LMFDB - Embedded newform 25.8.d.a.6.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,8,Mod(6,25)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("25.6");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	25.d (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.80962563710$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			6.9
Character	$\chi$	$=$	25.6
Dual form			25.8.d.a.21.9

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.247040 + 0.760310i) q^{2} +(-17.6400 + 12.8162i) q^{3} +(103.037 - 74.8609i) q^{4} +(-179.724 + 214.066i) q^{5} +(-14.1021 - 10.2458i) q^{6} +544.176 q^{7} +(165.157 + 119.993i) q^{8} +(-528.905 + 1627.80i) q^{9} +O(q^{10})$	\(q+(0.247040 + 0.760310i) q^{2} +(-17.6400 + 12.8162i) q^{3} +(103.037 - 74.8609i) q^{4} +(-179.724 + 214.066i) q^{5} +(-14.1021 - 10.2458i) q^{6} +544.176 q^{7} +(165.157 + 119.993i) q^{8} +(-528.905 + 1627.80i) q^{9} +(-207.155 - 83.7630i) q^{10} +(1200.38 + 3694.38i) q^{11} +(-858.144 + 2641.10i) q^{12} +(-4161.43 + 12807.6i) q^{13} +(134.433 + 413.742i) q^{14} +(426.814 - 6079.52i) q^{15} +(4987.22 - 15349.1i) q^{16} +(24281.8 + 17641.7i) q^{17} -1368.29 q^{18} +(-23566.1 - 17121.8i) q^{19} +(-2493.06 + 35511.0i) q^{20} +(-9599.29 + 6974.29i) q^{21} +(-2512.33 + 1825.32i) q^{22} +(1538.01 + 4733.50i) q^{23} -4451.23 q^{24} +(-13523.6 - 76945.6i) q^{25} -10765.7 q^{26} +(-26268.2 - 80845.1i) q^{27} +(56070.4 - 40737.5i) q^{28} +(153551. - 111561. i) q^{29} +(4727.76 - 1177.37i) q^{30} +(-133830. - 97233.0i) q^{31} +39032.7 q^{32} +(-68522.8 - 49784.7i) q^{33} +(-7414.63 + 22819.9i) q^{34} +(-97801.5 + 116490. i) q^{35} +(67361.8 + 207318. i) q^{36} +(-79799.8 + 245598. i) q^{37} +(7196.09 - 22147.3i) q^{38} +(-90737.0 - 279260. i) q^{39} +(-55369.1 + 13788.8i) q^{40} +(-150512. + 463227. i) q^{41} +(-7674.03 - 5575.51i) q^{42} +868259. q^{43} +(400248. + 290797. i) q^{44} +(-253401. - 405776. i) q^{45} +(-3218.98 + 2338.72i) q^{46} +(-226915. + 164863. i) q^{47} +(108743. + 334676. i) q^{48} -527415. q^{49} +(55161.6 - 29290.8i) q^{50} -654432. q^{51} +(530003. + 1.63118e6i) q^{52} +(326100. - 236925. i) q^{53} +(54978.1 - 39943.9i) q^{54} +(-1.00658e6 - 407008. i) q^{55} +(89874.4 + 65297.5i) q^{56} +635143. q^{57} +(122754. + 89186.1i) q^{58} +(659783. - 2.03060e6i) q^{59} +(-411140. - 658368. i) q^{60} +(80013.1 + 246255. i) q^{61} +(40865.9 - 125772. i) q^{62} +(-287818. + 885812. i) q^{63} +(-628722. - 1.93501e6i) q^{64} +(-1.99376e6 - 3.19265e6i) q^{65} +(20924.0 - 64397.3i) q^{66} +(1.27807e6 + 928572. i) q^{67} +3.82260e6 q^{68} +(-87796.2 - 63787.7i) q^{69} +(-112729. - 45581.8i) q^{70} +(-2.85481e6 + 2.07414e6i) q^{71} +(-282678. + 205377. i) q^{72} +(-1.07502e6 - 3.30856e6i) q^{73} -206445. q^{74} +(1.22471e6 + 1.18400e6i) q^{75} -3.70993e6 q^{76} +(653217. + 2.01039e6i) q^{77} +(189908. - 137976. i) q^{78} +(6.21591e6 - 4.51612e6i) q^{79} +(2.38940e6 + 3.82620e6i) q^{80} +(-1.52882e6 - 1.11075e6i) q^{81} -389378. q^{82} +(3.36350e6 + 2.44373e6i) q^{83} +(-466982. + 1.43722e6i) q^{84} +(-8.14052e6 + 2.02726e6i) q^{85} +(214494. + 660145. i) q^{86} +(-1.27885e6 + 3.93588e6i) q^{87} +(-245051. + 754189. i) q^{88} +(482259. + 1.48424e6i) q^{89} +(245915. - 292906. i) q^{90} +(-2.26455e6 + 6.96957e6i) q^{91} +(512826. + 372590. i) q^{92} +3.60692e6 q^{93} +(-181404. - 131798. i) q^{94} +(7.90058e6 - 1.96751e6i) q^{95} +(-688538. + 500252. i) q^{96} +(-918677. + 667458. i) q^{97} +(-130292. - 400999. i) q^{98} -6.64861e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 11 q^{2} + 23 q^{3} - 1091 q^{4} + 475 q^{5} - 179 q^{6} + 1734 q^{7} + 220 q^{8} - 14554 q^{9}+O(q^{10}) $ 68 * q - 11 * q^2 + 23 * q^3 - 1091 * q^4 + 475 * q^5 - 179 * q^6 + 1734 * q^7 + 220 * q^8 - 14554 * q^9	\( 68 q - 11 q^{2} + 23 q^{3} - 1091 q^{4} + 475 q^{5} - 179 q^{6} + 1734 q^{7} + 220 q^{8} - 14554 q^{9} + 4245 q^{10} + 466 q^{11} + 9979 q^{12} - 7407 q^{13} - 20177 q^{14} - 9285 q^{15} - 68527 q^{16} + 71504 q^{17} + 116208 q^{18} - 48685 q^{19} - 138265 q^{20} - 2274 q^{21} - 271952 q^{22} - 63227 q^{23} + 553980 q^{24} + 276615 q^{25} + 675246 q^{26} - 270235 q^{27} - 782613 q^{28} - 99655 q^{29} - 1011285 q^{30} + 39051 q^{31} + 1045974 q^{32} + 1766456 q^{33} + 605893 q^{34} - 476935 q^{35} - 2928227 q^{36} + 83909 q^{37} + 1937525 q^{38} + 1316257 q^{39} + 2903410 q^{40} - 1964944 q^{41} - 3462547 q^{42} - 3439822 q^{43} - 3557652 q^{44} - 2121790 q^{45} + 2982521 q^{46} + 1663474 q^{47} + 1678378 q^{48} + 6584354 q^{49} + 408485 q^{50} + 3922076 q^{51} - 5301176 q^{52} + 788553 q^{53} - 6946145 q^{54} - 2630560 q^{55} - 415350 q^{56} - 14598410 q^{57} + 4727030 q^{58} - 3625740 q^{59} + 29158890 q^{60} - 4161559 q^{61} + 19658928 q^{62} + 2426738 q^{63} - 4408596 q^{64} - 2030220 q^{65} - 6985528 q^{66} + 8470434 q^{67} - 29099218 q^{68} - 360673 q^{69} - 22417320 q^{70} - 4808044 q^{71} + 25676065 q^{72} + 5517633 q^{73} + 14050068 q^{74} + 257240 q^{75} + 22502000 q^{76} - 9936772 q^{77} + 14948561 q^{78} - 5343505 q^{79} - 3987180 q^{80} - 5865817 q^{81} - 76614542 q^{82} - 645927 q^{83} + 5992628 q^{84} + 48268560 q^{85} - 27540609 q^{86} + 65370380 q^{87} - 3612320 q^{88} + 11153500 q^{89} + 7267975 q^{90} - 9123484 q^{91} - 33863736 q^{92} - 118704764 q^{93} - 30761227 q^{94} - 26382485 q^{95} + 1256206 q^{96} + 55538244 q^{97} + 102201752 q^{98} + 71266232 q^{99}+O(q^{100}) \) 68 * q - 11 * q^2 + 23 * q^3 - 1091 * q^4 + 475 * q^5 - 179 * q^6 + 1734 * q^7 + 220 * q^8 - 14554 * q^9 + 4245 * q^10 + 466 * q^11 + 9979 * q^12 - 7407 * q^13 - 20177 * q^14 - 9285 * q^15 - 68527 * q^16 + 71504 * q^17 + 116208 * q^18 - 48685 * q^19 - 138265 * q^20 - 2274 * q^21 - 271952 * q^22 - 63227 * q^23 + 553980 * q^24 + 276615 * q^25 + 675246 * q^26 - 270235 * q^27 - 782613 * q^28 - 99655 * q^29 - 1011285 * q^30 + 39051 * q^31 + 1045974 * q^32 + 1766456 * q^33 + 605893 * q^34 - 476935 * q^35 - 2928227 * q^36 + 83909 * q^37 + 1937525 * q^38 + 1316257 * q^39 + 2903410 * q^40 - 1964944 * q^41 - 3462547 * q^42 - 3439822 * q^43 - 3557652 * q^44 - 2121790 * q^45 + 2982521 * q^46 + 1663474 * q^47 + 1678378 * q^48 + 6584354 * q^49 + 408485 * q^50 + 3922076 * q^51 - 5301176 * q^52 + 788553 * q^53 - 6946145 * q^54 - 2630560 * q^55 - 415350 * q^56 - 14598410 * q^57 + 4727030 * q^58 - 3625740 * q^59 + 29158890 * q^60 - 4161559 * q^61 + 19658928 * q^62 + 2426738 * q^63 - 4408596 * q^64 - 2030220 * q^65 - 6985528 * q^66 + 8470434 * q^67 - 29099218 * q^68 - 360673 * q^69 - 22417320 * q^70 - 4808044 * q^71 + 25676065 * q^72 + 5517633 * q^73 + 14050068 * q^74 + 257240 * q^75 + 22502000 * q^76 - 9936772 * q^77 + 14948561 * q^78 - 5343505 * q^79 - 3987180 * q^80 - 5865817 * q^81 - 76614542 * q^82 - 645927 * q^83 + 5992628 * q^84 + 48268560 * q^85 - 27540609 * q^86 + 65370380 * q^87 - 3612320 * q^88 + 11153500 * q^89 + 7267975 * q^90 - 9123484 * q^91 - 33863736 * q^92 - 118704764 * q^93 - 30761227 * q^94 - 26382485 * q^95 + 1256206 * q^96 + 55538244 * q^97 + 102201752 * q^98 + 71266232 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.247040	+	0.760310i	0.0218354	+	0.0672025i	0.961380	−	0.275223i	$-0.0887516\pi$
$2$	0.247040	+	0.760310i	0.0218354	+	0.0672025i	−0.939545	+	0.342425i	$0.888752\pi$
$3$	−17.6400	+	12.8162i	−0.377203	+	0.274054i	−0.760191	−	0.649699i	$-0.774895\pi$
$3$	−17.6400	+	12.8162i	−0.377203	+	0.274054i	0.382988	+	0.923753i	$0.374895\pi$
$4$	103.037	−	74.8609i	0.804978	−	0.584850i
$5$	−179.724	+	214.066i	−0.643000	+	0.765866i
$5$	−179.724	+	214.066i	−0.643000	+	0.765866i
$6$	−14.1021	−	10.2458i	−0.0266535	−	0.0193649i
$7$	544.176			0.599648			0.299824	−	0.953995i	$-0.403072\pi$
$7$	544.176			0.599648			0.299824	+	0.953995i	$0.403072\pi$
$8$	165.157	+	119.993i	0.114046	+	0.0828595i
$9$	−528.905	+	1627.80i	−0.241840	+	0.744309i
$10$	−207.155	−	83.7630i	−0.0655083	−	0.0264882i
$11$	1200.38	+	3694.38i	0.271921	+	0.836888i	0.990018	+	0.140944i	$0.0450138\pi$
$11$	1200.38	+	3694.38i	0.271921	+	0.836888i	−0.718096	+	0.695944i	$0.754986\pi$
$12$	−858.144	+	2641.10i	−0.143359	+	0.441215i
$13$	−4161.43	+	12807.6i	−0.525340	+	1.61683i	0.238302	+	0.971191i	$0.423409\pi$
$13$	−4161.43	+	12807.6i	−0.525340	+	1.61683i	−0.763642	+	0.645640i	$0.776591\pi$
$14$	134.433	+	413.742i	0.0130936	+	0.0402979i
$15$	426.814	−	6079.52i	0.0326527	−	0.465104i
$16$	4987.22	−	15349.1i	0.304396	−	0.936834i
$17$	24281.8	+	17641.7i	1.19870	+	0.870904i	0.994156	−	0.107954i	$-0.0344298\pi$
$17$	24281.8	+	17641.7i	1.19870	+	0.870904i	0.204541	+	0.978858i	$0.434430\pi$
$18$	−1368.29			−0.0553001
$19$	−23566.1	−	17121.8i	−0.788225	−	0.572679i	0.119212	−	0.992869i	$-0.461963\pi$
$19$	−23566.1	−	17121.8i	−0.788225	−	0.572679i	−0.907436	+	0.420190i	$0.861963\pi$
$20$	−2493.06	+	35511.0i	−0.0696832	+	0.992564i
$21$	−9599.29	+	6974.29i	−0.226189	+	0.164336i
$22$	−2512.33	+	1825.32i	−0.0503034	+	0.0365476i
$23$	1538.01	+	4733.50i	0.0263579	+	0.0811213i	0.963370	−	0.268175i	$-0.0864206\pi$
$23$	1538.01	+	4733.50i	0.0263579	+	0.0811213i	−0.937012	+	0.349296i	$0.886421\pi$
$24$	−4451.23			−0.0657266
$25$	−13523.6	−	76945.6i	−0.173102	−	0.984904i
$26$	−10765.7			−0.120126
$27$	−26268.2	−	80845.1i	−0.256837	−	0.790462i
$28$	56070.4	−	40737.5i	0.482703	−	0.350704i
$29$	153551.	−	111561.i	1.16912	−	0.849415i	0.178216	−	0.983991i	$-0.442967\pi$
$29$	153551.	−	111561.i	1.16912	−	0.849415i	0.990903	+	0.134577i	$0.0429674\pi$
$30$	4727.76	−	1177.37i	0.0319691	−	0.00796139i
$31$	−133830.	−	97233.0i	−0.806838	−	0.586202i	0.106074	−	0.994358i	$-0.466172\pi$
$31$	−133830.	−	97233.0i	−0.806838	−	0.586202i	−0.912912	+	0.408156i	$0.866172\pi$
$32$	39032.7			0.210573
$33$	−68522.8	−	49784.7i	−0.331922	−	0.241155i
$34$	−7414.63	+	22819.9i	−0.0323529	+	0.0995720i
$35$	−97801.5	+	116490.i	−0.385574	+	0.459250i
$36$	67361.8	+	207318.i	0.240633	+	0.740592i
$37$	−79799.8	+	245598.i	−0.258997	+	0.797112i	0.734018	+	0.679130i	$0.237643\pi$
$37$	−79799.8	+	245598.i	−0.258997	+	0.797112i	−0.993016	+	0.117982i	$0.962357\pi$
$38$	7196.09	−	22147.3i	0.0212742	−	0.0654753i
$39$	−90737.0	−	279260.i	−0.244939	−	0.753845i
$40$	−55369.1	+	13788.8i	−0.136791	+	0.0340656i
$41$	−150512.	+	463227.i	−0.341057	+	1.04966i	0.622605	+	0.782537i	$0.286075\pi$
$41$	−150512.	+	463227.i	−0.341057	+	1.04966i	−0.963661	+	0.267128i	$0.913925\pi$
$42$	−7674.03	−	5575.51i	−0.0159827	−	0.0116121i
$43$	868259.			1.66537			0.832683	−	0.553750i	$-0.186804\pi$
$43$	868259.			1.66537			0.832683	+	0.553750i	$0.186804\pi$
$44$	400248.	+	290797.i	0.708345	+	0.514643i
$45$	−253401.	−	405776.i	−0.414537	−	0.663808i
$46$	−3218.98	+	2338.72i	−0.00487602	+	0.00354264i
$47$	−226915.	+	164863.i	−0.318801	+	0.231623i	−0.735664	−	0.677347i	$-0.763130\pi$
$47$	−226915.	+	164863.i	−0.318801	+	0.231623i	0.416863	+	0.908970i	$0.363130\pi$
$48$	108743.	+	334676.i	0.141924	+	0.436798i
$49$	−527415.			−0.640422
$50$	55161.6	−	29290.8i	0.0624082	−	0.0331387i
$51$	−654432.			−0.690827
$52$	530003.	+	1.63118e6i	0.522717	+	1.60876i
$53$	326100.	−	236925.i	0.300874	−	0.218598i	−0.427097	−	0.904206i	$-0.640464\pi$
$53$	326100.	−	236925.i	0.300874	−	0.218598i	0.727971	+	0.685608i	$0.240464\pi$
$54$	54978.1	−	39943.9i	0.0475129	−	0.0345201i
$55$	−1.00658e6	−	407008.i	−0.815790	−	0.329863i
$56$	89874.4	+	65297.5i	0.0683877	+	0.0496865i
$57$	635143.			0.454266
$58$	122754.	+	89186.1i	0.0826110	+	0.0600204i
$59$	659783.	−	2.03060e6i	0.418234	−	1.28719i	−0.491092	−	0.871108i	$-0.663402\pi$
$59$	659783.	−	2.03060e6i	0.418234	−	1.28719i	0.909326	−	0.416084i	$-0.136598\pi$
$60$	−411140.	−	658368.i	−0.245731	−	0.393495i
$61$	80013.1	+	246255.i	0.0451343	+	0.138909i	0.971084	−	0.238737i	$-0.0767335\pi$
$61$	80013.1	+	246255.i	0.0451343	+	0.138909i	−0.925950	+	0.377646i	$0.876733\pi$
$62$	40865.9	−	125772.i	0.0217766	−	0.0670215i
$63$	−287818.	+	885812.i	−0.145019	+	0.446323i
$64$	−628722.	−	1.93501e6i	−0.299798	−	0.922683i
$65$	−1.99376e6	−	3.19265e6i	−0.900483	−	1.44196i
$66$	20924.0	−	64397.3i	0.00895860	−	0.0275717i
$67$	1.27807e6	+	928572.i	0.519150	+	0.377184i	0.816283	−	0.577652i	$-0.196031\pi$
$67$	1.27807e6	+	928572.i	0.519150	+	0.377184i	−0.297134	+	0.954836i	$0.596031\pi$
$68$	3.82260e6			1.47427
$69$	−87796.2	−	63787.7i	−0.0321739	−	0.0233757i
$70$	−112729.	−	45581.8i	−0.0392819	−	0.0158836i
$71$	−2.85481e6	+	2.07414e6i	−0.946614	+	0.687755i	−0.950004	−	0.312239i	$-0.898921\pi$
$71$	−2.85481e6	+	2.07414e6i	−0.946614	+	0.687755i	0.00338969	+	0.999994i	$0.498921\pi$
$72$	−282678.	+	205377.i	−0.0892540	+	0.0648469i
$73$	−1.07502e6	−	3.30856e6i	−0.323433	−	0.995425i	−0.972143	−	0.234389i	$-0.924691\pi$
$73$	−1.07502e6	−	3.30856e6i	−0.323433	−	0.995425i	0.648710	−	0.761036i	$-0.275309\pi$
$74$	−206445.			−0.0592233
$75$	1.22471e6	+	1.18400e6i	0.335212	+	0.324069i
$76$	−3.70993e6			−0.969434
$77$	653217.	+	2.01039e6i	0.163057	+	0.501838i
$78$	189908.	−	137976.i	0.0453119	−	0.0329210i
$79$	6.21591e6	−	4.51612e6i	1.41844	−	1.03055i	0.426410	−	0.904530i	$-0.359778\pi$
$79$	6.21591e6	−	4.51612e6i	1.41844	−	1.03055i	0.992027	−	0.126025i	$-0.0402219\pi$
$80$	2.38940e6	+	3.82620e6i	0.521763	+	0.835511i
$81$	−1.52882e6	−	1.11075e6i	−0.319638	−	0.232231i
$82$	−389378.			−0.0779872
$83$	3.36350e6	+	2.44373e6i	0.645681	+	0.469115i	0.861797	−	0.507253i	$-0.169339\pi$
$83$	3.36350e6	+	2.44373e6i	0.645681	+	0.469115i	−0.216116	+	0.976368i	$0.569339\pi$
$84$	−466982.	+	1.43722e6i	−0.0859652	+	0.264574i
$85$	−8.14052e6	+	2.02726e6i	−1.43776	+	0.358050i
$86$	214494.	+	660145.i	0.0363640	+	0.111917i
$87$	−1.27885e6	+	3.93588e6i	−0.208210	+	0.640804i
$88$	−245051.	+	754189.i	−0.0383325	+	0.117975i
$89$	482259.	+	1.48424e6i	0.0725130	+	0.223172i	0.980744	−	0.195297i	$-0.0625670\pi$
$89$	482259.	+	1.48424e6i	0.0725130	+	0.223172i	−0.908231	+	0.418469i	$0.862567\pi$
$90$	245915.	−	292906.i	0.0355579	−	0.0423525i
$91$	−2.26455e6	+	6.96957e6i	−0.315019	+	0.969530i
$92$	512826.	+	372590.i	0.0686614	+	0.0498854i
$93$	3.60692e6			0.464993
$94$	−181404.	−	131798.i	−0.0225268	−	0.0163667i
$95$	7.90058e6	−	1.96751e6i	0.945423	−	0.235442i
$96$	−688538.	+	500252.i	−0.0794289	+	0.0577084i
$97$	−918677.	+	667458.i	−0.102203	+	0.0742545i	−0.637713	−	0.770274i	$-0.720119\pi$
$97$	−918677.	+	667458.i	−0.102203	+	0.0742545i	0.535510	+	0.844529i	$0.320119\pi$
$98$	−130292.	−	400999.i	−0.0139839	−	0.0430380i
$99$	−6.64861e6			−0.688664
$100$	−7.15365e6	−	6.91586e6i	−0.715365	−	0.691586i
$101$	1.32945e7			1.28395			0.641974	−	0.766727i	$-0.278116\pi$
$101$	1.32945e7			1.28395			0.641974	+	0.766727i	$0.278116\pi$
$102$	−161671.	−	497571.i	−0.0150845	−	0.0464253i
$103$	−1.13693e6	+	826028.i	−0.102519	+	0.0744843i	−0.637864	−	0.770149i	$-0.720182\pi$
$103$	−1.13693e6	+	826028.i	−0.102519	+	0.0744843i	0.535345	+	0.844634i	$0.320182\pi$
$104$	−2.22411e6	+	1.61591e6i	−0.193883	+	0.140864i
$105$	232262.	−	3.30833e6i	0.0195801	−	0.278899i
$106$	260696.	+	189407.i	0.0212600	+	0.0154463i
$107$	7.66331e6			0.604747			0.302373	−	0.953190i	$-0.402221\pi$
$107$	7.66331e6			0.604747			0.302373	+	0.953190i	$0.402221\pi$
$108$	−8.75873e6	−	6.36359e6i	−0.669049	−	0.486093i
$109$	319291.	−	982676.i	0.0236153	−	0.0726804i	−0.938554	−	0.345132i	$-0.887834\pi$
$109$	319291.	−	982676.i	0.0236153	−	0.0726804i	0.962170	+	0.272451i	$0.0878343\pi$
$110$	60787.8	−	865858.i	0.00435454	−	0.0620258i
$111$	−1.73998e6	−	5.35510e6i	−0.120757	−	0.371652i
$112$	2.71393e6	−	8.35261e6i	0.182530	−	0.561771i
$113$	−4.58776e6	+	1.41197e7i	−0.299107	+	0.920556i	0.682704	+	0.730695i	$0.260804\pi$
$113$	−4.58776e6	+	1.41197e7i	−0.299107	+	0.920556i	−0.981811	+	0.189861i	$0.939196\pi$
$114$	156906.	+	482906.i	0.00991908	+	0.0305278i
$115$	−1.28970e6	−	521488.i	−0.0790762	−	0.0319744i
$116$	7.46986e6	−	2.29899e7i	0.444334	−	1.36752i
$117$	−1.86472e7	−	1.35480e7i	−1.07637	−	0.782030i
$118$	1.70688e6			0.0956348
$119$	1.32136e7	+	9.60022e6i	0.718796	+	0.522236i
$120$	799993.	−	952859.i	0.0422622	−	0.0503378i
$121$	3.55791e6	−	2.58497e6i	0.182577	−	0.132650i
$122$	−167464.	+	121670.i	−0.00834952	+	0.00606628i
$123$	−3.28180e6	−	1.01003e7i	−0.159017	−	0.489404i
$124$	−2.10684e7			−0.992327
$125$	1.89020e7	+	1.09340e7i	0.865610	+	0.500720i
$126$	−744593.			−0.0331606
$127$	954077.	+	2.93635e6i	0.0413305	+	0.127202i	0.969593	−	0.244724i	$-0.0786974\pi$
$127$	954077.	+	2.93635e6i	0.0413305	+	0.127202i	−0.928262	+	0.371926i	$0.878697\pi$
$128$	5.35788e6	−	3.89273e6i	0.225818	−	0.164066i
$129$	−1.53161e7	+	1.11278e7i	−0.628181	+	0.456400i
$130$	1.93486e6	−	2.30458e6i	0.0772411	−	0.0920005i
$131$	1.39481e7	+	1.01339e7i	0.542085	+	0.393847i	0.824859	−	0.565339i	$-0.191255\pi$
$131$	1.39481e7	+	1.01339e7i	0.542085	+	0.393847i	−0.282774	+	0.959187i	$0.591255\pi$
$132$	−1.07873e7			−0.408230
$133$	−1.28241e7	−	9.31726e6i	−0.472657	−	0.343406i
$134$	−390268.	+	1.20112e6i	−0.0140119	+	0.0431241i
$135$	2.20272e7	+	8.90668e6i	0.770534	+	0.311564i
$136$	1.89341e6	+	5.82731e6i	0.0645443	+	0.198647i
$137$	8.67081e6	−	2.66860e7i	0.288096	−	0.886669i	−0.697357	−	0.716724i	$-0.745641\pi$
$137$	8.67081e6	−	2.66860e7i	0.288096	−	0.886669i	0.985454	−	0.169945i	$-0.0543591\pi$
$138$	26809.2	−	82510.4i	0.000868376	−	0.00267259i
$139$	5.60522e6	+	1.72511e7i	0.177027	+	0.544835i	0.999720	−	0.0236517i	$-0.00752926\pi$
$139$	5.60522e6	+	1.72511e7i	0.177027	+	0.544835i	−0.822693	+	0.568486i	$0.807529\pi$
$140$	−1.35667e6	+	1.93243e7i	−0.0417854	+	0.595189i
$141$	1.88986e6	−	5.81638e6i	0.0567757	−	0.174737i
$142$	−2.28224e6	−	1.65814e6i	−0.0668886	−	0.0485974i
$143$	−5.23113e7			−1.49596
$144$	2.23475e7	+	1.62364e7i	0.623679	+	0.453129i
$145$	−3.71528e6	+	5.29202e7i	−0.101205	+	1.44156i
$146$	2.24996e6	−	1.63469e6i	0.0598328	−	0.0434710i
$147$	9.30362e6	−	6.75948e6i	0.241569	−	0.175510i
$148$	1.01634e7	+	3.12796e7i	0.257704	+	0.793132i
$149$	2.21569e7			0.548727			0.274364	−	0.961626i	$-0.411533\pi$
$149$	2.21569e7			0.548727			0.274364	+	0.961626i	$0.411533\pi$
$150$	−597656.	+	1.22365e6i	−0.0144588	+	0.0296033i
$151$	1.18067e7			0.279068			0.139534	−	0.990217i	$-0.455440\pi$
$151$	1.18067e7			0.279068			0.139534	+	0.990217i	$0.455440\pi$
$152$	−1.83760e6	−	5.65555e6i	−0.0424422	−	0.130624i
$153$	−4.15600e7	+	3.01951e7i	−0.938115	+	0.681580i
$154$	−1.36715e6	+	993294.i	−0.0301644	+	0.0219157i
$155$	4.48667e7	−	1.11733e7i	0.967750	−	0.241002i
$156$	−3.02549e7	−	2.19815e7i	−0.638057	−	0.463576i
$157$	−2.89844e7			−0.597744			−0.298872	−	0.954293i	$-0.596610\pi$
$157$	−2.89844e7			−0.597744			−0.298872	+	0.954293i	$0.596610\pi$
$158$	4.96923e6	+	3.61036e6i	0.100228	+	0.0728199i
$159$	−2.71592e6	+	8.35874e6i	−0.0535830	+	0.164912i
$160$	−7.01510e6	+	8.35557e6i	−0.135399	+	0.161271i
$161$	836947.	+	2.57586e6i	0.0158055	+	0.0486442i
$162$	466837.	−	1.43678e6i	0.00862705	−	0.0265513i
$163$	2.79779e7	−	8.61072e7i	0.506010	−	1.55734i	−0.293056	−	0.956095i	$-0.594672\pi$
$163$	2.79779e7	−	8.61072e7i	0.506010	−	1.55734i	0.799066	−	0.601243i	$-0.205328\pi$
$164$	1.91693e7	+	5.89970e7i	0.339354	+	1.04442i
$165$	2.29724e7	−	5.72090e6i	0.398119	−	0.0991450i
$166$	−1.02707e6	+	3.16100e6i	−0.0174270	+	0.0536347i
$167$	−4.44036e7	−	3.22611e7i	−0.737753	−	0.536009i	0.154254	−	0.988031i	$-0.450703\pi$
$167$	−4.44036e7	−	3.22611e7i	−0.737753	−	0.536009i	−0.892006	+	0.452023i	$0.850703\pi$
$168$	−2.42226e6			−0.0394128
$169$	−9.59514e7	−	6.97128e7i	−1.52914	−	1.11099i
$170$	−3.55238e6	−	5.68850e6i	−0.0554559	−	0.0888028i
$171$	4.03351e7	−	2.93052e7i	0.616874	−	0.448185i
$172$	8.94629e7	−	6.49986e7i	1.34058	−	0.973990i
$173$	6.53561e6	+	2.01145e7i	0.0959676	+	0.295358i	0.987505	−	0.157590i	$-0.0503724\pi$
$173$	6.53561e6	+	2.01145e7i	0.0959676	+	0.295358i	−0.891537	+	0.452948i	$0.850372\pi$
$174$	−3.30842e6			−0.0476100
$175$	−7.35924e6	−	4.18720e7i	−0.103801	−	0.590596i
$176$	6.26920e7			0.866797
$177$	1.43861e7	+	4.42759e7i	0.195001	+	0.600151i
$178$	−1.00935e6	+	733333.i	−0.0134144	+	0.00974611i
$179$	−1.13100e7	+	8.21717e6i	−0.147393	+	0.107087i	−0.659038	−	0.752110i	$-0.729036\pi$
$179$	−1.13100e7	+	8.21717e6i	−0.147393	+	0.107087i	0.511645	+	0.859197i	$0.329036\pi$
$180$	−5.64864e7	−	2.28402e7i	−0.721922	−	0.291908i
$181$	−3.28118e7	−	2.38392e7i	−0.411296	−	0.298824i	0.362830	−	0.931855i	$-0.381811\pi$
$181$	−3.28118e7	−	2.38392e7i	−0.411296	−	0.298824i	−0.774126	+	0.633031i	$0.781811\pi$
$182$	−5.85846e6			−0.0720334
$183$	−4.56750e6	−	3.31848e6i	−0.0550934	−	0.0400277i
$184$	−313976.	+	966320.i	−0.00371565	+	0.0114356i
$185$	−3.82324e7	−	6.12223e7i	−0.443946	−	0.710901i
$186$	891052.	+	2.74238e6i	0.0101533	+	0.0312487i
$187$	−3.60280e7	+	1.10883e8i	−0.402898	+	1.23999i
$188$	−1.10388e7	+	3.39740e7i	−0.121163	+	0.372902i
$189$	−1.42945e7	−	4.39940e7i	−0.154012	−	0.473999i
$190$	3.44767e6	+	5.52083e6i	0.0364660	+	0.0583939i
$191$	8.88379e6	−	2.73415e7i	0.0922532	−	0.283926i	−0.894275	−	0.447518i	$-0.852308\pi$
$191$	8.88379e6	−	2.73415e7i	0.0922532	−	0.283926i	0.986528	+	0.163592i	$0.0523080\pi$
$192$	3.58902e7	+	2.60758e7i	0.365950	+	0.265878i
$193$	−1.69920e7			−0.170135			−0.0850675	−	0.996375i	$-0.527111\pi$
$193$	−1.69920e7			−0.170135			−0.0850675	+	0.996375i	$0.527111\pi$
$194$	−734424.	−	533590.i	−0.00722172	−	0.00524689i
$195$	7.60876e7	+	3.07659e7i	0.734840	+	0.297132i
$196$	−5.43433e7	+	3.94828e7i	−0.515525	+	0.374551i
$197$	−3.00483e7	+	2.18314e7i	−0.280020	+	0.203446i	−0.718926	−	0.695087i	$-0.755366\pi$
$197$	−3.00483e7	+	2.18314e7i	−0.280020	+	0.203446i	0.438906	+	0.898533i	$0.355366\pi$
$198$	−1.64247e6	−	5.05500e6i	−0.0150373	−	0.0462800i
$199$	1.23476e8			1.11070			0.555349	−	0.831617i	$-0.312585\pi$
$199$	1.23476e8			1.11070			0.555349	+	0.831617i	$0.312585\pi$
$200$	6.99945e6	−	1.43308e7i	0.0618669	−	0.126668i
$201$	−3.44460e7			−0.299194
$202$	3.28427e6	+	1.01079e7i	0.0280355	+	0.0862845i
$203$	8.35587e7	−	6.07089e7i	0.701060	−	0.509350i
$204$	−6.74308e7	+	4.89914e7i	−0.556100	+	0.404030i
$205$	−7.21107e7	−	1.15472e8i	−0.584603	−	0.936138i
$206$	−908904.	−	660357.i	−0.00724407	−	0.00526313i
$207$	−8.51866e6			−0.0667537
$208$	1.75830e8	+	1.27748e8i	1.35479	+	0.984314i
$209$	3.49661e7	−	1.07615e8i	0.264933	−	0.815379i
$210$	2.57273e6	−	640697.i	0.0191702	−	0.00477403i
$211$	7.35401e7	+	2.26333e8i	0.538934	+	1.65867i	0.734991	+	0.678076i	$0.237186\pi$
$211$	7.35401e7	+	2.26333e8i	0.538934	+	1.65867i	−0.196057	+	0.980592i	$0.562814\pi$
$212$	1.58640e7	−	4.88242e7i	0.114350	−	0.351933i
$213$	2.37763e7	−	7.31758e7i	0.168584	−	0.518847i
$214$	1.89314e6	+	5.82649e6i	0.0132049	+	0.0406405i
$215$	−1.56047e8	+	1.85865e8i	−1.07083	+	1.27545i
$216$	5.36251e6	−	1.65041e7i	0.0362060	−	0.111431i
$217$	−7.28269e7	−	5.29119e7i	−0.483819	−	0.351515i
$218$	826015.			0.00539996
$219$	6.13666e7	+	4.45854e7i	0.394800	+	0.286839i
$220$	−1.34184e8	+	3.34163e7i	−0.849613	+	0.211582i
$221$	−3.26995e8	+	2.37575e8i	−2.03783	+	1.48057i
$222$	3.64169e6	−	2.64584e6i	0.0223392	−	0.0162304i
$223$	1.66267e7	+	5.11718e7i	0.100401	+	0.309003i	0.988624	−	0.150410i	$-0.0480595\pi$
$223$	1.66267e7	+	5.11718e7i	0.100401	+	0.309003i	−0.888222	+	0.459414i	$0.848059\pi$
$224$	2.12406e7			0.126270
$225$	1.32405e8	+	1.86831e7i	0.774935	+	0.109348i
$226$	−1.18687e7			−0.0683948
$227$	9.75291e7	+	3.00164e8i	0.553406	+	1.70321i	0.700116	+	0.714029i	$0.253132\pi$
$227$	9.75291e7	+	3.00164e8i	0.553406	+	1.70321i	−0.146710	+	0.989180i	$0.546868\pi$
$228$	6.54434e7	−	4.75474e7i	0.365674	−	0.265677i
$229$	1.81653e8	−	1.31979e8i	0.999581	−	0.726238i	0.0375829	−	0.999294i	$-0.488034\pi$
$229$	1.81653e8	−	1.31979e8i	0.999581	−	0.726238i	0.961998	+	0.273055i	$0.0880342\pi$
$230$	77885.6	−	1.10940e6i	0.000422094	−	0.00601229i
$231$	−3.72885e7	−	2.70917e7i	−0.199036	−	0.144608i
$232$	3.87465e7			0.203716
$233$	−1.23932e8	−	9.00421e7i	−0.641857	−	0.466337i	0.218630	−	0.975808i	$-0.429841\pi$
$233$	−1.23932e8	−	9.00421e7i	−0.641857	−	0.466337i	−0.860488	+	0.509471i	$0.829841\pi$
$234$	5.69406e6	−	1.75245e7i	0.0290514	−	0.0894109i
$235$	5.49037e6	−	7.82046e7i	0.0275971	−	0.393092i
$236$	−8.40306e7	−	2.58620e8i	−0.416146	−	1.28076i
$237$	−5.17692e7	+	1.59329e8i	−0.252611	+	0.777457i
$238$	−4.03487e6	+	1.24180e7i	−0.0194004	+	0.0597082i
$239$	−1.27272e8	−	3.91702e8i	−0.603031	−	1.85594i	−0.509800	−	0.860293i	$-0.670281\pi$
$239$	−1.27272e8	−	3.91702e8i	−0.603031	−	1.85594i	−0.0932306	−	0.995645i	$-0.529719\pi$
$240$	−9.11865e7	−	3.68711e7i	−0.425786	−	0.172166i
$241$	2.07110e7	−	6.37420e7i	0.0953107	−	0.293336i	−0.892024	−	0.451988i	$-0.850715\pi$
$241$	2.07110e7	−	6.37420e7i	0.0953107	−	0.293336i	0.987335	+	0.158652i	$0.0507148\pi$
$242$	2.84432e6	+	2.06652e6i	0.0129010	+	0.00937316i
$243$	2.27111e8			1.01535
$244$	2.66792e7	+	1.93836e7i	0.117573	+	0.0854219i
$245$	9.47891e7	−	1.12902e8i	0.411791	−	0.490478i
$246$	6.86865e6	−	4.99036e6i	0.0294170	−	0.0213727i
$247$	3.17357e8	−	2.30573e8i	1.34001	−	0.973575i
$248$	−1.04356e7	−	3.21173e7i	−0.0434445	−	0.133708i
$249$	−9.06517e7			−0.372116
$250$	−3.64370e6	+	1.70725e7i	−0.0147487	+	0.0691046i
$251$	1.83136e8			0.730997			0.365498	−	0.930812i	$-0.380899\pi$
$251$	1.83136e8			0.730997			0.365498	+	0.930812i	$0.380899\pi$
$252$	3.66567e7	+	1.12818e8i	0.144295	+	0.444095i
$253$	−1.56412e7	+	1.13640e7i	−0.0607222	+	0.0441172i
$254$	−1.99684e6	+	1.45079e6i	−0.00764584	+	0.00555503i
$255$	1.17617e8	−	1.40092e8i	0.444202	−	0.529081i
$256$	−2.06407e8	−	1.49963e8i	−0.768925	−	0.558657i
$257$	−3.98321e8			−1.46375			−0.731875	−	0.681438i	$-0.761355\pi$
$257$	−3.98321e8			−1.46375			−0.731875	+	0.681438i	$0.761355\pi$
$258$	−1.22443e7	−	8.89598e6i	−0.0443878	−	0.0322496i
$259$	−4.34251e7	+	1.33649e8i	−0.155307	+	0.477987i
$260$	−4.44435e8	−	1.79707e8i	−1.56820	−	0.634100i
$261$	1.00386e8	+	3.08956e8i	0.349486	+	1.07561i
$262$	−4.25917e6	+	1.31084e7i	−0.0146309	+	0.0450293i
$263$	−1.12237e8	+	3.45429e8i	−0.380444	+	1.17088i	0.559288	+	0.828973i	$0.311074\pi$
$263$	−1.12237e8	+	3.45429e8i	−0.380444	+	1.17088i	−0.939732	+	0.341912i	$0.888926\pi$
$264$	−5.34316e6	−	1.64446e7i	−0.0178725	−	0.0550058i
$265$	−7.89023e6	+	1.12388e8i	−0.0260453	+	0.370988i
$266$	3.91594e6	−	1.20520e7i	0.0127571	−	0.0392622i
$267$	−2.75295e7	−	2.00013e7i	−0.0885133	−	0.0643087i
$268$	2.01202e8			0.638500
$269$	−1.66195e8	−	1.20747e8i	−0.520576	−	0.378220i	0.296245	−	0.955112i	$-0.404266\pi$
$269$	−1.66195e8	−	1.20747e8i	−0.520576	−	0.378220i	−0.816821	+	0.576892i	$0.804266\pi$
$270$	−1.33024e6	+	1.89478e7i	−0.00411297	+	0.0585849i
$271$	7.50144e7	−	5.45012e7i	0.228956	−	0.166346i	−0.467393	−	0.884050i	$-0.654807\pi$
$271$	7.50144e7	−	5.45012e7i	0.228956	−	0.166346i	0.696349	+	0.717703i	$0.254807\pi$
$272$	3.91884e8	−	2.84720e8i	1.18077	−	0.857881i
$273$	−4.93769e7	−	1.51966e8i	−0.146877	−	0.452042i
$274$	2.24317e7			0.0658771
$275$	2.68033e8	−	1.42325e8i	0.777184	−	0.412684i
$276$	−1.38215e7			−0.0395706
$277$	1.01547e8	+	3.12529e8i	0.287069	+	0.883509i	0.985771	+	0.168095i	$0.0537617\pi$
$277$	1.01547e8	+	3.12529e8i	0.287069	+	0.883509i	−0.698701	+	0.715414i	$0.746238\pi$
$278$	−1.17315e7	+	8.52340e6i	−0.0327488	+	0.0237934i
$279$	2.29059e8	−	1.66421e8i	0.631442	−	0.458769i
$280$	−3.01306e7	+	7.50353e6i	−0.0820265	+	0.0204274i
$281$	4.20055e7	+	3.05188e7i	0.112937	+	0.0820532i	0.642820	−	0.766017i	$-0.277764\pi$
$281$	4.20055e7	+	3.05188e7i	0.112937	+	0.0820532i	−0.529883	+	0.848070i	$0.677764\pi$
$282$	4.88912e6			0.0129825
$283$	−2.22573e8	−	1.61709e8i	−0.583740	−	0.424112i	0.256330	−	0.966589i	$-0.417487\pi$
$283$	−2.22573e8	−	1.61709e8i	−0.583740	−	0.424112i	−0.840071	+	0.542477i	$0.817487\pi$
$284$	−1.38879e8	+	4.27427e8i	−0.359769	+	1.10726i
$285$	−1.14150e8	+	1.35963e8i	−0.292093	+	0.347907i
$286$	−1.29230e7	−	3.97728e7i	−0.0326649	−	0.100532i
$287$	−8.19048e7	+	2.52077e8i	−0.204514	+	0.629429i
$288$	−2.06446e7	+	6.35375e7i	−0.0509251	+	0.156731i
$289$	1.51572e8	+	4.66491e8i	0.369383	+	1.13684i
$290$	−4.11536e7	+	1.02486e7i	−0.0990865	+	0.0246759i
$291$	7.65120e6	−	2.35480e7i	0.0182014	−	0.0560180i
$292$	−3.58448e8	−	2.60428e8i	−0.842531	−	0.612135i
$293$	−1.02570e8			−0.238222			−0.119111	−	0.992881i	$-0.538004\pi$
$293$	−1.02570e8			−0.238222			−0.119111	+	0.992881i	$0.538004\pi$
$294$	7.43766e6	+	5.40378e6i	0.0170695	+	0.0124017i
$295$	3.16105e8	+	5.06185e8i	0.716893	+	1.14798i
$296$	−4.26496e7	+	3.09868e7i	−0.0955860	+	0.0694473i
$297$	2.67141e8	−	1.94089e8i	0.591688	−	0.429887i
$298$	5.47363e6	+	1.68461e7i	0.0119817	+	0.0368759i
$299$	−6.70249e7			−0.145006
$300$	2.14826e8	+	3.03132e7i	0.459370	+	0.0648198i
$301$	4.72486e8			0.998633
$302$	2.91673e6	+	8.97676e6i	0.00609357	+	0.0187541i
$303$	−2.34516e8	+	1.70386e8i	−0.484309	+	0.351871i
$304$	−3.80333e8	+	2.76328e8i	−0.776437	+	0.564115i
$305$	−6.70952e7	−	2.71298e7i	−0.135407	−	0.0547517i
$306$	−3.32246e7	−	2.41391e7i	−0.0662880	−	0.0481611i
$307$	−5.74681e8			−1.13355			−0.566777	−	0.823871i	$-0.691810\pi$
$307$	−5.74681e8			−1.13355			−0.566777	+	0.823871i	$0.691810\pi$
$308$	2.17805e8	+	1.58245e8i	0.424758	+	0.308605i
$309$	9.46892e6	−	2.91423e7i	0.0182577	−	0.0561914i
$310$	1.95790e7	+	3.13523e7i	0.0373272	+	0.0597728i
$311$	2.40181e8	+	7.39201e8i	0.452769	+	1.39348i	0.873734	+	0.486404i	$0.161692\pi$
$311$	2.40181e8	+	7.39201e8i	0.452769	+	1.39348i	−0.420965	+	0.907077i	$0.638308\pi$
$312$	1.85235e7	−	5.70094e7i	0.0345288	−	0.106269i
$313$	3.79090e7	−	1.16672e8i	0.0698775	−	0.215061i	−0.910019	−	0.414566i	$-0.863933\pi$
$313$	3.79090e7	−	1.16672e8i	0.0698775	−	0.215061i	0.979897	+	0.199505i	$0.0639334\pi$
$314$	−7.16029e6	−	2.20371e7i	−0.0130520	−	0.0401699i
$315$	−1.37895e8	−	2.20814e8i	−0.248577	−	0.398051i
$316$	3.02389e8	−	9.30657e8i	0.539090	−	1.65915i
$317$	−8.05936e8	−	5.85547e8i	−1.42100	−	1.03242i	−0.991606	−	0.129297i	$-0.958728\pi$
$317$	−8.05936e8	−	5.85547e8i	−1.42100	−	1.03242i	−0.429392	−	0.903118i	$-0.641272\pi$
$318$	−7.02617e6			−0.0122525
$319$	5.96468e8	+	4.33359e8i	1.02877	+	0.747448i
$320$	5.27216e8	+	2.13179e8i	0.899422	+	0.363680i
$321$	−1.35181e8	+	9.82149e7i	−0.228112	+	0.165733i
$322$	−1.75169e6	+	1.27268e6i	−0.00292390	+	0.00212433i
$323$	−2.70169e8	−	8.31494e8i	−0.446094	−	1.37294i
$324$	−2.40677e8			−0.393122
$325$	1.04176e9	+	1.46999e8i	1.68336	+	0.237532i
$326$	7.23798e7			0.115706
$327$	6.96191e6	+	2.14265e7i	0.0110106	+	0.0338872i
$328$	−8.04422e7	+	5.84447e7i	−0.125871	+	0.0914505i
$329$	−1.23482e8	+	8.97146e7i	−0.191169	+	0.138892i
$330$	1.00247e7	+	1.60528e7i	0.0153559	+	0.0245897i
$331$	−8.88953e8	−	6.45862e8i	−1.34735	−	0.978908i	−0.999139	−	0.0414918i	$-0.986789\pi$
$331$	−8.88953e8	−	6.45862e8i	−1.34735	−	0.978908i	−0.348212	−	0.937416i	$-0.613211\pi$
$332$	5.29505e8			0.794121
$333$	−3.57579e8	−	2.59797e8i	−0.530661	−	0.385548i
$334$	1.35590e7	−	4.17303e7i	0.0199120	−	0.0612828i
$335$	−4.28475e8	+	1.06705e8i	−0.622686	+	0.155070i
$336$	5.91753e7	+	1.82123e8i	0.0851046	+	0.261925i
$337$	3.14097e8	−	9.66692e8i	0.447053	−	1.37589i	−0.433163	−	0.901316i	$-0.642602\pi$
$337$	3.14097e8	−	9.66692e8i	0.447053	−	1.37589i	0.880216	−	0.474573i	$-0.157398\pi$
$338$	2.92995e7	−	9.01746e7i	0.0412717	−	0.127021i
$339$	−1.00033e8	−	3.07870e8i	−0.139458	−	0.429208i
$340$	−6.87013e8	+	8.18290e8i	−0.947957	+	1.12910i
$341$	1.98569e8	−	6.11134e8i	0.271189	−	0.834634i
$342$	3.22454e7	+	2.34276e7i	0.0435889	+	0.0316692i
$343$	−7.35159e8			−0.983676
$344$	1.43399e8	+	1.04185e8i	0.189929	+	0.137991i
$345$	2.94339e7	−	7.33002e6i	0.0385905	−	0.00961033i
$346$	−1.36787e7	+	9.93817e6i	−0.0177533	+	0.0128985i
$347$	5.30688e8	−	3.85567e8i	0.681845	−	0.495390i	−0.192124	−	0.981371i	$-0.561538\pi$
$347$	5.30688e8	−	3.85567e8i	0.681845	−	0.495390i	0.873969	+	0.485981i	$0.161538\pi$
$348$	1.62875e8	+	5.01278e8i	0.207170	+	0.637604i
$349$	−2.15754e8			−0.271687			−0.135844	−	0.990730i	$-0.543374\pi$
$349$	−2.15754e8			−0.271687			−0.135844	+	0.990730i	$0.543374\pi$
$350$	3.00176e7	−	1.59393e7i	0.0374230	−	0.0198716i
$351$	1.14474e9			1.41297
$352$	4.68539e7	+	1.44201e8i	0.0572594	+	0.176226i
$353$	−6.23266e8	+	4.52829e8i	−0.754157	+	0.547927i	−0.897113	−	0.441802i	$-0.854339\pi$
$353$	−6.23266e8	+	4.52829e8i	−0.754157	+	0.547927i	0.142955	+	0.989729i	$0.454339\pi$
$354$	−3.01094e7	+	2.18758e7i	−0.0360737	+	0.0262091i
$355$	6.90743e7	−	9.83891e8i	0.0819440	−	1.16721i
$356$	1.60802e8	+	1.16830e8i	0.188894	+	0.137239i
$357$	−3.56127e8			−0.414253
$358$	−9.04161e6	−	6.56911e6i	−0.0104149	−	0.00756687i
$359$	1.71800e8	−	5.28746e8i	0.195971	−	0.603138i	−0.803993	−	0.594639i	$-0.797295\pi$
$359$	1.71800e8	−	5.28746e8i	0.195971	−	0.603138i	0.999964	−	0.00849840i	$-0.00270516\pi$
$360$	6.83960e6	−	9.74230e7i	0.00772631	−	0.110053i
$361$	−1.40158e7	−	4.31363e7i	−0.0156799	−	0.0482579i
$362$	1.00193e7	−	3.08363e7i	0.0111009	−	0.0341651i
$363$	−2.96320e7	+	9.11980e7i	−0.0325153	+	0.100072i
$364$	2.88415e8	+	8.87651e8i	0.313446	+	0.964689i
$365$	9.01456e8	+	3.64502e8i	0.970330	+	0.392351i
$366$	1.39472e6	−	4.29251e6i	0.00148697	−	0.00457644i
$367$	−9.92281e8	−	7.20934e8i	−1.04786	−	0.761315i	−0.0760557	−	0.997104i	$-0.524233\pi$
$367$	−9.92281e8	−	7.20934e8i	−1.04786	−	0.761315i	−0.971804	+	0.235789i	$0.924233\pi$
$368$	8.03253e7			0.0840205
$369$	−6.74436e8	−	4.90006e8i	−0.698793	−	0.507703i
$370$	3.71030e7	−	4.41928e7i	0.0380806	−	0.0453571i
$371$	1.77456e8	−	1.28929e8i	0.180419	−	0.131082i
$372$	3.71647e8	−	2.70017e8i	0.374309	−	0.271951i
$373$	3.57206e8	+	1.09937e9i	0.356400	+	1.09689i	0.955193	+	0.295984i	$0.0956474\pi$
$373$	3.57206e8	+	1.09937e9i	0.356400	+	1.09689i	−0.598793	+	0.800904i	$0.704353\pi$
$374$	−9.32057e7			−0.0921280
$375$	−4.73564e8	+	4.93757e7i	−0.463735	+	0.0483508i
$376$	−5.72589e7			−0.0555502
$377$	7.89835e8	+	2.43086e9i	0.759175	+	2.33650i
$378$	2.99178e7	−	2.17365e7i	0.0284910	−	0.0206999i
$379$	−8.29688e8	+	6.02804e8i	−0.782848	+	0.568773i	−0.905833	−	0.423636i	$-0.860754\pi$
$379$	−8.29688e8	+	6.02804e8i	−0.782848	+	0.568773i	0.122984	+	0.992409i	$0.460754\pi$
$380$	6.66764e8	−	7.94171e8i	0.623346	−	0.742457i
$381$	−5.44629e7	−	3.95696e7i	−0.0504503	−	0.0366543i
$382$	2.29826e7			0.0210949
$383$	7.32628e7	+	5.32285e7i	0.0666328	+	0.0484115i	0.620603	−	0.784125i	$-0.286888\pi$
$383$	7.32628e7	+	5.32285e7i	0.0666328	+	0.0484115i	−0.553970	+	0.832536i	$0.686888\pi$
$384$	−4.46231e7	+	1.37336e8i	−0.0402161	+	0.123773i
$385$	−5.47756e8	−	2.21484e8i	−0.489187	−	0.197802i
$386$	−4.19769e6	−	1.29192e7i	−0.00371497	−	0.0114335i
$387$	−4.59226e8	+	1.41335e9i	−0.402753	+	1.23955i
$388$	−4.46914e7	+	1.37546e8i	−0.0388430	+	0.119546i
$389$	9.60125e7	+	2.95496e8i	0.0826997	+	0.254524i	0.983853	−	0.178976i	$-0.0572785\pi$
$389$	9.60125e7	+	2.95496e8i	0.0826997	+	0.254524i	−0.901154	+	0.433500i	$0.857279\pi$
$390$	−4.59497e6	+	6.54506e7i	−0.00392244	+	0.0558711i
$391$	−4.61617e7	+	1.42071e8i	−0.0390537	+	0.120195i
$392$	−8.71061e7	−	6.32863e7i	−0.0730378	−	0.0530651i
$393$	−3.75925e8			−0.312411
$394$	−2.40217e7	−	1.74528e7i	−0.0197864	−	0.0143757i
$395$	−1.50399e8	+	2.14227e9i	−0.122788	+	1.74898i
$396$	−6.85054e8	+	4.97721e8i	−0.554359	+	0.402766i
$397$	1.51008e9	−	1.09714e9i	1.21125	−	0.880024i	0.215906	−	0.976414i	$-0.430730\pi$
$397$	1.51008e9	−	1.09714e9i	1.21125	−	0.880024i	0.995344	+	0.0963902i	$0.0307297\pi$
$398$	3.05034e7	+	9.38799e7i	0.0242526	+	0.0746417i
$399$	3.45630e8			0.272399
$400$	−1.24849e9	−	1.76170e8i	−0.975384	−	0.137632i
$401$	−1.81324e8			−0.140427			−0.0702135	−	0.997532i	$-0.522368\pi$
$401$	−1.81324e8			−0.140427			−0.0702135	+	0.997532i	$0.522368\pi$
$402$	−8.50952e6	−	2.61896e7i	−0.00653302	−	0.0201066i
$403$	1.80224e9	−	1.30940e9i	1.37165	−	0.996565i
$404$	1.36983e9	−	9.95238e8i	1.03355	−	0.750917i
$405$	5.12540e8	−	1.27640e8i	0.383385	−	0.0954757i
$406$	6.67999e7	+	4.85329e7i	0.0495375	+	0.0359911i
$407$	−1.00312e9			−0.737521
$408$	−1.08084e8	−	7.85276e7i	−0.0787863	−	0.0572416i
$409$	1.84285e8	−	5.67170e8i	0.133186	−	0.409904i	−0.862118	−	0.506708i	$-0.830862\pi$
$409$	1.84285e8	−	5.67170e8i	0.133186	−	0.409904i	0.995303	+	0.0968045i	$0.0308622\pi$
$410$	6.99806e7	−	8.33527e7i	0.0501457	−	0.0597278i
$411$	1.89061e8	+	5.81869e8i	0.134324	+	0.413408i
$412$	−5.53089e7	+	1.70223e8i	−0.0389632	+	0.119916i
$413$	3.59038e8	−	1.10501e9i	0.250793	−	0.771862i
$414$	−2.10445e6	−	6.47682e6i	−0.00145759	−	0.00448602i
$415$	−1.12762e9	+	2.80816e8i	−0.774453	+	0.192865i
$416$	−1.62432e8	+	4.99913e8i	−0.110623	+	0.340461i
$417$	−3.19970e8	−	2.32472e8i	−0.216089	−	0.156998i
$418$	9.04585e7			0.0605804
$419$	−2.76684e8	−	2.01023e8i	−0.183753	−	0.133504i	0.492106	−	0.870535i	$-0.336227\pi$
$419$	−2.76684e8	−	2.01023e8i	−0.183753	−	0.133504i	−0.675859	+	0.737031i	$0.736227\pi$
$420$	−2.23733e8	−	3.58268e8i	−0.147352	−	0.235959i
$421$	−1.97786e9	+	1.43700e9i	−1.29184	+	0.938575i	−0.999841	−	0.0178444i	$-0.994320\pi$
$421$	−1.97786e9	+	1.43700e9i	−1.29184	+	0.938575i	−0.291997	+	0.956419i	$0.594320\pi$
$422$	−1.53916e8	+	1.11827e8i	−0.0996989	+	0.0724355i
$423$	−1.48348e8	−	4.56569e8i	−0.0952996	−	0.293302i
$424$	8.22870e7			0.0524265
$425$	1.02908e9	−	2.10696e9i	0.650260	−	1.33136i
$426$	6.15100e7			0.0385489
$427$	4.35413e7	+	1.34006e8i	0.0270647	+	0.0832966i
$428$	7.89606e8	−	5.73682e8i	0.486807	−	0.353686i
$429$	9.22773e8	−	6.70434e8i	0.564280	−	0.409973i
$430$	−1.79865e8	−	7.27280e7i	−0.109095	−	0.0441125i
$431$	−3.39857e8	−	2.46920e8i	−0.204468	−	0.148555i	0.480839	−	0.876809i	$-0.340332\pi$
$431$	−3.39857e8	−	2.46920e8i	−0.204468	−	0.148555i	−0.685307	+	0.728254i	$0.740332\pi$
$432$	−1.37191e9			−0.818712
$433$	2.08552e9	+	1.51522e9i	1.23454	+	0.896948i	0.997222	−	0.0744831i	$-0.0237307\pi$
$433$	2.08552e9	+	1.51522e9i	1.23454	+	0.896948i	0.237321	+	0.971431i	$0.423731\pi$
$434$	2.22383e7	−	6.84423e7i	0.0130583	−	0.0401893i
$435$	−6.12700e8	−	9.81130e8i	−0.356891	−	0.571497i
$436$	−4.06652e7	−	1.25154e8i	−0.0234974	−	0.0723175i
$437$	4.48011e7	−	1.37883e8i	0.0256805	−	0.0790364i
$438$	−1.87387e7	+	5.76719e7i	−0.0106557	+	0.0327948i
$439$	4.41120e7	+	1.35763e8i	0.0248846	+	0.0765869i	0.962728	−	0.270473i	$-0.0871801\pi$
$439$	4.41120e7	+	1.35763e8i	0.0248846	+	0.0765869i	−0.937843	+	0.347060i	$0.887180\pi$
$440$	−1.17405e8	−	1.88003e8i	−0.0657055	−	0.105216i
$441$	2.78953e8	−	8.58528e8i	0.154880	−	0.476672i
$442$	−2.61412e8	−	1.89927e8i	−0.143995	−	0.104618i
$443$	4.91223e8			0.268451			0.134226	−	0.990951i	$-0.457145\pi$
$443$	4.91223e8			0.268451			0.134226	+	0.990951i	$0.457145\pi$
$444$	−5.80169e8	−	4.21518e8i	−0.314568	−	0.228547i
$445$	−4.04399e8	−	1.63518e8i	−0.217546	−	0.0879643i
$446$	−3.47989e7	+	2.52829e7i	−0.0185735	+	0.0134944i
$447$	−3.90848e8	+	2.83968e8i	−0.206982	+	0.150381i
$448$	−3.42136e8	−	1.05299e9i	−0.179773	−	0.553285i
$449$	7.88092e8			0.410880			0.205440	−	0.978670i	$-0.434137\pi$
$449$	7.88092e8			0.410880			0.205440	+	0.978670i	$0.434137\pi$
$450$	1.85043e7	+	1.05284e8i	0.00957258	+	0.0544653i
$451$	−1.89201e9			−0.971192
$452$	5.84301e8	+	1.79829e9i	0.297613	+	0.915960i
$453$	−2.08271e8	+	1.51318e8i	−0.105265	+	0.0764797i
$454$	−2.04124e8	+	1.48305e8i	−0.102376	+	0.0743805i
$455$	−1.08495e9	−	1.73736e9i	−0.539973	−	0.864670i
$456$	1.04898e8	+	7.62130e7i	0.0518073	+	0.0376402i
$457$	2.31936e9			1.13674			0.568371	−	0.822772i	$-0.307574\pi$
$457$	2.31936e9			1.13674			0.568371	+	0.822772i	$0.307574\pi$
$458$	1.45220e8	+	1.05509e8i	0.0706313	+	0.0513167i
$459$	7.88411e8	−	2.42648e9i	0.380547	−	1.17120i
$460$	−1.71926e8	+	4.28153e7i	−0.0823548	+	0.0205091i
$461$	6.13939e8	+	1.88951e9i	0.291858	+	0.898247i	0.984259	+	0.176734i	$0.0565531\pi$
$461$	6.13939e8	+	1.88951e9i	0.291858	+	0.898247i	−0.692401	+	0.721513i	$0.743447\pi$
$462$	1.13863e7	−	3.50435e7i	0.00537201	−	0.0165333i
$463$	4.07008e8	−	1.25264e9i	0.190576	−	0.586534i	−0.809423	−	0.587225i	$-0.800220\pi$
$463$	4.07008e8	−	1.25264e9i	0.190576	−	0.586534i	1.00000		0.000691761i	$0.000220194\pi$
$464$	−9.46571e8	−	2.91324e9i	−0.439886	−	1.35383i
$465$	−6.48250e8	+	7.72120e8i	−0.298990	+	0.356122i
$466$	3.78437e7	−	1.16471e8i	0.0173238	−	0.0533171i
$467$	2.59590e9	+	1.88603e9i	1.17945	+	0.856918i	0.992109	−	0.125378i	$-0.0400143\pi$
$467$	2.59590e9	+	1.88603e9i	1.17945	+	0.856918i	0.187337	+	0.982296i	$0.440014\pi$
$468$	−2.93556e9			−1.32383
$469$	6.95495e8	+	5.05307e8i	0.311307	+	0.226178i
$470$	6.08160e7	−	1.51452e7i	0.0270194	−	0.00672874i
$471$	5.11286e8	−	3.71471e8i	0.225471	−	0.163814i
$472$	3.52627e8	−	2.56198e8i	0.154354	−	0.112145i
$473$	1.04224e9	+	3.20768e9i	0.452848	+	1.39372i
$474$	−1.33929e8			−0.0577629
$475$	−9.98746e8	+	2.04486e9i	−0.427590	+	0.875457i
$476$	2.08017e9			0.884045
$477$	2.13192e8	+	6.56137e8i	0.0899407	+	0.276809i
$478$	2.66374e8	−	1.93532e8i	0.111556	−	0.0810503i
$479$	−2.42670e9	+	1.76310e9i	−1.00888	+	0.732998i	−0.963975	−	0.265993i	$-0.914300\pi$
$479$	−2.42670e9	+	1.76310e9i	−1.00888	+	0.732998i	−0.0449100	+	0.998991i	$0.514300\pi$
$480$	1.66597e7	−	2.37300e8i	0.00687579	−	0.0979384i
$481$	−2.81343e9	−	2.04408e9i	−1.15273	−	0.837510i
$482$	5.35801e7			0.0217941
$483$	−4.77766e7	−	3.47117e7i	−0.0192930	−	0.0140172i
$484$	1.73083e8	−	5.32696e8i	0.0693900	−	0.213560i
$485$	2.22281e7	−	3.16616e8i	0.00884720	−	0.126019i
$486$	5.61055e7	+	1.72675e8i	0.0221706	+	0.0682342i
$487$	−5.75169e8	+	1.77019e9i	−0.225655	+	0.694494i	0.772570	+	0.634930i	$0.218971\pi$
$487$	−5.75169e8	+	1.77019e9i	−0.225655	+	0.694494i	−0.998225	+	0.0595638i	$0.981029\pi$
$488$	−1.63343e7	+	5.02717e7i	−0.00636254	+	0.0195819i
$489$	6.10039e8	+	1.87751e9i	0.235926	+	0.726107i
$490$	1.09257e8	+	4.41779e7i	0.0419530	+	0.0169636i
$491$	−2.23204e8	+	6.86953e8i	−0.0850977	+	0.261904i	−0.984547	−	0.175122i	$-0.943968\pi$
$491$	−2.23204e8	+	6.86953e8i	−0.0850977	+	0.261904i	0.899449	+	0.437026i	$0.143968\pi$
$492$	−1.09427e9	−	7.95031e8i	−0.414234	−	0.300958i
$493$	5.69662e9			2.14118
$494$	2.53707e8	+	1.84329e8i	0.0946863	+	0.0687937i
$495$	1.19491e9	−	1.42324e9i	0.442811	−	0.527425i
$496$	−2.15988e9	+	1.56924e9i	−0.794773	+	0.577436i
$497$	−1.55352e9	+	1.12870e9i	−0.567635	+	0.412411i
$498$	−2.23946e7	−	6.89234e7i	−0.00812531	−	0.0250071i
$499$	−8.37858e8			−0.301869			−0.150934	−	0.988544i	$-0.548228\pi$
$499$	−8.37858e8			−0.301869			−0.150934	+	0.988544i	$0.548228\pi$
$500$	2.76613e9	−	2.88408e8i	0.989642	−	0.103184i
$501$	1.19675e9			0.425178
$502$	4.52418e7	+	1.39240e8i	0.0159616	+	0.0491248i
$503$	−3.70637e9	+	2.69284e9i	−1.29856	+	0.943457i	−0.999940	−	0.0109164i	$-0.996525\pi$
$503$	−3.70637e9	+	2.69284e9i	−1.29856	+	0.943457i	−0.298616	+	0.954373i	$0.596525\pi$
$504$	−1.53827e8	+	1.11762e8i	−0.0535210	+	0.0388853i
$505$	−2.38934e9	+	2.84590e9i	−0.825578	+	0.983332i
$506$	−1.25041e7	−	9.08478e6i	−0.00429068	−	0.00311736i
$507$	2.58604e9			0.881268
$508$	3.18123e8	+	2.31130e8i	0.107664	+	0.0782227i
$509$	−6.10142e8	+	1.87782e9i	−0.205078	+	0.631164i	0.794633	+	0.607091i	$0.207664\pi$
$509$	−6.10142e8	+	1.87782e9i	−0.205078	+	0.631164i	−0.999710	+	0.0240734i	$0.992336\pi$
$510$	1.35569e8	+	5.48172e7i	0.0452549	+	0.0182988i
$511$	−5.84998e8	−	1.80044e9i	−0.193946	−	0.596905i
$512$	3.24983e8	−	1.00020e9i	0.107008	−	0.329337i
$513$	−7.65173e8	+	2.35496e9i	−0.250236	+	0.770146i
$514$	−9.84010e7	−	3.02847e8i	−0.0319616	−	0.0983677i
$515$	2.75089e7	−	3.91835e8i	0.00887458	−	0.126409i
$516$	−7.45091e8	+	2.29316e9i	−0.238746	+	0.734784i
$517$	−8.81450e8	−	6.40411e8i	−0.280531	−	0.203818i
$518$	−1.12342e8			−0.0355131
$519$	−3.73081e8	−	2.71059e8i	−0.117143	−	0.0851096i
$520$	5.38140e7	−	7.66524e8i	0.0167835	−	0.239064i
$521$	4.39569e9	−	3.19365e9i	1.36174	−	0.989363i	0.363410	−	0.931629i	$-0.381612\pi$
$521$	4.39569e9	−	3.19365e9i	1.36174	−	0.989363i	0.998332	−	0.0577340i	$-0.0183875\pi$
$522$	−2.10103e8	+	1.52648e8i	−0.0646524	+	0.0469727i
$523$	−8.22684e8	−	2.53196e9i	−0.251465	−	0.773929i	−0.994506	−	0.104683i	$-0.966617\pi$
$523$	−8.22684e8	−	2.53196e9i	−0.251465	−	0.773929i	0.743041	−	0.669246i	$-0.233383\pi$
$524$	2.19581e9			0.666708
$525$	6.66458e8	+	6.44306e8i	0.201009	+	0.194328i
$526$	−2.90360e8			−0.0869936
$527$	−1.53426e9	−	4.72198e9i	−0.456628	−	1.40536i
$528$	−1.10589e9	+	8.03475e8i	−0.326958	+	0.237549i
$529$	2.73452e9	−	1.98675e9i	0.803131	−	0.583509i
$530$	−8.73989e7	+	2.17653e7i	−0.0255000	+	0.00635037i
$531$	2.95646e9	+	2.14799e9i	0.856922	+	0.622590i
$532$	−2.01886e9			−0.581320
$533$	−5.30646e9	−	3.85537e9i	−1.51796	−	1.10286i
$534$	8.40634e6	−	2.58720e7i	0.00238898	−	0.00735252i
$535$	−1.37728e9	+	1.64046e9i	−0.388852	+	0.463155i
$536$	9.96593e7	+	3.06720e8i	0.0279538	+	0.0860330i
$537$	9.41950e7	−	2.89903e8i	0.0262493	−	0.0807871i
$538$	5.07488e7	−	1.56189e8i	0.0140504	−	0.0432426i
$539$	−6.33097e8	−	1.94847e9i	−0.174144	−	0.535962i
$540$	2.93638e9	−	7.31259e8i	0.802481	−	0.199845i
$541$	9.57567e8	−	2.94709e9i	0.260003	−	0.800208i	−0.732799	−	0.680445i	$-0.761787\pi$
$541$	9.57567e8	−	2.94709e9i	0.260003	−	0.800208i	0.992803	−	0.119763i	$-0.0382135\pi$
$542$	5.99693e7	+	4.35702e7i	0.0161782	+	0.0117542i
$543$	8.84329e8			0.237036
$544$	9.47783e8	+	6.88604e8i	0.252413	+	0.183389i
$545$	1.52973e8	+	2.44960e8i	0.0404789	+	0.0648197i
$546$	1.03344e8	−	7.50835e7i	0.0271712	−	0.0197410i
$547$	5.80268e9	−	4.21589e9i	1.51591	−	1.10137i	0.552439	−	0.833553i	$-0.313697\pi$
$547$	5.80268e9	−	4.21589e9i	1.51591	−	1.10137i	0.963469	−	0.267819i	$-0.0863028\pi$
$548$	−1.10432e9	−	3.39875e9i	−0.286658	−	0.882242i
$549$	−4.43174e8			−0.114307
$550$	1.74426e8	+	1.68628e8i	0.0447035	+	0.0432176i
$551$	−5.52871e9			−1.40797
$552$	−6.84603e6	−	2.10699e7i	−0.00173242	−	0.00533183i
$553$	3.38255e9	−	2.45757e9i	0.850563	−	0.617970i
$554$	−2.12533e8	+	1.54414e8i	−0.0531057	+	0.0385836i
$555$	1.45906e9	+	5.89969e8i	0.362283	+	0.146489i
$556$	1.86898e9	+	1.35789e9i	0.461150	+	0.335045i
$557$	−6.93492e9			−1.70039			−0.850194	−	0.526469i	$-0.823516\pi$
$557$	−6.93492e9			−1.70039			−0.850194	+	0.526469i	$0.823516\pi$
$558$	1.83118e8	+	1.33043e8i	0.0446182	+	0.0324170i
$559$	−3.61320e9	+	1.11203e10i	−0.874883	+	2.69261i
$560$	1.30025e9	+	2.08212e9i	0.312874	+	0.501013i
$561$	−7.85566e8	−	2.41772e9i	−0.187851	−	0.578145i
$562$	−1.28267e7	+	3.94766e7i	−0.00304816	+	0.00938128i
$563$	−4.29720e8	+	1.32254e9i	−0.101486	+	0.312342i	−0.988890	−	0.148651i	$-0.952507\pi$
$563$	−4.29720e8	+	1.32254e9i	−0.101486	+	0.312342i	0.887404	+	0.460993i	$0.152507\pi$
$564$	−2.40694e8	−	7.40780e8i	−0.0564922	−	0.173865i
$565$	−2.19801e9	−	3.51973e9i	−0.512697	−	0.820993i
$566$	6.79643e7	−	2.09173e8i	0.0157552	−	0.0484895i
$567$	−8.31947e8	−	6.04445e8i	−0.191670	−	0.139257i
$568$	−7.20374e8			−0.164945
$569$	−1.07096e9	−	7.78099e8i	−0.243714	−	0.177069i	0.459222	−	0.888321i	$-0.348128\pi$
$569$	−1.07096e9	−	7.78099e8i	−0.243714	−	0.177069i	−0.702936	+	0.711253i	$0.748128\pi$
$570$	−1.31573e8	−	5.32015e7i	−0.0297582	−	0.0120327i
$571$	1.95914e9	−	1.42340e9i	0.440391	−	0.319963i	−0.345399	−	0.938456i	$-0.612257\pi$
$571$	1.95914e9	−	1.42340e9i	0.440391	−	0.319963i	0.785790	+	0.618493i	$0.212257\pi$
$572$	−5.39000e9	+	3.91607e9i	−1.20421	+	0.874911i
$573$	1.93705e8	+	5.96162e8i	0.0430129	+	0.132380i
$574$	−2.11890e8			−0.0467649
$575$	3.43423e8	−	1.82357e8i	0.0753341	−	0.0400023i
$576$	3.48234e9			0.759264
$577$	−2.57847e9	−	7.93572e9i	−0.558788	−	1.71977i	−0.685724	−	0.727862i	$-0.740514\pi$
$577$	−2.57847e9	−	7.93572e9i	−0.558788	−	1.71977i	0.126936	−	0.991911i	$-0.459486\pi$
$578$	−3.17233e8	+	2.30483e8i	−0.0683331	+	0.0496469i
$579$	2.99739e8	−	2.17773e8i	0.0641754	−	0.0466262i
$580$	3.57884e9	+	5.73088e9i	0.761631	+	1.21962i
$581$	1.83034e9	+	1.32982e9i	0.387182	+	0.281304i
$582$	1.97939e7			0.00416199
$583$	1.26674e9	+	9.20337e8i	0.264756	+	0.192357i
$584$	2.19459e8	−	6.75425e8i	0.0455940	−	0.140324i
$585$	6.25150e9	−	1.55684e9i	1.29104	−	0.321512i
$586$	−2.53387e7	−	7.79846e7i	−0.00520168	−	0.0160091i
$587$	1.99018e9	−	6.12513e9i	0.406124	−	1.24992i	−0.513830	−	0.857892i	$-0.671774\pi$
$587$	1.99018e9	−	6.12513e9i	0.406124	−	1.24992i	0.919953	−	0.392028i	$-0.128226\pi$
$588$	4.52598e8	−	1.39295e9i	0.0918105	−	0.282564i
$589$	1.48904e9	+	4.58280e9i	0.300264	+	0.924118i
$590$	−3.06767e8	+	3.65385e8i	−0.0614932	+	0.0732435i
$591$	2.50257e8	−	7.70213e8i	0.0498690	−	0.153481i
$592$	3.37173e9	+	2.44971e9i	0.667924	+	0.485276i
$593$	−5.33292e9			−1.05020			−0.525102	−	0.851039i	$-0.675973\pi$
$593$	−5.33292e9			−1.05020			−0.525102	+	0.851039i	$0.675973\pi$
$594$	2.13562e8	+	1.55162e8i	0.0418092	+	0.0303762i
$595$	−4.42988e9	+	1.10319e9i	−0.862149	+	0.214704i
$596$	2.28298e9	−	1.65868e9i	0.441713	−	0.320924i
$597$	−2.17812e9	+	1.58250e9i	−0.418959	+	0.304391i
$598$	−1.65578e7	−	5.09597e7i	−0.00316627	−	0.00974479i
$599$	−3.45776e9			−0.657357			−0.328679	−	0.944442i	$-0.606603\pi$
$599$	−3.45776e9			−0.657357			−0.328679	+	0.944442i	$0.606603\pi$
$600$	6.01968e7	+	3.42503e8i	0.0113774	+	0.0647344i
$601$	2.45264e9			0.460865			0.230433	−	0.973088i	$-0.425986\pi$
$601$	2.45264e9			0.460865			0.230433	+	0.973088i	$0.425986\pi$
$602$	1.16723e8	+	3.59235e8i	0.0218056	+	0.0671107i
$603$	−2.18751e9	+	1.58932e9i	−0.406293	+	0.295189i
$604$	1.21653e9	−	8.83861e8i	0.224643	−	0.163213i
$605$	−8.60863e7	+	1.22621e9i	−0.0158048	+	0.225123i
$606$	−1.87480e8	−	1.36212e8i	−0.0342217	−	0.0248635i
$607$	7.55358e9			1.37086			0.685429	−	0.728140i	$-0.259615\pi$
$607$	7.55358e9			1.37086			0.685429	+	0.728140i	$0.259615\pi$
$608$	−9.19847e8	−	6.68308e8i	−0.165979	−	0.120591i
$609$	−6.95918e8	+	2.14182e9i	−0.124853	+	0.384257i
$610$	4.05191e6	−	5.77152e7i	0.000722779	−	0.0102952i
$611$	−1.16720e9	−	3.59229e9i	−0.207016	−	0.637128i
$612$	−2.02179e9	+	6.22244e9i	−0.356539	+	1.09731i
$613$	−3.38790e9	+	1.04269e10i	−0.594044	+	1.82828i	−0.0346149	+	0.999401i	$0.511020\pi$
$613$	−3.38790e9	+	1.04269e10i	−0.594044	+	1.82828i	−0.559429	+	0.828878i	$0.688980\pi$
$614$	−1.41969e8	−	4.36935e8i	−0.0247516	−	0.0761777i
$615$	2.75196e9	+	1.11275e9i	0.477066	+	0.192901i
$616$	−1.33351e8	+	4.10412e8i	−0.0229860	+	0.0707436i
$617$	4.47800e9	+	3.25345e9i	0.767513	+	0.557631i	0.901205	−	0.433392i	$-0.142683\pi$
$617$	4.47800e9	+	3.25345e9i	0.767513	+	0.557631i	−0.133693	+	0.991023i	$0.542683\pi$
$618$	2.44964e7			0.00417487
$619$	3.51460e9	+	2.55350e9i	0.595605	+	0.432732i	0.844316	−	0.535845i	$-0.180007\pi$
$619$	3.51460e9	+	2.55350e9i	0.595605	+	0.432732i	−0.248711	+	0.968578i	$0.580007\pi$
$620$	3.78649e9	−	4.51002e9i	0.638066	−	0.759990i
$621$	3.42280e8	−	2.48681e8i	0.0573536	−	0.0416698i
$622$	−5.02687e8	+	3.65224e8i	−0.0837590	+	0.0608545i
$623$	2.62434e8	+	8.07689e8i	0.0434823	+	0.133825i
$624$	−4.73891e9			−0.780786
$625$	−5.73774e9	+	2.08117e9i	−0.940071	+	0.340979i
$626$	9.80719e7			0.0159784
$627$	7.62412e8	+	2.34646e9i	0.123524	+	0.380169i
$628$	−2.98647e9	+	2.16980e9i	−0.481171	+	0.349591i
$629$	−6.27047e9	+	4.55576e9i	−1.00467	+	0.729934i
$630$	1.33821e8	−	1.59392e8i	0.0213223	−	0.0253966i
$631$	−8.05210e8	−	5.85019e8i	−0.127587	−	0.0926973i	0.522162	−	0.852847i	$-0.325126\pi$
$631$	−8.05210e8	−	5.85019e8i	−0.127587	−	0.0926973i	−0.649749	+	0.760149i	$0.725126\pi$
$632$	1.56850e9			0.247159
$633$	−4.19799e9	−	3.05002e9i	−0.657852	−	0.477958i
$634$	2.46099e8	−	7.57415e8i	0.0383528	−	0.118038i
$635$	−8.00043e8	−	3.23496e8i	−0.123995	−	0.0501373i
$636$	3.45902e8	+	1.06458e9i	0.0533155	+	0.164088i
$637$	2.19480e9	−	6.75490e9i	0.336439	−	1.03545i
$638$	−1.82136e8	+	5.60557e8i	−0.0277667	+	0.0854570i
$639$	−1.86637e9	−	5.74409e9i	−0.282973	−	0.870900i
$640$	−1.29638e8	+	1.84656e9i	−0.0195480	+	0.278441i
$641$	−2.76973e9	+	8.52436e9i	−0.415370	+	1.27838i	0.496550	+	0.868008i	$0.334600\pi$
$641$	−2.76973e9	+	8.52436e9i	−0.415370	+	1.27838i	−0.911920	+	0.410368i	$0.865400\pi$
$642$	−1.08069e8	−	7.85166e7i	−0.0161186	−	0.0117109i
$643$	8.54888e9			1.26815			0.634075	−	0.773271i	$-0.281381\pi$
$643$	8.54888e9			1.26815			0.634075	+	0.773271i	$0.281381\pi$
$644$	2.79068e8	+	2.02754e8i	0.0411727	+	0.0299137i
$645$	3.70585e8	−	5.27860e9i	0.0543787	−	0.774568i
$646$	5.65451e8	−	4.10824e8i	0.0825241	−	0.0599573i
$647$	−8.31943e9	+	6.04442e9i	−1.20762	+	0.877384i	−0.995012	−	0.0997546i	$-0.968194\pi$
$647$	−8.31943e9	+	6.04442e9i	−1.20762	+	0.877384i	−0.212603	+	0.977139i	$0.568194\pi$
$648$	−1.19212e8	−	3.66896e8i	−0.0172110	−	0.0529701i
$649$	8.29382e9			1.19096
$650$	1.45592e8	+	8.28377e8i	0.0207941	+	0.118313i
$651$	1.96280e9			0.278832
$652$	−3.56330e9	−	1.09667e10i	−0.503483	−	1.54956i
$653$	4.18191e9	−	3.03833e9i	0.587730	−	0.427011i	−0.253772	−	0.967264i	$-0.581671\pi$
$653$	4.18191e9	−	3.03833e9i	0.587730	−	0.427011i	0.841503	+	0.540253i	$0.181671\pi$
$654$	−1.45709e7	+	1.05864e7i	−0.00203688	+	0.00147988i
$655$	−4.67615e9	+	1.16452e9i	−0.650195	+	0.161920i
$656$	6.35948e9	+	4.62043e9i	0.879545	+	0.639027i
$657$	5.95426e9			0.819122
$658$	−9.87157e7	−	7.17211e7i	−0.0135081	−	0.00981424i
$659$	3.99804e9	−	1.23047e10i	0.544187	−	1.67484i	−0.178727	−	0.983899i	$-0.557198\pi$
$659$	3.99804e9	−	1.23047e10i	0.544187	−	1.67484i	0.722914	−	0.690938i	$-0.242802\pi$
$660$	1.93874e9	−	2.30920e9i	0.262492	−	0.312649i
$661$	−3.84982e9	−	1.18485e10i	−0.518484	−	1.59573i	−0.776851	−	0.629684i	$-0.783184\pi$
$661$	−3.84982e9	−	1.18485e10i	−0.518484	−	1.59573i	0.258367	−	0.966047i	$-0.416816\pi$
$662$	2.71449e8	−	8.35433e8i	0.0363651	−	0.111920i
$663$	2.72337e9	−	8.38168e9i	0.362919	−	1.11695i
$664$	2.62274e8	+	8.07196e8i	0.0347670	+	0.107002i
$665$	4.29931e9	−	1.07067e9i	0.566921	−	0.141183i
$666$	1.09190e8	−	3.36051e8i	0.0143226	−	0.0440804i
$667$	7.64237e8	+	5.55250e8i	0.0997212	+	0.0724517i
$668$	−6.99032e9			−0.907359
$669$	−9.49125e8	−	6.89580e8i	−0.122555	−	0.0890416i
$670$	−1.86979e8	−	2.99414e8i	−0.0240177	−	0.0384600i
$671$	−8.13714e8	+	5.91198e8i	−0.103978	+	0.0755447i
$672$	−3.74686e8	+	2.72225e8i	−0.0476294	+	0.0346048i
$673$	7.11583e8	+	2.19003e9i	0.0899856	+	0.276947i	0.985914	−	0.167250i	$-0.0534888\pi$
$673$	7.11583e8	+	2.19003e9i	0.0899856	+	0.276947i	−0.895929	+	0.444198i	$0.853489\pi$
$674$	8.12579e8			0.102225
$675$	−5.86544e9	+	3.11454e9i	−0.734070	+	0.389790i
$676$	−1.51053e10			−1.88069
$677$	−1.19584e8	−	3.68040e8i	−0.0148119	−	0.0455864i	0.943377	−	0.331721i	$-0.107629\pi$
$677$	−1.19584e8	−	3.68040e8i	−0.0148119	−	0.0455864i	−0.958189	+	0.286135i	$0.907629\pi$
$678$	2.09364e8	−	1.52112e8i	0.0257987	−	0.0187439i
$679$	−4.99922e8	+	3.63215e8i	−0.0612856	+	0.0445266i
$680$	−1.58772e9	−	6.41992e8i	−0.193639	−	0.0782976i
$681$	−5.56739e9	−	4.04494e9i	−0.675518	−	0.490792i
$682$	5.13706e8			0.0620110
$683$	9.71135e9	+	7.05571e9i	1.16629	+	0.847360i	0.990560	−	0.137078i	$-0.0437710\pi$
$683$	9.71135e9	+	7.05571e9i	1.16629	+	0.847360i	0.175731	+	0.984438i	$0.443771\pi$
$684$	1.96220e9	−	6.03904e9i	0.234449	−	0.721558i
$685$	4.15422e9	+	6.65224e9i	0.493824	+	0.790771i
$686$	−1.81613e8	−	5.58949e8i	−0.0214790	−	0.0661055i
$687$	−1.51290e9	+	4.65621e9i	−0.178017	+	0.547879i
$688$	4.33020e9	−	1.33270e10i	0.506930	−	1.56017i
$689$	1.67739e9	+	5.16249e9i	0.195375	+	0.601301i
$690$	1.28444e7	+	2.05680e7i	0.00148848	+	0.00238353i
$691$	−1.22664e9	+	3.77522e9i	−0.141431	+	0.435280i	−0.996535	−	0.0831769i	$-0.973493\pi$
$691$	−1.22664e9	+	3.77522e9i	−0.141431	+	0.435280i	0.855104	+	0.518457i	$0.173493\pi$
$692$	2.17920e9	+	1.58328e9i	0.249992	+	0.181630i
$693$	−3.61802e9			−0.412956
$694$	4.24251e8	+	3.08237e8i	0.0481798	+	0.0350047i
$695$	−4.70027e9	−	1.90055e9i	−0.531099	−	0.214749i
$696$	−6.83490e8	+	4.96585e8i	−0.0768422	+	0.0558291i
$697$	−1.18268e10	+	8.59269e9i	−1.32298	+	0.961201i
$698$	−5.32997e7	−	1.64040e8i	−0.00593241	−	0.0182581i
$699$	3.34017e9			0.369912
$700$	−3.89285e9	−	3.76345e9i	−0.428967	−	0.414709i
$701$	−6.54792e9			−0.717944			−0.358972	−	0.933348i	$-0.616873\pi$
$701$	−6.54792e9			−0.717944			−0.358972	+	0.933348i	$0.616873\pi$
$702$	2.82797e8	+	8.70358e8i	0.0308528	+	0.0949551i
$703$	6.08565e9	−	4.42148e9i	0.660637	−	0.479981i
$704$	6.39395e9	−	4.64548e9i	0.690661	−	0.501795i
$705$	9.05438e8	+	1.44990e9i	0.0973188	+	0.155839i
$706$	−4.98262e8	−	3.62008e8i	−0.0532894	−	0.0387170i
$707$	7.23455e9			0.769917
$708$	4.79683e9	+	3.48510e9i	0.507970	+	0.369062i
$709$	1.10211e9	−	3.39194e9i	0.116135	−	0.357426i	−0.876047	−	0.482225i	$-0.839829\pi$
$709$	1.10211e9	−	3.39194e9i	0.116135	−	0.357426i	0.992182	+	0.124799i	$0.0398286\pi$
$710$	7.65126e8	−	1.90542e8i	0.0802285	−	0.0199796i
$711$	4.06373e9	+	1.25069e10i	0.424015	+	1.30498i
$712$	−9.84508e7	+	3.03000e8i	−0.0102221	+	0.0314603i
$713$	2.54421e8	−	7.83028e8i	0.0262869	−	0.0809029i
$714$	−8.79774e7	−	2.70767e8i	−0.00904539	−	0.0278388i
$715$	9.40159e9	−	1.11981e10i	0.961900	−	1.14570i
$716$	−5.50202e8	+	1.69335e9i	−0.0560179	+	0.172405i
$717$	7.26523e9	+	5.27850e9i	0.736092	+	0.534802i
$718$	4.44452e8			0.0448115
$719$	−1.13227e10	−	8.22642e9i	−1.13605	−	0.825391i	−0.149489	−	0.988763i	$-0.547763\pi$
$719$	−1.13227e10	−	8.22642e9i	−1.13605	−	0.825391i	−0.986565	+	0.163372i	$0.947763\pi$
$720$	−7.49206e9	+	1.86577e9i	−0.748061	+	0.186293i
$721$	−6.18691e8	+	4.49505e8i	−0.0614752	+	0.0446644i
$722$	2.93345e7	−	2.13128e7i	0.00290067	−	0.00210746i
$723$	4.51589e8	+	1.38985e9i	0.0444385	+	0.136768i
$724$	−5.16545e9			−0.505852
$725$	−1.06607e10	−	1.03063e10i	−1.03897	−	1.00443i
$726$	−7.66590e7			−0.00743507
$727$	−1.27257e9	−	3.91656e9i	−0.122832	−	0.378037i	0.870668	−	0.491871i	$-0.163687\pi$
$727$	−1.27257e9	−	3.91656e9i	−0.122832	−	0.378037i	−0.993500	+	0.113834i	$0.963687\pi$
$728$	−1.21031e9	+	8.79340e8i	−0.116262	+	0.0844689i
$729$	−6.62727e8	+	4.81499e8i	−0.0633561	+	0.0460309i
$730$	−5.44394e7	+	7.75432e8i	−0.00517945	+	0.0737758i
$731$	2.10829e10	+	1.53176e10i	1.99627	+	1.45037i
$732$	−7.19046e8			−0.0677592
$733$	8.06909e9	+	5.86253e9i	0.756764	+	0.549821i	0.897916	−	0.440167i	$-0.145081\pi$
$733$	8.06909e9	+	5.86253e9i	0.756764	+	0.549821i	−0.141152	+	0.989988i	$0.545081\pi$
$734$	3.03001e8	−	9.32540e8i	0.0282818	−	0.0870425i
$735$	−2.25108e8	+	3.20643e9i	−0.0209115	+	0.297863i
$736$	6.00325e7	+	1.84761e8i	0.00555027	+	0.0170820i
$737$	−1.89633e9	+	5.83631e9i	−0.174493	+	0.537034i
$738$	2.05944e8	−	6.33831e8i	0.0188605	−	0.0580465i
$739$	3.07422e9	+	9.46148e9i	0.280207	+	0.862390i	0.987794	+	0.155763i	$0.0497837\pi$
$739$	3.07422e9	+	9.46148e9i	0.280207	+	0.862390i	−0.707587	+	0.706626i	$0.750216\pi$
$740$	−8.52251e9	−	3.44607e9i	−0.773137	−	0.312617i
$741$	−2.64310e9	+	8.13464e9i	−0.238644	+	0.734471i
$742$	1.41865e8	+	1.03071e8i	0.0127485	+	0.00926236i
$743$	2.37681e9			0.212585			0.106293	−	0.994335i	$-0.466102\pi$
$743$	2.37681e9			0.212585			0.106293	+	0.994335i	$0.466102\pi$
$744$	5.95707e8	+	4.32807e8i	0.0530307	+	0.0385291i
$745$	−3.98212e9	+	4.74304e9i	−0.352832	+	0.420252i
$746$	−7.47616e8	+	5.43175e8i	−0.0659315	+	0.0479020i
$747$	−5.75688e9	+	4.18262e9i	−0.505318	+	0.367135i
$748$	4.58856e9	+	1.41221e10i	0.400886	+	1.23380i
$749$	4.17019e9			0.362635
$750$	−1.54530e8	−	3.47858e8i	−0.0133751	−	0.0301084i
$751$	−8.05362e9			−0.693827			−0.346914	−	0.937897i	$-0.612770\pi$
$751$	−8.05362e9			−0.693827			−0.346914	+	0.937897i	$0.612770\pi$
$752$	1.39883e9	+	4.30514e9i	0.119950	+	0.369169i
$753$	−3.23053e9	+	2.34711e9i	−0.275734	+	0.200333i
$754$	−1.65309e9	+	1.20104e9i	−0.140442	+	0.102037i
$755$	−2.12195e9	+	2.52742e9i	−0.179441	+	0.213729i
$756$	−4.76630e9	−	3.46292e9i	−0.401194	−	0.291485i
$757$	−3.76157e9			−0.315162			−0.157581	−	0.987506i	$-0.550370\pi$
$757$	−3.76157e9			−0.315162			−0.157581	+	0.987506i	$0.550370\pi$
$758$	−6.63283e8	−	4.81904e8i	−0.0553168	−	0.0401900i
$759$	1.30267e8	−	4.00922e8i	0.0108141	−	0.0332823i
$760$	1.54092e9	+	6.23070e8i	0.127331	+	0.0514860i
$761$	−4.75847e9	−	1.46451e10i	−0.391400	−	1.20461i	−0.931730	−	0.363152i	$-0.881701\pi$
$761$	−4.75847e9	−	1.46451e10i	−0.391400	−	1.20461i	0.540330	−	0.841453i	$-0.318299\pi$
$762$	1.66307e7	−	5.11839e7i	0.00136166	−	0.00419074i
$763$	1.73750e8	−	5.34749e8i	0.0141609	−	0.0435827i
$764$	−1.13145e9	−	3.48224e9i	−0.0917926	−	0.282509i
$765$	1.00558e9	−	1.43234e10i	0.0812083	−	1.15673i
$766$	−2.23714e7	+	6.88520e7i	−0.00179842	+	0.00553498i
$767$	2.32614e10	+	1.69004e10i	1.86146	+	1.35243i
$768$	5.56299e9			0.443143
$769$	6.79539e8	+	4.93714e8i	0.0538855	+	0.0391501i	0.614402	−	0.788993i	$-0.289397\pi$
$769$	6.79539e8	+	4.93714e8i	0.0538855	+	0.0391501i	−0.560516	+	0.828143i	$0.689397\pi$
$770$	3.30793e7	−	4.71180e8i	0.00261119	−	0.0371937i
$771$	7.02640e9	−	5.10498e9i	0.552131	−	0.401147i
$772$	−1.75081e9	+	1.27203e9i	−0.136955	+	0.0995035i
$773$	−1.89694e8	−	5.83818e8i	−0.0147715	−	0.0454621i	0.943399	−	0.331660i	$-0.107609\pi$
$773$	−1.89694e8	−	5.83818e8i	−0.0147715	−	0.0454621i	−0.958171	+	0.286198i	$0.907609\pi$
$774$	−1.18803e9			−0.0920949
$775$	−5.67179e9	+	1.16125e10i	−0.437687	+	0.896131i
$776$	−2.31816e8			−0.0178085
$777$	−9.46854e8	−	2.91412e9i	−0.0724118	−	0.222861i
$778$	−2.00950e8	+	1.45998e8i	−0.0152988	+	0.0111153i
$779$	1.14782e10	−	8.33942e9i	0.869949	−	0.632055i
$780$	1.01430e10	−	2.52595e9i	0.765308	−	0.190587i
$781$	−1.10895e10	−	8.05700e9i	−0.832979	−	0.605194i
$782$	−1.19422e8			−0.00893017
$783$	−1.30527e10	−	9.48332e9i	−0.971702	−	0.705983i
$784$	−2.63034e9	+	8.09535e9i	−0.194942	+	0.599970i
$785$	5.20919e9	−	6.20458e9i	0.384349	−	0.457792i
$786$	−9.28683e7	−	2.85819e8i	−0.00682163	−	0.0209948i
$787$	4.52323e9	−	1.39211e10i	0.330778	−	1.01803i	−0.637986	−	0.770048i	$-0.720232\pi$
$787$	4.52323e9	−	1.39211e10i	0.330778	−	1.01803i	0.968764	−	0.247983i	$-0.0797677\pi$
$788$	−1.46178e9	+	4.49889e9i	−0.106424	+	0.327539i
$789$	−2.44724e9	−	7.53184e9i	−0.177381	−	0.545923i
$790$	−1.66594e9	+	4.14876e8i	−0.120217	+	0.0299381i
$791$	−2.49655e9	+	7.68359e9i	−0.179359	+	0.552010i
$792$	−1.09806e9	−	7.97789e8i	−0.0785396	−	0.0570624i
$793$	−3.48690e9			−0.248303
$794$	1.20721e9	+	8.77093e8i	0.0855880	+	0.0621833i
$795$	−1.30121e9	−	2.08365e9i	−0.0918463	−	0.147076i
$796$	1.27226e10	−	9.24351e9i	0.894088	−	0.649593i
$797$	−9.04435e9	+	6.57110e9i	−0.632810	+	0.459763i	−0.857373	−	0.514696i	$-0.827905\pi$
$797$	−9.04435e9	+	6.57110e9i	−0.632810	+	0.459763i	0.224563	+	0.974460i	$0.427905\pi$
$798$	8.53843e7	+	2.62786e8i	0.00594796	+	0.0183059i
$799$	−8.41836e9			−0.583867
$800$	−5.27863e8	−	3.00339e9i	−0.0364507	−	0.207394i
$801$	−2.67112e9			−0.183645
$802$	−4.47942e7	−	1.37863e8i	−0.00306628	−	0.00943704i
$803$	1.09326e10	−	7.94303e9i	0.745111	−	0.541355i
$804$	−3.54922e9	+	2.57866e9i	−0.240844	+	0.174984i
$805$	−7.01824e8	−	2.83781e8i	−0.0474179	−	0.0191734i
$806$	1.44078e9	+	1.04679e9i	0.0969224	+	0.0704182i
$807$	4.47921e9			0.300016
$808$	2.19568e9	+	1.59525e9i	0.146429	+	0.106387i
$809$	3.71355e9	−	1.14291e10i	0.246586	−	0.758915i	−0.748785	−	0.662813i	$-0.769363\pi$
$809$	3.71355e9	−	1.14291e10i	0.246586	−	0.758915i	0.995371	−	0.0961019i	$-0.0306375\pi$
$810$	2.23663e8	+	3.58157e8i	0.0147876	+	0.0236797i
$811$	3.69865e9	+	1.13833e10i	0.243484	+	0.749366i	0.995882	+	0.0906576i	$0.0288969\pi$
$811$	3.69865e9	+	1.13833e10i	0.243484	+	0.749366i	−0.752398	+	0.658708i	$0.771103\pi$
$812$	4.06492e9	−	1.25105e10i	0.266444	−	0.820031i
$813$	−6.24757e8	+	1.92281e9i	−0.0407750	+	0.125493i
$814$	−2.47811e8	−	7.62685e8i	−0.0161041	−	0.0495632i
$815$	1.34043e10	+	2.14647e10i	0.867349	+	1.38890i
$816$	−3.26380e9	+	1.00449e10i	−0.210285	+	0.647190i
$817$	−2.04615e10	−	1.48661e10i	−1.31268	−	0.953719i
$818$	4.76751e8			0.0304547
$819$	−1.01474e10	−	7.37248e9i	−0.645445	−	0.468943i
$820$	−1.60744e10	−	6.49968e9i	−1.01809	−	0.411664i
$821$	5.73354e9	−	4.16566e9i	0.361595	−	0.262714i	−0.392122	−	0.919913i	$-0.628259\pi$
$821$	5.73354e9	−	4.16566e9i	0.361595	−	0.262714i	0.753717	+	0.657199i	$0.228259\pi$
$822$	−3.95695e8	+	2.87489e8i	−0.0248490	+	0.0180539i
$823$	−3.55153e9	−	1.09305e10i	−0.222083	−	0.683502i	−0.998575	−	0.0533740i	$-0.983002\pi$
$823$	−3.55153e9	−	1.09305e10i	−0.222083	−	0.683502i	0.776491	−	0.630128i	$-0.216998\pi$
$824$	−2.86890e8			−0.0178636
$825$	−2.90404e9	+	5.94580e9i	−0.180058	+	0.368656i
$826$	9.28844e8			0.0573473
$827$	−3.52915e9	−	1.08616e10i	−0.216970	−	0.667766i	−0.999008	−	0.0445346i	$-0.985820\pi$
$827$	−3.52915e9	−	1.08616e10i	−0.216970	−	0.667766i	0.782038	−	0.623231i	$-0.214180\pi$
$828$	−8.77739e8	+	6.37715e8i	−0.0537352	+	0.0390409i
$829$	−1.31622e10	+	9.56286e9i	−0.802391	+	0.582971i	−0.911615	−	0.411046i	$-0.865164\pi$
$829$	−1.31622e10	+	9.56286e9i	−0.802391	+	0.582971i	0.109224	+	0.994017i	$0.465164\pi$
$830$	−4.92074e8	−	7.87968e8i	−0.0298715	−	0.0478339i
$831$	−5.79673e9	−	4.21157e9i	−0.350413	−	0.254590i
$832$	2.73991e10			1.64932
$833$	−1.28066e10	−	9.30453e9i	−0.767672	−	0.557746i
$834$	9.77054e7	−	3.00706e8i	0.00583227	−	0.0179499i
$835$	1.48864e10	−	3.70722e9i	0.884886	−	0.220366i
$836$	−4.45332e9	−	1.37059e10i	−0.263610	−	0.811308i
$837$	−4.34535e9	+	1.33736e10i	−0.256145	+	0.788333i
$838$	8.44875e7	−	2.60026e8i	0.00495951	−	0.0152638i
$839$	1.54156e9	+	4.74443e9i	0.0901143	+	0.277343i	0.985950	−	0.167043i	$-0.0534218\pi$
$839$	1.54156e9	+	4.74443e9i	0.0901143	+	0.277343i	−0.895835	+	0.444386i	$0.853422\pi$
$840$	4.35337e8	−	5.18523e8i	0.0253424	−	0.0301850i
$841$	5.80143e9	−	1.78550e10i	0.336317	−	1.03508i
$842$	−1.58117e9	−	1.14879e9i	−0.0912824	−	0.0663205i
$843$	−1.13212e9			−0.0650870
$844$	2.45209e10	+	1.78154e10i	1.40390	+	1.02000i
$845$	3.21679e10	−	8.01090e9i	1.83411	−	0.456754i
$846$	3.10486e8	−	2.25581e8i	0.0176297	−	0.0128088i
$847$	1.93613e9	−	1.40668e9i	0.109482	−	0.0795433i
$848$	−2.01026e9	−	6.18694e9i	−0.113205	−	0.348410i
$849$	5.99869e9			0.336418
$850$	1.85616e9	+	2.61916e8i	0.103669	+	0.0146283i
$851$	−1.28527e9			−0.0714894
$852$	−3.02817e9	−	9.31974e9i	−0.167742	−	0.516256i
$853$	−1.33327e10	+	9.68681e9i	−0.735526	+	0.534391i	−0.891307	−	0.453401i	$-0.850211\pi$
$853$	−1.33327e10	+	9.68681e9i	−0.735526	+	0.534391i	0.155781	+	0.987792i	$0.450211\pi$
$854$	−9.11298e7	+	6.62097e7i	−0.00500677	+	0.00363763i
$855$	−9.75938e8	+	1.39012e10i	−0.0533999	+	0.760626i
$856$	1.26565e9	+	9.19547e8i	0.0689691	+	0.0501090i
$857$	−2.18005e10			−1.18313			−0.591566	−	0.806256i	$-0.701490\pi$
$857$	−2.18005e10			−1.18313			−0.591566	+	0.806256i	$0.701490\pi$
$858$	7.37699e8	+	5.35970e8i	0.0398725	+	0.0289691i
$859$	3.18463e9	−	9.80128e9i	0.171428	−	0.527603i	−0.828024	−	0.560693i	$-0.810535\pi$
$859$	3.18463e9	−	9.80128e9i	0.171428	−	0.527603i	0.999452	+	0.0330902i	$0.0105349\pi$
$860$	−2.16462e9	+	3.08328e10i	−0.116048	+	1.65298i
$861$	−1.78588e9	−	5.49636e9i	−0.0953543	−	0.293470i
$862$	1.03778e8	−	3.19395e8i	0.00551860	−	0.0169845i
$863$	−6.30189e9	+	1.93952e10i	−0.333759	+	1.02720i	0.633571	+	0.773685i	$0.281588\pi$
$863$	−6.30189e9	+	1.93952e10i	−0.333759	+	1.02720i	−0.967330	+	0.253520i	$0.918412\pi$
$864$	−1.02532e9	−	3.15560e9i	−0.0540829	−	0.166450i
$865$	−5.48045e9	−	2.21601e9i	−0.287912	−	0.116417i
$866$	−6.36829e8	+	1.95996e9i	−0.0333204	+	0.102550i
$867$	−8.65240e9	−	6.28634e9i	−0.450889	−	0.327590i
$868$	−1.14649e10			−0.595047
$869$	2.41457e10	+	1.75429e10i	1.24816	+	0.906843i
$870$	5.94602e8	−	7.08220e8i	0.0306132	−	0.0364629i
$871$	−1.72113e10	+	1.25048e10i	−0.882573	+	0.641227i
$872$	1.70648e8	−	1.23983e8i	0.00871550	−	0.00633218i
$873$	−6.00597e8	−	1.84845e9i	−0.0305515	−	0.0940279i
$874$	1.15902e8			0.00587219
$875$	1.02860e10	+	5.95003e9i	0.519061	+	0.300256i
$876$	9.66074e9			0.485563
$877$	−2.97479e9	−	9.15546e9i	−0.148922	−	0.458333i	0.848573	−	0.529079i	$-0.177462\pi$
$877$	−2.97479e9	−	9.15546e9i	−0.148922	−	0.458333i	−0.997494	+	0.0707451i	$0.977462\pi$
$878$	−9.23243e7	+	6.70775e7i	−0.00460347	+	0.00334461i
$879$	1.80933e9	−	1.31456e9i	0.0898580	−	0.0652857i
$880$	−1.12672e10	+	1.34202e10i	−0.557350	+	0.663851i
$881$	2.98720e10	+	2.17033e10i	1.47180	+	1.06932i	0.980087	+	0.198567i	$0.0636287\pi$
$881$	2.98720e10	+	2.17033e10i	1.47180	+	1.06932i	0.491712	+	0.870758i	$0.336371\pi$
$882$	7.21659e8			0.0354154
$883$	−1.51467e10	−	1.10047e10i	−0.740380	−	0.537917i	0.152450	−	0.988311i	$-0.451284\pi$
$883$	−1.51467e10	−	1.10047e10i	−0.740380	−	0.537917i	−0.892830	+	0.450394i	$0.851284\pi$
$884$	−1.59075e10	+	4.89582e10i	−0.774495	+	2.38365i
$885$	−1.20635e10	−	4.87786e9i	−0.585021	−	0.236553i
$886$	1.21352e8	+	3.73482e8i	0.00586175	+	0.0180406i
$887$	3.14199e9	−	9.67006e9i	0.151172	−	0.465261i	−0.846581	−	0.532260i	$-0.821343\pi$
$887$	3.14199e9	−	9.67006e9i	0.151172	−	0.465261i	0.997753	+	0.0669998i	$0.0213427\pi$
$888$	3.55207e8	−	1.09322e9i	0.0170230	−	0.0523915i
$889$	5.19186e8	+	1.59789e9i	0.0247838	+	0.0762765i
$890$	2.44219e7	−	3.47864e8i	0.00116122	−	0.0165404i
$891$	2.26838e9	−	6.98136e9i	0.107435	−	0.330650i
$892$	5.54393e9	+	4.02790e9i	0.261542	+	0.190021i
$893$	8.17024e9			0.383932
$894$	−3.12458e8	−	2.27014e8i	−0.0146255	−	0.0106261i
$895$	2.73653e8	−	3.89790e9i	0.0127591	−	0.181740i
$896$	2.91563e9	−	2.11833e9i	0.135411	−	0.0983820i
$897$	1.18232e9	−	8.59007e8i	0.0546968	−	0.0397396i
$898$	1.94690e8	+	5.99194e8i	0.00897173	+	0.0276122i
$899$	−3.13971e10			−1.44122
$900$	1.50413e10	−	7.98689e9i	0.687758	−	0.365199i
$901$	1.20981e10			0.551035
$902$	−4.67401e8	−	1.43851e9i	−0.0212064	−	0.0652665i
$903$	−8.33467e9	+	6.05549e9i	−0.376687	+	0.273679i
$904$	−2.45197e9	+	1.78146e9i	−0.110389	+	0.0802022i
$905$	1.10002e10	−	2.73943e9i	0.493323	−	0.122854i
$906$	−1.66500e8	−	1.20969e8i	−0.00743814	−	0.00540412i
$907$	1.39668e9			0.0621544			0.0310772	−	0.999517i	$-0.490106\pi$
$907$	1.39668e9			0.0621544			0.0310772	+	0.999517i	$0.490106\pi$
$908$	3.25196e10	+	2.36269e10i	1.44160	+	1.04738i
$909$	−7.03153e9	+	2.16408e10i	−0.310510	+	0.955653i
$910$	1.05291e9	−	1.25410e9i	0.0463175	−	0.0551680i
$911$	2.34615e9	+	7.22071e9i	0.102812	+	0.316421i	0.989211	−	0.146501i	$-0.0468010\pi$
$911$	2.34615e9	+	7.22071e9i	0.102812	+	0.316421i	−0.886399	+	0.462922i	$0.846801\pi$
$912$	3.16760e9	−	9.74888e9i	0.138277	−	0.425572i
$913$	−4.99059e9	+	1.53595e10i	−0.217022	+	0.667925i
$914$	5.72975e8	+	1.76343e9i	0.0248213	+	0.0763920i
$915$	1.53126e9	−	3.81336e8i	0.0660809	−	0.0164564i
$916$	8.83696e9	−	2.71974e10i	0.379900	−	1.16921i
$917$	7.59025e9	+	5.51464e9i	0.325060	+	0.236170i
$918$	2.03965e9			0.0870172
$919$	−2.72058e10	−	1.97662e10i	−1.15626	−	0.840075i	−0.166963	−	0.985963i	$-0.553396\pi$
$919$	−2.72058e10	−	1.97662e10i	−1.15626	−	0.840075i	−0.989301	+	0.145888i	$0.953396\pi$
$920$	−1.50427e8	−	2.40883e8i	−0.00636897	−	0.0101988i
$921$	1.01374e10	−	7.36524e9i	0.427580	−	0.310655i
$922$	−1.28494e9	+	9.33567e8i	−0.0539916	+	0.0392272i
$923$	−1.46846e10	−	4.51945e10i	−0.614690	−	1.89182i
$924$	−5.87020e9			−0.244794
$925$	1.99769e10	+	2.81886e9i	0.829912	+	0.117106i
$926$	1.05294e9			0.0435779
$927$	−7.43283e8	−	2.28759e9i	−0.0306461	−	0.0943189i
$928$	5.99349e9	−	4.35453e9i	0.246185	−	0.178864i
$929$	2.46808e9	−	1.79316e9i	0.100996	−	0.0733778i	−0.536141	−	0.844128i	$-0.680119\pi$
$929$	2.46808e9	−	1.79316e9i	0.100996	−	0.0733778i	0.637137	+	0.770751i	$0.280119\pi$
$930$	−7.47194e8	−	3.02127e8i	−0.0304609	−	0.0123168i
$931$	1.24291e10	+	9.03028e9i	0.504796	+	0.366756i
$932$	−1.95102e10			−0.789418
$933$	−1.37106e10	−	9.96132e9i	−0.552675	−	0.401542i
$934$	−7.92677e8	+	2.43961e9i	−0.0318333	+	0.0979729i
$935$	−1.72612e10	−	2.76407e10i	−0.690605	−	1.10588i
$936$	−1.45404e9	−	4.47508e9i	−0.0579577	−	0.178375i
$937$	−9.83532e9	+	3.02700e10i	−0.390571	+	1.20205i	0.541786	+	0.840516i	$0.317748\pi$
$937$	−9.83532e9	+	3.02700e10i	−0.390571	+	1.20205i	−0.932357	+	0.361538i	$0.882252\pi$
$938$	−2.12375e8	+	6.53622e8i	−0.00840220	+	0.0258593i
$939$	8.26579e8	+	2.54395e9i	0.0325803	+	0.100272i
$940$	−5.28875e9	−	8.46899e9i	−0.207685	−	0.332571i
$941$	4.69388e9	−	1.44463e10i	0.183640	−	0.565187i	−0.816282	−	0.577654i	$-0.803968\pi$
$941$	4.69388e9	−	1.44463e10i	0.183640	−	0.565187i	0.999922	+	0.0124667i	$0.00396837\pi$
$942$	4.08741e8	+	2.96967e8i	0.0159320	+	0.0115753i
$943$	−2.42417e9			−0.0941397
$944$	−2.78775e10	−	2.02542e10i	−1.07858	−	0.783632i
$945$	1.19867e10	+	4.84680e9i	0.462049	+	0.186829i
$946$	−2.18135e9	+	1.58485e9i	−0.0837736	+	0.0608651i
$947$	2.10486e10	−	1.52927e10i	0.805373	−	0.585138i	−0.107112	−	0.994247i	$-0.534160\pi$
$947$	2.10486e10	−	1.52927e10i	0.805373	−	0.585138i	0.912486	+	0.409109i	$0.134160\pi$
$948$	6.59337e9	+	2.02923e10i	0.251350	+	0.773575i
$949$	4.68481e10			1.77935
$950$	−1.80145e9	−	2.54196e8i	−0.0681695	−	0.00961913i
$951$	2.17213e10			0.818942
$952$	1.03035e9	+	3.17108e9i	0.0387039	+	0.119118i
$953$	−2.35354e10	+	1.70995e10i	−0.880838	+	0.639966i	−0.933473	−	0.358648i	$-0.883238\pi$
$953$	−2.35354e10	+	1.70995e10i	−0.880838	+	0.639966i	0.0526350	+	0.998614i	$0.483238\pi$
$954$	−4.46201e8	+	3.24184e8i	−0.0166384	+	0.0120885i
$955$	4.25626e9	+	6.81564e9i	0.158131	+	0.253218i
$956$	−4.24369e10	−	3.08322e10i	−1.57087	−	1.14131i
$957$	−1.60758e10			−0.592898
$958$	−1.93999e9	−	1.40949e9i	−0.0712887	−	0.0517943i
$959$	4.71845e9	−	1.45219e10i	0.172756	−	0.531689i
$960$	−1.20323e10	+	2.99644e9i	−0.438933	+	0.109309i
$961$	−4.57292e7	−	1.40740e8i	−0.00166212	−	0.00511547i
$962$	8.59104e8	−	2.64405e9i	0.0311124	−	0.0957540i
$963$	−4.05317e9	+	1.24744e10i	−0.146252	+	0.450118i
$964$	−2.63777e9	−	8.11823e9i	−0.0948348	−	0.291872i
$965$	3.05387e9	−	3.63741e9i	0.109397	−	0.130301i
$966$	1.45890e7	−	4.49002e7i	0.000520720	−	0.00160261i
$967$	−2.58881e9	−	1.88088e9i	−0.0920677	−	0.0668911i	0.540799	−	0.841152i	$-0.318122\pi$
$967$	−2.58881e9	−	1.88088e9i	−0.0920677	−	0.0668911i	−0.632867	+	0.774261i	$0.718122\pi$
$968$	8.97792e8			0.0318135
$969$	1.54224e10	+	1.12050e10i	0.544527	+	0.395622i
$970$	2.46217e8	−	6.13164e7i	0.00866198	−	0.00215713i
$971$	1.71801e9	−	1.24821e9i	0.0602224	−	0.0437541i	−0.557267	−	0.830333i	$-0.688150\pi$
$971$	1.71801e9	−	1.24821e9i	0.0602224	−	0.0437541i	0.617489	+	0.786579i	$0.288150\pi$
$972$	2.34009e10	−	1.70017e10i	0.817336	−	0.593829i
$973$	3.05023e9	+	9.38763e9i	0.106154	+	0.326709i
$974$	−1.48798e9			−0.0515990
$975$	−2.02607e10	+	1.07584e10i	−0.700065	+	0.371734i
$976$	4.17884e9			0.143874
$977$	−3.31031e9	−	1.01881e10i	−0.113563	−	0.349511i	0.878082	−	0.478511i	$-0.158823\pi$
$977$	−3.31031e9	−	1.01881e10i	−0.113563	−	0.349511i	−0.991645	+	0.129000i	$0.958823\pi$
$978$	−1.27678e9	+	9.27637e8i	−0.0436447	+	0.0317097i
$979$	−4.90446e9	+	3.56330e9i	−0.167052	+	0.121370i
$980$	1.31488e9	−	1.87291e10i	0.0446267	−	0.635660i
$981$	1.43073e9	+	1.03948e9i	0.0483855	+	0.0351541i
$982$	−5.77437e8			−0.0194587
$983$	−1.82320e10	−	1.32463e10i	−0.612204	−	0.444792i	0.237986	−	0.971269i	$-0.423513\pi$
$983$	−1.82320e10	−	1.32463e10i	−0.612204	−	0.444792i	−0.850190	+	0.526477i	$0.823513\pi$
$984$	6.69962e8	−	2.06193e9i	0.0224165	−	0.0689908i
$985$	7.27042e8	−	1.03560e10i	0.0242400	−	0.345273i
$986$	1.40729e9	+	4.33119e9i	0.0467535	+	0.143893i
$987$	1.02842e9	−	3.16514e9i	0.0340454	−	0.104781i
$988$	1.54386e10	−	4.75152e10i	0.509283	−	1.56741i
$989$	1.33539e9	+	4.10990e9i	0.0438956	+	0.135097i
$990$	1.37730e9	+	5.56908e8i	0.0451132	+	0.0182415i
$991$	−1.45555e10	+	4.47971e10i	−0.475082	+	1.46215i	0.370766	+	0.928726i	$0.379095\pi$
$991$	−1.45555e10	+	4.47971e10i	−0.475082	+	1.46215i	−0.845848	+	0.533425i	$0.820905\pi$
$992$	−5.22373e9	−	3.79526e9i	−0.169899	−	0.123439i
$993$	2.39587e10			0.776498
$994$	−1.24194e9	−	9.02323e8i	−0.0401096	−	0.0291413i
$995$	−2.21916e10	+	2.64320e10i	−0.714179	+	0.850647i
$996$	−9.34049e9	+	6.78626e9i	−0.299545	+	0.217632i
$997$	9.00730e9	−	6.54419e9i	0.287847	−	0.209133i	−0.434486	−	0.900679i	$-0.643070\pi$
$997$	9.00730e9	−	6.54419e9i	0.287847	−	0.209133i	0.722333	+	0.691546i	$0.243070\pi$
$998$	−2.06984e8	−	6.37031e8i	−0.00659143	−	0.0202863i
$999$	2.19516e10			0.696607

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.8.d.a.6.9	✓	68
25.11	even	5		625.8.a.d.1.17		34
25.14	even	10		625.8.a.c.1.18		34
25.21	even	5	inner	25.8.d.a.21.9	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.8.d.a.6.9	✓	68	1.1	even	1	trivial
25.8.d.a.21.9	yes	68	25.21	even	5	inner
625.8.a.c.1.18		34	25.14	even	10
625.8.a.d.1.17		34	25.11	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	25.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.247040 + 0.760310i) q^{2} +(-17.6400 + 12.8162i) q^{3} +(103.037 - 74.8609i) q^{4} +(-179.724 + 214.066i) q^{5} +(-14.1021 - 10.2458i) q^{6} +544.176 q^{7} +(165.157 + 119.993i) q^{8} +(-528.905 + 1627.80i) q^{9} +O(q^{10})\)	\(q+(0.247040 + 0.760310i) q^{2} +(-17.6400 + 12.8162i) q^{3} +(103.037 - 74.8609i) q^{4} +(-179.724 + 214.066i) q^{5} +(-14.1021 - 10.2458i) q^{6} +544.176 q^{7} +(165.157 + 119.993i) q^{8} +(-528.905 + 1627.80i) q^{9} +(-207.155 - 83.7630i) q^{10} +(1200.38 + 3694.38i) q^{11} +(-858.144 + 2641.10i) q^{12} +(-4161.43 + 12807.6i) q^{13} +(134.433 + 413.742i) q^{14} +(426.814 - 6079.52i) q^{15} +(4987.22 - 15349.1i) q^{16} +(24281.8 + 17641.7i) q^{17} -1368.29 q^{18} +(-23566.1 - 17121.8i) q^{19} +(-2493.06 + 35511.0i) q^{20} +(-9599.29 + 6974.29i) q^{21} +(-2512.33 + 1825.32i) q^{22} +(1538.01 + 4733.50i) q^{23} -4451.23 q^{24} +(-13523.6 - 76945.6i) q^{25} -10765.7 q^{26} +(-26268.2 - 80845.1i) q^{27} +(56070.4 - 40737.5i) q^{28} +(153551. - 111561. i) q^{29} +(4727.76 - 1177.37i) q^{30} +(-133830. - 97233.0i) q^{31} +39032.7 q^{32} +(-68522.8 - 49784.7i) q^{33} +(-7414.63 + 22819.9i) q^{34} +(-97801.5 + 116490. i) q^{35} +(67361.8 + 207318. i) q^{36} +(-79799.8 + 245598. i) q^{37} +(7196.09 - 22147.3i) q^{38} +(-90737.0 - 279260. i) q^{39} +(-55369.1 + 13788.8i) q^{40} +(-150512. + 463227. i) q^{41} +(-7674.03 - 5575.51i) q^{42} +868259. q^{43} +(400248. + 290797. i) q^{44} +(-253401. - 405776. i) q^{45} +(-3218.98 + 2338.72i) q^{46} +(-226915. + 164863. i) q^{47} +(108743. + 334676. i) q^{48} -527415. q^{49} +(55161.6 - 29290.8i) q^{50} -654432. q^{51} +(530003. + 1.63118e6i) q^{52} +(326100. - 236925. i) q^{53} +(54978.1 - 39943.9i) q^{54} +(-1.00658e6 - 407008. i) q^{55} +(89874.4 + 65297.5i) q^{56} +635143. q^{57} +(122754. + 89186.1i) q^{58} +(659783. - 2.03060e6i) q^{59} +(-411140. - 658368. i) q^{60} +(80013.1 + 246255. i) q^{61} +(40865.9 - 125772. i) q^{62} +(-287818. + 885812. i) q^{63} +(-628722. - 1.93501e6i) q^{64} +(-1.99376e6 - 3.19265e6i) q^{65} +(20924.0 - 64397.3i) q^{66} +(1.27807e6 + 928572. i) q^{67} +3.82260e6 q^{68} +(-87796.2 - 63787.7i) q^{69} +(-112729. - 45581.8i) q^{70} +(-2.85481e6 + 2.07414e6i) q^{71} +(-282678. + 205377. i) q^{72} +(-1.07502e6 - 3.30856e6i) q^{73} -206445. q^{74} +(1.22471e6 + 1.18400e6i) q^{75} -3.70993e6 q^{76} +(653217. + 2.01039e6i) q^{77} +(189908. - 137976. i) q^{78} +(6.21591e6 - 4.51612e6i) q^{79} +(2.38940e6 + 3.82620e6i) q^{80} +(-1.52882e6 - 1.11075e6i) q^{81} -389378. q^{82} +(3.36350e6 + 2.44373e6i) q^{83} +(-466982. + 1.43722e6i) q^{84} +(-8.14052e6 + 2.02726e6i) q^{85} +(214494. + 660145. i) q^{86} +(-1.27885e6 + 3.93588e6i) q^{87} +(-245051. + 754189. i) q^{88} +(482259. + 1.48424e6i) q^{89} +(245915. - 292906. i) q^{90} +(-2.26455e6 + 6.96957e6i) q^{91} +(512826. + 372590. i) q^{92} +3.60692e6 q^{93} +(-181404. - 131798. i) q^{94} +(7.90058e6 - 1.96751e6i) q^{95} +(-688538. + 500252. i) q^{96} +(-918677. + 667458. i) q^{97} +(-130292. - 400999. i) q^{98} -6.64861e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 11 q^{2} + 23 q^{3} - 1091 q^{4} + 475 q^{5} - 179 q^{6} + 1734 q^{7} + 220 q^{8} - 14554 q^{9}+O(q^{10}) \) 68 * q - 11 * q^2 + 23 * q^3 - 1091 * q^4 + 475 * q^5 - 179 * q^6 + 1734 * q^7 + 220 * q^8 - 14554 * q^9	\( 68 q - 11 q^{2} + 23 q^{3} - 1091 q^{4} + 475 q^{5} - 179 q^{6} + 1734 q^{7} + 220 q^{8} - 14554 q^{9} + 4245 q^{10} + 466 q^{11} + 9979 q^{12} - 7407 q^{13} - 20177 q^{14} - 9285 q^{15} - 68527 q^{16} + 71504 q^{17} + 116208 q^{18} - 48685 q^{19} - 138265 q^{20} - 2274 q^{21} - 271952 q^{22} - 63227 q^{23} + 553980 q^{24} + 276615 q^{25} + 675246 q^{26} - 270235 q^{27} - 782613 q^{28} - 99655 q^{29} - 1011285 q^{30} + 39051 q^{31} + 1045974 q^{32} + 1766456 q^{33} + 605893 q^{34} - 476935 q^{35} - 2928227 q^{36} + 83909 q^{37} + 1937525 q^{38} + 1316257 q^{39} + 2903410 q^{40} - 1964944 q^{41} - 3462547 q^{42} - 3439822 q^{43} - 3557652 q^{44} - 2121790 q^{45} + 2982521 q^{46} + 1663474 q^{47} + 1678378 q^{48} + 6584354 q^{49} + 408485 q^{50} + 3922076 q^{51} - 5301176 q^{52} + 788553 q^{53} - 6946145 q^{54} - 2630560 q^{55} - 415350 q^{56} - 14598410 q^{57} + 4727030 q^{58} - 3625740 q^{59} + 29158890 q^{60} - 4161559 q^{61} + 19658928 q^{62} + 2426738 q^{63} - 4408596 q^{64} - 2030220 q^{65} - 6985528 q^{66} + 8470434 q^{67} - 29099218 q^{68} - 360673 q^{69} - 22417320 q^{70} - 4808044 q^{71} + 25676065 q^{72} + 5517633 q^{73} + 14050068 q^{74} + 257240 q^{75} + 22502000 q^{76} - 9936772 q^{77} + 14948561 q^{78} - 5343505 q^{79} - 3987180 q^{80} - 5865817 q^{81} - 76614542 q^{82} - 645927 q^{83} + 5992628 q^{84} + 48268560 q^{85} - 27540609 q^{86} + 65370380 q^{87} - 3612320 q^{88} + 11153500 q^{89} + 7267975 q^{90} - 9123484 q^{91} - 33863736 q^{92} - 118704764 q^{93} - 30761227 q^{94} - 26382485 q^{95} + 1256206 q^{96} + 55538244 q^{97} + 102201752 q^{98} + 71266232 q^{99}+O(q^{100}) \) 68 * q - 11 * q^2 + 23 * q^3 - 1091 * q^4 + 475 * q^5 - 179 * q^6 + 1734 * q^7 + 220 * q^8 - 14554 * q^9 + 4245 * q^10 + 466 * q^11 + 9979 * q^12 - 7407 * q^13 - 20177 * q^14 - 9285 * q^15 - 68527 * q^16 + 71504 * q^17 + 116208 * q^18 - 48685 * q^19 - 138265 * q^20 - 2274 * q^21 - 271952 * q^22 - 63227 * q^23 + 553980 * q^24 + 276615 * q^25 + 675246 * q^26 - 270235 * q^27 - 782613 * q^28 - 99655 * q^29 - 1011285 * q^30 + 39051 * q^31 + 1045974 * q^32 + 1766456 * q^33 + 605893 * q^34 - 476935 * q^35 - 2928227 * q^36 + 83909 * q^37 + 1937525 * q^38 + 1316257 * q^39 + 2903410 * q^40 - 1964944 * q^41 - 3462547 * q^42 - 3439822 * q^43 - 3557652 * q^44 - 2121790 * q^45 + 2982521 * q^46 + 1663474 * q^47 + 1678378 * q^48 + 6584354 * q^49 + 408485 * q^50 + 3922076 * q^51 - 5301176 * q^52 + 788553 * q^53 - 6946145 * q^54 - 2630560 * q^55 - 415350 * q^56 - 14598410 * q^57 + 4727030 * q^58 - 3625740 * q^59 + 29158890 * q^60 - 4161559 * q^61 + 19658928 * q^62 + 2426738 * q^63 - 4408596 * q^64 - 2030220 * q^65 - 6985528 * q^66 + 8470434 * q^67 - 29099218 * q^68 - 360673 * q^69 - 22417320 * q^70 - 4808044 * q^71 + 25676065 * q^72 + 5517633 * q^73 + 14050068 * q^74 + 257240 * q^75 + 22502000 * q^76 - 9936772 * q^77 + 14948561 * q^78 - 5343505 * q^79 - 3987180 * q^80 - 5865817 * q^81 - 76614542 * q^82 - 645927 * q^83 + 5992628 * q^84 + 48268560 * q^85 - 27540609 * q^86 + 65370380 * q^87 - 3612320 * q^88 + 11153500 * q^89 + 7267975 * q^90 - 9123484 * q^91 - 33863736 * q^92 - 118704764 * q^93 - 30761227 * q^94 - 26382485 * q^95 + 1256206 * q^96 + 55538244 * q^97 + 102201752 * q^98 + 71266232 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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