LMFDB - Embedded newform 25.8.d.a.6.2

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			6.2
Character	$\chi$	$=$	25.6
Dual form			25.8.d.a.21.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.60918 - 17.2633i) q^{2} +(68.4023 - 49.6972i) q^{3} +(-163.004 + 118.429i) q^{4} +(-18.3423 - 278.906i) q^{5} +(-1241.62 - 902.088i) q^{6} +935.944 q^{7} +(1079.11 + 784.017i) q^{8} +(1533.25 - 4718.84i) q^{9} +O(q^{10})$	\(q+(-5.60918 - 17.2633i) q^{2} +(68.4023 - 49.6972i) q^{3} +(-163.004 + 118.429i) q^{4} +(-18.3423 - 278.906i) q^{5} +(-1241.62 - 902.088i) q^{6} +935.944 q^{7} +(1079.11 + 784.017i) q^{8} +(1533.25 - 4718.84i) q^{9} +(-4711.95 + 1881.08i) q^{10} +(1278.00 + 3933.27i) q^{11} +(-5264.23 + 16201.6i) q^{12} +(-2601.70 + 8007.21i) q^{13} +(-5249.87 - 16157.5i) q^{14} +(-15115.5 - 18166.3i) q^{15} +(-487.714 + 1501.03i) q^{16} +(15171.3 + 11022.6i) q^{17} -90063.0 q^{18} +(16776.2 + 12188.6i) q^{19} +(36020.4 + 43290.4i) q^{20} +(64020.7 - 46513.8i) q^{21} +(60732.6 - 44124.8i) q^{22} +(-2529.45 - 7784.84i) q^{23} +112777. q^{24} +(-77452.1 + 10231.5i) q^{25} +152824. q^{26} +(-72495.2 - 223117. i) q^{27} +(-152562. + 110843. i) q^{28} +(74031.9 - 53787.3i) q^{29} +(-228824. + 362841. i) q^{30} +(-242622. - 176275. i) q^{31} +199381. q^{32} +(282890. + 205532. i) q^{33} +(105188. - 323735. i) q^{34} +(-17167.3 - 261040. i) q^{35} +(308924. + 950770. i) q^{36} +(-50651.7 + 155890. i) q^{37} +(116315. - 357981. i) q^{38} +(219974. + 677009. i) q^{39} +(198874. - 315350. i) q^{40} +(22913.2 - 70519.6i) q^{41} +(-1.16208e6 - 844303. i) q^{42} -190254. q^{43} +(-674132. - 489785. i) q^{44} +(-1.34424e6 - 341077. i) q^{45} +(-120204. + 87333.1i) q^{46} +(1.07627e6 - 781954. i) q^{47} +(41236.2 + 126912. i) q^{48} +52447.3 q^{49} +(611073. + 1.27969e6i) q^{50} +1.58555e6 q^{51} +(-524200. - 1.61332e6i) q^{52} +(-1.08698e6 + 789738. i) q^{53} +(-3.44510e6 + 2.50301e6i) q^{54} +(1.07357e6 - 428586. i) q^{55} +(1.00998e6 + 733796. i) q^{56} +1.75327e6 q^{57} +(-1.34380e6 - 976330. i) q^{58} +(-367866. + 1.13218e6i) q^{59} +(4.61529e6 + 1.17105e6i) q^{60} +(276424. + 850747. i) q^{61} +(-1.68218e6 + 5.17721e6i) q^{62} +(1.43503e6 - 4.41657e6i) q^{63} +(-1.05594e6 - 3.24984e6i) q^{64} +(2.28098e6 + 578759. i) q^{65} +(1.96137e6 - 6.03648e6i) q^{66} +(1.18038e6 + 857594. i) q^{67} -3.77838e6 q^{68} +(-559905. - 406795. i) q^{69} +(-4.41012e6 + 1.76059e6i) q^{70} +(-393843. + 286144. i) q^{71} +(5.35419e6 - 3.89005e6i) q^{72} +(208393. + 641367. i) q^{73} +2.97528e6 q^{74} +(-4.78943e6 + 4.54901e6i) q^{75} -4.17808e6 q^{76} +(1.19613e6 + 3.68132e6i) q^{77} +(1.04535e7 - 7.59493e6i) q^{78} +(2.65583e6 - 1.92957e6i) q^{79} +(427592. + 108494. i) q^{80} +(-7.26834e6 - 5.28076e6i) q^{81} -1.34592e6 q^{82} +(-3.88387e6 - 2.82179e6i) q^{83} +(-4.92702e6 + 1.51638e7i) q^{84} +(2.79600e6 - 4.43355e6i) q^{85} +(1.06717e6 + 3.28441e6i) q^{86} +(2.39087e6 - 7.35835e6i) q^{87} +(-1.70466e6 + 5.24639e6i) q^{88} +(1.49403e6 + 4.59815e6i) q^{89} +(1.65196e6 + 2.51191e7i) q^{90} +(-2.43504e6 + 7.49430e6i) q^{91} +(1.33426e6 + 969397. i) q^{92} -2.53563e7 q^{93} +(-1.95361e7 - 1.41938e7i) q^{94} +(3.09177e6 - 4.90256e6i) q^{95} +(1.36381e7 - 9.90868e6i) q^{96} +(-5.39967e6 + 3.92309e6i) q^{97} +(-294186. - 905411. i) q^{98} +2.05200e7 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 $

$2$	−5.60918	−	17.2633i	−0.495786	−	1.52587i	−0.815728	−	0.578435i	$-0.803664\pi$
$2$	−5.60918	−	17.2633i	−0.495786	−	1.52587i	0.319942	−	0.947437i	$-0.396336\pi$
$3$	68.4023	−	49.6972i	1.46267	−	1.06269i	0.480013	−	0.877261i	$-0.340632\pi$
$3$	68.4023	−	49.6972i	1.46267	−	1.06269i	0.982657	−	0.185431i	$-0.0593680\pi$
$4$	−163.004	+	118.429i	−1.27347	+	0.925227i
$5$	−18.3423	−	278.906i	−0.0656234	−	0.997844i
$5$	−18.3423	−	278.906i	−0.0656234	−	0.997844i
$6$	−1241.62	−	902.088i	−2.34670	−	1.70498i
$7$	935.944			1.03135			0.515676	−	0.856784i	$-0.327541\pi$
$7$	935.944			1.03135			0.515676	+	0.856784i	$0.327541\pi$
$8$	1079.11	+	784.017i	0.745160	+	0.541391i
$9$	1533.25	−	4718.84i	0.701073	−	2.15768i
$10$	−4711.95	+	1881.08i	−1.49005	+	0.594850i
$11$	1278.00	+	3933.27i	0.289505	+	0.891004i	0.985012	+	0.172485i	$0.0551796\pi$
$11$	1278.00	+	3933.27i	0.289505	+	0.891004i	−0.695508	+	0.718519i	$0.744820\pi$
$12$	−5264.23	+	16201.6i	−0.879429	+	2.70660i
$13$	−2601.70	+	8007.21i	−0.328440	+	1.01083i	0.641424	+	0.767186i	$0.278344\pi$
$13$	−2601.70	+	8007.21i	−0.328440	+	1.01083i	−0.969864	+	0.243647i	$0.921656\pi$
$14$	−5249.87	−	16157.5i	−0.511329	−	1.57371i
$15$	−15115.5	−	18166.3i	−1.15639	−	1.38978i
$16$	−487.714	+	1501.03i	−0.0297677	+	0.0916155i
$17$	15171.3	+	11022.6i	0.748949	+	0.544143i	0.895501	−	0.445060i	$-0.146818\pi$
$17$	15171.3	+	11022.6i	0.748949	+	0.544143i	−0.146552	+	0.989203i	$0.546818\pi$
$18$	−90063.0			−3.63993
$19$	16776.2	+	12188.6i	0.561121	+	0.407678i	0.831869	−	0.554972i	$-0.187271\pi$
$19$	16776.2	+	12188.6i	0.561121	+	0.407678i	−0.270748	+	0.962650i	$0.587271\pi$
$20$	36020.4	+	43290.4i	1.00680	+	1.21000i
$21$	64020.7	−	46513.8i	1.50853	−	1.09601i
$22$	60732.6	−	44124.8i	1.21603	−	0.883494i
$23$	−2529.45	−	7784.84i	−0.0433489	−	0.133414i	0.927040	−	0.374963i	$-0.122345\pi$
$23$	−2529.45	−	7784.84i	−0.0433489	−	0.133414i	−0.970389	+	0.241549i	$0.922345\pi$
$24$	112777.			1.66526
$25$	−77452.1	+	10231.5i	−0.991387	+	0.130964i
$26$	152824.			1.70524
$27$	−72495.2	−	223117.i	−0.708821	−	2.18153i
$28$	−152562.	+	110843.i	−1.31339	+	0.954234i
$29$	74031.9	−	53787.3i	0.563671	−	0.409531i	−0.269130	−	0.963104i	$-0.586736\pi$
$29$	74031.9	−	53787.3i	0.563671	−	0.409531i	0.832801	+	0.553573i	$0.186736\pi$
$30$	−228824.	+	362841.i	−1.54731	+	2.45353i
$31$	−242622.	−	176275.i	−1.46273	−	1.06274i	−0.982641	−	0.185517i	$-0.940604\pi$
$31$	−242622.	−	176275.i	−1.46273	−	1.06274i	−0.480090	−	0.877219i	$-0.659396\pi$
$32$	199381.			1.07562
$33$	282890.	+	205532.i	1.37031	+	0.995590i
$34$	105188.	−	323735.i	0.458975	−	1.41258i
$35$	−17167.3	−	261040.i	−0.0676807	−	1.02913i
$36$	308924.	+	950770.i	1.10355	+	3.39638i
$37$	−50651.7	+	155890.i	−0.164395	+	0.505955i	−0.998991	−	0.0449068i	$-0.985701\pi$
$37$	−50651.7	+	155890.i	−0.164395	+	0.505955i	0.834596	+	0.550862i	$0.185701\pi$
$38$	116315.	−	357981.i	0.343869	−	1.05832i
$39$	219974.	+	677009.i	0.593806	+	1.82755i
$40$	198874.	−	315350.i	0.491324	−	0.779082i
$41$	22913.2	−	70519.6i	0.0519209	−	0.159796i	−0.921734	−	0.387823i	$-0.873227\pi$
$41$	22913.2	−	70519.6i	0.0519209	−	0.159796i	0.973655	+	0.228027i	$0.0732273\pi$
$42$	−1.16208e6	−	844303.i	−2.42028	−	1.75843i
$43$	−190254.			−0.364917			−0.182459	−	0.983214i	$-0.558406\pi$
$43$	−190254.			−0.364917			−0.182459	+	0.983214i	$0.558406\pi$
$44$	−674132.	−	489785.i	−1.19305	−	0.866805i
$45$	−1.34424e6	−	341077.i	−2.19904	−	0.557967i
$46$	−120204.	+	87333.1i	−0.182081	+	0.132290i
$47$	1.07627e6	−	781954.i	1.51209	−	1.09860i	0.546851	−	0.837230i	$-0.315826\pi$
$47$	1.07627e6	−	781954.i	1.51209	−	1.09860i	0.965239	−	0.261368i	$-0.0841738\pi$
$48$	41236.2	+	126912.i	0.0538188	+	0.165637i
$49$	52447.3			0.0636849
$50$	611073.	+	1.27969e6i	0.691350	+	1.44780i
$51$	1.58555e6			1.67372
$52$	−524200.	−	1.61332e6i	−0.516994	−	1.59114i
$53$	−1.08698e6	+	789738.i	−1.00290	+	0.728647i	−0.962707	−	0.270545i	$-0.912796\pi$
$53$	−1.08698e6	+	789738.i	−1.00290	+	0.728647i	−0.0401897	+	0.999192i	$0.512796\pi$
$54$	−3.44510e6	+	2.50301e6i	−2.97731	+	2.16314i
$55$	1.07357e6	−	428586.i	0.870085	−	0.347351i
$56$	1.00998e6	+	733796.i	0.768522	+	0.558364i
$57$	1.75327e6			1.25397
$58$	−1.34380e6	−	976330.i	−0.904352	−	0.657050i
$59$	−367866.	+	1.13218e6i	−0.233189	+	0.717681i	0.764168	+	0.645018i	$0.223150\pi$
$59$	−367866.	+	1.13218e6i	−0.233189	+	0.717681i	−0.997356	+	0.0726638i	$0.976850\pi$
$60$	4.61529e6	+	1.17105e6i	2.75848	+	0.699917i
$61$	276424.	+	850747.i	0.155927	+	0.479895i	0.998254	−	0.0590730i	$-0.0188145\pi$
$61$	276424.	+	850747.i	0.155927	+	0.479895i	−0.842326	+	0.538968i	$0.818814\pi$
$62$	−1.68218e6	+	5.17721e6i	−0.896399	+	2.75883i
$63$	1.43503e6	−	4.41657e6i	0.723052	−	2.22532i
$64$	−1.05594e6	−	3.24984e6i	−0.503510	−	1.54964i
$65$	2.28098e6	+	578759.i	1.03021	+	0.261397i
$66$	1.96137e6	−	6.03648e6i	0.839762	−	2.58452i
$67$	1.18038e6	+	857594.i	0.479467	+	0.348353i	0.801119	−	0.598505i	$-0.204238\pi$
$67$	1.18038e6	+	857594.i	0.479467	+	0.348353i	−0.321652	+	0.946858i	$0.604238\pi$
$68$	−3.77838e6			−1.45722
$69$	−559905.	−	406795.i	−0.205183	−	0.149075i
$70$	−4.41012e6	+	1.76059e6i	−1.53676	+	0.613499i
$71$	−393843.	+	286144.i	−0.130593	+	0.0948811i	−0.651164	−	0.758937i	$-0.725719\pi$
$71$	−393843.	+	286144.i	−0.130593	+	0.0948811i	0.520571	+	0.853818i	$0.325719\pi$
$72$	5.35419e6	−	3.89005e6i	1.69056	−	1.22826i
$73$	208393.	+	641367.i	0.0626978	+	0.192964i	0.977499	−	0.210941i	$-0.0676527\pi$
$73$	208393.	+	641367.i	0.0626978	+	0.192964i	−0.914801	+	0.403905i	$0.867653\pi$
$74$	2.97528e6			0.853528
$75$	−4.78943e6	+	4.54901e6i	−1.31090	+	1.24510i
$76$	−4.17808e6			−1.09176
$77$	1.19613e6	+	3.68132e6i	0.298581	+	0.918937i
$78$	1.04535e7	−	7.59493e6i	2.49420	−	1.81214i
$79$	2.65583e6	−	1.92957e6i	0.606046	−	0.440318i	−0.241974	−	0.970283i	$-0.577795\pi$
$79$	2.65583e6	−	1.92957e6i	0.606046	−	0.440318i	0.848020	+	0.529965i	$0.177795\pi$
$80$	427592.	+	108494.i	0.0933715	+	0.0236914i
$81$	−7.26834e6	−	5.28076e6i	−1.51963	−	1.10408i
$82$	−1.34592e6			−0.269570
$83$	−3.88387e6	−	2.82179e6i	−0.745574	−	0.541692i	0.148878	−	0.988856i	$-0.452434\pi$
$83$	−3.88387e6	−	2.82179e6i	−0.745574	−	0.541692i	−0.894452	+	0.447164i	$0.852434\pi$
$84$	−4.92702e6	+	1.51638e7i	−0.907000	+	2.79146i
$85$	2.79600e6	−	4.43355e6i	0.493822	−	0.783043i
$86$	1.06717e6	+	3.28441e6i	0.180921	+	0.556817i
$87$	2.39087e6	−	7.35835e6i	0.389259	−	1.19802i
$88$	−1.70466e6	+	5.24639e6i	−0.266654	+	0.820675i
$89$	1.49403e6	+	4.59815e6i	0.224643	+	0.691382i	0.998328	+	0.0578100i	$0.0184118\pi$
$89$	1.49403e6	+	4.59815e6i	0.224643	+	0.691382i	−0.773684	+	0.633572i	$0.781588\pi$
$90$	1.65196e6	+	2.51191e7i	0.238864	+	3.63208i
$91$	−2.43504e6	+	7.49430e6i	−0.338737	+	1.04252i
$92$	1.33426e6	+	969397.i	0.178642	+	0.129791i
$93$	−2.53563e7			−3.26885
$94$	−1.95361e7	−	1.41938e7i	−2.42599	−	1.76259i
$95$	3.09177e6	−	4.90256e6i	0.369977	−	0.586665i
$96$	1.36381e7	−	9.90868e6i	1.57328	−	1.14305i
$97$	−5.39967e6	+	3.92309e6i	−0.600711	+	0.436442i	−0.846131	−	0.532975i	$-0.821074\pi$
$97$	−5.39967e6	+	3.92309e6i	−0.600711	+	0.436442i	0.245420	+	0.969417i	$0.421074\pi$
$98$	−294186.	−	905411.i	−0.0315741	−	0.0971750i
$99$	2.05200e7			2.12546
$100$	1.14133e7	−	1.08404e7i	1.14133	−	1.08404i
$101$	9.78559e6			0.945066			0.472533	−	0.881313i	$-0.343340\pi$
$101$	9.78559e6			0.945066			0.472533	+	0.881313i	$0.343340\pi$
$102$	−8.89361e6	−	2.73717e7i	−0.829808	−	2.55389i
$103$	804626.	−	584595.i	0.0725544	−	0.0527139i	−0.550917	−	0.834560i	$-0.685722\pi$
$103$	804626.	−	584595.i	0.0725544	−	0.0527139i	0.623471	+	0.781846i	$0.285722\pi$
$104$	−9.08531e6	+	6.60086e6i	−0.791996	+	0.575419i
$105$	−1.41473e7	−	1.70026e7i	−1.19264	−	1.43335i
$106$	1.97305e7	+	1.43351e7i	1.60905	+	1.16904i
$107$	−2.23938e7			−1.76720			−0.883600	−	0.468243i	$-0.844887\pi$
$107$	−2.23938e7			−1.76720			−0.883600	+	0.468243i	$0.844887\pi$
$108$	3.82406e7	+	2.77834e7i	2.92107	+	2.12228i
$109$	1.90070e6	−	5.84976e6i	0.140579	−	0.432659i	−0.855837	−	0.517246i	$-0.826957\pi$
$109$	1.90070e6	−	5.84976e6i	0.140579	−	0.432659i	0.996416	+	0.0845873i	$0.0269572\pi$
$110$	−1.34207e7	−	1.61293e7i	−0.961389	−	1.15543i
$111$	4.28260e6	+	1.31805e7i	0.297219	+	0.914746i
$112$	−456473.	+	1.40488e6i	−0.0307009	+	0.0944878i
$113$	−1.94935e6	+	5.99948e6i	−0.127091	+	0.391146i	−0.994276	−	0.106840i	$-0.965927\pi$
$113$	−1.94935e6	+	5.99948e6i	−0.127091	+	0.391146i	0.867185	+	0.497986i	$0.165927\pi$
$114$	−9.83443e6	−	3.02673e7i	−0.621702	−	1.91340i
$115$	−2.12484e6	+	848270.i	−0.130282	+	0.0520106i
$116$	−5.69748e6	+	1.75350e7i	−0.338907	+	1.04305i
$117$	3.37957e7	+	2.45540e7i	1.95079	+	1.41733i
$118$	2.16085e7			1.21070
$119$	1.41995e7	+	1.03165e7i	0.772429	+	0.561203i
$120$	−2.06859e6	−	3.14542e7i	−0.109280	−	1.66167i
$121$	1.92811e6	−	1.40085e6i	0.0989425	−	0.0718859i
$122$	1.31362e7	−	9.54398e6i	0.654952	−	0.475850i
$123$	−1.93731e6	−	5.96243e6i	−0.0938709	−	0.288905i
$124$	6.04244e7			2.84601
$125$	4.27429e6	+	2.14142e7i	0.195740	+	0.980656i
$126$	−8.42938e7			−3.75404
$127$	8.33826e6	+	2.56625e7i	0.361212	+	1.11170i	0.952319	+	0.305104i	$0.0986911\pi$
$127$	8.33826e6	+	2.56625e7i	0.361212	+	1.11170i	−0.591107	+	0.806593i	$0.701309\pi$
$128$	−2.95332e7	+	2.14571e7i	−1.24473	+	0.904350i
$129$	−1.30138e7	+	9.45509e6i	−0.533754	+	0.387795i
$130$	−2.80314e6	−	4.26236e7i	−0.111903	−	1.70156i
$131$	1.10532e7	+	8.03061e6i	0.429574	+	0.312104i	0.781479	−	0.623932i	$-0.214466\pi$
$131$	1.10532e7	+	8.03061e6i	0.429574	+	0.312104i	−0.351905	+	0.936036i	$0.614466\pi$
$132$	−7.04531e7			−2.66619
$133$	1.57016e7	+	1.14079e7i	0.578713	+	0.420460i
$134$	8.18394e6	−	2.51876e7i	0.293830	−	0.904314i
$135$	−6.08991e7	+	2.43118e7i	−2.13031	+	0.850452i
$136$	7.72957e6	+	2.37892e7i	0.263493	+	0.810948i
$137$	6.19530e6	−	1.90672e7i	0.205845	−	0.633526i	−0.793833	−	0.608136i	$-0.791917\pi$
$137$	6.19530e6	−	1.90672e7i	0.205845	−	0.633526i	0.999678	−	0.0253893i	$-0.00808255\pi$
$138$	−3.88200e6	+	1.19476e7i	−0.125742	+	0.386993i
$139$	−654802.	−	2.01527e6i	−0.0206804	−	0.0636476i	0.940184	−	0.340668i	$-0.110653\pi$
$139$	−654802.	−	2.01527e6i	−0.0206804	−	0.0636476i	−0.960864	+	0.277020i	$0.910653\pi$
$140$	3.37131e7	+	4.05174e7i	1.03837	+	1.24794i
$141$	3.47583e7	−	1.06975e8i	1.04422	−	3.21377i
$142$	7.14891e6	+	5.19399e6i	0.209522	+	0.152227i
$143$	−3.48195e7			−0.995741
$144$	6.33534e6	+	4.60289e6i	0.176808	+	0.128458i
$145$	−1.63595e7	−	1.96613e7i	−0.445638	−	0.535581i
$146$	9.90318e6	−	7.19508e6i	0.263354	−	0.191338i
$147$	3.58751e6	−	2.60648e6i	0.0931500	−	0.0676774i
$148$	−1.02055e7	−	3.14093e7i	−0.258772	−	0.796419i
$149$	−1.32162e7			−0.327306			−0.163653	−	0.986518i	$-0.552328\pi$
$149$	−1.32162e7			−0.327306			−0.163653	+	0.986518i	$0.552328\pi$
$150$	1.05396e8	+	5.71649e7i	2.54978	+	1.38296i
$151$	−5.97267e7			−1.41172			−0.705861	−	0.708351i	$-0.749440\pi$
$151$	−5.97267e7			−1.41172			−0.705861	+	0.708351i	$0.749440\pi$
$152$	8.54724e6	+	2.63057e7i	0.197412	+	0.607572i
$153$	7.52754e7	−	5.46908e7i	1.69915	−	1.23451i
$154$	5.68423e7	−	4.12984e7i	1.25415	−	0.911193i
$155$	−4.47140e7	+	7.09021e7i	−0.964456	+	1.52932i
$156$	−1.16034e8	−	8.43036e7i	−2.44709	−	1.77791i
$157$	3.94508e7			0.813593			0.406797	−	0.913519i	$-0.366646\pi$
$157$	3.94508e7			0.813593			0.406797	+	0.913519i	$0.366646\pi$
$158$	−4.82078e7	−	3.50250e7i	−0.972339	−	0.706445i
$159$	−3.51043e7	+	1.08040e8i	−0.692580	+	2.13154i
$160$	−3.65711e6	−	5.56086e7i	−0.0705858	−	1.07330i
$161$	−2.36742e6	−	7.28617e6i	−0.0447080	−	0.137597i
$162$	−5.03938e7	+	1.55096e8i	−0.931267	+	2.86614i
$163$	−1.33676e7	+	4.11413e7i	−0.241767	+	0.744083i	0.754384	+	0.656433i	$0.227936\pi$
$163$	−1.33676e7	+	4.11413e7i	−0.241767	+	0.744083i	−0.996151	+	0.0876497i	$0.972064\pi$
$164$	4.61663e6	+	1.42085e7i	0.0817282	+	0.251534i
$165$	5.21352e7	−	8.26698e7i	0.903520	−	1.43269i
$166$	−2.69281e7	+	8.28762e7i	−0.456907	+	1.40621i
$167$	−1.74608e7	−	1.26860e7i	−0.290105	−	0.210774i	0.433208	−	0.901294i	$-0.357382\pi$
$167$	−1.74608e7	−	1.26860e7i	−0.290105	−	0.210774i	−0.723313	+	0.690520i	$0.757382\pi$
$168$	1.05553e8			1.71746
$169$	−6.58196e6	−	4.78207e6i	−0.104894	−	0.0762101i
$170$	−9.22209e7	−	2.33995e7i	−1.43965	−	0.365287i
$171$	8.32384e7	−	6.04762e7i	1.27303	−	0.924908i
$172$	3.10121e7	−	2.25316e7i	0.464710	−	0.337631i
$173$	−843502.	−	2.59603e6i	−0.0123858	−	0.0381197i	0.944673	−	0.328015i	$-0.106380\pi$
$173$	−843502.	−	2.59603e6i	−0.0123858	−	0.0381197i	−0.957058	+	0.289895i	$0.906380\pi$
$174$	−1.40440e8			−2.02101
$175$	−7.24908e7	+	9.57615e6i	−1.02247	+	0.135070i
$176$	−6.52725e6			−0.0902477
$177$	3.11030e7	+	9.57253e7i	0.421596	+	1.29754i
$178$	7.09988e7	−	5.15836e7i	0.943585	−	0.685555i
$179$	9.99098e7	−	7.25888e7i	1.30204	−	0.945984i	0.302062	−	0.953288i	$-0.402325\pi$
$179$	9.99098e7	−	7.25888e7i	1.30204	−	0.945984i	0.999973	+	0.00730447i	$0.00232511\pi$
$180$	2.59509e8	−	1.03600e8i	3.31664	−	1.32405i
$181$	−9.05526e7	−	6.57903e7i	−1.13508	−	0.824683i	−0.148652	−	0.988890i	$-0.547494\pi$
$181$	−9.05526e7	−	6.57903e7i	−1.13508	−	0.824683i	−0.986426	+	0.164207i	$0.947494\pi$
$182$	1.43035e8			1.75870
$183$	6.11878e7	+	4.44555e7i	0.738051	+	0.536225i
$184$	3.37390e6	−	1.03838e7i	0.0399273	−	0.122884i
$185$	4.44077e7	+	1.12677e7i	0.515653	+	0.130838i
$186$	1.42228e8	+	4.37733e8i	1.62065	+	4.98786i
$187$	−2.39660e7	+	7.37598e7i	−0.268009	+	0.824848i
$188$	−8.28294e7	+	2.54923e8i	−0.909143	+	2.79805i
$189$	−6.78515e7	−	2.08825e8i	−0.731043	−	2.24992i
$190$	−1.01977e8	−	2.58748e7i	−1.07861	−	0.273677i
$191$	5.45694e7	−	1.67947e8i	0.566673	−	1.74404i	−0.0962563	−	0.995357i	$-0.530687\pi$
$191$	5.45694e7	−	1.67947e8i	0.566673	−	1.74404i	0.662929	−	0.748682i	$-0.269313\pi$
$192$	−2.33736e8	−	1.69819e8i	−2.38326	−	1.73154i
$193$	−5.00303e7			−0.500937			−0.250468	−	0.968125i	$-0.580585\pi$
$193$	−5.00303e7			−0.500937			−0.250468	+	0.968125i	$0.580585\pi$
$194$	9.80130e7	+	7.12106e7i	0.963780	+	0.700227i
$195$	1.84787e8	−	7.37698e7i	1.78464	−	0.712455i
$196$	−8.54909e6	+	6.21128e6i	−0.0811005	+	0.0589230i
$197$	4.80548e7	−	3.49139e7i	0.447822	−	0.325361i	−0.340913	−	0.940095i	$-0.610736\pi$
$197$	4.80548e7	−	3.49139e7i	0.447822	−	0.325361i	0.788735	+	0.614733i	$0.210736\pi$
$198$	−1.15100e8	−	3.54242e8i	−1.05378	−	3.24319i
$199$	−1.55951e8			−1.40282			−0.701411	−	0.712757i	$-0.747446\pi$
$199$	−1.55951e8			−1.40282			−0.701411	+	0.712757i	$0.747446\pi$
$200$	−9.16009e7	−	4.96829e7i	−0.809645	−	0.439139i
$201$	1.23361e8			1.07149
$202$	−5.48891e7	−	1.68931e8i	−0.468550	−	1.44205i
$203$	6.92896e7	−	5.03419e7i	0.581343	−	0.422370i
$204$	−2.58450e8	+	1.87775e8i	−2.13143	+	1.54857i
$205$	−2.00886e7	−	5.09714e6i	−0.162859	−	0.0413226i
$206$	−1.46053e7	−	1.06114e7i	−0.116406	−	0.0845740i
$207$	−4.06137e7			−0.318256
$208$	−1.07502e7	−	7.81046e6i	−0.0828311	−	0.0601803i
$209$	−2.65013e7	+	8.15625e7i	−0.200796	+	0.617986i
$210$	−2.14166e8	+	3.39598e8i	−1.59582	+	2.53045i
$211$	3.96595e7	+	1.22059e8i	0.290642	+	0.894505i	0.984650	+	0.174538i	$0.0558432\pi$
$211$	3.96595e7	+	1.22059e8i	0.290642	+	0.894505i	−0.694008	+	0.719967i	$0.744157\pi$
$212$	8.36539e7	−	2.57460e8i	0.602991	−	1.85582i
$213$	−1.27192e7	+	3.91458e7i	−0.0901846	+	0.277560i
$214$	1.25611e8	+	3.86591e8i	0.876153	+	2.69652i
$215$	3.48969e6	+	5.30630e7i	0.0239471	+	0.364131i
$216$	9.66978e7	−	2.97605e8i	0.652872	−	2.00933i
$217$	−2.27081e8	−	1.64984e8i	−1.50859	−	1.09605i
$218$	−1.11647e8			−0.729879
$219$	4.61287e7	+	3.35144e7i	0.296768	+	0.215614i
$220$	−1.24239e8	+	1.97003e8i	−0.786644	+	1.24737i
$221$	−1.27732e8	+	9.28025e7i	−0.796023	+	0.578344i
$222$	2.03516e8	−	1.47863e8i	1.24843	−	0.907037i
$223$	9.98966e7	+	3.07450e8i	0.603231	+	1.85655i	0.508522	+	0.861049i	$0.330192\pi$
$223$	9.98966e7	+	3.07450e8i	0.603231	+	1.85655i	0.0947090	+	0.995505i	$0.469808\pi$
$224$	1.86609e8			1.10934
$225$	−7.04720e7	+	3.81172e8i	−0.412456	+	2.23091i
$226$	1.14505e8			0.659849
$227$	4.95024e7	+	1.52353e8i	0.280890	+	0.864489i	0.987601	+	0.156987i	$0.0501781\pi$
$227$	4.95024e7	+	1.52353e8i	0.280890	+	0.864489i	−0.706711	+	0.707502i	$0.749822\pi$
$228$	−2.85790e8	+	2.07639e8i	−1.59689	+	1.16021i
$229$	1.71956e8	−	1.24933e8i	0.946223	−	0.687471i	−0.00368739	−	0.999993i	$-0.501174\pi$
$229$	1.71956e8	−	1.24933e8i	0.946223	−	0.687471i	0.949911	+	0.312522i	$0.101174\pi$
$230$	2.65625e7	+	3.19237e7i	0.143954	+	0.173008i
$231$	2.64770e8	+	1.92366e8i	1.41327	+	1.02680i
$232$	1.22058e8			0.641741
$233$	−7.13978e7	−	5.18735e7i	−0.369776	−	0.268658i	0.387342	−	0.921936i	$-0.373393\pi$
$233$	−7.13978e7	−	5.18735e7i	−0.369776	−	0.268658i	−0.757118	+	0.653278i	$0.773393\pi$
$234$	2.34317e8	−	7.21153e8i	1.19550	−	3.67936i
$235$	−2.37833e8	−	2.85835e8i	−1.19546	−	1.43674i
$236$	−7.41190e7	−	2.28115e8i	−0.367060	−	1.12970i
$237$	8.57706e7	−	2.63975e8i	0.418523	−	1.28808i
$238$	9.84498e7	−	3.02997e8i	0.473364	−	1.45687i
$239$	3.33971e7	+	1.02786e8i	0.158240	+	0.487012i	0.998475	−	0.0552104i	$-0.0175829\pi$
$239$	3.33971e7	+	1.02786e8i	0.158240	+	0.487012i	−0.840235	+	0.542223i	$0.817583\pi$
$240$	3.46401e7	−	1.38289e7i	0.161748	−	0.0645725i
$241$	−8.87742e7	+	2.73219e8i	−0.408533	+	1.25734i	0.509376	+	0.860544i	$0.329876\pi$
$241$	−8.87742e7	+	2.73219e8i	−0.408533	+	1.25734i	−0.917909	+	0.396791i	$0.870124\pi$
$242$	−3.49984e7	−	2.54278e7i	−0.158743	−	0.115334i
$243$	−2.46541e8			−1.10222
$244$	−1.45811e8	−	1.05938e8i	−0.642580	−	0.466861i
$245$	−962003.	−	1.46279e7i	−0.00417922	−	0.0635476i
$246$	−9.20643e7	+	6.68886e7i	−0.394292	+	0.286470i
$247$	−1.41244e8	+	1.02620e8i	−0.596389	+	0.433302i
$248$	−1.23612e8	−	3.80440e8i	−0.514614	−	1.58382i
$249$	−4.05901e8			−1.66618
$250$	3.45704e8	−	1.93904e8i	1.39931	−	0.784869i
$251$	−4.53219e7			−0.180905			−0.0904525	−	0.995901i	$-0.528831\pi$
$251$	−4.53219e7			−0.180905			−0.0904525	+	0.995901i	$0.528831\pi$
$252$	2.89135e8	+	8.89867e8i	1.13815	+	3.50286i
$253$	2.73873e7	−	1.98980e7i	0.106323	−	0.0772481i
$254$	3.96249e8	−	2.87891e8i	1.51722	−	1.10233i
$255$	−2.90825e7	−	4.42218e8i	−0.109835	−	1.67011i
$256$	1.82224e8	+	1.32393e8i	0.678836	+	0.493204i
$257$	3.95610e8			1.45379			0.726895	−	0.686749i	$-0.240963\pi$
$257$	3.95610e8			1.45379			0.726895	+	0.686749i	$0.240963\pi$
$258$	2.36223e8	+	1.71626e8i	0.856353	+	0.622177i
$259$	−4.74071e7	+	1.45904e8i	−0.169549	+	0.521817i
$260$	−4.40350e8	+	1.75794e8i	−1.55379	+	0.620295i
$261$	−1.40305e8	−	4.31814e8i	−0.488462	−	1.50333i
$262$	7.66353e7	−	2.35859e8i	0.263254	−	0.810212i
$263$	6.34813e7	−	1.95375e8i	0.215179	−	0.662254i	−0.783961	−	0.620810i	$-0.786804\pi$
$263$	6.34813e7	−	1.95375e8i	0.215179	−	0.662254i	0.999141	−	0.0414446i	$-0.0131960\pi$
$264$	1.44129e8	+	4.43582e8i	0.482099	+	1.48375i
$265$	2.40200e8	+	2.88680e8i	0.792890	+	0.952919i
$266$	1.08864e8	−	3.35050e8i	0.354650	−	1.09150i
$267$	3.30710e8	+	2.40275e8i	1.06331	+	0.772536i
$268$	−2.93970e8			−0.932891
$269$	−8.54979e6	−	6.21179e6i	−0.0267807	−	0.0194573i	0.574314	−	0.818635i	$-0.305269\pi$
$269$	−8.54979e6	−	6.21179e6i	−0.0267807	−	0.0194573i	−0.601095	+	0.799177i	$0.705269\pi$
$270$	7.61296e8	+	9.14948e8i	2.35386	+	2.82894i
$271$	3.53445e8	−	2.56792e8i	1.07877	−	0.783772i	0.101302	−	0.994856i	$-0.467699\pi$
$271$	3.53445e8	−	2.56792e8i	1.07877	−	0.783772i	0.977468	+	0.211084i	$0.0676993\pi$
$272$	−2.39445e7	+	1.73967e7i	−0.0721465	+	0.0524175i
$273$	2.05883e8	+	6.33642e8i	0.612422	+	1.88484i
$274$	−3.63912e8			−1.06873
$275$	−1.39227e8	−	2.91564e8i	−0.403700	−	0.845415i
$276$	1.39443e8			0.399222
$277$	−1.19069e8	−	3.66457e8i	−0.336605	−	1.03596i	−0.965926	−	0.258818i	$-0.916667\pi$
$277$	−1.19069e8	−	3.66457e8i	−0.336605	−	1.03596i	0.629321	−	0.777145i	$-0.283333\pi$
$278$	−3.11173e7	+	2.26080e7i	−0.0868651	+	0.0631112i
$279$	−1.20382e9	+	8.74623e8i	−3.31853	+	2.41105i
$280$	1.86135e8	−	2.95150e8i	0.506727	−	0.803507i
$281$	−2.16438e8	−	1.57252e8i	−0.581918	−	0.422788i	0.257497	−	0.966279i	$-0.417102\pi$
$281$	−2.16438e8	−	1.57252e8i	−0.581918	−	0.422788i	−0.839415	+	0.543491i	$0.817102\pi$
$282$	−2.04170e9			−5.42152
$283$	1.45532e8	+	1.05735e8i	0.381686	+	0.277311i	0.762040	−	0.647530i	$-0.224198\pi$
$283$	1.45532e8	+	1.05735e8i	0.381686	+	0.277311i	−0.380354	+	0.924841i	$0.624198\pi$
$284$	3.03101e7	−	9.32849e7i	0.0785187	−	0.241656i
$285$	−3.21591e7	−	4.88999e8i	−0.0822899	−	1.25127i
$286$	1.95309e8	+	6.01099e8i	0.493674	+	1.51937i
$287$	2.14455e7	−	6.60024e7i	0.0535487	−	0.164806i
$288$	3.05700e8	−	9.40849e8i	0.754088	−	2.32084i
$289$	−1.81305e7	−	5.58000e7i	−0.0441843	−	0.135985i
$290$	−2.47656e8	+	3.92703e8i	−0.596287	+	0.945521i
$291$	−1.74383e8	+	5.36696e8i	−0.414839	+	1.27674i
$292$	−1.09925e8	−	7.98653e7i	−0.258379	−	0.187723i
$293$	−1.53578e8			−0.356691			−0.178346	−	0.983968i	$-0.557075\pi$
$293$	−1.53578e8			−0.356691			−0.178346	+	0.983968i	$0.557075\pi$
$294$	−6.51194e7	−	4.73120e7i	−0.149450	−	0.108581i
$295$	3.22518e8	+	8.18334e7i	0.731437	+	0.185590i
$296$	−1.76879e8	+	1.28510e8i	−0.396420	+	0.288016i
$297$	7.84933e8	−	5.70287e8i	1.73854	−	1.26312i
$298$	7.41319e7	+	2.28155e8i	0.162274	+	0.499427i
$299$	6.89157e7			0.149097
$300$	2.41958e8	−	1.30871e9i	0.517387	−	2.79847i
$301$	−1.78067e8			−0.376358
$302$	3.35018e8	+	1.03108e9i	0.699912	+	2.15411i
$303$	6.69357e8	−	4.86316e8i	1.38232	−	1.00431i
$304$	−2.64775e7	+	1.92370e7i	−0.0540530	+	0.0392718i
$305$	2.32208e8	−	9.27011e7i	0.468628	−	0.187083i
$306$	−1.36637e9	−	9.92729e8i	−2.72612	−	1.98064i
$307$	5.02185e7			0.0990557			0.0495278	−	0.998773i	$-0.484228\pi$
$307$	5.02185e7			0.0990557			0.0495278	+	0.998773i	$0.484228\pi$
$308$	−6.30949e8	−	4.58411e8i	−1.23046	−	0.893980i
$309$	2.59856e7	−	7.99753e7i	0.0501046	−	0.154206i
$310$	1.47481e9	+	3.74208e8i	2.81171	+	0.713423i
$311$	−2.24936e8	−	6.92283e8i	−0.424032	−	1.30504i	−0.903918	−	0.427705i	$-0.859322\pi$
$311$	−2.24936e8	−	6.92283e8i	−0.424032	−	1.30504i	0.479886	−	0.877331i	$-0.340678\pi$
$312$	−2.93412e8	+	9.03028e8i	−0.546936	+	1.68330i
$313$	−2.51339e8	+	7.73543e8i	−0.463293	+	1.42587i	0.397825	+	0.917461i	$0.369765\pi$
$313$	−2.51339e8	+	7.73543e8i	−0.463293	+	1.42587i	−0.861117	+	0.508406i	$0.830235\pi$
$314$	−2.21287e8	−	6.81050e8i	−0.403368	−	1.24144i
$315$	−1.25813e9	−	3.19229e8i	−2.26798	−	0.575460i
$316$	−2.04392e8	+	6.29055e8i	−0.364385	+	1.12146i
$317$	1.66882e8	+	1.21247e8i	0.294239	+	0.213777i	0.725104	−	0.688639i	$-0.241791\pi$
$317$	1.66882e8	+	1.21247e8i	0.294239	+	0.213777i	−0.430865	+	0.902416i	$0.641791\pi$
$318$	2.06203e9			3.59583
$319$	3.06172e8	+	2.22447e8i	0.528079	+	0.383672i
$320$	−8.87032e8	+	3.54117e8i	−1.51326	+	0.604117i
$321$	−1.53179e9	+	1.11291e9i	−2.58483	+	1.87799i
$322$	−1.12504e8	+	8.17389e7i	−0.187790	+	0.136437i
$323$	1.20167e8	+	3.69836e8i	0.198416	+	0.610661i
$324$	1.81016e9			2.95672
$325$	1.19581e8	−	6.46795e8i	0.193228	−	1.04514i
$326$	7.85215e8			1.25524
$327$	−1.60704e8	−	4.94597e8i	−0.254162	−	0.782230i
$328$	8.00144e7	−	5.81339e7i	0.125202	−	0.0909643i
$329$	1.00733e9	−	7.31865e8i	1.55950	−	1.13304i
$330$	−1.71959e9	−	4.36315e8i	−2.63406	−	0.668347i
$331$	4.19216e8	+	3.04578e8i	0.635389	+	0.461637i	0.858263	−	0.513210i	$-0.171544\pi$
$331$	4.19216e8	+	3.04578e8i	0.635389	+	0.461637i	−0.222874	+	0.974847i	$0.571544\pi$
$332$	9.67267e8			1.45065
$333$	6.57959e8	+	4.78035e8i	0.976436	+	0.709422i
$334$	−1.21061e8	+	3.72588e8i	−0.177784	+	0.547162i
$335$	2.17537e8	−	3.44944e8i	0.316138	−	0.501294i
$336$	3.85947e7	+	1.18782e8i	0.0555061	+	0.170830i
$337$	−2.83240e7	+	8.71724e7i	−0.0403135	+	0.124072i	−0.969188	−	0.246323i	$-0.920778\pi$
$337$	−2.83240e7	+	8.71724e7i	−0.0403135	+	0.124072i	0.928874	+	0.370395i	$0.120778\pi$
$338$	−4.56349e7	+	1.40450e8i	−0.0642818	+	0.197839i
$339$	1.64817e8	+	5.07256e8i	0.229776	+	0.707177i
$340$	6.93041e7	+	1.05381e9i	0.0956275	+	1.45408i
$341$	3.83268e8	−	1.17958e9i	0.523435	−	1.61097i
$342$	−1.51092e9	−	1.09775e9i	−2.04244	−	1.48392i
$343$	−7.21702e8			−0.965670
$344$	−2.05305e8	−	1.49162e8i	−0.271922	−	0.197563i
$345$	−1.03188e8	+	1.63622e8i	−0.135288	+	0.214524i
$346$	−4.00847e7	+	2.91232e7i	−0.0520250	+	0.0377984i
$347$	−6.15611e8	+	4.47268e8i	−0.790958	+	0.574664i	−0.908247	−	0.418433i	$-0.862579\pi$
$347$	−6.15611e8	+	4.47268e8i	−0.790958	+	0.574664i	0.117290	+	0.993098i	$0.462579\pi$
$348$	4.81722e8	+	1.48259e9i	0.612729	+	1.88579i
$349$	−2.72785e8			−0.343504			−0.171752	−	0.985140i	$-0.554943\pi$
$349$	−2.72785e8			−0.343504			−0.171752	+	0.985140i	$0.554943\pi$
$350$	5.71930e8	+	1.19771e9i	0.713024	+	1.49319i
$351$	1.97516e9			2.43796
$352$	2.54809e8	+	7.84220e8i	0.311397	+	0.958382i
$353$	−1.31586e9	+	9.56029e8i	−1.59220	+	1.15680i	−0.691494	+	0.722382i	$0.743047\pi$
$353$	−1.31586e9	+	9.56029e8i	−1.59220	+	1.15680i	−0.900709	+	0.434422i	$0.856953\pi$
$354$	1.47807e9	−	1.07388e9i	1.77086	−	1.28660i
$355$	8.70311e7	+	1.04597e8i	0.103247	+	0.124085i
$356$	−7.88086e8	−	5.72578e8i	−0.925761	−	0.672605i
$357$	1.48398e9			1.72620
$358$	−1.81353e9	−	1.31761e9i	−2.08898	−	1.51773i
$359$	4.58057e7	−	1.40976e8i	0.0522504	−	0.160810i	−0.921526	−	0.388316i	$-0.873057\pi$
$359$	4.58057e7	−	1.40976e8i	0.0522504	−	0.160810i	0.973777	+	0.227506i	$0.0730570\pi$
$360$	−1.18317e9	−	1.42196e9i	−1.33656	−	1.60631i
$361$	−1.43343e8	−	4.41164e8i	−0.160362	−	0.493542i
$362$	−6.27831e8	+	1.93226e9i	−0.695605	+	2.14085i
$363$	6.22687e7	−	1.91643e8i	0.0683276	−	0.210291i
$364$	−4.90621e8	−	1.50998e9i	−0.533202	−	1.64103i
$365$	1.75059e8	−	6.98861e7i	0.188434	−	0.0752256i
$366$	4.24235e8	−	1.30566e9i	0.452296	−	1.39202i
$367$	−9.72761e8	−	7.06752e8i	−1.02725	−	0.746339i	−0.0594915	−	0.998229i	$-0.518948\pi$
$367$	−9.72761e8	−	7.06752e8i	−1.02725	−	0.746339i	−0.967756	+	0.251890i	$0.918948\pi$
$368$	1.29189e7			0.0135132
$369$	−2.97640e8	−	2.16248e8i	−0.308389	−	0.224057i
$370$	−5.45735e7	−	8.29825e8i	−0.0560113	−	0.851688i
$371$	−1.01735e9	+	7.39150e8i	−1.03434	+	0.751491i
$372$	4.13317e9	−	3.00292e9i	4.16277	−	3.02443i
$373$	−3.30731e8	−	1.01789e9i	−0.329985	−	1.01559i	−0.969140	−	0.246511i	$-0.920716\pi$
$373$	−3.30731e8	−	1.01789e9i	−0.329985	−	1.01559i	0.639155	−	0.769078i	$-0.279284\pi$
$374$	1.40777e9			1.39149
$375$	1.35660e9	+	1.25236e9i	1.32844	+	1.22637i
$376$	1.77447e9			1.72152
$377$	2.38077e8	+	7.32727e8i	0.228836	+	0.704284i
$378$	−3.22442e9	+	2.34268e9i	−3.07065	+	2.23096i
$379$	−5.43236e8	+	3.94684e8i	−0.512568	+	0.372402i	−0.813797	−	0.581150i	$-0.802603\pi$
$379$	−5.43236e8	+	3.94684e8i	−0.512568	+	0.372402i	0.301229	+	0.953552i	$0.402603\pi$
$380$	7.66355e7	+	1.16529e9i	0.0716452	+	1.08941i
$381$	1.84571e9	+	1.34099e9i	1.70973	+	1.24219i
$382$	−3.20541e9			−2.94213
$383$	−4.61605e8	−	3.35376e8i	−0.419831	−	0.305025i	0.357739	−	0.933822i	$-0.383548\pi$
$383$	−4.61605e8	−	3.35376e8i	−0.419831	−	0.305025i	−0.777570	+	0.628797i	$0.783548\pi$
$384$	−9.53780e8	+	2.93543e9i	−0.859585	+	2.64553i
$385$	1.00480e9	−	4.01133e8i	0.897363	−	0.358241i
$386$	2.80629e8	+	8.63688e8i	0.248357	+	0.764366i
$387$	−2.91706e8	+	8.97779e8i	−0.255833	+	0.787374i
$388$	4.15558e8	−	1.27895e9i	0.361177	−	1.11159i
$389$	−6.48239e8	−	1.99508e9i	−0.558357	−	1.71845i	−0.686909	−	0.726743i	$-0.741033\pi$
$389$	−6.48239e8	−	1.99508e9i	−0.558357	−	1.71845i	0.128553	−	0.991703i	$-0.458967\pi$
$390$	−2.31001e9	−	2.77624e9i	−1.97191	−	2.36991i
$391$	4.74342e7	−	1.45987e8i	0.0401304	−	0.123509i
$392$	5.65962e7	+	4.11196e7i	0.0474555	+	0.0344784i
$393$	1.15516e9			0.959995
$394$	−8.72276e8	−	6.33745e8i	−0.718484	−	0.522009i
$395$	−5.86884e8	−	7.05335e8i	−0.479140	−	0.575845i
$396$	−3.34483e9	+	2.43016e9i	−2.70671	+	1.96654i
$397$	−1.29889e8	+	9.43698e7i	−0.104185	+	0.0756948i	−0.638658	−	0.769491i	$-0.720510\pi$
$397$	−1.29889e8	+	9.43698e7i	−0.104185	+	0.0756948i	0.534473	+	0.845186i	$0.320510\pi$
$398$	8.74758e8	+	2.69223e9i	0.695500	+	2.14053i
$399$	1.64097e9			1.29329
$400$	2.24166e7	−	1.21248e8i	0.0175130	−	0.0947250i
$401$	5.56337e8			0.430856			0.215428	−	0.976520i	$-0.430885\pi$
$401$	5.56337e8			0.430856			0.215428	+	0.976520i	$0.430885\pi$
$402$	−6.91951e8	−	2.12961e9i	−0.531232	−	1.63496i
$403$	2.04270e9	−	1.48411e9i	1.55467	−	1.12953i
$404$	−1.59509e9	+	1.15890e9i	−1.20351	+	0.874401i
$405$	−1.33952e9	+	2.12404e9i	−1.00197	+	1.58881i
$406$	−1.25772e9	−	9.13790e8i	−0.932704	−	0.677649i
$407$	−6.77890e8			−0.498401
$408$	1.71097e9	+	1.24310e9i	1.24719	+	0.906137i
$409$	3.91183e8	−	1.20394e9i	0.282715	−	0.870106i	−0.704360	−	0.709843i	$-0.748766\pi$
$409$	3.91183e8	−	1.20394e9i	0.282715	−	0.870106i	0.987074	−	0.160263i	$-0.0512342\pi$
$410$	2.46873e7	+	3.75386e8i	0.0176901	+	0.268989i
$411$	−5.23812e8	−	1.61213e9i	−0.372159	−	1.14539i
$412$	−6.19239e7	+	1.90582e8i	−0.0436233	+	0.134259i
$413$	−3.44302e8	+	1.05965e9i	−0.240500	+	0.740181i
$414$	2.27810e8	+	7.01126e8i	0.157787	+	0.485618i
$415$	−7.15776e8	+	1.13499e9i	−0.491597	+	0.779515i
$416$	−5.18730e8	+	1.59649e9i	−0.353276	+	1.08727i
$417$	−1.44943e8	−	1.05308e8i	−0.0978863	−	0.0711186i
$418$	1.55669e9			1.04252
$419$	1.52133e9	+	1.10531e9i	1.01035	+	0.734065i	0.964283	−	0.264873i	$-0.0853301\pi$
$419$	1.52133e9	+	1.10531e9i	1.01035	+	0.734065i	0.0460706	+	0.998938i	$0.485330\pi$
$420$	4.31965e9	+	1.09604e9i	2.84496	+	0.721860i
$421$	−1.15523e8	+	8.39325e7i	−0.0754539	+	0.0548205i	−0.624873	−	0.780727i	$-0.714849\pi$
$421$	−1.15523e8	+	8.39325e7i	−0.0754539	+	0.0548205i	0.549419	+	0.835547i	$0.314849\pi$
$422$	1.88469e9	−	1.36931e9i	1.22080	−	0.886966i
$423$	−2.03974e9	−	6.27767e9i	−1.31034	−	4.03280i
$424$	−1.79214e9			−1.14180
$425$	−1.28783e9	−	6.98499e8i	−0.813762	−	0.441371i
$426$	7.47128e8			0.468233
$427$	2.58718e8	+	7.96251e8i	0.160816	+	0.494940i
$428$	3.65028e9	−	2.65208e9i	2.25047	−	1.63506i
$429$	−2.38173e9	+	1.73043e9i	−1.45644	+	1.05817i
$430$	8.96467e8	−	3.57883e8i	0.543744	−	0.217071i
$431$	−1.02789e9	−	7.46808e8i	−0.618411	−	0.449302i	0.233955	−	0.972247i	$-0.424833\pi$
$431$	−1.02789e9	−	7.46808e8i	−0.618411	−	0.449302i	−0.852366	+	0.522945i	$0.824833\pi$
$432$	3.70263e8			0.220962
$433$	1.05016e9	+	7.62984e8i	0.621651	+	0.451656i	0.853498	−	0.521096i	$-0.174477\pi$
$433$	1.05016e9	+	7.62984e8i	0.621651	+	0.451656i	−0.231847	+	0.972752i	$0.574477\pi$
$434$	−1.57442e9	+	4.84558e9i	−0.924502	+	2.84532i
$435$	−2.09614e9	−	5.31860e8i	−1.22098	−	0.309802i
$436$	3.82960e8	+	1.17863e9i	0.221285	+	0.681044i
$437$	5.24521e7	−	1.61431e8i	0.0300661	−	0.0925340i
$438$	3.19825e8	−	9.84320e8i	0.181867	−	0.559728i
$439$	3.43708e8	+	1.05783e9i	0.193894	+	0.596744i	0.999988	+	0.00495645i	$0.00157769\pi$
$439$	3.43708e8	+	1.05783e9i	0.193894	+	0.596744i	−0.806094	+	0.591788i	$0.798422\pi$
$440$	1.49452e9	+	3.79208e8i	0.836405	+	0.212223i
$441$	8.04145e7	−	2.47490e8i	0.0446477	−	0.137412i
$442$	2.31854e9	+	1.68452e9i	1.27714	+	0.927894i
$443$	2.97705e9			1.62695			0.813473	−	0.581602i	$-0.197574\pi$
$443$	2.97705e9			1.62695			0.813473	+	0.581602i	$0.197574\pi$
$444$	−2.25903e9	−	1.64128e9i	−1.22485	−	0.889903i
$445$	1.25505e9	−	5.01034e8i	0.675149	−	0.269530i
$446$	4.74726e9	−	3.44908e9i	2.53379	−	1.84091i
$447$	−9.04017e8	+	6.56807e8i	−0.478741	+	0.347825i
$448$	−9.88297e8	−	3.04167e9i	−0.519296	−	1.59823i
$449$	−2.92805e9			−1.52657			−0.763285	−	0.646062i	$-0.776415\pi$
$449$	−2.92805e9			−1.52657			−0.763285	+	0.646062i	$0.776415\pi$
$450$	6.97557e9	−	9.21483e8i	3.60858	−	0.476698i
$451$	3.06656e8			0.157410
$452$	−3.92762e8	−	1.20880e9i	−0.200053	−	0.615700i
$453$	−4.08544e9	+	2.96825e9i	−2.06488	+	1.50023i
$454$	2.35244e9	−	1.70915e9i	1.17984	−	0.857204i
$455$	2.13487e9	+	5.41686e8i	1.06251	+	0.269592i
$456$	1.89197e9	+	1.37460e9i	0.934410	+	0.678889i
$457$	−3.07172e9			−1.50548			−0.752739	−	0.658319i	$-0.771268\pi$
$457$	−3.07172e9			−1.50548			−0.752739	+	0.658319i	$0.771268\pi$
$458$	−3.12129e9	−	2.26775e9i	−1.51812	−	1.10298i
$459$	1.35949e9	−	4.18407e9i	0.656192	−	2.01955i
$460$	2.45897e8	−	3.89914e8i	0.117788	−	0.186774i
$461$	−9.05503e8	−	2.78685e9i	−0.430464	−	1.32483i	−0.897664	−	0.440680i	$-0.854737\pi$
$461$	−9.05503e8	−	2.78685e9i	−0.430464	−	1.32483i	0.467201	−	0.884151i	$-0.345263\pi$
$462$	1.83573e9	−	5.64981e9i	0.866089	−	2.66555i
$463$	−1.17380e9	+	3.61257e9i	−0.549616	+	1.69154i	0.160138	+	0.987095i	$0.448806\pi$
$463$	−1.17380e9	+	3.61257e9i	−0.549616	+	1.69154i	−0.709754	+	0.704450i	$0.751194\pi$
$464$	4.46299e7	+	1.37357e8i	0.0207402	+	0.0638318i
$465$	4.65093e8	+	7.07203e9i	0.214513	+	3.26181i
$466$	−4.95024e8	+	1.52353e9i	−0.226608	+	0.697429i
$467$	−9.14665e8	−	6.64543e8i	−0.415578	−	0.301935i	0.360278	−	0.932845i	$-0.382682\pi$
$467$	−9.14665e8	−	6.64543e8i	−0.415578	−	0.301935i	−0.775856	+	0.630910i	$0.782682\pi$
$468$	−8.41674e9			−3.79563
$469$	1.10477e9	+	8.02660e8i	0.494499	+	0.359275i
$470$	−3.60040e9	+	5.70907e9i	−1.59959	+	2.53643i
$471$	2.69853e9	−	1.96059e9i	1.19002	−	0.864599i
$472$	−1.28461e9	+	9.33325e8i	−0.562309	+	0.408541i
$473$	−2.43144e8	−	7.48321e8i	−0.105645	−	0.325143i
$474$	−5.03817e9			−2.17294
$475$	−1.42406e9	−	7.72390e8i	−0.609680	−	0.330681i
$476$	−3.53635e9			−1.50290
$477$	2.06004e9	+	6.34016e9i	0.869084	+	2.67477i
$478$	1.58709e9	−	1.15309e9i	0.664665	−	0.482908i
$479$	−2.23180e9	+	1.62150e9i	−0.927855	+	0.674126i	−0.945467	−	0.325718i	$-0.894394\pi$
$479$	−2.23180e9	+	1.62150e9i	−0.927855	+	0.674126i	0.0176114	+	0.999845i	$0.494394\pi$
$480$	−3.01375e9	−	3.62201e9i	−1.24383	−	1.49488i
$481$	−1.11646e9	−	8.11158e8i	−0.457442	−	0.332351i
$482$	5.21460e9			2.12108
$483$	−5.24039e8	−	3.80737e8i	−0.211616	−	0.153748i
$484$	−1.48387e8	+	4.56688e8i	−0.0594891	+	0.183089i
$485$	1.19321e9	+	1.43404e9i	0.474922	+	0.570776i
$486$	1.38289e9	+	4.25610e9i	0.546463	+	1.68184i
$487$	−5.24416e7	+	1.61399e8i	−0.0205743	+	0.0633211i	−0.960817	−	0.277185i	$-0.910598\pi$
$487$	−5.24416e7	+	1.61399e8i	−0.0205743	+	0.0633211i	0.940242	+	0.340506i	$0.110598\pi$
$488$	−3.68709e8	+	1.13477e9i	−0.143620	+	0.442016i
$489$	1.13023e9	+	3.47849e9i	0.437105	+	1.34527i
$490$	−2.47129e8	+	9.86576e7i	−0.0948936	+	0.0378830i
$491$	8.23857e8	−	2.53557e9i	0.314099	−	0.966698i	−0.662025	−	0.749482i	$-0.730303\pi$
$491$	8.23857e8	−	2.53557e9i	0.314099	−	0.966698i	0.976124	−	0.217216i	$-0.0696974\pi$
$492$	1.02191e9	+	7.42463e8i	0.386844	+	0.281059i
$493$	1.71604e9			0.645004
$494$	2.56381e9	+	1.86272e9i	0.956846	+	0.695189i
$495$	−3.76383e8	−	5.72315e9i	−0.139480	−	2.12088i
$496$	3.82925e8	−	2.78211e8i	0.140905	−	0.102374i
$497$	−3.68615e8	+	2.67814e8i	−0.134687	+	0.0978557i
$498$	2.27677e9	+	7.00718e9i	0.826069	+	2.54238i
$499$	4.56518e9			1.64477			0.822387	−	0.568928i	$-0.192642\pi$
$499$	4.56518e9			1.64477			0.822387	+	0.568928i	$0.192642\pi$
$500$	−3.23279e9	−	2.98439e9i	−1.15660	−	1.06773i
$501$	−1.82481e9			−0.648316
$502$	2.54219e8	+	7.82405e8i	0.0896902	+	0.276038i
$503$	1.69689e9	−	1.23287e9i	0.594520	−	0.431944i	−0.249409	−	0.968398i	$-0.580237\pi$
$503$	1.69689e9	−	1.23287e9i	0.594520	−	0.431944i	0.843930	+	0.536454i	$0.180237\pi$
$504$	5.01122e9	−	3.64087e9i	1.74356	−	1.26677i
$505$	−1.79490e8	−	2.72926e9i	−0.0620184	−	0.943029i
$506$	−4.97125e8	−	3.61182e8i	−0.170584	−	0.123937i
$507$	−6.87877e8			−0.234414
$508$	−4.39836e9	−	3.19559e9i	−1.48856	−	1.08150i
$509$	7.35811e8	−	2.26459e9i	0.247317	−	0.761164i	−0.747930	−	0.663778i	$-0.768952\pi$
$509$	7.35811e8	−	2.26459e9i	0.247317	−	0.761164i	0.995247	−	0.0973857i	$-0.0310480\pi$
$510$	−7.47101e9	+	2.98254e9i	−2.49393	+	0.995614i
$511$	1.95044e8	+	6.00283e8i	0.0646635	+	0.199014i
$512$	−1.80510e8	+	5.55552e8i	−0.0594368	+	0.182928i
$513$	1.50330e9	−	4.62669e9i	0.491627	−	1.51307i
$514$	−2.21905e9	−	6.82953e9i	−0.720769	−	2.21830i
$515$	−1.77806e8	−	2.13692e8i	−0.0573615	−	0.0689388i
$516$	1.00154e9	−	3.08243e9i	0.320919	−	0.987686i
$517$	4.45111e9	+	3.23392e9i	1.41661	+	1.02923i
$518$	2.78470e9			0.880286
$519$	−1.86713e8	−	1.35655e8i	−0.0586258	−	0.0425942i
$520$	2.00766e9	+	2.41287e9i	0.626152	+	0.752528i
$521$	−5.01739e9	+	3.64534e9i	−1.55434	+	1.12929i	−0.613871	+	0.789406i	$0.710389\pi$
$521$	−5.01739e9	+	3.64534e9i	−1.55434	+	1.12929i	−0.940466	+	0.339886i	$0.889611\pi$
$522$	−6.66753e9	+	4.84424e9i	−2.05172	+	1.49066i
$523$	1.88092e9	+	5.78888e9i	0.574930	+	1.76945i	0.636418	+	0.771344i	$0.280415\pi$
$523$	1.88092e9	+	5.78888e9i	0.574930	+	1.76945i	−0.0614885	+	0.998108i	$0.519585\pi$
$524$	−2.75277e9			−0.835814
$525$	−4.48263e9	+	4.25762e9i	−1.35200	+	1.28413i
$526$	−3.72890e9			−1.11720
$527$	−1.73789e9	−	5.34866e9i	−0.517230	−	1.59187i
$528$	−4.46479e8	+	3.24386e8i	−0.132003	+	0.0959055i
$529$	2.70036e9	−	1.96192e9i	0.793097	−	0.576219i
$530$	3.63623e9	−	5.76590e9i	1.06093	−	1.68229i
$531$	4.77853e9	+	3.47181e9i	1.38504	+	1.00629i
$532$	−3.91044e9			−1.12599
$533$	5.05052e8	+	3.66942e8i	0.144474	+	0.104967i
$534$	2.29292e9	−	7.05688e9i	0.651620	−	2.00548i
$535$	4.10754e8	+	6.24578e9i	0.115970	+	1.76339i
$536$	6.01385e8	+	1.85087e9i	0.168685	+	0.519158i
$537$	3.22661e9	−	9.93048e9i	0.899158	−	2.76732i
$538$	−5.92785e7	+	1.82440e8i	−0.0164119	+	0.0505107i
$539$	6.70274e7	+	2.06289e8i	0.0184371	+	0.0567435i
$540$	7.04754e9	−	1.11751e10i	1.92601	−	3.05404i
$541$	−1.81735e9	+	5.59322e9i	−0.493455	+	1.51870i	0.325895	+	0.945406i	$0.394334\pi$
$541$	−1.81735e9	+	5.59322e9i	−0.493455	+	1.51870i	−0.819350	+	0.573293i	$0.805666\pi$
$542$	−6.41561e9	−	4.66122e9i	−1.73078	−	1.25748i
$543$	−9.46360e9			−2.53663
$544$	3.02488e9	+	2.19770e9i	0.805585	+	0.585292i
$545$	−1.66640e9	−	4.22820e8i	−0.440951	−	0.111884i
$546$	9.78390e9	−	7.10842e9i	2.57240	−	1.86896i
$547$	2.15791e9	−	1.56781e9i	0.563738	−	0.409580i	−0.269087	−	0.963116i	$-0.586722\pi$
$547$	2.15791e9	−	1.56781e9i	0.563738	−	0.409580i	0.832825	+	0.553536i	$0.186722\pi$
$548$	1.24825e9	+	3.84172e9i	0.324018	+	0.997226i
$549$	4.43837e9			1.14478
$550$	−4.25241e9	+	4.03895e9i	−1.08985	+	1.03514i
$551$	1.89757e9			0.483245
$552$	−2.85263e8	−	8.77950e8i	−0.0721870	−	0.222169i
$553$	2.48571e9	−	1.80597e9i	0.625046	−	0.454123i
$554$	−5.65837e9	+	4.11105e9i	−1.41386	+	1.02723i
$555$	3.59756e9	−	1.43620e9i	0.893270	−	0.356607i
$556$	3.45402e8	+	2.50949e8i	0.0852242	+	0.0619190i
$557$	−1.03490e8			−0.0253750			−0.0126875	−	0.999920i	$-0.504039\pi$
$557$	−1.03490e8			−0.0253750			−0.0126875	+	0.999920i	$0.504039\pi$
$558$	2.18513e10	+	1.58759e10i	5.32423	+	3.86828i
$559$	4.94984e8	−	1.52340e9i	0.119853	−	0.368870i
$560$	4.00202e8	+	1.01544e8i	0.0962988	+	0.0244342i
$561$	2.02632e9	+	6.23638e9i	0.484550	+	1.49129i
$562$	−1.50064e9	+	4.61849e9i	−0.356614	+	1.09755i
$563$	−6.47622e8	+	1.99318e9i	−0.152947	+	0.470724i	−0.997947	−	0.0640429i	$-0.979601\pi$
$563$	−6.47622e8	+	1.99318e9i	−0.152947	+	0.470724i	0.845000	+	0.534767i	$0.179601\pi$
$564$	7.00322e9	+	2.15537e10i	1.64369	+	5.05877i
$565$	1.70905e9	+	4.33641e8i	0.398643	+	0.101149i
$566$	1.00902e9	−	3.10545e9i	0.233907	−	0.719892i
$567$	−6.80275e9	−	4.94249e9i	−1.56727	−	1.13869i
$568$	−6.49340e8			−0.148680
$569$	1.29018e9	+	9.37371e8i	0.293601	+	0.213314i	0.724828	−	0.688930i	$-0.241919\pi$
$569$	1.29018e9	+	9.37371e8i	0.293601	+	0.213314i	−0.431227	+	0.902243i	$0.641919\pi$
$570$	−8.26133e9	+	3.29805e9i	−1.86848	+	0.745925i
$571$	−3.62081e9	+	2.63067e9i	−0.813915	+	0.591344i	−0.914963	−	0.403538i	$-0.867780\pi$
$571$	−3.62081e9	+	2.63067e9i	−0.813915	+	0.591344i	0.101048	+	0.994882i	$0.467780\pi$
$572$	5.67570e9	−	4.12364e9i	1.26804	−	0.921286i
$573$	−4.61384e9	−	1.41999e10i	−1.02452	−	3.15315i
$574$	−1.25971e9			−0.278022
$575$	2.75562e8	+	5.77072e8i	0.0604480	+	0.126588i
$576$	−1.69545e10			−3.69663
$577$	3.66387e8	+	1.12762e9i	0.0794008	+	0.244370i	0.982875	−	0.184271i	$-0.0589924\pi$
$577$	3.66387e8	+	1.12762e9i	0.0794008	+	0.244370i	−0.903475	+	0.428641i	$0.858992\pi$
$578$	−8.61594e8	+	6.25985e8i	−0.185590	+	0.134839i
$579$	−3.42219e9	+	2.48637e9i	−0.732705	+	0.532342i
$580$	4.99513e9	+	1.26743e9i	1.06304	+	0.269728i
$581$	−3.63508e9	−	2.64104e9i	−0.768949	−	0.558674i
$582$	1.02433e10			2.15382
$583$	−4.49541e9	−	3.26611e9i	−0.939571	−	0.682638i
$584$	−2.77965e8	+	8.55487e8i	−0.0577490	+	0.177733i
$585$	6.22838e9	−	9.87621e9i	1.28626	−	2.03960i
$586$	8.61447e8	+	2.65126e9i	0.176843	+	0.544266i
$587$	−1.66584e9	+	5.12692e9i	−0.339937	+	1.04622i	0.624301	+	0.781184i	$0.285384\pi$
$587$	−1.66584e9	+	5.12692e9i	−0.339937	+	1.04622i	−0.964239	+	0.265036i	$0.914616\pi$
$588$	−2.76095e8	+	8.49732e8i	−0.0560063	+	0.172370i
$589$	−1.92173e9	−	5.91447e9i	−0.387515	−	1.19265i
$590$	−3.96349e8	−	6.02674e9i	−0.0794503	−	1.20809i
$591$	1.55194e9	−	4.77638e9i	0.309256	−	0.951793i
$592$	−2.09292e8	−	1.52059e8i	−0.0414597	−	0.0301222i
$593$	4.53623e8			0.0893314			0.0446657	−	0.999002i	$-0.485778\pi$
$593$	4.53623e8			0.0893314			0.0446657	+	0.999002i	$0.485778\pi$
$594$	−1.42478e10	−	1.03517e10i	−2.78931	−	2.02655i
$595$	2.61689e9	−	4.14956e9i	0.509304	−	0.807592i
$596$	2.15428e9	−	1.56518e9i	0.416813	−	0.302832i
$597$	−1.06674e10	+	7.75033e9i	−2.05187	+	1.49077i
$598$	−3.86561e8	−	1.18971e9i	−0.0739203	−	0.227503i
$599$	6.15429e8			0.117000			0.0584998	−	0.998287i	$-0.481368\pi$
$599$	6.15429e8			0.117000			0.0584998	+	0.998287i	$0.481368\pi$
$600$	−8.73481e9	+	1.15388e9i	−1.65091	+	0.218088i
$601$	2.63776e9			0.495650			0.247825	−	0.968805i	$-0.420284\pi$
$601$	2.63776e9			0.495650			0.247825	+	0.968805i	$0.420284\pi$
$602$	9.98810e8	+	3.07402e9i	0.186593	+	0.574274i
$603$	5.85666e9	−	4.25511e9i	1.08778	−	0.790316i
$604$	9.73567e9	−	7.07337e9i	1.79778	−	1.30616i
$605$	−4.26072e8	−	5.12066e8i	−0.0782239	−	0.0940118i
$606$	−1.21500e10	−	8.82746e9i	−2.21779	−	1.61132i
$607$	9.20548e9			1.67065			0.835326	−	0.549755i	$-0.185279\pi$
$607$	9.20548e9			1.67065			0.835326	+	0.549755i	$0.185279\pi$
$608$	3.34486e9	+	2.43019e9i	0.603554	+	0.438507i
$609$	2.23772e9	−	6.88700e9i	0.401463	−	1.23558i
$610$	−2.90282e9	−	3.48870e9i	−0.517805	−	0.622313i
$611$	3.46115e9	+	1.06523e10i	0.613869	+	1.88929i
$612$	−5.79318e9	+	1.78296e10i	−1.02161	+	3.14421i
$613$	−4.96639e8	+	1.52850e9i	−0.0870822	+	0.268011i	−0.985109	−	0.171928i	$-0.945000\pi$
$613$	−4.96639e8	+	1.52850e9i	−0.0870822	+	0.268011i	0.898027	+	0.439940i	$0.145000\pi$
$614$	−2.81685e8	−	8.66936e8i	−0.0491104	−	0.151146i
$615$	−1.62742e9	+	6.49692e8i	−0.282122	+	0.112628i
$616$	−1.59546e9	+	4.91033e9i	−0.275013	+	0.846404i
$617$	−8.60887e9	−	6.25471e9i	−1.47553	−	1.07204i	−0.978963	−	0.204037i	$-0.934594\pi$
$617$	−8.60887e9	−	6.25471e9i	−1.47553	−	1.07204i	−0.496567	−	0.867998i	$-0.665406\pi$
$618$	−1.52639e9			−0.260140
$619$	−9.48691e8	−	6.89264e8i	−0.160771	−	0.116807i	0.504491	−	0.863417i	$-0.331680\pi$
$619$	−9.48691e8	−	6.89264e8i	−0.160771	−	0.116807i	−0.665262	+	0.746610i	$0.731680\pi$
$620$	−1.10832e9	−	1.68527e10i	−0.186765	−	2.83988i
$621$	−1.55356e9	+	1.12873e9i	−0.260320	+	0.189134i
$622$	−1.06894e10	+	7.76628e9i	−1.78109	+	1.29404i
$623$	1.39833e9	+	4.30361e9i	0.231686	+	0.713057i
$624$	−1.12349e9			−0.185108
$625$	5.89415e9	−	1.58491e9i	0.965697	−	0.259672i
$626$	1.47637e10			2.40539
$627$	2.24068e9	+	6.89610e9i	0.363031	+	1.11729i
$628$	−6.43063e9	+	4.67212e9i	−1.03608	+	0.752758i
$629$	−2.48677e9	+	1.80674e9i	−0.398435	+	0.289480i
$630$	1.54614e9	+	2.35101e10i	0.246353	+	3.74595i
$631$	2.13373e8	+	1.55024e8i	0.0338093	+	0.0245639i	0.604562	−	0.796558i	$-0.293348\pi$
$631$	2.13373e8	+	1.55024e8i	0.0338093	+	0.0245639i	−0.570752	+	0.821122i	$0.693348\pi$
$632$	4.37875e9			0.689986
$633$	8.77881e9	+	6.37818e9i	1.37570	+	0.999503i
$634$	1.15704e9	−	3.56102e9i	0.180317	−	0.554960i
$635$	7.00449e9	−	2.79630e9i	1.08560	−	0.433387i
$636$	−7.07293e9	−	2.17682e10i	−1.09018	−	3.35524i
$637$	−1.36452e8	+	4.19956e8i	−0.0209166	+	0.0643748i
$638$	2.12279e9	−	6.53329e9i	0.323620	−	0.996000i
$639$	7.46409e8	+	2.29721e9i	0.113168	+	0.348296i
$640$	6.52623e9	+	7.84341e9i	0.984084	+	1.18270i
$641$	−3.65420e8	+	1.12465e9i	−0.0548011	+	0.168661i	−0.974711	−	0.223469i	$-0.928262\pi$
$641$	−3.65420e8	+	1.12465e9i	−0.0548011	+	0.168661i	0.919910	+	0.392130i	$0.128262\pi$
$642$	2.78046e10	+	2.02012e10i	4.14709	+	3.01304i
$643$	−1.07875e10			−1.60022			−0.800112	−	0.599851i	$-0.795227\pi$
$643$	−1.07875e10			−1.60022			−0.800112	+	0.599851i	$0.795227\pi$
$644$	1.24879e9	+	9.07301e8i	0.184242	+	0.133860i
$645$	2.87579e9	+	3.45620e9i	0.421985	+	0.507155i
$646$	5.71054e9	−	4.14895e9i	0.833419	−	0.605514i
$647$	−1.65281e8	+	1.20084e8i	−0.0239916	+	0.0174309i	−0.599716	−	0.800213i	$-0.704720\pi$
$647$	−1.65281e8	+	1.20084e8i	−0.0239916	+	0.0174309i	0.575725	+	0.817644i	$0.304720\pi$
$648$	−3.70311e9	−	1.13970e10i	−0.534631	−	1.64543i
$649$	−4.92328e9			−0.706966
$650$	−1.18365e10	+	1.56363e9i	−1.69055	+	0.223324i
$651$	−2.37321e10			−3.37134
$652$	−2.69335e9	−	8.28929e9i	−0.380563	−	1.17125i
$653$	5.52272e9	−	4.01249e9i	0.776170	−	0.563920i	−0.127657	−	0.991818i	$-0.540746\pi$
$653$	5.52272e9	−	4.01249e9i	0.776170	−	0.563920i	0.903827	+	0.427898i	$0.140746\pi$
$654$	−7.63694e9	+	5.54856e9i	−1.06757	+	0.775637i
$655$	2.03704e9	−	3.23010e9i	0.283241	−	0.449129i
$656$	9.46769e7	+	6.87868e7i	0.0130942	+	0.00951353i
$657$	3.34603e9			0.460310
$658$	−1.82847e10	−	1.32846e10i	−2.50205	−	1.81785i
$659$	−5.43195e8	+	1.67178e9i	−0.0739362	+	0.227552i	−0.981194	−	0.193022i	$-0.938171\pi$
$659$	−5.43195e8	+	1.67178e9i	−0.0739362	+	0.227552i	0.907258	+	0.420574i	$0.138171\pi$
$660$	1.29227e9	+	1.96498e10i	0.174964	+	2.66045i
$661$	−1.32937e9	−	4.09137e9i	−0.179036	−	0.551015i	0.820759	−	0.571274i	$-0.193551\pi$
$661$	−1.32937e9	−	4.09137e9i	−0.179036	−	0.551015i	−0.999795	+	0.0202594i	$0.993551\pi$
$662$	2.90656e9	−	8.94547e9i	0.389382	−	1.19840i
$663$	−4.12512e9	+	1.26958e10i	−0.549717	+	1.69185i
$664$	−1.97877e9	−	6.09004e9i	−0.262306	−	0.807294i
$665$	2.89372e9	−	4.58852e9i	0.381576	−	0.605058i
$666$	4.56184e9	−	1.40399e10i	0.598385	−	1.84164i
$667$	−6.05985e8	−	4.40274e8i	−0.0790718	−	0.0574490i
$668$	4.34856e9			0.564452
$669$	2.21126e10	+	1.60657e10i	2.85527	+	2.07448i
$670$	−7.17508e9	−	1.82055e9i	−0.921647	−	0.233852i
$671$	−2.99295e9	+	2.17450e9i	−0.382446	+	0.277864i
$672$	1.27645e10	−	9.27397e9i	1.62260	−	1.17889i
$673$	−1.50286e9	−	4.62531e9i	−0.190048	−	0.584909i	0.809950	−	0.586499i	$-0.199494\pi$
$673$	−1.50286e9	−	4.62531e9i	−0.190048	−	0.584909i	−0.999999	+	0.00158947i	$0.999494\pi$
$674$	1.66376e9			0.209305
$675$	7.89775e9	+	1.65392e10i	0.988417	+	2.06991i
$676$	1.63922e9			0.204091
$677$	−4.01773e9	−	1.23653e10i	−0.497646	−	1.53160i	−0.812793	−	0.582553i	$-0.802054\pi$
$677$	−4.01773e9	−	1.23653e10i	−0.497646	−	1.53160i	0.315147	−	0.949043i	$-0.397946\pi$
$678$	7.83241e9	−	5.69058e9i	0.965142	−	0.701217i
$679$	−5.05378e9	+	3.67179e9i	−0.619544	+	0.450125i
$680$	6.49316e9	−	2.59217e9i	0.791909	−	0.316142i
$681$	1.09576e10	+	7.96115e9i	1.32954	+	0.965964i
$682$	−2.25132e10			−2.71764
$683$	−1.13846e9	−	8.27140e8i	−0.136724	−	0.0993359i	0.517321	−	0.855791i	$-0.326929\pi$
$683$	−1.13846e9	−	8.27140e8i	−0.136724	−	0.0993359i	−0.654045	+	0.756456i	$0.726929\pi$
$684$	−6.40602e9	+	1.97157e10i	−0.765406	+	2.35568i
$685$	−5.43158e9	−	1.37817e9i	−0.645668	−	0.163827i
$686$	4.04816e9	+	1.24589e10i	0.478765	+	1.47349i
$687$	5.55336e9	−	1.70915e10i	0.653442	−	2.01109i
$688$	9.27896e7	−	2.85577e8i	0.0108627	−	0.0334321i
$689$	−3.49560e9	−	1.07583e10i	−0.407150	−	1.25308i
$690$	3.40346e9	+	8.63568e8i	0.394410	+	0.100075i
$691$	−1.05677e9	+	3.25241e9i	−0.121845	+	0.375000i	−0.993313	−	0.115452i	$-0.963168\pi$
$691$	−1.05677e9	+	3.25241e9i	−0.121845	+	0.375000i	0.871468	+	0.490452i	$0.163168\pi$
$692$	4.44940e8	+	3.23268e8i	0.0510423	+	0.0370844i
$693$	1.92055e10			2.19210
$694$	1.11744e10	+	8.11866e9i	1.26901	+	0.921990i
$695$	−5.50061e8	+	2.19593e8i	−0.0621533	+	0.0248125i
$696$	8.34908e9	−	6.06596e9i	0.938656	−	0.681973i
$697$	1.12493e9	−	8.17312e8i	0.125838	−	0.0914268i
$698$	1.53010e9	+	4.70917e9i	0.170304	+	0.524143i
$699$	−7.46175e9			−0.826362
$700$	1.06822e10	−	1.01460e10i	1.17711	−	1.11802i
$701$	1.39609e10			1.53074			0.765368	−	0.643593i	$-0.222557\pi$
$701$	1.39609e10			1.53074			0.765368	+	0.643593i	$0.222557\pi$
$702$	−1.10790e10	−	3.40977e10i	−1.20871	−	3.72002i
$703$	−2.74983e9	+	1.99787e9i	−0.298512	+	0.216882i
$704$	1.14330e10	−	8.30657e9i	1.23497	−	0.897258i
$705$	−3.04735e10	−	7.73213e9i	−3.27537	−	0.831069i
$706$	2.38851e10	+	1.73535e10i	2.55453	+	1.85597i
$707$	9.15876e9			0.974695
$708$	−1.64066e10	−	1.19201e10i	−1.73741	−	1.26230i
$709$	−4.27742e9	+	1.31646e10i	−0.450734	+	1.38722i	0.425337	+	0.905035i	$0.360155\pi$
$709$	−4.27742e9	+	1.31646e10i	−0.450734	+	1.38722i	−0.876071	+	0.482182i	$0.839845\pi$
$710$	1.31751e9	−	2.08914e9i	0.138149	−	0.219060i
$711$	−5.03332e9	−	1.54910e10i	−0.525183	−	1.61635i
$712$	−1.99281e9	+	6.13324e9i	−0.206912	+	0.636810i
$713$	−7.58575e8	+	2.33465e9i	−0.0783764	+	0.241218i
$714$	−8.32392e9	−	2.56184e10i	−0.855823	−	2.63395i
$715$	6.38669e8	+	9.71137e9i	0.0653439	+	0.993595i
$716$	−7.68905e9	+	2.36645e10i	−0.782847	+	2.40936i
$717$	7.39260e9	+	5.37104e9i	0.748997	+	0.544178i
$718$	−2.69063e9			−0.271281
$719$	−1.13457e10	−	8.24312e9i	−1.13836	−	0.827066i	−0.151469	−	0.988462i	$-0.548400\pi$
$719$	−1.13457e10	−	8.24312e9i	−1.13836	−	0.827066i	−0.986890	+	0.161396i	$0.948400\pi$
$720$	1.16757e9	−	1.85139e9i	0.116579	−	0.184856i
$721$	7.53085e8	−	5.47148e8i	0.0748291	−	0.0543665i
$722$	−6.81189e9	+	4.94913e9i	−0.673578	+	0.489383i
$723$	7.50585e9	+	2.31006e10i	0.738611	+	2.27321i
$724$	2.25519e10			2.20850
$725$	−5.18360e9	+	4.92340e9i	−0.505182	+	0.479824i
$726$	−3.65767e9			−0.354753
$727$	−1.38671e9	−	4.26786e9i	−0.133849	−	0.411945i	0.861560	−	0.507656i	$-0.169488\pi$
$727$	−1.38671e9	−	4.26786e9i	−0.133849	−	0.411945i	−0.995409	+	0.0957102i	$0.969488\pi$
$728$	−8.50333e9	+	6.17803e9i	−0.816826	+	0.593459i
$729$	−9.68099e8	+	7.03365e8i	−0.0925494	+	0.0672411i
$730$	−2.18840e9	−	2.63008e9i	−0.208207	−	0.250230i
$731$	−2.88641e9	−	2.09710e9i	−0.273304	−	0.198567i
$732$	−1.52387e10			−1.43601
$733$	−7.24204e9	−	5.26165e9i	−0.679199	−	0.493467i	0.193893	−	0.981023i	$-0.437889\pi$
$733$	−7.24204e9	−	5.26165e9i	−0.679199	−	0.493467i	−0.873092	+	0.487556i	$0.837889\pi$
$734$	−6.74447e9	+	2.07573e10i	−0.629523	+	1.93747i
$735$	−7.92766e8	−	9.52770e8i	−0.0736444	−	0.0885080i
$736$	−5.04324e8	−	1.55215e9i	−0.0466270	−	0.143503i
$737$	−1.86463e9	+	5.73875e9i	−0.171576	+	0.528057i
$738$	−2.06363e9	+	6.35121e9i	−0.188988	+	0.581646i
$739$	−2.13222e9	−	6.56229e9i	−0.194346	−	0.598136i	−0.999984	−	0.00572701i	$-0.998177\pi$
$739$	−2.13222e9	−	6.56229e9i	−0.194346	−	0.598136i	0.805637	−	0.592409i	$-0.201823\pi$
$740$	−8.57304e9	+	3.42249e9i	−0.777721	+	0.310478i
$741$	−4.56149e9	+	1.40388e10i	−0.411854	+	1.26756i
$742$	1.84667e10	+	1.34168e10i	1.65949	+	1.20569i
$743$	1.44134e10			1.28915			0.644576	−	0.764540i	$-0.277034\pi$
$743$	1.44134e10			1.28915			0.644576	+	0.764540i	$0.277034\pi$
$744$	−2.73622e10	−	1.98798e10i	−2.43582	−	1.76973i
$745$	2.42415e8	+	3.68607e9i	0.0214789	+	0.326600i
$746$	−1.57169e10	+	1.14190e10i	−1.38606	+	1.00703i
$747$	−1.92705e10	+	1.40009e10i	−1.69150	+	1.22895i
$748$	−4.82876e9	−	1.48614e10i	−0.421871	−	1.29839i
$749$	−2.09594e10			−1.82260
$750$	1.40104e10	−	3.04440e10i	1.21266	−	2.63504i
$751$	−3.95843e9			−0.341023			−0.170511	−	0.985356i	$-0.554542\pi$
$751$	−3.95843e9			−0.341023			−0.170511	+	0.985356i	$0.554542\pi$
$752$	6.48825e8	+	1.99688e9i	0.0556372	+	0.171234i
$753$	−3.10013e9	+	2.25237e9i	−0.264604	+	0.192246i
$754$	1.13139e10	−	8.21999e9i	0.961193	−	0.698348i
$755$	1.09552e9	+	1.66581e10i	0.0926419	+	1.40868i
$756$	3.57910e10	+	2.60037e10i	3.01264	+	2.18881i
$757$	−6.97998e9			−0.584815			−0.292407	−	0.956294i	$-0.594456\pi$
$757$	−6.97998e9			−0.584815			−0.292407	+	0.956294i	$0.594456\pi$
$758$	9.86065e9	+	7.16418e9i	0.822362	+	0.597481i
$759$	8.84477e8	−	2.72214e9i	0.0734244	−	0.225977i
$760$	7.18004e9	−	2.86638e9i	0.593307	−	0.236857i
$761$	−3.06549e9	−	9.43462e9i	−0.252147	−	0.776030i	−0.994378	−	0.105885i	$-0.966232\pi$
$761$	−3.06549e9	−	9.43462e9i	−0.252147	−	0.776030i	0.742231	−	0.670144i	$-0.233768\pi$
$762$	1.27969e10	−	3.93849e10i	1.04776	−	3.22468i
$763$	1.77895e9	−	5.47505e9i	0.144987	−	0.446223i
$764$	1.09948e10	+	3.38386e10i	0.891994	+	2.74527i
$765$	−1.66343e10	−	1.99916e10i	−1.34335	−	1.61448i
$766$	−3.20046e9	+	9.84999e9i	−0.257283	+	0.791836i
$767$	−8.10849e9	−	5.89116e9i	−0.648868	−	0.471430i
$768$	1.90441e10			1.51704
$769$	−1.37212e10	−	9.96905e9i	−1.08805	−	0.790518i	−0.108984	−	0.994043i	$-0.534760\pi$
$769$	−1.37212e10	−	9.96905e9i	−1.08805	−	0.790518i	−0.979070	+	0.203526i	$0.934760\pi$
$770$	−1.25610e10	−	1.50962e10i	−0.991530	−	1.19165i
$771$	2.70607e10	−	1.96607e10i	2.12642	−	1.54493i
$772$	8.15513e9	−	5.92505e9i	0.637926	−	0.463480i
$773$	2.39718e9	+	7.37777e9i	0.186669	+	0.574509i	0.999973	−	0.00733003i	$-0.00233324\pi$
$773$	2.39718e9	+	7.37777e9i	0.186669	+	0.574509i	−0.813304	+	0.581839i	$0.802333\pi$
$774$	1.71348e10			1.32827
$775$	2.05952e10	+	1.11705e10i	1.58931	+	0.862018i
$776$	−8.90259e9			−0.683912
$777$	4.00827e9	+	1.23362e10i	0.306537	+	0.943425i
$778$	−3.08055e10	+	2.23815e10i	−2.34530	+	1.70396i
$779$	1.24394e9	−	9.03772e8i	0.0942794	−	0.0684980i
$780$	−2.13845e10	+	3.39089e10i	−1.61349	+	2.55848i
$781$	−1.62881e9	−	1.18340e9i	−0.122347	−	0.0888900i
$782$	−2.78629e9			−0.208354
$783$	−1.73678e10	−	1.26185e10i	−1.29294	−	0.939379i
$784$	−2.55793e7	+	7.87249e7i	−0.00189575	+	0.00583453i
$785$	−7.23618e8	−	1.10031e10i	−0.0533907	−	0.811839i
$786$	−6.47951e9	−	1.99419e10i	−0.475952	−	1.46483i
$787$	6.89356e9	−	2.12162e10i	0.504118	−	1.55151i	−0.298131	−	0.954525i	$-0.596363\pi$
$787$	6.89356e9	−	2.12162e10i	0.504118	−	1.55151i	0.802249	−	0.596990i	$-0.203637\pi$
$788$	−3.69829e9	+	1.13822e10i	−0.269252	+	0.828673i
$789$	−5.36734e9	−	1.65190e10i	−0.389036	−	1.19733i
$790$	−8.88445e9	+	1.40879e10i	−0.641115	+	1.01660i
$791$	−1.82448e9	+	5.61518e9i	−0.131076	+	0.403409i
$792$	2.21433e10	+	1.60880e10i	1.58381	+	1.15071i
$793$	−7.53128e9			−0.536306
$794$	2.35770e9	+	1.71297e9i	0.167154	+	0.121445i
$795$	3.07768e10	+	7.80909e9i	2.17240	+	0.551208i
$796$	2.54206e10	−	1.84691e10i	1.78645	−	1.29793i
$797$	1.25124e10	−	9.09081e9i	0.875462	−	0.636060i	−0.0565851	−	0.998398i	$-0.518021\pi$
$797$	1.25124e10	−	9.09081e9i	0.875462	−	0.636060i	0.932047	+	0.362337i	$0.118021\pi$
$798$	−9.20447e9	−	2.83284e10i	−0.641193	−	1.97339i
$799$	2.49476e10			1.73027
$800$	−1.54425e10	+	2.03998e9i	−1.06636	+	0.140867i
$801$	2.39887e10			1.64927
$802$	−3.12059e9	−	9.60419e9i	−0.213612	−	0.657432i
$803$	−2.25634e9	+	1.63933e9i	−0.153780	+	0.111728i
$804$	−2.01082e10	+	1.46095e10i	−1.36451	+	0.991376i
$805$	−1.98873e9	+	7.93933e8i	−0.134366	+	0.0536412i
$806$	−3.70785e10	−	2.69391e10i	−2.49431	−	1.81222i
$807$	−8.93534e8			−0.0598486
$808$	1.05597e10	+	7.67207e9i	0.704226	+	0.511650i
$809$	3.93141e9	−	1.20996e10i	0.261053	−	0.803438i	−0.731524	−	0.681816i	$-0.761191\pi$
$809$	3.93141e9	−	1.20996e10i	0.261053	−	0.803438i	0.992577	−	0.121622i	$-0.0388095\pi$
$810$	4.41815e10	+	1.12103e10i	2.92108	+	0.741173i
$811$	−1.98271e8	−	6.10215e8i	−0.0130523	−	0.0401708i	0.944318	−	0.329033i	$-0.106723\pi$
$811$	−1.98271e8	−	6.10215e8i	−0.0130523	−	0.0401708i	−0.957371	+	0.288863i	$0.906723\pi$
$812$	−5.33252e9	+	1.64118e10i	−0.349532	+	1.07575i
$813$	1.14146e10	−	3.51304e10i	0.744976	−	2.29280i
$814$	3.80241e9	+	1.17026e10i	0.247100	+	0.760496i
$815$	1.17197e10	+	2.97368e9i	0.758345	+	0.192417i
$816$	−7.73293e8	+	2.37995e9i	−0.0498228	+	0.153339i
$817$	−3.19175e9	−	2.31894e9i	−0.204763	−	0.148769i
$818$	−2.29781e10			−1.46784
$819$	3.16309e10	+	2.29812e10i	2.01195	+	1.46177i
$820$	3.87817e9	−	1.54822e9i	0.245628	−	0.0980585i
$821$	1.39220e10	−	1.01149e10i	0.878013	−	0.637914i	−0.0547118	−	0.998502i	$-0.517424\pi$
$821$	1.39220e10	−	1.01149e10i	0.878013	−	0.637914i	0.932725	+	0.360588i	$0.117424\pi$
$822$	−2.48924e10	+	1.80854e10i	−1.56321	+	1.13574i
$823$	4.28395e9	+	1.31846e10i	0.267883	+	0.824459i	0.991015	+	0.133749i	$0.0427017\pi$
$823$	4.28395e9	+	1.31846e10i	0.267883	+	0.824459i	−0.723132	+	0.690710i	$0.757298\pi$
$824$	1.32661e9			0.0826034
$825$	−2.40134e10	−	1.30245e10i	−1.48890	−	0.807554i
$826$	2.02243e10			1.24866
$827$	3.43459e9	+	1.05706e10i	0.211157	+	0.649875i	0.999404	+	0.0345158i	$0.0109889\pi$
$827$	3.43459e9	+	1.05706e10i	0.211157	+	0.649875i	−0.788247	+	0.615359i	$0.789011\pi$
$828$	6.62018e9	−	4.80984e9i	0.405288	−	0.294459i
$829$	−1.19318e10	+	8.66894e9i	−0.727384	+	0.528476i	−0.888735	−	0.458421i	$-0.848415\pi$
$829$	−1.19318e10	+	8.66894e9i	−0.727384	+	0.528476i	0.161351	+	0.986897i	$0.448415\pi$
$830$	2.36086e10	+	5.99027e9i	1.43317	+	0.363641i
$831$	−2.63565e10	−	1.91491e10i	−1.59325	−	1.15756i
$832$	2.87694e10			1.73180
$833$	7.95694e8	+	5.78106e8i	0.0476967	+	0.0346537i
$834$	−1.00494e9	+	3.09289e9i	−0.0599872	+	0.184622i
$835$	−3.21793e9	+	5.10260e9i	−0.191282	+	0.303311i
$836$	−5.33957e9	−	1.64335e10i	−0.316071	−	0.972766i
$837$	−2.17411e10	+	6.69124e10i	−1.28157	+	3.94428i
$838$	1.05479e10	−	3.24630e10i	0.619170	−	1.90561i
$839$	8.18877e8	+	2.52024e9i	0.0478687	+	0.147325i	0.972134	−	0.234426i	$-0.0753212\pi$
$839$	8.18877e8	+	2.52024e9i	0.0478687	+	0.147325i	−0.924265	+	0.381751i	$0.875321\pi$
$840$	−1.93608e9	−	2.94393e10i	−0.112706	−	1.71376i
$841$	−2.74286e9	+	8.44166e9i	−0.159008	+	0.489375i
$842$	2.09694e9	+	1.52352e9i	0.121058	+	0.0879538i
$843$	−2.26198e10			−1.30045
$844$	−2.09200e10	−	1.51993e10i	−1.19774	−	0.870211i
$845$	−1.21302e9	+	1.92346e9i	−0.0691624	+	0.109669i
$846$	−9.69319e10	+	7.04251e10i	−5.50390	+	3.99881i
$847$	1.80460e9	−	1.31112e9i	0.102044	−	0.0741396i
$848$	−6.55284e8	−	2.01676e9i	−0.0369015	−	0.113571i
$849$	1.52095e10			0.852978
$850$	−4.83471e9	+	2.61502e10i	−0.270025	+	1.46052i
$851$	1.34170e9			0.0746280
$852$	−2.56272e9	−	7.88723e9i	−0.141959	−	0.436904i
$853$	1.22711e10	−	8.91544e9i	0.676956	−	0.491837i	−0.195391	−	0.980726i	$-0.562597\pi$
$853$	1.22711e10	−	8.91544e9i	0.676956	−	0.491837i	0.872346	+	0.488888i	$0.162597\pi$
$854$	1.22947e10	−	8.93263e9i	0.675485	−	0.490769i
$855$	−1.83940e10	−	2.21064e10i	−1.00645	−	1.20959i
$856$	−2.41654e10	−	1.75572e10i	−1.31685	−	0.956745i
$857$	2.49214e10			1.35251			0.676253	−	0.736670i	$-0.263603\pi$
$857$	2.49214e10			1.35251			0.676253	+	0.736670i	$0.263603\pi$
$858$	4.32325e10	+	3.14102e10i	2.33671	+	1.69772i
$859$	7.14436e8	−	2.19881e9i	0.0384580	−	0.118362i	−0.929984	−	0.367599i	$-0.880180\pi$
$859$	7.14436e8	−	2.19881e9i	0.0384580	−	0.118362i	0.968442	+	0.249237i	$0.0801799\pi$
$860$	−6.85303e9	−	8.23618e9i	−0.367399	−	0.441551i
$861$	−1.81321e9	−	5.58049e9i	−0.0968139	−	0.297963i
$862$	−7.12672e9	+	2.19338e10i	−0.378978	+	1.16637i
$863$	2.06134e9	−	6.34415e9i	0.109172	−	0.335997i	−0.881515	−	0.472156i	$-0.843476\pi$
$863$	2.06134e9	−	6.34415e9i	0.109172	−	0.335997i	0.990687	+	0.136159i	$0.0434759\pi$
$864$	−1.44542e10	−	4.44854e10i	−0.762422	−	2.34649i
$865$	−7.08578e8	+	2.82875e8i	−0.0372247	+	0.0148607i
$866$	7.28108e9	−	2.24089e10i	0.380964	−	1.17249i
$867$	−4.01327e9	−	2.91581e9i	−0.209138	−	0.151947i
$868$	5.65538e10			2.93524
$869$	1.09837e10	+	7.98011e9i	0.567778	+	0.412515i
$870$	2.57599e9	+	3.91696e10i	0.132626	+	2.01665i
$871$	−9.93792e9	+	7.22032e9i	−0.509603	+	0.370248i
$872$	6.63738e9	−	4.82234e9i	0.338992	−	0.246292i
$873$	1.02334e10	+	3.14952e10i	0.520560	+	1.60212i
$874$	−3.08104e9			−0.156101
$875$	4.00049e9	+	2.00425e10i	0.201876	+	1.01140i
$876$	−1.14882e10			−0.577415
$877$	3.37066e9	+	1.03738e10i	0.168739	+	0.519326i	0.999292	−	0.0376132i	$-0.0119755\pi$
$877$	3.37066e9	+	1.03738e10i	0.168739	+	0.519326i	−0.830553	+	0.556940i	$0.811975\pi$
$878$	1.63336e10	−	1.18671e10i	0.814426	−	0.591715i
$879$	−1.05051e10	+	7.63240e9i	−0.521722	+	0.379053i
$880$	1.19725e8	+	1.82049e9i	0.00592235	+	0.0900531i
$881$	1.08513e10	+	7.88390e9i	0.534643	+	0.388441i	0.822092	−	0.569355i	$-0.192807\pi$
$881$	1.08513e10	+	7.88390e9i	0.534643	+	0.388441i	−0.287448	+	0.957796i	$0.592807\pi$
$882$	−4.72356e9			−0.231808
$883$	−8.18341e9	−	5.94559e9i	−0.400011	−	0.290625i	0.369535	−	0.929217i	$-0.379517\pi$
$883$	−8.18341e9	−	5.94559e9i	−0.400011	−	0.290625i	−0.769545	+	0.638592i	$0.779517\pi$
$884$	9.83021e9	−	3.02543e10i	0.478608	−	1.47300i
$885$	2.61279e10	−	1.04306e10i	1.26708	−	0.505836i
$886$	−1.66988e10	−	5.13937e10i	−0.806617	−	2.48251i
$887$	−3.99565e9	+	1.22973e10i	−0.192245	+	0.591669i	0.807753	+	0.589521i	$0.200684\pi$
$887$	−3.99565e9	+	1.22973e10i	−0.192245	+	0.591669i	−0.999998	+	0.00214767i	$0.999316\pi$
$888$	−5.71234e9	+	1.75808e10i	−0.273759	+	0.842544i
$889$	7.80414e9	+	2.40187e10i	0.372537	+	1.14655i
$890$	−1.56893e10	−	1.88558e10i	−0.745998	−	0.896563i
$891$	1.14817e10	−	3.53371e10i	0.543795	−	1.67363i
$892$	−5.26945e10	−	3.82848e10i	−2.48593	−	1.80613i
$893$	2.75867e10			1.29634
$894$	1.64094e10	+	1.19221e10i	0.768090	+	0.558050i
$895$	−2.20780e10	−	2.65340e10i	−1.02939	−	1.23715i
$896$	−2.76414e10	+	2.00826e10i	−1.28375	+	0.932702i
$897$	4.71400e9	−	3.42492e9i	0.218080	−	0.158444i
$898$	1.64240e10	+	5.05478e10i	0.756852	+	2.32935i
$899$	−2.74431e10			−1.25972
$900$	−3.36546e10	−	7.04784e10i	−1.53885	−	3.22260i
$901$	−2.51959e10			−1.14761
$902$	−1.72009e9	−	5.29388e9i	−0.0780418	−	0.240188i
$903$	−1.21802e10	+	8.84943e9i	−0.550487	+	0.399952i
$904$	−6.80726e9	+	4.94576e9i	−0.306466	+	0.222661i
$905$	−1.66884e10	+	2.64624e10i	−0.748417	+	1.18675i
$906$	7.41577e10	+	5.38787e10i	3.31289	+	2.40696i
$907$	−3.07993e9			−0.137062			−0.0685308	−	0.997649i	$-0.521831\pi$
$907$	−3.07993e9			−0.137062			−0.0685308	+	0.997649i	$0.521831\pi$
$908$	−2.61121e10	−	1.89715e10i	−1.15755	−	0.841011i
$909$	1.50037e10	−	4.61767e10i	0.662560	−	2.03915i
$910$	−2.62358e9	−	3.98932e10i	−0.115412	−	1.75491i
$911$	3.51359e9	+	1.08137e10i	0.153970	+	0.473871i	0.998055	−	0.0623382i	$-0.0198557\pi$
$911$	3.51359e9	+	1.08137e10i	0.153970	+	0.473871i	−0.844085	+	0.536209i	$0.819856\pi$
$912$	−8.55096e8	+	2.63172e9i	−0.0373279	+	0.114883i
$913$	6.13531e9	−	1.88825e10i	0.266802	−	0.821132i
$914$	1.72298e10	+	5.30279e10i	0.746395	+	2.29717i
$915$	1.12766e10	−	1.78811e10i	0.486636	−	0.771649i
$916$	−1.32337e10	+	4.07292e10i	−0.568916	+	1.75094i
$917$	1.03452e10	+	7.51620e9i	0.443041	+	0.321888i
$918$	−7.98564e10			−3.40691
$919$	−2.14958e10	−	1.56176e10i	−0.913585	−	0.663759i	0.0283338	−	0.999599i	$-0.490980\pi$
$919$	−2.14958e10	−	1.56176e10i	−0.913585	−	0.663759i	−0.941919	+	0.335840i	$0.890980\pi$
$920$	−2.95799e9	−	7.50539e8i	−0.125239	−	0.0317772i
$921$	3.43506e9	−	2.49572e9i	0.144886	−	0.105266i
$922$	−4.30310e10	+	3.12639e10i	−1.80811	+	1.31367i
$923$	−1.26655e9	−	3.89804e9i	−0.0530172	−	0.163170i
$924$	−6.59401e10			−2.74978
$925$	2.32809e9	−	1.25922e10i	0.0967171	−	0.523127i
$926$	6.89489e10			2.85357
$927$	−1.52492e9	−	4.69323e9i	−0.0628737	−	0.193505i
$928$	1.47606e10	−	1.07242e10i	0.606296	−	0.440500i
$929$	−7.36785e9	+	5.35306e9i	−0.301499	+	0.219052i	−0.728240	−	0.685322i	$-0.759662\pi$
$929$	−7.36785e9	+	5.35306e9i	−0.301499	+	0.219052i	0.426741	+	0.904374i	$0.359662\pi$
$930$	1.19478e11	−	4.76973e10i	4.87075	−	1.94448i
$931$	8.79867e8	+	6.39261e8i	0.0357350	+	0.0259630i
$932$	1.77814e10			0.719467
$933$	−4.97907e10	−	3.61751e10i	−2.00707	−	1.45822i
$934$	−6.34167e9	+	1.95177e10i	−0.254677	+	0.783815i
$935$	2.10116e10	+	5.33134e9i	0.840658	+	0.213302i
$936$	1.72184e10	+	5.29929e10i	0.686322	+	2.11228i
$937$	1.44195e10	−	4.43786e10i	0.572612	−	1.76232i	−0.0715569	−	0.997437i	$-0.522797\pi$
$937$	1.44195e10	−	4.43786e10i	0.572612	−	1.76232i	0.644169	−	0.764883i	$-0.277203\pi$
$938$	7.65970e9	−	2.35741e10i	0.303041	−	0.932666i
$939$	2.12507e10	+	6.54030e10i	0.837614	+	2.57791i
$940$	7.26188e10	+	1.84258e10i	2.85168	+	0.723565i
$941$	1.36054e10	−	4.18732e10i	0.532291	−	1.63822i	−0.217141	−	0.976140i	$-0.569673\pi$
$941$	1.36054e10	−	4.18732e10i	0.532291	−	1.63822i	0.749432	−	0.662082i	$-0.230327\pi$
$942$	−4.89828e10	−	3.55881e10i	−1.90926	−	1.38716i
$943$	−6.06942e8			−0.0235698
$944$	−1.52001e9	−	1.10436e9i	−0.0588093	−	0.0427274i
$945$	−5.69981e10	+	2.27545e10i	−2.19710	+	0.877114i
$946$	−1.15546e10	+	8.39493e9i	−0.443749	+	0.322402i
$947$	2.18484e9	−	1.58738e9i	0.0835980	−	0.0607375i	−0.545201	−	0.838305i	$-0.683547\pi$
$947$	2.18484e9	−	1.58738e9i	0.0835980	−	0.0607375i	0.628799	+	0.777568i	$0.283547\pi$
$948$	1.72814e10	+	5.31866e10i	0.658793	+	2.02756i
$949$	−5.67773e9			−0.215647
$950$	−5.34615e9	+	2.89165e10i	−0.202306	+	1.09424i
$951$	1.74407e10			0.657555
$952$	7.23444e9	+	2.22653e10i	0.271754	+	0.836372i
$953$	−3.25662e10	+	2.36608e10i	−1.21883	+	0.885531i	−0.996002	−	0.0893275i	$-0.971528\pi$
$953$	−3.25662e10	+	2.36608e10i	−1.21883	+	0.885531i	−0.222826	+	0.974858i	$0.571528\pi$
$954$	9.78967e10	−	7.11261e10i	3.65047	−	2.65222i
$955$	−4.78424e10	−	1.21392e10i	−1.77747	−	0.451001i
$956$	−1.76167e10	−	1.27992e10i	−0.652110	−	0.473786i
$957$	3.19979e10			1.18013
$958$	4.05109e10	+	2.94329e10i	1.48865	+	1.08157i
$959$	5.79845e9	−	1.78458e10i	0.212298	−	0.653387i
$960$	−4.30764e10	+	6.83054e10i	−1.57141	+	2.49176i
$961$	1.92907e10	+	5.93705e10i	0.701157	+	2.15794i
$962$	−7.74080e9	+	2.38237e10i	−0.280332	+	0.862774i
$963$	−3.43353e10	+	1.05673e11i	−1.23893	+	3.81305i
$964$	−1.78865e10	−	5.50491e10i	−0.643068	−	1.97916i
$965$	9.17671e8	+	1.39538e10i	0.0328732	+	0.499857i
$966$	−3.63334e9	+	1.11823e10i	−0.129684	+	0.399125i
$967$	2.87788e10	+	2.09090e10i	1.02348	+	0.743603i	0.966994	−	0.254800i	$-0.0820096\pi$
$967$	2.87788e10	+	2.09090e10i	1.02348	+	0.743603i	0.0564885	+	0.998403i	$0.482010\pi$
$968$	3.17893e9			0.112646
$969$	2.65995e10	+	1.93257e10i	0.939161	+	0.682341i
$970$	1.80633e10	−	2.86426e10i	0.635471	−	1.00765i
$971$	2.15538e10	−	1.56598e10i	0.755539	−	0.548931i	−0.142000	−	0.989867i	$-0.545353\pi$
$971$	2.15538e10	−	1.56598e10i	0.755539	−	0.548931i	0.897539	+	0.440936i	$0.145353\pi$
$972$	4.01870e10	−	2.91976e10i	1.40363	−	1.01980i
$973$	−6.12857e8	−	1.88618e9i	−0.0213287	−	0.0656430i
$974$	3.08042e9			0.106820
$975$	−2.39643e10	−	5.01851e10i	−0.828034	−	1.73404i
$976$	−1.41181e9			−0.0486074
$977$	4.81157e9	+	1.48085e10i	0.165065	+	0.508019i	0.999041	−	0.0437824i	$-0.0139408\pi$
$977$	4.81157e9	+	1.48085e10i	0.165065	+	0.508019i	−0.833976	+	0.551801i	$0.813941\pi$
$978$	5.37105e10	−	3.90230e10i	1.83600	−	1.33393i
$979$	−1.61764e10	+	1.17528e10i	−0.550988	+	0.400316i
$980$	1.88917e9	+	2.27046e9i	0.0641181	+	0.0770590i
$981$	−2.46899e10	−	1.79382e10i	−0.834983	−	0.606650i
$982$	−4.83934e10			−1.63078
$983$	3.36514e10	+	2.44492e10i	1.12997	+	0.820970i	0.985690	−	0.168567i	$-0.0539141\pi$
$983$	3.36514e10	+	2.44492e10i	1.12997	+	0.820970i	0.144278	+	0.989537i	$0.453914\pi$
$984$	2.58408e9	−	7.95298e9i	0.0864616	−	0.266101i
$985$	−1.06191e10	−	1.27624e10i	−0.354048	−	0.425505i
$986$	−9.62556e9	−	2.96244e10i	−0.319784	−	0.984194i
$987$	3.25318e10	−	1.00123e11i	1.07696	−	3.31453i
$988$	1.08701e10	−	3.34547e10i	0.358579	−	1.10359i
$989$	4.81238e8	+	1.48110e9i	0.0158188	+	0.0486852i
$990$	−9.66890e10	+	3.85997e10i	−3.16704	+	1.26433i
$991$	5.48141e9	−	1.68701e10i	0.178910	−	0.550629i	−0.820880	−	0.571100i	$-0.806517\pi$
$991$	5.48141e9	−	1.68701e10i	0.178910	−	0.550629i	0.999790	+	0.0204716i	$0.00651676\pi$
$992$	−4.83743e10	−	3.51460e10i	−1.57334	−	1.14310i
$993$	4.38120e10			1.41994
$994$	6.69098e9	+	4.86128e9i	0.216091	+	0.156999i
$995$	2.86050e9	+	4.34957e10i	0.0920579	+	1.39980i
$996$	6.61633e10	−	4.80704e10i	2.12182	−	1.54160i
$997$	3.06086e10	−	2.22385e10i	0.978161	−	0.710676i	0.0208645	−	0.999782i	$-0.493358\pi$
$997$	3.06086e10	−	2.22385e10i	0.978161	−	0.710676i	0.957297	+	0.289106i	$0.0933581\pi$
$998$	−2.56069e10	−	7.88100e10i	−0.815456	−	2.50972i
$999$	3.84538e10			1.22028

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.8.d.a.6.2	✓	68
25.11	even	5		625.8.a.d.1.3		34
25.14	even	10		625.8.a.c.1.32		34
25.21	even	5	inner	25.8.d.a.21.2	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.8.d.a.6.2	✓	68	1.1	even	1	trivial
25.8.d.a.21.2	yes	68	25.21	even	5	inner
625.8.a.c.1.32		34	25.14	even	10
625.8.a.d.1.3		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)

\(f(q)\)	\(=\)	\(q+(-5.60918 - 17.2633i) q^{2} +(68.4023 - 49.6972i) q^{3} +(-163.004 + 118.429i) q^{4} +(-18.3423 - 278.906i) q^{5} +(-1241.62 - 902.088i) q^{6} +935.944 q^{7} +(1079.11 + 784.017i) q^{8} +(1533.25 - 4718.84i) q^{9} +O(q^{10})\)	\(q+(-5.60918 - 17.2633i) q^{2} +(68.4023 - 49.6972i) q^{3} +(-163.004 + 118.429i) q^{4} +(-18.3423 - 278.906i) q^{5} +(-1241.62 - 902.088i) q^{6} +935.944 q^{7} +(1079.11 + 784.017i) q^{8} +(1533.25 - 4718.84i) q^{9} +(-4711.95 + 1881.08i) q^{10} +(1278.00 + 3933.27i) q^{11} +(-5264.23 + 16201.6i) q^{12} +(-2601.70 + 8007.21i) q^{13} +(-5249.87 - 16157.5i) q^{14} +(-15115.5 - 18166.3i) q^{15} +(-487.714 + 1501.03i) q^{16} +(15171.3 + 11022.6i) q^{17} -90063.0 q^{18} +(16776.2 + 12188.6i) q^{19} +(36020.4 + 43290.4i) q^{20} +(64020.7 - 46513.8i) q^{21} +(60732.6 - 44124.8i) q^{22} +(-2529.45 - 7784.84i) q^{23} +112777. q^{24} +(-77452.1 + 10231.5i) q^{25} +152824. q^{26} +(-72495.2 - 223117. i) q^{27} +(-152562. + 110843. i) q^{28} +(74031.9 - 53787.3i) q^{29} +(-228824. + 362841. i) q^{30} +(-242622. - 176275. i) q^{31} +199381. q^{32} +(282890. + 205532. i) q^{33} +(105188. - 323735. i) q^{34} +(-17167.3 - 261040. i) q^{35} +(308924. + 950770. i) q^{36} +(-50651.7 + 155890. i) q^{37} +(116315. - 357981. i) q^{38} +(219974. + 677009. i) q^{39} +(198874. - 315350. i) q^{40} +(22913.2 - 70519.6i) q^{41} +(-1.16208e6 - 844303. i) q^{42} -190254. q^{43} +(-674132. - 489785. i) q^{44} +(-1.34424e6 - 341077. i) q^{45} +(-120204. + 87333.1i) q^{46} +(1.07627e6 - 781954. i) q^{47} +(41236.2 + 126912. i) q^{48} +52447.3 q^{49} +(611073. + 1.27969e6i) q^{50} +1.58555e6 q^{51} +(-524200. - 1.61332e6i) q^{52} +(-1.08698e6 + 789738. i) q^{53} +(-3.44510e6 + 2.50301e6i) q^{54} +(1.07357e6 - 428586. i) q^{55} +(1.00998e6 + 733796. i) q^{56} +1.75327e6 q^{57} +(-1.34380e6 - 976330. i) q^{58} +(-367866. + 1.13218e6i) q^{59} +(4.61529e6 + 1.17105e6i) q^{60} +(276424. + 850747. i) q^{61} +(-1.68218e6 + 5.17721e6i) q^{62} +(1.43503e6 - 4.41657e6i) q^{63} +(-1.05594e6 - 3.24984e6i) q^{64} +(2.28098e6 + 578759. i) q^{65} +(1.96137e6 - 6.03648e6i) q^{66} +(1.18038e6 + 857594. i) q^{67} -3.77838e6 q^{68} +(-559905. - 406795. i) q^{69} +(-4.41012e6 + 1.76059e6i) q^{70} +(-393843. + 286144. i) q^{71} +(5.35419e6 - 3.89005e6i) q^{72} +(208393. + 641367. i) q^{73} +2.97528e6 q^{74} +(-4.78943e6 + 4.54901e6i) q^{75} -4.17808e6 q^{76} +(1.19613e6 + 3.68132e6i) q^{77} +(1.04535e7 - 7.59493e6i) q^{78} +(2.65583e6 - 1.92957e6i) q^{79} +(427592. + 108494. i) q^{80} +(-7.26834e6 - 5.28076e6i) q^{81} -1.34592e6 q^{82} +(-3.88387e6 - 2.82179e6i) q^{83} +(-4.92702e6 + 1.51638e7i) q^{84} +(2.79600e6 - 4.43355e6i) q^{85} +(1.06717e6 + 3.28441e6i) q^{86} +(2.39087e6 - 7.35835e6i) q^{87} +(-1.70466e6 + 5.24639e6i) q^{88} +(1.49403e6 + 4.59815e6i) q^{89} +(1.65196e6 + 2.51191e7i) q^{90} +(-2.43504e6 + 7.49430e6i) q^{91} +(1.33426e6 + 969397. i) q^{92} -2.53563e7 q^{93} +(-1.95361e7 - 1.41938e7i) q^{94} +(3.09177e6 - 4.90256e6i) q^{95} +(1.36381e7 - 9.90868e6i) q^{96} +(-5.39967e6 + 3.92309e6i) q^{97} +(-294186. - 905411. i) q^{98} +2.05200e7 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

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Groups

Database

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