LMFDB - Embedded newform 25.8.d.a.6.6

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			6.6
Character	$\chi$	$=$	25.6
Dual form			25.8.d.a.21.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.92617 - 9.00581i) q^{2} +(22.7999 - 16.5651i) q^{3} +(31.0120 - 22.5315i) q^{4} +(233.049 + 154.315i) q^{5} +(-215.899 - 156.860i) q^{6} +1510.43 q^{7} +(-1274.24 - 925.792i) q^{8} +(-430.387 + 1324.59i) q^{9} +O(q^{10})$	\(q+(-2.92617 - 9.00581i) q^{2} +(22.7999 - 16.5651i) q^{3} +(31.0120 - 22.5315i) q^{4} +(233.049 + 154.315i) q^{5} +(-215.899 - 156.860i) q^{6} +1510.43 q^{7} +(-1274.24 - 925.792i) q^{8} +(-430.387 + 1324.59i) q^{9} +(707.789 - 2550.35i) q^{10} +(-824.075 - 2536.24i) q^{11} +(333.833 - 1027.43i) q^{12} +(1714.86 - 5277.79i) q^{13} +(-4419.77 - 13602.7i) q^{14} +(7869.75 - 342.124i) q^{15} +(-3092.64 + 9518.16i) q^{16} +(-21155.9 - 15370.7i) q^{17} +13188.4 q^{18} +(-4248.12 - 3086.44i) q^{19} +(10704.3 - 465.349i) q^{20} +(34437.7 - 25020.4i) q^{21} +(-20429.5 + 14842.9i) q^{22} +(32173.2 + 99018.8i) q^{23} -44388.5 q^{24} +(30498.9 + 71925.9i) q^{25} -52548.8 q^{26} +(31175.4 + 95948.0i) q^{27} +(46841.4 - 34032.3i) q^{28} +(35476.1 - 25774.9i) q^{29} +(-26109.3 - 69872.3i) q^{30} +(-172330. - 125205. i) q^{31} -106838. q^{32} +(-60801.9 - 44175.2i) q^{33} +(-76519.7 + 235503. i) q^{34} +(352005. + 233082. i) q^{35} +(16498.0 + 50775.5i) q^{36} +(-43390.0 + 133541. i) q^{37} +(-15365.2 + 47289.2i) q^{38} +(-48328.6 - 148740. i) q^{39} +(-154098. - 412390. i) q^{40} +(173954. - 535377. i) q^{41} +(-326100. - 236925. i) q^{42} +621050. q^{43} +(-82701.5 - 60086.1i) q^{44} +(-304706. + 242281. i) q^{45} +(797601. - 579491. i) q^{46} +(-666841. + 484489. i) q^{47} +(87157.5 + 268243. i) q^{48} +1.45786e6 q^{49} +(558506. - 485135. i) q^{50} -736970. q^{51} +(-65735.5 - 202313. i) q^{52} +(-1.27519e6 + 926478. i) q^{53} +(772866. - 561520. i) q^{54} +(199329. - 718236. i) q^{55} +(-1.92466e6 - 1.39834e6i) q^{56} -147984. q^{57} +(-335933. - 244070. i) q^{58} +(-333028. + 1.02495e6i) q^{59} +(236348. - 187927. i) q^{60} +(432651. + 1.33156e6i) q^{61} +(-623307. + 1.91834e6i) q^{62} +(-650069. + 2.00071e6i) q^{63} +(708484. + 2.18049e6i) q^{64} +(1.21409e6 - 965358. i) q^{65} +(-219917. + 676835. i) q^{66} +(-1.20496e6 - 875454. i) q^{67} -1.00241e6 q^{68} +(2.37380e6 + 1.72467e6i) q^{69} +(1.06907e6 - 3.85212e6i) q^{70} +(-1.07619e6 + 781901. i) q^{71} +(1.77472e6 - 1.28941e6i) q^{72} +(962881. + 2.96344e6i) q^{73} +1.32961e6 q^{74} +(1.88683e6 + 1.13469e6i) q^{75} -201285. q^{76} +(-1.24471e6 - 3.83081e6i) q^{77} +(-1.19811e6 + 870476. i) q^{78} +(316287. - 229796. i) q^{79} +(-2.18953e6 + 1.74096e6i) q^{80} +(-164053. - 119192. i) q^{81} -5.33052e6 q^{82} +(4.68875e6 + 3.40658e6i) q^{83} +(504232. - 1.55187e6i) q^{84} +(-2.55845e6 - 6.84680e6i) q^{85} +(-1.81730e6 - 5.59306e6i) q^{86} +(381889. - 1.17533e6i) q^{87} +(-1.29796e6 + 3.99471e6i) q^{88} +(-2.28979e6 - 7.04725e6i) q^{89} +(3.07355e6 + 2.03517e6i) q^{90} +(2.59017e6 - 7.97174e6i) q^{91} +(3.22880e6 + 2.34586e6i) q^{92} -6.00315e6 q^{93} +(6.31450e6 + 4.58775e6i) q^{94} +(-513738. - 1.37484e6i) q^{95} +(-2.43590e6 + 1.76979e6i) q^{96} +(-1.21732e6 + 884433. i) q^{97} +(-4.26593e6 - 1.31292e7i) q^{98} +3.71416e6 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 $

$2$	−2.92617	−	9.00581i	−0.258639	−	0.796009i	−0.993091	−	0.117348i	$-0.962561\pi$
$2$	−2.92617	−	9.00581i	−0.258639	−	0.796009i	0.734452	−	0.678661i	$-0.237439\pi$
$3$	22.7999	−	16.5651i	0.487539	−	0.354217i	−0.316698	−	0.948526i	$-0.602574\pi$
$3$	22.7999	−	16.5651i	0.487539	−	0.354217i	0.804237	+	0.594309i	$0.202574\pi$
$4$	31.0120	−	22.5315i	0.242281	−	0.176027i
$5$	233.049	+	154.315i	0.833782	+	0.552093i
$5$	233.049	+	154.315i	0.833782	+	0.552093i
$6$	−215.899	−	156.860i	−0.408057	−	0.296471i
$7$	1510.43			1.66440			0.832200	−	0.554476i	$-0.187081\pi$
$7$	1510.43			1.66440			0.832200	+	0.554476i	$0.187081\pi$
$8$	−1274.24	−	925.792i	−0.879908	−	0.639291i
$9$	−430.387	+	1324.59i	−0.196793	+	0.605667i
$10$	707.789	−	2550.35i	0.223822	−	0.806491i
$11$	−824.075	−	2536.24i	−0.186678	−	0.574534i	0.813296	−	0.581851i	$-0.197671\pi$
$11$	−824.075	−	2536.24i	−0.186678	−	0.574534i	−0.999973	+	0.00731619i	$0.997671\pi$
$12$	333.833	−	1027.43i	0.0557693	−	0.171640i
$13$	1714.86	−	5277.79i	0.216484	−	0.666270i	−0.782561	−	0.622575i	$-0.786087\pi$
$13$	1714.86	−	5277.79i	0.216484	−	0.666270i	0.999045	−	0.0436958i	$-0.0139132\pi$
$14$	−4419.77	−	13602.7i	−0.430479	−	1.32488i
$15$	7869.75	−	342.124i	0.602062	−	0.0261736i
$16$	−3092.64	+	9518.16i	−0.188760	+	0.580942i
$17$	−21155.9	−	15370.7i	−1.04439	−	0.758790i	−0.0732485	−	0.997314i	$-0.523337\pi$
$17$	−21155.9	−	15370.7i	−1.04439	−	0.758790i	−0.971137	+	0.238523i	$0.923337\pi$
$18$	13188.4			0.533015
$19$	−4248.12	−	3086.44i	−0.142089	−	0.103233i	0.514470	−	0.857508i	$-0.327989\pi$
$19$	−4248.12	−	3086.44i	−0.142089	−	0.103233i	−0.656559	+	0.754275i	$0.727989\pi$
$20$	10704.3	−	465.349i	0.299193	−	0.0130069i
$21$	34437.7	−	25020.4i	0.811459	−	0.589559i
$22$	−20429.5	+	14842.9i	−0.409052	+	0.297194i
$23$	32173.2	+	99018.8i	0.551374	+	1.69696i	0.705331	+	0.708878i	$0.250798\pi$
$23$	32173.2	+	99018.8i	0.551374	+	1.69696i	−0.153957	+	0.988078i	$0.549202\pi$
$24$	−44388.5			−0.655437
$25$	30498.9	+	71925.9i	0.390386	+	0.920651i
$26$	−52548.8			−0.586348
$27$	31175.4	+	95948.0i	0.304817	+	0.938130i
$28$	46841.4	−	34032.3i	0.403252	−	0.292980i
$29$	35476.1	−	25774.9i	0.270112	−	0.196248i	−0.444481	−	0.895788i	$-0.646612\pi$
$29$	35476.1	−	25774.9i	0.270112	−	0.196248i	0.714593	+	0.699541i	$0.246612\pi$
$30$	−26109.3	−	69872.3i	−0.176551	−	0.472477i
$31$	−172330.	−	125205.i	−1.03895	−	0.754842i	−0.0688701	−	0.997626i	$-0.521939\pi$
$31$	−172330.	−	125205.i	−1.03895	−	0.754842i	−0.970080	+	0.242784i	$0.921939\pi$
$32$	−106838.			−0.576371
$33$	−60801.9	−	44175.2i	−0.294523	−	0.213983i
$34$	−76519.7	+	235503.i	−0.333885	+	1.02759i
$35$	352005.	+	233082.i	1.38775	+	0.918903i
$36$	16498.0	+	50775.5i	0.0589348	+	0.181383i
$37$	−43390.0	+	133541.i	−0.140826	+	0.433418i	−0.996451	−	0.0841788i	$-0.973173\pi$
$37$	−43390.0	+	133541.i	−0.140826	+	0.433418i	0.855625	+	0.517597i	$0.173173\pi$
$38$	−15365.2	+	47289.2i	−0.0454251	+	0.139804i
$39$	−48328.6	−	148740.i	−0.130460	−	0.401515i
$40$	−154098.	−	412390.i	−0.380704	−	1.01882i
$41$	173954.	−	535377.i	0.394178	−	1.21315i	−0.535422	−	0.844585i	$-0.679848\pi$
$41$	173954.	−	535377.i	0.394178	−	1.21315i	0.929600	−	0.368570i	$-0.120152\pi$
$42$	−326100.	−	236925.i	−0.679169	−	0.493445i
$43$	621050.			1.19121			0.595603	−	0.803279i	$-0.296913\pi$
$43$	621050.			1.19121			0.595603	+	0.803279i	$0.296913\pi$
$44$	−82701.5	−	60086.1i	−0.146362	−	0.106338i
$45$	−304706.	+	242281.i	−0.498467	+	0.396346i
$46$	797601.	−	579491.i	1.20818	−	0.877798i
$47$	−666841.	+	484489.i	−0.936872	+	0.680677i	−0.947666	−	0.319265i	$-0.896564\pi$
$47$	−666841.	+	484489.i	−0.936872	+	0.680677i	0.0107940	+	0.999942i	$0.496564\pi$
$48$	87157.5	+	268243.i	0.113752	+	0.350094i
$49$	1.45786e6			1.77023
$50$	558506.	−	485135.i	0.631877	−	0.548867i
$51$	−736970.			−0.777955
$52$	−65735.5	−	202313.i	−0.0648318	−	0.199532i
$53$	−1.27519e6	+	926478.i	−1.17655	+	0.854810i	−0.991778	−	0.127972i	$-0.959153\pi$
$53$	−1.27519e6	+	926478.i	−1.17655	+	0.854810i	−0.184767	+	0.982782i	$0.559153\pi$
$54$	772866.	−	561520.i	0.667922	−	0.485274i
$55$	199329.	−	718236.i	0.161548	−	0.582100i
$56$	−1.92466e6	−	1.39834e6i	−1.46452	−	1.06404i
$57$	−147984.			−0.105841
$58$	−335933.	−	244070.i	−0.226076	−	0.164254i
$59$	−333028.	+	1.02495e6i	−0.211105	+	0.649714i	0.788302	+	0.615288i	$0.210960\pi$
$59$	−333028.	+	1.02495e6i	−0.211105	+	0.649714i	−0.999407	+	0.0344261i	$0.989040\pi$
$60$	236348.	−	187927.i	0.141261	−	0.112321i
$61$	432651.	+	1.33156e6i	0.244053	+	0.751117i	0.995791	+	0.0916550i	$0.0292157\pi$
$61$	432651.	+	1.33156e6i	0.244053	+	0.751117i	−0.751738	+	0.659462i	$0.770784\pi$
$62$	−623307.	+	1.91834e6i	−0.332148	+	1.02225i
$63$	−650069.	+	2.00071e6i	−0.327542	+	1.00807i
$64$	708484.	+	2.18049e6i	0.337831	+	1.03974i
$65$	1.21409e6	−	965358.i	0.548344	−	0.436005i
$66$	−219917.	+	676835.i	−0.0941575	+	0.289787i
$67$	−1.20496e6	−	875454.i	−0.489453	−	0.355608i	0.315521	−	0.948919i	$-0.397821\pi$
$67$	−1.20496e6	−	875454.i	−0.489453	−	0.355608i	−0.804974	+	0.593310i	$0.797821\pi$
$68$	−1.00241e6			−0.386602
$69$	2.37380e6	+	1.72467e6i	0.869907	+	0.632025i
$70$	1.06907e6	−	3.85212e6i	0.372530	−	1.34232i
$71$	−1.07619e6	+	781901.i	−0.356851	+	0.259267i	−0.751737	−	0.659463i	$-0.770784\pi$
$71$	−1.07619e6	+	781901.i	−0.356851	+	0.259267i	0.394887	+	0.918730i	$0.370784\pi$
$72$	1.77472e6	−	1.28941e6i	0.560357	−	0.407123i
$73$	962881.	+	2.96344e6i	0.289696	+	0.891593i	0.984952	+	0.172830i	$0.0552912\pi$
$73$	962881.	+	2.96344e6i	0.289696	+	0.891593i	−0.695255	+	0.718763i	$0.744709\pi$
$74$	1.32961e6			0.381428
$75$	1.88683e6	+	1.13469e6i	0.516439	+	0.310571i
$76$	−201285.			−0.0525972
$77$	−1.24471e6	−	3.83081e6i	−0.310706	−	0.956255i
$78$	−1.19811e6	+	870476.i	−0.285867	+	0.207695i
$79$	316287.	−	229796.i	0.0721750	−	0.0524382i	−0.551113	−	0.834431i	$-0.685797\pi$
$79$	316287.	−	229796.i	0.0721750	−	0.0524382i	0.623288	+	0.781993i	$0.285797\pi$
$80$	−2.18953e6	+	1.74096e6i	−0.478119	+	0.380166i
$81$	−164053.	−	119192.i	−0.0342995	−	0.0249200i
$82$	−5.33052e6			−1.06763
$83$	4.68875e6	+	3.40658e6i	0.900086	+	0.653950i	0.938488	−	0.345312i	$-0.112227\pi$
$83$	4.68875e6	+	3.40658e6i	0.900086	+	0.653950i	−0.0384024	+	0.999262i	$0.512227\pi$
$84$	504232.	−	1.55187e6i	0.0928224	−	0.285678i
$85$	−2.55845e6	−	6.84680e6i	−0.451867	−	1.20926i
$86$	−1.81730e6	−	5.59306e6i	−0.308093	−	0.948211i
$87$	381889.	−	1.17533e6i	0.0621755	−	0.191356i
$88$	−1.29796e6	+	3.99471e6i	−0.203035	+	0.624879i
$89$	−2.28979e6	−	7.04725e6i	−0.344295	−	1.05963i	−0.961960	−	0.273190i	$-0.911921\pi$
$89$	−2.28979e6	−	7.04725e6i	−0.344295	−	1.05963i	0.617665	−	0.786441i	$-0.288079\pi$
$90$	3.07355e6	+	2.03517e6i	0.444418	+	0.294274i
$91$	2.59017e6	−	7.97174e6i	0.360316	−	1.10894i
$92$	3.22880e6	+	2.34586e6i	0.432298	+	0.314083i
$93$	−6.00315e6			−0.773907
$94$	6.31450e6	+	4.58775e6i	0.784137	+	0.569709i
$95$	−513738.	−	1.37484e6i	−0.0614765	−	0.164520i
$96$	−2.43590e6	+	1.76979e6i	−0.281003	+	0.204161i
$97$	−1.21732e6	+	884433.i	−0.135426	+	0.0983929i	−0.653436	−	0.756982i	$-0.726673\pi$
$97$	−1.21732e6	+	884433.i	−0.135426	+	0.0983929i	0.518010	+	0.855375i	$0.326673\pi$
$98$	−4.26593e6	−	1.31292e7i	−0.457849	−	1.40912i
$99$	3.71416e6			0.384714
$100$	2.56643e6	+	1.54337e6i	0.256643	+	0.154337i
$101$	−8.66010e6			−0.836369			−0.418185	−	0.908362i	$-0.637333\pi$
$101$	−8.66010e6			−0.836369			−0.418185	+	0.908362i	$0.637333\pi$
$102$	2.15650e6	+	6.63702e6i	0.201209	+	0.619259i
$103$	1.22456e7	−	8.89691e6i	1.10420	−	0.802249i	0.122460	−	0.992473i	$-0.460922\pi$
$103$	1.22456e7	−	8.89691e6i	1.10420	−	0.802249i	0.981741	+	0.190225i	$0.0609216\pi$
$104$	−7.07128e6	+	5.13759e6i	−0.616427	+	0.447860i
$105$	1.18867e7	−	516754.i	1.00207	−	0.0435634i
$106$	1.20751e7	+	8.77307e6i	0.984737	+	0.715453i
$107$	−5.97103e6			−0.471201			−0.235600	−	0.971850i	$-0.575706\pi$
$107$	−5.97103e6			−0.471201			−0.235600	+	0.971850i	$0.575706\pi$
$108$	3.12866e6	+	2.27311e6i	0.238988	+	0.173635i
$109$	−2.61721e6	+	8.05495e6i	−0.193574	+	0.595758i	0.806417	+	0.591348i	$0.201404\pi$
$109$	−2.61721e6	+	8.05495e6i	−0.193574	+	0.595758i	−0.999990	+	0.00441039i	$0.998596\pi$
$110$	−7.05157e6	+	306555.i	−0.505140	+	0.0219601i
$111$	1.22283e6	+	3.76347e6i	0.0848661	+	0.261191i
$112$	−4.67121e6	+	1.43765e7i	−0.314171	+	0.966920i
$113$	−3.47916e6	+	1.07077e7i	−0.226829	+	0.698109i	0.771271	+	0.636506i	$0.219621\pi$
$113$	−3.47916e6	+	1.07077e7i	−0.226829	+	0.698109i	−0.998101	+	0.0616026i	$0.980379\pi$
$114$	433026.	+	1.33272e6i	0.0273745	+	0.0842502i
$115$	−7.78213e6	+	2.80411e7i	−0.477151	+	1.71930i
$116$	519436.	−	1.59866e6i	0.0308979	−	0.0950941i
$117$	6.25288e6	+	4.54298e6i	0.360935	+	0.262235i
$118$	1.02050e7			0.571778
$119$	−3.19545e7	−	2.32163e7i	−1.73827	−	1.26293i
$120$	−1.03447e7	−	6.84980e6i	−0.546492	−	0.361862i
$121$	1.00120e7	−	7.27417e6i	0.513776	−	0.373280i
$122$	1.07258e7	−	7.79275e6i	0.534774	−	0.388536i
$123$	−4.90243e6	−	1.50881e7i	−0.237544	−	0.731084i
$124$	−8.16535e6			−0.384591
$125$	−3.99147e6	+	2.14687e7i	−0.182788	+	0.983152i
$126$	1.99202e7			0.887150
$127$	1723.97	+	5305.83i	7.46821e−5	+	0.000229848i	0.951094	−	0.308902i	$-0.0999615\pi$
$127$	1723.97	+	5305.83i	7.46821e−5	+	0.000229848i	−0.951019	+	0.309132i	$0.899962\pi$
$128$	6.50039e6	−	4.72281e6i	0.273971	−	0.199052i
$129$	1.41599e7	−	1.02878e7i	0.580759	−	0.421946i
$130$	−1.22465e7	−	8.10905e6i	−0.488887	−	0.323719i
$131$	−1.57165e7	−	1.14187e7i	−0.610810	−	0.443780i	0.238889	−	0.971047i	$-0.423217\pi$
$131$	−1.57165e7	−	1.14187e7i	−0.610810	−	0.443780i	−0.849700	+	0.527267i	$0.823217\pi$
$132$	−2.88092e6			−0.109024
$133$	−6.41649e6	−	4.66185e6i	−0.236492	−	0.171822i
$134$	−4.35827e6	+	1.34134e7i	−0.156476	+	0.481583i
$135$	−7.54079e6	+	2.71714e7i	−0.263784	+	0.950483i
$136$	1.27277e7	+	3.91720e7i	0.433876	+	1.33533i
$137$	1.19279e7	−	3.67102e7i	0.396315	−	1.21973i	−0.531618	−	0.846984i	$-0.678416\pi$
$137$	1.19279e7	−	3.67102e7i	0.396315	−	1.21973i	0.927933	−	0.372747i	$-0.121584\pi$
$138$	8.58591e6	−	2.64247e7i	0.278105	−	0.855920i
$139$	−1.08554e7	−	3.34095e7i	−0.342842	−	1.05516i	−0.962729	−	0.270468i	$-0.912822\pi$
$139$	−1.08554e7	−	3.34095e7i	−0.342842	−	1.05516i	0.619887	−	0.784691i	$-0.287178\pi$
$140$	1.61680e7	−	702878.i	0.497977	−	0.0216487i
$141$	−7.17832e6	+	2.20926e7i	−0.215653	+	0.663713i
$142$	1.01908e7	+	7.40403e6i	0.298674	+	0.217000i
$143$	−1.47989e7			−0.423208
$144$	−1.12767e7	−	8.19298e6i	−0.314711	−	0.228651i
$145$	1.22451e7	−	532336.i	0.333561	−	0.0145010i
$146$	2.38707e7	−	1.73431e7i	0.634789	−	0.461201i
$147$	3.32390e7	−	2.41496e7i	0.863053	−	0.627045i
$148$	1.66326e6	+	5.11899e6i	0.0421740	+	0.129798i
$149$	1.82709e7			0.452490			0.226245	−	0.974070i	$-0.427355\pi$
$149$	1.82709e7			0.452490			0.226245	+	0.974070i	$0.427355\pi$
$150$	4.69758e6	−	2.03127e7i	0.113646	−	0.491416i
$151$	−7.37935e7			−1.74421			−0.872105	−	0.489319i	$-0.837245\pi$
$151$	−7.37935e7			−1.74421			−0.872105	+	0.489319i	$0.837245\pi$
$152$	2.55574e6	+	7.86575e6i	0.0590288	+	0.181672i
$153$	2.94651e7	−	2.14077e7i	0.665102	−	0.483225i
$154$	−3.08574e7	+	2.24192e7i	−0.680827	+	0.494649i
$155$	−2.08404e7	−	5.57720e7i	−0.449516	−	1.20297i
$156$	−4.85010e6	−	3.52380e6i	−0.102286	−	0.0743149i
$157$	8.23139e7			1.69756			0.848779	−	0.528748i	$-0.177338\pi$
$157$	8.23139e7			1.69756			0.848779	+	0.528748i	$0.177338\pi$
$158$	−2.99501e6	−	2.17600e6i	−0.0604086	−	0.0438894i
$159$	−1.37270e7	+	4.22473e7i	−0.270822	+	0.833506i
$160$	−2.48986e7	−	1.64867e7i	−0.480568	−	0.318210i
$161$	4.85953e7	+	1.49561e8i	0.917707	+	2.82441i
$162$	−593371.	+	1.82621e6i	−0.0109654	+	0.0337480i
$163$	3.10586e6	−	9.55884e6i	0.0561726	−	0.172882i	−0.919034	−	0.394179i	$-0.871029\pi$
$163$	3.10586e6	−	9.55884e6i	0.0561726	−	0.172882i	0.975206	+	0.221297i	$0.0710291\pi$
$164$	−6.66818e6	−	2.05225e7i	−0.118047	−	0.363310i
$165$	−7.35297e6	−	1.96776e7i	−0.127429	−	0.341019i
$166$	1.69589e7	−	5.21942e7i	0.287753	−	0.885613i
$167$	−6.46985e7	−	4.70062e7i	−1.07495	−	0.780994i	−0.0981512	−	0.995172i	$-0.531293\pi$
$167$	−6.46985e7	−	4.70062e7i	−1.07495	−	0.780994i	−0.976795	+	0.214178i	$0.931293\pi$
$168$	−6.70457e7			−1.09091
$169$	2.58503e7	+	1.87813e7i	0.411966	+	0.299311i
$170$	−5.41745e7	+	4.30758e7i	−0.845715	+	0.672453i
$171$	5.91661e6	−	4.29867e6i	0.0904871	−	0.0657428i
$172$	1.92600e7	−	1.39932e7i	0.288607	−	0.209685i
$173$	−1.99012e6	−	6.12497e6i	−0.0292226	−	0.0899379i	0.935381	−	0.353640i	$-0.115056\pi$
$173$	−1.99012e6	−	6.12497e6i	−0.0292226	−	0.0899379i	−0.964604	+	0.263702i	$0.915056\pi$
$174$	−1.17023e7			−0.168402
$175$	4.60665e7	+	1.08639e8i	0.649759	+	1.53233i
$176$	2.66889e7			0.369008
$177$	9.38547e6	+	2.88855e7i	0.127218	+	0.391538i
$178$	−5.67659e7	+	4.12429e7i	−0.754428	+	0.548124i
$179$	1.38618e7	−	1.00712e7i	0.180648	−	0.131249i	−0.493786	−	0.869583i	$-0.664388\pi$
$179$	1.38618e7	−	1.00712e7i	0.180648	−	0.131249i	0.674434	+	0.738335i	$0.264388\pi$
$180$	−3.99057e6	+	1.43791e7i	−0.0510013	+	0.183771i
$181$	−2.59989e7	−	1.88893e7i	−0.325897	−	0.236778i	0.412791	−	0.910826i	$-0.364554\pi$
$181$	−2.59989e7	−	1.88893e7i	−0.325897	−	0.236778i	−0.738688	+	0.674048i	$0.764554\pi$
$182$	−7.93712e7			−0.975918
$183$	3.19219e7	+	2.31926e7i	0.385044	+	0.279751i
$184$	5.06744e7	−	1.55960e8i	0.599689	−	1.84565i
$185$	−3.07193e7	+	2.44258e7i	−0.356706	+	0.283627i
$186$	1.75662e7	+	5.40632e7i	0.200162	+	0.616037i
$187$	−2.15497e7	+	6.63231e7i	−0.240988	+	0.741684i
$188$	−9.76380e6	+	3.00499e7i	−0.107168	+	0.329830i
$189$	4.70883e7	+	1.44923e8i	0.507337	+	1.56142i
$190$	−1.08783e7	+	8.64964e6i	−0.115059	+	0.0914872i
$191$	1.32138e7	−	4.06680e7i	0.137218	−	0.422315i	−0.858710	−	0.512462i	$-0.828734\pi$
$191$	1.32138e7	−	4.06680e7i	0.137218	−	0.422315i	0.995928	+	0.0901470i	$0.0287337\pi$
$192$	5.22734e7	+	3.79789e7i	0.532999	+	0.387247i
$193$	4.00516e6			0.0401023			0.0200512	−	0.999799i	$-0.493617\pi$
$193$	4.00516e6			0.0401023			0.0200512	+	0.999799i	$0.493617\pi$
$194$	1.15271e7	+	8.37494e6i	0.113348	+	0.0823523i
$195$	1.16898e7	−	4.21216e7i	0.112898	−	0.406802i
$196$	4.52110e7	−	3.28477e7i	0.428892	−	0.311608i
$197$	4.44543e7	−	3.22979e7i	0.414269	−	0.300984i	−0.361059	−	0.932543i	$-0.617585\pi$
$197$	4.44543e7	−	3.22979e7i	0.414269	−	0.300984i	0.775328	+	0.631559i	$0.217585\pi$
$198$	−1.08682e7	−	3.34490e7i	−0.0995019	−	0.306235i
$199$	2.64813e7			0.238207			0.119103	−	0.992882i	$-0.461998\pi$
$199$	2.64813e7			0.238207			0.119103	+	0.992882i	$0.461998\pi$
$200$	2.77253e7	−	1.19887e8i	0.245060	−	1.05966i
$201$	−4.19750e7			−0.364590
$202$	2.53409e7	+	7.79912e7i	0.216318	+	0.665757i
$203$	5.35842e7	−	3.89312e7i	0.449574	−	0.326634i
$204$	−2.28549e7	+	1.66050e7i	−0.188484	+	0.136941i
$205$	1.23157e8	−	9.79255e7i	0.998433	−	0.793884i
$206$	−1.15956e8	−	8.42473e7i	−0.924187	−	0.671461i
$207$	−1.45007e8			−1.13630
$208$	4.49314e7	+	3.26446e7i	0.346201	+	0.251530i
$209$	−4.32719e6	+	1.33177e7i	−0.0327864	+	0.100906i
$210$	−3.94363e7	−	1.05537e8i	−0.293852	−	0.786391i
$211$	−6.39383e7	−	1.96782e8i	−0.468568	−	1.44210i	−0.854439	−	0.519551i	$-0.826099\pi$
$211$	−6.39383e7	−	1.96782e8i	−0.468568	−	1.44210i	0.385872	−	0.922552i	$-0.373901\pi$
$212$	−1.86711e7	+	5.74638e7i	−0.134584	+	0.414208i
$213$	−1.15849e7	+	3.56546e7i	−0.0821415	+	0.252805i
$214$	1.74722e7	+	5.37740e7i	0.121871	+	0.375080i
$215$	1.44735e8	+	9.58372e7i	0.993207	+	0.657657i
$216$	4.91029e7	−	1.51123e8i	0.331527	−	1.02033i
$217$	−2.60292e8	−	1.89113e8i	−1.72923	−	1.25636i
$218$	8.01997e7			0.524294
$219$	7.10434e7	+	5.16160e7i	0.457056	+	0.332071i
$220$	−1.00013e7	−	2.67651e7i	−0.0633255	−	0.169469i
$221$	−1.17403e8	+	8.52980e7i	−0.731653	+	0.531577i
$222$	3.03149e7	−	2.20251e7i	0.185961	−	0.135108i
$223$	−1.93874e7	−	5.96682e7i	−0.117072	−	0.360310i	0.875302	−	0.483577i	$-0.160663\pi$
$223$	−1.93874e7	−	5.96682e7i	−0.117072	−	0.360310i	−0.992374	+	0.123267i	$0.960663\pi$
$224$	−1.61372e8			−0.959311
$225$	−1.08399e8	+	9.44277e6i	−0.634434	+	0.0552663i
$226$	1.06612e8			0.614368
$227$	5.52504e7	+	1.70043e8i	0.313506	+	0.964871i	0.976365	+	0.216127i	$0.0693426\pi$
$227$	5.52504e7	+	1.70043e8i	0.313506	+	0.964871i	−0.662860	+	0.748744i	$0.730657\pi$
$228$	−4.58927e6	+	3.33430e6i	−0.0256432	+	0.0186309i
$229$	7.52018e7	−	5.46373e7i	0.413813	−	0.300653i	−0.361331	−	0.932438i	$-0.617677\pi$
$229$	7.52018e7	−	5.46373e7i	0.413813	−	0.300653i	0.775144	+	0.631785i	$0.217677\pi$
$230$	2.75304e8	−	1.19684e7i	1.49199	−	0.0648617i
$231$	−9.18371e7	−	6.67236e7i	−0.490203	−	0.356154i
$232$	−6.90674e7			−0.363133
$233$	2.13815e8	+	1.55346e8i	1.10737	+	0.804552i	0.982247	−	0.187590i	$-0.0600675\pi$
$233$	2.13815e8	+	1.55346e8i	1.10737	+	0.804552i	0.125123	+	0.992141i	$0.460068\pi$
$234$	2.26163e7	−	6.96058e7i	0.115389	−	0.355132i
$235$	−2.30171e8	+	1.00063e7i	−1.15694	+	0.0502962i
$236$	1.27659e7	+	3.92894e7i	0.0632208	+	0.194574i
$237$	3.40473e6	−	1.04787e7i	0.0166136	−	0.0511313i
$238$	−1.15578e8	+	3.55712e8i	−0.555718	+	1.71032i
$239$	−4.39361e7	−	1.35221e8i	−0.208175	−	0.640697i	−0.999568	−	0.0293891i	$-0.990644\pi$
$239$	−4.39361e7	−	1.35221e8i	−0.208175	−	0.640697i	0.791393	−	0.611308i	$-0.209356\pi$
$240$	−2.10819e7	+	7.59635e7i	−0.0984396	+	0.354704i
$241$	7.27080e7	−	2.23772e8i	0.334598	−	1.02979i	−0.632322	−	0.774705i	$-0.717898\pi$
$241$	7.27080e7	−	2.23772e8i	0.334598	−	1.02979i	0.966920	−	0.255080i	$-0.0821018\pi$
$242$	−9.48067e7	−	6.88811e7i	−0.430017	−	0.312425i
$243$	−2.26352e8			−1.01196
$244$	4.34195e7	+	3.15461e7i	0.191346	+	0.139021i
$245$	3.39752e8	+	2.24969e8i	1.47598	+	0.977329i
$246$	−1.21536e8	+	8.83007e7i	−0.520512	+	0.378174i
$247$	−2.35745e7	+	1.71279e7i	−0.0995413	+	0.0723210i
$248$	1.03676e8	+	3.19083e8i	0.431618	+	1.32838i
$249$	1.63333e8			0.670467
$250$	2.05023e8	−	2.68746e7i	0.829874	−	0.108781i
$251$	−5.59433e6			−0.0223301			−0.0111650	−	0.999938i	$-0.503554\pi$
$251$	−5.59433e6			−0.0223301			−0.0111650	+	0.999938i	$0.503554\pi$
$252$	2.49190e7	+	7.66929e7i	0.0980910	+	0.301893i
$253$	2.24622e8	−	1.63198e8i	0.872030	−	0.633567i
$254$	42738.7	−	31051.5i	0.000163645	−	0.000118895i
$255$	−1.71750e8	−	1.13725e8i	−0.648645	−	0.429504i
$256$	1.75865e8	+	1.27773e8i	0.655148	+	0.475993i
$257$	−9.25883e7			−0.340244			−0.170122	−	0.985423i	$-0.554416\pi$
$257$	−9.25883e7			−0.340244			−0.170122	+	0.985423i	$0.554416\pi$
$258$	−1.34084e8	−	9.74177e7i	−0.486080	−	0.353158i
$259$	−6.55375e7	+	2.01704e8i	−0.234391	+	0.721381i
$260$	1.59003e7	−	5.72928e7i	0.0561045	−	0.202159i
$261$	1.88728e7	+	5.80846e7i	0.0657046	+	0.202218i
$262$	−5.68456e7	+	1.74953e8i	−0.195273	+	0.600989i
$263$	2.71135e7	−	8.34467e7i	0.0919052	−	0.282855i	−0.894530	−	0.447009i	$-0.852489\pi$
$263$	2.71135e7	−	8.34467e7i	0.0919052	−	0.282855i	0.986435	+	0.164154i	$0.0524893\pi$
$264$	3.65794e7	+	1.12580e8i	0.122355	+	0.376571i
$265$	−4.40151e8	+	1.91348e7i	−1.45292	+	0.0631631i
$266$	−2.32081e7	+	7.14271e7i	−0.0756054	+	0.232690i
$267$	−1.68946e8	−	1.22746e8i	−0.543197	−	0.394656i
$268$	−5.70935e7			−0.181182
$269$	1.94687e8	+	1.41448e8i	0.609823	+	0.443062i	0.849352	−	0.527827i	$-0.176993\pi$
$269$	1.94687e8	+	1.41448e8i	0.609823	+	0.443062i	−0.239529	+	0.970889i	$0.576993\pi$
$270$	2.66767e8	−	1.15972e7i	0.824818	−	0.0358576i
$271$	−3.38523e8	+	2.45951e8i	−1.03323	+	0.750684i	−0.968952	−	0.247249i	$-0.920474\pi$
$271$	−3.38523e8	+	2.45951e8i	−1.03323	+	0.750684i	−0.0642752	+	0.997932i	$0.520474\pi$
$272$	2.11728e8	−	1.53829e8i	0.637951	−	0.463499i
$273$	−7.29969e7	−	2.24661e8i	−0.217138	−	0.668281i
$274$	−3.65508e8			−1.07342
$275$	1.57288e8	−	1.36625e8i	0.456069	−	0.396155i
$276$	1.12476e8			0.322016
$277$	9.87162e7	+	3.03817e8i	0.279067	+	0.858881i	0.988114	+	0.153720i	$0.0491254\pi$
$277$	9.87162e7	+	3.03817e8i	0.279067	+	0.858881i	−0.709047	+	0.705161i	$0.750875\pi$
$278$	−2.69115e8	+	1.95523e8i	−0.751244	+	0.545810i
$279$	2.40014e8	−	1.74381e8i	0.661641	−	0.480711i
$280$	−2.32755e8	−	6.22886e8i	−0.633644	−	1.69572i
$281$	−2.63273e8	−	1.91279e8i	−0.707838	−	0.514275i	0.174637	−	0.984633i	$-0.444125\pi$
$281$	−2.63273e8	−	1.91279e8i	−0.707838	−	0.514275i	−0.882476	+	0.470358i	$0.844125\pi$
$282$	2.19967e8			0.584097
$283$	−3.52354e8	−	2.56000e8i	−0.924115	−	0.671409i	0.0204296	−	0.999791i	$-0.493497\pi$
$283$	−3.52354e8	−	2.56000e8i	−0.924115	−	0.671409i	−0.944545	+	0.328382i	$0.893497\pi$
$284$	−1.57575e7	+	4.84966e7i	−0.0408200	+	0.125631i
$285$	−3.44876e7	−	2.28361e7i	−0.0882481	−	0.0584339i
$286$	4.33041e7	+	1.33276e8i	0.109458	+	0.336877i
$287$	2.62746e8	−	8.08649e8i	0.656069	−	2.01917i
$288$	4.59818e7	−	1.41517e8i	0.113426	−	0.349089i
$289$	8.45137e7	+	2.60106e8i	0.205961	+	0.633882i
$290$	−4.06254e7	−	1.08720e8i	−0.0978149	−	0.261767i
$291$	−1.31040e7	+	4.03300e7i	−0.0311730	+	0.0959407i
$292$	9.66317e7	+	7.02070e7i	0.227133	+	0.165021i
$293$	3.87109e8			0.899076			0.449538	−	0.893261i	$-0.351589\pi$
$293$	3.87109e8			0.899076			0.449538	+	0.893261i	$0.351589\pi$
$294$	−3.14749e8	−	2.28679e8i	−0.722352	−	0.524820i
$295$	−2.35777e8	+	1.87474e8i	−0.534718	+	0.425171i
$296$	1.78920e8	−	1.29993e8i	0.400994	−	0.291339i
$297$	2.17656e8	−	1.58137e8i	0.482085	−	0.350255i
$298$	−5.34638e7	−	1.64545e8i	−0.117032	−	0.360186i
$299$	5.77773e8			1.24999
$300$	8.40806e7	−	7.32436e6i	0.179792	−	0.0156619i
$301$	9.38053e8			1.98264
$302$	2.15932e8	+	6.64570e8i	0.451121	+	1.38841i
$303$	−1.97450e8	+	1.43456e8i	−0.407762	+	0.296257i
$304$	4.25151e7	−	3.08890e7i	0.0867932	−	0.0630590i
$305$	−1.04651e8	+	3.77084e8i	−0.211200	+	0.761008i
$306$	−2.79013e8	−	2.02715e8i	−0.556673	−	0.404447i
$307$	−2.91081e8			−0.574156			−0.287078	−	0.957907i	$-0.592684\pi$
$307$	−2.91081e8			−0.574156			−0.287078	+	0.957907i	$0.592684\pi$
$308$	−1.24915e8	−	9.07559e7i	−0.243605	−	0.176989i
$309$	1.31819e8	−	4.05698e8i	0.254170	−	0.782254i
$310$	−4.41290e8	+	3.50883e8i	−0.841314	+	0.668954i
$311$	2.25905e8	+	6.95264e8i	0.425858	+	1.31065i	0.902171	+	0.431379i	$0.141973\pi$
$311$	2.25905e8	+	6.95264e8i	0.425858	+	1.31065i	−0.476313	+	0.879276i	$0.658027\pi$
$312$	−7.61200e7	+	2.34273e8i	−0.141892	+	0.436698i
$313$	2.63772e8	−	8.11808e8i	0.486210	−	1.49640i	−0.344011	−	0.938966i	$-0.611786\pi$
$313$	2.63772e8	−	8.11808e8i	0.486210	−	1.49640i	0.830221	−	0.557435i	$-0.188214\pi$
$314$	−2.40864e8	−	7.41304e8i	−0.439055	−	1.35127i
$315$	−4.60237e8	+	3.65948e8i	−0.829649	+	0.659679i
$316$	4.63103e6	−	1.42529e7i	0.00825607	−	0.0254096i
$317$	−5.94956e8	−	4.32261e8i	−1.04900	−	0.762146i	−0.0769815	−	0.997033i	$-0.524528\pi$
$317$	−5.94956e8	−	4.32261e8i	−1.04900	−	0.762146i	−0.972023	+	0.234886i	$0.924528\pi$
$318$	4.20638e8			0.733523
$319$	−9.46064e7	−	6.87355e7i	−0.163175	−	0.118553i
$320$	−1.71370e8	+	6.17491e8i	−0.292354	+	1.05343i
$321$	−1.36139e8	+	9.89107e7i	−0.229728	+	0.166907i
$322$	1.20472e9	−	8.75281e8i	2.01090	−	1.46101i
$323$	4.24322e7	+	1.30593e8i	0.0700627	+	0.215631i
$324$	−7.77318e6			−0.0126967
$325$	4.31911e8	−	3.76243e7i	0.697915	−	0.0607963i
$326$	−9.51734e7			−0.152144
$327$	7.37589e7	+	2.27007e8i	0.116653	+	0.359022i
$328$	−7.17308e8	+	5.21155e8i	−1.12240	+	0.815470i
$329$	−1.00722e9	+	7.31786e8i	−1.55933	+	1.13292i
$330$	−1.55697e8	+	1.23799e8i	−0.238496	+	0.189636i
$331$	1.17066e8	+	8.50536e7i	0.177433	+	0.128912i	0.672957	−	0.739682i	$-0.265024\pi$
$331$	1.17066e8	+	8.50536e7i	0.177433	+	0.128912i	−0.495524	+	0.868594i	$0.665024\pi$
$332$	2.22163e8			0.333187
$333$	−1.58213e8	−	1.14948e8i	−0.234794	−	0.170587i
$334$	−2.34011e8	+	7.20211e8i	−0.343655	+	1.05766i
$335$	−1.45719e8	−	3.89967e8i	−0.211768	−	0.566723i
$336$	1.31645e8	+	4.05162e8i	0.189329	+	0.582696i
$337$	−2.96859e8	+	9.13639e8i	−0.422519	+	1.30038i	0.482831	+	0.875713i	$0.339608\pi$
$337$	−2.96859e8	+	9.13639e8i	−0.422519	+	1.30038i	−0.905350	+	0.424666i	$0.860392\pi$
$338$	9.34989e7	−	2.87760e8i	0.131704	−	0.405342i
$339$	9.80504e7	+	3.01768e8i	0.136694	+	0.420702i
$340$	−2.33611e8	−	1.54687e8i	−0.322342	−	0.213441i
$341$	−1.75537e8	+	5.40249e8i	−0.239734	+	0.737825i
$342$	−5.60260e7	−	4.07053e7i	−0.0757353	−	0.0550249i
$343$	9.58086e8			1.28196
$344$	−7.91369e8	−	5.74963e8i	−1.04815	−	0.761528i
$345$	2.87071e8	+	7.68246e8i	0.376377	+	1.00724i
$346$	−4.93369e7	+	3.58454e7i	−0.0640333	+	0.0465229i
$347$	8.94350e8	−	6.49783e8i	1.14909	−	0.834863i	0.160731	−	0.986998i	$-0.448615\pi$
$347$	8.94350e8	−	6.49783e8i	1.14909	−	0.834863i	0.988360	+	0.152135i	$0.0486148\pi$
$348$	−1.46389e7	−	4.50539e7i	−0.0186200	−	0.0573066i
$349$	−1.33757e9			−1.68433			−0.842163	−	0.539222i	$-0.818718\pi$
$349$	−1.33757e9			−1.68433			−0.842163	+	0.539222i	$0.818718\pi$
$350$	8.43584e8	−	7.32762e8i	1.05170	−	0.913534i
$351$	5.59855e8			0.691036
$352$	8.80427e7	+	2.70968e8i	0.107595	+	0.331145i
$353$	6.78003e8	−	4.92598e8i	0.820390	−	0.596048i	−0.0964345	−	0.995339i	$-0.530744\pi$
$353$	6.78003e8	−	4.92598e8i	0.820390	−	0.596048i	0.916824	+	0.399291i	$0.130744\pi$
$354$	2.32674e8	−	1.69048e8i	0.278764	−	0.202534i
$355$	−3.71465e8	+	1.61488e7i	−0.440675	+	0.0191576i
$356$	−2.29796e8	−	1.66957e8i	−0.269940	−	0.196123i
$357$	−1.11314e9			−1.29483
$358$	−1.31261e8	−	9.53667e7i	−0.151198	−	0.109852i
$359$	1.94488e8	−	5.98572e8i	0.221851	−	0.682788i	−0.776745	−	0.629816i	$-0.783130\pi$
$359$	1.94488e8	−	5.98572e8i	0.221851	−	0.682788i	0.998596	−	0.0529727i	$-0.0168696\pi$
$360$	6.12571e8	−	2.66305e7i	0.691986	−	0.0300829i
$361$	−2.67701e8	−	8.23899e8i	−0.299485	−	0.921720i
$362$	−9.40366e7	+	2.89415e8i	−0.104188	+	0.320657i
$363$	1.07776e8	−	3.31701e8i	0.118263	−	0.363977i
$364$	−9.92888e7	−	3.05580e8i	−0.107906	−	0.332100i
$365$	−2.32904e8	+	8.39215e8i	−0.250699	+	0.903334i
$366$	1.15460e8	−	3.55348e8i	0.123097	−	0.378853i
$367$	8.08909e8	+	5.87706e8i	0.854217	+	0.620625i	0.926306	−	0.376773i	$-0.122966\pi$
$367$	8.08909e8	+	5.87706e8i	0.854217	+	0.620625i	−0.0720886	+	0.997398i	$0.522966\pi$
$368$	−1.04198e9			−1.08991
$369$	6.34289e8	+	4.60838e8i	0.657196	+	0.477481i
$370$	3.09864e8	+	2.05178e8i	0.318028	+	0.210584i
$371$	−1.92608e9	+	1.39938e9i	−1.95824	+	1.42275i
$372$	−1.86169e8	+	1.35260e8i	−0.187503	+	0.136229i
$373$	3.38649e8	+	1.04226e9i	0.337885	+	1.03990i	0.965283	+	0.261205i	$0.0841199\pi$
$373$	3.38649e8	+	1.04226e9i	0.337885	+	1.03990i	−0.627398	+	0.778699i	$0.715880\pi$
$374$	6.60351e8			0.652716
$375$	2.64626e8	+	5.55604e8i	0.259134	+	0.544071i
$376$	1.29825e9			1.25951
$377$	−7.51981e7	−	2.31436e8i	−0.0722790	−	0.222452i
$378$	1.16736e9	−	8.48136e8i	1.11169	−	0.807689i
$379$	5.02352e8	−	3.64980e8i	0.473992	−	0.344375i	−0.325003	−	0.945713i	$-0.605365\pi$
$379$	5.02352e8	−	3.64980e8i	0.473992	−	0.344375i	0.798995	+	0.601338i	$0.205365\pi$
$380$	−4.69092e7	−	3.10612e7i	−0.0438547	−	0.0290386i
$381$	127198.	+	92414.8i	0.000117827	+	8.56060e-5i
$382$	−4.04914e8			−0.371656
$383$	−3.60726e7	−	2.62083e7i	−0.0328082	−	0.0238365i	0.571260	−	0.820769i	$-0.306455\pi$
$383$	−3.60726e7	−	2.62083e7i	−0.0328082	−	0.0238365i	−0.604068	+	0.796932i	$0.706455\pi$
$384$	6.99745e7	−	2.15359e8i	0.0630639	−	0.194091i
$385$	3.01073e8	−	1.08485e9i	0.268880	−	0.968847i
$386$	−1.17198e7	−	3.60697e7i	−0.0103720	−	0.0319218i
$387$	−2.67292e8	+	8.22640e8i	−0.234421	+	0.721475i
$388$	−1.78238e7	+	5.48560e7i	−0.0154913	+	0.0476775i
$389$	−4.64030e8	−	1.42814e9i	−0.399689	−	1.23012i	−0.925249	−	0.379360i	$-0.876144\pi$
$389$	−4.64030e8	−	1.42814e9i	−0.399689	−	1.23012i	0.525560	−	0.850757i	$-0.323856\pi$
$390$	−4.13545e8	+	1.79782e7i	−0.353018	+	0.0153469i
$391$	8.41333e8	−	2.58936e9i	0.711786	−	2.19065i
$392$	−1.85766e9	−	1.34967e9i	−1.55764	−	1.13169i
$393$	−5.47487e8			−0.454988
$394$	−4.20950e8	−	3.05838e8i	−0.346732	−	0.251915i
$395$	1.09171e8	−	4.74605e6i	0.0891291	−	0.00387474i
$396$	1.15183e8	−	8.36856e7i	0.0932087	−	0.0677201i
$397$	1.46244e9	−	1.06252e9i	1.17303	−	0.852258i	0.181664	−	0.983361i	$-0.441852\pi$
$397$	1.46244e9	−	1.06252e9i	1.17303	−	0.852258i	0.991369	+	0.131102i	$0.0418516\pi$
$398$	−7.74887e7	−	2.38486e8i	−0.0616095	−	0.189615i
$399$	−2.23520e8			−0.176161
$400$	−7.78924e8	+	6.78530e7i	−0.608534	+	0.0530102i
$401$	1.43902e9			1.11445			0.557225	−	0.830362i	$-0.311866\pi$
$401$	1.43902e9			1.11445			0.557225	+	0.830362i	$0.311866\pi$
$402$	1.22826e8	+	3.78019e8i	0.0942971	+	0.290217i
$403$	−9.56328e8	+	6.94813e8i	−0.727845	+	0.528810i
$404$	−2.68567e8	+	1.95125e8i	−0.202636	+	0.147224i
$405$	−1.98395e7	−	5.30934e7i	−0.0148401	−	0.0397144i
$406$	−5.07404e8	−	3.68650e8i	−0.376281	−	0.273384i
$407$	3.74448e8			0.275303
$408$	9.39080e8	+	6.82281e8i	0.684529	+	0.497339i
$409$	−1.59672e8	+	4.91419e8i	−0.115398	+	0.355157i	−0.992030	−	0.126004i	$-0.959785\pi$
$409$	−1.59672e8	+	4.91419e8i	−0.115398	+	0.355157i	0.876632	+	0.481161i	$0.159785\pi$
$410$	−1.24227e9	−	8.22578e8i	−0.890172	−	0.589432i
$411$	−3.36154e8	−	1.03457e9i	−0.238831	−	0.735048i
$412$	1.79298e8	−	5.51821e8i	0.126309	−	0.388739i
$413$	−5.03015e8	+	1.54812e9i	−0.351363	+	1.08138i
$414$	4.24314e8	+	1.30590e9i	0.293891	+	0.904502i
$415$	5.67025e8	+	1.51744e9i	0.389434	+	1.04218i
$416$	−1.83212e8	+	5.63870e8i	−0.124775	+	0.384019i
$417$	−8.00934e8	−	5.81913e8i	−0.540904	−	0.392990i
$418$	1.32599e8			0.0888020
$419$	1.65448e9	+	1.20205e9i	1.09879	+	0.798315i	0.980861	−	0.194708i	$-0.0623758\pi$
$419$	1.65448e9	+	1.20205e9i	1.09879	+	0.798315i	0.117925	+	0.993023i	$0.462376\pi$
$420$	3.56987e8	−	2.83851e8i	0.235114	−	0.186947i
$421$	−1.61825e9	+	1.17573e9i	−1.05696	+	0.767924i	−0.973523	−	0.228589i	$-0.926589\pi$
$421$	−1.61825e9	+	1.17573e9i	−1.05696	+	0.767924i	−0.0834341	+	0.996513i	$0.526589\pi$
$422$	−1.58509e9	+	1.15163e9i	−1.02674	+	0.745968i
$423$	−3.54751e8	−	1.09181e9i	−0.227894	−	0.701385i
$424$	2.48263e9			1.58172
$425$	4.60316e8	−	1.99045e9i	0.290867	−	1.25774i
$426$	3.54998e8			0.222480
$427$	6.53489e8	+	2.01123e9i	0.406201	+	1.25016i
$428$	−1.85173e8	+	1.34536e8i	−0.114163	+	0.0829442i
$429$	−3.37414e8	+	2.45146e8i	−0.206330	+	0.149908i
$430$	4.39572e8	−	1.58390e9i	0.266619	−	0.960698i
$431$	−5.72897e8	−	4.16234e8i	−0.344672	−	0.250419i	0.401958	−	0.915658i	$-0.368330\pi$
$431$	−5.72897e8	−	4.16234e8i	−0.344672	−	0.250419i	−0.746630	+	0.665239i	$0.768330\pi$
$432$	−1.00966e9			−0.602536
$433$	−8.87395e8	−	6.44730e8i	−0.525302	−	0.381654i	0.293295	−	0.956022i	$-0.405248\pi$
$433$	−8.87395e8	−	6.44730e8i	−0.525302	−	0.381654i	−0.818598	+	0.574367i	$0.805248\pi$
$434$	−9.41462e8	+	2.89752e9i	−0.552826	+	1.70142i
$435$	2.70370e8	−	2.14979e8i	0.157487	−	0.125223i
$436$	1.00325e8	+	3.08769e8i	0.0579706	+	0.178415i
$437$	1.68940e8	−	5.19944e8i	0.0968385	−	0.298038i
$438$	2.56960e8	−	7.90841e8i	0.146119	−	0.449707i
$439$	4.64532e8	+	1.42968e9i	0.262053	+	0.806517i	0.992358	+	0.123395i	$0.0393783\pi$
$439$	4.64532e8	+	1.42968e9i	0.262053	+	0.806517i	−0.730304	+	0.683122i	$0.760622\pi$
$440$	−9.18931e8	+	7.30670e8i	−0.514279	+	0.408919i
$441$	−6.27442e8	+	1.93107e9i	−0.348368	+	1.07217i
$442$	1.11172e9	+	8.07710e8i	0.612374	+	0.444916i
$443$	−3.37903e8			−0.184662			−0.0923312	−	0.995728i	$-0.529432\pi$
$443$	−3.37903e8			−0.184662			−0.0923312	+	0.995728i	$0.529432\pi$
$444$	1.22719e8	+	8.91605e7i	0.0665382	+	0.0483429i
$445$	5.53861e8	−	1.99571e9i	0.297948	−	1.07359i
$446$	−4.80630e8	+	3.49198e8i	−0.256531	+	0.186380i
$447$	4.16576e8	−	3.02660e8i	0.220606	−	0.160280i
$448$	1.07012e9	+	3.29348e9i	0.562287	+	1.73054i
$449$	2.86539e9			1.49390			0.746950	−	0.664881i	$-0.231518\pi$
$449$	2.86539e9			1.49390			0.746950	+	0.664881i	$0.231518\pi$
$450$	4.02233e8	+	9.48589e8i	0.208082	+	0.490721i
$451$	−1.50120e9			−0.770583
$452$	1.33366e8	+	4.10459e8i	0.0679299	+	0.209067i
$453$	−1.68249e9	+	1.22240e9i	−0.850370	+	0.617830i
$454$	1.36971e9	−	9.95150e8i	0.686961	−	0.499106i
$455$	1.83379e9	−	1.45811e9i	0.912664	−	0.725686i
$456$	1.88568e8	+	1.37002e8i	0.0931301	+	0.0676630i
$457$	−8.92362e7			−0.0437355			−0.0218678	−	0.999761i	$-0.506961\pi$
$457$	−8.92362e7			−0.0437355			−0.0218678	+	0.999761i	$0.506961\pi$
$458$	−7.12107e8	−	5.17376e8i	−0.346350	−	0.251638i
$459$	8.15242e8	−	2.50906e9i	0.393498	−	1.21106i
$460$	3.90468e8	+	1.04495e9i	0.187039	+	0.500546i
$461$	−6.94151e8	−	2.13638e9i	−0.329990	−	1.01560i	−0.969138	−	0.246520i	$-0.920713\pi$
$461$	−6.94151e8	−	2.13638e9i	−0.329990	−	1.01560i	0.639148	−	0.769084i	$-0.279287\pi$
$462$	−3.32169e8	+	1.02231e9i	−0.156716	+	0.482321i
$463$	−1.01302e9	+	3.11775e9i	−0.474333	+	1.45985i	0.372522	+	0.928023i	$0.378493\pi$
$463$	−1.01302e9	+	3.11775e9i	−0.474333	+	1.45985i	−0.846855	+	0.531823i	$0.821507\pi$
$464$	1.35615e8	+	4.17380e8i	0.0630223	+	0.193963i
$465$	−1.39903e9	−	9.26374e8i	−0.645270	−	0.427269i
$466$	7.73357e8	−	2.38015e9i	0.354021	−	1.08957i
$467$	−2.15103e9	−	1.56281e9i	−0.977320	−	0.710064i	−0.0202117	−	0.999796i	$-0.506434\pi$
$467$	−2.15103e9	−	1.56281e9i	−0.977320	−	0.710064i	−0.957108	+	0.289731i	$0.906434\pi$
$468$	2.96274e8			0.133608
$469$	−1.82001e9	−	1.32231e9i	−0.814645	−	0.591874i
$470$	7.63632e8	+	2.04359e9i	0.339267	+	0.907929i
$471$	1.87675e9	−	1.36354e9i	0.827625	−	0.601305i
$472$	1.37325e9	−	9.97727e8i	0.601109	−	0.436732i
$473$	−5.11792e8	−	1.57513e9i	−0.222372	−	0.684389i
$474$	−1.04332e8			−0.0449979
$475$	9.24318e7	−	3.99683e8i	0.0395725	−	0.171115i
$476$	−1.51407e9			−0.643461
$477$	−6.78384e8	−	2.08785e9i	−0.286194	−	0.880816i
$478$	−1.08921e9	+	7.91360e8i	−0.456158	+	0.331418i
$479$	−2.82419e8	+	2.05189e8i	−0.117414	+	0.0853062i	−0.644943	−	0.764231i	$-0.723119\pi$
$479$	−2.82419e8	+	2.05189e8i	−0.117414	+	0.0853062i	0.527529	+	0.849537i	$0.323119\pi$
$480$	−8.40790e8	+	3.65519e7i	−0.347011	+	0.0150857i
$481$	6.30391e8	+	4.58006e8i	0.258287	+	0.187656i
$482$	−2.22801e9			−0.906258
$483$	3.58547e9	+	2.60499e9i	1.44787	+	1.05194i
$484$	1.46595e8	−	4.51172e8i	0.0587706	−	0.180877i
$485$	−4.20176e8	+	1.82664e7i	−0.167238	+	0.00727039i
$486$	6.62343e8	+	2.03848e9i	0.261732	+	0.805527i
$487$	1.00837e8	−	3.10346e8i	0.0395613	−	0.121757i	−0.929325	−	0.369262i	$-0.879611\pi$
$487$	1.00837e8	−	3.10346e8i	0.0395613	−	0.121757i	0.968887	+	0.247505i	$0.0796106\pi$
$488$	6.81448e8	−	2.09728e9i	0.265438	−	0.816934i
$489$	−8.75300e7	−	2.69390e8i	−0.0338513	−	0.104184i
$490$	1.03185e9	−	3.71804e9i	0.396216	−	1.42767i
$491$	−2.17036e8	+	6.67968e8i	−0.0827459	+	0.254666i	−0.983867	−	0.178902i	$-0.942745\pi$
$491$	−2.17036e8	+	6.67968e8i	−0.0827459	+	0.254666i	0.901121	+	0.433568i	$0.142745\pi$
$492$	−4.91992e8	−	3.57453e8i	−0.186243	−	0.135314i
$493$	−1.14671e9			−0.431011
$494$	2.23233e8	+	1.62189e8i	0.0833134	+	0.0605307i
$495$	8.65582e8	+	5.73150e8i	0.320767	+	0.212398i
$496$	1.72468e9	−	1.25305e9i	0.634631	−	0.461087i
$497$	−1.62552e9	+	1.18101e9i	−0.593942	+	0.431524i
$498$	−4.77941e8	−	1.47095e9i	−0.173409	−	0.533698i
$499$	−5.10368e9			−1.83879			−0.919394	−	0.393339i	$-0.871320\pi$
$499$	−5.10368e9			−1.83879			−0.919394	+	0.393339i	$0.871320\pi$
$500$	3.59939e8	+	7.55720e8i	0.128776	+	0.270375i
$501$	−2.25378e9			−0.800719
$502$	1.63699e7	+	5.03815e7i	0.00577543	+	0.0177749i
$503$	2.98138e9	−	2.16610e9i	1.04455	−	0.758911i	0.0733824	−	0.997304i	$-0.476621\pi$
$503$	2.98138e9	−	2.16610e9i	1.04455	−	0.758911i	0.971169	+	0.238393i	$0.0766206\pi$
$504$	2.68058e9	−	1.94756e9i	0.932659	−	0.677616i
$505$	−2.01823e9	−	1.33638e9i	−0.697350	−	0.461754i
$506$	−2.12701e9	−	1.54536e9i	−0.729866	−	0.530279i
$507$	9.00499e8			0.306871
$508$	173012.	+	125701.i	5.85536e−5	+	4.25416e-5i
$509$	2.58331e8	−	7.95061e8i	0.0868289	−	0.267232i	−0.898209	−	0.439568i	$-0.855132\pi$
$509$	2.58331e8	−	7.95061e8i	0.0868289	−	0.267232i	0.985038	+	0.172336i	$0.0551316\pi$
$510$	−5.21619e8	+	1.87953e9i	−0.174124	+	0.627414i
$511$	1.45436e9	+	4.47607e9i	0.482170	+	1.48397i
$512$	9.53908e8	−	2.93583e9i	0.314095	−	0.966686i
$513$	1.63701e8	−	5.03820e8i	0.0535353	−	0.164765i
$514$	2.70929e8	+	8.33833e8i	0.0880003	+	0.270837i
$515$	4.22674e9	−	1.83750e8i	1.36358	−	0.0592793i
$516$	2.07327e8	−	6.38088e8i	0.0664328	−	0.204459i
$517$	1.77831e9	+	1.29202e9i	0.565965	+	0.411198i
$518$	2.00828e9			0.634848
$519$	−1.46835e8	−	1.06682e8i	−0.0461047	−	0.0334970i
$520$	−2.44076e9	+	1.06108e8i	−0.761226	+	0.0330930i
$521$	3.73871e9	−	2.71633e9i	1.15822	−	0.841494i	0.168665	−	0.985673i	$-0.446054\pi$
$521$	3.73871e9	−	2.71633e9i	1.15822	−	0.841494i	0.989552	+	0.144180i	$0.0460543\pi$
$522$	4.67874e8	−	3.39931e8i	0.143973	−	0.104603i
$523$	5.47496e8	+	1.68502e9i	0.167350	+	0.515050i	0.999202	−	0.0399477i	$-0.0127191\pi$
$523$	5.47496e8	+	1.68502e9i	0.167350	+	0.515050i	−0.831852	+	0.554998i	$0.812719\pi$
$524$	−7.44680e8			−0.226105
$525$	2.84993e9	+	1.71386e9i	0.859561	+	0.516915i
$526$	−8.30844e8			−0.248926
$527$	1.72131e9	+	5.29766e9i	0.512298	+	1.57669i
$528$	6.08505e8	−	4.42105e8i	0.179906	−	0.130709i
$529$	−6.01506e9	+	4.37019e9i	−1.76663	+	1.28353i
$530$	1.46028e9	+	3.90792e9i	0.426060	+	1.14020i
$531$	−1.21432e9	−	8.82253e8i	−0.351967	−	0.255719i
$532$	−3.04026e8			−0.0875428
$533$	−2.52730e9	−	1.83619e9i	−0.722955	−	0.525258i
$534$	−6.11066e8	+	1.88067e9i	−0.173658	+	0.534463i
$535$	−1.39154e9	−	9.21417e8i	−0.392879	−	0.260147i
$536$	7.24923e8	+	2.23108e9i	0.203336	+	0.625805i
$537$	1.49217e8	−	4.59244e8i	0.0415824	−	0.127977i
$538$	7.04171e8	−	2.16722e9i	0.194958	−	0.600018i
$539$	−1.20138e9	−	3.69748e9i	−0.330461	−	1.01706i
$540$	3.78359e8	+	1.01254e9i	0.103401	+	0.276717i
$541$	4.52366e8	−	1.39224e9i	0.122829	−	0.378028i	−0.870671	−	0.491867i	$-0.836315\pi$
$541$	4.52366e8	−	1.39224e9i	0.122829	−	0.378028i	0.993499	+	0.113839i	$0.0363148\pi$
$542$	3.20557e9	+	2.32898e9i	0.864784	+	0.628302i
$543$	−9.05678e8			−0.242758
$544$	2.26026e9	+	1.64218e9i	0.601953	+	0.437345i
$545$	−1.85294e9	+	1.47333e9i	−0.490312	+	0.389862i
$546$	−1.80966e9	+	1.31479e9i	−0.475798	+	0.345687i
$547$	−3.64876e9	+	2.65098e9i	−0.953213	+	0.692550i	−0.951565	−	0.307449i	$-0.900525\pi$
$547$	−3.64876e9	+	2.65098e9i	−0.953213	+	0.692550i	−0.00164826	+	0.999999i	$0.500525\pi$
$548$	−4.57229e8	−	1.40721e9i	−0.118687	−	0.365280i
$549$	−1.94999e9			−0.502955
$550$	−1.69067e9	−	1.01672e9i	−0.433300	−	0.260574i
$551$	−2.30260e8			−0.0586391
$552$	−1.42812e9	−	4.39530e9i	−0.361391	−	1.11225i
$553$	4.77730e8	−	3.47091e8i	0.120128	−	0.0872782i
$554$	2.44726e9	−	1.77804e9i	0.611499	−	0.444280i
$555$	−2.95780e8	+	1.06577e9i	−0.0734419	+	0.264631i
$556$	−1.08941e9	−	7.91505e8i	−0.268801	−	0.195295i
$557$	6.36886e9			1.56160			0.780798	−	0.624784i	$-0.214813\pi$
$557$	6.36886e9			1.56160			0.780798	+	0.624784i	$0.214813\pi$
$558$	−2.27276e9	−	1.65126e9i	−0.553776	−	0.402342i
$559$	1.06501e9	−	3.27777e9i	0.257878	−	0.793666i
$560$	−3.30713e9	+	2.62960e9i	−0.795780	+	0.632749i
$561$	6.07318e8	+	1.86913e9i	0.145227	+	0.446962i
$562$	−9.52243e8	+	2.93070e9i	−0.226293	+	0.696457i
$563$	−5.59701e8	+	1.72258e9i	−0.132183	+	0.406818i	−0.995141	−	0.0984574i	$-0.968609\pi$
$563$	−5.59701e8	+	1.72258e9i	−0.132183	+	0.406818i	0.862958	+	0.505276i	$0.168609\pi$
$564$	2.75166e8	+	8.46873e8i	0.0645829	+	0.198766i
$565$	−2.46318e9	+	1.95855e9i	−0.574548	+	0.456840i
$566$	−1.27444e9	+	3.92233e9i	−0.295435	+	0.909257i
$567$	−2.47791e8	−	1.80031e8i	−0.0570880	−	0.0414769i
$568$	2.09521e9			0.479743
$569$	1.59599e9	+	1.15956e9i	0.363194	+	0.263876i	0.754383	−	0.656435i	$-0.227936\pi$
$569$	1.59599e9	+	1.15956e9i	0.363194	+	0.263876i	−0.391189	+	0.920310i	$0.627936\pi$
$570$	−1.04741e8	+	3.77411e8i	−0.0236895	+	0.0853596i
$571$	5.70078e9	−	4.14186e9i	1.28147	−	0.931042i	0.281873	−	0.959452i	$-0.409044\pi$
$571$	5.70078e9	−	4.14186e9i	1.28147	−	0.931042i	0.999596	+	0.0284098i	$0.00904433\pi$
$572$	−4.58943e8	+	3.33442e8i	−0.102535	+	0.0744962i
$573$	−3.72396e8	−	1.14612e9i	−0.0826920	−	0.254500i
$574$	−8.05138e9			−1.77697
$575$	−6.14077e9	+	5.33405e9i	−1.34705	+	1.17009i
$576$	−3.19319e9			−0.696218
$577$	−3.64193e8	−	1.12087e9i	−0.0789254	−	0.242907i	0.903807	−	0.427941i	$-0.140761\pi$
$577$	−3.64193e8	−	1.12087e9i	−0.0789254	−	0.242907i	−0.982732	+	0.185033i	$0.940761\pi$
$578$	2.09517e9	−	1.52223e9i	0.451307	−	0.327893i
$579$	9.13173e7	−	6.63459e7i	0.0195514	−	0.0142049i
$580$	3.67751e8	−	2.92410e8i	0.0782629	−	0.0622292i
$581$	7.08203e9	+	5.14540e9i	1.49810	+	1.08843i
$582$	4.01549e8			0.0844322
$583$	3.40062e9	+	2.47070e9i	0.710752	+	0.516392i
$584$	1.51659e9	−	4.66758e9i	0.315081	−	0.969720i
$585$	7.56180e8	+	2.02365e9i	0.156164	+	0.417917i
$586$	−1.13275e9	−	3.48623e9i	−0.232536	−	0.715673i
$587$	−3.72748e8	+	1.14720e9i	−0.0760645	+	0.234103i	−0.981858	−	0.189616i	$-0.939276\pi$
$587$	−3.72748e8	+	1.14720e9i	−0.0760645	+	0.234103i	0.905794	+	0.423719i	$0.139276\pi$
$588$	4.86681e8	−	1.49785e9i	0.0987242	−	0.303842i
$589$	3.45641e8	+	1.06377e9i	0.0696981	+	0.214509i
$590$	2.37828e9	+	1.57479e9i	0.476739	+	0.315675i
$591$	4.78536e8	−	1.47278e9i	0.0953582	−	0.293482i
$592$	−1.13687e9	−	8.25985e8i	−0.225209	−	0.163624i
$593$	−5.87513e8			−0.115698			−0.0578490	−	0.998325i	$-0.518424\pi$
$593$	−5.87513e8			−0.115698			−0.0578490	+	0.998325i	$0.518424\pi$
$594$	−2.06105e9	−	1.49744e9i	−0.403493	−	0.293154i
$595$	−3.86436e9	−	1.03416e10i	−0.752087	−	2.01270i
$596$	5.66617e8	−	4.11672e8i	0.109630	−	0.0796506i
$597$	6.03772e8	−	4.38666e8i	0.116135	−	0.0843769i
$598$	−1.69066e9	−	5.20332e9i	−0.323297	−	0.995007i
$599$	2.92828e9			0.556696			0.278348	−	0.960480i	$-0.410213\pi$
$599$	2.92828e9			0.556696			0.278348	+	0.960480i	$0.410213\pi$
$600$	−1.35380e9	−	3.19268e9i	−0.255874	−	0.603429i
$601$	7.04121e9			1.32308			0.661541	−	0.749909i	$-0.269903\pi$
$601$	7.04121e9			1.32308			0.661541	+	0.749909i	$0.269903\pi$
$602$	−2.74490e9	−	8.44793e9i	−0.512789	−	1.57820i
$603$	1.67822e9	−	1.21930e9i	0.311701	−	0.226464i
$604$	−2.28848e9	+	1.66268e9i	−0.422589	+	0.307029i
$605$	3.45581e9	−	1.50235e8i	0.634462	−	0.0275822i
$606$	1.86970e9	+	1.35842e9i	0.341286	+	0.247959i
$607$	9.04743e9			1.64197			0.820985	−	0.570950i	$-0.193425\pi$
$607$	9.04743e9			1.64197			0.820985	+	0.570950i	$0.193425\pi$
$608$	4.53862e8	+	3.29750e8i	0.0818957	+	0.0595007i
$609$	5.76816e8	−	1.77526e9i	0.103485	−	0.318494i
$610$	3.70218e9	−	1.60946e8i	0.660393	−	0.0287095i
$611$	1.41349e9	+	4.35028e9i	0.250697	+	0.771566i
$612$	4.31424e8	−	1.32779e9i	0.0760807	−	0.234152i
$613$	−2.08419e9	+	6.41449e9i	−0.365449	+	1.12474i	0.584251	+	0.811573i	$0.301388\pi$
$613$	−2.08419e9	+	6.41449e9i	−0.365449	+	1.12474i	−0.949700	+	0.313163i	$0.898612\pi$
$614$	8.51752e8	+	2.62142e9i	0.148499	+	0.457033i
$615$	1.18581e9	−	4.27279e9i	0.205567	−	0.740711i
$616$	−1.96048e9	+	6.03373e9i	−0.337932	+	1.04005i
$617$	4.04400e9	+	2.93814e9i	0.693127	+	0.503586i	0.877687	−	0.479235i	$-0.159086\pi$
$617$	4.04400e9	+	2.93814e9i	0.693127	+	0.503586i	−0.184560	+	0.982821i	$0.559086\pi$
$618$	−4.03936e9			−0.688420
$619$	−4.85791e9	−	3.52948e9i	−0.823251	−	0.598127i	0.0943905	−	0.995535i	$-0.469910\pi$
$619$	−4.85791e9	−	3.52948e9i	−0.823251	−	0.598127i	−0.917642	+	0.397408i	$0.869910\pi$
$620$	−1.90293e9	−	1.26003e9i	−0.320665	−	0.212330i
$621$	−8.49765e9	+	6.17390e9i	−1.42390	+	1.03452i
$622$	5.60038e9	−	4.06891e9i	0.933149	−	0.677973i
$623$	−3.45857e9	−	1.06444e10i	−0.573045	−	1.76365i
$624$	1.56519e9			0.257883
$625$	−4.24315e9	+	4.38732e9i	−0.695197	+	0.718819i
$626$	−8.08283e9			−1.31690
$627$	1.21950e8	+	3.75323e8i	0.0197581	+	0.0608091i
$628$	2.55272e9	−	1.85466e9i	0.411286	−	0.298817i
$629$	2.97056e9	−	2.15824e9i	0.475950	−	0.345798i
$630$	4.64239e9	+	3.07398e9i	0.739690	+	0.489789i
$631$	2.33975e9	+	1.69993e9i	0.370738	+	0.269357i	0.757517	−	0.652815i	$-0.226412\pi$
$631$	2.33975e9	+	1.69993e9i	0.370738	+	0.269357i	−0.386779	+	0.922173i	$0.626412\pi$
$632$	−6.15771e8			−0.0970307
$633$	−4.71750e9	−	3.42747e9i	−0.739263	−	0.537106i
$634$	−2.15192e9	+	6.62293e9i	−0.335362	+	1.03214i
$635$	−416998.	+	1.50255e6i	−6.46288e−5	+	0.000232875i
$636$	5.26194e8	+	1.61946e9i	0.0811047	+	0.249615i
$637$	2.50002e9	−	7.69426e9i	0.383226	−	1.17945i
$638$	−3.42186e8	+	1.05314e9i	−0.0521662	+	0.160551i
$639$	−5.72522e8	−	1.76204e9i	−0.0868038	−	0.267155i
$640$	2.24371e9	−	9.75415e7i	0.338327	−	0.0147082i
$641$	1.43321e9	−	4.41098e9i	0.214935	−	0.661503i	−0.784223	−	0.620479i	$-0.786938\pi$
$641$	1.43321e9	−	4.41098e9i	0.214935	−	0.661503i	0.999158	−	0.0410236i	$-0.0130619\pi$
$642$	1.28914e9	+	9.36613e8i	0.192277	+	0.139697i
$643$	−5.63996e9			−0.836639			−0.418319	−	0.908300i	$-0.637381\pi$
$643$	−5.63996e9			−0.836639			−0.418319	+	0.908300i	$0.637381\pi$
$644$	4.87687e9	+	3.54325e9i	0.719516	+	0.522759i
$645$	4.88751e9	−	2.12476e8i	0.717181	−	0.0311782i
$646$	1.05193e9	−	7.64273e8i	0.153523	−	0.111541i
$647$	−1.01263e10	+	7.35721e9i	−1.46990	+	1.06794i	−0.489254	+	0.872141i	$0.662731\pi$
$647$	−1.01263e10	+	7.35721e9i	−1.46990	+	1.06794i	−0.980643	+	0.195802i	$0.937269\pi$
$648$	9.86971e7	+	3.03758e8i	0.0142492	+	0.0438547i
$649$	2.87397e9			0.412692
$650$	−1.60268e9	−	3.77962e9i	−0.228902	−	0.539822i
$651$	−9.06733e9			−1.28809
$652$	−1.19056e8	−	3.66418e8i	−0.0168223	−	0.0517738i
$653$	−4.33118e9	+	3.14678e9i	−0.608709	+	0.442253i	−0.848960	−	0.528458i	$-0.822770\pi$
$653$	−4.33118e9	+	3.14678e9i	−0.608709	+	0.442253i	0.240250	+	0.970711i	$0.422770\pi$
$654$	1.82855e9	−	1.32852e9i	0.255614	−	0.185714i
$655$	−1.90064e9	−	5.08641e9i	−0.264275	−	0.707240i
$656$	4.55782e9	+	3.31145e9i	0.630368	+	0.457989i
$657$	−4.33977e9			−0.597019
$658$	9.53762e9	+	6.92948e9i	1.30512	+	0.948223i
$659$	−2.93268e9	+	9.02585e9i	−0.399177	+	1.22854i	0.526484	+	0.850185i	$0.323510\pi$
$659$	−2.93268e9	+	9.02585e9i	−0.399177	+	1.22854i	−0.925661	+	0.378355i	$0.876490\pi$
$660$	−6.71396e8	−	4.44568e8i	−0.0909024	−	0.0601915i
$661$	−3.82369e9	−	1.17681e10i	−0.514964	−	1.58490i	−0.783347	−	0.621585i	$-0.786489\pi$
$661$	−3.82369e9	−	1.17681e10i	−0.514964	−	1.58490i	0.268383	−	0.963312i	$-0.413511\pi$
$662$	4.23421e8	−	1.30316e9i	0.0567244	−	0.174580i
$663$	−1.26380e9	+	3.88958e9i	−0.168415	+	0.518328i
$664$	−2.82083e9	−	8.68162e9i	−0.373928	−	1.15083i
$665$	−7.75966e8	−	2.07660e9i	−0.102321	−	0.273828i
$666$	−5.72245e8	+	1.76119e9i	−0.0750624	+	0.231018i
$667$	3.69358e9	+	2.68354e9i	0.481956	+	0.350161i
$668$	−3.06555e9			−0.397915
$669$	−1.43044e9	−	1.03928e9i	−0.184705	−	0.134196i
$670$	−3.08557e9	+	2.45343e9i	−0.396345	+	0.315146i
$671$	3.02063e9	−	2.19461e9i	0.385983	−	0.280433i
$672$	−3.67926e9	+	2.67314e9i	−0.467701	+	0.339805i
$673$	4.83268e9	+	1.48735e10i	0.611133	+	1.88087i	0.447295	+	0.894386i	$0.352387\pi$
$673$	4.83268e9	+	1.48735e10i	0.611133	+	1.88087i	0.163838	+	0.986487i	$0.447613\pi$
$674$	9.09672e9			1.14439
$675$	−5.95033e9	+	5.16863e9i	−0.744694	+	0.646863i
$676$	1.22484e9			0.152499
$677$	−3.99345e8	−	1.22906e9i	−0.0494639	−	0.152234i	0.923274	−	0.384143i	$-0.125503\pi$
$677$	−3.99345e8	−	1.22906e9i	−0.0494639	−	0.152234i	−0.972738	+	0.231909i	$0.925503\pi$
$678$	2.43076e9	−	1.76605e9i	0.299528	−	0.217620i
$679$	−1.83867e9	+	1.33587e9i	−0.225403	+	0.163765i
$680$	−3.07862e9	+	1.10931e10i	−0.375470	+	1.35292i
$681$	4.07649e9	+	2.96175e9i	0.494620	+	0.359363i
$682$	5.37903e9			0.649320
$683$	3.75635e9	+	2.72915e9i	0.451122	+	0.327759i	0.790039	−	0.613057i	$-0.210060\pi$
$683$	3.75635e9	+	2.72915e9i	0.451122	+	0.327759i	−0.338917	+	0.940816i	$0.610060\pi$
$684$	8.66302e7	−	2.66620e8i	0.0103508	−	0.0318564i
$685$	8.44469e9	−	6.71463e9i	1.00385	−	0.798188i
$686$	−2.80352e9	−	8.62835e9i	−0.331565	−	1.02045i
$687$	8.09522e8	−	2.49145e9i	0.0952533	−	0.293160i
$688$	−1.92068e9	+	5.91125e9i	−0.224852	+	0.692022i
$689$	2.70299e9	+	8.31895e9i	0.314831	+	0.968950i
$690$	6.07866e9	−	4.83333e9i	0.704427	−	0.560111i
$691$	−1.95548e9	+	6.01834e9i	−0.225465	+	0.693911i	0.772779	+	0.634675i	$0.218866\pi$
$691$	−1.95548e9	+	6.01834e9i	−0.225465	+	0.693911i	−0.998244	+	0.0592352i	$0.981134\pi$
$692$	−1.99722e8	−	1.45107e8i	−0.0229116	−	0.0166463i
$693$	5.60998e9			0.640317
$694$	−8.46884e9	−	6.15298e9i	−0.961758	−	0.698758i
$695$	2.62573e9	−	9.46120e9i	0.296690	−	1.06905i
$696$	−1.57473e9	+	1.14411e9i	−0.177041	+	0.128628i
$697$	−1.19093e10	+	8.65259e9i	−1.33220	+	0.967902i
$698$	3.91394e9	+	1.20459e10i	0.435633	+	1.34074i
$699$	7.44829e9			0.824872
$700$	3.87641e9	+	2.33116e9i	0.427156	+	0.256879i
$701$	4.11606e9			0.451304			0.225652	−	0.974208i	$-0.427549\pi$
$701$	4.11606e9			0.451304			0.225652	+	0.974208i	$0.427549\pi$
$702$	−1.63823e9	−	5.04195e9i	−0.178729	−	0.550071i
$703$	5.96491e8	−	4.33376e8i	0.0647530	−	0.0470458i
$704$	4.94640e9	−	3.59377e9i	0.534300	−	0.388192i
$705$	−5.08212e9	+	4.04094e9i	−0.546239	+	0.434331i
$706$	−6.42020e9	−	4.66454e9i	−0.686644	−	0.498876i
$707$	−1.30805e10			−1.39205
$708$	9.41896e8	+	6.84327e8i	0.0997439	+	0.0724682i
$709$	−8.21397e8	+	2.52800e9i	−0.0865548	+	0.266388i	−0.984961	−	0.172777i	$-0.944726\pi$
$709$	−8.21397e8	+	2.52800e9i	−0.0865548	+	0.266388i	0.898406	+	0.439166i	$0.144726\pi$
$710$	1.23240e9	+	3.29809e9i	0.129225	+	0.345827i
$711$	1.68261e8	+	5.17854e8i	0.0175566	+	0.0540335i
$712$	−3.60654e9	+	1.10998e10i	−0.374465	+	1.15248i
$713$	6.85326e9	−	2.10922e10i	0.708082	−	2.17925i
$714$	3.25724e9	+	1.00248e10i	0.334893	+	1.03069i
$715$	−3.44888e9	−	2.28369e9i	−0.352863	−	0.233650i
$716$	2.02962e8	−	6.24653e8i	0.0206642	−	0.0635980i
$717$	−3.24169e9	−	2.35523e9i	−0.328439	−	0.238625i
$718$	−5.95974e9			−0.600885
$719$	6.15751e9	+	4.47369e9i	0.617809	+	0.448864i	0.852155	−	0.523289i	$-0.175295\pi$
$719$	6.15751e9	+	4.47369e9i	0.617809	+	0.448864i	−0.234347	+	0.972153i	$0.575295\pi$
$720$	−1.36372e9	−	3.64952e9i	−0.136164	−	0.364395i
$721$	1.84961e10	−	1.34382e10i	1.83783	−	1.33526i
$722$	−6.63655e9	+	4.82173e9i	−0.656239	+	0.476785i
$723$	−2.04908e9	−	6.30641e9i	−0.201639	−	0.620580i
$724$	−1.23188e9			−0.120638
$725$	2.93587e9	+	1.76554e9i	0.286123	+	0.172066i
$726$	−3.30261e9			−0.320316
$727$	−4.31896e9	−	1.32924e10i	−0.416878	−	1.28302i	−0.910560	−	0.413377i	$-0.864349\pi$
$727$	−4.31896e9	−	1.32924e10i	−0.416878	−	1.28302i	0.493682	−	0.869643i	$-0.335651\pi$
$728$	−1.06807e10	+	7.75997e9i	−1.02598	+	0.745418i
$729$	−4.80202e9	+	3.48887e9i	−0.459069	+	0.333533i
$730$	8.23933e9	−	3.58191e8i	0.783902	−	0.0340788i
$731$	−1.31389e10	−	9.54597e9i	−1.24408	−	0.903876i
$732$	1.51253e9			0.142532
$733$	−1.06836e10	−	7.76211e9i	−1.00197	−	0.727974i	−0.0394605	−	0.999221i	$-0.512564\pi$
$733$	−1.06836e10	−	7.76211e9i	−1.00197	−	0.727974i	−0.962510	+	0.271247i	$0.912564\pi$
$734$	2.92577e9	−	9.00461e9i	0.273089	−	0.840482i
$735$	1.14730e10	−	4.98768e8i	1.06579	−	0.0463332i
$736$	−3.43733e9	−	1.05790e10i	−0.317796	−	0.978075i
$737$	−1.22739e9	+	3.77751e9i	−0.112939	+	0.347591i
$738$	2.29419e9	−	7.06078e9i	0.210103	−	0.646629i
$739$	−3.47019e9	−	1.06802e10i	−0.316299	−	0.973469i	−0.975216	−	0.221254i	$-0.928985\pi$
$739$	−3.47019e9	−	1.06802e10i	−0.316299	−	0.973469i	0.658917	−	0.752216i	$-0.271015\pi$
$740$	−4.02314e8	+	1.44964e9i	−0.0364968	+	0.131507i
$741$	−2.53772e8	+	7.81029e8i	−0.0229129	+	0.0705185i
$742$	1.82386e10	+	1.32511e10i	1.63900	+	1.19080i
$743$	1.33511e10			1.19414			0.597071	−	0.802188i	$-0.296331\pi$
$743$	1.33511e10			1.19414			0.597071	+	0.802188i	$0.296331\pi$
$744$	7.64947e9	+	5.55766e9i	0.680967	+	0.494751i
$745$	4.25803e9	+	2.81947e9i	0.377278	+	0.249817i
$746$	8.39541e9	−	6.09962e9i	0.740382	−	0.537919i
$747$	−6.53031e9	+	4.74455e9i	−0.573207	+	0.416459i
$748$	8.26061e8	+	2.54236e9i	0.0721700	+	0.222116i
$749$	−9.01882e9			−0.784266
$750$	4.22932e9	−	4.00897e9i	0.366064	−	0.346991i
$751$	−1.63120e10			−1.40530			−0.702649	−	0.711536i	$-0.748000\pi$
$751$	−1.63120e10			−1.40530			−0.702649	+	0.711536i	$0.748000\pi$
$752$	−2.54914e9	−	7.84545e9i	−0.218591	−	0.672752i
$753$	−1.27550e8	+	9.26707e7i	−0.0108868	+	0.00790970i
$754$	−1.86423e9	+	1.35444e9i	−0.158379	+	0.115069i
$755$	−1.71975e10	−	1.13874e10i	−1.45429	−	0.962966i
$756$	4.72563e9	+	3.43337e9i	0.397771	+	0.288998i
$757$	1.13336e10			0.949581			0.474791	−	0.880099i	$-0.342524\pi$
$757$	1.13336e10			0.949581			0.474791	+	0.880099i	$0.342524\pi$
$758$	−4.75691e9	−	3.45610e9i	−0.396719	−	0.288233i
$759$	2.41799e9	−	7.44179e9i	0.200728	−	0.617777i
$760$	−6.18188e8	+	2.22750e9i	−0.0510826	+	0.184064i
$761$	−4.66616e9	−	1.43609e10i	−0.383807	−	1.18124i	−0.937342	−	0.348411i	$-0.886721\pi$
$761$	−4.66616e9	−	1.43609e10i	−0.383807	−	1.18124i	0.553535	−	0.832826i	$-0.313279\pi$
$762$	460068.	−	1.41594e6i	3.76686e−5	−	0.000115932i
$763$	−3.95311e9	+	1.21664e10i	−0.322184	+	0.991579i
$764$	−5.06524e8	−	1.55892e9i	−0.0410935	−	0.126473i
$765$	1.01703e10	−	4.42139e8i	0.821336	−	0.0357062i
$766$	−1.30473e8	+	4.01553e8i	−0.0104886	+	0.0322807i
$767$	4.83840e9	+	3.51530e9i	0.387184	+	0.281306i
$768$	6.12629e9			0.488015
$769$	5.75066e9	+	4.17810e9i	0.456011	+	0.331312i	0.791965	−	0.610567i	$-0.209058\pi$
$769$	5.75066e9	+	4.17810e9i	0.456011	+	0.331312i	−0.335953	+	0.941879i	$0.609058\pi$
$770$	−1.06509e10	+	4.63030e8i	−0.840754	+	0.0365504i
$771$	−2.11101e9	+	1.53374e9i	−0.165882	+	0.120520i
$772$	1.24208e8	−	9.02423e7i	0.00971602	−	0.00705910i
$773$	1.58755e9	+	4.88597e9i	0.123623	+	0.380472i	0.993648	−	0.112536i	$-0.0358973\pi$
$773$	1.58755e9	+	4.88597e9i	0.123623	+	0.380472i	−0.870025	+	0.493008i	$0.835897\pi$
$774$	8.19068e9			0.634931
$775$	3.74960e9	−	1.62136e10i	0.289354	−	1.25119i
$776$	2.36996e9			0.182064
$777$	1.84699e9	+	5.68446e9i	0.141251	+	0.434726i
$778$	−1.15037e10	+	8.35794e9i	−0.875809	+	0.636312i
$779$	−2.39139e9	+	1.73745e9i	−0.181246	+	0.131683i
$780$	−5.86537e8	−	1.56966e9i	−0.0442552	−	0.118434i
$781$	2.86995e9	+	2.08514e9i	0.215574	+	0.156624i
$782$	−2.57812e10			−1.92787
$783$	3.57903e9	+	2.60032e9i	0.266440	+	0.193580i
$784$	−4.50862e9	+	1.38761e10i	−0.334147	+	1.02840i
$785$	1.91832e10	+	1.27023e10i	1.41539	+	0.937210i
$786$	1.60204e9	+	4.93057e9i	0.117678	+	0.362175i
$787$	−9.20647e8	+	2.83346e9i	−0.0673258	+	0.207208i	−0.979060	−	0.203574i	$-0.934744\pi$
$787$	−9.20647e8	+	2.83346e9i	−0.0673258	+	0.207208i	0.911734	+	0.410782i	$0.134744\pi$
$788$	6.50894e8	−	2.00324e9i	0.0473880	−	0.145845i
$789$	−7.64119e8	−	2.35172e9i	−0.0553849	−	0.170457i
$790$	−3.62196e8	−	9.69290e8i	−0.0261366	−	0.0699454i
$791$	−5.25502e9	+	1.61733e10i	−0.377535	+	1.16193i
$792$	−4.73274e9	−	3.43854e9i	−0.338513	−	0.245944i
$793$	7.76965e9			0.553280
$794$	−1.38482e10	−	1.00613e10i	−0.981797	−	0.713318i
$795$	−9.71843e9	+	7.72742e9i	−0.685980	+	0.545443i
$796$	8.21237e8	−	5.96664e8i	0.0577129	−	0.0419309i
$797$	2.60615e9	−	1.89348e9i	0.182346	−	0.132482i	−0.492868	−	0.870104i	$-0.664051\pi$
$797$	2.60615e9	−	1.89348e9i	0.182346	−	0.132482i	0.675214	+	0.737622i	$0.264051\pi$
$798$	6.54055e8	+	2.01298e9i	0.0455622	+	0.140226i
$799$	2.15546e10			1.49495
$800$	−3.25845e9	−	7.68444e9i	−0.225007	−	0.530636i
$801$	1.03202e10			0.709539
$802$	−4.21080e9	−	1.29595e10i	−0.288240	−	0.887112i
$803$	6.72252e9	−	4.88420e9i	0.458171	−	0.332881i
$804$	−1.30173e9	+	9.45759e8i	−0.0883331	+	0.0641778i
$805$	−1.17544e10	+	4.23541e10i	−0.794170	+	2.86160i
$806$	9.05573e9	+	6.57937e9i	0.609187	+	0.442600i
$807$	6.78195e9			0.454253
$808$	1.10351e10	+	8.01745e9i	0.735928	+	0.534683i
$809$	3.76797e9	−	1.15966e10i	0.250200	−	0.770037i	−0.744537	−	0.667581i	$-0.767330\pi$
$809$	3.76797e9	−	1.15966e10i	0.250200	−	0.770037i	0.994738	−	0.102456i	$-0.0326702\pi$
$810$	−4.20095e8	+	3.34031e8i	−0.0277748	+	0.0220846i
$811$	3.05101e9	+	9.39003e9i	0.200849	+	0.618150i	0.999858	+	0.0168314i	$0.00535786\pi$
$811$	3.05101e9	+	9.39003e9i	0.200849	+	0.618150i	−0.799009	+	0.601319i	$0.794642\pi$
$812$	7.84572e8	−	2.41467e9i	0.0514265	−	0.158274i
$813$	−3.64409e9	+	1.12153e10i	−0.237833	+	0.731974i
$814$	−1.09570e9	−	3.37220e9i	−0.0712040	−	0.219143i
$815$	2.19889e9	−	1.74840e9i	0.142282	−	0.113133i
$816$	2.27918e9	−	7.01460e9i	0.146846	−	0.451947i
$817$	−2.63830e9	−	1.91683e9i	−0.169257	−	0.122972i
$818$	4.89285e9			0.312554
$819$	9.44454e9	+	6.86186e9i	0.600741	+	0.436464i
$820$	1.61292e9	−	5.81176e9i	0.102156	−	0.368094i
$821$	−2.31120e10	+	1.67919e10i	−1.45760	+	1.05900i	−0.473614	+	0.880733i	$0.657051\pi$
$821$	−2.31120e10	+	1.67919e10i	−1.45760	+	1.05900i	−0.983981	+	0.178272i	$0.942949\pi$
$822$	−8.33355e9	+	6.05467e9i	−0.523333	+	0.380224i
$823$	4.58443e9	+	1.41094e10i	0.286672	+	0.882287i	0.985892	+	0.167381i	$0.0535308\pi$
$823$	4.58443e9	+	1.41094e10i	0.286672	+	0.882287i	−0.699220	+	0.714907i	$0.746469\pi$
$824$	−2.38405e10			−1.48447
$825$	1.32295e9	−	5.72053e9i	0.0820263	−	0.354689i
$826$	1.54140e10			0.951667
$827$	−1.97253e9	−	6.07083e9i	−0.121270	−	0.373232i	0.871933	−	0.489626i	$-0.162867\pi$
$827$	−1.97253e9	−	6.07083e9i	−0.121270	−	0.373232i	−0.993203	+	0.116394i	$0.962867\pi$
$828$	−4.49694e9	+	3.26722e9i	−0.275303	+	0.200019i
$829$	−9.76243e9	+	7.09282e9i	−0.595137	+	0.432392i	−0.844149	−	0.536108i	$-0.819894\pi$
$829$	−9.76243e9	+	7.09282e9i	−0.595137	+	0.432392i	0.249012	+	0.968500i	$0.419894\pi$
$830$	1.20066e10	−	9.54681e9i	0.728865	−	0.579542i
$831$	7.28349e9	+	5.29176e9i	0.440287	+	0.319887i
$832$	1.27231e10			0.765882
$833$	−3.08423e10	−	2.24082e10i	−1.84880	−	1.34323i
$834$	−2.89693e9	+	8.91583e9i	−0.172925	+	0.532207i
$835$	−7.82419e9	−	2.09387e10i	−0.465090	−	1.24465i
$836$	1.65874e8	+	5.10506e8i	0.00981873	+	0.0302189i
$837$	6.64072e9	−	2.04380e10i	0.391450	−	1.20476i
$838$	5.98417e9	−	1.84174e10i	0.351277	−	1.08112i
$839$	4.15439e9	+	1.27859e10i	0.242851	+	0.747419i	0.995982	+	0.0895489i	$0.0285425\pi$
$839$	4.15439e9	+	1.27859e10i	0.242851	+	0.747419i	−0.753131	+	0.657870i	$0.771457\pi$
$840$	−1.56250e10	−	1.03461e10i	−0.909581	−	0.602283i
$841$	−4.73630e9	+	1.45768e10i	−0.274570	+	0.845039i
$842$	1.53236e10	+	1.11333e10i	0.884645	+	0.642732i
$843$	−9.17116e9			−0.527264
$844$	−6.41664e9	−	4.66196e9i	−0.367375	−	0.266913i
$845$	3.12615e9	+	8.36605e9i	0.178243	+	0.477004i
$846$	−8.79459e9	+	6.38964e9i	−0.499366	+	0.362811i
$847$	1.51225e10	−	1.09871e10i	0.855128	−	0.621287i
$848$	−4.87467e9	−	1.50027e10i	−0.274511	−	0.844858i
$849$	−1.22743e10			−0.688367
$850$	−1.92726e10	+	1.67886e9i	−1.07640	+	0.0937664i
$851$	−1.46190e10			−0.813139
$852$	4.44081e8	+	1.36674e9i	0.0245994	+	0.0757091i
$853$	−1.80519e8	+	1.31155e8i	−0.00995866	+	0.00723539i	−0.592753	−	0.805384i	$-0.701959\pi$
$853$	−1.80519e8	+	1.31155e8i	−0.00995866	+	0.00723539i	0.582795	+	0.812619i	$0.301959\pi$
$854$	1.62006e10	−	1.17704e10i	0.890078	−	0.646679i
$855$	2.04221e9	−	8.87817e7i	0.111743	−	0.00485783i
$856$	7.60854e9	+	5.52793e9i	0.414613	+	0.301234i
$857$	2.68550e10			1.45745			0.728724	−	0.684808i	$-0.240114\pi$
$857$	2.68550e10			1.45745			0.728724	+	0.684808i	$0.240114\pi$
$858$	3.19507e9	+	2.32135e9i	0.172693	+	0.125469i
$859$	−1.22402e9	+	3.76715e9i	−0.0658890	+	0.202785i	−0.978581	−	0.205863i	$-0.934000\pi$
$859$	−1.22402e9	+	3.76715e9i	−0.0658890	+	0.202785i	0.912692	+	0.408649i	$0.134000\pi$
$860$	6.64788e9	−	2.89005e8i	0.356401	−	0.0154939i
$861$	−7.40478e9	−	2.27896e10i	−0.395368	−	1.21682i
$862$	−2.07213e9	+	6.37737e9i	−0.110190	+	0.339130i
$863$	5.31167e8	−	1.63476e9i	0.0281315	−	0.0865800i	−0.936005	−	0.351987i	$-0.885506\pi$
$863$	5.31167e8	−	1.63476e9i	0.0281315	−	0.0865800i	0.964137	+	0.265407i	$0.0855062\pi$
$864$	−3.33073e9	−	1.02509e10i	−0.175687	−	0.540710i
$865$	4.81376e8	−	1.73453e9i	0.0252888	−	0.0911222i
$866$	−3.20965e9	+	9.87830e9i	−0.167937	+	0.516856i
$867$	6.23560e9	+	4.53043e9i	0.324946	+	0.236087i
$868$	−1.23332e10			−0.640112
$869$	−8.43463e8	−	6.12812e8i	−0.0436010	−	0.0316780i
$870$	−2.72721e9	−	1.80584e9i	−0.140411	−	0.0929738i
$871$	−6.68680e9	+	4.85824e9i	−0.342890	+	0.249124i
$872$	1.07922e10	−	7.84097e9i	0.551190	−	0.400463i
$873$	−6.47598e8	−	1.99310e9i	−0.0329424	−	0.101386i
$874$	−5.17687e9			−0.262287
$875$	−6.02883e9	+	3.24270e10i	−0.304232	+	1.63636i
$876$	3.36618e9			0.169189
$877$	−2.54091e9	−	7.82012e9i	−0.127201	−	0.391484i	0.867095	−	0.498143i	$-0.165985\pi$
$877$	−2.54091e9	−	7.82012e9i	−0.127201	−	0.391484i	−0.994296	+	0.106659i	$0.965985\pi$
$878$	1.15162e10	−	8.36697e9i	0.574218	−	0.417194i
$879$	8.82605e9	−	6.41250e9i	0.438334	−	0.318469i
$880$	6.21983e9	+	4.11849e9i	0.307673	+	0.203727i
$881$	3.96875e9	+	2.88347e9i	0.195541	+	0.142069i	0.681248	−	0.732053i	$-0.261438\pi$
$881$	3.96875e9	+	2.88347e9i	0.195541	+	0.142069i	−0.485707	+	0.874122i	$0.661438\pi$
$882$	1.92268e10			0.943556
$883$	−1.00100e10	−	7.27271e9i	−0.489298	−	0.355495i	0.315617	−	0.948887i	$-0.397789\pi$
$883$	−1.00100e10	−	7.27271e9i	−0.489298	−	0.355495i	−0.804914	+	0.593391i	$0.797789\pi$
$884$	−1.71899e9	+	5.29052e9i	−0.0836934	+	0.257582i
$885$	−2.27018e9	+	8.18007e9i	−0.110093	+	0.396694i
$886$	9.88760e8	+	3.04309e9i	0.0477609	+	0.146993i
$887$	1.44998e9	−	4.46259e9i	0.0697638	−	0.214711i	−0.910096	−	0.414397i	$-0.863992\pi$
$887$	1.44998e9	−	4.46259e9i	0.0697638	−	0.214711i	0.979860	+	0.199687i	$0.0639924\pi$
$888$	1.92601e9	−	5.92766e9i	0.0923027	−	0.284078i
$889$	2.60394e6	+	8.01409e6i	0.000124301	+	0.000382559i
$890$	−1.95936e10	+	8.51800e8i	−0.931644	+	0.0405017i
$891$	−1.67107e8	+	5.14301e8i	−0.00791447	+	0.0243582i
$892$	−1.94566e9	−	1.41360e9i	−0.0917887	−	0.0666884i
$893$	4.32817e9			0.203387
$894$	−3.94467e9	−	2.86597e9i	−0.184642	−	0.134150i
$895$	4.78461e9	−	2.08003e8i	0.223083	−	0.00969814i
$896$	9.81839e9	−	7.13347e9i	0.455997	−	0.331301i
$897$	1.31732e10	−	9.57088e9i	0.609421	−	0.442770i
$898$	−8.38460e9	−	2.58052e10i	−0.386381	−	1.18916i
$899$	−9.34075e9			−0.428768
$900$	−3.14890e9	+	2.73523e9i	−0.143983	+	0.125068i
$901$	4.12184e10			1.87739
$902$	4.39275e9	+	1.35195e10i	0.199303	+	0.613391i
$903$	2.13875e10	−	1.55390e10i	0.966615	−	0.702287i
$904$	1.43464e10	−	1.04233e10i	0.645884	−	0.469262i
$905$	−3.14413e9	−	8.41416e9i	−0.141004	−	0.377347i
$906$	1.59319e10	+	1.15752e10i	0.711737	+	0.517107i
$907$	−2.53809e10			−1.12949			−0.564744	−	0.825266i	$-0.691025\pi$
$907$	−2.53809e10			−1.12949			−0.564744	+	0.825266i	$0.691025\pi$
$908$	5.54476e9	+	4.02850e9i	0.245800	+	0.178584i
$909$	3.72719e9	−	1.14711e10i	0.164592	−	0.506561i
$910$	−1.84974e10	−	1.22482e10i	−0.813703	−	0.538798i
$911$	−1.03645e9	−	3.18987e9i	−0.0454186	−	0.139784i	0.925776	−	0.378074i	$-0.123413\pi$
$911$	−1.03645e9	−	3.18987e9i	−0.0454186	−	0.139784i	−0.971194	+	0.238289i	$0.923413\pi$
$912$	4.57661e8	−	1.40853e9i	0.0199784	−	0.0614873i
$913$	4.77602e9	−	1.46991e10i	0.207691	−	0.639208i
$914$	2.61120e8	+	8.03644e8i	0.0113117	+	0.0348139i
$915$	3.86041e9	+	1.03310e10i	0.166594	+	0.445831i
$916$	1.10109e9	−	3.38882e9i	0.0473359	−	0.145685i
$917$	−2.37387e10	−	1.72472e10i	−1.01663	−	0.738626i
$918$	−2.49816e10			−1.06579
$919$	−6.92301e9	−	5.02986e9i	−0.294233	−	0.213772i	0.430869	−	0.902415i	$-0.358207\pi$
$919$	−6.92301e9	−	5.02986e9i	−0.294233	−	0.213772i	−0.725101	+	0.688642i	$0.758207\pi$
$920$	3.58765e10	−	2.85265e10i	1.51898	−	1.20779i
$921$	−6.63663e9	+	4.82179e9i	−0.279923	+	0.203376i
$922$	−1.72086e10	+	1.25028e10i	−0.723082	+	0.525350i
$923$	2.28119e9	+	7.02078e9i	0.0954894	+	0.293886i
$924$	−4.35143e9			−0.181460
$925$	−1.09284e10	+	9.51984e8i	−0.454004	+	0.0395488i
$926$	3.10421e10			1.28473
$927$	6.51448e9	+	2.00495e10i	0.268597	+	0.826655i
$928$	−3.79021e9	+	2.75375e9i	−0.155684	+	0.113111i
$929$	−2.02982e10	+	1.47475e10i	−0.830619	+	0.603480i	−0.919734	−	0.392542i	$-0.871596\pi$
$929$	−2.02982e10	+	1.47475e10i	−0.830619	+	0.603480i	0.0891157	+	0.996021i	$0.471596\pi$
$930$	−4.24896e9	+	1.53101e10i	−0.173218	+	0.624149i
$931$	−6.19315e9	−	4.49959e9i	−0.251529	−	0.182746i
$932$	1.01310e10			0.409918
$933$	1.66677e10	+	1.21098e10i	0.671879	+	0.488148i
$934$	−7.78013e9	+	2.39448e10i	−0.312445	+	0.961606i
$935$	−1.52568e10	+	1.21311e10i	−0.610410	+	0.485356i
$936$	−3.76183e9	−	1.15777e10i	−0.149946	−	0.461485i
$937$	−2.94908e8	+	9.07632e8i	−0.0117111	+	0.0360430i	−0.956741	−	0.290940i	$-0.906032\pi$
$937$	−2.94908e8	+	9.07632e8i	−0.0117111	+	0.0360430i	0.945030	+	0.326983i	$0.106032\pi$
$938$	−6.58286e9	+	2.02600e10i	−0.260438	+	0.801546i
$939$	−7.43370e9	−	2.28786e10i	−0.293005	−	0.901777i
$940$	−6.91258e9	+	5.49640e9i	−0.271452	+	0.215840i
$941$	−4.73528e9	+	1.45737e10i	−0.185260	+	0.570172i	−0.999953	−	0.00972119i	$-0.996906\pi$
$941$	−4.73528e9	+	1.45737e10i	−0.185260	+	0.570172i	0.814693	+	0.579893i	$0.196906\pi$
$942$	−1.77715e10	−	1.29117e10i	−0.692700	−	0.503276i
$943$	5.86091e10			2.27601
$944$	−8.72574e9	−	6.33962e9i	−0.337598	−	0.245280i
$945$	−1.13898e10	+	4.10406e10i	−0.439042	+	1.58198i
$946$	−1.26878e10	+	9.21820e9i	−0.487266	+	0.354020i
$947$	−1.52901e10	+	1.11089e10i	−0.585038	+	0.425055i	−0.840537	−	0.541754i	$-0.817760\pi$
$947$	−1.52901e10	+	1.11089e10i	−0.585038	+	0.425055i	0.255499	+	0.966809i	$0.417760\pi$
$948$	−1.30513e8	−	4.01678e8i	−0.00497536	−	0.0153126i
$949$	1.72916e10			0.656757
$950$	−3.86994e9	+	3.37115e8i	−0.146444	+	0.0127569i
$951$	−2.07254e10			−0.781396
$952$	1.92244e10	+	5.91665e10i	0.722142	+	2.22253i
$953$	−2.80372e10	+	2.03702e10i	−1.04932	+	0.762378i	−0.972084	−	0.234635i	$-0.924611\pi$
$953$	−2.80372e10	+	2.03702e10i	−1.04932	+	0.762378i	−0.0772395	+	0.997013i	$0.524611\pi$
$954$	−1.68177e10	+	1.22188e10i	−0.627116	+	0.455627i
$955$	9.35515e9	−	7.43856e9i	0.347567	−	0.276361i
$956$	−4.40928e9	−	3.20353e9i	−0.163217	−	0.118584i
$957$	−3.29563e9			−0.121548
$958$	2.67430e9	+	1.94299e9i	0.0982723	+	0.0713990i
$959$	1.80162e10	−	5.54481e10i	0.659626	−	2.03012i
$960$	6.32159e9	+	1.69175e10i	0.230609	+	0.617145i
$961$	5.51945e9	+	1.69871e10i	0.200615	+	0.617430i
$962$	2.28009e9	−	7.01739e9i	0.0825732	−	0.254134i
$963$	2.56985e9	−	7.90919e9i	0.0927291	−	0.285391i
$964$	−2.78711e9	−	8.57784e9i	−0.100204	−	0.308396i
$965$	9.33400e8	+	6.18055e8i	0.0334366	+	0.0221402i
$966$	1.29684e10	−	3.99127e10i	0.462878	−	1.42459i
$967$	−7.40439e9	−	5.37960e9i	−0.263328	−	0.191319i	0.448285	−	0.893891i	$-0.352035\pi$
$967$	−7.40439e9	−	5.37960e9i	−0.263328	−	0.191319i	−0.711613	+	0.702572i	$0.752035\pi$
$968$	−1.94921e10			−0.690710
$969$	3.13074e9	+	2.27461e9i	0.110539	+	0.0803109i
$970$	1.39401e9	+	3.73058e9i	0.0490416	+	0.131243i
$971$	−1.26051e10	+	9.15813e9i	−0.441853	+	0.321025i	−0.786371	−	0.617755i	$-0.788043\pi$
$971$	−1.26051e10	+	9.15813e9i	−0.441853	+	0.321025i	0.344518	+	0.938780i	$0.388043\pi$
$972$	−7.01961e9	+	5.10005e9i	−0.245178	+	0.178132i
$973$	−1.63963e10	−	5.04627e10i	−0.570626	−	1.75621i
$974$	−3.08998e9			−0.107152
$975$	9.22429e9	−	8.01249e9i	0.318725	−	0.276854i
$976$	−1.40121e10			−0.482423
$977$	−1.29689e10	−	3.99143e10i	−0.444911	−	1.36930i	−0.882581	−	0.470160i	$-0.844196\pi$
$977$	−1.29689e10	−	3.99143e10i	−0.444911	−	1.36930i	0.437670	−	0.899136i	$-0.355804\pi$
$978$	−2.16995e9	+	1.57656e9i	−0.0741759	+	0.0538919i
$979$	−1.59866e10	+	1.16149e10i	−0.544523	+	0.395619i
$980$	1.56053e10	−	6.78413e8i	0.529639	−	0.0230252i
$981$	−9.54312e9	−	6.93348e9i	−0.322737	−	0.234482i
$982$	6.65068e9			0.224117
$983$	2.57112e10	+	1.86803e10i	0.863346	+	0.627258i	0.928793	−	0.370598i	$-0.120847\pi$
$983$	2.57112e10	+	1.86803e10i	0.863346	+	0.627258i	−0.0654472	+	0.997856i	$0.520847\pi$
$984$	−7.72158e9	+	2.37646e10i	−0.258359	+	0.795147i
$985$	1.53441e10	−	6.67058e8i	0.511581	−	0.0222401i
$986$	3.35546e9	+	1.03270e10i	0.111476	+	0.343089i
$987$	−1.08424e10	+	3.33693e10i	−0.358933	+	1.10468i
$988$	−3.45175e8	+	1.06234e9i	−0.0113865	+	0.0350440i
$989$	1.99812e10	+	6.14957e10i	0.656801	+	2.02142i
$990$	2.62884e9	−	9.47240e9i	0.0861075	−	0.310268i
$991$	9.92485e9	−	3.05455e10i	0.323941	−	0.996989i	−0.647975	−	0.761662i	$-0.724384\pi$
$991$	9.92485e9	−	3.05455e10i	0.323941	−	0.996989i	0.971916	−	0.235327i	$-0.0756161\pi$
$992$	1.84114e10	+	1.33767e10i	0.598821	+	0.435069i
$993$	4.07802e9			0.132168
$994$	1.53925e10	+	1.11833e10i	0.497114	+	0.361174i
$995$	6.17145e9	+	4.08646e9i	0.198612	+	0.131512i
$996$	5.06529e9	−	3.68015e9i	0.162441	−	0.118021i
$997$	2.11083e10	−	1.53361e10i	0.674559	−	0.490096i	−0.196989	−	0.980406i	$-0.563116\pi$
$997$	2.11083e10	−	1.53361e10i	0.674559	−	0.490096i	0.871548	+	0.490310i	$0.163116\pi$
$998$	1.49342e10	+	4.59628e10i	0.475582	+	1.46369i
$999$	−1.41656e10			−0.449529

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.8.d.a.6.6	✓	68
25.11	even	5		625.8.a.d.1.11		34
25.14	even	10		625.8.a.c.1.24		34
25.21	even	5	inner	25.8.d.a.21.6	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.8.d.a.6.6	✓	68	1.1	even	1	trivial
25.8.d.a.21.6	yes	68	25.21	even	5	inner
625.8.a.c.1.24		34	25.14	even	10
625.8.a.d.1.11		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)

\(f(q)\)	\(=\)	\(q+(-2.92617 - 9.00581i) q^{2} +(22.7999 - 16.5651i) q^{3} +(31.0120 - 22.5315i) q^{4} +(233.049 + 154.315i) q^{5} +(-215.899 - 156.860i) q^{6} +1510.43 q^{7} +(-1274.24 - 925.792i) q^{8} +(-430.387 + 1324.59i) q^{9} +O(q^{10})\)	\(q+(-2.92617 - 9.00581i) q^{2} +(22.7999 - 16.5651i) q^{3} +(31.0120 - 22.5315i) q^{4} +(233.049 + 154.315i) q^{5} +(-215.899 - 156.860i) q^{6} +1510.43 q^{7} +(-1274.24 - 925.792i) q^{8} +(-430.387 + 1324.59i) q^{9} +(707.789 - 2550.35i) q^{10} +(-824.075 - 2536.24i) q^{11} +(333.833 - 1027.43i) q^{12} +(1714.86 - 5277.79i) q^{13} +(-4419.77 - 13602.7i) q^{14} +(7869.75 - 342.124i) q^{15} +(-3092.64 + 9518.16i) q^{16} +(-21155.9 - 15370.7i) q^{17} +13188.4 q^{18} +(-4248.12 - 3086.44i) q^{19} +(10704.3 - 465.349i) q^{20} +(34437.7 - 25020.4i) q^{21} +(-20429.5 + 14842.9i) q^{22} +(32173.2 + 99018.8i) q^{23} -44388.5 q^{24} +(30498.9 + 71925.9i) q^{25} -52548.8 q^{26} +(31175.4 + 95948.0i) q^{27} +(46841.4 - 34032.3i) q^{28} +(35476.1 - 25774.9i) q^{29} +(-26109.3 - 69872.3i) q^{30} +(-172330. - 125205. i) q^{31} -106838. q^{32} +(-60801.9 - 44175.2i) q^{33} +(-76519.7 + 235503. i) q^{34} +(352005. + 233082. i) q^{35} +(16498.0 + 50775.5i) q^{36} +(-43390.0 + 133541. i) q^{37} +(-15365.2 + 47289.2i) q^{38} +(-48328.6 - 148740. i) q^{39} +(-154098. - 412390. i) q^{40} +(173954. - 535377. i) q^{41} +(-326100. - 236925. i) q^{42} +621050. q^{43} +(-82701.5 - 60086.1i) q^{44} +(-304706. + 242281. i) q^{45} +(797601. - 579491. i) q^{46} +(-666841. + 484489. i) q^{47} +(87157.5 + 268243. i) q^{48} +1.45786e6 q^{49} +(558506. - 485135. i) q^{50} -736970. q^{51} +(-65735.5 - 202313. i) q^{52} +(-1.27519e6 + 926478. i) q^{53} +(772866. - 561520. i) q^{54} +(199329. - 718236. i) q^{55} +(-1.92466e6 - 1.39834e6i) q^{56} -147984. q^{57} +(-335933. - 244070. i) q^{58} +(-333028. + 1.02495e6i) q^{59} +(236348. - 187927. i) q^{60} +(432651. + 1.33156e6i) q^{61} +(-623307. + 1.91834e6i) q^{62} +(-650069. + 2.00071e6i) q^{63} +(708484. + 2.18049e6i) q^{64} +(1.21409e6 - 965358. i) q^{65} +(-219917. + 676835. i) q^{66} +(-1.20496e6 - 875454. i) q^{67} -1.00241e6 q^{68} +(2.37380e6 + 1.72467e6i) q^{69} +(1.06907e6 - 3.85212e6i) q^{70} +(-1.07619e6 + 781901. i) q^{71} +(1.77472e6 - 1.28941e6i) q^{72} +(962881. + 2.96344e6i) q^{73} +1.32961e6 q^{74} +(1.88683e6 + 1.13469e6i) q^{75} -201285. q^{76} +(-1.24471e6 - 3.83081e6i) q^{77} +(-1.19811e6 + 870476. i) q^{78} +(316287. - 229796. i) q^{79} +(-2.18953e6 + 1.74096e6i) q^{80} +(-164053. - 119192. i) q^{81} -5.33052e6 q^{82} +(4.68875e6 + 3.40658e6i) q^{83} +(504232. - 1.55187e6i) q^{84} +(-2.55845e6 - 6.84680e6i) q^{85} +(-1.81730e6 - 5.59306e6i) q^{86} +(381889. - 1.17533e6i) q^{87} +(-1.29796e6 + 3.99471e6i) q^{88} +(-2.28979e6 - 7.04725e6i) q^{89} +(3.07355e6 + 2.03517e6i) q^{90} +(2.59017e6 - 7.97174e6i) q^{91} +(3.22880e6 + 2.34586e6i) q^{92} -6.00315e6 q^{93} +(6.31450e6 + 4.58775e6i) q^{94} +(-513738. - 1.37484e6i) q^{95} +(-2.43590e6 + 1.76979e6i) q^{96} +(-1.21732e6 + 884433. i) q^{97} +(-4.26593e6 - 1.31292e7i) q^{98} +3.71416e6 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

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