LMFDB - Embedded newform 250.2.g.b.231.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [250,2,Mod(11,250)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(250, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([38]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("250.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 250 = 2 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	250.g (of order $25$, degree $20$, 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:	$1.99626005053$
Analytic rank:	$0$
Dimension:	$140$
Relative dimension:	$7$ over $\Q(\zeta_{25})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{25}]$

Embedding invariants

Embedding label			231.7
Character	$\chi$	$=$	250.231
Dual form			250.2.g.b.171.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.535827 - 0.844328i) q^{2} +(2.45317 - 2.30368i) q^{3} +(-0.425779 - 0.904827i) q^{4} +(0.826966 + 2.07753i) q^{5} +(-0.630588 - 3.30566i) q^{6} +(-1.48185 + 1.07663i) q^{7} +(-0.992115 - 0.125333i) q^{8} +(0.522733 - 8.30860i) q^{9} +O(q^{10})$	\(q+(0.535827 - 0.844328i) q^{2} +(2.45317 - 2.30368i) q^{3} +(-0.425779 - 0.904827i) q^{4} +(0.826966 + 2.07753i) q^{5} +(-0.630588 - 3.30566i) q^{6} +(-1.48185 + 1.07663i) q^{7} +(-0.992115 - 0.125333i) q^{8} +(0.522733 - 8.30860i) q^{9} +(2.19723 + 0.414965i) q^{10} +(-1.26311 + 1.99034i) q^{11} +(-3.12895 - 1.23884i) q^{12} +(-0.224187 + 3.56335i) q^{13} +(0.115012 + 1.82806i) q^{14} +(6.81466 + 3.19147i) q^{15} +(-0.637424 + 0.770513i) q^{16} +(0.186113 - 0.395511i) q^{17} +(-6.73509 - 4.89333i) q^{18} +(0.151227 + 0.142011i) q^{19} +(1.52770 - 1.63283i) q^{20} +(-1.15503 + 6.05488i) q^{21} +(1.00369 + 2.13295i) q^{22} +(-3.49365 - 0.897017i) q^{23} +(-2.72256 + 1.97805i) q^{24} +(-3.63225 + 3.43609i) q^{25} +(2.88851 + 2.09862i) q^{26} +(-11.4227 - 13.8077i) q^{27} +(1.60511 + 0.882414i) q^{28} +(-0.0825469 - 0.0453805i) q^{29} +(6.34613 - 4.04373i) q^{30} +(-2.88930 + 6.14007i) q^{31} +(0.309017 + 0.951057i) q^{32} +(1.48649 + 7.79244i) q^{33} +(-0.234217 - 0.369066i) q^{34} +(-3.46217 - 2.18826i) q^{35} +(-7.74042 + 3.06465i) q^{36} +(7.52562 - 9.09691i) q^{37} +(0.200935 - 0.0515914i) q^{38} +(7.65886 + 9.25797i) q^{39} +(-0.560062 - 2.16479i) q^{40} +(10.9707 - 2.81679i) q^{41} +(4.49341 + 4.21959i) q^{42} +(2.87655 - 8.85310i) q^{43} +(2.33871 + 0.295448i) q^{44} +(17.6936 - 5.78494i) q^{45} +(-2.62937 + 2.46914i) q^{46} +(-8.41703 + 1.06332i) q^{47} +(0.211307 + 3.35863i) q^{48} +(-1.12636 + 3.46658i) q^{49} +(0.954929 + 4.90796i) q^{50} +(-0.454564 - 1.39900i) q^{51} +(3.31967 - 1.31435i) q^{52} +(-1.09003 + 5.71416i) q^{53} +(-17.7788 + 2.24599i) q^{54} +(-5.17953 - 0.978199i) q^{55} +(1.60511 - 0.882414i) q^{56} +0.698134 q^{57} +(-0.0825469 + 0.0453805i) q^{58} +(-10.7045 - 4.23819i) q^{59} +(-0.0138111 - 7.52496i) q^{60} +(3.76182 + 0.965870i) q^{61} +(3.63607 + 5.72952i) q^{62} +(8.17067 + 12.8749i) q^{63} +(0.968583 + 0.248690i) q^{64} +(-7.58835 + 2.48101i) q^{65} +(7.37587 + 2.92031i) q^{66} +(3.70745 - 2.03819i) q^{67} -0.437112 q^{68} +(-10.6370 + 5.84773i) q^{69} +(-3.70273 + 1.75068i) q^{70} +(11.4081 - 1.44118i) q^{71} +(-1.55995 + 8.17757i) q^{72} +(4.76908 - 1.88821i) q^{73} +(-3.64835 - 11.2285i) q^{74} +(-0.994885 + 16.7969i) q^{75} +(0.0641064 - 0.197299i) q^{76} +(-0.271117 - 4.30928i) q^{77} +(11.9206 - 1.50592i) q^{78} +(2.41586 - 2.26864i) q^{79} +(-2.12789 - 0.687079i) q^{80} +(-35.0524 - 4.42815i) q^{81} +(3.50009 - 10.7722i) q^{82} +(0.0752966 + 0.0707083i) q^{83} +(5.97041 - 1.53294i) q^{84} +(0.975596 + 0.0595818i) q^{85} +(-5.93359 - 7.17248i) q^{86} +(-0.307044 + 0.0788356i) q^{87} +(1.50260 - 1.81633i) q^{88} +(-9.61745 + 3.80782i) q^{89} +(4.59634 - 18.0390i) q^{90} +(-3.50419 - 5.52172i) q^{91} +(0.675879 + 3.54308i) q^{92} +(7.05683 + 21.7187i) q^{93} +(-3.61228 + 7.67649i) q^{94} +(-0.169973 + 0.431616i) q^{95} +(2.94901 + 1.62123i) q^{96} +(4.05624 + 2.22993i) q^{97} +(2.32340 + 2.80851i) q^{98} +(15.8766 + 11.5351i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q - 5 q^{5} - 10 q^{7} - 10 q^{9}+O(q^{10}) $ 140 * q - 5 * q^5 - 10 * q^7 - 10 * q^9	$ 140 q - 5 q^{5} - 10 q^{7} - 10 q^{9} + 20 q^{10} - 10 q^{11} + 20 q^{12} + 20 q^{14} - 10 q^{15} - 5 q^{17} - 50 q^{18} + 40 q^{19} - 10 q^{20} - 5 q^{21} - 10 q^{22} + 10 q^{23} - 5 q^{24} - 5 q^{25} - 35 q^{26} + 30 q^{27} - 5 q^{28} - 10 q^{29} - 10 q^{30} + 35 q^{31} - 35 q^{32} - 55 q^{33} - 15 q^{34} - 25 q^{35} - 10 q^{36} - 25 q^{37} - 30 q^{39} + 25 q^{41} - 5 q^{42} - 45 q^{43} + 40 q^{44} - 5 q^{45} + 90 q^{47} - 5 q^{48} - 65 q^{49} + 30 q^{50} - 80 q^{51} - 50 q^{53} - 5 q^{54} - 35 q^{55} - 5 q^{56} + 40 q^{57} - 10 q^{58} + 45 q^{59} + 15 q^{60} + 45 q^{61} - 45 q^{62} - 75 q^{63} - 60 q^{65} + 15 q^{66} - 45 q^{67} + 10 q^{68} - 125 q^{69} - 15 q^{70} - 5 q^{71} - 5 q^{72} - 50 q^{73} + 20 q^{74} - 130 q^{75} - 5 q^{76} + 10 q^{77} + 10 q^{78} - 50 q^{79} - 5 q^{80} + 15 q^{81} + 40 q^{82} + 25 q^{83} - 50 q^{84} - 95 q^{85} - 10 q^{86} + 80 q^{87} - 10 q^{88} - 65 q^{89} - 10 q^{90} + 65 q^{91} - 25 q^{92} - 10 q^{93} - 35 q^{94} + 80 q^{95} - 40 q^{97} - 25 q^{98} + 90 q^{99}+O(q^{100}) $ 140 * q - 5 * q^5 - 10 * q^7 - 10 * q^9 + 20 * q^10 - 10 * q^11 + 20 * q^12 + 20 * q^14 - 10 * q^15 - 5 * q^17 - 50 * q^18 + 40 * q^19 - 10 * q^20 - 5 * q^21 - 10 * q^22 + 10 * q^23 - 5 * q^24 - 5 * q^25 - 35 * q^26 + 30 * q^27 - 5 * q^28 - 10 * q^29 - 10 * q^30 + 35 * q^31 - 35 * q^32 - 55 * q^33 - 15 * q^34 - 25 * q^35 - 10 * q^36 - 25 * q^37 - 30 * q^39 + 25 * q^41 - 5 * q^42 - 45 * q^43 + 40 * q^44 - 5 * q^45 + 90 * q^47 - 5 * q^48 - 65 * q^49 + 30 * q^50 - 80 * q^51 - 50 * q^53 - 5 * q^54 - 35 * q^55 - 5 * q^56 + 40 * q^57 - 10 * q^58 + 45 * q^59 + 15 * q^60 + 45 * q^61 - 45 * q^62 - 75 * q^63 - 60 * q^65 + 15 * q^66 - 45 * q^67 + 10 * q^68 - 125 * q^69 - 15 * q^70 - 5 * q^71 - 5 * q^72 - 50 * q^73 + 20 * q^74 - 130 * q^75 - 5 * q^76 + 10 * q^77 + 10 * q^78 - 50 * q^79 - 5 * q^80 + 15 * q^81 + 40 * q^82 + 25 * q^83 - 50 * q^84 - 95 * q^85 - 10 * q^86 + 80 * q^87 - 10 * q^88 - 65 * q^89 - 10 * q^90 + 65 * q^91 - 25 * q^92 - 10 * q^93 - 35 * q^94 + 80 * q^95 - 40 * q^97 - 25 * q^98 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/250\mathbb{Z}\right)^\times$.

$n$	$127$
$\chi(n)$	$e\left(\frac{17}{25}\right)$

Coefficient data

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

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

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

$2$	0.535827	−	0.844328i	0.378887	−	0.597030i
$2$	0.535827	−	0.844328i	0.378887	−	0.597030i
$3$	2.45317	−	2.30368i	1.41634	−	1.33003i	0.545819	−	0.837903i	$-0.316218\pi$
$3$	2.45317	−	2.30368i	1.41634	−	1.33003i	0.870522	−	0.492130i	$-0.163782\pi$
$4$	−0.425779	−	0.904827i	−0.212890	−	0.452414i
$5$	0.826966	+	2.07753i	0.369830	+	0.929099i
$5$	0.826966	+	2.07753i	0.369830	+	0.929099i
$6$	−0.630588	−	3.30566i	−0.257437	−	1.34953i
$7$	−1.48185	+	1.07663i	−0.560088	+	0.406928i	−0.831491	−	0.555538i	$-0.812512\pi$
$7$	−1.48185	+	1.07663i	−0.560088	+	0.406928i	0.271403	+	0.962466i	$0.412512\pi$
$8$	−0.992115	−	0.125333i	−0.350766	−	0.0443120i
$9$	0.522733	−	8.30860i	0.174244	−	2.76953i
$10$	2.19723	+	0.414965i	0.694824	+	0.131224i
$11$	−1.26311	+	1.99034i	−0.380841	+	0.600109i	−0.979633	−	0.200795i	$-0.935647\pi$
$11$	−1.26311	+	1.99034i	−0.380841	+	0.600109i	0.598793	+	0.800904i	$0.295647\pi$
$12$	−3.12895	−	1.23884i	−0.903249	−	0.357622i
$13$	−0.224187	+	3.56335i	−0.0621782	+	0.988295i	0.836019	+	0.548701i	$0.184877\pi$
$13$	−0.224187	+	3.56335i	−0.0621782	+	0.988295i	−0.898197	+	0.439593i	$0.855123\pi$
$14$	0.115012	+	1.82806i	0.0307381	+	0.488569i
$15$	6.81466	+	3.19147i	1.75954	+	0.824035i
$16$	−0.637424	+	0.770513i	−0.159356	+	0.192628i
$17$	0.186113	−	0.395511i	0.0451391	−	0.0959256i	−0.880985	−	0.473143i	$-0.843119\pi$
$17$	0.186113	−	0.395511i	0.0451391	−	0.0959256i	0.926125	+	0.377218i	$0.123119\pi$
$18$	−6.73509	−	4.89333i	−1.58748	−	1.15337i
$19$	0.151227	+	0.142011i	0.0346938	+	0.0325796i	0.701700	−	0.712472i	$-0.252425\pi$
$19$	0.151227	+	0.142011i	0.0346938	+	0.0325796i	−0.667006	+	0.745052i	$0.732425\pi$
$20$	1.52770	−	1.63283i	0.341604	−	0.365112i
$21$	−1.15503	+	6.05488i	−0.252048	+	1.32128i
$22$	1.00369	+	2.13295i	0.213987	+	0.454747i
$23$	−3.49365	−	0.897017i	−0.728477	−	0.187041i	−0.133803	−	0.991008i	$-0.542719\pi$
$23$	−3.49365	−	0.897017i	−0.728477	−	0.187041i	−0.594674	+	0.803967i	$0.702719\pi$
$24$	−2.72256	+	1.97805i	−0.555740	+	0.403769i
$25$	−3.63225	+	3.43609i	−0.726451	+	0.687218i
$26$	2.88851	+	2.09862i	0.566483	+	0.411574i
$27$	−11.4227	−	13.8077i	−2.19831	−	2.65730i
$28$	1.60511	+	0.882414i	0.303336	+	0.166761i
$29$	−0.0825469	−	0.0453805i	−0.0153286	−	0.00842695i	0.474071	−	0.880487i	$-0.342784\pi$
$29$	−0.0825469	−	0.0453805i	−0.0153286	−	0.00842695i	−0.489400	+	0.872060i	$0.662784\pi$
$30$	6.34613	−	4.04373i	1.15864	−	0.738281i
$31$	−2.88930	+	6.14007i	−0.518933	+	1.10279i	0.457943	+	0.888981i	$0.348586\pi$
$31$	−2.88930	+	6.14007i	−0.518933	+	1.10279i	−0.976876	+	0.213807i	$0.931414\pi$
$32$	0.309017	+	0.951057i	0.0546270	+	0.168125i
$33$	1.48649	+	7.79244i	0.258764	+	1.35649i
$34$	−0.234217	−	0.369066i	−0.0401678	−	0.0632943i
$35$	−3.46217	−	2.18826i	−0.585214	−	0.369883i
$36$	−7.74042	+	3.06465i	−1.29007	+	0.510775i
$37$	7.52562	−	9.09691i	1.23720	−	1.49552i	0.432743	−	0.901517i	$-0.357546\pi$
$37$	7.52562	−	9.09691i	1.23720	−	1.49552i	0.804461	−	0.594006i	$-0.202454\pi$
$38$	0.200935	−	0.0515914i	0.0325960	−	0.00836923i
$39$	7.65886	+	9.25797i	1.22640	+	1.48246i
$40$	−0.560062	−	2.16479i	−0.0885535	−	0.342284i
$41$	10.9707	−	2.81679i	1.71333	−	0.439909i	0.740621	−	0.671923i	$-0.234531\pi$
$41$	10.9707	−	2.81679i	1.71333	−	0.439909i	0.972713	+	0.232013i	$0.0745312\pi$
$42$	4.49341	+	4.21959i	0.693348	+	0.651097i
$43$	2.87655	−	8.85310i	0.438669	−	1.35008i	−0.450610	−	0.892721i	$-0.648794\pi$
$43$	2.87655	−	8.85310i	0.438669	−	1.35008i	0.889280	−	0.457364i	$-0.151206\pi$
$44$	2.33871	+	0.295448i	0.352574	+	0.0445405i
$45$	17.6936	−	5.78494i	2.63761	−	0.862367i
$46$	−2.62937	+	2.46914i	−0.387679	+	0.364055i
$47$	−8.41703	+	1.06332i	−1.22775	+	0.155101i	−0.712335	−	0.701839i	$-0.752362\pi$
$47$	−8.41703	+	1.06332i	−1.22775	+	0.155101i	−0.515416	+	0.856940i	$0.672362\pi$
$48$	0.211307	+	3.35863i	0.0304995	+	0.484776i
$49$	−1.12636	+	3.46658i	−0.160909	+	0.495226i
$50$	0.954929	+	4.90796i	0.135047	+	0.694091i
$51$	−0.454564	−	1.39900i	−0.0636517	−	0.195900i
$52$	3.31967	−	1.31435i	0.460355	−	0.182267i
$53$	−1.09003	+	5.71416i	−0.149728	+	0.784900i	0.825620	+	0.564226i	$0.190826\pi$
$53$	−1.09003	+	5.71416i	−0.149728	+	0.784900i	−0.975348	+	0.220674i	$0.929174\pi$
$54$	−17.7788	+	2.24599i	−2.41939	+	0.305641i
$55$	−5.17953	−	0.978199i	−0.698407	−	0.131900i
$56$	1.60511	−	0.882414i	0.214491	−	0.117918i
$57$	0.698134			0.0924701
$58$	−0.0825469	+	0.0453805i	−0.0108389	+	0.00595875i
$59$	−10.7045	−	4.23819i	−1.39360	−	0.551766i	−0.453071	−	0.891475i	$-0.649671\pi$
$59$	−10.7045	−	4.23819i	−1.39360	−	0.551766i	−0.940531	+	0.339709i	$0.889671\pi$
$60$	−0.0138111	−	7.52496i	−0.00178300	−	0.971468i
$61$	3.76182	+	0.965870i	0.481651	+	0.123667i	0.481706	−	0.876333i	$-0.340017\pi$
$61$	3.76182	+	0.965870i	0.481651	+	0.123667i	−5.46291e−5		1.00000i	$0.500017\pi$
$62$	3.63607	+	5.72952i	0.461781	+	0.727650i
$63$	8.17067	+	12.8749i	1.02941	+	1.62209i
$64$	0.968583	+	0.248690i	0.121073	+	0.0310862i
$65$	−7.58835	+	2.48101i	−0.941219	+	0.307732i
$66$	7.37587	+	2.92031i	0.907907	+	0.359466i
$67$	3.70745	−	2.03819i	0.452937	−	0.249004i	−0.238919	−	0.971039i	$-0.576793\pi$
$67$	3.70745	−	2.03819i	0.452937	−	0.249004i	0.691856	+	0.722035i	$0.256793\pi$
$68$	−0.437112			−0.0530077
$69$	−10.6370	+	5.84773i	−1.28054	+	0.703984i
$70$	−3.70273	+	1.75068i	−0.442561	+	0.209246i
$71$	11.4081	−	1.44118i	1.35389	−	0.171036i	0.585321	−	0.810802i	$-0.300968\pi$
$71$	11.4081	−	1.44118i	1.35389	−	0.171036i	0.768570	+	0.639765i	$0.220968\pi$
$72$	−1.55995	+	8.17757i	−0.183842	+	0.963736i
$73$	4.76908	−	1.88821i	0.558179	−	0.220999i	−0.0720597	−	0.997400i	$-0.522957\pi$
$73$	4.76908	−	1.88821i	0.558179	−	0.220999i	0.630238	+	0.776402i	$0.282957\pi$
$74$	−3.64835	−	11.2285i	−0.424112	−	1.30528i
$75$	−0.994885	+	16.7969i	−0.114879	+	1.93954i
$76$	0.0641064	−	0.197299i	0.00735351	−	0.0226318i
$77$	−0.271117	−	4.30928i	−0.0308966	−	0.491088i
$78$	11.9206	−	1.50592i	1.34974	−	0.170512i
$79$	2.41586	−	2.26864i	0.271806	−	0.255242i	−0.536643	−	0.843810i	$-0.680308\pi$
$79$	2.41586	−	2.26864i	0.271806	−	0.255242i	0.808448	+	0.588567i	$0.200308\pi$
$80$	−2.12789	−	0.687079i	−0.237906	−	0.0768177i
$81$	−35.0524	−	4.42815i	−3.89471	−	0.492017i
$82$	3.50009	−	10.7722i	0.386520	−	1.18959i
$83$	0.0752966	+	0.0707083i	0.00826488	+	0.00776124i	0.688669	−	0.725076i	$-0.258196\pi$
$83$	0.0752966	+	0.0707083i	0.00826488	+	0.00776124i	−0.680404	+	0.732838i	$0.738196\pi$
$84$	5.97041	−	1.53294i	0.651425	−	0.167258i
$85$	0.975596	+	0.0595818i	0.105818	+	0.00646255i
$86$	−5.93359	−	7.17248i	−0.639835	−	0.773428i
$87$	−0.307044	+	0.0788356i	−0.0329186	+	0.00845206i
$88$	1.50260	−	1.81633i	0.160178	−	0.193622i
$89$	−9.61745	+	3.80782i	−1.01945	+	0.403628i	−0.817598	−	0.575789i	$-0.804695\pi$
$89$	−9.61745	+	3.80782i	−1.01945	+	0.403628i	−0.201849	+	0.979417i	$0.564695\pi$
$90$	4.59634	−	18.0390i	0.484497	−	1.90147i
$91$	−3.50419	−	5.52172i	−0.367339	−	0.578834i
$92$	0.675879	+	3.54308i	0.0704653	+	0.369392i
$93$	7.05683	+	21.7187i	0.731759	+	2.25212i
$94$	−3.61228	+	7.67649i	−0.372579	+	0.791770i
$95$	−0.169973	+	0.431616i	−0.0174389	+	0.0442829i
$96$	2.94901	+	1.62123i	0.300982	+	0.165466i
$97$	4.05624	+	2.22993i	0.411848	+	0.226416i	0.674188	−	0.738560i	$-0.264494\pi$
$97$	4.05624	+	2.22993i	0.411848	+	0.226416i	−0.262339	+	0.964976i	$0.584494\pi$
$98$	2.32340	+	2.80851i	0.234699	+	0.283702i
$99$	15.8766	+	11.5351i	1.59566	+	1.15932i
$100$	4.65561	+	1.82355i	0.465561	+	0.182355i
$101$	−12.5215	+	9.09737i	−1.24593	+	0.905222i	−0.997979	−	0.0635501i	$-0.979758\pi$
$101$	−12.5215	+	9.09737i	−1.24593	+	0.905222i	−0.247953	+	0.968772i	$0.579758\pi$
$102$	−1.42479	−	0.365823i	−0.141075	−	0.0362219i
$103$	−0.875569	−	1.86068i	−0.0862724	−	0.183338i	0.857035	−	0.515258i	$-0.172304\pi$
$103$	−0.875569	−	1.86068i	−0.0862724	−	0.183338i	−0.943308	+	0.331919i	$0.892304\pi$
$104$	0.669025	−	3.50715i	0.0656033	−	0.343904i
$105$	−13.5344	+	2.60757i	−1.32082	+	0.254473i
$106$	4.24055	+	3.98215i	0.411879	+	0.386780i
$107$	−2.25194	−	1.63613i	−0.217704	−	0.158171i	0.473589	−	0.880746i	$-0.342958\pi$
$107$	−2.25194	−	1.63613i	−0.217704	−	0.158171i	−0.691292	+	0.722575i	$0.742958\pi$
$108$	−7.63003	+	16.2146i	−0.734200	+	1.56025i
$109$	7.89700	−	9.54583i	0.756396	−	0.914325i	−0.242039	−	0.970267i	$-0.577816\pi$
$109$	7.89700	−	9.54583i	0.756396	−	0.914325i	0.998434	+	0.0559415i	$0.0178160\pi$
$110$	−3.60125	+	3.84907i	−0.343366	+	0.366995i
$111$	−2.49475	−	39.6530i	−0.236791	−	3.76369i
$112$	0.115012	−	1.82806i	0.0108676	−	0.172735i
$113$	−12.4207	−	4.91768i	−1.16844	−	0.462617i	−0.297841	−	0.954616i	$-0.596266\pi$
$113$	−12.4207	−	4.91768i	−1.16844	−	0.462617i	−0.870596	+	0.491999i	$0.836266\pi$
$114$	0.374079	−	0.589454i	0.0350357	−	0.0552074i
$115$	−1.02555	−	7.99997i	−0.0956332	−	0.746001i
$116$	−0.00591478	+	0.0940127i	−0.000549173	+	0.00872886i
$117$	29.4892	+	3.72536i	2.72628	+	0.344409i
$118$	−9.31416	+	6.76713i	−0.857438	+	0.622965i
$119$	0.150026	+	0.786465i	0.0137529	+	0.0720951i
$120$	−6.36093	−	4.02041i	−0.580671	−	0.367012i
$121$	2.31757	+	4.92509i	0.210688	+	0.447735i
$122$	2.83119	−	2.65867i	0.256324	−	0.240704i
$123$	20.4240	−	32.1831i	1.84157	−	2.90185i
$124$	6.78590			0.609392
$125$	−10.1423	−	4.70458i	−0.907158	−	0.420791i
$126$	15.2487			1.35846
$127$	4.19328	−	6.60755i	0.372093	−	0.586325i	−0.605752	−	0.795653i	$-0.707128\pi$
$127$	4.19328	−	6.60755i	0.372093	−	0.586325i	0.977845	+	0.209328i	$0.0671277\pi$
$128$	0.728969	−	0.684547i	0.0644323	−	0.0605060i
$129$	−13.3381	−	28.3449i	−1.17435	−	2.49563i
$130$	−1.97125	+	7.73645i	−0.172890	+	0.678531i
$131$	3.80907	+	19.9678i	0.332800	+	1.74460i	0.618044	+	0.786143i	$0.287925\pi$
$131$	3.80907	+	19.9678i	0.332800	+	1.74460i	−0.285244	+	0.958455i	$0.592075\pi$
$132$	6.41789	−	4.66287i	0.558606	−	0.405851i
$133$	−0.376989	−	0.0476248i	−0.0326891	−	0.00412959i
$134$	0.265652	−	4.22242i	0.0229488	−	0.364761i
$135$	19.2397	−	35.1496i	1.65589	−	3.02519i
$136$	−0.234217	+	0.369066i	−0.0200839	+	0.0316472i
$137$	−0.0823281	−	0.0325960i	−0.00703377	−	0.00278486i	0.364605	−	0.931162i	$-0.381204\pi$
$137$	−0.0823281	−	0.0325960i	−0.00703377	−	0.00278486i	−0.371639	+	0.928377i	$0.621204\pi$
$138$	−0.762178	+	12.1145i	−0.0648809	+	1.03125i
$139$	−0.176988	−	2.81315i	−0.0150119	−	0.238608i	−0.998376	−	0.0569637i	$-0.981858\pi$
$139$	−0.176988	−	2.81315i	−0.0150119	−	0.238608i	0.983364	−	0.181644i	$-0.0581419\pi$
$140$	−0.505874	+	4.06438i	−0.0427541	+	0.343503i
$141$	−18.1989	+	21.9987i	−1.53262	+	1.85262i
$142$	4.89593	−	10.4044i	0.410858	−	0.873117i
$143$	−6.80908	−	4.94709i	−0.569404	−	0.413696i
$144$	6.06868	+	5.69887i	0.505724	+	0.474906i
$145$	0.0260159	−	0.209022i	0.00216050	−	0.0173583i
$146$	0.961130	−	5.03842i	0.0795437	−	0.416983i
$147$	5.22275	+	11.0989i	0.430765	+	0.915423i
$148$	−11.4354	−	2.93611i	−0.939983	−	0.241347i
$149$	−0.135300	+	0.0983014i	−0.0110842	+	0.00805316i	−0.593314	−	0.804971i	$-0.702181\pi$
$149$	−0.135300	+	0.0983014i	−0.0110842	+	0.00805316i	0.582229	+	0.813025i	$0.302181\pi$
$150$	13.6490	+	9.84024i	1.11444	+	0.803452i
$151$	3.60619	+	2.62005i	0.293467	+	0.213216i	0.724770	−	0.688991i	$-0.241946\pi$
$151$	3.60619	+	2.62005i	0.293467	+	0.213216i	−0.431303	+	0.902207i	$0.641946\pi$
$152$	−0.132235	−	0.159845i	−0.0107257	−	0.0129651i
$153$	−3.18886	−	1.75309i	−0.257804	−	0.141729i
$154$	−3.78372	−	2.08012i	−0.304901	−	0.167621i
$155$	−15.1455	−	0.924971i	−1.21652	−	0.0742954i
$156$	5.11588	−	10.8718i	0.409598	−	0.870440i
$157$	−2.68540	−	8.26481i	−0.214318	−	0.659604i	−0.999201	−	0.0399597i	$-0.987277\pi$
$157$	−2.68540	−	8.26481i	−0.214318	−	0.659604i	0.784883	−	0.619644i	$-0.212723\pi$
$158$	−0.620997	−	3.25538i	−0.0494038	−	0.258984i
$159$	10.4896	+	16.5289i	0.831877	+	1.31083i
$160$	−1.72030	+	1.42848i	−0.136002	+	0.112932i
$161$	6.14283	−	2.43212i	0.484123	−	0.191678i
$162$	−22.5208	+	27.2230i	−1.76940	+	2.13884i
$163$	−6.37369	+	1.63648i	−0.499226	+	0.128179i	−0.489903	−	0.871777i	$-0.662968\pi$
$163$	−6.37369	+	1.63648i	−0.499226	+	0.128179i	−0.00932302	+	0.999957i	$0.502968\pi$
$164$	−7.21981	−	8.72725i	−0.563772	−	0.681483i
$165$	−14.9597	+	9.53230i	−1.16461	+	0.742089i
$166$	0.100047	−	0.0256877i	0.00776515	−	0.00199375i
$167$	−8.50894	−	7.99043i	−0.658442	−	0.618318i	0.281537	−	0.959550i	$-0.409156\pi$
$167$	−8.50894	−	7.99043i	−0.658442	−	0.618318i	−0.939979	+	0.341233i	$0.889156\pi$
$168$	1.90480	−	5.86237i	0.146959	−	0.452292i
$169$	0.250312	+	0.0316217i	0.0192548	+	0.00243244i
$170$	0.573057	−	0.791797i	0.0439515	−	0.0607281i
$171$	1.25897	−	1.18225i	0.0962755	−	0.0904087i
$172$	−9.23530	+	1.16669i	−0.704185	+	0.0889592i
$173$	−0.886334	−	14.0879i	−0.0673868	−	1.07108i	−0.875865	−	0.482556i	$-0.839708\pi$
$173$	−0.886334	−	14.0879i	−0.0673868	−	1.07108i	0.808478	−	0.588526i	$-0.200292\pi$
$174$	−0.0979595	+	0.301488i	−0.00742629	+	0.0228558i
$175$	1.68307	−	9.00237i	0.127228	−	0.680516i
$176$	−0.728446	−	2.24193i	−0.0549087	−	0.168992i
$177$	−36.0234	+	14.2627i	−2.70768	+	1.07205i
$178$	−1.93824	+	10.1606i	−0.145277	+	0.761570i
$179$	−11.7055	+	1.47875i	−0.874913	+	0.110527i	−0.549948	−	0.835199i	$-0.685353\pi$
$179$	−11.7055	+	1.47875i	−0.874913	+	0.110527i	−0.324965	+	0.945726i	$0.605353\pi$
$180$	−12.7680	−	13.5466i	−0.951667	−	1.00970i
$181$	−6.75083	+	3.71130i	−0.501785	+	0.275859i	−0.712479	−	0.701693i	$-0.752428\pi$
$181$	−6.75083	+	3.71130i	−0.501785	+	0.275859i	0.210694	+	0.977552i	$0.432428\pi$
$182$	−6.53978			−0.484761
$183$	11.4535	−	6.29659i	0.846664	−	0.465457i
$184$	3.35368	+	1.32782i	0.247236	+	0.0978878i
$185$	25.1225	+	8.11186i	1.84705	+	0.596396i
$186$	22.1189	+	5.67917i	1.62184	+	0.416417i
$187$	0.552119	+	0.870001i	0.0403750	+	0.0636207i
$188$	4.54592	+	7.16322i	0.331545	+	0.522432i
$189$	31.7926	+	8.16295i	2.31257	+	0.593767i
$190$	0.273349	+	0.374785i	0.0198308	+	0.0271897i
$191$	−2.56953	−	1.01735i	−0.185925	−	0.0736128i	0.273318	−	0.961924i	$-0.411879\pi$
$191$	−2.56953	−	1.01735i	−0.185925	−	0.0736128i	−0.459242	+	0.888311i	$0.651879\pi$
$192$	2.94901	−	1.62123i	0.212826	−	0.117002i
$193$	15.3069			1.10181			0.550906	−	0.834567i	$-0.314282\pi$
$193$	15.3069			1.10181			0.550906	+	0.834567i	$0.314282\pi$
$194$	4.05624	−	2.22993i	0.291221	−	0.160100i
$195$	−12.9001	+	23.5675i	−0.923794	+	1.68771i
$196$	3.61624	−	0.456837i	0.258303	−	0.0326312i
$197$	−2.93933	+	15.4085i	−0.209419	+	1.09781i	0.709901	+	0.704301i	$0.248740\pi$
$197$	−2.93933	+	15.4085i	−0.209419	+	1.09781i	−0.919320	+	0.393511i	$0.871260\pi$
$198$	18.2465	−	7.22430i	1.29672	−	0.513409i
$199$	0.361323	+	1.11204i	0.0256135	+	0.0788303i	0.963046	−	0.269336i	$-0.0868043\pi$
$199$	0.361323	+	1.11204i	0.0256135	+	0.0788303i	−0.937433	+	0.348167i	$0.886804\pi$
$200$	4.03427	−	2.95375i	0.285266	−	0.208862i
$201$	4.39968	−	13.5408i	0.310329	−	0.955096i
$202$	0.971832	+	15.4468i	0.0683779	+	1.08683i
$203$	0.171180	−	0.0216251i	0.0120145	−	0.00151778i
$204$	−1.07231	+	1.00697i	−0.0750769	+	0.0705019i
$205$	14.9244	+	20.4625i	1.04236	+	1.42917i
$206$	−2.04018	−	0.257734i	−0.142146	−	0.0179572i
$207$	−9.27921	+	28.5585i	−0.644949	+	1.98495i
$208$	−2.60270	−	2.44410i	−0.180465	−	0.169468i
$209$	−0.473665	+	0.121617i	−0.0327641	+	0.00841239i
$210$	−5.05043	+	12.8246i	−0.348513	+	0.884985i
$211$	1.92609	+	2.32824i	0.132597	+	0.160283i	0.832633	−	0.553825i	$-0.186833\pi$
$211$	1.92609	+	2.32824i	0.132597	+	0.160283i	−0.700036	+	0.714108i	$0.746833\pi$
$212$	5.63444	−	1.44668i	0.386975	−	0.0993583i
$213$	24.6660	−	29.8161i	1.69009	−	2.04297i
$214$	−2.58808	+	1.02470i	−0.176918	+	0.0700467i
$215$	20.7714	−	1.34510i	1.41660	−	0.0917352i
$216$	9.60209	+	15.1305i	0.653340	+	1.02950i
$217$	−2.32906	−	12.2094i	−0.158107	−	0.828826i
$218$	−3.82839	−	11.7826i	−0.259291	−	0.798016i
$219$	7.34954	−	15.6186i	0.496636	−	1.05541i
$220$	1.32023	+	5.10307i	0.0890102	+	0.344049i
$221$	1.36762	+	0.751855i	0.0919960	+	0.0505752i
$222$	−34.8169	−	19.1407i	−2.33675	−	1.28464i
$223$	−12.6201	−	15.2551i	−0.845107	−	1.02156i	−0.999437	−	0.0335399i	$-0.989322\pi$
$223$	−12.6201	−	15.2551i	−0.845107	−	1.02156i	0.154330	−	0.988019i	$-0.450678\pi$
$224$	−1.48185	−	1.07663i	−0.0990105	−	0.0719353i
$225$	26.6504	+	31.9751i	1.77669	+	2.13167i
$226$	−10.8075	+	7.85208i	−0.718901	+	0.522312i
$227$	6.86493	+	1.76261i	0.455641	+	0.116989i	0.469533	−	0.882915i	$-0.344422\pi$
$227$	6.86493	+	1.76261i	0.455641	+	0.116989i	−0.0138921	+	0.999903i	$0.504422\pi$
$228$	−0.297251	−	0.631691i	−0.0196859	−	0.0418347i
$229$	−2.82161	+	14.7914i	−0.186457	+	0.977442i	0.758851	+	0.651264i	$0.225761\pi$
$229$	−2.82161	+	14.7914i	−0.186457	+	0.977442i	−0.945308	+	0.326178i	$0.894239\pi$
$230$	−7.30411	−	3.42070i	−0.481619	−	0.225554i
$231$	−10.5923	−	9.94685i	−0.696924	−	0.654455i
$232$	0.0762083	+	0.0553685i	0.00500332	+	0.00363512i
$233$	−0.727210	+	1.54540i	−0.0476411	+	0.101243i	−0.927230	−	0.374491i	$-0.877817\pi$
$233$	−0.727210	+	1.54540i	−0.0476411	+	0.101243i	0.879589	+	0.475734i	$0.157817\pi$
$234$	18.9465	−	22.9024i	1.23857	−	1.49718i
$235$	−9.16968	−	16.6073i	−0.598164	−	1.08334i
$236$	0.722903	+	11.4902i	0.0470570	+	0.747949i
$237$	0.700288	−	11.1308i	0.0454886	−	0.723021i
$238$	0.744422	+	0.294738i	0.0482537	+	0.0191050i
$239$	−6.09260	+	9.60039i	−0.394097	+	0.620998i	−0.982211	−	0.187780i	$-0.939871\pi$
$239$	−6.09260	+	9.60039i	−0.394097	+	0.620998i	0.588114	+	0.808778i	$0.299871\pi$
$240$	−6.80290	+	3.21647i	−0.439125	+	0.207622i
$241$	−1.34935	+	21.4473i	−0.0869192	+	1.38154i	0.676883	+	0.736090i	$0.263330\pi$
$241$	−1.34935	+	21.4473i	−0.0869192	+	1.38154i	−0.763802	+	0.645450i	$0.776670\pi$
$242$	5.40021	+	0.682205i	0.347138	+	0.0438538i
$243$	−52.6976	+	38.2871i	−3.38056	+	2.45612i
$244$	−0.727758	−	3.81504i	−0.0465899	−	0.244233i
$245$	−8.13339	+	0.526698i	−0.519623	+	0.0336495i
$246$	−16.2294	−	34.4891i	−1.03475	−	2.19895i
$247$	−0.539938	+	0.507036i	−0.0343554	+	0.0322619i
$248$	3.63607	−	5.72952i	0.230890	−	0.363825i
$249$	0.347605			0.0220286
$250$	−9.40674	+	6.04261i	−0.594935	+	0.382168i
$251$	19.0624			1.20321			0.601605	−	0.798794i	$-0.294528\pi$
$251$	19.0624			1.20321			0.601605	+	0.798794i	$0.294528\pi$
$252$	8.17067	−	12.8749i	0.514704	−	0.811043i
$253$	6.19822	−	5.82051i	0.389679	−	0.365933i
$254$	−3.33207	−	7.08100i	−0.209072	−	0.444302i
$255$	2.53056	−	2.10130i	0.158470	−	0.131588i
$256$	−0.187381	−	0.982287i	−0.0117113	−	0.0613930i
$257$	5.08618	−	3.69533i	0.317267	−	0.230508i	−0.417741	−	0.908566i	$-0.637178\pi$
$257$	5.08618	−	3.69533i	0.317267	−	0.230508i	0.735008	+	0.678058i	$0.237178\pi$
$258$	−31.0792	−	3.92622i	−1.93491	−	0.244436i
$259$	−1.35786	+	21.5826i	−0.0843734	+	1.34108i
$260$	5.47585	+	5.80978i	0.339598	+	0.360307i
$261$	−0.420199	+	0.662127i	−0.0260096	+	0.0409846i
$262$	18.9004	+	7.48320i	1.16767	+	0.462314i
$263$	0.375657	−	5.97089i	0.0231640	−	0.368181i	−0.969320	−	0.245804i	$-0.920948\pi$
$263$	0.375657	−	5.97089i	0.0231640	−	0.368181i	0.992484	−	0.122377i	$-0.0390518\pi$
$264$	−0.498114	−	7.91730i	−0.0306568	−	0.487276i
$265$	−12.7728	+	2.46084i	−0.784624	+	0.151168i
$266$	−0.242212	+	0.292784i	−0.0148510	+	0.0179517i
$267$	−14.8213	+	31.4968i	−0.907047	+	1.92757i
$268$	−3.42276	−	2.48678i	−0.209078	−	0.151904i
$269$	−2.75587	−	2.58793i	−0.168028	−	0.157789i	0.595971	−	0.803006i	$-0.296767\pi$
$269$	−2.75587	−	2.58793i	−0.168028	−	0.157789i	−0.764000	+	0.645217i	$0.776767\pi$
$270$	−19.3686	−	35.0787i	−1.17874	−	2.13482i
$271$	−0.505086	+	2.64775i	−0.0306818	+	0.160839i	−0.994331	−	0.106333i	$-0.966089\pi$
$271$	−0.505086	+	2.64775i	−0.0306818	+	0.160839i	0.963649	+	0.267172i	$0.0860892\pi$
$272$	0.186113	+	0.395511i	0.0112848	+	0.0239814i
$273$	−21.3167	−	5.47320i	−1.29015	−	0.331253i
$274$	−0.0716353	+	0.0520461i	−0.00432765	+	0.00314422i
$275$	−2.25106	−	11.5696i	−0.135744	−	0.697670i
$276$	9.82019	+	7.13479i	0.591106	+	0.429464i
$277$	3.27816	+	3.96262i	0.196966	+	0.238091i	0.859744	−	0.510725i	$-0.170623\pi$
$277$	3.27816	+	3.96262i	0.196966	+	0.238091i	−0.662779	+	0.748815i	$0.730623\pi$
$278$	−2.47005	−	1.35792i	−0.148144	−	0.0814428i
$279$	49.5050	+	27.2156i	2.96379	+	1.62936i
$280$	3.16061	+	2.60493i	0.188883	+	0.155674i
$281$	9.60423	−	20.4100i	0.572940	−	1.21756i	−0.382932	−	0.923777i	$-0.625086\pi$
$281$	9.60423	−	20.4100i	0.572940	−	1.21756i	0.955872	−	0.293783i	$-0.0949144\pi$
$282$	8.82265	+	27.1533i	0.525381	+	1.61696i
$283$	−0.931245	−	4.88176i	−0.0553568	−	0.290190i	0.943834	−	0.330421i	$-0.107191\pi$
$283$	−0.931245	−	4.88176i	−0.0553568	−	0.290190i	−0.999190	+	0.0402307i	$0.987191\pi$
$284$	−6.16135	−	9.70873i	−0.365609	−	0.576107i
$285$	0.577333	+	1.45039i	0.0341983	+	0.0859139i
$286$	−7.82546	+	3.09832i	−0.462729	+	0.183207i
$287$	−13.2243	+	15.9854i	−0.780606	+	0.943591i
$288$	8.06348	−	2.07035i	0.475145	−	0.121997i
$289$	10.7144	+	12.9515i	0.630260	+	0.761853i
$290$	−0.162543	−	0.133965i	−0.00954484	−	0.00786672i
$291$	15.0877	−	3.87387i	0.884458	−	0.227090i
$292$	−3.73908	−	3.51123i	−0.218813	−	0.205479i
$293$	2.84979	−	8.77075i	0.166487	−	0.512393i	−0.832656	−	0.553790i	$-0.813181\pi$
$293$	2.84979	−	8.77075i	0.166487	−	0.512393i	0.999143	+	0.0413973i	$0.0131809\pi$
$294$	12.1696	+	1.53738i	0.709746	+	0.0896618i
$295$	−0.0472491	−	25.7437i	−0.00275095	−	1.49885i
$296$	−8.60642	+	8.08197i	−0.500238	+	0.469755i
$297$	41.9101	−	5.29448i	2.43187	−	0.307217i
$298$	0.0105011	+	0.166910i	0.000608313	+	0.00966885i
$299$	3.97961	−	12.2480i	0.230147	−	0.708320i
$300$	15.6219	−	6.25157i	0.901930	−	0.360935i
$301$	5.26889	+	16.2160i	0.303694	+	0.934673i
$302$	4.14447	−	1.64091i	0.238488	−	0.0944239i
$303$	−9.75985	+	51.1629i	−0.560689	+	2.93923i
$304$	−0.205817	+	0.0260007i	−0.0118044	+	0.00149124i
$305$	1.10427	+	8.61402i	0.0632303	+	0.493238i
$306$	−3.18886	+	1.75309i	−0.182295	+	0.100217i
$307$	21.3820			1.22034			0.610169	−	0.792272i	$-0.291102\pi$
$307$	21.3820			1.22034			0.610169	+	0.792272i	$0.291102\pi$
$308$	−3.78372	+	2.08012i	−0.215597	+	0.118526i
$309$	−6.43434	−	2.54754i	−0.366037	−	0.144924i
$310$	−8.89635	+	12.2922i	−0.505279	+	0.698148i
$311$	−1.36573	−	0.350660i	−0.0774435	−	0.0198841i	0.209769	−	0.977751i	$-0.432729\pi$
$311$	−1.36573	−	0.350660i	−0.0774435	−	0.0198841i	−0.287213	+	0.957867i	$0.592729\pi$
$312$	−6.43813	−	10.1449i	−0.364488	−	0.574340i
$313$	6.88045	+	10.8418i	0.388906	+	0.612817i	0.981221	−	0.192889i	$-0.0617858\pi$
$313$	6.88045	+	10.8418i	0.388906	+	0.612817i	−0.592315	+	0.805707i	$0.701786\pi$
$314$	−8.41712	−	2.16115i	−0.475005	−	0.121961i
$315$	−19.9911	+	27.6219i	−1.12637	+	1.55632i
$316$	−3.08135	−	1.21999i	−0.173340	−	0.0686300i
$317$	−4.72832	+	2.59942i	−0.265569	+	0.145998i	−0.608975	−	0.793189i	$-0.708419\pi$
$317$	−4.72832	+	2.59942i	−0.265569	+	0.145998i	0.343406	+	0.939187i	$0.388419\pi$
$318$	19.5764			1.09779
$319$	0.194588	−	0.106976i	0.0108948	−	0.00598948i
$320$	0.284325	+	2.21792i	0.0158942	+	0.123985i
$321$	−9.29355	+	1.17405i	−0.518715	+	0.0655290i
$322$	1.23799	−	6.48976i	0.0689904	−	0.361660i
$323$	0.0843123	−	0.0333816i	0.00469126	−	0.00185740i
$324$	10.9179	+	33.6018i	0.606549	+	1.86677i
$325$	−11.4297	−	13.7133i	−0.634005	−	0.760677i
$326$	−2.03346	+	6.25835i	−0.112623	+	0.346618i
$327$	−2.61787	−	41.6098i	−0.144768	−	2.30103i
$328$	−11.2372	+	1.41959i	−0.620472	+	0.0783838i
$329$	11.3280	−	10.6377i	0.624533	−	0.586476i
$330$	0.0325568	+	17.7386i	0.00179220	+	0.976477i
$331$	2.34561	+	0.296319i	0.128926	+	0.0162872i	0.189531	−	0.981875i	$-0.439303\pi$
$331$	2.34561	+	0.296319i	0.128926	+	0.0162872i	−0.0606053	+	0.998162i	$0.519303\pi$
$332$	0.0319190	−	0.0982366i	0.00175178	−	0.00539143i
$333$	−71.6487	−	67.2826i	−3.92633	−	3.68706i
$334$	−11.3059	+	2.90285i	−0.618629	+	0.158837i
$335$	7.30033	+	6.01682i	0.398859	+	0.328734i
$336$	−3.92912	−	4.74949i	−0.214351	−	0.259106i
$337$	19.5960	−	5.03139i	1.06746	−	0.274077i	0.326204	−	0.945299i	$-0.394230\pi$
$337$	19.5960	−	5.03139i	1.06746	−	0.274077i	0.741256	+	0.671222i	$0.234230\pi$
$338$	0.160823	−	0.194402i	0.00874762	−	0.0105741i
$339$	−41.7988	+	16.5493i	−2.27020	+	0.898836i
$340$	−0.361477	−	0.908114i	−0.0196039	−	0.0492494i
$341$	−8.57131	−	13.5062i	−0.464162	−	0.731403i
$342$	−0.323617	−	1.69646i	−0.0174992	−	0.0917340i
$343$	−6.02525	−	18.5438i	−0.325333	−	1.00127i
$344$	−3.96345	+	8.42276i	−0.213695	+	0.454125i
$345$	−20.9453	−	17.2628i	−1.12765	−	0.929396i
$346$	−12.3697	−	6.80031i	−0.665000	−	0.365587i
$347$	9.75182	+	5.36111i	0.523505	+	0.287799i	0.721513	−	0.692401i	$-0.243447\pi$
$347$	9.75182	+	5.36111i	0.523505	+	0.287799i	−0.198008	+	0.980200i	$0.563447\pi$
$348$	0.202066	+	0.244255i	0.0108319	+	0.0130935i
$349$	18.1485	+	13.1857i	0.971467	+	0.705812i	0.955785	−	0.294065i	$-0.0950082\pi$
$349$	18.1485	+	13.1857i	0.971467	+	0.705812i	0.0156817	+	0.999877i	$0.495008\pi$
$350$	−6.69912	−	6.24478i	−0.358083	−	0.333797i
$351$	51.7625	−	37.6076i	2.76288	−	2.00735i
$352$	−2.28324	−	0.586237i	−0.121697	−	0.0312465i
$353$	1.21021	+	2.57182i	0.0644127	+	0.136884i	0.934441	−	0.356117i	$-0.115900\pi$
$353$	1.21021	+	2.57182i	0.0644127	+	0.136884i	−0.870028	+	0.493001i	$0.835900\pi$
$354$	−7.25992	+	38.0578i	−0.385860	+	2.02275i
$355$	12.4282	+	22.5088i	0.659620	+	1.19465i
$356$	7.54033	+	7.08084i	0.399637	+	0.375284i
$357$	2.17981	+	1.58372i	0.115368	+	0.0838195i
$358$	−5.02359	+	10.6757i	−0.265505	+	0.564227i
$359$	−2.10814	+	2.54831i	−0.111263	+	0.134494i	−0.823205	−	0.567744i	$-0.807816\pi$
$359$	−2.10814	+	2.54831i	−0.111263	+	0.134494i	0.711941	+	0.702239i	$0.247816\pi$
$360$	−18.2792	+	3.52172i	−0.963397	+	0.185611i
$361$	−1.19032	−	18.9196i	−0.0626483	−	0.995766i
$362$	−0.483721	+	7.68852i	−0.0254238	+	0.404100i
$363$	17.0313	+	6.74315i	0.893909	+	0.353924i
$364$	−3.50419	+	5.52172i	−0.183670	+	0.289417i
$365$	7.86668	+	8.34641i	0.411761	+	0.436871i
$366$	0.820681	−	13.0443i	0.0428977	−	0.681839i
$367$	13.4429	+	1.69824i	0.701715	+	0.0886472i	0.468092	−	0.883680i	$-0.344942\pi$
$367$	13.4429	+	1.69824i	0.701715	+	0.0886472i	0.233623	+	0.972327i	$0.424942\pi$
$368$	2.91810	−	2.12013i	0.152117	−	0.110519i
$369$	−17.6689	−	92.6235i	−0.919805	−	4.82179i
$370$	20.3104	−	16.8651i	1.05589	−	0.876775i
$371$	−4.53676	−	9.64111i	−0.235537	−	0.500541i
$372$	16.6470	−	15.6326i	0.863107	−	0.810511i
$373$	−12.3535	+	19.4660i	−0.639641	+	1.00791i	0.357614	+	0.933869i	$0.383590\pi$
$373$	−12.3535	+	19.4660i	−0.639641	+	1.00791i	−0.997255	+	0.0740430i	$0.976410\pi$
$374$	1.03041			0.0532810
$375$	−35.7188	+	11.8236i	−1.84451	+	0.610566i
$376$	8.48393			0.437525
$377$	0.180212	−	0.283969i	0.00928141	−	0.0146252i
$378$	23.9275	−	22.4694i	1.23070	−	1.15570i
$379$	−3.92600	−	8.34318i	−0.201665	−	0.428560i	0.778256	−	0.627948i	$-0.216105\pi$
$379$	−3.92600	−	8.34318i	−0.201665	−	0.428560i	−0.979921	+	0.199387i	$0.936105\pi$
$380$	0.462909	−	0.0299768i	0.0237467	−	0.00153778i
$381$	−4.93486	−	25.8695i	−0.252821	−	1.32533i
$382$	−2.23580	+	1.62440i	−0.114393	+	0.0831117i
$383$	29.2403	+	3.69391i	1.49411	+	0.188750i	0.829527	−	0.558466i	$-0.188610\pi$
$383$	29.2403	+	3.69391i	1.49411	+	0.188750i	0.664581	+	0.747216i	$0.268610\pi$
$384$	0.211307	−	3.35863i	0.0107832	−	0.171394i
$385$	8.72845	−	4.12688i	0.444843	−	0.210325i
$386$	8.20183	−	12.9240i	0.417462	−	0.657815i
$387$	−72.0532	−	28.5279i	−3.66267	−	1.45015i
$388$	0.290644	−	4.61965i	0.0147552	−	0.234527i
$389$	1.11481	+	17.7194i	0.0565233	+	0.898412i	0.919481	+	0.393135i	$0.128610\pi$
$389$	1.11481	+	17.7194i	0.0565233	+	0.898412i	−0.862957	+	0.505277i	$0.831390\pi$
$390$	12.9865	+	23.5200i	0.657597	+	1.19098i
$391$	−1.00500	+	1.21483i	−0.0508248	+	0.0614367i
$392$	1.55196	−	3.29808i	0.0783857	−	0.166578i
$393$	55.3439	+	40.2097i	2.79173	+	2.02831i
$394$	11.4349	+	10.7381i	0.576080	+	0.540976i
$395$	6.71101	+	3.14293i	0.337667	+	0.158138i
$396$	3.67728	−	19.2770i	0.184790	−	0.968706i
$397$	5.62000	+	11.9431i	0.282060	+	0.599407i	0.994780	−	0.102041i	$-0.0325372\pi$
$397$	5.62000	+	11.9431i	0.282060	+	0.599407i	−0.712721	+	0.701448i	$0.752537\pi$
$398$	1.13253	+	0.290785i	0.0567687	+	0.0145757i
$399$	−1.03453	+	0.751632i	−0.0517914	+	0.0376286i
$400$	−0.332268	−	4.98895i	−0.0166134	−	0.249447i
$401$	0.288990	+	0.209964i	0.0144315	+	0.0104851i	0.594978	−	0.803742i	$-0.297161\pi$
$401$	0.288990	+	0.209964i	0.0144315	+	0.0104851i	−0.580546	+	0.814227i	$0.697161\pi$
$402$	−9.07543	−	10.9703i	−0.452641	−	0.547149i
$403$	−21.2314	−	11.6721i	−1.05761	−	0.581428i
$404$	13.5629	+	7.45628i	0.674781	+	0.370964i
$405$	−19.7875	−	76.4843i	−0.983251	−	3.80054i
$406$	0.0734643	−	0.156120i	0.00364597	−	0.00774809i
$407$	8.60026	+	26.4689i	0.426299	+	1.31201i
$408$	0.275638	+	1.44495i	0.0136461	+	0.0715354i
$409$	−9.00004	−	14.1818i	−0.445023	−	0.701245i	0.545573	−	0.838063i	$-0.316312\pi$
$409$	−9.00004	−	14.1818i	−0.445023	−	0.701245i	−0.990596	+	0.136819i	$0.956312\pi$
$410$	25.2740	−	1.63668i	1.24819	−	0.0808298i
$411$	−0.277056	+	0.109694i	−0.0136662	+	0.00541082i
$412$	−1.31079	+	1.58448i	−0.0645782	+	0.0780616i
$413$	20.4254	−	5.24435i	1.00507	−	0.258058i
$414$	19.1407	+	23.1371i	0.940712	+	1.13713i
$415$	−0.0846307	+	0.214904i	−0.00415436	+	0.0105492i
$416$	−3.45822	+	0.887920i	−0.169553	+	0.0435339i
$417$	−6.91478	−	6.49341i	−0.338618	−	0.317984i
$418$	−0.151118	+	0.465094i	−0.00739143	+	0.0227485i
$419$	20.6943	+	2.61429i	1.01098	+	0.127717i	0.613335	−	0.789823i	$-0.289828\pi$
$419$	20.6943	+	2.61429i	1.01098	+	0.127717i	0.397645	+	0.917539i	$0.369828\pi$
$420$	8.12205	+	11.1360i	0.396316	+	0.543382i
$421$	20.3823	−	19.1403i	0.993374	−	0.932841i	−0.00436855	−	0.999990i	$-0.501391\pi$
$421$	20.3823	−	19.1403i	0.993374	−	0.932841i	0.997743	+	0.0671498i	$0.0213906\pi$
$422$	2.99785	−	0.378716i	0.145933	−	0.0184356i
$423$	4.43483	+	70.4896i	0.215629	+	3.42732i
$424$	1.79761	−	5.53248i	0.0872998	−	0.268681i
$425$	0.683001	+	2.07610i	0.0331304	+	0.100706i
$426$	−11.9579	−	36.8025i	−0.579360	−	1.78309i
$427$	−6.61434	+	2.61880i	−0.320090	+	0.126733i
$428$	−0.521586	+	2.73425i	−0.0252118	+	0.132165i
$429$	−28.1004	+	3.54991i	−1.35670	+	0.171391i
$430$	9.99415	−	18.2586i	0.481961	−	0.880508i
$431$	22.9715	−	12.6287i	1.10650	−	0.608304i	0.179648	−	0.983731i	$-0.442504\pi$
$431$	22.9715	−	12.6287i	1.10650	−	0.608304i	0.926852	+	0.375427i	$0.122504\pi$
$432$	17.9201			0.862183
$433$	20.7751	−	11.4212i	0.998388	−	0.548869i	0.103249	−	0.994656i	$-0.467076\pi$
$433$	20.7751	−	11.4212i	0.998388	−	0.548869i	0.895139	+	0.445787i	$0.147076\pi$
$434$	−11.5567	−	4.57562i	−0.554739	−	0.219637i
$435$	−0.417698	−	0.572699i	−0.0200271	−	0.0274588i
$436$	−11.9997	−	3.08100i	−0.574682	−	0.147553i
$437$	−0.400947	−	0.631791i	−0.0191799	−	0.0302226i
$438$	−9.24911	−	14.5743i	−0.441940	−	0.696386i
$439$	−26.8775	−	6.90098i	−1.28279	−	0.329366i	−0.455048	−	0.890467i	$-0.650378\pi$
$439$	−26.8775	−	6.90098i	−1.28279	−	0.329366i	−0.827747	+	0.561101i	$0.810378\pi$
$440$	5.01608	+	1.61965i	0.239132	+	0.0772139i
$441$	28.2137	+	11.1706i	1.34351	+	0.531932i
$442$	1.36762	−	0.751855i	0.0650510	−	0.0357621i
$443$	−9.21146			−0.437650			−0.218825	−	0.975764i	$-0.570222\pi$
$443$	−9.21146			−0.437650			−0.218825	+	0.975764i	$0.570222\pi$
$444$	−34.8169	+	19.1407i	−1.65234	+	0.908379i
$445$	−15.8642	−	16.8316i	−0.752033	−	0.797894i
$446$	−19.6425	+	2.48143i	−0.930102	+	0.117499i
$447$	−0.105460	+	0.552840i	−0.00498808	+	0.0261484i
$448$	−1.70304	+	0.674283i	−0.0804613	+	0.0318569i
$449$	−5.89829	−	18.1531i	−0.278357	−	0.856696i	−0.988311	−	0.152448i	$-0.951284\pi$
$449$	−5.89829	−	18.1531i	−0.278357	−	0.856696i	0.709954	−	0.704248i	$-0.248716\pi$
$450$	41.2775	−	5.36857i	1.94584	−	0.253077i
$451$	−8.25077	+	25.3933i	−0.388514	+	1.19572i
$452$	0.838803	+	13.3324i	0.0394540	+	0.627103i
$453$	14.8824	−	1.88008i	0.699235	−	0.0883339i
$454$	5.16664	−	4.85180i	0.242482	−	0.227706i
$455$	8.57369	−	11.8463i	0.401941	−	0.555365i
$456$	−0.692629	−	0.0874994i	−0.0324353	−	0.00409754i
$457$	−4.97234	+	15.3033i	−0.232596	+	0.715857i	0.764835	+	0.644226i	$0.222820\pi$
$457$	−4.97234	+	15.3033i	−0.232596	+	0.715857i	−0.997431	+	0.0716312i	$0.977180\pi$
$458$	10.9769	+	10.3080i	0.512916	+	0.481660i
$459$	−7.58703	+	1.94802i	−0.354132	+	0.0909257i
$460$	−6.80193	+	4.33417i	−0.317142	+	0.202082i
$461$	26.4203	+	31.9367i	1.23052	+	1.48744i	0.816683	+	0.577086i	$0.195810\pi$
$461$	26.4203	+	31.9367i	1.23052	+	1.48744i	0.413834	+	0.910353i	$0.364190\pi$
$462$	−14.0741	+	3.61360i	−0.654784	+	0.168120i
$463$	5.47827	−	6.62209i	0.254597	−	0.307755i	−0.627693	−	0.778461i	$-0.716001\pi$
$463$	5.47827	−	6.62209i	0.254597	−	0.307755i	0.882290	+	0.470706i	$0.156001\pi$
$464$	0.0875836	−	0.0346768i	0.00406597	−	0.00160983i
$465$	−39.2854	+	32.6214i	−1.82182	+	1.51278i
$466$	0.915166	+	1.44207i	0.0423942	+	0.0668026i
$467$	−5.55227	−	29.1060i	−0.256928	−	1.34687i	−0.843570	−	0.537019i	$-0.819550\pi$
$467$	−5.55227	−	29.1060i	−0.256928	−	1.34687i	0.586642	−	0.809847i	$-0.300450\pi$
$468$	−9.18510	−	28.2688i	−0.424581	−	1.30673i
$469$	−3.29952	+	7.01184i	−0.152358	+	0.323777i
$470$	−18.9354	−	1.15643i	−0.873424	−	0.0533419i
$471$	−25.6273	−	14.0887i	−1.18084	−	0.649173i
$472$	10.0889	+	5.54640i	0.464377	+	0.255294i
$473$	13.9873	+	16.9077i	0.643135	+	0.777416i
$474$	−9.02278	−	6.55543i	−0.414430	−	0.301101i
$475$	−1.03726	+	0.00380751i	−0.0475926	+	0.000174700i
$476$	0.647736	−	0.470608i	0.0296890	−	0.0215703i
$477$	46.9069	+	12.0436i	2.14772	+	0.551440i
$478$	4.84131	+	10.2883i	0.221436	+	0.470576i
$479$	−7.16028	+	37.5355i	−0.327162	+	1.71504i	0.315529	+	0.948916i	$0.397818\pi$
$479$	−7.16028	+	37.5355i	−0.327162	+	1.71504i	−0.642690	+	0.766126i	$0.722182\pi$
$480$	−0.929425	+	7.46735i	−0.0424222	+	0.340836i
$481$	30.7283	+	28.8558i	1.40109	+	1.31571i
$482$	17.3855	+	12.6313i	0.791889	+	0.575341i
$483$	9.46661	−	20.1176i	0.430746	−	0.915381i
$484$	3.46958	−	4.19400i	0.157708	−	0.190636i
$485$	−1.27839	+	10.2710i	−0.0580485	+	0.466383i
$486$	4.09004	+	65.0093i	0.185528	+	2.94888i
$487$	1.73938	−	27.6466i	0.0788188	−	1.25279i	−0.737564	−	0.675277i	$-0.764024\pi$
$487$	1.73938	−	27.6466i	0.0788188	−	1.25279i	0.816383	−	0.577511i	$-0.195976\pi$
$488$	−3.61110	−	1.42973i	−0.163467	−	0.0647210i
$489$	−11.8658	+	18.6975i	−0.536591	+	0.845532i
$490$	−3.91338	+	7.14947i	−0.176789	+	0.322980i
$491$	1.00934	−	16.0430i	0.0455509	−	0.724011i	−0.907283	−	0.420520i	$-0.861848\pi$
$491$	1.00934	−	16.0430i	0.0455509	−	0.724011i	0.952834	−	0.303491i	$-0.0981523\pi$
$492$	−37.8163	−	4.77730i	−1.70489	−	0.215378i
$493$	−0.0333116	+	0.0242023i	−0.00150028	+	0.00109002i
$494$	0.138791	+	0.727568i	0.00624450	+	0.0327348i
$495$	−10.8350	+	42.5233i	−0.486996	+	1.91128i
$496$	−2.88930	−	6.14007i	−0.129733	−	0.275697i
$497$	−15.3535	+	14.4179i	−0.688699	+	0.646731i
$498$	0.186256	−	0.293493i	0.00834634	−	0.0131517i
$499$	14.6484			0.655752			0.327876	−	0.944721i	$-0.393667\pi$
$499$	14.6484			0.655752			0.327876	+	0.944721i	$0.393667\pi$
$500$	0.0615597	+	11.1802i	0.00275303	+	0.499992i
$501$	−39.2813			−1.75496
$502$	10.2142	−	16.0949i	0.455880	−	0.718352i
$503$	−26.4285	+	24.8181i	−1.17839	+	1.10658i	−0.186115	+	0.982528i	$0.559590\pi$
$503$	−26.4285	+	24.8181i	−1.17839	+	1.10658i	−0.992275	+	0.124055i	$0.960410\pi$
$504$	−6.49259	−	13.7974i	−0.289203	−	0.614587i
$505$	−29.2549	−	18.4905i	−1.30182	−	0.822815i
$506$	−1.59325	−	8.35212i	−0.0708287	−	0.371297i
$507$	0.686905	−	0.499066i	0.0305065	−	0.0221643i
$508$	−7.76410	−	0.980834i	−0.344476	−	0.0435175i
$509$	−0.0472390	+	0.750843i	−0.00209383	+	0.0332805i	−0.998935	−	0.0461415i	$-0.985307\pi$
$509$	−0.0472390	+	0.750843i	−0.00209383	+	0.0332805i	0.996841	+	0.0794221i	$0.0253075\pi$
$510$	−0.418242	−	3.26256i	−0.0185201	−	0.144469i
$511$	−5.03417	+	7.93258i	−0.222699	+	0.350917i
$512$	−0.929776	−	0.368125i	−0.0410907	−	0.0162690i
$513$	0.233429	−	3.71025i	0.0103061	−	0.163811i
$514$	−0.394755	−	6.27446i	−0.0174119	−	0.276754i
$515$	3.14155	−	3.35774i	0.138433	−	0.147960i
$516$	−19.9681	+	24.1373i	−0.879047	+	1.06259i
$517$	8.51524	−	18.0958i	0.374500	−	0.795853i
$518$	17.4952	+	12.7110i	0.768695	+	0.558490i
$519$	−34.6284	−	32.5182i	−1.52002	−	1.42739i
$520$	7.83947	−	1.51038i	0.343783	−	0.0662344i
$521$	1.87452	−	9.82660i	0.0821244	−	0.430511i	−0.917350	−	0.398083i	$-0.869676\pi$
$521$	1.87452	−	9.82660i	0.0821244	−	0.430511i	0.999474	−	0.0324288i	$-0.0103242\pi$
$522$	0.333899	+	0.709571i	0.0146143	+	0.0310571i
$523$	−30.0424	−	7.71359i	−1.31366	−	0.337292i	−0.474061	−	0.880492i	$-0.657213\pi$
$523$	−30.0424	−	7.71359i	−1.31366	−	0.337292i	−0.839603	+	0.543200i	$0.817213\pi$
$524$	16.4456	−	11.9484i	0.718430	−	0.521970i
$525$	−16.6098	−	25.9617i	−0.724909	−	1.13306i
$526$	−4.84010	−	3.51654i	−0.211038	−	0.153328i
$527$	1.89073	+	2.28550i	0.0823614	+	0.0995578i
$528$	−6.95170	−	3.82173i	−0.302534	−	0.166319i
$529$	−8.75409	−	4.81260i	−0.380612	−	0.209243i
$530$	−4.76623	+	12.1030i	−0.207032	+	0.525720i
$531$	−40.8090	+	86.7236i	−1.77096	+	3.76348i
$532$	0.117422	+	0.361387i	0.00509088	+	0.0156681i
$533$	7.57773	+	39.7239i	0.328228	+	1.72063i
$534$	18.6520	+	29.3908i	0.807151	+	1.27187i
$535$	1.53683	−	6.03151i	0.0664431	−	0.260765i
$536$	−3.93367	+	1.55745i	−0.169909	+	0.0672715i
$537$	−25.3092	+	30.5935i	−1.09217	+	1.32021i
$538$	−3.66173	+	0.940174i	−0.157869	+	0.0405338i
$539$	−5.47695	−	6.62050i	−0.235909	−	0.285165i
$540$	−39.9961	−	2.44265i	−1.72116	−	0.105115i
$541$	−19.7406	+	5.06854i	−0.848717	+	0.217913i	−0.647909	−	0.761717i	$-0.724356\pi$
$541$	−19.7406	+	5.06854i	−0.848717	+	0.217913i	−0.200807	+	0.979631i	$0.564356\pi$
$542$	1.96493	+	1.84519i	0.0844011	+	0.0792579i
$543$	−8.01130	+	24.6562i	−0.343798	+	1.05810i
$544$	0.433666	+	0.0547847i	0.0185933	+	0.00234888i
$545$	26.3623	+	8.51217i	1.12924	+	0.364621i
$546$	−16.0432	+	15.0656i	−0.686587	+	0.644748i
$547$	−32.5214	+	4.10841i	−1.39052	+	0.175663i	−0.784668	−	0.619917i	$-0.787166\pi$
$547$	−32.5214	+	4.10841i	−1.39052	+	0.175663i	−0.605849	+	0.795580i	$0.707166\pi$
$548$	0.00555986	+	0.0883714i	0.000237505	+	0.00377504i
$549$	9.99145	−	30.7505i	0.426425	−	1.31240i
$550$	−10.9747	−	4.29865i	−0.467962	−	0.183295i
$551$	−0.00603874	−	0.0185853i	−0.000257259	−	0.000791761i
$552$	11.2860	−	4.46845i	0.480365	−	0.190190i
$553$	−1.13746	+	5.96278i	−0.0483698	+	0.253563i
$554$	5.10227	−	0.644567i	0.216775	−	0.0273850i
$555$	80.3171	−	37.9746i	3.40927	−	1.61193i
$556$	−2.47005	+	1.35792i	−0.104754	+	0.0575887i
$557$	−19.5483			−0.828288			−0.414144	−	0.910211i	$-0.635919\pi$
$557$	−19.5483			−0.828288			−0.414144	+	0.910211i	$0.635919\pi$
$558$	49.5050	−	27.2156i	2.09571	−	1.15213i
$559$	30.9018	+	12.2349i	1.30701	+	0.517480i
$560$	3.89295	−	1.27280i	0.164507	−	0.0537856i
$561$	3.35865	+	0.862355i	0.141802	+	0.0364087i
$562$	−12.0866	−	19.0454i	−0.509840	−	0.803380i
$563$	1.35800	+	2.13987i	0.0572330	+	0.0901848i	0.871739	−	0.489970i	$-0.162992\pi$
$563$	1.35800	+	2.13987i	0.0572330	+	0.0901848i	−0.814506	+	0.580155i	$0.802992\pi$
$564$	27.6537	+	7.10027i	1.16443	+	0.298975i
$565$	−0.0548243	−	29.8710i	−0.00230648	−	1.25668i
$566$	−4.62079	−	1.82950i	−0.194226	−	0.0768996i
$567$	56.7100	−	31.1766i	2.38160	−	1.30929i
$568$	−11.4988			−0.482477
$569$	−1.11989	+	0.615663i	−0.0469481	+	0.0258099i	−0.505055	−	0.863087i	$-0.668528\pi$
$569$	−1.11989	+	0.615663i	−0.0469481	+	0.0258099i	0.458107	+	0.888897i	$0.348528\pi$
$570$	1.53396	+	0.289701i	0.0642505	+	0.0121343i
$571$	−45.7802	+	5.78339i	−1.91584	+	0.242027i	−0.990543	−	0.137206i	$-0.956188\pi$
$571$	−45.7802	+	5.78339i	−1.91584	+	0.242027i	−0.925301	+	0.379233i	$0.876188\pi$
$572$	−1.57709	+	8.26741i	−0.0659416	+	0.345678i
$573$	−8.64716	+	3.42365i	−0.361240	+	0.143025i
$574$	6.41102	+	19.7311i	0.267591	+	0.823559i
$575$	15.7721	−	8.74631i	0.657741	−	0.364747i
$576$	2.57258	−	7.91757i	0.107191	−	0.329899i
$577$	2.39904	+	38.1316i	0.0998733	+	1.58744i	0.654970	+	0.755655i	$0.272681\pi$
$577$	2.39904	+	38.1316i	0.0998733	+	1.58744i	−0.555097	+	0.831786i	$0.687319\pi$
$578$	16.6764	−	2.10672i	0.693646	−	0.0876279i
$579$	37.5504	−	35.2622i	1.56054	−	1.46545i
$580$	−0.200205	+	0.0654572i	−0.00831308	+	0.00271796i
$581$	−0.187705	−	0.0237127i	−0.00778732	−	0.000983767i
$582$	4.81359	−	14.8147i	0.199530	−	0.614089i
$583$	−9.99627	−	9.38712i	−0.414003	−	0.388775i
$584$	−4.96813	+	1.27560i	−0.205583	+	0.0527847i
$585$	16.6471	+	64.3455i	0.688271	+	2.66036i
$586$	−5.87840	−	7.10576i	−0.242834	−	0.293536i
$587$	−10.1972	+	2.61820i	−0.420884	+	0.108065i	−0.453191	−	0.891413i	$-0.649715\pi$
$587$	−10.1972	+	2.61820i	−0.420884	+	0.108065i	0.0323070	+	0.999478i	$0.489715\pi$
$588$	7.81886	−	9.45138i	0.322444	−	0.389768i
$589$	−1.30890	+	0.518229i	−0.0539321	+	0.0213532i
$590$	−21.7614	−	13.7542i	−0.895903	−	0.566253i
$591$	28.2857	+	44.5711i	1.16352	+	1.83341i
$592$	2.21228	+	11.5972i	0.0909242	+	0.476641i
$593$	−2.24358	−	6.90502i	−0.0921327	−	0.283555i	0.894363	−	0.447342i	$-0.147629\pi$
$593$	−2.24358	−	6.90502i	−0.0921327	−	0.283555i	−0.986496	+	0.163786i	$0.947629\pi$
$594$	17.9863	−	38.2228i	0.737986	−	1.56830i
$595$	−1.50984	+	0.962063i	−0.0618973	+	0.0394407i
$596$	0.146554	+	0.0805686i	0.00600308	+	0.00330022i
$597$	3.44818	+	1.89565i	0.141124	+	0.0775838i
$598$	−8.20894	−	9.92290i	−0.335689	−	0.405778i
$599$	2.91401	+	2.11715i	0.119063	+	0.0865044i	0.645723	−	0.763572i	$-0.276556\pi$
$599$	2.91401	+	2.11715i	0.119063	+	0.0865044i	−0.526660	+	0.850076i	$0.676556\pi$
$600$	3.09225	−	16.5398i	0.126241	−	0.675233i
$601$	7.14238	−	5.18924i	0.291344	−	0.211674i	−0.432506	−	0.901631i	$-0.642371\pi$
$601$	7.14238	−	5.18924i	0.291344	−	0.211674i	0.723850	+	0.689957i	$0.242371\pi$
$602$	16.5148	+	4.24028i	0.673093	+	0.172821i
$603$	−14.9965	−	31.8691i	−0.610704	−	1.29781i
$604$	0.835251	−	4.37854i	0.0339859	−	0.178160i
$605$	−8.31546	+	8.88770i	−0.338072	+	0.361337i
$606$	37.9687	+	35.6550i	1.54237	+	1.44838i
$607$	7.92338	+	5.75667i	0.321600	+	0.233656i	0.736858	−	0.676048i	$-0.236309\pi$
$607$	7.92338	+	5.75667i	0.321600	+	0.233656i	−0.415258	+	0.909704i	$0.636309\pi$
$608$	−0.0883291	+	0.187709i	−0.00358222	+	0.00761260i
$609$	0.370118	−	0.447396i	0.0149979	−	0.0181294i
$610$	7.86476	+	3.68326i	0.318435	+	0.149131i
$611$	−1.90199	−	30.2312i	−0.0769461	−	1.22302i
$612$	−0.228493	+	3.63179i	−0.00923628	+	0.146807i
$613$	−21.2559	−	8.41582i	−0.858520	−	0.339912i	−0.102716	−	0.994711i	$-0.532753\pi$
$613$	−21.2559	−	8.41582i	−0.858520	−	0.339912i	−0.755803	+	0.654799i	$0.772753\pi$
$614$	11.4571	−	18.0535i	0.462370	−	0.728578i
$615$	83.7513	+	15.8172i	3.37718	+	0.637810i
$616$	−0.271117	+	4.30928i	−0.0109236	+	0.173626i
$617$	−32.5472	−	4.11167i	−1.31030	−	0.165530i	−0.561032	−	0.827794i	$-0.689596\pi$
$617$	−32.5472	−	4.11167i	−1.31030	−	0.165530i	−0.749270	+	0.662264i	$0.769596\pi$
$618$	−5.59865	+	4.06766i	−0.225211	+	0.163625i
$619$	8.53926	+	44.7643i	0.343222	+	1.79923i	0.566047	+	0.824373i	$0.308472\pi$
$619$	8.53926	+	44.7643i	0.343222	+	1.79923i	−0.222826	+	0.974858i	$0.571528\pi$
$620$	5.61171	+	14.0979i	0.225372	+	0.566185i
$621$	27.5213	+	58.4857i	1.10439	+	2.34695i
$622$	−1.02787	+	0.965231i	−0.0412137	+	0.0387022i
$623$	10.1520	−	15.9971i	0.406733	−	0.640908i
$624$	−12.0153			−0.480998
$625$	1.38655	−	24.9615i	0.0554619	−	0.998461i
$626$	12.8408			0.513222
$627$	−0.881817	+	1.38952i	−0.0352164	+	0.0554921i
$628$	−6.33484	+	5.94881i	−0.252787	+	0.237383i
$629$	−2.19731	−	4.66952i	−0.0876125	−	0.186186i
$630$	12.6102	+	31.6796i	0.502401	+	1.26215i
$631$	−1.56235	−	8.19011i	−0.0621960	−	0.326043i	0.937567	−	0.347804i	$-0.113073\pi$
$631$	−1.56235	−	8.19011i	−0.0621960	−	0.326043i	−0.999763	+	0.0217613i	$0.993073\pi$
$632$	−2.68115	+	1.94797i	−0.106650	+	0.0774860i
$633$	10.0886	+	1.27448i	0.400984	+	0.0506561i
$634$	−0.338801	+	5.38509i	−0.0134555	+	0.213869i
$635$	17.1951	+	3.24744i	0.682366	+	0.128871i
$636$	10.4896	−	16.5289i	0.415939	−	0.655414i
$637$	−12.1001	−	4.79078i	−0.479424	−	0.189818i
$638$	0.0139429	−	0.221616i	0.000552005	−	0.00877387i
$639$	−6.01078	−	95.5386i	−0.237783	−	3.77945i
$640$	2.02500	+	0.948356i	0.0800451	+	0.0374871i
$641$	20.4794	−	24.7554i	0.808889	−	0.977779i	−0.191104	−	0.981570i	$-0.561207\pi$
$641$	20.4794	−	24.7554i	0.808889	−	0.977779i	0.999993	+	0.00379107i	$0.00120674\pi$
$642$	−3.98845	+	8.47589i	−0.157412	+	0.334517i
$643$	34.3069	+	24.9254i	1.35293	+	0.982962i	0.998860	+	0.0477437i	$0.0152031\pi$
$643$	34.3069	+	24.9254i	1.35293	+	0.982962i	0.354072	+	0.935218i	$0.384797\pi$
$644$	−4.81614	−	4.52266i	−0.189783	−	0.178218i
$645$	47.8571	−	51.1505i	1.88437	−	2.01405i
$646$	0.0169918	−	0.0890740i	0.000668532	−	0.00350457i
$647$	−5.70023	−	12.1136i	−0.224099	−	0.476235i	0.760884	−	0.648888i	$-0.224766\pi$
$647$	−5.70023	−	12.1136i	−0.224099	−	0.476235i	−0.984983	+	0.172654i	$0.944766\pi$
$648$	34.2210	+	8.78646i	1.34433	+	0.345165i
$649$	21.9563	−	15.9522i	0.861860	−	0.626178i
$650$	−17.7029	+	2.30244i	−0.694363	+	0.0903092i
$651$	−33.8401	−	24.5863i	−1.32630	−	0.963613i
$652$	4.19452	+	5.07030i	0.164270	+	0.198568i
$653$	−30.1025	−	16.5490i	−1.17800	−	0.647611i	−0.232298	−	0.972645i	$-0.574624\pi$
$653$	−30.1025	−	16.5490i	−1.17800	−	0.647611i	−0.945702	+	0.325034i	$0.894624\pi$
$654$	−36.5350	−	20.0853i	−1.42863	−	0.785398i
$655$	−38.3338	+	24.4262i	−1.49783	+	0.954410i
$656$	−4.82260	+	10.2486i	−0.188291	+	0.400139i
$657$	−13.1954	−	40.6114i	−0.514803	−	1.58440i
$658$	−2.91186	−	15.2645i	−0.113516	−	0.595073i
$659$	−0.897255	−	1.41385i	−0.0349521	−	0.0550757i	0.826403	−	0.563080i	$-0.190384\pi$
$659$	−0.897255	−	1.41385i	−0.0349521	−	0.0550757i	−0.861355	+	0.508004i	$0.830384\pi$
$660$	14.9946	+	9.47732i	0.583665	+	0.368904i
$661$	8.68758	−	3.43965i	0.337908	−	0.133787i	−0.193042	−	0.981190i	$-0.561835\pi$
$661$	8.68758	−	3.43965i	0.337908	−	0.133787i	0.530950	+	0.847403i	$0.321835\pi$
$662$	1.50703	−	1.82168i	0.0585723	−	0.0708018i
$663$	5.08705	−	1.30613i	0.197564	−	0.0507259i
$664$	−0.0658408	−	0.0795879i	−0.00255512	−	0.00308861i
$665$	−0.212815	−	0.822590i	−0.00825262	−	0.0318987i
$666$	−95.1999	+	24.4432i	−3.68892	+	0.947154i
$667$	0.247683	+	0.232590i	0.00959032	+	0.00900591i
$668$	−3.60702	+	11.1013i	−0.139560	+	0.429521i
$669$	−66.1024	−	8.35068i	−2.55567	−	0.322856i
$670$	8.99188	−	2.93990i	0.347387	−	0.113578i
$671$	−6.67398	+	6.26728i	−0.257646	+	0.241946i
$672$	−6.11546	+	0.772562i	−0.235909	+	0.0298022i
$673$	−1.83604	−	29.1830i	−0.0707741	−	1.12492i	−0.859823	−	0.510592i	$-0.829426\pi$
$673$	−1.83604	−	29.1830i	−0.0707741	−	1.12492i	0.789049	−	0.614330i	$-0.210574\pi$
$674$	6.25190	−	19.2414i	0.240814	−	0.741150i
$675$	88.9348	+	10.9036i	3.42310	+	0.419679i
$676$	−0.0779654	−	0.239953i	−0.00299867	−	0.00922896i
$677$	5.31493	−	2.10433i	0.204269	−	0.0808760i	−0.263762	−	0.964588i	$-0.584963\pi$
$677$	5.31493	−	2.10433i	0.204269	−	0.0808760i	0.468031	+	0.883712i	$0.344963\pi$
$678$	−8.42387	+	44.1595i	−0.323517	+	1.69593i
$679$	−8.41156	+	1.06263i	−0.322806	+	0.0407799i
$680$	−0.960435	−	0.181387i	−0.0368310	−	0.00695586i
$681$	20.9014	−	11.4906i	0.800942	−	0.440322i
$682$	−15.9964			−0.612534
$683$	−26.2480	+	14.4300i	−1.00435	+	0.552148i	−0.896980	−	0.442071i	$-0.854244\pi$
$683$	−26.2480	+	14.4300i	−1.00435	+	0.552148i	−0.107373	+	0.994219i	$0.534244\pi$
$684$	−1.60577	−	0.635770i	−0.0613982	−	0.0243093i
$685$	−0.000363393	−	0.197995i	−1.38845e−5	−	0.00756499i
$686$	−18.8855	−	4.84898i	−0.721053	−	0.185135i
$687$	27.1528	+	42.7859i	1.03594	+	1.63238i
$688$	4.98785	+	7.85959i	0.190160	+	0.299644i
$689$	−20.1172	−	5.16521i	−0.766403	−	0.196779i
$690$	−25.7985	+	8.43481i	−0.982131	+	0.321108i
$691$	−27.1009	−	10.7300i	−1.03097	−	0.408189i	−0.209116	−	0.977891i	$-0.567059\pi$
$691$	−27.1009	−	10.7300i	−1.03097	−	0.408189i	−0.821852	+	0.569702i	$0.807059\pi$
$692$	−12.3697	+	6.80031i	−0.470226	+	0.258509i
$693$	−35.9458			−1.36547
$694$	9.75182	−	5.36111i	0.370174	−	0.203505i
$695$	5.69803	−	2.69407i	0.216139	−	0.102192i
$696$	0.314504	−	0.0397311i	0.0119212	−	0.00150600i
$697$	0.927719	−	4.86327i	0.0351399	−	0.184210i
$698$	20.8575	−	8.25806i	0.789467	−	0.312572i
$699$	1.77614	+	5.46640i	0.0671798	+	0.206758i
$700$	−8.86221	+	2.31014i	−0.334960	+	0.0873150i
$701$	−4.38324	+	13.4902i	−0.165553	+	0.509519i	−0.999077	−	0.0429646i	$-0.986320\pi$
$701$	−4.38324	+	13.4902i	−0.165553	+	0.509519i	0.833524	+	0.552483i	$0.186320\pi$
$702$	−4.01746	−	63.8557i	−0.151629	−	2.41008i
$703$	2.42994	−	0.306972i	0.0916468	−	0.0115777i
$704$	−1.71840	+	1.61368i	−0.0647646	+	0.0608180i
$705$	−60.7528	−	19.6166i	−2.28808	−	0.738803i
$706$	2.81992	+	0.356238i	0.106129	+	0.0134072i
$707$	8.76046	−	26.9619i	0.329471	−	1.01401i
$708$	28.2432	+	26.5222i	1.06145	+	0.996764i
$709$	−6.33379	+	1.62624i	−0.237870	+	0.0610747i	−0.365743	−	0.930716i	$-0.619185\pi$
$709$	−6.33379	+	1.62624i	−0.237870	+	0.0610747i	0.127873	+	0.991791i	$0.459185\pi$
$710$	25.6642	+	1.56737i	0.963160	+	0.0588224i
$711$	−17.5864	−	21.2583i	−0.659542	−	0.797249i
$712$	10.0189	−	2.57241i	0.375473	−	0.0964050i
$713$	15.6019	−	18.8595i	0.584297	−	0.706294i
$714$	2.50518	−	0.991871i	0.0937540	−	0.0371198i
$715$	4.64684	−	18.2371i	0.173782	−	0.682031i
$716$	6.32200	+	9.96187i	0.236264	+	0.372293i
$717$	7.17008	+	37.5869i	0.267771	+	1.40371i
$718$	1.02201	+	3.14541i	0.0381409	+	0.117386i
$719$	−1.49027	+	3.16699i	−0.0555778	+	0.118109i	−0.930687	−	0.365817i	$-0.880790\pi$
$719$	−1.49027	+	3.16699i	−0.0555778	+	0.118109i	0.875109	+	0.483926i	$0.160790\pi$
$720$	−6.82098	+	17.3206i	−0.254203	+	0.645502i
$721$	3.30073	+	1.81459i	0.122926	+	0.0675789i
$722$	−16.6121	−	9.13259i	−0.618239	−	0.339880i
$723$	46.0976	+	55.7224i	1.71439	+	2.07234i
$724$	6.23244	+	4.52814i	0.231627	+	0.168287i
$725$	0.455763	−	0.118805i	0.0169266	−	0.00441231i
$726$	14.8192	−	10.7668i	0.549993	−	0.399594i
$727$	−27.1927	−	6.98189i	−1.00852	−	0.258944i	−0.291931	−	0.956439i	$-0.594298\pi$
$727$	−27.1927	−	6.98189i	−1.00852	−	0.258944i	−0.716589	+	0.697495i	$0.754298\pi$
$728$	2.78450	+	5.91737i	0.103201	+	0.219312i
$729$	−21.2141	+	111.208i	−0.785706	+	4.11882i
$730$	11.2623	−	2.16983i	0.416836	−	0.0803089i
$731$	−2.96614	−	2.78539i	−0.109706	−	0.103021i
$732$	−10.5740	−	7.68244i	−0.390825	−	0.283951i
$733$	−4.17523	+	8.87281i	−0.154215	+	0.327725i	−0.966974	−	0.254877i	$-0.917965\pi$
$733$	−4.17523	+	8.87281i	−0.154215	+	0.327725i	0.812758	+	0.582601i	$0.197965\pi$
$734$	8.63695	−	10.4403i	0.318796	−	0.385358i
$735$	−18.7393	+	20.0288i	−0.691209	+	0.738775i
$736$	−0.226484	−	3.59985i	−0.00834830	−	0.132692i
$737$	−0.626222	+	9.95351i	−0.0230672	+	0.366642i
$738$	−87.6721	−	34.7118i	−3.22725	−	1.27776i
$739$	13.0127	−	20.5047i	0.478679	−	0.754277i	−0.516079	−	0.856541i	$-0.672609\pi$
$739$	13.0127	−	20.5047i	0.478679	−	0.754277i	0.994757	+	0.102264i	$0.0326087\pi$
$740$	−3.35682	−	26.1854i	−0.123399	−	0.962595i
$741$	−0.156512	+	2.48769i	−0.00574963	+	0.0913877i
$742$	−10.5712	−	1.33545i	−0.388080	−	0.0490259i
$743$	30.2757	−	21.9966i	1.11071	−	0.806977i	0.127934	−	0.991783i	$-0.459165\pi$
$743$	30.2757	−	21.9966i	1.11071	−	0.806977i	0.982775	+	0.184805i	$0.0591654\pi$
$744$	−4.27911	−	22.4319i	−0.156880	−	0.822392i
$745$	−0.316113	−	0.199798i	−0.0115815	−	0.00732004i
$746$	9.81636	+	20.8608i	0.359403	+	0.763769i
$747$	0.626847	−	0.588648i	0.0229351	−	0.0215375i
$748$	0.552119	−	0.870001i	0.0201875	−	0.0318104i
$749$	5.09856			0.186297
$750$	−9.15612	+	36.4938i	−0.334334	+	1.33256i
$751$	−39.1514			−1.42866			−0.714328	−	0.699811i	$-0.753268\pi$
$751$	−39.1514			−1.42866			−0.714328	+	0.699811i	$0.753268\pi$
$752$	4.54592	−	7.16322i	0.165773	−	0.261216i
$753$	46.7635	−	43.9138i	1.70416	−	1.60031i
$754$	−0.143201	−	0.304317i	−0.00521506	−	0.0110826i
$755$	−2.46103	+	9.65865i	−0.0895661	+	0.351514i
$756$	−6.15057	−	32.2424i	−0.223694	−	1.17265i
$757$	18.0695	−	13.1282i	0.656746	−	0.477154i	−0.208816	−	0.977955i	$-0.566961\pi$
$757$	18.0695	−	13.1282i	0.656746	−	0.477154i	0.865562	+	0.500801i	$0.166961\pi$
$758$	−9.14804	−	1.15567i	−0.332272	−	0.0419757i
$759$	1.79668	−	28.5575i	0.0652155	−	1.03657i
$760$	0.222729	−	0.406909i	0.00807922	−	0.0147602i
$761$	−5.73624	+	9.03886i	−0.207938	+	0.327659i	−0.932250	−	0.361814i	$-0.882158\pi$
$761$	−5.73624	+	9.03886i	−0.207938	+	0.327659i	0.724312	+	0.689472i	$0.242158\pi$
$762$	−24.4865	−	9.69491i	−0.887054	−	0.351209i
$763$	−1.42487	+	22.6477i	−0.0515838	+	0.819901i
$764$	0.173528	+	2.75815i	0.00627802	+	0.0997862i
$765$	1.00502	−	8.07469i	0.0363365	−	0.291941i
$766$	18.7866	−	22.7091i	0.678787	−	0.820513i
$767$	17.5020	−	37.1935i	0.631959	−	1.34298i
$768$	−2.72256	−	1.97805i	−0.0982419	−	0.0713769i
$769$	32.7982	+	30.7995i	1.18273	+	1.11066i	0.991633	+	0.129088i	$0.0412051\pi$
$769$	32.7982	+	30.7995i	1.18273	+	1.11066i	0.191099	+	0.981571i	$0.438795\pi$
$770$	1.19250	−	9.58097i	0.0429746	−	0.345274i
$771$	3.96442	−	20.7822i	0.142775	−	0.748454i
$772$	−6.51734	−	13.8501i	−0.234564	−	0.498475i
$773$	−9.21214	−	2.36528i	−0.331338	−	0.0850731i	0.0793562	−	0.996846i	$-0.474714\pi$
$773$	−9.21214	−	2.36528i	−0.331338	−	0.0850731i	−0.410694	+	0.911773i	$0.634714\pi$
$774$	−62.6949	+	45.5505i	−2.25352	+	1.63728i
$775$	−10.6032	−	32.2302i	−0.380877	−	1.15774i
$776$	−3.74477	−	2.72073i	−0.134429	−	0.0976686i
$777$	46.3884	+	56.0739i	1.66417	+	2.01164i
$778$	15.5584	+	8.55329i	0.557795	+	0.306650i
$779$	2.05908	+	1.13199i	0.0737741	+	0.0405576i
$780$	26.8171	+	1.63778i	0.960207	+	0.0586420i
$781$	−11.5412	+	24.5263i	−0.412976	+	0.877620i
$782$	0.487212	+	1.49949i	0.0174227	+	0.0536215i
$783$	0.316309	+	1.65815i	0.0113040	+	0.0592575i
$784$	−1.95308	−	3.07756i	−0.0697528	−	0.109913i
$785$	14.9496	−	12.4137i	0.533576	−	0.443064i
$786$	63.6049	−	25.1830i	2.26871	−	0.898247i
$787$	−3.45670	+	4.17844i	−0.123218	+	0.148945i	−0.828515	−	0.559967i	$-0.810814\pi$
$787$	−3.45670	+	4.17844i	−0.123218	+	0.148945i	0.705297	+	0.708912i	$0.250814\pi$
$788$	15.1936	−	3.90104i	0.541248	−	0.138969i
$789$	−12.8335	−	15.5130i	−0.456885	−	0.552278i
$790$	6.24960	−	3.98223i	0.222351	−	0.141681i
$791$	23.7001	−	6.08515i	0.842679	−	0.216363i
$792$	−14.3057	−	13.4340i	−0.508332	−	0.477355i
$793$	−4.28508	+	13.1881i	−0.152168	+	0.468324i
$794$	13.0952	+	1.65431i	0.464733	+	0.0587094i
$795$	−25.6648	+	35.4613i	−0.910237	+	1.25768i
$796$	0.852359	−	0.800418i	0.0302111	−	0.0283701i
$797$	−36.3246	+	4.58886i	−1.28668	+	0.162546i	−0.738752	−	0.673978i	$-0.764584\pi$
$797$	−36.3246	+	4.58886i	−1.28668	+	0.162546i	−0.547931	+	0.836524i	$0.684584\pi$
$798$	0.0802935	+	1.27623i	0.00284236	+	0.0451780i
$799$	−1.14597	+	3.52693i	−0.0405415	+	0.124774i
$800$	−4.39035	−	2.39267i	−0.155222	−	0.0845936i
$801$	26.6103	+	81.8980i	0.940228	+	2.89372i
$802$	0.332127	−	0.131498i	0.0117278	−	0.00464337i
$803$	−2.26567	+	11.8771i	−0.0799539	+	0.419133i
$804$	−14.1254	+	1.78445i	−0.498164	+	0.0629328i
$805$	10.1327	+	10.7506i	0.357131	+	0.378910i
$806$	−21.2314	+	11.6721i	−0.747846	+	0.411132i
$807$	−12.7224			−0.447850
$808$	13.5629	−	7.45628i	0.477142	−	0.262311i
$809$	5.28745	+	2.09345i	0.185897	+	0.0736017i	0.459229	−	0.888318i	$-0.348126\pi$
$809$	5.28745	+	2.09345i	0.185897	+	0.0736017i	−0.273332	+	0.961920i	$0.588126\pi$
$810$	−75.1806	−	24.2752i	−2.64158	−	0.852943i
$811$	−2.46171	−	0.632060i	−0.0864423	−	0.0221946i	0.205221	−	0.978716i	$-0.434209\pi$
$811$	−2.46171	−	0.632060i	−0.0864423	−	0.0221946i	−0.291663	+	0.956521i	$0.594209\pi$
$812$	−0.0924520	−	0.145681i	−0.00324443	−	0.00511240i
$813$	4.86052	+	7.65896i	0.170466	+	0.268611i
$814$	26.9567	+	6.92129i	0.944830	+	0.242591i
$815$	−8.67066	−	11.8882i	−0.303720	−	0.416426i
$816$	1.36770	+	0.541511i	0.0478791	+	0.0189567i
$817$	1.69225	−	0.930322i	0.0592043	−	0.0325478i
$818$	−16.7965			−0.587277
$819$	−47.7095	+	26.2285i	−1.66711	+	0.916499i
$820$	12.1606	−	22.2165i	0.424666	−	0.775833i
$821$	−13.2394	+	1.67252i	−0.462057	+	0.0583713i	−0.352916	−	0.935655i	$-0.614810\pi$
$821$	−13.2394	+	1.67252i	−0.462057	+	0.0583713i	−0.109141	+	0.994026i	$0.534810\pi$
$822$	−0.0558362	+	0.292703i	−0.00194751	+	0.0102092i
$823$	−40.5744	+	16.0645i	−1.41433	+	0.559974i	−0.946171	−	0.323668i	$-0.895084\pi$
$823$	−40.5744	+	16.0645i	−1.41433	+	0.559974i	−0.468163	+	0.883642i	$0.655084\pi$
$824$	0.635460	+	1.95575i	0.0221373	+	0.0681316i
$825$	−32.1748	−	23.1964i	−1.12018	−	0.807595i
$826$	6.51652	−	20.0558i	0.226739	−	0.697830i
$827$	−0.766695	−	12.1863i	−0.0266606	−	0.423758i	−0.988607	−	0.150520i	$-0.951905\pi$
$827$	−0.766695	−	12.1863i	−0.0266606	−	0.423758i	0.961946	−	0.273238i	$-0.0880947\pi$
$828$	29.7914	−	3.76352i	1.03532	−	0.130792i
$829$	3.66597	−	3.44258i	0.127324	−	0.119566i	−0.618269	−	0.785966i	$-0.712166\pi$
$829$	3.66597	−	3.44258i	0.127324	−	0.119566i	0.745594	+	0.666401i	$0.232166\pi$
$830$	0.136102	+	0.186608i	0.00472418	+	0.00647724i
$831$	17.1705	+	2.16914i	0.595639	+	0.0752467i
$832$	−1.10331	+	3.39564i	−0.0382505	+	0.117723i
$833$	1.16144	+	1.09067i	0.0402416	+	0.0377893i
$834$	−9.18769	+	2.35900i	−0.318144	+	0.0816855i
$835$	9.56374	−	24.2854i	0.330967	−	0.840430i
$836$	0.311719	+	0.376803i	0.0107810	+	0.0130320i
$837$	117.784	−	30.2418i	4.07121	−	1.04531i
$838$	13.2959	−	16.0719i	0.459298	−	0.555195i
$839$	−30.0204	+	11.8859i	−1.03642	+	0.410347i	−0.823855	−	0.566800i	$-0.808181\pi$
$839$	−30.0204	+	11.8859i	−1.03642	+	0.410347i	−0.212564	+	0.977147i	$0.568181\pi$
$840$	13.7545	−	0.890704i	0.474574	−	0.0307322i
$841$	−15.5342	−	24.4780i	−0.535663	−	0.844070i
$842$	−5.23928	−	27.4653i	−0.180557	−	0.946515i
$843$	−23.4574	−	72.1945i	−0.807916	−	2.48651i
$844$	1.28657	−	2.73409i	0.0442854	−	0.0941113i
$845$	0.141304	+	0.546180i	0.00486102	+	0.0187892i
$846$	61.8926	+	34.0258i	2.12791	+	1.16983i
$847$	−8.73680	−	4.80309i	−0.300200	−	0.165036i
$848$	−3.70802	−	4.48223i	−0.127334	−	0.153920i
$849$	−13.5305	−	9.83051i	−0.464367	−	0.337382i
$850$	2.11888	+	0.535753i	0.0726770	+	0.0183762i
$851$	−34.4520	+	25.0308i	−1.18100	+	0.858046i
$852$	−37.4807	−	9.62341i	−1.28407	−	0.329693i
$853$	−1.75748	−	3.73484i	−0.0601751	−	0.127879i	0.872478	−	0.488654i	$-0.162512\pi$
$853$	−1.75748	−	3.73484i	−0.0601751	−	0.127879i	−0.932653	+	0.360776i	$0.882512\pi$
$854$	−1.33301	+	6.98790i	−0.0456148	+	0.239121i
$855$	3.49727	+	1.63786i	0.119604	+	0.0560136i
$856$	2.02913	+	1.90548i	0.0693541	+	0.0651278i
$857$	5.78935	+	4.20621i	0.197760	+	0.143681i	0.682259	−	0.731111i	$-0.260998\pi$
$857$	5.78935	+	4.20621i	0.197760	+	0.143681i	−0.484498	+	0.874792i	$0.660998\pi$
$858$	−12.0597	+	25.6281i	−0.411710	+	0.874929i
$859$	−11.8279	+	14.2975i	−0.403563	+	0.487824i	−0.932670	−	0.360731i	$-0.882527\pi$
$859$	−11.8279	+	14.2975i	−0.403563	+	0.487824i	0.529107	+	0.848555i	$0.322527\pi$
$860$	−10.0611	−	18.2218i	−0.343081	−	0.621358i
$861$	4.38388	+	69.6797i	0.149402	+	2.37468i
$862$	1.64599	−	26.1623i	0.0560628	−	0.891092i
$863$	26.9017	+	10.6511i	0.915745	+	0.362569i	0.778265	−	0.627936i	$-0.216100\pi$
$863$	26.9017	+	10.6511i	0.915745	+	0.362569i	0.137479	+	0.990505i	$0.456100\pi$
$864$	9.60209	−	15.1305i	0.326670	−	0.514749i
$865$	28.5350	−	13.4916i	0.970220	−	0.458728i
$866$	1.48861	−	23.6608i	0.0505851	−	0.804027i
$867$	56.1205	+	7.08967i	1.90595	+	0.240778i
$868$	−10.0557	+	7.30590i	−0.341313	+	0.247978i
$869$	1.46388	+	7.67391i	0.0496586	+	0.260320i
$870$	−0.707360	+	0.0458069i	−0.0239817	+	0.00155300i
$871$	6.43161	+	13.6679i	0.217927	+	0.463118i
$872$	−9.03114	+	8.48081i	−0.305833	+	0.287196i
$873$	20.6480	−	32.5360i	0.698828	−	1.10118i
$874$	−0.748276			−0.0253108
$875$	20.0945	−	3.94803i	0.679319	−	0.133468i
$876$	−17.2614			−0.583208
$877$	−19.4979	+	30.7237i	−0.658396	+	1.03747i	0.336989	+	0.941509i	$0.390591\pi$
$877$	−19.4979	+	30.7237i	−0.658396	+	1.03747i	−0.995385	+	0.0959579i	$0.969409\pi$
$878$	−20.2284	+	18.9957i	−0.682675	+	0.641075i
$879$	−13.2140	−	28.0812i	−0.445698	−	0.947156i
$880$	4.05527	−	3.36737i	0.136703	−	0.113514i
$881$	−10.5996	−	55.5650i	−0.357110	−	1.87203i	−0.476482	−	0.879184i	$-0.658088\pi$
$881$	−10.5996	−	55.5650i	−0.357110	−	1.87203i	0.119372	−	0.992850i	$-0.461912\pi$
$882$	24.5493	−	17.8361i	0.826617	−	0.600572i
$883$	5.05100	+	0.638089i	0.169980	+	0.0214734i	0.209862	−	0.977731i	$-0.432698\pi$
$883$	5.05100	+	0.638089i	0.169980	+	0.0214734i	−0.0398827	+	0.999204i	$0.512698\pi$
$884$	0.0979948	−	1.55758i	0.00329592	−	0.0523872i
$885$	−59.4212	−	63.0448i	−1.99742	−	2.11923i
$886$	−4.93575	+	7.77749i	−0.165820	+	0.261290i
$887$	45.4057	+	17.9774i	1.52457	+	0.603621i	0.973061	−	0.230546i	$-0.0740512\pi$
$887$	45.4057	+	17.9774i	1.52457	+	0.603621i	0.551512	+	0.834167i	$0.314051\pi$
$888$	−2.49475	+	39.6530i	−0.0837184	+	1.33067i
$889$	0.900059	+	14.3060i	0.0301870	+	0.479809i
$890$	−22.7118	+	4.37573i	−0.761302	+	0.146675i
$891$	53.0884	−	64.1729i	1.77853	−	2.14987i
$892$	−8.42986	+	17.9144i	−0.282253	+	0.599817i
$893$	−1.42388	−	1.03451i	−0.0476484	−	0.0346186i
$894$	0.410270	+	0.385269i	0.0137215	+	0.0128853i
$895$	−12.7522	−	23.0957i	−0.426260	−	0.772005i
$896$	−0.343221	+	1.79923i	−0.0114662	+	0.0601080i
$897$	−18.4528	−	39.2142i	−0.616122	−	1.30933i
$898$	−18.4876	−	4.74681i	−0.616939	−	0.158403i
$899$	0.517142	−	0.375725i	0.0172476	−	0.0125311i
$900$	17.5848	−	37.7284i	0.586158	−	1.25761i
$901$	2.05714	+	1.49460i	0.0685334	+	0.0497924i
$902$	17.0193	+	20.5728i	0.566679	+	0.684998i
$903$	50.2820	+	27.6427i	1.67328	+	0.919893i
$904$	11.7064	+	6.43563i	0.389348	+	0.214046i
$905$	−13.2930	−	10.9559i	−0.441875	−	0.364187i
$906$	6.38697	−	13.5730i	0.212193	−	0.450933i
$907$	6.46481	+	19.8966i	0.214660	+	0.660657i	0.999178	+	0.0405496i	$0.0129109\pi$
$907$	6.46481	+	19.8966i	0.214660	+	0.660657i	−0.784517	+	0.620107i	$0.787089\pi$
$908$	−1.32808	−	6.96206i	−0.0440740	−	0.231044i
$909$	69.0410	+	108.791i	2.28995	+	3.60838i
$910$	−5.40818	−	13.5866i	−0.179279	−	0.450391i
$911$	17.6587	−	6.99159i	0.585060	−	0.231642i	−0.0568996	−	0.998380i	$-0.518121\pi$
$911$	17.6587	−	6.99159i	0.585060	−	0.231642i	0.641960	+	0.766738i	$0.278121\pi$
$912$	−0.445007	+	0.537922i	−0.0147357	+	0.0178124i
$913$	−0.235841	+	0.0605536i	−0.00780519	+	0.00200403i
$914$	10.2567	+	12.3982i	0.339261	+	0.410096i
$915$	22.5530	+	18.5878i	0.745578	+	0.614494i
$916$	14.5850	−	3.74480i	0.481903	−	0.123732i
$917$	−27.1424	−	25.4884i	−0.896322	−	0.841703i
$918$	−2.42057	+	7.44974i	−0.0798906	+	0.245878i
$919$	23.5398	+	2.97377i	0.776507	+	0.0980957i	0.503591	−	0.863942i	$-0.332012\pi$
$919$	23.5398	+	2.97377i	0.776507	+	0.0980957i	0.272916	+	0.962038i	$0.412012\pi$
$920$	0.0148030	+	8.06542i	0.000488041	+	0.265909i
$921$	52.4539	−	49.2575i	1.72841	−	1.62309i
$922$	41.1217	−	5.19488i	1.35427	−	0.171084i
$923$	2.57787	+	40.9741i	0.0848516	+	1.34868i
$924$	−4.49019	+	13.8194i	−0.147716	+	0.454624i
$925$	3.92285	+	58.9010i	0.128983	+	1.93665i
$926$	−2.65581	−	8.17375i	−0.0872754	−	0.268606i
$927$	−15.9173	+	6.30212i	−0.522794	+	0.206989i
$928$	0.0176511	−	0.0925301i	0.000579424	−	0.00303745i
$929$	31.1336	−	3.93309i	1.02146	−	0.129040i	0.403280	−	0.915077i	$-0.367870\pi$
$929$	31.1336	−	3.93309i	1.02146	−	0.129040i	0.618180	+	0.786036i	$0.287870\pi$
$930$	6.49295	+	50.6492i	0.212912	+	1.66085i
$931$	−0.662629	+	0.364284i	−0.0217168	+	0.0119389i
$932$	1.70795			0.0559458
$933$	−4.15819	+	2.28598i	−0.136133	+	0.0748397i
$934$	−27.5501	−	10.9078i	−0.901466	−	0.356916i
$935$	−1.35087	+	1.86650i	−0.0441781	+	0.0610412i
$936$	−28.7898	−	7.39196i	−0.941024	−	0.241614i
$937$	−24.8474	−	39.1532i	−0.811728	−	1.27908i	−0.957116	−	0.289704i	$-0.906443\pi$
$937$	−24.8474	−	39.1532i	−0.811728	−	1.27908i	0.145388	−	0.989375i	$-0.453557\pi$
$938$	4.15232	+	6.54301i	0.135578	+	0.213637i
$939$	41.8551	+	10.7466i	1.36589	+	0.350701i
$940$	−11.1225	+	15.3680i	−0.362775	+	0.501250i
$941$	−32.6436	−	12.9245i	−1.06415	−	0.421327i	−0.230186	−	0.973147i	$-0.573934\pi$
$941$	−32.6436	−	12.9245i	−1.06415	−	0.421327i	−0.833963	+	0.551820i	$0.813934\pi$
$942$	−25.6273	+	14.0887i	−0.834981	+	0.459035i
$943$	−40.8545			−1.33041
$944$	10.0889	−	5.54640i	0.328364	−	0.180520i
$945$	9.33262	+	72.8005i	0.303590	+	2.36820i
$946$	21.7704	−	2.75024i	0.707816	−	0.0894180i
$947$	−10.3122	+	54.0583i	−0.335100	+	1.75666i	0.272253	+	0.962226i	$0.412231\pi$
$947$	−10.3122	+	54.0583i	−0.335100	+	1.75666i	−0.607353	+	0.794432i	$0.707769\pi$
$948$	−10.3696	+	4.10561i	−0.336788	+	0.133344i
$949$	5.65919	+	17.4172i	0.183705	+	0.565386i
$950$	−0.552575	+	0.877825i	−0.0179279	+	0.0284804i
$951$	−5.61116	+	17.2694i	−0.181954	+	0.559998i
$952$	−0.0502730	−	0.799066i	−0.00162936	−	0.0258979i
$953$	9.16881	−	1.15829i	0.297007	−	0.0375207i	0.0245822	−	0.999698i	$-0.492174\pi$
$953$	9.16881	−	1.15829i	0.297007	−	0.0375207i	0.272425	+	0.962177i	$0.412174\pi$
$954$	35.3027	−	33.1515i	1.14297	−	1.07332i
$955$	−0.0113418	−	6.17959i	−0.000367012	−	0.199967i
$956$	11.2808	+	1.42510i	0.364847	+	0.0460909i
$957$	0.230920	−	0.710699i	0.00746458	−	0.0229736i
$958$	27.8556	+	26.1582i	0.899974	+	0.845132i
$959$	0.157092	−	0.0403344i	0.00507276	−	0.00130246i
$960$	5.80688	+	4.78595i	0.187416	+	0.154466i
$961$	−9.59223	−	11.5950i	−0.309427	−	0.374033i
$962$	40.8288	−	10.4831i	1.31637	−	0.337987i
$963$	−14.7711	+	17.8552i	−0.475993	+	0.575377i
$964$	19.9806	−	7.91088i	0.643532	−	0.254792i
$965$	12.6583	+	31.8004i	0.407484	+	1.02369i
$966$	−11.9134	−	18.7725i	−0.383306	−	0.603994i
$967$	2.99064	+	15.6775i	0.0961725	+	0.504154i	0.997478	+	0.0709708i	$0.0226097\pi$
$967$	2.99064	+	15.6775i	0.0961725	+	0.504154i	−0.901306	+	0.433183i	$0.857390\pi$
$968$	−1.68202	−	5.17672i	−0.0540621	−	0.166386i
$969$	0.129932	−	0.276120i	0.00417402	−	0.00887025i
$970$	7.98712	+	6.58287i	0.256451	+	0.211363i
$971$	−47.1910	−	25.9435i	−1.51443	−	0.832566i	−0.514739	−	0.857347i	$-0.672111\pi$
$971$	−47.1910	−	25.9435i	−1.51443	−	0.832566i	−0.999693	+	0.0247805i	$0.992111\pi$
$972$	57.0808	+	31.3804i	1.83087	+	1.00653i
$973$	3.29098	+	3.97812i	0.105504	+	0.127533i
$974$	−22.4108	−	16.2824i	−0.718089	−	0.521722i
$975$	−59.6301	−	7.31076i	−1.90969	−	0.234132i
$976$	−3.14209	+	2.28286i	−0.100576	+	0.0730726i
$977$	−38.9644	−	10.0043i	−1.24658	−	0.320067i	−0.432933	−	0.901426i	$-0.642521\pi$
$977$	−38.9644	−	10.0043i	−1.24658	−	0.320067i	−0.813647	+	0.581359i	$0.802521\pi$
$978$	9.42883	+	20.0373i	0.301501	+	0.640722i
$979$	4.56902	−	23.9516i	0.146026	−	0.765497i
$980$	3.93960	+	7.13505i	0.125846	+	0.227921i
$981$	−75.1845	−	70.6029i	−2.40046	−	2.25418i
$982$	−13.0047	−	9.44849i	−0.414998	−	0.301513i
$983$	−0.402052	+	0.854403i	−0.0128235	+	0.0272512i	−0.911136	−	0.412105i	$-0.864794\pi$
$983$	−0.402052	+	0.854403i	−0.0128235	+	0.0272512i	0.898313	+	0.439357i	$0.144794\pi$
$984$	−24.2966	+	29.3695i	−0.774547	+	0.936266i
$985$	−34.4424	+	6.63577i	−1.09743	+	0.211433i
$986$	0.00258542	+	0.0410941i	8.23367e−5	+	0.00130870i
$987$	3.28366	−	52.1923i	0.104520	−	1.66130i
$988$	0.688674	+	0.272665i	0.0219096	+	0.00867464i
$989$	−17.9910	+	28.3493i	−0.572082	+	0.901456i
$990$	30.0979	+	31.9334i	0.956575	+	1.01491i
$991$	−1.43725	+	22.8444i	−0.0456558	+	0.725677i	0.906906	+	0.421333i	$0.138437\pi$
$991$	−1.43725	+	22.8444i	−0.0456558	+	0.725677i	−0.952562	+	0.304345i	$0.901563\pi$
$992$	−6.73239	−	0.850499i	−0.213754	−	0.0270034i
$993$	6.43680	−	4.67661i	0.204266	−	0.148408i
$994$	3.94662	+	20.6889i	0.125179	+	0.656212i
$995$	−2.01149	+	1.67028i	−0.0637685	+	0.0529514i
$996$	−0.148003	−	0.314523i	−0.00468966	−	0.00996603i
$997$	23.4869	−	22.0557i	0.743838	−	0.698510i	−0.216830	−	0.976209i	$-0.569572\pi$
$997$	23.4869	−	22.0557i	0.743838	−	0.698510i	0.960668	+	0.277699i	$0.0895718\pi$
$998$	7.84900	−	12.3681i	0.248456	−	0.391504i
$999$	−211.571			−6.69380

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.2.g.b.231.7	yes	140
125.46	even	25	inner	250.2.g.b.171.7	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
250.2.g.b.171.7	✓	140	125.46	even	25	inner
250.2.g.b.231.7	yes	140	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 250 = 2 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	250.g (of order \(25\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.535827 - 0.844328i) q^{2} +(2.45317 - 2.30368i) q^{3} +(-0.425779 - 0.904827i) q^{4} +(0.826966 + 2.07753i) q^{5} +(-0.630588 - 3.30566i) q^{6} +(-1.48185 + 1.07663i) q^{7} +(-0.992115 - 0.125333i) q^{8} +(0.522733 - 8.30860i) q^{9} +O(q^{10})\)	\(q+(0.535827 - 0.844328i) q^{2} +(2.45317 - 2.30368i) q^{3} +(-0.425779 - 0.904827i) q^{4} +(0.826966 + 2.07753i) q^{5} +(-0.630588 - 3.30566i) q^{6} +(-1.48185 + 1.07663i) q^{7} +(-0.992115 - 0.125333i) q^{8} +(0.522733 - 8.30860i) q^{9} +(2.19723 + 0.414965i) q^{10} +(-1.26311 + 1.99034i) q^{11} +(-3.12895 - 1.23884i) q^{12} +(-0.224187 + 3.56335i) q^{13} +(0.115012 + 1.82806i) q^{14} +(6.81466 + 3.19147i) q^{15} +(-0.637424 + 0.770513i) q^{16} +(0.186113 - 0.395511i) q^{17} +(-6.73509 - 4.89333i) q^{18} +(0.151227 + 0.142011i) q^{19} +(1.52770 - 1.63283i) q^{20} +(-1.15503 + 6.05488i) q^{21} +(1.00369 + 2.13295i) q^{22} +(-3.49365 - 0.897017i) q^{23} +(-2.72256 + 1.97805i) q^{24} +(-3.63225 + 3.43609i) q^{25} +(2.88851 + 2.09862i) q^{26} +(-11.4227 - 13.8077i) q^{27} +(1.60511 + 0.882414i) q^{28} +(-0.0825469 - 0.0453805i) q^{29} +(6.34613 - 4.04373i) q^{30} +(-2.88930 + 6.14007i) q^{31} +(0.309017 + 0.951057i) q^{32} +(1.48649 + 7.79244i) q^{33} +(-0.234217 - 0.369066i) q^{34} +(-3.46217 - 2.18826i) q^{35} +(-7.74042 + 3.06465i) q^{36} +(7.52562 - 9.09691i) q^{37} +(0.200935 - 0.0515914i) q^{38} +(7.65886 + 9.25797i) q^{39} +(-0.560062 - 2.16479i) q^{40} +(10.9707 - 2.81679i) q^{41} +(4.49341 + 4.21959i) q^{42} +(2.87655 - 8.85310i) q^{43} +(2.33871 + 0.295448i) q^{44} +(17.6936 - 5.78494i) q^{45} +(-2.62937 + 2.46914i) q^{46} +(-8.41703 + 1.06332i) q^{47} +(0.211307 + 3.35863i) q^{48} +(-1.12636 + 3.46658i) q^{49} +(0.954929 + 4.90796i) q^{50} +(-0.454564 - 1.39900i) q^{51} +(3.31967 - 1.31435i) q^{52} +(-1.09003 + 5.71416i) q^{53} +(-17.7788 + 2.24599i) q^{54} +(-5.17953 - 0.978199i) q^{55} +(1.60511 - 0.882414i) q^{56} +0.698134 q^{57} +(-0.0825469 + 0.0453805i) q^{58} +(-10.7045 - 4.23819i) q^{59} +(-0.0138111 - 7.52496i) q^{60} +(3.76182 + 0.965870i) q^{61} +(3.63607 + 5.72952i) q^{62} +(8.17067 + 12.8749i) q^{63} +(0.968583 + 0.248690i) q^{64} +(-7.58835 + 2.48101i) q^{65} +(7.37587 + 2.92031i) q^{66} +(3.70745 - 2.03819i) q^{67} -0.437112 q^{68} +(-10.6370 + 5.84773i) q^{69} +(-3.70273 + 1.75068i) q^{70} +(11.4081 - 1.44118i) q^{71} +(-1.55995 + 8.17757i) q^{72} +(4.76908 - 1.88821i) q^{73} +(-3.64835 - 11.2285i) q^{74} +(-0.994885 + 16.7969i) q^{75} +(0.0641064 - 0.197299i) q^{76} +(-0.271117 - 4.30928i) q^{77} +(11.9206 - 1.50592i) q^{78} +(2.41586 - 2.26864i) q^{79} +(-2.12789 - 0.687079i) q^{80} +(-35.0524 - 4.42815i) q^{81} +(3.50009 - 10.7722i) q^{82} +(0.0752966 + 0.0707083i) q^{83} +(5.97041 - 1.53294i) q^{84} +(0.975596 + 0.0595818i) q^{85} +(-5.93359 - 7.17248i) q^{86} +(-0.307044 + 0.0788356i) q^{87} +(1.50260 - 1.81633i) q^{88} +(-9.61745 + 3.80782i) q^{89} +(4.59634 - 18.0390i) q^{90} +(-3.50419 - 5.52172i) q^{91} +(0.675879 + 3.54308i) q^{92} +(7.05683 + 21.7187i) q^{93} +(-3.61228 + 7.67649i) q^{94} +(-0.169973 + 0.431616i) q^{95} +(2.94901 + 1.62123i) q^{96} +(4.05624 + 2.22993i) q^{97} +(2.32340 + 2.80851i) q^{98} +(15.8766 + 11.5351i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 5 q^{5} - 10 q^{7} - 10 q^{9}+O(q^{10}) \) 140 * q - 5 * q^5 - 10 * q^7 - 10 * q^9	\( 140 q - 5 q^{5} - 10 q^{7} - 10 q^{9} + 20 q^{10} - 10 q^{11} + 20 q^{12} + 20 q^{14} - 10 q^{15} - 5 q^{17} - 50 q^{18} + 40 q^{19} - 10 q^{20} - 5 q^{21} - 10 q^{22} + 10 q^{23} - 5 q^{24} - 5 q^{25} - 35 q^{26} + 30 q^{27} - 5 q^{28} - 10 q^{29} - 10 q^{30} + 35 q^{31} - 35 q^{32} - 55 q^{33} - 15 q^{34} - 25 q^{35} - 10 q^{36} - 25 q^{37} - 30 q^{39} + 25 q^{41} - 5 q^{42} - 45 q^{43} + 40 q^{44} - 5 q^{45} + 90 q^{47} - 5 q^{48} - 65 q^{49} + 30 q^{50} - 80 q^{51} - 50 q^{53} - 5 q^{54} - 35 q^{55} - 5 q^{56} + 40 q^{57} - 10 q^{58} + 45 q^{59} + 15 q^{60} + 45 q^{61} - 45 q^{62} - 75 q^{63} - 60 q^{65} + 15 q^{66} - 45 q^{67} + 10 q^{68} - 125 q^{69} - 15 q^{70} - 5 q^{71} - 5 q^{72} - 50 q^{73} + 20 q^{74} - 130 q^{75} - 5 q^{76} + 10 q^{77} + 10 q^{78} - 50 q^{79} - 5 q^{80} + 15 q^{81} + 40 q^{82} + 25 q^{83} - 50 q^{84} - 95 q^{85} - 10 q^{86} + 80 q^{87} - 10 q^{88} - 65 q^{89} - 10 q^{90} + 65 q^{91} - 25 q^{92} - 10 q^{93} - 35 q^{94} + 80 q^{95} - 40 q^{97} - 25 q^{98} + 90 q^{99}+O(q^{100}) \) 140 * q - 5 * q^5 - 10 * q^7 - 10 * q^9 + 20 * q^10 - 10 * q^11 + 20 * q^12 + 20 * q^14 - 10 * q^15 - 5 * q^17 - 50 * q^18 + 40 * q^19 - 10 * q^20 - 5 * q^21 - 10 * q^22 + 10 * q^23 - 5 * q^24 - 5 * q^25 - 35 * q^26 + 30 * q^27 - 5 * q^28 - 10 * q^29 - 10 * q^30 + 35 * q^31 - 35 * q^32 - 55 * q^33 - 15 * q^34 - 25 * q^35 - 10 * q^36 - 25 * q^37 - 30 * q^39 + 25 * q^41 - 5 * q^42 - 45 * q^43 + 40 * q^44 - 5 * q^45 + 90 * q^47 - 5 * q^48 - 65 * q^49 + 30 * q^50 - 80 * q^51 - 50 * q^53 - 5 * q^54 - 35 * q^55 - 5 * q^56 + 40 * q^57 - 10 * q^58 + 45 * q^59 + 15 * q^60 + 45 * q^61 - 45 * q^62 - 75 * q^63 - 60 * q^65 + 15 * q^66 - 45 * q^67 + 10 * q^68 - 125 * q^69 - 15 * q^70 - 5 * q^71 - 5 * q^72 - 50 * q^73 + 20 * q^74 - 130 * q^75 - 5 * q^76 + 10 * q^77 + 10 * q^78 - 50 * q^79 - 5 * q^80 + 15 * q^81 + 40 * q^82 + 25 * q^83 - 50 * q^84 - 95 * q^85 - 10 * q^86 + 80 * q^87 - 10 * q^88 - 65 * q^89 - 10 * q^90 + 65 * q^91 - 25 * q^92 - 10 * q^93 - 35 * q^94 + 80 * q^95 - 40 * q^97 - 25 * q^98 + 90 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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