LMFDB - Embedded newform 640.2.bm.a.221.31

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(21,640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(640, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 13, 0]))

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

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

chi := DirichletCharacter("640.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.bm (of order $32$, degree $16$, 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:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			221.31
Character	$\chi$	$=$	640.221
Dual form			640.2.bm.a.501.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0696611 + 1.41250i) q^{2} +(-2.70800 - 0.266714i) q^{3} +(-1.99029 - 0.196792i) q^{4} +(0.471397 + 0.881921i) q^{5} +(0.565375 - 3.80646i) q^{6} +(0.732825 + 3.68416i) q^{7} +(0.416614 - 2.79758i) q^{8} +(4.31976 + 0.859253i) q^{9} +O(q^{10})$	\(q+(-0.0696611 + 1.41250i) q^{2} +(-2.70800 - 0.266714i) q^{3} +(-1.99029 - 0.196792i) q^{4} +(0.471397 + 0.881921i) q^{5} +(0.565375 - 3.80646i) q^{6} +(0.732825 + 3.68416i) q^{7} +(0.416614 - 2.79758i) q^{8} +(4.31976 + 0.859253i) q^{9} +(-1.27855 + 0.604411i) q^{10} +(4.10442 + 3.36841i) q^{11} +(5.33723 + 1.06375i) q^{12} +(0.315885 + 0.168844i) q^{13} +(-5.25492 + 0.778471i) q^{14} +(-1.04132 - 2.51397i) q^{15} +(3.92255 + 0.783349i) q^{16} +(-0.190272 + 0.459358i) q^{17} +(-1.51461 + 6.04179i) q^{18} +(2.44121 - 0.740534i) q^{19} +(-0.764663 - 1.84805i) q^{20} +(-1.00187 - 10.1722i) q^{21} +(-5.04379 + 5.56284i) q^{22} +(-6.43045 + 4.29669i) q^{23} +(-1.87434 + 7.46471i) q^{24} +(-0.555570 + 0.831470i) q^{25} +(-0.260497 + 0.434425i) q^{26} +(-3.65692 - 1.10932i) q^{27} +(-0.733524 - 7.47678i) q^{28} +(-4.28923 - 5.22644i) q^{29} +(3.62351 - 1.29574i) q^{30} +(-3.47723 + 3.47723i) q^{31} +(-1.37973 + 5.48601i) q^{32} +(-10.2164 - 10.2164i) q^{33} +(-0.635587 - 0.300758i) q^{34} +(-2.90369 + 2.38300i) q^{35} +(-8.42849 - 2.56026i) q^{36} +(0.445183 - 1.46757i) q^{37} +(0.875944 + 3.49979i) q^{38} +(-0.810384 - 0.541481i) q^{39} +(2.66363 - 0.951347i) q^{40} +(4.16253 + 6.22967i) q^{41} +(14.4379 - 0.706534i) q^{42} +(-11.8221 + 1.16438i) q^{43} +(-7.50613 - 7.51185i) q^{44} +(1.27853 + 4.21473i) q^{45} +(-5.62111 - 9.38231i) q^{46} +(0.594046 + 0.246062i) q^{47} +(-10.4133 - 3.16751i) q^{48} +(-6.56886 + 2.72091i) q^{49} +(-1.13575 - 0.842662i) q^{50} +(0.637774 - 1.19319i) q^{51} +(-0.595478 - 0.398214i) q^{52} +(7.99729 - 9.74472i) q^{53} +(1.82165 - 5.08812i) q^{54} +(-1.03586 + 5.20764i) q^{55} +(10.6120 - 0.515260i) q^{56} +(-6.80831 + 1.35426i) q^{57} +(7.68112 - 5.69444i) q^{58} +(1.83492 - 0.980786i) q^{59} +(1.57780 + 5.20846i) q^{60} +(0.763163 - 7.74853i) q^{61} +(-4.66934 - 5.15380i) q^{62} +16.5444i q^{63} +(-7.65286 - 2.33102i) q^{64} +0.358179i q^{65} +(15.1423 - 13.7189i) q^{66} +(-0.372938 + 3.78650i) q^{67} +(0.469096 - 0.876813i) q^{68} +(18.5596 - 9.92033i) q^{69} +(-3.16370 - 4.26745i) q^{70} +(-3.34194 + 0.664753i) q^{71} +(4.20350 - 11.7269i) q^{72} +(-2.75549 + 13.8528i) q^{73} +(2.04193 + 0.731051i) q^{74} +(1.72625 - 2.10344i) q^{75} +(-5.00447 + 0.993469i) q^{76} +(-9.40195 + 17.5898i) q^{77} +(0.821292 - 1.10694i) q^{78} +(8.64105 - 3.57924i) q^{79} +(1.15822 + 3.82864i) q^{80} +(-2.60030 - 1.07708i) q^{81} +(-9.08935 + 5.44560i) q^{82} +(2.29476 + 7.56482i) q^{83} +(-0.00778440 + 20.4427i) q^{84} +(-0.494811 + 0.0487346i) q^{85} +(-0.821138 - 16.7798i) q^{86} +(10.2213 + 15.2972i) q^{87} +(11.1334 - 10.0791i) q^{88} +(-1.50062 - 1.00268i) q^{89} +(-6.04236 + 1.51231i) q^{90} +(-0.390561 + 1.28751i) q^{91} +(13.6441 - 7.28622i) q^{92} +(10.3437 - 8.48889i) q^{93} +(-0.388944 + 0.821948i) q^{94} +(1.80387 + 1.80387i) q^{95} +(5.19950 - 14.4881i) q^{96} +(-8.38097 + 8.38097i) q^{97} +(-3.38568 - 9.46803i) q^{98} +(14.8358 + 18.0775i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q+O(q^{10}) $ 1024 * q	$ 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) $ 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{11}{32}\right)$	$1$

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 $

$2$	−0.0696611	+	1.41250i	−0.0492578	+	0.998786i
$2$	−0.0696611	+	1.41250i	−0.0492578	+	0.998786i
$3$	−2.70800	−	0.266714i	−1.56346	−	0.153988i	−0.721074	−	0.692858i	$-0.756351\pi$
$3$	−2.70800	−	0.266714i	−1.56346	−	0.153988i	−0.842389	+	0.538870i	$0.818851\pi$
$4$	−1.99029	−	0.196792i	−0.995147	−	0.0983961i
$5$	0.471397	+	0.881921i	0.210815	+	0.394407i
$5$	0.471397	+	0.881921i	0.210815	+	0.394407i
$6$	0.565375	−	3.80646i	0.230814	−	1.55398i
$7$	0.732825	+	3.68416i	0.276982	+	1.39248i	0.829279	+	0.558835i	$0.188751\pi$
$7$	0.732825	+	3.68416i	0.276982	+	1.39248i	−0.552297	+	0.833647i	$0.686249\pi$
$8$	0.416614	−	2.79758i	0.147295	−	0.989093i
$9$	4.31976	+	0.859253i	1.43992	+	0.286418i
$10$	−1.27855	+	0.604411i	−0.404313	+	0.191131i
$11$	4.10442	+	3.36841i	1.23753	+	1.01561i	0.999010	+	0.0444771i	$0.0141622\pi$
$11$	4.10442	+	3.36841i	1.23753	+	1.01561i	0.238520	+	0.971138i	$0.423338\pi$
$12$	5.33723	+	1.06375i	1.54072	+	0.307079i
$13$	0.315885	+	0.168844i	0.0876108	+	0.0468290i	0.514620	−	0.857418i	$-0.327933\pi$
$13$	0.315885	+	0.168844i	0.0876108	+	0.0468290i	−0.427009	+	0.904247i	$0.640433\pi$
$14$	−5.25492	+	0.778471i	−1.40444	+	0.208055i
$15$	−1.04132	−	2.51397i	−0.268868	−	0.649104i
$16$	3.92255	+	0.783349i	0.980636	+	0.195837i
$17$	−0.190272	+	0.459358i	−0.0461478	+	0.111411i	−0.945273	−	0.326282i	$-0.894204\pi$
$17$	−0.190272	+	0.459358i	−0.0461478	+	0.111411i	0.899125	+	0.437692i	$0.144204\pi$
$18$	−1.51461	+	6.04179i	−0.356997	+	1.42406i
$19$	2.44121	−	0.740534i	0.560053	−	0.169890i	0.00244844	−	0.999997i	$-0.499221\pi$
$19$	2.44121	−	0.740534i	0.560053	−	0.169890i	0.557604	+	0.830107i	$0.311721\pi$
$20$	−0.764663	−	1.84805i	−0.170984	−	0.413237i
$21$	−1.00187	−	10.1722i	−0.218626	−	2.21975i
$22$	−5.04379	+	5.56284i	−1.07534	+	1.18600i
$23$	−6.43045	+	4.29669i	−1.34084	+	0.895922i	−0.999038	−	0.0438490i	$-0.986038\pi$
$23$	−6.43045	+	4.29669i	−1.34084	+	0.895922i	−0.341804	+	0.939771i	$0.611038\pi$
$24$	−1.87434	+	7.46471i	−0.382599	+	1.52373i
$25$	−0.555570	+	0.831470i	−0.111114	+	0.166294i
$26$	−0.260497	+	0.434425i	−0.0510876	+	0.0851978i
$27$	−3.65692	−	1.10932i	−0.703775	−	0.213488i
$28$	−0.733524	−	7.47678i	−0.138623	−	1.41298i
$29$	−4.28923	−	5.22644i	−0.796490	−	0.970526i	0.203473	−	0.979080i	$-0.434777\pi$
$29$	−4.28923	−	5.22644i	−0.796490	−	0.970526i	−0.999963	+	0.00855468i	$0.997277\pi$
$30$	3.62351	−	1.29574i	0.661560	−	0.236568i
$31$	−3.47723	+	3.47723i	−0.624528	+	0.624528i	−0.946686	−	0.322158i	$-0.895592\pi$
$31$	−3.47723	+	3.47723i	−0.624528	+	0.624528i	0.322158	+	0.946686i	$0.395592\pi$
$32$	−1.37973	+	5.48601i	−0.243904	+	0.969800i
$33$	−10.2164	−	10.2164i	−1.77844	−	1.77844i
$34$	−0.635587	−	0.300758i	−0.109002	−	0.0515796i
$35$	−2.90369	+	2.38300i	−0.490813	+	0.402800i
$36$	−8.42849	−	2.56026i	−1.40475	−	0.426710i
$37$	0.445183	−	1.46757i	0.0731876	−	0.241267i	−0.912712	−	0.408602i	$-0.866016\pi$
$37$	0.445183	−	1.46757i	0.0731876	−	0.241267i	0.985900	+	0.167335i	$0.0535163\pi$
$38$	0.875944	+	3.49979i	0.142097	+	0.567741i
$39$	−0.810384	−	0.541481i	−0.129765	−	0.0867063i
$40$	2.66363	−	0.951347i	0.421157	−	0.150421i
$41$	4.16253	+	6.22967i	0.650078	+	0.972911i	0.999356	+	0.0358914i	$0.0114270\pi$
$41$	4.16253	+	6.22967i	0.650078	+	0.972911i	−0.349278	+	0.937019i	$0.613573\pi$
$42$	14.4379	−	0.706534i	2.22782	−	0.109021i
$43$	−11.8221	+	1.16438i	−1.80286	+	0.177566i	−0.942961	−	0.332903i	$-0.891972\pi$
$43$	−11.8221	+	1.16438i	−1.80286	+	0.177566i	−0.859896	+	0.510469i	$0.829472\pi$
$44$	−7.50613	−	7.51185i	−1.13159	−	1.13245i
$45$	1.27853	+	4.21473i	0.190591	+	0.628296i
$46$	−5.62111	−	9.38231i	−0.828788	−	1.38335i
$47$	0.594046	+	0.246062i	0.0866506	+	0.0358918i	0.425588	−	0.904917i	$-0.360067\pi$
$47$	0.594046	+	0.246062i	0.0866506	+	0.0358918i	−0.338937	+	0.940809i	$0.610067\pi$
$48$	−10.4133	−	3.16751i	−1.50303	−	0.457190i
$49$	−6.56886	+	2.72091i	−0.938408	+	0.388701i
$50$	−1.13575	−	0.842662i	−0.160619	−	0.119170i
$51$	0.637774	−	1.19319i	0.0893062	−	0.167080i
$52$	−0.595478	−	0.398214i	−0.0825779	−	0.0552223i
$53$	7.99729	−	9.74472i	1.09851	−	1.33854i	0.162445	−	0.986718i	$-0.448062\pi$
$53$	7.99729	−	9.74472i	1.09851	−	1.33854i	0.936067	−	0.351823i	$-0.114438\pi$
$54$	1.82165	−	5.08812i	0.247895	−	0.692405i
$55$	−1.03586	+	5.20764i	−0.139676	+	0.702198i
$56$	10.6120	−	0.515260i	1.41809	−	0.0688545i
$57$	−6.80831	+	1.35426i	−0.901783	+	0.179376i
$58$	7.68112	−	5.69444i	1.00858	−	0.747717i
$59$	1.83492	−	0.980786i	0.238886	−	0.127687i	−0.347610	−	0.937639i	$-0.613007\pi$
$59$	1.83492	−	0.980786i	0.238886	−	0.127687i	0.586497	+	0.809952i	$0.300507\pi$
$60$	1.57780	+	5.20846i	0.203694	+	0.672410i
$61$	0.763163	−	7.74853i	0.0977131	−	0.992097i	−0.813888	−	0.581022i	$-0.802653\pi$
$61$	0.763163	−	7.74853i	0.0977131	−	0.992097i	0.911601	−	0.411076i	$-0.134847\pi$
$62$	−4.66934	−	5.15380i	−0.593007	−	0.654533i
$63$			16.5444i			2.08439i
$64$	−7.65286	−	2.33102i	−0.956608	−	0.291378i
$65$			0.358179i			0.0444266i
$66$	15.1423	−	13.7189i	1.86388	−	1.68868i
$67$	−0.372938	+	3.78650i	−0.0455616	+	0.462595i	0.945152	+	0.326631i	$0.105913\pi$
$67$	−0.372938	+	3.78650i	−0.0455616	+	0.462595i	−0.990714	+	0.135964i	$0.956587\pi$
$68$	0.469096	−	0.876813i	0.0568862	−	0.106329i
$69$	18.5596	−	9.92033i	2.23432	−	1.19427i
$70$	−3.16370	−	4.26745i	−0.378134	−	0.510058i
$71$	−3.34194	+	0.664753i	−0.396615	+	0.0788916i	−0.389368	−	0.921082i	$-0.627307\pi$
$71$	−3.34194	+	0.664753i	−0.396615	+	0.0788916i	−0.00724659	+	0.999974i	$0.502307\pi$
$72$	4.20350	−	11.7269i	0.495387	−	1.38203i
$73$	−2.75549	+	13.8528i	−0.322506	+	1.62135i	0.390787	+	0.920481i	$0.372203\pi$
$73$	−2.75549	+	13.8528i	−0.322506	+	1.62135i	−0.713293	+	0.700866i	$0.752797\pi$
$74$	2.04193	+	0.731051i	0.237369	+	0.0849830i
$75$	1.72625	−	2.10344i	0.199330	−	0.242884i
$76$	−5.00447	+	0.993469i	−0.574052	+	0.113959i
$77$	−9.40195	+	17.5898i	−1.07145	+	2.00455i
$78$	0.821292	−	1.10694i	0.0929930	−	0.125337i
$79$	8.64105	−	3.57924i	0.972194	−	0.402696i	0.160666	−	0.987009i	$-0.448636\pi$
$79$	8.64105	−	3.57924i	0.972194	−	0.402696i	0.811528	+	0.584313i	$0.198636\pi$
$80$	1.15822	+	3.82864i	0.129493	+	0.428055i
$81$	−2.60030	−	1.07708i	−0.288922	−	0.119675i
$82$	−9.08935	+	5.44560i	−1.00375	+	0.601366i
$83$	2.29476	+	7.56482i	0.251883	+	0.830347i	0.988128	+	0.153632i	$0.0490971\pi$
$83$	2.29476	+	7.56482i	0.251883	+	0.830347i	−0.736245	+	0.676715i	$0.763403\pi$
$84$	−0.00778440	+	20.4427i	−0.000849348	+	2.23049i
$85$	−0.494811	+	0.0487346i	−0.0536698	+	0.00528601i
$86$	−0.821138	−	16.7798i	−0.0885456	−	1.80942i
$87$	10.2213	+	15.2972i	1.09583	+	1.64003i
$88$	11.1334	−	10.0791i	1.18682	−	1.07444i
$89$	−1.50062	−	1.00268i	−0.159065	−	0.106284i	0.473490	−	0.880799i	$-0.342994\pi$
$89$	−1.50062	−	1.00268i	−0.159065	−	0.106284i	−0.632555	+	0.774515i	$0.717994\pi$
$90$	−6.04236	+	1.51231i	−0.636921	+	0.159412i
$91$	−0.390561	+	1.28751i	−0.0409419	+	0.134967i
$92$	13.6441	−	7.28622i	1.42249	−	0.759641i
$93$	10.3437	−	8.48889i	1.07260	−	0.880257i
$94$	−0.388944	+	0.821948i	−0.0401165	+	0.0847774i
$95$	1.80387	+	1.80387i	0.185073	+	0.185073i
$96$	5.19950	−	14.4881i	0.530671	−	1.47869i
$97$	−8.38097	+	8.38097i	−0.850958	+	0.850958i	−0.990251	−	0.139293i	$-0.955517\pi$
$97$	−8.38097	+	8.38097i	−0.850958	+	0.850958i	0.139293	+	0.990251i	$0.455517\pi$
$98$	−3.38568	−	9.46803i	−0.342006	−	0.956416i
$99$	14.8358	+	18.0775i	1.49105	+	1.81685i
$100$	1.26938	−	1.54554i	0.126938	−	0.154554i
$101$	−9.27667	−	2.81405i	−0.923063	−	0.280008i	−0.207240	−	0.978290i	$-0.566448\pi$
$101$	−9.27667	−	2.81405i	−0.923063	−	0.280008i	−0.715823	+	0.698282i	$0.753948\pi$
$102$	1.64095	+	0.983973i	0.162478	+	0.0974278i
$103$	−1.08005	+	1.61641i	−0.106421	+	0.159270i	−0.880858	−	0.473381i	$-0.843033\pi$
$103$	−1.08005	+	1.61641i	−0.106421	+	0.159270i	0.774437	+	0.632651i	$0.218033\pi$
$104$	0.603957	−	0.813370i	0.0592229	−	0.0797575i
$105$	8.49876	−	5.67869i	0.829394	−	0.554183i
$106$	13.2073	+	11.9750i	1.28281	+	1.16311i
$107$	−1.32027	−	13.4049i	−0.127635	−	1.29590i	−0.819167	−	0.573555i	$-0.805564\pi$
$107$	−1.32027	−	13.4049i	−0.127635	−	1.29590i	0.691532	−	0.722346i	$-0.256936\pi$
$108$	7.06005	+	2.92752i	0.679354	+	0.281701i
$109$	−0.488577	+	0.148208i	−0.0467972	+	0.0141958i	−0.313596	−	0.949556i	$-0.601534\pi$
$109$	−0.488577	+	0.148208i	−0.0467972	+	0.0141958i	0.266799	+	0.963752i	$0.414034\pi$
$110$	−7.28361	−	1.82592i	−0.694465	−	0.174095i
$111$	−1.59698	+	3.85544i	−0.151578	+	0.365942i
$112$	−0.0114430	+	15.0254i	−0.00108126	+	1.41976i
$113$	−1.22863	−	2.96617i	−0.115580	−	0.279034i	0.855495	−	0.517812i	$-0.173253\pi$
$113$	−1.22863	−	2.96617i	−0.115580	−	0.279034i	−0.971074	+	0.238778i	$0.923253\pi$
$114$	−1.43861	−	9.71106i	−0.134738	−	0.909524i
$115$	−6.82064	−	3.64571i	−0.636028	−	0.339964i
$116$	7.50831	+	11.2462i	0.697129	+	1.04419i
$117$	1.21947	+	1.00079i	0.112740	+	0.0925232i
$118$	1.25753	+	2.66014i	0.115765	+	0.244886i
$119$	−1.83178	−	0.364365i	−0.167919	−	0.0334013i
$120$	−7.46685	+	1.86582i	−0.681627	+	0.170325i
$121$	3.35409	+	16.8621i	0.304917	+	1.53292i
$122$	10.8916	+	1.61774i	0.986080	+	0.146463i
$123$	−9.61058	−	17.9801i	−0.866557	−	1.62121i
$124$	7.60500	−	6.23641i	0.682949	−	0.560047i
$125$	−0.995185	−	0.0980171i	−0.0890120	−	0.00876692i
$126$	−23.3689	−	1.15250i	−2.08186	−	0.102673i
$127$	5.43130			0.481950			0.240975	−	0.970531i	$-0.422533\pi$
$127$	5.43130			0.481950			0.240975	+	0.970531i	$0.422533\pi$
$128$	3.82567	−	10.6473i	0.338144	−	0.941094i
$129$	32.3248			2.84604
$130$	−0.505926	−	0.0249511i	−0.0443727	−	0.00218836i
$131$	−15.4151	−	1.51825i	−1.34682	−	0.132650i	−0.601242	−	0.799067i	$-0.705327\pi$
$131$	−15.4151	−	1.51825i	−1.34682	−	0.132650i	−0.745579	+	0.666417i	$0.767827\pi$
$132$	18.3231	+	22.3441i	1.59482	+	1.94480i
$133$	4.51723	+	8.45114i	0.391694	+	0.732807i
$134$	−5.32245	−	0.790546i	−0.459789	−	0.0682928i
$135$	−0.745533	−	3.74805i	−0.0641652	−	0.322580i
$136$	1.20582	+	0.723676i	0.103398	+	0.0620547i
$137$	11.9677	+	2.38053i	1.02247	+	0.203382i	0.677726	−	0.735314i	$-0.262965\pi$
$137$	11.9677	+	2.38053i	1.02247	+	0.203382i	0.344745	+	0.938696i	$0.387965\pi$
$138$	12.7196	+	26.9065i	1.08276	+	2.29043i
$139$	10.2550	+	8.41609i	0.869820	+	0.713843i	0.959374	−	0.282139i	$-0.0910439\pi$
$139$	10.2550	+	8.41609i	0.869820	+	0.713843i	−0.0895532	+	0.995982i	$0.528544\pi$
$140$	6.24815	−	4.17144i	0.528065	−	0.352551i
$141$	−1.54305	−	0.824776i	−0.129948	−	0.0694587i
$142$	−0.706158	−	4.76678i	−0.0592595	−	0.400020i
$143$	0.727790	+	1.75704i	0.0608609	+	0.146931i
$144$	16.2713	+	6.75434i	1.35595	+	0.562861i
$145$	2.58738	−	6.24649i	0.214870	−	0.518743i
$146$	−19.3751	−	4.85713i	−1.60349	−	0.401979i
$147$	18.5142	−	5.61621i	1.52702	−	0.463217i
$148$	−1.17485	+	2.83329i	−0.0965721	+	0.232895i
$149$	1.26462	+	12.8399i	0.103602	+	1.05189i	0.896653	+	0.442734i	$0.145991\pi$
$149$	1.26462	+	12.8399i	0.103602	+	1.05189i	−0.793051	+	0.609155i	$0.791509\pi$
$150$	2.85085	+	2.58485i	0.232771	+	0.211052i
$151$	11.6267	−	7.76873i	0.946170	−	0.632211i	0.0162090	−	0.999869i	$-0.494840\pi$
$151$	11.6267	−	7.76873i	0.946170	−	0.632211i	0.929961	+	0.367658i	$0.119840\pi$
$152$	−1.05466	−	7.13800i	−0.0855439	−	0.578968i
$153$	−1.21663	+	1.82082i	−0.0983591	+	0.147205i
$154$	−24.1906	−	14.5056i	−1.94934	−	1.16889i
$155$	−4.70579	−	1.42749i	−0.377978	−	0.114658i
$156$	1.50634	+	1.23718i	0.120604	+	0.0990540i
$157$	−2.95679	−	3.60286i	−0.235978	−	0.287540i	0.641534	−	0.767094i	$-0.278298\pi$
$157$	−2.95679	−	3.60286i	−0.235978	−	0.287540i	−0.877512	+	0.479555i	$0.840798\pi$
$158$	4.45372	+	12.4548i	0.354319	+	0.990850i
$159$	−24.2557	+	24.2557i	−1.92360	+	1.92360i
$160$	−5.48863	+	1.36928i	−0.433914	+	0.108251i
$161$	−20.5421	−	20.5421i	−1.61894	−	1.61894i
$162$	1.70251	−	3.59788i	0.133762	−	0.282676i
$163$	3.75452	−	3.08125i	0.294076	−	0.241342i	−0.475773	−	0.879568i	$-0.657831\pi$
$163$	3.75452	−	3.08125i	0.294076	−	0.241342i	0.769849	+	0.638226i	$0.220331\pi$
$164$	−7.05871	−	13.2180i	−0.551193	−	1.03215i
$165$	4.19407	−	13.8260i	0.326508	−	1.07635i
$166$	−10.8451	+	2.71437i	−0.841747	+	0.210676i
$167$	−20.2107	−	13.5043i	−1.56395	−	1.04500i	−0.970796	−	0.239907i	$-0.922883\pi$
$167$	−20.2107	−	13.5043i	−1.56395	−	1.04500i	−0.593152	−	0.805090i	$-0.702117\pi$
$168$	−28.8748	−	1.43506i	−2.22774	−	0.110717i
$169$	−7.15114	−	10.7024i	−0.550088	−	0.823264i
$170$	−0.0343684	−	0.702314i	−0.00263594	−	0.0538650i
$171$	11.1818	−	1.10131i	0.855090	−	0.0842190i
$172$	23.7587	+	0.00904707i	1.81158	+	0.000689833i
$173$	2.05882	+	6.78701i	0.156529	+	0.516007i	0.999768	−	0.0215318i	$-0.00685432\pi$
$173$	2.05882	+	6.78701i	0.156529	+	0.516007i	−0.843239	+	0.537538i	$0.819354\pi$
$174$	−22.3193	+	13.3719i	−1.69202	+	1.01372i
$175$	−3.47040	−	1.43749i	−0.262338	−	0.108664i
$176$	13.4611	+	16.4279i	1.01467	+	1.23830i
$177$	−5.23055	+	2.16657i	−0.393152	+	0.162849i
$178$	1.52082	−	2.04977i	0.113990	−	0.153637i
$179$	−3.66392	+	6.85471i	−0.273854	+	0.512345i	−0.980823	−	0.194899i	$-0.937562\pi$
$179$	−3.66392	+	6.85471i	−0.273854	+	0.512345i	0.706969	+	0.707244i	$0.250062\pi$
$180$	−1.71522	−	8.64017i	−0.127845	−	0.644000i
$181$	−9.79351	+	11.9334i	−0.727946	+	0.887005i	−0.997101	−	0.0760923i	$-0.975756\pi$
$181$	−9.79351	+	11.9334i	−0.727946	+	0.887005i	0.269155	+	0.963097i	$0.413256\pi$
$182$	−1.79139	−	0.641355i	−0.132787	−	0.0475404i
$183$	−4.13329	+	20.7794i	−0.305542	+	1.53606i
$184$	9.34130	+	19.7797i	0.688650	+	1.45818i
$185$	1.50414	−	0.299192i	0.110586	−	0.0219970i
$186$	11.2700	+	15.2019i	0.826355	+	1.11465i
$187$	−2.32826	+	1.24448i	−0.170260	+	0.0910056i
$188$	−1.13390	−	0.606640i	−0.0826985	−	0.0442437i
$189$	1.40701	−	14.2856i	0.102345	−	1.03913i
$190$	−2.67362	+	2.42230i	−0.193965	+	0.175732i
$191$		−	23.4563i		−	1.69724i	−0.529005	−	0.848619i	$-0.677435\pi$
$191$		−	23.4563i		−	1.69724i	0.529005	−	0.848619i	$-0.322565\pi$
$192$	20.1022	+	8.35353i	1.45075	+	0.602864i
$193$			25.1487i			1.81025i	0.425150	+	0.905123i	$0.360221\pi$
$193$			25.1487i			1.81025i	−0.425150	+	0.905123i	$0.639779\pi$
$194$	−11.2543	−	12.4219i	−0.808009	−	0.891842i
$195$	0.0955314	−	0.969947i	0.00684115	−	0.0694593i
$196$	13.6094	−	4.12271i	0.972101	−	0.294479i
$197$	17.4850	−	9.34594i	1.24576	−	0.665871i	0.289158	−	0.957281i	$-0.406625\pi$
$197$	17.4850	−	9.34594i	1.24576	−	0.665871i	0.956598	+	0.291411i	$0.0941246\pi$
$198$	−26.5678	+	19.6962i	−1.88809	+	1.39975i
$199$	−17.7138	+	3.52349i	−1.25570	+	0.249773i	−0.777726	−	0.628603i	$-0.783627\pi$
$199$	−17.7138	+	3.52349i	−1.25570	+	0.249773i	−0.477970	+	0.878376i	$0.658627\pi$
$200$	2.09464	+	1.90065i	0.148113	+	0.134396i
$201$	2.01983	−	10.1544i	0.142468	−	0.716234i
$202$	4.62105	−	12.9072i	0.325136	−	0.908150i
$203$	16.1118	−	19.6323i	1.13083	−	1.37792i
$204$	−1.50417	+	2.24929i	−0.105313	+	0.157482i
$205$	−3.53187	+	6.60767i	−0.246677	+	0.461500i
$206$	−2.20794	−	1.63817i	−0.153834	−	0.114137i
$207$	−31.4699	+	13.0353i	−2.18731	+	0.906014i
$208$	1.10681	+	0.909748i	0.0767435	+	0.0630797i
$209$	12.5142	+	5.18355i	0.865625	+	0.358554i
$210$	7.42910	+	12.4001i	0.512657	+	0.855685i
$211$	4.39339	+	14.4831i	0.302454	+	0.997056i	0.968053	+	0.250747i	$0.0806761\pi$
$211$	4.39339	+	14.4831i	0.302454	+	0.997056i	−0.665599	+	0.746310i	$0.731824\pi$
$212$	−17.8346	+	17.8211i	−1.22489	+	1.22396i
$213$	9.22726	−	0.908805i	0.632241	−	0.0622703i
$214$	19.0264	−	0.931074i	1.30061	−	0.0636469i
$215$	−6.59980	−	9.87730i	−0.450103	−	0.673626i
$216$	−4.62692	+	9.76836i	−0.314822	+	0.664653i
$217$	−15.3589	−	10.2625i	−1.04263	−	0.696662i
$218$	−0.175309	−	0.700438i	−0.0118734	−	0.0474396i
$219$	11.1566	−	36.7784i	0.753894	−	2.48525i
$220$	3.08650	−	10.1609i	0.208092	−	0.685047i
$221$	−0.137664	+	0.112978i	−0.00926029	+	0.00759973i
$222$	−5.33455	−	2.52430i	−0.358031	−	0.169420i
$223$	3.34620	+	3.34620i	0.224078	+	0.224078i	0.810213	−	0.586135i	$-0.199351\pi$
$223$	3.34620	+	3.34620i	0.224078	+	0.224078i	−0.586135	+	0.810213i	$0.699351\pi$
$224$	−21.2225	−	1.06285i	−1.41799	−	0.0710144i
$225$	−3.11437	+	3.11437i	−0.207625	+	0.207625i
$226$	4.27529	−	1.52881i	0.284388	−	0.101695i
$227$	4.79034	+	5.83705i	0.317946	+	0.387418i	0.907319	−	0.420443i	$-0.138125\pi$
$227$	4.79034	+	5.83705i	0.317946	+	0.387418i	−0.589373	+	0.807861i	$0.700625\pi$
$228$	13.8171	−	1.35555i	0.915057	−	0.0897734i
$229$	17.5287	+	5.31727i	1.15833	+	0.351375i	0.810247	−	0.586089i	$-0.199333\pi$
$229$	17.5287	+	5.31727i	1.15833	+	0.351375i	0.348082	+	0.937464i	$0.386833\pi$
$230$	5.62468	−	9.38017i	0.370881	−	0.618510i
$231$	30.1519	−	45.1255i	1.98385	−	2.96904i
$232$	−16.4083	+	9.82204i	−1.07726	+	0.644848i
$233$	14.9962	−	10.0201i	0.982433	−	0.656441i	0.0429646	−	0.999077i	$-0.486320\pi$
$233$	14.9962	−	10.0201i	0.982433	−	0.656441i	0.939468	+	0.342636i	$0.111320\pi$
$234$	−1.49856	+	1.65278i	−0.0979642	+	0.108046i
$235$	0.0630241	+	0.639895i	0.00411124	+	0.0417421i
$236$	−3.84505	+	1.59096i	−0.250291	+	0.103562i
$237$	−24.3546	+	7.38788i	−1.58200	+	0.479894i
$238$	0.642268	−	2.56201i	0.0416321	−	0.166070i
$239$	9.26626	−	22.3707i	0.599385	−	1.44704i	−0.274825	−	0.961494i	$-0.588620\pi$
$239$	9.26626	−	22.3707i	0.599385	−	1.44704i	0.874210	−	0.485548i	$-0.161380\pi$
$240$	−2.11531	−	10.6769i	−0.136543	−	0.689189i
$241$	11.0793	+	26.7479i	0.713683	+	1.72298i	0.690586	+	0.723250i	$0.257353\pi$
$241$	11.0793	+	26.7479i	0.713683	+	1.72298i	0.0230968	+	0.999733i	$0.492647\pi$
$242$	−24.0514	+	3.56301i	−1.54608	+	0.229039i
$243$	16.8650	+	9.01456i	1.08189	+	0.578284i
$244$	−3.04377	+	15.2717i	−0.194857	+	0.977669i
$245$	−5.49617	−	4.51059i	−0.351137	−	0.288171i
$246$	26.0664	−	12.3224i	1.66193	−	0.785647i
$247$	0.896179	+	0.178261i	0.0570225	+	0.0113425i
$248$	8.27914	+	11.1765i	0.525726	+	0.709707i
$249$	−4.19657	−	21.0976i	−0.265947	−	1.33700i
$250$	0.207775	−	1.39887i	0.0131408	−	0.0884721i
$251$	4.49574	+	8.41093i	0.283768	+	0.530893i	0.982909	−	0.184091i	$-0.0589340\pi$
$251$	4.49574	+	8.41093i	0.283768	+	0.530893i	−0.699141	+	0.714984i	$0.746434\pi$
$252$	3.25580	−	32.9282i	0.205096	−	2.07428i
$253$	−40.8663	−	4.02498i	−2.56924	−	0.253049i
$254$	−0.378350	+	7.67169i	−0.0237398	+	0.481365i
$255$	1.35295			0.0847247
$256$	14.7727	+	6.14544i	0.923296	+	0.384090i
$257$	−7.22845			−0.450898			−0.225449	−	0.974255i	$-0.572385\pi$
$257$	−7.22845			−0.450898			−0.225449	+	0.974255i	$0.572385\pi$
$258$	−2.25178	+	45.6587i	−0.140190	+	2.84259i
$259$	5.73301	+	0.564652i	0.356232	+	0.0350858i
$260$	0.0704868	−	0.712881i	0.00437140	−	0.0442110i
$261$	−14.0376	−	26.2625i	−0.868905	−	1.62561i
$262$	3.21836	−	21.6680i	0.198831	−	1.33865i
$263$	−5.24535	−	26.3702i	−0.323442	−	1.62605i	−0.710289	−	0.703910i	$-0.751436\pi$
$263$	−5.24535	−	26.3702i	−0.323442	−	1.62605i	0.386846	−	0.922144i	$-0.373564\pi$
$264$	−32.8373	+	24.3248i	−2.02100	+	1.49709i
$265$	12.3640	+	2.45935i	0.759513	+	0.151076i
$266$	−12.2519	+	5.79186i	−0.751211	+	0.355122i
$267$	3.79623	+	3.11549i	0.232326	+	0.190665i
$268$	1.48741	−	7.46287i	0.0908581	−	0.455867i
$269$	9.67696	+	5.17244i	0.590015	+	0.315369i	0.739249	−	0.673432i	$-0.235181\pi$
$269$	9.67696	+	5.17244i	0.590015	+	0.315369i	−0.149234	+	0.988802i	$0.547681\pi$
$270$	5.34604	−	0.791970i	0.325349	−	0.0481977i
$271$	8.47180	+	20.4527i	0.514625	+	1.24241i	0.941165	+	0.337946i	$0.109732\pi$
$271$	8.47180	+	20.4527i	0.514625	+	1.24241i	−0.426540	+	0.904469i	$0.640268\pi$
$272$	−1.10619	+	1.65280i	−0.0670726	+	0.100216i
$273$	1.40103	−	3.38239i	0.0847944	−	0.204712i
$274$	−4.19617	+	16.7385i	−0.253500	+	1.01121i
$275$	−5.08103	+	1.54131i	−0.306398	+	0.0929447i
$276$	−38.8914	+	16.0920i	−2.34099	+	0.968624i
$277$	0.190584	+	1.93503i	0.0114511	+	0.116265i	0.999211	−	0.0397173i	$-0.0126457\pi$
$277$	0.190584	+	1.93503i	0.0114511	+	0.116265i	−0.987760	+	0.155982i	$0.950146\pi$
$278$	−12.6021	+	13.8989i	−0.755822	+	0.833602i
$279$	−18.0086	+	12.0330i	−1.07815	+	0.720394i
$280$	5.45689	+	9.11608i	0.326112	+	0.544790i
$281$	5.58290	−	8.35540i	0.333048	−	0.498441i	−0.626717	−	0.779247i	$-0.715602\pi$
$281$	5.58290	−	8.35540i	0.333048	−	0.498441i	0.959765	+	0.280806i	$0.0906017\pi$
$282$	1.27248	−	2.12209i	0.0757753	−	0.126369i
$283$	1.09487	+	0.332126i	0.0650834	+	0.0197428i	0.322659	−	0.946515i	$-0.395423\pi$
$283$	1.09487	+	0.332126i	0.0650834	+	0.0197428i	−0.257575	+	0.966258i	$0.582923\pi$
$284$	6.78226	−	0.665386i	0.402453	−	0.0394834i
$285$	−4.40376	−	5.36600i	−0.260856	−	0.317855i
$286$	−2.53251	+	0.905604i	−0.149751	+	0.0535495i
$287$	−19.9007	+	19.9007i	−1.17470	+	1.17470i
$288$	−10.6740	+	22.5127i	−0.628969	+	1.32657i
$289$	11.8460	+	11.8460i	0.696824	+	0.696824i
$290$	8.64291	+	4.08980i	0.507529	+	0.240162i
$291$	24.9310	−	20.4603i	1.46148	−	1.19940i
$292$	8.21036	−	27.0289i	0.480475	−	1.58175i
$293$	3.94395	−	13.0014i	0.230408	−	0.759553i	−0.763150	−	0.646222i	$-0.776348\pi$
$293$	3.94395	−	13.0014i	0.230408	−	0.759553i	0.993557	−	0.113331i	$-0.0361520\pi$
$294$	6.64316	+	26.5424i	0.387437	+	1.54799i
$295$	1.72995	+	1.15592i	0.100722	+	0.0673001i
$296$	−3.92017	−	1.85684i	−0.227855	−	0.107927i
$297$	−11.2729	−	16.8711i	−0.654122	−	0.978962i
$298$	−18.2245	+	0.891833i	−1.05572	+	0.0516625i
$299$	−2.75676	+	0.271517i	−0.159427	+	0.0157022i
$300$	−3.84968	+	3.84675i	−0.222261	+	0.222092i
$301$	−12.9533	−	42.7013i	−0.746616	−	2.46126i
$302$	10.1634	+	16.9639i	0.584837	+	0.976163i
$303$	24.3706	+	10.0946i	1.40006	+	0.579922i
$304$	10.1559	−	0.992457i	0.582479	−	0.0569213i
$305$	7.19335	−	2.97958i	0.411890	−	0.170610i
$306$	−2.48715	−	1.84533i	−0.142181	−	0.105491i
$307$	12.9117	−	24.1562i	0.736912	−	1.37866i	−0.181641	−	0.983365i	$-0.558141\pi$
$307$	12.9117	−	24.1562i	0.736912	−	1.37866i	0.918552	−	0.395300i	$-0.129359\pi$
$308$	22.1742	−	33.1587i	1.26349	−	1.88939i
$309$	3.35590	−	4.08917i	0.190910	−	0.232625i
$310$	2.34413	−	6.54748i	0.133138	−	0.371872i
$311$	3.36075	−	16.8956i	0.190571	−	0.958063i	−0.760558	−	0.649270i	$-0.775075\pi$
$311$	3.36075	−	16.8956i	0.190571	−	0.958063i	0.951129	−	0.308794i	$-0.0999253\pi$
$312$	−1.85245	+	2.04152i	−0.104874	+	0.115578i
$313$	17.0794	−	3.39730i	0.965384	−	0.192027i	0.312864	−	0.949798i	$-0.398712\pi$
$313$	17.0794	−	3.39730i	0.965384	−	0.192027i	0.652520	+	0.757771i	$0.273712\pi$
$314$	5.29500	−	3.92548i	0.298814	−	0.221528i
$315$	−14.5908	+	7.79896i	−0.822100	+	0.439422i
$316$	−17.9026	+	5.42325i	−1.00710	+	0.305082i
$317$	0.589250	−	5.98275i	0.0330956	−	0.336025i	−0.964352	−	0.264623i	$-0.914753\pi$
$317$	0.589250	−	5.98275i	0.0330956	−	0.336025i	0.997448	−	0.0714022i	$-0.0227474\pi$
$318$	−32.5714	−	35.9508i	−1.82651	−	2.01602i
$319$		−	35.8994i		−	2.00998i
$320$	−1.55176	−	7.84806i	−0.0867459	−	0.438720i
$321$			36.6526i			2.04575i
$322$	30.4466	−	27.5847i	1.69673	−	1.53723i
$323$	−0.124325	+	1.26229i	−0.00691763	+	0.0702359i
$324$	4.96340	+	2.65542i	0.275744	+	0.147523i
$325$	−0.315885	+	0.168844i	−0.0175222	+	0.00936579i
$326$	4.09071	+	5.51789i	0.226564	+	0.305607i
$327$	1.36259	−	0.271037i	0.0753516	−	0.0149884i
$328$	19.1621	−	9.04963i	1.05805	−	0.499682i
$329$	−0.471200	+	2.36888i	−0.0259781	+	0.130601i
$330$	19.2370	+	6.88724i	1.05896	+	0.379130i
$331$	−5.36455	+	6.53672i	−0.294862	+	0.359291i	−0.899277	−	0.437379i	$-0.855907\pi$
$331$	−5.36455	+	6.53672i	−0.294862	+	0.359291i	0.604415	+	0.796670i	$0.293407\pi$
$332$	−3.07856	−	15.5078i	−0.168958	−	0.851102i
$333$	3.18409	−	5.95702i	0.174487	−	0.326443i
$334$	20.4827	−	27.6068i	1.12077	−	1.51058i
$335$	−3.51520	+	1.45604i	−0.192056	+	0.0795522i
$336$	4.03847	−	40.6856i	0.220316	−	2.21958i
$337$	2.60003	+	1.07697i	0.141633	+	0.0586661i	0.452374	−	0.891828i	$-0.350577\pi$
$337$	2.60003	+	1.07697i	0.141633	+	0.0586661i	−0.310741	+	0.950495i	$0.600577\pi$
$338$	15.6153	−	9.35542i	0.849361	−	0.508868i
$339$	2.53600	+	8.36007i	0.137737	+	0.454057i
$340$	0.994411		0.000378662i	0.0539295		2.05358e-5i
$341$	−25.9847	+	2.55927i	−1.40715	+	0.138592i
$342$	0.776659	+	15.8709i	0.0419969	+	0.858201i
$343$	−0.229727	−	0.343811i	−0.0124041	−	0.0185641i
$344$	−1.66783	+	33.5584i	−0.0899235	+	1.80935i
$345$	17.4979	+	11.6917i	0.942056	+	0.629462i
$346$	−9.73004	+	2.43528i	−0.523090	+	0.130921i
$347$	−6.67103	+	21.9914i	−0.358120	+	1.18056i	0.574135	+	0.818761i	$0.305338\pi$
$347$	−6.67103	+	21.9914i	−0.358120	+	1.18056i	−0.932255	+	0.361802i	$0.882162\pi$
$348$	−17.3329	−	32.4574i	−0.929143	−	1.73990i
$349$	−14.6671	+	12.0370i	−0.785111	+	0.644324i	−0.939059	−	0.343755i	$-0.888301\pi$
$349$	−14.6671	+	12.0370i	−0.785111	+	0.644324i	0.153948	+	0.988079i	$0.450801\pi$
$350$	2.27220	−	4.80180i	0.121454	−	0.256667i
$351$	−0.967867	−	0.967867i	−0.0516609	−	0.0516609i
$352$	−24.1421	+	17.8694i	−1.28678	+	0.952444i
$353$	19.7570	−	19.7570i	1.05156	−	1.05156i	0.0529631	−	0.998596i	$-0.483133\pi$
$353$	19.7570	−	19.7570i	1.05156	−	1.05156i	0.998596	−	0.0529631i	$-0.0168666\pi$
$354$	−2.69590	−	7.53906i	−0.143286	−	0.400697i
$355$	−2.16164	−	2.63396i	−0.114728	−	0.139796i
$356$	2.78935	+	2.29094i	0.147835	+	0.121419i
$357$	4.86329	+	1.47526i	0.257392	+	0.0780791i
$358$	−9.42702	−	5.65278i	−0.498234	−	0.298759i
$359$	−15.1825	+	22.7222i	−0.801301	+	1.19923i	0.175373	+	0.984502i	$0.443887\pi$
$359$	−15.1825	+	22.7222i	−0.801301	+	1.19923i	−0.976674	+	0.214729i	$0.931113\pi$
$360$	12.3237	−	1.82085i	0.649516	−	0.0959674i
$361$	−10.3868	+	6.94023i	−0.546673	+	0.365275i
$362$	−16.1737	−	14.6646i	−0.850071	−	0.770754i
$363$	−4.58549	−	46.5572i	−0.240676	−	2.44362i
$364$	1.03070	−	2.48566i	0.0540235	−	0.130284i
$365$	−13.5160	+	4.10004i	−0.707460	+	0.214606i
$366$	−29.0630	−	7.28578i	−1.51915	−	0.380834i
$367$	−8.67931	+	20.9537i	−0.453056	+	1.09377i	0.518098	+	0.855321i	$0.326640\pi$
$367$	−8.67931	+	20.9537i	−0.453056	+	1.09377i	−0.971154	+	0.238453i	$0.923360\pi$
$368$	−28.5896	+	11.8167i	−1.49033	+	0.615987i
$369$	12.6283	+	30.4873i	0.657401	+	1.58711i
$370$	0.317828	+	2.14543i	0.0165231	+	0.111536i
$371$	41.7617	+	22.3221i	2.16816	+	1.15891i
$372$	−22.2577	+	14.8598i	−1.15401	+	0.770446i
$373$	−1.75710	−	1.44202i	−0.0909793	−	0.0746647i	0.587804	−	0.809003i	$-0.299993\pi$
$373$	−1.75710	−	1.44202i	−0.0909793	−	0.0746647i	−0.678784	+	0.734338i	$0.737493\pi$
$374$	−1.59564	−	3.37536i	−0.0825085	−	0.174536i
$375$	2.66881	+	0.530860i	0.137817	+	0.0274135i
$376$	0.935866	−	1.55938i	0.0482636	−	0.0804187i
$377$	−0.472450	−	2.37517i	−0.0243324	−	0.122327i
$378$	20.0804	+	2.98255i	1.03282	+	0.153406i
$379$	0.488383	+	0.913701i	0.0250866	+	0.0469337i	0.894152	−	0.447763i	$-0.147779\pi$
$379$	0.488383	+	0.913701i	0.0250866	+	0.0469337i	−0.869066	+	0.494697i	$0.835279\pi$
$380$	−3.23525	−	3.94523i	−0.165965	−	0.202386i
$381$	−14.7079	−	1.44861i	−0.753511	−	0.0742144i
$382$	33.1319	+	1.63399i	1.69518	+	0.0836023i
$383$	−12.3110			−0.629063			−0.314532	−	0.949247i	$-0.601847\pi$
$383$	−12.3110			−0.629063			−0.314532	+	0.949247i	$0.601847\pi$
$384$	−13.1997	+	27.8124i	−0.673593	+	1.41930i
$385$	−19.9449			−1.01649
$386$	−35.5225	−	1.75189i	−1.80805	−	0.0891688i
$387$	−52.0692	−	5.12837i	−2.64683	−	0.260690i
$388$	18.3299	−	15.0313i	0.930560	−	0.763098i
$389$	10.6516	+	19.9278i	0.540060	+	1.01038i	0.992918	+	0.118799i	$0.0379043\pi$
$389$	10.6516	+	19.9278i	0.540060	+	1.01038i	−0.452858	+	0.891582i	$0.649596\pi$
$390$	1.36339	+	0.202505i	0.0690380	+	0.0102543i
$391$	−0.750182	−	3.77142i	−0.0379383	−	0.190729i
$392$	4.87527	+	19.5104i	0.246238	+	0.985427i
$393$	41.3390	+	8.22284i	2.08528	+	0.414788i
$394$	11.9831	+	25.3486i	0.603699	+	1.27704i
$395$	7.22997	+	5.93348i	0.363779	+	0.298546i
$396$	−25.9701	−	38.8990i	−1.30505	−	1.95475i
$397$	−6.45938	−	3.45261i	−0.324187	−	0.173282i	0.301273	−	0.953538i	$-0.402589\pi$
$397$	−6.45938	−	3.45261i	−0.324187	−	0.173282i	−0.625460	+	0.780256i	$0.715089\pi$
$398$	−3.74296	−	25.2661i	−0.187617	−	1.26648i
$399$	−9.97861	−	24.0905i	−0.499555	−	1.20603i
$400$	−2.83058	+	2.82627i	−0.141529	+	0.141314i
$401$	−11.0591	+	26.6990i	−0.552265	+	1.33329i	0.363509	+	0.931591i	$0.381579\pi$
$401$	−11.0591	+	26.6990i	−0.552265	+	1.33329i	−0.915774	+	0.401695i	$0.868421\pi$
$402$	14.2023	+	3.56037i	0.708347	+	0.177575i
$403$	−1.68551	+	0.511295i	−0.0839615	+	0.0254694i
$404$	17.9095	+	7.42636i	0.891032	+	0.369475i
$405$	−0.275873	−	2.80099i	−0.0137083	−	0.139182i
$406$	26.6082	+	24.1255i	1.32054	+	1.19733i
$407$	6.77060	−	4.52397i	0.335606	−	0.224245i
$408$	−3.07234	−	2.28132i	−0.152103	−	0.112942i
$409$	8.80812	−	13.1823i	0.435534	−	0.651822i	−0.547167	−	0.837024i	$-0.684294\pi$
$409$	8.80812	−	13.1823i	0.435534	−	0.651822i	0.982701	+	0.185201i	$0.0592937\pi$
$410$	−9.08728	−	5.44906i	−0.448789	−	0.269110i
$411$	−31.7736	−	9.63843i	−1.56728	−	0.475428i
$412$	2.46772	−	3.00459i	0.121576	−	0.148026i
$413$	4.95805	+	6.04140i	0.243970	+	0.297278i
$414$	−16.2201	−	45.3592i	−0.797172	−	2.22929i
$415$	−5.58983	+	5.58983i	−0.274394	+	0.274394i
$416$	−1.36212	+	1.49999i	−0.0667833	+	0.0735432i
$417$	−25.5259	−	25.5259i	−1.25001	−	1.25001i
$418$	−8.19350	+	17.3152i	−0.400757	+	0.846913i
$419$	−24.5070	+	20.1124i	−1.19725	+	0.982556i	−0.197250	+	0.980353i	$0.563201\pi$
$419$	−24.5070	+	20.1124i	−1.19725	+	0.982556i	−0.999998	+	0.00220224i	$0.999299\pi$
$420$	−18.0326	+	9.62978i	−0.879899	+	0.469885i
$421$	8.77009	−	28.9111i	0.427428	−	1.40904i	−0.433885	−	0.900968i	$-0.642858\pi$
$421$	8.77009	−	28.9111i	0.427428	−	1.40904i	0.861314	−	0.508074i	$-0.169642\pi$
$422$	−20.7634	+	5.19675i	−1.01074	+	0.252974i
$423$	2.35471	+	1.57336i	0.114490	+	0.0764996i
$424$	−23.9298	−	26.4328i	−1.16213	−	1.28369i
$425$	−0.276232	−	0.413411i	−0.0133992	−	0.0200534i
$426$	0.640904	+	13.0968i	0.0310519	+	0.634541i
$427$	29.1061	−	2.86670i	1.40854	−	0.138729i
$428$	−0.0102583	+	26.9395i	−0.000495854	+	1.30217i
$429$	−1.50223	−	4.95217i	−0.0725281	−	0.239093i
$430$	14.4114	−	8.63414i	0.694980	−	0.416375i
$431$	23.7778	+	9.84907i	1.14533	+	0.474413i	0.872967	−	0.487780i	$-0.162193\pi$
$431$	23.7778	+	9.84907i	1.14533	+	0.474413i	0.272368	+	0.962193i	$0.412193\pi$
$432$	−13.4755	−	7.21599i	−0.648339	−	0.347179i
$433$	3.38128	−	1.40057i	0.162494	−	0.0673072i	−0.299954	−	0.953954i	$-0.596971\pi$
$433$	3.38128	−	1.40057i	0.162494	−	0.0673072i	0.462448	+	0.886647i	$0.346971\pi$
$434$	15.5656	−	20.9795i	0.747173	−	1.00705i
$435$	−8.67265	+	16.2254i	−0.415822	+	0.777948i
$436$	1.00158	−	0.198830i	0.0479669	−	0.00952222i
$437$	−12.5163	+	15.2511i	−0.598734	+	0.729560i
$438$	51.1722	+	18.3207i	2.44510	+	0.875397i
$439$	−3.72694	+	18.7366i	−0.177877	+	0.894248i	0.783999	+	0.620762i	$0.213177\pi$
$439$	−3.72694	+	18.7366i	−0.177877	+	0.894248i	−0.961876	+	0.273486i	$0.911823\pi$
$440$	14.1372	+	5.06748i	0.673965	+	0.241583i
$441$	−30.7138	+	6.10936i	−1.46256	+	0.290922i
$442$	−0.149991	−	0.202320i	−0.00713436	−	0.00962340i
$443$	−19.4487	+	10.3955i	−0.924034	+	0.493907i	−0.863550	−	0.504263i	$-0.831764\pi$
$443$	−19.4487	+	10.3955i	−0.924034	+	0.493907i	−0.0604838	+	0.998169i	$0.519264\pi$
$444$	3.93717	−	7.35919i	0.186850	−	0.349252i
$445$	0.176899	−	1.79608i	0.00838581	−	0.0851426i
$446$	−4.95960	+	4.49340i	−0.234844	+	0.212768i
$447$		−	35.1078i		−	1.66054i
$448$	2.97965	−	29.9026i	0.140775	−	1.41277i
$449$		−	6.77200i		−	0.319590i	−0.987150	−	0.159795i	$-0.948917\pi$
$449$		−	6.77200i		−	0.319590i	0.987150	−	0.159795i	$-0.0510834\pi$
$450$	−4.18209	−	4.61599i	−0.197146	−	0.217600i
$451$	−3.89931	+	39.5903i	−0.183611	+	1.86424i
$452$	1.86161	+	6.14533i	0.0875628	+	0.289052i
$453$	−33.5572	+	17.9367i	−1.57665	+	0.842739i
$454$	−8.57851	+	6.35973i	−0.402610	+	0.298477i
$455$	−1.31959	+	0.262482i	−0.0618632	+	0.0123054i
$456$	0.952197	+	19.6110i	0.0445907	+	0.918368i
$457$	−7.74502	+	38.9369i	−0.362297	+	1.82139i	0.182960	+	0.983120i	$0.441432\pi$
$457$	−7.74502	+	38.9369i	−0.362297	+	1.82139i	−0.545256	+	0.838269i	$0.683568\pi$
$458$	−8.73170	+	24.3888i	−0.408006	+	1.13962i
$459$	1.20538	−	1.46876i	0.0562625	−	0.0685560i
$460$	12.8576	+	8.59828i	0.599490	+	0.400897i
$461$	−3.93097	+	7.35433i	−0.183084	+	0.342525i	−0.956674	−	0.291160i	$-0.905959\pi$
$461$	−3.93097	+	7.35433i	−0.183084	+	0.342525i	0.773591	+	0.633686i	$0.218459\pi$
$462$	61.6393	+	45.7330i	2.86772	+	2.12769i
$463$	21.4783	−	8.89661i	0.998182	−	0.413460i	0.177052	−	0.984202i	$-0.443344\pi$
$463$	21.4783	−	8.89661i	0.998182	−	0.413460i	0.821130	+	0.570741i	$0.193344\pi$
$464$	−12.7306	−	23.8609i	−0.591002	−	1.10772i
$465$	12.3625	+	5.12073i	0.573299	+	0.237468i
$466$	13.1088	+	21.8801i	0.607251	+	1.01358i
$467$	1.96244	+	6.46930i	0.0908109	+	0.299363i	0.990567	−	0.137030i	$-0.0437557\pi$
$467$	1.96244	+	6.46930i	0.0908109	+	0.299363i	−0.899756	+	0.436393i	$0.856256\pi$
$468$	−2.23015	−	2.23185i	−0.103089	−	0.103167i
$469$	−14.2234	+	1.40088i	−0.656775	+	0.0646867i
$470$	−0.908240	+	0.0444456i	−0.0418940	+	0.00205012i
$471$	7.04605	+	10.5452i	0.324665	+	0.485895i
$472$	−1.97937	−	5.54194i	−0.0911078	−	0.255089i
$473$	−52.4451	−	35.0427i	−2.41143	−	1.61127i
$474$	−8.73879	−	34.9154i	−0.401386	−	1.60372i
$475$	−0.740534	+	2.44121i	−0.0339780	+	0.112011i
$476$	3.57409	+	1.08567i	0.163818	+	0.0497618i
$477$	42.9195	−	35.2231i	1.96515	−	1.61276i
$478$	30.9531	+	14.6469i	1.41576	+	0.669935i
$479$	26.4436	+	26.4436i	1.20824	+	1.20824i	0.971597	+	0.236644i	$0.0760474\pi$
$479$	26.4436	+	26.4436i	1.20824	+	1.20824i	0.236644	+	0.971597i	$0.423953\pi$
$480$	15.2284	−	2.24411i	0.695078	−	0.102429i
$481$	0.388417	−	0.388417i	0.0177103	−	0.0177103i
$482$	−38.5531	+	13.7862i	−1.75605	+	0.627946i
$483$	50.1491	+	61.1068i	2.28186	+	2.78046i
$484$	−3.35729	−	34.2207i	−0.152604	−	1.55549i
$485$	−11.3421	−	3.44059i	−0.515019	−	0.156229i
$486$	−13.9079	+	23.1939i	−0.630874	+	1.05209i
$487$	2.98221	−	4.46319i	0.135137	−	0.202246i	−0.757729	−	0.652569i	$-0.773691\pi$
$487$	2.98221	−	4.46319i	0.135137	−	0.202246i	0.892866	+	0.450323i	$0.148691\pi$
$488$	−21.3592	−	5.36316i	−0.966884	−	0.242779i
$489$	−10.9890	+	7.34264i	−0.496941	+	0.332046i
$490$	6.75406	−	7.44911i	0.305117	−	0.336516i
$491$	−1.65770	−	16.8309i	−0.0748110	−	0.759569i	−0.957273	−	0.289185i	$-0.906616\pi$
$491$	−1.65770	−	16.8309i	−0.0748110	−	0.759569i	0.882462	−	0.470383i	$-0.155884\pi$
$492$	15.5895	+	37.6770i	0.702831	+	1.69861i
$493$	3.21693	−	0.975844i	0.144883	−	0.0439498i
$494$	−0.314222	+	1.25343i	−0.0141375	+	0.0563946i
$495$	−8.94936	+	21.6057i	−0.402244	+	0.971102i
$496$	−16.3635	+	10.9157i	−0.734741	+	0.490129i
$497$	−4.89811	−	11.8251i	−0.219710	−	0.530428i
$498$	30.0926	−	4.45796i	1.34848	−	0.199766i
$499$	−14.9315	−	7.98105i	−0.668426	−	0.357281i	0.102024	−	0.994782i	$-0.467468\pi$
$499$	−14.9315	−	7.98105i	−0.668426	−	0.357281i	−0.770449	+	0.637501i	$0.779968\pi$
$500$	1.96142	+	0.390928i	0.0877175	+	0.0174828i
$501$	51.1286	+	41.9602i	2.28426	+	1.87464i
$502$	−12.1936	+	5.76430i	−0.544227	+	0.257273i
$503$	−2.57603	−	0.512405i	−0.114860	−	0.0228470i	0.137326	−	0.990526i	$-0.456149\pi$
$503$	−2.57603	−	0.512405i	−0.114860	−	0.0228470i	−0.252185	+	0.967679i	$0.581149\pi$
$504$	46.2841	+	6.89262i	2.06166	+	0.307022i
$505$	−1.89122	−	9.50782i	−0.0841583	−	0.423092i
$506$	8.53207	−	57.4432i	0.379297	−	2.55366i
$507$	16.5108	+	30.8895i	0.733269	+	1.37185i
$508$	−10.8099	−	1.06884i	−0.479611	−	0.0474220i
$509$	16.8663	+	1.66119i	0.747587	+	0.0736309i	0.464634	−	0.885503i	$-0.346186\pi$
$509$	16.8663	+	1.66119i	0.747587	+	0.0736309i	0.282953	+	0.959134i	$0.408686\pi$
$510$	−0.0942477	+	1.91103i	−0.00417336	+	0.0846219i
$511$	−53.0552			−2.34703
$512$	−9.70950	+	20.4383i	−0.429104	+	0.903255i
$513$	−9.74882			−0.430421
$514$	0.503542	−	10.2102i	0.0222103	−	0.450351i
$515$	−1.93468	−	0.190549i	−0.0852522	−	0.00839661i
$516$	−64.3360	−	6.36128i	−2.83223	−	0.280040i
$517$	1.60938	+	3.01094i	0.0707804	+	0.132421i
$518$	−1.19694	+	8.05852i	−0.0525904	+	0.354071i
$519$	−3.76508	−	18.9283i	−0.165268	−	0.830861i
$520$	1.00203	+	0.149222i	0.0439420	+	0.00654384i
$521$	28.4113	+	5.65137i	1.24472	+	0.247591i	0.773143	−	0.634232i	$-0.218684\pi$
$521$	28.4113	+	5.65137i	1.24472	+	0.247591i	0.471581	+	0.881823i	$0.343684\pi$
$522$	38.0736	−	17.9986i	1.66643	−	0.787777i
$523$	−4.80239	−	3.94122i	−0.209994	−	0.172338i	0.523517	−	0.852015i	$-0.324620\pi$
$523$	−4.80239	−	3.94122i	−0.209994	−	0.172338i	−0.733511	+	0.679678i	$0.762120\pi$
$524$	30.3818	+	6.05533i	1.32723	+	0.264529i
$525$	9.01445	+	4.81832i	0.393423	+	0.210289i
$526$	37.6132	−	5.57207i	1.64001	−	0.242954i
$527$	−0.935672	−	2.25891i	−0.0407585	−	0.0983997i
$528$	−32.0712	−	48.0771i	−1.39572	−	2.09229i
$529$	14.0875	−	34.0101i	0.612498	−	1.47870i
$530$	−4.33511	+	17.2927i	−0.188305	+	0.751149i
$531$	8.76916	−	2.66010i	0.380549	−	0.115438i
$532$	−7.32750	−	17.7092i	−0.317687	−	0.767792i
$533$	0.263039	+	2.67068i	0.0113935	+	0.115680i
$534$	−4.66507	+	5.14514i	−0.201877	+	0.222652i
$535$	11.1997	−	7.48340i	0.484205	−	0.323536i
$536$	10.4377	+	2.62083i	0.450838	+	0.113203i
$537$	11.7501	−	17.5853i	0.507056	−	0.758862i
$538$	−7.98017	+	13.3084i	−0.344049	+	0.573764i
$539$	−36.1265	−	10.9589i	−1.55608	−	0.472032i
$540$	0.746244	+	7.60643i	0.0321132	+	0.327329i
$541$	15.5909	+	18.9976i	0.670306	+	0.816770i	0.991481	−	0.130250i	$-0.0415779\pi$
$541$	15.5909	+	18.9976i	0.670306	+	0.816770i	−0.321175	+	0.947020i	$0.604078\pi$
$542$	−29.4796	+	10.5416i	−1.26626	+	0.452802i
$543$	29.7036	−	29.7036i	1.27470	−	1.27470i
$544$	−2.25752	−	1.67762i	−0.0967904	−	0.0719276i
$545$	−0.361022	−	0.361022i	−0.0154645	−	0.0154645i
$546$	4.68002	+	2.21458i	0.200287	+	0.0947752i
$547$	12.6031	−	10.3431i	0.538868	−	0.442237i	−0.325176	−	0.945653i	$-0.605424\pi$
$547$	12.6031	−	10.3431i	0.538868	−	0.442237i	0.864044	+	0.503416i	$0.167924\pi$
$548$	−23.3508	−	7.09310i	−0.997498	−	0.303002i
$549$	9.95463	−	32.8160i	0.424853	−	1.40055i
$550$	−1.82315	−	7.28431i	−0.0777394	−	0.310604i
$551$	−14.3413	−	9.58254i	−0.610959	−	0.408230i
$552$	−20.0207	−	56.0550i	−0.852137	−	2.38586i
$553$	19.5189	+	29.2121i	0.830027	+	1.24222i
$554$	−2.74651	+	0.134403i	−0.116688	+	0.00571024i
$555$	−4.15300	+	0.409035i	−0.176285	+	0.0173626i
$556$	−18.7543	−	18.7686i	−0.795360	−	0.795966i
$557$	−0.872935	−	2.87768i	−0.0369874	−	0.121931i	0.936503	−	0.350661i	$-0.114043\pi$
$557$	−0.872935	−	2.87768i	−0.0369874	−	0.121931i	−0.973490	+	0.228729i	$0.926543\pi$
$558$	−15.7420	−	26.2753i	−0.666413	−	1.11232i
$559$	−3.93104	−	1.62829i	−0.166265	−	0.0688693i
$560$	−13.2566	+	7.07281i	−0.560192	+	0.298881i
$561$	6.63686	−	2.74908i	0.280208	−	0.116066i
$562$	11.4131	+	8.46787i	0.481431	+	0.357196i
$563$	15.5527	−	29.0970i	0.655466	−	1.22629i	−0.306173	−	0.951976i	$-0.599049\pi$
$563$	15.5527	−	29.0970i	0.655466	−	1.22629i	0.961640	−	0.274315i	$-0.0884512\pi$
$564$	2.90881	+	1.94521i	0.122483	+	0.0819080i
$565$	2.03676	−	2.48179i	0.0856870	−	0.104410i
$566$	−0.545397	+	1.52337i	−0.0229248	+	0.0640320i
$567$	2.06257	−	10.3692i	0.0866197	−	0.435467i
$568$	0.467397	+	9.62627i	0.0196115	+	0.403909i
$569$	−9.73174	+	1.93576i	−0.407976	+	0.0811515i	−0.394812	−	0.918762i	$-0.629190\pi$
$569$	−9.73174	+	1.93576i	−0.407976	+	0.0811515i	−0.0131639	+	0.999913i	$0.504190\pi$
$570$	7.88623	−	5.84650i	0.330318	−	0.244883i
$571$	−16.4501	+	8.79277i	−0.688416	+	0.367966i	−0.778218	−	0.627994i	$-0.783876\pi$
$571$	−16.4501	+	8.79277i	−0.688416	+	0.367966i	0.0898027	+	0.995960i	$0.471376\pi$
$572$	−1.10274	−	3.64025i	−0.0461081	−	0.152207i
$573$	−6.25613	+	63.5196i	−0.261354	+	2.65357i
$574$	−26.7234	−	29.4960i	−1.11541	−	1.23114i
$575$		−	7.73384i		−	0.322523i
$576$	−31.0556	−	16.6452i	−1.29398	−	0.693550i
$577$			12.3423i			0.513816i	0.966436	+	0.256908i	$0.0827037\pi$
$577$			12.3423i			0.513816i	−0.966436	+	0.256908i	$0.917296\pi$
$578$	−17.5577	+	15.9072i	−0.730302	+	0.661654i
$579$	6.70753	−	68.1027i	0.278756	−	2.83025i
$580$	−6.37891	+	11.9232i	−0.264870	+	0.495083i
$581$	−26.1884	+	13.9980i	−1.08648	+	0.580734i
$582$	27.1634	+	36.6402i	1.12596	+	1.51878i
$583$	65.6485	−	13.0583i	2.71888	−	0.540819i
$584$	37.6063	+	13.4800i	1.55616	+	0.557805i
$585$	−0.307766	+	1.54724i	−0.0127246	+	0.0639707i
$586$	18.0898	+	6.47651i	0.747281	+	0.267542i
$587$	16.1445	−	19.6721i	0.666355	−	0.811956i	−0.324642	−	0.945837i	$-0.605244\pi$
$587$	16.1445	−	19.6721i	0.666355	−	0.811956i	0.990997	+	0.133881i	$0.0427438\pi$
$588$	−37.9538	+	7.53447i	−1.56519	+	0.310716i
$589$	−5.91365	+	11.0637i	−0.243668	+	0.455870i
$590$	−1.75324	+	2.36303i	−0.0721797	+	0.0972844i
$591$	−49.8421	+	20.6453i	−2.05023	+	0.849233i
$592$	2.89587	−	5.40788i	0.119019	−	0.222262i
$593$	8.81540	+	3.65146i	0.362005	+	0.149948i	0.556270	−	0.831002i	$-0.312232\pi$
$593$	8.81540	+	3.65146i	0.362005	+	0.149948i	−0.194265	+	0.980949i	$0.562232\pi$
$594$	24.6157	−	14.7477i	1.00999	−	0.605106i
$595$	−0.542156	−	1.78725i	−0.0222262	−	0.0732701i
$596$	0.00982597	−	25.8041i	0.000402487	−	1.05698i
$597$	48.9086	−	4.81708i	2.00170	−	0.197150i
$598$	−0.191478	−	3.91283i	−0.00783012	−	0.160007i
$599$	6.23048	+	9.32458i	0.254571	+	0.380992i	0.936639	−	0.350297i	$-0.113919\pi$
$599$	6.23048	+	9.32458i	0.254571	+	0.380992i	−0.682068	+	0.731289i	$0.738919\pi$
$600$	−5.16535	−	5.70563i	−0.210875	−	0.232931i
$601$	7.27506	+	4.86104i	0.296756	+	0.198286i	0.695030	−	0.718980i	$-0.255391\pi$
$601$	7.27506	+	4.86104i	0.296756	+	0.198286i	−0.398275	+	0.917266i	$0.630391\pi$
$602$	61.2179	−	15.3219i	2.49505	−	0.624474i
$603$	−4.86457	+	16.0363i	−0.198100	+	0.653050i
$604$	−24.6695	+	13.1740i	−1.00379	+	0.536043i
$605$	−13.2900	+	10.9068i	−0.540315	+	0.443425i
$606$	−15.9563	+	33.7202i	−0.648182	+	1.36979i
$607$	3.87021	+	3.87021i	0.157087	+	0.157087i	0.781275	−	0.624188i	$-0.214570\pi$
$607$	3.87021	+	3.87021i	0.157087	+	0.157087i	−0.624188	+	0.781275i	$0.714570\pi$
$608$	0.694373	+	14.4143i	0.0281605	+	0.584576i
$609$	−48.8669	+	48.8669i	−1.98019	+	1.98019i
$610$	3.70755	+	10.3681i	0.150114	+	0.419794i
$611$	0.146104	+	0.178029i	0.00591075	+	0.00720227i
$612$	2.77978	−	3.38455i	0.112366	−	0.136812i
$613$	10.9207	+	3.31275i	0.441082	+	0.133801i	0.503011	−	0.864280i	$-0.332225\pi$
$613$	10.9207	+	3.31275i	0.441082	+	0.133801i	−0.0619293	+	0.998081i	$0.519725\pi$
$614$	33.2210	+	19.9205i	1.34069	+	0.803927i
$615$	11.3267	−	16.9516i	0.456735	−	0.683553i
$616$	45.2919	+	33.6309i	1.82486	+	1.35503i
$617$	6.94744	−	4.64213i	0.279693	−	0.186885i	−0.407809	−	0.913067i	$-0.633707\pi$
$617$	6.94744	−	4.64213i	0.279693	−	0.186885i	0.687502	+	0.726182i	$0.258707\pi$
$618$	5.54217	+	5.02505i	0.222939	+	0.202137i
$619$	−1.32640	−	13.4672i	−0.0533126	−	0.541292i	−0.984332	−	0.176323i	$-0.943580\pi$
$619$	−1.32640	−	13.4672i	−0.0533126	−	0.541292i	0.931020	−	0.364969i	$-0.118920\pi$
$620$	9.08500	+	3.76718i	0.364862	+	0.151294i
$621$	28.2821	−	8.57927i	1.13492	−	0.344274i
$622$	23.6309	+	5.92402i	0.947513	+	0.237531i
$623$	2.59434	−	6.26330i	0.103940	−	0.250934i
$624$	−2.75460	−	2.75880i	−0.110272	−	0.110440i
$625$	−0.382683	−	0.923880i	−0.0153073	−	0.0369552i
$626$	3.60891	+	24.3612i	0.144241	+	0.973671i
$627$	−32.5059	−	17.3748i	−1.29816	−	0.693881i
$628$	5.17587	+	7.75263i	0.206540	+	0.309364i
$629$	0.589434	+	0.483736i	0.0235023	+	0.0192878i
$630$	−9.99959	−	21.1528i	−0.398393	−	0.842747i
$631$	−12.3470	−	2.45597i	−0.491526	−	0.0977707i	−0.0568969	−	0.998380i	$-0.518121\pi$
$631$	−12.3470	−	2.45597i	−0.491526	−	0.0977707i	−0.434629	+	0.900609i	$0.643121\pi$
$632$	−6.41321	−	25.6652i	−0.255104	−	1.02091i
$633$	−8.03445	−	40.3919i	−0.319341	−	1.60543i
$634$	8.40957	+	1.24908i	0.333987	+	0.0496072i
$635$	2.56030	+	4.78998i	0.101602	+	0.190085i
$636$	53.0493	−	43.5026i	2.10354	−	1.72499i
$637$	−2.53442	−	0.249618i	−0.100417	−	0.00989023i
$638$	50.7078	+	2.50079i	2.00754	+	0.0990074i
$639$	−15.0075			−0.593689
$640$	11.1935	−	1.64515i	0.442460	−	0.0650302i
$641$	49.3627			1.94971			0.974855	−	0.222839i	$-0.0715325\pi$
$641$	49.3627			1.94971			0.974855	+	0.222839i	$0.0715325\pi$
$642$	−51.7717	−	2.55326i	−2.04326	−	0.100769i
$643$	−14.3835	−	1.41665i	−0.567229	−	0.0558672i	−0.189662	−	0.981849i	$-0.560739\pi$
$643$	−14.3835	−	1.41665i	−0.567229	−	0.0558672i	−0.377567	+	0.925982i	$0.623239\pi$
$644$	36.8423	+	44.9274i	1.45179	+	1.77039i
$645$	15.2378	+	28.5080i	0.599989	+	1.12250i
$646$	−1.77433	−	0.263542i	−0.0698099	−	0.0103689i
$647$	7.28031	+	36.6006i	0.286219	+	1.43892i	0.809682	+	0.586869i	$0.199640\pi$
$647$	7.28031	+	36.6006i	0.286219	+	1.43892i	−0.523463	+	0.852048i	$0.675360\pi$
$648$	−4.09653	+	6.82581i	−0.160927	+	0.268143i
$649$	10.8350	+	2.15521i	0.425310	+	0.0845995i
$650$	−0.216487	−	0.457949i	−0.00849132	−	0.0179622i
$651$	38.8546	+	31.8872i	1.52283	+	1.24976i
$652$	−8.07896	+	5.39374i	−0.316397	+	0.211235i
$653$	−28.6827	−	15.3312i	−1.12244	−	0.599957i	−0.197589	−	0.980285i	$-0.563311\pi$
$653$	−28.6827	−	15.3312i	−1.12244	−	0.599957i	−0.924852	+	0.380328i	$0.875811\pi$
$654$	0.287919	+	1.94354i	0.0112585	+	0.0759985i
$655$	−5.92764	−	14.3106i	−0.231612	−	0.559161i
$656$	11.4477	+	27.6969i	0.446958	+	1.08138i
$657$	−23.8061	+	57.4730i	−0.928765	+	2.24224i
$658$	−3.31322	−	0.830588i	−0.129163	−	0.0323797i
$659$	5.51547	−	1.67310i	0.214852	−	0.0651746i	−0.181024	−	0.983479i	$-0.557941\pi$
$659$	5.51547	−	1.67310i	0.214852	−	0.0651746i	0.395876	+	0.918304i	$0.370441\pi$
$660$	−11.0683	+	26.6924i	−0.430832	+	1.03900i
$661$	3.16461	+	32.1308i	0.123089	+	1.24974i	0.836095	+	0.548585i	$0.184833\pi$
$661$	3.16461	+	32.1308i	0.123089	+	1.24974i	−0.713006	+	0.701158i	$0.752667\pi$
$662$	−8.85940	−	8.03277i	−0.344330	−	0.312202i
$663$	0.402927	−	0.269227i	0.0156484	−	0.0104559i
$664$	22.1192	−	3.26816i	0.858392	−	0.126829i
$665$	−5.32384	+	7.96768i	−0.206449	+	0.308973i
$666$	8.19247	+	4.91250i	0.317452	+	0.190355i
$667$	50.0381	+	15.1789i	1.93748	+	0.587729i
$668$	37.5676	+	30.8549i	1.45354	+	1.19381i
$669$	−8.16902	−	9.95398i	−0.315833	−	0.384843i
$670$	−1.81178	−	5.06664i	−0.0699953	−	0.195741i
$671$	29.2326	−	29.2326i	1.12851	−	1.12851i
$672$	57.1869	+	8.53852i	2.20603	+	0.329381i
$673$	3.70513	+	3.70513i	0.142822	+	0.142822i	0.774903	−	0.632081i	$-0.217799\pi$
$673$	3.70513	+	3.70513i	0.142822	+	0.142822i	−0.632081	+	0.774903i	$0.717799\pi$
$674$	−1.70233	+	3.59751i	−0.0655714	+	0.138571i
$675$	2.95404	−	2.42432i	0.113701	−	0.0933120i
$676$	12.1267	+	22.7083i	0.466412	+	0.873396i
$677$	9.45380	−	31.1650i	0.363339	−	1.19777i	−0.564703	−	0.825294i	$-0.691009\pi$
$677$	9.45380	−	31.1650i	0.363339	−	1.19777i	0.928042	−	0.372475i	$-0.121491\pi$
$678$	−11.9852	+	2.99972i	−0.460290	+	0.115203i
$679$	−37.0186	−	24.7351i	−1.42064	−	0.949244i
$680$	−0.0698066	+	1.40458i	−0.00267696	+	0.0538630i
$681$	−11.4154	−	17.0844i	−0.437439	−	0.654674i
$682$	−1.80484	−	36.8817i	−0.0691109	−	1.41227i
$683$	34.2305	−	3.37141i	1.30979	−	0.129003i	0.581093	−	0.813837i	$-0.302625\pi$
$683$	34.2305	−	3.37141i	1.30979	−	0.129003i	0.728699	+	0.684834i	$0.240125\pi$
$684$	−22.4717	−	0.00855701i	−0.859228	−	0.000327186i
$685$	3.54211	+	11.6768i	0.135337	+	0.446146i
$686$	0.501635	−	0.300539i	0.0191525	−	0.0114746i
$687$	−46.0495	−	19.0743i	−1.75690	−	0.727731i
$688$	−47.2849	−	4.69352i	−1.80272	−	0.178939i
$689$	4.17157	−	1.72792i	0.158924	−	0.0658285i
$690$	−17.7335	+	23.9013i	−0.675101	+	0.909906i
$691$	5.79734	−	10.8461i	0.220541	−	0.412603i	−0.747182	−	0.664620i	$-0.768594\pi$
$691$	5.79734	−	10.8461i	0.220541	−	0.412603i	0.967723	+	0.252016i	$0.0810936\pi$
$692$	−2.76202	−	13.9133i	−0.104996	−	0.528904i
$693$	−55.7283	+	67.9051i	−2.11694	+	2.57950i
$694$	−30.5981	−	10.9548i	−1.16149	−	0.415837i
$695$	−2.58814	+	13.0114i	−0.0981737	+	0.493552i
$696$	47.0534	−	22.2217i	1.78355	−	0.842312i
$697$	−3.65366	+	0.726758i	−0.138392	+	0.0275279i
$698$	−15.9805	−	21.5557i	−0.604869	−	0.815896i
$699$	−43.2821	+	23.1348i	−1.63708	+	0.875038i
$700$	6.62424	+	3.54397i	0.250373	+	0.133950i
$701$	0.169750	−	1.72351i	0.00641139	−	0.0650959i	−0.991447	−	0.130513i	$-0.958338\pi$
$701$	0.169750	−	1.72351i	0.00641139	−	0.0650959i	0.997858	+	0.0654168i	$0.0208377\pi$
$702$	1.43453	−	1.29969i	0.0541429	−	0.0490535i
$703$		−	3.91232i		−	0.147556i
$704$	−23.5588	−	35.3455i	−0.887904	−	1.33213i
$705$		−	1.74964i		−	0.0658954i
$706$	26.5304	+	29.2830i	0.998486	+	1.10208i
$707$	3.56922	−	36.2389i	0.134234	−	1.36291i
$708$	10.8367	−	3.28277i	0.407268	−	0.123374i
$709$	−18.4652	+	9.86988i	−0.693477	+	0.370671i	−0.780173	−	0.625564i	$-0.784869\pi$
$709$	−18.4652	+	9.86988i	−0.693477	+	0.370671i	0.0866964	+	0.996235i	$0.472369\pi$
$710$	3.87105	−	2.86982i	0.145278	−	0.107702i
$711$	40.4027	−	8.03660i	1.51522	−	0.301396i
$712$	−3.43025	+	3.78036i	−0.128554	+	0.141675i
$713$	7.41957	−	37.3007i	0.277865	−	1.39692i
$714$	−2.42258	+	6.76661i	−0.0906630	+	0.253234i
$715$	−1.20649	+	1.47012i	−0.0451203	+	0.0549793i
$716$	8.64123	−	12.9219i	0.322938	−	0.482913i
$717$	−31.0596	+	58.1084i	−1.15994	+	2.17010i
$718$	−31.0374	−	23.0281i	−1.15830	−	0.859399i
$719$	5.27595	−	2.18537i	0.196760	−	0.0815005i	−0.282128	−	0.959377i	$-0.591040\pi$
$719$	5.27595	−	2.18537i	0.196760	−	0.0815005i	0.478887	+	0.877876i	$0.341040\pi$
$720$	1.71347	+	17.5340i	0.0638572	+	0.653454i
$721$	−6.74661	−	2.79454i	−0.251257	−	0.104074i
$722$	−9.07950	−	15.1548i	−0.337904	−	0.564002i
$723$	−22.8688	−	75.3882i	−0.850499	−	2.80372i
$724$	21.8404	−	21.8237i	0.811691	−	0.811073i
$725$	6.72860	−	0.662709i	0.249894	−	0.0246124i
$726$	66.0814	−	3.23376i	2.45251	−	0.120016i
$727$	−5.23757	−	7.83858i	−0.194251	−	0.290717i	0.721540	−	0.692373i	$-0.243435\pi$
$727$	−5.23757	−	7.83858i	−0.194251	−	0.290717i	−0.915791	+	0.401656i	$0.868435\pi$
$728$	3.43918	+	1.62902i	0.127465	+	0.0603754i
$729$	−36.2456	−	24.2185i	−1.34243	−	0.896982i
$730$	−4.84975	−	19.3769i	−0.179497	−	0.717172i
$731$	1.71456	−	5.65214i	0.0634152	−	0.209052i
$732$	12.3157	−	40.5438i	0.455201	−	1.49854i
$733$	−23.1013	+	18.9588i	−0.853266	+	0.700257i	−0.955655	−	0.294487i	$-0.904851\pi$
$733$	−23.1013	+	18.9588i	−0.853266	+	0.700257i	0.102389	+	0.994744i	$0.467351\pi$
$734$	−28.9924	−	13.7192i	−1.07013	−	0.506383i
$735$	13.6806	+	13.6806i	0.504615	+	0.504615i
$736$	−14.6994	−	41.2058i	−0.541829	−	1.51887i
$737$	−14.2852	+	14.2852i	−0.526202	+	0.526202i
$738$	−43.9429	+	15.7136i	−1.61756	+	0.578426i
$739$	−2.65248	−	3.23206i	−0.0975731	−	0.118893i	0.721935	−	0.691961i	$-0.243253\pi$
$739$	−2.65248	−	3.23206i	−0.0975731	−	0.118893i	−0.819508	+	0.573068i	$0.805753\pi$
$740$	−3.05256	+	0.299477i	−0.112214	+	0.0110090i
$741$	−2.37930	−	0.721754i	−0.0874059	−	0.0265143i
$742$	−34.4391	+	57.4333i	−1.26430	+	2.10844i
$743$	7.80082	−	11.6748i	0.286185	−	0.428305i	−0.660326	−	0.750979i	$-0.729582\pi$
$743$	7.80082	−	11.6748i	0.286185	−	0.428305i	0.946510	+	0.322674i	$0.104582\pi$
$744$	−19.4390	−	32.4740i	−0.712667	−	1.19056i
$745$	−10.7277	+	7.16801i	−0.393032	+	0.262616i
$746$	2.15924	−	2.38145i	0.0790555	−	0.0871910i
$747$	3.41273	+	34.6500i	0.124865	+	1.26778i
$748$	4.87884	−	2.01870i	0.178388	−	0.0738111i
$749$	48.4183	−	14.6875i	1.76917	−	0.536671i
$750$	−0.935751	+	3.73271i	−0.0341688	+	0.136299i
$751$	−11.5683	+	27.9284i	−0.422134	+	1.01912i	0.559583	+	0.828775i	$0.310961\pi$
$751$	−11.5683	+	27.9284i	−0.422134	+	1.01912i	−0.981717	+	0.190347i	$0.939039\pi$
$752$	2.13742	+	1.43053i	0.0779437	+	0.0521662i
$753$	−9.93113	−	23.9759i	−0.361910	−	0.873729i
$754$	3.38783	−	0.501878i	0.123377	−	0.0182773i
$755$	12.3322	+	6.59171i	0.448815	+	0.239897i
$756$	−5.61167	+	28.1557i	−0.204094	+	1.02401i
$757$	−19.1903	−	15.7491i	−0.697482	−	0.572409i	0.217423	−	0.976077i	$-0.430235\pi$
$757$	−19.1903	−	15.7491i	−0.697482	−	0.572409i	−0.914905	+	0.403668i	$0.867735\pi$
$758$	−1.32462	+	0.626190i	−0.0481124	+	0.0227443i
$759$	109.592	+	21.7993i	3.97795	+	0.791264i
$760$	5.79799	−	4.29495i	0.210315	−	0.155794i
$761$	−1.08874	−	5.47345i	−0.0394667	−	0.198412i	0.956022	−	0.293296i	$-0.0947521\pi$
$761$	−1.08874	−	5.47345i	−0.0394667	−	0.198412i	−0.995488	+	0.0948835i	$0.969752\pi$
$762$	3.07072	−	20.6740i	0.111241	−	0.748941i
$763$	−0.904065	−	1.69139i	−0.0327293	−	0.0612323i
$764$	−4.61601	+	46.6849i	−0.167002	+	1.68900i
$765$	−2.17934	−	0.214646i	−0.0787942	−	0.00776055i
$766$	0.857598	−	17.3893i	0.0309863	−	0.628299i
$767$	0.745225			0.0269085
$768$	−38.3654	−	20.5819i	−1.38439	−	0.742687i
$769$	27.3682			0.986924			0.493462	−	0.869767i	$-0.335731\pi$
$769$	27.3682			0.986924			0.493462	+	0.869767i	$0.335731\pi$
$770$	1.38938	−	28.1721i	0.0500699	−	1.01525i
$771$	19.5746	+	1.92793i	0.704963	+	0.0694328i
$772$	4.94908	−	50.0534i	0.178121	−	1.80146i
$773$	−3.66151	−	6.85020i	−0.131695	−	0.246385i	0.807427	−	0.589967i	$-0.200859\pi$
$773$	−3.66151	−	6.85020i	−0.131695	−	0.246385i	−0.939122	+	0.343583i	$0.888359\pi$
$774$	10.8710	−	73.1903i	0.390750	−	2.63077i
$775$	−0.959365	−	4.82305i	−0.0344614	−	0.173249i
$776$	19.9548	+	26.9380i	0.716334	+	0.967019i
$777$	−15.3744	−	3.05815i	−0.551552	−	0.109711i
$778$	−28.8900	+	13.6572i	−1.03576	+	0.489635i
$779$	14.7749	+	12.1255i	0.529366	+	0.434440i
$780$	−0.381014	+	1.91168i	−0.0136425	+	0.0684491i
$781$	−15.9559	−	8.52860i	−0.570946	−	0.305177i
$782$	5.37938	−	0.796909i	0.192366	−	0.0284974i
$783$	9.88761	+	23.8708i	0.353354	+	0.853073i
$784$	−27.8981	+	5.52719i	−0.996359	+	0.197400i
$785$	1.78362	−	4.30603i	0.0636601	−	0.153689i
$786$	−14.4945	+	57.8184i	−0.517000	+	2.06232i
$787$	48.6125	−	14.7464i	1.73285	−	0.525654i	0.743188	−	0.669082i	$-0.233313\pi$
$787$	48.6125	−	14.7464i	1.73285	−	0.525654i	0.989661	+	0.143428i	$0.0458126\pi$
$788$	−36.6396	+	15.1603i	−1.30523	+	0.540062i
$789$	7.17110	+	72.8094i	0.255298	+	2.59208i
$790$	−8.88468	+	9.79898i	−0.316103	+	0.348632i
$791$	10.0275	−	6.70014i	0.356536	−	0.238230i
$792$	56.7539	−	33.9729i	2.01666	−	1.20718i
$793$	1.54937	−	2.31879i	0.0550196	−	0.0823427i
$794$	5.32677	−	8.88334i	0.189040	−	0.315258i
$795$	−32.8257	−	9.95755i	−1.16421	−	0.353158i
$796$	35.9490	−	3.52685i	1.27418	−	0.125006i
$797$	8.31430	+	10.1310i	0.294507	+	0.358858i	0.899152	−	0.437637i	$-0.144185\pi$
$797$	8.31430	+	10.1310i	0.294507	+	0.358858i	−0.604644	+	0.796496i	$0.706685\pi$
$798$	34.7229	−	12.4166i	1.22918	−	0.439542i
$799$	−0.226061	+	0.226061i	−0.00799746	+	0.00799746i
$800$	−3.79492	−	4.19507i	−0.134171	−	0.148318i
$801$	−5.62074	−	5.62074i	−0.198599	−	0.198599i
$802$	−36.9419	−	17.4808i	−1.30446	−	0.617269i
$803$	−57.9717	+	47.5761i	−2.04578	+	1.67892i
$804$	−6.01836	+	19.8127i	−0.212251	+	0.698740i
$805$	8.43304	−	27.8000i	0.297226	−	0.979821i
$806$	−0.604788	−	2.41640i	−0.0213028	−	0.0851141i
$807$	−24.8256	−	16.5879i	−0.873903	−	0.583923i
$808$	−11.7373	+	24.7798i	−0.412917	+	0.871751i
$809$	−9.41570	−	14.0916i	−0.331038	−	0.495434i	0.628192	−	0.778058i	$-0.283795\pi$
$809$	−9.41570	−	14.0916i	−0.331038	−	0.495434i	−0.959231	+	0.282624i	$0.908795\pi$
$810$	3.97561	−	0.194550i	0.139689	−	0.00683580i
$811$	−43.2860	+	4.26330i	−1.51998	+	0.149705i	−0.823269	−	0.567652i	$-0.807852\pi$
$811$	−43.2860	+	4.26330i	−1.51998	+	0.149705i	−0.696707	+	0.717356i	$0.745352\pi$
$812$	−35.9307	+	35.9034i	−1.26092	+	1.25996i
$813$	−17.4866	−	57.6455i	−0.613281	−	2.02172i
$814$	5.91845	+	9.87860i	0.207441	+	0.346245i
$815$	4.48729	+	1.85870i	0.157183	+	0.0651073i
$816$	3.43638	−	4.18075i	0.120297	−	0.146355i
$817$	−27.9981	+	11.5972i	−0.979529	+	0.405734i
$818$	18.0064	+	13.3597i	0.629578	+	0.467112i
$819$	−2.79342	+	5.22612i	−0.0976100	+	0.182616i
$820$	8.32981	−	12.4562i	0.290889	−	0.434988i
$821$	5.67001	−	6.90893i	0.197885	−	0.241123i	−0.664609	−	0.747192i	$-0.731402\pi$
$821$	5.67001	−	6.90893i	0.197885	−	0.241123i	0.862493	+	0.506069i	$0.168902\pi$
$822$	15.8276	−	44.2087i	0.552052	−	1.54196i
$823$	3.10528	−	15.6113i	0.108243	−	0.544176i	−0.888167	−	0.459521i	$-0.848021\pi$
$823$	3.10528	−	15.6113i	0.108243	−	0.544176i	0.996410	−	0.0846552i	$-0.0269789\pi$
$824$	4.07207	+	3.69495i	0.141857	+	0.128720i
$825$	14.1705	−	2.81869i	0.493354	−	0.0981341i
$826$	−8.87885	+	6.58238i	−0.308935	+	0.229030i
$827$	25.9537	−	13.8725i	0.902498	−	0.482395i	0.0462323	−	0.998931i	$-0.485279\pi$
$827$	25.9537	−	13.8725i	0.902498	−	0.482395i	0.856266	+	0.516535i	$0.172779\pi$
$828$	65.1997	−	19.7510i	2.26585	−	0.686395i
$829$	2.29583	−	23.3099i	0.0797374	−	0.809588i	−0.869271	−	0.494336i	$-0.835411\pi$
$829$	2.29583	−	23.3099i	0.0797374	−	0.809588i	0.949008	−	0.315251i	$-0.102089\pi$
$830$	−7.50623	−	8.28502i	−0.260545	−	0.287577i
$831$		−	5.29090i		−	0.183539i
$832$	−2.02385	−	2.02848i	−0.0701643	−	0.0703248i
$833$		−	3.53517i		−	0.122486i
$834$	37.8334	−	34.2771i	1.31006	−	1.18692i
$835$	2.38252	−	24.1901i	0.0824505	−	0.837134i
$836$	−23.8869	−	12.7795i	−0.826144	−	0.441988i
$837$	16.5733	−	8.85861i	0.572857	−	0.306198i
$838$	−26.7015	−	36.0172i	−0.922389	−	1.24419i
$839$	−40.7254	+	8.10079i	−1.40600	+	0.279670i	−0.839037	−	0.544074i	$-0.816881\pi$
$839$	−40.7254	+	8.10079i	−1.40600	+	0.279670i	−0.566961	+	0.823745i	$0.691881\pi$
$840$	−12.3459	−	26.1418i	−0.425973	−	0.901976i
$841$	−3.26058	+	16.3920i	−0.112434	+	0.565243i
$842$	40.2259	+	14.4017i	1.38628	+	0.496316i
$843$	−17.3470	+	21.1374i	−0.597462	+	0.728009i
$844$	−5.89399	−	29.6902i	−0.202880	−	1.02198i
$845$	6.06768	−	11.3518i	0.208735	−	0.390515i
$846$	−2.38640	+	3.21641i	−0.0820462	+	0.110583i
$847$	−59.6649	+	24.7140i	−2.05011	+	0.849184i
$848$	39.0032	−	31.9594i	1.33938	−	1.09749i
$849$	−2.87633	−	1.19142i	−0.0987154	−	0.0408893i
$850$	0.603185	−	0.361379i	0.0206891	−	0.0123952i
$851$	3.44297	+	11.3500i	0.118024	+	0.389071i
$852$	−18.5438	−	0.00706130i	−0.635300	−	0.000241916i
$853$	−0.508632	+	0.0500959i	−0.0174152	+	0.00171525i	−0.106721	−	0.994289i	$-0.534035\pi$
$853$	−0.508632	+	0.0500959i	−0.0174152	+	0.00171525i	0.0893058	+	0.996004i	$0.471535\pi$
$854$	2.02164	+	41.3120i	0.0691792	+	1.41367i
$855$	6.24231	+	9.34228i	0.213482	+	0.319499i
$856$	−38.0513	−	1.89113i	−1.30057	−	0.0646374i
$857$	8.03364	+	5.36790i	0.274424	+	0.183364i	0.685165	−	0.728388i	$-0.259730\pi$
$857$	8.03364	+	5.36790i	0.274424	+	0.183364i	−0.410741	+	0.911752i	$0.634730\pi$
$858$	7.09958	−	1.77691i	0.242376	−	0.0606629i
$859$	10.5627	−	34.8205i	0.360394	−	1.18806i	−0.570046	−	0.821613i	$-0.693075\pi$
$859$	10.5627	−	34.8205i	0.360394	−	1.18806i	0.930439	−	0.366446i	$-0.119425\pi$
$860$	11.1918	+	20.9575i	0.381636	+	0.714646i
$861$	59.1988	−	48.5832i	2.01749	−	1.65571i
$862$	−15.5682	+	32.8999i	−0.530254	+	1.12058i
$863$	24.5428	+	24.5428i	0.835445	+	0.835445i	0.988256	−	0.152810i	$-0.0488324\pi$
$863$	24.5428	+	24.5428i	0.835445	+	0.835445i	−0.152810	+	0.988256i	$0.548832\pi$
$864$	11.1313	−	18.5314i	0.378694	−	0.630450i
$865$	−5.01509	+	5.01509i	−0.170518	+	0.170518i
$866$	1.74276	+	4.87361i	0.0592214	+	0.165612i
$867$	−28.9195	−	35.2385i	−0.982156	−	1.19676i
$868$	28.5491	+	23.4478i	0.969019	+	0.795871i
$869$	47.5229	+	14.4159i	1.61210	+	0.489026i
$870$	−22.3142	−	13.3804i	−0.756521	−	0.453637i
$871$	−0.757135	+	1.13313i	−0.0256545	+	0.0383947i
$872$	0.211076	+	1.42858i	0.00714792	+	0.0483777i
$873$	−43.4051	+	29.0024i	−1.46904	+	0.981582i
$874$	−20.6703	−	18.7416i	−0.699182	−	0.633944i
$875$	−0.368186	−	3.73825i	−0.0124469	−	0.126376i
$876$	−29.4426	+	71.0043i	−0.994775	+	2.39901i
$877$	−21.7824	+	6.60763i	−0.735540	+	0.223124i	−0.635761	−	0.771886i	$-0.719314\pi$
$877$	−21.7824	+	6.60763i	−0.735540	+	0.223124i	−0.0997792	+	0.995010i	$0.531814\pi$
$878$	−26.2057	−	6.56950i	−0.884401	−	0.221710i
$879$	−14.1479	+	34.1560i	−0.477196	+	1.15205i
$880$	−8.14262	+	19.6158i	−0.274488	+	0.661247i
$881$	1.62258	+	3.91724i	0.0546659	+	0.131975i	0.948853	−	0.315718i	$-0.102245\pi$
$881$	1.62258	+	3.91724i	0.0546659	+	0.131975i	−0.894187	+	0.447694i	$0.852245\pi$
$882$	−6.48989	−	43.8088i	−0.218526	−	1.47512i
$883$	30.0670	+	16.0712i	1.01184	+	0.540837i	0.892038	−	0.451961i	$-0.149275\pi$
$883$	30.0670	+	16.0712i	1.01184	+	0.540837i	0.119798	+	0.992798i	$0.461775\pi$
$884$	0.296225	−	0.197768i	0.00996314	−	0.00665167i
$885$	−4.37641	−	3.59162i	−0.147111	−	0.120731i
$886$	−13.3288	−	28.1953i	−0.447791	−	0.947241i
$887$	21.1934	+	4.21563i	0.711605	+	0.141547i	0.537603	−	0.843198i	$-0.319330\pi$
$887$	21.1934	+	4.21563i	0.711605	+	0.141547i	0.174002	+	0.984745i	$0.444330\pi$
$888$	10.1206	+	6.07389i	0.339624	+	0.203826i
$889$	3.98019	+	20.0098i	0.133491	+	0.671107i
$890$	2.52464	+	0.374986i	0.0846261	+	0.0125696i
$891$	−7.04468	−	13.1797i	−0.236006	−	0.441535i
$892$	−6.00142	−	7.31843i	−0.200942	−	0.245039i
$893$	1.63241	+	0.160778i	0.0546266	+	0.00538025i
$894$	49.5897	+	2.44565i	1.65853	+	0.0817948i
$895$	−7.77247			−0.259805
$896$	42.0298	+	6.29179i	1.40412	+	0.210194i
$897$	7.53771			0.251677
$898$	9.56543	+	0.471745i	0.319202	+	0.0157423i
$899$	33.0881	+	3.25890i	1.10355	+	0.108690i
$900$	6.81140	−	5.58563i	0.227047	−	0.186188i
$901$	2.95465	+	5.52777i	0.0984337	+	0.184157i
$902$	−55.6496	−	8.26566i	−1.85293	−	0.275216i
$903$	23.6885	+	119.090i	0.788303	+	3.96307i
$904$	−8.80994	+	2.20143i	−0.293014	+	0.0732184i
$905$	−15.1410	−	3.01173i	−0.503303	−	0.100113i
$906$	−22.9979	−	48.6489i	−0.764054	−	1.61625i
$907$	2.19479	+	1.80121i	0.0728767	+	0.0598084i	0.670126	−	0.742247i	$-0.266240\pi$
$907$	2.19479	+	1.80121i	0.0728767	+	0.0598084i	−0.597250	+	0.802055i	$0.703740\pi$
$908$	−8.38551	−	12.5601i	−0.278283	−	0.416823i
$909$	−37.6550	−	20.1270i	−1.24894	−	0.667570i
$910$	−0.278832	−	1.88220i	−0.00924318	−	0.0623943i
$911$	−6.75517	−	16.3084i	−0.223809	−	0.540322i	0.771592	−	0.636118i	$-0.219461\pi$
$911$	−6.75517	−	16.3084i	−0.223809	−	0.540322i	−0.995401	+	0.0957950i	$0.969461\pi$
$912$	−27.7668	−	0.0211466i	−0.919450	−	0.000700235i
$913$	−16.0628	+	38.7790i	−0.531600	+	1.28340i
$914$	−54.4587	−	13.6522i	−1.80133	−	0.451575i
$915$	−20.2743	+	6.15013i	−0.670246	+	0.203317i
$916$	−33.8409	−	14.0325i	−1.11813	−	0.463645i
$917$	−5.70307	−	57.9042i	−0.188332	−	1.91217i
$918$	1.99066	+	1.80492i	0.0657015	+	0.0595711i
$919$	10.9793	−	7.33612i	0.362173	−	0.241996i	−0.361147	−	0.932509i	$-0.617615\pi$
$919$	10.9793	−	7.33612i	0.362173	−	0.241996i	0.723321	+	0.690512i	$0.242615\pi$
$920$	−13.0407	+	17.5624i	−0.429940	+	0.579015i
$921$	−41.4077	+	61.9711i	−1.36443	+	2.04202i
$922$	−10.1141	−	6.06480i	−0.333091	−	0.199733i
$923$	−1.16791	−	0.354281i	−0.0384422	−	0.0116613i
$924$	−68.8916	+	83.8795i	−2.26637	+	2.75943i
$925$	0.972910	+	1.18549i	0.0319891	+	0.0389788i
$926$	11.0702	+	30.9578i	0.363790	+	1.01734i
$927$	−6.05447	+	6.05447i	−0.198855	+	0.198855i
$928$	34.5903	−	16.3197i	1.13548	−	0.535721i
$929$	12.3172	+	12.3172i	0.404113	+	0.404113i	0.879680	−	0.475567i	$-0.157757\pi$
$929$	12.3172	+	12.3172i	0.404113	+	0.404113i	−0.475567	+	0.879680i	$0.657757\pi$
$930$	−8.09421	+	17.1053i	−0.265420	+	0.560906i
$931$	−14.0211	+	11.5068i	−0.459522	+	0.377120i
$932$	−31.8187	+	16.9919i	−1.04226	+	0.556588i
$933$	−13.6072	+	44.8570i	−0.445480	+	1.46855i
$934$	−9.27457	+	2.32128i	−0.303473	+	0.0759546i
$935$	−2.19507	−	1.46670i	−0.0717866	−	0.0479662i
$936$	3.30784	−	2.99461i	0.108120	−	0.0978819i
$937$	−9.75227	−	14.5953i	−0.318593	−	0.476808i	0.637262	−	0.770647i	$-0.280067\pi$
$937$	−9.75227	−	14.5953i	−0.318593	−	0.476808i	−0.955855	+	0.293839i	$0.905067\pi$
$938$	−0.987924	−	20.1881i	−0.0322569	−	0.659164i
$939$	−47.1570	+	4.64456i	−1.53891	+	0.151570i
$940$	0.000489690	−	1.28598i	1.59719e−5	−	0.0419441i
$941$	−4.28689	−	14.1320i	−0.139749	−	0.460689i	0.858929	−	0.512094i	$-0.171130\pi$
$941$	−4.28689	−	14.1320i	−0.139749	−	0.460689i	−0.998678	+	0.0514048i	$0.983630\pi$
$942$	−15.3858	+	9.21793i	−0.501298	+	0.300337i
$943$	−53.5339	−	22.1745i	−1.74330	−	0.722100i
$944$	7.96586	−	2.40979i	0.259267	−	0.0784321i
$945$	13.2621	−	5.49333i	0.431415	−	0.178698i
$946$	53.1511	−	71.6375i	1.72809	−	2.32913i
$947$	−14.3933	+	26.9280i	−0.467720	+	0.875042i	0.531882	+	0.846819i	$0.321485\pi$
$947$	−14.3933	+	26.9280i	−0.467720	+	0.875042i	−0.999602	+	0.0282237i	$0.991015\pi$
$948$	49.9267	−	9.91127i	1.62154	−	0.321903i
$949$	−3.20938	+	3.91065i	−0.104181	+	0.126945i
$950$	−3.39662	−	1.21606i	−0.110201	−	0.0394542i
$951$	−3.19137	+	16.0441i	−0.103487	+	0.520266i
$952$	−1.78249	+	4.97276i	−0.0577707	+	0.161168i
$953$	−14.7819	+	2.94030i	−0.478833	+	0.0952458i	−0.428605	−	0.903492i	$-0.640995\pi$
$953$	−14.7819	+	2.94030i	−0.478833	+	0.0952458i	−0.0502280	+	0.998738i	$0.515995\pi$
$954$	46.7627	+	63.0774i	1.51400	+	2.04220i
$955$	20.6866	−	11.0572i	0.669403	−	0.357803i
$956$	−22.8450	+	42.7008i	−0.738859	+	1.38104i
$957$	−9.57490	+	97.2155i	−0.309512	+	3.14253i
$958$	−39.1936	+	35.5094i	−1.26629	+	1.14726i
$959$			45.8355i			1.48011i
$960$	2.10897	+	21.6664i	0.0680666	+	0.699280i
$961$			6.81779i			0.219929i
$962$	0.521581	+	0.575696i	0.0168164	+	0.0185612i
$963$	5.81497	−	59.0404i	0.187385	−	1.90255i
$964$	−16.7874	−	55.4165i	−0.540685	−	1.78485i
$965$	−22.1792	+	11.8550i	−0.713974	+	0.381627i
$966$	−89.8067	+	66.5787i	−2.88948	+	2.14213i
$967$	54.3011	−	10.8012i	1.74621	−	0.347342i	0.784228	−	0.620472i	$-0.213059\pi$
$967$	54.3011	−	10.8012i	1.74621	−	0.347342i	0.961977	+	0.273131i	$0.0880591\pi$
$968$	48.5705	−	2.35831i	1.56112	−	0.0757989i
$969$	0.673344	−	3.38513i	0.0216309	−	0.108746i
$970$	5.64993	−	15.7810i	0.181408	−	0.506698i
$971$	−32.4008	+	39.4805i	−1.03979	+	1.26699i	−0.0769166	+	0.997038i	$0.524508\pi$
$971$	−32.4008	+	39.4805i	−1.03979	+	1.26699i	−0.962874	+	0.269951i	$0.912992\pi$
$972$	−31.7924	−	21.2605i	−1.01974	−	0.681932i
$973$	−23.4911	+	43.9487i	−0.753089	+	1.40893i
$974$	6.09649	+	4.52327i	0.195344	+	0.144935i
$975$	0.900450	−	0.372979i	0.0288375	−	0.0119449i
$976$	9.06334	−	29.7961i	0.290111	−	0.953751i
$977$	−9.58979	−	3.97222i	−0.306805	−	0.127083i	0.223969	−	0.974596i	$-0.428099\pi$
$977$	−9.58979	−	3.97222i	−0.306805	−	0.127083i	−0.530774	+	0.847514i	$0.678099\pi$
$978$	−9.60595	−	16.0335i	−0.307164	−	0.512694i
$979$	−2.78172	−	9.17011i	−0.0889043	−	0.293078i
$980$	10.0513	+	10.0590i	0.321078	+	0.321323i
$981$	−2.23788	+	0.220412i	−0.0714501	+	0.00703722i
$982$	23.8891	−	1.16904i	0.762332	−	0.0373055i
$983$	5.59822	+	8.37833i	0.178555	+	0.267227i	0.909942	−	0.414736i	$-0.136126\pi$
$983$	5.59822	+	8.37833i	0.178555	+	0.267227i	−0.731386	+	0.681964i	$0.761126\pi$
$984$	−54.3047	+	19.3955i	−1.73117	+	0.618308i
$985$	16.4848	+	11.0148i	0.525248	+	0.350960i
$986$	1.15428	+	4.61188i	0.0367598	+	0.146872i
$987$	1.90782	−	6.28925i	0.0607267	−	0.200189i
$988$	−1.74858	−	0.531153i	−0.0556297	−	0.0168982i
$989$	71.0187	−	58.2835i	2.25826	−	1.85331i
$990$	−29.8945	−	14.1460i	−0.950110	−	0.449590i
$991$	0.100443	+	0.100443i	0.00319069	+	0.00319069i	0.708700	−	0.705510i	$-0.249282\pi$
$991$	0.100443	+	0.100443i	0.00319069	+	0.00319069i	−0.705510	+	0.708700i	$0.749282\pi$
$992$	−14.2785	−	23.8737i	−0.453343	−	0.757992i
$993$	16.2706	−	16.2706i	0.516333	−	0.516333i
$994$	17.0441	−	6.09482i	0.540606	−	0.193316i
$995$	−11.4577	−	13.9612i	−0.363232	−	0.442600i
$996$	4.20057	+	42.8162i	0.133100	+	1.35668i
$997$	31.7486	+	9.63085i	1.00549	+	0.305012i	0.749741	−	0.661731i	$-0.230178\pi$
$997$	31.7486	+	9.63085i	1.00549	+	0.305012i	0.255749	+	0.966743i	$0.417678\pi$
$998$	12.3134	−	20.5347i	0.389772	−	0.650015i
$999$	−3.25600	+	4.87294i	−0.103015	+	0.154173i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.bm.a.221.31	✓	1024
128.117	even	32	inner	640.2.bm.a.501.31	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.bm.a.221.31	✓	1024	1.1	even	1	trivial
640.2.bm.a.501.31	yes	1024	128.117	even	32	inner

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:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.bm (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0696611 + 1.41250i) q^{2} +(-2.70800 - 0.266714i) q^{3} +(-1.99029 - 0.196792i) q^{4} +(0.471397 + 0.881921i) q^{5} +(0.565375 - 3.80646i) q^{6} +(0.732825 + 3.68416i) q^{7} +(0.416614 - 2.79758i) q^{8} +(4.31976 + 0.859253i) q^{9} +O(q^{10})\)	\(q+(-0.0696611 + 1.41250i) q^{2} +(-2.70800 - 0.266714i) q^{3} +(-1.99029 - 0.196792i) q^{4} +(0.471397 + 0.881921i) q^{5} +(0.565375 - 3.80646i) q^{6} +(0.732825 + 3.68416i) q^{7} +(0.416614 - 2.79758i) q^{8} +(4.31976 + 0.859253i) q^{9} +(-1.27855 + 0.604411i) q^{10} +(4.10442 + 3.36841i) q^{11} +(5.33723 + 1.06375i) q^{12} +(0.315885 + 0.168844i) q^{13} +(-5.25492 + 0.778471i) q^{14} +(-1.04132 - 2.51397i) q^{15} +(3.92255 + 0.783349i) q^{16} +(-0.190272 + 0.459358i) q^{17} +(-1.51461 + 6.04179i) q^{18} +(2.44121 - 0.740534i) q^{19} +(-0.764663 - 1.84805i) q^{20} +(-1.00187 - 10.1722i) q^{21} +(-5.04379 + 5.56284i) q^{22} +(-6.43045 + 4.29669i) q^{23} +(-1.87434 + 7.46471i) q^{24} +(-0.555570 + 0.831470i) q^{25} +(-0.260497 + 0.434425i) q^{26} +(-3.65692 - 1.10932i) q^{27} +(-0.733524 - 7.47678i) q^{28} +(-4.28923 - 5.22644i) q^{29} +(3.62351 - 1.29574i) q^{30} +(-3.47723 + 3.47723i) q^{31} +(-1.37973 + 5.48601i) q^{32} +(-10.2164 - 10.2164i) q^{33} +(-0.635587 - 0.300758i) q^{34} +(-2.90369 + 2.38300i) q^{35} +(-8.42849 - 2.56026i) q^{36} +(0.445183 - 1.46757i) q^{37} +(0.875944 + 3.49979i) q^{38} +(-0.810384 - 0.541481i) q^{39} +(2.66363 - 0.951347i) q^{40} +(4.16253 + 6.22967i) q^{41} +(14.4379 - 0.706534i) q^{42} +(-11.8221 + 1.16438i) q^{43} +(-7.50613 - 7.51185i) q^{44} +(1.27853 + 4.21473i) q^{45} +(-5.62111 - 9.38231i) q^{46} +(0.594046 + 0.246062i) q^{47} +(-10.4133 - 3.16751i) q^{48} +(-6.56886 + 2.72091i) q^{49} +(-1.13575 - 0.842662i) q^{50} +(0.637774 - 1.19319i) q^{51} +(-0.595478 - 0.398214i) q^{52} +(7.99729 - 9.74472i) q^{53} +(1.82165 - 5.08812i) q^{54} +(-1.03586 + 5.20764i) q^{55} +(10.6120 - 0.515260i) q^{56} +(-6.80831 + 1.35426i) q^{57} +(7.68112 - 5.69444i) q^{58} +(1.83492 - 0.980786i) q^{59} +(1.57780 + 5.20846i) q^{60} +(0.763163 - 7.74853i) q^{61} +(-4.66934 - 5.15380i) q^{62} +16.5444i q^{63} +(-7.65286 - 2.33102i) q^{64} +0.358179i q^{65} +(15.1423 - 13.7189i) q^{66} +(-0.372938 + 3.78650i) q^{67} +(0.469096 - 0.876813i) q^{68} +(18.5596 - 9.92033i) q^{69} +(-3.16370 - 4.26745i) q^{70} +(-3.34194 + 0.664753i) q^{71} +(4.20350 - 11.7269i) q^{72} +(-2.75549 + 13.8528i) q^{73} +(2.04193 + 0.731051i) q^{74} +(1.72625 - 2.10344i) q^{75} +(-5.00447 + 0.993469i) q^{76} +(-9.40195 + 17.5898i) q^{77} +(0.821292 - 1.10694i) q^{78} +(8.64105 - 3.57924i) q^{79} +(1.15822 + 3.82864i) q^{80} +(-2.60030 - 1.07708i) q^{81} +(-9.08935 + 5.44560i) q^{82} +(2.29476 + 7.56482i) q^{83} +(-0.00778440 + 20.4427i) q^{84} +(-0.494811 + 0.0487346i) q^{85} +(-0.821138 - 16.7798i) q^{86} +(10.2213 + 15.2972i) q^{87} +(11.1334 - 10.0791i) q^{88} +(-1.50062 - 1.00268i) q^{89} +(-6.04236 + 1.51231i) q^{90} +(-0.390561 + 1.28751i) q^{91} +(13.6441 - 7.28622i) q^{92} +(10.3437 - 8.48889i) q^{93} +(-0.388944 + 0.821948i) q^{94} +(1.80387 + 1.80387i) q^{95} +(5.19950 - 14.4881i) q^{96} +(-8.38097 + 8.38097i) q^{97} +(-3.38568 - 9.46803i) q^{98} +(14.8358 + 18.0775i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q+O(q^{10}) \) 1024 * q	\( 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) \) 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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