LMFDB - Embedded newform 875.2.q.b.226.29

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [875,2,Mod(51,875)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(875, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([24, 10]))

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

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

chi := DirichletCharacter("875.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.q (of order $15$, degree $8$, not 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:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$36$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			226.29
Character	$\chi$	$=$	875.226
Dual form			875.2.q.b.151.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.18897 + 1.32048i) q^{2} +(-0.0142295 + 0.135384i) q^{3} +(-0.120974 + 1.15099i) q^{4} +(-0.195691 + 0.142178i) q^{6} +(1.81810 + 1.92211i) q^{7} +(1.21137 - 0.880110i) q^{8} +(2.91632 + 0.619882i) q^{9} +O(q^{10})$	\(q+(1.18897 + 1.32048i) q^{2} +(-0.0142295 + 0.135384i) q^{3} +(-0.120974 + 1.15099i) q^{4} +(-0.195691 + 0.142178i) q^{6} +(1.81810 + 1.92211i) q^{7} +(1.21137 - 0.880110i) q^{8} +(2.91632 + 0.619882i) q^{9} +(0.876154 - 0.186232i) q^{11} +(-0.154104 - 0.0327559i) q^{12} +(-1.82766 - 5.62497i) q^{13} +(-0.376443 + 4.68611i) q^{14} +(4.86653 + 1.03441i) q^{16} +(-1.86670 - 0.831108i) q^{17} +(2.64887 + 4.58797i) q^{18} +(0.385351 + 3.66637i) q^{19} +(-0.286094 + 0.218792i) q^{21} +(1.28764 + 0.935524i) q^{22} +(0.131400 + 0.145934i) q^{23} +(0.101916 + 0.176524i) q^{24} +(5.25465 - 9.10133i) q^{26} +(-0.251619 + 0.774405i) q^{27} +(-2.43227 + 1.86009i) q^{28} +(1.19212 + 0.866123i) q^{29} +(-1.46865 - 0.653883i) q^{31} +(2.92289 + 5.06260i) q^{32} +(0.0127457 + 0.121268i) q^{33} +(-1.12198 - 3.45311i) q^{34} +(-1.06627 + 3.28166i) q^{36} +(8.53955 + 1.81514i) q^{37} +(-4.38322 + 4.86805i) q^{38} +(0.787540 - 0.167397i) q^{39} +(1.96439 + 6.04579i) q^{41} +(-0.629069 - 0.117645i) q^{42} -11.5179 q^{43} +(0.108360 + 1.03097i) q^{44} +(-0.0364735 + 0.347022i) q^{46} +(-11.0000 + 4.89753i) q^{47} +(-0.209291 + 0.644132i) q^{48} +(-0.388997 + 6.98918i) q^{49} +(0.139081 - 0.240896i) q^{51} +(6.69538 - 1.42315i) q^{52} +(-0.219388 + 2.08734i) q^{53} +(-1.32176 + 0.588484i) q^{54} +(3.89406 + 0.728248i) q^{56} -0.501852 q^{57} +(0.273688 + 2.60397i) q^{58} +(5.44105 - 6.04289i) q^{59} +(1.69386 + 1.88122i) q^{61} +(-0.882733 - 2.71677i) q^{62} +(4.11069 + 6.73248i) q^{63} +(-0.134982 + 0.415431i) q^{64} +(-0.144978 + 0.161014i) q^{66} +(-9.29355 - 4.13775i) q^{67} +(1.18242 - 2.04801i) q^{68} +(-0.0216269 + 0.0157129i) q^{69} +(-9.11276 - 6.62080i) q^{71} +(4.07830 - 1.81577i) q^{72} +(9.78179 - 2.07918i) q^{73} +(7.75640 + 13.4345i) q^{74} -4.26657 q^{76} +(1.95090 + 1.34547i) q^{77} +(1.15741 + 0.840905i) q^{78} +(3.29105 - 1.46527i) q^{79} +(8.06986 + 3.59293i) q^{81} +(-5.64776 + 9.78221i) q^{82} +(2.17252 - 1.57843i) q^{83} +(-0.217217 - 0.355759i) q^{84} +(-13.6945 - 15.2092i) q^{86} +(-0.134223 + 0.149069i) q^{87} +(0.897440 - 0.996708i) q^{88} +(-4.43903 - 4.93004i) q^{89} +(7.48892 - 13.7398i) q^{91} +(-0.183864 + 0.133585i) q^{92} +(0.109424 - 0.189527i) q^{93} +(-19.5458 - 8.70236i) q^{94} +(-0.726988 + 0.323676i) q^{96} +(-14.2589 - 10.3597i) q^{97} +(-9.69161 + 7.79626i) q^{98} +2.67059 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q + 38 q^{4} - 24 q^{6} + 34 q^{9}+O(q^{10}) $ 288 * q + 38 * q^4 - 24 * q^6 + 34 * q^9	$ 288 q + 38 q^{4} - 24 q^{6} + 34 q^{9} + 36 q^{14} + 10 q^{16} + 22 q^{19} - 18 q^{21} - 100 q^{24} - 120 q^{26} + 48 q^{29} + 30 q^{31} + 40 q^{34} + 32 q^{36} - 26 q^{39} - 124 q^{41} + 30 q^{44} - 54 q^{46} + 76 q^{49} - 16 q^{51} + 58 q^{54} + 64 q^{56} + 78 q^{59} + 14 q^{61} - 68 q^{64} + 22 q^{66} - 148 q^{69} - 92 q^{71} - 12 q^{74} + 360 q^{76} - 18 q^{79} - 118 q^{81} + 102 q^{84} + 22 q^{86} + 84 q^{89} + 44 q^{91} - 10 q^{94} + 106 q^{96} + 88 q^{99}+O(q^{100}) $ 288 * q + 38 * q^4 - 24 * q^6 + 34 * q^9 + 36 * q^14 + 10 * q^16 + 22 * q^19 - 18 * q^21 - 100 * q^24 - 120 * q^26 + 48 * q^29 + 30 * q^31 + 40 * q^34 + 32 * q^36 - 26 * q^39 - 124 * q^41 + 30 * q^44 - 54 * q^46 + 76 * q^49 - 16 * q^51 + 58 * q^54 + 64 * q^56 + 78 * q^59 + 14 * q^61 - 68 * q^64 + 22 * q^66 - 148 * q^69 - 92 * q^71 - 12 * q^74 + 360 * q^76 - 18 * q^79 - 118 * q^81 + 102 * q^84 + 22 * q^86 + 84 * q^89 + 44 * q^91 - 10 * q^94 + 106 * q^96 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.18897	+	1.32048i	0.840728	+	0.933724i	0.998555	−	0.0537433i	$-0.0171153\pi$
$2$	1.18897	+	1.32048i	0.840728	+	0.933724i	−0.157826	+	0.987467i	$0.550449\pi$
$3$	−0.0142295	+	0.135384i	−0.00821539	+	0.0781642i	−0.997861	−	0.0653656i	$-0.979179\pi$
$3$	−0.0142295	+	0.135384i	−0.00821539	+	0.0781642i	0.989646	+	0.143530i	$0.0458453\pi$
$4$	−0.120974	+	1.15099i	−0.0604869	+	0.575494i
$5$		0			0
$5$		0			0
$6$	−0.195691	+	0.142178i	−0.0798906	+	0.0580439i
$7$	1.81810	+	1.92211i	0.687179	+	0.726488i
$7$	1.81810	+	1.92211i	0.687179	+	0.726488i
$8$	1.21137	−	0.880110i	0.428283	−	0.311166i
$9$	2.91632	+	0.619882i	0.972105	+	0.206627i
$10$		0			0
$11$	0.876154	−	0.186232i	0.264170	−	0.0561512i	−0.0739221	−	0.997264i	$-0.523552\pi$
$11$	0.876154	−	0.186232i	0.264170	−	0.0561512i	0.338093	+	0.941113i	$0.390218\pi$
$12$	−0.154104	−	0.0327559i	−0.0444861	−	0.00945581i
$13$	−1.82766	−	5.62497i	−0.506903	−	1.56009i	−0.797548	−	0.603256i	$-0.793870\pi$
$13$	−1.82766	−	5.62497i	−0.506903	−	1.56009i	0.290645	−	0.956831i	$-0.406130\pi$
$14$	−0.376443	+	4.68611i	−0.100609	+	1.25241i
$15$		0			0
$16$	4.86653	+	1.03441i	1.21663	+	0.258603i
$17$	−1.86670	−	0.831108i	−0.452741	−	0.201573i	0.167681	−	0.985841i	$-0.446372\pi$
$17$	−1.86670	−	0.831108i	−0.452741	−	0.201573i	−0.620422	+	0.784268i	$0.713039\pi$
$18$	2.64887	+	4.58797i	0.624344	+	1.08140i
$19$	0.385351	+	3.66637i	0.0884056	+	0.841123i	0.945425	+	0.325839i	$0.105647\pi$
$19$	0.385351	+	3.66637i	0.0884056	+	0.841123i	−0.857020	+	0.515284i	$0.827686\pi$
$20$		0			0
$21$	−0.286094	+	0.218792i	−0.0624308	+	0.0477444i
$22$	1.28764	+	0.935524i	0.274525	+	0.199454i
$23$	0.131400	+	0.145934i	0.0273987	+	0.0304293i	0.756688	−	0.653776i	$-0.226816\pi$
$23$	0.131400	+	0.145934i	0.0273987	+	0.0304293i	−0.729290	+	0.684205i	$0.760149\pi$
$24$	0.101916	+	0.176524i	0.0208035	+	0.0360328i
$25$		0			0
$26$	5.25465	−	9.10133i	1.03052	−	1.78492i
$27$	−0.251619	+	0.774405i	−0.0484242	+	0.149034i
$28$	−2.43227	+	1.86009i	−0.459655	+	0.351524i
$29$	1.19212	+	0.866123i	0.221370	+	0.160835i	0.692943	−	0.720992i	$-0.256314\pi$
$29$	1.19212	+	0.866123i	0.221370	+	0.160835i	−0.471573	+	0.881827i	$0.656314\pi$
$30$		0			0
$31$	−1.46865	−	0.653883i	−0.263777	−	0.117441i	0.270587	−	0.962695i	$-0.412782\pi$
$31$	−1.46865	−	0.653883i	−0.263777	−	0.117441i	−0.534364	+	0.845255i	$0.679449\pi$
$32$	2.92289	+	5.06260i	0.516700	+	0.894950i
$33$	0.0127457	+	0.121268i	0.00221875	+	0.0211100i
$34$	−1.12198	−	3.45311i	−0.192419	−	0.592204i
$35$		0			0
$36$	−1.06627	+	3.28166i	−0.177712	+	0.546943i
$37$	8.53955	+	1.81514i	1.40389	+	0.298407i	0.846742	−	0.532004i	$-0.178561\pi$
$37$	8.53955	+	1.81514i	1.40389	+	0.298407i	0.557151	+	0.830411i	$0.311894\pi$
$38$	−4.38322	+	4.86805i	−0.711051	+	0.789703i
$39$	0.787540	−	0.167397i	0.126107	−	0.0268049i
$40$		0			0
$41$	1.96439	+	6.04579i	0.306787	+	0.944193i	0.979004	+	0.203839i	$0.0653420\pi$
$41$	1.96439	+	6.04579i	0.306787	+	0.944193i	−0.672217	+	0.740354i	$0.734658\pi$
$42$	−0.629069	−	0.117645i	−0.0970674	−	0.0181531i
$43$	−11.5179			−1.75647			−0.878233	−	0.478232i	$-0.841278\pi$
$43$	−11.5179			−1.75647			−0.878233	+	0.478232i	$0.841278\pi$
$44$	0.108360	+	1.03097i	0.0163358	+	0.155425i
$45$		0			0
$46$	−0.0364735	+	0.347022i	−0.00537772	+	0.0511656i
$47$	−11.0000	+	4.89753i	−1.60452	+	0.714379i	−0.996812	−	0.0797819i	$-0.974578\pi$
$47$	−11.0000	+	4.89753i	−1.60452	+	0.714379i	−0.607708	+	0.794160i	$0.707911\pi$
$48$	−0.209291	+	0.644132i	−0.0302086	+	0.0929725i
$49$	−0.388997	+	6.98918i	−0.0555710	+	0.998455i
$50$		0			0
$51$	0.139081	−	0.240896i	0.0194753	−	0.0337321i
$52$	6.69538	−	1.42315i	0.928482	−	0.197355i
$53$	−0.219388	+	2.08734i	−0.0301353	+	0.286718i	0.969067	+	0.246796i	$0.0793777\pi$
$53$	−0.219388	+	2.08734i	−0.0301353	+	0.286718i	−0.999203	+	0.0399223i	$0.987289\pi$
$54$	−1.32176	+	0.588484i	−0.179868	+	0.0800826i
$55$		0			0
$56$	3.89406	+	0.728248i	0.520366	+	0.0973162i
$57$	−0.501852			−0.0664720
$58$	0.273688	+	2.60397i	0.0359370	+	0.341917i
$59$	5.44105	−	6.04289i	0.708364	−	0.786718i	−0.276320	−	0.961066i	$-0.589115\pi$
$59$	5.44105	−	6.04289i	0.708364	−	0.786718i	0.984684	+	0.174348i	$0.0557817\pi$
$60$		0			0
$61$	1.69386	+	1.88122i	0.216876	+	0.240865i	0.841759	−	0.539853i	$-0.181520\pi$
$61$	1.69386	+	1.88122i	0.216876	+	0.240865i	−0.624883	+	0.780718i	$0.714853\pi$
$62$	−0.882733	−	2.71677i	−0.112107	−	0.345030i
$63$	4.11069	+	6.73248i	0.517898	+	0.848213i
$64$	−0.134982	+	0.415431i	−0.0168727	+	0.0519289i
$65$		0			0
$66$	−0.144978	+	0.161014i	−0.0178455	+	0.0198194i
$67$	−9.29355	−	4.13775i	−1.13539	−	0.505507i	−0.249024	−	0.968497i	$-0.580110\pi$
$67$	−9.29355	−	4.13775i	−1.13539	−	0.505507i	−0.886363	+	0.462990i	$0.846777\pi$
$68$	1.18242	−	2.04801i	0.143389	−	0.248357i
$69$	−0.0216269	+	0.0157129i	−0.00260358	+	0.00189161i
$70$		0			0
$71$	−9.11276	−	6.62080i	−1.08149	−	0.785745i	−0.103544	−	0.994625i	$-0.533018\pi$
$71$	−9.11276	−	6.62080i	−1.08149	−	0.785745i	−0.977941	+	0.208880i	$0.933018\pi$
$72$	4.07830	−	1.81577i	0.480632	−	0.213991i
$73$	9.78179	−	2.07918i	1.14487	−	0.243350i	0.403846	−	0.914827i	$-0.367673\pi$
$73$	9.78179	−	2.07918i	1.14487	−	0.243350i	0.741026	+	0.671477i	$0.234340\pi$
$74$	7.75640	+	13.4345i	0.901663	+	1.56173i
$75$		0			0
$76$	−4.26657			−0.489409
$77$	1.95090	+	1.34547i	0.222325	+	0.153331i
$78$	1.15741	+	0.840905i	0.131050	+	0.0952137i
$79$	3.29105	−	1.46527i	0.370272	−	0.164856i	−0.213161	−	0.977017i	$-0.568376\pi$
$79$	3.29105	−	1.46527i	0.370272	−	0.164856i	0.583433	+	0.812161i	$0.301709\pi$
$80$		0			0
$81$	8.06986	+	3.59293i	0.896651	+	0.399215i
$82$	−5.64776	+	9.78221i	−0.623691	+	1.08026i
$83$	2.17252	−	1.57843i	0.238465	−	0.173255i	−0.462134	−	0.886810i	$-0.652916\pi$
$83$	2.17252	−	1.57843i	0.238465	−	0.173255i	0.700599	+	0.713555i	$0.252916\pi$
$84$	−0.217217	−	0.355759i	−0.0237004	−	0.0388165i
$85$		0			0
$86$	−13.6945	−	15.2092i	−1.47671	−	1.64005i
$87$	−0.134223	+	0.149069i	−0.0143902	+	0.0159819i
$88$	0.897440	−	0.996708i	0.0956674	−	0.106249i
$89$	−4.43903	−	4.93004i	−0.470536	−	0.522584i	0.460426	−	0.887698i	$-0.347697\pi$
$89$	−4.43903	−	4.93004i	−0.470536	−	0.522584i	−0.930963	+	0.365114i	$0.881030\pi$
$90$		0			0
$91$	7.48892	−	13.7398i	0.785052	−	1.44032i
$92$	−0.183864	+	0.133585i	−0.0191692	+	0.0139272i
$93$	0.109424	−	0.189527i	0.0113467	−	0.0196531i
$94$	−19.5458	−	8.70236i	−2.01600	−	0.897580i
$95$		0			0
$96$	−0.726988	+	0.323676i	−0.0741979	+	0.0330350i
$97$	−14.2589	−	10.3597i	−1.44777	−	1.05187i	−0.986346	−	0.164688i	$-0.947338\pi$
$97$	−14.2589	−	10.3597i	−1.44777	−	1.05187i	−0.461425	−	0.887179i	$-0.652662\pi$
$98$	−9.69161	+	7.79626i	−0.979001	+	0.787541i
$99$	2.67059			0.268404
$100$		0			0
$101$	−4.58094	−	7.93442i	−0.455820	−	0.789504i	0.542915	−	0.839788i	$-0.317321\pi$
$101$	−4.58094	−	7.93442i	−0.455820	−	0.789504i	−0.998735	+	0.0502839i	$0.983987\pi$
$102$	0.483462	−	0.102763i	0.0478699	−	0.0101751i
$103$	−2.58534	+	1.15107i	−0.254741	+	0.113418i	−0.530135	−	0.847914i	$-0.677859\pi$
$103$	−2.58534	+	1.15107i	−0.254741	+	0.113418i	0.275393	+	0.961332i	$0.411192\pi$
$104$	−7.16457	−	5.20537i	−0.702544	−	0.510428i
$105$		0			0
$106$	−3.01715	+	2.19209i	−0.293051	+	0.212914i
$107$	−5.57806	+	9.66149i	−0.539252	+	0.934011i	0.459693	+	0.888078i	$0.347960\pi$
$107$	−5.57806	+	9.66149i	−0.539252	+	0.934011i	−0.998945	+	0.0459333i	$0.985374\pi$
$108$	−0.860892	−	0.383294i	−0.0828393	−	0.0368824i
$109$	4.07926	−	4.53048i	0.390722	−	0.433941i	−0.515405	−	0.856947i	$-0.672358\pi$
$109$	4.07926	−	4.53048i	0.390722	−	0.433941i	0.906127	+	0.423006i	$0.139025\pi$
$110$		0			0
$111$	−0.367254	+	1.13029i	−0.0348582	+	0.107283i
$112$	6.85960	+	11.2347i	0.648171	+	1.06158i
$113$	−1.68628	−	5.18982i	−0.158631	−	0.488217i	0.839879	−	0.542773i	$-0.182626\pi$
$113$	−1.68628	−	5.18982i	−0.158631	−	0.488217i	−0.998511	+	0.0545558i	$0.982626\pi$
$114$	−0.596687	−	0.662688i	−0.0558849	−	0.0620665i
$115$		0			0
$116$	−1.14111	+	1.26733i	−0.105950	+	0.117669i
$117$	−1.84323	−	17.5371i	−0.170406	−	1.62131i
$118$	14.4488			1.33012
$119$	−1.79637	−	5.09904i	−0.164673	−	0.467428i
$120$		0			0
$121$	−9.31604	+	4.14777i	−0.846912	+	0.377070i
$122$	−0.470176	+	4.47342i	−0.0425677	+	0.405005i
$123$	−0.846457	+	0.179920i	−0.0763224	+	0.0162228i
$124$	0.930280	−	1.61129i	0.0835416	−	0.144698i
$125$		0			0
$126$	−4.00266	+	13.4328i	−0.356585	+	1.19669i
$127$	3.84194	−	11.8243i	0.340917	−	1.04923i	−0.622817	−	0.782368i	$-0.714012\pi$
$127$	3.84194	−	11.8243i	0.340917	−	1.04923i	0.963734	−	0.266866i	$-0.0859881\pi$
$128$	9.97173	−	4.43970i	0.881384	−	0.392418i
$129$	0.163894	−	1.55935i	0.0144301	−	0.137293i
$130$		0			0
$131$	0.335067	+	3.18795i	0.0292749	+	0.278532i	0.999360	+	0.0357675i	$0.0113876\pi$
$131$	0.335067	+	3.18795i	0.0292749	+	0.278532i	−0.970085	+	0.242765i	$0.921946\pi$
$132$	−0.141119			−0.0122829
$133$	−6.34655	+	7.40653i	−0.550316	+	0.642228i
$134$	−5.58591	−	17.1916i	−0.482549	−	1.48513i
$135$		0			0
$136$	−2.99273	+	0.636124i	−0.256624	+	0.0545472i
$137$	1.12467	−	1.24907i	0.0960871	−	0.106716i	−0.693183	−	0.720761i	$-0.743792\pi$
$137$	1.12467	−	1.24907i	0.0960871	−	0.106716i	0.789270	+	0.614046i	$0.210459\pi$
$138$	−0.0464624	−	0.00987588i	−0.00395514	−	0.000840691i
$139$	−0.0192250	+	0.0591686i	−0.00163065	+	0.00501861i	−0.951869	−	0.306507i	$-0.900840\pi$
$139$	−0.0192250	+	0.0591686i	−0.00163065	+	0.00501861i	0.950238	+	0.311525i	$0.100840\pi$
$140$		0			0
$141$	−0.506524	−	1.55892i	−0.0426571	−	0.131285i
$142$	−2.09212	−	19.9052i	−0.175567	−	1.67041i
$143$	−2.64887	−	4.58797i	−0.221510	−	0.383666i
$144$	13.5511	+	6.03335i	1.12926	+	0.502779i
$145$		0			0
$146$	14.3758	+	10.4446i	1.18975	+	0.864403i
$147$	−0.940691	−	0.152116i	−0.0775868	−	0.0125464i
$148$	−3.12226	+	9.60933i	−0.256648	+	0.789882i
$149$	10.9267	−	18.9256i	0.895149	−	1.55044i	0.0615297	−	0.998105i	$-0.480402\pi$
$149$	10.9267	−	18.9256i	0.895149	−	1.55044i	0.833620	−	0.552339i	$-0.186265\pi$
$150$		0			0
$151$	2.73477	+	4.73676i	0.222552	+	0.385472i	0.955582	−	0.294724i	$-0.0952278\pi$
$151$	2.73477	+	4.73676i	0.222552	+	0.385472i	−0.733030	+	0.680196i	$0.761894\pi$
$152$	3.69361	+	4.10217i	0.299592	+	0.332730i
$153$	−4.92870	−	3.58091i	−0.398462	−	0.289499i
$154$	0.542882	+	4.17586i	0.0437467	+	0.336500i
$155$		0			0
$156$	0.0974001	+	0.926700i	0.00779825	+	0.0741954i
$157$	−3.89986	−	6.75475i	−0.311243	−	0.539088i	0.667389	−	0.744709i	$-0.267412\pi$
$157$	−3.89986	−	6.75475i	−0.311243	−	0.539088i	−0.978632	+	0.205621i	$0.934078\pi$
$158$	5.84783	+	2.60362i	0.465228	+	0.207133i
$159$	−0.279471	−	0.0594035i	−0.0221635	−	0.00471100i
$160$		0			0
$161$	−0.0416028	+	0.517887i	−0.00327876	+	0.0408152i
$162$	4.85041	+	14.9280i	0.381084	+	1.17286i
$163$	17.3497	+	3.68779i	1.35893	+	0.288850i	0.829028	−	0.559206i	$-0.188894\pi$
$163$	17.3497	+	3.68779i	1.35893	+	0.288850i	0.529905	+	0.848057i	$0.322227\pi$
$164$	−7.19627	+	1.52961i	−0.561934	+	0.119443i
$165$		0			0
$166$	4.66735	+	0.992076i	0.362257	+	0.0770000i
$167$	−7.96812	+	5.78918i	−0.616591	+	0.447980i	−0.851729	−	0.523982i	$-0.824446\pi$
$167$	−7.96812	+	5.78918i	−0.616591	+	0.447980i	0.235138	+	0.971962i	$0.424446\pi$
$168$	−0.154004	+	0.516832i	−0.0118816	+	0.0398745i
$169$	−17.7828	+	12.9199i	−1.36790	+	0.993841i
$170$		0			0
$171$	−1.14891	+	10.9312i	−0.0878595	+	0.835927i
$172$	1.39337	−	13.2570i	0.106243	−	1.01084i
$173$	−13.3027	−	14.7742i	−1.01139	−	1.12326i	−0.992352	−	0.123440i	$-0.960607\pi$
$173$	−13.3027	−	14.7742i	−1.01139	−	1.12326i	−0.0190351	−	0.999819i	$-0.506059\pi$
$174$	−0.356431			−0.0270209
$175$		0			0
$176$	4.45647			0.335919
$177$	0.740690	+	0.822620i	0.0556737	+	0.0618319i
$178$	1.23217	−	11.7233i	0.0923553	−	0.878702i
$179$	−1.87236	+	17.8143i	−0.139947	+	1.33150i	0.668842	+	0.743405i	$0.266790\pi$
$179$	−1.87236	+	17.8143i	−0.139947	+	1.33150i	−0.808789	+	0.588099i	$0.799876\pi$
$180$		0			0
$181$	−6.41485	+	4.66066i	−0.476812	+	0.346424i	−0.800090	−	0.599880i	$-0.795215\pi$
$181$	−6.41485	+	4.66066i	−0.476812	+	0.346424i	0.323278	+	0.946304i	$0.395215\pi$
$182$	27.0472	−	6.44715i	2.00487	−	0.477894i
$183$	−0.278790	+	0.202553i	−0.0206088	+	0.0149731i
$184$	0.287611	+	0.0611337i	0.0212030	+	0.00450683i
$185$		0			0
$186$	0.380369	−	0.0808500i	0.0278900	−	0.00592821i
$187$	−1.79030	−	0.380539i	−0.130919	−	0.0278278i
$188$	−4.30629	−	13.2534i	−0.314068	−	0.966602i
$189$	−1.94596	+	0.924309i	−0.141548	+	0.0672336i
$190$		0			0
$191$	−5.30465	−	1.12754i	−0.383831	−	0.0815858i	0.0119551	−	0.999929i	$-0.496194\pi$
$191$	−5.30465	−	1.12754i	−0.383831	−	0.0815858i	−0.395786	+	0.918343i	$0.629528\pi$
$192$	−0.0543221	−	0.0241858i	−0.00392036	−	0.00174546i
$193$	−3.76790	−	6.52619i	−0.271219	−	0.469765i	0.697955	−	0.716142i	$-0.254093\pi$
$193$	−3.76790	−	6.52619i	−0.271219	−	0.469765i	−0.969174	+	0.246376i	$0.920760\pi$
$194$	−3.27358	−	31.1460i	−0.235029	−	2.23615i
$195$		0			0
$196$	−7.99741	−	1.29324i	−0.571243	−	0.0923742i
$197$	9.65536	+	7.01503i	0.687916	+	0.499800i	0.875974	−	0.482358i	$-0.160219\pi$
$197$	9.65536	+	7.01503i	0.687916	+	0.499800i	−0.188059	+	0.982158i	$0.560219\pi$
$198$	3.17524	+	3.52647i	0.225655	+	0.250615i
$199$	10.1092	+	17.5097i	0.716623	+	1.24123i	0.962330	+	0.271883i	$0.0876463\pi$
$199$	10.1092	+	17.5097i	0.716623	+	1.24123i	−0.245708	+	0.969344i	$0.579020\pi$
$200$		0			0
$201$	0.692429	−	1.19932i	0.0488402	−	0.0845937i
$202$	5.03068	−	15.4828i	0.353957	−	1.08937i
$203$	0.502609	+	3.86608i	0.0352762	+	0.271346i
$204$	0.260443	+	0.189223i	0.0182346	+	0.0132482i
$205$		0			0
$206$	−4.59386	−	2.04532i	−0.320069	−	0.142504i
$207$	0.292741	+	0.507042i	0.0203469	+	0.0352419i
$208$	−3.07584	−	29.2646i	−0.213271	−	2.02914i
$209$	1.02042	+	3.14054i	0.0705842	+	0.217236i
$210$		0			0
$211$	−0.0373383	+	0.114915i	−0.00257047	+	0.00791110i	−0.952334	−	0.305059i	$-0.901324\pi$
$211$	−0.0373383	+	0.114915i	−0.00257047	+	0.00791110i	0.949763	+	0.312970i	$0.101324\pi$
$212$	−2.37596	−	0.505027i	−0.163182	−	0.0346854i
$213$	1.02602	−	1.13951i	0.0703019	−	0.0780782i
$214$	−19.3900	+	4.12147i	−1.32547	+	0.281738i
$215$		0			0
$216$	0.376758	+	1.15954i	0.0256351	+	0.0788969i
$217$	−1.41332	−	4.01172i	−0.0959422	−	0.272334i
$218$	10.8325			0.733672
$219$	0.142299	+	1.35389i	0.00961569	+	0.0914872i
$220$		0			0
$221$	−1.26326	+	12.0191i	−0.0849761	+	0.808494i
$222$	−1.92919	+	0.858930i	−0.129479	+	0.0576476i
$223$	5.92362	−	18.2310i	0.396675	−	1.22084i	−0.530975	−	0.847388i	$-0.678174\pi$
$223$	5.92362	−	18.2310i	0.396675	−	1.22084i	0.927650	−	0.373452i	$-0.121826\pi$
$224$	−4.41674	+	14.8225i	−0.295106	+	0.990367i
$225$		0			0
$226$	4.84815	−	8.39724i	0.322494	−	0.558576i
$227$	−11.6976	+	2.48639i	−0.776394	+	0.165028i	−0.579034	−	0.815303i	$-0.696570\pi$
$227$	−11.6976	+	2.48639i	−0.776394	+	0.165028i	−0.197360	+	0.980331i	$0.563237\pi$
$228$	0.0607110	−	0.577626i	0.00402068	−	0.0382542i
$229$	12.4325	−	5.53533i	0.821566	−	0.365785i	0.0474854	−	0.998872i	$-0.484879\pi$
$229$	12.4325	−	5.53533i	0.821566	−	0.365785i	0.774080	+	0.633087i	$0.218213\pi$
$230$		0			0
$231$	−0.209916	+	0.244976i	−0.0138115	+	0.0161182i
$232$	2.20638			0.144856
$233$	0.378605	+	3.60218i	0.0248032	+	0.235987i	0.999899	+	0.0142032i	$0.00452118\pi$
$233$	0.378605	+	3.60218i	0.0248032	+	0.235987i	−0.975096	+	0.221784i	$0.928812\pi$
$234$	20.9660	−	23.2851i	1.37059	−	1.52219i
$235$		0			0
$236$	6.29708	+	6.99361i	0.409905	+	0.455245i
$237$	0.151545	+	0.466407i	0.00984389	+	0.0302964i
$238$	4.59737	−	8.43469i	0.298003	−	0.546740i
$239$	−5.63387	+	17.3393i	−0.364425	+	1.12158i	0.585916	+	0.810372i	$0.300735\pi$
$239$	−5.63387	+	17.3393i	−0.364425	+	1.12158i	−0.950341	+	0.311212i	$0.899265\pi$
$240$		0			0
$241$	−9.80898	+	10.8940i	−0.631852	+	0.701743i	−0.971024	−	0.238981i	$-0.923186\pi$
$241$	−9.80898	+	10.8940i	−0.631852	+	0.701743i	0.339172	+	0.940724i	$0.389853\pi$
$242$	−16.5535	−	7.37011i	−1.06410	−	0.473769i
$243$	−1.82264	+	3.15691i	−0.116923	+	0.202516i
$244$	−2.37017	+	1.72203i	−0.151735	+	0.110242i
$245$		0			0
$246$	−1.24399	−	0.903814i	−0.0793141	−	0.0576251i
$247$	19.9189	−	8.86849i	1.26741	−	0.564288i
$248$	−2.35456	+	0.500477i	−0.149515	+	0.0317803i
$249$	0.182781	+	0.316585i	0.0115833	+	0.0200628i
$250$		0			0
$251$	3.37510			0.213034			0.106517	−	0.994311i	$-0.466030\pi$
$251$	3.37510			0.213034			0.106517	+	0.994311i	$0.466030\pi$
$252$	−8.24629	+	3.91690i	−0.519468	+	0.246741i
$253$	0.142304	+	0.103390i	0.00894657	+	0.00650006i
$254$	20.1817	−	8.98547i	1.26631	−	0.563799i
$255$		0			0
$256$	18.5167	+	8.24418i	1.15730	+	0.515261i
$257$	−3.53064	+	6.11524i	−0.220235	+	0.381458i	−0.954879	−	0.296994i	$-0.904016\pi$
$257$	−3.53064	+	6.11524i	−0.220235	+	0.381458i	0.734644	+	0.678453i	$0.237349\pi$
$258$	2.25396	−	1.63760i	0.140325	−	0.101952i
$259$	12.0369	+	19.7140i	0.747936	+	1.22497i
$260$		0			0
$261$	2.93969	+	3.26486i	0.181963	+	0.202090i
$262$	−3.81125	+	4.23282i	−0.235460	+	0.261505i
$263$	−19.0297	+	21.1346i	−1.17342	+	1.30322i	−0.229402	+	0.973332i	$0.573677\pi$
$263$	−19.0297	+	21.1346i	−1.17342	+	1.30322i	−0.944021	+	0.329886i	$0.892990\pi$
$264$	0.122169	+	0.135682i	0.00751896	+	0.00835065i
$265$		0			0
$266$	−17.3261	+	0.425615i	−1.06233	+	0.0260961i
$267$	0.730616	−	0.530823i	0.0447130	−	0.0324859i
$268$	5.88678	−	10.1962i	0.359592	−	0.622832i
$269$	−14.4783	−	6.44613i	−0.882755	−	0.393028i	−0.0852637	−	0.996358i	$-0.527173\pi$
$269$	−14.4783	−	6.44613i	−0.882755	−	0.393028i	−0.797491	+	0.603331i	$0.793840\pi$
$270$		0			0
$271$	9.27705	−	4.13041i	0.563540	−	0.250904i	−0.105136	−	0.994458i	$-0.533528\pi$
$271$	9.27705	−	4.13041i	0.563540	−	0.250904i	0.668676	+	0.743553i	$0.266861\pi$
$272$	−8.22464	−	5.97555i	−0.498692	−	0.362321i
$273$	1.75358	+	1.20939i	0.106132	+	0.0731957i
$274$	2.98658			0.180426
$275$		0			0
$276$	−0.0154690	−	0.0267932i	−0.000931127	−	0.00161276i
$277$	20.7779	−	4.41649i	1.24842	−	0.265361i	0.464140	−	0.885762i	$-0.346363\pi$
$277$	20.7779	−	4.41649i	1.24842	−	0.265361i	0.784285	+	0.620401i	$0.213030\pi$
$278$	−0.100989	+	0.0449633i	−0.00605693	+	0.00269672i
$279$	−3.87771	−	2.81732i	−0.232152	−	0.168668i
$280$		0			0
$281$	−16.1276	+	11.7174i	−0.962094	+	0.699003i	−0.953636	−	0.300962i	$-0.902692\pi$
$281$	−16.1276	+	11.7174i	−0.962094	+	0.699003i	−0.00845822	+	0.999964i	$0.502692\pi$
$282$	1.45629	−	2.52237i	0.0867208	−	0.150205i
$283$	−12.6819	−	5.64634i	−0.753860	−	0.335640i	−0.00642906	−	0.999979i	$-0.502046\pi$
$283$	−12.6819	−	5.64634i	−0.753860	−	0.335640i	−0.747431	+	0.664339i	$0.768713\pi$
$284$	8.72287	−	9.68773i	0.517607	−	0.574861i
$285$		0			0
$286$	2.90893	−	8.95275i	0.172008	−	0.529387i
$287$	−8.04918	+	14.7676i	−0.475128	+	0.871706i
$288$	5.38587	+	16.5760i	0.317365	+	0.976750i
$289$	−8.58139	−	9.53060i	−0.504788	−	0.560624i
$290$		0			0
$291$	1.60544	−	1.78302i	0.0941123	−	0.104522i
$292$	1.20978	+	11.5103i	0.0707968	+	0.673587i
$293$	−8.17516			−0.477598			−0.238799	−	0.971069i	$-0.576754\pi$
$293$	−8.17516			−0.477598			−0.238799	+	0.971069i	$0.576754\pi$
$294$	−0.917585	−	1.42303i	−0.0535146	−	0.0829927i
$295$		0			0
$296$	11.9421	−	5.31694i	0.694118	−	0.309041i
$297$	−0.0762382	+	0.725358i	−0.00442379	+	0.0420895i
$298$	37.9824	−	8.07342i	2.20026	−	0.467680i
$299$	0.580721	−	1.00584i	0.0335839	−	0.0581691i
$300$		0			0
$301$	−20.9408	−	22.1387i	−1.20701	−	1.27605i
$302$	−3.00326	+	9.24309i	−0.172818	+	0.531880i
$303$	1.13938	−	0.507285i	0.0654557	−	0.0291427i
$304$	−1.91722	+	18.2411i	−0.109960	+	1.04620i
$305$		0			0
$306$	−1.13154	−	10.7659i	−0.0646857	−	0.615443i
$307$	21.6183			1.23382			0.616911	−	0.787033i	$-0.288384\pi$
$307$	21.6183			1.23382			0.616911	+	0.787033i	$0.288384\pi$
$308$	−1.78463	+	2.08269i	−0.101689	+	0.118672i
$309$	−0.119049	−	0.366394i	−0.00677244	−	0.0208434i
$310$		0			0
$311$	6.07359	−	1.29098i	0.344402	−	0.0732049i	−0.0324635	−	0.999473i	$-0.510335\pi$
$311$	6.07359	−	1.29098i	0.344402	−	0.0732049i	0.376865	+	0.926268i	$0.377002\pi$
$312$	0.806673	−	0.895901i	0.0456689	−	0.0507204i
$313$	9.51653	+	2.02280i	0.537906	+	0.114335i	0.468851	−	0.883277i	$-0.344668\pi$
$313$	9.51653	+	2.02280i	0.537906	+	0.114335i	0.0690553	+	0.997613i	$0.478002\pi$
$314$	4.28273	−	13.1809i	0.241689	−	0.743841i
$315$		0			0
$316$	1.28838	+	3.96522i	0.0724770	+	0.223061i
$317$	2.17289	+	20.6737i	0.122042	+	1.16115i	0.868490	+	0.495707i	$0.165091\pi$
$317$	2.17289	+	20.6737i	0.122042	+	1.16115i	−0.746448	+	0.665444i	$0.768242\pi$
$318$	−0.253842	−	0.439666i	−0.0142347	−	0.0246553i
$319$	1.20578	+	0.536847i	0.0675106	+	0.0300577i
$320$		0			0
$321$	−1.22864	−	0.892660i	−0.0685761	−	0.0498234i
$322$	−0.733327	+	0.560816i	−0.0408667	+	0.0312531i
$323$	2.32782	−	7.16428i	0.129523	−	0.398631i
$324$	−5.11166	+	8.85366i	−0.283981	+	0.491870i
$325$		0			0
$326$	15.7586	+	27.2947i	0.872788	+	1.51171i
$327$	0.555310	+	0.616734i	0.0307087	+	0.0341055i
$328$	7.70056	+	5.59479i	0.425192	+	0.308920i
$329$	−29.4128	−	12.2390i	−1.62158	−	0.674760i
$330$		0			0
$331$	−0.772681	−	7.35156i	−0.0424704	−	0.404079i	−0.995018	−	0.0996905i	$-0.968215\pi$
$331$	−0.772681	−	7.35156i	−0.0424704	−	0.404079i	0.952548	−	0.304388i	$-0.0984519\pi$
$332$	1.55393	+	2.69149i	0.0852832	+	0.147715i
$333$	23.7788	+	10.5870i	1.30307	+	0.580165i
$334$	−17.1184	−	3.63862i	−0.936675	−	0.199097i
$335$		0			0
$336$	−1.61860	+	0.768819i	−0.0883021	+	0.0419425i
$337$	−8.86877	−	27.2953i	−0.483113	−	1.48687i	−0.834696	−	0.550711i	$-0.814357\pi$
$337$	−8.86877	−	27.2953i	−0.483113	−	1.48687i	0.351583	−	0.936157i	$-0.385643\pi$
$338$	−38.2037	−	8.12045i	−2.07801	−	0.441694i
$339$	0.726615	−	0.154447i	0.0394643	−	0.00838840i
$340$		0			0
$341$	−1.40853	−	0.299393i	−0.0762764	−	0.0162131i
$342$	−15.8005	+	11.4797i	−0.854391	+	0.620752i
$343$	−14.1412	+	11.9594i	−0.763553	+	0.645745i
$344$	−13.9524	+	10.1370i	−0.752265	+	0.546553i
$345$		0			0
$346$	3.69253	−	35.1321i	0.198512	−	1.88871i
$347$	1.66988	−	15.8878i	0.0896438	−	0.852904i	−0.853628	−	0.520883i	$-0.825603\pi$
$347$	1.66988	−	15.8878i	0.0896438	−	0.852904i	0.943272	−	0.332021i	$-0.107731\pi$
$348$	−0.155340	−	0.172522i	−0.00832708	−	0.00924816i
$349$	30.2549			1.61951			0.809754	−	0.586770i	$-0.199601\pi$
$349$	30.2549			1.61951			0.809754	+	0.586770i	$0.199601\pi$
$350$		0			0
$351$	4.81588			0.257053
$352$	3.50373	+	3.89128i	0.186749	+	0.207406i
$353$	−0.951741	+	9.05521i	−0.0506561	+	0.481960i	0.939557	+	0.342394i	$0.111238\pi$
$353$	−0.951741	+	9.05521i	−0.0506561	+	0.481960i	−0.990213	+	0.139567i	$0.955429\pi$
$354$	−0.205599	+	1.95614i	−0.0109274	+	0.103968i
$355$		0			0
$356$	6.21143	−	4.51287i	0.329205	−	0.239181i
$357$	0.715892	−	0.170644i	0.0378890	−	0.00903146i
$358$	−25.7497	+	18.7083i	−1.36091	+	0.988762i
$359$	−23.0329	−	4.89579i	−1.21563	−	0.258390i	−0.444916	−	0.895572i	$-0.646767\pi$
$359$	−23.0329	−	4.89579i	−1.21563	−	0.258390i	−0.770713	+	0.637182i	$0.780100\pi$
$360$		0			0
$361$	5.29102	−	1.12464i	0.278475	−	0.0591917i
$362$	−13.7814	−	2.92933i	−0.724334	−	0.153962i
$363$	−0.428980	−	1.32027i	−0.0225156	−	0.0692960i
$364$	14.9083	+	10.2818i	0.781409	+	0.538913i
$365$		0			0
$366$	−0.598941	−	0.127309i	−0.0313072	−	0.00665454i
$367$	32.8548	+	14.6279i	1.71500	+	0.763569i	0.997771	+	0.0667361i	$0.0212585\pi$
$367$	32.8548	+	14.6279i	1.71500	+	0.763569i	0.717233	+	0.696833i	$0.245408\pi$
$368$	0.488504	+	0.846113i	0.0254650	+	0.0441067i
$369$	1.98112	+	18.8491i	0.103133	+	0.981246i
$370$		0			0
$371$	−4.41096	+	3.37331i	−0.229006	+	0.175134i
$372$	0.204906	+	0.148873i	0.0106239	+	0.00771871i
$373$	4.76070	+	5.28729i	0.246500	+	0.273765i	0.853679	−	0.520799i	$-0.174366\pi$
$373$	4.76070	+	5.28729i	0.246500	+	0.273765i	−0.607180	+	0.794564i	$0.707699\pi$
$374$	−1.62611	−	2.81651i	−0.0840842	−	0.145638i
$375$		0			0
$376$	−9.01472	+	15.6140i	−0.464899	+	0.805229i
$377$	2.69313	−	8.28861i	0.138703	−	0.426885i
$378$	−3.53422	−	1.47063i	−0.181781	−	0.0756413i
$379$	−7.76350	−	5.64052i	−0.398784	−	0.289734i	0.370261	−	0.928928i	$-0.379268\pi$
$379$	−7.76350	−	5.64052i	−0.398784	−	0.289734i	−0.769046	+	0.639194i	$0.779268\pi$
$380$		0			0
$381$	1.54615	+	0.688391i	0.0792117	+	0.0352673i
$382$	−4.81817	−	8.34532i	−0.246519	−	0.426983i
$383$	0.470515	+	4.47665i	0.0240422	+	0.228746i	0.999944	+	0.0105382i	$0.00335448\pi$
$383$	0.470515	+	4.47665i	0.0240422	+	0.228746i	−0.975902	+	0.218208i	$0.929979\pi$
$384$	0.459173	+	1.41319i	0.0234321	+	0.0721165i
$385$		0			0
$386$	4.13782	−	12.7349i	0.210609	−	0.648189i
$387$	−33.5899	−	7.13976i	−1.70747	−	0.362934i
$388$	13.6488	−	15.1586i	0.692914	−	0.769559i
$389$	20.6389	−	4.38693i	1.04643	−	0.222426i	0.347549	−	0.937662i	$-0.387014\pi$
$389$	20.6389	−	4.38693i	1.04643	−	0.222426i	0.698884	+	0.715235i	$0.253681\pi$
$390$		0			0
$391$	−0.123997	−	0.381622i	−0.00627078	−	0.0192995i
$392$	5.68003	+	8.80883i	0.286885	+	0.444913i
$393$	−0.436366			−0.0220117
$394$	2.21669	+	21.0904i	0.111675	+	1.06252i
$395$		0			0
$396$	−0.323071	+	3.07381i	−0.0162349	+	0.154465i
$397$	−4.29081	+	1.91039i	−0.215350	+	0.0958799i	−0.511576	−	0.859238i	$-0.670938\pi$
$397$	−4.29081	+	1.91039i	−0.215350	+	0.0958799i	0.296227	+	0.955118i	$0.404272\pi$
$398$	−11.1017	+	34.1675i	−0.556478	+	1.71266i
$399$	−0.912420	−	0.964615i	−0.0456781	−	0.0482911i
$400$		0			0
$401$	−0.532582	+	0.922460i	−0.0265959	+	0.0460654i	−0.879017	−	0.476790i	$-0.841800\pi$
$401$	−0.532582	+	0.922460i	−0.0265959	+	0.0460654i	0.852421	+	0.522856i	$0.175133\pi$
$402$	2.40696	−	0.511616i	0.120048	−	0.0255171i
$403$	−0.993884	+	9.45618i	−0.0495089	+	0.471046i
$404$	9.68659	−	4.31275i	0.481926	−	0.214567i
$405$		0			0
$406$	−4.50751	+	5.26034i	−0.223704	+	0.261066i
$407$	7.82000			0.387623
$408$	−0.0435363	−	0.414220i	−0.00215537	−	0.0205069i
$409$	11.4795	−	12.7492i	0.567623	−	0.630410i	−0.389174	−	0.921164i	$-0.627240\pi$
$409$	11.4795	−	12.7492i	0.567623	−	0.630410i	0.956798	+	0.290755i	$0.0939063\pi$
$410$		0			0
$411$	0.153102	+	0.170036i	0.00755194	+	0.00838728i
$412$	−1.01211	−	3.11495i	−0.0498630	−	0.153462i
$413$	21.5075	−	0.528331i	1.05831	−	0.0259975i
$414$	−0.321481	+	0.989417i	−0.0157999	+	0.0486272i
$415$		0			0
$416$	23.1349	−	25.6939i	1.13428	−	1.25975i
$417$	−0.00773694	−	0.00344471i	−0.000378879	−	0.000168688i
$418$	−2.93378	+	5.08146i	−0.143496	+	0.248542i
$419$	20.0431	−	14.5622i	0.979170	−	0.711409i	0.0216469	−	0.999766i	$-0.493109\pi$
$419$	20.0431	−	14.5622i	0.979170	−	0.711409i	0.957523	+	0.288357i	$0.0931090\pi$
$420$		0			0
$421$	−8.45029	−	6.13949i	−0.411842	−	0.299221i	0.362505	−	0.931982i	$-0.381921\pi$
$421$	−8.45029	−	6.13949i	−0.411842	−	0.299221i	−0.774347	+	0.632761i	$0.781921\pi$
$422$	−0.196138	+	0.0873263i	−0.00954785	+	0.00425098i
$423$	−35.1155	+	7.46403i	−1.70737	+	0.362913i
$424$	1.57133	+	2.72162i	0.0763105	+	0.132174i
$425$		0			0
$426$	2.72462			0.132008
$427$	−0.536298	+	6.67603i	−0.0259533	+	0.323076i
$428$	−10.4455	−	7.58907i	−0.504900	−	0.366832i
$429$	0.658832	−	0.293331i	0.0318087	−	0.0141621i
$430$		0			0
$431$	−28.9662	−	12.8966i	−1.39525	−	0.621206i	−0.435022	−	0.900420i	$-0.643259\pi$
$431$	−28.9662	−	12.8966i	−1.39525	−	0.621206i	−0.960229	+	0.279214i	$0.909926\pi$
$432$	−2.02557	+	3.50838i	−0.0974551	+	0.168797i
$433$	−15.3387	+	11.1442i	−0.737130	+	0.535556i	−0.891811	−	0.452408i	$-0.850565\pi$
$433$	−15.3387	+	11.1442i	−0.737130	+	0.535556i	0.154681	+	0.987964i	$0.450565\pi$
$434$	3.61703	−	6.63608i	0.173623	−	0.318542i
$435$		0			0
$436$	4.72104	+	5.24325i	0.226097	+	0.251106i
$437$	−0.484413	+	0.537995i	−0.0231726	+	0.0257358i
$438$	−1.61860	+	1.79763i	−0.0773396	+	0.0858943i
$439$	−3.34415	−	3.71405i	−0.159608	−	0.177262i	0.658037	−	0.752986i	$-0.271387\pi$
$439$	−3.34415	−	3.71405i	−0.159608	−	0.177262i	−0.817644	+	0.575724i	$0.804720\pi$
$440$		0			0
$441$	−5.46691	+	20.1415i	−0.260329	+	0.959121i
$442$	−17.3731	+	12.6223i	−0.826352	+	0.600380i
$443$	1.62942	−	2.82224i	0.0774162	−	0.134089i	−0.824718	−	0.565544i	$-0.808666\pi$
$443$	1.62942	−	2.82224i	0.0774162	−	0.134089i	0.902134	+	0.431455i	$0.142000\pi$
$444$	−1.25652	−	0.559441i	−0.0596320	−	0.0265499i
$445$		0			0
$446$	31.1168	−	13.8541i	1.47342	−	0.656010i
$447$	2.40675	+	1.74860i	0.113835	+	0.0827061i
$448$	−1.04391	+	0.495847i	−0.0493203	+	0.0234266i
$449$	−18.7348			−0.884151			−0.442076	−	0.896978i	$-0.645758\pi$
$449$	−18.7348			−0.884151			−0.442076	+	0.896978i	$0.645758\pi$
$450$		0			0
$451$	2.84703	+	4.93121i	0.134062	+	0.232201i
$452$	6.17742	−	1.31305i	0.290561	−	0.0617607i
$453$	−0.680198	+	0.302843i	−0.0319585	+	0.0142288i
$454$	−17.1913	−	12.4902i	−0.806827	−	0.586194i
$455$		0			0
$456$	−0.607928	+	0.441686i	−0.0284688	+	0.0206838i
$457$	−13.5813	+	23.5235i	−0.635306	+	1.10038i	0.351144	+	0.936322i	$0.385793\pi$
$457$	−13.5813	+	23.5235i	−0.635306	+	1.10038i	−0.986450	+	0.164061i	$0.947541\pi$
$458$	22.0912	+	9.83565i	1.03226	+	0.459590i
$459$	1.11331	−	1.23646i	0.0519650	−	0.0577130i
$460$		0			0
$461$	−4.36190	+	13.4245i	−0.203154	+	0.625243i	0.796630	+	0.604467i	$0.206614\pi$
$461$	−4.36190	+	13.4245i	−0.203154	+	0.625243i	−0.999784	+	0.0207762i	$0.993386\pi$
$462$	−0.573071	+	0.0140775i	−0.0266617	+	0.000654943i
$463$	5.57173	+	17.1480i	0.258940	+	0.796936i	0.993028	+	0.117881i	$0.0376103\pi$
$463$	5.57173	+	17.1480i	0.258940	+	0.796936i	−0.734087	+	0.679055i	$0.762390\pi$
$464$	4.90554	+	5.44815i	0.227734	+	0.252924i
$465$		0			0
$466$	−4.30648	+	4.78283i	−0.199494	+	0.221560i
$467$	1.93956	+	18.4537i	0.0897522	+	0.853935i	0.943081	+	0.332562i	$0.107913\pi$
$467$	1.93956	+	18.4537i	0.0897522	+	0.853935i	−0.853329	+	0.521373i	$0.825420\pi$
$468$	20.4080			0.943361
$469$	−8.94343	−	25.3861i	−0.412969	−	1.17222i
$470$		0			0
$471$	0.969980	−	0.431863i	0.0446943	−	0.0198992i
$472$	1.27270	−	12.1089i	0.0585806	−	0.557357i
$473$	−10.0915	+	2.14501i	−0.464007	+	0.0986277i
$474$	−0.435701	+	0.754656i	−0.0200124	+	0.0346625i
$475$		0			0
$476$	6.08625	−	1.45076i	0.278963	−	0.0664953i
$477$	−1.93371	+	5.95135i	−0.0885385	+	0.272494i
$478$	−29.5947	+	13.1764i	−1.35363	+	0.602675i
$479$	−3.68019	+	35.0147i	−0.168152	+	1.59986i	0.506842	+	0.862039i	$0.330813\pi$
$479$	−3.68019	+	35.0147i	−0.168152	+	1.59986i	−0.674994	+	0.737823i	$0.735854\pi$
$480$		0			0
$481$	−5.39733	−	51.3522i	−0.246097	−	2.34146i
$482$	−26.0479			−1.18645
$483$	−0.0695218	−	0.0130016i	−0.00316335	−	0.000591595i
$484$	−3.64703	−	11.2244i	−0.165774	−	0.510201i
$485$		0			0
$486$	−6.33572	+	1.34670i	−0.287394	+	0.0610875i
$487$	−6.78987	+	7.54091i	−0.307678	+	0.341711i	−0.877077	−	0.480350i	$-0.840510\pi$
$487$	−6.78987	+	7.54091i	−0.307678	+	0.341711i	0.569398	+	0.822062i	$0.307176\pi$
$488$	3.70756	+	0.788067i	0.167834	+	0.0356741i
$489$	−0.746147	+	2.29640i	−0.0337419	+	0.103847i
$490$		0			0
$491$	−5.28524	−	16.2663i	−0.238520	−	0.734088i	−0.996635	−	0.0819676i	$-0.973880\pi$
$491$	−5.28524	−	16.2663i	−0.238520	−	0.734088i	0.758115	−	0.652121i	$-0.226120\pi$
$492$	−0.104687	−	0.996027i	−0.00471964	−	0.0449044i
$493$	−1.50548	−	2.60757i	−0.0678035	−	0.117439i
$494$	35.3937	+	15.7583i	1.59244	+	0.709000i
$495$		0			0
$496$	−6.47082	−	4.70133i	−0.290548	−	0.211096i
$497$	−3.84204	−	29.5530i	−0.172339	−	1.32563i
$498$	−0.200725	+	0.617769i	−0.00899472	+	0.0276829i
$499$	−7.24707	+	12.5523i	−0.324423	+	0.561918i	−0.981395	−	0.191997i	$-0.938504\pi$
$499$	−7.24707	+	12.5523i	−0.324423	+	0.561918i	0.656972	+	0.753915i	$0.271837\pi$
$500$		0			0
$501$	−0.670382	−	1.16114i	−0.0299504	−	0.0518757i
$502$	4.01289	+	4.45676i	0.179104	+	0.198915i
$503$	16.1604	+	11.7412i	0.720558	+	0.523516i	0.886562	−	0.462609i	$-0.153087\pi$
$503$	16.1604	+	11.7412i	0.720558	+	0.523516i	−0.166005	+	0.986125i	$0.553087\pi$
$504$	10.9049	+	4.53766i	0.485742	+	0.202123i
$505$		0			0
$506$	0.0326703	+	0.310838i	0.00145237	+	0.0138184i
$507$	−1.49612	−	2.59135i	−0.0664449	−	0.115086i
$508$	13.1448	+	5.85245i	0.583207	+	0.259660i
$509$	4.10387	+	0.872305i	0.181901	+	0.0386642i	0.297961	−	0.954578i	$-0.403693\pi$
$509$	4.10387	+	0.872305i	0.181901	+	0.0386642i	−0.116061	+	0.993242i	$0.537027\pi$
$510$		0			0
$511$	21.7807	+	15.0215i	0.963523	+	0.664511i
$512$	4.38342	+	13.4908i	0.193722	+	0.596214i
$513$	−2.93622	−	0.624112i	−0.129637	−	0.0275552i
$514$	−12.2729	+	2.60869i	−0.541335	+	0.115064i
$515$		0			0
$516$	1.77496	+	0.377280i	0.0781383	+	0.0166088i
$517$	−8.72565	+	6.33956i	−0.383754	+	0.278813i
$518$	−11.7206	+	39.3339i	−0.514973	+	1.72823i
$519$	2.18948	−	1.59075i	0.0961076	−	0.0698262i
$520$		0			0
$521$	−1.08972	+	10.3680i	−0.0477414	+	0.454229i	0.944371	+	0.328881i	$0.106671\pi$
$521$	−1.08972	+	10.3680i	−0.0477414	+	0.454229i	−0.992113	+	0.125348i	$0.959995\pi$
$522$	−0.815992	+	7.76364i	−0.0357150	+	0.339805i
$523$	−12.1520	−	13.4962i	−0.531370	−	0.590146i	0.416368	−	0.909196i	$-0.363303\pi$
$523$	−12.1520	−	13.4962i	−0.531370	−	0.590146i	−0.947738	+	0.319050i	$0.896636\pi$
$524$	−3.70982			−0.162064
$525$		0			0
$526$	−50.5337			−2.20337
$527$	2.19807	+	2.44121i	0.0957496	+	0.106341i
$528$	−0.0634132	+	0.603336i	−0.00275970	+	0.0262568i
$529$	2.40012	−	22.8357i	0.104353	−	0.992854i
$530$		0			0
$531$	19.6137	−	14.2502i	0.851162	−	0.618405i
$532$	−7.75706	−	8.20080i	−0.336311	−	0.355550i
$533$	30.4171	−	22.0993i	1.31751	−	0.957229i
$534$	1.56962	+	0.333634i	0.0679243	+	0.0144377i
$535$		0			0
$536$	−14.8996	+	3.16700i	−0.643564	+	0.136794i
$537$	−2.38514	−	0.506976i	−0.102926	−	0.0218776i
$538$	−8.70218	−	26.7826i	−0.375178	−	1.15468i
$539$	0.960791	+	6.19605i	0.0413842	+	0.266883i
$540$		0			0
$541$	7.24876	+	1.54077i	0.311649	+	0.0662429i	0.361081	−	0.932535i	$-0.382408\pi$
$541$	7.24876	+	1.54077i	0.311649	+	0.0662429i	−0.0494322	+	0.998777i	$0.515741\pi$
$542$	16.4843	+	7.33927i	0.708060	+	0.315249i
$543$	−0.539701	−	0.934789i	−0.0231608	−	0.0401156i
$544$	−1.24860	−	11.8796i	−0.0535331	−	0.509334i
$545$		0			0
$546$	0.487975	+	3.75351i	0.0208834	+	0.160635i
$547$	28.6018	+	20.7804i	1.22293	+	0.888508i	0.996340	−	0.0854834i	$-0.0272435\pi$
$547$	28.6018	+	20.7804i	1.22293	+	0.888508i	0.226586	+	0.973991i	$0.427243\pi$
$548$	1.30161	+	1.44559i	0.0556022	+	0.0617525i
$549$	3.77369	+	6.53622i	0.161057	+	0.278959i
$550$		0			0
$551$	−2.71615	+	4.70450i	−0.115712	+	0.200419i
$552$	−0.0123691	+	0.0380681i	−0.000526463	+	0.00162029i
$553$	8.79989	+	3.66174i	0.374209	+	0.155713i
$554$	30.5362	+	22.1859i	1.29736	+	0.942587i
$555$		0			0
$556$	−0.0657766	−	0.0292856i	−0.00278955	−	0.00124199i
$557$	−11.6999	−	20.2649i	−0.495742	−	0.858650i	0.504246	−	0.863560i	$-0.331770\pi$
$557$	−11.6999	−	20.2649i	−0.495742	−	0.858650i	−0.999988	+	0.00490988i	$0.998437\pi$
$558$	−0.890249	−	8.47016i	−0.0376873	−	0.358570i
$559$	21.0509	+	64.7880i	0.890358	+	2.74024i
$560$		0			0
$561$	0.0769940	−	0.236963i	0.00325069	−	0.0100046i
$562$	−34.6479	−	7.36465i	−1.46154	−	0.310659i
$563$	−12.0159	+	13.3450i	−0.506409	+	0.562425i	−0.941088	−	0.338161i	$-0.890195\pi$
$563$	−12.0159	+	13.3450i	−0.506409	+	0.562425i	0.434679	+	0.900586i	$0.356862\pi$
$564$	1.85558	−	0.394415i	0.0781339	−	0.0166079i
$565$		0			0
$566$	−7.62248	−	23.4596i	−0.320397	−	0.986080i
$567$	7.76584	+	22.0435i	0.326135	+	0.925739i
$568$	−16.8659			−0.707679
$569$	4.49348	+	42.7526i	0.188376	+	1.79228i	0.525471	+	0.850811i	$0.323889\pi$
$569$	4.49348	+	42.7526i	0.188376	+	1.79228i	−0.337095	+	0.941471i	$0.609444\pi$
$570$		0			0
$571$	2.31535	−	22.0290i	0.0968942	−	0.921887i	−0.832805	−	0.553567i	$-0.813266\pi$
$571$	2.31535	−	22.0290i	0.0968942	−	0.921887i	0.929699	−	0.368320i	$-0.120067\pi$
$572$	5.60115	−	2.49379i	0.234196	−	0.104271i
$573$	0.228133	−	0.702122i	0.00953040	−	0.0293316i
$574$	−29.0707	+	6.92947i	−1.21339	+	0.289230i
$575$		0			0
$576$	−0.651168	+	1.12786i	−0.0271320	+	0.0469940i
$577$	−29.1697	+	6.20020i	−1.21435	+	0.258118i	−0.770181	−	0.637826i	$-0.779834\pi$
$577$	−29.1697	+	6.20020i	−1.21435	+	0.258118i	−0.444168	+	0.895943i	$0.646501\pi$
$578$	2.38200	−	22.6632i	0.0990780	−	0.942664i
$579$	0.937159	−	0.417250i	0.0389470	−	0.0173403i
$580$		0			0
$581$	6.98378	+	1.30607i	0.289736	+	0.0541850i
$582$	4.26326			0.176718
$583$	0.196512	+	1.86969i	0.00813871	+	0.0774346i
$584$	10.0194	−	11.1277i	0.414607	−	0.460468i
$585$		0			0
$586$	−9.72002	−	10.7952i	−0.401530	−	0.445944i
$587$	12.5015	+	38.4758i	0.515994	+	1.58807i	0.781467	+	0.623947i	$0.214472\pi$
$587$	12.5015	+	38.4758i	0.515994	+	1.58807i	−0.265473	+	0.964118i	$0.585528\pi$
$588$	0.288883	−	1.06432i	0.0119133	−	0.0438919i
$589$	1.83143	−	5.63658i	0.0754630	−	0.232251i
$590$		0			0
$591$	−1.08712	+	1.20736i	−0.0447179	+	0.0496643i
$592$	39.6803	+	17.6668i	1.63085	+	0.726102i
$593$	−0.312216	+	0.540774i	−0.0128212	+	0.0222069i	−0.872365	−	0.488855i	$-0.837415\pi$
$593$	−0.312216	+	0.540774i	−0.0128212	+	0.0222069i	0.859544	+	0.511062i	$0.170748\pi$
$594$	−1.04847	+	0.761757i	−0.0430192	+	0.0312553i
$595$		0			0
$596$	20.4613	+	14.8660i	0.838127	+	0.608935i
$597$	−2.51438	+	1.11947i	−0.102907	+	0.0458171i
$598$	2.01865	−	0.429078i	0.0825488	−	0.0175463i
$599$	−6.69211	−	11.5911i	−0.273432	−	0.473599i	0.696306	−	0.717745i	$-0.254826\pi$
$599$	−6.69211	−	11.5911i	−0.273432	−	0.473599i	−0.969738	+	0.244146i	$0.921492\pi$
$600$		0			0
$601$	39.9880			1.63114			0.815572	−	0.578656i	$-0.196423\pi$
$601$	39.9880			1.63114			0.815572	+	0.578656i	$0.196423\pi$
$602$	4.33585	−	53.9742i	0.176716	−	2.19982i
$603$	−24.5380	−	17.8279i	−0.999265	−	0.726008i
$604$	−5.78279	+	2.57466i	−0.235298	+	0.104762i
$605$		0			0
$606$	2.02455	+	0.901388i	0.0822417	+	0.0366164i
$607$	12.2530	−	21.2227i	0.497332	−	0.861405i	−0.502663	−	0.864482i	$-0.667646\pi$
$607$	12.2530	−	21.2227i	0.497332	−	0.861405i	0.999995	+	0.00307784i	$0.000979707\pi$
$608$	−17.4350	+	12.6673i	−0.707084	+	0.513727i
$609$	−0.530558	+	0.0130332i	−0.0214993	+	0.000528130i
$610$		0			0
$611$	47.6529	+	52.9239i	1.92783	+	2.14107i
$612$	4.71783	−	5.23968i	0.190707	−	0.211801i
$613$	22.5063	−	24.9958i	0.909021	−	1.00957i	−0.0908854	−	0.995861i	$-0.528970\pi$
$613$	22.5063	−	24.9958i	0.909021	−	1.00957i	0.999906	−	0.0137084i	$-0.00436365\pi$
$614$	25.7035	+	28.5466i	1.03731	+	1.15205i
$615$		0			0
$616$	3.54742	−	0.0871424i	0.142930	−	0.00351107i
$617$	27.3814	−	19.8937i	1.10233	−	0.800891i	0.120893	−	0.992666i	$-0.461424\pi$
$617$	27.3814	−	19.8937i	1.10233	−	0.800891i	0.981439	+	0.191774i	$0.0614242\pi$
$618$	0.342272	−	0.592833i	0.0137682	−	0.0238472i
$619$	−24.2226	−	10.7846i	−0.973587	−	0.433469i	−0.142612	−	0.989779i	$-0.545550\pi$
$619$	−24.2226	−	10.7846i	−0.973587	−	0.433469i	−0.830975	+	0.556310i	$0.812217\pi$
$620$		0			0
$621$	−0.146075	+	0.0650366i	−0.00586178	+	0.00260983i
$622$	8.92604	+	6.48515i	0.357902	+	0.260031i
$623$	1.40546	−	17.4956i	0.0563084	−	0.700948i
$624$	4.00574			0.160358
$625$		0			0
$626$	8.64379	+	14.9715i	0.345475	+	0.598381i
$627$	−0.439700	+	0.0934612i	−0.0175599	+	0.00373248i
$628$	8.24642	−	3.67154i	0.329068	−	0.146510i
$629$	−14.4322	−	10.4856i	−0.575449	−	0.418088i
$630$		0			0
$631$	27.4224	−	19.9235i	1.09167	−	0.793144i	0.111988	−	0.993710i	$-0.464278\pi$
$631$	27.4224	−	19.9235i	1.09167	−	0.793144i	0.979680	+	0.200566i	$0.0642781\pi$
$632$	2.69708	−	4.67147i	0.107284	−	0.185821i
$633$	−0.0150264	−	0.00669020i	−0.000597247	−	0.000265912i
$634$	−24.7158	+	27.4497i	−0.981589	+	1.09017i
$635$		0			0
$636$	0.102181	−	0.314482i	0.00405175	−	0.0124700i
$637$	40.0249	−	10.5858i	1.58585	−	0.419424i
$638$	0.724735	+	2.23051i	0.0286925	+	0.0883066i
$639$	−22.4716	−	24.9572i	−0.888961	−	0.987291i
$640$		0			0
$641$	−23.8022	+	26.4350i	−0.940131	+	1.04412i	0.0588174	+	0.998269i	$0.481267\pi$
$641$	−23.8022	+	26.4350i	−0.940131	+	1.04412i	−0.998948	+	0.0458523i	$0.985400\pi$
$642$	−0.282073	−	2.68375i	−0.0111325	−	0.105919i
$643$	32.5951			1.28542			0.642712	−	0.766108i	$-0.277809\pi$
$643$	32.5951			1.28542			0.642712	+	0.766108i	$0.277809\pi$
$644$	−0.591049	−	0.110535i	−0.0232906	−	0.00435569i
$645$		0			0
$646$	12.2280	−	5.44427i	0.481105	−	0.214202i
$647$	−4.11533	+	39.1547i	−0.161790	+	1.53933i	0.548937	+	0.835864i	$0.315033\pi$
$647$	−4.11533	+	39.1547i	−0.161790	+	1.53933i	−0.710728	+	0.703467i	$0.751634\pi$
$648$	12.9377	−	2.75000i	0.508243	−	0.108030i
$649$	3.64181	−	6.30781i	0.142954	−	0.247603i
$650$		0			0
$651$	0.563235	−	0.134256i	0.0220749	−	0.00526192i
$652$	−6.34347	+	19.5232i	−0.248429	+	0.764587i
$653$	26.1104	−	11.6251i	1.02178	−	0.454926i	0.173703	−	0.984798i	$-0.444427\pi$
$653$	26.1104	−	11.6251i	1.02178	−	0.454926i	0.848078	+	0.529872i	$0.177760\pi$
$654$	−0.154141	+	1.46656i	−0.00602740	+	0.0573469i
$655$		0			0
$656$	3.30595	+	31.4540i	0.129075	+	1.22807i
$657$	29.8156			1.16322
$658$	−18.8095	−	53.3910i	−0.733269	−	2.08140i
$659$	−3.08756	−	9.50254i	−0.120274	−	0.370166i	0.872736	−	0.488192i	$-0.162343\pi$
$659$	−3.08756	−	9.50254i	−0.120274	−	0.370166i	−0.993011	+	0.118026i	$0.962343\pi$
$660$		0			0
$661$	−8.30978	+	1.76630i	−0.323213	+	0.0687010i	−0.366661	−	0.930355i	$-0.619499\pi$
$661$	−8.30978	+	1.76630i	−0.323213	+	0.0687010i	0.0434480	+	0.999056i	$0.486166\pi$
$662$	8.78893	−	9.76110i	0.341592	−	0.379376i
$663$	−1.60923	−	0.342051i	−0.0624971	−	0.0132842i
$664$	1.24253	−	3.82412i	0.0482195	−	0.148404i
$665$		0			0
$666$	14.2923	+	43.9873i	0.553816	+	1.70447i
$667$	0.0302467	+	0.287779i	0.00117116	+	0.0111428i
$668$	−5.69934	−	9.87155i	−0.220514	−	0.381942i
$669$	2.38390	+	1.06138i	0.0921671	+	0.0410354i
$670$		0			0
$671$	1.83442	+	1.33279i	0.0708172	+	0.0514517i
$672$	−1.94388	−	0.808873i	−0.0749868	−	0.0312029i
$673$	5.45660	−	16.7937i	0.210336	−	0.647349i	−0.789116	−	0.614245i	$-0.789461\pi$
$673$	5.45660	−	16.7937i	0.210336	−	0.647349i	0.999452	−	0.0331038i	$-0.0105392\pi$
$674$	25.4983	−	44.1643i	0.982157	−	1.70115i
$675$		0			0
$676$	−12.7194	−	22.0307i	−0.489209	−	0.847335i
$677$	2.67229	+	2.96788i	0.102704	+	0.114065i	0.792305	−	0.610125i	$-0.208881\pi$
$677$	2.67229	+	2.96788i	0.102704	+	0.114065i	−0.689601	+	0.724190i	$0.742214\pi$
$678$	1.06787	+	0.775852i	0.0410112	+	0.0297964i
$679$	−6.01170	−	46.2421i	−0.230708	−	1.77461i
$680$		0			0
$681$	−0.170169	−	1.61905i	−0.00652087	−	0.0620419i
$682$	−1.27936	−	2.21592i	−0.0489893	−	0.0848519i
$683$	8.80674	+	3.92101i	0.336980	+	0.150033i	0.568249	−	0.822857i	$-0.307621\pi$
$683$	8.80674	+	3.92101i	0.336980	+	0.150033i	−0.231269	+	0.972890i	$0.574288\pi$
$684$	−12.4427	−	2.64477i	−0.475757	−	0.101125i
$685$		0			0
$686$	−32.6056	−	4.45391i	−1.24489	−	0.170051i
$687$	0.572488	+	1.76194i	0.0218418	+	0.0672221i
$688$	−56.0523	−	11.9143i	−2.13697	−	0.454228i
$689$	12.1422	−	2.58090i	0.462581	−	0.0983246i
$690$		0			0
$691$	−6.25348	−	1.32922i	−0.237894	−	0.0505658i	0.0874219	−	0.996171i	$-0.472137\pi$
$691$	−6.25348	−	1.32922i	−0.237894	−	0.0505658i	−0.325315	+	0.945606i	$0.605470\pi$
$692$	18.6142	−	13.5240i	0.707605	−	0.514105i
$693$	4.85540	+	5.13315i	0.184441	+	0.194992i
$694$	22.9651	−	16.6851i	0.871743	−	0.633358i
$695$		0			0
$696$	−0.0313955	+	0.298709i	−0.00119004	+	0.0113225i
$697$	1.35777	−	12.9183i	0.0514291	−	0.489315i
$698$	35.9721	+	39.9511i	1.36157	+	1.51217i
$699$	−0.493066			−0.0186495
$700$		0			0
$701$	13.7697			0.520075			0.260037	−	0.965599i	$-0.416265\pi$
$701$	13.7697			0.520075			0.260037	+	0.965599i	$0.416265\pi$
$702$	5.72594	+	6.35930i	0.216112	+	0.240016i
$703$	−3.36424	+	32.0086i	−0.126885	+	1.20723i
$704$	−0.0408981	+	0.389120i	−0.00154141	+	0.0146655i
$705$		0			0
$706$	−13.0889	+	9.50961i	−0.492606	+	0.357899i
$707$	6.92219	−	23.2307i	0.260336	−	0.873679i
$708$	−1.03643	+	0.753010i	−0.0389514	+	0.0282998i
$709$	−47.0675	−	10.0045i	−1.76766	−	0.375727i	−0.794752	−	0.606934i	$-0.792399\pi$
$709$	−47.0675	−	10.0045i	−1.76766	−	0.375727i	−0.972905	+	0.231207i	$0.925733\pi$
$710$		0			0
$711$	10.5060	−	2.23313i	0.394008	−	0.0837489i
$712$	−9.71628	−	2.06526i	−0.364133	−	0.0773989i
$713$	−0.0975556	−	0.300245i	−0.00365349	−	0.0112443i
$714$	1.07651	+	0.742433i	0.0402872	+	0.0277848i
$715$		0			0
$716$	−20.2776	−	4.31013i	−0.757808	−	0.161077i
$717$	−2.26730	−	1.00947i	−0.0846738	−	0.0376992i
$718$	−20.9206	−	36.2355i	−0.780750	−	1.35230i
$719$	0.565884	+	5.38402i	0.0211039	+	0.200790i	0.999994	−	0.00359939i	$-0.00114572\pi$
$719$	0.565884	+	5.38402i	0.0211039	+	0.200790i	−0.978890	+	0.204390i	$0.934479\pi$
$720$		0			0
$721$	−6.91290	−	2.87654i	−0.257450	−	0.107128i
$722$	7.77594	+	5.64955i	0.289390	+	0.210254i
$723$	−1.33530	−	1.48300i	−0.0496602	−	0.0551533i
$724$	−4.58834	−	7.94723i	−0.170524	−	0.295357i
$725$		0			0
$726$	1.23335	−	2.13622i	0.0457738	−	0.0792825i
$727$	0.502260	−	1.54580i	0.0186278	−	0.0573305i	−0.941311	−	0.337542i	$-0.890405\pi$
$727$	0.502260	−	1.54580i	0.0186278	−	0.0573305i	0.959938	+	0.280211i	$0.0904046\pi$
$728$	−3.02066	−	23.2350i	−0.111953	−	0.861146i
$729$	21.0380	+	15.2850i	0.779187	+	0.566112i
$730$		0			0
$731$	21.5005	+	9.57264i	0.795225	+	0.354057i
$732$	−0.199410	−	0.345388i	−0.00737040	−	0.0127659i
$733$	1.93192	+	18.3810i	0.0713572	+	0.678919i	0.970473	+	0.241208i	$0.0775438\pi$
$733$	1.93192	+	18.3810i	0.0713572	+	0.678919i	−0.899116	+	0.437710i	$0.855790\pi$
$734$	19.7474	+	60.7763i	0.728890	+	2.24329i
$735$		0			0
$736$	−0.354739	+	1.09177i	−0.0130758	+	0.0402433i
$737$	−8.91317	−	1.89455i	−0.328321	−	0.0697867i
$738$	−22.5345	+	25.0271i	−0.829505	+	0.921259i
$739$	3.91680	−	0.832542i	0.144082	−	0.0306256i	−0.135306	−	0.990804i	$-0.543202\pi$
$739$	3.91680	−	0.832542i	0.144082	−	0.0306256i	0.279388	+	0.960178i	$0.409868\pi$
$740$		0			0
$741$	0.917218	+	2.82291i	0.0336948	+	0.103702i
$742$	−9.69891	−	1.81384i	−0.356058	−	0.0665882i
$743$	−20.9549			−0.768760			−0.384380	−	0.923175i	$-0.625585\pi$
$743$	−20.9549			−0.768760			−0.384380	+	0.923175i	$0.625585\pi$
$744$	−0.0342526	−	0.325892i	−0.00125576	−	0.0119478i
$745$		0			0
$746$	−1.32146	+	12.5729i	−0.0483821	+	0.460325i
$747$	7.31420	−	3.25649i	0.267612	−	0.119149i
$748$	0.654575	−	2.01457i	0.0239336	−	0.0736601i
$749$	−28.7119	+	6.84395i	−1.04911	+	0.250073i
$750$		0			0
$751$	1.95354	−	3.38362i	0.0712855	−	0.123470i	−0.828179	−	0.560463i	$-0.810623\pi$
$751$	1.95354	−	3.38362i	0.0712855	−	0.123470i	0.899465	+	0.436993i	$0.143957\pi$
$752$	−58.5980	+	12.4554i	−2.13685	+	0.454202i
$753$	−0.0480258	+	0.456935i	−0.00175016	+	0.0166516i
$754$	14.1470	−	6.29866i	0.515204	−	0.229384i
$755$		0			0
$756$	−0.828459	−	2.35159i	−0.0301307	−	0.0855266i
$757$	−28.1928			−1.02469			−0.512343	−	0.858781i	$-0.671222\pi$
$757$	−28.1928			−1.02469			−0.512343	+	0.858781i	$0.671222\pi$
$758$	−1.78236	−	16.9580i	−0.0647381	−	0.615942i
$759$	−0.0160223	+	0.0177945i	−0.000581572	+	0.000645901i
$760$		0			0
$761$	1.56426	+	1.73728i	0.0567043	+	0.0629765i	0.770830	−	0.637041i	$-0.219842\pi$
$761$	1.56426	+	1.73728i	0.0567043	+	0.0629765i	−0.714125	+	0.700018i	$0.753175\pi$
$762$	0.929317	+	2.86014i	0.0336656	+	0.103612i
$763$	16.1246	−	0.396100i	0.583749	−	0.0143398i
$764$	1.93951	−	5.96919i	0.0701689	−	0.215958i
$765$		0			0
$766$	−5.35192	+	5.94391i	−0.193373	+	0.214762i
$767$	−43.9355	−	19.5614i	−1.58642	−	0.706320i
$768$	−1.37962	+	2.38956i	−0.0497826	+	0.0862260i
$769$	−4.40134	+	3.19776i	−0.158716	+	0.115314i	−0.664309	−	0.747458i	$-0.731274\pi$
$769$	−4.40134	+	3.19776i	−0.158716	+	0.115314i	0.505592	+	0.862772i	$0.331274\pi$
$770$		0			0
$771$	−0.777669	−	0.565009i	−0.0280071	−	0.0203483i
$772$	7.96738	−	3.54731i	0.286752	−	0.127670i
$773$	29.9626	−	6.36875i	1.07768	−	0.229068i	0.365320	−	0.930882i	$-0.380960\pi$
$773$	29.9626	−	6.36875i	1.07768	−	0.229068i	0.712360	+	0.701814i	$0.247626\pi$
$774$	−30.5094	−	52.8439i	−1.09664	−	1.89944i
$775$		0			0
$776$	−26.3904			−0.947361
$777$	−2.84025	+	1.34909i	−0.101893	+	0.0483982i
$778$	30.3319	+	22.0374i	1.08745	+	0.790079i
$779$	−21.4091	+	9.53195i	−0.767061	+	0.341518i
$780$		0			0
$781$	−9.21719	−	4.10376i	−0.329817	−	0.146844i
$782$	0.356498	−	0.617473i	0.0127483	−	0.0220808i
$783$	−0.970690	+	0.705247i	−0.0346896	+	0.0252035i
$784$	−9.12276	+	33.6107i	−0.325813	+	1.20038i
$785$		0			0
$786$	−0.518825	−	0.576214i	−0.0185059	−	0.0205529i
$787$	12.8691	−	14.2925i	0.458733	−	0.509474i	−0.468755	−	0.883328i	$-0.655297\pi$
$787$	12.8691	−	14.2925i	0.458733	−	0.509474i	0.927488	+	0.373854i	$0.121964\pi$
$788$	−9.24226	+	10.2646i	−0.329242	+	0.365660i
$789$	−2.59052	−	2.87706i	−0.0922248	−	0.102426i
$790$		0			0
$791$	6.90958	−	12.6768i	0.245676	−	0.450737i
$792$	3.23506	−	2.35041i	0.114953	−	0.0835182i
$793$	7.48601	−	12.9661i	0.265836	−	0.460441i
$794$	−7.62429	−	3.39455i	−0.270576	−	0.120468i
$795$		0			0
$796$	−21.3764	+	9.51737i	−0.757665	+	0.337334i
$797$	22.0460	+	16.0174i	0.780911	+	0.567365i	0.905252	−	0.424874i	$-0.139682\pi$
$797$	22.0460	+	16.0174i	0.780911	+	0.567365i	−0.124341	+	0.992240i	$0.539682\pi$
$798$	0.188919	−	2.35173i	0.00668766	−	0.0832505i
$799$	24.6042			0.870432
$800$		0			0
$801$	−9.88957	−	17.1292i	−0.349431	−	0.605232i
$802$	−1.85132	+	0.393510i	−0.0653723	+	0.0138953i
$803$	8.18315	−	3.64337i	0.288777	−	0.128572i
$804$	1.29664	+	0.942064i	0.0457290	+	0.0332240i
$805$		0			0
$806$	−13.6684	+	9.93070i	−0.481450	+	0.349794i
$807$	1.07872	−	1.86840i	0.0379729	−	0.0657709i
$808$	−12.5324	−	5.57977i	−0.440887	−	0.196296i
$809$	10.3329	−	11.4759i	0.363287	−	0.403471i	−0.533596	−	0.845740i	$-0.679160\pi$
$809$	10.3329	−	11.4759i	0.363287	−	0.403471i	0.896883	+	0.442269i	$0.145826\pi$
$810$		0			0
$811$	7.57398	−	23.3103i	0.265958	−	0.818536i	−0.725513	−	0.688209i	$-0.758397\pi$
$811$	7.57398	−	23.3103i	0.265958	−	0.818536i	0.991471	−	0.130327i	$-0.0416027\pi$
$812$	−4.51061	+	0.110803i	−0.158291	+	0.00388843i
$813$	0.427185	+	1.31474i	0.0149820	+	0.0461099i
$814$	9.29774	+	10.3262i	0.325886	+	0.361933i
$815$		0			0
$816$	0.926028	−	1.02846i	0.0324175	−	0.0360032i
$817$	−4.43845	−	42.2290i	−0.155282	−	1.47741i
$818$	30.4839			1.06585
$819$	30.3571	−	35.4272i	1.06076	−	1.23793i
$820$		0			0
$821$	−26.9382	+	11.9937i	−0.940151	+	0.418582i	−0.818833	−	0.574032i	$-0.805379\pi$
$821$	−26.9382	+	11.9937i	−0.940151	+	0.418582i	−0.121318	+	0.992614i	$0.538712\pi$
$822$	−0.0424975	+	0.404336i	−0.00148227	+	0.0141029i
$823$	7.51501	−	1.59736i	0.261957	−	0.0556806i	−0.0750609	−	0.997179i	$-0.523915\pi$
$823$	7.51501	−	1.59736i	0.261957	−	0.0556806i	0.337018	+	0.941498i	$0.390582\pi$
$824$	−2.11873	+	3.66975i	−0.0738096	+	0.127842i
$825$		0			0
$826$	26.2694	+	27.7721i	0.914029	+	0.966316i
$827$	1.75253	−	5.39373i	0.0609414	−	0.187558i	−0.915951	−	0.401290i	$-0.868562\pi$
$827$	1.75253	−	5.39373i	0.0609414	−	0.187558i	0.976892	+	0.213732i	$0.0685619\pi$
$828$	−0.619013	+	0.275602i	−0.0215122	+	0.00957785i
$829$	−1.61187	+	15.3359i	−0.0559824	+	0.532637i	0.930209	+	0.367030i	$0.119625\pi$
$829$	−1.61187	+	15.3359i	−0.0559824	+	0.532637i	−0.986192	+	0.165608i	$0.947041\pi$
$830$		0			0
$831$	0.302264	+	2.87585i	0.0104854	+	0.0997621i
$832$	2.58349			0.0895664
$833$	6.53491	−	12.7234i	0.226421	−	0.440840i
$834$	−0.00465030	−	0.0143122i	−0.000161027	−	0.000495589i
$835$		0			0
$836$	−3.73817	+	0.794573i	−0.129287	+	0.0274809i
$837$	0.875911	−	0.972797i	0.0302759	−	0.0336248i
$838$	43.0598	+	9.15264i	1.48747	+	0.316173i
$839$	12.6424	−	38.9093i	0.436464	−	1.34330i	−0.455115	−	0.890433i	$-0.650402\pi$
$839$	12.6424	−	38.9093i	0.436464	−	1.34330i	0.891579	−	0.452865i	$-0.149598\pi$
$840$		0			0
$841$	−8.29052	−	25.5156i	−0.285880	−	0.879848i
$842$	−1.94003	−	18.4581i	−0.0668578	−	0.636110i
$843$	−1.35687	−	2.35016i	−0.0467330	−	0.0809439i
$844$	−0.127749	−	0.0568777i	−0.00439731	−	0.00195781i
$845$		0			0
$846$	−51.6074	−	37.4950i	−1.77430	−	1.28910i
$847$	−24.9100	−	10.3654i	−0.855917	−	0.356158i
$848$	−3.22683	+	9.93116i	−0.110810	+	0.341037i
$849$	0.944883	−	1.63659i	0.0324283	−	0.0561675i
$850$		0			0
$851$	0.857203	+	1.48472i	0.0293845	+	0.0508955i
$852$	1.18744	+	1.31879i	0.0406812	+	0.0451810i
$853$	−13.9621	−	10.1441i	−0.478053	−	0.347326i	0.322519	−	0.946563i	$-0.395471\pi$
$853$	−13.9621	−	10.1441i	−0.478053	−	0.347326i	−0.800571	+	0.599237i	$0.795471\pi$
$854$	−9.45323	+	7.22942i	−0.323483	+	0.247386i
$855$		0			0
$856$	1.74609	+	16.6129i	0.0596801	+	0.567818i
$857$	−21.6693	−	37.5323i	−0.740208	−	1.28208i	−0.952400	−	0.304850i	$-0.901394\pi$
$857$	−21.6693	−	37.5323i	−0.740208	−	1.28208i	0.212192	−	0.977228i	$-0.431940\pi$
$858$	1.17067	+	0.521216i	0.0399660	+	0.0177940i
$859$	−17.4422	−	3.70745i	−0.595120	−	0.126497i	−0.0995020	−	0.995037i	$-0.531725\pi$
$859$	−17.4422	−	3.70745i	−0.595120	−	0.126497i	−0.495618	+	0.868541i	$0.665058\pi$
$860$		0			0
$861$	−1.88477	−	1.29987i	−0.0642329	−	0.0442994i
$862$	−17.4102	−	53.5830i	−0.592993	−	1.82504i
$863$	34.3026	+	7.29125i	1.16768	+	0.248197i	0.750652	−	0.660698i	$-0.229740\pi$
$863$	34.3026	+	7.29125i	1.16768	+	0.248197i	0.417024	+	0.908895i	$0.363073\pi$
$864$	−4.65596	+	0.989655i	−0.158399	+	0.0336687i
$865$		0			0
$866$	−32.9530	−	7.00437i	−1.11979	−	0.238018i
$867$	1.41240	−	1.02617i	0.0479677	−	0.0348506i
$868$	4.78842	−	1.14140i	0.162530	−	0.0387416i
$869$	2.61059	−	1.89670i	0.0885582	−	0.0643413i
$870$		0			0
$871$	−6.28927	+	59.8384i	−0.213104	+	2.02755i
$872$	0.954165	−	9.07827i	0.0323121	−	0.307429i
$873$	−35.1616	−	39.0510i	−1.19004	−	1.32167i
$874$	−1.28637			−0.0435120
$875$		0			0
$876$	−1.57552			−0.0532320
$877$	26.8879	+	29.8620i	0.907940	+	1.00837i	0.999921	+	0.0126089i	$0.00401364\pi$
$877$	26.8879	+	29.8620i	0.907940	+	1.00837i	−0.0919803	+	0.995761i	$0.529320\pi$
$878$	0.928259	−	8.83180i	0.0313272	−	0.298059i
$879$	0.116328	−	1.10679i	0.00392365	−	0.0373310i
$880$		0			0
$881$	−13.0284	+	9.46567i	−0.438937	+	0.318907i	−0.785213	−	0.619226i	$-0.787446\pi$
$881$	−13.0284	+	9.46567i	−0.438937	+	0.318907i	0.346275	+	0.938133i	$0.387446\pi$
$882$	−33.0966	+	16.7287i	−1.11442	+	0.563285i
$883$	−1.27404	+	0.925642i	−0.0428748	+	0.0311503i	−0.609016	−	0.793158i	$-0.708436\pi$
$883$	−1.27404	+	0.925642i	−0.0428748	+	0.0311503i	0.566141	+	0.824308i	$0.308436\pi$
$884$	−13.6811	−	2.90800i	−0.460144	−	0.0978065i
$885$		0			0
$886$	5.66406	−	1.20393i	0.190288	−	0.0404469i
$887$	9.68421	+	2.05844i	0.325164	+	0.0691157i	0.367602	−	0.929983i	$-0.380179\pi$
$887$	9.68421	+	2.05844i	0.325164	+	0.0691157i	−0.0424376	+	0.999099i	$0.513512\pi$
$888$	0.549902	+	1.69242i	0.0184535	+	0.0567940i
$889$	29.7125	−	14.1131i	0.996527	−	0.473339i
$890$		0			0
$891$	7.73956	+	1.64509i	0.259285	+	0.0551127i
$892$	20.2671	+	9.02349i	0.678592	+	0.302129i
$893$	−22.1950	−	38.4430i	−0.742729	−	1.28644i
$894$	0.552544	+	5.25711i	0.0184798	+	0.175824i
$895$		0			0
$896$	26.6632	+	11.0949i	0.890755	+	0.370655i
$897$	0.127911	+	0.0929330i	0.00427083	+	0.00310294i
$898$	−22.2751	−	24.7390i	−0.743331	−	0.825553i
$899$	−1.18445	−	2.05153i	−0.0395037	−	0.0684225i
$900$		0			0
$901$	2.14434	−	3.71410i	0.0714383	−	0.123735i
$902$	−3.12655	+	9.62252i	−0.104103	+	0.320395i
$903$	3.29521	−	2.52003i	0.109658	−	0.0838614i
$904$	−6.61032	−	4.80268i	−0.219856	−	0.159735i
$905$		0			0
$906$	−1.20863	−	0.538119i	−0.0401542	−	0.0178778i
$907$	14.5476	+	25.1973i	0.483047	+	0.836661i	0.999811	−	0.0194668i	$-0.00619686\pi$
$907$	14.5476	+	25.1973i	0.483047	+	0.836661i	−0.516764	+	0.856128i	$0.672864\pi$
$908$	−1.44671	−	13.7645i	−0.0480108	−	0.456792i
$909$	−8.44106	−	25.9789i	−0.279972	−	0.861666i
$910$		0			0
$911$	10.9862	−	33.8121i	0.363989	−	1.12024i	−0.586622	−	0.809861i	$-0.699543\pi$
$911$	10.9862	−	33.8121i	0.363989	−	1.12024i	0.950612	−	0.310383i	$-0.100457\pi$
$912$	−2.44228	−	0.519122i	−0.0808719	−	0.0171899i
$913$	1.60951	−	1.78754i	0.0532670	−	0.0591590i
$914$	−47.2102	+	10.0348i	−1.56157	+	0.331923i
$915$		0			0
$916$	4.86708	+	14.9793i	0.160813	+	0.494931i
$917$	−5.51839	+	6.44005i	−0.182233	+	0.212669i
$918$	2.95642			0.0975764
$919$	3.05900	+	29.1044i	0.100907	+	0.960067i	0.921454	+	0.388488i	$0.127002\pi$
$919$	3.05900	+	29.1044i	0.100907	+	0.960067i	−0.820547	+	0.571579i	$0.806331\pi$
$920$		0			0
$921$	−0.307617	+	2.92678i	−0.0101363	+	0.0964407i
$922$	−22.9131	+	10.2015i	−0.754601	+	0.335970i
$923$	−20.5868	+	63.3596i	−0.677623	+	2.08551i
$924$	−0.256570	−	0.271247i	−0.00844052	−	0.00892336i
$925$		0			0
$926$	−16.0191	+	27.7459i	−0.526420	+	0.911786i
$927$	−8.25320	+	1.75427i	−0.271071	+	0.0576178i
$928$	−0.900407	+	8.56680i	−0.0295573	+	0.281219i
$929$	31.7179	−	14.1217i	1.04063	−	0.463319i	0.185997	−	0.982550i	$-0.440448\pi$
$929$	31.7179	−	14.1217i	1.04063	−	0.463319i	0.854634	+	0.519231i	$0.173782\pi$
$930$		0			0
$931$	−25.7748	+	1.26708i	−0.844736	+	0.0415269i
$932$	−4.19187			−0.137309
$933$	0.0883548	+	0.840639i	0.00289260	+	0.0275213i
$934$	−22.0617	+	24.5020i	−0.721882	+	0.801731i
$935$		0			0
$936$	−17.6674	−	19.6217i	−0.577479	−	0.641355i
$937$	1.44334	+	4.44214i	0.0471519	+	0.145119i	0.971861	−	0.235557i	$-0.0756915\pi$
$937$	1.44334	+	4.44214i	0.0471519	+	0.145119i	−0.924709	+	0.380676i	$0.875691\pi$
$938$	22.8884	−	41.9929i	0.747334	−	1.37112i
$939$	−0.409271	+	1.25961i	−0.0133560	+	0.0411057i
$940$		0			0
$941$	24.7415	−	27.4782i	0.806550	−	0.895765i	−0.189739	−	0.981835i	$-0.560764\pi$
$941$	24.7415	−	27.4782i	0.806550	−	0.895765i	0.996289	+	0.0860698i	$0.0274308\pi$
$942$	1.72355	+	0.767372i	0.0561562	+	0.0250023i
$943$	−0.624165	+	1.08109i	−0.0203256	+	0.0352050i
$944$	32.7298	−	23.7796i	1.06527	−	0.773961i
$945$		0			0
$946$	−14.8309	−	10.7753i	−0.482195	−	0.350335i
$947$	−39.3642	+	17.5261i	−1.27916	+	0.569521i	−0.930006	−	0.367543i	$-0.880199\pi$
$947$	−39.3642	+	17.5261i	−1.27916	+	0.569521i	−0.349158	+	0.937064i	$0.613532\pi$
$948$	−0.555162	+	0.118003i	−0.0180308	+	0.00383257i
$949$	−29.5732	−	51.2223i	−0.959986	−	1.66275i
$950$		0			0
$951$	−2.82981			−0.0917630
$952$	−6.66379	−	4.59581i	−0.215975	−	0.148951i
$953$	14.0927	+	10.2390i	0.456508	+	0.331672i	0.792160	−	0.610314i	$-0.208957\pi$
$953$	14.0927	+	10.2390i	0.456508	+	0.331672i	−0.335652	+	0.941986i	$0.608957\pi$
$954$	−10.1578	+	4.52254i	−0.328871	+	0.146423i
$955$		0			0
$956$	−19.2757	−	8.58211i	−0.623422	−	0.277565i
$957$	−0.0898382	+	0.155604i	−0.00290406	+	0.00502998i
$958$	−50.6120	+	36.7718i	−1.63520	+	1.18804i
$959$	4.44562	−	0.109207i	0.143557	−	0.00352647i
$960$		0			0
$961$	−19.0137	−	21.1168i	−0.613345	−	0.681188i
$962$	61.3925	−	68.1833i	1.97937	−	2.19832i
$963$	−22.2564	+	24.7182i	−0.717202	+	0.796533i
$964$	−11.3522	−	12.6079i	−0.365630	−	0.406073i
$965$		0			0
$966$	−0.0654909	−	0.107261i	−0.00210713	−	0.00345107i
$967$	−5.93845	+	4.31454i	−0.190968	+	0.138746i	−0.679161	−	0.733989i	$-0.737656\pi$
$967$	−5.93845	+	4.31454i	−0.190968	+	0.138746i	0.488193	+	0.872736i	$0.337656\pi$
$968$	−7.63466	+	13.2236i	−0.245387	+	0.425023i
$969$	0.936808	+	0.417094i	0.0300946	+	0.0133990i
$970$		0			0
$971$	−27.1712	+	12.0974i	−0.871966	+	0.388224i	−0.793411	−	0.608686i	$-0.791697\pi$
$971$	−27.1712	+	12.0974i	−0.871966	+	0.388224i	−0.0785541	+	0.996910i	$0.525030\pi$
$972$	−3.41307	−	2.47974i	−0.109474	−	0.0795378i
$973$	−0.148682	+	0.0706220i	−0.00476651	+	0.00226404i
$974$	−18.0306			−0.577738
$975$		0			0
$976$	6.29725	+	10.9071i	0.201570	+	0.349129i
$977$	−33.6351	+	7.14936i	−1.07608	+	0.228728i	−0.711673	−	0.702511i	$-0.752062\pi$
$977$	−33.6351	+	7.14936i	−1.07608	+	0.228728i	−0.364408	+	0.931239i	$0.618729\pi$
$978$	−3.91951	+	1.74508i	−0.125332	+	0.0558014i
$979$	−4.80741	−	3.49279i	−0.153646	−	0.111630i
$980$		0			0
$981$	14.7048	−	10.6836i	0.469487	−	0.341103i
$982$	15.1954	−	26.3192i	0.484905	−	0.839880i
$983$	10.5553	+	4.69953i	0.336662	+	0.149892i	0.568103	−	0.822957i	$-0.307677\pi$
$983$	10.5553	+	4.69953i	0.336662	+	0.149892i	−0.231441	+	0.972849i	$0.574344\pi$
$984$	−0.867021	+	0.962925i	−0.0276396	+	0.0306969i
$985$		0			0
$986$	1.65328	−	5.08829i	0.0526513	−	0.162044i
$987$	2.07550	−	3.80788i	0.0660640	−	0.121206i
$988$	7.79785	+	23.9993i	0.248083	+	0.763520i
$989$	−1.51345	−	1.68086i	−0.0481249	−	0.0534481i
$990$		0			0
$991$	15.4926	−	17.2063i	0.492138	−	0.546575i	−0.445001	−	0.895530i	$-0.646797\pi$
$991$	15.4926	−	17.2063i	0.492138	−	0.546575i	0.937139	+	0.348955i	$0.113463\pi$
$992$	−0.982346	−	9.34640i	−0.0311895	−	0.296749i
$993$	1.00628			0.0319334
$994$	34.4562	−	40.2110i	1.09289	−	1.27541i
$995$		0			0
$996$	−0.386498	+	0.172080i	−0.0122466	+	0.00545256i
$997$	−5.49557	+	52.2869i	−0.174047	+	1.65594i	0.463919	+	0.885877i	$0.346443\pi$
$997$	−5.49557	+	52.2869i	−0.174047	+	1.65594i	−0.637966	+	0.770065i	$0.720224\pi$
$998$	−25.1917	+	5.35465i	−0.797428	+	0.169499i
$999$	−3.55437	+	6.15634i	−0.112455	+	0.194778i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.q.b.226.29		288
5.2	odd	4		175.2.t.a.79.4	yes	144
5.3	odd	4		875.2.u.a.149.15		144
5.4	even	2	inner	875.2.q.b.226.8		288
7.4	even	3	inner	875.2.q.b.851.8		288
25.6	even	5	inner	875.2.q.b.401.8		288
25.8	odd	20		175.2.t.a.44.4	yes	144
25.17	odd	20		875.2.u.a.849.15		144
25.19	even	10	inner	875.2.q.b.401.29		288
35.4	even	6	inner	875.2.q.b.851.29		288
35.18	odd	12		875.2.u.a.774.15		144
35.32	odd	12		175.2.t.a.4.4	✓	144
175.67	odd	60		875.2.u.a.599.15		144
175.81	even	15	inner	875.2.q.b.151.29		288
175.144	even	30	inner	875.2.q.b.151.8		288
175.158	odd	60		175.2.t.a.144.4	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.t.a.4.4	✓	144	35.32	odd	12
175.2.t.a.44.4	yes	144	25.8	odd	20
175.2.t.a.79.4	yes	144	5.2	odd	4
175.2.t.a.144.4	yes	144	175.158	odd	60
875.2.q.b.151.8		288	175.144	even	30	inner
875.2.q.b.151.29		288	175.81	even	15	inner
875.2.q.b.226.8		288	5.4	even	2	inner
875.2.q.b.226.29		288	1.1	even	1	trivial
875.2.q.b.401.8		288	25.6	even	5	inner
875.2.q.b.401.29		288	25.19	even	10	inner
875.2.q.b.851.8		288	7.4	even	3	inner
875.2.q.b.851.29		288	35.4	even	6	inner
875.2.u.a.149.15		144	5.3	odd	4
875.2.u.a.599.15		144	175.67	odd	60
875.2.u.a.774.15		144	35.18	odd	12
875.2.u.a.849.15		144	25.17	odd	20

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:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.q (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.18897 + 1.32048i) q^{2} +(-0.0142295 + 0.135384i) q^{3} +(-0.120974 + 1.15099i) q^{4} +(-0.195691 + 0.142178i) q^{6} +(1.81810 + 1.92211i) q^{7} +(1.21137 - 0.880110i) q^{8} +(2.91632 + 0.619882i) q^{9} +O(q^{10})\)	\(q+(1.18897 + 1.32048i) q^{2} +(-0.0142295 + 0.135384i) q^{3} +(-0.120974 + 1.15099i) q^{4} +(-0.195691 + 0.142178i) q^{6} +(1.81810 + 1.92211i) q^{7} +(1.21137 - 0.880110i) q^{8} +(2.91632 + 0.619882i) q^{9} +(0.876154 - 0.186232i) q^{11} +(-0.154104 - 0.0327559i) q^{12} +(-1.82766 - 5.62497i) q^{13} +(-0.376443 + 4.68611i) q^{14} +(4.86653 + 1.03441i) q^{16} +(-1.86670 - 0.831108i) q^{17} +(2.64887 + 4.58797i) q^{18} +(0.385351 + 3.66637i) q^{19} +(-0.286094 + 0.218792i) q^{21} +(1.28764 + 0.935524i) q^{22} +(0.131400 + 0.145934i) q^{23} +(0.101916 + 0.176524i) q^{24} +(5.25465 - 9.10133i) q^{26} +(-0.251619 + 0.774405i) q^{27} +(-2.43227 + 1.86009i) q^{28} +(1.19212 + 0.866123i) q^{29} +(-1.46865 - 0.653883i) q^{31} +(2.92289 + 5.06260i) q^{32} +(0.0127457 + 0.121268i) q^{33} +(-1.12198 - 3.45311i) q^{34} +(-1.06627 + 3.28166i) q^{36} +(8.53955 + 1.81514i) q^{37} +(-4.38322 + 4.86805i) q^{38} +(0.787540 - 0.167397i) q^{39} +(1.96439 + 6.04579i) q^{41} +(-0.629069 - 0.117645i) q^{42} -11.5179 q^{43} +(0.108360 + 1.03097i) q^{44} +(-0.0364735 + 0.347022i) q^{46} +(-11.0000 + 4.89753i) q^{47} +(-0.209291 + 0.644132i) q^{48} +(-0.388997 + 6.98918i) q^{49} +(0.139081 - 0.240896i) q^{51} +(6.69538 - 1.42315i) q^{52} +(-0.219388 + 2.08734i) q^{53} +(-1.32176 + 0.588484i) q^{54} +(3.89406 + 0.728248i) q^{56} -0.501852 q^{57} +(0.273688 + 2.60397i) q^{58} +(5.44105 - 6.04289i) q^{59} +(1.69386 + 1.88122i) q^{61} +(-0.882733 - 2.71677i) q^{62} +(4.11069 + 6.73248i) q^{63} +(-0.134982 + 0.415431i) q^{64} +(-0.144978 + 0.161014i) q^{66} +(-9.29355 - 4.13775i) q^{67} +(1.18242 - 2.04801i) q^{68} +(-0.0216269 + 0.0157129i) q^{69} +(-9.11276 - 6.62080i) q^{71} +(4.07830 - 1.81577i) q^{72} +(9.78179 - 2.07918i) q^{73} +(7.75640 + 13.4345i) q^{74} -4.26657 q^{76} +(1.95090 + 1.34547i) q^{77} +(1.15741 + 0.840905i) q^{78} +(3.29105 - 1.46527i) q^{79} +(8.06986 + 3.59293i) q^{81} +(-5.64776 + 9.78221i) q^{82} +(2.17252 - 1.57843i) q^{83} +(-0.217217 - 0.355759i) q^{84} +(-13.6945 - 15.2092i) q^{86} +(-0.134223 + 0.149069i) q^{87} +(0.897440 - 0.996708i) q^{88} +(-4.43903 - 4.93004i) q^{89} +(7.48892 - 13.7398i) q^{91} +(-0.183864 + 0.133585i) q^{92} +(0.109424 - 0.189527i) q^{93} +(-19.5458 - 8.70236i) q^{94} +(-0.726988 + 0.323676i) q^{96} +(-14.2589 - 10.3597i) q^{97} +(-9.69161 + 7.79626i) q^{98} +2.67059 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q + 38 q^{4} - 24 q^{6} + 34 q^{9}+O(q^{10}) \) 288 * q + 38 * q^4 - 24 * q^6 + 34 * q^9	\( 288 q + 38 q^{4} - 24 q^{6} + 34 q^{9} + 36 q^{14} + 10 q^{16} + 22 q^{19} - 18 q^{21} - 100 q^{24} - 120 q^{26} + 48 q^{29} + 30 q^{31} + 40 q^{34} + 32 q^{36} - 26 q^{39} - 124 q^{41} + 30 q^{44} - 54 q^{46} + 76 q^{49} - 16 q^{51} + 58 q^{54} + 64 q^{56} + 78 q^{59} + 14 q^{61} - 68 q^{64} + 22 q^{66} - 148 q^{69} - 92 q^{71} - 12 q^{74} + 360 q^{76} - 18 q^{79} - 118 q^{81} + 102 q^{84} + 22 q^{86} + 84 q^{89} + 44 q^{91} - 10 q^{94} + 106 q^{96} + 88 q^{99}+O(q^{100}) \) 288 * q + 38 * q^4 - 24 * q^6 + 34 * q^9 + 36 * q^14 + 10 * q^16 + 22 * q^19 - 18 * q^21 - 100 * q^24 - 120 * q^26 + 48 * q^29 + 30 * q^31 + 40 * q^34 + 32 * q^36 - 26 * q^39 - 124 * q^41 + 30 * q^44 - 54 * q^46 + 76 * q^49 - 16 * q^51 + 58 * q^54 + 64 * q^56 + 78 * q^59 + 14 * q^61 - 68 * q^64 + 22 * q^66 - 148 * q^69 - 92 * q^71 - 12 * q^74 + 360 * q^76 - 18 * q^79 - 118 * q^81 + 102 * q^84 + 22 * q^86 + 84 * q^89 + 44 * q^91 - 10 * q^94 + 106 * q^96 + 88 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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