LMFDB - Embedded newform 725.2.bd.b.482.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [725,2,Mod(43,725)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("725.43"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(725, base_ring=CyclotomicField(28)) chi = DirichletCharacter(H, H._module([21, 13])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	725.bd (of order $28$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [156] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.78915414654$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$13$ over $\Q(\zeta_{28})$
Twist minimal:	no (minimal twist has level 145)
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			482.5
Character	$\chi$	$=$	725.482
Dual form			725.2.bd.b.543.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.443182 + 0.920277i) q^{2} +(0.973467 - 1.22069i) q^{3} +(0.596480 + 0.747962i) q^{4} +(0.691949 + 1.43685i) q^{6} +(3.19267 - 0.359728i) q^{7} +(-2.94432 + 0.672023i) q^{8} +(0.125119 + 0.548181i) q^{9} +(-0.282265 + 0.177359i) q^{11} +1.49368 q^{12} +(-3.66774 + 2.30460i) q^{13} +(-1.08389 + 3.09757i) q^{14} +(0.260662 - 1.14204i) q^{16} +7.42290i q^{17} +(-0.559929 - 0.127800i) q^{18} +(5.42486 + 0.611234i) q^{19} +(2.66885 - 4.24744i) q^{21} +(-0.0381244 - 0.338364i) q^{22} +(1.34116 - 3.83282i) q^{23} +(-2.04587 + 4.24830i) q^{24} +(-0.495389 - 4.39670i) q^{26} +(5.01106 + 2.41320i) q^{27} +(2.17343 + 2.17343i) q^{28} +(-0.0218780 - 5.38512i) q^{29} +(0.716676 + 2.04814i) q^{31} +(-3.78686 - 3.01992i) q^{32} +(-0.0582756 + 0.517210i) q^{33} +(-6.83113 - 3.28970i) q^{34} +(-0.335388 + 0.420563i) q^{36} +(-1.62587 - 7.12342i) q^{37} +(-2.96670 + 4.72148i) q^{38} +(-0.757232 + 6.72062i) q^{39} +(1.70982 - 1.70982i) q^{41} +(2.72604 + 4.33847i) q^{42} +(6.20526 - 2.98830i) q^{43} +(-0.301023 - 0.105332i) q^{44} +(2.93288 + 2.93288i) q^{46} +(-2.16272 + 9.47549i) q^{47} +(-1.14032 - 1.42992i) q^{48} +(3.23926 - 0.739339i) q^{49} +(9.06106 + 7.22595i) q^{51} +(-3.91149 - 1.36869i) q^{52} +(-6.89339 + 2.41210i) q^{53} +(-4.44163 + 3.54208i) q^{54} +(-9.15852 + 3.20470i) q^{56} +(6.02705 - 6.02705i) q^{57} +(4.96550 + 2.36646i) q^{58} -6.55260i q^{59} +(6.95855 - 0.784041i) q^{61} +(-2.20248 - 0.248159i) q^{62} +(0.596659 + 1.70515i) q^{63} +(6.56823 - 3.16309i) q^{64} +(-0.450150 - 0.282848i) q^{66} +(6.35336 + 3.99208i) q^{67} +(-5.55205 + 4.42761i) q^{68} +(-3.37311 - 5.36827i) q^{69} +(-3.19119 - 0.728367i) q^{71} +(-0.736780 - 1.52994i) q^{72} +(-1.83366 - 3.80763i) q^{73} +(7.27608 + 1.66072i) q^{74} +(2.77864 + 4.42218i) q^{76} +(-0.837377 + 0.667786i) q^{77} +(-5.84924 - 3.67532i) q^{78} +(1.68732 + 1.06021i) q^{79} +(6.30409 - 3.03589i) q^{81} +(0.815745 + 2.33127i) q^{82} +(7.58032 + 0.854097i) q^{83} +(4.76884 - 0.537319i) q^{84} +7.03492i q^{86} +(-6.59486 - 5.21553i) q^{87} +(0.711889 - 0.711889i) q^{88} +(-9.71523 + 3.39950i) q^{89} +(-10.8809 + 8.67721i) q^{91} +(3.66678 - 1.28306i) q^{92} +(3.19781 + 1.11896i) q^{93} +(-7.76160 - 6.18967i) q^{94} +(-7.37277 + 1.68279i) q^{96} +(-0.740965 - 0.929141i) q^{97} +(-0.755184 + 3.30868i) q^{98} +(-0.132541 - 0.132541i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q + 14 q^{2} + 10 q^{3} + 22 q^{4} - 28 q^{6} + 10 q^{7} + 14 q^{8} - 10 q^{9} - 20 q^{11} + 20 q^{12} + 28 q^{13} - 4 q^{14} - 34 q^{16} - 84 q^{18} - 16 q^{21} + 22 q^{22} + 10 q^{23} - 56 q^{24}+ \cdots - 76 q^{99}+O(q^{100}) $ 156 * q + 14 * q^2 + 10 * q^3 + 22 * q^4 - 28 * q^6 + 10 * q^7 + 14 * q^8 - 10 * q^9 - 20 * q^11 + 20 * q^12 + 28 * q^13 - 4 * q^14 - 34 * q^16 - 84 * q^18 - 16 * q^21 + 22 * q^22 + 10 * q^23 - 56 * q^24 + 36 * q^26 - 32 * q^27 + 8 * q^28 - 8 * q^31 + 14 * q^32 + 14 * q^33 + 24 * q^34 + 78 * q^36 + 72 * q^37 + 120 * q^38 - 16 * q^39 - 22 * q^41 + 18 * q^42 - 2 * q^43 + 112 * q^44 + 4 * q^46 - 22 * q^47 - 38 * q^48 - 84 * q^49 - 28 * q^51 - 86 * q^52 - 56 * q^53 + 4 * q^56 + 12 * q^57 - 96 * q^58 - 46 * q^61 + 112 * q^62 - 158 * q^63 + 30 * q^64 - 48 * q^66 - 18 * q^67 - 140 * q^68 + 124 * q^69 - 28 * q^71 + 98 * q^72 + 84 * q^73 - 112 * q^74 - 48 * q^76 - 28 * q^77 - 70 * q^78 + 4 * q^79 + 58 * q^81 - 16 * q^82 - 46 * q^83 - 120 * q^84 - 68 * q^87 - 40 * q^88 - 46 * q^89 - 28 * q^91 + 14 * q^92 + 22 * q^93 + 84 * q^94 - 28 * q^96 + 76 * q^97 + 160 * q^98 - 76 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/725\mathbb{Z}\right)^\times$.

$n$	$176$	$552$
$\chi(n)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.443182	+	0.920277i	−0.313377	+	0.650734i	−0.996856	−	0.0792362i	$-0.974752\pi$
$2$	−0.443182	+	0.920277i	−0.313377	+	0.650734i	0.683479	+	0.729970i	$0.260466\pi$
$3$	0.973467	−	1.22069i	0.562032	−	0.704765i	−0.416900	−	0.908952i	$-0.636884\pi$
$3$	0.973467	−	1.22069i	0.562032	−	0.704765i	0.978932	+	0.204187i	$0.0654550\pi$
$4$	0.596480	+	0.747962i	0.298240	+	0.373981i
$5$		0			0
$5$		0			0
$6$	0.691949	+	1.43685i	0.282487	+	0.586591i
$7$	3.19267	−	0.359728i	1.20672	−	0.135964i	0.514395	−	0.857553i	$-0.328017\pi$
$7$	3.19267	−	0.359728i	1.20672	−	0.135964i	0.692322	+	0.721589i	$0.256588\pi$
$8$	−2.94432	+	0.672023i	−1.04098	+	0.237596i
$9$	0.125119	+	0.548181i	0.0417063	+	0.182727i
$10$		0			0
$11$	−0.282265	+	0.177359i	−0.0851060	+	0.0534756i	−0.573913	−	0.818916i	$-0.694575\pi$
$11$	−0.282265	+	0.177359i	−0.0851060	+	0.0534756i	0.488807	+	0.872392i	$0.337432\pi$
$12$	1.49368			0.431189
$13$	−3.66774	+	2.30460i	−1.01725	+	0.639180i	−0.933972	−	0.357347i	$-0.883681\pi$
$13$	−3.66774	+	2.30460i	−1.01725	+	0.639180i	−0.0832770	+	0.996526i	$0.526539\pi$
$14$	−1.08389	+	3.09757i	−0.289681	+	0.827860i
$15$		0			0
$16$	0.260662	−	1.14204i	0.0651655	−	0.285509i
$17$			7.42290i			1.80032i	0.435561	+	0.900159i	$0.356550\pi$
$17$			7.42290i			1.80032i	−0.435561	+	0.900159i	$0.643450\pi$
$18$	−0.559929	−	0.127800i	−0.131977	−	0.0301228i
$19$	5.42486	+	0.611234i	1.24455	+	0.140227i	0.709567	−	0.704638i	$-0.248890\pi$
$19$	5.42486	+	0.611234i	1.24455	+	0.140227i	0.534980	+	0.844865i	$0.320319\pi$
$20$		0			0
$21$	2.66885	−	4.24744i	0.582390	−	0.926868i
$22$	−0.0381244	−	0.338364i	−0.00812816	−	0.0721394i
$23$	1.34116	−	3.83282i	0.279652	−	0.799199i	−0.715297	−	0.698820i	$-0.753709\pi$
$23$	1.34116	−	3.83282i	0.279652	−	0.799199i	0.994949	−	0.100379i	$-0.0320055\pi$
$24$	−2.04587	+	4.24830i	−0.417612	+	0.867180i
$25$		0			0
$26$	−0.495389	−	4.39670i	−0.0971537	−	0.862263i
$27$	5.01106	+	2.41320i	0.964379	+	0.464421i
$28$	2.17343	+	2.17343i	0.410739	+	0.410739i
$29$	−0.0218780	−	5.38512i	−0.00406265	−	0.999992i
$29$	−0.0218780	−	5.38512i	−0.00406265	−	0.999992i
$30$		0			0
$31$	0.716676	+	2.04814i	0.128719	+	0.367857i	0.990149	−	0.140019i	$-0.0447164\pi$
$31$	0.716676	+	2.04814i	0.128719	+	0.367857i	−0.861430	+	0.507876i	$0.830431\pi$
$32$	−3.78686	−	3.01992i	−0.669429	−	0.533852i
$33$	−0.0582756	+	0.517210i	−0.0101445	+	0.0900347i
$34$	−6.83113	−	3.28970i	−1.17153	−	0.564178i
$35$		0			0
$36$	−0.335388	+	0.420563i	−0.0558980	+	0.0700939i
$37$	−1.62587	−	7.12342i	−0.267292	−	1.17108i	−0.913149	−	0.407625i	$-0.866357\pi$
$37$	−1.62587	−	7.12342i	−0.267292	−	1.17108i	0.645857	−	0.763458i	$-0.276500\pi$
$38$	−2.96670	+	4.72148i	−0.481263	+	0.765926i
$39$	−0.757232	+	6.72062i	−0.121254	+	1.07616i
$40$		0			0
$41$	1.70982	−	1.70982i	0.267029	−	0.267029i	−0.560873	−	0.827902i	$-0.689534\pi$
$41$	1.70982	−	1.70982i	0.267029	−	0.267029i	0.827902	+	0.560873i	$0.189534\pi$
$42$	2.72604	+	4.33847i	0.420637	+	0.669440i
$43$	6.20526	−	2.98830i	0.946294	−	0.455711i	0.103908	−	0.994587i	$-0.466865\pi$
$43$	6.20526	−	2.98830i	0.946294	−	0.455711i	0.842385	+	0.538876i	$0.181151\pi$
$44$	−0.301023	−	0.105332i	−0.0453809	−	0.0158795i
$45$		0			0
$46$	2.93288	+	2.93288i	0.432430	+	0.432430i
$47$	−2.16272	+	9.47549i	−0.315465	+	1.38214i	0.529949	+	0.848030i	$0.322211\pi$
$47$	−2.16272	+	9.47549i	−0.315465	+	1.38214i	−0.845414	+	0.534112i	$0.820646\pi$
$48$	−1.14032	−	1.42992i	−0.164592	−	0.206391i
$49$	3.23926	−	0.739339i	0.462751	−	0.105620i
$50$		0			0
$51$	9.06106	+	7.22595i	1.26880	+	1.01184i
$52$	−3.91149	−	1.36869i	−0.542425	−	0.189803i
$53$	−6.89339	+	2.41210i	−0.946880	+	0.331328i	−0.759167	−	0.650896i	$-0.774393\pi$
$53$	−6.89339	+	2.41210i	−0.946880	+	0.331328i	−0.187713	+	0.982224i	$0.560108\pi$
$54$	−4.44163	+	3.54208i	−0.604429	+	0.482016i
$55$		0			0
$56$	−9.15852	+	3.20470i	−1.22386	+	0.428247i
$57$	6.02705	−	6.02705i	0.798302	−	0.798302i
$58$	4.96550	+	2.36646i	0.652002	+	0.310731i
$59$		−	6.55260i		−	0.853075i	−0.904470	−	0.426538i	$-0.859733\pi$
$59$		−	6.55260i		−	0.853075i	0.904470	−	0.426538i	$-0.140267\pi$
$60$		0			0
$61$	6.95855	−	0.784041i	0.890952	−	0.100386i	0.345392	−	0.938458i	$-0.387746\pi$
$61$	6.95855	−	0.784041i	0.890952	−	0.100386i	0.545559	+	0.838072i	$0.316317\pi$
$62$	−2.20248	−	0.248159i	−0.279715	−	0.0315163i
$63$	0.596659	+	1.70515i	0.0751720	+	0.214829i
$64$	6.56823	−	3.16309i	0.821029	−	0.395387i
$65$		0			0
$66$	−0.450150	−	0.282848i	−0.0554096	−	0.0348162i
$67$	6.35336	+	3.99208i	0.776186	+	0.487710i	0.860949	−	0.508691i	$-0.169870\pi$
$67$	6.35336	+	3.99208i	0.776186	+	0.487710i	−0.0847630	+	0.996401i	$0.527013\pi$
$68$	−5.55205	+	4.42761i	−0.673285	+	0.536927i
$69$	−3.37311	−	5.36827i	−0.406075	−	0.646264i
$70$		0			0
$71$	−3.19119	−	0.728367i	−0.378724	−	0.0864413i	0.0289212	−	0.999582i	$-0.490793\pi$
$71$	−3.19119	−	0.728367i	−0.378724	−	0.0864413i	−0.407645	+	0.913140i	$0.633650\pi$
$72$	−0.736780	−	1.52994i	−0.0868304	−	0.180305i
$73$	−1.83366	−	3.80763i	−0.214614	−	0.445650i	0.765673	−	0.643230i	$-0.222406\pi$
$73$	−1.83366	−	3.80763i	−0.214614	−	0.445650i	−0.980287	+	0.197580i	$0.936692\pi$
$74$	7.27608	+	1.66072i	0.845827	+	0.193055i
$75$		0			0
$76$	2.77864	+	4.42218i	0.318732	+	0.507258i
$77$	−0.837377	+	0.667786i	−0.0954280	+	0.0761013i
$78$	−5.84924	−	3.67532i	−0.662296	−	0.416148i
$79$	1.68732	+	1.06021i	0.189838	+	0.119283i	0.623598	−	0.781746i	$-0.285670\pi$
$79$	1.68732	+	1.06021i	0.189838	+	0.119283i	−0.433760	+	0.901029i	$0.642813\pi$
$80$		0			0
$81$	6.30409	−	3.03589i	0.700454	−	0.337321i
$82$	0.815745	+	2.33127i	0.0900840	+	0.257445i
$83$	7.58032	+	0.854097i	0.832048	+	0.0937493i	0.517704	−	0.855560i	$-0.326787\pi$
$83$	7.58032	+	0.854097i	0.832048	+	0.0937493i	0.314344	+	0.949309i	$0.398215\pi$
$84$	4.76884	−	0.537319i	0.520323	−	0.0586264i
$85$		0			0
$86$			7.03492i			0.758595i
$87$	−6.59486	−	5.21553i	−0.707043	−	0.559164i
$88$	0.711889	−	0.711889i	0.0758877	−	0.0758877i
$89$	−9.71523	+	3.39950i	−1.02981	+	0.360347i	−0.791712	−	0.610894i	$-0.790810\pi$
$89$	−9.71523	+	3.39950i	−1.02981	+	0.360347i	−0.238100	+	0.971241i	$0.576524\pi$
$90$		0			0
$91$	−10.8809	+	8.67721i	−1.14063	+	0.909618i
$92$	3.66678	−	1.28306i	0.382289	−	0.133769i
$93$	3.19781	+	1.11896i	0.331597	+	0.116031i
$94$	−7.76160	−	6.18967i	−0.800547	−	0.638415i
$95$		0			0
$96$	−7.37277	+	1.68279i	−0.752480	+	0.171749i
$97$	−0.740965	−	0.929141i	−0.0752336	−	0.0943400i	0.742790	−	0.669524i	$-0.233502\pi$
$97$	−0.740965	−	0.929141i	−0.0752336	−	0.0943400i	−0.818024	+	0.575184i	$0.804930\pi$
$98$	−0.755184	+	3.30868i	−0.0762851	+	0.334227i
$99$	−0.132541	−	0.132541i	−0.0133209	−	0.0133209i
$100$		0			0
$101$	−8.62410	−	3.01770i	−0.858130	−	0.300273i	−0.134882	−	0.990862i	$-0.543066\pi$
$101$	−8.62410	−	3.01770i	−0.858130	−	0.300273i	−0.723247	+	0.690589i	$0.757351\pi$
$102$	−10.6656	+	5.13627i	−1.05605	+	0.508567i
$103$	−5.62139	−	8.94639i	−0.553892	−	0.881514i	0.446017	−	0.895025i	$-0.352842\pi$
$103$	−5.62139	−	8.94639i	−0.553892	−	0.881514i	−0.999909	+	0.0135104i	$0.995699\pi$
$104$	9.25028	−	9.25028i	0.907065	−	0.907065i
$105$		0			0
$106$	0.835225	−	7.41283i	0.0811242	−	0.719997i
$107$	4.63405	−	7.37505i	0.447990	−	0.712973i	−0.544028	−	0.839067i	$-0.683101\pi$
$107$	4.63405	−	7.37505i	0.447990	−	0.712973i	0.992018	+	0.126094i	$0.0402443\pi$
$108$	1.18402	+	5.18751i	0.113932	+	0.499168i
$109$	−3.50666	+	4.39721i	−0.335877	+	0.421177i	−0.920875	−	0.389858i	$-0.872524\pi$
$109$	−3.50666	+	4.39721i	−0.335877	+	0.421177i	0.584998	+	0.811035i	$0.301095\pi$
$110$		0			0
$111$	−10.2782	−	4.94973i	−0.975566	−	0.469808i
$112$	0.421387	−	3.73991i	0.0398173	−	0.353388i
$113$	0.182774	+	0.145757i	0.0171939	+	0.0137117i	0.632049	−	0.774928i	$-0.282214\pi$
$113$	0.182774	+	0.145757i	0.0171939	+	0.0137117i	−0.614855	+	0.788640i	$0.710786\pi$
$114$	2.87547	+	8.21763i	0.269313	+	0.769652i
$115$		0			0
$116$	4.01482	−	3.22848i	0.372766	−	0.299757i
$117$	−1.72224	−	1.72224i	−0.159221	−	0.159221i
$118$	6.03020	+	2.90399i	0.555125	+	0.267334i
$119$	2.67022	+	23.6989i	0.244779	+	2.17247i
$120$		0			0
$121$	−4.72450	+	9.81053i	−0.429500	+	0.891867i
$122$	−2.36237	+	6.75127i	−0.213879	+	0.611231i
$123$	−0.422705	−	3.75161i	−0.0381140	−	0.338271i
$124$	−1.10445	+	1.75772i	−0.0991826	+	0.157848i
$125$		0			0
$126$	−1.83364	−	0.206602i	−0.163354	−	0.0184056i
$127$	−5.26685	−	1.20212i	−0.467358	−	0.106671i	−0.0176444	−	0.999844i	$-0.505617\pi$
$127$	−5.26685	−	1.20212i	−0.467358	−	0.106671i	−0.449713	+	0.893173i	$0.648474\pi$
$128$		−	2.24073i		−	0.198055i
$129$	2.39284	−	10.4837i	0.210678	−	0.923039i
$130$		0			0
$131$	2.90820	−	8.31115i	0.254091	−	0.726149i	−0.744214	−	0.667941i	$-0.767176\pi$
$131$	2.90820	−	8.31115i	0.254091	−	0.726149i	0.998304	−	0.0582077i	$-0.0185386\pi$
$132$	−0.421614	+	0.264918i	−0.0366968	+	0.0230581i
$133$	17.5397			1.52088
$134$	−6.48951	+	4.07763i	−0.560609	+	0.352254i
$135$		0			0
$136$	−4.98836	−	21.8554i	−0.427748	−	1.87409i
$137$	−5.93617	+	1.35489i	−0.507161	+	0.115756i	−0.468443	−	0.883494i	$-0.655185\pi$
$137$	−5.93617	+	1.35489i	−0.507161	+	0.115756i	−0.0387184	+	0.999250i	$0.512328\pi$
$138$	6.43520	−	0.725073i	0.547801	−	0.0617223i
$139$	−8.13195	−	16.8862i	−0.689743	−	1.43227i	−0.891588	−	0.452848i	$-0.850408\pi$
$139$	−8.13195	−	16.8862i	−0.689743	−	1.43227i	0.201845	−	0.979418i	$-0.435306\pi$
$140$		0			0
$141$	9.46129	+	11.8641i	0.796784	+	0.999136i
$142$	2.08458	−	2.61398i	0.174934	−	0.219360i
$143$	0.626534	−	1.30101i	0.0523934	−	0.108796i
$144$	0.658656			0.0548880
$145$		0			0
$146$	4.31672			0.357255
$147$	2.25081	−	4.67385i	0.185643	−	0.385493i
$148$	4.35825	−	5.46507i	0.358246	−	0.449226i
$149$	−12.0345	−	15.0908i	−0.985904	−	1.23628i	−0.971659	−	0.236386i	$-0.924037\pi$
$149$	−12.0345	−	15.0908i	−0.985904	−	1.23628i	−0.0142448	−	0.999899i	$-0.504534\pi$
$150$		0			0
$151$	−7.58945	−	15.7597i	−0.617621	−	1.28250i	−0.941694	−	0.336471i	$-0.890767\pi$
$151$	−7.58945	−	15.7597i	−0.617621	−	1.28250i	0.324073	−	0.946032i	$-0.394948\pi$
$152$	−16.3833	+	1.84595i	−1.32886	+	0.149727i
$153$	−4.06909	+	0.928744i	−0.328967	+	0.0750845i
$154$	−0.243438	−	1.06657i	−0.0196168	−	0.0859467i
$155$		0			0
$156$	−5.47845	+	3.44234i	−0.438627	+	0.275607i
$157$	18.5421			1.47982			0.739910	−	0.672706i	$-0.234868\pi$
$157$	18.5421			1.47982			0.739910	+	0.672706i	$0.234868\pi$
$158$	−1.72348	+	1.08293i	−0.137112	+	0.0861534i
$159$	−3.76606	+	10.7628i	−0.298668	+	0.853545i
$160$		0			0
$161$	2.90312	−	12.7194i	0.228798	−	1.00243i
$162$			7.14696i			0.561518i
$163$	−1.92140	−	0.438548i	−0.150496	−	0.0343497i	0.146609	−	0.989195i	$-0.453164\pi$
$163$	−1.92140	−	0.438548i	−0.150496	−	0.0343497i	−0.297105	+	0.954845i	$0.596021\pi$
$164$	2.29875	+	0.259007i	0.179502	+	0.0202250i
$165$		0			0
$166$	−4.14547	+	6.59747i	−0.321751	+	0.512063i
$167$	−1.08881	−	9.66345i	−0.0842546	−	0.747780i	−0.962817	−	0.270153i	$-0.912926\pi$
$167$	−1.08881	−	9.66345i	−0.0842546	−	0.747780i	0.878563	−	0.477627i	$-0.158503\pi$
$168$	−5.00357	+	14.2994i	−0.386034	+	1.10322i
$169$	2.50069	−	5.19273i	0.192361	−	0.399441i
$170$		0			0
$171$	0.343684	+	3.05028i	0.0262822	+	0.233261i
$172$	5.93645	+	2.85884i	0.452650	+	0.217985i
$173$	−0.563496	−	0.563496i	−0.0428418	−	0.0428418i	0.685361	−	0.728203i	$-0.259644\pi$
$173$	−0.563496	−	0.563496i	−0.0428418	−	0.0428418i	−0.728203	+	0.685361i	$0.759644\pi$
$174$	7.72246	−	3.75767i	0.585438	−	0.284868i
$175$		0			0
$176$	0.128974	+	0.368587i	0.00972179	+	0.0277833i
$177$	−7.99868	−	6.37874i	−0.601218	−	0.479455i
$178$	1.17713	−	10.4473i	0.0882295	−	0.783058i
$179$	1.04193	+	0.501769i	0.0778778	+	0.0375040i	0.472417	−	0.881375i	$-0.343382\pi$
$179$	1.04193	+	0.501769i	0.0778778	+	0.0375040i	−0.394539	+	0.918879i	$0.629096\pi$
$180$		0			0
$181$	−8.53309	+	10.7002i	−0.634260	+	0.795337i	−0.990272	−	0.139145i	$-0.955565\pi$
$181$	−8.53309	+	10.7002i	−0.634260	+	0.795337i	0.356012	+	0.934481i	$0.384136\pi$
$182$	−3.16323	−	13.8590i	−0.234474	−	1.02730i
$183$	5.81685	−	9.25747i	0.429994	−	0.684332i
$184$	−1.37307	+	12.1864i	−0.101224	+	0.898391i
$185$		0			0
$186$	−2.44696	+	2.44696i	−0.179420	+	0.179420i
$187$	−1.31652	−	2.09522i	−0.0962731	−	0.153218i
$188$	−8.37732	+	4.03431i	−0.610979	+	0.294232i
$189$	16.8668	+	5.90194i	1.22688	+	0.429303i
$190$		0			0
$191$	10.1739	+	10.1739i	0.736156	+	0.736156i	0.971832	−	0.235676i	$-0.0757304\pi$
$191$	10.1739	+	10.1739i	0.736156	+	0.736156i	−0.235676	+	0.971832i	$0.575730\pi$
$192$	2.53280	−	11.0969i	0.182789	−	0.800853i
$193$	−0.132503	−	0.166154i	−0.00953779	−	0.0119600i	0.777040	−	0.629452i	$-0.216720\pi$
$193$	−0.132503	−	0.166154i	−0.00953779	−	0.0119600i	−0.786578	+	0.617492i	$0.788149\pi$
$194$	1.18345	−	0.270115i	0.0849667	−	0.0193931i
$195$		0			0
$196$	2.48515	+	1.98184i	0.177511	+	0.141560i
$197$	1.29341	+	0.452582i	0.0921514	+	0.0322452i	0.375961	−	0.926635i	$-0.377313\pi$
$197$	1.29341	+	0.452582i	0.0921514	+	0.0322452i	−0.283810	+	0.958881i	$0.591598\pi$
$198$	0.180715	−	0.0632348i	0.0128428	−	0.00449390i
$199$	16.6181	−	13.2525i	1.17802	−	0.939443i	0.179011	−	0.983847i	$-0.442710\pi$
$199$	16.6181	−	13.2525i	1.17802	−	0.939443i	0.999014	+	0.0444042i	$0.0141389\pi$
$200$		0			0
$201$	11.0579	−	3.86932i	0.779962	−	0.272921i
$202$	6.59917	−	6.59917i	0.464316	−	0.464316i
$203$	−2.00703	−	17.1851i	−0.140866	−	1.20615i
$204$			11.0875i			0.776278i
$205$		0			0
$206$	10.7245	−	1.20836i	0.747209	−	0.0841902i
$207$	2.26889	+	0.255642i	0.157699	+	0.0177684i
$208$	1.67589	+	4.78941i	0.116202	+	0.332086i
$209$	−1.63965	+	0.789615i	−0.113417	+	0.0546188i
$210$		0			0
$211$	0.0410704	+	0.0258062i	0.00282740	+	0.00177657i	0.533445	−	0.845835i	$-0.320897\pi$
$211$	0.0410704	+	0.0258062i	0.00282740	+	0.00177657i	−0.530618	+	0.847611i	$0.678040\pi$
$212$	−5.91593	−	3.71722i	−0.406308	−	0.255300i
$213$	−3.99562	+	3.18640i	−0.273776	+	0.218329i
$214$	4.73336	+	7.53310i	0.323566	+	0.514952i
$215$		0			0
$216$	−16.3759	−	3.73770i	−1.11424	−	0.254318i
$217$	3.02488	+	6.28124i	0.205343	+	0.426398i
$218$	−2.49257	−	5.17587i	−0.168818	−	0.350554i
$219$	−6.43295	−	1.46828i	−0.434698	−	0.0992170i
$220$		0			0
$221$	−17.1068	−	27.2253i	−1.15073	−	1.83137i
$222$	9.11025	−	7.26518i	0.611440	−	0.487607i
$223$	−10.4384	−	6.55891i	−0.699010	−	0.439217i	0.135088	−	0.990834i	$-0.456868\pi$
$223$	−10.4384	−	6.55891i	−0.699010	−	0.439217i	−0.834098	+	0.551616i	$0.814011\pi$
$224$	−13.1766	−	8.27938i	−0.880396	−	0.553189i
$225$		0			0
$226$	−0.215139	+	0.103606i	−0.0143108	+	0.00689174i
$227$	−3.37134	−	9.63473i	−0.223764	−	0.639480i	−0.999960	−	0.00898794i	$-0.997139\pi$
$227$	−3.37134	−	9.63473i	−0.223764	−	0.639480i	0.776196	−	0.630492i	$-0.217147\pi$
$228$	8.10302	+	0.912991i	0.536635	+	0.0604643i
$229$	20.6689	−	2.32882i	1.36584	−	0.153893i	0.601584	−	0.798810i	$-0.294537\pi$
$229$	20.6689	−	2.32882i	1.36584	−	0.153893i	0.764253	+	0.644917i	$0.223108\pi$
$230$		0			0
$231$			1.67225i			0.110026i
$232$	3.68334	+	15.8408i	0.241823	+	1.04000i
$233$	15.9794	−	15.9794i	1.04684	−	1.04684i	0.0479964	−	0.998848i	$-0.484716\pi$
$233$	15.9794	−	15.9794i	1.04684	−	1.04684i	0.998848	−	0.0479964i	$-0.0152836\pi$
$234$	2.34820	−	0.821672i	0.153507	−	0.0537144i
$235$		0			0
$236$	4.90109	−	3.90849i	0.319034	−	0.254421i
$237$	2.93674	−	1.02761i	0.190761	−	0.0667503i
$238$	−22.9929	−	8.04558i	−1.49041	−	0.521517i
$239$	−10.5217	−	8.39081i	−0.680595	−	0.542757i	0.221034	−	0.975266i	$-0.429057\pi$
$239$	−10.5217	−	8.39081i	−0.680595	−	0.542757i	−0.901629	+	0.432509i	$0.857628\pi$
$240$		0			0
$241$	7.37877	−	1.68416i	0.475309	−	0.108486i	0.0218459	−	0.999761i	$-0.493046\pi$
$241$	7.37877	−	1.68416i	0.475309	−	0.108486i	0.453463	+	0.891275i	$0.350189\pi$
$242$	−6.93459	−	8.69571i	−0.445773	−	0.558981i
$243$	−1.28194	+	5.61656i	−0.0822368	+	0.360303i
$244$	4.73707	+	4.73707i	0.303260	+	0.303260i
$245$		0			0
$246$	3.63985	+	1.27364i	0.232069	+	0.0812043i
$247$	−21.3056	+	10.2602i	−1.35564	+	0.652844i
$248$	−3.48652	−	5.54877i	−0.221395	−	0.352347i
$249$	8.42178	−	8.42178i	0.533709	−	0.533709i
$250$		0			0
$251$	−2.50604	+	22.2418i	−0.158180	+	1.40389i	0.624287	+	0.781195i	$0.285390\pi$
$251$	−2.50604	+	22.2418i	−0.158180	+	1.40389i	−0.782467	+	0.622692i	$0.786039\pi$
$252$	−0.919496	+	1.46337i	−0.0579228	+	0.0921836i
$253$	0.301221	+	1.31974i	0.0189376	+	0.0829712i
$254$	3.44046	−	4.31420i	0.215874	−	0.270697i
$255$		0			0
$256$	15.1986	+	7.31924i	0.949910	+	0.457453i
$257$	1.87619	−	16.6517i	0.117034	−	1.03870i	−0.788677	−	0.614807i	$-0.789234\pi$
$257$	1.87619	−	16.6517i	0.117034	−	1.03870i	0.905711	−	0.423895i	$-0.139338\pi$
$258$	8.58745	+	6.84827i	0.534632	+	0.426354i
$259$	−7.75338	−	22.1579i	−0.481771	−	1.37682i
$260$		0			0
$261$	2.94928	−	0.685773i	0.182556	−	0.0424483i
$262$	6.35970	+	6.35970i	0.392904	+	0.392904i
$263$	−8.21450	−	3.95590i	−0.506528	−	0.243931i	0.163125	−	0.986605i	$-0.447843\pi$
$263$	−8.21450	−	3.95590i	−0.506528	−	0.243931i	−0.669653	+	0.742674i	$0.733557\pi$
$264$	−0.175995	−	1.56200i	−0.0108317	−	0.0961343i
$265$		0			0
$266$	−7.77327	+	16.1414i	−0.476610	+	0.989690i
$267$	−5.30772	+	15.1686i	−0.324827	+	0.928302i
$268$	0.803726	+	7.13327i	0.0490954	+	0.435734i
$269$	2.83114	−	4.50574i	0.172618	−	0.274720i	−0.749199	−	0.662344i	$-0.769562\pi$
$269$	2.83114	−	4.50574i	0.172618	−	0.274720i	0.921817	+	0.387625i	$0.126704\pi$
$270$		0			0
$271$	1.33774	+	0.150727i	0.0812619	+	0.00915602i	0.152502	−	0.988303i	$-0.451267\pi$
$271$	1.33774	+	0.150727i	0.0812619	+	0.00915602i	−0.0712399	+	0.997459i	$0.522696\pi$
$272$	8.47722	+	1.93487i	0.514007	+	0.117319i
$273$			21.7291i			1.31511i
$274$	1.38393	−	6.06338i	0.0836061	−	0.366302i
$275$		0			0
$276$	2.00327	−	5.72503i	0.120583	−	0.344606i
$277$	−18.9088	+	11.8812i	−1.13612	+	0.713871i	−0.962591	−	0.270958i	$-0.912660\pi$
$277$	−18.9088	+	11.8812i	−1.13612	+	0.713871i	−0.173528	+	0.984829i	$0.555517\pi$
$278$	19.1439			1.14817
$279$	−1.03308	+	0.649129i	−0.0618491	+	0.0388624i
$280$		0			0
$281$	−1.16627	−	5.10977i	−0.0695739	−	0.304823i	0.928154	−	0.372197i	$-0.121395\pi$
$281$	−1.16627	−	5.10977i	−0.0695739	−	0.304823i	−0.997728	+	0.0673733i	$0.978538\pi$
$282$	−15.1113	+	3.44906i	−0.899866	+	0.205389i
$283$	25.7594	−	2.90239i	1.53124	−	0.172529i	0.694244	−	0.719739i	$-0.255739\pi$
$283$	25.7594	−	2.90239i	1.53124	−	0.172529i	0.836995	+	0.547210i	$0.184310\pi$
$284$	−1.35869	−	2.82134i	−0.0806232	−	0.167416i
$285$		0			0
$286$	0.919622	+	1.15317i	0.0543784	+	0.0681884i
$287$	4.84382	−	6.07395i	0.285921	−	0.358534i
$288$	1.18166	−	2.45373i	0.0696298	−	0.144588i
$289$	−38.0995			−2.24115
$290$		0			0
$291$	−1.85550			−0.108771
$292$	1.75422	−	3.64269i	0.102658	−	0.213172i
$293$	−14.2954	+	17.9259i	−0.835149	+	1.04724i	0.163012	+	0.986624i	$0.447879\pi$
$293$	−14.2954	+	17.9259i	−0.835149	+	1.04724i	−0.998161	+	0.0606195i	$0.980692\pi$
$294$	3.30372	+	4.14273i	0.192677	+	0.241609i
$295$		0			0
$296$	9.57420	+	19.8810i	0.556489	+	1.15556i
$297$	−1.84245	+	0.207594i	−0.106910	+	0.0120458i
$298$	19.2212	−	4.38711i	1.11345	−	0.254138i
$299$	3.91407	+	17.1487i	0.226356	+	0.991732i
$300$		0			0
$301$	18.7364	−	11.7729i	1.07995	−	0.678576i
$302$	17.8668			1.02812
$303$	−12.0790	+	7.58971i	−0.693918	+	0.436017i
$304$	2.11211	−	6.03605i	0.121138	−	0.346191i
$305$		0			0
$306$	0.948648	−	4.15630i	0.0542306	−	0.237600i
$307$			31.7559i			1.81240i	0.422844	+	0.906202i	$0.361032\pi$
$307$			31.7559i			1.81240i	−0.422844	+	0.906202i	$0.638968\pi$
$308$	−0.998958	−	0.228006i	−0.0569209	−	0.0129918i
$309$	−16.3930	−	1.84705i	−0.932566	−	0.105075i
$310$		0			0
$311$	−1.19084	+	1.89521i	−0.0675263	+	0.107468i	−0.878781	−	0.477226i	$-0.841642\pi$
$311$	−1.19084	+	1.89521i	−0.0675263	+	0.107468i	0.811254	+	0.584693i	$0.198785\pi$
$312$	−2.28687	−	20.2966i	−0.129469	−	1.14907i
$313$	3.53606	−	10.1055i	0.199870	−	0.571196i	−0.799704	−	0.600395i	$-0.795010\pi$
$313$	3.53606	−	10.1055i	0.199870	−	0.571196i	0.999574	+	0.0291992i	$0.00929571\pi$
$314$	−8.21752	+	17.0639i	−0.463741	+	0.962969i
$315$		0			0
$316$	0.213453	+	1.89444i	0.0120076	+	0.106571i
$317$	20.1277	+	9.69299i	1.13048	+	0.544413i	0.903116	−	0.429396i	$-0.141274\pi$
$317$	20.1277	+	9.69299i	1.13048	+	0.544413i	0.227368	+	0.973809i	$0.426988\pi$
$318$	−8.23570	−	8.23570i	−0.461835	−	0.461835i
$319$	0.961273	+	1.51615i	0.0538209	+	0.0848880i
$320$		0			0
$321$	−4.49155	−	12.8361i	−0.250694	−	0.716441i
$322$	10.4188	+	8.30869i	0.580615	+	0.463025i
$323$	−4.53713	+	40.2682i	−0.252453	+	2.24058i
$324$	6.03099	+	2.90437i	0.335055	+	0.161354i
$325$		0			0
$326$	1.25512	−	1.57387i	0.0695146	−	0.0871685i
$327$	1.95401	+	8.56109i	0.108057	+	0.473429i
$328$	−3.88522	+	6.18329i	−0.214525	+	0.341415i
$329$	−3.49625	+	31.0301i	−0.192755	+	1.71075i
$330$		0			0
$331$	−8.77860	+	8.77860i	−0.482516	+	0.482516i	−0.905934	−	0.423418i	$-0.860830\pi$
$331$	−8.77860	+	8.77860i	−0.482516	+	0.482516i	0.423418	+	0.905934i	$0.360830\pi$
$332$	3.88268	+	6.17924i	0.213090	+	0.339130i
$333$	3.70150	−	1.78255i	0.202841	−	0.0976830i
$334$	9.37559	+	3.28066i	0.513009	+	0.179510i
$335$		0			0
$336$	−4.15506	−	4.15506i	−0.226677	−	0.226677i
$337$	0.316965	−	1.38871i	0.0172662	−	0.0756481i	−0.965561	−	0.260177i	$-0.916219\pi$
$337$	0.316965	−	1.38871i	0.0172662	−	0.0756481i	0.982827	+	0.184529i	$0.0590761\pi$
$338$	3.67049	+	4.60265i	0.199648	+	0.250351i
$339$	0.355849	−	0.0812201i	0.0193270	−	0.00441127i
$340$		0			0
$341$	−0.565548	−	0.451009i	−0.0306261	−	0.0244235i
$342$	−2.95942	−	1.03555i	−0.160027	−	0.0559959i
$343$	−11.1521	+	3.90230i	−0.602158	+	0.210704i
$344$	−16.2621	+	12.9686i	−0.876794	+	0.699220i
$345$		0			0
$346$	0.768304	−	0.268841i	0.0413043	−	0.0144530i
$347$	−14.4583	+	14.4583i	−0.776163	+	0.776163i	−0.979176	−	0.203013i	$-0.934927\pi$
$347$	−14.4583	+	14.4583i	−0.776163	+	0.776163i	0.203013	+	0.979176i	$0.434927\pi$
$348$	−0.0326789	−	8.04366i	−0.00175177	−	0.431186i
$349$			28.1957i			1.50928i	0.656138	+	0.754641i	$0.272189\pi$
$349$			28.1957i			1.50928i	−0.656138	+	0.754641i	$0.727811\pi$
$350$		0			0
$351$	−23.9407	+	2.69747i	−1.27786	+	0.143980i
$352$	1.60451	+	0.180784i	0.0855204	+	0.00963584i
$353$	1.86690	+	5.33528i	0.0993648	+	0.283968i	0.982826	−	0.184537i	$-0.0590785\pi$
$353$	1.86690	+	5.33528i	0.0993648	+	0.283968i	−0.883461	+	0.468505i	$0.844793\pi$
$354$	9.41508	−	4.53406i	0.500406	−	0.240983i
$355$		0			0
$356$	−8.33764	−	5.23889i	−0.441894	−	0.277660i
$357$	31.5284	+	19.8106i	1.66866	+	1.04849i
$358$	−0.923533	+	0.736493i	−0.0488103	+	0.0389249i
$359$	−0.405361	−	0.645128i	−0.0213941	−	0.0340486i	0.835856	−	0.548949i	$-0.184972\pi$
$359$	−0.405361	−	0.645128i	−0.0213941	−	0.0340486i	−0.857250	+	0.514900i	$0.827829\pi$
$360$		0			0
$361$	10.5318	+	2.40382i	0.554307	+	0.126517i
$362$	−6.06540	−	12.5949i	−0.318790	−	0.661975i
$363$	7.37646	+	15.3174i	0.387164	+	0.803954i
$364$	−12.9804	−	2.96270i	−0.680360	−	0.155288i
$365$		0			0
$366$	5.94151	+	9.45586i	0.310568	+	0.494266i
$367$	1.86997	−	1.49125i	0.0976119	−	0.0778429i	−0.573468	−	0.819228i	$-0.694402\pi$
$367$	1.86997	−	1.49125i	0.0976119	−	0.0778429i	0.671080	+	0.741385i	$0.265831\pi$
$368$	−4.02763	−	2.53073i	−0.209955	−	0.131923i
$369$	1.15122	+	0.723359i	0.0599301	+	0.0376566i
$370$		0			0
$371$	−21.1406	+	10.1808i	−1.09757	+	0.528560i
$372$	1.07049	+	3.05928i	0.0555022	+	0.158616i
$373$	−15.9897	−	1.80161i	−0.827916	−	0.0932837i	−0.312171	−	0.950026i	$-0.601056\pi$
$373$	−15.9897	−	1.80161i	−0.827916	−	0.0932837i	−0.515745	+	0.856742i	$0.672485\pi$
$374$	2.51164	−	0.282994i	0.129874	−	0.0146333i
$375$		0			0
$376$		−	29.3523i		−	1.51373i
$377$	12.4908	+	19.7008i	0.643307	+	1.01464i
$378$	−12.9065	+	12.9065i	−0.663837	+	0.663837i
$379$	−15.5819	+	5.45235i	−0.800390	+	0.280069i	−0.699318	−	0.714811i	$-0.746513\pi$
$379$	−15.5819	+	5.45235i	−0.800390	+	0.280069i	−0.101072	+	0.994879i	$0.532227\pi$
$380$		0			0
$381$	−6.59453	+	5.25896i	−0.337848	+	0.269425i
$382$	−13.8717	+	4.85391i	−0.709736	+	0.248347i
$383$	4.41190	+	1.54379i	0.225437	+	0.0788840i	0.440634	−	0.897687i	$-0.354754\pi$
$383$	4.41190	+	1.54379i	0.225437	+	0.0788840i	−0.215197	+	0.976571i	$0.569039\pi$
$384$	−2.73524	−	2.18128i	−0.139582	−	0.111313i
$385$		0			0
$386$	0.211631	−	0.0483033i	0.0107717	−	0.00245857i
$387$	2.41452	+	3.02772i	0.122737	+	0.153907i
$388$	0.252991	−	1.10843i	0.0128437	−	0.0562719i
$389$	26.3154	+	26.3154i	1.33424	+	1.33424i	0.901533	+	0.432711i	$0.142443\pi$
$389$	26.3154	+	26.3154i	1.33424	+	1.33424i	0.432711	+	0.901533i	$0.357557\pi$
$390$		0			0
$391$	28.4507	+	9.95532i	1.43881	+	0.503462i
$392$	−9.04057	+	4.35371i	−0.456618	+	0.219895i
$393$	−7.31430	−	11.6406i	−0.368958	−	0.587193i
$394$	−0.989716	+	0.989716i	−0.0498612	+	0.0498612i
$395$		0			0
$396$	0.0200776	−	0.178194i	0.00100894	−	0.00895459i
$397$	16.0938	−	25.6132i	0.807726	−	1.28549i	−0.147337	−	0.989086i	$-0.547070\pi$
$397$	16.0938	−	25.6132i	0.807726	−	1.28549i	0.955063	−	0.296402i	$-0.0957869\pi$
$398$	4.83111	+	21.1665i	0.242162	+	1.06098i
$399$	17.0743	−	21.4105i	0.854784	−	1.07186i
$400$		0			0
$401$	−2.42926	−	1.16987i	−0.121311	−	0.0584205i	0.372244	−	0.928135i	$-0.378589\pi$
$401$	−2.42926	−	1.16987i	−0.121311	−	0.0584205i	−0.493555	+	0.869715i	$0.664303\pi$
$402$	−1.33981	+	11.8911i	−0.0668235	+	0.593075i
$403$	−7.34872	−	5.86041i	−0.366066	−	0.291928i
$404$	−2.88697	−	8.25050i	−0.143632	−	0.410478i
$405$		0			0
$406$	16.7045	+	5.76909i	0.829030	+	0.286315i
$407$	1.72233	+	1.72233i	0.0853726	+	0.0853726i
$408$	−31.5347	−	15.1863i	−1.56120	−	0.751834i
$409$	−1.94353	−	17.2493i	−0.0961013	−	0.852922i	−0.945600	−	0.325332i	$-0.894524\pi$
$409$	−1.94353	−	17.2493i	−0.0961013	−	0.852922i	0.849499	−	0.527591i	$-0.176905\pi$
$410$		0			0
$411$	−4.12476	+	8.56516i	−0.203460	+	0.422488i
$412$	3.33852	−	9.54093i	0.164477	−	0.470048i
$413$	−2.35715	−	20.9203i	−0.115988	−	1.02942i
$414$	−1.24079	+	1.97471i	−0.0609816	+	0.0970516i
$415$		0			0
$416$	20.8489	+	2.34911i	1.02220	+	0.115175i
$417$	−28.5290	−	6.51155i	−1.39707	−	0.318872i
$418$		−	1.85888i		−	0.0909207i
$419$	1.52289	−	6.67222i	0.0743981	−	0.325960i	−0.924010	−	0.382369i	$-0.875108\pi$
$419$	1.52289	−	6.67222i	0.0743981	−	0.325960i	0.998408	+	0.0564098i	$0.0179653\pi$
$420$		0			0
$421$	2.91469	−	8.32970i	0.142053	−	0.405965i	−0.850773	−	0.525534i	$-0.823866\pi$
$421$	2.91469	−	8.32970i	0.142053	−	0.405965i	0.992826	+	0.119569i	$0.0381513\pi$
$422$	−0.0419505	+	0.0263593i	−0.00204212	+	0.00128315i
$423$	−5.46488			−0.265712
$424$	18.6754	−	11.7345i	0.906957	−	0.569879i
$425$		0			0
$426$	−1.16159	−	5.08924i	−0.0562790	−	0.246574i
$427$	21.9343	−	5.00637i	1.06148	−	0.242275i
$428$	8.28037	−	0.932974i	0.400247	−	0.0450970i
$429$	−0.978220	−	2.03130i	−0.0472289	−	0.0980719i
$430$		0			0
$431$	10.0620	+	12.6174i	0.484671	+	0.607758i	0.962695	−	0.270589i	$-0.0872183\pi$
$431$	10.0620	+	12.6174i	0.484671	+	0.607758i	−0.478024	+	0.878347i	$0.658647\pi$
$432$	4.06215	−	5.09378i	0.195440	−	0.245075i
$433$	−1.77627	+	3.68847i	−0.0853622	+	0.177257i	−0.939280	−	0.343151i	$-0.888506\pi$
$433$	−1.77627	+	3.68847i	−0.0853622	+	0.177257i	0.853918	+	0.520408i	$0.174220\pi$
$434$	−7.12105			−0.341822
$435$		0			0
$436$	−5.38060			−0.257684
$437$	9.61837	−	19.9728i	0.460109	−	0.955426i
$438$	4.20219	−	5.26938i	0.200788	−	0.251781i
$439$	−11.9256	−	14.9542i	−0.569177	−	0.713725i	0.411048	−	0.911614i	$-0.365163\pi$
$439$	−11.9256	−	14.9542i	−0.569177	−	0.713725i	−0.980224	+	0.197889i	$0.936592\pi$
$440$		0			0
$441$	0.810583	+	1.68319i	0.0385992	+	0.0801521i
$442$	32.6362	−	3.67722i	1.55235	−	0.174908i
$443$	−29.1934	+	6.66320i	−1.38702	+	0.316578i	−0.849908	−	0.526932i	$-0.823342\pi$
$443$	−29.1934	+	6.66320i	−1.38702	+	0.316578i	−0.537113	+	0.843510i	$0.680485\pi$
$444$	−2.42854	−	10.6401i	−0.115254	−	0.504959i
$445$		0			0
$446$	10.6621	−	6.69947i	0.504867	−	0.317229i
$447$	−30.1363			−1.42540
$448$	19.8324	−	12.4615i	0.936991	−	0.588750i
$449$	0.137280	−	0.392324i	0.00647865	−	0.0185149i	−0.940599	−	0.339521i	$-0.889735\pi$
$449$	0.137280	−	0.392324i	0.00647865	−	0.0185149i	0.947077	+	0.321006i	$0.104021\pi$
$450$		0			0
$451$	−0.179370	+	0.785871i	−0.00844621	+	0.0370052i
$452$			0.223649i			0.0105196i
$453$	−26.6257	−	6.07715i	−1.25099	−	0.285529i
$454$	10.3607	+	1.16738i	0.486254	+	0.0547876i
$455$		0			0
$456$	−13.6953	+	21.7959i	−0.641340	+	1.02069i
$457$	3.15663	+	28.0159i	0.147661	+	1.31053i	0.820887	+	0.571091i	$0.193480\pi$
$457$	3.15663	+	28.0159i	0.147661	+	1.31053i	−0.673226	+	0.739437i	$0.735092\pi$
$458$	−7.01691	+	20.0532i	−0.327879	+	0.937023i
$459$	−17.9129	+	37.1966i	−0.836105	+	1.73619i
$460$		0			0
$461$	−1.94340	−	17.2482i	−0.0905133	−	0.803328i	−0.954174	−	0.299254i	$-0.903262\pi$
$461$	−1.94340	−	17.2482i	−0.0905133	−	0.803328i	0.863660	−	0.504074i	$-0.168166\pi$
$462$	−1.53893	−	0.741109i	−0.0715975	−	0.0344795i
$463$	−10.1426	−	10.1426i	−0.471365	−	0.471365i	0.430991	−	0.902356i	$-0.358164\pi$
$463$	−10.1426	−	10.1426i	−0.471365	−	0.471365i	−0.902356	+	0.430991i	$0.858164\pi$
$464$	−6.15570	−	1.37871i	−0.285771	−	0.0640051i
$465$		0			0
$466$	7.62368	+	21.7872i	0.353160	+	1.00927i
$467$	4.24669	+	3.38662i	0.196513	+	0.156714i	0.716803	−	0.697276i	$-0.245605\pi$
$467$	4.24669	+	3.38662i	0.196513	+	0.156714i	−0.520290	+	0.853990i	$0.674176\pi$
$468$	0.260889	−	2.31545i	0.0120596	−	0.107032i
$469$	21.7202	+	10.4599i	1.00295	+	0.482994i
$470$		0			0
$471$	18.0501	−	22.6341i	0.831705	−	1.04293i
$472$	4.40349	+	19.2930i	0.202687	+	0.888031i
$473$	−1.22153	+	1.94405i	−0.0561658	+	0.0893874i
$474$	−0.355824	+	3.15803i	−0.0163436	+	0.145053i
$475$		0			0
$476$	−16.1331	+	16.1331i	−0.739461	+	0.739461i
$477$	−2.18476	−	3.47703i	−0.100033	−	0.159202i
$478$	12.3849	−	5.96427i	0.566473	−	0.272799i
$479$	−7.85928	−	2.75008i	−0.359100	−	0.125654i	0.144698	−	0.989476i	$-0.453779\pi$
$479$	−7.85928	−	2.75008i	−0.359100	−	0.125654i	−0.503798	+	0.863821i	$0.668064\pi$
$480$		0			0
$481$	22.3799	+	22.3799i	1.02044	+	1.02044i
$482$	−1.72025	+	7.53690i	−0.0783552	+	0.343297i
$483$	−12.7003	−	15.9257i	−0.577886	−	0.724646i
$484$	−10.1560	+	2.31804i	−0.461635	+	0.105365i
$485$		0			0
$486$	−4.60066	−	3.66890i	−0.208690	−	0.166425i
$487$	−18.1215	−	6.34097i	−0.821161	−	0.287337i	−0.113186	−	0.993574i	$-0.536106\pi$
$487$	−18.1215	−	6.34097i	−0.821161	−	0.287337i	−0.707975	+	0.706237i	$0.750391\pi$
$488$	−19.9613	+	6.98478i	−0.903608	+	0.316186i
$489$	−2.40576	+	1.91853i	−0.108792	+	0.0867588i
$490$		0			0
$491$	9.42610	−	3.29834i	0.425394	−	0.148852i	−0.109087	−	0.994032i	$-0.534793\pi$
$491$	9.42610	−	3.29834i	0.425394	−	0.148852i	0.534481	+	0.845180i	$0.320507\pi$
$492$	2.55393	−	2.55393i	0.115140	−	0.115140i
$493$	39.9732	−	0.162399i	1.80030	−	0.00731406i
$494$		−	24.1542i		−	1.08675i
$495$		0			0
$496$	2.52586	−	0.284596i	0.113415	−	0.0127787i
$497$	−10.4504	−	1.17748i	−0.468766	−	0.0528172i
$498$	4.01799	+	11.4828i	0.180050	+	0.514555i
$499$	6.72572	−	3.23894i	0.301085	−	0.144995i	−0.277242	−	0.960800i	$-0.589420\pi$
$499$	6.72572	−	3.23894i	0.301085	−	0.144995i	0.578326	+	0.815805i	$0.303706\pi$
$500$		0			0
$501$	−12.8560	−	8.07795i	−0.574363	−	0.360896i
$502$	−19.3579	−	12.1634i	−0.863987	−	0.542879i
$503$	29.7509	−	23.7256i	1.32653	−	1.05787i	0.333163	−	0.942869i	$-0.391884\pi$
$503$	29.7509	−	23.7256i	1.32653	−	1.05787i	0.993365	−	0.115001i	$-0.0366873\pi$
$504$	−2.90266	−	4.61956i	−0.129295	−	0.205771i
$505$		0			0
$506$	−1.34802	−	0.307677i	−0.0599268	−	0.0136779i
$507$	−3.90438	−	8.10752i	−0.173399	−	0.360068i
$508$	−2.24243	−	4.65645i	−0.0994917	−	0.206597i
$509$	17.5133	+	3.99729i	0.776263	+	0.177177i	0.592258	−	0.805748i	$-0.298237\pi$
$509$	17.5133	+	3.99729i	0.776263	+	0.177177i	0.184005	+	0.982925i	$0.441094\pi$
$510$		0			0
$511$	−7.22399	−	11.4969i	−0.319570	−	0.508593i
$512$	−9.96771	+	7.94898i	−0.440515	+	0.351299i
$513$	25.7093	+	16.1542i	1.13509	+	0.713225i
$514$	14.4927	+	9.10634i	0.639244	+	0.401663i
$515$		0			0
$516$	9.26870	−	4.46357i	0.408032	−	0.196498i
$517$	−1.07010	−	3.05817i	−0.0470630	−	0.134498i
$518$	23.8275	+	2.68472i	1.04692	+	0.117960i
$519$	−1.23640	+	0.139309i	−0.0542719	+	0.00611498i
$520$		0			0
$521$			15.7501i			0.690024i	0.938598	+	0.345012i	$0.112125\pi$
$521$			15.7501i			0.690024i	−0.938598	+	0.345012i	$0.887875\pi$
$522$	−0.675969	+	3.01808i	−0.0295864	+	0.132098i
$523$	8.21538	−	8.21538i	0.359233	−	0.359233i	−0.504297	−	0.863530i	$-0.668248\pi$
$523$	8.21538	−	8.21538i	0.359233	−	0.359233i	0.863530	+	0.504297i	$0.168248\pi$
$524$	7.95111	−	2.78221i	0.347346	−	0.121542i
$525$		0			0
$526$	7.28104	−	5.80644i	0.317468	−	0.253173i
$527$	−15.2032	+	5.31982i	−0.662260	+	0.231735i
$528$	0.575482	+	0.201370i	0.0250446	+	0.00876350i
$529$	5.09030	+	4.05938i	0.221318	+	0.176495i
$530$		0			0
$531$	3.59201	−	0.819853i	0.155880	−	0.0355786i
$532$	10.4621	+	13.1190i	0.453588	+	0.568781i
$533$	−2.33073	+	10.2116i	−0.100955	+	0.442314i
$534$	−11.6070	−	11.6070i	−0.502285	−	0.502285i
$535$		0			0
$536$	−21.3891	−	7.48437i	−0.923869	−	0.323276i
$537$	1.62679	−	0.783422i	0.0702013	−	0.0338072i
$538$	2.89181	+	4.60230i	0.124675	+	0.198419i
$539$	−0.783199	+	0.783199i	−0.0337348	+	0.0337348i
$540$		0			0
$541$	3.67537	−	32.6198i	0.158016	−	1.40243i	−0.625093	−	0.780551i	$-0.714939\pi$
$541$	3.67537	−	32.6198i	0.158016	−	1.40243i	0.783109	−	0.621884i	$-0.213633\pi$
$542$	−0.731573	+	1.16429i	−0.0314238	+	0.0500106i
$543$	4.75488	+	20.8325i	0.204052	+	0.894009i
$544$	22.4166	−	28.1095i	0.961103	−	1.20518i
$545$		0			0
$546$	−19.9968	−	9.62997i	−0.855786	−	0.412125i
$547$	1.12606	−	9.99406i	0.0481468	−	0.427315i	−0.946398	−	0.323003i	$-0.895307\pi$
$547$	1.12606	−	9.99406i	0.0481468	−	0.427315i	0.994545	−	0.104312i	$-0.0332639\pi$
$548$	−4.55421	−	3.63186i	−0.194546	−	0.155145i
$549$	1.30044	+	3.71645i	0.0555015	+	0.158614i
$550$		0			0
$551$	3.17289	−	29.2269i	0.135169	−	1.24511i
$552$	13.5391	+	13.5391i	0.576264	+	0.576264i
$553$	5.76843	+	2.77793i	0.245299	+	0.118130i
$554$	−2.55394	−	22.6669i	−0.108507	−	0.963023i
$555$		0			0
$556$	7.77967	−	16.1547i	0.329931	−	0.685110i
$557$	12.4775	−	35.6586i	0.528688	−	1.51090i	−0.301525	−	0.953458i	$-0.597496\pi$
$557$	12.4775	−	35.6586i	0.528688	−	1.51090i	0.830213	−	0.557446i	$-0.188219\pi$
$558$	−0.139535	−	1.23841i	−0.00590698	−	0.0524259i
$559$	−15.8725	+	25.2609i	−0.671335	+	1.06842i
$560$		0			0
$561$	−3.83920	−	0.432574i	−0.162091	−	0.0182633i
$562$	5.21927	+	1.19127i	0.220162	+	0.0502505i
$563$		−	0.0469315i		−	0.00197793i	−1.00000		0.000988963i	$-0.999685\pi$
$563$		−	0.0469315i		−	0.00197793i	1.00000		0.000988963i	$-0.000314797\pi$
$564$	−3.23042	+	14.1534i	−0.136025	+	0.595965i
$565$		0			0
$566$	−8.74512	+	24.9921i	−0.367585	+	1.05050i
$567$	19.0348	−	11.9603i	0.799386	−	0.502287i
$568$	9.88536			0.414781
$569$	−24.4344	+	15.3531i	−1.02434	+	0.643637i	−0.935835	−	0.352438i	$-0.885353\pi$
$569$	−24.4344	+	15.3531i	−1.02434	+	0.643637i	−0.0885075	+	0.996076i	$0.528210\pi$
$570$		0			0
$571$	9.57895	+	41.9681i	0.400867	+	1.75631i	0.623903	+	0.781502i	$0.285546\pi$
$571$	9.57895	+	41.9681i	0.400867	+	1.75631i	−0.223036	+	0.974810i	$0.571597\pi$
$572$	1.34682	−	0.307403i	0.0563135	−	0.0128532i
$573$	22.3231	−	2.51521i	0.932560	−	0.105074i
$574$	3.44303	+	7.14952i	0.143709	+	0.298415i
$575$		0			0
$576$	2.55576	+	3.20482i	0.106490	+	0.133534i
$577$	17.0518	−	21.3823i	0.709875	−	0.890155i	−0.287843	−	0.957678i	$-0.592938\pi$
$577$	17.0518	−	21.3823i	0.709875	−	0.890155i	0.997718	+	0.0675225i	$0.0215094\pi$
$578$	16.8850	−	35.0621i	0.702324	−	1.45839i
$579$	−0.331810			−0.0137895
$580$		0			0
$581$	24.5087			1.01679
$582$	0.822324	−	1.70757i	0.0340864	−	0.0707812i
$583$	1.51795	−	1.90345i	0.0628672	−	0.0788329i
$584$	7.95770	+	9.97865i	0.329292	+	0.412919i
$585$		0			0
$586$	−10.1613	−	21.1002i	−0.419761	−	0.871642i
$587$	2.19250	−	0.247035i	0.0904941	−	0.0101962i	−0.0666013	−	0.997780i	$-0.521216\pi$
$587$	2.19250	−	0.247035i	0.0904941	−	0.0101962i	0.157095	+	0.987583i	$0.449787\pi$
$588$	4.83842	−	1.10434i	0.199533	−	0.0455422i
$589$	2.63597	+	11.5489i	0.108613	+	0.475866i
$590$		0			0
$591$	1.81155	−	1.13827i	0.0745173	−	0.0468223i
$592$	−8.55900			−0.351773
$593$	−1.33905	+	0.841384i	−0.0549884	+	0.0345515i	−0.559246	−	0.829002i	$-0.688909\pi$
$593$	−1.33905	+	0.841384i	−0.0549884	+	0.0345515i	0.504257	+	0.863553i	$0.331766\pi$
$594$	0.625496	−	1.78756i	0.0256644	−	0.0733446i
$595$		0			0
$596$	4.10900	−	18.0027i	0.168311	−	0.737419i
$597$		−	33.1864i		−	1.35823i
$598$	−17.5162	−	3.99795i	−0.716289	−	0.163488i
$599$	25.1241	+	2.83081i	1.02654	+	0.115664i	0.609144	−	0.793060i	$-0.291513\pi$
$599$	25.1241	+	2.83081i	1.02654	+	0.115664i	0.417399	+	0.908723i	$0.362942\pi$
$600$		0			0
$601$	−14.9382	+	23.7740i	−0.609342	+	0.969762i	0.389471	+	0.921039i	$0.372658\pi$
$601$	−14.9382	+	23.7740i	−0.609342	+	0.969762i	−0.998812	+	0.0487229i	$0.984485\pi$
$602$	2.53066	+	22.4602i	0.103142	+	0.915409i
$603$	−1.39346	+	3.98227i	−0.0567460	+	0.162171i
$604$	7.26068	−	15.0769i	0.295433	−	0.613472i
$605$		0			0
$606$	−1.63146	−	14.4796i	−0.0662735	−	0.588194i
$607$	−30.3818	−	14.6311i	−1.23316	−	0.593859i	−0.300213	−	0.953872i	$-0.597058\pi$
$607$	−30.3818	−	14.6311i	−1.23316	−	0.593859i	−0.932947	+	0.360013i	$0.882772\pi$
$608$	−18.6973	−	18.6973i	−0.758276	−	0.758276i
$609$	−22.9314	−	14.2791i	−0.929227	−	0.578620i
$610$		0			0
$611$	−13.9049	−	39.7378i	−0.562531	−	1.60762i
$612$	−3.12180	−	2.48955i	−0.126191	−	0.100634i
$613$	4.15227	−	36.8524i	0.167709	−	1.48846i	−0.574620	−	0.818420i	$-0.694850\pi$
$613$	4.15227	−	36.8524i	0.167709	−	1.48846i	0.742329	−	0.670036i	$-0.233721\pi$
$614$	−29.2242	−	14.0736i	−1.17939	−	0.567966i
$615$		0			0
$616$	2.01674	−	2.52892i	0.0812569	−	0.101893i
$617$	5.39870	+	23.6532i	0.217343	+	0.952243i	0.959432	+	0.281941i	$0.0909783\pi$
$617$	5.39870	+	23.6532i	0.217343	+	0.952243i	−0.742088	+	0.670302i	$0.766165\pi$
$618$	8.96488	−	14.2675i	0.360621	−	0.573924i
$619$	4.24442	−	37.6702i	0.170598	−	1.51410i	−0.558396	−	0.829574i	$-0.688583\pi$
$619$	4.24442	−	37.6702i	0.170598	−	1.51410i	0.728994	−	0.684521i	$-0.239988\pi$
$620$		0			0
$621$	15.9700	−	15.9700i	0.640855	−	0.640855i
$622$	−1.21636	−	1.93583i	−0.0487716	−	0.0776195i
$623$	−29.7946	+	14.3483i	−1.19370	+	0.574854i
$624$	7.47781	+	2.61660i	0.299352	+	0.104748i
$625$		0			0
$626$	7.73273	+	7.73273i	0.309062	+	0.309062i
$627$	−0.632273	+	2.77017i	−0.0252506	+	0.110630i
$628$	11.0600	+	13.8688i	0.441341	+	0.553424i
$629$	52.8765	−	12.0687i	2.10832	−	0.481211i
$630$		0			0
$631$	15.9303	+	12.7040i	0.634175	+	0.505737i	0.886997	−	0.461775i	$-0.152787\pi$
$631$	15.9303	+	12.7040i	0.634175	+	0.505737i	−0.252822	+	0.967513i	$0.581359\pi$
$632$	−5.68049	−	1.98769i	−0.225958	−	0.0790661i
$633$	0.0714821	−	0.0250127i	0.00284116	−	0.000994164i
$634$	−17.8405	+	14.2273i	−0.708536	+	0.565038i
$635$		0			0
$636$	−10.2965	+	3.60291i	−0.408284	+	0.142865i
$637$	−10.1769	+	10.1769i	−0.403223	+	0.403223i
$638$	−1.82130	+	0.212707i	−0.0721058	+	0.00842117i
$639$		−	1.84048i		−	0.0728083i
$640$		0			0
$641$	−20.0334	+	2.25723i	−0.791273	+	0.0891550i	−0.498344	−	0.866979i	$-0.666058\pi$
$641$	−20.0334	+	2.25723i	−0.791273	+	0.0891550i	−0.292929	+	0.956134i	$0.594630\pi$
$642$	13.8033	+	1.55526i	0.544775	+	0.0613813i
$643$	14.5417	+	41.5577i	0.573467	+	1.63887i	0.755176	+	0.655522i	$0.227551\pi$
$643$	14.5417	+	41.5577i	0.573467	+	1.63887i	−0.181709	+	0.983352i	$0.558163\pi$
$644$	11.2453	−	5.41544i	0.443126	−	0.213398i
$645$		0			0
$646$	−35.0471	−	22.0216i	−1.37891	−	0.866426i
$647$	−34.5951	−	21.7375i	−1.36007	−	0.854591i	−0.363056	−	0.931767i	$-0.618267\pi$
$647$	−34.5951	−	21.7375i	−1.36007	−	0.854591i	−0.997017	+	0.0771768i	$0.975409\pi$
$648$	−16.5211	+	13.1751i	−0.649010	+	0.517568i
$649$	1.16216	+	1.84957i	0.0456187	+	0.0726018i
$650$		0			0
$651$	10.6121	+	2.42214i	0.415920	+	0.0949310i
$652$	−0.818062	−	1.69872i	−0.0320378	−	0.0665271i
$653$	18.4814	+	38.3770i	0.723233	+	1.50181i	0.859499	+	0.511137i	$0.170776\pi$
$653$	18.4814	+	38.3770i	0.723233	+	1.50181i	−0.136266	+	0.990672i	$0.543510\pi$
$654$	−8.74456	−	1.99589i	−0.341939	−	0.0780454i
$655$		0			0
$656$	−1.50699	−	2.39836i	−0.0588379	−	0.0936401i
$657$	1.85785	−	1.48158i	0.0724815	−	0.0578021i
$658$	−27.0068	−	16.9695i	−1.05284	−	0.661540i
$659$	29.0653	+	18.2629i	1.13222	+	0.711423i	0.961747	−	0.273939i	$-0.0883267\pi$
$659$	29.0653	+	18.2629i	1.13222	+	0.711423i	0.170476	+	0.985362i	$0.445470\pi$
$660$		0			0
$661$	−42.5571	+	20.4944i	−1.65528	+	0.797141i	−0.656187	+	0.754599i	$0.727832\pi$
$661$	−42.5571	+	20.4944i	−1.65528	+	0.797141i	−0.999095	+	0.0425427i	$0.986454\pi$
$662$	−4.18823	−	11.9693i	−0.162780	−	0.465199i
$663$	−49.8865	−	5.62086i	−1.93743	−	0.218296i
$664$	−22.8929	+	2.57941i	−0.888417	+	0.100100i
$665$		0			0
$666$			4.19640i			0.162607i
$667$	−20.6696	−	7.13847i	−0.800329	−	0.276403i
$668$	6.57844	−	6.57844i	0.254528	−	0.254528i
$669$	−18.1679	+	6.35722i	−0.702411	+	0.245784i
$670$		0			0
$671$	−1.82510	+	1.45547i	−0.0704571	+	0.0561877i
$672$	−22.9335	+	8.02478i	−0.884679	+	0.309563i
$673$	34.5971	+	12.1061i	1.33362	+	0.466654i	0.900569	−	0.434714i	$-0.143151\pi$
$673$	34.5971	+	12.1061i	1.33362	+	0.466654i	0.433053	+	0.901368i	$0.357436\pi$
$674$	1.13753	+	0.907149i	0.0438160	+	0.0349421i
$675$		0			0
$676$	5.37558	−	1.22694i	0.206753	−	0.0471900i
$677$	16.8329	+	21.1078i	0.646942	+	0.811240i	0.991852	−	0.127396i	$-0.0406619\pi$
$677$	16.8329	+	21.1078i	0.646942	+	0.811240i	−0.344910	+	0.938636i	$0.612090\pi$
$678$	−0.0829607	+	0.363475i	−0.00318609	+	0.0139592i
$679$	−2.69990	−	2.69990i	−0.103613	−	0.103613i
$680$		0			0
$681$	−15.0429	−	5.26374i	−0.576445	−	0.201707i
$682$	0.665694	−	0.320581i	0.0254908	−	0.0122757i
$683$	6.09521	+	9.70047i	0.233227	+	0.371178i	0.942748	−	0.333506i	$-0.108232\pi$
$683$	6.09521	+	9.70047i	0.233227	+	0.371178i	−0.709521	+	0.704684i	$0.751089\pi$
$684$	−2.07649	+	2.07649i	−0.0793967	+	0.0793967i
$685$		0			0
$686$	1.35123	−	11.9925i	0.0515901	−	0.457875i
$687$	17.2777	−	27.4973i	0.659185	−	1.04909i
$688$	−1.79526	−	7.86556i	−0.0684438	−	0.299872i
$689$	19.7243	−	24.7334i	0.751434	−	0.942269i
$690$		0			0
$691$	−15.3535	−	7.39386i	−0.584075	−	0.281276i	0.118421	−	0.992964i	$-0.462217\pi$
$691$	−15.3535	−	7.39386i	−0.584075	−	0.281276i	−0.702496	+	0.711688i	$0.747931\pi$
$692$	0.0853597	−	0.757588i	0.00324489	−	0.0287992i
$693$	−0.470839	−	0.375482i	−0.0178857	−	0.0142634i
$694$	−6.89799	−	19.7133i	−0.261844	−	0.748308i
$695$		0			0
$696$	22.9224	+	10.9243i	0.868870	+	0.414085i
$697$	12.6918	+	12.6918i	0.480736	+	0.480736i
$698$	−25.9479	−	12.4958i	−0.982141	−	0.472974i
$699$	−3.95046	−	35.0613i	−0.149420	−	1.32614i
$700$		0			0
$701$	−9.35305	+	19.4218i	−0.353260	+	0.733552i	−0.999564	−	0.0295282i	$-0.990600\pi$
$701$	−9.35305	+	19.4218i	−0.353260	+	0.733552i	0.646304	+	0.763080i	$0.276314\pi$
$702$	8.12768	−	23.2276i	0.306760	−	0.876669i
$703$	−4.46605	−	39.6373i	−0.168440	−	1.49495i
$704$	−1.29298	+	2.05776i	−0.0487309	+	0.0775548i
$705$		0			0
$706$	−5.73731	−	0.646440i	−0.215927	−	0.0243291i
$707$	−28.6195	−	6.53221i	−1.07635	−	0.245669i
$708$		−	9.78750i		−	0.367837i
$709$	−5.43528	+	23.8135i	−0.204126	+	0.894336i	0.764266	+	0.644902i	$0.223102\pi$
$709$	−5.43528	+	23.8135i	−0.204126	+	0.894336i	−0.968392	+	0.249434i	$0.919755\pi$
$710$		0			0
$711$	−0.370073	+	1.05761i	−0.0138788	+	0.0396634i
$712$	26.3202	−	16.5381i	0.986392	−	0.619791i
$713$	8.81135			0.329988
$714$	−32.2040	+	20.2351i	−1.20521	+	0.757281i
$715$		0			0
$716$	0.246189	+	1.07862i	0.00920050	+	0.0403100i
$717$	−20.4852	+	4.67560i	−0.765032	+	0.174614i
$718$	0.773345	−	0.0871351i	0.0288610	−	0.00325185i
$719$	12.1135	+	25.1540i	0.451758	+	0.938086i	0.995128	+	0.0985924i	$0.0314340\pi$
$719$	12.1135	+	25.1540i	0.451758	+	0.938086i	−0.543369	+	0.839494i	$0.682852\pi$
$720$		0			0
$721$	−21.1655	−	26.5407i	−0.788245	−	0.988428i
$722$	−6.87970	+	8.62687i	−0.256036	+	0.321059i
$723$	5.12716	−	10.6467i	0.190681	−	0.395954i
$724$	−13.0931			−0.486602
$725$		0			0
$726$	−17.3654			−0.644489
$727$	−1.90781	+	3.96162i	−0.0707569	+	0.146928i	−0.933347	−	0.358975i	$-0.883126\pi$
$727$	−1.90781	+	3.96162i	−0.0707569	+	0.146928i	0.862590	+	0.505903i	$0.168841\pi$
$728$	26.2055	−	32.8607i	0.971242	−	1.21790i
$729$	18.6958	+	23.4438i	0.692438	+	0.868290i
$730$		0			0
$731$	22.1818	+	46.0611i	0.820425	+	1.70363i
$732$	10.3939	−	1.17111i	0.384169	−	0.0432854i
$733$	−25.3994	+	5.79725i	−0.938149	+	0.214126i	−0.664146	−	0.747603i	$-0.731205\pi$
$733$	−25.3994	+	5.79725i	−0.938149	+	0.214126i	−0.274003	+	0.961729i	$0.588348\pi$
$734$	0.543629	+	2.38179i	0.0200657	+	0.0879136i
$735$		0			0
$736$	−16.6536	+	10.4642i	−0.613861	+	0.385714i
$737$	−2.50136			−0.0921387
$738$	−1.17589	+	0.738861i	−0.0432851	+	0.0271979i
$739$	1.95496	−	5.58694i	0.0719142	−	0.205519i	−0.902316	−	0.431075i	$-0.858134\pi$
$739$	1.95496	−	5.58694i	0.0719142	−	0.205519i	0.974230	+	0.225556i	$0.0724200\pi$
$740$		0			0
$741$	−8.21575	+	35.9956i	−0.301813	+	1.32233i
$742$		−	23.9672i		−	0.879863i
$743$	−6.86085	−	1.56594i	−0.251700	−	0.0574489i	0.0948090	−	0.995495i	$-0.469776\pi$
$743$	−6.86085	−	1.56594i	−0.251700	−	0.0574489i	−0.346509	+	0.938047i	$0.612633\pi$
$744$	−10.1673	−	1.14558i	−0.372753	−	0.0419992i
$745$		0			0
$746$	8.74433	−	13.9165i	0.320153	−	0.509520i
$747$	0.480240	+	4.26225i	0.0175711	+	0.155948i
$748$	0.781872	−	2.23446i	0.0285881	−	0.0817000i
$749$	12.1420	−	25.2131i	0.443659	−	0.921267i
$750$		0			0
$751$	5.32203	+	47.2343i	0.194203	+	1.72360i	0.591836	+	0.806059i	$0.298403\pi$
$751$	5.32203	+	47.2343i	0.194203	+	1.72360i	−0.397632	+	0.917545i	$0.630168\pi$
$752$	10.2576	+	4.93980i	0.374056	+	0.180136i
$753$	24.7107	+	24.7107i	0.900509	+	0.900509i
$754$	−23.6659	+	2.76392i	−0.861861	+	0.100656i
$755$		0			0
$756$	5.64626	+	16.1361i	0.205353	+	0.586864i
$757$	−14.3815	−	11.4688i	−0.522704	−	0.416842i	0.326271	−	0.945276i	$-0.394208\pi$
$757$	−14.3815	−	11.4688i	−0.522704	−	0.416842i	−0.848974	+	0.528434i	$0.822779\pi$
$758$	1.88796	−	16.7561i	0.0685737	−	0.608608i
$759$	1.90422	+	0.917023i	0.0691188	+	0.0332858i
$760$		0			0
$761$	−12.2089	+	15.3094i	−0.442571	+	0.554966i	−0.952219	−	0.305417i	$-0.901204\pi$
$761$	−12.2089	+	15.3094i	−0.442571	+	0.554966i	0.509648	+	0.860383i	$0.329776\pi$
$762$	−1.91713	−	8.39947i	−0.0694501	−	0.304281i
$763$	−9.61382	+	15.3003i	−0.348044	+	0.553908i
$764$	−1.54116	+	13.6782i	−0.0557573	+	0.494860i
$765$		0			0
$766$	−3.37599	+	3.37599i	−0.121979	+	0.121979i
$767$	15.1011	+	24.0332i	0.545268	+	0.867790i
$768$	23.7298	−	11.4277i	0.856276	−	0.412361i
$769$	15.5886	+	5.45470i	0.562141	+	0.196702i	0.596366	−	0.802713i	$-0.296611\pi$
$769$	15.5886	+	5.45470i	0.562141	+	0.196702i	−0.0342253	+	0.999414i	$0.510896\pi$
$770$		0			0
$771$	−18.5001	−	18.5001i	−0.666265	−	0.666265i
$772$	0.0452412	−	0.198215i	0.00162827	−	0.00713391i
$773$	−12.7969	−	16.0469i	−0.460274	−	0.577166i	0.496486	−	0.868045i	$-0.334624\pi$
$773$	−12.7969	−	16.0469i	−0.460274	−	0.577166i	−0.956760	+	0.290879i	$0.906052\pi$
$774$	−3.85641	+	0.880201i	−0.138616	+	0.0316382i
$775$		0			0
$776$	2.80605	+	2.23775i	0.100731	+	0.0803304i
$777$	−34.5956	−	12.1055i	−1.24111	−	0.434283i
$778$	−35.8800	+	12.5549i	−1.28636	+	0.450117i
$779$	10.3206	−	8.23041i	0.369774	−	0.294885i
$780$		0			0
$781$	1.02994	−	0.360392i	0.0368542	−	0.0128958i
$782$	−21.7705	+	21.7705i	−0.778511	+	0.778511i
$783$	12.8857	−	27.0380i	0.460499	−	0.966258i
$784$		−	3.89206i		−	0.139002i
$785$		0			0
$786$	13.9542	−	1.57226i	0.497729	−	0.0560806i
$787$	−34.1359	−	3.84619i	−1.21681	−	0.137102i	−0.519880	−	0.854239i	$-0.674023\pi$
$787$	−34.1359	−	3.84619i	−1.21681	−	0.137102i	−0.696932	+	0.717137i	$0.745452\pi$
$788$	0.432976	+	1.23738i	0.0154241	+	0.0440797i
$789$	−12.8255	+	6.17642i	−0.456599	+	0.219886i
$790$		0			0
$791$	0.635969	+	0.399606i	0.0226125	+	0.0142084i
$792$	0.479315	+	0.301174i	0.0170317	+	0.0107017i
$793$	−23.7153	+	18.9123i	−0.842155	+	0.671596i
$794$	16.4387	+	26.1621i	0.583388	+	0.928457i
$795$		0			0
$796$	19.8247	+	4.52486i	0.702668	+	0.160379i
$797$	5.98688	+	12.4319i	0.212066	+	0.440360i	0.979684	−	0.200548i	$-0.0642723\pi$
$797$	5.98688	+	12.4319i	0.212066	+	0.440360i	−0.767618	+	0.640908i	$0.778558\pi$
$798$	12.1366	+	25.2018i	0.429630	+	0.892135i
$799$	−70.3356	−	16.0536i	−2.48829	−	0.567937i
$800$		0			0
$801$	−3.07910	−	4.90036i	−0.108795	−	0.173146i
$802$	2.15321	−	1.71713i	0.0760324	−	0.0606338i
$803$	1.19289	+	0.749545i	0.0420963	+	0.0264509i
$804$	9.48990	+	5.96290i	0.334683	+	0.210295i
$805$		0			0
$806$	8.65002	−	4.16563i	0.304684	−	0.146728i
$807$	−2.74408	−	7.84213i	−0.0965962	−	0.276056i
$808$	27.4201	+	3.08950i	0.964636	+	0.108688i
$809$	−19.1241	+	2.15477i	−0.672367	+	0.0757576i	−0.441546	−	0.897239i	$-0.645570\pi$
$809$	−19.1241	+	2.15477i	−0.672367	+	0.0757576i	−0.230821	+	0.972996i	$0.574141\pi$
$810$		0			0
$811$		−	46.6872i		−	1.63941i	−0.572787	−	0.819704i	$-0.694138\pi$
$811$		−	46.6872i		−	1.63941i	0.572787	−	0.819704i	$-0.305862\pi$
$812$	11.6566	−	11.7517i	0.409067	−	0.412405i
$813$	1.48624	−	1.48624i	0.0521246	−	0.0521246i
$814$	−2.34832	+	0.821714i	−0.0823087	+	0.0288010i
$815$		0			0
$816$	10.6142	−	8.46452i	0.371570	−	0.296317i
$817$	35.4892	−	12.4182i	1.24161	−	0.434458i
$818$	16.7355	+	5.85599i	0.585142	+	0.204750i
$819$	−6.11808	−	4.87901i	−0.213783	−	0.170486i
$820$		0			0
$821$	−8.38107	+	1.91292i	−0.292501	+	0.0667615i	−0.366254	−	0.930515i	$-0.619360\pi$
$821$	−8.38107	+	1.91292i	−0.292501	+	0.0667615i	0.0737522	+	0.997277i	$0.476503\pi$
$822$	−6.05430	−	7.59185i	−0.211168	−	0.264796i
$823$	−3.81633	+	16.7204i	−0.133029	+	0.582838i	0.863840	+	0.503766i	$0.168053\pi$
$823$	−3.81633	+	16.7204i	−0.133029	+	0.582838i	−0.996869	+	0.0790717i	$0.974804\pi$
$824$	22.5634	+	22.5634i	0.786033	+	0.786033i
$825$		0			0
$826$	20.2971	+	7.10227i	0.706227	+	0.247119i
$827$	23.3648	−	11.2519i	0.812474	−	0.391267i	0.0189613	−	0.999820i	$-0.493964\pi$
$827$	23.3648	−	11.2519i	0.812474	−	0.391267i	0.793513	+	0.608553i	$0.208250\pi$
$828$	1.16213	+	1.84953i	0.0403870	+	0.0642755i
$829$	8.01072	−	8.01072i	0.278224	−	0.278224i	−0.554176	−	0.832400i	$-0.686966\pi$
$829$	8.01072	−	8.01072i	0.278224	−	0.278224i	0.832400	+	0.554176i	$0.186966\pi$
$830$		0			0
$831$	−3.90386	+	34.6477i	−0.135423	+	1.20192i
$832$	−16.8009	+	26.7385i	−0.582468	+	0.926992i
$833$	5.48804	+	24.0447i	0.190149	+	0.833099i
$834$	18.6359	−	23.3687i	0.645310	−	0.809193i
$835$		0			0
$836$	−1.56862	−	0.755409i	−0.0542519	−	0.0261264i
$837$	−1.35127	+	11.9928i	−0.0467067	+	0.414533i
$838$	5.46538	+	4.35849i	0.188798	+	0.150562i
$839$	1.26460	+	3.61402i	0.0436588	+	0.124770i	0.963649	−	0.267172i	$-0.0860892\pi$
$839$	1.26460	+	3.61402i	0.0436588	+	0.124770i	−0.919990	+	0.391942i	$0.871803\pi$
$840$		0			0
$841$	−28.9990	+	0.235632i	−0.999967	+	0.00812523i
$842$	6.37389	+	6.37389i	0.219659	+	0.219659i
$843$	−7.37277	−	3.55054i	−0.253932	−	0.122287i
$844$	0.00519557	+	0.0461120i	0.000178839	+	0.00158724i
$845$		0			0
$846$	2.42194	−	5.02920i	0.0832679	−	0.172908i
$847$	−11.5547	+	33.0214i	−0.397023	+	1.13463i
$848$	0.957859	+	8.50124i	0.0328930	+	0.291934i
$849$	21.5331	−	34.2697i	0.739013	−	1.17613i
$850$		0			0
$851$	−29.4834	−	3.32198i	−1.01068	−	0.113876i
$852$	−4.76662	−	1.08795i	−0.163302	−	0.0372726i
$853$			39.2828i			1.34502i	0.740089	+	0.672509i	$0.234783\pi$
$853$			39.2828i			1.34502i	−0.740089	+	0.672509i	$0.765217\pi$
$854$	−5.11366	+	22.4044i	−0.174986	+	0.766663i
$855$		0			0
$856$	−8.68794	+	24.8287i	−0.296948	+	0.848628i
$857$	47.4255	−	29.7994i	1.62002	−	1.01793i	0.655048	−	0.755587i	$-0.272648\pi$
$857$	47.4255	−	29.7994i	1.62002	−	1.01793i	0.964975	−	0.262341i	$-0.0844946\pi$
$858$	2.30288			0.0786192
$859$	3.31692	−	2.08416i	0.113172	−	0.0711105i	−0.474257	−	0.880387i	$-0.657283\pi$
$859$	3.31692	−	2.08416i	0.113172	−	0.0711105i	0.587429	+	0.809276i	$0.300140\pi$
$860$		0			0
$861$	−2.69911	−	11.8256i	−0.0919856	−	0.403015i
$862$	−16.0708	+	3.66805i	−0.547374	+	0.124934i
$863$	34.7264	−	3.91273i	1.18210	−	0.133191i	0.501045	−	0.865421i	$-0.332949\pi$
$863$	34.7264	−	3.91273i	1.18210	−	0.133191i	0.681057	+	0.732231i	$0.261521\pi$
$864$	−11.6885	−	24.2715i	−0.397652	−	0.825732i
$865$		0			0
$866$	−2.60720	−	3.26933i	−0.0885963	−	0.111096i
$867$	−37.0886	+	46.5076i	−1.25959	+	1.57948i
$868$	−2.89385	+	6.00913i	−0.0982235	+	0.203963i
$869$	−0.664307			−0.0225351
$870$		0			0
$871$	−32.5026			−1.10131
$872$	7.36972	−	15.3034i	0.249570	−	0.518238i
$873$	0.416629	−	0.522436i	0.0141008	−	0.0176818i
$874$	14.1178	+	17.7031i	0.477541	+	0.598817i
$875$		0			0
$876$	−2.73891	−	5.68740i	−0.0925391	−	0.192159i
$877$	−10.1148	+	1.13966i	−0.341553	+	0.0384837i	−0.281075	−	0.959686i	$-0.590691\pi$
$877$	−10.1148	+	1.13966i	−0.341553	+	0.0384837i	−0.0604776	+	0.998170i	$0.519262\pi$
$878$	19.0472	−	4.34740i	0.642812	−	0.146718i
$879$	7.96583	+	34.9006i	0.268681	+	1.17717i
$880$		0			0
$881$	−10.5567	+	6.63321i	−0.355664	+	0.223479i	−0.697998	−	0.716100i	$-0.745925\pi$
$881$	−10.5567	+	6.63321i	−0.355664	+	0.223479i	0.342334	+	0.939578i	$0.388783\pi$
$882$	−1.90824			−0.0642538
$883$	8.92134	−	5.60565i	0.300227	−	0.188645i	−0.373491	−	0.927634i	$-0.621839\pi$
$883$	8.92134	−	5.60565i	0.300227	−	0.188645i	0.673718	+	0.738989i	$0.264696\pi$
$884$	10.1596	−	29.0346i	0.341706	−	0.976538i
$885$		0			0
$886$	6.80600	−	29.8190i	0.228652	−	1.00179i
$887$			10.4690i			0.351515i	0.984433	+	0.175758i	$0.0562375\pi$
$887$			10.4690i			0.351515i	−0.984433	+	0.175758i	$0.943763\pi$
$888$	33.5888	+	7.66641i	1.12716	+	0.257268i
$889$	−17.2478	−	1.94336i	−0.578472	−	0.0651781i
$890$		0			0
$891$	−1.24098	+	1.97501i	−0.0415744	+	0.0661652i
$892$	−1.32051	−	11.7198i	−0.0442138	−	0.392409i
$893$	−17.5242	+	50.0812i	−0.586424	+	1.67590i
$894$	13.3559	−	27.7338i	0.446688	−	0.927556i
$895$		0			0
$896$	−0.806054	−	7.15393i	−0.0269284	−	0.238996i
$897$	24.7434	+	11.9158i	0.826158	+	0.397857i
$898$	0.300207	+	0.300207i	0.0100180	+	0.0100180i
$899$	11.0138	−	3.90420i	0.367331	−	0.130212i
$900$		0			0
$901$	−17.9048	−	51.1689i	−0.596495	−	1.70468i
$902$	−0.643726	−	0.513354i	−0.0214337	−	0.0170928i
$903$	3.86827	−	34.3318i	0.128728	−	1.14249i
$904$	−0.636097	−	0.306328i	−0.0211563	−	0.0101883i
$905$		0			0
$906$	17.3927	−	21.8098i	0.577834	−	0.724581i
$907$	8.36134	+	36.6334i	0.277634	+	1.21639i	0.900776	+	0.434284i	$0.142999\pi$
$907$	8.36134	+	36.6334i	0.277634	+	1.21639i	−0.623142	+	0.782109i	$0.714144\pi$
$908$	5.19548	−	8.26856i	0.172418	−	0.274402i
$909$	0.575211	−	5.10514i	0.0190785	−	0.169327i
$910$		0			0
$911$	27.7673	−	27.7673i	0.919972	−	0.919972i	−0.0770545	−	0.997027i	$-0.524552\pi$
$911$	27.7673	−	27.7673i	0.919972	−	0.919972i	0.997027	+	0.0770545i	$0.0245516\pi$
$912$	−5.31208	−	8.45412i	−0.175900	−	0.279944i
$913$	−2.29114	+	1.10335i	−0.0758256	+	0.0365157i
$914$	−27.1813	−	9.51116i	−0.899079	−	0.314601i
$915$		0			0
$916$	14.0704	+	14.0704i	0.464900	+	0.464900i
$917$	6.29517	−	27.5810i	0.207885	−	0.910803i
$918$	−26.2925	−	32.9697i	−0.867782	−	1.08816i
$919$	−26.5398	+	6.05753i	−0.875466	+	0.199819i	−0.636564	−	0.771224i	$-0.719645\pi$
$919$	−26.5398	+	6.05753i	−0.875466	+	0.199819i	−0.238902	+	0.971044i	$0.576788\pi$
$920$		0			0
$921$	38.7641	+	30.9133i	1.27732	+	1.01863i
$922$	16.7344	+	5.85561i	0.551118	+	0.192844i
$923$	13.3830	−	4.68293i	0.440508	−	0.154140i
$924$	−1.25078	+	0.997461i	−0.0411475	+	0.0328141i
$925$		0			0
$926$	13.8290	−	4.83896i	0.454448	−	0.159018i
$927$	4.20090	−	4.20090i	0.137976	−	0.137976i
$928$	−16.1798	+	20.4588i	−0.531128	+	0.671592i
$929$		−	42.3538i		−	1.38958i	−0.719211	−	0.694792i	$-0.755496\pi$
$929$		−	42.3538i		−	1.38958i	0.719211	−	0.694792i	$-0.244504\pi$
$930$		0			0
$931$	18.0244	−	2.03086i	0.590726	−	0.0665588i
$932$	21.4834	+	2.42059i	0.703711	+	0.0792891i
$933$	1.15422	+	3.29857i	0.0377875	+	0.107990i
$934$	−4.99869	+	2.40724i	−0.163562	+	0.0787674i
$935$		0			0
$936$	6.22821	+	3.91345i	0.203576	+	0.127915i
$937$	−5.38668	−	3.38468i	−0.175975	−	0.110573i	0.441164	−	0.897426i	$-0.354566\pi$
$937$	−5.38668	−	3.38468i	−0.175975	−	0.110573i	−0.617139	+	0.786854i	$0.711709\pi$
$938$	−19.2521	+	15.3530i	−0.628602	+	0.501293i
$939$	−8.89342	−	14.1538i	−0.290226	−	0.461892i
$940$		0			0
$941$	43.5932	+	9.94986i	1.42110	+	0.324356i	0.862910	−	0.505358i	$-0.168640\pi$
$941$	43.5932	+	9.94986i	1.42110	+	0.324356i	0.558188	+	0.829715i	$0.311497\pi$
$942$	12.8302	+	26.6421i	0.418030	+	0.868048i
$943$	−4.26028	−	8.84657i	−0.138734	−	0.288084i
$944$	−7.48330	−	1.70801i	−0.243561	−	0.0555911i
$945$		0			0
$946$	−1.24770	−	1.98571i	−0.0405663	−	0.0645610i
$947$	15.8121	−	12.6098i	0.513825	−	0.409762i	−0.331954	−	0.943296i	$-0.607708\pi$
$947$	15.8121	−	12.6098i	0.513825	−	0.409762i	0.845779	+	0.533534i	$0.179136\pi$
$948$	2.52032	+	1.58362i	0.0818561	+	0.0514336i
$949$	15.5004	+	9.73958i	0.503166	+	0.316160i
$950$		0			0
$951$	31.4258	−	15.1339i	1.01905	−	0.490749i
$952$	−23.7882	−	67.9828i	−0.770980	−	2.20333i
$953$	−37.0553	−	4.17513i	−1.20034	−	0.135246i	−0.510933	−	0.859621i	$-0.670700\pi$
$953$	−37.0553	−	4.17513i	−1.20034	−	0.135246i	−0.689406	+	0.724375i	$0.742128\pi$
$954$	4.16807	−	0.469629i	0.134946	−	0.0152048i
$955$		0			0
$956$		−	12.8748i		−	0.416402i
$957$	2.78651	+	0.302506i	0.0900752	+	0.00977862i
$958$	6.01393	−	6.01393i	0.194301	−	0.194301i
$959$	−18.4648	+	6.46113i	−0.596261	+	0.208641i
$960$		0			0
$961$	20.5555	−	16.3925i	0.663081	−	0.528790i
$962$	−30.5141	+	10.6773i	−0.983813	+	0.344251i
$963$	4.62267	+	1.61754i	0.148963	+	0.0521245i
$964$	5.66098	+	4.51448i	0.182328	+	0.145402i
$965$		0			0
$966$	20.2847	−	4.62984i	0.652648	−	0.148963i
$967$	−23.5211	−	29.4946i	−0.756389	−	0.948482i	0.243381	−	0.969931i	$-0.421743\pi$
$967$	−23.5211	−	29.4946i	−0.756389	−	0.948482i	−0.999770	+	0.0214491i	$0.993172\pi$
$968$	7.31757	−	32.0604i	0.235196	−	1.03046i
$969$	44.7382	+	44.7382i	1.43720	+	1.43720i
$970$		0			0
$971$	−37.0487	−	12.9639i	−1.18895	−	0.416031i	−0.337933	−	0.941170i	$-0.609728\pi$
$971$	−37.0487	−	12.9639i	−1.18895	−	0.416031i	−0.851016	+	0.525139i	$0.824013\pi$
$972$	−4.96563	+	2.39132i	−0.159273	+	0.0767017i
$973$	−32.0371	−	50.9867i	−1.02706	−	1.63456i
$974$	13.8666	−	13.8666i	0.444313	−	0.444313i
$975$		0			0
$976$	0.918429	−	8.15128i	0.0293982	−	0.260916i
$977$	10.3799	−	16.5196i	0.332083	−	0.528508i	−0.638391	−	0.769712i	$-0.720400\pi$
$977$	10.3799	−	16.5196i	0.332083	−	0.528508i	0.970474	+	0.241205i	$0.0775425\pi$
$978$	−0.699388	−	3.06422i	−0.0223640	−	0.0979829i
$979$	2.13933	−	2.68264i	0.0683734	−	0.0857375i
$980$		0			0
$981$	−2.84922	−	1.37211i	−0.0909686	−	0.0438081i
$982$	−1.14210	+	10.1364i	−0.0364458	+	0.323465i
$983$	13.1719	+	10.5042i	0.420118	+	0.335033i	0.810624	−	0.585568i	$-0.199128\pi$
$983$	13.1719	+	10.5042i	0.420118	+	0.335033i	−0.390505	+	0.920601i	$0.627700\pi$
$984$	3.76574	+	10.7619i	0.120048	+	0.343076i
$985$		0			0
$986$	−17.5660	+	36.8584i	−0.559414	+	1.17381i
$987$	34.4746	+	34.4746i	1.09734	+	1.09734i
$988$	−20.3827	−	9.81577i	−0.648459	−	0.312281i
$989$	−3.13135	−	27.7915i	−0.0995710	−	0.883717i
$990$		0			0
$991$	−1.37219	+	2.84939i	−0.0435892	+	0.0905139i	−0.921626	−	0.388079i	$-0.873139\pi$
$991$	−1.37219	+	2.84939i	−0.0435892	+	0.0905139i	0.878037	+	0.478593i	$0.158853\pi$
$992$	3.47128	−	9.92033i	0.110213	−	0.314971i
$993$	2.17026	+	19.2616i	0.0688713	+	0.611249i
$994$	5.71505	−	9.09545i	0.181270	−	0.288490i
$995$		0			0
$996$	11.3226	+	1.27575i	0.358770	+	0.0404237i
$997$	13.9139	+	3.17575i	0.440657	+	0.100577i	0.437092	−	0.899417i	$-0.356008\pi$
$997$	13.9139	+	3.17575i	0.440657	+	0.100577i	0.00356433	+	0.999994i	$0.498865\pi$
$998$			7.62497i			0.241364i
$999$	9.04288	−	39.6195i	0.286104	−	1.25350i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.2.bd.b.482.5		156
5.2	odd	4		145.2.o.a.18.5	✓	156
5.3	odd	4		725.2.y.b.18.9		156
5.4	even	2		145.2.t.a.47.9	yes	156
29.21	odd	28		725.2.y.b.282.9		156
145.79	odd	28		145.2.o.a.137.5	yes	156
145.108	even	28	inner	725.2.bd.b.543.5		156
145.137	even	28		145.2.t.a.108.9	yes	156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.2.o.a.18.5	✓	156	5.2	odd	4
145.2.o.a.137.5	yes	156	145.79	odd	28
145.2.t.a.47.9	yes	156	5.4	even	2
145.2.t.a.108.9	yes	156	145.137	even	28
725.2.y.b.18.9		156	5.3	odd	4
725.2.y.b.282.9		156	29.21	odd	28
725.2.bd.b.482.5		156	1.1	even	1	trivial
725.2.bd.b.543.5		156	145.108	even	28	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	725.bd (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.443182 + 0.920277i) q^{2} +(0.973467 - 1.22069i) q^{3} +(0.596480 + 0.747962i) q^{4} +(0.691949 + 1.43685i) q^{6} +(3.19267 - 0.359728i) q^{7} +(-2.94432 + 0.672023i) q^{8} +(0.125119 + 0.548181i) q^{9} +(-0.282265 + 0.177359i) q^{11} +1.49368 q^{12} +(-3.66774 + 2.30460i) q^{13} +(-1.08389 + 3.09757i) q^{14} +(0.260662 - 1.14204i) q^{16} +7.42290i q^{17} +(-0.559929 - 0.127800i) q^{18} +(5.42486 + 0.611234i) q^{19} +(2.66885 - 4.24744i) q^{21} +(-0.0381244 - 0.338364i) q^{22} +(1.34116 - 3.83282i) q^{23} +(-2.04587 + 4.24830i) q^{24} +(-0.495389 - 4.39670i) q^{26} +(5.01106 + 2.41320i) q^{27} +(2.17343 + 2.17343i) q^{28} +(-0.0218780 - 5.38512i) q^{29} +(0.716676 + 2.04814i) q^{31} +(-3.78686 - 3.01992i) q^{32} +(-0.0582756 + 0.517210i) q^{33} +(-6.83113 - 3.28970i) q^{34} +(-0.335388 + 0.420563i) q^{36} +(-1.62587 - 7.12342i) q^{37} +(-2.96670 + 4.72148i) q^{38} +(-0.757232 + 6.72062i) q^{39} +(1.70982 - 1.70982i) q^{41} +(2.72604 + 4.33847i) q^{42} +(6.20526 - 2.98830i) q^{43} +(-0.301023 - 0.105332i) q^{44} +(2.93288 + 2.93288i) q^{46} +(-2.16272 + 9.47549i) q^{47} +(-1.14032 - 1.42992i) q^{48} +(3.23926 - 0.739339i) q^{49} +(9.06106 + 7.22595i) q^{51} +(-3.91149 - 1.36869i) q^{52} +(-6.89339 + 2.41210i) q^{53} +(-4.44163 + 3.54208i) q^{54} +(-9.15852 + 3.20470i) q^{56} +(6.02705 - 6.02705i) q^{57} +(4.96550 + 2.36646i) q^{58} -6.55260i q^{59} +(6.95855 - 0.784041i) q^{61} +(-2.20248 - 0.248159i) q^{62} +(0.596659 + 1.70515i) q^{63} +(6.56823 - 3.16309i) q^{64} +(-0.450150 - 0.282848i) q^{66} +(6.35336 + 3.99208i) q^{67} +(-5.55205 + 4.42761i) q^{68} +(-3.37311 - 5.36827i) q^{69} +(-3.19119 - 0.728367i) q^{71} +(-0.736780 - 1.52994i) q^{72} +(-1.83366 - 3.80763i) q^{73} +(7.27608 + 1.66072i) q^{74} +(2.77864 + 4.42218i) q^{76} +(-0.837377 + 0.667786i) q^{77} +(-5.84924 - 3.67532i) q^{78} +(1.68732 + 1.06021i) q^{79} +(6.30409 - 3.03589i) q^{81} +(0.815745 + 2.33127i) q^{82} +(7.58032 + 0.854097i) q^{83} +(4.76884 - 0.537319i) q^{84} +7.03492i q^{86} +(-6.59486 - 5.21553i) q^{87} +(0.711889 - 0.711889i) q^{88} +(-9.71523 + 3.39950i) q^{89} +(-10.8809 + 8.67721i) q^{91} +(3.66678 - 1.28306i) q^{92} +(3.19781 + 1.11896i) q^{93} +(-7.76160 - 6.18967i) q^{94} +(-7.37277 + 1.68279i) q^{96} +(-0.740965 - 0.929141i) q^{97} +(-0.755184 + 3.30868i) q^{98} +(-0.132541 - 0.132541i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q + 14 q^{2} + 10 q^{3} + 22 q^{4} - 28 q^{6} + 10 q^{7} + 14 q^{8} - 10 q^{9} - 20 q^{11} + 20 q^{12} + 28 q^{13} - 4 q^{14} - 34 q^{16} - 84 q^{18} - 16 q^{21} + 22 q^{22} + 10 q^{23} - 56 q^{24}+ \cdots - 76 q^{99}+O(q^{100}) \) 156 * q + 14 * q^2 + 10 * q^3 + 22 * q^4 - 28 * q^6 + 10 * q^7 + 14 * q^8 - 10 * q^9 - 20 * q^11 + 20 * q^12 + 28 * q^13 - 4 * q^14 - 34 * q^16 - 84 * q^18 - 16 * q^21 + 22 * q^22 + 10 * q^23 - 56 * q^24 + 36 * q^26 - 32 * q^27 + 8 * q^28 - 8 * q^31 + 14 * q^32 + 14 * q^33 + 24 * q^34 + 78 * q^36 + 72 * q^37 + 120 * q^38 - 16 * q^39 - 22 * q^41 + 18 * q^42 - 2 * q^43 + 112 * q^44 + 4 * q^46 - 22 * q^47 - 38 * q^48 - 84 * q^49 - 28 * q^51 - 86 * q^52 - 56 * q^53 + 4 * q^56 + 12 * q^57 - 96 * q^58 - 46 * q^61 + 112 * q^62 - 158 * q^63 + 30 * q^64 - 48 * q^66 - 18 * q^67 - 140 * q^68 + 124 * q^69 - 28 * q^71 + 98 * q^72 + 84 * q^73 - 112 * q^74 - 48 * q^76 - 28 * q^77 - 70 * q^78 + 4 * q^79 + 58 * q^81 - 16 * q^82 - 46 * q^83 - 120 * q^84 - 68 * q^87 - 40 * q^88 - 46 * q^89 - 28 * q^91 + 14 * q^92 + 22 * q^93 + 84 * q^94 - 28 * q^96 + 76 * q^97 + 160 * q^98 - 76 * q^99

Introduction

L-functions

Modular forms

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Database

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