LMFDB - Embedded newform 775.2.ck.a.524.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [775,2,Mod(49,775)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(775, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([15, 26])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("775.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.ck (of order $30$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,28] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			524.1
Character	$\chi$	$=$	775.524
Dual form			775.2.ck.a.599.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.744490 - 1.02470i) q^{2} +(1.47618 + 0.155153i) q^{3} +(0.122284 - 0.376353i) q^{4} +(-0.940018 - 1.62816i) q^{6} +(-0.455117 - 2.14115i) q^{7} +(-2.88591 + 0.937688i) q^{8} +(-0.779397 - 0.165666i) q^{9} +(-0.636073 - 0.706430i) q^{11} +(0.238907 - 0.536593i) q^{12} +(-0.0683897 - 0.153606i) q^{13} +(-1.85522 + 2.06043i) q^{14} +(2.46909 + 1.79390i) q^{16} +(-4.88741 - 4.40064i) q^{17} +(0.410495 + 0.921986i) q^{18} +(1.05317 + 0.468903i) q^{19} +(-0.339629 - 3.23135i) q^{21} +(-0.250331 + 1.17772i) q^{22} +(-4.40197 + 1.43029i) q^{23} +(-4.40562 + 0.936443i) q^{24} +(-0.106485 + 0.184437i) q^{26} +(-5.35983 - 1.74151i) q^{27} +(-0.861483 - 0.0905455i) q^{28} +(1.08143 - 0.785701i) q^{29} +(5.56350 + 0.217815i) q^{31} +2.20322i q^{32} +(-0.829355 - 1.14151i) q^{33} +(-0.870722 + 8.28437i) q^{34} +(-0.157657 + 0.273070i) q^{36} +(-3.35295 + 1.93582i) q^{37} +(-0.303591 - 1.42828i) q^{38} +(-0.0771233 - 0.237361i) q^{39} +(-0.0343065 - 0.326405i) q^{41} +(-3.05832 + 2.75373i) q^{42} +(3.91711 - 8.79797i) q^{43} +(-0.343649 + 0.153002i) q^{44} +(4.74283 + 3.44587i) q^{46} +(3.31427 - 4.56170i) q^{47} +(3.36650 + 3.03121i) q^{48} +(2.01741 - 0.898207i) q^{49} +(-6.53194 - 7.25445i) q^{51} +(-0.0661729 + 0.00695505i) q^{52} +(1.52460 - 7.17270i) q^{53} +(2.20581 + 6.78877i) q^{54} +(3.32116 + 5.75242i) q^{56} +(1.48193 + 0.855590i) q^{57} +(-1.61022 - 0.523192i) q^{58} +(-0.277326 + 2.63859i) q^{59} -1.74967 q^{61} +(-3.91877 - 5.86309i) q^{62} +1.74421i q^{63} +(7.19583 - 5.22808i) q^{64} +(-0.552261 + 1.69968i) q^{66} +(-0.478052 - 0.276003i) q^{67} +(-2.25385 + 1.30126i) q^{68} +(-6.72002 + 1.42838i) q^{69} +(-1.11214 - 0.236393i) q^{71} +(2.40461 - 0.252735i) q^{72} +(-5.88764 + 5.30125i) q^{73} +(4.47988 + 1.99457i) q^{74} +(0.305260 - 0.339025i) q^{76} +(-1.22309 + 1.68344i) q^{77} +(-0.185807 + 0.255741i) q^{78} +(-3.03938 + 3.37557i) q^{79} +(-5.45813 - 2.43012i) q^{81} +(-0.308927 + 0.278159i) q^{82} +(-0.324608 + 0.0341177i) q^{83} +(-1.25766 - 0.267324i) q^{84} +(-11.9315 + 2.53613i) q^{86} +(1.71829 - 0.992053i) q^{87} +(2.49806 + 1.44225i) q^{88} +(4.54569 - 13.9902i) q^{89} +(-0.297768 + 0.216341i) q^{91} +1.83159i q^{92} +(8.17896 + 1.18473i) q^{93} -7.14183 q^{94} +(-0.341837 + 3.25236i) q^{96} +(14.7596 + 4.79569i) q^{97} +(-2.42233 - 1.39853i) q^{98} +(0.378722 + 0.655965i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 28 q^{4} + 22 q^{6} + 20 q^{9} - 14 q^{11} + 12 q^{14} - 4 q^{16} - 32 q^{19} + 18 q^{21} + 40 q^{24} + 18 q^{26} + 28 q^{29} + 30 q^{31} + 64 q^{34} + 2 q^{36} + 6 q^{39} - 16 q^{41} - 78 q^{44}+ \cdots - 12 q^{99}+O(q^{100}) $ 32 * q + 28 * q^4 + 22 * q^6 + 20 * q^9 - 14 * q^11 + 12 * q^14 - 4 * q^16 - 32 * q^19 + 18 * q^21 + 40 * q^24 + 18 * q^26 + 28 * q^29 + 30 * q^31 + 64 * q^34 + 2 * q^36 + 6 * q^39 - 16 * q^41 - 78 * q^44 + 68 * q^46 - 4 * q^49 - 84 * q^51 + 92 * q^54 - 60 * q^56 - 8 * q^59 - 120 * q^61 - 46 * q^64 - 60 * q^66 - 76 * q^69 - 28 * q^71 - 26 * q^74 - 24 * q^76 - 36 * q^79 + 46 * q^81 - 16 * q^84 - 52 * q^86 - 2 * q^89 + 16 * q^91 - 88 * q^94 + 16 * q^96 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/775\mathbb{Z}\right)^\times$.

$n$	$251$	$652$
$\chi(n)$	$e\left(\frac{8}{15}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.744490	−	1.02470i	−0.526434	−	0.724574i	0.460148	−	0.887842i	$-0.347796\pi$
$2$	−0.744490	−	1.02470i	−0.526434	−	0.724574i	−0.986582	+	0.163268i	$0.947796\pi$
$3$	1.47618	+	0.155153i	0.852275	+	0.0895777i	0.520584	−	0.853810i	$-0.325714\pi$
$3$	1.47618	+	0.155153i	0.852275	+	0.0895777i	0.331691	+	0.943388i	$0.392381\pi$
$4$	0.122284	−	0.376353i	0.0611422	−	0.188176i
$5$		0			0
$5$		0			0
$6$	−0.940018	−	1.62816i	−0.383761	−	0.664693i
$7$	−0.455117	−	2.14115i	−0.172018	−	0.809280i	−0.976536	−	0.215353i	$-0.930910\pi$
$7$	−0.455117	−	2.14115i	−0.172018	−	0.809280i	0.804518	−	0.593928i	$-0.202423\pi$
$8$	−2.88591	+	0.937688i	−1.02032	+	0.331523i
$9$	−0.779397	−	0.165666i	−0.259799	−	0.0552220i
$10$		0			0
$11$	−0.636073	−	0.706430i	−0.191783	−	0.212997i	0.639583	−	0.768722i	$-0.279107\pi$
$11$	−0.636073	−	0.706430i	−0.191783	−	0.212997i	−0.831366	+	0.555726i	$0.812441\pi$
$12$	0.238907	−	0.536593i	0.0689664	−	0.154901i
$13$	−0.0683897	−	0.153606i	−0.0189679	−	0.0426026i	0.903813	−	0.427927i	$-0.140756\pi$
$13$	−0.0683897	−	0.153606i	−0.0189679	−	0.0426026i	−0.922781	+	0.385325i	$0.874089\pi$
$14$	−1.85522	+	2.06043i	−0.495827	+	0.550672i
$15$		0			0
$16$	2.46909	+	1.79390i	0.617273	+	0.448475i
$17$	−4.88741	−	4.40064i	−1.18537	−	1.06731i	−0.996352	−	0.0853387i	$-0.972803\pi$
$17$	−4.88741	−	4.40064i	−1.18537	−	1.06731i	−0.189018	−	0.981974i	$-0.560531\pi$
$18$	0.410495	+	0.921986i	0.0967546	+	0.217314i
$19$	1.05317	+	0.468903i	0.241615	+	0.107574i	0.523972	−	0.851736i	$-0.324450\pi$
$19$	1.05317	+	0.468903i	0.241615	+	0.107574i	−0.282357	+	0.959309i	$0.591116\pi$
$20$		0			0
$21$	−0.339629	−	3.23135i	−0.0741130	−	0.705139i
$22$	−0.250331	+	1.17772i	−0.0533708	+	0.251090i
$23$	−4.40197	+	1.43029i	−0.917873	+	0.298235i	−0.729594	−	0.683880i	$-0.760291\pi$
$23$	−4.40197	+	1.43029i	−0.917873	+	0.298235i	−0.188279	+	0.982116i	$0.560291\pi$
$24$	−4.40562	+	0.936443i	−0.899293	+	0.191151i
$25$		0			0
$26$	−0.106485	+	0.184437i	−0.0208834	+	0.0361711i
$27$	−5.35983	−	1.74151i	−1.03150	−	0.335155i
$28$	−0.861483	−	0.0905455i	−0.162805	−	0.0171115i
$29$	1.08143	−	0.785701i	0.200816	−	0.145901i	−0.482833	−	0.875713i	$-0.660392\pi$
$29$	1.08143	−	0.785701i	0.200816	−	0.145901i	0.683649	+	0.729811i	$0.260392\pi$
$30$		0			0
$31$	5.56350	+	0.217815i	0.999234	+	0.0391208i
$31$	5.56350	+	0.217815i	0.999234	+	0.0391208i
$32$			2.20322i			0.389479i
$33$	−0.829355	−	1.14151i	−0.144372	−	0.198711i
$34$	−0.870722	+	8.28437i	−0.149328	+	1.42076i
$35$		0			0
$36$	−0.157657	+	0.273070i	−0.0262762	+	0.0455116i
$37$	−3.35295	+	1.93582i	−0.551221	+	0.318248i	−0.749614	−	0.661875i	$-0.769761\pi$
$37$	−3.35295	+	1.93582i	−0.551221	+	0.318248i	0.198393	+	0.980122i	$0.436428\pi$
$38$	−0.303591	−	1.42828i	−0.0492489	−	0.231698i
$39$	−0.0771233	−	0.237361i	−0.0123496	−	0.0380082i
$40$		0			0
$41$	−0.0343065	−	0.326405i	−0.00535778	−	0.0509758i	0.991516	−	0.129982i	$-0.0414920\pi$
$41$	−0.0343065	−	0.326405i	−0.00535778	−	0.0509758i	−0.996874	+	0.0790062i	$0.974825\pi$
$42$	−3.05832	+	2.75373i	−0.471909	+	0.424909i
$43$	3.91711	−	8.79797i	0.597353	−	1.34168i	−0.321437	−	0.946931i	$-0.604166\pi$
$43$	3.91711	−	8.79797i	0.597353	−	1.34168i	0.918790	−	0.394746i	$-0.129167\pi$
$44$	−0.343649	+	0.153002i	−0.0518070	+	0.0230660i
$45$		0			0
$46$	4.74283	+	3.44587i	0.699293	+	0.508066i
$47$	3.31427	−	4.56170i	0.483436	−	0.665393i	−0.495725	−	0.868480i	$-0.665097\pi$
$47$	3.31427	−	4.56170i	0.483436	−	0.665393i	0.979161	+	0.203087i	$0.0650974\pi$
$48$	3.36650	+	3.03121i	0.485913	+	0.437518i
$49$	2.01741	−	0.898207i	0.288201	−	0.128315i
$50$		0			0
$51$	−6.53194	−	7.25445i	−0.914654	−	1.01583i
$52$	−0.0661729	+	0.00695505i	−0.00917653	+	0.000964493i
$53$	1.52460	−	7.17270i	0.209421	−	0.985246i	−0.740331	−	0.672242i	$-0.765331\pi$
$53$	1.52460	−	7.17270i	0.209421	−	0.985246i	0.949752	−	0.313004i	$-0.101335\pi$
$54$	2.20581	+	6.78877i	0.300172	+	0.923835i
$55$		0			0
$56$	3.32116	+	5.75242i	0.443809	+	0.768699i
$57$	1.48193	+	0.855590i	0.196286	+	0.113326i
$58$	−1.61022	−	0.523192i	−0.211432	−	0.0686985i
$59$	−0.277326	+	2.63859i	−0.0361048	+	0.343515i	0.961526	+	0.274715i	$0.0885835\pi$
$59$	−0.277326	+	2.63859i	−0.0361048	+	0.343515i	−0.997631	+	0.0687995i	$0.978083\pi$
$60$		0			0
$61$	−1.74967			−0.224023			−0.112011	−	0.993707i	$-0.535729\pi$
$61$	−1.74967			−0.224023			−0.112011	+	0.993707i	$0.535729\pi$
$62$	−3.91877	−	5.86309i	−0.497685	−	0.744614i
$63$			1.74421i			0.219749i
$64$	7.19583	−	5.22808i	0.899479	−	0.653510i
$65$		0			0
$66$	−0.552261	+	1.69968i	−0.0679786	+	0.209217i
$67$	−0.478052	−	0.276003i	−0.0584033	−	0.0337192i	0.470514	−	0.882393i	$-0.344069\pi$
$67$	−0.478052	−	0.276003i	−0.0584033	−	0.0337192i	−0.528917	+	0.848673i	$0.677402\pi$
$68$	−2.25385	+	1.30126i	−0.273319	+	0.157801i
$69$	−6.72002	+	1.42838i	−0.808996	+	0.171957i
$70$		0			0
$71$	−1.11214	−	0.236393i	−0.131987	−	0.0280547i	0.141444	−	0.989946i	$-0.454825\pi$
$71$	−1.11214	−	0.236393i	−0.131987	−	0.0280547i	−0.273431	+	0.961891i	$0.588159\pi$
$72$	2.40461	−	0.252735i	0.283386	−	0.0297851i
$73$	−5.88764	+	5.30125i	−0.689096	+	0.620465i	−0.937415	−	0.348214i	$-0.886788\pi$
$73$	−5.88764	+	5.30125i	−0.689096	+	0.620465i	0.248319	+	0.968678i	$0.420122\pi$
$74$	4.47988	+	1.99457i	0.520775	+	0.231864i
$75$		0			0
$76$	0.305260	−	0.339025i	0.0350157	−	0.0388888i
$77$	−1.22309	+	1.68344i	−0.139384	+	0.191846i
$78$	−0.185807	+	0.255741i	−0.0210385	+	0.0289570i
$79$	−3.03938	+	3.37557i	−0.341957	+	0.379782i	−0.889453	−	0.457027i	$-0.848914\pi$
$79$	−3.03938	+	3.37557i	−0.341957	+	0.379782i	0.547496	+	0.836808i	$0.315581\pi$
$80$		0			0
$81$	−5.45813	−	2.43012i	−0.606459	−	0.270013i
$82$	−0.308927	+	0.278159i	−0.0341152	+	0.0307175i
$83$	−0.324608	+	0.0341177i	−0.0356303	+	0.00374490i	−0.122327	−	0.992490i	$-0.539036\pi$
$83$	−0.324608	+	0.0341177i	−0.0356303	+	0.00374490i	0.0866965	+	0.996235i	$0.472369\pi$
$84$	−1.25766	−	0.267324i	−0.137222	−	0.0291674i
$85$		0			0
$86$	−11.9315	+	2.53613i	−1.28661	+	0.273478i
$87$	1.71829	−	0.992053i	0.184220	−	0.106359i
$88$	2.49806	+	1.44225i	0.266294	+	0.153745i
$89$	4.54569	−	13.9902i	0.481842	−	1.48296i	−0.354661	−	0.934995i	$-0.615404\pi$
$89$	4.54569	−	13.9902i	0.481842	−	1.48296i	0.836503	−	0.547962i	$-0.184596\pi$
$90$		0			0
$91$	−0.297768	+	0.216341i	−0.0312146	+	0.0226787i
$92$			1.83159i			0.190957i
$93$	8.17896	+	1.18473i	0.848118	+	0.122851i
$94$	−7.14183			−0.736623
$95$		0			0
$96$	−0.341837	+	3.25236i	−0.0348886	+	0.331943i
$97$	14.7596	+	4.79569i	1.49861	+	0.486929i	0.939613	−	0.342239i	$-0.111185\pi$
$97$	14.7596	+	4.79569i	1.49861	+	0.486929i	0.559000	+	0.829168i	$0.311185\pi$
$98$	−2.42233	−	1.39853i	−0.244692	−	0.141273i
$99$	0.378722	+	0.655965i	0.0380630	+	0.0659270i
$100$		0			0
$101$	1.50602	+	4.63507i	0.149855	+	0.461206i	0.997603	−	0.0691923i	$-0.0220422\pi$
$101$	1.50602	+	4.63507i	0.149855	+	0.461206i	−0.847748	+	0.530399i	$0.822042\pi$
$102$	−2.57069	+	12.0942i	−0.254536	+	1.19750i
$103$	−1.92004	+	0.201805i	−0.189187	+	0.0198844i	−0.198648	−	0.980071i	$-0.563655\pi$
$103$	−1.92004	+	0.201805i	−0.189187	+	0.0198844i	0.00946083	+	0.999955i	$0.496988\pi$
$104$	0.341401	+	0.379164i	0.0334771	+	0.0371801i
$105$		0			0
$106$	−8.48494	+	3.77774i	−0.824130	+	0.366926i
$107$	9.30976	+	8.38254i	0.900008	+	0.810371i	0.982508	−	0.186220i	$-0.0596238\pi$
$107$	9.30976	+	8.38254i	0.900008	+	0.810371i	−0.0824999	+	0.996591i	$0.526290\pi$
$108$	−1.31085	+	1.80423i	−0.126136	+	0.173612i
$109$	−8.30253	−	6.03214i	−0.795238	−	0.577774i	0.114275	−	0.993449i	$-0.463545\pi$
$109$	−8.30253	−	6.03214i	−0.795238	−	0.577774i	−0.909513	+	0.415675i	$0.863545\pi$
$110$		0			0
$111$	−5.24991	+	2.33741i	−0.498300	+	0.221857i
$112$	2.71729	−	6.10314i	0.256760	−	0.576692i
$113$	−2.85586	+	2.57143i	−0.268657	+	0.241900i	−0.792437	−	0.609954i	$-0.791188\pi$
$113$	−2.85586	+	2.57143i	−0.268657	+	0.241900i	0.523780	+	0.851854i	$0.324521\pi$
$114$	−0.226553	−	2.15551i	−0.0212187	−	0.201882i
$115$		0			0
$116$	−0.163459	−	0.503076i	−0.0151768	−	0.0467095i
$117$	0.0278555	+	0.131050i	0.00257524	+	0.0121155i
$118$	2.91023	−	1.68022i	0.267908	−	0.154677i
$119$	−7.19811	+	12.4675i	−0.659850	+	1.14289i
$120$		0			0
$121$	1.05536	−	10.0411i	0.0959416	−	0.912824i
$122$	1.30261	+	1.79289i	0.117933	+	0.162321i
$123$		−	0.487156i		−	0.0439254i
$124$	0.762305	−	2.06720i	0.0684570	−	0.185640i
$125$		0			0
$126$	1.78729	−	1.29854i	0.159225	−	0.115684i
$127$	−7.30366	−	0.767645i	−0.648095	−	0.0681175i	−0.225223	−	0.974307i	$-0.572311\pi$
$127$	−7.30366	−	0.767645i	−0.648095	−	0.0681175i	−0.422871	+	0.906190i	$0.638978\pi$
$128$	−6.52366	−	2.11967i	−0.576616	−	0.187354i
$129$	7.14740	−	12.3797i	0.629294	−	1.08997i
$130$		0			0
$131$	−12.7489	+	2.70985i	−1.11387	+	0.236761i	−0.727855	−	0.685731i	$-0.759483\pi$
$131$	−12.7489	+	2.70985i	−1.11387	+	0.236761i	−0.386017	+	0.922492i	$0.626149\pi$
$132$	−0.531027	+	0.172541i	−0.0462200	+	0.0150178i
$133$	0.524677	−	2.46841i	0.0454953	−	0.214039i
$134$	0.0730834	+	0.695342i	0.00631345	+	0.0600684i
$135$		0			0
$136$	18.2310	+	8.11698i	1.56330	+	0.696025i
$137$	−0.0546244	−	0.122689i	−0.00466688	−	0.0104820i	0.911197	−	0.411971i	$-0.135159\pi$
$137$	−0.0546244	−	0.122689i	−0.00466688	−	0.0104820i	−0.915864	+	0.401489i	$0.868493\pi$
$138$	6.46666	+	5.82260i	0.550478	+	0.495653i
$139$	9.32593	+	6.77569i	0.791015	+	0.574706i	0.908265	−	0.418396i	$-0.137408\pi$
$139$	9.32593	+	6.77569i	0.791015	+	0.574706i	−0.117249	+	0.993103i	$0.537408\pi$
$140$		0			0
$141$	5.60024	−	6.21969i	0.471625	−	0.523793i
$142$	0.585746	+	1.31561i	0.0491547	+	0.110403i
$143$	−0.0650109	+	0.146017i	−0.00543649	+	0.0122106i
$144$	−1.62721	−	1.80720i	−0.135601	−	0.150600i
$145$		0			0
$146$	9.81549	+	2.08635i	0.812336	+	0.172667i
$147$	3.11742	−	1.01291i	0.257120	−	0.0835435i
$148$	0.318540	+	1.49861i	0.0261838	+	0.123185i
$149$	−2.72054	−	4.71211i	−0.222875	−	0.386031i	0.732805	−	0.680439i	$-0.238211\pi$
$149$	−2.72054	−	4.71211i	−0.222875	−	0.386031i	−0.955680	+	0.294408i	$0.904878\pi$
$150$		0			0
$151$	4.23019	−	13.0192i	0.344248	−	1.05949i	−0.617737	−	0.786385i	$-0.711950\pi$
$151$	4.23019	−	13.0192i	0.344248	−	1.05949i	0.961985	−	0.273102i	$-0.0880496\pi$
$152$	−3.47905	−	0.365662i	−0.282188	−	0.0296591i
$153$	3.08019	+	4.23952i	0.249019	+	0.342745i
$154$	2.63560			0.212383
$155$		0			0
$156$	−0.0987625			−0.00790733
$157$	8.84931	+	12.1800i	0.706252	+	0.972072i	0.999870	+	0.0161493i	$0.00514071\pi$
$157$	8.84931	+	12.1800i	0.706252	+	0.972072i	−0.293618	+	0.955923i	$0.594859\pi$
$158$	5.72174	+	0.601379i	0.455197	+	0.0478432i
$159$	3.36346	−	10.3517i	0.266740	−	0.820942i
$160$		0			0
$161$	5.06587	+	8.77434i	0.399246	+	0.691515i
$162$	1.57338	+	7.40215i	0.123616	+	0.581568i
$163$	16.2042	−	5.26506i	1.26921	−	0.412391i	0.404443	−	0.914563i	$-0.367466\pi$
$163$	16.2042	−	5.26506i	1.26921	−	0.412391i	0.864768	+	0.502172i	$0.167466\pi$
$164$	−0.127038	−	0.0270028i	−0.00992003	−	0.00210857i
$165$		0			0
$166$	0.276628	+	0.307226i	0.0214705	+	0.0238454i
$167$	6.58842	−	14.7978i	0.509827	−	1.14509i	−0.456955	−	0.889490i	$-0.651060\pi$
$167$	6.58842	−	14.7978i	0.509827	−	1.14509i	0.966782	−	0.255601i	$-0.0822732\pi$
$168$	4.01014	+	9.00692i	0.309389	+	0.694899i
$169$	8.67978	−	9.63987i	0.667675	−	0.741529i
$170$		0			0
$171$	−0.743159	−	0.539937i	−0.0568308	−	0.0412900i
$172$	−2.83214	−	2.55007i	−0.215948	−	0.194441i
$173$	0.948192	+	2.12967i	0.0720897	+	0.161916i	0.945996	−	0.324178i	$-0.105088\pi$
$173$	0.948192	+	2.12967i	0.0720897	+	0.161916i	−0.873906	+	0.486094i	$0.838421\pi$
$174$	−2.29581	−	1.02216i	−0.174045	−	0.0774896i
$175$		0			0
$176$	−0.303256	−	2.88529i	−0.0228588	−	0.217487i
$177$	−0.818770	+	3.85201i	−0.0615425	+	0.289535i
$178$	−17.7200	+	5.75758i	−1.32817	+	0.431549i
$179$	−16.5998	+	3.52839i	−1.24073	+	0.263724i	−0.781110	−	0.624394i	$-0.785346\pi$
$179$	−16.5998	+	3.52839i	−1.24073	+	0.263724i	−0.459616	+	0.888118i	$0.652013\pi$
$180$		0			0
$181$	3.66788	−	6.35296i	0.272631	−	0.472211i	−0.696903	−	0.717165i	$-0.745439\pi$
$181$	3.66788	−	6.35296i	0.272631	−	0.472211i	0.969535	+	0.244954i	$0.0787727\pi$
$182$	0.443371	+	0.144060i	0.0328648	+	0.0106784i
$183$	−2.58284	−	0.271467i	−0.190929	−	0.0200674i
$184$	11.3625	−	8.25534i	0.837655	−	0.608592i
$185$		0			0
$186$	−4.87515	−	9.26301i	−0.357464	−	0.679197i
$187$			6.25174i			0.457173i
$188$	−1.31153	−	1.80516i	−0.0956528	−	0.131655i
$189$	−1.28951	+	12.2688i	−0.0937977	+	0.892425i
$190$		0			0
$191$	−3.91138	+	6.77471i	−0.283018	+	0.490201i	−0.972127	−	0.234457i	$-0.924669\pi$
$191$	−3.91138	+	6.77471i	−0.283018	+	0.490201i	0.689109	+	0.724658i	$0.258002\pi$
$192$	11.4335	−	6.60115i	0.825143	−	0.476397i
$193$	−0.962944	−	4.53030i	−0.0693142	−	0.326098i	0.929805	−	0.368052i	$-0.119975\pi$
$193$	−0.962944	−	4.53030i	−0.0693142	−	0.326098i	−0.999120	+	0.0419539i	$0.986642\pi$
$194$	−6.07423	−	18.6946i	−0.436104	−	1.34219i
$195$		0			0
$196$	−0.0913453	−	0.869092i	−0.00652466	−	0.0620780i
$197$	16.6348	−	14.9781i	1.18518	−	1.06714i	0.188813	−	0.982013i	$-0.439536\pi$
$197$	16.6348	−	14.9781i	1.18518	−	1.06714i	0.996370	−	0.0851305i	$-0.0271307\pi$
$198$	0.390215	−	0.876436i	0.0277313	−	0.0622856i
$199$	24.3037	−	10.8207i	1.72285	−	0.767061i	0.726001	−	0.687694i	$-0.241377\pi$
$199$	24.3037	−	10.8207i	1.72285	−	0.767061i	0.996845	−	0.0793670i	$-0.0252899\pi$
$200$		0			0
$201$	−0.662869	−	0.481603i	−0.0467552	−	0.0339696i
$202$	3.62834	−	4.99399i	0.255289	−	0.351376i
$203$	−2.17448	−	1.95791i	−0.152619	−	0.137419i
$204$	−3.52899	+	1.57121i	−0.247078	+	0.110006i
$205$		0			0
$206$	1.63624	+	1.81723i	0.114002	+	0.126612i
$207$	3.66783	−	0.385504i	0.254932	−	0.0267944i
$208$	0.106693	−	0.501951i	0.00739782	−	0.0348040i
$209$	−0.338648	−	1.04225i	−0.0234247	−	0.0720939i
$210$		0			0
$211$	−0.663069	−	1.14847i	−0.0456476	−	0.0790639i	0.842299	−	0.539011i	$-0.181202\pi$
$211$	−0.663069	−	1.14847i	−0.0456476	−	0.0790639i	−0.887946	+	0.459947i	$0.847868\pi$
$212$	−2.51303	−	1.45090i	−0.172596	−	0.0996481i
$213$	−1.60505	−	0.521512i	−0.109976	−	0.0357334i
$214$	1.65859	−	15.7804i	0.113379	−	1.07873i
$215$		0			0
$216$	17.1010			1.16357
$217$	−2.06567	−	12.0115i	−0.140227	−	0.815390i
$218$			12.9985i			0.880368i
$219$	−9.51374	+	6.91214i	−0.642879	+	0.467079i
$220$		0			0
$221$	−0.341716	+	1.05169i	−0.0229863	+	0.0707445i
$222$	6.30366	+	3.63942i	0.423074	+	0.244262i
$223$	10.4962	−	6.05997i	0.702876	−	0.405806i	−0.105542	−	0.994415i	$-0.533658\pi$
$223$	10.4962	−	6.05997i	0.702876	−	0.405806i	0.808418	+	0.588609i	$0.200324\pi$
$224$	4.71744	−	1.00272i	0.315198	−	0.0669973i
$225$		0			0
$226$	4.76111	+	1.01201i	0.316704	+	0.0673176i
$227$	−15.8150	+	1.66223i	−1.04968	+	0.110326i	−0.613628	−	0.789595i	$-0.710291\pi$
$227$	−15.8150	+	1.66223i	−1.04968	+	0.110326i	−0.436053	+	0.899921i	$0.643624\pi$
$228$	0.503220	−	0.453101i	0.0333266	−	0.0300074i
$229$	14.8895	+	6.62924i	0.983927	+	0.438073i	0.834685	−	0.550728i	$-0.185650\pi$
$229$	14.8895	+	6.62924i	0.983927	+	0.438073i	0.149242	+	0.988801i	$0.452317\pi$
$230$		0			0
$231$	−2.06670	+	2.29530i	−0.135979	+	0.151020i
$232$	−2.38415	+	3.28150i	−0.156527	+	0.215441i
$233$	3.01120	−	4.14456i	0.197270	−	0.271519i	−0.698910	−	0.715210i	$-0.746331\pi$
$233$	3.01120	−	4.14456i	0.197270	−	0.271519i	0.896180	+	0.443691i	$0.146331\pi$
$234$	0.113549	−	0.126109i	0.00742292	−	0.00824399i
$235$		0			0
$236$	0.959126	+	0.427030i	0.0624338	+	0.0277973i
$237$	−5.01041	+	4.51140i	−0.325461	+	0.293047i
$238$	18.1344	−	1.90600i	1.17548	−	0.123548i
$239$	8.38077	+	1.78139i	0.542107	+	0.115228i	0.470823	−	0.882228i	$-0.343957\pi$
$239$	8.38077	+	1.78139i	0.542107	+	0.115228i	0.0712838	+	0.997456i	$0.477290\pi$
$240$		0			0
$241$	6.69714	−	1.42352i	0.431401	−	0.0916971i	0.0129071	−	0.999917i	$-0.495891\pi$
$241$	6.69714	−	1.42352i	0.431401	−	0.0916971i	0.418494	+	0.908220i	$0.362558\pi$
$242$	−11.0748	+	6.39404i	−0.711915	+	0.411024i
$243$	6.96171	+	4.01935i	0.446594	+	0.257841i
$244$	−0.213958	+	0.658494i	−0.0136972	+	0.0421558i
$245$		0			0
$246$	−0.499190	+	0.362683i	−0.0318272	+	0.0231238i
$247$		−	0.193842i		−	0.0123338i
$248$	−16.2600	+	4.58824i	−1.03251	+	0.291353i
$249$	−0.484474			−0.0307023
$250$		0			0
$251$	−2.36925	+	22.5419i	−0.149546	+	1.42283i	0.620180	+	0.784460i	$0.287060\pi$
$251$	−2.36925	+	22.5419i	−0.149546	+	1.42283i	−0.769726	+	0.638375i	$0.779607\pi$
$252$	0.656437	+	0.213289i	0.0413516	+	0.0134360i
$253$	3.81037	+	2.19992i	0.239556	+	0.138308i
$254$	4.65089	+	8.05558i	0.291823	+	0.505452i
$255$		0			0
$256$	−2.81235	−	8.65553i	−0.175772	−	0.540971i
$257$	−3.46347	+	16.2943i	−0.216045	+	1.01641i	0.727740	+	0.685853i	$0.240571\pi$
$257$	−3.46347	+	16.2943i	−0.216045	+	1.01641i	−0.943785	+	0.330560i	$0.892763\pi$
$258$	−18.0066	+	1.89257i	−1.12104	+	0.117826i
$259$	5.67088	+	6.29815i	0.352371	+	0.391348i
$260$		0			0
$261$	−0.973024	+	0.433218i	−0.0602286	+	0.0268155i
$262$	12.2682	+	11.0463i	0.757931	+	0.682444i
$263$	14.4515	−	19.8908i	0.891118	−	1.22652i	−0.0820979	−	0.996624i	$-0.526162\pi$
$263$	14.4515	−	19.8908i	0.891118	−	1.22652i	0.973216	−	0.229894i	$-0.0738380\pi$
$264$	3.46382	+	2.51661i	0.213184	+	0.154887i
$265$		0			0
$266$	−2.92000	+	1.30007i	−0.179037	+	0.0797124i
$267$	8.88089	−	19.9468i	0.543502	−	1.22073i
$268$	−0.162333	+	0.146165i	−0.00991606	+	0.00892846i
$269$	1.30808	+	12.4456i	0.0797553	+	0.758821i	0.959182	+	0.282788i	$0.0912592\pi$
$269$	1.30808	+	12.4456i	0.0797553	+	0.758821i	−0.879427	+	0.476033i	$0.842074\pi$
$270$		0			0
$271$	−8.39516	−	25.8376i	−0.509969	−	1.56952i	−0.792252	−	0.610194i	$-0.791092\pi$
$271$	−8.39516	−	25.8376i	−0.509969	−	1.56952i	0.282283	−	0.959331i	$-0.408908\pi$
$272$	−4.17314	−	19.6331i	−0.253034	−	1.19043i
$273$	−0.473127	+	0.273160i	−0.0286349	+	0.0165324i
$274$	−0.0850519	+	0.147314i	−0.00513817	+	0.00889957i
$275$		0			0
$276$	−0.284177	+	2.70377i	−0.0171055	+	0.162748i
$277$	8.90926	+	12.2625i	0.535305	+	0.736785i	0.987927	−	0.154918i	$-0.0495113\pi$
$277$	8.90926	+	12.2625i	0.535305	+	0.736785i	−0.452622	+	0.891703i	$0.649511\pi$
$278$		−	14.6007i		−	0.875694i
$279$	−4.30009	−	1.09145i	−0.257440	−	0.0653433i
$280$		0			0
$281$	−24.4709	+	17.7792i	−1.45981	+	1.06062i	−0.476401	+	0.879228i	$0.658059\pi$
$281$	−24.4709	+	17.7792i	−1.45981	+	1.06062i	−0.983412	+	0.181387i	$0.941941\pi$
$282$	−10.5426	−	1.10808i	−0.627806	−	0.0659850i
$283$	−2.99138	−	0.971958i	−0.177819	−	0.0577769i	0.218754	−	0.975780i	$-0.429801\pi$
$283$	−2.99138	−	0.971958i	−0.177819	−	0.0577769i	−0.396573	+	0.918003i	$0.629801\pi$
$284$	−0.224965	+	0.389651i	−0.0133492	+	0.0231215i
$285$		0			0
$286$	0.198024	−	0.0420913i	0.0117094	−	0.00248891i
$287$	−0.683269	+	0.222008i	−0.0403321	+	0.0131047i
$288$	0.364999	−	1.71719i	0.0215078	−	0.101186i
$289$	2.74412	+	26.1086i	0.161419	+	1.53580i
$290$		0			0
$291$	21.0438	+	9.36932i	1.23361	+	0.549239i
$292$	1.27517	+	2.86409i	0.0746239	+	0.167608i
$293$	−1.41204	−	1.27140i	−0.0824920	−	0.0742761i	0.626853	−	0.779137i	$-0.284343\pi$
$293$	−1.41204	−	1.27140i	−0.0824920	−	0.0742761i	−0.709345	+	0.704861i	$0.751009\pi$
$294$	−3.35882	−	2.44033i	−0.195890	−	0.142323i
$295$		0			0
$296$	7.86109	−	8.73063i	0.456917	−	0.507458i
$297$	2.17898	+	4.89408i	0.126437	+	0.283983i
$298$	−2.80310	+	6.29586i	−0.162379	+	0.364709i
$299$	0.520749	+	0.578350i	0.0301157	+	0.0334469i
$300$		0			0
$301$	−20.6205	−	4.38303i	−1.18855	−	0.252634i
$302$	−16.4901	+	5.35797i	−0.948900	+	0.308316i
$303$	1.50402	+	7.07588i	0.0864039	+	0.406498i
$304$	1.75922	+	3.04705i	0.100898	+	0.174760i
$305$		0			0
$306$	2.05108	−	6.31256i	0.117252	−	0.360865i
$307$	−22.6036	−	2.37573i	−1.29005	−	0.135590i	−0.565466	−	0.824772i	$-0.691304\pi$
$307$	−22.6036	−	2.37573i	−1.29005	−	0.135590i	−0.724589	+	0.689181i	$0.757970\pi$
$308$	0.484002	+	0.666171i	0.0275786	+	0.0379586i
$309$	−2.86565			−0.163021
$310$		0			0
$311$	15.8754			0.900213			0.450106	−	0.892975i	$-0.351386\pi$
$311$	15.8754			0.900213			0.450106	+	0.892975i	$0.351386\pi$
$312$	0.445142	+	0.612685i	0.0252012	+	0.0346865i
$313$	6.31457	+	0.663688i	0.356920	+	0.0375138i	0.281292	−	0.959622i	$-0.409237\pi$
$313$	6.31457	+	0.663688i	0.356920	+	0.0375138i	0.0756284	+	0.997136i	$0.475904\pi$
$314$	5.89268	−	18.1358i	0.332543	−	1.02346i
$315$		0			0
$316$	0.898737	+	1.55666i	0.0505579	+	0.0875689i
$317$	3.18126	+	14.9666i	0.178677	+	0.840610i	0.972581	+	0.232566i	$0.0747122\pi$
$317$	3.18126	+	14.9666i	0.178677	+	0.840610i	−0.793903	+	0.608044i	$0.791954\pi$
$318$	−13.1115	+	4.26017i	−0.735254	+	0.238898i
$319$	−1.24291	−	0.264188i	−0.0695895	−	0.0147917i
$320$		0			0
$321$	12.4423	+	13.8186i	0.694463	+	0.771280i
$322$	5.21960	−	11.7234i	0.290877	−	0.653320i
$323$	−3.08381	−	6.92636i	−0.171588	−	0.385393i
$324$	−1.58202	+	1.75702i	−0.0878903	+	0.0976120i
$325$		0			0
$326$	−17.4590	−	12.6847i	−0.966963	−	0.702540i
$327$	−11.3201	−	10.1927i	−0.626006	−	0.563658i
$328$	0.405071	+	0.909805i	0.0223663	+	0.0502356i
$329$	−11.2757	−	5.02026i	−0.621649	−	0.276776i
$330$		0			0
$331$	0.937407	+	8.91883i	0.0515245	+	0.490223i	0.989606	+	0.143808i	$0.0459346\pi$
$331$	0.937407	+	8.91883i	0.0515245	+	0.490223i	−0.938081	+	0.346416i	$0.887399\pi$
$332$	−0.0268542	+	0.126339i	−0.00147382	+	0.00693376i
$333$	2.93398	−	0.953307i	0.160781	−	0.0522409i
$334$	−20.0684	+	4.26566i	−1.09809	+	0.233407i
$335$		0			0
$336$	4.95814	−	8.58776i	0.270489	−	0.468501i
$337$	−4.15495	−	1.35002i	−0.226334	−	0.0735405i	0.193654	−	0.981070i	$-0.437966\pi$
$337$	−4.15495	−	1.35002i	−0.226334	−	0.0735405i	−0.419989	+	0.907529i	$0.637966\pi$
$338$	−16.3400	−	1.71740i	−0.888779	−	0.0934144i
$339$	−4.61474	+	3.35281i	−0.250638	+	0.182100i
$340$		0			0
$341$	−3.38492	−	4.06877i	−0.183304	−	0.220336i
$342$			1.16349i			0.0629145i
$343$	−11.8479	−	16.3073i	−0.639729	−	0.880511i
$344$	−3.05466	+	29.0631i	−0.164696	+	1.56698i
$345$		0			0
$346$	1.47636	−	2.55713i	0.0793697	−	0.137472i
$347$	21.1356	−	12.2026i	1.13462	−	0.655073i	0.189526	−	0.981876i	$-0.439305\pi$
$347$	21.1356	−	12.2026i	1.13462	−	0.655073i	0.945092	+	0.326803i	$0.105971\pi$
$348$	−0.163242	−	0.767994i	−0.00875070	−	0.0411688i
$349$	−4.03079	−	12.4055i	−0.215763	−	0.664051i	−0.999099	−	0.0424515i	$-0.986483\pi$
$349$	−4.03079	−	12.4055i	−0.215763	−	0.664051i	0.783335	−	0.621599i	$-0.213517\pi$
$350$		0			0
$351$	0.0990505	+	0.942403i	0.00528692	+	0.0503017i
$352$	1.55642	−	1.40141i	0.0829577	−	0.0746955i
$353$	4.40285	−	9.88896i	0.234340	−	0.526336i	−0.757649	−	0.652662i	$-0.773652\pi$
$353$	4.40285	−	9.88896i	0.234340	−	0.526336i	0.991989	+	0.126326i	$0.0403187\pi$
$354$	4.55673	−	2.02879i	0.242187	−	0.107829i
$355$		0			0
$356$	−4.70938	−	3.42156i	−0.249597	−	0.181343i
$357$	−12.5601	+	17.2875i	−0.664752	+	0.914952i
$358$	15.9739	+	14.3830i	0.844248	+	0.760164i
$359$	−30.8627	+	13.7409i	−1.62887	+	0.725220i	−0.998687	−	0.0512273i	$-0.983687\pi$
$359$	−30.8627	+	13.7409i	−1.62887	+	0.725220i	−0.630183	+	0.776447i	$0.717020\pi$
$360$		0			0
$361$	−11.8242	−	13.1321i	−0.622325	−	0.691162i
$362$	−9.24059	+	0.971225i	−0.485674	+	0.0510464i
$363$	3.11580	−	14.6587i	0.163537	−	0.769382i
$364$	0.0450082	+	0.138521i	0.00235907	+	0.00726048i
$365$		0			0
$366$	1.64472	+	2.84875i	0.0859711	+	0.148906i
$367$	−19.5993	−	11.3157i	−1.02308	−	0.590673i	−0.108082	−	0.994142i	$-0.534471\pi$
$367$	−19.5993	−	11.3157i	−1.02308	−	0.590673i	−0.914993	+	0.403469i	$0.867804\pi$
$368$	−13.4346	−	4.36518i	−0.700329	−	0.227551i
$369$	−0.0273357	+	0.260082i	−0.00142304	+	0.0135393i
$370$		0			0
$371$	−16.0517			−0.833365
$372$	1.44604	−	2.93330i	0.0749734	−	0.152084i
$373$			32.9720i			1.70723i	0.520908	+	0.853613i	$0.325593\pi$
$373$			32.9720i			1.70723i	−0.520908	+	0.853613i	$0.674407\pi$
$374$	6.40617	−	4.65436i	0.331255	−	0.240671i
$375$		0			0
$376$	−5.28723	+	16.2724i	−0.272668	+	0.839185i
$377$	−0.194647	−	0.112379i	−0.0100248	−	0.00578783i
$378$	13.5319	−	7.81265i	0.696006	−	0.401840i
$379$	−31.7818	+	6.75544i	−1.63252	+	0.347004i	−0.930824	−	0.365469i	$-0.880909\pi$
$379$	−31.7818	+	6.75544i	−1.63252	+	0.347004i	−0.701700	+	0.712472i	$0.747575\pi$
$380$		0			0
$381$	−10.6624	−	2.26637i	−0.546253	−	0.116110i
$382$	9.85404	−	1.03570i	0.504177	−	0.0529911i
$383$	−19.9017	+	17.9196i	−1.01693	+	0.915649i	−0.996454	−	0.0841414i	$-0.973185\pi$
$383$	−19.9017	+	17.9196i	−1.01693	+	0.915649i	−0.0204773	+	0.999790i	$0.506519\pi$
$384$	−9.30125	−	4.14118i	−0.474652	−	0.211329i
$385$		0			0
$386$	−3.92530	+	4.35949i	−0.199793	+	0.221892i
$387$	−4.51050	+	6.20818i	−0.229282	+	0.315579i
$388$	3.60974	−	4.96838i	0.183257	−	0.252232i
$389$	11.8687	−	13.1815i	0.601767	−	0.668330i	−0.362892	−	0.931831i	$-0.618211\pi$
$389$	11.8687	−	13.1815i	0.601767	−	0.668330i	0.964659	+	0.263501i	$0.0848772\pi$
$390$		0			0
$391$	27.8084	+	12.3811i	1.40633	+	0.626138i
$392$	−4.97981	+	4.48384i	−0.251518	+	0.226468i
$393$	−19.2401	+	2.02222i	−0.970534	+	0.102007i
$394$	−27.7325	−	5.89473i	−1.39714	−	0.296972i
$395$		0			0
$396$	0.293186	−	0.0623186i	0.0147332	−	0.00313163i
$397$	8.61654	−	4.97476i	0.432452	−	0.249676i	−0.267939	−	0.963436i	$-0.586342\pi$
$397$	8.61654	−	4.97476i	0.432452	−	0.249676i	0.700391	+	0.713760i	$0.253009\pi$
$398$	−29.1819	−	16.8482i	−1.46276	−	0.844523i
$399$	1.15750	−	3.56243i	0.0579476	−	0.178344i
$400$		0			0
$401$	−16.0959	+	11.6943i	−0.803789	+	0.583987i	−0.912023	−	0.410138i	$-0.865480\pi$
$401$	−16.0959	+	11.6943i	−0.803789	+	0.583987i	0.108234	+	0.994125i	$0.465480\pi$
$402$			1.03779i			0.0517604i
$403$	−0.347028	−	0.869482i	−0.0172867	−	0.0433120i
$404$	1.92858			0.0959506
$405$		0			0
$406$	−0.387398	+	3.68584i	−0.0192262	+	0.182925i
$407$	3.50024	+	1.13730i	0.173501	+	0.0563738i
$408$	25.6530	+	14.8108i	1.27001	+	0.733242i
$409$	−12.1628	−	21.0665i	−0.601410	−	1.04167i	−0.992608	−	0.121365i	$-0.961273\pi$
$409$	−12.1628	−	21.0665i	−0.601410	−	1.04167i	0.391198	−	0.920306i	$-0.372061\pi$
$410$		0			0
$411$	−0.0616002	−	0.189586i	−0.00303851	−	0.00935159i
$412$	−0.158842	+	0.747291i	−0.00782556	+	0.0368164i
$413$	5.77584	−	0.607065i	0.284210	−	0.0298717i
$414$	−3.12569	−	3.47143i	−0.153619	−	0.170611i
$415$		0			0
$416$	0.338428	−	0.150678i	0.0165928	−	0.00738759i
$417$	12.7155	+	11.4491i	0.622682	+	0.560665i
$418$	−0.815876	+	1.12296i	−0.0399058	+	0.0549256i
$419$	−3.56513	−	2.59022i	−0.174168	−	0.126541i	0.497286	−	0.867587i	$-0.334330\pi$
$419$	−3.56513	−	2.59022i	−0.174168	−	0.126541i	−0.671454	+	0.741046i	$0.734330\pi$
$420$		0			0
$421$	−11.3496	+	5.05316i	−0.553145	+	0.246276i	−0.664222	−	0.747536i	$-0.731237\pi$
$421$	−11.3496	+	5.05316i	−0.553145	+	0.246276i	0.111076	+	0.993812i	$0.464570\pi$
$422$	−0.683191	+	1.53447i	−0.0332572	+	0.0746969i
$423$	−3.33885	+	3.00632i	−0.162341	+	0.146172i
$424$	2.32589	+	22.1294i	0.112955	+	1.07470i
$425$		0			0
$426$	0.660548	+	2.03296i	0.0320037	+	0.0984972i
$427$	0.796305	+	3.74632i	0.0385359	+	0.181297i
$428$	4.29323	−	2.47870i	0.207521	−	0.119812i
$429$	−0.118623	+	0.205461i	−0.00572718	+	0.00991976i
$430$		0			0
$431$	1.94060	−	18.4636i	0.0934755	−	0.889360i	−0.842831	−	0.538178i	$-0.819113\pi$
$431$	1.94060	−	18.4636i	0.0934755	−	0.889360i	0.936307	−	0.351183i	$-0.114220\pi$
$432$	−10.1098	−	13.9150i	−0.486408	−	0.669484i
$433$			36.1204i			1.73584i	0.496708	+	0.867918i	$0.334542\pi$
$433$			36.1204i			1.73584i	−0.496708	+	0.867918i	$0.665458\pi$
$434$	−10.7703	+	11.0591i	−0.516991	+	0.530853i
$435$		0			0
$436$	−3.28548	+	2.38704i	−0.157346	+	0.114319i
$437$	−5.30670	−	0.557756i	−0.253854	−	0.0266811i
$438$	14.1658	+	4.60274i	0.676866	+	0.219927i
$439$	−9.50469	+	16.4626i	−0.453634	+	0.785718i	−0.998609	−	0.0527352i	$-0.983206\pi$
$439$	−9.50469	+	16.4626i	−0.453634	+	0.785718i	0.544974	+	0.838453i	$0.316539\pi$
$440$		0			0
$441$	−1.72116	+	0.365844i	−0.0819601	+	0.0174212i
$442$	1.33208	−	0.432817i	0.0633603	−	0.0205870i
$443$	−2.58934	+	12.1819i	−0.123023	+	0.578779i	0.872847	+	0.487993i	$0.162271\pi$
$443$	−2.58934	+	12.1819i	−0.123023	+	0.578779i	−0.995870	+	0.0907852i	$0.971062\pi$
$444$	0.237709	+	2.26165i	0.0112812	+	0.107333i
$445$		0			0
$446$	−14.0240	−	6.24387i	−0.664054	−	0.295656i
$447$	−3.28492	−	7.37804i	−0.155371	−	0.348969i
$448$	−14.4691	−	13.0280i	−0.683599	−	0.615515i
$449$	20.5786	+	14.9513i	0.971166	+	0.705593i	0.955717	−	0.294287i	$-0.0950822\pi$
$449$	20.5786	+	14.9513i	0.971166	+	0.705593i	0.0154490	+	0.999881i	$0.495082\pi$
$450$		0			0
$451$	−0.208761	+	0.231852i	−0.00983016	+	0.0109175i
$452$	0.618537	+	1.38926i	0.0290935	+	0.0653452i
$453$	8.26451	−	18.5624i	0.388300	−	0.872137i
$454$	13.4774	+	14.9682i	0.632527	+	0.702492i
$455$		0			0
$456$	−5.07898	−	1.07957i	−0.237845	−	0.0505555i
$457$	−30.4090	+	9.88049i	−1.42247	+	0.462190i	−0.916388	−	0.400292i	$-0.868909\pi$
$457$	−30.4090	+	9.88049i	−1.42247	+	0.462190i	−0.506087	+	0.862482i	$0.668909\pi$
$458$	−4.29210	−	20.1927i	−0.200556	−	0.943544i
$459$	18.5319	+	32.0982i	0.864995	+	1.49822i
$460$		0			0
$461$	5.97950	−	18.4030i	0.278493	−	0.857114i	−0.709781	−	0.704423i	$-0.751206\pi$
$461$	5.97950	−	18.4030i	0.278493	−	0.857114i	0.988274	−	0.152691i	$-0.0487940\pi$
$462$	3.89063	+	0.408922i	0.181008	+	0.0190248i
$463$	0.0243710	+	0.0335439i	0.00113262	+	0.00155892i	0.809583	−	0.587006i	$-0.199693\pi$
$463$	0.0243710	+	0.0335439i	0.00113262	+	0.00155892i	−0.808450	+	0.588564i	$0.799693\pi$
$464$	4.07961			0.189391
$465$		0			0
$466$	−6.48875			−0.300586
$467$	−14.8758	−	20.4748i	−0.688372	−	0.947462i	0.311625	−	0.950205i	$-0.399127\pi$
$467$	−14.8758	−	20.4748i	−0.688372	−	0.947462i	−0.999996	+	0.00274297i	$0.999127\pi$
$468$	0.0527272	+	0.00554185i	0.00243732	+	0.000256172i
$469$	−0.373397	+	1.14920i	−0.0172419	+	0.0530650i
$470$		0			0
$471$	11.1734	+	19.3530i	0.514845	+	0.891737i
$472$	−1.67383	−	7.87476i	−0.0770444	−	0.362465i
$473$	−8.70671	+	2.82898i	−0.400335	+	0.130077i
$474$	8.35304	+	1.77549i	0.383668	+	0.0815511i
$475$		0			0
$476$	3.81196	+	4.23361i	0.174721	+	0.194047i
$477$	−2.37655	+	5.33781i	−0.108815	+	0.244401i
$478$	−4.41400	−	9.91401i	−0.201892	−	0.453456i
$479$	14.2131	−	15.7852i	0.649413	−	0.721246i	−0.325074	−	0.945689i	$-0.605389\pi$
$479$	14.2131	−	15.7852i	0.649413	−	0.721246i	0.974487	+	0.224442i	$0.0720559\pi$
$480$		0			0
$481$	0.526661	+	0.382641i	0.0240137	+	0.0174469i
$482$	−6.44464	−	5.80278i	−0.293545	−	0.264309i
$483$	6.11679	+	13.7385i	0.278323	+	0.625125i
$484$	−3.64993	−	1.62505i	−0.165906	−	0.0738660i
$485$		0			0
$486$	−1.06429	−	10.1260i	−0.0482772	−	0.459327i
$487$	5.56413	−	26.1772i	0.252135	−	1.18620i	−0.651753	−	0.758431i	$-0.725966\pi$
$487$	5.56413	−	26.1772i	0.252135	−	1.18620i	0.903888	−	0.427769i	$-0.140700\pi$
$488$	5.04940	−	1.64065i	0.228575	−	0.0742687i
$489$	24.7373	−	5.25807i	1.11866	−	0.237778i
$490$		0			0
$491$	6.28320	−	10.8828i	0.283557	−	0.491135i	−0.688701	−	0.725045i	$-0.741819\pi$
$491$	6.28320	−	10.8828i	0.283557	−	0.491135i	0.972258	+	0.233910i	$0.0751522\pi$
$492$	−0.183342	−	0.0595716i	−0.00826572	−	0.00268569i
$493$	−8.74296	−	0.918922i	−0.393763	−	0.0413861i
$494$	−0.198630	+	0.144313i	−0.00893678	+	0.00649295i
$495$		0			0
$496$	13.3461	+	10.5182i	0.599255	+	0.472280i
$497$			2.48886i			0.111640i
$498$	0.360686	+	0.496442i	0.0161627	+	0.0222461i
$499$	−2.40733	+	22.9042i	−0.107767	+	1.02533i	0.798318	+	0.602236i	$0.205724\pi$
$499$	−2.40733	+	22.9042i	−0.107767	+	1.02533i	−0.906085	+	0.423097i	$0.860943\pi$
$500$		0			0
$501$	12.0216	−	20.8221i	0.537087	−	0.930263i
$502$	24.8626	−	14.3545i	1.10967	−	0.640671i
$503$	0.137550	+	0.647121i	0.00613305	+	0.0288537i	0.981108	−	0.193462i	$-0.0619717\pi$
$503$	0.137550	+	0.647121i	0.00613305	+	0.0288537i	−0.974975	+	0.222316i	$0.928638\pi$
$504$	−1.63552	−	5.03362i	−0.0728520	−	0.224215i
$505$		0			0
$506$	−0.582520	−	5.54231i	−0.0258962	−	0.246386i
$507$	14.3086	−	12.8835i	0.635468	−	0.572178i
$508$	−1.18203	+	2.65488i	−0.0524440	+	0.117791i
$509$	10.6587	−	4.74556i	0.472439	−	0.210343i	−0.156685	−	0.987649i	$-0.550081\pi$
$509$	10.6587	−	4.74556i	0.472439	−	0.210343i	0.629124	+	0.777305i	$0.283414\pi$
$510$		0			0
$511$	14.0304	+	10.1937i	0.620667	+	0.450941i
$512$	−14.8393	+	20.4245i	−0.655809	+	0.902644i
$513$	−4.82823	−	4.34736i	−0.213172	−	0.191941i
$514$	19.2754	−	8.58194i	0.850200	−	0.378533i
$515$		0			0
$516$	−3.78510	−	4.20378i	−0.166630	−	0.185061i
$517$	−5.33064	+	0.560273i	−0.234441	+	0.0246408i
$518$	2.23182	−	10.4999i	0.0980604	−	0.461338i
$519$	1.06928	+	3.29090i	0.0469362	+	0.144455i
$520$		0			0
$521$	15.9592	+	27.6422i	0.699186	+	1.21103i	0.968749	+	0.248043i	$0.0797874\pi$
$521$	15.9592	+	27.6422i	0.699186	+	1.21103i	−0.269563	+	0.962983i	$0.586879\pi$
$522$	1.16833	+	0.674533i	0.0511362	+	0.0295235i
$523$	0.00394726	+	0.00128254i	0.000172602	+	5.60817e-5i	0.309103	−	0.951028i	$-0.399971\pi$
$523$	0.00394726	+	0.00128254i	0.000172602	+	5.60817e-5i	−0.308931	+	0.951085i	$0.599971\pi$
$524$	−0.539126	+	5.12944i	−0.0235518	+	0.224081i
$525$		0			0
$526$	−31.1411			−1.35782
$527$	−26.2326	−	25.5475i	−1.14271	−	1.11287i
$528$		−	4.30627i		−	0.187406i
$529$	−1.27581	+	0.926929i	−0.0554699	+	0.0403013i
$530$		0			0
$531$	0.653271	−	2.01056i	0.0283496	−	0.0872510i
$532$	−0.864834	−	0.499312i	−0.0374953	−	0.0216479i
$533$	−0.0477914	+	0.0275924i	−0.00207008	+	0.00119516i
$534$	−27.0513	+	5.74993i	−1.17062	+	0.248824i
$535$		0			0
$536$	1.63842	+	0.348257i	0.0707689	+	0.0150424i
$537$	−25.0518	+	2.63305i	−1.08106	+	0.113624i
$538$	11.7792	−	10.6060i	0.507836	−	0.457258i
$539$	−1.91774	−	0.853831i	−0.0826028	−	0.0367771i
$540$		0			0
$541$	19.5888	−	21.7556i	0.842189	−	0.935346i	−0.156440	−	0.987687i	$-0.550002\pi$
$541$	19.5888	−	21.7556i	0.842189	−	0.935346i	0.998629	+	0.0523416i	$0.0166685\pi$
$542$	−20.2258	+	27.8384i	−0.868771	+	1.19576i
$543$	6.40015	−	8.80905i	0.274657	−	0.378032i
$544$	9.69560	−	10.7681i	0.415695	−	0.461677i
$545$		0			0
$546$	0.632146	+	0.281449i	0.0270533	+	0.0120449i
$547$	−30.5918	+	27.5450i	−1.30801	+	1.17774i	−0.336248	+	0.941773i	$0.609158\pi$
$547$	−30.5918	+	27.5450i	−1.30801	+	1.17774i	−0.971762	+	0.235964i	$0.924175\pi$
$548$	−0.0528539	+	0.00555517i	−0.00225781	+	0.000237305i
$549$	1.36369	+	0.289861i	0.0582009	+	0.0123710i
$550$		0			0
$551$	1.50735	−	0.320396i	0.0642151	−	0.0136493i
$552$	18.0540	−	10.4235i	0.768429	−	0.443653i
$553$	8.61089	+	4.97150i	0.366172	+	0.211410i
$554$	5.93260	−	18.2587i	0.252052	−	0.775737i
$555$		0			0
$556$	3.69046	−	2.68128i	0.156511	−	0.113712i
$557$		−	5.73810i		−	0.243131i	−0.992583	−	0.121566i	$-0.961209\pi$
$557$		−	5.73810i		−	0.243131i	0.992583	−	0.121566i	$-0.0387915\pi$
$558$	2.08297	+	5.21889i	0.0881790	+	0.220933i
$559$	−1.61931			−0.0684894
$560$		0			0
$561$	−0.969977	+	9.22872i	−0.0409525	+	0.389637i
$562$	36.4367	+	11.8390i	1.53699	+	0.499398i
$563$	−12.3791	−	7.14710i	−0.521718	−	0.301214i	0.215919	−	0.976411i	$-0.430725\pi$
$563$	−12.3791	−	7.14710i	−0.521718	−	0.301214i	−0.737637	+	0.675197i	$0.764059\pi$
$564$	−1.65598	−	2.86823i	−0.0697292	−	0.120774i
$565$		0			0
$566$	1.23108	+	3.78889i	0.0517463	+	0.159259i
$567$	−2.71917	+	12.7927i	−0.114194	+	0.537242i
$568$	3.43121	−	0.360634i	0.143970	−	0.0151319i
$569$	−9.60991	−	10.6729i	−0.402869	−	0.447431i	0.507237	−	0.861806i	$-0.330667\pi$
$569$	−9.60991	−	10.6729i	−0.402869	−	0.447431i	−0.910106	+	0.414375i	$0.864000\pi$
$570$		0			0
$571$	30.4932	−	13.5765i	1.27610	−	0.568157i	0.346960	−	0.937880i	$-0.387214\pi$
$571$	30.4932	−	13.5765i	1.27610	−	0.568157i	0.929142	+	0.369722i	$0.120547\pi$
$572$	0.0470040	+	0.0423226i	0.00196534	+	0.00176960i
$573$	−6.82503	+	9.39385i	−0.285120	+	0.392434i
$574$	0.736179	+	0.534865i	0.0307275	+	0.0223248i
$575$		0			0
$576$	−6.47452	+	2.88264i	−0.269772	+	0.120110i
$577$	9.14328	−	20.5361i	0.380640	−	0.854931i	−0.617045	−	0.786928i	$-0.711670\pi$
$577$	9.14328	−	20.5361i	0.380640	−	0.854931i	0.997685	−	0.0680033i	$-0.0216628\pi$
$578$	24.7105	−	22.2495i	1.02782	−	0.925456i
$579$	−0.718593	−	6.83695i	−0.0298637	−	0.284134i
$580$		0			0
$581$	0.220786	+	0.679508i	0.00915973	+	0.0281908i
$582$	−6.06616	−	28.5390i	−0.251450	−	1.18298i
$583$	−6.03677	+	3.48533i	−0.250018	+	0.144348i
$584$	12.0203	−	20.8197i	0.497402	−	0.861525i
$585$		0			0
$586$	−0.251563	+	2.39346i	−0.0103920	+	0.0988730i
$587$	3.77133	+	5.19079i	0.155659	+	0.214247i	0.879723	−	0.475486i	$-0.157728\pi$
$587$	3.77133	+	5.19079i	0.155659	+	0.214247i	−0.724064	+	0.689733i	$0.757728\pi$
$588$		−	1.29711i		−	0.0534920i
$589$	5.75720	+	2.83814i	0.237221	+	0.116944i
$590$		0			0
$591$	26.8800	−	19.5294i	1.10569	−	0.803334i
$592$	−11.7514	−	1.23512i	−0.482980	−	0.0507632i
$593$	19.8392	+	6.44614i	0.814697	+	0.264711i	0.686586	−	0.727049i	$-0.259109\pi$
$593$	19.8392	+	6.44614i	0.814697	+	0.264711i	0.128111	+	0.991760i	$0.459109\pi$
$594$	3.39274	−	5.87640i	0.139206	−	0.241112i
$595$		0			0
$596$	−2.10610	+	0.447664i	−0.0862690	+	0.0183370i
$597$	37.5557	−	12.2026i	1.53705	−	0.499418i
$598$	0.204945	−	0.964189i	0.00838081	−	0.0394286i
$599$	−1.20818	−	11.4951i	−0.0493649	−	0.469676i	−0.991080	−	0.133265i	$-0.957454\pi$
$599$	−1.20818	−	11.4951i	−0.0493649	−	0.469676i	0.941715	−	0.336410i	$-0.109213\pi$
$600$		0			0
$601$	3.94416	+	1.75605i	0.160885	+	0.0716308i	0.485599	−	0.874181i	$-0.338601\pi$
$601$	3.94416	+	1.75605i	0.160885	+	0.0716308i	−0.324714	+	0.945812i	$0.605268\pi$
$602$	10.8605	+	24.3930i	0.442640	+	0.994186i
$603$	0.326868	+	0.294313i	0.0133111	+	0.0119854i
$604$	−4.38252	−	3.18409i	−0.178322	−	0.129559i
$605$		0			0
$606$	6.13093	−	6.80909i	0.249052	−	0.276600i
$607$	18.2662	+	41.0266i	0.741404	+	1.66522i	0.746635	+	0.665234i	$0.231668\pi$
$607$	18.2662	+	41.0266i	0.741404	+	1.66522i	−0.00523163	+	0.999986i	$0.501665\pi$
$608$	−1.03310	+	2.32038i	−0.0418977	+	0.0941037i
$609$	−2.90616	−	3.22762i	−0.117764	−	0.130790i
$610$		0			0
$611$	−0.927366	−	0.197118i	−0.0375172	−	0.00797453i
$612$	1.97222	−	0.640812i	0.0797221	−	0.0259033i
$613$	−0.541644	−	2.54823i	−0.0218768	−	0.102922i	0.965855	−	0.259085i	$-0.0834209\pi$
$613$	−0.541644	−	2.54823i	−0.0218768	−	0.102922i	−0.987731	+	0.156163i	$0.950088\pi$
$614$	14.3937	+	24.9306i	0.580883	+	1.00612i
$615$		0			0
$616$	1.95118	−	6.00512i	0.0786154	−	0.241953i
$617$	24.8499	+	2.61183i	1.00042	+	0.105148i	0.590555	−	0.806998i	$-0.298909\pi$
$617$	24.8499	+	2.61183i	1.00042	+	0.105148i	0.409865	+	0.912146i	$0.365576\pi$
$618$	2.13344	+	2.93643i	0.0858197	+	0.118121i
$619$	−31.9083			−1.28250			−0.641252	−	0.767330i	$-0.721585\pi$
$619$	−31.9083			−1.28250			−0.641252	+	0.767330i	$0.721585\pi$
$620$		0			0
$621$	26.0847			1.04674
$622$	−11.8191	−	16.2676i	−0.473902	−	0.652271i
$623$	−32.0240	−	3.36586i	−1.28301	−	0.134850i
$624$	0.235378	−	0.724418i	0.00942264	−	0.0289999i
$625$		0			0
$626$	−4.02105	−	6.96466i	−0.160713	−	0.278364i
$627$	−0.338198	−	1.59109i	−0.0135063	−	0.0635422i
$628$	5.66612	−	1.84103i	0.226103	−	0.0734652i
$629$	24.9061	+	5.29395i	0.993071	+	0.211084i
$630$		0			0
$631$	−0.240720	−	0.267347i	−0.00958293	−	0.0106429i	0.738334	−	0.674435i	$-0.235613\pi$
$631$	−0.240720	−	0.267347i	−0.00958293	−	0.0106429i	−0.747917	+	0.663792i	$0.768946\pi$
$632$	5.60613	−	12.5916i	0.223000	−	0.500866i
$633$	−0.800623	−	1.79823i	−0.0318219	−	0.0714732i
$634$	12.9679	−	14.4024i	0.515022	−	0.571990i
$635$		0			0
$636$	−3.48458	−	2.53170i	−0.138173	−	0.100388i
$637$	−0.275939	−	0.248457i	−0.0109331	−	0.00984422i
$638$	0.654618	+	1.47030i	0.0259166	+	0.0582096i
$639$	0.827639	+	0.368488i	0.0327409	+	0.0145772i
$640$		0			0
$641$	3.22020	+	30.6382i	0.127190	+	1.21013i	0.852878	+	0.522110i	$0.174855\pi$
$641$	3.22020	+	30.6382i	0.127190	+	1.21013i	−0.725688	+	0.688024i	$0.758478\pi$
$642$	4.89677	−	23.0375i	0.193260	−	0.909218i
$643$	−1.66609	+	0.541347i	−0.0657044	+	0.0213486i	−0.341685	−	0.939815i	$-0.610998\pi$
$643$	−1.66609	+	0.541347i	−0.0657044	+	0.0213486i	0.275980	+	0.961163i	$0.410998\pi$
$644$	3.92172	−	0.833588i	0.154538	−	0.0328480i
$645$		0			0
$646$	−4.80159	+	8.31659i	−0.188916	+	0.327212i
$647$	−23.4439	−	7.61739i	−0.921675	−	0.299470i	−0.190521	−	0.981683i	$-0.561018\pi$
$647$	−23.4439	−	7.61739i	−0.921675	−	0.299470i	−0.731154	+	0.682213i	$0.761018\pi$
$648$	18.0304	+	1.89507i	0.708299	+	0.0744452i
$649$	2.04038	−	1.48242i	0.0800918	−	0.0581901i
$650$		0			0
$651$	−1.18569	−	18.0516i	−0.0464707	−	0.707498i
$652$		−	6.74233i		−	0.264050i
$653$	−0.167909	−	0.231107i	−0.00657080	−	0.00904393i	0.805719	−	0.592298i	$-0.201779\pi$
$653$	−0.167909	−	0.231107i	−0.00657080	−	0.00904393i	−0.812290	+	0.583254i	$0.801779\pi$
$654$	−2.01676	+	19.1881i	−0.0788614	+	0.750316i
$655$		0			0
$656$	0.500831	−	0.867465i	0.0195542	−	0.0338688i
$657$	5.46704	−	3.15640i	0.213290	−	0.123143i
$658$	3.25036	+	15.2918i	0.126712	+	0.596135i
$659$	−11.5649	−	35.5930i	−0.450503	−	1.38651i	−0.876335	−	0.481703i	$-0.840018\pi$
$659$	−11.5649	−	35.5930i	−0.450503	−	1.38651i	0.425832	−	0.904802i	$-0.359982\pi$
$660$		0			0
$661$	−0.438139	−	4.16861i	−0.0170416	−	0.162140i	0.982691	−	0.185251i	$-0.0593097\pi$
$661$	−0.438139	−	4.16861i	−0.0170416	−	0.162140i	−0.999733	+	0.0231105i	$0.992643\pi$
$662$	8.44125	−	7.60054i	0.328079	−	0.295403i
$663$	−0.667608	+	1.49947i	−0.0259278	+	0.0582347i
$664$	0.904797	−	0.402841i	0.0351129	−	0.0156333i
$665$		0			0
$666$	−3.16117	−	2.29673i	−0.122493	−	0.0889963i
$667$	−3.63662	+	5.00538i	−0.140810	+	0.193809i
$668$	−4.76354	−	4.28911i	−0.184307	−	0.165951i
$669$	16.4345	−	7.31712i	0.635395	−	0.282896i
$670$		0			0
$671$	1.11292	+	1.23602i	0.0429638	+	0.0477161i
$672$	7.11939	−	0.748278i	0.274636	−	0.0288655i
$673$	−2.07343	+	9.75474i	−0.0799250	+	0.376018i	−0.999872	−	0.0160261i	$-0.994899\pi$
$673$	−2.07343	+	9.75474i	−0.0799250	+	0.376018i	0.919947	+	0.392044i	$0.128232\pi$
$674$	1.70994	+	5.26266i	0.0658645	+	0.202710i
$675$		0			0
$676$	−2.56659	−	4.44546i	−0.0987150	−	0.170979i
$677$	41.3594	+	23.8788i	1.58957	+	0.917738i	0.993377	+	0.114896i	$0.0366536\pi$
$677$	41.3594	+	23.8788i	1.58957	+	0.917738i	0.596192	+	0.802842i	$0.296680\pi$
$678$	6.87126	+	2.23261i	0.263889	+	0.0857428i
$679$	3.55097	−	33.7852i	0.136274	−	1.29656i
$680$		0			0
$681$	−23.6038			−0.904500
$682$	−1.64924	+	6.49769i	−0.0631527	+	0.248810i
$683$		−	27.7600i		−	1.06221i	−0.847307	−	0.531104i	$-0.821777\pi$
$683$		−	27.7600i		−	1.06221i	0.847307	−	0.531104i	$-0.178223\pi$
$684$	−0.294083	+	0.213664i	−0.0112446	+	0.00816965i
$685$		0			0
$686$	−7.88945	+	24.2812i	−0.301221	+	0.927062i
$687$	20.9511	+	12.0961i	0.799335	+	0.461496i
$688$	25.4544	−	14.6961i	0.970438	−	0.560283i
$689$	−1.20604	+	0.256351i	−0.0459463	+	0.00976619i
$690$		0			0
$691$	−37.1999	−	7.90708i	−1.41515	−	0.300800i	−0.564023	−	0.825759i	$-0.690747\pi$
$691$	−37.1999	−	7.90708i	−1.41515	−	0.300800i	−0.851127	+	0.524959i	$0.824081\pi$
$692$	0.917457	−	0.0964286i	0.0348765	−	0.00366567i
$693$	1.23216	−	1.10944i	0.0468059	−	0.0421442i
$694$	−28.2393	−	12.5730i	−1.07195	−	0.477263i
$695$		0			0
$696$	−4.02858	+	4.47419i	−0.152703	+	0.169594i
$697$	−1.26872	+	1.74624i	−0.0480562	+	0.0661437i
$698$	−9.71106	+	13.3661i	−0.367569	+	0.505915i
$699$	5.08813	−	5.65094i	0.192451	−	0.213738i
$700$		0			0
$701$	37.5067	+	16.6991i	1.41661	+	0.630716i	0.965179	−	0.261590i	$-0.0842469\pi$
$701$	37.5067	+	16.6991i	1.41661	+	0.630716i	0.451431	+	0.892306i	$0.350914\pi$
$702$	0.891940	−	0.803106i	0.0336641	−	0.0303113i
$703$	−4.43895	+	0.466552i	−0.167418	+	0.0175963i
$704$	−8.27034	−	1.75792i	−0.311700	−	0.0662539i
$705$		0			0
$706$	−13.4111	+	2.85062i	−0.504734	+	0.107284i
$707$	9.23898	−	5.33413i	0.347468	−	0.200611i
$708$	1.34959	+	0.779187i	0.0507207	+	0.0292836i
$709$	−12.9990	+	40.0069i	−0.488188	+	1.50249i	0.339121	+	0.940743i	$0.389870\pi$
$709$	−12.9990	+	40.0069i	−0.488188	+	1.50249i	−0.827309	+	0.561747i	$0.810130\pi$
$710$		0			0
$711$	2.92810	−	2.12739i	0.109812	−	0.0797833i
$712$			44.6368i			1.67284i
$713$	−24.8019	+	6.99858i	−0.928838	+	0.262099i
$714$	27.0654			1.01290
$715$		0			0
$716$	−0.701974	+	6.67884i	−0.0262340	+	0.249600i
$717$	12.0952	+	3.92996i	0.451702	+	0.146767i
$718$	37.0573	+	21.3951i	1.38297	+	0.798456i
$719$	−16.6345	−	28.8118i	−0.620362	−	1.07450i	−0.989418	−	0.145092i	$-0.953652\pi$
$719$	−16.6345	−	28.8118i	−0.620362	−	1.07450i	0.369056	−	0.929407i	$-0.379681\pi$
$720$		0			0
$721$	1.30594	+	4.01926i	0.0486357	+	0.149685i
$722$	−4.65349	+	21.8930i	−0.173185	+	0.814772i
$723$	10.1071	−	1.06230i	0.375886	−	0.0395072i
$724$	−1.94243	−	2.15728i	−0.0721897	−	0.0801748i
$725$		0			0
$726$	−17.3405	+	7.72048i	−0.643566	+	0.286534i
$727$	−24.3179	−	21.8959i	−0.901899	−	0.812074i	0.0809055	−	0.996722i	$-0.474219\pi$
$727$	−24.3179	−	21.8959i	−0.901899	−	0.812074i	−0.982805	+	0.184648i	$0.940885\pi$
$728$	0.656471	−	0.903555i	0.0243305	−	0.0334880i
$729$	24.1540	+	17.5489i	0.894592	+	0.649959i
$730$		0			0
$731$	−57.8612	+	25.7615i	−2.14007	+	0.952822i
$732$	−0.418008	+	0.938862i	−0.0154500	+	0.0347014i
$733$	−7.40463	+	6.66715i	−0.273496	+	0.246257i	−0.794452	−	0.607326i	$-0.792242\pi$
$733$	−7.40463	+	6.66715i	−0.273496	+	0.246257i	0.520956	+	0.853583i	$0.325575\pi$
$734$	2.99629	+	28.5078i	0.110595	+	1.05224i
$735$		0			0
$736$	−3.15124	−	9.69852i	−0.116156	−	0.357492i
$737$	0.109099	+	0.513268i	0.00401870	+	0.0189065i
$738$	0.286858	−	0.165618i	0.0105594	−	0.00609647i
$739$	15.4792	−	26.8108i	0.569412	−	0.986251i	−0.427212	−	0.904152i	$-0.640504\pi$
$739$	15.4792	−	26.8108i	0.569412	−	0.986251i	0.996624	−	0.0820995i	$-0.0261625\pi$
$740$		0			0
$741$	0.0300751	−	0.286146i	0.00110484	−	0.0105118i
$742$	11.9504	+	16.4483i	0.438711	+	0.603834i
$743$		−	1.11003i		−	0.0407231i	−0.999793	−	0.0203615i	$-0.993518\pi$
$743$		−	1.11003i		−	0.0407231i	0.999793	−	0.0203615i	$-0.00648173\pi$
$744$	−24.7146	+	4.25029i	−0.906082	+	0.155823i
$745$		0			0
$746$	33.7865	−	24.5473i	1.23701	−	0.898741i
$747$	0.258651	+	0.0271853i	0.00946353	+	0.000994657i
$748$	2.35286	+	0.764490i	0.0860290	+	0.0279525i
$749$	13.7113	−	23.7487i	0.501000	−	0.867757i
$750$		0			0
$751$	−27.5400	+	5.85382i	−1.00495	+	0.213609i	−0.680857	−	0.732416i	$-0.738393\pi$
$751$	−27.5400	+	5.85382i	−1.00495	+	0.213609i	−0.324093	+	0.946025i	$0.605059\pi$
$752$	16.3665	−	5.31779i	0.596824	−	0.193920i
$753$	−6.99490	+	32.9084i	−0.254908	+	1.19925i
$754$	0.0297571	+	0.283120i	0.00108369	+	0.0103106i
$755$		0			0
$756$	4.45972	+	1.98559i	0.162198	+	0.0722154i
$757$	15.7498	+	35.3746i	0.572436	+	1.28571i	0.935295	+	0.353868i	$0.115134\pi$
$757$	15.7498	+	35.3746i	0.572436	+	1.28571i	−0.362860	+	0.931844i	$0.618200\pi$
$758$	30.5836	+	27.5376i	1.11085	+	1.00021i
$759$	5.28348	+	3.83867i	0.191778	+	0.139335i
$760$		0			0
$761$	29.0649	−	32.2799i	1.05360	−	1.17014i	0.0685936	−	0.997645i	$-0.478149\pi$
$761$	29.0649	−	32.2799i	1.05360	−	1.17014i	0.985010	−	0.172500i	$-0.0551845\pi$
$762$	5.61572	+	12.6131i	0.203436	+	0.456925i
$763$	−9.13713	+	20.5223i	−0.330786	+	0.742958i
$764$	2.07138	+	2.30050i	0.0749399	+	0.0832292i
$765$		0			0
$766$	33.1789	+	7.05239i	1.19880	+	0.254813i
$767$	0.424268	−	0.137853i	0.0153194	−	0.00497759i
$768$	−2.80862	−	13.2135i	−0.101347	−	0.476801i
$769$	−1.55509	−	2.69350i	−0.0560781	−	0.0971302i	0.836624	−	0.547778i	$-0.184526\pi$
$769$	−1.55509	−	2.69350i	−0.0560781	−	0.0971302i	−0.892702	+	0.450648i	$0.851193\pi$
$770$		0			0
$771$	−7.64083	+	23.5161i	−0.275178	+	0.846910i
$772$	−1.82274	−	0.191578i	−0.0656019	−	0.00689504i
$773$	12.7198	+	17.5073i	0.457499	+	0.629693i	0.973988	−	0.226601i	$-0.0727613\pi$
$773$	12.7198	+	17.5073i	0.457499	+	0.629693i	−0.516489	+	0.856294i	$0.672761\pi$
$774$	9.71956			0.349362
$775$		0			0
$776$	−47.0918			−1.69050
$777$	7.39408	+	10.1771i	0.265261	+	0.365101i
$778$	−22.3433	−	2.34837i	−0.801045	−	0.0841932i
$779$	0.116921	−	0.359847i	0.00418914	−	0.0128929i
$780$		0			0
$781$	0.540408	+	0.936015i	0.0193373	+	0.0334932i
$782$	−8.01612	−	37.7129i	−0.286656	−	1.34861i
$783$	−7.16457	+	2.32791i	−0.256041	+	0.0831927i
$784$	6.59245	+	1.40127i	0.235445	+	0.0500453i
$785$		0			0
$786$	16.3962	+	18.2098i	0.584834	+	0.649524i
$787$	3.20368	−	7.19557i	0.114199	−	0.256494i	−0.847399	−	0.530956i	$-0.821833\pi$
$787$	3.20368	−	7.19557i	0.114199	−	0.256494i	0.961598	+	0.274462i	$0.0884996\pi$
$788$	−3.60286	−	8.09215i	−0.128346	−	0.288271i
$789$	24.4192	−	27.1203i	0.869346	−	0.965507i
$790$		0			0
$791$	6.80558	+	4.94454i	0.241979	+	0.175808i
$792$	−1.70805	−	1.53793i	−0.0606928	−	0.0546481i
$793$	0.119660	+	0.268760i	0.00424924	+	0.00954395i
$794$	−11.5126	−	5.12573i	−0.408566	−	0.181905i
$795$		0			0
$796$	−1.10044	−	10.4700i	−0.0390040	−	0.371099i
$797$	6.13717	−	28.8731i	0.217390	−	1.02274i	−0.725136	−	0.688605i	$-0.758223\pi$
$797$	6.13717	−	28.8731i	0.217390	−	1.02274i	0.942526	−	0.334133i	$-0.108443\pi$
$798$	−4.51217	+	1.46609i	−0.159729	+	0.0518992i
$799$	−36.2726	+	7.70998i	−1.28323	+	0.272760i
$800$		0			0
$801$	−5.86059	+	10.1508i	−0.207074	+	0.358663i
$802$	23.9664	+	7.78716i	0.846283	+	0.274974i
$803$	7.48993	+	0.787223i	0.264314	+	0.0277805i
$804$	−0.262311	+	0.190580i	−0.00925100	+	0.00672124i
$805$		0			0
$806$	−0.632601	+	1.00292i	−0.0222824	+	0.0353264i
$807$			18.5749i			0.653869i
$808$	−8.69250	−	11.9642i	−0.305801	−	0.420899i
$809$	−0.222387	+	2.11587i	−0.00781871	+	0.0743901i	−0.997735	−	0.0672603i	$-0.978574\pi$
$809$	−0.222387	+	2.11587i	−0.00781871	+	0.0743901i	0.989917	+	0.141650i	$0.0452409\pi$
$810$		0			0
$811$	−3.60252	+	6.23975i	−0.126502	+	0.219107i	−0.922319	−	0.386430i	$-0.873708\pi$
$811$	−3.60252	+	6.23975i	−0.126502	+	0.219107i	0.795817	+	0.605537i	$0.207042\pi$
$812$	−1.00277	+	0.578950i	−0.0351904	+	0.0203172i
$813$	−8.38400	−	39.4436i	−0.294040	−	1.38335i
$814$	−1.44050	−	4.43341i	−0.0504896	−	0.155391i
$815$		0			0
$816$	−3.11419	−	29.6295i	−0.109018	−	1.03724i
$817$	8.25078	−	7.42904i	0.288658	−	0.259909i
$818$	−12.5319	+	28.1470i	−0.438166	+	0.984137i
$819$	0.267920	−	0.119286i	0.00936189	−	0.00416818i
$820$		0			0
$821$	−34.0270	−	24.7221i	−1.18755	−	0.862807i	−0.194548	−	0.980893i	$-0.562324\pi$
$821$	−34.0270	−	24.7221i	−1.18755	−	0.862807i	−0.993003	+	0.118086i	$0.962324\pi$
$822$	−0.148408	+	0.204267i	−0.00517634	+	0.00712462i
$823$	22.4229	+	20.1897i	0.781613	+	0.703767i	0.959940	−	0.280204i	$-0.0904021\pi$
$823$	22.4229	+	20.1897i	0.781613	+	0.703767i	−0.178328	+	0.983971i	$0.557069\pi$
$824$	5.35184	−	2.38279i	0.186440	−	0.0830085i
$825$		0			0
$826$	−4.92211	−	5.46656i	−0.171262	−	0.190206i
$827$	−3.84925	+	0.404573i	−0.133852	+	0.0140684i	−0.171217	−	0.985233i	$-0.554770\pi$
$827$	−3.84925	+	0.404573i	−0.133852	+	0.0140684i	0.0373657	+	0.999302i	$0.488103\pi$
$828$	0.303433	−	1.42754i	0.0105450	−	0.0496104i
$829$	−4.07025	−	12.5269i	−0.141366	−	0.435079i	0.855160	−	0.518364i	$-0.173459\pi$
$829$	−4.07025	−	12.5269i	−0.141366	−	0.435079i	−0.996526	+	0.0832851i	$0.973459\pi$
$830$		0			0
$831$	11.2491	+	19.4841i	0.390228	+	0.675895i
$832$	−1.29518	−	0.747774i	−0.0449024	−	0.0259244i
$833$	−13.8126	−	4.48797i	−0.478577	−	0.155499i
$834$	2.26535	−	21.5534i	0.0784427	−	0.746332i
$835$		0			0
$836$	−0.433665			−0.0149986
$837$	−29.4401	−	10.8564i	−1.01760	−	0.375251i
$838$			5.58159i			0.192813i
$839$	−27.7080	+	20.1311i	−0.956588	+	0.695002i	−0.952356	−	0.304989i	$-0.901347\pi$
$839$	−27.7080	+	20.1311i	−0.956588	+	0.695002i	−0.00423187	+	0.999991i	$0.501347\pi$
$840$		0			0
$841$	−8.40934	+	25.8813i	−0.289977	+	0.892458i
$842$	13.6276	+	7.86792i	0.469640	+	0.271147i
$843$	−38.8821	+	22.4486i	−1.33917	+	0.773170i
$844$	−0.513313	+	0.109108i	−0.0176689	+	0.00375565i
$845$		0			0
$846$	5.56632	+	1.18316i	0.191374	+	0.0406778i
$847$	−21.9798	+	2.31017i	−0.755234	+	0.0793783i
$848$	16.6315	−	14.9751i	0.571128	−	0.514246i
$849$	−4.26502	−	1.89891i	−0.146375	−	0.0651704i
$850$		0			0
$851$	11.9908	−	13.3171i	0.411038	−	0.456504i
$852$	−0.392545	+	0.540292i	−0.0134484	+	0.0185101i
$853$	8.49225	−	11.6886i	0.290769	−	0.400209i	−0.638495	−	0.769626i	$-0.720443\pi$
$853$	8.49225	−	11.6886i	0.290769	−	0.400209i	0.929264	+	0.369417i	$0.120443\pi$
$854$	3.24602	−	3.60507i	0.111077	−	0.123363i
$855$		0			0
$856$	−34.7273	−	15.4616i	−1.18696	−	0.528466i
$857$	−20.6840	+	18.6239i	−0.706552	+	0.636182i	−0.941964	−	0.335714i	$-0.891023\pi$
$857$	−20.6840	+	18.6239i	−0.706552	+	0.636182i	0.235413	+	0.971896i	$0.424356\pi$
$858$	0.298850	−	0.0314104i	0.0102026	−	0.00107233i
$859$	−46.2861	−	9.83842i	−1.57926	−	0.335682i	−0.666925	−	0.745124i	$-0.732390\pi$
$859$	−46.2861	−	9.83842i	−1.57926	−	0.335682i	−0.912336	+	0.409442i	$0.865723\pi$
$860$		0			0
$861$	−1.04308	+	0.221713i	−0.0355479	+	0.00755595i
$862$	−20.3644	+	11.7574i	−0.693616	+	0.400459i
$863$	22.5629	+	13.0267i	0.768049	+	0.443434i	0.832178	−	0.554508i	$-0.187094\pi$
$863$	22.5629	+	13.0267i	0.768049	+	0.443434i	−0.0641289	+	0.997942i	$0.520427\pi$
$864$	3.83695	−	11.8089i	0.130536	−	0.401747i
$865$		0			0
$866$	37.0127	−	26.8913i	1.25774	−	0.913802i
$867$			38.9668i			1.32338i
$868$	−4.77314	−	0.691394i	−0.162011	−	0.0234675i
$869$	4.31787			0.146474
$870$		0			0
$871$	−0.00970189	+	0.0923073i	−0.000328736	+	0.00312771i
$872$	29.6166	+	9.62302i	1.00294	+	0.325876i
$873$	−10.7091	−	6.18291i	−0.362449	−	0.209260i
$874$	3.37925	+	5.85303i	0.114305	+	0.197982i
$875$		0			0
$876$	1.43802	+	4.42577i	0.0485862	+	0.149533i
$877$	−7.13584	+	33.5715i	−0.240960	+	1.13363i	0.676699	+	0.736260i	$0.263410\pi$
$877$	−7.13584	+	33.5715i	−0.240960	+	1.13363i	−0.917659	+	0.397368i	$0.869924\pi$
$878$	23.9454	−	2.51676i	0.808119	−	0.0849367i
$879$	−1.88716	−	2.09591i	−0.0636524	−	0.0706931i
$880$		0			0
$881$	−3.32044	+	1.47835i	−0.111868	+	0.0498070i	−0.461908	−	0.886928i	$-0.652835\pi$
$881$	−3.32044	+	1.47835i	−0.111868	+	0.0498070i	0.350039	+	0.936735i	$0.386168\pi$
$882$	1.65627	+	1.49131i	0.0557695	+	0.0502151i
$883$	−23.1925	+	31.9217i	−0.780489	+	1.07425i	0.214739	+	0.976671i	$0.431110\pi$
$883$	−23.1925	+	31.9217i	−0.780489	+	1.07425i	−0.995228	+	0.0975789i	$0.968890\pi$
$884$	0.354021	+	0.257211i	0.0119070	+	0.00865095i
$885$		0			0
$886$	14.4105	−	6.41598i	0.484131	−	0.215549i
$887$	17.2061	−	38.6455i	0.577723	−	1.29759i	−0.354280	−	0.935139i	$-0.615274\pi$
$887$	17.2061	−	38.6455i	0.577723	−	1.29759i	0.932004	−	0.362449i	$-0.118059\pi$
$888$	12.9590	−	11.6683i	0.434876	−	0.391564i
$889$	1.68037	+	15.9876i	0.0563577	+	0.536208i
$890$		0			0
$891$	1.75506	+	5.40152i	0.0587967	+	0.180958i
$892$	−0.997168	−	4.69131i	−0.0333876	−	0.157077i
$893$	5.62950	−	3.25019i	0.188384	−	0.108764i
$894$	−5.11471	+	8.85894i	−0.171062	+	0.296287i
$895$		0			0
$896$	−1.56951	+	14.9329i	−0.0524336	+	0.498872i
$897$	0.678988	+	0.934547i	0.0226708	+	0.0312036i
$898$		−	32.2180i		−	1.07513i
$899$	6.18765	−	4.13570i	0.206370	−	0.137933i
$900$		0			0
$901$	−39.0159	+	28.3467i	−1.29981	+	0.944365i
$902$	0.393000	+	0.0413059i	0.0130855	+	0.00137534i
$903$	−29.7597	−	9.66950i	−0.990340	−	0.321781i
$904$	5.83056	−	10.0988i	0.193921	−	0.335882i
$905$		0			0
$906$	−25.1738	+	5.35085i	−0.836342	+	0.177770i
$907$	30.7838	−	10.0023i	1.02216	−	0.332120i	0.250474	−	0.968123i	$-0.419414\pi$
$907$	30.7838	−	10.0023i	1.02216	−	0.332120i	0.771686	+	0.636003i	$0.219414\pi$
$908$	−1.30835	+	6.15530i	−0.0434191	+	0.204271i
$909$	−0.405918	−	3.86206i	−0.0134635	−	0.128096i
$910$		0			0
$911$	−24.7212	−	11.0066i	−0.819051	−	0.364665i	−0.0459464	−	0.998944i	$-0.514630\pi$
$911$	−24.7212	−	11.0066i	−0.819051	−	0.364665i	−0.773104	+	0.634279i	$0.781297\pi$
$912$	2.12417	+	4.77095i	0.0703382	+	0.157982i
$913$	0.230576	+	0.207612i	0.00763095	+	0.00687094i
$914$	32.7638	+	23.8043i	1.08373	+	0.787376i
$915$		0			0
$916$	4.31569	−	4.79306i	0.142594	−	0.158367i
$917$	11.6044	+	26.0640i	0.383212	+	0.860708i
$918$	19.0943	−	42.8864i	0.630205	−	1.41546i
$919$	−13.8945	−	15.4314i	−0.458336	−	0.509033i	0.469034	−	0.883180i	$-0.344602\pi$
$919$	−13.8945	−	15.4314i	−0.458336	−	0.509033i	−0.927369	+	0.374147i	$0.877936\pi$
$920$		0			0
$921$	−32.9984	−	7.01403i	−1.08734	−	0.231120i
$922$	−23.3093	+	7.57365i	−0.767651	+	0.249425i
$923$	0.0397477	+	0.186998i	0.00130831	+	0.00615513i
$924$	0.611117	+	1.05849i	0.0201043	+	0.0348216i
$925$		0			0
$926$	0.0162285	−	0.0499461i	0.000533301	−	0.00164133i
$927$	1.52991	+	0.160800i	0.0502488	+	0.00528136i
$928$	1.73108	+	2.38262i	0.0568254	+	0.0782134i
$929$	20.6589			0.677798			0.338899	−	0.940823i	$-0.389945\pi$
$929$	20.6589			0.677798			0.338899	+	0.940823i	$0.389945\pi$
$930$		0			0
$931$	2.54585			0.0834368
$932$	−1.19159	−	1.64009i	−0.0390320	−	0.0537229i
$933$	23.4350	+	2.46312i	0.767229	+	0.0806390i
$934$	−9.90570	+	30.4866i	−0.324124	+	0.997552i
$935$		0			0
$936$	−0.203272	−	0.352078i	−0.00664416	−	0.0115080i
$937$	−0.607227	−	2.85678i	−0.0198372	−	0.0933269i	0.967115	−	0.254338i	$-0.0818577\pi$
$937$	−0.607227	−	2.85678i	−0.0198372	−	0.0933269i	−0.986953	+	0.161012i	$0.948524\pi$
$938$	1.45557	−	0.472945i	0.0475262	−	0.0154422i
$939$	9.21849	+	1.95945i	0.300834	+	0.0639442i
$940$		0			0
$941$	21.9810	+	24.4124i	0.716560	+	0.795821i	0.985920	−	0.167219i	$-0.0534787\pi$
$941$	21.9810	+	24.4124i	0.716560	+	0.795821i	−0.269360	+	0.963040i	$0.586812\pi$
$942$	11.5125	−	25.8575i	0.375098	−	0.842484i
$943$	0.617868	+	1.38775i	0.0201205	+	0.0451915i
$944$	−5.41810	+	6.01741i	−0.176344	+	0.195850i
$945$		0			0
$946$	9.38092	+	6.81564i	0.305000	+	0.221596i
$947$	29.0753	+	26.1796i	0.944822	+	0.850721i	0.988942	−	0.148305i	$-0.0473817\pi$
$947$	29.0753	+	26.1796i	0.944822	+	0.850721i	−0.0441199	+	0.999026i	$0.514048\pi$
$948$	1.08518	+	2.43736i	0.0352450	+	0.0791616i
$949$	1.21696	+	0.541824i	0.0395041	+	0.0175883i
$950$		0			0
$951$	2.37400	+	22.5871i	0.0769822	+	0.732437i
$952$	9.08247	−	42.7296i	0.294364	−	1.38488i
$953$	5.72512	−	1.86020i	0.185455	−	0.0602579i	−0.214817	−	0.976654i	$-0.568916\pi$
$953$	5.72512	−	1.86020i	0.185455	−	0.0602579i	0.400272	+	0.916396i	$0.368916\pi$
$954$	7.23898	−	1.53869i	0.234371	−	0.0498170i
$955$		0			0
$956$	1.69527	−	2.93629i	0.0548288	−	0.0949663i
$957$	−1.79377	−	0.582832i	−0.0579844	−	0.0188403i
$958$	−26.7567	−	2.81224i	−0.864469	−	0.0908594i
$959$	−0.237835	+	0.172797i	−0.00768008	+	0.00557991i
$960$		0			0
$961$	30.9051	+	2.42363i	0.996939	+	0.0781816i
$962$		−	0.824543i		−	0.0265843i
$963$	−5.86729	−	8.07564i	−0.189071	−	0.260234i
$964$	0.283210	−	2.69456i	0.00912158	−	0.0867860i
$965$		0			0
$966$	9.52401	−	16.4961i	0.306430	−	0.530753i
$967$	22.7854	−	13.1552i	0.732730	−	0.423042i	−0.0866903	−	0.996235i	$-0.527629\pi$
$967$	22.7854	−	13.1552i	0.732730	−	0.423042i	0.819420	+	0.573194i	$0.194296\pi$
$968$	6.36972	+	29.9672i	0.204731	+	0.963181i
$969$	−3.47763	−	10.7030i	−0.111718	−	0.343831i
$970$		0			0
$971$	0.495033	+	4.70993i	0.0158864	+	0.151149i	0.999589	−	0.0286519i	$-0.00912142\pi$
$971$	0.495033	+	4.70993i	0.0158864	+	0.151149i	−0.983703	+	0.179801i	$0.942455\pi$
$972$	2.36400	−	2.12856i	0.0758254	−	0.0682735i
$973$	10.2634	−	23.0520i	0.329030	−	0.739013i
$974$	−30.9662	+	13.7870i	−0.992222	+	0.441766i
$975$		0			0
$976$	−4.32010	−	3.13874i	−0.138283	−	0.100469i
$977$	−10.1569	+	13.9798i	−0.324950	+	0.447255i	−0.939970	−	0.341256i	$-0.889148\pi$
$977$	−10.1569	+	13.9798i	−0.324950	+	0.447255i	0.615021	+	0.788511i	$0.289148\pi$
$978$	−23.8046	−	21.4337i	−0.761187	−	0.685376i
$979$	−12.7745	+	5.68757i	−0.408274	+	0.181775i
$980$		0			0
$981$	5.47165	+	6.07688i	0.174696	+	0.194020i
$982$	−15.8294	+	1.66374i	−0.505137	+	0.0530921i
$983$	8.51742	−	40.0713i	0.271663	−	1.27808i	−0.604711	−	0.796445i	$-0.706711\pi$
$983$	8.51742	−	40.0713i	0.271663	−	1.27808i	0.876374	−	0.481631i	$-0.159955\pi$
$984$	0.456801	+	1.40589i	0.0145623	+	0.0448181i
$985$		0			0
$986$	5.56742	+	9.64305i	0.177303	+	0.307097i
$987$	−15.8661	−	9.16029i	−0.505023	−	0.291575i
$988$	−0.0729528	−	0.0237038i	−0.00232094	−	0.000754118i
$989$	−4.65937	+	44.3309i	−0.148159	+	1.40964i
$990$		0			0
$991$	14.1338			0.448975			0.224487	−	0.974477i	$-0.427929\pi$
$991$	14.1338			0.448975			0.224487	+	0.974477i	$0.427929\pi$
$992$	−0.479896	+	12.2576i	−0.0152367	+	0.389181i
$993$			13.3113i			0.422420i
$994$	2.55034	−	1.85293i	0.0808918	−	0.0587713i
$995$		0			0
$996$	−0.0592436	+	0.182333i	−0.00187721	+	0.00577745i
$997$	−13.3834	−	7.72692i	−0.423857	−	0.244714i	0.272869	−	0.962051i	$-0.412027\pi$
$997$	−13.3834	−	7.72692i	−0.423857	−	0.244714i	−0.696726	+	0.717337i	$0.745361\pi$
$998$	25.2622	−	14.5852i	0.799662	−	0.461685i
$999$	21.3425	−	4.53649i	0.675247	−	0.143528i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.ck.a.524.1		32
5.2	odd	4		775.2.bl.a.276.2		16
5.3	odd	4		31.2.g.a.28.1	yes	16
5.4	even	2	inner	775.2.ck.a.524.4		32
15.8	even	4		279.2.y.c.28.2		16
20.3	even	4		496.2.bg.c.369.2		16
31.10	even	15	inner	775.2.ck.a.599.4		32
155.3	even	60		961.2.d.q.531.3		16
155.8	odd	20		961.2.c.j.521.6		16
155.13	even	60		961.2.g.m.547.2		16
155.18	odd	60		961.2.g.s.547.2		16
155.23	even	20		961.2.c.i.521.6		16
155.28	odd	60		961.2.d.p.531.3		16
155.33	odd	20		961.2.g.k.732.1		16
155.38	odd	60		961.2.d.p.628.3		16
155.43	even	60		961.2.d.n.374.2		16
155.48	even	60		961.2.a.j.1.6		8
155.53	even	60		961.2.c.i.439.6		16
155.58	even	20		961.2.g.m.448.2		16
155.68	even	12		961.2.d.n.388.2		16
155.72	odd	60		775.2.bl.a.351.2		16
155.73	even	60		961.2.g.n.846.2		16
155.78	odd	20		961.2.g.t.844.2		16
155.83	even	60		961.2.g.l.816.1		16
155.88	even	12		961.2.g.j.235.1		16
155.98	odd	12		961.2.g.k.235.1		16
155.103	odd	60		31.2.g.a.10.1	✓	16
155.108	even	20		961.2.g.n.844.2		16
155.113	odd	60		961.2.g.t.846.2		16
155.118	odd	12		961.2.d.o.388.2		16
155.123	even	4		961.2.g.l.338.1		16
155.128	odd	20		961.2.g.s.448.2		16
155.133	odd	60		961.2.c.j.439.6		16
155.134	even	30	inner	775.2.ck.a.599.1		32
155.138	odd	60		961.2.a.i.1.6		8
155.143	odd	60		961.2.d.o.374.2		16
155.148	even	60		961.2.d.q.628.3		16
155.153	even	20		961.2.g.j.732.1		16
465.203	odd	60		8649.2.a.be.1.3		8
465.293	even	60		8649.2.a.bf.1.3		8
465.413	even	60		279.2.y.c.10.2		16
620.103	even	60		496.2.bg.c.289.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.10.1	✓	16	155.103	odd	60
31.2.g.a.28.1	yes	16	5.3	odd	4
279.2.y.c.10.2		16	465.413	even	60
279.2.y.c.28.2		16	15.8	even	4
496.2.bg.c.289.2		16	620.103	even	60
496.2.bg.c.369.2		16	20.3	even	4
775.2.bl.a.276.2		16	5.2	odd	4
775.2.bl.a.351.2		16	155.72	odd	60
775.2.ck.a.524.1		32	1.1	even	1	trivial
775.2.ck.a.524.4		32	5.4	even	2	inner
775.2.ck.a.599.1		32	155.134	even	30	inner
775.2.ck.a.599.4		32	31.10	even	15	inner
961.2.a.i.1.6		8	155.138	odd	60
961.2.a.j.1.6		8	155.48	even	60
961.2.c.i.439.6		16	155.53	even	60
961.2.c.i.521.6		16	155.23	even	20
961.2.c.j.439.6		16	155.133	odd	60
961.2.c.j.521.6		16	155.8	odd	20
961.2.d.n.374.2		16	155.43	even	60
961.2.d.n.388.2		16	155.68	even	12
961.2.d.o.374.2		16	155.143	odd	60
961.2.d.o.388.2		16	155.118	odd	12
961.2.d.p.531.3		16	155.28	odd	60
961.2.d.p.628.3		16	155.38	odd	60
961.2.d.q.531.3		16	155.3	even	60
961.2.d.q.628.3		16	155.148	even	60
961.2.g.j.235.1		16	155.88	even	12
961.2.g.j.732.1		16	155.153	even	20
961.2.g.k.235.1		16	155.98	odd	12
961.2.g.k.732.1		16	155.33	odd	20
961.2.g.l.338.1		16	155.123	even	4
961.2.g.l.816.1		16	155.83	even	60
961.2.g.m.448.2		16	155.58	even	20
961.2.g.m.547.2		16	155.13	even	60
961.2.g.n.844.2		16	155.108	even	20
961.2.g.n.846.2		16	155.73	even	60
961.2.g.s.448.2		16	155.128	odd	20
961.2.g.s.547.2		16	155.18	odd	60
961.2.g.t.844.2		16	155.78	odd	20
961.2.g.t.846.2		16	155.113	odd	60
8649.2.a.be.1.3		8	465.203	odd	60
8649.2.a.bf.1.3		8	465.293	even	60

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:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.ck (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.744490 - 1.02470i) q^{2} +(1.47618 + 0.155153i) q^{3} +(0.122284 - 0.376353i) q^{4} +(-0.940018 - 1.62816i) q^{6} +(-0.455117 - 2.14115i) q^{7} +(-2.88591 + 0.937688i) q^{8} +(-0.779397 - 0.165666i) q^{9} +(-0.636073 - 0.706430i) q^{11} +(0.238907 - 0.536593i) q^{12} +(-0.0683897 - 0.153606i) q^{13} +(-1.85522 + 2.06043i) q^{14} +(2.46909 + 1.79390i) q^{16} +(-4.88741 - 4.40064i) q^{17} +(0.410495 + 0.921986i) q^{18} +(1.05317 + 0.468903i) q^{19} +(-0.339629 - 3.23135i) q^{21} +(-0.250331 + 1.17772i) q^{22} +(-4.40197 + 1.43029i) q^{23} +(-4.40562 + 0.936443i) q^{24} +(-0.106485 + 0.184437i) q^{26} +(-5.35983 - 1.74151i) q^{27} +(-0.861483 - 0.0905455i) q^{28} +(1.08143 - 0.785701i) q^{29} +(5.56350 + 0.217815i) q^{31} +2.20322i q^{32} +(-0.829355 - 1.14151i) q^{33} +(-0.870722 + 8.28437i) q^{34} +(-0.157657 + 0.273070i) q^{36} +(-3.35295 + 1.93582i) q^{37} +(-0.303591 - 1.42828i) q^{38} +(-0.0771233 - 0.237361i) q^{39} +(-0.0343065 - 0.326405i) q^{41} +(-3.05832 + 2.75373i) q^{42} +(3.91711 - 8.79797i) q^{43} +(-0.343649 + 0.153002i) q^{44} +(4.74283 + 3.44587i) q^{46} +(3.31427 - 4.56170i) q^{47} +(3.36650 + 3.03121i) q^{48} +(2.01741 - 0.898207i) q^{49} +(-6.53194 - 7.25445i) q^{51} +(-0.0661729 + 0.00695505i) q^{52} +(1.52460 - 7.17270i) q^{53} +(2.20581 + 6.78877i) q^{54} +(3.32116 + 5.75242i) q^{56} +(1.48193 + 0.855590i) q^{57} +(-1.61022 - 0.523192i) q^{58} +(-0.277326 + 2.63859i) q^{59} -1.74967 q^{61} +(-3.91877 - 5.86309i) q^{62} +1.74421i q^{63} +(7.19583 - 5.22808i) q^{64} +(-0.552261 + 1.69968i) q^{66} +(-0.478052 - 0.276003i) q^{67} +(-2.25385 + 1.30126i) q^{68} +(-6.72002 + 1.42838i) q^{69} +(-1.11214 - 0.236393i) q^{71} +(2.40461 - 0.252735i) q^{72} +(-5.88764 + 5.30125i) q^{73} +(4.47988 + 1.99457i) q^{74} +(0.305260 - 0.339025i) q^{76} +(-1.22309 + 1.68344i) q^{77} +(-0.185807 + 0.255741i) q^{78} +(-3.03938 + 3.37557i) q^{79} +(-5.45813 - 2.43012i) q^{81} +(-0.308927 + 0.278159i) q^{82} +(-0.324608 + 0.0341177i) q^{83} +(-1.25766 - 0.267324i) q^{84} +(-11.9315 + 2.53613i) q^{86} +(1.71829 - 0.992053i) q^{87} +(2.49806 + 1.44225i) q^{88} +(4.54569 - 13.9902i) q^{89} +(-0.297768 + 0.216341i) q^{91} +1.83159i q^{92} +(8.17896 + 1.18473i) q^{93} -7.14183 q^{94} +(-0.341837 + 3.25236i) q^{96} +(14.7596 + 4.79569i) q^{97} +(-2.42233 - 1.39853i) q^{98} +(0.378722 + 0.655965i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 28 q^{4} + 22 q^{6} + 20 q^{9} - 14 q^{11} + 12 q^{14} - 4 q^{16} - 32 q^{19} + 18 q^{21} + 40 q^{24} + 18 q^{26} + 28 q^{29} + 30 q^{31} + 64 q^{34} + 2 q^{36} + 6 q^{39} - 16 q^{41} - 78 q^{44}+ \cdots - 12 q^{99}+O(q^{100}) \) 32 * q + 28 * q^4 + 22 * q^6 + 20 * q^9 - 14 * q^11 + 12 * q^14 - 4 * q^16 - 32 * q^19 + 18 * q^21 + 40 * q^24 + 18 * q^26 + 28 * q^29 + 30 * q^31 + 64 * q^34 + 2 * q^36 + 6 * q^39 - 16 * q^41 - 78 * q^44 + 68 * q^46 - 4 * q^49 - 84 * q^51 + 92 * q^54 - 60 * q^56 - 8 * q^59 - 120 * q^61 - 46 * q^64 - 60 * q^66 - 76 * q^69 - 28 * q^71 - 26 * q^74 - 24 * q^76 - 36 * q^79 + 46 * q^81 - 16 * q^84 - 52 * q^86 - 2 * q^89 + 16 * q^91 - 88 * q^94 + 16 * q^96 - 12 * q^99

Introduction

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