LMFDB - Embedded newform 775.2.ck.a.599.1

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			599.1
Character	$\chi$	$=$	775.599
Dual form			775.2.ck.a.524.1

$q$-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 $\left(\mathbb{Z}/775\mathbb{Z}\right)^\times$.

$n$	$251$	$652$
$\chi(n)$	$e\left(\frac{7}{15}\right)$	$-1$

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	−0.986582	−	0.163268i	$-0.947796\pi$
$2$	−0.744490	+	1.02470i	−0.526434	+	0.724574i	0.460148	+	0.887842i	$0.347796\pi$
$3$	1.47618	−	0.155153i	0.852275	−	0.0895777i	0.331691	−	0.943388i	$-0.392381\pi$
$3$	1.47618	−	0.155153i	0.852275	−	0.0895777i	0.520584	+	0.853810i	$0.325714\pi$
$4$	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	0.804518	+	0.593928i	$0.202423\pi$
$7$	−0.455117	+	2.14115i	−0.172018	+	0.809280i	−0.976536	+	0.215353i	$0.930910\pi$
$8$	−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	−0.831366	−	0.555726i	$-0.812441\pi$
$11$	−0.636073	+	0.706430i	−0.191783	+	0.212997i	0.639583	+	0.768722i	$0.279107\pi$
$12$	0.238907	+	0.536593i	0.0689664	+	0.154901i
$13$	−0.0683897	+	0.153606i	−0.0189679	+	0.0426026i	−0.922781	−	0.385325i	$-0.874089\pi$
$13$	−0.0683897	+	0.153606i	−0.0189679	+	0.0426026i	0.903813	+	0.427927i	$0.140756\pi$
$14$	−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	−0.189018	+	0.981974i	$0.560531\pi$
$17$	−4.88741	+	4.40064i	−1.18537	+	1.06731i	−0.996352	+	0.0853387i	$0.972803\pi$
$18$	0.410495	−	0.921986i	0.0967546	−	0.217314i
$19$	1.05317	−	0.468903i	0.241615	−	0.107574i	−0.282357	−	0.959309i	$-0.591116\pi$
$19$	1.05317	−	0.468903i	0.241615	−	0.107574i	0.523972	+	0.851736i	$0.324450\pi$
$20$		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	−0.188279	−	0.982116i	$-0.560291\pi$
$23$	−4.40197	−	1.43029i	−0.917873	−	0.298235i	−0.729594	+	0.683880i	$0.760291\pi$
$24$	−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	0.683649	−	0.729811i	$-0.260392\pi$
$29$	1.08143	+	0.785701i	0.200816	+	0.145901i	−0.482833	+	0.875713i	$0.660392\pi$
$30$		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	0.198393	−	0.980122i	$-0.436428\pi$
$37$	−3.35295	−	1.93582i	−0.551221	−	0.318248i	−0.749614	+	0.661875i	$0.769761\pi$
$38$	−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	−0.996874	−	0.0790062i	$-0.974825\pi$
$41$	−0.0343065	+	0.326405i	−0.00535778	+	0.0509758i	0.991516	+	0.129982i	$0.0414920\pi$
$42$	−3.05832	−	2.75373i	−0.471909	−	0.424909i
$43$	3.91711	+	8.79797i	0.597353	+	1.34168i	0.918790	+	0.394746i	$0.129167\pi$
$43$	3.91711	+	8.79797i	0.597353	+	1.34168i	−0.321437	+	0.946931i	$0.604166\pi$
$44$	−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	0.979161	−	0.203087i	$-0.0650974\pi$
$47$	3.31427	+	4.56170i	0.483436	+	0.665393i	−0.495725	+	0.868480i	$0.665097\pi$
$48$	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	0.949752	+	0.313004i	$0.101335\pi$
$53$	1.52460	+	7.17270i	0.209421	+	0.985246i	−0.740331	+	0.672242i	$0.765331\pi$
$54$	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	−0.997631	−	0.0687995i	$-0.978083\pi$
$59$	−0.277326	−	2.63859i	−0.0361048	−	0.343515i	0.961526	−	0.274715i	$-0.0885835\pi$
$60$		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	−0.528917	−	0.848673i	$-0.677402\pi$
$67$	−0.478052	+	0.276003i	−0.0584033	+	0.0337192i	0.470514	+	0.882393i	$0.344069\pi$
$68$	−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	−0.273431	−	0.961891i	$-0.588159\pi$
$71$	−1.11214	+	0.236393i	−0.131987	+	0.0280547i	0.141444	+	0.989946i	$0.454825\pi$
$72$	2.40461	+	0.252735i	0.283386	+	0.0297851i
$73$	−5.88764	−	5.30125i	−0.689096	−	0.620465i	0.248319	−	0.968678i	$-0.420122\pi$
$73$	−5.88764	−	5.30125i	−0.689096	−	0.620465i	−0.937415	+	0.348214i	$0.886788\pi$
$74$	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	0.547496	−	0.836808i	$-0.315581\pi$
$79$	−3.03938	−	3.37557i	−0.341957	−	0.379782i	−0.889453	+	0.457027i	$0.848914\pi$
$80$		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	0.0866965	−	0.996235i	$-0.472369\pi$
$83$	−0.324608	−	0.0341177i	−0.0356303	−	0.00374490i	−0.122327	+	0.992490i	$0.539036\pi$
$84$	−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	0.836503	+	0.547962i	$0.184596\pi$
$89$	4.54569	+	13.9902i	0.481842	+	1.48296i	−0.354661	+	0.934995i	$0.615404\pi$
$90$		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	0.559000	−	0.829168i	$-0.311185\pi$
$97$	14.7596	−	4.79569i	1.49861	−	0.486929i	0.939613	+	0.342239i	$0.111185\pi$
$98$	−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	−0.847748	−	0.530399i	$-0.822042\pi$
$101$	1.50602	−	4.63507i	0.149855	−	0.461206i	0.997603	+	0.0691923i	$0.0220422\pi$
$102$	−2.57069	−	12.0942i	−0.254536	−	1.19750i
$103$	−1.92004	−	0.201805i	−0.189187	−	0.0198844i	0.00946083	−	0.999955i	$-0.496988\pi$
$103$	−1.92004	−	0.201805i	−0.189187	−	0.0198844i	−0.198648	+	0.980071i	$0.563655\pi$
$104$	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	−0.0824999	−	0.996591i	$-0.526290\pi$
$107$	9.30976	−	8.38254i	0.900008	−	0.810371i	0.982508	+	0.186220i	$0.0596238\pi$
$108$	−1.31085	−	1.80423i	−0.126136	−	0.173612i
$109$	−8.30253	+	6.03214i	−0.795238	+	0.577774i	−0.909513	−	0.415675i	$-0.863545\pi$
$109$	−8.30253	+	6.03214i	−0.795238	+	0.577774i	0.114275	+	0.993449i	$0.463545\pi$
$110$		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	0.523780	−	0.851854i	$-0.324521\pi$
$113$	−2.85586	−	2.57143i	−0.268657	−	0.241900i	−0.792437	+	0.609954i	$0.791188\pi$
$114$	−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	−0.422871	−	0.906190i	$-0.638978\pi$
$127$	−7.30366	+	0.767645i	−0.648095	+	0.0681175i	−0.225223	+	0.974307i	$0.572311\pi$
$128$	−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	−0.386017	−	0.922492i	$-0.626149\pi$
$131$	−12.7489	−	2.70985i	−1.11387	−	0.236761i	−0.727855	+	0.685731i	$0.759483\pi$
$132$	−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	−0.915864	−	0.401489i	$-0.868493\pi$
$137$	−0.0546244	+	0.122689i	−0.00466688	+	0.0104820i	0.911197	+	0.411971i	$0.135159\pi$
$138$	6.46666	−	5.82260i	0.550478	−	0.495653i
$139$	9.32593	−	6.77569i	0.791015	−	0.574706i	−0.117249	−	0.993103i	$-0.537408\pi$
$139$	9.32593	−	6.77569i	0.791015	−	0.574706i	0.908265	+	0.418396i	$0.137408\pi$
$140$		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	−0.955680	−	0.294408i	$-0.904878\pi$
$149$	−2.72054	+	4.71211i	−0.222875	+	0.386031i	0.732805	+	0.680439i	$0.238211\pi$
$150$		0			0
$151$	4.23019	+	13.0192i	0.344248	+	1.05949i	0.961985	+	0.273102i	$0.0880496\pi$
$151$	4.23019	+	13.0192i	0.344248	+	1.05949i	−0.617737	+	0.786385i	$0.711950\pi$
$152$	−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	−0.293618	−	0.955923i	$-0.594859\pi$
$157$	8.84931	−	12.1800i	0.706252	−	0.972072i	0.999870	−	0.0161493i	$-0.00514071\pi$
$158$	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	0.864768	−	0.502172i	$-0.167466\pi$
$163$	16.2042	+	5.26506i	1.26921	+	0.412391i	0.404443	+	0.914563i	$0.367466\pi$
$164$	−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	0.966782	+	0.255601i	$0.0822732\pi$
$167$	6.58842	+	14.7978i	0.509827	+	1.14509i	−0.456955	+	0.889490i	$0.651060\pi$
$168$	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	−0.873906	−	0.486094i	$-0.838421\pi$
$173$	0.948192	−	2.12967i	0.0720897	−	0.161916i	0.945996	+	0.324178i	$0.105088\pi$
$174$	−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	−0.459616	−	0.888118i	$-0.652013\pi$
$179$	−16.5998	−	3.52839i	−1.24073	−	0.263724i	−0.781110	+	0.624394i	$0.785346\pi$
$180$		0			0
$181$	3.66788	+	6.35296i	0.272631	+	0.472211i	0.969535	−	0.244954i	$-0.0787727\pi$
$181$	3.66788	+	6.35296i	0.272631	+	0.472211i	−0.696903	+	0.717165i	$0.745439\pi$
$182$	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	0.689109	−	0.724658i	$-0.258002\pi$
$191$	−3.91138	−	6.77471i	−0.283018	−	0.490201i	−0.972127	+	0.234457i	$0.924669\pi$
$192$	11.4335	+	6.60115i	0.825143	+	0.476397i
$193$	−0.962944	+	4.53030i	−0.0693142	+	0.326098i	−0.999120	−	0.0419539i	$-0.986642\pi$
$193$	−0.962944	+	4.53030i	−0.0693142	+	0.326098i	0.929805	+	0.368052i	$0.119975\pi$
$194$	−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	0.996370	+	0.0851305i	$0.0271307\pi$
$197$	16.6348	+	14.9781i	1.18518	+	1.06714i	0.188813	+	0.982013i	$0.439536\pi$
$198$	0.390215	+	0.876436i	0.0277313	+	0.0622856i
$199$	24.3037	+	10.8207i	1.72285	+	0.767061i	0.996845	+	0.0793670i	$0.0252899\pi$
$199$	24.3037	+	10.8207i	1.72285	+	0.767061i	0.726001	+	0.687694i	$0.241377\pi$
$200$		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	−0.887946	−	0.459947i	$-0.847868\pi$
$211$	−0.663069	+	1.14847i	−0.0456476	+	0.0790639i	0.842299	+	0.539011i	$0.181202\pi$
$212$	−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	0.808418	−	0.588609i	$-0.200324\pi$
$223$	10.4962	+	6.05997i	0.702876	+	0.405806i	−0.105542	+	0.994415i	$0.533658\pi$
$224$	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	−0.436053	−	0.899921i	$-0.643624\pi$
$227$	−15.8150	−	1.66223i	−1.04968	−	0.110326i	−0.613628	+	0.789595i	$0.710291\pi$
$228$	0.503220	+	0.453101i	0.0333266	+	0.0300074i
$229$	14.8895	−	6.62924i	0.983927	−	0.438073i	0.149242	−	0.988801i	$-0.452317\pi$
$229$	14.8895	−	6.62924i	0.983927	−	0.438073i	0.834685	+	0.550728i	$0.185650\pi$
$230$		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	0.896180	−	0.443691i	$-0.146331\pi$
$233$	3.01120	+	4.14456i	0.197270	+	0.271519i	−0.698910	+	0.715210i	$0.746331\pi$
$234$	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	0.0712838	−	0.997456i	$-0.477290\pi$
$239$	8.38077	−	1.78139i	0.542107	−	0.115228i	0.470823	+	0.882228i	$0.343957\pi$
$240$		0			0
$241$	6.69714	+	1.42352i	0.431401	+	0.0916971i	0.418494	−	0.908220i	$-0.362558\pi$
$241$	6.69714	+	1.42352i	0.431401	+	0.0916971i	0.0129071	+	0.999917i	$0.495891\pi$
$242$	−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	−0.769726	−	0.638375i	$-0.779607\pi$
$251$	−2.36925	−	22.5419i	−0.149546	−	1.42283i	0.620180	−	0.784460i	$-0.287060\pi$
$252$	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	−0.943785	−	0.330560i	$-0.892763\pi$
$257$	−3.46347	−	16.2943i	−0.216045	−	1.01641i	0.727740	−	0.685853i	$-0.240571\pi$
$258$	−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	0.973216	+	0.229894i	$0.0738380\pi$
$263$	14.4515	+	19.8908i	0.891118	+	1.22652i	−0.0820979	+	0.996624i	$0.526162\pi$
$264$	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	−0.879427	−	0.476033i	$-0.842074\pi$
$269$	1.30808	−	12.4456i	0.0797553	−	0.758821i	0.959182	−	0.282788i	$-0.0912592\pi$
$270$		0			0
$271$	−8.39516	+	25.8376i	−0.509969	+	1.56952i	0.282283	+	0.959331i	$0.408908\pi$
$271$	−8.39516	+	25.8376i	−0.509969	+	1.56952i	−0.792252	+	0.610194i	$0.791092\pi$
$272$	−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	−0.452622	−	0.891703i	$-0.649511\pi$
$277$	8.90926	−	12.2625i	0.535305	−	0.736785i	0.987927	+	0.154918i	$0.0495113\pi$
$278$			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	−0.983412	−	0.181387i	$-0.941941\pi$
$281$	−24.4709	−	17.7792i	−1.45981	−	1.06062i	−0.476401	−	0.879228i	$-0.658059\pi$
$282$	−10.5426	+	1.10808i	−0.627806	+	0.0659850i
$283$	−2.99138	+	0.971958i	−0.177819	+	0.0577769i	−0.396573	−	0.918003i	$-0.629801\pi$
$283$	−2.99138	+	0.971958i	−0.177819	+	0.0577769i	0.218754	+	0.975780i	$0.429801\pi$
$284$	−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	−0.709345	−	0.704861i	$-0.751009\pi$
$293$	−1.41204	+	1.27140i	−0.0824920	+	0.0742761i	0.626853	+	0.779137i	$0.284343\pi$
$294$	−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	−0.724589	−	0.689181i	$-0.757970\pi$
$307$	−22.6036	+	2.37573i	−1.29005	+	0.135590i	−0.565466	+	0.824772i	$0.691304\pi$
$308$	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	0.0756284	−	0.997136i	$-0.475904\pi$
$313$	6.31457	−	0.663688i	0.356920	−	0.0375138i	0.281292	+	0.959622i	$0.409237\pi$
$314$	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	−0.793903	−	0.608044i	$-0.791954\pi$
$317$	3.18126	−	14.9666i	0.178677	−	0.840610i	0.972581	−	0.232566i	$-0.0747122\pi$
$318$	−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	−0.938081	−	0.346416i	$-0.887399\pi$
$331$	0.937407	−	8.91883i	0.0515245	−	0.490223i	0.989606	−	0.143808i	$-0.0459346\pi$
$332$	−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	−0.419989	−	0.907529i	$-0.637966\pi$
$337$	−4.15495	+	1.35002i	−0.226334	+	0.0735405i	0.193654	+	0.981070i	$0.437966\pi$
$338$	−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	0.945092	−	0.326803i	$-0.105971\pi$
$347$	21.1356	+	12.2026i	1.13462	+	0.655073i	0.189526	+	0.981876i	$0.439305\pi$
$348$	−0.163242	+	0.767994i	−0.00875070	+	0.0411688i
$349$	−4.03079	+	12.4055i	−0.215763	+	0.664051i	0.783335	+	0.621599i	$0.213517\pi$
$349$	−4.03079	+	12.4055i	−0.215763	+	0.664051i	−0.999099	+	0.0424515i	$0.986483\pi$
$350$		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	0.991989	−	0.126326i	$-0.0403187\pi$
$353$	4.40285	+	9.88896i	0.234340	+	0.526336i	−0.757649	+	0.652662i	$0.773652\pi$
$354$	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	−0.630183	−	0.776447i	$-0.717020\pi$
$359$	−30.8627	−	13.7409i	−1.62887	−	0.725220i	−0.998687	+	0.0512273i	$0.983687\pi$
$360$		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	−0.914993	−	0.403469i	$-0.867804\pi$
$367$	−19.5993	+	11.3157i	−1.02308	+	0.590673i	−0.108082	+	0.994142i	$0.534471\pi$
$368$	−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	$-0.674407\pi$
$373$		−	32.9720i		−	1.70723i	0.520908	−	0.853613i	$-0.325593\pi$
$374$	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	−0.701700	−	0.712472i	$-0.747575\pi$
$379$	−31.7818	−	6.75544i	−1.63252	−	0.347004i	−0.930824	+	0.365469i	$0.880909\pi$
$380$		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	−0.0204773	−	0.999790i	$-0.506519\pi$
$383$	−19.9017	−	17.9196i	−1.01693	−	0.915649i	−0.996454	+	0.0841414i	$0.973185\pi$
$384$	−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	0.964659	−	0.263501i	$-0.0848772\pi$
$389$	11.8687	+	13.1815i	0.601767	+	0.668330i	−0.362892	+	0.931831i	$0.618211\pi$
$390$		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	0.700391	−	0.713760i	$-0.253009\pi$
$397$	8.61654	+	4.97476i	0.432452	+	0.249676i	−0.267939	+	0.963436i	$0.586342\pi$
$398$	−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	0.108234	−	0.994125i	$-0.465480\pi$
$401$	−16.0959	−	11.6943i	−0.803789	−	0.583987i	−0.912023	+	0.410138i	$0.865480\pi$
$402$		−	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	0.391198	+	0.920306i	$0.372061\pi$
$409$	−12.1628	+	21.0665i	−0.601410	+	1.04167i	−0.992608	+	0.121365i	$0.961273\pi$
$410$		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	−0.671454	−	0.741046i	$-0.734330\pi$
$419$	−3.56513	+	2.59022i	−0.174168	+	0.126541i	0.497286	+	0.867587i	$0.334330\pi$
$420$		0			0
$421$	−11.3496	−	5.05316i	−0.553145	−	0.246276i	0.111076	−	0.993812i	$-0.464570\pi$
$421$	−11.3496	−	5.05316i	−0.553145	−	0.246276i	−0.664222	+	0.747536i	$0.731237\pi$
$422$	−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	0.936307	+	0.351183i	$0.114220\pi$
$431$	1.94060	+	18.4636i	0.0934755	+	0.889360i	−0.842831	+	0.538178i	$0.819113\pi$
$432$	−10.1098	+	13.9150i	−0.486408	+	0.669484i
$433$		−	36.1204i		−	1.73584i	−0.496708	−	0.867918i	$-0.665458\pi$
$433$		−	36.1204i		−	1.73584i	0.496708	−	0.867918i	$-0.334542\pi$
$434$	−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	0.544974	−	0.838453i	$-0.316539\pi$
$439$	−9.50469	−	16.4626i	−0.453634	−	0.785718i	−0.998609	+	0.0527352i	$0.983206\pi$
$440$		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	−0.995870	−	0.0907852i	$-0.971062\pi$
$443$	−2.58934	−	12.1819i	−0.123023	−	0.578779i	0.872847	−	0.487993i	$-0.162271\pi$
$444$	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	0.0154490	−	0.999881i	$-0.495082\pi$
$449$	20.5786	−	14.9513i	0.971166	−	0.705593i	0.955717	+	0.294287i	$0.0950822\pi$
$450$		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	−0.506087	−	0.862482i	$-0.668909\pi$
$457$	−30.4090	−	9.88049i	−1.42247	−	0.462190i	−0.916388	+	0.400292i	$0.868909\pi$
$458$	−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	0.988274	+	0.152691i	$0.0487940\pi$
$461$	5.97950	+	18.4030i	0.278493	+	0.857114i	−0.709781	+	0.704423i	$0.751206\pi$
$462$	3.89063	−	0.408922i	0.181008	−	0.0190248i
$463$	0.0243710	−	0.0335439i	0.00113262	−	0.00155892i	−0.808450	−	0.588564i	$-0.799693\pi$
$463$	0.0243710	−	0.0335439i	0.00113262	−	0.00155892i	0.809583	+	0.587006i	$0.199693\pi$
$464$	4.07961			0.189391
$465$		0			0
$466$	−6.48875			−0.300586
$467$	−14.8758	+	20.4748i	−0.688372	+	0.947462i	−0.999996	−	0.00274297i	$-0.999127\pi$
$467$	−14.8758	+	20.4748i	−0.688372	+	0.947462i	0.311625	+	0.950205i	$0.399127\pi$
$468$	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	0.974487	−	0.224442i	$-0.0720559\pi$
$479$	14.2131	+	15.7852i	0.649413	+	0.721246i	−0.325074	+	0.945689i	$0.605389\pi$
$480$		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	0.903888	+	0.427769i	$0.140700\pi$
$487$	5.56413	+	26.1772i	0.252135	+	1.18620i	−0.651753	+	0.758431i	$0.725966\pi$
$488$	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	0.972258	−	0.233910i	$-0.0751522\pi$
$491$	6.28320	+	10.8828i	0.283557	+	0.491135i	−0.688701	+	0.725045i	$0.741819\pi$
$492$	−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	−0.906085	−	0.423097i	$-0.860943\pi$
$499$	−2.40733	−	22.9042i	−0.107767	−	1.02533i	0.798318	−	0.602236i	$-0.205724\pi$
$500$		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	−0.974975	−	0.222316i	$-0.928638\pi$
$503$	0.137550	−	0.647121i	0.00613305	−	0.0288537i	0.981108	+	0.193462i	$0.0619717\pi$
$504$	−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	0.629124	−	0.777305i	$-0.283414\pi$
$509$	10.6587	+	4.74556i	0.472439	+	0.210343i	−0.156685	+	0.987649i	$0.550081\pi$
$510$		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	−0.269563	−	0.962983i	$-0.586879\pi$
$521$	15.9592	−	27.6422i	0.699186	−	1.21103i	0.968749	−	0.248043i	$-0.0797874\pi$
$522$	1.16833	−	0.674533i	0.0511362	−	0.0295235i
$523$	0.00394726	−	0.00128254i	0.000172602	−	5.60817e-5i	−0.308931	−	0.951085i	$-0.599971\pi$
$523$	0.00394726	−	0.00128254i	0.000172602	−	5.60817e-5i	0.309103	+	0.951028i	$0.399971\pi$
$524$	−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	0.998629	−	0.0523416i	$-0.0166685\pi$
$541$	19.5888	+	21.7556i	0.842189	+	0.935346i	−0.156440	+	0.987687i	$0.550002\pi$
$542$	−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	−0.971762	−	0.235964i	$-0.924175\pi$
$547$	−30.5918	−	27.5450i	−1.30801	−	1.17774i	−0.336248	−	0.941773i	$-0.609158\pi$
$548$	−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	$0.0387915\pi$
$557$			5.73810i			0.243131i	−0.992583	+	0.121566i	$0.961209\pi$
$558$	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	−0.737637	−	0.675197i	$-0.764059\pi$
$563$	−12.3791	+	7.14710i	−0.521718	+	0.301214i	0.215919	+	0.976411i	$0.430725\pi$
$564$	−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	−0.910106	−	0.414375i	$-0.864000\pi$
$569$	−9.60991	+	10.6729i	−0.402869	+	0.447431i	0.507237	+	0.861806i	$0.330667\pi$
$570$		0			0
$571$	30.4932	+	13.5765i	1.27610	+	0.568157i	0.929142	−	0.369722i	$-0.120547\pi$
$571$	30.4932	+	13.5765i	1.27610	+	0.568157i	0.346960	+	0.937880i	$0.387214\pi$
$572$	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	0.997685	+	0.0680033i	$0.0216628\pi$
$577$	9.14328	+	20.5361i	0.380640	+	0.854931i	−0.617045	+	0.786928i	$0.711670\pi$
$578$	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	−0.724064	−	0.689733i	$-0.757728\pi$
$587$	3.77133	−	5.19079i	0.155659	−	0.214247i	0.879723	+	0.475486i	$0.157728\pi$
$588$			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	0.128111	−	0.991760i	$-0.459109\pi$
$593$	19.8392	−	6.44614i	0.814697	−	0.264711i	0.686586	+	0.727049i	$0.259109\pi$
$594$	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	0.941715	+	0.336410i	$0.109213\pi$
$599$	−1.20818	+	11.4951i	−0.0493649	+	0.469676i	−0.991080	+	0.133265i	$0.957454\pi$
$600$		0			0
$601$	3.94416	−	1.75605i	0.160885	−	0.0716308i	−0.324714	−	0.945812i	$-0.605268\pi$
$601$	3.94416	−	1.75605i	0.160885	−	0.0716308i	0.485599	+	0.874181i	$0.338601\pi$
$602$	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	−0.00523163	−	0.999986i	$-0.501665\pi$
$607$	18.2662	−	41.0266i	0.741404	−	1.66522i	0.746635	−	0.665234i	$-0.231668\pi$
$608$	−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	−0.987731	−	0.156163i	$-0.950088\pi$
$613$	−0.541644	+	2.54823i	−0.0218768	+	0.102922i	0.965855	+	0.259085i	$0.0834209\pi$
$614$	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	0.409865	−	0.912146i	$-0.365576\pi$
$617$	24.8499	−	2.61183i	1.00042	−	0.105148i	0.590555	+	0.806998i	$0.298909\pi$
$618$	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	−0.747917	−	0.663792i	$-0.768946\pi$
$631$	−0.240720	+	0.267347i	−0.00958293	+	0.0106429i	0.738334	+	0.674435i	$0.235613\pi$
$632$	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	−0.725688	−	0.688024i	$-0.758478\pi$
$641$	3.22020	−	30.6382i	0.127190	−	1.21013i	0.852878	−	0.522110i	$-0.174855\pi$
$642$	4.89677	+	23.0375i	0.193260	+	0.909218i
$643$	−1.66609	−	0.541347i	−0.0657044	−	0.0213486i	0.275980	−	0.961163i	$-0.410998\pi$
$643$	−1.66609	−	0.541347i	−0.0657044	−	0.0213486i	−0.341685	+	0.939815i	$0.610998\pi$
$644$	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	−0.731154	−	0.682213i	$-0.761018\pi$
$647$	−23.4439	+	7.61739i	−0.921675	+	0.299470i	−0.190521	+	0.981683i	$0.561018\pi$
$648$	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	−0.812290	−	0.583254i	$-0.801779\pi$
$653$	−0.167909	+	0.231107i	−0.00657080	+	0.00904393i	0.805719	+	0.592298i	$0.201779\pi$
$654$	−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	0.425832	+	0.904802i	$0.359982\pi$
$659$	−11.5649	+	35.5930i	−0.450503	+	1.38651i	−0.876335	+	0.481703i	$0.840018\pi$
$660$		0			0
$661$	−0.438139	+	4.16861i	−0.0170416	+	0.162140i	−0.999733	−	0.0231105i	$-0.992643\pi$
$661$	−0.438139	+	4.16861i	−0.0170416	+	0.162140i	0.982691	+	0.185251i	$0.0593097\pi$
$662$	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	0.919947	−	0.392044i	$-0.128232\pi$
$673$	−2.07343	−	9.75474i	−0.0799250	−	0.376018i	−0.999872	+	0.0160261i	$0.994899\pi$
$674$	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	0.596192	−	0.802842i	$-0.296680\pi$
$677$	41.3594	−	23.8788i	1.58957	−	0.917738i	0.993377	−	0.114896i	$-0.0366536\pi$
$678$	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	$0.178223\pi$
$683$			27.7600i			1.06221i	−0.847307	+	0.531104i	$0.821777\pi$
$684$	−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	−0.851127	−	0.524959i	$-0.824081\pi$
$691$	−37.1999	+	7.90708i	−1.41515	+	0.300800i	−0.564023	+	0.825759i	$0.690747\pi$
$692$	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	0.451431	−	0.892306i	$-0.350914\pi$
$701$	37.5067	−	16.6991i	1.41661	−	0.630716i	0.965179	+	0.261590i	$0.0842469\pi$
$702$	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	−0.827309	−	0.561747i	$-0.810130\pi$
$709$	−12.9990	−	40.0069i	−0.488188	−	1.50249i	0.339121	−	0.940743i	$-0.389870\pi$
$710$		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	0.369056	+	0.929407i	$0.379681\pi$
$719$	−16.6345	+	28.8118i	−0.620362	+	1.07450i	−0.989418	+	0.145092i	$0.953652\pi$
$720$		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	−0.982805	−	0.184648i	$-0.940885\pi$
$727$	−24.3179	+	21.8959i	−0.901899	+	0.812074i	0.0809055	+	0.996722i	$0.474219\pi$
$728$	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	0.520956	−	0.853583i	$-0.325575\pi$
$733$	−7.40463	−	6.66715i	−0.273496	−	0.246257i	−0.794452	+	0.607326i	$0.792242\pi$
$734$	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	0.996624	+	0.0820995i	$0.0261625\pi$
$739$	15.4792	+	26.8108i	0.569412	+	0.986251i	−0.427212	+	0.904152i	$0.640504\pi$
$740$		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	$0.00648173\pi$
$743$			1.11003i			0.0407231i	−0.999793	+	0.0203615i	$0.993518\pi$
$744$	−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	−0.324093	−	0.946025i	$-0.605059\pi$
$751$	−27.5400	−	5.85382i	−1.00495	−	0.213609i	−0.680857	+	0.732416i	$0.738393\pi$
$752$	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	−0.362860	−	0.931844i	$-0.618200\pi$
$757$	15.7498	−	35.3746i	0.572436	−	1.28571i	0.935295	−	0.353868i	$-0.115134\pi$
$758$	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	0.985010	+	0.172500i	$0.0551845\pi$
$761$	29.0649	+	32.2799i	1.05360	+	1.17014i	0.0685936	+	0.997645i	$0.478149\pi$
$762$	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	−0.892702	−	0.450648i	$-0.851193\pi$
$769$	−1.55509	+	2.69350i	−0.0560781	+	0.0971302i	0.836624	+	0.547778i	$0.184526\pi$
$770$		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	−0.516489	−	0.856294i	$-0.672761\pi$
$773$	12.7198	−	17.5073i	0.457499	−	0.629693i	0.973988	+	0.226601i	$0.0727613\pi$
$774$	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	0.961598	−	0.274462i	$-0.0884996\pi$
$787$	3.20368	+	7.19557i	0.114199	+	0.256494i	−0.847399	+	0.530956i	$0.821833\pi$
$788$	−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	0.942526	+	0.334133i	$0.108443\pi$
$797$	6.13717	+	28.8731i	0.217390	+	1.02274i	−0.725136	+	0.688605i	$0.758223\pi$
$798$	−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	0.989917	−	0.141650i	$-0.0452409\pi$
$809$	−0.222387	−	2.11587i	−0.00781871	−	0.0743901i	−0.997735	+	0.0672603i	$0.978574\pi$
$810$		0			0
$811$	−3.60252	−	6.23975i	−0.126502	−	0.219107i	0.795817	−	0.605537i	$-0.207042\pi$
$811$	−3.60252	−	6.23975i	−0.126502	−	0.219107i	−0.922319	+	0.386430i	$0.873708\pi$
$812$	−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	−0.993003	−	0.118086i	$-0.962324\pi$
$821$	−34.0270	+	24.7221i	−1.18755	+	0.862807i	−0.194548	+	0.980893i	$0.562324\pi$
$822$	−0.148408	−	0.204267i	−0.00517634	−	0.00712462i
$823$	22.4229	−	20.1897i	0.781613	−	0.703767i	−0.178328	−	0.983971i	$-0.557069\pi$
$823$	22.4229	−	20.1897i	0.781613	−	0.703767i	0.959940	+	0.280204i	$0.0904021\pi$
$824$	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	0.0373657	−	0.999302i	$-0.488103\pi$
$827$	−3.84925	−	0.404573i	−0.133852	−	0.0140684i	−0.171217	+	0.985233i	$0.554770\pi$
$828$	0.303433	+	1.42754i	0.0105450	+	0.0496104i
$829$	−4.07025	+	12.5269i	−0.141366	+	0.435079i	−0.996526	−	0.0832851i	$-0.973459\pi$
$829$	−4.07025	+	12.5269i	−0.141366	+	0.435079i	0.855160	+	0.518364i	$0.173459\pi$
$830$		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	−0.00423187	−	0.999991i	$-0.501347\pi$
$839$	−27.7080	−	20.1311i	−0.956588	−	0.695002i	−0.952356	+	0.304989i	$0.901347\pi$
$840$		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	0.929264	−	0.369417i	$-0.120443\pi$
$853$	8.49225	+	11.6886i	0.290769	+	0.400209i	−0.638495	+	0.769626i	$0.720443\pi$
$854$	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	0.235413	−	0.971896i	$-0.424356\pi$
$857$	−20.6840	−	18.6239i	−0.706552	−	0.636182i	−0.941964	+	0.335714i	$0.891023\pi$
$858$	0.298850	+	0.0314104i	0.0102026	+	0.00107233i
$859$	−46.2861	+	9.83842i	−1.57926	+	0.335682i	−0.912336	−	0.409442i	$-0.865723\pi$
$859$	−46.2861	+	9.83842i	−1.57926	+	0.335682i	−0.666925	+	0.745124i	$0.732390\pi$
$860$		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	−0.0641289	−	0.997942i	$-0.520427\pi$
$863$	22.5629	−	13.0267i	0.768049	−	0.443434i	0.832178	+	0.554508i	$0.187094\pi$
$864$	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	−0.917659	−	0.397368i	$-0.869924\pi$
$877$	−7.13584	−	33.5715i	−0.240960	−	1.13363i	0.676699	−	0.736260i	$-0.263410\pi$
$878$	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	0.350039	−	0.936735i	$-0.386168\pi$
$881$	−3.32044	−	1.47835i	−0.111868	−	0.0498070i	−0.461908	+	0.886928i	$0.652835\pi$
$882$	1.65627	−	1.49131i	0.0557695	−	0.0502151i
$883$	−23.1925	−	31.9217i	−0.780489	−	1.07425i	−0.995228	−	0.0975789i	$-0.968890\pi$
$883$	−23.1925	−	31.9217i	−0.780489	−	1.07425i	0.214739	−	0.976671i	$-0.431110\pi$
$884$	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	0.932004	+	0.362449i	$0.118059\pi$
$887$	17.2061	+	38.6455i	0.577723	+	1.29759i	−0.354280	+	0.935139i	$0.615274\pi$
$888$	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	0.771686	−	0.636003i	$-0.219414\pi$
$907$	30.7838	+	10.0023i	1.02216	+	0.332120i	0.250474	+	0.968123i	$0.419414\pi$
$908$	−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	−0.773104	−	0.634279i	$-0.781297\pi$
$911$	−24.7212	+	11.0066i	−0.819051	+	0.364665i	−0.0459464	+	0.998944i	$0.514630\pi$
$912$	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	−0.927369	−	0.374147i	$-0.877936\pi$
$919$	−13.8945	+	15.4314i	−0.458336	+	0.509033i	0.469034	+	0.883180i	$0.344602\pi$
$920$		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	−0.986953	−	0.161012i	$-0.948524\pi$
$937$	−0.607227	+	2.85678i	−0.0198372	+	0.0933269i	0.967115	+	0.254338i	$0.0818577\pi$
$938$	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	−0.269360	−	0.963040i	$-0.586812\pi$
$941$	21.9810	−	24.4124i	0.716560	−	0.795821i	0.985920	+	0.167219i	$0.0534787\pi$
$942$	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	−0.0441199	−	0.999026i	$-0.514048\pi$
$947$	29.0753	−	26.1796i	0.944822	−	0.850721i	0.988942	+	0.148305i	$0.0473817\pi$
$948$	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	0.400272	−	0.916396i	$-0.368916\pi$
$953$	5.72512	+	1.86020i	0.185455	+	0.0602579i	−0.214817	+	0.976654i	$0.568916\pi$
$954$	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	0.819420	−	0.573194i	$-0.194296\pi$
$967$	22.7854	+	13.1552i	0.732730	+	0.423042i	−0.0866903	+	0.996235i	$0.527629\pi$
$968$	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	−0.983703	−	0.179801i	$-0.942455\pi$
$971$	0.495033	−	4.70993i	0.0158864	−	0.151149i	0.999589	+	0.0286519i	$0.00912142\pi$
$972$	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	0.615021	−	0.788511i	$-0.289148\pi$
$977$	−10.1569	−	13.9798i	−0.324950	−	0.447255i	−0.939970	+	0.341256i	$0.889148\pi$
$978$	−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	0.876374	+	0.481631i	$0.159955\pi$
$983$	8.51742	+	40.0713i	0.271663	+	1.27808i	−0.604711	+	0.796445i	$0.706711\pi$
$984$	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	−0.696726	−	0.717337i	$-0.745361\pi$
$997$	−13.3834	+	7.72692i	−0.423857	+	0.244714i	0.272869	+	0.962051i	$0.412027\pi$
$998$	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.599.1		32
5.2	odd	4		31.2.g.a.10.1	✓	16
5.3	odd	4		775.2.bl.a.351.2		16
5.4	even	2	inner	775.2.ck.a.599.4		32
15.2	even	4		279.2.y.c.10.2		16
20.7	even	4		496.2.bg.c.289.2		16
31.28	even	15	inner	775.2.ck.a.524.4		32
155.2	odd	20		961.2.g.t.846.2		16
155.7	odd	60		961.2.c.j.521.6		16
155.12	even	60		961.2.g.m.448.2		16
155.17	even	60		961.2.g.n.844.2		16
155.22	even	60		961.2.d.q.531.3		16
155.27	even	20		961.2.c.i.439.6		16
155.28	odd	60		775.2.bl.a.276.2		16
155.37	even	12		961.2.g.j.732.1		16
155.42	even	60		961.2.a.j.1.6		8
155.47	odd	20		961.2.g.k.235.1		16
155.52	even	60		961.2.d.q.628.3		16
155.57	even	12		961.2.d.n.374.2		16
155.59	even	30	inner	775.2.ck.a.524.1		32
155.67	odd	12		961.2.d.o.374.2		16
155.72	odd	60		961.2.d.p.628.3		16
155.77	even	20		961.2.g.j.235.1		16
155.82	odd	60		961.2.a.i.1.6		8
155.87	odd	12		961.2.g.k.732.1		16
155.92	even	4		961.2.g.l.816.1		16
155.97	odd	20		961.2.c.j.439.6		16
155.102	odd	60		961.2.d.p.531.3		16
155.107	odd	60		961.2.g.t.844.2		16
155.112	odd	60		961.2.g.s.448.2		16
155.117	even	60		961.2.c.i.521.6		16
155.122	even	20		961.2.g.n.846.2		16
155.127	even	60		961.2.g.l.338.1		16
155.132	odd	20		961.2.g.s.547.2		16
155.137	even	60		961.2.d.n.388.2		16
155.142	odd	60		961.2.d.o.388.2		16
155.147	even	20		961.2.g.m.547.2		16
155.152	odd	60		31.2.g.a.28.1	yes	16
465.152	even	60		279.2.y.c.28.2		16
465.197	odd	60		8649.2.a.be.1.3		8
465.392	even	60		8649.2.a.bf.1.3		8
620.307	even	60		496.2.bg.c.369.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.10.1	✓	16	5.2	odd	4
31.2.g.a.28.1	yes	16	155.152	odd	60
279.2.y.c.10.2		16	15.2	even	4
279.2.y.c.28.2		16	465.152	even	60
496.2.bg.c.289.2		16	20.7	even	4
496.2.bg.c.369.2		16	620.307	even	60
775.2.bl.a.276.2		16	155.28	odd	60
775.2.bl.a.351.2		16	5.3	odd	4
775.2.ck.a.524.1		32	155.59	even	30	inner
775.2.ck.a.524.4		32	31.28	even	15	inner
775.2.ck.a.599.1		32	1.1	even	1	trivial
775.2.ck.a.599.4		32	5.4	even	2	inner
961.2.a.i.1.6		8	155.82	odd	60
961.2.a.j.1.6		8	155.42	even	60
961.2.c.i.439.6		16	155.27	even	20
961.2.c.i.521.6		16	155.117	even	60
961.2.c.j.439.6		16	155.97	odd	20
961.2.c.j.521.6		16	155.7	odd	60
961.2.d.n.374.2		16	155.57	even	12
961.2.d.n.388.2		16	155.137	even	60
961.2.d.o.374.2		16	155.67	odd	12
961.2.d.o.388.2		16	155.142	odd	60
961.2.d.p.531.3		16	155.102	odd	60
961.2.d.p.628.3		16	155.72	odd	60
961.2.d.q.531.3		16	155.22	even	60
961.2.d.q.628.3		16	155.52	even	60
961.2.g.j.235.1		16	155.77	even	20
961.2.g.j.732.1		16	155.37	even	12
961.2.g.k.235.1		16	155.47	odd	20
961.2.g.k.732.1		16	155.87	odd	12
961.2.g.l.338.1		16	155.127	even	60
961.2.g.l.816.1		16	155.92	even	4
961.2.g.m.448.2		16	155.12	even	60
961.2.g.m.547.2		16	155.147	even	20
961.2.g.n.844.2		16	155.17	even	60
961.2.g.n.846.2		16	155.122	even	20
961.2.g.s.448.2		16	155.112	odd	60
961.2.g.s.547.2		16	155.132	odd	20
961.2.g.t.844.2		16	155.107	odd	60
961.2.g.t.846.2		16	155.2	odd	20
8649.2.a.be.1.3		8	465.197	odd	60
8649.2.a.bf.1.3		8	465.392	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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