LMFDB - Embedded newform 213.2.e.a.196.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [213,2,Mod(25,213)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("213.25"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(213, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 213 = 3 \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	213.e (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.70081356305$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			196.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	213.196
Dual form			213.2.e.a.25.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.30902 + 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.190983 + 0.587785i) q^{4} +(-0.881966 + 2.71441i) q^{5} +(0.500000 + 1.53884i) q^{6} +(1.30902 + 0.951057i) q^{7} +(0.690983 - 2.12663i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-3.73607 + 2.71441i) q^{10} +(-4.92705 - 3.57971i) q^{11} +(-0.190983 + 0.587785i) q^{12} +(1.80902 - 1.31433i) q^{13} +(0.809017 + 2.48990i) q^{14} +(-2.30902 + 1.67760i) q^{15} +(3.92705 - 2.85317i) q^{16} +(-0.500000 + 1.53884i) q^{18} +(5.73607 + 4.16750i) q^{19} -1.76393 q^{20} +(0.500000 + 1.53884i) q^{21} +(-3.04508 - 9.37181i) q^{22} -3.47214 q^{23} +(1.80902 - 1.31433i) q^{24} +(-2.54508 - 1.84911i) q^{25} +3.61803 q^{26} +(-0.309017 + 0.951057i) q^{27} +(-0.309017 + 0.951057i) q^{28} +(2.88197 - 8.86978i) q^{29} -4.61803 q^{30} +(-6.04508 - 4.39201i) q^{31} +3.38197 q^{32} +(-1.88197 - 5.79210i) q^{33} +(-3.73607 + 2.71441i) q^{35} +(-0.500000 + 0.363271i) q^{36} -2.38197 q^{37} +(3.54508 + 10.9106i) q^{38} +2.23607 q^{39} +(5.16312 + 3.75123i) q^{40} +3.09017 q^{41} +(-0.809017 + 2.48990i) q^{42} +(-0.118034 + 0.363271i) q^{43} +(1.16312 - 3.57971i) q^{44} -2.85410 q^{45} +(-4.54508 - 3.30220i) q^{46} +(-5.42705 + 3.94298i) q^{47} +4.85410 q^{48} +(-1.35410 - 4.16750i) q^{49} +(-1.57295 - 4.84104i) q^{50} +(1.11803 + 0.812299i) q^{52} +(-3.89919 + 12.0005i) q^{53} +(-1.30902 + 0.951057i) q^{54} +(14.0623 - 10.2169i) q^{55} +(2.92705 - 2.12663i) q^{56} +(2.19098 + 6.74315i) q^{57} +(12.2082 - 8.86978i) q^{58} +(1.80902 - 5.56758i) q^{59} +(-1.42705 - 1.03681i) q^{60} +(-5.16312 + 3.75123i) q^{61} +(-3.73607 - 11.4984i) q^{62} +(-0.500000 + 1.53884i) q^{63} +(-3.42705 - 2.48990i) q^{64} +(1.97214 + 6.06961i) q^{65} +(3.04508 - 9.37181i) q^{66} +(-0.472136 - 1.45309i) q^{67} +(-2.80902 - 2.04087i) q^{69} -7.47214 q^{70} +(-1.95492 + 8.19624i) q^{71} +2.23607 q^{72} +(8.35410 + 6.06961i) q^{73} +(-3.11803 - 2.26538i) q^{74} +(-0.972136 - 2.99193i) q^{75} +(-1.35410 + 4.16750i) q^{76} +(-3.04508 - 9.37181i) q^{77} +(2.92705 + 2.12663i) q^{78} +(-0.600813 + 1.84911i) q^{79} +(4.28115 + 13.1760i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(4.04508 + 2.93893i) q^{82} +(-3.69098 + 11.3597i) q^{83} +(-0.809017 + 0.587785i) q^{84} +(-0.500000 + 0.363271i) q^{86} +(7.54508 - 5.48183i) q^{87} +(-11.0172 + 8.00448i) q^{88} +(-0.972136 + 2.99193i) q^{89} +(-3.73607 - 2.71441i) q^{90} +3.61803 q^{91} +(-0.663119 - 2.04087i) q^{92} +(-2.30902 - 7.10642i) q^{93} -10.8541 q^{94} +(-16.3713 + 11.8945i) q^{95} +(2.73607 + 1.98787i) q^{96} -5.94427 q^{97} +(2.19098 - 6.74315i) q^{98} +(1.88197 - 5.79210i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} + q^{3} + 3 q^{4} - 8 q^{5} + 2 q^{6} + 3 q^{7} + 5 q^{8} - q^{9} - 6 q^{10} - 13 q^{11} - 3 q^{12} + 5 q^{13} + q^{14} - 7 q^{15} + 9 q^{16} - 2 q^{18} + 14 q^{19} - 16 q^{20} + 2 q^{21}+ \cdots + 12 q^{99}+O(q^{100}) $ 4 * q + 3 * q^2 + q^3 + 3 * q^4 - 8 * q^5 + 2 * q^6 + 3 * q^7 + 5 * q^8 - q^9 - 6 * q^10 - 13 * q^11 - 3 * q^12 + 5 * q^13 + q^14 - 7 * q^15 + 9 * q^16 - 2 * q^18 + 14 * q^19 - 16 * q^20 + 2 * q^21 - q^22 + 4 * q^23 + 5 * q^24 + q^25 + 10 * q^26 + q^27 + q^28 + 16 * q^29 - 14 * q^30 - 13 * q^31 + 18 * q^32 - 12 * q^33 - 6 * q^35 - 2 * q^36 - 14 * q^37 + 3 * q^38 + 5 * q^40 - 10 * q^41 - q^42 + 4 * q^43 - 11 * q^44 + 2 * q^45 - 7 * q^46 - 15 * q^47 + 6 * q^48 + 8 * q^49 - 13 * q^50 + 9 * q^53 - 3 * q^54 + 16 * q^55 + 5 * q^56 + 11 * q^57 + 22 * q^58 + 5 * q^59 + q^60 - 5 * q^61 - 6 * q^62 - 2 * q^63 - 7 * q^64 - 10 * q^65 + q^66 + 16 * q^67 - 9 * q^69 - 12 * q^70 - 19 * q^71 + 20 * q^73 - 8 * q^74 + 14 * q^75 + 8 * q^76 - q^77 + 5 * q^78 - 27 * q^79 - 3 * q^80 - q^81 + 5 * q^82 - 17 * q^83 - q^84 - 2 * q^86 + 19 * q^87 - 15 * q^88 + 14 * q^89 - 6 * q^90 + 10 * q^91 + 13 * q^92 - 7 * q^93 - 30 * q^94 - 23 * q^95 + 2 * q^96 + 12 * q^97 + 11 * q^98 + 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/213\mathbb{Z}\right)^\times$.

$n$	$7$	$143$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

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 $

$2$	1.30902	+	0.951057i	0.925615	+	0.672499i	0.944915	−	0.327315i	$-0.106144\pi$
$2$	1.30902	+	0.951057i	0.925615	+	0.672499i	−0.0193004	+	0.999814i	$0.506144\pi$
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$4$	0.190983	+	0.587785i	0.0954915	+	0.293893i
$5$	−0.881966	+	2.71441i	−0.394427	+	1.21392i	0.534980	+	0.844865i	$0.320319\pi$
$5$	−0.881966	+	2.71441i	−0.394427	+	1.21392i	−0.929407	+	0.369057i	$0.879681\pi$
$6$	0.500000	+	1.53884i	0.204124	+	0.628230i
$7$	1.30902	+	0.951057i	0.494762	+	0.359466i	0.807013	−	0.590534i	$-0.201083\pi$
$7$	1.30902	+	0.951057i	0.494762	+	0.359466i	−0.312251	+	0.950000i	$0.601083\pi$
$8$	0.690983	−	2.12663i	0.244299	−	0.751876i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$	−3.73607	+	2.71441i	−1.18145	+	0.858373i
$11$	−4.92705	−	3.57971i	−1.48556	−	1.07932i	−0.975711	−	0.219061i	$-0.929701\pi$
$11$	−4.92705	−	3.57971i	−1.48556	−	1.07932i	−0.509851	−	0.860263i	$-0.670299\pi$
$12$	−0.190983	+	0.587785i	−0.0551320	+	0.169679i
$13$	1.80902	−	1.31433i	0.501731	−	0.364529i	−0.307947	−	0.951404i	$-0.599642\pi$
$13$	1.80902	−	1.31433i	0.501731	−	0.364529i	0.809678	+	0.586875i	$0.199642\pi$
$14$	0.809017	+	2.48990i	0.216219	+	0.665453i
$15$	−2.30902	+	1.67760i	−0.596186	+	0.433154i
$16$	3.92705	−	2.85317i	0.981763	−	0.713292i
$17$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$17$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$18$	−0.500000	+	1.53884i	−0.117851	+	0.362708i
$19$	5.73607	+	4.16750i	1.31594	+	0.956089i	0.999973	+	0.00732062i	$0.00233025\pi$
$19$	5.73607	+	4.16750i	1.31594	+	0.956089i	0.315971	+	0.948769i	$0.397670\pi$
$20$	−1.76393			−0.394427
$21$	0.500000	+	1.53884i	0.109109	+	0.335803i
$22$	−3.04508	−	9.37181i	−0.649214	−	1.99808i
$23$	−3.47214			−0.723990			−0.361995	−	0.932180i	$-0.617904\pi$
$23$	−3.47214			−0.723990			−0.361995	+	0.932180i	$0.617904\pi$
$24$	1.80902	−	1.31433i	0.369264	−	0.268286i
$25$	−2.54508	−	1.84911i	−0.509017	−	0.369822i
$26$	3.61803			0.709555
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	−0.309017	+	0.951057i	−0.0583987	+	0.179733i
$29$	2.88197	−	8.86978i	0.535168	−	1.64708i	−0.208119	−	0.978104i	$-0.566734\pi$
$29$	2.88197	−	8.86978i	0.535168	−	1.64708i	0.743287	−	0.668973i	$-0.233266\pi$
$30$	−4.61803			−0.843134
$31$	−6.04508	−	4.39201i	−1.08573	−	0.788829i	−0.107056	−	0.994253i	$-0.534143\pi$
$31$	−6.04508	−	4.39201i	−1.08573	−	0.788829i	−0.978673	+	0.205424i	$0.934143\pi$
$32$	3.38197			0.597853
$33$	−1.88197	−	5.79210i	−0.327608	−	1.00827i
$34$		0			0
$35$	−3.73607	+	2.71441i	−0.631511	+	0.458819i
$36$	−0.500000	+	0.363271i	−0.0833333	+	0.0605452i
$37$	−2.38197			−0.391593			−0.195796	−	0.980645i	$-0.562729\pi$
$37$	−2.38197			−0.391593			−0.195796	+	0.980645i	$0.562729\pi$
$38$	3.54508	+	10.9106i	0.575089	+	1.76994i
$39$	2.23607			0.358057
$40$	5.16312	+	3.75123i	0.816361	+	0.593121i
$41$	3.09017			0.482603			0.241302	−	0.970450i	$-0.422426\pi$
$41$	3.09017			0.482603			0.241302	+	0.970450i	$0.422426\pi$
$42$	−0.809017	+	2.48990i	−0.124834	+	0.384200i
$43$	−0.118034	+	0.363271i	−0.0180000	+	0.0553983i	−0.959653	−	0.281187i	$-0.909272\pi$
$43$	−0.118034	+	0.363271i	−0.0180000	+	0.0553983i	0.941653	+	0.336585i	$0.109272\pi$
$44$	1.16312	−	3.57971i	0.175347	−	0.539662i
$45$	−2.85410			−0.425464
$46$	−4.54508	−	3.30220i	−0.670136	−	0.486882i
$47$	−5.42705	+	3.94298i	−0.791617	+	0.575143i	−0.908443	−	0.418009i	$-0.862728\pi$
$47$	−5.42705	+	3.94298i	−0.791617	+	0.575143i	0.116826	+	0.993152i	$0.462728\pi$
$48$	4.85410			0.700629
$49$	−1.35410	−	4.16750i	−0.193443	−	0.595357i
$50$	−1.57295	−	4.84104i	−0.222449	−	0.684626i
$51$		0			0
$52$	1.11803	+	0.812299i	0.155043	+	0.112646i
$53$	−3.89919	+	12.0005i	−0.535595	+	1.64839i	0.206766	+	0.978390i	$0.433706\pi$
$53$	−3.89919	+	12.0005i	−0.535595	+	1.64839i	−0.742361	+	0.670000i	$0.766294\pi$
$54$	−1.30902	+	0.951057i	−0.178135	+	0.129422i
$55$	14.0623	−	10.2169i	1.89616	−	1.37764i
$56$	2.92705	−	2.12663i	0.391144	−	0.284182i
$57$	2.19098	+	6.74315i	0.290203	+	0.893152i
$58$	12.2082	−	8.86978i	1.60302	−	1.16466i
$59$	1.80902	−	5.56758i	0.235514	−	0.724837i	−0.761539	−	0.648119i	$-0.775556\pi$
$59$	1.80902	−	5.56758i	0.235514	−	0.724837i	0.997053	−	0.0767182i	$-0.0244442\pi$
$60$	−1.42705	−	1.03681i	−0.184231	−	0.133852i
$61$	−5.16312	+	3.75123i	−0.661070	+	0.480295i	−0.867024	−	0.498266i	$-0.833970\pi$
$61$	−5.16312	+	3.75123i	−0.661070	+	0.480295i	0.205954	+	0.978562i	$0.433970\pi$
$62$	−3.73607	−	11.4984i	−0.474481	−	1.46030i
$63$	−0.500000	+	1.53884i	−0.0629941	+	0.193876i
$64$	−3.42705	−	2.48990i	−0.428381	−	0.311237i
$65$	1.97214	+	6.06961i	0.244613	+	0.752843i
$66$	3.04508	−	9.37181i	0.374824	−	1.15359i
$67$	−0.472136	−	1.45309i	−0.0576806	−	0.177523i	0.918065	−	0.396430i	$-0.129751\pi$
$67$	−0.472136	−	1.45309i	−0.0576806	−	0.177523i	−0.975746	+	0.218907i	$0.929751\pi$
$68$		0			0
$69$	−2.80902	−	2.04087i	−0.338166	−	0.245692i
$70$	−7.47214			−0.893091
$71$	−1.95492	+	8.19624i	−0.232006	+	0.972714i
$71$	−1.95492	+	8.19624i	−0.232006	+	0.972714i
$72$	2.23607			0.263523
$73$	8.35410	+	6.06961i	0.977774	+	0.710394i	0.957210	−	0.289394i	$-0.0934539\pi$
$73$	8.35410	+	6.06961i	0.977774	+	0.710394i	0.0205637	+	0.999789i	$0.493454\pi$
$74$	−3.11803	−	2.26538i	−0.362464	−	0.263346i
$75$	−0.972136	−	2.99193i	−0.112253	−	0.345478i
$76$	−1.35410	+	4.16750i	−0.155326	+	0.478045i
$77$	−3.04508	−	9.37181i	−0.347020	−	1.06802i
$78$	2.92705	+	2.12663i	0.331423	+	0.240793i
$79$	−0.600813	+	1.84911i	−0.0675968	+	0.208041i	−0.979149	−	0.203142i	$-0.934885\pi$
$79$	−0.600813	+	1.84911i	−0.0675968	+	0.208041i	0.911552	+	0.411184i	$0.134885\pi$
$80$	4.28115	+	13.1760i	0.478647	+	1.47313i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	4.04508	+	2.93893i	0.446705	+	0.324550i
$83$	−3.69098	+	11.3597i	−0.405138	+	1.24689i	0.515642	+	0.856804i	$0.327553\pi$
$83$	−3.69098	+	11.3597i	−0.405138	+	1.24689i	−0.920780	+	0.390082i	$0.872447\pi$
$84$	−0.809017	+	0.587785i	−0.0882710	+	0.0641326i
$85$		0			0
$86$	−0.500000	+	0.363271i	−0.0539164	+	0.0391725i
$87$	7.54508	−	5.48183i	0.808918	−	0.587713i
$88$	−11.0172	+	8.00448i	−1.17444	+	0.853280i
$89$	−0.972136	+	2.99193i	−0.103046	+	0.317144i	−0.989267	−	0.146120i	$-0.953322\pi$
$89$	−0.972136	+	2.99193i	−0.103046	+	0.317144i	0.886221	+	0.463263i	$0.153322\pi$
$90$	−3.73607	−	2.71441i	−0.393816	−	0.286124i
$91$	3.61803			0.379273
$92$	−0.663119	−	2.04087i	−0.0691349	−	0.212775i
$93$	−2.30902	−	7.10642i	−0.239434	−	0.736902i
$94$	−10.8541			−1.11952
$95$	−16.3713	+	11.8945i	−1.67966	+	1.22035i
$96$	2.73607	+	1.98787i	0.279249	+	0.202886i
$97$	−5.94427			−0.603549			−0.301775	−	0.953379i	$-0.597579\pi$
$97$	−5.94427			−0.603549			−0.301775	+	0.953379i	$0.597579\pi$
$98$	2.19098	−	6.74315i	0.221323	−	0.681161i
$99$	1.88197	−	5.79210i	0.189145	−	0.582128i
$100$	0.600813	−	1.84911i	0.0600813	−	0.184911i
$101$	17.5623			1.74751			0.873757	−	0.486362i	$-0.161676\pi$
$101$	17.5623			1.74751			0.873757	+	0.486362i	$0.161676\pi$
$102$		0			0
$103$	−8.14590			−0.802639			−0.401320	−	0.915938i	$-0.631448\pi$
$103$	−8.14590			−0.802639			−0.401320	+	0.915938i	$0.631448\pi$
$104$	−1.54508	−	4.75528i	−0.151508	−	0.466294i
$105$	−4.61803			−0.450674
$106$	−16.5172	+	12.0005i	−1.60429	+	1.16559i
$107$	16.3992	−	11.9147i	1.58537	−	1.15184i	0.675174	−	0.737658i	$-0.264068\pi$
$107$	16.3992	−	11.9147i	1.58537	−	1.15184i	0.910195	−	0.414180i	$-0.135932\pi$
$108$	−0.618034			−0.0594703
$109$	0.736068	+	2.26538i	0.0705025	+	0.216984i	0.980099	−	0.198508i	$-0.0636094\pi$
$109$	0.736068	+	2.26538i	0.0705025	+	0.216984i	−0.909597	+	0.415492i	$0.863609\pi$
$110$	28.1246			2.68158
$111$	−1.92705	−	1.40008i	−0.182908	−	0.132890i
$112$	7.85410			0.742143
$113$	−2.63525	+	8.11048i	−0.247904	+	0.762970i	0.747241	+	0.664553i	$0.231378\pi$
$113$	−2.63525	+	8.11048i	−0.247904	+	0.762970i	−0.995145	+	0.0984171i	$0.968622\pi$
$114$	−3.54508	+	10.9106i	−0.332028	+	1.02188i
$115$	3.06231	−	9.42481i	0.285561	−	0.878868i
$116$	5.76393			0.535168
$117$	1.80902	+	1.31433i	0.167244	+	0.121510i
$118$	7.66312	−	5.56758i	0.705447	−	0.512537i
$119$		0			0
$120$	1.97214	+	6.06961i	0.180031	+	0.554077i
$121$	8.06231	+	24.8132i	0.732937	+	2.25575i
$122$	−10.3262			−0.934894
$123$	2.50000	+	1.81636i	0.225417	+	0.163775i
$124$	1.42705	−	4.39201i	0.128153	−	0.394414i
$125$	−4.28115	+	3.11044i	−0.382918	+	0.278206i
$126$	−2.11803	+	1.53884i	−0.188689	+	0.137091i
$127$	−6.04508	+	4.39201i	−0.536415	+	0.389728i	−0.822752	−	0.568401i	$-0.807562\pi$
$127$	−6.04508	+	4.39201i	−0.536415	+	0.389728i	0.286337	+	0.958129i	$0.407562\pi$
$128$	−4.20820	−	12.9515i	−0.371956	−	1.14476i
$129$	−0.309017	+	0.224514i	−0.0272074	+	0.0197674i
$130$	−3.19098	+	9.82084i	−0.279868	+	0.861344i
$131$	−15.0902	−	10.9637i	−1.31843	−	0.957899i	−0.999950	−	0.00997032i	$-0.996826\pi$
$131$	−15.0902	−	10.9637i	−1.31843	−	0.957899i	−0.318484	−	0.947928i	$-0.603174\pi$
$132$	3.04508	−	2.21238i	0.265041	−	0.192563i
$133$	3.54508	+	10.9106i	0.307398	+	0.946073i
$134$	0.763932	−	2.35114i	0.0659937	−	0.203108i
$135$	−2.30902	−	1.67760i	−0.198729	−	0.144385i
$136$		0			0
$137$	1.98278	−	6.10237i	0.169400	−	0.521360i	−0.829933	−	0.557863i	$-0.811622\pi$
$137$	1.98278	−	6.10237i	0.169400	−	0.521360i	0.999334	+	0.0365022i	$0.0116216\pi$
$138$	−1.73607	−	5.34307i	−0.147784	−	0.454832i
$139$	−2.47214	−	1.79611i	−0.209684	−	0.152344i	0.477987	−	0.878367i	$-0.341367\pi$
$139$	−2.47214	−	1.79611i	−0.209684	−	0.152344i	−0.687671	+	0.726023i	$0.741367\pi$
$140$	−2.30902	−	1.67760i	−0.195148	−	0.141783i
$141$	−6.70820			−0.564933
$142$	−10.3541	+	8.86978i	−0.868897	+	0.744335i
$143$	−13.6180			−1.13880
$144$	3.92705	+	2.85317i	0.327254	+	0.237764i
$145$	21.5344	+	15.6457i	1.78834	+	1.29930i
$146$	5.16312	+	15.8904i	0.427303	+	1.31510i
$147$	1.35410	−	4.16750i	0.111684	−	0.343729i
$148$	−0.454915	−	1.40008i	−0.0373938	−	0.115086i
$149$	1.23607	+	0.898056i	0.101263	+	0.0735716i	0.637264	−	0.770645i	$-0.280066\pi$
$149$	1.23607	+	0.898056i	0.101263	+	0.0735716i	−0.536002	+	0.844217i	$0.680066\pi$
$150$	1.57295	−	4.84104i	0.128431	−	0.395269i
$151$	−1.90983	−	5.87785i	−0.155420	−	0.478333i	0.842783	−	0.538253i	$-0.180915\pi$
$151$	−1.90983	−	5.87785i	−0.155420	−	0.478333i	−0.998203	+	0.0599200i	$0.980915\pi$
$152$	12.8262	−	9.31881i	1.04035	−	0.755855i
$153$		0			0
$154$	4.92705	−	15.1639i	0.397033	−	1.22194i
$155$	17.2533	−	12.5352i	1.38582	−	1.00686i
$156$	0.427051	+	1.31433i	0.0341914	+	0.105230i
$157$	13.9721	−	10.1514i	1.11510	−	0.810166i	0.131639	−	0.991298i	$-0.457976\pi$
$157$	13.9721	−	10.1514i	1.11510	−	0.810166i	0.983459	+	0.181132i	$0.0579760\pi$
$158$	−2.54508	+	1.84911i	−0.202476	+	0.147107i
$159$	−10.2082	+	7.41669i	−0.809563	+	0.588182i
$160$	−2.98278	+	9.18005i	−0.235809	+	0.725747i
$161$	−4.54508	−	3.30220i	−0.358203	−	0.260250i
$162$	−1.61803			−0.127125
$163$	−1.47214	−	4.53077i	−0.115307	−	0.354877i	0.876704	−	0.481030i	$-0.159737\pi$
$163$	−1.47214	−	4.53077i	−0.115307	−	0.354877i	−0.992011	+	0.126153i	$0.959737\pi$
$164$	0.590170	+	1.81636i	0.0460845	+	0.141834i
$165$	17.3820			1.35318
$166$	−15.6353	+	11.3597i	−1.21353	+	0.881682i
$167$	−0.263932	−	0.191758i	−0.0204237	−	0.0148387i	0.577527	−	0.816372i	$-0.304018\pi$
$167$	−0.263932	−	0.191758i	−0.0204237	−	0.0148387i	−0.597950	+	0.801533i	$0.704018\pi$
$168$	3.61803			0.279137
$169$	−2.47214	+	7.60845i	−0.190164	+	0.585266i
$170$		0			0
$171$	−2.19098	+	6.74315i	−0.167549	+	0.515662i
$172$	−0.236068			−0.0180000
$173$	4.80902	+	3.49396i	0.365623	+	0.265641i	0.755394	−	0.655271i	$-0.227446\pi$
$173$	4.80902	+	3.49396i	0.365623	+	0.265641i	−0.389771	+	0.920912i	$0.627446\pi$
$174$	15.0902			1.14398
$175$	−1.57295	−	4.84104i	−0.118904	−	0.365948i
$176$	−29.5623			−2.22834
$177$	4.73607	−	3.44095i	0.355985	−	0.258638i
$178$	−4.11803	+	2.99193i	−0.308660	+	0.224254i
$179$	7.18034			0.536684			0.268342	−	0.963324i	$-0.413524\pi$
$179$	7.18034			0.536684			0.268342	+	0.963324i	$0.413524\pi$
$180$	−0.545085	−	1.67760i	−0.0406282	−	0.125041i
$181$	13.7984			1.02563			0.512813	−	0.858501i	$-0.328604\pi$
$181$	13.7984			1.02563			0.512813	+	0.858501i	$0.328604\pi$
$182$	4.73607	+	3.44095i	0.351061	+	0.255061i
$183$	−6.38197			−0.471769
$184$	−2.39919	+	7.38394i	−0.176870	+	0.544351i
$185$	2.10081	−	6.46564i	0.154455	−	0.475363i
$186$	3.73607	−	11.4984i	0.273942	−	0.843106i
$187$		0			0
$188$	−3.35410	−	2.43690i	−0.244623	−	0.177729i
$189$	−1.30902	+	0.951057i	−0.0952170	+	0.0691792i
$190$	−32.7426			−2.37540
$191$	−3.52786	−	10.8576i	−0.255267	−	0.785632i	−0.993777	−	0.111389i	$-0.964470\pi$
$191$	−3.52786	−	10.8576i	−0.255267	−	0.785632i	0.738510	−	0.674243i	$-0.235530\pi$
$192$	−1.30902	−	4.02874i	−0.0944702	−	0.290749i
$193$	8.79837			0.633321			0.316660	−	0.948539i	$-0.397438\pi$
$193$	8.79837			0.633321			0.316660	+	0.948539i	$0.397438\pi$
$194$	−7.78115	−	5.65334i	−0.558654	−	0.405886i
$195$	−1.97214	+	6.06961i	−0.141228	+	0.434654i
$196$	2.19098	−	1.59184i	0.156499	−	0.113703i
$197$	−2.19098	+	1.59184i	−0.156101	+	0.113414i	−0.663094	−	0.748536i	$-0.730757\pi$
$197$	−2.19098	+	1.59184i	−0.156101	+	0.113414i	0.506993	+	0.861950i	$0.330757\pi$
$198$	7.97214	−	5.79210i	0.566555	−	0.411626i
$199$	−4.10081	−	12.6210i	−0.290699	−	0.894679i	−0.984632	−	0.174640i	$-0.944124\pi$
$199$	−4.10081	−	12.6210i	−0.290699	−	0.894679i	0.693933	−	0.720039i	$-0.255876\pi$
$200$	−5.69098	+	4.13474i	−0.402413	+	0.292370i
$201$	0.472136	−	1.45309i	0.0333019	−	0.102493i
$202$	22.9894	+	16.7027i	1.61753	+	1.17520i
$203$	12.2082	−	8.86978i	0.856848	−	0.622536i
$204$		0			0
$205$	−2.72542	+	8.38800i	−0.190352	+	0.585843i
$206$	−10.6631	−	7.74721i	−0.742935	−	0.539774i
$207$	−1.07295	−	3.30220i	−0.0745751	−	0.229519i
$208$	3.35410	−	10.3229i	0.232565	−	0.715762i
$209$	−13.3435	−	41.0669i	−0.922986	−	2.84066i
$210$	−6.04508	−	4.39201i	−0.417150	−	0.303078i
$211$	−15.5623	−	11.3067i	−1.07135	−	0.778384i	−0.0951983	−	0.995458i	$-0.530349\pi$
$211$	−15.5623	−	11.3067i	−1.07135	−	0.778384i	−0.976155	+	0.217075i	$0.930349\pi$
$212$	−7.79837			−0.535595
$213$	−6.39919	+	5.48183i	−0.438465	+	0.375608i
$214$	32.7984			2.24205
$215$	−0.881966	−	0.640786i	−0.0601496	−	0.0437012i
$216$	1.80902	+	1.31433i	0.123088	+	0.0894287i
$217$	−3.73607	−	11.4984i	−0.253621	−	0.780565i
$218$	−1.19098	+	3.66547i	−0.0806635	+	0.248257i
$219$	3.19098	+	9.82084i	0.215627	+	0.663631i
$220$	8.69098	+	6.31437i	0.585946	+	0.425715i
$221$		0			0
$222$	−1.19098	−	3.66547i	−0.0799335	−	0.246010i
$223$	−4.61803	+	3.35520i	−0.309246	+	0.224681i	−0.731573	−	0.681763i	$-0.761214\pi$
$223$	−4.61803	+	3.35520i	−0.309246	+	0.224681i	0.422327	+	0.906444i	$0.361214\pi$
$224$	4.42705	+	3.21644i	0.295795	+	0.214907i
$225$	0.972136	−	2.99193i	0.0648091	−	0.199462i
$226$	−11.1631	+	8.11048i	−0.742560	+	0.539501i
$227$	−0.954915	−	2.93893i	−0.0633799	−	0.195063i	0.914352	−	0.404919i	$-0.132700\pi$
$227$	−0.954915	−	2.93893i	−0.0633799	−	0.195063i	−0.977732	+	0.209856i	$0.932700\pi$
$228$	−3.54508	+	2.57565i	−0.234779	+	0.170577i
$229$	−6.11803	+	4.44501i	−0.404291	+	0.293735i	−0.771287	−	0.636488i	$-0.780386\pi$
$229$	−6.11803	+	4.44501i	−0.404291	+	0.293735i	0.366995	+	0.930223i	$0.380386\pi$
$230$	12.9721	−	9.42481i	0.855357	−	0.621453i
$231$	3.04508	−	9.37181i	0.200352	−	0.616620i
$232$	−16.8713	−	12.2577i	−1.10766	−	0.804760i
$233$	5.09017			0.333468			0.166734	−	0.986002i	$-0.446678\pi$
$233$	5.09017			0.333468			0.166734	+	0.986002i	$0.446678\pi$
$234$	1.11803	+	3.44095i	0.0730882	+	0.224942i
$235$	−5.91641	−	18.2088i	−0.385944	−	1.18781i
$236$	3.61803			0.235514
$237$	−1.57295	+	1.14281i	−0.102174	+	0.0742338i
$238$		0			0
$239$	19.0902			1.23484			0.617420	−	0.786634i	$-0.288178\pi$
$239$	19.0902			1.23484			0.617420	+	0.786634i	$0.288178\pi$
$240$	−4.28115	+	13.1760i	−0.276347	+	0.850509i
$241$	5.48936	−	16.8945i	0.353601	−	1.08827i	−0.603216	−	0.797578i	$-0.706114\pi$
$241$	5.48936	−	16.8945i	0.353601	−	1.08827i	0.956816	−	0.290693i	$-0.0938857\pi$
$242$	−13.0451	+	40.1486i	−0.838570	+	2.58085i
$243$	−1.00000			−0.0641500
$244$	−3.19098	−	2.31838i	−0.204282	−	0.148419i
$245$	12.5066			0.799016
$246$	1.54508	+	4.75528i	0.0985110	+	0.303186i
$247$	15.8541			1.00877
$248$	−13.5172	+	9.82084i	−0.858344	+	0.623624i
$249$	−9.66312	+	7.02067i	−0.612375	+	0.444917i
$250$	−8.56231			−0.541528
$251$	−2.20820	−	6.79615i	−0.139381	−	0.428969i	0.856865	−	0.515541i	$-0.172409\pi$
$251$	−2.20820	−	6.79615i	−0.139381	−	0.428969i	−0.996246	+	0.0865714i	$0.972409\pi$
$252$	−1.00000			−0.0629941
$253$	17.1074	+	12.4292i	1.07553	+	0.781420i
$254$	−12.0902			−0.758605
$255$		0			0
$256$	4.19098	−	12.8985i	0.261936	−	0.806157i
$257$	1.76393	−	5.42882i	0.110031	−	0.338641i	−0.880847	−	0.473401i	$-0.843026\pi$
$257$	1.76393	−	5.42882i	0.110031	−	0.338641i	0.990878	+	0.134760i	$0.0430263\pi$
$258$	−0.618034			−0.0384771
$259$	−3.11803	−	2.26538i	−0.193745	−	0.140764i
$260$	−3.19098	+	2.31838i	−0.197896	+	0.143780i
$261$	9.32624			0.577280
$262$	−9.32624	−	28.7032i	−0.576177	−	1.77329i
$263$	5.66312	+	17.4293i	0.349203	+	1.07474i	0.959295	+	0.282406i	$0.0911324\pi$
$263$	5.66312	+	17.4293i	0.349203	+	1.07474i	−0.610092	+	0.792330i	$0.708868\pi$
$264$	−13.6180			−0.838132
$265$	−29.1353	−	21.1680i	−1.78976	−	1.30034i
$266$	−5.73607	+	17.6538i	−0.351701	+	1.08242i
$267$	−2.54508	+	1.84911i	−0.155757	+	0.113164i
$268$	0.763932	−	0.555029i	0.0466646	−	0.0339038i
$269$	9.66312	−	7.02067i	0.589171	−	0.428058i	−0.252848	−	0.967506i	$-0.581367\pi$
$269$	9.66312	−	7.02067i	0.589171	−	0.428058i	0.842019	+	0.539448i	$0.181367\pi$
$270$	−1.42705	−	4.39201i	−0.0868476	−	0.267289i
$271$	−14.1353	+	10.2699i	−0.858656	+	0.623850i	−0.927519	−	0.373776i	$-0.878063\pi$
$271$	−14.1353	+	10.2699i	−0.858656	+	0.623850i	0.0688633	+	0.997626i	$0.478063\pi$
$272$		0			0
$273$	2.92705	+	2.12663i	0.177153	+	0.128709i
$274$	8.39919	−	6.10237i	0.507413	−	0.368657i
$275$	5.92047	+	18.2213i	0.357018	+	1.09879i
$276$	0.663119	−	2.04087i	0.0399151	−	0.122846i
$277$	−7.82624	−	5.68609i	−0.470233	−	0.341644i	0.327299	−	0.944921i	$-0.393862\pi$
$277$	−7.82624	−	5.68609i	−0.470233	−	0.341644i	−0.797532	+	0.603276i	$0.793862\pi$
$278$	−1.52786	−	4.70228i	−0.0916352	−	0.282024i
$279$	2.30902	−	7.10642i	0.138237	−	0.425450i
$280$	3.19098	+	9.82084i	0.190698	+	0.586907i
$281$	13.6353	+	9.90659i	0.813411	+	0.590978i	0.914818	−	0.403867i	$-0.132334\pi$
$281$	13.6353	+	9.90659i	0.813411	+	0.590978i	−0.101406	+	0.994845i	$0.532334\pi$
$282$	−8.78115	−	6.37988i	−0.522910	−	0.379916i
$283$	19.1803			1.14015			0.570076	−	0.821592i	$-0.306914\pi$
$283$	19.1803			1.14015			0.570076	+	0.821592i	$0.306914\pi$
$284$	−5.19098	+	0.416272i	−0.308028	+	0.0247012i
$285$	−20.2361			−1.19868
$286$	−17.8262	−	12.9515i	−1.05409	−	0.765839i
$287$	4.04508	+	2.93893i	0.238774	+	0.173479i
$288$	1.04508	+	3.21644i	0.0615822	+	0.189531i
$289$	−5.25329	+	16.1680i	−0.309017	+	0.951057i
$290$	13.3090	+	40.9609i	0.781532	+	2.40531i
$291$	−4.80902	−	3.49396i	−0.281910	−	0.204819i
$292$	−1.97214	+	6.06961i	−0.115411	+	0.355197i
$293$	4.73607	+	14.5761i	0.276684	+	0.851546i	0.988769	+	0.149453i	$0.0477511\pi$
$293$	4.73607	+	14.5761i	0.276684	+	0.851546i	−0.712085	+	0.702093i	$0.752249\pi$
$294$	5.73607	−	4.16750i	0.334534	−	0.243053i
$295$	13.5172	+	9.82084i	0.787003	+	0.571791i
$296$	−1.64590	+	5.06555i	−0.0956659	+	0.294429i
$297$	4.92705	−	3.57971i	0.285896	−	0.207716i
$298$	0.763932	+	2.35114i	0.0442534	+	0.136198i
$299$	−6.28115	+	4.56352i	−0.363248	+	0.263915i
$300$	1.57295	−	1.14281i	0.0908143	−	0.0659804i
$301$	−0.500000	+	0.363271i	−0.0288195	+	0.0209386i
$302$	3.09017	−	9.51057i	0.177819	−	0.547272i
$303$	14.2082	+	10.3229i	0.816240	+	0.593033i
$304$	34.4164			1.97392
$305$	−5.62868	−	17.3233i	−0.322297	−	0.991929i
$306$		0			0
$307$	23.1246			1.31979			0.659896	−	0.751357i	$-0.270600\pi$
$307$	23.1246			1.31979			0.659896	+	0.751357i	$0.270600\pi$
$308$	4.92705	−	3.57971i	0.280745	−	0.203973i
$309$	−6.59017	−	4.78804i	−0.374902	−	0.272382i
$310$	34.5066			1.95984
$311$	−10.8435	+	33.3727i	−0.614876	+	1.89239i	−0.211419	+	0.977395i	$0.567809\pi$
$311$	−10.8435	+	33.3727i	−0.614876	+	1.89239i	−0.403457	+	0.914999i	$0.632191\pi$
$312$	1.54508	−	4.75528i	0.0874732	−	0.269215i
$313$	4.10081	−	12.6210i	0.231792	−	0.713381i	−0.765739	−	0.643151i	$-0.777627\pi$
$313$	4.10081	−	12.6210i	0.231792	−	0.713381i	0.997531	−	0.0702301i	$-0.0223734\pi$
$314$	27.9443			1.57699
$315$	−3.73607	−	2.71441i	−0.210504	−	0.152940i
$316$	−1.20163			−0.0675968
$317$	5.60739	+	17.2578i	0.314942	+	0.969293i	0.975778	+	0.218763i	$0.0702020\pi$
$317$	5.60739	+	17.2578i	0.314942	+	0.969293i	−0.660836	+	0.750531i	$0.729798\pi$
$318$	−20.4164			−1.14490
$319$	−45.9508	+	33.3852i	−2.57275	+	1.86921i
$320$	9.78115	−	7.10642i	0.546783	−	0.397261i
$321$	20.2705			1.13139
$322$	−2.80902	−	8.64527i	−0.156540	−	0.481782i
$323$		0			0
$324$	−0.500000	−	0.363271i	−0.0277778	−	0.0201817i
$325$	−7.03444			−0.390201
$326$	2.38197	−	7.33094i	0.131925	−	0.406023i
$327$	−0.736068	+	2.26538i	−0.0407047	+	0.125276i
$328$	2.13525	−	6.57164i	0.117900	−	0.362858i
$329$	−10.8541			−0.598406
$330$	22.7533	+	16.5312i	1.25253	+	0.910014i
$331$	28.0795	−	20.4010i	1.54339	−	1.12134i	0.595226	−	0.803558i	$-0.297063\pi$
$331$	28.0795	−	20.4010i	1.54339	−	1.12134i	0.948164	−	0.317780i	$-0.102937\pi$
$332$	−7.38197			−0.405138
$333$	−0.736068	−	2.26538i	−0.0403363	−	0.124142i
$334$	−0.163119	−	0.502029i	−0.00892547	−	0.0274698i
$335$	4.36068			0.238249
$336$	6.35410	+	4.61653i	0.346645	+	0.251852i
$337$	−6.29837	+	19.3844i	−0.343094	+	1.05594i	0.619502	+	0.784995i	$0.287335\pi$
$337$	−6.29837	+	19.3844i	−0.343094	+	1.05594i	−0.962596	+	0.270940i	$0.912665\pi$
$338$	−10.4721	+	7.60845i	−0.569609	+	0.413845i
$339$	−6.89919	+	5.01255i	−0.374712	+	0.272244i
$340$		0			0
$341$	14.0623	+	43.2793i	0.761517	+	2.34371i
$342$	−9.28115	+	6.74315i	−0.501867	+	0.364628i
$343$	5.69098	−	17.5150i	0.307284	−	0.945724i
$344$	0.690983	+	0.502029i	0.0372553	+	0.0270676i
$345$	8.01722	−	5.82485i	0.431633	−	0.313599i
$346$	2.97214	+	9.14729i	0.159783	+	0.491762i
$347$	4.23607	−	13.0373i	0.227404	−	0.699878i	−0.770635	−	0.637277i	$-0.780061\pi$
$347$	4.23607	−	13.0373i	0.227404	−	0.699878i	0.998039	−	0.0626004i	$-0.0199394\pi$
$348$	4.66312	+	3.38795i	0.249969	+	0.181613i
$349$	5.12868	+	15.7844i	0.274532	+	0.844922i	0.989343	+	0.145604i	$0.0465127\pi$
$349$	5.12868	+	15.7844i	0.274532	+	0.844922i	−0.714811	+	0.699318i	$0.753487\pi$
$350$	2.54508	−	7.83297i	0.136041	−	0.418690i
$351$	0.690983	+	2.12663i	0.0368819	+	0.113511i
$352$	−16.6631	−	12.1065i	−0.888147	−	0.645277i
$353$	−24.2254	−	17.6008i	−1.28939	−	0.936796i	−0.289596	−	0.957149i	$-0.593521\pi$
$353$	−24.2254	−	17.6008i	−1.28939	−	0.936796i	−0.999793	+	0.0203527i	$0.993521\pi$
$354$	9.47214			0.503438
$355$	−20.5238	−	12.5352i	−1.08929	−	0.665302i
$356$	−1.94427			−0.103046
$357$		0			0
$358$	9.39919	+	6.82891i	0.496762	+	0.360919i
$359$	−10.1074	−	31.1074i	−0.533448	−	1.64178i	−0.746980	−	0.664847i	$-0.768497\pi$
$359$	−10.1074	−	31.1074i	−0.533448	−	1.64178i	0.213532	−	0.976936i	$-0.431503\pi$
$360$	−1.97214	+	6.06961i	−0.103941	+	0.319897i
$361$	9.66312	+	29.7400i	0.508585	+	1.56526i
$362$	18.0623	+	13.1230i	0.949334	+	0.689731i
$363$	−8.06231	+	24.8132i	−0.423161	+	1.30236i
$364$	0.690983	+	2.12663i	0.0362174	+	0.111466i
$365$	−23.8435	+	17.3233i	−1.24802	+	0.906742i
$366$	−8.35410	−	6.06961i	−0.436676	−	0.317264i
$367$	2.30902	−	7.10642i	0.120530	−	0.370952i	−0.872530	−	0.488560i	$-0.837522\pi$
$367$	2.30902	−	7.10642i	0.120530	−	0.370952i	0.993060	+	0.117607i	$0.0375224\pi$
$368$	−13.6353	+	9.90659i	−0.710787	+	0.516417i
$369$	0.954915	+	2.93893i	0.0497109	+	0.152994i
$370$	8.89919	−	6.46564i	0.462647	−	0.336133i
$371$	−16.5172	+	12.0005i	−0.857531	+	0.623033i
$372$	3.73607	−	2.71441i	0.193706	−	0.140736i
$373$	0.798374	−	2.45714i	0.0413382	−	0.127226i	−0.928258	−	0.371938i	$-0.878693\pi$
$373$	0.798374	−	2.45714i	0.0413382	−	0.127226i	0.969596	+	0.244712i	$0.0786934\pi$
$374$		0			0
$375$	−5.29180			−0.273267
$376$	4.63525	+	14.2658i	0.239045	+	0.735705i
$377$	−6.44427	−	19.8334i	−0.331897	−	1.02147i
$378$	−2.61803			−0.134657
$379$	−2.09017	+	1.51860i	−0.107365	+	0.0780051i	−0.640172	−	0.768231i	$-0.721137\pi$
$379$	−2.09017	+	1.51860i	−0.107365	+	0.0780051i	0.532807	+	0.846237i	$0.321137\pi$
$380$	−10.1180	−	7.35118i	−0.519044	−	0.377108i
$381$	−7.47214			−0.382809
$382$	5.70820	−	17.5680i	0.292057	−	0.898859i
$383$	1.54508	−	4.75528i	0.0789502	−	0.242984i	−0.903790	−	0.427977i	$-0.859226\pi$
$383$	1.54508	−	4.75528i	0.0789502	−	0.242984i	0.982740	+	0.184993i	$0.0592264\pi$
$384$	4.20820	−	12.9515i	0.214749	−	0.660929i
$385$	28.1246			1.43336
$386$	11.5172	+	8.36775i	0.586211	+	0.425907i
$387$	−0.381966			−0.0194164
$388$	−1.13525	−	3.49396i	−0.0576338	−	0.177379i
$389$	4.79837			0.243287			0.121644	−	0.992574i	$-0.461184\pi$
$389$	4.79837			0.243287			0.121644	+	0.992574i	$0.461184\pi$
$390$	−8.35410	+	6.06961i	−0.423026	+	0.307347i
$391$		0			0
$392$	−9.79837			−0.494893
$393$	−5.76393	−	17.7396i	−0.290752	−	0.894842i
$394$	−4.38197			−0.220760
$395$	−4.48936	−	3.26171i	−0.225884	−	0.164114i
$396$	3.76393			0.189145
$397$	7.38197	−	22.7194i	0.370490	−	1.14025i	−0.575981	−	0.817463i	$-0.695380\pi$
$397$	7.38197	−	22.7194i	0.370490	−	1.14025i	0.946471	−	0.322789i	$-0.104620\pi$
$398$	6.63525	−	20.4212i	0.332595	−	1.02362i
$399$	−3.54508	+	10.9106i	−0.177476	+	0.546216i
$400$	−15.2705			−0.763525
$401$	−12.8541	−	9.33905i	−0.641903	−	0.466370i	0.218600	−	0.975814i	$-0.429851\pi$
$401$	−12.8541	−	9.33905i	−0.641903	−	0.466370i	−0.860504	+	0.509444i	$0.829851\pi$
$402$	2.00000	−	1.45309i	0.0997509	−	0.0724733i
$403$	−16.7082			−0.832295
$404$	3.35410	+	10.3229i	0.166873	+	0.513582i
$405$	−0.881966	−	2.71441i	−0.0438252	−	0.134880i
$406$	24.4164			1.21177
$407$	11.7361	+	8.52675i	0.581735	+	0.422655i
$408$		0			0
$409$	5.70820	−	4.14725i	0.282253	−	0.205068i	−0.437647	−	0.899147i	$-0.644188\pi$
$409$	5.70820	−	4.14725i	0.282253	−	0.205068i	0.719899	+	0.694079i	$0.244188\pi$
$410$	−11.5451	+	8.38800i	−0.570171	+	0.414254i
$411$	5.19098	−	3.77147i	0.256052	−	0.186033i
$412$	−1.55573	−	4.78804i	−0.0766452	−	0.235890i
$413$	7.66312	−	5.56758i	0.377077	−	0.273963i
$414$	1.73607	−	5.34307i	0.0853231	−	0.262597i
$415$	−27.5795	−	20.0377i	−1.35383	−	0.983612i
$416$	6.11803	−	4.44501i	0.299961	−	0.217935i
$417$	−0.944272	−	2.90617i	−0.0462412	−	0.142316i
$418$	21.5902	−	66.4477i	1.05601	−	3.25006i
$419$	7.80902	+	5.67358i	0.381495	+	0.277173i	0.761962	−	0.647622i	$-0.224236\pi$
$419$	7.80902	+	5.67358i	0.381495	+	0.277173i	−0.380466	+	0.924795i	$0.624236\pi$
$420$	−0.881966	−	2.71441i	−0.0430355	−	0.132450i
$421$	−11.7705	+	36.2259i	−0.573660	+	1.76554i	0.0670394	+	0.997750i	$0.478645\pi$
$421$	−11.7705	+	36.2259i	−0.573660	+	1.76554i	−0.640699	+	0.767792i	$0.721355\pi$
$422$	−9.61803	−	29.6013i	−0.468199	−	1.44097i
$423$	−5.42705	−	3.94298i	−0.263872	−	0.191714i
$424$	22.8262	+	16.5842i	1.10854	+	0.805402i
$425$		0			0
$426$	−13.5902	+	1.08981i	−0.658446	+	0.0528017i
$427$	−10.3262			−0.499722
$428$	10.1353	+	7.36369i	0.489906	+	0.355938i
$429$	−11.0172	−	8.00448i	−0.531916	−	0.386460i
$430$	−0.545085	−	1.67760i	−0.0262863	−	0.0809010i
$431$	−6.83688	+	21.0418i	−0.329321	+	1.01355i	0.640131	+	0.768266i	$0.278880\pi$
$431$	−6.83688	+	21.0418i	−0.329321	+	1.01355i	−0.969452	+	0.245280i	$0.921120\pi$
$432$	1.50000	+	4.61653i	0.0721688	+	0.222113i
$433$	−21.2533	−	15.4414i	−1.02137	−	0.742067i	−0.0548050	−	0.998497i	$-0.517454\pi$
$433$	−21.2533	−	15.4414i	−1.02137	−	0.742067i	−0.966563	+	0.256430i	$0.917454\pi$
$434$	6.04508	−	18.6049i	0.290173	−	0.893062i
$435$	8.22542	+	25.3153i	0.394379	+	1.21377i
$436$	−1.19098	+	0.865300i	−0.0570377	+	0.0414403i
$437$	−19.9164	−	14.4701i	−0.952731	−	0.692200i
$438$	−5.16312	+	15.8904i	−0.246703	+	0.759275i
$439$	−25.6525	+	18.6376i	−1.22433	+	0.889525i	−0.996452	−	0.0841658i	$-0.973177\pi$
$439$	−25.6525	+	18.6376i	−1.22433	+	0.889525i	−0.227874	+	0.973691i	$0.573177\pi$
$440$	−12.0106	−	36.9650i	−0.572585	−	1.76224i
$441$	3.54508	−	2.57565i	0.168814	−	0.122650i
$442$		0			0
$443$	−19.2082	+	13.9556i	−0.912609	+	0.663049i	−0.941673	−	0.336528i	$-0.890747\pi$
$443$	−19.2082	+	13.9556i	−0.912609	+	0.663049i	0.0290641	+	0.999578i	$0.490747\pi$
$444$	0.454915	−	1.40008i	0.0215893	−	0.0664451i
$445$	−7.26393	−	5.27756i	−0.344343	−	0.250180i
$446$	−9.23607			−0.437340
$447$	0.472136	+	1.45309i	0.0223313	+	0.0687286i
$448$	−2.11803	−	6.51864i	−0.100068	−	0.307977i
$449$	19.3262			0.912062			0.456031	−	0.889964i	$-0.349271\pi$
$449$	19.3262			0.912062			0.456031	+	0.889964i	$0.349271\pi$
$450$	4.11803	−	2.99193i	0.194126	−	0.141041i
$451$	−15.2254	−	11.0619i	−0.716937	−	0.520885i
$452$	−5.27051			−0.247904
$453$	1.90983	−	5.87785i	0.0897316	−	0.276166i
$454$	1.54508	−	4.75528i	0.0725144	−	0.223176i
$455$	−3.19098	+	9.82084i	−0.149596	+	0.460408i
$456$	15.8541			0.742436
$457$	−8.04508	−	5.84510i	−0.376333	−	0.273422i	0.383499	−	0.923541i	$-0.374719\pi$
$457$	−8.04508	−	5.84510i	−0.376333	−	0.273422i	−0.759832	+	0.650119i	$0.774719\pi$
$458$	−12.2361			−0.571754
$459$		0			0
$460$	6.12461			0.285561
$461$	12.7533	−	9.26581i	0.593980	−	0.431552i	−0.249757	−	0.968309i	$-0.580351\pi$
$461$	12.7533	−	9.26581i	0.593980	−	0.431552i	0.843737	+	0.536757i	$0.180351\pi$
$462$	12.8992	−	9.37181i	0.600124	−	0.436016i
$463$	−6.18034			−0.287225			−0.143612	−	0.989634i	$-0.545872\pi$
$463$	−6.18034			−0.287225			−0.143612	+	0.989634i	$0.545872\pi$
$464$	−13.9894	−	43.0548i	−0.649440	−	1.99877i
$465$	21.3262			0.988981
$466$	6.66312	+	4.84104i	0.308663	+	0.224257i
$467$	37.3262			1.72725			0.863626	−	0.504133i	$-0.168188\pi$
$467$	37.3262			1.72725			0.863626	+	0.504133i	$0.168188\pi$
$468$	−0.427051	+	1.31433i	−0.0197404	+	0.0607548i
$469$	0.763932	−	2.35114i	0.0352751	−	0.108566i
$470$	9.57295	−	29.4625i	0.441567	−	1.35900i
$471$	17.2705			0.795783
$472$	−10.5902	−	7.69421i	−0.487452	−	0.354155i
$473$	1.88197	−	1.36733i	0.0865329	−	0.0628698i
$474$	−3.14590			−0.144496
$475$	−6.89261	−	21.2133i	−0.316255	−	0.973332i
$476$		0			0
$477$	−12.6180			−0.577740
$478$	24.9894	+	18.1558i	1.14299	+	0.830428i
$479$	0.0729490	−	0.224514i	0.00333313	−	0.0102583i	−0.949376	−	0.314142i	$-0.898283\pi$
$479$	0.0729490	−	0.224514i	0.00333313	−	0.0102583i	0.952709	+	0.303883i	$0.0982833\pi$
$480$	−7.80902	+	5.67358i	−0.356431	+	0.258962i
$481$	−4.30902	+	3.13068i	−0.196474	+	0.142747i
$482$	23.2533	−	16.8945i	1.05916	−	0.769524i
$483$	−1.73607	−	5.34307i	−0.0789938	−	0.243118i
$484$	−13.0451	+	9.47781i	−0.592958	+	0.430810i
$485$	5.24265	−	16.1352i	0.238056	−	0.732662i
$486$	−1.30902	−	0.951057i	−0.0593782	−	0.0431408i
$487$	−23.1353	+	16.8087i	−1.04836	+	0.761677i	−0.971900	−	0.235396i	$-0.924361\pi$
$487$	−23.1353	+	16.8087i	−1.04836	+	0.761677i	−0.0764589	+	0.997073i	$0.524361\pi$
$488$	4.40983	+	13.5721i	0.199624	+	0.614378i
$489$	1.47214	−	4.53077i	0.0665723	−	0.204888i
$490$	16.3713	+	11.8945i	0.739581	+	0.537337i
$491$	−10.7639	−	33.1280i	−0.485769	−	1.49504i	−0.830863	−	0.556476i	$-0.812153\pi$
$491$	−10.7639	−	33.1280i	−0.485769	−	1.49504i	0.345094	−	0.938568i	$-0.387847\pi$
$492$	−0.590170	+	1.81636i	−0.0266069	+	0.0818877i
$493$		0			0
$494$	20.7533	+	15.0781i	0.933735	+	0.678398i
$495$	14.0623	+	10.2169i	0.632054	+	0.459214i
$496$	−36.2705			−1.62859
$497$	−10.3541	+	8.86978i	−0.464445	+	0.397864i
$498$	−19.3262			−0.866029
$499$	1.54508	+	1.12257i	0.0691675	+	0.0502531i	0.621832	−	0.783151i	$-0.286389\pi$
$499$	1.54508	+	1.12257i	0.0691675	+	0.0502531i	−0.552664	+	0.833404i	$0.686389\pi$
$500$	−2.64590	−	1.92236i	−0.118328	−	0.0859704i
$501$	−0.100813	−	0.310271i	−0.00450400	−	0.0138619i
$502$	3.57295	−	10.9964i	0.159469	−	0.490794i
$503$	7.17376	+	22.0786i	0.319862	+	0.984435i	0.973707	+	0.227806i	$0.0731551\pi$
$503$	7.17376	+	22.0786i	0.319862	+	0.984435i	−0.653844	+	0.756629i	$0.726845\pi$
$504$	2.92705	+	2.12663i	0.130381	+	0.0947275i
$505$	−15.4894	+	47.6713i	−0.689267	+	2.12135i
$506$	10.5729	+	32.5402i	0.470025	+	1.44659i
$507$	−6.47214	+	4.70228i	−0.287438	+	0.208836i
$508$	−3.73607	−	2.71441i	−0.165761	−	0.120433i
$509$	−5.98278	+	18.4131i	−0.265182	+	0.816146i	0.726469	+	0.687199i	$0.241160\pi$
$509$	−5.98278	+	18.4131i	−0.265182	+	0.816146i	−0.991651	+	0.128948i	$0.958840\pi$
$510$		0			0
$511$	5.16312	+	15.8904i	0.228403	+	0.702952i
$512$	−4.28115	+	3.11044i	−0.189202	+	0.137463i
$513$	−5.73607	+	4.16750i	−0.253254	+	0.184000i
$514$	7.47214	−	5.42882i	0.329582	−	0.239455i
$515$	7.18441	−	22.1113i	0.316583	−	0.974341i
$516$	−0.190983	−	0.138757i	−0.00840756	−	0.00610845i
$517$	40.8541			1.79676
$518$	−1.92705	−	5.93085i	−0.0846698	−	0.260587i
$519$	1.83688	+	5.65334i	0.0806301	+	0.248154i
$520$	14.2705			0.625803
$521$	−9.51722	+	6.91467i	−0.416957	+	0.302937i	−0.776412	−	0.630225i	$-0.782963\pi$
$521$	−9.51722	+	6.91467i	−0.416957	+	0.302937i	0.359455	+	0.933162i	$0.382963\pi$
$522$	12.2082	+	8.86978i	0.534339	+	0.388220i
$523$	35.3951			1.54772			0.773860	−	0.633356i	$-0.218323\pi$
$523$	35.3951			1.54772			0.773860	+	0.633356i	$0.218323\pi$
$524$	3.56231	−	10.9637i	0.155620	−	0.478949i
$525$	1.57295	−	4.84104i	0.0686491	−	0.211280i
$526$	−9.16312	+	28.2012i	−0.399531	+	1.22963i
$527$		0			0
$528$	−23.9164	−	17.3763i	−1.04083	−	0.756206i
$529$	−10.9443			−0.475838
$530$	−18.0066	−	55.4185i	−0.782156	−	2.40723i
$531$	5.85410			0.254046
$532$	−5.73607	+	4.16750i	−0.248690	+	0.180684i
$533$	5.59017	−	4.06150i	0.242137	−	0.175923i
$534$	−5.09017			−0.220273
$535$	17.8779	+	55.0225i	0.772929	+	2.37883i
$536$	−3.41641			−0.147566
$537$	5.80902	+	4.22050i	0.250678	+	0.182128i
$538$	19.3262			0.833213
$539$	−8.24671	+	25.3808i	−0.355211	+	1.09323i
$540$	0.545085	−	1.67760i	0.0234567	−	0.0721924i
$541$	1.59017	−	4.89404i	0.0683667	−	0.210411i	−0.911036	−	0.412326i	$-0.864716\pi$
$541$	1.59017	−	4.89404i	0.0683667	−	0.210411i	0.979403	+	0.201915i	$0.0647164\pi$
$542$	−28.2705			−1.21432
$543$	11.1631	+	8.11048i	0.479055	+	0.348054i
$544$		0			0
$545$	−6.79837			−0.291210
$546$	1.80902	+	5.56758i	0.0774188	+	0.238271i
$547$	−5.26393	−	16.2007i	−0.225069	−	0.692693i	−0.998285	−	0.0585488i	$-0.981353\pi$
$547$	−5.26393	−	16.2007i	−0.225069	−	0.692693i	0.773215	−	0.634144i	$-0.218647\pi$
$548$	3.96556			0.169400
$549$	−5.16312	−	3.75123i	−0.220357	−	0.160098i
$550$	−9.57953	+	29.4828i	−0.408472	+	1.25715i
$551$	53.4959	−	38.8671i	2.27900	−	1.65579i
$552$	−6.28115	+	4.56352i	−0.267344	+	0.194237i
$553$	−2.54508	+	1.84911i	−0.108228	+	0.0786323i
$554$	−4.83688	−	14.8864i	−0.205499	−	0.632462i
$555$	5.50000	−	3.99598i	0.233462	−	0.169620i
$556$	0.583592	−	1.79611i	0.0247498	−	0.0761721i
$557$	13.9164	+	10.1109i	0.589657	+	0.428411i	0.842193	−	0.539177i	$-0.181264\pi$
$557$	13.9164	+	10.1109i	0.589657	+	0.428411i	−0.252536	+	0.967588i	$0.581264\pi$
$558$	9.78115	−	7.10642i	0.414069	−	0.300839i
$559$	0.263932	+	0.812299i	0.0111631	+	0.0343566i
$560$	−6.92705	+	21.3193i	−0.292721	+	0.900904i
$561$		0			0
$562$	8.42705	+	25.9358i	0.355474	+	1.09404i
$563$	1.95492	−	6.01661i	0.0823898	−	0.253570i	−0.901373	−	0.433044i	$-0.857440\pi$
$563$	1.95492	−	6.01661i	0.0823898	−	0.253570i	0.983763	+	0.179474i	$0.0574395\pi$
$564$	−1.28115	−	3.94298i	−0.0539463	−	0.166030i
$565$	−19.6910	−	14.3063i	−0.828406	−	0.601872i
$566$	25.1074	+	18.2416i	1.05534	+	0.766751i
$567$	−1.61803			−0.0679510
$568$	16.0795	+	9.82084i	0.674682	+	0.412073i
$569$	16.0344			0.672199			0.336099	−	0.941827i	$-0.390892\pi$
$569$	16.0344			0.672199			0.336099	+	0.941827i	$0.390892\pi$
$570$	−26.4894	−	19.2456i	−1.10952	−	0.806111i
$571$	−24.3262	−	17.6740i	−1.01802	−	0.739636i	−0.0521450	−	0.998640i	$-0.516606\pi$
$571$	−24.3262	−	17.6740i	−1.01802	−	0.739636i	−0.965876	+	0.259004i	$0.916606\pi$
$572$	−2.60081	−	8.00448i	−0.108745	−	0.334684i
$573$	3.52786	−	10.8576i	0.147379	−	0.453585i
$574$	2.50000	+	7.69421i	0.104348	+	0.321150i
$575$	8.83688	+	6.42037i	0.368523	+	0.267748i
$576$	1.30902	−	4.02874i	0.0545424	−	0.167864i
$577$	7.22542	+	22.2376i	0.300798	+	0.925762i	0.981212	+	0.192934i	$0.0618002\pi$
$577$	7.22542	+	22.2376i	0.300798	+	0.925762i	−0.680413	+	0.732828i	$0.738200\pi$
$578$	−22.2533	+	16.1680i	−0.925615	+	0.672499i
$579$	7.11803	+	5.17155i	0.295815	+	0.214922i
$580$	−5.08359	+	15.6457i	−0.211085	+	0.649652i
$581$	−15.6353	+	11.3597i	−0.648660	+	0.471279i
$582$	−2.97214	−	9.14729i	−0.123199	−	0.379168i
$583$	62.1697	−	45.1689i	2.57481	−	1.87071i
$584$	18.6803	−	13.5721i	0.772998	−	0.561616i
$585$	−5.16312	+	3.75123i	−0.213469	+	0.155094i
$586$	−7.66312	+	23.5847i	−0.316561	+	0.974273i
$587$	14.1803	+	10.3026i	0.585285	+	0.425235i	0.840626	−	0.541617i	$-0.182188\pi$
$587$	14.1803	+	10.3026i	0.585285	+	0.425235i	−0.255340	+	0.966851i	$0.582188\pi$
$588$	2.70820			0.111684
$589$	−16.3713	−	50.3858i	−0.674569	−	2.07611i
$590$	8.35410	+	25.7113i	0.343933	+	1.05852i
$591$	−2.70820			−0.111401
$592$	−9.35410	+	6.79615i	−0.384451	+	0.279320i
$593$	23.8992	+	17.3638i	0.981422	+	0.713045i	0.958026	−	0.286681i	$-0.0925521\pi$
$593$	23.8992	+	17.3638i	0.981422	+	0.713045i	0.0233960	+	0.999726i	$0.492552\pi$
$594$	9.85410			0.404319
$595$		0			0
$596$	−0.291796	+	0.898056i	−0.0119524	+	0.0367858i
$597$	4.10081	−	12.6210i	0.167835	−	0.516543i
$598$	−12.5623			−0.513711
$599$	−8.19098	−	5.95110i	−0.334674	−	0.243155i	0.407737	−	0.913099i	$-0.366318\pi$
$599$	−8.19098	−	5.95110i	−0.334674	−	0.243155i	−0.742411	+	0.669944i	$0.766318\pi$
$600$	−7.03444			−0.287180
$601$	1.20163	+	3.69822i	0.0490154	+	0.150854i	0.972568	−	0.232617i	$-0.0747288\pi$
$601$	1.20163	+	3.69822i	0.0490154	+	0.150854i	−0.923553	+	0.383470i	$0.874729\pi$
$602$	−1.00000			−0.0407570
$603$	1.23607	−	0.898056i	0.0503366	−	0.0365717i
$604$	3.09017	−	2.24514i	0.125737	−	0.0913534i
$605$	−74.4640			−3.02739
$606$	8.78115	+	27.0256i	0.356710	+	1.09784i
$607$	21.0902			0.856024			0.428012	−	0.903773i	$-0.359214\pi$
$607$	21.0902			0.856024			0.428012	+	0.903773i	$0.359214\pi$
$608$	19.3992	+	14.0943i	0.786741	+	0.571601i
$609$	15.0902			0.611485
$610$	9.10739	−	28.0297i	0.368747	−	1.13489i
$611$	−4.63525	+	14.2658i	−0.187522	+	0.577134i
$612$		0			0
$613$	−13.2918			−0.536851			−0.268425	−	0.963301i	$-0.586503\pi$
$613$	−13.2918			−0.536851			−0.268425	+	0.963301i	$0.586503\pi$
$614$	30.2705	+	21.9928i	1.22162	+	0.887558i
$615$	−7.13525	+	5.18407i	−0.287721	+	0.209042i
$616$	−22.0344			−0.887793
$617$	−0.291796	−	0.898056i	−0.0117473	−	0.0361544i	0.945011	−	0.327038i	$-0.106051\pi$
$617$	−0.291796	−	0.898056i	−0.0117473	−	0.0361544i	−0.956758	+	0.290884i	$0.906051\pi$
$618$	−4.07295	−	12.5352i	−0.163838	−	0.504242i
$619$	−28.3607			−1.13991			−0.569956	−	0.821675i	$-0.693040\pi$
$619$	−28.3607			−1.13991			−0.569956	+	0.821675i	$0.693040\pi$
$620$	10.6631	+	7.74721i	0.428241	+	0.311135i
$621$	1.07295	−	3.30220i	0.0430560	−	0.132513i
$622$	−45.9336	+	33.3727i	−1.84177	+	1.33812i
$623$	−4.11803	+	2.99193i	−0.164986	+	0.119869i
$624$	8.78115	−	6.37988i	0.351527	−	0.255400i
$625$	−9.52786	−	29.3238i	−0.381115	−	1.17295i
$626$	17.3713	−	12.6210i	0.694298	−	0.504437i
$627$	13.3435	−	41.0669i	0.532886	−	1.64006i
$628$	8.63525	+	6.27388i	0.344584	+	0.250355i
$629$		0			0
$630$	−2.30902	−	7.10642i	−0.0919934	−	0.283127i
$631$	−14.7254	+	45.3202i	−0.586210	+	1.80417i	0.00814648	+	0.999967i	$0.497407\pi$
$631$	−14.7254	+	45.3202i	−0.586210	+	1.80417i	−0.594356	+	0.804202i	$0.702593\pi$
$632$	3.51722	+	2.55541i	0.139908	+	0.101649i
$633$	−5.94427	−	18.2946i	−0.236264	−	0.727145i
$634$	−9.07295	+	27.9237i	−0.360333	+	1.10899i
$635$	−6.59017	−	20.2825i	−0.261523	−	0.804885i
$636$	−6.30902	−	4.58377i	−0.250169	−	0.181758i
$637$	−7.92705	−	5.75934i	−0.314081	−	0.228193i
$638$	−91.9017			−3.63842
$639$	−8.39919	+	0.673542i	−0.332267	+	0.0266449i
$640$	38.8673			1.53636
$641$	−16.5172	−	12.0005i	−0.652391	−	0.473990i	0.211694	−	0.977336i	$-0.432102\pi$
$641$	−16.5172	−	12.0005i	−0.652391	−	0.473990i	−0.864085	+	0.503346i	$0.832102\pi$
$642$	26.5344	+	19.2784i	1.04723	+	0.760858i
$643$	−7.01722	−	21.5968i	−0.276732	−	0.851694i	−0.988756	−	0.149539i	$-0.952221\pi$
$643$	−7.01722	−	21.5968i	−0.276732	−	0.851694i	0.712024	−	0.702155i	$-0.247779\pi$
$644$	1.07295	−	3.30220i	0.0422801	−	0.130125i
$645$	−0.336881	−	1.03681i	−0.0132647	−	0.0408245i
$646$		0			0
$647$	−6.85410	+	21.0948i	−0.269463	+	0.829320i	0.721169	+	0.692759i	$0.243605\pi$
$647$	−6.85410	+	21.0948i	−0.269463	+	0.829320i	−0.990632	+	0.136561i	$0.956395\pi$
$648$	0.690983	+	2.12663i	0.0271444	+	0.0835418i
$649$	−28.8435	+	20.9560i	−1.13220	+	0.822595i
$650$	−9.20820	−	6.69015i	−0.361175	−	0.262409i
$651$	3.73607	−	11.4984i	0.146428	−	0.450659i
$652$	2.38197	−	1.73060i	0.0932850	−	0.0677755i
$653$	−12.5344	−	38.5770i	−0.490511	−	1.50964i	−0.823838	−	0.566825i	$-0.808171\pi$
$653$	−12.5344	−	38.5770i	−0.490511	−	1.50964i	0.333327	−	0.942811i	$-0.391829\pi$
$654$	−3.11803	+	2.26538i	−0.121925	+	0.0885835i
$655$	43.0689	−	31.2914i	1.68284	−	1.22266i
$656$	12.1353	−	8.81678i	0.473802	−	0.344237i
$657$	−3.19098	+	9.82084i	−0.124492	+	0.383147i
$658$	−14.2082	−	10.3229i	−0.553893	−	0.402427i
$659$	−16.6180			−0.647347			−0.323673	−	0.946169i	$-0.604918\pi$
$659$	−16.6180			−0.647347			−0.323673	+	0.946169i	$0.604918\pi$
$660$	3.31966	+	10.2169i	0.129218	+	0.397691i
$661$	7.09017	+	21.8213i	0.275776	+	0.848750i	0.989013	+	0.147828i	$0.0472281\pi$
$661$	7.09017	+	21.8213i	0.275776	+	0.848750i	−0.713237	+	0.700922i	$0.752772\pi$
$662$	56.1591			2.18268
$663$		0			0
$664$	21.6074	+	15.6987i	0.838529	+	0.609227i
$665$	−32.7426			−1.26971
$666$	1.19098	−	3.66547i	0.0461497	−	0.142034i
$667$	−10.0066	+	30.7971i	−0.387456	+	1.19247i
$668$	0.0623059	−	0.191758i	0.00241069	−	0.00741933i
$669$	−5.70820			−0.220692
$670$	5.70820	+	4.14725i	0.220527	+	0.160222i
$671$	38.8673			1.50045
$672$	1.69098	+	5.20431i	0.0652311	+	0.200761i
$673$	−16.3607			−0.630658			−0.315329	−	0.948982i	$-0.602115\pi$
$673$	−16.3607			−0.630658			−0.315329	+	0.948982i	$0.602115\pi$
$674$	−26.6803	+	19.3844i	−1.02769	+	0.746659i
$675$	2.54508	−	1.84911i	0.0979604	−	0.0711724i
$676$	−4.94427			−0.190164
$677$	−8.20163	−	25.2420i	−0.315214	−	0.970129i	−0.975666	−	0.219261i	$-0.929635\pi$
$677$	−8.20163	−	25.2420i	−0.315214	−	0.970129i	0.660452	−	0.750868i	$-0.270365\pi$
$678$	−13.7984			−0.529923
$679$	−7.78115	−	5.65334i	−0.298613	−	0.216955i
$680$		0			0
$681$	0.954915	−	2.93893i	0.0365924	−	0.112620i
$682$	−22.7533	+	70.0274i	−0.871268	+	2.68149i
$683$	−8.24671	+	25.3808i	−0.315552	+	0.971168i	0.659975	+	0.751287i	$0.270567\pi$
$683$	−8.24671	+	25.3808i	−0.315552	+	0.971168i	−0.975527	+	0.219881i	$0.929433\pi$
$684$	−4.38197			−0.167549
$685$	14.8156	+	10.7642i	0.566075	+	0.411277i
$686$	24.1074	−	17.5150i	0.920424	−	0.668728i
$687$	−7.56231			−0.288520
$688$	0.572949	+	1.76336i	0.0218435	+	0.0672273i
$689$	8.71885	+	26.8339i	0.332162	+	1.02229i
$690$	16.0344			0.610421
$691$	38.3885	+	27.8909i	1.46037	+	1.06102i	0.983267	+	0.182173i	$0.0583129\pi$
$691$	38.3885	+	27.8909i	1.46037	+	1.06102i	0.477102	+	0.878848i	$0.341687\pi$
$692$	−1.13525	+	3.49396i	−0.0431559	+	0.132820i
$693$	7.97214	−	5.79210i	0.302836	−	0.220024i
$694$	17.9443	−	13.0373i	0.681155	−	0.494888i
$695$	7.05573	−	5.12629i	0.267639	−	0.194451i
$696$	−6.44427	−	19.8334i	−0.244269	−	0.751784i
$697$		0			0
$698$	−8.29837	+	25.5398i	−0.314098	+	0.966695i
$699$	4.11803	+	2.99193i	0.155758	+	0.113165i
$700$	2.54508	−	1.84911i	0.0961952	−	0.0698899i
$701$	−7.86068	−	24.1927i	−0.296894	−	0.913745i	−0.982579	−	0.185847i	$-0.940497\pi$
$701$	−7.86068	−	24.1927i	−0.296894	−	0.913745i	0.685685	−	0.727898i	$-0.259503\pi$
$702$	−1.11803	+	3.44095i	−0.0421975	+	0.129870i
$703$	−13.6631	−	9.92684i	−0.515314	−	0.374398i
$704$	7.97214	+	24.5357i	0.300461	+	0.924724i
$705$	5.91641	−	18.2088i	0.222825	−	0.685784i
$706$	−14.9721	−	46.0795i	−0.563484	−	1.73422i
$707$	22.9894	+	16.7027i	0.864604	+	0.628171i
$708$	2.92705	+	2.12663i	0.110005	+	0.0799235i
$709$	−16.7082			−0.627490			−0.313745	−	0.949507i	$-0.601584\pi$
$709$	−16.7082			−0.627490			−0.313745	+	0.949507i	$0.601584\pi$
$710$	−14.9443	−	35.9281i	−0.560849	−	1.34836i
$711$	−1.94427			−0.0729159
$712$	5.69098	+	4.13474i	0.213279	+	0.154956i
$713$	20.9894	+	15.2497i	0.786058	+	0.571104i
$714$		0			0
$715$	12.0106	−	36.9650i	0.449173	−	1.38241i
$716$	1.37132	+	4.22050i	0.0512487	+	0.157727i
$717$	15.4443	+	11.2209i	0.576777	+	0.419053i
$718$	16.3541	−	50.3328i	0.610330	−	1.87840i
$719$	−1.70820	−	5.25731i	−0.0637053	−	0.196065i	0.914138	−	0.405403i	$-0.132869\pi$
$719$	−1.70820	−	5.25731i	−0.0637053	−	0.196065i	−0.977843	+	0.209339i	$0.932869\pi$
$720$	−11.2082	+	8.14324i	−0.417705	+	0.303481i
$721$	−10.6631	−	7.74721i	−0.397115	−	0.288521i
$722$	−15.6353	+	48.1204i	−0.581884	+	1.79085i
$723$	14.3713	−	10.4414i	0.534475	−	0.388319i
$724$	2.63525	+	8.11048i	0.0979385	+	0.301424i
$725$	−23.7361	+	17.2453i	−0.881535	+	0.640473i
$726$	−34.1525	+	24.8132i	−1.26752	+	0.920905i
$727$	10.2812	−	7.46969i	0.381307	−	0.277036i	−0.380577	−	0.924749i	$-0.624275\pi$
$727$	10.2812	−	7.46969i	0.381307	−	0.277036i	0.761884	+	0.647714i	$0.224275\pi$
$728$	2.50000	−	7.69421i	0.0926562	−	0.285166i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	−47.6869			−1.76497
$731$		0			0
$732$	−1.21885	−	3.75123i	−0.0450499	−	0.138649i
$733$	−32.8885			−1.21477			−0.607383	−	0.794409i	$-0.707781\pi$
$733$	−32.8885			−1.21477			−0.607383	+	0.794409i	$0.707781\pi$
$734$	9.78115	−	7.10642i	0.361029	−	0.262303i
$735$	10.1180	+	7.35118i	0.373209	+	0.271152i
$736$	−11.7426			−0.432840
$737$	−2.87539	+	8.84953i	−0.105916	+	0.325977i
$738$	−1.54508	+	4.75528i	−0.0568754	+	0.175044i
$739$	14.6525	−	45.0957i	0.539000	−	1.65887i	−0.195844	−	0.980635i	$-0.562745\pi$
$739$	14.6525	−	45.0957i	0.539000	−	1.65887i	0.734844	−	0.678236i	$-0.237255\pi$
$740$	4.20163			0.154455
$741$	12.8262	+	9.31881i	0.471184	+	0.342335i
$742$	−33.0344			−1.21273
$743$	−10.2188	−	31.4504i	−0.374893	−	1.15380i	−0.943551	−	0.331228i	$-0.892537\pi$
$743$	−10.2188	−	31.4504i	−0.374893	−	1.15380i	0.568658	−	0.822574i	$-0.307463\pi$
$744$	−16.7082			−0.612552
$745$	−3.52786	+	2.56314i	−0.129251	+	0.0939063i
$746$	3.38197	−	2.45714i	0.123823	−	0.0899624i
$747$	−11.9443			−0.437018
$748$		0			0
$749$	32.7984			1.19843
$750$	−6.92705	−	5.03280i	−0.252940	−	0.183772i
$751$	39.5967			1.44491			0.722453	−	0.691420i	$-0.243015\pi$
$751$	39.5967			1.44491			0.722453	+	0.691420i	$0.243015\pi$
$752$	−10.0623	+	30.9686i	−0.366935	+	1.12931i
$753$	2.20820	−	6.79615i	0.0804714	−	0.247666i
$754$	10.4271	−	32.0912i	0.379731	−	1.16869i
$755$	17.6393			0.641961
$756$	−0.809017	−	0.587785i	−0.0294237	−	0.0213775i
$757$	37.3607	−	27.1441i	1.35790	−	0.986570i	0.359321	−	0.933214i	$-0.383008\pi$
$757$	37.3607	−	27.1441i	1.35790	−	0.986570i	0.998576	−	0.0533561i	$-0.0169918\pi$
$758$	−4.18034			−0.151837
$759$	6.53444	+	20.1109i	0.237185	+	0.729981i
$760$	13.9828	+	43.0346i	0.507209	+	1.56103i
$761$	19.0902			0.692018			0.346009	−	0.938231i	$-0.387537\pi$
$761$	19.0902			0.692018			0.346009	+	0.938231i	$0.387537\pi$
$762$	−9.78115	−	7.10642i	−0.354334	−	0.257439i
$763$	−1.19098	+	3.66547i	−0.0431165	+	0.132699i
$764$	5.70820	−	4.14725i	0.206516	−	0.150042i
$765$		0			0
$766$	6.54508	−	4.75528i	0.236484	−	0.171815i
$767$	−4.04508	−	12.4495i	−0.146060	−	0.449525i
$768$	10.9721	−	7.97172i	0.395923	−	0.287655i
$769$	−10.9721	+	33.7688i	−0.395665	+	1.21773i	0.532777	+	0.846256i	$0.321149\pi$
$769$	−10.9721	+	33.7688i	−0.395665	+	1.21773i	−0.928442	+	0.371477i	$0.878851\pi$
$770$	36.8156	+	26.7481i	1.32674	+	0.963934i
$771$	4.61803	−	3.35520i	0.166314	−	0.120835i
$772$	1.68034	+	5.17155i	0.0604768	+	0.186128i
$773$	3.52786	−	10.8576i	0.126888	−	0.390522i	−0.867352	−	0.497695i	$-0.834180\pi$
$773$	3.52786	−	10.8576i	0.126888	−	0.390522i	0.994240	+	0.107173i	$0.0341798\pi$
$774$	−0.500000	−	0.363271i	−0.0179721	−	0.0130575i
$775$	7.26393	+	22.3561i	0.260928	+	0.803054i
$776$	−4.10739	+	12.6412i	−0.147447	+	0.453794i
$777$	−1.19098	−	3.66547i	−0.0427263	−	0.131498i
$778$	6.28115	+	4.56352i	0.225190	+	0.163610i
$779$	17.7254	+	12.8783i	0.635079	+	0.461412i
$780$	−3.94427			−0.141228
$781$	38.9721	−	33.3852i	1.39453	−	1.19462i
$782$		0			0
$783$	7.54508	+	5.48183i	0.269639	+	0.195904i
$784$	−17.2082	−	12.5025i	−0.614579	−	0.446518i
$785$	15.2320	+	46.8793i	0.543653	+	1.67319i
$786$	9.32624	−	28.7032i	0.332656	−	1.02381i
$787$	13.1803	+	40.5649i	0.469828	+	1.44598i	0.852807	+	0.522226i	$0.174898\pi$
$787$	13.1803	+	40.5649i	0.469828	+	1.44598i	−0.382979	+	0.923757i	$0.625102\pi$
$788$	−1.35410	−	0.983813i	−0.0482379	−	0.0350469i
$789$	−5.66312	+	17.4293i	−0.201612	+	0.620499i
$790$	−2.77458	−	8.53926i	−0.0987150	−	0.303813i
$791$	−11.1631	+	8.11048i	−0.396915	+	0.288375i
$792$	−11.0172	−	8.00448i	−0.391480	−	0.284427i
$793$	−4.40983	+	13.5721i	−0.156598	+	0.481958i
$794$	31.2705	−	22.7194i	1.10975	−	0.806280i
$795$	−11.1287	−	34.2505i	−0.394694	−	1.21474i
$796$	6.63525	−	4.82079i	0.235180	−	0.170869i
$797$	38.0344	−	27.6336i	1.34725	−	0.978834i	0.348106	−	0.937455i	$-0.386825\pi$
$797$	38.0344	−	27.6336i	1.34725	−	0.978834i	0.999144	−	0.0413784i	$-0.0131749\pi$
$798$	−15.0172	+	10.9106i	−0.531604	+	0.386233i
$799$		0			0
$800$	−8.60739	−	6.25364i	−0.304317	−	0.221099i
$801$	−3.14590			−0.111155
$802$	−7.94427	−	24.4500i	−0.280522	−	0.863358i
$803$	−19.4336	−	59.8106i	−0.685798	−	2.11067i
$804$	0.944272			0.0333019
$805$	12.9721	−	9.42481i	0.457208	−	0.332181i
$806$	−21.8713	−	15.8904i	−0.770384	−	0.559717i
$807$	11.9443			0.420458
$808$	12.1353	−	37.3485i	0.426917	−	1.31391i
$809$	−1.28115	+	3.94298i	−0.0450429	+	0.138628i	−0.971049	−	0.238881i	$-0.923219\pi$
$809$	−1.28115	+	3.94298i	−0.0450429	+	0.138628i	0.926006	+	0.377509i	$0.123219\pi$
$810$	1.42705	−	4.39201i	0.0501415	−	0.154320i
$811$	−14.8328			−0.520851			−0.260425	−	0.965494i	$-0.583863\pi$
$811$	−14.8328			−0.520851			−0.260425	+	0.965494i	$0.583863\pi$
$812$	7.54508	+	5.48183i	0.264781	+	0.192374i
$813$	−17.4721			−0.612775
$814$	7.25329	+	22.3233i	0.254228	+	0.782432i
$815$	13.5967			0.476273
$816$		0			0
$817$	−2.19098	+	1.59184i	−0.0766528	+	0.0556915i
$818$	11.4164			0.399165
$819$	1.11803	+	3.44095i	0.0390673	+	0.120237i
$820$	−5.45085			−0.190352
$821$	−13.1631	−	9.56357i	−0.459396	−	0.333771i	0.333898	−	0.942609i	$-0.391636\pi$
$821$	−13.1631	−	9.56357i	−0.459396	−	0.333771i	−0.793294	+	0.608838i	$0.791636\pi$
$822$	10.3820			0.362113
$823$	0.0623059	−	0.191758i	0.00217185	−	0.00668426i	−0.949965	−	0.312357i	$-0.898881\pi$
$823$	0.0623059	−	0.191758i	0.00217185	−	0.00668426i	0.952137	+	0.305673i	$0.0988814\pi$
$824$	−5.62868	+	17.3233i	−0.196084	+	0.603485i
$825$	−5.92047	+	18.2213i	−0.206124	+	0.634386i
$826$	15.3262			0.533268
$827$	29.0066	+	21.0745i	1.00866	+	0.732833i	0.963927	−	0.266166i	$-0.0857571\pi$
$827$	29.0066	+	21.0745i	1.00866	+	0.732833i	0.0447305	+	0.998999i	$0.485757\pi$
$828$	1.73607	−	1.26133i	0.0603325	−	0.0438342i
$829$	0.124612			0.00432795			0.00216397	−	0.999998i	$-0.499311\pi$
$829$	0.124612			0.00432795			0.00216397	+	0.999998i	$0.499311\pi$
$830$	−17.0451	−	52.4594i	−0.591644	−	1.82089i
$831$	−2.98936	−	9.20029i	−0.103700	−	0.319155i
$832$	−9.47214			−0.328387
$833$		0			0
$834$	1.52786	−	4.70228i	0.0529056	−	0.162827i
$835$	0.753289	−	0.547296i	0.0260686	−	0.0189400i
$836$	21.5902	−	15.6862i	0.746712	−	0.542518i
$837$	6.04508	−	4.39201i	0.208949	−	0.151810i
$838$	4.82624	+	14.8536i	0.166720	+	0.513110i
$839$	−38.4615	+	27.9439i	−1.32784	+	0.964731i	−0.328040	+	0.944664i	$0.606388\pi$
$839$	−38.4615	+	27.9439i	−1.32784	+	0.964731i	−0.999799	+	0.0200669i	$0.993612\pi$
$840$	−3.19098	+	9.82084i	−0.110099	+	0.338851i
$841$	−46.9058	−	34.0790i	−1.61744	−	1.17514i
$842$	−49.8607	+	36.2259i	−1.71831	+	1.24843i
$843$	5.20820	+	16.0292i	0.179380	+	0.552075i
$844$	3.67376	−	11.3067i	0.126456	−	0.389192i
$845$	−18.4721	−	13.4208i	−0.635461	−	0.461689i
$846$	−3.35410	−	10.3229i	−0.115316	−	0.354907i
$847$	−13.0451	+	40.1486i	−0.448234	+	1.37952i
$848$	18.9271	+	58.2515i	0.649958	+	2.00036i
$849$	15.5172	+	11.2739i	0.532550	+	0.386920i
$850$		0			0
$851$	8.27051			0.283509
$852$	−4.44427	−	2.71441i	−0.152258	−	0.0929942i
$853$	−5.32624			−0.182367			−0.0911835	−	0.995834i	$-0.529065\pi$
$853$	−5.32624			−0.182367			−0.0911835	+	0.995834i	$0.529065\pi$
$854$	−13.5172	−	9.82084i	−0.462550	−	0.336062i
$855$	−16.3713	−	11.8945i	−0.559887	−	0.406782i
$856$	−14.0066	−	43.1078i	−0.478735	−	1.47339i
$857$	12.9894	−	39.9771i	0.443708	−	1.36559i	−0.440187	−	0.897906i	$-0.645088\pi$
$857$	12.9894	−	39.9771i	0.443708	−	1.36559i	0.883894	−	0.467686i	$-0.154912\pi$
$858$	−6.80902	−	20.9560i	−0.232456	−	0.715426i
$859$	4.70820	+	3.42071i	0.160642	+	0.116713i	0.665202	−	0.746663i	$-0.268345\pi$
$859$	4.70820	+	3.42071i	0.160642	+	0.116713i	−0.504560	+	0.863376i	$0.668345\pi$
$860$	0.208204	−	0.640786i	0.00709970	−	0.0218506i
$861$	1.54508	+	4.75528i	0.0526564	+	0.162060i
$862$	−28.9615	+	21.0418i	−0.986432	+	0.716685i
$863$	34.8156	+	25.2950i	1.18514	+	0.861052i	0.992742	−	0.120265i	$-0.0383746\pi$
$863$	34.8156	+	25.2950i	1.18514	+	0.861052i	0.192395	+	0.981318i	$0.438375\pi$
$864$	−1.04508	+	3.21644i	−0.0355545	+	0.109426i
$865$	−13.7254	+	9.97210i	−0.466678	+	0.339062i
$866$	−13.1353	−	40.4262i	−0.446354	−	1.37374i
$867$	−13.7533	+	9.99235i	−0.467086	+	0.339358i
$868$	6.04508	−	4.39201i	0.205184	−	0.149075i
$869$	9.57953	−	6.95993i	0.324963	−	0.236100i
$870$	−13.3090	+	40.9609i	−0.451218	+	1.38871i
$871$	−2.76393	−	2.00811i	−0.0936523	−	0.0680424i
$872$	5.32624			0.180369
$873$	−1.83688	−	5.65334i	−0.0621690	−	0.191337i
$874$	−12.3090	−	37.8833i	−0.416359	−	1.28142i
$875$	−8.56231			−0.289459
$876$	−5.16312	+	3.75123i	−0.174446	+	0.126742i
$877$	−9.63525	−	7.00042i	−0.325359	−	0.236387i	0.413100	−	0.910686i	$-0.364446\pi$
$877$	−9.63525	−	7.00042i	−0.325359	−	0.236387i	−0.738459	+	0.674298i	$0.764446\pi$
$878$	−51.3050			−1.73146
$879$	−4.73607	+	14.5761i	−0.159744	+	0.491640i
$880$	26.0729	−	80.2443i	0.878919	−	2.70503i
$881$	15.2599	−	46.9650i	0.514118	−	1.58229i	−0.270763	−	0.962646i	$-0.587276\pi$
$881$	15.2599	−	46.9650i	0.514118	−	1.58229i	0.784881	−	0.619646i	$-0.212724\pi$
$882$	7.09017			0.238738
$883$	−12.5451	−	9.11454i	−0.422176	−	0.306729i	0.356337	−	0.934358i	$-0.384026\pi$
$883$	−12.5451	−	9.11454i	−0.422176	−	0.306729i	−0.778513	+	0.627629i	$0.784026\pi$
$884$		0			0
$885$	5.16312	+	15.8904i	0.173556	+	0.534152i
$886$	−38.4164			−1.29062
$887$	−0.236068	+	0.171513i	−0.00792639	+	0.00575886i	−0.591741	−	0.806128i	$-0.701559\pi$
$887$	−0.236068	+	0.171513i	−0.00792639	+	0.00575886i	0.583815	+	0.811887i	$0.301559\pi$
$888$	−4.30902	+	3.13068i	−0.144601	+	0.105059i
$889$	−12.0902			−0.405491
$890$	−4.48936	−	13.8168i	−0.150484	−	0.463141i
$891$	6.09017			0.204028
$892$	−2.85410	−	2.07363i	−0.0955624	−	0.0694301i
$893$	−47.5623			−1.59161
$894$	−0.763932	+	2.35114i	−0.0255497	+	0.0786339i
$895$	−6.33282	+	19.4904i	−0.211683	+	0.651492i
$896$	6.80902	−	20.9560i	0.227473	−	0.700091i
$897$	−7.76393			−0.259230
$898$	25.2984	+	18.3803i	0.844218	+	0.613360i
$899$	−56.3779	+	40.9609i	−1.88031	+	1.36612i
$900$	1.94427			0.0648091
$901$		0			0
$902$	−9.40983	−	28.9605i	−0.313313	−	0.964278i
$903$	−0.618034			−0.0205669
$904$	15.4271	+	11.2084i	0.513096	+	0.372786i
$905$	−12.1697	+	37.4545i	−0.404534	+	1.24503i
$906$	8.09017	−	5.87785i	0.268778	−	0.195279i
$907$	−27.4164	+	19.9192i	−0.910347	+	0.661406i	−0.941103	−	0.338121i	$-0.890209\pi$
$907$	−27.4164	+	19.9192i	−0.910347	+	0.661406i	0.0307557	+	0.999527i	$0.490209\pi$
$908$	1.54508	−	1.12257i	0.0512754	−	0.0372538i
$909$	5.42705	+	16.7027i	0.180004	+	0.553995i
$910$	−13.5172	+	9.82084i	−0.448092	+	0.325558i
$911$	−9.34346	+	28.7562i	−0.309563	+	0.952736i	0.668372	+	0.743827i	$0.266991\pi$
$911$	−9.34346	+	28.7562i	−0.309563	+	0.952736i	−0.977935	+	0.208909i	$0.933009\pi$
$912$	27.8435	+	20.2295i	0.921989	+	0.669864i
$913$	58.8500	−	42.7571i	1.94765	−	1.41505i
$914$	−4.97214	−	15.3027i	−0.164464	−	0.506167i
$915$	5.62868	−	17.3233i	0.186078	−	0.572690i
$916$	−3.78115	−	2.74717i	−0.124933	−	0.0907690i
$917$	−9.32624	−	28.7032i	−0.307980	−	0.947863i
$918$		0			0
$919$	−9.69098	−	29.8258i	−0.319676	−	0.983862i	−0.973787	−	0.227463i	$-0.926957\pi$
$919$	−9.69098	−	29.8258i	−0.319676	−	0.983862i	0.654111	−	0.756399i	$-0.273043\pi$
$920$	−17.9271	−	13.0248i	−0.591037	−	0.429414i
$921$	18.7082	+	13.5923i	0.616456	+	0.447882i
$922$	25.5066			0.840014
$923$	7.23607	+	17.3965i	0.238178	+	0.572614i
$924$	6.09017			0.200352
$925$	6.06231	+	4.40452i	0.199327	+	0.144820i
$926$	−8.09017	−	5.87785i	−0.265859	−	0.193158i
$927$	−2.51722	−	7.74721i	−0.0826764	−	0.254452i
$928$	9.74671	−	29.9973i	0.319951	−	0.984709i
$929$	−17.1697	−	52.8429i	−0.563319	−	1.73372i	−0.672892	−	0.739740i	$-0.734948\pi$
$929$	−17.1697	−	52.8429i	−0.563319	−	1.73372i	0.109573	−	0.993979i	$-0.465052\pi$
$930$	27.9164	+	20.2825i	0.915415	+	0.665088i
$931$	9.60081	−	29.5483i	0.314654	−	0.968405i
$932$	0.972136	+	2.99193i	0.0318434	+	0.0980038i
$933$	−28.3885	+	20.6255i	−0.929399	+	0.675248i
$934$	48.8607	+	35.4994i	1.59877	+	1.16157i
$935$		0			0
$936$	4.04508	−	2.93893i	0.132218	−	0.0960618i
$937$	15.4377	+	47.5123i	0.504327	+	1.55216i	0.801898	+	0.597461i	$0.203824\pi$
$937$	15.4377	+	47.5123i	0.504327	+	1.55216i	−0.297571	+	0.954700i	$0.596176\pi$
$938$	3.23607	−	2.35114i	0.105661	−	0.0767675i
$939$	10.7361	−	7.80021i	0.350358	−	0.254550i
$940$	9.57295	−	6.95515i	0.312235	−	0.226852i
$941$	−3.11803	+	9.59632i	−0.101645	+	0.312831i	−0.988928	−	0.148394i	$-0.952590\pi$
$941$	−3.11803	+	9.59632i	−0.101645	+	0.312831i	0.887283	+	0.461225i	$0.152590\pi$
$942$	22.6074	+	16.4252i	0.736589	+	0.535163i
$943$	−10.7295			−0.349400
$944$	−8.78115	−	27.0256i	−0.285802	−	0.879609i
$945$	−1.42705	−	4.39201i	−0.0464220	−	0.142872i
$946$	3.76393			0.122376
$947$	10.7984	−	7.84548i	0.350900	−	0.254944i	−0.398346	−	0.917235i	$-0.630416\pi$
$947$	10.7984	−	7.84548i	0.350900	−	0.254944i	0.749246	+	0.662291i	$0.230416\pi$
$948$	−0.972136	−	0.706298i	−0.0315735	−	0.0229395i
$949$	23.0902			0.749539
$950$	11.1525	−	34.3238i	0.361834	−	1.11361i
$951$	−5.60739	+	17.2578i	−0.181832	+	0.559622i
$952$		0			0
$953$	28.7984			0.932871			0.466435	−	0.884555i	$-0.345538\pi$
$953$	28.7984			0.932871			0.466435	+	0.884555i	$0.345538\pi$
$954$	−16.5172	−	12.0005i	−0.534765	−	0.388529i
$955$	32.5836			1.05438
$956$	3.64590	+	11.2209i	0.117917	+	0.362911i
$957$	−56.7984			−1.83603
$958$	0.309017	−	0.224514i	0.00998389	−	0.00725372i
$959$	8.39919	−	6.10237i	0.271224	−	0.197056i
$960$	12.0902			0.390209
$961$	7.67376	+	23.6174i	0.247541	+	0.761852i
$962$	−8.61803			−0.277857
$963$	16.3992	+	11.9147i	0.528456	+	0.383946i
$964$	10.9787			0.353601
$965$	−7.75987	+	23.8824i	−0.249799	+	0.768802i
$966$	2.80902	−	8.64527i	0.0903786	−	0.278157i
$967$	4.64590	−	14.2986i	0.149402	−	0.459812i	−0.848149	−	0.529758i	$-0.822283\pi$
$967$	4.64590	−	14.2986i	0.149402	−	0.459812i	0.997551	+	0.0699460i	$0.0222827\pi$
$968$	58.3394			1.87510
$969$		0			0
$970$	22.2082	−	16.1352i	0.713062	−	0.518070i
$971$	−0.0557281			−0.00178840			−0.000894200	−	1.00000i	$-0.500285\pi$
$971$	−0.0557281			−0.00178840			−0.000894200		1.00000i	$0.500285\pi$
$972$	−0.190983	−	0.587785i	−0.00612578	−	0.0188532i
$973$	−1.52786	−	4.70228i	−0.0489811	−	0.150748i
$974$	−46.2705			−1.48260
$975$	−5.69098	−	4.13474i	−0.182257	−	0.132418i
$976$	−9.57295	+	29.4625i	−0.306423	+	0.943072i
$977$	34.5795	−	25.1235i	1.10630	−	0.803772i	0.124221	−	0.992255i	$-0.460357\pi$
$977$	34.5795	−	25.1235i	1.10630	−	0.803772i	0.982076	+	0.188483i	$0.0603570\pi$
$978$	6.23607	−	4.53077i	0.199407	−	0.144878i
$979$	15.5000	−	11.2614i	0.495382	−	0.359916i
$980$	2.38854	+	7.35118i	0.0762992	+	0.234825i
$981$	−1.92705	+	1.40008i	−0.0615260	+	0.0447013i
$982$	17.4164	−	53.6022i	0.555780	−	1.71051i
$983$	20.7533	+	15.0781i	0.661927	+	0.480918i	0.867313	−	0.497763i	$-0.165845\pi$
$983$	20.7533	+	15.0781i	0.661927	+	0.480918i	−0.205386	+	0.978681i	$0.565845\pi$
$984$	5.59017	−	4.06150i	0.178208	−	0.129476i
$985$	−2.38854	−	7.35118i	−0.0761053	−	0.234228i
$986$		0			0
$987$	−8.78115	−	6.37988i	−0.279507	−	0.203074i
$988$	3.02786	+	9.31881i	0.0963292	+	0.296471i
$989$	0.409830	−	1.26133i	0.0130318	−	0.0401079i
$990$	8.69098	+	26.7481i	0.276218	+	0.850110i
$991$	−17.9894	−	13.0700i	−0.571451	−	0.415183i	0.264181	−	0.964473i	$-0.414898\pi$
$991$	−17.9894	−	13.0700i	−0.571451	−	0.415183i	−0.835632	+	0.549290i	$0.814898\pi$
$992$	−20.4443	−	14.8536i	−0.649106	−	0.471603i
$993$	34.7082			1.10143
$994$	−21.9894	+	1.76336i	−0.697460	+	0.0559302i
$995$	37.8754			1.20073
$996$	−5.97214	−	4.33901i	−0.189234	−	0.137487i
$997$	−5.35410	−	3.88998i	−0.169566	−	0.123197i	0.499766	−	0.866161i	$-0.333419\pi$
$997$	−5.35410	−	3.88998i	−0.169566	−	0.123197i	−0.669332	+	0.742964i	$0.733419\pi$
$998$	0.954915	+	2.93893i	0.0302273	+	0.0930301i
$999$	0.736068	−	2.26538i	0.0232882	−	0.0716736i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	213.2.e.a.196.1	yes	4
3.2	odd	2		639.2.f.a.622.1		4
71.25	even	5	inner	213.2.e.a.25.1	✓	4
213.167	odd	10		639.2.f.a.451.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
213.2.e.a.25.1	✓	4	71.25	even	5	inner
213.2.e.a.196.1	yes	4	1.1	even	1	trivial
639.2.f.a.451.1		4	213.167	odd	10
639.2.f.a.622.1		4	3.2	odd	2

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:	\( N \)	\(=\)	\( 213 = 3 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	213.e (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.30902 + 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.190983 + 0.587785i) q^{4} +(-0.881966 + 2.71441i) q^{5} +(0.500000 + 1.53884i) q^{6} +(1.30902 + 0.951057i) q^{7} +(0.690983 - 2.12663i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-3.73607 + 2.71441i) q^{10} +(-4.92705 - 3.57971i) q^{11} +(-0.190983 + 0.587785i) q^{12} +(1.80902 - 1.31433i) q^{13} +(0.809017 + 2.48990i) q^{14} +(-2.30902 + 1.67760i) q^{15} +(3.92705 - 2.85317i) q^{16} +(-0.500000 + 1.53884i) q^{18} +(5.73607 + 4.16750i) q^{19} -1.76393 q^{20} +(0.500000 + 1.53884i) q^{21} +(-3.04508 - 9.37181i) q^{22} -3.47214 q^{23} +(1.80902 - 1.31433i) q^{24} +(-2.54508 - 1.84911i) q^{25} +3.61803 q^{26} +(-0.309017 + 0.951057i) q^{27} +(-0.309017 + 0.951057i) q^{28} +(2.88197 - 8.86978i) q^{29} -4.61803 q^{30} +(-6.04508 - 4.39201i) q^{31} +3.38197 q^{32} +(-1.88197 - 5.79210i) q^{33} +(-3.73607 + 2.71441i) q^{35} +(-0.500000 + 0.363271i) q^{36} -2.38197 q^{37} +(3.54508 + 10.9106i) q^{38} +2.23607 q^{39} +(5.16312 + 3.75123i) q^{40} +3.09017 q^{41} +(-0.809017 + 2.48990i) q^{42} +(-0.118034 + 0.363271i) q^{43} +(1.16312 - 3.57971i) q^{44} -2.85410 q^{45} +(-4.54508 - 3.30220i) q^{46} +(-5.42705 + 3.94298i) q^{47} +4.85410 q^{48} +(-1.35410 - 4.16750i) q^{49} +(-1.57295 - 4.84104i) q^{50} +(1.11803 + 0.812299i) q^{52} +(-3.89919 + 12.0005i) q^{53} +(-1.30902 + 0.951057i) q^{54} +(14.0623 - 10.2169i) q^{55} +(2.92705 - 2.12663i) q^{56} +(2.19098 + 6.74315i) q^{57} +(12.2082 - 8.86978i) q^{58} +(1.80902 - 5.56758i) q^{59} +(-1.42705 - 1.03681i) q^{60} +(-5.16312 + 3.75123i) q^{61} +(-3.73607 - 11.4984i) q^{62} +(-0.500000 + 1.53884i) q^{63} +(-3.42705 - 2.48990i) q^{64} +(1.97214 + 6.06961i) q^{65} +(3.04508 - 9.37181i) q^{66} +(-0.472136 - 1.45309i) q^{67} +(-2.80902 - 2.04087i) q^{69} -7.47214 q^{70} +(-1.95492 + 8.19624i) q^{71} +2.23607 q^{72} +(8.35410 + 6.06961i) q^{73} +(-3.11803 - 2.26538i) q^{74} +(-0.972136 - 2.99193i) q^{75} +(-1.35410 + 4.16750i) q^{76} +(-3.04508 - 9.37181i) q^{77} +(2.92705 + 2.12663i) q^{78} +(-0.600813 + 1.84911i) q^{79} +(4.28115 + 13.1760i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(4.04508 + 2.93893i) q^{82} +(-3.69098 + 11.3597i) q^{83} +(-0.809017 + 0.587785i) q^{84} +(-0.500000 + 0.363271i) q^{86} +(7.54508 - 5.48183i) q^{87} +(-11.0172 + 8.00448i) q^{88} +(-0.972136 + 2.99193i) q^{89} +(-3.73607 - 2.71441i) q^{90} +3.61803 q^{91} +(-0.663119 - 2.04087i) q^{92} +(-2.30902 - 7.10642i) q^{93} -10.8541 q^{94} +(-16.3713 + 11.8945i) q^{95} +(2.73607 + 1.98787i) q^{96} -5.94427 q^{97} +(2.19098 - 6.74315i) q^{98} +(1.88197 - 5.79210i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} + q^{3} + 3 q^{4} - 8 q^{5} + 2 q^{6} + 3 q^{7} + 5 q^{8} - q^{9} - 6 q^{10} - 13 q^{11} - 3 q^{12} + 5 q^{13} + q^{14} - 7 q^{15} + 9 q^{16} - 2 q^{18} + 14 q^{19} - 16 q^{20} + 2 q^{21}+ \cdots + 12 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 + q^3 + 3 * q^4 - 8 * q^5 + 2 * q^6 + 3 * q^7 + 5 * q^8 - q^9 - 6 * q^10 - 13 * q^11 - 3 * q^12 + 5 * q^13 + q^14 - 7 * q^15 + 9 * q^16 - 2 * q^18 + 14 * q^19 - 16 * q^20 + 2 * q^21 - q^22 + 4 * q^23 + 5 * q^24 + q^25 + 10 * q^26 + q^27 + q^28 + 16 * q^29 - 14 * q^30 - 13 * q^31 + 18 * q^32 - 12 * q^33 - 6 * q^35 - 2 * q^36 - 14 * q^37 + 3 * q^38 + 5 * q^40 - 10 * q^41 - q^42 + 4 * q^43 - 11 * q^44 + 2 * q^45 - 7 * q^46 - 15 * q^47 + 6 * q^48 + 8 * q^49 - 13 * q^50 + 9 * q^53 - 3 * q^54 + 16 * q^55 + 5 * q^56 + 11 * q^57 + 22 * q^58 + 5 * q^59 + q^60 - 5 * q^61 - 6 * q^62 - 2 * q^63 - 7 * q^64 - 10 * q^65 + q^66 + 16 * q^67 - 9 * q^69 - 12 * q^70 - 19 * q^71 + 20 * q^73 - 8 * q^74 + 14 * q^75 + 8 * q^76 - q^77 + 5 * q^78 - 27 * q^79 - 3 * q^80 - q^81 + 5 * q^82 - 17 * q^83 - q^84 - 2 * q^86 + 19 * q^87 - 15 * q^88 + 14 * q^89 - 6 * q^90 + 10 * q^91 + 13 * q^92 - 7 * q^93 - 30 * q^94 - 23 * q^95 + 2 * q^96 + 12 * q^97 + 11 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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