LMFDB - Embedded newform 605.2.g.l.81.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [605,2,Mod(81,605)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(605, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("605.81"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.g (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.64000000.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 2x^{6} + 4x^{4} + 8x^{2} + 16 $ x^8 + 2x^6 + 4x^4 + 8*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.1
Root			$0.437016 - 1.34500i$ of defining polynomial
Character	$\chi$	$=$	605.81
Dual form			605.2.g.l.366.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.335106 - 0.243469i) q^{2} +(0.874032 - 2.68999i) q^{3} +(-0.565015 - 1.73894i) q^{4} +(0.809017 - 0.587785i) q^{5} +(-0.947822 + 0.688633i) q^{6} +(0.618034 + 1.90211i) q^{7} +(-0.490035 + 1.50817i) q^{8} +(-4.04508 - 2.93893i) q^{9} -0.414214 q^{10} -5.17157 q^{12} +(-5.52431 - 4.01365i) q^{13} +(0.255998 - 0.787881i) q^{14} +(-0.874032 - 2.68999i) q^{15} +(-2.42705 + 1.76336i) q^{16} +(0.947822 - 0.688633i) q^{17} +(0.639995 + 1.96970i) q^{18} +(-1.47923 - 1.07472i) q^{20} +5.65685 q^{21} +2.82843 q^{23} +(3.62867 + 2.63638i) q^{24} +(0.309017 - 0.951057i) q^{25} +(0.874032 + 2.68999i) q^{26} +(-4.57649 + 3.32502i) q^{27} +(2.95846 - 2.14944i) q^{28} +(-2.36610 - 7.28210i) q^{29} +(-0.362036 + 1.11423i) q^{30} +4.41421 q^{32} -0.485281 q^{34} +(1.61803 + 1.17557i) q^{35} +(-2.82508 + 8.69469i) q^{36} +(1.13003 + 3.47788i) q^{37} +(-15.6251 + 11.3523i) q^{39} +(0.490035 + 1.50817i) q^{40} +(-1.85410 + 5.70634i) q^{41} +(-1.89564 - 1.37727i) q^{42} +6.00000 q^{43} -5.00000 q^{45} +(-0.947822 - 0.688633i) q^{46} +(-0.874032 + 2.68999i) q^{47} +(2.62210 + 8.06998i) q^{48} +(2.42705 - 1.76336i) q^{49} +(-0.335106 + 0.243469i) q^{50} +(-1.02399 - 3.15152i) q^{51} +(-3.85816 + 11.8742i) q^{52} +(-0.277611 - 0.201696i) q^{53} +2.34315 q^{54} -3.17157 q^{56} +(-0.980070 + 3.01635i) q^{58} +(-2.98413 - 9.18421i) q^{59} +(-4.18389 + 3.03977i) q^{60} +(10.7710 - 7.82560i) q^{61} +(3.09017 - 9.51057i) q^{63} +(3.37487 + 2.45199i) q^{64} -6.82843 q^{65} -4.48528 q^{67} +(-1.73302 - 1.25912i) q^{68} +(2.47214 - 7.60845i) q^{69} +(-0.255998 - 0.787881i) q^{70} +(9.15298 - 6.65003i) q^{71} +(6.41464 - 4.66051i) q^{72} +(2.11010 + 6.49422i) q^{73} +(0.468074 - 1.44058i) q^{74} +(-2.28825 - 1.66251i) q^{75} +8.00000 q^{78} +(3.23607 + 2.35114i) q^{79} +(-0.927051 + 2.85317i) q^{80} +(0.309017 + 0.951057i) q^{81} +(2.01063 - 1.46081i) q^{82} +(-4.85410 + 3.52671i) q^{83} +(-3.19621 - 9.83692i) q^{84} +(0.362036 - 1.11423i) q^{85} +(-2.01063 - 1.46081i) q^{86} -21.6569 q^{87} +9.31371 q^{89} +(1.67553 + 1.21734i) q^{90} +(4.22020 - 12.9884i) q^{91} +(-1.59810 - 4.91846i) q^{92} +(0.947822 - 0.688633i) q^{94} +(3.85816 - 11.8742i) q^{96} +(6.19453 + 4.50059i) q^{97} -1.24264 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{8} - 10 q^{9} + 8 q^{10} - 64 q^{12} - 8 q^{13} + 4 q^{14} - 6 q^{16} + 8 q^{17} + 10 q^{18} + 2 q^{20} - 8 q^{24} - 2 q^{25} - 4 q^{28} + 4 q^{29}+ \cdots + 24 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^8 - 10 * q^9 + 8 * q^10 - 64 * q^12 - 8 * q^13 + 4 * q^14 - 6 * q^16 + 8 * q^17 + 10 * q^18 + 2 * q^20 - 8 * q^24 - 2 * q^25 - 4 * q^28 + 4 * q^29 + 8 * q^30 + 24 * q^32 + 64 * q^34 + 4 * q^35 - 10 * q^36 + 4 * q^37 - 16 * q^39 - 6 * q^40 + 12 * q^41 - 16 * q^42 + 48 * q^43 - 40 * q^45 - 8 * q^46 + 6 * q^49 + 2 * q^50 - 16 * q^51 + 8 * q^52 - 12 * q^53 + 64 * q^54 - 48 * q^56 + 12 * q^58 + 8 * q^59 - 16 * q^60 + 4 * q^61 - 20 * q^63 + 14 * q^64 - 32 * q^65 + 32 * q^67 + 24 * q^68 - 16 * q^69 - 4 * q^70 + 30 * q^72 - 8 * q^73 - 20 * q^74 + 64 * q^78 + 8 * q^79 + 6 * q^80 - 2 * q^81 - 12 * q^82 - 12 * q^83 + 32 * q^84 - 8 * q^85 + 12 * q^86 - 128 * q^87 - 16 * q^89 - 10 * q^90 - 16 * q^91 + 16 * q^92 + 8 * q^94 - 8 * q^96 + 4 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	−0.335106	−	0.243469i	−0.236956	−	0.172158i	0.462970	−	0.886374i	$-0.346784\pi$
$2$	−0.335106	−	0.243469i	−0.236956	−	0.172158i	−0.699926	+	0.714215i	$0.746784\pi$
$3$	0.874032	−	2.68999i	0.504623	−	1.55307i	−0.296781	−	0.954945i	$-0.595913\pi$
$3$	0.874032	−	2.68999i	0.504623	−	1.55307i	0.801404	−	0.598123i	$-0.204087\pi$
$4$	−0.565015	−	1.73894i	−0.282508	−	0.869469i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$6$	−0.947822	+	0.688633i	−0.386947	+	0.281133i
$7$	0.618034	+	1.90211i	0.233595	+	0.718931i	0.997305	+	0.0733714i	$0.0233759\pi$
$7$	0.618034	+	1.90211i	0.233595	+	0.718931i	−0.763710	+	0.645560i	$0.776624\pi$
$8$	−0.490035	+	1.50817i	−0.173254	+	0.533220i
$9$	−4.04508	−	2.93893i	−1.34836	−	0.979642i
$10$	−0.414214			−0.130986
$11$		0			0
$11$		0			0
$12$	−5.17157			−1.49290
$13$	−5.52431	−	4.01365i	−1.53217	−	1.11319i	−0.955018	−	0.296549i	$-0.904164\pi$
$13$	−5.52431	−	4.01365i	−1.53217	−	1.11319i	−0.577151	−	0.816637i	$-0.695836\pi$
$14$	0.255998	−	0.787881i	0.0684184	−	0.210570i
$15$	−0.874032	−	2.68999i	−0.225674	−	0.694553i
$16$	−2.42705	+	1.76336i	−0.606763	+	0.440839i
$17$	0.947822	−	0.688633i	0.229881	−	0.167018i	−0.466882	−	0.884319i	$-0.654623\pi$
$17$	0.947822	−	0.688633i	0.229881	−	0.167018i	0.696763	+	0.717301i	$0.254623\pi$
$18$	0.639995	+	1.96970i	0.150848	+	0.464263i
$19$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$19$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$20$	−1.47923	−	1.07472i	−0.330766	−	0.240315i
$21$	5.65685			1.23443
$22$		0			0
$23$	2.82843			0.589768			0.294884	−	0.955533i	$-0.404719\pi$
$23$	2.82843			0.589768			0.294884	+	0.955533i	$0.404719\pi$
$24$	3.62867	+	2.63638i	0.740699	+	0.538149i
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$	0.874032	+	2.68999i	0.171412	+	0.527551i
$27$	−4.57649	+	3.32502i	−0.880746	+	0.639900i
$28$	2.95846	−	2.14944i	0.559096	−	0.406207i
$29$	−2.36610	−	7.28210i	−0.439373	−	1.35225i	−0.888538	−	0.458803i	$-0.848278\pi$
$29$	−2.36610	−	7.28210i	−0.439373	−	1.35225i	0.449165	−	0.893449i	$-0.351722\pi$
$30$	−0.362036	+	1.11423i	−0.0660984	+	0.203430i
$31$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$31$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$32$	4.41421			0.780330
$33$		0			0
$34$	−0.485281			−0.0832251
$35$	1.61803	+	1.17557i	0.273498	+	0.198708i
$36$	−2.82508	+	8.69469i	−0.470846	+	1.44911i
$37$	1.13003	+	3.47788i	0.185776	+	0.571759i	0.999961	−	0.00884630i	$-0.00281590\pi$
$37$	1.13003	+	3.47788i	0.185776	+	0.571759i	−0.814185	+	0.580605i	$0.802816\pi$
$38$		0			0
$39$	−15.6251	+	11.3523i	−2.50202	+	1.81782i
$40$	0.490035	+	1.50817i	0.0774813	+	0.238463i
$41$	−1.85410	+	5.70634i	−0.289562	+	0.891180i	0.695432	+	0.718592i	$0.255213\pi$
$41$	−1.85410	+	5.70634i	−0.289562	+	0.891180i	−0.984994	+	0.172588i	$0.944787\pi$
$42$	−1.89564	−	1.37727i	−0.292504	−	0.212517i
$43$	6.00000			0.914991			0.457496	−	0.889212i	$-0.348747\pi$
$43$	6.00000			0.914991			0.457496	+	0.889212i	$0.348747\pi$
$44$		0			0
$45$	−5.00000			−0.745356
$46$	−0.947822	−	0.688633i	−0.139749	−	0.101533i
$47$	−0.874032	+	2.68999i	−0.127491	+	0.392376i	−0.994347	−	0.106183i	$-0.966137\pi$
$47$	−0.874032	+	2.68999i	−0.127491	+	0.392376i	0.866856	+	0.498559i	$0.166137\pi$
$48$	2.62210	+	8.06998i	0.378467	+	1.16480i
$49$	2.42705	−	1.76336i	0.346722	−	0.251908i
$50$	−0.335106	+	0.243469i	−0.0473911	+	0.0344317i
$51$	−1.02399	−	3.15152i	−0.143388	−	0.441302i
$52$	−3.85816	+	11.8742i	−0.535031	+	1.64666i
$53$	−0.277611	−	0.201696i	−0.0381328	−	0.0277051i	0.568556	−	0.822645i	$-0.307502\pi$
$53$	−0.277611	−	0.201696i	−0.0381328	−	0.0277051i	−0.606688	+	0.794940i	$0.707502\pi$
$54$	2.34315			0.318862
$55$		0			0
$56$	−3.17157			−0.423819
$57$		0			0
$58$	−0.980070	+	3.01635i	−0.128689	+	0.396066i
$59$	−2.98413	−	9.18421i	−0.388501	−	1.19568i	−0.933909	−	0.357512i	$-0.883625\pi$
$59$	−2.98413	−	9.18421i	−0.388501	−	1.19568i	0.545408	−	0.838171i	$-0.316375\pi$
$60$	−4.18389	+	3.03977i	−0.540138	+	0.392433i
$61$	10.7710	−	7.82560i	1.37909	−	1.00197i	0.382123	−	0.924112i	$-0.375193\pi$
$61$	10.7710	−	7.82560i	1.37909	−	1.00197i	0.996965	−	0.0778539i	$-0.0248068\pi$
$62$		0			0
$63$	3.09017	−	9.51057i	0.389325	−	1.19822i
$64$	3.37487	+	2.45199i	0.421859	+	0.306499i
$65$	−6.82843			−0.846962
$66$		0			0
$67$	−4.48528			−0.547964			−0.273982	−	0.961735i	$-0.588341\pi$
$67$	−4.48528			−0.547964			−0.273982	+	0.961735i	$0.588341\pi$
$68$	−1.73302	−	1.25912i	−0.210160	−	0.152690i
$69$	2.47214	−	7.60845i	0.297610	−	0.915950i
$70$	−0.255998	−	0.787881i	−0.0305976	−	0.0941698i
$71$	9.15298	−	6.65003i	1.08626	−	0.789213i	0.107496	−	0.994206i	$-0.465717\pi$
$71$	9.15298	−	6.65003i	1.08626	−	0.789213i	0.978764	+	0.204992i	$0.0657169\pi$
$72$	6.41464	−	4.66051i	0.755973	−	0.549246i
$73$	2.11010	+	6.49422i	0.246969	+	0.760091i	0.995306	+	0.0967733i	$0.0308522\pi$
$73$	2.11010	+	6.49422i	0.246969	+	0.760091i	−0.748338	+	0.663318i	$0.769148\pi$
$74$	0.468074	−	1.44058i	0.0544125	−	0.167464i
$75$	−2.28825	−	1.66251i	−0.264224	−	0.191970i
$76$		0			0
$77$		0			0
$78$	8.00000			0.905822
$79$	3.23607	+	2.35114i	0.364086	+	0.264524i	0.754754	−	0.656007i	$-0.227756\pi$
$79$	3.23607	+	2.35114i	0.364086	+	0.264524i	−0.390668	+	0.920532i	$0.627756\pi$
$80$	−0.927051	+	2.85317i	−0.103647	+	0.318994i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	2.01063	−	1.46081i	0.222037	−	0.161320i
$83$	−4.85410	+	3.52671i	−0.532807	+	0.387107i	−0.821407	−	0.570343i	$-0.806810\pi$
$83$	−4.85410	+	3.52671i	−0.532807	+	0.387107i	0.288600	+	0.957450i	$0.406810\pi$
$84$	−3.19621	−	9.83692i	−0.348735	−	1.07330i
$85$	0.362036	−	1.11423i	0.0392683	−	0.120855i
$86$	−2.01063	−	1.46081i	−0.216812	−	0.157523i
$87$	−21.6569			−2.32186
$88$		0			0
$89$	9.31371			0.987251			0.493626	−	0.869675i	$-0.335671\pi$
$89$	9.31371			0.987251			0.493626	+	0.869675i	$0.335671\pi$
$90$	1.67553	+	1.21734i	0.176616	+	0.128319i
$91$	4.22020	−	12.9884i	0.442397	−	1.36156i
$92$	−1.59810	−	4.91846i	−0.166614	−	0.512785i
$93$		0			0
$94$	0.947822	−	0.688633i	0.0977604	−	0.0710271i
$95$		0			0
$96$	3.85816	−	11.8742i	0.393772	−	1.21191i
$97$	6.19453	+	4.50059i	0.628959	+	0.456965i	0.856039	−	0.516911i	$-0.172918\pi$
$97$	6.19453	+	4.50059i	0.628959	+	0.456965i	−0.227081	+	0.973876i	$0.572918\pi$
$98$	−1.24264			−0.125526
$99$		0			0
$100$	−1.82843			−0.182843
$101$	−10.7710	−	7.82560i	−1.07176	−	0.778676i	−0.0955291	−	0.995427i	$-0.530454\pi$
$101$	−10.7710	−	7.82560i	−1.07176	−	0.778676i	−0.976227	+	0.216750i	$0.930454\pi$
$102$	−0.424151	+	1.30540i	−0.0419973	+	0.129254i
$103$	0.362036	+	1.11423i	0.0356725	+	0.109789i	0.967307	−	0.253608i	$-0.0816172\pi$
$103$	0.362036	+	1.11423i	0.0356725	+	0.109789i	−0.931635	+	0.363396i	$0.881617\pi$
$104$	8.76038	−	6.36479i	0.859026	−	0.624119i
$105$	4.57649	−	3.32502i	0.446620	−	0.324488i
$106$	0.0439223	+	0.135179i	0.00426611	+	0.0131297i
$107$	1.13003	−	3.47788i	0.109244	−	0.336219i	−0.881459	−	0.472261i	$-0.843438\pi$
$107$	1.13003	−	3.47788i	0.109244	−	0.336219i	0.990703	+	0.136042i	$0.0434381\pi$
$108$	8.36778	+	6.07955i	0.805190	+	0.585005i
$109$	−3.65685			−0.350263			−0.175132	−	0.984545i	$-0.556035\pi$
$109$	−3.65685			−0.350263			−0.175132	+	0.984545i	$0.556035\pi$
$110$		0			0
$111$	10.3431			0.981728
$112$	−4.85410	−	3.52671i	−0.458670	−	0.333243i
$113$	2.57817	−	7.93480i	0.242534	−	0.746443i	−0.753498	−	0.657450i	$-0.771635\pi$
$113$	2.57817	−	7.93480i	0.242534	−	0.746443i	0.996032	−	0.0889933i	$-0.0283650\pi$
$114$		0			0
$115$	2.28825	−	1.66251i	0.213380	−	0.155030i
$116$	−11.3262	+	8.22899i	−1.05161	+	0.764043i
$117$	10.5505	+	32.4711i	0.975394	+	3.00195i
$118$	−1.23607	+	3.80423i	−0.113789	+	0.350207i
$119$	1.89564	+	1.37727i	0.173773	+	0.126254i
$120$	4.48528			0.409448
$121$		0			0
$122$	−5.51472			−0.499279
$123$	13.7295	+	9.97505i	1.23794	+	0.899420i
$124$		0			0
$125$	−0.309017	−	0.951057i	−0.0276393	−	0.0850651i
$126$	−3.35106	+	2.43469i	−0.298536	+	0.216899i
$127$	12.6667	−	9.20287i	1.12398	−	0.816622i	0.139176	−	0.990268i	$-0.455555\pi$
$127$	12.6667	−	9.20287i	1.12398	−	0.816622i	0.984808	+	0.173645i	$0.0555546\pi$
$128$	−3.26209	−	10.0397i	−0.288331	−	0.887391i
$129$	5.24419	−	16.1400i	0.461725	−	1.42104i
$130$	2.28825	+	1.66251i	0.200692	+	0.145812i
$131$	−11.3137			−0.988483			−0.494242	−	0.869325i	$-0.664554\pi$
$131$	−11.3137			−0.988483			−0.494242	+	0.869325i	$0.664554\pi$
$132$		0			0
$133$		0			0
$134$	1.50304	+	1.09203i	0.129843	+	0.0943366i
$135$	−1.74806	+	5.37999i	−0.150449	+	0.463036i
$136$	0.574112	+	1.76693i	0.0492297	+	0.151513i
$137$	−18.5836	+	13.5018i	−1.58770	+	1.15353i	−0.680573	+	0.732680i	$0.738269\pi$
$137$	−18.5836	+	13.5018i	−1.58770	+	1.15353i	−0.907129	+	0.420853i	$0.861731\pi$
$138$	−2.68085	+	1.94775i	−0.228209	+	0.165803i
$139$	1.23607	+	3.80423i	0.104842	+	0.322670i	0.989693	−	0.143203i	$-0.0457402\pi$
$139$	1.23607	+	3.80423i	0.104842	+	0.322670i	−0.884851	+	0.465873i	$0.845740\pi$
$140$	1.13003	−	3.47788i	0.0955050	−	0.293934i
$141$	6.47214	+	4.70228i	0.545052	+	0.396004i
$142$	−4.68629			−0.393265
$143$		0			0
$144$	15.0000			1.25000
$145$	−6.19453	−	4.50059i	−0.514427	−	0.373753i
$146$	0.874032	−	2.68999i	0.0723354	−	0.222625i
$147$	−2.62210	−	8.06998i	−0.216267	−	0.665601i
$148$	5.40932	−	3.93010i	0.444644	−	0.323053i
$149$	9.43059	−	6.85173i	0.772584	−	0.561315i	−0.130160	−	0.991493i	$-0.541549\pi$
$149$	9.43059	−	6.85173i	0.772584	−	0.561315i	0.902744	+	0.430178i	$0.141549\pi$
$150$	0.362036	+	1.11423i	0.0295601	+	0.0909767i
$151$	3.70820	−	11.4127i	0.301769	−	0.928751i	−0.679094	−	0.734052i	$-0.737627\pi$
$151$	3.70820	−	11.4127i	0.301769	−	0.928751i	0.980863	−	0.194699i	$-0.0623730\pi$
$152$		0			0
$153$	−5.85786			−0.473580
$154$		0			0
$155$		0			0
$156$	28.5694	+	20.7569i	2.28738	+	1.66188i
$157$	−4.32624	+	13.3148i	−0.345271	+	1.06264i	0.616167	+	0.787616i	$0.288685\pi$
$157$	−4.32624	+	13.3148i	−0.345271	+	1.06264i	−0.961438	+	0.275020i	$0.911315\pi$
$158$	−0.511996	−	1.57576i	−0.0407322	−	0.125361i
$159$	−0.785202	+	0.570482i	−0.0622705	+	0.0452422i
$160$	3.57117	−	2.59461i	0.282326	−	0.205122i
$161$	1.74806	+	5.37999i	0.137767	+	0.424002i
$162$	0.127999	−	0.393941i	0.0100566	−	0.0309509i
$163$	0.392601	+	0.285241i	0.0307509	+	0.0223418i	0.603055	−	0.797700i	$-0.293950\pi$
$163$	0.392601	+	0.285241i	0.0307509	+	0.0223418i	−0.572304	+	0.820042i	$0.693950\pi$
$164$	10.9706			0.856657
$165$		0			0
$166$	2.48528			0.192895
$167$	8.87537	+	6.44833i	0.686797	+	0.498987i	0.875606	−	0.483027i	$-0.160463\pi$
$167$	8.87537	+	6.44833i	0.686797	+	0.498987i	−0.188809	+	0.982014i	$0.560463\pi$
$168$	−2.77206	+	8.53151i	−0.213869	+	0.658220i
$169$	10.3914	+	31.9816i	0.799342	+	2.46012i
$170$	−0.392601	+	0.285241i	−0.0301111	+	0.0218770i
$171$		0			0
$172$	−3.39009	−	10.4336i	−0.258492	−	0.795556i
$173$	−1.89802	+	5.84152i	−0.144304	+	0.444122i	−0.996921	−	0.0784144i	$-0.975014\pi$
$173$	−1.89802	+	5.84152i	−0.144304	+	0.444122i	0.852617	+	0.522537i	$0.175014\pi$
$174$	7.25734	+	5.27276i	0.550177	+	0.399727i
$175$	2.00000			0.151186
$176$		0			0
$177$	−27.3137			−2.05302
$178$	−3.12108	−	2.26760i	−0.233935	−	0.169963i
$179$	−0.511996	+	1.57576i	−0.0382684	+	0.117778i	−0.968366	−	0.249535i	$-0.919722\pi$
$179$	−0.511996	+	1.57576i	−0.0382684	+	0.117778i	0.930097	+	0.367313i	$0.119722\pi$
$180$	2.82508	+	8.69469i	0.210569	+	0.648064i
$181$	1.06281	−	0.772178i	0.0789982	−	0.0573956i	−0.547585	−	0.836750i	$-0.684453\pi$
$181$	1.06281	−	0.772178i	0.0789982	−	0.0573956i	0.626583	+	0.779354i	$0.284453\pi$
$182$	−4.57649	+	3.32502i	−0.339232	+	0.246467i
$183$	−11.6366	−	35.8138i	−0.860203	−	2.64743i
$184$	−1.38603	+	4.26576i	−0.102179	+	0.314476i
$185$	2.95846	+	2.14944i	0.217510	+	0.158030i
$186$		0			0
$187$		0			0
$188$	5.17157			0.377176
$189$	−9.15298	−	6.65003i	−0.665782	−	0.483719i
$190$		0			0
$191$	−5.96826	−	18.3684i	−0.431848	−	1.32909i	−0.896282	−	0.443485i	$-0.853742\pi$
$191$	−5.96826	−	18.3684i	−0.431848	−	1.32909i	0.464433	−	0.885608i	$-0.346258\pi$
$192$	9.54558	−	6.93527i	0.688893	−	0.500510i
$193$	−5.52431	+	4.01365i	−0.397649	+	0.288909i	−0.768583	−	0.639751i	$-0.779038\pi$
$193$	−5.52431	+	4.01365i	−0.397649	+	0.288909i	0.370934	+	0.928659i	$0.379038\pi$
$194$	−0.980070	−	3.01635i	−0.0703649	−	0.216561i
$195$	−5.96826	+	18.3684i	−0.427396	+	1.31539i
$196$	−4.43769	−	3.22417i	−0.316978	−	0.230298i
$197$	5.17157			0.368459			0.184230	−	0.982883i	$-0.441021\pi$
$197$	5.17157			0.368459			0.184230	+	0.982883i	$0.441021\pi$
$198$		0			0
$199$	21.6569			1.53521			0.767607	−	0.640921i	$-0.221447\pi$
$199$	21.6569			1.53521			0.767607	+	0.640921i	$0.221447\pi$
$200$	1.28293	+	0.932102i	0.0907167	+	0.0659096i
$201$	−3.92028	+	12.0654i	−0.276515	+	0.851026i
$202$	1.70414	+	5.24481i	0.119903	+	0.369023i
$203$	12.3891	−	9.00117i	0.869541	−	0.631758i
$204$	−4.90173	+	3.56132i	−0.343190	+	0.249342i
$205$	1.85410	+	5.70634i	0.129496	+	0.398548i
$206$	0.149960	−	0.461530i	0.0104482	−	0.0321563i
$207$	−11.4412	−	8.31254i	−0.795220	−	0.577761i
$208$	20.4853			1.42040
$209$		0			0
$210$	−2.34315			−0.161692
$211$	−12.9443	−	9.40456i	−0.891120	−	0.647437i	0.0450495	−	0.998985i	$-0.485655\pi$
$211$	−12.9443	−	9.40456i	−0.891120	−	0.647437i	−0.936170	+	0.351548i	$0.885655\pi$
$212$	−0.193883	+	0.596709i	−0.0133159	+	0.0409821i
$213$	−9.88854	−	30.4338i	−0.677552	−	2.08529i
$214$	−1.22543	+	0.890329i	−0.0837689	+	0.0608617i
$215$	4.85410	−	3.52671i	0.331047	−	0.240520i
$216$	−2.77206	−	8.53151i	−0.188615	−	0.580496i
$217$		0			0
$218$	1.22543	+	0.890329i	0.0829968	+	0.0603007i
$219$	19.3137			1.30510
$220$		0			0
$221$	−8.00000			−0.538138
$222$	−3.46605	−	2.51823i	−0.232626	−	0.169013i
$223$	−1.59810	+	4.91846i	−0.107017	+	0.329364i	−0.990199	−	0.139667i	$-0.955397\pi$
$223$	−1.59810	+	4.91846i	−0.107017	+	0.329364i	0.883182	+	0.469031i	$0.155397\pi$
$224$	2.72813	+	8.39633i	0.182281	+	0.561004i
$225$	−4.04508	+	2.93893i	−0.269672	+	0.195928i
$226$	−2.79584	+	2.03129i	−0.185976	+	0.135120i
$227$	−0.830110	−	2.55482i	−0.0550963	−	0.169569i	0.919722	−	0.392571i	$-0.128414\pi$
$227$	−0.830110	−	2.55482i	−0.0550963	−	0.169569i	−0.974818	+	0.223002i	$0.928414\pi$
$228$		0			0
$229$	17.2432	+	12.5279i	1.13946	+	0.827866i	0.987044	−	0.160451i	$-0.0512947\pi$
$229$	17.2432	+	12.5279i	1.13946	+	0.827866i	0.152416	+	0.988316i	$0.451295\pi$
$230$	−1.17157			−0.0772512
$231$		0			0
$232$	12.1421			0.797170
$233$	17.9134	+	13.0148i	1.17354	+	0.852629i	0.991429	−	0.130648i	$-0.0417058\pi$
$233$	17.9134	+	13.0148i	1.17354	+	0.852629i	0.182115	+	0.983277i	$0.441706\pi$
$234$	4.37016	−	13.4500i	0.285686	−	0.879252i
$235$	0.874032	+	2.68999i	0.0570156	+	0.175476i
$236$	−14.2847	+	10.3784i	−0.929854	+	0.675579i
$237$	9.15298	−	6.65003i	0.594550	−	0.431966i
$238$	−0.299920	−	0.923060i	−0.0194410	−	0.0598331i
$239$	0.212076	−	0.652702i	0.0137180	−	0.0422198i	−0.943963	−	0.330051i	$-0.892934\pi$
$239$	0.212076	−	0.652702i	0.0137180	−	0.0422198i	0.957681	+	0.287831i	$0.0929341\pi$
$240$	6.86474	+	4.98752i	0.443117	+	0.321943i
$241$	−6.00000			−0.386494			−0.193247	−	0.981150i	$-0.561902\pi$
$241$	−6.00000			−0.386494			−0.193247	+	0.981150i	$0.561902\pi$
$242$		0			0
$243$	−14.1421			−0.907218
$244$	−19.6940	−	14.3085i	−1.26078	−	0.916011i
$245$	0.927051	−	2.85317i	0.0592271	−	0.182282i
$246$	−2.17222	−	6.68539i	−0.138495	−	0.426245i
$247$		0			0
$248$		0			0
$249$	5.24419	+	16.1400i	0.332337	+	1.02283i
$250$	−0.127999	+	0.393941i	−0.00809537	+	0.0249150i
$251$	−9.70820	−	7.05342i	−0.612776	−	0.445208i	0.237614	−	0.971360i	$-0.423635\pi$
$251$	−9.70820	−	7.05342i	−0.612776	−	0.445208i	−0.850391	+	0.526151i	$0.823635\pi$
$252$	−18.2843			−1.15180
$253$		0			0
$254$	−6.48528			−0.406923
$255$	−2.68085	−	1.94775i	−0.167881	−	0.121973i
$256$	1.22697	−	3.77623i	0.0766857	−	0.236014i
$257$	4.11416	+	12.6621i	0.256634	+	0.789839i	0.993503	+	0.113804i	$0.0363035\pi$
$257$	4.11416	+	12.6621i	0.256634	+	0.789839i	−0.736869	+	0.676036i	$0.763696\pi$
$258$	−5.68693	+	4.13180i	−0.354053	+	0.257235i
$259$	−5.91691	+	4.29889i	−0.367659	+	0.267120i
$260$	3.85816	+	11.8742i	0.239273	+	0.736407i
$261$	−11.8305	+	36.4105i	−0.732289	+	2.25375i
$262$	3.79129	+	2.75453i	0.234227	+	0.170176i
$263$	−22.9706			−1.41643			−0.708213	−	0.705999i	$-0.750498\pi$
$263$	−22.9706			−1.41643			−0.708213	+	0.705999i	$0.750498\pi$
$264$		0			0
$265$	−0.343146			−0.0210793
$266$		0			0
$267$	8.14048	−	25.0538i	0.498189	−	1.53327i
$268$	2.53425	+	7.79962i	0.154804	+	0.476438i
$269$	4.29888	−	3.12332i	0.262107	−	0.190432i	−0.448968	−	0.893548i	$-0.648208\pi$
$269$	4.29888	−	3.12332i	0.262107	−	0.190432i	0.711076	+	0.703116i	$0.248208\pi$
$270$	1.89564	−	1.37727i	0.115365	−	0.0838178i
$271$	4.73220	+	14.5642i	0.287460	+	0.884712i	0.985650	+	0.168800i	$0.0539891\pi$
$271$	4.73220	+	14.5642i	0.287460	+	0.884712i	−0.698190	+	0.715913i	$0.746011\pi$
$272$	−1.08611	+	3.34270i	−0.0658550	+	0.202681i
$273$	−31.2502	−	22.7046i	−1.89135	−	1.37415i
$274$	9.51472			0.574805
$275$		0			0
$276$	−14.6274			−0.880467
$277$	0.947822	+	0.688633i	0.0569491	+	0.0413760i	0.615896	−	0.787828i	$-0.288794\pi$
$277$	0.947822	+	0.688633i	0.0569491	+	0.0413760i	−0.558947	+	0.829204i	$0.688794\pi$
$278$	0.511996	−	1.57576i	0.0307075	−	0.0945079i
$279$		0			0
$280$	−2.56586	+	1.86420i	−0.153339	+	0.111407i
$281$	−4.29888	+	3.12332i	−0.256450	+	0.186322i	−0.708580	−	0.705630i	$-0.750664\pi$
$281$	−4.29888	+	3.12332i	−0.256450	+	0.186322i	0.452131	+	0.891952i	$0.350664\pi$
$282$	−1.02399	−	3.15152i	−0.0609779	−	0.187671i
$283$	3.90209	−	12.0094i	0.231955	−	0.713884i	−0.765556	−	0.643370i	$-0.777536\pi$
$283$	3.90209	−	12.0094i	0.231955	−	0.713884i	0.997511	−	0.0705145i	$-0.0224641\pi$
$284$	−16.7356	−	12.1591i	−0.993073	−	0.721510i
$285$		0			0
$286$		0			0
$287$	−12.0000			−0.708338
$288$	−17.8559	−	12.9730i	−1.05217	−	0.764444i
$289$	−4.82914	+	14.8626i	−0.284067	+	0.874268i
$290$	0.980070	+	3.01635i	0.0575517	+	0.177126i
$291$	17.5208	−	12.7296i	1.02709	−	0.746221i
$292$	10.1008	−	7.33866i	0.591105	−	0.429463i
$293$	4.58224	+	14.1027i	0.267697	+	0.823887i	0.991060	+	0.133419i	$0.0425955\pi$
$293$	4.58224	+	14.1027i	0.267697	+	0.823887i	−0.723363	+	0.690468i	$0.757405\pi$
$294$	−1.08611	+	3.34270i	−0.0633431	+	0.194950i
$295$	−7.81256	−	5.67616i	−0.454865	−	0.330479i
$296$	−5.79899			−0.337059
$297$		0			0
$298$	−4.82843			−0.279703
$299$	−15.6251	−	11.3523i	−0.903624	−	0.656521i
$300$	−1.59810	+	4.91846i	−0.0922666	+	0.283967i
$301$	3.70820	+	11.4127i	0.213737	+	0.657816i
$302$	−4.02127	+	2.92162i	−0.231398	+	0.168121i
$303$	−30.4650	+	22.1341i	−1.75017	+	1.27157i
$304$		0			0
$305$	4.11416	−	12.6621i	0.235576	−	0.725029i
$306$	1.96300	+	1.42621i	0.112217	+	0.0815308i
$307$	27.6569			1.57846			0.789230	−	0.614098i	$-0.210480\pi$
$307$	27.6569			1.57846			0.789230	+	0.614098i	$0.210480\pi$
$308$		0			0
$309$	3.31371			0.188510
$310$		0			0
$311$	8.44040	−	25.9769i	0.478611	−	1.47301i	−0.362414	−	0.932017i	$-0.618047\pi$
$311$	8.44040	−	25.9769i	0.478611	−	1.47301i	0.841025	−	0.540996i	$-0.181953\pi$
$312$	−9.46439	−	29.1284i	−0.535816	−	1.64907i
$313$	−17.2432	+	12.5279i	−0.974641	+	0.708118i	−0.956504	−	0.291718i	$-0.905773\pi$
$313$	−17.2432	+	12.5279i	−0.974641	+	0.708118i	−0.0181361	+	0.999836i	$0.505773\pi$
$314$	4.69148	−	3.40856i	0.264756	−	0.192356i
$315$	−3.09017	−	9.51057i	−0.174111	−	0.535860i
$316$	2.26006	−	6.95575i	0.127138	−	0.391292i
$317$	−17.2432	−	12.5279i	−0.968472	−	0.703636i	−0.0133691	−	0.999911i	$-0.504256\pi$
$317$	−17.2432	−	12.5279i	−0.968472	−	0.703636i	−0.955103	+	0.296275i	$0.904256\pi$
$318$	0.402020			0.0225442
$319$		0			0
$320$	4.17157			0.233198
$321$	−8.36778	−	6.07955i	−0.467044	−	0.339327i
$322$	0.724072	−	2.22846i	0.0403509	−	0.124187i
$323$		0			0
$324$	1.47923	−	1.07472i	0.0821794	−	0.0597068i
$325$	−5.52431	+	4.01365i	−0.306434	+	0.222637i
$326$	−0.0621155	−	0.191172i	−0.00344026	−	0.0105880i
$327$	−3.19621	+	9.83692i	−0.176751	+	0.543983i
$328$	−7.69757	−	5.59261i	−0.425027	−	0.308800i
$329$	−5.65685			−0.311872
$330$		0			0
$331$	15.3137			0.841718			0.420859	−	0.907126i	$-0.361729\pi$
$331$	15.3137			0.841718			0.420859	+	0.907126i	$0.361729\pi$
$332$	8.87537	+	6.44833i	0.487099	+	0.353898i
$333$	5.65015	−	17.3894i	0.309626	−	0.952932i
$334$	−1.40422	−	4.32175i	−0.0768356	−	0.236476i
$335$	−3.62867	+	2.63638i	−0.198255	+	0.144041i
$336$	−13.7295	+	9.97505i	−0.749004	+	0.544183i
$337$	1.08611	+	3.34270i	0.0591641	+	0.182088i	0.976271	−	0.216554i	$-0.0694816\pi$
$337$	1.08611	+	3.34270i	0.0591641	+	0.182088i	−0.917107	+	0.398642i	$0.869482\pi$
$338$	4.30428	−	13.2472i	0.234122	−	0.720553i
$339$	−19.0912	−	13.8705i	−1.03689	−	0.753345i
$340$	−2.14214			−0.116174
$341$		0			0
$342$		0			0
$343$	16.1803	+	11.7557i	0.873656	+	0.634748i
$344$	−2.94021	+	9.04904i	−0.158525	+	0.487891i
$345$	−2.47214	−	7.60845i	−0.133095	−	0.409625i
$346$	2.05827	−	1.49542i	0.110653	−	0.0803941i
$347$	−18.5836	+	13.5018i	−0.997619	+	0.724812i	−0.961576	−	0.274538i	$-0.911475\pi$
$347$	−18.5836	+	13.5018i	−0.997619	+	0.724812i	−0.0360423	+	0.999350i	$0.511475\pi$
$348$	12.2364	+	37.6599i	0.655943	+	2.01878i
$349$	2.15402	−	6.62940i	0.115302	−	0.354864i	−0.876708	−	0.481023i	$-0.840265\pi$
$349$	2.15402	−	6.62940i	0.115302	−	0.354864i	0.992010	+	0.126160i	$0.0402652\pi$
$350$	−0.670212	−	0.486937i	−0.0358243	−	0.0260279i
$351$	38.6274			2.06178
$352$		0			0
$353$	−1.31371			−0.0699216			−0.0349608	−	0.999389i	$-0.511131\pi$
$353$	−1.31371			−0.0699216			−0.0349608	+	0.999389i	$0.511131\pi$
$354$	9.15298	+	6.65003i	0.486476	+	0.353445i
$355$	3.49613	−	10.7600i	0.185555	−	0.571080i
$356$	−5.26239	−	16.1960i	−0.278906	−	0.858384i
$357$	5.36169	−	3.89550i	0.283771	−	0.206172i
$358$	0.555221	−	0.403392i	0.0293444	−	0.0213199i
$359$	−7.20433	−	22.1727i	−0.380230	−	1.17023i	−0.939882	−	0.341500i	$-0.889065\pi$
$359$	−7.20433	−	22.1727i	−0.380230	−	1.17023i	0.559652	−	0.828728i	$-0.310935\pi$
$360$	2.45017	−	7.54086i	0.129136	−	0.397438i
$361$	15.3713	+	11.1679i	0.809017	+	0.587785i
$362$	−0.544156			−0.0286002
$363$		0			0
$364$	−24.9706			−1.30881
$365$	5.52431	+	4.01365i	0.289156	+	0.210084i
$366$	−4.82004	+	14.8346i	−0.251948	+	0.775415i
$367$	2.62210	+	8.06998i	0.136872	+	0.421250i	0.995877	−	0.0907188i	$-0.0289165\pi$
$367$	2.62210	+	8.06998i	0.136872	+	0.421250i	−0.859004	+	0.511968i	$0.828916\pi$
$368$	−6.86474	+	4.98752i	−0.357849	+	0.259993i
$369$	24.2705	−	17.6336i	1.26347	−	0.917966i
$370$	−0.468074	−	1.44058i	−0.0243340	−	0.0748923i
$371$	0.212076	−	0.652702i	0.0110104	−	0.0338866i
$372$		0			0
$373$	3.79899			0.196704			0.0983521	−	0.995152i	$-0.468643\pi$
$373$	3.79899			0.196704			0.0983521	+	0.995152i	$0.468643\pi$
$374$		0			0
$375$	−2.82843			−0.146059
$376$	−3.62867	−	2.63638i	−0.187134	−	0.135961i
$377$	−16.1567	+	49.7253i	−0.832114	+	2.56098i
$378$	1.44814	+	4.45693i	0.0744845	+	0.229240i
$379$	−18.0760	+	13.1330i	−0.928501	+	0.674595i	−0.945625	−	0.325258i	$-0.894549\pi$
$379$	−18.0760	+	13.1330i	−0.928501	+	0.674595i	0.0171244	+	0.999853i	$0.494549\pi$
$380$		0			0
$381$	−13.6846	−	42.1168i	−0.701083	−	2.15771i
$382$	−2.47214	+	7.60845i	−0.126485	+	0.389282i
$383$	27.6216	+	20.0682i	1.41140	+	1.02544i	0.993118	+	0.117121i	$0.0373664\pi$
$383$	27.6216	+	20.0682i	1.41140	+	1.02544i	0.418278	+	0.908319i	$0.362634\pi$
$384$	−29.8579			−1.52368
$385$		0			0
$386$	2.82843			0.143963
$387$	−24.2705	−	17.6336i	−1.23374	−	0.896364i
$388$	4.32624	−	13.3148i	0.219631	−	0.675956i
$389$	−7.61029	−	23.4221i	−0.385857	−	1.18755i	−0.935857	−	0.352381i	$-0.885372\pi$
$389$	−7.61029	−	23.4221i	−0.385857	−	1.18755i	0.550000	−	0.835165i	$-0.314628\pi$
$390$	6.47214	−	4.70228i	0.327729	−	0.238109i
$391$	2.68085	−	1.94775i	0.135576	−	0.0985019i
$392$	1.47010	+	4.52452i	0.0742515	+	0.228523i
$393$	−9.88854	+	30.4338i	−0.498811	+	1.53518i
$394$	−1.73302	−	1.25912i	−0.0873085	−	0.0634333i
$395$	4.00000			0.201262
$396$		0			0
$397$	13.3137			0.668196			0.334098	−	0.942538i	$-0.391568\pi$
$397$	13.3137			0.668196			0.334098	+	0.942538i	$0.391568\pi$
$398$	−7.25734	−	5.27276i	−0.363777	−	0.264300i
$399$		0			0
$400$	0.927051	+	2.85317i	0.0463525	+	0.142658i
$401$	−14.0071	+	10.1767i	−0.699480	+	0.508202i	−0.879763	−	0.475413i	$-0.842299\pi$
$401$	−14.0071	+	10.1767i	−0.699480	+	0.508202i	0.180283	+	0.983615i	$0.442299\pi$
$402$	4.25125	−	3.08871i	0.212033	−	0.154051i
$403$		0			0
$404$	−7.52245	+	23.1517i	−0.374256	+	1.15184i
$405$	0.809017	+	0.587785i	0.0402004	+	0.0292073i
$406$	−6.34315			−0.314805
$407$		0			0
$408$	5.25483			0.260153
$409$	28.2918	+	20.5552i	1.39894	+	1.01639i	0.994817	+	0.101683i	$0.0324227\pi$
$409$	28.2918	+	20.5552i	1.39894	+	1.01639i	0.404122	+	0.914705i	$0.367577\pi$
$410$	0.767994	−	2.36364i	0.0379285	−	0.116732i
$411$	20.0770	+	61.7907i	0.990326	+	3.04791i
$412$	1.73302	−	1.25912i	0.0853800	−	0.0620322i
$413$	15.6251	−	11.3523i	0.768862	−	0.558611i
$414$	1.81018	+	5.57116i	0.0889655	+	0.273808i
$415$	−1.85410	+	5.70634i	−0.0910143	+	0.280113i
$416$	−24.3855	−	17.7171i	−1.19560	−	0.868652i
$417$	11.3137			0.554035
$418$		0			0
$419$	−14.3431			−0.700709			−0.350354	−	0.936617i	$-0.613939\pi$
$419$	−14.3431			−0.700709			−0.350354	+	0.936617i	$0.613939\pi$
$420$	−8.36778	−	6.07955i	−0.408306	−	0.296652i
$421$	−1.85410	+	5.70634i	−0.0903634	+	0.278110i	−0.986018	−	0.166641i	$-0.946708\pi$
$421$	−1.85410	+	5.70634i	−0.0903634	+	0.278110i	0.895654	+	0.444751i	$0.146708\pi$
$422$	2.04798	+	6.30305i	0.0996943	+	0.306828i
$423$	11.4412	−	8.31254i	0.556292	−	0.404169i
$424$	0.440231	−	0.319847i	0.0213795	−	0.0155331i
$425$	−0.362036	−	1.11423i	−0.0175613	−	0.0540482i
$426$	−4.09597	+	12.6061i	−0.198450	+	0.610767i
$427$	21.5420	+	15.6512i	1.04249	+	0.757415i
$428$	−6.68629			−0.323194
$429$		0			0
$430$	−2.48528			−0.119851
$431$	9.15298	+	6.65003i	0.440884	+	0.320321i	0.785986	−	0.618244i	$-0.212156\pi$
$431$	9.15298	+	6.65003i	0.440884	+	0.320321i	−0.345102	+	0.938565i	$0.612156\pi$
$432$	5.24419	−	16.1400i	0.252311	−	0.776534i
$433$	1.13003	+	3.47788i	0.0543058	+	0.167136i	0.974531	−	0.224254i	$-0.0719944\pi$
$433$	1.13003	+	3.47788i	0.0543058	+	0.167136i	−0.920225	+	0.391390i	$0.871994\pi$
$434$		0			0
$435$	−17.5208	+	12.7296i	−0.840056	+	0.610337i
$436$	2.06618	+	6.35904i	0.0989520	+	0.304543i
$437$		0			0
$438$	−6.47214	−	4.70228i	−0.309251	−	0.224684i
$439$	16.0000			0.763638			0.381819	−	0.924237i	$-0.375298\pi$
$439$	16.0000			0.763638			0.381819	+	0.924237i	$0.375298\pi$
$440$		0			0
$441$	−15.0000			−0.714286
$442$	2.68085	+	1.94775i	0.127515	+	0.0926450i
$443$	−6.54238	+	20.1354i	−0.310838	+	0.956660i	0.666596	+	0.745419i	$0.267751\pi$
$443$	−6.54238	+	20.1354i	−0.310838	+	0.956660i	−0.977434	+	0.211241i	$0.932249\pi$
$444$	−5.84403	−	17.9861i	−0.277346	−	0.853582i
$445$	7.53495	−	5.47446i	0.357191	−	0.259514i
$446$	1.73302	−	1.25912i	0.0820611	−	0.0596209i
$447$	−10.1885	−	31.3569i	−0.481898	−	1.48313i
$448$	−2.57817	+	7.93480i	−0.121807	+	0.374884i
$449$	13.4519	+	9.77335i	0.634833	+	0.461233i	0.858071	−	0.513531i	$-0.171663\pi$
$449$	13.4519	+	9.77335i	0.634833	+	0.461233i	−0.223238	+	0.974764i	$0.571663\pi$
$450$	2.07107			0.0976311
$451$		0			0
$452$	−15.2548			−0.717527
$453$	−27.4589	−	19.9501i	−1.29013	−	0.937337i
$454$	−0.343843	+	1.05824i	−0.0161373	+	0.0496656i
$455$	−4.22020	−	12.9884i	−0.197846	−	0.608907i
$456$		0			0
$457$	−13.3369	+	9.68981i	−0.623873	+	0.453270i	−0.854272	−	0.519826i	$-0.825997\pi$
$457$	−13.3369	+	9.68981i	−0.623873	+	0.453270i	0.230399	+	0.973096i	$0.425997\pi$
$458$	−2.72813	−	8.39633i	−0.127477	−	0.392335i
$459$	−2.04798	+	6.30305i	−0.0955917	+	0.294201i
$460$	−4.18389	−	3.03977i	−0.195075	−	0.141730i
$461$	32.6274			1.51961			0.759805	−	0.650151i	$-0.225294\pi$
$461$	32.6274			1.51961			0.759805	+	0.650151i	$0.225294\pi$
$462$		0			0
$463$	22.1421			1.02903			0.514516	−	0.857481i	$-0.327972\pi$
$463$	22.1421			1.02903			0.514516	+	0.857481i	$0.327972\pi$
$464$	18.5836	+	13.5018i	0.862721	+	0.626803i
$465$		0			0
$466$	−2.83417	−	8.72268i	−0.131290	−	0.404071i
$467$	7.41996	−	5.39092i	0.343355	−	0.249462i	−0.402721	−	0.915323i	$-0.631936\pi$
$467$	7.41996	−	5.39092i	0.343355	−	0.249462i	0.746076	+	0.665861i	$0.231936\pi$
$468$	50.5040	−	36.6933i	2.33455	−	1.69615i
$469$	−2.77206	−	8.53151i	−0.128002	−	0.393949i
$470$	0.362036	−	1.11423i	0.0166995	−	0.0513957i
$471$	32.0354	+	23.2751i	1.47612	+	1.07246i
$472$	15.3137			0.704871
$473$		0			0
$474$	−4.68629			−0.215248
$475$		0			0
$476$	1.32391	−	4.07458i	0.0606814	−	0.186758i
$477$	0.530189	+	1.63176i	0.0242757	+	0.0747129i
$478$	−0.229980	+	0.167090i	−0.0105191	+	0.00764254i
$479$	−29.1246	+	21.1603i	−1.33074	+	0.966837i	−0.331007	+	0.943628i	$0.607388\pi$
$479$	−29.1246	+	21.1603i	−1.33074	+	0.966837i	−0.999731	+	0.0232090i	$0.992612\pi$
$480$	−3.85816	−	11.8742i	−0.176100	−	0.541981i
$481$	7.71633	−	23.7484i	0.351834	−	1.08283i
$482$	2.01063	+	1.46081i	0.0915819	+	0.0665382i
$483$	16.0000			0.728025
$484$		0			0
$485$	7.65685			0.347680
$486$	4.73911	+	3.44317i	0.214970	+	0.156185i
$487$	−2.32218	+	7.14692i	−0.105228	+	0.323858i	−0.989784	−	0.142576i	$-0.954461\pi$
$487$	−2.32218	+	7.14692i	−0.105228	+	0.323858i	0.884556	+	0.466434i	$0.154461\pi$
$488$	6.52418	+	20.0794i	0.295336	+	0.908950i
$489$	1.11044	−	0.806784i	0.0502160	−	0.0364840i
$490$	−1.00532	+	0.730406i	−0.0454156	+	0.0329964i
$491$	7.20433	+	22.1727i	0.325127	+	1.00064i	0.971383	+	0.237517i	$0.0763337\pi$
$491$	7.20433	+	22.1727i	0.325127	+	1.00064i	−0.646256	+	0.763120i	$0.723666\pi$
$492$	9.58862	−	29.5107i	0.432289	−	1.33045i
$493$	−7.25734	−	5.27276i	−0.326854	−	0.237473i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	18.3060	+	13.3001i	0.821135	+	0.596589i
$498$	2.17222	−	6.68539i	0.0973393	−	0.299580i
$499$	−0.511996	−	1.57576i	−0.0229201	−	0.0705408i	0.938942	−	0.344075i	$-0.111807\pi$
$499$	−0.511996	−	1.57576i	−0.0229201	−	0.0705408i	−0.961862	+	0.273534i	$0.911807\pi$
$500$	−1.47923	+	1.07472i	−0.0661531	+	0.0480631i
$501$	25.1033	−	18.2386i	1.12153	−	0.814843i
$502$	1.53599	+	4.72729i	0.0685545	+	0.210989i
$503$	8.84636	−	27.2263i	0.394440	−	1.21396i	−0.534957	−	0.844879i	$-0.679672\pi$
$503$	8.84636	−	27.2263i	0.394440	−	1.21396i	0.929397	−	0.369081i	$-0.120328\pi$
$504$	12.8293	+	9.32102i	0.571462	+	0.415191i
$505$	−13.3137			−0.592452
$506$		0			0
$507$	95.1127			4.22410
$508$	−23.1601	−	16.8268i	−1.02756	−	0.746567i
$509$	2.87809	−	8.85786i	0.127569	−	0.392618i	−0.866791	−	0.498671i	$-0.833821\pi$
$509$	2.87809	−	8.85786i	0.127569	−	0.392618i	0.994360	+	0.106053i	$0.0338215\pi$
$510$	0.424151	+	1.30540i	0.0187817	+	0.0578043i
$511$	−11.0486	+	8.02730i	−0.488762	+	0.355107i
$512$	−18.4111	+	13.3764i	−0.813663	+	0.591161i
$513$		0			0
$514$	1.70414	−	5.24481i	0.0751665	−	0.231339i
$515$	0.947822	+	0.688633i	0.0417660	+	0.0303448i
$516$	−31.0294			−1.36599
$517$		0			0
$518$	3.02944			0.133106
$519$	14.0547	+	10.2113i	0.616934	+	0.448228i
$520$	3.34617	−	10.2984i	0.146739	−	0.451617i
$521$	0.830110	+	2.55482i	0.0363678	+	0.111928i	0.967592	−	0.252517i	$-0.0812585\pi$
$521$	0.830110	+	2.55482i	0.0363678	+	0.111928i	−0.931225	+	0.364446i	$0.881258\pi$
$522$	12.8293	−	9.32102i	0.561522	−	0.407970i
$523$	30.4174	−	22.0995i	1.33006	−	0.966345i	0.330313	−	0.943872i	$-0.392846\pi$
$523$	30.4174	−	22.0995i	1.33006	−	0.966345i	0.999747	−	0.0224738i	$-0.00715424\pi$
$524$	6.39242	+	19.6738i	0.279254	+	0.859455i
$525$	1.74806	−	5.37999i	0.0762918	−	0.234802i
$526$	7.69757	+	5.59261i	0.335630	+	0.243849i
$527$		0			0
$528$		0			0
$529$	−15.0000			−0.652174
$530$	0.114990	+	0.0835452i	0.00499485	+	0.00362897i
$531$	−14.9207	+	45.9211i	−0.647502	+	1.99280i
$532$		0			0
$533$	33.1459	−	24.0819i	1.43571	−	1.04310i
$534$	−8.82774	+	6.41373i	−0.382014	+	0.277549i
$535$	−1.13003	−	3.47788i	−0.0488555	−	0.150362i
$536$	2.19794	−	6.76458i	0.0949368	−	0.292185i
$537$	3.79129	+	2.75453i	0.163606	+	0.118867i
$538$	−2.20101			−0.0948923
$539$		0			0
$540$	10.3431			0.445098
$541$	4.85410	+	3.52671i	0.208694	+	0.151625i	0.687223	−	0.726447i	$-0.258830\pi$
$541$	4.85410	+	3.52671i	0.208694	+	0.151625i	−0.478529	+	0.878072i	$0.658830\pi$
$542$	1.96014	−	6.03269i	0.0841952	−	0.259126i
$543$	−1.14822	−	3.53387i	−0.0492750	−	0.151653i
$544$	4.18389	−	3.03977i	0.179383	−	0.130329i
$545$	−2.95846	+	2.14944i	−0.126726	+	0.0920721i
$546$	4.94427	+	15.2169i	0.211595	+	0.651223i
$547$	10.5066	−	32.3359i	0.449229	−	1.38258i	−0.428550	−	0.903518i	$-0.640975\pi$
$547$	10.5066	−	32.3359i	0.449229	−	1.38258i	0.877779	−	0.479066i	$-0.159025\pi$
$548$	33.9787	+	24.6870i	1.45150	+	1.05458i
$549$	−66.5685			−2.84108
$550$		0			0
$551$		0			0
$552$	10.2634	+	7.45682i	0.436840	+	0.317383i
$553$	−2.47214	+	7.60845i	−0.105126	+	0.323544i
$554$	−0.149960	−	0.461530i	−0.00637120	−	0.0196085i
$555$	8.36778	−	6.07955i	0.355193	−	0.258062i
$556$	5.91691	−	4.29889i	0.250933	−	0.182314i
$557$	−11.7866	−	36.2753i	−0.499413	−	1.53703i	−0.809965	−	0.586478i	$-0.800514\pi$
$557$	−11.7866	−	36.2753i	−0.499413	−	1.53703i	0.310552	−	0.950556i	$-0.399486\pi$
$558$		0			0
$559$	−33.1459	−	24.0819i	−1.40192	−	1.01856i
$560$	−6.00000			−0.253546
$561$		0			0
$562$	2.20101			0.0928440
$563$	9.43059	+	6.85173i	0.397452	+	0.288766i	0.768502	−	0.639847i	$-0.221002\pi$
$563$	9.43059	+	6.85173i	0.397452	+	0.288766i	−0.371050	+	0.928613i	$0.621002\pi$
$564$	4.52012	−	13.9115i	0.190331	−	0.585780i
$565$	−2.57817	−	7.93480i	−0.108465	−	0.333820i
$566$	−4.23152	+	3.07438i	−0.177864	+	0.129226i
$567$	−1.61803	+	1.17557i	−0.0679510	+	0.0493693i
$568$	5.54411	+	17.0630i	0.232626	+	0.715949i
$569$	−6.28638	+	19.3475i	−0.263539	+	0.811089i	0.728488	+	0.685059i	$0.240224\pi$
$569$	−6.28638	+	19.3475i	−0.263539	+	0.811089i	−0.992026	+	0.126030i	$0.959776\pi$
$570$		0			0
$571$	−45.9411			−1.92258			−0.961288	−	0.275545i	$-0.911142\pi$
$571$	−45.9411			−1.92258			−0.961288	+	0.275545i	$0.911142\pi$
$572$		0			0
$573$	−54.6274			−2.28209
$574$	4.02127	+	2.92162i	0.167845	+	0.121946i
$575$	0.874032	−	2.68999i	0.0364497	−	0.112181i
$576$	−6.44543	−	19.8370i	−0.268560	−	0.826542i
$577$	−5.63930	+	4.09719i	−0.234767	+	0.170568i	−0.698949	−	0.715172i	$-0.746349\pi$
$577$	−5.63930	+	4.09719i	−0.234767	+	0.170568i	0.464182	+	0.885740i	$0.346349\pi$
$578$	5.23684	−	3.80479i	0.217824	−	0.158258i
$579$	5.96826	+	18.3684i	0.248033	+	0.763366i
$580$	−4.32624	+	13.3148i	−0.179637	+	0.552867i
$581$	−9.70820	−	7.05342i	−0.402764	−	0.292625i
$582$	−8.97056			−0.371842
$583$		0			0
$584$	−10.8284			−0.448084
$585$	27.6216	+	20.0682i	1.14201	+	0.829720i
$586$	1.89802	−	5.84152i	0.0784067	−	0.241311i
$587$	8.07836	+	24.8626i	0.333430	+	1.02619i	0.967490	+	0.252908i	$0.0813870\pi$
$587$	8.07836	+	24.8626i	0.333430	+	1.02619i	−0.634061	+	0.773283i	$0.718613\pi$
$588$	−12.5517	+	9.11932i	−0.517622	+	0.376075i
$589$		0			0
$590$	1.23607	+	3.80423i	0.0508881	+	0.156618i
$591$	4.52012	−	13.9115i	0.185933	−	0.572243i
$592$	−8.87537	−	6.44833i	−0.364776	−	0.265025i
$593$	−20.4853			−0.841230			−0.420615	−	0.907239i	$-0.638186\pi$
$593$	−20.4853			−0.841230			−0.420615	+	0.907239i	$0.638186\pi$
$594$		0			0
$595$	2.34315			0.0960596
$596$	−17.2432	−	12.5279i	−0.706307	−	0.513162i
$597$	18.9288	−	58.2568i	0.774704	−	2.38429i
$598$	2.47214	+	7.60845i	0.101093	+	0.311133i
$599$	−4.57649	+	3.32502i	−0.186990	+	0.135856i	−0.677342	−	0.735668i	$-0.736868\pi$
$599$	−4.57649	+	3.32502i	−0.186990	+	0.135856i	0.490352	+	0.871525i	$0.336868\pi$
$600$	3.62867	−	2.63638i	0.148140	−	0.107630i
$601$	13.5786	+	41.7905i	0.553881	+	1.70467i	0.698881	+	0.715238i	$0.253682\pi$
$601$	13.5786	+	41.7905i	0.553881	+	1.70467i	−0.145000	+	0.989432i	$0.546318\pi$
$602$	1.53599	−	4.72729i	0.0626022	−	0.192670i
$603$	18.1433	+	13.1819i	0.738854	+	0.536809i
$604$	−21.9411			−0.892772
$605$		0			0
$606$	15.5980			0.633625
$607$	−14.7923	−	10.7472i	−0.600400	−	0.436216i	0.245621	−	0.969366i	$-0.421008\pi$
$607$	−14.7923	−	10.7472i	−0.600400	−	0.436216i	−0.846021	+	0.533150i	$0.821008\pi$
$608$		0			0
$609$	−13.3847	−	41.1938i	−0.542374	−	1.66926i
$610$	−4.46150	+	3.24147i	−0.180641	+	0.131243i
$611$	15.6251	−	11.3523i	0.632125	−	0.459265i
$612$	3.30978	+	10.1865i	0.133790	+	0.411763i
$613$	−7.86629	+	24.2099i	−0.317716	+	0.977831i	0.656905	+	0.753973i	$0.271865\pi$
$613$	−7.86629	+	24.2099i	−0.317716	+	0.977831i	−0.974622	+	0.223858i	$0.928135\pi$
$614$	−9.26797	−	6.73358i	−0.374025	−	0.271745i
$615$	16.9706			0.684319
$616$		0			0
$617$	11.6569			0.469287			0.234644	−	0.972081i	$-0.424608\pi$
$617$	11.6569			0.469287			0.234644	+	0.972081i	$0.424608\pi$
$618$	−1.11044	−	0.806784i	−0.0446686	−	0.0324536i
$619$	−7.92840	+	24.4011i	−0.318669	+	0.980764i	0.655548	+	0.755153i	$0.272438\pi$
$619$	−7.92840	+	24.4011i	−0.318669	+	0.980764i	−0.974218	+	0.225610i	$0.927562\pi$
$620$		0			0
$621$	−12.9443	+	9.40456i	−0.519436	+	0.377392i
$622$	−9.15298	+	6.65003i	−0.367001	+	0.266642i
$623$	5.75619	+	17.7157i	0.230617	+	0.709766i
$624$	17.9048	−	55.1053i	0.716765	−	2.20598i
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$	8.82843			0.352855
$627$		0			0
$628$	25.5980			1.02147
$629$	3.46605	+	2.51823i	0.138200	+	0.100408i
$630$	−1.27999	+	3.93941i	−0.0509960	+	0.156950i
$631$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$631$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$632$	−5.13171	+	3.72841i	−0.204129	+	0.148308i
$633$	−36.6119	+	26.6001i	−1.45519	+	1.05726i
$634$	2.72813	+	8.39633i	0.108348	+	0.333461i
$635$	4.83823	−	14.8906i	0.191999	−	0.590914i
$636$	1.43568	+	1.04309i	0.0569286	+	0.0413610i
$637$	−20.4853			−0.811656
$638$		0			0
$639$	−56.5685			−2.23782
$640$	−8.54027	−	6.20487i	−0.337584	−	0.245269i
$641$	9.27051	−	28.5317i	0.366163	−	1.12693i	−0.583086	−	0.812410i	$-0.698155\pi$
$641$	9.27051	−	28.5317i	0.366163	−	1.12693i	0.949250	−	0.314524i	$-0.101845\pi$
$642$	1.32391	+	4.07458i	0.0522507	+	0.160811i
$643$	−40.0106	+	29.0694i	−1.57786	+	1.14639i	−0.658773	+	0.752341i	$0.728924\pi$
$643$	−40.0106	+	29.0694i	−1.57786	+	1.14639i	−0.919091	+	0.394044i	$0.871076\pi$
$644$	8.36778	−	6.07955i	0.329737	−	0.239568i
$645$	−5.24419	−	16.1400i	−0.206490	−	0.635510i
$646$		0			0
$647$	28.4068	+	20.6387i	1.11679	+	0.811392i	0.983719	−	0.179715i	$-0.0575176\pi$
$647$	28.4068	+	20.6387i	1.11679	+	0.811392i	0.133067	+	0.991107i	$0.457518\pi$
$648$	−1.58579			−0.0622956
$649$		0			0
$650$	2.82843			0.110940
$651$		0			0
$652$	0.274191	−	0.843874i	0.0107382	−	0.0330487i
$653$	0.106038	+	0.326351i	0.00414958	+	0.0127711i	0.953110	−	0.302624i	$-0.0978628\pi$
$653$	0.106038	+	0.326351i	0.00414958	+	0.0127711i	−0.948960	+	0.315396i	$0.897863\pi$
$654$	3.46605	−	2.51823i	0.135533	−	0.0984706i
$655$	−9.15298	+	6.65003i	−0.357637	+	0.259838i
$656$	−5.56231	−	17.1190i	−0.217172	−	0.668385i
$657$	10.5505	−	32.4711i	0.411614	−	1.26682i
$658$	1.89564	+	1.37727i	0.0738999	+	0.0536914i
$659$	21.9411			0.854705			0.427352	−	0.904085i	$-0.359446\pi$
$659$	21.9411			0.854705			0.427352	+	0.904085i	$0.359446\pi$
$660$		0			0
$661$	−0.627417			−0.0244037			−0.0122018	−	0.999926i	$-0.503884\pi$
$661$	−0.627417			−0.0244037			−0.0122018	+	0.999926i	$0.503884\pi$
$662$	−5.13171	−	3.72841i	−0.199450	−	0.144909i
$663$	−6.99226	+	21.5200i	−0.271557	+	0.835766i
$664$	−2.94021	−	9.04904i	−0.114102	−	0.351171i
$665$		0			0
$666$	−6.12717	+	4.45165i	−0.237423	+	0.172498i
$667$	−6.69234	−	20.5969i	−0.259128	−	0.797515i
$668$	6.19853	−	19.0771i	0.239828	−	0.738116i
$669$	11.8338	+	8.59778i	0.457522	+	0.332409i
$670$	1.85786			0.0717756
$671$		0			0
$672$	24.9706			0.963260
$673$	3.62867	+	2.63638i	0.139875	+	0.101625i	0.655522	−	0.755176i	$-0.272449\pi$
$673$	3.62867	+	2.63638i	0.139875	+	0.101625i	−0.515647	+	0.856801i	$0.672449\pi$
$674$	0.449881	−	1.38459i	0.0173288	−	0.0533324i
$675$	1.74806	+	5.37999i	0.0672830	+	0.207076i
$676$	49.7426	−	36.1401i	1.91318	−	1.39001i
$677$	13.8921	−	10.0932i	0.533917	−	0.387913i	−0.287904	−	0.957659i	$-0.592958\pi$
$677$	13.8921	−	10.0932i	0.533917	−	0.387913i	0.821821	+	0.569746i	$0.192958\pi$
$678$	3.02052	+	9.29620i	0.116002	+	0.357018i
$679$	−4.73220	+	14.5642i	−0.181605	+	0.558923i
$680$	1.50304	+	1.09203i	0.0576391	+	0.0418773i
$681$	−7.59798			−0.291155
$682$		0			0
$683$	31.7990			1.21675			0.608377	−	0.793648i	$-0.291821\pi$
$683$	31.7990			1.21675			0.608377	+	0.793648i	$0.291821\pi$
$684$		0			0
$685$	−7.09829	+	21.8463i	−0.271212	+	0.834704i
$686$	−2.55998	−	7.87881i	−0.0977405	−	0.300814i
$687$	48.7710	−	35.4342i	1.86073	−	1.35190i
$688$	−14.5623	+	10.5801i	−0.555183	+	0.403364i
$689$	0.724072	+	2.22846i	0.0275849	+	0.0848977i
$690$	−1.02399	+	3.15152i	−0.0389827	+	0.119976i
$691$	13.4995	+	9.80796i	0.513545	+	0.373112i	0.814167	−	0.580631i	$-0.197194\pi$
$691$	13.4995	+	9.80796i	0.513545	+	0.373112i	−0.300622	+	0.953743i	$0.597194\pi$
$692$	11.2304			0.426918
$693$		0			0
$694$	9.51472			0.361174
$695$	3.23607	+	2.35114i	0.122751	+	0.0891839i
$696$	10.6126	−	32.6623i	0.402270	−	1.23806i
$697$	2.17222	+	6.68539i	0.0822785	+	0.253227i
$698$	−2.33588	+	1.69711i	−0.0884142	+	0.0642367i
$699$	50.6666	−	36.8115i	1.91639	−	1.39234i
$700$	−1.13003	−	3.47788i	−0.0427111	−	0.131451i
$701$	−10.0824	+	31.0305i	−0.380808	+	1.17201i	0.558668	+	0.829391i	$0.311313\pi$
$701$	−10.0824	+	31.0305i	−0.380808	+	1.17201i	−0.939476	+	0.342615i	$0.888687\pi$
$702$	−12.9443	−	9.40456i	−0.488550	−	0.354952i
$703$		0			0
$704$		0			0
$705$	8.00000			0.301297
$706$	0.440231	+	0.319847i	0.0165683	+	0.0120376i
$707$	8.22832	−	25.3242i	0.309458	−	0.952414i
$708$	15.4327	+	47.4968i	0.579995	+	1.78504i
$709$	16.6879	−	12.1245i	0.626728	−	0.455345i	−0.228537	−	0.973535i	$-0.573394\pi$
$709$	16.6879	−	12.1245i	0.626728	−	0.455345i	0.855265	+	0.518190i	$0.173394\pi$
$710$	−3.79129	+	2.75453i	−0.142285	+	0.103376i
$711$	−6.18034	−	19.0211i	−0.231781	−	0.713348i
$712$	−4.56404	+	14.0467i	−0.171045	+	0.526422i
$713$		0			0
$714$	−2.74517			−0.102735
$715$		0			0
$716$	3.02944			0.113215
$717$	−1.57040	−	1.14096i	−0.0586478	−	0.0426101i
$718$	−2.98413	+	9.18421i	−0.111367	+	0.342752i
$719$	9.16447	+	28.2053i	0.341777	+	1.05188i	0.963287	+	0.268475i	$0.0865197\pi$
$719$	9.16447	+	28.2053i	0.341777	+	1.05188i	−0.621509	+	0.783407i	$0.713480\pi$
$720$	12.1353	−	8.81678i	0.452254	−	0.328582i
$721$	−1.89564	+	1.37727i	−0.0705975	+	0.0512921i
$722$	−2.43198	−	7.48487i	−0.0905090	−	0.278558i
$723$	−5.24419	+	16.1400i	−0.195034	+	0.600252i
$724$	−1.94328	−	1.41187i	−0.0722213	−	0.0524718i
$725$	−7.65685			−0.284368
$726$		0			0
$727$	−36.4853			−1.35316			−0.676582	−	0.736367i	$-0.736540\pi$
$727$	−36.4853			−1.35316			−0.676582	+	0.736367i	$0.736540\pi$
$728$	17.5208	+	12.7296i	0.649363	+	0.471790i
$729$	−13.2877	+	40.8954i	−0.492138	+	1.51465i
$730$	−0.874032	−	2.68999i	−0.0323494	−	0.0995611i
$731$	5.68693	−	4.13180i	0.210339	−	0.152820i
$732$	−55.7031	+	40.4707i	−2.05885	+	1.49584i
$733$	−10.3384	−	31.8184i	−0.381858	−	1.17524i	−0.938734	−	0.344643i	$-0.888000\pi$
$733$	−10.3384	−	31.8184i	−0.381858	−	1.17524i	0.556875	−	0.830596i	$-0.312000\pi$
$734$	1.08611	−	3.34270i	0.0400890	−	0.123381i
$735$	−6.86474	−	4.98752i	−0.253210	−	0.183968i
$736$	12.4853			0.460214
$737$		0			0
$738$	−12.4264			−0.457422
$739$	−30.6950	−	22.3012i	−1.12913	−	0.820364i	−0.143566	−	0.989641i	$-0.545857\pi$
$739$	−30.6950	−	22.3012i	−1.12913	−	0.820364i	−0.985569	+	0.169277i	$0.945857\pi$
$740$	2.06618	−	6.35904i	0.0759542	−	0.233763i
$741$		0			0
$742$	−0.229980	+	0.167090i	−0.00844284	+	0.00613408i
$743$	23.9453	−	17.3973i	0.878467	−	0.638243i	−0.0543787	−	0.998520i	$-0.517318\pi$
$743$	23.9453	−	17.3973i	0.878467	−	0.638243i	0.932845	+	0.360277i	$0.117318\pi$
$744$		0			0
$745$	3.60217	−	11.0863i	0.131973	−	0.406172i
$746$	−1.27306	−	0.924935i	−0.0466102	−	0.0338643i
$747$	30.0000			1.09764
$748$		0			0
$749$	7.31371			0.267237
$750$	0.947822	+	0.688633i	0.0346096	+	0.0251453i
$751$	−4.94427	+	15.2169i	−0.180419	+	0.555273i	−0.999839	−	0.0179203i	$-0.994295\pi$
$751$	−4.94427	+	15.2169i	−0.180419	+	0.555273i	0.819420	+	0.573193i	$0.194295\pi$
$752$	−2.62210	−	8.06998i	−0.0956180	−	0.294282i
$753$	−27.4589	+	19.9501i	−1.00066	+	0.727022i
$754$	17.5208	−	12.7296i	0.638069	−	0.463584i
$755$	−3.70820	−	11.4127i	−0.134955	−	0.415350i
$756$	−6.39242	+	19.6738i	−0.232490	+	0.715530i
$757$	7.53495	+	5.47446i	0.273862	+	0.198973i	0.716236	−	0.697858i	$-0.245863\pi$
$757$	7.53495	+	5.47446i	0.273862	+	0.198973i	−0.442374	+	0.896831i	$0.645863\pi$
$758$	9.25483			0.336151
$759$		0			0
$760$		0			0
$761$	−24.2705	−	17.6336i	−0.879805	−	0.639216i	0.0533947	−	0.998573i	$-0.482996\pi$
$761$	−24.2705	−	17.6336i	−0.879805	−	0.639216i	−0.933200	+	0.359358i	$0.882996\pi$
$762$	−5.66834	+	17.4454i	−0.205342	+	0.631979i
$763$	−2.26006	−	6.95575i	−0.0818197	−	0.251815i
$764$	−28.5694	+	20.7569i	−1.03360	+	0.750957i
$765$	−4.73911	+	3.44317i	−0.171343	+	0.124488i
$766$	−4.37016	−	13.4500i	−0.157900	−	0.485967i
$767$	−20.3769	+	62.7137i	−0.735768	+	2.26446i
$768$	−9.08562	−	6.60109i	−0.327849	−	0.238196i
$769$	−14.9706			−0.539852			−0.269926	−	0.962881i	$-0.586999\pi$
$769$	−14.9706			−0.539852			−0.269926	+	0.962881i	$0.586999\pi$
$770$		0			0
$771$	37.6569			1.35618
$772$	10.1008	+	7.33866i	0.363536	+	0.264124i
$773$	−9.35835	+	28.8021i	−0.336597	+	1.03594i	0.629334	+	0.777135i	$0.283328\pi$
$773$	−9.35835	+	28.8021i	−0.336597	+	1.03594i	−0.965930	+	0.258803i	$0.916672\pi$
$774$	3.83997	+	11.8182i	0.138025	+	0.424797i
$775$		0			0
$776$	−9.82319	+	7.13697i	−0.352632	+	0.256202i
$777$	6.39242	+	19.6738i	0.229327	+	0.705795i
$778$	−3.15229	+	9.70174i	−0.113015	+	0.347824i
$779$		0			0
$780$	35.3137			1.26443
$781$		0			0
$782$	−1.37258			−0.0490835
$783$	35.0415	+	25.4592i	1.25228	+	0.909836i
$784$	−2.78115	+	8.55951i	−0.0993269	+	0.305697i
$785$	4.32624	+	13.3148i	0.154410	+	0.475225i
$786$	10.7234	−	7.79100i	0.382491	−	0.277896i
$787$	15.3475	−	11.1506i	0.547080	−	0.397477i	−0.279628	−	0.960108i	$-0.590211\pi$
$787$	15.3475	−	11.1506i	0.547080	−	0.397477i	0.826708	+	0.562632i	$0.190211\pi$
$788$	−2.92202	−	8.99304i	−0.104093	−	0.320364i
$789$	−20.0770	+	61.7907i	−0.714760	+	2.19981i
$790$	−1.34042	−	0.973874i	−0.0476901	−	0.0346489i
$791$	16.6863			0.593296
$792$		0			0
$793$	−90.9117			−3.22837
$794$	−4.46150	−	3.24147i	−0.158333	−	0.115035i
$795$	−0.299920	+	0.923060i	−0.0106371	+	0.0327376i
$796$	−12.2364	−	37.6599i	−0.433709	−	1.33482i
$797$	10.2158	−	7.42221i	0.361862	−	0.262908i	−0.391966	−	0.919980i	$-0.628205\pi$
$797$	10.2158	−	7.42221i	0.361862	−	0.262908i	0.753828	+	0.657071i	$0.228205\pi$
$798$		0			0
$799$	1.02399	+	3.15152i	0.0362262	+	0.111493i
$800$	1.36407	−	4.19817i	0.0482271	−	0.148428i
$801$	−37.6747	−	27.3723i	−1.33117	−	0.967153i
$802$	7.17157			0.253237
$803$		0			0
$804$	23.1960			0.818058
$805$	4.57649	+	3.32502i	0.161300	+	0.117191i
$806$		0			0
$807$	−4.64435	−	14.2938i	−0.163489	−	0.503167i
$808$	17.0805	−	12.4097i	0.600891	−	0.436573i
$809$	18.5836	−	13.5018i	0.653364	−	0.474697i	−0.211052	−	0.977475i	$-0.567689\pi$
$809$	18.5836	−	13.5018i	0.653364	−	0.474697i	0.864415	+	0.502778i	$0.167689\pi$
$810$	−0.127999	−	0.393941i	−0.00449743	−	0.0138417i
$811$	4.30804	−	13.2588i	0.151276	−	0.465579i	−0.846489	−	0.532407i	$-0.821288\pi$
$811$	4.30804	−	13.2588i	0.151276	−	0.465579i	0.997765	+	0.0668274i	$0.0212877\pi$
$812$	−22.6525	−	16.4580i	−0.794946	−	0.577562i
$813$	43.3137			1.51908
$814$		0			0
$815$	0.485281			0.0169987
$816$	8.04254	+	5.84325i	0.281545	+	0.204555i
$817$		0			0
$818$	−4.47620	−	13.7763i	−0.156507	−	0.481678i
$819$	−55.2431	+	40.1365i	−1.93035	+	1.40248i
$820$	8.87537	−	6.44833i	0.309941	−	0.225186i
$821$	5.77438	+	17.7717i	0.201527	+	0.620237i	0.999838	+	0.0179916i	$0.00572722\pi$
$821$	5.77438	+	17.7717i	0.201527	+	0.620237i	−0.798311	+	0.602246i	$0.794273\pi$
$822$	8.31617	−	25.5945i	0.290060	−	0.892712i
$823$	−29.5172	−	21.4455i	−1.02891	−	0.747543i	−0.0608161	−	0.998149i	$-0.519370\pi$
$823$	−29.5172	−	21.4455i	−1.02891	−	0.747543i	−0.968089	+	0.250605i	$0.919370\pi$
$824$	−1.85786			−0.0647218
$825$		0			0
$826$	−8.00000			−0.278356
$827$	−27.7366	−	20.1518i	−0.964495	−	0.700746i	−0.0103044	−	0.999947i	$-0.503280\pi$
$827$	−27.7366	−	20.1518i	−0.964495	−	0.700746i	−0.954190	+	0.299201i	$0.903280\pi$
$828$	−7.99052	+	24.5923i	−0.277690	+	0.854641i
$829$	5.56231	+	17.1190i	0.193187	+	0.594568i	0.999993	+	0.00375172i	$0.00119421\pi$
$829$	5.56231	+	17.1190i	0.193187	+	0.594568i	−0.806806	+	0.590816i	$0.798806\pi$
$830$	2.01063	−	1.46081i	0.0697902	−	0.0507055i
$831$	2.68085	−	1.94775i	0.0929975	−	0.0675667i
$832$	−8.80244	−	27.0911i	−0.305170	−	0.939215i
$833$	1.08611	−	3.34270i	0.0376314	−	0.115818i
$834$	−3.79129	−	2.75453i	−0.131282	−	0.0953817i
$835$	10.9706			0.379652
$836$		0			0
$837$		0			0
$838$	4.80647	+	3.49211i	0.166037	+	0.120633i
$839$	11.6366	−	35.8138i	0.401740	−	1.23643i	−0.521846	−	0.853040i	$-0.674757\pi$
$839$	11.6366	−	35.8138i	0.401740	−	1.23643i	0.923587	−	0.383390i	$-0.125243\pi$
$840$	2.77206	+	8.53151i	0.0956450	+	0.294365i
$841$	−23.9691	+	17.4146i	−0.826520	+	0.600502i
$842$	2.01063	−	1.46081i	0.0692911	−	0.0503429i
$843$	4.64435	+	14.2938i	0.159960	+	0.492306i
$844$	−9.04024	+	27.8230i	−0.311178	+	0.957707i
$845$	27.2052	+	19.7657i	0.935886	+	0.679961i
$846$	−5.85786			−0.201398
$847$		0			0
$848$	1.02944			0.0353510
$849$	−28.8946	−	20.9932i	−0.991661	−	0.720484i
$850$	−0.149960	+	0.461530i	−0.00514359	+	0.0158303i
$851$	3.19621	+	9.83692i	0.109565	+	0.337205i
$852$	−47.3353	+	34.3911i	−1.62168	+	1.17822i
$853$	−26.2811	+	19.0944i	−0.899849	+	0.653779i	−0.938427	−	0.345477i	$-0.887717\pi$
$853$	−26.2811	+	19.0944i	−0.899849	+	0.653779i	0.0385780	+	0.999256i	$0.487717\pi$
$854$	−3.40828	−	10.4896i	−0.116629	−	0.358947i
$855$		0			0
$856$	4.69148	+	3.40856i	0.160352	+	0.116502i
$857$	48.7696			1.66594			0.832968	−	0.553321i	$-0.186640\pi$
$857$	48.7696			1.66594			0.832968	+	0.553321i	$0.186640\pi$
$858$		0			0
$859$	−32.2843			−1.10153			−0.550763	−	0.834662i	$-0.685663\pi$
$859$	−32.2843			−1.10153			−0.550763	+	0.834662i	$0.685663\pi$
$860$	−8.87537	−	6.44833i	−0.302648	−	0.219886i
$861$	−10.4884	+	32.2799i	−0.357443	+	1.10010i
$862$	−1.44814	−	4.45693i	−0.0493240	−	0.151804i
$863$	11.9964	−	8.71593i	0.408364	−	0.296694i	−0.364575	−	0.931174i	$-0.618786\pi$
$863$	11.9964	−	8.71593i	0.408364	−	0.296694i	0.772939	+	0.634480i	$0.218786\pi$
$864$	−20.2016	+	14.6773i	−0.687273	+	0.499333i
$865$	1.89802	+	5.84152i	0.0645348	+	0.198618i
$866$	0.468074	−	1.44058i	0.0159058	−	0.0489530i
$867$	35.7594	+	25.9807i	1.21445	+	0.882351i
$868$		0			0
$869$		0			0
$870$	8.97056			0.304131
$871$	24.7781	+	18.0023i	0.839574	+	0.609986i
$872$	1.79199	−	5.51517i	0.0606843	−	0.186767i
$873$	−11.8305	−	36.4105i	−0.400401	−	1.23231i
$874$		0			0
$875$	1.61803	−	1.17557i	0.0546995	−	0.0397415i
$876$	−10.9125	−	33.5853i	−0.368700	−	1.13474i
$877$	−0.449881	+	1.38459i	−0.0151914	+	0.0467543i	−0.958365	−	0.285546i	$-0.907825\pi$
$877$	−0.449881	+	1.38459i	−0.0151914	+	0.0467543i	0.943173	+	0.332301i	$0.107825\pi$
$878$	−5.36169	−	3.89550i	−0.180948	−	0.131467i
$879$	41.9411			1.41464
$880$		0			0
$881$	−52.6274			−1.77306			−0.886531	−	0.462668i	$-0.846892\pi$
$881$	−52.6274			−1.77306			−0.886531	+	0.462668i	$0.846892\pi$
$882$	5.02659	+	3.65203i	0.169254	+	0.122970i
$883$	13.2347	−	40.7323i	0.445384	−	1.37075i	−0.436679	−	0.899617i	$-0.643845\pi$
$883$	13.2347	−	40.7323i	0.445384	−	1.37075i	0.882063	−	0.471132i	$-0.156155\pi$
$884$	4.52012	+	13.9115i	0.152028	+	0.467894i
$885$	−22.0973	+	16.0546i	−0.742791	+	0.539669i
$886$	7.09472	−	5.15461i	0.238352	−	0.173173i
$887$	5.65015	+	17.3894i	0.189713	+	0.583878i	0.999998	−	0.00215907i	$-0.000687255\pi$
$887$	5.65015	+	17.3894i	0.189713	+	0.583878i	−0.810284	+	0.586037i	$0.800687\pi$
$888$	−5.06850	+	15.5992i	−0.170088	+	0.523476i
$889$	25.3333	+	18.4057i	0.849652	+	0.617309i
$890$	−3.85786			−0.129316
$891$		0			0
$892$	9.45584			0.316605
$893$		0			0
$894$	−4.22020	+	12.9884i	−0.141145	+	0.434398i
$895$	0.511996	+	1.57576i	0.0171141	+	0.0526719i
$896$	17.0805	−	12.4097i	0.570621	−	0.414580i
$897$	−44.1945	+	32.1092i	−1.47561	+	1.07209i
$898$	−2.12829	−	6.55021i	−0.0710221	−	0.218583i
$899$		0			0
$900$	7.39614	+	5.37361i	0.246538	+	0.179120i
$901$	−0.402020			−0.0133932
$902$		0			0
$903$	33.9411			1.12949
$904$	10.7037	+	7.77666i	0.355998	+	0.258648i
$905$	0.405958	−	1.24941i	0.0134945	−	0.0415318i
$906$	4.34443	+	13.3708i	0.144334	+	0.444215i
$907$	35.9893	−	26.1478i	1.19501	−	0.868223i	0.201222	−	0.979546i	$-0.435509\pi$
$907$	35.9893	−	26.1478i	1.19501	−	0.868223i	0.993784	+	0.111322i	$0.0355086\pi$
$908$	−3.97364	+	2.88702i	−0.131870	+	0.0958091i
$909$	20.5708	+	63.3104i	0.682291	+	2.09987i
$910$	−1.74806	+	5.37999i	−0.0579478	+	0.178345i
$911$	−46.8754	−	34.0569i	−1.55305	−	1.12836i	−0.941432	−	0.337204i	$-0.890519\pi$
$911$	−46.8754	−	34.0569i	−1.55305	−	1.12836i	−0.611618	−	0.791153i	$-0.709481\pi$
$912$		0			0
$913$		0			0
$914$	6.82843			0.225864
$915$	−30.4650	−	22.1341i	−1.00714	−	0.731732i
$916$	12.0426	−	37.0632i	0.397898	−	1.22460i
$917$	−6.99226	−	21.5200i	−0.230905	−	0.710651i
$918$	2.22089	−	1.61357i	0.0733002	−	0.0532557i
$919$	−25.8885	+	18.8091i	−0.853984	+	0.620456i	−0.926242	−	0.376930i	$-0.876980\pi$
$919$	−25.8885	+	18.8091i	−0.853984	+	0.620456i	0.0722574	+	0.997386i	$0.476980\pi$
$920$	1.38603	+	4.26576i	0.0456960	+	0.140638i
$921$	24.1730	−	74.3968i	0.796527	−	2.45146i
$922$	−10.9336	−	7.94375i	−0.360080	−	0.261614i
$923$	−77.2548			−2.54287
$924$		0			0
$925$	3.65685			0.120237
$926$	−7.41996	−	5.39092i	−0.243835	−	0.177156i
$927$	1.81018	−	5.57116i	0.0594541	−	0.182981i
$928$	−10.4445	−	32.1447i	−0.342856	−	1.05520i
$929$	14.0071	−	10.1767i	0.459558	−	0.333888i	−0.333800	−	0.942644i	$-0.608331\pi$
$929$	14.0071	−	10.1767i	0.459558	−	0.333888i	0.793358	+	0.608756i	$0.208331\pi$
$930$		0			0
$931$		0			0
$932$	12.5106	−	38.5038i	0.409800	−	1.26123i
$933$	−62.5005	−	45.4093i	−2.04617	−	1.48663i
$934$	−3.79899			−0.124307
$935$		0			0
$936$	−54.1421			−1.76969
$937$	40.0106	+	29.0694i	1.30709	+	0.949656i	0.999998	−	0.00202342i	$-0.000644075\pi$
$937$	40.0106	+	29.0694i	1.30709	+	0.949656i	0.307092	+	0.951680i	$0.400644\pi$
$938$	−1.14822	+	3.53387i	−0.0374908	+	0.115385i
$939$	18.6289	+	57.3337i	0.607930	+	1.87102i
$940$	4.18389	−	3.03977i	0.136463	−	0.0991465i
$941$	−23.7153	+	17.2302i	−0.773096	+	0.561687i	−0.902899	−	0.429852i	$-0.858566\pi$
$941$	−23.7153	+	17.2302i	−0.773096	+	0.561687i	0.129803	+	0.991540i	$0.458566\pi$
$942$	−5.06850	−	15.5992i	−0.165141	−	0.508251i
$943$	−5.24419	+	16.1400i	−0.170774	+	0.525590i
$944$	23.4377	+	17.0285i	0.762831	+	0.554229i
$945$	−11.3137			−0.368035
$946$		0			0
$947$	46.8284			1.52172			0.760860	−	0.648916i	$-0.224778\pi$
$947$	46.8284			1.52172			0.760860	+	0.648916i	$0.224778\pi$
$948$	−16.7356	−	12.1591i	−0.543546	−	0.394909i
$949$	14.4087	−	44.3453i	0.467725	−	1.43951i
$950$		0			0
$951$	−48.7710	+	35.4342i	−1.58151	+	1.14903i
$952$	−3.00609	+	2.18405i	−0.0974279	+	0.0707855i
$953$	−18.1790	−	55.9492i	−0.588875	−	1.81237i	−0.583118	−	0.812388i	$-0.698167\pi$
$953$	−18.1790	−	55.9492i	−0.588875	−	1.81237i	−0.00575724	−	0.999983i	$-0.501833\pi$
$954$	0.219612	−	0.675895i	0.00711019	−	0.0218829i
$955$	−15.6251	−	11.3523i	−0.505617	−	0.367352i
$956$	−1.25483			−0.0405842
$957$		0			0
$958$	14.9117			0.481775
$959$	−37.1672	−	27.0035i	−1.20019	−	0.871989i
$960$	3.64609	−	11.2215i	0.117677	−	0.362173i
$961$	−9.57953	−	29.4828i	−0.309017	−	0.951057i
$962$	−8.36778	+	6.07955i	−0.269788	+	0.196013i
$963$	−14.7923	+	10.7472i	−0.476675	+	0.346324i
$964$	3.39009	+	10.4336i	0.109187	+	0.336044i
$965$	−2.11010	+	6.49422i	−0.0679265	+	0.209056i
$966$	−5.36169	−	3.89550i	−0.172510	−	0.125336i
$967$	−18.9706			−0.610052			−0.305026	−	0.952344i	$-0.598665\pi$
$967$	−18.9706			−0.610052			−0.305026	+	0.952344i	$0.598665\pi$
$968$		0			0
$969$		0			0
$970$	−2.56586	−	1.86420i	−0.0823847	−	0.0598560i
$971$	−9.67647	+	29.7811i	−0.310533	+	0.955721i	0.667022	+	0.745038i	$0.267569\pi$
$971$	−9.67647	+	29.7811i	−0.310533	+	0.955721i	−0.977554	+	0.210683i	$0.932431\pi$
$972$	7.99052	+	24.5923i	0.256296	+	0.788798i
$973$	−6.47214	+	4.70228i	−0.207487	+	0.150748i
$974$	2.51823	−	1.82960i	0.0806892	−	0.0586241i
$975$	5.96826	+	18.3684i	0.191137	+	0.588261i
$976$	−12.3425	+	37.9863i	−0.395073	+	1.21591i
$977$	−35.3191	−	25.6609i	−1.12996	−	0.820963i	−0.144270	−	0.989538i	$-0.546084\pi$
$977$	−35.3191	−	25.6609i	−1.12996	−	0.820963i	−0.985689	+	0.168575i	$0.946084\pi$
$978$	−0.568542			−0.0181800
$979$		0			0
$980$	−5.48528			−0.175221
$981$	14.7923	+	10.7472i	0.472281	+	0.343132i
$982$	2.98413	−	9.18421i	0.0952275	−	0.293080i
$983$	−15.4948	−	47.6880i	−0.494206	−	1.52101i	−0.818190	−	0.574948i	$-0.805022\pi$
$983$	−15.4948	−	47.6880i	−0.494206	−	1.52101i	0.323983	−	0.946063i	$-0.394978\pi$
$984$	−21.7720	+	15.8183i	−0.694066	+	0.504269i
$985$	4.18389	−	3.03977i	0.133310	−	0.0968553i
$986$	1.14822	+	3.53387i	0.0365669	+	0.112541i
$987$	−4.94427	+	15.2169i	−0.157378	+	0.484359i
$988$		0			0
$989$	16.9706			0.539633
$990$		0			0
$991$	9.94113			0.315790			0.157895	−	0.987456i	$-0.449529\pi$
$991$	9.94113			0.315790			0.157895	+	0.987456i	$0.449529\pi$
$992$		0			0
$993$	13.3847	−	41.1938i	0.424750	−	1.30725i
$994$	−2.89629	−	8.91386i	−0.0918647	−	0.282730i
$995$	17.5208	−	12.7296i	0.555446	−	0.403555i
$996$	25.1033	−	18.2386i	0.795430	−	0.577914i
$997$	−2.92202	−	8.99304i	−0.0925412	−	0.284813i	0.894064	−	0.447939i	$-0.147842\pi$
$997$	−2.92202	−	8.99304i	−0.0925412	−	0.284813i	−0.986605	+	0.163127i	$0.947842\pi$
$998$	−0.212076	+	0.652702i	−0.00671314	+	0.0206609i
$999$	−16.7356	−	12.1591i	−0.529490	−	0.384697i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.g.l.81.1		8
11.2	odd	10		605.2.g.f.511.1		8
11.3	even	5	inner	605.2.g.l.366.1		8
11.4	even	5	inner	605.2.g.l.251.2		8
11.5	even	5		605.2.a.d.1.2		2
11.6	odd	10		55.2.a.b.1.1	✓	2
11.7	odd	10		605.2.g.f.251.1		8
11.8	odd	10		605.2.g.f.366.2		8
11.9	even	5	inner	605.2.g.l.511.2		8
11.10	odd	2		605.2.g.f.81.2		8
33.5	odd	10		5445.2.a.y.1.1		2
33.17	even	10		495.2.a.b.1.2		2
44.27	odd	10		9680.2.a.bn.1.1		2
44.39	even	10		880.2.a.m.1.1		2
55.17	even	20		275.2.b.d.199.2		4
55.28	even	20		275.2.b.d.199.3		4
55.39	odd	10		275.2.a.c.1.2		2
55.49	even	10		3025.2.a.o.1.1		2
77.6	even	10		2695.2.a.f.1.1		2
88.61	odd	10		3520.2.a.bn.1.1		2
88.83	even	10		3520.2.a.bo.1.2		2
132.83	odd	10		7920.2.a.ch.1.1		2
143.116	odd	10		9295.2.a.g.1.2		2
165.17	odd	20		2475.2.c.l.199.3		4
165.83	odd	20		2475.2.c.l.199.2		4
165.149	even	10		2475.2.a.x.1.1		2
220.39	even	10		4400.2.a.bn.1.2		2
220.83	odd	20		4400.2.b.q.4049.1		4
220.127	odd	20		4400.2.b.q.4049.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.a.b.1.1	✓	2	11.6	odd	10
275.2.a.c.1.2		2	55.39	odd	10
275.2.b.d.199.2		4	55.17	even	20
275.2.b.d.199.3		4	55.28	even	20
495.2.a.b.1.2		2	33.17	even	10
605.2.a.d.1.2		2	11.5	even	5
605.2.g.f.81.2		8	11.10	odd	2
605.2.g.f.251.1		8	11.7	odd	10
605.2.g.f.366.2		8	11.8	odd	10
605.2.g.f.511.1		8	11.2	odd	10
605.2.g.l.81.1		8	1.1	even	1	trivial
605.2.g.l.251.2		8	11.4	even	5	inner
605.2.g.l.366.1		8	11.3	even	5	inner
605.2.g.l.511.2		8	11.9	even	5	inner
880.2.a.m.1.1		2	44.39	even	10
2475.2.a.x.1.1		2	165.149	even	10
2475.2.c.l.199.2		4	165.83	odd	20
2475.2.c.l.199.3		4	165.17	odd	20
2695.2.a.f.1.1		2	77.6	even	10
3025.2.a.o.1.1		2	55.49	even	10
3520.2.a.bn.1.1		2	88.61	odd	10
3520.2.a.bo.1.2		2	88.83	even	10
4400.2.a.bn.1.2		2	220.39	even	10
4400.2.b.q.4049.1		4	220.83	odd	20
4400.2.b.q.4049.4		4	220.127	odd	20
5445.2.a.y.1.1		2	33.5	odd	10
7920.2.a.ch.1.1		2	132.83	odd	10
9295.2.a.g.1.2		2	143.116	odd	10
9680.2.a.bn.1.1		2	44.27	odd	10

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.335106 - 0.243469i) q^{2} +(0.874032 - 2.68999i) q^{3} +(-0.565015 - 1.73894i) q^{4} +(0.809017 - 0.587785i) q^{5} +(-0.947822 + 0.688633i) q^{6} +(0.618034 + 1.90211i) q^{7} +(-0.490035 + 1.50817i) q^{8} +(-4.04508 - 2.93893i) q^{9} -0.414214 q^{10} -5.17157 q^{12} +(-5.52431 - 4.01365i) q^{13} +(0.255998 - 0.787881i) q^{14} +(-0.874032 - 2.68999i) q^{15} +(-2.42705 + 1.76336i) q^{16} +(0.947822 - 0.688633i) q^{17} +(0.639995 + 1.96970i) q^{18} +(-1.47923 - 1.07472i) q^{20} +5.65685 q^{21} +2.82843 q^{23} +(3.62867 + 2.63638i) q^{24} +(0.309017 - 0.951057i) q^{25} +(0.874032 + 2.68999i) q^{26} +(-4.57649 + 3.32502i) q^{27} +(2.95846 - 2.14944i) q^{28} +(-2.36610 - 7.28210i) q^{29} +(-0.362036 + 1.11423i) q^{30} +4.41421 q^{32} -0.485281 q^{34} +(1.61803 + 1.17557i) q^{35} +(-2.82508 + 8.69469i) q^{36} +(1.13003 + 3.47788i) q^{37} +(-15.6251 + 11.3523i) q^{39} +(0.490035 + 1.50817i) q^{40} +(-1.85410 + 5.70634i) q^{41} +(-1.89564 - 1.37727i) q^{42} +6.00000 q^{43} -5.00000 q^{45} +(-0.947822 - 0.688633i) q^{46} +(-0.874032 + 2.68999i) q^{47} +(2.62210 + 8.06998i) q^{48} +(2.42705 - 1.76336i) q^{49} +(-0.335106 + 0.243469i) q^{50} +(-1.02399 - 3.15152i) q^{51} +(-3.85816 + 11.8742i) q^{52} +(-0.277611 - 0.201696i) q^{53} +2.34315 q^{54} -3.17157 q^{56} +(-0.980070 + 3.01635i) q^{58} +(-2.98413 - 9.18421i) q^{59} +(-4.18389 + 3.03977i) q^{60} +(10.7710 - 7.82560i) q^{61} +(3.09017 - 9.51057i) q^{63} +(3.37487 + 2.45199i) q^{64} -6.82843 q^{65} -4.48528 q^{67} +(-1.73302 - 1.25912i) q^{68} +(2.47214 - 7.60845i) q^{69} +(-0.255998 - 0.787881i) q^{70} +(9.15298 - 6.65003i) q^{71} +(6.41464 - 4.66051i) q^{72} +(2.11010 + 6.49422i) q^{73} +(0.468074 - 1.44058i) q^{74} +(-2.28825 - 1.66251i) q^{75} +8.00000 q^{78} +(3.23607 + 2.35114i) q^{79} +(-0.927051 + 2.85317i) q^{80} +(0.309017 + 0.951057i) q^{81} +(2.01063 - 1.46081i) q^{82} +(-4.85410 + 3.52671i) q^{83} +(-3.19621 - 9.83692i) q^{84} +(0.362036 - 1.11423i) q^{85} +(-2.01063 - 1.46081i) q^{86} -21.6569 q^{87} +9.31371 q^{89} +(1.67553 + 1.21734i) q^{90} +(4.22020 - 12.9884i) q^{91} +(-1.59810 - 4.91846i) q^{92} +(0.947822 - 0.688633i) q^{94} +(3.85816 - 11.8742i) q^{96} +(6.19453 + 4.50059i) q^{97} -1.24264 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{8} - 10 q^{9} + 8 q^{10} - 64 q^{12} - 8 q^{13} + 4 q^{14} - 6 q^{16} + 8 q^{17} + 10 q^{18} + 2 q^{20} - 8 q^{24} - 2 q^{25} - 4 q^{28} + 4 q^{29}+ \cdots + 24 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^8 - 10 * q^9 + 8 * q^10 - 64 * q^12 - 8 * q^13 + 4 * q^14 - 6 * q^16 + 8 * q^17 + 10 * q^18 + 2 * q^20 - 8 * q^24 - 2 * q^25 - 4 * q^28 + 4 * q^29 + 8 * q^30 + 24 * q^32 + 64 * q^34 + 4 * q^35 - 10 * q^36 + 4 * q^37 - 16 * q^39 - 6 * q^40 + 12 * q^41 - 16 * q^42 + 48 * q^43 - 40 * q^45 - 8 * q^46 + 6 * q^49 + 2 * q^50 - 16 * q^51 + 8 * q^52 - 12 * q^53 + 64 * q^54 - 48 * q^56 + 12 * q^58 + 8 * q^59 - 16 * q^60 + 4 * q^61 - 20 * q^63 + 14 * q^64 - 32 * q^65 + 32 * q^67 + 24 * q^68 - 16 * q^69 - 4 * q^70 + 30 * q^72 - 8 * q^73 - 20 * q^74 + 64 * q^78 + 8 * q^79 + 6 * q^80 - 2 * q^81 - 12 * q^82 - 12 * q^83 + 32 * q^84 - 8 * q^85 + 12 * q^86 - 128 * q^87 - 16 * q^89 - 10 * q^90 - 16 * q^91 + 16 * q^92 + 8 * q^94 - 8 * q^96 + 4 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more