LMFDB - Embedded newform 675.2.u.e.49.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(49,675)] 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("675.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([14, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.u (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [132] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			49.14
Character	$\chi$	$=$	675.49
Dual form			675.2.u.e.124.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.499186 + 0.594907i) q^{2} +(-1.47949 - 0.900618i) q^{3} +(0.242569 - 1.37568i) q^{4} +(-0.202756 - 1.32973i) q^{6} +(4.84944 - 0.855088i) q^{7} +(2.28459 - 1.31901i) q^{8} +(1.37777 + 2.66491i) q^{9} +(-3.17186 - 1.15446i) q^{11} +(-1.59784 + 1.81684i) q^{12} +(-0.504276 + 0.600973i) q^{13} +(2.92947 + 2.45812i) q^{14} +(-0.700189 - 0.254848i) q^{16} +(4.95771 + 2.86234i) q^{17} +(-0.897607 + 2.14993i) q^{18} +(-2.16649 - 3.75247i) q^{19} +(-7.94481 - 3.10240i) q^{21} +(-0.896551 - 2.46325i) q^{22} +(1.21828 + 0.214816i) q^{23} +(-4.56795 - 0.106085i) q^{24} -0.609251 q^{26} +(0.361665 - 5.18355i) q^{27} -6.87869i q^{28} +(-1.75863 + 1.47566i) q^{29} +(1.42301 - 8.07028i) q^{31} +(-2.00242 - 5.50161i) q^{32} +(3.65300 + 4.56465i) q^{33} +(0.771998 + 4.37822i) q^{34} +(4.00026 - 1.24895i) q^{36} +(2.68123 + 1.54801i) q^{37} +(1.15089 - 3.16204i) q^{38} +(1.28732 - 0.434973i) q^{39} +(4.54071 + 3.81011i) q^{41} +(-2.12029 - 6.27510i) q^{42} +(0.144385 - 0.396695i) q^{43} +(-2.35756 + 4.08342i) q^{44} +(0.480353 + 0.831996i) q^{46} +(-7.90806 + 1.39441i) q^{47} +(0.806401 + 1.00765i) q^{48} +(16.2081 - 5.89926i) q^{49} +(-4.75701 - 8.69981i) q^{51} +(0.704423 + 0.839499i) q^{52} -12.8380i q^{53} +(3.26427 - 2.37240i) q^{54} +(9.95112 - 8.34998i) q^{56} +(-0.174246 + 7.50292i) q^{57} +(-1.75576 - 0.309589i) q^{58} +(-6.94844 + 2.52902i) q^{59} +(-0.679578 - 3.85408i) q^{61} +(5.51141 - 3.18202i) q^{62} +(8.96017 + 11.7452i) q^{63} +(1.52824 - 2.64699i) q^{64} +(-0.892014 + 4.45180i) q^{66} +(2.05797 - 2.45259i) q^{67} +(5.14024 - 6.12590i) q^{68} +(-1.60896 - 1.41502i) q^{69} +(-4.92735 + 8.53442i) q^{71} +(6.66269 + 4.27093i) q^{72} +(-3.07968 + 1.77806i) q^{73} +(0.417511 + 2.36782i) q^{74} +(-5.68772 + 2.07016i) q^{76} +(-16.3689 - 2.88628i) q^{77} +(0.901380 + 0.548702i) q^{78} +(-1.31333 + 1.10201i) q^{79} +(-5.20348 + 7.34328i) q^{81} +4.60325i q^{82} +(10.4548 + 12.4596i) q^{83} +(-6.19507 + 10.1769i) q^{84} +(0.308071 - 0.112129i) q^{86} +(3.93088 - 0.599376i) q^{87} +(-8.76914 + 1.54624i) q^{88} +(-1.10530 - 1.91444i) q^{89} +(-1.93158 + 3.34559i) q^{91} +(0.591034 - 1.62385i) q^{92} +(-9.37357 + 10.6583i) q^{93} +(-4.77714 - 4.00849i) q^{94} +(-1.99229 + 9.94300i) q^{96} +(-5.21207 + 14.3200i) q^{97} +(11.6004 + 6.69747i) q^{98} +(-1.29357 - 10.0433i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 12 q^{6} + 12 q^{9} + 30 q^{11} - 30 q^{14} + 36 q^{16} - 24 q^{19} + 24 q^{21} + 78 q^{24} + 12 q^{26} + 30 q^{29} + 6 q^{31} + 60 q^{36} + 30 q^{39} + 78 q^{41} - 102 q^{44} + 18 q^{46} + 12 q^{49}+ \cdots + 96 q^{99}+O(q^{100}) $ 132 * q - 12 * q^6 + 12 * q^9 + 30 * q^11 - 30 * q^14 + 36 * q^16 - 24 * q^19 + 24 * q^21 + 78 * q^24 + 12 * q^26 + 30 * q^29 + 6 * q^31 + 60 * q^36 + 30 * q^39 + 78 * q^41 - 102 * q^44 + 18 * q^46 + 12 * q^49 - 150 * q^54 + 288 * q^56 - 90 * q^59 - 108 * q^61 + 48 * q^64 + 96 * q^66 - 102 * q^69 - 30 * q^71 - 192 * q^74 - 96 * q^76 - 96 * q^79 - 108 * q^81 - 114 * q^84 - 222 * q^86 + 24 * q^89 + 18 * q^91 - 72 * q^94 - 498 * q^96 + 96 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.499186	+	0.594907i	0.352978	+	0.420663i	0.913092	−	0.407752i	$-0.133687\pi$
$2$	0.499186	+	0.594907i	0.352978	+	0.420663i	−0.560115	+	0.828415i	$0.689243\pi$
$3$	−1.47949	−	0.900618i	−0.854183	−	0.519972i
$3$	−1.47949	−	0.900618i	−0.854183	−	0.519972i
$4$	0.242569	−	1.37568i	0.121285	−	0.687839i
$5$		0			0
$5$		0			0
$6$	−0.202756	−	1.32973i	−0.0827749	−	0.542862i
$7$	4.84944	−	0.855088i	1.83292	−	0.323193i	0.852896	−	0.522082i	$-0.174844\pi$
$7$	4.84944	−	0.855088i	1.83292	−	0.323193i	0.980022	+	0.198889i	$0.0637332\pi$
$8$	2.28459	−	1.31901i	0.807724	−	0.466340i
$9$	1.37777	+	2.66491i	0.459258	+	0.888303i
$10$		0			0
$11$	−3.17186	−	1.15446i	−0.956352	−	0.348084i	−0.183749	−	0.982973i	$-0.558823\pi$
$11$	−3.17186	−	1.15446i	−0.956352	−	0.348084i	−0.772603	+	0.634890i	$0.781046\pi$
$12$	−1.59784	+	1.81684i	−0.461256	+	0.524476i
$13$	−0.504276	+	0.600973i	−0.139861	+	0.166680i	−0.831428	−	0.555632i	$-0.812476\pi$
$13$	−0.504276	+	0.600973i	−0.139861	+	0.166680i	0.691567	+	0.722312i	$0.256921\pi$
$14$	2.92947	+	2.45812i	0.782934	+	0.656960i
$15$		0			0
$16$	−0.700189	−	0.254848i	−0.175047	−	0.0637120i
$17$	4.95771	+	2.86234i	1.20242	+	0.694219i	0.961093	−	0.276224i	$-0.0890833\pi$
$17$	4.95771	+	2.86234i	1.20242	+	0.694219i	0.241329	+	0.970443i	$0.422417\pi$
$18$	−0.897607	+	2.14993i	−0.211568	+	0.506744i
$19$	−2.16649	−	3.75247i	−0.497027	−	0.860877i	0.502967	−	0.864306i	$-0.332242\pi$
$19$	−2.16649	−	3.75247i	−0.497027	−	0.860877i	−0.999994	+	0.00342920i	$0.998908\pi$
$20$		0			0
$21$	−7.94481	−	3.10240i	−1.73370	−	0.677000i
$22$	−0.896551	−	2.46325i	−0.191145	−	0.525167i
$23$	1.21828	+	0.214816i	0.254029	+	0.0447921i	0.299212	−	0.954187i	$-0.403276\pi$
$23$	1.21828	+	0.214816i	0.254029	+	0.0447921i	−0.0451834	+	0.998979i	$0.514387\pi$
$24$	−4.56795	−	0.106085i	−0.932428	−	0.0216545i
$25$		0			0
$26$	−0.609251			−0.119484
$27$	0.361665	−	5.18355i	0.0696024	−	0.997575i
$28$		−	6.87869i		−	1.29995i
$29$	−1.75863	+	1.47566i	−0.326569	+	0.274024i	−0.791300	−	0.611428i	$-0.790595\pi$
$29$	−1.75863	+	1.47566i	−0.326569	+	0.274024i	0.464731	+	0.885452i	$0.346151\pi$
$30$		0			0
$31$	1.42301	−	8.07028i	0.255580	−	1.44947i	−0.539000	−	0.842306i	$-0.681198\pi$
$31$	1.42301	−	8.07028i	0.255580	−	1.44947i	0.794580	−	0.607160i	$-0.207691\pi$
$32$	−2.00242	−	5.50161i	−0.353982	−	0.972557i
$33$	3.65300	+	4.56465i	0.635906	+	0.794603i
$34$	0.771998	+	4.37822i	0.132397	+	0.750858i
$35$		0			0
$36$	4.00026	−	1.24895i	0.666710	−	0.208158i
$37$	2.68123	+	1.54801i	0.440791	+	0.254491i	0.703933	−	0.710266i	$-0.251425\pi$
$37$	2.68123	+	1.54801i	0.440791	+	0.254491i	−0.263142	+	0.964757i	$0.584759\pi$
$38$	1.15089	−	3.16204i	0.186699	−	0.512951i
$39$	1.28732	−	0.434973i	0.206136	−	0.0696514i
$40$		0			0
$41$	4.54071	+	3.81011i	0.709140	+	0.595039i	0.924358	−	0.381527i	$-0.124602\pi$
$41$	4.54071	+	3.81011i	0.709140	+	0.595039i	−0.215218	+	0.976566i	$0.569046\pi$
$42$	−2.12029	−	6.27510i	−0.327169	−	0.968268i
$43$	0.144385	−	0.396695i	0.0220185	−	0.0604954i	−0.928196	−	0.372091i	$-0.878641\pi$
$43$	0.144385	−	0.396695i	0.0220185	−	0.0604954i	0.950215	+	0.311595i	$0.100863\pi$
$44$	−2.35756	+	4.08342i	−0.355416	+	0.615599i
$45$		0			0
$46$	0.480353	+	0.831996i	0.0708242	+	0.122671i
$47$	−7.90806	+	1.39441i	−1.15351	+	0.203395i	−0.717508	−	0.696551i	$-0.754717\pi$
$47$	−7.90806	+	1.39441i	−1.15351	+	0.203395i	−0.436002	+	0.899946i	$0.643606\pi$
$48$	0.806401	+	1.00765i	0.116394	+	0.145441i
$49$	16.2081	−	5.89926i	2.31544	−	0.842752i
$50$		0			0
$51$	−4.75701	−	8.69981i	−0.666115	−	1.21822i
$52$	0.704423	+	0.839499i	0.0976859	+	0.116418i
$53$		−	12.8380i		−	1.76343i	−0.471779	−	0.881717i	$-0.656388\pi$
$53$		−	12.8380i		−	1.76343i	0.471779	−	0.881717i	$-0.343612\pi$
$54$	3.26427	−	2.37240i	0.444211	−	0.322843i
$55$		0			0
$56$	9.95112	−	8.34998i	1.32977	−	1.11581i
$57$	−0.174246	+	7.50292i	−0.0230795	+	0.993787i
$58$	−1.75576	−	0.309589i	−0.230543	−	0.0406510i
$59$	−6.94844	+	2.52902i	−0.904609	+	0.329251i	−0.752098	−	0.659051i	$-0.770958\pi$
$59$	−6.94844	+	2.52902i	−0.904609	+	0.329251i	−0.152511	+	0.988302i	$0.548736\pi$
$60$		0			0
$61$	−0.679578	−	3.85408i	−0.0870111	−	0.493464i	−0.996904	−	0.0786222i	$-0.974948\pi$
$61$	−0.679578	−	3.85408i	−0.0870111	−	0.493464i	0.909893	−	0.414842i	$-0.136163\pi$
$62$	5.51141	−	3.18202i	0.699950	−	0.404116i
$63$	8.96017	+	11.7452i	1.12888	+	1.47976i
$64$	1.52824	−	2.64699i	0.191030	−	0.330874i
$65$		0			0
$66$	−0.892014	+	4.45180i	−0.109799	+	0.547979i
$67$	2.05797	−	2.45259i	0.251421	−	0.299631i	−0.625542	−	0.780191i	$-0.715122\pi$
$67$	2.05797	−	2.45259i	0.251421	−	0.299631i	0.876962	+	0.480559i	$0.159566\pi$
$68$	5.14024	−	6.12590i	0.623346	−	0.742875i
$69$	−1.60896	−	1.41502i	−0.193697	−	0.170349i
$70$		0			0
$71$	−4.92735	+	8.53442i	−0.584769	+	1.01285i	0.410135	+	0.912025i	$0.365482\pi$
$71$	−4.92735	+	8.53442i	−0.584769	+	1.01285i	−0.994904	+	0.100825i	$0.967852\pi$
$72$	6.66269	+	4.27093i	0.785205	+	0.503334i
$73$	−3.07968	+	1.77806i	−0.360450	+	0.208106i	−0.669278	−	0.743012i	$-0.733396\pi$
$73$	−3.07968	+	1.77806i	−0.360450	+	0.208106i	0.308828	+	0.951118i	$0.400063\pi$
$74$	0.417511	+	2.36782i	0.0485347	+	0.275254i
$75$		0			0
$76$	−5.68772	+	2.07016i	−0.652426	+	0.237464i
$77$	−16.3689	−	2.88628i	−1.86541	−	0.328922i
$78$	0.901380	+	0.548702i	0.102061	+	0.0621283i
$79$	−1.31333	+	1.10201i	−0.147761	+	0.123986i	−0.713672	−	0.700480i	$-0.752969\pi$
$79$	−1.31333	+	1.10201i	−0.147761	+	0.123986i	0.565911	+	0.824467i	$0.308525\pi$
$80$		0			0
$81$	−5.20348	+	7.34328i	−0.578164	+	0.815920i
$82$			4.60325i			0.508344i
$83$	10.4548	+	12.4596i	1.14757	+	1.36762i	0.919079	+	0.394073i	$0.128934\pi$
$83$	10.4548	+	12.4596i	1.14757	+	1.36762i	0.228490	+	0.973546i	$0.426621\pi$
$84$	−6.19507	+	10.1769i	−0.675938	+	1.11040i
$85$		0			0
$86$	0.308071	−	0.112129i	0.0332202	−	0.0120912i
$87$	3.93088	−	0.599376i	0.421434	−	0.0642598i
$88$	−8.76914	+	1.54624i	−0.934794	+	0.164829i
$89$	−1.10530	−	1.91444i	−0.117162	−	0.202930i	0.801480	−	0.598021i	$-0.204046\pi$
$89$	−1.10530	−	1.91444i	−0.117162	−	0.202930i	−0.918642	+	0.395091i	$0.870713\pi$
$90$		0			0
$91$	−1.93158	+	3.34559i	−0.202484	+	0.350713i
$92$	0.591034	−	1.62385i	0.0616195	−	0.169298i
$93$	−9.37357	+	10.6583i	−0.971994	+	1.10522i
$94$	−4.77714	−	4.00849i	−0.492724	−	0.413445i
$95$		0			0
$96$	−1.99229	+	9.94300i	−0.203337	+	1.01480i
$97$	−5.21207	+	14.3200i	−0.529205	+	1.45398i	0.330804	+	0.943700i	$0.392680\pi$
$97$	−5.21207	+	14.3200i	−0.529205	+	1.45398i	−0.860009	+	0.510279i	$0.829542\pi$
$98$	11.6004	+	6.69747i	1.17181	+	0.676547i
$99$	−1.29357	−	10.0433i	−0.130008	−	1.00939i
$100$		0			0
$101$	3.25498	+	18.4599i	0.323882	+	1.83683i	0.517417	+	0.855733i	$0.326894\pi$
$101$	3.25498	+	18.4599i	0.323882	+	1.83683i	−0.193535	+	0.981093i	$0.561995\pi$
$102$	2.80094	−	7.17280i	0.277334	−	0.710213i
$103$	0.474488	+	1.30365i	0.0467527	+	0.128452i	0.960872	−	0.276994i	$-0.0893383\pi$
$103$	0.474488	+	1.30365i	0.0467527	+	0.128452i	−0.914119	+	0.405446i	$0.867116\pi$
$104$	−0.359376	+	2.03812i	−0.0352397	+	0.199854i
$105$		0			0
$106$	7.63741	−	6.40854i	0.741810	−	0.622453i
$107$			6.79809i			0.657196i	0.944470	+	0.328598i	$0.106576\pi$
$107$			6.79809i			0.657196i	−0.944470	+	0.328598i	$0.893424\pi$
$108$	−7.04316	−	1.75490i	−0.677729	−	0.168866i
$109$	−3.70718			−0.355084			−0.177542	−	0.984113i	$-0.556815\pi$
$109$	−3.70718			−0.355084			−0.177542	+	0.984113i	$0.556815\pi$
$110$		0			0
$111$	−2.57268	−	4.70502i	−0.244188	−	0.446581i
$112$	−3.61345	−	0.637148i	−0.341439	−	0.0602048i
$113$	−3.50908	−	9.64111i	−0.330106	−	0.906959i	−0.988083	−	0.153921i	$-0.950810\pi$
$113$	−3.50908	−	9.64111i	−0.330106	−	0.906959i	0.657977	−	0.753038i	$-0.271412\pi$
$114$	−4.55052	+	3.64169i	−0.426195	+	0.341076i
$115$		0			0
$116$	1.60345	+	2.77725i	0.148876	+	0.257862i
$117$	−2.29632	−	0.515846i	−0.212295	−	0.0476899i
$118$	−4.97310	−	2.87122i	−0.457811	−	0.264317i
$119$	26.4897	+	9.64147i	2.42831	+	0.883832i
$120$		0			0
$121$	0.301422	+	0.252923i	0.0274020	+	0.0229930i
$122$	1.95358	−	2.32819i	0.176869	−	0.210784i
$123$	−3.28648	−	9.72646i	−0.296332	−	0.877005i
$124$	−10.7569	−	3.91520i	−0.966001	−	0.351596i
$125$		0			0
$126$	−2.51451	+	11.1935i	−0.224011	+	0.997197i
$127$	15.4077	−	8.89562i	1.36721	−	0.789359i	0.376639	−	0.926360i	$-0.377080\pi$
$127$	15.4077	−	8.89562i	1.36721	−	0.789359i	0.990571	+	0.137002i	$0.0437466\pi$
$128$	−9.19391	+	1.62113i	−0.812635	+	0.143289i
$129$	−0.570887	+	0.456870i	−0.0502638	+	0.0402251i
$130$		0			0
$131$	1.04732	−	5.93962i	0.0915044	−	0.518947i	−0.904258	−	0.426986i	$-0.859575\pi$
$131$	1.04732	−	5.93962i	0.0915044	−	0.518947i	0.995763	−	0.0919612i	$-0.0293136\pi$
$132$	7.16559	−	3.91811i	0.623684	−	0.341027i
$133$	−13.7150	−	16.3449i	−1.18924	−	1.41728i
$134$	2.48637			0.214790
$135$		0			0
$136$	15.1018			1.29497
$137$	9.66943	+	11.5236i	0.826115	+	0.984525i	1.00000		0.000240652i	$-7.66018e-5\pi$
$137$	9.66943	+	11.5236i	0.826115	+	0.984525i	−0.173885	+	0.984766i	$0.555632\pi$
$138$	0.0386337	−	1.66354i	0.00328872	−	0.141610i
$139$	1.48204	−	8.40509i	0.125705	−	0.712911i	−0.855181	−	0.518330i	$-0.826554\pi$
$139$	1.48204	−	8.40509i	0.125705	−	0.712911i	0.980886	−	0.194581i	$-0.0623348\pi$
$140$		0			0
$141$	12.9557	+	5.05914i	1.09107	+	0.426056i
$142$	−7.53685	+	1.32895i	−0.632479	+	0.111523i
$143$	2.29330	−	1.32403i	0.191775	−	0.110721i
$144$	−0.285556	−	2.21706i	−0.0237963	−	0.184755i
$145$		0			0
$146$	−2.59511	−	0.944544i	−0.214773	−	0.0781710i
$147$	−29.2927	−	5.86941i	−2.41602	−	0.484101i
$148$	2.77994	−	3.31301i	0.228510	−	0.272327i
$149$	−7.57146	−	6.35321i	−0.620278	−	0.520475i	0.277613	−	0.960693i	$-0.410457\pi$
$149$	−7.57146	−	6.35321i	−0.620278	−	0.520475i	−0.897891	+	0.440218i	$0.854901\pi$
$150$		0			0
$151$	3.18979	+	1.16099i	0.259582	+	0.0944800i	0.468533	−	0.883446i	$-0.344783\pi$
$151$	3.18979	+	1.16099i	0.259582	+	0.0944800i	−0.208951	+	0.977926i	$0.567005\pi$
$152$	−9.89909	−	5.71524i	−0.802922	−	0.463567i
$153$	−0.797261	+	17.1555i	−0.0644547	+	1.38694i
$154$	−6.45407	−	11.1788i	−0.520084	−	0.900811i
$155$		0			0
$156$	−0.286118	−	1.87645i	−0.0229078	−	0.150236i
$157$	7.39131	+	20.3075i	0.589891	+	1.62071i	0.770703	+	0.637195i	$0.219905\pi$
$157$	7.39131	+	20.3075i	0.589891	+	1.62071i	−0.180812	+	0.983518i	$0.557873\pi$
$158$	−1.31119	−	0.231198i	−0.104313	−	0.0183931i
$159$	−11.5621	+	18.9937i	−0.916936	+	1.50630i
$160$		0			0
$161$	6.09166			0.480090
$162$	−6.96607	+	0.570079i	−0.547306	+	0.0447897i
$163$			6.62741i			0.519099i	0.965730	+	0.259549i	$0.0835741\pi$
$163$			6.62741i			0.519099i	−0.965730	+	0.259549i	$0.916426\pi$
$164$	6.34292	−	5.32234i	0.495299	−	0.415605i
$165$		0			0
$166$	−2.19339	+	12.4393i	−0.170240	+	0.965479i
$167$	6.48077	+	17.8058i	0.501497	+	1.37785i	0.889813	+	0.456326i	$0.150835\pi$
$167$	6.48077	+	17.8058i	0.501497	+	1.37785i	−0.388315	+	0.921527i	$0.626943\pi$
$168$	−22.2427	+	3.39154i	−1.71606	+	0.261663i
$169$	2.15055	+	12.1964i	0.165427	+	0.938184i
$170$		0			0
$171$	7.01507	−	10.9436i	0.536455	−	0.836875i
$172$	−0.510701	−	0.294853i	−0.0389406	−	0.0224823i
$173$	−0.200504	+	0.550879i	−0.0152440	+	0.0418826i	−0.947081	−	0.320994i	$-0.895983\pi$
$173$	−0.200504	+	0.550879i	−0.0152440	+	0.0418826i	0.931837	+	0.362876i	$0.118205\pi$
$174$	2.31881	+	2.03931i	0.175789	+	0.154599i
$175$		0			0
$176$	1.92669	+	1.61668i	0.145230	+	0.121862i
$177$	12.5578	+	2.51623i	0.943903	+	0.189131i
$178$	0.587161	−	1.61321i	0.0440096	−	0.120915i
$179$	10.0081	−	17.3345i	0.748037	−	1.29564i	−0.200725	−	0.979648i	$-0.564330\pi$
$179$	10.0081	−	17.3345i	0.748037	−	1.29564i	0.948762	−	0.315991i	$-0.102337\pi$
$180$		0			0
$181$	7.25247	+	12.5617i	0.539072	+	0.933700i	0.998954	+	0.0457203i	$0.0145583\pi$
$181$	7.25247	+	12.5617i	0.539072	+	0.933700i	−0.459882	+	0.887980i	$0.652108\pi$
$182$	−2.95453	+	0.520963i	−0.219004	+	0.0386163i
$183$	−2.46563	+	6.31411i	−0.182264	+	0.466752i
$184$	3.06661	−	1.11616i	0.226074	−	0.0822841i
$185$		0			0
$186$	−11.0199	−	0.255922i	−0.808015	−	0.0187651i
$187$	−12.4207	−	14.8024i	−0.908293	−	1.08246i
$188$			11.2172i			0.818097i
$189$	−2.67852	−	25.4466i	−0.194834	−	1.85097i
$190$		0			0
$191$	−3.01864	+	2.53294i	−0.218421	+	0.183277i	−0.745432	−	0.666581i	$-0.767757\pi$
$191$	−3.01864	+	2.53294i	−0.218421	+	0.183277i	0.527011	+	0.849858i	$0.323312\pi$
$192$	−4.64494	+	2.53983i	−0.335220	+	0.183296i
$193$	−5.95297	−	1.04967i	−0.428504	−	0.0755568i	−0.0447632	−	0.998998i	$-0.514253\pi$
$193$	−5.95297	−	1.04967i	−0.428504	−	0.0755568i	−0.383741	+	0.923441i	$0.625364\pi$
$194$	−11.1209	+	4.04767i	−0.798432	+	0.290606i
$195$		0			0
$196$	−4.18390	−	23.7281i	−0.298850	−	1.69486i
$197$	0.694457	−	0.400945i	0.0494780	−	0.0285662i	−0.475057	−	0.879955i	$-0.657573\pi$
$197$	0.694457	−	0.400945i	0.0494780	−	0.0285662i	0.524535	+	0.851389i	$0.324239\pi$
$198$	5.32910	−	5.78303i	0.378723	−	0.410982i
$199$	2.31981	−	4.01802i	0.164447	−	0.284830i	−0.772012	−	0.635608i	$-0.780749\pi$
$199$	2.31981	−	4.01802i	0.164447	−	0.284830i	0.936459	+	0.350778i	$0.114083\pi$
$200$		0			0
$201$	−5.25358	+	1.77514i	−0.370559	+	0.125208i
$202$	−9.35707	+	11.1513i	−0.658361	+	0.784604i
$203$	−7.26654	+	8.65993i	−0.510011	+	0.607808i
$204$	−13.1220	+	4.43381i	−0.918726	+	0.310429i
$205$		0			0
$206$	−0.538690	+	0.933038i	−0.0375323	+	0.0650078i
$207$	1.10605	+	3.54257i	0.0768758	+	0.246226i
$208$	0.506246	−	0.292281i	0.0351018	−	0.0202661i
$209$	2.53972	+	14.4035i	0.175676	+	0.996308i
$210$		0			0
$211$	5.90447	−	2.14905i	0.406480	−	0.147947i	−0.130684	−	0.991424i	$-0.541717\pi$
$211$	5.90447	−	2.14905i	0.406480	−	0.147947i	0.537165	+	0.843477i	$0.319495\pi$
$212$	−17.6609	−	3.11410i	−1.21296	−	0.213877i
$213$	14.9762	−	8.18892i	1.02615	−	0.561096i
$214$	−4.04423	+	3.39351i	−0.276458	+	0.231976i
$215$		0			0
$216$	−6.01089	−	12.3193i	−0.408989	−	0.838224i
$217$		−	40.3532i		−	2.73935i
$218$	−1.85057	−	2.20543i	−0.125337	−	0.149370i
$219$	6.15771	+	0.143005i	0.416099	+	0.00966339i
$220$		0			0
$221$	−4.22025	+	1.53604i	−0.283885	+	0.103326i
$222$	1.51480	−	3.87919i	0.101667	−	0.260354i
$223$	−0.207803	+	0.0366413i	−0.0139155	+	0.00245368i	−0.180602	−	0.983556i	$-0.557804\pi$
$223$	−0.207803	+	0.0366413i	−0.0139155	+	0.00245368i	0.166686	+	0.986010i	$0.446693\pi$
$224$	−14.4150	−	24.9675i	−0.963143	−	1.66821i
$225$		0			0
$226$	3.98388	−	6.90028i	0.265004	−	0.459000i
$227$	2.41142	−	6.62533i	0.160052	−	0.439739i	−0.833582	−	0.552395i	$-0.813714\pi$
$227$	2.41142	−	6.62533i	0.160052	−	0.439739i	0.993634	+	0.112657i	$0.0359361\pi$
$228$	10.2793	+	2.05968i	0.680766	+	0.136406i
$229$	17.0605	+	14.3154i	1.12739	+	0.945991i	0.998954	−	0.0457276i	$-0.0145606\pi$
$229$	17.0605	+	14.3154i	1.12739	+	0.945991i	0.128434	+	0.991718i	$0.459005\pi$
$230$		0			0
$231$	21.6182	+	19.0124i	1.42237	+	1.25092i
$232$	−2.07133	+	5.69093i	−0.135989	+	0.373628i
$233$	11.7402	+	6.77819i	0.769124	+	0.444054i	0.832562	−	0.553932i	$-0.186873\pi$
$233$	11.7402	+	6.77819i	0.769124	+	0.444054i	−0.0634379	+	0.997986i	$0.520206\pi$
$234$	−0.839410	−	1.62360i	−0.0548739	−	0.106138i
$235$		0			0
$236$	1.79365	+	10.1723i	0.116756	+	0.662158i
$237$	2.93555	−	0.447609i	0.190684	−	0.0290753i
$238$	7.48752	+	20.5718i	0.485344	+	1.33347i
$239$	−1.06063	+	6.01513i	−0.0686065	+	0.389087i	0.931098	+	0.364770i	$0.118852\pi$
$239$	−1.06063	+	6.01513i	−0.0686065	+	0.389087i	−0.999704	+	0.0243171i	$0.992259\pi$
$240$		0			0
$241$	−14.7499	+	12.3766i	−0.950123	+	0.797248i	−0.979318	−	0.202326i	$-0.935150\pi$
$241$	−14.7499	+	12.3766i	−0.950123	+	0.797248i	0.0291956	+	0.999574i	$0.490705\pi$
$242$			0.305574i			0.0196430i
$243$	14.3120	−	6.17796i	0.918114	−	0.396316i
$244$	−5.46681			−0.349977
$245$		0			0
$246$	4.14577	−	6.81046i	0.264325	−	0.434219i
$247$	3.34765	+	0.590280i	0.213006	+	0.0375586i
$248$	−7.39378	−	20.3143i	−0.469506	−	1.28996i
$249$	−4.24648	−	27.8497i	−0.269110	−	1.76490i
$250$		0			0
$251$	−0.695671	−	1.20494i	−0.0439104	−	0.0760550i	0.843235	−	0.537545i	$-0.180648\pi$
$251$	−0.695671	−	1.20494i	−0.0439104	−	0.0760550i	−0.887145	+	0.461490i	$0.847315\pi$
$252$	18.3311	−	9.47728i	1.15475	−	0.597012i
$253$	−3.61622	−	2.08782i	−0.227350	−	0.131260i
$254$	12.9834	+	4.72556i	0.814648	+	0.296508i
$255$		0			0
$256$	−10.2367	−	8.58961i	−0.639793	−	0.536850i
$257$	2.68508	−	3.19995i	0.167491	−	0.199608i	−0.675770	−	0.737113i	$-0.736189\pi$
$257$	2.68508	−	3.19995i	0.167491	−	0.199608i	0.843261	+	0.537505i	$0.180633\pi$
$258$	−0.556773	−	0.111561i	−0.0346632	−	0.00694551i
$259$	14.3261	+	5.21429i	0.890184	+	0.324000i
$260$		0			0
$261$	−6.35550	−	2.65345i	−0.393396	−	0.164245i
$262$	4.05633	−	2.34192i	0.250601	−	0.144684i
$263$	−8.59885	+	1.51621i	−0.530228	+	0.0934934i	−0.432351	−	0.901705i	$-0.642316\pi$
$263$	−8.59885	+	1.51621i	−0.530228	+	0.0934934i	−0.0978761	+	0.995199i	$0.531205\pi$
$264$	14.3664	+	5.61001i	0.884192	+	0.345272i
$265$		0			0
$266$	2.87735	−	16.3183i	0.176422	−	1.00054i
$267$	−0.0888969	+	3.82784i	−0.00544040	+	0.234260i
$268$	−2.87477	−	3.42602i	−0.175605	−	0.209277i
$269$	−3.57322			−0.217863			−0.108931	−	0.994049i	$-0.534743\pi$
$269$	−3.57322			−0.217863			−0.108931	+	0.994049i	$0.534743\pi$
$270$		0			0
$271$	−13.9724			−0.848765			−0.424383	−	0.905483i	$-0.639509\pi$
$271$	−13.9724			−0.848765			−0.424383	+	0.905483i	$0.639509\pi$
$272$	−2.74188	−	3.26764i	−0.166251	−	0.198130i
$273$	5.87084	−	3.21015i	0.355319	−	0.194287i
$274$	−2.02861	+	11.5048i	−0.122553	+	0.695031i
$275$		0			0
$276$	−2.33690	+	1.87017i	−0.140665	+	0.112571i
$277$	−19.1250	+	3.37225i	−1.14911	+	0.202619i	−0.715587	−	0.698524i	$-0.753841\pi$
$277$	−19.1250	+	3.37225i	−1.14911	+	0.202619i	−0.433523	+	0.901143i	$0.642730\pi$
$278$	5.74006	−	3.31403i	0.344266	−	0.198762i
$279$	23.4672	−	7.32684i	1.40494	−	0.438646i
$280$		0			0
$281$	−18.7960	−	6.84119i	−1.12128	−	0.408111i	−0.286158	−	0.958182i	$-0.592378\pi$
$281$	−18.7960	−	6.84119i	−1.12128	−	0.408111i	−0.835118	+	0.550071i	$0.814600\pi$
$282$	3.45760	+	10.2329i	0.205897	+	0.609360i
$283$	−7.03336	+	8.38203i	−0.418090	+	0.498260i	−0.933447	−	0.358715i	$-0.883215\pi$
$283$	−7.03336	+	8.38203i	−0.418090	+	0.498260i	0.515357	+	0.856976i	$0.327659\pi$
$284$	10.5454	+	8.84863i	0.625754	+	0.525070i
$285$		0			0
$286$	1.93246	+	0.703357i	0.114269	+	0.0415904i
$287$	25.2779	+	14.5942i	1.49211	+	0.861469i
$288$	11.9024	−	12.9163i	0.701356	−	0.761098i
$289$	7.88596	+	13.6589i	0.463880	+	0.803464i
$290$		0			0
$291$	20.6081	−	16.4922i	1.20807	−	0.966792i
$292$	1.69900	+	4.66795i	0.0994262	+	0.273171i
$293$	6.31252	+	1.11307i	0.368781	+	0.0650261i	0.354968	−	0.934879i	$-0.384492\pi$
$293$	6.31252	+	1.11307i	0.368781	+	0.0650261i	0.0138134	+	0.999905i	$0.495603\pi$
$294$	−11.1307	−	20.3563i	−0.649158	−	1.18721i
$295$		0			0
$296$	8.16734			0.474717
$297$	−7.13137	+	16.0240i	−0.413804	+	0.929805i
$298$		−	7.67575i		−	0.444644i
$299$	−0.743448	+	0.623827i	−0.0429947	+	0.0360768i
$300$		0			0
$301$	0.360979	−	2.04721i	0.0208065	−	0.117999i
$302$	0.901619	+	2.47718i	0.0518823	+	0.142546i
$303$	11.8096	−	30.2427i	0.678444	−	1.73740i
$304$	0.560644	+	3.17957i	0.0321551	+	0.182361i
$305$		0			0
$306$	−10.6039	+	8.08950i	−0.606185	+	0.462446i
$307$	9.86017	+	5.69277i	0.562750	+	0.324904i	0.754248	−	0.656589i	$-0.228001\pi$
$307$	9.86017	+	5.69277i	0.562750	+	0.324904i	−0.191499	+	0.981493i	$0.561335\pi$
$308$	−7.94119	+	21.8182i	−0.452491	+	1.24321i
$309$	0.472087	−	2.35606i	0.0268561	−	0.134032i
$310$		0			0
$311$	−1.58925	−	1.33354i	−0.0901183	−	0.0756182i	0.596616	−	0.802527i	$-0.296512\pi$
$311$	−1.58925	−	1.33354i	−0.0901183	−	0.0756182i	−0.686734	+	0.726909i	$0.740956\pi$
$312$	2.36726	−	2.69172i	0.134020	−	0.152389i
$313$	−8.22881	+	22.6085i	−0.465120	+	1.27791i	0.456469	+	0.889739i	$0.349114\pi$
$313$	−8.22881	+	22.6085i	−0.465120	+	1.27791i	−0.921589	+	0.388167i	$0.873108\pi$
$314$	−8.39141	+	14.5343i	−0.473555	+	0.820221i
$315$		0			0
$316$	1.19744	+	2.07403i	0.0673614	+	0.116673i
$317$	7.25490	−	1.27924i	0.407476	−	0.0718490i	0.0338465	−	0.999427i	$-0.489224\pi$
$317$	7.25490	−	1.27924i	0.407476	−	0.0718490i	0.373629	+	0.927578i	$0.378113\pi$
$318$	−17.0711	+	2.60298i	−0.957300	+	0.145968i
$319$	7.28172	−	2.65033i	0.407698	−	0.148390i
$320$		0			0
$321$	6.12248	−	10.0577i	0.341724	−	0.561366i
$322$	3.04087	+	3.62397i	0.169461	+	0.201956i
$323$		−	24.8049i		−	1.38018i
$324$	8.83978	+	8.93956i	0.491099	+	0.496642i
$325$		0			0
$326$	−3.94269	+	3.30831i	−0.218366	+	0.183230i
$327$	5.48473	+	3.33876i	0.303307	+	0.184634i
$328$	15.3992	+	2.71530i	0.850280	+	0.149927i
$329$	−37.1574	+	13.5242i	−2.04855	+	0.745612i
$330$		0			0
$331$	−0.0223761	−	0.126901i	−0.00122990	−	0.00697513i	0.984187	−	0.177135i	$-0.0566828\pi$
$331$	−0.0223761	−	0.126901i	−0.00122990	−	0.00697513i	−0.985417	+	0.170160i	$0.945572\pi$
$332$	19.6764	−	11.3602i	1.07988	−	0.623471i
$333$	−0.431174	+	9.27803i	−0.0236282	+	0.508433i
$334$	−7.35767	+	12.7439i	−0.402594	+	0.697312i
$335$		0			0
$336$	4.77223	+	4.19699i	0.260346	+	0.228965i
$337$	7.89430	−	9.40807i	0.430030	−	0.512490i	−0.506901	−	0.862004i	$-0.669209\pi$
$337$	7.89430	−	9.40807i	0.430030	−	0.512490i	0.936931	+	0.349514i	$0.113653\pi$
$338$	−6.18219	+	7.36764i	−0.336267	+	0.400747i
$339$	−3.49132	+	17.4243i	−0.189622	+	0.946355i
$340$		0			0
$341$	−13.8304	+	23.9550i	−0.748960	+	1.29724i
$342$	10.0122	−	1.28956i	0.541399	−	0.0697316i
$343$	43.7041	−	25.2326i	2.35980	−	1.36243i
$344$	−0.193383	−	1.09673i	−0.0104265	−	0.0591317i
$345$		0			0
$346$	−0.427810	+	0.155710i	−0.0229992	+	0.00837104i
$347$	−5.83965	−	1.02969i	−0.313489	−	0.0552765i	0.0146902	−	0.999892i	$-0.495324\pi$
$347$	−5.83965	−	1.02969i	−0.313489	−	0.0552765i	−0.328179	+	0.944616i	$0.606435\pi$
$348$	0.128962	−	5.55301i	0.00691308	−	0.297673i
$349$	−22.5465	+	18.9188i	−1.20689	+	1.01270i	−0.207483	+	0.978239i	$0.566527\pi$
$349$	−22.5465	+	18.9188i	−1.20689	+	1.01270i	−0.999406	+	0.0344616i	$0.989028\pi$
$350$		0			0
$351$	2.93280	+	2.83129i	0.156541	+	0.151123i
$352$			19.7621i			1.05332i
$353$	−3.78753	−	4.51380i	−0.201590	−	0.240246i	0.655773	−	0.754958i	$-0.272343\pi$
$353$	−3.78753	−	4.51380i	−0.201590	−	0.240246i	−0.857363	+	0.514713i	$0.827899\pi$
$354$	4.77177	+	8.72679i	0.253617	+	0.463824i
$355$		0			0
$356$	−2.90176	+	1.05615i	−0.153793	+	0.0559760i
$357$	−30.5079	−	38.1216i	−1.61465	−	2.01761i
$358$	15.3083	−	2.69926i	0.809067	−	0.142660i
$359$	−10.0448	−	17.3981i	−0.530145	−	0.918239i	−0.999381	−	0.0351660i	$-0.988804\pi$
$359$	−10.0448	−	17.3981i	−0.530145	−	0.918239i	0.469236	−	0.883073i	$-0.344529\pi$
$360$		0			0
$361$	0.112627	−	0.195076i	0.00592776	−	0.0102672i
$362$	−3.85268	+	10.5851i	−0.202492	+	0.556343i
$363$	−0.218164	−	0.645664i	−0.0114506	−	0.0338886i
$364$	4.13391	+	3.46876i	0.216676	+	0.181812i
$365$		0			0
$366$	−4.98711	+	1.68510i	−0.260680	+	0.0880814i
$367$	8.05989	−	22.1444i	0.420723	−	1.15593i	−0.530571	−	0.847640i	$-0.678023\pi$
$367$	8.05989	−	22.1444i	0.420723	−	1.15593i	0.951294	−	0.308286i	$-0.0997553\pi$
$368$	−0.798281	−	0.460888i	−0.0416133	−	0.0240254i
$369$	−3.89752	+	17.3500i	−0.202897	+	0.903207i
$370$		0			0
$371$	−10.9776	−	62.2571i	−0.569929	−	3.23223i
$372$	12.3887	+	15.4804i	0.642322	+	0.802620i
$373$	4.91475	+	13.5032i	0.254476	+	0.699167i	0.999484	+	0.0321116i	$0.0102232\pi$
$373$	4.91475	+	13.5032i	0.254476	+	0.699167i	−0.745008	+	0.667055i	$0.767555\pi$
$374$	2.60582	−	14.7783i	0.134744	−	0.764169i
$375$		0			0
$376$	−16.2275	+	13.6164i	−0.836867	+	0.702215i
$377$		−	1.80103i		−	0.0927578i
$378$	13.8013	−	14.2961i	0.709861	−	0.735310i
$379$	−32.6347			−1.67633			−0.838165	−	0.545417i	$-0.816371\pi$
$379$	−32.6347			−1.67633			−0.838165	+	0.545417i	$0.816371\pi$
$380$		0			0
$381$	−30.8070	−	0.715455i	−1.57829	−	0.0366539i
$382$	−3.01372	−	0.531401i	−0.154196	−	0.0271888i
$383$	1.87730	+	5.15784i	0.0959255	+	0.263553i	0.978370	−	0.206864i	$-0.0663257\pi$
$383$	1.87730	+	5.15784i	0.0959255	+	0.263553i	−0.882444	+	0.470417i	$0.844103\pi$
$384$	15.0623	+	5.88175i	0.768645	+	0.300152i
$385$		0			0
$386$	−2.34718	−	4.06544i	−0.119469	−	0.206926i
$387$	1.25609	−	0.161782i	0.0638504	−	0.00822387i
$388$	18.4355	+	10.6437i	0.935918	+	0.540353i
$389$	−16.4485	−	5.98677i	−0.833973	−	0.303541i	−0.110484	−	0.993878i	$-0.535240\pi$
$389$	−16.4485	−	5.98677i	−0.833973	−	0.303541i	−0.723488	+	0.690337i	$0.757462\pi$
$390$		0			0
$391$	5.42501	+	4.55212i	0.274354	+	0.230211i
$392$	29.2477	−	34.8560i	1.47723	−	1.76049i
$393$	−6.89883	+	7.84437i	−0.348000	+	0.395696i
$394$	0.585188	+	0.212991i	0.0294814	+	0.0107303i
$395$		0			0
$396$	−14.1301	−	0.656663i	−0.710066	−	0.0329986i
$397$	3.83373	−	2.21340i	0.192409	−	0.111088i	−0.400701	−	0.916209i	$-0.631233\pi$
$397$	3.83373	−	2.21340i	0.192409	−	0.111088i	0.593110	+	0.805121i	$0.297900\pi$
$398$	3.54836	−	0.625672i	0.177863	−	0.0313621i
$399$	5.57066	+	36.5340i	0.278882	+	1.82899i
$400$		0			0
$401$	5.70218	−	32.3387i	0.284754	−	1.61492i	−0.421411	−	0.906870i	$-0.638465\pi$
$401$	5.70218	−	32.3387i	0.284754	−	1.61492i	0.706165	−	0.708048i	$-0.250424\pi$
$402$	−3.67856	−	2.23927i	−0.183470	−	0.111685i
$403$	4.13244	+	4.92484i	0.205851	+	0.245324i
$404$	26.1844			1.30272
$405$		0			0
$406$	−8.77921			−0.435705
$407$	−6.71736	−	8.00544i	−0.332967	−	0.396815i
$408$	−22.3429	−	13.6009i	−1.10614	−	0.673347i
$409$	4.60541	−	26.1186i	0.227723	−	1.29148i	−0.629688	−	0.776848i	$-0.716817\pi$
$409$	4.60541	−	26.1186i	0.227723	−	1.29148i	0.857411	−	0.514633i	$-0.172072\pi$
$410$		0			0
$411$	−3.92747	−	25.7575i	−0.193728	−	1.27052i
$412$	1.90849	−	0.336519i	0.0940246	−	0.0165791i
$413$	−31.5335	+	18.2059i	−1.55166	+	0.895853i
$414$	−1.55538	+	2.42640i	−0.0764425	+	0.119251i
$415$		0			0
$416$	4.31610	+	1.57093i	0.211614	+	0.0770212i
$417$	−9.76245	+	11.1005i	−0.478069	+	0.543593i
$418$	−7.30092	+	8.70090i	−0.357100	+	0.425575i
$419$	21.0958	+	17.7015i	1.03060	+	0.864774i	0.990922	−	0.134439i	$-0.0429232\pi$
$419$	21.0958	+	17.7015i	1.03060	+	0.864774i	0.0396754	+	0.999213i	$0.487368\pi$
$420$		0			0
$421$	25.5292	+	9.29186i	1.24422	+	0.452857i	0.878443	−	0.477847i	$-0.158583\pi$
$421$	25.5292	+	9.29186i	1.24422	+	0.452857i	0.365772	+	0.930704i	$0.380805\pi$
$422$	4.22591	+	2.43983i	0.205714	+	0.118769i
$423$	−14.6115	−	19.1531i	−0.710435	−	0.931255i
$424$	−16.9334	−	29.3295i	−0.822359	−	1.42437i
$425$		0			0
$426$	12.3476	+	4.82166i	0.598241	+	0.233610i
$427$	−6.59115	−	18.1090i	−0.318968	−	0.876358i
$428$	9.35198	+	1.64901i	0.452045	+	0.0797077i
$429$	−4.58535	−	0.106489i	−0.221383	−	0.00514134i
$430$		0			0
$431$	−6.47039			−0.311668			−0.155834	−	0.987783i	$-0.549806\pi$
$431$	−6.47039			−0.311668			−0.155834	+	0.987783i	$0.549806\pi$
$432$	−1.57425	+	3.53730i	−0.0757412	+	0.170188i
$433$		−	18.9751i		−	0.911883i	−0.890010	−	0.455942i	$-0.849303\pi$
$433$		−	18.9751i		−	0.911883i	0.890010	−	0.455942i	$-0.150697\pi$
$434$	24.0064	−	20.1438i	1.15234	−	0.966931i
$435$		0			0
$436$	−0.899248	+	5.09989i	−0.0430661	+	0.244240i
$437$	−1.83330	−	5.03696i	−0.0876988	−	0.240950i
$438$	2.98877	+	3.73465i	0.142809	+	0.178448i
$439$	5.12907	+	29.0884i	0.244797	+	1.38831i	0.820963	+	0.570981i	$0.193437\pi$
$439$	5.12907	+	29.0884i	0.244797	+	1.38831i	−0.576166	+	0.817333i	$0.695452\pi$
$440$		0			0
$441$	38.0521	+	35.0652i	1.81200	+	1.66977i
$442$	−3.02049	−	1.74388i	−0.143670	−	0.0829480i
$443$	−4.68628	+	12.8754i	−0.222652	+	0.611731i	−0.999846	−	0.0175297i	$-0.994420\pi$
$443$	−4.68628	+	12.8754i	−0.222652	+	0.611731i	0.777195	+	0.629260i	$0.216642\pi$
$444$	−7.09665	+	2.39789i	−0.336792	+	0.113799i
$445$		0			0
$446$	−0.125531	−	0.105333i	−0.00594405	−	0.00498765i
$447$	5.48007	+	16.2185i	0.259199	+	0.767109i
$448$	5.14770	−	14.1432i	0.243206	−	0.668203i
$449$	16.2238	−	28.1005i	0.765649	−	1.32614i	−0.174253	−	0.984701i	$-0.555751\pi$
$449$	16.2238	−	28.1005i	0.765649	−	1.32614i	0.939903	−	0.341443i	$-0.110915\pi$
$450$		0			0
$451$	−10.0039	−	17.3272i	−0.471064	−	0.815907i
$452$	−14.1142	+	2.48872i	−0.663878	+	0.117060i
$453$	−3.67365	−	4.59045i	−0.172603	−	0.215678i
$454$	5.14520	−	1.87270i	0.241476	−	0.0878902i
$455$		0			0
$456$	9.49834	+	17.3709i	0.444801	+	0.813469i
$457$	−10.6990	−	12.7506i	−0.500478	−	0.596446i	0.455372	−	0.890301i	$-0.349506\pi$
$457$	−10.6990	−	12.7506i	−0.500478	−	0.596446i	−0.955850	+	0.293855i	$0.905062\pi$
$458$			17.2955i			0.808163i
$459$	16.6301	−	24.6634i	0.776227	−	1.15119i
$460$		0			0
$461$	−25.2927	+	21.2231i	−1.17800	+	0.988460i	−0.178010	+	0.984029i	$0.556966\pi$
$461$	−25.2927	+	21.2231i	−1.17800	+	0.988460i	−0.999990	+	0.00443082i	$0.998590\pi$
$462$	−0.519086	+	22.3515i	−0.0241501	+	1.03989i
$463$	33.4802	+	5.90347i	1.55596	+	0.274357i	0.884448	−	0.466638i	$-0.154535\pi$
$463$	33.4802	+	5.90347i	1.55596	+	0.274357i	0.671510	+	0.740996i	$0.265646\pi$
$464$	1.60744	−	0.585061i	0.0746236	−	0.0271608i
$465$		0			0
$466$	1.82814	+	10.3679i	0.0846869	+	0.480283i
$467$	−1.54822	+	0.893863i	−0.0716429	+	0.0413630i	−0.535394	−	0.844603i	$-0.679837\pi$
$467$	−1.54822	+	0.893863i	−0.0716429	+	0.0413630i	0.463751	+	0.885966i	$0.346503\pi$
$468$	−1.26665	+	3.03386i	−0.0585510	+	0.140240i
$469$	7.88281	−	13.6534i	0.363995	−	0.630457i
$470$		0			0
$471$	7.35391	−	36.7014i	0.338850	−	1.69111i
$472$	−12.5385	+	14.9428i	−0.577132	+	0.687799i
$473$	−0.915938	+	1.09157i	−0.0421149	+	0.0501906i
$474$	1.73167	+	1.52294i	0.0795382	+	0.0699508i
$475$		0			0
$476$	19.6891	−	34.1026i	0.902450	−	1.56309i
$477$	34.2121	−	17.6878i	1.56646	−	0.809871i
$478$	−4.10790	+	2.37169i	−0.187891	+	0.108479i
$479$	−3.22748	−	18.3040i	−0.147467	−	0.836329i	−0.965353	−	0.260948i	$-0.915965\pi$
$479$	−3.22748	−	18.3040i	−0.147467	−	0.836329i	0.817886	−	0.575381i	$-0.195146\pi$
$480$		0			0
$481$	−2.28239	+	0.830722i	−0.104068	+	0.0378777i
$482$	−14.7259	−	2.59657i	−0.670744	−	0.118270i
$483$	−9.01255	−	5.48626i	−0.410085	−	0.249634i
$484$	0.421057	−	0.353309i	0.0191389	−	0.0160595i
$485$		0			0
$486$	10.8196	+	5.43035i	0.490789	+	0.246325i
$487$			16.9037i			0.765979i	0.923753	+	0.382989i	$0.125105\pi$
$487$			16.9037i			0.765979i	−0.923753	+	0.382989i	$0.874895\pi$
$488$	−6.63612	−	7.90862i	−0.300403	−	0.358006i
$489$	5.96877	−	9.80518i	0.269917	−	0.443406i
$490$		0			0
$491$	−1.02681	+	0.373728i	−0.0463392	+	0.0168661i	−0.365086	−	0.930974i	$-0.618960\pi$
$491$	−1.02681	+	0.373728i	−0.0463392	+	0.0168661i	0.318747	+	0.947840i	$0.396738\pi$
$492$	−14.1777	+	2.16179i	−0.639179	+	0.0974612i
$493$	−12.9426	+	2.28213i	−0.582906	+	0.102782i
$494$	1.31994	+	2.28620i	0.0593868	+	0.102861i
$495$		0			0
$496$	−3.05307	+	5.28808i	−0.137087	+	0.237442i
$497$	−16.5972	+	45.6005i	−0.744488	+	2.04546i
$498$	14.4482	−	16.4284i	0.647438	−	0.736176i
$499$	−1.10500	−	0.927202i	−0.0494664	−	0.0415073i	0.617719	−	0.786399i	$-0.288057\pi$
$499$	−1.10500	−	0.927202i	−0.0494664	−	0.0415073i	−0.667186	+	0.744891i	$0.732501\pi$
$500$		0			0
$501$	6.44798	−	32.1801i	0.288074	−	1.43770i
$502$	0.369556	−	1.01535i	0.0164941	−	0.0453172i
$503$	−20.6911	−	11.9460i	−0.922569	−	0.532645i	−0.0381151	−	0.999273i	$-0.512135\pi$
$503$	−20.6911	−	11.9460i	−0.922569	−	0.532645i	−0.884454	+	0.466628i	$0.845469\pi$
$504$	35.9623	+	15.0144i	1.60189	+	0.668797i
$505$		0			0
$506$	−0.563104	−	3.19352i	−0.0250330	−	0.141969i
$507$	7.80257	−	19.9812i	0.346524	−	0.887398i
$508$	−8.50008	−	23.3538i	−0.377130	−	1.03616i
$509$	0.690844	−	3.91797i	0.0306211	−	0.173661i	−0.965662	−	0.259802i	$-0.916343\pi$
$509$	0.690844	−	3.91797i	0.0306211	−	0.173661i	0.996283	+	0.0861414i	$0.0274537\pi$
$510$		0			0
$511$	−13.4144	+	11.2560i	−0.593416	+	0.497936i
$512$			8.29380i			0.366537i
$513$	−20.2347	+	9.87298i	−0.893383	+	0.435903i
$514$	3.24403			0.143088
$515$		0			0
$516$	0.490026	+	0.896178i	0.0215722	+	0.0394520i
$517$	26.6931	+	4.70671i	1.17396	+	0.207001i
$518$	4.04940	+	11.1256i	0.177920	+	0.488832i
$519$	0.792775	−	0.634442i	0.0347990	−	0.0278489i
$520$		0			0
$521$	11.2999	+	19.5719i	0.495055	+	0.857461i	0.999984	−	0.00570007i	$-0.00181440\pi$
$521$	11.2999	+	19.5719i	0.495055	+	0.857461i	−0.504928	+	0.863161i	$0.668481\pi$
$522$	−1.59402	−	5.10550i	−0.0697684	−	0.223461i
$523$	25.9568	+	14.9862i	1.13501	+	0.655299i	0.945190	−	0.326520i	$-0.105876\pi$
$523$	25.9568	+	14.9862i	1.13501	+	0.655299i	0.189821	+	0.981819i	$0.439209\pi$
$524$	−7.91696	−	2.88154i	−0.345854	−	0.125881i
$525$		0			0
$526$	−5.19443	−	4.35864i	−0.226488	−	0.190046i
$527$	30.1548	−	35.9370i	1.31356	−	1.56544i
$528$	−1.39450	−	4.12708i	−0.0606878	−	0.179608i
$529$	−20.1749	−	7.34305i	−0.877168	−	0.319263i
$530$		0			0
$531$	−16.3130	−	15.0325i	−0.707923	−	0.652356i
$532$	−25.8121	+	14.9026i	−1.11910	+	0.646111i
$533$	−4.57955	+	0.807498i	−0.198362	+	0.0349766i
$534$	−2.32159	+	1.85792i	−0.100465	+	0.0804001i
$535$		0			0
$536$	1.46662	−	8.31764i	0.0633485	−	0.359267i
$537$	−30.4185	+	16.6327i	−1.31266	+	0.717754i
$538$	−1.78370	−	2.12573i	−0.0769008	−	0.0916468i
$539$	−58.2203			−2.50772
$540$		0			0
$541$	3.99696			0.171843			0.0859215	−	0.996302i	$-0.472617\pi$
$541$	3.99696			0.171843			0.0859215	+	0.996302i	$0.472617\pi$
$542$	−6.97485	−	8.31230i	−0.299595	−	0.357044i
$543$	0.583300	−	25.1165i	0.0250318	−	1.07785i
$544$	5.82003	−	33.0070i	0.249532	−	1.41517i
$545$		0			0
$546$	4.84038	+	1.89014i	0.207149	+	0.0808906i
$547$	33.3096	−	5.87339i	1.42422	−	0.251128i	0.592161	−	0.805819i	$-0.298275\pi$
$547$	33.3096	−	5.87339i	1.42422	−	0.251128i	0.832056	+	0.554692i	$0.187164\pi$
$548$	18.1982	−	10.5067i	0.777389	−	0.448826i
$549$	9.33447	−	7.12106i	0.398385	−	0.303920i
$550$		0			0
$551$	9.34744	+	3.40219i	0.398214	+	0.144938i
$552$	−5.54225	−	1.11051i	−0.235894	−	0.0472663i
$553$	−5.42660	+	6.46716i	−0.230762	+	0.275012i
$554$	−11.5531	−	9.69421i	−0.490844	−	0.411867i
$555$		0			0
$556$	−11.2032	−	4.07763i	−0.475121	−	0.172930i
$557$	−21.9093	−	12.6493i	−0.928326	−	0.535969i	−0.0420444	−	0.999116i	$-0.513387\pi$
$557$	−21.9093	−	12.6493i	−0.928326	−	0.535969i	−0.886282	+	0.463146i	$0.846720\pi$
$558$	16.0733	+	10.3033i	0.680435	+	0.436174i
$559$	0.165593	+	0.286815i	0.00700383	+	0.0121310i
$560$		0			0
$561$	5.04497	+	33.0864i	0.212999	+	1.39691i
$562$	−5.31284	−	14.5969i	−0.224108	−	0.615733i
$563$	−39.8845	−	7.03270i	−1.68093	−	0.296393i	−0.749958	−	0.661486i	$-0.769926\pi$
$563$	−39.8845	−	7.03270i	−1.68093	−	0.296393i	−0.930971	+	0.365092i	$0.881037\pi$
$564$	10.1024	−	16.5957i	0.425388	−	0.698805i
$565$		0			0
$566$	−8.49748			−0.357176
$567$	−18.9548	+	40.0603i	−0.796028	+	1.68237i
$568$			25.9969i			1.09080i
$569$	−7.94639	+	6.66781i	−0.333130	+	0.279529i	−0.793974	−	0.607952i	$-0.791991\pi$
$569$	−7.94639	+	6.66781i	−0.333130	+	0.279529i	0.460844	+	0.887481i	$0.347547\pi$
$570$		0			0
$571$	−1.66139	+	9.42220i	−0.0695269	+	0.394307i	0.930108	+	0.367286i	$0.119713\pi$
$571$	−1.66139	+	9.42220i	−0.0695269	+	0.394307i	−0.999635	+	0.0270205i	$0.991398\pi$
$572$	−1.26516	−	3.47600i	−0.0528991	−	0.145339i
$573$	6.74725	−	1.02881i	0.281870	−	0.0429793i
$574$	3.93619	+	22.3232i	0.164293	+	0.931753i
$575$		0			0
$576$	9.15955	+	0.425668i	0.381648	+	0.0177362i
$577$	−18.2058	−	10.5111i	−0.757919	−	0.437585i	0.0706290	−	0.997503i	$-0.477499\pi$
$577$	−18.2058	−	10.5111i	−0.757919	−	0.437585i	−0.828548	+	0.559918i	$0.810833\pi$
$578$	−4.18920	+	11.5097i	−0.174248	+	0.478742i
$579$	7.86200	+	6.91433i	0.326734	+	0.287350i
$580$		0			0
$581$	61.3543	+	51.4823i	2.54540	+	2.13585i
$582$	20.0986	+	4.02718i	0.833114	+	0.166932i
$583$	−14.8210	+	40.7203i	−0.613822	+	1.68646i
$584$	−4.69054	+	8.12426i	−0.194096	+	0.336184i
$585$		0			0
$586$	2.48895	+	4.31099i	0.102818	+	0.178085i
$587$	25.4966	−	4.49575i	1.05236	−	0.185559i	0.379395	−	0.925235i	$-0.376132\pi$
$587$	25.4966	−	4.49575i	1.05236	−	0.185559i	0.672964	+	0.739675i	$0.265021\pi$
$588$	−15.1799	+	38.8735i	−0.626009	+	1.60312i
$589$	−33.3665	+	12.1444i	−1.37484	+	0.500401i
$590$		0			0
$591$	−1.38854	−	0.0322471i	−0.0571169	−	0.00132647i
$592$	−1.48286	−	1.76720i	−0.0609452	−	0.0726317i
$593$			7.66640i			0.314821i	0.987533	+	0.157411i	$0.0503146\pi$
$593$			7.66640i			0.314821i	−0.987533	+	0.157411i	$0.949685\pi$
$594$	−13.0926	+	3.75644i	−0.537198	+	0.154129i
$595$		0			0
$596$	−10.5766	+	8.87479i	−0.433233	+	0.363526i
$597$	−7.05083	+	3.85536i	−0.288571	+	0.157789i
$598$	−0.742238	−	0.130877i	−0.0303524	−	0.00535194i
$599$	−35.3351	+	12.8609i	−1.44375	+	0.525483i	−0.940839	−	0.338854i	$-0.889961\pi$
$599$	−35.3351	+	12.8609i	−1.44375	+	0.525483i	−0.502914	+	0.864337i	$0.667739\pi$
$600$		0			0
$601$	−2.37700	−	13.4806i	−0.0969599	−	0.549887i	−0.994129	−	0.108200i	$-0.965491\pi$
$601$	−2.37700	−	13.4806i	−0.0969599	−	0.549887i	0.897169	−	0.441687i	$-0.145620\pi$
$602$	1.39810	−	0.807191i	0.0569821	−	0.0328986i
$603$	9.37134	+	2.10518i	0.381630	+	0.0857296i
$604$	2.37089	−	4.10650i	0.0964702	−	0.167091i
$605$		0			0
$606$	23.8868	−	8.07111i	0.970333	−	0.327866i
$607$	−22.2667	+	26.5364i	−0.903776	+	1.07708i	0.0929052	+	0.995675i	$0.470385\pi$
$607$	−22.2667	+	26.5364i	−0.903776	+	1.07708i	−0.996681	+	0.0814033i	$0.974060\pi$
$608$	−16.3064	+	19.4332i	−0.661313	+	0.788122i
$609$	18.5501	−	6.26789i	0.751686	−	0.253988i
$610$		0			0
$611$	3.14985	−	5.45570i	0.127429	−	0.220714i
$612$	23.4071	+	5.25817i	0.946174	+	0.212549i
$613$	−13.6596	+	7.88639i	−0.551708	+	0.318528i	−0.749810	−	0.661653i	$-0.769855\pi$
$613$	−13.6596	+	7.88639i	−0.551708	+	0.318528i	0.198103	+	0.980181i	$0.436522\pi$
$614$	1.53539	+	8.70763i	0.0619633	+	0.351412i
$615$		0			0
$616$	−41.2033	+	14.9968i	−1.66013	+	0.604237i
$617$	−34.5615	−	6.09413i	−1.39139	−	0.245340i	−0.572792	−	0.819701i	$-0.694140\pi$
$617$	−34.5615	−	6.09413i	−1.39139	−	0.245340i	−0.818603	+	0.574360i	$0.805251\pi$
$618$	1.63730	−	0.895265i	0.0658617	−	0.0360129i
$619$	14.1386	−	11.8637i	0.568278	−	0.476842i	−0.312796	−	0.949820i	$-0.601266\pi$
$619$	14.1386	−	11.8637i	0.568278	−	0.476842i	0.881074	+	0.472978i	$0.156821\pi$
$620$		0			0
$621$	1.55412	−	6.23732i	0.0623645	−	0.250295i
$622$		−	1.61114i		−	0.0646010i
$623$	−6.99711	−	8.33883i	−0.280333	−	0.334088i
$624$	−1.01222	−	0.0235075i	−0.0405212	−	0.000941054i
$625$		0			0
$626$	−17.5576	+	6.39046i	−0.701745	+	0.255414i
$627$	9.21453	−	23.5971i	0.367993	−	0.942376i
$628$	29.7294	−	5.24210i	1.18633	−	0.209183i
$629$	8.86184	+	15.3492i	0.353345	+	0.612011i
$630$		0			0
$631$	−16.7999	+	29.0983i	−0.668793	+	1.15838i	0.309449	+	0.950916i	$0.399855\pi$
$631$	−16.7999	+	29.0983i	−0.668793	+	1.15838i	−0.978242	+	0.207467i	$0.933478\pi$
$632$	−1.54685	+	4.24994i	−0.0615305	+	0.169054i
$633$	−10.6711	−	2.13818i	−0.424137	−	0.0849849i
$634$	4.38257	+	3.67741i	0.174054	+	0.146049i
$635$		0			0
$636$	23.3245	+	20.5130i	0.924878	+	0.813394i
$637$	−4.62806	+	12.7155i	−0.183370	+	0.503806i
$638$	5.21163	+	3.00894i	0.206330	+	0.119125i
$639$	−29.5322	−	1.37244i	−1.16828	−	0.0542929i
$640$		0			0
$641$	−5.20105	−	29.4966i	−0.205429	−	1.16505i	−0.896763	−	0.442511i	$-0.854088\pi$
$641$	−5.20105	−	29.4966i	−0.205429	−	1.16505i	0.691334	−	0.722536i	$-0.257023\pi$
$642$	9.03965	−	1.37836i	0.356767	−	0.0543994i
$643$	4.45660	+	12.2444i	0.175751	+	0.482873i	0.996022	−	0.0891022i	$-0.0283998\pi$
$643$	4.45660	+	12.2444i	0.175751	+	0.482873i	−0.820271	+	0.571975i	$0.806178\pi$
$644$	1.47765	−	8.38016i	0.0582275	−	0.330225i
$645$		0			0
$646$	14.7566	−	12.3823i	0.580591	−	0.487174i
$647$		−	36.7940i		−	1.44652i	−0.690576	−	0.723260i	$-0.742643\pi$
$647$		−	36.7940i		−	1.44652i	0.690576	−	0.723260i	$-0.257357\pi$
$648$	−2.20196	+	23.6398i	−0.0865013	+	0.928660i
$649$	24.9591			0.979731
$650$		0			0
$651$	−36.3428	+	59.7021i	−1.42439	+	2.33991i
$652$	9.11718	+	1.60760i	0.357056	+	0.0629587i
$653$	−14.4650	−	39.7421i	−0.566057	−	1.55523i	−0.810606	−	0.585592i	$-0.800862\pi$
$653$	−14.4650	−	39.7421i	−0.566057	−	1.55523i	0.244548	−	0.969637i	$-0.421360\pi$
$654$	0.751654	+	4.92957i	0.0293920	+	0.192761i
$655$		0			0
$656$	−2.20836	−	3.82499i	−0.0862219	−	0.149341i
$657$	−8.98147	−	5.75732i	−0.350400	−	0.224614i
$658$	−26.5941	−	15.3541i	−1.03674	−	0.598565i
$659$	−28.0790	−	10.2199i	−1.09380	−	0.398111i	−0.268773	−	0.963203i	$-0.586618\pi$
$659$	−28.0790	−	10.2199i	−1.09380	−	0.398111i	−0.825028	+	0.565092i	$0.808840\pi$
$660$		0			0
$661$	30.7868	+	25.8332i	1.19747	+	1.00480i	0.999699	+	0.0245465i	$0.00781419\pi$
$661$	30.7868	+	25.8332i	1.19747	+	1.00480i	0.197769	+	0.980249i	$0.436630\pi$
$662$	0.0643246	−	0.0766591i	0.00250005	−	0.00297944i
$663$	7.62720	+	1.52827i	0.296216	+	0.0593531i
$664$	40.3194	+	14.6750i	1.56469	+	0.569502i
$665$		0			0
$666$	−5.73480	+	4.37496i	−0.222219	+	0.169526i
$667$	−2.45950	+	1.41999i	−0.0952320	+	0.0549822i
$668$	26.0670	−	4.59632i	1.00856	−	0.177837i
$669$	0.340442	+	0.132941i	0.0131623	+	0.00513980i
$670$		0			0
$671$	−2.29386	+	13.0091i	−0.0885536	+	0.502213i
$672$	−1.15937	+	49.9216i	−0.0447235	+	1.92577i
$673$	−13.6066	−	16.2157i	−0.524496	−	0.625070i	0.437142	−	0.899393i	$-0.355991\pi$
$673$	−13.6066	−	16.2157i	−0.524496	−	0.625070i	−0.961638	+	0.274322i	$0.911546\pi$
$674$	9.53765			0.367376
$675$		0			0
$676$	17.2999			0.665383
$677$	−4.85067	−	5.78080i	−0.186426	−	0.222174i	0.664734	−	0.747080i	$-0.268545\pi$
$677$	−4.85067	−	5.78080i	−0.186426	−	0.222174i	−0.851160	+	0.524906i	$0.824100\pi$
$678$	−12.1086	+	6.62093i	−0.465029	+	0.254275i
$679$	−13.0307	+	73.9010i	−0.500074	+	2.83606i
$680$		0			0
$681$	−9.53457	+	7.63033i	−0.365365	+	0.292395i
$682$	−21.1549	+	3.73019i	−0.810065	+	0.142836i
$683$	2.15819	−	1.24603i	0.0825810	−	0.0476781i	−0.458141	−	0.888880i	$-0.651484\pi$
$683$	2.15819	−	1.24603i	0.0825810	−	0.0476781i	0.540722	+	0.841201i	$0.318151\pi$
$684$	−13.3532	−	12.3050i	−0.510571	−	0.470495i
$685$		0			0
$686$	36.8275	+	13.4041i	1.40608	+	0.511772i
$687$	−12.3480	−	36.5445i	−0.471107	−	1.39426i
$688$	−0.202194	+	0.240965i	−0.00770857	+	0.00918671i
$689$	7.71529	+	6.47389i	0.293929	+	0.246636i
$690$		0			0
$691$	40.1126	+	14.5998i	1.52595	+	0.555402i	0.962627	−	0.270831i	$-0.0872986\pi$
$691$	40.1126	+	14.5998i	1.52595	+	0.555402i	0.563328	+	0.826234i	$0.309521\pi$
$692$	0.709196	+	0.409455i	0.0269596	+	0.0155651i
$693$	−14.8610	−	47.5983i	−0.564522	−	1.80811i
$694$	−2.30250	−	3.98805i	−0.0874018	−	0.151384i
$695$		0			0
$696$	8.18986	−	6.55419i	0.310436	−	0.248436i
$697$	11.6057	+	31.8865i	0.439598	+	1.20779i
$698$	−22.5098	−	3.96909i	−0.852010	−	0.150232i
$699$	−11.2649	−	20.6017i	−0.426077	−	0.779227i
$700$		0			0
$701$	−0.600532			−0.0226818			−0.0113409	−	0.999936i	$-0.503610\pi$
$701$	−0.600532			−0.0226818			−0.0113409	+	0.999936i	$0.503610\pi$
$702$	−0.220345	+	3.15808i	−0.00831637	+	0.119194i
$703$		−	13.4150i		−	0.505956i
$704$	−7.90321	+	6.63158i	−0.297863	+	0.249937i
$705$		0			0
$706$	0.794610	−	4.50646i	0.0299055	−	0.169603i
$707$	31.5696	+	86.7369i	1.18730	+	3.26208i
$708$	6.50765	−	16.6651i	0.244573	−	0.626314i
$709$	−8.93134	−	50.6521i	−0.335423	−	1.90228i	−0.423012	−	0.906124i	$-0.639027\pi$
$709$	−8.93134	−	50.6521i	−0.335423	−	1.90228i	0.0875888	−	0.996157i	$-0.472084\pi$
$710$		0			0
$711$	−4.74624	−	1.98158i	−0.177998	−	0.0743149i
$712$	−5.05032	−	2.91580i	−0.189269	−	0.109274i
$713$	3.46725	−	9.52618i	0.129849	−	0.356758i
$714$	7.44963	−	37.1791i	0.278795	−	1.39139i
$715$		0			0
$716$	−21.4190	−	17.9727i	−0.800465	−	0.671670i
$717$	6.98653	−	7.94410i	0.260917	−	0.296678i
$718$	5.33604	−	14.6606i	0.199139	−	0.547130i
$719$	2.39613	−	4.15021i	0.0893604	−	0.154777i	−0.817881	−	0.575388i	$-0.804851\pi$
$719$	2.39613	−	4.15021i	0.0893604	−	0.154777i	0.907241	+	0.420611i	$0.138184\pi$
$720$		0			0
$721$	3.41574	+	5.91623i	0.127209	+	0.220332i
$722$	0.172274	−	0.0303766i	0.00641139	−	0.00113050i
$723$	32.9689	−	5.02705i	1.22613	−	0.186958i
$724$	19.0400	−	6.92999i	0.707616	−	0.257551i
$725$		0			0
$726$	0.275206	−	0.452093i	0.0102138	−	0.0167788i
$727$	−10.1481	−	12.0941i	−0.376373	−	0.448544i	0.544293	−	0.838895i	$-0.316798\pi$
$727$	−10.1481	−	12.0941i	−0.376373	−	0.448544i	−0.920666	+	0.390351i	$0.872354\pi$
$728$			10.1911i			0.377706i
$729$	−26.7384	−	3.74942i	−0.990311	−	0.138867i
$730$		0			0
$731$	1.85129	−	1.55342i	0.0684726	−	0.0574553i
$732$	8.08809	+	4.92351i	0.298944	+	0.181978i
$733$	2.52244	+	0.444773i	0.0931683	+	0.0164281i	0.220038	−	0.975491i	$-0.429382\pi$
$733$	2.52244	+	0.444773i	0.0931683	+	0.0164281i	−0.126870	+	0.991919i	$0.540493\pi$
$734$	17.1972	−	6.25927i	0.634761	−	0.231034i
$735$		0			0
$736$	−1.25768	−	7.13266i	−0.0463587	−	0.262913i
$737$	−9.35900	+	5.40342i	−0.344743	+	0.199038i
$738$	−12.2672	+	6.34224i	−0.451564	+	0.233461i
$739$	−12.4456	+	21.5564i	−0.457818	+	0.792964i	−0.998845	−	0.0480413i	$-0.984702\pi$
$739$	−12.4456	+	21.5564i	−0.457818	+	0.792964i	0.541028	+	0.841005i	$0.318035\pi$
$740$		0			0
$741$	−4.42119	−	3.88827i	−0.162416	−	0.142839i
$742$	31.5573	−	37.6085i	1.15851	−	1.38065i
$743$	−0.918468	+	1.09459i	−0.0336953	+	0.0401565i	−0.782629	−	0.622489i	$-0.786122\pi$
$743$	−0.918468	+	1.09459i	−0.0336953	+	0.0401565i	0.748934	+	0.662645i	$0.230566\pi$
$744$	−7.35637	+	36.7137i	−0.269697	+	1.34599i
$745$		0			0
$746$	−5.57974	+	9.66440i	−0.204289	+	0.353839i
$747$	−18.7993	+	45.0277i	−0.687830	+	1.64748i
$748$	−23.3762	+	13.4963i	−0.854720	+	0.493473i
$749$	5.81296	+	32.9670i	0.212401	+	1.20459i
$750$		0			0
$751$	24.5964	−	8.95234i	0.897534	−	0.326676i	0.148270	−	0.988947i	$-0.452630\pi$
$751$	24.5964	−	8.95234i	0.897534	−	0.326676i	0.749264	+	0.662271i	$0.230407\pi$
$752$	5.89250	+	1.03901i	0.214878	+	0.0378887i
$753$	−0.0559513	+	2.40923i	−0.00203898	+	0.0877971i
$754$	1.07145	−	0.899049i	0.0390197	−	0.0327414i
$755$		0			0
$756$	−35.6560	−	2.48778i	−1.29680	−	0.0904797i
$757$		−	13.5023i		−	0.490750i	−0.969428	−	0.245375i	$-0.921089\pi$
$757$		−	13.5023i		−	0.490750i	0.969428	−	0.245375i	$-0.0789111\pi$
$758$	−16.2908	−	19.4146i	−0.591707	−	0.705169i
$759$	3.46982	+	6.34574i	0.125946	+	0.230336i
$760$		0			0
$761$	−38.1386	+	13.8813i	−1.38252	+	0.503197i	−0.922942	−	0.384939i	$-0.874222\pi$
$761$	−38.1386	+	13.8813i	−1.38252	+	0.503197i	−0.459580	+	0.888136i	$0.652000\pi$
$762$	−14.9528	−	18.6845i	−0.541683	−	0.676866i
$763$	−17.9778	+	3.16997i	−0.650839	+	0.114761i
$764$	2.75228	+	4.76708i	0.0995739	+	0.172467i
$765$		0			0
$766$	−2.13131	+	3.69154i	−0.0770074	+	0.133381i
$767$	1.98406	−	5.45115i	0.0716401	−	0.196830i
$768$	7.40912	+	21.9276i	0.267354	+	0.791243i
$769$	13.6615	+	11.4634i	0.492647	+	0.413380i	0.854974	−	0.518671i	$-0.173573\pi$
$769$	13.6615	+	11.4634i	0.492647	+	0.413380i	−0.362327	+	0.932051i	$0.618018\pi$
$770$		0			0
$771$	−6.85448	+	2.31606i	−0.246858	+	0.0834110i
$772$	−2.88801	+	7.93475i	−0.103942	+	0.285578i
$773$	21.3604	+	12.3324i	0.768279	+	0.443566i	0.832260	−	0.554385i	$-0.187046\pi$
$773$	21.3604	+	12.3324i	0.768279	+	0.443566i	−0.0639812	+	0.997951i	$0.520380\pi$
$774$	0.723266	+	0.666494i	0.0259973	+	0.0239566i
$775$		0			0
$776$	6.98081	+	39.5902i	0.250597	+	1.42120i
$777$	−16.4993	−	20.6169i	−0.591909	−	0.739626i
$778$	−4.64930	−	12.7738i	−0.166685	−	0.457965i
$779$	4.45992	−	25.2935i	0.159793	−	0.906233i
$780$		0			0
$781$	25.4815	−	21.3816i	0.911801	−	0.765092i
$782$			5.49973i			0.196670i
$783$	7.01314	+	9.64963i	0.250629	+	0.344850i
$784$	−12.8521			−0.459005
$785$		0			0
$786$	−8.11047	−	0.188356i	−0.289291	−	0.00671842i
$787$	1.27156	+	0.224210i	0.0453261	+	0.00799222i	0.196265	−	0.980551i	$-0.437119\pi$
$787$	1.27156	+	0.224210i	0.0453261	+	0.00799222i	−0.150939	+	0.988543i	$0.548230\pi$
$788$	−0.383117	−	1.05261i	−0.0136480	−	0.0374975i
$789$	14.0874	+	5.50106i	0.501525	+	0.195843i
$790$		0			0
$791$	−25.2611	−	43.7535i	−0.898180	−	1.55569i
$792$	−16.2025	−	21.2386i	−0.575730	−	0.754681i
$793$	2.65889	+	1.53511i	0.0944201	+	0.0545135i
$794$	3.23051	+	1.17581i	0.114647	+	0.0417280i
$795$		0			0
$796$	−4.96479	−	4.16595i	−0.175972	−	0.147658i
$797$	−13.5891	+	16.1949i	−0.481351	+	0.573652i	−0.950996	−	0.309203i	$-0.899938\pi$
$797$	−13.5891	+	16.1949i	−0.481351	+	0.573652i	0.469645	+	0.882856i	$0.344382\pi$
$798$	−18.9535	+	21.5513i	−0.670948	+	0.762907i
$799$	−43.1972	−	15.7225i	−1.52821	−	0.556222i
$800$		0			0
$801$	3.57895	−	5.58319i	0.126456	−	0.197272i
$802$	22.0850	−	12.7508i	0.779847	−	0.450245i
$803$	11.8210	−	2.08437i	0.417155	−	0.0735557i
$804$	1.16766	+	7.65783i	0.0411801	+	0.270071i
$805$		0			0
$806$	−0.866969	+	4.91683i	−0.0305377	+	0.173188i
$807$	5.28654	+	3.21811i	0.186095	+	0.113283i
$808$	31.7850	+	37.8799i	1.11819	+	1.33261i
$809$	41.8122			1.47004			0.735019	−	0.678047i	$-0.237173\pi$
$809$	41.8122			1.47004			0.735019	+	0.678047i	$0.237173\pi$
$810$		0			0
$811$	1.20717			0.0423894			0.0211947	−	0.999775i	$-0.493253\pi$
$811$	1.20717			0.0423894			0.0211947	+	0.999775i	$0.493253\pi$
$812$	10.1506	+	12.0970i	0.356217	+	0.424523i
$813$	20.6721	+	12.5838i	0.725001	+	0.441334i
$814$	1.40928	−	7.99241i	0.0493951	−	0.280134i
$815$		0			0
$816$	1.11368	+	7.30383i	0.0389866	+	0.255685i
$817$	−1.80140	+	0.317635i	−0.0630229	+	0.0111126i
$818$	17.8371	−	10.2982i	0.623659	−	0.360070i
$819$	−11.5770	−	0.538011i	−0.404532	−	0.0187996i
$820$		0			0
$821$	14.8150	+	5.39222i	0.517047	+	0.188190i	0.587346	−	0.809336i	$-0.300173\pi$
$821$	14.8150	+	5.39222i	0.517047	+	0.188190i	−0.0702986	+	0.997526i	$0.522395\pi$
$822$	13.3627	−	15.1942i	0.466079	−	0.529960i
$823$	18.1599	−	21.6421i	0.633015	−	0.754398i	−0.350235	−	0.936662i	$-0.613898\pi$
$823$	18.1599	−	21.6421i	0.633015	−	0.754398i	0.983250	+	0.182264i	$0.0583427\pi$
$824$	2.80353	+	2.35244i	0.0976656	+	0.0819512i
$825$		0			0
$826$	−26.5719	−	9.67138i	−0.924554	−	0.336510i
$827$	−16.4770	−	9.51297i	−0.572960	−	0.330799i	0.185371	−	0.982669i	$-0.440651\pi$
$827$	−16.4770	−	9.51297i	−0.572960	−	0.330799i	−0.758331	+	0.651870i	$0.773985\pi$
$828$	5.14173	−	0.662249i	0.178687	−	0.0230148i
$829$	−8.50721	−	14.7349i	−0.295468	−	0.511765i	0.679626	−	0.733559i	$-0.262142\pi$
$829$	−8.50721	−	14.7349i	−0.295468	−	0.511765i	−0.975094	+	0.221794i	$0.928809\pi$
$830$		0			0
$831$	31.3323	+	12.2351i	1.08691	+	0.424431i
$832$	0.820114	+	2.25324i	0.0284323	+	0.0781172i
$833$	97.2407	+	17.1462i	3.36919	+	0.594079i
$834$	−11.4770	−	0.266540i	−0.397417	−	0.00922952i
$835$		0			0
$836$	20.4306			0.706606
$837$	−41.3181	−	10.2950i	−1.42816	−	0.355846i
$838$			21.3864i			0.738780i
$839$	−0.767986	+	0.644416i	−0.0265138	+	0.0222477i	−0.655948	−	0.754806i	$-0.727731\pi$
$839$	−0.767986	+	0.644416i	−0.0265138	+	0.0222477i	0.629434	+	0.777054i	$0.283287\pi$
$840$		0			0
$841$	−4.12061	+	23.3691i	−0.142090	+	0.805832i
$842$	7.21601	+	19.8258i	0.248680	+	0.683243i
$843$	21.6472	+	27.0495i	0.745569	+	0.931634i
$844$	−1.52416	−	8.64394i	−0.0524637	−	0.297537i
$845$		0			0
$846$	4.10046	−	18.2534i	0.140977	−	0.627566i
$847$	1.67800	+	0.968796i	0.0576569	+	0.0332882i
$848$	−3.27174	+	8.98902i	−0.112352	+	0.308684i
$849$	17.9548	−	6.06675i	0.616207	−	0.208210i
$850$		0			0
$851$	2.93395	+	2.46188i	0.100574	+	0.0843920i
$852$	−7.63255	−	22.5888i	−0.261487	−	0.773880i
$853$	10.1529	−	27.8950i	0.347630	−	0.955106i	−0.635484	−	0.772114i	$-0.719200\pi$
$853$	10.1529	−	27.8950i	0.347630	−	0.955106i	0.983114	−	0.182992i	$-0.0585783\pi$
$854$	7.48298	−	12.9609i	0.256062	−	0.443513i
$855$		0			0
$856$	8.96674	+	15.5308i	0.306477	+	0.530833i
$857$	33.9292	−	5.98263i	1.15900	−	0.204363i	0.439097	−	0.898439i	$-0.355298\pi$
$857$	33.9292	−	5.98263i	1.15900	−	0.204363i	0.719901	+	0.694077i	$0.244187\pi$
$858$	−2.22559	−	2.78102i	−0.0759805	−	0.0949423i
$859$	−21.6343	+	7.87422i	−0.738151	+	0.268665i	−0.683611	−	0.729847i	$-0.739592\pi$
$859$	−21.6343	+	7.87422i	−0.738151	+	0.268665i	−0.0545401	+	0.998512i	$0.517369\pi$
$860$		0			0
$861$	−24.2546	−	44.3577i	−0.826593	−	1.51171i
$862$	−3.22993	−	3.84928i	−0.110012	−	0.131107i
$863$			17.0095i			0.579009i	0.957177	+	0.289504i	$0.0934905\pi$
$863$			17.0095i			0.579009i	−0.957177	+	0.289504i	$0.906509\pi$
$864$	−29.2421	+	8.38993i	−0.994837	+	0.285431i
$865$		0			0
$866$	11.2884	−	9.47209i	0.383595	−	0.321875i
$867$	0.634250	−	27.3104i	0.0215403	−	0.927510i
$868$	−55.5130	−	9.78843i	−1.88423	−	0.332241i
$869$	5.43793	−	1.97924i	0.184469	−	0.0671412i
$870$		0			0
$871$	0.436156	+	2.47357i	0.0147786	+	0.0838136i
$872$	−8.46939	+	4.88981i	−0.286810	+	0.165590i
$873$	−45.3426	+	5.84008i	−1.53462	+	0.197657i
$874$	2.08136	−	3.60502i	0.0704031	−	0.121942i
$875$		0			0
$876$	1.69040	−	8.43633i	0.0571133	−	0.285037i
$877$	9.26361	−	11.0399i	0.312810	−	0.372792i	−0.586616	−	0.809865i	$-0.699540\pi$
$877$	9.26361	−	11.0399i	0.312810	−	0.372792i	0.899426	+	0.437073i	$0.143985\pi$
$878$	−14.7445	+	17.5718i	−0.497604	+	0.593021i
$879$	−8.33685	−	7.33194i	−0.281195	−	0.247300i
$880$		0			0
$881$	−3.76414	+	6.51968i	−0.126817	+	0.219654i	−0.922442	−	0.386136i	$-0.873809\pi$
$881$	−3.76414	+	6.51968i	−0.126817	+	0.219654i	0.795625	+	0.605790i	$0.207143\pi$
$882$	−1.86548	+	40.1415i	−0.0628140	+	1.35163i
$883$	−28.8410	+	16.6514i	−0.970578	+	0.560363i	−0.899412	−	0.437101i	$-0.856005\pi$
$883$	−28.8410	+	16.6514i	−0.970578	+	0.560363i	−0.0711656	+	0.997465i	$0.522672\pi$
$884$	1.08940	+	6.17829i	0.0366405	+	0.207799i
$885$		0			0
$886$	−9.99901	+	3.63934i	−0.335923	+	0.122266i
$887$	−16.6274	−	2.93186i	−0.558294	−	0.0984423i	−0.112621	−	0.993638i	$-0.535925\pi$
$887$	−16.6274	−	2.93186i	−0.558294	−	0.0984423i	−0.445673	+	0.895196i	$0.647036\pi$
$888$	−12.0835	−	7.35566i	−0.405495	−	0.246840i
$889$	67.1121	−	56.3137i	2.25087	−	1.88870i
$890$		0			0
$891$	24.9823	−	17.2846i	0.836937	−	0.579057i
$892$			0.294758i			0.00986924i
$893$	22.3652	+	26.6538i	0.748424	+	0.891937i
$894$	−6.91292	+	11.3562i	−0.231203	+	0.379807i
$895$		0			0
$896$	−43.1992	+	15.7232i	−1.44318	+	0.525275i
$897$	1.66175	−	0.253382i	0.0554843	−	0.00846018i
$898$	24.8159	−	4.37571i	0.828116	−	0.146019i
$899$	9.40648	+	16.2925i	0.313724	+	0.543386i
$900$		0			0
$901$	36.7467	−	63.6471i	1.22421	−	2.12039i
$902$	5.31428	−	14.6009i	0.176946	−	0.486156i
$903$	−2.37782	+	2.70372i	−0.0791289	+	0.0899742i
$904$	−20.7335	−	17.3975i	−0.689586	−	0.578631i
$905$		0			0
$906$	0.897056	−	4.47697i	0.0298027	−	0.148737i
$907$	−2.57952	+	7.08716i	−0.0856514	+	0.235325i	−0.975123	−	0.221666i	$-0.928851\pi$
$907$	−2.57952	+	7.08716i	−0.0856514	+	0.235325i	0.889471	+	0.456991i	$0.151073\pi$
$908$	−8.52938	−	4.92444i	−0.283057	−	0.163423i
$909$	−44.7093	+	34.1078i	−1.48291	+	1.13128i
$910$		0			0
$911$	1.57637	+	8.94003i	0.0522274	+	0.296196i	0.999722	−	0.0235753i	$-0.00750494\pi$
$911$	1.57637	+	8.94003i	0.0522274	+	0.296196i	−0.947495	+	0.319772i	$0.896394\pi$
$912$	2.03411	−	5.20906i	0.0673562	−	0.172489i
$913$	−18.7772	−	51.5898i	−0.621434	−	1.70737i
$914$	2.24461	−	12.7298i	0.0742451	−	0.421065i
$915$		0			0
$916$	23.8318	−	19.9972i	0.787423	−	0.660727i
$917$		−	29.6994i		−	0.980761i
$918$	22.9739	−	2.41824i	0.758252	−	0.0798139i
$919$	27.0698			0.892951			0.446475	−	0.894796i	$-0.352679\pi$
$919$	27.0698			0.892951			0.446475	+	0.894796i	$0.352679\pi$
$920$		0			0
$921$	−9.46100	−	17.3026i	−0.311750	−	0.570141i
$922$	−25.2516	−	4.45253i	−0.831616	−	0.146636i
$923$	−2.64421	−	7.26492i	−0.0870353	−	0.239128i
$924$	31.3988	−	25.1279i	1.03294	−	0.826646i
$925$		0			0
$926$	13.2008	+	22.8645i	0.433807	+	0.751375i
$927$	−2.82036	+	3.06060i	−0.0926328	+	0.100523i
$928$	11.6400	+	6.72039i	0.382103	+	0.220607i
$929$	30.5625	+	11.1238i	1.00272	+	0.364962i	0.790634	−	0.612289i	$-0.209751\pi$
$929$	30.5625	+	11.1238i	1.00272	+	0.364962i	0.212090	+	0.977250i	$0.431973\pi$
$930$		0			0
$931$	−57.2515	−	48.0397i	−1.87634	−	1.57444i
$932$	12.1724	−	14.5065i	0.398720	−	0.475176i
$933$	1.15027	+	3.40427i	0.0376582	+	0.111451i
$934$	−1.30461	−	0.474840i	−0.0426882	−	0.0155372i
$935$		0			0
$936$	−5.92655	+	1.85037i	−0.193715	+	0.0604811i
$937$	−18.8358	+	10.8749i	−0.615340	+	0.355267i	−0.775052	−	0.631897i	$-0.782277\pi$
$937$	−18.8358	+	10.8749i	−0.615340	+	0.355267i	0.159713	+	0.987164i	$0.448943\pi$
$938$	12.0575	−	2.12606i	0.393692	−	0.0694185i
$939$	32.5360	−	26.0380i	1.06177	−	0.849717i
$940$		0			0
$941$	0.523029	−	2.96625i	0.0170503	−	0.0966969i	−0.975095	−	0.221787i	$-0.928811\pi$
$941$	0.523029	−	2.96625i	0.0170503	−	0.0966969i	0.992145	+	0.125090i	$0.0399221\pi$
$942$	25.5049	−	13.9459i	0.830994	−	0.454383i
$943$	4.71338	+	5.61719i	0.153489	+	0.182921i
$944$	5.50974			0.179327
$945$		0			0
$946$	−1.10661			−0.0359789
$947$	10.6073	+	12.6413i	0.344692	+	0.410787i	0.910341	−	0.413858i	$-0.135819\pi$
$947$	10.6073	+	12.6413i	0.344692	+	0.410787i	−0.565650	+	0.824646i	$0.691375\pi$
$948$	0.0963076	−	4.14694i	0.00312793	−	0.134686i
$949$	0.484448	−	2.74744i	0.0157258	−	0.0891857i
$950$		0			0
$951$	−11.8857	−	4.64128i	−0.385419	−	0.150504i
$952$	73.2353	−	12.9134i	2.37357	−	0.418524i
$953$	24.2702	−	14.0124i	0.786190	−	0.453907i	−0.0524298	−	0.998625i	$-0.516697\pi$
$953$	24.2702	−	14.0124i	0.786190	−	0.453907i	0.838619	+	0.544718i	$0.183363\pi$
$954$	27.6008	+	11.5235i	0.893609	+	0.373086i
$955$		0			0
$956$	8.01761	+	2.91817i	0.259308	+	0.0943804i
$957$	−13.1602	−	2.63692i	−0.425407	−	0.0852394i
$958$	9.27803	−	11.0571i	0.299760	−	0.357240i
$959$	56.7450	+	47.6147i	1.83239	+	1.53756i
$960$		0			0
$961$	−33.9741	−	12.3656i	−1.09594	−	0.398889i
$962$	−1.63354	−	0.943125i	−0.0526675	−	0.0304076i
$963$	−18.1163	+	9.36623i	−0.583789	+	0.301823i
$964$	13.4484	+	23.2932i	0.433142	+	0.750225i
$965$		0			0
$966$	−1.23512	−	8.10029i	−0.0397394	−	0.260623i
$967$	−4.22850	−	11.6177i	−0.135979	−	0.373601i	0.852949	−	0.521995i	$-0.174812\pi$
$967$	−4.22850	−	11.6177i	−0.135979	−	0.373601i	−0.988928	+	0.148394i	$0.952590\pi$
$968$	1.02223	+	0.180248i	0.0328559	+	0.00579338i
$969$	−22.3398	+	36.6986i	−0.717657	+	1.17893i
$970$		0			0
$971$	−24.0943			−0.773224			−0.386612	−	0.922242i	$-0.626355\pi$
$971$	−24.0943			−0.773224			−0.386612	+	0.922242i	$0.626355\pi$
$972$	−5.02723	−	21.1872i	−0.161248	−	0.679581i
$973$		−	42.0273i		−	1.34733i
$974$	−10.0561	+	8.43808i	−0.322219	+	0.270374i
$975$		0			0
$976$	−0.506371	+	2.87177i	−0.0162086	+	0.0919233i
$977$	14.5207	+	39.8952i	0.464558	+	1.27636i	0.922023	+	0.387134i	$0.126535\pi$
$977$	14.5207	+	39.8952i	0.464558	+	1.27636i	−0.457466	+	0.889227i	$0.651243\pi$
$978$	8.81269	−	1.34375i	0.281799	−	0.0429684i
$979$	1.29571	+	7.34835i	0.0414112	+	0.234854i
$980$		0			0
$981$	−5.10766	−	9.87930i	−0.163075	−	0.315422i
$982$	−0.734902	−	0.424296i	−0.0234517	−	0.0135398i
$983$	17.6012	−	48.3589i	0.561392	−	1.54241i	−0.256207	−	0.966622i	$-0.582473\pi$
$983$	17.6012	−	48.3589i	0.561392	−	1.54241i	0.817598	−	0.575789i	$-0.195305\pi$
$984$	−20.3375	−	17.8861i	−0.648337	−	0.570187i
$985$		0			0
$986$	−7.81843	−	6.56044i	−0.248990	−	0.208927i
$987$	67.1540	+	13.4557i	2.13754	+	0.428301i
$988$	1.62407	−	4.46210i	0.0516686	−	0.141958i
$989$	0.261118	−	0.452269i	0.00830306	−	0.0143813i
$990$		0			0
$991$	−16.2637	−	28.1695i	−0.516632	−	0.894833i	−0.999813	−	0.0193130i	$-0.993852\pi$
$991$	−16.2637	−	28.1695i	−0.516632	−	0.894833i	0.483181	−	0.875520i	$-0.339481\pi$
$992$	−47.2491	+	8.33128i	−1.50016	+	0.264519i
$993$	−0.0811844	+	0.207901i	−0.00257631	+	0.00659755i
$994$	−35.4132	+	12.8893i	−1.12324	+	0.408825i
$995$		0			0
$996$	−39.3422	−	0.913674i	−1.24661	−	0.0289509i
$997$	5.40517	+	6.44164i	0.171184	+	0.204009i	0.844815	−	0.535059i	$-0.179711\pi$
$997$	5.40517	+	6.44164i	0.171184	+	0.204009i	−0.673631	+	0.739068i	$0.735266\pi$
$998$		−	1.12022i		−	0.0354598i
$999$	8.99388	−	13.3384i	0.284554	−	0.422009i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.u.e.49.14		132
5.2	odd	4		675.2.l.f.76.5	✓	66
5.3	odd	4		675.2.l.g.76.7	yes	66
5.4	even	2	inner	675.2.u.e.49.9		132
27.16	even	9	inner	675.2.u.e.124.9		132
135.43	odd	36		675.2.l.g.151.7	yes	66
135.97	odd	36		675.2.l.f.151.5	yes	66
135.124	even	18	inner	675.2.u.e.124.14		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
675.2.l.f.76.5	✓	66	5.2	odd	4
675.2.l.f.151.5	yes	66	135.97	odd	36
675.2.l.g.76.7	yes	66	5.3	odd	4
675.2.l.g.151.7	yes	66	135.43	odd	36
675.2.u.e.49.9		132	5.4	even	2	inner
675.2.u.e.49.14		132	1.1	even	1	trivial
675.2.u.e.124.9		132	27.16	even	9	inner
675.2.u.e.124.14		132	135.124	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.499186 + 0.594907i) q^{2} +(-1.47949 - 0.900618i) q^{3} +(0.242569 - 1.37568i) q^{4} +(-0.202756 - 1.32973i) q^{6} +(4.84944 - 0.855088i) q^{7} +(2.28459 - 1.31901i) q^{8} +(1.37777 + 2.66491i) q^{9} +(-3.17186 - 1.15446i) q^{11} +(-1.59784 + 1.81684i) q^{12} +(-0.504276 + 0.600973i) q^{13} +(2.92947 + 2.45812i) q^{14} +(-0.700189 - 0.254848i) q^{16} +(4.95771 + 2.86234i) q^{17} +(-0.897607 + 2.14993i) q^{18} +(-2.16649 - 3.75247i) q^{19} +(-7.94481 - 3.10240i) q^{21} +(-0.896551 - 2.46325i) q^{22} +(1.21828 + 0.214816i) q^{23} +(-4.56795 - 0.106085i) q^{24} -0.609251 q^{26} +(0.361665 - 5.18355i) q^{27} -6.87869i q^{28} +(-1.75863 + 1.47566i) q^{29} +(1.42301 - 8.07028i) q^{31} +(-2.00242 - 5.50161i) q^{32} +(3.65300 + 4.56465i) q^{33} +(0.771998 + 4.37822i) q^{34} +(4.00026 - 1.24895i) q^{36} +(2.68123 + 1.54801i) q^{37} +(1.15089 - 3.16204i) q^{38} +(1.28732 - 0.434973i) q^{39} +(4.54071 + 3.81011i) q^{41} +(-2.12029 - 6.27510i) q^{42} +(0.144385 - 0.396695i) q^{43} +(-2.35756 + 4.08342i) q^{44} +(0.480353 + 0.831996i) q^{46} +(-7.90806 + 1.39441i) q^{47} +(0.806401 + 1.00765i) q^{48} +(16.2081 - 5.89926i) q^{49} +(-4.75701 - 8.69981i) q^{51} +(0.704423 + 0.839499i) q^{52} -12.8380i q^{53} +(3.26427 - 2.37240i) q^{54} +(9.95112 - 8.34998i) q^{56} +(-0.174246 + 7.50292i) q^{57} +(-1.75576 - 0.309589i) q^{58} +(-6.94844 + 2.52902i) q^{59} +(-0.679578 - 3.85408i) q^{61} +(5.51141 - 3.18202i) q^{62} +(8.96017 + 11.7452i) q^{63} +(1.52824 - 2.64699i) q^{64} +(-0.892014 + 4.45180i) q^{66} +(2.05797 - 2.45259i) q^{67} +(5.14024 - 6.12590i) q^{68} +(-1.60896 - 1.41502i) q^{69} +(-4.92735 + 8.53442i) q^{71} +(6.66269 + 4.27093i) q^{72} +(-3.07968 + 1.77806i) q^{73} +(0.417511 + 2.36782i) q^{74} +(-5.68772 + 2.07016i) q^{76} +(-16.3689 - 2.88628i) q^{77} +(0.901380 + 0.548702i) q^{78} +(-1.31333 + 1.10201i) q^{79} +(-5.20348 + 7.34328i) q^{81} +4.60325i q^{82} +(10.4548 + 12.4596i) q^{83} +(-6.19507 + 10.1769i) q^{84} +(0.308071 - 0.112129i) q^{86} +(3.93088 - 0.599376i) q^{87} +(-8.76914 + 1.54624i) q^{88} +(-1.10530 - 1.91444i) q^{89} +(-1.93158 + 3.34559i) q^{91} +(0.591034 - 1.62385i) q^{92} +(-9.37357 + 10.6583i) q^{93} +(-4.77714 - 4.00849i) q^{94} +(-1.99229 + 9.94300i) q^{96} +(-5.21207 + 14.3200i) q^{97} +(11.6004 + 6.69747i) q^{98} +(-1.29357 - 10.0433i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 12 q^{6} + 12 q^{9} + 30 q^{11} - 30 q^{14} + 36 q^{16} - 24 q^{19} + 24 q^{21} + 78 q^{24} + 12 q^{26} + 30 q^{29} + 6 q^{31} + 60 q^{36} + 30 q^{39} + 78 q^{41} - 102 q^{44} + 18 q^{46} + 12 q^{49}+ \cdots + 96 q^{99}+O(q^{100}) \) 132 * q - 12 * q^6 + 12 * q^9 + 30 * q^11 - 30 * q^14 + 36 * q^16 - 24 * q^19 + 24 * q^21 + 78 * q^24 + 12 * q^26 + 30 * q^29 + 6 * q^31 + 60 * q^36 + 30 * q^39 + 78 * q^41 - 102 * q^44 + 18 * q^46 + 12 * q^49 - 150 * q^54 + 288 * q^56 - 90 * q^59 - 108 * q^61 + 48 * q^64 + 96 * q^66 - 102 * q^69 - 30 * q^71 - 192 * q^74 - 96 * q^76 - 96 * q^79 - 108 * q^81 - 114 * q^84 - 222 * q^86 + 24 * q^89 + 18 * q^91 - 72 * q^94 - 498 * q^96 + 96 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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