LMFDB - Embedded newform 675.2.u.e.49.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(49,675)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			49.9
Character	$\chi$	$=$	675.49
Dual form			675.2.u.e.124.9

$q$-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	0.560115	−	0.828415i	$-0.310757\pi$
$2$	−0.499186	−	0.594907i	−0.352978	−	0.420663i	−0.913092	+	0.407752i	$0.866313\pi$
$3$	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	−0.980022	−	0.198889i	$-0.936267\pi$
$7$	−4.84944	+	0.855088i	−1.83292	+	0.323193i	−0.852896	+	0.522082i	$0.825156\pi$
$8$	−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	−0.691567	−	0.722312i	$-0.743079\pi$
$13$	0.504276	−	0.600973i	0.139861	−	0.166680i	0.831428	+	0.555632i	$0.187524\pi$
$14$	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	−0.241329	−	0.970443i	$-0.577583\pi$
$17$	−4.95771	−	2.86234i	−1.20242	−	0.694219i	−0.961093	+	0.276224i	$0.910917\pi$
$18$	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	0.0451834	−	0.998979i	$-0.485613\pi$
$23$	−1.21828	−	0.214816i	−0.254029	−	0.0447921i	−0.299212	+	0.954187i	$0.596724\pi$
$24$	−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	0.263142	−	0.964757i	$-0.415241\pi$
$37$	−2.68123	−	1.54801i	−0.440791	−	0.254491i	−0.703933	+	0.710266i	$0.748575\pi$
$38$	−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	−0.950215	−	0.311595i	$-0.899137\pi$
$43$	−0.144385	+	0.396695i	−0.0220185	+	0.0604954i	0.928196	+	0.372091i	$0.121359\pi$
$44$	−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	0.436002	−	0.899946i	$-0.356394\pi$
$47$	7.90806	−	1.39441i	1.15351	−	0.203395i	0.717508	+	0.696551i	$0.245283\pi$
$48$	−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	$0.343612\pi$
$53$			12.8380i			1.76343i	−0.471779	+	0.881717i	$0.656388\pi$
$54$	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	−0.876962	−	0.480559i	$-0.840434\pi$
$67$	−2.05797	+	2.45259i	−0.251421	+	0.299631i	0.625542	+	0.780191i	$0.284878\pi$
$68$	−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	−0.308828	−	0.951118i	$-0.599937\pi$
$73$	3.07968	−	1.77806i	0.360450	−	0.208106i	0.669278	+	0.743012i	$0.266604\pi$
$74$	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	$-0.871066\pi$
$83$	−10.4548	−	12.4596i	−1.14757	−	1.36762i	−0.228490	−	0.973546i	$-0.573379\pi$
$84$	−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	$-0.607320\pi$
$97$	5.21207	−	14.3200i	0.529205	−	1.45398i	0.860009	−	0.510279i	$-0.170458\pi$
$98$	−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	0.914119	−	0.405446i	$-0.132884\pi$
$103$	−0.474488	−	1.30365i	−0.0467527	−	0.128452i	−0.960872	+	0.276994i	$0.910662\pi$
$104$	−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	$-0.893424\pi$
$107$		−	6.79809i		−	0.657196i	0.944470	−	0.328598i	$-0.106576\pi$
$108$	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	$0.0491902\pi$
$113$	3.50908	+	9.64111i	0.330106	+	0.906959i	−0.657977	+	0.753038i	$0.728588\pi$
$114$	−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	−0.990571	−	0.137002i	$-0.956253\pi$
$127$	−15.4077	+	8.89562i	−1.36721	+	0.789359i	−0.376639	+	0.926360i	$0.622920\pi$
$128$	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	0.173885	−	0.984766i	$-0.444368\pi$
$137$	−9.66943	−	11.5236i	−0.826115	−	0.984525i	−1.00000		0.000240652i	$0.999923\pi$
$138$	−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	$-0.780095\pi$
$157$	−7.39131	−	20.3075i	−0.589891	−	1.62071i	0.180812	−	0.983518i	$-0.442127\pi$
$158$	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	$-0.916426\pi$
$163$		−	6.62741i		−	0.519099i	0.965730	−	0.259549i	$-0.0835741\pi$
$164$	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	$-0.849165\pi$
$167$	−6.48077	−	17.8058i	−0.501497	−	1.37785i	0.388315	−	0.921527i	$-0.373057\pi$
$168$	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	−0.931837	−	0.362876i	$-0.881795\pi$
$173$	0.200504	−	0.550879i	0.0152440	−	0.0418826i	0.947081	+	0.320994i	$0.104017\pi$
$174$	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	0.383741	−	0.923441i	$-0.374636\pi$
$193$	5.95297	+	1.04967i	0.428504	+	0.0755568i	0.0447632	+	0.998998i	$0.485747\pi$
$194$	−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	−0.524535	−	0.851389i	$-0.675761\pi$
$197$	−0.694457	+	0.400945i	−0.0494780	+	0.0285662i	0.475057	+	0.879955i	$0.342427\pi$
$198$	−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	−0.166686	−	0.986010i	$-0.553307\pi$
$223$	0.207803	−	0.0366413i	0.0139155	−	0.00245368i	0.180602	+	0.983556i	$0.442196\pi$
$224$	−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	−0.993634	−	0.112657i	$-0.964064\pi$
$227$	−2.41142	+	6.62533i	−0.160052	+	0.439739i	0.833582	+	0.552395i	$0.186286\pi$
$228$	−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	0.0634379	−	0.997986i	$-0.479794\pi$
$233$	−11.7402	−	6.77819i	−0.769124	−	0.444054i	−0.832562	+	0.553932i	$0.813127\pi$
$234$	−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	−0.843261	−	0.537505i	$-0.819367\pi$
$257$	−2.68508	+	3.19995i	−0.167491	+	0.199608i	0.675770	+	0.737113i	$0.263811\pi$
$258$	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	0.0978761	−	0.995199i	$-0.468795\pi$
$263$	8.59885	−	1.51621i	0.530228	−	0.0934934i	0.432351	+	0.901705i	$0.357684\pi$
$264$	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	0.433523	−	0.901143i	$-0.357270\pi$
$277$	19.1250	−	3.37225i	1.14911	−	0.202619i	0.715587	+	0.698524i	$0.246159\pi$
$278$	−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	−0.515357	−	0.856976i	$-0.672341\pi$
$283$	7.03336	−	8.38203i	0.418090	−	0.498260i	0.933447	+	0.358715i	$0.116785\pi$
$284$	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	−0.0138134	−	0.999905i	$-0.504397\pi$
$293$	−6.31252	−	1.11307i	−0.368781	−	0.0650261i	−0.354968	+	0.934879i	$0.615508\pi$
$294$	−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	0.191499	−	0.981493i	$-0.438665\pi$
$307$	−9.86017	−	5.69277i	−0.562750	−	0.324904i	−0.754248	+	0.656589i	$0.771999\pi$
$308$	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	$-0.650886\pi$
$313$	8.22881	−	22.6085i	0.465120	−	1.27791i	0.921589	−	0.388167i	$-0.126892\pi$
$314$	−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	−0.373629	−	0.927578i	$-0.621887\pi$
$317$	−7.25490	+	1.27924i	−0.407476	+	0.0718490i	−0.0338465	+	0.999427i	$0.510776\pi$
$318$	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	−0.936931	−	0.349514i	$-0.886347\pi$
$337$	−7.89430	+	9.40807i	−0.430030	+	0.512490i	0.506901	+	0.862004i	$0.330791\pi$
$338$	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	0.328179	−	0.944616i	$-0.393565\pi$
$347$	5.83965	+	1.02969i	0.313489	+	0.0552765i	−0.0146902	+	0.999892i	$0.504676\pi$
$348$	−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	0.857363	−	0.514713i	$-0.172101\pi$
$353$	3.78753	+	4.51380i	0.201590	+	0.240246i	−0.655773	+	0.754958i	$0.727657\pi$
$354$	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	$0.321977\pi$
$367$	−8.05989	+	22.1444i	−0.420723	+	1.15593i	−0.951294	+	0.308286i	$0.900245\pi$
$368$	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	$-0.989777\pi$
$373$	−4.91475	−	13.5032i	−0.254476	−	0.699167i	0.745008	−	0.667055i	$-0.232445\pi$
$374$	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	0.882444	−	0.470417i	$-0.155897\pi$
$383$	−1.87730	−	5.15784i	−0.0959255	−	0.263553i	−0.978370	+	0.206864i	$0.933674\pi$
$384$	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	−0.593110	−	0.805121i	$-0.702100\pi$
$397$	−3.83373	+	2.21340i	−0.192409	+	0.111088i	0.400701	+	0.916209i	$0.368767\pi$
$398$	−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	$0.150697\pi$
$433$			18.9751i			0.911883i	−0.890010	+	0.455942i	$0.849303\pi$
$434$	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	−0.777195	−	0.629260i	$-0.783358\pi$
$443$	4.68628	−	12.8754i	0.222652	−	0.611731i	0.999846	+	0.0175297i	$0.00558017\pi$
$444$	−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	0.955850	−	0.293855i	$-0.0949382\pi$
$457$	10.6990	+	12.7506i	0.500478	+	0.596446i	−0.455372	+	0.890301i	$0.650494\pi$
$458$		−	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	−0.671510	−	0.740996i	$-0.734354\pi$
$463$	−33.4802	−	5.90347i	−1.55596	−	0.274357i	−0.884448	+	0.466638i	$0.845465\pi$
$464$	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	−0.463751	−	0.885966i	$-0.653497\pi$
$467$	1.54822	−	0.893863i	0.0716429	−	0.0413630i	0.535394	+	0.844603i	$0.320163\pi$
$468$	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	$-0.874895\pi$
$487$		−	16.9037i		−	0.765979i	0.923753	−	0.382989i	$-0.125105\pi$
$488$	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	0.884454	−	0.466628i	$-0.154531\pi$
$503$	20.6911	+	11.9460i	0.922569	+	0.532645i	0.0381151	+	0.999273i	$0.487865\pi$
$504$	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	−0.189821	−	0.981819i	$-0.560791\pi$
$523$	−25.9568	−	14.9862i	−1.13501	−	0.655299i	−0.945190	+	0.326520i	$0.894124\pi$
$524$	−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	−0.832056	−	0.554692i	$-0.812836\pi$
$547$	−33.3096	+	5.87339i	−1.42422	+	0.251128i	−0.592161	+	0.805819i	$0.701725\pi$
$548$	−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	0.886282	−	0.463146i	$-0.153280\pi$
$557$	21.9093	+	12.6493i	0.928326	+	0.535969i	0.0420444	+	0.999116i	$0.486613\pi$
$558$	−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	0.930971	−	0.365092i	$-0.118963\pi$
$563$	39.8845	+	7.03270i	1.68093	+	0.296393i	0.749958	+	0.661486i	$0.230074\pi$
$564$	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	0.828548	−	0.559918i	$-0.189167\pi$
$577$	18.2058	+	10.5111i	0.757919	+	0.437585i	−0.0706290	+	0.997503i	$0.522501\pi$
$578$	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	−0.672964	−	0.739675i	$-0.734979\pi$
$587$	−25.4966	+	4.49575i	−1.05236	+	0.185559i	−0.379395	+	0.925235i	$0.623868\pi$
$588$	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	$-0.949685\pi$
$593$		−	7.66640i		−	0.314821i	0.987533	−	0.157411i	$-0.0503146\pi$
$594$	−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	$-0.529615\pi$
$607$	22.2667	−	26.5364i	0.903776	−	1.07708i	0.996681	−	0.0814033i	$-0.0259402\pi$
$608$	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	−0.198103	−	0.980181i	$-0.563478\pi$
$613$	13.6596	−	7.88639i	0.551708	−	0.318528i	0.749810	+	0.661653i	$0.230145\pi$
$614$	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	0.818603	−	0.574360i	$-0.194749\pi$
$617$	34.5615	+	6.09413i	1.39139	+	0.245340i	0.572792	+	0.819701i	$0.305860\pi$
$618$	−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	0.820271	−	0.571975i	$-0.193822\pi$
$643$	−4.45660	−	12.2444i	−0.175751	−	0.482873i	−0.996022	+	0.0891022i	$0.971600\pi$
$644$	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	$0.257357\pi$
$647$			36.7940i			1.44652i	−0.690576	+	0.723260i	$0.742643\pi$
$648$	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	$0.199138\pi$
$653$	14.4650	+	39.7421i	0.566057	+	1.55523i	−0.244548	+	0.969637i	$0.578640\pi$
$654$	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	0.961638	−	0.274322i	$-0.0884536\pi$
$673$	13.6066	+	16.2157i	0.524496	+	0.625070i	−0.437142	+	0.899393i	$0.644009\pi$
$674$	9.53765			0.367376
$675$		0			0
$676$	17.2999			0.665383
$677$	4.85067	+	5.78080i	0.186426	+	0.222174i	0.851160	−	0.524906i	$-0.175900\pi$
$677$	4.85067	+	5.78080i	0.186426	+	0.222174i	−0.664734	+	0.747080i	$0.731455\pi$
$678$	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	−0.540722	−	0.841201i	$-0.681849\pi$
$683$	−2.15819	+	1.24603i	−0.0825810	+	0.0476781i	0.458141	+	0.888880i	$0.348516\pi$
$684$	−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	0.920666	−	0.390351i	$-0.127646\pi$
$727$	10.1481	+	12.0941i	0.376373	+	0.448544i	−0.544293	+	0.838895i	$0.683202\pi$
$728$		−	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	0.126870	−	0.991919i	$-0.459507\pi$
$733$	−2.52244	−	0.444773i	−0.0931683	−	0.0164281i	−0.220038	+	0.975491i	$0.570618\pi$
$734$	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	−0.748934	−	0.662645i	$-0.769434\pi$
$743$	0.918468	−	1.09459i	0.0336953	−	0.0401565i	0.782629	+	0.622489i	$0.213878\pi$
$744$	−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	$0.0789111\pi$
$757$			13.5023i			0.490750i	−0.969428	+	0.245375i	$0.921089\pi$
$758$	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	0.0639812	−	0.997951i	$-0.479620\pi$
$773$	−21.3604	−	12.3324i	−0.768279	−	0.443566i	−0.832260	+	0.554385i	$0.812954\pi$
$774$	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	0.150939	−	0.988543i	$-0.451770\pi$
$787$	−1.27156	−	0.224210i	−0.0453261	−	0.00799222i	−0.196265	+	0.980551i	$0.562881\pi$
$788$	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	−0.469645	−	0.882856i	$-0.655618\pi$
$797$	13.5891	−	16.1949i	0.481351	−	0.573652i	0.950996	+	0.309203i	$0.100062\pi$
$798$	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	−0.983250	−	0.182264i	$-0.941657\pi$
$823$	−18.1599	+	21.6421i	−0.633015	+	0.754398i	0.350235	+	0.936662i	$0.386102\pi$
$824$	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	0.758331	−	0.651870i	$-0.226015\pi$
$827$	16.4770	+	9.51297i	0.572960	+	0.330799i	−0.185371	+	0.982669i	$0.559349\pi$
$828$	−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	$0.280800\pi$
$853$	−10.1529	+	27.8950i	−0.347630	+	0.955106i	−0.983114	+	0.182992i	$0.941422\pi$
$854$	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	−0.719901	−	0.694077i	$-0.755813\pi$
$857$	−33.9292	+	5.98263i	−1.15900	+	0.204363i	−0.439097	+	0.898439i	$0.644702\pi$
$858$	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	$-0.906509\pi$
$863$		−	17.0095i		−	0.579009i	0.957177	−	0.289504i	$-0.0934905\pi$
$864$	−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	−0.899426	−	0.437073i	$-0.856015\pi$
$877$	−9.26361	+	11.0399i	−0.312810	+	0.372792i	0.586616	+	0.809865i	$0.300460\pi$
$878$	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	0.0711656	−	0.997465i	$-0.477328\pi$
$883$	28.8410	−	16.6514i	0.970578	−	0.560363i	0.899412	+	0.437101i	$0.143995\pi$
$884$	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	0.445673	−	0.895196i	$-0.352964\pi$
$887$	16.6274	+	2.93186i	0.558294	+	0.0984423i	0.112621	+	0.993638i	$0.464075\pi$
$888$	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	−0.889471	−	0.456991i	$-0.848927\pi$
$907$	2.57952	−	7.08716i	0.0856514	−	0.235325i	0.975123	+	0.221666i	$0.0711494\pi$
$908$	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	−0.159713	−	0.987164i	$-0.551057\pi$
$937$	18.8358	−	10.8749i	0.615340	−	0.355267i	0.775052	+	0.631897i	$0.217723\pi$
$938$	−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	0.565650	−	0.824646i	$-0.308625\pi$
$947$	−10.6073	−	12.6413i	−0.344692	−	0.410787i	−0.910341	+	0.413858i	$0.864181\pi$
$948$	−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	−0.838619	−	0.544718i	$-0.816637\pi$
$953$	−24.2702	+	14.0124i	−0.786190	+	0.453907i	0.0524298	+	0.998625i	$0.483303\pi$
$954$	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	0.988928	−	0.148394i	$-0.0474104\pi$
$967$	4.22850	+	11.6177i	0.135979	+	0.373601i	−0.852949	+	0.521995i	$0.825188\pi$
$968$	−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	$-0.873465\pi$
$977$	−14.5207	−	39.8952i	−0.464558	−	1.27636i	0.457466	−	0.889227i	$-0.348757\pi$
$978$	−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	$0.417527\pi$
$983$	−17.6012	+	48.3589i	−0.561392	+	1.54241i	−0.817598	+	0.575789i	$0.804695\pi$
$984$	−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	0.673631	−	0.739068i	$-0.264734\pi$
$997$	−5.40517	−	6.44164i	−0.171184	−	0.204009i	−0.844815	+	0.535059i	$0.820289\pi$
$998$			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.49.9		132
5.2	odd	4		675.2.l.g.76.7	yes	66
5.3	odd	4		675.2.l.f.76.5	✓	66
5.4	even	2	inner	675.2.u.e.49.14		132
27.16	even	9	inner	675.2.u.e.124.14		132
135.43	odd	36		675.2.l.f.151.5	yes	66
135.97	odd	36		675.2.l.g.151.7	yes	66
135.124	even	18	inner	675.2.u.e.124.9		132

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

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

Fields

Representations

Groups

Database

Properties

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