LMFDB - Embedded newform 675.2.l.f.151.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(76,675)] 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("675.76"); 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, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.l (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [66,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$11$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			151.5
Character	$\chi$	$=$	675.151
Dual form			675.2.l.f.76.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.594907 - 0.499186i) q^{2} +(-0.900618 - 1.47949i) q^{3} +(-0.242569 - 1.37568i) q^{4} +(-0.202756 + 1.32973i) q^{6} +(0.855088 - 4.84944i) q^{7} +(-1.31901 + 2.28459i) q^{8} +(-1.37777 + 2.66491i) q^{9} +(-3.17186 + 1.15446i) q^{11} +(-1.81684 + 1.59784i) q^{12} +(0.600973 - 0.504276i) q^{13} +(-2.92947 + 2.45812i) q^{14} +(-0.700189 + 0.254848i) q^{16} +(-2.86234 - 4.95771i) q^{17} +(2.14993 - 0.897607i) q^{18} +(2.16649 - 3.75247i) q^{19} +(-7.94481 + 3.10240i) q^{21} +(2.46325 + 0.896551i) q^{22} +(0.214816 + 1.21828i) q^{23} +(4.56795 - 0.106085i) q^{24} -0.609251 q^{26} +(5.18355 - 0.361665i) q^{27} -6.87869 q^{28} +(1.75863 + 1.47566i) q^{29} +(1.42301 + 8.07028i) q^{31} +(5.50161 + 2.00242i) q^{32} +(4.56465 + 3.65300i) q^{33} +(-0.771998 + 4.37822i) q^{34} +(4.00026 + 1.24895i) q^{36} +(-1.54801 - 2.68123i) q^{37} +(-3.16204 + 1.15089i) q^{38} +(-1.28732 - 0.434973i) q^{39} +(4.54071 - 3.81011i) q^{41} +(6.27510 + 2.12029i) q^{42} +(-0.396695 + 0.144385i) q^{43} +(2.35756 + 4.08342i) q^{44} +(0.480353 - 0.831996i) q^{46} +(-1.39441 + 7.90806i) q^{47} +(1.00765 + 0.806401i) q^{48} +(-16.2081 - 5.89926i) q^{49} +(-4.75701 + 8.69981i) q^{51} +(-0.839499 - 0.704423i) q^{52} -12.8380 q^{53} +(-3.26427 - 2.37240i) q^{54} +(9.95112 + 8.34998i) q^{56} +(-7.50292 + 0.174246i) q^{57} +(-0.309589 - 1.75576i) q^{58} +(6.94844 + 2.52902i) q^{59} +(-0.679578 + 3.85408i) q^{61} +(3.18202 - 5.51141i) q^{62} +(11.7452 + 8.96017i) q^{63} +(-1.52824 - 2.64699i) q^{64} +(-0.892014 - 4.45180i) q^{66} +(2.45259 - 2.05797i) q^{67} +(-6.12590 + 5.14024i) q^{68} +(1.60896 - 1.41502i) q^{69} +(-4.92735 - 8.53442i) q^{71} +(-4.27093 - 6.66269i) q^{72} +(1.77806 - 3.07968i) q^{73} +(-0.417511 + 2.36782i) q^{74} +(-5.68772 - 2.07016i) q^{76} +(2.88628 + 16.3689i) q^{77} +(0.548702 + 0.901380i) q^{78} +(1.31333 + 1.10201i) q^{79} +(-5.20348 - 7.34328i) q^{81} -4.60325 q^{82} +(12.4596 + 10.4548i) q^{83} +(6.19507 + 10.1769i) q^{84} +(0.308071 + 0.112129i) q^{86} +(0.599376 - 3.93088i) q^{87} +(1.54624 - 8.76914i) q^{88} +(1.10530 - 1.91444i) q^{89} +(-1.93158 - 3.34559i) q^{91} +(1.62385 - 0.591034i) q^{92} +(10.6583 - 9.37357i) q^{93} +(4.77714 - 4.00849i) q^{94} +(-1.99229 - 9.94300i) q^{96} +(-14.3200 + 5.21207i) q^{97} +(6.69747 + 11.6004i) q^{98} +(1.29357 - 10.0433i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q - 6 q^{2} - 6 q^{6} - 6 q^{7} - 12 q^{8} - 6 q^{9} + 15 q^{11} - 18 q^{12} + 15 q^{14} + 18 q^{16} - 30 q^{17} + 12 q^{18} + 12 q^{19} + 12 q^{21} + 45 q^{22} - 36 q^{23} - 39 q^{24} + 6 q^{26} - 51 q^{27}+ \cdots - 48 q^{99}+O(q^{100}) $ 66 * q - 6 * q^2 - 6 * q^6 - 6 * q^7 - 12 * q^8 - 6 * q^9 + 15 * q^11 - 18 * q^12 + 15 * q^14 + 18 * q^16 - 30 * q^17 + 12 * q^18 + 12 * q^19 + 12 * q^21 + 45 * q^22 - 36 * q^23 - 39 * q^24 + 6 * q^26 - 51 * q^27 + 36 * q^28 - 15 * q^29 + 3 * q^31 - 27 * q^32 + 3 * q^33 + 30 * q^36 - 6 * q^37 + 12 * q^38 - 15 * q^39 + 39 * q^41 - 48 * q^42 - 12 * q^43 + 51 * q^44 + 9 * q^46 - 30 * q^47 + 132 * q^48 - 6 * q^49 - 9 * q^52 + 24 * q^53 + 75 * q^54 + 144 * q^56 - 33 * q^57 - 27 * q^58 + 45 * q^59 - 54 * q^61 - 66 * q^62 + 120 * q^63 - 24 * q^64 + 48 * q^66 - 9 * q^67 + 69 * q^68 + 51 * q^69 - 15 * q^71 - 9 * q^72 + 15 * q^73 + 96 * q^74 - 48 * q^76 + 36 * q^77 + 18 * q^78 + 48 * q^79 - 54 * q^81 + 36 * q^82 - 30 * q^83 + 57 * q^84 - 111 * q^86 + 33 * q^87 - 36 * q^88 - 12 * q^89 + 9 * q^91 + 219 * q^92 - 63 * q^93 + 36 * q^94 - 249 * q^96 - 57 * q^97 - 75 * q^98 - 48 * q^99

Character values

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

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$

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 $

$2$	−0.594907	−	0.499186i	−0.420663	−	0.352978i	0.407752	−	0.913092i	$-0.366313\pi$
$2$	−0.594907	−	0.499186i	−0.420663	−	0.352978i	−0.828415	+	0.560115i	$0.810757\pi$
$3$	−0.900618	−	1.47949i	−0.519972	−	0.854183i
$3$	−0.900618	−	1.47949i	−0.519972	−	0.854183i
$4$	−0.242569	−	1.37568i	−0.121285	−	0.687839i
$5$		0			0
$5$		0			0
$6$	−0.202756	+	1.32973i	−0.0827749	+	0.542862i
$7$	0.855088	−	4.84944i	0.323193	−	1.83292i	−0.198889	−	0.980022i	$-0.563733\pi$
$7$	0.855088	−	4.84944i	0.323193	−	1.83292i	0.522082	−	0.852896i	$-0.325156\pi$
$8$	−1.31901	+	2.28459i	−0.466340	+	0.807724i
$9$	−1.37777	+	2.66491i	−0.459258	+	0.888303i
$10$		0			0
$11$	−3.17186	+	1.15446i	−0.956352	+	0.348084i	−0.772603	−	0.634890i	$-0.781046\pi$
$11$	−3.17186	+	1.15446i	−0.956352	+	0.348084i	−0.183749	+	0.982973i	$0.558823\pi$
$12$	−1.81684	+	1.59784i	−0.524476	+	0.461256i
$13$	0.600973	−	0.504276i	0.166680	−	0.139861i	−0.555632	−	0.831428i	$-0.687524\pi$
$13$	0.600973	−	0.504276i	0.166680	−	0.139861i	0.722312	+	0.691567i	$0.243079\pi$
$14$	−2.92947	+	2.45812i	−0.782934	+	0.656960i
$15$		0			0
$16$	−0.700189	+	0.254848i	−0.175047	+	0.0637120i
$17$	−2.86234	−	4.95771i	−0.694219	−	1.20242i	−0.970443	−	0.241329i	$-0.922417\pi$
$17$	−2.86234	−	4.95771i	−0.694219	−	1.20242i	0.276224	−	0.961093i	$-0.410917\pi$
$18$	2.14993	−	0.897607i	0.506744	−	0.211568i
$19$	2.16649	−	3.75247i	0.497027	−	0.860877i	−0.502967	−	0.864306i	$-0.667758\pi$
$19$	2.16649	−	3.75247i	0.497027	−	0.860877i	0.999994	+	0.00342920i	$0.00109155\pi$
$20$		0			0
$21$	−7.94481	+	3.10240i	−1.73370	+	0.677000i
$22$	2.46325	+	0.896551i	0.525167	+	0.191145i
$23$	0.214816	+	1.21828i	0.0447921	+	0.254029i	0.998979	−	0.0451834i	$-0.0143872\pi$
$23$	0.214816	+	1.21828i	0.0447921	+	0.254029i	−0.954187	+	0.299212i	$0.903276\pi$
$24$	4.56795	−	0.106085i	0.932428	−	0.0216545i
$25$		0			0
$26$	−0.609251			−0.119484
$27$	5.18355	−	0.361665i	0.997575	−	0.0696024i
$28$	−6.87869			−1.29995
$29$	1.75863	+	1.47566i	0.326569	+	0.274024i	0.791300	−	0.611428i	$-0.209405\pi$
$29$	1.75863	+	1.47566i	0.326569	+	0.274024i	−0.464731	+	0.885452i	$0.653849\pi$
$30$		0			0
$31$	1.42301	+	8.07028i	0.255580	+	1.44947i	0.794580	+	0.607160i	$0.207691\pi$
$31$	1.42301	+	8.07028i	0.255580	+	1.44947i	−0.539000	+	0.842306i	$0.681198\pi$
$32$	5.50161	+	2.00242i	0.972557	+	0.353982i
$33$	4.56465	+	3.65300i	0.794603	+	0.635906i
$34$	−0.771998	+	4.37822i	−0.132397	+	0.750858i
$35$		0			0
$36$	4.00026	+	1.24895i	0.666710	+	0.208158i
$37$	−1.54801	−	2.68123i	−0.254491	−	0.440791i	0.710266	−	0.703933i	$-0.248575\pi$
$37$	−1.54801	−	2.68123i	−0.254491	−	0.440791i	−0.964757	+	0.263142i	$0.915241\pi$
$38$	−3.16204	+	1.15089i	−0.512951	+	0.186699i
$39$	−1.28732	−	0.434973i	−0.206136	−	0.0696514i
$40$		0			0
$41$	4.54071	−	3.81011i	0.709140	−	0.595039i	−0.215218	−	0.976566i	$-0.569046\pi$
$41$	4.54071	−	3.81011i	0.709140	−	0.595039i	0.924358	+	0.381527i	$0.124602\pi$
$42$	6.27510	+	2.12029i	0.968268	+	0.327169i
$43$	−0.396695	+	0.144385i	−0.0604954	+	0.0220185i	−0.372091	−	0.928196i	$-0.621359\pi$
$43$	−0.396695	+	0.144385i	−0.0604954	+	0.0220185i	0.311595	+	0.950215i	$0.399137\pi$
$44$	2.35756	+	4.08342i	0.355416	+	0.615599i
$45$		0			0
$46$	0.480353	−	0.831996i	0.0708242	−	0.122671i
$47$	−1.39441	+	7.90806i	−0.203395	+	1.15351i	0.696551	+	0.717508i	$0.254717\pi$
$47$	−1.39441	+	7.90806i	−0.203395	+	1.15351i	−0.899946	+	0.436002i	$0.856394\pi$
$48$	1.00765	+	0.806401i	0.145441	+	0.116394i
$49$	−16.2081	−	5.89926i	−2.31544	−	0.842752i
$50$		0			0
$51$	−4.75701	+	8.69981i	−0.666115	+	1.21822i
$52$	−0.839499	−	0.704423i	−0.116418	−	0.0976859i
$53$	−12.8380			−1.76343			−0.881717	−	0.471779i	$-0.843612\pi$
$53$	−12.8380			−1.76343			−0.881717	+	0.471779i	$0.843612\pi$
$54$	−3.26427	−	2.37240i	−0.444211	−	0.322843i
$55$		0			0
$56$	9.95112	+	8.34998i	1.32977	+	1.11581i
$57$	−7.50292	+	0.174246i	−0.993787	+	0.0230795i
$58$	−0.309589	−	1.75576i	−0.0406510	−	0.230543i
$59$	6.94844	+	2.52902i	0.904609	+	0.329251i	0.752098	−	0.659051i	$-0.229042\pi$
$59$	6.94844	+	2.52902i	0.904609	+	0.329251i	0.152511	+	0.988302i	$0.451264\pi$
$60$		0			0
$61$	−0.679578	+	3.85408i	−0.0870111	+	0.493464i	0.909893	+	0.414842i	$0.136163\pi$
$61$	−0.679578	+	3.85408i	−0.0870111	+	0.493464i	−0.996904	+	0.0786222i	$0.974948\pi$
$62$	3.18202	−	5.51141i	0.404116	−	0.699950i
$63$	11.7452	+	8.96017i	1.47976	+	1.12888i
$64$	−1.52824	−	2.64699i	−0.191030	−	0.330874i
$65$		0			0
$66$	−0.892014	−	4.45180i	−0.109799	−	0.547979i
$67$	2.45259	−	2.05797i	0.299631	−	0.251421i	−0.480559	−	0.876962i	$-0.659566\pi$
$67$	2.45259	−	2.05797i	0.299631	−	0.251421i	0.780191	+	0.625542i	$0.215122\pi$
$68$	−6.12590	+	5.14024i	−0.742875	+	0.623346i
$69$	1.60896	−	1.41502i	0.193697	−	0.170349i
$70$		0			0
$71$	−4.92735	−	8.53442i	−0.584769	−	1.01285i	−0.994904	−	0.100825i	$-0.967852\pi$
$71$	−4.92735	−	8.53442i	−0.584769	−	1.01285i	0.410135	−	0.912025i	$-0.365482\pi$
$72$	−4.27093	−	6.66269i	−0.503334	−	0.785205i
$73$	1.77806	−	3.07968i	0.208106	−	0.360450i	−0.743012	−	0.669278i	$-0.766604\pi$
$73$	1.77806	−	3.07968i	0.208106	−	0.360450i	0.951118	+	0.308828i	$0.0999368\pi$
$74$	−0.417511	+	2.36782i	−0.0485347	+	0.275254i
$75$		0			0
$76$	−5.68772	−	2.07016i	−0.652426	−	0.237464i
$77$	2.88628	+	16.3689i	0.328922	+	1.86541i
$78$	0.548702	+	0.901380i	0.0621283	+	0.102061i
$79$	1.31333	+	1.10201i	0.147761	+	0.123986i	0.713672	−	0.700480i	$-0.247031\pi$
$79$	1.31333	+	1.10201i	0.147761	+	0.123986i	−0.565911	+	0.824467i	$0.691475\pi$
$80$		0			0
$81$	−5.20348	−	7.34328i	−0.578164	−	0.815920i
$82$	−4.60325			−0.508344
$83$	12.4596	+	10.4548i	1.36762	+	1.14757i	0.973546	+	0.228490i	$0.0733787\pi$
$83$	12.4596	+	10.4548i	1.36762	+	1.14757i	0.394073	+	0.919079i	$0.371066\pi$
$84$	6.19507	+	10.1769i	0.675938	+	1.11040i
$85$		0			0
$86$	0.308071	+	0.112129i	0.0332202	+	0.0120912i
$87$	0.599376	−	3.93088i	0.0642598	−	0.421434i
$88$	1.54624	−	8.76914i	0.164829	−	0.934794i
$89$	1.10530	−	1.91444i	0.117162	−	0.202930i	−0.801480	−	0.598021i	$-0.795954\pi$
$89$	1.10530	−	1.91444i	0.117162	−	0.202930i	0.918642	+	0.395091i	$0.129287\pi$
$90$		0			0
$91$	−1.93158	−	3.34559i	−0.202484	−	0.350713i
$92$	1.62385	−	0.591034i	0.169298	−	0.0616195i
$93$	10.6583	−	9.37357i	1.10522	−	0.971994i
$94$	4.77714	−	4.00849i	0.492724	−	0.413445i
$95$		0			0
$96$	−1.99229	−	9.94300i	−0.203337	−	1.01480i
$97$	−14.3200	+	5.21207i	−1.45398	+	0.529205i	−0.943700	−	0.330804i	$-0.892680\pi$
$97$	−14.3200	+	5.21207i	−1.45398	+	0.529205i	−0.510279	+	0.860009i	$0.670458\pi$
$98$	6.69747	+	11.6004i	0.676547	+	1.17181i
$99$	1.29357	−	10.0433i	0.130008	−	1.00939i
$100$		0			0
$101$	3.25498	−	18.4599i	0.323882	−	1.83683i	−0.193535	−	0.981093i	$-0.561995\pi$
$101$	3.25498	−	18.4599i	0.323882	−	1.83683i	0.517417	−	0.855733i	$-0.326894\pi$
$102$	7.17280	−	2.80094i	0.710213	−	0.277334i
$103$	1.30365	+	0.474488i	0.128452	+	0.0467527i	0.405446	−	0.914119i	$-0.367116\pi$
$103$	1.30365	+	0.474488i	0.128452	+	0.0467527i	−0.276994	+	0.960872i	$0.589338\pi$
$104$	0.359376	+	2.03812i	0.0352397	+	0.199854i
$105$		0			0
$106$	7.63741	+	6.40854i	0.741810	+	0.622453i
$107$	−6.79809			−0.657196			−0.328598	−	0.944470i	$-0.606576\pi$
$107$	−6.79809			−0.657196			−0.328598	+	0.944470i	$0.606576\pi$
$108$	−1.75490	−	7.04316i	−0.168866	−	0.677729i
$109$	3.70718			0.355084			0.177542	−	0.984113i	$-0.443185\pi$
$109$	3.70718			0.355084			0.177542	+	0.984113i	$0.443185\pi$
$110$		0			0
$111$	−2.57268	+	4.70502i	−0.244188	+	0.446581i
$112$	0.637148	+	3.61345i	0.0602048	+	0.341439i
$113$	−9.64111	−	3.50908i	−0.906959	−	0.330106i	−0.153921	−	0.988083i	$-0.549190\pi$
$113$	−9.64111	−	3.50908i	−0.906959	−	0.330106i	−0.753038	+	0.657977i	$0.771412\pi$
$114$	4.55052	+	3.64169i	0.426195	+	0.341076i
$115$		0			0
$116$	1.60345	−	2.77725i	0.148876	−	0.257862i
$117$	0.515846	+	2.29632i	0.0476899	+	0.212295i
$118$	−2.87122	−	4.97310i	−0.264317	−	0.457811i
$119$	−26.4897	+	9.64147i	−2.42831	+	0.883832i
$120$		0			0
$121$	0.301422	−	0.252923i	0.0274020	−	0.0229930i
$122$	2.32819	−	1.95358i	0.210784	−	0.176869i
$123$	−9.72646	−	3.28648i	−0.877005	−	0.296332i
$124$	10.7569	−	3.91520i	0.966001	−	0.351596i
$125$		0			0
$126$	−2.51451	−	11.1935i	−0.224011	−	0.997197i
$127$	8.89562	−	15.4077i	0.789359	−	1.36721i	−0.137002	−	0.990571i	$-0.543747\pi$
$127$	8.89562	−	15.4077i	0.789359	−	1.36721i	0.926360	−	0.376639i	$-0.122920\pi$
$128$	1.62113	−	9.19391i	0.143289	−	0.812635i
$129$	0.570887	+	0.456870i	0.0502638	+	0.0402251i
$130$		0			0
$131$	1.04732	+	5.93962i	0.0915044	+	0.518947i	0.995763	+	0.0919612i	$0.0293136\pi$
$131$	1.04732	+	5.93962i	0.0915044	+	0.518947i	−0.904258	+	0.426986i	$0.859575\pi$
$132$	3.91811	−	7.16559i	0.341027	−	0.623684i
$133$	−16.3449	−	13.7150i	−1.41728	−	1.18924i
$134$	−2.48637			−0.214790
$135$		0			0
$136$	15.1018			1.29497
$137$	−11.5236	−	9.66943i	−0.984525	−	0.826115i	0.000240652	−	1.00000i	$-0.499923\pi$
$137$	−11.5236	−	9.66943i	−0.984525	−	0.826115i	−0.984766	+	0.173885i	$0.944368\pi$
$138$	−1.66354	+	0.0386337i	−0.141610	+	0.00328872i
$139$	−1.48204	−	8.40509i	−0.125705	−	0.712911i	−0.980886	−	0.194581i	$-0.937665\pi$
$139$	−1.48204	−	8.40509i	−0.125705	−	0.712911i	0.855181	−	0.518330i	$-0.173446\pi$
$140$		0			0
$141$	12.9557	−	5.05914i	1.09107	−	0.426056i
$142$	−1.32895	+	7.53685i	−0.111523	+	0.632479i
$143$	−1.32403	+	2.29330i	−0.110721	+	0.191775i
$144$	0.285556	−	2.21706i	0.0237963	−	0.184755i
$145$		0			0
$146$	−2.59511	+	0.944544i	−0.214773	+	0.0781710i
$147$	5.86941	+	29.2927i	0.484101	+	2.41602i
$148$	−3.31301	+	2.77994i	−0.272327	+	0.228510i
$149$	7.57146	−	6.35321i	0.620278	−	0.520475i	−0.277613	−	0.960693i	$-0.589543\pi$
$149$	7.57146	−	6.35321i	0.620278	−	0.520475i	0.897891	+	0.440218i	$0.145099\pi$
$150$		0			0
$151$	3.18979	−	1.16099i	0.259582	−	0.0944800i	−0.208951	−	0.977926i	$-0.567005\pi$
$151$	3.18979	−	1.16099i	0.259582	−	0.0944800i	0.468533	+	0.883446i	$0.344783\pi$
$152$	5.71524	+	9.89909i	0.463567	+	0.802922i
$153$	17.1555	−	0.797261i	1.38694	−	0.0644547i
$154$	6.45407	−	11.1788i	0.520084	−	0.900811i
$155$		0			0
$156$	−0.286118	+	1.87645i	−0.0229078	+	0.150236i
$157$	−20.3075	−	7.39131i	−1.62071	−	0.589891i	−0.637195	−	0.770703i	$-0.719905\pi$
$157$	−20.3075	−	7.39131i	−1.62071	−	0.589891i	−0.983518	+	0.180812i	$0.942127\pi$
$158$	−0.231198	−	1.31119i	−0.0183931	−	0.104313i
$159$	11.5621	+	18.9937i	0.916936	+	1.50630i
$160$		0			0
$161$	6.09166			0.480090
$162$	−0.570079	+	6.96607i	−0.0447897	+	0.547306i
$163$	6.62741			0.519099			0.259549	−	0.965730i	$-0.416426\pi$
$163$	6.62741			0.519099			0.259549	+	0.965730i	$0.416426\pi$
$164$	−6.34292	−	5.32234i	−0.495299	−	0.415605i
$165$		0			0
$166$	−2.19339	−	12.4393i	−0.170240	−	0.965479i
$167$	−17.8058	−	6.48077i	−1.37785	−	0.501497i	−0.456326	−	0.889813i	$-0.650835\pi$
$167$	−17.8058	−	6.48077i	−1.37785	−	0.501497i	−0.921527	+	0.388315i	$0.873057\pi$
$168$	3.39154	−	22.2427i	0.261663	−	1.71606i
$169$	−2.15055	+	12.1964i	−0.165427	+	0.938184i
$170$		0			0
$171$	7.01507	+	10.9436i	0.536455	+	0.836875i
$172$	0.294853	+	0.510701i	0.0224823	+	0.0389406i
$173$	0.550879	−	0.200504i	0.0418826	−	0.0152440i	−0.320994	−	0.947081i	$-0.604017\pi$
$173$	0.550879	−	0.200504i	0.0418826	−	0.0152440i	0.362876	+	0.931837i	$0.381795\pi$
$174$	−2.31881	+	2.03931i	−0.175789	+	0.154599i
$175$		0			0
$176$	1.92669	−	1.61668i	0.145230	−	0.121862i
$177$	−2.51623	−	12.5578i	−0.189131	−	0.943903i
$178$	−1.61321	+	0.587161i	−0.120915	+	0.0440096i
$179$	−10.0081	−	17.3345i	−0.748037	−	1.29564i	−0.948762	−	0.315991i	$-0.897663\pi$
$179$	−10.0081	−	17.3345i	−0.748037	−	1.29564i	0.200725	−	0.979648i	$-0.435670\pi$
$180$		0			0
$181$	7.25247	−	12.5617i	0.539072	−	0.933700i	−0.459882	−	0.887980i	$-0.652108\pi$
$181$	7.25247	−	12.5617i	0.539072	−	0.933700i	0.998954	−	0.0457203i	$-0.0145583\pi$
$182$	−0.520963	+	2.95453i	−0.0386163	+	0.219004i
$183$	6.31411	−	2.46563i	0.466752	−	0.182264i
$184$	−3.06661	−	1.11616i	−0.226074	−	0.0822841i
$185$		0			0
$186$	−11.0199	+	0.255922i	−0.808015	+	0.0187651i
$187$	14.8024	+	12.4207i	1.08246	+	0.908293i
$188$	11.2172			0.818097
$189$	2.67852	−	25.4466i	0.194834	−	1.85097i
$190$		0			0
$191$	−3.01864	−	2.53294i	−0.218421	−	0.183277i	0.527011	−	0.849858i	$-0.323312\pi$
$191$	−3.01864	−	2.53294i	−0.218421	−	0.183277i	−0.745432	+	0.666581i	$0.767757\pi$
$192$	−2.53983	+	4.64494i	−0.183296	+	0.335220i
$193$	−1.04967	−	5.95297i	−0.0755568	−	0.428504i	−0.998998	−	0.0447632i	$-0.985747\pi$
$193$	−1.04967	−	5.95297i	−0.0755568	−	0.428504i	0.923441	−	0.383741i	$-0.125364\pi$
$194$	11.1209	+	4.04767i	0.798432	+	0.290606i
$195$		0			0
$196$	−4.18390	+	23.7281i	−0.298850	+	1.69486i
$197$	0.400945	−	0.694457i	0.0285662	−	0.0494780i	−0.851389	−	0.524535i	$-0.824239\pi$
$197$	0.400945	−	0.694457i	0.0285662	−	0.0494780i	0.879955	+	0.475057i	$0.157573\pi$
$198$	−5.78303	+	5.32910i	−0.410982	+	0.378723i
$199$	−2.31981	−	4.01802i	−0.164447	−	0.284830i	0.772012	−	0.635608i	$-0.219251\pi$
$199$	−2.31981	−	4.01802i	−0.164447	−	0.284830i	−0.936459	+	0.350778i	$0.885917\pi$
$200$		0			0
$201$	−5.25358	−	1.77514i	−0.370559	−	0.125208i
$202$	−11.1513	+	9.35707i	−0.784604	+	0.658361i
$203$	8.65993	−	7.26654i	0.607808	−	0.510011i
$204$	13.1220	+	4.43381i	0.918726	+	0.310429i
$205$		0			0
$206$	−0.538690	−	0.933038i	−0.0375323	−	0.0650078i
$207$	−3.54257	−	1.10605i	−0.246226	−	0.0768758i
$208$	−0.292281	+	0.506246i	−0.0202661	+	0.0351018i
$209$	−2.53972	+	14.4035i	−0.175676	+	0.996308i
$210$		0			0
$211$	5.90447	+	2.14905i	0.406480	+	0.147947i	0.537165	−	0.843477i	$-0.319495\pi$
$211$	5.90447	+	2.14905i	0.406480	+	0.147947i	−0.130684	+	0.991424i	$0.541717\pi$
$212$	3.11410	+	17.6609i	0.213877	+	1.21296i
$213$	−8.18892	+	14.9762i	−0.561096	+	1.02615i
$214$	4.04423	+	3.39351i	0.276458	+	0.231976i
$215$		0			0
$216$	−6.01089	+	12.3193i	−0.408989	+	0.838224i
$217$	40.3532			2.73935
$218$	−2.20543	−	1.85057i	−0.149370	−	0.125337i
$219$	−6.15771	+	0.143005i	−0.416099	+	0.00966339i
$220$		0			0
$221$	−4.22025	−	1.53604i	−0.283885	−	0.103326i
$222$	3.87919	−	1.51480i	0.260354	−	0.101667i
$223$	0.0366413	−	0.207803i	0.00245368	−	0.0139155i	−0.983556	−	0.180602i	$-0.942196\pi$
$223$	0.0366413	−	0.207803i	0.00245368	−	0.0139155i	0.986010	+	0.166686i	$0.0533066\pi$
$224$	14.4150	−	24.9675i	0.963143	−	1.66821i
$225$		0			0
$226$	3.98388	+	6.90028i	0.265004	+	0.459000i
$227$	6.62533	−	2.41142i	0.439739	−	0.160052i	−0.112657	−	0.993634i	$-0.535936\pi$
$227$	6.62533	−	2.41142i	0.439739	−	0.160052i	0.552395	+	0.833582i	$0.313714\pi$
$228$	2.05968	+	10.2793i	0.136406	+	0.680766i
$229$	−17.0605	+	14.3154i	−1.12739	+	0.945991i	−0.998954	−	0.0457276i	$-0.985439\pi$
$229$	−17.0605	+	14.3154i	−1.12739	+	0.945991i	−0.128434	+	0.991718i	$0.540995\pi$
$230$		0			0
$231$	21.6182	−	19.0124i	1.42237	−	1.25092i
$232$	−5.69093	+	2.07133i	−0.373628	+	0.135989i
$233$	6.77819	+	11.7402i	0.444054	+	0.769124i	0.997986	−	0.0634379i	$-0.0202065\pi$
$233$	6.77819	+	11.7402i	0.444054	+	0.769124i	−0.553932	+	0.832562i	$0.686873\pi$
$234$	0.839410	−	1.62360i	0.0548739	−	0.106138i
$235$		0			0
$236$	1.79365	−	10.1723i	0.116756	−	0.662158i
$237$	0.447609	−	2.93555i	0.0290753	−	0.190684i
$238$	20.5718	+	7.48752i	1.33347	+	0.485344i
$239$	1.06063	+	6.01513i	0.0686065	+	0.389087i	0.999704	+	0.0243171i	$0.00774114\pi$
$239$	1.06063	+	6.01513i	0.0686065	+	0.389087i	−0.931098	+	0.364770i	$0.881148\pi$
$240$		0			0
$241$	−14.7499	−	12.3766i	−0.950123	−	0.797248i	0.0291956	−	0.999574i	$-0.490705\pi$
$241$	−14.7499	−	12.3766i	−0.950123	−	0.797248i	−0.979318	+	0.202326i	$0.935150\pi$
$242$	−0.305574			−0.0196430
$243$	−6.17796	+	14.3120i	−0.396316	+	0.918114i
$244$	5.46681			0.349977
$245$		0			0
$246$	4.14577	+	6.81046i	0.264325	+	0.434219i
$247$	−0.590280	−	3.34765i	−0.0375586	−	0.213006i
$248$	−20.3143	−	7.39378i	−1.28996	−	0.469506i
$249$	4.24648	−	27.8497i	0.269110	−	1.76490i
$250$		0			0
$251$	−0.695671	+	1.20494i	−0.0439104	+	0.0760550i	−0.887145	−	0.461490i	$-0.847315\pi$
$251$	−0.695671	+	1.20494i	−0.0439104	+	0.0760550i	0.843235	+	0.537545i	$0.180648\pi$
$252$	9.47728	−	18.3311i	0.597012	−	1.15475i
$253$	−2.08782	−	3.61622i	−0.131260	−	0.227350i
$254$	−12.9834	+	4.72556i	−0.814648	+	0.296508i
$255$		0			0
$256$	−10.2367	+	8.58961i	−0.639793	+	0.536850i
$257$	3.19995	−	2.68508i	0.199608	−	0.167491i	−0.537505	−	0.843261i	$-0.680633\pi$
$257$	3.19995	−	2.68508i	0.199608	−	0.167491i	0.737113	+	0.675770i	$0.236189\pi$
$258$	−0.111561	−	0.556773i	−0.00694551	−	0.0346632i
$259$	−14.3261	+	5.21429i	−0.890184	+	0.324000i
$260$		0			0
$261$	−6.35550	+	2.65345i	−0.393396	+	0.164245i
$262$	2.34192	−	4.05633i	0.144684	−	0.250601i
$263$	1.51621	−	8.59885i	0.0934934	−	0.530228i	−0.901705	−	0.432351i	$-0.857684\pi$
$263$	1.51621	−	8.59885i	0.0934934	−	0.530228i	0.995199	−	0.0978761i	$-0.0312049\pi$
$264$	−14.3664	+	5.61001i	−0.884192	+	0.345272i
$265$		0			0
$266$	2.87735	+	16.3183i	0.176422	+	1.00054i
$267$	−3.82784	+	0.0888969i	−0.234260	+	0.00544040i
$268$	−3.42602	−	2.87477i	−0.209277	−	0.175605i
$269$	3.57322			0.217863			0.108931	−	0.994049i	$-0.465257\pi$
$269$	3.57322			0.217863			0.108931	+	0.994049i	$0.465257\pi$
$270$		0			0
$271$	−13.9724			−0.848765			−0.424383	−	0.905483i	$-0.639509\pi$
$271$	−13.9724			−0.848765			−0.424383	+	0.905483i	$0.639509\pi$
$272$	3.26764	+	2.74188i	0.198130	+	0.166251i
$273$	−3.21015	+	5.87084i	−0.194287	+	0.355319i
$274$	2.02861	+	11.5048i	0.122553	+	0.695031i
$275$		0			0
$276$	−2.33690	−	1.87017i	−0.140665	−	0.112571i
$277$	−3.37225	+	19.1250i	−0.202619	+	1.14911i	0.698524	+	0.715587i	$0.253841\pi$
$277$	−3.37225	+	19.1250i	−0.202619	+	1.14911i	−0.901143	+	0.433523i	$0.857270\pi$
$278$	−3.31403	+	5.74006i	−0.198762	+	0.344266i
$279$	−23.4672	−	7.32684i	−1.40494	−	0.438646i
$280$		0			0
$281$	−18.7960	+	6.84119i	−1.12128	+	0.408111i	−0.835118	−	0.550071i	$-0.814600\pi$
$281$	−18.7960	+	6.84119i	−1.12128	+	0.408111i	−0.286158	+	0.958182i	$0.592378\pi$
$282$	−10.2329	−	3.45760i	−0.609360	−	0.205897i
$283$	8.38203	−	7.03336i	0.498260	−	0.418090i	−0.358715	−	0.933447i	$-0.616785\pi$
$283$	8.38203	−	7.03336i	0.498260	−	0.418090i	0.856976	+	0.515357i	$0.172341\pi$
$284$	−10.5454	+	8.84863i	−0.625754	+	0.525070i
$285$		0			0
$286$	1.93246	−	0.703357i	0.114269	−	0.0415904i
$287$	−14.5942	−	25.2779i	−0.861469	−	1.49211i
$288$	−12.9163	+	11.9024i	−0.761098	+	0.701356i
$289$	−7.88596	+	13.6589i	−0.463880	+	0.803464i
$290$		0			0
$291$	20.6081	+	16.4922i	1.20807	+	0.966792i
$292$	−4.66795	−	1.69900i	−0.273171	−	0.0994262i
$293$	1.11307	+	6.31252i	0.0650261	+	0.368781i	0.999905	+	0.0138134i	$0.00439707\pi$
$293$	1.11307	+	6.31252i	0.0650261	+	0.368781i	−0.934879	+	0.354968i	$0.884492\pi$
$294$	11.1307	−	20.3563i	0.649158	−	1.18721i
$295$		0			0
$296$	8.16734			0.474717
$297$	−16.0240	+	7.13137i	−0.929805	+	0.413804i
$298$	−7.67575			−0.444644
$299$	0.743448	+	0.623827i	0.0429947	+	0.0360768i
$300$		0			0
$301$	0.360979	+	2.04721i	0.0208065	+	0.117999i
$302$	−2.47718	−	0.901619i	−0.142546	−	0.0518823i
$303$	−30.2427	+	11.8096i	−1.73740	+	0.678444i
$304$	−0.560644	+	3.17957i	−0.0321551	+	0.182361i
$305$		0			0
$306$	−10.6039	−	8.08950i	−0.606185	−	0.462446i
$307$	−5.69277	−	9.86017i	−0.324904	−	0.562750i	0.656589	−	0.754248i	$-0.271999\pi$
$307$	−5.69277	−	9.86017i	−0.324904	−	0.562750i	−0.981493	+	0.191499i	$0.938665\pi$
$308$	21.8182	−	7.94119i	1.24321	−	0.452491i
$309$	−0.472087	−	2.35606i	−0.0268561	−	0.134032i
$310$		0			0
$311$	−1.58925	+	1.33354i	−0.0901183	+	0.0756182i	−0.686734	−	0.726909i	$-0.740956\pi$
$311$	−1.58925	+	1.33354i	−0.0901183	+	0.0756182i	0.596616	+	0.802527i	$0.296512\pi$
$312$	2.69172	−	2.36726i	0.152389	−	0.134020i
$313$	22.6085	−	8.22881i	1.27791	−	0.465120i	0.388167	−	0.921589i	$-0.373108\pi$
$313$	22.6085	−	8.22881i	1.27791	−	0.465120i	0.889739	+	0.456469i	$0.150886\pi$
$314$	8.39141	+	14.5343i	0.473555	+	0.820221i
$315$		0			0
$316$	1.19744	−	2.07403i	0.0673614	−	0.116673i
$317$	1.27924	−	7.25490i	0.0718490	−	0.407476i	−0.927578	−	0.373629i	$-0.878113\pi$
$317$	1.27924	−	7.25490i	0.0718490	−	0.407476i	0.999427	−	0.0338465i	$-0.0107757\pi$
$318$	2.60298	−	17.0711i	0.145968	−	0.957300i
$319$	−7.28172	−	2.65033i	−0.407698	−	0.148390i
$320$		0			0
$321$	6.12248	+	10.0577i	0.341724	+	0.561366i
$322$	−3.62397	−	3.04087i	−0.201956	−	0.169461i
$323$	−24.8049			−1.38018
$324$	−8.83978	+	8.93956i	−0.491099	+	0.496642i
$325$		0			0
$326$	−3.94269	−	3.30831i	−0.218366	−	0.183230i
$327$	−3.33876	−	5.48473i	−0.184634	−	0.303307i
$328$	2.71530	+	15.3992i	0.149927	+	0.850280i
$329$	37.1574	+	13.5242i	2.04855	+	0.745612i
$330$		0			0
$331$	−0.0223761	+	0.126901i	−0.00122990	+	0.00697513i	−0.985417	−	0.170160i	$-0.945572\pi$
$331$	−0.0223761	+	0.126901i	−0.00122990	+	0.00697513i	0.984187	+	0.177135i	$0.0566828\pi$
$332$	11.3602	−	19.6764i	0.623471	−	1.07988i
$333$	9.27803	−	0.431174i	0.508433	−	0.0236282i
$334$	7.35767	+	12.7439i	0.402594	+	0.697312i
$335$		0			0
$336$	4.77223	−	4.19699i	0.260346	−	0.228965i
$337$	9.40807	−	7.89430i	0.512490	−	0.430030i	−0.349514	−	0.936931i	$-0.613653\pi$
$337$	9.40807	−	7.89430i	0.512490	−	0.430030i	0.862004	+	0.506901i	$0.169209\pi$
$338$	7.36764	−	6.18219i	0.400747	−	0.336267i
$339$	3.49132	+	17.4243i	0.189622	+	0.946355i
$340$		0			0
$341$	−13.8304	−	23.9550i	−0.748960	−	1.29724i
$342$	1.28956	−	10.0122i	0.0697316	−	0.541399i
$343$	−25.2326	+	43.7041i	−1.36243	+	2.35980i
$344$	0.193383	−	1.09673i	0.0104265	−	0.0591317i
$345$		0			0
$346$	−0.427810	−	0.155710i	−0.0229992	−	0.00837104i
$347$	1.02969	+	5.83965i	0.0552765	+	0.313489i	0.999892	−	0.0146902i	$-0.00467619\pi$
$347$	1.02969	+	5.83965i	0.0552765	+	0.313489i	−0.944616	+	0.328179i	$0.893565\pi$
$348$	−5.55301	+	0.128962i	−0.297673	+	0.00691308i
$349$	22.5465	+	18.9188i	1.20689	+	1.01270i	0.999406	+	0.0344616i	$0.0109716\pi$
$349$	22.5465	+	18.9188i	1.20689	+	1.01270i	0.207483	+	0.978239i	$0.433473\pi$
$350$		0			0
$351$	2.93280	−	2.83129i	0.156541	−	0.151123i
$352$	−19.7621			−1.05332
$353$	−4.51380	−	3.78753i	−0.240246	−	0.201590i	0.514713	−	0.857363i	$-0.327899\pi$
$353$	−4.51380	−	3.78753i	−0.240246	−	0.201590i	−0.754958	+	0.655773i	$0.772343\pi$
$354$	−4.77177	+	8.72679i	−0.253617	+	0.463824i
$355$		0			0
$356$	−2.90176	−	1.05615i	−0.153793	−	0.0559760i
$357$	38.1216	+	30.5079i	2.01761	+	1.61465i
$358$	−2.69926	+	15.3083i	−0.142660	+	0.809067i
$359$	10.0448	−	17.3981i	0.530145	−	0.918239i	−0.469236	−	0.883073i	$-0.655471\pi$
$359$	10.0448	−	17.3981i	0.530145	−	0.918239i	0.999381	−	0.0351660i	$-0.0111960\pi$
$360$		0			0
$361$	0.112627	+	0.195076i	0.00592776	+	0.0102672i
$362$	−10.5851	+	3.85268i	−0.556343	+	0.202492i
$363$	−0.645664	−	0.218164i	−0.0338886	−	0.0114506i
$364$	−4.13391	+	3.46876i	−0.216676	+	0.181812i
$365$		0			0
$366$	−4.98711	−	1.68510i	−0.260680	−	0.0880814i
$367$	22.1444	−	8.05989i	1.15593	−	0.420723i	0.308286	−	0.951294i	$-0.400245\pi$
$367$	22.1444	−	8.05989i	1.15593	−	0.420723i	0.847640	+	0.530571i	$0.178023\pi$
$368$	−0.460888	−	0.798281i	−0.0240254	−	0.0416133i
$369$	3.89752	+	17.3500i	0.202897	+	0.903207i
$370$		0			0
$371$	−10.9776	+	62.2571i	−0.569929	+	3.23223i
$372$	−15.4804	−	12.3887i	−0.802620	−	0.642322i
$373$	13.5032	+	4.91475i	0.699167	+	0.254476i	0.667055	−	0.745008i	$-0.267555\pi$
$373$	13.5032	+	4.91475i	0.699167	+	0.254476i	0.0321116	+	0.999484i	$0.489777\pi$
$374$	−2.60582	−	14.7783i	−0.134744	−	0.764169i
$375$		0			0
$376$	−16.2275	−	13.6164i	−0.836867	−	0.702215i
$377$	1.80103			0.0927578
$378$	−14.2961	+	13.8013i	−0.735310	+	0.709861i
$379$	32.6347			1.67633			0.838165	−	0.545417i	$-0.183629\pi$
$379$	32.6347			1.67633			0.838165	+	0.545417i	$0.183629\pi$
$380$		0			0
$381$	−30.8070	+	0.715455i	−1.57829	+	0.0366539i
$382$	0.531401	+	3.01372i	0.0271888	+	0.154196i
$383$	5.15784	+	1.87730i	0.263553	+	0.0959255i	0.470417	−	0.882444i	$-0.344103\pi$
$383$	5.15784	+	1.87730i	0.263553	+	0.0959255i	−0.206864	+	0.978370i	$0.566326\pi$
$384$	−15.0623	+	5.88175i	−0.768645	+	0.300152i
$385$		0			0
$386$	−2.34718	+	4.06544i	−0.119469	+	0.206926i
$387$	0.161782	−	1.25609i	0.00822387	−	0.0638504i
$388$	10.6437	+	18.4355i	0.540353	+	0.935918i
$389$	16.4485	−	5.98677i	0.833973	−	0.303541i	0.110484	−	0.993878i	$-0.464760\pi$
$389$	16.4485	−	5.98677i	0.833973	−	0.303541i	0.723488	+	0.690337i	$0.242538\pi$
$390$		0			0
$391$	5.42501	−	4.55212i	0.274354	−	0.230211i
$392$	34.8560	−	29.2477i	1.76049	−	1.47723i
$393$	7.84437	−	6.89883i	0.395696	−	0.348000i
$394$	−0.585188	+	0.212991i	−0.0294814	+	0.0107303i
$395$		0			0
$396$	−14.1301	+	0.656663i	−0.710066	+	0.0329986i
$397$	2.21340	−	3.83373i	0.111088	−	0.192409i	−0.805121	−	0.593110i	$-0.797900\pi$
$397$	2.21340	−	3.83373i	0.111088	−	0.192409i	0.916209	+	0.400701i	$0.131233\pi$
$398$	−0.625672	+	3.54836i	−0.0313621	+	0.177863i
$399$	−5.57066	+	36.5340i	−0.278882	+	1.82899i
$400$		0			0
$401$	5.70218	+	32.3387i	0.284754	+	1.61492i	0.706165	+	0.708048i	$0.250424\pi$
$401$	5.70218	+	32.3387i	0.284754	+	1.61492i	−0.421411	+	0.906870i	$0.638465\pi$
$402$	2.23927	+	3.67856i	0.111685	+	0.183470i
$403$	4.92484	+	4.13244i	0.245324	+	0.205851i
$404$	−26.1844			−1.30272
$405$		0			0
$406$	−8.77921			−0.435705
$407$	8.00544	+	6.71736i	0.396815	+	0.332967i
$408$	−13.6009	−	22.3429i	−0.673347	−	1.10614i
$409$	−4.60541	−	26.1186i	−0.227723	−	1.29148i	−0.857411	−	0.514633i	$-0.827928\pi$
$409$	−4.60541	−	26.1186i	−0.227723	−	1.29148i	0.629688	−	0.776848i	$-0.283183\pi$
$410$		0			0
$411$	−3.92747	+	25.7575i	−0.193728	+	1.27052i
$412$	0.336519	−	1.90849i	0.0165791	−	0.0940246i
$413$	18.2059	−	31.5335i	0.895853	−	1.55166i
$414$	1.55538	+	2.42640i	0.0764425	+	0.119251i
$415$		0			0
$416$	4.31610	−	1.57093i	0.211614	−	0.0770212i
$417$	−11.1005	+	9.76245i	−0.543593	+	0.478069i
$418$	8.70090	−	7.30092i	0.425575	−	0.357100i
$419$	−21.0958	+	17.7015i	−1.03060	+	0.864774i	−0.990922	−	0.134439i	$-0.957077\pi$
$419$	−21.0958	+	17.7015i	−1.03060	+	0.864774i	−0.0396754	+	0.999213i	$0.512632\pi$
$420$		0			0
$421$	25.5292	−	9.29186i	1.24422	−	0.452857i	0.365772	−	0.930704i	$-0.380805\pi$
$421$	25.5292	−	9.29186i	1.24422	−	0.452857i	0.878443	+	0.477847i	$0.158583\pi$
$422$	−2.43983	−	4.22591i	−0.118769	−	0.205714i
$423$	−19.1531	−	14.6115i	−0.931255	−	0.710435i
$424$	16.9334	−	29.3295i	0.822359	−	1.42437i
$425$		0			0
$426$	12.3476	−	4.82166i	0.598241	−	0.233610i
$427$	18.1090	+	6.59115i	0.876358	+	0.318968i
$428$	1.64901	+	9.35198i	0.0797077	+	0.452045i
$429$	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	$0.549806\pi$
$432$	−3.53730	+	1.57425i	−0.170188	+	0.0757412i
$433$	−18.9751			−0.911883			−0.455942	−	0.890010i	$-0.650697\pi$
$433$	−18.9751			−0.911883			−0.455942	+	0.890010i	$0.650697\pi$
$434$	−24.0064	−	20.1438i	−1.15234	−	0.966931i
$435$		0			0
$436$	−0.899248	−	5.09989i	−0.0430661	−	0.244240i
$437$	5.03696	+	1.83330i	0.240950	+	0.0876988i
$438$	3.73465	+	2.98877i	0.178448	+	0.142809i
$439$	−5.12907	+	29.0884i	−0.244797	+	1.38831i	0.576166	+	0.817333i	$0.304548\pi$
$439$	−5.12907	+	29.0884i	−0.244797	+	1.38831i	−0.820963	+	0.570981i	$0.806563\pi$
$440$		0			0
$441$	38.0521	−	35.0652i	1.81200	−	1.66977i
$442$	1.74388	+	3.02049i	0.0829480	+	0.143670i
$443$	12.8754	−	4.68628i	0.611731	−	0.222652i	−0.0175297	−	0.999846i	$-0.505580\pi$
$443$	12.8754	−	4.68628i	0.611731	−	0.222652i	0.629260	+	0.777195i	$0.283358\pi$
$444$	7.09665	+	2.39789i	0.336792	+	0.113799i
$445$		0			0
$446$	−0.125531	+	0.105333i	−0.00594405	+	0.00498765i
$447$	−16.2185	−	5.48007i	−0.767109	−	0.259199i
$448$	−14.1432	+	5.14770i	−0.668203	+	0.243206i
$449$	−16.2238	−	28.1005i	−0.765649	−	1.32614i	−0.939903	−	0.341443i	$-0.889085\pi$
$449$	−16.2238	−	28.1005i	−0.765649	−	1.32614i	0.174253	−	0.984701i	$-0.444249\pi$
$450$		0			0
$451$	−10.0039	+	17.3272i	−0.471064	+	0.815907i
$452$	−2.48872	+	14.1142i	−0.117060	+	0.663878i
$453$	−4.59045	−	3.67365i	−0.215678	−	0.172603i
$454$	−5.14520	−	1.87270i	−0.241476	−	0.0878902i
$455$		0			0
$456$	9.49834	−	17.3709i	0.444801	−	0.813469i
$457$	12.7506	+	10.6990i	0.596446	+	0.500478i	0.890301	−	0.455372i	$-0.150494\pi$
$457$	12.7506	+	10.6990i	0.596446	+	0.500478i	−0.293855	+	0.955850i	$0.594938\pi$
$458$	17.2955			0.808163
$459$	−16.6301	−	24.6634i	−0.776227	−	1.15119i
$460$		0			0
$461$	−25.2927	−	21.2231i	−1.17800	−	0.988460i	−0.999990	−	0.00443082i	$-0.998590\pi$
$461$	−25.2927	−	21.2231i	−1.17800	−	0.988460i	−0.178010	−	0.984029i	$-0.556966\pi$
$462$	−22.3515	+	0.519086i	−1.03989	+	0.0241501i
$463$	5.90347	+	33.4802i	0.274357	+	1.55596i	0.740996	+	0.671510i	$0.234354\pi$
$463$	5.90347	+	33.4802i	0.274357	+	1.55596i	−0.466638	+	0.884448i	$0.654535\pi$
$464$	−1.60744	−	0.585061i	−0.0746236	−	0.0271608i
$465$		0			0
$466$	1.82814	−	10.3679i	0.0846869	−	0.480283i
$467$	−0.893863	+	1.54822i	−0.0413630	+	0.0716429i	−0.885966	−	0.463751i	$-0.846503\pi$
$467$	−0.893863	+	1.54822i	−0.0413630	+	0.0716429i	0.844603	+	0.535394i	$0.179837\pi$
$468$	3.03386	−	1.26665i	0.140240	−	0.0585510i
$469$	−7.88281	−	13.6534i	−0.363995	−	0.630457i
$470$		0			0
$471$	7.35391	+	36.7014i	0.338850	+	1.69111i
$472$	−14.9428	+	12.5385i	−0.687799	+	0.577132i
$473$	1.09157	−	0.915938i	0.0501906	−	0.0421149i
$474$	−1.73167	+	1.52294i	−0.0795382	+	0.0699508i
$475$		0			0
$476$	19.6891	+	34.1026i	0.902450	+	1.56309i
$477$	17.6878	−	34.2121i	0.809871	−	1.56646i
$478$	2.37169	−	4.10790i	0.108479	−	0.187891i
$479$	3.22748	−	18.3040i	0.147467	−	0.836329i	−0.817886	−	0.575381i	$-0.804854\pi$
$479$	3.22748	−	18.3040i	0.147467	−	0.836329i	0.965353	−	0.260948i	$-0.0840351\pi$
$480$		0			0
$481$	−2.28239	−	0.830722i	−0.104068	−	0.0378777i
$482$	2.59657	+	14.7259i	0.118270	+	0.670744i
$483$	−5.48626	−	9.01255i	−0.249634	−	0.410085i
$484$	−0.421057	−	0.353309i	−0.0191389	−	0.0160595i
$485$		0			0
$486$	10.8196	−	5.43035i	0.490789	−	0.246325i
$487$	−16.9037			−0.765979			−0.382989	−	0.923753i	$-0.625105\pi$
$487$	−16.9037			−0.765979			−0.382989	+	0.923753i	$0.625105\pi$
$488$	−7.90862	−	6.63612i	−0.358006	−	0.300403i
$489$	−5.96877	−	9.80518i	−0.269917	−	0.443406i
$490$		0			0
$491$	−1.02681	−	0.373728i	−0.0463392	−	0.0168661i	0.318747	−	0.947840i	$-0.396738\pi$
$491$	−1.02681	−	0.373728i	−0.0463392	−	0.0168661i	−0.365086	+	0.930974i	$0.618960\pi$
$492$	−2.16179	+	14.1777i	−0.0974612	+	0.639179i
$493$	2.28213	−	12.9426i	0.102782	−	0.582906i
$494$	−1.31994	+	2.28620i	−0.0593868	+	0.102861i
$495$		0			0
$496$	−3.05307	−	5.28808i	−0.137087	−	0.237442i
$497$	−45.6005	+	16.5972i	−2.04546	+	0.744488i
$498$	−16.4284	+	14.4482i	−0.736176	+	0.647438i
$499$	1.10500	−	0.927202i	0.0494664	−	0.0415073i	−0.617719	−	0.786399i	$-0.711943\pi$
$499$	1.10500	−	0.927202i	0.0494664	−	0.0415073i	0.667186	+	0.744891i	$0.267499\pi$
$500$		0			0
$501$	6.44798	+	32.1801i	0.288074	+	1.43770i
$502$	1.01535	−	0.369556i	0.0453172	−	0.0164941i
$503$	−11.9460	−	20.6911i	−0.532645	−	0.922569i	−0.999273	−	0.0381151i	$-0.987865\pi$
$503$	−11.9460	−	20.6911i	−0.532645	−	0.922569i	0.466628	−	0.884454i	$-0.345469\pi$
$504$	−35.9623	+	15.0144i	−1.60189	+	0.668797i
$505$		0			0
$506$	−0.563104	+	3.19352i	−0.0250330	+	0.141969i
$507$	19.9812	−	7.80257i	0.887398	−	0.346524i
$508$	−23.3538	−	8.50008i	−1.03616	−	0.377130i
$509$	−0.690844	−	3.91797i	−0.0306211	−	0.173661i	0.965662	−	0.259802i	$-0.0836574\pi$
$509$	−0.690844	−	3.91797i	−0.0306211	−	0.173661i	−0.996283	+	0.0861414i	$0.972546\pi$
$510$		0			0
$511$	−13.4144	−	11.2560i	−0.593416	−	0.497936i
$512$	−8.29380			−0.366537
$513$	9.87298	−	20.2347i	0.435903	−	0.893383i
$514$	−3.24403			−0.143088
$515$		0			0
$516$	0.490026	−	0.896178i	0.0215722	−	0.0394520i
$517$	−4.70671	−	26.6931i	−0.207001	−	1.17396i
$518$	11.1256	+	4.04940i	0.488832	+	0.177920i
$519$	−0.792775	−	0.634442i	−0.0347990	−	0.0278489i
$520$		0			0
$521$	11.2999	−	19.5719i	0.495055	−	0.857461i	−0.504928	−	0.863161i	$-0.668481\pi$
$521$	11.2999	−	19.5719i	0.495055	−	0.857461i	0.999984	+	0.00570007i	$0.00181440\pi$
$522$	5.10550	+	1.59402i	0.223461	+	0.0697684i
$523$	14.9862	+	25.9568i	0.655299	+	1.13501i	0.981819	+	0.189821i	$0.0607907\pi$
$523$	14.9862	+	25.9568i	0.655299	+	1.13501i	−0.326520	+	0.945190i	$0.605876\pi$
$524$	7.91696	−	2.88154i	0.345854	−	0.125881i
$525$		0			0
$526$	−5.19443	+	4.35864i	−0.226488	+	0.190046i
$527$	35.9370	−	30.1548i	1.56544	−	1.31356i
$528$	−4.12708	−	1.39450i	−0.179608	−	0.0606878i
$529$	20.1749	−	7.34305i	0.877168	−	0.319263i
$530$		0			0
$531$	−16.3130	+	15.0325i	−0.707923	+	0.652356i
$532$	−14.9026	+	25.8121i	−0.646111	+	1.11910i
$533$	0.807498	−	4.57955i	0.0349766	−	0.198362i
$534$	2.32159	+	1.85792i	0.100465	+	0.0804001i
$535$		0			0
$536$	1.46662	+	8.31764i	0.0633485	+	0.359267i
$537$	−16.6327	+	30.4185i	−0.717754	+	1.31266i
$538$	−2.12573	−	1.78370i	−0.0916468	−	0.0769008i
$539$	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	$0.472617\pi$
$542$	8.31230	+	6.97485i	0.357044	+	0.299595i
$543$	−25.1165	+	0.583300i	−1.07785	+	0.0250318i
$544$	−5.82003	−	33.0070i	−0.249532	−	1.41517i
$545$		0			0
$546$	4.84038	−	1.89014i	0.207149	−	0.0808906i
$547$	5.87339	−	33.3096i	0.251128	−	1.42422i	−0.554692	−	0.832056i	$-0.687164\pi$
$547$	5.87339	−	33.3096i	0.251128	−	1.42422i	0.805819	−	0.592161i	$-0.201725\pi$
$548$	−10.5067	+	18.1982i	−0.448826	+	0.777389i
$549$	−9.33447	−	7.12106i	−0.398385	−	0.303920i
$550$		0			0
$551$	9.34744	−	3.40219i	0.398214	−	0.144938i
$552$	1.11051	+	5.54225i	0.0472663	+	0.235894i
$553$	6.46716	−	5.42660i	0.275012	−	0.230762i
$554$	11.5531	−	9.69421i	0.490844	−	0.411867i
$555$		0			0
$556$	−11.2032	+	4.07763i	−0.475121	+	0.172930i
$557$	12.6493	+	21.9093i	0.535969	+	0.928326i	0.999116	+	0.0420444i	$0.0133871\pi$
$557$	12.6493	+	21.9093i	0.535969	+	0.928326i	−0.463146	+	0.886282i	$0.653280\pi$
$558$	10.3033	+	16.0733i	0.436174	+	0.680435i
$559$	−0.165593	+	0.286815i	−0.00700383	+	0.0121310i
$560$		0			0
$561$	5.04497	−	33.0864i	0.212999	−	1.39691i
$562$	14.5969	+	5.31284i	0.615733	+	0.224108i
$563$	−7.03270	−	39.8845i	−0.296393	−	1.68093i	−0.661486	−	0.749958i	$-0.730074\pi$
$563$	−7.03270	−	39.8845i	−0.296393	−	1.68093i	0.365092	−	0.930971i	$-0.381037\pi$
$564$	−10.1024	−	16.5957i	−0.425388	−	0.698805i
$565$		0			0
$566$	−8.49748			−0.357176
$567$	−40.0603	+	18.9548i	−1.68237	+	0.796028i
$568$	25.9969			1.09080
$569$	7.94639	+	6.66781i	0.333130	+	0.279529i	0.793974	−	0.607952i	$-0.208009\pi$
$569$	7.94639	+	6.66781i	0.333130	+	0.279529i	−0.460844	+	0.887481i	$0.652453\pi$
$570$		0			0
$571$	−1.66139	−	9.42220i	−0.0695269	−	0.394307i	−0.999635	−	0.0270205i	$-0.991398\pi$
$571$	−1.66139	−	9.42220i	−0.0695269	−	0.394307i	0.930108	−	0.367286i	$-0.119713\pi$
$572$	3.47600	+	1.26516i	0.145339	+	0.0528991i
$573$	−1.02881	+	6.74725i	−0.0429793	+	0.281870i
$574$	−3.93619	+	22.3232i	−0.164293	+	0.931753i
$575$		0			0
$576$	9.15955	−	0.425668i	0.381648	−	0.0177362i
$577$	10.5111	+	18.2058i	0.437585	+	0.757919i	0.997503	−	0.0706290i	$-0.0225006\pi$
$577$	10.5111	+	18.2058i	0.437585	+	0.757919i	−0.559918	+	0.828548i	$0.689167\pi$
$578$	11.5097	−	4.18920i	0.478742	−	0.174248i
$579$	−7.86200	+	6.91433i	−0.326734	+	0.287350i
$580$		0			0
$581$	61.3543	−	51.4823i	2.54540	−	2.13585i
$582$	−4.02718	−	20.0986i	−0.166932	−	0.833114i
$583$	40.7203	−	14.8210i	1.68646	−	0.613822i
$584$	4.69054	+	8.12426i	0.194096	+	0.336184i
$585$		0			0
$586$	2.48895	−	4.31099i	0.102818	−	0.178085i
$587$	4.49575	−	25.4966i	0.185559	−	1.05236i	−0.739675	−	0.672964i	$-0.765021\pi$
$587$	4.49575	−	25.4966i	0.185559	−	1.05236i	0.925235	−	0.379395i	$-0.123868\pi$
$588$	38.8735	−	15.1799i	1.60312	−	0.626009i
$589$	33.3665	+	12.1444i	1.37484	+	0.500401i
$590$		0			0
$591$	−1.38854	+	0.0322471i	−0.0571169	+	0.00132647i
$592$	1.76720	+	1.48286i	0.0726317	+	0.0609452i
$593$	7.66640			0.314821			0.157411	−	0.987533i	$-0.449685\pi$
$593$	7.66640			0.314821			0.157411	+	0.987533i	$0.449685\pi$
$594$	13.0926	+	3.75644i	0.537198	+	0.154129i
$595$		0			0
$596$	−10.5766	−	8.87479i	−0.433233	−	0.363526i
$597$	−3.85536	+	7.05083i	−0.157789	+	0.288571i
$598$	−0.130877	−	0.742238i	−0.00535194	−	0.0303524i
$599$	35.3351	+	12.8609i	1.44375	+	0.525483i	0.940839	−	0.338854i	$-0.110039\pi$
$599$	35.3351	+	12.8609i	1.44375	+	0.525483i	0.502914	+	0.864337i	$0.332261\pi$
$600$		0			0
$601$	−2.37700	+	13.4806i	−0.0969599	+	0.549887i	0.897169	+	0.441687i	$0.145620\pi$
$601$	−2.37700	+	13.4806i	−0.0969599	+	0.549887i	−0.994129	+	0.108200i	$0.965491\pi$
$602$	0.807191	−	1.39810i	0.0328986	−	0.0569821i
$603$	2.10518	+	9.37134i	0.0857296	+	0.381630i
$604$	−2.37089	−	4.10650i	−0.0964702	−	0.167091i
$605$		0			0
$606$	23.8868	+	8.07111i	0.970333	+	0.327866i
$607$	−26.5364	+	22.2667i	−1.07708	+	0.903776i	−0.995675	−	0.0929052i	$-0.970385\pi$
$607$	−26.5364	+	22.2667i	−1.07708	+	0.903776i	−0.0814033	+	0.996681i	$0.525940\pi$
$608$	19.4332	−	16.3064i	0.788122	−	0.661313i
$609$	−18.5501	−	6.26789i	−0.751686	−	0.253988i
$610$		0			0
$611$	3.14985	+	5.45570i	0.127429	+	0.220714i
$612$	−5.25817	−	23.4071i	−0.212549	−	0.946174i
$613$	7.88639	−	13.6596i	0.318528	−	0.551708i	−0.661653	−	0.749810i	$-0.730145\pi$
$613$	7.88639	−	13.6596i	0.318528	−	0.551708i	0.980181	+	0.198103i	$0.0634780\pi$
$614$	−1.53539	+	8.70763i	−0.0619633	+	0.351412i
$615$		0			0
$616$	−41.2033	−	14.9968i	−1.66013	−	0.604237i
$617$	6.09413	+	34.5615i	0.245340	+	1.39139i	0.819701	+	0.572792i	$0.194140\pi$
$617$	6.09413	+	34.5615i	0.245340	+	1.39139i	−0.574360	+	0.818603i	$0.694749\pi$
$618$	−0.895265	+	1.63730i	−0.0360129	+	0.0658617i
$619$	−14.1386	−	11.8637i	−0.568278	−	0.476842i	0.312796	−	0.949820i	$-0.398734\pi$
$619$	−14.1386	−	11.8637i	−0.568278	−	0.476842i	−0.881074	+	0.472978i	$0.843179\pi$
$620$		0			0
$621$	1.55412	+	6.23732i	0.0623645	+	0.250295i
$622$	1.61114			0.0646010
$623$	−8.33883	−	6.99711i	−0.334088	−	0.280333i
$624$	1.01222	−	0.0235075i	0.0405212	−	0.000941054i
$625$		0			0
$626$	−17.5576	−	6.39046i	−0.701745	−	0.255414i
$627$	23.5971	−	9.21453i	0.942376	−	0.367993i
$628$	−5.24210	+	29.7294i	−0.209183	+	1.18633i
$629$	−8.86184	+	15.3492i	−0.353345	+	0.612011i
$630$		0			0
$631$	−16.7999	−	29.0983i	−0.668793	−	1.15838i	−0.978242	−	0.207467i	$-0.933478\pi$
$631$	−16.7999	−	29.0983i	−0.668793	−	1.15838i	0.309449	−	0.950916i	$-0.399855\pi$
$632$	−4.24994	+	1.54685i	−0.169054	+	0.0615305i
$633$	−2.13818	−	10.6711i	−0.0849849	−	0.424137i
$634$	−4.38257	+	3.67741i	−0.174054	+	0.146049i
$635$		0			0
$636$	23.3245	−	20.5130i	0.924878	−	0.813394i
$637$	−12.7155	+	4.62806i	−0.503806	+	0.183370i
$638$	3.00894	+	5.21163i	0.119125	+	0.206330i
$639$	29.5322	−	1.37244i	1.16828	−	0.0542929i
$640$		0			0
$641$	−5.20105	+	29.4966i	−0.205429	+	1.16505i	0.691334	+	0.722536i	$0.257023\pi$
$641$	−5.20105	+	29.4966i	−0.205429	+	1.16505i	−0.896763	+	0.442511i	$0.854088\pi$
$642$	1.37836	−	9.03965i	0.0543994	−	0.356767i
$643$	12.2444	+	4.45660i	0.482873	+	0.175751i	0.571975	−	0.820271i	$-0.306178\pi$
$643$	12.2444	+	4.45660i	0.482873	+	0.175751i	−0.0891022	+	0.996022i	$0.528400\pi$
$644$	−1.47765	−	8.38016i	−0.0582275	−	0.330225i
$645$		0			0
$646$	14.7566	+	12.3823i	0.580591	+	0.487174i
$647$	36.7940			1.44652			0.723260	−	0.690576i	$-0.242643\pi$
$647$	36.7940			1.44652			0.723260	+	0.690576i	$0.242643\pi$
$648$	23.6398	−	2.20196i	0.928660	−	0.0865013i
$649$	−24.9591			−0.979731
$650$		0			0
$651$	−36.3428	−	59.7021i	−1.42439	−	2.33991i
$652$	−1.60760	−	9.11718i	−0.0629587	−	0.357056i
$653$	−39.7421	−	14.4650i	−1.55523	−	0.566057i	−0.585592	−	0.810606i	$-0.699138\pi$
$653$	−39.7421	−	14.4650i	−1.55523	−	0.566057i	−0.969637	+	0.244548i	$0.921360\pi$
$654$	−0.751654	+	4.92957i	−0.0293920	+	0.192761i
$655$		0			0
$656$	−2.20836	+	3.82499i	−0.0862219	+	0.149341i
$657$	5.75732	+	8.98147i	0.224614	+	0.350400i
$658$	−15.3541	−	26.5941i	−0.598565	−	1.03674i
$659$	28.0790	−	10.2199i	1.09380	−	0.398111i	0.268773	−	0.963203i	$-0.413382\pi$
$659$	28.0790	−	10.2199i	1.09380	−	0.398111i	0.825028	+	0.565092i	$0.191160\pi$
$660$		0			0
$661$	30.7868	−	25.8332i	1.19747	−	1.00480i	0.197769	−	0.980249i	$-0.436630\pi$
$661$	30.7868	−	25.8332i	1.19747	−	1.00480i	0.999699	−	0.0245465i	$-0.00781419\pi$
$662$	0.0766591	−	0.0643246i	0.00297944	−	0.00250005i
$663$	1.52827	+	7.62720i	0.0593531	+	0.296216i
$664$	−40.3194	+	14.6750i	−1.56469	+	0.569502i
$665$		0			0
$666$	−5.73480	−	4.37496i	−0.222219	−	0.169526i
$667$	−1.41999	+	2.45950i	−0.0549822	+	0.0952320i
$668$	−4.59632	+	26.0670i	−0.177837	+	1.00856i
$669$	−0.340442	+	0.132941i	−0.0131623	+	0.00513980i
$670$		0			0
$671$	−2.29386	−	13.0091i	−0.0885536	−	0.502213i
$672$	−49.9216	+	1.15937i	−1.92577	+	0.0447235i
$673$	−16.2157	−	13.6066i	−0.625070	−	0.524496i	0.274322	−	0.961638i	$-0.411546\pi$
$673$	−16.2157	−	13.6066i	−0.625070	−	0.524496i	−0.899393	+	0.437142i	$0.855991\pi$
$674$	−9.53765			−0.367376
$675$		0			0
$676$	17.2999			0.665383
$677$	5.78080	+	4.85067i	0.222174	+	0.186426i	0.747080	−	0.664734i	$-0.231455\pi$
$677$	5.78080	+	4.85067i	0.222174	+	0.186426i	−0.524906	+	0.851160i	$0.675900\pi$
$678$	6.62093	−	12.1086i	0.254275	−	0.465029i
$679$	13.0307	+	73.9010i	0.500074	+	2.83606i
$680$		0			0
$681$	−9.53457	−	7.63033i	−0.365365	−	0.292395i
$682$	−3.73019	+	21.1549i	−0.142836	+	0.810065i
$683$	−1.24603	+	2.15819i	−0.0476781	+	0.0825810i	−0.888880	−	0.458141i	$-0.848516\pi$
$683$	−1.24603	+	2.15819i	−0.0476781	+	0.0825810i	0.841201	+	0.540722i	$0.181849\pi$
$684$	13.3532	−	12.3050i	0.510571	−	0.470495i
$685$		0			0
$686$	36.8275	−	13.4041i	1.40608	−	0.511772i
$687$	36.5445	+	12.3480i	1.39426	+	0.471107i
$688$	0.240965	−	0.202194i	0.00918671	−	0.00770857i
$689$	−7.71529	+	6.47389i	−0.293929	+	0.246636i
$690$		0			0
$691$	40.1126	−	14.5998i	1.52595	−	0.555402i	0.563328	−	0.826234i	$-0.309521\pi$
$691$	40.1126	−	14.5998i	1.52595	−	0.555402i	0.962627	+	0.270831i	$0.0872986\pi$
$692$	−0.409455	−	0.709196i	−0.0155651	−	0.0269596i
$693$	−47.5983	−	14.8610i	−1.80811	−	0.564522i
$694$	2.30250	−	3.98805i	0.0874018	−	0.151384i
$695$		0			0
$696$	8.18986	+	6.55419i	0.310436	+	0.248436i
$697$	−31.8865	−	11.6057i	−1.20779	−	0.439598i
$698$	−3.96909	−	22.5098i	−0.150232	−	0.852010i
$699$	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	$0.503610\pi$
$702$	−3.15808	+	0.220345i	−0.119194	+	0.00831637i
$703$	−13.4150			−0.505956
$704$	7.90321	+	6.63158i	0.297863	+	0.249937i
$705$		0			0
$706$	0.794610	+	4.50646i	0.0299055	+	0.169603i
$707$	−86.7369	−	31.5696i	−3.26208	−	1.18730i
$708$	−16.6651	+	6.50765i	−0.626314	+	0.244573i
$709$	8.93134	−	50.6521i	0.335423	−	1.90228i	−0.0875888	−	0.996157i	$-0.527916\pi$
$709$	8.93134	−	50.6521i	0.335423	−	1.90228i	0.423012	−	0.906124i	$-0.360973\pi$
$710$		0			0
$711$	−4.74624	+	1.98158i	−0.177998	+	0.0743149i
$712$	2.91580	+	5.05032i	0.109274	+	0.189269i
$713$	−9.52618	+	3.46725i	−0.356758	+	0.129849i
$714$	−7.44963	−	37.1791i	−0.278795	−	1.39139i
$715$		0			0
$716$	−21.4190	+	17.9727i	−0.800465	+	0.671670i
$717$	7.94410	−	6.98653i	0.296678	−	0.260917i
$718$	−14.6606	+	5.33604i	−0.547130	+	0.199139i
$719$	−2.39613	−	4.15021i	−0.0893604	−	0.154777i	0.817881	−	0.575388i	$-0.195149\pi$
$719$	−2.39613	−	4.15021i	−0.0893604	−	0.154777i	−0.907241	+	0.420611i	$0.861816\pi$
$720$		0			0
$721$	3.41574	−	5.91623i	0.127209	−	0.220332i
$722$	0.0303766	−	0.172274i	0.00113050	−	0.00641139i
$723$	−5.02705	+	32.9689i	−0.186958	+	1.22613i
$724$	−19.0400	−	6.92999i	−0.707616	−	0.257551i
$725$		0			0
$726$	0.275206	+	0.452093i	0.0102138	+	0.0167788i
$727$	12.0941	+	10.1481i	0.448544	+	0.376373i	0.838895	−	0.544293i	$-0.183202\pi$
$727$	12.0941	+	10.1481i	0.448544	+	0.376373i	−0.390351	+	0.920666i	$0.627646\pi$
$728$	10.1911			0.377706
$729$	26.7384	−	3.74942i	0.990311	−	0.138867i
$730$		0			0
$731$	1.85129	+	1.55342i	0.0684726	+	0.0574553i
$732$	−4.92351	−	8.08809i	−0.181978	−	0.298944i
$733$	0.444773	+	2.52244i	0.0164281	+	0.0931683i	0.991919	−	0.126870i	$-0.0404930\pi$
$733$	0.444773	+	2.52244i	0.0164281	+	0.0931683i	−0.975491	+	0.220038i	$0.929382\pi$
$734$	−17.1972	−	6.25927i	−0.634761	−	0.231034i
$735$		0			0
$736$	−1.25768	+	7.13266i	−0.0463587	+	0.262913i
$737$	−5.40342	+	9.35900i	−0.199038	+	0.344743i
$738$	6.34224	−	12.2672i	0.233461	−	0.451564i
$739$	12.4456	+	21.5564i	0.457818	+	0.792964i	0.998845	−	0.0480413i	$-0.0152979\pi$
$739$	12.4456	+	21.5564i	0.457818	+	0.792964i	−0.541028	+	0.841005i	$0.681965\pi$
$740$		0			0
$741$	−4.42119	+	3.88827i	−0.162416	+	0.142839i
$742$	37.6085	−	31.5573i	1.38065	−	1.15851i
$743$	1.09459	−	0.918468i	0.0401565	−	0.0336953i	−0.622489	−	0.782629i	$-0.713878\pi$
$743$	1.09459	−	0.918468i	0.0401565	−	0.0336953i	0.662645	+	0.748934i	$0.269434\pi$
$744$	7.35637	+	36.7137i	0.269697	+	1.34599i
$745$		0			0
$746$	−5.57974	−	9.66440i	−0.204289	−	0.353839i
$747$	−45.0277	+	18.7993i	−1.64748	+	0.687830i
$748$	13.4963	−	23.3762i	0.493473	−	0.854720i
$749$	−5.81296	+	32.9670i	−0.212401	+	1.20459i
$750$		0			0
$751$	24.5964	+	8.95234i	0.897534	+	0.326676i	0.749264	−	0.662271i	$-0.230407\pi$
$751$	24.5964	+	8.95234i	0.897534	+	0.326676i	0.148270	+	0.988947i	$0.452630\pi$
$752$	−1.03901	−	5.89250i	−0.0378887	−	0.214878i
$753$	2.40923	−	0.0559513i	0.0877971	−	0.00203898i
$754$	−1.07145	−	0.899049i	−0.0390197	−	0.0327414i
$755$		0			0
$756$	−35.6560	+	2.48778i	−1.29680	+	0.0904797i
$757$	13.5023			0.490750			0.245375	−	0.969428i	$-0.421089\pi$
$757$	13.5023			0.490750			0.245375	+	0.969428i	$0.421089\pi$
$758$	−19.4146	−	16.2908i	−0.705169	−	0.591707i
$759$	−3.46982	+	6.34574i	−0.125946	+	0.230336i
$760$		0			0
$761$	−38.1386	−	13.8813i	−1.38252	−	0.503197i	−0.459580	−	0.888136i	$-0.652000\pi$
$761$	−38.1386	−	13.8813i	−1.38252	−	0.503197i	−0.922942	+	0.384939i	$0.874222\pi$
$762$	18.6845	+	14.9528i	0.676866	+	0.541683i
$763$	3.16997	−	17.9778i	0.114761	−	0.650839i
$764$	−2.75228	+	4.76708i	−0.0995739	+	0.172467i
$765$		0			0
$766$	−2.13131	−	3.69154i	−0.0770074	−	0.133381i
$767$	5.45115	−	1.98406i	0.196830	−	0.0716401i
$768$	21.9276	+	7.40912i	0.791243	+	0.267354i
$769$	−13.6615	+	11.4634i	−0.492647	+	0.413380i	−0.854974	−	0.518671i	$-0.826427\pi$
$769$	−13.6615	+	11.4634i	−0.492647	+	0.413380i	0.362327	+	0.932051i	$0.381982\pi$
$770$		0			0
$771$	−6.85448	−	2.31606i	−0.246858	−	0.0834110i
$772$	−7.93475	+	2.88801i	−0.285578	+	0.103942i
$773$	12.3324	+	21.3604i	0.443566	+	0.768279i	0.997951	−	0.0639812i	$-0.0203798\pi$
$773$	12.3324	+	21.3604i	0.443566	+	0.768279i	−0.554385	+	0.832260i	$0.687046\pi$
$774$	−0.723266	+	0.666494i	−0.0259973	+	0.0239566i
$775$		0			0
$776$	6.98081	−	39.5902i	0.250597	−	1.42120i
$777$	20.6169	+	16.4993i	0.739626	+	0.591909i
$778$	−12.7738	−	4.64930i	−0.457965	−	0.166685i
$779$	−4.45992	−	25.2935i	−0.159793	−	0.906233i
$780$		0			0
$781$	25.4815	+	21.3816i	0.911801	+	0.765092i
$782$	−5.49973			−0.196670
$783$	9.64963	+	7.01314i	0.344850	+	0.250629i
$784$	12.8521			0.459005
$785$		0			0
$786$	−8.11047	+	0.188356i	−0.289291	+	0.00671842i
$787$	−0.224210	−	1.27156i	−0.00799222	−	0.0453261i	0.980551	−	0.196265i	$-0.0628814\pi$
$787$	−0.224210	−	1.27156i	−0.00799222	−	0.0453261i	−0.988543	+	0.150939i	$0.951770\pi$
$788$	−1.05261	−	0.383117i	−0.0374975	−	0.0136480i
$789$	−14.0874	+	5.50106i	−0.501525	+	0.195843i
$790$		0			0
$791$	−25.2611	+	43.7535i	−0.898180	+	1.55569i
$792$	21.2386	+	16.2025i	0.754681	+	0.575730i
$793$	1.53511	+	2.65889i	0.0545135	+	0.0944201i
$794$	−3.23051	+	1.17581i	−0.114647	+	0.0417280i
$795$		0			0
$796$	−4.96479	+	4.16595i	−0.175972	+	0.147658i
$797$	−16.1949	+	13.5891i	−0.573652	+	0.481351i	−0.882856	−	0.469645i	$-0.844382\pi$
$797$	−16.1949	+	13.5891i	−0.573652	+	0.481351i	0.309203	+	0.950996i	$0.399938\pi$
$798$	21.5513	−	18.9535i	0.762907	−	0.670948i
$799$	43.1972	−	15.7225i	1.52821	−	0.556222i
$800$		0			0
$801$	3.57895	+	5.58319i	0.126456	+	0.197272i
$802$	12.7508	−	22.0850i	0.450245	−	0.779847i
$803$	−2.08437	+	11.8210i	−0.0735557	+	0.417155i
$804$	−1.16766	+	7.65783i	−0.0411801	+	0.270071i
$805$		0			0
$806$	−0.866969	−	4.91683i	−0.0305377	−	0.173188i
$807$	−3.21811	−	5.28654i	−0.113283	−	0.186095i
$808$	37.8799	+	31.7850i	1.33261	+	1.11819i
$809$	−41.8122			−1.47004			−0.735019	−	0.678047i	$-0.762827\pi$
$809$	−41.8122			−1.47004			−0.735019	+	0.678047i	$0.762827\pi$
$810$		0			0
$811$	1.20717			0.0423894			0.0211947	−	0.999775i	$-0.493253\pi$
$811$	1.20717			0.0423894			0.0211947	+	0.999775i	$0.493253\pi$
$812$	−12.0970	−	10.1506i	−0.424523	−	0.356217i
$813$	12.5838	+	20.6721i	0.441334	+	0.725001i
$814$	−1.40928	−	7.99241i	−0.0493951	−	0.280134i
$815$		0			0
$816$	1.11368	−	7.30383i	0.0389866	−	0.255685i
$817$	−0.317635	+	1.80140i	−0.0111126	+	0.0630229i
$818$	−10.2982	+	17.8371i	−0.360070	+	0.623659i
$819$	11.5770	−	0.538011i	0.404532	−	0.0187996i
$820$		0			0
$821$	14.8150	−	5.39222i	0.517047	−	0.188190i	−0.0702986	−	0.997526i	$-0.522395\pi$
$821$	14.8150	−	5.39222i	0.517047	−	0.188190i	0.587346	+	0.809336i	$0.300173\pi$
$822$	15.1942	−	13.3627i	0.529960	−	0.466079i
$823$	−21.6421	+	18.1599i	−0.754398	+	0.633015i	−0.936662	−	0.350235i	$-0.886102\pi$
$823$	−21.6421	+	18.1599i	−0.754398	+	0.633015i	0.182264	+	0.983250i	$0.441657\pi$
$824$	−2.80353	+	2.35244i	−0.0976656	+	0.0819512i
$825$		0			0
$826$	−26.5719	+	9.67138i	−0.924554	+	0.336510i
$827$	9.51297	+	16.4770i	0.330799	+	0.572960i	0.982669	−	0.185371i	$-0.0593486\pi$
$827$	9.51297	+	16.4770i	0.330799	+	0.572960i	−0.651870	+	0.758331i	$0.726015\pi$
$828$	−0.662249	+	5.14173i	−0.0230148	+	0.178687i
$829$	8.50721	−	14.7349i	0.295468	−	0.511765i	−0.679626	−	0.733559i	$-0.737858\pi$
$829$	8.50721	−	14.7349i	0.295468	−	0.511765i	0.975094	+	0.221794i	$0.0711912\pi$
$830$		0			0
$831$	31.3323	−	12.2351i	1.08691	−	0.424431i
$832$	−2.25324	−	0.820114i	−0.0781172	−	0.0284323i
$833$	17.1462	+	97.2407i	0.594079	+	3.36919i
$834$	11.4770	−	0.266540i	0.397417	−	0.00922952i
$835$		0			0
$836$	20.4306			0.706606
$837$	10.2950	+	41.3181i	0.355846	+	1.42816i
$838$	21.3864			0.738780
$839$	0.767986	+	0.644416i	0.0265138	+	0.0222477i	0.655948	−	0.754806i	$-0.272269\pi$
$839$	0.767986	+	0.644416i	0.0265138	+	0.0222477i	−0.629434	+	0.777054i	$0.716713\pi$
$840$		0			0
$841$	−4.12061	−	23.3691i	−0.142090	−	0.805832i
$842$	−19.8258	−	7.21601i	−0.683243	−	0.248680i
$843$	27.0495	+	21.6472i	0.931634	+	0.745569i
$844$	1.52416	−	8.64394i	0.0524637	−	0.297537i
$845$		0			0
$846$	4.10046	+	18.2534i	0.140977	+	0.627566i
$847$	−0.968796	−	1.67800i	−0.0332882	−	0.0576569i
$848$	8.98902	−	3.27174i	0.308684	−	0.112352i
$849$	−17.9548	−	6.06675i	−0.616207	−	0.208210i
$850$		0			0
$851$	2.93395	−	2.46188i	0.100574	−	0.0843920i
$852$	22.5888	+	7.63255i	0.773880	+	0.261487i
$853$	−27.8950	+	10.1529i	−0.955106	+	0.347630i	−0.772114	−	0.635484i	$-0.780800\pi$
$853$	−27.8950	+	10.1529i	−0.955106	+	0.347630i	−0.182992	+	0.983114i	$0.558578\pi$
$854$	−7.48298	−	12.9609i	−0.256062	−	0.443513i
$855$		0			0
$856$	8.96674	−	15.5308i	0.306477	−	0.530833i
$857$	5.98263	−	33.9292i	0.204363	−	1.15900i	−0.694077	−	0.719901i	$-0.744187\pi$
$857$	5.98263	−	33.9292i	0.204363	−	1.15900i	0.898439	−	0.439097i	$-0.144702\pi$
$858$	−2.78102	−	2.22559i	−0.0949423	−	0.0759805i
$859$	21.6343	+	7.87422i	0.738151	+	0.268665i	0.683611	−	0.729847i	$-0.260408\pi$
$859$	21.6343	+	7.87422i	0.738151	+	0.268665i	0.0545401	+	0.998512i	$0.482631\pi$
$860$		0			0
$861$	−24.2546	+	44.3577i	−0.826593	+	1.51171i
$862$	3.84928	+	3.22993i	0.131107	+	0.110012i
$863$	17.0095			0.579009			0.289504	−	0.957177i	$-0.406509\pi$
$863$	17.0095			0.579009			0.289504	+	0.957177i	$0.406509\pi$
$864$	29.2421	+	8.38993i	0.994837	+	0.285431i
$865$		0			0
$866$	11.2884	+	9.47209i	0.383595	+	0.321875i
$867$	27.3104	−	0.634250i	0.927510	−	0.0215403i
$868$	−9.78843	−	55.5130i	−0.332241	−	1.88423i
$869$	−5.43793	−	1.97924i	−0.184469	−	0.0671412i
$870$		0			0
$871$	0.436156	−	2.47357i	0.0147786	−	0.0838136i
$872$	−4.88981	+	8.46939i	−0.165590	+	0.286810i
$873$	5.84008	−	45.3426i	0.197657	−	1.53462i
$874$	−2.08136	−	3.60502i	−0.0704031	−	0.121942i
$875$		0			0
$876$	1.69040	+	8.43633i	0.0571133	+	0.285037i
$877$	11.0399	−	9.26361i	0.372792	−	0.312810i	−0.437073	−	0.899426i	$-0.643985\pi$
$877$	11.0399	−	9.26361i	0.372792	−	0.312810i	0.809865	+	0.586616i	$0.199540\pi$
$878$	17.5718	−	14.7445i	0.593021	−	0.497604i
$879$	8.33685	−	7.33194i	0.281195	−	0.247300i
$880$		0			0
$881$	−3.76414	−	6.51968i	−0.126817	−	0.219654i	0.795625	−	0.605790i	$-0.207143\pi$
$881$	−3.76414	−	6.51968i	−0.126817	−	0.219654i	−0.922442	+	0.386136i	$0.873809\pi$
$882$	−40.1415	+	1.86548i	−1.35163	+	0.0628140i
$883$	16.6514	−	28.8410i	0.560363	−	0.970578i	−0.437101	−	0.899412i	$-0.643995\pi$
$883$	16.6514	−	28.8410i	0.560363	−	0.970578i	0.997465	−	0.0711656i	$-0.0226719\pi$
$884$	−1.08940	+	6.17829i	−0.0366405	+	0.207799i
$885$		0			0
$886$	−9.99901	−	3.63934i	−0.335923	−	0.122266i
$887$	2.93186	+	16.6274i	0.0984423	+	0.558294i	0.993638	+	0.112621i	$0.0359245\pi$
$887$	2.93186	+	16.6274i	0.0984423	+	0.558294i	−0.895196	+	0.445673i	$0.852964\pi$
$888$	−7.35566	−	12.0835i	−0.246840	−	0.405495i
$889$	−67.1121	−	56.3137i	−2.25087	−	1.88870i
$890$		0			0
$891$	24.9823	+	17.2846i	0.836937	+	0.579057i
$892$	−0.294758			−0.00986924
$893$	26.6538	+	22.3652i	0.891937	+	0.748424i
$894$	6.91292	+	11.3562i	0.231203	+	0.379807i
$895$		0			0
$896$	−43.1992	−	15.7232i	−1.44318	−	0.525275i
$897$	0.253382	−	1.66175i	0.00846018	−	0.0554843i
$898$	−4.37571	+	24.8159i	−0.146019	+	0.828116i
$899$	−9.40648	+	16.2925i	−0.313724	+	0.543386i
$900$		0			0
$901$	36.7467	+	63.6471i	1.22421	+	2.12039i
$902$	14.6009	−	5.31428i	0.486156	−	0.176946i
$903$	2.70372	−	2.37782i	0.0899742	−	0.0791289i
$904$	20.7335	−	17.3975i	0.689586	−	0.578631i
$905$		0			0
$906$	0.897056	+	4.47697i	0.0298027	+	0.148737i
$907$	−7.08716	+	2.57952i	−0.235325	+	0.0856514i	−0.456991	−	0.889471i	$-0.651073\pi$
$907$	−7.08716	+	2.57952i	−0.235325	+	0.0856514i	0.221666	+	0.975123i	$0.428851\pi$
$908$	−4.92444	−	8.52938i	−0.163423	−	0.283057i
$909$	44.7093	+	34.1078i	1.48291	+	1.13128i
$910$		0			0
$911$	1.57637	−	8.94003i	0.0522274	−	0.296196i	−0.947495	−	0.319772i	$-0.896394\pi$
$911$	1.57637	−	8.94003i	0.0522274	−	0.296196i	0.999722	+	0.0235753i	$0.00750494\pi$
$912$	5.20906	−	2.03411i	0.172489	−	0.0673562i
$913$	−51.5898	−	18.7772i	−1.70737	−	0.621434i
$914$	−2.24461	−	12.7298i	−0.0742451	−	0.421065i
$915$		0			0
$916$	23.8318	+	19.9972i	0.787423	+	0.660727i
$917$	29.6994			0.980761
$918$	−2.41824	+	22.9739i	−0.0798139	+	0.758252i
$919$	−27.0698			−0.892951			−0.446475	−	0.894796i	$-0.647321\pi$
$919$	−27.0698			−0.892951			−0.446475	+	0.894796i	$0.647321\pi$
$920$		0			0
$921$	−9.46100	+	17.3026i	−0.311750	+	0.570141i
$922$	4.45253	+	25.2516i	0.146636	+	0.831616i
$923$	−7.26492	−	2.64421i	−0.239128	−	0.0870353i
$924$	−31.3988	−	25.1279i	−1.03294	−	0.826646i
$925$		0			0
$926$	13.2008	−	22.8645i	0.433807	−	0.751375i
$927$	−3.06060	+	2.82036i	−0.100523	+	0.0926328i
$928$	6.72039	+	11.6400i	0.220607	+	0.382103i
$929$	−30.5625	+	11.1238i	−1.00272	+	0.364962i	−0.790634	−	0.612289i	$-0.790249\pi$
$929$	−30.5625	+	11.1238i	−1.00272	+	0.364962i	−0.212090	+	0.977250i	$0.568027\pi$
$930$		0			0
$931$	−57.2515	+	48.0397i	−1.87634	+	1.57444i
$932$	14.5065	−	12.1724i	0.475176	−	0.398720i
$933$	3.40427	+	1.15027i	0.111451	+	0.0376582i
$934$	1.30461	−	0.474840i	0.0426882	−	0.0155372i
$935$		0			0
$936$	−5.92655	−	1.85037i	−0.193715	−	0.0604811i
$937$	−10.8749	+	18.8358i	−0.355267	+	0.615340i	−0.987164	−	0.159713i	$-0.948943\pi$
$937$	−10.8749	+	18.8358i	−0.355267	+	0.615340i	0.631897	+	0.775052i	$0.282277\pi$
$938$	−2.12606	+	12.0575i	−0.0694185	+	0.393692i
$939$	−32.5360	−	26.0380i	−1.06177	−	0.849717i
$940$		0			0
$941$	0.523029	+	2.96625i	0.0170503	+	0.0966969i	0.992145	−	0.125090i	$-0.0399221\pi$
$941$	0.523029	+	2.96625i	0.0170503	+	0.0966969i	−0.975095	+	0.221787i	$0.928811\pi$
$942$	13.9459	−	25.5049i	0.454383	−	0.830994i
$943$	5.61719	+	4.71338i	0.182921	+	0.153489i
$944$	−5.50974			−0.179327
$945$		0			0
$946$	−1.10661			−0.0359789
$947$	−12.6413	−	10.6073i	−0.410787	−	0.344692i	0.413858	−	0.910341i	$-0.364181\pi$
$947$	−12.6413	−	10.6073i	−0.410787	−	0.344692i	−0.824646	+	0.565650i	$0.808625\pi$
$948$	−4.14694	+	0.0963076i	−0.134686	+	0.00312793i
$949$	−0.484448	−	2.74744i	−0.0157258	−	0.0891857i
$950$		0			0
$951$	−11.8857	+	4.64128i	−0.385419	+	0.150504i
$952$	12.9134	−	73.2353i	0.418524	−	2.37357i
$953$	−14.0124	+	24.2702i	−0.453907	+	0.786190i	−0.998625	−	0.0524298i	$-0.983303\pi$
$953$	−14.0124	+	24.2702i	−0.453907	+	0.786190i	0.544718	+	0.838619i	$0.316637\pi$
$954$	−27.6008	+	11.5235i	−0.893609	+	0.373086i
$955$		0			0
$956$	8.01761	−	2.91817i	0.259308	−	0.0943804i
$957$	2.63692	+	13.1602i	0.0852394	+	0.425407i
$958$	−11.0571	+	9.27803i	−0.357240	+	0.299760i
$959$	−56.7450	+	47.6147i	−1.83239	+	1.53756i
$960$		0			0
$961$	−33.9741	+	12.3656i	−1.09594	+	0.398889i
$962$	0.943125	+	1.63354i	0.0304076	+	0.0526675i
$963$	9.36623	−	18.1163i	0.301823	−	0.583789i
$964$	−13.4484	+	23.2932i	−0.433142	+	0.750225i
$965$		0			0
$966$	−1.23512	+	8.10029i	−0.0397394	+	0.260623i
$967$	11.6177	+	4.22850i	0.373601	+	0.135979i	0.521995	−	0.852949i	$-0.325188\pi$
$967$	11.6177	+	4.22850i	0.373601	+	0.135979i	−0.148394	+	0.988928i	$0.547410\pi$
$968$	0.180248	+	1.02223i	0.00579338	+	0.0328559i
$969$	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	$0.626355\pi$
$972$	21.1872	+	5.02723i	0.679581	+	0.161248i
$973$	−42.0273			−1.34733
$974$	10.0561	+	8.43808i	0.322219	+	0.270374i
$975$		0			0
$976$	−0.506371	−	2.87177i	−0.0162086	−	0.0919233i
$977$	−39.8952	−	14.5207i	−1.27636	−	0.464558i	−0.387134	−	0.922023i	$-0.626535\pi$
$977$	−39.8952	−	14.5207i	−1.27636	−	0.464558i	−0.889227	+	0.457466i	$0.848757\pi$
$978$	−1.34375	+	8.81269i	−0.0429684	+	0.281799i
$979$	−1.29571	+	7.34835i	−0.0414112	+	0.234854i
$980$		0			0
$981$	−5.10766	+	9.87930i	−0.163075	+	0.315422i
$982$	0.424296	+	0.734902i	0.0135398	+	0.0234517i
$983$	−48.3589	+	17.6012i	−1.54241	+	0.561392i	−0.966622	−	0.256207i	$-0.917527\pi$
$983$	−48.3589	+	17.6012i	−1.54241	+	0.561392i	−0.575789	+	0.817598i	$0.695305\pi$
$984$	20.3375	−	17.8861i	0.648337	−	0.570187i
$985$		0			0
$986$	−7.81843	+	6.56044i	−0.248990	+	0.208927i
$987$	−13.4557	−	67.1540i	−0.428301	−	2.13754i
$988$	−4.46210	+	1.62407i	−0.141958	+	0.0516686i
$989$	−0.261118	−	0.452269i	−0.00830306	−	0.0143813i
$990$		0			0
$991$	−16.2637	+	28.1695i	−0.516632	+	0.894833i	0.483181	+	0.875520i	$0.339481\pi$
$991$	−16.2637	+	28.1695i	−0.516632	+	0.894833i	−0.999813	+	0.0193130i	$0.993852\pi$
$992$	−8.33128	+	47.2491i	−0.264519	+	1.50016i
$993$	0.207901	−	0.0811844i	0.00659755	−	0.00257631i
$994$	35.4132	+	12.8893i	1.12324	+	0.408825i
$995$		0			0
$996$	−39.3422	+	0.913674i	−1.24661	+	0.0289509i
$997$	−6.44164	−	5.40517i	−0.204009	−	0.171184i	0.535059	−	0.844815i	$-0.320289\pi$
$997$	−6.44164	−	5.40517i	−0.204009	−	0.171184i	−0.739068	+	0.673631i	$0.764734\pi$
$998$	−1.12022			−0.0354598
$999$	−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.l.f.151.5	yes	66
5.2	odd	4		675.2.u.e.124.14		132
5.3	odd	4		675.2.u.e.124.9		132
5.4	even	2		675.2.l.g.151.7	yes	66
27.22	even	9	inner	675.2.l.f.76.5	✓	66
135.22	odd	36		675.2.u.e.49.9		132
135.49	even	18		675.2.l.g.76.7	yes	66
135.103	odd	36		675.2.u.e.49.14		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
675.2.l.f.76.5	✓	66	27.22	even	9	inner
675.2.l.f.151.5	yes	66	1.1	even	1	trivial
675.2.l.g.76.7	yes	66	135.49	even	18
675.2.l.g.151.7	yes	66	5.4	even	2
675.2.u.e.49.9		132	135.22	odd	36
675.2.u.e.49.14		132	135.103	odd	36
675.2.u.e.124.9		132	5.3	odd	4
675.2.u.e.124.14		132	5.2	odd	4

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.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.594907 - 0.499186i) q^{2} +(-0.900618 - 1.47949i) q^{3} +(-0.242569 - 1.37568i) q^{4} +(-0.202756 + 1.32973i) q^{6} +(0.855088 - 4.84944i) q^{7} +(-1.31901 + 2.28459i) q^{8} +(-1.37777 + 2.66491i) q^{9} +(-3.17186 + 1.15446i) q^{11} +(-1.81684 + 1.59784i) q^{12} +(0.600973 - 0.504276i) q^{13} +(-2.92947 + 2.45812i) q^{14} +(-0.700189 + 0.254848i) q^{16} +(-2.86234 - 4.95771i) q^{17} +(2.14993 - 0.897607i) q^{18} +(2.16649 - 3.75247i) q^{19} +(-7.94481 + 3.10240i) q^{21} +(2.46325 + 0.896551i) q^{22} +(0.214816 + 1.21828i) q^{23} +(4.56795 - 0.106085i) q^{24} -0.609251 q^{26} +(5.18355 - 0.361665i) q^{27} -6.87869 q^{28} +(1.75863 + 1.47566i) q^{29} +(1.42301 + 8.07028i) q^{31} +(5.50161 + 2.00242i) q^{32} +(4.56465 + 3.65300i) q^{33} +(-0.771998 + 4.37822i) q^{34} +(4.00026 + 1.24895i) q^{36} +(-1.54801 - 2.68123i) q^{37} +(-3.16204 + 1.15089i) q^{38} +(-1.28732 - 0.434973i) q^{39} +(4.54071 - 3.81011i) q^{41} +(6.27510 + 2.12029i) q^{42} +(-0.396695 + 0.144385i) q^{43} +(2.35756 + 4.08342i) q^{44} +(0.480353 - 0.831996i) q^{46} +(-1.39441 + 7.90806i) q^{47} +(1.00765 + 0.806401i) q^{48} +(-16.2081 - 5.89926i) q^{49} +(-4.75701 + 8.69981i) q^{51} +(-0.839499 - 0.704423i) q^{52} -12.8380 q^{53} +(-3.26427 - 2.37240i) q^{54} +(9.95112 + 8.34998i) q^{56} +(-7.50292 + 0.174246i) q^{57} +(-0.309589 - 1.75576i) q^{58} +(6.94844 + 2.52902i) q^{59} +(-0.679578 + 3.85408i) q^{61} +(3.18202 - 5.51141i) q^{62} +(11.7452 + 8.96017i) q^{63} +(-1.52824 - 2.64699i) q^{64} +(-0.892014 - 4.45180i) q^{66} +(2.45259 - 2.05797i) q^{67} +(-6.12590 + 5.14024i) q^{68} +(1.60896 - 1.41502i) q^{69} +(-4.92735 - 8.53442i) q^{71} +(-4.27093 - 6.66269i) q^{72} +(1.77806 - 3.07968i) q^{73} +(-0.417511 + 2.36782i) q^{74} +(-5.68772 - 2.07016i) q^{76} +(2.88628 + 16.3689i) q^{77} +(0.548702 + 0.901380i) q^{78} +(1.31333 + 1.10201i) q^{79} +(-5.20348 - 7.34328i) q^{81} -4.60325 q^{82} +(12.4596 + 10.4548i) q^{83} +(6.19507 + 10.1769i) q^{84} +(0.308071 + 0.112129i) q^{86} +(0.599376 - 3.93088i) q^{87} +(1.54624 - 8.76914i) q^{88} +(1.10530 - 1.91444i) q^{89} +(-1.93158 - 3.34559i) q^{91} +(1.62385 - 0.591034i) q^{92} +(10.6583 - 9.37357i) q^{93} +(4.77714 - 4.00849i) q^{94} +(-1.99229 - 9.94300i) q^{96} +(-14.3200 + 5.21207i) q^{97} +(6.69747 + 11.6004i) q^{98} +(1.29357 - 10.0433i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 6 q^{2} - 6 q^{6} - 6 q^{7} - 12 q^{8} - 6 q^{9} + 15 q^{11} - 18 q^{12} + 15 q^{14} + 18 q^{16} - 30 q^{17} + 12 q^{18} + 12 q^{19} + 12 q^{21} + 45 q^{22} - 36 q^{23} - 39 q^{24} + 6 q^{26} - 51 q^{27}+ \cdots - 48 q^{99}+O(q^{100}) \) 66 * q - 6 * q^2 - 6 * q^6 - 6 * q^7 - 12 * q^8 - 6 * q^9 + 15 * q^11 - 18 * q^12 + 15 * q^14 + 18 * q^16 - 30 * q^17 + 12 * q^18 + 12 * q^19 + 12 * q^21 + 45 * q^22 - 36 * q^23 - 39 * q^24 + 6 * q^26 - 51 * q^27 + 36 * q^28 - 15 * q^29 + 3 * q^31 - 27 * q^32 + 3 * q^33 + 30 * q^36 - 6 * q^37 + 12 * q^38 - 15 * q^39 + 39 * q^41 - 48 * q^42 - 12 * q^43 + 51 * q^44 + 9 * q^46 - 30 * q^47 + 132 * q^48 - 6 * q^49 - 9 * q^52 + 24 * q^53 + 75 * q^54 + 144 * q^56 - 33 * q^57 - 27 * q^58 + 45 * q^59 - 54 * q^61 - 66 * q^62 + 120 * q^63 - 24 * q^64 + 48 * q^66 - 9 * q^67 + 69 * q^68 + 51 * q^69 - 15 * q^71 - 9 * q^72 + 15 * q^73 + 96 * q^74 - 48 * q^76 + 36 * q^77 + 18 * q^78 + 48 * q^79 - 54 * q^81 + 36 * q^82 - 30 * q^83 + 57 * q^84 - 111 * q^86 + 33 * q^87 - 36 * q^88 - 12 * q^89 + 9 * q^91 + 219 * q^92 - 63 * q^93 + 36 * q^94 - 249 * q^96 - 57 * q^97 - 75 * q^98 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more