LMFDB - Embedded newform 675.2.u.e.49.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(49,675)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("675.49"); S:= CuspForms(chi, 2); N := Newforms(S);

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			49.12
Character	$\chi$	$=$	675.49
Dual form			675.2.u.e.124.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.163444 + 0.194784i) q^{2} +(0.154950 + 1.72511i) q^{3} +(0.336069 - 1.90594i) q^{4} +(-0.310698 + 0.312139i) q^{6} +(2.55151 - 0.449901i) q^{7} +(0.866590 - 0.500326i) q^{8} +(-2.95198 + 0.534610i) q^{9} +(2.07133 + 0.753901i) q^{11} +(3.34003 + 0.284429i) q^{12} +(0.932020 - 1.11074i) q^{13} +(0.504662 + 0.423462i) q^{14} +(-3.39816 - 1.23683i) q^{16} +(2.04069 + 1.17819i) q^{17} +(-0.586616 - 0.487621i) q^{18} +(-2.22207 - 3.84874i) q^{19} +(1.17148 + 4.33192i) q^{21} +(0.191697 + 0.526682i) q^{22} +(6.94755 + 1.22504i) q^{23} +(0.997394 + 1.41743i) q^{24} +0.368687 q^{26} +(-1.37967 - 5.00964i) q^{27} -5.01424i q^{28} +(4.88786 - 4.10140i) q^{29} +(-1.13861 + 6.45736i) q^{31} +(-0.998979 - 2.74467i) q^{32} +(-0.979608 + 3.69007i) q^{33} +(0.104044 + 0.590063i) q^{34} +(0.0268659 + 5.80597i) q^{36} +(3.93474 + 2.27172i) q^{37} +(0.386492 - 1.06188i) q^{38} +(2.06056 + 1.43572i) q^{39} +(5.08374 + 4.26577i) q^{41} +(-0.652319 + 0.936211i) q^{42} +(2.10913 - 5.79479i) q^{43} +(2.13300 - 3.69447i) q^{44} +(0.896913 + 1.55350i) q^{46} +(-9.40977 + 1.65920i) q^{47} +(1.60712 - 6.05384i) q^{48} +(-0.270040 + 0.0982866i) q^{49} +(-1.71630 + 3.70297i) q^{51} +(-1.80378 - 2.14966i) q^{52} +13.3683i q^{53} +(0.750303 - 1.08753i) q^{54} +(1.98602 - 1.66647i) q^{56} +(6.29518 - 4.42967i) q^{57} +(1.59778 + 0.281731i) q^{58} +(-3.10061 + 1.12853i) q^{59} +(-1.57865 - 8.95295i) q^{61} +(-1.44389 + 0.833631i) q^{62} +(-7.29150 + 2.69216i) q^{63} +(-3.24491 + 5.62035i) q^{64} +(-0.878880 + 0.412306i) q^{66} +(-3.43334 + 4.09170i) q^{67} +(2.93138 - 3.49349i) q^{68} +(-1.03680 + 12.1751i) q^{69} +(-1.67410 + 2.89963i) q^{71} +(-2.29068 + 1.94024i) q^{72} +(4.41805 - 2.55076i) q^{73} +(0.200612 + 1.13773i) q^{74} +(-8.08225 + 2.94170i) q^{76} +(5.62420 + 0.991698i) q^{77} +(0.0571280 + 0.636024i) q^{78} +(-3.14132 + 2.63588i) q^{79} +(8.42838 - 3.15632i) q^{81} +1.68745i q^{82} +(2.22867 + 2.65602i) q^{83} +(8.65009 - 0.776955i) q^{84} +(1.47346 - 0.536295i) q^{86} +(7.83272 + 7.79656i) q^{87} +(2.17219 - 0.383015i) q^{88} +(-7.60791 - 13.1773i) q^{89} +(1.87834 - 3.25338i) q^{91} +(4.66971 - 12.8299i) q^{92} +(-11.3161 - 0.963650i) q^{93} +(-1.86115 - 1.56169i) q^{94} +(4.58006 - 2.14863i) q^{96} +(-1.43431 + 3.94072i) q^{97} +(-0.0632810 - 0.0365353i) q^{98} +(-6.51756 - 1.11815i) 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 $

$2$	0.163444	+	0.194784i	0.115572	+	0.137733i	0.820729	−	0.571318i	$-0.193568\pi$
$2$	0.163444	+	0.194784i	0.115572	+	0.137733i	−0.705157	+	0.709052i	$0.749123\pi$
$3$	0.154950	+	1.72511i	0.0894603	+	0.995990i
$3$	0.154950	+	1.72511i	0.0894603	+	0.995990i
$4$	0.336069	−	1.90594i	0.168035	−	0.952971i
$5$		0			0
$5$		0			0
$6$	−0.310698	+	0.312139i	−0.126842	+	0.127430i
$7$	2.55151	−	0.449901i	0.964381	−	0.170046i	0.330781	−	0.943707i	$-0.392688\pi$
$7$	2.55151	−	0.449901i	0.964381	−	0.170046i	0.633600	+	0.773661i	$0.281577\pi$
$8$	0.866590	−	0.500326i	0.306386	−	0.176892i
$9$	−2.95198	+	0.534610i	−0.983994	+	0.178203i
$10$		0			0
$11$	2.07133	+	0.753901i	0.624528	+	0.227310i	0.634848	−	0.772637i	$-0.281063\pi$
$11$	2.07133	+	0.753901i	0.624528	+	0.227310i	−0.0103197	+	0.999947i	$0.503285\pi$
$12$	3.34003	+	0.284429i	0.964183	+	0.0821077i
$13$	0.932020	−	1.11074i	0.258496	−	0.308063i	−0.621151	−	0.783691i	$-0.713335\pi$
$13$	0.932020	−	1.11074i	0.258496	−	0.308063i	0.879647	+	0.475628i	$0.157779\pi$
$14$	0.504662	+	0.423462i	0.134877	+	0.113175i
$15$		0			0
$16$	−3.39816	−	1.23683i	−0.849541	−	0.309208i
$17$	2.04069	+	1.17819i	0.494940	+	0.285754i	0.726622	−	0.687038i	$-0.241089\pi$
$17$	2.04069	+	1.17819i	0.494940	+	0.285754i	−0.231681	+	0.972792i	$0.574423\pi$
$18$	−0.586616	−	0.487621i	−0.138267	−	0.114933i
$19$	−2.22207	−	3.84874i	−0.509778	−	0.882962i	−0.999936	−	0.0113281i	$-0.996394\pi$
$19$	−2.22207	−	3.84874i	−0.509778	−	0.882962i	0.490157	−	0.871634i	$-0.336939\pi$
$20$		0			0
$21$	1.17148	+	4.33192i	0.255638	+	0.945302i
$22$	0.191697	+	0.526682i	0.0408699	+	0.112289i
$23$	6.94755	+	1.22504i	1.44866	+	0.255439i	0.841982	−	0.539506i	$-0.181389\pi$
$23$	6.94755	+	1.22504i	1.44866	+	0.255439i	0.606682	+	0.794944i	$0.292500\pi$
$24$	0.997394	+	1.41743i	0.203592	+	0.289333i
$25$		0			0
$26$	0.368687			0.0723055
$27$	−1.37967	−	5.00964i	−0.265517	−	0.964106i
$28$		−	5.01424i		−	0.947602i
$29$	4.88786	−	4.10140i	0.907652	−	0.761611i	−0.0640188	−	0.997949i	$-0.520392\pi$
$29$	4.88786	−	4.10140i	0.907652	−	0.761611i	0.971671	+	0.236338i	$0.0759473\pi$
$30$		0			0
$31$	−1.13861	+	6.45736i	−0.204500	+	1.15978i	0.693725	+	0.720240i	$0.255968\pi$
$31$	−1.13861	+	6.45736i	−0.204500	+	1.15978i	−0.898225	+	0.439536i	$0.855143\pi$
$32$	−0.998979	−	2.74467i	−0.176596	−	0.485194i
$33$	−0.979608	+	3.69007i	−0.170528	+	0.642359i
$34$	0.104044	+	0.590063i	0.0178434	+	0.101195i
$35$		0			0
$36$	0.0268659	+	5.80597i	0.00447766	+	0.967662i
$37$	3.93474	+	2.27172i	0.646868	+	0.373469i	0.787255	−	0.616627i	$-0.211501\pi$
$37$	3.93474	+	2.27172i	0.646868	+	0.373469i	−0.140387	+	0.990097i	$0.544835\pi$
$38$	0.386492	−	1.06188i	0.0626972	−	0.172259i
$39$	2.06056	+	1.43572i	0.329953	+	0.229900i
$40$		0			0
$41$	5.08374	+	4.26577i	0.793947	+	0.666201i	0.946719	−	0.322061i	$-0.104375\pi$
$41$	5.08374	+	4.26577i	0.793947	+	0.666201i	−0.152772	+	0.988262i	$0.548820\pi$
$42$	−0.652319	+	0.936211i	−0.100655	+	0.144460i
$43$	2.10913	−	5.79479i	0.321640	−	0.883697i	−0.668512	−	0.743701i	$-0.733069\pi$
$43$	2.10913	−	5.79479i	0.321640	−	0.883697i	0.990152	−	0.139996i	$-0.0447091\pi$
$44$	2.13300	−	3.69447i	0.321562	−	0.556962i
$45$		0			0
$46$	0.896913	+	1.55350i	0.132243	+	0.229051i
$47$	−9.40977	+	1.65920i	−1.37256	+	0.242019i	−0.810819	−	0.585297i	$-0.800978\pi$
$47$	−9.40977	+	1.65920i	−1.37256	+	0.242019i	−0.561737	+	0.827316i	$0.689867\pi$
$48$	1.60712	−	6.05384i	0.231968	−	0.873797i
$49$	−0.270040	+	0.0982866i	−0.0385772	+	0.0140409i
$50$		0			0
$51$	−1.71630	+	3.70297i	−0.240331	+	0.518519i
$52$	−1.80378	−	2.14966i	−0.250139	−	0.298104i
$53$			13.3683i			1.83627i	0.396263	+	0.918137i	$0.370307\pi$
$53$			13.3683i			1.83627i	−0.396263	+	0.918137i	$0.629693\pi$
$54$	0.750303	−	1.08753i	0.102103	−	0.147994i
$55$		0			0
$56$	1.98602	−	1.66647i	0.265393	−	0.222691i
$57$	6.29518	−	4.42967i	0.833817	−	0.586724i
$58$	1.59778	+	0.281731i	0.209798	+	0.0369931i
$59$	−3.10061	+	1.12853i	−0.403665	+	0.146922i	−0.535870	−	0.844300i	$-0.680016\pi$
$59$	−3.10061	+	1.12853i	−0.403665	+	0.146922i	0.132205	+	0.991222i	$0.457794\pi$
$60$		0			0
$61$	−1.57865	−	8.95295i	−0.202125	−	1.14631i	−0.901900	−	0.431945i	$-0.857828\pi$
$61$	−1.57865	−	8.95295i	−0.202125	−	1.14631i	0.699775	−	0.714363i	$-0.253284\pi$
$62$	−1.44389	+	0.833631i	−0.183374	+	0.105871i
$63$	−7.29150	+	2.69216i	−0.918642	+	0.339181i
$64$	−3.24491	+	5.62035i	−0.405614	+	0.702543i
$65$		0			0
$66$	−0.878880	+	0.412306i	−0.108183	+	0.0507514i
$67$	−3.43334	+	4.09170i	−0.419450	+	0.499881i	−0.933848	−	0.357671i	$-0.883571\pi$
$67$	−3.43334	+	4.09170i	−0.419450	+	0.499881i	0.514398	+	0.857552i	$0.328015\pi$
$68$	2.93138	−	3.49349i	0.355482	−	0.423647i
$69$	−1.03680	+	12.1751i	−0.124816	+	1.46571i
$70$		0			0
$71$	−1.67410	+	2.89963i	−0.198680	+	0.344123i	−0.948101	−	0.317971i	$-0.896999\pi$
$71$	−1.67410	+	2.89963i	−0.198680	+	0.344123i	0.749421	+	0.662094i	$0.230332\pi$
$72$	−2.29068	+	1.94024i	−0.269959	+	0.228660i
$73$	4.41805	−	2.55076i	0.517094	−	0.298544i	−0.218651	−	0.975803i	$-0.570166\pi$
$73$	4.41805	−	2.55076i	0.517094	−	0.298544i	0.735745	+	0.677259i	$0.236832\pi$
$74$	0.200612	+	1.13773i	0.0233206	+	0.132258i
$75$		0			0
$76$	−8.08225	+	2.94170i	−0.927098	+	0.337436i
$77$	5.62420	+	0.991698i	0.640937	+	0.113014i
$78$	0.0571280	+	0.636024i	0.00646847	+	0.0720156i
$79$	−3.14132	+	2.63588i	−0.353426	+	0.296560i	−0.802164	−	0.597104i	$-0.796318\pi$
$79$	−3.14132	+	2.63588i	−0.353426	+	0.296560i	0.448738	+	0.893663i	$0.351874\pi$
$80$		0			0
$81$	8.42838	−	3.15632i	0.936487	−	0.350702i
$82$			1.68745i			0.186347i
$83$	2.22867	+	2.65602i	0.244628	+	0.291536i	0.874362	−	0.485275i	$-0.161280\pi$
$83$	2.22867	+	2.65602i	0.244628	+	0.291536i	−0.629734	+	0.776811i	$0.716836\pi$
$84$	8.65009	−	0.776955i	0.943802	−	0.0847727i
$85$		0			0
$86$	1.47346	−	0.536295i	0.158887	−	0.0578302i
$87$	7.83272	+	7.79656i	0.839756	+	0.835879i
$88$	2.17219	−	0.383015i	0.231556	−	0.0408296i
$89$	−7.60791	−	13.1773i	−0.806437	−	1.39679i	−0.915317	−	0.402734i	$-0.868060\pi$
$89$	−7.60791	−	13.1773i	−0.806437	−	1.39679i	0.108880	−	0.994055i	$-0.465274\pi$
$90$		0			0
$91$	1.87834	−	3.25338i	0.196903	−	0.341047i
$92$	4.66971	−	12.8299i	0.486851	−	1.33761i
$93$	−11.3161	−	0.963650i	−1.17342	−	0.0999259i
$94$	−1.86115	−	1.56169i	−0.191963	−	0.161076i
$95$		0			0
$96$	4.58006	−	2.14863i	0.467450	−	0.219294i
$97$	−1.43431	+	3.94072i	−0.145632	+	0.400120i	−0.990965	−	0.134119i	$-0.957179\pi$
$97$	−1.43431	+	3.94072i	−0.145632	+	0.400120i	0.845334	+	0.534239i	$0.179402\pi$
$98$	−0.0632810	−	0.0365353i	−0.00639235	−	0.00369063i
$99$	−6.51756	−	1.11815i	−0.655039	−	0.112378i
$100$		0			0
$101$	−2.48305	−	14.0821i	−0.247073	−	1.40122i	−0.815629	−	0.578575i	$-0.803609\pi$
$101$	−2.48305	−	14.0821i	−0.247073	−	1.40122i	0.568557	−	0.822644i	$-0.307502\pi$
$102$	−1.00180	+	0.270917i	−0.0991929	+	0.0268248i
$103$	−2.95323	−	8.11392i	−0.290990	−	0.799489i	−0.995922	−	0.0902141i	$-0.971245\pi$
$103$	−2.95323	−	8.11392i	−0.290990	−	0.799489i	0.704932	−	0.709275i	$-0.250977\pi$
$104$	0.251948	−	1.42887i	0.0247055	−	0.140112i
$105$		0			0
$106$	−2.60393	+	2.18496i	−0.252916	+	0.212222i
$107$			5.67259i			0.548390i	0.961674	+	0.274195i	$0.0884113\pi$
$107$			5.67259i			0.548390i	−0.961674	+	0.274195i	$0.911589\pi$
$108$	−10.0118	+	0.945981i	−0.963382	+	0.0910271i
$109$	−18.9591			−1.81595			−0.907975	−	0.419025i	$-0.862372\pi$
$109$	−18.9591			−1.81595			−0.907975	+	0.419025i	$0.862372\pi$
$110$		0			0
$111$	−3.30928	+	7.13985i	−0.314103	+	0.677685i
$112$	−9.22691	−	1.62695i	−0.871861	−	0.153733i
$113$	3.91044	+	10.7438i	0.367863	+	1.01070i	0.976172	+	0.216996i	$0.0696259\pi$
$113$	3.91044	+	10.7438i	0.367863	+	1.01070i	−0.608309	+	0.793700i	$0.708152\pi$
$114$	1.89174	+	0.502201i	0.177177	+	0.0470355i
$115$		0			0
$116$	−6.17437	−	10.6943i	−0.573276	−	0.992943i
$117$	−2.15749	+	3.77714i	−0.199460	+	0.349197i
$118$	−0.726595	−	0.419500i	−0.0668884	−	0.0386181i
$119$	5.73692	+	2.08807i	0.525903	+	0.191413i
$120$		0			0
$121$	−4.70446	−	3.94751i	−0.427679	−	0.358865i
$122$	1.48588	−	1.77080i	0.134525	−	0.160321i
$123$	−6.57118	+	9.43098i	−0.592503	+	0.850362i
$124$	11.9247	+	4.34024i	1.07087	+	0.389765i
$125$		0			0
$126$	−1.71614	−	0.980254i	−0.152886	−	0.0873279i
$127$	−2.86168	+	1.65219i	−0.253933	+	0.146608i	−0.621564	−	0.783363i	$-0.713502\pi$
$127$	−2.86168	+	1.65219i	−0.253933	+	0.146608i	0.367631	+	0.929972i	$0.380169\pi$
$128$	−7.37801	+	1.30094i	−0.652130	+	0.114988i
$129$	10.3234	+	2.74057i	0.908928	+	0.241294i
$130$		0			0
$131$	2.70616	−	15.3474i	0.236439	−	1.34091i	−0.603124	−	0.797647i	$-0.706078\pi$
$131$	2.70616	−	15.3474i	0.236439	−	1.34091i	0.839563	−	0.543263i	$-0.182811\pi$
$132$	6.70385	+	3.10720i	0.583496	+	0.270447i
$133$	−7.40120	−	8.82040i	−0.641765	−	0.764826i
$134$	−1.35816			−0.117327
$135$		0			0
$136$	2.35792			0.202190
$137$	−7.73491	−	9.21811i	−0.660838	−	0.787556i	0.326668	−	0.945139i	$-0.394074\pi$
$137$	−7.73491	−	9.21811i	−0.660838	−	0.787556i	−0.987506	+	0.157583i	$0.949630\pi$
$138$	−2.54098	+	1.78799i	−0.216302	+	0.152203i
$139$	3.09573	−	17.5568i	0.262577	−	1.48915i	−0.513271	−	0.858227i	$-0.671566\pi$
$139$	3.09573	−	17.5568i	0.262577	−	1.48915i	0.775848	−	0.630920i	$-0.217323\pi$
$140$		0			0
$141$	−4.32033	−	15.9758i	−0.363838	−	1.34540i
$142$	−0.838425	+	0.147837i	−0.0703591	+	0.0124062i
$143$	2.76790	−	1.59805i	0.231464	−	0.133636i
$144$	10.6925	+	1.83441i	0.891045	+	0.152867i
$145$		0			0
$146$	1.21895	+	0.443662i	0.100881	+	0.0367177i
$147$	−0.211398	−	0.450619i	−0.0174358	−	0.0371664i
$148$	5.65212	−	6.73594i	0.464602	−	0.553691i
$149$	16.4176	+	13.7760i	1.34498	+	1.12857i	0.980316	+	0.197433i	$0.0632606\pi$
$149$	16.4176	+	13.7760i	1.34498	+	1.12857i	0.364664	+	0.931139i	$0.381184\pi$
$150$		0			0
$151$	−7.24523	−	2.63705i	−0.589608	−	0.214600i	0.0299488	−	0.999551i	$-0.490466\pi$
$151$	−7.24523	−	2.63705i	−0.589608	−	0.214600i	−0.619557	+	0.784952i	$0.712688\pi$
$152$	−3.85125	−	2.22352i	−0.312378	−	0.180351i
$153$	−6.65396	−	2.38703i	−0.537940	−	0.192980i
$154$	0.726071	+	1.25759i	0.0585085	+	0.101340i
$155$		0			0
$156$	3.42890	−	3.44480i	0.274532	−	0.275805i
$157$	0.264975	+	0.728013i	0.0211473	+	0.0581018i	0.949817	−	0.312806i	$-0.101269\pi$
$157$	0.264975	+	0.728013i	0.0211473	+	0.0581018i	−0.928670	+	0.370908i	$0.879047\pi$
$158$	−1.02686	−	0.181063i	−0.0816924	−	0.0144046i
$159$	−23.0617	+	2.07141i	−1.82891	+	0.164274i
$160$		0			0
$161$	18.2779			1.44050
$162$	1.99237	+	1.12584i	0.156535	+	0.0884542i
$163$			16.3075i			1.27731i	0.769495	+	0.638653i	$0.220508\pi$
$163$			16.3075i			1.27731i	−0.769495	+	0.638653i	$0.779492\pi$
$164$	9.83880	−	8.25573i	0.768281	−	0.644664i
$165$		0			0
$166$	−0.153090	+	0.868219i	−0.0118821	+	0.0673869i
$167$	−2.36980	−	6.51098i	−0.183381	−	0.503835i	0.813605	−	0.581418i	$-0.197502\pi$
$167$	−2.36980	−	6.51098i	−0.183381	−	0.503835i	−0.996986	+	0.0775833i	$0.975280\pi$
$168$	3.18257	+	3.16787i	0.245540	+	0.244407i
$169$	1.89235	+	10.7320i	0.145565	+	0.825542i
$170$		0			0
$171$	8.61709	+	10.1735i	0.658965	+	0.777985i
$172$	−10.3357	−	5.96733i	−0.788092	−	0.455005i
$173$	2.55019	−	7.00660i	0.193888	−	0.532702i	−0.804211	−	0.594344i	$-0.797412\pi$
$173$	2.55019	−	7.00660i	0.193888	−	0.532702i	0.998098	+	0.0616426i	$0.0196339\pi$
$174$	−0.238441	+	2.79999i	−0.0180762	+	0.212267i
$175$		0			0
$176$	−6.10626	−	5.12376i	−0.460277	−	0.386218i
$177$	−2.42727	−	5.17401i	−0.182445	−	0.388903i
$178$	1.32327	−	3.63564i	0.0991830	−	0.272503i
$179$	−7.25608	+	12.5679i	−0.542345	+	0.939369i	0.456424	+	0.889762i	$0.349130\pi$
$179$	−7.25608	+	12.5679i	−0.542345	+	0.939369i	−0.998769	+	0.0496065i	$0.984203\pi$
$180$		0			0
$181$	−4.13864	−	7.16833i	−0.307622	−	0.532818i	0.670219	−	0.742163i	$-0.266200\pi$
$181$	−4.13864	−	7.16833i	−0.307622	−	0.532818i	−0.977842	+	0.209345i	$0.932867\pi$
$182$	0.940710	−	0.165873i	0.0697301	−	0.0122953i
$183$	15.2002	−	4.11059i	1.12363	−	0.303864i
$184$	6.63360	−	2.41443i	0.489035	−	0.177994i
$185$		0			0
$186$	−1.66183	−	2.36169i	−0.121851	−	0.173168i
$187$	3.33870	+	3.97890i	0.244150	+	0.290966i
$188$			18.4921i			1.34867i
$189$	−5.77408	−	12.1615i	−0.420003	−	0.884616i
$190$		0			0
$191$	−18.3309	+	15.3815i	−1.32638	+	1.11297i	−0.341472	+	0.939892i	$0.610925\pi$
$191$	−18.3309	+	15.3815i	−1.32638	+	1.11297i	−0.984909	+	0.173074i	$0.944630\pi$
$192$	−10.1985	−	4.72694i	−0.736013	−	0.341137i
$193$	−23.6651	−	4.17280i	−1.70345	−	0.300364i	−0.764553	−	0.644560i	$-0.777040\pi$
$193$	−23.6651	−	4.17280i	−1.70345	−	0.300364i	−0.938898	+	0.344196i	$0.888152\pi$
$194$	−1.00202	+	0.364705i	−0.0719408	+	0.0261843i
$195$		0			0
$196$	0.0965765	+	0.547712i	0.00689832	+	0.0391223i
$197$	−20.3050	+	11.7231i	−1.44667	+	0.835235i	−0.998281	−	0.0586045i	$-0.981335\pi$
$197$	−20.3050	+	11.7231i	−1.44667	+	0.835235i	−0.448388	+	0.893839i	$0.648002\pi$
$198$	−0.847455	−	1.45227i	−0.0602260	−	0.103209i
$199$	−3.92254	+	6.79404i	−0.278061	+	0.481617i	−0.970903	−	0.239473i	$-0.923025\pi$
$199$	−3.92254	+	6.79404i	−0.278061	+	0.481617i	0.692841	+	0.721090i	$0.256359\pi$
$200$		0			0
$201$	−7.59061	−	5.28887i	−0.535401	−	0.373048i
$202$	2.33713	−	2.78528i	0.164440	−	0.195972i
$203$	10.6262	−	12.6638i	0.745814	−	0.888826i
$204$	6.48085	+	4.51563i	0.453750	+	0.316157i
$205$		0			0
$206$	1.09778	−	1.90141i	0.0764860	−	0.132478i
$207$	−21.1640	+	0.0979318i	−1.47100	+	0.00680673i
$208$	−4.54095	+	2.62172i	−0.314858	+	0.181784i
$209$	−1.70107	−	9.64722i	−0.117665	−	0.667312i
$210$		0			0
$211$	4.73989	−	1.72518i	0.326307	−	0.118766i	−0.173672	−	0.984804i	$-0.555563\pi$
$211$	4.73989	−	1.72518i	0.326307	−	0.118766i	0.499979	+	0.866037i	$0.333341\pi$
$212$	25.4792	+	4.49267i	1.74992	+	0.308558i
$213$	−5.26158	−	2.43871i	−0.360517	−	0.167098i
$214$	−1.10493	+	0.927148i	−0.0755316	+	0.0633785i
$215$		0			0
$216$	−3.70206	−	3.65102i	−0.251893	−	0.248421i
$217$			16.9883i			1.15324i
$218$	−3.09874	−	3.69293i	−0.209873	−	0.250117i
$219$	5.08492	+	7.22637i	0.343607	+	0.488313i
$220$		0			0
$221$	3.21063	−	1.16857i	0.215970	−	0.0786067i
$222$	−1.93161	+	0.522367i	−0.129641	+	0.0350590i
$223$	18.5966	−	3.27908i	1.24532	−	0.219583i	0.488125	−	0.872774i	$-0.337681\pi$
$223$	18.5966	−	3.27908i	1.24532	−	0.219583i	0.757193	+	0.653191i	$0.226570\pi$
$224$	−3.78374	−	6.55363i	−0.252812	−	0.437883i
$225$		0			0
$226$	−1.45360	+	2.51771i	−0.0966919	+	0.167475i
$227$	−1.27969	+	3.51591i	−0.0849358	+	0.233359i	−0.974888	−	0.222694i	$-0.928515\pi$
$227$	−1.27969	+	3.51591i	−0.0849358	+	0.233359i	0.889953	+	0.456053i	$0.150737\pi$
$228$	−6.32709	−	13.4869i	−0.419022	−	0.893194i
$229$	−6.44759	−	5.41017i	−0.426069	−	0.357514i	0.404397	−	0.914583i	$-0.367481\pi$
$229$	−6.44759	−	5.41017i	−0.426069	−	0.357514i	−0.830466	+	0.557069i	$0.811926\pi$
$230$		0			0
$231$	−0.839315	+	9.85600i	−0.0552229	+	0.648477i
$232$	2.18373	−	5.99975i	0.143369	−	0.393903i
$233$	−9.73700	−	5.62166i	−0.637892	−	0.368287i	0.145910	−	0.989298i	$-0.453389\pi$
$233$	−9.73700	−	5.62166i	−0.637892	−	0.368287i	−0.783802	+	0.621011i	$0.786722\pi$
$234$	−1.08836	+	0.197104i	−0.0711481	+	0.0128851i
$235$		0			0
$236$	1.10889	+	6.28885i	0.0721828	+	0.409369i
$237$	−5.03392	−	5.01068i	−0.326988	−	0.325479i
$238$	0.530939	+	1.45874i	0.0344157	+	0.0945563i
$239$	−3.13312	+	17.7688i	−0.202665	+	1.14937i	0.698408	+	0.715700i	$0.253892\pi$
$239$	−3.13312	+	17.7688i	−0.202665	+	1.14937i	−0.901073	+	0.433668i	$0.857219\pi$
$240$		0			0
$241$	11.6762	−	9.79751i	0.752131	−	0.631113i	−0.183934	−	0.982939i	$-0.558883\pi$
$241$	11.6762	−	9.79751i	0.752131	−	0.631113i	0.936066	+	0.351826i	$0.114439\pi$
$242$		−	1.56155i		−	0.100380i
$243$	6.75096	+	14.0508i	0.433074	+	0.901358i
$244$	−17.5943			−1.12636
$245$		0			0
$246$	−2.91102	+	0.261470i	−0.185600	+	0.0166707i
$247$	−6.34596	−	1.11896i	−0.403784	−	0.0711980i
$248$	2.24408	+	6.16556i	0.142499	+	0.391513i
$249$	−4.23659	+	4.25624i	−0.268483	+	0.269728i
$250$		0			0
$251$	10.1160	+	17.5214i	0.638515	+	1.10594i	0.985759	+	0.168165i	$0.0537843\pi$
$251$	10.1160	+	17.5214i	0.638515	+	1.10594i	−0.347244	+	0.937775i	$0.612882\pi$
$252$	2.68066	+	14.8019i	0.168866	+	0.932434i
$253$	13.4671	+	7.77522i	0.846668	+	0.488824i
$254$	−0.789545	−	0.287371i	−0.0495405	−	0.0180312i
$255$		0			0
$256$	8.48369	+	7.11866i	0.530230	+	0.444916i
$257$	−18.7141	+	22.3026i	−1.16735	+	1.39120i	−0.262795	+	0.964852i	$0.584644\pi$
$257$	−18.7141	+	22.3026i	−1.16735	+	1.39120i	−0.904560	+	0.426347i	$0.859800\pi$
$258$	1.15348	+	2.45877i	0.0718124	+	0.153077i
$259$	11.0616	+	4.02609i	0.687334	+	0.250169i
$260$		0			0
$261$	−12.2362	+	14.7203i	−0.757402	+	0.911167i
$262$	3.43174	−	1.98132i	0.212014	−	0.122406i
$263$	1.14764	−	0.202359i	0.0707663	−	0.0124780i	−0.138153	−	0.990411i	$-0.544117\pi$
$263$	1.14764	−	0.202359i	0.0707663	−	0.0124780i	0.208919	+	0.977933i	$0.433005\pi$
$264$	0.997322	+	3.68791i	0.0613809	+	0.226975i
$265$		0			0
$266$	0.508399	−	2.88328i	0.0311720	−	0.176785i
$267$	21.5534	−	15.1663i	1.31904	−	0.928160i
$268$	6.64471	+	7.91885i	0.405890	+	0.483721i
$269$	−3.89377			−0.237407			−0.118704	−	0.992930i	$-0.537874\pi$
$269$	−3.89377			−0.237407			−0.118704	+	0.992930i	$0.537874\pi$
$270$		0			0
$271$	−1.01175			−0.0614596			−0.0307298	−	0.999528i	$-0.509783\pi$
$271$	−1.01175			−0.0614596			−0.0307298	+	0.999528i	$0.509783\pi$
$272$	−5.47738	−	6.52769i	−0.332115	−	0.395799i
$273$	5.90347	+	2.73622i	0.357294	+	0.165604i
$274$	0.531323	−	3.01328i	0.0320984	−	0.182039i
$275$		0			0
$276$	22.8566	+	6.06776i	1.37580	+	0.365236i
$277$	30.5191	−	5.38133i	1.83371	−	0.323333i	0.853471	−	0.521140i	$-0.174493\pi$
$277$	30.5191	−	5.38133i	1.83371	−	0.323333i	0.980241	+	0.197807i	$0.0633818\pi$
$278$	3.92577	−	2.26654i	0.235452	−	0.135938i
$279$	−0.0910221	−	19.6707i	−0.00544935	−	1.17765i
$280$		0			0
$281$	−2.69096	−	0.979428i	−0.160529	−	0.0584278i	0.260506	−	0.965472i	$-0.416111\pi$
$281$	−2.69096	−	0.979428i	−0.160529	−	0.0584278i	−0.421035	+	0.907045i	$0.638333\pi$
$282$	2.40570	−	3.45267i	0.143257	−	0.205603i
$283$	−15.8369	+	18.8737i	−0.941405	+	1.12192i	0.0509739	+	0.998700i	$0.483767\pi$
$283$	−15.8369	+	18.8737i	−0.941405	+	1.12192i	−0.992379	+	0.123223i	$0.960677\pi$
$284$	4.96392	+	4.16523i	0.294555	+	0.247161i
$285$		0			0
$286$	0.763671	+	0.277954i	0.0451568	+	0.0164357i
$287$	14.8904	+	8.59698i	0.878953	+	0.507464i
$288$	4.41630	+	7.56816i	0.260233	+	0.445958i
$289$	−5.72372	−	9.91377i	−0.336689	−	0.583163i
$290$		0			0
$291$	−7.02041	−	1.86371i	−0.411544	−	0.109253i
$292$	−3.37684	−	9.27779i	−0.197615	−	0.542942i
$293$	−5.71323	−	1.00740i	−0.333771	−	0.0588527i	0.00425146	−	0.999991i	$-0.498647\pi$
$293$	−5.71323	−	1.00740i	−0.333771	−	0.0588527i	−0.338022	+	0.941138i	$0.609758\pi$
$294$	0.0532219	−	0.114828i	0.00310397	−	0.00669688i
$295$		0			0
$296$	4.54641			0.264255
$297$	0.919033	−	11.4167i	0.0533277	−	0.662466i
$298$			5.44948i			0.315680i
$299$	7.83595	−	6.57515i	0.453165	−	0.380250i
$300$		0			0
$301$	2.77440	−	15.7344i	0.159914	−	0.906915i
$302$	−0.670530	−	1.84227i	−0.0385847	−	0.106011i
$303$	23.9083	−	6.46554i	1.37350	−	0.371435i
$304$	2.79073	+	15.8270i	0.160059	+	0.907740i
$305$		0			0
$306$	−0.622589	−	1.68623i	−0.0355911	−	0.0963955i
$307$	26.8124	+	15.4802i	1.53027	+	0.883500i	0.999349	+	0.0360759i	$0.0114858\pi$
$307$	26.8124	+	15.4802i	1.53027	+	0.883500i	0.530917	+	0.847424i	$0.321848\pi$
$308$	3.78024	−	10.3861i	0.215399	−	0.591804i
$309$	13.5398	−	6.35188i	0.770251	−	0.361346i
$310$		0			0
$311$	7.44776	+	6.24942i	0.422324	+	0.354372i	0.829046	−	0.559180i	$-0.188884\pi$
$311$	7.44776	+	6.24942i	0.422324	+	0.354372i	−0.406722	+	0.913552i	$0.633328\pi$
$312$	2.50399	+	0.213234i	0.141760	+	0.0120720i
$313$	4.15409	−	11.4133i	0.234803	−	0.645116i	−0.765196	−	0.643797i	$-0.777358\pi$
$313$	4.15409	−	11.4133i	0.234803	−	0.645116i	0.999999	−	0.00131881i	$-0.000419789\pi$
$314$	−0.0984972	+	0.170602i	−0.00555852	+	0.00962763i
$315$		0			0
$316$	3.96814	+	6.87301i	0.223225	+	0.386637i
$317$	5.20964	−	0.918600i	0.292603	−	0.0515937i	−0.0254200	−	0.999677i	$-0.508092\pi$
$317$	5.20964	−	0.918600i	0.292603	−	0.0515937i	0.318023	+	0.948083i	$0.396981\pi$
$318$	−4.17276	−	4.15350i	−0.233997	−	0.232917i
$319$	13.2164	−	4.81037i	0.739976	−	0.269329i
$320$		0			0
$321$	−9.78581	+	0.878966i	−0.546191	+	0.0490591i
$322$	2.98741	+	3.56025i	0.166482	+	0.198405i
$323$		−	10.4721i		−	0.582685i
$324$	−3.18324	−	17.1248i	−0.176847	−	0.951376i
$325$		0			0
$326$	−3.17646	+	2.66536i	−0.175928	+	0.147621i
$327$	−2.93770	−	32.7064i	−0.162455	−	1.80867i
$328$	6.53980	+	1.15314i	0.361100	+	0.0636717i
$329$	−23.2627	+	8.46692i	−1.28251	+	0.466797i
$330$		0			0
$331$	4.36397	+	24.7493i	0.239866	+	1.36035i	0.832121	+	0.554595i	$0.187127\pi$
$331$	4.36397	+	24.7493i	0.239866	+	1.36035i	−0.592255	+	0.805750i	$0.701762\pi$
$332$	5.81121	−	3.35510i	0.318932	−	0.184135i
$333$	−12.8298	−	4.60254i	−0.703067	−	0.252217i
$334$	0.880908	−	1.52578i	0.0482012	−	0.0834868i
$335$		0			0
$336$	1.37696	−	16.1695i	0.0751193	−	0.882118i
$337$	−3.24968	+	3.87282i	−0.177021	+	0.210966i	−0.847258	−	0.531182i	$-0.821748\pi$
$337$	−3.24968	+	3.87282i	−0.177021	+	0.210966i	0.670237	+	0.742147i	$0.266193\pi$
$338$	−1.78114	+	2.12268i	−0.0968814	+	0.115459i
$339$	−17.9284	+	8.41068i	−0.973734	+	0.456806i
$340$		0			0
$341$	−7.22663	+	12.5169i	−0.391344	+	0.677828i
$342$	−0.573226	+	3.34126i	−0.0309965	+	0.180675i
$343$	−16.3511	+	9.44033i	−0.882878	+	0.509730i
$344$	−1.07153	−	6.07696i	−0.0577732	−	0.327648i
$345$		0			0
$346$	1.78159	−	0.648445i	0.0957788	−	0.0348606i
$347$	26.6058	+	4.69131i	1.42827	+	0.251843i	0.833708	−	0.552206i	$-0.186214\pi$
$347$	26.6058	+	4.69131i	1.42827	+	0.251843i	0.594564	+	0.804048i	$0.297325\pi$
$348$	17.4921	−	12.3085i	0.937677	−	0.659807i
$349$	17.9519	−	15.0634i	0.960941	−	0.806326i	−0.0201645	−	0.999797i	$-0.506419\pi$
$349$	17.9519	−	15.0634i	0.960941	−	0.806326i	0.981106	+	0.193471i	$0.0619746\pi$
$350$		0			0
$351$	−6.85028	−	3.13664i	−0.365641	−	0.167421i
$352$		−	6.43824i		−	0.343160i
$353$	−11.4710	−	13.6706i	−0.610538	−	0.727611i	0.368875	−	0.929479i	$-0.379743\pi$
$353$	−11.4710	−	13.6706i	−0.610538	−	0.727611i	−0.979413	+	0.201868i	$0.935299\pi$
$354$	0.611095	−	1.31845i	0.0324794	−	0.0700750i
$355$		0			0
$356$	−27.6719	+	10.0718i	−1.46661	+	0.533802i
$357$	−2.71320	+	10.2203i	−0.143598	+	0.540918i
$358$	−3.63399	+	0.640771i	−0.192062	+	0.0338658i
$359$	−12.7067	−	22.0086i	−0.670633	−	1.16157i	−0.977725	−	0.209891i	$-0.932689\pi$
$359$	−12.7067	−	22.0086i	−0.670633	−	1.16157i	0.307092	−	0.951680i	$-0.400644\pi$
$360$		0			0
$361$	−0.375211	+	0.649885i	−0.0197480	+	0.0342045i
$362$	0.719845	−	1.97776i	0.0378342	−	0.103949i
$363$	6.08092	−	8.72737i	0.319166	−	0.458068i
$364$	−5.56950	−	4.67337i	−0.291921	−	0.244951i
$365$		0			0
$366$	3.28505	+	2.28891i	0.171712	+	0.119643i
$367$	12.1787	−	33.4606i	0.635721	−	1.74663i	−0.0290451	−	0.999578i	$-0.509247\pi$
$367$	12.1787	−	33.4606i	0.635721	−	1.74663i	0.664766	−	0.747051i	$-0.268531\pi$
$368$	−22.0938	−	12.7558i	−1.15172	−	0.664944i
$369$	−17.2876	−	9.87465i	−0.899958	−	0.514054i
$370$		0			0
$371$	6.01439	+	34.1093i	0.312252	+	1.77087i
$372$	−5.63964	+	21.2439i	−0.292402	+	1.10144i
$373$	−1.97686	−	5.43137i	−0.102358	−	0.281226i	0.877934	−	0.478782i	$-0.158922\pi$
$373$	−1.97686	−	5.43137i	−0.102358	−	0.281226i	−0.980291	+	0.197557i	$0.936699\pi$
$374$	−0.229340	+	1.30065i	−0.0118589	+	0.0672551i
$375$		0			0
$376$	−7.32428	+	6.14580i	−0.377721	+	0.316945i
$377$		−	9.25171i		−	0.476487i
$378$	1.42513	−	3.11241i	0.0733006	−	0.160085i
$379$	27.7158			1.42366			0.711832	−	0.702350i	$-0.247866\pi$
$379$	27.7158			1.42366			0.711832	+	0.702350i	$0.247866\pi$
$380$		0			0
$381$	−3.29362	−	4.68070i	−0.168737	−	0.239799i
$382$	−5.99215	−	1.05658i	−0.306585	−	0.0540592i
$383$	−1.88281	−	5.17297i	−0.0962069	−	0.264326i	0.882249	−	0.470784i	$-0.156029\pi$
$383$	−1.88281	−	5.17297i	−0.0962069	−	0.264326i	−0.978456	+	0.206457i	$0.933807\pi$
$384$	−3.38748	−	12.5263i	−0.172867	−	0.639228i
$385$		0			0
$386$	−3.05511	−	5.29161i	−0.155501	−	0.269336i
$387$	−3.12816	+	18.2337i	−0.159014	+	0.926870i
$388$	7.02876	+	4.05806i	0.356831	+	0.206017i
$389$	33.7465	+	12.2827i	1.71101	+	0.622758i	0.997002	−	0.0773745i	$-0.0246537\pi$
$389$	33.7465	+	12.2827i	1.71101	+	0.622758i	0.714013	+	0.700133i	$0.246876\pi$
$390$		0			0
$391$	12.7345	+	10.6855i	0.644010	+	0.540388i
$392$	−0.184839	+	0.220282i	−0.00933577	+	0.0111259i
$393$	26.8952	+	2.29034i	1.35669	+	0.115532i
$394$	−5.60219	−	2.03903i	−0.282234	−	0.102725i
$395$		0			0
$396$	−4.32148	+	12.0463i	−0.217163	+	0.605350i
$397$	−7.32719	+	4.23035i	−0.367741	+	0.212315i	−0.672471	−	0.740123i	$-0.734767\pi$
$397$	−7.32719	+	4.23035i	−0.367741	+	0.212315i	0.304730	+	0.952439i	$0.401434\pi$
$398$	−1.96449	+	0.346392i	−0.0984708	+	0.0173631i
$399$	14.0693	−	14.1346i	0.704347	−	0.707614i
$400$		0			0
$401$	4.71483	−	26.7391i	0.235447	−	1.33529i	−0.606222	−	0.795296i	$-0.707316\pi$
$401$	4.71483	−	26.7391i	0.235447	−	1.33529i	0.841669	−	0.539993i	$-0.181573\pi$
$402$	−0.210446	−	2.34297i	−0.0104961	−	0.116857i
$403$	6.11123	+	7.28308i	0.304422	+	0.362796i
$404$	−27.6741			−1.37684
$405$		0			0
$406$	4.20350			0.208616
$407$	6.43748	+	7.67189i	0.319094	+	0.380281i
$408$	0.365360	+	4.06767i	0.0180880	+	0.201380i
$409$	0.359891	−	2.04104i	0.0177954	−	0.100923i	−0.974616	−	0.223882i	$-0.928127\pi$
$409$	0.359891	−	2.04104i	0.0177954	−	0.100923i	0.992412	+	0.122959i	$0.0392382\pi$
$410$		0			0
$411$	14.7037	−	14.7719i	0.725280	−	0.728643i
$412$	−16.4572	+	2.90184i	−0.810786	+	0.142964i
$413$	−7.40352	+	4.27442i	−0.364303	+	0.210331i
$414$	−3.47819	−	4.10640i	−0.170944	−	0.201819i
$415$		0			0
$416$	−3.97968	−	1.44849i	−0.195120	−	0.0710178i
$417$	30.7670	+	2.62005i	1.50667	+	0.128304i
$418$	1.60110	−	1.90812i	0.0783124	−	0.0933291i
$419$	19.8184	+	16.6296i	0.968190	+	0.812408i	0.982266	−	0.187493i	$-0.0600362\pi$
$419$	19.8184	+	16.6296i	0.968190	+	0.812408i	−0.0140758	+	0.999901i	$0.504481\pi$
$420$		0			0
$421$	9.37834	+	3.41344i	0.457073	+	0.166361i	0.560287	−	0.828298i	$-0.310691\pi$
$421$	9.37834	+	3.41344i	0.457073	+	0.166361i	−0.103215	+	0.994659i	$0.532913\pi$
$422$	1.11074	+	0.641287i	0.0540700	+	0.0312174i
$423$	26.8904	−	9.92847i	1.30746	−	0.482739i
$424$	6.68850	+	11.5848i	0.324822	+	0.562608i
$425$		0			0
$426$	−0.384948	−	1.42347i	−0.0186508	−	0.0689671i
$427$	−8.05588	−	22.1333i	−0.389851	−	1.07111i
$428$	10.8116	+	1.90638i	0.522600	+	0.0921484i
$429$	3.18569	+	4.52731i	0.153807	+	0.218581i
$430$		0			0
$431$	2.41940			0.116538			0.0582692	−	0.998301i	$-0.481442\pi$
$431$	2.41940			0.116538			0.0582692	+	0.998301i	$0.481442\pi$
$432$	−1.50774	+	18.7300i	−0.0725413	+	0.901148i
$433$			19.8081i			0.951915i	0.879468	+	0.475957i	$0.157898\pi$
$433$			19.8081i			0.951915i	−0.879468	+	0.475957i	$0.842102\pi$
$434$	−3.30906	+	2.77663i	−0.158840	+	0.133282i
$435$		0			0
$436$	−6.37156	+	36.1349i	−0.305142	+	1.73055i
$437$	−10.7231	−	29.4615i	−0.512955	−	1.40933i
$438$	−0.576488	+	2.17157i	−0.0275457	+	0.103761i
$439$	−0.697642	−	3.95652i	−0.0332966	−	0.188835i	0.963623	−	0.267266i	$-0.0861201\pi$
$439$	−0.697642	−	3.95652i	−0.0332966	−	0.188835i	−0.996920	+	0.0784310i	$0.975009\pi$
$440$		0			0
$441$	0.744609	−	0.434506i	0.0354576	−	0.0206908i
$442$	0.752376	+	0.434385i	0.0357869	+	0.0206616i
$443$	−1.71466	+	4.71098i	−0.0814658	+	0.223826i	−0.973738	−	0.227673i	$-0.926888\pi$
$443$	−1.71466	+	4.71098i	−0.0814658	+	0.223826i	0.892272	+	0.451499i	$0.149110\pi$
$444$	12.4960	+	8.70678i	0.593034	+	0.413205i
$445$		0			0
$446$	3.67820	+	3.08638i	0.174168	+	0.146144i
$447$	−21.2211	+	30.4566i	−1.00373	+	1.44055i
$448$	−5.75083	+	15.8003i	−0.271701	+	0.746493i
$449$	−9.48026	+	16.4203i	−0.447401	+	0.774922i	−0.998216	−	0.0597059i	$-0.980984\pi$
$449$	−9.48026	+	16.4203i	−0.447401	+	0.774922i	0.550815	+	0.834627i	$0.314317\pi$
$450$		0			0
$451$	7.31412	+	12.6684i	0.344409	+	0.596533i
$452$	21.7913	−	3.84240i	1.02498	−	0.180731i
$453$	3.42654	−	12.9074i	0.160993	−	0.606442i
$454$	−0.894001	+	0.325390i	−0.0419575	+	0.0152713i
$455$		0			0
$456$	3.23906	−	6.98835i	0.151683	−	0.327260i
$457$	−7.31683	−	8.71986i	−0.342267	−	0.407898i	0.567263	−	0.823537i	$-0.308002\pi$
$457$	−7.31683	−	8.71986i	−0.342267	−	0.407898i	−0.909530	+	0.415639i	$0.863558\pi$
$458$		−	2.14015i		−	0.100002i
$459$	3.08685	−	11.8486i	0.144082	−	0.553048i
$460$		0			0
$461$	−3.34271	+	2.80487i	−0.155686	+	0.130636i	−0.717303	−	0.696761i	$-0.754624\pi$
$461$	−3.34271	+	2.80487i	−0.155686	+	0.130636i	0.561617	+	0.827397i	$0.310179\pi$
$462$	−2.05698	+	1.44741i	−0.0956992	+	0.0673398i
$463$	−7.13335	−	1.25780i	−0.331515	−	0.0584550i	0.00541334	−	0.999985i	$-0.498277\pi$
$463$	−7.13335	−	1.25780i	−0.331515	−	0.0584550i	−0.336928	+	0.941530i	$0.609388\pi$
$464$	−21.6825	+	7.89178i	−1.00658	+	0.366367i
$465$		0			0
$466$	−0.496438	−	2.81544i	−0.0229970	−	0.130423i
$467$	3.10264	−	1.79131i	0.143573	−	0.0828919i	−0.426493	−	0.904491i	$-0.640251\pi$
$467$	3.10264	−	1.79131i	0.143573	−	0.0828919i	0.570066	+	0.821599i	$0.306918\pi$
$468$	6.47395	+	5.38144i	0.299259	+	0.248757i
$469$	−6.91936	+	11.9847i	−0.319507	+	0.553402i
$470$		0			0
$471$	−1.21484	+	0.569916i	−0.0559770	+	0.0262603i
$472$	−2.12232	+	2.52929i	−0.0976879	+	0.116420i
$473$	8.73740	−	10.4128i	0.401746	−	0.478782i
$474$	0.153241	−	1.79949i	0.00703858	−	0.0826534i
$475$		0			0
$476$	5.90774	−	10.2325i	0.270781	−	0.469006i
$477$	−7.14681	−	39.4629i	−0.327230	−	1.80688i
$478$	−3.97317	+	2.29391i	−0.181729	+	0.104921i
$479$	−0.329444	−	1.86837i	−0.0150527	−	0.0853680i	0.976356	−	0.216169i	$-0.0693562\pi$
$479$	−0.329444	−	1.86837i	−0.0150527	−	0.0853680i	−0.991409	+	0.130801i	$0.958245\pi$
$480$		0			0
$481$	6.19055	−	2.25318i	0.282265	−	0.102736i
$482$	3.81680	+	0.673006i	0.173851	+	0.0306546i
$483$	2.83216	+	31.5313i	0.128868	+	1.43473i
$484$	−9.10476	+	7.63980i	−0.413853	+	0.347264i
$485$		0			0
$486$	−1.63347	+	3.61149i	−0.0740959	+	0.163821i
$487$			13.6444i			0.618286i	0.951016	+	0.309143i	$0.100042\pi$
$487$			13.6444i			0.618286i	−0.951016	+	0.309143i	$0.899958\pi$
$488$	−5.84743	−	6.96870i	−0.264701	−	0.315458i
$489$	−28.1322	+	2.52685i	−1.27218	+	0.114268i
$490$		0			0
$491$	−37.0378	+	13.4806i	−1.67149	+	0.608373i	−0.992105	−	0.125408i	$-0.959976\pi$
$491$	−37.0378	+	13.4806i	−1.67149	+	0.608373i	−0.679386	+	0.733781i	$0.737754\pi$
$492$	15.7665	+	15.6937i	0.710810	+	0.707529i
$493$	14.8068	−	2.61085i	0.666867	−	0.117587i
$494$	−0.819249	−	1.41898i	−0.0368598	−	0.0638430i
$495$		0			0
$496$	11.8558	−	20.5349i	0.532343	−	0.922044i
$497$	−2.96695	+	8.15164i	−0.133086	+	0.365651i
$498$	−1.52149	−	0.129567i	−0.0681797	−	0.00580603i
$499$	20.0062	+	16.7872i	0.895599	+	0.751497i	0.969325	−	0.245781i	$-0.0790446\pi$
$499$	20.0062	+	16.7872i	0.895599	+	0.751497i	−0.0737260	+	0.997279i	$0.523489\pi$
$500$		0			0
$501$	10.8649	−	5.09703i	0.485409	−	0.227719i
$502$	−1.75950	+	4.83419i	−0.0785304	+	0.215761i
$503$	5.65434	+	3.26454i	0.252115	+	0.145558i	0.620732	−	0.784023i	$-0.286835\pi$
$503$	5.65434	+	3.26454i	0.252115	+	0.145558i	−0.368618	+	0.929581i	$0.620169\pi$
$504$	−4.97178	+	5.98113i	−0.221461	+	0.266421i
$505$		0			0
$506$	0.686615	+	3.89399i	0.0305238	+	0.173109i
$507$	−18.2207	+	4.92743i	−0.809209	+	0.218835i
$508$	2.18726	+	6.00945i	0.0970441	+	0.266626i
$509$	0.633039	−	3.59014i	0.0280590	−	0.159130i	−0.967559	−	0.252646i	$-0.918699\pi$
$509$	0.633039	−	3.59014i	0.0280590	−	0.159130i	0.995618	+	0.0935154i	$0.0298104\pi$
$510$		0			0
$511$	10.1251	−	8.49600i	0.447910	−	0.375841i
$512$			17.7996i			0.786640i
$513$	−16.2151	+	16.4418i	−0.715914	+	0.725922i
$514$	−7.40290			−0.326528
$515$		0			0
$516$	8.69277	−	18.7549i	0.382678	−	0.825637i
$517$	−20.7416	−	3.65730i	−0.912214	−	0.160848i
$518$	1.02373	+	2.81267i	0.0449800	+	0.123581i
$519$	12.4823	+	3.31368i	0.547911	+	0.145454i
$520$		0			0
$521$	5.35490	+	9.27496i	0.234603	+	0.406344i	0.959157	−	0.282874i	$-0.0912878\pi$
$521$	5.35490	+	9.27496i	0.234603	+	0.406344i	−0.724555	+	0.689217i	$0.757954\pi$
$522$	−4.86722	+	0.0225221i	−0.213033	+	0.000985764i
$523$	−2.58057	−	1.48990i	−0.112841	−	0.0651486i	0.442517	−	0.896760i	$-0.354085\pi$
$523$	−2.58057	−	1.48990i	−0.112841	−	0.0651486i	−0.555358	+	0.831611i	$0.687419\pi$
$524$	−28.3418	−	10.3156i	−1.23812	−	0.450639i
$525$		0			0
$526$	0.226990	+	0.190467i	0.00989724	+	0.00830477i
$527$	−9.93156	+	11.8360i	−0.432626	+	0.515583i
$528$	7.89287	−	11.3279i	0.343493	−	0.492982i
$529$	25.1548	+	9.15560i	1.09369	+	0.398069i
$530$		0			0
$531$	8.54962	−	4.98901i	0.371022	−	0.216505i
$532$	−19.2985	+	11.1420i	−0.836696	+	0.483067i
$533$	9.47630	−	1.67093i	0.410464	−	0.0723759i
$534$	6.47691	+	1.71943i	0.280283	+	0.0744071i
$535$		0			0
$536$	−0.928118	+	5.26362i	−0.0400886	+	0.227354i
$537$	−22.8053	−	10.5701i	−0.984121	−	0.456134i
$538$	−0.636411	−	0.758445i	−0.0274376	−	0.0326989i
$539$	−0.633440			−0.0272842
$540$		0			0
$541$	9.02469			0.388002			0.194001	−	0.981001i	$-0.437854\pi$
$541$	9.02469			0.388002			0.194001	+	0.981001i	$0.437854\pi$
$542$	−0.165364	−	0.197074i	−0.00710301	−	0.00846504i
$543$	11.7248	−	8.25032i	0.503161	−	0.354055i
$544$	1.19515	−	6.77802i	0.0512415	−	0.290605i
$545$		0			0
$546$	0.431911	+	1.59712i	0.0184841	+	0.0683505i
$547$	10.5473	−	1.85977i	0.450969	−	0.0795180i	0.0564494	−	0.998405i	$-0.482022\pi$
$547$	10.5473	−	1.85977i	0.450969	−	0.0795180i	0.394520	+	0.918887i	$0.370911\pi$
$548$	−20.1687	+	11.6444i	−0.861562	+	0.497423i
$549$	9.44647	+	25.5850i	0.403166	+	1.09194i
$550$		0			0
$551$	−26.6464	−	9.69849i	−1.13517	−	0.413170i
$552$	5.19303	+	11.0695i	0.221030	+	0.471151i
$553$	−6.82923	+	8.13876i	−0.290409	+	0.346095i
$554$	6.03634	+	5.06509i	0.256460	+	0.215195i
$555$		0			0
$556$	−32.4218	−	11.8006i	−1.37499	−	0.500456i
$557$	−8.87931	−	5.12647i	−0.376228	−	0.217216i	0.299948	−	0.953956i	$-0.403031\pi$
$557$	−8.87931	−	5.12647i	−0.376228	−	0.217216i	−0.676176	+	0.736740i	$0.736364\pi$
$558$	3.81667	−	3.23278i	0.161573	−	0.136855i
$559$	−4.47074	−	7.74355i	−0.189092	−	0.327517i
$560$		0			0
$561$	−6.34670	+	6.37613i	−0.267958	+	0.269201i
$562$	−0.249042	−	0.684238i	−0.0105052	−	0.0288628i
$563$	−41.2043	−	7.26542i	−1.73655	−	0.306201i	−0.786338	−	0.617797i	$-0.788025\pi$
$563$	−41.2043	−	7.26542i	−1.73655	−	0.306201i	−0.950215	+	0.311596i	$0.899136\pi$
$564$	−31.9008	+	2.86535i	−1.34327	+	0.120653i
$565$		0			0
$566$	−6.26473			−0.263326
$567$	20.0851	−	11.8453i	0.843495	−	0.497457i
$568$			3.35039i			0.140579i
$569$	6.82704	−	5.72857i	0.286205	−	0.240154i	−0.488370	−	0.872637i	$-0.662408\pi$
$569$	6.82704	−	5.72857i	0.286205	−	0.240154i	0.774575	+	0.632482i	$0.217964\pi$
$570$		0			0
$571$	3.12283	−	17.7104i	0.130686	−	0.741159i	−0.847081	−	0.531464i	$-0.821642\pi$
$571$	3.12283	−	17.7104i	0.130686	−	0.741159i	0.977767	−	0.209695i	$-0.0672470\pi$
$572$	−2.11558	−	5.81252i	−0.0884570	−	0.243034i
$573$	−29.3751	−	29.2395i	−1.22716	−	1.22150i
$574$	0.759183	+	4.30554i	0.0316877	+	0.179710i
$575$		0			0
$576$	6.57422	−	18.3259i	0.273926	−	0.763580i
$577$	−6.31165	−	3.64403i	−0.262757	−	0.151703i	0.362834	−	0.931854i	$-0.381809\pi$
$577$	−6.31165	−	3.64403i	−0.262757	−	0.151703i	−0.625592	+	0.780151i	$0.715142\pi$
$578$	0.995544	−	2.73523i	0.0414092	−	0.113771i
$579$	3.53161	−	41.4714i	0.146769	−	1.72349i
$580$		0			0
$581$	6.88142	+	5.77419i	0.285489	+	0.239554i
$582$	−0.784418	−	1.67208i	−0.0325152	−	0.0693099i
$583$	−10.0784	+	27.6901i	−0.417403	+	1.14680i
$584$	2.55243	−	4.42094i	0.105620	−	0.182940i
$585$		0			0
$586$	−0.737566	−	1.27750i	−0.0304686	−	0.0527731i
$587$	−29.6830	+	5.23392i	−1.22515	+	0.216027i	−0.748541	−	0.663089i	$-0.769245\pi$
$587$	−29.6830	+	5.23392i	−1.22515	+	0.216027i	−0.476608	+	0.879116i	$0.658134\pi$
$588$	−0.929897	+	0.251473i	−0.0383483	+	0.0103706i
$589$	27.3828	−	9.96652i	1.12829	−	0.410663i
$590$		0			0
$591$	−23.3698	−	33.2117i	−0.961305	−	1.36615i
$592$	−10.5612	−	12.5863i	−0.434061	−	0.517294i
$593$			3.49473i			0.143511i	0.997422	+	0.0717557i	$0.0228602\pi$
$593$			3.49473i			0.143511i	−0.997422	+	0.0717557i	$0.977140\pi$
$594$	2.37401	−	1.68698i	0.0974069	−	0.0692176i
$595$		0			0
$596$	31.7737	−	26.6613i	1.30150	−	1.09209i
$597$	−12.3282	−	5.71406i	−0.504561	−	0.233861i
$598$	2.56147	+	0.451657i	0.104746	+	0.0184696i
$599$	−24.8902	+	9.05928i	−1.01698	+	0.370152i	−0.796111	−	0.605150i	$-0.793113\pi$
$599$	−24.8902	+	9.05928i	−1.01698	+	0.370152i	−0.220873	+	0.975302i	$0.570891\pi$
$600$		0			0
$601$	−2.02684	−	11.4948i	−0.0826764	−	0.468881i	−0.997834	−	0.0657845i	$-0.979045\pi$
$601$	−2.02684	−	11.4948i	−0.0826764	−	0.468881i	0.915157	−	0.403096i	$-0.132066\pi$
$602$	3.51827	−	2.03127i	0.143394	−	0.0827886i
$603$	7.94770	−	13.9141i	0.323656	−	0.566627i
$604$	−7.46096	+	12.9228i	−0.303582	+	0.525820i
$605$		0			0
$606$	5.16705	+	3.60022i	0.209897	+	0.146249i
$607$	3.50795	−	4.18061i	0.142383	−	0.169686i	−0.690140	−	0.723676i	$-0.742451\pi$
$607$	3.50795	−	4.18061i	0.142383	−	0.169686i	0.832523	+	0.553990i	$0.186895\pi$
$608$	−8.34373	+	9.94367i	−0.338383	+	0.403269i
$609$	23.4930	+	16.3691i	0.951983	+	0.663308i
$610$		0			0
$611$	−6.92716	+	11.9982i	−0.280243	+	0.485395i
$612$	−6.78574	+	11.8799i	−0.274297	+	0.480215i
$613$	6.02950	−	3.48113i	0.243529	−	0.140602i	−0.373269	−	0.927723i	$-0.621763\pi$
$613$	6.02950	−	3.48113i	0.243529	−	0.140602i	0.616798	+	0.787122i	$0.288430\pi$
$614$	1.36702	+	7.75278i	0.0551686	+	0.312877i
$615$		0			0
$616$	5.37005	−	1.95454i	0.216365	−	0.0787505i
$617$	18.7560	+	3.30719i	0.755089	+	0.133143i	0.537925	−	0.842993i	$-0.319208\pi$
$617$	18.7560	+	3.30719i	0.755089	+	0.133143i	0.217164	+	0.976135i	$0.430319\pi$
$618$	3.45024	+	1.59916i	0.138789	+	0.0643278i
$619$	−10.9809	+	9.21409i	−0.441360	+	0.370345i	−0.836218	−	0.548397i	$-0.815238\pi$
$619$	−10.9809	+	9.21409i	−0.441360	+	0.370345i	0.394858	+	0.918742i	$0.370794\pi$
$620$		0			0
$621$	−3.44829	−	36.4949i	−0.138375	−	1.46449i
$622$			2.47214i			0.0991236i
$623$	−25.3401	−	30.1992i	−1.01523	−	1.20991i
$624$	−5.22636	−	7.42739i	−0.209222	−	0.297333i
$625$		0			0
$626$	2.90209	−	1.05627i	0.115991	−	0.0422172i
$627$	16.3789	−	4.42935i	0.654110	−	0.176891i
$628$	1.47660	−	0.260365i	0.0589228	−	0.0103897i
$629$	5.35306	+	9.27178i	0.213441	+	0.369690i
$630$		0			0
$631$	−5.23437	+	9.06620i	−0.208377	+	0.360920i	−0.951203	−	0.308564i	$-0.900151\pi$
$631$	−5.23437	+	9.06620i	−0.208377	+	0.360920i	0.742826	+	0.669484i	$0.233485\pi$
$632$	−1.40344	+	3.85591i	−0.0558257	+	0.153380i
$633$	3.71056	+	7.90949i	0.147481	+	0.314374i
$634$	1.03041	+	0.864618i	0.0409229	+	0.0343384i
$635$		0			0
$636$	−3.80233	+	44.6504i	−0.150772	+	1.77050i
$637$	−0.142512	+	0.391549i	−0.00564654	+	0.0155137i
$638$	3.09712	+	1.78812i	0.122616	+	0.0707925i
$639$	3.39175	−	9.45466i	0.134176	−	0.374021i
$640$		0			0
$641$	−1.94620	−	11.0374i	−0.0768701	−	0.435952i	−0.998817	−	0.0486349i	$-0.984513\pi$
$641$	−1.94620	−	11.0374i	−0.0768701	−	0.435952i	0.921947	−	0.387317i	$-0.126598\pi$
$642$	−1.77064	−	1.76246i	−0.0698815	−	0.0695588i
$643$	−1.36924	−	3.76197i	−0.0539977	−	0.148357i	0.909761	−	0.415132i	$-0.136264\pi$
$643$	−1.36924	−	3.76197i	−0.0539977	−	0.148357i	−0.963759	+	0.266774i	$0.914042\pi$
$644$	6.14264	−	34.8367i	0.242054	−	1.37276i
$645$		0			0
$646$	2.03981	−	1.71160i	0.0802551	−	0.0673421i
$647$			23.5060i			0.924118i	0.886849	+	0.462059i	$0.152889\pi$
$647$			23.5060i			0.924118i	−0.886849	+	0.462059i	$0.847111\pi$
$648$	5.72477	−	6.95217i	0.224890	−	0.273107i
$649$	−7.27317			−0.285497
$650$		0			0
$651$	−29.3066	+	2.63233i	−1.14862	+	0.103169i
$652$	31.0812	+	5.48046i	1.21724	+	0.214631i
$653$	−3.66017	−	10.0562i	−0.143233	−	0.393531i	0.847244	−	0.531203i	$-0.178260\pi$
$653$	−3.66017	−	10.0562i	−0.143233	−	0.393531i	−0.990478	+	0.137673i	$0.956038\pi$
$654$	5.89055	−	5.91787i	0.230339	−	0.231407i
$655$		0			0
$656$	−11.9994	−	20.7835i	−0.468497	−	0.811460i
$657$	−11.6783	+	9.89175i	−0.455616	+	0.385914i
$658$	−5.45136	−	3.14734i	−0.212516	−	0.122696i
$659$	5.16703	+	1.88064i	0.201279	+	0.0732595i	0.440692	−	0.897658i	$-0.354733\pi$
$659$	5.16703	+	1.88064i	0.201279	+	0.0732595i	−0.239414	+	0.970918i	$0.576955\pi$
$660$		0			0
$661$	−29.3397	−	24.6189i	−1.14118	−	0.957565i	−0.141705	−	0.989909i	$-0.545258\pi$
$661$	−29.3397	−	24.6189i	−1.14118	−	0.957565i	−0.999477	+	0.0323440i	$0.989703\pi$
$662$	−4.10752	+	4.89515i	−0.159643	+	0.190255i
$663$	2.51340	+	5.35760i	0.0976123	+	0.208072i
$664$	3.26022	+	1.18662i	0.126521	+	0.0460499i
$665$		0			0
$666$	−1.20044	−	3.25130i	−0.0465161	−	0.125985i
$667$	38.9830	−	22.5068i	1.50943	−	0.871469i
$668$	−13.2060	+	2.32857i	−0.510954	+	0.0900950i
$669$	8.53829	+	31.5730i	0.330109	+	1.22068i
$670$		0			0
$671$	3.47975	−	19.7346i	0.134334	−	0.761847i
$672$	10.7194	−	7.54283i	0.413510	−	0.290971i
$673$	−13.5100	−	16.1006i	−0.520771	−	0.620631i	0.439992	−	0.898002i	$-0.354981\pi$
$673$	−13.5100	−	16.1006i	−0.520771	−	0.620631i	−0.960763	+	0.277371i	$0.910537\pi$
$674$	−1.28550			−0.0495158
$675$		0			0
$676$	21.0906			0.811178
$677$	1.79711	+	2.14171i	0.0690685	+	0.0823126i	0.799472	−	0.600703i	$-0.205113\pi$
$677$	1.79711	+	2.14171i	0.0690685	+	0.0823126i	−0.730404	+	0.683016i	$0.760668\pi$
$678$	−4.56854	−	2.11749i	−0.175454	−	0.0813218i
$679$	−1.88672	+	10.7001i	−0.0724055	+	0.410632i
$680$		0			0
$681$	−6.26360	−	1.66280i	−0.240022	−	0.0637188i
$682$	−3.61924	+	0.638170i	−0.138588	+	0.0244368i
$683$	1.94224	−	1.12135i	0.0743176	−	0.0429073i	−0.462381	−	0.886681i	$-0.653005\pi$
$683$	1.94224	−	1.12135i	0.0743176	−	0.0429073i	0.536698	+	0.843774i	$0.319671\pi$
$684$	22.2860	−	13.0047i	0.852126	−	0.497247i
$685$		0			0
$686$	−4.51132	−	1.64199i	−0.172243	−	0.0626913i
$687$	8.33406	−	11.9611i	0.317964	−	0.456343i
$688$	−14.3344	+	17.0830i	−0.546492	+	0.651284i
$689$	14.8487	+	12.4595i	0.565689	+	0.474669i
$690$		0			0
$691$	27.0475	+	9.84448i	1.02893	+	0.374502i	0.800675	−	0.599099i	$-0.204474\pi$
$691$	27.0475	+	9.84448i	1.02893	+	0.374502i	0.228260	+	0.973600i	$0.426697\pi$
$692$	−12.4971	−	7.21522i	−0.475070	−	0.274282i
$693$	−17.1327	+	0.0792780i	−0.650817	+	0.00301152i
$694$	3.43474	+	5.94915i	0.130381	+	0.225827i
$695$		0			0
$696$	10.6886	+	2.83751i	0.405150	+	0.107555i
$697$	5.34845	+	14.6947i	0.202587	+	0.556603i
$698$	5.86823	+	1.03473i	0.222116	+	0.0391650i
$699$	8.18921	−	17.6684i	0.309744	−	0.668281i
$700$		0			0
$701$	−19.7581			−0.746255			−0.373127	−	0.927780i	$-0.621715\pi$
$701$	−19.7581			−0.746255			−0.373127	+	0.927780i	$0.621715\pi$
$702$	−0.508666	−	1.84699i	−0.0191983	−	0.0697102i
$703$		−	20.1917i		−	0.761546i
$704$	−10.9584	+	9.19523i	−0.413012	+	0.346558i
$705$		0			0
$706$	0.787958	−	4.46873i	0.0296552	−	0.168183i
$707$	−12.6711	−	34.8135i	−0.476544	−	1.30930i
$708$	−10.6771	+	2.88741i	−0.401270	+	0.108516i
$709$	0.688034	+	3.90203i	0.0258397	+	0.146544i	0.994998	−	0.0998949i	$-0.0318507\pi$
$709$	0.688034	+	3.90203i	0.0258397	+	0.146544i	−0.969158	+	0.246439i	$0.920740\pi$
$710$		0			0
$711$	7.86395	−	9.46045i	0.294921	−	0.354795i
$712$	−13.1859	−	7.61287i	−0.494162	−	0.285304i
$713$	−15.8211	+	43.4680i	−0.592503	+	1.62789i
$714$	−2.43422	+	1.14196i	−0.0910984	+	0.0427367i
$715$		0			0
$716$	21.5152	+	18.0534i	0.804059	+	0.674686i
$717$	−31.1385	−	2.65169i	−1.16289	−	0.0990291i
$718$	2.21011	−	6.07223i	0.0824806	−	0.226614i
$719$	13.6807	−	23.6957i	0.510204	−	0.883699i	−0.489726	−	0.871876i	$-0.662903\pi$
$719$	13.6807	−	23.6957i	0.510204	−	0.883699i	0.999930	−	0.0118228i	$-0.00376341\pi$
$720$		0			0
$721$	−11.1857	−	19.3741i	−0.416576	−	0.721530i
$722$	−0.187913	+	0.0331342i	−0.00699341	+	0.00123313i
$723$	18.7110	+	18.6246i	0.695868	+	0.692656i
$724$	−15.0533	+	5.47895i	−0.559451	+	0.203624i
$725$		0			0
$726$	2.69384	−	0.241962i	0.0999779	−	0.00898006i
$727$	7.91094	+	9.42789i	0.293401	+	0.349661i	0.892528	−	0.450993i	$-0.148930\pi$
$727$	7.91094	+	9.42789i	0.293401	+	0.349661i	−0.599127	+	0.800654i	$0.704486\pi$
$728$		−	3.75913i		−	0.139323i
$729$	−23.1930	+	13.8233i	−0.859001	+	0.511973i
$730$		0			0
$731$	11.1315	−	9.34041i	0.411712	−	0.345468i
$732$	−2.72624	−	30.3521i	−0.100765	−	1.12185i
$733$	2.30089	+	0.405710i	0.0849854	+	0.0149852i	0.215979	−	0.976398i	$-0.430706\pi$
$733$	2.30089	+	0.405710i	0.0849854	+	0.0149852i	−0.130994	+	0.991383i	$0.541817\pi$
$734$	8.50813	−	3.09671i	0.314041	−	0.114302i
$735$		0			0
$736$	−3.57812	−	20.2925i	−0.131891	−	0.747993i
$737$	−10.1963	+	5.88684i	−0.375586	+	0.216845i
$738$	−0.902125	−	4.98131i	−0.0332077	−	0.183365i
$739$	26.0513	−	45.1221i	0.958311	−	1.65984i	0.231710	−	0.972785i	$-0.425568\pi$
$739$	26.0513	−	45.1221i	0.958311	−	1.65984i	0.726602	−	0.687059i	$-0.241099\pi$
$740$		0			0
$741$	0.947026	−	11.1208i	0.0347899	−	0.408534i
$742$	−5.66095	+	6.74646i	−0.207820	+	0.247670i
$743$	25.9544	−	30.9313i	0.952175	−	1.13476i	−0.0386016	−	0.999255i	$-0.512290\pi$
$743$	25.9544	−	30.9313i	0.952175	−	1.13476i	0.990777	−	0.135504i	$-0.0432652\pi$
$744$	−10.2885	+	4.82663i	−0.377195	+	0.176953i
$745$		0			0
$746$	0.734841	−	1.27278i	0.0269045	−	0.0465999i
$747$	−7.99892	−	6.64906i	−0.292665	−	0.243276i
$748$	8.70559	−	5.02618i	0.318308	−	0.183775i
$749$	2.55210	+	14.4737i	0.0932517	+	0.528857i
$750$		0			0
$751$	−25.8917	+	9.42382i	−0.944803	+	0.343880i	−0.768061	−	0.640377i	$-0.778778\pi$
$751$	−25.8917	+	9.42382i	−0.944803	+	0.343880i	−0.176742	+	0.984257i	$0.556556\pi$
$752$	34.0281	+	6.00007i	1.24088	+	0.218800i
$753$	−28.6588	+	20.1661i	−1.04438	+	0.734892i
$754$	1.80209	−	1.51213i	0.0656282	−	0.0550686i
$755$		0			0
$756$	−25.1195	+	6.91798i	−0.913588	+	0.251604i
$757$		−	13.2447i		−	0.481386i	−0.970601	−	0.240693i	$-0.922625\pi$
$757$		−	13.2447i		−	0.481386i	0.970601	−	0.240693i	$-0.0773746\pi$
$758$	4.52996	+	5.39860i	0.164536	+	0.196086i
$759$	−11.3264	+	24.4369i	−0.411121	+	0.887004i
$760$		0			0
$761$	35.4594	−	12.9062i	1.28540	−	0.467848i	0.393187	−	0.919459i	$-0.371373\pi$
$761$	35.4594	−	12.9062i	1.28540	−	0.467848i	0.892215	+	0.451611i	$0.149150\pi$
$762$	0.373405	−	1.40658i	0.0135270	−	0.0509549i
$763$	−48.3743	+	8.52970i	−1.75127	+	0.308796i
$764$	23.1558	+	40.1070i	0.837747	+	1.45102i
$765$		0			0
$766$	0.699881	−	1.21223i	0.0252877	−	0.0437997i
$767$	−1.63633	+	4.49578i	−0.0590844	+	0.162333i
$768$	−10.9659	+	15.7383i	−0.395698	+	0.567907i
$769$	−39.2960	−	32.9733i	−1.41705	−	1.18905i	−0.952898	−	0.303292i	$-0.901914\pi$
$769$	−39.2960	−	32.9733i	−1.41705	−	1.18905i	−0.464153	−	0.885755i	$-0.653641\pi$
$770$		0			0
$771$	−41.3741	−	28.8280i	−1.49005	−	1.03822i
$772$	−15.9062	+	43.7020i	−0.572477	+	1.57287i
$773$	37.1420	+	21.4439i	1.33590	+	0.771285i	0.986197	−	0.165574i	$-0.0529478\pi$
$773$	37.1420	+	21.4439i	1.33590	+	0.771285i	0.349707	+	0.936859i	$0.386281\pi$
$774$	−4.06291	+	2.37086i	−0.146038	+	0.0852188i
$775$		0			0
$776$	0.728691	+	4.13261i	0.0261585	+	0.148352i
$777$	−5.23144	+	19.7063i	−0.187677	+	0.706959i
$778$	3.12316	+	8.58082i	0.111971	+	0.307637i
$779$	5.12139	−	29.0449i	0.183493	−	1.04064i
$780$		0			0
$781$	−5.65365	+	4.74398i	−0.202304	+	0.169753i
$782$			4.22695i			0.151155i
$783$	−27.2902	−	18.8278i	−0.975271	−	0.672852i
$784$	1.03921			0.0371145
$785$		0			0
$786$	3.94973	+	5.61312i	0.140882	+	0.200213i
$787$	38.1836	+	6.73280i	1.36110	+	0.239998i	0.806063	−	0.591829i	$-0.201594\pi$
$787$	38.1836	+	6.73280i	1.36110	+	0.239998i	0.555034	+	0.831827i	$0.312705\pi$
$788$	15.5196	+	42.6399i	0.552864	+	1.51898i
$789$	0.526917	+	1.94844i	0.0187588	+	0.0693663i
$790$		0			0
$791$	14.8112	+	25.6538i	0.526626	+	0.912143i
$792$	−6.20749	+	2.29193i	−0.220574	+	0.0814401i
$793$	−11.4157	−	6.59086i	−0.405384	−	0.234048i
$794$	−2.02159	−	0.735798i	−0.0717435	−	0.0261125i
$795$		0			0
$796$	11.6308	+	9.75940i	0.412243	+	0.345913i
$797$	−28.1529	+	33.5513i	−0.997228	+	1.18845i	−0.0151670	+	0.999885i	$0.504828\pi$
$797$	−28.1529	+	33.5513i	−0.997228	+	1.18845i	−0.982061	+	0.188565i	$0.939616\pi$
$798$	5.05273	+	0.430280i	0.178865	+	0.0152317i
$799$	−21.1573	−	7.70063i	−0.748491	−	0.272429i
$800$		0			0
$801$	29.5031	+	34.8318i	1.04244	+	1.23072i
$802$	5.97898	−	3.45196i	0.211125	−	0.121893i
$803$	11.0743	−	1.95269i	0.390802	−	0.0689089i
$804$	−12.6313	+	12.6898i	−0.445470	+	0.447536i
$805$		0			0
$806$	−0.419790	+	2.38074i	−0.0147865	+	0.0838582i
$807$	−0.603338	−	6.71716i	−0.0212385	−	0.236455i
$808$	−9.19742	−	10.9611i	−0.323564	−	0.385608i
$809$	20.1808			0.709518			0.354759	−	0.934958i	$-0.384563\pi$
$809$	20.1808			0.709518			0.354759	+	0.934958i	$0.384563\pi$
$810$		0			0
$811$	−9.77975			−0.343413			−0.171707	−	0.985148i	$-0.554928\pi$
$811$	−9.77975			−0.343413			−0.171707	+	0.985148i	$0.554928\pi$
$812$	−20.5654	−	24.5089i	−0.721703	−	0.860093i
$813$	−0.156771	−	1.74538i	−0.00549820	−	0.0612132i
$814$	−0.442200	+	2.50784i	−0.0154991	+	0.0878998i
$815$		0			0
$816$	10.4122	−	10.4605i	0.364501	−	0.366192i
$817$	−26.9893	+	4.75894i	−0.944236	+	0.166494i
$818$	0.456385	−	0.263494i	0.0159571	−	0.00921285i
$819$	−3.80553	+	10.6081i	−0.132976	+	0.370677i
$820$		0			0
$821$	−5.74874	−	2.09237i	−0.200632	−	0.0730242i	0.239749	−	0.970835i	$-0.422935\pi$
$821$	−5.74874	−	2.09237i	−0.200632	−	0.0730242i	−0.440382	+	0.897811i	$0.645157\pi$
$822$	5.28056	+	0.449681i	0.184181	+	0.0156844i
$823$	27.7805	−	33.1075i	0.968366	−	1.15405i	−0.0196667	−	0.999807i	$-0.506261\pi$
$823$	27.7805	−	33.1075i	0.968366	−	1.15405i	0.988032	−	0.154247i	$-0.0492950\pi$
$824$	−6.61885	−	5.55387i	−0.230578	−	0.193478i
$825$		0			0
$826$	−2.04265	−	0.743463i	−0.0710728	−	0.0258684i
$827$	−2.44008	−	1.40878i	−0.0848499	−	0.0489881i	0.456975	−	0.889480i	$-0.348933\pi$
$827$	−2.44008	−	1.40878i	−0.0848499	−	0.0489881i	−0.541825	+	0.840492i	$0.682266\pi$
$828$	−6.92590	+	40.3702i	−0.240692	+	1.40296i
$829$	10.5567	+	18.2847i	0.366649	+	0.635054i	0.989039	−	0.147653i	$-0.0471718\pi$
$829$	10.5567	+	18.2847i	0.366649	+	0.635054i	−0.622391	+	0.782707i	$0.713838\pi$
$830$		0			0
$831$	14.0123	+	51.8148i	0.486081	+	1.79743i
$832$	3.21841	+	8.84252i	0.111578	+	0.306559i
$833$	−0.666869	−	0.117587i	−0.0231057	−	0.00407415i
$834$	4.51832	+	6.42116i	0.156457	+	0.222347i
$835$		0			0
$836$	−18.9587			−0.655701
$837$	33.9200	−	3.20500i	1.17245	−	0.110781i
$838$			6.57831i			0.227244i
$839$	−21.2831	+	17.8586i	−0.734774	+	0.616549i	−0.931429	−	0.363924i	$-0.881437\pi$
$839$	−21.2831	+	17.8586i	−0.734774	+	0.616549i	0.196655	+	0.980473i	$0.436992\pi$
$840$		0			0
$841$	2.03387	−	11.5347i	0.0701335	−	0.397747i
$842$	0.867945	+	2.38466i	0.0299114	+	0.0821808i
$843$	1.27265	−	4.79395i	0.0438325	−	0.165112i
$844$	−1.69516	−	9.61373i	−0.0583498	−	0.330918i
$845$		0			0
$846$	6.32898	+	3.61510i	0.217595	+	0.124290i
$847$	−13.7795	−	7.95559i	−0.473469	−	0.273357i
$848$	16.5343	−	45.4276i	0.567790	−	1.55999i
$849$	−35.0130	−	24.3958i	−1.20164	−	0.837263i
$850$		0			0
$851$	24.5539	+	20.6031i	0.841696	+	0.706267i
$852$	−6.41630	+	9.20869i	−0.219819	+	0.315485i
$853$	14.0482	−	38.5970i	0.481000	−	1.32154i	−0.427637	−	0.903950i	$-0.640654\pi$
$853$	14.0482	−	38.5970i	0.481000	−	1.32154i	0.908637	−	0.417586i	$-0.137124\pi$
$854$	2.99455	−	5.18671i	0.102471	−	0.177486i
$855$		0			0
$856$	2.83814	+	4.91581i	0.0970057	+	0.168019i
$857$	9.34103	−	1.64708i	0.319084	−	0.0562630i	−0.0118126	−	0.999930i	$-0.503760\pi$
$857$	9.34103	−	1.64708i	0.319084	−	0.0562630i	0.330896	+	0.943667i	$0.392649\pi$
$858$	−0.361169	+	1.36048i	−0.0123301	+	0.0464461i
$859$	−29.4183	+	10.7074i	−1.00374	+	0.365332i	−0.791026	−	0.611783i	$-0.790453\pi$
$859$	−29.4183	+	10.7074i	−1.00374	+	0.365332i	−0.212715	+	0.977114i	$0.568231\pi$
$860$		0			0
$861$	−12.5234	+	27.0196i	−0.426798	+	0.920827i
$862$	0.395435	+	0.471261i	0.0134686	+	0.0160512i
$863$		−	34.9043i		−	1.18816i	−0.804407	−	0.594078i	$-0.797517\pi$
$863$		−	34.9043i		−	1.18816i	0.804407	−	0.594078i	$-0.202483\pi$
$864$	−12.3716	+	8.79126i	−0.420889	+	0.299085i
$865$		0			0
$866$	−3.85830	+	3.23750i	−0.131110	+	0.110015i
$867$	16.2154	−	11.4102i	0.550705	−	0.387509i
$868$	32.3787	+	5.70924i	1.09901	+	0.193784i
$869$	−8.49389	+	3.09152i	−0.288136	+	0.104873i
$870$		0			0
$871$	1.34486	+	7.62709i	0.0455689	+	0.258434i
$872$	−16.4297	+	9.48572i	−0.556381	+	0.321227i
$873$	2.12729	−	12.3997i	0.0719980	−	0.419667i
$874$	3.98601	−	6.90398i	0.134829	−	0.233531i
$875$		0			0
$876$	15.4819	−	7.26300i	0.523086	−	0.245394i
$877$	11.1162	−	13.2477i	0.375366	−	0.447344i	−0.544980	−	0.838449i	$-0.683463\pi$
$877$	11.1162	−	13.2477i	0.375366	−	0.447344i	0.920346	+	0.391105i	$0.127907\pi$
$878$	0.656644	−	0.782558i	0.0221607	−	0.0264101i
$879$	0.852602	−	10.0120i	0.0287576	−	0.337697i
$880$		0			0
$881$	10.5256	−	18.2309i	0.354618	−	0.614216i	−0.632435	−	0.774614i	$-0.717944\pi$
$881$	10.5256	−	18.2309i	0.354618	−	0.614216i	0.987052	+	0.160398i	$0.0512777\pi$
$882$	0.206337	+	0.0740209i	0.00694771	+	0.00249241i
$883$	27.1348	−	15.6663i	0.913158	−	0.527212i	0.0317123	−	0.999497i	$-0.489904\pi$
$883$	27.1348	−	15.6663i	0.913158	−	0.527212i	0.881446	+	0.472285i	$0.156571\pi$
$884$	−1.14824	−	6.51200i	−0.0386195	−	0.219022i
$885$		0			0
$886$	−1.19788	+	0.435991i	−0.0402434	+	0.0146474i
$887$	29.5237	+	5.20582i	0.991309	+	0.174794i	0.645706	−	0.763586i	$-0.276563\pi$
$887$	29.5237	+	5.20582i	0.991309	+	0.174794i	0.345603	+	0.938381i	$0.387674\pi$
$888$	0.704466	+	7.84304i	0.0236403	+	0.263195i
$889$	−6.55830	+	5.50306i	−0.219958	+	0.184567i
$890$		0			0
$891$	19.8375	−	0.183592i	0.664581	−	0.00615055i
$892$		−	36.5460i		−	1.22365i
$893$	27.2950	+	32.5289i	0.913393	+	1.08854i
$894$	−9.40094	+	0.844397i	−0.314414	+	0.0282409i
$895$		0			0
$896$	−18.2398	+	6.63874i	−0.609349	+	0.221785i
$897$	12.5570	+	12.4990i	0.419266	+	0.417331i
$898$	−4.74791	+	0.837184i	−0.158440	+	0.0279372i
$899$	20.9189	+	36.2325i	0.697683	+	1.20842i
$900$		0			0
$901$	−15.7504	+	27.2805i	−0.524722	+	0.908846i
$902$	−1.27217	+	3.49525i	−0.0423585	+	0.116379i
$903$	27.5734	+	2.34809i	0.917584	+	0.0781395i
$904$	8.76418	+	7.35402i	0.291492	+	0.244591i
$905$		0			0
$906$	3.07421	−	1.44219i	0.102134	−	0.0479137i
$907$	−7.49886	+	20.6029i	−0.248995	+	0.684109i	0.750728	+	0.660611i	$0.229703\pi$
$907$	−7.49886	+	20.6029i	−0.248995	+	0.684109i	−0.999724	+	0.0234984i	$0.992520\pi$
$908$	6.27106	+	3.62060i	0.208112	+	0.120154i
$909$	14.8583	+	40.2426i	0.492820	+	1.33476i
$910$		0			0
$911$	−4.98714	−	28.2835i	−0.165231	−	0.937073i	−0.948826	−	0.315800i	$-0.897727\pi$
$911$	−4.98714	−	28.2835i	−0.165231	−	0.937073i	0.783594	−	0.621273i	$-0.213384\pi$
$912$	−26.8708	+	7.26669i	−0.889781	+	0.240624i
$913$	2.61392	+	7.18168i	0.0865080	+	0.237679i
$914$	0.502604	−	2.85041i	0.0166247	−	0.0942832i
$915$		0			0
$916$	−12.4783	+	10.4705i	−0.412295	+	0.345956i
$917$		−	40.3766i		−	1.33335i
$918$	2.81246	−	1.33531i	0.0928250	−	0.0440719i
$919$	1.97798			0.0652474			0.0326237	−	0.999468i	$-0.489614\pi$
$919$	1.97798			0.0652474			0.0326237	+	0.999468i	$0.489614\pi$
$920$		0			0
$921$	−22.5503	+	48.6529i	−0.743059	+	1.60317i
$922$	−1.09269	−	0.192671i	−0.0359858	−	0.00634527i
$923$	1.66044	+	4.56201i	0.0546539	+	0.150160i
$924$	18.5029	+	4.91198i	0.608701	+	0.161592i
$925$		0			0
$926$	−0.920900	−	1.59505i	−0.0302626	−	0.0524164i
$927$	13.0557	+	22.3733i	0.428804	+	0.734837i
$928$	−16.1399	−	9.31835i	−0.529817	−	0.305890i
$929$	3.58721	+	1.30564i	0.117693	+	0.0428366i	0.400195	−	0.916430i	$-0.368942\pi$
$929$	3.58721	+	1.30564i	0.117693	+	0.0428366i	−0.282502	+	0.959267i	$0.591165\pi$
$930$		0			0
$931$	0.978329	+	0.820915i	0.0320634	+	0.0269044i
$932$	−13.9869	+	16.6689i	−0.458155	+	0.546008i
$933$	−9.62687	+	13.8165i	−0.315170	+	0.452333i
$934$	0.856025	+	0.311568i	0.0280100	+	0.0101948i
$935$		0			0
$936$	0.0201412	+	4.35269i	0.000658334	+	0.142272i
$937$	−35.8550	+	20.7009i	−1.17133	+	0.676269i	−0.953994	−	0.299827i	$-0.903071\pi$
$937$	−35.8550	+	20.7009i	−1.17133	+	0.676269i	−0.217339	+	0.976096i	$0.569738\pi$
$938$	−3.46536	+	0.611036i	−0.113148	+	0.0199510i
$939$	20.3328	+	5.39776i	0.663535	+	0.176149i
$940$		0			0
$941$	2.51391	−	14.2571i	0.0819512	−	0.464768i	−0.916022	−	0.401129i	$-0.868618\pi$
$941$	2.51391	−	14.2571i	0.0819512	−	0.464768i	0.997973	−	0.0636397i	$-0.0202708\pi$
$942$	−0.309569	−	0.143483i	−0.0100863	−	0.00467494i
$943$	30.0938	+	35.8644i	0.979990	+	1.16791i
$944$	11.9322			0.388359
$945$		0			0
$946$	3.45633			0.112375
$947$	13.6373	+	16.2523i	0.443152	+	0.528128i	0.940669	−	0.339326i	$-0.110199\pi$
$947$	13.6373	+	16.2523i	0.443152	+	0.528128i	−0.497517	+	0.867454i	$0.665755\pi$
$948$	−11.2418	+	7.91043i	−0.365117	+	0.256919i
$949$	1.28448	−	7.28466i	0.0416961	−	0.236470i
$950$		0			0
$951$	2.39192	+	8.84485i	0.0775632	+	0.286814i
$952$	6.01627	−	1.06083i	0.194989	−	0.0343817i
$953$	22.1452	−	12.7855i	0.717354	−	0.414165i	−0.0964240	−	0.995340i	$-0.530740\pi$
$953$	22.1452	−	12.7855i	0.717354	−	0.414165i	0.813778	+	0.581176i	$0.197407\pi$
$954$	6.51866	−	7.84204i	0.211049	−	0.253896i
$955$		0			0
$956$	32.8134	+	11.9431i	1.06126	+	0.386267i
$957$	10.3463	+	22.0543i	0.334448	+	0.712915i
$958$	0.310084	−	0.369544i	0.0100184	−	0.0119394i
$959$	−23.8830	−	20.0402i	−0.771221	−	0.647131i
$960$		0			0
$961$	−11.2706	−	4.10216i	−0.363567	−	0.132328i
$962$	1.45069	+	0.837556i	0.0467721	+	0.0270039i
$963$	−3.03262	−	16.7454i	−0.0977248	−	0.539612i
$964$	−14.7495	−	25.5468i	−0.475049	−	0.822808i
$965$		0			0
$966$	−5.67892	+	5.70525i	−0.182716	+	0.183564i
$967$	19.1595	+	52.6404i	0.616129	+	1.69280i	0.716266	+	0.697827i	$0.245850\pi$
$967$	19.1595	+	52.6404i	0.616129	+	1.69280i	−0.100137	+	0.994974i	$0.531928\pi$
$968$	−6.05189	−	1.06711i	−0.194515	−	0.0342982i
$969$	18.0655	−	1.62265i	0.580348	−	0.0521272i
$970$		0			0
$971$	−13.1661			−0.422521			−0.211261	−	0.977430i	$-0.567757\pi$
$971$	−13.1661			−0.422521			−0.211261	+	0.977430i	$0.567757\pi$
$972$	29.0488	−	8.14490i	0.931740	−	0.261248i
$973$		−	46.1891i		−	1.48076i
$974$	−2.65771	+	2.23009i	−0.0851587	+	0.0714566i
$975$		0			0
$976$	−5.70878	+	32.3761i	−0.182734	+	1.03633i
$977$	−19.4053	−	53.3156i	−0.620831	−	1.70572i	−0.704945	−	0.709262i	$-0.749028\pi$
$977$	−19.4053	−	53.3156i	−0.620831	−	1.70572i	0.0841143	−	0.996456i	$-0.473194\pi$
$978$	−5.09022	−	5.06672i	−0.162767	−	0.162016i
$979$	−5.82409	−	33.0301i	−0.186139	−	1.05565i
$980$		0			0
$981$	55.9668	−	10.1357i	1.78688	−	0.323608i
$982$	−8.67940	−	5.01106i	−0.276971	−	0.159909i
$983$	−11.4913	+	31.5720i	−0.366515	+	1.00699i	0.610162	+	0.792277i	$0.291104\pi$
$983$	−11.4913	+	31.5720i	−0.366515	+	1.00699i	−0.976677	+	0.214715i	$0.931118\pi$
$984$	−0.975953	+	11.4605i	−0.0311122	+	0.365348i
$985$		0			0
$986$	2.92864	+	2.45742i	0.0932668	+	0.0782601i
$987$	−18.2109	−	38.8186i	−0.579659	−	1.23561i
$988$	−4.26536	+	11.7190i	−0.135699	+	0.372831i
$989$	21.7522	−	37.6758i	0.691678	−	1.19802i
$990$		0			0
$991$	10.8153	+	18.7327i	0.343559	+	0.595062i	0.985091	−	0.172034i	$-0.0550340\pi$
$991$	10.8153	+	18.7327i	0.343559	+	0.595062i	−0.641532	+	0.767097i	$0.721701\pi$
$992$	18.8608	−	3.32566i	0.598830	−	0.105590i
$993$	−42.0190	+	11.3632i	−1.33343	+	0.360601i
$994$	−2.07274	+	0.754416i	−0.0657434	+	0.0239286i
$995$		0			0
$996$	6.68836	+	9.50508i	0.211929	+	0.301180i
$997$	−22.1024	−	26.3406i	−0.699989	−	0.834214i	0.292536	−	0.956254i	$-0.405501\pi$
$997$	−22.1024	−	26.3406i	−0.699989	−	0.834214i	−0.992525	+	0.122040i	$0.961056\pi$
$998$			6.64065i			0.210206i
$999$	5.95189	−	22.8459i	0.188310	−	0.722812i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.u.e.49.12		132
5.2	odd	4		675.2.l.g.76.6	yes	66
5.3	odd	4		675.2.l.f.76.6	✓	66
5.4	even	2	inner	675.2.u.e.49.11		132
27.16	even	9	inner	675.2.u.e.124.11		132
135.43	odd	36		675.2.l.f.151.6	yes	66
135.97	odd	36		675.2.l.g.151.6	yes	66
135.124	even	18	inner	675.2.u.e.124.12		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
675.2.l.f.76.6	✓	66	5.3	odd	4
675.2.l.f.151.6	yes	66	135.43	odd	36
675.2.l.g.76.6	yes	66	5.2	odd	4
675.2.l.g.151.6	yes	66	135.97	odd	36
675.2.u.e.49.11		132	5.4	even	2	inner
675.2.u.e.49.12		132	1.1	even	1	trivial
675.2.u.e.124.11		132	27.16	even	9	inner
675.2.u.e.124.12		132	135.124	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.163444 + 0.194784i) q^{2} +(0.154950 + 1.72511i) q^{3} +(0.336069 - 1.90594i) q^{4} +(-0.310698 + 0.312139i) q^{6} +(2.55151 - 0.449901i) q^{7} +(0.866590 - 0.500326i) q^{8} +(-2.95198 + 0.534610i) q^{9} +(2.07133 + 0.753901i) q^{11} +(3.34003 + 0.284429i) q^{12} +(0.932020 - 1.11074i) q^{13} +(0.504662 + 0.423462i) q^{14} +(-3.39816 - 1.23683i) q^{16} +(2.04069 + 1.17819i) q^{17} +(-0.586616 - 0.487621i) q^{18} +(-2.22207 - 3.84874i) q^{19} +(1.17148 + 4.33192i) q^{21} +(0.191697 + 0.526682i) q^{22} +(6.94755 + 1.22504i) q^{23} +(0.997394 + 1.41743i) q^{24} +0.368687 q^{26} +(-1.37967 - 5.00964i) q^{27} -5.01424i q^{28} +(4.88786 - 4.10140i) q^{29} +(-1.13861 + 6.45736i) q^{31} +(-0.998979 - 2.74467i) q^{32} +(-0.979608 + 3.69007i) q^{33} +(0.104044 + 0.590063i) q^{34} +(0.0268659 + 5.80597i) q^{36} +(3.93474 + 2.27172i) q^{37} +(0.386492 - 1.06188i) q^{38} +(2.06056 + 1.43572i) q^{39} +(5.08374 + 4.26577i) q^{41} +(-0.652319 + 0.936211i) q^{42} +(2.10913 - 5.79479i) q^{43} +(2.13300 - 3.69447i) q^{44} +(0.896913 + 1.55350i) q^{46} +(-9.40977 + 1.65920i) q^{47} +(1.60712 - 6.05384i) q^{48} +(-0.270040 + 0.0982866i) q^{49} +(-1.71630 + 3.70297i) q^{51} +(-1.80378 - 2.14966i) q^{52} +13.3683i q^{53} +(0.750303 - 1.08753i) q^{54} +(1.98602 - 1.66647i) q^{56} +(6.29518 - 4.42967i) q^{57} +(1.59778 + 0.281731i) q^{58} +(-3.10061 + 1.12853i) q^{59} +(-1.57865 - 8.95295i) q^{61} +(-1.44389 + 0.833631i) q^{62} +(-7.29150 + 2.69216i) q^{63} +(-3.24491 + 5.62035i) q^{64} +(-0.878880 + 0.412306i) q^{66} +(-3.43334 + 4.09170i) q^{67} +(2.93138 - 3.49349i) q^{68} +(-1.03680 + 12.1751i) q^{69} +(-1.67410 + 2.89963i) q^{71} +(-2.29068 + 1.94024i) q^{72} +(4.41805 - 2.55076i) q^{73} +(0.200612 + 1.13773i) q^{74} +(-8.08225 + 2.94170i) q^{76} +(5.62420 + 0.991698i) q^{77} +(0.0571280 + 0.636024i) q^{78} +(-3.14132 + 2.63588i) q^{79} +(8.42838 - 3.15632i) q^{81} +1.68745i q^{82} +(2.22867 + 2.65602i) q^{83} +(8.65009 - 0.776955i) q^{84} +(1.47346 - 0.536295i) q^{86} +(7.83272 + 7.79656i) q^{87} +(2.17219 - 0.383015i) q^{88} +(-7.60791 - 13.1773i) q^{89} +(1.87834 - 3.25338i) q^{91} +(4.66971 - 12.8299i) q^{92} +(-11.3161 - 0.963650i) q^{93} +(-1.86115 - 1.56169i) q^{94} +(4.58006 - 2.14863i) q^{96} +(-1.43431 + 3.94072i) q^{97} +(-0.0632810 - 0.0365353i) q^{98} +(-6.51756 - 1.11815i) 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

Related objects

Downloads

Learn more