LMFDB - Embedded newform 950.2.u.g.149.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(99,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("950.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.u (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			149.5
Character	$\chi$	$=$	950.149
Dual form			950.2.u.g.899.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.642788 - 0.766044i) q^{2} +(0.197144 + 0.541649i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(0.541649 + 0.197144i) q^{6} +(-4.21251 + 2.43209i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(2.04362 - 1.71480i) q^{9} +O(q^{10})$	\(q+(0.642788 - 0.766044i) q^{2} +(0.197144 + 0.541649i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(0.541649 + 0.197144i) q^{6} +(-4.21251 + 2.43209i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(2.04362 - 1.71480i) q^{9} +(2.68454 - 4.64975i) q^{11} +(0.499186 - 0.288205i) q^{12} +(1.31923 - 3.62457i) q^{13} +(-0.844657 + 4.79029i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(-0.901248 + 1.07407i) q^{17} -2.66775i q^{18} +(-4.35299 + 0.226908i) q^{19} +(-2.14781 - 1.80223i) q^{21} +(-1.83633 - 5.04528i) q^{22} +(5.25780 - 0.927092i) q^{23} +(0.100093 - 0.567654i) q^{24} +(-1.92859 - 3.34042i) q^{26} +(2.82926 + 1.63348i) q^{27} +(3.12664 + 3.72618i) q^{28} +(2.78364 - 2.33575i) q^{29} +(-4.10189 - 7.10468i) q^{31} +(-0.342020 + 0.939693i) q^{32} +(3.04777 + 0.537405i) q^{33} +(0.243471 + 1.38079i) q^{34} +(-2.04362 - 1.71480i) q^{36} -10.4594i q^{37} +(-2.62423 + 3.48044i) q^{38} +2.22332 q^{39} +(1.79322 - 0.652678i) q^{41} +(-2.76117 + 0.486869i) q^{42} +(-1.45618 - 0.256764i) q^{43} +(-5.04528 - 1.83633i) q^{44} +(2.66945 - 4.62363i) q^{46} +(-2.00570 - 2.39030i) q^{47} +(-0.370510 - 0.441556i) q^{48} +(8.33016 - 14.4283i) q^{49} +(-0.759442 - 0.276414i) q^{51} +(-3.79858 - 0.669793i) q^{52} +(-1.77266 + 0.312568i) q^{53} +(3.06993 - 1.11736i) q^{54} +4.86419 q^{56} +(-0.981070 - 2.31306i) q^{57} -3.63378i q^{58} +(5.61133 + 4.70846i) q^{59} +(1.40916 + 7.99176i) q^{61} +(-8.07914 - 1.42457i) q^{62} +(-4.43820 + 12.1939i) q^{63} +(0.500000 + 0.866025i) q^{64} +(2.37075 - 1.98929i) q^{66} +(5.42827 + 6.46916i) q^{67} +(1.21425 + 0.701047i) q^{68} +(1.53870 + 2.66511i) q^{69} +(1.04647 - 5.93485i) q^{71} +(-2.62722 + 0.463250i) q^{72} +(-0.436515 - 1.19931i) q^{73} +(-8.01234 - 6.72316i) q^{74} +(0.979350 + 4.24746i) q^{76} +26.1162i q^{77} +(1.42912 - 1.70316i) q^{78} +(-15.6290 + 5.68848i) q^{79} +(1.06275 - 6.02717i) q^{81} +(0.652678 - 1.79322i) q^{82} +(-12.5236 + 7.23049i) q^{83} +(-1.40188 + 2.42814i) q^{84} +(-1.13271 + 0.950453i) q^{86} +(1.81393 + 1.04727i) q^{87} +(-4.64975 + 2.68454i) q^{88} +(9.02905 + 3.28630i) q^{89} +(3.25800 + 18.4770i) q^{91} +(-1.82601 - 5.01693i) q^{92} +(3.03958 - 3.62243i) q^{93} -3.12031 q^{94} -0.576411 q^{96} +(3.90758 - 4.65687i) q^{97} +(-5.69817 - 15.6556i) q^{98} +(-2.48722 - 14.1057i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 36 q^{9}+O(q^{10}) $ 36 * q + 36 * q^9	$ 36 q + 36 q^{9} - 24 q^{11} - 12 q^{14} + 24 q^{21} - 18 q^{26} + 12 q^{29} - 12 q^{31} - 36 q^{34} - 36 q^{36} - 96 q^{39} - 42 q^{41} - 6 q^{44} + 36 q^{46} + 78 q^{49} + 84 q^{51} + 108 q^{54} + 60 q^{59} + 96 q^{61} + 18 q^{64} + 48 q^{66} + 60 q^{69} + 60 q^{71} + 6 q^{74} - 42 q^{76} - 60 q^{79} + 36 q^{81} - 12 q^{84} + 72 q^{86} - 60 q^{89} - 120 q^{91} - 12 q^{94} - 342 q^{99}+O(q^{100}) $ 36 * q + 36 * q^9 - 24 * q^11 - 12 * q^14 + 24 * q^21 - 18 * q^26 + 12 * q^29 - 12 * q^31 - 36 * q^34 - 36 * q^36 - 96 * q^39 - 42 * q^41 - 6 * q^44 + 36 * q^46 + 78 * q^49 + 84 * q^51 + 108 * q^54 + 60 * q^59 + 96 * q^61 + 18 * q^64 + 48 * q^66 + 60 * q^69 + 60 * q^71 + 6 * q^74 - 42 * q^76 - 60 * q^79 + 36 * q^81 - 12 * q^84 + 72 * q^86 - 60 * q^89 - 120 * q^91 - 12 * q^94 - 342 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{2}{9}\right)$

Coefficient data

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

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

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

$2$	0.642788	−	0.766044i	0.454519	−	0.541675i
$2$	0.642788	−	0.766044i	0.454519	−	0.541675i
$3$	0.197144	+	0.541649i	0.113821	+	0.312721i	0.983503	−	0.180892i	$-0.0578983\pi$
$3$	0.197144	+	0.541649i	0.113821	+	0.312721i	−0.869682	+	0.493613i	$0.835676\pi$
$4$	−0.173648	−	0.984808i	−0.0868241	−	0.492404i
$5$		0			0
$5$		0			0
$6$	0.541649	+	0.197144i	0.221127	+	0.0804837i
$7$	−4.21251	+	2.43209i	−1.59218	+	0.919245i	−0.599247	+	0.800564i	$0.704533\pi$
$7$	−4.21251	+	2.43209i	−1.59218	+	0.919245i	−0.992932	+	0.118681i	$0.962134\pi$
$8$	−0.866025	−	0.500000i	−0.306186	−	0.176777i
$9$	2.04362	−	1.71480i	0.681205	−	0.571599i
$10$		0			0
$11$	2.68454	−	4.64975i	0.809418	−	1.40195i	−0.103850	−	0.994593i	$-0.533116\pi$
$11$	2.68454	−	4.64975i	0.809418	−	1.40195i	0.913268	−	0.407360i	$-0.133550\pi$
$12$	0.499186	−	0.288205i	0.144103	−	0.0831977i
$13$	1.31923	−	3.62457i	0.365890	−	1.00527i	−0.611019	−	0.791616i	$-0.709240\pi$
$13$	1.31923	−	3.62457i	0.365890	−	1.00527i	0.976909	−	0.213658i	$-0.0685377\pi$
$14$	−0.844657	+	4.79029i	−0.225744	+	1.28026i
$15$		0			0
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−0.901248	+	1.07407i	−0.218585	+	0.260499i	−0.864183	−	0.503178i	$-0.832164\pi$
$17$	−0.901248	+	1.07407i	−0.218585	+	0.260499i	0.645598	+	0.763678i	$0.276608\pi$
$18$		−	2.66775i		−	0.628795i
$19$	−4.35299	+	0.226908i	−0.998644	+	0.0520563i
$19$	−4.35299	+	0.226908i	−0.998644	+	0.0520563i
$20$		0			0
$21$	−2.14781	−	1.80223i	−0.468691	−	0.393278i
$22$	−1.83633	−	5.04528i	−0.391507	−	1.07566i
$23$	5.25780	−	0.927092i	1.09633	−	0.193312i	0.403902	−	0.914802i	$-0.367654\pi$
$23$	5.25780	−	0.927092i	1.09633	−	0.193312i	0.692425	+	0.721490i	$0.256543\pi$
$24$	0.100093	−	0.567654i	0.0204313	−	0.115872i
$25$		0			0
$26$	−1.92859	−	3.34042i	−0.378228	−	0.655110i
$27$	2.82926	+	1.63348i	0.544492	+	0.314363i
$28$	3.12664	+	3.72618i	0.590879	+	0.704183i
$29$	2.78364	−	2.33575i	0.516908	−	0.433738i	−0.346644	−	0.937997i	$-0.612679\pi$
$29$	2.78364	−	2.33575i	0.516908	−	0.433738i	0.863552	+	0.504259i	$0.168234\pi$
$30$		0			0
$31$	−4.10189	−	7.10468i	−0.736721	−	1.27604i	−0.953964	−	0.299920i	$-0.903040\pi$
$31$	−4.10189	−	7.10468i	−0.736721	−	1.27604i	0.217244	−	0.976117i	$-0.430293\pi$
$32$	−0.342020	+	0.939693i	−0.0604612	+	0.166116i
$33$	3.04777	+	0.537405i	0.530549	+	0.0935501i
$34$	0.243471	+	1.38079i	0.0417549	+	0.236804i
$35$		0			0
$36$	−2.04362	−	1.71480i	−0.340603	−	0.285800i
$37$		−	10.4594i		−	1.71951i	−0.510706	−	0.859755i	$-0.670616\pi$
$37$		−	10.4594i		−	1.71951i	0.510706	−	0.859755i	$-0.329384\pi$
$38$	−2.62423	+	3.48044i	−0.425706	+	0.564601i
$39$	2.22332			0.356016
$40$		0			0
$41$	1.79322	−	0.652678i	0.280054	−	0.101931i	−0.198175	−	0.980167i	$-0.563501\pi$
$41$	1.79322	−	0.652678i	0.280054	−	0.101931i	0.478228	+	0.878236i	$0.341279\pi$
$42$	−2.76117	+	0.486869i	−0.426058	+	0.0751256i
$43$	−1.45618	−	0.256764i	−0.222065	−	0.0391561i	0.0615084	−	0.998107i	$-0.480409\pi$
$43$	−1.45618	−	0.256764i	−0.222065	−	0.0391561i	−0.283574	+	0.958950i	$0.591520\pi$
$44$	−5.04528	−	1.83633i	−0.760604	−	0.276837i
$45$		0			0
$46$	2.66945	−	4.62363i	0.393590	−	0.681717i
$47$	−2.00570	−	2.39030i	−0.292561	−	0.348661i	0.599664	−	0.800252i	$-0.295301\pi$
$47$	−2.00570	−	2.39030i	−0.292561	−	0.348661i	−0.892225	+	0.451591i	$0.850857\pi$
$48$	−0.370510	−	0.441556i	−0.0534785	−	0.0637331i
$49$	8.33016	−	14.4283i	1.19002	−	2.06118i
$50$		0			0
$51$	−0.759442	−	0.276414i	−0.106343	−	0.0387058i
$52$	−3.79858	−	0.669793i	−0.526769	−	0.0928835i
$53$	−1.77266	+	0.312568i	−0.243494	+	0.0429346i	−0.294063	−	0.955786i	$-0.595008\pi$
$53$	−1.77266	+	0.312568i	−0.243494	+	0.0429346i	0.0505691	+	0.998721i	$0.483896\pi$
$54$	3.06993	−	1.11736i	0.417765	−	0.152054i
$55$		0			0
$56$	4.86419			0.650004
$57$	−0.981070	−	2.31306i	−0.129946	−	0.306372i
$58$		−	3.63378i		−	0.477139i
$59$	5.61133	+	4.70846i	0.730532	+	0.612990i	0.930277	−	0.366859i	$-0.119567\pi$
$59$	5.61133	+	4.70846i	0.730532	+	0.612990i	−0.199744	+	0.979848i	$0.564011\pi$
$60$		0			0
$61$	1.40916	+	7.99176i	0.180425	+	1.02324i	0.931694	+	0.363244i	$0.118331\pi$
$61$	1.40916	+	7.99176i	0.180425	+	1.02324i	−0.751269	+	0.659996i	$0.770558\pi$
$62$	−8.07914	−	1.42457i	−1.02605	−	0.180921i
$63$	−4.43820	+	12.1939i	−0.559161	+	1.53628i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$		0			0
$66$	2.37075	−	1.98929i	0.291819	−	0.244865i
$67$	5.42827	+	6.46916i	0.663169	+	0.790334i	0.987837	−	0.155494i	$-0.0496970\pi$
$67$	5.42827	+	6.46916i	0.663169	+	0.790334i	−0.324668	+	0.945828i	$0.605253\pi$
$68$	1.21425	+	0.701047i	0.147249	+	0.0850144i
$69$	1.53870	+	2.66511i	0.185238	+	0.320842i
$70$		0			0
$71$	1.04647	−	5.93485i	0.124194	−	0.704337i	−0.857590	−	0.514334i	$-0.828039\pi$
$71$	1.04647	−	5.93485i	0.124194	−	0.704337i	0.981783	−	0.190003i	$-0.0608498\pi$
$72$	−2.62722	+	0.463250i	−0.309621	+	0.0545945i
$73$	−0.436515	−	1.19931i	−0.0510902	−	0.140369i	0.911523	−	0.411249i	$-0.134907\pi$
$73$	−0.436515	−	1.19931i	−0.0510902	−	0.140369i	−0.962613	+	0.270880i	$0.912685\pi$
$74$	−8.01234	−	6.72316i	−0.931416	−	0.781551i
$75$		0			0
$76$	0.979350	+	4.24746i	0.112339	+	0.487217i
$77$			26.1162i			2.97621i
$78$	1.42912	−	1.70316i	0.161816	−	0.192845i
$79$	−15.6290	+	5.68848i	−1.75840	+	0.640004i	−0.999931	−	0.0117101i	$-0.996272\pi$
$79$	−15.6290	+	5.68848i	−1.75840	+	0.640004i	−0.758465	+	0.651714i	$0.774050\pi$
$80$		0			0
$81$	1.06275	−	6.02717i	0.118084	−	0.669685i
$82$	0.652678	−	1.79322i	0.0720762	−	0.198028i
$83$	−12.5236	+	7.23049i	−1.37464	+	0.793649i	−0.991508	−	0.130044i	$-0.958488\pi$
$83$	−12.5236	+	7.23049i	−1.37464	+	0.793649i	−0.383133	+	0.923693i	$0.625155\pi$
$84$	−1.40188	+	2.42814i	−0.152958	+	0.264931i
$85$		0			0
$86$	−1.13271	+	0.950453i	−0.122143	+	0.102490i
$87$	1.81393	+	1.04727i	0.194474	+	0.112280i
$88$	−4.64975	+	2.68454i	−0.495665	+	0.286172i
$89$	9.02905	+	3.28630i	0.957077	+	0.348348i	0.772887	−	0.634543i	$-0.218812\pi$
$89$	9.02905	+	3.28630i	0.957077	+	0.348348i	0.184190	+	0.982891i	$0.441034\pi$
$90$		0			0
$91$	3.25800	+	18.4770i	0.341531	+	1.93692i
$92$	−1.82601	−	5.01693i	−0.190375	−	0.523051i
$93$	3.03958	−	3.62243i	0.315189	−	0.375628i
$94$	−3.12031			−0.321836
$95$		0			0
$96$	−0.576411			−0.0588297
$97$	3.90758	−	4.65687i	0.396755	−	0.472834i	−0.530273	−	0.847827i	$-0.677911\pi$
$97$	3.90758	−	4.65687i	0.396755	−	0.472834i	0.927028	+	0.374993i	$0.122355\pi$
$98$	−5.69817	−	15.6556i	−0.575602	−	1.58145i
$99$	−2.48722	−	14.1057i	−0.249975	−	1.41768i
$100$		0			0
$101$	−1.17995	−	0.429466i	−0.117409	−	0.0427335i	0.282647	−	0.959224i	$-0.408787\pi$
$101$	−1.17995	−	0.429466i	−0.117409	−	0.0427335i	−0.400057	+	0.916490i	$0.631010\pi$
$102$	−0.699906	+	0.404091i	−0.0693010	+	0.0400109i
$103$	6.38005	+	3.68352i	0.628645	+	0.362948i	0.780227	−	0.625496i	$-0.215103\pi$
$103$	6.38005	+	3.68352i	0.628645	+	0.362948i	−0.151582	+	0.988445i	$0.548437\pi$
$104$	−2.95477	+	2.47935i	−0.289739	+	0.243120i
$105$		0			0
$106$	−0.900005	+	1.55885i	−0.0874162	+	0.151409i
$107$	−7.56108	+	4.36539i	−0.730957	+	0.422018i	−0.818772	−	0.574119i	$-0.805345\pi$
$107$	−7.56108	+	4.36539i	−0.730957	+	0.422018i	0.0878153	+	0.996137i	$0.472011\pi$
$108$	1.11736	−	3.06993i	0.107518	−	0.295404i
$109$	−1.41173	+	8.00630i	−0.135219	+	0.766865i	0.839488	+	0.543378i	$0.182855\pi$
$109$	−1.41173	+	8.00630i	−0.135219	+	0.766865i	−0.974707	+	0.223487i	$0.928256\pi$
$110$		0			0
$111$	5.66531	−	2.06200i	0.537727	−	0.195717i
$112$	3.12664	−	3.72618i	0.295440	−	0.352091i
$113$			4.48210i			0.421640i	0.977525	+	0.210820i	$0.0676134\pi$
$113$			4.48210i			0.421640i	−0.977525	+	0.210820i	$0.932387\pi$
$114$	−2.40253	−	0.735261i	−0.225017	−	0.0688635i
$115$		0			0
$116$	−2.78364	−	2.33575i	−0.258454	−	0.216869i
$117$	−3.51939	−	9.66944i	−0.325368	−	0.893940i
$118$	7.21378	−	1.27198i	0.664082	−	0.117096i
$119$	1.18429	−	6.71643i	0.108564	−	0.615694i
$120$		0			0
$121$	−8.91346	−	15.4386i	−0.810314	−	1.40351i
$122$	7.02784	+	4.05753i	0.636271	+	0.367351i
$123$	0.707045	+	0.842623i	0.0637521	+	0.0759768i
$124$	−6.28445	+	5.27328i	−0.564361	+	0.473555i
$125$		0			0
$126$	6.48822	+	11.2379i	0.578017	+	1.00115i
$127$	−0.0476033	+	0.130789i	−0.00422411	+	0.0116057i	−0.941787	−	0.336211i	$-0.890855\pi$
$127$	−0.0476033	+	0.130789i	−0.00422411	+	0.0116057i	0.937563	+	0.347816i	$0.113077\pi$
$128$	0.984808	+	0.173648i	0.0870455	+	0.0153485i
$129$	−0.148001	−	0.839357i	−0.0130308	−	0.0739013i
$130$		0			0
$131$	9.52200	+	7.98991i	0.831941	+	0.698082i	0.955736	−	0.294226i	$-0.0950620\pi$
$131$	9.52200	+	7.98991i	0.831941	+	0.698082i	−0.123795	+	0.992308i	$0.539506\pi$
$132$		−	3.09479i		−	0.269367i
$133$	17.7851	−	11.5427i	1.54217	−	1.00088i
$134$	8.44489			0.729528
$135$		0			0
$136$	1.31754	−	0.479544i	0.112978	−	0.0411206i
$137$	14.1631	−	2.49734i	1.21004	−	0.213362i	0.468004	−	0.883726i	$-0.344973\pi$
$137$	14.1631	−	2.49734i	1.21004	−	0.213362i	0.742032	+	0.670364i	$0.233862\pi$
$138$	3.03065	+	0.534386i	0.257986	+	0.0454899i
$139$	16.7746	+	6.10544i	1.42280	+	0.517857i	0.934859	−	0.355020i	$-0.115526\pi$
$139$	16.7746	+	6.10544i	1.42280	+	0.517857i	0.487941	+	0.872877i	$0.337748\pi$
$140$		0			0
$141$	0.899291	−	1.55762i	0.0757340	−	0.131175i
$142$	−3.87370	−	4.61650i	−0.325074	−	0.387408i
$143$	−13.3118	−	15.8644i	−1.11319	−	1.32665i
$144$	−1.33388	+	2.31034i	−0.111156	+	0.192528i
$145$		0			0
$146$	−1.19931	−	0.436515i	−0.0992559	−	0.0361262i
$147$	9.45729	+	1.66758i	0.780024	+	0.137539i
$148$	−10.3005	+	1.81625i	−0.846694	+	0.149295i
$149$	−2.71250	+	0.987271i	−0.222217	+	0.0808804i	−0.450729	−	0.892661i	$-0.648836\pi$
$149$	−2.71250	+	0.987271i	−0.222217	+	0.0808804i	0.228512	+	0.973541i	$0.426614\pi$
$150$		0			0
$151$	2.01805			0.164226			0.0821132	−	0.996623i	$-0.473833\pi$
$151$	2.01805			0.164226			0.0821132	+	0.996623i	$0.473833\pi$
$152$	3.88325	+	1.97999i	0.314973	+	0.160598i
$153$			3.74044i			0.302396i
$154$	20.0061	+	16.7871i	1.61214	+	1.35275i
$155$		0			0
$156$	−0.386076	−	2.18954i	−0.0309108	−	0.175304i
$157$	−10.8717	−	1.91697i	−0.867655	−	0.152991i	−0.277936	−	0.960600i	$-0.589650\pi$
$157$	−10.8717	−	1.91697i	−0.867655	−	0.152991i	−0.589719	+	0.807609i	$0.700761\pi$
$158$	−5.68848	+	15.6290i	−0.452551	+	1.24337i
$159$	−0.518772	−	0.898540i	−0.0411413	−	0.0712589i
$160$		0			0
$161$	−19.8938	+	16.6928i	−1.56785	+	1.31558i
$162$	−3.93395	−	4.68830i	−0.309081	−	0.368348i
$163$	−5.13439	−	2.96434i	−0.402157	−	0.232185i	0.285257	−	0.958451i	$-0.407921\pi$
$163$	−5.13439	−	2.96434i	−0.402157	−	0.232185i	−0.687414	+	0.726266i	$0.741254\pi$
$164$	−0.954151	−	1.65264i	−0.0745067	−	0.129049i
$165$		0			0
$166$	−2.51112	+	14.2413i	−0.194901	+	1.10534i
$167$	−7.11784	+	1.25507i	−0.550795	+	0.0971200i	−0.442118	−	0.896957i	$-0.645773\pi$
$167$	−7.11784	+	1.25507i	−0.550795	+	0.0971200i	−0.108677	+	0.994077i	$0.534661\pi$
$168$	0.958946	+	2.63468i	0.0739843	+	0.203270i
$169$	−1.43852	−	1.20707i	−0.110656	−	0.0928512i
$170$		0			0
$171$	−8.50673	+	7.92821i	−0.650526	+	0.606285i
$172$			1.47864i			0.112745i
$173$	−3.31585	+	3.95167i	−0.252099	+	0.300440i	−0.877221	−	0.480087i	$-0.840605\pi$
$173$	−3.31585	+	3.95167i	−0.252099	+	0.300440i	0.625121	+	0.780528i	$0.285049\pi$
$174$	1.96823	−	0.716378i	0.149211	−	0.0543085i
$175$		0			0
$176$	−0.932329	+	5.28750i	−0.0702770	+	0.398560i
$177$	−1.44409	+	3.96761i	−0.108545	+	0.298224i
$178$	8.32122	−	4.80426i	0.623701	−	0.360094i
$179$	4.09186	−	7.08730i	0.305840	−	0.529730i	−0.671608	−	0.740906i	$-0.734396\pi$
$179$	4.09186	−	7.08730i	0.305840	−	0.529730i	0.977448	+	0.211177i	$0.0677295\pi$
$180$		0			0
$181$	−2.62934	+	2.20628i	−0.195437	+	0.163991i	−0.735255	−	0.677791i	$-0.762938\pi$
$181$	−2.62934	+	2.20628i	−0.195437	+	0.163991i	0.539818	+	0.841782i	$0.318493\pi$
$182$	16.2484	+	9.38103i	1.20441	+	0.695368i
$183$	−4.05092	+	2.33880i	−0.299453	+	0.172889i
$184$	−5.01693	−	1.82601i	−0.369853	−	0.134616i
$185$		0			0
$186$	−0.821137	−	4.65690i	−0.0602087	−	0.341461i
$187$	2.57471	+	7.07395i	0.188281	+	0.517298i
$188$	−2.00570	+	2.39030i	−0.146281	+	0.174330i
$189$	−15.8911			−1.15591
$190$		0			0
$191$	3.77584			0.273210			0.136605	−	0.990626i	$-0.456381\pi$
$191$	3.77584			0.273210			0.136605	+	0.990626i	$0.456381\pi$
$192$	−0.370510	+	0.441556i	−0.0267392	+	0.0318666i
$193$	4.16508	+	11.4435i	0.299809	+	0.823718i	0.994531	+	0.104440i	$0.0333050\pi$
$193$	4.16508	+	11.4435i	0.299809	+	0.823718i	−0.694722	+	0.719278i	$0.744473\pi$
$194$	−1.05563	−	5.98676i	−0.0757896	−	0.429824i
$195$		0			0
$196$	−15.6556	−	5.69817i	−1.11826	−	0.407012i
$197$	6.23743	−	3.60118i	0.444399	−	0.256574i	−0.261063	−	0.965322i	$-0.584073\pi$
$197$	6.23743	−	3.60118i	0.444399	−	0.256574i	0.705462	+	0.708748i	$0.250740\pi$
$198$	−12.4044	−	7.16167i	−0.881541	−	0.508958i
$199$	−4.47147	+	3.75201i	−0.316974	+	0.265973i	−0.787367	−	0.616484i	$-0.788557\pi$
$199$	−4.47147	+	3.75201i	−0.316974	+	0.265973i	0.470393	+	0.882457i	$0.344112\pi$
$200$		0			0
$201$	−2.43386	+	4.21557i	−0.171671	+	0.297344i
$202$	−1.08745	+	0.627838i	−0.0765125	+	0.0441745i
$203$	−6.04534	+	16.6094i	−0.424299	+	1.16575i
$204$	−0.140339	+	0.795903i	−0.00982571	+	0.0557244i
$205$		0			0
$206$	6.92276	−	2.51968i	0.482332	−	0.175554i
$207$	9.15514	−	10.9107i	0.636327	−	0.758344i
$208$			3.85718i			0.267448i
$209$	−10.6307	+	20.8495i	−0.735340	+	1.44219i
$210$		0			0
$211$	8.17443	+	6.85916i	0.562751	+	0.472204i	0.879231	−	0.476395i	$-0.158057\pi$
$211$	8.17443	+	6.85916i	0.562751	+	0.472204i	−0.316481	+	0.948599i	$0.602501\pi$
$212$	0.615640	+	1.69146i	0.0422823	+	0.116170i
$213$	3.42091	−	0.603199i	0.234397	−	0.0413305i
$214$	−1.51608	+	8.59814i	−0.103637	+	0.587757i
$215$		0			0
$216$	−1.63348	−	2.82926i	−0.111144	−	0.192507i
$217$	34.5585	+	19.9523i	2.34598	+	1.35445i
$218$	5.22574	+	6.22780i	0.353932	+	0.421800i
$219$	0.563551	−	0.472875i	0.0380812	−	0.0319539i
$220$		0			0
$221$	2.70407	+	4.68358i	0.181895	+	0.315052i
$222$	2.06200	−	5.66531i	0.138393	−	0.380231i
$223$	0.0979573	+	0.0172725i	0.00655971	+	0.00115665i	0.176927	−	0.984224i	$-0.443384\pi$
$223$	0.0979573	+	0.0172725i	0.00655971	+	0.00115665i	−0.170367	+	0.985381i	$0.554495\pi$
$224$	−0.844657	−	4.79029i	−0.0564360	−	0.320065i
$225$		0			0
$226$	3.43349	+	2.88104i	0.228392	+	0.191644i
$227$		−	13.8262i		−	0.917680i	−0.888519	−	0.458840i	$-0.848265\pi$
$227$		−	13.8262i		−	0.917680i	0.888519	−	0.458840i	$-0.151735\pi$
$228$	−2.10756	+	1.36782i	−0.139576	+	0.0905864i
$229$	−15.5752			−1.02924			−0.514619	−	0.857419i	$-0.672066\pi$
$229$	−15.5752			−1.02924			−0.514619	+	0.857419i	$0.672066\pi$
$230$		0			0
$231$	−14.1458	+	5.14865i	−0.930725	+	0.338756i
$232$	−3.57857	+	0.630999i	−0.234945	+	0.0414271i
$233$	15.0095	+	2.64658i	0.983307	+	0.173384i	0.642113	−	0.766610i	$-0.278058\pi$
$233$	15.0095	+	2.64658i	0.983307	+	0.173384i	0.341193	+	0.939993i	$0.389169\pi$
$234$	−9.66944	−	3.51939i	−0.632111	−	0.230070i
$235$		0			0
$236$	3.66253	−	6.34369i	0.238411	−	0.412939i
$237$	−6.16232	−	7.34396i	−0.400285	−	0.477042i
$238$	−4.38384	−	5.22446i	−0.284162	−	0.338651i
$239$	8.41167	−	14.5694i	0.544106	−	0.942419i	−0.454557	−	0.890718i	$-0.650202\pi$
$239$	8.41167	−	14.5694i	0.544106	−	0.942419i	0.998663	−	0.0517011i	$-0.0164643\pi$
$240$		0			0
$241$	8.55776	+	3.11477i	0.551254	+	0.200640i	0.602604	−	0.798041i	$-0.294130\pi$
$241$	8.55776	+	3.11477i	0.551254	+	0.200640i	−0.0513496	+	0.998681i	$0.516352\pi$
$242$	−17.5561	−	3.09561i	−1.12855	−	0.198993i
$243$	13.1261	−	2.31448i	0.842039	−	0.148474i
$244$	7.62565	−	2.77551i	0.488182	−	0.177684i
$245$		0			0
$246$	1.09997			0.0701313
$247$	−4.92017	+	16.0770i	−0.313063	+	1.02296i
$248$			8.20377i			0.520940i
$249$	−6.38533	−	5.35793i	−0.404654	−	0.339545i
$250$		0			0
$251$	2.91829	+	16.5504i	0.184201	+	1.04465i	0.926978	+	0.375116i	$0.122397\pi$
$251$	2.91829	+	16.5504i	0.184201	+	1.04465i	−0.742777	+	0.669539i	$0.766492\pi$
$252$	12.7793	+	2.25334i	0.805020	+	0.141947i
$253$	9.80400	−	26.9363i	0.616372	−	1.69347i
$254$	0.0695914	+	0.120536i	0.00436655	+	0.00756309i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−6.36185	−	7.58176i	−0.396841	−	0.472937i	0.530213	−	0.847865i	$-0.322112\pi$
$257$	−6.36185	−	7.58176i	−0.396841	−	0.472937i	−0.927054	+	0.374927i	$0.877668\pi$
$258$	−0.738118	−	0.426153i	−0.0459532	−	0.0265311i
$259$	25.4382	+	44.0602i	1.58065	+	2.73777i
$260$		0			0
$261$	1.68335	−	9.54674i	0.104197	−	0.590929i
$262$	12.2412	−	2.15846i	0.756267	−	0.133350i
$263$	−7.66554	−	21.0609i	−0.472677	−	1.29867i	−0.915593	−	0.402107i	$-0.868278\pi$
$263$	−7.66554	−	21.0609i	−0.472677	−	1.29867i	0.442915	−	0.896564i	$-0.353944\pi$
$264$	−2.37075	−	1.98929i	−0.145909	−	0.122432i
$265$		0			0
$266$	2.58983	−	21.0437i	0.158793	−	1.29027i
$267$			5.53845i			0.338948i
$268$	5.42827	−	6.46916i	0.331584	−	0.395167i
$269$	7.02217	−	2.55586i	0.428149	−	0.155834i	−0.118952	−	0.992900i	$-0.537953\pi$
$269$	7.02217	−	2.55586i	0.428149	−	0.155834i	0.547101	+	0.837066i	$0.315731\pi$
$270$		0			0
$271$	−1.84950	+	10.4890i	−0.112349	+	0.637163i	0.875680	+	0.482893i	$0.160414\pi$
$271$	−1.84950	+	10.4890i	−0.112349	+	0.637163i	−0.988029	+	0.154271i	$0.950697\pi$
$272$	0.479544	−	1.31754i	0.0290766	−	0.0798874i
$273$	−9.36576	+	5.40733i	−0.566842	+	0.327266i
$274$	7.19080	−	12.4548i	0.434412	−	0.752424i
$275$		0			0
$276$	2.35743	−	1.97812i	0.141900	−	0.119069i
$277$	2.01467	+	1.16317i	0.121050	+	0.0698880i	0.559302	−	0.828964i	$-0.311069\pi$
$277$	2.01467	+	1.16317i	0.121050	+	0.0698880i	−0.438253	+	0.898852i	$0.644402\pi$
$278$	15.4595	−	8.92555i	0.927200	−	0.535319i
$279$	−20.5658	−	7.48532i	−1.23124	−	0.448135i
$280$		0			0
$281$	−2.96472	−	16.8137i	−0.176860	−	1.00302i	−0.935975	−	0.352067i	$-0.885479\pi$
$281$	−2.96472	−	16.8137i	−0.176860	−	1.00302i	0.759115	−	0.650957i	$-0.225632\pi$
$282$	−0.615151	−	1.69011i	−0.0366317	−	0.100645i
$283$	5.44307	−	6.48680i	0.323557	−	0.385600i	−0.579607	−	0.814896i	$-0.696794\pi$
$283$	5.44307	−	6.48680i	0.323557	−	0.385600i	0.903164	+	0.429296i	$0.141238\pi$
$284$	−6.02641			−0.357601
$285$		0			0
$286$	−20.7095			−1.22458
$287$	−5.96658	+	7.11069i	−0.352196	+	0.419731i
$288$	0.912424	+	2.50687i	0.0537651	+	0.147718i
$289$	2.61065	+	14.8057i	0.153568	+	0.870925i
$290$		0			0
$291$	3.29275	+	1.19846i	0.193024	+	0.0702551i
$292$	−1.10529	+	0.638142i	−0.0646824	+	0.0373444i
$293$	−2.24512	−	1.29622i	−0.131161	−	0.0757260i	0.432984	−	0.901402i	$-0.357461\pi$
$293$	−2.24512	−	1.29622i	−0.131161	−	0.0757260i	−0.564145	+	0.825676i	$0.690794\pi$
$294$	7.35647	−	6.17281i	0.429038	−	0.360006i
$295$		0			0
$296$	−5.22969	+	9.05808i	−0.303969	+	0.526490i
$297$	15.1905	−	8.77025i	0.881443	−	0.508901i
$298$	−0.987271	+	2.71250i	−0.0571911	+	0.157131i
$299$	3.57596	−	20.2803i	0.206803	−	1.17284i
$300$		0			0
$301$	6.75864	−	2.45994i	0.389562	−	0.141789i
$302$	1.29718	−	1.54591i	0.0746441	−	0.0889573i
$303$		−	0.723785i		−	0.0415804i
$304$	4.01286	−	1.70203i	0.230154	−	0.0976183i
$305$		0			0
$306$	2.86534	+	2.40431i	0.163801	+	0.137445i
$307$	1.40970	+	3.87311i	0.0804557	+	0.221050i	0.973398	−	0.229121i	$-0.0735852\pi$
$307$	1.40970	+	3.87311i	0.0804557	+	0.221050i	−0.892942	+	0.450171i	$0.851363\pi$
$308$	25.7194	−	4.53502i	1.46550	−	0.258407i
$309$	−0.737387	+	4.18193i	−0.0419485	+	0.237902i
$310$		0			0
$311$	−1.24153	−	2.15040i	−0.0704008	−	0.121938i	0.828676	−	0.559728i	$-0.189094\pi$
$311$	−1.24153	−	2.15040i	−0.0704008	−	0.121938i	−0.899077	+	0.437791i	$0.855761\pi$
$312$	−1.92545	−	1.11166i	−0.109007	−	0.0629354i
$313$	−3.45913	−	4.12243i	−0.195522	−	0.233014i	0.659372	−	0.751817i	$-0.270822\pi$
$313$	−3.45913	−	4.12243i	−0.195522	−	0.233014i	−0.854894	+	0.518803i	$0.826378\pi$
$314$	−8.45667	+	7.09599i	−0.477238	+	0.400450i
$315$		0			0
$316$	8.31600	+	14.4037i	0.467812	+	0.810273i
$317$	6.65753	−	18.2914i	0.373924	−	1.02735i	−0.599906	−	0.800071i	$-0.704795\pi$
$317$	6.65753	−	18.2914i	0.373924	−	1.02735i	0.973830	−	0.227278i	$-0.0729825\pi$
$318$	−1.02178	−	0.180168i	−0.0572987	−	0.0101033i
$319$	−3.38788	−	19.2136i	−0.189685	−	1.07576i
$320$		0			0
$321$	−3.85513	−	3.23484i	−0.215172	−	0.180551i
$322$			25.9695i			1.44722i
$323$	3.67941	−	4.87990i	0.204728	−	0.271525i
$324$	−6.12015			−0.340008
$325$		0			0
$326$	−5.57114	+	2.02773i	−0.308557	+	0.112306i
$327$	−4.61492	+	0.813735i	−0.255206	+	0.0449996i
$328$	−1.87931	−	0.331373i	−0.103768	−	0.0182970i
$329$	14.2625	+	5.19111i	0.786315	+	0.286195i
$330$		0			0
$331$	9.35511	−	16.2035i	0.514203	−	0.890626i	−0.485661	−	0.874147i	$-0.661421\pi$
$331$	9.35511	−	16.2035i	0.514203	−	0.890626i	0.999864	−	0.0164787i	$-0.00524557\pi$
$332$	9.29534	+	11.0778i	0.510148	+	0.607971i
$333$	−17.9357	−	21.3749i	−0.982870	−	1.17134i
$334$	−3.61382	+	6.25932i	−0.197739	+	0.342495i
$335$		0			0
$336$	2.63468	+	0.958946i	0.143734	+	0.0523148i
$337$	−24.7159	−	4.35808i	−1.34636	−	0.237400i	−0.546436	−	0.837501i	$-0.684016\pi$
$337$	−24.7159	−	4.35808i	−1.34636	−	0.237400i	−0.799924	+	0.600101i	$0.795127\pi$
$338$	−1.84933	+	0.326087i	−0.100590	+	0.0177368i
$339$	−2.42772	+	0.883619i	−0.131856	+	0.0479916i
$340$		0			0
$341$	−44.0466			−2.38526
$342$	0.605335	+	11.6127i	0.0327328	+	0.627942i
$343$			46.9896i			2.53720i
$344$	1.13271	+	0.950453i	0.0610714	+	0.0512450i
$345$		0			0
$346$	0.895772	+	5.08018i	0.0481570	+	0.273112i
$347$	22.4078	+	3.95111i	1.20292	+	0.212107i	0.738958	−	0.673751i	$-0.235318\pi$
$347$	22.4078	+	3.95111i	1.20292	+	0.212107i	0.463957	+	0.885857i	$0.346429\pi$
$348$	0.716378	−	1.96823i	0.0384019	−	0.105508i
$349$	6.58190	+	11.4002i	0.352321	+	0.610238i	0.986656	−	0.162820i	$-0.0520591\pi$
$349$	6.58190	+	11.4002i	0.352321	+	0.610238i	−0.634335	+	0.773059i	$0.718726\pi$
$350$		0			0
$351$	9.65310	−	8.09992i	0.515245	−	0.432341i
$352$	3.45117	+	4.11295i	0.183948	+	0.219221i
$353$	−10.6570	−	6.15281i	−0.567213	−	0.327481i	0.188822	−	0.982011i	$-0.439533\pi$
$353$	−10.6570	−	6.15281i	−0.567213	−	0.327481i	−0.756036	+	0.654530i	$0.772866\pi$
$354$	2.11112	+	3.65657i	0.112205	+	0.194345i
$355$		0			0
$356$	1.66850	−	9.46254i	0.0884304	−	0.501513i
$357$	3.87142	−	0.682636i	0.204897	−	0.0361290i
$358$	−2.79899	−	7.69017i	−0.147931	−	0.406438i
$359$	−9.62244	−	8.07418i	−0.507853	−	0.426139i	0.352520	−	0.935804i	$-0.385325\pi$
$359$	−9.62244	−	8.07418i	−0.507853	−	0.426139i	−0.860373	+	0.509665i	$0.829769\pi$
$360$		0			0
$361$	18.8970	−	1.97546i	0.994580	−	0.103972i
$362$			3.43236i			0.180401i
$363$	6.60504	−	7.87158i	0.346675	−	0.413151i
$364$	17.6306	−	6.41700i	0.924093	−	0.336342i
$365$		0			0
$366$	−0.812257	+	4.60654i	−0.0424574	+	0.240788i
$367$	0.918156	−	2.52261i	0.0479274	−	0.131679i	−0.913420	−	0.407019i	$-0.866568\pi$
$367$	0.918156	−	2.52261i	0.0479274	−	0.131679i	0.961347	+	0.275340i	$0.0887904\pi$
$368$	−4.62363	+	2.66945i	−0.241023	+	0.139155i
$369$	2.54544	−	4.40883i	0.132510	−	0.229514i
$370$		0			0
$371$	6.70717	−	5.62798i	0.348219	−	0.292190i
$372$	−4.09521	−	2.36437i	−0.212327	−	0.122587i
$373$	16.0582	−	9.27119i	0.831461	−	0.480044i	−0.0228917	−	0.999738i	$-0.507287\pi$
$373$	16.0582	−	9.27119i	0.831461	−	0.480044i	0.854353	+	0.519694i	$0.173954\pi$
$374$	7.07395	+	2.57471i	0.365785	+	0.133135i
$375$		0			0
$376$	0.541837	+	3.07291i	0.0279431	+	0.158473i
$377$	−4.79381	−	13.1709i	−0.246894	−	0.678334i
$378$	−10.2146	+	12.1733i	−0.525381	+	0.626125i
$379$	−11.5855			−0.595108			−0.297554	−	0.954705i	$-0.596171\pi$
$379$	−11.5855			−0.595108			−0.297554	+	0.954705i	$0.596171\pi$
$380$		0			0
$381$	−0.0802265			−0.00411013
$382$	2.42706	−	2.89246i	0.124179	−	0.147991i
$383$	9.94564	+	27.3254i	0.508199	+	1.39626i	0.883094	+	0.469197i	$0.155457\pi$
$383$	9.94564	+	27.3254i	0.508199	+	1.39626i	−0.374895	+	0.927067i	$0.622321\pi$
$384$	0.100093	+	0.567654i	0.00510783	+	0.0289680i
$385$		0			0
$386$	11.4435	+	4.16508i	0.582457	+	0.211997i
$387$	−3.41617	+	1.97233i	−0.173654	+	0.100259i
$388$	−5.26467	−	3.03956i	−0.267273	−	0.154310i
$389$	−22.8144	+	19.1436i	−1.15674	+	0.970618i	−0.999856	−	0.0169993i	$-0.994589\pi$
$389$	−22.8144	+	19.1436i	−1.15674	+	0.970618i	−0.156882	+	0.987617i	$0.550144\pi$
$390$		0			0
$391$	−3.74282	+	6.48276i	−0.189283	+	0.327847i
$392$	−14.4283	+	8.33016i	−0.728737	+	0.420737i
$393$	−2.45052	+	6.73274i	−0.123612	+	0.339622i
$394$	1.25068	−	7.09294i	0.0630082	−	0.357337i
$395$		0			0
$396$	−13.4595	+	4.89887i	−0.676367	+	0.246178i
$397$	−4.03025	+	4.80307i	−0.202273	+	0.241059i	−0.857639	−	0.514252i	$-0.828070\pi$
$397$	−4.03025	+	4.80307i	−0.202273	+	0.241059i	0.655367	+	0.755311i	$0.272514\pi$
$398$			5.83709i			0.292587i
$399$	9.75834	+	7.35772i	0.488528	+	0.368347i
$400$		0			0
$401$	7.58485	+	6.36445i	0.378769	+	0.317825i	0.812219	−	0.583353i	$-0.198259\pi$
$401$	7.58485	+	6.36445i	0.378769	+	0.317825i	−0.433450	+	0.901178i	$0.642704\pi$
$402$	1.66486	+	4.57417i	0.0830357	+	0.228139i
$403$	−31.1627	+	5.49483i	−1.55233	+	0.273717i
$404$	−0.218046	+	1.23660i	−0.0108482	+	0.0615231i
$405$		0			0
$406$	8.83769	+	15.3073i	0.438607	+	0.759690i
$407$	−48.6335	−	28.0786i	−2.41067	−	1.39180i
$408$	0.519489	+	0.619103i	0.0257185	+	0.0306502i
$409$	23.4859	−	19.7070i	1.16130	−	0.974449i	0.161380	−	0.986892i	$-0.448405\pi$
$409$	23.4859	−	19.7070i	1.16130	−	0.974449i	0.999923	+	0.0124433i	$0.00396092\pi$
$410$		0			0
$411$	4.14486	+	7.17910i	0.204451	+	0.354119i
$412$	2.51968	−	6.92276i	0.124136	−	0.341060i
$413$	−35.0892	−	6.18717i	−1.72663	−	0.304451i
$414$	−2.47325	−	14.0265i	−0.121554	−	0.689365i
$415$		0			0
$416$	2.95477	+	2.47935i	0.144870	+	0.121560i
$417$			10.2896i			0.503882i
$418$	9.13834	+	21.5454i	0.446971	+	1.05382i
$419$	−17.9296			−0.875916			−0.437958	−	0.898995i	$-0.644298\pi$
$419$	−17.9296			−0.875916			−0.437958	+	0.898995i	$0.644298\pi$
$420$		0			0
$421$	30.2850	−	11.0228i	1.47600	−	0.537220i	0.526278	−	0.850313i	$-0.323587\pi$
$421$	30.2850	−	11.0228i	1.47600	−	0.537220i	0.949723	+	0.313093i	$0.101365\pi$
$422$	10.5088	−	1.85299i	0.511562	−	0.0902022i
$423$	−8.19775	−	1.44549i	−0.398588	−	0.0702819i
$424$	1.69146	+	0.615640i	0.0821444	+	0.0298981i
$425$		0			0
$426$	1.73684	−	3.00830i	0.0841503	−	0.145753i
$427$	−25.3728	−	30.2382i	−1.22788	−	1.46333i
$428$	5.61204	+	6.68816i	0.271268	+	0.323285i
$429$	5.96858	−	10.3379i	0.288166	−	0.499118i
$430$		0			0
$431$	1.30703	+	0.475720i	0.0629575	+	0.0229146i	0.373307	−	0.927708i	$-0.378224\pi$
$431$	1.30703	+	0.475720i	0.0629575	+	0.0229146i	−0.310349	+	0.950623i	$0.600446\pi$
$432$	−3.21732	−	0.567300i	−0.154793	−	0.0272942i
$433$	32.7483	−	5.77441i	1.57378	−	0.277500i	0.682478	−	0.730906i	$-0.260902\pi$
$433$	32.7483	−	5.77441i	1.57378	−	0.277500i	0.891304	+	0.453406i	$0.149791\pi$
$434$	37.4981	−	13.6482i	1.79997	−	0.655135i
$435$		0			0
$436$	8.12981			0.389347
$437$	−22.6768	+	5.22866i	−1.08478	+	0.250121i
$438$		−	0.735663i		−	0.0351513i
$439$	27.6648	+	23.2135i	1.32037	+	1.10792i	0.986227	+	0.165397i	$0.0528906\pi$
$439$	27.6648	+	23.2135i	1.32037	+	1.10792i	0.334141	+	0.942523i	$0.391554\pi$
$440$		0			0
$441$	−7.71789	−	43.7704i	−0.367519	−	2.08430i
$442$	5.32597	+	0.939112i	0.253330	+	0.0446690i
$443$	−10.9404	+	30.0586i	−0.519795	+	1.42813i	0.350951	+	0.936394i	$0.385858\pi$
$443$	−10.9404	+	30.0586i	−0.519795	+	1.42813i	−0.870746	+	0.491732i	$0.836364\pi$
$444$	−3.01445	−	5.22118i	−0.143059	−	0.247786i
$445$		0			0
$446$	0.0761973	−	0.0639371i	0.00360805	−	0.00302751i
$447$	−1.06951	−	1.27459i	−0.0505860	−	0.0602860i
$448$	−4.21251	−	2.43209i	−0.199022	−	0.114906i
$449$	−1.09116	−	1.88995i	−0.0514951	−	0.0891922i	0.839129	−	0.543933i	$-0.183065\pi$
$449$	−1.09116	−	1.88995i	−0.0514951	−	0.0891922i	−0.890624	+	0.454741i	$0.849732\pi$
$450$		0			0
$451$	1.77917	−	10.0902i	0.0837777	−	0.475127i
$452$	4.41400	−	0.778308i	0.207617	−	0.0366085i
$453$	0.397846	+	1.09307i	0.0186924	+	0.0513570i
$454$	−10.5915	−	8.88734i	−0.497084	−	0.417103i
$455$		0			0
$456$	−0.306897	+	2.49370i	−0.0143718	+	0.116778i
$457$		−	37.2037i		−	1.74031i	−0.492774	−	0.870157i	$-0.664017\pi$
$457$		−	37.2037i		−	1.74031i	0.492774	−	0.870157i	$-0.335983\pi$
$458$	−10.0115	+	11.9313i	−0.467808	+	0.557512i
$459$	−4.30433	+	1.56665i	−0.200909	+	0.0731248i
$460$		0			0
$461$	−0.847556	+	4.80673i	−0.0394746	+	0.223872i	−0.998163	−	0.0605870i	$-0.980703\pi$
$461$	−0.847556	+	4.80673i	−0.0394746	+	0.223872i	0.958688	+	0.284459i	$0.0918138\pi$
$462$	−5.14865	+	14.1458i	−0.239537	+	0.658122i
$463$	17.5133	−	10.1113i	0.813914	−	0.469913i	−0.0343994	−	0.999408i	$-0.510952\pi$
$463$	17.5133	−	10.1113i	0.813914	−	0.469913i	0.848313	+	0.529495i	$0.177619\pi$
$464$	−1.81689	+	3.14694i	−0.0843470	+	0.146093i
$465$		0			0
$466$	11.6753	−	9.79677i	0.540850	−	0.453827i
$467$	−33.7859	−	19.5063i	−1.56342	−	0.902644i	−0.996907	−	0.0785944i	$-0.974957\pi$
$467$	−33.7859	−	19.5063i	−1.56342	−	0.902644i	−0.566518	−	0.824049i	$-0.691710\pi$
$468$	−8.91140	+	5.14500i	−0.411930	+	0.237828i
$469$	−38.6003	−	14.0493i	−1.78239	−	0.648739i
$470$		0			0
$471$	−1.10496	−	6.26656i	−0.0509140	−	0.288748i
$472$	−2.50532	−	6.88331i	−0.115317	−	0.316830i
$473$	−5.10305	+	6.08158i	−0.234639	+	0.279631i
$474$	−9.58686			−0.440339
$475$		0			0
$476$	−6.82004			−0.312596
$477$	−3.08665	+	3.67853i	−0.141328	+	0.168428i
$478$	−5.75392	−	15.8088i	−0.263178	−	0.723076i
$479$	5.39865	+	30.6172i	0.246670	+	1.39894i	0.816581	+	0.577231i	$0.195867\pi$
$479$	5.39865	+	30.6172i	0.246670	+	1.39894i	−0.569911	+	0.821707i	$0.693022\pi$
$480$		0			0
$481$	−37.9107	−	13.7984i	−1.72858	−	0.629151i
$482$	7.88688	−	4.55349i	0.359237	−	0.207406i
$483$	−12.9636	−	7.48453i	−0.589864	−	0.340558i
$484$	−13.6562	+	11.4589i	−0.620737	+	0.520860i
$485$		0			0
$486$	6.66429	−	11.5429i	0.302298	−	0.523596i
$487$	−24.2263	+	13.9870i	−1.09780	+	0.633813i	−0.935641	−	0.352952i	$-0.885178\pi$
$487$	−24.2263	+	13.9870i	−1.09780	+	0.633813i	−0.162155	+	0.986765i	$0.551845\pi$
$488$	2.77551	−	7.62565i	0.125641	−	0.345197i
$489$	0.593418	−	3.36544i	0.0268353	−	0.152191i
$490$		0			0
$491$	−2.79400	+	1.01693i	−0.126091	+	0.0458935i	−0.404295	−	0.914629i	$-0.632483\pi$
$491$	−2.79400	+	1.01693i	−0.126091	+	0.0458935i	0.278204	+	0.960522i	$0.410261\pi$
$492$	0.707045	−	0.842623i	0.0318760	−	0.0379884i
$493$			5.09490i			0.229463i
$494$	9.15311	+	14.1032i	0.411818	+	0.634533i
$495$		0			0
$496$	6.28445	+	5.27328i	0.282180	+	0.236777i
$497$	10.0258	+	27.5458i	0.449720	+	1.23560i
$498$	−8.20883	+	1.44744i	−0.367846	+	0.0648612i
$499$	−3.20155	+	18.1569i	−0.143321	+	0.812815i	0.825379	+	0.564580i	$0.190962\pi$
$499$	−3.20155	+	18.1569i	−0.143321	+	0.812815i	−0.968700	+	0.248235i	$0.920149\pi$
$500$		0			0
$501$	−2.08304	−	3.60794i	−0.0930636	−	0.161191i
$502$	14.5542	+	8.40288i	0.649586	+	0.375039i
$503$	−2.10120	−	2.50412i	−0.0936881	−	0.111653i	0.717163	−	0.696905i	$-0.245440\pi$
$503$	−2.10120	−	2.50412i	−0.0936881	−	0.111653i	−0.810852	+	0.585252i	$0.800996\pi$
$504$	9.94053	−	8.34110i	0.442786	−	0.371542i
$505$		0			0
$506$	−14.3325	−	24.8246i	−0.637157	−	1.10359i
$507$	0.370209	−	1.01714i	0.0164416	−	0.0451728i
$508$	0.137068	+	0.0241688i	0.00608142	+	0.00107232i
$509$	−6.53272	−	37.0489i	−0.289558	−	1.64216i	−0.688536	−	0.725202i	$-0.741746\pi$
$509$	−6.53272	−	37.0489i	−0.289558	−	1.64216i	0.398978	−	0.916960i	$-0.369365\pi$
$510$		0			0
$511$	4.75567	+	3.99048i	0.210378	+	0.176528i
$512$		−	1.00000i		−	0.0441942i
$513$	−12.6864	−	6.46852i	−0.560118	−	0.285592i
$514$	−9.89728			−0.436550
$515$		0			0
$516$	−0.800905	+	0.291506i	−0.0352579	+	0.0128328i
$517$	−16.4987	+	2.90916i	−0.725610	+	0.127945i
$518$	50.1034	+	8.83459i	2.20142	+	0.388169i
$519$	−2.79412	−	1.01698i	−0.122648	−	0.0446403i
$520$		0			0
$521$	−15.7203	+	27.2284i	−0.688719	+	1.19290i	0.283533	+	0.958962i	$0.408493\pi$
$521$	−15.7203	+	27.2284i	−0.688719	+	1.19290i	−0.972252	+	0.233934i	$0.924840\pi$
$522$	−6.23119	−	7.42605i	−0.272732	−	0.325029i
$523$	−2.88381	−	3.43679i	−0.126100	−	0.150280i	0.699300	−	0.714828i	$-0.253495\pi$
$523$	−2.88381	−	3.43679i	−0.126100	−	0.150280i	−0.825400	+	0.564548i	$0.809051\pi$
$524$	6.21505	−	10.7648i	0.271506	−	0.470261i
$525$		0			0
$526$	−21.0609	−	7.66554i	−0.918299	−	0.334233i
$527$	11.3277	+	1.99738i	0.493443	+	0.0870073i
$528$	−3.04777	+	0.537405i	−0.132637	+	0.0233875i
$529$	5.17201	−	1.88246i	0.224870	−	0.0818460i
$530$		0			0
$531$	19.5415			0.848027
$532$	−14.4557	−	15.5106i	−0.626735	−	0.672469i
$533$		−	7.36067i		−	0.318826i
$534$	4.24270	+	3.56005i	0.183599	+	0.154058i
$535$		0			0
$536$	−1.46644	−	8.31660i	−0.0633406	−	0.359222i
$537$	4.64551	+	0.819129i	0.200469	+	0.0353480i
$538$	2.55586	−	7.02217i	0.110191	−	0.302747i
$539$	−44.7252	−	77.4664i	−1.92645	−	3.33671i
$540$		0			0
$541$	17.0269	−	14.2873i	0.732045	−	0.614259i	−0.198643	−	0.980072i	$-0.563653\pi$
$541$	17.0269	−	14.2873i	0.732045	−	0.614259i	0.930688	+	0.365813i	$0.119209\pi$
$542$	6.84623	+	8.15902i	0.294071	+	0.350460i
$543$	−1.71339	−	0.989225i	−0.0735285	−	0.0424517i
$544$	−0.701047	−	1.21425i	−0.0300571	−	0.0520605i
$545$		0			0
$546$	−1.87794	+	10.6504i	−0.0803686	+	0.455793i
$547$	28.4071	−	5.00894i	1.21460	−	0.214167i	0.470600	−	0.882347i	$-0.344038\pi$
$547$	28.4071	−	5.00894i	1.21460	−	0.214167i	0.744000	+	0.668180i	$0.232926\pi$
$548$	−4.91880	−	13.5143i	−0.210121	−	0.577302i
$549$	16.5840	+	13.9157i	0.707790	+	0.593906i
$550$		0			0
$551$	−11.5871	+	10.7991i	−0.493629	+	0.460058i
$552$		−	3.07740i		−	0.130983i
$553$	52.0023	−	61.9739i	2.21136	−	2.63540i
$554$	2.18604	−	0.795654i	0.0928760	−	0.0338041i
$555$		0			0
$556$	3.09981	−	17.5799i	0.131461	−	0.745554i
$557$	−9.58721	+	26.3406i	−0.406223	+	1.11609i	0.552937	+	0.833223i	$0.313507\pi$
$557$	−9.58721	+	26.3406i	−0.406223	+	1.11609i	−0.959160	+	0.282865i	$0.908715\pi$
$558$	−18.9535	+	10.9428i	−0.802366	+	0.463246i
$559$	−2.85170	+	4.93929i	−0.120614	+	0.208910i
$560$		0			0
$561$	−3.32401	+	2.78917i	−0.140340	+	0.117759i
$562$	−14.7858	−	8.53656i	−0.623699	−	0.360093i
$563$	5.69177	−	3.28614i	0.239879	−	0.138494i	−0.375242	−	0.926927i	$-0.622440\pi$
$563$	5.69177	−	3.28614i	0.239879	−	0.138494i	0.615121	+	0.788432i	$0.289107\pi$
$564$	−1.69011	−	0.615151i	−0.0711666	−	0.0259025i
$565$		0			0
$566$	−1.47044	−	8.33927i	−0.0618071	−	0.350526i
$567$	10.1818	+	27.9742i	0.427595	+	1.17481i
$568$	−3.87370	+	4.61650i	−0.162537	+	0.193704i
$569$	−3.90032			−0.163510			−0.0817549	−	0.996652i	$-0.526052\pi$
$569$	−3.90032			−0.163510			−0.0817549	+	0.996652i	$0.526052\pi$
$570$		0			0
$571$	18.1559			0.759802			0.379901	−	0.925027i	$-0.375958\pi$
$571$	18.1559			0.759802			0.379901	+	0.925027i	$0.375958\pi$
$572$	−13.3118	+	15.8644i	−0.556594	+	0.663323i
$573$	0.744385	+	2.04518i	0.0310971	+	0.0854386i
$574$	1.61186	+	9.14132i	0.0672778	+	0.381551i
$575$		0			0
$576$	2.50687	+	0.912424i	0.104453	+	0.0380177i
$577$	12.1402	−	7.00915i	0.505403	−	0.291795i	−0.225539	−	0.974234i	$-0.572414\pi$
$577$	12.1402	−	7.00915i	0.505403	−	0.291795i	0.730942	+	0.682439i	$0.239081\pi$
$578$	13.0199	+	7.51707i	0.541558	+	0.312669i
$579$	−5.37721	+	4.51202i	−0.223469	+	0.187513i
$580$		0			0
$581$	35.1705	−	60.9170i	1.45912	−	2.52726i
$582$	3.03461	−	1.75203i	0.125789	−	0.0726241i
$583$	−3.30541	+	9.08155i	−0.136896	+	0.376119i
$584$	−0.221624	+	1.25689i	−0.00917088	+	0.0520106i
$585$		0			0
$586$	−2.43610	+	0.886667i	−0.100634	+	0.0366279i
$587$	4.89246	−	5.83061i	0.201933	−	0.240655i	−0.655568	−	0.755136i	$-0.727571\pi$
$587$	4.89246	−	5.83061i	0.201933	−	0.240655i	0.857502	+	0.514481i	$0.172015\pi$
$588$		−	9.60319i		−	0.396029i
$589$	19.4676	+	29.9958i	0.802148	+	1.23596i
$590$		0			0
$591$	3.18025	+	2.66855i	0.130818	+	0.109769i
$592$	3.57732	+	9.82860i	0.147027	+	0.403953i
$593$	−9.27933	+	1.63620i	−0.381056	+	0.0671905i	−0.360896	−	0.932606i	$-0.617529\pi$
$593$	−9.27933	+	1.63620i	−0.381056	+	0.0671905i	−0.0201608	+	0.999797i	$0.506418\pi$
$594$	3.04587	−	17.2740i	0.124974	−	0.708761i
$595$		0			0
$596$	1.44329	+	2.49986i	0.0591196	+	0.102398i
$597$	−2.91380	−	1.68228i	−0.119254	−	0.0688512i
$598$	−13.2370	−	15.7753i	−0.541302	−	0.645099i
$599$	−10.7502	+	9.02053i	−0.439243	+	0.368569i	−0.835426	−	0.549603i	$-0.814779\pi$
$599$	−10.7502	+	9.02053i	−0.439243	+	0.368569i	0.396183	+	0.918172i	$0.370335\pi$
$600$		0			0
$601$	6.78599	+	11.7537i	0.276806	+	0.479443i	0.970589	−	0.240742i	$-0.0773906\pi$
$601$	6.78599	+	11.7537i	0.276806	+	0.479443i	−0.693783	+	0.720184i	$0.744057\pi$
$602$	2.45994	−	6.75864i	0.100260	−	0.275462i
$603$	22.1866	+	3.91210i	0.903508	+	0.159313i
$604$	−0.350430	−	1.98739i	−0.0142588	−	0.0808657i
$605$		0			0
$606$	−0.554451	−	0.465240i	−0.0225231	−	0.0188991i
$607$			2.07689i			0.0842984i	0.999111	+	0.0421492i	$0.0134205\pi$
$607$			2.07689i			0.0842984i	−0.999111	+	0.0421492i	$0.986580\pi$
$608$	1.27559	−	4.16808i	0.0517318	−	0.169038i
$609$	−10.1883			−0.412850
$610$		0			0
$611$	−11.3098	+	4.11642i	−0.457545	+	0.166533i
$612$	3.68361	−	0.649520i	0.148901	−	0.0262553i
$613$	16.2680	+	2.86849i	0.657059	+	0.115857i	0.492230	−	0.870465i	$-0.336182\pi$
$613$	16.2680	+	2.86849i	0.657059	+	0.115857i	0.164828	+	0.986322i	$0.447293\pi$
$614$	3.87311	+	1.40970i	0.156306	+	0.0568908i
$615$		0			0
$616$	13.0581	−	22.6173i	0.526125	−	0.911275i
$617$	14.7080	+	17.5283i	0.592120	+	0.705661i	0.976012	−	0.217717i	$-0.0698610\pi$
$617$	14.7080	+	17.5283i	0.592120	+	0.705661i	−0.383892	+	0.923378i	$0.625417\pi$
$618$	2.72956	+	3.25297i	0.109799	+	0.130853i
$619$	−6.66514	+	11.5444i	−0.267895	+	0.464007i	−0.968318	−	0.249721i	$-0.919661\pi$
$619$	−6.66514	+	11.5444i	−0.267895	+	0.464007i	0.700423	+	0.713728i	$0.252995\pi$
$620$		0			0
$621$	16.3901	+	5.96550i	0.657711	+	0.239387i
$622$	−2.44534	−	0.431179i	−0.0980492	−	0.0172887i
$623$	−46.0276	+	8.11590i	−1.84406	+	0.325157i
$624$	−2.08924	+	0.760421i	−0.0836365	+	0.0304412i
$625$		0			0
$626$	−5.38145			−0.215086
$627$	−13.3889	−	1.64775i	−0.534700	−	0.0658048i
$628$			11.0394i			0.440520i
$629$	11.2341	+	9.42649i	0.447931	+	0.375859i
$630$		0			0
$631$	1.51546	+	8.59462i	0.0603297	+	0.342147i	1.00000		6.52024e-5i	$2.07546e-5\pi$
$631$	1.51546	+	8.59462i	0.0603297	+	0.342147i	−0.939670	+	0.342081i	$0.888868\pi$
$632$	16.3793	+	2.88812i	0.651534	+	0.114883i
$633$	−2.10372	+	5.77991i	−0.0836152	+	0.229731i
$634$	−9.73266	−	16.8575i	−0.386533	−	0.669495i
$635$		0			0
$636$	−0.794805	+	0.666921i	−0.0315161	+	0.0264451i
$637$	−41.3068	−	49.2275i	−1.63663	−	1.95046i
$638$	−16.8962	−	9.75501i	−0.668926	−	0.386204i
$639$	−8.03848	−	13.9230i	−0.317997	−	0.550787i
$640$		0			0
$641$	−0.151753	+	0.860632i	−0.00599387	+	0.0339929i	−0.987658	−	0.156626i	$-0.949938\pi$
$641$	−0.151753	+	0.860632i	−0.00599387	+	0.0339929i	0.981664	+	0.190619i	$0.0610494\pi$
$642$	−4.95606	+	0.873887i	−0.195600	+	0.0344896i
$643$	−6.50122	−	17.8620i	−0.256383	−	0.704407i	−0.999383	−	0.0351158i	$-0.988820\pi$
$643$	−6.50122	−	17.8620i	−0.256383	−	0.704407i	0.743000	−	0.669291i	$-0.233402\pi$
$644$	19.8938	+	16.6928i	0.783924	+	0.657790i
$645$		0			0
$646$	−1.37314	−	5.95533i	−0.0540255	−	0.234309i
$647$			14.4175i			0.566810i	0.959000	+	0.283405i	$0.0914641\pi$
$647$			14.4175i			0.566810i	−0.959000	+	0.283405i	$0.908536\pi$
$648$	−3.93395	+	4.68830i	−0.154540	+	0.184174i
$649$	36.9570	−	13.4512i	1.45069	−	0.528007i
$650$		0			0
$651$	−3.99417	+	22.6520i	−0.156544	+	0.887804i
$652$	−2.02773	+	5.57114i	−0.0794121	+	0.218183i
$653$	−9.06528	+	5.23384i	−0.354752	+	0.204816i	−0.666776	−	0.745258i	$-0.732326\pi$
$653$	−9.06528	+	5.23384i	−0.354752	+	0.204816i	0.312024	+	0.950074i	$0.398993\pi$
$654$	−2.34306	+	4.05829i	−0.0916207	+	0.158692i
$655$		0			0
$656$	−1.46184	+	1.22663i	−0.0570755	+	0.0478920i
$657$	−2.94865	−	1.70240i	−0.115038	−	0.0664171i
$658$	13.1444	−	7.58889i	0.512420	−	0.295846i
$659$	5.20991	+	1.89625i	0.202949	+	0.0738675i	0.441495	−	0.897264i	$-0.354448\pi$
$659$	5.20991	+	1.89625i	0.202949	+	0.0738675i	−0.238545	+	0.971131i	$0.576671\pi$
$660$		0			0
$661$	5.00125	+	28.3635i	0.194526	+	1.10321i	0.913092	+	0.407753i	$0.133688\pi$
$661$	5.00125	+	28.3635i	0.194526	+	1.10321i	−0.718566	+	0.695459i	$0.755201\pi$
$662$	−6.39927	−	17.5818i	−0.248715	−	0.683338i
$663$	−2.00376	+	2.38799i	−0.0778198	+	0.0927420i
$664$	14.4610			0.561195
$665$		0			0
$666$	−27.9030			−1.08122
$667$	12.4703	−	14.8616i	0.482854	−	0.575443i
$668$	2.47200	+	6.79176i	0.0956445	+	0.262781i
$669$	0.00995606	+	0.0564636i	0.000384924	+	0.00218301i
$670$		0			0
$671$	40.9427	+	14.9019i	1.58057	+	0.575282i
$672$	2.42814	−	1.40188i	0.0936674	−	0.0540789i
$673$	34.5899	+	19.9705i	1.33334	+	0.769807i	0.985811	−	0.167861i	$-0.0536860\pi$
$673$	34.5899	+	19.9705i	1.33334	+	0.769807i	0.347533	+	0.937668i	$0.387019\pi$
$674$	−19.2255	+	16.1322i	−0.740540	+	0.621387i
$675$		0			0
$676$	−0.938930	+	1.62627i	−0.0361127	+	0.0625490i
$677$	12.6270	−	7.29022i	0.485296	−	0.280186i	−0.237325	−	0.971430i	$-0.576271\pi$
$677$	12.6270	−	7.29022i	0.485296	−	0.280186i	0.722621	+	0.691245i	$0.242937\pi$
$678$	−0.883619	+	2.42772i	−0.0339352	+	0.0932361i
$679$	−5.13477	+	29.1207i	−0.197054	+	1.11755i
$680$		0			0
$681$	7.48897	−	2.72576i	0.286978	−	0.104451i
$682$	−28.3126	+	33.7417i	−1.08415	+	1.29204i
$683$			26.6159i			1.01843i	0.860640	+	0.509214i	$0.170064\pi$
$683$			26.6159i			1.01843i	−0.860640	+	0.509214i	$0.829936\pi$
$684$	9.28494	+	7.00078i	0.355018	+	0.267681i
$685$		0			0
$686$	35.9961	+	30.2043i	1.37434	+	1.15321i
$687$	−3.07056	−	8.43628i	−0.117149	−	0.321864i
$688$	1.45618	−	0.256764i	0.0555163	−	0.00978902i
$689$	−1.20563	+	6.83749i	−0.0459310	+	0.260488i
$690$		0			0
$691$	−18.6248	−	32.2591i	−0.708521	−	1.22719i	−0.965406	−	0.260752i	$-0.916029\pi$
$691$	−18.6248	−	32.2591i	−0.708521	−	1.22719i	0.256885	−	0.966442i	$-0.417304\pi$
$692$	4.46743	+	2.57927i	0.169826	+	0.0980492i
$693$	44.7839	+	53.3714i	1.70120	+	2.02741i
$694$	17.4302	−	14.6257i	0.661642	−	0.555183i
$695$		0			0
$696$	−1.04727	−	1.81393i	−0.0396968	−	0.0687569i
$697$	−0.915115	+	2.51426i	−0.0346625	+	0.0952344i
$698$	12.9638	+	2.28587i	0.490688	+	0.0865215i
$699$	1.52552	+	8.65165i	0.0577004	+	0.327235i
$700$		0			0
$701$	−30.3425	−	25.4604i	−1.14602	−	0.961626i	−0.146402	−	0.989225i	$-0.546769\pi$
$701$	−30.3425	−	25.4604i	−1.14602	−	0.961626i	−0.999619	+	0.0275989i	$0.991214\pi$
$702$		−	12.6012i		−	0.475603i
$703$	2.37332	+	45.5295i	0.0895114	+	1.71718i
$704$	5.36907			0.202354
$705$		0			0
$706$	−11.5635	+	4.20877i	−0.435198	+	0.158399i
$707$	6.01505	−	1.06062i	0.226219	−	0.0398886i
$708$	4.15810	+	0.733185i	0.156271	+	0.0275548i
$709$	−34.4453	−	12.5371i	−1.29362	−	0.470839i	−0.398707	−	0.917079i	$-0.630541\pi$
$709$	−34.4453	−	12.5371i	−1.29362	−	0.470839i	−0.894914	+	0.446239i	$0.852763\pi$
$710$		0			0
$711$	−22.1850	+	38.4256i	−0.832003	+	1.44107i
$712$	−6.17623	−	7.36055i	−0.231464	−	0.275848i
$713$	−28.1536	−	33.5521i	−1.05436	−	1.25654i
$714$	1.96557	−	3.40447i	0.0735597	−	0.127409i
$715$		0			0
$716$	−7.69017	−	2.79899i	−0.287395	−	0.104603i
$717$	9.54983	+	1.68389i	0.356645	+	0.0628861i
$718$	−12.3704	+	2.18123i	−0.461658	+	0.0814028i
$719$	10.3333	−	3.76101i	0.385367	−	0.140262i	−0.142069	−	0.989857i	$-0.545376\pi$
$719$	10.3333	−	3.76101i	0.385367	−	0.140262i	0.527436	+	0.849595i	$0.323153\pi$
$720$		0			0
$721$	−35.8347			−1.33455
$722$	10.6335	−	15.7458i	0.395737	−	0.585997i
$723$			5.24936i			0.195226i
$724$	2.62934	+	2.20628i	0.0977187	+	0.0819957i
$725$		0			0
$726$	−1.78434	−	10.1195i	−0.0662232	−	0.375570i
$727$	44.7236	+	7.88597i	1.65871	+	0.292475i	0.922992	−	0.384818i	$-0.125736\pi$
$727$	44.7236	+	7.88597i	1.65871	+	0.292475i	0.735714	+	0.677293i	$0.236847\pi$
$728$	6.41700	−	17.6306i	0.237830	−	0.653432i
$729$	−5.33885	−	9.24717i	−0.197735	−	0.342488i
$730$		0			0
$731$	1.58816	−	1.33262i	0.0587402	−	0.0492889i
$732$	3.00670	+	3.58325i	0.111131	+	0.132441i
$733$	−23.4118	−	13.5168i	−0.864735	−	0.499255i	0.000859816	−	1.00000i	$-0.499726\pi$
$733$	−23.4118	−	13.5168i	−0.864735	−	0.499255i	−0.865595	+	0.500744i	$0.833060\pi$
$734$	−1.34225	−	2.32485i	−0.0495435	−	0.0858119i
$735$		0			0
$736$	−0.927092	+	5.25780i	−0.0341731	+	0.193805i
$737$	44.6524	−	7.87342i	1.64479	−	0.290021i
$738$	−1.74118	−	4.78386i	−0.0640938	−	0.176096i
$739$	0.964167	+	0.809032i	0.0354675	+	0.0297607i	0.660349	−	0.750959i	$-0.270408\pi$
$739$	0.964167	+	0.809032i	0.0354675	+	0.0297607i	−0.624882	+	0.780720i	$0.714853\pi$
$740$		0			0
$741$	−9.67809	+	0.504490i	−0.355534	+	0.0185329i
$742$		−	8.75559i		−	0.321428i
$743$	33.5678	−	40.0045i	1.23148	−	1.46762i	0.395867	−	0.918308i	$-0.370444\pi$
$743$	33.5678	−	40.0045i	1.23148	−	1.46762i	0.835615	−	0.549315i	$-0.185111\pi$
$744$	−4.44356	+	1.61733i	−0.162909	+	0.0592940i
$745$		0			0
$746$	3.21985	−	18.2607i	0.117887	−	0.668571i
$747$	−13.1945	+	36.2517i	−0.482763	+	1.32638i
$748$	6.51938	−	3.76397i	0.238372	−	0.137624i
$749$	21.2341	−	36.7785i	0.775876	−	1.34386i
$750$		0			0
$751$	0.810409	−	0.680014i	0.0295723	−	0.0248141i	−0.627882	−	0.778309i	$-0.716078\pi$
$751$	0.810409	−	0.680014i	0.0295723	−	0.0248141i	0.657454	+	0.753495i	$0.271633\pi$
$752$	2.70227	+	1.56016i	0.0985417	+	0.0568931i
$753$	−8.38920	+	4.84351i	−0.305720	+	0.176507i
$754$	−13.1709	−	4.79381i	−0.479655	−	0.174580i
$755$		0			0
$756$	2.75945	+	15.6496i	0.100360	+	0.569172i
$757$	−0.632944	−	1.73900i	−0.0230047	−	0.0632050i	0.927659	−	0.373429i	$-0.121818\pi$
$757$	−0.632944	−	1.73900i	−0.0230047	−	0.0632050i	−0.950663	+	0.310224i	$0.899596\pi$
$758$	−7.44703	+	8.87503i	−0.270488	+	0.322355i
$759$	16.5228			0.599739
$760$		0			0
$761$	−31.8442			−1.15435			−0.577176	−	0.816620i	$-0.695845\pi$
$761$	−31.8442			−1.15435			−0.577176	+	0.816620i	$0.695845\pi$
$762$	−0.0515686	+	0.0614570i	−0.00186813	+	0.00222635i
$763$	−13.5252	−	37.1601i	−0.489644	−	1.34529i
$764$	−0.655668	−	3.71848i	−0.0237212	−	0.134530i
$765$		0			0
$766$	27.3254	+	9.94564i	0.987308	+	0.359351i
$767$	24.4688	−	14.1271i	0.883517	−	0.510099i
$768$	0.499186	+	0.288205i	0.0180128	+	0.0103997i
$769$	−0.0929228	+	0.0779715i	−0.00335088	+	0.00281172i	−0.644462	−	0.764637i	$-0.722918\pi$
$769$	−0.0929228	+	0.0779715i	−0.00335088	+	0.00281172i	0.641111	+	0.767448i	$0.278474\pi$
$770$		0			0
$771$	2.85245	−	4.94059i	0.102728	−	0.177931i
$772$	10.5463	−	6.08894i	0.379571	−	0.219146i
$773$	11.9131	−	32.7308i	0.428483	−	1.17725i	−0.518251	−	0.855229i	$-0.673417\pi$
$773$	11.9131	−	32.7308i	0.428483	−	1.17725i	0.946734	−	0.322018i	$-0.104361\pi$
$774$	−0.684981	+	3.88472i	−0.0246211	+	0.139633i
$775$		0			0
$776$	−5.71250	+	2.07918i	−0.205067	+	0.0746382i
$777$	−18.8502	+	22.4648i	−0.676246	+	0.805919i
$778$			29.7821i			1.06774i
$779$	−7.65776	+	3.24800i	−0.274368	+	0.116372i
$780$		0			0
$781$	−24.7863	−	20.7982i	−0.886923	−	0.744217i
$782$	2.56024	+	7.03421i	0.0915541	+	0.251543i
$783$	11.6910	−	2.06144i	0.417803	−	0.0736700i
$784$	−2.89303	+	16.4072i	−0.103323	+	0.585972i
$785$		0			0
$786$	3.58242	+	6.20493i	0.127781	+	0.221323i
$787$	−16.6039	−	9.58626i	−0.591865	−	0.341713i	0.173970	−	0.984751i	$-0.444340\pi$
$787$	−16.6039	−	9.58626i	−0.591865	−	0.341713i	−0.765834	+	0.643038i	$0.777674\pi$
$788$	−4.62959	−	5.51733i	−0.164922	−	0.196547i
$789$	9.89640	−	8.30406i	0.352321	−	0.295632i
$790$		0			0
$791$	−10.9009	−	18.8809i	−0.387591	−	0.671327i
$792$	−4.89887	+	13.4595i	−0.174074	+	0.478264i
$793$	30.8257	+	5.43540i	1.09465	+	0.193017i
$794$	1.08877	+	6.17471i	0.0386389	+	0.219132i
$795$		0			0
$796$	4.47147	+	3.75201i	0.158487	+	0.132986i
$797$		−	22.4041i		−	0.793593i	−0.917907	−	0.396796i	$-0.870122\pi$
$797$		−	22.4041i		−	0.793593i	0.917907	−	0.396796i	$-0.129878\pi$
$798$	11.9089	−	2.74587i	0.421570	−	0.0972028i
$799$	4.37497			0.154775
$800$		0			0
$801$	24.0872	−	8.76704i	0.851081	−	0.309768i
$802$	9.75090	−	1.71935i	0.344316	−	0.0607122i
$803$	−6.74835	−	1.18992i	−0.238144	−	0.0419912i
$804$	4.57417	+	1.66486i	0.161318	+	0.0587151i
$805$		0			0
$806$	−15.8217	+	27.4040i	−0.557297	+	0.965266i
$807$	2.76876	+	3.29968i	0.0974649	+	0.116154i
$808$	0.807133	+	0.961904i	0.0283948	+	0.0338396i
$809$	22.7973	−	39.4861i	0.801511	−	1.38826i	−0.117110	−	0.993119i	$-0.537363\pi$
$809$	22.7973	−	39.4861i	0.801511	−	1.38826i	0.918621	−	0.395139i	$-0.129304\pi$
$810$		0			0
$811$	−35.6230	−	12.9657i	−1.25089	−	0.455288i	−0.370191	−	0.928956i	$-0.620708\pi$
$811$	−35.6230	−	12.9657i	−1.25089	−	0.455288i	−0.880704	+	0.473667i	$0.842930\pi$
$812$	17.4069	+	3.06930i	0.610861	+	0.107711i
$813$	−6.04599	+	1.06607i	−0.212042	+	0.0373888i
$814$	−52.7704	+	19.2069i	−1.84960	+	0.673200i
$815$		0			0
$816$	0.808181			0.0282920
$817$	6.39699	+	0.787270i	0.223802	+	0.0275431i
$818$		−	30.6587i		−	1.07196i
$819$	38.3424	+	32.1731i	1.33979	+	1.12422i
$820$		0			0
$821$	9.63416	+	54.6380i	0.336235	+	1.90688i	0.414689	+	0.909963i	$0.363890\pi$
$821$	9.63416	+	54.6380i	0.336235	+	1.90688i	−0.0784541	+	0.996918i	$0.524998\pi$
$822$	8.16377	+	1.43949i	0.284744	+	0.0502081i
$823$	2.19203	−	6.02255i	0.0764094	−	0.209933i	−0.895607	−	0.444846i	$-0.853258\pi$
$823$	2.19203	−	6.02255i	0.0764094	−	0.209933i	0.972016	+	0.234913i	$0.0754806\pi$
$824$	−3.68352	−	6.38005i	−0.128322	−	0.222260i
$825$		0			0
$826$	−27.2945	+	22.9028i	−0.949699	+	0.796892i
$827$	2.82341	+	3.36481i	0.0981796	+	0.117006i	0.812897	−	0.582407i	$-0.197889\pi$
$827$	2.82341	+	3.36481i	0.0981796	+	0.117006i	−0.714717	+	0.699413i	$0.753445\pi$
$828$	−12.3347	−	7.12144i	−0.428660	−	0.247487i
$829$	25.0469	+	43.3826i	0.869916	+	1.50674i	0.862082	+	0.506769i	$0.169160\pi$
$829$	25.0469	+	43.3826i	0.869916	+	1.50674i	0.00783422	+	0.999969i	$0.497506\pi$
$830$		0			0
$831$	−0.232849	+	1.32055i	−0.00807745	+	0.0458095i
$832$	3.79858	−	0.669793i	0.131692	−	0.0232209i
$833$	7.98936	+	21.9506i	0.276815	+	0.760543i
$834$	7.88227	+	6.61401i	0.272941	+	0.229024i
$835$		0			0
$836$	22.3787	+	6.84871i	0.773984	+	0.236868i
$837$		−	26.8013i		−	0.926390i
$838$	−11.5249	+	13.7348i	−0.398121	+	0.474462i
$839$	28.3895	−	10.3329i	0.980115	−	0.356733i	0.198230	−	0.980156i	$-0.436481\pi$
$839$	28.3895	−	10.3329i	0.980115	−	0.356733i	0.781885	+	0.623423i	$0.214258\pi$
$840$		0			0
$841$	−2.74289	+	15.5557i	−0.0945823	+	0.536403i
$842$	11.0228	−	30.2850i	0.379872	−	1.04369i
$843$	8.52266	−	4.92056i	0.293536	−	0.169473i
$844$	5.33548	−	9.24132i	0.183655	−	0.318099i
$845$		0			0
$846$	−6.37672	+	5.35070i	−0.219236	+	0.183961i
$847$	75.0961	+	43.3567i	2.58033	+	1.48975i
$848$	1.55885	−	0.900005i	0.0535313	−	0.0309063i
$849$	4.58664	+	1.66940i	0.157413	+	0.0572937i
$850$		0			0
$851$	−9.69680	−	54.9933i	−0.332402	−	1.88515i
$852$	−1.18807	−	3.26420i	−0.0407026	−	0.111830i
$853$	−7.61549	+	9.07579i	−0.260750	+	0.310749i	−0.880497	−	0.474052i	$-0.842791\pi$
$853$	−7.61549	+	9.07579i	−0.260750	+	0.310749i	0.619747	+	0.784802i	$0.287235\pi$
$854$	−39.4731			−1.35074
$855$		0			0
$856$	8.73078			0.298412
$857$	−30.5978	+	36.4650i	−1.04520	+	1.24562i	−0.0765828	+	0.997063i	$0.524401\pi$
$857$	−30.5978	+	36.4650i	−1.04520	+	1.24562i	−0.968617	+	0.248558i	$0.920043\pi$
$858$	−4.08275	−	11.2173i	−0.139383	−	0.382951i
$859$	−1.97498	−	11.2007i	−0.0673853	−	0.382161i	−0.999785	−	0.0207325i	$-0.993400\pi$
$859$	−1.97498	−	11.2007i	−0.0673853	−	0.382161i	0.932400	−	0.361429i	$-0.117711\pi$
$860$		0			0
$861$	−5.02777	−	1.82996i	−0.171346	−	0.0623648i
$862$	1.20457	−	0.695457i	0.0410277	−	0.0236873i
$863$	−42.3239	−	24.4357i	−1.44072	−	0.831801i	−0.442825	−	0.896608i	$-0.646024\pi$
$863$	−42.3239	−	24.4357i	−1.44072	−	0.831801i	−0.997898	+	0.0648068i	$0.979357\pi$
$864$	−2.50263	+	2.09996i	−0.0851412	+	0.0714420i
$865$		0			0
$866$	16.6267	−	28.7984i	0.565000	−	0.978608i
$867$	−7.50483	+	4.33292i	−0.254878	+	0.147154i
$868$	13.6482	−	37.4981i	0.463250	−	1.27277i
$869$	−15.5065	+	87.9417i	−0.526022	+	2.98322i
$870$		0			0
$871$	30.6091	−	11.1408i	1.03715	−	0.377491i
$872$	5.22574	−	6.22780i	0.176966	−	0.210900i
$873$		−	16.2176i		−	0.548882i
$874$	−10.5710	+	20.7323i	−0.357568	+	0.701282i
$875$		0			0
$876$	−0.563551	−	0.472875i	−0.0190406	−	0.0159770i
$877$	10.0837	+	27.7048i	0.340503	+	0.935524i	0.985249	+	0.171127i	$0.0547410\pi$
$877$	10.0837	+	27.7048i	0.340503	+	0.935524i	−0.644746	+	0.764397i	$0.723037\pi$
$878$	35.5652	−	6.27110i	1.20027	−	0.211639i
$879$	0.259484	−	1.47161i	0.00875218	−	0.0496361i
$880$		0			0
$881$	20.8616	+	36.1334i	0.702846	+	1.21736i	0.967463	+	0.253011i	$0.0814209\pi$
$881$	20.8616	+	36.1334i	0.702846	+	1.21736i	−0.264618	+	0.964353i	$0.585246\pi$
$882$	−38.4910	−	22.2228i	−1.29606	−	0.748280i
$883$	−3.80618	−	4.53603i	−0.128088	−	0.152650i	0.698189	−	0.715914i	$-0.253990\pi$
$883$	−3.80618	−	4.53603i	−0.128088	−	0.152650i	−0.826277	+	0.563264i	$0.809545\pi$
$884$	4.14287	−	3.47628i	0.139340	−	0.116920i
$885$		0			0
$886$	15.9938	+	27.7021i	0.537323	+	0.930672i
$887$	−4.72909	+	12.9931i	−0.158787	+	0.436265i	−0.993418	−	0.114545i	$-0.963459\pi$
$887$	−4.72909	+	12.9931i	−0.158787	+	0.436265i	0.834631	+	0.550810i	$0.185681\pi$
$888$	−5.93730	−	1.04691i	−0.199243	−	0.0351319i
$889$	−0.117562	−	0.666726i	−0.00394290	−	0.0223613i
$890$		0			0
$891$	−25.1718	−	21.1217i	−0.843288	−	0.707603i
$892$		−	0.0994685i		−	0.00333045i
$893$	9.27316	+	9.94983i	0.310315	+	0.332958i
$894$	−1.66386			−0.0556478
$895$		0			0
$896$	−4.57084	+	1.66365i	−0.152701	+	0.0555787i
$897$	11.6898	−	2.06122i	0.390310	−	0.0688222i
$898$	−2.14917	−	0.378957i	−0.0717187	−	0.0126459i
$899$	−28.0129	−	10.1959i	−0.934282	−	0.340051i
$900$		0			0
$901$	1.26189	−	2.18566i	0.0420397	−	0.0728149i
$902$	−6.58588	−	7.84875i	−0.219286	−	0.261335i
$903$	2.66485	+	3.17585i	0.0886807	+	0.105686i
$904$	2.24105	−	3.88161i	0.0745362	−	0.129100i
$905$		0			0
$906$	1.09307	+	0.397846i	0.0363149	+	0.0132175i
$907$	8.22903	+	1.45100i	0.273240	+	0.0481797i	0.308589	−	0.951195i	$-0.400143\pi$
$907$	8.22903	+	1.45100i	0.273240	+	0.0481797i	−0.0353489	+	0.999375i	$0.511254\pi$
$908$	−13.6162	+	2.40090i	−0.451869	+	0.0796767i
$909$	−3.14781	+	1.14571i	−0.104406	+	0.0380008i
$910$		0			0
$911$	39.5762			1.31122			0.655609	−	0.755101i	$-0.272412\pi$
$911$	39.5762			1.31122			0.655609	+	0.755101i	$0.272412\pi$
$912$	1.71302	+	1.83802i	0.0567237	+	0.0608628i
$913$			77.6420i			2.56958i
$914$	−28.4997	−	23.9141i	−0.942685	−	0.791007i
$915$		0			0
$916$	2.70460	+	15.3386i	0.0893626	+	0.506800i
$917$	−59.5437	−	10.4992i	−1.96631	−	0.346713i
$918$	−1.56665	+	4.30433i	−0.0517071	+	0.142064i
$919$	−19.0623	−	33.0169i	−0.628807	−	1.08913i	−0.987791	−	0.155782i	$-0.950210\pi$
$919$	−19.0623	−	33.0169i	−0.628807	−	1.08913i	0.358984	−	0.933344i	$-0.383123\pi$
$920$		0			0
$921$	−1.81995	+	1.52712i	−0.0599695	+	0.0503204i
$922$	3.13737	+	3.73897i	0.103324	+	0.123136i
$923$	−20.1307	−	11.6225i	−0.662611	−	0.382559i
$924$	7.52682	+	13.0368i	0.247614	+	0.428880i
$925$		0			0
$926$	3.51163	−	19.9154i	0.115399	−	0.654462i
$927$	19.3549	−	3.41279i	0.635697	−	0.112091i
$928$	1.24283	+	3.41464i	0.0407977	+	0.112091i
$929$	−29.3240	−	24.6058i	−0.962090	−	0.807289i	0.0192022	−	0.999816i	$-0.493887\pi$
$929$	−29.3240	−	24.6058i	−0.962090	−	0.807289i	−0.981292	+	0.192527i	$0.938332\pi$
$930$		0			0
$931$	−32.9872	+	64.6962i	−1.08111	+	2.12033i
$932$		−	15.2411i		−	0.499238i
$933$	0.919999	−	1.09641i	0.0301194	−	0.0358949i
$934$	−36.6598	+	13.3431i	−1.19955	+	0.436599i
$935$		0			0
$936$	−1.78684	+	10.1337i	−0.0584047	+	0.331230i
$937$	0.644843	−	1.77169i	0.0210661	−	0.0578787i	−0.928714	−	0.370797i	$-0.879084\pi$
$937$	0.644843	−	1.77169i	0.0210661	−	0.0578787i	0.949780	+	0.312919i	$0.101307\pi$
$938$	−35.5742	+	20.5388i	−1.16154	+	0.670615i
$939$	1.55096	−	2.68635i	0.0506138	−	0.0876656i
$940$		0			0
$941$	−11.3282	+	9.50548i	−0.369288	+	0.309870i	−0.808480	−	0.588524i	$-0.799709\pi$
$941$	−11.3282	+	9.50548i	−0.369288	+	0.309870i	0.439192	+	0.898393i	$0.355265\pi$
$942$	−5.51072	−	3.18161i	−0.179549	−	0.103663i
$943$	8.82329	−	5.09413i	0.287326	−	0.165888i
$944$	−6.88331	−	2.50532i	−0.224033	−	0.0815412i
$945$		0			0
$946$	1.37858	+	7.81833i	0.0448216	+	0.254196i
$947$	1.94275	+	5.33767i	0.0631310	+	0.173451i	0.967248	−	0.253835i	$-0.0816920\pi$
$947$	1.94275	+	5.33767i	0.0631310	+	0.173451i	−0.904117	+	0.427286i	$0.859470\pi$
$948$	−6.16232	+	7.34396i	−0.200143	+	0.238521i
$949$	−4.92286			−0.159803
$950$		0			0
$951$	11.2200			0.363834
$952$	−4.38384	+	5.22446i	−0.142081	+	0.169326i
$953$	−4.40396	−	12.0998i	−0.142658	−	0.391950i	0.847701	−	0.530475i	$-0.177986\pi$
$953$	−4.40396	−	12.0998i	−0.142658	−	0.391950i	−0.990359	+	0.138524i	$0.955764\pi$
$954$	0.833855	+	4.72902i	0.0269970	+	0.153108i
$955$		0			0
$956$	−15.8088	−	5.75392i	−0.511292	−	0.186095i
$957$	9.73913	−	5.62289i	0.314821	−	0.181762i
$958$	26.9244	+	15.5448i	0.869886	+	0.502229i
$959$	−53.5885	+	44.9661i	−1.73046	+	1.45203i
$960$		0			0
$961$	−18.1509	+	31.4384i	−0.585514	+	1.01414i
$962$	−34.9387	+	20.1719i	−1.12647	+	0.650367i
$963$	−7.96618	+	21.8869i	−0.256706	+	0.705295i
$964$	1.58141	−	8.96862i	0.0509338	−	0.288860i
$965$		0			0
$966$	−14.0663	+	5.11972i	−0.452577	+	0.164724i
$967$	31.3467	−	37.3576i	1.00804	−	1.20134i	0.0286047	−	0.999591i	$-0.490894\pi$
$967$	31.3467	−	37.3576i	1.00804	−	1.20134i	0.979438	−	0.201747i	$-0.0646620\pi$
$968$			17.8269i			0.572979i
$969$	3.36856	+	1.03090i	0.108214	+	0.0331174i
$970$		0			0
$971$	22.9752	+	19.2784i	0.737308	+	0.618675i	0.932113	−	0.362167i	$-0.117963\pi$
$971$	22.9752	+	19.2784i	0.737308	+	0.618675i	−0.194805	+	0.980842i	$0.562407\pi$
$972$	−4.55864	−	12.5248i	−0.146218	−	0.401732i
$973$	−85.5120	+	15.0781i	−2.74139	+	0.483381i
$974$	−4.85765	+	27.5491i	−0.155649	+	0.882730i
$975$		0			0
$976$	−4.05753	−	7.02784i	−0.129878	−	0.224956i
$977$	46.5081	+	26.8514i	1.48792	+	0.859054i	0.999905	−	0.0137792i	$-0.00438620\pi$
$977$	46.5081	+	26.8514i	1.48792	+	0.859054i	0.488019	+	0.872833i	$0.337720\pi$
$978$	−2.19664	−	2.61785i	−0.0702407	−	0.0837096i
$979$	39.5193	−	33.1606i	1.26304	−	1.05982i
$980$		0			0
$981$	10.8442	+	18.7826i	0.346227	+	0.599683i
$982$	−1.01693	+	2.79400i	−0.0324516	+	0.0891600i
$983$	57.0469	+	10.0589i	1.81951	+	0.320829i	0.976246	−	0.216665i	$-0.0695180\pi$
$983$	57.0469	+	10.0589i	1.81951	+	0.320829i	0.843267	+	0.537495i	$0.180629\pi$
$984$	−0.191007	−	1.08326i	−0.00608908	−	0.0345329i
$985$		0			0
$986$	3.90292	+	3.27494i	0.124294	+	0.104295i
$987$			8.74864i			0.278472i
$988$	16.6872	+	2.05367i	0.530890	+	0.0653360i
$989$	−7.89434			−0.251025
$990$		0			0
$991$	6.56906	−	2.39094i	0.208673	−	0.0759508i	−0.235569	−	0.971858i	$-0.575695\pi$
$991$	6.56906	−	2.39094i	0.208673	−	0.0759508i	0.444242	+	0.895907i	$0.353473\pi$
$992$	8.07914	−	1.42457i	0.256513	−	0.0452302i
$993$	10.6209	+	1.87275i	0.337045	+	0.0594301i
$994$	27.5458	+	10.0258i	0.873698	+	0.318000i
$995$		0			0
$996$	−4.16773	+	7.21872i	−0.132060	+	0.228734i
$997$	24.4042	+	29.0837i	0.772887	+	0.921091i	0.998589	−	0.0531052i	$-0.0169119\pi$
$997$	24.4042	+	29.0837i	0.772887	+	0.921091i	−0.225702	+	0.974196i	$0.572467\pi$
$998$	11.8511	+	14.1236i	0.375140	+	0.447074i
$999$	17.0851	−	29.5923i	0.540550	−	0.936260i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.u.g.149.5		36
5.2	odd	4		950.2.l.i.301.2		18
5.3	odd	4		190.2.k.d.111.2	yes	18
5.4	even	2	inner	950.2.u.g.149.2		36
19.6	even	9	inner	950.2.u.g.899.2		36
95.33	even	36		3610.2.a.bj.1.4		9
95.43	odd	36		3610.2.a.bi.1.6		9
95.44	even	18	inner	950.2.u.g.899.5		36
95.63	odd	36		190.2.k.d.101.2	✓	18
95.82	odd	36		950.2.l.i.101.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.d.101.2	✓	18	95.63	odd	36
190.2.k.d.111.2	yes	18	5.3	odd	4
950.2.l.i.101.2		18	95.82	odd	36
950.2.l.i.301.2		18	5.2	odd	4
950.2.u.g.149.2		36	5.4	even	2	inner
950.2.u.g.149.5		36	1.1	even	1	trivial
950.2.u.g.899.2		36	19.6	even	9	inner
950.2.u.g.899.5		36	95.44	even	18	inner
3610.2.a.bi.1.6		9	95.43	odd	36
3610.2.a.bj.1.4		9	95.33	even	36

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.642788 - 0.766044i) q^{2} +(0.197144 + 0.541649i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(0.541649 + 0.197144i) q^{6} +(-4.21251 + 2.43209i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(2.04362 - 1.71480i) q^{9} +O(q^{10})\)	\(q+(0.642788 - 0.766044i) q^{2} +(0.197144 + 0.541649i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(0.541649 + 0.197144i) q^{6} +(-4.21251 + 2.43209i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(2.04362 - 1.71480i) q^{9} +(2.68454 - 4.64975i) q^{11} +(0.499186 - 0.288205i) q^{12} +(1.31923 - 3.62457i) q^{13} +(-0.844657 + 4.79029i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(-0.901248 + 1.07407i) q^{17} -2.66775i q^{18} +(-4.35299 + 0.226908i) q^{19} +(-2.14781 - 1.80223i) q^{21} +(-1.83633 - 5.04528i) q^{22} +(5.25780 - 0.927092i) q^{23} +(0.100093 - 0.567654i) q^{24} +(-1.92859 - 3.34042i) q^{26} +(2.82926 + 1.63348i) q^{27} +(3.12664 + 3.72618i) q^{28} +(2.78364 - 2.33575i) q^{29} +(-4.10189 - 7.10468i) q^{31} +(-0.342020 + 0.939693i) q^{32} +(3.04777 + 0.537405i) q^{33} +(0.243471 + 1.38079i) q^{34} +(-2.04362 - 1.71480i) q^{36} -10.4594i q^{37} +(-2.62423 + 3.48044i) q^{38} +2.22332 q^{39} +(1.79322 - 0.652678i) q^{41} +(-2.76117 + 0.486869i) q^{42} +(-1.45618 - 0.256764i) q^{43} +(-5.04528 - 1.83633i) q^{44} +(2.66945 - 4.62363i) q^{46} +(-2.00570 - 2.39030i) q^{47} +(-0.370510 - 0.441556i) q^{48} +(8.33016 - 14.4283i) q^{49} +(-0.759442 - 0.276414i) q^{51} +(-3.79858 - 0.669793i) q^{52} +(-1.77266 + 0.312568i) q^{53} +(3.06993 - 1.11736i) q^{54} +4.86419 q^{56} +(-0.981070 - 2.31306i) q^{57} -3.63378i q^{58} +(5.61133 + 4.70846i) q^{59} +(1.40916 + 7.99176i) q^{61} +(-8.07914 - 1.42457i) q^{62} +(-4.43820 + 12.1939i) q^{63} +(0.500000 + 0.866025i) q^{64} +(2.37075 - 1.98929i) q^{66} +(5.42827 + 6.46916i) q^{67} +(1.21425 + 0.701047i) q^{68} +(1.53870 + 2.66511i) q^{69} +(1.04647 - 5.93485i) q^{71} +(-2.62722 + 0.463250i) q^{72} +(-0.436515 - 1.19931i) q^{73} +(-8.01234 - 6.72316i) q^{74} +(0.979350 + 4.24746i) q^{76} +26.1162i q^{77} +(1.42912 - 1.70316i) q^{78} +(-15.6290 + 5.68848i) q^{79} +(1.06275 - 6.02717i) q^{81} +(0.652678 - 1.79322i) q^{82} +(-12.5236 + 7.23049i) q^{83} +(-1.40188 + 2.42814i) q^{84} +(-1.13271 + 0.950453i) q^{86} +(1.81393 + 1.04727i) q^{87} +(-4.64975 + 2.68454i) q^{88} +(9.02905 + 3.28630i) q^{89} +(3.25800 + 18.4770i) q^{91} +(-1.82601 - 5.01693i) q^{92} +(3.03958 - 3.62243i) q^{93} -3.12031 q^{94} -0.576411 q^{96} +(3.90758 - 4.65687i) q^{97} +(-5.69817 - 15.6556i) q^{98} +(-2.48722 - 14.1057i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 36 q^{9}+O(q^{10}) \) 36 * q + 36 * q^9	\( 36 q + 36 q^{9} - 24 q^{11} - 12 q^{14} + 24 q^{21} - 18 q^{26} + 12 q^{29} - 12 q^{31} - 36 q^{34} - 36 q^{36} - 96 q^{39} - 42 q^{41} - 6 q^{44} + 36 q^{46} + 78 q^{49} + 84 q^{51} + 108 q^{54} + 60 q^{59} + 96 q^{61} + 18 q^{64} + 48 q^{66} + 60 q^{69} + 60 q^{71} + 6 q^{74} - 42 q^{76} - 60 q^{79} + 36 q^{81} - 12 q^{84} + 72 q^{86} - 60 q^{89} - 120 q^{91} - 12 q^{94} - 342 q^{99}+O(q^{100}) \) 36 * q + 36 * q^9 - 24 * q^11 - 12 * q^14 + 24 * q^21 - 18 * q^26 + 12 * q^29 - 12 * q^31 - 36 * q^34 - 36 * q^36 - 96 * q^39 - 42 * q^41 - 6 * q^44 + 36 * q^46 + 78 * q^49 + 84 * q^51 + 108 * q^54 + 60 * q^59 + 96 * q^61 + 18 * q^64 + 48 * q^66 + 60 * q^69 + 60 * q^71 + 6 * q^74 - 42 * q^76 - 60 * q^79 + 36 * q^81 - 12 * q^84 + 72 * q^86 - 60 * q^89 - 120 * q^91 - 12 * q^94 - 342 * q^99

Introduction

L-functions

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