LMFDB - Embedded newform 950.2.q.g.293.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(107,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 10]))

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

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

chi := DirichletCharacter("950.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.q (of order $12$, degree $4$, 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:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			293.1
Character	$\chi$	$=$	950.293
Dual form			950.2.q.g.107.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(-0.570807 - 2.13028i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.10271 + 1.90996i) q^{6} +(-0.526345 + 0.526345i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.61420 + 0.931958i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.570807 - 2.13028i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.10271 + 1.90996i) q^{6} +(-0.526345 + 0.526345i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.61420 + 0.931958i) q^{9} -1.06054 q^{11} +(-1.55947 - 1.55947i) q^{12} +(-2.86922 - 0.768805i) q^{13} +(0.372182 - 0.644639i) q^{14} +(0.500000 - 0.866025i) q^{16} +(1.37028 + 5.11396i) q^{17} +(1.31799 - 1.31799i) q^{18} +(-0.610346 + 4.31596i) q^{19} +(1.42170 + 0.820821i) q^{21} +(1.02440 - 0.274488i) q^{22} +(-1.88935 + 7.05116i) q^{23} +(1.90996 + 1.10271i) q^{24} +2.97044 q^{26} +(-1.77169 - 1.77169i) q^{27} +(-0.192656 + 0.719001i) q^{28} +(-2.09166 - 3.62286i) q^{29} -0.212537i q^{31} +(-0.258819 + 0.965926i) q^{32} +(0.605364 + 2.25925i) q^{33} +(-2.64718 - 4.58505i) q^{34} +(-0.931958 + 1.61420i) q^{36} +(-0.476282 - 0.476282i) q^{37} +(-0.527502 - 4.32686i) q^{38} +6.55108i q^{39} +(-3.02929 - 1.74896i) q^{41} +(-1.58571 - 0.424888i) q^{42} +(-1.89630 + 0.508111i) q^{43} +(-0.918455 + 0.530270i) q^{44} -7.29989i q^{46} +(-2.97966 - 0.798398i) q^{47} +(-2.13028 - 0.570807i) q^{48} +6.44592i q^{49} +(10.1120 - 5.83817i) q^{51} +(-2.86922 + 0.768805i) q^{52} +(13.5838 + 3.63976i) q^{53} +(2.16987 + 1.25278i) q^{54} -0.744364i q^{56} +(9.54259 - 1.16337i) q^{57} +(2.95805 + 2.95805i) q^{58} +(-6.92591 + 11.9960i) q^{59} +(-2.71555 - 4.70348i) q^{61} +(0.0550088 + 0.205295i) q^{62} +(0.359094 - 1.34016i) q^{63} -1.00000i q^{64} +(-1.16947 - 2.02559i) q^{66} +(0.292219 - 1.09057i) q^{67} +(3.74368 + 3.74368i) q^{68} +16.0994 q^{69} +(11.0186 + 6.36159i) q^{71} +(0.482417 - 1.80040i) q^{72} +(10.5463 - 2.82587i) q^{73} +(0.583324 + 0.336782i) q^{74} +(1.62940 + 4.04290i) q^{76} +(0.558210 - 0.558210i) q^{77} +(-1.69555 - 6.32786i) q^{78} +(-2.13430 + 3.69672i) q^{79} +(-5.55878 + 9.62809i) q^{81} +(3.37874 + 0.905330i) q^{82} +(5.50824 + 5.50824i) q^{83} +1.64164 q^{84} +(1.70017 - 0.981595i) q^{86} +(-6.52378 + 6.52378i) q^{87} +(0.749915 - 0.749915i) q^{88} +(0.831602 + 1.44038i) q^{89} +(1.91486 - 1.10554i) q^{91} +(1.88935 + 7.05116i) q^{92} +(-0.452764 + 0.121318i) q^{93} +3.08477 q^{94} +2.20543 q^{96} +(-11.7778 + 3.15584i) q^{97} +(-1.66833 - 6.22628i) q^{98} +(1.71192 - 0.988379i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 12 q^{3} - 24 q^{7}+O(q^{10}) $ 32 * q + 12 * q^3 - 24 * q^7	$ 32 q + 12 q^{3} - 24 q^{7} - 16 q^{11} - 24 q^{13} + 16 q^{16} + 8 q^{17} + 12 q^{22} - 4 q^{23} - 16 q^{26} + 12 q^{28} + 24 q^{33} - 8 q^{36} - 16 q^{38} + 24 q^{41} - 20 q^{42} + 24 q^{43} + 36 q^{47} + 12 q^{48} + 24 q^{51} - 24 q^{52} + 72 q^{53} + 24 q^{57} - 24 q^{58} - 48 q^{61} + 4 q^{62} - 16 q^{63} + 32 q^{66} - 36 q^{67} - 16 q^{68} + 24 q^{71} - 8 q^{73} + 24 q^{77} + 24 q^{78} + 56 q^{81} - 8 q^{82} - 24 q^{83} - 104 q^{87} - 24 q^{91} + 4 q^{92} - 52 q^{93} + 24 q^{97} - 72 q^{98}+O(q^{100}) $ 32 * q + 12 * q^3 - 24 * q^7 - 16 * q^11 - 24 * q^13 + 16 * q^16 + 8 * q^17 + 12 * q^22 - 4 * q^23 - 16 * q^26 + 12 * q^28 + 24 * q^33 - 8 * q^36 - 16 * q^38 + 24 * q^41 - 20 * q^42 + 24 * q^43 + 36 * q^47 + 12 * q^48 + 24 * q^51 - 24 * q^52 + 72 * q^53 + 24 * q^57 - 24 * q^58 - 48 * q^61 + 4 * q^62 - 16 * q^63 + 32 * q^66 - 36 * q^67 - 16 * q^68 + 24 * q^71 - 8 * q^73 + 24 * q^77 + 24 * q^78 + 56 * q^81 - 8 * q^82 - 24 * q^83 - 104 * q^87 - 24 * q^91 + 4 * q^92 - 52 * q^93 + 24 * q^97 - 72 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$	−0.570807	−	2.13028i	−0.329556	−	1.22992i	−0.909652	−	0.415370i	$-0.863652\pi$
$3$	−0.570807	−	2.13028i	−0.329556	−	1.22992i	0.580097	−	0.814548i	$-0.303015\pi$
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$	1.10271	+	1.90996i	0.450181	+	0.779737i
$7$	−0.526345	+	0.526345i	−0.198940	+	0.198940i	−0.799545	−	0.600606i	$-0.794926\pi$
$7$	−0.526345	+	0.526345i	−0.198940	+	0.198940i	0.600606	+	0.799545i	$0.294926\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−1.61420	+	0.931958i	−0.538066	+	0.310653i
$10$		0			0
$11$	−1.06054			−0.319765			−0.159883	−	0.987136i	$-0.551112\pi$
$11$	−1.06054			−0.319765			−0.159883	+	0.987136i	$0.551112\pi$
$12$	−1.55947	−	1.55947i	−0.450181	−	0.450181i
$13$	−2.86922	−	0.768805i	−0.795779	−	0.213228i	−0.162049	−	0.986783i	$-0.551810\pi$
$13$	−2.86922	−	0.768805i	−0.795779	−	0.213228i	−0.633730	+	0.773554i	$0.718477\pi$
$14$	0.372182	−	0.644639i	0.0994699	−	0.172287i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	1.37028	+	5.11396i	0.332342	+	1.24032i	0.906722	+	0.421729i	$0.138577\pi$
$17$	1.37028	+	5.11396i	0.332342	+	1.24032i	−0.574380	+	0.818589i	$0.694757\pi$
$18$	1.31799	−	1.31799i	0.310653	−	0.310653i
$19$	−0.610346	+	4.31596i	−0.140023	+	0.990148i
$19$	−0.610346	+	4.31596i	−0.140023	+	0.990148i
$20$		0			0
$21$	1.42170	+	0.820821i	0.310241	+	0.179118i
$22$	1.02440	−	0.274488i	0.218404	−	0.0585211i
$23$	−1.88935	+	7.05116i	−0.393957	+	1.47027i	0.429592	+	0.903023i	$0.358657\pi$
$23$	−1.88935	+	7.05116i	−0.393957	+	1.47027i	−0.823549	+	0.567245i	$0.808009\pi$
$24$	1.90996	+	1.10271i	0.389868	+	0.225091i
$25$		0			0
$26$	2.97044			0.582550
$27$	−1.77169	−	1.77169i	−0.340963	−	0.340963i
$28$	−0.192656	+	0.719001i	−0.0364085	+	0.135878i
$29$	−2.09166	−	3.62286i	−0.388412	−	0.672749i	0.603824	−	0.797117i	$-0.293643\pi$
$29$	−2.09166	−	3.62286i	−0.388412	−	0.672749i	−0.992236	+	0.124369i	$0.960309\pi$
$30$		0			0
$31$		−	0.212537i		−	0.0381729i	−0.999818	−	0.0190864i	$-0.993924\pi$
$31$		−	0.212537i		−	0.0381729i	0.999818	−	0.0190864i	$-0.00607577\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	0.605364	+	2.25925i	0.105380	+	0.393285i
$34$	−2.64718	−	4.58505i	−0.453988	−	0.786330i
$35$		0			0
$36$	−0.931958	+	1.61420i	−0.155326	+	0.269033i
$37$	−0.476282	−	0.476282i	−0.0783002	−	0.0783002i	0.666872	−	0.745172i	$-0.267633\pi$
$37$	−0.476282	−	0.476282i	−0.0783002	−	0.0783002i	−0.745172	+	0.666872i	$0.767633\pi$
$38$	−0.527502	−	4.32686i	−0.0855722	−	0.701910i
$39$			6.55108i			1.04901i
$40$		0			0
$41$	−3.02929	−	1.74896i	−0.473096	−	0.273142i	0.244439	−	0.969665i	$-0.421396\pi$
$41$	−3.02929	−	1.74896i	−0.473096	−	0.273142i	−0.717535	+	0.696522i	$0.754730\pi$
$42$	−1.58571	−	0.424888i	−0.244680	−	0.0655617i
$43$	−1.89630	+	0.508111i	−0.289182	+	0.0774862i	−0.400494	−	0.916299i	$-0.631161\pi$
$43$	−1.89630	+	0.508111i	−0.289182	+	0.0774862i	0.111312	+	0.993786i	$0.464495\pi$
$44$	−0.918455	+	0.530270i	−0.138462	+	0.0799413i
$45$		0			0
$46$		−	7.29989i		−	1.07631i
$47$	−2.97966	−	0.798398i	−0.434628	−	0.116458i	0.0348697	−	0.999392i	$-0.488898\pi$
$47$	−2.97966	−	0.798398i	−0.434628	−	0.116458i	−0.469498	+	0.882934i	$0.655565\pi$
$48$	−2.13028	−	0.570807i	−0.307479	−	0.0823889i
$49$			6.44592i			0.920846i
$50$		0			0
$51$	10.1120	−	5.83817i	1.41596	−	0.817507i
$52$	−2.86922	+	0.768805i	−0.397889	+	0.106614i
$53$	13.5838	+	3.63976i	1.86588	+	0.499960i	1.00000		0.000297173i	$-9.45930e-5\pi$
$53$	13.5838	+	3.63976i	1.86588	+	0.499960i	0.865877	+	0.500257i	$0.166761\pi$
$54$	2.16987	+	1.25278i	0.295282	+	0.170481i
$55$		0			0
$56$		−	0.744364i		−	0.0994699i
$57$	9.54259	−	1.16337i	1.26395	−	0.154092i
$58$	2.95805	+	2.95805i	0.388412	+	0.388412i
$59$	−6.92591	+	11.9960i	−0.901677	+	1.56175i	−0.0763602	+	0.997080i	$0.524330\pi$
$59$	−6.92591	+	11.9960i	−0.901677	+	1.56175i	−0.825317	+	0.564670i	$0.809003\pi$
$60$		0			0
$61$	−2.71555	−	4.70348i	−0.347691	−	0.602219i	0.638148	−	0.769914i	$-0.279701\pi$
$61$	−2.71555	−	4.70348i	−0.347691	−	0.602219i	−0.985839	+	0.167695i	$0.946368\pi$
$62$	0.0550088	+	0.205295i	0.00698612	+	0.0260725i
$63$	0.359094	−	1.34016i	0.0452416	−	0.168844i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	−1.16947	−	2.02559i	−0.143952	−	0.249333i
$67$	0.292219	−	1.09057i	0.0357002	−	0.133235i	−0.945776	−	0.324820i	$-0.894696\pi$
$67$	0.292219	−	1.09057i	0.0357002	−	0.133235i	0.981476	+	0.191585i	$0.0613629\pi$
$68$	3.74368	+	3.74368i	0.453988	+	0.453988i
$69$	16.0994			1.93814
$70$		0			0
$71$	11.0186	+	6.36159i	1.30767	+	0.754982i	0.981706	−	0.190401i	$-0.0609790\pi$
$71$	11.0186	+	6.36159i	1.30767	+	0.754982i	0.325961	+	0.945383i	$0.394312\pi$
$72$	0.482417	−	1.80040i	0.0568534	−	0.212180i
$73$	10.5463	−	2.82587i	1.23435	−	0.330744i	0.418079	−	0.908411i	$-0.362703\pi$
$73$	10.5463	−	2.82587i	1.23435	−	0.330744i	0.816272	+	0.577667i	$0.196037\pi$
$74$	0.583324	+	0.336782i	0.0678100	+	0.0391501i
$75$		0			0
$76$	1.62940	+	4.04290i	0.186905	+	0.463753i
$77$	0.558210	−	0.558210i	0.0636140	−	0.0636140i
$78$	−1.69555	−	6.32786i	−0.191983	−	0.716489i
$79$	−2.13430	+	3.69672i	−0.240128	+	0.415914i	−0.960751	−	0.277414i	$-0.910523\pi$
$79$	−2.13430	+	3.69672i	−0.240128	+	0.415914i	0.720623	+	0.693327i	$0.243856\pi$
$80$		0			0
$81$	−5.55878	+	9.62809i	−0.617643	+	1.06979i
$82$	3.37874	+	0.905330i	0.373119	+	0.0999770i
$83$	5.50824	+	5.50824i	0.604608	+	0.604608i	0.941532	−	0.336924i	$-0.109387\pi$
$83$	5.50824	+	5.50824i	0.604608	+	0.604608i	−0.336924	+	0.941532i	$0.609387\pi$
$84$	1.64164			0.179118
$85$		0			0
$86$	1.70017	−	0.981595i	0.183334	−	0.105848i
$87$	−6.52378	+	6.52378i	−0.699422	+	0.699422i
$88$	0.749915	−	0.749915i	0.0799413	−	0.0799413i
$89$	0.831602	+	1.44038i	0.0881496	+	0.152680i	0.906729	−	0.421714i	$-0.138571\pi$
$89$	0.831602	+	1.44038i	0.0881496	+	0.152680i	−0.818579	+	0.574393i	$0.805238\pi$
$90$		0			0
$91$	1.91486	−	1.10554i	0.200732	−	0.115892i
$92$	1.88935	+	7.05116i	0.196979	+	0.735134i
$93$	−0.452764	+	0.121318i	−0.0469495	+	0.0125801i
$94$	3.08477			0.318170
$95$		0			0
$96$	2.20543			0.225091
$97$	−11.7778	+	3.15584i	−1.19585	+	0.320427i	−0.801196	−	0.598402i	$-0.795802\pi$
$97$	−11.7778	+	3.15584i	−1.19585	+	0.320427i	−0.394655	+	0.918830i	$0.629136\pi$
$98$	−1.66833	−	6.22628i	−0.168527	−	0.628949i
$99$	1.71192	−	0.988379i	0.172055	−	0.0993358i
$100$		0			0
$101$	7.25213	+	12.5611i	0.721614	+	1.24987i	0.960353	+	0.278788i	$0.0899328\pi$
$101$	7.25213	+	12.5611i	0.721614	+	1.24987i	−0.238738	+	0.971084i	$0.576734\pi$
$102$	−8.25642	+	8.25642i	−0.817507	+	0.817507i
$103$	−10.0636	+	10.0636i	−0.991596	+	0.991596i	−0.999965	−	0.00836877i	$-0.997336\pi$
$103$	−10.0636	+	10.0636i	−0.991596	+	0.991596i	0.00836877	+	0.999965i	$0.497336\pi$
$104$	2.57247	−	1.48522i	0.252252	−	0.145638i
$105$		0			0
$106$	−14.0630			−1.36592
$107$	−9.27061	−	9.27061i	−0.896224	−	0.896224i	0.0988761	−	0.995100i	$-0.468475\pi$
$107$	−9.27061	−	9.27061i	−0.896224	−	0.896224i	−0.995100	+	0.0988761i	$0.968475\pi$
$108$	−2.42018	−	0.648485i	−0.232882	−	0.0624005i
$109$	6.82603	−	11.8230i	0.653815	−	1.13244i	−0.328374	−	0.944548i	$-0.606501\pi$
$109$	6.82603	−	11.8230i	0.653815	−	1.13244i	0.982189	−	0.187893i	$-0.0601659\pi$
$110$		0			0
$111$	−0.742749	+	1.28648i	−0.0704986	+	0.122107i
$112$	0.192656	+	0.719001i	0.0182043	+	0.0679392i
$113$	3.56502	−	3.56502i	0.335369	−	0.335369i	−0.519252	−	0.854621i	$-0.673790\pi$
$113$	3.56502	−	3.56502i	0.335369	−	0.335369i	0.854621	+	0.519252i	$0.173790\pi$
$114$	−8.91633	+	3.59353i	−0.835091	+	0.336565i
$115$		0			0
$116$	−3.62286	−	2.09166i	−0.336374	−	0.194206i
$117$	5.34798	−	1.43299i	0.494421	−	0.132480i
$118$	3.58512	−	13.3798i	0.330037	−	1.23171i
$119$	−3.41295	−	1.97047i	−0.312865	−	0.180633i
$120$		0			0
$121$	−9.87525			−0.897750
$122$	3.84037	+	3.84037i	0.347691	+	0.347691i
$123$	−1.99664	+	7.45157i	−0.180031	+	0.671885i
$124$	−0.106269	−	0.184063i	−0.00954322	−	0.0165293i
$125$		0			0
$126$			1.38743i			0.123602i
$127$	1.60526	−	5.99091i	0.142444	−	0.531607i	−0.857412	−	0.514630i	$-0.827929\pi$
$127$	1.60526	−	5.99091i	0.142444	−	0.531607i	0.999856	−	0.0169768i	$-0.00540416\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	2.16484	+	3.74961i	0.190603	+	0.330135i
$130$		0			0
$131$	2.17592	−	3.76880i	0.190111	−	0.329281i	−0.755176	−	0.655522i	$-0.772449\pi$
$131$	2.17592	−	3.76880i	0.190111	−	0.329281i	0.945287	+	0.326241i	$0.105782\pi$
$132$	1.65388	+	1.65388i	0.143952	+	0.143952i
$133$	−1.95043	−	2.59294i	−0.169124	−	0.224836i
$134$			1.12905i			0.0975347i
$135$		0			0
$136$	−4.58505	−	2.64718i	−0.393165	−	0.226994i
$137$	17.9819	+	4.81823i	1.53630	+	0.411649i	0.925067	−	0.379804i	$-0.124009\pi$
$137$	17.9819	+	4.81823i	1.53630	+	0.411649i	0.611229	+	0.791454i	$0.290675\pi$
$138$	−15.5508	+	4.16683i	−1.32377	+	0.354704i
$139$	−8.68264	+	5.01293i	−0.736452	+	0.425191i	−0.820778	−	0.571247i	$-0.806460\pi$
$139$	−8.68264	+	5.01293i	−0.736452	+	0.425191i	0.0843257	+	0.996438i	$0.473126\pi$
$140$		0			0
$141$			6.80325i			0.572937i
$142$	−12.2896	−	3.29300i	−1.03132	−	0.276343i
$143$	3.04293	+	0.815349i	0.254462	+	0.0681829i
$144$			1.86392i			0.155326i
$145$		0			0
$146$	−9.45556	+	5.45917i	−0.782548	+	0.451804i
$147$	13.7316	−	3.67938i	1.13256	−	0.303470i
$148$	−0.650613	−	0.174331i	−0.0534801	−	0.0143299i
$149$	−12.2575	−	7.07688i	−1.00418	−	0.579761i	−0.0946943	−	0.995506i	$-0.530187\pi$
$149$	−12.2575	−	7.07688i	−1.00418	−	0.579761i	−0.909481	+	0.415746i	$0.863521\pi$
$150$		0			0
$151$			0.0824251i			0.00670766i	0.999994	+	0.00335383i	$0.00106756\pi$
$151$			0.0824251i			0.00670766i	−0.999994	+	0.00335383i	$0.998932\pi$
$152$	−2.62026	−	3.48342i	−0.212531	−	0.282543i
$153$	−6.97790	−	6.97790i	−0.564130	−	0.564130i
$154$	−0.394714	+	0.683665i	−0.0318070	+	0.0550913i
$155$		0			0
$156$	3.27554	+	5.67341i	0.262253	+	0.454236i
$157$	−0.788803	−	2.94385i	−0.0629533	−	0.234945i	0.927279	−	0.374370i	$-0.122141\pi$
$157$	−0.788803	−	2.94385i	−0.0629533	−	0.234945i	−0.990233	+	0.139425i	$0.955474\pi$
$158$	1.10480	−	4.12316i	0.0878929	−	0.328021i
$159$		−	31.0149i		−	2.45964i
$160$		0			0
$161$	−2.71689	−	4.70579i	−0.214121	−	0.370868i
$162$	2.87744	−	10.7387i	0.226073	−	0.843715i
$163$	−13.5003	−	13.5003i	−1.05742	−	1.05742i	−0.998248	−	0.0591770i	$-0.981152\pi$
$163$	−13.5003	−	13.5003i	−1.05742	−	1.05742i	−0.0591770	−	0.998248i	$-0.518848\pi$
$164$	−3.49793			−0.273142
$165$		0			0
$166$	−6.74619	−	3.89491i	−0.523606	−	0.302304i
$167$	−3.88702	+	14.5066i	−0.300787	+	1.12255i	0.635725	+	0.771915i	$0.280701\pi$
$167$	−3.88702	+	14.5066i	−0.300787	+	1.12255i	−0.936512	+	0.350636i	$0.885966\pi$
$168$	−1.58571	+	0.424888i	−0.122340	+	0.0327809i
$169$	−3.61696	−	2.08825i	−0.278228	−	0.160635i
$170$		0			0
$171$	−3.03707	−	7.53562i	−0.232250	−	0.576264i
$172$	−1.38818	+	1.38818i	−0.105848	+	0.105848i
$173$	5.75359	+	21.4727i	0.437438	+	1.63254i	0.735165	+	0.677888i	$0.237105\pi$
$173$	5.75359	+	21.4727i	0.437438	+	1.63254i	−0.297727	+	0.954651i	$0.596229\pi$
$174$	4.61301	−	7.98996i	0.349711	−	0.605718i
$175$		0			0
$176$	−0.530270	+	0.918455i	−0.0399706	+	0.0692312i
$177$	29.5083	+	7.90672i	2.21798	+	0.594305i
$178$	−1.17606	−	1.17606i	−0.0881496	−	0.0881496i
$179$	−3.26598			−0.244111			−0.122055	−	0.992523i	$-0.538949\pi$
$179$	−3.26598			−0.244111			−0.122055	+	0.992523i	$0.538949\pi$
$180$		0			0
$181$	11.6168	−	6.70695i	0.863469	−	0.498524i	−0.00170370	−	0.999999i	$-0.500542\pi$
$181$	11.6168	−	6.70695i	0.863469	−	0.498524i	0.865172	+	0.501475i	$0.167209\pi$
$182$	−1.56347	+	1.56347i	−0.115892	+	0.115892i
$183$	−8.46967	+	8.46967i	−0.626096	+	0.626096i
$184$	−3.64995	−	6.32189i	−0.269078	−	0.466056i
$185$		0			0
$186$	0.405938	−	0.234368i	0.0297648	−	0.0171847i
$187$	−1.45324	−	5.42356i	−0.106271	−	0.396610i
$188$	−2.97966	+	0.798398i	−0.217314	+	0.0582291i
$189$	1.86505			0.135662
$190$		0			0
$191$	−18.7214			−1.35463			−0.677315	−	0.735693i	$-0.736856\pi$
$191$	−18.7214			−1.35463			−0.677315	+	0.735693i	$0.736856\pi$
$192$	−2.13028	+	0.570807i	−0.153740	+	0.0411944i
$193$	−0.260402	−	0.971835i	−0.0187442	−	0.0699542i	0.955920	−	0.293626i	$-0.0948622\pi$
$193$	−0.260402	−	0.971835i	−0.0187442	−	0.0699542i	−0.974664	+	0.223672i	$0.928195\pi$
$194$	10.5596	−	6.09662i	0.758139	−	0.437712i
$195$		0			0
$196$	3.22296	+	5.58233i	0.230211	+	0.398738i
$197$	−6.69899	+	6.69899i	−0.477283	+	0.477283i	−0.904262	−	0.426979i	$-0.859578\pi$
$197$	−6.69899	+	6.69899i	−0.477283	+	0.477283i	0.426979	+	0.904262i	$0.359578\pi$
$198$	−1.39778	+	1.39778i	−0.0993358	+	0.0993358i
$199$	0.787477	−	0.454650i	0.0558227	−	0.0322293i	−0.471829	−	0.881690i	$-0.656406\pi$
$199$	0.787477	−	0.454650i	0.0558227	−	0.0322293i	0.527652	+	0.849461i	$0.323073\pi$
$200$		0			0
$201$	−2.49003			−0.175633
$202$	−10.2561	−	10.2561i	−0.721614	−	0.721614i
$203$	3.00781	+	0.805941i	0.211107	+	0.0565659i
$204$	5.83817	−	10.1120i	0.408754	−	0.707982i
$205$		0			0
$206$	7.11604	−	12.3253i	0.495798	−	0.858748i
$207$	−3.52159	−	13.1428i	−0.244767	−	0.913485i
$208$	−2.10042	+	2.10042i	−0.145638	+	0.145638i
$209$	0.647297	−	4.57725i	0.0447745	−	0.316615i
$210$		0			0
$211$	−19.9485	−	11.5173i	−1.37331	−	0.792882i	−0.381968	−	0.924175i	$-0.624754\pi$
$211$	−19.9485	−	11.5173i	−1.37331	−	0.792882i	−0.991344	+	0.131294i	$0.958087\pi$
$212$	13.5838	−	3.63976i	0.932938	−	0.249980i
$213$	7.26248	−	27.1039i	0.497617	−	1.85713i
$214$	11.3541	+	6.55531i	0.776152	+	0.448112i
$215$		0			0
$216$	2.50555			0.170481
$217$	0.111868	+	0.111868i	0.00759410	+	0.00759410i
$218$	−3.53341	+	13.1869i	−0.239313	+	0.893128i
$219$	−12.0398	−	20.8536i	−0.813575	−	1.40915i
$220$		0			0
$221$		−	15.7266i		−	1.05788i
$222$	0.384475	−	1.43488i	0.0258043	−	0.0963029i
$223$	−2.34651	−	8.75728i	−0.157134	−	0.586431i	−0.998913	−	0.0466094i	$-0.985158\pi$
$223$	−2.34651	−	8.75728i	−0.157134	−	0.586431i	0.841779	−	0.539822i	$-0.181508\pi$
$224$	−0.372182	−	0.644639i	−0.0248675	−	0.0430717i
$225$		0			0
$226$	−2.52085	+	4.36624i	−0.167684	+	0.290438i
$227$	−8.32995	−	8.32995i	−0.552878	−	0.552878i	0.374392	−	0.927270i	$-0.377851\pi$
$227$	−8.32995	−	8.32995i	−0.552878	−	0.552878i	−0.927270	+	0.374392i	$0.877851\pi$
$228$	7.68244	−	5.77880i	0.508782	−	0.382710i
$229$			1.57480i			0.104066i	0.998645	+	0.0520328i	$0.0165700\pi$
$229$			1.57480i			0.104066i	−0.998645	+	0.0520328i	$0.983430\pi$
$230$		0			0
$231$	−1.50778	−	0.870514i	−0.0992043	−	0.0572756i
$232$	4.04078	+	1.08272i	0.265290	+	0.0710843i
$233$	−24.1552	+	6.47235i	−1.58246	+	0.424018i	−0.939685	−	0.342040i	$-0.888882\pi$
$233$	−24.1552	+	6.47235i	−1.58246	+	0.424018i	−0.642771	+	0.766058i	$0.722216\pi$
$234$	−4.79487	+	2.76832i	−0.313451	+	0.180971i
$235$		0			0
$236$			13.8518i			0.901677i
$237$	9.09333	+	2.43655i	0.590675	+	0.158271i
$238$	3.80665	+	1.01999i	0.246749	+	0.0661161i
$239$			27.3266i			1.76761i	0.467852	+	0.883807i	$0.345028\pi$
$239$			27.3266i			1.76761i	−0.467852	+	0.883807i	$0.654972\pi$
$240$		0			0
$241$	7.63547	−	4.40834i	0.491844	−	0.283966i	−0.233495	−	0.972358i	$-0.575016\pi$
$241$	7.63547	−	4.40834i	0.491844	−	0.283966i	0.725339	+	0.688392i	$0.241683\pi$
$242$	9.53876	−	2.55590i	0.613175	−	0.164300i
$243$	16.4230	+	4.40053i	1.05354	+	0.282294i
$244$	−4.70348	−	2.71555i	−0.301109	−	0.173846i
$245$		0			0
$246$		−	7.71443i		−	0.491854i
$247$	5.06935	−	11.9142i	0.322555	−	0.758082i
$248$	0.150287	+	0.150287i	0.00954322	+	0.00954322i
$249$	8.58995	−	14.8782i	0.544366	−	0.942870i
$250$		0			0
$251$	8.56706	+	14.8386i	0.540748	+	0.936603i	0.998861	+	0.0477090i	$0.0151920\pi$
$251$	8.56706	+	14.8386i	0.540748	+	0.936603i	−0.458113	+	0.888894i	$0.651475\pi$
$252$	−0.359094	−	1.34016i	−0.0226208	−	0.0844219i
$253$	2.00373	−	7.47804i	0.125974	−	0.470140i
$254$			6.20224i			0.389163i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.10918	−	26.5318i	0.443458	−	1.65501i	−0.276517	−	0.961009i	$-0.589180\pi$
$257$	7.10918	−	26.5318i	0.443458	−	1.65501i	0.719975	−	0.694000i	$-0.244153\pi$
$258$	−3.06154	−	3.06154i	−0.190603	−	0.190603i
$259$	0.501377			0.0311541
$260$		0			0
$261$	6.75271	+	3.89868i	0.417982	+	0.241322i
$262$	−1.12634	+	4.20355i	−0.0695854	+	0.259696i
$263$	−16.2841	+	4.36332i	−1.00412	+	0.269054i	−0.723172	−	0.690668i	$-0.757317\pi$
$263$	−16.2841	+	4.36332i	−1.00412	+	0.269054i	−0.280951	+	0.959722i	$0.590650\pi$
$264$	−2.02559	−	1.16947i	−0.124666	−	0.0719761i
$265$		0			0
$266$	2.55507	+	1.99977i	0.156661	+	0.122614i
$267$	2.59372	−	2.59372i	0.158733	−	0.158733i
$268$	−0.292219	−	1.09057i	−0.0178501	−	0.0666174i
$269$	2.80111	−	4.85166i	0.170787	−	0.295811i	−0.767909	−	0.640560i	$-0.778702\pi$
$269$	2.80111	−	4.85166i	0.170787	−	0.295811i	0.938695	+	0.344749i	$0.112036\pi$
$270$		0			0
$271$	0.597168	−	1.03433i	0.0362754	−	0.0628308i	−0.847318	−	0.531086i	$-0.821784\pi$
$271$	0.597168	−	1.03433i	0.0362754	−	0.0628308i	0.883593	+	0.468256i	$0.155117\pi$
$272$	5.11396	+	1.37028i	0.310080	+	0.0830856i
$273$	−3.44813	−	3.44813i	−0.208690	−	0.208690i
$274$	−18.6162			−1.12465
$275$		0			0
$276$	13.9425	−	8.04970i	0.839239	−	0.484535i
$277$	−18.5238	+	18.5238i	−1.11299	+	1.11299i	−0.120246	+	0.992744i	$0.538368\pi$
$277$	−18.5238	+	18.5238i	−1.11299	+	1.11299i	−0.992744	+	0.120246i	$0.961632\pi$
$278$	7.08935	−	7.08935i	0.425191	−	0.425191i
$279$	0.198076	+	0.343078i	0.0118585	+	0.0205395i
$280$		0			0
$281$	4.21180	−	2.43169i	0.251255	−	0.145062i	−0.369084	−	0.929396i	$-0.620328\pi$
$281$	4.21180	−	2.43169i	0.251255	−	0.145062i	0.620339	+	0.784334i	$0.286995\pi$
$282$	−1.76081	−	6.57143i	−0.104855	−	0.391323i
$283$	22.6837	−	6.07808i	1.34841	−	0.361305i	0.488861	−	0.872362i	$-0.337413\pi$
$283$	22.6837	−	6.07808i	1.34841	−	0.361305i	0.859547	+	0.511057i	$0.170746\pi$
$284$	12.7232			0.754982
$285$		0			0
$286$	−3.15027			−0.186279
$287$	2.51501	−	0.673896i	0.148457	−	0.0397788i
$288$	−0.482417	−	1.80040i	−0.0284267	−	0.106090i
$289$	−9.55251	+	5.51514i	−0.561912	+	0.324420i
$290$		0			0
$291$	13.4457	+	23.2886i	0.788198	+	1.36520i
$292$	7.72043	−	7.72043i	0.451804	−	0.451804i
$293$	−6.38942	+	6.38942i	−0.373274	+	0.373274i	−0.868668	−	0.495394i	$-0.835024\pi$
$293$	−6.38942	+	6.38942i	−0.373274	+	0.373274i	0.495394	+	0.868668i	$0.335024\pi$
$294$	−12.3114	+	7.10801i	−0.718017	+	0.414548i
$295$		0			0
$296$	0.673564			0.0391501
$297$	1.87895	+	1.87895i	0.109028	+	0.109028i
$298$	13.6715	+	3.66326i	0.791968	+	0.212207i
$299$	10.8419	−	18.7788i	0.627005	−	1.08600i
$300$		0			0
$301$	0.730664	−	1.26555i	0.0421148	−	0.0729449i
$302$	−0.0213332	−	0.0796166i	−0.00122759	−	0.00458142i
$303$	22.6190	−	22.6190i	1.29943	−	1.29943i
$304$	3.43255	+	2.68655i	0.196871	+	0.154084i
$305$		0			0
$306$	8.54615	+	4.93412i	0.488551	+	0.282065i
$307$	−26.9385	+	7.21815i	−1.53746	+	0.411962i	−0.925445	−	0.378882i	$-0.876309\pi$
$307$	−26.9385	+	7.21815i	−1.53746	+	0.411962i	−0.612018	+	0.790844i	$0.709642\pi$
$308$	0.204319	−	0.762530i	0.0116422	−	0.0434492i
$309$	27.1827	+	15.6939i	1.54637	+	0.892796i
$310$		0			0
$311$	−4.80047			−0.272210			−0.136105	−	0.990694i	$-0.543458\pi$
$311$	−4.80047			−0.272210			−0.136105	+	0.990694i	$0.543458\pi$
$312$	−4.63232	−	4.63232i	−0.262253	−	0.262253i
$313$	4.02579	−	15.0244i	0.227551	−	0.849232i	−0.753815	−	0.657086i	$-0.771789\pi$
$313$	4.02579	−	15.0244i	0.227551	−	0.849232i	0.981366	−	0.192146i	$-0.0615446\pi$
$314$	1.52385	+	2.63939i	0.0859959	+	0.148949i
$315$		0			0
$316$			4.26861i			0.240128i
$317$	4.90704	−	18.3133i	0.275607	−	1.02858i	−0.679827	−	0.733373i	$-0.737945\pi$
$317$	4.90704	−	18.3133i	0.275607	−	1.02858i	0.955434	−	0.295206i	$-0.0953884\pi$
$318$	8.02724	+	29.9581i	0.450145	+	1.67997i
$319$	2.21829	+	3.84219i	0.124200	+	0.215121i
$320$		0			0
$321$	−14.4573	+	25.0407i	−0.806926	+	1.39764i
$322$	3.84226	+	3.84226i	0.214121	+	0.214121i
$323$	−22.9080	+	2.79279i	−1.27463	+	0.155395i
$324$			11.1176i			0.617643i
$325$		0			0
$326$	16.5344	+	9.54615i	0.915756	+	0.528712i
$327$	−29.0827	−	7.79269i	−1.60828	−	0.430937i
$328$	3.37874	−	0.905330i	0.186560	−	0.0499885i
$329$	1.98856	−	1.14810i	0.109633	−	0.0632967i
$330$		0			0
$331$		−	26.4861i		−	1.45581i	−0.685678	−	0.727905i	$-0.740494\pi$
$331$		−	26.4861i		−	1.45581i	0.685678	−	0.727905i	$-0.259506\pi$
$332$	7.52439	+	2.01616i	0.412955	+	0.110651i
$333$	1.21269	+	0.324939i	0.0664549	+	0.0178065i
$334$		−	15.0183i		−	0.821765i
$335$		0			0
$336$	1.42170	−	0.820821i	0.0775603	−	0.0447795i
$337$	−9.19179	+	2.46293i	−0.500709	+	0.134165i	−0.500329	−	0.865835i	$-0.666788\pi$
$337$	−9.19179	+	2.46293i	−0.500709	+	0.134165i	−0.000379952		1.00000i	$0.500121\pi$
$338$	4.03420	+	1.08096i	0.219431	+	0.0587965i
$339$	−9.62942	−	5.55955i	−0.522998	−	0.301953i
$340$		0			0
$341$			0.225405i			0.0122063i
$342$	4.88395	+	6.49280i	0.264094	+	0.351091i
$343$	−7.07720	−	7.07720i	−0.382133	−	0.382133i
$344$	0.981595	−	1.70017i	0.0529240	−	0.0916671i
$345$		0			0
$346$	−11.1151	−	19.2519i	−0.597551	−	1.03499i
$347$	−4.29550	−	16.0310i	−0.230595	−	0.860591i	−0.980085	−	0.198576i	$-0.936368\pi$
$347$	−4.29550	−	16.0310i	−0.230595	−	0.860591i	0.749491	−	0.662015i	$-0.230298\pi$
$348$	−2.38787	+	8.91165i	−0.128003	+	0.477714i
$349$			11.0407i			0.590993i	0.955344	+	0.295497i	$0.0954851\pi$
$349$			11.0407i			0.590993i	−0.955344	+	0.295497i	$0.904515\pi$
$350$		0			0
$351$	3.72129	+	6.44547i	0.198628	+	0.344034i
$352$	0.274488	−	1.02440i	0.0146303	−	0.0546009i
$353$	−10.4033	−	10.4033i	−0.553713	−	0.553713i	0.373797	−	0.927511i	$-0.378056\pi$
$353$	−10.4033	−	10.4033i	−0.553713	−	0.553713i	−0.927511	+	0.373797i	$0.878056\pi$
$354$	−30.5492			−1.62367
$355$		0			0
$356$	1.44038	+	0.831602i	0.0763398	+	0.0440748i
$357$	−2.24951	+	8.39530i	−0.119057	+	0.444326i
$358$	3.15469	−	0.845298i	0.166731	−	0.0446754i
$359$	15.5898	+	9.00075i	0.822796	+	0.475042i	0.851380	−	0.524550i	$-0.175766\pi$
$359$	15.5898	+	9.00075i	0.822796	+	0.475042i	−0.0285837	+	0.999591i	$0.509100\pi$
$360$		0			0
$361$	−18.2550	−	5.26846i	−0.960787	−	0.277287i
$362$	−9.48506	+	9.48506i	−0.498524	+	0.498524i
$363$	5.63686	+	21.0371i	0.295859	+	1.10416i
$364$	1.10554	−	1.91486i	0.0579462	−	0.100366i
$365$		0			0
$366$	5.98896	−	10.3732i	0.313048	−	0.542215i
$367$	24.2299	+	6.49239i	1.26479	+	0.338900i	0.828033	−	0.560679i	$-0.189460\pi$
$367$	24.2299	+	6.49239i	1.26479	+	0.338900i	0.436758	+	0.899579i	$0.356126\pi$
$368$	5.16180	+	5.16180i	0.269078	+	0.269078i
$369$	6.51984			0.339409
$370$		0			0
$371$	−9.06553	+	5.23399i	−0.470659	+	0.271735i
$372$	−0.331447	+	0.331447i	−0.0171847	+	0.0171847i
$373$	1.41651	−	1.41651i	0.0733441	−	0.0733441i	−0.669483	−	0.742827i	$-0.733484\pi$
$373$	1.41651	−	1.41651i	0.0733441	−	0.0733441i	0.742827	+	0.669483i	$0.233484\pi$
$374$	2.80744	+	4.86263i	0.145169	+	0.251441i
$375$		0			0
$376$	2.67149	−	1.54239i	0.137772	−	0.0795425i
$377$	3.21616	+	12.0029i	0.165641	+	0.618179i
$378$	−1.80150	+	0.482709i	−0.0926589	+	0.0248279i
$379$	−1.62081			−0.0832554			−0.0416277	−	0.999133i	$-0.513254\pi$
$379$	−1.62081			−0.0832554			−0.0416277	+	0.999133i	$0.513254\pi$
$380$		0			0
$381$	−13.6786			−0.700776
$382$	18.0834	−	4.84544i	0.925229	−	0.247914i
$383$	6.45289	+	24.0825i	0.329727	+	1.23056i	0.909474	+	0.415761i	$0.136485\pi$
$383$	6.45289	+	24.0825i	0.329727	+	1.23056i	−0.579747	+	0.814797i	$0.696849\pi$
$384$	1.90996	−	1.10271i	0.0974671	−	0.0562727i
$385$		0			0
$386$	0.503059	+	0.871323i	0.0256050	+	0.0443492i
$387$	2.58746	−	2.58746i	0.131528	−	0.131528i
$388$	−8.62192	+	8.62192i	−0.437712	+	0.437712i
$389$	−16.2493	+	9.38152i	−0.823870	+	0.475662i	−0.851749	−	0.523950i	$-0.824458\pi$
$389$	−16.2493	+	9.38152i	−0.823870	+	0.475662i	0.0278790	+	0.999611i	$0.491125\pi$
$390$		0			0
$391$	−38.6483			−1.95453
$392$	−4.55795	−	4.55795i	−0.230211	−	0.230211i
$393$	−9.27063	−	2.48406i	−0.467641	−	0.125304i
$394$	4.73690	−	8.20455i	0.238642	−	0.413339i
$395$		0			0
$396$	0.988379	−	1.71192i	0.0496679	−	0.0860273i
$397$	4.82505	+	18.0073i	0.242163	+	0.903763i	0.974788	+	0.223131i	$0.0716279\pi$
$397$	4.82505	+	18.0073i	0.242163	+	0.903763i	−0.732626	+	0.680632i	$0.761705\pi$
$398$	−0.642972	+	0.642972i	−0.0322293	+	0.0322293i
$399$	−4.41036	+	5.63503i	−0.220794	+	0.282104i
$400$		0			0
$401$	14.4535	+	8.34471i	0.721772	+	0.416715i	0.815404	−	0.578892i	$-0.196515\pi$
$401$	14.4535	+	8.34471i	0.721772	+	0.416715i	−0.0936326	+	0.995607i	$0.529848\pi$
$402$	2.40518	−	0.644467i	0.119960	−	0.0321431i
$403$	−0.163400	+	0.609817i	−0.00813953	+	0.0303772i
$404$	12.5611	+	7.25213i	0.624936	+	0.360807i
$405$		0			0
$406$	−3.11392			−0.154541
$407$	0.505116	+	0.505116i	0.0250377	+	0.0250377i
$408$	−3.02206	+	11.2785i	−0.149614	+	0.558368i
$409$	1.71847	+	2.97648i	0.0849729	+	0.147177i	0.905380	−	0.424603i	$-0.139586\pi$
$409$	1.71847	+	2.97648i	0.0849729	+	0.147177i	−0.820407	+	0.571780i	$0.806253\pi$
$410$		0			0
$411$		−	41.0567i		−	2.02518i
$412$	−3.68353	+	13.7471i	−0.181475	+	0.677273i
$413$	−2.66863	−	9.95947i	−0.131315	−	0.490074i
$414$	6.80319	+	11.7835i	0.334359	+	0.579126i
$415$		0			0
$416$	1.48522	−	2.57247i	0.0728188	−	0.126126i
$417$	15.6351	+	15.6351i	0.765652	+	0.765652i
$418$	0.559438	+	4.58881i	0.0273630	+	0.224446i
$419$		−	11.5819i		−	0.565811i	−0.959148	−	0.282906i	$-0.908702\pi$
$419$		−	11.5819i		−	0.565811i	0.959148	−	0.282906i	$-0.0912983\pi$
$420$		0			0
$421$	28.7795	+	16.6158i	1.40263	+	0.809807i	0.994662	−	0.103191i	$-0.0329052\pi$
$421$	28.7795	+	16.6158i	1.40263	+	0.809807i	0.407965	+	0.912998i	$0.366239\pi$
$422$	22.2497	+	5.96178i	1.08310	+	0.290215i
$423$	5.55384	−	1.48815i	0.270037	−	0.0723561i
$424$	−12.1789	+	7.03149i	−0.591459	+	0.341479i
$425$		0			0
$426$			28.0601i			1.35951i
$427$	3.90497	+	1.04633i	0.188975	+	0.0506356i
$428$	−12.6639	−	3.39328i	−0.612132	−	0.164020i
$429$		−	6.94769i		−	0.335438i
$430$		0			0
$431$	5.28977	−	3.05405i	0.254799	−	0.147108i	−0.367161	−	0.930158i	$-0.619670\pi$
$431$	5.28977	−	3.05405i	0.254799	−	0.147108i	0.621960	+	0.783049i	$0.286337\pi$
$432$	−2.42018	+	0.648485i	−0.116441	+	0.0312003i
$433$	−1.64906	−	0.441865i	−0.0792489	−	0.0212347i	0.218977	−	0.975730i	$-0.429728\pi$
$433$	−1.64906	−	0.441865i	−0.0792489	−	0.0212347i	−0.298226	+	0.954495i	$0.596395\pi$
$434$	−0.137010	−	0.0791027i	−0.00657668	−	0.00379705i
$435$		0			0
$436$		−	13.6521i		−	0.653815i
$437$	−29.2793	−	12.4580i	−1.40062	−	0.595947i
$438$	17.0269	+	17.0269i	0.813575	+	0.813575i
$439$	−14.3230	+	24.8081i	−0.683599	+	1.18403i	0.290276	+	0.956943i	$0.406253\pi$
$439$	−14.3230	+	24.8081i	−0.683599	+	1.18403i	−0.973875	+	0.227085i	$0.927080\pi$
$440$		0			0
$441$	−6.00733	−	10.4050i	−0.286063	−	0.495476i
$442$	4.07034	+	15.1907i	0.193606	+	0.722548i
$443$	1.75901	−	6.56472i	0.0835731	−	0.311899i	−0.911467	−	0.411373i	$-0.865049\pi$
$443$	1.75901	−	6.56472i	0.0835731	−	0.311899i	0.995040	+	0.0994739i	$0.0317160\pi$
$444$			1.48550i			0.0704986i
$445$		0			0
$446$	4.53310	+	7.85156i	0.214649	+	0.371782i
$447$	−8.07907	+	30.1515i	−0.382127	+	1.42612i
$448$	0.526345	+	0.526345i	0.0248675	+	0.0248675i
$449$	34.6251			1.63406			0.817030	−	0.576595i	$-0.195619\pi$
$449$	34.6251			1.63406			0.817030	+	0.576595i	$0.195619\pi$
$450$		0			0
$451$	3.21269	+	1.85485i	0.151280	+	0.0873414i
$452$	1.30489	−	4.86990i	0.0613767	−	0.229061i
$453$	0.175589	−	0.0470488i	0.00824988	−	0.00221055i
$454$	10.2021	+	5.89016i	0.478806	+	0.276439i
$455$		0			0
$456$	−5.92500	+	7.57025i	−0.277464	+	0.354510i
$457$	−21.1038	+	21.1038i	−0.987193	+	0.987193i	−0.999919	−	0.0127255i	$-0.995949\pi$
$457$	−21.1038	+	21.1038i	−0.987193	+	0.987193i	0.0127255	+	0.999919i	$0.495949\pi$
$458$	−0.407588	−	1.52114i	−0.0190453	−	0.0710781i
$459$	6.63266	−	11.4881i	0.309586	−	0.536219i
$460$		0			0
$461$	−17.6007	+	30.4854i	−0.819748	+	1.41984i	0.0861203	+	0.996285i	$0.472553\pi$
$461$	−17.6007	+	30.4854i	−0.819748	+	1.41984i	−0.905868	+	0.423560i	$0.860780\pi$
$462$	1.68170	+	0.450611i	0.0782400	+	0.0209643i
$463$	−6.22371	−	6.22371i	−0.289240	−	0.289240i	0.547539	−	0.836780i	$-0.315565\pi$
$463$	−6.22371	−	6.22371i	−0.289240	−	0.289240i	−0.836780	+	0.547539i	$0.815565\pi$
$464$	−4.18332			−0.194206
$465$		0			0
$466$	21.6569	−	12.5036i	1.00324	−	0.579219i
$467$	−12.6457	+	12.6457i	−0.585175	+	0.585175i	−0.936321	−	0.351146i	$-0.885792\pi$
$467$	−12.6457	+	12.6457i	−0.585175	+	0.585175i	0.351146	+	0.936321i	$0.385792\pi$
$468$	3.91500	−	3.91500i	0.180971	−	0.180971i
$469$	0.420211	+	0.727826i	0.0194035	+	0.0336079i
$470$		0			0
$471$	−5.82098	+	3.36074i	−0.268217	+	0.154855i
$472$	−3.58512	−	13.3798i	−0.165018	−	0.615857i
$473$	2.01110	−	0.538872i	0.0924704	−	0.0247774i
$474$	−9.41411			−0.432404
$475$		0			0
$476$	−3.94094			−0.180633
$477$	−25.3190	+	6.78421i	−1.15928	+	0.310628i
$478$	−7.07266	−	26.3955i	−0.323496	−	1.20730i
$479$	3.13243	−	1.80851i	0.143124	−	0.0826329i	−0.426728	−	0.904380i	$-0.640334\pi$
$479$	3.13243	−	1.80851i	0.143124	−	0.0826329i	0.569852	+	0.821747i	$0.307000\pi$
$480$		0			0
$481$	1.00039	+	1.73273i	0.0456138	+	0.0790055i
$482$	−6.23434	+	6.23434i	−0.283966	+	0.283966i
$483$	−8.47384	+	8.47384i	−0.385573	+	0.385573i
$484$	−8.55222	+	4.93763i	−0.388737	+	0.224438i
$485$		0			0
$486$	−17.0023			−0.771242
$487$	19.8549	+	19.8549i	0.899710	+	0.899710i	0.995410	−	0.0957001i	$-0.0305090\pi$
$487$	19.8549	+	19.8549i	0.899710	+	0.899710i	−0.0957001	+	0.995410i	$0.530509\pi$
$488$	5.24605	+	1.40567i	0.237477	+	0.0636319i
$489$	−21.0533	+	36.4655i	−0.952065	+	1.64903i
$490$		0			0
$491$	15.7856	−	27.3414i	0.712392	−	1.23390i	−0.251565	−	0.967840i	$-0.580945\pi$
$491$	15.7856	−	27.3414i	0.712392	−	1.23390i	0.963957	−	0.266059i	$-0.0857215\pi$
$492$	1.99664	+	7.45157i	0.0900156	+	0.335943i
$493$	15.6610	−	15.6610i	0.705337	−	0.705337i
$494$	−1.81299	+	12.8203i	−0.0815705	+	0.576811i
$495$		0			0
$496$	−0.184063	−	0.106269i	−0.00826467	−	0.00477161i
$497$	−9.14798	+	2.45119i	−0.410343	+	0.109951i
$498$	−4.44649	+	16.5945i	−0.199252	+	0.743618i
$499$	−29.9079	−	17.2674i	−1.33886	−	0.772993i	−0.352225	−	0.935915i	$-0.614575\pi$
$499$	−29.9079	−	17.2674i	−1.33886	−	0.772993i	−0.986639	+	0.162922i	$0.947908\pi$
$500$		0			0
$501$	33.1218			1.47977
$502$	−12.1156	−	12.1156i	−0.540748	−	0.540748i
$503$	−6.02305	+	22.4783i	−0.268555	+	1.00226i	0.691484	+	0.722392i	$0.256957\pi$
$503$	−6.02305	+	22.4783i	−0.268555	+	1.00226i	−0.960039	+	0.279867i	$0.909709\pi$
$504$	0.693716	+	1.20155i	0.0309006	+	0.0535214i
$505$		0			0
$506$			7.74183i			0.344166i
$507$	−2.38398	+	8.89713i	−0.105876	+	0.395136i
$508$	−1.60526	−	5.99091i	−0.0712219	−	0.265804i
$509$	11.2770	+	19.5324i	0.499845	+	0.865758i	1.00000		0.000178436i	$-5.67980e-5\pi$
$509$	11.2770	+	19.5324i	0.499845	+	0.865758i	−0.500155	+	0.865936i	$0.666723\pi$
$510$		0			0
$511$	−4.06361	+	7.03838i	−0.179764	+	0.311360i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	8.72790	−	6.56521i	0.385346	−	0.289861i
$514$			27.4678i			1.21155i
$515$		0			0
$516$	3.74961	+	2.16484i	0.165067	+	0.0953016i
$517$	3.16005	+	0.846733i	0.138979	+	0.0372393i
$518$	−0.484293	+	0.129766i	−0.0212786	+	0.00570159i
$519$	42.4587	−	24.5135i	1.86373	−	1.07602i
$520$		0			0
$521$		−	0.968119i		−	0.0424141i	−0.999775	−	0.0212070i	$-0.993249\pi$
$521$		−	0.968119i		−	0.0424141i	0.999775	−	0.0212070i	$-0.00675092\pi$
$522$	−7.53167	−	2.01810i	−0.329652	−	0.0883300i
$523$	1.16271	+	0.311548i	0.0508419	+	0.0136231i	0.284150	−	0.958780i	$-0.408289\pi$
$523$	1.16271	+	0.311548i	0.0508419	+	0.0136231i	−0.233308	+	0.972403i	$0.574955\pi$
$524$		−	4.35183i		−	0.190111i
$525$		0			0
$526$	14.6000	−	8.42929i	0.636588	−	0.367534i
$527$	1.08691	−	0.291236i	0.0473465	−	0.0126865i
$528$	2.25925	+	0.605364i	0.0983212	+	0.0263451i
$529$	−26.2306	−	15.1442i	−1.14046	−	0.658445i
$530$		0			0
$531$		−	25.8186i		−	1.12043i
$532$	−2.98559	−	1.27033i	−0.129442	−	0.0550759i
$533$	7.34710	+	7.34710i	0.318238	+	0.318238i
$534$	−1.83404	+	3.17665i	−0.0793666	+	0.137467i
$535$		0			0
$536$	0.564523	+	0.977782i	0.0243837	+	0.0422338i
$537$	1.86424	+	6.95745i	0.0804480	+	0.300236i
$538$	−1.44996	+	5.41132i	−0.0625122	+	0.233299i
$539$		−	6.83616i		−	0.294454i
$540$		0			0
$541$	12.7328	+	22.0539i	0.547426	+	0.948170i	0.998450	+	0.0556584i	$0.0177258\pi$
$541$	12.7328	+	22.0539i	0.547426	+	0.948170i	−0.451023	+	0.892512i	$0.648941\pi$
$542$	−0.309117	+	1.15364i	−0.0132777	+	0.0495531i
$543$	−20.9186	−	20.9186i	−0.897704	−	0.897704i
$544$	−5.29436			−0.226994
$545$		0			0
$546$	4.22308	+	2.43820i	0.180731	+	0.104345i
$547$	3.19441	−	11.9217i	0.136583	−	0.509736i	−0.863403	−	0.504515i	$-0.831671\pi$
$547$	3.19441	−	11.9217i	0.136583	−	0.509736i	0.999986	−	0.00522100i	$-0.00166190\pi$
$548$	17.9819	−	4.81823i	0.768148	−	0.205825i
$549$	8.76688	+	5.06156i	0.374161	+	0.216022i
$550$		0			0
$551$	16.9128	−	6.81631i	0.720507	−	0.290385i
$552$	−11.3840	+	11.3840i	−0.484535	+	0.484535i
$553$	−0.822371	−	3.06913i	−0.0349708	−	0.130513i
$554$	13.0983	−	22.6870i	0.556495	−	0.963877i
$555$		0			0
$556$	−5.01293	+	8.68264i	−0.212595	+	0.368226i
$557$	4.26796	+	1.14360i	0.180839	+	0.0484558i	0.348102	−	0.937457i	$-0.386826\pi$
$557$	4.26796	+	1.14360i	0.180839	+	0.0484558i	−0.167263	+	0.985912i	$0.553493\pi$
$558$	−0.280122	−	0.280122i	−0.0118585	−	0.0118585i
$559$	5.83153			0.246647
$560$		0			0
$561$	−10.7242	+	6.19162i	−0.452776	+	0.261410i
$562$	−3.43892	+	3.43892i	−0.145062	+	0.145062i
$563$	29.6545	−	29.6545i	1.24979	−	1.24979i	0.293976	−	0.955813i	$-0.405021\pi$
$563$	29.6545	−	29.6545i	1.24979	−	1.24979i	0.955813	−	0.293976i	$-0.0949787\pi$
$564$	3.40162	+	5.89178i	0.143234	+	0.248089i
$565$		0			0
$566$	−20.3377	+	11.7420i	−0.854856	+	0.493551i
$567$	−2.14186	−	7.99354i	−0.0899498	−	0.335697i
$568$	−12.2896	+	3.29300i	−0.515662	+	0.138171i
$569$	−34.3603			−1.44046			−0.720230	−	0.693735i	$-0.755964\pi$
$569$	−34.3603			−1.44046			−0.720230	+	0.693735i	$0.755964\pi$
$570$		0			0
$571$	−0.576302			−0.0241175			−0.0120588	−	0.999927i	$-0.503839\pi$
$571$	−0.576302			−0.0241175			−0.0120588	+	0.999927i	$0.503839\pi$
$572$	3.04293	−	0.815349i	0.127231	−	0.0340915i
$573$	10.6863	+	39.8817i	0.446426	+	1.66608i
$574$	−2.25490	+	1.30187i	−0.0941177	+	0.0543389i
$575$		0			0
$576$	0.931958	+	1.61420i	0.0388316	+	0.0672582i
$577$	8.23167	−	8.23167i	0.342689	−	0.342689i	−0.514688	−	0.857377i	$-0.672092\pi$
$577$	8.23167	−	8.23167i	0.342689	−	0.342689i	0.857377	+	0.514688i	$0.172092\pi$
$578$	7.79959	−	7.79959i	0.324420	−	0.324420i
$579$	−1.92164	+	1.10946i	−0.0798607	+	0.0461076i
$580$		0			0
$581$	−5.79847			−0.240561
$582$	−19.0150	−	19.0150i	−0.788198	−	0.788198i
$583$	−14.4062	−	3.86012i	−0.596642	−	0.159870i
$584$	−5.45917	+	9.45556i	−0.225902	+	0.391274i
$585$		0			0
$586$	4.51800	−	7.82541i	0.186637	−	0.323265i
$587$	−1.23950	−	4.62587i	−0.0511595	−	0.190930i	0.935617	−	0.353017i	$-0.114844\pi$
$587$	−1.23950	−	4.62587i	−0.0511595	−	0.190930i	−0.986776	+	0.162087i	$0.948177\pi$
$588$	10.0522	−	10.0522i	0.414548	−	0.414548i
$589$	0.917303	+	0.129721i	0.0377968	+	0.00534508i
$590$		0			0
$591$	18.0946	+	10.4469i	0.744311	+	0.429728i
$592$	−0.650613	+	0.174331i	−0.0267400	+	0.00716497i
$593$	4.09509	−	15.2831i	0.168165	−	0.627601i	−0.829450	−	0.558581i	$-0.811346\pi$
$593$	4.09509	−	15.2831i	0.168165	−	0.627601i	0.997615	−	0.0690202i	$-0.0219873\pi$
$594$	−2.30124	−	1.32862i	−0.0944210	−	0.0545140i
$595$		0			0
$596$	−14.1538			−0.579761
$597$	−1.41803	−	1.41803i	−0.0580361	−	0.0580361i
$598$	−5.61220	+	20.9450i	−0.229500	+	0.856505i
$599$	12.9609	+	22.4489i	0.529568	+	0.917238i	0.999405	+	0.0344854i	$0.0109792\pi$
$599$	12.9609	+	22.4489i	0.529568	+	0.917238i	−0.469837	+	0.882753i	$0.655687\pi$
$600$		0			0
$601$		−	16.4012i		−	0.669019i	−0.942392	−	0.334510i	$-0.891429\pi$
$601$		−	16.4012i		−	0.669019i	0.942392	−	0.334510i	$-0.108571\pi$
$602$	−0.378220	+	1.41153i	−0.0154151	+	0.0575299i
$603$	0.544671	+	2.03274i	0.0221807	+	0.0827795i
$604$	0.0412126	+	0.0713823i	0.00167692	+	0.00290450i
$605$		0			0
$606$	−15.9941	+	27.7025i	−0.649714	+	1.12534i
$607$	−26.1059	−	26.1059i	−1.05961	−	1.05961i	−0.998107	−	0.0614991i	$-0.980412\pi$
$607$	−26.1059	−	26.1059i	−1.05961	−	1.05961i	−0.0614991	−	0.998107i	$-0.519588\pi$
$608$	−4.01092	−	1.70660i	−0.162664	−	0.0692118i
$609$		−	6.86752i		−	0.278286i
$610$		0			0
$611$	7.93549	+	4.58156i	0.321036	+	0.185350i
$612$	−9.53199	−	2.55409i	−0.385308	−	0.103243i
$613$	35.4676	−	9.50350i	1.43252	−	0.383843i	0.542613	−	0.839983i	$-0.317435\pi$
$613$	35.4676	−	9.50350i	1.43252	−	0.383843i	0.889908	+	0.456140i	$0.150768\pi$
$614$	24.1524	−	13.9444i	0.974712	−	0.562750i
$615$		0			0
$616$			0.789429i			0.0318070i
$617$	23.0104	+	6.16563i	0.926366	+	0.248219i	0.690304	−	0.723519i	$-0.257477\pi$
$617$	23.0104	+	6.16563i	0.926366	+	0.248219i	0.236061	+	0.971738i	$0.424143\pi$
$618$	−30.3183	−	8.12377i	−1.21958	−	0.326786i
$619$			25.5915i			1.02861i	0.857607	+	0.514305i	$0.171950\pi$
$619$			25.5915i			1.02861i	−0.857607	+	0.514305i	$0.828050\pi$
$620$		0			0
$621$	15.8398	−	9.14514i	0.635631	−	0.366982i
$622$	4.63690	−	1.24245i	0.185923	−	0.0498178i
$623$	−1.19585	−	0.320426i	−0.0479105	−	0.0128376i
$624$	5.67341	+	3.27554i	0.227118	+	0.131127i
$625$		0			0
$626$			15.5544i			0.621681i
$627$	−10.1203	+	1.23380i	−0.404166	+	0.0492732i
$628$	−2.15505	−	2.15505i	−0.0859959	−	0.0859959i
$629$	1.78305	−	3.08833i	0.0710947	−	0.123140i
$630$		0			0
$631$	−2.83321	−	4.90727i	−0.112788	−	0.195355i	0.804105	−	0.594487i	$-0.202645\pi$
$631$	−2.83321	−	4.90727i	−0.112788	−	0.195355i	−0.916894	+	0.399132i	$0.869312\pi$
$632$	−1.10480	−	4.12316i	−0.0439465	−	0.164010i
$633$	−13.1483	+	49.0700i	−0.522597	+	1.95036i
$634$			18.9594i			0.752972i
$635$		0			0
$636$	−15.5074	−	26.8597i	−0.614910	−	1.06506i
$637$	4.95566	−	18.4948i	0.196350	−	0.732790i
$638$	−3.13714	−	3.13714i	−0.124200	−	0.124200i
$639$	−23.7149			−0.938148
$640$		0			0
$641$	23.7139	+	13.6912i	0.936644	+	0.540771i	0.888907	−	0.458088i	$-0.151466\pi$
$641$	23.7139	+	13.6912i	0.936644	+	0.540771i	0.0477371	+	0.998860i	$0.484799\pi$
$642$	7.48363	−	27.9293i	0.295355	−	1.10228i
$643$	46.1844	−	12.3751i	1.82133	−	0.488025i	0.824381	−	0.566035i	$-0.191523\pi$
$643$	46.1844	−	12.3751i	1.82133	−	0.488025i	0.996953	+	0.0780102i	$0.0248567\pi$
$644$	−4.70579	−	2.71689i	−0.185434	−	0.107061i
$645$		0			0
$646$	21.4046	−	8.62665i	0.842152	−	0.339411i
$647$	11.2759	−	11.2759i	0.443300	−	0.443300i	−0.449819	−	0.893120i	$-0.648512\pi$
$647$	11.2759	−	11.2759i	0.443300	−	0.443300i	0.893120	+	0.449819i	$0.148512\pi$
$648$	−2.87744	−	10.7387i	−0.113036	−	0.421858i
$649$	7.34521	−	12.7223i	0.288325	−	0.499393i
$650$		0			0
$651$	0.174455	−	0.302165i	0.00683744	−	0.0118428i
$652$	−18.4417	−	4.94145i	−0.722234	−	0.193522i
$653$	−6.72143	−	6.72143i	−0.263030	−	0.263030i	0.563254	−	0.826284i	$-0.309549\pi$
$653$	−6.72143	−	6.72143i	−0.263030	−	0.263030i	−0.826284	+	0.563254i	$0.809549\pi$
$654$	30.1086			1.17734
$655$		0			0
$656$	−3.02929	+	1.74896i	−0.118274	+	0.0682856i
$657$	−14.3902	+	14.3902i	−0.561416	+	0.561416i
$658$	−1.62366	+	1.62366i	−0.0632967	+	0.0632967i
$659$	−16.3232	−	28.2726i	−0.635862	−	1.10134i	−0.986332	−	0.164771i	$-0.947312\pi$
$659$	−16.3232	−	28.2726i	−0.635862	−	1.10134i	0.350470	−	0.936574i	$-0.386022\pi$
$660$		0			0
$661$	−9.29737	+	5.36784i	−0.361626	+	0.208785i	−0.669794	−	0.742547i	$-0.733617\pi$
$661$	−9.29737	+	5.36784i	−0.361626	+	0.208785i	0.308168	+	0.951332i	$0.400284\pi$
$662$	6.85512	+	25.5836i	0.266432	+	0.994337i
$663$	−33.5020	+	8.97683i	−1.30111	+	0.348631i
$664$	−7.78983			−0.302304
$665$		0			0
$666$	−1.25547			−0.0486483
$667$	29.4972	−	7.90376i	1.14214	−	0.306035i
$668$	3.88702	+	14.5066i	0.150393	+	0.561276i
$669$	−17.3161	+	9.99743i	−0.669478	+	0.386523i
$670$		0			0
$671$	2.87996	+	4.98823i	0.111179	+	0.192568i
$672$	−1.16082	+	1.16082i	−0.0447795	+	0.0447795i
$673$	−21.6092	+	21.6092i	−0.832972	+	0.832972i	−0.987922	−	0.154950i	$-0.950478\pi$
$673$	−21.6092	+	21.6092i	−0.832972	+	0.832972i	0.154950	+	0.987922i	$0.450478\pi$
$674$	8.24114	−	4.75802i	0.317437	−	0.183272i
$675$		0			0
$676$	−4.17651			−0.160635
$677$	−3.10659	−	3.10659i	−0.119396	−	0.119396i	0.644884	−	0.764280i	$-0.276906\pi$
$677$	−3.10659	−	3.10659i	−0.119396	−	0.119396i	−0.764280	+	0.644884i	$0.776906\pi$
$678$	10.7402	+	2.87783i	0.412476	+	0.110523i
$679$	4.53810	−	7.86023i	0.174156	−	0.301648i
$680$		0			0
$681$	−12.9903	+	22.4999i	−0.497791	+	0.862199i
$682$	−0.0583390	−	0.217724i	−0.00223392	−	0.00833709i
$683$	−12.3419	+	12.3419i	−0.472248	+	0.472248i	−0.902642	−	0.430393i	$-0.858375\pi$
$683$	−12.3419	+	12.3419i	−0.472248	+	0.472248i	0.430393	+	0.902642i	$0.358375\pi$
$684$	−6.39799	−	5.00751i	−0.244633	−	0.191467i
$685$		0			0
$686$	8.66776	+	5.00433i	0.330937	+	0.191066i
$687$	3.35476	−	0.898906i	0.127992	−	0.0342954i
$688$	−0.508111	+	1.89630i	−0.0193715	+	0.0722956i
$689$	−36.1766	−	20.8866i	−1.37822	−	0.795715i
$690$		0			0
$691$	38.3587			1.45923			0.729617	−	0.683856i	$-0.239699\pi$
$691$	38.3587			1.45923			0.729617	+	0.683856i	$0.239699\pi$
$692$	15.7191	+	15.7191i	0.597551	+	0.597551i
$693$	−0.380834	+	1.42129i	−0.0144667	+	0.0539904i
$694$	8.29828	+	14.3730i	0.314998	+	0.545593i
$695$		0			0
$696$		−	9.22602i		−	0.349711i
$697$	4.79315	−	17.8883i	0.181553	−	0.677567i
$698$	−2.85753	−	10.6645i	−0.108159	−	0.403656i
$699$	27.5759	+	47.7628i	1.04301	+	1.80655i
$700$		0			0
$701$	22.9091	−	39.6798i	0.865266	−	1.49869i	−0.00151588	−	0.999999i	$-0.500483\pi$
$701$	22.9091	−	39.6798i	0.865266	−	1.49869i	0.866782	−	0.498687i	$-0.166184\pi$
$702$	−5.26271	−	5.26271i	−0.198628	−	0.198628i
$703$	2.34631	−	1.76491i	0.0884927	−	0.0665650i
$704$			1.06054i			0.0399706i
$705$		0			0
$706$	12.7414	+	7.35627i	0.479530	+	0.276857i
$707$	−10.4286	−	2.79433i	−0.392207	−	0.105092i
$708$	29.5083	−	7.90672i	1.10899	−	0.297153i
$709$	21.8003	−	12.5864i	0.818727	−	0.472692i	−0.0312505	−	0.999512i	$-0.509949\pi$
$709$	21.8003	−	12.5864i	0.818727	−	0.472692i	0.849977	+	0.526820i	$0.176616\pi$
$710$		0			0
$711$		−	7.95632i		−	0.298385i
$712$	−1.60653	−	0.430469i	−0.0602073	−	0.0161325i
$713$	1.49864	+	0.401558i	0.0561243	+	0.0150385i
$714$		−	8.69145i		−	0.325269i
$715$		0			0
$716$	−2.82842	+	1.63299i	−0.105703	+	0.0610277i
$717$	58.2134	−	15.5982i	2.17402	−	0.582527i
$718$	−17.3881	−	4.65913i	−0.648919	−	0.173877i
$719$	10.1580	+	5.86473i	0.378830	+	0.218718i	0.677309	−	0.735699i	$-0.263146\pi$
$719$	10.1580	+	5.86473i	0.378830	+	0.218718i	−0.298479	+	0.954416i	$0.596479\pi$
$720$		0			0
$721$		−	10.5939i		−	0.394536i
$722$	18.9965	+	0.364207i	0.706977	+	0.0135544i
$723$	−13.7494	−	13.7494i	−0.511345	−	0.511345i
$724$	6.70695	−	11.6168i	0.249262	−	0.431734i
$725$		0			0
$726$	−10.8896	−	18.8613i	−0.404150	−	0.700009i
$727$	2.65461	+	9.90713i	0.0984540	+	0.367435i	0.997520	−	0.0703769i	$-0.0224202\pi$
$727$	2.65461	+	9.90713i	0.0984540	+	0.367435i	−0.899067	+	0.437812i	$0.855754\pi$
$728$	−0.572271	+	2.13575i	−0.0212098	+	0.0791560i
$729$		−	4.14474i		−	0.153509i
$730$		0			0
$731$	−5.19692	−	9.00133i	−0.192215	−	0.332926i
$732$	−3.10011	+	11.5698i	−0.114584	+	0.427631i
$733$	14.6696	+	14.6696i	0.541835	+	0.541835i	0.924067	−	0.382231i	$-0.124844\pi$
$733$	14.6696	+	14.6696i	0.541835	+	0.541835i	−0.382231	+	0.924067i	$0.624844\pi$
$734$	−25.0847			−0.925892
$735$		0			0
$736$	−6.32189	−	3.64995i	−0.233028	−	0.134539i
$737$	−0.309910	+	1.15660i	−0.0114157	+	0.0426038i
$738$	−6.29768	+	1.68746i	−0.231821	+	0.0621162i
$739$	23.0232	+	13.2924i	0.846922	+	0.488971i	0.859611	−	0.510949i	$-0.170706\pi$
$739$	23.0232	+	13.2924i	0.846922	+	0.488971i	−0.0126893	+	0.999919i	$0.504039\pi$
$740$		0			0
$741$	−28.2742	−	3.99843i	−1.03868	−	0.146886i
$742$	7.40198	−	7.40198i	0.271735	−	0.271735i
$743$	−4.99074	−	18.6257i	−0.183093	−	0.683311i	−0.995031	−	0.0995676i	$-0.968254\pi$
$743$	−4.99074	−	18.6257i	−0.183093	−	0.683311i	0.811938	−	0.583743i	$-0.198413\pi$
$744$	0.234368	−	0.405938i	0.00859235	−	0.0148824i
$745$		0			0
$746$	−1.00162	+	1.73486i	−0.0366720	+	0.0635178i
$747$	−14.0248	−	3.75794i	−0.513142	−	0.137496i
$748$	−3.97032	−	3.97032i	−0.145169	−	0.145169i
$749$	9.75908			0.356589
$750$		0			0
$751$	−25.0396	+	14.4566i	−0.913709	+	0.527530i	−0.881623	−	0.471955i	$-0.843549\pi$
$751$	−25.0396	+	14.4566i	−0.913709	+	0.527530i	−0.0320866	+	0.999485i	$0.510215\pi$
$752$	−2.18126	+	2.18126i	−0.0795425	+	0.0795425i
$753$	26.7202	−	26.7202i	0.973738	−	0.973738i
$754$	−6.21314	−	10.7615i	−0.226269	−	0.391910i
$755$		0			0
$756$	1.61518	−	0.932523i	0.0587434	−	0.0339155i
$757$	−7.05405	−	26.3261i	−0.256384	−	0.956837i	−0.967315	−	0.253576i	$-0.918393\pi$
$757$	−7.05405	−	26.3261i	−0.256384	−	0.956837i	0.710932	−	0.703261i	$-0.248274\pi$
$758$	1.56558	−	0.419496i	0.0568645	−	0.0152368i
$759$	−17.0741			−0.619749
$760$		0			0
$761$	11.7519			0.426005			0.213002	−	0.977052i	$-0.431676\pi$
$761$	11.7519			0.426005			0.213002	+	0.977052i	$0.431676\pi$
$762$	13.2125	−	3.54028i	0.478639	−	0.128251i
$763$	2.63015	+	9.81584i	0.0952177	+	0.355357i
$764$	−16.2132	+	9.36068i	−0.586572	+	0.338657i
$765$		0			0
$766$	−12.4660	−	21.5918i	−0.450415	−	0.780143i
$767$	29.0946	−	29.0946i	1.05054	−	1.05054i
$768$	−1.55947	+	1.55947i	−0.0562727	+	0.0562727i
$769$	15.8245	−	9.13626i	0.570645	−	0.329462i	−0.186762	−	0.982405i	$-0.559799\pi$
$769$	15.8245	−	9.13626i	0.570645	−	0.329462i	0.757407	+	0.652943i	$0.226466\pi$
$770$		0			0
$771$	−60.5782			−2.18167
$772$	−0.711432	−	0.711432i	−0.0256050	−	0.0256050i
$773$	7.26094	+	1.94556i	0.261158	+	0.0699770i	0.387022	−	0.922070i	$-0.373504\pi$
$773$	7.26094	+	1.94556i	0.261158	+	0.0699770i	−0.125864	+	0.992047i	$0.540170\pi$
$774$	−1.82961	+	3.16898i	−0.0657639	+	0.113906i
$775$		0			0
$776$	6.09662	−	10.5596i	0.218856	−	0.379069i
$777$	−0.286190	−	1.06807i	−0.0102670	−	0.0383169i
$778$	13.2675	−	13.2675i	0.475662	−	0.475662i
$779$	9.39737	−	12.0068i	0.336696	−	0.430189i
$780$		0			0
$781$	−11.6857	−	6.74672i	−0.418146	−	0.241417i
$782$	37.3314	−	10.0029i	1.33497	−	0.357703i
$783$	−2.71282	+	10.1244i	−0.0969483	+	0.361816i
$784$	5.58233	+	3.22296i	0.199369	+	0.115106i
$785$		0			0
$786$	9.59766			0.342337
$787$	13.1228	+	13.1228i	0.467777	+	0.467777i	0.901194	−	0.433417i	$-0.142692\pi$
$787$	13.1228	+	13.1228i	0.467777	+	0.467777i	−0.433417	+	0.901194i	$0.642692\pi$
$788$	−2.45200	+	9.15099i	−0.0873489	+	0.325991i
$789$	18.5902	+	32.1992i	0.661828	+	1.14632i
$790$		0			0
$791$			3.75286i			0.133436i
$792$	−0.511622	+	1.90940i	−0.0181797	+	0.0678476i
$793$	4.17547	+	15.5830i	0.148275	+	0.553370i
$794$	−9.32129	−	16.1449i	−0.330800	−	0.572963i
$795$		0			0
$796$	0.454650	−	0.787477i	0.0161146	−	0.0279114i
$797$	6.37552	+	6.37552i	0.225833	+	0.225833i	0.810949	−	0.585117i	$-0.198951\pi$
$797$	6.37552	+	6.37552i	0.225833	+	0.225833i	−0.585117	+	0.810949i	$0.698951\pi$
$798$	2.80163	−	6.58450i	0.0991766	−	0.233089i
$799$		−	16.3319i		−	0.577781i
$800$		0			0
$801$	−2.68474	−	1.55004i	−0.0948606	−	0.0547678i
$802$	−16.1208	−	4.31954i	−0.569243	−	0.152528i
$803$	−11.1848	+	2.99695i	−0.394702	+	0.105760i
$804$	−2.15643	+	1.24501i	−0.0760514	+	0.0439083i
$805$		0			0
$806$		−	0.631329i		−	0.0222376i
$807$	−11.9343	−	3.19778i	−0.420107	−	0.112567i
$808$	−14.0100	−	3.75398i	−0.492872	−	0.132065i
$809$		−	11.3870i		−	0.400346i	−0.979761	−	0.200173i	$-0.935850\pi$
$809$		−	11.3870i		−	0.400346i	0.979761	−	0.200173i	$-0.0641505\pi$
$810$		0			0
$811$	−2.69596	+	1.55651i	−0.0946679	+	0.0546565i	−0.546587	−	0.837403i	$-0.684073\pi$
$811$	−2.69596	+	1.55651i	−0.0946679	+	0.0546565i	0.451919	+	0.892059i	$0.350740\pi$
$812$	3.00781	−	0.805941i	0.105553	−	0.0282830i
$813$	−2.54427	−	0.681736i	−0.0892315	−	0.0239095i
$814$	−0.618638	−	0.357171i	−0.0216833	−	0.0125188i
$815$		0			0
$816$		−	11.6763i		−	0.408754i
$817$	−1.03559	−	8.49445i	−0.0362306	−	0.297183i
$818$	−2.43028	−	2.43028i	−0.0849729	−	0.0849729i
$819$	−2.06064	+	3.56913i	−0.0720046	+	0.124716i
$820$		0			0
$821$	−16.2587	−	28.1609i	−0.567433	−	0.982823i	−0.996819	−	0.0797017i	$-0.974603\pi$
$821$	−16.2587	−	28.1609i	−0.567433	−	0.982823i	0.429386	−	0.903121i	$-0.358730\pi$
$822$	10.6263	+	39.6578i	0.370634	+	1.38322i
$823$	−10.3748	+	38.7193i	−0.361643	+	1.34967i	0.510272	+	0.860013i	$0.329545\pi$
$823$	−10.3748	+	38.7193i	−0.361643	+	1.34967i	−0.871915	+	0.489657i	$0.837122\pi$
$824$		−	14.2321i		−	0.495798i
$825$		0			0
$826$	5.15540	+	8.92942i	0.179379	+	0.310694i
$827$	−1.63119	+	6.08768i	−0.0567220	+	0.211689i	−0.988470	−	0.151416i	$-0.951617\pi$
$827$	−1.63119	+	6.08768i	−0.0567220	+	0.211689i	0.931748	+	0.363105i	$0.118283\pi$
$828$	−9.62117	−	9.62117i	−0.334359	−	0.334359i
$829$	−6.05110			−0.210163			−0.105082	−	0.994464i	$-0.533510\pi$
$829$	−6.05110			−0.210163			−0.105082	+	0.994464i	$0.533510\pi$
$830$		0			0
$831$	50.0345	+	28.8874i	1.73568	+	1.00209i
$832$	−0.768805	+	2.86922i	−0.0266535	+	0.0994723i
$833$	−32.9642	+	8.83273i	−1.14214	+	0.306036i
$834$	−19.1490	−	11.0557i	−0.663074	−	0.382826i
$835$		0			0
$836$	−1.72805	−	4.28766i	−0.0597658	−	0.148292i
$837$	−0.376551	+	0.376551i	−0.0130155	+	0.0130155i
$838$	2.99761	+	11.1872i	0.103551	+	0.386456i
$839$	14.2455	−	24.6740i	0.491811	−	0.851841i	−0.508145	−	0.861272i	$-0.669669\pi$
$839$	14.2455	−	24.6740i	0.491811	−	0.851841i	0.999956	+	0.00943063i	$0.00300191\pi$
$840$		0			0
$841$	5.74991	−	9.95914i	0.198273	−	0.343419i
$842$	−32.0994	−	8.60100i	−1.10622	−	0.296410i
$843$	−7.58430	−	7.58430i	−0.261217	−	0.261217i
$844$	−23.0345			−0.792882
$845$		0			0
$846$	−4.97943	+	2.87488i	−0.171196	+	0.0988403i
$847$	5.19779	−	5.19779i	0.178598	−	0.178598i
$848$	9.94402	−	9.94402i	0.341479	−	0.341479i
$849$	−25.8960	−	44.8533i	−0.888750	−	1.53936i
$850$		0			0
$851$	4.25820	−	2.45847i	0.145969	−	0.0842754i
$852$	−7.26248	−	27.1039i	−0.248808	−	0.928566i
$853$	−5.96837	+	1.59922i	−0.204353	+	0.0547562i	−0.359543	−	0.933128i	$-0.617068\pi$
$853$	−5.96837	+	1.59922i	−0.204353	+	0.0547562i	0.155190	+	0.987885i	$0.450401\pi$
$854$	−4.04272			−0.138339
$855$		0			0
$856$	13.1106			0.448112
$857$	−39.0373	+	10.4600i	−1.33349	+	0.357307i	−0.854015	−	0.520248i	$-0.825839\pi$
$857$	−39.0373	+	10.4600i	−1.33349	+	0.357307i	−0.479475	+	0.877556i	$0.659173\pi$
$858$	1.79819	+	6.71095i	0.0613894	+	0.229108i
$859$	15.0491	−	8.68862i	0.513470	−	0.296452i	−0.220789	−	0.975322i	$-0.570863\pi$
$859$	15.0491	−	8.68862i	0.513470	−	0.296452i	0.734259	+	0.678870i	$0.237530\pi$
$860$		0			0
$861$	−2.87117	−	4.97302i	−0.0978494	−	0.169480i
$862$	−4.31908	+	4.31908i	−0.147108	+	0.147108i
$863$	7.65509	−	7.65509i	0.260582	−	0.260582i	−0.564708	−	0.825291i	$-0.691011\pi$
$863$	7.65509	−	7.65509i	0.260582	−	0.260582i	0.825291	+	0.564708i	$0.191011\pi$
$864$	2.16987	−	1.25278i	0.0738206	−	0.0426203i
$865$		0			0
$866$	1.70724			0.0580142
$867$	17.2014	+	17.2014i	0.584191	+	0.584191i
$868$	0.152815	+	0.0409466i	0.00518687	+	0.00138982i
$869$	2.26352	−	3.92052i	0.0767845	−	0.132995i
$870$		0			0
$871$	−1.67688	+	2.90444i	−0.0568189	+	0.0984132i
$872$	3.53341	+	13.1869i	0.119656	+	0.446564i
$873$	16.0705	−	16.0705i	0.543905	−	0.543905i
$874$	31.5060	+	4.45546i	1.06571	+	0.150708i
$875$		0			0
$876$	−20.8536	−	12.0398i	−0.704576	−	0.406787i
$877$	4.62562	−	1.23943i	0.156196	−	0.0418526i	−0.179874	−	0.983690i	$-0.557569\pi$
$877$	4.62562	−	1.23943i	0.156196	−	0.0418526i	0.336070	+	0.941837i	$0.390902\pi$
$878$	7.41412	−	27.6699i	0.250215	−	0.933813i
$879$	17.2584	+	9.96414i	0.582111	+	0.336082i
$880$		0			0
$881$	−48.4187			−1.63127			−0.815633	−	0.578569i	$-0.803611\pi$
$881$	−48.4187			−1.63127			−0.815633	+	0.578569i	$0.803611\pi$
$882$	8.49564	+	8.49564i	0.286063	+	0.286063i
$883$	2.46247	−	9.19005i	0.0828686	−	0.309270i	−0.912033	−	0.410116i	$-0.865488\pi$
$883$	2.46247	−	9.19005i	0.0828686	−	0.309270i	0.994902	+	0.100846i	$0.0321549\pi$
$884$	−7.86328	−	13.6196i	−0.264471	−	0.458077i
$885$		0			0
$886$			6.79630i			0.228326i
$887$	−0.476878	+	1.77973i	−0.0160120	+	0.0597576i	−0.973470	−	0.228816i	$-0.926514\pi$
$887$	−0.476878	+	1.77973i	−0.0160120	+	0.0597576i	0.957458	+	0.288574i	$0.0931811\pi$
$888$	−0.384475	−	1.43488i	−0.0129021	−	0.0481514i
$889$	2.30837	+	3.99821i	0.0774201	+	0.134096i
$890$		0			0
$891$	5.89531	−	10.2110i	0.197500	−	0.342081i
$892$	−6.41078	−	6.41078i	−0.214649	−	0.214649i
$893$	5.26448	−	12.3728i	0.176169	−	0.414040i
$894$		−	31.2151i		−	1.04399i
$895$		0			0
$896$	−0.644639	−	0.372182i	−0.0215359	−	0.0124337i
$897$	−46.1927	−	12.3773i	−1.54233	−	0.413266i
$898$	−33.4453	+	8.96164i	−1.11608	+	0.299054i
$899$	−0.769994	+	0.444556i	−0.0256807	+	0.0148268i
$900$		0			0
$901$			74.4545i			2.48044i
$902$	−3.58329	−	0.960140i	−0.119311	−	0.0319692i
$903$	−3.11304	−	0.834136i	−0.103595	−	0.0277583i
$904$			5.04170i			0.167684i
$905$		0			0
$906$	−0.157429	+	0.0908914i	−0.00523021	+	0.00301966i
$907$	−1.31840	+	0.353264i	−0.0437767	+	0.0117299i	−0.280641	−	0.959813i	$-0.590547\pi$
$907$	−1.31840	+	0.353264i	−0.0437767	+	0.0117299i	0.236864	+	0.971543i	$0.423880\pi$
$908$	−11.3789	−	3.04897i	−0.377623	−	0.101184i
$909$	−23.4128	−	13.5174i	−0.776552	−	0.448342i
$910$		0			0
$911$		−	20.2019i		−	0.669320i	−0.942339	−	0.334660i	$-0.891379\pi$
$911$		−	20.2019i		−	0.669320i	0.942339	−	0.334660i	$-0.108621\pi$
$912$	3.76379	−	8.84581i	0.124631	−	0.292914i
$913$	−5.84171	−	5.84171i	−0.193332	−	0.193332i
$914$	14.9226	−	25.8468i	0.493597	−	0.854935i
$915$		0			0
$916$	0.787399	+	1.36382i	0.0260164	+	0.0450617i
$917$	0.838406	+	3.12897i	0.0276866	+	0.103328i
$918$	−3.43332	+	12.8133i	−0.113316	+	0.422902i
$919$		−	10.3200i		−	0.340426i	−0.985407	−	0.170213i	$-0.945554\pi$
$919$		−	10.3200i		−	0.340426i	0.985407	−	0.170213i	$-0.0544456\pi$
$920$		0			0
$921$	30.7534	+	53.2664i	1.01336	+	1.75519i
$922$	9.11081	−	34.0020i	0.300049	−	1.11980i
$923$	−26.7240	−	26.7240i	−0.879630	−	0.879630i
$924$	−1.74103			−0.0572756
$925$		0			0
$926$	7.62246	+	4.40083i	0.250489	+	0.144620i
$927$	6.86579	−	25.6235i	0.225502	−	0.841586i
$928$	4.04078	−	1.08272i	0.132645	−	0.0355421i
$929$	−23.1172	−	13.3467i	−0.758451	−	0.437892i	0.0702885	−	0.997527i	$-0.477608\pi$
$929$	−23.1172	−	13.3467i	−0.758451	−	0.437892i	−0.828739	+	0.559635i	$0.810941\pi$
$930$		0			0
$931$	−27.8203	−	3.93424i	−0.911774	−	0.128940i
$932$	−17.6828	+	17.6828i	−0.579219	+	0.579219i
$933$	2.74014	+	10.2263i	0.0897082	+	0.334795i
$934$	8.94189	−	15.4878i	0.292588	−	0.506777i
$935$		0			0
$936$	−2.76832	+	4.79487i	−0.0904854	+	0.156725i
$937$	−7.30133	−	1.95639i	−0.238524	−	0.0639123i	0.137577	−	0.990491i	$-0.456069\pi$
$937$	−7.30133	−	1.95639i	−0.238524	−	0.0639123i	−0.376101	+	0.926579i	$0.622735\pi$
$938$	−0.594268	−	0.594268i	−0.0194035	−	0.0194035i
$939$	−34.3042			−1.11948
$940$		0			0
$941$	−44.4168	+	25.6440i	−1.44795	+	0.835972i	−0.998359	−	0.0572653i	$-0.981762\pi$
$941$	−44.4168	+	25.6440i	−1.44795	+	0.835972i	−0.449586	+	0.893237i	$0.648429\pi$
$942$	4.75281	−	4.75281i	0.154855	−	0.154855i
$943$	18.0556	−	18.0556i	0.587972	−	0.587972i
$944$	6.92591	+	11.9960i	0.225419	+	0.390438i
$945$		0			0
$946$	−1.80310	+	1.04102i	−0.0586239	+	0.0338465i
$947$	−3.61202	−	13.4802i	−0.117375	−	0.438049i	0.882079	−	0.471102i	$-0.156144\pi$
$947$	−3.61202	−	13.4802i	−0.117375	−	0.438049i	−0.999454	+	0.0330532i	$0.989477\pi$
$948$	9.09333	−	2.43655i	0.295338	−	0.0791355i
$949$	−32.4322			−1.05279
$950$		0			0
$951$	−41.8135			−1.35590
$952$	3.80665	−	1.01999i	0.123374	−	0.0330580i
$953$	0.244682	+	0.913164i	0.00792601	+	0.0295803i	0.969776	−	0.243999i	$-0.0784592\pi$
$953$	0.244682	+	0.913164i	0.00792601	+	0.0295803i	−0.961850	+	0.273579i	$0.911793\pi$
$954$	22.7004	−	13.1061i	0.734953	−	0.424325i
$955$		0			0
$956$	13.6633	+	23.6656i	0.441903	+	0.765399i
$957$	6.91873	−	6.91873i	0.223651	−	0.223651i
$958$	−2.55762	+	2.55762i	−0.0826329	+	0.0826329i
$959$	−12.0007	+	6.92862i	−0.387524	+	0.223737i
$960$		0			0
$961$	30.9548			0.998543
$962$	−1.41476	−	1.41476i	−0.0456138	−	0.0456138i
$963$	23.6044	+	6.32478i	0.760642	+	0.203813i
$964$	4.40834	−	7.63547i	0.141983	−	0.245922i
$965$		0			0
$966$	5.99191	−	10.3783i	0.192787	−	0.333916i
$967$	4.64699	+	17.3428i	0.149437	+	0.557707i	0.999518	+	0.0310541i	$0.00988642\pi$
$967$	4.64699	+	17.3428i	0.149437	+	0.557707i	−0.850081	+	0.526652i	$0.823447\pi$
$968$	6.98286	−	6.98286i	0.224438	−	0.224438i
$969$	19.0255	+	47.2063i	0.611186	+	1.51648i
$970$		0			0
$971$	16.8767	+	9.74378i	0.541600	+	0.312693i	0.745727	−	0.666251i	$-0.232102\pi$
$971$	16.8767	+	9.74378i	0.541600	+	0.312693i	−0.204127	+	0.978944i	$0.565436\pi$
$972$	16.4230	−	4.40053i	0.526768	−	0.141147i
$973$	1.93154	−	7.20860i	0.0619223	−	0.231097i
$974$	−24.3172	−	14.0395i	−0.779172	−	0.449855i
$975$		0			0
$976$	−5.43111			−0.173846
$977$	21.0974	+	21.0974i	0.674966	+	0.674966i	0.958857	−	0.283890i	$-0.0916252\pi$
$977$	21.0974	+	21.0974i	0.674966	+	0.674966i	−0.283890	+	0.958857i	$0.591625\pi$
$978$	10.8980	−	40.6719i	0.348480	−	1.30055i
$979$	−0.881948	−	1.52758i	−0.0281872	−	0.0488216i
$980$		0			0
$981$			25.4463i			0.812437i
$982$	−8.17120	+	30.4953i	−0.260754	+	0.973145i
$983$	−0.350930	−	1.30969i	−0.0111929	−	0.0417726i	0.960104	−	0.279645i	$-0.0902167\pi$
$983$	−0.350930	−	1.30969i	−0.0111929	−	0.0417726i	−0.971296	+	0.237872i	$0.923550\pi$
$984$	−3.85722	−	6.68089i	−0.122964	−	0.212979i
$985$		0			0
$986$	−11.0740	+	19.1807i	−0.352668	+	0.610839i
$987$	−3.58086	−	3.58086i	−0.113980	−	0.113980i
$988$	−1.56691	−	12.8527i	−0.0498501	−	0.408898i
$989$		−	14.3311i		−	0.455702i
$990$		0			0
$991$	−7.90763	−	4.56547i	−0.251194	−	0.145027i	0.369117	−	0.929383i	$-0.379660\pi$
$991$	−7.90763	−	4.56547i	−0.251194	−	0.145027i	−0.620311	+	0.784356i	$0.712994\pi$
$992$	0.205295	+	0.0550088i	0.00651814	+	0.00174653i
$993$	−56.4229	+	15.1185i	−1.79053	+	0.479770i
$994$	8.20185	−	4.73534i	0.260147	−	0.150196i
$995$		0			0
$996$		−	17.1799i		−	0.544366i
$997$	48.0084	+	12.8638i	1.52044	+	0.407401i	0.919887	−	0.392183i	$-0.128280\pi$
$997$	48.0084	+	12.8638i	1.52044	+	0.407401i	0.600554	+	0.799584i	$0.294947\pi$
$998$	33.3580	+	8.93824i	1.05593	+	0.282935i
$999$			1.68765i			0.0533949i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.q.g.293.1		32
5.2	odd	4	inner	950.2.q.g.407.1		32
5.3	odd	4		190.2.m.b.27.8	✓	32
5.4	even	2		190.2.m.b.103.8	yes	32
19.12	odd	6	inner	950.2.q.g.943.1		32
95.12	even	12	inner	950.2.q.g.107.1		32
95.69	odd	6		190.2.m.b.183.8	yes	32
95.88	even	12		190.2.m.b.107.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.m.b.27.8	✓	32	5.3	odd	4
190.2.m.b.103.8	yes	32	5.4	even	2
190.2.m.b.107.8	yes	32	95.88	even	12
190.2.m.b.183.8	yes	32	95.69	odd	6
950.2.q.g.107.1		32	95.12	even	12	inner
950.2.q.g.293.1		32	1.1	even	1	trivial
950.2.q.g.407.1		32	5.2	odd	4	inner
950.2.q.g.943.1		32	19.12	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.q (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.570807 - 2.13028i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.10271 + 1.90996i) q^{6} +(-0.526345 + 0.526345i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.61420 + 0.931958i) q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.570807 - 2.13028i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.10271 + 1.90996i) q^{6} +(-0.526345 + 0.526345i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.61420 + 0.931958i) q^{9} -1.06054 q^{11} +(-1.55947 - 1.55947i) q^{12} +(-2.86922 - 0.768805i) q^{13} +(0.372182 - 0.644639i) q^{14} +(0.500000 - 0.866025i) q^{16} +(1.37028 + 5.11396i) q^{17} +(1.31799 - 1.31799i) q^{18} +(-0.610346 + 4.31596i) q^{19} +(1.42170 + 0.820821i) q^{21} +(1.02440 - 0.274488i) q^{22} +(-1.88935 + 7.05116i) q^{23} +(1.90996 + 1.10271i) q^{24} +2.97044 q^{26} +(-1.77169 - 1.77169i) q^{27} +(-0.192656 + 0.719001i) q^{28} +(-2.09166 - 3.62286i) q^{29} -0.212537i q^{31} +(-0.258819 + 0.965926i) q^{32} +(0.605364 + 2.25925i) q^{33} +(-2.64718 - 4.58505i) q^{34} +(-0.931958 + 1.61420i) q^{36} +(-0.476282 - 0.476282i) q^{37} +(-0.527502 - 4.32686i) q^{38} +6.55108i q^{39} +(-3.02929 - 1.74896i) q^{41} +(-1.58571 - 0.424888i) q^{42} +(-1.89630 + 0.508111i) q^{43} +(-0.918455 + 0.530270i) q^{44} -7.29989i q^{46} +(-2.97966 - 0.798398i) q^{47} +(-2.13028 - 0.570807i) q^{48} +6.44592i q^{49} +(10.1120 - 5.83817i) q^{51} +(-2.86922 + 0.768805i) q^{52} +(13.5838 + 3.63976i) q^{53} +(2.16987 + 1.25278i) q^{54} -0.744364i q^{56} +(9.54259 - 1.16337i) q^{57} +(2.95805 + 2.95805i) q^{58} +(-6.92591 + 11.9960i) q^{59} +(-2.71555 - 4.70348i) q^{61} +(0.0550088 + 0.205295i) q^{62} +(0.359094 - 1.34016i) q^{63} -1.00000i q^{64} +(-1.16947 - 2.02559i) q^{66} +(0.292219 - 1.09057i) q^{67} +(3.74368 + 3.74368i) q^{68} +16.0994 q^{69} +(11.0186 + 6.36159i) q^{71} +(0.482417 - 1.80040i) q^{72} +(10.5463 - 2.82587i) q^{73} +(0.583324 + 0.336782i) q^{74} +(1.62940 + 4.04290i) q^{76} +(0.558210 - 0.558210i) q^{77} +(-1.69555 - 6.32786i) q^{78} +(-2.13430 + 3.69672i) q^{79} +(-5.55878 + 9.62809i) q^{81} +(3.37874 + 0.905330i) q^{82} +(5.50824 + 5.50824i) q^{83} +1.64164 q^{84} +(1.70017 - 0.981595i) q^{86} +(-6.52378 + 6.52378i) q^{87} +(0.749915 - 0.749915i) q^{88} +(0.831602 + 1.44038i) q^{89} +(1.91486 - 1.10554i) q^{91} +(1.88935 + 7.05116i) q^{92} +(-0.452764 + 0.121318i) q^{93} +3.08477 q^{94} +2.20543 q^{96} +(-11.7778 + 3.15584i) q^{97} +(-1.66833 - 6.22628i) q^{98} +(1.71192 - 0.988379i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 12 q^{3} - 24 q^{7}+O(q^{10}) \) 32 * q + 12 * q^3 - 24 * q^7	\( 32 q + 12 q^{3} - 24 q^{7} - 16 q^{11} - 24 q^{13} + 16 q^{16} + 8 q^{17} + 12 q^{22} - 4 q^{23} - 16 q^{26} + 12 q^{28} + 24 q^{33} - 8 q^{36} - 16 q^{38} + 24 q^{41} - 20 q^{42} + 24 q^{43} + 36 q^{47} + 12 q^{48} + 24 q^{51} - 24 q^{52} + 72 q^{53} + 24 q^{57} - 24 q^{58} - 48 q^{61} + 4 q^{62} - 16 q^{63} + 32 q^{66} - 36 q^{67} - 16 q^{68} + 24 q^{71} - 8 q^{73} + 24 q^{77} + 24 q^{78} + 56 q^{81} - 8 q^{82} - 24 q^{83} - 104 q^{87} - 24 q^{91} + 4 q^{92} - 52 q^{93} + 24 q^{97} - 72 q^{98}+O(q^{100}) \) 32 * q + 12 * q^3 - 24 * q^7 - 16 * q^11 - 24 * q^13 + 16 * q^16 + 8 * q^17 + 12 * q^22 - 4 * q^23 - 16 * q^26 + 12 * q^28 + 24 * q^33 - 8 * q^36 - 16 * q^38 + 24 * q^41 - 20 * q^42 + 24 * q^43 + 36 * q^47 + 12 * q^48 + 24 * q^51 - 24 * q^52 + 72 * q^53 + 24 * q^57 - 24 * q^58 - 48 * q^61 + 4 * q^62 - 16 * q^63 + 32 * q^66 - 36 * q^67 - 16 * q^68 + 24 * q^71 - 8 * q^73 + 24 * q^77 + 24 * q^78 + 56 * q^81 - 8 * q^82 - 24 * q^83 - 104 * q^87 - 24 * q^91 + 4 * q^92 - 52 * q^93 + 24 * q^97 - 72 * q^98

Introduction

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