LMFDB - Embedded newform 950.2.u.f.149.1

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:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			149.1
Character	$\chi$	$=$	950.149
Dual form			950.2.u.f.899.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.642788 + 0.766044i) q^{2} +(-0.936765 - 2.57374i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(2.57374 + 0.936765i) q^{6} +(3.33331 - 1.92448i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-3.44848 + 2.89362i) q^{9} +O(q^{10})$	\(q+(-0.642788 + 0.766044i) q^{2} +(-0.936765 - 2.57374i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(2.57374 + 0.936765i) q^{6} +(3.33331 - 1.92448i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-3.44848 + 2.89362i) q^{9} +(-2.86418 + 4.96090i) q^{11} +(-2.37197 + 1.36946i) q^{12} +(-1.84169 + 5.05999i) q^{13} +(-0.668367 + 3.79050i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(-0.883218 + 1.05258i) q^{17} -4.50167i q^{18} +(-4.23364 + 1.03746i) q^{19} +(-8.07565 - 6.77628i) q^{21} +(-1.95921 - 5.38289i) q^{22} +(1.55399 - 0.274010i) q^{23} +(0.475608 - 2.69731i) q^{24} +(-2.69236 - 4.66331i) q^{26} +(3.56193 + 2.05648i) q^{27} +(-2.47407 - 2.94848i) q^{28} +(-5.22668 + 4.38571i) q^{29} +(3.07565 + 5.32718i) q^{31} +(0.342020 - 0.939693i) q^{32} +(15.4511 + 2.72445i) q^{33} +(-0.238600 - 1.35317i) q^{34} +(3.44848 + 2.89362i) q^{36} -1.89405i q^{37} +(1.92659 - 3.91002i) q^{38} +14.7483 q^{39} +(-3.39002 + 1.23387i) q^{41} +(10.3819 - 1.83060i) q^{42} +(-3.22670 - 0.568954i) q^{43} +(5.38289 + 1.95921i) q^{44} +(-0.788981 + 1.36656i) q^{46} +(4.65857 + 5.55187i) q^{47} +(1.76054 + 2.09813i) q^{48} +(3.90728 - 6.76762i) q^{49} +(3.53643 + 1.28716i) q^{51} +(5.30292 + 0.935048i) q^{52} +(-11.5955 + 2.04459i) q^{53} +(-3.86492 + 1.40672i) q^{54} +3.84897 q^{56} +(6.63607 + 9.92443i) q^{57} -6.82295i q^{58} +(2.00293 + 1.68066i) q^{59} +(-1.05728 - 5.99615i) q^{61} +(-6.05785 - 1.06816i) q^{62} +(-5.92612 + 16.2819i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-12.0189 + 10.0850i) q^{66} +(-4.03673 - 4.81079i) q^{67} +(1.18996 + 0.687022i) q^{68} +(-2.16096 - 3.74288i) q^{69} +(-2.16096 + 12.2554i) q^{71} +(-4.43328 + 0.781707i) q^{72} +(-3.22433 - 8.85877i) q^{73} +(1.45093 + 1.21747i) q^{74} +(1.75686 + 3.98917i) q^{76} +22.0483i q^{77} +(-9.48004 + 11.2979i) q^{78} +(7.27101 - 2.64643i) q^{79} +(-0.388964 + 2.20593i) q^{81} +(1.23387 - 3.39002i) q^{82} +(3.88794 - 2.24471i) q^{83} +(-5.27101 + 9.12965i) q^{84} +(2.50993 - 2.10608i) q^{86} +(16.1838 + 9.34375i) q^{87} +(-4.96090 + 2.86418i) q^{88} +(-0.964940 - 0.351210i) q^{89} +(3.59897 + 20.4108i) q^{91} +(-0.539695 - 1.48280i) q^{92} +(10.8296 - 12.9063i) q^{93} -7.24746 q^{94} -2.73892 q^{96} +(0.849299 - 1.01216i) q^{97} +(2.67274 + 7.34329i) q^{98} +(-4.47790 - 25.3954i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{6} - 18 q^{9}+O(q^{10}) $ 24 * q + 6 * q^6 - 18 * q^9	$ 24 q + 6 q^{6} - 18 q^{9} - 12 q^{11} + 12 q^{14} - 12 q^{19} - 72 q^{21} - 6 q^{24} - 6 q^{26} - 72 q^{29} - 48 q^{31} + 12 q^{34} + 18 q^{36} + 24 q^{39} - 24 q^{41} + 18 q^{44} - 36 q^{46} - 54 q^{51} - 18 q^{54} + 24 q^{56} + 54 q^{59} + 108 q^{61} + 12 q^{64} - 78 q^{66} + 48 q^{69} + 48 q^{71} - 30 q^{74} + 18 q^{76} + 72 q^{79} - 18 q^{81} - 24 q^{84} + 48 q^{86} - 36 q^{89} + 24 q^{91} - 36 q^{94} - 36 q^{99}+O(q^{100}) $ 24 * q + 6 * q^6 - 18 * q^9 - 12 * q^11 + 12 * q^14 - 12 * q^19 - 72 * q^21 - 6 * q^24 - 6 * q^26 - 72 * q^29 - 48 * q^31 + 12 * q^34 + 18 * q^36 + 24 * q^39 - 24 * q^41 + 18 * q^44 - 36 * q^46 - 54 * q^51 - 18 * q^54 + 24 * q^56 + 54 * q^59 + 108 * q^61 + 12 * q^64 - 78 * q^66 + 48 * q^69 + 48 * q^71 - 30 * q^74 + 18 * q^76 + 72 * q^79 - 18 * q^81 - 24 * q^84 + 48 * q^86 - 36 * q^89 + 24 * q^91 - 36 * q^94 - 36 * 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
$3$	−0.936765	−	2.57374i	−0.540842	−	1.48595i	−0.845756	−	0.533570i	$-0.820850\pi$
$3$	−0.936765	−	2.57374i	−0.540842	−	1.48595i	0.304914	−	0.952380i	$-0.401372\pi$
$4$	−0.173648	−	0.984808i	−0.0868241	−	0.492404i
$5$		0			0
$5$		0			0
$6$	2.57374	+	0.936765i	1.05073	+	0.382433i
$7$	3.33331	−	1.92448i	1.25987	−	0.727387i	0.286822	−	0.957984i	$-0.407401\pi$
$7$	3.33331	−	1.92448i	1.25987	−	0.727387i	0.973049	+	0.230597i	$0.0740679\pi$
$8$	0.866025	+	0.500000i	0.306186	+	0.176777i
$9$	−3.44848	+	2.89362i	−1.14949	+	0.964540i
$10$		0			0
$11$	−2.86418	+	4.96090i	−0.863582	+	1.49577i	0.00486621	+	0.999988i	$0.498451\pi$
$11$	−2.86418	+	4.96090i	−0.863582	+	1.49577i	−0.868448	+	0.495780i	$0.834882\pi$
$12$	−2.37197	+	1.36946i	−0.684730	+	0.395329i
$13$	−1.84169	+	5.05999i	−0.510792	+	1.40339i	0.369622	+	0.929182i	$0.379487\pi$
$13$	−1.84169	+	5.05999i	−0.510792	+	1.40339i	−0.880414	+	0.474206i	$0.842735\pi$
$14$	−0.668367	+	3.79050i	−0.178628	+	1.01305i
$15$		0			0
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−0.883218	+	1.05258i	−0.214212	+	0.255288i	−0.862441	−	0.506158i	$-0.831065\pi$
$17$	−0.883218	+	1.05258i	−0.214212	+	0.255288i	0.648229	+	0.761445i	$0.275510\pi$
$18$		−	4.50167i		−	1.06105i
$19$	−4.23364	+	1.03746i	−0.971263	+	0.238009i
$19$	−4.23364	+	1.03746i	−0.971263	+	0.238009i
$20$		0			0
$21$	−8.07565	−	6.77628i	−1.76225	−	1.47870i
$22$	−1.95921	−	5.38289i	−0.417706	−	1.14764i
$23$	1.55399	−	0.274010i	0.324029	−	0.0571351i	−0.00926752	−	0.999957i	$-0.502950\pi$
$23$	1.55399	−	0.274010i	0.324029	−	0.0571351i	0.333297	+	0.942822i	$0.391839\pi$
$24$	0.475608	−	2.69731i	0.0970831	−	0.550586i
$25$		0			0
$26$	−2.69236	−	4.66331i	−0.528016	−	0.914550i
$27$	3.56193	+	2.05648i	0.685494	+	0.395770i
$28$	−2.47407	−	2.94848i	−0.467555	−	0.557211i
$29$	−5.22668	+	4.38571i	−0.970570	+	0.814405i	−0.982640	−	0.185522i	$-0.940602\pi$
$29$	−5.22668	+	4.38571i	−0.970570	+	0.814405i	0.0120697	+	0.999927i	$0.496158\pi$
$30$		0			0
$31$	3.07565	+	5.32718i	0.552403	+	0.956791i	0.998100	+	0.0616068i	$0.0196225\pi$
$31$	3.07565	+	5.32718i	0.552403	+	0.956791i	−0.445697	+	0.895184i	$0.647044\pi$
$32$	0.342020	−	0.939693i	0.0604612	−	0.166116i
$33$	15.4511	+	2.72445i	2.68970	+	0.474266i
$34$	−0.238600	−	1.35317i	−0.0409196	−	0.232066i
$35$		0			0
$36$	3.44848	+	2.89362i	0.574747	+	0.482270i
$37$		−	1.89405i		−	0.311381i	−0.987806	−	0.155690i	$-0.950240\pi$
$37$		−	1.89405i		−	0.311381i	0.987806	−	0.155690i	$-0.0497602\pi$
$38$	1.92659	−	3.91002i	0.312534	−	0.634289i
$39$	14.7483			2.36162
$40$		0			0
$41$	−3.39002	+	1.23387i	−0.529433	+	0.192698i	−0.592885	−	0.805287i	$-0.702011\pi$
$41$	−3.39002	+	1.23387i	−0.529433	+	0.192698i	0.0634522	+	0.997985i	$0.479789\pi$
$42$	10.3819	−	1.83060i	1.60196	−	0.282468i
$43$	−3.22670	−	0.568954i	−0.492067	−	0.0867647i	−0.0778917	−	0.996962i	$-0.524819\pi$
$43$	−3.22670	−	0.568954i	−0.492067	−	0.0867647i	−0.414175	+	0.910197i	$0.635930\pi$
$44$	5.38289	+	1.95921i	0.811502	+	0.295362i
$45$		0			0
$46$	−0.788981	+	1.36656i	−0.116329	+	0.201488i
$47$	4.65857	+	5.55187i	0.679523	+	0.809824i	0.990046	−	0.140742i	$-0.0449487\pi$
$47$	4.65857	+	5.55187i	0.679523	+	0.809824i	−0.310523	+	0.950566i	$0.600504\pi$
$48$	1.76054	+	2.09813i	0.254112	+	0.302839i
$49$	3.90728	−	6.76762i	0.558184	−	0.966802i
$50$		0			0
$51$	3.53643	+	1.28716i	0.495199	+	0.180238i
$52$	5.30292	+	0.935048i	0.735383	+	0.129668i
$53$	−11.5955	+	2.04459i	−1.59276	+	0.280847i	−0.898532	−	0.438908i	$-0.855365\pi$
$53$	−11.5955	+	2.04459i	−1.59276	+	0.280847i	−0.694229	+	0.719755i	$0.744254\pi$
$54$	−3.86492	+	1.40672i	−0.525949	+	0.191430i
$55$		0			0
$56$	3.84897			0.514340
$57$	6.63607	+	9.92443i	0.878969	+	1.31452i
$58$		−	6.82295i		−	0.895897i
$59$	2.00293	+	1.68066i	0.260759	+	0.218803i	0.763789	−	0.645466i	$-0.223337\pi$
$59$	2.00293	+	1.68066i	0.260759	+	0.218803i	−0.503030	+	0.864269i	$0.667781\pi$
$60$		0			0
$61$	−1.05728	−	5.99615i	−0.135371	−	0.767728i	−0.974600	−	0.223951i	$-0.928105\pi$
$61$	−1.05728	−	5.99615i	−0.135371	−	0.767728i	0.839229	−	0.543778i	$-0.183007\pi$
$62$	−6.05785	−	1.06816i	−0.769348	−	0.135657i
$63$	−5.92612	+	16.2819i	−0.746621	+	2.05132i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$		0			0
$66$	−12.0189	+	10.0850i	−1.47942	+	1.24138i
$67$	−4.03673	−	4.81079i	−0.493166	−	0.587732i	0.460854	−	0.887476i	$-0.347543\pi$
$67$	−4.03673	−	4.81079i	−0.493166	−	0.587732i	−0.954020	+	0.299744i	$0.903099\pi$
$68$	1.18996	+	0.687022i	0.144303	+	0.0833136i
$69$	−2.16096	−	3.74288i	−0.260148	−	0.450590i
$70$		0			0
$71$	−2.16096	+	12.2554i	−0.256458	+	1.45445i	0.535843	+	0.844317i	$0.319994\pi$
$71$	−2.16096	+	12.2554i	−0.256458	+	1.45445i	−0.792302	+	0.610130i	$0.791117\pi$
$72$	−4.43328	+	0.781707i	−0.522467	+	0.0921251i
$73$	−3.22433	−	8.85877i	−0.377379	−	1.03684i	−0.972439	−	0.233159i	$-0.925094\pi$
$73$	−3.22433	−	8.85877i	−0.377379	−	1.03684i	0.595060	−	0.803682i	$-0.297128\pi$
$74$	1.45093	+	1.21747i	0.168667	+	0.141529i
$75$		0			0
$76$	1.75686	+	3.98917i	0.201526	+	0.457589i
$77$			22.0483i			2.51263i
$78$	−9.48004	+	11.2979i	−1.07340	+	1.27923i
$79$	7.27101	−	2.64643i	0.818052	−	0.297747i	0.101106	−	0.994876i	$-0.467762\pi$
$79$	7.27101	−	2.64643i	0.818052	−	0.297747i	0.716946	+	0.697129i	$0.245540\pi$
$80$		0			0
$81$	−0.388964	+	2.20593i	−0.0432182	+	0.245103i
$82$	1.23387	−	3.39002i	0.136258	−	0.374366i
$83$	3.88794	−	2.24471i	0.426757	−	0.246388i	−0.271207	−	0.962521i	$-0.587423\pi$
$83$	3.88794	−	2.24471i	0.426757	−	0.246388i	0.697964	+	0.716133i	$0.254089\pi$
$84$	−5.27101	+	9.12965i	−0.575114	+	0.996127i
$85$		0			0
$86$	2.50993	−	2.10608i	0.270652	−	0.227104i
$87$	16.1838	+	9.34375i	1.73509	+	1.00176i
$88$	−4.96090	+	2.86418i	−0.528834	+	0.305322i
$89$	−0.964940	−	0.351210i	−0.102283	−	0.0372281i	0.290372	−	0.956914i	$-0.406221\pi$
$89$	−0.964940	−	0.351210i	−0.102283	−	0.0372281i	−0.392655	+	0.919686i	$0.628443\pi$
$90$		0			0
$91$	3.59897	+	20.4108i	0.377275	+	2.13963i
$92$	−0.539695	−	1.48280i	−0.0562671	−	0.154593i
$93$	10.8296	−	12.9063i	1.12298	−	1.33832i
$94$	−7.24746			−0.747518
$95$		0			0
$96$	−2.73892			−0.279540
$97$	0.849299	−	1.01216i	0.0862332	−	0.102769i	−0.721203	−	0.692724i	$-0.756410\pi$
$97$	0.849299	−	1.01216i	0.0862332	−	0.102769i	0.807436	+	0.589956i	$0.200855\pi$
$98$	2.67274	+	7.34329i	0.269988	+	0.741785i
$99$	−4.47790	−	25.3954i	−0.450046	−	2.55234i
$100$		0			0
$101$	13.6667	+	4.97428i	1.35989	+	0.494960i	0.916021	−	0.401131i	$-0.131383\pi$
$101$	13.6667	+	4.97428i	1.35989	+	0.494960i	0.443870	+	0.896091i	$0.353605\pi$
$102$	−3.25919	+	1.88170i	−0.322708	+	0.186316i
$103$	6.57398	+	3.79549i	0.647754	+	0.373981i	0.787595	−	0.616193i	$-0.211326\pi$
$103$	6.57398	+	3.79549i	0.647754	+	0.373981i	−0.139841	+	0.990174i	$0.544659\pi$
$104$	−4.12494	+	3.46124i	−0.404484	+	0.339402i
$105$		0			0
$106$	5.88718	−	10.1969i	0.571813	−	0.990409i
$107$	1.18180	−	0.682312i	0.114249	−	0.0659616i	−0.441787	−	0.897120i	$-0.645655\pi$
$107$	1.18180	−	0.682312i	0.114249	−	0.0659616i	0.556035	+	0.831159i	$0.312322\pi$
$108$	1.40672	−	3.86492i	0.135361	−	0.371902i
$109$	−1.23433	+	7.00026i	−0.118228	+	0.670503i	0.866873	+	0.498528i	$0.166126\pi$
$109$	−1.23433	+	7.00026i	−0.118228	+	0.670503i	−0.985101	+	0.171975i	$0.944985\pi$
$110$		0			0
$111$	−4.87481	+	1.77428i	−0.462696	+	0.168408i
$112$	−2.47407	+	2.94848i	−0.233778	+	0.278605i
$113$		−	11.0635i		−	1.04077i	−0.853932	−	0.520385i	$-0.825788\pi$
$113$		−	11.0635i		−	1.04077i	0.853932	−	0.520385i	$-0.174212\pi$
$114$	−11.8681	−	1.29577i	−1.11155	−	0.121360i
$115$		0			0
$116$	5.22668	+	4.38571i	0.485285	+	0.407203i
$117$	−8.29067	−	22.7784i	−0.766472	−	2.10587i
$118$	−2.57491	+	0.454027i	−0.237040	+	0.0417965i
$119$	−0.918365	+	5.20830i	−0.0841863	+	0.477444i
$120$		0			0
$121$	−10.9070	−	18.8915i	−0.991548	−	1.71741i
$122$	5.27293	+	3.04433i	0.477388	+	0.275620i
$123$	6.35131	+	7.56920i	0.572679	+	0.682492i
$124$	4.71217	−	3.95398i	0.423166	−	0.355078i
$125$		0			0
$126$	−8.66340	−	15.0055i	−0.771797	−	1.33679i
$127$	0.111515	−	0.306386i	0.00989538	−	0.0271873i	−0.934647	−	0.355578i	$-0.884284\pi$
$127$	0.111515	−	0.306386i	0.00989538	−	0.0271873i	0.944542	+	0.328391i	$0.106506\pi$
$128$	−0.984808	−	0.173648i	−0.0870455	−	0.0153485i
$129$	1.55832	+	8.83766i	0.137202	+	0.778113i
$130$		0			0
$131$	−4.03121	−	3.38258i	−0.352208	−	0.295538i	0.449468	−	0.893296i	$-0.351614\pi$
$131$	−4.03121	−	3.38258i	−0.352208	−	0.295538i	−0.801676	+	0.597759i	$0.796058\pi$
$132$		−	15.6895i		−	1.36560i
$133$	−12.1154	+	11.6057i	−1.05054	+	1.00634i
$134$	6.28004			0.542513
$135$		0			0
$136$	−1.29118	+	0.469950i	−0.110718	+	0.0402979i
$137$	−12.2383	+	2.15794i	−1.04559	+	0.184365i	−0.669953	−	0.742403i	$-0.733686\pi$
$137$	−12.2383	+	2.15794i	−1.04559	+	0.184365i	−0.375633	+	0.926768i	$0.622575\pi$
$138$	4.25625	+	0.750492i	0.362316	+	0.0638861i
$139$	−5.85434	−	2.13081i	−0.496559	−	0.180733i	0.0815867	−	0.996666i	$-0.474001\pi$
$139$	−5.85434	−	2.13081i	−0.496559	−	0.180733i	−0.578146	+	0.815934i	$0.696223\pi$
$140$		0			0
$141$	9.92509	−	17.1908i	0.835844	−	1.44772i
$142$	−7.99914	−	9.53300i	−0.671273	−	0.799992i
$143$	−19.8272	−	23.6291i	−1.65803	−	1.97597i
$144$	2.25084	−	3.89856i	0.187570	−	0.324880i
$145$		0			0
$146$	8.85877	+	3.22433i	0.733157	+	0.266847i
$147$	−21.0783	−	3.71667i	−1.73851	−	0.306546i
$148$	−1.86528	+	0.328899i	−0.153325	+	0.0270353i
$149$	21.4638	−	7.81220i	1.75839	−	0.640000i	0.758456	−	0.651725i	$-0.225954\pi$
$149$	21.4638	−	7.81220i	1.75839	−	0.640000i	0.999931	+	0.0117242i	$0.00373201\pi$
$150$		0			0
$151$	6.70041			0.545272			0.272636	−	0.962117i	$-0.412105\pi$
$151$	6.70041			0.545272			0.272636	+	0.962117i	$0.412105\pi$
$152$	−4.18517	−	1.21835i	−0.339462	−	0.0988215i
$153$		−	6.18549i		−	0.500068i
$154$	−16.8900	−	14.1724i	−1.36103	−	1.14204i
$155$		0			0
$156$	−2.56102	−	14.5243i	−0.205046	−	1.16287i
$157$	−0.0371436	−	0.00654942i	−0.00296438	−	0.000522700i	0.172166	−	0.985068i	$-0.444924\pi$
$157$	−0.0371436	−	0.00654942i	−0.00296438	−	0.000522700i	−0.175130	+	0.984545i	$0.556035\pi$
$158$	−2.64643	+	7.27101i	−0.210539	+	0.578450i
$159$	16.1245	+	27.9284i	1.27876	+	2.21487i
$160$		0			0
$161$	4.65259	−	3.90399i	0.366676	−	0.307678i
$162$	−1.43982	−	1.71591i	−0.113123	−	0.134814i
$163$	10.0740	+	5.81624i	0.789059	+	0.455563i	0.839631	−	0.543157i	$-0.182771\pi$
$163$	10.0740	+	5.81624i	0.789059	+	0.455563i	−0.0505722	+	0.998720i	$0.516105\pi$
$164$	1.80379	+	3.12426i	0.140853	+	0.243964i
$165$		0			0
$166$	−0.779578	+	4.42121i	−0.0605070	+	0.343152i
$167$	−10.5469	+	1.85971i	−0.816146	+	0.143909i	−0.566112	−	0.824328i	$-0.691553\pi$
$167$	−10.5469	+	1.85971i	−0.816146	+	0.143909i	−0.250034	+	0.968237i	$0.580442\pi$
$168$	−3.60558	−	9.90625i	−0.278177	−	0.764284i
$169$	−12.2531	−	10.2816i	−0.942546	−	0.790890i
$170$		0			0
$171$	11.5976	−	15.8282i	0.886891	−	1.21041i
$172$			3.27648i			0.249829i
$173$	−1.99680	+	2.37970i	−0.151814	+	0.180925i	−0.836591	−	0.547827i	$-0.815455\pi$
$173$	−1.99680	+	2.37970i	−0.151814	+	0.180925i	0.684777	+	0.728752i	$0.259899\pi$
$174$	−17.5605	+	6.39150i	−1.33126	+	0.484538i
$175$		0			0
$176$	0.994718	−	5.64133i	0.0749797	−	0.425231i
$177$	2.44930	−	6.72939i	0.184101	−	0.505812i
$178$	0.889294	−	0.513434i	0.0666554	−	0.0384835i
$179$	−10.5528	+	18.2779i	−0.788751	+	1.36616i	0.137981	+	0.990435i	$0.455939\pi$
$179$	−10.5528	+	18.2779i	−0.788751	+	1.36616i	−0.926732	+	0.375723i	$0.877395\pi$
$180$		0			0
$181$	−3.41410	+	2.86477i	−0.253768	+	0.212936i	−0.760793	−	0.648995i	$-0.775190\pi$
$181$	−3.41410	+	2.86477i	−0.253768	+	0.212936i	0.507025	+	0.861931i	$0.330745\pi$
$182$	−17.9489	−	10.3628i	−1.33046	−	0.768144i
$183$	−14.4421	+	8.33816i	−1.06759	+	0.616374i
$184$	1.48280	+	0.539695i	0.109313	+	0.0397868i
$185$		0			0
$186$	2.92561	+	16.5920i	0.214516	+	1.21658i
$187$	−2.69204	−	7.39633i	−0.196862	−	0.540873i
$188$	4.65857	−	5.55187i	0.339761	−	0.404912i
$189$	15.8307			1.15151
$190$		0			0
$191$	−8.06392			−0.583485			−0.291743	−	0.956497i	$-0.594235\pi$
$191$	−8.06392			−0.583485			−0.291743	+	0.956497i	$0.594235\pi$
$192$	1.76054	−	2.09813i	0.127056	−	0.151420i
$193$	0.230531	+	0.633380i	0.0165940	+	0.0455917i	0.947713	−	0.319124i	$-0.103389\pi$
$193$	0.230531	+	0.633380i	0.0165940	+	0.0455917i	−0.931119	+	0.364715i	$0.881166\pi$
$194$	0.229437	+	1.30120i	0.0164726	+	0.0934208i
$195$		0			0
$196$	−7.34329	−	2.67274i	−0.524521	−	0.190910i
$197$	6.37075	−	3.67816i	0.453897	−	0.262058i	−0.255577	−	0.966789i	$-0.582266\pi$
$197$	6.37075	−	3.67816i	0.453897	−	0.262058i	0.709475	+	0.704731i	$0.248932\pi$
$198$	22.3324	+	12.8936i	1.58709	+	0.916308i
$199$	21.0911	−	17.6976i	1.49511	−	1.25455i	0.607185	−	0.794561i	$-0.292299\pi$
$199$	21.0911	−	17.6976i	1.49511	−	1.25455i	0.887926	−	0.459986i	$-0.152146\pi$
$200$		0			0
$201$	−8.60026	+	14.8961i	−0.606616	+	1.05069i
$202$	−12.5953	+	7.27192i	−0.886204	+	0.511650i
$203$	−8.98190	+	24.6776i	−0.630406	+	1.73203i
$204$	0.653506	−	3.70622i	0.0457546	−	0.259487i
$205$		0			0
$206$	−7.13319	+	2.59627i	−0.496993	+	0.180891i
$207$	−4.56602	+	5.44158i	−0.317361	+	0.378216i
$208$		−	5.38473i		−	0.373364i
$209$	6.97916	−	23.9741i	0.482759	−	1.65832i
$210$		0			0
$211$	−16.3598	−	13.7275i	−1.12625	−	0.945038i	−0.127349	−	0.991858i	$-0.540647\pi$
$211$	−16.3598	−	13.7275i	−1.12625	−	0.945038i	−0.998903	+	0.0468202i	$0.985091\pi$
$212$	4.02706	+	11.0643i	0.276580	+	0.759897i
$213$	33.5665	−	5.91868i	2.29994	−	0.405541i
$214$	−0.236964	+	1.34389i	−0.0161986	+	0.0918665i
$215$		0			0
$216$	2.05648	+	3.56193i	0.139926	+	0.242359i
$217$	20.5042	+	11.8381i	1.39191	+	0.803622i
$218$	−4.56910	−	5.44524i	−0.309458	−	0.368798i
$219$	−19.7797	+	16.5972i	−1.33659	+	1.12153i
$220$		0			0
$221$	−3.69942	−	6.40759i	−0.248850	−	0.431021i
$222$	1.77428	−	4.87481i	0.119082	−	0.327176i
$223$	−18.5726	−	3.27485i	−1.24371	−	0.219300i	−0.487207	−	0.873286i	$-0.661984\pi$
$223$	−18.5726	−	3.27485i	−1.24371	−	0.219300i	−0.756506	+	0.653986i	$0.773095\pi$
$224$	−0.668367	−	3.79050i	−0.0446571	−	0.253263i
$225$		0			0
$226$	8.47516	+	7.11151i	0.563759	+	0.473050i
$227$		−	5.24641i		−	0.348217i	−0.984727	−	0.174108i	$-0.944296\pi$
$227$		−	5.24641i		−	0.348217i	0.984727	−	0.174108i	$-0.0557043\pi$
$228$	8.62131	−	8.25862i	0.570961	−	0.546940i
$229$	3.56871			0.235827			0.117913	−	0.993024i	$-0.462379\pi$
$229$	3.56871			0.235827			0.117913	+	0.993024i	$0.462379\pi$
$230$		0			0
$231$	56.7465	−	20.6541i	3.73365	−	1.35894i
$232$	−6.71929	+	1.18479i	−0.441143	+	0.0777854i
$233$	−5.45334	−	0.961571i	−0.357260	−	0.0629946i	−0.00786247	−	0.999969i	$-0.502503\pi$
$233$	−5.45334	−	0.961571i	−0.357260	−	0.0629946i	−0.349398	+	0.936974i	$0.613614\pi$
$234$	22.7784	+	8.29067i	1.48907	+	0.541978i
$235$		0			0
$236$	1.30732	−	2.26434i	0.0850991	−	0.147396i
$237$	−13.6225	−	16.2346i	−0.884873	−	1.05455i
$238$	−3.39948	−	4.05134i	−0.220355	−	0.262609i
$239$	−5.69086	+	9.85686i	−0.368111	+	0.637587i	−0.989270	−	0.146097i	$-0.953329\pi$
$239$	−5.69086	+	9.85686i	−0.368111	+	0.637587i	0.621159	+	0.783684i	$0.286662\pi$
$240$		0			0
$241$	−10.4113	−	3.78939i	−0.670649	−	0.244096i	−0.0158218	−	0.999875i	$-0.505036\pi$
$241$	−10.4113	−	3.78939i	−0.670649	−	0.244096i	−0.654827	+	0.755778i	$0.727259\pi$
$242$	21.4826	+	3.78797i	1.38096	+	0.243500i
$243$	18.1933	−	3.20797i	1.16710	−	0.205791i
$244$	−5.72146	+	2.08244i	−0.366279	+	0.133315i
$245$		0			0
$246$	−9.88089			−0.629983
$247$	2.54750	−	23.3328i	0.162094	−	1.48463i
$248$			6.15130i			0.390608i
$249$	−9.41938	−	7.90380i	−0.596929	−	0.500883i
$250$		0			0
$251$	0.628522	+	3.56453i	0.0396720	+	0.224991i	0.998197	−	0.0600161i	$-0.0191152\pi$
$251$	0.628522	+	3.56453i	0.0396720	+	0.224991i	−0.958525	+	0.285007i	$0.908004\pi$
$252$	17.0636	+	3.00877i	1.07490	+	0.189535i
$253$	−3.09156	+	8.49400i	−0.194365	+	0.534014i
$254$	0.163024	+	0.282367i	0.0102291	+	0.0177173i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−6.97027	−	8.30685i	−0.434794	−	0.518167i	0.503505	−	0.863992i	$-0.332043\pi$
$257$	−6.97027	−	8.30685i	−0.434794	−	0.518167i	−0.938299	+	0.345825i	$0.887599\pi$
$258$	−7.77171	−	4.48700i	−0.483846	−	0.279348i
$259$	−3.64508	−	6.31346i	−0.226494	−	0.392299i
$260$		0			0
$261$	5.33355	−	30.2481i	0.330138	−	1.87231i
$262$	5.18242	−	0.913800i	0.320171	−	0.0564548i
$263$	3.29831	+	9.06203i	0.203383	+	0.558789i	0.998887	−	0.0471583i	$-0.0150165\pi$
$263$	3.29831	+	9.06203i	0.203383	+	0.558789i	−0.795505	+	0.605947i	$0.792794\pi$
$264$	12.0189	+	10.0850i	0.739709	+	0.620690i
$265$		0			0
$266$	−1.10286	−	16.7410i	−0.0676206	−	1.02646i
$267$			2.81251i			0.172123i
$268$	−4.03673	+	4.81079i	−0.246583	+	0.293866i
$269$	−7.01729	+	2.55409i	−0.427852	+	0.155725i	−0.546965	−	0.837155i	$-0.684217\pi$
$269$	−7.01729	+	2.55409i	−0.427852	+	0.155725i	0.119113	+	0.992881i	$0.461995\pi$
$270$		0			0
$271$	−5.28922	+	29.9967i	−0.321297	+	1.82217i	0.213212	+	0.977006i	$0.431607\pi$
$271$	−5.28922	+	29.9967i	−0.321297	+	1.82217i	−0.534509	+	0.845162i	$0.679504\pi$
$272$	0.469950	−	1.29118i	0.0284949	−	0.0782892i
$273$	49.1607	−	28.3829i	2.97534	−	1.71781i
$274$	6.21353	−	10.7622i	0.375373	−	0.650166i
$275$		0			0
$276$	−3.31078	+	2.77807i	−0.199285	+	0.167220i
$277$	8.58624	+	4.95727i	0.515897	+	0.297853i	0.735254	−	0.677791i	$-0.237063\pi$
$277$	8.58624	+	4.95727i	0.515897	+	0.297853i	−0.219357	+	0.975645i	$0.570396\pi$
$278$	5.39539	−	3.11503i	0.323594	−	0.186827i
$279$	−26.0212	−	9.47093i	−1.55785	−	0.567010i
$280$		0			0
$281$	−2.79030	−	15.8246i	−0.166455	−	0.944015i	−0.947551	−	0.319604i	$-0.896450\pi$
$281$	−2.79030	−	15.8246i	−0.166455	−	0.944015i	0.781096	−	0.624411i	$-0.214661\pi$
$282$	6.78916	+	18.6531i	0.404289	+	1.11077i
$283$	−6.48413	+	7.72748i	−0.385441	+	0.459351i	−0.923524	−	0.383541i	$-0.874704\pi$
$283$	−6.48413	+	7.72748i	−0.385441	+	0.459351i	0.538082	+	0.842892i	$0.319149\pi$
$284$	12.4444			0.738442
$285$		0			0
$286$	30.8456			1.82394
$287$	−8.92543	+	10.6369i	−0.526851	+	0.627877i
$288$	1.53966	+	4.23019i	0.0907255	+	0.249266i
$289$	2.62417	+	14.8824i	0.154363	+	0.875436i
$290$		0			0
$291$	−3.40062	−	1.23772i	−0.199348	−	0.0725567i
$292$	−8.16429	+	4.71365i	−0.477779	+	0.275846i
$293$	4.55971	+	2.63255i	0.266381	+	0.153795i	0.627242	−	0.778824i	$-0.284184\pi$
$293$	4.55971	+	2.63255i	0.266381	+	0.153795i	−0.360861	+	0.932620i	$0.617517\pi$
$294$	16.3960	−	13.7579i	0.956235	−	0.802376i
$295$		0			0
$296$	0.947027	−	1.64030i	0.0550448	−	0.0953405i
$297$	−20.4040	+	11.7803i	−1.18396	+	0.683560i
$298$	−7.81220	+	21.4638i	−0.452549	+	1.24337i
$299$	−1.47547	+	8.36781i	−0.0853287	+	0.483923i
$300$		0			0
$301$	−11.8505	+	4.31324i	−0.683052	+	0.248611i
$302$	−4.30694	+	5.13281i	−0.247837	+	0.295360i
$303$		−	39.8344i		−	2.28843i
$304$	3.62349	−	2.42288i	0.207821	−	0.138962i
$305$		0			0
$306$	4.73836	+	3.97596i	0.270874	+	0.227290i
$307$	10.6272	+	29.1979i	0.606524	+	1.66641i	0.737762	+	0.675061i	$0.235883\pi$
$307$	10.6272	+	29.1979i	0.606524	+	1.66641i	−0.131238	+	0.991351i	$0.541895\pi$
$308$	21.7133	−	3.82864i	1.23723	−	0.218157i
$309$	3.61033	−	20.4752i	0.205385	−	1.16479i
$310$		0			0
$311$	8.97919	+	15.5524i	0.509163	+	0.881897i	0.999944	+	0.0106135i	$0.00337844\pi$
$311$	8.97919	+	15.5524i	0.509163	+	0.881897i	−0.490780	+	0.871283i	$0.663288\pi$
$312$	12.7724	+	7.37416i	0.723096	+	0.417480i
$313$	−9.59739	−	11.4377i	−0.542477	−	0.646499i	0.423264	−	0.906006i	$-0.360884\pi$
$313$	−9.59739	−	11.4377i	−0.542477	−	0.646499i	−0.965741	+	0.259508i	$0.916440\pi$
$314$	0.0288926	−	0.0242438i	0.00163050	−	0.00136815i
$315$		0			0
$316$	−3.86882	−	6.70100i	−0.217638	−	0.376961i
$317$	3.08921	−	8.48754i	0.173507	−	0.476708i	−0.822207	−	0.569188i	$-0.807257\pi$
$317$	3.08921	−	8.48754i	0.173507	−	0.476708i	0.995714	+	0.0924808i	$0.0294797\pi$
$318$	−31.7590	−	5.59998i	−1.78096	−	0.314031i
$319$	−6.78691	−	38.4905i	−0.379994	−	2.15505i
$320$		0			0
$321$	−2.86316	−	2.40248i	−0.159806	−	0.134093i
$322$			6.07353i			0.338465i
$323$	2.64722	−	5.37253i	0.147295	−	0.298936i
$324$	2.23996			0.124442
$325$		0			0
$326$	−10.9310	+	3.97855i	−0.605410	+	0.220351i
$327$	19.1731	−	3.38074i	1.06028	−	0.186955i
$328$	−3.55278	−	0.626451i	−0.196170	−	0.0345900i
$329$	26.2130	+	9.54073i	1.44517	+	0.525998i
$330$		0			0
$331$	17.1733	−	29.7451i	0.943931	−	1.63494i	0.186054	−	0.982540i	$-0.440430\pi$
$331$	17.1733	−	29.7451i	0.943931	−	1.63494i	0.757877	−	0.652397i	$-0.226237\pi$
$332$	−2.88574	−	3.43909i	−0.158375	−	0.188744i
$333$	5.48067	+	6.53161i	0.300339	+	0.357930i
$334$	5.35482	−	9.27482i	0.293003	−	0.507495i
$335$		0			0
$336$	9.90625	+	3.60558i	0.540430	+	0.196701i
$337$	−11.4013	−	2.01036i	−0.621068	−	0.109511i	−0.145745	−	0.989322i	$-0.546558\pi$
$337$	−11.4013	−	2.01036i	−0.621068	−	0.109511i	−0.475323	+	0.879811i	$0.657669\pi$
$338$	15.7523	−	2.77755i	0.856811	−	0.151079i
$339$	−28.4747	+	10.3639i	−1.54653	+	0.562892i
$340$		0			0
$341$	−35.2368			−1.90818
$342$	4.67030	+	19.0585i	0.252541	+	1.03056i
$343$		−	3.13526i		−	0.169288i
$344$	−2.50993	−	2.10608i	−0.135326	−	0.113552i
$345$		0			0
$346$	−0.539433	−	3.05928i	−0.0290001	−	0.164468i
$347$	1.71163	+	0.301806i	0.0918849	+	0.0162018i	0.219402	−	0.975635i	$-0.429590\pi$
$347$	1.71163	+	0.301806i	0.0918849	+	0.0162018i	−0.127517	+	0.991836i	$0.540701\pi$
$348$	6.39150	−	17.5605i	0.342620	−	0.941342i
$349$	−1.15031	−	1.99239i	−0.0615744	−	0.106650i	0.833595	−	0.552376i	$-0.186279\pi$
$349$	−1.15031	−	1.99239i	−0.0615744	−	0.106650i	−0.895169	+	0.445726i	$0.852945\pi$
$350$		0			0
$351$	−16.9657	+	14.2359i	−0.905563	+	0.759858i
$352$	3.68212	+	4.38817i	0.196257	+	0.233890i
$353$	25.5226	+	14.7355i	1.35843	+	0.784291i	0.989413	−	0.145130i	$-0.0463600\pi$
$353$	25.5226	+	14.7355i	1.35843	+	0.784291i	0.369020	+	0.929421i	$0.379693\pi$
$354$	3.58064	+	6.20184i	0.190309	+	0.329624i
$355$		0			0
$356$	−0.178314	+	1.01127i	−0.00945061	+	0.0535971i
$357$	14.2651	−	2.51533i	0.754990	−	0.133125i
$358$	−7.21852	−	19.8327i	−0.381511	−	1.04819i
$359$	−10.6986	−	8.97719i	−0.564651	−	0.473798i	0.315215	−	0.949020i	$-0.397923\pi$
$359$	−10.6986	−	8.97719i	−0.564651	−	0.473798i	−0.879866	+	0.475222i	$0.842368\pi$
$360$		0			0
$361$	16.8474	−	8.78444i	0.886703	−	0.462339i
$362$		−	4.45679i		−	0.234243i
$363$	−38.4046	+	45.7688i	−2.01572	+	2.40224i
$364$	19.4757	−	7.08859i	1.02081	−	0.371543i
$365$		0			0
$366$	2.89581	−	16.4230i	0.151367	−	0.858442i
$367$	−10.1569	+	27.9058i	−0.530185	+	1.45667i	0.328666	+	0.944446i	$0.393401\pi$
$367$	−10.1569	+	27.9058i	−0.530185	+	1.45667i	−0.858851	+	0.512226i	$0.828821\pi$
$368$	−1.36656	+	0.788981i	−0.0712366	+	0.0411285i
$369$	8.12009	−	14.0644i	0.422715	−	0.732164i
$370$		0			0
$371$	−34.7165	+	29.1306i	−1.80239	+	1.51238i
$372$	−14.5907	−	8.42396i	−0.756494	−	0.436762i
$373$	−9.99697	+	5.77175i	−0.517624	+	0.298850i	−0.735962	−	0.677023i	$-0.763270\pi$
$373$	−9.99697	+	5.77175i	−0.517624	+	0.298850i	0.218338	+	0.975873i	$0.429936\pi$
$374$	7.39633	+	2.69204i	0.382455	+	0.139202i
$375$		0			0
$376$	1.25851	+	7.13735i	0.0649026	+	0.368081i
$377$	−12.5657	−	34.5240i	−0.647168	−	1.77808i
$378$	−10.1758	+	12.1270i	−0.523384	+	0.623745i
$379$	−8.96195			−0.460345			−0.230172	−	0.973150i	$-0.573929\pi$
$379$	−8.96195			−0.460345			−0.230172	+	0.973150i	$0.573929\pi$
$380$		0			0
$381$	−0.893021			−0.0457509
$382$	5.18339	−	6.17732i	0.265205	−	0.316059i
$383$	9.90707	+	27.2194i	0.506227	+	1.39085i	0.885101	+	0.465400i	$0.154089\pi$
$383$	9.90707	+	27.2194i	0.506227	+	1.39085i	−0.378873	+	0.925449i	$0.623688\pi$
$384$	0.475608	+	2.69731i	0.0242708	+	0.137646i
$385$		0			0
$386$	−0.633380	−	0.230531i	−0.0322382	−	0.0117337i
$387$	12.7735	−	7.37481i	0.649316	−	0.374883i
$388$	−1.14426	−	0.660637i	−0.0580909	−	0.0335388i
$389$	−13.7913	+	11.5723i	−0.699247	+	0.586738i	−0.921559	−	0.388238i	$-0.873084\pi$
$389$	−13.7913	+	11.5723i	−0.699247	+	0.586738i	0.222312	+	0.974976i	$0.428640\pi$
$390$		0			0
$391$	−1.08409	+	1.87771i	−0.0548250	+	0.0949597i
$392$	6.76762	−	3.90728i	0.341816	−	0.197348i
$393$	−4.92960	+	13.5440i	−0.248665	+	0.683203i
$394$	−1.27741	+	7.24455i	−0.0643550	+	0.364975i
$395$		0			0
$396$	−24.2320	+	8.81974i	−1.21771	+	0.443208i
$397$	11.9441	−	14.2345i	0.599458	−	0.714407i	−0.377936	−	0.925832i	$-0.623366\pi$
$397$	11.9441	−	14.2345i	0.599458	−	0.714407i	0.977394	+	0.211425i	$0.0678104\pi$
$398$			27.5325i			1.38008i
$399$	41.2195	+	20.3101i	2.06356	+	1.01678i
$400$		0			0
$401$	21.6450	+	18.1623i	1.08090	+	0.906981i	0.995995	−	0.0894080i	$-0.0284975\pi$
$401$	21.6450	+	18.1623i	1.08090	+	0.906981i	0.0849030	+	0.996389i	$0.472942\pi$
$402$	−5.88293	−	16.1632i	−0.293414	−	0.806148i
$403$	−32.6199	+	5.75176i	−1.62491	+	0.286516i
$404$	2.52551	−	14.3229i	0.125649	−	0.712590i
$405$		0			0
$406$	−13.1307	−	22.7430i	−0.651664	−	1.12871i
$407$	9.39622	+	5.42491i	0.465753	+	0.268903i
$408$	2.41906	+	2.88293i	0.119761	+	0.142726i
$409$	−26.3573	+	22.1164i	−1.30329	+	1.09359i	−0.313718	+	0.949516i	$0.601575\pi$
$409$	−26.3573	+	22.1164i	−1.30329	+	1.09359i	−0.989567	+	0.144071i	$0.953981\pi$
$410$		0			0
$411$	17.0184	+	29.4767i	0.839454	+	1.45398i
$412$	2.59627	−	7.13319i	0.127909	−	0.351427i
$413$	9.91076	+	1.74753i	0.487677	+	0.0859906i
$414$	−1.23351	−	6.99556i	−0.0606235	−	0.343813i
$415$		0			0
$416$	4.12494	+	3.46124i	0.202242	+	0.169701i
$417$			17.0636i			0.835610i
$418$	13.8791	+	20.7566i	0.678850	+	1.01524i
$419$	−0.950291			−0.0464248			−0.0232124	−	0.999731i	$-0.507389\pi$
$419$	−0.950291			−0.0464248			−0.0232124	+	0.999731i	$0.507389\pi$
$420$		0			0
$421$	−20.5965	+	7.49650i	−1.00381	+	0.365357i	−0.791052	−	0.611748i	$-0.790467\pi$
$421$	−20.5965	+	7.49650i	−1.00381	+	0.365357i	−0.212757	+	0.977105i	$0.568244\pi$
$422$	21.0317	−	3.70846i	1.02381	−	0.180525i
$423$	−32.1300	−	5.66539i	−1.56222	−	0.275461i
$424$	−11.0643	−	4.02706i	−0.537328	−	0.195572i
$425$		0			0
$426$	−17.0422	+	29.5179i	−0.825695	+	1.43015i
$427$	−15.0638	−	17.9523i	−0.728986	−	0.868772i
$428$	−0.877163	−	1.04536i	−0.0423993	−	0.0505295i
$429$	−42.2418	+	73.1650i	−2.03945	+	3.53244i
$430$		0			0
$431$	23.5122	+	8.55773i	1.13254	+	0.412211i	0.839214	−	0.543801i	$-0.183015\pi$
$431$	23.5122	+	8.55773i	1.13254	+	0.412211i	0.293327	+	0.956012i	$0.405238\pi$
$432$	−4.05048	−	0.714208i	−0.194879	−	0.0343624i
$433$	−38.3559	+	6.76319i	−1.84327	+	0.325018i	−0.982827	−	0.184531i	$-0.940923\pi$
$433$	−38.3559	+	6.76319i	−1.84327	+	0.325018i	−0.860442	+	0.509549i	$0.829812\pi$
$434$	−22.2483	+	8.09773i	−1.06795	+	0.388704i
$435$		0			0
$436$	7.10825			0.340424
$437$	−6.29475	+	2.77226i	−0.301119	+	0.132615i
$438$		−	25.8206i		−	1.23376i
$439$	−3.73509	−	3.13411i	−0.178266	−	0.149583i	0.549289	−	0.835633i	$-0.314899\pi$
$439$	−3.73509	−	3.13411i	−0.178266	−	0.149583i	−0.727555	+	0.686050i	$0.759343\pi$
$440$		0			0
$441$	6.10871	+	34.6442i	0.290891	+	1.64972i
$442$	7.28644	+	1.28480i	0.346581	+	0.0611115i
$443$	7.08698	−	19.4713i	0.336712	−	0.925110i	−0.649608	−	0.760269i	$-0.725067\pi$
$443$	7.08698	−	19.4713i	0.336712	−	0.925110i	0.986320	−	0.164840i	$-0.0527109\pi$
$444$	2.59383	+	4.49265i	0.123098	+	0.213212i
$445$		0			0
$446$	14.4469	−	12.1224i	0.684082	−	0.574013i
$447$	−40.2132	−	47.9242i	−1.90202	−	2.26674i
$448$	3.33331	+	1.92448i	0.157484	+	0.0909234i
$449$	8.39412	+	14.5390i	0.396143	+	0.686140i	0.993246	−	0.116024i	$-0.0370151\pi$
$449$	8.39412	+	14.5390i	0.396143	+	0.686140i	−0.597103	+	0.802164i	$0.703682\pi$
$450$		0			0
$451$	3.58853	−	20.3516i	0.168978	−	0.958319i
$452$	−10.8955	+	1.92116i	−0.512479	+	0.0903639i
$453$	−6.27671	−	17.2451i	−0.294906	−	0.810247i
$454$	4.01899	+	3.37233i	0.188620	+	0.158271i
$455$		0			0
$456$	0.784792	+	11.9128i	0.0367513	+	0.557870i
$457$			8.48651i			0.396982i	0.980103	+	0.198491i	$0.0636041\pi$
$457$			8.48651i			0.396982i	−0.980103	+	0.198491i	$0.936396\pi$
$458$	−2.29392	+	2.73379i	−0.107188	+	0.127742i
$459$	−5.31057	+	1.93289i	−0.247876	+	0.0902195i
$460$		0			0
$461$	−5.74433	+	32.5777i	−0.267540	+	1.51730i	0.494163	+	0.869369i	$0.335475\pi$
$461$	−5.74433	+	32.5777i	−0.267540	+	1.51730i	−0.761703	+	0.647926i	$0.775637\pi$
$462$	−20.6541	+	56.7465i	−0.960913	+	2.64009i
$463$	27.0264	−	15.6037i	1.25602	−	0.725165i	0.283724	−	0.958906i	$-0.408430\pi$
$463$	27.0264	−	15.6037i	1.25602	−	0.725165i	0.972299	+	0.233741i	$0.0750969\pi$
$464$	3.41147	−	5.90885i	0.158374	−	0.274311i
$465$		0			0
$466$	4.24195	−	3.55942i	0.196504	−	0.164887i
$467$	−15.2665	−	8.81413i	−0.706450	−	0.407869i	0.103295	−	0.994651i	$-0.467061\pi$
$467$	−15.2665	−	8.81413i	−0.706450	−	0.407869i	−0.809745	+	0.586782i	$0.800395\pi$
$468$	−20.9927	+	12.1201i	−0.970388	+	0.560254i
$469$	−22.7140	−	8.26721i	−1.04883	−	0.381744i
$470$		0			0
$471$	0.0179383	+	0.101733i	0.000826554	+	0.00468762i
$472$	0.894258	+	2.45695i	0.0411616	+	0.113090i
$473$	12.0644	−	14.3777i	0.554720	−	0.661090i
$474$	21.1928			0.973416
$475$		0			0
$476$	5.28865			0.242405
$477$	34.0705	−	40.6036i	1.55998	−	1.85911i
$478$	−3.89278	−	10.6953i	−0.178051	−	0.489192i
$479$	−2.69595	−	15.2895i	−0.123181	−	0.698596i	−0.982371	−	0.186939i	$-0.940143\pi$
$479$	−2.69595	−	15.2895i	−0.123181	−	0.698596i	0.859190	−	0.511656i	$-0.170968\pi$
$480$		0			0
$481$	9.58389	+	3.48825i	0.436988	+	0.159051i
$482$	9.59508	−	5.53972i	0.437044	−	0.252328i
$483$	−14.4063	−	8.31745i	−0.655507	−	0.378457i
$484$	−16.7105	+	14.0218i	−0.759570	+	0.637355i
$485$		0			0
$486$	−9.23697	+	15.9989i	−0.418997	+	0.725725i
$487$	20.9286	−	12.0831i	0.948364	−	0.547538i	0.0557919	−	0.998442i	$-0.482232\pi$
$487$	20.9286	−	12.0831i	0.948364	−	0.547538i	0.892572	+	0.450904i	$0.148898\pi$
$488$	2.08244	−	5.72146i	0.0942677	−	0.258998i
$489$	5.53251	−	31.3764i	0.250189	−	1.41889i
$490$		0			0
$491$	−5.53601	+	2.01494i	−0.249837	+	0.0909331i	−0.463903	−	0.885886i	$-0.653551\pi$
$491$	−5.53601	+	2.01494i	−0.249837	+	0.0909331i	0.214066	+	0.976819i	$0.431329\pi$
$492$	6.35131	−	7.56920i	0.286339	−	0.341246i
$493$		−	9.37502i		−	0.422230i
$494$	16.2365	+	16.9495i	0.730514	+	0.762596i
$495$		0			0
$496$	−4.71217	−	3.95398i	−0.211583	−	0.177539i
$497$	16.3822	+	45.0097i	0.734841	+	2.01896i
$498$	12.1093	−	2.13520i	0.542632	−	0.0956806i
$499$	4.15373	−	23.5570i	0.185947	−	1.05456i	−0.738786	−	0.673940i	$-0.764601\pi$
$499$	4.15373	−	23.5570i	0.185947	−	1.05456i	0.924733	−	0.380616i	$-0.124288\pi$
$500$		0			0
$501$	14.6664	+	25.4030i	0.655247	+	1.13492i
$502$	−3.13459	−	1.80976i	−0.139904	−	0.0807734i
$503$	−18.5683	−	22.1288i	−0.827919	−	0.986675i	−0.999999	−	0.00159206i	$-0.999493\pi$
$503$	−18.5683	−	22.1288i	−0.827919	−	0.986675i	0.172080	−	0.985083i	$-0.444951\pi$
$504$	−13.2731	+	11.1375i	−0.591231	+	0.496102i
$505$		0			0
$506$	−4.51957	−	7.82812i	−0.200919	−	0.348002i
$507$	−14.9838	+	41.1677i	−0.665455	+	1.82832i
$508$	−0.321096	−	0.0566178i	−0.0142463	−	0.00251201i
$509$	3.15957	+	17.9188i	0.140046	+	0.794238i	0.971212	+	0.238215i	$0.0765622\pi$
$509$	3.15957	+	17.9188i	0.140046	+	0.794238i	−0.831167	+	0.556023i	$0.812327\pi$
$510$		0			0
$511$	−27.7962	−	23.3238i	−1.22963	−	1.03178i
$512$			1.00000i			0.0441942i
$513$	−17.2134	−	5.01104i	−0.759991	−	0.221243i
$514$	10.8438			0.478301
$515$		0			0
$516$	8.43280	−	3.06929i	0.371233	−	0.135118i
$517$	−40.8853	+	7.20918i	−1.79813	+	0.317059i
$518$	7.17940	+	1.26592i	0.315445	+	0.0556215i
$519$	7.99525	+	2.91003i	0.350953	+	0.127736i
$520$		0			0
$521$	−7.21014	+	12.4883i	−0.315882	+	0.547124i	−0.979625	−	0.200837i	$-0.935634\pi$
$521$	−7.21014	+	12.4883i	−0.315882	+	0.547124i	0.663743	+	0.747961i	$0.268967\pi$
$522$	19.7430	+	23.5288i	0.864128	+	1.02983i
$523$	12.4712	+	14.8626i	0.545326	+	0.649895i	0.966373	−	0.257144i	$-0.0827816\pi$
$523$	12.4712	+	14.8626i	0.545326	+	0.649895i	−0.421047	+	0.907039i	$0.638337\pi$
$524$	−2.63118	+	4.55734i	−0.114944	+	0.199088i
$525$		0			0
$526$	−9.06203	−	3.29831i	−0.395123	−	0.143813i
$527$	−8.32375	−	1.46770i	−0.362588	−	0.0639341i
$528$	−15.4511	+	2.72445i	−0.672424	+	0.118567i
$529$	−19.2731	+	7.01484i	−0.837962	+	0.304993i
$530$		0			0
$531$	−11.7702			−0.510785
$532$	13.5332	+	9.91606i	0.586740	+	0.429916i
$533$		−	19.4259i		−	0.841428i
$534$	−2.15451	−	1.80784i	−0.0932346	−	0.0782331i
$535$		0			0
$536$	−1.09052	−	6.18464i	−0.0471032	−	0.267136i
$537$	56.9282	+	10.0380i	2.45663	+	0.433171i
$538$	2.55409	−	7.01729i	0.110114	−	0.302537i
$539$	22.3823	+	38.7673i	0.964075	+	1.66983i
$540$		0			0
$541$	13.0794	−	10.9749i	0.562328	−	0.471849i	−0.316762	−	0.948505i	$-0.602596\pi$
$541$	13.0794	−	10.9749i	0.562328	−	0.471849i	0.879090	+	0.476656i	$0.158151\pi$
$542$	−19.5789	−	23.3333i	−0.840988	−	1.00225i
$543$	10.5714	+	6.10339i	0.453661	+	0.261921i
$544$	0.687022	+	1.18996i	0.0294558	+	0.0510190i
$545$		0			0
$546$	−9.85729	+	55.9035i	−0.421853	+	2.39245i
$547$	27.9866	−	4.93480i	1.19662	−	0.210997i	0.460384	−	0.887720i	$-0.347712\pi$
$547$	27.9866	−	4.93480i	1.19662	−	0.210997i	0.736238	+	0.676723i	$0.236601\pi$
$548$	4.25031	+	11.6776i	0.181564	+	0.498843i
$549$	20.9966	+	17.6182i	0.896113	+	0.751928i
$550$		0			0
$551$	17.5779	−	23.9900i	0.748843	−	1.02201i
$552$		−	4.32191i		−	0.183953i
$553$	19.1435	−	22.8143i	0.814063	−	0.970163i
$554$	−9.31661	+	3.39097i	−0.395825	+	0.144068i
$555$		0			0
$556$	−1.08184	+	6.13541i	−0.0458802	+	0.260200i
$557$	12.3640	−	33.9699i	0.523881	−	1.43935i	−0.342286	−	0.939596i	$-0.611201\pi$
$557$	12.3640	−	33.9699i	0.523881	−	1.43935i	0.866167	−	0.499755i	$-0.166576\pi$
$558$	23.9812	−	13.8456i	1.01521	−	0.586130i
$559$	8.82146	−	15.2792i	0.373108	−	0.646242i
$560$		0			0
$561$	−16.5144	+	13.8572i	−0.697239	+	0.585053i
$562$	13.9159	+	8.03435i	0.587007	+	0.338908i
$563$	−0.397587	+	0.229547i	−0.0167563	+	0.00967424i	−0.508355	−	0.861148i	$-0.669746\pi$
$563$	−0.397587	+	0.229547i	−0.0167563	+	0.00967424i	0.491598	+	0.870822i	$0.336413\pi$
$564$	−18.6531	−	6.78916i	−0.785436	−	0.285875i
$565$		0			0
$566$	−1.75168	−	9.93426i	−0.0736285	−	0.417568i
$567$	2.94873	+	8.10158i	0.123835	+	0.340234i
$568$	−7.99914	+	9.53300i	−0.335636	+	0.399996i
$569$	−11.7203			−0.491339			−0.245670	−	0.969354i	$-0.579008\pi$
$569$	−11.7203			−0.491339			−0.245670	+	0.969354i	$0.579008\pi$
$570$		0			0
$571$	2.30956			0.0966521			0.0483260	−	0.998832i	$-0.484611\pi$
$571$	2.30956			0.0966521			0.0483260	+	0.998832i	$0.484611\pi$
$572$	−19.8272	+	23.6291i	−0.829016	+	0.987983i
$573$	7.55400	+	20.7545i	0.315573	+	0.867030i
$574$	−2.41119	−	13.6745i	−0.100641	−	0.570765i
$575$		0			0
$576$	−4.23019	−	1.53966i	−0.176258	−	0.0641526i
$577$	40.3059	−	23.2706i	1.67796	−	0.968768i	0.714994	−	0.699131i	$-0.246430\pi$
$577$	40.3059	−	23.2706i	1.67796	−	0.968768i	0.962962	−	0.269637i	$-0.0869038\pi$
$578$	−13.0874	−	7.55600i	−0.544363	−	0.314288i
$579$	1.41420	−	1.18666i	0.0587722	−	0.0493158i
$580$		0			0
$581$	8.63980	−	14.9646i	0.358439	−	0.620835i
$582$	3.13403	−	1.80943i	0.129910	−	0.0750034i
$583$	23.0685	−	63.3801i	0.955398	−	2.62493i
$584$	1.63703	−	9.28408i	0.0677410	−	0.384178i
$585$		0			0
$586$	−4.94758	+	1.80077i	−0.204383	+	0.0743892i
$587$	−1.87738	+	2.23737i	−0.0774876	+	0.0923462i	−0.803395	−	0.595446i	$-0.796975\pi$
$587$	−1.87738	+	2.23737i	−0.0774876	+	0.0923462i	0.725908	+	0.687792i	$0.241420\pi$
$588$			21.4035i			0.882664i
$589$	−18.5479	−	19.3625i	−0.764254	−	0.797818i
$590$		0			0
$591$	−15.4345	−	12.9511i	−0.634891	−	0.532737i
$592$	0.647805	+	1.77983i	0.0266246	+	0.0731505i
$593$	−14.5170	+	2.55975i	−0.596144	+	0.105116i	−0.463575	−	0.886058i	$-0.653434\pi$
$593$	−14.5170	+	2.55975i	−0.596144	+	0.105116i	−0.132569	+	0.991174i	$0.542322\pi$
$594$	4.09124	−	23.2026i	0.167866	−	0.952013i
$595$		0			0
$596$	−11.4207	−	19.7812i	−0.467809	−	0.810269i
$597$	−65.3064	−	37.7047i	−2.67281	−	1.54315i
$598$	−5.46170	−	6.50900i	−0.223346	−	0.266173i
$599$	−4.45027	+	3.73422i	−0.181833	+	0.152576i	−0.729161	−	0.684342i	$-0.760089\pi$
$599$	−4.45027	+	3.73422i	−0.181833	+	0.152576i	0.547328	+	0.836918i	$0.315645\pi$
$600$		0			0
$601$	3.34531	+	5.79425i	0.136458	+	0.236352i	0.926153	−	0.377147i	$-0.123095\pi$
$601$	3.34531	+	5.79425i	0.136458	+	0.236352i	−0.789695	+	0.613499i	$0.789761\pi$
$602$	4.31324	−	11.8505i	0.175794	−	0.482991i
$603$	27.8412	+	4.90916i	1.13378	+	0.199916i
$604$	−1.16351	−	6.59862i	−0.0473427	−	0.268494i
$605$		0			0
$606$	30.5149	+	25.6050i	1.23958	+	1.04013i
$607$			40.7346i			1.65337i	0.562667	+	0.826684i	$0.309775\pi$
$607$			40.7346i			1.65337i	−0.562667	+	0.826684i	$0.690225\pi$
$608$	−0.473097	+	4.33315i	−0.0191866	+	0.175732i
$609$	71.9276			2.91465
$610$		0			0
$611$	−36.6720	+	13.3475i	−1.48359	+	0.539983i
$612$	−6.09152	+	1.07410i	−0.246235	+	0.0434179i
$613$	−5.61324	−	0.989765i	−0.226716	−	0.0399762i	0.0591357	−	0.998250i	$-0.481166\pi$
$613$	−5.61324	−	0.989765i	−0.226716	−	0.0399762i	−0.285852	+	0.958274i	$0.592277\pi$
$614$	−29.1979	−	10.6272i	−1.17833	−	0.428877i
$615$		0			0
$616$	−11.0241	+	19.0944i	−0.444175	+	0.769334i
$617$	3.25873	+	3.88361i	0.131192	+	0.156348i	0.827641	−	0.561258i	$-0.189682\pi$
$617$	3.25873	+	3.88361i	0.131192	+	0.156348i	−0.696449	+	0.717606i	$0.745238\pi$
$618$	13.3643	+	15.9269i	0.537589	+	0.640674i
$619$	−4.89822	+	8.48397i	−0.196876	+	0.341000i	−0.947514	−	0.319714i	$-0.896413\pi$
$619$	−4.89822	+	8.48397i	−0.196876	+	0.341000i	0.750638	+	0.660714i	$0.229746\pi$
$620$		0			0
$621$	6.09870	+	2.21974i	0.244732	+	0.0890753i
$622$	−17.6856	−	3.11844i	−0.709126	−	0.125038i
$623$	−3.89234	+	0.686324i	−0.155943	+	0.0274970i
$624$	−13.8589	+	5.04423i	−0.554800	+	0.201931i
$625$		0			0
$626$	14.9309			0.596759
$627$	−68.2410	+	4.49557i	−2.72528	+	0.179536i
$628$			0.0377166i			0.00150506i
$629$	1.99364	+	1.67286i	0.0794916	+	0.0667014i
$630$		0			0
$631$	−3.95112	−	22.4079i	−0.157292	−	0.892045i	−0.956661	−	0.291205i	$-0.905944\pi$
$631$	−3.95112	−	22.4079i	−0.157292	−	0.892045i	0.799369	−	0.600840i	$-0.205167\pi$
$632$	7.62009	+	1.34363i	0.303111	+	0.0534466i
$633$	−20.0057	+	54.9652i	−0.795155	+	2.18467i
$634$	4.51612	+	7.82216i	0.179358	+	0.310658i
$635$		0			0
$636$	24.7042	−	20.7292i	0.979583	−	0.821968i
$637$	27.0481	+	32.2346i	1.07168	+	1.27718i
$638$	33.8480	+	19.5421i	1.34005	+	0.773681i
$639$	−28.0104	−	48.5155i	−1.10808	−	1.91924i
$640$		0			0
$641$	7.58983	−	43.0441i	0.299780	−	1.70014i	−0.347331	−	0.937742i	$-0.612912\pi$
$641$	7.58983	−	43.0441i	0.299780	−	1.70014i	0.647112	−	0.762395i	$-0.275977\pi$
$642$	3.68081	−	0.649026i	0.145270	−	0.0256150i
$643$	15.3392	+	42.1442i	0.604921	+	1.66201i	0.741159	+	0.671330i	$0.234276\pi$
$643$	15.3392	+	42.1442i	0.604921	+	1.66201i	−0.136238	+	0.990676i	$0.543501\pi$
$644$	−4.65259	−	3.90399i	−0.183338	−	0.153839i
$645$		0			0
$646$	2.41400	+	5.48129i	0.0949776	+	0.215658i
$647$			3.04207i			0.119596i	0.998210	+	0.0597981i	$0.0190457\pi$
$647$			3.04207i			0.119596i	−0.998210	+	0.0597981i	$0.980954\pi$
$648$	−1.43982	+	1.71591i	−0.0565613	+	0.0674071i
$649$	−14.0743	+	5.12263i	−0.552465	+	0.201081i
$650$		0			0
$651$	11.2606	−	63.8620i	0.441337	−	2.50295i
$652$	3.97855	−	10.9310i	0.155812	−	0.428090i
$653$	−3.18983	+	1.84165i	−0.124828	+	0.0720694i	−0.561114	−	0.827739i	$-0.689627\pi$
$653$	−3.18983	+	1.84165i	−0.124828	+	0.0720694i	0.436286	+	0.899808i	$0.356294\pi$
$654$	−9.73446	+	16.8606i	−0.380648	+	0.659301i
$655$		0			0
$656$	2.76357	−	2.31891i	0.107899	−	0.0905383i
$657$	36.7530	+	21.2193i	1.43387	+	0.827845i
$658$	−24.1580	+	13.9476i	−0.941776	+	0.543735i
$659$	39.2902	+	14.3005i	1.53053	+	0.557067i	0.963751	−	0.266803i	$-0.0859674\pi$
$659$	39.2902	+	14.3005i	1.53053	+	0.557067i	0.566778	+	0.823870i	$0.308190\pi$
$660$		0			0
$661$	0.336551	+	1.90867i	0.0130903	+	0.0742388i	0.990653	−	0.136405i	$-0.0435550\pi$
$661$	0.336551	+	1.90867i	0.0130903	+	0.0742388i	−0.977563	+	0.210644i	$0.932444\pi$
$662$	11.7472	+	32.2753i	0.456570	+	1.25441i
$663$	−13.0260	+	15.5238i	−0.505887	+	0.602893i
$664$	4.48941			0.174223
$665$		0			0
$666$	−8.52641			−0.330392
$667$	−6.92048	+	8.24751i	−0.267962	+	0.319345i
$668$	3.66291	+	10.0638i	0.141722	+	0.389379i
$669$	8.96955	+	50.8688i	0.346783	+	1.96670i
$670$		0			0
$671$	32.7746	+	11.9290i	1.26525	+	0.460513i
$672$	−9.12965	+	5.27101i	−0.352184	+	0.203334i
$673$	38.8439	+	22.4265i	1.49732	+	0.864479i	0.999995	−	0.00308384i	$-0.000981617\pi$
$673$	38.8439	+	22.4265i	1.49732	+	0.864479i	0.497327	+	0.867563i	$0.334315\pi$
$674$	8.86863	−	7.44166i	0.341607	−	0.286642i
$675$		0			0
$676$	−7.99764	+	13.8523i	−0.307602	+	0.532782i
$677$	−27.4179	+	15.8298i	−1.05376	+	0.608387i	−0.923699	−	0.383119i	$-0.874850\pi$
$677$	−27.4179	+	15.8298i	−1.05376	+	0.608387i	−0.130058	+	0.991506i	$0.541516\pi$
$678$	10.3639	−	28.4747i	0.398025	−	1.09356i
$679$	0.883096	−	5.00829i	0.0338901	−	0.192200i
$680$		0			0
$681$	−13.5029	+	4.91466i	−0.517433	+	0.188330i
$682$	22.6498	−	26.9930i	0.867306	−	1.03362i
$683$		−	46.7025i		−	1.78702i	−0.449042	−	0.893511i	$-0.648235\pi$
$683$		−	46.7025i		−	1.78702i	0.449042	−	0.893511i	$-0.351765\pi$
$684$	−17.6016	−	8.67288i	−0.673015	−	0.331616i
$685$		0			0
$686$	2.40174	+	2.01530i	0.0916990	+	0.0769446i
$687$	−3.34304	−	9.18494i	−0.127545	−	0.350427i
$688$	3.22670	−	0.568954i	0.123017	−	0.0216912i
$689$	11.0096	−	62.4385i	0.419432	−	2.37872i
$690$		0			0
$691$	15.2738	+	26.4549i	0.581041	+	1.00639i	0.995356	+	0.0962590i	$0.0306877\pi$
$691$	15.2738	+	26.4549i	0.581041	+	1.00639i	−0.414315	+	0.910133i	$0.635979\pi$
$692$	2.69028	+	1.55324i	0.102269	+	0.0590452i
$693$	−63.7993	−	76.0331i	−2.42354	−	2.88826i
$694$	−1.33141	+	1.11718i	−0.0505396	+	0.0424077i
$695$		0			0
$696$	9.34375	+	16.1838i	0.354174	+	0.613447i
$697$	1.69539	−	4.65804i	0.0642174	−	0.176436i
$698$	2.26566	+	0.399497i	0.0857564	+	0.0151212i
$699$	2.63367	+	14.9363i	0.0996144	+	0.564941i
$700$		0			0
$701$	21.6536	+	18.1696i	0.817847	+	0.686255i	0.952467	−	0.304642i	$-0.0985370\pi$
$701$	21.6536	+	18.1696i	0.817847	+	0.686255i	−0.134620	+	0.990897i	$0.542981\pi$
$702$		−	22.1472i		−	0.835891i
$703$	1.96500	+	8.01874i	0.0741115	+	0.302432i
$704$	−5.72836			−0.215896
$705$		0			0
$706$	−27.6937	+	10.0797i	−1.04227	+	0.379354i
$707$	55.1283	−	9.72061i	2.07331	−	0.365581i
$708$	−7.05248	−	1.24354i	−0.265048	−	0.0467352i
$709$	−15.9283	−	5.79743i	−0.598200	−	0.217727i	0.0251320	−	0.999684i	$-0.491999\pi$
$709$	−15.9283	−	5.79743i	−0.598200	−	0.217727i	−0.623332	+	0.781957i	$0.714222\pi$
$710$		0			0
$711$	−17.4162	+	30.1657i	−0.653158	+	1.13130i
$712$	−0.660058	−	0.786626i	−0.0247367	−	0.0294801i
$713$	6.23924	+	7.43563i	0.233661	+	0.278467i
$714$	−7.24259	+	12.5445i	−0.271047	+	0.469467i
$715$		0			0
$716$	19.8327	+	7.21852i	0.741184	+	0.269769i
$717$	30.7000	+	5.41324i	1.14651	+	0.202161i
$718$	13.7539	−	2.42518i	0.513289	−	0.0905068i
$719$	26.7072	−	9.72061i	0.996009	−	0.362518i	0.207965	−	0.978136i	$-0.433316\pi$
$719$	26.7072	−	9.72061i	0.996009	−	0.362518i	0.788044	+	0.615619i	$0.211094\pi$
$720$		0			0
$721$	29.2175			1.08812
$722$	−4.10000	+	18.5524i	−0.152586	+	0.690447i
$723$			30.3457i			1.12857i
$724$	3.41410	+	2.86477i	0.126884	+	0.106468i
$725$		0			0
$726$	−10.3749	−	58.8392i	−0.385050	−	2.18373i
$727$	−9.78007	−	1.72449i	−0.362723	−	0.0639578i	−0.0106831	−	0.999943i	$-0.503401\pi$
$727$	−9.78007	−	1.72449i	−0.362723	−	0.0639578i	−0.352039	+	0.935985i	$0.614512\pi$
$728$	−7.08859	+	19.4757i	−0.262721	+	0.721819i
$729$	−21.9394	−	38.0001i	−0.812569	−	1.40741i
$730$		0			0
$731$	3.44875	−	2.89384i	0.127556	−	0.107033i
$732$	10.7193	+	12.7748i	0.396198	+	0.472170i
$733$	1.21761	+	0.702986i	0.0449734	+	0.0259654i	0.522318	−	0.852751i	$-0.325067\pi$
$733$	1.21761	+	0.702986i	0.0449734	+	0.0259654i	−0.477345	+	0.878716i	$0.658401\pi$
$734$	−14.8484	−	25.7181i	−0.548064	−	0.949274i
$735$		0			0
$736$	0.274010	−	1.55399i	0.0101002	−	0.0572808i
$737$	35.4278	−	6.24688i	1.30500	−	0.230107i
$738$	5.55447	+	15.2608i	0.204463	+	0.561757i
$739$	36.0542	+	30.2530i	1.32627	+	1.11288i	0.984933	+	0.172937i	$0.0553257\pi$
$739$	36.0542	+	30.2530i	1.32627	+	1.11288i	0.341342	+	0.939939i	$0.389119\pi$
$740$		0			0
$741$	−62.4391	+	15.3008i	−2.29376	+	0.562088i
$742$		−	45.3191i		−	1.66372i
$743$	−8.78794	+	10.4731i	−0.322398	+	0.384219i	−0.902764	−	0.430137i	$-0.858465\pi$
$743$	−8.78794	+	10.4731i	−0.322398	+	0.384219i	0.580365	+	0.814356i	$0.302910\pi$
$744$	15.8319	−	5.76233i	0.580424	−	0.211257i
$745$		0			0
$746$	2.00451	−	11.3681i	0.0733903	−	0.416217i
$747$	−6.91218	+	18.9911i	−0.252903	+	0.694846i
$748$	−6.81649	+	3.93550i	−0.249236	+	0.143896i
$749$	2.62620	−	4.54871i	0.0959592	−	0.166206i
$750$		0			0
$751$	14.2856	−	11.9871i	0.521290	−	0.437414i	−0.343791	−	0.939046i	$-0.611711\pi$
$751$	14.2856	−	11.9871i	0.521290	−	0.437414i	0.865081	+	0.501632i	$0.167267\pi$
$752$	−6.27648	−	3.62373i	−0.228880	−	0.132144i
$753$	8.58539	−	4.95678i	0.312869	−	0.180635i
$754$	34.5240	+	12.5657i	1.25729	+	0.457617i
$755$		0			0
$756$	−2.74897	−	15.5902i	−0.0999789	−	0.567009i
$757$	−7.20316	−	19.7905i	−0.261803	−	0.719299i	−0.999046	−	0.0436709i	$-0.986095\pi$
$757$	−7.20316	−	19.7905i	−0.261803	−	0.719299i	0.737243	−	0.675628i	$-0.236128\pi$
$758$	5.76063	−	6.86525i	0.209236	−	0.249357i
$759$	24.7574			0.898638
$760$		0			0
$761$	−10.4369			−0.378338			−0.189169	−	0.981945i	$-0.560579\pi$
$761$	−10.4369			−0.378338			−0.189169	+	0.981945i	$0.560579\pi$
$762$	0.574023	−	0.684094i	0.0207947	−	0.0247821i
$763$	9.35748	+	25.7095i	0.338764	+	0.930745i
$764$	1.40029	+	7.94142i	0.0506606	+	0.287310i
$765$		0			0
$766$	−27.2194	−	9.90707i	−0.983478	−	0.357957i
$767$	−12.1929	+	7.03955i	−0.440258	+	0.254183i
$768$	−2.37197	−	1.36946i	−0.0855912	−	0.0494161i
$769$	27.7366	−	23.2738i	1.00021	−	0.839275i	0.0131956	−	0.999913i	$-0.495800\pi$
$769$	27.7366	−	23.2738i	1.00021	−	0.839275i	0.987013	+	0.160638i	$0.0513552\pi$
$770$		0			0
$771$	−14.8502	+	25.7213i	−0.534816	+	0.926328i
$772$	0.583726	−	0.337014i	0.0210088	−	0.0121294i
$773$	4.10232	−	11.2710i	0.147550	−	0.405391i	−0.843796	−	0.536664i	$-0.819684\pi$
$773$	4.10232	−	11.2710i	0.147550	−	0.405391i	0.991346	+	0.131273i	$0.0419065\pi$
$774$	−2.56125	+	14.5255i	−0.0920621	+	0.522110i
$775$		0			0
$776$	1.24159	−	0.451903i	0.0445706	−	0.0162224i
$777$	−12.8346	+	15.2957i	−0.460440	+	0.548731i
$778$		−	18.0033i		−	0.645449i
$779$	13.0720	−	8.74076i	0.468355	−	0.313170i
$780$		0			0
$781$	−54.6084	−	45.8219i	−1.95404	−	1.63964i
$782$	−0.741564	−	2.03743i	−0.0265183	−	0.0728584i
$783$	−27.6362	+	4.87301i	−0.987637	+	0.174147i
$784$	−1.35699	+	7.69585i	−0.0484638	+	0.274852i
$785$		0			0
$786$	−7.20659	−	12.4822i	−0.257051	−	0.445225i
$787$	17.3546	+	10.0197i	0.618624	+	0.357163i	0.776333	−	0.630323i	$-0.217078\pi$
$787$	17.3546	+	10.0197i	0.618624	+	0.357163i	−0.157709	+	0.987486i	$0.550411\pi$
$788$	−4.72855	−	5.63526i	−0.168447	−	0.200748i
$789$	20.2336	−	16.9780i	0.720335	−	0.604433i
$790$		0			0
$791$	−21.2916	−	36.8782i	−0.757043	−	1.31124i
$792$	8.81974	−	24.2320i	0.313396	−	0.861048i
$793$	32.2876	+	5.69318i	1.14657	+	0.202171i
$794$	3.22669	+	18.2995i	0.114511	+	0.649424i
$795$		0			0
$796$	−21.0911	−	17.6976i	−0.747555	−	0.627273i
$797$		−	17.2997i		−	0.612788i	−0.951905	−	0.306394i	$-0.900878\pi$
$797$		−	17.2997i		−	0.612788i	0.951905	−	0.306394i	$-0.0991224\pi$
$798$	−42.0538	+	18.5208i	−1.48869	+	0.655631i
$799$	−9.95832			−0.352300
$800$		0			0
$801$	4.34385	−	1.58103i	0.153482	−	0.0558630i
$802$	−27.8262	+	4.90652i	−0.982578	+	0.173255i
$803$	53.1825	+	9.37751i	1.87677	+	0.330925i
$804$	16.1632	+	5.88293i	0.570032	+	0.207475i
$805$		0			0
$806$	16.5615	−	28.6854i	0.583356	−	1.01040i
$807$	13.1471	+	15.6681i	0.462800	+	0.551544i
$808$	9.34860	+	11.1412i	0.328883	+	0.391947i
$809$	−13.6286	+	23.6054i	−0.479156	+	0.829922i	−0.999714	−	0.0239039i	$-0.992390\pi$
$809$	−13.6286	+	23.6054i	−0.479156	+	0.829922i	0.520558	+	0.853826i	$0.325724\pi$
$810$		0			0
$811$	49.4372	+	17.9937i	1.73598	+	0.631843i	0.999027	−	0.0441053i	$-0.0140437\pi$
$811$	49.4372	+	17.9937i	1.73598	+	0.631843i	0.736949	+	0.675949i	$0.236266\pi$
$812$	25.8624	+	4.56023i	0.907591	+	0.160033i
$813$	82.1585	−	14.4868i	2.88142	−	0.508073i
$814$	−10.1955	+	3.71086i	−0.357352	+	0.130065i
$815$		0			0
$816$	−3.76339			−0.131745
$817$	14.2509	−	0.938820i	0.498577	−	0.0328452i
$818$		−	34.4070i		−	1.20301i
$819$	−71.4720	−	59.9722i	−2.49744	−	2.09560i
$820$		0			0
$821$	3.56727	+	20.2310i	0.124498	+	0.706066i	0.981604	+	0.190926i	$0.0611490\pi$
$821$	3.56727	+	20.2310i	0.124498	+	0.706066i	−0.857106	+	0.515140i	$0.827740\pi$
$822$	−33.5196	−	5.91041i	−1.16913	−	0.206149i
$823$	18.5700	−	51.0206i	0.647309	−	1.77847i	0.0198664	−	0.999803i	$-0.493676\pi$
$823$	18.5700	−	51.0206i	0.647309	−	1.77847i	0.627442	−	0.778663i	$-0.284102\pi$
$824$	3.79549	+	6.57398i	0.132222	+	0.229016i
$825$		0			0
$826$	−7.70920	+	6.46879i	−0.268238	+	0.225078i
$827$	7.66257	+	9.13189i	0.266454	+	0.317547i	0.882637	−	0.470056i	$-0.155766\pi$
$827$	7.66257	+	9.13189i	0.266454	+	0.317547i	−0.616183	+	0.787603i	$0.711322\pi$
$828$	6.15179	+	3.55174i	0.213789	+	0.123431i
$829$	−7.12734	−	12.3449i	−0.247543	−	0.428757i	0.715301	−	0.698817i	$-0.246290\pi$
$829$	−7.12734	−	12.3449i	−0.247543	−	0.428757i	−0.962843	+	0.270060i	$0.912956\pi$
$830$		0			0
$831$	4.71543	−	26.7425i	0.163577	−	0.927689i
$832$	−5.30292	+	0.935048i	−0.183846	+	0.0324170i
$833$	3.67246	+	10.0900i	0.127243	+	0.349598i
$834$	−13.0715	−	10.9683i	−0.452629	−	0.379801i
$835$		0			0
$836$	−24.8218	−	2.71007i	−0.858480	−	0.0937297i
$837$			25.3001i			0.874498i
$838$	0.610835	−	0.727965i	0.0211010	−	0.0251471i
$839$	−13.7410	+	5.00130i	−0.474391	+	0.172664i	−0.568140	−	0.822932i	$-0.692337\pi$
$839$	−13.7410	+	5.00130i	−0.474391	+	0.172664i	0.0937496	+	0.995596i	$0.470115\pi$
$840$		0			0
$841$	3.04798	−	17.2860i	0.105103	−	0.596068i
$842$	7.49650	−	20.5965i	0.258346	−	0.709801i
$843$	−38.1145	+	22.0054i	−1.31273	+	0.757907i
$844$	−10.6781	+	18.4950i	−0.367554	+	0.636623i
$845$		0			0
$846$	24.9927	−	20.9714i	0.859267	−	0.721011i
$847$	−72.7129	−	41.9808i	−2.49845	−	1.44248i
$848$	10.1969	−	5.88718i	0.350163	−	0.202166i
$849$	25.9626	+	9.44963i	0.891036	+	0.324310i
$850$		0			0
$851$	−0.518991	−	2.94334i	−0.0177908	−	0.100896i
$852$	−11.6575	−	32.0288i	−0.399380	−	1.09729i
$853$	−24.8236	+	29.5837i	−0.849945	+	1.01293i	0.149762	+	0.988722i	$0.452149\pi$
$853$	−24.8236	+	29.5837i	−0.849945	+	1.01293i	−0.999707	+	0.0242034i	$0.992295\pi$
$854$	23.4350			0.801930
$855$		0			0
$856$	1.36462			0.0466419
$857$	−25.2057	+	30.0390i	−0.861012	+	1.02611i	0.138349	+	0.990383i	$0.455820\pi$
$857$	−25.2057	+	30.0390i	−0.861012	+	1.02611i	−0.999361	+	0.0357307i	$0.988624\pi$
$858$	−28.8951	−	79.3887i	−0.986463	−	2.71028i
$859$	0.982011	+	5.56926i	0.0335058	+	0.190021i	0.996967	−	0.0778278i	$-0.0247984\pi$
$859$	0.982011	+	5.56926i	0.0335058	+	0.190021i	−0.963461	+	0.267849i	$0.913687\pi$
$860$		0			0
$861$	35.7377	+	13.0075i	1.21794	+	0.443293i
$862$	−21.6689	+	12.5106i	−0.738046	+	0.426111i
$863$	−8.89440	−	5.13518i	−0.302769	−	0.174804i	0.340917	−	0.940093i	$-0.389262\pi$
$863$	−8.89440	−	5.13518i	−0.302769	−	0.174804i	−0.643686	+	0.765290i	$0.722596\pi$
$864$	3.15071	−	2.64376i	0.107189	−	0.0899426i
$865$		0			0
$866$	19.4738	−	33.7296i	0.661747	−	1.14618i
$867$	35.8453	−	20.6953i	1.21737	−	0.702848i
$868$	8.09773	−	22.2483i	0.274855	−	0.755158i
$869$	−7.69678	+	43.6506i	−0.261095	+	1.48074i
$870$		0			0
$871$	31.7770	−	11.5659i	1.07672	−	0.391894i
$872$	−4.56910	+	5.44524i	−0.154729	+	0.184399i
$873$			5.94795i			0.201308i
$874$	1.92252	−	6.60404i	0.0650301	−	0.223385i
$875$		0			0
$876$	19.7797	+	16.5972i	0.668296	+	0.560767i
$877$	−16.6745	−	45.8127i	−0.563056	−	1.54698i	−0.815131	−	0.579277i	$-0.803335\pi$
$877$	−16.6745	−	45.8127i	−0.563056	−	1.54698i	0.252075	−	0.967708i	$-0.418887\pi$
$878$	4.80173	−	0.846675i	0.162051	−	0.0285739i
$879$	2.50413	−	14.2016i	0.0844620	−	0.479008i
$880$		0			0
$881$	21.8207	+	37.7945i	0.735157	+	1.27333i	0.954654	+	0.297717i	$0.0962250\pi$
$881$	21.8207	+	37.7945i	0.735157	+	1.27333i	−0.219497	+	0.975613i	$0.570442\pi$
$882$	−30.4656	−	17.5893i	−1.02583	−	0.592263i
$883$	31.0341	+	36.9850i	1.04438	+	1.24464i	0.968888	+	0.247498i	$0.0796083\pi$
$883$	31.0341	+	36.9850i	1.04438	+	1.24464i	0.0754921	+	0.997146i	$0.475947\pi$
$884$	−5.66785	+	4.75589i	−0.190630	+	0.159958i
$885$		0			0
$886$	10.3605	+	17.9449i	0.348067	+	0.602869i
$887$	12.0546	−	33.1197i	0.404753	−	1.11205i	−0.555158	−	0.831745i	$-0.687342\pi$
$887$	12.0546	−	33.1197i	0.404753	−	1.11205i	0.959911	−	0.280305i	$-0.0904357\pi$
$888$	−5.10885	−	0.900828i	−0.171442	−	0.0302298i
$889$	−0.217920	−	1.23589i	−0.00730881	−	0.0414503i
$890$		0			0
$891$	−9.82932	−	8.24778i	−0.329294	−	0.276311i
$892$			18.8591i			0.631450i
$893$	−25.4826	−	18.6715i	−0.852741	−	0.624819i
$894$	62.5606			2.09234
$895$		0			0
$896$	−3.61685	+	1.31643i	−0.120830	+	0.0439787i
$897$	22.9188	−	4.04119i	0.765235	−	0.134932i
$898$	−16.5332	−	2.91525i	−0.551720	−	0.0972831i
$899$	−39.4389	−	14.3546i	−1.31536	−	0.478752i
$900$		0			0
$901$	8.08923	−	14.0110i	0.269491	−	0.466773i
$902$	13.2836	+	15.8307i	0.442294	+	0.527106i
$903$	22.2023	+	26.4597i	0.738846	+	0.880523i
$904$	5.53177	−	9.58131i	0.183984	−	0.318670i
$905$		0			0
$906$	17.2451	+	6.27671i	0.572931	+	0.208530i
$907$	−45.8015	−	8.07604i	−1.52081	−	0.268160i	−0.650061	−	0.759882i	$-0.725257\pi$
$907$	−45.8015	−	8.07604i	−1.52081	−	0.268160i	−0.870752	+	0.491722i	$0.836368\pi$
$908$	−5.16671	+	0.911030i	−0.171463	+	0.0302336i
$909$	−61.5232	+	22.3926i	−2.04060	+	0.742716i
$910$		0			0
$911$	−13.1421			−0.435416			−0.217708	−	0.976014i	$-0.569858\pi$
$911$	−13.1421			−0.435416			−0.217708	+	0.976014i	$0.569858\pi$
$912$	−9.63022	−	7.05624i	−0.318889	−	0.233656i
$913$			25.7169i			0.851106i
$914$	−6.50105	−	5.45503i	−0.215036	−	0.180436i
$915$		0			0
$916$	−0.619700	−	3.51449i	−0.0204755	−	0.116122i
$917$	−19.9470	−	3.51719i	−0.658707	−	0.116148i
$918$	1.93289	−	5.31057i	0.0637948	−	0.175275i
$919$	14.1951	+	24.5866i	0.468252	+	0.811037i	0.999342	−	0.0362788i	$-0.0115504\pi$
$919$	14.1951	+	24.5866i	0.468252	+	0.811037i	−0.531089	+	0.847316i	$0.678217\pi$
$920$		0			0
$921$	65.1927	−	54.7031i	2.14817	−	1.80253i
$922$	−21.2636	−	25.3410i	−0.700279	−	0.834560i
$923$	−58.0323	−	33.5050i	−1.91016	−	1.10283i
$924$	−30.1942	−	52.2979i	−0.993316	−	1.72047i
$925$		0			0
$926$	−5.41910	+	30.7333i	−0.178083	+	1.00996i
$927$	−33.6530	+	5.93393i	−1.10531	+	0.194896i
$928$	2.33359	+	6.41147i	0.0766037	+	0.210467i
$929$	−6.10973	−	5.12667i	−0.200454	−	0.168201i	0.537035	−	0.843560i	$-0.319544\pi$
$929$	−6.10973	−	5.12667i	−0.200454	−	0.168201i	−0.737489	+	0.675359i	$0.763989\pi$
$930$		0			0
$931$	−9.52091	+	32.7053i	−0.312035	+	1.07187i
$932$			5.53747i			0.181386i
$933$	31.6165	−	37.6791i	1.03508	−	1.23356i
$934$	16.5651	−	6.02922i	0.542028	−	0.197282i
$935$		0			0
$936$	4.20928	−	23.8720i	0.137585	−	0.780281i
$937$	−11.7475	+	32.2761i	−0.383775	+	1.05441i	0.585978	+	0.810327i	$0.300711\pi$
$937$	−11.7475	+	32.2761i	−0.383775	+	1.05441i	−0.969753	+	0.244087i	$0.921512\pi$
$938$	20.9333	−	12.0859i	0.683497	−	0.394617i
$939$	−20.4473	+	35.4157i	−0.667271	+	1.15575i
$940$		0			0
$941$	14.2992	−	11.9984i	0.466140	−	0.391138i	−0.379244	−	0.925297i	$-0.623816\pi$
$941$	14.2992	−	11.9984i	0.466140	−	0.391138i	0.845384	+	0.534159i	$0.179372\pi$
$942$	−0.0894627	−	0.0516513i	−0.00291485	−	0.00168289i
$943$	−4.92997	+	2.84632i	−0.160542	+	0.0926889i
$944$	−2.45695	−	0.894258i	−0.0799670	−	0.0291056i
$945$		0			0
$946$	3.25917	+	18.4837i	0.105965	+	0.600956i
$947$	−6.93088	−	19.0424i	−0.225223	−	0.618796i	0.774685	−	0.632348i	$-0.217909\pi$
$947$	−6.93088	−	19.0424i	−0.225223	−	0.618796i	−0.999908	+	0.0135513i	$0.995686\pi$
$948$	−13.6225	+	16.2346i	−0.442437	+	0.527276i
$949$	50.7635			1.64785
$950$		0			0
$951$	−24.7386			−0.802204
$952$	−3.39948	+	4.05134i	−0.110178	+	0.131305i
$953$	1.02416	+	2.81385i	0.0331757	+	0.0911496i	0.955175	−	0.296043i	$-0.0956671\pi$
$953$	1.02416	+	2.81385i	0.0331757	+	0.0911496i	−0.921999	+	0.387192i	$0.873445\pi$
$954$	9.20410	+	52.1990i	0.297994	+	1.69001i
$955$		0			0
$956$	10.6953	+	3.89278i	0.345911	+	0.125901i
$957$	−92.7068	+	53.5243i	−2.99679	+	1.73020i
$958$	13.4454	+	7.76269i	0.434400	+	0.250801i
$959$	−36.6410	+	30.7454i	−1.18320	+	0.992822i
$960$		0			0
$961$	−3.41927	+	5.92234i	−0.110299	+	0.191043i
$962$	−8.83256	+	5.09948i	−0.284773	+	0.164414i
$963$	−2.10106	+	5.77262i	−0.0677057	+	0.186020i
$964$	−1.92393	+	10.9111i	−0.0619655	+	0.351424i
$965$		0			0
$966$	15.6317	−	5.68947i	0.502942	−	0.183056i
$967$	−25.0727	+	29.8805i	−0.806284	+	0.960892i	−0.999796	−	0.0202060i	$-0.993568\pi$
$967$	−25.0727	+	29.8805i	−0.806284	+	0.960892i	0.193512	+	0.981098i	$0.438012\pi$
$968$		−	21.8141i		−	0.701130i
$969$	−16.3073	−	1.78045i	−0.523867	−	0.0571963i
$970$		0			0
$971$	26.6945	+	22.3993i	0.856667	+	0.718829i	0.961247	−	0.275688i	$-0.0889055\pi$
$971$	26.6945	+	22.3993i	0.856667	+	0.718829i	−0.104580	+	0.994516i	$0.533350\pi$
$972$	−6.31846	−	17.3598i	−0.202665	−	0.556817i
$973$	−23.6150	+	4.16397i	−0.757063	+	0.133491i
$974$	−4.19642	+	23.7991i	−0.134462	+	0.762572i
$975$		0			0
$976$	3.04433	+	5.27293i	0.0974465	+	0.168782i
$977$	−45.9323	−	26.5190i	−1.46951	−	0.848420i	−0.470091	−	0.882618i	$-0.655779\pi$
$977$	−45.9323	−	26.5190i	−1.46951	−	0.848420i	−0.999415	+	0.0341985i	$0.989112\pi$
$978$	20.4795	+	24.4065i	0.654862	+	0.780434i
$979$	4.50608	−	3.78105i	0.144015	−	0.120843i
$980$		0			0
$981$	−15.9995	−	27.7120i	−0.510825	−	0.884775i
$982$	2.01494	−	5.53601i	0.0642994	−	0.176661i
$983$	−12.2225	−	2.15515i	−0.389836	−	0.0687387i	−0.0247053	−	0.999695i	$-0.507865\pi$
$983$	−12.2225	−	2.15515i	−0.389836	−	0.0687387i	−0.365131	+	0.930956i	$0.618976\pi$
$984$	1.71580	+	9.73078i	0.0546977	+	0.310206i
$985$		0			0
$986$	7.18169	+	6.02615i	0.228711	+	0.191912i
$987$		−	76.4028i		−	2.43193i
$988$	−23.4207	+	1.54291i	−0.745112	+	0.0490864i
$989$	−5.17016			−0.164401
$990$		0			0
$991$	48.0653	−	17.4943i	1.52684	−	0.555726i	0.563998	−	0.825776i	$-0.309262\pi$
$991$	48.0653	−	17.4943i	1.52684	−	0.555726i	0.962846	+	0.270050i	$0.0870403\pi$
$992$	6.05785	−	1.06816i	0.192337	−	0.0339142i
$993$	−92.6435	−	16.3355i	−2.93995	−	0.518393i
$994$	−45.0097	−	16.3822i	−1.42762	−	0.519611i
$995$		0			0
$996$	−6.14806	+	10.6488i	−0.194809	+	0.337419i
$997$	12.1556	+	14.4865i	0.384973	+	0.458793i	0.923377	−	0.383894i	$-0.125417\pi$
$997$	12.1556	+	14.4865i	0.384973	+	0.458793i	−0.538405	+	0.842687i	$0.680973\pi$
$998$	15.3757	+	18.3241i	0.486711	+	0.580039i
$999$	3.89509	−	6.74649i	0.123235	−	0.213449i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.u.f.149.1		24
5.2	odd	4		950.2.l.g.301.1		12
5.3	odd	4		190.2.k.c.111.2	yes	12
5.4	even	2	inner	950.2.u.f.149.4		24
19.6	even	9	inner	950.2.u.f.899.4		24
95.33	even	36		3610.2.a.bd.1.5		6
95.43	odd	36		3610.2.a.bf.1.2		6
95.44	even	18	inner	950.2.u.f.899.1		24
95.63	odd	36		190.2.k.c.101.2	✓	12
95.82	odd	36		950.2.l.g.101.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.c.101.2	✓	12	95.63	odd	36
190.2.k.c.111.2	yes	12	5.3	odd	4
950.2.l.g.101.1		12	95.82	odd	36
950.2.l.g.301.1		12	5.2	odd	4
950.2.u.f.149.1		24	1.1	even	1	trivial
950.2.u.f.149.4		24	5.4	even	2	inner
950.2.u.f.899.1		24	95.44	even	18	inner
950.2.u.f.899.4		24	19.6	even	9	inner
3610.2.a.bd.1.5		6	95.33	even	36
3610.2.a.bf.1.2		6	95.43	odd	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)

\(f(q)\)	\(=\)	\(q+(-0.642788 + 0.766044i) q^{2} +(-0.936765 - 2.57374i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(2.57374 + 0.936765i) q^{6} +(3.33331 - 1.92448i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-3.44848 + 2.89362i) q^{9} +O(q^{10})\)	\(q+(-0.642788 + 0.766044i) q^{2} +(-0.936765 - 2.57374i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(2.57374 + 0.936765i) q^{6} +(3.33331 - 1.92448i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-3.44848 + 2.89362i) q^{9} +(-2.86418 + 4.96090i) q^{11} +(-2.37197 + 1.36946i) q^{12} +(-1.84169 + 5.05999i) q^{13} +(-0.668367 + 3.79050i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(-0.883218 + 1.05258i) q^{17} -4.50167i q^{18} +(-4.23364 + 1.03746i) q^{19} +(-8.07565 - 6.77628i) q^{21} +(-1.95921 - 5.38289i) q^{22} +(1.55399 - 0.274010i) q^{23} +(0.475608 - 2.69731i) q^{24} +(-2.69236 - 4.66331i) q^{26} +(3.56193 + 2.05648i) q^{27} +(-2.47407 - 2.94848i) q^{28} +(-5.22668 + 4.38571i) q^{29} +(3.07565 + 5.32718i) q^{31} +(0.342020 - 0.939693i) q^{32} +(15.4511 + 2.72445i) q^{33} +(-0.238600 - 1.35317i) q^{34} +(3.44848 + 2.89362i) q^{36} -1.89405i q^{37} +(1.92659 - 3.91002i) q^{38} +14.7483 q^{39} +(-3.39002 + 1.23387i) q^{41} +(10.3819 - 1.83060i) q^{42} +(-3.22670 - 0.568954i) q^{43} +(5.38289 + 1.95921i) q^{44} +(-0.788981 + 1.36656i) q^{46} +(4.65857 + 5.55187i) q^{47} +(1.76054 + 2.09813i) q^{48} +(3.90728 - 6.76762i) q^{49} +(3.53643 + 1.28716i) q^{51} +(5.30292 + 0.935048i) q^{52} +(-11.5955 + 2.04459i) q^{53} +(-3.86492 + 1.40672i) q^{54} +3.84897 q^{56} +(6.63607 + 9.92443i) q^{57} -6.82295i q^{58} +(2.00293 + 1.68066i) q^{59} +(-1.05728 - 5.99615i) q^{61} +(-6.05785 - 1.06816i) q^{62} +(-5.92612 + 16.2819i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-12.0189 + 10.0850i) q^{66} +(-4.03673 - 4.81079i) q^{67} +(1.18996 + 0.687022i) q^{68} +(-2.16096 - 3.74288i) q^{69} +(-2.16096 + 12.2554i) q^{71} +(-4.43328 + 0.781707i) q^{72} +(-3.22433 - 8.85877i) q^{73} +(1.45093 + 1.21747i) q^{74} +(1.75686 + 3.98917i) q^{76} +22.0483i q^{77} +(-9.48004 + 11.2979i) q^{78} +(7.27101 - 2.64643i) q^{79} +(-0.388964 + 2.20593i) q^{81} +(1.23387 - 3.39002i) q^{82} +(3.88794 - 2.24471i) q^{83} +(-5.27101 + 9.12965i) q^{84} +(2.50993 - 2.10608i) q^{86} +(16.1838 + 9.34375i) q^{87} +(-4.96090 + 2.86418i) q^{88} +(-0.964940 - 0.351210i) q^{89} +(3.59897 + 20.4108i) q^{91} +(-0.539695 - 1.48280i) q^{92} +(10.8296 - 12.9063i) q^{93} -7.24746 q^{94} -2.73892 q^{96} +(0.849299 - 1.01216i) q^{97} +(2.67274 + 7.34329i) q^{98} +(-4.47790 - 25.3954i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{6} - 18 q^{9}+O(q^{10}) \) 24 * q + 6 * q^6 - 18 * q^9	\( 24 q + 6 q^{6} - 18 q^{9} - 12 q^{11} + 12 q^{14} - 12 q^{19} - 72 q^{21} - 6 q^{24} - 6 q^{26} - 72 q^{29} - 48 q^{31} + 12 q^{34} + 18 q^{36} + 24 q^{39} - 24 q^{41} + 18 q^{44} - 36 q^{46} - 54 q^{51} - 18 q^{54} + 24 q^{56} + 54 q^{59} + 108 q^{61} + 12 q^{64} - 78 q^{66} + 48 q^{69} + 48 q^{71} - 30 q^{74} + 18 q^{76} + 72 q^{79} - 18 q^{81} - 24 q^{84} + 48 q^{86} - 36 q^{89} + 24 q^{91} - 36 q^{94} - 36 q^{99}+O(q^{100}) \) 24 * q + 6 * q^6 - 18 * q^9 - 12 * q^11 + 12 * q^14 - 12 * q^19 - 72 * q^21 - 6 * q^24 - 6 * q^26 - 72 * q^29 - 48 * q^31 + 12 * q^34 + 18 * q^36 + 24 * q^39 - 24 * q^41 + 18 * q^44 - 36 * q^46 - 54 * q^51 - 18 * q^54 + 24 * q^56 + 54 * q^59 + 108 * q^61 + 12 * q^64 - 78 * q^66 + 48 * q^69 + 48 * q^71 - 30 * q^74 + 18 * q^76 + 72 * q^79 - 18 * q^81 - 24 * q^84 + 48 * q^86 - 36 * q^89 + 24 * q^91 - 36 * q^94 - 36 * q^99

Introduction

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