LMFDB - Embedded newform 950.2.u.h.99.7

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:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			99.7
Character	$\chi$	$=$	950.99
Dual form			950.2.u.h.499.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.342020 - 0.939693i) q^{2} +(1.28901 - 0.227288i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.227288 - 1.28901i) q^{6} +(-1.93191 - 1.11539i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-1.20918 + 0.440106i) q^{9} +O(q^{10})$	\(q+(0.342020 - 0.939693i) q^{2} +(1.28901 - 0.227288i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.227288 - 1.28901i) q^{6} +(-1.93191 - 1.11539i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-1.20918 + 0.440106i) q^{9} +(-2.90465 - 5.03101i) q^{11} +(-1.13354 - 0.654450i) q^{12} +(-2.79302 - 0.492485i) q^{13} +(-1.70888 + 1.43392i) q^{14} +(0.173648 + 0.984808i) q^{16} +(0.366339 - 1.00651i) q^{17} +1.28678i q^{18} +(2.13101 + 3.80247i) q^{19} +(-2.74378 - 0.998653i) q^{21} +(-5.72105 + 1.00878i) q^{22} +(-2.90709 + 3.46454i) q^{23} +(-1.00267 + 0.841344i) q^{24} +(-1.41805 + 2.45614i) q^{26} +(-4.85924 + 2.80548i) q^{27} +(0.762972 + 2.09625i) q^{28} +(-0.483478 + 0.175971i) q^{29} +(3.47213 - 6.01390i) q^{31} +(0.984808 + 0.173648i) q^{32} +(-4.88763 - 5.82484i) q^{33} +(-0.820514 - 0.688493i) q^{34} +(1.20918 + 0.440106i) q^{36} +2.58207i q^{37} +(4.30200 - 0.701975i) q^{38} -3.71218 q^{39} +(-0.665458 - 3.77400i) q^{41} +(-1.87685 + 2.23675i) q^{42} +(-5.38018 - 6.41185i) q^{43} +(-1.00878 + 5.72105i) q^{44} +(2.26132 + 3.91672i) q^{46} +(-3.77288 - 10.3659i) q^{47} +(0.447670 + 1.22996i) q^{48} +(-1.01181 - 1.75251i) q^{49} +(0.243449 - 1.38067i) q^{51} +(1.82302 + 2.17259i) q^{52} +(1.89969 - 2.26396i) q^{53} +(0.974334 + 5.52572i) q^{54} +2.23078 q^{56} +(3.61116 + 4.41709i) q^{57} +0.514506i q^{58} +(6.57499 + 2.39310i) q^{59} +(11.2875 + 9.47136i) q^{61} +(-4.46368 - 5.31961i) q^{62} +(2.82692 + 0.498462i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-7.14523 + 2.60065i) q^{66} +(-2.77800 - 7.63250i) q^{67} +(-0.927604 + 0.535552i) q^{68} +(-2.95984 + 5.12659i) q^{69} +(5.09076 - 4.27166i) q^{71} +(0.827128 - 0.985733i) q^{72} +(-3.34414 + 0.589662i) q^{73} +(2.42635 + 0.883120i) q^{74} +(0.811731 - 4.28265i) q^{76} +12.9593i q^{77} +(-1.26964 + 3.48831i) q^{78} +(0.901573 + 5.11307i) q^{79} +(-2.66878 + 2.23937i) q^{81} +(-3.77400 - 0.665458i) q^{82} +(-14.3386 - 8.27838i) q^{83} +(1.45993 + 2.52868i) q^{84} +(-7.86530 + 2.86273i) q^{86} +(-0.583213 + 0.336718i) q^{87} +(5.03101 + 2.90465i) q^{88} +(-0.355224 + 2.01458i) q^{89} +(4.84656 + 4.06675i) q^{91} +(4.45392 - 0.785347i) q^{92} +(3.10873 - 8.54118i) q^{93} -11.0312 q^{94} +1.30890 q^{96} +(1.70458 - 4.68331i) q^{97} +(-1.99288 + 0.351398i) q^{98} +(5.72642 + 4.80504i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 12 q^{11} + 30 q^{14} + 30 q^{19} - 36 q^{21} - 18 q^{26} + 24 q^{29} + 18 q^{31} + 18 q^{34} - 132 q^{39} + 36 q^{41} - 6 q^{46} + 54 q^{49} - 6 q^{51} - 54 q^{54} - 12 q^{56} - 72 q^{59} + 24 q^{61} + 24 q^{64} + 96 q^{66} - 42 q^{69} - 78 q^{71} - 36 q^{74} + 12 q^{76} + 84 q^{79} - 72 q^{81} - 18 q^{84} - 78 q^{86} + 72 q^{89} + 24 q^{91} - 24 q^{94} + 12 q^{96} - 102 q^{99}+O(q^{100}) $ 48 * q - 12 * q^11 + 30 * q^14 + 30 * q^19 - 36 * q^21 - 18 * q^26 + 24 * q^29 + 18 * q^31 + 18 * q^34 - 132 * q^39 + 36 * q^41 - 6 * q^46 + 54 * q^49 - 6 * q^51 - 54 * q^54 - 12 * q^56 - 72 * q^59 + 24 * q^61 + 24 * q^64 + 96 * q^66 - 42 * q^69 - 78 * q^71 - 36 * q^74 + 12 * q^76 + 84 * q^79 - 72 * q^81 - 18 * q^84 - 78 * q^86 + 72 * q^89 + 24 * q^91 - 24 * q^94 + 12 * q^96 - 102 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.342020	−	0.939693i	0.241845	−	0.664463i
$2$	0.342020	−	0.939693i	0.241845	−	0.664463i
$3$	1.28901	−	0.227288i	0.744213	−	0.131225i	0.211331	−	0.977415i	$-0.432220\pi$
$3$	1.28901	−	0.227288i	0.744213	−	0.131225i	0.532882	+	0.846190i	$0.321109\pi$
$4$	−0.766044	−	0.642788i	−0.383022	−	0.321394i
$5$		0			0
$5$		0			0
$6$	0.227288	−	1.28901i	0.0927899	−	0.526238i
$7$	−1.93191	−	1.11539i	−0.730194	−	0.421578i	0.0882992	−	0.996094i	$-0.471857\pi$
$7$	−1.93191	−	1.11539i	−0.730194	−	0.421578i	−0.818493	+	0.574516i	$0.805190\pi$
$8$	−0.866025	+	0.500000i	−0.306186	+	0.176777i
$9$	−1.20918	+	0.440106i	−0.403060	+	0.146702i
$10$		0			0
$11$	−2.90465	−	5.03101i	−0.875786	−	1.51691i	−0.855923	−	0.517103i	$-0.827011\pi$
$11$	−2.90465	−	5.03101i	−0.875786	−	1.51691i	−0.0198623	−	0.999803i	$-0.506323\pi$
$12$	−1.13354	−	0.654450i	−0.327225	−	0.188923i
$13$	−2.79302	−	0.492485i	−0.774645	−	0.136591i	−0.227668	−	0.973739i	$-0.573110\pi$
$13$	−2.79302	−	0.492485i	−0.774645	−	0.136591i	−0.546977	+	0.837148i	$0.684221\pi$
$14$	−1.70888	+	1.43392i	−0.456716	+	0.383231i
$15$		0			0
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	0.366339	−	1.00651i	0.0888504	−	0.244114i	−0.887307	−	0.461180i	$-0.847426\pi$
$17$	0.366339	−	1.00651i	0.0888504	−	0.244114i	0.976157	+	0.217065i	$0.0696485\pi$
$18$			1.28678i			0.303298i
$19$	2.13101	+	3.80247i	0.488888	+	0.872347i
$19$	2.13101	+	3.80247i	0.488888	+	0.872347i
$20$		0			0
$21$	−2.74378	−	0.998653i	−0.598741	−	0.217924i
$22$	−5.72105	+	1.00878i	−1.21973	+	0.215072i
$23$	−2.90709	+	3.46454i	−0.606171	+	0.722406i	−0.978627	−	0.205644i	$-0.934071\pi$
$23$	−2.90709	+	3.46454i	−0.606171	+	0.722406i	0.372456	+	0.928050i	$0.378516\pi$
$24$	−1.00267	+	0.841344i	−0.204670	+	0.171739i
$25$		0			0
$26$	−1.41805	+	2.45614i	−0.278103	+	0.481689i
$27$	−4.85924	+	2.80548i	−0.935161	+	0.539916i
$28$	0.762972	+	2.09625i	0.144188	+	0.396153i
$29$	−0.483478	+	0.175971i	−0.0897795	+	0.0326771i	−0.386519	−	0.922281i	$-0.626323\pi$
$29$	−0.483478	+	0.175971i	−0.0897795	+	0.0326771i	0.296740	+	0.954958i	$0.404101\pi$
$30$		0			0
$31$	3.47213	−	6.01390i	0.623613	−	1.08013i	−0.365195	−	0.930931i	$-0.618998\pi$
$31$	3.47213	−	6.01390i	0.623613	−	1.08013i	0.988807	−	0.149198i	$-0.0476690\pi$
$32$	0.984808	+	0.173648i	0.174091	+	0.0306970i
$33$	−4.88763	−	5.82484i	−0.850826	−	1.01398i
$34$	−0.820514	−	0.688493i	−0.140717	−	0.118076i
$35$		0			0
$36$	1.20918	+	0.440106i	0.201530	+	0.0733509i
$37$			2.58207i			0.424490i	0.977217	+	0.212245i	$0.0680774\pi$
$37$			2.58207i			0.424490i	−0.977217	+	0.212245i	$0.931923\pi$
$38$	4.30200	−	0.701975i	0.697877	−	0.113875i
$39$	−3.71218			−0.594425
$40$		0			0
$41$	−0.665458	−	3.77400i	−0.103927	−	0.589400i	−0.991643	−	0.129009i	$-0.958820\pi$
$41$	−0.665458	−	3.77400i	−0.103927	−	0.589400i	0.887716	−	0.460391i	$-0.152291\pi$
$42$	−1.87685	+	2.23675i	−0.289605	+	0.345138i
$43$	−5.38018	−	6.41185i	−0.820470	−	0.977798i	0.179512	−	0.983756i	$-0.442548\pi$
$43$	−5.38018	−	6.41185i	−0.820470	−	0.977798i	−0.999982	+	0.00595783i	$0.998104\pi$
$44$	−1.00878	+	5.72105i	−0.152079	+	0.862481i
$45$		0			0
$46$	2.26132	+	3.91672i	0.333413	+	0.577488i
$47$	−3.77288	−	10.3659i	−0.550331	−	1.51202i	−0.833260	−	0.552881i	$-0.813528\pi$
$47$	−3.77288	−	10.3659i	−0.550331	−	1.51202i	0.282929	−	0.959141i	$-0.408694\pi$
$48$	0.447670	+	1.22996i	0.0646156	+	0.177530i
$49$	−1.01181	−	1.75251i	−0.144545	−	0.250358i
$50$		0			0
$51$	0.243449	−	1.38067i	0.0340897	−	0.193332i
$52$	1.82302	+	2.17259i	0.252807	+	0.301283i
$53$	1.89969	−	2.26396i	0.260942	−	0.310979i	−0.619627	−	0.784897i	$-0.712716\pi$
$53$	1.89969	−	2.26396i	0.260942	−	0.310979i	0.880569	+	0.473917i	$0.157161\pi$
$54$	0.974334	+	5.52572i	0.132590	+	0.751956i
$55$		0			0
$56$	2.23078			0.298100
$57$	3.61116	+	4.41709i	0.478310	+	0.585057i
$58$			0.514506i			0.0675580i
$59$	6.57499	+	2.39310i	0.855991	+	0.311555i	0.732480	−	0.680788i	$-0.238363\pi$
$59$	6.57499	+	2.39310i	0.855991	+	0.311555i	0.123510	+	0.992343i	$0.460585\pi$
$60$		0			0
$61$	11.2875	+	9.47136i	1.44522	+	1.21268i	0.935977	+	0.352061i	$0.114519\pi$
$61$	11.2875	+	9.47136i	1.44522	+	1.21268i	0.509243	+	0.860623i	$0.329925\pi$
$62$	−4.46368	−	5.31961i	−0.566888	−	0.675591i
$63$	2.82692	+	0.498462i	0.356158	+	0.0628003i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$		0			0
$66$	−7.14523	+	2.60065i	−0.879517	+	0.320118i
$67$	−2.77800	−	7.63250i	−0.339387	−	0.932458i	−0.985569	−	0.169275i	$-0.945857\pi$
$67$	−2.77800	−	7.63250i	−0.339387	−	0.932458i	0.646182	−	0.763183i	$-0.276365\pi$
$68$	−0.927604	+	0.535552i	−0.112488	+	0.0649453i
$69$	−2.95984	+	5.12659i	−0.356322	+	0.617168i
$70$		0			0
$71$	5.09076	−	4.27166i	0.604162	−	0.506952i	−0.288618	−	0.957444i	$-0.593196\pi$
$71$	5.09076	−	4.27166i	0.604162	−	0.506952i	0.892780	+	0.450492i	$0.148751\pi$
$72$	0.827128	−	0.985733i	0.0974780	−	0.116170i
$73$	−3.34414	+	0.589662i	−0.391402	+	0.0690147i	−0.365886	−	0.930660i	$-0.619234\pi$
$73$	−3.34414	+	0.589662i	−0.391402	+	0.0690147i	−0.0255158	+	0.999674i	$0.508123\pi$
$74$	2.42635	+	0.883120i	0.282058	+	0.102661i
$75$		0			0
$76$	0.811731	−	4.28265i	0.0931119	−	0.491254i
$77$			12.9593i			1.47685i
$78$	−1.26964	+	3.48831i	−0.143758	+	0.394973i
$79$	0.901573	+	5.11307i	0.101435	+	0.575266i	0.992585	+	0.121556i	$0.0387885\pi$
$79$	0.901573	+	5.11307i	0.101435	+	0.575266i	−0.891150	+	0.453709i	$0.850100\pi$
$80$		0			0
$81$	−2.66878	+	2.23937i	−0.296531	+	0.248819i
$82$	−3.77400	−	0.665458i	−0.416769	−	0.0734876i
$83$	−14.3386	−	8.27838i	−1.57386	−	0.908670i	−0.995689	−	0.0927571i	$-0.970432\pi$
$83$	−14.3386	−	8.27838i	−1.57386	−	0.908670i	−0.578174	−	0.815913i	$-0.696235\pi$
$84$	1.45993	+	2.52868i	0.159292	+	0.275901i
$85$		0			0
$86$	−7.86530	+	2.86273i	−0.848137	+	0.308697i
$87$	−0.583213	+	0.336718i	−0.0625270	+	0.0361000i
$88$	5.03101	+	2.90465i	0.536307	+	0.309637i
$89$	−0.355224	+	2.01458i	−0.0376537	+	0.213545i	−0.997829	−	0.0658523i	$-0.979023\pi$
$89$	−0.355224	+	2.01458i	−0.0376537	+	0.213545i	0.960176	+	0.279397i	$0.0901345\pi$
$90$		0			0
$91$	4.84656	+	4.06675i	0.508057	+	0.426311i
$92$	4.45392	−	0.785347i	0.464354	−	0.0818781i
$93$	3.10873	−	8.54118i	0.322361	−	0.885679i
$94$	−11.0312			−1.13778
$95$		0			0
$96$	1.30890			0.133589
$97$	1.70458	−	4.68331i	0.173074	−	0.475518i	−0.822579	−	0.568650i	$-0.807466\pi$
$97$	1.70458	−	4.68331i	0.173074	−	0.475518i	0.995654	+	0.0931326i	$0.0296880\pi$
$98$	−1.99288	+	0.351398i	−0.201311	+	0.0354966i
$99$	5.72642	+	4.80504i	0.575527	+	0.482925i
$100$		0			0
$101$	2.06712	−	11.7232i	0.205686	−	1.16650i	−0.690670	−	0.723170i	$-0.742684\pi$
$101$	2.06712	−	11.7232i	0.205686	−	1.16650i	0.896356	−	0.443334i	$-0.146204\pi$
$102$	−1.21414	−	0.700984i	−0.120218	−	0.0694078i
$103$	0.455266	−	0.262848i	0.0448587	−	0.0258992i	−0.477403	−	0.878684i	$-0.658422\pi$
$103$	0.455266	−	0.262848i	0.0448587	−	0.0258992i	0.522262	+	0.852785i	$0.325088\pi$
$104$	2.66507	−	0.970006i	0.261332	−	0.0951169i
$105$		0			0
$106$	−1.47770	−	2.55944i	−0.143527	−	0.248595i
$107$	10.0386	+	5.79580i	0.970471	+	0.560301i	0.899380	−	0.437168i	$-0.144019\pi$
$107$	10.0386	+	5.79580i	0.970471	+	0.560301i	0.0710909	+	0.997470i	$0.477352\pi$
$108$	5.52572	+	0.974334i	0.531713	+	0.0937553i
$109$	6.32655	−	5.30860i	0.605973	−	0.508472i	−0.287386	−	0.957815i	$-0.592786\pi$
$109$	6.32655	−	5.30860i	0.605973	−	0.508472i	0.893359	+	0.449343i	$0.148342\pi$
$110$		0			0
$111$	0.586873	+	3.32832i	0.0557035	+	0.315910i
$112$	0.762972	−	2.09625i	0.0720940	−	0.198077i
$113$			13.3771i			1.25841i	0.777239	+	0.629205i	$0.216619\pi$
$113$			13.3771i			1.25841i	−0.777239	+	0.629205i	$0.783381\pi$
$114$	5.38579	−	1.88265i	0.504426	−	0.176326i
$115$		0			0
$116$	0.483478	+	0.175971i	0.0448898	+	0.0163385i
$117$	3.59401	−	0.633721i	0.332267	−	0.0585876i
$118$	4.49756	−	5.35998i	0.414034	−	0.493426i
$119$	−1.83039	+	1.53588i	−0.167791	+	0.140793i
$120$		0			0
$121$	−11.3740	+	19.7004i	−1.03400	+	1.79094i
$122$	12.7607	−	7.36741i	1.15530	−	0.667014i
$123$	−1.71557	−	4.71349i	−0.154688	−	0.425001i
$124$	−6.52547	+	2.37508i	−0.586004	+	0.213288i
$125$		0			0
$126$	1.43526	−	2.48595i	0.127864	−	0.221466i
$127$	17.2810	+	3.04711i	1.53344	+	0.270388i	0.875701	−	0.482854i	$-0.160400\pi$
$127$	17.2810	+	3.04711i	1.53344	+	0.270388i	0.657744	+	0.753242i	$0.271511\pi$
$128$	−0.642788	−	0.766044i	−0.0568149	−	0.0677094i
$129$	−8.39246	−	7.04211i	−0.738915	−	0.620024i
$130$		0			0
$131$	3.68597	+	1.34158i	0.322044	+	0.117215i	0.497984	−	0.867186i	$-0.334074\pi$
$131$	3.68597	+	1.34158i	0.322044	+	0.117215i	−0.175939	+	0.984401i	$0.556296\pi$
$132$			7.60379i			0.661825i
$133$	0.124309	−	9.72295i	0.0107790	−	0.843086i
$134$	−8.12234			−0.701663
$135$		0			0
$136$	0.185995	+	1.05483i	0.0159490	+	0.0904511i
$137$	−1.70408	+	2.03084i	−0.145589	+	0.173507i	−0.833911	−	0.551899i	$-0.813903\pi$
$137$	−1.70408	+	2.03084i	−0.145589	+	0.173507i	0.688322	+	0.725406i	$0.258348\pi$
$138$	3.80509	+	4.53473i	0.323911	+	0.386022i
$139$	2.79736	−	15.8646i	0.237269	−	1.34562i	−0.600513	−	0.799615i	$-0.705037\pi$
$139$	2.79736	−	15.8646i	0.237269	−	1.34562i	0.837782	−	0.546005i	$-0.183852\pi$
$140$		0			0
$141$	−7.21934	−	12.5043i	−0.607978	−	1.05305i
$142$	−2.27290	−	6.24474i	−0.190738	−	0.524047i
$143$	5.63506	+	15.4822i	0.471228	+	1.29469i
$144$	−0.643391	−	1.11439i	−0.0536160	−	0.0928656i
$145$		0			0
$146$	−0.589662	+	3.34414i	−0.0488007	+	0.276763i
$147$	−1.70256	−	2.02904i	−0.140425	−	0.167352i
$148$	1.65972	−	1.97798i	0.136428	−	0.162589i
$149$	−2.40712	−	13.6515i	−0.197199	−	1.11837i	−0.909252	−	0.416246i	$-0.863346\pi$
$149$	−2.40712	−	13.6515i	−0.197199	−	1.11837i	0.712053	−	0.702126i	$-0.247766\pi$
$150$		0			0
$151$	−8.66473			−0.705125			−0.352563	−	0.935788i	$-0.614690\pi$
$151$	−8.66473			−0.705125			−0.352563	+	0.935788i	$0.614690\pi$
$152$	−3.74675	−	2.22753i	−0.303901	−	0.180677i
$153$			1.37828i			0.111427i
$154$	12.1777	+	4.43233i	0.981310	+	0.357168i
$155$		0			0
$156$	2.84369	+	2.38614i	0.227678	+	0.191044i
$157$	2.56383	+	3.05546i	0.204616	+	0.243852i	0.858587	−	0.512667i	$-0.171343\pi$
$157$	2.56383	+	3.05546i	0.204616	+	0.243852i	−0.653971	+	0.756520i	$0.726898\pi$
$158$	5.11307	+	0.901573i	0.406774	+	0.0717253i
$159$	1.93415	−	3.35005i	0.153388	−	0.265677i
$160$		0			0
$161$	9.48056	−	3.45064i	0.747173	−	0.271949i
$162$	1.19154	+	3.27374i	0.0936165	+	0.257209i
$163$	−15.9771	+	9.22440i	−1.25143	+	0.722511i	−0.971393	−	0.237479i	$-0.923679\pi$
$163$	−15.9771	+	9.22440i	−1.25143	+	0.722511i	−0.280033	+	0.959990i	$0.590346\pi$
$164$	−1.91611	+	3.31880i	−0.149623	+	0.259155i
$165$		0			0
$166$	−12.6832	+	10.6425i	−0.984408	+	0.826017i
$167$	−4.10123	+	4.88766i	−0.317363	+	0.378218i	−0.901017	−	0.433784i	$-0.857178\pi$
$167$	−4.10123	+	4.88766i	−0.317363	+	0.378218i	0.583654	+	0.812002i	$0.301622\pi$
$168$	2.87551	−	0.507029i	0.221850	−	0.0391182i
$169$	−4.65758	−	1.69522i	−0.358275	−	0.130401i
$170$		0			0
$171$	−4.25027	−	3.66000i	−0.325026	−	0.279887i
$172$			8.37008i			0.638212i
$173$	−3.75610	+	10.3198i	−0.285571	+	0.784600i	0.711101	+	0.703090i	$0.248197\pi$
$173$	−3.75610	+	10.3198i	−0.285571	+	0.784600i	−0.996672	+	0.0815108i	$0.974025\pi$
$174$	0.116941	+	0.663206i	0.00886528	+	0.0502775i
$175$		0			0
$176$	4.45019	−	3.73415i	0.335445	−	0.281472i
$177$	9.01918	+	1.59032i	0.677923	+	0.119536i
$178$	1.77159	+	1.02283i	0.132786	+	0.0766641i
$179$	1.72523	+	2.98818i	0.128950	+	0.223347i	0.923270	−	0.384152i	$-0.125506\pi$
$179$	1.72523	+	2.98818i	0.128950	+	0.223347i	−0.794320	+	0.607499i	$0.792173\pi$
$180$		0			0
$181$	−10.4671	+	3.80969i	−0.778010	+	0.283172i	−0.700343	−	0.713807i	$-0.746969\pi$
$181$	−10.4671	+	3.80969i	−0.778010	+	0.283172i	−0.0776672	+	0.996979i	$0.524747\pi$
$182$	5.47911	−	3.16337i	0.406139	−	0.234484i
$183$	16.7025	+	9.64320i	1.23469	+	0.712846i
$184$	0.785347	−	4.45392i	0.0578966	−	0.328348i
$185$		0			0
$186$	−6.96283	−	5.84251i	−0.510540	−	0.428394i
$187$	−6.12784	+	1.08050i	−0.448112	+	0.0790143i
$188$	−3.77288	+	10.3659i	−0.275166	+	0.756011i
$189$	12.5168			0.910465
$190$		0			0
$191$	9.70152			0.701977			0.350989	−	0.936380i	$-0.385846\pi$
$191$	9.70152			0.701977			0.350989	+	0.936380i	$0.385846\pi$
$192$	0.447670	−	1.22996i	0.0323078	−	0.0887649i
$193$	3.50514	−	0.618052i	0.252306	−	0.0444883i	−0.0460647	−	0.998938i	$-0.514668\pi$
$193$	3.50514	−	0.618052i	0.252306	−	0.0444883i	0.298370	+	0.954450i	$0.403557\pi$
$194$	−3.81787	−	3.20357i	−0.274107	−	0.230003i
$195$		0			0
$196$	−0.351398	+	1.99288i	−0.0250999	+	0.142349i
$197$	2.90411	+	1.67669i	0.206909	+	0.119459i	0.599874	−	0.800094i	$-0.295217\pi$
$197$	2.90411	+	1.67669i	0.206909	+	0.119459i	−0.392965	+	0.919553i	$0.628551\pi$
$198$	6.47381	−	3.73766i	0.460074	−	0.265624i
$199$	17.4134	−	6.33797i	1.23441	−	0.449287i	0.359302	−	0.933222i	$-0.383015\pi$
$199$	17.4134	−	6.33797i	1.23441	−	0.449287i	0.875104	+	0.483935i	$0.160793\pi$
$200$		0			0
$201$	−5.31566	−	9.20699i	−0.374938	−	0.649411i
$202$	−10.3092	−	5.95203i	−0.725355	−	0.418784i
$203$	1.13031	+	0.199305i	0.0793324	+	0.0139884i
$204$	−1.07397	+	0.901168i	−0.0751929	+	0.0630944i
$205$		0			0
$206$	−0.0912862	−	0.517710i	−0.00636021	−	0.0360705i
$207$	1.99044	−	5.46868i	0.138345	−	0.380100i
$208$		−	2.83611i		−	0.196649i
$209$	12.9404	−	21.7660i	0.895106	−	1.50559i
$210$		0			0
$211$	24.3786	+	8.87308i	1.67829	+	0.610848i	0.993074	−	0.117490i	$-0.0374847\pi$
$211$	24.3786	+	8.87308i	1.67829	+	0.610848i	0.685218	+	0.728338i	$0.259707\pi$
$212$	−2.91049	+	0.513198i	−0.199893	+	0.0352466i
$213$	5.59117	−	6.66329i	0.383100	−	0.456561i
$214$	8.87969	−	7.45094i	0.607003	−	0.509336i
$215$		0			0
$216$	2.80548	−	4.85924i	0.190889	−	0.330629i
$217$	−13.4157	+	7.74555i	−0.910716	+	0.525802i
$218$	−2.82465	−	7.76066i	−0.191309	−	0.525618i
$219$	−4.17662	+	1.52016i	−0.282230	+	0.102723i
$220$		0			0
$221$	−1.51888	+	2.63079i	−0.102171	+	0.176966i
$222$	3.32832	+	0.586873i	0.223382	+	0.0393884i
$223$	3.42681	+	4.08391i	0.229476	+	0.273479i	0.868480	−	0.495725i	$-0.165098\pi$
$223$	3.42681	+	4.08391i	0.229476	+	0.273479i	−0.639004	+	0.769204i	$0.720653\pi$
$224$	−1.70888	−	1.43392i	−0.114179	−	0.0958076i
$225$		0			0
$226$	12.5703	+	4.57523i	0.836167	+	0.304340i
$227$		−	23.7640i		−	1.57727i	−0.614860	−	0.788636i	$-0.710788\pi$
$227$		−	23.7640i		−	1.57727i	0.614860	−	0.788636i	$-0.289212\pi$
$228$	0.0729378	−	5.70489i	0.00483042	−	0.377816i
$229$	−21.1887			−1.40019			−0.700094	−	0.714051i	$-0.746859\pi$
$229$	−21.1887			−1.40019			−0.700094	+	0.714051i	$0.746859\pi$
$230$		0			0
$231$	2.94549	+	16.7047i	0.193799	+	1.09909i
$232$	0.330718	−	0.394135i	0.0217127	−	0.0258762i
$233$	−9.81621	−	11.6985i	−0.643082	−	0.766395i	0.341772	−	0.939783i	$-0.388973\pi$
$233$	−9.81621	−	11.6985i	−0.643082	−	0.766395i	−0.984854	+	0.173388i	$0.944528\pi$
$234$	0.633721	−	3.59401i	0.0414277	−	0.234948i
$235$		0			0
$236$	−3.49848	−	6.05954i	−0.227732	−	0.394443i
$237$	2.32428	+	6.38591i	0.150978	+	0.414809i
$238$	0.817222	+	2.24530i	0.0529727	+	0.145541i
$239$	−9.80155	−	16.9768i	−0.634010	−	1.09814i	−0.986724	−	0.162406i	$-0.948075\pi$
$239$	−9.80155	−	16.9768i	−0.634010	−	1.09814i	0.352714	−	0.935731i	$-0.385259\pi$
$240$		0			0
$241$	−1.58431	+	8.98507i	−0.102054	+	0.578779i	0.890302	+	0.455371i	$0.150493\pi$
$241$	−1.58431	+	8.98507i	−0.102054	+	0.578779i	−0.992356	+	0.123408i	$0.960618\pi$
$242$	14.6221	+	17.4260i	0.939947	+	1.12019i
$243$	7.88887	−	9.40159i	0.506071	−	0.603112i
$244$	−2.55868	−	14.5110i	−0.163802	−	0.928970i
$245$		0			0
$246$	−5.01599			−0.319808
$247$	−4.07930	−	11.6699i	−0.259560	−	0.742536i
$248$			6.94426i			0.440961i
$249$	−20.3642	−	7.41196i	−1.29053	−	0.469714i
$250$		0			0
$251$	6.49099	+	5.44659i	0.409708	+	0.343786i	0.824232	−	0.566253i	$-0.191607\pi$
$251$	6.49099	+	5.44659i	0.409708	+	0.343786i	−0.414524	+	0.910038i	$0.636052\pi$
$252$	−1.84514	−	2.19895i	−0.116233	−	0.138521i
$253$	25.8742	+	4.56232i	1.62670	+	0.286831i
$254$	8.77382	−	15.1967i	0.550518	−	0.953525i
$255$		0			0
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−1.67522	−	4.60263i	−0.104497	−	0.287104i	0.876414	−	0.481558i	$-0.159929\pi$
$257$	−1.67522	−	4.60263i	−0.104497	−	0.287104i	−0.980912	+	0.194454i	$0.937707\pi$
$258$	−9.48781	+	5.47779i	−0.590686	+	0.341032i
$259$	2.88001	−	4.98833i	0.178955	−	0.309960i
$260$		0			0
$261$	0.507166	−	0.425562i	0.0313928	−	0.0263417i
$262$	2.52135	−	3.00483i	0.155770	−	0.185639i
$263$	12.4030	−	2.18699i	0.764805	−	0.134856i	0.222380	−	0.974960i	$-0.428617\pi$
$263$	12.4030	−	2.18699i	0.764805	−	0.134856i	0.542425	+	0.840104i	$0.317506\pi$
$264$	7.14523	+	2.60065i	0.439758	+	0.160059i
$265$		0			0
$266$	−9.09407	−	3.44226i	−0.557593	−	0.211058i
$267$			2.67755i			0.163864i
$268$	−2.77800	+	7.63250i	−0.169694	+	0.466229i
$269$	0.460372	+	2.61090i	0.0280694	+	0.159190i	0.995621	−	0.0934853i	$-0.0298008\pi$
$269$	0.460372	+	2.61090i	0.0280694	+	0.159190i	−0.967551	+	0.252675i	$0.918690\pi$
$270$		0			0
$271$	−16.0350	+	13.4549i	−0.974055	+	0.817329i	−0.983182	−	0.182629i	$-0.941539\pi$
$271$	−16.0350	+	13.4549i	−0.974055	+	0.817329i	0.00912662	+	0.999958i	$0.497095\pi$
$272$	1.05483	+	0.185995i	0.0639586	+	0.0112776i
$273$	7.17160	+	4.14053i	0.434045	+	0.250596i
$274$	1.32554	+	2.29590i	0.0800787	+	0.138700i
$275$		0			0
$276$	5.56267	−	2.02465i	0.334834	−	0.121869i
$277$	−12.6107	+	7.28081i	−0.757705	+	0.437461i	−0.828471	−	0.560032i	$-0.810789\pi$
$277$	−12.6107	+	7.28081i	−0.757705	+	0.437461i	0.0707659	+	0.997493i	$0.477456\pi$
$278$	−13.9511	−	8.05468i	−0.836732	−	0.483087i
$279$	−1.55168	+	8.80000i	−0.0928964	+	0.526842i
$280$		0			0
$281$	−25.2645	−	21.1994i	−1.50715	−	1.26465i	−0.869072	−	0.494685i	$-0.835283\pi$
$281$	−25.2645	−	21.1994i	−1.50715	−	1.26465i	−0.638082	−	0.769968i	$-0.720272\pi$
$282$	−14.2193	+	2.50725i	−0.846748	+	0.149305i
$283$	−0.288929	+	0.793827i	−0.0171751	+	0.0471881i	−0.947984	−	0.318318i	$-0.896882\pi$
$283$	−0.288929	+	0.793827i	−0.0171751	+	0.0471881i	0.930809	+	0.365506i	$0.119104\pi$
$284$	−6.64552			−0.394339
$285$		0			0
$286$	16.4758			0.974236
$287$	−2.92388	+	8.03328i	−0.172591	+	0.474190i
$288$	−1.26723	+	0.223448i	−0.0746725	+	0.0131668i
$289$	12.1439	+	10.1899i	0.714347	+	0.599408i
$290$		0			0
$291$	1.13277	−	6.42428i	0.0664044	−	0.376598i
$292$	2.94078	+	1.69786i	0.172096	+	0.0993599i
$293$	21.3463	−	12.3243i	1.24706	−	0.719992i	0.276541	−	0.961002i	$-0.410812\pi$
$293$	21.3463	−	12.3243i	1.24706	−	0.719992i	0.970523	+	0.241010i	$0.0774787\pi$
$294$	−2.48898	+	0.905915i	−0.145160	+	0.0528340i
$295$		0			0
$296$	−1.29103	−	2.23614i	−0.0750399	−	0.129973i
$297$	28.2288	+	16.2979i	1.63800	+	0.945701i
$298$	−13.6515	−	2.40712i	−0.790808	−	0.139441i
$299$	9.82581	−	8.24483i	0.568241	−	0.476811i
$300$		0			0
$301$	3.24232	+	18.3881i	0.186884	+	1.05987i
$302$	−2.96351	+	8.14218i	−0.170531	+	0.468530i
$303$		−	15.5812i		−	0.895118i
$304$	−3.37466	+	2.75893i	−0.193550	+	0.158235i
$305$		0			0
$306$	1.29516	+	0.471399i	0.0740393	+	0.0269481i
$307$	−33.4659	+	5.90094i	−1.91000	+	0.336785i	−0.997400	−	0.0720678i	$-0.977040\pi$
$307$	−33.4659	+	5.90094i	−1.91000	+	0.336785i	−0.912601	+	0.408852i	$0.865929\pi$
$308$	8.33006	−	9.92738i	0.474649	−	0.565665i
$309$	0.527102	−	0.442291i	0.0299858	−	0.0251611i
$310$		0			0
$311$	14.7721	−	25.5861i	0.837650	−	1.45085i	−0.0542040	−	0.998530i	$-0.517262\pi$
$311$	14.7721	−	25.5861i	0.837650	−	1.45085i	0.891854	−	0.452323i	$-0.149405\pi$
$312$	3.21484	−	1.85609i	0.182005	−	0.105080i
$313$	1.21889	+	3.34887i	0.0688956	+	0.189289i	0.969362	−	0.245636i	$-0.0789969\pi$
$313$	1.21889	+	3.34887i	0.0688956	+	0.189289i	−0.900466	+	0.434926i	$0.856775\pi$
$314$	3.74808	−	1.36419i	0.211516	−	0.0769856i
$315$		0			0
$316$	2.59598	−	4.49636i	0.146035	−	0.252940i
$317$	26.7764	+	4.72141i	1.50391	+	0.265181i	0.864089	−	0.503340i	$-0.167895\pi$
$317$	26.7764	+	4.72141i	1.50391	+	0.265181i	0.639826	+	0.768520i	$0.279007\pi$
$318$	−2.48650	−	2.96330i	−0.139436	−	0.166173i
$319$	2.28965	+	1.92124i	0.128196	+	0.107569i
$320$		0			0
$321$	14.2572	+	5.18921i	0.795762	+	0.289634i
$322$		−	10.0890i		−	0.562238i
$323$	4.60790	−	0.751889i	0.256390	−	0.0418362i
$324$	3.48384			0.193547
$325$		0			0
$326$	3.20360	+	18.1685i	0.177431	+	1.00626i
$327$	6.94843	−	8.28081i	0.384249	−	0.457930i
$328$	2.46330	+	2.93565i	0.136013	+	0.162094i
$329$	−4.27315	+	24.2342i	−0.235586	+	1.33608i
$330$		0			0
$331$	−14.6651	−	25.4007i	−0.806066	−	1.39615i	−0.915569	−	0.402160i	$-0.868259\pi$
$331$	−14.6651	−	25.4007i	−0.806066	−	1.39615i	0.109503	−	0.993986i	$-0.465074\pi$
$332$	5.66275	+	15.5583i	0.310784	+	0.853871i
$333$	−1.13638	−	3.12219i	−0.0622734	−	0.171095i
$334$	3.19019	+	5.52557i	0.174560	+	0.302346i
$335$		0			0
$336$	0.507029	−	2.87551i	0.0276607	−	0.156872i
$337$	6.38152	+	7.60520i	0.347624	+	0.414282i	0.911319	−	0.411701i	$-0.135065\pi$
$337$	6.38152	+	7.60520i	0.347624	+	0.414282i	−0.563695	+	0.825983i	$0.690621\pi$
$338$	−3.18597	+	3.79689i	−0.173294	+	0.206524i
$339$	3.04045	+	17.2433i	0.165135	+	0.936525i
$340$		0			0
$341$	−40.3413			−2.18460
$342$	−4.89295	+	2.74215i	−0.264581	+	0.148279i
$343$			20.1297i			1.08690i
$344$	7.86530	+	2.86273i	0.424068	+	0.154348i
$345$		0			0
$346$	8.41278	+	7.05916i	0.452274	+	0.379503i
$347$	−20.5362	−	24.4740i	−1.10244	−	1.31384i	−0.945279	−	0.326262i	$-0.894211\pi$
$347$	−20.5362	−	24.4740i	−1.10244	−	1.31384i	−0.157159	−	0.987573i	$-0.550234\pi$
$348$	0.663206	+	0.116941i	0.0355516	+	0.00626870i
$349$	−9.46630	+	16.3961i	−0.506719	+	0.877664i	0.493250	+	0.869887i	$0.335809\pi$
$349$	−9.46630	+	16.3961i	−0.506719	+	0.877664i	−0.999970	+	0.00777642i	$0.997525\pi$
$350$		0			0
$351$	14.9536	−	5.44267i	0.798165	−	0.290508i
$352$	−1.98690	−	5.45896i	−0.105902	−	0.290964i
$353$	2.77214	−	1.60049i	0.147546	−	0.0851857i	−0.424410	−	0.905470i	$-0.639518\pi$
$353$	2.77214	−	1.60049i	0.147546	−	0.0851857i	0.571956	+	0.820285i	$0.306185\pi$
$354$	4.57916	−	7.93133i	0.243379	−	0.421546i
$355$		0			0
$356$	1.56706	−	1.31492i	0.0830541	−	0.0696906i
$357$	−2.01031	+	2.39579i	−0.106397	+	0.126799i
$358$	3.39804	−	0.599165i	0.179592	−	0.0316669i
$359$	21.1480	+	7.69725i	1.11615	+	0.406245i	0.833246	−	0.552903i	$-0.186480\pi$
$359$	21.1480	+	7.69725i	1.11615	+	0.406245i	0.282904	+	0.959148i	$0.408702\pi$
$360$		0			0
$361$	−9.91757	+	16.2062i	−0.521977	+	0.852959i
$362$			11.1388i			0.585442i
$363$	−10.1836	+	27.9792i	−0.534501	+	1.46853i
$364$	−1.09863	−	6.23062i	−0.0575836	−	0.326573i
$365$		0			0
$366$	14.7742	−	12.3971i	0.772262	−	0.648005i
$367$	−5.05702	−	0.891689i	−0.263974	−	0.0465458i	0.0400944	−	0.999196i	$-0.487234\pi$
$367$	−5.05702	−	0.891689i	−0.263974	−	0.0465458i	−0.304069	+	0.952650i	$0.598345\pi$
$368$	−3.91672	−	2.26132i	−0.204173	−	0.117879i
$369$	2.46562	+	4.27058i	0.128355	+	0.222317i
$370$		0			0
$371$	−6.19523	+	2.25488i	−0.321640	+	0.117068i
$372$	−7.87159	+	4.54467i	−0.408123	+	0.235630i
$373$	−28.1039	−	16.2258i	−1.45517	−	0.840141i	−0.456400	−	0.889775i	$-0.650861\pi$
$373$	−28.1039	−	16.2258i	−1.45517	−	0.840141i	−0.998767	+	0.0496338i	$0.984195\pi$
$374$	−1.08050	+	6.12784i	−0.0558715	+	0.316863i
$375$		0			0
$376$	8.45036	+	7.09070i	0.435794	+	0.365675i
$377$	1.43703	−	0.253387i	0.0740106	−	0.0130501i
$378$	4.28101	−	11.7620i	0.220191	−	0.604971i
$379$	24.1904			1.24258			0.621288	−	0.783582i	$-0.286610\pi$
$379$	24.1904			1.24258			0.621288	+	0.783582i	$0.286610\pi$
$380$		0			0
$381$	22.9681			1.17669
$382$	3.31812	−	9.11645i	0.169770	−	0.466438i
$383$	7.89057	−	1.39132i	0.403189	−	0.0710932i	0.0316238	−	0.999500i	$-0.489932\pi$
$383$	7.89057	−	1.39132i	0.403189	−	0.0710932i	0.371566	+	0.928407i	$0.378821\pi$
$384$	−1.00267	−	0.841344i	−0.0511675	−	0.0429347i
$385$		0			0
$386$	0.618052	−	3.50514i	0.0314580	−	0.178407i
$387$	9.32750	+	5.38523i	0.474143	+	0.273747i
$388$	−4.31616	+	2.49193i	−0.219120	+	0.126509i
$389$	−11.8250	+	4.30396i	−0.599553	+	0.218220i	−0.623926	−	0.781483i	$-0.714463\pi$
$389$	−11.8250	+	4.30396i	−0.599553	+	0.218220i	0.0243728	+	0.999703i	$0.492241\pi$
$390$		0			0
$391$	2.42211	+	4.19521i	0.122491	+	0.212161i
$392$	1.75251	+	1.01181i	0.0885151	+	0.0511042i
$393$	5.05619	+	0.891543i	0.255051	+	0.0449724i
$394$	2.56883	−	2.15551i	0.129416	−	0.108593i
$395$		0			0
$396$	−1.29807	−	7.36175i	−0.0652307	−	0.369942i
$397$	0.382338	−	1.05047i	0.0191890	−	0.0527214i	−0.929728	−	0.368246i	$-0.879958\pi$
$397$	0.382338	−	1.05047i	0.0191890	−	0.0527214i	0.948917	+	0.315525i	$0.102181\pi$
$398$		−	18.5310i		−	0.928875i
$399$	−2.04967	−	12.5613i	−0.102612	−	0.628850i
$400$		0			0
$401$	−16.9221	−	6.15915i	−0.845050	−	0.307573i	−0.117030	−	0.993128i	$-0.537337\pi$
$401$	−16.9221	−	6.15915i	−0.845050	−	0.307573i	−0.728021	+	0.685555i	$0.759559\pi$
$402$	−10.4698	+	1.84611i	−0.522186	+	0.0920756i
$403$	−12.6595	+	15.0870i	−0.630614	+	0.751536i
$404$	−9.11905	+	7.65179i	−0.453689	+	0.380691i
$405$		0			0
$406$	0.573875	−	0.993980i	0.0284809	−	0.0493304i
$407$	12.9904	−	7.50001i	0.643910	−	0.371762i
$408$	0.479501	+	1.31742i	0.0237389	+	0.0652220i
$409$	−22.8966	+	8.33368i	−1.13216	+	0.412074i	−0.839077	−	0.544012i	$-0.816904\pi$
$409$	−22.8966	+	8.33368i	−1.13216	+	0.412074i	−0.293086	+	0.956086i	$0.594682\pi$
$410$		0			0
$411$	−1.73500	+	3.00510i	−0.0855810	+	0.148231i
$412$	−0.517710	−	0.0912862i	−0.0255057	−	0.00449735i
$413$	−10.0331	−	11.9569i	−0.493695	−	0.588362i
$414$	−4.45811	−	3.74080i	−0.219104	−	0.183850i
$415$		0			0
$416$	−2.66507	−	0.970006i	−0.130666	−	0.0475585i
$417$		−	21.0855i		−	1.03256i
$418$	−16.0275	−	19.6044i	−0.783929	−	0.958883i
$419$	−17.2621			−0.843311			−0.421655	−	0.906756i	$-0.638551\pi$
$419$	−17.2621			−0.843311			−0.421655	+	0.906756i	$0.638551\pi$
$420$		0			0
$421$	5.85430	+	33.2014i	0.285321	+	1.61814i	0.704137	+	0.710064i	$0.251334\pi$
$421$	5.85430	+	33.2014i	0.285321	+	1.61814i	−0.418816	+	0.908071i	$0.637555\pi$
$422$	16.6759	−	19.8736i	0.811772	−	0.967433i
$423$	9.12419	+	10.8738i	0.443633	+	0.528701i
$424$	−0.513198	+	2.91049i	−0.0249231	+	0.141346i
$425$		0			0
$426$	−4.34916	−	7.53296i	−0.210717	−	0.364973i
$427$	−11.2423	−	30.8878i	−0.544051	−	1.49477i
$428$	−3.96456	−	10.8925i	−0.191634	−	0.526511i
$429$	10.7826	+	18.6760i	0.520589	+	0.901686i
$430$		0			0
$431$	4.99240	−	28.3133i	0.240475	−	1.36380i	−0.590295	−	0.807188i	$-0.700989\pi$
$431$	4.99240	−	28.3133i	0.240475	−	1.36380i	0.830770	−	0.556615i	$-0.187900\pi$
$432$	−3.60666	−	4.29825i	−0.173526	−	0.206800i
$433$	−8.19027	+	9.76078i	−0.393599	+	0.469073i	−0.926057	−	0.377383i	$-0.876824\pi$
$433$	−8.19027	+	9.76078i	−0.393599	+	0.469073i	0.532458	+	0.846456i	$0.321268\pi$
$434$	2.69000	+	15.2558i	0.129124	+	0.732300i
$435$		0			0
$436$	−8.25872			−0.395521
$437$	−19.3689	−	3.67116i	−0.926538	−	0.175615i
$438$			4.44466i			0.212374i
$439$	−28.3251	−	10.3095i	−1.35188	−	0.492045i	−0.438347	−	0.898806i	$-0.644436\pi$
$439$	−28.3251	−	10.3095i	−1.35188	−	0.492045i	−0.913535	+	0.406761i	$0.866658\pi$
$440$		0			0
$441$	1.99475	+	1.67380i	0.0949882	+	0.0797046i
$442$	1.95264	+	2.32707i	0.0928776	+	0.110687i
$443$	32.0964	+	5.65947i	1.52495	+	0.268889i	0.872375	−	0.488837i	$-0.162579\pi$
$443$	32.0964	+	5.65947i	1.52495	+	0.268889i	0.652572	+	0.757726i	$0.273690\pi$
$444$	1.68983	−	2.92688i	0.0801960	−	0.138904i
$445$		0			0
$446$	5.00966	−	1.82337i	0.237214	−	0.0863389i
$447$	−6.20563	−	17.0498i	−0.293516	−	0.806429i
$448$	−1.93191	+	1.11539i	−0.0912742	+	0.0526972i
$449$	−8.38799	+	14.5284i	−0.395854	+	0.685638i	−0.993210	−	0.116338i	$-0.962885\pi$
$449$	−8.38799	+	14.5284i	−0.395854	+	0.685638i	0.597356	+	0.801976i	$0.296218\pi$
$450$		0			0
$451$	−17.0541	+	14.3101i	−0.803046	+	0.673836i
$452$	8.59862	−	10.2474i	0.404445	−	0.481999i
$453$	−11.1690	+	1.96939i	−0.524763	+	0.0925299i
$454$	−22.3309	−	8.12777i	−1.04804	−	0.381455i
$455$		0			0
$456$	−5.33590	−	2.01973i	−0.249876	−	0.0945824i
$457$			16.4975i			0.771722i	0.922557	+	0.385861i	$0.126096\pi$
$457$			16.4975i			0.771722i	−0.922557	+	0.385861i	$0.873904\pi$
$458$	−7.24696	+	19.9109i	−0.338628	+	0.930373i
$459$	1.04361	+	5.91863i	0.0487117	+	0.276258i
$460$		0			0
$461$	11.1486	−	9.35479i	0.519242	−	0.435696i	−0.345125	−	0.938557i	$-0.612164\pi$
$461$	11.1486	−	9.35479i	0.519242	−	0.435696i	0.864367	+	0.502861i	$0.167719\pi$
$462$	16.7047	+	2.94549i	0.777173	+	0.137037i
$463$	−16.4068	−	9.47245i	−0.762487	−	0.440222i	0.0677011	−	0.997706i	$-0.478434\pi$
$463$	−16.4068	−	9.47245i	−0.762487	−	0.440222i	−0.830188	+	0.557484i	$0.811767\pi$
$464$	−0.257253	−	0.445575i	−0.0119427	−	0.0206853i
$465$		0			0
$466$	−14.3503	+	5.22310i	−0.664767	+	0.241955i
$467$	12.5838	−	7.26529i	0.582311	−	0.336197i	−0.179740	−	0.983714i	$-0.557526\pi$
$467$	12.5838	−	7.26529i	0.582311	−	0.336197i	0.762051	+	0.647517i	$0.224192\pi$
$468$	−3.16052	−	1.82473i	−0.146095	−	0.0843481i
$469$	−3.14636	+	17.8439i	−0.145285	+	0.823953i
$470$		0			0
$471$	3.99929	+	3.35580i	0.184277	+	0.154627i
$472$	−6.89066	+	1.21501i	−0.317168	+	0.0559253i
$473$	−16.6305	+	45.6919i	−0.764671	+	2.10092i
$474$	6.79574			0.312139
$475$		0			0
$476$	2.38940			0.109518
$477$	−1.30068	+	3.57360i	−0.0595543	+	0.163624i
$478$	−19.3053	+	3.40404i	−0.883004	+	0.155697i
$479$	−3.70285	−	3.10706i	−0.169188	−	0.141965i	0.554263	−	0.832342i	$-0.313000\pi$
$479$	−3.70285	−	3.10706i	−0.169188	−	0.141965i	−0.723450	+	0.690377i	$0.757445\pi$
$480$		0			0
$481$	1.27163	−	7.21178i	0.0579814	−	0.328829i
$482$	7.90134	+	4.56184i	0.359896	+	0.207786i
$483$	11.4363	−	6.60274i	0.520369	−	0.300435i
$484$	21.3762	−	7.78028i	0.971643	−	0.353649i
$485$		0			0
$486$	−6.13645	−	10.6286i	−0.278355	−	0.482125i
$487$	23.9912	+	13.8513i	1.08715	+	0.627664i	0.932815	−	0.360356i	$-0.117345\pi$
$487$	23.9912	+	13.8513i	1.08715	+	0.627664i	0.154330	+	0.988019i	$0.450678\pi$
$488$	−14.5110	−	2.55868i	−0.656881	−	0.115826i
$489$	−18.4982	+	15.5218i	−0.836516	+	0.701920i
$490$		0			0
$491$	5.69883	+	32.3197i	0.257185	+	1.45857i	0.790402	+	0.612588i	$0.209872\pi$
$491$	5.69883	+	32.3197i	0.257185	+	1.45857i	−0.533218	+	0.845978i	$0.679017\pi$
$492$	−1.71557	+	4.71349i	−0.0773439	+	0.212501i
$493$			0.551090i			0.0248198i
$494$	−12.3613	−	0.158041i	−0.556161	−	0.00711059i
$495$		0			0
$496$	6.52547	+	2.37508i	0.293002	+	0.106644i
$497$	−14.5995	+	2.57428i	−0.654875	+	0.115472i
$498$	−13.9299	+	16.6010i	−0.624215	+	0.743911i
$499$	−14.9188	+	12.5184i	−0.667857	+	0.560399i	−0.912430	−	0.409232i	$-0.865797\pi$
$499$	−14.9188	+	12.5184i	−0.667857	+	0.560399i	0.244573	+	0.969631i	$0.421352\pi$
$500$		0			0
$501$	−4.17564	+	7.23242i	−0.186554	+	0.323121i
$502$	7.33817	−	4.23670i	0.327519	−	0.189093i
$503$	−9.86583	−	27.1062i	−0.439896	−	1.20860i	−0.939560	−	0.342384i	$-0.888765\pi$
$503$	−9.86583	−	27.1062i	−0.439896	−	1.20860i	0.499664	−	0.866219i	$-0.333457\pi$
$504$	−2.69741	+	0.981779i	−0.120152	+	0.0437319i
$505$		0			0
$506$	13.1367	−	22.7534i	0.583997	−	1.01151i
$507$	−6.38898	−	1.12655i	−0.283745	−	0.0500319i
$508$	−11.2794	−	13.4423i	−0.500442	−	0.596404i
$509$	23.1340	+	19.4117i	1.02540	+	0.860410i	0.990296	−	0.138974i	$-0.0443804\pi$
$509$	23.1340	+	19.4117i	1.02540	+	0.860410i	0.0351005	+	0.999384i	$0.488825\pi$
$510$		0			0
$511$	7.11828	+	2.59084i	0.314894	+	0.114612i
$512$			1.00000i			0.0441942i
$513$	−21.0229	−	12.4986i	−0.928182	−	0.551827i
$514$	−4.89802			−0.216042
$515$		0			0
$516$	1.90242	+	10.7891i	0.0837493	+	0.474966i
$517$	−41.1920	+	49.0907i	−1.81162	+	2.15901i
$518$	−3.70247	−	4.41244i	−0.162677	−	0.193871i
$519$	−2.49610	+	14.1561i	−0.109567	+	0.621384i
$520$		0			0
$521$	−18.6288	−	32.2661i	−0.816144	−	1.41360i	−0.908504	−	0.417877i	$-0.862774\pi$
$521$	−18.6288	−	32.2661i	−0.816144	−	1.41360i	0.0923600	−	0.995726i	$-0.470559\pi$
$522$	−0.226437	−	0.622131i	−0.00991088	−	0.0272299i
$523$	2.62859	+	7.22198i	0.114940	+	0.315795i	0.983802	−	0.179260i	$-0.0573702\pi$
$523$	2.62859	+	7.22198i	0.114940	+	0.315795i	−0.868862	+	0.495055i	$0.835148\pi$
$524$	−1.96126	−	3.39701i	−0.0856781	−	0.148399i
$525$		0			0
$526$	2.18699	−	12.4030i	0.0953574	−	0.540798i
$527$	−4.78107	−	5.69786i	−0.208267	−	0.248203i
$528$	4.88763	−	5.82484i	0.212707	−	0.253494i
$529$	0.442071	+	2.50711i	0.0192205	+	0.109005i
$530$		0			0
$531$	−9.00357			−0.390721
$532$	−6.34502	+	7.36831i	−0.275091	+	0.319457i
$533$			10.8686i			0.470771i
$534$	2.51608	+	0.915777i	0.108881	+	0.0396296i
$535$		0			0
$536$	6.22207	+	5.22094i	0.268753	+	0.225510i
$537$	2.90302	+	3.45969i	0.125275	+	0.149296i
$538$	2.61090	+	0.460372i	0.112564	+	0.0198481i
$539$	−5.87792	+	10.1809i	−0.253180	+	0.438521i
$540$		0			0
$541$	10.8889	−	3.96325i	0.468152	−	0.170393i	−0.0971632	−	0.995268i	$-0.530977\pi$
$541$	10.8889	−	3.96325i	0.468152	−	0.170393i	0.565315	+	0.824875i	$0.308755\pi$
$542$	7.15922	+	19.6698i	0.307515	+	0.844891i
$543$	−12.6263	+	7.28978i	−0.541845	+	0.312835i
$544$	0.535552	−	0.927604i	0.0229616	−	0.0397707i
$545$		0			0
$546$	6.34366	−	5.32296i	0.271483	−	0.227802i
$547$	9.30744	−	11.0922i	0.397958	−	0.474267i	−0.529438	−	0.848348i	$-0.677597\pi$
$547$	9.30744	−	11.0922i	0.397958	−	0.474267i	0.927396	+	0.374081i	$0.122042\pi$
$548$	2.61080	−	0.460355i	0.111528	−	0.0196654i
$549$	−17.8171	−	6.48488i	−0.760414	−	0.276768i
$550$		0			0
$551$	−1.69942	−	1.46341i	−0.0723979	−	0.0623435i
$552$		−	5.91967i		−	0.251958i
$553$	3.96131	−	10.8836i	0.168452	−	0.462818i
$554$	2.52860	+	14.3404i	0.107430	+	0.609265i
$555$		0			0
$556$	−12.3405	+	10.3549i	−0.523353	+	0.439145i
$557$	−39.0853	−	6.89180i	−1.65610	−	0.292015i	−0.734052	−	0.679094i	$-0.762373\pi$
$557$	−39.0853	−	6.89180i	−1.65610	−	0.292015i	−0.922047	+	0.387079i	$0.873484\pi$
$558$	7.73859	+	4.46787i	0.327600	+	0.189140i
$559$	11.8692	+	20.5581i	0.502015	+	0.869515i
$560$		0			0
$561$	−7.65329	+	2.78557i	−0.323122	+	0.117607i
$562$	−28.5619	+	16.4902i	−1.20481	+	0.695599i
$563$	10.7400	+	6.20077i	0.452639	+	0.261331i	0.708944	−	0.705265i	$-0.249172\pi$
$563$	10.7400	+	6.20077i	0.452639	+	0.261331i	−0.256305	+	0.966596i	$0.582505\pi$
$564$	−2.50725	+	14.2193i	−0.105574	+	0.598742i
$565$		0			0
$566$	0.647134	+	0.543009i	0.0272011	+	0.0228244i
$567$	7.65361	−	1.34954i	0.321421	−	0.0566753i
$568$	−2.27290	+	6.24474i	−0.0953688	+	0.262024i
$569$	−33.6313			−1.40990			−0.704949	−	0.709258i	$-0.749030\pi$
$569$	−33.6313			−1.40990			−0.704949	+	0.709258i	$0.749030\pi$
$570$		0			0
$571$	−4.64608			−0.194432			−0.0972162	−	0.995263i	$-0.530994\pi$
$571$	−4.64608			−0.194432			−0.0972162	+	0.995263i	$0.530994\pi$
$572$	5.63506	−	15.4822i	0.235614	−	0.647344i
$573$	12.5054	−	2.20504i	0.522421	−	0.0921168i
$574$	6.54879	+	5.49509i	0.273341	+	0.229361i
$575$		0			0
$576$	−0.223448	+	1.26723i	−0.00931031	+	0.0528014i
$577$	−18.0303	−	10.4098i	−0.750612	−	0.433366i	0.0753028	−	0.997161i	$-0.476008\pi$
$577$	−18.0303	−	10.4098i	−0.750612	−	0.433366i	−0.825915	+	0.563794i	$0.809341\pi$
$578$	13.7289	−	7.92637i	0.571046	−	0.329693i
$579$	4.37770	−	1.59335i	0.181931	−	0.0662175i
$580$		0			0
$581$	18.4672	+	31.9862i	0.766150	+	1.32701i
$582$	−5.64942	−	3.26169i	−0.234176	−	0.135201i
$583$	−16.9079	−	2.98133i	−0.700255	−	0.123474i
$584$	2.60128	−	2.18273i	0.107642	−	0.0903220i
$585$		0			0
$586$	−4.28018	−	24.2741i	−0.176813	−	1.00275i
$587$	−1.34529	+	3.69616i	−0.0555262	+	0.152557i	−0.964355	−	0.264613i	$-0.914756\pi$
$587$	−1.34529	+	3.69616i	−0.0555262	+	0.152557i	0.908828	+	0.417170i	$0.136978\pi$
$588$			2.64872i			0.109231i
$589$	30.2668	+	0.386965i	1.24712	+	0.0159446i
$590$		0			0
$591$	4.12453	+	1.50120i	0.169660	+	0.0617513i
$592$	−2.54284	+	0.448372i	−0.104510	+	0.0184280i
$593$	0.192194	−	0.229047i	0.00789244	−	0.00940585i	−0.762084	−	0.647478i	$-0.775824\pi$
$593$	0.192194	−	0.229047i	0.00789244	−	0.00940585i	0.769976	+	0.638073i	$0.220268\pi$
$594$	24.9698	−	20.9522i	1.02453	−	0.859679i
$595$		0			0
$596$	−6.93103	+	12.0049i	−0.283906	+	0.491740i
$597$	21.0056	−	12.1276i	0.859703	−	0.496350i
$598$	−4.38698	−	12.0531i	−0.179397	−	0.492889i
$599$	20.7035	−	7.53546i	0.845922	−	0.307891i	0.117546	−	0.993067i	$-0.462497\pi$
$599$	20.7035	−	7.53546i	0.845922	−	0.307891i	0.728377	+	0.685177i	$0.240275\pi$
$600$		0			0
$601$	18.1695	−	31.4705i	0.741150	−	1.28371i	−0.210822	−	0.977524i	$-0.567614\pi$
$601$	18.1695	−	31.4705i	0.741150	−	1.28371i	0.951972	−	0.306185i	$-0.0990525\pi$
$602$	18.3881	+	3.24232i	0.749444	+	0.132147i
$603$	6.71821	+	8.00645i	0.273587	+	0.326048i
$604$	6.63757	+	5.56958i	0.270079	+	0.226623i
$605$		0			0
$606$	−14.6416	−	5.32909i	−0.594773	−	0.216480i
$607$			21.1463i			0.858301i	0.903233	+	0.429150i	$0.141187\pi$
$607$			21.1463i			0.858301i	−0.903233	+	0.429150i	$0.858813\pi$
$608$	1.43835	+	4.11475i	0.0583326	+	0.166875i
$609$	1.50229			0.0608758
$610$		0			0
$611$	5.43268	+	30.8103i	0.219783	+	1.24645i
$612$	0.885941	−	1.05582i	0.0358120	−	0.0426791i
$613$	−25.6199	−	30.5326i	−1.03478	−	1.23320i	−0.971953	−	0.235174i	$-0.924434\pi$
$613$	−25.6199	−	30.5326i	−1.03478	−	1.23320i	−0.0628228	−	0.998025i	$-0.520010\pi$
$614$	−5.90094	+	33.4659i	−0.238143	+	1.35057i
$615$		0			0
$616$	−6.47964	−	11.2231i	−0.261072	−	0.452190i
$617$	−1.59546	−	4.38350i	−0.0642309	−	0.176473i	0.903425	−	0.428746i	$-0.141044\pi$
$617$	−1.59546	−	4.38350i	−0.0642309	−	0.176473i	−0.967656	+	0.252272i	$0.918822\pi$
$618$	−0.235338	−	0.646587i	−0.00946669	−	0.0260095i
$619$	−11.5280	−	19.9671i	−0.463351	−	0.802547i	0.535775	−	0.844361i	$-0.320020\pi$
$619$	−11.5280	−	19.9671i	−0.463351	−	0.802547i	−0.999125	+	0.0418139i	$0.986686\pi$
$620$		0			0
$621$	4.40656	−	24.9908i	0.176829	−	1.00285i
$622$	−18.9907	−	22.6322i	−0.761457	−	0.907469i
$623$	2.93330	−	3.49577i	0.117520	−	0.140055i
$624$	−0.644613	−	3.65578i	−0.0258052	−	0.146348i
$625$		0			0
$626$	3.56379			0.142438
$627$	11.7332	−	30.9979i	0.468579	−	1.23794i
$628$		−	3.98862i		−	0.159163i
$629$	2.59888	+	0.945914i	0.103624	+	0.0377160i
$630$		0			0
$631$	26.1036	+	21.9035i	1.03917	+	0.871964i	0.991913	−	0.126919i	$-0.0405089\pi$
$631$	26.1036	+	21.9035i	1.03917	+	0.871964i	0.0472529	+	0.998883i	$0.484953\pi$
$632$	−3.33732	−	3.97726i	−0.132752	−	0.158207i
$633$	33.4411	+	5.89657i	1.32916	+	0.234368i
$634$	13.5948	−	23.5468i	0.539917	−	0.935163i
$635$		0			0
$636$	−3.63502	+	1.32304i	−0.144138	+	0.0524619i
$637$	1.96293	+	5.39310i	0.0777740	+	0.213682i
$638$	2.58848	−	1.49446i	0.102479	−	0.0591663i
$639$	−4.27567	+	7.40568i	−0.169143	+	0.292964i
$640$		0			0
$641$	−30.9804	+	25.9956i	−1.22365	+	1.02676i	−0.225025	+	0.974353i	$0.572246\pi$
$641$	−30.9804	+	25.9956i	−1.22365	+	1.02676i	−0.998626	+	0.0524120i	$0.983309\pi$
$642$	9.75253	−	11.6226i	0.384902	−	0.458708i
$643$	31.2148	−	5.50401i	1.23099	−	0.217057i	0.479940	−	0.877301i	$-0.340658\pi$
$643$	31.2148	−	5.50401i	1.23099	−	0.217057i	0.751051	+	0.660244i	$0.229547\pi$
$644$	−9.48056	−	3.45064i	−0.373586	−	0.135974i
$645$		0			0
$646$	0.869449	−	4.58717i	0.0342080	−	0.180480i
$647$		−	0.479708i		−	0.0188593i	−0.999956	−	0.00942963i	$-0.996998\pi$
$647$		−	0.479708i		−	0.0188593i	0.999956	−	0.00942963i	$-0.00300159\pi$
$648$	1.19154	−	3.27374i	0.0468083	−	0.128605i
$649$	−7.05836	−	40.0299i	−0.277065	−	1.57131i
$650$		0			0
$651$	−15.5325	+	13.0333i	−0.608768	+	0.510817i
$652$	18.1685	+	3.20360i	0.711535	+	0.125463i
$653$	−10.4302	−	6.02190i	−0.408167	−	0.235655i	0.281835	−	0.959463i	$-0.409057\pi$
$653$	−10.4302	−	6.02190i	−0.408167	−	0.235655i	−0.690002	+	0.723808i	$0.742390\pi$
$654$	−5.40492	−	9.36159i	−0.211349	−	0.366067i
$655$		0			0
$656$	3.60111	−	1.31070i	0.140600	−	0.0511741i
$657$	3.78415	−	2.18478i	0.147634	−	0.0852364i
$658$	21.3112	+	12.3040i	0.830798	+	0.479662i
$659$	6.50457	−	36.8893i	0.253382	−	1.43700i	−0.546809	−	0.837257i	$-0.684158\pi$
$659$	6.50457	−	36.8893i	0.253382	−	1.43700i	0.800192	−	0.599744i	$-0.204731\pi$
$660$		0			0
$661$	6.71174	+	5.63182i	0.261056	+	0.219052i	0.763916	−	0.645316i	$-0.223274\pi$
$661$	6.71174	+	5.63182i	0.261056	+	0.219052i	−0.502859	+	0.864368i	$0.667719\pi$
$662$	−28.8846	+	5.09313i	−1.12263	+	0.197950i
$663$	−1.35992	+	3.73634i	−0.0528148	+	0.145108i
$664$	16.5568			0.642527
$665$		0			0
$666$	−3.32256			−0.128747
$667$	0.795855	−	2.18659i	0.0308156	−	0.0846652i
$668$	6.28345	−	1.10794i	0.243114	−	0.0428676i
$669$	5.34543	+	4.48534i	0.206666	+	0.173413i
$670$		0			0
$671$	14.8641	−	84.2986i	0.573823	−	3.25431i
$672$	−2.52868	−	1.45993i	−0.0975459	−	0.0563181i
$673$	−38.6790	+	22.3313i	−1.49097	+	0.860810i	−0.999947	−	0.0103382i	$-0.996709\pi$
$673$	−38.6790	+	22.3313i	−1.49097	+	0.860810i	−0.491020	+	0.871148i	$0.663376\pi$
$674$	9.32916	−	3.39554i	0.359346	−	0.130791i
$675$		0			0
$676$	2.47824	+	4.29245i	0.0953171	+	0.165094i
$677$	4.32076	+	2.49459i	0.166060	+	0.0958750i	0.580727	−	0.814098i	$-0.302768\pi$
$677$	4.32076	+	2.49459i	0.166060	+	0.0958750i	−0.414667	+	0.909973i	$0.636102\pi$
$678$	17.2433	+	3.04045i	0.662223	+	0.116768i
$679$	−8.51682	+	7.14646i	−0.326845	+	0.274256i
$680$		0			0
$681$	−5.40127	−	30.6321i	−0.206977	−	1.17383i
$682$	−13.7975	+	37.9084i	−0.528335	+	1.45159i
$683$		−	28.7691i		−	1.10082i	−0.834895	−	0.550409i	$-0.814472\pi$
$683$		−	28.7691i		−	1.10082i	0.834895	−	0.550409i	$-0.185528\pi$
$684$	0.903289	+	5.53574i	0.0345381	+	0.211664i
$685$		0			0
$686$	18.9157	+	6.88477i	0.722206	+	0.262862i
$687$	−27.3125	+	4.81594i	−1.04204	+	0.183739i
$688$	5.38018	−	6.41185i	0.205117	−	0.244449i
$689$	−6.42084	+	5.38772i	−0.244615	+	0.205256i
$690$		0			0
$691$	−12.7430	+	22.0716i	−0.484767	+	0.839642i	−0.999847	−	0.0175008i	$-0.994429\pi$
$691$	−12.7430	+	22.0716i	−0.484767	+	0.839642i	0.515080	+	0.857142i	$0.327762\pi$
$692$	9.51079	−	5.49105i	0.361546	−	0.208739i
$693$	−5.70345	−	15.6701i	−0.216656	−	0.595258i
$694$	−30.0218	+	10.9271i	−1.13961	+	0.414785i
$695$		0			0
$696$	0.336718	−	0.583213i	0.0127633	−	0.0221066i
$697$	−4.04235	−	0.712775i	−0.153115	−	0.0269983i
$698$	12.1696	+	14.5032i	0.460628	+	0.548955i
$699$	−15.3122	−	12.8484i	−0.579159	−	0.485972i
$700$		0			0
$701$	27.6845	+	10.0763i	1.04563	+	0.380578i	0.807011	−	0.590536i	$-0.201084\pi$
$701$	27.6845	+	10.0763i	1.04563	+	0.380578i	0.238617	+	0.971114i	$0.423306\pi$
$702$		−	15.9133i		−	0.600609i
$703$	−9.81824	+	5.50242i	−0.370302	+	0.207528i
$704$	−5.80931			−0.218946
$705$		0			0
$706$	−0.555846	−	3.15236i	−0.0209195	−	0.118641i
$707$	−17.0695	+	20.3426i	−0.641963	+	0.765061i
$708$	−5.88685	−	7.01567i	−0.221241	−	0.263665i
$709$	0.217936	−	1.23598i	0.00818476	−	0.0464181i	−0.980442	−	0.196809i	$-0.936942\pi$
$709$	0.217936	−	1.23598i	0.00818476	−	0.0464181i	0.988627	+	0.150391i	$0.0480532\pi$
$710$		0			0
$711$	−3.34046	−	5.78584i	−0.125277	−	0.216986i
$712$	−0.699655	−	1.92229i	−0.0262207	−	0.0720407i
$713$	10.7416	+	29.5123i	0.402276	+	1.10524i
$714$	1.56374	+	2.70848i	0.0585215	+	0.101362i
$715$		0			0
$716$	0.599165	−	3.39804i	0.0223919	−	0.126991i
$717$	−16.4930	−	19.6555i	−0.615941	−	0.734050i
$718$	14.4661	−	17.2400i	0.539870	−	0.643392i
$719$	4.48596	+	25.4412i	0.167298	+	0.948795i	0.946663	+	0.322225i	$0.104431\pi$
$719$	4.48596	+	25.4412i	0.167298	+	0.948795i	−0.779365	+	0.626570i	$0.784458\pi$
$720$		0			0
$721$	−1.17271			−0.0436741
$722$	11.8369	+	14.8623i	0.440522	+	0.553118i
$723$			11.9420i			0.444127i
$724$	10.4671	+	3.80969i	0.389005	+	0.141586i
$725$		0			0
$726$	22.8089	+	19.1389i	0.846517	+	0.710312i
$727$	20.9853	+	25.0093i	0.778301	+	0.927543i	0.998855	−	0.0478314i	$-0.0152310\pi$
$727$	20.9853	+	25.0093i	0.778301	+	0.927543i	−0.220554	+	0.975375i	$0.570787\pi$
$728$	−6.23062	−	1.09863i	−0.230922	−	0.0407178i
$729$	13.2578	−	22.9631i	0.491028	−	0.850486i
$730$		0			0
$731$	−8.42456	+	3.06629i	−0.311594	+	0.113411i
$732$	−6.59634	−	18.1233i	−0.243808	−	0.669856i
$733$	30.1077	−	17.3827i	1.11205	−	0.642044i	0.172693	−	0.984976i	$-0.444753\pi$
$733$	30.1077	−	17.3827i	1.11205	−	0.642044i	0.939360	+	0.342932i	$0.111420\pi$
$734$	−2.56752	+	4.44707i	−0.0947687	+	0.164144i
$735$		0			0
$736$	−3.46454	+	2.90709i	−0.127705	+	0.107157i
$737$	−30.3300	+	36.1459i	−1.11722	+	1.33145i
$738$	4.85632	−	0.856300i	0.178764	−	0.0315208i
$739$	28.3181	+	10.3069i	1.04170	+	0.379147i	0.805523	−	0.592564i	$-0.201884\pi$
$739$	28.3181	+	10.3069i	1.04170	+	0.379147i	0.236174	+	0.971711i	$0.424107\pi$
$740$		0			0
$741$	−7.91070	−	14.1155i	−0.290607	−	0.518544i
$742$			6.59283i			0.242030i
$743$	6.40141	−	17.5877i	0.234845	−	0.645231i	−0.765154	−	0.643847i	$-0.777337\pi$
$743$	6.40141	−	17.5877i	0.234845	−	0.645231i	0.999999	−	0.00138410i	$-0.000440573\pi$
$744$	1.57835	+	8.95124i	0.0578650	+	0.328168i
$745$		0			0
$746$	−24.8594	+	20.8595i	−0.910167	+	0.763721i
$747$	20.9813	+	3.69957i	0.767665	+	0.135360i
$748$	5.38873	+	3.11119i	0.197032	+	0.113756i
$749$	−12.9292	−	22.3940i	−0.472421	−	0.818258i
$750$		0			0
$751$	5.65553	−	2.05844i	0.206373	−	0.0751137i	−0.236765	−	0.971567i	$-0.576087\pi$
$751$	5.65553	−	2.05844i	0.206373	−	0.0751137i	0.443138	+	0.896453i	$0.353865\pi$
$752$	9.55327	−	5.51558i	0.348372	−	0.201133i
$753$	9.60493	+	5.54541i	0.350023	+	0.202086i
$754$	0.253387	−	1.43703i	0.00922780	−	0.0523334i
$755$		0			0
$756$	−9.58845	−	8.04566i	−0.348728	−	0.292618i
$757$	40.0667	−	7.06485i	1.45625	−	0.256776i	0.611206	−	0.791472i	$-0.290685\pi$
$757$	40.0667	−	7.06485i	1.45625	−	0.256776i	0.845045	+	0.534695i	$0.179574\pi$
$758$	8.27360	−	22.7315i	0.300511	−	0.825646i
$759$	34.3892			1.24825
$760$		0			0
$761$	39.9978			1.44992			0.724960	−	0.688791i	$-0.241858\pi$
$761$	39.9978			1.44992			0.724960	+	0.688791i	$0.241858\pi$
$762$	7.85555	−	21.5829i	0.284576	−	0.781867i
$763$	−18.1435	+	3.19919i	−0.656838	+	0.115818i
$764$	−7.43180	−	6.23602i	−0.268873	−	0.225611i
$765$		0			0
$766$	1.39132	−	7.89057i	0.0502705	−	0.285098i
$767$	−17.1855	−	9.92207i	−0.620533	−	0.358265i
$768$	−1.13354	+	0.654450i	−0.0409031	+	0.0236154i
$769$	21.0594	−	7.66500i	0.759422	−	0.276407i	0.0668569	−	0.997763i	$-0.478703\pi$
$769$	21.0594	−	7.66500i	0.759422	−	0.276407i	0.692565	+	0.721356i	$0.256481\pi$
$770$		0			0
$771$	−3.20551	−	5.55210i	−0.115444	−	0.199954i
$772$	−3.08237	−	1.77961i	−0.110937	−	0.0640495i
$773$	51.3378	+	9.05225i	1.84649	+	0.325587i	0.983679	−	0.179933i	$-0.0575881\pi$
$773$	51.3378	+	9.05225i	1.84649	+	0.325587i	0.862815	+	0.505520i	$0.168699\pi$
$774$	8.25066	−	6.92312i	0.296564	−	0.248847i
$775$		0			0
$776$	0.865440	+	4.90815i	0.0310675	+	0.176192i
$777$	2.57859	−	7.08462i	0.0925064	−	0.254159i
$778$			12.5839i			0.451156i
$779$	12.9324	−	10.5728i	0.463352	−	0.378811i
$780$		0			0
$781$	−36.2776	−	13.2040i	−1.29812	−	0.472475i
$782$	4.77062	−	0.841189i	0.170597	−	0.0300809i
$783$	1.85565	−	2.21148i	0.0663155	−	0.0790317i
$784$	1.55019	−	1.30076i	0.0553638	−	0.0464557i
$785$		0			0
$786$	2.56709	−	4.44634i	0.0915652	−	0.158596i
$787$	−5.63724	+	3.25466i	−0.200946	+	0.116016i	−0.597097	−	0.802169i	$-0.703679\pi$
$787$	−5.63724	+	3.25466i	−0.200946	+	0.116016i	0.396151	+	0.918186i	$0.370346\pi$
$788$	−1.14692	−	3.15114i	−0.0408574	−	0.112255i
$789$	15.4906	−	5.63813i	0.551481	−	0.200723i
$790$		0			0
$791$	14.9207	−	25.8433i	0.530518	−	0.918884i
$792$	−7.36175	−	1.29807i	−0.261588	−	0.0461251i
$793$	−26.8618	−	32.0127i	−0.953891	−	1.13680i
$794$	−0.856348	−	0.718561i	−0.0303906	−	0.0255008i
$795$		0			0
$796$	−17.4134	−	6.33797i	−0.617203	−	0.224643i
$797$			3.20848i			0.113650i	0.998384	+	0.0568251i	$0.0180977\pi$
$797$			3.20848i			0.113650i	−0.998384	+	0.0568251i	$0.981902\pi$
$798$	−12.5048	−	2.37015i	−0.442664	−	0.0839022i
$799$	−11.8155			−0.418003
$800$		0			0
$801$	−0.457096	−	2.59232i	−0.0161507	−	0.0915952i
$802$	−11.5754	+	13.7950i	−0.408742	+	0.487120i
$803$	12.6801	+	15.1116i	0.447473	+	0.533277i
$804$	−1.84611	+	10.4698i	−0.0651073	+	0.369242i
$805$		0			0
$806$	9.84733	+	17.0561i	0.346857	+	0.600775i
$807$	1.18685	+	3.26085i	0.0417792	+	0.114787i
$808$	4.07143	+	11.1862i	0.143232	+	0.393528i
$809$	3.42148	+	5.92617i	0.120293	+	0.208353i	0.919883	−	0.392193i	$-0.128283\pi$
$809$	3.42148	+	5.92617i	0.120293	+	0.208353i	−0.799590	+	0.600546i	$0.794950\pi$
$810$		0			0
$811$	0.958834	−	5.43782i	0.0336692	−	0.190948i	−0.963334	−	0.268304i	$-0.913537\pi$
$811$	0.958834	−	5.43782i	0.0336692	−	0.190948i	0.997004	+	0.0773564i	$0.0246479\pi$
$812$	−0.737759	−	0.879227i	−0.0258903	−	0.0308548i
$813$	−17.6112	+	20.9882i	−0.617650	+	0.736087i
$814$	−2.60473	−	14.7721i	−0.0912957	−	0.517763i
$815$		0			0
$816$	1.40197			0.0490787
$817$	12.9156	−	34.1217i	0.451861	−	1.19377i
$818$			24.3660i			0.851939i
$819$	−7.65016	−	2.78443i	−0.267318	−	0.0972959i
$820$		0			0
$821$	19.7227	+	16.5493i	0.688326	+	0.577574i	0.918426	−	0.395593i	$-0.129461\pi$
$821$	19.7227	+	16.5493i	0.688326	+	0.577574i	−0.230100	+	0.973167i	$0.573905\pi$
$822$	2.23047	+	2.65817i	0.0777965	+	0.0927143i
$823$	16.7613	+	2.95546i	0.584260	+	0.103021i	0.457963	−	0.888971i	$-0.348579\pi$
$823$	16.7613	+	2.95546i	0.584260	+	0.103021i	0.126298	+	0.991992i	$0.459690\pi$
$824$	−0.262848	+	0.455266i	−0.00915674	+	0.0158599i
$825$		0			0
$826$	−14.6674	+	5.33848i	−0.510342	+	0.185749i
$827$	13.4210	+	36.8739i	0.466695	+	1.28223i	0.920364	+	0.391063i	$0.127892\pi$
$827$	13.4210	+	36.8739i	0.466695	+	1.28223i	−0.453669	+	0.891170i	$0.649885\pi$
$828$	−5.03996	+	2.90982i	−0.175151	+	0.101123i
$829$	3.37098	−	5.83871i	0.117079	−	0.202787i	−0.801530	−	0.597955i	$-0.795980\pi$
$829$	3.37098	−	5.83871i	0.117079	−	0.202787i	0.918609	+	0.395168i	$0.129314\pi$
$830$		0			0
$831$	−14.6006	+	12.2513i	−0.506488	+	0.424994i
$832$	−1.82302	+	2.17259i	−0.0632017	+	0.0753208i
$833$	−2.13458	+	0.376385i	−0.0739589	+	0.0130410i
$834$	−19.8139	−	7.21167i	−0.686100	−	0.249720i
$835$		0			0
$836$	−23.9038	+	8.35579i	−0.826731	+	0.288991i
$837$			38.9640i			1.34679i
$838$	−5.90400	+	16.2211i	−0.203950	+	0.560349i
$839$	−8.81270	−	49.9793i	−0.304248	−	1.72548i	−0.627022	−	0.779002i	$-0.715726\pi$
$839$	−8.81270	−	49.9793i	−0.304248	−	1.72548i	0.322773	−	0.946476i	$-0.395385\pi$
$840$		0			0
$841$	−22.0125	+	18.4707i	−0.759052	+	0.636920i
$842$	33.2014	+	5.85430i	1.14419	+	0.201752i
$843$	−37.3847	−	21.5841i	−1.28760	−	0.743395i
$844$	−12.9716	−	22.4674i	−0.446500	−	0.773361i
$845$		0			0
$846$	13.3387	−	4.85488i	0.458593	−	0.166914i
$847$	43.9472	−	25.3729i	1.51004	−	0.871824i
$848$	2.55944	+	1.47770i	0.0878917	+	0.0507443i
$849$	−0.192007	+	1.08892i	−0.00658965	+	0.0373718i
$850$		0			0
$851$	−8.94568	−	7.50632i	−0.306654	−	0.257313i
$852$	−8.56616	+	1.51045i	−0.293472	+	0.0517470i
$853$	9.91768	−	27.2486i	0.339575	−	0.932974i	−0.645940	−	0.763388i	$-0.723535\pi$
$853$	9.91768	−	27.2486i	0.339575	−	0.932974i	0.985515	−	0.169587i	$-0.0542432\pi$
$854$	−32.8701			−1.12479
$855$		0			0
$856$	−11.5916			−0.396193
$857$	−6.86388	+	18.8584i	−0.234466	+	0.644189i	0.765534	+	0.643395i	$0.222475\pi$
$857$	−6.86388	+	18.8584i	−0.234466	+	0.644189i	−1.00000		0.000793759i	$0.999747\pi$
$858$	21.2376	−	3.74476i	0.725038	−	0.127844i
$859$	−25.1028	−	21.0638i	−0.856498	−	0.718687i	0.104713	−	0.994502i	$-0.466608\pi$
$859$	−25.1028	−	21.0638i	−0.856498	−	0.718687i	−0.961211	+	0.275816i	$0.911052\pi$
$860$		0			0
$861$	−1.94305	+	11.0196i	−0.0662189	+	0.375546i
$862$	−24.8983	−	14.3750i	−0.848039	−	0.489616i
$863$	27.7154	−	16.0015i	0.943444	−	0.544698i	0.0524056	−	0.998626i	$-0.483311\pi$
$863$	27.7154	−	16.0015i	0.943444	−	0.544698i	0.891038	+	0.453928i	$0.149978\pi$
$864$	−5.27258	+	1.91906i	−0.179377	+	0.0652879i
$865$		0			0
$866$	6.37090	+	11.0347i	0.216492	+	0.374975i
$867$	17.9697	+	10.3748i	0.610283	+	0.352347i
$868$	15.2558	+	2.69000i	0.517814	+	0.0913046i
$869$	23.1051	−	19.3875i	0.783788	−	0.657676i
$870$		0			0
$871$	4.00013	+	22.6859i	0.135539	+	0.768681i
$872$	−2.82465	+	7.76066i	−0.0956547	+	0.262809i
$873$			6.41316i			0.217053i
$874$	−10.0743	+	16.9452i	−0.340768	+	0.573179i
$875$		0			0
$876$	4.17662	+	1.52016i	0.141115	+	0.0513616i
$877$	33.9423	−	5.98494i	1.14615	−	0.202097i	0.431856	−	0.901943i	$-0.357859\pi$
$877$	33.9423	−	5.98494i	1.14615	−	0.202097i	0.714294	+	0.699846i	$0.246748\pi$
$878$	−19.3755	+	23.0908i	−0.653891	+	0.779277i
$879$	24.7145	−	20.7379i	0.833599	−	0.699473i
$880$		0			0
$881$	−18.6285	+	32.2656i	−0.627612	+	1.08706i	0.360418	+	0.932791i	$0.382634\pi$
$881$	−18.6285	+	32.2656i	−0.627612	+	1.08706i	−0.988030	+	0.154264i	$0.950699\pi$
$882$	2.25510	−	1.30198i	0.0759331	−	0.0438400i
$883$	−8.49776	−	23.3474i	−0.285972	−	0.785702i	−0.996620	−	0.0821540i	$-0.973820\pi$
$883$	−8.49776	−	23.3474i	−0.285972	−	0.785702i	0.710647	−	0.703548i	$-0.248402\pi$
$884$	2.85457	−	1.03898i	0.0960096	−	0.0349446i
$885$		0			0
$886$	16.2958	−	28.2251i	0.547468	−	0.948242i
$887$	−32.9254	−	5.80563i	−1.10553	−	0.194934i	−0.409049	−	0.912513i	$-0.634139\pi$
$887$	−32.9254	−	5.80563i	−1.10553	−	0.194934i	−0.696478	+	0.717578i	$0.745251\pi$
$888$	−2.17241	−	2.58898i	−0.0729013	−	0.0868804i
$889$	−29.9867	−	25.1619i	−1.00572	−	0.843902i
$890$		0			0
$891$	19.0182	+	6.92204i	0.637132	+	0.231897i
$892$		−	5.33117i		−	0.178501i
$893$	31.3760	−	36.4361i	1.04996	−	1.21929i
$894$	−18.1440			−0.606828
$895$		0			0
$896$	0.387371	+	2.19689i	0.0129411	+	0.0733929i
$897$	10.7917	−	12.8610i	0.360323	−	0.429416i
$898$	10.7834	+	12.8511i	0.359846	+	0.428848i
$899$	−0.620421	+	3.51858i	−0.0206922	+	0.117351i
$900$		0			0
$901$	−1.58277	−	2.74143i	−0.0527296	−	0.0913304i
$902$	7.61424	+	20.9199i	0.253526	+	0.696558i
$903$	8.35880	+	22.9656i	0.278163	+	0.764248i
$904$	−6.68854	−	11.5849i	−0.222458	−	0.385308i
$905$		0			0
$906$	−1.96939	+	11.1690i	−0.0654285	+	0.371064i
$907$	−16.3574	−	19.4940i	−0.543139	−	0.647288i	0.422749	−	0.906247i	$-0.361065\pi$
$907$	−16.3574	−	19.4940i	−0.543139	−	0.647288i	−0.965888	+	0.258958i	$0.916621\pi$
$908$	−15.2752	+	18.2043i	−0.506926	+	0.604130i
$909$	2.65993	+	15.0852i	0.0882245	+	0.500346i
$910$		0			0
$911$	−0.722711			−0.0239445			−0.0119722	−	0.999928i	$-0.503811\pi$
$911$	−0.722711			−0.0239445			−0.0119722	+	0.999928i	$0.503811\pi$
$912$	−3.72291	+	4.32332i	−0.123278	+	0.143159i
$913$			96.1833i			3.18320i
$914$	15.5026	+	5.64249i	0.512781	+	0.186637i
$915$		0			0
$916$	16.2315	+	13.6198i	0.536303	+	0.450012i
$917$	−5.62458	−	6.70311i	−0.185740	−	0.221356i
$918$	5.91863	+	1.04361i	0.195344	+	0.0344444i
$919$	1.12765	−	1.95314i	0.0371976	−	0.0644281i	−0.846827	−	0.531868i	$-0.821490\pi$
$919$	1.12765	−	1.95314i	0.0371976	−	0.0644281i	0.884025	+	0.467440i	$0.154824\pi$
$920$		0			0
$921$	−41.7968	+	15.2128i	−1.37725	+	0.501279i
$922$	−4.97758	−	13.6758i	−0.163928	−	0.450388i
$923$	−16.3223	+	9.42370i	−0.537256	+	0.310185i
$924$	8.48119	−	14.6899i	0.279011	−	0.483261i
$925$		0			0
$926$	−14.5126	+	12.1775i	−0.476915	+	0.400179i
$927$	−0.434818	+	0.518196i	−0.0142813	+	0.0170198i
$928$	−0.506690	+	0.0893431i	−0.0166329	+	0.00293283i
$929$	1.24934	+	0.454722i	0.0409895	+	0.0149189i	0.362434	−	0.932010i	$-0.381946\pi$
$929$	1.24934	+	0.454722i	0.0409895	+	0.0149189i	−0.321444	+	0.946929i	$0.604168\pi$
$930$		0			0
$931$	4.50768	−	7.58200i	0.147733	−	0.248490i
$932$			15.2713i			0.500229i
$933$	13.2261	−	36.3383i	0.433002	−	1.18966i
$934$	−2.52321	−	14.3098i	−0.0825619	−	0.468232i
$935$		0			0
$936$	−2.79565	+	2.34583i	−0.0913785	+	0.0766757i
$937$	38.4407	+	6.77813i	1.25580	+	0.221432i	0.761676	−	0.647959i	$-0.224377\pi$
$937$	38.4407	+	6.77813i	1.25580	+	0.221432i	0.494126	+	0.869390i	$0.335488\pi$
$938$	15.6916	+	9.05957i	0.512350	+	0.295805i
$939$	2.33232	+	4.03970i	0.0761124	+	0.131831i
$940$		0			0
$941$	12.0825	−	4.39766i	0.393878	−	0.143360i	−0.137486	−	0.990504i	$-0.543902\pi$
$941$	12.0825	−	4.39766i	0.393878	−	0.143360i	0.531363	+	0.847144i	$0.321680\pi$
$942$	4.52126	−	2.61035i	0.147311	−	0.0850498i
$943$	15.0097	+	8.66587i	0.488784	+	0.282199i
$944$	−1.21501	+	6.89066i	−0.0395452	+	0.224272i
$945$		0			0
$946$	37.2484	+	31.2551i	1.21105	+	1.01619i
$947$	46.2414	−	8.15361i	1.50264	−	0.264957i	0.639058	−	0.769158i	$-0.279324\pi$
$947$	46.2414	−	8.15361i	1.50264	−	0.264957i	0.863586	+	0.504202i	$0.168213\pi$
$948$	2.32428	−	6.38591i	0.0754891	−	0.207405i
$949$	9.63065			0.312624
$950$		0			0
$951$	35.5883			1.15403
$952$	0.817222	−	2.24530i	0.0264863	−	0.0727706i
$953$	−17.4656	+	3.07965i	−0.565765	+	0.0997596i	−0.449213	−	0.893425i	$-0.648295\pi$
$953$	−17.4656	+	3.07965i	−0.565765	+	0.0997596i	−0.116552	+	0.993185i	$0.537184\pi$
$954$	2.91323	+	2.44449i	0.0943192	+	0.0791432i
$955$		0			0
$956$	−3.40404	+	19.3053i	−0.110095	+	0.624378i
$957$	3.38806	+	1.95610i	0.109521	+	0.0632317i
$958$	−4.18613	+	2.41686i	−0.135248	+	0.0780853i
$959$	5.55731	−	2.02270i	0.179455	−	0.0653163i
$960$		0			0
$961$	−8.61134	−	14.9153i	−0.277785	−	0.481138i
$962$	−6.34193	−	3.66151i	−0.204472	−	0.118052i
$963$	−14.6893	−	2.59012i	−0.473355	−	0.0834653i
$964$	6.98914	−	5.86459i	0.225105	−	0.188886i
$965$		0			0
$966$	−2.29311	−	13.0049i	−0.0737795	−	0.418425i
$967$	3.32511	−	9.13568i	0.106928	−	0.293784i	−0.874676	−	0.484707i	$-0.838926\pi$
$967$	3.32511	−	9.13568i	0.106928	−	0.293784i	0.981605	+	0.190924i	$0.0611483\pi$
$968$		−	22.7480i		−	0.731149i
$969$	5.76875	−	2.01651i	0.185319	−	0.0647798i
$970$		0			0
$971$	−34.4686	−	12.5455i	−1.10615	−	0.402606i	−0.276570	−	0.960994i	$-0.589198\pi$
$971$	−34.4686	−	12.5455i	−1.10615	−	0.402606i	−0.829580	+	0.558388i	$0.811420\pi$
$972$	−12.0865	+	2.13117i	−0.387673	+	0.0683572i
$973$	−23.0995	+	27.5289i	−0.740536	+	0.882536i
$974$	21.2215	−	17.8069i	0.679980	−	0.570571i
$975$		0			0
$976$	−7.36741	+	12.7607i	−0.235825	+	0.408461i
$977$	32.3814	−	18.6954i	1.03597	−	0.598119i	0.117283	−	0.993099i	$-0.462582\pi$
$977$	32.3814	−	18.6954i	1.03597	−	0.598119i	0.918690	+	0.394980i	$0.129248\pi$
$978$	8.25898	+	22.6914i	0.264093	+	0.725589i
$979$	11.1671	−	4.06451i	0.356903	−	0.129902i
$980$		0			0
$981$	−5.31359	+	9.20341i	−0.169650	+	0.293842i
$982$	32.3197	+	5.69883i	1.03136	+	0.181857i
$983$	−7.41304	−	8.83452i	−0.236439	−	0.281777i	0.634757	−	0.772711i	$-0.281100\pi$
$983$	−7.41304	−	8.83452i	−0.236439	−	0.281777i	−0.871197	+	0.490934i	$0.836656\pi$
$984$	3.84247	+	3.22422i	0.122494	+	0.102784i
$985$		0			0
$986$	0.517855	+	0.188484i	0.0164919	+	0.00600255i
$987$			32.2095i			1.02524i
$988$	−4.37632	+	11.5618i	−0.139229	+	0.367829i
$989$	37.8548			1.20371
$990$		0			0
$991$	4.49126	+	25.4712i	0.142670	+	0.809119i	0.969209	+	0.246240i	$0.0791952\pi$
$991$	4.49126	+	25.4712i	0.142670	+	0.809119i	−0.826539	+	0.562879i	$0.809694\pi$
$992$	4.46368	−	5.31961i	0.141722	−	0.168898i
$993$	−24.6768	−	29.4086i	−0.783093	−	0.933254i
$994$	−2.57428	+	14.5995i	−0.0816512	+	0.463067i
$995$		0			0
$996$	10.8356	+	18.7678i	0.343338	+	0.594679i
$997$	0.249388	+	0.685188i	0.00789819	+	0.0217001i	0.943579	−	0.331147i	$-0.107436\pi$
$997$	0.249388	+	0.685188i	0.00789819	+	0.0217001i	−0.935681	+	0.352847i	$0.885213\pi$
$998$	6.66088	+	18.3006i	0.210846	+	0.579296i
$999$	−7.24395	−	12.5469i	−0.229189	−	0.396966i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.u.h.99.7		48
5.2	odd	4		950.2.l.j.251.2	✓	24
5.3	odd	4		950.2.l.k.251.3	yes	24
5.4	even	2	inner	950.2.u.h.99.2		48
19.5	even	9	inner	950.2.u.h.499.2		48
95.24	even	18	inner	950.2.u.h.499.7		48
95.43	odd	36		950.2.l.k.651.3	yes	24
95.62	odd	36		950.2.l.j.651.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.l.j.251.2	✓	24	5.2	odd	4
950.2.l.j.651.2	yes	24	95.62	odd	36
950.2.l.k.251.3	yes	24	5.3	odd	4
950.2.l.k.651.3	yes	24	95.43	odd	36
950.2.u.h.99.2		48	5.4	even	2	inner
950.2.u.h.99.7		48	1.1	even	1	trivial
950.2.u.h.499.2		48	19.5	even	9	inner
950.2.u.h.499.7		48	95.24	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.342020 - 0.939693i) q^{2} +(1.28901 - 0.227288i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.227288 - 1.28901i) q^{6} +(-1.93191 - 1.11539i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-1.20918 + 0.440106i) q^{9} +O(q^{10})\)	\(q+(0.342020 - 0.939693i) q^{2} +(1.28901 - 0.227288i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.227288 - 1.28901i) q^{6} +(-1.93191 - 1.11539i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-1.20918 + 0.440106i) q^{9} +(-2.90465 - 5.03101i) q^{11} +(-1.13354 - 0.654450i) q^{12} +(-2.79302 - 0.492485i) q^{13} +(-1.70888 + 1.43392i) q^{14} +(0.173648 + 0.984808i) q^{16} +(0.366339 - 1.00651i) q^{17} +1.28678i q^{18} +(2.13101 + 3.80247i) q^{19} +(-2.74378 - 0.998653i) q^{21} +(-5.72105 + 1.00878i) q^{22} +(-2.90709 + 3.46454i) q^{23} +(-1.00267 + 0.841344i) q^{24} +(-1.41805 + 2.45614i) q^{26} +(-4.85924 + 2.80548i) q^{27} +(0.762972 + 2.09625i) q^{28} +(-0.483478 + 0.175971i) q^{29} +(3.47213 - 6.01390i) q^{31} +(0.984808 + 0.173648i) q^{32} +(-4.88763 - 5.82484i) q^{33} +(-0.820514 - 0.688493i) q^{34} +(1.20918 + 0.440106i) q^{36} +2.58207i q^{37} +(4.30200 - 0.701975i) q^{38} -3.71218 q^{39} +(-0.665458 - 3.77400i) q^{41} +(-1.87685 + 2.23675i) q^{42} +(-5.38018 - 6.41185i) q^{43} +(-1.00878 + 5.72105i) q^{44} +(2.26132 + 3.91672i) q^{46} +(-3.77288 - 10.3659i) q^{47} +(0.447670 + 1.22996i) q^{48} +(-1.01181 - 1.75251i) q^{49} +(0.243449 - 1.38067i) q^{51} +(1.82302 + 2.17259i) q^{52} +(1.89969 - 2.26396i) q^{53} +(0.974334 + 5.52572i) q^{54} +2.23078 q^{56} +(3.61116 + 4.41709i) q^{57} +0.514506i q^{58} +(6.57499 + 2.39310i) q^{59} +(11.2875 + 9.47136i) q^{61} +(-4.46368 - 5.31961i) q^{62} +(2.82692 + 0.498462i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-7.14523 + 2.60065i) q^{66} +(-2.77800 - 7.63250i) q^{67} +(-0.927604 + 0.535552i) q^{68} +(-2.95984 + 5.12659i) q^{69} +(5.09076 - 4.27166i) q^{71} +(0.827128 - 0.985733i) q^{72} +(-3.34414 + 0.589662i) q^{73} +(2.42635 + 0.883120i) q^{74} +(0.811731 - 4.28265i) q^{76} +12.9593i q^{77} +(-1.26964 + 3.48831i) q^{78} +(0.901573 + 5.11307i) q^{79} +(-2.66878 + 2.23937i) q^{81} +(-3.77400 - 0.665458i) q^{82} +(-14.3386 - 8.27838i) q^{83} +(1.45993 + 2.52868i) q^{84} +(-7.86530 + 2.86273i) q^{86} +(-0.583213 + 0.336718i) q^{87} +(5.03101 + 2.90465i) q^{88} +(-0.355224 + 2.01458i) q^{89} +(4.84656 + 4.06675i) q^{91} +(4.45392 - 0.785347i) q^{92} +(3.10873 - 8.54118i) q^{93} -11.0312 q^{94} +1.30890 q^{96} +(1.70458 - 4.68331i) q^{97} +(-1.99288 + 0.351398i) q^{98} +(5.72642 + 4.80504i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 12 q^{11} + 30 q^{14} + 30 q^{19} - 36 q^{21} - 18 q^{26} + 24 q^{29} + 18 q^{31} + 18 q^{34} - 132 q^{39} + 36 q^{41} - 6 q^{46} + 54 q^{49} - 6 q^{51} - 54 q^{54} - 12 q^{56} - 72 q^{59} + 24 q^{61} + 24 q^{64} + 96 q^{66} - 42 q^{69} - 78 q^{71} - 36 q^{74} + 12 q^{76} + 84 q^{79} - 72 q^{81} - 18 q^{84} - 78 q^{86} + 72 q^{89} + 24 q^{91} - 24 q^{94} + 12 q^{96} - 102 q^{99}+O(q^{100}) \) 48 * q - 12 * q^11 + 30 * q^14 + 30 * q^19 - 36 * q^21 - 18 * q^26 + 24 * q^29 + 18 * q^31 + 18 * q^34 - 132 * q^39 + 36 * q^41 - 6 * q^46 + 54 * q^49 - 6 * q^51 - 54 * q^54 - 12 * q^56 - 72 * q^59 + 24 * q^61 + 24 * q^64 + 96 * q^66 - 42 * q^69 - 78 * q^71 - 36 * q^74 + 12 * q^76 + 84 * q^79 - 72 * q^81 - 18 * q^84 - 78 * q^86 + 72 * q^89 + 24 * q^91 - 24 * q^94 + 12 * q^96 - 102 * q^99

Introduction

L-functions

Modular forms

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Database

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