LMFDB - Embedded newform 475.2.u.c.74.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(24,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 16]))

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

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

chi := DirichletCharacter("475.24");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			74.1
Character	$\chi$	$=$	475.74
Dual form			475.2.u.c.199.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.58240 - 0.455347i) q^{2} +(0.597006 - 0.711484i) q^{3} +(4.58206 + 1.66773i) q^{4} +(-1.86568 + 1.56549i) q^{6} +(3.31824 - 1.91579i) q^{7} +(-6.53146 - 3.77094i) q^{8} +(0.371151 + 2.10490i) q^{9} +O(q^{10})$	\(q+(-2.58240 - 0.455347i) q^{2} +(0.597006 - 0.711484i) q^{3} +(4.58206 + 1.66773i) q^{4} +(-1.86568 + 1.56549i) q^{6} +(3.31824 - 1.91579i) q^{7} +(-6.53146 - 3.77094i) q^{8} +(0.371151 + 2.10490i) q^{9} +(1.63362 - 2.82951i) q^{11} +(3.92208 - 2.26441i) q^{12} +(-0.234066 - 0.278949i) q^{13} +(-9.44137 + 3.43638i) q^{14} +(7.67910 + 6.44353i) q^{16} +(0.673822 + 0.118813i) q^{17} -5.60470i q^{18} +(3.86613 - 2.01323i) q^{19} +(0.617958 - 3.50461i) q^{21} +(-5.50706 + 6.56305i) q^{22} +(-3.20407 + 8.80310i) q^{23} +(-6.58228 + 2.39576i) q^{24} +(0.477433 + 0.826939i) q^{26} +(4.13222 + 2.38574i) q^{27} +(18.3994 - 3.24431i) q^{28} +(-0.267393 - 1.51646i) q^{29} +(1.22444 + 2.12080i) q^{31} +(-7.20079 - 8.58157i) q^{32} +(-1.03787 - 2.85152i) q^{33} +(-1.68598 - 0.613646i) q^{34} +(-1.80978 + 10.2638i) q^{36} -0.163399i q^{37} +(-10.9006 + 3.43852i) q^{38} -0.338206 q^{39} +(-5.64858 - 4.73972i) q^{41} +(-3.19163 + 8.76892i) q^{42} +(-0.885107 - 2.43181i) q^{43} +(12.2042 - 10.2405i) q^{44} +(12.2826 - 21.2742i) q^{46} +(8.66316 - 1.52755i) q^{47} +(9.16893 - 1.61673i) q^{48} +(3.84048 - 6.65191i) q^{49} +(0.486809 - 0.408482i) q^{51} +(-0.607292 - 1.66852i) q^{52} +(3.80291 - 10.4484i) q^{53} +(-9.58469 - 8.04251i) q^{54} -28.8973 q^{56} +(0.875722 - 3.95259i) q^{57} +4.03786i q^{58} +(1.35268 - 7.67146i) q^{59} +(-2.27305 - 0.827322i) q^{61} +(-2.19630 - 6.03429i) q^{62} +(5.26412 + 6.27353i) q^{63} +(4.66339 + 8.07723i) q^{64} +(1.38176 + 7.83636i) q^{66} +(-9.41216 + 1.65962i) q^{67} +(2.88935 + 1.66816i) q^{68} +(4.35042 + 7.53515i) q^{69} +(4.81203 - 1.75144i) q^{71} +(5.51331 - 15.1477i) q^{72} +(5.06782 - 6.03960i) q^{73} +(-0.0744033 + 0.421962i) q^{74} +(21.0723 - 2.77705i) q^{76} -12.5186i q^{77} +(0.873384 + 0.154001i) q^{78} +(7.14004 + 5.99121i) q^{79} +(-1.86106 + 0.677369i) q^{81} +(12.4287 + 14.8119i) q^{82} +(0.631436 - 0.364559i) q^{83} +(8.67627 - 15.0277i) q^{84} +(1.17838 + 6.68294i) q^{86} +(-1.23857 - 0.715090i) q^{87} +(-21.3398 + 12.3205i) q^{88} +(-9.68319 + 8.12516i) q^{89} +(-1.31109 - 0.477199i) q^{91} +(-29.3625 + 34.9928i) q^{92} +(2.23991 + 0.394957i) q^{93} -23.0673 q^{94} -10.4046 q^{96} +(7.43249 + 1.31055i) q^{97} +(-12.9466 + 15.4291i) q^{98} +(6.56216 + 2.38843i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 6 q^{4} - 12 q^{6} + 42 q^{9}+O(q^{10}) $ 36 * q + 6 * q^4 - 12 * q^6 + 42 * q^9	$ 36 q + 6 q^{4} - 12 q^{6} + 42 q^{9} - 48 q^{14} + 42 q^{16} + 24 q^{19} + 6 q^{21} - 42 q^{24} - 42 q^{26} + 18 q^{29} + 60 q^{31} - 48 q^{34} - 42 q^{36} - 24 q^{39} - 12 q^{41} + 60 q^{44} + 42 q^{46} + 6 q^{49} + 54 q^{51} - 60 q^{54} - 144 q^{56} - 36 q^{59} + 12 q^{61} + 48 q^{64} - 66 q^{66} - 54 q^{69} + 48 q^{71} + 78 q^{74} + 54 q^{76} - 18 q^{79} + 30 q^{81} + 24 q^{84} - 66 q^{86} + 12 q^{89} - 12 q^{91} + 132 q^{94} - 36 q^{96} - 6 q^{99}+O(q^{100}) $ 36 * q + 6 * q^4 - 12 * q^6 + 42 * q^9 - 48 * q^14 + 42 * q^16 + 24 * q^19 + 6 * q^21 - 42 * q^24 - 42 * q^26 + 18 * q^29 + 60 * q^31 - 48 * q^34 - 42 * q^36 - 24 * q^39 - 12 * q^41 + 60 * q^44 + 42 * q^46 + 6 * q^49 + 54 * q^51 - 60 * q^54 - 144 * q^56 - 36 * q^59 + 12 * q^61 + 48 * q^64 - 66 * q^66 - 54 * q^69 + 48 * q^71 + 78 * q^74 + 54 * q^76 - 18 * q^79 + 30 * q^81 + 24 * q^84 - 66 * q^86 + 12 * q^89 - 12 * q^91 + 132 * q^94 - 36 * q^96 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{5}{9}\right)$

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 $

$2$	−2.58240	−	0.455347i	−1.82603	−	0.321979i	−0.847930	−	0.530108i	$-0.822152\pi$
$2$	−2.58240	−	0.455347i	−1.82603	−	0.321979i	−0.978101	+	0.208129i	$0.933263\pi$
$3$	0.597006	−	0.711484i	0.344681	−	0.410775i	−0.565657	−	0.824641i	$-0.691377\pi$
$3$	0.597006	−	0.711484i	0.344681	−	0.410775i	0.910338	+	0.413866i	$0.135822\pi$
$4$	4.58206	+	1.66773i	2.29103	+	0.833867i
$5$		0			0
$5$		0			0
$6$	−1.86568	+	1.56549i	−0.761660	+	0.639109i
$7$	3.31824	−	1.91579i	1.25418	−	0.724100i	0.282241	−	0.959344i	$-0.408922\pi$
$7$	3.31824	−	1.91579i	1.25418	−	0.724100i	0.971936	+	0.235244i	$0.0755889\pi$
$8$	−6.53146	−	3.77094i	−2.30922	−	1.33323i
$9$	0.371151	+	2.10490i	0.123717	+	0.701634i
$10$		0			0
$11$	1.63362	−	2.82951i	0.492554	−	0.853128i	−0.507409	−	0.861705i	$-0.669397\pi$
$11$	1.63362	−	2.82951i	0.492554	−	0.853128i	0.999963	+	0.00857679i	$0.00273011\pi$
$12$	3.92208	−	2.26441i	1.13221	−	0.653680i
$13$	−0.234066	−	0.278949i	−0.0649182	−	0.0773665i	0.732608	−	0.680651i	$-0.238303\pi$
$13$	−0.234066	−	0.278949i	−0.0649182	−	0.0773665i	−0.797526	+	0.603284i	$0.793858\pi$
$14$	−9.44137	+	3.43638i	−2.52331	+	0.918411i
$15$		0			0
$16$	7.67910	+	6.44353i	1.91977	+	1.61088i
$17$	0.673822	+	0.118813i	0.163426	+	0.0288164i	0.254762	−	0.967004i	$-0.418003\pi$
$17$	0.673822	+	0.118813i	0.163426	+	0.0288164i	−0.0913364	+	0.995820i	$0.529114\pi$
$18$		−	5.60470i		−	1.32104i
$19$	3.86613	−	2.01323i	0.886950	−	0.461866i
$19$	3.86613	−	2.01323i	0.886950	−	0.461866i
$20$		0			0
$21$	0.617958	−	3.50461i	0.134849	−	0.764769i
$22$	−5.50706	+	6.56305i	−1.17411	+	1.39925i
$23$	−3.20407	+	8.80310i	−0.668094	+	1.83557i	−0.132331	+	0.991206i	$0.542246\pi$
$23$	−3.20407	+	8.80310i	−0.668094	+	1.83557i	−0.535763	+	0.844368i	$0.679976\pi$
$24$	−6.58228	+	2.39576i	−1.34360	+	0.489031i
$25$		0			0
$26$	0.477433	+	0.826939i	0.0936324	+	0.162176i
$27$	4.13222	+	2.38574i	0.795245	+	0.459135i
$28$	18.3994	−	3.24431i	3.47716	−	0.613117i
$29$	−0.267393	−	1.51646i	−0.0496536	−	0.281600i	0.949864	−	0.312664i	$-0.101221\pi$
$29$	−0.267393	−	1.51646i	−0.0496536	−	0.281600i	−0.999517	+	0.0310645i	$0.990110\pi$
$30$		0			0
$31$	1.22444	+	2.12080i	0.219916	+	0.380906i	0.954782	−	0.297306i	$-0.0960882\pi$
$31$	1.22444	+	2.12080i	0.219916	+	0.380906i	−0.734866	+	0.678213i	$0.762755\pi$
$32$	−7.20079	−	8.58157i	−1.27293	−	1.51702i
$33$	−1.03787	−	2.85152i	−0.180670	−	0.496387i
$34$	−1.68598	−	0.613646i	−0.289143	−	0.105239i
$35$		0			0
$36$	−1.80978	+	10.2638i	−0.301630	+	1.71063i
$37$		−	0.163399i		−	0.0268627i	−0.999910	−	0.0134313i	$-0.995725\pi$
$37$		−	0.163399i		−	0.0268627i	0.999910	−	0.0134313i	$-0.00427545\pi$
$38$	−10.9006	+	3.43852i	−1.76831	+	0.557802i
$39$	−0.338206			−0.0541564
$40$		0			0
$41$	−5.64858	−	4.73972i	−0.882160	−	0.740220i	0.0844622	−	0.996427i	$-0.473083\pi$
$41$	−5.64858	−	4.73972i	−0.882160	−	0.740220i	−0.966622	+	0.256207i	$0.917527\pi$
$42$	−3.19163	+	8.76892i	−0.492479	+	1.35307i
$43$	−0.885107	−	2.43181i	−0.134978	−	0.370848i	0.853728	−	0.520719i	$-0.174336\pi$
$43$	−0.885107	−	2.43181i	−0.134978	−	0.370848i	−0.988705	+	0.149872i	$0.952114\pi$
$44$	12.2042	−	10.2405i	1.83985	−	1.54382i
$45$		0			0
$46$	12.2826	−	21.2742i	1.81098	−	3.13670i
$47$	8.66316	−	1.52755i	1.26365	−	0.222816i	0.498627	−	0.866817i	$-0.333838\pi$
$47$	8.66316	−	1.52755i	1.26365	−	0.222816i	0.765025	+	0.644001i	$0.222727\pi$
$48$	9.16893	−	1.61673i	1.32342	−	0.233355i
$49$	3.84048	−	6.65191i	0.548640	−	0.950273i
$50$		0			0
$51$	0.486809	−	0.408482i	0.0681670	−	0.0571989i
$52$	−0.607292	−	1.66852i	−0.0842162	−	0.231382i
$53$	3.80291	−	10.4484i	0.522370	−	1.43520i	−0.345505	−	0.938417i	$-0.612292\pi$
$53$	3.80291	−	10.4484i	0.522370	−	1.43520i	0.867875	−	0.496783i	$-0.165485\pi$
$54$	−9.58469	−	8.04251i	−1.30431	−	1.09445i
$55$		0			0
$56$	−28.8973			−3.86156
$57$	0.875722	−	3.95259i	0.115992	−	0.523534i
$58$			4.03786i			0.530197i
$59$	1.35268	−	7.67146i	0.176105	−	0.998739i	−0.760757	−	0.649037i	$-0.775172\pi$
$59$	1.35268	−	7.67146i	0.176105	−	0.998739i	0.936861	−	0.349701i	$-0.113717\pi$
$60$		0			0
$61$	−2.27305	−	0.827322i	−0.291034	−	0.105928i	0.192377	−	0.981321i	$-0.438380\pi$
$61$	−2.27305	−	0.827322i	−0.291034	−	0.105928i	−0.483411	+	0.875393i	$0.660602\pi$
$62$	−2.19630	−	6.03429i	−0.278931	−	0.766356i
$63$	5.26412	+	6.27353i	0.663216	+	0.790391i
$64$	4.66339	+	8.07723i	0.582924	+	1.00965i
$65$		0			0
$66$	1.38176	+	7.83636i	0.170083	+	0.964590i
$67$	−9.41216	+	1.65962i	−1.14988	+	0.202755i	−0.715923	−	0.698180i	$-0.753994\pi$
$67$	−9.41216	+	1.65962i	−1.14988	+	0.202755i	−0.433956	+	0.900934i	$0.642883\pi$
$68$	2.88935	+	1.66816i	0.350385	+	0.202295i
$69$	4.35042	+	7.53515i	0.523729	+	0.907125i
$70$		0			0
$71$	4.81203	−	1.75144i	0.571083	−	0.207857i	−0.0403062	−	0.999187i	$-0.512833\pi$
$71$	4.81203	−	1.75144i	0.571083	−	0.207857i	0.611389	+	0.791330i	$0.290611\pi$
$72$	5.51331	−	15.1477i	0.649749	−	1.78517i
$73$	5.06782	−	6.03960i	0.593144	−	0.706881i	−0.383063	−	0.923722i	$-0.625131\pi$
$73$	5.06782	−	6.03960i	0.593144	−	0.706881i	0.976207	+	0.216841i	$0.0695753\pi$
$74$	−0.0744033	+	0.421962i	−0.00864920	+	0.0490521i
$75$		0			0
$76$	21.0723	−	2.77705i	2.41716	−	0.318550i
$77$		−	12.5186i		−	1.42663i
$78$	0.873384	+	0.154001i	0.0988913	+	0.0174372i
$79$	7.14004	+	5.99121i	0.803317	+	0.674063i	0.949003	−	0.315268i	$-0.102094\pi$
$79$	7.14004	+	5.99121i	0.803317	+	0.674063i	−0.145685	+	0.989331i	$0.546539\pi$
$80$		0			0
$81$	−1.86106	+	0.677369i	−0.206784	+	0.0752633i
$82$	12.4287	+	14.8119i	1.37252	+	1.63570i
$83$	0.631436	−	0.364559i	0.0693091	−	0.0400156i	−0.464945	−	0.885340i	$-0.653926\pi$
$83$	0.631436	−	0.364559i	0.0693091	−	0.0400156i	0.534254	+	0.845324i	$0.320593\pi$
$84$	8.67627	−	15.0277i	0.946659	−	1.63966i
$85$		0			0
$86$	1.17838	+	6.68294i	0.127068	+	0.720640i
$87$	−1.23857	−	0.715090i	−0.132789	−	0.0766657i
$88$	−21.3398	+	12.3205i	−2.27483	+	1.31337i
$89$	−9.68319	+	8.12516i	−1.02642	+	0.861265i	−0.990420	−	0.138087i	$-0.955905\pi$
$89$	−9.68319	+	8.12516i	−1.02642	+	0.861265i	−0.0359958	+	0.999352i	$0.511460\pi$
$90$		0			0
$91$	−1.31109	−	0.477199i	−0.137440	−	0.0500241i
$92$	−29.3625	+	34.9928i	−3.06125	+	3.64825i
$93$	2.23991	+	0.394957i	0.232268	+	0.0409551i
$94$	−23.0673			−2.37921
$95$		0			0
$96$	−10.4046			−1.06191
$97$	7.43249	+	1.31055i	0.754655	+	0.133066i	0.537724	−	0.843121i	$-0.319284\pi$
$97$	7.43249	+	1.31055i	0.754655	+	0.133066i	0.216931	+	0.976187i	$0.430395\pi$
$98$	−12.9466	+	15.4291i	−1.30780	+	1.55858i
$99$	6.56216	+	2.38843i	0.659522	+	0.240046i
$100$		0			0
$101$	3.10910	−	2.60884i	0.309367	−	0.259589i	−0.474864	−	0.880059i	$-0.657503\pi$
$101$	3.10910	−	2.60884i	0.309367	−	0.259589i	0.784230	+	0.620470i	$0.213058\pi$
$102$	−1.44314	+	0.833196i	−0.142892	+	0.0824987i
$103$	−11.9321	−	6.88900i	−1.17571	−	0.678794i	−0.220688	−	0.975344i	$-0.570830\pi$
$103$	−11.9321	−	6.88900i	−1.17571	−	0.678794i	−0.955017	+	0.296551i	$0.904164\pi$
$104$	0.476893	+	2.70459i	0.0467632	+	0.265207i
$105$		0			0
$106$	−14.5783	+	25.2503i	−1.41597	+	2.45253i
$107$	−5.65047	+	3.26230i	−0.546252	+	0.315379i	−0.747609	−	0.664139i	$-0.768798\pi$
$107$	−5.65047	+	3.26230i	−0.546252	+	0.315379i	0.201357	+	0.979518i	$0.435465\pi$
$108$	14.9553	+	17.8230i	1.43907	+	1.71502i
$109$	−8.46545	+	3.08117i	−0.810843	+	0.295123i	−0.713972	−	0.700174i	$-0.753106\pi$
$109$	−8.46545	+	3.08117i	−0.810843	+	0.295123i	−0.0968707	+	0.995297i	$0.530883\pi$
$110$		0			0
$111$	−0.116256	−	0.0975503i	−0.0110345	−	0.00925906i
$112$	37.8255	+	6.66966i	3.57418	+	0.630224i
$113$			13.1464i			1.23670i	0.785901	+	0.618352i	$0.212200\pi$
$113$			13.1464i			1.23670i	−0.785901	+	0.618352i	$0.787800\pi$
$114$	−4.06126	+	9.80841i	−0.380372	+	0.918642i
$115$		0			0
$116$	1.30384	−	7.39445i	0.121059	−	0.686557i
$117$	0.500287	−	0.596218i	0.0462515	−	0.0551204i
$118$	−6.98634	+	19.1948i	−0.643145	+	1.76703i
$119$	2.46353	−	0.896650i	0.225831	−	0.0821958i
$120$		0			0
$121$	0.162595	+	0.281622i	0.0147813	+	0.0256020i
$122$	5.49320	+	3.17150i	0.497331	+	0.287134i
$123$	−6.74447	+	1.18923i	−0.608128	+	0.107229i
$124$	2.07355	+	11.7597i	0.186210	+	1.05605i
$125$		0			0
$126$	−10.7374	−	18.5978i	−0.956565	−	1.65682i
$127$	5.63783	+	6.71890i	0.500276	+	0.596206i	0.955800	−	0.294018i	$-0.0949924\pi$
$127$	5.63783	+	6.71890i	0.500276	+	0.596206i	−0.455524	+	0.890224i	$0.650548\pi$
$128$	−0.701866	−	1.92836i	−0.0620368	−	0.170445i
$129$	−2.25861	−	0.822066i	−0.198859	−	0.0723789i
$130$		0			0
$131$	1.80469	−	10.2349i	0.157676	−	0.894226i	−0.798622	−	0.601833i	$-0.794437\pi$
$131$	1.80469	−	10.2349i	0.157676	−	0.894226i	0.956298	−	0.292393i	$-0.0944515\pi$
$132$		−	14.7967i		−	1.28789i
$133$	8.97182	−	14.0870i	0.777956	−	1.22150i
$134$	25.0616			2.16500
$135$		0			0
$136$	−3.95301	−	3.31697i	−0.338968	−	0.284428i
$137$	−1.21940	+	3.35026i	−0.104180	+	0.286232i	−0.980820	−	0.194914i	$-0.937557\pi$
$137$	−1.21940	+	3.35026i	−0.104180	+	0.286232i	0.876640	+	0.481146i	$0.159779\pi$
$138$	−7.80341	−	21.4397i	−0.664271	−	1.82507i
$139$	−6.64270	+	5.57389i	−0.563427	+	0.472771i	−0.879457	−	0.475978i	$-0.842094\pi$
$139$	−6.64270	+	5.57389i	−0.563427	+	0.472771i	0.316030	+	0.948749i	$0.397650\pi$
$140$		0			0
$141$	4.08513	−	7.07565i	0.344030	−	0.595877i
$142$	−13.2241	+	2.33176i	−1.10974	+	0.195677i
$143$	−1.17166	+	0.206596i	−0.0979793	+	0.0172764i
$144$	−10.7129	+	18.5553i	−0.892741	+	1.54627i
$145$		0			0
$146$	−15.8373	+	13.2890i	−1.31070	+	1.09981i
$147$	−2.43994	−	6.70367i	−0.201243	−	0.552910i
$148$	0.272506	−	0.748705i	0.0223999	−	0.0615431i
$149$	12.9946	+	10.9038i	1.06456	+	0.893274i	0.994549	−	0.104272i	$-0.0332513\pi$
$149$	12.9946	+	10.9038i	1.06456	+	0.893274i	0.0700136	+	0.997546i	$0.477696\pi$
$150$		0			0
$151$	−11.0821			−0.901849			−0.450925	−	0.892562i	$-0.648906\pi$
$151$	−11.0821			−0.901849			−0.450925	+	0.892562i	$0.648906\pi$
$152$	−32.8432	−	1.42963i	−2.66394	−	0.115958i
$153$			1.46243i			0.118230i
$154$	−5.70032	+	32.3281i	−0.459345	+	2.60508i
$155$		0			0
$156$	−1.54968	−	0.564038i	−0.124074	−	0.0451592i
$157$	−0.318919	−	0.876222i	−0.0254525	−	0.0699302i	0.926316	−	0.376748i	$-0.122958\pi$
$157$	−0.318919	−	0.876222i	−0.0254525	−	0.0699302i	−0.951768	+	0.306818i	$0.900736\pi$
$158$	−15.7104	−	18.7229i	−1.24985	−	1.48951i
$159$	−5.16352	−	8.94347i	−0.409493	−	0.709264i
$160$		0			0
$161$	6.23301	+	35.3491i	0.491230	+	2.78590i
$162$	5.11443	−	0.901812i	0.401828	−	0.0708530i
$163$	−6.99149	−	4.03654i	−0.547616	−	0.316166i	0.200544	−	0.979685i	$-0.435729\pi$
$163$	−6.99149	−	4.03654i	−0.547616	−	0.316166i	−0.748160	+	0.663519i	$0.769062\pi$
$164$	−17.9775	−	31.1380i	−1.40381	−	2.43147i
$165$		0			0
$166$	−1.79662	+	0.653916i	−0.139445	+	0.0507537i
$167$	4.66839	−	12.8263i	0.361251	−	0.992529i	−0.617337	−	0.786699i	$-0.711788\pi$
$167$	4.66839	−	12.8263i	0.361251	−	0.992529i	0.978588	−	0.205830i	$-0.0659895\pi$
$168$	−17.2518	+	20.5599i	−1.33101	+	1.58623i
$169$	2.23440	−	12.6719i	0.171877	−	0.974763i
$170$		0			0
$171$	5.67256	+	7.39061i	0.433792	+	0.565174i
$172$		−	12.6188i		−	0.962176i
$173$	8.24695	+	1.45416i	0.627004	+	0.110558i	0.478117	−	0.878296i	$-0.341320\pi$
$173$	8.24695	+	1.45416i	0.627004	+	0.110558i	0.148888	+	0.988854i	$0.452431\pi$
$174$	2.87287	+	2.41063i	0.217792	+	0.182749i
$175$		0			0
$176$	30.7767	−	11.2018i	2.31988	−	0.844368i
$177$	−4.65056	−	5.54232i	−0.349557	−	0.416586i
$178$	28.7056	−	16.5732i	2.15158	−	1.24221i
$179$	−2.85227	+	4.94028i	−0.213189	+	0.369254i	−0.952711	−	0.303879i	$-0.901718\pi$
$179$	−2.85227	+	4.94028i	−0.213189	+	0.369254i	0.739522	+	0.673132i	$0.235052\pi$
$180$		0			0
$181$	2.57719	+	14.6160i	0.191561	+	1.08640i	0.917231	+	0.398355i	$0.130419\pi$
$181$	2.57719	+	14.6160i	0.191561	+	1.08640i	−0.725670	+	0.688043i	$0.758470\pi$
$182$	3.16848	+	1.82932i	0.234863	+	0.135598i
$183$	−1.94565	+	1.12332i	−0.143827	+	0.0830383i
$184$	54.1232	−	45.4148i	3.99002	−	3.34802i
$185$		0			0
$186$	−5.60451	−	2.03987i	−0.410942	−	0.149571i
$187$	1.43695	−	1.71249i	0.105080	−	0.125230i
$188$	42.2426	+	7.44852i	3.08086	+	0.543239i
$189$	18.2822			1.32984
$190$		0			0
$191$	−19.7204			−1.42692			−0.713460	−	0.700695i	$-0.752873\pi$
$191$	−19.7204			−1.42692			−0.713460	+	0.700695i	$0.752873\pi$
$192$	8.53088	+	1.50423i	0.615664	+	0.108558i
$193$	2.65500	−	3.16411i	0.191111	−	0.227758i	−0.661977	−	0.749524i	$-0.730282\pi$
$193$	2.65500	−	3.16411i	0.191111	−	0.227758i	0.853088	+	0.521767i	$0.174727\pi$
$194$	−18.5969	−	6.76871i	−1.33518	−	0.485965i
$195$		0			0
$196$	28.6909	−	24.0746i	2.04935	−	1.71961i
$197$	−0.144293	+	0.0833078i	−0.0102805	+	0.00593544i	−0.505131	−	0.863042i	$-0.668556\pi$
$197$	−0.144293	+	0.0833078i	−0.0102805	+	0.00593544i	0.494851	+	0.868978i	$0.335223\pi$
$198$	−15.8585	−	9.15593i	−1.12702	−	0.650684i
$199$	0.900606	+	5.10759i	0.0638423	+	0.362068i	0.999946	+	0.0103448i	$0.00329292\pi$
$199$	0.900606	+	5.10759i	0.0638423	+	0.362068i	−0.936104	+	0.351723i	$0.885596\pi$
$200$		0			0
$201$	−4.43832	+	7.68740i	−0.313055	+	0.542227i
$202$	−9.21685	+	5.32135i	−0.648495	+	0.374409i
$203$	−3.79249	−	4.51971i	−0.266181	−	0.317222i
$204$	2.91183	−	1.05982i	0.203869	−	0.0742022i
$205$		0			0
$206$	27.6766	+	23.2234i	1.92832	+	1.61805i
$207$	−19.7189	−	3.47697i	−1.37056	−	0.241666i
$208$		−	3.65029i		−	0.253102i
$209$	0.619331	−	14.2281i	0.0428400	−	0.984176i
$210$		0			0
$211$	−0.853752	+	4.84187i	−0.0587747	+	0.333328i	−0.999990	−	0.00447940i	$-0.998574\pi$
$211$	−0.853752	+	4.84187i	−0.0587747	+	0.333328i	0.941215	+	0.337807i	$0.109685\pi$
$212$	34.8503	−	41.5330i	2.39353	−	2.85250i
$213$	1.62669	−	4.46930i	0.111459	−	0.306231i
$214$	16.0772	−	5.85164i	1.09902	−	0.400010i
$215$		0			0
$216$	−17.9929	−	31.1647i	−1.22426	−	2.12049i
$217$	8.12599	+	4.69155i	0.551628	+	0.318483i
$218$	23.2642	−	4.10210i	1.57565	−	0.277829i
$219$	−1.27156	−	7.21135i	−0.0859237	−	0.487298i
$220$		0			0
$221$	−0.124576	−	0.215772i	−0.00837990	−	0.0145144i
$222$	0.255800	+	0.304850i	0.0171682	+	0.0204602i
$223$	2.99672	+	8.23341i	0.200675	+	0.551350i	0.998683	−	0.0512961i	$-0.0163352\pi$
$223$	2.99672	+	8.23341i	0.200675	+	0.551350i	−0.798008	+	0.602646i	$0.794113\pi$
$224$	−40.3344	−	14.6805i	−2.69496	−	0.980885i
$225$		0			0
$226$	5.98615	−	33.9491i	0.398193	−	2.25826i
$227$			5.53943i			0.367665i	0.982958	+	0.183833i	$0.0588504\pi$
$227$			5.53943i			0.367665i	−0.982958	+	0.183833i	$0.941150\pi$
$228$	10.6045	−	16.6505i	0.702299	−	1.10271i
$229$	−26.8762			−1.77603			−0.888014	−	0.459816i	$-0.847915\pi$
$229$	−26.8762			−1.77603			−0.888014	+	0.459816i	$0.847915\pi$
$230$		0			0
$231$	−8.90682	−	7.47371i	−0.586025	−	0.491734i
$232$	−3.97201	+	10.9130i	−0.260776	+	0.716475i
$233$	−0.873055	−	2.39870i	−0.0571958	−	0.157144i	0.907804	−	0.419394i	$-0.137758\pi$
$233$	−0.873055	−	2.39870i	−0.0571958	−	0.157144i	−0.965000	+	0.262250i	$0.915535\pi$
$234$	−1.56343	+	1.31187i	−0.102204	+	0.0857596i
$235$		0			0
$236$	18.9920	−	32.8952i	1.23628	−	2.14129i
$237$	8.52529	−	1.50324i	0.553777	−	0.0976459i
$238$	−6.77009	+	1.19375i	−0.438840	+	0.0773793i
$239$	−12.7663	+	22.1119i	−0.825784	+	1.43030i	0.0755339	+	0.997143i	$0.475934\pi$
$239$	−12.7663	+	22.1119i	−0.825784	+	1.43030i	−0.901318	+	0.433157i	$0.857399\pi$
$240$		0			0
$241$	−0.759825	+	0.637569i	−0.0489446	+	0.0410694i	−0.666932	−	0.745119i	$-0.732393\pi$
$241$	−0.759825	+	0.637569i	−0.0489446	+	0.0410694i	0.617987	+	0.786188i	$0.287948\pi$
$242$	−0.291648	−	0.801298i	−0.0187479	−	0.0515094i
$243$	−5.52494	+	15.1797i	−0.354425	+	0.973775i
$244$	−9.03549	−	7.58168i	−0.578438	−	0.485367i
$245$		0			0
$246$	17.9584			1.14499
$247$	−1.46652	−	0.607224i	−0.0933121	−	0.0386367i
$248$		−	18.4692i		−	1.17280i
$249$	0.117593	−	0.666900i	0.00745212	−	0.0422631i
$250$		0			0
$251$	13.6599	+	4.97181i	0.862207	+	0.313818i	0.735007	−	0.678059i	$-0.237179\pi$
$251$	13.6599	+	4.97181i	0.862207	+	0.313818i	0.127200	+	0.991877i	$0.459401\pi$
$252$	13.6579	+	37.5248i	0.860368	+	2.36384i
$253$	19.6742	+	23.4468i	1.23691	+	1.47409i
$254$	−11.4997	−	19.9180i	−0.721555	−	1.24977i
$255$		0			0
$256$	−2.30473	−	13.0708i	−0.144046	−	0.816923i
$257$	−16.9069	+	2.98115i	−1.05463	+	0.185959i	−0.673971	−	0.738758i	$-0.735413\pi$
$257$	−16.9069	+	2.98115i	−1.05463	+	0.185959i	−0.380655	+	0.924717i	$0.624302\pi$
$258$	5.45830	+	3.15135i	0.339819	+	0.196195i
$259$	−0.313038	−	0.542198i	−0.0194512	−	0.0336905i
$260$		0			0
$261$	3.09276	−	1.12567i	0.191437	−	0.0696773i
$262$	−9.32083	+	25.6088i	−0.575843	+	1.58212i
$263$	−0.806105	+	0.960678i	−0.0497066	+	0.0592380i	−0.790325	−	0.612688i	$-0.790088\pi$
$263$	−0.806105	+	0.960678i	−0.0497066	+	0.0592380i	0.740618	+	0.671926i	$0.234533\pi$
$264$	−3.97412	+	22.5384i	−0.244590	+	1.38714i
$265$		0			0
$266$	−29.5833	+	32.2931i	−1.81387	+	1.98002i
$267$			11.7402i			0.718489i
$268$	−45.8949	−	8.09250i	−2.80347	−	0.494328i
$269$	10.4753	+	8.78981i	0.638689	+	0.535924i	0.903615	−	0.428345i	$-0.140903\pi$
$269$	10.4753	+	8.78981i	0.638689	+	0.535924i	−0.264926	+	0.964269i	$0.585348\pi$
$270$		0			0
$271$	−12.6289	+	4.59653i	−0.767150	+	0.279220i	−0.695804	−	0.718232i	$-0.744952\pi$
$271$	−12.6289	+	4.59653i	−0.767150	+	0.279220i	−0.0713459	+	0.997452i	$0.522729\pi$
$272$	4.40877	+	5.25417i	0.267321	+	0.318581i
$273$	−1.12225	+	0.647932i	−0.0679217	+	0.0392146i
$274$	4.67450	−	8.09647i	0.282397	−	0.489126i
$275$		0			0
$276$	7.36726	+	41.7818i	0.443457	+	2.51497i
$277$	−10.4219	−	6.01711i	−0.626194	−	0.361533i	0.153083	−	0.988213i	$-0.451080\pi$
$277$	−10.4219	−	6.01711i	−0.626194	−	0.361533i	−0.779277	+	0.626680i	$0.784413\pi$
$278$	19.6922	−	11.3693i	1.18106	−	0.681884i
$279$	−4.00962	+	3.36447i	−0.240050	+	0.201426i
$280$		0			0
$281$	13.4574	+	4.89810i	0.802802	+	0.292196i	0.710647	−	0.703549i	$-0.248402\pi$
$281$	13.4574	+	4.89810i	0.802802	+	0.292196i	0.0921549	+	0.995745i	$0.470625\pi$
$282$	−13.7713	+	16.4120i	−0.820069	+	0.977321i
$283$	5.22943	+	0.922089i	0.310857	+	0.0548125i	0.326900	−	0.945059i	$-0.393996\pi$
$283$	5.22943	+	0.922089i	0.310857	+	0.0548125i	−0.0160432	+	0.999871i	$0.505107\pi$
$284$	24.9699			1.48169
$285$		0			0
$286$	3.11977			0.184476
$287$	−27.8236	−	4.90606i	−1.64238	−	0.289596i
$288$	15.3908	−	18.3420i	0.906911	−	1.08081i
$289$	−15.5349	−	5.65422i	−0.913815	−	0.332601i
$290$		0			0
$291$	5.36967	−	4.50569i	0.314776	−	0.264128i
$292$	33.2935	−	19.2220i	1.94835	−	1.12488i
$293$	0.766360	+	0.442458i	0.0447712	+	0.0258487i	0.522219	−	0.852812i	$-0.325105\pi$
$293$	0.766360	+	0.442458i	0.0447712	+	0.0258487i	−0.477447	+	0.878660i	$0.658438\pi$
$294$	3.24840	+	18.4226i	0.189450	+	1.07443i
$295$		0			0
$296$	−0.616169	+	1.06724i	−0.0358141	+	0.0620318i
$297$	13.5009	−	7.79475i	0.783402	−	0.452297i
$298$	−28.5923	−	34.0750i	−1.65631	−	1.97391i
$299$	3.20558	−	1.16674i	0.185383	−	0.0674741i
$300$		0			0
$301$	−7.59583	−	6.37366i	−0.437816	−	0.367372i
$302$	28.6184	+	5.04620i	1.64681	+	0.290376i
$303$		−	3.76956i		−	0.216556i
$304$	42.6606	+	9.45173i	2.44675	+	0.542094i
$305$		0			0
$306$	0.665912	−	3.77657i	0.0380677	−	0.215892i
$307$	−15.9728	+	19.0356i	−0.911614	+	1.08642i	0.0843293	+	0.996438i	$0.473125\pi$
$307$	−15.9728	+	19.0356i	−0.911614	+	1.08642i	−0.995943	+	0.0899815i	$0.971319\pi$
$308$	20.8778	−	57.3612i	1.18962	−	3.26846i
$309$	−12.0250	+	4.37672i	−0.684076	+	0.248983i
$310$		0			0
$311$	−9.25003	−	16.0215i	−0.524521	−	0.908497i	−0.999592	−	0.0285497i	$-0.990911\pi$
$311$	−9.25003	−	16.0215i	−0.524521	−	0.908497i	0.475071	−	0.879947i	$-0.342422\pi$
$312$	2.20898	+	1.27536i	0.125059	+	0.0722028i
$313$	−32.7069	+	5.76710i	−1.84870	+	0.325976i	−0.984256	−	0.176751i	$-0.943441\pi$
$313$	−32.7069	+	5.76710i	−1.84870	+	0.325976i	−0.864445	+	0.502727i	$0.832330\pi$
$314$	0.424591	+	2.40797i	0.0239611	+	0.135890i
$315$		0			0
$316$	22.7244	+	39.3597i	1.27835	+	2.21416i
$317$	−4.24865	−	5.06335i	−0.238628	−	0.284386i	0.633418	−	0.773810i	$-0.281651\pi$
$317$	−4.24865	−	5.06335i	−0.238628	−	0.284386i	−0.872046	+	0.489424i	$0.837207\pi$
$318$	9.26188	+	25.4468i	0.519380	+	1.42699i
$319$	−4.72765	−	1.72072i	−0.264698	−	0.0963420i
$320$		0			0
$321$	−1.05229	+	5.96783i	−0.0587331	+	0.333092i
$322$		−	94.1237i		−	5.24531i
$323$	2.84428	−	0.897210i	0.158260	−	0.0499221i
$324$	−9.65715			−0.536508
$325$		0			0
$326$	16.2168	+	13.6075i	0.898165	+	0.753650i
$327$	−2.86172	+	7.86250i	−0.158253	+	0.434797i
$328$	19.0203	+	52.2578i	1.05022	+	2.88545i
$329$	25.8200	−	21.6655i	1.42350	−	1.19446i
$330$		0			0
$331$	−8.25075	+	14.2907i	−0.453502	+	0.785489i	−0.998601	−	0.0528830i	$-0.983159\pi$
$331$	−8.25075	+	14.2907i	−0.453502	+	0.785489i	0.545098	+	0.838372i	$0.316492\pi$
$332$	3.50126	−	0.617367i	0.192157	−	0.0338824i
$333$	0.343939	−	0.0606458i	0.0188478	−	0.00332337i
$334$	−17.8961	+	30.9969i	−0.979229	+	1.69608i
$335$		0			0
$336$	27.3274	−	22.9304i	1.49083	−	1.25096i
$337$	−2.03595	−	5.59372i	−0.110905	−	0.304709i	0.871807	−	0.489849i	$-0.162948\pi$
$337$	−2.03595	−	5.59372i	−0.110905	−	0.304709i	−0.982712	+	0.185140i	$0.940726\pi$
$338$	−11.5402	+	31.7065i	−0.627706	+	1.72461i
$339$	9.35342	+	7.84845i	0.508008	+	0.426269i
$340$		0			0
$341$	8.00108			0.433283
$342$	−11.2835	−	21.6685i	−0.610143	−	1.17170i
$343$		−	2.60918i		−	0.140882i
$344$	−3.38917	+	19.2210i	−0.182732	+	1.03632i
$345$		0			0
$346$	−20.6348	−	7.51044i	−1.10933	−	0.403764i
$347$	7.39194	+	20.3092i	0.396820	+	1.09025i	0.963824	+	0.266539i	$0.0858802\pi$
$347$	7.39194	+	20.3092i	0.396820	+	1.09025i	−0.567004	+	0.823715i	$0.691898\pi$
$348$	−4.48263	−	5.34219i	−0.240294	−	0.286371i
$349$	−1.21095	−	2.09743i	−0.0648208	−	0.112273i	0.831794	−	0.555085i	$-0.187314\pi$
$349$	−1.21095	−	2.09743i	−0.0648208	−	0.112273i	−0.896614	+	0.442812i	$0.853981\pi$
$350$		0			0
$351$	−0.301713	−	1.71110i	−0.0161042	−	0.0913316i
$352$	−36.0450	+	6.35570i	−1.92120	+	0.338760i
$353$	−6.62643	−	3.82577i	−0.352690	−	0.203625i	0.313180	−	0.949694i	$-0.398606\pi$
$353$	−6.62643	−	3.82577i	−0.352690	−	0.203625i	−0.665869	+	0.746069i	$0.731939\pi$
$354$	9.48592	+	16.4301i	0.504171	+	0.873250i
$355$		0			0
$356$	−57.9195	+	21.0810i	−3.06973	+	1.11729i
$357$	0.832787	−	2.28806i	0.0440758	−	0.121097i
$358$	9.61525	−	11.4590i	0.508182	−	0.605627i
$359$	−1.18268	+	6.70733i	−0.0624197	+	0.353999i	0.937561	+	0.347820i	$0.113078\pi$
$359$	−1.18268	+	6.70733i	−0.0624197	+	0.353999i	−0.999981	+	0.00617924i	$0.998033\pi$
$360$		0			0
$361$	10.8938	−	15.5668i	0.573360	−	0.819303i
$362$		−	38.9178i		−	2.04548i
$363$	0.297440	+	0.0524466i	0.0156115	+	0.00275273i
$364$	−5.21167	−	4.37311i	−0.273166	−	0.229213i
$365$		0			0
$366$	5.53595	−	2.01492i	0.289369	−	0.105322i
$367$	8.84542	+	10.5416i	0.461727	+	0.550265i	0.945795	−	0.324766i	$-0.105285\pi$
$367$	8.84542	+	10.5416i	0.461727	+	0.550265i	−0.484067	+	0.875031i	$0.660841\pi$
$368$	−81.3274	+	46.9544i	−4.23948	+	2.44767i
$369$	7.88018	−	13.6489i	0.410226	−	0.710532i
$370$		0			0
$371$	−7.39796	−	41.9559i	−0.384083	−	2.17824i
$372$	9.60473	+	5.54529i	0.497982	+	0.287510i
$373$	26.2495	−	15.1552i	1.35915	−	0.784705i	0.369640	−	0.929175i	$-0.379481\pi$
$373$	26.2495	−	15.1552i	1.35915	−	0.784705i	0.989509	+	0.144470i	$0.0461477\pi$
$374$	−4.49055	+	3.76802i	−0.232201	+	0.194840i
$375$		0			0
$376$	−62.3434	−	22.6911i	−3.21511	−	1.17021i
$377$	−0.360427	+	0.429541i	−0.0185630	+	0.0221225i
$378$	−47.2121	−	8.32476i	−2.42833	−	0.428179i
$379$	3.43860			0.176629			0.0883144	−	0.996093i	$-0.471852\pi$
$379$	3.43860			0.176629			0.0883144	+	0.996093i	$0.471852\pi$
$380$		0			0
$381$	8.14620			0.417343
$382$	50.9260	+	8.97964i	2.60560	+	0.459438i
$383$	−11.7836	+	14.0432i	−0.602114	+	0.717572i	−0.977886	−	0.209141i	$-0.932933\pi$
$383$	−11.7836	+	14.0432i	−0.602114	+	0.717572i	0.375771	+	0.926712i	$0.377378\pi$
$384$	−1.79102	−	0.651876i	−0.0913974	−	0.0332659i
$385$		0			0
$386$	−8.29704	+	6.96205i	−0.422308	+	0.354359i
$387$	4.79022	−	2.76563i	0.243500	−	0.140585i
$388$	31.8704	+	18.4004i	1.61798	+	0.934139i
$389$	−0.723319	−	4.10215i	−0.0366737	−	0.207987i	0.960965	−	0.276671i	$-0.0892312\pi$
$389$	−0.723319	−	4.10215i	−0.0366737	−	0.207987i	−0.997638	+	0.0686838i	$0.978120\pi$
$390$		0			0
$391$	−3.20490	+	5.55104i	−0.162079	+	0.280728i
$392$	−50.1679	+	28.9645i	−2.53386	+	1.46293i
$393$	−6.20454	−	7.39429i	−0.312978	−	0.372992i
$394$	0.410557	−	0.149431i	0.0206836	−	0.00752820i
$395$		0			0
$396$	26.0849	+	21.8879i	1.31082	+	1.09991i
$397$	19.5995	+	3.45592i	0.983669	+	0.173447i	0.642276	−	0.766473i	$-0.277990\pi$
$397$	19.5995	+	3.45592i	0.983669	+	0.173447i	0.341393	+	0.939921i	$0.389101\pi$
$398$		−	13.5999i		−	0.681703i
$399$	−4.66647	−	14.7934i	−0.233616	−	0.740594i
$400$		0			0
$401$	−1.64601	+	9.33496i	−0.0821976	+	0.466166i	0.915729	+	0.401797i	$0.131614\pi$
$401$	−1.64601	+	9.33496i	−0.0821976	+	0.466166i	−0.997926	+	0.0643684i	$0.979497\pi$
$402$	14.9619	−	17.8310i	0.746234	−	0.889327i
$403$	0.304994	−	0.837964i	0.0151928	−	0.0417419i
$404$	18.5969	−	6.76872i	0.925231	−	0.336756i
$405$		0			0
$406$	7.73568	+	13.3986i	0.383915	+	0.664961i
$407$	−0.462339	−	0.266932i	−0.0229173	−	0.0132313i
$408$	−4.71994	+	0.832252i	−0.233672	+	0.0412026i
$409$	4.04137	+	22.9197i	0.199833	+	1.13331i	0.905366	+	0.424632i	$0.139596\pi$
$409$	4.04137	+	22.9197i	0.199833	+	1.13331i	−0.705533	+	0.708677i	$0.749292\pi$
$410$		0			0
$411$	1.65567	+	2.86771i	0.0816682	+	0.141454i
$412$	−43.1846	−	51.4654i	−2.12755	−	2.53552i
$413$	−10.2083	−	28.0472i	−0.502320	−	1.38011i
$414$	49.3388	+	17.9578i	2.42487	+	0.882580i
$415$		0			0
$416$	−0.708360	+	4.01731i	−0.0347302	+	0.196965i
$417$			8.05382i			0.394397i
$418$	−8.07806	+	36.4605i	−0.395111	+	1.78334i
$419$	−3.05296			−0.149147			−0.0745735	−	0.997216i	$-0.523760\pi$
$419$	−3.05296			−0.149147			−0.0745735	+	0.997216i	$0.523760\pi$
$420$		0			0
$421$	21.4803	+	18.0241i	1.04689	+	0.878441i	0.992763	−	0.120093i	$-0.0383194\pi$
$421$	21.4803	+	18.0241i	1.04689	+	0.878441i	0.0541226	+	0.998534i	$0.482764\pi$
$422$	4.40946	−	12.1149i	0.214649	−	0.589743i
$423$	6.43068	+	17.6682i	0.312670	+	0.859055i
$424$	−64.2389	+	53.9028i	−3.11972	+	2.61775i
$425$		0			0
$426$	−6.23585	+	10.8008i	−0.302128	+	0.523301i
$427$	−9.12750	+	1.60942i	−0.441711	+	0.0778855i
$428$	−31.3314	+	5.52458i	−1.51446	+	0.267041i
$429$	−0.552500	+	0.956957i	−0.0266749	+	0.0462023i
$430$		0			0
$431$	23.1461	−	19.4219i	1.11491	−	0.935521i	0.116574	−	0.993182i	$-0.462809\pi$
$431$	23.1461	−	19.4219i	1.11491	−	0.935521i	0.998336	+	0.0576610i	$0.0183642\pi$
$432$	16.3591	+	44.9463i	0.787079	+	2.16248i
$433$	5.14314	−	14.1306i	0.247163	−	0.679076i	−0.752624	−	0.658451i	$-0.771212\pi$
$433$	5.14314	−	14.1306i	0.247163	−	0.679076i	0.999787	−	0.0206251i	$-0.00656563\pi$
$434$	−18.8483	−	15.8156i	−0.904746	−	0.759172i
$435$		0			0
$436$	−43.9277			−2.10376
$437$	5.33530	+	40.4844i	0.255222	+	1.93663i
$438$			19.2016i			0.917487i
$439$	6.70915	−	38.0495i	0.320210	−	1.81600i	−0.221181	−	0.975233i	$-0.570991\pi$
$439$	6.70915	−	38.0495i	0.320210	−	1.81600i	0.541391	−	0.840771i	$-0.317898\pi$
$440$		0			0
$441$	15.4270	+	5.61498i	0.734621	+	0.267380i
$442$	0.223454	+	0.613935i	0.0106286	+	0.0292019i
$443$	2.82052	+	3.36137i	0.134007	+	0.159703i	0.828875	−	0.559434i	$-0.188982\pi$
$443$	2.82052	+	3.36137i	0.134007	+	0.159703i	−0.694868	+	0.719138i	$0.744537\pi$
$444$	−0.370003	−	0.640865i	−0.0175596	−	0.0304141i
$445$		0			0
$446$	−3.98966	−	22.6265i	−0.188916	−	1.07140i
$447$	15.5158	−	2.73585i	0.733870	−	0.129401i
$448$	30.9485	+	17.8681i	1.46218	+	0.844189i
$449$	−12.3966	−	21.4716i	−0.585032	−	1.01331i	−0.994871	−	0.101148i	$-0.967749\pi$
$449$	−12.3966	−	21.4716i	−0.585032	−	1.01331i	0.409839	−	0.912158i	$-0.365585\pi$
$450$		0			0
$451$	−22.6387	+	8.23981i	−1.06601	+	0.387997i
$452$	−21.9246	+	60.2374i	−1.03125	+	2.83333i
$453$	−6.61608	+	7.88474i	−0.310851	+	0.370457i
$454$	2.52236	−	14.3050i	0.118380	−	0.671368i
$455$		0			0
$456$	−20.6247	+	22.5139i	−0.965842	+	1.05431i
$457$			21.1249i			0.988182i	0.869410	+	0.494091i	$0.164499\pi$
$457$			21.1249i			0.988182i	−0.869410	+	0.494091i	$0.835501\pi$
$458$	69.4051	+	12.2380i	3.24309	+	0.571843i
$459$	2.50092	+	2.09852i	0.116733	+	0.0979507i
$460$		0			0
$461$	10.4865	−	3.81677i	0.488405	−	0.177765i	−0.0860668	−	0.996289i	$-0.527430\pi$
$461$	10.4865	−	3.81677i	0.488405	−	0.177765i	0.574471	+	0.818525i	$0.305208\pi$
$462$	19.5978	+	23.3558i	0.911773	+	1.08661i
$463$	−3.50260	+	2.02223i	−0.162779	+	0.0939808i	−0.579177	−	0.815202i	$-0.696626\pi$
$463$	−3.50260	+	2.02223i	−0.162779	+	0.0939808i	0.416397	+	0.909183i	$0.363293\pi$
$464$	7.71801	−	13.3680i	0.358300	−	0.620593i
$465$		0			0
$466$	1.16234	+	6.59194i	0.0538442	+	0.305366i
$467$	18.2919	+	10.5608i	0.846448	+	0.488697i	0.859451	−	0.511218i	$-0.170806\pi$
$467$	18.2919	+	10.5608i	0.846448	+	0.488697i	−0.0130026	+	0.999915i	$0.504139\pi$
$468$	3.28668	−	1.89756i	0.151927	−	0.0877149i
$469$	−28.0523	+	23.5387i	−1.29534	+	1.08692i
$470$		0			0
$471$	−0.813815	−	0.296204i	−0.0374986	−	0.0136484i
$472$	−37.7636	+	45.0049i	−1.73821	+	2.07152i
$473$	−8.32675	−	1.46823i	−0.382864	−	0.0675093i
$474$	−22.7002			−1.04265
$475$		0			0
$476$	12.7834			0.585926
$477$	23.4044	+	4.12682i	1.07161	+	0.188954i
$478$	43.0363	−	51.2887i	1.96844	−	2.34589i
$479$	32.1446	+	11.6997i	1.46872	+	0.534572i	0.947754	−	0.319003i	$-0.103348\pi$
$479$	32.1446	+	11.6997i	1.46872	+	0.534572i	0.520971	+	0.853575i	$0.325570\pi$
$480$		0			0
$481$	−0.0455800	+	0.0382462i	−0.00207827	+	0.00174388i
$482$	2.25249	−	1.30047i	0.102598	−	0.0592349i
$483$	28.8715	+	16.6690i	1.31370	+	0.758464i
$484$	0.275348	+	1.56157i	0.0125158	+	0.0709806i
$485$		0			0
$486$	21.1796	−	36.6842i	0.960727	−	1.66403i
$487$	−1.53876	+	0.888403i	−0.0697278	+	0.0402574i	−0.534459	−	0.845195i	$-0.679484\pi$
$487$	−1.53876	+	0.888403i	−0.0697278	+	0.0402574i	0.464731	+	0.885452i	$0.346151\pi$
$488$	11.7265	+	13.9752i	0.530836	+	0.632626i
$489$	−7.04589	+	2.56449i	−0.318626	+	0.115970i
$490$		0			0
$491$	−15.8336	−	13.2860i	−0.714562	−	0.599589i	0.211313	−	0.977418i	$-0.432226\pi$
$491$	−15.8336	−	13.2860i	−0.714562	−	0.599589i	−0.925875	+	0.377830i	$0.876670\pi$
$492$	−32.8869	−	5.79884i	−1.48265	−	0.261432i
$493$		−	1.05359i		−	0.0474515i
$494$	3.51063	+	2.23587i	0.157951	+	0.100596i
$495$		0			0
$496$	−4.26280	+	24.1755i	−0.191405	+	1.08551i
$497$	12.6121	−	15.0305i	0.565730	−	0.674211i
$498$	−0.607342	+	1.66866i	−0.0272156	+	0.0747743i
$499$	−40.0666	+	14.5830i	−1.79363	+	0.652826i	−0.794675	+	0.607036i	$0.792359\pi$
$499$	−40.0666	+	14.5830i	−1.79363	+	0.652826i	−0.998951	+	0.0457908i	$0.985419\pi$
$500$		0			0
$501$	−6.33865	−	10.9789i	−0.283190	−	0.490500i
$502$	−33.0115	−	19.0592i	−1.47338	−	0.850654i
$503$	−24.0995	+	4.24940i	−1.07455	+	0.189471i	−0.682802	−	0.730603i	$-0.739239\pi$
$503$	−24.0995	+	4.24940i	−1.07455	+	0.189471i	−0.391743	+	0.920075i	$0.628128\pi$
$504$	−10.7253	−	60.8260i	−0.477741	−	2.70940i
$505$		0			0
$506$	−40.1303	−	69.5076i	−1.78401	−	3.08999i
$507$	−7.68191	−	9.15495i	−0.341166	−	0.406585i
$508$	14.6275	+	40.1888i	0.648991	+	1.78309i
$509$	31.7212	+	11.5456i	1.40602	+	0.511749i	0.929959	−	0.367664i	$-0.119842\pi$
$509$	31.7212	+	11.5456i	1.40602	+	0.511749i	0.476060	+	0.879413i	$0.342064\pi$
$510$		0			0
$511$	5.24568	−	29.7497i	0.232055	−	1.31605i
$512$			38.9076i			1.71949i
$513$	20.7787	+	0.904472i	0.917401	+	0.0399334i
$514$	45.0179			1.98566
$515$		0			0
$516$	−8.97809	−	7.53351i	−0.395238	−	0.331644i
$517$	9.83007	−	27.0079i	0.432326	−	1.18781i
$518$	0.561501	+	1.54271i	0.0246710	+	0.0677829i
$519$	5.95809	−	4.99943i	0.261531	−	0.219451i
$520$		0			0
$521$	0.743494	−	1.28777i	0.0325731	−	0.0564182i	−0.849279	−	0.527944i	$-0.822963\pi$
$521$	0.743494	−	1.28777i	0.0325731	−	0.0564182i	0.881852	+	0.471526i	$0.156297\pi$
$522$	−8.49931	+	1.49866i	−0.372005	+	0.0655944i
$523$	−6.21793	+	1.09639i	−0.271891	+	0.0479417i	−0.307931	−	0.951409i	$-0.599637\pi$
$523$	−6.21793	+	1.09639i	−0.271891	+	0.0479417i	0.0360402	+	0.999350i	$0.488526\pi$
$524$	25.3382	−	43.8871i	1.10691	−	1.91722i
$525$		0			0
$526$	2.51913	−	2.11380i	0.109839	−	0.0921660i
$527$	0.573079	+	1.57452i	0.0249637	+	0.0685872i
$528$	10.4040	−	28.5847i	0.452775	−	1.24399i
$529$	−49.6096	−	41.6274i	−2.15694	−	1.80989i
$530$		0			0
$531$	16.6497			0.722537
$532$	64.6029	−	49.5850i	2.80089	−	2.14978i
$533$			2.68507i			0.116303i
$534$	5.34586	−	30.3179i	0.231338	−	1.31198i
$535$		0			0
$536$	67.7335	+	24.6530i	2.92564	+	1.06485i
$537$	1.81211	+	4.97872i	0.0781982	+	0.214848i
$538$	−23.0490	−	27.4687i	−0.993711	−	1.18426i
$539$	−12.5478	−	21.7333i	−0.540470	−	0.936122i
$540$		0			0
$541$	−5.19461	−	29.4601i	−0.223334	−	1.26659i	−0.865845	−	0.500312i	$-0.833218\pi$
$541$	−5.19461	−	29.4601i	−0.223334	−	1.26659i	0.642511	−	0.766276i	$-0.277893\pi$
$542$	34.7058	−	6.11957i	1.49074	−	0.262858i
$543$	11.9376	+	6.89220i	0.512293	+	0.295773i
$544$	−3.83245	−	6.63800i	−0.164315	−	0.284602i
$545$		0			0
$546$	3.19313	−	1.16220i	0.136653	−	0.0497378i
$547$	10.2591	−	28.1867i	0.438648	−	1.20518i	−0.501724	−	0.865028i	$-0.667301\pi$
$547$	10.2591	−	28.1867i	0.438648	−	1.20518i	0.940372	−	0.340147i	$-0.110477\pi$
$548$	−11.1747	+	13.3175i	−0.477359	+	0.568894i
$549$	0.897788	−	5.09161i	0.0383167	−	0.217305i
$550$		0			0
$551$	−4.08675	−	5.32450i	−0.174101	−	0.226831i
$552$		−	65.6207i		−	2.79300i
$553$	35.1703	+	6.20147i	1.49559	+	0.263713i
$554$	24.1737	+	20.2842i	1.02704	+	0.861792i
$555$		0			0
$556$	−39.7330	+	14.4616i	−1.68506	+	0.613310i
$557$	−17.4418	−	20.7864i	−0.739034	−	0.880746i	0.257297	−	0.966332i	$-0.417168\pi$
$557$	−17.4418	−	20.7864i	−0.739034	−	0.880746i	−0.996331	+	0.0855864i	$0.972724\pi$
$558$	11.8864	−	6.86264i	0.503193	−	0.290519i
$559$	−0.471178	+	0.816104i	−0.0199287	+	0.0345175i
$560$		0			0
$561$	−0.360542	−	2.04473i	−0.0152221	−	0.0863287i
$562$	−32.5221	−	18.7766i	−1.37186	−	0.792044i
$563$	−34.4334	+	19.8801i	−1.45119	+	0.837847i	−0.998549	−	0.0538451i	$-0.982852\pi$
$563$	−34.4334	+	19.8801i	−1.45119	+	0.837847i	−0.452643	+	0.891692i	$0.649519\pi$
$564$	30.5186	−	25.6081i	1.28506	−	1.07830i
$565$		0			0
$566$	−13.0846	−	4.76241i	−0.549987	−	0.200179i
$567$	−4.87774	+	5.81307i	−0.204846	+	0.244126i
$568$	−38.0341	−	6.70644i	−1.59588	−	0.281396i
$569$	6.66486			0.279405			0.139703	−	0.990194i	$-0.455385\pi$
$569$	6.66486			0.279405			0.139703	+	0.990194i	$0.455385\pi$
$570$		0			0
$571$	−27.6502			−1.15713			−0.578563	−	0.815638i	$-0.696386\pi$
$571$	−27.6502			−1.15713			−0.578563	+	0.815638i	$0.696386\pi$
$572$	−5.71317	−	1.00739i	−0.238880	−	0.0421209i
$573$	−11.7732	+	14.0308i	−0.491833	+	0.586144i
$574$	69.6178	+	25.3388i	2.90579	+	1.05762i
$575$		0			0
$576$	−15.2710	+	12.8139i	−0.636290	+	0.533911i
$577$	−26.0039	+	15.0134i	−1.08256	+	0.625015i	−0.931585	−	0.363523i	$-0.881574\pi$
$577$	−26.0039	+	15.0134i	−1.08256	+	0.625015i	−0.150972	+	0.988538i	$0.548240\pi$
$578$	37.5426	+	21.6752i	1.56156	+	0.901570i
$579$	−0.666160	−	3.77798i	−0.0276847	−	0.157008i
$580$		0			0
$581$	1.39684	−	2.41939i	0.0579506	−	0.100373i
$582$	−15.9183	+	9.19042i	−0.659834	+	0.380955i
$583$	−23.3514	−	27.8291i	−0.967114	−	1.15256i
$584$	−55.8752	+	20.3369i	−2.31213	+	0.841548i
$585$		0			0
$586$	−1.77757	−	1.49156i	−0.0734309	−	0.0616159i
$587$	13.0717	+	2.30489i	0.539527	+	0.0951332i	0.436770	−	0.899573i	$-0.356122\pi$
$587$	13.0717	+	2.30489i	0.539527	+	0.0951332i	0.102757	+	0.994706i	$0.467234\pi$
$588$		−	34.7858i		−	1.43454i
$589$	9.00349	+	5.73419i	0.370982	+	0.236273i
$590$		0			0
$591$	−0.0268718	+	0.152398i	−0.00110536	+	0.00626880i
$592$	1.05287	−	1.25476i	0.0432726	−	0.0515702i
$593$	4.26638	−	11.7218i	0.175199	−	0.481356i	−0.820748	−	0.571290i	$-0.806443\pi$
$593$	4.26638	−	11.7218i	0.175199	−	0.481356i	0.995948	+	0.0899335i	$0.0286655\pi$
$594$	−38.4141	+	13.9816i	−1.57615	+	0.573671i
$595$		0			0
$596$	41.3576	+	71.6334i	1.69407	+	2.93422i
$597$	4.17164	+	2.40850i	0.170734	+	0.0985732i
$598$	−8.80935	+	1.55333i	−0.360241	+	0.0635203i
$599$	5.75729	+	32.6512i	0.235237	+	1.33409i	0.842115	+	0.539298i	$0.181310\pi$
$599$	5.75729	+	32.6512i	0.235237	+	1.33409i	−0.606878	+	0.794795i	$0.707578\pi$
$600$		0			0
$601$	12.4753	+	21.6079i	0.508879	+	0.881404i	0.999947	+	0.0102826i	$0.00327313\pi$
$601$	12.4753	+	21.6079i	0.508879	+	0.881404i	−0.491069	+	0.871121i	$0.663394\pi$
$602$	16.7132	+	19.9181i	0.681181	+	0.811800i
$603$	−6.98667	−	19.1957i	−0.284519	−	0.781710i
$604$	−50.7789	−	18.4820i	−2.06616	−	0.752022i
$605$		0			0
$606$	−1.71646	+	9.73452i	−0.0697264	+	0.395438i
$607$			3.04625i			0.123644i	0.998087	+	0.0618218i	$0.0196911\pi$
$607$			3.04625i			0.123644i	−0.998087	+	0.0618218i	$0.980309\pi$
$608$	−45.1158	−	18.6806i	−1.82969	−	0.757599i
$609$	−5.47984			−0.222054
$610$		0			0
$611$	−2.45386	−	2.05903i	−0.0992725	−	0.0832995i
$612$	−2.43894	+	6.70093i	−0.0985883	+	0.270869i
$613$	−7.55293	−	20.7515i	−0.305060	−	0.838145i	−0.993601	−	0.112948i	$-0.963971\pi$
$613$	−7.55293	−	20.7515i	−0.305060	−	0.838145i	0.688541	−	0.725197i	$-0.258251\pi$
$614$	49.9159	−	41.8844i	2.01444	−	1.69032i
$615$		0			0
$616$	−47.2071	+	81.7651i	−1.90203	+	3.29441i
$617$	−44.1410	+	7.78325i	−1.77705	+	0.313342i	−0.963411	−	0.268030i	$-0.913628\pi$
$617$	−44.1410	+	7.78325i	−1.77705	+	0.313342i	−0.813638	+	0.581371i	$0.802516\pi$
$618$	33.0462	−	5.82693i	1.32931	−	0.234393i
$619$	3.64323	−	6.31025i	0.146434	−	0.253630i	−0.783473	−	0.621425i	$-0.786554\pi$
$619$	3.64323	−	6.31025i	0.146434	−	0.253630i	0.929907	+	0.367795i	$0.119887\pi$
$620$		0			0
$621$	−34.2418	+	28.7323i	−1.37408	+	1.15299i
$622$	16.5919	+	45.5859i	0.665275	+	1.82783i
$623$	−16.5651	+	45.5122i	−0.663666	+	1.82341i
$624$	−2.59712	−	2.17924i	−0.103968	−	0.0872395i
$625$		0			0
$626$	87.0882			3.48074
$627$	−9.75329	−	8.93488i	−0.389509	−	0.356825i
$628$		−	4.54677i		−	0.181436i
$629$	0.0194140	−	0.110102i	0.000774085	−	0.00439006i
$630$		0			0
$631$	37.7879	+	13.7537i	1.50431	+	0.547525i	0.957173	−	0.289517i	$-0.0934945\pi$
$631$	37.7879	+	13.7537i	1.50431	+	0.547525i	0.547139	+	0.837042i	$0.315717\pi$
$632$	−24.0424	−	66.0560i	−0.956356	−	2.62757i
$633$	2.93522	+	3.49806i	0.116664	+	0.139035i
$634$	8.66614	+	15.0102i	0.344176	+	0.596131i
$635$		0			0
$636$	−8.74421	−	49.5909i	−0.346731	−	1.96641i
$637$	−2.75447	+	0.485687i	−0.109136	+	0.0192436i
$638$	11.4252	+	6.59632i	0.452326	+	0.261151i
$639$	5.47259	+	9.47881i	0.216492	+	0.374976i
$640$		0			0
$641$	23.9377	−	8.71261i	0.945482	−	0.344127i	0.177154	−	0.984183i	$-0.443311\pi$
$641$	23.9377	−	8.71261i	0.945482	−	0.344127i	0.768328	+	0.640056i	$0.221089\pi$
$642$	5.43486	−	14.9322i	0.214497	−	0.589326i
$643$	27.1888	−	32.4023i	1.07222	−	1.27782i	0.113480	−	0.993540i	$-0.463800\pi$
$643$	27.1888	−	32.4023i	1.07222	−	1.27782i	0.958741	−	0.284283i	$-0.0917554\pi$
$644$	−30.3929	+	172.367i	−1.19765	+	6.79220i
$645$		0			0
$646$	−7.75361	+	1.02182i	−0.305062	+	0.0402030i
$647$		−	1.66919i		−	0.0656226i	−0.999462	−	0.0328113i	$-0.989554\pi$
$647$		−	1.66919i		−	0.0656226i	0.999462	−	0.0328113i	$-0.0104460\pi$
$648$	14.7097	+	2.59372i	0.577853	+	0.101891i
$649$	−19.4967	−	16.3597i	−0.765311	−	0.642172i
$650$		0			0
$651$	8.18922	−	2.98063i	0.320961	−	0.116820i
$652$	−25.3035	−	30.1556i	−0.990963	−	1.18098i
$653$	5.01760	−	2.89691i	0.196354	−	0.113365i	−0.398600	−	0.917125i	$-0.630504\pi$
$653$	5.01760	−	2.89691i	0.196354	−	0.113365i	0.594954	+	0.803760i	$0.297170\pi$
$654$	10.9703	−	19.0010i	0.428971	−	0.743000i
$655$		0			0
$656$	−12.8355	−	72.7935i	−0.501141	−	2.84211i
$657$	14.5937	+	8.42567i	0.569354	+	0.328717i
$658$	−76.5428	+	44.1920i	−2.98395	+	1.72278i
$659$	−17.0351	+	14.2942i	−0.663595	+	0.556822i	−0.911162	−	0.412049i	$-0.864813\pi$
$659$	−17.0351	+	14.2942i	−0.663595	+	0.556822i	0.247567	+	0.968871i	$0.420369\pi$
$660$		0			0
$661$	8.72292	+	3.17488i	0.339282	+	0.123489i	0.506042	−	0.862509i	$-0.331108\pi$
$661$	8.72292	+	3.17488i	0.339282	+	0.123489i	−0.166759	+	0.985998i	$0.553330\pi$
$662$	27.8140	−	33.1474i	1.08102	−	1.28831i
$663$	−0.227891	−	0.0401833i	−0.00885056	−	0.00156059i
$664$	−5.49893			−0.213400
$665$		0			0
$666$	−0.915804			−0.0354867
$667$	14.2063	+	2.50495i	0.550070	+	0.0969922i
$668$	42.7817	−	50.9853i	1.65527	−	1.97268i
$669$	7.64700	+	2.78328i	0.295650	+	0.107608i
$670$		0			0
$671$	−6.05420	+	5.08008i	−0.233720	+	0.196114i
$672$	−34.5249	+	19.9329i	−1.33183	+	0.768930i
$673$	−26.7229	−	15.4285i	−1.03009	−	0.594723i	−0.113080	−	0.993586i	$-0.536072\pi$
$673$	−26.7229	−	15.4285i	−1.03009	−	0.594723i	−0.917011	+	0.398862i	$0.869405\pi$
$674$	2.71055	+	15.3723i	0.104406	+	0.592118i
$675$		0			0
$676$	31.3715	−	54.3371i	1.20660	−	2.08989i
$677$	35.2722	−	20.3644i	1.35562	−	0.782669i	0.366592	−	0.930382i	$-0.380525\pi$
$677$	35.2722	−	20.3644i	1.35562	−	0.782669i	0.989030	+	0.147713i	$0.0471913\pi$
$678$	−20.5805	−	24.5269i	−0.790389	−	0.941949i
$679$	27.1735	−	9.89035i	1.04282	−	0.379557i
$680$		0			0
$681$	3.94122	+	3.30707i	0.151028	+	0.126727i
$682$	−20.6620	−	3.64327i	−0.791188	−	0.139508i
$683$			16.1788i			0.619066i	0.950889	+	0.309533i	$0.100173\pi$
$683$			16.1788i			0.619066i	−0.950889	+	0.309533i	$0.899827\pi$
$684$	13.6665	+	43.3245i	0.522550	+	1.65655i
$685$		0			0
$686$	−1.18808	+	6.73793i	−0.0453611	+	0.257255i
$687$	−16.0452	+	19.1220i	−0.612164	+	0.729549i
$688$	8.87262	−	24.3773i	0.338265	−	0.929376i
$689$	−3.80471	+	1.38480i	−0.144948	+	0.0527567i
$690$		0			0
$691$	−7.33032	−	12.6965i	−0.278859	−	0.482997i	0.692243	−	0.721665i	$-0.256623\pi$
$691$	−7.33032	−	12.6965i	−0.278859	−	0.482997i	−0.971101	+	0.238667i	$0.923289\pi$
$692$	35.3629	+	20.4168i	1.34429	+	0.776129i
$693$	26.3505	−	4.64631i	1.00097	−	0.176499i
$694$	−9.84122	−	55.8123i	−0.373568	−	2.11861i
$695$		0			0
$696$	5.39312	+	9.34116i	0.204426	+	0.354076i
$697$	−3.24300	−	3.86485i	−0.122837	−	0.146392i
$698$	2.17210	+	5.96781i	0.0822153	+	0.225885i
$699$	−2.22786	−	0.810873i	−0.0842652	−	0.0306700i
$700$		0			0
$701$	−2.53070	+	14.3523i	−0.0955833	+	0.542080i	0.898984	+	0.437982i	$0.144307\pi$
$701$	−2.53070	+	14.3523i	−0.0955833	+	0.542080i	−0.994567	+	0.104098i	$0.966804\pi$
$702$			4.55612i			0.171960i
$703$	−0.328959	−	0.631722i	−0.0124069	−	0.0238258i
$704$	30.4728			1.14848
$705$		0			0
$706$	15.3700	+	12.8970i	0.578459	+	0.485385i
$707$	5.31874	−	14.6131i	0.200032	−	0.549583i
$708$	−12.0660	−	33.1511i	−0.453469	−	1.24590i
$709$	9.07912	−	7.61829i	0.340974	−	0.286111i	−0.456180	−	0.889888i	$-0.650783\pi$
$709$	9.07912	−	7.61829i	0.340974	−	0.286111i	0.797153	+	0.603777i	$0.206338\pi$
$710$		0			0
$711$	−9.96088	+	17.2527i	−0.373562	+	0.647028i
$712$	93.8849	−	16.5544i	3.51848	−	0.620404i
$713$	−22.5928	+	3.98372i	−0.846107	+	0.149191i
$714$	−3.19245	+	5.52949i	−0.119474	+	0.206936i
$715$		0			0
$716$	−21.3083	+	17.8798i	−0.796330	+	0.668201i
$717$	8.11070	+	22.2840i	0.302900	+	0.832210i
$718$	6.10832	−	16.7825i	0.227961	−	0.626316i
$719$	−13.0707	−	10.9676i	−0.487455	−	0.409023i	0.365658	−	0.930749i	$-0.380844\pi$
$719$	−13.0707	−	10.9676i	−0.487455	−	0.409023i	−0.853113	+	0.521726i	$0.825288\pi$
$720$		0			0
$721$	−52.7915			−1.96606
$722$	−35.2205	+	35.2391i	−1.31077	+	1.31146i
$723$			0.921235i			0.0342611i
$724$	−12.5667	+	71.2694i	−0.467039	+	2.64871i
$725$		0			0
$726$	−0.744226	−	0.270876i	−0.0276208	−	0.0100532i
$727$	−4.52829	−	12.4414i	−0.167945	−	0.461425i	0.826958	−	0.562264i	$-0.190070\pi$
$727$	−4.52829	−	12.4414i	−0.167945	−	0.461425i	−0.994903	+	0.100839i	$0.967847\pi$
$728$	6.76387	+	8.06087i	0.250686	+	0.298756i
$729$	4.53091	+	7.84777i	0.167812	+	0.290658i
$730$		0			0
$731$	−0.307474	−	1.74377i	−0.0113723	−	0.0644957i
$732$	−10.7885	+	1.90230i	−0.398754	+	0.0703111i
$733$	46.3491	+	26.7597i	1.71194	+	0.988391i	0.931938	+	0.362618i	$0.118117\pi$
$733$	46.3491	+	26.7597i	1.71194	+	0.988391i	0.780005	+	0.625773i	$0.215216\pi$
$734$	−18.0423	−	31.2503i	−0.665955	−	1.15347i
$735$		0			0
$736$	98.6163	−	35.8934i	3.63505	−	1.32305i
$737$	−10.6800	+	29.3429i	−0.393401	+	1.08086i
$738$	−26.5647	+	31.6586i	−0.977861	+	1.16537i
$739$	7.32823	−	41.5604i	0.269573	−	1.52883i	−0.486116	−	0.873894i	$-0.661587\pi$
$739$	7.32823	−	41.5604i	0.269573	−	1.52883i	0.755689	−	0.654931i	$-0.227302\pi$
$740$		0			0
$741$	−1.30755	+	0.680886i	−0.0480340	+	0.0250130i
$742$			111.716i			4.10121i
$743$	−17.8079	−	3.14002i	−0.653310	−	0.115196i	−0.162838	−	0.986653i	$-0.552065\pi$
$743$	−17.8079	−	3.14002i	−0.653310	−	0.115196i	−0.490472	+	0.871457i	$0.663176\pi$
$744$	−13.1405	−	11.0262i	−0.481756	−	0.404241i
$745$		0			0
$746$	−74.6876	+	27.1841i	−2.73451	+	0.995280i
$747$	1.00172	+	1.19380i	0.0366510	+	0.0436790i
$748$	9.44016	−	5.45028i	0.345167	−	0.199282i
$749$	−12.4998	+	21.6502i	−0.456731	+	0.791081i
$750$		0			0
$751$	0.514525	+	2.91802i	0.0187753	+	0.106480i	0.992755	−	0.120154i	$-0.0383389\pi$
$751$	0.514525	+	2.91802i	0.0187753	+	0.106480i	−0.973980	+	0.226634i	$0.927228\pi$
$752$	76.3680	+	44.0911i	2.78485	+	1.60784i
$753$	11.6924	−	6.75062i	0.426096	−	0.246006i
$754$	1.12636	−	0.945126i	0.0410195	−	0.0344194i
$755$		0			0
$756$	83.7703	+	30.4899i	3.04670	+	1.10891i
$757$	3.06821	−	3.65655i	0.111516	−	0.132900i	−0.707399	−	0.706814i	$-0.750132\pi$
$757$	3.06821	−	3.65655i	0.111516	−	0.132900i	0.818915	+	0.573915i	$0.194576\pi$
$758$	−8.87983	−	1.56575i	−0.322530	−	0.0568707i
$759$	28.4277			1.03186
$760$		0			0
$761$	31.1552			1.12938			0.564688	−	0.825305i	$-0.308997\pi$
$761$	31.1552			1.12938			0.564688	+	0.825305i	$0.308997\pi$
$762$	−21.0367	−	3.70935i	−0.762081	−	0.134375i
$763$	−22.1875	+	26.4421i	−0.803242	+	0.957267i
$764$	−90.3602	−	32.8884i	−3.26912	−	1.18986i
$765$		0			0
$766$	36.8245	−	30.8994i	1.33052	−	1.11644i
$767$	−2.45656	+	1.41830i	−0.0887013	+	0.0512117i
$768$	−10.6756	−	6.16355i	−0.385222	−	0.222408i
$769$	8.40236	+	47.6522i	0.302997	+	1.71838i	0.632786	+	0.774327i	$0.281911\pi$
$769$	8.40236	+	47.6522i	0.302997	+	1.71838i	−0.329789	+	0.944055i	$0.606978\pi$
$770$		0			0
$771$	−7.97250	+	13.8088i	−0.287123	+	0.497311i
$772$	17.4423	−	10.0703i	0.627761	−	0.362438i
$773$	−30.1312	−	35.9089i	−1.08374	−	1.29155i	−0.953934	−	0.300015i	$-0.903008\pi$
$773$	−30.1312	−	35.9089i	−1.08374	−	1.29155i	−0.129808	−	0.991539i	$-0.541436\pi$
$774$	−13.6296	+	4.96076i	−0.489905	+	0.178311i
$775$		0			0
$776$	−43.6030	−	36.5873i	−1.56526	−	1.31341i
$777$	−0.572651	−	0.100974i	−0.0205437	−	0.00362241i
$778$			10.9227i			0.391599i
$779$	−31.3802	−	6.95249i	−1.12431	−	0.249099i
$780$		0			0
$781$	2.90531	−	16.4768i	0.103960	−	0.589588i
$782$	10.8040	−	12.8757i	0.386349	−	0.460433i
$783$	2.51295	−	6.90427i	0.0898054	−	0.246738i
$784$	72.3532	−	26.3344i	2.58404	−	0.940515i
$785$		0			0
$786$	12.6556	+	21.9202i	0.451412	+	0.781868i
$787$	−43.9042	−	25.3481i	−1.56502	−	0.903563i	−0.996736	−	0.0807272i	$-0.974276\pi$
$787$	−43.9042	−	25.3481i	−1.56502	−	0.903563i	−0.568280	−	0.822835i	$-0.692391\pi$
$788$	−0.800096	+	0.141079i	−0.0285022	+	0.00502571i
$789$	0.202258	+	1.14706i	0.00720057	+	0.0408365i
$790$		0			0
$791$	25.1856	+	43.6228i	0.895497	+	1.55105i
$792$	−33.8538	−	40.3454i	−1.20294	−	1.43361i
$793$	0.301263	+	0.827713i	0.0106982	+	0.0293929i
$794$	−49.0400	−	17.8491i	−1.74036	−	0.633441i
$795$		0			0
$796$	−4.39147	+	24.9053i	−0.155652	+	0.882744i
$797$			11.3007i			0.400291i	0.979766	+	0.200146i	$0.0641415\pi$
$797$			11.3007i			0.400291i	−0.979766	+	0.200146i	$0.935858\pi$
$798$	5.31459	+	40.3272i	0.188134	+	1.42757i
$799$	6.01892			0.212934
$800$		0			0
$801$	−20.6966	−	17.3665i	−0.731279	−	0.613616i
$802$	8.50129	−	23.3571i	0.300191	−	0.824768i
$803$	−8.81020	−	24.2058i	−0.310905	−	0.854205i
$804$	−33.1572	+	27.8222i	−1.16936	+	0.981213i
$805$		0			0
$806$	−1.16918	+	2.02508i	−0.0411826	+	0.0713303i
$807$	12.5076	−	2.20543i	0.440289	−	0.0776348i
$808$	−30.1447	+	5.31533i	−1.06049	+	0.186993i
$809$	−2.98372	+	5.16796i	−0.104902	+	0.181696i	−0.913698	−	0.406393i	$-0.866786\pi$
$809$	−2.98372	+	5.16796i	−0.104902	+	0.181696i	0.808796	+	0.588089i	$0.200120\pi$
$810$		0			0
$811$	−18.0275	+	15.1268i	−0.633030	+	0.531175i	−0.901869	−	0.432010i	$-0.857804\pi$
$811$	−18.0275	+	15.1268i	−0.633030	+	0.531175i	0.268839	+	0.963185i	$0.413360\pi$
$812$	−9.83973	−	27.0344i	−0.345307	−	0.948723i
$813$	−4.26915	+	11.7294i	−0.149726	+	0.411368i
$814$	1.07240	+	0.899848i	0.0375875	+	0.0315397i
$815$		0			0
$816$	6.37032			0.223006
$817$	−8.31772	−	7.61977i	−0.291000	−	0.266582i
$818$		−	61.0282i		−	2.13380i
$819$	0.517844	−	2.93684i	0.0180949	−	0.102621i
$820$		0			0
$821$	−28.1921	−	10.2611i	−0.983911	−	0.358114i	−0.200551	−	0.979683i	$-0.564273\pi$
$821$	−28.1921	−	10.2611i	−0.983911	−	0.358114i	−0.783359	+	0.621569i	$0.786496\pi$
$822$	−2.96980	−	8.15947i	−0.103584	−	0.284594i
$823$	5.40876	+	6.44591i	0.188538	+	0.224690i	0.852030	−	0.523492i	$-0.175371\pi$
$823$	5.40876	+	6.44591i	0.188538	+	0.224690i	−0.663493	+	0.748183i	$0.730927\pi$
$824$	51.9561	+	89.9905i	1.80997	+	3.13497i
$825$		0			0
$826$	13.5908	+	77.0774i	0.472885	+	2.68187i
$827$	27.2794	−	4.81009i	0.948597	−	0.167263i	0.322116	−	0.946700i	$-0.395606\pi$
$827$	27.2794	−	4.81009i	0.948597	−	0.167263i	0.626481	+	0.779437i	$0.284495\pi$
$828$	−84.5544	−	48.8175i	−2.93847	−	1.69653i
$829$	24.1279	+	41.7908i	0.837998	+	1.45145i	0.891566	+	0.452890i	$0.149607\pi$
$829$	24.1279	+	41.7908i	0.837998	+	1.45145i	−0.0535685	+	0.998564i	$0.517060\pi$
$830$		0			0
$831$	−10.5030	+	3.82279i	−0.364346	+	0.132611i
$832$	1.16159	−	3.19145i	0.0402710	−	0.110644i
$833$	3.37814	−	4.02591i	0.117046	−	0.139489i
$834$	3.66728	−	20.7982i	0.126988	−	0.720182i
$835$		0			0
$836$	26.5664	−	64.1610i	0.918819	−	2.21905i
$837$			11.6848i			0.403885i
$838$	7.88397	+	1.39016i	0.272347	+	0.0480222i
$839$	14.9006	+	12.5031i	0.514425	+	0.431653i	0.862683	−	0.505745i	$-0.168782\pi$
$839$	14.9006	+	12.5031i	0.514425	+	0.431653i	−0.348258	+	0.937399i	$0.613227\pi$
$840$		0			0
$841$	25.0229	−	9.10760i	0.862860	−	0.314055i
$842$	−47.2635	−	56.3264i	−1.62881	−	1.94114i
$843$	11.5191	−	6.65054i	0.396738	−	0.229057i
$844$	−11.9869	+	20.7619i	−0.412606	+	0.714654i
$845$		0			0
$846$	−8.56145	−	48.5544i	−0.294349	−	1.66934i
$847$	1.07906	+	0.622993i	0.0370768	+	0.0214063i
$848$	96.5275	−	55.7302i	3.31477	−	1.91378i
$849$	3.77805	−	3.17016i	0.129662	−	0.108800i
$850$		0			0
$851$	1.43842	+	0.523542i	0.0493084	+	0.0179468i
$852$	14.9072	−	17.7657i	0.510712	−	0.608643i
$853$	35.5818	+	6.27404i	1.21830	+	0.214819i	0.745593	−	0.666401i	$-0.232166\pi$
$853$	35.5818	+	6.27404i	1.21830	+	0.214819i	0.472706	+	0.881220i	$0.343277\pi$
$854$	24.3037			0.831655
$855$		0			0
$856$	49.2078			1.68189
$857$	−46.1479	−	8.13712i	−1.57638	−	0.277959i	−0.684083	−	0.729404i	$-0.739797\pi$
$857$	−46.1479	−	8.13712i	−1.57638	−	0.277959i	−0.892299	+	0.451446i	$0.850908\pi$
$858$	1.86252	−	2.21967i	0.0635854	−	0.0757782i
$859$	13.1861	+	4.79933i	0.449903	+	0.163751i	0.557027	−	0.830494i	$-0.311942\pi$
$859$	13.1861	+	4.79933i	0.449903	+	0.163751i	−0.107124	+	0.994246i	$0.534164\pi$
$860$		0			0
$861$	−20.1015	+	16.8671i	−0.685056	+	0.574830i
$862$	−68.6163	+	39.6156i	−2.33708	+	1.34931i
$863$	35.1649	+	20.3025i	1.19703	+	0.691105i	0.959892	−	0.280371i	$-0.0904576\pi$
$863$	35.1649	+	20.3025i	1.19703	+	0.691105i	0.237137	+	0.971476i	$0.423791\pi$
$864$	−9.28187	−	52.6401i	−0.315776	−	1.79085i
$865$		0			0
$866$	−19.7160	+	34.1491i	−0.669976	+	1.16043i
$867$	−13.2973	+	7.67719i	−0.451600	+	0.260731i
$868$	29.4095	+	35.0489i	0.998225	+	1.18964i
$869$	28.6162	−	10.4155i	0.970740	−	0.353320i
$870$		0			0
$871$	2.66601	+	2.23705i	0.0903344	+	0.0757996i
$872$	66.9106	+	11.7981i	2.26588	+	0.399536i
$873$			16.1311i			0.545954i
$874$	4.65655	−	106.976i	0.157510	−	3.61853i
$875$		0			0
$876$	6.20026	−	35.1634i	0.209487	−	1.18806i
$877$	17.2321	−	20.5365i	0.581888	−	0.693467i	−0.392137	−	0.919907i	$-0.628264\pi$
$877$	17.2321	−	20.5365i	0.581888	−	0.693467i	0.974025	+	0.226439i	$0.0727085\pi$
$878$	−34.6514	+	95.2040i	−1.16943	+	3.21298i
$879$	0.772323	−	0.281103i	0.0260498	−	0.00948135i
$880$		0			0
$881$	−25.1410	−	43.5454i	−0.847021	−	1.46708i	−0.883855	−	0.467761i	$-0.845061\pi$
$881$	−25.1410	−	43.5454i	−0.847021	−	1.46708i	0.0368343	−	0.999321i	$-0.488273\pi$
$882$	−37.2820	−	21.5248i	−1.25535	−	0.724777i
$883$	−10.9144	+	1.92450i	−0.367298	+	0.0647645i	−0.354251	−	0.935150i	$-0.615264\pi$
$883$	−10.9144	+	1.92450i	−0.367298	+	0.0647645i	−0.0130467	+	0.999915i	$0.504153\pi$
$884$	−0.210965	−	1.19644i	−0.00709551	−	0.0402406i
$885$		0			0
$886$	−5.75313	−	9.96471i	−0.193280	−	0.334771i
$887$	−6.37238	−	7.59431i	−0.213964	−	0.254992i	0.648378	−	0.761318i	$-0.275448\pi$
$887$	−6.37238	−	7.59431i	−0.213964	−	0.254992i	−0.862342	+	0.506326i	$0.831003\pi$
$888$	0.391464	+	1.07554i	0.0131367	+	0.0360927i
$889$	31.5797	+	11.4941i	1.05915	+	0.385498i
$890$		0			0
$891$	−1.12363	+	6.37244i	−0.0376431	+	0.213485i
$892$			42.7237i			1.43050i
$893$	30.4175	−	23.3466i	1.01788	−	0.781263i
$894$	−41.3136			−1.38173
$895$		0			0
$896$	−6.02329	−	5.05414i	−0.201224	−	0.168847i
$897$	1.08364	−	2.97727i	0.0361816	−	0.0994080i
$898$	22.2360	+	61.0929i	0.742025	+	2.03870i
$899$	2.88870	−	2.42390i	0.0963434	−	0.0808417i
$900$		0			0
$901$	3.80390	−	6.58854i	0.126726	−	0.219496i
$902$	62.2141	−	10.9700i	2.07150	−	0.365262i
$903$	−9.06951	+	1.59920i	−0.301814	+	0.0532180i
$904$	49.5741	−	85.8649i	1.64881	−	2.85582i
$905$		0			0
$906$	20.6757	−	17.3489i	0.686903	−	0.576380i
$907$	6.23529	+	17.1313i	0.207039	+	0.568836i	0.999136	−	0.0415596i	$-0.0132326\pi$
$907$	6.23529	+	17.1313i	0.207039	+	0.568836i	−0.792097	+	0.610396i	$0.791010\pi$
$908$	−9.23830	+	25.3820i	−0.306584	+	0.842332i
$909$	6.64530	+	5.57607i	0.220411	+	0.184947i
$910$		0			0
$911$	21.7792			0.721576			0.360788	−	0.932648i	$-0.382508\pi$
$911$	21.7792			0.721576			0.360788	+	0.932648i	$0.382508\pi$
$912$	32.1934	−	24.7096i	1.06603	−	0.818217i
$913$		−	2.38220i		−	0.0788394i
$914$	9.61916	−	54.5530i	0.318174	−	1.80445i
$915$		0			0
$916$	−123.148	−	44.8223i	−4.06893	−	1.48097i
$917$	−13.6195	−	37.4192i	−0.449755	−	1.23569i
$918$	−5.50283	−	6.55801i	−0.181620	−	0.216447i
$919$	−13.1150	−	22.7158i	−0.432623	−	0.749325i	0.564475	−	0.825450i	$-0.309079\pi$
$919$	−13.1150	−	22.7158i	−0.432623	−	0.749325i	−0.997098	+	0.0761249i	$0.975745\pi$
$920$		0			0
$921$	4.00769	+	22.7287i	0.132058	+	0.748937i
$922$	−28.8183	+	5.08144i	−0.949079	+	0.167348i
$923$	−1.61489	−	0.932359i	−0.0531549	−	0.0306890i
$924$	−28.3474	−	49.0991i	−0.932561	−	1.61524i
$925$		0			0
$926$	9.96592	−	3.62730i	0.327500	−	0.119200i
$927$	10.0721	−	27.6728i	0.330810	−	0.908894i
$928$	−11.0882	+	13.2144i	−0.363987	+	0.433783i
$929$	1.81278	−	10.2808i	0.0594754	−	0.337302i	−0.940522	−	0.339734i	$-0.889663\pi$
$929$	1.81278	−	10.2808i	0.0594754	−	0.337302i	0.999997	+	0.00243204i	$0.000774142\pi$
$930$		0			0
$931$	1.45599	−	33.4489i	0.0477182	−	1.09624i
$932$		−	12.4470i		−	0.407715i
$933$	−16.9214	−	2.98369i	−0.553981	−	0.0976818i
$934$	−42.4282	−	35.6014i	−1.38829	−	1.16491i
$935$		0			0
$936$	−5.51591	+	2.00763i	−0.180293	+	0.0656213i
$937$	−13.6398	−	16.2552i	−0.445591	−	0.531035i	0.495762	−	0.868459i	$-0.334889\pi$
$937$	−13.6398	−	16.2552i	−0.445591	−	0.531035i	−0.941353	+	0.337424i	$0.890445\pi$
$938$	83.1606	−	48.0128i	2.71529	−	1.56767i
$939$	−15.4230	+	26.7134i	−0.503310	+	0.871759i
$940$		0			0
$941$	8.76643	+	49.7169i	0.285778	+	1.62072i	0.702495	+	0.711689i	$0.252069\pi$
$941$	8.76643	+	49.7169i	0.285778	+	1.62072i	−0.416717	+	0.909036i	$0.636820\pi$
$942$	1.96672	+	1.13549i	0.0640791	+	0.0369961i
$943$	59.8227	−	34.5386i	1.94809	−	1.12473i
$944$	59.8186	−	50.1938i	1.94693	−	1.63367i
$945$		0			0
$946$	20.8344	+	7.58312i	0.677386	+	0.246548i
$947$	7.70259	−	9.17959i	0.250301	−	0.298297i	−0.626234	−	0.779635i	$-0.715405\pi$
$947$	7.70259	−	9.17959i	0.250301	−	0.298297i	0.876535	+	0.481338i	$0.159849\pi$
$948$	41.5704	+	7.32998i	1.35014	+	0.238067i
$949$	−2.87094			−0.0931948
$950$		0			0
$951$	−6.13896			−0.199069
$952$	−19.4716	−	3.43338i	−0.631079	−	0.111276i
$953$	−21.9823	+	26.1975i	−0.712077	+	0.848620i	−0.993835	−	0.110865i	$-0.964638\pi$
$953$	−21.9823	+	26.1975i	−0.712077	+	0.848620i	0.281759	+	0.959485i	$0.409082\pi$
$954$	−58.5602	−	21.3142i	−1.89596	−	0.690072i
$955$		0			0
$956$	−95.3728	+	80.0273i	−3.08458	+	2.58827i
$957$	−4.04670	+	2.33636i	−0.130811	+	0.0755239i
$958$	−77.6828	−	44.8502i	−2.50982	−	1.44904i
$959$	2.37214	+	13.4531i	0.0766005	+	0.434423i
$960$		0			0
$961$	12.5015	−	21.6532i	0.403274	−	0.698490i
$962$	0.135121	−	0.0780122i	0.00435648	−	0.00251521i
$963$	−8.96401	−	10.6829i	−0.288861	−	0.344251i
$964$	−4.54486	+	1.65419i	−0.146380	+	0.0532780i
$965$		0			0
$966$	−66.9675	−	56.1924i	−2.15464	−	1.80796i
$967$	12.0223	+	2.11985i	0.386610	+	0.0681698i	0.363575	−	0.931565i	$-0.381556\pi$
$967$	12.0223	+	2.11985i	0.386610	+	0.0681698i	0.0230349	+	0.999735i	$0.492667\pi$
$968$		−	2.45254i		−	0.0788276i
$969$	1.05970	−	2.55930i	0.0340425	−	0.0822165i
$970$		0			0
$971$	−2.56830	+	14.5656i	−0.0824207	+	0.467431i	0.915463	+	0.402403i	$0.131825\pi$
$971$	−2.56830	+	14.5656i	−0.0824207	+	0.467431i	−0.997883	+	0.0650281i	$0.979286\pi$
$972$	−50.6312	+	60.3399i	−1.62400	+	1.93540i
$973$	−11.3637	+	31.2215i	−0.364304	+	1.00092i
$974$	4.37822	−	1.59354i	0.140287	−	0.0510604i
$975$		0			0
$976$	−12.1241	−	20.9995i	−0.388083	−	0.672179i
$977$	11.6876	+	6.74782i	0.373919	+	0.215882i	0.675169	−	0.737663i	$-0.264071\pi$
$977$	11.6876	+	6.74782i	0.373919	+	0.215882i	−0.301250	+	0.953545i	$0.597404\pi$
$978$	19.3630	−	3.41423i	0.619162	−	0.109175i
$979$	7.17158	+	40.6720i	0.229205	+	1.29988i
$980$		0			0
$981$	−9.62753	−	16.6754i	−0.307383	−	0.532403i
$982$	34.8390	+	41.5195i	1.11176	+	1.32494i
$983$	−16.4163	−	45.1035i	−0.523600	−	1.43858i	−0.866486	−	0.499202i	$-0.833627\pi$
$983$	−16.4163	−	45.1035i	−0.523600	−	1.43858i	0.342886	−	0.939377i	$-0.388596\pi$
$984$	48.5358	+	17.6656i	1.54726	+	0.563158i
$985$		0			0
$986$	−0.479751	+	2.72080i	−0.0152784	+	0.0866480i
$987$		−	31.3050i		−	0.996448i
$988$	−5.70697	−	5.22809i	−0.181563	−	0.166328i
$989$	24.2434			0.770896
$990$		0			0
$991$	41.3075	+	34.6611i	1.31217	+	1.10105i	0.987902	+	0.155081i	$0.0495640\pi$
$991$	41.3075	+	34.6611i	1.31217	+	1.10105i	0.324273	+	0.945964i	$0.394880\pi$
$992$	9.38282	−	25.7791i	0.297905	−	0.818486i
$993$	5.24187	+	14.4019i	0.166346	+	0.457031i
$994$	−39.4136	+	33.0719i	−1.25012	+	1.04898i
$995$		0			0
$996$	1.65103	−	2.85966i	0.0523148	−	0.0906119i
$997$	33.0855	−	5.83386i	1.04783	−	0.184760i	0.376878	−	0.926263i	$-0.376998\pi$
$997$	33.0855	−	5.83386i	1.04783	−	0.184760i	0.670950	+	0.741503i	$0.265887\pi$
$998$	110.108	−	19.4150i	3.48541	−	0.614572i
$999$	0.389827	−	0.675201i	0.0123336	−	0.0213624i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.u.c.74.1		36
5.2	odd	4		95.2.k.b.36.3	✓	18
5.3	odd	4		475.2.l.b.226.1		18
5.4	even	2	inner	475.2.u.c.74.6		36
15.2	even	4		855.2.bs.b.226.1		18
19.9	even	9	inner	475.2.u.c.199.6		36
95.3	even	36		9025.2.a.cd.1.9		9
95.9	even	18	inner	475.2.u.c.199.1		36
95.22	even	36		1805.2.a.u.1.1		9
95.28	odd	36		475.2.l.b.351.1		18
95.47	odd	36		95.2.k.b.66.3	yes	18
95.73	odd	36		9025.2.a.ce.1.1		9
95.92	odd	36		1805.2.a.t.1.9		9
285.47	even	36		855.2.bs.b.541.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.b.36.3	✓	18	5.2	odd	4
95.2.k.b.66.3	yes	18	95.47	odd	36
475.2.l.b.226.1		18	5.3	odd	4
475.2.l.b.351.1		18	95.28	odd	36
475.2.u.c.74.1		36	1.1	even	1	trivial
475.2.u.c.74.6		36	5.4	even	2	inner
475.2.u.c.199.1		36	95.9	even	18	inner
475.2.u.c.199.6		36	19.9	even	9	inner
855.2.bs.b.226.1		18	15.2	even	4
855.2.bs.b.541.1		18	285.47	even	36
1805.2.a.t.1.9		9	95.92	odd	36
1805.2.a.u.1.1		9	95.22	even	36
9025.2.a.cd.1.9		9	95.3	even	36
9025.2.a.ce.1.1		9	95.73	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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.58240 - 0.455347i) q^{2} +(0.597006 - 0.711484i) q^{3} +(4.58206 + 1.66773i) q^{4} +(-1.86568 + 1.56549i) q^{6} +(3.31824 - 1.91579i) q^{7} +(-6.53146 - 3.77094i) q^{8} +(0.371151 + 2.10490i) q^{9} +O(q^{10})\)	\(q+(-2.58240 - 0.455347i) q^{2} +(0.597006 - 0.711484i) q^{3} +(4.58206 + 1.66773i) q^{4} +(-1.86568 + 1.56549i) q^{6} +(3.31824 - 1.91579i) q^{7} +(-6.53146 - 3.77094i) q^{8} +(0.371151 + 2.10490i) q^{9} +(1.63362 - 2.82951i) q^{11} +(3.92208 - 2.26441i) q^{12} +(-0.234066 - 0.278949i) q^{13} +(-9.44137 + 3.43638i) q^{14} +(7.67910 + 6.44353i) q^{16} +(0.673822 + 0.118813i) q^{17} -5.60470i q^{18} +(3.86613 - 2.01323i) q^{19} +(0.617958 - 3.50461i) q^{21} +(-5.50706 + 6.56305i) q^{22} +(-3.20407 + 8.80310i) q^{23} +(-6.58228 + 2.39576i) q^{24} +(0.477433 + 0.826939i) q^{26} +(4.13222 + 2.38574i) q^{27} +(18.3994 - 3.24431i) q^{28} +(-0.267393 - 1.51646i) q^{29} +(1.22444 + 2.12080i) q^{31} +(-7.20079 - 8.58157i) q^{32} +(-1.03787 - 2.85152i) q^{33} +(-1.68598 - 0.613646i) q^{34} +(-1.80978 + 10.2638i) q^{36} -0.163399i q^{37} +(-10.9006 + 3.43852i) q^{38} -0.338206 q^{39} +(-5.64858 - 4.73972i) q^{41} +(-3.19163 + 8.76892i) q^{42} +(-0.885107 - 2.43181i) q^{43} +(12.2042 - 10.2405i) q^{44} +(12.2826 - 21.2742i) q^{46} +(8.66316 - 1.52755i) q^{47} +(9.16893 - 1.61673i) q^{48} +(3.84048 - 6.65191i) q^{49} +(0.486809 - 0.408482i) q^{51} +(-0.607292 - 1.66852i) q^{52} +(3.80291 - 10.4484i) q^{53} +(-9.58469 - 8.04251i) q^{54} -28.8973 q^{56} +(0.875722 - 3.95259i) q^{57} +4.03786i q^{58} +(1.35268 - 7.67146i) q^{59} +(-2.27305 - 0.827322i) q^{61} +(-2.19630 - 6.03429i) q^{62} +(5.26412 + 6.27353i) q^{63} +(4.66339 + 8.07723i) q^{64} +(1.38176 + 7.83636i) q^{66} +(-9.41216 + 1.65962i) q^{67} +(2.88935 + 1.66816i) q^{68} +(4.35042 + 7.53515i) q^{69} +(4.81203 - 1.75144i) q^{71} +(5.51331 - 15.1477i) q^{72} +(5.06782 - 6.03960i) q^{73} +(-0.0744033 + 0.421962i) q^{74} +(21.0723 - 2.77705i) q^{76} -12.5186i q^{77} +(0.873384 + 0.154001i) q^{78} +(7.14004 + 5.99121i) q^{79} +(-1.86106 + 0.677369i) q^{81} +(12.4287 + 14.8119i) q^{82} +(0.631436 - 0.364559i) q^{83} +(8.67627 - 15.0277i) q^{84} +(1.17838 + 6.68294i) q^{86} +(-1.23857 - 0.715090i) q^{87} +(-21.3398 + 12.3205i) q^{88} +(-9.68319 + 8.12516i) q^{89} +(-1.31109 - 0.477199i) q^{91} +(-29.3625 + 34.9928i) q^{92} +(2.23991 + 0.394957i) q^{93} -23.0673 q^{94} -10.4046 q^{96} +(7.43249 + 1.31055i) q^{97} +(-12.9466 + 15.4291i) q^{98} +(6.56216 + 2.38843i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{4} - 12 q^{6} + 42 q^{9}+O(q^{10}) \) 36 * q + 6 * q^4 - 12 * q^6 + 42 * q^9	\( 36 q + 6 q^{4} - 12 q^{6} + 42 q^{9} - 48 q^{14} + 42 q^{16} + 24 q^{19} + 6 q^{21} - 42 q^{24} - 42 q^{26} + 18 q^{29} + 60 q^{31} - 48 q^{34} - 42 q^{36} - 24 q^{39} - 12 q^{41} + 60 q^{44} + 42 q^{46} + 6 q^{49} + 54 q^{51} - 60 q^{54} - 144 q^{56} - 36 q^{59} + 12 q^{61} + 48 q^{64} - 66 q^{66} - 54 q^{69} + 48 q^{71} + 78 q^{74} + 54 q^{76} - 18 q^{79} + 30 q^{81} + 24 q^{84} - 66 q^{86} + 12 q^{89} - 12 q^{91} + 132 q^{94} - 36 q^{96} - 6 q^{99}+O(q^{100}) \) 36 * q + 6 * q^4 - 12 * q^6 + 42 * q^9 - 48 * q^14 + 42 * q^16 + 24 * q^19 + 6 * q^21 - 42 * q^24 - 42 * q^26 + 18 * q^29 + 60 * q^31 - 48 * q^34 - 42 * q^36 - 24 * q^39 - 12 * q^41 + 60 * q^44 + 42 * q^46 + 6 * q^49 + 54 * q^51 - 60 * q^54 - 144 * q^56 - 36 * q^59 + 12 * q^61 + 48 * q^64 - 66 * q^66 - 54 * q^69 + 48 * q^71 + 78 * q^74 + 54 * q^76 - 18 * q^79 + 30 * q^81 + 24 * q^84 - 66 * q^86 + 12 * q^89 - 12 * q^91 + 132 * q^94 - 36 * q^96 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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