LMFDB - Embedded newform 190.2.m.a.107.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [190,2,Mod(27,190)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(190, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("190.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 190 = 2 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	190.m (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.51715763840$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			107.1
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	190.107
Dual form			190.2.m.a.103.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(0.633975 - 2.36603i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-2.03906 + 0.917738i) q^{5} +(-1.22474 + 2.12132i) q^{6} +(-3.22474 - 3.22474i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.59808 - 1.50000i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(0.633975 - 2.36603i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-2.03906 + 0.917738i) q^{5} +(-1.22474 + 2.12132i) q^{6} +(-3.22474 - 3.22474i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.59808 - 1.50000i) q^{9} +(2.20711 - 0.358719i) q^{10} +3.44949 q^{11} +(1.73205 - 1.73205i) q^{12} +(-4.73205 + 1.26795i) q^{13} +(2.28024 + 3.94949i) q^{14} +(0.878680 + 5.40629i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.732051 - 2.73205i) q^{17} +(2.12132 + 2.12132i) q^{18} +(-1.25529 - 4.17423i) q^{19} +(-2.22474 - 0.224745i) q^{20} +(-9.67423 + 5.58542i) q^{21} +(-3.33195 - 0.892794i) q^{22} +(1.34486 + 5.01910i) q^{23} +(-2.12132 + 1.22474i) q^{24} +(3.31552 - 3.74264i) q^{25} +4.89898 q^{26} +(-1.18034 - 4.40508i) q^{28} +(0.389270 - 0.674235i) q^{29} +(0.550510 - 5.44949i) q^{30} -7.70674i q^{31} +(-0.258819 - 0.965926i) q^{32} +(2.18689 - 8.16158i) q^{33} +(-1.41421 + 2.44949i) q^{34} +(9.53491 + 3.61597i) q^{35} +(-1.50000 - 2.59808i) q^{36} +(0.389270 - 0.389270i) q^{37} +(0.132150 + 4.35690i) q^{38} +12.0000i q^{39} +(2.09077 + 0.792893i) q^{40} +(-1.50000 + 0.866025i) q^{41} +(10.7902 - 2.89123i) q^{42} +(3.48406 + 0.933552i) q^{43} +(2.98735 + 1.72474i) q^{44} +(6.67423 + 0.674235i) q^{45} -5.19615i q^{46} +(6.69213 - 1.79315i) q^{47} +(2.36603 - 0.633975i) q^{48} +13.7980i q^{49} +(-4.17121 + 2.75699i) q^{50} +(-6.00000 - 3.46410i) q^{51} +(-4.73205 - 1.26795i) q^{52} +(9.99585 - 2.67838i) q^{53} +(-7.03371 + 3.16573i) q^{55} +4.56048i q^{56} +(-10.6722 + 0.323701i) q^{57} +(-0.550510 + 0.550510i) q^{58} +(-1.73205 - 3.00000i) q^{59} +(-1.94218 + 5.12132i) q^{60} +(4.00000 - 6.92820i) q^{61} +(-1.99465 + 7.44414i) q^{62} +(3.54102 + 13.2153i) q^{63} +1.00000i q^{64} +(8.48528 - 6.92820i) q^{65} +(-4.22474 + 7.31747i) q^{66} +(2.47185 + 9.22508i) q^{67} +(2.00000 - 2.00000i) q^{68} +12.7279 q^{69} +(-8.27414 - 5.96058i) q^{70} +(-3.00000 + 1.73205i) q^{71} +(0.776457 + 2.89778i) q^{72} +(2.11804 + 0.567526i) q^{73} +(-0.476756 + 0.275255i) q^{74} +(-6.75323 - 10.2173i) q^{75} +(1.00000 - 4.24264i) q^{76} +(-11.1237 - 11.1237i) q^{77} +(3.10583 - 11.5911i) q^{78} +(-5.97469 - 10.3485i) q^{79} +(-1.81431 - 1.30701i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(1.67303 - 0.448288i) q^{82} +(-2.34847 + 2.34847i) q^{83} -11.1708 q^{84} +(1.01461 + 6.24264i) q^{85} +(-3.12372 - 1.80348i) q^{86} +(-1.34847 - 1.34847i) q^{87} +(-2.43916 - 2.43916i) q^{88} +(1.64456 - 2.84847i) q^{89} +(-6.27231 - 2.37868i) q^{90} +(19.3485 + 11.1708i) q^{91} +(-1.34486 + 5.01910i) q^{92} +(-18.2343 - 4.88588i) q^{93} -6.92820 q^{94} +(6.39047 + 7.35948i) q^{95} -2.44949 q^{96} +(-9.22508 - 2.47185i) q^{97} +(3.57117 - 13.3278i) q^{98} +(-8.96204 - 5.17423i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 12 q^{3} + 4 q^{5} - 16 q^{7}+O(q^{10}) $ 8 * q + 12 * q^3 + 4 * q^5 - 16 * q^7	$ 8 q + 12 q^{3} + 4 q^{5} - 16 q^{7} + 12 q^{10} + 8 q^{11} - 24 q^{13} + 24 q^{15} + 4 q^{16} - 8 q^{17} - 8 q^{20} - 48 q^{21} - 12 q^{22} + 8 q^{28} + 24 q^{30} + 12 q^{33} + 12 q^{35} - 12 q^{36} - 12 q^{38} - 12 q^{41} + 12 q^{42} + 20 q^{43} + 24 q^{45} + 12 q^{48} - 48 q^{51} - 24 q^{52} + 36 q^{53} - 8 q^{55} - 12 q^{57} - 24 q^{58} + 32 q^{61} + 12 q^{62} - 24 q^{63} - 24 q^{66} - 12 q^{67} + 16 q^{68} - 36 q^{70} - 24 q^{71} + 16 q^{73} + 8 q^{76} - 40 q^{77} - 4 q^{80} - 36 q^{81} + 40 q^{83} + 24 q^{86} + 48 q^{87} + 96 q^{91} - 24 q^{93} + 32 q^{95} + 12 q^{97} + 48 q^{98}+O(q^{100}) $ 8 * q + 12 * q^3 + 4 * q^5 - 16 * q^7 + 12 * q^10 + 8 * q^11 - 24 * q^13 + 24 * q^15 + 4 * q^16 - 8 * q^17 - 8 * q^20 - 48 * q^21 - 12 * q^22 + 8 * q^28 + 24 * q^30 + 12 * q^33 + 12 * q^35 - 12 * q^36 - 12 * q^38 - 12 * q^41 + 12 * q^42 + 20 * q^43 + 24 * q^45 + 12 * q^48 - 48 * q^51 - 24 * q^52 + 36 * q^53 - 8 * q^55 - 12 * q^57 - 24 * q^58 + 32 * q^61 + 12 * q^62 - 24 * q^63 - 24 * q^66 - 12 * q^67 + 16 * q^68 - 36 * q^70 - 24 * q^71 + 16 * q^73 + 8 * q^76 - 40 * q^77 - 4 * q^80 - 36 * q^81 + 40 * q^83 + 24 * q^86 + 48 * q^87 + 96 * q^91 - 24 * q^93 + 32 * q^95 + 12 * q^97 + 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/190\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	0.633975	−	2.36603i	0.366025	−	1.36603i	−0.500000	−	0.866025i	$-0.666667\pi$
$3$	0.633975	−	2.36603i	0.366025	−	1.36603i	0.866025	−	0.500000i	$-0.166667\pi$
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	−2.03906	+	0.917738i	−0.911894	+	0.410425i
$5$	−2.03906	+	0.917738i	−0.911894	+	0.410425i
$6$	−1.22474	+	2.12132i	−0.500000	+	0.866025i
$7$	−3.22474	−	3.22474i	−1.21884	−	1.21884i	−0.968039	−	0.250800i	$-0.919306\pi$
$7$	−3.22474	−	3.22474i	−1.21884	−	1.21884i	−0.250800	−	0.968039i	$-0.580694\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−2.59808	−	1.50000i	−0.866025	−	0.500000i
$10$	2.20711	−	0.358719i	0.697948	−	0.113437i
$11$	3.44949			1.04006			0.520030	−	0.854148i	$-0.325921\pi$
$11$	3.44949			1.04006			0.520030	+	0.854148i	$0.325921\pi$
$12$	1.73205	−	1.73205i	0.500000	−	0.500000i
$13$	−4.73205	+	1.26795i	−1.31243	+	0.351666i	−0.846139	−	0.532963i	$-0.821079\pi$
$13$	−4.73205	+	1.26795i	−1.31243	+	0.351666i	−0.466296	+	0.884629i	$0.654412\pi$
$14$	2.28024	+	3.94949i	0.609419	+	1.05555i
$15$	0.878680	+	5.40629i	0.226874	+	1.39590i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	0.732051	−	2.73205i	0.177548	−	0.662620i	−0.818555	−	0.574428i	$-0.805225\pi$
$17$	0.732051	−	2.73205i	0.177548	−	0.662620i	0.996104	−	0.0881917i	$-0.0281088\pi$
$18$	2.12132	+	2.12132i	0.500000	+	0.500000i
$19$	−1.25529	−	4.17423i	−0.287984	−	0.957635i
$19$	−1.25529	−	4.17423i	−0.287984	−	0.957635i
$20$	−2.22474	−	0.224745i	−0.497468	−	0.0502545i
$21$	−9.67423	+	5.58542i	−2.11109	+	1.21884i
$22$	−3.33195	−	0.892794i	−0.710374	−	0.190344i
$23$	1.34486	+	5.01910i	0.280423	+	1.04655i	0.952119	+	0.305727i	$0.0988995\pi$
$23$	1.34486	+	5.01910i	0.280423	+	1.04655i	−0.671696	+	0.740827i	$0.734434\pi$
$24$	−2.12132	+	1.22474i	−0.433013	+	0.250000i
$25$	3.31552	−	3.74264i	0.663103	−	0.748528i
$26$	4.89898			0.960769
$27$		0			0
$28$	−1.18034	−	4.40508i	−0.223063	−	0.832483i
$29$	0.389270	−	0.674235i	0.0722855	−	0.125202i	−0.827617	−	0.561293i	$-0.810304\pi$
$29$	0.389270	−	0.674235i	0.0722855	−	0.125202i	0.899903	+	0.436091i	$0.143637\pi$
$30$	0.550510	−	5.44949i	0.100509	−	0.994936i
$31$		−	7.70674i		−	1.38417i	−0.721815	−	0.692086i	$-0.756692\pi$
$31$		−	7.70674i		−	1.38417i	0.721815	−	0.692086i	$-0.243308\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	2.18689	−	8.16158i	0.380688	−	1.42075i
$34$	−1.41421	+	2.44949i	−0.242536	+	0.420084i
$35$	9.53491	+	3.61597i	1.61169	+	0.611211i
$36$	−1.50000	−	2.59808i	−0.250000	−	0.433013i
$37$	0.389270	−	0.389270i	0.0639955	−	0.0639955i	−0.674385	−	0.738380i	$-0.735591\pi$
$37$	0.389270	−	0.389270i	0.0639955	−	0.0639955i	0.738380	+	0.674385i	$0.235591\pi$
$38$	0.132150	+	4.35690i	0.0214376	+	0.706782i
$39$			12.0000i			1.92154i
$40$	2.09077	+	0.792893i	0.330580	+	0.125367i
$41$	−1.50000	+	0.866025i	−0.234261	+	0.135250i	−0.612536	−	0.790443i	$-0.709851\pi$
$41$	−1.50000	+	0.866025i	−0.234261	+	0.135250i	0.378275	+	0.925693i	$0.376517\pi$
$42$	10.7902	−	2.89123i	1.66497	−	0.446126i
$43$	3.48406	+	0.933552i	0.531314	+	0.142365i	0.514495	−	0.857493i	$-0.327979\pi$
$43$	3.48406	+	0.933552i	0.531314	+	0.142365i	0.0168193	+	0.999859i	$0.494646\pi$
$44$	2.98735	+	1.72474i	0.450359	+	0.260015i
$45$	6.67423	+	0.674235i	0.994936	+	0.100509i
$46$		−	5.19615i		−	0.766131i
$47$	6.69213	−	1.79315i	0.976148	−	0.261558i	0.264726	−	0.964324i	$-0.414718\pi$
$47$	6.69213	−	1.79315i	0.976148	−	0.261558i	0.711421	+	0.702766i	$0.248052\pi$
$48$	2.36603	−	0.633975i	0.341506	−	0.0915064i
$49$			13.7980i			1.97114i
$50$	−4.17121	+	2.75699i	−0.589898	+	0.389898i
$51$	−6.00000	−	3.46410i	−0.840168	−	0.485071i
$52$	−4.73205	−	1.26795i	−0.656217	−	0.175833i
$53$	9.99585	−	2.67838i	1.37304	−	0.367904i	0.504449	−	0.863441i	$-0.331695\pi$
$53$	9.99585	−	2.67838i	1.37304	−	0.367904i	0.868587	+	0.495537i	$0.165029\pi$
$54$		0			0
$55$	−7.03371	+	3.16573i	−0.948425	+	0.426866i
$56$			4.56048i			0.609419i
$57$	−10.6722	+	0.323701i	−1.41356	+	0.0428752i
$58$	−0.550510	+	0.550510i	−0.0722855	+	0.0722855i
$59$	−1.73205	−	3.00000i	−0.225494	−	0.390567i	0.730974	−	0.682406i	$-0.239066\pi$
$59$	−1.73205	−	3.00000i	−0.225494	−	0.390567i	−0.956467	+	0.291839i	$0.905733\pi$
$60$	−1.94218	+	5.12132i	−0.250735	+	0.661160i
$61$	4.00000	−	6.92820i	0.512148	−	0.887066i	−0.487753	−	0.872982i	$-0.662183\pi$
$61$	4.00000	−	6.92820i	0.512148	−	0.887066i	0.999901	−	0.0140840i	$-0.00448323\pi$
$62$	−1.99465	+	7.44414i	−0.253321	+	0.945407i
$63$	3.54102	+	13.2153i	0.446126	+	1.66497i
$64$			1.00000i			0.125000i
$65$	8.48528	−	6.92820i	1.05247	−	0.859338i
$66$	−4.22474	+	7.31747i	−0.520030	+	0.900719i
$67$	2.47185	+	9.22508i	0.301985	+	1.12702i	0.935510	+	0.353301i	$0.114941\pi$
$67$	2.47185	+	9.22508i	0.301985	+	1.12702i	−0.633525	+	0.773722i	$0.718392\pi$
$68$	2.00000	−	2.00000i	0.242536	−	0.242536i
$69$	12.7279			1.53226
$70$	−8.27414	−	5.96058i	−0.988948	−	0.712425i
$71$	−3.00000	+	1.73205i	−0.356034	+	0.205557i	−0.667340	−	0.744753i	$-0.732567\pi$
$71$	−3.00000	+	1.73205i	−0.356034	+	0.205557i	0.311305	+	0.950310i	$0.399234\pi$
$72$	0.776457	+	2.89778i	0.0915064	+	0.341506i
$73$	2.11804	+	0.567526i	0.247897	+	0.0664239i	0.380628	−	0.924728i	$-0.375708\pi$
$73$	2.11804	+	0.567526i	0.247897	+	0.0664239i	−0.132731	+	0.991152i	$0.542375\pi$
$74$	−0.476756	+	0.275255i	−0.0554217	+	0.0319978i
$75$	−6.75323	−	10.2173i	−0.779796	−	1.17980i
$76$	1.00000	−	4.24264i	0.114708	−	0.486664i
$77$	−11.1237	−	11.1237i	−1.26767	−	1.26767i
$78$	3.10583	−	11.5911i	0.351666	−	1.31243i
$79$	−5.97469	−	10.3485i	−0.672205	−	1.16429i	−0.977277	−	0.211964i	$-0.932014\pi$
$79$	−5.97469	−	10.3485i	−0.672205	−	1.16429i	0.305072	−	0.952329i	$-0.401319\pi$
$80$	−1.81431	−	1.30701i	−0.202846	−	0.146128i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	1.67303	−	0.448288i	0.184756	−	0.0495051i
$83$	−2.34847	+	2.34847i	−0.257778	+	0.257778i	−0.824150	−	0.566372i	$-0.808347\pi$
$83$	−2.34847	+	2.34847i	−0.257778	+	0.257778i	0.566372	+	0.824150i	$0.308347\pi$
$84$	−11.1708			−1.21884
$85$	1.01461	+	6.24264i	0.110050	+	0.677109i
$86$	−3.12372	−	1.80348i	−0.336840	−	0.194475i
$87$	−1.34847	−	1.34847i	−0.144571	−	0.144571i
$88$	−2.43916	−	2.43916i	−0.260015	−	0.260015i
$89$	1.64456	−	2.84847i	0.174323	−	0.301937i	−0.765603	−	0.643313i	$-0.777559\pi$
$89$	1.64456	−	2.84847i	0.174323	−	0.301937i	0.939927	+	0.341376i	$0.110893\pi$
$90$	−6.27231	−	2.37868i	−0.661160	−	0.250735i
$91$	19.3485	+	11.1708i	2.02827	+	1.17102i
$92$	−1.34486	+	5.01910i	−0.140212	+	0.523277i
$93$	−18.2343	−	4.88588i	−1.89081	−	0.506642i
$94$	−6.92820			−0.714590
$95$	6.39047	+	7.35948i	0.655649	+	0.755066i
$96$	−2.44949			−0.250000
$97$	−9.22508	−	2.47185i	−0.936665	−	0.250979i	−0.241971	−	0.970284i	$-0.577794\pi$
$97$	−9.22508	−	2.47185i	−0.936665	−	0.250979i	−0.694695	+	0.719305i	$0.744460\pi$
$98$	3.57117	−	13.3278i	0.360743	−	1.34631i
$99$	−8.96204	−	5.17423i	−0.900719	−	0.520030i
$100$	4.74264	−	1.58346i	0.474264	−	0.158346i
$101$	−8.34847	+	14.4600i	−0.830704	+	1.43882i	0.0667772	+	0.997768i	$0.478728\pi$
$101$	−8.34847	+	14.4600i	−0.830704	+	1.43882i	−0.897481	+	0.441053i	$0.854605\pi$
$102$	4.89898	+	4.89898i	0.485071	+	0.485071i
$103$	5.58542	+	5.58542i	0.550348	+	0.550348i	0.926541	−	0.376193i	$-0.122767\pi$
$103$	5.58542	+	5.58542i	0.550348	+	0.550348i	−0.376193	+	0.926541i	$0.622767\pi$
$104$	4.24264	+	2.44949i	0.416025	+	0.240192i
$105$	14.6004	−	20.2674i	1.42485	−	1.97790i
$106$	−10.3485			−1.00513
$107$	−8.66025	+	8.66025i	−0.837218	+	0.837218i	−0.988492	−	0.151274i	$-0.951663\pi$
$107$	−8.66025	+	8.66025i	−0.837218	+	0.837218i	0.151274	+	0.988492i	$0.451663\pi$
$108$		0			0
$109$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$109$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$110$	7.61339	−	1.23740i	0.725908	−	0.117981i
$111$	−0.674235	−	1.16781i	−0.0639955	−	0.110843i
$112$	1.18034	−	4.40508i	0.111532	−	0.416241i
$113$	−4.41761	−	4.41761i	−0.415574	−	0.415574i	0.468101	−	0.883675i	$-0.344938\pi$
$113$	−4.41761	−	4.41761i	−0.415574	−	0.415574i	−0.883675	+	0.468101i	$0.844938\pi$
$114$	10.3923	+	2.44949i	0.973329	+	0.229416i
$115$	−7.34847	−	9.00000i	−0.685248	−	0.839254i
$116$	0.674235	−	0.389270i	0.0626011	−	0.0361428i
$117$	14.1962	+	3.80385i	1.31243	+	0.351666i
$118$	0.896575	+	3.34607i	0.0825365	+	0.308030i
$119$	−11.1708	+	6.44949i	−1.02403	+	0.591224i
$120$	3.20150	−	4.44414i	0.292256	−	0.405693i
$121$	0.898979			0.0817254
$122$	−5.65685	+	5.65685i	−0.512148	+	0.512148i
$123$	1.09808	+	4.09808i	0.0990102	+	0.369511i
$124$	3.85337	−	6.67423i	0.346043	−	0.599364i
$125$	−3.32577	+	10.6742i	−0.297465	+	0.954733i
$126$		−	13.6814i		−	1.21884i
$127$	1.06142	+	3.96128i	0.0941860	+	0.351507i	0.996895	−	0.0787452i	$-0.0250913\pi$
$127$	1.06142	+	3.96128i	0.0941860	+	0.351507i	−0.902709	+	0.430252i	$0.858425\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	4.41761	−	7.65153i	0.388949	−	0.673680i
$130$	−9.98930	+	4.49598i	−0.876120	+	0.394323i
$131$	8.62372	+	14.9367i	0.753458	+	1.30503i	0.946137	+	0.323766i	$0.104949\pi$
$131$	8.62372	+	14.9367i	0.753458	+	1.30503i	−0.192679	+	0.981262i	$0.561718\pi$
$132$	5.97469	−	5.97469i	0.520030	−	0.520030i
$133$	−9.41284	+	17.5088i	−0.816196	+	1.51821i
$134$		−	9.55051i		−	0.825038i
$135$		0			0
$136$	−2.44949	+	1.41421i	−0.210042	+	0.121268i
$137$	−2.73205	+	0.732051i	−0.233415	+	0.0625433i	−0.373630	−	0.927578i	$-0.621887\pi$
$137$	−2.73205	+	0.732051i	−0.233415	+	0.0625433i	0.140215	+	0.990121i	$0.455220\pi$
$138$	−12.2942	−	3.29423i	−1.04655	−	0.280423i
$139$	6.14966	+	3.55051i	0.521608	+	0.301150i	0.737592	−	0.675246i	$-0.235963\pi$
$139$	6.14966	+	3.55051i	0.521608	+	0.301150i	−0.215984	+	0.976397i	$0.569296\pi$
$140$	6.44949	+	7.89898i	0.545081	+	0.667586i
$141$		−	16.9706i		−	1.42918i
$142$	3.34607	−	0.896575i	0.280796	−	0.0752389i
$143$	−16.3232	+	4.37378i	−1.36501	+	0.365754i
$144$		−	3.00000i		−	0.250000i
$145$	−0.174973	+	1.73205i	−0.0145307	+	0.143839i
$146$	−1.89898	−	1.09638i	−0.157161	−	0.0907367i
$147$	32.6463	+	8.74756i	2.69262	+	0.721486i
$148$	0.531752	−	0.142483i	0.0437098	−	0.0117120i
$149$	1.34278	−	0.775255i	0.110005	−	0.0635114i	−0.443988	−	0.896033i	$-0.646437\pi$
$149$	1.34278	−	0.775255i	0.110005	−	0.0635114i	0.553993	+	0.832521i	$0.313103\pi$
$150$	3.87868	+	11.6170i	0.316693	+	0.948528i
$151$		−	8.48528i		−	0.690522i	−0.938507	−	0.345261i	$-0.887790\pi$
$151$		−	8.48528i		−	0.690522i	0.938507	−	0.345261i	$-0.112210\pi$
$152$	−2.06400	+	3.83926i	−0.167413	+	0.311405i
$153$	−6.00000	+	6.00000i	−0.485071	+	0.485071i
$154$	7.86566	+	13.6237i	0.633833	+	1.09783i
$155$	7.07277	+	15.7145i	0.568098	+	1.26222i
$156$	−6.00000	+	10.3923i	−0.480384	+	0.832050i
$157$	0.978838	−	3.65307i	0.0781198	−	0.291547i	−0.915803	−	0.401628i	$-0.868444\pi$
$157$	0.978838	−	3.65307i	0.0781198	−	0.291547i	0.993923	+	0.110081i	$0.0351111\pi$
$158$	3.09273	+	11.5422i	0.246044	+	0.918250i
$159$		−	25.3485i		−	2.01026i
$160$	1.41421	+	1.73205i	0.111803	+	0.136931i
$161$	11.8485	−	20.5222i	0.933790	−	1.61737i
$162$	2.32937	+	8.69333i	0.183013	+	0.683013i
$163$	5.34847	−	5.34847i	0.418924	−	0.418924i	−0.465908	−	0.884833i	$-0.654272\pi$
$163$	5.34847	−	5.34847i	0.418924	−	0.418924i	0.884833	+	0.465908i	$0.154272\pi$
$164$	−1.73205			−0.135250
$165$	3.03100	+	18.6489i	0.235963	+	1.45182i
$166$	2.87628	−	1.66062i	0.223242	−	0.128889i
$167$	−6.13322	−	22.8895i	−0.474603	−	1.77124i	−0.622903	−	0.782299i	$-0.714047\pi$
$167$	−6.13322	−	22.8895i	−0.474603	−	1.77124i	0.148300	−	0.988942i	$-0.452620\pi$
$168$	10.7902	+	2.89123i	0.832483	+	0.223063i
$169$	9.52628	−	5.50000i	0.732791	−	0.423077i
$170$	0.635674	−	6.29253i	0.0487540	−	0.482615i
$171$	−3.00000	+	12.7279i	−0.229416	+	0.973329i
$172$	2.55051	+	2.55051i	0.194475	+	0.194475i
$173$	1.41043	−	5.26380i	0.107233	−	0.400200i	−0.891356	−	0.453304i	$-0.850245\pi$
$173$	1.41043	−	5.26380i	0.107233	−	0.400200i	0.998589	+	0.0531048i	$0.0169117\pi$
$174$	0.953512	+	1.65153i	0.0722855	+	0.125202i
$175$	−22.7608	+	1.37737i	−1.72055	+	0.104119i
$176$	1.72474	+	2.98735i	0.130008	+	0.225180i
$177$	−8.19615	+	2.19615i	−0.616061	+	0.165073i
$178$	−2.32577	+	2.32577i	−0.174323	+	0.174323i
$179$	−5.97469			−0.446569			−0.223285	−	0.974753i	$-0.571678\pi$
$179$	−5.97469			−0.446569			−0.223285	+	0.974753i	$0.571678\pi$
$180$	5.44294	+	3.92102i	0.405693	+	0.292256i
$181$	11.3258	+	6.53893i	0.841838	+	0.486035i	0.857888	−	0.513836i	$-0.171776\pi$
$181$	11.3258	+	6.53893i	0.841838	+	0.486035i	−0.0160509	+	0.999871i	$0.505109\pi$
$182$	−15.7980	−	15.7980i	−1.17102	−	1.17102i
$183$	−13.8564	−	13.8564i	−1.02430	−	1.02430i
$184$	2.59808	−	4.50000i	0.191533	−	0.331744i
$185$	−0.436496	+	1.15099i	−0.0320918	+	0.0846225i
$186$	16.3485	+	9.43879i	1.19873	+	0.692086i
$187$	2.52520	−	9.42418i	0.184661	−	0.689164i
$188$	6.69213	+	1.79315i	0.488074	+	0.130779i
$189$		0			0
$190$	−4.26795	−	8.76268i	−0.309630	−	0.635712i
$191$	8.24745			0.596764			0.298382	−	0.954446i	$-0.403553\pi$
$191$	8.24745			0.596764			0.298382	+	0.954446i	$0.403553\pi$
$192$	2.36603	+	0.633975i	0.170753	+	0.0457532i
$193$	−0.349010	+	1.30252i	−0.0251223	+	0.0937575i	−0.977349	−	0.211635i	$-0.932121\pi$
$193$	−0.349010	+	1.30252i	−0.0251223	+	0.0937575i	0.952226	+	0.305393i	$0.0987878\pi$
$194$	8.27098	+	4.77526i	0.593822	+	0.342843i
$195$	−11.0129	−	24.4687i	−0.788647	−	1.75224i
$196$	−6.89898	+	11.9494i	−0.492784	+	0.853527i
$197$	12.6742	+	12.6742i	0.903002	+	0.903002i	0.995695	−	0.0926929i	$-0.0295475\pi$
$197$	12.6742	+	12.6742i	0.903002	+	0.903002i	−0.0926929	+	0.995695i	$0.529547\pi$
$198$	7.31747	+	7.31747i	0.520030	+	0.520030i
$199$	8.48528	+	4.89898i	0.601506	+	0.347279i	0.769634	−	0.638486i	$-0.220439\pi$
$199$	8.48528	+	4.89898i	0.601506	+	0.347279i	−0.168128	+	0.985765i	$0.553772\pi$
$200$	−4.99087	+	0.302023i	−0.352908	+	0.0213563i
$201$	23.3939			1.65008
$202$	11.8065	−	11.8065i	0.830704	−	0.830704i
$203$	−3.42953	+	0.918940i	−0.240706	+	0.0644969i
$204$	−3.46410	−	6.00000i	−0.242536	−	0.420084i
$205$	2.26380	−	3.14248i	0.158111	−	0.219481i
$206$	−3.94949	−	6.84072i	−0.275174	−	0.476615i
$207$	4.03459	−	15.0573i	0.280423	−	1.04655i
$208$	−3.46410	−	3.46410i	−0.240192	−	0.240192i
$209$	−4.33013	−	14.3990i	−0.299521	−	0.995998i
$210$	−19.3485	+	15.7980i	−1.33517	+	1.09016i
$211$	23.1742	−	13.3797i	1.59538	−	0.921093i	0.603019	−	0.797727i	$-0.293964\pi$
$211$	23.1742	−	13.3797i	1.59538	−	0.921093i	0.992361	−	0.123366i	$-0.0393690\pi$
$212$	9.99585	+	2.67838i	0.686518	+	0.183952i
$213$	2.19615	+	8.19615i	0.150478	+	0.561591i
$214$	10.6066	−	6.12372i	0.725052	−	0.418609i
$215$	−7.96096	+	1.29389i	−0.542933	+	0.0882425i
$216$		0			0
$217$	−24.8523	+	24.8523i	−1.68708	+	1.68708i
$218$		0			0
$219$	2.68556	−	4.65153i	0.181473	−	0.314321i
$220$	−7.67423	−	0.775255i	−0.517397	−	0.0522677i
$221$			13.8564i			0.932083i
$222$	0.349010	+	1.30252i	0.0234240	+	0.0874195i
$223$	4.58030	−	17.0939i	0.306720	−	1.14469i	−0.624735	−	0.780837i	$-0.714793\pi$
$223$	4.58030	−	17.0939i	0.306720	−	1.14469i	0.931455	−	0.363857i	$-0.118540\pi$
$224$	−2.28024	+	3.94949i	−0.152355	+	0.263886i
$225$	−14.2279	+	4.75039i	−0.948528	+	0.316693i
$226$	3.12372	+	5.41045i	0.207787	+	0.359898i
$227$	14.4600	−	14.4600i	0.959742	−	0.959742i	−0.0394783	−	0.999220i	$-0.512570\pi$
$227$	14.4600	−	14.4600i	0.959742	−	0.959742i	0.999220	+	0.0394783i	$0.0125696\pi$
$228$	−9.40422	−	5.05575i	−0.622810	−	0.334825i
$229$			20.4495i			1.35134i	0.737204	+	0.675670i	$0.236146\pi$
$229$			20.4495i			1.35134i	−0.737204	+	0.675670i	$0.763854\pi$
$230$	4.76870	+	10.5953i	0.314439	+	0.698631i
$231$	−33.3712	+	19.2669i	−2.19566	+	1.26767i
$232$	−0.752011	+	0.201501i	−0.0493719	+	0.0132292i
$233$	−3.34607	−	0.896575i	−0.219208	−	0.0587366i	0.147543	−	0.989056i	$-0.452863\pi$
$233$	−3.34607	−	0.896575i	−0.219208	−	0.0587366i	−0.366751	+	0.930319i	$0.619530\pi$
$234$	−12.7279	−	7.34847i	−0.832050	−	0.480384i
$235$	−12.0000	+	9.79796i	−0.782794	+	0.639148i
$236$		−	3.46410i		−	0.225494i
$237$	−28.2725	+	7.57561i	−1.83650	+	0.492088i
$238$	12.4595	−	3.33850i	0.807627	−	0.216403i
$239$		−	5.79796i		−	0.375039i	−0.982261	−	0.187519i	$-0.939955\pi$
$239$		−	5.79796i		−	0.375039i	0.982261	−	0.187519i	$-0.0600447\pi$
$240$	−4.24264	+	3.46410i	−0.273861	+	0.223607i
$241$	−5.69694	−	3.28913i	−0.366972	−	0.211871i	0.305163	−	0.952300i	$-0.401289\pi$
$241$	−5.69694	−	3.28913i	−0.366972	−	0.211871i	−0.672135	+	0.740429i	$0.734622\pi$
$242$	−0.868348	−	0.232673i	−0.0558195	−	0.0149568i
$243$	−21.2942	+	5.70577i	−1.36603	+	0.366025i
$244$	6.92820	−	4.00000i	0.443533	−	0.256074i
$245$	−12.6629	−	28.1348i	−0.809003	−	1.79747i
$246$		−	4.24264i		−	0.270501i
$247$	11.2328	+	18.1610i	0.714728	+	1.15556i
$248$	−5.44949	+	5.44949i	−0.346043	+	0.346043i
$249$	4.06767	+	7.04541i	0.257778	+	0.446485i
$250$	5.97514	−	9.44975i	0.377901	−	0.597655i
$251$	−4.44949	+	7.70674i	−0.280849	+	0.486445i	−0.971594	−	0.236653i	$-0.923949\pi$
$251$	−4.44949	+	7.70674i	−0.280849	+	0.486445i	0.690745	+	0.723099i	$0.257283\pi$
$252$	−3.54102	+	13.2153i	−0.223063	+	0.832483i
$253$	4.63909	+	17.3133i	0.291657	+	1.08848i
$254$		−	4.10102i		−	0.257321i
$255$	15.4135	+	1.55708i	0.965230	+	0.0975080i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.73980	+	13.9571i	0.233283	+	0.870622i	0.978916	+	0.204265i	$0.0654806\pi$
$257$	3.73980	+	13.9571i	0.233283	+	0.870622i	−0.745633	+	0.666357i	$0.767853\pi$
$258$	−6.24745	+	6.24745i	−0.388949	+	0.388949i
$259$	−2.51059			−0.156000
$260$	10.8126	−	1.75736i	0.670567	−	0.108987i
$261$	−2.02270	+	1.16781i	−0.125202	+	0.0722855i
$262$	−4.46397	−	16.6598i	−0.275785	−	1.02924i
$263$	27.8275	+	7.45637i	1.71592	+	0.459779i	0.976863	−	0.213864i	$-0.0686051\pi$
$263$	27.8275	+	7.45637i	1.71592	+	0.459779i	0.739056	+	0.673644i	$0.235272\pi$
$264$	−7.31747	+	4.22474i	−0.450359	+	0.260015i
$265$	−17.9241	+	14.6349i	−1.10107	+	0.899018i
$266$	13.6237	−	14.4760i	0.835324	−	0.887582i
$267$	−5.69694	−	5.69694i	−0.348647	−	0.348647i
$268$	−2.47185	+	9.22508i	−0.150993	+	0.563512i
$269$	−3.46410	−	6.00000i	−0.211210	−	0.365826i	0.740883	−	0.671634i	$-0.234407\pi$
$269$	−3.46410	−	6.00000i	−0.211210	−	0.365826i	−0.952093	+	0.305807i	$0.901074\pi$
$270$		0			0
$271$	−16.3485	−	28.3164i	−0.993099	−	1.72010i	−0.598118	−	0.801408i	$-0.704084\pi$
$271$	−16.3485	−	28.3164i	−0.993099	−	1.72010i	−0.394981	−	0.918689i	$-0.629249\pi$
$272$	2.73205	−	0.732051i	0.165655	−	0.0443871i
$273$	38.6969	−	38.6969i	2.34205	−	2.34205i
$274$	2.82843			0.170872
$275$	11.4368	−	12.9102i	0.689667	−	0.778514i
$276$	11.0227	+	6.36396i	0.663489	+	0.383065i
$277$	−5.79796	−	5.79796i	−0.348366	−	0.348366i	0.511135	−	0.859500i	$-0.329225\pi$
$277$	−5.79796	−	5.79796i	−0.348366	−	0.348366i	−0.859500	+	0.511135i	$0.829225\pi$
$278$	−5.02118	−	5.02118i	−0.301150	−	0.301150i
$279$	−11.5601	+	20.0227i	−0.692086	+	1.19873i
$280$	−4.18532	−	9.29908i	−0.250121	−	0.555726i
$281$	−10.5000	−	6.06218i	−0.626377	−	0.361639i	0.152970	−	0.988231i	$-0.451116\pi$
$281$	−10.5000	−	6.06218i	−0.626377	−	0.361639i	−0.779348	+	0.626592i	$0.784449\pi$
$282$	−4.39230	+	16.3923i	−0.261558	+	0.976148i
$283$	6.07812	+	1.62863i	0.361306	+	0.0968118i	0.434905	−	0.900476i	$-0.356782\pi$
$283$	6.07812	+	1.62863i	0.361306	+	0.0968118i	−0.0735989	+	0.997288i	$0.523448\pi$
$284$	−3.46410			−0.205557
$285$	21.4641	−	10.4543i	1.27142	−	0.619259i
$286$	16.8990			0.999258
$287$	7.62983	+	2.04441i	0.450375	+	0.120677i
$288$	−0.776457	+	2.89778i	−0.0457532	+	0.170753i
$289$	7.79423	+	4.50000i	0.458484	+	0.264706i
$290$	0.617298	−	1.62775i	0.0362490	−	0.0955846i
$291$	−11.6969	+	20.2597i	−0.685687	+	1.18764i
$292$	1.55051	+	1.55051i	0.0907367	+	0.0907367i
$293$	−1.94635	−	1.94635i	−0.113707	−	0.113707i	0.647964	−	0.761671i	$-0.275621\pi$
$293$	−1.94635	−	1.94635i	−0.113707	−	0.113707i	−0.761671	+	0.647964i	$0.775621\pi$
$294$	−29.2699	−	16.8990i	−1.70705	−	0.985568i
$295$	6.28497	+	4.52761i	0.365925	+	0.263607i
$296$	−0.550510			−0.0319978
$297$		0			0
$298$	−1.49768	+	0.401302i	−0.0867582	+	0.0232468i
$299$	−12.7279	−	22.0454i	−0.736075	−	1.27492i
$300$	−0.739803	−	12.2251i	−0.0427126	−	0.705816i
$301$	−8.22474	−	14.2457i	−0.474066	−	0.821107i
$302$	−2.19615	+	8.19615i	−0.126374	+	0.471636i
$303$	28.9199	+	28.9199i	1.66141	+	1.66141i
$304$	2.98735	−	3.17423i	0.171336	−	0.182055i
$305$	−1.79796	+	17.7980i	−0.102951	+	1.01911i
$306$	7.34847	−	4.24264i	0.420084	−	0.242536i
$307$	−1.30252	−	0.349010i	−0.0743388	−	0.0199190i	0.221458	−	0.975170i	$-0.428918\pi$
$307$	−1.30252	−	0.349010i	−0.0743388	−	0.0199190i	−0.295797	+	0.955251i	$0.595585\pi$
$308$	−4.07157	−	15.1953i	−0.231999	−	0.865832i
$309$	16.7563	−	9.67423i	0.953231	−	0.550348i
$310$	−2.76456	−	17.0096i	−0.157016	−	0.966081i
$311$	6.20204			0.351685			0.175843	−	0.984418i	$-0.443735\pi$
$311$	6.20204			0.351685			0.175843	+	0.984418i	$0.443735\pi$
$312$	8.48528	−	8.48528i	0.480384	−	0.480384i
$313$	−8.43520	−	31.4806i	−0.476786	−	1.77939i	−0.614499	−	0.788917i	$-0.710642\pi$
$313$	−8.43520	−	31.4806i	−0.476786	−	1.77939i	0.137713	−	0.990472i	$-0.456025\pi$
$314$	−1.89097	+	3.27526i	−0.106714	+	0.184833i
$315$	−19.3485	−	23.6969i	−1.09016	−	1.33517i
$316$		−	11.9494i		−	0.672205i
$317$	2.39342	+	8.93235i	0.134428	+	0.501691i	1.00000		0.000906171i	$0.000288443\pi$
$317$	2.39342	+	8.93235i	0.134428	+	0.501691i	−0.865572	+	0.500785i	$0.833045\pi$
$318$	−6.56067	+	24.4847i	−0.367904	+	1.37304i
$319$	1.34278	−	2.32577i	0.0751813	−	0.130218i
$320$	−0.917738	−	2.03906i	−0.0513031	−	0.113987i
$321$	15.0000	+	25.9808i	0.837218	+	1.45010i
$322$	−16.7563	+	16.7563i	−0.933790	+	0.933790i
$323$	−12.3232	+	0.373778i	−0.685679	+	0.0207975i
$324$		−	9.00000i		−	0.500000i
$325$	−10.9437	+	21.9143i	−0.607048	+	1.21559i
$326$	−6.55051	+	3.78194i	−0.362799	+	0.209462i
$327$		0			0
$328$	1.67303	+	0.448288i	0.0923778	+	0.0247525i
$329$	−27.3629	−	15.7980i	−1.50856	−	0.870970i
$330$	1.89898	−	18.7980i	0.104535	−	1.03479i
$331$			21.3882i			1.17560i	0.809006	+	0.587800i	$0.200006\pi$
$331$			21.3882i			1.17560i	−0.809006	+	0.587800i	$0.799994\pi$
$332$	−3.20807	+	0.859599i	−0.176066	+	0.0471766i
$333$	−1.59526	+	0.427448i	−0.0874195	+	0.0234240i
$334$			23.6969i			1.29664i
$335$	−13.5065	−	16.5420i	−0.737937	−	0.903784i
$336$	−9.67423	−	5.58542i	−0.527773	−	0.304710i
$337$	17.3867	+	4.65874i	0.947112	+	0.253778i	0.699136	−	0.714988i	$-0.253568\pi$
$337$	17.3867	+	4.65874i	0.947112	+	0.253778i	0.247976	+	0.968766i	$0.420235\pi$
$338$	−10.6252	+	2.84701i	−0.577934	+	0.154857i
$339$	−13.2528	+	7.65153i	−0.719795	+	0.415574i
$340$	−2.24264	+	5.91359i	−0.121624	+	0.320710i
$341$		−	26.5843i		−	1.43962i
$342$	6.19201	−	11.5178i	0.334825	−	0.622810i
$343$	21.9217	−	21.9217i	1.18366	−	1.18366i
$344$	−1.80348	−	3.12372i	−0.0972373	−	0.168420i
$345$	−25.9530	+	11.6809i	−1.39726	+	0.628878i
$346$	−2.72474	+	4.71940i	−0.146483	+	0.253716i
$347$	7.81408	−	29.1626i	0.419482	−	1.56553i	−0.356204	−	0.934408i	$-0.615929\pi$
$347$	7.81408	−	29.1626i	0.419482	−	1.56553i	0.775686	−	0.631119i	$-0.217404\pi$
$348$	−0.493574	−	1.84204i	−0.0264583	−	0.0987439i
$349$			28.8990i			1.54693i	0.633841	+	0.773463i	$0.281477\pi$
$349$			28.8990i			1.54693i	−0.633841	+	0.773463i	$0.718523\pi$
$350$	22.3417	+	4.56048i	1.19421	+	0.243768i
$351$		0			0
$352$	−0.892794	−	3.33195i	−0.0475861	−	0.177594i
$353$	−16.3485	+	16.3485i	−0.870141	+	0.870141i	−0.992487	−	0.122346i	$-0.960958\pi$
$353$	−16.3485	+	16.3485i	−0.870141	+	0.870141i	0.122346	+	0.992487i	$0.460958\pi$
$354$	8.48528			0.450988
$355$	4.52761	−	6.28497i	0.240300	−	0.333571i
$356$	2.84847	−	1.64456i	0.150969	−	0.0871617i
$357$	8.17763	+	30.5193i	0.432806	+	1.61525i
$358$	5.77111	+	1.54636i	0.305013	+	0.0817279i
$359$	3.63907	−	2.10102i	0.192063	−	0.110888i	−0.400885	−	0.916128i	$-0.631297\pi$
$359$	3.63907	−	2.10102i	0.192063	−	0.110888i	0.592948	+	0.805241i	$0.297964\pi$
$360$	−4.24264	−	5.19615i	−0.223607	−	0.273861i
$361$	−15.8485	+	10.4798i	−0.834130	+	0.551568i
$362$	−9.24745	−	9.24745i	−0.486035	−	0.486035i
$363$	0.569930	−	2.12701i	0.0299136	−	0.111639i
$364$	11.1708	+	19.3485i	0.585511	+	1.01414i
$365$	−4.83964	+	0.786583i	−0.253318	+	0.0411716i
$366$	9.79796	+	16.9706i	0.512148	+	0.887066i
$367$	25.5405	−	6.84355i	1.33320	−	0.357231i	0.479295	−	0.877654i	$-0.340893\pi$
$367$	25.5405	−	6.84355i	1.33320	−	0.357231i	0.853908	+	0.520423i	$0.174226\pi$
$368$	−3.67423	+	3.67423i	−0.191533	+	0.191533i
$369$	5.19615			0.270501
$370$	0.719521	−	0.998798i	0.0374061	−	0.0519250i
$371$	−40.8712	−	23.5970i	−2.12193	−	1.22509i
$372$	−13.3485	−	13.3485i	−0.692086	−	0.692086i
$373$	−12.6886	−	12.6886i	−0.656991	−	0.656991i	0.297676	−	0.954667i	$-0.403788\pi$
$373$	−12.6886	−	12.6886i	−0.656991	−	0.656991i	−0.954667	+	0.297676i	$0.903788\pi$
$374$	−4.87832	+	8.44949i	−0.252252	+	0.436913i
$375$	23.1471	+	14.6360i	1.19531	+	0.755802i
$376$	−6.00000	−	3.46410i	−0.309426	−	0.178647i
$377$	−0.987148	+	3.68409i	−0.0508407	+	0.189740i
$378$		0			0
$379$	21.9917			1.12964			0.564820	−	0.825214i	$-0.308946\pi$
$379$	21.9917			1.12964			0.564820	+	0.825214i	$0.308946\pi$
$380$	1.85457	+	9.56873i	0.0951376	+	0.490865i
$381$	10.0454			0.514642
$382$	−7.96642	−	2.13460i	−0.407598	−	0.109215i
$383$	2.53590	−	9.46410i	0.129578	−	0.483593i	−0.870383	−	0.492375i	$-0.836129\pi$
$383$	2.53590	−	9.46410i	0.129578	−	0.483593i	0.999961	+	0.00878215i	$0.00279548\pi$
$384$	−2.12132	−	1.22474i	−0.108253	−	0.0625000i
$385$	32.8906	+	12.4733i	1.67626	+	0.635696i
$386$	0.674235	−	1.16781i	0.0343176	−	0.0594399i
$387$	−7.65153	−	7.65153i	−0.388949	−	0.388949i
$388$	−6.75323	−	6.75323i	−0.342843	−	0.342843i
$389$	5.97469	+	3.44949i	0.302929	+	0.174896i	0.643758	−	0.765229i	$-0.277374\pi$
$389$	5.97469	+	3.44949i	0.302929	+	0.174896i	−0.340829	+	0.940125i	$0.610708\pi$
$390$	4.30463	+	26.4853i	0.217974	+	1.34113i
$391$	14.6969			0.743256
$392$	9.75663	−	9.75663i	0.492784	−	0.492784i
$393$	40.8079	−	10.9344i	2.05849	−	0.551570i
$394$	−8.96204	−	15.5227i	−0.451501	−	0.782023i
$395$	21.6799	+	15.6179i	1.09084	+	0.785823i
$396$	−5.17423	−	8.96204i	−0.260015	−	0.450359i
$397$	3.01047	−	11.2352i	0.151091	−	0.563879i	−0.848318	−	0.529488i	$-0.822384\pi$
$397$	3.01047	−	11.2352i	0.151091	−	0.563879i	0.999408	−	0.0343912i	$-0.0109492\pi$
$398$	−6.92820	−	6.92820i	−0.347279	−	0.347279i
$399$	35.4589	+	33.3712i	1.77516	+	1.67065i
$400$	4.89898	+	1.00000i	0.244949	+	0.0500000i
$401$	−15.0000	+	8.66025i	−0.749064	+	0.432472i	−0.825356	−	0.564613i	$-0.809025\pi$
$401$	−15.0000	+	8.66025i	−0.749064	+	0.432472i	0.0762914	+	0.997086i	$0.475692\pi$
$402$	−22.5967	−	6.05478i	−1.12702	−	0.301985i
$403$	9.77176	+	36.4687i	0.486766	+	1.81664i
$404$	−14.4600	+	8.34847i	−0.719411	+	0.415352i
$405$	16.3288	+	11.7631i	0.811386	+	0.584511i
$406$	3.55051			0.176209
$407$	1.34278	−	1.34278i	0.0665592	−	0.0665592i
$408$	1.79315	+	6.69213i	0.0887742	+	0.331310i
$409$	−7.79423	+	13.5000i	−0.385400	+	0.667532i	−0.991825	−	0.127609i	$-0.959270\pi$
$409$	−7.79423	+	13.5000i	−0.385400	+	0.667532i	0.606425	+	0.795141i	$0.292603\pi$
$410$	−3.00000	+	2.44949i	−0.148159	+	0.120972i
$411$			6.92820i			0.341743i
$412$	2.04441	+	7.62983i	0.100721	+	0.375895i
$413$	−4.08881	+	15.2597i	−0.201197	+	0.750879i
$414$	−7.79423	+	13.5000i	−0.383065	+	0.663489i
$415$	2.63339	−	6.94394i	0.129268	−	0.340865i
$416$	2.44949	+	4.24264i	0.120096	+	0.208013i
$417$	12.2993	−	12.2993i	0.602301	−	0.602301i
$418$	0.455851	+	15.0291i	0.0222964	+	0.735096i
$419$			6.34847i			0.310143i	0.987903	+	0.155072i	$0.0495608\pi$
$419$			6.34847i			0.310143i	−0.987903	+	0.155072i	$0.950439\pi$
$420$	22.7780	−	10.2519i	1.11145	−	0.500242i
$421$	15.6742	−	9.04952i	0.763915	−	0.441047i	−0.0667843	−	0.997767i	$-0.521274\pi$
$421$	15.6742	−	9.04952i	0.763915	−	0.441047i	0.830700	+	0.556721i	$0.187941\pi$
$422$	−25.8475	+	6.92582i	−1.25824	+	0.337143i
$423$	−20.0764	−	5.37945i	−0.976148	−	0.261558i
$424$	−8.96204	−	5.17423i	−0.435235	−	0.251283i
$425$	−7.79796	−	11.7980i	−0.378257	−	0.572285i
$426$		−	8.48528i		−	0.411113i
$427$	−35.2407	+	9.44271i	−1.70542	+	0.456965i
$428$	−11.8301	+	3.16987i	−0.571831	+	0.153222i
$429$			41.3939i			1.99852i
$430$	8.02458	+	0.810647i	0.386980	+	0.0390929i
$431$	−2.02270	−	1.16781i	−0.0974302	−	0.0562514i	0.450493	−	0.892780i	$-0.351248\pi$
$431$	−2.02270	−	1.16781i	−0.0974302	−	0.0562514i	−0.547923	+	0.836528i	$0.684581\pi$
$432$		0			0
$433$	4.49303	−	1.20390i	0.215921	−	0.0578560i	−0.149237	−	0.988802i	$-0.547682\pi$
$433$	4.49303	−	1.20390i	0.215921	−	0.0578560i	0.365158	+	0.930946i	$0.381015\pi$
$434$	30.4377	−	17.5732i	1.46106	−	0.843541i
$435$	3.98715	+	1.51207i	0.191169	+	0.0724980i
$436$		0			0
$437$	19.2627	−	11.9142i	0.921460	−	0.569935i
$438$	−3.79796	+	3.79796i	−0.181473	+	0.181473i
$439$	−15.8028	−	27.3712i	−0.754224	−	1.30635i	−0.945759	−	0.324869i	$-0.894680\pi$
$439$	−15.8028	−	27.3712i	−0.754224	−	1.30635i	0.191535	−	0.981486i	$-0.438654\pi$
$440$	7.21209	+	2.73508i	0.343823	+	0.130390i
$441$	20.6969	−	35.8481i	0.985568	−	1.70705i
$442$	3.58630	−	13.3843i	0.170583	−	0.636624i
$443$	−7.97861	−	29.7766i	−0.379075	−	1.41473i	−0.847298	−	0.531117i	$-0.821772\pi$
$443$	−7.97861	−	29.7766i	−0.379075	−	1.41473i	0.468223	−	0.883610i	$-0.344894\pi$
$444$		−	1.34847i		−	0.0639955i
$445$	−0.739215	+	7.31747i	−0.0350421	+	0.346881i
$446$	−8.84847	+	15.3260i	−0.418987	+	0.725707i
$447$	−0.982984	−	3.66855i	−0.0464936	−	0.173516i
$448$	3.22474	−	3.22474i	0.152355	−	0.152355i
$449$	8.66025			0.408703			0.204351	−	0.978898i	$-0.434492\pi$
$449$	8.66025			0.408703			0.204351	+	0.978898i	$0.434492\pi$
$450$	14.9726	−	0.906070i	0.705816	−	0.0427126i
$451$	−5.17423	+	2.98735i	−0.243645	+	0.140669i
$452$	−1.61696	−	6.03457i	−0.0760553	−	0.283842i
$453$	−20.0764	−	5.37945i	−0.943271	−	0.252749i
$454$	−17.7098	+	10.2247i	−0.831161	+	0.479871i
$455$	−49.7046	−	5.02118i	−2.33019	−	0.235397i
$456$	7.77526	+	7.31747i	0.364110	+	0.342672i
$457$	5.24745	+	5.24745i	0.245465	+	0.245465i	0.819107	−	0.573641i	$-0.194470\pi$
$457$	5.24745	+	5.24745i	0.245465	+	0.245465i	−0.573641	+	0.819107i	$0.694470\pi$
$458$	5.29272	−	19.7527i	0.247312	−	0.922983i
$459$		0			0
$460$	−1.86396	−	11.4685i	−0.0869076	−	0.534720i
$461$	17.8990	+	31.0019i	0.833639	+	1.44390i	0.895134	+	0.445797i	$0.147080\pi$
$461$	17.8990	+	31.0019i	0.833639	+	1.44390i	−0.0614955	+	0.998107i	$0.519587\pi$
$462$	37.2207	−	9.97326i	1.73166	−	0.463998i
$463$	−8.77526	+	8.77526i	−0.407821	+	0.407821i	−0.880978	−	0.473157i	$-0.843114\pi$
$463$	−8.77526	+	8.77526i	−0.407821	+	0.407821i	0.473157	+	0.880978i	$0.343114\pi$
$464$	0.778539			0.0361428
$465$	41.6648	−	6.77176i	1.93216	−	0.314033i
$466$	3.00000	+	1.73205i	0.138972	+	0.0802357i
$467$	18.5505	+	18.5505i	0.858415	+	0.858415i	0.991151	−	0.132736i	$-0.0423763\pi$
$467$	18.5505	+	18.5505i	0.858415	+	0.858415i	−0.132736	+	0.991151i	$0.542376\pi$
$468$	10.3923	+	10.3923i	0.480384	+	0.480384i
$469$	21.7774	−	37.7196i	1.00559	−	1.74173i
$470$	14.1270	−	6.35827i	0.651630	−	0.293285i
$471$	−8.02270	−	4.63191i	−0.369667	−	0.213427i
$472$	−0.896575	+	3.34607i	−0.0412682	+	0.154015i
$473$	12.0182	+	3.22028i	0.552599	+	0.148068i
$474$	29.2699			1.34441
$475$	−19.7846	−	9.14162i	−0.907780	−	0.419446i
$476$	−12.8990			−0.591224
$477$	−29.9876	−	8.03514i	−1.37304	−	0.367904i
$478$	−1.50062	+	5.60040i	−0.0686369	+	0.256156i
$479$	27.1879	+	15.6969i	1.24225	+	0.717211i	0.969551	−	0.244889i	$-0.0787515\pi$
$479$	27.1879	+	15.6969i	1.24225	+	0.717211i	0.272695	+	0.962100i	$0.412085\pi$
$480$	4.99465	−	2.24799i	0.227974	−	0.102606i
$481$	−1.34847	+	2.33562i	−0.0614849	+	0.106495i
$482$	4.65153	+	4.65153i	0.211871	+	0.211871i
$483$	−41.0443	−	41.0443i	−1.86758	−	1.86758i
$484$	0.778539	+	0.449490i	0.0353881	+	0.0204314i
$485$	21.0790	−	3.42595i	0.957148	−	0.155565i
$486$	22.0454			1.00000
$487$	−30.2627	+	30.2627i	−1.37134	+	1.37134i	−0.512867	+	0.858468i	$0.671417\pi$
$487$	−30.2627	+	30.2627i	−1.37134	+	1.37134i	−0.858468	+	0.512867i	$0.828583\pi$
$488$	−7.72741	+	2.07055i	−0.349803	+	0.0937295i
$489$	−9.26382	−	16.0454i	−0.418924	−	0.725598i
$490$	4.94960	+	30.4536i	0.223600	+	1.37575i
$491$	−2.82577	−	4.89437i	−0.127525	−	0.220880i	0.795192	−	0.606358i	$-0.207370\pi$
$491$	−2.82577	−	4.89437i	−0.127525	−	0.220880i	−0.922717	+	0.385478i	$0.874037\pi$
$492$	−1.09808	+	4.09808i	−0.0495051	+	0.184756i
$493$	−1.55708	−	1.55708i	−0.0701273	−	0.0701273i
$494$	−6.14966	−	20.4495i	−0.276686	−	0.920066i
$495$	23.0227	+	2.32577i	1.03479	+	0.104535i
$496$	6.67423	−	3.85337i	0.299682	−	0.173021i
$497$	15.2597	+	4.08881i	0.684489	+	0.183408i
$498$	−2.10558	−	7.85813i	−0.0943533	−	0.352131i
$499$	−2.81237	+	1.62372i	−0.125899	+	0.0726879i	−0.561627	−	0.827391i	$-0.689824\pi$
$499$	−2.81237	+	1.62372i	−0.125899	+	0.0726879i	0.435728	+	0.900078i	$0.356491\pi$
$500$	−8.21731	+	7.58128i	−0.367489	+	0.339045i
$501$	−58.0454			−2.59328
$502$	6.29253	−	6.29253i	0.280849	−	0.280849i
$503$	9.15895	+	34.1816i	0.408377	+	1.52408i	0.797741	+	0.603000i	$0.206028\pi$
$503$	9.15895	+	34.1816i	0.408377	+	1.52408i	−0.389364	+	0.921084i	$0.627305\pi$
$504$	6.84072	−	11.8485i	0.304710	−	0.527773i
$505$	3.75255	−	37.1464i	0.166986	−	1.65299i
$506$		−	17.9241i		−	0.796822i
$507$	−6.97372	−	26.0263i	−0.309714	−	1.15587i
$508$	−1.06142	+	3.96128i	−0.0470930	+	0.175753i
$509$	6.53893	−	11.3258i	0.289833	−	0.502006i	−0.683937	−	0.729541i	$-0.739734\pi$
$509$	6.53893	−	11.3258i	0.289833	−	0.502006i	0.973770	+	0.227536i	$0.0730669\pi$
$510$	−14.4853	−	5.49333i	−0.641419	−	0.243249i
$511$	−5.00000	−	8.66025i	−0.221187	−	0.383107i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$		−	14.4495i		−	0.637340i
$515$	−16.5150	−	6.26305i	−0.727736	−	0.275983i
$516$	7.65153	−	4.41761i	0.336840	−	0.194475i
$517$	23.0844	−	6.18546i	1.01525	−	0.272036i
$518$	2.42504	+	0.649788i	0.106550	+	0.0285501i
$519$	−11.5601	−	6.67423i	−0.507433	−	0.292966i
$520$	−10.8990	−	1.10102i	−0.477952	−	0.0482829i
$521$			15.0635i			0.659946i	0.943990	+	0.329973i	$0.107040\pi$
$521$			15.0635i			0.659946i	−0.943990	+	0.329973i	$0.892960\pi$
$522$	2.25603	−	0.604502i	0.0987439	−	0.0264583i
$523$	−33.9488	+	9.09656i	−1.48448	+	0.397765i	−0.907869	−	0.419254i	$-0.862292\pi$
$523$	−33.9488	+	9.09656i	−1.48448	+	0.397765i	−0.576610	+	0.817019i	$0.695625\pi$
$524$			17.2474i			0.753458i
$525$	−11.1708	+	54.7257i	−0.487536	+	2.38843i
$526$	−24.9495	−	14.4046i	−1.08785	−	0.628070i
$527$	−21.0552	−	5.64173i	−0.917179	−	0.245757i
$528$	8.16158	−	2.18689i	0.355187	−	0.0951721i
$529$	−3.46410	+	2.00000i	−0.150613	+	0.0869565i
$530$	21.1011	−	9.49718i	0.916574	−	0.412531i
$531$			10.3923i			0.450988i
$532$	−16.9062	+	10.4567i	−0.732976	+	0.453355i
$533$	6.00000	−	6.00000i	0.259889	−	0.259889i
$534$	4.02834	+	6.97730i	0.174323	+	0.301937i
$535$	9.71092	−	25.6066i	0.419840	−	1.10707i
$536$	4.77526	−	8.27098i	0.206260	−	0.357252i
$537$	−3.78780	+	14.1363i	−0.163456	+	0.610025i
$538$	1.79315	+	6.69213i	0.0773082	+	0.288518i
$539$			47.5959i			2.05010i
$540$		0			0
$541$	4.77526	−	8.27098i	0.205304	−	0.355597i	−0.744925	−	0.667148i	$-0.767515\pi$
$541$	4.77526	−	8.27098i	0.205304	−	0.355597i	0.950230	+	0.311550i	$0.100848\pi$
$542$	8.46259	+	31.5828i	0.363499	+	1.35660i
$543$	22.6515	−	22.6515i	0.972070	−	0.972070i
$544$	−2.82843			−0.121268
$545$		0			0
$546$	−47.3939	+	27.3629i	−2.02827	+	1.17102i
$547$	−4.65874	−	17.3867i	−0.199193	−	0.743400i	−0.991141	−	0.132811i	$-0.957600\pi$
$547$	−4.65874	−	17.3867i	−0.199193	−	0.743400i	0.791948	−	0.610589i	$-0.209067\pi$
$548$	−2.73205	−	0.732051i	−0.116707	−	0.0312717i
$549$	−20.7846	+	12.0000i	−0.887066	+	0.512148i
$550$	−14.3885	+	9.51023i	−0.613529	+	0.405517i
$551$	−3.30306	−	0.778539i	−0.140715	−	0.0331669i
$552$	−9.00000	−	9.00000i	−0.383065	−	0.383065i
$553$	−14.1043	+	52.6380i	−0.599777	+	2.23840i
$554$	4.09978	+	7.10102i	0.174183	+	0.301693i
$555$	2.44655	+	1.76246i	0.103850	+	0.0748122i
$556$	3.55051	+	6.14966i	0.150575	+	0.260804i
$557$	−16.9753	+	4.54852i	−0.719267	+	0.192727i	−0.599844	−	0.800117i	$-0.704771\pi$
$557$	−16.9753	+	4.54852i	−0.719267	+	0.192727i	−0.119422	+	0.992844i	$0.538104\pi$
$558$	16.3485	−	16.3485i	0.692086	−	0.692086i
$559$	−17.6705			−0.747381
$560$	1.63593	+	10.0655i	0.0691308	+	0.425343i
$561$	−20.6969	−	11.9494i	−0.873825	−	0.504503i
$562$	8.57321	+	8.57321i	0.361639	+	0.361639i
$563$	16.9706	+	16.9706i	0.715224	+	0.715224i	0.967623	−	0.252399i	$-0.0812196\pi$
$563$	16.9706	+	16.9706i	0.715224	+	0.715224i	−0.252399	+	0.967623i	$0.581220\pi$
$564$	8.48528	−	14.6969i	0.357295	−	0.618853i
$565$	13.0620	+	4.95356i	0.549522	+	0.208398i
$566$	−5.44949	−	3.14626i	−0.229059	−	0.132247i
$567$	−10.6230	+	39.6458i	−0.446126	+	1.66497i
$568$	3.34607	+	0.896575i	0.140398	+	0.0376195i
$569$	−18.7026			−0.784054			−0.392027	−	0.919954i	$-0.628226\pi$
$569$	−18.7026			−0.784054			−0.392027	+	0.919954i	$0.628226\pi$
$570$	−23.4385	+	4.54276i	−0.981731	+	0.190275i
$571$	−12.0000			−0.502184			−0.251092	−	0.967963i	$-0.580790\pi$
$571$	−12.0000			−0.502184			−0.251092	+	0.967963i	$0.580790\pi$
$572$	−16.3232	−	4.37378i	−0.682506	−	0.182877i
$573$	5.22867	−	19.5137i	0.218431	−	0.815195i
$574$	−6.84072	−	3.94949i	−0.285526	−	0.164849i
$575$	23.2436	+	11.6076i	0.969325	+	0.484069i
$576$	1.50000	−	2.59808i	0.0625000	−	0.108253i
$577$	−19.2474	−	19.2474i	−0.801282	−	0.801282i	0.182014	−	0.983296i	$-0.441738\pi$
$577$	−19.2474	−	19.2474i	−0.801282	−	0.801282i	−0.983296	+	0.182014i	$0.941738\pi$
$578$	−6.36396	−	6.36396i	−0.264706	−	0.264706i
$579$	2.86054	+	1.65153i	0.118880	+	0.0686353i
$580$	−1.01756	+	1.41251i	−0.0422517	+	0.0586514i
$581$	15.1464			0.628380
$582$	16.5420	−	16.5420i	0.685687	−	0.685687i
$583$	34.4806	−	9.23905i	1.42804	−	0.382642i
$584$	−1.09638	−	1.89898i	−0.0453684	−	0.0785803i
$585$	−32.4377	+	5.27208i	−1.34113	+	0.217974i
$586$	1.37628	+	2.38378i	0.0568534	+	0.0984730i
$587$	3.58630	−	13.3843i	0.148023	−	0.552428i	−0.851580	−	0.524225i	$-0.824355\pi$
$587$	3.58630	−	13.3843i	0.148023	−	0.552428i	0.999602	−	0.0282024i	$-0.00897830\pi$
$588$	23.8988	+	23.8988i	0.985568	+	0.985568i
$589$	−32.1698	+	9.67423i	−1.32553	+	0.398620i
$590$	−4.89898	−	6.00000i	−0.201688	−	0.247016i
$591$	38.0227	−	21.9524i	1.56405	−	0.903002i
$592$	0.531752	+	0.142483i	0.0218549	+	0.00585600i
$593$	−10.6147	−	39.6147i	−0.435895	−	1.62678i	−0.738915	−	0.673798i	$-0.764662\pi$
$593$	−10.6147	−	39.6147i	−0.435895	−	1.62678i	0.303020	−	0.952984i	$-0.402005\pi$
$594$		0			0
$595$	16.8591	−	23.4028i	0.691154	−	0.959421i
$596$	1.55051			0.0635114
$597$	16.9706	−	16.9706i	0.694559	−	0.694559i
$598$	6.58846	+	24.5885i	0.269422	+	1.00550i
$599$	6.14966	−	10.6515i	0.251268	−	0.435210i	−0.712607	−	0.701564i	$-0.752486\pi$
$599$	6.14966	−	10.6515i	0.251268	−	0.435210i	0.963875	+	0.266354i	$0.0858190\pi$
$600$	−2.44949	+	12.0000i	−0.100000	+	0.489898i
$601$		−	17.1455i		−	0.699381i	−0.936865	−	0.349690i	$-0.886287\pi$
$601$		−	17.1455i		−	0.699381i	0.936865	−	0.349690i	$-0.113713\pi$
$602$	4.25744	+	15.8890i	0.173520	+	0.647587i
$603$	7.41556	−	27.6753i	0.301985	−	1.12702i
$604$	4.24264	−	7.34847i	0.172631	−	0.299005i
$605$	−1.83307	+	0.825027i	−0.0745249	+	0.0335421i
$606$	−20.4495	−	35.4196i	−0.830704	−	1.43882i
$607$	−5.58542	+	5.58542i	−0.226705	+	0.226705i	−0.811315	−	0.584610i	$-0.801248\pi$
$607$	−5.58542	+	5.58542i	−0.226705	+	0.226705i	0.584610	+	0.811315i	$0.301248\pi$
$608$	−3.70711	+	2.29289i	−0.150343	+	0.0929891i
$609$			8.69694i			0.352418i
$610$	6.34315	−	16.7262i	0.256826	−	0.677223i
$611$	−29.3939	+	16.9706i	−1.18915	+	0.686555i
$612$	−8.19615	+	2.19615i	−0.331310	+	0.0887742i
$613$	−40.4598	−	10.8412i	−1.63416	−	0.437871i	−0.679039	−	0.734102i	$-0.737603\pi$
$613$	−40.4598	−	10.8412i	−1.63416	−	0.437871i	−0.955116	+	0.296231i	$0.904270\pi$
$614$	1.16781	+	0.674235i	0.0471289	+	0.0272099i
$615$	−6.00000	−	7.34847i	−0.241943	−	0.296319i
$616$			15.7313i			0.633833i
$617$	28.7486	−	7.70315i	1.15737	−	0.310117i	0.371457	−	0.928450i	$-0.378858\pi$
$617$	28.7486	−	7.70315i	1.15737	−	0.310117i	0.785916	+	0.618333i	$0.212192\pi$
$618$	−18.6892	+	5.00775i	−0.751789	+	0.201441i
$619$			25.0454i			1.00666i	0.864094	+	0.503330i	$0.167892\pi$
$619$			25.0454i			1.00666i	−0.864094	+	0.503330i	$0.832108\pi$
$620$	−1.73205	+	17.1455i	−0.0695608	+	0.688581i
$621$		0			0
$622$	−5.99071	−	1.60521i	−0.240206	−	0.0643629i
$623$	−14.4889	+	3.88229i	−0.580485	+	0.155540i
$624$	−10.3923	+	6.00000i	−0.416025	+	0.240192i
$625$	−3.01472	−	24.8176i	−0.120589	−	0.992703i
$626$			32.5911i			1.30260i
$627$	−36.8135	+	1.11660i	−1.47019	+	0.0445928i
$628$	2.67423	−	2.67423i	0.106714	−	0.106714i
$629$	−0.778539	−	1.34847i	−0.0310424	−	0.0537670i
$630$	12.5560	+	27.8972i	0.500242	+	1.11145i
$631$	−1.00000	+	1.73205i	−0.0398094	+	0.0689519i	−0.885244	−	0.465128i	$-0.846008\pi$
$631$	−1.00000	+	1.73205i	−0.0398094	+	0.0689519i	0.845434	+	0.534080i	$0.179342\pi$
$632$	−3.09273	+	11.5422i	−0.123022	+	0.459125i
$633$	−16.9647	−	63.3132i	−0.674287	−	2.51647i
$634$		−	9.24745i		−	0.367263i
$635$	−5.79972	−	7.10318i	−0.230155	−	0.281881i
$636$	12.6742	−	21.9524i	0.502566	−	0.870470i
$637$	−17.4951	−	65.2926i	−0.693182	−	2.58699i
$638$	−1.89898	+	1.89898i	−0.0751813	+	0.0751813i
$639$	10.3923			0.411113
$640$	0.358719	+	2.20711i	0.0141796	+	0.0872436i
$641$	−7.65153	+	4.41761i	−0.302217	+	0.174485i	−0.643439	−	0.765498i	$-0.722493\pi$
$641$	−7.65153	+	4.41761i	−0.302217	+	0.174485i	0.341221	+	0.939983i	$0.389159\pi$
$642$	−7.76457	−	28.9778i	−0.306443	−	1.14366i
$643$	24.0365	+	6.44055i	0.947906	+	0.253991i	0.699473	−	0.714659i	$-0.253418\pi$
$643$	24.0365	+	6.44055i	0.947906	+	0.253991i	0.248432	+	0.968649i	$0.420085\pi$
$644$	20.5222	−	11.8485i	0.808686	−	0.466895i
$645$	−1.98567	+	19.6561i	−0.0781858	+	0.773959i
$646$	12.0000	+	2.82843i	0.472134	+	0.111283i
$647$	−17.6742	−	17.6742i	−0.694846	−	0.694846i	0.268448	−	0.963294i	$-0.413489\pi$
$647$	−17.6742	−	17.6742i	−0.694846	−	0.694846i	−0.963294	+	0.268448i	$0.913489\pi$
$648$	−2.32937	+	8.69333i	−0.0915064	+	0.341506i
$649$	−5.97469	−	10.3485i	−0.234527	−	0.406213i
$650$	16.2426	−	18.3351i	0.637089	−	0.719163i
$651$	43.0454	+	74.5568i	1.68708	+	2.92211i
$652$	7.30614	−	1.95768i	0.286131	−	0.0766685i
$653$	12.0227	−	12.0227i	0.470485	−	0.470485i	−0.431587	−	0.902071i	$-0.642046\pi$
$653$	12.0227	−	12.0227i	0.470485	−	0.470485i	0.902071	+	0.431587i	$0.142046\pi$
$654$		0			0
$655$	−31.2923	−	22.5425i	−1.22269	−	0.880810i
$656$	−1.50000	−	0.866025i	−0.0585652	−	0.0338126i
$657$	−4.65153	−	4.65153i	−0.181473	−	0.181473i
$658$	22.3417	+	22.3417i	0.870970	+	0.870970i
$659$	−14.1582	+	24.5227i	−0.551525	+	0.955269i	0.446640	+	0.894714i	$0.352620\pi$
$659$	−14.1582	+	24.5227i	−0.551525	+	0.955269i	−0.998165	+	0.0605552i	$0.980713\pi$
$660$	−6.69954	+	17.6659i	−0.260779	+	0.687646i
$661$	33.0681	+	19.0919i	1.28620	+	0.742588i	0.977974	−	0.208725i	$-0.0669313\pi$
$661$	33.0681	+	19.0919i	1.28620	+	0.742588i	0.308226	+	0.951313i	$0.400265\pi$
$662$	5.53567	−	20.6594i	0.215150	−	0.802950i
$663$	32.7846	+	8.78461i	1.27325	+	0.341166i
$664$	3.32124			0.128889
$665$	3.12479	−	44.3401i	0.121174	−	1.71943i
$666$	1.65153			0.0639955
$667$	3.90756	+	1.04703i	0.151301	+	0.0405411i
$668$	6.13322	−	22.8895i	0.237301	−	0.885621i
$669$	−37.5409	−	21.6742i	−1.45141	−	0.837974i
$670$	8.76486	+	19.4740i	0.338616	+	0.752348i
$671$	13.7980	−	23.8988i	0.532664	−	0.922602i
$672$	7.89898	+	7.89898i	0.304710	+	0.304710i
$673$	30.8270	+	30.8270i	1.18829	+	1.18829i	0.977539	+	0.210753i	$0.0675916\pi$
$673$	30.8270	+	30.8270i	1.18829	+	1.18829i	0.210753	+	0.977539i	$0.432408\pi$
$674$	−15.5885	−	9.00000i	−0.600445	−	0.346667i
$675$		0			0
$676$	11.0000			0.423077
$677$	−21.9524	+	21.9524i	−0.843700	+	0.843700i	−0.989338	−	0.145638i	$-0.953477\pi$
$677$	−21.9524	+	21.9524i	−0.843700	+	0.843700i	0.145638	+	0.989338i	$0.453477\pi$
$678$	14.7816	−	3.96072i	0.567685	−	0.152111i
$679$	21.7774	+	37.7196i	0.835742	+	1.44755i
$680$	3.69677	−	5.13165i	0.141765	−	0.196790i
$681$	−25.0454	−	43.3799i	−0.959742	−	1.66232i
$682$	−6.88053	+	25.6785i	−0.263469	+	0.983280i
$683$	8.83523	+	8.83523i	0.338071	+	0.338071i	0.855641	−	0.517570i	$-0.173163\pi$
$683$	8.83523	+	8.83523i	0.338071	+	0.338071i	−0.517570	+	0.855641i	$0.673163\pi$
$684$	−8.96204	+	9.52270i	−0.342672	+	0.364110i
$685$	4.89898	−	4.00000i	0.187180	−	0.152832i
$686$	−26.8485	+	15.5010i	−1.02508	+	0.591830i
$687$	48.3840	+	12.9645i	1.84597	+	0.494625i
$688$	0.933552	+	3.48406i	0.0355913	+	0.132829i
$689$	−43.9048	+	25.3485i	−1.67264	+	0.965700i
$690$	28.0919	−	4.56575i	1.06944	−	0.173815i
$691$	11.4495			0.435559			0.217780	−	0.975998i	$-0.430119\pi$
$691$	11.4495			0.435559			0.217780	+	0.975998i	$0.430119\pi$
$692$	3.85337	−	3.85337i	0.146483	−	0.146483i
$693$	12.2147	+	45.5859i	0.463998	+	1.73166i
$694$	−15.0956	+	26.1464i	−0.573023	+	0.992505i
$695$	−15.7980	−	1.59592i	−0.599251	−	0.0605366i
$696$			1.90702i			0.0722855i
$697$	1.26795	+	4.73205i	0.0480270	+	0.179239i
$698$	7.47961	−	27.9143i	0.283107	−	1.05657i
$699$	−4.24264	+	7.34847i	−0.160471	+	0.277945i
$700$	−20.4001	−	10.1875i	−0.771050	−	0.385053i
$701$	2.67423	+	4.63191i	0.101004	+	0.174945i	0.912099	−	0.409971i	$-0.134461\pi$
$701$	2.67423	+	4.63191i	0.101004	+	0.174945i	−0.811094	+	0.584915i	$0.801128\pi$
$702$		0			0
$703$	−2.11355	−	1.13625i	−0.0797141	−	0.0428546i
$704$			3.44949i			0.130008i
$705$	15.5745	+	34.6040i	0.586571	+	1.30326i
$706$	20.0227	−	11.5601i	0.753564	−	0.435071i
$707$	73.5514	−	19.7080i	2.76619	−	0.741197i
$708$	−8.19615	−	2.19615i	−0.308030	−	0.0825365i
$709$	2.33562	+	1.34847i	0.0877159	+	0.0506428i	0.543216	−	0.839593i	$-0.317206\pi$
$709$	2.33562	+	1.34847i	0.0877159	+	0.0506428i	−0.455500	+	0.890236i	$0.650540\pi$
$710$	−6.00000	+	4.89898i	−0.225176	+	0.183855i
$711$			35.8481i			1.34441i
$712$	−3.17705	+	0.851289i	−0.119065	+	0.0319034i
$713$	38.6809	−	10.3645i	1.44861	−	0.388154i
$714$		−	31.5959i		−	1.18245i
$715$	29.2699	−	23.8988i	1.09463	−	0.893763i
$716$	−5.17423	−	2.98735i	−0.193370	−	0.111642i
$717$	−13.7181	−	3.67576i	−0.512313	−	0.137274i
$718$	−4.05886	+	1.08757i	−0.151475	+	0.0405877i
$719$	−1.51775	+	0.876276i	−0.0566027	+	0.0326796i	−0.528034	−	0.849223i	$-0.677071\pi$
$719$	−1.51775	+	0.876276i	−0.0566027	+	0.0326796i	0.471432	+	0.881903i	$0.343737\pi$
$720$	2.75321	+	6.11717i	0.102606	+	0.227974i
$721$		−	36.0231i		−	1.34157i
$722$	18.0208	−	6.02082i	0.670665	−	0.224072i
$723$	−11.3939	+	11.3939i	−0.423743	+	0.423743i
$724$	6.53893	+	11.3258i	0.243018	+	0.420919i
$725$	−1.23279	−	3.69233i	−0.0457846	−	0.137130i
$726$	−1.10102	+	1.90702i	−0.0408627	+	0.0707763i
$727$	1.86710	−	6.96812i	0.0692470	−	0.258433i	−0.922620	−	0.385709i	$-0.873957\pi$
$727$	1.86710	−	6.96812i	0.0692470	−	0.258433i	0.991867	+	0.127276i	$0.0406234\pi$
$728$	−5.78245	−	21.5804i	−0.214312	−	0.799823i
$729$			27.0000i			1.00000i
$730$	4.87832	+	0.492810i	0.180555	+	0.0182397i
$731$	5.10102	−	8.83523i	0.188668	−	0.326783i
$732$	−5.07180	−	18.9282i	−0.187459	−	0.699607i
$733$	−10.0227	+	10.0227i	−0.370197	+	0.370197i	−0.867549	−	0.497352i	$-0.834306\pi$
$733$	−10.0227	+	10.0227i	−0.370197	+	0.370197i	0.497352	+	0.867549i	$0.334306\pi$
$734$	−26.4415			−0.975972
$735$	−74.5957	+	12.1240i	−2.75150	+	0.447200i
$736$	4.50000	−	2.59808i	0.165872	−	0.0957664i
$737$	8.52663	+	31.8218i	0.314083	+	1.17217i
$738$	−5.01910	−	1.34486i	−0.184756	−	0.0495051i
$739$	25.6790	−	14.8258i	0.944617	−	0.545375i	0.0532120	−	0.998583i	$-0.483054\pi$
$739$	25.6790	−	14.8258i	0.944617	−	0.545375i	0.891404	+	0.453209i	$0.149721\pi$
$740$	−0.953512	+	0.778539i	−0.0350518	+	0.0286197i
$741$	50.0908	−	15.0635i	1.84013	−	0.553373i
$742$	33.3712	+	33.3712i	1.22509	+	1.22509i
$743$	−4.99336	+	18.6355i	−0.183189	+	0.683669i	0.811822	+	0.583904i	$0.198476\pi$
$743$	−4.99336	+	18.6355i	−0.183189	+	0.683669i	−0.995011	+	0.0997647i	$0.968191\pi$
$744$	9.43879	+	16.3485i	0.346043	+	0.599364i
$745$	−2.02653	+	2.81311i	−0.0742462	+	0.103064i
$746$	8.97219	+	15.5403i	0.328495	+	0.568971i
$747$	9.62421	−	2.57880i	0.352131	−	0.0943533i
$748$	6.89898	−	6.89898i	0.252252	−	0.252252i
$749$	55.8542			2.04087
$750$	−18.5703	−	20.1282i	−0.678090	−	0.734979i
$751$	−15.9773	−	9.22450i	−0.583020	−	0.336607i	0.179313	−	0.983792i	$-0.442613\pi$
$751$	−15.9773	−	9.22450i	−0.583020	−	0.336607i	−0.762333	+	0.647185i	$0.775946\pi$
$752$	4.89898	+	4.89898i	0.178647	+	0.178647i
$753$	15.4135	+	15.4135i	0.561699	+	0.561699i
$754$	1.90702	−	3.30306i	0.0694497	−	0.120290i
$755$	7.78726	+	17.3020i	0.283407	+	0.629684i
$756$		0			0
$757$	−9.68950	+	36.1617i	−0.352171	+	1.31432i	0.531837	+	0.846847i	$0.321502\pi$
$757$	−9.68950	+	36.1617i	−0.352171	+	1.31432i	−0.884008	+	0.467472i	$0.845165\pi$
$758$	−21.2424	−	5.69188i	−0.771558	−	0.206738i
$759$	43.9048			1.59364
$760$	0.685189	−	9.72268i	0.0248544	−	0.352679i
$761$	10.7980			0.391426			0.195713	−	0.980661i	$-0.437298\pi$
$761$	10.7980			0.391426			0.195713	+	0.980661i	$0.437298\pi$
$762$	−9.70312	−	2.59994i	−0.351507	−	0.0941860i
$763$		0			0
$764$	7.14250	+	4.12372i	0.258407	+	0.149191i
$765$	6.72792	−	17.7408i	0.243249	−	0.641419i
$766$	−4.89898	+	8.48528i	−0.177007	+	0.306586i
$767$	12.0000	+	12.0000i	0.433295	+	0.433295i
$768$	1.73205	+	1.73205i	0.0625000	+	0.0625000i
$769$	3.81405	+	2.20204i	0.137538	+	0.0794076i	0.567190	−	0.823587i	$-0.308030\pi$
$769$	3.81405	+	2.20204i	0.137538	+	0.0794076i	−0.429652	+	0.902995i	$0.641364\pi$
$770$	−28.5415	−	20.5610i	−1.02857	−	0.740965i
$771$	35.3939			1.27468
$772$	−0.953512	+	0.953512i	−0.0343176	+	0.0343176i
$773$	−21.5870	+	5.78421i	−0.776429	+	0.208044i	−0.625210	−	0.780457i	$-0.714987\pi$
$773$	−21.5870	+	5.78421i	−0.776429	+	0.208044i	−0.151219	+	0.988500i	$0.548320\pi$
$774$	5.41045	+	9.37117i	0.194475	+	0.336840i
$775$	−28.8436	−	25.5518i	−1.03609	−	0.917848i
$776$	4.77526	+	8.27098i	0.171422	+	0.296911i
$777$	−1.59165	+	5.94012i	−0.0571001	+	0.213101i
$778$	−4.87832	−	4.87832i	−0.174896	−	0.174896i
$779$	5.49794	+	5.17423i	0.196984	+	0.185386i
$780$	2.69694	−	26.6969i	0.0965659	−	0.955904i
$781$	−10.3485	+	5.97469i	−0.370297	+	0.213791i
$782$	−14.1962	−	3.80385i	−0.507653	−	0.136025i
$783$		0			0
$784$	−11.9494	+	6.89898i	−0.426764	+	0.246392i
$785$	1.35666	+	8.34714i	0.0484211	+	0.297922i
$786$	−42.2474			−1.50692
$787$	7.88171	−	7.88171i	0.280953	−	0.280953i	−0.552536	−	0.833489i	$-0.686340\pi$
$787$	7.88171	−	7.88171i	0.280953	−	0.280953i	0.833489	+	0.552536i	$0.186340\pi$
$788$	4.63909	+	17.3133i	0.165261	+	0.616762i
$789$	35.2839	−	61.1135i	1.25614	−	2.17570i
$790$	−16.8990	−	20.6969i	−0.601239	−	0.736364i
$791$			28.4914i			1.01304i
$792$	2.67838	+	9.99585i	0.0951721	+	0.355187i
$793$	−10.1436	+	37.8564i	−0.360210	+	1.34432i
$794$	−5.81577	+	10.0732i	−0.206394	+	0.357485i
$795$	23.2632	+	51.6870i	0.825062	+	1.83315i
$796$	4.89898	+	8.48528i	0.173640	+	0.300753i
$797$	−20.0454	+	20.0454i	−0.710044	+	0.710044i	−0.966544	−	0.256500i	$-0.917431\pi$
$797$	−20.0454	+	20.0454i	−0.710044	+	0.710044i	0.256500	+	0.966544i	$0.417431\pi$
$798$	−25.6136	−	41.4115i	−0.906710	−	1.46595i
$799$		−	19.5959i		−	0.693254i
$800$	−4.47323	−	2.23388i	−0.158153	−	0.0789794i
$801$	−8.54541	+	4.93369i	−0.301937	+	0.174323i
$802$	16.7303	−	4.48288i	0.590768	−	0.158296i
$803$	7.30614	+	1.95768i	0.257828	+	0.0690849i
$804$	20.2597	+	11.6969i	0.714504	+	0.412519i
$805$	−5.32577	+	52.7196i	−0.187709	+	1.85812i
$806$		−	37.7552i		−	1.32987i
$807$	−16.3923	+	4.39230i	−0.577036	+	0.154616i
$808$	16.1280	−	4.32149i	0.567381	−	0.152029i
$809$		−	37.7980i		−	1.32891i	−0.747330	−	0.664453i	$-0.768665\pi$
$809$		−	37.7980i		−	1.32891i	0.747330	−	0.664453i	$-0.231335\pi$
$810$	−12.7279	−	15.5885i	−0.447214	−	0.547723i
$811$	−15.5227	−	8.96204i	−0.545076	−	0.314700i	0.202058	−	0.979374i	$-0.435237\pi$
$811$	−15.5227	−	8.96204i	−0.545076	−	0.314700i	−0.747134	+	0.664674i	$0.768570\pi$
$812$	−3.42953	−	0.918940i	−0.120353	−	0.0322485i
$813$	−77.3618	+	20.7290i	−2.71320	+	0.726999i
$814$	−1.64456	+	0.949490i	−0.0576420	+	0.0332796i
$815$	−5.99735	+	15.8143i	−0.210078	+	0.553952i
$816$		−	6.92820i		−	0.242536i
$817$	−0.476662	−	15.7152i	−0.0166763	−	0.549804i
$818$	11.0227	−	11.0227i	0.385400	−	0.385400i
$819$	−33.5125	−	58.0454i	−1.17102	−	2.02827i
$820$	3.53175	−	1.58957i	0.123334	−	0.0555101i
$821$	−23.2474	+	40.2658i	−0.811342	+	1.40528i	0.100584	+	0.994929i	$0.467929\pi$
$821$	−23.2474	+	40.2658i	−0.811342	+	1.40528i	−0.911925	+	0.410356i	$0.865404\pi$
$822$	1.79315	−	6.69213i	0.0625433	−	0.233415i
$823$	4.10854	+	15.3333i	0.143215	+	0.534485i	0.999828	+	0.0185263i	$0.00589745\pi$
$823$	4.10854	+	15.3333i	0.143215	+	0.534485i	−0.856614	+	0.515958i	$0.827436\pi$
$824$		−	7.89898i		−	0.275174i
$825$	−23.2952	−	35.2446i	−0.811035	−	1.22706i
$826$	7.89898	−	13.6814i	0.274841	−	0.476038i
$827$	12.3305	+	46.0180i	0.428773	+	1.60020i	0.755543	+	0.655099i	$0.227373\pi$
$827$	12.3305	+	46.0180i	0.428773	+	1.60020i	−0.326771	+	0.945104i	$0.605960\pi$
$828$	11.0227	−	11.0227i	0.383065	−	0.383065i
$829$	41.5692			1.44376			0.721879	−	0.692019i	$-0.243279\pi$
$829$	41.5692			1.44376			0.721879	+	0.692019i	$0.243279\pi$
$830$	−4.34088	+	6.02576i	−0.150674	+	0.209157i
$831$	−17.3939	+	10.0424i	−0.603387	+	0.348366i
$832$	−1.26795	−	4.73205i	−0.0439582	−	0.164054i
$833$	37.6967	+	10.1008i	1.30611	+	0.349972i
$834$	−15.0635	+	8.69694i	−0.521608	+	0.301150i
$835$	33.5125	+	41.0443i	1.15975	+	1.42040i
$836$	3.44949	−	14.6349i	0.119303	−	0.506160i
$837$		0			0
$838$	1.64310	−	6.13215i	0.0567601	−	0.211832i
$839$	−20.2204	−	35.0227i	−0.698085	−	1.20912i	−0.969130	−	0.246551i	$-0.920703\pi$
$839$	−20.2204	−	35.0227i	−0.698085	−	1.20912i	0.271045	−	0.962567i	$-0.412631\pi$
$840$	−24.6552	+	4.00720i	−0.850687	+	0.138262i
$841$	14.1969	+	24.5898i	0.489550	+	0.847925i
$842$	−17.4823	+	4.68438i	−0.602481	+	0.161434i
$843$	−21.0000	+	21.0000i	−0.723278	+	0.723278i
$844$	26.7593			0.921093
$845$	−14.3771	+	19.9574i	−0.494587	+	0.686557i
$846$	18.0000	+	10.3923i	0.618853	+	0.357295i
$847$	−2.89898	−	2.89898i	−0.0996101	−	0.0996101i
$848$	7.31747	+	7.31747i	0.251283	+	0.251283i
$849$	7.70674	−	13.3485i	0.264495	−	0.458118i
$850$	4.47871	+	13.4142i	0.153619	+	0.460104i
$851$	2.47730	+	1.43027i	0.0849206	+	0.0490289i
$852$	−2.19615	+	8.19615i	−0.0752389	+	0.280796i
$853$	−51.0810	−	13.6871i	−1.74898	−	0.468638i	−0.764572	−	0.644539i	$-0.777049\pi$
$853$	−51.0810	−	13.6871i	−1.74898	−	0.468638i	−0.984408	+	0.175901i	$0.943716\pi$
$854$	36.4838			1.24845
$855$	−5.56372	−	28.7062i	−0.190275	−	0.981731i
$856$	12.2474			0.418609
$857$	8.98607	+	2.40781i	0.306958	+	0.0822492i	0.409010	−	0.912530i	$-0.365874\pi$
$857$	8.98607	+	2.40781i	0.306958	+	0.0822492i	−0.102052	+	0.994779i	$0.532541\pi$
$858$	10.7135	−	39.9834i	0.365754	−	1.36501i
$859$	−21.0864	−	12.1742i	−0.719458	−	0.415380i	0.0950949	−	0.995468i	$-0.469685\pi$
$859$	−21.0864	−	12.1742i	−0.719458	−	0.415380i	−0.814553	+	0.580089i	$0.803018\pi$
$860$	−7.54134	−	2.85994i	−0.257157	−	0.0975231i
$861$	9.67423	−	16.7563i	0.329697	−	0.571052i
$862$	1.65153	+	1.65153i	0.0562514	+	0.0562514i
$863$	7.92104	+	7.92104i	0.269635	+	0.269635i	0.828953	−	0.559318i	$-0.188937\pi$
$863$	7.92104	+	7.92104i	0.269635	+	0.269635i	−0.559318	+	0.828953i	$0.688937\pi$
$864$		0			0
$865$	1.95484	+	12.0276i	0.0664665	+	0.408951i
$866$	−4.65153			−0.158065
$867$	15.5885	−	15.5885i	0.529412	−	0.529412i
$868$	−33.9488	+	9.09656i	−1.15230	+	0.308758i
$869$	−20.6096	−	35.6969i	−0.699134	−	1.21094i
$870$	−3.45994	−	2.49249i	−0.117303	−	0.0845034i
$871$	−23.3939	−	40.5194i	−0.792671	−	1.37295i
$872$		0			0
$873$	20.2597	+	20.2597i	0.685687	+	0.685687i
$874$	−21.6900	+	6.52270i	−0.733674	+	0.220634i
$875$	45.1464	−	23.6969i	1.52623	−	0.801103i
$876$	4.65153	−	2.68556i	0.157161	−	0.0907367i
$877$	34.7196	+	9.30309i	1.17240	+	0.314143i	0.791907	−	0.610642i	$-0.209088\pi$
$877$	34.7196	+	9.30309i	1.17240	+	0.314143i	0.380491	+	0.924785i	$0.375755\pi$
$878$	8.18011	+	30.5286i	0.276065	+	1.03029i
$879$	−5.83904	+	3.37117i	−0.196946	+	0.113707i
$880$	−6.25845	−	4.50851i	−0.210972	−	0.151982i
$881$	−23.2929			−0.784756			−0.392378	−	0.919804i	$-0.628348\pi$
$881$	−23.2929			−0.784756			−0.392378	+	0.919804i	$0.628348\pi$
$882$	−29.2699	+	29.2699i	−0.985568	+	0.985568i
$883$	−8.74763	−	32.6466i	−0.294381	−	1.09865i	−0.941707	−	0.336433i	$-0.890779\pi$
$883$	−8.74763	−	32.6466i	−0.294381	−	1.09865i	0.647326	−	0.762213i	$-0.275887\pi$
$884$	−6.92820	+	12.0000i	−0.233021	+	0.403604i
$885$	14.6969	−	12.0000i	0.494032	−	0.403376i
$886$			30.8270i			1.03565i
$887$	14.1043	+	52.6380i	0.473577	+	1.76741i	0.626758	+	0.779214i	$0.284381\pi$
$887$	14.1043	+	52.6380i	0.473577	+	1.76741i	−0.153181	+	0.988198i	$0.548952\pi$
$888$	−0.349010	+	1.30252i	−0.0117120	+	0.0437098i
$889$	9.35131	−	16.1969i	0.313633	−	0.543228i
$890$	2.60793	−	6.87681i	0.0874179	−	0.230511i
$891$	−15.5227	−	26.8861i	−0.520030	−	0.900719i
$892$	12.5136	−	12.5136i	0.418987	−	0.418987i
$893$	−15.8856	−	25.6836i	−0.531592	−	0.859469i
$894$			3.79796i			0.127023i
$895$	12.1827	−	5.48320i	0.407224	−	0.183283i
$896$	−3.94949	+	2.28024i	−0.131943	+	0.0761774i
$897$	−60.2292	+	16.1384i	−2.01099	+	0.538844i
$898$	−8.36516	−	2.24144i	−0.279149	−	0.0747978i
$899$	−5.19615	−	3.00000i	−0.173301	−	0.100056i
$900$	−14.6969	−	3.00000i	−0.489898	−	0.100000i
$901$		−	29.2699i		−	0.975121i
$902$	5.77111	−	1.54636i	0.192157	−	0.0514883i
$903$	−38.9199	+	10.4286i	−1.29517	+	0.347041i
$904$			6.24745i			0.207787i
$905$	−29.0949	−	2.93918i	−0.967148	−	0.0977018i
$906$	18.0000	+	10.3923i	0.598010	+	0.345261i
$907$	−52.8770	−	14.1684i	−1.75575	−	0.470453i	−0.769914	−	0.638147i	$-0.779701\pi$
$907$	−52.8770	−	14.1684i	−1.75575	−	0.470453i	−0.985839	+	0.167694i	$0.946368\pi$
$908$	19.7527	−	5.29272i	0.655516	−	0.175645i
$909$	43.3799	−	25.0454i	1.43882	−	0.830704i
$910$	46.7113	+	17.7146i	1.54847	+	0.587232i
$911$			22.6916i			0.751807i	0.926659	+	0.375904i	$0.122668\pi$
$911$			22.6916i			0.751807i	−0.926659	+	0.375904i	$0.877332\pi$
$912$	−5.61642	−	9.08052i	−0.185978	−	0.300686i
$913$	−8.10102	+	8.10102i	−0.268105	+	0.268105i
$914$	−3.71051	−	6.42679i	−0.122733	−	0.212579i
$915$	40.9706	+	15.5375i	1.35445	+	0.513653i
$916$	−10.2247	+	17.7098i	−0.337835	+	0.585148i
$917$	20.3578	−	75.9765i	0.672275	−	2.50896i
$918$		0			0
$919$		−	54.0908i		−	1.78429i	−0.451748	−	0.892146i	$-0.649199\pi$
$919$		−	54.0908i		−	1.78429i	0.451748	−	0.892146i	$-0.350801\pi$
$920$	−1.16781	+	11.5601i	−0.0385015	+	0.381126i
$921$	−1.65153	+	2.86054i	−0.0544198	+	0.0942578i
$922$	−9.26519	−	34.5782i	−0.305133	−	1.13877i
$923$	12.0000	−	12.0000i	0.394985	−	0.394985i
$924$	−38.5337			−1.26767
$925$	−0.166267	−	2.74753i	−0.00546682	−	0.0903381i
$926$	10.7474	−	6.20504i	0.353183	−	0.203910i
$927$	−6.13322	−	22.8895i	−0.201441	−	0.751789i
$928$	−0.752011	−	0.201501i	−0.0246860	−	0.00661459i
$929$	−9.00136	+	5.19694i	−0.295325	+	0.170506i	−0.640341	−	0.768091i	$-0.721207\pi$
$929$	−9.00136	+	5.19694i	−0.295325	+	0.170506i	0.345016	+	0.938597i	$0.387874\pi$
$930$	−41.9978	−	4.24264i	−1.37716	−	0.139122i
$931$	57.5959	−	17.3205i	1.88763	−	0.567657i
$932$	−2.44949	−	2.44949i	−0.0802357	−	0.0802357i
$933$	3.93194	−	14.6742i	0.128726	−	0.480411i
$934$	−13.1172	−	22.7196i	−0.429208	−	0.743409i
$935$	3.49989	+	21.5339i	0.114459	+	0.704235i
$936$	−7.34847	−	12.7279i	−0.240192	−	0.416025i
$937$	43.0988	−	11.5483i	1.40798	−	0.377266i	0.526774	−	0.850005i	$-0.323401\pi$
$937$	43.0988	−	11.5483i	1.40798	−	0.377266i	0.881202	+	0.472739i	$0.156735\pi$
$938$	−30.7980	+	30.7980i	−1.00559	+	1.00559i
$939$	−79.8316			−2.60521
$940$	−15.2913	+	2.48528i	−0.498747	+	0.0810609i
$941$	45.3712	+	26.1951i	1.47906	+	0.853935i	0.999719	−	0.0236955i	$-0.00754320\pi$
$941$	45.3712	+	26.1951i	1.47906	+	0.853935i	0.479339	+	0.877630i	$0.340877\pi$
$942$	6.55051	+	6.55051i	0.213427	+	0.213427i
$943$	−6.36396	−	6.36396i	−0.207239	−	0.207239i
$944$	1.73205	−	3.00000i	0.0563735	−	0.0976417i
$945$		0			0
$946$	−10.7753	−	6.22110i	−0.350334	−	0.202265i
$947$	2.92820	−	10.9282i	0.0951538	−	0.355119i	−0.901889	−	0.431968i	$-0.857819\pi$
$947$	2.92820	−	10.9282i	0.0951538	−	0.355119i	0.997043	+	0.0768492i	$0.0244860\pi$
$948$	−28.2725	−	7.57561i	−0.918250	−	0.246044i
$949$	−10.7423			−0.348708
$950$	16.7444	+	13.9508i	0.543261	+	0.452622i
$951$	22.6515			0.734526
$952$	12.4595	+	3.33850i	0.403813	+	0.108201i
$953$	−8.17763	+	30.5193i	−0.264899	+	0.988618i	0.697413	+	0.716670i	$0.254334\pi$
$953$	−8.17763	+	30.5193i	−0.264899	+	0.988618i	−0.962312	+	0.271948i	$0.912332\pi$
$954$	26.8861	+	15.5227i	0.870470	+	0.502566i
$955$	−16.8170	+	7.56899i	−0.544186	+	0.244927i
$956$	2.89898	−	5.02118i	0.0937597	−	0.162397i
$957$	−4.65153	−	4.65153i	−0.150363	−	0.150363i
$958$	−22.1988	−	22.1988i	−0.717211	−	0.717211i
$959$	11.1708	+	6.44949i	0.360725	+	0.208265i
$960$	−5.40629	+	0.878680i	−0.174487	+	0.0283593i
$961$	−28.3939			−0.915932
$962$	1.90702	−	1.90702i	0.0614849	−	0.0614849i
$963$	35.4904	−	9.50962i	1.14366	−	0.306443i
$964$	−3.28913	−	5.69694i	−0.105936	−	0.183486i
$965$	−0.483722	−	2.97622i	−0.0155716	−	0.0958078i
$966$	29.0227	+	50.2688i	0.933790	+	1.61737i
$967$	−0.732051	+	2.73205i	−0.0235412	+	0.0878568i	−0.976697	−	0.214623i	$-0.931148\pi$
$967$	−0.732051	+	2.73205i	−0.0235412	+	0.0878568i	0.953156	+	0.302480i	$0.0978144\pi$
$968$	−0.635674	−	0.635674i	−0.0204314	−	0.0204314i
$969$	−6.92820	+	29.3939i	−0.222566	+	0.944267i
$970$	−21.2474	−	2.14643i	−0.682214	−	0.0689177i
$971$	−28.0454	+	16.1920i	−0.900020	+	0.519627i	−0.877207	−	0.480113i	$-0.840596\pi$
$971$	−28.0454	+	16.1920i	−0.900020	+	0.519627i	−0.0228133	+	0.999740i	$0.507262\pi$
$972$	−21.2942	−	5.70577i	−0.683013	−	0.183013i
$973$	−8.38161	−	31.2806i	−0.268702	−	1.00281i
$974$	37.0641	−	21.3990i	1.18761	−	0.685668i
$975$	44.9117	+	39.7862i	1.43833	+	1.27418i
$976$	8.00000			0.256074
$977$	8.31031	−	8.31031i	0.265870	−	0.265870i	−0.561563	−	0.827434i	$-0.689800\pi$
$977$	8.31031	−	8.31031i	0.265870	−	0.265870i	0.827434	+	0.561563i	$0.189800\pi$
$978$	4.79531	+	17.8963i	0.153337	+	0.572261i
$979$	5.67291	−	9.82577i	0.181307	−	0.314033i
$980$	3.10102	−	30.6969i	0.0990585	−	0.980578i
$981$		0			0
$982$	1.46272	+	5.45896i	0.0466774	+	0.174202i
$983$	2.45746	−	9.17137i	0.0783808	−	0.292521i	−0.915598	−	0.402095i	$-0.868282\pi$
$983$	2.45746	−	9.17137i	0.0783808	−	0.292521i	0.993979	+	0.109574i	$0.0349487\pi$
$984$	2.12132	−	3.67423i	0.0676252	−	0.117130i
$985$	−37.4751	−	14.2119i	−1.19406	−	0.452828i
$986$	1.10102	+	1.90702i	0.0350636	+	0.0607320i
$987$	−54.7257	+	54.7257i	−1.74194	+	1.74194i
$988$	0.647402	+	21.3443i	0.0205966	+	0.679054i
$989$			18.7423i			0.595972i
$990$	−21.6363	−	8.20523i	−0.687646	−	0.260779i
$991$	−18.9773	+	10.9565i	−0.602834	+	0.348046i	−0.770156	−	0.637856i	$-0.779821\pi$
$991$	−18.9773	+	10.9565i	−0.602834	+	0.348046i	0.167322	+	0.985902i	$0.446488\pi$
$992$	−7.44414	+	1.99465i	−0.236352	+	0.0633303i
$993$	50.6050	+	13.5596i	1.60590	+	0.430300i
$994$	−13.6814	−	7.89898i	−0.433949	−	0.250540i
$995$	−21.7980	−	2.20204i	−0.691042	−	0.0698094i
$996$			8.13534i			0.257778i
$997$	3.99109	−	1.06941i	0.126399	−	0.0338686i	−0.195065	−	0.980790i	$-0.562492\pi$
$997$	3.99109	−	1.06941i	0.126399	−	0.0338686i	0.321464	+	0.946922i	$0.395825\pi$
$998$	3.13679	−	0.840502i	0.0992935	−	0.0266056i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	190.2.m.a.107.1	yes	8
5.2	odd	4		950.2.q.a.943.2		8
5.3	odd	4	inner	190.2.m.a.183.1	yes	8
5.4	even	2		950.2.q.a.107.2		8
19.8	odd	6	inner	190.2.m.a.27.1	✓	8
95.8	even	12	inner	190.2.m.a.103.1	yes	8
95.27	even	12		950.2.q.a.293.2		8
95.84	odd	6		950.2.q.a.407.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.m.a.27.1	✓	8	19.8	odd	6	inner
190.2.m.a.103.1	yes	8	95.8	even	12	inner
190.2.m.a.107.1	yes	8	1.1	even	1	trivial
190.2.m.a.183.1	yes	8	5.3	odd	4	inner
950.2.q.a.107.2		8	5.4	even	2
950.2.q.a.293.2		8	95.27	even	12
950.2.q.a.407.2		8	95.84	odd	6
950.2.q.a.943.2		8	5.2	odd	4

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:	\( N \)	\(=\)	\( 190 = 2 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	190.m (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(0.633975 - 2.36603i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-2.03906 + 0.917738i) q^{5} +(-1.22474 + 2.12132i) q^{6} +(-3.22474 - 3.22474i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.59808 - 1.50000i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(0.633975 - 2.36603i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-2.03906 + 0.917738i) q^{5} +(-1.22474 + 2.12132i) q^{6} +(-3.22474 - 3.22474i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.59808 - 1.50000i) q^{9} +(2.20711 - 0.358719i) q^{10} +3.44949 q^{11} +(1.73205 - 1.73205i) q^{12} +(-4.73205 + 1.26795i) q^{13} +(2.28024 + 3.94949i) q^{14} +(0.878680 + 5.40629i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.732051 - 2.73205i) q^{17} +(2.12132 + 2.12132i) q^{18} +(-1.25529 - 4.17423i) q^{19} +(-2.22474 - 0.224745i) q^{20} +(-9.67423 + 5.58542i) q^{21} +(-3.33195 - 0.892794i) q^{22} +(1.34486 + 5.01910i) q^{23} +(-2.12132 + 1.22474i) q^{24} +(3.31552 - 3.74264i) q^{25} +4.89898 q^{26} +(-1.18034 - 4.40508i) q^{28} +(0.389270 - 0.674235i) q^{29} +(0.550510 - 5.44949i) q^{30} -7.70674i q^{31} +(-0.258819 - 0.965926i) q^{32} +(2.18689 - 8.16158i) q^{33} +(-1.41421 + 2.44949i) q^{34} +(9.53491 + 3.61597i) q^{35} +(-1.50000 - 2.59808i) q^{36} +(0.389270 - 0.389270i) q^{37} +(0.132150 + 4.35690i) q^{38} +12.0000i q^{39} +(2.09077 + 0.792893i) q^{40} +(-1.50000 + 0.866025i) q^{41} +(10.7902 - 2.89123i) q^{42} +(3.48406 + 0.933552i) q^{43} +(2.98735 + 1.72474i) q^{44} +(6.67423 + 0.674235i) q^{45} -5.19615i q^{46} +(6.69213 - 1.79315i) q^{47} +(2.36603 - 0.633975i) q^{48} +13.7980i q^{49} +(-4.17121 + 2.75699i) q^{50} +(-6.00000 - 3.46410i) q^{51} +(-4.73205 - 1.26795i) q^{52} +(9.99585 - 2.67838i) q^{53} +(-7.03371 + 3.16573i) q^{55} +4.56048i q^{56} +(-10.6722 + 0.323701i) q^{57} +(-0.550510 + 0.550510i) q^{58} +(-1.73205 - 3.00000i) q^{59} +(-1.94218 + 5.12132i) q^{60} +(4.00000 - 6.92820i) q^{61} +(-1.99465 + 7.44414i) q^{62} +(3.54102 + 13.2153i) q^{63} +1.00000i q^{64} +(8.48528 - 6.92820i) q^{65} +(-4.22474 + 7.31747i) q^{66} +(2.47185 + 9.22508i) q^{67} +(2.00000 - 2.00000i) q^{68} +12.7279 q^{69} +(-8.27414 - 5.96058i) q^{70} +(-3.00000 + 1.73205i) q^{71} +(0.776457 + 2.89778i) q^{72} +(2.11804 + 0.567526i) q^{73} +(-0.476756 + 0.275255i) q^{74} +(-6.75323 - 10.2173i) q^{75} +(1.00000 - 4.24264i) q^{76} +(-11.1237 - 11.1237i) q^{77} +(3.10583 - 11.5911i) q^{78} +(-5.97469 - 10.3485i) q^{79} +(-1.81431 - 1.30701i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(1.67303 - 0.448288i) q^{82} +(-2.34847 + 2.34847i) q^{83} -11.1708 q^{84} +(1.01461 + 6.24264i) q^{85} +(-3.12372 - 1.80348i) q^{86} +(-1.34847 - 1.34847i) q^{87} +(-2.43916 - 2.43916i) q^{88} +(1.64456 - 2.84847i) q^{89} +(-6.27231 - 2.37868i) q^{90} +(19.3485 + 11.1708i) q^{91} +(-1.34486 + 5.01910i) q^{92} +(-18.2343 - 4.88588i) q^{93} -6.92820 q^{94} +(6.39047 + 7.35948i) q^{95} -2.44949 q^{96} +(-9.22508 - 2.47185i) q^{97} +(3.57117 - 13.3278i) q^{98} +(-8.96204 - 5.17423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 12 q^{3} + 4 q^{5} - 16 q^{7}+O(q^{10}) \) 8 * q + 12 * q^3 + 4 * q^5 - 16 * q^7	\( 8 q + 12 q^{3} + 4 q^{5} - 16 q^{7} + 12 q^{10} + 8 q^{11} - 24 q^{13} + 24 q^{15} + 4 q^{16} - 8 q^{17} - 8 q^{20} - 48 q^{21} - 12 q^{22} + 8 q^{28} + 24 q^{30} + 12 q^{33} + 12 q^{35} - 12 q^{36} - 12 q^{38} - 12 q^{41} + 12 q^{42} + 20 q^{43} + 24 q^{45} + 12 q^{48} - 48 q^{51} - 24 q^{52} + 36 q^{53} - 8 q^{55} - 12 q^{57} - 24 q^{58} + 32 q^{61} + 12 q^{62} - 24 q^{63} - 24 q^{66} - 12 q^{67} + 16 q^{68} - 36 q^{70} - 24 q^{71} + 16 q^{73} + 8 q^{76} - 40 q^{77} - 4 q^{80} - 36 q^{81} + 40 q^{83} + 24 q^{86} + 48 q^{87} + 96 q^{91} - 24 q^{93} + 32 q^{95} + 12 q^{97} + 48 q^{98}+O(q^{100}) \) 8 * q + 12 * q^3 + 4 * q^5 - 16 * q^7 + 12 * q^10 + 8 * q^11 - 24 * q^13 + 24 * q^15 + 4 * q^16 - 8 * q^17 - 8 * q^20 - 48 * q^21 - 12 * q^22 + 8 * q^28 + 24 * q^30 + 12 * q^33 + 12 * q^35 - 12 * q^36 - 12 * q^38 - 12 * q^41 + 12 * q^42 + 20 * q^43 + 24 * q^45 + 12 * q^48 - 48 * q^51 - 24 * q^52 + 36 * q^53 - 8 * q^55 - 12 * q^57 - 24 * q^58 + 32 * q^61 + 12 * q^62 - 24 * q^63 - 24 * q^66 - 12 * q^67 + 16 * q^68 - 36 * q^70 - 24 * q^71 + 16 * q^73 + 8 * q^76 - 40 * q^77 - 4 * q^80 - 36 * q^81 + 40 * q^83 + 24 * q^86 + 48 * q^87 + 96 * q^91 - 24 * q^93 + 32 * q^95 + 12 * q^97 + 48 * q^98

Introduction

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