LMFDB - Embedded newform 605.2.e.a.483.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(362,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("605.362");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.e (of order $4$, degree $2$, 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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 67x^{16} + 1315x^{12} + 9193x^{8} + 16040x^{4} + 16 $ x^20 + 67x^16 + 1315x^12 + 9193x^8 + 16040x^4 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			483.3
Root			$-1.31283 - 1.31283i$ of defining polynomial
Character	$\chi$	$=$	605.483
Dual form			605.2.e.a.362.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31283 - 1.31283i) q^{2} +(-1.09155 - 1.09155i) q^{3} +1.44706i q^{4} +(2.21808 + 0.283032i) q^{5} +2.86605i q^{6} +(1.45954 + 1.45954i) q^{7} +(-0.725917 + 0.725917i) q^{8} -0.617036i q^{9} +O(q^{10})$	\(q+(-1.31283 - 1.31283i) q^{2} +(-1.09155 - 1.09155i) q^{3} +1.44706i q^{4} +(2.21808 + 0.283032i) q^{5} +2.86605i q^{6} +(1.45954 + 1.45954i) q^{7} +(-0.725917 + 0.725917i) q^{8} -0.617036i q^{9} +(-2.54040 - 3.28355i) q^{10} +(1.57954 - 1.57954i) q^{12} +(-2.13060 + 2.13060i) q^{13} -3.83226i q^{14} +(-2.11221 - 2.73009i) q^{15} +4.80014 q^{16} +(4.86718 + 4.86718i) q^{17} +(-0.810065 + 0.810065i) q^{18} +4.07750 q^{19} +(-0.409565 + 3.20970i) q^{20} -3.18632i q^{21} +(5.40871 + 5.40871i) q^{23} +1.58475 q^{24} +(4.83979 + 1.25558i) q^{25} +5.59425 q^{26} +(-3.94818 + 3.94818i) q^{27} +(-2.11204 + 2.11204i) q^{28} -5.13382 q^{29} +(-0.811184 + 6.35713i) q^{30} +2.74917 q^{31} +(-4.84994 - 4.84994i) q^{32} -12.7796i q^{34} +(2.82428 + 3.65047i) q^{35} +0.892888 q^{36} +(3.38434 - 3.38434i) q^{37} +(-5.35308 - 5.35308i) q^{38} +4.65132 q^{39} +(-1.81560 + 1.40469i) q^{40} -7.55673i q^{41} +(-4.18310 + 4.18310i) q^{42} +(-2.58034 + 2.58034i) q^{43} +(0.174641 - 1.36864i) q^{45} -14.2015i q^{46} +(0.313348 - 0.313348i) q^{47} +(-5.23959 - 5.23959i) q^{48} -2.73950i q^{49} +(-4.70546 - 8.00220i) q^{50} -10.6255i q^{51} +(-3.08311 - 3.08311i) q^{52} +(-5.18310 - 5.18310i) q^{53} +10.3666 q^{54} -2.11900 q^{56} +(-4.45080 - 4.45080i) q^{57} +(6.73985 + 6.73985i) q^{58} +12.9685i q^{59} +(3.95061 - 3.05649i) q^{60} -5.35564i q^{61} +(-3.60920 - 3.60920i) q^{62} +(0.900586 - 0.900586i) q^{63} +3.13406i q^{64} +(-5.32888 + 4.12282i) q^{65} +(-3.40871 + 3.40871i) q^{67} +(-7.04310 + 7.04310i) q^{68} -11.8078i q^{69} +(1.08465 - 8.50026i) q^{70} -4.38126 q^{71} +(0.447916 + 0.447916i) q^{72} +(6.35783 - 6.35783i) q^{73} -8.88615 q^{74} +(-3.91234 - 6.65340i) q^{75} +5.90039i q^{76} +(-6.10640 - 6.10640i) q^{78} +12.6989 q^{79} +(10.6471 + 1.35859i) q^{80} +6.76816 q^{81} +(-9.92072 + 9.92072i) q^{82} +(-0.789678 + 0.789678i) q^{83} +4.61079 q^{84} +(9.41823 + 12.1734i) q^{85} +6.77512 q^{86} +(5.60383 + 5.60383i) q^{87} +13.5666i q^{89} +(-2.02607 + 1.56752i) q^{90} -6.21938 q^{91} +(-7.82674 + 7.82674i) q^{92} +(-3.00085 - 3.00085i) q^{93} -0.822748 q^{94} +(9.04423 + 1.15406i) q^{95} +10.5879i q^{96} +(5.96130 - 5.96130i) q^{97} +(-3.59651 + 3.59651i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{3} + 4 q^{5}+O(q^{10}) $ 20 * q + 4 * q^3 + 4 * q^5	$ 20 q + 4 q^{3} + 4 q^{5} - 16 q^{12} + 16 q^{15} + 12 q^{16} + 16 q^{20} + 12 q^{23} + 16 q^{25} + 56 q^{26} - 20 q^{27} - 16 q^{31} - 20 q^{36} - 72 q^{37} - 32 q^{38} - 32 q^{42} - 28 q^{45} + 16 q^{47} - 104 q^{48} - 52 q^{53} - 32 q^{56} + 12 q^{58} + 112 q^{60} + 28 q^{67} + 104 q^{70} + 24 q^{71} + 64 q^{75} + 104 q^{78} + 44 q^{80} + 100 q^{81} - 124 q^{82} + 128 q^{86} - 16 q^{92} - 132 q^{93} + 32 q^{97}+O(q^{100}) $ 20 * q + 4 * q^3 + 4 * q^5 - 16 * q^12 + 16 * q^15 + 12 * q^16 + 16 * q^20 + 12 * q^23 + 16 * q^25 + 56 * q^26 - 20 * q^27 - 16 * q^31 - 20 * q^36 - 72 * q^37 - 32 * q^38 - 32 * q^42 - 28 * q^45 + 16 * q^47 - 104 * q^48 - 52 * q^53 - 32 * q^56 + 12 * q^58 + 112 * q^60 + 28 * q^67 + 104 * q^70 + 24 * q^71 + 64 * q^75 + 104 * q^78 + 44 * q^80 + 100 * q^81 - 124 * q^82 + 128 * q^86 - 16 * q^92 - 132 * q^93 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−1.31283	−	1.31283i	−0.928313	−	0.928313i	0.0692839	−	0.997597i	$-0.477929\pi$
$2$	−1.31283	−	1.31283i	−0.928313	−	0.928313i	−0.997597	+	0.0692839i	$0.977929\pi$
$3$	−1.09155	−	1.09155i	−0.630207	−	0.630207i	0.317913	−	0.948120i	$-0.397018\pi$
$3$	−1.09155	−	1.09155i	−0.630207	−	0.630207i	−0.948120	+	0.317913i	$0.897018\pi$
$4$			1.44706i			0.723531i
$5$	2.21808	+	0.283032i	0.991957	+	0.126576i
$5$	2.21808	+	0.283032i	0.991957	+	0.126576i
$6$			2.86605i			1.17006i
$7$	1.45954	+	1.45954i	0.551653	+	0.551653i	0.926918	−	0.375265i	$-0.122448\pi$
$7$	1.45954	+	1.45954i	0.551653	+	0.551653i	−0.375265	+	0.926918i	$0.622448\pi$
$8$	−0.725917	+	0.725917i	−0.256650	+	0.256650i
$9$		−	0.617036i		−	0.205679i
$10$	−2.54040	−	3.28355i	−0.803345	−	1.03835i
$11$		0			0
$11$		0			0
$12$	1.57954	−	1.57954i	0.455974	−	0.455974i
$13$	−2.13060	+	2.13060i	−0.590923	+	0.590923i	−0.937881	−	0.346958i	$-0.887215\pi$
$13$	−2.13060	+	2.13060i	−0.590923	+	0.590923i	0.346958	+	0.937881i	$0.387215\pi$
$14$		−	3.83226i		−	1.02421i
$15$	−2.11221	−	2.73009i	−0.545369	−	0.704907i
$16$	4.80014			1.20003
$17$	4.86718	+	4.86718i	1.18046	+	1.18046i	0.979624	+	0.200840i	$0.0643670\pi$
$17$	4.86718	+	4.86718i	1.18046	+	1.18046i	0.200840	+	0.979624i	$0.435633\pi$
$18$	−0.810065	+	0.810065i	−0.190934	+	0.190934i
$19$	4.07750			0.935442			0.467721	−	0.883876i	$-0.345075\pi$
$19$	4.07750			0.935442			0.467721	+	0.883876i	$0.345075\pi$
$20$	−0.409565	+	3.20970i	−0.0915816	+	0.717711i
$21$		−	3.18632i		−	0.695311i
$22$		0			0
$23$	5.40871	+	5.40871i	1.12779	+	1.12779i	0.990535	+	0.137259i	$0.0438294\pi$
$23$	5.40871	+	5.40871i	1.12779	+	1.12779i	0.137259	+	0.990535i	$0.456171\pi$
$24$	1.58475			0.323485
$25$	4.83979	+	1.25558i	0.967957	+	0.251116i
$26$	5.59425			1.09712
$27$	−3.94818	+	3.94818i	−0.759827	+	0.759827i
$28$	−2.11204	+	2.11204i	−0.399138	+	0.399138i
$29$	−5.13382			−0.953327			−0.476664	−	0.879086i	$-0.658154\pi$
$29$	−5.13382			−0.953327			−0.476664	+	0.879086i	$0.658154\pi$
$30$	−0.811184	+	6.35713i	−0.148101	+	1.16065i
$31$	2.74917			0.493765			0.246882	−	0.969045i	$-0.420594\pi$
$31$	2.74917			0.493765			0.246882	+	0.969045i	$0.420594\pi$
$32$	−4.84994	−	4.84994i	−0.857357	−	0.857357i
$33$		0			0
$34$		−	12.7796i		−	2.19168i
$35$	2.82428	+	3.65047i	0.477390	+	0.617042i
$36$	0.892888			0.148815
$37$	3.38434	−	3.38434i	0.556383	−	0.556383i	−0.371893	−	0.928276i	$-0.621291\pi$
$37$	3.38434	−	3.38434i	0.556383	−	0.556383i	0.928276	+	0.371893i	$0.121291\pi$
$38$	−5.35308	−	5.35308i	−0.868383	−	0.868383i
$39$	4.65132			0.744807
$40$	−1.81560	+	1.40469i	−0.287072	+	0.222100i
$41$		−	7.55673i		−	1.18016i	−0.807344	−	0.590081i	$-0.799096\pi$
$41$		−	7.55673i		−	1.18016i	0.807344	−	0.590081i	$-0.200904\pi$
$42$	−4.18310	+	4.18310i	−0.645466	+	0.645466i
$43$	−2.58034	+	2.58034i	−0.393499	+	0.393499i	−0.875932	−	0.482434i	$-0.839753\pi$
$43$	−2.58034	+	2.58034i	−0.393499	+	0.393499i	0.482434	+	0.875932i	$0.339753\pi$
$44$		0			0
$45$	0.174641	−	1.36864i	0.0260340	−	0.204024i
$46$		−	14.2015i		−	2.09389i
$47$	0.313348	−	0.313348i	0.0457066	−	0.0457066i	−0.683884	−	0.729591i	$-0.739711\pi$
$47$	0.313348	−	0.313348i	0.0457066	−	0.0457066i	0.729591	+	0.683884i	$0.239711\pi$
$48$	−5.23959	−	5.23959i	−0.756270	−	0.756270i
$49$		−	2.73950i		−	0.391358i
$50$	−4.70546	−	8.00220i	−0.665453	−	1.13168i
$51$		−	10.6255i		−	1.48787i
$52$	−3.08311	−	3.08311i	−0.427551	−	0.427551i
$53$	−5.18310	−	5.18310i	−0.711954	−	0.711954i	0.254990	−	0.966944i	$-0.417928\pi$
$53$	−5.18310	−	5.18310i	−0.711954	−	0.711954i	−0.966944	+	0.254990i	$0.917928\pi$
$54$	10.3666			1.41071
$55$		0			0
$56$	−2.11900			−0.283164
$57$	−4.45080	−	4.45080i	−0.589522	−	0.589522i
$58$	6.73985	+	6.73985i	0.884986	+	0.884986i
$59$			12.9685i			1.68836i	0.536059	+	0.844181i	$0.319913\pi$
$59$			12.9685i			1.68836i	−0.536059	+	0.844181i	$0.680087\pi$
$60$	3.95061	−	3.05649i	0.510022	−	0.394591i
$61$		−	5.35564i		−	0.685720i	−0.939387	−	0.342860i	$-0.888604\pi$
$61$		−	5.35564i		−	0.685720i	0.939387	−	0.342860i	$-0.111396\pi$
$62$	−3.60920	−	3.60920i	−0.458368	−	0.458368i
$63$	0.900586	−	0.900586i	0.113463	−	0.113463i
$64$			3.13406i			0.391758i
$65$	−5.32888	+	4.12282i	−0.660966	+	0.511373i
$66$		0			0
$67$	−3.40871	+	3.40871i	−0.416441	+	0.416441i	−0.883975	−	0.467534i	$-0.845142\pi$
$67$	−3.40871	+	3.40871i	−0.416441	+	0.416441i	0.467534	+	0.883975i	$0.345142\pi$
$68$	−7.04310	+	7.04310i	−0.854102	+	0.854102i
$69$		−	11.8078i		−	1.42149i
$70$	1.08465	−	8.50026i	0.129641	−	1.01598i
$71$	−4.38126			−0.519960			−0.259980	−	0.965614i	$-0.583716\pi$
$71$	−4.38126			−0.519960			−0.259980	+	0.965614i	$0.583716\pi$
$72$	0.447916	+	0.447916i	0.0527875	+	0.0527875i
$73$	6.35783	−	6.35783i	0.744128	−	0.744128i	−0.229241	−	0.973370i	$-0.573625\pi$
$73$	6.35783	−	6.35783i	0.744128	−	0.744128i	0.973370	+	0.229241i	$0.0736245\pi$
$74$	−8.88615			−1.03299
$75$	−3.91234	−	6.65340i	−0.451758	−	0.768268i
$76$			5.90039i			0.676821i
$77$		0			0
$78$	−6.10640	−	6.10640i	−0.691414	−	0.691414i
$79$	12.6989			1.42873			0.714366	−	0.699772i	$-0.246715\pi$
$79$	12.6989			1.42873			0.714366	+	0.699772i	$0.246715\pi$
$80$	10.6471	+	1.35859i	1.19038	+	0.151895i
$81$	6.76816			0.752018
$82$	−9.92072	+	9.92072i	−1.09556	+	1.09556i
$83$	−0.789678	+	0.789678i	−0.0866784	+	0.0866784i	−0.749117	−	0.662438i	$-0.769522\pi$
$83$	−0.789678	+	0.789678i	−0.0866784	+	0.0866784i	0.662438	+	0.749117i	$0.269522\pi$
$84$	4.61079			0.503079
$85$	9.41823	+	12.1734i	1.02155	+	1.32039i
$86$	6.77512			0.730580
$87$	5.60383	+	5.60383i	0.600793	+	0.600793i
$88$		0			0
$89$			13.5666i			1.43806i	0.694981	+	0.719028i	$0.255413\pi$
$89$			13.5666i			1.43806i	−0.694981	+	0.719028i	$0.744587\pi$
$90$	−2.02607	+	1.56752i	−0.213566	+	0.165231i
$91$	−6.21938			−0.651969
$92$	−7.82674	+	7.82674i	−0.815994	+	0.815994i
$93$	−3.00085	−	3.00085i	−0.311174	−	0.311174i
$94$	−0.822748			−0.0848600
$95$	9.04423	+	1.15406i	0.927919	+	0.118405i
$96$			10.5879i			1.08062i
$97$	5.96130	−	5.96130i	0.605279	−	0.605279i	−0.336430	−	0.941708i	$-0.609220\pi$
$97$	5.96130	−	5.96130i	0.605279	−	0.605279i	0.941708	+	0.336430i	$0.109220\pi$
$98$	−3.59651	+	3.59651i	−0.363303	+	0.363303i
$99$		0			0
$100$	−1.81690	+	7.00346i	−0.181690	+	0.700346i
$101$			1.49186i			0.148446i	0.997242	+	0.0742230i	$0.0236477\pi$
$101$			1.49186i			0.148446i	−0.997242	+	0.0742230i	$0.976352\pi$
$102$	−13.9496	+	13.9496i	−1.38121	+	1.38121i
$103$	−5.01348	−	5.01348i	−0.493992	−	0.493992i	0.415569	−	0.909562i	$-0.363582\pi$
$103$	−5.01348	−	5.01348i	−0.493992	−	0.493992i	−0.909562	+	0.415569i	$0.863582\pi$
$104$		−	3.09328i		−	0.303321i
$105$	0.901831	−	7.06751i	0.0880097	−	0.689719i
$106$			13.6091i			1.32183i
$107$	−10.7299	−	10.7299i	−1.03730	−	1.03730i	−0.999277	−	0.0380264i	$-0.987893\pi$
$107$	−10.7299	−	10.7299i	−1.03730	−	1.03730i	−0.0380264	−	0.999277i	$-0.512107\pi$
$108$	−5.71325	−	5.71325i	−0.549758	−	0.549758i
$109$	1.85686			0.177855			0.0889275	−	0.996038i	$-0.471656\pi$
$109$	1.85686			0.177855			0.0889275	+	0.996038i	$0.471656\pi$
$110$		0			0
$111$	−7.38836			−0.701272
$112$	7.00598	+	7.00598i	0.662003	+	0.662003i
$113$	−5.93505	−	5.93505i	−0.558323	−	0.558323i	0.370507	−	0.928830i	$-0.379184\pi$
$113$	−5.93505	−	5.93505i	−0.558323	−	0.558323i	−0.928830	+	0.370507i	$0.879184\pi$
$114$			11.6863i			1.09452i
$115$	10.4661	+	13.5278i	0.975972	+	1.26148i
$116$		−	7.42896i		−	0.689761i
$117$	1.31466	+	1.31466i	0.121540	+	0.121540i
$118$	17.0255	−	17.0255i	1.56733	−	1.56733i
$119$			14.2076i			1.30241i
$120$	3.51510	+	0.448535i	0.320884	+	0.0409455i
$121$		0			0
$122$	−7.03106	+	7.03106i	−0.636563	+	0.636563i
$123$	−8.24855	+	8.24855i	−0.743747	+	0.743747i
$124$			3.97821i			0.357254i
$125$	10.3797	+	4.15479i	0.928386	+	0.371616i
$126$	−2.36464			−0.210659
$127$	0.938206	+	0.938206i	0.0832523	+	0.0832523i	0.747507	−	0.664254i	$-0.231251\pi$
$127$	0.938206	+	0.938206i	0.0832523	+	0.0832523i	−0.664254	+	0.747507i	$0.731251\pi$
$128$	−5.58539	+	5.58539i	−0.493683	+	0.493683i
$129$	5.63315			0.495971
$130$	12.4085	+	1.58335i	1.08830	+	0.138869i
$131$		−	9.41359i		−	0.822469i	−0.911530	−	0.411235i	$-0.865098\pi$
$131$		−	9.41359i		−	0.822469i	0.911530	−	0.411235i	$-0.134902\pi$
$132$		0			0
$133$	5.95126	+	5.95126i	0.516040	+	0.516040i
$134$	8.95014			0.773174
$135$	−9.87485	+	7.63992i	−0.849891	+	0.657540i
$136$	−7.06633			−0.605933
$137$	8.62931	−	8.62931i	0.737252	−	0.737252i	−0.234794	−	0.972045i	$-0.575441\pi$
$137$	8.62931	−	8.62931i	0.737252	−	0.737252i	0.972045	+	0.234794i	$0.0754414\pi$
$138$	−15.5016	+	15.5016i	−1.31959	+	1.31959i
$139$	7.02028			0.595452			0.297726	−	0.954651i	$-0.403772\pi$
$139$	7.02028			0.595452			0.297726	+	0.954651i	$0.403772\pi$
$140$	−5.28245	+	4.08690i	−0.446449	+	0.345406i
$141$	−0.684071			−0.0576092
$142$	5.75186	+	5.75186i	0.482686	+	0.482686i
$143$		0			0
$144$		−	2.96186i		−	0.246821i
$145$	−11.3872	−	1.45304i	−0.945659	−	0.120668i
$146$	−16.6936			−1.38157
$147$	−2.99031	+	2.99031i	−0.246636	+	0.246636i
$148$	4.89735	+	4.89735i	0.402560	+	0.402560i
$149$	−1.34529			−0.110210			−0.0551050	−	0.998481i	$-0.517549\pi$
$149$	−1.34529			−0.110210			−0.0551050	+	0.998481i	$0.517549\pi$
$150$	−3.59855	+	13.8711i	−0.293820	+	1.13257i
$151$		−	2.94909i		−	0.239994i	−0.992774	−	0.119997i	$-0.961712\pi$
$151$		−	2.94909i		−	0.239994i	0.992774	−	0.119997i	$-0.0382884\pi$
$152$	−2.95992	+	2.95992i	−0.240082	+	0.240082i
$153$	3.00322	−	3.00322i	0.242796	−	0.242796i
$154$		0			0
$155$	6.09788	+	0.778103i	0.489793	+	0.0624987i
$156$			6.73074i			0.538891i
$157$	−1.75195	+	1.75195i	−0.139821	+	0.139821i	−0.773553	−	0.633732i	$-0.781522\pi$
$157$	−1.75195	+	1.75195i	−0.139821	+	0.139821i	0.633732	+	0.773553i	$0.281522\pi$
$158$	−16.6715	−	16.6715i	−1.32631	−	1.32631i
$159$			11.3152i			0.897356i
$160$	−9.38489	−	12.1303i	−0.741941	−	0.958982i
$161$			15.7884i			1.24430i
$162$	−8.88546	−	8.88546i	−0.698108	−	0.698108i
$163$	6.75298	+	6.75298i	0.528934	+	0.528934i	0.920255	−	0.391320i	$-0.127982\pi$
$163$	6.75298	+	6.75298i	0.528934	+	0.528934i	−0.391320	+	0.920255i	$0.627982\pi$
$164$	10.9350			0.853884
$165$		0			0
$166$	2.07343			0.160929
$167$	5.42613	+	5.42613i	0.419886	+	0.419886i	0.885165	−	0.465278i	$-0.154046\pi$
$167$	5.42613	+	5.42613i	0.419886	+	0.419886i	−0.465278	+	0.885165i	$0.654046\pi$
$168$	2.31300	+	2.31300i	0.178452	+	0.178452i
$169$			3.92107i			0.301621i
$170$	3.61704	−	28.3462i	0.277414	−	2.17405i
$171$		−	2.51596i		−	0.192400i
$172$	−3.73391	−	3.73391i	−0.284708	−	0.284708i
$173$	−9.68297	+	9.68297i	−0.736183	+	0.736183i	−0.971837	−	0.235654i	$-0.924277\pi$
$173$	−9.68297	+	9.68297i	−0.736183	+	0.736183i	0.235654	+	0.971837i	$0.424277\pi$
$174$		−	14.7138i		−	1.11545i
$175$	5.23128	+	8.89641i	0.395448	+	0.672505i
$176$		0			0
$177$	14.1558	−	14.1558i	1.06402	−	1.06402i
$178$	17.8107	−	17.8107i	1.33497	−	1.33497i
$179$			13.9546i			1.04301i	0.853247	+	0.521507i	$0.174630\pi$
$179$			13.9546i			1.04301i	−0.853247	+	0.521507i	$0.825370\pi$
$180$	1.98050	+	0.252716i	0.147618	+	0.0188364i
$181$	19.7953			1.47137			0.735687	−	0.677322i	$-0.236860\pi$
$181$	19.7953			1.47137			0.735687	+	0.677322i	$0.236860\pi$
$182$	8.16501	+	8.16501i	0.605231	+	0.605231i
$183$	−5.84595	+	5.84595i	−0.432145	+	0.432145i
$184$	−7.85255			−0.578898
$185$	8.46463	−	6.54887i	0.622332	−	0.481483i
$186$			7.87924i			0.577734i
$187$		0			0
$188$	0.453434	+	0.453434i	0.0330701	+	0.0330701i
$189$	−11.5250			−0.838322
$190$	−10.3585	−	13.3887i	−0.751483	−	0.971315i
$191$	−0.549146			−0.0397348			−0.0198674	−	0.999803i	$-0.506324\pi$
$191$	−0.549146			−0.0397348			−0.0198674	+	0.999803i	$0.506324\pi$
$192$	3.42099	−	3.42099i	0.246888	−	0.246888i
$193$	−3.57704	+	3.57704i	−0.257481	+	0.257481i	−0.824029	−	0.566548i	$-0.808279\pi$
$193$	−3.57704	+	3.57704i	−0.257481	+	0.257481i	0.566548	+	0.824029i	$0.308279\pi$
$194$	−15.6524			−1.12378
$195$	10.3170	+	1.31647i	0.738816	+	0.0942747i
$196$	3.96423			0.283159
$197$	5.33112	+	5.33112i	0.379827	+	0.379827i	0.871040	−	0.491213i	$-0.163446\pi$
$197$	5.33112	+	5.33112i	0.379827	+	0.379827i	−0.491213	+	0.871040i	$0.663446\pi$
$198$		0			0
$199$		−	5.88702i		−	0.417320i	−0.977988	−	0.208660i	$-0.933090\pi$
$199$		−	5.88702i		−	0.417320i	0.977988	−	0.208660i	$-0.0669102\pi$
$200$	−4.42473	+	2.60183i	−0.312875	+	0.183977i
$201$	7.44156			0.524887
$202$	1.95857	−	1.95857i	0.137804	−	0.137804i
$203$	−7.49301	−	7.49301i	−0.525906	−	0.525906i
$204$	15.3758			1.07652
$205$	2.13880	−	16.7615i	0.149380	−	1.17067i
$206$			13.1637i			0.917159i
$207$	3.33737	−	3.33737i	0.231963	−	0.231963i
$208$	−10.2272	+	10.2272i	−0.709127	+	0.709127i
$209$		0			0
$210$	−10.4624	+	8.09451i	−0.721975	+	0.558574i
$211$			15.1670i			1.04414i	0.852903	+	0.522069i	$0.174840\pi$
$211$			15.1670i			1.04414i	−0.852903	+	0.522069i	$0.825160\pi$
$212$	7.50026	−	7.50026i	0.515120	−	0.515120i
$213$	4.78236	+	4.78236i	0.327682	+	0.327682i
$214$			28.1733i			1.92588i
$215$	−6.45374	+	4.99309i	−0.440141	+	0.340526i
$216$		−	5.73209i		−	0.390020i
$217$	4.01251	+	4.01251i	0.272387	+	0.272387i
$218$	−2.43775	−	2.43775i	−0.165105	−	0.165105i
$219$	−13.8798			−0.937910
$220$		0			0
$221$	−20.7400			−1.39513
$222$	9.69968	+	9.69968i	0.651000	+	0.651000i
$223$	2.12144	+	2.12144i	0.142062	+	0.142062i	0.774561	−	0.632499i	$-0.217971\pi$
$223$	2.12144	+	2.12144i	0.142062	+	0.142062i	−0.632499	+	0.774561i	$0.717971\pi$
$224$		−	14.1573i		−	0.945927i
$225$	0.774737	−	2.98632i	0.0516491	−	0.199088i
$226$			15.5835i			1.03660i
$227$	−0.530734	−	0.530734i	−0.0352261	−	0.0352261i	0.689274	−	0.724500i	$-0.257929\pi$
$227$	−0.530734	−	0.530734i	−0.0352261	−	0.0352261i	−0.724500	+	0.689274i	$0.757929\pi$
$228$	6.44057	−	6.44057i	0.426537	−	0.426537i
$229$			8.06680i			0.533069i	0.963825	+	0.266535i	$0.0858786\pi$
$229$			8.06680i			0.533069i	−0.963825	+	0.266535i	$0.914121\pi$
$230$	4.01948	−	31.5000i	0.265037	−	2.07705i
$231$		0			0
$232$	3.72673	−	3.72673i	0.244672	−	0.244672i
$233$	1.18349	−	1.18349i	0.0775328	−	0.0775328i	−0.667277	−	0.744810i	$-0.732540\pi$
$233$	1.18349	−	1.18349i	0.0775328	−	0.0775328i	0.744810	+	0.667277i	$0.232540\pi$
$234$		−	3.45185i		−	0.225655i
$235$	0.783721	−	0.606345i	0.0511243	−	0.0395536i
$236$	−18.7663			−1.22158
$237$	−13.8614	−	13.8614i	−0.900397	−	0.900397i
$238$	18.6523	−	18.6523i	1.20905	−	1.20905i
$239$	−16.5020			−1.06743			−0.533713	−	0.845666i	$-0.679204\pi$
$239$	−16.5020			−1.06743			−0.533713	+	0.845666i	$0.679204\pi$
$240$	−10.1389	−	13.1048i	−0.654461	−	0.845913i
$241$		−	21.2562i		−	1.36923i	−0.728903	−	0.684617i	$-0.759970\pi$
$241$		−	21.2562i		−	1.36923i	0.728903	−	0.684617i	$-0.240030\pi$
$242$		0			0
$243$	4.45674	+	4.45674i	0.285900	+	0.285900i
$244$	7.74994			0.496139
$245$	0.775369	−	6.07645i	0.0495365	−	0.388210i
$246$	21.6579			1.38086
$247$	−8.68753	+	8.68753i	−0.552774	+	0.552774i
$248$	−1.99566	+	1.99566i	−0.126725	+	0.126725i
$249$	1.72395			0.109251
$250$	−8.17223	−	19.0813i	−0.516857	−	1.20681i
$251$	−26.0502			−1.64428			−0.822138	−	0.569288i	$-0.807219\pi$
$251$	−26.0502			−1.64428			−0.822138	+	0.569288i	$0.807219\pi$
$252$	1.30320	+	1.30320i	0.0820941	+	0.0820941i
$253$		0			0
$254$		−	2.46342i		−	0.154568i
$255$	3.00737	−	23.5683i	0.188329	−	1.47591i
$256$	20.9335			1.30834
$257$	−1.73727	+	1.73727i	−0.108368	+	0.108368i	−0.759212	−	0.650844i	$-0.774415\pi$
$257$	−1.73727	+	1.73727i	−0.108368	+	0.108368i	0.650844	+	0.759212i	$0.274415\pi$
$258$	−7.39538	−	7.39538i	−0.460416	−	0.460416i
$259$	9.87915			0.613860
$260$	−5.96598	−	7.71122i	−0.369994	−	0.478229i
$261$			3.16775i			0.196079i
$262$	−12.3585	+	12.3585i	−0.763509	+	0.763509i
$263$	−14.2199	+	14.2199i	−0.876839	+	0.876839i	−0.993206	−	0.116367i	$-0.962875\pi$
$263$	−14.2199	+	14.2199i	−0.876839	+	0.876839i	0.116367	+	0.993206i	$0.462875\pi$
$264$		0			0
$265$	−10.0296	−	12.9635i	−0.616111	−	0.796344i
$266$		−	15.6260i		−	0.958093i
$267$	14.8086	−	14.8086i	0.906273	−	0.906273i
$268$	−4.93262	−	4.93262i	−0.301307	−	0.301307i
$269$		−	2.23801i		−	0.136454i	−0.997670	−	0.0682269i	$-0.978266\pi$
$269$		−	2.23801i		−	0.136454i	0.997670	−	0.0682269i	$-0.0217342\pi$
$270$	22.9940	+	2.93408i	1.39937	+	0.178563i
$271$		−	2.95960i		−	0.179783i	−0.995952	−	0.0898914i	$-0.971348\pi$
$271$		−	2.95960i		−	0.179783i	0.995952	−	0.0898914i	$-0.0286520\pi$
$272$	23.3631	+	23.3631i	1.41660	+	1.41660i
$273$	6.78877	+	6.78877i	0.410875	+	0.410875i
$274$	−22.6577			−1.36880
$275$		0			0
$276$	17.0866			1.02849
$277$	−19.5458	−	19.5458i	−1.17439	−	1.17439i	−0.981152	−	0.193239i	$-0.938101\pi$
$277$	−19.5458	−	19.5458i	−1.17439	−	1.17439i	−0.193239	−	0.981152i	$-0.561899\pi$
$278$	−9.21645	−	9.21645i	−0.552766	−	0.552766i
$279$		−	1.69633i		−	0.101557i
$280$	−4.70013	−	0.599747i	−0.280886	−	0.0358417i
$281$		−	29.6489i		−	1.76870i	−0.466822	−	0.884351i	$-0.654601\pi$
$281$		−	29.6489i		−	1.76870i	0.466822	−	0.884351i	$-0.345399\pi$
$282$	0.898071	+	0.898071i	0.0534794	+	0.0534794i
$283$	6.46389	−	6.46389i	0.384238	−	0.384238i	−0.488388	−	0.872626i	$-0.662415\pi$
$283$	6.46389	−	6.46389i	0.384238	−	0.384238i	0.872626	+	0.488388i	$0.162415\pi$
$284$		−	6.33995i		−	0.376207i
$285$	−8.61251	−	11.1320i	−0.510161	−	0.659400i
$286$		0			0
$287$	11.0293	−	11.0293i	0.651040	−	0.651040i
$288$	−2.99259	+	2.99259i	−0.176340	+	0.176340i
$289$			30.3788i			1.78699i
$290$	13.0420	+	16.8572i	0.765850	+	0.989886i
$291$	−13.0141			−0.762901
$292$	9.20018	+	9.20018i	0.538400	+	0.538400i
$293$	1.24653	−	1.24653i	0.0728229	−	0.0728229i	−0.669757	−	0.742580i	$-0.733602\pi$
$293$	1.24653	−	1.24653i	0.0728229	−	0.0728229i	0.742580	+	0.669757i	$0.233602\pi$
$294$	7.85155			0.457912
$295$	−3.67052	+	28.7653i	−0.213706	+	1.67478i
$296$			4.91350i			0.285591i
$297$		0			0
$298$	1.76613	+	1.76613i	0.102309	+	0.102309i
$299$	−23.0476			−1.33288
$300$	9.62787	−	5.66140i	0.555865	−	0.326861i
$301$	−7.53221			−0.434149
$302$	−3.87166	+	3.87166i	−0.222789	+	0.222789i
$303$	1.62844	−	1.62844i	0.0935517	−	0.0935517i
$304$	19.5726			1.12256
$305$	1.51582	−	11.8793i	0.0867956	−	0.680204i
$306$	−7.88546			−0.450782
$307$	10.6721	+	10.6721i	0.609087	+	0.609087i	0.942707	−	0.333621i	$-0.108270\pi$
$307$	10.6721	+	10.6721i	0.609087	+	0.609087i	−0.333621	+	0.942707i	$0.608270\pi$
$308$		0			0
$309$			10.9449i			0.622635i
$310$	−6.98398	−	9.02701i	−0.396663	−	0.512700i
$311$	27.3038			1.54826			0.774129	−	0.633028i	$-0.218188\pi$
$311$	27.3038			1.54826			0.774129	+	0.633028i	$0.218188\pi$
$312$	−3.37647	+	3.37647i	−0.191155	+	0.191155i
$313$	−18.9653	−	18.9653i	−1.07198	−	1.07198i	−0.997200	−	0.0747818i	$-0.976174\pi$
$313$	−18.9653	−	18.9653i	−1.07198	−	1.07198i	−0.0747818	−	0.997200i	$-0.523826\pi$
$314$	4.60004			0.259595
$315$	2.25247	−	1.74268i	0.126912	−	0.0981889i
$316$			18.3760i			1.03373i
$317$	1.39021	−	1.39021i	0.0780820	−	0.0780820i	−0.666987	−	0.745069i	$-0.732416\pi$
$317$	1.39021	−	1.39021i	0.0780820	−	0.0780820i	0.745069	+	0.666987i	$0.232416\pi$
$318$	14.8550	−	14.8550i	0.833027	−	0.833027i
$319$		0			0
$320$	−0.887041	+	6.95161i	−0.0495871	+	0.388607i
$321$			23.4246i			1.30743i
$322$	20.7276	−	20.7276i	1.15510	−	1.15510i
$323$	19.8459	+	19.8459i	1.10426	+	1.10426i
$324$			9.79394i			0.544108i
$325$	−12.9868	+	7.63652i	−0.720378	+	0.423598i
$326$		−	17.7311i		−	0.982033i
$327$	−2.02686	−	2.02686i	−0.112085	−	0.112085i
$328$	5.48555	+	5.48555i	0.302889	+	0.302889i
$329$	0.914687			0.0504283
$330$		0			0
$331$	24.3840			1.34027			0.670133	−	0.742241i	$-0.266237\pi$
$331$	24.3840			1.34027			0.670133	+	0.742241i	$0.266237\pi$
$332$	−1.14271	−	1.14271i	−0.0627145	−	0.0627145i
$333$	−2.08826	−	2.08826i	−0.114436	−	0.114436i
$334$		−	14.2472i		−	0.779572i
$335$	−8.52558	+	6.59603i	−0.465802	+	0.360380i
$336$		−	15.2948i		−	0.834397i
$337$	−5.70583	−	5.70583i	−0.310816	−	0.310816i	0.534410	−	0.845226i	$-0.320534\pi$
$337$	−5.70583	−	5.70583i	−0.310816	−	0.310816i	−0.845226	+	0.534410i	$0.820534\pi$
$338$	5.14771	−	5.14771i	0.279999	−	0.279999i
$339$			12.9568i			0.703717i
$340$	−17.6156	+	13.6288i	−0.955341	+	0.739123i
$341$		0			0
$342$	−3.30304	+	3.30304i	−0.178608	+	0.178608i
$343$	14.2152	−	14.2152i	0.767547	−	0.767547i
$344$		−	3.74623i		−	0.201983i
$345$	3.34198	−	26.1906i	0.179926	−	1.41005i
$346$	25.4242			1.36682
$347$	20.5054	+	20.5054i	1.10079	+	1.10079i	0.994316	+	0.106470i	$0.0339547\pi$
$347$	20.5054	+	20.5054i	1.10079	+	1.10079i	0.106470	+	0.994316i	$0.466045\pi$
$348$	−8.10908	+	8.10908i	−0.434692	+	0.434692i
$349$	−3.44459			−0.184385			−0.0921924	−	0.995741i	$-0.529387\pi$
$349$	−3.44459			−0.184385			−0.0921924	+	0.995741i	$0.529387\pi$
$350$	4.81170	−	18.5473i	0.257196	−	0.991395i
$351$		−	16.8240i		−	0.897998i
$352$		0			0
$353$	−7.44497	−	7.44497i	−0.396256	−	0.396256i	0.480654	−	0.876910i	$-0.340399\pi$
$353$	−7.44497	−	7.44497i	−0.396256	−	0.396256i	−0.876910	+	0.480654i	$0.840399\pi$
$354$	−37.1685			−1.97548
$355$	−9.71800	−	1.24004i	−0.515778	−	0.0658144i
$356$	−19.6317			−1.04048
$357$	15.5084	−	15.5084i	0.820790	−	0.820790i
$358$	18.3200	−	18.3200i	0.968244	−	0.968244i
$359$	−15.1005			−0.796972			−0.398486	−	0.917174i	$-0.630464\pi$
$359$	−15.1005			−0.796972			−0.398486	+	0.917174i	$0.630464\pi$
$360$	0.866741	+	1.12029i	0.0456813	+	0.0590445i
$361$	−2.37400			−0.124947
$362$	−25.9879	−	25.9879i	−1.36590	−	1.36590i
$363$		0			0
$364$		−	8.99983i		−	0.471719i
$365$	15.9017	−	12.3027i	0.832332	−	0.643954i
$366$	15.3495			0.802332
$367$	−23.6545	+	23.6545i	−1.23476	+	1.23476i	−0.272639	+	0.962117i	$0.587896\pi$
$367$	−23.6545	+	23.6545i	−1.23476	+	1.23476i	−0.962117	+	0.272639i	$0.912104\pi$
$368$	25.9626	+	25.9626i	1.35339	+	1.35339i
$369$	−4.66277			−0.242734
$370$	−19.7102	−	2.51507i	−1.02469	−	0.130752i
$371$		−	15.1299i		−	0.785503i
$372$	4.34242	−	4.34242i	0.225144	−	0.225144i
$373$	0.821903	−	0.821903i	0.0425565	−	0.0425565i	−0.685508	−	0.728065i	$-0.740420\pi$
$373$	0.821903	−	0.821903i	0.0425565	−	0.0425565i	0.728065	+	0.685508i	$0.240420\pi$
$374$		0			0
$375$	−6.79477	−	15.8651i	−0.350881	−	0.819271i
$376$			0.454930i			0.0234612i
$377$	10.9381	−	10.9381i	0.563343	−	0.563343i
$378$	15.1304	+	15.1304i	0.778225	+	0.778225i
$379$		−	11.9529i		−	0.613978i	−0.951713	−	0.306989i	$-0.900679\pi$
$379$		−	11.9529i		−	0.613978i	0.951713	−	0.306989i	$-0.0993215\pi$
$380$	−1.67000	+	13.0876i	−0.0856693	+	0.671377i
$381$		−	2.04820i		−	0.104932i
$382$	0.720937	+	0.720937i	0.0368863	+	0.0368863i
$383$	−13.8803	−	13.8803i	−0.709251	−	0.709251i	0.257127	−	0.966378i	$-0.417224\pi$
$383$	−13.8803	−	13.8803i	−0.709251	−	0.709251i	−0.966378	+	0.257127i	$0.917224\pi$
$384$	12.1935			0.622245
$385$		0			0
$386$	9.39212			0.478046
$387$	1.59216	+	1.59216i	0.0809342	+	0.0809342i
$388$	8.62637	+	8.62637i	0.437938	+	0.437938i
$389$		−	35.4108i		−	1.79540i	−0.440609	−	0.897699i	$-0.645237\pi$
$389$		−	35.4108i		−	1.79540i	0.440609	−	0.897699i	$-0.354763\pi$
$390$	−11.8162	−	15.2728i	−0.598337	−	0.773369i
$391$			52.6503i			2.66264i
$392$	1.98865	+	1.98865i	0.100442	+	0.100442i
$393$	−10.2754	+	10.2754i	−0.518326	+	0.518326i
$394$		−	13.9977i		−	0.705196i
$395$	28.1671	+	3.59419i	1.41724	+	0.180843i
$396$		0			0
$397$	−13.8345	+	13.8345i	−0.694333	+	0.694333i	−0.963182	−	0.268849i	$-0.913357\pi$
$397$	−13.8345	+	13.8345i	−0.694333	+	0.694333i	0.268849	+	0.963182i	$0.413357\pi$
$398$	−7.72867	+	7.72867i	−0.387403	+	0.387403i
$399$		−	12.9922i		−	0.650424i
$400$	23.2316	+	6.02695i	1.16158	+	0.301348i
$401$	6.64954			0.332062			0.166031	−	0.986121i	$-0.446905\pi$
$401$	6.64954			0.332062			0.166031	+	0.986121i	$0.446905\pi$
$402$	−9.76953	−	9.76953i	−0.487260	−	0.487260i
$403$	−5.85738	+	5.85738i	−0.291777	+	0.291777i
$404$	−2.15882			−0.107405
$405$	15.0123	+	1.91561i	0.745969	+	0.0951874i
$406$			19.6741i			0.976411i
$407$		0			0
$408$	7.71325	+	7.71325i	0.381863	+	0.381863i
$409$	29.2129			1.44448			0.722242	−	0.691640i	$-0.243111\pi$
$409$	29.2129			1.44448			0.722242	+	0.691640i	$0.243111\pi$
$410$	−24.8129	+	19.1971i	−1.22542	+	0.948077i
$411$	−18.8387			−0.929242
$412$	7.25480	−	7.25480i	0.357419	−	0.357419i
$413$	−18.9281	+	18.9281i	−0.931390	+	0.931390i
$414$	−8.76282			−0.430669
$415$	−1.97507	+	1.52807i	−0.0969526	+	0.0750098i
$416$	20.6666			1.01326
$417$	−7.66299	−	7.66299i	−0.375258	−	0.375258i
$418$		0			0
$419$		−	19.2755i		−	0.941672i	−0.882221	−	0.470836i	$-0.843952\pi$
$419$		−	19.2755i		−	0.941672i	0.882221	−	0.470836i	$-0.156048\pi$
$420$	10.2271	+	1.30500i	0.499033	+	0.0636777i
$421$	−36.5249			−1.78011			−0.890056	−	0.455850i	$-0.849335\pi$
$421$	−36.5249			−1.78011			−0.890056	+	0.455850i	$0.849335\pi$
$422$	19.9117	−	19.9117i	0.969287	−	0.969287i
$423$	−0.193347	−	0.193347i	−0.00940086	−	0.00940086i
$424$	7.52500			0.365446
$425$	17.4450	+	29.6672i	0.846205	+	1.43907i
$426$		−	12.5569i		−	0.608383i
$427$	7.81676	−	7.81676i	0.378279	−	0.378279i
$428$	15.5269	−	15.5269i	0.750520	−	0.750520i
$429$		0			0
$430$	15.0278	+	1.91758i	0.724704	+	0.0924738i
$431$			12.1197i			0.583786i	0.956451	+	0.291893i	$0.0942851\pi$
$431$			12.1197i			0.583786i	−0.956451	+	0.291893i	$0.905715\pi$
$432$	−18.9518	+	18.9518i	−0.911818	+	0.911818i
$433$	3.34776	+	3.34776i	0.160883	+	0.160883i	0.782958	−	0.622075i	$-0.213710\pi$
$433$	3.34776	+	3.34776i	0.160883	+	0.160883i	−0.622075	+	0.782958i	$0.713710\pi$
$434$		−	10.5355i		−	0.505721i
$435$	10.8437	+	14.0158i	0.519915	+	0.672007i
$436$			2.68699i			0.128684i
$437$	22.0540	+	22.0540i	1.05499	+	1.05499i
$438$	18.2219	+	18.2219i	0.870674	+	0.870674i
$439$	−26.1692			−1.24899			−0.624494	−	0.781029i	$-0.714695\pi$
$439$	−26.1692			−1.24899			−0.624494	+	0.781029i	$0.714695\pi$
$440$		0			0
$441$	−1.69037			−0.0804939
$442$	27.2282	+	27.2282i	1.29511	+	1.29511i
$443$	−20.2145	−	20.2145i	−0.960422	−	0.960422i	0.0388240	−	0.999246i	$-0.487639\pi$
$443$	−20.2145	−	20.2145i	−0.960422	−	0.960422i	−0.999246	+	0.0388240i	$0.987639\pi$
$444$		−	10.6914i		−	0.507392i
$445$	−3.83979	+	30.0918i	−0.182023	+	1.42649i
$446$		−	5.57019i		−	0.263756i
$447$	1.46845	+	1.46845i	0.0694551	+	0.0694551i
$448$	−4.57428	+	4.57428i	−0.216114	+	0.216114i
$449$		−	4.74429i		−	0.223897i	−0.993714	−	0.111949i	$-0.964291\pi$
$449$		−	4.74429i		−	0.223897i	0.993714	−	0.111949i	$-0.0357092\pi$
$450$	−4.93764	+	2.90344i	−0.232763	+	0.136869i
$451$		0			0
$452$	8.58838	−	8.58838i	0.403963	−	0.403963i
$453$	−3.21908	+	3.21908i	−0.151246	+	0.151246i
$454$			1.39353i			0.0654016i
$455$	−13.7951	−	1.76029i	−0.646725	−	0.0825235i
$456$	6.46181			0.302602
$457$	−23.9375	−	23.9375i	−1.11975	−	1.11975i	−0.991778	−	0.127969i	$-0.959154\pi$
$457$	−23.9375	−	23.9375i	−1.11975	−	1.11975i	−0.127969	−	0.991778i	$-0.540846\pi$
$458$	10.5904	−	10.5904i	0.494855	−	0.494855i
$459$	−38.4329			−1.79390
$460$	−19.5756	+	15.1451i	−0.912716	+	0.706145i
$461$			28.3761i			1.32161i	0.750559	+	0.660803i	$0.229784\pi$
$461$			28.3761i			1.32161i	−0.750559	+	0.660803i	$0.770216\pi$
$462$		0			0
$463$	−16.0155	−	16.0155i	−0.744304	−	0.744304i	0.229099	−	0.973403i	$-0.426422\pi$
$463$	−16.0155	−	16.0155i	−0.744304	−	0.744304i	−0.973403	+	0.229099i	$0.926422\pi$
$464$	−24.6431			−1.14403
$465$	−5.80680	−	7.50548i	−0.269284	−	0.348058i
$466$	−3.10744			−0.143949
$467$	−3.11810	+	3.11810i	−0.144289	+	0.144289i	−0.775561	−	0.631273i	$-0.782533\pi$
$467$	−3.11810	+	3.11810i	−0.144289	+	0.144289i	0.631273	+	0.775561i	$0.282533\pi$
$468$	−1.90239	+	1.90239i	−0.0879380	+	0.0879380i
$469$	−9.95028			−0.459461
$470$	−1.82492	−	0.232865i	−0.0841775	−	0.0107412i
$471$	3.82468			0.176232
$472$	−9.41408	−	9.41408i	−0.433318	−	0.433318i
$473$		0			0
$474$			36.3955i			1.67170i
$475$	19.7342	+	5.11962i	0.905468	+	0.234904i
$476$	−20.5593			−0.942335
$477$	−3.19816	+	3.19816i	−0.146434	+	0.146434i
$478$	21.6644	+	21.6644i	0.990905	+	0.990905i
$479$	−17.4799			−0.798678			−0.399339	−	0.916803i	$-0.630760\pi$
$479$	−17.4799			−0.798678			−0.399339	+	0.916803i	$0.630760\pi$
$480$	−2.99672	+	23.4849i	−0.136781	+	1.07193i
$481$			14.4214i			0.657558i
$482$	−27.9059	+	27.9059i	−1.27108	+	1.27108i
$483$	17.2339	−	17.2339i	0.784168	−	0.784168i
$484$		0			0
$485$	14.9099	−	11.5354i	0.677024	−	0.523797i
$486$		−	11.7019i		−	0.530810i
$487$	−13.0589	+	13.0589i	−0.591754	+	0.591754i	−0.938105	−	0.346351i	$-0.887421\pi$
$487$	−13.0589	+	13.0589i	−0.591754	+	0.591754i	0.346351	+	0.938105i	$0.387421\pi$
$488$	3.88775	+	3.88775i	0.175990	+	0.175990i
$489$		−	14.7424i		−	0.666676i
$490$	−8.99529	+	6.95943i	−0.406366	+	0.314395i
$491$			13.2524i			0.598071i	0.954242	+	0.299035i	$0.0966649\pi$
$491$			13.2524i			0.598071i	−0.954242	+	0.299035i	$0.903335\pi$
$492$	−11.9362	−	11.9362i	−0.538123	−	0.538123i
$493$	−24.9872	−	24.9872i	−1.12537	−	1.12537i
$494$	22.8105			1.02629
$495$		0			0
$496$	13.1964			0.592534
$497$	−6.39461	−	6.39461i	−0.286837	−	0.286837i
$498$	−2.26325	−	2.26325i	−0.101419	−	0.101419i
$499$		−	11.6010i		−	0.519331i	−0.965699	−	0.259665i	$-0.916388\pi$
$499$		−	11.6010i		−	0.519331i	0.965699	−	0.259665i	$-0.0836123\pi$
$500$	−6.01224	+	15.0200i	−0.268876	+	0.671716i
$501$		−	11.8458i		−	0.529230i
$502$	34.1996	+	34.1996i	1.52640	+	1.52640i
$503$	2.98395	−	2.98395i	0.133048	−	0.133048i	−0.637447	−	0.770494i	$-0.720009\pi$
$503$	2.98395	−	2.98395i	0.133048	−	0.133048i	0.770494	+	0.637447i	$0.220009\pi$
$504$			1.30750i			0.0582407i
$505$	−0.422246	+	3.30908i	−0.0187897	+	0.147252i
$506$		0			0
$507$	4.28005	−	4.28005i	0.190084	−	0.190084i
$508$	−1.35764	+	1.35764i	−0.0602356	+	0.0602356i
$509$			27.1372i			1.20283i	0.798936	+	0.601417i	$0.205397\pi$
$509$			27.1372i			1.20283i	−0.798936	+	0.601417i	$0.794603\pi$
$510$	−34.8894	+	26.9931i	−1.54493	+	1.19527i
$511$	18.5590			0.821001
$512$	−16.3114	−	16.3114i	−0.720869	−	0.720869i
$513$	−16.0987	+	16.0987i	−0.710774	+	0.710774i
$514$	4.56150			0.201199
$515$	−9.70133	−	12.5393i	−0.427492	−	0.552547i
$516$			8.15151i			0.358850i
$517$		0			0
$518$	−12.9697	−	12.9697i	−0.569855	−	0.569855i
$519$	21.1389			0.927895
$520$	0.875498	−	6.86115i	0.0383931	−	0.300881i
$521$	11.5548			0.506226			0.253113	−	0.967437i	$-0.418545\pi$
$521$	11.5548			0.506226			0.253113	+	0.967437i	$0.418545\pi$
$522$	4.15873	−	4.15873i	0.182023	−	0.182023i
$523$	20.1714	−	20.1714i	0.882034	−	0.882034i	−0.111707	−	0.993741i	$-0.535632\pi$
$523$	20.1714	−	20.1714i	0.882034	−	0.882034i	0.993741	+	0.111707i	$0.0356319\pi$
$524$	13.6220			0.595082
$525$	4.00067	−	15.4211i	0.174604	−	0.673031i
$526$	37.3368			1.62796
$527$	13.3807	+	13.3807i	0.582871	+	0.582871i
$528$		0			0
$529$			35.5083i			1.54384i
$530$	−3.85181	+	30.1861i	−0.167312	+	1.31120i
$531$	8.00206			0.347260
$532$	−8.61184	+	8.61184i	−0.373370	+	0.373370i
$533$	16.1004	+	16.1004i	0.697385	+	0.697385i
$534$	−38.8825			−1.68261
$535$	−20.7630	−	26.8368i	−0.897662	−	1.16026i
$536$		−	4.94888i		−	0.213759i
$537$	15.2321	−	15.2321i	0.657315	−	0.657315i
$538$	−2.93813	+	2.93813i	−0.126672	+	0.126672i
$539$		0			0
$540$	−11.0554	−	14.2895i	−0.475750	−	0.614922i
$541$		−	21.4079i		−	0.920398i	−0.887816	−	0.460199i	$-0.847778\pi$
$541$		−	21.4079i		−	0.920398i	0.887816	−	0.460199i	$-0.152222\pi$
$542$	−3.88546	+	3.88546i	−0.166895	+	0.166895i
$543$	−21.6076	−	21.6076i	−0.927270	−	0.927270i
$544$		−	47.2111i		−	2.02416i
$545$	4.11867	+	0.525552i	0.176425	+	0.0225122i
$546$		−	17.8250i		−	0.762841i
$547$	−3.21652	−	3.21652i	−0.137528	−	0.137528i	0.634991	−	0.772520i	$-0.281004\pi$
$547$	−3.21652	−	3.21652i	−0.137528	−	0.137528i	−0.772520	+	0.634991i	$0.781004\pi$
$548$	12.4871	+	12.4871i	0.533424	+	0.533424i
$549$	−3.30462			−0.141038
$550$		0			0
$551$	−20.9332			−0.891783
$552$	8.57145	+	8.57145i	0.364825	+	0.364825i
$553$	18.5344	+	18.5344i	0.788165	+	0.788165i
$554$			51.3206i			2.18041i
$555$	−16.3880	−	2.09115i	−0.695632	−	0.0887642i
$556$			10.1588i			0.430828i
$557$	−6.68376	−	6.68376i	−0.283200	−	0.283200i	0.551184	−	0.834384i	$-0.314176\pi$
$557$	−6.68376	−	6.68376i	−0.283200	−	0.283200i	−0.834384	+	0.551184i	$0.814176\pi$
$558$	−2.22700	+	2.22700i	−0.0942765	+	0.0942765i
$559$		−	10.9954i		−	0.465054i
$560$	13.5569	+	17.5228i	0.572884	+	0.740472i
$561$		0			0
$562$	−38.9240	+	38.9240i	−1.64191	+	1.64191i
$563$	−23.5546	+	23.5546i	−0.992709	+	0.992709i	−0.999974	−	0.00726468i	$-0.997688\pi$
$563$	−23.5546	+	23.5546i	−0.992709	+	0.992709i	0.00726468	+	0.999974i	$0.497688\pi$
$564$		−	0.989893i		−	0.0416820i
$565$	−11.4846	−	14.8442i	−0.483162	−	0.624502i
$566$	−16.9720			−0.713387
$567$	9.87838	+	9.87838i	0.414853	+	0.414853i
$568$	3.18043	−	3.18043i	0.133448	−	0.133448i
$569$	38.1684			1.60010			0.800052	−	0.599931i	$-0.204805\pi$
$569$	38.1684			1.60010			0.800052	+	0.599931i	$0.204805\pi$
$570$	−3.30760	+	25.9212i	−0.138540	+	1.08572i
$571$			0.631817i			0.0264407i	0.999913	+	0.0132204i	$0.00420829\pi$
$571$			0.631817i			0.0264407i	−0.999913	+	0.0132204i	$0.995792\pi$
$572$		0			0
$573$	0.599420	+	0.599420i	0.0250411	+	0.0250411i
$574$	−28.9593			−1.20874
$575$	19.3859	+	32.9681i	0.808450	+	1.37486i
$576$	1.93383			0.0805762
$577$	6.92463	−	6.92463i	0.288276	−	0.288276i	−0.548122	−	0.836398i	$-0.684657\pi$
$577$	6.92463	−	6.92463i	0.288276	−	0.288276i	0.836398	+	0.548122i	$0.184657\pi$
$578$	39.8823	−	39.8823i	1.65889	−	1.65889i
$579$	7.80904			0.324533
$580$	2.10264	−	16.4780i	0.0873072	−	0.684213i
$581$	−2.30513			−0.0956328
$582$	17.0854	+	17.0854i	0.708211	+	0.708211i
$583$		0			0
$584$			9.23051i			0.381961i
$585$	2.54393	+	3.28811i	0.105179	+	0.135947i
$586$	−3.27296			−0.135205
$587$	9.62241	−	9.62241i	0.397159	−	0.397159i	−0.480070	−	0.877230i	$-0.659389\pi$
$587$	9.62241	−	9.62241i	0.397159	−	0.397159i	0.877230	+	0.480070i	$0.159389\pi$
$588$	−4.32716	−	4.32716i	−0.178449	−	0.178449i
$589$	11.2097			0.461888
$590$	42.5828	−	32.9453i	1.75311	−	1.35634i
$591$		−	11.6384i		−	0.478739i
$592$	16.2453	−	16.2453i	0.667678	−	0.667678i
$593$	6.27189	−	6.27189i	0.257555	−	0.257555i	−0.566504	−	0.824059i	$-0.691704\pi$
$593$	6.27189	−	6.27189i	0.257555	−	0.257555i	0.824059	+	0.566504i	$0.191704\pi$
$594$		0			0
$595$	−4.02123	+	31.5137i	−0.164854	+	1.29194i
$596$		−	1.94671i		−	0.0797403i
$597$	−6.42598	+	6.42598i	−0.262998	+	0.262998i
$598$	30.2577	+	30.2577i	1.23733	+	1.23733i
$599$			24.2660i			0.991482i	0.868470	+	0.495741i	$0.165104\pi$
$599$			24.2660i			0.991482i	−0.868470	+	0.495741i	$0.834896\pi$
$600$	7.66984	+	1.98978i	0.313120	+	0.0812323i
$601$			23.3691i			0.953247i	0.879107	+	0.476624i	$0.158140\pi$
$601$			23.3691i			0.953247i	−0.879107	+	0.476624i	$0.841860\pi$
$602$	9.88853	+	9.88853i	0.403027	+	0.403027i
$603$	2.10330	+	2.10330i	0.0856529	+	0.0856529i
$604$	4.26751			0.173643
$605$		0			0
$606$	−4.27575			−0.173691
$607$	−12.6775	−	12.6775i	−0.514563	−	0.514563i	0.401358	−	0.915921i	$-0.368538\pi$
$607$	−12.6775	−	12.6775i	−0.514563	−	0.514563i	−0.915921	+	0.401358i	$0.868538\pi$
$608$	−19.7756	−	19.7756i	−0.802008	−	0.802008i
$609$			16.3580i			0.662859i
$610$	−17.5855	+	13.6055i	−0.712016	+	0.550869i
$611$			1.33524i			0.0540181i
$612$	4.34585	+	4.34585i	0.175670	+	0.175670i
$613$	−27.0000	+	27.0000i	−1.09052	+	1.09052i	−0.0950448	+	0.995473i	$0.530299\pi$
$613$	−27.0000	+	27.0000i	−1.09052	+	1.09052i	−0.995473	+	0.0950448i	$0.969701\pi$
$614$		−	28.0213i		−	1.13085i
$615$	−20.6306	+	15.9614i	−0.831905	+	0.643624i
$616$		0			0
$617$	−9.02298	+	9.02298i	−0.363252	+	0.363252i	−0.865009	−	0.501757i	$-0.832687\pi$
$617$	−9.02298	+	9.02298i	−0.363252	+	0.363252i	0.501757	+	0.865009i	$0.332687\pi$
$618$	14.3689	−	14.3689i	0.578000	−	0.578000i
$619$		−	39.9556i		−	1.60595i	−0.596011	−	0.802976i	$-0.703249\pi$
$619$		−	39.9556i		−	1.60595i	0.596011	−	0.802976i	$-0.296751\pi$
$620$	−1.12596	+	8.82400i	−0.0452197	+	0.354380i
$621$	−42.7091			−1.71386
$622$	−35.8454	−	35.8454i	−1.43727	−	1.43727i
$623$	−19.8009	+	19.8009i	−0.793308	+	0.793308i
$624$	22.3270			0.893794
$625$	21.8470	+	12.1535i	0.873882	+	0.486139i
$626$			49.7965i			1.99027i
$627$		0			0
$628$	−2.53518	−	2.53518i	−0.101165	−	0.101165i
$629$	32.9444			1.31358
$630$	−5.24497	−	0.669270i	−0.208964	−	0.0266643i
$631$	−8.73741			−0.347831			−0.173915	−	0.984761i	$-0.555642\pi$
$631$	−8.73741			−0.347831			−0.173915	+	0.984761i	$0.555642\pi$
$632$	−9.21831	+	9.21831i	−0.366685	+	0.366685i
$633$	16.5555	−	16.5555i	0.658023	−	0.658023i
$634$	−3.65023			−0.144969
$635$	1.81548	+	2.34656i	0.0720450	+	0.0931205i
$636$	−16.3738			−0.649265
$637$	5.83679	+	5.83679i	0.231262	+	0.231262i
$638$		0			0
$639$			2.70339i			0.106945i
$640$	−13.9697	+	10.8080i	−0.552201	+	0.427224i
$641$	22.0310			0.870174			0.435087	−	0.900389i	$-0.356718\pi$
$641$	22.0310			0.870174			0.435087	+	0.900389i	$0.356718\pi$
$642$	30.7525	−	30.7525i	1.21371	−	1.21371i
$643$	−31.1418	−	31.1418i	−1.22811	−	1.22811i	−0.964677	−	0.263435i	$-0.915145\pi$
$643$	−31.1418	−	31.1418i	−1.22811	−	1.22811i	−0.263435	−	0.964677i	$-0.584855\pi$
$644$	−22.8468			−0.900291
$645$	12.4948	+	1.59436i	0.491982	+	0.0627780i
$646$		−	52.1087i		−	2.05019i
$647$	26.8448	−	26.8448i	1.05538	−	1.05538i	0.0570061	−	0.998374i	$-0.481845\pi$
$647$	26.8448	−	26.8448i	1.05538	−	1.05538i	0.998374	−	0.0570061i	$-0.0181555\pi$
$648$	−4.91312	+	4.91312i	−0.193006	+	0.193006i
$649$		0			0
$650$	27.0750	+	7.02402i	1.06197	+	0.275505i
$651$		−	8.75971i		−	0.343320i
$652$	−9.77197	+	9.77197i	−0.382700	+	0.382700i
$653$	5.74292	+	5.74292i	0.224738	+	0.224738i	0.810490	−	0.585752i	$-0.199201\pi$
$653$	5.74292	+	5.74292i	0.224738	+	0.224738i	−0.585752	+	0.810490i	$0.699201\pi$
$654$			5.32185i			0.208101i
$655$	2.66435	−	20.8801i	0.104105	−	0.815854i
$656$		−	36.2733i		−	1.41624i
$657$	−3.92301	−	3.92301i	−0.153051	−	0.153051i
$658$	−1.20083	−	1.20083i	−0.0468133	−	0.0468133i
$659$	35.1688			1.36998			0.684990	−	0.728552i	$-0.259806\pi$
$659$	35.1688			1.36998			0.684990	+	0.728552i	$0.259806\pi$
$660$		0			0
$661$	−40.3405			−1.56906			−0.784531	−	0.620090i	$-0.787096\pi$
$661$	−40.3405			−1.56906			−0.784531	+	0.620090i	$0.787096\pi$
$662$	−32.0121	−	32.0121i	−1.24419	−	1.24419i
$663$	22.6388	+	22.6388i	0.879218	+	0.879218i
$664$		−	1.14648i		−	0.0444921i
$665$	11.5160	+	14.8848i	0.446571	+	0.577207i
$666$			5.48307i			0.212465i
$667$	−27.7674	−	27.7674i	−1.07516	−	1.07516i
$668$	−7.85194	+	7.85194i	−0.303801	+	0.303801i
$669$		−	4.63132i		−	0.179057i
$670$	19.8522	+	2.53318i	0.766956	+	0.0978653i
$671$		0			0
$672$	−15.4535	+	15.4535i	−0.596130	+	0.596130i
$673$	21.1364	−	21.1364i	0.814747	−	0.814747i	−0.170594	−	0.985341i	$-0.554569\pi$
$673$	21.1364	−	21.1364i	0.814747	−	0.814747i	0.985341	+	0.170594i	$0.0545687\pi$
$674$			14.9816i			0.577069i
$675$	−24.0656	+	14.1511i	−0.926284	+	0.544675i
$676$	−5.67403			−0.218232
$677$	8.89652	+	8.89652i	0.341921	+	0.341921i	0.857089	−	0.515168i	$-0.172271\pi$
$677$	8.89652	+	8.89652i	0.341921	+	0.341921i	−0.515168	+	0.857089i	$0.672271\pi$
$678$	17.0101	−	17.0101i	0.653270	−	0.653270i
$679$	17.4015			0.667808
$680$	−15.6737	−	2.00000i	−0.601059	−	0.0766965i
$681$			1.15865i			0.0443994i
$682$		0			0
$683$	1.03200	+	1.03200i	0.0394883	+	0.0394883i	0.726575	−	0.687087i	$-0.241111\pi$
$683$	1.03200	+	1.03200i	0.0394883	+	0.0394883i	−0.687087	+	0.726575i	$0.741111\pi$
$684$	3.64075			0.139208
$685$	21.5829	−	16.6982i	0.824640	−	0.638004i
$686$	−37.3243			−1.42505
$687$	8.80532	−	8.80532i	0.335944	−	0.335944i
$688$	−12.3860	+	12.3860i	−0.472212	+	0.472212i
$689$	22.0862			0.841419
$690$	−38.7713	+	29.9964i	−1.47600	+	1.14194i
$691$	−39.5634			−1.50506			−0.752532	−	0.658556i	$-0.771168\pi$
$691$	−39.5634			−1.50506			−0.752532	+	0.658556i	$0.771168\pi$
$692$	−14.0118	−	14.0118i	−0.532651	−	0.532651i
$693$		0			0
$694$		−	53.8402i		−	2.04375i
$695$	15.5716	+	1.98697i	0.590663	+	0.0753699i
$696$	−8.13582			−0.308388
$697$	36.7799	−	36.7799i	1.39314	−	1.39314i
$698$	4.52217	+	4.52217i	0.171167	+	0.171167i
$699$	−2.58367			−0.0977234
$700$	−12.8736	+	7.56998i	−0.486578	+	0.286118i
$701$			1.17600i			0.0444169i	0.999753	+	0.0222085i	$0.00706976\pi$
$701$			1.17600i			0.0444169i	−0.999753	+	0.0222085i	$0.992930\pi$
$702$	−22.0871	+	22.0871i	−0.833623	+	0.833623i
$703$	13.7997	−	13.7997i	0.520464	−	0.520464i
$704$		0			0
$705$	−1.51733	−	0.193614i	−0.0571458	−	0.00729194i
$706$			19.5480i			0.735699i
$707$	−2.17743	+	2.17743i	−0.0818907	+	0.0818907i
$708$	20.4843	+	20.4843i	0.769849	+	0.769849i
$709$		−	29.4591i		−	1.10636i	−0.833062	−	0.553179i	$-0.813415\pi$
$709$		−	29.4591i		−	1.10636i	0.833062	−	0.553179i	$-0.186585\pi$
$710$	11.1301	+	14.3861i	0.417707	+	0.539900i
$711$		−	7.83565i		−	0.293860i
$712$	−9.84821	−	9.84821i	−0.369077	−	0.369077i
$713$	14.8694	+	14.8694i	0.556865	+	0.556865i
$714$	−40.7198			−1.52390
$715$		0			0
$716$	−20.1931			−0.754653
$717$	18.0128	+	18.0128i	0.672699	+	0.672699i
$718$	19.8244	+	19.8244i	0.739839	+	0.739839i
$719$		−	15.1589i		−	0.565331i	−0.959219	−	0.282665i	$-0.908781\pi$
$719$		−	15.1589i		−	0.565331i	0.959219	−	0.282665i	$-0.0912186\pi$
$720$	0.838301	−	6.56964i	0.0312416	−	0.244836i
$721$		−	14.6347i		−	0.545025i
$722$	3.11667	+	3.11667i	0.115990	+	0.115990i
$723$	−23.2022	+	23.2022i	−0.862900	+	0.862900i
$724$			28.6450i			1.06458i
$725$	−24.8466	−	6.44592i	−0.922780	−	0.239395i
$726$		0			0
$727$	6.89315	−	6.89315i	0.255653	−	0.255653i	−0.567631	−	0.823283i	$-0.692140\pi$
$727$	6.89315	−	6.89315i	0.255653	−	0.255653i	0.823283	+	0.567631i	$0.192140\pi$
$728$	4.51475	−	4.51475i	0.167328	−	0.167328i
$729$		−	30.0340i		−	1.11237i
$730$	−37.0277	−	4.72482i	−1.37046	−	0.174873i
$731$	−25.1180			−0.929022
$732$	−8.45945	−	8.45945i	−0.312670	−	0.312670i
$733$	6.35783	−	6.35783i	0.234832	−	0.234832i	−0.579874	−	0.814706i	$-0.696898\pi$
$733$	6.35783	−	6.35783i	0.234832	−	0.234832i	0.814706	+	0.579874i	$0.196898\pi$
$734$	62.1088			2.29248
$735$	−7.47910	+	5.78640i	−0.275871	+	0.213434i
$736$		−	52.4639i		−	1.93385i
$737$		0			0
$738$	6.12144	+	6.12144i	0.225333	+	0.225333i
$739$	−9.01466			−0.331610			−0.165805	−	0.986159i	$-0.553022\pi$
$739$	−9.01466			−0.331610			−0.165805	+	0.986159i	$0.553022\pi$
$740$	9.47662	+	12.2488i	0.348368	+	0.450276i
$741$	18.9657			0.696724
$742$	−19.8630	+	19.8630i	−0.729193	+	0.729193i
$743$	25.3482	−	25.3482i	0.929935	−	0.929935i	−0.0677663	−	0.997701i	$-0.521587\pi$
$743$	25.3482	−	25.3482i	0.929935	−	0.929935i	0.997701	+	0.0677663i	$0.0215872\pi$
$744$	4.35674			0.159726
$745$	−2.98395	−	0.380759i	−0.109324	−	0.0139499i
$746$	−2.15804			−0.0790116
$747$	0.487259	+	0.487259i	0.0178279	+	0.0178279i
$748$		0			0
$749$		−	31.3215i		−	1.14446i
$750$	−11.9078	+	29.7486i	−0.434813	+	1.08627i
$751$	−27.9110			−1.01849			−0.509244	−	0.860622i	$-0.670075\pi$
$751$	−27.9110			−1.01849			−0.509244	+	0.860622i	$0.670075\pi$
$752$	1.50412	−	1.50412i	0.0548494	−	0.0548494i
$753$	28.4351	+	28.4351i	1.03623	+	1.03623i
$754$	−28.7199			−1.04592
$755$	0.834688	−	6.54133i	0.0303774	−	0.238063i
$756$		−	16.6774i		−	0.606551i
$757$	−30.7120	+	30.7120i	−1.11625	+	1.11625i	−0.123961	+	0.992287i	$0.539560\pi$
$757$	−30.7120	+	30.7120i	−1.11625	+	1.11625i	−0.992287	+	0.123961i	$0.960440\pi$
$758$	−15.6921	+	15.6921i	−0.569964	+	0.569964i
$759$		0			0
$760$	−7.40311	+	5.72760i	−0.268539	+	0.207762i
$761$			3.22860i			0.117037i	0.998286	+	0.0585184i	$0.0186376\pi$
$761$			3.22860i			0.117037i	−0.998286	+	0.0585184i	$0.981362\pi$
$762$	−2.68894	+	2.68894i	−0.0974101	+	0.0974101i
$763$	2.71016	+	2.71016i	0.0981143	+	0.0981143i
$764$		−	0.794648i		−	0.0287493i
$765$	7.51141	−	5.81139i	0.271575	−	0.210111i
$766$			36.4451i			1.31681i
$767$	−27.6308	−	27.6308i	−0.997691	−	0.997691i
$768$	−22.8500	−	22.8500i	−0.824527	−	0.824527i
$769$	−5.00727			−0.180567			−0.0902834	−	0.995916i	$-0.528777\pi$
$769$	−5.00727			−0.180567			−0.0902834	+	0.995916i	$0.528777\pi$
$770$		0			0
$771$	3.79264			0.136589
$772$	−5.17620	−	5.17620i	−0.186295	−	0.186295i
$773$	−5.97152	−	5.97152i	−0.214781	−	0.214781i	0.591514	−	0.806295i	$-0.298530\pi$
$773$	−5.97152	−	5.97152i	−0.214781	−	0.214781i	−0.806295	+	0.591514i	$0.798530\pi$
$774$		−	4.18049i		−	0.150265i
$775$	13.3054	+	3.45179i	0.477943	+	0.123992i
$776$			8.65482i			0.310690i
$777$	−10.7836	−	10.7836i	−0.386859	−	0.386859i
$778$	−46.4885	+	46.4885i	−1.66669	+	1.66669i
$779$		−	30.8126i		−	1.10397i
$780$	−1.90502	+	14.9293i	−0.0682106	+	0.534556i
$781$		0			0
$782$	69.1211	−	69.1211i	2.47176	−	2.47176i
$783$	20.2692	−	20.2692i	0.724364	−	0.724364i
$784$		−	13.1500i		−	0.469643i
$785$	−4.38183	+	3.39011i	−0.156394	+	0.120998i
$786$	26.9798			0.962337
$787$	−8.07988	−	8.07988i	−0.288016	−	0.288016i	0.548279	−	0.836295i	$-0.315283\pi$
$787$	−8.07988	−	8.07988i	−0.288016	−	0.288016i	−0.836295	+	0.548279i	$0.815283\pi$
$788$	−7.71446	+	7.71446i	−0.274816	+	0.274816i
$789$	31.0435			1.10518
$790$	−32.2601	−	41.6973i	−1.14776	−	1.48352i
$791$		−	17.3249i		−	0.616001i
$792$		0			0
$793$	11.4107	+	11.4107i	0.405207	+	0.405207i
$794$	36.3247			1.28912
$795$	−3.20258	+	25.0981i	−0.113584	+	0.890139i
$796$	8.51888			0.301944
$797$	13.2627	−	13.2627i	0.469790	−	0.469790i	−0.432056	−	0.901847i	$-0.642212\pi$
$797$	13.2627	−	13.2627i	0.469790	−	0.469790i	0.901847	+	0.432056i	$0.142212\pi$
$798$	−17.0566	+	17.0566i	−0.603797	+	0.603797i
$799$	3.05024			0.107910
$800$	−17.3832	−	29.5622i	−0.614589	−	1.04518i
$801$	8.37107			0.295777
$802$	−8.72973	−	8.72973i	−0.308258	−	0.308258i
$803$		0			0
$804$			10.7684i			0.379772i
$805$	−4.46864	+	35.0201i	−0.157499	+	1.23429i
$806$	15.3795			0.541720
$807$	−2.44290	+	2.44290i	−0.0859941	+	0.0859941i
$808$	−1.08297	−	1.08297i	−0.0380987	−	0.0380987i
$809$	−50.7258			−1.78342			−0.891711	−	0.452605i	$-0.850495\pi$
$809$	−50.7258			−1.78342			−0.891711	+	0.452605i	$0.850495\pi$
$810$	−17.1938	−	22.2236i	−0.604129	−	0.780857i
$811$			36.0745i			1.26675i	0.773846	+	0.633373i	$0.218330\pi$
$811$			36.0745i			1.26675i	−0.773846	+	0.633373i	$0.781670\pi$
$812$	10.8428	−	10.8428i	0.380509	−	0.380509i
$813$	−3.23055	+	3.23055i	−0.113300	+	0.113300i
$814$		0			0
$815$	13.0674	+	16.8900i	0.457730	+	0.591630i
$816$		−	51.0040i		−	1.78550i
$817$	−10.5213	+	10.5213i	−0.368095	+	0.368095i
$818$	−38.3517	−	38.3517i	−1.34093	−	1.34093i
$819$			3.83758i			0.134096i
$820$	24.2548	+	3.09497i	0.847016	+	0.108081i
$821$			10.3135i			0.359945i	0.983672	+	0.179972i	$0.0576009\pi$
$821$			10.3135i			0.359945i	−0.983672	+	0.179972i	$0.942399\pi$
$822$	24.7320	+	24.7320i	0.862628	+	0.862628i
$823$	38.8814	+	38.8814i	1.35532	+	1.35532i	0.879591	+	0.475731i	$0.157817\pi$
$823$	38.8814	+	38.8814i	1.35532	+	1.35532i	0.475731	+	0.879591i	$0.342183\pi$
$824$	7.27873			0.253567
$825$		0			0
$826$	49.6988			1.72924
$827$	−19.0643	−	19.0643i	−0.662930	−	0.662930i	0.293139	−	0.956070i	$-0.405300\pi$
$827$	−19.0643	−	19.0643i	−0.662930	−	0.662930i	−0.956070	+	0.293139i	$0.905300\pi$
$828$	4.82938	+	4.82938i	0.167832	+	0.167832i
$829$		−	5.15854i		−	0.179163i	−0.995979	−	0.0895817i	$-0.971447\pi$
$829$		−	5.15854i		−	0.179163i	0.995979	−	0.0895817i	$-0.0285530\pi$
$830$	4.59904	+	0.586848i	0.159635	+	0.0203698i
$831$			42.6704i			1.48022i
$832$	−6.67744	−	6.67744i	−0.231498	−	0.231498i
$833$	13.3337	−	13.3337i	0.461984	−	0.461984i
$834$			20.1204i			0.696714i
$835$	10.4998	+	13.5714i	0.363362	+	0.469657i
$836$		0			0
$837$	−10.8542	+	10.8542i	−0.375176	+	0.375176i
$838$	−25.3056	+	25.3056i	−0.874166	+	0.874166i
$839$		−	48.4883i		−	1.67400i	−0.547201	−	0.837001i	$-0.684307\pi$
$839$		−	48.4883i		−	1.67400i	0.547201	−	0.837001i	$-0.315693\pi$
$840$	4.47577	+	5.78508i	0.154429	+	0.199604i
$841$	−2.64385			−0.0911673
$842$	47.9510	+	47.9510i	1.65250	+	1.65250i
$843$	−32.3632	+	32.3632i	−1.11465	+	1.11465i
$844$	−21.9475			−0.755466
$845$	−1.10979	+	8.69726i	−0.0381780	+	0.299195i
$846$			0.507665i			0.0174539i
$847$		0			0
$848$	−24.8796	−	24.8796i	−0.854369	−	0.854369i
$849$	−14.1113			−0.484299
$850$	16.0458	−	61.8504i	0.550365	−	2.12145i
$851$	36.6099			1.25497
$852$	−6.92037	+	6.92037i	−0.237088	+	0.237088i
$853$	−9.94531	+	9.94531i	−0.340521	+	0.340521i	−0.856563	−	0.516042i	$-0.827405\pi$
$853$	−9.94531	+	9.94531i	−0.340521	+	0.340521i	0.516042	+	0.856563i	$0.327405\pi$
$854$	−20.5242			−0.702323
$855$	0.712099	−	5.58061i	0.0243533	−	0.190853i
$856$	15.5781			0.532448
$857$	−25.9087	−	25.9087i	−0.885023	−	0.885023i	0.109017	−	0.994040i	$-0.465230\pi$
$857$	−25.9087	−	25.9087i	−0.885023	−	0.885023i	−0.994040	+	0.109017i	$0.965230\pi$
$858$		0			0
$859$		−	12.2122i		−	0.416675i	−0.978057	−	0.208337i	$-0.933195\pi$
$859$		−	12.2122i		−	0.416675i	0.978057	−	0.208337i	$-0.0668052\pi$
$860$	−7.22531	−	9.33895i	−0.246381	−	0.318456i
$861$	−24.0781			−0.820580
$862$	15.9112	−	15.9112i	0.541936	−	0.541936i
$863$	5.95005	+	5.95005i	0.202542	+	0.202542i	0.801088	−	0.598546i	$-0.204255\pi$
$863$	5.95005	+	5.95005i	0.202542	+	0.202542i	−0.598546	+	0.801088i	$0.704255\pi$
$864$	38.2969			1.30289
$865$	−24.2182	+	18.7370i	−0.823444	+	0.637078i
$866$		−	8.79010i		−	0.298700i
$867$	33.1600	−	33.1600i	1.12617	−	1.12617i
$868$	−5.80634	+	5.80634i	−0.197080	+	0.197080i
$869$		0			0
$870$	4.16448	−	32.6364i	0.141189	−	1.10648i
$871$		−	14.5252i		−	0.492168i
$872$	−1.34793	+	1.34793i	−0.0456465	+	0.0456465i
$873$	−3.67834	−	3.67834i	−0.124493	−	0.124493i
$874$		−	57.9065i		−	1.95872i
$875$	9.08544	+	21.2136i	0.307144	+	0.717150i
$876$		−	20.0849i		−	0.678606i
$877$	19.3868	+	19.3868i	0.654645	+	0.654645i	0.954108	−	0.299463i	$-0.0968076\pi$
$877$	19.3868	+	19.3868i	0.654645	+	0.654645i	−0.299463	+	0.954108i	$0.596808\pi$
$878$	34.3558	+	34.3558i	1.15945	+	1.15945i
$879$	−2.72129			−0.0917870
$880$		0			0
$881$	13.9259			0.469176			0.234588	−	0.972095i	$-0.424626\pi$
$881$	13.9259			0.469176			0.234588	+	0.972095i	$0.424626\pi$
$882$	2.21918	+	2.21918i	0.0747236	+	0.0747236i
$883$	2.09557	+	2.09557i	0.0705215	+	0.0705215i	0.741488	−	0.670966i	$-0.234121\pi$
$883$	2.09557	+	2.09557i	0.0705215	+	0.0705215i	−0.670966	+	0.741488i	$0.734121\pi$
$884$		−	30.0121i		−	1.00942i
$885$	35.4054	−	27.3922i	1.19014	−	0.920780i
$886$			53.0766i			1.78314i
$887$	25.6385	+	25.6385i	0.860856	+	0.860856i	0.991438	−	0.130582i	$-0.0416845\pi$
$887$	25.6385	+	25.6385i	0.860856	+	0.860856i	−0.130582	+	0.991438i	$0.541685\pi$
$888$	5.36333	−	5.36333i	0.179982	−	0.179982i
$889$			2.73869i			0.0918528i
$890$	44.5465	−	34.4645i	1.49320	−	1.15525i
$891$		0			0
$892$	−3.06985	+	3.06985i	−0.102786	+	0.102786i
$893$	1.27768	−	1.27768i	0.0427559	−	0.0427559i
$894$		−	3.85565i		−	0.128952i
$895$	−3.94960	+	30.9524i	−0.132021	+	1.03463i
$896$	−16.3042			−0.544684
$897$	25.1576	+	25.1576i	0.839989	+	0.839989i
$898$	−6.22847	+	6.22847i	−0.207847	+	0.207847i
$899$	−14.1137			−0.470719
$900$	4.32139	+	1.12109i	0.144046	+	0.0373697i
$901$		−	50.4541i		−	1.68087i
$902$		0			0
$903$	8.22179	+	8.22179i	0.273604	+	0.273604i
$904$	8.61670			0.286587
$905$	43.9076	+	5.60271i	1.45954	+	0.186241i
$906$	8.45223			0.280807
$907$	14.7629	−	14.7629i	0.490193	−	0.490193i	−0.418174	−	0.908367i	$-0.637330\pi$
$907$	14.7629	−	14.7629i	0.490193	−	0.490193i	0.908367	+	0.418174i	$0.137330\pi$
$908$	0.768005	−	0.768005i	0.0254871	−	0.0254871i
$909$	0.920533			0.0305322
$910$	15.7997	+	20.4216i	0.523755	+	0.676971i
$911$	6.84296			0.226717			0.113359	−	0.993554i	$-0.463839\pi$
$911$	6.84296			0.226717			0.113359	+	0.993554i	$0.463839\pi$
$912$	−21.3644	−	21.3644i	−0.707447	−	0.707447i
$913$		0			0
$914$			62.8518i			2.07895i
$915$	−14.6214	+	11.3122i	−0.483369	+	0.373970i
$916$	−11.6732			−0.385692
$917$	13.7395	−	13.7395i	0.453718	−	0.453718i
$918$	50.4560	+	50.4560i	1.66530	+	1.66530i
$919$	27.7193			0.914374			0.457187	−	0.889371i	$-0.348857\pi$
$919$	27.7193			0.914374			0.457187	+	0.889371i	$0.348857\pi$
$920$	−17.4176	−	2.22253i	−0.574241	−	0.0732745i
$921$		−	23.2982i		−	0.767702i
$922$	37.2531	−	37.2531i	1.22686	−	1.22686i
$923$	9.33472	−	9.33472i	0.307256	−	0.307256i
$924$		0			0
$925$	20.6288	−	12.1302i	0.678271	−	0.398838i
$926$			42.0514i			1.38190i
$927$	−3.09349	+	3.09349i	−0.101604	+	0.101604i
$928$	24.8988	+	24.8988i	0.817342	+	0.817342i
$929$			34.7438i			1.13991i	0.821677	+	0.569953i	$0.193039\pi$
$929$			34.7438i			1.13991i	−0.821677	+	0.569953i	$0.806961\pi$
$930$	−2.23008	+	17.4768i	−0.0731272	+	0.573087i
$931$		−	11.1703i		−	0.366093i
$932$	1.71258	+	1.71258i	0.0560973	+	0.0560973i
$933$	−29.8035	−	29.8035i	−0.975723	−	0.975723i
$934$	8.18709			0.267890
$935$		0			0
$936$	−1.90866			−0.0623866
$937$	−32.2307	−	32.2307i	−1.05293	−	1.05293i	−0.998518	−	0.0544137i	$-0.982671\pi$
$937$	−32.2307	−	32.2307i	−1.05293	−	1.05293i	−0.0544137	−	0.998518i	$-0.517329\pi$
$938$	13.0631	+	13.0631i	0.426524	+	0.426524i
$939$			41.4031i			1.35114i
$940$	0.877419	+	1.13409i	0.0286182	+	0.0369900i
$941$		−	8.74290i		−	0.285010i	−0.989794	−	0.142505i	$-0.954484\pi$
$941$		−	8.74290i		−	0.285010i	0.989794	−	0.142505i	$-0.0455158\pi$
$942$	−5.02117	−	5.02117i	−0.163599	−	0.163599i
$943$	40.8722	−	40.8722i	1.33098	−	1.33098i
$944$			62.2508i			2.02609i
$945$	−25.5634	−	3.26195i	−0.831579	−	0.106111i
$946$		0			0
$947$	−8.84044	+	8.84044i	−0.287276	+	0.287276i	−0.836002	−	0.548726i	$-0.815113\pi$
$947$	−8.84044	+	8.84044i	−0.287276	+	0.287276i	0.548726	+	0.836002i	$0.315113\pi$
$948$	20.0583	−	20.0583i	0.651465	−	0.651465i
$949$			27.0920i			0.879444i
$950$	−19.1865	−	32.6289i	−0.622493	−	1.05862i
$951$	−3.03497			−0.0984157
$952$	−10.3136	−	10.3136i	−0.334265	−	0.334265i
$953$	11.2689	−	11.2689i	0.365035	−	0.365035i	−0.500628	−	0.865663i	$-0.666897\pi$
$953$	11.2689	−	11.2689i	0.365035	−	0.365035i	0.865663	+	0.500628i	$0.166897\pi$
$954$	8.39730			0.271873
$955$	−1.21805	−	0.155426i	−0.0394152	−	0.00502947i
$956$		−	23.8794i		−	0.772315i
$957$		0			0
$958$	22.9482	+	22.9482i	0.741424	+	0.741424i
$959$	25.1896			0.813414
$960$	8.55628	−	6.61978i	0.276153	−	0.213653i
$961$	−23.4421			−0.756196
$962$	18.9329	−	18.9329i	0.610420	−	0.610420i
$963$	−6.62076	+	6.62076i	−0.213351	+	0.213351i
$964$	30.7590			0.990682
$965$	−8.94659	+	6.92176i	−0.288001	+	0.222819i
$966$	−45.2504			−1.45591
$967$	12.0840	+	12.0840i	0.388597	+	0.388597i	0.874187	−	0.485590i	$-0.161395\pi$
$967$	12.0840	+	12.0840i	0.388597	+	0.388597i	−0.485590	+	0.874187i	$0.661395\pi$
$968$		0			0
$969$		−	43.3256i		−	1.39182i
$970$	−34.7183	−	4.43013i	−1.11474	−	0.142243i
$971$	−38.0475			−1.22100			−0.610501	−	0.792016i	$-0.709032\pi$
$971$	−38.0475			−1.22100			−0.610501	+	0.792016i	$0.709032\pi$
$972$	−6.44918	+	6.44918i	−0.206858	+	0.206858i
$973$	10.2464	+	10.2464i	0.328483	+	0.328483i
$974$	34.2882			1.09867
$975$	22.5114	+	5.84010i	0.720941	+	0.187033i
$976$		−	25.7078i		−	0.822887i
$977$	−20.2744	+	20.2744i	−0.648637	+	0.648637i	−0.952663	−	0.304027i	$-0.901669\pi$
$977$	−20.2744	+	20.2744i	−0.648637	+	0.648637i	0.304027	+	0.952663i	$0.401669\pi$
$978$	−19.3544	+	19.3544i	−0.618884	+	0.618884i
$979$		0			0
$980$	8.79299	+	1.12201i	0.280882	+	0.0358412i
$981$		−	1.14575i		−	0.0365810i
$982$	17.3981	−	17.3981i	0.555197	−	0.555197i
$983$	1.31893	+	1.31893i	0.0420673	+	0.0420673i	0.727828	−	0.685760i	$-0.240530\pi$
$983$	1.31893	+	1.31893i	0.0420673	+	0.0420673i	−0.685760	+	0.727828i	$0.740530\pi$
$984$		−	11.9755i		−	0.381766i
$985$	10.3160	+	13.3337i	0.328695	+	0.424848i
$986$			65.6081i			2.08939i
$987$	−0.998427	−	0.998427i	−0.0317803	−	0.0317803i
$988$	−12.5714	−	12.5714i	−0.399949	−	0.399949i
$989$	−27.9127			−0.887571
$990$		0			0
$991$	44.4865			1.41316			0.706580	−	0.707634i	$-0.250237\pi$
$991$	44.4865			1.41316			0.706580	+	0.707634i	$0.250237\pi$
$992$	−13.3333	−	13.3333i	−0.423333	−	0.423333i
$993$	−26.6164	−	26.6164i	−0.844645	−	0.844645i
$994$			16.7901i			0.532550i
$995$	1.66622	−	13.0579i	0.0528227	−	0.413963i
$996$			2.49465i			0.0790462i
$997$	−5.88973	−	5.88973i	−0.186530	−	0.186530i	0.607664	−	0.794194i	$-0.292107\pi$
$997$	−5.88973	−	5.88973i	−0.186530	−	0.186530i	−0.794194	+	0.607664i	$0.792107\pi$
$998$	−15.2301	+	15.2301i	−0.482102	+	0.482102i
$999$			26.7240i			0.845509i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.e.a.483.3	yes	20
5.2	odd	4	inner	605.2.e.a.362.8	yes	20
11.2	odd	10		605.2.m.f.403.3		80
11.3	even	5		605.2.m.f.233.3		80
11.4	even	5		605.2.m.f.578.8		80
11.5	even	5		605.2.m.f.118.8		80
11.6	odd	10		605.2.m.f.118.3		80
11.7	odd	10		605.2.m.f.578.3		80
11.8	odd	10		605.2.m.f.233.8		80
11.9	even	5		605.2.m.f.403.8		80
11.10	odd	2	inner	605.2.e.a.483.8	yes	20
55.2	even	20		605.2.m.f.282.8		80
55.7	even	20		605.2.m.f.457.3		80
55.17	even	20		605.2.m.f.602.8		80
55.27	odd	20		605.2.m.f.602.3		80
55.32	even	4	inner	605.2.e.a.362.3	✓	20
55.37	odd	20		605.2.m.f.457.8		80
55.42	odd	20		605.2.m.f.282.3		80
55.47	odd	20		605.2.m.f.112.3		80
55.52	even	20		605.2.m.f.112.8		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.e.a.362.3	✓	20	55.32	even	4	inner
605.2.e.a.362.8	yes	20	5.2	odd	4	inner
605.2.e.a.483.3	yes	20	1.1	even	1	trivial
605.2.e.a.483.8	yes	20	11.10	odd	2	inner
605.2.m.f.112.3		80	55.47	odd	20
605.2.m.f.112.8		80	55.52	even	20
605.2.m.f.118.3		80	11.6	odd	10
605.2.m.f.118.8		80	11.5	even	5
605.2.m.f.233.3		80	11.3	even	5
605.2.m.f.233.8		80	11.8	odd	10
605.2.m.f.282.3		80	55.42	odd	20
605.2.m.f.282.8		80	55.2	even	20
605.2.m.f.403.3		80	11.2	odd	10
605.2.m.f.403.8		80	11.9	even	5
605.2.m.f.457.3		80	55.7	even	20
605.2.m.f.457.8		80	55.37	odd	20
605.2.m.f.578.3		80	11.7	odd	10
605.2.m.f.578.8		80	11.4	even	5
605.2.m.f.602.3		80	55.27	odd	20
605.2.m.f.602.8		80	55.17	even	20

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31283 - 1.31283i) q^{2} +(-1.09155 - 1.09155i) q^{3} +1.44706i q^{4} +(2.21808 + 0.283032i) q^{5} +2.86605i q^{6} +(1.45954 + 1.45954i) q^{7} +(-0.725917 + 0.725917i) q^{8} -0.617036i q^{9} +O(q^{10})\)	\(q+(-1.31283 - 1.31283i) q^{2} +(-1.09155 - 1.09155i) q^{3} +1.44706i q^{4} +(2.21808 + 0.283032i) q^{5} +2.86605i q^{6} +(1.45954 + 1.45954i) q^{7} +(-0.725917 + 0.725917i) q^{8} -0.617036i q^{9} +(-2.54040 - 3.28355i) q^{10} +(1.57954 - 1.57954i) q^{12} +(-2.13060 + 2.13060i) q^{13} -3.83226i q^{14} +(-2.11221 - 2.73009i) q^{15} +4.80014 q^{16} +(4.86718 + 4.86718i) q^{17} +(-0.810065 + 0.810065i) q^{18} +4.07750 q^{19} +(-0.409565 + 3.20970i) q^{20} -3.18632i q^{21} +(5.40871 + 5.40871i) q^{23} +1.58475 q^{24} +(4.83979 + 1.25558i) q^{25} +5.59425 q^{26} +(-3.94818 + 3.94818i) q^{27} +(-2.11204 + 2.11204i) q^{28} -5.13382 q^{29} +(-0.811184 + 6.35713i) q^{30} +2.74917 q^{31} +(-4.84994 - 4.84994i) q^{32} -12.7796i q^{34} +(2.82428 + 3.65047i) q^{35} +0.892888 q^{36} +(3.38434 - 3.38434i) q^{37} +(-5.35308 - 5.35308i) q^{38} +4.65132 q^{39} +(-1.81560 + 1.40469i) q^{40} -7.55673i q^{41} +(-4.18310 + 4.18310i) q^{42} +(-2.58034 + 2.58034i) q^{43} +(0.174641 - 1.36864i) q^{45} -14.2015i q^{46} +(0.313348 - 0.313348i) q^{47} +(-5.23959 - 5.23959i) q^{48} -2.73950i q^{49} +(-4.70546 - 8.00220i) q^{50} -10.6255i q^{51} +(-3.08311 - 3.08311i) q^{52} +(-5.18310 - 5.18310i) q^{53} +10.3666 q^{54} -2.11900 q^{56} +(-4.45080 - 4.45080i) q^{57} +(6.73985 + 6.73985i) q^{58} +12.9685i q^{59} +(3.95061 - 3.05649i) q^{60} -5.35564i q^{61} +(-3.60920 - 3.60920i) q^{62} +(0.900586 - 0.900586i) q^{63} +3.13406i q^{64} +(-5.32888 + 4.12282i) q^{65} +(-3.40871 + 3.40871i) q^{67} +(-7.04310 + 7.04310i) q^{68} -11.8078i q^{69} +(1.08465 - 8.50026i) q^{70} -4.38126 q^{71} +(0.447916 + 0.447916i) q^{72} +(6.35783 - 6.35783i) q^{73} -8.88615 q^{74} +(-3.91234 - 6.65340i) q^{75} +5.90039i q^{76} +(-6.10640 - 6.10640i) q^{78} +12.6989 q^{79} +(10.6471 + 1.35859i) q^{80} +6.76816 q^{81} +(-9.92072 + 9.92072i) q^{82} +(-0.789678 + 0.789678i) q^{83} +4.61079 q^{84} +(9.41823 + 12.1734i) q^{85} +6.77512 q^{86} +(5.60383 + 5.60383i) q^{87} +13.5666i q^{89} +(-2.02607 + 1.56752i) q^{90} -6.21938 q^{91} +(-7.82674 + 7.82674i) q^{92} +(-3.00085 - 3.00085i) q^{93} -0.822748 q^{94} +(9.04423 + 1.15406i) q^{95} +10.5879i q^{96} +(5.96130 - 5.96130i) q^{97} +(-3.59651 + 3.59651i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{3} + 4 q^{5}+O(q^{10}) \) 20 * q + 4 * q^3 + 4 * q^5	\( 20 q + 4 q^{3} + 4 q^{5} - 16 q^{12} + 16 q^{15} + 12 q^{16} + 16 q^{20} + 12 q^{23} + 16 q^{25} + 56 q^{26} - 20 q^{27} - 16 q^{31} - 20 q^{36} - 72 q^{37} - 32 q^{38} - 32 q^{42} - 28 q^{45} + 16 q^{47} - 104 q^{48} - 52 q^{53} - 32 q^{56} + 12 q^{58} + 112 q^{60} + 28 q^{67} + 104 q^{70} + 24 q^{71} + 64 q^{75} + 104 q^{78} + 44 q^{80} + 100 q^{81} - 124 q^{82} + 128 q^{86} - 16 q^{92} - 132 q^{93} + 32 q^{97}+O(q^{100}) \) 20 * q + 4 * q^3 + 4 * q^5 - 16 * q^12 + 16 * q^15 + 12 * q^16 + 16 * q^20 + 12 * q^23 + 16 * q^25 + 56 * q^26 - 20 * q^27 - 16 * q^31 - 20 * q^36 - 72 * q^37 - 32 * q^38 - 32 * q^42 - 28 * q^45 + 16 * q^47 - 104 * q^48 - 52 * q^53 - 32 * q^56 + 12 * q^58 + 112 * q^60 + 28 * q^67 + 104 * q^70 + 24 * q^71 + 64 * q^75 + 104 * q^78 + 44 * q^80 + 100 * q^81 - 124 * q^82 + 128 * q^86 - 16 * q^92 - 132 * q^93 + 32 * q^97

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