LMFDB - Embedded newform 483.2.y.b.193.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(4,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 44, 12]))

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

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

chi := DirichletCharacter("483.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.y (of order $33$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			193.3
Character	$\chi$	$=$	483.193
Dual form			483.2.y.b.478.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.47170 - 1.40327i) q^{2} +(0.981929 - 0.189251i) q^{3} +(0.101591 + 2.13265i) q^{4} +(-2.78466 + 2.18988i) q^{5} +(-1.71068 - 1.09939i) q^{6} +(1.30031 - 2.30417i) q^{7} +(0.179868 - 0.207579i) q^{8} +(0.928368 - 0.371662i) q^{9} +O(q^{10})$	\(q+(-1.47170 - 1.40327i) q^{2} +(0.981929 - 0.189251i) q^{3} +(0.101591 + 2.13265i) q^{4} +(-2.78466 + 2.18988i) q^{5} +(-1.71068 - 1.09939i) q^{6} +(1.30031 - 2.30417i) q^{7} +(0.179868 - 0.207579i) q^{8} +(0.928368 - 0.371662i) q^{9} +(7.17119 + 0.684765i) q^{10} +(2.88075 - 2.74679i) q^{11} +(0.503362 + 2.07489i) q^{12} +(-0.232566 - 0.509248i) q^{13} +(-5.14704 + 1.56637i) q^{14} +(-2.31990 + 2.67731i) q^{15} +(3.69481 - 0.352811i) q^{16} +(1.29502 - 0.667632i) q^{17} +(-1.88782 - 0.755771i) q^{18} +(-4.09269 - 2.10993i) q^{19} +(-4.95315 - 5.71625i) q^{20} +(0.840747 - 2.50861i) q^{21} -8.09408 q^{22} +(-4.34591 - 2.02806i) q^{23} +(0.137333 - 0.237868i) q^{24} +(1.77996 - 7.33710i) q^{25} +(-0.372343 + 1.07581i) q^{26} +(0.841254 - 0.540641i) q^{27} +(5.04609 + 2.53903i) q^{28} +(-5.64801 - 3.62976i) q^{29} +(7.17119 - 0.684765i) q^{30} +(-1.49725 - 4.32601i) q^{31} +(-6.36455 - 5.00514i) q^{32} +(2.30885 - 3.24233i) q^{33} +(-2.84276 - 0.834709i) q^{34} +(1.42493 + 9.26386i) q^{35} +(0.886941 + 1.94213i) q^{36} +(7.32613 - 2.93294i) q^{37} +(3.06243 + 8.84832i) q^{38} +(-0.324739 - 0.456031i) q^{39} +(-0.0462986 + 0.971928i) q^{40} +(-0.713712 - 4.96398i) q^{41} +(-4.75759 + 2.51215i) q^{42} +(-0.474440 - 0.547532i) q^{43} +(6.15060 + 5.86458i) q^{44} +(-1.77129 + 3.06797i) q^{45} +(3.54999 + 9.08318i) q^{46} +(4.46117 + 7.72697i) q^{47} +(3.56127 - 1.04568i) q^{48} +(-3.61838 - 5.99227i) q^{49} +(-12.9155 + 8.30028i) q^{50} +(1.14527 - 0.900652i) q^{51} +(1.06242 - 0.547717i) q^{52} +(-4.94305 - 6.94154i) q^{53} +(-1.99674 - 0.384840i) q^{54} +(-2.00677 + 13.9574i) q^{55} +(-0.244412 - 0.684365i) q^{56} +(-4.41803 - 1.29725i) q^{57} +(3.21869 + 13.2676i) q^{58} +(0.656185 + 0.0626581i) q^{59} +(-5.94545 - 4.67555i) q^{60} +(-1.15192 - 0.222014i) q^{61} +(-3.86704 + 8.46765i) q^{62} +(0.350795 - 2.62239i) q^{63} +(1.28676 + 8.94959i) q^{64} +(1.76281 + 0.908791i) q^{65} +(-7.94781 + 1.53181i) q^{66} +(1.02512 - 4.22560i) q^{67} +(1.55539 + 2.69401i) q^{68} +(-4.65119 - 1.16894i) q^{69} +(10.9026 - 15.6332i) q^{70} +(5.70982 - 1.67656i) q^{71} +(0.0898346 - 0.259560i) q^{72} +(0.0496571 + 1.04243i) q^{73} +(-14.8976 - 5.96410i) q^{74} +(0.359240 - 7.54137i) q^{75} +(4.08396 - 8.94263i) q^{76} +(-2.58319 - 10.2094i) q^{77} +(-0.162015 + 1.12684i) q^{78} +(-3.72598 + 5.23240i) q^{79} +(-9.51617 + 9.07365i) q^{80} +(0.723734 - 0.690079i) q^{81} +(-5.91541 + 8.30704i) q^{82} +(-0.499366 + 3.47317i) q^{83} +(5.43542 + 1.53817i) q^{84} +(-2.14417 + 4.69508i) q^{85} +(-0.0700996 + 1.47157i) q^{86} +(-6.23288 - 2.49527i) q^{87} +(-0.0520204 - 1.09204i) q^{88} +(4.48147 - 12.9484i) q^{89} +(6.91200 - 2.02955i) q^{90} +(-1.47580 - 0.126311i) q^{91} +(3.88365 - 9.47436i) q^{92} +(-2.28889 - 3.96448i) q^{93} +(4.27748 - 17.6320i) q^{94} +(16.0172 - 3.08707i) q^{95} +(-7.19677 - 3.71019i) q^{96} +(0.828262 + 5.76069i) q^{97} +(-3.08358 + 13.8964i) q^{98} +(1.65351 - 3.62069i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 2 q^{2} + 16 q^{3} + 18 q^{4} - 2 q^{5} + 18 q^{6} + 2 q^{7} - 12 q^{8} + 16 q^{9}+O(q^{10}) $ 320 * q + 2 * q^2 + 16 * q^3 + 18 * q^4 - 2 * q^5 + 18 * q^6 + 2 * q^7 - 12 * q^8 + 16 * q^9	\( 320 q + 2 q^{2} + 16 q^{3} + 18 q^{4} - 2 q^{5} + 18 q^{6} + 2 q^{7} - 12 q^{8} + 16 q^{9} + 2 q^{11} + 18 q^{12} + 18 q^{14} - 18 q^{15} - 8 q^{16} + 4 q^{17} + 2 q^{18} + 8 q^{19} - 162 q^{20} - 4 q^{21} + 144 q^{22} - 26 q^{23} + 6 q^{24} - 8 q^{25} - 14 q^{26} - 32 q^{27} + 86 q^{28} - 74 q^{29} - 56 q^{31} - 28 q^{32} + 13 q^{33} + 40 q^{34} - 32 q^{35} - 14 q^{36} + 2 q^{37} - 39 q^{38} - 52 q^{40} + 60 q^{41} - 61 q^{42} + 16 q^{43} - 75 q^{44} - 2 q^{45} - 4 q^{46} - 40 q^{47} - 28 q^{48} - 100 q^{49} + 146 q^{50} - 18 q^{51} - 18 q^{52} + 34 q^{53} + 2 q^{54} + 36 q^{55} - 102 q^{56} + 28 q^{57} - 17 q^{58} - 102 q^{59} - 18 q^{60} - 18 q^{61} - 88 q^{62} + 2 q^{63} - 252 q^{64} - 78 q^{65} + 16 q^{66} + 12 q^{67} + 34 q^{68} + 8 q^{69} + 264 q^{70} + 160 q^{71} + 6 q^{72} - 8 q^{73} + 70 q^{74} + 14 q^{75} - 40 q^{76} - 90 q^{77} - 16 q^{78} + 26 q^{79} - 103 q^{80} + 16 q^{81} - 30 q^{82} - 80 q^{83} - 52 q^{84} - 128 q^{85} + 90 q^{86} + 4 q^{87} - 293 q^{88} - 36 q^{89} + 16 q^{91} - 174 q^{92} + 32 q^{93} + 57 q^{94} - 85 q^{95} - 50 q^{96} - 8 q^{97} - 193 q^{98} - 26 q^{99}+O(q^{100}) \) 320 * q + 2 * q^2 + 16 * q^3 + 18 * q^4 - 2 * q^5 + 18 * q^6 + 2 * q^7 - 12 * q^8 + 16 * q^9 + 2 * q^11 + 18 * q^12 + 18 * q^14 - 18 * q^15 - 8 * q^16 + 4 * q^17 + 2 * q^18 + 8 * q^19 - 162 * q^20 - 4 * q^21 + 144 * q^22 - 26 * q^23 + 6 * q^24 - 8 * q^25 - 14 * q^26 - 32 * q^27 + 86 * q^28 - 74 * q^29 - 56 * q^31 - 28 * q^32 + 13 * q^33 + 40 * q^34 - 32 * q^35 - 14 * q^36 + 2 * q^37 - 39 * q^38 - 52 * q^40 + 60 * q^41 - 61 * q^42 + 16 * q^43 - 75 * q^44 - 2 * q^45 - 4 * q^46 - 40 * q^47 - 28 * q^48 - 100 * q^49 + 146 * q^50 - 18 * q^51 - 18 * q^52 + 34 * q^53 + 2 * q^54 + 36 * q^55 - 102 * q^56 + 28 * q^57 - 17 * q^58 - 102 * q^59 - 18 * q^60 - 18 * q^61 - 88 * q^62 + 2 * q^63 - 252 * q^64 - 78 * q^65 + 16 * q^66 + 12 * q^67 + 34 * q^68 + 8 * q^69 + 264 * q^70 + 160 * q^71 + 6 * q^72 - 8 * q^73 + 70 * q^74 + 14 * q^75 - 40 * q^76 - 90 * q^77 - 16 * q^78 + 26 * q^79 - 103 * q^80 + 16 * q^81 - 30 * q^82 - 80 * q^83 - 52 * q^84 - 128 * q^85 + 90 * q^86 + 4 * q^87 - 293 * q^88 - 36 * q^89 + 16 * q^91 - 174 * q^92 + 32 * q^93 + 57 * q^94 - 85 * q^95 - 50 * q^96 - 8 * q^97 - 193 * q^98 - 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{11}\right)$

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 $

$2$	−1.47170	−	1.40327i	−1.04065	−	0.992260i	−0.0406759	−	0.999172i	$-0.512951\pi$
$2$	−1.47170	−	1.40327i	−1.04065	−	0.992260i	−0.999976	+	0.00691272i	$0.997800\pi$
$3$	0.981929	−	0.189251i	0.566917	−	0.109264i
$3$	0.981929	−	0.189251i	0.566917	−	0.109264i
$4$	0.101591	+	2.13265i	0.0507954	+	1.06633i
$5$	−2.78466	+	2.18988i	−1.24534	+	0.979345i	−0.245388	+	0.969425i	$0.578915\pi$
$5$	−2.78466	+	2.18988i	−1.24534	+	0.979345i	−0.999951	+	0.00991984i	$0.996842\pi$
$6$	−1.71068	−	1.09939i	−0.698382	−	0.448823i
$7$	1.30031	−	2.30417i	0.491472	−	0.870894i
$7$	1.30031	−	2.30417i	0.491472	−	0.870894i
$8$	0.179868	−	0.207579i	0.0635931	−	0.0733903i
$9$	0.928368	−	0.371662i	0.309456	−	0.123887i
$10$	7.17119	+	0.684765i	2.26773	+	0.216542i
$11$	2.88075	−	2.74679i	0.868578	−	0.828187i	−0.117740	−	0.993044i	$-0.537565\pi$
$11$	2.88075	−	2.74679i	0.868578	−	0.828187i	0.986317	+	0.164857i	$0.0527164\pi$
$12$	0.503362	+	2.07489i	0.145308	+	0.598968i
$13$	−0.232566	−	0.509248i	−0.0645021	−	0.141240i	0.874635	−	0.484781i	$-0.161101\pi$
$13$	−0.232566	−	0.509248i	−0.0645021	−	0.141240i	−0.939138	+	0.343541i	$0.888373\pi$
$14$	−5.14704	+	1.56637i	−1.37560	+	0.418630i
$15$	−2.31990	+	2.67731i	−0.598996	+	0.691278i
$16$	3.69481	−	0.352811i	0.923701	−	0.0882028i
$17$	1.29502	−	0.667632i	0.314090	−	0.161924i	−0.293973	−	0.955814i	$-0.594977\pi$
$17$	1.29502	−	0.667632i	0.314090	−	0.161924i	0.608062	+	0.793889i	$0.291947\pi$
$18$	−1.88782	−	0.755771i	−0.444965	−	0.178137i
$19$	−4.09269	−	2.10993i	−0.938927	−	0.484050i	−0.0803679	−	0.996765i	$-0.525610\pi$
$19$	−4.09269	−	2.10993i	−0.938927	−	0.484050i	−0.858559	+	0.512715i	$0.828640\pi$
$20$	−4.95315	−	5.71625i	−1.10756	−	1.27819i
$21$	0.840747	−	2.50861i	0.183466	−	0.547424i
$22$	−8.09408			−1.72566
$23$	−4.34591	−	2.02806i	−0.906186	−	0.422880i
$23$	−4.34591	−	2.02806i	−0.906186	−	0.422880i
$24$	0.137333	−	0.237868i	0.0280330	−	0.0485547i
$25$	1.77996	−	7.33710i	0.355992	−	1.46742i
$26$	−0.372343	+	1.07581i	−0.0730224	+	0.210984i
$27$	0.841254	−	0.540641i	0.161899	−	0.104046i
$28$	5.04609	+	2.53903i	0.953622	+	0.479832i
$29$	−5.64801	−	3.62976i	−1.04881	−	0.674029i	−0.101660	−	0.994819i	$-0.532415\pi$
$29$	−5.64801	−	3.62976i	−1.04881	−	0.674029i	−0.947150	+	0.320790i	$0.896052\pi$
$30$	7.17119	−	0.684765i	1.30927	−	0.125020i
$31$	−1.49725	−	4.32601i	−0.268913	−	0.776975i	−0.995911	−	0.0903349i	$-0.971206\pi$
$31$	−1.49725	−	4.32601i	−0.268913	−	0.776975i	0.726998	−	0.686640i	$-0.240915\pi$
$32$	−6.36455	−	5.00514i	−1.12510	−	0.884792i
$33$	2.30885	−	3.24233i	0.401920	−	0.564418i
$34$	−2.84276	−	0.834709i	−0.487529	−	0.143151i
$35$	1.42493	+	9.26386i	0.240857	+	1.56588i
$36$	0.886941	+	1.94213i	0.147823	+	0.323688i
$37$	7.32613	−	2.93294i	1.20441	−	0.482172i	0.319343	−	0.947639i	$-0.396538\pi$
$37$	7.32613	−	2.93294i	1.20441	−	0.482172i	0.885065	+	0.465467i	$0.154114\pi$
$38$	3.06243	+	8.84832i	0.496792	+	1.43539i
$39$	−0.324739	−	0.456031i	−0.0519998	−	0.0730235i
$40$	−0.0462986	+	0.971928i	−0.00732046	+	0.153675i
$41$	−0.713712	−	4.96398i	−0.111463	−	0.775243i	−0.966498	−	0.256673i	$-0.917374\pi$
$41$	−0.713712	−	4.96398i	−0.111463	−	0.775243i	0.855035	−	0.518570i	$-0.173535\pi$
$42$	−4.75759	+	2.51215i	−0.734112	+	0.387632i
$43$	−0.474440	−	0.547532i	−0.0723514	−	0.0834979i	0.718420	−	0.695610i	$-0.244866\pi$
$43$	−0.474440	−	0.547532i	−0.0723514	−	0.0834979i	−0.790771	+	0.612112i	$0.790320\pi$
$44$	6.15060	+	5.86458i	0.927238	+	0.884119i
$45$	−1.77129	+	3.06797i	−0.264049	+	0.457346i
$46$	3.54999	+	9.08318i	0.523417	+	1.33924i
$47$	4.46117	+	7.72697i	0.650728	+	1.12709i	0.982946	+	0.183892i	$0.0588697\pi$
$47$	4.46117	+	7.72697i	0.650728	+	1.12709i	−0.332218	+	0.943203i	$0.607797\pi$
$48$	3.56127	−	1.04568i	0.514024	−	0.150931i
$49$	−3.61838	−	5.99227i	−0.516911	−	0.856039i
$50$	−12.9155	+	8.30028i	−1.82653	+	1.17384i
$51$	1.14527	−	0.900652i	0.160370	−	0.126116i
$52$	1.06242	−	0.547717i	0.147331	−	0.0759546i
$53$	−4.94305	−	6.94154i	−0.678980	−	0.953494i	−0.999979	−	0.00641467i	$-0.997958\pi$
$53$	−4.94305	−	6.94154i	−0.678980	−	0.953494i	0.320999	−	0.947079i	$-0.395981\pi$
$54$	−1.99674	−	0.384840i	−0.271722	−	0.0523701i
$55$	−2.00677	+	13.9574i	−0.270592	+	1.88201i
$56$	−0.244412	−	0.684365i	−0.0326610	−	0.0914521i
$57$	−4.41803	−	1.29725i	−0.585183	−	0.171825i
$58$	3.21869	+	13.2676i	0.422634	+	1.74212i
$59$	0.656185	+	0.0626581i	0.0854280	+	0.00815738i	0.137682	−	0.990476i	$-0.456035\pi$
$59$	0.656185	+	0.0626581i	0.0854280	+	0.00815738i	−0.0522545	+	0.998634i	$0.516641\pi$
$60$	−5.94545	−	4.67555i	−0.767554	−	0.603611i
$61$	−1.15192	−	0.222014i	−0.147488	−	0.0284259i	0.114973	−	0.993369i	$-0.463322\pi$
$61$	−1.15192	−	0.222014i	−0.147488	−	0.0284259i	−0.262461	+	0.964943i	$0.584534\pi$
$62$	−3.86704	+	8.46765i	−0.491115	+	1.07539i
$63$	0.350795	−	2.62239i	0.0441961	−	0.330390i
$64$	1.28676	+	8.94959i	0.160845	+	1.11870i
$65$	1.76281	+	0.908791i	0.218649	+	0.112722i
$66$	−7.94781	+	1.53181i	−0.978308	+	0.188553i
$67$	1.02512	−	4.22560i	0.125238	−	0.516239i	−0.874286	−	0.485410i	$-0.838670\pi$
$67$	1.02512	−	4.22560i	0.125238	−	0.516239i	0.999525	−	0.0308288i	$-0.00981466\pi$
$68$	1.55539	+	2.69401i	0.188619	+	0.326697i
$69$	−4.65119	−	1.16894i	−0.559938	−	0.140724i
$70$	10.9026	−	15.6332i	1.30311	−	1.86853i
$71$	5.70982	−	1.67656i	0.677631	−	0.198971i	0.0752328	−	0.997166i	$-0.476030\pi$
$71$	5.70982	−	1.67656i	0.677631	−	0.198971i	0.602399	+	0.798195i	$0.294212\pi$
$72$	0.0898346	−	0.259560i	0.0105871	−	0.0305895i
$73$	0.0496571	+	1.04243i	0.00581192	+	0.122007i	0.999909	+	0.0135106i	$0.00430067\pi$
$73$	0.0496571	+	1.04243i	0.00581192	+	0.122007i	−0.994097	+	0.108497i	$0.965396\pi$
$74$	−14.8976	−	5.96410i	−1.73181	−	0.693312i
$75$	0.359240	−	7.54137i	0.0414814	−	0.870802i
$76$	4.08396	−	8.94263i	0.468463	−	1.02579i
$77$	−2.58319	−	10.2094i	−0.294381	−	1.16347i
$78$	−0.162015	+	1.12684i	−0.0183446	+	0.127589i
$79$	−3.72598	+	5.23240i	−0.419205	+	0.588691i	−0.969138	−	0.246517i	$-0.920714\pi$
$79$	−3.72598	+	5.23240i	−0.419205	+	0.588691i	0.549933	+	0.835209i	$0.314653\pi$
$80$	−9.51617	+	9.07365i	−1.06394	+	1.01446i
$81$	0.723734	−	0.690079i	0.0804149	−	0.0766754i
$82$	−5.91541	+	8.30704i	−0.653248	+	0.917359i
$83$	−0.499366	+	3.47317i	−0.0548125	+	0.381230i	0.943888	+	0.330266i	$0.107138\pi$
$83$	−0.499366	+	3.47317i	−0.0548125	+	0.381230i	−0.998701	+	0.0509638i	$0.983771\pi$
$84$	5.43542	+	1.53817i	0.593053	+	0.167828i
$85$	−2.14417	+	4.69508i	−0.232568	+	0.509253i
$86$	−0.0700996	+	1.47157i	−0.00755903	+	0.158684i
$87$	−6.23288	−	2.49527i	−0.668235	−	0.267521i
$88$	−0.0520204	−	1.09204i	−0.00554539	−	0.116412i
$89$	4.48147	−	12.9484i	0.475035	−	1.37252i	−0.412153	−	0.911115i	$-0.635223\pi$
$89$	4.48147	−	12.9484i	0.475035	−	1.37252i	0.887188	−	0.461409i	$-0.152656\pi$
$90$	6.91200	−	2.02955i	0.728589	−	0.213933i
$91$	−1.47580	−	0.126311i	−0.154706	−	0.0132409i
$92$	3.88365	−	9.47436i	0.404898	−	0.987770i
$93$	−2.28889	−	3.96448i	−0.237347	−	0.411097i
$94$	4.27748	−	17.6320i	0.441189	−	1.81860i
$95$	16.0172	−	3.08707i	1.64333	−	0.316727i
$96$	−7.19677	−	3.71019i	−0.734517	−	0.378670i
$97$	0.828262	+	5.76069i	0.0840973	+	0.584909i	0.987679	+	0.156494i	$0.0500190\pi$
$97$	0.828262	+	5.76069i	0.0840973	+	0.584909i	−0.903582	+	0.428416i	$0.859072\pi$
$98$	−3.08358	+	13.8964i	−0.311489	+	1.40375i
$99$	1.65351	−	3.62069i	0.166185	−	0.363893i
$100$	15.8283	+	3.05066i	1.58283	+	0.305066i
$101$	8.73555	+	6.86971i	0.869220	+	0.683562i	0.949689	−	0.313195i	$-0.101399\pi$
$101$	8.73555	+	6.86971i	0.869220	+	0.683562i	−0.0804691	+	0.996757i	$0.525642\pi$
$102$	−2.94936	−	0.281629i	−0.292030	−	0.0278855i
$103$	3.44828	+	14.2140i	0.339769	+	1.40055i	0.843706	+	0.536806i	$0.180369\pi$
$103$	3.44828	+	14.2140i	0.339769	+	1.40055i	−0.503937	+	0.863740i	$0.668116\pi$
$104$	−0.147540	−	0.0433218i	−0.0144675	−	0.00424805i
$105$	3.15237	+	8.82678i	0.307640	+	0.861405i
$106$	−2.46613	+	17.1523i	−0.239532	+	1.66598i
$107$	11.9238	+	2.29812i	1.15272	+	0.222168i	0.729579	−	0.683897i	$-0.239716\pi$
$107$	11.9238	+	2.29812i	1.15272	+	0.222168i	0.423138	+	0.906065i	$0.360928\pi$
$108$	1.23846	+	1.73918i	0.119171	+	0.167352i
$109$	−6.42873	+	3.31424i	−0.615761	+	0.317447i	−0.737739	−	0.675086i	$-0.764107\pi$
$109$	−6.42873	+	3.31424i	−0.615761	+	0.317447i	0.121978	+	0.992533i	$0.461076\pi$
$110$	22.5393	−	17.7251i	2.14904	−	1.69002i
$111$	6.63867	−	4.26642i	0.630115	−	0.404950i
$112$	3.99146	−	8.97222i	0.377158	−	0.847795i
$113$	17.1388	−	5.03241i	1.61229	−	0.473410i	0.653355	−	0.757052i	$-0.273361\pi$
$113$	17.1388	−	5.03241i	1.61229	−	0.473410i	0.958930	+	0.283642i	$0.0915427\pi$
$114$	4.68165	+	8.10885i	0.438476	+	0.759464i
$115$	16.5431	−	3.86958i	1.54265	−	0.360840i
$116$	7.16723	−	12.4140i	0.665461	−	1.15261i
$117$	−0.405175	−	0.386333i	−0.0374584	−	0.0357165i
$118$	−0.877784	−	1.01302i	−0.0808066	−	0.0932557i
$119$	0.145601	−	3.85208i	0.0133472	−	0.353120i
$120$	0.138477	+	0.963126i	0.0126411	+	0.0879210i
$121$	0.230464	−	4.83804i	0.0209513	−	0.439822i
$122$	1.38374	+	1.94318i	0.125278	+	0.175928i
$123$	−1.64025	−	4.73920i	−0.147897	−	0.427319i
$124$	9.07378	−	3.63259i	0.814849	−	0.326216i
$125$	3.75257	+	8.21699i	0.335640	+	0.734950i
$126$	−4.19618	+	3.36713i	−0.373826	+	0.299967i
$127$	12.2255	+	3.58972i	1.08483	+	0.318536i	0.774811	−	0.632193i	$-0.217845\pi$
$127$	12.2255	+	3.58972i	1.08483	+	0.318536i	0.310023	+	0.950729i	$0.399663\pi$
$128$	1.27167	−	1.78581i	0.112401	−	0.157845i
$129$	−0.569487	−	0.447850i	−0.0501405	−	0.0394310i
$130$	−1.31906	−	3.81116i	−0.115689	−	0.334261i
$131$	−14.9714	+	1.42959i	−1.30806	+	0.124904i	−0.725689	−	0.688023i	$-0.758479\pi$
$131$	−14.9714	+	1.42959i	−1.30806	+	0.124904i	−0.582366	+	0.812927i	$0.697873\pi$
$132$	7.14933	+	4.59460i	0.622269	+	0.399908i
$133$	−10.1834	+	6.68668i	−0.883012	+	0.579808i
$134$	−7.43832	+	4.78032i	−0.642573	+	0.412956i
$135$	−1.15867	+	3.34775i	−0.0997221	+	0.288128i
$136$	0.0943476	−	0.388906i	0.00809024	−	0.0333484i
$137$	11.4922	−	19.9050i	0.981842	−	1.70060i	0.326634	−	0.945151i	$-0.394086\pi$
$137$	11.4922	−	19.9050i	0.981842	−	1.70060i	0.655208	−	0.755449i	$-0.272581\pi$
$138$	5.20484	+	8.24720i	0.443065	+	0.702048i
$139$	−16.8065			−1.42551			−0.712756	−	0.701412i	$-0.752553\pi$
$139$	−16.8065			−1.42551			−0.712756	+	0.701412i	$0.752553\pi$
$140$	−19.6118	+	3.98000i	−1.65750	+	0.336371i
$141$	5.84289	+	6.74305i	0.492060	+	0.567868i
$142$	−10.7558	−	5.54501i	−0.902609	−	0.465327i
$143$	−2.06876	−	0.828205i	−0.172998	−	0.0692580i
$144$	3.29901	−	1.70076i	0.274918	−	0.141730i
$145$	23.6765	−	2.26084i	1.96623	−	0.187752i
$146$	1.38973	−	1.60383i	0.115015	−	0.132734i
$147$	−4.68703	−	5.19920i	−0.386580	−	0.428823i
$148$	6.99921	+	15.3261i	0.575332	+	1.25980i
$149$	−3.20910	−	13.2281i	−0.262900	−	1.08369i	−0.938186	−	0.346132i	$-0.887495\pi$
$149$	−3.20910	−	13.2281i	−0.262900	−	1.08369i	0.675286	−	0.737556i	$-0.264020\pi$
$150$	−11.1112	+	10.5946i	−0.907230	+	0.865042i
$151$	−17.7985	−	1.69955i	−1.44842	−	0.138308i	−0.658994	−	0.752148i	$-0.729018\pi$
$151$	−17.7985	−	1.69955i	−1.44842	−	0.138308i	−0.789430	+	0.613840i	$0.789624\pi$
$152$	−1.17412	+	0.470048i	−0.0952339	+	0.0381259i
$153$	0.954126	−	1.10112i	0.0771365	−	0.0890203i
$154$	−10.5248	+	18.6501i	−0.848115	+	1.50287i
$155$	13.6428	+	8.76768i	1.09581	+	0.704237i
$156$	0.939567	−	0.738883i	0.0752255	−	0.0591580i
$157$	1.16184	+	24.3900i	0.0927248	+	1.94653i	0.271058	+	0.962563i	$0.412626\pi$
$157$	1.16184	+	24.3900i	0.0927248	+	1.94653i	−0.178333	+	0.983970i	$0.557071\pi$
$158$	12.8260	−	2.47201i	1.02038	−	0.196662i
$159$	−6.16742	−	5.88062i	−0.489108	−	0.466364i
$160$	28.6838			2.26765
$161$	−10.3240	+	7.37660i	−0.813648	+	0.581358i
$162$	−2.03349			−0.159766
$163$	1.52667	+	1.45568i	0.119578	+	0.114018i	0.747509	−	0.664251i	$-0.231250\pi$
$163$	1.52667	+	1.45568i	0.119578	+	0.114018i	−0.627931	+	0.778269i	$0.716098\pi$
$164$	10.5139	−	2.02640i	0.821001	−	0.158235i
$165$	0.670947	+	14.0849i	0.0522332	+	1.09651i
$166$	5.60870	−	4.41073i	0.435320	−	0.342339i
$167$	−6.52096	−	4.19077i	−0.504607	−	0.324291i	0.263449	−	0.964673i	$-0.415140\pi$
$167$	−6.52096	−	4.19077i	−0.504607	−	0.324291i	−0.768057	+	0.640382i	$0.778776\pi$
$168$	−0.369512	−	0.625742i	−0.0285085	−	0.0482770i
$169$	8.30794	−	9.58788i	0.639073	−	0.737529i
$170$	9.74403	−	3.90092i	0.747333	−	0.299187i
$171$	−4.58370	−	0.437690i	−0.350524	−	0.0334710i
$172$	1.11950	−	1.06744i	0.0853609	−	0.0813915i
$173$	5.53529	+	22.8168i	0.420840	+	1.73473i	0.648711	+	0.761035i	$0.275309\pi$
$173$	5.53529	+	22.8168i	0.420840	+	1.73473i	−0.227870	+	0.973691i	$0.573176\pi$
$174$	5.67143	+	12.4187i	0.429950	+	0.941459i
$175$	−14.5914	−	13.6418i	−1.10301	−	1.03123i
$176$	9.67470	−	11.1652i	0.729258	−	0.841609i
$177$	0.656185	−	0.0626581i	0.0493219	−	0.00470967i
$178$	−24.7654	+	12.7675i	−1.85625	+	0.956961i
$179$	15.1850	+	6.07915i	1.13498	+	0.454377i	0.861629	−	0.507538i	$-0.169444\pi$
$179$	15.1850	+	6.07915i	1.13498	+	0.454377i	0.273349	+	0.961915i	$0.411869\pi$
$180$	−6.72286	−	3.46588i	−0.501093	−	0.258331i
$181$	−9.72501	−	11.2233i	−0.722854	−	0.834219i	0.268793	−	0.963198i	$-0.413375\pi$
$181$	−9.72501	−	11.2233i	−0.722854	−	0.834219i	−0.991647	+	0.128980i	$0.958830\pi$
$182$	1.99469	+	2.25683i	0.147856	+	0.167288i
$183$	−1.17312			−0.0867192
$184$	−1.20268	+	0.537337i	−0.0886624	+	0.0396130i
$185$	−13.9780	+	24.2106i	−1.02768	+	1.78000i
$186$	−2.19465	+	9.04647i	−0.160919	+	0.663319i
$187$	1.89680	−	5.48043i	0.138707	−	0.400769i
$188$	−16.0257	+	10.2991i	−1.16880	+	0.751140i
$189$	−0.151835	−	2.64139i	−0.0110444	−	0.192133i
$190$	−27.9046	−	17.9332i	−2.02441	−	1.30101i
$191$	−15.7232	+	1.50139i	−1.13769	+	0.108636i	−0.646854	−	0.762614i	$-0.723916\pi$
$191$	−15.7232	+	1.50139i	−1.13769	+	0.108636i	−0.490839	+	0.871250i	$0.663310\pi$
$192$	2.95722	+	8.54434i	0.213419	+	0.616635i
$193$	1.39152	+	1.09430i	0.100164	+	0.0787697i	0.666985	−	0.745071i	$-0.267585\pi$
$193$	1.39152	+	1.09430i	0.100164	+	0.0787697i	−0.566821	+	0.823841i	$0.691827\pi$
$194$	6.86483	−	9.64030i	0.492866	−	0.692133i
$195$	1.90294	+	0.558754i	0.136272	+	0.0400132i
$196$	12.4118	−	8.32551i	0.886561	−	0.594679i
$197$	−10.8694	−	23.8008i	−0.774415	−	1.69573i	−0.716681	−	0.697401i	$-0.754339\pi$
$197$	−10.8694	−	23.8008i	−0.774415	−	1.69573i	−0.0577348	−	0.998332i	$-0.518388\pi$
$198$	−7.51428	+	3.00827i	−0.534017	+	0.213788i
$199$	0.0610608	+	0.176424i	0.00432849	+	0.0125063i	0.947144	−	0.320808i	$-0.103954\pi$
$199$	0.0610608	+	0.176424i	0.00432849	+	0.0125063i	−0.942816	+	0.333314i	$0.891833\pi$
$200$	−1.20287	−	1.68920i	−0.0850558	−	0.119444i
$201$	0.206894	−	4.34324i	0.0145932	−	0.306349i
$202$	−3.21610	−	22.3685i	−0.226284	−	1.57384i
$203$	−15.7078	+	8.29415i	−1.10247	+	0.582136i
$204$	2.03713	+	2.35097i	0.142627	+	0.164601i
$205$	12.8580	+	12.2601i	0.898040	+	0.856279i
$206$	14.8712	−	25.7576i	1.03612	−	1.79462i
$207$	−4.78836	−	0.267573i	−0.332814	−	0.0185976i
$208$	−1.03895	−	1.79952i	−0.0720384	−	0.124774i
$209$	−17.5855	+	5.16357i	−1.21642	+	0.357172i
$210$	7.74697	−	17.4140i	0.534591	−	1.20168i
$211$	−4.32568	+	2.77994i	−0.297792	+	0.191379i	−0.681001	−	0.732282i	$-0.738455\pi$
$211$	−4.32568	+	2.77994i	−0.297792	+	0.191379i	0.383209	+	0.923662i	$0.374819\pi$
$212$	14.3017	−	11.2470i	0.982247	−	0.772448i
$213$	5.28935	−	2.72685i	0.362420	−	0.186841i
$214$	−14.3234	−	20.1144i	−0.979129	−	1.37499i
$215$	2.52018	+	0.485726i	0.171875	+	0.0331262i
$216$	0.0390891	−	0.271871i	0.00265968	−	0.0184985i
$217$	−11.9147	−	2.17526i	−0.808825	−	0.147666i
$218$	14.1120	+	4.14365i	0.955783	+	0.280643i
$219$	0.246041	+	1.01420i	0.0166259	+	0.0685329i
$220$	−29.9701	−	2.86180i	−2.02058	−	0.192942i
$221$	−0.641168	−	0.504220i	−0.0431296	−	0.0339175i
$222$	−15.7571	−	3.03693i	−1.05755	−	0.203825i
$223$	4.88505	−	10.6968i	0.327127	−	0.716309i	−0.672592	−	0.740014i	$-0.734819\pi$
$223$	4.88505	−	10.6968i	0.327127	−	0.716309i	0.999719	+	0.0237047i	$0.00754615\pi$
$224$	−19.8086	+	8.15676i	−1.32352	+	0.544996i
$225$	−1.07447	−	7.47307i	−0.0716310	−	0.498205i
$226$	−32.2851	−	16.6441i	−2.14757	−	1.10715i
$227$	6.14310	−	1.18399i	0.407732	−	0.0785839i	0.0187385	−	0.999824i	$-0.494035\pi$
$227$	6.14310	−	1.18399i	0.407732	−	0.0785839i	0.388993	+	0.921241i	$0.372823\pi$
$228$	2.31776	−	9.55392i	0.153497	−	0.632724i
$229$	9.84000	+	17.0434i	0.650246	+	1.12626i	0.983063	+	0.183267i	$0.0586674\pi$
$229$	9.84000	+	17.0434i	0.650246	+	1.12626i	−0.332817	+	0.942991i	$0.607999\pi$
$230$	−29.7766	−	17.5195i	−1.96341	−	1.15520i
$231$	−4.46865	−	9.53603i	−0.294015	−	0.627425i
$232$	−1.76936	+	0.519531i	−0.116164	+	0.0341089i
$233$	−9.32791	+	26.9512i	−0.611092	+	1.76563i	0.0315907	+	0.999501i	$0.489943\pi$
$233$	−9.32791	+	26.9512i	−0.611092	+	1.76563i	−0.642682	+	0.766133i	$0.722179\pi$
$234$	0.0541685	+	1.13714i	0.00354110	+	0.0743369i
$235$	−29.3440	−	11.7476i	−1.91419	−	0.766327i
$236$	−0.0669656	+	1.40578i	−0.00435909	+	0.0915085i
$237$	−2.66841	+	5.84299i	−0.173332	+	0.379543i
$238$	−5.61978	+	5.46481i	−0.364276	+	0.354231i
$239$	−2.28964	+	15.9248i	−0.148104	+	1.03009i	0.771214	+	0.636575i	$0.219650\pi$
$239$	−2.28964	+	15.9248i	−0.148104	+	1.03009i	−0.919319	+	0.393513i	$0.871259\pi$
$240$	−7.62700	+	10.7106i	−0.492321	+	0.691368i
$241$	20.7787	−	19.8125i	1.33848	−	1.27624i	0.406531	−	0.913637i	$-0.366738\pi$
$241$	20.7787	−	19.8125i	1.33848	−	1.27624i	0.931946	−	0.362598i	$-0.118110\pi$
$242$	−7.12824	+	6.79676i	−0.458221	+	0.436913i
$243$	0.580057	−	0.814576i	0.0372107	−	0.0522551i
$244$	0.356454	−	2.47919i	0.0228196	−	0.158714i
$245$	23.1983	+	8.76263i	1.48209	+	0.559824i
$246$	−4.23640	+	9.27642i	−0.270103	+	0.591443i
$247$	−0.122657	+	2.57489i	−0.00780448	+	0.163836i
$248$	−1.16730	−	0.467315i	−0.0741234	−	0.0296746i
$249$	0.166959	+	3.50491i	0.0105806	+	0.222115i
$250$	6.00795	−	17.3588i	0.379976	−	1.09787i
$251$	6.16591	−	1.81047i	0.389189	−	0.114276i	−0.0812833	−	0.996691i	$-0.525902\pi$
$251$	6.16591	−	1.81047i	0.389189	−	0.114276i	0.470472	+	0.882415i	$0.344084\pi$
$252$	5.62829	+	0.481714i	0.354549	+	0.0303451i
$253$	−18.0901	+	6.09497i	−1.13732	+	0.383187i
$254$	−12.9549	−	22.4386i	−0.812865	−	1.40792i
$255$	−1.21687	+	5.01602i	−0.0762036	+	0.314115i
$256$	13.3790	−	2.57858i	0.836185	−	0.161161i
$257$	3.56791	+	1.83939i	0.222560	+	0.114738i	0.565901	−	0.824473i	$-0.308528\pi$
$257$	3.56791	+	1.83939i	0.222560	+	0.114738i	−0.343341	+	0.939211i	$0.611559\pi$
$258$	0.209664	+	1.45824i	0.0130531	+	0.0907863i
$259$	2.76827	−	20.6944i	0.172012	−	1.28589i
$260$	−1.75905	+	3.85178i	−0.109092	+	0.238877i
$261$	−6.59248	−	1.27060i	−0.408064	−	0.0786479i
$262$	24.0395	+	18.9049i	1.48517	+	1.16795i
$263$	−11.9970	−	1.14557i	−0.739766	−	0.0706391i	−0.281632	−	0.959522i	$-0.590876\pi$
$263$	−11.9970	−	1.14557i	−0.739766	−	0.0706391i	−0.458134	+	0.888883i	$0.651482\pi$
$264$	−0.257751	−	1.06246i	−0.0158635	−	0.0653901i
$265$	28.9659	+	8.50515i	1.77936	+	0.522467i
$266$	24.3701	+	4.44922i	1.49423	+	0.272799i
$267$	1.94999	−	13.5625i	0.119338	−	0.830011i
$268$	9.11588	+	1.75694i	0.556841	+	0.107322i
$269$	12.2078	+	17.1435i	0.744324	+	1.04526i	0.996977	+	0.0776996i	$0.0247575\pi$
$269$	12.2078	+	17.1435i	0.744324	+	1.04526i	−0.252653	+	0.967557i	$0.581303\pi$
$270$	6.40300	−	3.30097i	0.389674	−	0.200891i
$271$	4.09355	−	3.21920i	0.248666	−	0.195553i	−0.486044	−	0.873934i	$-0.661561\pi$
$271$	4.09355	−	3.21920i	0.248666	−	0.195553i	0.734710	+	0.678381i	$0.237318\pi$
$272$	4.54932	−	2.92367i	0.275843	−	0.177273i
$273$	−1.47303	+	0.155269i	−0.0891521	+	0.00939730i
$274$	−44.8451	+	13.1677i	−2.70919	+	0.795490i
$275$	−15.0258	−	26.0255i	−0.906091	−	1.56940i
$276$	2.02043	−	10.0381i	0.121615	−	0.604225i
$277$	−11.1571	+	19.3246i	−0.670364	+	1.16111i	0.307436	+	0.951569i	$0.400529\pi$
$277$	−11.1571	+	19.3246i	−0.670364	+	1.16111i	−0.977801	+	0.209537i	$0.932804\pi$
$278$	24.7343	+	23.5841i	1.48346	+	1.41448i
$279$	−2.99781	−	3.45966i	−0.179474	−	0.207124i
$280$	2.17928	+	1.37049i	0.130237	+	0.0819024i
$281$	1.27691	+	8.88110i	0.0761740	+	0.529802i	0.991803	+	0.127777i	$0.0407843\pi$
$281$	1.27691	+	8.88110i	0.0761740	+	0.529802i	−0.915629	+	0.402025i	$0.868307\pi$
$282$	0.863301	−	18.1229i	0.0514088	−	1.07920i
$283$	5.90277	+	8.28928i	0.350883	+	0.492746i	0.951866	−	0.306516i	$-0.0991632\pi$
$283$	5.90277	+	8.28928i	0.350883	+	0.492746i	−0.600982	+	0.799262i	$0.705224\pi$
$284$	4.15558	+	12.0068i	0.246588	+	0.712470i
$285$	15.1436	−	6.06256i	0.897027	−	0.359115i
$286$	1.88240	+	4.12189i	0.111309	+	0.243732i
$287$	−12.3659	−	4.81021i	−0.729935	−	0.283938i
$288$	−7.76887	−	2.28115i	−0.457785	−	0.134418i
$289$	−8.62961	+	12.1186i	−0.507624	+	0.712858i
$290$	−38.0174	−	29.8972i	−2.23246	−	1.75563i
$291$	1.90351	+	5.49984i	0.111586	+	0.322406i
$292$	−2.21810	+	0.211803i	−0.129804	+	0.0123948i
$293$	−8.62602	−	5.54361i	−0.503938	−	0.323861i	0.263852	−	0.964563i	$-0.415007\pi$
$293$	−8.62602	−	5.54361i	−0.503938	−	0.323861i	−0.767790	+	0.640702i	$0.778643\pi$
$294$	−0.397943	+	14.2288i	−0.0232085	+	0.829843i
$295$	−1.96447	+	1.26249i	−0.114376	+	0.0735048i
$296$	0.708922	−	2.04829i	0.0412052	−	0.119055i
$297$	0.938413	−	3.86819i	0.0544523	−	0.224455i
$298$	−13.8397	+	23.9711i	−0.801713	+	1.38861i
$299$	−0.0220749	+	2.68480i	−0.00127662	+	0.155266i
$300$	16.1196			0.930667
$301$	−1.87853	+	0.381225i	−0.108276	+	0.0219735i
$302$	23.8092	+	27.4773i	1.37007	+	1.58114i
$303$	9.87779	+	5.09235i	0.567464	+	0.292548i
$304$	−15.8661	−	6.35182i	−0.909983	−	0.364302i
$305$	3.69388	−	1.90433i	0.211511	−	0.109041i
$306$	−2.94936	+	0.281629i	−0.168603	+	0.0160997i
$307$	−21.0712	+	24.3174i	−1.20260	+	1.38787i	−0.301946	+	0.953325i	$0.597636\pi$
$307$	−21.0712	+	24.3174i	−1.20260	+	1.38787i	−0.900650	+	0.434545i	$0.856909\pi$
$308$	21.5107	−	6.54622i	1.22568	−	0.373006i
$309$	6.07598	+	13.3045i	0.345650	+	0.756868i
$310$	−7.77474	−	32.0479i	−0.441575	−	1.82020i
$311$	10.2630	−	9.78580i	0.581964	−	0.554902i	−0.340864	−	0.940112i	$-0.610720\pi$
$311$	10.2630	−	9.78580i	0.581964	−	0.554902i	0.922829	+	0.385211i	$0.125871\pi$
$312$	−0.153073	−	0.0146167i	−0.00866604	−	0.000827507i
$313$	13.8350	−	5.53869i	0.781999	−	0.313065i	0.0539082	−	0.998546i	$-0.482832\pi$
$313$	13.8350	−	5.53869i	0.781999	−	0.313065i	0.728091	+	0.685481i	$0.240408\pi$
$314$	32.5158	−	37.5252i	1.83497	−	2.11767i
$315$	4.76588	+	8.07067i	0.268527	+	0.454731i
$316$	−11.5374	−	7.41466i	−0.649031	−	0.417107i
$317$	−24.7360	+	19.4526i	−1.38931	+	1.09257i	−0.405355	+	0.914159i	$0.632852\pi$
$317$	−24.7360	+	19.4526i	−1.38931	+	1.09257i	−0.983957	+	0.178407i	$0.942906\pi$
$318$	0.824533	+	17.3091i	0.0462375	+	0.970644i
$319$	−26.2407	+	5.05747i	−1.46920	+	0.283164i
$320$	−23.1817	−	22.1037i	−1.29590	−	1.23564i
$321$	12.1432			0.677770
$322$	25.5453	+	3.63120i	1.42358	+	0.202359i
$323$	−6.70879			−0.373287
$324$	1.54522	+	1.47337i	0.0858458	+	0.0818538i
$325$	−4.15036	+	0.799916i	−0.230220	+	0.0443713i
$326$	−0.204104	−	4.28466i	−0.0113043	−	0.237306i
$327$	−5.68533	+	4.47100i	−0.314400	+	0.247247i
$328$	−1.15879	−	0.744711i	−0.0639836	−	0.0411198i
$329$	23.6052	−	0.231808i	1.30139	−	0.0127800i
$330$	18.7775	−	21.6703i	1.03367	−	1.19291i
$331$	20.3561	−	8.14934i	1.11887	−	0.447928i	0.262833	−	0.964841i	$-0.415343\pi$
$331$	20.3561	−	8.14934i	1.11887	−	0.447928i	0.856038	+	0.516913i	$0.172919\pi$
$332$	−7.45779	−	0.712133i	−0.409300	−	0.0390834i
$333$	5.71128	−	5.44569i	0.312976	−	0.298422i
$334$	3.71616	+	15.3182i	0.203339	+	0.838176i
$335$	6.39895	+	14.0118i	0.349612	+	0.765544i
$336$	2.22133	−	9.56547i	0.121183	−	0.521839i
$337$	6.26155	−	7.22621i	0.341088	−	0.393637i	−0.559127	−	0.829082i	$-0.688864\pi$
$337$	6.26155	−	7.22621i	0.341088	−	0.393637i	0.900215	+	0.435445i	$0.143409\pi$
$338$	−25.6812	+	2.45226i	−1.39687	+	0.133385i
$339$	15.8767	−	8.18502i	0.862305	−	0.444549i
$340$	−10.2308	−	4.09580i	−0.554843	−	0.222126i
$341$	−16.1958	−	8.34952i	−0.877052	−	0.452152i
$342$	6.13165	+	7.07631i	0.331562	+	0.382643i
$343$	−18.5122	+	0.545524i	−0.999566	+	0.0294555i
$344$	−0.198993			−0.0107290
$345$	15.5118	−	6.93045i	0.835129	−	0.373123i
$346$	23.8717	−	41.3470i	1.28335	−	2.22283i
$347$	−4.71445	+	19.4332i	−0.253085	+	1.04323i	0.693418	+	0.720536i	$0.256104\pi$
$347$	−4.71445	+	19.4332i	−0.253085	+	1.04323i	−0.946503	+	0.322695i	$0.895411\pi$
$348$	4.68834	−	13.5461i	0.251322	−	0.726146i
$349$	−2.68749	+	1.72714i	−0.143858	+	0.0924518i	−0.610590	−	0.791947i	$-0.709068\pi$
$349$	−2.68749	+	1.72714i	−0.143858	+	0.0924518i	0.466732	+	0.884399i	$0.345431\pi$
$350$	2.33107	+	40.5524i	0.124601	+	2.16762i
$351$	−0.470967	−	0.302672i	−0.0251383	−	0.0161554i
$352$	−32.0827	+	3.06353i	−1.71001	+	0.163287i
$353$	−0.314422	−	0.908464i	−0.0167350	−	0.0483527i	0.936324	−	0.351137i	$-0.114205\pi$
$353$	−0.314422	−	0.908464i	−0.0167350	−	0.0483527i	−0.953059	+	0.302785i	$0.902084\pi$
$354$	−1.05364	−	0.828588i	−0.0560001	−	0.0440390i
$355$	−12.2285	+	17.1725i	−0.649020	+	0.911420i
$356$	28.0696	+	8.24199i	1.48769	+	0.436825i
$357$	−0.586042	−	3.81003i	−0.0310166	−	0.201648i
$358$	−13.8171	−	30.2553i	−0.730258	−	1.59904i
$359$	32.9595	−	13.1950i	1.73953	−	0.696404i	0.739812	−	0.672814i	$-0.234915\pi$
$359$	32.9595	−	13.1950i	1.73953	−	0.696404i	0.999722	−	0.0235900i	$-0.00750963\pi$
$360$	0.318247	+	0.919514i	0.0167731	+	0.0484627i
$361$	1.27722	+	1.79360i	0.0672220	+	0.0944001i
$362$	−1.43689	+	30.1641i	−0.0755215	+	1.58539i
$363$	−0.689306	−	4.79423i	−0.0361792	−	0.251632i
$364$	0.119449	−	3.16020i	0.00626083	−	0.165640i
$365$	−2.42108	−	2.79407i	−0.126725	−	0.146248i
$366$	1.72648	+	1.64619i	0.0902445	+	0.0860480i
$367$	14.0335	−	24.3068i	0.732543	−	1.26880i	−0.223249	−	0.974761i	$-0.571666\pi$
$367$	14.0335	−	24.3068i	0.732543	−	1.26880i	0.955793	−	0.294041i	$-0.0950003\pi$
$368$	−16.7728	−	5.96000i	−0.874344	−	0.310687i
$369$	−2.50751	−	4.34314i	−0.130536	−	0.226095i
$370$	54.5454	−	16.0160i	2.83568	−	0.832631i
$371$	−22.4220	+	2.36345i	−1.16409	+	0.122704i
$372$	8.22233	−	5.28417i	0.426308	−	0.273971i
$373$	−5.21700	+	4.10270i	−0.270126	+	0.212430i	−0.744029	−	0.668148i	$-0.767087\pi$
$373$	−5.21700	+	4.10270i	−0.270126	+	0.212430i	0.473902	+	0.880577i	$0.342845\pi$
$374$	−10.4820	+	5.40386i	−0.542013	+	0.279427i
$375$	5.23984	+	7.35832i	0.270584	+	0.379982i
$376$	2.40638	+	0.463792i	0.124100	+	0.0239182i
$377$	−0.534912	+	3.72039i	−0.0275494	+	0.191610i
$378$	−3.48312	+	4.10041i	−0.179152	+	0.210902i
$379$	5.04490	+	1.48132i	0.259139	+	0.0760902i	0.408722	−	0.912659i	$-0.365975\pi$
$379$	5.04490	+	1.48132i	0.259139	+	0.0760902i	−0.149582	+	0.988749i	$0.547793\pi$
$380$	8.21085	+	33.8456i	0.421208	+	1.73624i
$381$	12.6839	+	1.21117i	0.649816	+	0.0620499i
$382$	25.2468	+	19.8543i	1.29174	+	1.01583i
$383$	8.15979	+	1.57267i	0.416946	+	0.0803597i	0.393410	−	0.919363i	$-0.371295\pi$
$383$	8.15979	+	1.57267i	0.416946	+	0.0803597i	0.0235361	+	0.999723i	$0.492508\pi$
$384$	0.910723	−	1.99421i	0.0464752	−	0.101766i
$385$	29.5507	+	22.7728i	1.50604	+	1.16061i
$386$	−0.512306	−	3.56316i	−0.0260757	−	0.181360i
$387$	−0.643952	−	0.331980i	−0.0327339	−	0.0168755i
$388$	−12.2014	+	2.35163i	−0.619433	+	0.119386i
$389$	5.27061	−	21.7257i	0.267231	−	1.10154i	−0.667054	−	0.745010i	$-0.732445\pi$
$389$	5.27061	−	21.7257i	0.267231	−	1.10154i	0.934284	−	0.356529i	$-0.116040\pi$
$390$	−2.01649	−	3.49266i	−0.102109	−	0.176858i
$391$	−6.98206	+	0.275081i	−0.353098	+	0.0139115i
$392$	−1.89470	−	0.326721i	−0.0956969	−	0.0165019i
$393$	−14.4303	+	4.23711i	−0.727911	+	0.213734i
$394$	−17.4022	+	50.2804i	−0.876711	+	2.53309i
$395$	−1.08276	−	22.7299i	−0.0544796	−	1.14367i
$396$	7.88966	+	3.15855i	0.396471	+	0.158723i
$397$	−0.276840	+	5.81160i	−0.0138942	+	0.291676i	0.981216	+	0.192910i	$0.0617925\pi$
$397$	−0.276840	+	5.81160i	−0.0138942	+	0.291676i	−0.995111	+	0.0987658i	$0.968511\pi$
$398$	0.157706	−	0.345328i	0.00790509	−	0.0173097i
$399$	−8.73391	+	8.49306i	−0.437242	+	0.425185i
$400$	3.98800	−	27.7371i	0.199400	−	1.38686i
$401$	5.45250	−	7.65696i	0.272285	−	0.382371i	−0.655680	−	0.755039i	$-0.727618\pi$
$401$	5.45250	−	7.65696i	0.272285	−	0.382371i	0.927964	+	0.372669i	$0.121557\pi$
$402$	−6.39922	+	6.10164i	−0.319164	+	0.304322i
$403$	−1.85480	+	1.76855i	−0.0923943	+	0.0880978i
$404$	−13.7633	+	19.3278i	−0.684748	+	0.961594i
$405$	−0.504163	+	3.50653i	−0.0250520	+	0.174241i
$406$	34.7561	+	9.83563i	1.72492	+	0.488134i
$407$	13.0486	−	28.5724i	0.646793	−	1.41628i
$408$	0.0190416	−	0.399733i	0.000942702	−	0.0197897i
$409$	12.9441	+	5.18203i	0.640044	+	0.256235i	0.668905	−	0.743348i	$-0.266763\pi$
$409$	12.9441	+	5.18203i	0.640044	+	0.256235i	−0.0288601	+	0.999583i	$0.509188\pi$
$410$	−1.71900	−	36.0863i	−0.0848956	−	1.78218i
$411$	7.51744	−	21.7202i	0.370808	−	1.07138i
$412$	−29.9632	+	8.79799i	−1.47618	+	0.433446i
$413$	0.997620	−	1.43048i	0.0490897	−	0.0703896i
$414$	6.67157	+	7.11314i	0.327890	+	0.349592i
$415$	−6.21526	−	10.7651i	−0.305095	−	0.528440i
$416$	−1.06868	+	4.40516i	−0.0523963	+	0.215981i
$417$	−16.5028	+	3.18066i	−0.808147	+	0.155758i
$418$	33.1265	+	17.0779i	1.62027	+	0.835308i
$419$	−0.956137	−	6.65008i	−0.0467104	−	0.324878i	−0.999757	−	0.0220535i	$-0.992980\pi$
$419$	−0.956137	−	6.65008i	−0.0467104	−	0.324878i	0.953046	−	0.302824i	$-0.0979295\pi$
$420$	−18.5042	+	7.61964i	−0.902913	+	0.371800i
$421$	8.98692	−	19.6786i	0.437996	−	0.959077i	−0.553966	−	0.832539i	$-0.686886\pi$
$421$	8.98692	−	19.6786i	0.437996	−	0.959077i	0.991962	−	0.126538i	$-0.0403864\pi$
$422$	10.2671	+	1.97883i	0.499796	+	0.0963277i
$423$	7.01343	+	5.51542i	0.341005	+	0.268169i
$424$	−2.33002	−	0.222490i	−0.113156	−	0.0108051i
$425$	−2.59339	−	10.6901i	−0.125798	−	0.518545i
$426$	−11.6109	−	3.40925i	−0.562548	−	0.165179i
$427$	−2.00941	+	2.36552i	−0.0972420	+	0.114476i
$428$	−3.68975	+	25.6628i	−0.178351	+	1.24046i
$429$	−2.18811	−	0.421724i	−0.105643	−	0.0203610i
$430$	−3.02736	−	4.25134i	−0.145992	−	0.205018i
$431$	23.9867	−	12.3660i	1.15540	−	0.595649i	0.229458	−	0.973319i	$-0.426305\pi$
$431$	23.9867	−	12.3660i	1.15540	−	0.595649i	0.925940	+	0.377670i	$0.123274\pi$
$432$	2.91752	−	2.29437i	0.140369	−	0.110388i
$433$	26.7014	−	17.1599i	1.28319	−	0.824654i	0.291909	−	0.956446i	$-0.405710\pi$
$433$	26.7014	−	17.1599i	1.28319	−	0.824654i	0.991277	+	0.131792i	$0.0420732\pi$
$434$	14.4825	+	19.9209i	0.695183	+	0.956234i
$435$	22.8208	−	6.70080i	1.09417	−	0.321279i
$436$	−7.72123	−	13.3736i	−0.369780	−	0.640478i
$437$	13.5074	+	17.4698i	0.646147	+	0.835693i
$438$	1.06109	−	1.83786i	0.0507007	−	0.0878162i
$439$	0.846769	+	0.807393i	0.0404141	+	0.0385348i	0.710017	−	0.704185i	$-0.248687\pi$
$439$	0.846769	+	0.807393i	0.0404141	+	0.0385348i	−0.669603	+	0.742719i	$0.733536\pi$
$440$	2.53630	+	2.92705i	0.120914	+	0.139542i
$441$	−5.58629	−	4.21822i	−0.266014	−	0.200868i
$442$	0.236054	+	1.64179i	0.0112280	+	0.0780921i
$443$	0.622821	−	13.0746i	0.0295911	−	0.621194i	−0.934554	−	0.355820i	$-0.884202\pi$
$443$	0.622821	−	13.0746i	0.0295911	−	0.621194i	0.964146	−	0.265374i	$-0.0854955\pi$
$444$	9.77321	+	13.7246i	0.463816	+	0.651339i
$445$	15.8760	+	45.8707i	0.752595	+	2.17448i
$446$	−22.1998	+	8.88746i	−1.05119	+	0.420833i
$447$	−5.65454	−	12.3817i	−0.267451	−	0.585635i
$448$	22.2945	+	8.67236i	1.05332	+	0.409730i
$449$	−24.7447	−	7.26569i	−1.16777	−	0.342889i	−0.360324	−	0.932827i	$-0.617334\pi$
$449$	−24.7447	−	7.26569i	−1.16777	−	0.342889i	−0.807448	+	0.589938i	$0.799152\pi$
$450$	−8.90542	+	12.5059i	−0.419806	+	0.589534i
$451$	−15.6910	−	12.3395i	−0.738861	−	0.581046i
$452$	12.4735	+	36.0399i	0.586706	+	1.69518i
$453$	−17.7985	+	1.69955i	−0.836248	+	0.0798520i
$454$	−10.7023	−	6.87793i	−0.502283	−	0.322797i
$455$	4.38621	−	2.88009i	0.205629	−	0.135021i
$456$	−1.06395	+	0.683757i	−0.0498239	+	0.0320199i
$457$	4.05836	−	11.7259i	0.189842	−	0.548513i	−0.809407	−	0.587248i	$-0.800211\pi$
$457$	4.05836	−	11.7259i	0.189842	−	0.548513i	0.999250	+	0.0387346i	$0.0123327\pi$
$458$	9.43485	−	38.8910i	0.440862	−	1.81726i
$459$	0.728495	−	1.26179i	0.0340032	−	0.0588953i
$460$	9.93309	+	34.8876i	0.463133	+	1.62664i
$461$	9.77832			0.455422			0.227711	−	0.973729i	$-0.426876\pi$
$461$	9.77832			0.455422			0.227711	+	0.973729i	$0.426876\pi$
$462$	−6.80507	+	20.3049i	−0.316601	+	0.944670i
$463$	−0.342783	−	0.395593i	−0.0159305	−	0.0183848i	0.747728	−	0.664005i	$-0.231145\pi$
$463$	−0.342783	−	0.395593i	−0.0159305	−	0.0183848i	−0.763659	+	0.645620i	$0.776599\pi$
$464$	−22.1489	−	11.4186i	−1.02824	−	0.530094i
$465$	15.0555	+	6.02733i	0.698183	+	0.279511i
$466$	51.5477	−	26.5747i	2.38790	−	1.23105i
$467$	−34.9568	+	3.33797i	−1.61761	+	0.154463i	−0.864219	−	0.503115i	$-0.832187\pi$
$467$	−34.9568	+	3.33797i	−1.61761	+	0.154463i	−0.753387	+	0.657578i	$0.771581\pi$
$468$	0.782753	−	0.903345i	0.0361828	−	0.0417571i
$469$	−8.40352	−	7.85665i	−0.388038	−	0.362786i
$470$	26.7007	+	58.4664i	1.23161	+	2.69685i
$471$	5.75668	+	23.7294i	0.265254	+	1.09339i
$472$	0.131033	−	0.124940i	0.00603130	−	0.00575083i
$473$	−2.87069	−	0.274118i	−0.131995	−	0.0126040i
$474$	12.1264	−	4.85467i	0.556983	−	0.222982i
$475$	−22.7656	+	26.2729i	−1.04456	+	1.20548i
$476$	8.22995	−	0.0808201i	0.377219	−	0.00370438i
$477$	−7.16888	−	4.60716i	−0.328240	−	0.210947i
$478$	25.7164	−	20.2236i	1.17624	−	0.925006i
$479$	0.303293	+	6.36690i	0.0138578	+	0.290911i	0.995149	+	0.0983807i	$0.0313663\pi$
$479$	0.303293	+	6.36690i	0.0138578	+	0.290911i	−0.981291	+	0.192530i	$0.938331\pi$
$480$	28.1654	−	5.42844i	1.28557	−	0.247773i
$481$	−3.19740	−	3.04871i	−0.145789	−	0.139009i
$482$	−58.3824			−2.65925
$483$	−8.74144	+	9.19714i	−0.397749	+	0.418484i
$484$	10.3413			0.470058
$485$	−14.9217	−	14.2278i	−0.677557	−	0.646050i
$486$	−1.99674	+	0.384840i	−0.0905740	+	0.0174567i
$487$	1.07028	+	22.4679i	0.0484989	+	1.01812i	0.883665	+	0.468119i	$0.155068\pi$
$487$	1.07028	+	22.4679i	0.0484989	+	1.01812i	−0.835166	+	0.549997i	$0.814629\pi$
$488$	−0.253279	+	0.199181i	−0.0114654	+	0.00901648i
$489$	1.77457	+	1.14045i	0.0802490	+	0.0515729i
$490$	−21.8448	−	45.4495i	−0.986846	−	2.05320i
$491$	−0.845195	+	0.975407i	−0.0381431	+	0.0440195i	−0.774501	−	0.632573i	$-0.781999\pi$
$491$	−0.845195	+	0.975407i	−0.0381431	+	0.0440195i	0.736357	+	0.676593i	$0.236544\pi$
$492$	9.94044	−	3.97955i	0.448150	−	0.179412i
$493$	−9.73766	−	0.929834i	−0.438562	−	0.0418776i
$494$	3.79377	−	3.61735i	0.170690	−	0.162752i
$495$	3.32441	+	13.7034i	0.149421	+	0.615922i
$496$	−7.05830	−	15.4555i	−0.316927	−	0.693974i
$497$	3.56149	−	15.3364i	0.159755	−	0.687933i
$498$	4.67261	−	5.39248i	0.209385	−	0.241643i
$499$	−13.3155	+	1.27148i	−0.596084	+	0.0569191i	−0.388738	−	0.921349i	$-0.627089\pi$
$499$	−13.3155	+	1.27148i	−0.596084	+	0.0569191i	−0.207346	+	0.978268i	$0.566483\pi$
$500$	−17.1428	+	8.83771i	−0.766648	+	0.395234i
$501$	−7.19623	−	2.88094i	−0.321504	−	0.128711i
$502$	−11.6150	−	5.98793i	−0.518401	−	0.267255i
$503$	11.5839	+	13.3686i	0.516502	+	0.596075i	0.952751	−	0.303751i	$-0.0982391\pi$
$503$	11.5839	+	13.3686i	0.516502	+	0.596075i	−0.436250	+	0.899826i	$0.643694\pi$
$504$	−0.481257	−	0.544503i	−0.0214369	−	0.0242541i
$505$	−39.3694			−1.75192
$506$	35.1762	+	16.4153i	1.56377	+	0.729748i
$507$	6.34329	−	10.9869i	0.281715	−	0.487945i
$508$	−6.41364	+	26.4374i	−0.284559	+	1.17297i
$509$	−2.78955	+	8.05989i	−0.123645	+	0.357248i	−0.989788	−	0.142548i	$-0.954471\pi$
$509$	−2.78955	+	8.05989i	−0.123645	+	0.357248i	0.866143	+	0.499796i	$0.166592\pi$
$510$	8.82969	−	5.67450i	0.390985	−	0.251271i
$511$	2.46651	+	1.24107i	0.109112	+	0.0549016i
$512$	−26.9969	−	17.3499i	−1.19311	−	0.766763i
$513$	−4.58370	+	0.437690i	−0.202375	+	0.0193245i
$514$	−2.66976	−	7.71376i	−0.117758	−	0.340239i
$515$	−40.7292	−	32.0298i	−1.79474	−	1.41140i
$516$	0.897253	−	1.26002i	0.0394994	−	0.0554691i
$517$	34.0758	+	10.0056i	1.49865	+	0.440044i
$518$	−33.1138	+	26.5714i	−1.45494	+	1.16748i
$519$	9.75336	+	21.3569i	0.428125	+	0.937463i
$520$	0.505719	−	0.202460i	0.0221773	−	0.00887844i
$521$	4.37069	+	12.6283i	0.191484	+	0.553255i	0.999348	−	0.0361133i	$-0.0114977\pi$
$521$	4.37069	+	12.6283i	0.191484	+	0.553255i	−0.807864	+	0.589369i	$0.799377\pi$
$522$	7.91920	+	11.1210i	0.346614	+	0.486751i
$523$	1.38523	−	29.0795i	0.0605717	−	1.27156i	−0.740118	−	0.672477i	$-0.765230\pi$
$523$	1.38523	−	29.0795i	0.0605717	−	1.27156i	0.800690	−	0.599079i	$-0.204467\pi$
$524$	−4.56978	−	31.7835i	−0.199632	−	1.38847i
$525$	−16.9095	−	10.6339i	−0.737989	−	0.464101i
$526$	16.0485	+	18.5209i	0.699747	+	0.807551i
$527$	−4.82715	−	4.60268i	−0.210274	−	0.200496i
$528$	7.38684	−	12.7944i	0.321471	−	0.556804i
$529$	14.7739	+	17.6276i	0.642345	+	0.766415i
$530$	−30.6942	−	53.1639i	−1.33327	−	2.30929i
$531$	0.632469	−	0.185710i	0.0274468	−	0.00805911i
$532$	−15.2949	−	21.0383i	−0.663118	−	0.912128i
$533$	−2.36191	+	1.51791i	−0.102306	+	0.0657478i
$534$	−21.9016	+	17.2236i	−0.947775	+	0.745339i
$535$	−38.2364	+	19.7122i	−1.65310	+	0.852233i
$536$	−0.692760	−	0.972845i	−0.0299227	−	0.0420205i
$537$	16.0611	+	3.09551i	0.693085	+	0.133581i
$538$	6.09059	−	42.3610i	0.262584	−	1.82631i
$539$	−26.8831	−	7.32331i	−1.15794	−	0.315437i
$540$	−7.25729	−	2.13093i	−0.312304	−	0.0917008i
$541$	−6.32102	−	26.0556i	−0.271762	−	1.12022i	−0.930044	−	0.367447i	$-0.880232\pi$
$541$	−6.32102	−	26.0556i	−0.271762	−	1.12022i	0.658283	−	0.752771i	$-0.271283\pi$
$542$	−10.5419	−	1.00663i	−0.452813	−	0.0432384i
$543$	−11.6733	−	9.17997i	−0.500949	−	0.393950i
$544$	−11.5838	−	2.23260i	−0.496653	−	0.0957221i
$545$	10.6440	−	23.3072i	0.455941	−	0.998371i
$546$	2.38575	+	1.83855i	0.102101	+	0.0786827i
$547$	−3.42516	−	23.8225i	−0.146449	−	1.01858i	−0.921972	−	0.387256i	$-0.873423\pi$
$547$	−3.42516	−	23.8225i	−0.146449	−	1.01858i	0.775523	−	0.631319i	$-0.217486\pi$
$548$	43.6180	+	22.4866i	1.86327	+	0.960581i
$549$	−1.15192	+	0.222014i	−0.0491626	+	0.00947531i
$550$	−14.4071	+	59.3871i	−0.614323	+	2.53227i
$551$	15.4570	+	26.7724i	0.658492	+	1.14054i
$552$	−1.07925	+	0.755235i	−0.0459359	+	0.0321449i
$553$	7.21140	+	15.3890i	0.306660	+	0.654408i
$554$	43.5376	−	12.7838i	1.84973	−	0.543131i
$555$	−9.14351	+	26.4184i	−0.388120	+	1.12140i
$556$	−1.70739	−	35.8425i	−0.0724095	−	1.52006i
$557$	31.1567	+	12.4733i	1.32015	+	0.528509i	0.921423	−	0.388560i	$-0.127027\pi$
$557$	31.1567	+	12.4733i	1.32015	+	0.528509i	0.398728	+	0.917069i	$0.369452\pi$
$558$	−0.442934	+	9.29833i	−0.0187509	+	0.393630i
$559$	−0.168491	+	0.368944i	−0.00712642	+	0.0156047i
$560$	8.53322	+	33.7254i	0.360594	+	1.42516i
$561$	0.825340	−	5.74036i	0.0348459	−	0.242358i
$562$	10.5833	−	14.8622i	0.446431	−	0.626924i
$563$	−13.6674	+	13.0318i	−0.576010	+	0.549225i	−0.921091	−	0.389348i	$-0.872700\pi$
$563$	−13.6674	+	13.0318i	−0.576010	+	0.549225i	0.345080	+	0.938573i	$0.387852\pi$
$564$	−13.7870	+	13.1459i	−0.580538	+	0.553542i
$565$	−36.7054	+	51.5456i	−1.54421	+	2.16854i
$566$	2.94494	−	20.4825i	0.123785	−	0.860945i
$567$	−0.648978	−	2.56492i	−0.0272545	−	0.107717i
$568$	0.678999	−	1.48680i	0.0284901	−	0.0623847i
$569$	−0.123845	+	2.59983i	−0.00519186	+	0.108991i	0.994784	+	0.102006i	$0.0325262\pi$
$569$	−0.123845	+	2.59983i	−0.00519186	+	0.108991i	−0.999976	+	0.00698426i	$0.997777\pi$
$570$	−30.7942	−	12.3282i	−1.28983	−	0.516369i
$571$	−0.583960	−	12.2588i	−0.0244380	−	0.513016i	−0.977589	−	0.210522i	$-0.932484\pi$
$571$	−0.583960	−	12.2588i	−0.0244380	−	0.513016i	0.953151	−	0.302494i	$-0.0978193\pi$
$572$	1.55611	−	4.49608i	0.0650641	−	0.187990i
$573$	−15.1549	+	4.44989i	−0.633107	+	0.185897i
$574$	11.4489	+	24.4318i	0.477869	+	1.01977i
$575$	−22.6156	+	28.2765i	−0.943137	+	1.17921i
$576$	4.52081	+	7.83027i	0.188367	+	0.326261i
$577$	5.59855	−	23.0775i	0.233071	−	0.960731i	−0.728253	−	0.685309i	$-0.759667\pi$
$577$	5.59855	−	23.0775i	0.233071	−	0.960731i	0.961323	−	0.275422i	$-0.0888176\pi$
$578$	29.7059	−	5.72533i	1.23560	−	0.238143i
$579$	1.57347	+	0.811181i	0.0653912	+	0.0337115i
$580$	7.22690	+	50.2642i	0.300081	+	2.08711i
$581$	7.35343	+	5.66682i	0.305072	+	0.235099i
$582$	4.91633	−	10.7653i	0.203789	−	0.446235i
$583$	−33.3066	−	6.41932i	−1.37942	−	0.265861i
$584$	0.225319	+	0.177193i	0.00932375	+	0.00733228i
$585$	1.97430	+	0.188523i	0.0816272	+	0.00779445i
$586$	4.91579	+	20.2632i	0.203069	+	0.837064i
$587$	13.4559	+	3.95100i	0.555383	+	0.163075i	0.547367	−	0.836893i	$-0.315630\pi$
$587$	13.4559	+	3.95100i	0.555383	+	0.163075i	0.00801630	+	0.999968i	$0.497448\pi$
$588$	10.6119	−	10.5240i	0.437629	−	0.434003i
$589$	−2.99980	+	20.8641i	−0.123605	+	0.859690i
$590$	4.66272	+	0.898665i	0.191961	+	0.0369975i
$591$	−15.1773	−	21.3136i	−0.624312	−	0.876724i
$592$	26.0338	−	13.4214i	1.06998	−	0.551615i
$593$	31.7307	−	24.9533i	1.30302	−	1.02471i	0.305660	−	0.952141i	$-0.401123\pi$
$593$	31.7307	−	24.9533i	1.30302	−	1.02471i	0.997363	−	0.0725682i	$-0.0231195\pi$
$594$	−6.80917	+	4.37599i	−0.279384	+	0.179549i
$595$	8.03016	+	11.0456i	0.329204	+	0.452825i
$596$	27.8849	−	8.18776i	1.14221	−	0.335384i
$597$	0.0933457	+	0.161680i	0.00382039	+	0.00661710i
$598$	3.79998	−	3.92026i	0.155393	−	0.160311i
$599$	−15.8794	+	27.5040i	−0.648816	+	1.12378i	0.334590	+	0.942364i	$0.391402\pi$
$599$	−15.8794	+	27.5040i	−0.648816	+	1.12378i	−0.983406	+	0.181418i	$0.941931\pi$
$600$	−1.50082	−	1.43102i	−0.0612705	−	0.0584213i
$601$	−15.5698	−	17.9686i	−0.635107	−	0.732953i	0.343395	−	0.939191i	$-0.388423\pi$
$601$	−15.5698	−	17.9686i	−0.635107	−	0.732953i	−0.978502	+	0.206238i	$0.933878\pi$
$602$	3.29960	+	2.07502i	0.134481	+	0.0845716i
$603$	−0.618809	−	4.30391i	−0.0251998	−	0.175269i
$604$	1.81639	−	38.1308i	0.0739079	−	1.55152i
$605$	9.95298	+	13.9770i	0.404646	+	0.568246i
$606$	−7.39125	−	21.3556i	−0.300249	−	0.867512i
$607$	15.2172	−	6.09204i	0.617646	−	0.247268i	−0.0416733	−	0.999131i	$-0.513269\pi$
$607$	15.2172	−	6.09204i	0.617646	−	0.247268i	0.659319	+	0.751863i	$0.270845\pi$
$608$	15.4877	+	33.9132i	0.628107	+	1.37536i
$609$	−13.8542	+	11.1170i	−0.561401	+	0.450483i
$610$	−8.10858	−	2.38089i	−0.328307	−	0.0963996i
$611$	2.89743	−	4.06887i	0.117217	−	0.164609i
$612$	2.44524	+	1.92296i	0.0988429	+	0.0777309i
$613$	−3.75670	−	10.8543i	−0.151732	−	0.438400i	0.843361	−	0.537348i	$-0.180574\pi$
$613$	−3.75670	−	10.8543i	−0.151732	−	0.438400i	−0.995093	+	0.0989473i	$0.968452\pi$
$614$	65.1344	−	6.21958i	2.62861	−	0.251002i
$615$	14.9458	+	9.60511i	0.602674	+	0.387315i
$616$	−2.58389	−	1.30013i	−0.104108	−	0.0523838i
$617$	−12.3354	+	7.92749i	−0.496605	+	0.319149i	−0.764857	−	0.644200i	$-0.777190\pi$
$617$	−12.3354	+	7.92749i	−0.496605	+	0.319149i	0.268252	+	0.963349i	$0.413554\pi$
$618$	9.72777	−	28.1066i	0.391308	−	1.13061i
$619$	−7.05582	+	29.0845i	−0.283597	+	1.16900i	0.634588	+	0.772851i	$0.281170\pi$
$619$	−7.05582	+	29.0845i	−0.283597	+	1.16900i	−0.918185	+	0.396153i	$0.870345\pi$
$620$	−17.3124	+	29.9860i	−0.695284	+	1.20427i
$621$	−4.75247	+	0.643465i	−0.190710	+	0.0258214i
$622$	−28.8363			−1.15623
$623$	−24.0079	−	27.1630i	−0.961856	−	1.08826i
$624$	−1.36074	−	1.57038i	−0.0544731	−	0.0628654i
$625$	5.10930	+	2.63403i	0.204372	+	0.105361i
$626$	−28.1332	−	11.2629i	−1.12443	−	0.450154i
$627$	−16.2905	+	8.39834i	−0.650580	+	0.335397i
$628$	−51.8974	+	4.95560i	−2.07093	+	0.197750i
$629$	7.52939	−	8.68938i	0.300217	−	0.346468i
$630$	4.31134	−	18.5655i	0.171768	−	0.739665i
$631$	−5.98115	−	13.0969i	−0.238106	−	0.521379i	0.752424	−	0.658679i	$-0.228885\pi$
$631$	−5.98115	−	13.0969i	−0.238106	−	0.521379i	−0.990529	+	0.137301i	$0.956157\pi$
$632$	0.415952	+	1.71458i	0.0165457	+	0.0682023i
$633$	−3.72140	+	3.54835i	−0.147912	+	0.141034i
$634$	63.7012	+	6.08273i	2.52990	+	0.241576i
$635$	−41.9048	+	16.7762i	−1.66294	+	0.665742i
$636$	11.9148	−	13.7504i	0.472451	−	0.545238i
$637$	−2.21004	+	3.23625i	−0.0875650	+	0.128225i
$638$	45.7155	+	29.3796i	1.80989	+	1.16315i
$639$	4.67770	−	3.67859i	0.185047	−	0.145523i
$640$	0.369544	+	7.75769i	0.0146075	+	0.306650i
$641$	12.6208	−	2.43246i	0.498492	−	0.0960764i	0.0661929	−	0.997807i	$-0.478915\pi$
$641$	12.6208	−	2.43246i	0.498492	−	0.0960764i	0.432299	+	0.901730i	$0.357703\pi$
$642$	−17.8713	−	17.0402i	−0.705322	−	0.672523i
$643$	−20.1183			−0.793387			−0.396693	−	0.917951i	$-0.629842\pi$
$643$	−20.1183			−0.793387			−0.396693	+	0.917951i	$0.629842\pi$
$644$	−16.7806	−	21.2682i	−0.661247	−	0.838084i
$645$	2.56657			0.101058
$646$	9.87335	+	9.41422i	0.388462	+	0.370397i
$647$	−25.5608	+	4.92644i	−1.00490	+	0.193678i	−0.665047	−	0.746801i	$-0.731589\pi$
$647$	−25.5608	+	4.92644i	−1.00490	+	0.193678i	−0.339851	+	0.940479i	$0.610377\pi$
$648$	−0.0130692	−	0.274355i	−0.000513405	−	0.0107777i
$649$	2.06241	−	1.62190i	0.0809567	−	0.0636650i
$650$	7.23059	+	4.64682i	0.283607	+	0.182263i
$651$	−12.1111	+	0.118934i	−0.474671	+	0.00466139i
$652$	−2.94937	+	3.40375i	−0.115506	+	0.133301i
$653$	2.21397	−	0.886338i	0.0866392	−	0.0346851i	−0.327938	−	0.944699i	$-0.606354\pi$
$653$	2.21397	−	0.886338i	0.0866392	−	0.0346851i	0.414577	+	0.910014i	$0.363929\pi$
$654$	14.6411	+	1.39806i	0.572513	+	0.0546684i
$655$	38.5596	−	36.7665i	1.50665	−	1.43659i
$656$	−4.38837	−	18.0891i	−0.171337	−	0.706262i
$657$	0.433532	+	0.949304i	0.0169137	+	0.0370359i
$658$	−35.0651	−	32.7832i	−1.36698	−	1.27802i
$659$	26.2078	−	30.2454i	1.02091	−	1.17819i	0.0370410	−	0.999314i	$-0.488207\pi$
$659$	26.2078	−	30.2454i	1.02091	−	1.17819i	0.983871	−	0.178881i	$-0.0572478\pi$
$660$	−29.9701	+	2.86180i	−1.16658	+	0.111395i
$661$	−11.0260	+	5.68431i	−0.428863	+	0.221094i	−0.659123	−	0.752035i	$-0.729072\pi$
$661$	−11.0260	+	5.68431i	−0.428863	+	0.221094i	0.230261	+	0.973129i	$0.426042\pi$
$662$	−41.3938	−	16.5716i	−1.60882	−	0.644073i
$663$	−0.725005	−	0.373766i	−0.0281569	−	0.0145159i
$664$	0.631137	+	0.728371i	0.0244929	+	0.0282663i
$665$	13.7143	−	40.9206i	0.531817	−	1.58683i
$666$	−16.0471			−0.621812
$667$	17.1844	+	27.2291i	0.665383	+	1.05432i
$668$	8.27499	−	14.3327i	0.320169	−	0.554549i
$669$	2.77240	−	11.4280i	0.107187	−	0.441831i
$670$	10.2449	−	29.6006i	0.395794	−	1.14357i
$671$	−3.92820	+	2.52450i	−0.151647	+	0.0974573i
$672$	−17.9069	+	11.7582i	−0.690775	+	0.453581i
$673$	12.7162	+	8.17219i	0.490172	+	0.315015i	0.762275	−	0.647254i	$-0.224083\pi$
$673$	12.7162	+	8.17219i	0.490172	+	0.315015i	−0.272102	+	0.962268i	$0.587719\pi$
$674$	−19.3554	+	1.84822i	−0.745544	+	0.0711908i
$675$	−2.46934	−	7.13468i	−0.0950448	−	0.274614i
$676$	21.2916	+	16.7439i	0.818909	+	0.643997i
$677$	15.1798	−	21.3170i	0.583407	−	0.819281i	−0.412377	−	0.911013i	$-0.635301\pi$
$677$	15.1798	−	21.3170i	0.583407	−	0.819281i	0.995784	+	0.0917328i	$0.0292406\pi$
$678$	−34.8516	−	10.2334i	−1.33847	−	0.393009i
$679$	14.3506	+	5.58224i	0.550725	+	0.214227i
$680$	0.588932	+	1.28958i	0.0225845	+	0.0494532i
$681$	5.80802	−	2.32518i	0.222564	−	0.0891010i
$682$	12.1188	+	35.0151i	0.464054	+	1.34080i
$683$	19.5373	+	27.4363i	0.747574	+	1.04982i	0.996686	+	0.0813457i	$0.0259218\pi$
$683$	19.5373	+	27.4363i	0.747574	+	1.04982i	−0.249112	+	0.968475i	$0.580139\pi$
$684$	0.467780	−	9.81991i	0.0178860	−	0.375474i
$685$	11.5878	+	80.5952i	0.442748	+	3.07938i
$686$	28.0100	+	25.1747i	1.06943	+	0.961176i
$687$	12.8877	+	14.8732i	0.491695	+	0.567446i
$688$	−1.94614	−	1.85564i	−0.0741958	−	0.0707456i
$689$	−2.38538	+	4.13160i	−0.0908757	+	0.157401i
$690$	−32.5541	−	11.5677i	−1.23931	−	0.440374i
$691$	−21.9081	−	37.9459i	−0.833423	−	1.44353i	−0.895308	−	0.445447i	$-0.853045\pi$
$691$	−21.9081	−	37.9459i	−0.833423	−	1.44353i	0.0618852	−	0.998083i	$-0.480289\pi$
$692$	−48.0979	+	14.1228i	−1.82841	+	0.536869i
$693$	−6.19260	−	8.51801i	−0.235237	−	0.323572i
$694$	34.2083	−	21.9843i	1.29853	−	0.834514i
$695$	46.8005	−	36.8044i	1.77525	−	1.39607i
$696$	−1.63906	+	0.844997i	−0.0621286	+	0.0320295i
$697$	−4.23838	−	5.95198i	−0.160540	−	0.225447i
$698$	6.37883	+	1.22942i	0.241442	+	0.0465342i
$699$	−4.05879	+	28.2295i	−0.153518	+	1.06774i
$700$	27.6110	−	32.5043i	1.04360	−	1.22855i
$701$	−32.6924	−	9.59934i	−1.23477	−	0.362562i	−0.401724	−	0.915761i	$-0.631589\pi$
$701$	−32.6924	−	9.59934i	−1.23477	−	0.362562i	−0.833049	+	0.553199i	$0.813407\pi$
$702$	0.268394	+	1.10634i	0.0101299	+	0.0417559i
$703$	−36.1718	−	3.45399i	−1.36425	−	0.130270i
$704$	28.2894	+	22.2470i	1.06620	+	0.838467i
$705$	−31.0370	−	5.98188i	−1.16892	−	0.225291i
$706$	−0.812081	+	1.77821i	−0.0305631	+	0.0669238i
$707$	27.1879	−	11.1954i	1.02251	−	0.421046i
$708$	0.200290	+	1.39305i	0.00752737	+	0.0523540i
$709$	−5.58508	−	2.87931i	−0.209752	−	0.108135i	0.350150	−	0.936694i	$-0.386131\pi$
$709$	−5.58508	−	2.87931i	−0.209752	−	0.108135i	−0.559902	+	0.828559i	$0.689161\pi$
$710$	42.0943	−	8.11300i	1.57977	−	0.304476i
$711$	−1.51439	+	6.24240i	−0.0567941	+	0.234108i
$712$	−1.88174	−	3.25926i	−0.0705210	−	0.122146i
$713$	−2.26651	+	21.8370i	−0.0848813	+	0.817801i
$714$	−4.48400	+	6.42961i	−0.167810	+	0.240622i
$715$	7.57446	−	2.22406i	0.283269	−	0.0831752i
$716$	−11.4221	+	33.0019i	−0.426862	+	1.23334i
$717$	0.765524	+	16.0703i	0.0285890	+	0.600157i
$718$	−67.0226	−	26.8318i	−2.50126	−	1.00135i
$719$	2.23714	−	46.9634i	0.0834314	−	1.75144i	−0.438753	−	0.898608i	$-0.644580\pi$
$719$	2.23714	−	46.9634i	0.0834314	−	1.75144i	0.522185	−	0.852832i	$-0.325117\pi$
$720$	−5.46217	+	11.9605i	−0.203563	+	0.445741i
$721$	37.2352	+	10.5372i	1.38671	+	0.392426i
$722$	0.637215	−	4.43193i	0.0237147	−	0.164939i
$723$	16.6537	−	23.3869i	0.619358	−	0.869767i
$724$	22.9474	−	21.8803i	0.852832	−	0.813173i
$725$	−36.6851	+	34.9792i	−1.36245	+	1.29910i
$726$	−5.71313	+	8.02297i	−0.212034	+	0.297760i
$727$	−3.41819	+	23.7740i	−0.126774	+	0.881730i	0.822832	+	0.568284i	$0.192393\pi$
$727$	−3.41819	+	23.7740i	−0.126774	+	0.881730i	−0.949606	+	0.313446i	$0.898517\pi$
$728$	−0.291669	+	0.283626i	−0.0108100	+	0.0105119i
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$	−0.357720	+	7.50947i	−0.0132398	+	0.277938i
$731$	−0.979961	−	0.392317i	−0.0362452	−	0.0145104i
$732$	−0.119178	−	2.50185i	−0.00440494	−	0.0924710i
$733$	10.3939	−	30.0313i	0.383908	−	1.10923i	−0.573179	−	0.819430i	$-0.694290\pi$
$733$	10.3939	−	30.0313i	0.383908	−	1.10923i	0.957087	−	0.289800i	$-0.0935888\pi$
$734$	−54.7621	+	16.0796i	−2.02130	+	0.593509i
$735$	24.4374	+	4.21397i	0.901389	+	0.155435i
$736$	17.5091	+	34.6596i	0.645393	+	1.27757i
$737$	−8.65371	−	14.9887i	−0.318763	−	0.552115i
$738$	−2.40427	+	9.91052i	−0.0885023	+	0.364811i
$739$	21.8542	−	4.21205i	0.803920	−	0.154943i	0.229292	−	0.973358i	$-0.426359\pi$
$739$	21.8542	−	4.21205i	0.803920	−	0.154943i	0.574628	+	0.818415i	$0.305147\pi$
$740$	−53.0528	−	27.3506i	−1.95026	−	1.00543i
$741$	0.366860	+	2.55157i	0.0134769	+	0.0937342i
$742$	36.3151	+	27.9857i	1.33317	+	1.02739i
$743$	−7.56190	+	16.5583i	−0.277419	+	0.607463i	−0.996134	−	0.0878411i	$-0.972003\pi$
$743$	−7.56190	+	16.5583i	−0.277419	+	0.607463i	0.718715	+	0.695305i	$0.244730\pi$
$744$	−1.23464	−	0.237958i	−0.0452642	−	0.00872396i
$745$	37.9042	+	29.8082i	1.38870	+	1.09209i
$746$	13.4351	+	1.28289i	0.491893	+	0.0469701i
$747$	0.827250	+	3.40997i	0.0302675	+	0.124764i
$748$	11.8806	+	3.48845i	0.434396	+	0.127550i
$749$	20.7999	−	24.4862i	0.760012	−	0.894704i
$750$	2.61420	−	18.1822i	0.0954571	−	0.663919i
$751$	16.3136	+	3.14418i	0.595290	+	0.114733i	0.477992	−	0.878364i	$-0.341365\pi$
$751$	16.3136	+	3.14418i	0.595290	+	0.114733i	0.117298	+	0.993097i	$0.462577\pi$
$752$	19.2093	+	26.9757i	0.700492	+	0.983703i
$753$	5.71185	−	2.94466i	0.208151	−	0.107309i
$754$	6.00794	−	4.72470i	0.218796	−	0.172063i
$755$	53.2847	−	34.2440i	1.93923	−	1.24627i
$756$	5.61775	−	0.592153i	0.204315	−	0.0215364i
$757$	40.2103	−	11.8068i	1.46147	−	0.429126i	0.548154	−	0.836378i	$-0.315331\pi$
$757$	40.2103	−	11.8068i	1.46147	−	0.429126i	0.913316	+	0.407251i	$0.133513\pi$
$758$	−5.34592	−	9.25941i	−0.194173	−	0.336317i
$759$	−16.6097	+	9.40840i	−0.602895	+	0.341503i
$760$	2.24018	−	3.88011i	0.0812600	−	0.140746i
$761$	−22.6595	−	21.6058i	−0.821406	−	0.783209i	0.157501	−	0.987519i	$-0.449656\pi$
$761$	−22.6595	−	21.6058i	−0.821406	−	0.783209i	−0.978906	+	0.204310i	$0.934505\pi$
$762$	−16.9674	−	19.5814i	−0.614662	−	0.709358i
$763$	−0.722789	+	19.1224i	−0.0261667	+	0.692278i
$764$	−4.79927	−	33.3797i	−0.173632	−	1.20763i
$765$	−0.245595	+	5.15567i	−0.00887950	+	0.186404i
$766$	−9.80192	−	13.7649i	−0.354158	−	0.497345i
$767$	−0.120698	−	0.348733i	−0.00435814	−	0.0125920i
$768$	12.6492	−	5.06397i	0.456438	−	0.182730i
$769$	−4.47408	−	9.79686i	−0.161339	−	0.353284i	0.811646	−	0.584149i	$-0.198572\pi$
$769$	−4.47408	−	9.79686i	−0.161339	−	0.353284i	−0.972986	+	0.230865i	$0.925844\pi$
$770$	−11.5335	−	74.9824i	−0.415637	−	2.70218i
$771$	3.85154	+	1.13091i	0.138710	+	0.0407289i
$772$	−2.19240	+	3.07880i	−0.0789063	+	0.110808i
$773$	16.6050	+	13.0583i	0.597242	+	0.469676i	0.870435	−	0.492283i	$-0.163838\pi$
$773$	16.6050	+	13.0583i	0.597242	+	0.469676i	−0.273194	+	0.961959i	$0.588080\pi$
$774$	0.481850	+	1.39221i	0.0173197	+	0.0500421i
$775$	−34.4054	+	3.28532i	−1.23588	+	0.118012i
$776$	1.34478	+	0.864236i	0.0482747	+	0.0310243i
$777$	−1.19819	−	20.8443i	−0.0429849	−	0.747785i
$778$	−38.2438	+	24.5778i	−1.37111	+	0.881157i
$779$	−7.55263	+	21.8219i	−0.270601	+	0.781850i
$780$	−0.998307	+	4.11508i	−0.0357451	+	0.147343i
$781$	11.8434	−	20.5134i	0.423791	−	0.734027i
$782$	10.6615	+	9.39286i	0.381256	+	0.335888i
$783$	−6.71381			−0.239932
$784$	−15.4833	−	20.8637i	−0.552977	−	0.745132i
$785$	−56.6465	−	65.3736i	−2.02180	−	2.33328i
$786$	27.1829	+	14.0138i	0.969582	+	0.499854i
$787$	2.79867	+	1.12042i	0.0997619	+	0.0399386i	0.421007	−	0.907058i	$-0.361677\pi$
$787$	2.79867	+	1.12042i	0.0997619	+	0.0399386i	−0.321245	+	0.946996i	$0.604101\pi$
$788$	49.6545	−	25.5987i	1.76887	−	0.911915i
$789$	−11.9970	+	1.14557i	−0.427104	+	0.0407835i
$790$	−30.3027	+	34.9711i	−1.07812	+	1.24422i
$791$	10.6903	−	46.0344i	0.380103	−	1.63680i
$792$	−0.454165	−	0.994483i	−0.0161381	−	0.0353374i
$793$	0.154836	+	0.638243i	0.00549839	+	0.0226647i
$794$	8.56265	−	8.16447i	0.303877	−	0.289746i
$795$	30.0520	+	2.86962i	1.06584	+	0.101775i
$796$	−0.370047	+	0.148145i	−0.0131160	+	0.00525084i
$797$	−3.64534	+	4.20694i	−0.129124	+	0.149018i	−0.816630	−	0.577162i	$-0.804160\pi$
$797$	−3.64534	+	4.20694i	−0.129124	+	0.149018i	0.687505	+	0.726179i	$0.258706\pi$
$798$	24.7718	−	0.243265i	0.876911	−	0.00861148i
$799$	10.9361	+	7.02820i	0.386891	+	0.248640i
$800$	−48.0519	+	37.7884i	−1.69889	+	1.33602i
$801$	−0.651965	−	13.6864i	−0.0230361	−	0.483587i
$802$	−18.7692	+	3.61747i	−0.662765	+	0.127737i
$803$	3.00638	+	2.86658i	0.106093	+	0.101159i
$804$	9.28365			0.327409
$805$	12.5951	−	43.1498i	0.443917	−	1.52083i
$806$	5.21147			0.183566
$807$	15.2316	+	14.5233i	0.536179	+	0.511246i
$808$	2.99726	−	0.577674i	0.105443	−	0.0203225i
$809$	1.17412	+	24.6478i	0.0412798	+	0.866570i	0.920640	+	0.390413i	$0.127668\pi$
$809$	1.17412	+	24.6478i	0.0412798	+	0.866570i	−0.879360	+	0.476157i	$0.842029\pi$
$810$	5.66257	−	4.45310i	0.198963	−	0.156466i
$811$	32.0908	+	20.6235i	1.12686	+	0.724188i	0.964902	−	0.262610i	$-0.0845832\pi$
$811$	32.0908	+	20.6235i	1.12686	+	0.724188i	0.161957	+	0.986798i	$0.448220\pi$
$812$	−19.2843	−	32.6566i	−0.676747	−	1.14602i
$813$	3.41034	−	3.93574i	0.119606	−	0.138032i
$814$	−59.2983	+	23.7394i	−2.07840	+	0.832067i
$815$	−7.43904	−	0.710342i	−0.260578	−	0.0248822i
$816$	3.91380	−	3.73180i	0.137010	−	0.130639i
$817$	0.786479	+	3.24191i	0.0275154	+	0.113420i
$818$	−11.7781	−	25.7904i	−0.411812	−	0.901742i
$819$	−1.41703	+	0.431237i	−0.0495150	+	0.0150686i
$820$	−24.8402	+	28.6671i	−0.867457	+	1.00110i
$821$	25.0825	−	2.39509i	0.875384	−	0.0835890i	0.352317	−	0.935881i	$-0.385394\pi$
$821$	25.0825	−	2.39509i	0.875384	−	0.0835890i	0.523067	+	0.852292i	$0.324788\pi$
$822$	−41.5427	+	21.4167i	−1.44897	+	0.746995i
$823$	5.32377	+	2.13131i	0.185575	+	0.0742930i	0.462589	−	0.886573i	$-0.346921\pi$
$823$	5.32377	+	2.13131i	0.185575	+	0.0742930i	−0.277014	+	0.960866i	$0.589345\pi$
$824$	3.57076	+	1.84086i	0.124393	+	0.0641293i
$825$	−19.6796	−	22.7115i	−0.685157	−	0.790714i
$826$	−3.47555	+	0.705324i	−0.120930	+	0.0245414i
$827$	45.6769			1.58834			0.794171	−	0.607695i	$-0.207906\pi$
$827$	45.6769			1.58834			0.794171	+	0.607695i	$0.207906\pi$
$828$	0.0841876	−	10.2391i	0.00292572	−	0.355833i
$829$	5.00361	−	8.66650i	0.173782	−	0.301000i	−0.765957	−	0.642892i	$-0.777734\pi$
$829$	5.00361	−	8.66650i	0.173782	−	0.301000i	0.939739	+	0.341892i	$0.111068\pi$
$830$	−5.95935	+	24.5648i	−0.206852	+	0.852656i
$831$	−7.29825	+	21.0869i	−0.253174	+	0.731497i
$832$	4.25830	−	2.73664i	0.147630	−	0.0948761i
$833$	−8.68652	−	5.34440i	−0.300970	−	0.185172i
$834$	28.7506	+	18.4769i	0.995552	+	0.639802i
$835$	27.3360	−	2.61027i	0.946000	−	0.0903321i
$836$	−12.7986	−	36.9792i	−0.442650	−	1.27895i
$837$	−3.59838	−	2.82980i	−0.124378	−	0.0978122i
$838$	−7.92469	+	11.1287i	−0.273754	+	0.384433i
$839$	11.6415	+	3.41825i	0.401908	+	0.118011i	0.476438	−	0.879208i	$-0.341927\pi$
$839$	11.6415	+	3.41825i	0.401908	+	0.118011i	−0.0745301	+	0.997219i	$0.523746\pi$
$840$	2.39927	+	0.933291i	0.0827826	+	0.0322016i
$841$	6.67789	+	14.6225i	0.230272	+	0.504225i
$842$	−40.8404	+	16.3500i	−1.40745	+	0.563460i
$843$	2.93459	+	8.47895i	0.101073	+	0.292031i
$844$	−6.36811	−	8.94276i	−0.219199	−	0.307822i
$845$	−2.13849	+	44.8924i	−0.0735663	+	1.54435i
$846$	−2.58208	−	17.9588i	−0.0887739	−	0.617436i
$847$	−10.8480	−	6.82199i	−0.372741	−	0.234406i
$848$	−20.7127	−	23.9037i	−0.711276	−	0.820856i
$849$	7.36485	+	7.02237i	0.252761	+	0.241007i
$850$	−11.1843	+	19.3719i	−0.383620	+	0.664449i
$851$	−37.7869	−	2.11153i	−1.29532	−	0.0723823i
$852$	6.35277	+	11.0033i	0.217642	+	0.376968i
$853$	1.95711	−	0.574660i	0.0670102	−	0.0196760i	−0.248056	−	0.968746i	$-0.579792\pi$
$853$	1.95711	−	0.574660i	0.0670102	−	0.0196760i	0.315066	+	0.949070i	$0.397973\pi$
$854$	6.27671	−	0.661612i	0.214785	−	0.0226399i
$855$	13.7225	−	8.81894i	0.469301	−	0.301601i
$856$	2.62176	−	2.06177i	0.0896098	−	0.0704699i
$857$	0.385803	−	0.198895i	0.0131788	−	0.00679414i	−0.451625	−	0.892208i	$-0.649155\pi$
$857$	0.385803	−	0.198895i	0.0131788	−	0.00679414i	0.464803	+	0.885414i	$0.346125\pi$
$858$	2.62846	+	3.69115i	0.0897341	+	0.126014i
$859$	45.5159	+	8.77247i	1.55298	+	0.299313i	0.892332	−	0.451381i	$-0.149068\pi$
$859$	45.5159	+	8.77247i	1.55298	+	0.299313i	0.660651	+	0.750693i	$0.270280\pi$
$860$	−0.779857	+	5.42403i	−0.0265929	+	0.184958i
$861$	−13.0528	−	2.38302i	−0.444837	−	0.0812131i
$862$	−52.6541	−	15.4606i	−1.79341	−	0.526592i
$863$	−0.557873	−	2.29958i	−0.0189902	−	0.0782787i	0.961528	−	0.274707i	$-0.0885809\pi$
$863$	−0.557873	−	2.29958i	−0.0189902	−	0.0782787i	−0.980518	+	0.196428i	$0.937066\pi$
$864$	−8.06019	−	0.769655i	−0.274213	−	0.0261842i
$865$	−65.3799	−	51.4153i	−2.22298	−	1.74817i
$866$	−63.3765	−	12.2148i	−2.15362	−	0.415076i
$867$	−6.18020	+	13.5328i	−0.209891	+	0.459597i
$868$	3.42864	−	25.6310i	0.116376	−	0.869973i
$869$	3.63870	+	25.3077i	0.123434	+	0.858505i
$870$	−42.9885	−	22.1621i	−1.45745	−	0.751366i
$871$	−2.39028	+	0.460689i	−0.0809917	+	0.0156099i
$872$	−0.468358	+	1.93060i	−0.0158606	+	0.0653783i
$873$	2.90996	+	5.04020i	0.0984873	+	0.170585i
$874$	4.63586	−	44.6649i	0.156810	−	1.51081i
$875$	23.8128	+	2.03809i	0.805021	+	0.0689001i
$876$	−2.13793	+	0.627753i	−0.0722340	+	0.0212098i
$877$	1.04851	−	3.02948i	0.0354058	−	0.102298i	−0.925913	−	0.377738i	$-0.876702\pi$
$877$	1.04851	−	3.02948i	0.0354058	−	0.102298i	0.961318	+	0.275439i	$0.0888233\pi$
$878$	−0.113206	−	2.37649i	−0.00382052	−	0.0802026i
$879$	−9.51928	−	3.81094i	−0.321077	−	0.128540i
$880$	−2.49030	+	52.2777i	−0.0839479	+	1.76228i
$881$	−12.8144	+	28.0596i	−0.431727	+	0.945350i	0.561316	+	0.827601i	$0.310295\pi$
$881$	−12.8144	+	28.0596i	−0.431727	+	0.945350i	−0.993043	+	0.117749i	$0.962432\pi$
$882$	2.30208	+	14.0470i	0.0775149	+	0.472988i
$883$	−0.721723	+	5.01969i	−0.0242879	+	0.168926i	−0.998355	−	0.0573327i	$-0.981740\pi$
$883$	−0.721723	+	5.01969i	−0.0242879	+	0.168926i	0.974067	+	0.226259i	$0.0726495\pi$
$884$	1.01019	−	1.41861i	0.0339764	−	0.0477131i
$885$	−1.69004	+	1.61145i	−0.0568100	+	0.0541683i
$886$	−19.2638	+	18.3680i	−0.647180	+	0.617085i
$887$	−7.69172	+	10.8015i	−0.258263	+	0.362679i	−0.923266	−	0.384161i	$-0.874491\pi$
$887$	−7.69172	+	10.8015i	−0.258263	+	0.362679i	0.665003	+	0.746840i	$0.268430\pi$
$888$	0.308468	−	2.14544i	0.0103515	−	0.0719964i
$889$	24.1682	−	23.5018i	0.810577	−	0.788224i
$890$	41.0041	−	89.7864i	1.37446	−	3.00965i
$891$	0.189395	−	3.97588i	0.00634496	−	0.133197i
$892$	23.3088	+	9.33143i	0.780436	+	0.312440i
$893$	−1.95482	−	41.0368i	−0.0654157	−	1.37324i
$894$	−9.05305	+	26.1571i	−0.302779	+	0.874823i
$895$	−55.5976	+	16.3249i	−1.85842	+	0.545682i
$896$	−2.46124	−	5.25226i	−0.0822243	−	0.175466i
$897$	0.486426	+	2.64046i	0.0162413	+	0.0881625i
$898$	26.2211	+	45.4163i	0.875010	+	1.51556i
$899$	−7.24590	+	29.8680i	−0.241664	+	0.996154i
$900$	15.8283	−	3.05066i	0.527611	−	0.101689i
$901$	−11.0358	−	5.68933i	−0.367655	−	0.189539i
$902$	5.77684	+	40.1788i	0.192348	+	1.33781i
$903$	−1.77243	+	0.729849i	−0.0589828	+	0.0242879i
$904$	2.03811	−	4.46284i	0.0677865	−	0.148432i
$905$	51.6585	+	9.95636i	1.71719	+	0.330960i
$906$	28.5791	+	22.4749i	0.949477	+	0.746677i
$907$	−6.39279	−	0.610437i	−0.212269	−	0.0202692i	−0.0116202	−	0.999932i	$-0.503699\pi$
$907$	−6.39279	−	0.610437i	−0.212269	−	0.0202692i	−0.200649	+	0.979663i	$0.564305\pi$
$908$	3.14911	+	12.9808i	0.104507	+	0.430784i
$909$	10.6630	+	3.13094i	0.353670	+	0.103847i
$910$	−10.4967	−	1.91637i	−0.347964	−	0.0635272i
$911$	−5.20244	+	36.1837i	−0.172364	+	1.19882i	0.701507	+	0.712663i	$0.252511\pi$
$911$	−5.20244	+	36.1837i	−0.172364	+	1.19882i	−0.873871	+	0.486158i	$0.838398\pi$
$912$	−16.7815	−	3.23436i	−0.555690	−	0.107100i
$913$	8.10150	+	11.3770i	0.268120	+	0.376523i
$914$	−22.4272	+	11.5620i	−0.741827	+	0.382438i
$915$	3.26673	−	2.56899i	0.107995	−	0.0849280i
$916$	−35.3480	+	22.7168i	−1.16793	+	0.750583i
$917$	−16.1734	+	36.3555i	−0.534094	+	1.20056i
$918$	−2.84276	+	0.834709i	−0.0938250	+	0.0275495i
$919$	−8.94244	−	15.4888i	−0.294984	−	0.510927i	0.679997	−	0.733215i	$-0.261981\pi$
$919$	−8.94244	−	15.4888i	−0.294984	−	0.510927i	−0.974981	+	0.222287i	$0.928648\pi$
$920$	2.17234	−	4.13002i	0.0716199	−	0.136163i
$921$	−16.0883	+	27.8657i	−0.530127	+	0.918207i
$922$	−14.3908	−	13.7216i	−0.473936	−	0.451897i
$923$	−2.18169	−	2.51780i	−0.0718112	−	0.0828745i
$924$	19.8831	−	10.4988i	0.654105	−	0.345387i
$925$	−8.47904	−	58.9731i	−0.278789	−	1.93902i
$926$	−0.0506471	+	1.06321i	−0.00166437	+	0.0349393i
$927$	8.48408	+	11.9142i	0.278654	+	0.391314i
$928$	17.7796	+	51.3709i	0.583645	+	1.68633i
$929$	−15.7629	+	6.31051i	−0.517164	+	0.207041i	−0.615536	−	0.788108i	$-0.711061\pi$
$929$	−15.7629	+	6.31051i	−0.517164	+	0.207041i	0.0983724	+	0.995150i	$0.468636\pi$
$930$	−13.6993	−	29.9974i	−0.449219	−	0.983652i
$931$	2.16563	+	32.1590i	0.0709756	+	1.05397i
$932$	−58.4253	−	17.1552i	−1.91378	−	0.561937i
$933$	8.22561	−	11.5513i	0.269294	−	0.378171i
$934$	56.1301	+	44.1412i	1.83663	+	1.44434i
$935$	6.71956	+	19.4149i	0.219753	+	0.634935i
$936$	−0.153073	+	0.0146167i	−0.00500334	+	0.000477761i
$937$	−39.1355	−	25.1509i	−1.27850	−	0.821644i	−0.287800	−	0.957690i	$-0.592924\pi$
$937$	−39.1355	−	25.1509i	−1.27850	−	0.821644i	−0.990702	+	0.136047i	$0.956560\pi$
$938$	1.34252	+	23.3550i	0.0438348	+	0.762569i
$939$	12.5368	−	8.05688i	0.409122	−	0.262926i
$940$	22.0724	−	63.7740i	0.719922	−	2.08008i
$941$	−6.47477	+	26.6894i	−0.211071	+	0.870048i	0.763470	+	0.645843i	$0.223494\pi$
$941$	−6.47477	+	26.6894i	−0.211071	+	0.870048i	−0.974542	+	0.224206i	$0.928021\pi$
$942$	24.8265	−	43.0007i	0.808891	−	1.40104i
$943$	−6.96552	+	23.0205i	−0.226828	+	0.749650i
$944$	2.44658			0.0796295
$945$	6.20714	+	7.02288i	0.201918	+	0.228454i
$946$	3.84015	+	4.43177i	0.124854	+	0.144089i
$947$	9.47934	+	4.88694i	0.308037	+	0.158804i	0.605313	−	0.795987i	$-0.293048\pi$
$947$	9.47934	+	4.88694i	0.308037	+	0.158804i	−0.297276	+	0.954792i	$0.596078\pi$
$948$	−12.7322	−	5.09719i	−0.413522	−	0.165549i
$949$	0.519307	−	0.267721i	0.0168574	−	0.00869060i
$950$	70.3720	−	6.71971i	2.28317	−	0.218016i
$951$	−20.6075	+	23.7824i	−0.668246	+	0.771196i
$952$	−0.773423	−	0.723092i	−0.0250668	−	0.0234355i
$953$	6.48305	+	14.1959i	0.210007	+	0.459850i	0.985097	−	0.172000i	$-0.0550230\pi$
$953$	6.48305	+	14.1959i	0.210007	+	0.459850i	−0.775090	+	0.631850i	$0.782296\pi$
$954$	4.08539	+	16.8402i	0.132270	+	0.545222i
$955$	40.4960	−	38.6129i	1.31042	−	1.24948i
$956$	−34.1947	−	3.26519i	−1.10593	−	0.105604i
$957$	−24.8093	+	9.93216i	−0.801972	+	0.321061i
$958$	8.48810	−	9.79579i	0.274238	−	0.316488i
$959$	−30.9211	−	52.3626i	−0.998494	−	1.69088i
$960$	−26.9460	−	17.3171i	−0.869677	−	0.558908i
$961$	7.89502	−	6.20871i	0.254678	−	0.200281i
$962$	0.427465	+	8.97360i	0.0137820	+	0.289321i
$963$	11.9238	−	2.29812i	0.384239	−	0.0740560i
$964$	44.3641	+	42.3011i	1.42887	+	1.36243i
$965$	−6.27131			−0.201880
$966$	25.7708	−	1.26889i	0.829163	−	0.0408260i
$967$	10.7226			0.344815			0.172408	−	0.985026i	$-0.444845\pi$
$967$	10.7226			0.344815			0.172408	+	0.985026i	$0.444845\pi$
$968$	−0.962823	−	0.918050i	−0.0309463	−	0.0295073i
$969$	−6.58755	+	1.26965i	−0.211623	+	0.0407869i
$970$	1.99490	+	41.8781i	0.0640524	+	1.34463i
$971$	−21.4372	+	16.8584i	−0.687953	+	0.541012i	−0.899807	−	0.436289i	$-0.856293\pi$
$971$	−21.4372	+	16.8584i	−0.687953	+	0.541012i	0.211853	+	0.977301i	$0.432050\pi$
$972$	1.79614	+	1.15431i	0.0576111	+	0.0370244i
$973$	−21.8538	+	38.7251i	−0.700599	+	1.24147i
$974$	29.9533	−	34.5679i	0.959766	−	1.10763i
$975$	−3.92397	+	1.57092i	−0.125668	+	0.0503097i
$976$	−4.33444	−	0.413888i	−0.138742	−	0.0132482i
$977$	5.37698	−	5.12694i	0.172025	−	0.164025i	−0.599176	−	0.800617i	$-0.704505\pi$
$977$	5.37698	−	5.12694i	0.172025	−	0.164025i	0.771201	+	0.636592i	$0.219656\pi$
$978$	−1.01129	−	4.16861i	−0.0323376	−	0.133297i
$979$	−22.6564	−	49.6106i	−0.724101	−	1.58556i
$980$	−16.3309	+	50.3642i	−0.521672	+	1.60883i
$981$	−4.73645	+	5.46616i	−0.151223	+	0.174521i
$982$	2.61263	−	0.249476i	0.0833725	−	0.00796111i
$983$	−11.0095	+	5.67577i	−0.351147	+	0.181029i	−0.624771	−	0.780808i	$-0.714808\pi$
$983$	−11.0095	+	5.67577i	−0.351147	+	0.181029i	0.273624	+	0.961837i	$0.411778\pi$
$984$	−1.27879	−	0.511950i	−0.0407663	−	0.0163204i
$985$	82.3885	+	42.4742i	2.62512	+	1.35334i
$986$	13.0261	+	15.0330i	0.414837	+	0.478748i
$987$	23.1347	−	4.69492i	0.736386	−	0.149441i
$988$	−5.50380			−0.175099
$989$	0.951445	+	3.34172i	0.0302542	+	0.106261i
$990$	14.3370	−	24.8324i	0.455659	−	0.789225i
$991$	7.46336	−	30.7644i	0.237081	−	0.977263i	−0.721493	−	0.692421i	$-0.756544\pi$
$991$	7.46336	−	30.7644i	0.237081	−	0.977263i	0.958575	−	0.284841i	$-0.0919409\pi$
$992$	−12.1230	+	35.0271i	−0.384905	+	1.11211i
$993$	18.4459	−	11.8545i	0.585364	−	0.376190i
$994$	−26.7626	+	17.5730i	−0.848857	+	0.557381i
$995$	−0.556381	−	0.357564i	−0.0176384	−	0.0113355i
$996$	−7.45779	+	0.712133i	−0.236309	+	0.0225648i
$997$	−0.887356	−	2.56385i	−0.0281028	−	0.0811978i	0.930077	−	0.367365i	$-0.119740\pi$
$997$	−0.887356	−	2.56385i	−0.0281028	−	0.0811978i	−0.958180	+	0.286167i	$0.907619\pi$
$998$	21.3807	+	16.8140i	0.676794	+	0.532237i
$999$	4.57746	−	6.42815i	0.144825	−	0.203378i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.y.b.193.3	✓	320
7.2	even	3	inner	483.2.y.b.331.3	yes	320
23.18	even	11	inner	483.2.y.b.340.3	yes	320
161.156	even	33	inner	483.2.y.b.478.3	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.y.b.193.3	✓	320	1.1	even	1	trivial
483.2.y.b.331.3	yes	320	7.2	even	3	inner
483.2.y.b.340.3	yes	320	23.18	even	11	inner
483.2.y.b.478.3	yes	320	161.156	even	33	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.47170 - 1.40327i) q^{2} +(0.981929 - 0.189251i) q^{3} +(0.101591 + 2.13265i) q^{4} +(-2.78466 + 2.18988i) q^{5} +(-1.71068 - 1.09939i) q^{6} +(1.30031 - 2.30417i) q^{7} +(0.179868 - 0.207579i) q^{8} +(0.928368 - 0.371662i) q^{9} +O(q^{10})\)	\(q+(-1.47170 - 1.40327i) q^{2} +(0.981929 - 0.189251i) q^{3} +(0.101591 + 2.13265i) q^{4} +(-2.78466 + 2.18988i) q^{5} +(-1.71068 - 1.09939i) q^{6} +(1.30031 - 2.30417i) q^{7} +(0.179868 - 0.207579i) q^{8} +(0.928368 - 0.371662i) q^{9} +(7.17119 + 0.684765i) q^{10} +(2.88075 - 2.74679i) q^{11} +(0.503362 + 2.07489i) q^{12} +(-0.232566 - 0.509248i) q^{13} +(-5.14704 + 1.56637i) q^{14} +(-2.31990 + 2.67731i) q^{15} +(3.69481 - 0.352811i) q^{16} +(1.29502 - 0.667632i) q^{17} +(-1.88782 - 0.755771i) q^{18} +(-4.09269 - 2.10993i) q^{19} +(-4.95315 - 5.71625i) q^{20} +(0.840747 - 2.50861i) q^{21} -8.09408 q^{22} +(-4.34591 - 2.02806i) q^{23} +(0.137333 - 0.237868i) q^{24} +(1.77996 - 7.33710i) q^{25} +(-0.372343 + 1.07581i) q^{26} +(0.841254 - 0.540641i) q^{27} +(5.04609 + 2.53903i) q^{28} +(-5.64801 - 3.62976i) q^{29} +(7.17119 - 0.684765i) q^{30} +(-1.49725 - 4.32601i) q^{31} +(-6.36455 - 5.00514i) q^{32} +(2.30885 - 3.24233i) q^{33} +(-2.84276 - 0.834709i) q^{34} +(1.42493 + 9.26386i) q^{35} +(0.886941 + 1.94213i) q^{36} +(7.32613 - 2.93294i) q^{37} +(3.06243 + 8.84832i) q^{38} +(-0.324739 - 0.456031i) q^{39} +(-0.0462986 + 0.971928i) q^{40} +(-0.713712 - 4.96398i) q^{41} +(-4.75759 + 2.51215i) q^{42} +(-0.474440 - 0.547532i) q^{43} +(6.15060 + 5.86458i) q^{44} +(-1.77129 + 3.06797i) q^{45} +(3.54999 + 9.08318i) q^{46} +(4.46117 + 7.72697i) q^{47} +(3.56127 - 1.04568i) q^{48} +(-3.61838 - 5.99227i) q^{49} +(-12.9155 + 8.30028i) q^{50} +(1.14527 - 0.900652i) q^{51} +(1.06242 - 0.547717i) q^{52} +(-4.94305 - 6.94154i) q^{53} +(-1.99674 - 0.384840i) q^{54} +(-2.00677 + 13.9574i) q^{55} +(-0.244412 - 0.684365i) q^{56} +(-4.41803 - 1.29725i) q^{57} +(3.21869 + 13.2676i) q^{58} +(0.656185 + 0.0626581i) q^{59} +(-5.94545 - 4.67555i) q^{60} +(-1.15192 - 0.222014i) q^{61} +(-3.86704 + 8.46765i) q^{62} +(0.350795 - 2.62239i) q^{63} +(1.28676 + 8.94959i) q^{64} +(1.76281 + 0.908791i) q^{65} +(-7.94781 + 1.53181i) q^{66} +(1.02512 - 4.22560i) q^{67} +(1.55539 + 2.69401i) q^{68} +(-4.65119 - 1.16894i) q^{69} +(10.9026 - 15.6332i) q^{70} +(5.70982 - 1.67656i) q^{71} +(0.0898346 - 0.259560i) q^{72} +(0.0496571 + 1.04243i) q^{73} +(-14.8976 - 5.96410i) q^{74} +(0.359240 - 7.54137i) q^{75} +(4.08396 - 8.94263i) q^{76} +(-2.58319 - 10.2094i) q^{77} +(-0.162015 + 1.12684i) q^{78} +(-3.72598 + 5.23240i) q^{79} +(-9.51617 + 9.07365i) q^{80} +(0.723734 - 0.690079i) q^{81} +(-5.91541 + 8.30704i) q^{82} +(-0.499366 + 3.47317i) q^{83} +(5.43542 + 1.53817i) q^{84} +(-2.14417 + 4.69508i) q^{85} +(-0.0700996 + 1.47157i) q^{86} +(-6.23288 - 2.49527i) q^{87} +(-0.0520204 - 1.09204i) q^{88} +(4.48147 - 12.9484i) q^{89} +(6.91200 - 2.02955i) q^{90} +(-1.47580 - 0.126311i) q^{91} +(3.88365 - 9.47436i) q^{92} +(-2.28889 - 3.96448i) q^{93} +(4.27748 - 17.6320i) q^{94} +(16.0172 - 3.08707i) q^{95} +(-7.19677 - 3.71019i) q^{96} +(0.828262 + 5.76069i) q^{97} +(-3.08358 + 13.8964i) q^{98} +(1.65351 - 3.62069i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 2 q^{2} + 16 q^{3} + 18 q^{4} - 2 q^{5} + 18 q^{6} + 2 q^{7} - 12 q^{8} + 16 q^{9}+O(q^{10}) \) 320 * q + 2 * q^2 + 16 * q^3 + 18 * q^4 - 2 * q^5 + 18 * q^6 + 2 * q^7 - 12 * q^8 + 16 * q^9	\( 320 q + 2 q^{2} + 16 q^{3} + 18 q^{4} - 2 q^{5} + 18 q^{6} + 2 q^{7} - 12 q^{8} + 16 q^{9} + 2 q^{11} + 18 q^{12} + 18 q^{14} - 18 q^{15} - 8 q^{16} + 4 q^{17} + 2 q^{18} + 8 q^{19} - 162 q^{20} - 4 q^{21} + 144 q^{22} - 26 q^{23} + 6 q^{24} - 8 q^{25} - 14 q^{26} - 32 q^{27} + 86 q^{28} - 74 q^{29} - 56 q^{31} - 28 q^{32} + 13 q^{33} + 40 q^{34} - 32 q^{35} - 14 q^{36} + 2 q^{37} - 39 q^{38} - 52 q^{40} + 60 q^{41} - 61 q^{42} + 16 q^{43} - 75 q^{44} - 2 q^{45} - 4 q^{46} - 40 q^{47} - 28 q^{48} - 100 q^{49} + 146 q^{50} - 18 q^{51} - 18 q^{52} + 34 q^{53} + 2 q^{54} + 36 q^{55} - 102 q^{56} + 28 q^{57} - 17 q^{58} - 102 q^{59} - 18 q^{60} - 18 q^{61} - 88 q^{62} + 2 q^{63} - 252 q^{64} - 78 q^{65} + 16 q^{66} + 12 q^{67} + 34 q^{68} + 8 q^{69} + 264 q^{70} + 160 q^{71} + 6 q^{72} - 8 q^{73} + 70 q^{74} + 14 q^{75} - 40 q^{76} - 90 q^{77} - 16 q^{78} + 26 q^{79} - 103 q^{80} + 16 q^{81} - 30 q^{82} - 80 q^{83} - 52 q^{84} - 128 q^{85} + 90 q^{86} + 4 q^{87} - 293 q^{88} - 36 q^{89} + 16 q^{91} - 174 q^{92} + 32 q^{93} + 57 q^{94} - 85 q^{95} - 50 q^{96} - 8 q^{97} - 193 q^{98} - 26 q^{99}+O(q^{100}) \) 320 * q + 2 * q^2 + 16 * q^3 + 18 * q^4 - 2 * q^5 + 18 * q^6 + 2 * q^7 - 12 * q^8 + 16 * q^9 + 2 * q^11 + 18 * q^12 + 18 * q^14 - 18 * q^15 - 8 * q^16 + 4 * q^17 + 2 * q^18 + 8 * q^19 - 162 * q^20 - 4 * q^21 + 144 * q^22 - 26 * q^23 + 6 * q^24 - 8 * q^25 - 14 * q^26 - 32 * q^27 + 86 * q^28 - 74 * q^29 - 56 * q^31 - 28 * q^32 + 13 * q^33 + 40 * q^34 - 32 * q^35 - 14 * q^36 + 2 * q^37 - 39 * q^38 - 52 * q^40 + 60 * q^41 - 61 * q^42 + 16 * q^43 - 75 * q^44 - 2 * q^45 - 4 * q^46 - 40 * q^47 - 28 * q^48 - 100 * q^49 + 146 * q^50 - 18 * q^51 - 18 * q^52 + 34 * q^53 + 2 * q^54 + 36 * q^55 - 102 * q^56 + 28 * q^57 - 17 * q^58 - 102 * q^59 - 18 * q^60 - 18 * q^61 - 88 * q^62 + 2 * q^63 - 252 * q^64 - 78 * q^65 + 16 * q^66 + 12 * q^67 + 34 * q^68 + 8 * q^69 + 264 * q^70 + 160 * q^71 + 6 * q^72 - 8 * q^73 + 70 * q^74 + 14 * q^75 - 40 * q^76 - 90 * q^77 - 16 * q^78 + 26 * q^79 - 103 * q^80 + 16 * q^81 - 30 * q^82 - 80 * q^83 - 52 * q^84 - 128 * q^85 + 90 * q^86 + 4 * q^87 - 293 * q^88 - 36 * q^89 + 16 * q^91 - 174 * q^92 + 32 * q^93 + 57 * q^94 - 85 * q^95 - 50 * q^96 - 8 * q^97 - 193 * q^98 - 26 * q^99

Introduction

L-functions

Modular forms

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