LMFDB - Embedded newform 230.2.l.a.83.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(7,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([11, 38]))

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

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

chi := DirichletCharacter("230.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, 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:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			83.3
Character	$\chi$	$=$	230.83
Dual form			230.2.l.a.97.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.479249 + 0.877679i) q^{2} +(-0.0925997 + 1.29471i) q^{3} +(-0.540641 - 0.841254i) q^{4} +(1.32676 - 1.79992i) q^{5} +(-1.09196 - 0.701763i) q^{6} +(2.84106 - 1.05966i) q^{7} +(0.997452 - 0.0713392i) q^{8} +(1.30176 + 0.187165i) q^{9} +O(q^{10})$	\(q+(-0.479249 + 0.877679i) q^{2} +(-0.0925997 + 1.29471i) q^{3} +(-0.540641 - 0.841254i) q^{4} +(1.32676 - 1.79992i) q^{5} +(-1.09196 - 0.701763i) q^{6} +(2.84106 - 1.05966i) q^{7} +(0.997452 - 0.0713392i) q^{8} +(1.30176 + 0.187165i) q^{9} +(0.943903 + 2.02708i) q^{10} +(-0.916945 + 3.12283i) q^{11} +(1.13924 - 0.622075i) q^{12} +(0.938652 - 2.51662i) q^{13} +(-0.431533 + 3.00138i) q^{14} +(2.20752 + 1.88444i) q^{15} +(-0.415415 + 0.909632i) q^{16} +(0.118421 + 0.544374i) q^{17} +(-0.788137 + 1.05283i) q^{18} +(-7.04270 + 4.52607i) q^{19} +(-2.23149 - 0.143031i) q^{20} +(1.10887 + 3.77648i) q^{21} +(-2.30140 - 2.30140i) q^{22} +(4.21877 - 2.28078i) q^{23} +1.29802i q^{24} +(-1.47942 - 4.77612i) q^{25} +(1.75894 + 2.02992i) q^{26} +(-1.19061 + 5.47314i) q^{27} +(-2.42744 - 1.81716i) q^{28} +(-3.68158 + 5.72866i) q^{29} +(-2.71189 + 1.03438i) q^{30} +(5.42542 - 6.26127i) q^{31} +(-0.599278 - 0.800541i) q^{32} +(-3.95826 - 1.47635i) q^{33} +(-0.534539 - 0.156955i) q^{34} +(1.86210 - 6.51959i) q^{35} +(-0.546331 - 1.19630i) q^{36} +(6.02087 - 4.50717i) q^{37} +(-0.597229 - 8.35035i) q^{38} +(3.17138 + 1.44832i) q^{39} +(1.19497 - 1.88998i) q^{40} +(0.0516552 + 0.359270i) q^{41} +(-3.84596 - 0.836638i) q^{42} +(1.30617 + 0.0934194i) q^{43} +(3.12283 - 0.916945i) q^{44} +(2.06400 - 2.09474i) q^{45} +(-0.0200519 + 4.79579i) q^{46} +(-7.80610 + 7.80610i) q^{47} +(-1.13924 - 0.622075i) q^{48} +(1.65849 - 1.43709i) q^{49} +(4.90091 + 0.990495i) q^{50} +(-0.715774 + 0.102913i) q^{51} +(-2.62459 + 0.570945i) q^{52} +(-3.43834 - 9.21854i) q^{53} +(-4.23306 - 3.66797i) q^{54} +(4.40427 + 5.79367i) q^{55} +(2.75823 - 1.25964i) q^{56} +(-5.20781 - 9.53739i) q^{57} +(-3.26353 - 5.97670i) q^{58} +(-0.549862 + 0.251113i) q^{59} +(0.391819 - 2.87589i) q^{60} +(-5.69461 - 4.93441i) q^{61} +(2.89526 + 7.76249i) q^{62} +(3.89670 - 0.847676i) q^{63} +(0.989821 - 0.142315i) q^{64} +(-3.28435 - 5.02845i) q^{65} +(3.19275 - 2.76654i) q^{66} +(-4.15784 - 2.27035i) q^{67} +(0.393933 - 0.393933i) q^{68} +(2.56230 + 5.67330i) q^{69} +(4.82970 + 4.75883i) q^{70} +(-6.48944 + 1.90547i) q^{71} +(1.31179 + 0.0938213i) q^{72} +(-14.4254 - 3.13806i) q^{73} +(1.07035 + 7.44445i) q^{74} +(6.32070 - 1.47316i) q^{75} +(7.61515 + 3.47772i) q^{76} +(0.704042 + 9.84379i) q^{77} +(-2.79105 + 2.08935i) q^{78} +(-4.19131 - 9.17769i) q^{79} +(1.08611 + 1.95458i) q^{80} +(-3.19028 - 0.936750i) q^{81} +(-0.340079 - 0.126843i) q^{82} +(6.24597 + 8.34364i) q^{83} +(2.57747 - 2.97456i) q^{84} +(1.13695 + 0.509104i) q^{85} +(-0.707975 + 1.10163i) q^{86} +(-7.07605 - 5.29706i) q^{87} +(-0.691829 + 3.18029i) q^{88} +(0.294495 + 0.339866i) q^{89} +(0.849336 + 2.81543i) q^{90} -8.14453i q^{91} +(-4.19955 - 2.31598i) q^{92} +(7.60415 + 7.60415i) q^{93} +(-3.11018 - 10.5923i) q^{94} +(-1.19741 + 18.6813i) q^{95} +(1.09196 - 0.701763i) q^{96} +(-1.66526 + 2.22452i) q^{97} +(0.466475 + 2.14435i) q^{98} +(-1.77812 + 3.89355i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 8 q^{6}+O(q^{10}) $ 240 * q - 8 * q^3 - 8 * q^6	$ 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46} - 80 q^{47} + 8 q^{48} + 8 q^{50} + 16 q^{52} - 44 q^{56} - 88 q^{57} - 176 q^{61} - 32 q^{62} - 176 q^{66} + 24 q^{70} - 336 q^{71} + 16 q^{72} - 88 q^{73} - 36 q^{75} - 24 q^{77} + 40 q^{78} - 136 q^{81} + 40 q^{82} - 100 q^{85} - 44 q^{86} + 40 q^{87} + 8 q^{92} + 56 q^{93} + 52 q^{95} + 8 q^{96} + 132 q^{97} + 24 q^{98}+O(q^{100}) $ 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{21}{22}\right)$

Coefficient data

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

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

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

$2$	−0.479249	+	0.877679i	−0.338880	+	0.620613i
$2$	−0.479249	+	0.877679i	−0.338880	+	0.620613i
$3$	−0.0925997	+	1.29471i	−0.0534625	+	0.747503i	0.898050	+	0.439893i	$0.144984\pi$
$3$	−0.0925997	+	1.29471i	−0.0534625	+	0.747503i	−0.951513	+	0.307610i	$0.900471\pi$
$4$	−0.540641	−	0.841254i	−0.270320	−	0.420627i
$5$	1.32676	−	1.79992i	0.593345	−	0.804948i
$5$	1.32676	−	1.79992i	0.593345	−	0.804948i
$6$	−1.09196	−	0.701763i	−0.445792	−	0.286493i
$7$	2.84106	−	1.05966i	1.07382	−	0.400514i	0.250514	−	0.968113i	$-0.419400\pi$
$7$	2.84106	−	1.05966i	1.07382	−	0.400514i	0.823305	+	0.567599i	$0.192128\pi$
$8$	0.997452	−	0.0713392i	0.352653	−	0.0252222i
$9$	1.30176	+	0.187165i	0.433919	+	0.0623882i
$10$	0.943903	+	2.02708i	0.298488	+	0.641018i
$11$	−0.916945	+	3.12283i	−0.276469	+	0.941568i	0.697821	+	0.716272i	$0.254153\pi$
$11$	−0.916945	+	3.12283i	−0.276469	+	0.941568i	−0.974290	+	0.225296i	$0.927665\pi$
$12$	1.13924	−	0.622075i	0.328872	−	0.179578i
$13$	0.938652	−	2.51662i	0.260335	−	0.697986i	−0.739360	−	0.673310i	$-0.764872\pi$
$13$	0.938652	−	2.51662i	0.260335	−	0.697986i	0.999696	−	0.0246756i	$-0.00785529\pi$
$14$	−0.431533	+	3.00138i	−0.115332	+	0.802152i
$15$	2.20752	+	1.88444i	0.569979	+	0.486561i
$16$	−0.415415	+	0.909632i	−0.103854	+	0.227408i
$17$	0.118421	+	0.544374i	0.0287214	+	0.132030i	0.989275	−	0.146065i	$-0.0466607\pi$
$17$	0.118421	+	0.544374i	0.0287214	+	0.132030i	−0.960554	+	0.278095i	$0.910297\pi$
$18$	−0.788137	+	1.05283i	−0.185766	+	0.248154i
$19$	−7.04270	+	4.52607i	−1.61571	+	1.03835i	−0.657026	+	0.753868i	$0.728186\pi$
$19$	−7.04270	+	4.52607i	−1.61571	+	1.03835i	−0.958681	+	0.284484i	$0.908178\pi$
$20$	−2.23149	−	0.143031i	−0.498976	−	0.0319827i
$21$	1.10887	+	3.77648i	0.241976	+	0.824096i
$22$	−2.30140	−	2.30140i	−0.490659	−	0.490659i
$23$	4.21877	−	2.28078i	0.879675	−	0.475575i
$23$	4.21877	−	2.28078i	0.879675	−	0.475575i
$24$			1.29802i			0.264957i
$25$	−1.47942	−	4.77612i	−0.295884	−	0.955224i
$26$	1.75894	+	2.02992i	0.344956	+	0.398101i
$27$	−1.19061	+	5.47314i	−0.229133	+	1.05331i
$28$	−2.42744	−	1.81716i	−0.458742	−	0.343410i
$29$	−3.68158	+	5.72866i	−0.683653	+	1.06378i	0.309939	+	0.950756i	$0.399691\pi$
$29$	−3.68158	+	5.72866i	−0.683653	+	1.06378i	−0.993592	+	0.113028i	$0.963945\pi$
$30$	−2.71189	+	1.03438i	−0.495121	+	0.188850i
$31$	5.42542	−	6.26127i	0.974435	−	1.12456i	−0.0177580	−	0.999842i	$-0.505653\pi$
$31$	5.42542	−	6.26127i	0.974435	−	1.12456i	0.992193	−	0.124715i	$-0.0398017\pi$
$32$	−0.599278	−	0.800541i	−0.105938	−	0.141517i
$33$	−3.95826	−	1.47635i	−0.689044	−	0.257000i
$34$	−0.534539	−	0.156955i	−0.0916727	−	0.0269175i
$35$	1.86210	−	6.51959i	0.314752	−	1.10201i
$36$	−0.546331	−	1.19630i	−0.0910551	−	0.199383i
$37$	6.02087	−	4.50717i	0.989826	−	0.740974i	0.0238789	−	0.999715i	$-0.492398\pi$
$37$	6.02087	−	4.50717i	0.989826	−	0.740974i	0.965947	+	0.258741i	$0.0833075\pi$
$38$	−0.597229	−	8.35035i	−0.0968833	−	1.35461i
$39$	3.17138	+	1.44832i	0.507828	+	0.231917i
$40$	1.19497	−	1.88998i	0.188942	−	0.298833i
$41$	0.0516552	+	0.359270i	0.00806719	+	0.0561085i	0.993457	−	0.114203i	$-0.0364316\pi$
$41$	0.0516552	+	0.359270i	0.00806719	+	0.0561085i	−0.985390	+	0.170312i	$0.945522\pi$
$42$	−3.84596	−	0.836638i	−0.593445	−	0.129096i
$43$	1.30617	+	0.0934194i	0.199190	+	0.0142463i	0.170577	−	0.985344i	$-0.445437\pi$
$43$	1.30617	+	0.0934194i	0.199190	+	0.0142463i	0.0286121	+	0.999591i	$0.490891\pi$
$44$	3.12283	−	0.916945i	0.470784	−	0.138235i
$45$	2.06400	−	2.09474i	0.307683	−	0.312265i
$46$	−0.0200519	+	4.79579i	−0.00295649	+	0.707101i
$47$	−7.80610	+	7.80610i	−1.13864	+	1.13864i	−0.149942	+	0.988695i	$0.547909\pi$
$47$	−7.80610	+	7.80610i	−1.13864	+	1.13864i	−0.988695	+	0.149942i	$0.952091\pi$
$48$	−1.13924	−	0.622075i	−0.164436	−	0.0897888i
$49$	1.65849	−	1.43709i	0.236928	−	0.205299i
$50$	4.90091	+	0.990495i	0.693093	+	0.140077i
$51$	−0.715774	+	0.102913i	−0.100228	+	0.0144107i
$52$	−2.62459	+	0.570945i	−0.363965	+	0.0791758i
$53$	−3.43834	−	9.21854i	−0.472292	−	1.26626i	−0.926811	−	0.375527i	$-0.877462\pi$
$53$	−3.43834	−	9.21854i	−0.472292	−	1.26626i	0.454519	−	0.890737i	$-0.349811\pi$
$54$	−4.23306	−	3.66797i	−0.576047	−	0.499147i
$55$	4.40427	+	5.79367i	0.593872	+	0.781218i
$56$	2.75823	−	1.25964i	0.368583	−	0.168326i
$57$	−5.20781	−	9.53739i	−0.689791	−	1.26326i
$58$	−3.26353	−	5.97670i	−0.428522	−	0.784779i
$59$	−0.549862	+	0.251113i	−0.0715859	+	0.0326922i	−0.450886	−	0.892581i	$-0.648892\pi$
$59$	−0.549862	+	0.251113i	−0.0715859	+	0.0326922i	0.379300	+	0.925274i	$0.376165\pi$
$60$	0.391819	−	2.87589i	0.0505837	−	0.371276i
$61$	−5.69461	−	4.93441i	−0.729121	−	0.631787i	0.209072	−	0.977900i	$-0.432956\pi$
$61$	−5.69461	−	4.93441i	−0.729121	−	0.631787i	−0.938193	+	0.346114i	$0.887501\pi$
$62$	2.89526	+	7.76249i	0.367698	+	0.985837i
$63$	3.89670	−	0.847676i	0.490938	−	0.106797i
$64$	0.989821	−	0.142315i	0.123728	−	0.0177894i
$65$	−3.28435	−	5.02845i	−0.407374	−	0.623702i
$66$	3.19275	−	2.76654i	0.393001	−	0.340537i
$67$	−4.15784	−	2.27035i	−0.507961	−	0.277368i	0.204764	−	0.978811i	$-0.434357\pi$
$67$	−4.15784	−	2.27035i	−0.507961	−	0.277368i	−0.712725	+	0.701444i	$0.752539\pi$
$68$	0.393933	−	0.393933i	0.0477714	−	0.0477714i
$69$	2.56230	+	5.67330i	0.308464	+	0.682985i
$70$	4.82970	+	4.75883i	0.577260	+	0.568789i
$71$	−6.48944	+	1.90547i	−0.770155	+	0.226138i	−0.643125	−	0.765761i	$-0.722363\pi$
$71$	−6.48944	+	1.90547i	−0.770155	+	0.226138i	−0.127030	+	0.991899i	$0.540544\pi$
$72$	1.31179	+	0.0938213i	0.154596	+	0.0110569i
$73$	−14.4254	−	3.13806i	−1.68837	−	0.367282i	−0.737134	−	0.675747i	$-0.763821\pi$
$73$	−14.4254	−	3.13806i	−1.68837	−	0.367282i	−0.951236	+	0.308464i	$0.900185\pi$
$74$	1.07035	+	7.44445i	0.124426	+	0.865400i
$75$	6.32070	−	1.47316i	0.729851	−	0.170105i
$76$	7.61515	+	3.47772i	0.873517	+	0.398922i
$77$	0.704042	+	9.84379i	0.0802330	+	1.12180i
$78$	−2.79105	+	2.08935i	−0.316024	+	0.236572i
$79$	−4.19131	−	9.17769i	−0.471559	−	1.03257i	−0.984699	−	0.174265i	$-0.944245\pi$
$79$	−4.19131	−	9.17769i	−0.471559	−	1.03257i	0.513140	−	0.858305i	$-0.328482\pi$
$80$	1.08611	+	1.95458i	0.121431	+	0.218528i
$81$	−3.19028	−	0.936750i	−0.354475	−	0.104083i
$82$	−0.340079	−	0.126843i	−0.0375555	−	0.0140075i
$83$	6.24597	+	8.34364i	0.685585	+	0.915834i	0.999434	−	0.0336390i	$-0.0107097\pi$
$83$	6.24597	+	8.34364i	0.685585	+	0.915834i	−0.313850	+	0.949473i	$0.601619\pi$
$84$	2.57747	−	2.97456i	0.281226	−	0.324552i
$85$	1.13695	+	0.509104i	0.123319	+	0.0552201i
$86$	−0.707975	+	1.10163i	−0.0763429	+	0.118792i
$87$	−7.07605	−	5.29706i	−0.758632	−	0.567905i
$88$	−0.691829	+	3.18029i	−0.0737492	+	0.339020i
$89$	0.294495	+	0.339866i	0.0312164	+	0.0360257i	0.771143	−	0.636662i	$-0.219685\pi$
$89$	0.294495	+	0.339866i	0.0312164	+	0.0360257i	−0.739927	+	0.672688i	$0.765140\pi$
$90$	0.849336	+	2.81543i	0.0895279	+	0.296772i
$91$		−	8.14453i		−	0.853778i
$92$	−4.19955	−	2.31598i	−0.437834	−	0.241457i
$93$	7.60415	+	7.60415i	0.788514	+	0.788514i
$94$	−3.11018	−	10.5923i	−0.320791	−	1.09251i
$95$	−1.19741	+	18.6813i	−0.122852	+	1.91666i
$96$	1.09196	−	0.701763i	0.111448	−	0.0716233i
$97$	−1.66526	+	2.22452i	−0.169081	+	0.225866i	−0.877076	−	0.480352i	$-0.840509\pi$
$97$	−1.66526	+	2.22452i	−0.169081	+	0.225866i	0.707995	+	0.706218i	$0.249600\pi$
$98$	0.466475	+	2.14435i	0.0471211	+	0.216612i
$99$	−1.77812	+	3.89355i	−0.178708	+	0.391316i
$100$	−3.21809	+	3.82673i	−0.321809	+	0.382673i
$101$	−0.864027	+	6.00944i	−0.0859739	+	0.597962i	0.900600	+	0.434648i	$0.143127\pi$
$101$	−0.864027	+	6.00944i	−0.0859739	+	0.597962i	−0.986574	+	0.163313i	$0.947782\pi$
$102$	0.252709	−	0.677540i	0.0250220	−	0.0670865i
$103$	8.87454	−	4.84586i	0.874434	−	0.477477i	0.0216650	−	0.999765i	$-0.493103\pi$
$103$	8.87454	−	4.84586i	0.874434	−	0.477477i	0.852769	+	0.522288i	$0.174921\pi$
$104$	0.756726	−	2.57717i	0.0742031	−	0.252713i
$105$	8.26857	+	3.01460i	0.806930	+	0.294194i
$106$	9.73874	+	1.40022i	0.945910	+	0.136001i
$107$	2.31074	−	0.165268i	0.223388	−	0.0159770i	0.0408036	−	0.999167i	$-0.487008\pi$
$107$	2.31074	−	0.165268i	0.223388	−	0.0159770i	0.182585	+	0.983190i	$0.441554\pi$
$108$	5.24799	−	1.95740i	0.504988	−	0.188351i
$109$	−9.29120	−	5.97109i	−0.889935	−	0.571927i	0.0138543	−	0.999904i	$-0.495590\pi$
$109$	−9.29120	−	5.97109i	−0.889935	−	0.571927i	−0.903789	+	0.427977i	$0.859226\pi$
$110$	−7.19572	+	1.08893i	−0.686085	+	0.103825i
$111$	5.27796	+	8.21267i	0.500962	+	0.779512i
$112$	−0.216318	+	3.02452i	−0.0204401	+	0.285790i
$113$	−0.785015	+	1.43765i	−0.0738480	+	0.135243i	−0.911994	−	0.410203i	$-0.865458\pi$
$113$	−0.785015	+	1.43765i	−0.0738480	+	0.135243i	0.838146	+	0.545446i	$0.183640\pi$
$114$	10.8666			1.01775
$115$	1.49208	−	10.6195i	0.139137	−	0.990273i
$116$	6.80967			0.632262
$117$	1.69292	−	3.10035i	0.156510	−	0.286628i
$118$	0.0431237	−	0.602948i	0.00396986	−	0.0555059i
$119$	0.913293	+	1.42111i	0.0837215	+	0.130273i
$120$	2.33633	+	1.72216i	0.213277	+	0.157211i
$121$	0.342523	+	0.220126i	0.0311384	+	0.0200115i
$122$	7.05997	−	2.63323i	0.639179	−	0.238402i
$123$	−0.469934	+	0.0336104i	−0.0423726	+	0.00303055i
$124$	−8.20052	−	1.17906i	−0.736429	−	0.105882i
$125$	−10.5595	−	3.67393i	−0.944467	−	0.328606i
$126$	−1.12350	+	3.82630i	−0.100090	+	0.340874i
$127$	6.32744	−	3.45505i	0.561470	−	0.306586i	−0.173337	−	0.984863i	$-0.555455\pi$
$127$	6.32744	−	3.45505i	0.561470	−	0.306586i	0.734806	+	0.678277i	$0.237273\pi$
$128$	−0.349464	+	0.936950i	−0.0308886	+	0.0828154i
$129$	−0.241902	+	1.68247i	−0.0212983	+	0.148133i
$130$	5.98739	−	0.472728i	0.525129	−	0.0414610i
$131$	−3.35857	+	7.35424i	−0.293439	+	0.642543i	−0.997728	−	0.0673712i	$-0.978539\pi$
$131$	−3.35857	+	7.35424i	−0.293439	+	0.642543i	0.704289	+	0.709914i	$0.251266\pi$
$132$	0.898007	+	4.12807i	0.0781615	+	0.359303i
$133$	−15.2126	+	20.3217i	−1.31910	+	1.76212i
$134$	3.98528	−	2.56119i	0.344276	−	0.221253i
$135$	8.27156	+	9.40454i	0.711902	+	0.809414i
$136$	0.156955	+	0.534539i	0.0134588	+	0.0458363i
$137$	2.77999	+	2.77999i	0.237510	+	0.237510i	0.815818	−	0.578308i	$-0.196287\pi$
$137$	2.77999	+	2.77999i	0.237510	+	0.237510i	−0.578308	+	0.815818i	$0.696287\pi$
$138$	−6.20731	−	0.470050i	−0.528402	−	0.0400133i
$139$			9.64862i			0.818385i	0.912448	+	0.409193i	$0.134190\pi$
$139$			9.64862i			0.818385i	−0.912448	+	0.409193i	$0.865810\pi$
$140$	−6.49136	+	1.95826i	−0.548620	+	0.165503i
$141$	−9.38381	−	10.8295i	−0.790260	−	0.912008i
$142$	1.43767	−	6.60884i	0.120646	−	0.554602i
$143$	6.99829	+	5.23885i	0.585226	+	0.438095i
$144$	−0.711021	+	1.10637i	−0.0592517	+	0.0921975i
$145$	5.42654	+	14.2271i	0.450650	+	1.18150i
$146$	9.66759	−	11.1570i	0.800095	−	0.923359i
$147$	1.70705	+	2.28035i	0.140795	+	0.188080i
$148$	−7.04680	−	2.62832i	−0.579244	−	0.216047i
$149$	15.1524	+	4.44915i	1.24133	+	0.364488i	0.835516	−	0.549466i	$-0.185169\pi$
$149$	15.1524	+	4.44915i	1.24133	+	0.364488i	0.405817	+	0.913954i	$0.366987\pi$
$150$	−1.73623	+	6.25355i	−0.141763	+	0.510600i
$151$	−0.612556	−	1.34131i	−0.0498491	−	0.109154i	0.883069	−	0.469244i	$-0.155473\pi$
$151$	−0.612556	−	1.34131i	−0.0498491	−	0.109154i	−0.932918	+	0.360089i	$0.882746\pi$
$152$	−6.70187	+	5.01696i	−0.543594	+	0.406929i
$153$	0.0522684	+	0.730807i	0.00422565	+	0.0590823i
$154$	−8.97710	−	4.09970i	−0.723395	−	0.330364i
$155$	−4.07155	−	18.0725i	−0.327035	−	1.45162i
$156$	−0.496173	−	3.45096i	−0.0397257	−	0.276298i
$157$	−1.05217	−	0.228885i	−0.0839722	−	0.0182670i	0.170383	−	0.985378i	$-0.445500\pi$
$157$	−1.05217	−	0.228885i	−0.0839722	−	0.0182670i	−0.254355	+	0.967111i	$0.581863\pi$
$158$	10.0637	+	0.719773i	0.800628	+	0.0572621i
$159$	12.2537	−	3.59803i	0.971786	−	0.285342i
$160$	−2.23601	+	0.0165259i	−0.176772	+	0.00130648i
$161$	9.56894	−	10.9503i	0.754138	−	0.863004i
$162$	2.35110	−	2.35110i	0.184720	−	0.184720i
$163$	−1.04991	−	0.573294i	−0.0822352	−	0.0449038i	0.437605	−	0.899167i	$-0.355827\pi$
$163$	−1.04991	−	0.573294i	−0.0822352	−	0.0449038i	−0.519840	+	0.854263i	$0.674009\pi$
$164$	0.274310	−	0.237691i	0.0214200	−	0.0185606i
$165$	−7.90897	+	5.16578i	−0.615712	+	0.402155i
$166$	−10.3164	+	1.48328i	−0.800709	+	0.115125i
$167$	4.54884	−	0.989539i	0.351999	−	0.0765728i	−0.0330892	−	0.999452i	$-0.510535\pi$
$167$	4.54884	−	0.989539i	0.351999	−	0.0765728i	0.385089	+	0.922880i	$0.374171\pi$
$168$	1.37546	+	3.68775i	0.106119	+	0.284516i
$169$	4.37242	+	3.78873i	0.336340	+	0.291440i
$170$	−0.991710	+	0.753886i	−0.0760607	+	0.0578204i
$171$	−10.0150	+	4.57370i	−0.765867	+	0.349760i
$172$	−0.627581	−	1.14933i	−0.0478526	−	0.0876355i
$173$	−9.02575	−	16.5294i	−0.686215	−	1.25671i	−0.955881	−	0.293755i	$-0.905095\pi$
$173$	−9.02575	−	16.5294i	−0.686215	−	1.25671i	0.269665	−	0.962954i	$-0.413087\pi$
$174$	8.04031	−	3.67189i	0.609534	−	0.278365i
$175$	−9.26418	−	12.0016i	−0.700306	−	0.907233i
$176$	−2.45971	−	2.13135i	−0.185408	−	0.160657i
$177$	−0.274203	−	0.735166i	−0.0206103	−	0.0552585i
$178$	−0.439429	+	0.0955920i	−0.0329366	+	0.00716492i
$179$	−5.06495	+	0.728230i	−0.378572	+	0.0544304i	−0.328974	−	0.944339i	$-0.606703\pi$
$179$	−5.06495	+	0.728230i	−0.378572	+	0.0544304i	−0.0495976	+	0.998769i	$0.515794\pi$
$180$	−2.87809	−	0.603848i	−0.214520	−	0.0450081i
$181$	−8.44055	+	7.31377i	−0.627381	+	0.543629i	−0.909475	−	0.415758i	$-0.863516\pi$
$181$	−8.44055	+	7.31377i	−0.627381	+	0.543629i	0.282094	+	0.959387i	$0.408971\pi$
$182$	7.14828	+	3.90326i	0.529866	+	0.289329i
$183$	6.91596	−	6.91596i	0.511243	−	0.511243i
$184$	4.04532	−	2.57593i	0.298225	−	0.189900i
$185$	−0.124291	−	16.8170i	−0.00913806	−	1.23641i
$186$	−10.3183	+	3.02972i	−0.756574	+	0.222150i
$187$	−1.80857	−	0.129352i	−0.132256	−	0.00945913i
$188$	10.7872	+	2.34661i	0.786738	+	0.171144i
$189$	2.41708	+	16.8112i	0.175817	+	1.22283i
$190$	−15.8223	−	10.0039i	−1.14787	−	0.725762i
$191$	−21.5985	−	9.86371i	−1.56281	−	0.713713i	−0.568750	−	0.822511i	$-0.692573\pi$
$191$	−21.5985	−	9.86371i	−1.56281	−	0.713713i	−0.994064	+	0.108798i	$0.965300\pi$
$192$	0.0925997	+	1.29471i	0.00668281	+	0.0934378i
$193$	11.3534	−	8.49908i	0.817239	−	0.611777i	−0.106712	−	0.994290i	$-0.534032\pi$
$193$	11.3534	−	8.49908i	0.817239	−	0.611777i	0.923950	+	0.382513i	$0.124941\pi$
$194$	−1.15434	−	2.52766i	−0.0828770	−	0.181475i
$195$	6.81453	−	3.78666i	0.487998	−	0.271168i
$196$	−2.10561	−	0.618262i	−0.150401	−	0.0441616i
$197$	3.48361	+	1.29932i	0.248197	+	0.0925728i	0.470484	−	0.882409i	$-0.344079\pi$
$197$	3.48361	+	1.29932i	0.248197	+	0.0925728i	−0.222287	+	0.974981i	$0.571352\pi$
$198$	−2.56512	−	3.42660i	−0.182295	−	0.243518i
$199$	−6.22217	+	7.18076i	−0.441078	+	0.509031i	−0.932142	−	0.362092i	$-0.882062\pi$
$199$	−6.22217	+	7.18076i	−0.441078	+	0.509031i	0.491065	+	0.871123i	$0.336608\pi$
$200$	−1.81637	−	4.65841i	−0.128437	−	0.329399i
$201$	3.32447	−	5.17298i	0.234490	−	0.364874i
$202$	−4.86027	−	3.63836i	−0.341968	−	0.255994i
$203$	−4.38917	+	20.1767i	−0.308059	+	1.41613i
$204$	0.473552	+	0.546508i	0.0331553	+	0.0382632i
$205$	0.715191	+	0.383689i	0.0499511	+	0.0267980i
$206$			10.1114i			0.704492i
$207$	5.91870	−	2.17942i	0.411378	−	0.151480i
$208$	1.89927	+	1.89927i	0.131691	+	0.131691i
$209$	−7.67637	−	26.1433i	−0.530985	−	1.80837i
$210$	−6.60855	+	5.81241i	−0.456033	+	0.401094i
$211$	8.37030	−	5.37926i	0.576235	−	0.370324i	−0.219827	−	0.975539i	$-0.570549\pi$
$211$	8.37030	−	5.37926i	0.576235	−	0.370324i	0.796062	+	0.605215i	$0.206913\pi$
$212$	−5.89622	+	7.87643i	−0.404954	+	0.540956i
$213$	−1.86612	−	8.57841i	−0.127864	−	0.587783i
$214$	−0.962370	+	2.10730i	−0.0657863	+	0.144052i
$215$	1.90113	−	2.22706i	0.129656	−	0.151884i
$216$	−0.797126	+	5.54413i	−0.0542375	+	0.377230i
$217$	8.77913	−	23.5377i	0.595966	−	1.59785i
$218$	9.69350	−	5.29305i	0.656526	−	0.358491i
$219$	5.39868	−	18.3862i	0.364809	−	1.24243i
$220$	2.49281	−	6.83740i	0.168065	−	0.460978i
$221$	1.48114	+	0.212956i	0.0996323	+	0.0143250i
$222$	−9.73754	+	0.696443i	−0.653541	+	0.0467422i
$223$	2.32709	−	0.867961i	0.155834	−	0.0581230i	−0.270337	−	0.962766i	$-0.587135\pi$
$223$	2.32709	−	0.867961i	0.155834	−	0.0581230i	0.426171	+	0.904643i	$0.359862\pi$
$224$	−2.55089	−	1.63935i	−0.170438	−	0.109534i
$225$	−1.03193	−	6.49425i	−0.0687950	−	0.432950i
$226$	−0.885576	−	1.37798i	−0.0589076	−	0.0916621i
$227$	0.779412	−	10.8976i	0.0517314	−	0.723299i	−0.903715	−	0.428135i	$-0.859171\pi$
$227$	0.779412	−	10.8976i	0.0517314	−	0.723299i	0.955446	−	0.295165i	$-0.0953745\pi$
$228$	−5.20781	+	9.53739i	−0.344896	+	0.631629i
$229$	27.8750			1.84203			0.921015	−	0.389526i	$-0.127361\pi$
$229$	27.8750			1.84203			0.921015	+	0.389526i	$0.127361\pi$
$230$	8.60543	+	6.39895i	0.567425	+	0.421934i
$231$	−12.8101			−0.842841
$232$	−3.26353	+	5.97670i	−0.214261	+	0.392390i
$233$	−2.01709	+	28.2026i	−0.132144	+	1.84761i	0.310085	+	0.950709i	$0.399642\pi$
$233$	−2.01709	+	28.2026i	−0.132144	+	1.84761i	−0.442229	+	0.896902i	$0.645812\pi$
$234$	1.90978	+	2.97168i	0.124846	+	0.194265i
$235$	3.69353	+	24.4072i	0.240940	+	1.59215i
$236$	0.508528	+	0.326811i	0.0331023	+	0.0212736i
$237$	12.2706	−	4.57669i	0.797060	−	0.297288i
$238$	−1.68498	+	0.120512i	−0.109221	+	0.00781162i
$239$	−26.7158	−	3.84115i	−1.72810	−	0.248464i	−0.794625	−	0.607100i	$-0.792333\pi$
$239$	−26.7158	−	3.84115i	−1.72810	−	0.248464i	−0.933477	+	0.358636i	$0.883242\pi$
$240$	−2.63119	+	1.22521i	−0.169842	+	0.0790867i
$241$	0.828558	−	2.82181i	0.0533721	−	0.181769i	−0.928493	−	0.371350i	$-0.878895\pi$
$241$	0.828558	−	2.82181i	0.0533721	−	0.181769i	0.981865	+	0.189582i	$0.0607131\pi$
$242$	−0.357354	+	0.195130i	−0.0229716	+	0.0125434i
$243$	−4.36396	+	11.7002i	−0.279948	+	0.750569i
$244$	−1.07235	+	7.45836i	−0.0686502	+	0.477472i
$245$	−0.386229	−	4.89183i	−0.0246753	−	0.312528i
$246$	0.195716	−	0.428559i	0.0124784	−	0.0273239i
$247$	4.77977	+	21.9722i	0.304129	+	1.39806i
$248$	4.96492	−	6.63236i	0.315273	−	0.421155i
$249$	−11.3810	+	7.31412i	−0.721241	+	0.463514i
$250$	8.28514	−	7.50709i	0.523998	−	0.474790i
$251$	−1.74927	−	5.95747i	−0.110413	−	0.376032i	0.885685	−	0.464287i	$-0.153689\pi$
$251$	−1.74927	−	5.95747i	−0.110413	−	0.376032i	−0.996098	+	0.0882546i	$0.971871\pi$
$252$	−2.81983	−	2.81983i	−0.177632	−	0.177632i
$253$	3.25409	+	15.2659i	0.204583	+	0.959756i
$254$			7.20929i			0.452351i
$255$	−0.764425	+	1.42488i	−0.0478701	+	0.0892291i
$256$	−0.654861	−	0.755750i	−0.0409288	−	0.0472343i
$257$	2.41174	−	11.0866i	0.150440	−	0.691563i	−0.838701	−	0.544593i	$-0.816684\pi$
$257$	2.41174	−	11.0866i	0.150440	−	0.691563i	0.989141	−	0.146970i	$-0.0469522\pi$
$258$	−1.36074	−	1.01863i	−0.0847157	−	0.0634174i
$259$	12.3296	−	19.1852i	0.766124	−	1.19211i
$260$	−2.45455	+	5.48156i	−0.152224	+	0.339952i
$261$	−5.86473	+	6.76826i	−0.363018	+	0.418945i
$262$	−4.84507	−	6.47225i	−0.299329	−	0.399857i
$263$	1.04239	+	0.388792i	0.0642766	+	0.0239739i	0.381397	−	0.924411i	$-0.375443\pi$
$263$	1.04239	+	0.388792i	0.0642766	+	0.0239739i	−0.317120	+	0.948385i	$0.602716\pi$
$264$	−4.05349	−	1.19021i	−0.249475	−	0.0732525i
$265$	−21.1545	−	6.04205i	−1.29951	−	0.371160i
$266$	−10.5453	−	23.0910i	−0.646574	−	1.41580i
$267$	−0.467298	+	0.349815i	−0.0285982	+	0.0214083i
$268$	0.337956	+	4.72525i	0.0206440	+	0.288640i
$269$	−7.62696	−	3.48312i	−0.465024	−	0.212369i	0.169103	−	0.985598i	$-0.445913\pi$
$269$	−7.62696	−	3.48312i	−0.465024	−	0.212369i	−0.634127	+	0.773229i	$0.718640\pi$
$270$	−12.2183	+	2.75266i	−0.743582	+	0.167521i
$271$	4.22052	+	29.3543i	0.256378	+	1.78315i	0.558120	+	0.829760i	$0.311523\pi$
$271$	4.22052	+	29.3543i	0.256378	+	1.78315i	−0.301742	+	0.953390i	$0.597568\pi$
$272$	−0.544374	−	0.118421i	−0.0330075	−	0.00718035i
$273$	10.5448	+	0.754181i	0.638202	+	0.0456451i
$274$	−3.77224	+	1.10763i	−0.227889	+	0.0669144i
$275$	16.2715	−	0.240532i	0.981211	−	0.0145046i
$276$	3.38740	−	5.22276i	0.203898	−	0.314373i
$277$	−12.1450	+	12.1450i	−0.729722	+	0.729722i	−0.970564	−	0.240842i	$-0.922576\pi$
$277$	−12.1450	+	12.1450i	−0.729722	+	0.729722i	0.240842	+	0.970564i	$0.422576\pi$
$278$	−8.46839	−	4.62409i	−0.507900	−	0.277335i
$279$	8.23447	−	7.13521i	0.492985	−	0.427174i
$280$	1.39225	−	6.63582i	0.0832030	−	0.396566i
$281$	24.2561	−	3.48750i	1.44700	−	0.208047i	0.626376	−	0.779521i	$-0.284538\pi$
$281$	24.2561	−	3.48750i	1.44700	−	0.208047i	0.820620	+	0.571475i	$0.193628\pi$
$282$	14.0020	−	3.04595i	0.833807	−	0.181384i
$283$	−2.07467	−	5.56241i	−0.123326	−	0.330651i	0.860585	−	0.509306i	$-0.170098\pi$
$283$	−2.07467	−	5.56241i	−0.123326	−	0.330651i	−0.983912	+	0.178655i	$0.942825\pi$
$284$	5.11144	+	4.42909i	0.303308	+	0.262818i
$285$	−24.0760	−	3.28019i	−1.42614	−	0.194301i
$286$	−7.95195	+	3.63154i	−0.470209	+	0.214737i
$287$	0.527459	+	0.965970i	0.0311349	+	0.0570194i
$288$	−0.630282	−	1.15427i	−0.0371397	−	0.0680163i
$289$	15.1814	−	6.93312i	0.893025	−	0.407831i
$290$	−15.0875	−	2.05556i	−0.885968	−	0.120707i
$291$	−2.72591	−	2.36202i	−0.159796	−	0.138464i
$292$	5.15908	+	13.8320i	0.301912	+	0.809458i
$293$	14.7239	−	3.20298i	0.860177	−	0.187120i	0.239220	−	0.970965i	$-0.423108\pi$
$293$	14.7239	−	3.20298i	0.860177	−	0.187120i	0.620956	+	0.783845i	$0.286745\pi$
$294$	−2.81951	+	0.405385i	−0.164437	+	0.0236425i
$295$	−0.277550	+	1.32287i	−0.0161596	+	0.0770207i
$296$	5.68400	−	4.92521i	0.330376	−	0.286272i
$297$	−16.0000	−	8.73663i	−0.928411	−	0.506951i
$298$	−11.1667	+	11.1667i	−0.646869	+	0.646869i
$299$	−1.77990	−	12.7579i	−0.102934	−	0.737809i
$300$	−4.65652	−	4.52086i	−0.268845	−	0.261012i
$301$	3.80991	−	1.11869i	0.219600	−	0.0644802i
$302$	1.47081	+	0.105194i	0.0846354	+	0.00605324i
$303$	−7.70049	−	1.67514i	−0.442382	−	0.0962342i
$304$	−1.19141	−	8.28647i	−0.0683323	−	0.475261i
$305$	−16.4369	+	3.70307i	−0.941175	+	0.212037i
$306$	−0.666464	−	0.304364i	−0.0380992	−	0.0173993i
$307$	0.721723	+	10.0910i	0.0411909	+	0.575924i	0.975576	+	0.219660i	$0.0704949\pi$
$307$	0.721723	+	10.0910i	0.0411909	+	0.575924i	−0.934386	+	0.356263i	$0.884051\pi$
$308$	7.90049	−	5.91423i	0.450172	−	0.336995i
$309$	5.45222	+	11.9387i	0.310166	+	0.679169i
$310$	17.8132	+	5.08772i	1.01172	+	0.288963i
$311$	8.10917	+	2.38107i	0.459829	+	0.135018i	0.503439	−	0.864031i	$-0.332068\pi$
$311$	8.10917	+	2.38107i	0.459829	+	0.135018i	−0.0436102	+	0.999049i	$0.513886\pi$
$312$	3.26663	+	1.21839i	0.184936	+	0.0689777i
$313$	7.77062	+	10.3803i	0.439221	+	0.586731i	0.964462	−	0.264223i	$-0.0851155\pi$
$313$	7.77062	+	10.3803i	0.439221	+	0.586731i	−0.525240	+	0.850954i	$0.676025\pi$
$314$	0.705139	−	0.813774i	0.0397933	−	0.0459239i
$315$	3.64424	−	8.13841i	0.205330	−	0.458548i
$316$	−5.45477	+	8.48779i	−0.306855	+	0.477475i
$317$	23.8063	+	17.8212i	1.33710	+	1.00094i	0.998191	+	0.0601176i	$0.0191476\pi$
$317$	23.8063	+	17.8212i	1.33710	+	1.00094i	0.338905	+	0.940820i	$0.389943\pi$
$318$	−2.71469	+	12.4792i	−0.152232	+	0.699799i
$319$	−14.5138	−	16.7498i	−0.812617	−	0.937809i
$320$	1.05710	−	1.97042i	0.0590937	−	0.110150i
$321$			3.00705i			0.167837i
$322$	5.02494	+	13.6464i	0.280029	+	0.760483i
$323$	−3.29788	−	3.29788i	−0.183499	−	0.183499i
$324$	0.936750	+	3.19028i	0.0520417	+	0.177238i
$325$	−13.4083	−	0.759973i	−0.743761	−	0.0421557i
$326$	1.00634	−	0.646733i	0.0557358	−	0.0358192i
$327$	8.59121	−	11.4765i	0.475095	−	0.634652i
$328$	0.0771536	+	0.354669i	0.00426009	+	0.0195833i
$329$	−13.9058	+	30.4494i	−0.766650	+	1.67873i
$330$	−0.743527	−	9.41723i	−0.0409298	−	0.518401i
$331$	−3.18139	+	22.1270i	−0.174865	+	1.21621i	0.693563	+	0.720396i	$0.256040\pi$
$331$	−3.18139	+	22.1270i	−0.174865	+	1.21621i	−0.868428	+	0.495816i	$0.834869\pi$
$332$	3.64229	−	9.76536i	0.199897	−	0.535944i
$333$	8.68130	−	4.74035i	0.475733	−	0.259770i
$334$	−1.31153	+	4.46665i	−0.0717636	+	0.244404i
$335$	−9.60291	+	4.47157i	−0.524663	+	0.244308i
$336$	−3.89585	−	0.560139i	−0.212536	−	0.0305581i
$337$	32.7077	−	2.33930i	1.78170	−	0.127430i	0.858761	−	0.512377i	$-0.171235\pi$
$337$	32.7077	−	2.33930i	1.78170	−	0.127430i	0.922939	+	0.384947i	$0.125780\pi$
$338$	−5.42076	+	2.02184i	−0.294851	+	0.109974i
$339$	−1.78865	−	1.14950i	−0.0971461	−	0.0624320i
$340$	−0.186393	−	1.23170i	−0.0101086	−	0.0667984i
$341$	14.5781	+	22.6839i	0.789446	+	1.22840i
$342$	0.785442	−	10.9819i	0.0424718	−	0.593834i
$343$	−6.98335	+	12.7891i	−0.377065	+	0.690544i
$344$	1.30951			0.0706040
$345$	13.6110	+	2.91518i	0.732793	+	0.156948i
$346$	18.8331			1.01247
$347$	2.86056	−	5.23873i	0.153563	−	0.281230i	−0.789560	−	0.613673i	$-0.789691\pi$
$347$	2.86056	−	5.23873i	0.153563	−	0.281230i	0.943123	+	0.332443i	$0.107873\pi$
$348$	−0.630573	+	8.81656i	−0.0338023	+	0.472617i
$349$	15.9501	+	24.8188i	0.853788	+	1.32852i	0.943097	+	0.332517i	$0.107898\pi$
$349$	15.9501	+	24.8188i	0.853788	+	1.32852i	−0.0893091	+	0.996004i	$0.528466\pi$
$350$	14.9734	−	2.37924i	0.800360	−	0.127176i
$351$	12.6563	+	8.13368i	0.675541	+	0.434144i
$352$	3.04946	−	1.13739i	0.162537	−	0.0606230i
$353$	4.55914	−	0.326076i	0.242659	−	0.0173553i	0.0505199	−	0.998723i	$-0.483912\pi$
$353$	4.55914	−	0.326076i	0.242659	−	0.0173553i	0.192139	+	0.981368i	$0.438458\pi$
$354$	0.776651	+	0.111666i	0.0412785	+	0.00593496i
$355$	−5.18023	+	14.2086i	−0.274938	+	0.754113i
$356$	0.126697	−	0.431490i	0.00671493	−	0.0228689i
$357$	−1.92450	+	1.05086i	−0.101856	+	0.0556173i
$358$	1.78822	−	4.79440i	0.0945103	−	0.253392i
$359$	1.14223	−	7.94435i	0.0602843	−	0.419287i	−0.937223	−	0.348730i	$-0.886613\pi$
$359$	1.14223	−	7.94435i	0.0602843	−	0.419287i	0.997508	−	0.0705572i	$-0.0224777\pi$
$360$	1.90931	−	2.23664i	0.100629	−	0.117881i
$361$	21.2215	−	46.4685i	1.11692	−	2.44571i
$362$	−2.37402	−	10.9132i	−0.124776	−	0.573585i
$363$	−0.316718	+	0.423085i	−0.0166234	+	0.0222062i
$364$	−6.85161	+	4.40326i	−0.359122	+	0.230794i
$365$	−24.7873	+	21.8012i	−1.29743	+	1.14113i
$366$	2.75553	+	9.38446i	0.144034	+	0.490534i
$367$	−22.1581	−	22.1581i	−1.15664	−	1.15664i	−0.985193	−	0.171449i	$-0.945155\pi$
$367$	−22.1581	−	22.1581i	−1.15664	−	1.15664i	−0.171449	−	0.985193i	$-0.554845\pi$
$368$	0.322127	+	4.78500i	0.0167920	+	0.249435i
$369$			0.477350i			0.0248499i
$370$	14.8195	+	7.95045i	0.770430	+	0.413324i
$371$	−19.5370	−	22.5470i	−1.01431	−	1.17058i
$372$	2.28591	−	10.5081i	0.118519	−	0.544822i
$373$	−7.39018	−	5.53222i	−0.382649	−	0.286447i	0.390587	−	0.920566i	$-0.372272\pi$
$373$	−7.39018	−	5.53222i	−0.382649	−	0.286447i	−0.773236	+	0.634119i	$0.781363\pi$
$374$	0.980285	−	1.52535i	0.0506894	−	0.0788742i
$375$	5.73448	−	13.3313i	0.296127	−	0.688424i
$376$	−7.22933	+	8.34309i	−0.372824	+	0.430262i
$377$	10.9611	+	14.6424i	0.564527	+	0.754120i
$378$	−15.9132	−	5.93531i	−0.818486	−	0.305279i
$379$	28.5690	+	8.38862i	1.46749	+	0.430895i	0.915283	−	0.402811i	$-0.131967\pi$
$379$	28.5690	+	8.38862i	1.46749	+	0.430895i	0.552209	+	0.833706i	$0.313785\pi$
$380$	16.3631	−	9.09255i	0.839408	−	0.466438i
$381$	3.88737	+	8.51216i	0.199156	+	0.436091i
$382$	19.0082	−	14.2294i	0.972546	−	0.728039i
$383$	−1.42054	−	19.8617i	−0.0725862	−	1.01489i	−0.895020	−	0.446026i	$-0.852839\pi$
$383$	−1.42054	−	19.8617i	−0.0725862	−	1.01489i	0.822434	−	0.568861i	$-0.192616\pi$
$384$	−1.18072	−	0.539217i	−0.0602534	−	0.0275168i
$385$	18.6521	+	11.7931i	0.950600	+	0.601033i
$386$	2.01834	+	14.0379i	0.102731	+	0.714508i
$387$	1.68284	+	0.366079i	0.0855434	+	0.0186088i
$388$	2.77169	+	0.198235i	0.140711	+	0.0100639i
$389$	−7.85349	+	2.30599i	−0.398188	+	0.116918i	−0.474695	−	0.880151i	$-0.657441\pi$
$389$	−7.85349	+	2.30599i	−0.398188	+	0.116918i	0.0765069	+	0.997069i	$0.475623\pi$
$390$	0.0576165	+	7.79572i	0.00291753	+	0.394752i
$391$	1.74119	+	2.02650i	0.0880557	+	0.102484i
$392$	1.55175	−	1.55175i	0.0783750	−	0.0783750i
$393$	−9.21062	−	5.02938i	−0.464614	−	0.253699i
$394$	−2.80991	+	2.43480i	−0.141561	+	0.122663i
$395$	−22.0800	−	4.63256i	−1.11096	−	0.233090i
$396$	4.23679	−	0.609158i	0.212906	−	0.0306113i
$397$	−18.7441	+	4.07752i	−0.940737	+	0.204645i	−0.656686	−	0.754164i	$-0.728042\pi$
$397$	−18.7441	+	4.07752i	−0.940737	+	0.204645i	−0.284051	+	0.958809i	$0.591679\pi$
$398$	−3.32044	−	8.90244i	−0.166439	−	0.446239i
$399$	−24.9021	−	21.5778i	−1.24666	−	1.08024i
$400$	4.95908	+	0.638345i	0.247954	+	0.0319172i
$401$	21.0320	−	9.60501i	1.05029	−	0.479651i	0.185950	−	0.982559i	$-0.440464\pi$
$401$	21.0320	−	9.60501i	1.05029	−	0.479651i	0.864340	+	0.502908i	$0.167737\pi$
$402$	2.94696	+	5.39696i	0.146981	+	0.269176i
$403$	−10.6647	−	19.5309i	−0.531245	−	0.972903i
$404$	5.52259	−	2.52208i	0.274759	−	0.125478i
$405$	−5.91881	+	4.49940i	−0.294108	+	0.223577i
$406$	−15.6051	−	13.5219i	−0.774470	−	0.671082i
$407$	8.55431	+	22.9350i	0.424021	+	1.13684i
$408$	−0.706608	+	0.153713i	−0.0349823	+	0.00760994i
$409$	−21.7383	+	3.12549i	−1.07489	+	0.154546i	−0.656953	−	0.753931i	$-0.728155\pi$
$409$	−21.7383	+	3.12549i	−1.07489	+	0.154546i	−0.417935	+	0.908477i	$0.637246\pi$
$410$	−0.679510	+	0.443825i	−0.0335586	+	0.0219190i
$411$	−3.85671	+	3.34186i	−0.190237	+	0.164842i
$412$	−8.87454	−	4.84586i	−0.437217	−	0.238739i
$413$	−1.29610	+	1.29610i	−0.0637767	+	0.0637767i
$414$	−0.923704	+	6.23920i	−0.0453976	+	0.306640i
$415$	23.3048	−	0.172241i	1.14399	−	0.00845496i
$416$	−2.57717	+	0.756726i	−0.126356	+	0.0371016i
$417$	−12.4922	−	0.893459i	−0.611745	−	0.0437529i
$418$	26.6243	+	5.79177i	1.30224	+	0.283285i
$419$	−5.23943	−	36.4411i	−0.255963	−	1.78026i	−0.560894	−	0.827887i	$-0.689543\pi$
$419$	−5.23943	−	36.4411i	−0.255963	−	1.78026i	0.304931	−	0.952374i	$-0.401367\pi$
$420$	−1.93429	−	8.58578i	−0.0943835	−	0.418943i
$421$	13.4811	+	6.15663i	0.657031	+	0.300056i	0.715893	−	0.698210i	$-0.246020\pi$
$421$	13.4811	+	6.15663i	0.657031	+	0.300056i	−0.0588619	+	0.998266i	$0.518747\pi$
$422$	0.709810	+	9.92444i	0.0345530	+	0.483114i
$423$	−11.6227	+	8.70063i	−0.565114	+	0.423039i
$424$	−4.08722	−	8.94976i	−0.198493	−	0.434639i
$425$	2.42480	−	1.37095i	0.117620	−	0.0665009i
$426$	8.42343	+	2.47334i	0.408116	+	0.119834i
$427$	−21.4075	−	7.98460i	−1.03598	−	0.386402i
$428$	−1.38831	−	1.85457i	−0.0671067	−	0.0896441i
$429$	−7.43085	+	8.57566i	−0.358765	+	0.414037i
$430$	1.04353	+	2.73589i	0.0503236	+	0.131937i
$431$	8.01116	−	12.4656i	0.385884	−	0.600447i	−0.592916	−	0.805264i	$-0.702023\pi$
$431$	8.01116	−	12.4656i	0.385884	−	0.600447i	0.978800	+	0.204817i	$0.0656598\pi$
$432$	−4.48395	−	3.35664i	−0.215734	−	0.161496i
$433$	−0.555258	+	2.55248i	−0.0266840	+	0.122664i	−0.988562	−	0.150814i	$-0.951811\pi$
$433$	−0.555258	+	2.55248i	−0.0266840	+	0.122664i	0.961878	+	0.273478i	$0.0881742\pi$
$434$	16.4512	+	18.9857i	0.789683	+	0.911343i
$435$	−18.9225	+	5.70839i	−0.907265	+	0.273696i
$436$			11.0445i			0.528934i
$437$	−19.3886	+	35.1573i	−0.927483	+	1.68180i
$438$	13.5499	+	13.5499i	0.647439	+	0.647439i
$439$	4.27885	+	14.5724i	0.204218	+	0.695504i	0.996366	+	0.0851744i	$0.0271447\pi$
$439$	4.27885	+	14.5724i	0.204218	+	0.695504i	−0.792148	+	0.610329i	$0.791037\pi$
$440$	4.80637	+	5.46471i	0.229135	+	0.260520i
$441$	2.42793	−	1.56034i	0.115616	−	0.0743017i
$442$	−0.896742	+	1.19791i	−0.0426537	+	0.0569786i
$443$	−2.15886	−	9.92413i	−0.102571	−	0.471510i	−0.999566	−	0.0294692i	$-0.990618\pi$
$443$	−2.15886	−	9.92413i	−0.102571	−	0.471510i	0.896995	−	0.442041i	$-0.145745\pi$
$444$	4.05545	−	8.88020i	0.192463	−	0.421436i
$445$	1.00245	−	0.0791478i	0.0475209	−	0.00375196i
$446$	−0.353466	+	2.45841i	−0.0167371	+	0.116409i
$447$	−7.16347	+	19.2060i	−0.338821	+	0.908413i
$448$	2.66134	−	1.45320i	0.125736	−	0.0686572i
$449$	0.309809	−	1.05511i	0.0146208	−	0.0497938i	−0.951860	−	0.306535i	$-0.900830\pi$
$449$	0.309809	−	1.05511i	0.0146208	−	0.0497938i	0.966480	+	0.256741i	$0.0826487\pi$
$450$	6.19441	+	2.20666i	0.292007	+	0.104023i
$451$	−1.16930	−	0.168120i	−0.0550603	−	0.00791648i
$452$	1.63384	−	0.116854i	0.0768493	−	0.00549637i
$453$	1.79333	−	0.668879i	0.0842582	−	0.0314267i
$454$	9.19106	+	5.90674i	0.431358	+	0.277217i
$455$	−14.6595	−	10.8058i	−0.687248	−	0.506585i
$456$	−5.87493	−	9.14157i	−0.275119	−	0.428093i
$457$	0.175441	−	2.45299i	0.00820679	−	0.114746i	−0.991697	−	0.128594i	$-0.958954\pi$
$457$	0.175441	−	2.45299i	0.00820679	−	0.114746i	0.999904	+	0.0138481i	$0.00440814\pi$
$458$	−13.3591	+	24.4653i	−0.624228	+	1.14319i
$459$	−3.12043			−0.145649
$460$	−9.74037	+	4.48611i	−0.454147	+	0.209166i
$461$	−20.1778			−0.939775			−0.469887	−	0.882726i	$-0.655706\pi$
$461$	−20.1778			−0.939775			−0.469887	+	0.882726i	$0.655706\pi$
$462$	6.13922	−	11.2431i	0.285622	−	0.523078i
$463$	2.22953	−	31.1729i	0.103615	−	1.44873i	−0.633910	−	0.773406i	$-0.718551\pi$
$463$	2.22953	−	31.1729i	0.103615	−	1.44873i	0.737525	−	0.675319i	$-0.235994\pi$
$464$	−3.68158	−	5.72866i	−0.170913	−	0.265946i
$465$	23.7757	−	3.59798i	1.10257	−	0.166852i
$466$	−23.7861	−	15.2864i	−1.10187	−	0.708129i
$467$	−17.2024	+	6.41616i	−0.796032	+	0.296904i	−0.714381	−	0.699757i	$-0.753292\pi$
$467$	−17.2024	+	6.41616i	−0.796032	+	0.296904i	−0.0816503	+	0.996661i	$0.526019\pi$
$468$	−3.52344	+	0.252002i	−0.162871	+	0.0116488i
$469$	−14.2185	−	2.04431i	−0.656549	−	0.0943974i
$470$	−23.1918	−	8.45537i	−1.06976	−	0.390017i
$471$	0.393771	−	1.34106i	0.0181440	−	0.0617929i
$472$	−0.530547	+	0.289700i	−0.0244204	+	0.0133345i
$473$	−1.48942	+	3.99329i	−0.0684837	+	0.183612i
$474$	−1.86380	+	12.9630i	−0.0856071	+	0.595411i
$475$	32.0362	+	26.9408i	1.46992	+	1.23613i
$476$	0.701752	−	1.53662i	0.0321648	−	0.0704310i
$477$	−2.75050	−	12.6438i	−0.125937	−	0.578922i
$478$	16.1748	−	21.6070i	0.739820	−	0.988283i
$479$	−22.0117	+	14.1461i	−1.00574	+	0.646351i	−0.936288	−	0.351234i	$-0.885762\pi$
$479$	−22.0117	+	14.1461i	−1.00574	+	0.646351i	−0.0694542	+	0.997585i	$0.522126\pi$
$480$	0.185657	−	2.89652i	0.00847406	−	0.132207i
$481$	−5.69134	−	19.3829i	−0.259503	−	0.883786i
$482$	2.07956	+	2.07956i	0.0947212	+	0.0947212i
$483$	13.2914	+	13.4030i	0.604780	+	0.609858i
$484$		−	0.407158i		−	0.0185072i
$485$	1.79457	+	5.94873i	0.0814870	+	0.270118i
$486$	−8.17761	−	9.43747i	−0.370944	−	0.428092i
$487$	−4.30505	+	19.7900i	−0.195081	+	0.896771i	0.770657	+	0.637250i	$0.219928\pi$
$487$	−4.30505	+	19.7900i	−0.195081	+	0.896771i	−0.965738	+	0.259521i	$0.916435\pi$
$488$	−6.03212	−	4.51559i	−0.273061	−	0.204411i
$489$	0.839472	−	1.30624i	0.0379622	−	0.0590704i
$490$	4.47856	+	2.00542i	0.202321	+	0.0905956i
$491$	−7.15615	+	8.25864i	−0.322953	+	0.372707i	−0.893890	−	0.448286i	$-0.852034\pi$
$491$	−7.15615	+	8.25864i	−0.322953	+	0.372707i	0.570937	+	0.820994i	$0.306580\pi$
$492$	0.282341	+	0.377163i	0.0127289	+	0.0170038i
$493$	−3.55451	−	1.32576i	−0.160087	−	0.0597094i
$494$	−21.5753	−	6.33507i	−0.970717	−	0.285028i
$495$	4.64893	+	8.36628i	0.208954	+	0.376036i
$496$	3.44165	+	7.53616i	0.154535	+	0.338384i
$497$	−16.4177	+	12.2902i	−0.736436	+	0.551289i
$498$	−0.965120	−	13.4941i	−0.0432481	−	0.604687i
$499$	19.9333	+	9.10325i	0.892339	+	0.407517i	0.808180	−	0.588935i	$-0.200453\pi$
$499$	19.9333	+	9.10325i	0.892339	+	0.407517i	0.0841583	+	0.996452i	$0.473180\pi$
$500$	2.61817	+	10.8695i	0.117088	+	0.486097i
$501$	0.859947	+	5.98107i	0.0384196	+	0.267214i
$502$	6.06708	+	1.31981i	0.270787	+	0.0589061i
$503$	18.3798	+	1.31455i	0.819513	+	0.0586127i	0.474798	−	0.880095i	$-0.342521\pi$
$503$	18.3798	+	1.31455i	0.819513	+	0.0586127i	0.344715	+	0.938708i	$0.387976\pi$
$504$	3.82630	−	1.12350i	0.170437	−	0.0500448i
$505$	9.67015	+	9.52826i	0.430316	+	0.424002i
$506$	−14.9580	−	4.46009i	−0.664966	−	0.198275i
$507$	−5.31020	+	5.31020i	−0.235834	+	0.235834i
$508$	−6.32744	−	3.45505i	−0.280735	−	0.153293i
$509$	27.3941	−	23.7371i	1.21422	−	1.05213i	0.217114	−	0.976146i	$-0.430336\pi$
$509$	27.3941	−	23.7371i	1.21422	−	1.05213i	0.997109	−	0.0759841i	$-0.0242098\pi$
$510$	−0.884233	−	1.35379i	−0.0391545	−	0.0599468i
$511$	−44.3088	+	6.37065i	−1.96011	+	0.281821i
$512$	0.977147	−	0.212565i	0.0431842	−	0.00939415i
$513$	−16.3867	−	43.9345i	−0.723491	−	1.93975i
$514$	8.57465	+	7.42998i	0.378212	+	0.327722i
$515$	3.05221	−	22.4027i	0.134496	−	0.987183i
$516$	1.54617	−	0.706110i	0.0680661	−	0.0310848i
$517$	−17.2193	−	31.5349i	−0.757306	−	1.38690i
$518$	10.9295	+	20.0159i	0.480216	+	0.879449i
$519$	22.2367	−	10.1551i	0.976081	−	0.445761i
$520$	−3.63471	−	4.78134i	−0.159393	−	0.209675i
$521$	14.6669	+	12.7090i	0.642569	+	0.556790i	0.914023	−	0.405662i	$-0.132959\pi$
$521$	14.6669	+	12.7090i	0.642569	+	0.556790i	−0.271454	+	0.962451i	$0.587504\pi$
$522$	−3.12969	−	8.39103i	−0.136983	−	0.367266i
$523$	−30.4374	+	6.62126i	−1.33094	+	0.289528i	−0.821120	−	0.570756i	$-0.806650\pi$
$523$	−30.4374	+	6.62126i	−1.33094	+	0.289528i	−0.509817	+	0.860283i	$0.670287\pi$
$524$	8.00256	−	1.15059i	0.349593	−	0.0502639i
$525$	16.3964	−	10.8831i	0.715599	−	0.474978i
$526$	−0.840799	+	0.728557i	−0.0366606	+	0.0317666i
$527$	4.05096	+	2.21199i	0.176462	+	0.0963558i
$528$	2.98726	−	2.98726i	0.130004	−	0.130004i
$529$	12.5961	−	19.2442i	0.547657	−	0.836703i
$530$	15.4412	−	15.6712i	0.670725	−	0.680713i
$531$	−0.762786	+	0.223974i	−0.0331021	+	0.00971966i
$532$	25.3203	+	1.81094i	1.09777	+	0.0785143i
$533$	0.952633	+	0.207233i	0.0412631	+	0.00897624i
$534$	−0.0830732	−	0.577787i	−0.00359493	−	0.0250033i
$535$	2.76833	−	4.37842i	0.119685	−	0.189296i
$536$	−4.30921	−	1.96795i	−0.186130	−	0.0850026i
$537$	−0.473836	−	6.62509i	−0.0204475	−	0.285894i
$538$	6.71227	−	5.02474i	0.289386	−	0.216632i
$539$	2.96705	+	6.49692i	0.127800	+	0.279842i
$540$	3.43966	−	12.0430i	0.148019	−	0.518246i
$541$	−24.5392	−	7.20535i	−1.05502	−	0.309782i	−0.292177	−	0.956364i	$-0.594380\pi$
$541$	−24.5392	−	7.20535i	−1.05502	−	0.309782i	−0.762845	+	0.646582i	$0.776198\pi$
$542$	−27.7864	−	10.3638i	−1.19353	−	0.445162i
$543$	−8.68764	−	11.6053i	−0.372823	−	0.498033i
$544$	0.364827	−	0.421032i	0.0156418	−	0.0180516i
$545$	−23.0747	+	8.80120i	−0.988410	+	0.377002i
$546$	−5.71552	+	8.89353i	−0.244602	+	0.380608i
$547$	−7.48128	−	5.60042i	−0.319876	−	0.239456i	0.427258	−	0.904130i	$-0.359480\pi$
$547$	−7.48128	−	5.60042i	−0.319876	−	0.239456i	−0.747134	+	0.664673i	$0.768571\pi$
$548$	0.835699	−	3.84165i	0.0356993	−	0.164107i
$549$	−6.48946	−	7.48924i	−0.276963	−	0.319633i
$550$	−7.58701	+	14.3965i	−0.323511	+	0.613867i
$551$		−	57.0083i		−	2.42864i
$552$	2.96050	+	5.47605i	0.126007	+	0.233076i
$553$	−21.6330	−	21.6330i	−0.919928	−	0.919928i
$554$	−4.83893	−	16.4799i	−0.205586	−	0.700163i
$555$	21.7847	+	1.39633i	0.924710	+	0.0592709i
$556$	8.11693	−	5.21644i	0.344235	−	0.221226i
$557$	11.9402	−	15.9503i	0.505924	−	0.675835i	−0.472764	−	0.881189i	$-0.656744\pi$
$557$	11.9402	−	15.9503i	0.505924	−	0.675835i	0.978688	+	0.205354i	$0.0658346\pi$
$558$	2.31606	+	10.6468i	0.0980468	+	0.450714i
$559$	1.46114	−	3.19946i	0.0617998	−	0.135323i
$560$	5.15689	+	4.40216i	0.217918	+	0.186025i
$561$	0.334946	−	2.32960i	0.0141414	−	0.0983559i
$562$	−8.56379	+	22.9604i	−0.361242	+	0.968527i
$563$	15.7404	−	8.59490i	0.663378	−	0.362232i	−0.112019	−	0.993706i	$-0.535732\pi$
$563$	15.7404	−	8.59490i	0.663378	−	0.362232i	0.775397	+	0.631474i	$0.217550\pi$
$564$	−4.03708	+	13.7490i	−0.169992	+	0.578939i
$565$	1.54612	+	3.32038i	0.0650460	+	0.139689i
$566$	5.87629	+	0.844884i	0.246999	+	0.0355131i
$567$	−10.0564	+	0.719249i	−0.422329	+	0.0302056i
$568$	−6.33697	+	2.36357i	−0.265894	+	0.0991732i
$569$	29.1395	+	18.7268i	1.22159	+	0.785069i	0.982561	−	0.185943i	$-0.0595340\pi$
$569$	29.1395	+	18.7268i	1.22159	+	0.785069i	0.239031	+	0.971012i	$0.423170\pi$
$570$	14.4174	−	19.5590i	0.603877	−	0.819237i
$571$	6.56960	+	10.2225i	0.274929	+	0.427798i	0.951071	−	0.308974i	$-0.0999856\pi$
$571$	6.56960	+	10.2225i	0.274929	+	0.427798i	−0.676142	+	0.736772i	$0.736349\pi$
$572$	0.623643	−	8.71967i	0.0260758	−	0.364588i
$573$	14.7707	−	27.0505i	0.617054	−	1.13005i
$574$	−1.10060			−0.0459380
$575$	−17.1346	−	16.7751i	−0.714562	−	0.699572i
$576$	1.31514			0.0547977
$577$	8.39086	−	15.3667i	0.349316	−	0.639724i	−0.642660	−	0.766152i	$-0.722169\pi$
$577$	8.39086	−	15.3667i	0.349316	−	0.639724i	0.991976	+	0.126427i	$0.0403510\pi$
$578$	−1.19062	+	16.6471i	−0.0495235	+	0.692428i
$579$	9.95254	+	15.4865i	0.413613	+	0.643595i
$580$	9.03479	−	12.2568i	0.375149	−	0.508938i
$581$	26.5866	+	17.0862i	1.10300	+	0.708854i
$582$	3.37949	−	1.26048i	0.140084	−	0.0522487i
$583$	31.9407	−	2.28444i	1.32285	−	0.0946119i
$584$	−14.6126	−	2.10097i	−0.604672	−	0.0869387i
$585$	−3.33428	−	7.16054i	−0.137856	−	0.296052i
$586$	−4.24520	+	14.4578i	−0.175368	+	0.597248i
$587$	−23.0766	+	12.6008i	−0.952475	+	0.520091i	−0.878799	−	0.477191i	$-0.841655\pi$
$587$	−23.0766	+	12.6008i	−0.952475	+	0.520091i	−0.0736759	+	0.997282i	$0.523473\pi$
$588$	0.995451	−	2.66891i	0.0410517	−	0.110064i
$589$	−9.87068	+	68.6521i	−0.406714	+	2.82876i
$590$	−1.02804	−	0.877586i	−0.0423239	−	0.0361296i
$591$	−2.00483	+	4.38996i	−0.0824676	+	0.180579i
$592$	1.59870	+	7.34913i	0.0657064	+	0.302047i
$593$	−13.0033	+	17.3703i	−0.533980	+	0.713314i	−0.983692	−	0.179860i	$-0.942436\pi$
$593$	−13.0033	+	17.3703i	−0.533980	+	0.713314i	0.449712	+	0.893174i	$0.351527\pi$
$594$	15.3359	−	9.85580i	0.629240	−	0.404388i
$595$	3.76961	+	0.241620i	0.154539	+	0.00990544i
$596$	−4.44915	−	15.1524i	−0.182244	−	0.620667i
$597$	−8.72085	−	8.72085i	−0.356921	−	0.356921i
$598$	12.0504	+	4.55204i	0.492776	+	0.186147i
$599$		−	18.6106i		−	0.760410i	−0.924902	−	0.380205i	$-0.875853\pi$
$599$		−	18.6106i		−	0.760410i	0.924902	−	0.380205i	$-0.124147\pi$
$600$	6.19950	−	1.92032i	0.253093	−	0.0783966i
$601$	22.5879	+	26.0679i	0.921382	+	1.06333i	0.997803	+	0.0662553i	$0.0211052\pi$
$601$	22.5879	+	26.0679i	0.921382	+	1.06333i	−0.0764212	+	0.997076i	$0.524349\pi$
$602$	−0.844044	+	3.88001i	−0.0344007	+	0.158137i
$603$	−4.98757	−	3.73365i	−0.203110	−	0.152046i
$604$	−0.797209	+	1.24048i	−0.0324380	+	0.0504745i
$605$	0.850655	−	0.324459i	0.0345840	−	0.0131911i
$606$	5.16069	−	5.95575i	0.209639	−	0.241936i
$607$	−8.89601	−	11.8837i	−0.361078	−	0.482344i	0.582811	−	0.812608i	$-0.301953\pi$
$607$	−8.89601	−	11.8837i	−0.361078	−	0.482344i	−0.943888	+	0.330264i	$0.892862\pi$
$608$	7.84384	+	2.92560i	0.318110	+	0.118649i
$609$	−25.7166	−	7.55107i	−1.04209	−	0.305985i
$610$	4.62727	−	16.2010i	0.187353	−	0.655961i
$611$	12.3178	+	26.9722i	0.498325	+	1.09118i
$612$	0.586536	−	0.439075i	0.0237093	−	0.0177486i
$613$	0.729459	+	10.1992i	0.0294626	+	0.411940i	0.990686	+	0.136169i	$0.0434789\pi$
$613$	0.729459	+	10.1992i	0.0294626	+	0.411940i	−0.961223	+	0.275772i	$0.911067\pi$
$614$	−9.20254	−	4.20266i	−0.371384	−	0.169606i
$615$	−0.562994	+	0.890437i	−0.0227021	+	0.0359059i
$616$	1.40450	+	9.76848i	0.0565888	+	0.393583i
$617$	−0.315657	−	0.0686669i	−0.0127079	−	0.00276442i	0.206207	−	0.978508i	$-0.433888\pi$
$617$	−0.315657	−	0.0686669i	−0.0127079	−	0.00276442i	−0.218915	+	0.975744i	$0.570252\pi$
$618$	−13.0913	−	0.936310i	−0.526610	−	0.0376639i
$619$	8.73143	−	2.56378i	0.350946	−	0.103047i	−0.101508	−	0.994835i	$-0.532367\pi$
$619$	8.73143	−	2.56378i	0.350946	−	0.103047i	0.452454	+	0.891788i	$0.350549\pi$
$620$	−13.0023	+	13.1960i	−0.522186	+	0.529962i
$621$	7.46011	+	25.8055i	0.299364	+	1.03554i
$622$	−5.97613	+	5.97613i	−0.239621	+	0.239621i
$623$	1.19682	+	0.653513i	0.0479496	+	0.0261825i
$624$	−2.63488	+	2.28314i	−0.105480	+	0.0913987i
$625$	−20.6226	+	14.1318i	−0.824906	+	0.565271i
$626$	−12.8347	+	1.84535i	−0.512976	+	0.0737548i
$627$	34.5589	−	7.51783i	1.38015	−	0.300233i
$628$	0.376295	+	1.00889i	0.0150158	+	0.0402589i
$629$	3.16659	+	2.74386i	0.126260	+	0.109405i
$630$	5.39642	+	7.09880i	0.214998	+	0.282823i
$631$	16.5604	−	7.56288i	0.659259	−	0.301074i	−0.0575504	−	0.998343i	$-0.518329\pi$
$631$	16.5604	−	7.56288i	0.659259	−	0.301074i	0.716809	+	0.697269i	$0.245602\pi$
$632$	−4.83536	−	8.85530i	−0.192340	−	0.352245i
$633$	6.18951	+	11.3352i	0.246011	+	0.450536i
$634$	−27.0504	+	12.3535i	−1.07431	+	0.490621i
$635$	2.17619	−	15.9729i	0.0863595	−	0.633865i
$636$	−9.65173	−	8.36327i	−0.382716	−	0.331625i
$637$	−2.05987	−	5.52273i	−0.0816151	−	0.218819i
$638$	21.6567	−	4.71112i	0.857396	−	0.186515i
$639$	−8.80432	+	1.26587i	−0.348294	+	0.0500771i
$640$	1.22278	+	1.87211i	0.0483346	+	0.0740018i
$641$	−6.95573	+	6.02717i	−0.274735	+	0.238059i	−0.781320	−	0.624131i	$-0.785453\pi$
$641$	−6.95573	+	6.02717i	−0.274735	+	0.238059i	0.506585	+	0.862190i	$0.330908\pi$
$642$	−2.63923	−	1.44113i	−0.104162	−	0.0568768i
$643$	−21.8882	+	21.8882i	−0.863186	+	0.863186i	−0.991707	−	0.128521i	$-0.958977\pi$
$643$	−21.8882	+	21.8882i	−0.863186	+	0.863186i	0.128521	+	0.991707i	$0.458977\pi$
$644$	−14.3853	−	2.12973i	−0.566862	−	0.0839230i
$645$	2.70736	+	2.66764i	0.106602	+	0.105038i
$646$	4.47499	−	1.31397i	0.176066	−	0.0516976i
$647$	5.97794	+	0.427551i	0.235017	+	0.0168088i	0.188351	−	0.982102i	$-0.439686\pi$
$647$	5.97794	+	0.427551i	0.235017	+	0.0168088i	0.0466662	+	0.998911i	$0.485140\pi$
$648$	−3.24898	−	0.706772i	−0.127632	−	0.0277646i
$649$	−0.279991	−	1.94738i	−0.0109906	−	0.0764414i
$650$	7.09295	−	11.4040i	0.278208	−	0.447302i
$651$	29.6617	+	13.5460i	1.16253	+	0.530911i
$652$	0.0853383	+	1.19319i	0.00334211	+	0.0467288i
$653$	20.6357	−	15.4477i	0.807538	−	0.604515i	−0.113700	−	0.993515i	$-0.536270\pi$
$653$	20.6357	−	15.4477i	0.807538	−	0.604515i	0.921238	+	0.389000i	$0.127179\pi$
$654$	5.95536	+	13.0404i	0.232873	+	0.509921i
$655$	8.78102	+	15.8025i	0.343103	+	0.617453i
$656$	−0.348262	−	0.102259i	−0.0135973	−	0.00399254i
$657$	−18.1911	−	6.78493i	−0.709702	−	0.264705i
$658$	−20.0605	−	26.7977i	−0.782039	−	1.04468i
$659$	12.7910	−	14.7616i	0.498265	−	0.575028i	−0.449790	−	0.893134i	$-0.648501\pi$
$659$	12.7910	−	14.7616i	0.498265	−	0.575028i	0.948055	+	0.318106i	$0.103047\pi$
$660$	8.62164	+	3.86062i	0.335597	+	0.150274i
$661$	−11.0683	+	17.2226i	−0.430507	+	0.669882i	−0.986954	−	0.161001i	$-0.948528\pi$
$661$	−11.0683	+	17.2226i	−0.430507	+	0.669882i	0.556447	+	0.830883i	$0.312164\pi$
$662$	−17.8958	−	13.3966i	−0.695539	−	0.520674i
$663$	−0.412870	+	1.89793i	−0.0160345	+	0.0737095i
$664$	6.82529	+	7.87680i	0.264873	+	0.305679i
$665$	16.3939	+	54.3436i	0.635729	+	2.10735i
$666$			9.89121i			0.383276i
$667$	−2.46597	+	32.5648i	−0.0954829	+	1.26091i
$668$	−3.29174	−	3.29174i	−0.127361	−	0.127361i
$669$	0.908272	+	3.09329i	0.0351158	+	0.119594i
$670$	0.677584	−	10.5713i	0.0261773	−	0.408404i
$671$	20.6310	−	13.2587i	0.796449	−	0.511847i
$672$	2.35870	−	3.15086i	0.0909890	−	0.121547i
$673$	−1.72429	−	7.92644i	−0.0664666	−	0.305542i	0.931897	−	0.362722i	$-0.118153\pi$
$673$	−1.72429	−	7.92644i	−0.0664666	−	0.305542i	−0.998364	+	0.0571803i	$0.981789\pi$
$674$	−13.6220	+	29.8279i	−0.524698	+	1.14893i
$675$	27.9018	−	2.41058i	1.07394	−	0.0927832i
$676$	0.823369	−	5.72666i	0.0316680	−	0.220256i
$677$	12.4407	−	33.3548i	0.478136	−	1.28193i	−0.444334	−	0.895861i	$-0.646560\pi$
$677$	12.4407	−	33.3548i	0.478136	−	1.28193i	0.922470	−	0.386070i	$-0.126168\pi$
$678$	1.86610	−	1.01897i	0.0716670	−	0.0391331i
$679$	−2.37385	+	8.08460i	−0.0911002	+	0.310259i
$680$	1.17037	+	0.426698i	0.0448816	+	0.0163631i
$681$	14.0371	+	2.01823i	0.537902	+	0.0773387i
$682$	−26.8957	+	1.92362i	−1.02989	+	0.0736592i
$683$	4.54626	−	1.69567i	0.173958	−	0.0648828i	−0.260976	−	0.965345i	$-0.584044\pi$
$683$	4.54626	−	1.69567i	0.173958	−	0.0648828i	0.434934	+	0.900462i	$0.356772\pi$
$684$	9.26217	+	5.95244i	0.354148	+	0.227597i
$685$	8.69213	−	1.31538i	0.332109	−	0.0502580i
$686$	−7.87792	−	12.2583i	−0.300780	−	0.468023i
$687$	−2.58121	+	36.0901i	−0.0984795	+	1.37692i
$688$	−0.627581	+	1.14933i	−0.0239263	+	0.0438178i
$689$	−26.4270			−1.00679
$690$	−9.08166	+	10.5490i	−0.345733	+	0.401594i
$691$	14.4220			0.548640			0.274320	−	0.961639i	$-0.411547\pi$
$691$	14.4220			0.548640			0.274320	+	0.961639i	$0.411547\pi$
$692$	−9.02575	+	16.5294i	−0.343108	+	0.628355i
$693$	−0.925917	+	12.9460i	−0.0351727	+	0.491778i
$694$	3.22700	+	5.02131i	0.122495	+	0.190606i
$695$	17.3667	+	12.8014i	0.658758	+	0.485585i
$696$	−7.43591	−	4.77877i	−0.281857	−	0.181139i
$697$	−0.189460	+	0.0706649i	−0.00717631	+	0.00267663i
$698$	−29.4270	+	2.10466i	−1.11383	+	0.0796626i
$699$	−36.3274	−	5.22310i	−1.37403	−	0.197556i
$700$	−5.08776	+	14.2821i	−0.192299	+	0.539811i
$701$	−9.00874	+	30.6809i	−0.340255	+	1.15880i	0.594673	+	0.803967i	$0.297281\pi$
$701$	−9.00874	+	30.6809i	−0.340255	+	1.15880i	−0.934929	+	0.354836i	$0.884537\pi$
$702$	−13.2043	+	7.21007i	−0.498363	+	0.272127i
$703$	−22.0035	+	58.9936i	−0.829876	+	2.22498i
$704$	−0.463187	+	3.22154i	−0.0174570	+	0.121416i
$705$	−31.9423	+	2.52197i	−1.20302	+	0.0949828i
$706$	−1.89877	+	4.15774i	−0.0714613	+	0.156478i
$707$	3.91321	+	17.9888i	0.147172	+	0.676537i
$708$	−0.470216	+	0.628135i	−0.0176718	+	0.0236068i
$709$	28.7677	−	18.4879i	1.08039	−	0.694327i	0.125746	−	0.992062i	$-0.459868\pi$
$709$	28.7677	−	18.4879i	1.08039	−	0.694327i	0.954648	+	0.297735i	$0.0962312\pi$
$710$	−9.98795	−	11.3560i	−0.374841	−	0.426184i
$711$	−3.73833	−	12.7316i	−0.140198	−	0.477472i
$712$	0.317991	+	0.317991i	0.0119172	+	0.0119172i
$713$	8.60806	−	38.7891i	0.322374	−	1.45266i
$714$		−	2.19272i		−	0.0820604i
$715$	18.7146	−	5.64566i	0.699885	−	0.211136i
$716$	3.35094	+	3.86719i	0.125231	+	0.144524i
$717$	7.44707	−	34.2336i	0.278116	−	1.27848i
$718$	6.42518	+	4.80983i	0.239786	+	0.179501i
$719$	−9.52760	+	14.8252i	−0.355320	+	0.552888i	−0.972195	−	0.234173i	$-0.924762\pi$
$719$	−9.52760	+	14.8252i	−0.355320	+	0.552888i	0.616875	+	0.787061i	$0.288398\pi$
$720$	1.04802	+	2.74767i	0.0390575	+	0.102399i
$721$	20.0781	−	23.1714i	0.747748	−	0.862947i
$722$	30.6141	+	40.8956i	1.13934	+	1.52198i
$723$	3.57671	+	1.33404i	0.133019	+	0.0496136i
$724$	10.7160	+	3.14651i	0.398259	+	0.116939i
$725$	32.8073	+	9.10860i	1.21843	+	0.338285i
$726$	−0.219546	−	0.480740i	−0.00814813	−	0.0178419i
$727$	37.9009	−	28.3722i	1.40567	−	1.05227i	0.415924	−	0.909400i	$-0.363458\pi$
$727$	37.9009	−	28.3722i	1.40567	−	1.05227i	0.989742	−	0.142868i	$-0.0456325\pi$
$728$	−0.581024	−	8.12378i	−0.0215342	−	0.301087i
$729$	−23.8178	−	10.8772i	−0.882141	−	0.402860i
$730$	−7.25512	−	32.2035i	−0.268524	−	1.19191i
$731$	0.103824	+	0.722110i	0.00384006	+	0.0267082i
$732$	−9.55713	−	2.07903i	−0.353242	−	0.0768430i
$733$	−3.61955	−	0.258875i	−0.133691	−	0.00956177i	0.00433328	−	0.999991i	$-0.498621\pi$
$733$	−3.61955	−	0.258875i	−0.133691	−	0.00956177i	−0.138024	+	0.990429i	$0.544075\pi$
$734$	30.0669	−	8.82844i	1.10979	−	0.325864i
$735$	6.36928	−	0.0470740i	0.234934	−	0.00173635i
$736$	−4.35407	−	2.01048i	−0.160493	−	0.0741074i
$737$	10.9024	−	10.9024i	0.401596	−	0.401596i
$738$	−0.418960	−	0.228770i	−0.0154221	−	0.00842113i
$739$	7.01482	−	6.07838i	0.258044	−	0.223597i	−0.516225	−	0.856453i	$-0.672663\pi$
$739$	7.01482	−	6.07838i	0.258044	−	0.223597i	0.774269	+	0.632856i	$0.218118\pi$
$740$	−14.0802	+	9.19653i	−0.517598	+	0.338071i
$741$	−28.8903	+	4.15380i	−1.06131	+	0.152594i
$742$	29.1521	−	6.34165i	1.07021	−	0.232809i
$743$	0.459880	+	1.23299i	0.0168714	+	0.0452339i	0.945112	−	0.326745i	$-0.105952\pi$
$743$	0.459880	+	1.23299i	0.0168714	+	0.0452339i	−0.928241	+	0.371979i	$0.878679\pi$
$744$	8.12725	+	7.04231i	0.297960	+	0.258183i
$745$	28.1117	−	21.3702i	1.02993	−	0.782942i
$746$	8.39725	−	3.83490i	0.307445	−	0.140405i
$747$	6.56911	+	12.0304i	0.240351	+	0.440170i
$748$	0.868970	+	1.59140i	0.0317727	+	0.0581874i
$749$	6.38984	−	2.91814i	0.233480	−	0.106627i
$750$	8.95233	+	11.4220i	0.326893	+	0.417074i
$751$	20.4804	+	17.7463i	0.747339	+	0.647573i	0.942884	−	0.333122i	$-0.108102\pi$
$751$	20.4804	+	17.7463i	0.747339	+	0.647573i	−0.195545	+	0.980695i	$0.562648\pi$
$752$	−3.85791	−	10.3434i	−0.140683	−	0.377187i
$753$	7.87519	−	1.71314i	0.286988	−	0.0624304i
$754$	−18.1044	+	2.60302i	−0.659324	+	0.0947965i
$755$	−3.22696	−	0.677045i	−0.117441	−	0.0246402i
$756$	12.8357	−	11.1222i	0.466829	−	0.404510i
$757$	4.99399	+	2.72693i	0.181510	+	0.0991119i	0.567435	−	0.823418i	$-0.307936\pi$
$757$	4.99399	+	2.72693i	0.181510	+	0.0991119i	−0.385925	+	0.922530i	$0.626118\pi$
$758$	−21.0542	+	21.0542i	−0.764723	+	0.764723i
$759$	−20.0662	+	2.79950i	−0.728358	+	0.101616i
$760$	0.138349	+	18.7191i	0.00501845	+	0.679014i
$761$	−27.0418	+	7.94019i	−0.980264	+	0.287832i	−0.732333	−	0.680946i	$-0.761569\pi$
$761$	−27.0418	+	7.94019i	−0.980264	+	0.287832i	−0.247931	+	0.968778i	$0.579751\pi$
$762$	−9.33396	−	0.667578i	−0.338134	−	0.0241838i
$763$	−32.7242	−	7.11871i	−1.18469	−	0.257715i
$764$	3.37916	+	23.5025i	0.122254	+	0.850292i
$765$	1.38474	+	0.875527i	0.0500654	+	0.0316547i
$766$	18.1130	+	8.27194i	0.654450	+	0.298877i
$767$	0.115829	+	1.61950i	0.00418235	+	0.0584768i
$768$	1.03912	−	0.777874i	0.0374960	−	0.0280691i
$769$	20.6072	+	45.1234i	0.743113	+	1.62719i	0.778364	+	0.627813i	$0.216050\pi$
$769$	20.6072	+	45.1234i	0.743113	+	1.62719i	−0.0352509	+	0.999378i	$0.511223\pi$
$770$	−19.2896	+	10.7187i	−0.695149	+	0.386276i
$771$	14.1306	+	4.14913i	0.508902	+	0.149427i
$772$	−13.2880	−	4.95617i	−0.478246	−	0.178377i
$773$	12.6153	+	16.8520i	0.453740	+	0.606125i	0.967828	−	0.251612i	$-0.0809607\pi$
$773$	12.6153	+	16.8520i	0.453740	+	0.606125i	−0.514089	+	0.857737i	$0.671870\pi$
$774$	−1.12780	+	1.30155i	−0.0405378	+	0.0467832i
$775$	−37.9311	−	16.6494i	−1.36252	−	0.598065i
$776$	−1.50232	+	2.33765i	−0.0539301	+	0.0839168i
$777$	23.6976	+	17.7398i	0.850148	+	0.636413i
$778$	1.73986	−	7.99799i	0.0623768	−	0.286742i
$779$	−1.98987	−	2.29644i	−0.0712946	−	0.0822783i
$780$	−6.86975	−	3.68552i	−0.245977	−	0.131963i
$781$		−	22.0126i		−	0.787674i
$782$	−2.61308	+	0.557008i	−0.0934435	+	0.0199186i
$783$	−26.9704	−	26.9704i	−0.963844	−	0.963844i
$784$	0.618262	+	2.10561i	0.0220808	+	0.0752003i
$785$	−1.80795	+	1.59014i	−0.0645285	+	0.0567547i
$786$	8.82836	−	5.67364i	0.314897	−	0.202372i
$787$	−4.34583	+	5.80534i	−0.154912	+	0.206938i	−0.871282	−	0.490782i	$-0.836711\pi$
$787$	−4.34583	+	5.80534i	−0.154912	+	0.206938i	0.716370	+	0.697720i	$0.245802\pi$
$788$	−0.790326	−	3.63307i	−0.0281542	−	0.129423i
$789$	−0.599899	+	1.31359i	−0.0213570	+	0.0467652i
$790$	14.6477	−	17.1590i	0.521142	−	0.610488i
$791$	−0.706857	+	4.91630i	−0.0251329	+	0.174803i
$792$	−1.49583	+	4.01048i	−0.0531520	+	0.142506i
$793$	−17.7633	+	9.69950i	−0.630794	+	0.344439i
$794$	5.40432	−	18.4054i	0.191792	−	0.653184i
$795$	9.78162	−	26.8295i	0.346918	−	0.951543i
$796$	9.40480	+	1.35221i	0.333344	+	0.0479277i
$797$	−29.6760	+	2.12247i	−1.05118	+	0.0751818i	−0.586221	−	0.810151i	$-0.699385\pi$
$797$	−29.6760	+	2.12247i	−1.05118	+	0.0751818i	−0.464958	+	0.885333i	$0.653930\pi$
$798$	30.8727	−	11.5149i	1.09288	−	0.407623i
$799$	−5.17384	−	3.32503i	−0.183037	−	0.117631i
$800$	−2.93690	+	4.04656i	−0.103835	+	0.143067i
$801$	0.319751	+	0.497542i	0.0112978	+	0.0175798i
$802$	−1.64947	+	23.0626i	−0.0582447	+	0.814367i
$803$	23.0270	−	42.1707i	0.812604	−	1.48817i
$804$	−6.14913			−0.216863
$805$	−7.01397	−	31.7517i	−0.247210	−	1.11910i
$806$	22.2529			0.783825
$807$	5.21589	−	9.55219i	0.183608	−	0.336253i
$808$	−0.433117	+	6.05577i	−0.0152370	+	0.213041i
$809$	−8.96760	−	13.9539i	−0.315284	−	0.490592i	0.647055	−	0.762443i	$-0.276000\pi$
$809$	−8.96760	−	13.9539i	−0.315284	−	0.490592i	−0.962339	+	0.271852i	$0.912364\pi$
$810$	−1.11245	−	7.35115i	−0.0390874	−	0.258293i
$811$	−11.0488	−	7.10066i	−0.387977	−	0.249338i	0.332082	−	0.943251i	$-0.392249\pi$
$811$	−11.0488	−	7.10066i	−0.387977	−	0.249338i	−0.720059	+	0.693913i	$0.755885\pi$
$812$	19.3467	−	7.21593i	0.678935	−	0.253230i
$813$	−38.3963	+	2.74615i	−1.34662	+	0.0963119i
$814$	−24.2292	−	3.48363i	−0.849233	−	0.122101i
$815$	−2.42486	+	1.12913i	−0.0849391	+	0.0395517i
$816$	0.203730	−	0.693842i	0.00713199	−	0.0242893i
$817$	−9.62182	+	5.25391i	−0.336625	+	0.183811i
$818$	7.67487	−	20.5771i	0.268345	−	0.719462i
$819$	1.52437	−	10.6022i	0.0532657	−	0.370471i
$820$	−0.0638812	−	0.809095i	−0.00223083	−	0.0282548i
$821$	−0.743767	+	1.62862i	−0.0259576	+	0.0568393i	−0.922167	−	0.386793i	$-0.873583\pi$
$821$	−0.743767	+	1.62862i	−0.0259576	+	0.0568393i	0.896209	+	0.443632i	$0.146310\pi$
$822$	−1.08475	−	4.98654i	−0.0378352	−	0.173925i
$823$	23.5369	−	31.4416i	0.820445	−	1.09599i	−0.173361	−	0.984858i	$-0.555463\pi$
$823$	23.5369	−	31.4416i	0.820445	−	1.09599i	0.993806	−	0.111128i	$-0.0354465\pi$
$824$	8.50623	−	5.46662i	0.296328	−	0.190439i
$825$	−1.19532	+	21.0893i	−0.0416157	+	0.734233i
$826$	−0.516403	−	1.75871i	−0.0179680	−	0.0611933i
$827$	−19.2848	−	19.2848i	−0.670598	−	0.670598i	0.287256	−	0.957854i	$-0.407257\pi$
$827$	−19.2848	−	19.2848i	−0.670598	−	0.670598i	−0.957854	+	0.287256i	$0.907257\pi$
$828$	−5.03333	−	3.80085i	−0.174920	−	0.132089i
$829$		−	34.7915i		−	1.20836i	−0.796849	−	0.604179i	$-0.793501\pi$
$829$		−	34.7915i		−	1.20836i	0.796849	−	0.604179i	$-0.206499\pi$
$830$	−11.0176	+	20.5367i	−0.382427	+	0.712838i
$831$	−14.5997	−	16.8489i	−0.506457	−	0.584482i
$832$	0.570945	−	2.62459i	0.0197940	−	0.0909913i
$833$	0.978717	+	0.732658i	0.0339105	+	0.0253851i
$834$	6.77104	−	10.5359i	0.234462	−	0.364830i
$835$	4.25412	−	9.50042i	0.147220	−	0.328775i
$836$	−17.8430	+	20.5919i	−0.617113	+	0.712186i
$837$	27.8093	+	37.1488i	0.961228	+	1.28405i
$838$	34.4945	+	12.8658i	1.19159	+	0.444442i
$839$	−25.7061	−	7.54800i	−0.887474	−	0.260586i	−0.193943	−	0.981013i	$-0.562128\pi$
$839$	−25.7061	−	7.54800i	−0.887474	−	0.260586i	−0.693531	+	0.720427i	$0.743946\pi$
$840$	8.46256	+	2.41704i	0.291986	+	0.0833959i
$841$	−7.21640	−	15.8017i	−0.248841	−	0.544887i
$842$	−11.8644	+	8.88156i	−0.408873	+	0.306079i
$843$	2.26920	+	31.7276i	0.0781554	+	1.09276i
$844$	−9.05065	−	4.13329i	−0.311536	−	0.142274i
$845$	12.6206	−	2.84328i	0.434160	−	0.0978118i
$846$	−2.06620	−	14.3707i	−0.0710375	−	0.494076i
$847$	1.20639	+	0.262433i	0.0414520	+	0.00901732i
$848$	9.81382	+	0.701898i	0.337008	+	0.0241033i
$849$	7.39384	−	2.17103i	0.253756	−	0.0745094i
$850$	0.0411722	+	2.78522i	0.00141220	+	0.0955324i
$851$	15.1209	−	32.7470i	0.518336	−	1.12255i
$852$	−6.20772	+	6.20772i	−0.212673	+	0.212673i
$853$	10.7943	+	5.89414i	0.369590	+	0.201811i	0.653301	−	0.757099i	$-0.273384\pi$
$853$	10.7943	+	5.89414i	0.369590	+	0.201811i	−0.283711	+	0.958910i	$0.591566\pi$
$854$	17.2675	−	14.9623i	0.590880	−	0.512001i
$855$	−5.05522	+	24.0944i	−0.172885	+	0.824012i
$856$	2.29307	−	0.329693i	0.0783754	−	0.0112687i
$857$	−12.9284	+	2.81239i	−0.441625	+	0.0960696i	−0.427879	−	0.903836i	$-0.640739\pi$
$857$	−12.9284	+	2.81239i	−0.441625	+	0.0960696i	−0.0137456	+	0.999906i	$0.504375\pi$
$858$	−3.96545	−	10.6318i	−0.135378	−	0.362963i
$859$	−25.5954	−	22.1786i	−0.873305	−	0.756723i	0.0978424	−	0.995202i	$-0.468806\pi$
$859$	−25.5954	−	22.1786i	−0.873305	−	0.756723i	−0.971148	+	0.238478i	$0.923351\pi$
$860$	−2.90135	−	0.395288i	−0.0989352	−	0.0134792i
$861$	−1.29950	+	0.593460i	−0.0442867	+	0.0202251i
$862$	7.10146	+	13.0054i	0.241877	+	0.442964i
$863$	18.9026	+	34.6174i	0.643450	+	1.17839i	0.972239	+	0.233988i	$0.0751777\pi$
$863$	18.9026	+	34.6174i	0.643450	+	1.17839i	−0.328789	+	0.944403i	$0.606641\pi$
$864$	5.09498	−	2.32680i	0.173335	−	0.0791593i
$865$	−41.7267	−	5.68495i	−1.41875	−	0.193294i
$866$	−1.97415	−	1.71061i	−0.0670844	−	0.0581290i
$867$	7.57061	+	20.2976i	0.257111	+	0.689342i
$868$	−24.5476	+	5.34000i	−0.833199	+	0.181251i
$869$	32.5035	−	4.67330i	1.10261	−	0.158531i
$870$	4.05846	−	19.3436i	0.137595	−	0.655810i
$871$	−9.61639	+	8.33265i	−0.325839	+	0.282341i
$872$	−9.69350	−	5.29305i	−0.328263	−	0.179245i
$873$	−2.58411	+	2.58411i	−0.0874589	+	0.0874589i
$874$	−21.5649	−	33.8661i	−0.729442	−	1.14554i
$875$	−33.8932	+	0.751601i	−1.14580	+	0.0254088i
$876$	−18.3862	+	5.39868i	−0.621213	+	0.182405i
$877$	−25.7724	−	1.84328i	−0.870274	−	0.0622432i	−0.370944	−	0.928655i	$-0.620966\pi$
$877$	−25.7724	−	1.84328i	−0.870274	−	0.0622432i	−0.499330	+	0.866412i	$0.666420\pi$
$878$	−14.8405	−	3.22836i	−0.500844	−	0.108952i
$879$	2.78351	+	19.3598i	0.0938855	+	0.652988i
$880$	−7.09971	+	1.59949i	−0.239331	+	0.0539188i
$881$	−21.5299	−	9.83238i	−0.725361	−	0.331261i	0.0182868	−	0.999833i	$-0.494179\pi$
$881$	−21.5299	−	9.83238i	−0.725361	−	0.331261i	−0.743648	+	0.668572i	$0.766906\pi$
$882$	0.205891	+	2.87873i	0.00693271	+	0.0969319i
$883$	33.0746	−	24.7593i	1.11305	−	0.833218i	0.125745	−	0.992063i	$-0.459868\pi$
$883$	33.0746	−	24.7593i	1.11305	−	0.833218i	0.987304	+	0.158845i	$0.0507769\pi$
$884$	−0.621615	−	1.36115i	−0.0209072	−	0.0457803i
$885$	−1.68704	−	0.481846i	−0.0567092	−	0.0161971i
$886$	9.74484	+	2.86134i	0.327384	+	0.0961287i
$887$	−8.53284	−	3.18258i	−0.286505	−	0.106861i	0.202103	−	0.979364i	$-0.435222\pi$
$887$	−8.53284	−	3.18258i	−0.286505	−	0.106861i	−0.488608	+	0.872504i	$0.662495\pi$
$888$	5.85040	+	7.81522i	0.196326	+	0.262261i
$889$	14.3155	−	16.5209i	0.480125	−	0.554094i
$890$	−0.410959	+	0.917765i	−0.0137754	+	0.0307636i
$891$	5.85062	−	9.10374i	0.196003	−	0.304987i
$892$	−1.98830	−	1.48842i	−0.0665731	−	0.0498360i
$893$	19.6451	−	90.3070i	0.657398	−	3.02201i
$894$	−13.4236	−	15.4917i	−0.448953	−	0.518120i
$895$	−5.40921	+	10.0827i	−0.180810	+	0.337027i
$896$			3.03224i			0.101300i
$897$	16.6827	−	1.12308i	0.557018	−	0.0374985i
$898$	0.777574	+	0.777574i	0.0259480	+	0.0259480i
$899$	15.8945	+	54.1318i	0.530112	+	1.80540i
$900$	−4.90541	+	4.37917i	−0.163514	+	0.145972i
$901$	4.61116	−	2.96341i	0.153620	−	0.0987256i
$902$	0.707943	−	0.945701i	0.0235719	−	0.0314884i
$903$	1.09559	+	5.03633i	0.0364588	+	0.167599i
$904$	−0.680455	+	1.48999i	−0.0226316	+	0.0495563i
$905$	1.96563	+	24.8959i	0.0653398	+	0.827568i
$906$	−0.272392	+	1.89453i	−0.00904963	+	0.0629416i
$907$	13.4278	−	36.0013i	0.445863	−	1.19540i	−0.498613	−	0.866825i	$-0.666157\pi$
$907$	13.4278	−	36.0013i	0.445863	−	1.19540i	0.944476	−	0.328580i	$-0.106570\pi$
$908$	−9.58903	+	5.23600i	−0.318223	+	0.173763i
$909$	−2.24951	+	7.66112i	−0.0746115	+	0.254103i
$910$	16.5096	−	7.68765i	0.547288	−	0.254843i
$911$	1.51508	+	0.217836i	0.0501969	+	0.00721723i	0.167368	−	0.985895i	$-0.446473\pi$
$911$	1.51508	+	0.217836i	0.0501969	+	0.00721723i	−0.117171	+	0.993112i	$0.537382\pi$
$912$	10.8389	−	0.775215i	0.358912	−	0.0256699i
$913$	−31.7830	+	11.8544i	−1.05186	+	0.392325i
$914$	2.06886	+	1.32957i	0.0684316	+	0.0439783i
$915$	−3.27236	−	21.6240i	−0.108181	−	0.714867i
$916$	−15.0704	−	23.4499i	−0.497939	−	0.774808i
$917$	−1.74890	+	24.4528i	−0.0577536	+	0.807501i
$918$	1.49546	−	2.73873i	0.0493576	−	0.0903917i
$919$	56.2155			1.85438			0.927189	−	0.374593i	$-0.122218\pi$
$919$	56.2155			1.85438			0.927189	+	0.374593i	$0.122218\pi$
$920$	0.730693	−	10.6989i	0.0240902	−	0.352732i
$921$	−13.1318			−0.432707
$922$	9.67020	−	17.7097i	0.318471	−	0.583236i
$923$	−1.29597	+	18.1201i	−0.0426574	+	0.596429i
$924$	6.92565	+	10.7765i	0.227837	+	0.354522i
$925$	−30.4342	−	22.0884i	−1.00067	−	0.726263i
$926$	26.2913	+	16.8964i	0.863985	+	0.555249i
$927$	12.4595	−	4.64714i	0.409223	−	0.152632i
$928$	6.79232	−	0.485796i	0.222969	−	0.0159470i
$929$	−31.0170	−	4.45958i	−1.01764	−	0.146314i	−0.386746	−	0.922186i	$-0.626401\pi$
$929$	−31.0170	−	4.45958i	−1.01764	−	0.146314i	−0.630890	+	0.775872i	$0.717310\pi$
$930$	−8.23663	+	22.5918i	−0.270090	+	0.740814i
$931$	−5.17589	+	17.6275i	−0.169633	+	0.577717i
$932$	24.8160	−	13.5506i	0.812876	−	0.443864i
$933$	−3.83371	+	10.2786i	−0.125510	+	0.336505i
$934$	2.61290	−	18.1731i	0.0854967	−	0.594642i
$935$	−2.63236	+	3.08366i	−0.0860874	+	0.100847i
$936$	1.46743	−	3.21322i	0.0479644	−	0.105027i
$937$	−5.86715	−	26.9708i	−0.191671	−	0.881099i	−0.968035	−	0.250814i	$-0.919302\pi$
$937$	−5.86715	−	26.9708i	−0.191671	−	0.881099i	0.776364	−	0.630285i	$-0.217062\pi$
$938$	8.60844	−	11.4995i	0.281076	−	0.375473i
$939$	−14.1591	+	9.09950i	−0.462065	+	0.296951i
$940$	18.5357	−	16.3027i	0.604569	−	0.531736i
$941$	−7.30425	−	24.8760i	−0.238112	−	0.810935i	−0.988667	−	0.150126i	$-0.952032\pi$
$941$	−7.30425	−	24.8760i	−0.238112	−	0.810935i	0.750555	−	0.660808i	$-0.229786\pi$
$942$	0.988307	+	0.988307i	0.0322008	+	0.0322008i
$943$	1.03734	+	1.39786i	0.0337803	+	0.0455207i
$944$		−	0.604488i		−	0.0196744i
$945$	33.4656	+	17.9538i	1.08864	+	0.584038i
$946$	−2.79103	−	3.22102i	−0.0907441	−	0.104724i
$947$	−4.98974	+	22.9375i	−0.162145	+	0.745368i	0.822212	+	0.569182i	$0.192740\pi$
$947$	−4.98974	+	22.9375i	−0.162145	+	0.745368i	−0.984357	+	0.176187i	$0.943624\pi$
$948$	−10.4841	−	7.84832i	−0.340509	−	0.254902i
$949$	−21.4378	+	33.3578i	−0.695900	+	1.08284i
$950$	−38.9987	+	15.2061i	−1.26529	+	0.493351i
$951$	−25.2778	+	29.1721i	−0.819688	+	0.945971i
$952$	1.01235	+	1.35234i	0.0328104	+	0.0438295i
$953$	−20.1828	−	7.52778i	−0.653784	−	0.243849i	0.000613126	−	1.00000i	$-0.499805\pi$
$953$	−20.1828	−	7.52778i	−0.653784	−	0.243849i	−0.654397	+	0.756151i	$0.727078\pi$
$954$	12.4154	+	3.64549i	0.401964	+	0.118027i
$955$	−46.4099	+	25.7888i	−1.50179	+	0.834506i
$956$	11.2123	+	24.5515i	0.362631	+	0.794051i
$957$	23.0302	−	17.2402i	0.744460	−	0.557295i
$958$	−1.86662	−	26.0987i	−0.0603077	−	0.843212i
$959$	10.8440	+	4.95227i	0.350169	+	0.159917i
$960$	2.45324	+	1.55110i	0.0791778	+	0.0500615i
$961$	−5.35655	−	37.2556i	−0.172792	−	1.20179i
$962$	19.7396	+	4.29408i	0.636429	+	0.138447i
$963$	3.03896	+	0.217351i	0.0979292	+	0.00700403i
$964$	−2.82181	+	0.828558i	−0.0908843	+	0.0266860i
$965$	−0.234373	−	31.7115i	−0.00754473	−	1.02083i
$966$	−18.1334	+	5.24220i	−0.583434	+	0.168665i
$967$	6.12082	−	6.12082i	0.196832	−	0.196832i	−0.601808	−	0.798641i	$-0.705553\pi$
$967$	6.12082	−	6.12082i	0.196832	−	0.196832i	0.798641	+	0.601808i	$0.205553\pi$
$968$	0.357354	+	0.195130i	0.0114858	+	0.00627171i
$969$	4.57519	−	3.96443i	0.146976	−	0.127356i
$970$	−6.08112	−	1.27587i	−0.195253	−	0.0409658i
$971$	−3.17353	+	0.456285i	−0.101843	+	0.0146429i	−0.193048	−	0.981189i	$-0.561837\pi$
$971$	−3.17353	+	0.456285i	−0.101843	+	0.0146429i	0.0912047	+	0.995832i	$0.470928\pi$
$972$	12.2022	−	2.65442i	0.391385	−	0.0851406i
$973$	10.2243	+	27.4123i	0.327775	+	0.878798i
$974$	−15.3061	−	13.2628i	−0.490438	−	0.424967i
$975$	2.22556	−	17.2896i	0.0712748	−	0.553710i
$976$	6.85413	−	3.13017i	0.219395	−	0.100194i
$977$	12.8629	+	23.5567i	0.411522	+	0.753646i	0.998430	−	0.0560073i	$-0.0178370\pi$
$977$	12.8629	+	23.5567i	0.411522	+	0.753646i	−0.586909	+	0.809653i	$0.699655\pi$
$978$	0.744147	+	1.36280i	0.0237952	+	0.0435776i
$979$	−1.33138	+	0.608020i	−0.0425510	+	0.0194324i
$980$	−3.90646	+	2.96964i	−0.124787	+	0.0948617i
$981$	−10.9773	−	9.51190i	−0.350479	−	0.303691i
$982$	−3.81886	−	10.2388i	−0.121865	−	0.326732i
$983$	−21.2885	+	4.63102i	−0.678996	+	0.147707i	−0.538821	−	0.842420i	$-0.681130\pi$
$983$	−21.2885	+	4.63102i	−0.678996	+	0.147707i	−0.140175	+	0.990127i	$0.544767\pi$
$984$	−0.466339	+	0.0670495i	−0.0148664	+	0.00213746i
$985$	6.96059	−	4.54634i	0.221783	−	0.144858i
$986$	2.86709	−	2.48435i	0.0913067	−	0.0791177i
$987$	−38.1356	−	20.8236i	−1.21387	−	0.662822i
$988$	15.9001	−	15.9001i	0.505849	−	0.505849i
$989$	5.72352	−	2.58498i	0.181997	−	0.0821975i
$990$	−9.57090	+	0.0707365i	−0.304183	+	0.00224815i
$991$	−41.1091	+	12.0707i	−1.30587	+	0.383439i	−0.859376	−	0.511345i	$-0.829147\pi$
$991$	−41.1091	+	12.0707i	−1.30587	+	0.383439i	−0.446499	+	0.894784i	$0.647329\pi$
$992$	−8.26374	−	0.591034i	−0.262374	−	0.0187654i
$993$	−28.3536	−	6.16794i	−0.899773	−	0.195734i
$994$	−2.91864	−	20.2996i	−0.0925735	−	0.643863i
$995$	4.66948	+	20.7265i	0.148032	+	0.657076i
$996$	12.3061	+	5.61999i	0.389932	+	0.178076i
$997$	−3.59988	−	50.3329i	−0.114009	−	1.59406i	−0.656717	−	0.754137i	$-0.728056\pi$
$997$	−3.59988	−	50.3329i	−0.114009	−	1.59406i	0.542708	−	0.839921i	$-0.317399\pi$
$998$	−17.5428	+	13.1323i	−0.555306	+	0.415697i
$999$	17.4999	+	38.3194i	0.553671	+	1.21237i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.83.3	yes	240
5.2	odd	4	inner	230.2.l.a.37.4	✓	240
23.5	odd	22	inner	230.2.l.a.143.4	yes	240
115.97	even	44	inner	230.2.l.a.97.3	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.37.4	✓	240	5.2	odd	4	inner
230.2.l.a.83.3	yes	240	1.1	even	1	trivial
230.2.l.a.97.3	yes	240	115.97	even	44	inner
230.2.l.a.143.4	yes	240	23.5	odd	22	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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.479249 + 0.877679i) q^{2} +(-0.0925997 + 1.29471i) q^{3} +(-0.540641 - 0.841254i) q^{4} +(1.32676 - 1.79992i) q^{5} +(-1.09196 - 0.701763i) q^{6} +(2.84106 - 1.05966i) q^{7} +(0.997452 - 0.0713392i) q^{8} +(1.30176 + 0.187165i) q^{9} +O(q^{10})\)	\(q+(-0.479249 + 0.877679i) q^{2} +(-0.0925997 + 1.29471i) q^{3} +(-0.540641 - 0.841254i) q^{4} +(1.32676 - 1.79992i) q^{5} +(-1.09196 - 0.701763i) q^{6} +(2.84106 - 1.05966i) q^{7} +(0.997452 - 0.0713392i) q^{8} +(1.30176 + 0.187165i) q^{9} +(0.943903 + 2.02708i) q^{10} +(-0.916945 + 3.12283i) q^{11} +(1.13924 - 0.622075i) q^{12} +(0.938652 - 2.51662i) q^{13} +(-0.431533 + 3.00138i) q^{14} +(2.20752 + 1.88444i) q^{15} +(-0.415415 + 0.909632i) q^{16} +(0.118421 + 0.544374i) q^{17} +(-0.788137 + 1.05283i) q^{18} +(-7.04270 + 4.52607i) q^{19} +(-2.23149 - 0.143031i) q^{20} +(1.10887 + 3.77648i) q^{21} +(-2.30140 - 2.30140i) q^{22} +(4.21877 - 2.28078i) q^{23} +1.29802i q^{24} +(-1.47942 - 4.77612i) q^{25} +(1.75894 + 2.02992i) q^{26} +(-1.19061 + 5.47314i) q^{27} +(-2.42744 - 1.81716i) q^{28} +(-3.68158 + 5.72866i) q^{29} +(-2.71189 + 1.03438i) q^{30} +(5.42542 - 6.26127i) q^{31} +(-0.599278 - 0.800541i) q^{32} +(-3.95826 - 1.47635i) q^{33} +(-0.534539 - 0.156955i) q^{34} +(1.86210 - 6.51959i) q^{35} +(-0.546331 - 1.19630i) q^{36} +(6.02087 - 4.50717i) q^{37} +(-0.597229 - 8.35035i) q^{38} +(3.17138 + 1.44832i) q^{39} +(1.19497 - 1.88998i) q^{40} +(0.0516552 + 0.359270i) q^{41} +(-3.84596 - 0.836638i) q^{42} +(1.30617 + 0.0934194i) q^{43} +(3.12283 - 0.916945i) q^{44} +(2.06400 - 2.09474i) q^{45} +(-0.0200519 + 4.79579i) q^{46} +(-7.80610 + 7.80610i) q^{47} +(-1.13924 - 0.622075i) q^{48} +(1.65849 - 1.43709i) q^{49} +(4.90091 + 0.990495i) q^{50} +(-0.715774 + 0.102913i) q^{51} +(-2.62459 + 0.570945i) q^{52} +(-3.43834 - 9.21854i) q^{53} +(-4.23306 - 3.66797i) q^{54} +(4.40427 + 5.79367i) q^{55} +(2.75823 - 1.25964i) q^{56} +(-5.20781 - 9.53739i) q^{57} +(-3.26353 - 5.97670i) q^{58} +(-0.549862 + 0.251113i) q^{59} +(0.391819 - 2.87589i) q^{60} +(-5.69461 - 4.93441i) q^{61} +(2.89526 + 7.76249i) q^{62} +(3.89670 - 0.847676i) q^{63} +(0.989821 - 0.142315i) q^{64} +(-3.28435 - 5.02845i) q^{65} +(3.19275 - 2.76654i) q^{66} +(-4.15784 - 2.27035i) q^{67} +(0.393933 - 0.393933i) q^{68} +(2.56230 + 5.67330i) q^{69} +(4.82970 + 4.75883i) q^{70} +(-6.48944 + 1.90547i) q^{71} +(1.31179 + 0.0938213i) q^{72} +(-14.4254 - 3.13806i) q^{73} +(1.07035 + 7.44445i) q^{74} +(6.32070 - 1.47316i) q^{75} +(7.61515 + 3.47772i) q^{76} +(0.704042 + 9.84379i) q^{77} +(-2.79105 + 2.08935i) q^{78} +(-4.19131 - 9.17769i) q^{79} +(1.08611 + 1.95458i) q^{80} +(-3.19028 - 0.936750i) q^{81} +(-0.340079 - 0.126843i) q^{82} +(6.24597 + 8.34364i) q^{83} +(2.57747 - 2.97456i) q^{84} +(1.13695 + 0.509104i) q^{85} +(-0.707975 + 1.10163i) q^{86} +(-7.07605 - 5.29706i) q^{87} +(-0.691829 + 3.18029i) q^{88} +(0.294495 + 0.339866i) q^{89} +(0.849336 + 2.81543i) q^{90} -8.14453i q^{91} +(-4.19955 - 2.31598i) q^{92} +(7.60415 + 7.60415i) q^{93} +(-3.11018 - 10.5923i) q^{94} +(-1.19741 + 18.6813i) q^{95} +(1.09196 - 0.701763i) q^{96} +(-1.66526 + 2.22452i) q^{97} +(0.466475 + 2.14435i) q^{98} +(-1.77812 + 3.89355i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 8 q^{6}+O(q^{10}) \) 240 * q - 8 * q^3 - 8 * q^6	\( 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46} - 80 q^{47} + 8 q^{48} + 8 q^{50} + 16 q^{52} - 44 q^{56} - 88 q^{57} - 176 q^{61} - 32 q^{62} - 176 q^{66} + 24 q^{70} - 336 q^{71} + 16 q^{72} - 88 q^{73} - 36 q^{75} - 24 q^{77} + 40 q^{78} - 136 q^{81} + 40 q^{82} - 100 q^{85} - 44 q^{86} + 40 q^{87} + 8 q^{92} + 56 q^{93} + 52 q^{95} + 8 q^{96} + 132 q^{97} + 24 q^{98}+O(q^{100}) \) 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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