LMFDB - Embedded newform 230.2.l.a.217.6

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			217.6
Character	$\chi$	$=$	230.217
Dual form			230.2.l.a.53.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0713392 + 0.997452i) q^{2} +(2.50200 - 0.544276i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(1.09283 + 1.95083i) q^{5} +(0.364399 + 2.53445i) q^{6} +(0.862032 - 0.470705i) q^{7} +(0.212565 - 0.977147i) q^{8} +(3.23486 - 1.47731i) q^{9} +O(q^{10})$	\(q+(-0.0713392 + 0.997452i) q^{2} +(2.50200 - 0.544276i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(1.09283 + 1.95083i) q^{5} +(0.364399 + 2.53445i) q^{6} +(0.862032 - 0.470705i) q^{7} +(0.212565 - 0.977147i) q^{8} +(3.23486 - 1.47731i) q^{9} +(-2.02382 + 0.950875i) q^{10} +(-4.13264 - 3.58095i) q^{11} +(-2.55399 + 0.182665i) q^{12} +(-1.66485 + 3.04895i) q^{13} +(0.408009 + 0.893415i) q^{14} +(3.79605 + 4.28616i) q^{15} +(0.959493 + 0.281733i) q^{16} +(0.137398 + 0.102855i) q^{17} +(1.24278 + 3.33201i) q^{18} +(0.241301 - 1.67828i) q^{19} +(-0.804074 - 2.08650i) q^{20} +(1.90061 - 1.64689i) q^{21} +(3.86665 - 3.86665i) q^{22} +(2.13500 - 4.29439i) q^{23} -2.56051i q^{24} +(-2.61145 + 4.26384i) q^{25} +(-2.92241 - 1.87812i) q^{26} +(1.14017 - 0.853517i) q^{27} +(-0.920246 + 0.343234i) q^{28} +(5.01202 - 0.720619i) q^{29} +(-4.54605 + 3.48060i) q^{30} +(-8.53830 + 5.48723i) q^{31} +(-0.349464 + 0.936950i) q^{32} +(-12.2889 - 6.71024i) q^{33} +(-0.112394 + 0.129710i) q^{34} +(1.86032 + 1.16727i) q^{35} +(-3.41218 + 1.00191i) q^{36} +(4.75179 + 1.77232i) q^{37} +(1.65679 + 0.360413i) q^{38} +(-2.50598 + 8.53460i) q^{39} +(2.13854 - 0.653177i) q^{40} +(1.70890 - 3.74198i) q^{41} +(1.50710 + 2.01325i) q^{42} +(-1.12179 - 5.15679i) q^{43} +(3.58095 + 4.13264i) q^{44} +(6.41713 + 4.69621i) q^{45} +(4.13114 + 2.43592i) q^{46} +(-5.74203 - 5.74203i) q^{47} +(2.55399 + 0.182665i) q^{48} +(-3.26295 + 5.07725i) q^{49} +(-4.06668 - 2.90897i) q^{50} +(0.399750 + 0.182560i) q^{51} +(2.08182 - 2.78098i) q^{52} +(-5.01582 - 9.18578i) q^{53} +(0.770004 + 1.19815i) q^{54} +(2.46955 - 11.9754i) q^{55} +(-0.276710 - 0.942387i) q^{56} +(-0.309716 - 4.33039i) q^{57} +(0.361230 + 5.05066i) q^{58} +(-0.184613 - 0.628733i) q^{59} +(-3.14742 - 4.78277i) q^{60} +(2.53267 + 3.94090i) q^{61} +(-4.86414 - 8.90800i) q^{62} +(2.09318 - 2.79616i) q^{63} +(-0.909632 - 0.415415i) q^{64} +(-7.76736 + 0.0841432i) q^{65} +(7.56982 - 11.7789i) q^{66} +(0.295442 + 0.0211304i) q^{67} +(-0.121361 - 0.121361i) q^{68} +(3.00444 - 11.9066i) q^{69} +(-1.29701 + 1.77231i) q^{70} +(6.31730 + 7.29055i) q^{71} +(-0.755932 - 3.47496i) q^{72} +(1.15831 + 1.54732i) q^{73} +(-2.10680 + 4.61324i) q^{74} +(-4.21313 + 12.0895i) q^{75} +(-0.477689 + 1.62686i) q^{76} +(-5.24804 - 1.14164i) q^{77} +(-8.33408 - 3.10845i) q^{78} +(16.2406 - 4.76868i) q^{79} +(0.498951 + 2.17969i) q^{80} +(-4.59837 + 5.30680i) q^{81} +(3.61053 + 1.97150i) q^{82} +(1.60007 - 4.28996i) q^{83} +(-2.11564 + 1.35964i) q^{84} +(-0.0504993 + 0.380441i) q^{85} +(5.22368 - 0.751051i) q^{86} +(12.1478 - 4.53091i) q^{87} +(-4.37757 + 3.27701i) q^{88} +(-8.23324 - 5.29118i) q^{89} +(-5.14203 + 6.06576i) q^{90} +3.41194i q^{91} +(-2.72443 + 3.94683i) q^{92} +(-18.3762 + 18.3762i) q^{93} +(6.13703 - 5.31777i) q^{94} +(3.53774 - 1.36334i) q^{95} +(-0.364399 + 2.53445i) q^{96} +(-3.64640 - 9.77637i) q^{97} +(-4.83154 - 3.61684i) q^{98} +(-18.6587 - 5.47869i) 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 $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{22}\right)$

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 $

$2$	−0.0713392	+	0.997452i	−0.0504444	+	0.705305i
$2$	−0.0713392	+	0.997452i	−0.0504444	+	0.705305i
$3$	2.50200	−	0.544276i	1.44453	−	0.314238i	0.579095	−	0.815260i	$-0.303406\pi$
$3$	2.50200	−	0.544276i	1.44453	−	0.314238i	0.865435	+	0.501022i	$0.167042\pi$
$4$	−0.989821	−	0.142315i	−0.494911	−	0.0711574i
$5$	1.09283	+	1.95083i	0.488728	+	0.872436i
$5$	1.09283	+	1.95083i	0.488728	+	0.872436i
$6$	0.364399	+	2.53445i	0.148765	+	1.03469i
$7$	0.862032	−	0.470705i	0.325817	−	0.177910i	−0.308012	−	0.951382i	$-0.599664\pi$
$7$	0.862032	−	0.470705i	0.325817	−	0.177910i	0.633830	+	0.773473i	$0.281482\pi$
$8$	0.212565	−	0.977147i	0.0751532	−	0.345474i
$9$	3.23486	−	1.47731i	1.07829	−	0.492438i
$10$	−2.02382	+	0.950875i	−0.639987	+	0.300693i
$11$	−4.13264	−	3.58095i	−1.24604	−	1.07970i	−0.993702	−	0.112058i	$-0.964256\pi$
$11$	−4.13264	−	3.58095i	−1.24604	−	1.07970i	−0.252336	−	0.967640i	$-0.581199\pi$
$12$	−2.55399	+	0.182665i	−0.737274	+	0.0527308i
$13$	−1.66485	+	3.04895i	−0.461746	+	0.845625i	0.538250	+	0.842786i	$0.319086\pi$
$13$	−1.66485	+	3.04895i	−0.461746	+	0.845625i	−0.999996	+	0.00283996i	$0.999096\pi$
$14$	0.408009	+	0.893415i	0.109045	+	0.238775i
$15$	3.79605	+	4.28616i	0.980135	+	1.10668i
$16$	0.959493	+	0.281733i	0.239873	+	0.0704331i
$17$	0.137398	+	0.102855i	0.0333238	+	0.0249459i	0.615810	−	0.787895i	$-0.288829\pi$
$17$	0.137398	+	0.102855i	0.0333238	+	0.0249459i	−0.582486	+	0.812841i	$0.697920\pi$
$18$	1.24278	+	3.33201i	0.292925	+	0.785363i
$19$	0.241301	−	1.67828i	0.0553581	−	0.385024i	−0.943241	−	0.332109i	$-0.892240\pi$
$19$	0.241301	−	1.67828i	0.0553581	−	0.385024i	0.998599	−	0.0529149i	$-0.0168512\pi$
$20$	−0.804074	−	2.08650i	−0.179796	−	0.466555i
$21$	1.90061	−	1.64689i	0.414747	−	0.359380i
$22$	3.86665	−	3.86665i	0.824372	−	0.824372i
$23$	2.13500	−	4.29439i	0.445179	−	0.895442i
$23$	2.13500	−	4.29439i	0.445179	−	0.895442i
$24$		−	2.56051i		−	0.522663i
$25$	−2.61145	+	4.26384i	−0.522290	+	0.852768i
$26$	−2.92241	−	1.87812i	−0.573131	−	0.368329i
$27$	1.14017	−	0.853517i	0.219425	−	0.164259i
$28$	−0.920246	+	0.343234i	−0.173910	+	0.0648651i
$29$	5.01202	−	0.720619i	0.930708	−	0.133816i	0.339748	−	0.940516i	$-0.389658\pi$
$29$	5.01202	−	0.720619i	0.930708	−	0.133816i	0.590960	+	0.806701i	$0.298749\pi$
$30$	−4.54605	+	3.48060i	−0.829991	+	0.635468i
$31$	−8.53830	+	5.48723i	−1.53352	+	0.985536i	−0.544339	+	0.838866i	$0.683219\pi$
$31$	−8.53830	+	5.48723i	−1.53352	+	0.985536i	−0.989185	+	0.146670i	$0.953144\pi$
$32$	−0.349464	+	0.936950i	−0.0617771	+	0.165631i
$33$	−12.2889	−	6.71024i	−2.13922	−	1.16810i
$34$	−0.112394	+	0.129710i	−0.0192755	+	0.0222451i
$35$	1.86032	+	1.16727i	0.314451	+	0.197305i
$36$	−3.41218	+	1.00191i	−0.568697	+	0.166984i
$37$	4.75179	+	1.77232i	0.781189	+	0.291368i	0.708244	−	0.705968i	$-0.249488\pi$
$37$	4.75179	+	1.77232i	0.781189	+	0.291368i	0.0729448	+	0.997336i	$0.476760\pi$
$38$	1.65679	+	0.360413i	0.268767	+	0.0584667i
$39$	−2.50598	+	8.53460i	−0.401279	+	1.36663i
$40$	2.13854	−	0.653177i	0.338133	−	0.103276i
$41$	1.70890	−	3.74198i	0.266886	−	0.584399i	−0.727980	−	0.685598i	$-0.759541\pi$
$41$	1.70890	−	3.74198i	0.266886	−	0.584399i	0.994866	+	0.101199i	$0.0322680\pi$
$42$	1.50710	+	2.01325i	0.232551	+	0.310652i
$43$	−1.12179	−	5.15679i	−0.171071	−	0.786403i	−0.980080	−	0.198605i	$-0.936359\pi$
$43$	−1.12179	−	5.15679i	−0.171071	−	0.786403i	0.809008	−	0.587797i	$-0.200005\pi$
$44$	3.58095	+	4.13264i	0.539849	+	0.623019i
$45$	6.41713	+	4.69621i	0.956610	+	0.700069i
$46$	4.13114	+	2.43592i	0.609103	+	0.359157i
$47$	−5.74203	−	5.74203i	−0.837561	−	0.837561i	0.150976	−	0.988537i	$-0.451758\pi$
$47$	−5.74203	−	5.74203i	−0.837561	−	0.837561i	−0.988537	+	0.150976i	$0.951758\pi$
$48$	2.55399	+	0.182665i	0.368637	+	0.0263654i
$49$	−3.26295	+	5.07725i	−0.466136	+	0.725321i
$50$	−4.06668	−	2.90897i	−0.575115	−	0.411391i
$51$	0.399750	+	0.182560i	0.0559762	+	0.0255635i
$52$	2.08182	−	2.78098i	0.288696	−	0.385652i
$53$	−5.01582	−	9.18578i	−0.688975	−	1.26176i	−0.954658	−	0.297704i	$-0.903779\pi$
$53$	−5.01582	−	9.18578i	−0.688975	−	1.26176i	0.265683	−	0.964060i	$-0.414403\pi$
$54$	0.770004	+	1.19815i	0.104784	+	0.163047i
$55$	2.46955	−	11.9754i	0.332994	−	1.61477i
$56$	−0.276710	−	0.942387i	−0.0369769	−	0.125932i
$57$	−0.309716	−	4.33039i	−0.0410229	−	0.573575i
$58$	0.361230	+	5.05066i	0.0474318	+	0.663184i
$59$	−0.184613	−	0.628733i	−0.0240345	−	0.0818541i	0.946602	−	0.322403i	$-0.104491\pi$
$59$	−0.184613	−	0.628733i	−0.0240345	−	0.0818541i	−0.970637	+	0.240549i	$0.922672\pi$
$60$	−3.14742	−	4.78277i	−0.406331	−	0.617453i
$61$	2.53267	+	3.94090i	0.324275	+	0.504581i	0.964669	−	0.263465i	$-0.0848654\pi$
$61$	2.53267	+	3.94090i	0.324275	+	0.504581i	−0.640394	+	0.768046i	$0.721229\pi$
$62$	−4.86414	−	8.90800i	−0.617746	−	1.13132i
$63$	2.09318	−	2.79616i	0.263716	−	0.352283i
$64$	−0.909632	−	0.415415i	−0.113704	−	0.0519269i
$65$	−7.76736	+	0.0841432i	−0.963423	+	0.0104367i
$66$	7.56982	−	11.7789i	0.931781	−	1.44988i
$67$	0.295442	+	0.0211304i	0.0360940	+	0.00258149i	0.0893745	−	0.995998i	$-0.471513\pi$
$67$	0.295442	+	0.0211304i	0.0360940	+	0.00258149i	−0.0532805	+	0.998580i	$0.516968\pi$
$68$	−0.121361	−	0.121361i	−0.0147172	−	0.0147172i
$69$	3.00444	−	11.9066i	0.361692	−	1.43338i
$70$	−1.29701	+	1.77231i	−0.155023	+	0.211831i
$71$	6.31730	+	7.29055i	0.749726	+	0.865230i	0.994542	−	0.104340i	$-0.0332730\pi$
$71$	6.31730	+	7.29055i	0.749726	+	0.865230i	−0.244816	+	0.969570i	$0.578728\pi$
$72$	−0.755932	−	3.47496i	−0.0890874	−	0.409528i
$73$	1.15831	+	1.54732i	0.135570	+	0.181100i	0.863189	−	0.504882i	$-0.168464\pi$
$73$	1.15831	+	1.54732i	0.135570	+	0.181100i	−0.727619	+	0.685982i	$0.759373\pi$
$74$	−2.10680	+	4.61324i	−0.244910	+	0.536279i
$75$	−4.21313	+	12.0895i	−0.486490	+	1.39597i
$76$	−0.477689	+	1.62686i	−0.0547947	+	0.186614i
$77$	−5.24804	−	1.14164i	−0.598070	−	0.130102i
$78$	−8.33408	−	3.10845i	−0.943648	−	0.351963i
$79$	16.2406	−	4.76868i	1.82722	−	0.536519i	0.827525	−	0.561428i	$-0.189748\pi$
$79$	16.2406	−	4.76868i	1.82722	−	0.536519i	0.999690	+	0.0249096i	$0.00792979\pi$
$80$	0.498951	+	2.17969i	0.0557844	+	0.243697i
$81$	−4.59837	+	5.30680i	−0.510930	+	0.589645i
$82$	3.61053	+	1.97150i	0.398717	+	0.217716i
$83$	1.60007	−	4.28996i	0.175631	−	0.470885i	−0.819070	−	0.573693i	$-0.805510\pi$
$83$	1.60007	−	4.28996i	0.175631	−	0.470885i	0.994701	+	0.102809i	$0.0327829\pi$
$84$	−2.11564	+	1.35964i	−0.230835	+	0.148349i
$85$	−0.0504993	+	0.380441i	−0.00547742	+	0.0412647i
$86$	5.22368	−	0.751051i	0.563283	−	0.0809879i
$87$	12.1478	−	4.53091i	1.30239	−	0.485765i
$88$	−4.37757	+	3.27701i	−0.466651	+	0.349330i
$89$	−8.23324	−	5.29118i	−0.872722	−	0.560864i	0.0258624	−	0.999666i	$-0.491767\pi$
$89$	−8.23324	−	5.29118i	−0.872722	−	0.560864i	−0.898584	+	0.438801i	$0.855403\pi$
$90$	−5.14203	+	6.06576i	−0.542018	+	0.639387i
$91$			3.41194i			0.357669i
$92$	−2.72443	+	3.94683i	−0.284041	+	0.411486i
$93$	−18.3762	+	18.3762i	−1.90553	+	1.90553i
$94$	6.13703	−	5.31777i	0.632986	−	0.548486i
$95$	3.53774	−	1.36334i	0.362964	−	0.139876i
$96$	−0.364399	+	2.53445i	−0.0371913	+	0.258671i
$97$	−3.64640	−	9.77637i	−0.370235	−	0.992640i	−0.979814	−	0.199914i	$-0.935934\pi$
$97$	−3.64640	−	9.77637i	−0.370235	−	0.992640i	0.609578	−	0.792726i	$-0.291339\pi$
$98$	−4.83154	−	3.61684i	−0.488059	−	0.365356i
$99$	−18.6587	−	5.47869i	−1.87527	−	0.550629i
$100$	3.19168	−	3.84879i	0.319168	−	0.384879i
$101$	4.80496	+	10.5214i	0.478111	+	1.04692i	0.982978	+	0.183721i	$0.0588142\pi$
$101$	4.80496	+	10.5214i	0.478111	+	1.04692i	−0.504867	+	0.863197i	$0.668459\pi$
$102$	−0.210612	+	0.385708i	−0.0208537	+	0.0381908i
$103$	−1.33152	+	0.0952323i	−0.131199	+	0.00938352i	−0.136784	−	0.990601i	$-0.543677\pi$
$103$	−1.33152	+	0.0952323i	−0.131199	+	0.00938352i	0.00558538	+	0.999984i	$0.498222\pi$
$104$	2.62538	+	2.27490i	0.257440	+	0.223073i
$105$	5.28983	+	1.90799i	0.516235	+	0.186201i
$106$	9.52020	−	4.34773i	0.924684	−	0.422289i
$107$	−3.32677	+	15.2929i	−0.321611	+	1.47842i	0.478244	+	0.878227i	$0.341273\pi$
$107$	−3.32677	+	15.2929i	−0.321611	+	1.47842i	−0.799855	+	0.600193i	$0.795090\pi$
$108$	−1.25003	+	0.682567i	−0.120284	+	0.0656800i
$109$	2.02885	+	14.1109i	0.194328	+	1.35158i	0.820388	+	0.571808i	$0.193758\pi$
$109$	2.02885	+	14.1109i	0.194328	+	1.35158i	−0.626059	+	0.779775i	$0.715333\pi$
$110$	11.7687	+	3.31757i	1.12211	+	0.316318i
$111$	12.8536	+	1.84807i	1.22001	+	0.175411i
$112$	0.959727	−	0.208776i	0.0906856	−	0.0197275i
$113$	−0.909094	+	12.7108i	−0.0855203	+	1.19573i	0.755656	+	0.654969i	$0.227318\pi$
$113$	−0.909094	+	12.7108i	−0.0855203	+	1.19573i	−0.841176	+	0.540761i	$0.818136\pi$
$114$	4.34145			0.406614
$115$	10.7108	−	0.528015i	0.998787	−	0.0492376i
$116$	−5.06356			−0.470140
$117$	−0.881318	+	12.3224i	−0.0814778	+	1.13921i
$118$	0.640301	−	0.139289i	0.0589445	−	0.0128226i
$119$	0.166855	+	0.0239902i	0.0152956	+	0.00219918i
$120$	4.99512	−	2.79821i	0.455990	−	0.255440i
$121$	2.69002	+	18.7095i	0.244548	+	1.70087i
$122$	−4.11154	+	2.24507i	−0.372241	+	0.203259i
$123$	2.23901	−	10.2925i	0.201884	−	0.928047i
$124$	9.23231	−	4.21625i	0.829086	−	0.378631i
$125$	−11.1719	−	0.434832i	−0.999243	−	0.0388925i
$126$	2.63971	+	2.28732i	0.235164	+	0.203771i
$127$	19.4735	−	1.39277i	1.72799	−	0.123589i	0.828350	−	0.560211i	$-0.189280\pi$
$127$	19.4735	−	1.39277i	1.72799	−	0.123589i	0.899645	+	0.436623i	$0.143826\pi$
$128$	0.479249	−	0.877679i	0.0423600	−	0.0775766i
$129$	−5.61344	−	12.2917i	−0.494235	−	1.08222i
$130$	0.470188	−	7.75357i	0.0412383	−	0.680033i
$131$	1.20305	+	0.353248i	0.105111	+	0.0308634i	0.333865	−	0.942621i	$-0.391647\pi$
$131$	1.20305	+	0.353248i	0.105111	+	0.0308634i	−0.228754	+	0.973484i	$0.573465\pi$
$132$	11.2088	+	8.39083i	0.975604	+	0.730328i
$133$	−0.581967	−	1.56031i	−0.0504629	−	0.135296i
$134$	−0.0421532	+	0.293182i	−0.00364148	+	0.0253270i
$135$	2.91107	+	1.29152i	0.250545	+	0.111156i
$136$	0.129710	−	0.112394i	0.0111225	−	0.00963774i
$137$	−3.52577	+	3.52577i	−0.301227	+	0.301227i	−0.841494	−	0.540267i	$-0.818323\pi$
$137$	−3.52577	+	3.52577i	−0.301227	+	0.301227i	0.540267	+	0.841494i	$0.318323\pi$
$138$	11.6619	+	3.84619i	0.992728	+	0.327409i
$139$			18.3939i			1.56015i	0.625685	+	0.780076i	$0.284819\pi$
$139$			18.3939i			1.56015i	−0.625685	+	0.780076i	$0.715181\pi$
$140$	−1.67526	−	1.42014i	−0.141585	−	0.120024i
$141$	−17.4918	−	11.2413i	−1.47308	−	0.946688i
$142$	−7.72265	+	5.78110i	−0.648070	+	0.485139i
$143$	17.7984	−	6.63844i	1.48837	−	0.555135i
$144$	3.52004	−	0.506105i	0.293336	−	0.0421754i
$145$	6.88308	+	8.99006i	0.571609	+	0.746584i
$146$	−1.62601	+	1.04497i	−0.134570	+	0.0864827i
$147$	−5.40047	+	14.4792i	−0.445423	+	1.19423i
$148$	−4.45119	−	2.43053i	−0.365886	−	0.199789i
$149$	7.16272	−	8.26622i	0.586793	−	0.677195i	−0.382258	−	0.924056i	$-0.624853\pi$
$149$	7.16272	−	8.26622i	0.586793	−	0.677195i	0.969051	+	0.246860i	$0.0793989\pi$
$150$	−11.7581	−	5.06485i	−0.960046	−	0.413543i
$151$	−17.9797	+	5.27931i	−1.46316	+	0.429624i	−0.913871	−	0.406005i	$-0.866922\pi$
$151$	−17.9797	+	5.27931i	−1.46316	+	0.429624i	−0.549294	+	0.835629i	$0.685103\pi$
$152$	−1.58864	−	0.592531i	−0.128855	−	0.0480606i
$153$	0.596411	+	0.129741i	0.0482170	+	0.0104890i
$154$	1.51312	−	5.15322i	0.121931	−	0.415259i
$155$	−20.0355	−	10.6601i	−1.60929	−	0.856243i
$156$	3.69508	−	8.09109i	0.295843	−	0.647806i
$157$	−3.81022	−	5.08986i	−0.304089	−	0.406215i	0.622303	−	0.782777i	$-0.286197\pi$
$157$	−3.81022	−	5.08986i	−0.304089	−	0.406215i	−0.926392	+	0.376562i	$0.877106\pi$
$158$	3.59794	+	16.5395i	0.286237	+	1.31581i
$159$	−17.5492	−	20.2528i	−1.39174	−	1.60615i
$160$	−2.20973	+	0.342182i	−0.174695	+	0.0270519i
$161$	−0.180950	−	4.70686i	−0.0142609	−	0.370952i
$162$	−4.96524	−	4.96524i	−0.390106	−	0.390106i
$163$	16.6331	+	1.18962i	1.30280	+	0.0931783i	0.705427	−	0.708783i	$-0.250755\pi$
$163$	16.6331	+	1.18962i	1.30280	+	0.0931783i	0.597376	+	0.801961i	$0.296210\pi$
$164$	−2.22405	+	3.46069i	−0.173669	+	0.270234i
$165$	−0.339142	−	31.3066i	−0.0264022	−	2.43722i
$166$	4.16489	+	1.90204i	0.323258	+	0.147627i
$167$	7.89664	−	10.5487i	0.611060	−	0.816281i	−0.383155	−	0.923684i	$-0.625163\pi$
$167$	7.89664	−	10.5487i	0.611060	−	0.816281i	0.994216	+	0.107403i	$0.0342535\pi$
$168$	−1.20525	−	2.20725i	−0.0929868	−	0.170293i
$169$	0.503986	+	0.784217i	0.0387681	+	0.0603244i
$170$	−0.375870	−	0.0775110i	−0.0288279	−	0.00594482i
$171$	−1.69877	−	5.78549i	−0.129908	−	0.442427i
$172$	0.376485	+	5.26395i	0.0287067	+	0.401372i
$173$	−0.861075	−	12.0394i	−0.0654663	−	0.915338i	−0.918989	−	0.394283i	$-0.870993\pi$
$173$	−0.861075	−	12.0394i	−0.0654663	−	0.915338i	0.853523	−	0.521055i	$-0.174462\pi$
$174$	3.65275	+	12.4401i	0.276914	+	0.943084i
$175$	−0.244140	+	4.90479i	−0.0184553	+	0.370767i
$176$	−2.95637	−	4.60020i	−0.222845	−	0.346753i
$177$	−0.804105	−	1.47261i	−0.0604402	−	0.110688i
$178$	5.86505	−	7.83479i	0.439604	−	0.587243i
$179$	5.27780	+	2.41029i	0.394482	+	0.180154i	0.602772	−	0.797913i	$-0.294063\pi$
$179$	5.27780	+	2.41029i	0.394482	+	0.180154i	−0.208291	+	0.978067i	$0.566790\pi$
$180$	−5.68348	−	5.56166i	−0.423621	−	0.414542i
$181$	−1.79055	+	2.78615i	−0.133091	+	0.207093i	−0.901402	−	0.432983i	$-0.857461\pi$
$181$	−1.79055	+	2.78615i	−0.133091	+	0.207093i	0.768311	+	0.640076i	$0.221097\pi$
$182$	−3.40325	−	0.243405i	−0.252266	−	0.0180424i
$183$	8.48167	+	8.48167i	0.626983	+	0.626983i
$184$	−3.74242	−	2.99905i	−0.275895	−	0.221093i
$185$	1.73539	+	11.2068i	0.127589	+	0.823937i
$186$	−17.0185	−	19.6404i	−1.24786	−	1.44010i
$187$	−0.199498	−	0.917075i	−0.0145887	−	0.0670632i
$188$	4.86641	+	6.50076i	0.354919	+	0.474117i
$189$	0.581104	−	1.27244i	0.0422691	−	0.0925564i
$190$	1.10749	+	3.62598i	0.0803456	+	0.263056i
$191$	2.03282	−	6.92315i	0.147090	−	0.500942i	−0.852679	−	0.522435i	$-0.825024\pi$
$191$	2.03282	−	6.92315i	0.147090	−	0.500942i	0.999769	+	0.0214931i	$0.00684198\pi$
$192$	−2.50200	−	0.544276i	−0.180566	−	0.0392798i
$193$	−5.01166	−	1.86925i	−0.360747	−	0.134552i	0.162554	−	0.986700i	$-0.448027\pi$
$193$	−5.01166	−	1.86925i	−0.360747	−	0.134552i	−0.523301	+	0.852148i	$0.675300\pi$
$194$	10.0116	−	2.93967i	0.718790	−	0.211056i
$195$	−19.3881	+	4.43812i	−1.38841	+	0.317820i
$196$	3.95231	−	4.56120i	0.282308	−	0.325800i
$197$	8.35528	+	4.56233i	0.595289	+	0.325052i	0.748494	−	0.663142i	$-0.230777\pi$
$197$	8.35528	+	4.56233i	0.595289	+	0.325052i	−0.153204	+	0.988195i	$0.548959\pi$
$198$	6.79583	−	18.2203i	0.482959	−	1.29486i
$199$	−9.68462	+	6.22393i	−0.686525	+	0.441203i	−0.836849	−	0.547434i	$-0.815605\pi$
$199$	−9.68462	+	6.22393i	−0.686525	+	0.441203i	0.150324	+	0.988637i	$0.451968\pi$
$200$	3.61130	+	3.45811i	0.255357	+	0.244526i
$201$	0.750696	−	0.107934i	0.0529500	−	0.00761306i
$202$	−10.8374	+	4.04213i	−0.762515	+	0.284403i
$203$	3.98132	−	2.98038i	0.279434	−	0.209182i
$204$	−0.369700	−	0.237592i	−0.0258842	−	0.0166348i
$205$	9.16749	−	0.755568i	0.640285	−	0.0527712i
$206$		−	1.33492i		−	0.0930085i
$207$	0.562287	−	17.0458i	0.0390816	−	1.18477i
$208$	−2.45640	+	2.45640i	−0.170321	+	0.170321i
$209$	−7.00706	+	6.07165i	−0.484688	+	0.419985i
$210$	−2.28050	+	5.14024i	−0.157370	+	0.354710i
$211$	2.53957	−	17.6631i	0.174831	−	1.21598i	−0.693672	−	0.720291i	$-0.744008\pi$
$211$	2.53957	−	17.6631i	0.174831	−	1.21598i	0.868503	−	0.495684i	$-0.165083\pi$
$212$	3.65749	+	9.80611i	0.251197	+	0.673486i
$213$	19.7740	+	14.8026i	1.35489	+	1.01426i
$214$	−15.0166	−	4.40927i	−1.02651	−	0.301412i
$215$	8.83407	−	7.82391i	0.602479	−	0.533586i
$216$	−0.591652	−	1.29554i	−0.0402568	−	0.0881501i
$217$	−4.77742	+	8.74919i	−0.324312	+	0.593934i
$218$	−14.2197	+	1.01701i	−0.963081	+	0.0688809i
$219$	3.74026	+	3.24095i	0.252743	+	0.219003i
$220$	−4.14869	+	11.5021i	−0.279705	+	0.775470i
$221$	−0.542345	+	0.247680i	−0.0364820	+	0.0166608i
$222$	−2.76032	+	12.6890i	−0.185261	+	0.851631i
$223$	−5.84075	+	3.18929i	−0.391126	+	0.213571i	−0.662764	−	0.748829i	$-0.730617\pi$
$223$	−5.84075	+	3.18929i	−0.391126	+	0.213571i	0.271638	+	0.962400i	$0.412435\pi$
$224$	0.139778	+	0.972175i	0.00933929	+	0.0649562i
$225$	−2.14865	+	17.6509i	−0.143243	+	1.17672i
$226$	−12.6135	−	1.81355i	−0.839041	−	0.120636i
$227$	−2.96721	+	0.645476i	−0.196940	+	0.0428418i	−0.309953	−	0.950752i	$-0.600313\pi$
$227$	−2.96721	+	0.645476i	−0.196940	+	0.0428418i	0.113013	+	0.993594i	$0.463950\pi$
$228$	−0.309716	+	4.33039i	−0.0205114	+	0.286787i
$229$	20.0994			1.32821			0.664104	−	0.747641i	$-0.268813\pi$
$229$	20.0994			1.32821			0.664104	+	0.747641i	$0.268813\pi$
$230$	−0.237430	+	10.7212i	−0.0156557	+	0.706933i
$231$	−13.7520			−0.904812
$232$	0.361230	−	5.05066i	0.0237159	−	0.331592i
$233$	15.4572	−	3.36250i	1.01263	−	0.220285i	0.324513	−	0.945881i	$-0.394800\pi$
$233$	15.4572	−	3.36250i	1.01263	−	0.220285i	0.688121	+	0.725596i	$0.258436\pi$
$234$	−12.2282	−	1.75814i	−0.799380	−	0.114933i
$235$	4.92665	−	17.4768i	0.321379	−	1.14006i
$236$	0.0932555	+	0.648607i	0.00607042	+	0.0422207i
$237$	38.0386	−	20.7706i	2.47087	−	1.34920i
$238$	−0.0358324	+	0.164719i	−0.00232267	+	0.0106771i
$239$	−1.08709	+	0.496459i	−0.0703183	+	0.0321133i	−0.450264	−	0.892896i	$-0.648670\pi$
$239$	−1.08709	+	0.496459i	−0.0703183	+	0.0321133i	0.379945	+	0.925009i	$0.375943\pi$
$240$	2.43473	+	5.18201i	0.157161	+	0.334498i
$241$	−10.9334	−	9.47388i	−0.704285	−	0.610266i	0.227285	−	0.973828i	$-0.427015\pi$
$241$	−10.9334	−	9.47388i	−0.704285	−	0.610266i	−0.931570	+	0.363562i	$0.881560\pi$
$242$	−18.8538	+	1.34845i	−1.21197	+	0.0866815i
$243$	−10.6644	+	19.5305i	−0.684125	+	1.25288i
$244$	−1.94604	−	4.26123i	−0.124582	−	0.272797i
$245$	−13.4707	−	0.816882i	−0.860610	−	0.0521887i
$246$	10.1066	+	2.96756i	0.644372	+	0.189205i
$247$	4.71526	+	3.52980i	0.300025	+	0.224596i
$248$	3.54689	+	9.50957i	0.225227	+	0.603858i
$249$	1.66846	−	11.6044i	0.105734	−	0.735397i
$250$	1.23072	−	11.1124i	0.0778374	−	0.702810i
$251$	16.7278	−	14.4947i	1.05585	−	0.914900i	0.0593299	−	0.998238i	$-0.481104\pi$
$251$	16.7278	−	14.4947i	1.05585	−	0.914900i	0.996521	+	0.0833381i	$0.0265582\pi$
$252$	−2.46981	+	2.46981i	−0.155583	+	0.155583i
$253$	−24.2012	+	10.1018i	−1.52152	+	0.635096i
$254$			19.5232i			1.22500i
$255$	0.0807162	+	0.979349i	0.00505465	+	0.0613292i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	−24.2156	+	18.1276i	−1.51053	+	1.13077i	−0.556578	+	0.830795i	$0.687886\pi$
$257$	−24.2156	+	18.1276i	−1.51053	+	1.13077i	−0.953948	+	0.299971i	$0.903023\pi$
$258$	12.6608	−	4.72225i	0.788230	−	0.293995i
$259$	4.93043	−	0.708890i	0.306362	−	0.0440483i
$260$	7.70028	+	1.02212i	0.477551	+	0.0633894i
$261$	15.1486	−	9.73542i	0.937676	−	0.602608i
$262$	−0.438173	+	1.17479i	−0.0270704	+	0.0725786i
$263$	−0.345827	−	0.188836i	−0.0213246	−	0.0116441i	0.468551	−	0.883436i	$-0.344776\pi$
$263$	−0.345827	−	0.188836i	−0.0213246	−	0.0116441i	−0.489876	+	0.871792i	$0.662958\pi$
$264$	−9.16908	+	10.5817i	−0.564318	+	0.651257i
$265$	12.4384	−	19.8235i	0.764087	−	1.21775i
$266$	1.59786	−	0.469173i	0.0979708	−	0.0287668i
$267$	−23.4794	−	8.75737i	−1.43692	−	0.535942i
$268$	−0.289427	−	0.0629611i	−0.0176796	−	0.00384596i
$269$	0.661200	−	2.25184i	0.0403141	−	0.137297i	−0.936877	−	0.349659i	$-0.886297\pi$
$269$	0.661200	−	2.25184i	0.0403141	−	0.137297i	0.977191	+	0.212362i	$0.0681156\pi$
$270$	−1.49590	+	2.81152i	−0.0910375	+	0.171103i
$271$	−7.20738	+	15.7820i	−0.437817	+	0.958685i	0.554177	+	0.832399i	$0.313033\pi$
$271$	−7.20738	+	15.7820i	−0.437817	+	0.958685i	−0.991994	+	0.126286i	$0.959694\pi$
$272$	0.102855	+	0.137398i	0.00623647	+	0.00833096i
$273$	1.85704	+	8.53668i	0.112393	+	0.516663i
$274$	−3.26526	−	3.76832i	−0.197262	−	0.227652i
$275$	26.0608	−	8.26945i	1.57152	−	0.498666i
$276$	−4.66834	+	11.3578i	−0.281001	+	0.683660i
$277$	11.0319	+	11.0319i	0.662840	+	0.662840i	0.956049	−	0.293208i	$-0.0947229\pi$
$277$	11.0319	+	11.0319i	0.662840	+	0.662840i	−0.293208	+	0.956049i	$0.594723\pi$
$278$	−18.3470	−	1.31221i	−1.10038	−	0.0787009i
$279$	−19.5139	+	30.3642i	−1.16827	+	1.81786i
$280$	1.53604	−	1.56968i	0.0917958	−	0.0938064i
$281$	−15.5856	−	7.11770i	−0.929758	−	0.424606i	−0.107812	−	0.994171i	$-0.534384\pi$
$281$	−15.5856	−	7.11770i	−0.929758	−	0.424606i	−0.821946	+	0.569565i	$0.807112\pi$
$282$	12.4605	−	16.6453i	0.742012	−	0.991213i
$283$	−7.57458	−	13.8718i	−0.450262	−	0.824593i	0.549680	−	0.835375i	$-0.314750\pi$
$283$	−7.57458	−	13.8718i	−0.450262	−	0.824593i	−0.999942	+	0.0107821i	$0.996568\pi$
$284$	−5.21545	−	8.11539i	−0.309480	−	0.481560i
$285$	8.10938	−	5.33658i	0.480358	−	0.316112i
$286$	5.35181	+	18.2266i	0.316459	+	1.07776i
$287$	−0.288238	−	4.03010i	−0.0170142	−	0.237889i
$288$	0.253699	+	3.54717i	0.0149493	+	0.209019i
$289$	−4.78115	−	16.2831i	−0.281244	−	0.957830i
$290$	−9.45819	+	6.22420i	−0.555404	+	0.365498i
$291$	−14.4443	−	22.4758i	−0.846741	−	1.31756i
$292$	−0.926313	−	1.69642i	−0.0542084	−	0.0992752i
$293$	14.9076	−	19.9142i	0.870912	−	1.16340i	−0.114535	−	0.993419i	$-0.536538\pi$
$293$	14.9076	−	19.9142i	0.870912	−	1.16340i	0.985447	−	0.169983i	$-0.0543714\pi$
$294$	−14.0571	−	6.41964i	−0.819824	−	0.374401i
$295$	1.02480	−	1.04725i	0.0596661	−	0.0609730i
$296$	2.74189	−	4.26646i	0.159369	−	0.247983i
$297$	−7.76829	−	0.555599i	−0.450762	−	0.0322391i
$298$	7.73418	+	7.73418i	0.448029	+	0.448029i
$299$	9.53890	+	13.6590i	0.551649	+	0.789922i
$300$	5.89076	−	11.3668i	0.340103	−	0.656264i
$301$	−3.39434	−	3.91728i	−0.195647	−	0.225788i
$302$	−3.98320	−	18.3105i	−0.229208	−	1.05365i
$303$	17.7485	+	23.7093i	1.01963	+	1.36206i
$304$	0.704353	−	1.54232i	0.0403974	−	0.0884580i
$305$	−4.92025	+	9.24753i	−0.281733	+	0.529512i
$306$	−0.171958	+	0.585636i	−0.00983019	+	0.0334786i
$307$	−21.4335	−	4.66256i	−1.22327	−	0.266107i	−0.445863	−	0.895101i	$-0.647103\pi$
$307$	−21.4335	−	4.66256i	−1.22327	−	0.266107i	−0.777410	+	0.628995i	$0.783467\pi$
$308$	5.03215	+	1.87689i	0.286733	+	0.106946i
$309$	−3.27963	+	0.962987i	−0.186572	+	0.0547824i
$310$	12.0623	−	19.2240i	0.685092	−	1.09185i
$311$	4.62138	−	5.33335i	0.262054	−	0.302427i	−0.609440	−	0.792832i	$-0.708606\pi$
$311$	4.62138	−	5.33335i	0.262054	−	0.302427i	0.871495	+	0.490405i	$0.163151\pi$
$312$	7.80687	+	4.26287i	0.441977	+	0.241338i
$313$	7.26325	−	19.4735i	0.410543	−	1.10071i	−0.553006	−	0.833177i	$-0.686519\pi$
$313$	7.26325	−	19.4735i	0.410543	−	1.10071i	0.963549	−	0.267532i	$-0.0862080\pi$
$314$	5.34871	−	3.43741i	0.301845	−	0.193984i
$315$	7.74230	+	1.02770i	0.436229	+	0.0579045i
$316$	−16.7540	+	2.40886i	−0.942486	+	0.135509i
$317$	−20.2173	+	7.54065i	−1.13552	+	0.423525i	−0.845754	−	0.533574i	$-0.820849\pi$
$317$	−20.2173	+	7.54065i	−1.13552	+	0.423525i	−0.289761	+	0.957099i	$0.593576\pi$
$318$	21.4532	−	16.0596i	1.20303	−	0.900580i
$319$	−23.2934	−	14.9697i	−1.30418	−	0.838145i
$320$	−0.183670	−	2.22851i	−0.0102675	−	0.124578i
$321$			40.0735i			2.23668i
$322$	4.70777	+	0.155294i	0.262354	+	0.00865421i
$323$	0.205773	−	0.205773i	0.0114495	−	0.0114495i
$324$	5.30680	−	4.59837i	0.294822	−	0.255465i
$325$	−8.65255	−	15.0608i	−0.479957	−	0.835424i
$326$	−2.37318	+	16.5058i	−0.131438	+	0.914174i
$327$	12.7564	+	34.2013i	0.705432	+	1.89134i
$328$	−3.29321	−	2.46527i	−0.181837	−	0.136121i
$329$	−7.65262	−	2.24701i	−0.421902	−	0.123882i
$330$	31.2511	+	1.89511i	1.72031	+	0.104322i
$331$	−3.44212	−	7.53718i	−0.189196	−	0.414281i	0.791135	−	0.611641i	$-0.209490\pi$
$331$	−3.44212	−	7.53718i	−0.189196	−	0.414281i	−0.980331	+	0.197360i	$0.936763\pi$
$332$	−2.19431	+	4.01858i	−0.120429	+	0.220548i
$333$	17.9897	−	1.28665i	0.985827	−	0.0705078i
$334$	9.95846	+	8.62905i	0.544903	+	0.472161i
$335$	0.281646	+	0.599448i	0.0153879	+	0.0327513i
$336$	2.28760	−	1.04471i	0.124799	−	0.0569938i
$337$	3.40949	−	15.6732i	0.185727	−	0.853773i	−0.786104	−	0.618094i	$-0.787905\pi$
$337$	3.40949	−	15.6732i	0.185727	−	0.853773i	0.971831	−	0.235679i	$-0.0757313\pi$
$338$	−0.818173	+	0.446756i	−0.0445027	+	0.0243003i
$339$	4.64363	+	32.2972i	0.252207	+	1.75414i
$340$	0.104128	−	0.369382i	0.00564712	−	0.0200326i
$341$	54.9352	+	7.89849i	2.97491	+	0.427727i
$342$	5.89194	−	1.28171i	0.318600	−	0.0693071i
$343$	−0.913352	+	12.7703i	−0.0493164	+	0.689533i
$344$	−5.27739			−0.284538
$345$	26.5110	−	7.15073i	1.42731	−	0.384982i
$346$	12.0701			0.648895
$347$	0.764815	−	10.6935i	0.0410574	−	0.574057i	−0.934733	−	0.355350i	$-0.884362\pi$
$347$	0.764815	−	10.6935i	0.0410574	−	0.574057i	0.975791	−	0.218707i	$-0.0701839\pi$
$348$	−12.6690	+	2.75598i	−0.679130	+	0.147736i
$349$	−4.34521	−	0.624747i	−0.232594	−	0.0334420i	0.0250322	−	0.999687i	$-0.492031\pi$
$349$	−4.34521	−	0.624747i	−0.232594	−	0.0334420i	−0.257626	+	0.966245i	$0.582940\pi$
$350$	−4.87488	−	0.593422i	−0.260573	−	0.0317197i
$351$	0.704123	+	4.89728i	0.0375833	+	0.261397i
$352$	4.79938	−	2.62066i	0.255808	−	0.139682i
$353$	2.99134	−	13.7510i	0.159213	−	0.731890i	−0.826429	−	0.563041i	$-0.809631\pi$
$353$	2.99134	−	13.7510i	0.159213	−	0.731890i	0.985642	−	0.168849i	$-0.0540051\pi$
$354$	1.52622	−	0.697002i	0.0811177	−	0.0370452i
$355$	−7.31887	+	20.2913i	−0.388446	+	1.07695i
$356$	7.39642	+	6.40904i	0.392010	+	0.339678i
$357$	0.430529	−	0.0307920i	0.0227860	−	0.00162969i
$358$	−2.78067	+	5.09241i	−0.146963	+	0.269142i
$359$	10.3530	+	22.6699i	0.546410	+	1.19647i	0.958438	+	0.285301i	$0.0920934\pi$
$359$	10.3530	+	22.6699i	0.546410	+	1.19647i	−0.412028	+	0.911171i	$0.635179\pi$
$360$	5.95294	−	5.27223i	0.313748	−	0.277871i
$361$	15.4720	+	4.54298i	0.814314	+	0.239104i
$362$	−2.65132	−	1.98475i	−0.139350	−	0.104316i
$363$	16.9136	+	45.3471i	0.887734	+	2.38011i
$364$	0.485570	−	3.37721i	0.0254508	−	0.177014i
$365$	−1.75272	+	3.95062i	−0.0917415	+	0.206785i
$366$	−9.06513	+	7.85498i	−0.473842	+	0.410586i
$367$	−17.9948	+	17.9948i	−0.939321	+	0.939321i	−0.998262	−	0.0589403i	$-0.981228\pi$
$367$	−17.9948	+	17.9948i	−0.939321	+	0.939321i	0.0589403	+	0.998262i	$0.481228\pi$
$368$	3.25839	−	3.51894i	0.169855	−	0.183437i
$369$		−	14.6294i		−	0.761575i
$370$	−11.3020	+	0.931491i	−0.587563	+	0.0484259i
$371$	−8.64759	−	5.55747i	−0.448960	−	0.288529i
$372$	20.8044	−	15.5740i	1.07866	−	0.807474i
$373$	3.28799	−	1.22636i	0.170246	−	0.0634983i	−0.262896	−	0.964824i	$-0.584678\pi$
$373$	3.28799	−	1.22636i	0.170246	−	0.0634983i	0.433142	+	0.901326i	$0.357405\pi$
$374$	0.928971	−	0.133566i	0.0480359	−	0.00690652i
$375$	−28.1887	+	4.99264i	−1.45566	+	0.257819i
$376$	−6.83136	+	4.39025i	−0.352301	+	0.226410i
$377$	−6.14713	+	16.4811i	−0.316593	+	0.848820i
$378$	1.22774	+	0.670398i	0.0631483	+	0.0344816i
$379$	−22.4911	+	25.9561i	−1.15529	+	1.33328i	−0.221623	+	0.975132i	$0.571135\pi$
$379$	−22.4911	+	25.9561i	−1.15529	+	1.33328i	−0.933667	+	0.358143i	$0.883410\pi$
$380$	−3.69575	+	0.845991i	−0.189588	+	0.0433984i
$381$	47.9646	−	14.0837i	2.45730	−	0.721529i
$382$	6.76049	+	2.52153i	0.345897	+	0.129013i
$383$	−36.6547	−	7.97374i	−1.87297	−	0.407439i	−0.875802	−	0.482671i	$-0.839667\pi$
$383$	−36.6547	−	7.97374i	−1.87297	−	0.407439i	−0.997166	+	0.0752314i	$0.976030\pi$
$384$	0.721380	−	2.45680i	0.0368128	−	0.125373i
$385$	−3.50807	−	11.4856i	−0.178788	−	0.585362i
$386$	2.22202	−	4.86554i	0.113098	−	0.247650i
$387$	−11.2470	−	15.0243i	−0.571718	−	0.763726i
$388$	2.21796	+	10.1958i	0.112600	+	0.517613i
$389$	17.2453	+	19.9021i	0.874370	+	1.00908i	0.999856	+	0.0169818i	$0.00540574\pi$
$389$	17.2453	+	19.9021i	0.874370	+	1.00908i	−0.125485	+	0.992095i	$0.540049\pi$
$390$	−3.04368	−	19.6553i	−0.154123	−	0.995287i
$391$	0.735042	−	0.370444i	0.0371727	−	0.0187342i
$392$	4.26763	+	4.26763i	0.215548	+	0.215548i
$393$	3.20230	+	0.229033i	0.161535	+	0.0115532i
$394$	−5.14676	+	8.00852i	−0.259290	+	0.403463i
$395$	27.0511	+	26.4713i	1.36109	+	1.33192i
$396$	17.6891	+	8.07834i	0.888910	+	0.405952i
$397$	7.64263	−	10.2094i	0.383573	−	0.512393i	−0.566652	−	0.823957i	$-0.691762\pi$
$397$	7.64263	−	10.2094i	0.383573	−	0.512393i	0.950225	+	0.311564i	$0.100853\pi$
$398$	−5.51718	−	10.1040i	−0.276551	−	0.506466i
$399$	−2.30532	−	3.58715i	−0.115411	−	0.179582i
$400$	−3.70693	+	3.35540i	−0.185346	+	0.167770i
$401$	−0.760440	−	2.58982i	−0.0379745	−	0.129329i	0.938324	−	0.345757i	$-0.112378\pi$
$401$	−0.760440	−	2.58982i	−0.0379745	−	0.129329i	−0.976299	+	0.216427i	$0.930560\pi$
$402$	0.0541047	+	0.756483i	0.00269850	+	0.0377299i
$403$	−2.51528	−	35.1682i	−0.125295	−	1.75185i
$404$	−3.25870	−	11.0981i	−0.162126	−	0.552152i
$405$	−15.3779	−	3.17119i	−0.764133	−	0.157578i
$406$	2.68876	+	4.18380i	0.133441	+	0.207638i
$407$	−13.2908	−	24.3403i	−0.658801	−	1.20650i
$408$	0.263361	−	0.351809i	0.0130383	−	0.0174171i
$409$	−22.5455	−	10.2962i	−1.11480	−	0.509114i	−0.229118	−	0.973399i	$-0.573584\pi$
$409$	−22.5455	−	10.2962i	−1.11480	−	0.509114i	−0.885686	+	0.464285i	$0.846311\pi$
$410$	0.0996416	+	9.19803i	0.00492095	+	0.454259i
$411$	−6.90248	+	10.7405i	−0.340474	+	0.529788i
$412$	1.33152	+	0.0952323i	0.0655994	+	0.00469176i
$413$	−0.455090	−	0.455090i	−0.0223935	−	0.0223935i
$414$	16.9623	+	1.77689i	0.833651	+	0.0873293i
$415$	10.1176	−	1.56673i	0.496653	−	0.0769078i
$416$	−2.27490	−	2.62538i	−0.111536	−	0.128720i
$417$	10.0114	+	46.0215i	0.490259	+	2.25368i
$418$	−5.55630	−	7.42235i	−0.271768	−	0.363039i
$419$	6.88135	−	15.0681i	0.336176	−	0.736122i	−0.663754	−	0.747951i	$-0.731038\pi$
$419$	6.88135	−	15.0681i	0.336176	−	0.736122i	0.999930	+	0.0118283i	$0.00376516\pi$
$420$	−4.96445	−	2.64139i	−0.242241	−	0.128887i
$421$	3.98170	−	13.5604i	0.194056	−	0.660895i	−0.803767	−	0.594945i	$-0.797174\pi$
$421$	3.98170	−	13.5604i	0.194056	−	0.660895i	0.997823	−	0.0659503i	$-0.0210079\pi$
$422$	17.4369	+	3.79316i	0.848815	+	0.184648i
$423$	−27.0575	−	10.0919i	−1.31558	−	0.490685i
$424$	−10.0420	+	2.94861i	−0.487685	+	0.143197i
$425$	−0.797362	+	0.317242i	−0.0386778	+	0.0153885i
$426$	−16.1755	+	18.6676i	−0.783707	+	0.904447i
$427$	4.03824	+	2.20505i	0.195424	+	0.106710i
$428$	5.46931	−	14.6638i	0.264369	−	0.708801i
$429$	40.9183	−	26.2966i	1.97555	−	1.26961i
$430$	7.17376	+	9.36971i	0.345949	+	0.451848i
$431$	−34.3181	+	4.93420i	−1.65305	+	0.237672i	−0.904827	−	0.425780i	$-0.860000\pi$
$431$	−34.3181	+	4.93420i	−1.65305	+	0.237672i	−0.748219	+	0.663452i	$0.769091\pi$
$432$	1.33444	−	0.497722i	0.0642035	−	0.0239467i
$433$	−9.97627	+	7.46814i	−0.479429	+	0.358896i	−0.811494	−	0.584360i	$-0.801346\pi$
$433$	−9.97627	+	7.46814i	−0.479429	+	0.358896i	0.332065	+	0.943256i	$0.392255\pi$
$434$	−8.38608	−	5.38941i	−0.402545	−	0.258700i
$435$	22.1145	+	18.7468i	1.06031	+	0.898842i
$436$		−	14.2561i		−	0.682741i
$437$	−6.69202	−	4.61937i	−0.320123	−	0.220975i
$438$	−3.49952	+	3.49952i	−0.167214	+	0.167214i
$439$	−11.6089	+	10.0592i	−0.554064	+	0.480099i	−0.886309	−	0.463094i	$-0.846739\pi$
$439$	−11.6089	+	10.0592i	−0.554064	+	0.480099i	0.332245	+	0.943193i	$0.392194\pi$
$440$	−11.1768	−	4.95867i	−0.532834	−	0.236395i
$441$	−3.05451	+	21.2446i	−0.145453	+	1.01165i
$442$	−0.208359	−	0.558632i	−0.00991063	−	0.0265714i
$443$	−8.66962	−	6.48999i	−0.411906	−	0.308349i	0.373153	−	0.927770i	$-0.378277\pi$
$443$	−8.66962	−	6.48999i	−0.411906	−	0.308349i	−0.785059	+	0.619421i	$0.787367\pi$
$444$	−12.4598	−	3.65852i	−0.591314	−	0.173625i
$445$	1.32465	−	21.8440i	0.0627945	−	1.03550i
$446$	−2.76449	−	6.05339i	−0.130903	−	0.286636i
$447$	13.4220	−	24.5806i	0.634839	−	1.16262i
$448$	−0.979670	+	0.0700674i	−0.0462851	+	0.00331037i
$449$	8.63127	+	7.47904i	0.407335	+	0.352958i	0.834300	−	0.551310i	$-0.185872\pi$
$449$	8.63127	+	7.47904i	0.407335	+	0.352958i	−0.426965	+	0.904268i	$0.640417\pi$
$450$	−17.4526	−	3.40238i	−0.822724	−	0.160390i
$451$	−20.4621	+	9.34474i	−0.963524	+	0.440027i
$452$	2.70877	−	12.4520i	0.127410	−	0.585694i
$453$	−42.1117	+	22.9947i	−1.97858	+	1.08039i
$454$	−0.432154	−	3.00569i	−0.0202820	−	0.141064i
$455$	−6.65611	+	3.72867i	−0.312043	+	0.174803i
$456$	−4.29726	−	0.617853i	−0.201238	−	0.0289336i
$457$	4.97639	−	1.08255i	0.232786	−	0.0506394i	−0.0946590	−	0.995510i	$-0.530176\pi$
$457$	4.97639	−	1.08255i	0.232786	−	0.0506394i	0.327445	+	0.944870i	$0.393812\pi$
$458$	−1.43388	+	20.0482i	−0.0670006	+	0.936791i
$459$	0.244444			0.0114097
$460$	−10.6769	−	1.00167i	−0.497814	−	0.0467029i
$461$	−20.4621			−0.953013			−0.476506	−	0.879171i	$-0.658097\pi$
$461$	−20.4621			−0.953013			−0.476506	+	0.879171i	$0.658097\pi$
$462$	0.981053	−	13.7169i	0.0456427	−	0.638169i
$463$	28.0893	−	6.11046i	1.30542	−	0.283977i	0.494523	−	0.869164i	$-0.335343\pi$
$463$	28.0893	−	6.11046i	1.30542	−	0.283977i	0.810898	+	0.585187i	$0.198979\pi$
$464$	5.01202	+	0.720619i	0.232677	+	0.0334539i
$465$	−55.9310	−	15.7668i	−2.59374	−	0.731166i
$466$	2.25123	+	15.6577i	0.104286	+	0.725328i
$467$	1.18345	−	0.646211i	0.0547634	−	0.0299031i	−0.451634	−	0.892203i	$-0.649159\pi$
$467$	1.18345	−	0.646211i	0.0547634	−	0.0299031i	0.506397	+	0.862300i	$0.330977\pi$
$468$	2.62601	−	12.0716i	0.121387	−	0.558009i
$469$	0.264626	−	0.120851i	0.0122193	−	0.00558037i
$470$	17.0808	+	6.16087i	0.787877	+	0.284180i
$471$	−12.3035	−	10.6610i	−0.566913	−	0.491233i
$472$	−0.653607	+	0.0467469i	−0.0300847	+	0.00215170i
$473$	−13.8303	+	25.3282i	−0.635916	+	1.16459i
$474$	18.0041	+	39.4234i	0.826955	+	1.81078i
$475$	6.52578	+	5.41161i	0.299423	+	0.248302i
$476$	−0.161743	−	0.0474920i	−0.00741347	−	0.00217679i
$477$	−29.7958	−	22.3048i	−1.36425	−	1.02127i
$478$	−0.417642	−	1.11974i	−0.0191025	−	0.0512158i
$479$	−1.22456	+	8.51702i	−0.0559517	+	0.389153i	0.942533	+	0.334114i	$0.108437\pi$
$479$	−1.22456	+	8.51702i	−0.0559517	+	0.389153i	−0.998484	+	0.0550383i	$0.982472\pi$
$480$	−5.34250	+	2.05884i	−0.243851	+	0.0939729i
$481$	−13.3147	+	11.5373i	−0.607100	+	0.526055i
$482$	10.2297	−	10.2297i	0.465951	−	0.465951i
$483$	−3.01457	−	11.6781i	−0.137168	−	0.531370i
$484$		−	18.9019i		−	0.859179i
$485$	15.0871	−	17.7974i	0.685070	−	0.808138i
$486$	−18.7199	−	12.0306i	−0.849153	−	0.545718i
$487$	4.81942	−	3.60777i	0.218389	−	0.163484i	−0.484482	−	0.874801i	$-0.660992\pi$
$487$	4.81942	−	3.60777i	0.218389	−	0.163484i	0.702871	+	0.711317i	$0.251901\pi$
$488$	4.38920	−	1.63709i	0.198690	−	0.0741074i
$489$	42.2634	−	6.07656i	1.91122	−	0.274792i
$490$	1.77579	−	13.3781i	0.0802219	−	0.604360i
$491$	35.9776	−	23.1214i	1.62365	−	1.04346i	0.670076	−	0.742293i	$-0.266262\pi$
$491$	35.9776	−	23.1214i	1.62365	−	1.04346i	0.953573	−	0.301163i	$-0.0973747\pi$
$492$	−3.68100	+	9.86913i	−0.165952	+	0.444935i
$493$	0.762759	+	0.416498i	0.0343529	+	0.0187581i
$494$	−3.85719	+	4.45143i	−0.173543	+	0.200280i
$495$	−9.70281	−	42.3872i	−0.436109	−	1.90516i
$496$	−9.73837	+	2.85944i	−0.437266	+	0.128393i
$497$	8.87742	+	3.31111i	0.398207	+	0.148523i
$498$	11.4558	+	2.49205i	0.513345	+	0.111671i
$499$	5.51281	−	18.7749i	0.246787	−	0.840480i	−0.739175	−	0.673513i	$-0.764785\pi$
$499$	5.51281	−	18.7749i	0.246787	−	0.840480i	0.985963	−	0.166967i	$-0.0533973\pi$
$500$	10.9963	+	2.02033i	0.491769	+	0.0903519i
$501$	14.0160	−	30.6907i	0.626188	−	1.37116i
$502$	13.2645	+	17.7193i	0.592022	+	0.790849i
$503$	−2.42767	−	11.1598i	−0.108244	−	0.497591i	−0.999065	−	0.0432360i	$-0.986233\pi$
$503$	−2.42767	−	11.1598i	−0.108244	−	0.497591i	0.890821	−	0.454355i	$-0.150130\pi$
$504$	−2.28732	−	2.63971i	−0.101885	−	0.117582i
$505$	−15.2744	+	20.8717i	−0.679702	+	0.928780i
$506$	−8.34958	−	24.8602i	−0.371184	−	1.10517i
$507$	1.68780	+	1.68780i	0.0749579	+	0.0749579i
$508$	−19.4735	−	1.39277i	−0.863997	−	0.0617943i
$509$	5.84113	−	9.08898i	0.258904	−	0.402862i	−0.687330	−	0.726345i	$-0.741217\pi$
$509$	5.84113	−	9.08898i	0.258904	−	0.402862i	0.946234	+	0.323483i	$0.104854\pi$
$510$	−0.982612	+	0.0106446i	−0.0435108	+	0.000471349i
$511$	1.72683	+	0.788618i	0.0763906	+	0.0348864i
$512$	−0.599278	+	0.800541i	−0.0264846	+	0.0353793i
$513$	−1.15732	−	2.11947i	−0.0510969	−	0.0935770i
$514$	−16.3539	−	25.4471i	−0.721337	−	1.12242i
$515$	−1.64091	−	2.49349i	−0.0723070	−	0.109876i
$516$	3.80701	+	12.9655i	0.167594	+	0.570773i
$517$	3.16780	+	44.2917i	0.139320	+	1.94795i
$518$	0.355350	+	4.96844i	0.0156132	+	0.218301i
$519$	−8.70717	−	29.6539i	−0.382202	−	1.30166i
$520$	−1.56885	+	7.60774i	−0.0687987	+	0.333621i
$521$	−7.00871	−	10.9058i	−0.307057	−	0.477790i	0.653092	−	0.757279i	$-0.273471\pi$
$521$	−7.00871	−	10.9058i	−0.307057	−	0.477790i	−0.960149	+	0.279489i	$0.909835\pi$
$522$	8.62993	+	15.8045i	0.377722	+	0.691746i
$523$	1.90361	−	2.54293i	0.0832392	−	0.111195i	−0.756989	−	0.653428i	$-0.773330\pi$
$523$	1.90361	−	2.54293i	0.0832392	−	0.111195i	0.840228	+	0.542233i	$0.182421\pi$
$524$	−1.14053	−	0.520865i	−0.0498245	−	0.0227541i
$525$	2.05872	+	12.4047i	0.0898500	+	0.541384i
$526$	0.213026	−	0.331475i	0.00928837	−	0.0144530i
$527$	−1.73753	−	0.124271i	−0.0756880	−	0.00541331i
$528$	−9.90061	−	9.90061i	−0.430869	−	0.430869i
$529$	−13.8835	−	18.3371i	−0.603632	−	0.797263i
$530$	18.8856	+	13.8209i	0.820339	+	0.600343i
$531$	−1.52603	−	1.76113i	−0.0662241	−	0.0764267i
$532$	0.353988	+	1.62726i	0.0153473	+	0.0705505i
$533$	8.56402	+	11.4402i	0.370949	+	0.495530i
$534$	10.4101	−	22.7949i	0.450487	−	0.986430i
$535$	−33.4694	+	10.2226i	−1.44701	+	0.441961i
$536$	0.0834482	−	0.284198i	0.00360441	−	0.0122755i
$537$	14.5169	+	3.15796i	0.626451	+	0.136276i
$538$	2.19893	+	0.820159i	0.0948027	+	0.0353596i
$539$	31.6660	−	9.29797i	1.36395	−	0.400492i
$540$	−2.69764	−	1.69266i	−0.116088	−	0.0728404i
$541$	−5.26412	+	6.07512i	−0.226322	+	0.261190i	−0.857542	−	0.514414i	$-0.828009\pi$
$541$	−5.26412	+	6.07512i	−0.226322	+	0.261190i	0.631219	+	0.775604i	$0.282555\pi$
$542$	−15.2276	−	8.31488i	−0.654080	−	0.357155i
$543$	−2.96352	+	7.94551i	−0.127177	+	0.340974i
$544$	−0.144385	+	0.0927907i	−0.00619046	+	0.00397837i
$545$	−25.3108	+	19.3788i	−1.08420	+	0.830096i
$546$	−8.64740	+	1.24331i	−0.370075	+	0.0532087i
$547$	18.6183	−	6.94426i	0.796060	−	0.296915i	0.0816671	−	0.996660i	$-0.473976\pi$
$547$	18.6183	−	6.94426i	0.796060	−	0.296915i	0.714393	+	0.699745i	$0.246703\pi$
$548$	3.99166	−	2.98812i	0.170515	−	0.127646i
$549$	14.0148	+	9.00675i	0.598136	+	0.384399i
$550$	6.38922	+	26.5843i	0.272437	+	1.13356i
$551$		−	8.58547i		−	0.365753i
$552$	−10.9958	−	5.46670i	−0.468014	−	0.232678i
$553$	11.7553	−	11.7553i	0.499887	−	0.499887i
$554$	−11.7908	+	10.2168i	−0.500941	+	0.434068i
$555$	10.4415	+	27.0948i	0.443218	+	1.15011i
$556$	2.61773	−	18.2067i	0.111016	−	0.772136i
$557$	6.07240	+	16.2807i	0.257296	+	0.689837i	0.999800	+	0.0199955i	$0.00636519\pi$
$557$	6.07240	+	16.2807i	0.257296	+	0.689837i	−0.742504	+	0.669841i	$0.766362\pi$
$558$	−28.8947	−	21.6303i	−1.22321	−	0.915684i
$559$	17.5904	+	5.16500i	0.743994	+	0.218456i
$560$	1.45610	+	1.64410i	0.0615316	+	0.0694761i
$561$	−0.998285	−	2.18594i	−0.0421476	−	0.0922904i
$562$	8.21142	−	15.0381i	0.346378	−	0.634344i
$563$	−20.9749	+	1.50016i	−0.883988	+	0.0632241i	−0.505947	−	0.862565i	$-0.668857\pi$
$563$	−20.9749	+	1.50016i	−0.883988	+	0.0632241i	−0.378041	+	0.925789i	$0.623402\pi$
$564$	15.7140	+	13.6162i	0.661677	+	0.573346i
$565$	−25.7900	+	12.1172i	−1.08499	+	0.509776i
$566$	14.3768	−	6.56568i	0.604303	−	0.275976i
$567$	−1.46600	+	6.73911i	−0.0615664	+	0.283016i
$568$	8.46678	−	4.62321i	0.355258	−	0.193986i
$569$	1.73171	+	12.0443i	0.0725969	+	0.504922i	0.993382	+	0.114853i	$0.0366398\pi$
$569$	1.73171	+	12.0443i	0.0725969	+	0.504922i	−0.920786	+	0.390069i	$0.872451\pi$
$570$	4.74447	+	8.46942i	0.198724	+	0.354745i
$571$	21.1486	+	3.04072i	0.885043	+	0.127250i	0.569822	−	0.821768i	$-0.307012\pi$
$571$	21.1486	+	3.04072i	0.885043	+	0.127250i	0.315221	+	0.949018i	$0.397921\pi$
$572$	−18.5619	+	4.03790i	−0.776114	+	0.168833i
$573$	1.31801	−	18.4281i	0.0550605	−	0.769846i
$574$	4.04039			0.168643
$575$	12.7351	+	20.3179i	0.531092	+	0.847314i
$576$	−3.55623			−0.148176
$577$	1.66736	−	23.3127i	0.0694130	−	0.970520i	−0.836748	−	0.547588i	$-0.815546\pi$
$577$	1.66736	−	23.3127i	0.0694130	−	0.970520i	0.906161	−	0.422933i	$-0.138999\pi$
$578$	16.5827	−	3.60735i	0.689750	−	0.150046i
$579$	−13.5566	−	1.94914i	−0.563392	−	0.0810035i
$580$	−5.53361	−	9.87812i	−0.229770	−	0.410167i
$581$	−0.639993	−	4.45125i	−0.0265514	−	0.184669i
$582$	23.4490	−	12.8041i	0.971992	−	0.530748i
$583$	−12.1653	+	55.9229i	−0.503835	+	2.31609i
$584$	1.75818	−	0.802932i	0.0727539	−	0.0332256i
$585$	−25.0021	+	11.7470i	−1.03371	+	0.485679i
$586$	18.8000	+	16.2903i	0.776621	+	0.672946i
$587$	−6.75845	+	0.483374i	−0.278951	+	0.0199510i	−0.210114	−	0.977677i	$-0.567383\pi$
$587$	−6.75845	+	0.483374i	−0.278951	+	0.0199510i	−0.0688373	+	0.997628i	$0.521929\pi$
$588$	7.40611	−	13.5633i	0.305423	−	0.559340i
$589$	7.14883	+	15.6537i	0.294562	+	0.645001i
$590$	0.971469	+	1.09690i	0.0399947	+	0.0451586i
$591$	23.3881	+	6.86736i	0.962056	+	0.282485i
$592$	4.05998	+	3.03927i	0.166864	+	0.124913i
$593$	−7.15907	−	19.1942i	−0.293988	−	0.788212i	−0.997026	−	0.0770602i	$-0.975447\pi$
$593$	−7.15907	−	19.1942i	−0.293988	−	0.788212i	0.703039	−	0.711152i	$-0.251826\pi$
$594$	1.10837	−	7.70887i	0.0454769	−	0.316299i
$595$	0.135544	+	0.351723i	0.00555675	+	0.0144192i
$596$	−8.26622	+	7.16272i	−0.338598	+	0.293397i
$597$	−20.8434	+	20.8434i	−0.853062	+	0.853062i
$598$	−14.3047	+	8.54017i	−0.584963	+	0.349234i
$599$		−	22.1792i		−	0.906216i	−0.891456	−	0.453108i	$-0.850315\pi$
$599$		−	22.1792i		−	0.906216i	0.891456	−	0.453108i	$-0.149685\pi$
$600$	10.9176	+	6.68665i	0.445710	+	0.272981i
$601$	8.66226	+	5.56690i	0.353341	+	0.227079i	0.705255	−	0.708954i	$-0.250833\pi$
$601$	8.66226	+	5.56690i	0.353341	+	0.227079i	−0.351914	+	0.936032i	$0.614469\pi$
$602$	4.14945	−	3.10624i	0.169119	−	0.126601i
$603$	0.986930	−	0.368106i	0.0401909	−	0.0149904i
$604$	18.5480	−	2.66680i	0.754707	−	0.108510i
$605$	−33.5593	+	25.6941i	−1.36438	+	1.04461i
$606$	−24.9150	+	16.0119i	−1.01210	+	0.650440i
$607$	2.48839	−	6.67162i	0.101000	−	0.270793i	−0.876615	−	0.481192i	$-0.840204\pi$
$607$	2.48839	−	6.67162i	0.101000	−	0.270793i	0.977615	+	0.210400i	$0.0674765\pi$
$608$	1.48814	+	0.812586i	0.0603520	+	0.0329547i
$609$	8.33911	−	9.62385i	0.337918	−	0.389978i
$610$	−8.87296	−	5.56742i	−0.359256	−	0.225418i
$611$	27.0668	−	7.94752i	1.09500	−	0.321522i
$612$	−0.571876	−	0.213299i	−0.0231167	−	0.00862209i
$613$	11.7125	+	2.54791i	0.473065	+	0.102909i	0.442776	−	0.896632i	$-0.353994\pi$
$613$	11.7125	+	2.54791i	0.473065	+	0.102909i	0.0302890	+	0.999541i	$0.490357\pi$
$614$	6.17973	−	21.0462i	0.249394	−	0.849357i
$615$	22.5258	−	6.88008i	0.908328	−	0.277432i
$616$	−2.23110	+	4.88543i	−0.0898937	+	0.196840i
$617$	−4.73177	−	6.32090i	−0.190494	−	0.254470i	0.695119	−	0.718895i	$-0.255352\pi$
$617$	−4.73177	−	6.32090i	−0.190494	−	0.254470i	−0.885612	+	0.464425i	$0.846261\pi$
$618$	−0.726567	−	3.33997i	−0.0292268	−	0.134353i
$619$	−13.8197	−	15.9488i	−0.555461	−	0.641036i	0.406686	−	0.913568i	$-0.366684\pi$
$619$	−13.8197	−	15.9488i	−0.555461	−	0.641036i	−0.962147	+	0.272532i	$0.912139\pi$
$620$	18.3145	+	13.4030i	0.735529	+	0.538277i
$621$	−1.23108	−	6.71857i	−0.0494015	−	0.269607i
$622$	4.99008	+	4.99008i	0.200084	+	0.200084i
$623$	−9.58790	−	0.685740i	−0.384131	−	0.0274736i
$624$	−4.80895	+	7.48287i	−0.192512	+	0.299554i
$625$	−11.3607	−	22.2696i	−0.454427	−	0.890784i
$626$	18.9058	+	8.63397i	0.755626	+	0.345083i
$627$	−14.2270	+	19.0050i	−0.568171	+	0.758988i
$628$	3.04707	+	5.58030i	0.121592	+	0.222678i
$629$	0.470593	+	0.732256i	0.0187638	+	0.0291970i
$630$	−1.57741	+	7.64926i	−0.0628457	+	0.304754i
$631$	2.05380	+	6.99460i	0.0817605	+	0.278451i	0.990218	−	0.139526i	$-0.0445577\pi$
$631$	2.05380	+	6.99460i	0.0817605	+	0.278451i	−0.908458	+	0.417976i	$0.862740\pi$
$632$	−1.20751	−	16.8831i	−0.0480320	−	0.671576i
$633$	−3.25960	−	45.5752i	−0.129558	−	1.81145i
$634$	−6.07916	−	20.7037i	−0.241434	−	0.822249i
$635$	23.9983	+	36.4674i	0.952343	+	1.44716i
$636$	14.4883	+	22.5442i	0.574497	+	0.893935i
$637$	−10.0479	−	18.4014i	−0.398114	−	0.729091i
$638$	16.5933	−	22.1661i	0.656936	−	0.877564i
$639$	31.2060	+	14.2513i	1.23449	+	0.563773i
$640$	2.23594	−	0.0242217i	0.0883832	−	0.000957448i
$641$	−10.9663	+	17.0639i	−0.433142	+	0.673982i	−0.987379	−	0.158377i	$-0.949374\pi$
$641$	−10.9663	+	17.0639i	−0.433142	+	0.673982i	0.554237	+	0.832359i	$0.313010\pi$
$642$	−39.9714	−	2.85881i	−1.57754	−	0.112828i
$643$	0.374000	+	0.374000i	0.0147491	+	0.0147491i	0.714443	−	0.699694i	$-0.246680\pi$
$643$	0.374000	+	0.374000i	0.0147491	+	0.0147491i	−0.699694	+	0.714443i	$0.746680\pi$
$644$	−0.490747	+	4.68470i	−0.0193381	+	0.184603i
$645$	17.8445	−	24.3836i	0.702625	−	0.960102i
$646$	0.190569	+	0.219929i	0.00749784	+	0.00865297i
$647$	−5.33115	−	24.5069i	−0.209589	−	0.963465i	−0.954941	−	0.296795i	$-0.904082\pi$
$647$	−5.33115	−	24.5069i	−0.209589	−	0.963465i	0.745352	−	0.666671i	$-0.232281\pi$
$648$	4.20807	+	5.62132i	0.165309	+	0.220826i
$649$	−1.48853	+	3.25942i	−0.0584297	+	0.127943i
$650$	15.6397	−	7.55608i	0.613440	−	0.296374i
$651$	−7.19112	+	24.4907i	−0.281842	+	0.959866i
$652$	−16.2945	−	3.54465i	−0.638141	−	0.138819i
$653$	8.43644	+	3.14663i	0.330143	+	0.123137i	0.509070	−	0.860725i	$-0.329990\pi$
$653$	8.43644	+	3.14663i	0.330143	+	0.123137i	−0.178926	+	0.983862i	$0.557262\pi$
$654$	−35.0242	+	10.2840i	−1.36955	+	0.402137i
$655$	0.625605	+	2.73299i	0.0244444	+	0.106787i
$656$	2.69392	−	3.10895i	0.105180	−	0.121384i
$657$	6.03285	+	3.29419i	0.235364	+	0.128518i
$658$	2.78722	−	7.47282i	0.108657	−	0.291321i
$659$	25.2459	−	16.2245i	0.983439	−	0.632018i	0.0530503	−	0.998592i	$-0.483106\pi$
$659$	25.2459	−	16.2245i	0.983439	−	0.632018i	0.930389	+	0.366574i	$0.119469\pi$
$660$	−4.11971	+	31.0362i	−0.160359	+	1.20808i
$661$	−21.9067	+	3.14972i	−0.852074	+	0.122510i	−0.554495	−	0.832187i	$-0.687088\pi$
$661$	−21.9067	+	3.14972i	−0.852074	+	0.122510i	−0.297579	+	0.954697i	$0.596179\pi$
$662$	7.76354	−	2.89565i	0.301738	−	0.112543i
$663$	−1.22214	+	0.914882i	−0.0474639	+	0.0355311i
$664$	−3.85180	−	2.47540i	−0.149479	−	0.0960643i
$665$	2.40791	−	2.84047i	0.0933748	−	0.110149i
$666$			18.0356i			0.698866i
$667$	7.60605	−	23.0621i	0.294507	−	0.892967i
$668$	−9.31749	+	9.31749i	−0.360505	+	0.360505i
$669$	−12.8777	+	11.1586i	−0.497881	+	0.431416i
$670$	−0.618013	+	0.238164i	−0.0238759	+	0.00920108i
$671$	3.64560	−	25.3557i	0.140737	−	0.978846i
$672$	0.878856	+	2.35630i	0.0339026	+	0.0908964i
$673$	20.6527	+	15.4604i	0.796102	+	0.595955i	0.917997	−	0.396588i	$-0.129806\pi$
$673$	20.6527	+	15.4604i	0.796102	+	0.595955i	−0.121894	+	0.992543i	$0.538897\pi$
$674$	15.3900	+	4.51892i	0.592801	+	0.174062i
$675$	0.661778	+	7.09040i	0.0254719	+	0.272910i
$676$	−0.387250	−	0.847959i	−0.0148942	−	0.0326138i
$677$	17.9641	−	32.8988i	0.690416	−	1.26440i	−0.263595	−	0.964633i	$-0.584908\pi$
$677$	17.9641	−	32.8988i	0.690416	−	1.26440i	0.954012	−	0.299770i	$-0.0969099\pi$
$678$	−32.5462	+	2.32775i	−1.24993	+	0.0893966i
$679$	−7.74510	−	6.71116i	−0.297230	−	0.257551i
$680$	0.361013	+	0.130214i	0.0138442	+	0.00499347i
$681$	−7.07263	+	3.22996i	−0.271024	+	0.123772i
$682$	−11.7974	+	54.2318i	−0.451746	+	2.07664i
$683$	27.8738	−	15.2203i	1.06656	−	0.582387i	0.152643	−	0.988281i	$-0.451222\pi$
$683$	27.8738	−	15.2203i	1.06656	−	0.582387i	0.913920	+	0.405894i	$0.133040\pi$
$684$	0.858121	+	5.96836i	0.0328111	+	0.228206i
$685$	−10.7312	−	3.02510i	−0.410020	−	0.115583i
$686$	−12.6726	−	1.82205i	−0.483843	−	0.0695662i
$687$	50.2887	−	10.9396i	1.91863	−	0.417373i
$688$	0.376485	−	5.26395i	0.0143533	−	0.200686i
$689$	36.3575			1.38511
$690$	5.24123	+	26.9536i	0.199530	+	1.02611i
$691$	−34.1617			−1.29957			−0.649786	−	0.760117i	$-0.725142\pi$
$691$	−34.1617			−1.29957			−0.649786	+	0.760117i	$0.725142\pi$
$692$	−0.861075	+	12.0394i	−0.0327331	+	0.457669i
$693$	−18.6633	+	4.05994i	−0.708958	+	0.154224i
$694$	10.6117	+	1.52573i	0.402815	+	0.0579160i
$695$	−35.8833	+	20.1014i	−1.36113	+	0.762490i
$696$	−1.84516	−	12.8333i	−0.0699405	−	0.486447i
$697$	0.619679	−	0.338370i	0.0234720	−	0.0128167i
$698$	0.933139	−	4.28957i	0.0353198	−	0.162363i
$699$	36.8437	−	16.8260i	1.39356	−	0.636416i
$700$	0.939680	−	4.82012i	0.0355165	−	0.182183i
$701$	15.9847	+	13.8508i	0.603734	+	0.523138i	0.902220	−	0.431275i	$-0.141936\pi$
$701$	15.9847	+	13.8508i	0.603734	+	0.523138i	−0.298486	+	0.954414i	$0.596482\pi$
$702$	−4.93503	+	0.352961i	−0.186261	+	0.0133216i
$703$	4.12107	−	7.54718i	0.155429	−	0.284647i
$704$	2.27160	+	4.97411i	0.0856141	+	0.187469i
$705$	2.81427	−	46.4083i	0.105991	−	1.74784i
$706$	13.5025	+	3.96470i	0.508175	+	0.149214i
$707$	9.09450	+	6.80806i	0.342034	+	0.256043i
$708$	0.586346	+	1.57206i	0.0220362	+	0.0590815i
$709$	−4.76319	+	33.1287i	−0.178885	+	1.24417i	0.680462	+	0.732783i	$0.261779\pi$
$709$	−4.76319	+	33.1287i	−0.178885	+	1.24417i	−0.859348	+	0.511392i	$0.829130\pi$
$710$	−19.7175	−	8.74779i	−0.739983	−	0.328299i
$711$	45.4914	−	39.4185i	1.70606	−	1.47831i
$712$	−6.92036	+	6.92036i	−0.259352	+	0.259352i
$713$	5.33502	+	48.3820i	0.199798	+	1.81192i
$714$			0.431629i			0.0161533i
$715$	32.4010	+	27.4668i	1.21173	+	1.02720i
$716$	−4.88106	−	3.13687i	−0.182414	−	0.117230i
$717$	−2.44970	+	1.83382i	−0.0914856	+	0.0684853i
$718$	−23.3507	+	8.70937i	−0.871441	+	0.325031i
$719$	−14.6856	+	2.11147i	−0.547679	+	0.0787444i	−0.410600	−	0.911816i	$-0.634681\pi$
$719$	−14.6856	+	2.11147i	−0.547679	+	0.0787444i	−0.137079	+	0.990560i	$0.543772\pi$
$720$	4.83412	+	6.31389i	0.180157	+	0.235305i
$721$	−1.10299	+	0.708847i	−0.0410774	+	0.0263988i
$722$	−5.63516	+	15.1084i	−0.209719	+	0.562278i
$723$	−32.5119	−	17.7528i	−1.20913	−	0.660234i
$724$	2.16884	−	2.50297i	0.0806042	−	0.0930222i
$725$	−10.0160	+	23.2523i	−0.371986	+	0.863569i
$726$	−46.4382	+	13.6355i	−1.72348	+	0.506060i
$727$	−28.3336	−	10.5679i	−1.05084	−	0.391941i	−0.236072	−	0.971735i	$-0.575860\pi$
$727$	−28.3336	−	10.5679i	−1.05084	−	0.391941i	−0.814763	+	0.579794i	$0.803133\pi$
$728$	3.33397	+	0.725261i	0.123565	+	0.0268799i
$729$	−10.1176	+	34.4572i	−0.374724	+	1.27619i
$730$	−3.81552	−	2.03009i	−0.141219	−	0.0751369i
$731$	0.376268	−	0.823912i	0.0139168	−	0.0304735i
$732$	−7.18827	−	9.60240i	−0.265686	−	0.354915i
$733$	−3.19783	−	14.7002i	−0.118115	−	0.542964i	−0.997734	−	0.0672855i	$-0.978566\pi$
$733$	−3.19783	−	14.7002i	−0.118115	−	0.542964i	0.879619	−	0.475679i	$-0.157797\pi$
$734$	−16.6652	−	19.2327i	−0.615125	−	0.709892i
$735$	−34.1482	+	5.28794i	−1.25958	+	0.195048i
$736$	3.27752	+	3.50112i	0.120811	+	0.129053i
$737$	−1.14529	−	1.14529i	−0.0421872	−	0.0421872i
$738$	14.5921	+	1.04365i	0.537143	+	0.0384172i
$739$	−6.31805	+	9.83108i	−0.232413	+	0.361642i	−0.937797	−	0.347183i	$-0.887138\pi$
$739$	−6.31805	+	9.83108i	−0.232413	+	0.361642i	0.705384	+	0.708825i	$0.250775\pi$
$740$	−0.122842	−	11.3397i	−0.00451575	−	0.416854i
$741$	13.7188	+	6.26515i	0.503971	+	0.230156i
$742$	6.16022	−	8.22909i	0.226149	−	0.302099i
$743$	20.8218	+	38.1323i	0.763877	+	1.39894i	0.912094	+	0.409982i	$0.134465\pi$
$743$	20.8218	+	38.1323i	0.763877	+	1.39894i	−0.148216	+	0.988955i	$0.547353\pi$
$744$	14.0501	+	21.8624i	0.515103	+	0.801516i
$745$	23.9536	+	4.93966i	0.877592	+	0.180975i
$746$	0.988669	+	3.36710i	0.0361977	+	0.123278i
$747$	−1.16160	−	16.2413i	−0.0425006	−	0.594236i
$748$	0.0669535	+	0.936132i	0.00244806	+	0.0342284i
$749$	4.33067	+	14.7489i	0.158239	+	0.538913i
$750$	−2.96896	−	28.4730i	−0.108411	−	1.03969i
$751$	14.5006	+	22.5634i	0.529136	+	0.823351i	0.998210	−	0.0598077i	$-0.0190488\pi$
$751$	14.5006	+	22.5634i	0.529136	+	0.823351i	−0.469074	+	0.883159i	$0.655412\pi$
$752$	−3.89172	−	7.12715i	−0.141916	−	0.259901i
$753$	33.9639	−	45.3704i	1.23771	−	1.65339i
$754$	−16.0006	−	7.30722i	−0.582707	−	0.266113i
$755$	−29.9477	−	29.3058i	−1.08991	−	1.06655i
$756$	−0.756276	+	1.17679i	−0.0275055	+	0.0427994i
$757$	45.5724	+	3.25941i	1.65636	+	0.118465i	0.867938	−	0.496672i	$-0.165445\pi$
$757$	45.5724	+	3.25941i	1.65636	+	0.118465i	0.788420	+	0.615137i	$0.210899\pi$
$758$	−24.2855	−	24.2855i	−0.882088	−	0.882088i
$759$	−55.0532	+	38.4469i	−1.99830	+	1.39553i
$760$	−0.580184	−	3.74669i	−0.0210455	−	0.135907i
$761$	29.7315	+	34.3120i	1.07777	+	1.24381i	0.968293	+	0.249818i	$0.0803707\pi$
$761$	29.7315	+	34.3120i	1.07777	+	1.24381i	0.109473	+	0.993990i	$0.465084\pi$
$762$	10.6260	+	48.8471i	0.384941	+	1.76955i
$763$	8.39102	+	11.2091i	0.303775	+	0.405797i
$764$	−2.99740	+	6.56338i	−0.108442	+	0.237455i
$765$	0.398673	+	1.30528i	0.0144140	+	0.0471925i
$766$	10.5683	−	35.9925i	0.381850	−	1.30046i
$767$	2.22433	+	0.483872i	0.0803157	+	0.0174716i
$768$	2.39907	+	0.894808i	0.0865691	+	0.0322886i
$769$	13.3546	−	3.92127i	0.481580	−	0.141405i	−0.0319265	−	0.999490i	$-0.510164\pi$
$769$	13.3546	−	3.92127i	0.481580	−	0.141405i	0.513507	+	0.858085i	$0.328346\pi$
$770$	11.7066	−	2.67975i	0.421878	−	0.0965716i
$771$	−50.7209	+	58.5351i	−1.82667	+	2.10809i
$772$	4.69463	+	2.56346i	0.168963	+	0.0922610i
$773$	3.98001	−	10.6708i	0.143151	−	0.383803i	−0.845512	−	0.533957i	$-0.820704\pi$
$773$	3.98001	−	10.6708i	0.143151	−	0.383803i	0.988663	+	0.150154i	$0.0479771\pi$
$774$	15.7883	−	10.1465i	0.567500	−	0.364710i
$775$	−1.09936	−	50.7356i	−0.0394901	−	1.82248i
$776$	−10.3280	+	1.48495i	−0.370755	+	0.0533065i
$777$	11.9501	−	4.45716i	0.428708	−	0.159900i
$778$	−21.0817	+	15.7815i	−0.755815	+	0.565796i
$779$	−5.86774	−	3.77096i	−0.210233	−	0.135109i
$780$	19.8224	−	1.63373i	0.709756	−	0.0584968i
$781$		−	52.7512i		−	1.88759i
$782$	0.317063	+	0.759596i	0.0113381	+	0.0271631i
$783$	5.09947	−	5.09947i	0.182240	−	0.182240i
$784$	−4.56120	+	3.95231i	−0.162900	+	0.141154i
$785$	5.76551	−	12.9954i	0.205780	−	0.463827i
$786$	−0.456899	+	3.17780i	−0.0162970	+	0.113348i
$787$	9.48065	+	25.4186i	0.337949	+	0.906075i	0.989116	+	0.147141i	$0.0470070\pi$
$787$	9.48065	+	25.4186i	0.337949	+	0.906075i	−0.651167	+	0.758934i	$0.725720\pi$
$788$	−7.62095	−	5.70497i	−0.271485	−	0.203231i
$789$	−0.968038	−	0.284242i	−0.0344631	−	0.0101193i
$790$	−28.3337	+	25.0938i	−1.00807	+	0.892796i
$791$	5.19937	+	11.3850i	0.184868	+	0.404805i
$792$	−9.31968	+	17.0677i	−0.331160	+	0.606475i
$793$	−16.2321	+	1.16094i	−0.576419	+	0.0412263i
$794$	9.63813	+	8.35149i	0.342045	+	0.296383i
$795$	20.3315	−	56.3683i	0.721084	−	1.99918i
$796$	10.4718	−	4.78231i	0.371163	−	0.169505i
$797$	−6.07411	+	27.9223i	−0.215156	+	0.989057i	0.735190	+	0.677861i	$0.237093\pi$
$797$	−6.07411	+	27.9223i	−0.215156	+	0.989057i	−0.950346	+	0.311196i	$0.899271\pi$
$798$	3.74247	−	2.04354i	0.132482	−	0.0723407i
$799$	−0.198347	−	1.37954i	−0.00701702	−	0.0488045i
$800$	−3.08240	−	3.93686i	−0.108979	−	0.139189i
$801$	−34.4501	−	4.95318i	−1.21724	−	0.175012i
$802$	2.63747	−	0.573746i	0.0931323	−	0.0202597i
$803$	0.754005	−	10.5424i	0.0266083	−	0.372032i
$804$	−0.758415			−0.0267472
$805$	8.98451	−	5.49679i	0.316662	−	0.193736i
$806$	35.2581			1.24191
$807$	0.428697	−	5.99397i	0.0150909	−	0.210998i
$808$	11.3023	−	2.45867i	0.397614	−	0.0864956i
$809$	−40.9101	−	5.88198i	−1.43832	−	0.206799i	−0.621375	−	0.783513i	$-0.713426\pi$
$809$	−40.9101	−	5.88198i	−1.43832	−	0.206799i	−0.816946	+	0.576714i	$0.804335\pi$
$810$	4.26016	−	15.1125i	0.149687	−	0.530998i
$811$	−1.16548	−	8.10609i	−0.0409255	−	0.284643i	−0.999999	−	0.00148562i	$-0.999527\pi$
$811$	−1.16548	−	8.10609i	−0.0409255	−	0.284643i	0.959073	−	0.283158i	$-0.0913820\pi$
$812$	−4.36495	+	2.38344i	−0.153180	+	0.0836424i
$813$	−9.44310	+	43.4092i	−0.331184	+	1.52243i
$814$	25.2264	−	11.5205i	0.884186	−	0.403794i
$815$	15.8564	+	33.7483i	0.555424	+	1.18215i
$816$	0.332124	+	0.287787i	0.0116267	+	0.0100746i
$817$	−8.92523	+	0.638345i	−0.312254	+	0.0223329i
$818$	11.8783	−	21.7535i	0.415316	−	0.760595i
$819$	5.04051	+	11.0372i	0.176130	+	0.385670i
$820$	−9.18171	−	0.556793i	−0.320639	−	0.0194440i
$821$	−38.9805	−	11.4457i	−1.36043	−	0.399458i	−0.481514	−	0.876438i	$-0.659913\pi$
$821$	−38.9805	−	11.4457i	−1.36043	−	0.399458i	−0.878914	+	0.476981i	$0.841731\pi$
$822$	−10.2207	−	7.65111i	−0.356487	−	0.266863i
$823$	−0.0764573	−	0.204990i	−0.00266513	−	0.00714550i	0.935610	−	0.353034i	$-0.114850\pi$
$823$	−0.0764573	−	0.204990i	−0.00266513	−	0.00714550i	−0.938275	+	0.345889i	$0.887577\pi$
$824$	−0.189979	+	1.32134i	−0.00661824	+	0.0460309i
$825$	60.7032	−	34.8744i	2.11341	−	1.21417i
$826$	0.486396	−	0.421465i	0.0169239	−	0.0146646i
$827$	26.5057	−	26.5057i	0.921693	−	0.921693i	−0.0754559	−	0.997149i	$-0.524041\pi$
$827$	26.5057	−	26.5057i	0.921693	−	0.921693i	0.997149	+	0.0754559i	$0.0240412\pi$
$828$	−2.98244	+	16.7923i	−0.103647	+	0.583573i
$829$			47.4529i			1.64811i	0.566512	+	0.824054i	$0.308293\pi$
$829$			47.4529i			1.64811i	−0.566512	+	0.824054i	$0.691707\pi$
$830$	0.840960	+	10.2036i	0.0291902	+	0.354171i
$831$	33.6061	+	21.5973i	1.16578	+	0.749203i
$832$	2.78098	−	2.08182i	0.0964131	−	0.0721739i
$833$	−0.970540	+	0.361993i	−0.0336272	+	0.0125423i
$834$	−46.6185	+	6.70273i	−1.61427	+	0.232096i
$835$	29.2083	+	3.87707i	1.01080	+	0.134172i
$836$	7.79982	−	5.01264i	0.269762	−	0.173366i
$837$	−5.05163	+	13.5439i	−0.174610	+	0.468147i
$838$	14.5387	+	7.93876i	0.502233	+	0.274240i
$839$	1.47534	−	1.70264i	0.0509345	−	0.0587815i	−0.729711	−	0.683756i	$-0.760345\pi$
$839$	1.47534	−	1.70264i	0.0509345	−	0.0587815i	0.780645	+	0.624975i	$0.214891\pi$
$840$	2.98882	−	4.76337i	0.103124	−	0.164352i
$841$	−3.22426	+	0.946728i	−0.111181	+	0.0326458i
$842$	13.2418	+	4.93895i	0.456344	+	0.170207i
$843$	−42.8691	−	9.32560i	−1.47649	−	0.321191i
$844$	−5.02743	+	17.1219i	−0.173051	+	0.589359i
$845$	−0.979101	+	1.84020i	−0.0336821	+	0.0633049i
$846$	11.9965	−	26.2686i	0.412447	−	0.903132i
$847$	11.1256	+	14.8620i	0.382279	+	0.510665i
$848$	−2.22471	−	10.2268i	−0.0763967	−	0.351190i
$849$	−26.5017	−	30.5846i	−0.909535	−	1.04966i
$850$	−0.259551	−	0.817963i	−0.00890252	−	0.0280559i
$851$	17.7561	−	16.6221i	0.608672	−	0.569798i
$852$	−17.4661	−	17.4661i	−0.598377	−	0.598377i
$853$	52.8544	+	3.78022i	1.80970	+	0.129432i	0.934869	−	0.354993i	$-0.115517\pi$
$853$	52.8544	+	3.78022i	1.80970	+	0.129432i	0.874833	+	0.484425i	$0.160971\pi$
$854$	−2.48751	+	3.87065i	−0.0851210	+	0.132451i
$855$	9.43002	−	9.63656i	0.322500	−	0.329564i
$856$	14.2363	+	6.50148i	0.486585	+	0.222216i
$857$	12.6762	−	16.9334i	0.433011	−	0.578435i	−0.529966	−	0.848019i	$-0.677795\pi$
$857$	12.6762	−	16.9334i	0.433011	−	0.578435i	0.962977	+	0.269584i	$0.0868862\pi$
$858$	23.3105	+	42.6900i	0.795808	+	1.45741i
$859$	−3.07912	−	4.79121i	−0.105058	−	0.163474i	0.784744	−	0.619820i	$-0.212794\pi$
$859$	−3.07912	−	4.79121i	−0.105058	−	0.163474i	−0.889802	+	0.456346i	$0.849158\pi$
$860$	−9.85761	+	6.48705i	−0.336142	+	0.221207i
$861$	−2.91466	−	9.92641i	−0.0993312	−	0.338291i
$862$	−2.47340	−	34.5827i	−0.0842444	−	1.17789i
$863$	0.418015	+	5.84461i	0.0142294	+	0.198953i	0.999594	+	0.0284929i	$0.00907080\pi$
$863$	0.418015	+	5.84461i	0.0142294	+	0.198953i	−0.985365	+	0.170460i	$0.945475\pi$
$864$	0.401256	+	1.36655i	0.0136510	+	0.0464910i
$865$	22.5458	−	14.8368i	0.766579	−	0.504467i
$866$	−6.73742	−	10.4836i	−0.228947	−	0.356248i
$867$	−20.8250	−	38.1381i	−0.707253	−	1.29524i
$868$	5.97393	−	7.98024i	0.202768	−	0.270867i
$869$	−84.1931	−	38.4497i	−2.85606	−	1.30432i
$870$	−20.2767	+	20.7208i	−0.687444	+	0.702502i
$871$	−0.556292	+	0.865607i	−0.0188492	+	0.0293300i
$872$	14.2197	+	1.01701i	0.481541	+	0.0344405i
$873$	−26.2383	−	26.2383i	−0.888033	−	0.888033i
$874$	5.08501	−	6.34542i	0.172003	−	0.214637i
$875$	−9.83520	+	4.88382i	−0.332490	+	0.165103i
$876$	−3.24095	−	3.74026i	−0.109502	−	0.126372i
$877$	−8.74194	−	40.1860i	−0.295194	−	1.35699i	−0.850778	−	0.525525i	$-0.823869\pi$
$877$	−8.74194	−	40.1860i	−0.295194	−	1.35699i	0.555584	−	0.831461i	$-0.312495\pi$
$878$	−9.20539	−	12.2970i	−0.310667	−	0.415002i
$879$	26.4600	−	57.9393i	0.892473	−	1.95424i
$880$	5.74338	−	10.7946i	0.193609	−	0.363886i
$881$	−14.4785	+	49.3093i	−0.487794	+	1.66127i	0.236383	+	0.971660i	$0.424038\pi$
$881$	−14.4785	+	49.3093i	−0.487794	+	1.66127i	−0.724177	+	0.689614i	$0.757780\pi$
$882$	−20.9726	−	4.56230i	−0.706183	−	0.153621i
$883$	−5.28066	−	1.96958i	−0.177708	−	0.0662818i	0.259035	−	0.965868i	$-0.416596\pi$
$883$	−5.28066	−	1.96958i	−0.177708	−	0.0662818i	−0.436743	+	0.899586i	$0.643868\pi$
$884$	0.572073	−	0.167976i	0.0192409	−	0.00564964i
$885$	1.99405	−	3.17798i	0.0670294	−	0.106827i
$886$	7.09194	−	8.18454i	0.238258	−	0.274965i
$887$	−11.0417	−	6.02923i	−0.370745	−	0.202442i	0.283065	−	0.959101i	$-0.408649\pi$
$887$	−11.0417	−	6.02923i	−0.370745	−	0.202442i	−0.653810	+	0.756659i	$0.726830\pi$
$888$	4.53806	−	12.1670i	0.152287	−	0.408298i
$889$	16.1312	−	10.3669i	0.541023	−	0.347694i
$890$	21.6938	+	2.87961i	0.727179	+	0.0965247i
$891$	38.0068	−	5.46455i	1.27328	−	0.183069i
$892$	6.23519	−	2.32560i	0.208769	−	0.0778670i
$893$	−11.0223	+	8.25119i	−0.368847	+	0.276116i
$894$	23.5604	+	15.1414i	0.787979	+	0.506403i
$895$	1.06568	+	12.9301i	0.0356216	+	0.432206i
$896$		−	0.982172i		−	0.0328121i
$897$	31.3006	+	28.9830i	1.04510	+	0.967716i
$898$	−8.07573	+	8.07573i	−0.269491	+	0.269491i
$899$	−38.8399	+	33.6550i	−1.29538	+	1.12246i
$900$	4.63876	−	17.1654i	0.154625	−	0.572181i
$901$	0.255638	−	1.77800i	0.00851655	−	0.0592339i
$902$	−7.86118	−	21.0766i	−0.261749	−	0.701775i
$903$	−10.6247	−	7.95357i	−0.353569	−	0.264678i
$904$	12.2271	+	3.59019i	0.406666	+	0.119408i
$905$	−7.39207	−	0.448266i	−0.245721	−	0.0149009i
$906$	−19.9319	−	43.6448i	−0.662194	−	1.45000i
$907$	19.4866	−	35.6870i	0.647042	−	1.18497i	−0.324000	−	0.946057i	$-0.605028\pi$
$907$	19.4866	−	35.6870i	0.647042	−	1.18497i	0.971041	−	0.238911i	$-0.0767904\pi$
$908$	3.02887	−	0.216629i	0.100516	−	0.00718908i
$909$	31.0868	+	26.9368i	1.03108	+	0.893439i
$910$	−3.24433	−	6.90515i	−0.107548	−	0.228903i
$911$	−31.3361	+	14.3107i	−1.03821	+	0.474135i	−0.860234	−	0.509900i	$-0.829683\pi$
$911$	−31.3361	+	14.3107i	−1.03821	+	0.474135i	−0.177977	+	0.984035i	$0.556955\pi$
$912$	0.922843	−	4.24224i	0.0305584	−	0.140475i
$913$	−21.9747	+	11.9991i	−0.727256	+	0.397112i
$914$	0.724778	+	5.04094i	0.0239735	+	0.166739i
$915$	−7.27725	+	25.8153i	−0.240578	+	0.853427i
$916$	−19.8948	−	2.86045i	−0.657344	−	0.0945118i
$917$	1.20335	−	0.261772i	0.0397380	−	0.00864447i
$918$	−0.0174384	+	0.243821i	−0.000575554	+	0.00804730i
$919$	−25.7553			−0.849588			−0.424794	−	0.905290i	$-0.639653\pi$
$919$	−25.7553			−0.849588			−0.424794	+	0.905290i	$0.639653\pi$
$920$	1.76080	−	10.5783i	0.0580517	−	0.348755i
$921$	−56.1642			−1.85067
$922$	1.45975	−	20.4099i	0.0480742	−	0.672165i
$923$	−32.7459	+	7.12343i	−1.07784	+	0.234470i
$924$	13.6120	+	1.95711i	0.447801	+	0.0643841i
$925$	−19.9660	+	15.6325i	−0.656477	+	0.513994i
$926$	4.09102	+	28.4537i	0.134439	+	0.935046i
$927$	−4.16660	+	2.27514i	−0.136849	+	0.0747253i
$928$	−1.07634	+	4.94784i	−0.0353325	+	0.162421i
$929$	−24.0797	+	10.9968i	−0.790031	+	0.360795i	−0.769216	−	0.638988i	$-0.779353\pi$
$929$	−24.0797	+	10.9968i	−0.790031	+	0.360795i	−0.0208143	+	0.999783i	$0.506626\pi$
$930$	19.7167	−	54.6637i	0.646535	−	1.79249i
$931$	7.73370	+	6.70129i	0.253462	+	0.219626i
$932$	−15.7784	+	1.12849i	−0.516838	+	0.0369650i
$933$	8.65986	−	15.8594i	0.283511	−	0.519212i
$934$	0.560138	+	1.22653i	0.0183283	+	0.0401333i
$935$	1.57104	−	1.39139i	0.0513784	−	0.0455034i
$936$	11.8535	+	3.48050i	0.387443	+	0.113764i
$937$	−10.5351	−	7.88648i	−0.344167	−	0.257640i	0.413185	−	0.910647i	$-0.364416\pi$
$937$	−10.5351	−	7.88648i	−0.344167	−	0.257640i	−0.757352	+	0.653007i	$0.773507\pi$
$938$	0.101665	+	0.272574i	0.00331947	+	0.00889984i
$939$	7.57366	−	52.6760i	0.247157	−	1.71902i
$940$	−7.36370	+	16.5977i	−0.240177	+	0.541359i
$941$	7.93208	−	6.87319i	0.258578	−	0.224059i	−0.515918	−	0.856638i	$-0.672549\pi$
$941$	7.93208	−	6.87319i	0.258578	−	0.224059i	0.774496	+	0.632579i	$0.218004\pi$
$942$	11.5116	−	11.5116i	0.375067	−	0.375067i
$943$	−12.4210	−	15.3278i	−0.404483	−	0.499143i
$944$		−	0.655276i		−	0.0213274i
$945$	3.11736	−	0.256927i	0.101408	−	0.00835784i
$946$	−24.2770	−	15.6019i	−0.789315	−	0.507262i
$947$	−30.7872	+	23.0470i	−1.00045	+	0.748928i	−0.968104	−	0.250549i	$-0.919389\pi$
$947$	−30.7872	+	23.0470i	−1.00045	+	0.748928i	−0.0323465	+	0.999477i	$0.510298\pi$
$948$	−40.6074	+	15.1458i	−1.31887	+	0.491912i
$949$	−6.64611	+	0.955567i	−0.215742	+	0.0310190i
$950$	−5.86337	+	6.12310i	−0.190233	+	0.198659i
$951$	−46.4794	+	29.8705i	−1.50720	+	0.968617i
$952$	0.0589096	−	0.157943i	0.00190927	−	0.00511895i
$953$	−29.7699	−	16.2556i	−0.964341	−	0.526570i	−0.0817201	−	0.996655i	$-0.526041\pi$
$953$	−29.7699	−	16.2556i	−0.964341	−	0.526570i	−0.882621	+	0.470085i	$0.844223\pi$
$954$	24.3736	−	28.1286i	0.789124	−	0.910698i
$955$	15.7274	−	3.60014i	0.508927	−	0.116498i
$956$	1.14668	−	0.336696i	0.0370864	−	0.0108895i
$957$	−66.4277	−	24.7762i	−2.14730	−	0.800902i
$958$	−8.40796	−	1.82904i	−0.271649	−	0.0590936i
$959$	−1.37973	+	4.69893i	−0.0445538	+	0.151736i
$960$	−1.67247	−	5.47577i	−0.0539787	−	0.176730i
$961$	29.9150	−	65.5047i	0.965000	−	2.11305i
$962$	−10.5580	−	14.1039i	−0.340404	−	0.454727i
$963$	11.8308	+	54.3851i	0.381241	+	1.75254i
$964$	9.47388	+	10.9334i	0.305133	+	0.352142i
$965$	−1.83030	−	11.8197i	−0.0589195	−	0.380488i
$966$	11.8634	−	2.17378i	0.381697	−	0.0699403i
$967$	−15.9732	−	15.9732i	−0.513663	−	0.513663i	0.401984	−	0.915647i	$-0.368321\pi$
$967$	−15.9732	−	15.9732i	−0.513663	−	0.513663i	−0.915647	+	0.401984i	$0.868321\pi$
$968$	18.8538	+	1.34845i	0.605983	+	0.0433408i
$969$	0.402847	−	0.626841i	0.0129413	−	0.0201370i
$970$	16.6757	+	16.3183i	0.535426	+	0.523950i
$971$	14.2140	+	6.49133i	0.456150	+	0.208317i	0.630220	−	0.776417i	$-0.282965\pi$
$971$	14.2140	+	6.49133i	0.456150	+	0.208317i	−0.174070	+	0.984733i	$0.555692\pi$
$972$	13.3354	−	17.8140i	0.427732	−	0.571384i
$973$	8.65811	+	15.8561i	0.277566	+	0.508325i
$974$	3.25477	+	5.06452i	0.104289	+	0.162278i
$975$	−29.8459	−	32.9728i	−0.955834	−	1.05597i
$976$	1.31979	+	4.49480i	0.0422456	+	0.143875i
$977$	1.42417	+	19.9125i	0.0455633	+	0.637059i	0.968006	+	0.250926i	$0.0807349\pi$
$977$	1.42417	+	19.9125i	0.0455633	+	0.637059i	−0.922443	+	0.386133i	$0.873811\pi$
$978$	3.04604	+	42.5892i	0.0974017	+	1.36185i
$979$	15.0775	+	51.3494i	0.481880	+	1.64113i
$980$	13.2173	+	2.72565i	0.422212	+	0.0870675i
$981$	27.4093	+	42.6497i	0.875112	+	1.36170i
$982$	20.4959	+	37.5354i	0.654051	+	1.19780i
$983$	−31.4328	+	41.9893i	−1.00255	+	1.33925i	−0.0625624	+	0.998041i	$0.519927\pi$
$983$	−31.4328	+	41.9893i	−1.00255	+	1.33925i	−0.939988	+	0.341209i	$0.889164\pi$
$984$	−9.58139	−	4.37567i	−0.305444	−	0.139491i
$985$	0.230585	+	21.2855i	0.00734704	+	0.678214i
$986$	−0.469851	+	0.731102i	−0.0149631	+	0.0232830i
$987$	−20.3698	−	1.45688i	−0.648379	−	0.0463730i
$988$	−4.16492	−	4.16492i	−0.132504	−	0.132504i
$989$	−24.5403	−	6.19235i	−0.780335	−	0.196905i
$990$	42.9714	−	6.65422i	1.36572	−	0.211485i
$991$	−8.64352	−	9.97515i	−0.274570	−	0.316871i	0.601671	−	0.798744i	$-0.294502\pi$
$991$	−8.64352	−	9.97515i	−0.274570	−	0.316871i	−0.876241	+	0.481873i	$0.839957\pi$
$992$	−2.15743	−	9.91755i	−0.0684985	−	0.314883i
$993$	−12.7145	−	16.9846i	−0.403482	−	0.538989i
$994$	−3.93598	+	8.61859i	−0.124842	+	0.273365i
$995$	−22.7254	−	12.0913i	−0.720445	−	0.383321i
$996$	−3.30295	+	11.2488i	−0.104658	+	0.356432i
$997$	−23.3969	−	5.08969i	−0.740988	−	0.161192i	−0.173801	−	0.984781i	$-0.555605\pi$
$997$	−23.3969	−	5.08969i	−0.740988	−	0.161192i	−0.567187	+	0.823589i	$0.691968\pi$
$998$	18.3338	+	6.83815i	0.580346	+	0.216458i
$999$	6.93053	−	2.03499i	0.219272	−	0.0643842i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.217.6	yes	240
5.3	odd	4	inner	230.2.l.a.33.12	yes	240
23.7	odd	22	inner	230.2.l.a.7.12	✓	240
115.53	even	44	inner	230.2.l.a.53.6	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.7.12	✓	240	23.7	odd	22	inner
230.2.l.a.33.12	yes	240	5.3	odd	4	inner
230.2.l.a.53.6	yes	240	115.53	even	44	inner
230.2.l.a.217.6	yes	240	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-0.0713392 + 0.997452i) q^{2} +(2.50200 - 0.544276i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(1.09283 + 1.95083i) q^{5} +(0.364399 + 2.53445i) q^{6} +(0.862032 - 0.470705i) q^{7} +(0.212565 - 0.977147i) q^{8} +(3.23486 - 1.47731i) q^{9} +O(q^{10})\)	\(q+(-0.0713392 + 0.997452i) q^{2} +(2.50200 - 0.544276i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(1.09283 + 1.95083i) q^{5} +(0.364399 + 2.53445i) q^{6} +(0.862032 - 0.470705i) q^{7} +(0.212565 - 0.977147i) q^{8} +(3.23486 - 1.47731i) q^{9} +(-2.02382 + 0.950875i) q^{10} +(-4.13264 - 3.58095i) q^{11} +(-2.55399 + 0.182665i) q^{12} +(-1.66485 + 3.04895i) q^{13} +(0.408009 + 0.893415i) q^{14} +(3.79605 + 4.28616i) q^{15} +(0.959493 + 0.281733i) q^{16} +(0.137398 + 0.102855i) q^{17} +(1.24278 + 3.33201i) q^{18} +(0.241301 - 1.67828i) q^{19} +(-0.804074 - 2.08650i) q^{20} +(1.90061 - 1.64689i) q^{21} +(3.86665 - 3.86665i) q^{22} +(2.13500 - 4.29439i) q^{23} -2.56051i q^{24} +(-2.61145 + 4.26384i) q^{25} +(-2.92241 - 1.87812i) q^{26} +(1.14017 - 0.853517i) q^{27} +(-0.920246 + 0.343234i) q^{28} +(5.01202 - 0.720619i) q^{29} +(-4.54605 + 3.48060i) q^{30} +(-8.53830 + 5.48723i) q^{31} +(-0.349464 + 0.936950i) q^{32} +(-12.2889 - 6.71024i) q^{33} +(-0.112394 + 0.129710i) q^{34} +(1.86032 + 1.16727i) q^{35} +(-3.41218 + 1.00191i) q^{36} +(4.75179 + 1.77232i) q^{37} +(1.65679 + 0.360413i) q^{38} +(-2.50598 + 8.53460i) q^{39} +(2.13854 - 0.653177i) q^{40} +(1.70890 - 3.74198i) q^{41} +(1.50710 + 2.01325i) q^{42} +(-1.12179 - 5.15679i) q^{43} +(3.58095 + 4.13264i) q^{44} +(6.41713 + 4.69621i) q^{45} +(4.13114 + 2.43592i) q^{46} +(-5.74203 - 5.74203i) q^{47} +(2.55399 + 0.182665i) q^{48} +(-3.26295 + 5.07725i) q^{49} +(-4.06668 - 2.90897i) q^{50} +(0.399750 + 0.182560i) q^{51} +(2.08182 - 2.78098i) q^{52} +(-5.01582 - 9.18578i) q^{53} +(0.770004 + 1.19815i) q^{54} +(2.46955 - 11.9754i) q^{55} +(-0.276710 - 0.942387i) q^{56} +(-0.309716 - 4.33039i) q^{57} +(0.361230 + 5.05066i) q^{58} +(-0.184613 - 0.628733i) q^{59} +(-3.14742 - 4.78277i) q^{60} +(2.53267 + 3.94090i) q^{61} +(-4.86414 - 8.90800i) q^{62} +(2.09318 - 2.79616i) q^{63} +(-0.909632 - 0.415415i) q^{64} +(-7.76736 + 0.0841432i) q^{65} +(7.56982 - 11.7789i) q^{66} +(0.295442 + 0.0211304i) q^{67} +(-0.121361 - 0.121361i) q^{68} +(3.00444 - 11.9066i) q^{69} +(-1.29701 + 1.77231i) q^{70} +(6.31730 + 7.29055i) q^{71} +(-0.755932 - 3.47496i) q^{72} +(1.15831 + 1.54732i) q^{73} +(-2.10680 + 4.61324i) q^{74} +(-4.21313 + 12.0895i) q^{75} +(-0.477689 + 1.62686i) q^{76} +(-5.24804 - 1.14164i) q^{77} +(-8.33408 - 3.10845i) q^{78} +(16.2406 - 4.76868i) q^{79} +(0.498951 + 2.17969i) q^{80} +(-4.59837 + 5.30680i) q^{81} +(3.61053 + 1.97150i) q^{82} +(1.60007 - 4.28996i) q^{83} +(-2.11564 + 1.35964i) q^{84} +(-0.0504993 + 0.380441i) q^{85} +(5.22368 - 0.751051i) q^{86} +(12.1478 - 4.53091i) q^{87} +(-4.37757 + 3.27701i) q^{88} +(-8.23324 - 5.29118i) q^{89} +(-5.14203 + 6.06576i) q^{90} +3.41194i q^{91} +(-2.72443 + 3.94683i) q^{92} +(-18.3762 + 18.3762i) q^{93} +(6.13703 - 5.31777i) q^{94} +(3.53774 - 1.36334i) q^{95} +(-0.364399 + 2.53445i) q^{96} +(-3.64640 - 9.77637i) q^{97} +(-4.83154 - 3.61684i) q^{98} +(-18.6587 - 5.47869i) 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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