LMFDB - Embedded newform 230.2.g.d.41.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(31,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("230.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.g (of order $11$, degree $10$, 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:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			41.2
Character	$\chi$	$=$	230.41
Dual form			230.2.g.d.101.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.959493 - 0.281733i) q^{2} +(-0.858654 + 0.990939i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.142315 - 0.989821i) q^{5} +(1.10305 - 0.708888i) q^{6} +(-1.50220 - 3.28936i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(0.182270 + 1.26772i) q^{9} +O(q^{10})$	\(q+(-0.959493 - 0.281733i) q^{2} +(-0.858654 + 0.990939i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.142315 - 0.989821i) q^{5} +(1.10305 - 0.708888i) q^{6} +(-1.50220 - 3.28936i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(0.182270 + 1.26772i) q^{9} +(-0.415415 + 0.909632i) q^{10} +(3.02193 - 0.887318i) q^{11} +(-1.25809 + 0.369408i) q^{12} +(1.46316 - 3.20388i) q^{13} +(0.514631 + 3.57934i) q^{14} +(0.858654 + 0.990939i) q^{15} +(0.415415 + 0.909632i) q^{16} +(4.17898 - 2.68567i) q^{17} +(0.182270 - 1.26772i) q^{18} +(-0.977173 - 0.627991i) q^{19} +(0.654861 - 0.755750i) q^{20} +(4.54943 + 1.33583i) q^{21} -3.14951 q^{22} +(4.77746 - 0.419424i) q^{23} +1.31120 q^{24} +(-0.959493 - 0.281733i) q^{25} +(-2.30653 + 2.66188i) q^{26} +(-4.72189 - 3.03458i) q^{27} +(0.514631 - 3.57934i) q^{28} +(4.24421 - 2.72759i) q^{29} +(-0.544692 - 1.19271i) q^{30} +(-4.03260 - 4.65386i) q^{31} +(-0.142315 - 0.989821i) q^{32} +(-1.71551 + 3.75645i) q^{33} +(-4.76634 + 1.39952i) q^{34} +(-3.46966 + 1.01879i) q^{35} +(-0.532044 + 1.16501i) q^{36} +(0.136316 + 0.948096i) q^{37} +(0.760665 + 0.877854i) q^{38} +(1.91850 + 4.20092i) q^{39} +(-0.841254 + 0.540641i) q^{40} +(-0.313345 + 2.17936i) q^{41} +(-3.98879 - 2.56344i) q^{42} +(-5.53392 + 6.38648i) q^{43} +(3.02193 + 0.887318i) q^{44} +1.28075 q^{45} +(-4.70210 - 0.943530i) q^{46} -6.16026 q^{47} +(-1.25809 - 0.369408i) q^{48} +(-3.97926 + 4.59231i) q^{49} +(0.841254 + 0.540641i) q^{50} +(-0.926963 + 6.44717i) q^{51} +(2.96304 - 1.90423i) q^{52} +(5.13871 + 11.2522i) q^{53} +(3.67568 + 4.24197i) q^{54} +(-0.448221 - 3.11745i) q^{55} +(-1.50220 + 3.28936i) q^{56} +(1.46135 - 0.429092i) q^{57} +(-4.84074 + 1.42137i) q^{58} +(3.30335 - 7.23333i) q^{59} +(0.186603 + 1.29785i) q^{60} +(5.74850 + 6.63412i) q^{61} +(2.55810 + 5.60146i) q^{62} +(3.89617 - 2.50392i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(-2.96304 - 1.90423i) q^{65} +(2.70433 - 3.12097i) q^{66} +(-14.8839 - 4.37030i) q^{67} +4.96756 q^{68} +(-3.68656 + 5.09431i) q^{69} +3.61614 q^{70} +(-1.03568 - 0.304104i) q^{71} +(0.838715 - 0.967929i) q^{72} +(-1.97436 - 1.26884i) q^{73} +(0.136316 - 0.948096i) q^{74} +(1.10305 - 0.708888i) q^{75} +(-0.482533 - 1.05660i) q^{76} +(-7.45825 - 8.60728i) q^{77} +(-0.657248 - 4.57126i) q^{78} +(3.03627 - 6.64851i) q^{79} +(0.959493 - 0.281733i) q^{80} +(3.37493 - 0.990969i) q^{81} +(0.914650 - 2.00280i) q^{82} +(2.08646 + 14.5117i) q^{83} +(3.10501 + 3.58338i) q^{84} +(-2.06360 - 4.51865i) q^{85} +(7.10903 - 4.56870i) q^{86} +(-0.941433 + 6.54781i) q^{87} +(-2.64953 - 1.70275i) q^{88} +(-1.03857 + 1.19857i) q^{89} +(-1.22887 - 0.360830i) q^{90} -12.7367 q^{91} +(4.24581 + 2.23005i) q^{92} +8.07430 q^{93} +(5.91073 + 1.73555i) q^{94} +(-0.760665 + 0.877854i) q^{95} +(1.10305 + 0.708888i) q^{96} +(0.0192305 - 0.133751i) q^{97} +(5.11187 - 3.28520i) q^{98} +(1.67568 + 3.66922i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{2} - q^{3} - 3 q^{4} + 3 q^{5} - q^{6} + 8 q^{7} - 3 q^{8} + 12 q^{9}+O(q^{10}) $ 30 * q - 3 * q^2 - q^3 - 3 * q^4 + 3 * q^5 - q^6 + 8 * q^7 - 3 * q^8 + 12 * q^9	\( 30 q - 3 q^{2} - q^{3} - 3 q^{4} + 3 q^{5} - q^{6} + 8 q^{7} - 3 q^{8} + 12 q^{9} + 3 q^{10} - 3 q^{11} - q^{12} + 12 q^{13} - 3 q^{14} + q^{15} - 3 q^{16} - 26 q^{17} + 12 q^{18} - 25 q^{19} + 3 q^{20} - 11 q^{21} - 14 q^{22} + 14 q^{23} + 10 q^{24} - 3 q^{25} - 10 q^{26} - 52 q^{27} - 3 q^{28} + 4 q^{29} + q^{30} + 5 q^{31} - 3 q^{32} + 9 q^{33} + 7 q^{34} + 3 q^{35} + 12 q^{36} - 20 q^{37} + 19 q^{38} + 41 q^{39} + 3 q^{40} + 32 q^{41} + 22 q^{42} - 46 q^{43} - 3 q^{44} - 56 q^{45} + 3 q^{46} + 80 q^{47} - q^{48} - 41 q^{49} - 3 q^{50} - 34 q^{51} - 21 q^{52} + 29 q^{53} + 47 q^{54} + 3 q^{55} + 8 q^{56} - 33 q^{57} - 7 q^{58} - 3 q^{59} + q^{60} - q^{61} - 28 q^{62} - 8 q^{63} - 3 q^{64} + 21 q^{65} - 46 q^{66} - 63 q^{67} - 4 q^{68} + 78 q^{69} - 8 q^{70} + 55 q^{71} - 32 q^{72} - 36 q^{73} - 20 q^{74} - q^{75} - 3 q^{76} - 9 q^{77} - 80 q^{78} - 29 q^{79} + 3 q^{80} + 15 q^{81} - 23 q^{82} - 63 q^{83} + 4 q^{85} + 31 q^{86} + 63 q^{87} - 3 q^{88} - 95 q^{89} + 10 q^{90} - 12 q^{91} + 14 q^{92} + 126 q^{93} + 3 q^{94} - 19 q^{95} - q^{96} + 11 q^{97} + 58 q^{98} + 97 q^{99}+O(q^{100}) \) 30 * q - 3 * q^2 - q^3 - 3 * q^4 + 3 * q^5 - q^6 + 8 * q^7 - 3 * q^8 + 12 * q^9 + 3 * q^10 - 3 * q^11 - q^12 + 12 * q^13 - 3 * q^14 + q^15 - 3 * q^16 - 26 * q^17 + 12 * q^18 - 25 * q^19 + 3 * q^20 - 11 * q^21 - 14 * q^22 + 14 * q^23 + 10 * q^24 - 3 * q^25 - 10 * q^26 - 52 * q^27 - 3 * q^28 + 4 * q^29 + q^30 + 5 * q^31 - 3 * q^32 + 9 * q^33 + 7 * q^34 + 3 * q^35 + 12 * q^36 - 20 * q^37 + 19 * q^38 + 41 * q^39 + 3 * q^40 + 32 * q^41 + 22 * q^42 - 46 * q^43 - 3 * q^44 - 56 * q^45 + 3 * q^46 + 80 * q^47 - q^48 - 41 * q^49 - 3 * q^50 - 34 * q^51 - 21 * q^52 + 29 * q^53 + 47 * q^54 + 3 * q^55 + 8 * q^56 - 33 * q^57 - 7 * q^58 - 3 * q^59 + q^60 - q^61 - 28 * q^62 - 8 * q^63 - 3 * q^64 + 21 * q^65 - 46 * q^66 - 63 * q^67 - 4 * q^68 + 78 * q^69 - 8 * q^70 + 55 * q^71 - 32 * q^72 - 36 * q^73 - 20 * q^74 - q^75 - 3 * q^76 - 9 * q^77 - 80 * q^78 - 29 * q^79 + 3 * q^80 + 15 * q^81 - 23 * q^82 - 63 * q^83 + 4 * q^85 + 31 * q^86 + 63 * q^87 - 3 * q^88 - 95 * q^89 + 10 * q^90 - 12 * q^91 + 14 * q^92 + 126 * q^93 + 3 * q^94 - 19 * q^95 - q^96 + 11 * q^97 + 58 * q^98 + 97 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{6}{11}\right)$

Coefficient data

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

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

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

$2$	−0.959493	−	0.281733i	−0.678464	−	0.199215i
$2$	−0.959493	−	0.281733i	−0.678464	−	0.199215i
$3$	−0.858654	+	0.990939i	−0.495744	+	0.572119i	−0.947391	−	0.320078i	$-0.896291\pi$
$3$	−0.858654	+	0.990939i	−0.495744	+	0.572119i	0.451647	+	0.892196i	$0.350836\pi$
$4$	0.841254	+	0.540641i	0.420627	+	0.270320i
$5$	0.142315	−	0.989821i	0.0636451	−	0.442662i
$5$	0.142315	−	0.989821i	0.0636451	−	0.442662i
$6$	1.10305	−	0.708888i	0.450319	−	0.289402i
$7$	−1.50220	−	3.28936i	−0.567778	−	1.24326i	−0.947972	−	0.318354i	$-0.896870\pi$
$7$	−1.50220	−	3.28936i	−0.567778	−	1.24326i	0.380193	−	0.924907i	$-0.375857\pi$
$8$	−0.654861	−	0.755750i	−0.231528	−	0.267198i
$9$	0.182270	+	1.26772i	0.0607567	+	0.422572i
$10$	−0.415415	+	0.909632i	−0.131366	+	0.287651i
$11$	3.02193	−	0.887318i	0.911146	−	0.267537i	0.207623	−	0.978209i	$-0.433427\pi$
$11$	3.02193	−	0.887318i	0.911146	−	0.267537i	0.703523	+	0.710672i	$0.251609\pi$
$12$	−1.25809	+	0.369408i	−0.363179	+	0.106639i
$13$	1.46316	−	3.20388i	0.405808	−	0.888596i	−0.590840	−	0.806789i	$-0.701204\pi$
$13$	1.46316	−	3.20388i	0.405808	−	0.888596i	0.996648	−	0.0818070i	$-0.0260691\pi$
$14$	0.514631	+	3.57934i	0.137541	+	0.956618i
$15$	0.858654	+	0.990939i	0.221703	+	0.255859i
$16$	0.415415	+	0.909632i	0.103854	+	0.227408i
$17$	4.17898	−	2.68567i	1.01355	−	0.651370i	0.0752414	−	0.997165i	$-0.476027\pi$
$17$	4.17898	−	2.68567i	1.01355	−	0.651370i	0.938310	+	0.345795i	$0.112391\pi$
$18$	0.182270	−	1.26772i	0.0429615	−	0.298804i
$19$	−0.977173	−	0.627991i	−0.224179	−	0.144071i	0.423731	−	0.905788i	$-0.360720\pi$
$19$	−0.977173	−	0.627991i	−0.224179	−	0.144071i	−0.647910	+	0.761717i	$0.724357\pi$
$20$	0.654861	−	0.755750i	0.146431	−	0.168991i
$21$	4.54943	+	1.33583i	0.992766	+	0.291502i
$22$	−3.14951			−0.671477
$23$	4.77746	−	0.419424i	0.996168	−	0.0874559i
$23$	4.77746	−	0.419424i	0.996168	−	0.0874559i
$24$	1.31120			0.267648
$25$	−0.959493	−	0.281733i	−0.191899	−	0.0563465i
$26$	−2.30653	+	2.66188i	−0.452348	+	0.522037i
$27$	−4.72189	−	3.03458i	−0.908729	−	0.584005i
$28$	0.514631	−	3.57934i	0.0972561	−	0.676431i
$29$	4.24421	−	2.72759i	0.788130	−	0.506501i	−0.0835924	−	0.996500i	$-0.526639\pi$
$29$	4.24421	−	2.72759i	0.788130	−	0.506501i	0.871723	+	0.489999i	$0.163003\pi$
$30$	−0.544692	−	1.19271i	−0.0994468	−	0.217758i
$31$	−4.03260	−	4.65386i	−0.724275	−	0.835858i	0.267539	−	0.963547i	$-0.413790\pi$
$31$	−4.03260	−	4.65386i	−0.724275	−	0.835858i	−0.991814	+	0.127689i	$0.959244\pi$
$32$	−0.142315	−	0.989821i	−0.0251579	−	0.174977i
$33$	−1.71551	+	3.75645i	−0.298632	+	0.653913i
$34$	−4.76634	+	1.39952i	−0.817421	+	0.240016i
$35$	−3.46966	+	1.01879i	−0.586480	+	0.172206i
$36$	−0.532044	+	1.16501i	−0.0886740	+	0.194169i
$37$	0.136316	+	0.948096i	0.0224102	+	0.155866i	0.997954	−	0.0639400i	$-0.0203666\pi$
$37$	0.136316	+	0.948096i	0.0224102	+	0.155866i	−0.975544	+	0.219806i	$0.929458\pi$
$38$	0.760665	+	0.877854i	0.123396	+	0.142407i
$39$	1.91850	+	4.20092i	0.307206	+	0.672686i
$40$	−0.841254	+	0.540641i	−0.133014	+	0.0854828i
$41$	−0.313345	+	2.17936i	−0.0489363	+	0.340359i	0.950614	+	0.310375i	$0.100455\pi$
$41$	−0.313345	+	2.17936i	−0.0489363	+	0.340359i	−0.999550	+	0.0299839i	$0.990454\pi$
$42$	−3.98879	−	2.56344i	−0.615484	−	0.395548i
$43$	−5.53392	+	6.38648i	−0.843914	+	0.973929i	−0.999904	−	0.0138297i	$-0.995598\pi$
$43$	−5.53392	+	6.38648i	−0.843914	+	0.973929i	0.155990	+	0.987759i	$0.450143\pi$
$44$	3.02193	+	0.887318i	0.455573	+	0.133768i
$45$	1.28075			0.190923
$46$	−4.70210	−	0.943530i	−0.693287	−	0.139116i
$47$	−6.16026			−0.898567			−0.449283	−	0.893389i	$-0.648321\pi$
$47$	−6.16026			−0.898567			−0.449283	+	0.893389i	$0.648321\pi$
$48$	−1.25809	−	0.369408i	−0.181589	−	0.0533194i
$49$	−3.97926	+	4.59231i	−0.568465	+	0.656044i
$50$	0.841254	+	0.540641i	0.118971	+	0.0764582i
$51$	−0.926963	+	6.44717i	−0.129801	+	0.902785i
$52$	2.96304	−	1.90423i	0.410899	−	0.264069i
$53$	5.13871	+	11.2522i	0.705856	+	1.54561i	0.832724	+	0.553689i	$0.186780\pi$
$53$	5.13871	+	11.2522i	0.705856	+	1.54561i	−0.126868	+	0.991920i	$0.540492\pi$
$54$	3.67568	+	4.24197i	0.500197	+	0.577258i
$55$	−0.448221	−	3.11745i	−0.0604382	−	0.420357i
$56$	−1.50220	+	3.28936i	−0.200740	+	0.439559i
$57$	1.46135	−	0.429092i	0.193561	−	0.0568346i
$58$	−4.84074	+	1.42137i	−0.635621	+	0.186635i
$59$	3.30335	−	7.23333i	0.430060	−	0.941699i	−0.563258	−	0.826281i	$-0.690452\pi$
$59$	3.30335	−	7.23333i	0.430060	−	0.941699i	0.993317	−	0.115418i	$-0.0368206\pi$
$60$	0.186603	+	1.29785i	0.0240904	+	0.167552i
$61$	5.74850	+	6.63412i	0.736020	+	0.849412i	0.993136	−	0.116968i	$-0.0373176\pi$
$61$	5.74850	+	6.63412i	0.736020	+	0.849412i	−0.257116	+	0.966381i	$0.582772\pi$
$62$	2.55810	+	5.60146i	0.324879	+	0.711386i
$63$	3.89617	−	2.50392i	0.490872	−	0.315464i
$64$	−0.142315	+	0.989821i	−0.0177894	+	0.123728i
$65$	−2.96304	−	1.90423i	−0.367519	−	0.236190i
$66$	2.70433	−	3.12097i	0.332881	−	0.384165i
$67$	−14.8839	−	4.37030i	−1.81836	−	0.533918i	−0.819143	−	0.573589i	$-0.805551\pi$
$67$	−14.8839	−	4.37030i	−1.81836	−	0.533918i	−0.999213	+	0.0396714i	$0.987369\pi$
$68$	4.96756			0.602405
$69$	−3.68656	+	5.09431i	−0.443809	+	0.613283i
$70$	3.61614			0.432212
$71$	−1.03568	−	0.304104i	−0.122913	−	0.0360905i	0.219698	−	0.975568i	$-0.429493\pi$
$71$	−1.03568	−	0.304104i	−0.122913	−	0.0360905i	−0.342611	+	0.939478i	$0.611311\pi$
$72$	0.838715	−	0.967929i	0.0988435	−	0.114072i
$73$	−1.97436	−	1.26884i	−0.231081	−	0.148507i	0.419977	−	0.907535i	$-0.362038\pi$
$73$	−1.97436	−	1.26884i	−0.231081	−	0.148507i	−0.651058	+	0.759028i	$0.725674\pi$
$74$	0.136316	−	0.948096i	0.0158464	−	0.110214i
$75$	1.10305	−	0.708888i	0.127369	−	0.0818554i
$76$	−0.482533	−	1.05660i	−0.0553503	−	0.121200i
$77$	−7.45825	−	8.60728i	−0.849947	−	0.980891i
$78$	−0.657248	−	4.57126i	−0.0744187	−	0.517593i
$79$	3.03627	−	6.64851i	0.341607	−	0.748016i	−0.658382	−	0.752684i	$-0.728759\pi$
$79$	3.03627	−	6.64851i	0.341607	−	0.748016i	0.999989	+	0.00466846i	$0.00148602\pi$
$80$	0.959493	−	0.281733i	0.107275	−	0.0314987i
$81$	3.37493	−	0.990969i	0.374992	−	0.110108i
$82$	0.914650	−	2.00280i	0.101006	−	0.221173i
$83$	2.08646	+	14.5117i	0.229019	+	1.59286i	0.702253	+	0.711927i	$0.252177\pi$
$83$	2.08646	+	14.5117i	0.229019	+	1.59286i	−0.473234	+	0.880937i	$0.656914\pi$
$84$	3.10501	+	3.58338i	0.338785	+	0.390979i
$85$	−2.06360	−	4.51865i	−0.223829	−	0.490117i
$86$	7.10903	−	4.56870i	0.766587	−	0.492655i
$87$	−0.941433	+	6.54781i	−0.100932	+	0.701999i
$88$	−2.64953	−	1.70275i	−0.282441	−	0.181514i
$89$	−1.03857	+	1.19857i	−0.110088	+	0.127049i	−0.808119	−	0.589019i	$-0.799514\pi$
$89$	−1.03857	+	1.19857i	−0.110088	+	0.127049i	0.698031	+	0.716068i	$0.254060\pi$
$90$	−1.22887	−	0.360830i	−0.129535	−	0.0380348i
$91$	−12.7367			−1.33517
$92$	4.24581	+	2.23005i	0.442656	+	0.232498i
$93$	8.07430			0.837266
$94$	5.91073	+	1.73555i	0.609645	+	0.179008i
$95$	−0.760665	+	0.877854i	−0.0780426	+	0.0900659i
$96$	1.10305	+	0.708888i	0.112580	+	0.0723506i
$97$	0.0192305	−	0.133751i	0.00195257	−	0.0135804i	−0.988822	−	0.149102i	$-0.952362\pi$
$97$	0.0192305	−	0.133751i	0.00195257	−	0.0135804i	0.990774	+	0.135521i	$0.0432709\pi$
$98$	5.11187	−	3.28520i	0.516377	−	0.331855i
$99$	1.67568	+	3.66922i	0.168412	+	0.368770i
$100$	−0.654861	−	0.755750i	−0.0654861	−	0.0755750i
$101$	−1.83654	−	12.7734i	−0.182742	−	1.27100i	−0.850242	−	0.526392i	$-0.823545\pi$
$101$	−1.83654	−	12.7734i	−0.182742	−	1.27100i	0.667500	−	0.744610i	$-0.267364\pi$
$102$	2.70579	−	5.92486i	0.267913	−	0.586649i
$103$	6.46188	−	1.89738i	0.636708	−	0.186954i	0.0525813	−	0.998617i	$-0.483255\pi$
$103$	6.46188	−	1.89738i	0.636708	−	0.186954i	0.584127	+	0.811662i	$0.301437\pi$
$104$	−3.37950	+	0.992309i	−0.331387	+	0.0973040i
$105$	1.96969	−	4.31301i	0.192222	−	0.420907i
$106$	−1.76044	−	12.2441i	−0.170989	−	1.18926i
$107$	9.86869	+	11.3891i	0.954043	+	1.10102i	0.994799	+	0.101855i	$0.0324777\pi$
$107$	9.86869	+	11.3891i	0.954043	+	1.10102i	−0.0407565	+	0.999169i	$0.512977\pi$
$108$	−2.33169	−	5.10570i	−0.224367	−	0.491296i
$109$	10.6841	−	6.86628i	1.02335	−	0.657670i	0.0825389	−	0.996588i	$-0.473697\pi$
$109$	10.6841	−	6.86628i	1.02335	−	0.657670i	0.940816	+	0.338918i	$0.110061\pi$
$110$	−0.448221	+	3.11745i	−0.0427362	+	0.297237i
$111$	−1.05655	−	0.679006i	−0.100284	−	0.0644484i
$112$	2.36807	−	2.73290i	0.223762	−	0.258235i
$113$	−13.5163	−	3.96874i	−1.27151	−	0.373348i	−0.424740	−	0.905315i	$-0.639635\pi$
$113$	−13.5163	−	3.96874i	−1.27151	−	0.373348i	−0.846765	+	0.531968i	$0.821453\pi$
$114$	−1.52305			−0.142646
$115$	0.264748	−	4.78852i	0.0246879	−	0.446532i
$116$	5.04510			0.468426
$117$	4.32830	+	1.27090i	0.400152	+	0.117495i
$118$	−5.20740	+	6.00967i	−0.479380	+	0.553235i
$119$	−15.1118	−	9.71176i	−1.38530	−	0.890275i
$120$	0.186603	−	1.29785i	0.0170345	−	0.118477i
$121$	−0.909068	+	0.584223i	−0.0826426	+	0.0531112i
$122$	−3.64660	−	7.98493i	−0.330147	−	0.722922i
$123$	−1.89056	−	2.18182i	−0.170466	−	0.196728i
$124$	−0.876367	−	6.09526i	−0.0787001	−	0.547371i
$125$	−0.415415	+	0.909632i	−0.0371558	+	0.0813600i
$126$	−4.44379	+	1.30481i	−0.395884	+	0.116242i
$127$	3.22050	−	0.945625i	0.285773	−	0.0839106i	−0.135704	−	0.990749i	$-0.543330\pi$
$127$	3.22050	−	0.945625i	0.285773	−	0.0839106i	0.421478	+	0.906839i	$0.361512\pi$
$128$	0.415415	−	0.909632i	0.0367178	−	0.0804009i
$129$	−1.57690	−	10.9675i	−0.138838	−	0.965639i
$130$	2.30653	+	2.66188i	0.202296	+	0.233462i
$131$	7.04793	+	15.4328i	0.615780	+	1.34837i	0.918549	+	0.395307i	$0.129362\pi$
$131$	7.04793	+	15.4328i	0.615780	+	1.34837i	−0.302769	+	0.953064i	$0.597911\pi$
$132$	−3.47407	+	2.23265i	−0.302379	+	0.194327i
$133$	−0.597778	+	4.15764i	−0.0518340	+	0.360513i
$134$	13.0497	+	8.38655i	1.12732	+	0.724488i
$135$	−3.67568	+	4.24197i	−0.316353	+	0.365090i
$136$	−4.76634	−	1.39952i	−0.408710	−	0.120008i
$137$	14.4268			1.23257			0.616284	−	0.787524i	$-0.288637\pi$
$137$	14.4268			1.23257			0.616284	+	0.787524i	$0.288637\pi$
$138$	4.97246	−	3.84933i	0.423284	−	0.327677i
$139$	11.0105			0.933901			0.466950	−	0.884283i	$-0.345353\pi$
$139$	11.0105			0.933901			0.466950	+	0.884283i	$0.345353\pi$
$140$	−3.46966	−	1.01879i	−0.293240	−	0.0861031i
$141$	5.28953	−	6.10445i	0.445459	−	0.514087i
$142$	0.908055	+	0.583571i	0.0762023	+	0.0489722i
$143$	1.57871	−	10.9802i	0.132018	−	0.918209i
$144$	−1.07744	+	0.692428i	−0.0897865	+	0.0577023i
$145$	−2.09581	−	4.58919i	−0.174048	−	0.381111i
$146$	1.53691	+	1.77368i	0.127195	+	0.146791i
$147$	−1.13389	−	7.88640i	−0.0935220	−	0.650460i
$148$	−0.397904	+	0.871287i	−0.0327075	+	0.0716194i
$149$	−1.18838	+	0.348940i	−0.0973560	+	0.0285863i	−0.330048	−	0.943964i	$-0.607065\pi$
$149$	−1.18838	+	0.348940i	−0.0973560	+	0.0285863i	0.232692	+	0.972551i	$0.425247\pi$
$150$	−1.25809	+	0.369408i	−0.102722	+	0.0301620i
$151$	−9.44180	+	20.6747i	−0.768362	+	1.68248i	−0.0381374	+	0.999273i	$0.512142\pi$
$151$	−9.44180	+	20.6747i	−0.768362	+	1.68248i	−0.730225	+	0.683207i	$0.760585\pi$
$152$	0.165308	+	1.14974i	0.0134083	+	0.0932566i
$153$	4.16637	+	4.80825i	0.336831	+	0.388724i
$154$	4.73119	+	10.3599i	0.381250	+	0.834821i
$155$	−5.18039	+	3.32924i	−0.416099	+	0.267411i
$156$	−0.657248	+	4.57126i	−0.0526220	+	0.365994i
$157$	13.6098	+	8.74647i	1.08618	+	0.698044i	0.955977	−	0.293443i	$-0.0948011\pi$
$157$	13.6098	+	8.74647i	1.08618	+	0.698044i	0.130202	+	0.991488i	$0.458437\pi$
$158$	−4.78638	+	5.52378i	−0.380784	+	0.439448i
$159$	−15.5626	−	4.56960i	−1.23420	−	0.362393i
$160$	−1.00000			−0.0790569
$161$	−8.55633	−	15.0847i	−0.674333	−	1.18884i
$162$	−3.51741			−0.276354
$163$	11.2022	+	3.28926i	0.877424	+	0.257635i	0.689270	−	0.724505i	$-0.257931\pi$
$163$	11.2022	+	3.28926i	0.877424	+	0.257635i	0.188154	+	0.982140i	$0.439750\pi$
$164$	−1.44185	+	1.66399i	−0.112590	+	0.129936i
$165$	3.47407	+	2.23265i	0.270456	+	0.173811i
$166$	2.08646	−	14.5117i	0.161941	−	1.12632i
$167$	5.71245	−	3.67117i	0.442043	−	0.284084i	−0.300627	−	0.953742i	$-0.597196\pi$
$167$	5.71245	−	3.67117i	0.442043	−	0.284084i	0.742669	+	0.669658i	$0.233559\pi$
$168$	−1.96969	−	4.31301i	−0.151965	−	0.332756i
$169$	0.389204	+	0.449165i	0.0299387	+	0.0345511i
$170$	0.706958	+	4.91700i	0.0542212	+	0.377117i
$171$	0.618005	−	1.35324i	0.0472600	−	0.103485i
$172$	−8.10822	+	2.38079i	−0.618246	+	0.181533i
$173$	3.61801	−	1.06234i	0.275072	−	0.0807684i	−0.141287	−	0.989969i	$-0.545124\pi$
$173$	3.61801	−	1.06234i	0.275072	−	0.0807684i	0.416359	+	0.909200i	$0.363306\pi$
$174$	2.74803	−	6.01735i	0.208328	−	0.456174i
$175$	0.514631	+	3.57934i	0.0389024	+	0.270572i
$176$	2.06249	+	2.38024i	0.155466	+	0.179417i
$177$	4.33135	+	9.48434i	0.325564	+	0.712887i
$178$	1.33418	−	0.857424i	0.100001	−	0.0642666i
$179$	−1.64460	+	11.4384i	−0.122923	+	0.854949i	0.831294	+	0.555834i	$0.187601\pi$
$179$	−1.64460	+	11.4384i	−0.122923	+	0.854949i	−0.954217	+	0.299116i	$0.903308\pi$
$180$	1.07744	+	0.692428i	0.0803075	+	0.0516105i
$181$	−10.6100	+	12.2446i	−0.788638	+	0.910137i	−0.997701	−	0.0677653i	$-0.978413\pi$
$181$	−10.6100	+	12.2446i	−0.788638	+	0.910137i	0.209063	+	0.977902i	$0.432959\pi$
$182$	12.2207	+	3.58833i	0.905862	+	0.265985i
$183$	−11.5100			−0.850842
$184$	−3.44555	−	3.33590i	−0.254009	−	0.245926i
$185$	0.957846			0.0704222
$186$	−7.74723	−	2.27479i	−0.568055	−	0.166796i
$187$	10.2455	−	11.8240i	0.749228	−	0.864655i
$188$	−5.18234	−	3.33049i	−0.377961	−	0.242901i
$189$	−2.88858	+	20.0905i	−0.210114	+	1.46137i
$190$	0.977173	−	0.627991i	0.0708916	−	0.0455592i
$191$	−1.59948	−	3.50238i	−0.115735	−	0.253423i	0.842896	−	0.538076i	$-0.180849\pi$
$191$	−1.59948	−	3.50238i	−0.115735	−	0.253423i	−0.958631	+	0.284653i	$0.908122\pi$
$192$	−0.858654	−	0.990939i	−0.0619680	−	0.0715149i
$193$	−2.51576	−	17.4975i	−0.181088	−	1.25950i	−0.854195	−	0.519952i	$-0.825950\pi$
$193$	−2.51576	−	17.4975i	−0.181088	−	1.25950i	0.673107	−	0.739545i	$-0.264959\pi$
$194$	−0.0561337	+	0.122916i	−0.00403016	+	0.00882483i
$195$	4.43120	−	1.30112i	0.317325	−	0.0931749i
$196$	−5.83035	+	1.71195i	−0.416454	+	0.122282i
$197$	−11.0222	+	24.1353i	−0.785301	+	1.71957i	−0.0956641	+	0.995414i	$0.530497\pi$
$197$	−11.0222	+	24.1353i	−0.785301	+	1.71957i	−0.689637	+	0.724155i	$0.742230\pi$
$198$	−0.574061	−	3.99268i	−0.0407968	−	0.283748i
$199$	−5.66294	−	6.53538i	−0.401435	−	0.463281i	0.518657	−	0.854982i	$-0.326432\pi$
$199$	−5.66294	−	6.53538i	−0.401435	−	0.463281i	−0.920092	+	0.391702i	$0.871887\pi$
$200$	0.415415	+	0.909632i	0.0293743	+	0.0643207i
$201$	17.1108	−	10.9964i	1.20690	−	0.775630i
$202$	−1.83654	+	12.7734i	−0.129218	+	0.898734i
$203$	−15.3477	−	9.86335i	−1.07720	−	0.692272i
$204$	−4.26542	+	4.92255i	−0.298639	+	0.344648i
$205$	2.11259	+	0.620311i	0.147549	+	0.0433244i
$206$	−6.73469			−0.469228
$207$	1.40250	+	5.98002i	0.0974804	+	0.415640i
$208$	3.52217			0.244218
$209$	−3.51017	−	1.03068i	−0.242804	−	0.0712936i
$210$	−3.10501	+	3.58338i	−0.214266	+	0.247277i
$211$	−0.418335	−	0.268848i	−0.0287994	−	0.0185082i	0.526162	−	0.850384i	$-0.323631\pi$
$211$	−0.418335	−	0.268848i	−0.0287994	−	0.0185082i	−0.554961	+	0.831876i	$0.687267\pi$
$212$	−1.76044	+	12.2441i	−0.120908	+	0.840932i
$213$	1.19064	−	0.765179i	0.0815814	−	0.0524292i
$214$	−6.26027	−	13.7081i	−0.427943	−	0.937065i
$215$	5.53392	+	6.38648i	0.377410	+	0.435554i
$216$	0.798803	+	5.55579i	0.0543516	+	0.378024i
$217$	−9.25046	+	20.2557i	−0.627962	+	1.37505i
$218$	−12.1858	+	3.57808i	−0.825327	+	0.242338i
$219$	2.95263	−	0.866971i	0.199520	−	0.0585845i
$220$	1.30835	−	2.86489i	0.0882091	−	0.193151i
$221$	−2.49002	−	17.3185i	−0.167497	−	1.16497i
$222$	0.822458	+	0.949167i	0.0551998	+	0.0637039i
$223$	−1.46684	−	3.21192i	−0.0982266	−	0.215086i	0.854139	−	0.520045i	$-0.174085\pi$
$223$	−1.46684	−	3.21192i	−0.0982266	−	0.215086i	−0.952366	+	0.304958i	$0.901357\pi$
$224$	−3.04209	+	1.95503i	−0.203258	+	0.130626i
$225$	0.182270	−	1.26772i	0.0121513	−	0.0845145i
$226$	11.8507	+	7.61595i	0.788294	+	0.506606i
$227$	8.39818	−	9.69201i	0.557407	−	0.643281i	−0.405186	−	0.914234i	$-0.632793\pi$
$227$	8.39818	−	9.69201i	0.557407	−	0.643281i	0.962593	+	0.270953i	$0.0873387\pi$
$228$	1.46135	+	0.429092i	0.0967805	+	0.0284173i
$229$	−13.3800			−0.884178			−0.442089	−	0.896971i	$-0.645762\pi$
$229$	−13.3800			−0.884178			−0.442089	+	0.896971i	$0.645762\pi$
$230$	−1.60311	+	4.51996i	−0.105706	+	0.298037i
$231$	14.9333			0.982542
$232$	−4.84074	−	1.42137i	−0.317810	−	0.0933175i
$233$	−18.6144	+	21.4821i	−1.21947	+	1.40734i	−0.334043	+	0.942558i	$0.608413\pi$
$233$	−18.6144	+	21.4821i	−1.21947	+	1.40734i	−0.885424	+	0.464783i	$0.846132\pi$
$234$	−3.79492	−	2.43885i	−0.248082	−	0.159432i
$235$	−0.876697	+	6.09756i	−0.0571894	+	0.397761i
$236$	6.68959	−	4.29914i	0.435455	−	0.279850i
$237$	3.98116	+	8.71753i	0.258604	+	0.566264i
$238$	11.7635	+	13.5758i	0.762517	+	0.879991i
$239$	−2.07803	−	14.4530i	−0.134417	−	0.934889i	−0.939700	−	0.341999i	$-0.888896\pi$
$239$	−2.07803	−	14.4530i	−0.134417	−	0.934889i	0.805284	−	0.592890i	$-0.202013\pi$
$240$	−0.544692	+	1.19271i	−0.0351597	+	0.0769891i
$241$	−20.4663	+	6.00944i	−1.31835	+	0.387102i	−0.863896	−	0.503670i	$-0.831983\pi$
$241$	−20.4663	+	6.00944i	−1.31835	+	0.387102i	−0.454451	+	0.890772i	$0.650165\pi$
$242$	1.03684	−	0.304443i	0.0666505	−	0.0195704i
$243$	5.07917	−	11.1218i	0.325829	−	0.713466i
$244$	1.24927	+	8.68885i	0.0799762	+	0.556247i
$245$	3.97926	+	4.59231i	0.254225	+	0.293392i
$246$	1.19929	+	2.62608i	0.0764639	+	0.167433i
$247$	−3.44177	+	2.21189i	−0.218994	+	0.140739i
$248$	−0.876367	+	6.09526i	−0.0556493	+	0.387050i
$249$	−16.1717	−	10.3929i	−1.02484	−	0.658626i
$250$	0.654861	−	0.755750i	0.0414170	−	0.0477978i
$251$	16.4050	+	4.81694i	1.03547	+	0.304043i	0.754935	−	0.655800i	$-0.227669\pi$
$251$	16.4050	+	4.81694i	1.03547	+	0.304043i	0.280539	+	0.959843i	$0.409487\pi$
$252$	4.63139			0.291750
$253$	14.0650	−	5.50659i	0.884257	−	0.346197i
$254$	−3.35646			−0.210603
$255$	6.24963	+	1.83506i	0.391367	+	0.114916i
$256$	−0.654861	+	0.755750i	−0.0409288	+	0.0472343i
$257$	−25.1991	−	16.1945i	−1.57188	−	1.01019i	−0.978745	−	0.205082i	$-0.934254\pi$
$257$	−25.1991	−	16.1945i	−1.57188	−	1.01019i	−0.593135	−	0.805103i	$-0.702110\pi$
$258$	−1.57690	+	10.9675i	−0.0981732	+	0.682810i
$259$	2.91386	−	1.87262i	0.181058	−	0.116359i
$260$	−1.46316	−	3.20388i	−0.0907414	−	0.198696i
$261$	4.23141	+	4.88330i	0.261917	+	0.302269i
$262$	−2.41451	−	16.7933i	−0.149169	−	1.03749i
$263$	−1.02464	+	2.24364i	−0.0631819	+	0.138349i	−0.938589	−	0.345038i	$-0.887866\pi$
$263$	−1.02464	+	2.24364i	−0.0631819	+	0.138349i	0.875407	+	0.483387i	$0.160593\pi$
$264$	3.96235	−	1.16345i	0.243866	−	0.0716055i
$265$	11.8690	−	3.48505i	0.729106	−	0.214085i
$266$	1.74491	−	3.82081i	0.106987	−	0.234269i
$267$	−0.295942	−	2.05832i	−0.0181113	−	0.125967i
$268$	−10.1584	−	11.7234i	−0.620520	−	0.716119i
$269$	1.69634	+	3.71447i	0.103428	+	0.226475i	0.954270	−	0.298946i	$-0.0966350\pi$
$269$	1.69634	+	3.71447i	0.103428	+	0.226475i	−0.850842	+	0.525421i	$0.823908\pi$
$270$	4.72189	−	3.03458i	0.287365	−	0.184678i
$271$	−1.83675	+	12.7749i	−0.111575	+	0.776019i	0.854814	+	0.518934i	$0.173671\pi$
$271$	−1.83675	+	12.7749i	−0.111575	+	0.776019i	−0.966389	+	0.257085i	$0.917238\pi$
$272$	4.17898	+	2.68567i	0.253388	+	0.162842i
$273$	10.9364	−	12.6213i	0.661900	−	0.763873i
$274$	−13.8424	−	4.06451i	−0.836253	−	0.245546i
$275$	−3.14951			−0.189922
$276$	−5.85552	+	2.29250i	−0.352461	+	0.137992i
$277$	14.8828			0.894218			0.447109	−	0.894479i	$-0.352454\pi$
$277$	14.8828			0.894218			0.447109	+	0.894479i	$0.352454\pi$
$278$	−10.5645	−	3.10202i	−0.633618	−	0.186047i
$279$	5.16476	−	5.96045i	0.309206	−	0.356843i
$280$	3.04209	+	1.95503i	0.181800	+	0.116836i
$281$	2.63057	−	18.2960i	0.156926	−	1.09145i	−0.747329	−	0.664455i	$-0.768664\pi$
$281$	2.63057	−	18.2960i	0.156926	−	1.09145i	0.904255	−	0.426993i	$-0.140427\pi$
$282$	−6.79509	+	4.36694i	−0.404642	+	0.260047i
$283$	−5.34850	−	11.7116i	−0.317935	−	0.696181i	0.681427	−	0.731886i	$-0.261360\pi$
$283$	−5.34850	−	11.7116i	−0.317935	−	0.696181i	−0.999362	+	0.0357048i	$0.988632\pi$
$284$	−0.706861	−	0.815761i	−0.0419445	−	0.0484065i
$285$	−0.216752	−	1.50755i	−0.0128393	−	0.0892993i
$286$	−4.60824	+	10.0906i	−0.272491	+	0.596671i
$287$	7.63941	−	2.24313i	0.450940	−	0.132408i
$288$	1.22887	−	0.360830i	0.0724121	−	0.0212621i
$289$	3.18901	−	6.98295i	0.187589	−	0.410762i
$290$	0.717993	+	4.99375i	0.0421620	+	0.293243i
$291$	0.116027	+	0.133902i	0.00680163	+	0.00784950i
$292$	−0.974946	−	2.13483i	−0.0570544	−	0.124932i
$293$	14.1182	−	9.07324i	0.824796	−	0.530064i	−0.0588243	−	0.998268i	$-0.518735\pi$
$293$	14.1182	−	9.07324i	0.824796	−	0.530064i	0.883620	+	0.468204i	$0.155099\pi$
$294$	−1.13389	+	7.88640i	−0.0661300	+	0.459944i
$295$	−6.68959	−	4.29914i	−0.389483	−	0.250305i
$296$	0.627256	−	0.723892i	0.0364585	−	0.0420753i
$297$	−16.9619	−	4.98045i	−0.984227	−	0.288995i
$298$	1.23855			0.0717474
$299$	5.64641	−	15.9201i	0.326540	−	0.920681i
$300$	1.31120			0.0757022
$301$	29.3205	+	8.60927i	1.69000	+	0.496230i
$302$	14.8841	−	17.1771i	0.856481	−	0.988432i
$303$	14.2346	+	9.14803i	0.817758	+	0.525541i
$304$	0.165308	−	1.14974i	0.00948108	−	0.0659424i
$305$	7.38469	−	4.74585i	0.422846	−	0.271747i
$306$	−2.64296	−	5.78728i	−0.151088	−	0.330837i
$307$	−0.238380	−	0.275105i	−0.0136050	−	0.0157011i	0.748906	−	0.662676i	$-0.230579\pi$
$307$	−0.238380	−	0.275105i	−0.0136050	−	0.0157011i	−0.762511	+	0.646975i	$0.776034\pi$
$308$	−1.62083	−	11.2731i	−0.0923555	−	0.642347i
$309$	−3.66833	+	8.03253i	−0.208684	+	0.456954i
$310$	5.90850	−	1.73489i	0.335580	−	0.0985353i
$311$	6.99805	−	2.05481i	0.396823	−	0.116518i	−0.0772315	−	0.997013i	$-0.524608\pi$
$311$	6.99805	−	2.05481i	0.396823	−	0.116518i	0.474055	+	0.880495i	$0.342790\pi$
$312$	1.91850	−	4.20092i	0.108614	−	0.237831i
$313$	3.69629	+	25.7083i	0.208927	+	1.45312i	0.776668	+	0.629910i	$0.216908\pi$
$313$	3.69629	+	25.7083i	0.208927	+	1.45312i	−0.567741	+	0.823207i	$0.692182\pi$
$314$	−10.5943	−	12.2265i	−0.597872	−	0.689981i
$315$	−1.92395	−	4.21286i	−0.108402	−	0.237368i
$316$	6.14873	−	3.95155i	0.345893	−	0.222292i
$317$	1.42839	−	9.93469i	0.0802265	−	0.557988i	−0.909576	−	0.415539i	$-0.863593\pi$
$317$	1.42839	−	9.93469i	0.0802265	−	0.557988i	0.989802	−	0.142449i	$-0.0454978\pi$
$318$	13.6448	+	8.76899i	0.765163	+	0.491741i
$319$	10.4055	−	12.0085i	0.582594	−	0.672350i
$320$	0.959493	+	0.281733i	0.0536373	+	0.0157493i
$321$	−19.7597			−1.10288
$322$	3.95989	+	16.8843i	0.220676	+	0.940924i
$323$	−5.77016			−0.321060
$324$	3.37493	+	0.990969i	0.187496	+	0.0550538i
$325$	−2.30653	+	2.66188i	−0.127943	+	0.147654i
$326$	−9.82174	−	6.31205i	−0.543976	−	0.349592i
$327$	−2.36991	+	16.4831i	−0.131056	+	0.911517i
$328$	1.85225	−	1.19037i	0.102273	−	0.0657271i
$329$	9.25395	+	20.2633i	0.510187	+	1.11715i
$330$	−2.70433	−	3.12097i	−0.148869	−	0.171804i
$331$	4.01096	+	27.8968i	0.220462	+	1.53335i	0.736296	+	0.676660i	$0.236573\pi$
$331$	4.01096	+	27.8968i	0.220462	+	1.53335i	−0.515833	+	0.856689i	$0.672518\pi$
$332$	−6.09036	+	13.3360i	−0.334252	+	0.731910i
$333$	−1.17707	+	0.345620i	−0.0645031	+	0.0189398i
$334$	−6.51535	+	1.91308i	−0.356504	+	0.104679i
$335$	−6.44402	+	14.1104i	−0.352074	+	0.770935i
$336$	0.674784	+	4.69323i	0.0368125	+	0.256037i
$337$	14.7576	+	17.0312i	0.803897	+	0.927747i	0.998588	−	0.0531176i	$-0.0169158\pi$
$337$	14.7576	+	17.0312i	0.803897	+	0.927747i	−0.194691	+	0.980865i	$0.562370\pi$
$338$	−0.246894	−	0.540622i	−0.0134292	−	0.0294059i
$339$	15.5386	−	9.98604i	0.843940	−	0.542367i
$340$	0.706958	−	4.91700i	0.0383402	−	0.266662i
$341$	−16.3157	−	10.4854i	−0.883543	−	0.567819i
$342$	−0.974224	+	1.12431i	−0.0526800	+	0.0607960i
$343$	−3.20425	−	0.940854i	−0.173013	−	0.0508013i
$344$	8.45052			0.455622
$345$	4.51780	+	4.37403i	0.243230	+	0.235490i
$346$	−3.77075			−0.202717
$347$	−15.3363	−	4.50313i	−0.823293	−	0.241741i	−0.157160	−	0.987573i	$-0.550234\pi$
$347$	−15.3363	−	4.50313i	−0.823293	−	0.241741i	−0.666134	+	0.745832i	$0.732052\pi$
$348$	−4.33200	+	4.99939i	−0.232219	+	0.267995i
$349$	−17.4077	−	11.1872i	−0.931810	−	0.598838i	−0.0157489	−	0.999876i	$-0.505013\pi$
$349$	−17.4077	−	11.1872i	−0.931810	−	0.598838i	−0.916062	+	0.401038i	$0.868650\pi$
$350$	0.514631	−	3.57934i	0.0275082	−	0.191324i
$351$	−16.6313	+	10.6883i	−0.887713	+	0.570499i
$352$	−1.30835	−	2.86489i	−0.0697354	−	0.152699i
$353$	−7.02411	−	8.10625i	−0.373856	−	0.431452i	0.537379	−	0.843341i	$-0.319415\pi$
$353$	−7.02411	−	8.10625i	−0.373856	−	0.431452i	−0.911234	+	0.411889i	$0.864869\pi$
$354$	−1.48386	−	10.3204i	−0.0788660	−	0.548525i
$355$	−0.448402	+	0.981863i	−0.0237987	+	0.0521119i
$356$	−1.52170	+	0.446811i	−0.0806498	+	0.0236809i
$357$	22.5996	−	6.63583i	1.19610	−	0.351205i
$358$	4.80056	−	10.5118i	0.253718	−	0.555564i
$359$	2.16731	+	15.0740i	0.114386	+	0.795575i	0.963566	+	0.267471i	$0.0861879\pi$
$359$	2.16731	+	15.0740i	0.114386	+	0.795575i	−0.849180	+	0.528104i	$0.822903\pi$
$360$	−0.838715	−	0.967929i	−0.0442042	−	0.0510143i
$361$	−7.33239	−	16.0557i	−0.385915	−	0.845037i
$362$	13.6300	−	8.75945i	0.716375	−	0.460387i
$363$	0.201646	−	1.40248i	0.0105837	−	0.0736109i
$364$	−10.7148	−	6.88596i	−0.561606	−	0.360922i
$365$	−1.53691	+	1.77368i	−0.0804453	+	0.0928389i
$366$	11.0437	+	3.24274i	0.577266	+	0.169501i
$367$	15.5272			0.810516			0.405258	−	0.914202i	$-0.367182\pi$
$367$	15.5272			0.810516			0.405258	+	0.914202i	$0.367182\pi$
$368$	2.36615	+	4.17149i	0.123344	+	0.217454i
$369$	−2.81993			−0.146800
$370$	−0.919046	−	0.269856i	−0.0477789	−	0.0140292i
$371$	29.2932	−	33.8061i	1.52083	−	1.75513i
$372$	6.79253	+	4.36529i	0.352176	+	0.226330i
$373$	−2.94697	+	20.4966i	−0.152588	+	1.06127i	0.759272	+	0.650773i	$0.225555\pi$
$373$	−2.94697	+	20.4966i	−0.152588	+	1.06127i	−0.911860	+	0.410501i	$0.865354\pi$
$374$	−13.1617	+	8.45852i	−0.680576	+	0.437380i
$375$	−0.544692	−	1.19271i	−0.0281278	−	0.0615913i
$376$	4.03411	+	4.65562i	0.208044	+	0.240095i
$377$	−2.52889	−	17.5888i	−0.130245	−	0.905871i
$378$	8.43174	−	18.4629i	0.433682	−	0.949631i
$379$	−4.86878	+	1.42960i	−0.250093	+	0.0734338i	−0.404376	−	0.914593i	$-0.632511\pi$
$379$	−4.86878	+	1.42960i	−0.250093	+	0.0734338i	0.154283	+	0.988027i	$0.450693\pi$
$380$	−1.11452	+	0.327251i	−0.0571735	+	0.0167876i
$381$	−1.82824	+	4.00329i	−0.0936636	+	0.205095i
$382$	0.547958	+	3.81113i	0.0280360	+	0.194995i
$383$	1.16166	+	1.34063i	0.0593580	+	0.0685028i	0.784652	−	0.619936i	$-0.212842\pi$
$383$	1.16166	+	1.34063i	0.0593580	+	0.0685028i	−0.725294	+	0.688439i	$0.758296\pi$
$384$	0.544692	+	1.19271i	0.0277962	+	0.0608652i
$385$	−9.58109	+	6.15739i	−0.488298	+	0.313810i
$386$	−2.51576	+	17.4975i	−0.128049	+	0.890599i
$387$	−9.10492	−	5.85138i	−0.462829	−	0.297442i
$388$	0.0884892	−	0.102122i	0.00449236	−	0.00518446i
$389$	4.85565	+	1.42575i	0.246191	+	0.0722883i	0.402500	−	0.915420i	$-0.368141\pi$
$389$	4.85565	+	1.42575i	0.246191	+	0.0722883i	−0.156309	+	0.987708i	$0.549960\pi$
$390$	−4.61827			−0.233855
$391$	18.8385	−	14.5834i	0.952702	−	0.737515i
$392$	6.07649			0.306909
$393$	−21.3447	−	6.26737i	−1.07670	−	0.316147i
$394$	17.3754	−	20.0523i	0.875362	−	1.01022i
$395$	−6.14873	−	3.95155i	−0.309376	−	0.198824i
$396$	−0.574061	+	3.99268i	−0.0288477	+	0.200640i
$397$	−2.00398	+	1.28788i	−0.100577	+	0.0646367i	−0.589962	−	0.807431i	$-0.700857\pi$
$397$	−2.00398	+	1.28788i	−0.100577	+	0.0646367i	0.489386	+	0.872067i	$0.337221\pi$
$398$	3.59232	+	7.86608i	0.180067	+	0.394291i
$399$	−3.60668	−	4.16234i	−0.180560	−	0.208377i
$400$	−0.142315	−	0.989821i	−0.00711574	−	0.0494911i
$401$	−6.80365	+	14.8979i	−0.339758	+	0.743966i	−0.999975	−	0.00710908i	$-0.997737\pi$
$401$	−6.80365	+	14.8979i	−0.339758	+	0.743966i	0.660217	+	0.751075i	$0.270464\pi$
$402$	−19.5158	+	5.73034i	−0.973357	+	0.285804i
$403$	−20.8107	+	6.11059i	−1.03666	+	0.304390i
$404$	5.36083	−	11.7386i	0.266711	−	0.584016i
$405$	−0.500580	−	3.48161i	−0.0248740	−	0.173002i
$406$	11.9472	+	13.7878i	0.592928	+	0.684275i
$407$	1.25320	+	2.74412i	0.0621188	+	0.136021i
$408$	5.47948	−	3.52145i	0.271275	−	0.174338i
$409$	5.70500	−	39.6792i	0.282094	−	1.96201i	0.00922712	−	0.999957i	$-0.497063\pi$
$409$	5.70500	−	39.6792i	0.282094	−	1.96201i	0.272867	−	0.962052i	$-0.412028\pi$
$410$	−1.85225	−	1.19037i	−0.0914761	−	0.0587881i
$411$	−12.3877	+	14.2961i	−0.611038	+	0.705175i
$412$	6.46188	+	1.89738i	0.318354	+	0.0934772i
$413$	−28.7553			−1.41496
$414$	0.339077	−	6.13291i	0.0166647	−	0.301416i
$415$	14.6609			0.719676
$416$	−3.37950	−	0.992309i	−0.165693	−	0.0486520i
$417$	−9.45423	+	10.9108i	−0.462976	+	0.534302i
$418$	3.07761	+	1.97786i	0.150531	+	0.0967403i
$419$	−3.88956	+	27.0525i	−0.190017	+	1.32160i	0.641938	+	0.766757i	$0.278131\pi$
$419$	−3.88956	+	27.0525i	−0.190017	+	1.32160i	−0.831955	+	0.554843i	$0.812778\pi$
$420$	3.98879	−	2.56344i	0.194633	−	0.125083i
$421$	−12.4444	−	27.2494i	−0.606503	−	1.32806i	−0.924941	−	0.380112i	$-0.875885\pi$
$421$	−12.4444	−	27.2494i	−0.606503	−	1.32806i	0.318438	−	0.947944i	$-0.396842\pi$
$422$	0.325647	+	0.375816i	0.0158522	+	0.0182944i
$423$	−1.12283	−	7.80947i	−0.0545940	−	0.379710i
$424$	5.13871	−	11.2522i	0.249558	−	0.546455i
$425$	−4.76634	+	1.39952i	−0.231202	+	0.0678869i
$426$	−1.35799	+	0.398741i	−0.0657947	+	0.0193191i
$427$	13.1866	−	28.8747i	0.638145	−	1.39734i
$428$	2.14467	+	14.9165i	0.103667	+	0.721017i
$429$	9.52512	+	10.9926i	0.459877	+	0.530727i
$430$	−3.51047	−	7.68687i	−0.169290	−	0.370694i
$431$	−9.37540	+	6.02520i	−0.451597	+	0.290224i	−0.746601	−	0.665272i	$-0.768315\pi$
$431$	−9.37540	+	6.02520i	−0.451597	+	0.290224i	0.295004	+	0.955496i	$0.404679\pi$
$432$	0.798803	−	5.55579i	0.0384324	−	0.267303i
$433$	13.4226	+	8.62618i	0.645049	+	0.414548i	0.821854	−	0.569698i	$-0.192940\pi$
$433$	13.4226	+	8.62618i	0.645049	+	0.414548i	−0.176805	+	0.984246i	$0.556576\pi$
$434$	14.5824	−	16.8290i	0.699980	−	0.807820i
$435$	6.34718	+	1.86370i	0.304324	+	0.0893576i
$436$	12.7003			0.608232
$437$	−4.93179	−	2.59035i	−0.235920	−	0.123913i
$438$	−3.07728			−0.147038
$439$	18.8150	+	5.52459i	0.897993	+	0.263674i	0.697979	−	0.716119i	$-0.254083\pi$
$439$	18.8150	+	5.52459i	0.897993	+	0.263674i	0.200014	+	0.979793i	$0.435901\pi$
$440$	−2.06249	+	2.38024i	−0.0983253	+	0.113473i
$441$	−6.54705	−	4.20753i	−0.311764	−	0.200359i
$442$	−2.49002	+	17.3185i	−0.118438	+	0.823757i
$443$	−18.3580	+	11.7979i	−0.872213	+	0.560537i	−0.898429	−	0.439119i	$-0.855291\pi$
$443$	−18.3580	+	11.7979i	−0.872213	+	0.560537i	0.0262158	+	0.999656i	$0.491654\pi$
$444$	−0.521731	−	1.14243i	−0.0247603	−	0.0542174i
$445$	1.03857	+	1.19857i	0.0492329	+	0.0568178i
$446$	0.502516	+	3.49507i	0.0237948	+	0.165497i
$447$	0.674630	−	1.47723i	0.0319089	−	0.0698707i
$448$	3.46966	−	1.01879i	0.163926	−	0.0481331i
$449$	10.3781	−	3.04728i	0.489773	−	0.143810i	−0.0275158	−	0.999621i	$-0.508760\pi$
$449$	10.3781	−	3.04728i	0.489773	−	0.143810i	0.517288	+	0.855811i	$0.326941\pi$
$450$	−0.532044	+	1.16501i	−0.0250808	+	0.0549193i
$451$	0.986882	+	6.86391i	0.0464705	+	0.323209i
$452$	−9.22496	−	10.6462i	−0.433906	−	0.500754i
$453$	−12.3801	−	27.1086i	−0.581667	−	1.27367i
$454$	−10.7885	+	6.93338i	−0.506332	+	0.325400i
$455$	−1.81262	+	12.6070i	−0.0849768	+	0.591026i
$456$	−1.28127	−	0.823422i	−0.0600009	−	0.0385603i
$457$	−14.3796	+	16.5949i	−0.672648	+	0.776277i	−0.984788	−	0.173759i	$-0.944409\pi$
$457$	−14.3796	+	16.5949i	−0.672648	+	0.776277i	0.312140	+	0.950036i	$0.398954\pi$
$458$	12.8381	+	3.76959i	0.599883	+	0.176142i
$459$	−27.8826			−1.30145
$460$	2.81159	−	3.88522i	0.131091	−	0.181150i
$461$	37.0763			1.72682			0.863408	−	0.504507i	$-0.168326\pi$
$461$	37.0763			1.72682			0.863408	+	0.504507i	$0.168326\pi$
$462$	−14.3284	−	4.20721i	−0.666619	−	0.195737i
$463$	18.5796	−	21.4420i	0.863469	−	0.996496i	−0.136514	−	0.990638i	$-0.543590\pi$
$463$	18.5796	−	21.4420i	0.863469	−	0.996496i	0.999983	−	0.00585821i	$-0.00186474\pi$
$464$	4.24421	+	2.72759i	0.197033	+	0.126625i
$465$	1.14909	−	7.99211i	0.0532879	−	0.370625i
$466$	23.9126	−	15.3677i	1.10773	−	0.711894i
$467$	3.94724	+	8.64325i	0.182656	+	0.399962i	0.978705	−	0.205271i	$-0.0658074\pi$
$467$	3.94724	+	8.64325i	0.182656	+	0.399962i	−0.796049	+	0.605232i	$0.793080\pi$
$468$	2.95410	+	3.40921i	0.136553	+	0.157591i
$469$	7.98308	+	55.5235i	0.368624	+	2.56384i
$470$	2.55907	−	5.60357i	0.118041	−	0.258474i
$471$	−20.3533	+	5.97627i	−0.937831	+	0.275372i
$472$	−7.62982	+	2.24032i	−0.351191	+	0.103119i
$473$	−11.0563	+	24.2098i	−0.508367	+	1.11317i
$474$	−1.36389	−	9.48603i	−0.0626453	−	0.435708i
$475$	0.760665	+	0.877854i	0.0349017	+	0.0402787i
$476$	−7.46227	−	16.3401i	−0.342033	−	0.748947i
$477$	−13.3280	+	8.56537i	−0.610246	+	0.392181i
$478$	−2.07803	+	14.4530i	−0.0950470	+	0.661066i
$479$	4.79721	+	3.08298i	0.219190	+	0.140865i	0.645629	−	0.763652i	$-0.276595\pi$
$479$	4.79721	+	3.08298i	0.219190	+	0.140865i	−0.426438	+	0.904517i	$0.640232\pi$
$480$	0.858654	−	0.990939i	0.0391920	−	0.0452300i
$481$	3.23704	+	0.950480i	0.147596	+	0.0433381i
$482$	21.3303			0.971568
$483$	22.2950	+	4.47374i	1.01446	+	0.203562i
$484$	−1.08061			−0.0491187
$485$	−0.129653	−	0.0380696i	−0.00588725	−	0.00172865i
$486$	−8.00682	+	9.24036i	−0.363197	+	0.419151i
$487$	15.9024	+	10.2198i	0.720605	+	0.463104i	0.848847	−	0.528638i	$-0.177297\pi$
$487$	15.9024	+	10.2198i	0.720605	+	0.463104i	−0.128243	+	0.991743i	$0.540934\pi$
$488$	1.24927	−	8.68885i	0.0565517	−	0.393326i
$489$	−12.8783	+	8.27636i	−0.582375	+	0.374270i
$490$	−2.52427	−	5.52737i	−0.114035	−	0.249701i
$491$	−4.95699	−	5.72068i	−0.223706	−	0.258170i	0.632791	−	0.774323i	$-0.281909\pi$
$491$	−4.95699	−	5.72068i	−0.223706	−	0.258170i	−0.856497	+	0.516152i	$0.827364\pi$
$492$	−0.410858	−	2.85758i	−0.0185229	−	0.128830i
$493$	10.4111	−	22.7971i	0.468891	−	1.02673i
$494$	3.92551	−	1.15263i	0.176617	−	0.0518595i
$495$	3.87035	−	1.13644i	0.173959	−	0.0510790i
$496$	2.55810	−	5.60146i	0.114862	−	0.251513i
$497$	0.555496	+	3.86356i	0.0249174	+	0.173304i
$498$	12.5886	+	14.5281i	0.564110	+	0.651018i
$499$	8.73980	+	19.1375i	0.391247	+	0.856712i	0.998083	+	0.0618849i	$0.0197112\pi$
$499$	8.73980	+	19.1375i	0.391247	+	0.856712i	−0.606836	+	0.794827i	$0.707562\pi$
$500$	−0.841254	+	0.540641i	−0.0376220	+	0.0241782i
$501$	−1.26711	+	8.81296i	−0.0566104	+	0.393734i
$502$	−14.3834	−	9.24364i	−0.641962	−	0.412564i
$503$	−7.29205	+	8.41548i	−0.325137	+	0.375228i	−0.894660	−	0.446747i	$-0.852582\pi$
$503$	−7.29205	+	8.41548i	−0.325137	+	0.375228i	0.569524	+	0.821975i	$0.307128\pi$
$504$	−4.44379	−	1.30481i	−0.197942	−	0.0581210i
$505$	−12.9048			−0.574254
$506$	−15.0466	+	1.32098i	−0.668904	+	0.0587247i
$507$	−0.779286			−0.0346093
$508$	3.22050	+	0.945625i	0.142887	+	0.0419553i
$509$	−24.7525	+	28.5660i	−1.09714	+	1.26616i	−0.135816	+	0.990734i	$0.543365\pi$
$509$	−24.7525	+	28.5660i	−1.09714	+	1.26616i	−0.961321	+	0.275429i	$0.911180\pi$
$510$	−5.47948	−	3.52145i	−0.242635	−	0.155932i
$511$	−1.20780	+	8.40042i	−0.0534298	+	0.371613i
$512$	0.841254	−	0.540641i	0.0371785	−	0.0238932i
$513$	2.70842	+	5.93061i	0.119580	+	0.261843i
$514$	19.6159	+	22.6379i	0.865219	+	0.998516i
$515$	−0.958446	−	6.66614i	−0.0422342	−	0.293745i
$516$	4.60293	−	10.0790i	0.202633	−	0.443704i
$517$	−18.6159	+	5.46611i	−0.818725	+	0.240399i
$518$	−3.32340	+	0.975839i	−0.146022	+	0.0428759i
$519$	−2.05390	+	4.49741i	−0.0901561	+	0.197414i
$520$	0.501257	+	3.48632i	0.0219816	+	0.152885i
$521$	−24.4154	−	28.1769i	−1.06966	−	1.23445i	−0.970936	−	0.239339i	$-0.923069\pi$
$521$	−24.4154	−	28.1769i	−1.06966	−	1.23445i	−0.0987238	−	0.995115i	$-0.531476\pi$
$522$	−2.68422	−	5.87762i	−0.117485	−	0.257256i
$523$	−2.59594	+	1.66831i	−0.113512	+	0.0729500i	−0.596165	−	0.802862i	$-0.703310\pi$
$523$	−2.59594	+	1.66831i	−0.113512	+	0.0729500i	0.482653	+	0.875812i	$0.339673\pi$
$524$	−2.41451	+	16.7933i	−0.105478	+	0.733619i
$525$	−3.98879	−	2.56344i	−0.174085	−	0.111878i
$526$	1.61524	−	1.86409i	0.0704278	−	0.0812780i
$527$	−29.3509	−	8.61819i	−1.27854	−	0.375414i
$528$	−4.12963			−0.179719
$529$	22.6482	−	4.00756i	0.984703	−	0.174242i
$530$	−12.3701			−0.537321
$531$	9.77192	+	2.86929i	0.424065	+	0.124517i
$532$	−2.75067	+	3.17445i	−0.119257	+	0.137630i
$533$	6.52393	+	4.19268i	0.282583	+	0.181605i
$534$	−0.295942	+	2.05832i	−0.0128066	+	0.0890722i
$535$	12.6776	−	8.14741i	0.548101	−	0.352243i
$536$	6.44402	+	14.1104i	0.278339	+	0.609478i
$537$	−9.92266	−	11.4514i	−0.428194	−	0.494163i
$538$	−0.581141	−	4.04192i	−0.0250548	−	0.174260i
$539$	−7.95019	+	17.4085i	−0.342439	+	0.749837i
$540$	−5.38556	+	1.58134i	−0.231758	+	0.0680502i
$541$	−24.0892	+	7.07324i	−1.03568	+	0.304102i	−0.755017	−	0.655705i	$-0.772372\pi$
$541$	−24.0892	+	7.07324i	−1.03568	+	0.304102i	−0.280660	+	0.959807i	$0.590553\pi$
$542$	5.36145	−	11.7399i	0.230294	−	0.504273i
$543$	−3.02334	−	21.0278i	−0.129744	−	0.902390i
$544$	−3.25306	−	3.75423i	−0.139474	−	0.160961i
$545$	−5.27588	−	11.5526i	−0.225994	−	0.494857i
$546$	−14.0492	+	9.02888i	−0.601250	+	0.386400i
$547$	3.97619	−	27.6550i	0.170010	−	1.18244i	−0.708849	−	0.705361i	$-0.750785\pi$
$547$	3.97619	−	27.6550i	0.170010	−	1.18244i	0.878858	−	0.477083i	$-0.158306\pi$
$548$	12.1366	+	7.79973i	0.518451	+	0.333188i
$549$	−7.36241	+	8.49668i	−0.314220	+	0.362629i
$550$	3.02193	+	0.887318i	0.128855	+	0.0378354i
$551$	−5.86023			−0.249654
$552$	6.26420	−	0.549949i	0.266622	−	0.0234074i
$553$	−26.4304			−1.12394
$554$	−14.2799	−	4.19296i	−0.606695	−	0.178142i
$555$	−0.822458	+	0.949167i	−0.0349114	+	0.0402899i
$556$	9.26265	+	5.95274i	0.392824	+	0.252452i
$557$	−0.995735	+	6.92549i	−0.0421906	+	0.293442i	0.957791	+	0.287464i	$0.0928121\pi$
$557$	−0.995735	+	6.92549i	−0.0421906	+	0.293442i	−0.999982	+	0.00597853i	$0.998097\pi$
$558$	−6.63481	+	4.26393i	−0.280874	+	0.180507i
$559$	12.3645	+	27.0744i	0.522962	+	1.14513i
$560$	−2.36807	−	2.73290i	−0.100069	−	0.115486i
$561$	2.91948	+	20.3054i	0.123260	+	0.857295i
$562$	−7.67858	+	16.8138i	−0.323902	+	0.709245i
$563$	19.6124	−	5.75872i	0.826564	−	0.242701i	0.159024	−	0.987275i	$-0.449165\pi$
$563$	19.6124	−	5.75872i	0.826564	−	0.242701i	0.667540	+	0.744574i	$0.267347\pi$
$564$	7.75015	−	2.27565i	0.326340	−	0.0958221i
$565$	−5.85191	+	12.8139i	−0.246192	+	0.539085i
$566$	1.83231	+	12.7440i	0.0770179	+	0.535671i
$567$	−8.32947	−	9.61272i	−0.349805	−	0.403696i
$568$	0.448402	+	0.981863i	0.0188145	+	0.0411981i
$569$	−5.01918	+	3.22563i	−0.210415	+	0.135226i	−0.641604	−	0.767036i	$-0.721731\pi$
$569$	−5.01918	+	3.22563i	−0.210415	+	0.135226i	0.431189	+	0.902262i	$0.358094\pi$
$570$	−0.216752	+	1.50755i	−0.00907875	+	0.0631441i
$571$	−5.67133	−	3.64475i	−0.237338	−	0.152528i	0.416566	−	0.909106i	$-0.363234\pi$
$571$	−5.67133	−	3.64475i	−0.237338	−	0.152528i	−0.653904	+	0.756578i	$0.726870\pi$
$572$	7.26443	−	8.38360i	0.303741	−	0.350536i
$573$	4.84405	+	1.42234i	0.202363	+	0.0594191i
$574$	−7.96193			−0.332324
$575$	−4.70210	−	0.943530i	−0.196091	−	0.0393479i
$576$	−1.28075			−0.0533647
$577$	−34.8112	−	10.2215i	−1.44921	−	0.425527i	−0.539930	−	0.841710i	$-0.681549\pi$
$577$	−34.8112	−	10.2215i	−1.44921	−	0.425527i	−0.909281	+	0.416183i	$0.863368\pi$
$578$	−5.02715	+	5.80164i	−0.209102	+	0.241317i
$579$	19.4991	+	12.5313i	0.810356	+	0.520784i
$580$	0.717993	−	4.99375i	0.0298130	−	0.207354i
$581$	44.5998	−	28.6626i	1.85031	−	1.18912i
$582$	−0.0736025	−	0.161167i	−0.00305092	−	0.00668059i
$583$	25.5131	+	29.4437i	1.05664	+	1.21943i
$584$	0.334002	+	2.32303i	0.0138211	+	0.0961278i
$585$	1.87395	−	4.10338i	0.0774783	−	0.169654i
$586$	−16.1026	+	4.72814i	−0.665191	+	0.195318i
$587$	25.9454	−	7.61825i	1.07088	−	0.314439i	0.301655	−	0.953417i	$-0.402461\pi$
$587$	25.9454	−	7.61825i	1.07088	−	0.314439i	0.769225	+	0.638978i	$0.220643\pi$
$588$	3.30982	−	7.24749i	0.136495	−	0.298882i
$589$	1.01796	+	7.08006i	0.0419443	+	0.291729i
$590$	5.20740	+	6.00967i	0.214385	+	0.247414i
$591$	−14.4523	−	31.6462i	−0.594490	−	1.30175i
$592$	−0.805791	+	0.517851i	−0.0331178	+	0.0212835i
$593$	3.17490	−	22.0819i	0.130377	−	0.906795i	−0.814685	−	0.579904i	$-0.803090\pi$
$593$	3.17490	−	22.0819i	0.130377	−	0.906795i	0.945062	−	0.326891i	$-0.106001\pi$
$594$	14.8716	+	9.55742i	0.610190	+	0.392146i
$595$	−11.7635	+	13.5758i	−0.482258	+	0.556555i
$596$	−1.18838	−	0.348940i	−0.0486780	−	0.0142932i
$597$	11.3387			0.464060
$598$	−9.90289	+	13.6844i	−0.404959	+	0.559597i
$599$	23.9530			0.978693			0.489347	−	0.872089i	$-0.337235\pi$
$599$	23.9530			0.978693			0.489347	+	0.872089i	$0.337235\pi$
$600$	−1.25809	−	0.369408i	−0.0513612	−	0.0150810i
$601$	−0.594726	+	0.686351i	−0.0242594	+	0.0279968i	−0.767750	−	0.640750i	$-0.778624\pi$
$601$	−0.594726	+	0.686351i	−0.0242594	+	0.0279968i	0.743490	+	0.668747i	$0.233169\pi$
$602$	−25.7073	−	16.5211i	−1.04775	−	0.673348i
$603$	2.82742	−	19.6651i	0.115141	−	0.800826i
$604$	−19.1205	+	12.2880i	−0.778002	+	0.499992i
$605$	0.448902	+	0.982959i	0.0182505	+	0.0399630i
$606$	−11.0807	−	12.7878i	−0.450123	−	0.519470i
$607$	−4.43109	−	30.8189i	−0.179852	−	1.25090i	−0.857102	−	0.515147i	$-0.827737\pi$
$607$	−4.43109	−	30.8189i	−0.179852	−	1.25090i	0.677250	−	0.735753i	$-0.263172\pi$
$608$	−0.482533	+	1.05660i	−0.0195693	+	0.0428507i
$609$	22.9523	−	6.73941i	0.930075	−	0.273095i
$610$	−8.42262	+	2.47311i	−0.341022	+	0.100133i
$611$	−9.01346	+	19.7367i	−0.364646	+	0.798462i
$612$	0.905439	+	6.29747i	0.0366002	+	0.254560i
$613$	10.5371	+	12.1605i	0.425591	+	0.491158i	0.927532	−	0.373744i	$-0.121926\pi$
$613$	10.5371	+	12.1605i	0.425591	+	0.491158i	−0.501941	+	0.864902i	$0.667381\pi$
$614$	0.151218	+	0.331120i	0.00610265	+	0.0133629i
$615$	−2.42867	+	1.56081i	−0.0979334	+	0.0629380i
$616$	−1.62083	+	11.2731i	−0.0653052	+	0.454208i
$617$	18.7979	+	12.0807i	0.756775	+	0.486350i	0.861252	−	0.508178i	$-0.169681\pi$
$617$	18.7979	+	12.0807i	0.756775	+	0.486350i	−0.104477	+	0.994527i	$0.533317\pi$
$618$	5.78276	−	6.67366i	0.232617	−	0.268454i
$619$	12.6656	+	3.71895i	0.509072	+	0.149477i	0.526174	−	0.850377i	$-0.323626\pi$
$619$	12.6656	+	3.71895i	0.509072	+	0.149477i	−0.0171022	+	0.999854i	$0.505444\pi$
$620$	−6.15794			−0.247309
$621$	−23.8314	−	12.5171i	−0.956322	−	0.502293i
$622$	−7.29349			−0.292442
$623$	5.50268	+	1.61573i	0.220460	+	0.0647329i
$624$	−3.02432	+	3.49025i	−0.121070	+	0.139722i
$625$	0.841254	+	0.540641i	0.0336501	+	0.0216256i
$626$	3.69629	−	25.7083i	0.147734	−	1.02751i
$627$	4.03537	−	2.59337i	0.161157	−	0.103569i
$628$	6.72057	+	14.7160i	0.268180	+	0.587232i
$629$	3.11593	+	3.59598i	0.124240	+	0.143381i
$630$	0.659115	+	4.58425i	0.0262598	+	0.182641i
$631$	−11.5882	+	25.3747i	−0.461321	+	1.01015i	0.525864	+	0.850569i	$0.323742\pi$
$631$	−11.5882	+	25.3747i	−0.461321	+	1.01015i	−0.987185	+	0.159583i	$0.948985\pi$
$632$	−7.01294	+	2.05919i	−0.278960	+	0.0819100i
$633$	0.625617	−	0.183698i	0.0248660	−	0.00730133i
$634$	−4.16946	+	9.12984i	−0.165590	+	0.362592i
$635$	−0.477675	−	3.32230i	−0.0189559	−	0.131841i
$636$	−10.6216	−	12.2580i	−0.421174	−	0.486060i
$637$	8.89089	+	19.4683i	0.352270	+	0.771364i
$638$	−13.3672	+	8.59056i	−0.529211	+	0.340103i
$639$	0.196744	−	1.36838i	0.00778306	−	0.0541324i
$640$	−0.841254	−	0.540641i	−0.0332535	−	0.0213707i
$641$	10.4317	−	12.0389i	0.412029	−	0.475506i	−0.511363	−	0.859365i	$-0.670859\pi$
$641$	10.4317	−	12.0389i	0.412029	−	0.475506i	0.923392	+	0.383858i	$0.125405\pi$
$642$	18.9593	+	5.56694i	0.748263	+	0.219710i
$643$	−21.7301			−0.856952			−0.428476	−	0.903553i	$-0.640949\pi$
$643$	−21.7301			−0.856952			−0.428476	+	0.903553i	$0.640949\pi$
$644$	0.957367	−	17.3160i	0.0377255	−	0.682345i
$645$	−11.0803			−0.436287
$646$	5.53643	+	1.62564i	0.217828	+	0.0639600i
$647$	12.9844	−	14.9848i	0.510468	−	0.589112i	−0.440750	−	0.897630i	$-0.645288\pi$
$647$	12.9844	−	14.9848i	0.510468	−	0.589112i	0.951219	+	0.308518i	$0.0998330\pi$
$648$	−2.95903	−	1.90166i	−0.116242	−	0.0747041i
$649$	3.56422	−	24.7897i	0.139908	−	0.973082i
$650$	2.96304	−	1.90423i	0.116220	−	0.0746900i
$651$	−12.1292	−	26.5593i	−0.475381	−	1.04094i
$652$	7.64558	+	8.82347i	0.299424	+	0.345554i
$653$	−0.994634	−	6.91783i	−0.0389230	−	0.270716i	0.961061	−	0.276336i	$-0.0891202\pi$
$653$	−0.994634	−	6.91783i	−0.0389230	−	0.270716i	−0.999984	+	0.00562002i	$0.998211\pi$
$654$	6.91773	−	15.1477i	0.270505	−	0.592323i
$655$	16.2787	−	4.77987i	0.636063	−	0.186765i
$656$	−2.11259	+	0.620311i	−0.0824826	+	0.0242191i
$657$	1.24867	−	2.73420i	0.0487151	−	0.106671i
$658$	−3.17026	−	22.0497i	−0.123590	−	0.859585i
$659$	−10.9577	−	12.6459i	−0.426852	−	0.492613i	0.501060	−	0.865412i	$-0.332943\pi$
$659$	−10.9577	−	12.6459i	−0.426852	−	0.492613i	−0.927912	+	0.372799i	$0.878398\pi$
$660$	1.71551	+	3.75645i	0.0667762	+	0.146219i
$661$	1.58924	−	1.02134i	0.0618141	−	0.0397255i	−0.509369	−	0.860548i	$-0.670121\pi$
$661$	1.58924	−	1.02134i	0.0618141	−	0.0397255i	0.571183	+	0.820823i	$0.306485\pi$
$662$	4.01096	−	27.8968i	0.155890	−	1.08424i
$663$	19.2996	+	12.4031i	0.749536	+	0.481698i
$664$	9.60085	−	11.0800i	0.372585	−	0.429986i
$665$	4.03025	+	1.18339i	0.156286	+	0.0458898i
$666$	1.22676			0.0475362
$667$	19.1325	−	14.8111i	0.740814	−	0.573487i
$668$	6.79041			0.262729
$669$	4.44233	+	1.30438i	0.171750	+	0.0504304i
$670$	10.1584	−	11.7234i	0.392452	−	0.452913i
$671$	23.2581	+	14.9471i	0.897870	+	0.577026i
$672$	0.674784	−	4.69323i	0.0260304	−	0.181045i
$673$	29.1568	−	18.7379i	1.12391	−	0.722294i	0.159630	−	0.987177i	$-0.448970\pi$
$673$	29.1568	−	18.7379i	1.12391	−	0.722294i	0.964281	+	0.264883i	$0.0853334\pi$
$674$	−9.36157	−	20.4990i	−0.360594	−	0.789591i
$675$	3.67568	+	4.24197i	0.141477	+	0.163273i
$676$	0.0845820	+	0.588281i	0.00325315	+	0.0226262i
$677$	10.2409	−	22.4244i	0.393589	−	0.861840i	−0.604291	−	0.796764i	$-0.706544\pi$
$677$	10.2409	−	22.4244i	0.393589	−	0.861840i	0.997880	−	0.0650766i	$-0.0207292\pi$
$678$	−17.7226	+	5.20381i	−0.680631	+	0.199851i
$679$	−0.468844	+	0.137665i	−0.0179926	+	0.00528310i
$680$	−2.06360	+	4.51865i	−0.0791354	+	0.173282i
$681$	2.39307	+	16.6442i	0.0917026	+	0.637806i
$682$	12.7007	+	14.6574i	0.486334	+	0.561260i
$683$	7.42772	+	16.2644i	0.284214	+	0.622342i	0.996860	−	0.0791819i	$-0.0252308\pi$
$683$	7.42772	+	16.2644i	0.284214	+	0.622342i	−0.712646	+	0.701524i	$0.752504\pi$
$684$	1.25152	−	0.804301i	0.0478530	−	0.0307532i
$685$	2.05315	−	14.2800i	0.0784469	−	0.545610i
$686$	2.80939	+	1.80549i	0.107263	+	0.0689338i
$687$	11.4888	−	13.2588i	0.438326	−	0.505855i
$688$	−8.10822	−	2.38079i	−0.309123	−	0.0907667i
$689$	43.5694			1.65986
$690$	−3.10249	−	5.46966i	−0.118110	−	0.208226i
$691$	−17.8803			−0.680197			−0.340099	−	0.940390i	$-0.610460\pi$
$691$	−17.8803			−0.680197			−0.340099	+	0.940390i	$0.610460\pi$
$692$	3.61801	+	1.06234i	0.137536	+	0.0403842i
$693$	9.55218	−	11.0238i	0.362857	−	0.418760i
$694$	13.4464	+	8.64145i	0.510417	+	0.328025i
$695$	1.56696	−	10.8985i	0.0594382	−	0.413402i
$696$	5.56501	−	3.57642i	0.210941	−	0.135564i
$697$	4.54358	+	9.94905i	0.172100	+	0.376847i
$698$	13.5507	+	15.6384i	0.512902	+	0.591921i
$699$	−5.30418	−	36.8914i	−0.200623	−	1.39536i
$700$	−1.50220	+	3.28936i	−0.0567778	+	0.124326i
$701$	39.7579	−	11.6740i	1.50164	−	0.440920i	0.575403	−	0.817870i	$-0.304845\pi$
$701$	39.7579	−	11.6740i	1.50164	−	0.440920i	0.926234	+	0.376950i	$0.123027\pi$
$702$	18.9689	−	5.56976i	0.715933	−	0.210217i
$703$	0.462192	−	1.01206i	0.0174319	−	0.0381705i
$704$	0.448221	+	3.11745i	0.0168930	+	0.117493i
$705$	−5.28953	−	6.10445i	−0.199215	−	0.229907i
$706$	4.45579	+	9.75681i	0.167696	+	0.367203i
$707$	−39.2575	+	25.2293i	−1.47643	+	0.948844i
$708$	−1.48386	+	10.3204i	−0.0557667	+	0.387866i
$709$	32.2759	+	20.7424i	1.21215	+	0.778998i	0.981016	−	0.193925i	$-0.0621218\pi$
$709$	32.2759	+	20.7424i	1.21215	+	0.778998i	0.231129	+	0.972923i	$0.425758\pi$
$710$	0.706861	−	0.815761i	0.0265280	−	0.0306150i
$711$	8.98185	+	2.63731i	0.336846	+	0.0989068i
$712$	1.58594			0.0594356
$713$	−21.2175	−	20.5423i	−0.794601	−	0.769314i
$714$	−23.5536			−0.881473
$715$	−10.6437	−	3.12528i	−0.398053	−	0.116879i
$716$	−7.56761	+	8.73349i	−0.282815	+	0.326386i
$717$	16.1064	+	10.3509i	0.601504	+	0.386563i
$718$	2.16731	−	15.0740i	0.0808834	−	0.562557i
$719$	−1.97642	+	1.27017i	−0.0737079	+	0.0473692i	−0.576976	−	0.816761i	$-0.695767\pi$
$719$	−1.97642	+	1.27017i	−0.0737079	+	0.0473692i	0.503268	+	0.864130i	$0.332131\pi$
$720$	0.532044	+	1.16501i	0.0198281	+	0.0434175i
$721$	−15.9482	−	18.4052i	−0.593942	−	0.685446i
$722$	2.51197	+	17.4711i	0.0934857	+	0.650207i
$723$	11.6184	−	25.4408i	0.432095	−	0.946155i
$724$	−15.5457	+	4.56462i	−0.577751	+	0.169643i
$725$	−4.84074	+	1.42137i	−0.179781	+	0.0527884i
$726$	−0.588601	+	1.28886i	−0.0218450	+	0.0478339i
$727$	−7.07603	−	49.2149i	−0.262435	−	1.82528i	−0.514409	−	0.857545i	$-0.671989\pi$
$727$	−7.07603	−	49.2149i	−0.262435	−	1.82528i	0.251974	−	0.967734i	$-0.418920\pi$
$728$	8.34074	+	9.62573i	0.309128	+	0.356753i
$729$	11.0434	+	24.1816i	0.409014	+	0.895615i
$730$	1.97436	−	1.26884i	0.0730742	−	0.0469619i
$731$	−5.97416	+	41.5512i	−0.220962	+	1.53683i
$732$	−9.68281	−	6.22277i	−0.357887	−	0.230000i
$733$	27.3902	−	31.6100i	1.01168	−	1.16754i	0.0258722	−	0.999665i	$-0.491764\pi$
$733$	27.3902	−	31.6100i	1.01168	−	1.16754i	0.985808	−	0.167876i	$-0.0536908\pi$
$734$	−14.8983	−	4.37453i	−0.549906	−	0.161467i
$735$	−7.96750			−0.293886
$736$	−1.09506	−	4.66914i	−0.0403644	−	0.172107i
$737$	−48.8559			−1.79963
$738$	2.70570	+	0.794466i	0.0995983	+	0.0292447i
$739$	3.47080	−	4.00551i	0.127675	−	0.147345i	−0.688312	−	0.725414i	$-0.741648\pi$
$739$	3.47080	−	4.00551i	0.127675	−	0.147345i	0.815988	+	0.578069i	$0.196194\pi$
$740$	0.805791	+	0.517851i	0.0296215	+	0.0190366i
$741$	0.763438	−	5.30983i	0.0280456	−	0.195061i
$742$	−37.6309	+	24.1839i	−1.38147	+	0.887819i
$743$	20.4492	+	44.7775i	0.750209	+	1.64273i	0.765990	+	0.642853i	$0.222249\pi$
$743$	20.4492	+	44.7775i	0.750209	+	1.64273i	−0.0157806	+	0.999875i	$0.505023\pi$
$744$	−5.28754	−	6.10215i	−0.193851	−	0.223716i
$745$	0.176264	+	1.22595i	0.00645782	+	0.0449152i
$746$	8.60215	−	18.8361i	0.314947	−	0.689638i
$747$	−18.0164	+	5.29009i	−0.659186	+	0.193554i
$748$	15.0116	−	4.40781i	0.548879	−	0.161165i
$749$	22.6380	−	49.5704i	0.827176	−	1.81126i
$750$	0.186603	+	1.29785i	0.00681379	+	0.0473909i
$751$	−26.2315	−	30.2728i	−0.957201	−	1.10467i	−0.994434	−	0.105363i	$-0.966400\pi$
$751$	−26.2315	−	30.2728i	−0.957201	−	1.10467i	0.0372324	−	0.999307i	$-0.488146\pi$
$752$	−2.55907	−	5.60357i	−0.0933195	−	0.204341i
$753$	−18.8595	+	12.1203i	−0.687278	+	0.441687i
$754$	−2.52889	+	17.5888i	−0.0920968	+	0.640548i
$755$	19.1205	+	12.2880i	0.695866	+	0.447206i
$756$	−13.2918	+	15.3396i	−0.483418	+	0.557894i
$757$	−39.3627	−	11.5579i	−1.43066	−	0.420080i	−0.527563	−	0.849516i	$-0.676894\pi$
$757$	−39.3627	−	11.5579i	−1.43066	−	0.420080i	−0.903097	+	0.429436i	$0.858712\pi$
$758$	5.07433			0.184308
$759$	−6.62024	+	18.6658i	−0.240299	+	0.677525i
$760$	1.16157			0.0421345
$761$	44.4783	+	13.0600i	1.61234	+	0.473425i	0.958944	−	0.283595i	$-0.0915272\pi$
$761$	44.4783	+	13.0600i	1.61234	+	0.473425i	0.653392	+	0.757020i	$0.273345\pi$
$762$	2.88204	−	3.32605i	0.104405	−	0.120490i
$763$	−38.6354	−	24.8295i	−1.39869	−	0.898887i
$764$	0.547958	−	3.81113i	0.0198244	−	0.137882i
$765$	5.35224	−	3.43968i	0.193511	−	0.124362i
$766$	−0.736906	−	1.61360i	−0.0266255	−	0.0583017i
$767$	−18.3414	−	21.1671i	−0.662268	−	0.764298i
$768$	−0.186603	−	1.29785i	−0.00673347	−	0.0468323i
$769$	−7.89684	+	17.2917i	−0.284767	+	0.623553i	−0.996916	−	0.0784753i	$-0.974995\pi$
$769$	−7.89684	+	17.2917i	−0.284767	+	0.623553i	0.712149	+	0.702028i	$0.247722\pi$
$770$	10.9277	−	3.20867i	0.393808	−	0.115632i
$771$	37.6851	−	11.0653i	1.35720	−	0.398509i
$772$	7.34347	−	16.0800i	0.264297	−	0.578730i
$773$	3.40228	+	23.6633i	0.122371	+	0.851111i	0.954857	+	0.297065i	$0.0960078\pi$
$773$	3.40228	+	23.6633i	0.122371	+	0.851111i	−0.832486	+	0.554046i	$0.813083\pi$
$774$	7.08758	+	8.17951i	0.254758	+	0.294006i
$775$	2.55810	+	5.60146i	0.0918897	+	0.201210i
$776$	−0.113676	+	0.0730550i	−0.00408073	+	0.00262252i
$777$	−0.646339	+	4.49539i	−0.0231873	+	0.161271i
$778$	−4.25728	−	2.73599i	−0.152631	−	0.0980900i
$779$	1.67481	−	1.93284i	0.0600064	−	0.0692510i
$780$	4.43120	+	1.30112i	0.158662	+	0.0465874i
$781$	−3.39960			−0.121647
$782$	−22.1840	+	8.68528i	−0.793298	+	0.310585i
$783$	−28.3178			−1.01200
$784$	−5.83035	−	1.71195i	−0.208227	−	0.0611409i
$785$	10.5943	−	12.2265i	0.378127	−	0.436382i
$786$	18.7144	+	12.0270i	0.667519	+	0.428989i
$787$	−3.98466	+	27.7139i	−0.142038	+	0.987895i	0.786747	+	0.617276i	$0.211764\pi$
$787$	−3.98466	+	27.7139i	−0.142038	+	0.987895i	−0.928785	+	0.370620i	$0.879145\pi$
$788$	−22.3210	+	14.3448i	−0.795153	+	0.511014i
$789$	−1.34351	−	2.94187i	−0.0478301	−	0.104733i
$790$	4.78638	+	5.52378i	0.170292	+	0.196527i
$791$	7.24956	+	50.4218i	0.257765	+	1.79279i
$792$	1.67568	−	3.66922i	0.0595426	−	0.130380i
$793$	29.6659	−	8.71069i	1.05347	−	0.309326i
$794$	2.28564	−	0.671124i	0.0811143	−	0.0238173i
$795$	−6.73788	+	14.7539i	−0.238968	+	0.523267i
$796$	−1.23067	−	8.55952i	−0.0436201	−	0.303384i
$797$	1.63051	+	1.88171i	0.0577557	+	0.0666537i	0.783892	−	0.620897i	$-0.213231\pi$
$797$	1.63051	+	1.88171i	0.0577557	+	0.0666537i	−0.726137	+	0.687551i	$0.758686\pi$
$798$	2.28792	+	5.00985i	0.0809916	+	0.177347i
$799$	−25.7436	+	16.5444i	−0.910743	+	0.585299i
$800$	−0.142315	+	0.989821i	−0.00503159	+	0.0349955i
$801$	−1.70875	−	1.09815i	−0.0603758	−	0.0388012i
$802$	10.7253	−	12.3776i	0.378723	−	0.437069i
$803$	−7.09223	−	2.08247i	−0.250279	−	0.0734886i
$804$	20.3397			0.717324
$805$	−16.1489	+	6.32246i	−0.569173	+	0.222838i
$806$	21.6893			0.763973
$807$	−5.13739	−	1.50847i	−0.180845	−	0.0531007i
$808$	−8.45082	+	9.75277i	−0.297299	+	0.343101i
$809$	−27.4102	−	17.6155i	−0.963692	−	0.619327i	−0.0386745	−	0.999252i	$-0.512314\pi$
$809$	−27.4102	−	17.6155i	−0.963692	−	0.619327i	−0.925017	+	0.379925i	$0.875950\pi$
$810$	−0.500580	+	3.48161i	−0.0175886	+	0.122331i
$811$	16.1601	−	10.3855i	0.567459	−	0.364684i	−0.225234	−	0.974305i	$-0.572315\pi$
$811$	16.1601	−	10.3855i	0.567459	−	0.364684i	0.792693	+	0.609621i	$0.208678\pi$
$812$	−7.57876	−	16.5952i	−0.265962	−	0.582376i
$813$	−11.0820	−	12.7893i	−0.388663	−	0.448541i
$814$	−0.429327	−	2.98604i	−0.0150479	−	0.104660i
$815$	4.85002	−	10.6201i	0.169889	−	0.372005i
$816$	−6.24963	+	1.83506i	−0.218781	+	0.0642398i
$817$	9.41824	−	2.76545i	0.329503	−	0.0967507i
$818$	−16.6528	+	36.4646i	−0.582252	+	1.27496i
$819$	−2.32152	−	16.1465i	−0.0811203	−	0.564204i
$820$	1.44185	+	1.66399i	0.0503518	+	0.0581090i
$821$	−14.3019	−	31.3169i	−0.499141	−	1.09297i	−0.976748	−	0.214393i	$-0.931223\pi$
$821$	−14.3019	−	31.3169i	−0.499141	−	1.09297i	0.477606	−	0.878574i	$-0.341505\pi$
$822$	15.9135	−	10.2270i	0.555049	−	0.356708i
$823$	8.04128	−	55.9283i	0.280301	−	1.94954i	−0.0318132	−	0.999494i	$-0.510128\pi$
$823$	8.04128	−	55.9283i	0.280301	−	1.94954i	0.312114	−	0.950044i	$-0.398963\pi$
$824$	−5.66558	−	3.64105i	−0.197370	−	0.126842i
$825$	2.70433	−	3.12097i	0.0941529	−	0.108658i
$826$	27.5905	+	8.10131i	0.959997	+	0.281881i
$827$	33.4116			1.16184			0.580918	−	0.813962i	$-0.302694\pi$
$827$	33.4116			1.16184			0.580918	+	0.813962i	$0.302694\pi$
$828$	−2.05318	+	5.78896i	−0.0713530	+	0.201180i
$829$	−45.4187			−1.57746			−0.788728	−	0.614742i	$-0.789260\pi$
$829$	−45.4187			−1.57746			−0.788728	+	0.614742i	$0.789260\pi$
$830$	−14.0670	−	4.13045i	−0.488274	−	0.143370i
$831$	−12.7791	+	14.7479i	−0.443303	+	0.511599i
$832$	2.96304	+	1.90423i	0.102725	+	0.0660172i
$833$	−4.29583	+	29.8781i	−0.148842	+	1.03522i
$834$	12.1452	−	7.80524i	0.420553	−	0.270273i
$835$	−2.82084	−	6.17677i	−0.0976191	−	0.213756i
$836$	−2.39572	−	2.76481i	−0.0828577	−	0.0956228i
$837$	4.91898	+	34.2123i	0.170025	+	1.18255i
$838$	11.3536	−	24.8608i	0.392202	−	0.858803i
$839$	−20.2022	+	5.93190i	−0.697457	+	0.204792i	−0.611194	−	0.791481i	$-0.709311\pi$
$839$	−20.2022	+	5.93190i	−0.697457	+	0.204792i	−0.0862625	+	0.996272i	$0.527492\pi$
$840$	−4.54943	+	1.33583i	−0.156970	+	0.0460906i
$841$	−1.47345	+	3.22640i	−0.0508085	+	0.111255i
$842$	4.26326	+	29.6516i	0.146922	+	1.02186i
$843$	15.8715	+	18.3166i	0.546642	+	0.630859i
$844$	−0.206576	−	0.452338i	−0.00711064	−	0.0155701i
$845$	0.499982	−	0.321319i	0.0171999	−	0.0110537i
$846$	−1.12283	+	7.80947i	−0.0386038	+	0.268495i
$847$	3.28732	+	2.11263i	0.112954	+	0.0725909i
$848$	−8.10067	+	9.34867i	−0.278178	+	0.321035i
$849$	16.1980	+	4.75615i	0.555913	+	0.163231i
$850$	4.96756			0.170386
$851$	1.04890	+	4.47231i	0.0359557	+	0.153309i
$852$	1.41532			0.0484880
$853$	−7.34056	−	2.15538i	−0.251336	−	0.0737989i	0.153638	−	0.988127i	$-0.450901\pi$
$853$	−7.34056	−	2.15538i	−0.251336	−	0.0737989i	−0.404974	+	0.914328i	$0.632719\pi$
$854$	−20.7874	+	23.9899i	−0.711330	+	0.820919i
$855$	−1.25152	−	0.804301i	−0.0428010	−	0.0275065i
$856$	2.14467	−	14.9165i	0.0733034	−	0.509836i
$857$	−10.5459	+	6.77744i	−0.360241	+	0.231513i	−0.708224	−	0.705988i	$-0.750503\pi$
$857$	−10.5459	+	6.77744i	−0.360241	+	0.231513i	0.347983	+	0.937501i	$0.386867\pi$
$858$	−6.04232	−	13.2308i	−0.206281	−	0.451693i
$859$	−27.9356	−	32.2394i	−0.953151	−	1.09999i	−0.994900	−	0.100866i	$-0.967839\pi$
$859$	−27.9356	−	32.2394i	−0.953151	−	1.09999i	0.0417493	−	0.999128i	$-0.486707\pi$
$860$	1.20263	+	8.36451i	0.0410095	+	0.285227i
$861$	−4.33680	+	9.49627i	−0.147798	+	0.323632i
$862$	10.6931	−	3.13978i	0.364209	−	0.106941i
$863$	−42.5184	+	12.4845i	−1.44734	+	0.424978i	−0.908662	−	0.417532i	$-0.862895\pi$
$863$	−42.5184	+	12.4845i	−1.44734	+	0.424978i	−0.538680	+	0.842510i	$0.681077\pi$
$864$	−2.33169	+	5.10570i	−0.0793258	+	0.173699i
$865$	−0.536633	−	3.73237i	−0.0182461	−	0.126904i
$866$	−10.4486	−	12.0583i	−0.355058	−	0.409759i
$867$	4.18143	+	9.15605i	0.142009	+	0.310956i
$868$	−18.7330	+	12.0390i	−0.635841	+	0.408630i
$869$	3.27605	−	22.7855i	0.111133	−	0.772944i
$870$	−5.56501	−	3.57642i	−0.188672	−	0.121252i
$871$	−35.7794	+	41.2917i	−1.21234	+	1.39912i
$872$	−12.1858	−	3.57808i	−0.412664	−	0.121169i
$873$	0.173064			0.00585733
$874$	4.00224	+	3.87487i	0.135378	+	0.131069i
$875$	3.61614			0.122248
$876$	2.95263	+	0.866971i	0.0997602	+	0.0292922i
$877$	−30.9787	+	35.7513i	−1.04608	+	1.20724i	−0.0682816	+	0.997666i	$0.521752\pi$
$877$	−30.9787	+	35.7513i	−1.04608	+	1.20724i	−0.977794	+	0.209569i	$0.932794\pi$
$878$	−16.4964	−	10.6016i	−0.556728	−	0.357787i
$879$	−3.13165	+	21.7811i	−0.105628	+	0.734657i
$880$	2.64953	−	1.70275i	0.0893157	−	0.0573997i
$881$	19.9423	+	43.6675i	0.671872	+	1.47120i	0.871031	+	0.491228i	$0.163452\pi$
$881$	19.9423	+	43.6675i	0.671872	+	1.47120i	−0.199159	+	0.979967i	$0.563821\pi$
$882$	5.09645	+	5.88162i	0.171606	+	0.198044i
$883$	5.82419	+	40.5082i	0.196000	+	1.36321i	0.815748	+	0.578407i	$0.196326\pi$
$883$	5.82419	+	40.5082i	0.196000	+	1.36321i	−0.619748	+	0.784801i	$0.712765\pi$
$884$	7.26835	−	15.9155i	0.244461	−	0.535295i
$885$	10.0042	−	2.93750i	0.336288	−	0.0987431i
$886$	20.9382	−	6.14801i	0.703433	−	0.206546i
$887$	−18.3427	+	40.1649i	−0.615888	+	1.34861i	0.302586	+	0.953122i	$0.402150\pi$
$887$	−18.3427	+	40.1649i	−0.615888	+	1.34861i	−0.918473	+	0.395483i	$0.870577\pi$
$888$	0.178737	+	1.24314i	0.00599803	+	0.0417172i
$889$	−7.94834	−	9.17287i	−0.266579	−	0.307648i
$890$	−0.658823	−	1.44262i	−0.0220838	−	0.0483568i
$891$	9.31949	−	5.98927i	0.312215	−	0.200648i
$892$	0.502516	−	3.49507i	0.0168255	−	0.117024i
$893$	6.01964	+	3.86859i	0.201440	+	0.129457i
$894$	−1.06349	+	1.22733i	−0.0355683	+	0.0410480i
$895$	11.0880	+	3.25572i	0.370630	+	0.108827i
$896$	−3.61614			−0.120807
$897$	10.9275	+	19.2651i	0.364859	+	0.643242i
$898$	−10.8162			−0.360942
$899$	−29.8090	−	8.75272i	−0.994186	−	0.291919i
$900$	0.838715	−	0.967929i	0.0279572	−	0.0322643i
$901$	51.6942	+	33.2219i	1.72218	+	1.10678i
$902$	0.986882	−	6.86391i	0.0328596	−	0.228543i
$903$	−33.7074	+	21.6624i	−1.12171	+	0.720880i
$904$	5.85191	+	12.8139i	0.194632	+	0.426184i
$905$	10.6100	+	12.2446i	0.352690	+	0.407026i
$906$	4.24123	+	29.4984i	0.140905	+	0.980018i
$907$	−0.345721	+	0.757024i	−0.0114795	+	0.0251366i	−0.915285	−	0.402807i	$-0.868035\pi$
$907$	−0.345721	+	0.757024i	−0.0114795	+	0.0251366i	0.903805	+	0.427944i	$0.140762\pi$
$908$	12.3049	−	3.61304i	0.408352	−	0.119903i
$909$	15.8583	−	4.65642i	0.525987	−	0.154444i
$910$	5.29100	−	11.5857i	0.175395	−	0.384062i
$911$	−3.75363	−	26.1071i	−0.124363	−	0.864967i	−0.952521	−	0.304472i	$-0.901520\pi$
$911$	−3.75363	−	26.1071i	−0.124363	−	0.864967i	0.828158	−	0.560495i	$-0.189389\pi$
$912$	0.997384	+	1.15104i	0.0330267	+	0.0381148i
$913$	19.1816	+	42.0019i	0.634819	+	1.39006i
$914$	18.4724	−	11.8715i	0.611013	−	0.392674i
$915$	−1.63804	+	11.3928i	−0.0541520	+	0.376635i
$916$	−11.2560	−	7.23380i	−0.371909	−	0.239011i
$917$	40.1767	−	46.3663i	1.32675	−	1.53115i
$918$	26.7531	+	7.85542i	0.882984	+	0.259268i
$919$	14.7025			0.484990			0.242495	−	0.970153i	$-0.422034\pi$
$919$	14.7025			0.484990			0.242495	+	0.970153i	$0.422034\pi$
$920$	−3.79229	+	2.93573i	−0.125028	+	0.0967881i
$921$	0.477298			0.0157275
$922$	−35.5745	−	10.4456i	−1.17158	−	0.344008i
$923$	−2.48968	+	2.87325i	−0.0819489	+	0.0945741i
$924$	12.5627	+	8.07358i	0.413284	+	0.265601i
$925$	0.136316	−	0.948096i	0.00448203	−	0.0311732i
$926$	−23.8680	+	15.3390i	−0.784350	+	0.504071i
$927$	3.58315	+	7.84601i	0.117686	+	0.257697i
$928$	−3.30384	−	3.81284i	−0.108454	−	0.125162i
$929$	1.30107	+	9.04915i	0.0426868	+	0.296893i	0.999970	+	0.00774121i	$0.00246413\pi$
$929$	1.30107	+	9.04915i	0.0426868	+	0.296893i	−0.957283	+	0.289152i	$0.906627\pi$
$930$	−3.35418	+	7.34464i	−0.109988	+	0.240840i
$931$	6.77235	−	1.98854i	0.221955	−	0.0651718i
$932$	−27.2735	+	8.00823i	−0.893374	+	0.262318i
$933$	−3.97271	+	8.69902i	−0.130061	+	0.284793i
$934$	−1.35226	−	9.40520i	−0.0442474	−	0.307748i
$935$	−10.2455	−	11.8240i	−0.335065	−	0.386685i
$936$	−1.87395	−	4.10338i	−0.0612520	−	0.134123i
$937$	14.1390	−	9.08661i	0.461903	−	0.296847i	−0.288917	−	0.957354i	$-0.593295\pi$
$937$	14.1390	−	9.08661i	0.461903	−	0.296847i	0.750820	+	0.660507i	$0.229659\pi$
$938$	7.98308	−	55.5235i	0.260657	−	1.81291i
$939$	−28.6492	−	18.4117i	−0.934930	−	0.600843i
$940$	−4.03411	+	4.65562i	−0.131578	+	0.151849i
$941$	−18.5036	−	5.43313i	−0.603199	−	0.177115i	−0.0341469	−	0.999417i	$-0.510871\pi$
$941$	−18.5036	−	5.43313i	−0.603199	−	0.177115i	−0.569052	+	0.822302i	$0.692690\pi$
$942$	21.2126			0.691143
$943$	−0.582915	+	10.5432i	−0.0189823	+	0.343335i
$944$	7.95193			0.258813
$945$	19.4750	+	5.71837i	0.633521	+	0.186018i
$946$	17.4291	−	20.1143i	0.566669	−	0.653971i
$947$	37.9486	+	24.3881i	1.23316	+	0.792506i	0.984381	−	0.176053i	$-0.0563331\pi$
$947$	37.9486	+	24.3881i	1.23316	+	0.792506i	0.248783	+	0.968559i	$0.419969\pi$
$948$	−1.36389	+	9.48603i	−0.0442969	+	0.308092i
$949$	−6.95401	+	4.46907i	−0.225737	+	0.145072i
$950$	−0.482533	−	1.05660i	−0.0156554	−	0.0342806i
$951$	8.61818	+	9.94591i	0.279464	+	0.322518i
$952$	2.55646	+	17.7806i	0.0828554	+	0.576272i
$953$	−11.0284	+	24.1488i	−0.357245	+	0.782256i	0.642626	+	0.766180i	$0.277845\pi$
$953$	−11.0284	+	24.1488i	−0.357245	+	0.782256i	−0.999871	+	0.0160766i	$0.994882\pi$
$954$	15.2012	−	4.46349i	0.492158	−	0.144511i
$955$	−3.69436	+	1.08476i	−0.119547	+	0.0351021i
$956$	6.06575	−	13.2821i	0.196180	−	0.429575i
$957$	2.96505	+	20.6224i	0.0958464	+	0.666626i
$958$	−3.73432	−	4.30963i	−0.120650	−	0.139238i
$959$	−21.6720	−	47.4550i	−0.699825	−	1.53240i
$960$	−1.10305	+	0.708888i	−0.0356008	+	0.0228793i
$961$	−0.984856	+	6.84983i	−0.0317696	+	0.220962i
$962$	−2.83813	−	1.82396i	−0.0915051	−	0.0588067i
$963$	−12.6394	+	14.5866i	−0.407298	+	0.470047i
$964$	−20.4663	−	6.00944i	−0.659174	−	0.193551i
$965$	−17.6774			−0.569056
$966$	−20.1315	−	10.5737i	−0.647719	−	0.340204i
$967$	0.555100			0.0178508			0.00892541	−	0.999960i	$-0.497159\pi$
$967$	0.555100			0.0178508			0.00892541	+	0.999960i	$0.497159\pi$
$968$	1.03684	+	0.304443i	0.0333253	+	0.00978518i
$969$	4.95457	−	5.71788i	0.159164	−	0.183685i
$970$	0.113676	+	0.0730550i	0.00364991	+	0.00234566i
$971$	5.15101	−	35.8261i	0.165304	−	1.14971i	−0.723131	−	0.690711i	$-0.757298\pi$
$971$	5.15101	−	35.8261i	0.165304	−	1.14971i	0.888435	−	0.459003i	$-0.151793\pi$
$972$	10.2858	−	6.61028i	0.329917	−	0.212025i
$973$	−16.5400	−	36.2176i	−0.530249	−	1.16108i
$974$	−12.3789	−	14.2861i	−0.396647	−	0.457755i
$975$	−0.657248	−	4.57126i	−0.0210488	−	0.146398i
$976$	−3.64660	+	7.98493i	−0.116725	+	0.255592i
$977$	18.7446	−	5.50391i	0.599693	−	0.176086i	0.0322242	−	0.999481i	$-0.489741\pi$
$977$	18.7446	−	5.50391i	0.599693	−	0.176086i	0.567469	+	0.823395i	$0.307923\pi$
$978$	14.6883	−	4.31288i	0.469681	−	0.137911i
$979$	−2.07497	+	4.54355i	−0.0663163	+	0.145212i
$980$	0.864775	+	6.01464i	0.0276242	+	0.192131i
$981$	10.6519	+	12.2930i	0.340089	+	0.392484i
$982$	3.14450	+	6.88549i	0.100345	+	0.219725i
$983$	10.2108	−	6.56208i	0.325674	−	0.209298i	−0.367579	−	0.929992i	$-0.619813\pi$
$983$	10.2108	−	6.56208i	0.325674	−	0.209298i	0.693253	+	0.720694i	$0.256177\pi$
$984$	−0.410858	+	2.85758i	−0.0130977	+	0.0910963i
$985$	22.3210	+	14.3448i	0.711207	+	0.457065i
$986$	−16.4120	+	18.9405i	−0.522666	+	0.603188i
$987$	−28.0257	−	8.22907i	−0.892066	−	0.261934i
$988$	−4.09124			−0.130160
$989$	−23.7594	+	32.8322i	−0.755505	+	1.04400i
$990$	−4.03374			−0.128201
$991$	−15.9769	−	4.69125i	−0.507524	−	0.149023i	0.0179387	−	0.999839i	$-0.494290\pi$
$991$	−15.9769	−	4.69125i	−0.507524	−	0.149023i	−0.525463	+	0.850817i	$0.676108\pi$
$992$	−4.03260	+	4.65386i	−0.128035	+	0.147760i
$993$	−31.0881	−	19.9791i	−0.986551	−	0.634018i
$994$	0.555496	−	3.86356i	0.0176193	−	0.122545i
$995$	−7.27478	+	4.67521i	−0.230626	+	0.148214i
$996$	−7.98568	−	17.4862i	−0.253036	−	0.554072i
$997$	−13.3931	−	15.4564i	−0.424162	−	0.489509i	0.502938	−	0.864322i	$-0.332252\pi$
$997$	−13.3931	−	15.4564i	−0.424162	−	0.489509i	−0.927100	+	0.374813i	$0.877707\pi$
$998$	−2.99412	−	20.8246i	−0.0947773	−	0.659191i
$999$	2.23340	−	4.89047i	0.0706617	−	0.154728i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.g.d.41.2	✓	30
23.3	even	11		5290.2.a.bk.1.10		15
23.9	even	11	inner	230.2.g.d.101.2	yes	30
23.20	odd	22		5290.2.a.bl.1.10		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.g.d.41.2	✓	30	1.1	even	1	trivial
230.2.g.d.101.2	yes	30	23.9	even	11	inner
5290.2.a.bk.1.10		15	23.3	even	11
5290.2.a.bl.1.10		15	23.20	odd	22

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.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.959493 - 0.281733i) q^{2} +(-0.858654 + 0.990939i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.142315 - 0.989821i) q^{5} +(1.10305 - 0.708888i) q^{6} +(-1.50220 - 3.28936i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(0.182270 + 1.26772i) q^{9} +O(q^{10})\)	\(q+(-0.959493 - 0.281733i) q^{2} +(-0.858654 + 0.990939i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.142315 - 0.989821i) q^{5} +(1.10305 - 0.708888i) q^{6} +(-1.50220 - 3.28936i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(0.182270 + 1.26772i) q^{9} +(-0.415415 + 0.909632i) q^{10} +(3.02193 - 0.887318i) q^{11} +(-1.25809 + 0.369408i) q^{12} +(1.46316 - 3.20388i) q^{13} +(0.514631 + 3.57934i) q^{14} +(0.858654 + 0.990939i) q^{15} +(0.415415 + 0.909632i) q^{16} +(4.17898 - 2.68567i) q^{17} +(0.182270 - 1.26772i) q^{18} +(-0.977173 - 0.627991i) q^{19} +(0.654861 - 0.755750i) q^{20} +(4.54943 + 1.33583i) q^{21} -3.14951 q^{22} +(4.77746 - 0.419424i) q^{23} +1.31120 q^{24} +(-0.959493 - 0.281733i) q^{25} +(-2.30653 + 2.66188i) q^{26} +(-4.72189 - 3.03458i) q^{27} +(0.514631 - 3.57934i) q^{28} +(4.24421 - 2.72759i) q^{29} +(-0.544692 - 1.19271i) q^{30} +(-4.03260 - 4.65386i) q^{31} +(-0.142315 - 0.989821i) q^{32} +(-1.71551 + 3.75645i) q^{33} +(-4.76634 + 1.39952i) q^{34} +(-3.46966 + 1.01879i) q^{35} +(-0.532044 + 1.16501i) q^{36} +(0.136316 + 0.948096i) q^{37} +(0.760665 + 0.877854i) q^{38} +(1.91850 + 4.20092i) q^{39} +(-0.841254 + 0.540641i) q^{40} +(-0.313345 + 2.17936i) q^{41} +(-3.98879 - 2.56344i) q^{42} +(-5.53392 + 6.38648i) q^{43} +(3.02193 + 0.887318i) q^{44} +1.28075 q^{45} +(-4.70210 - 0.943530i) q^{46} -6.16026 q^{47} +(-1.25809 - 0.369408i) q^{48} +(-3.97926 + 4.59231i) q^{49} +(0.841254 + 0.540641i) q^{50} +(-0.926963 + 6.44717i) q^{51} +(2.96304 - 1.90423i) q^{52} +(5.13871 + 11.2522i) q^{53} +(3.67568 + 4.24197i) q^{54} +(-0.448221 - 3.11745i) q^{55} +(-1.50220 + 3.28936i) q^{56} +(1.46135 - 0.429092i) q^{57} +(-4.84074 + 1.42137i) q^{58} +(3.30335 - 7.23333i) q^{59} +(0.186603 + 1.29785i) q^{60} +(5.74850 + 6.63412i) q^{61} +(2.55810 + 5.60146i) q^{62} +(3.89617 - 2.50392i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(-2.96304 - 1.90423i) q^{65} +(2.70433 - 3.12097i) q^{66} +(-14.8839 - 4.37030i) q^{67} +4.96756 q^{68} +(-3.68656 + 5.09431i) q^{69} +3.61614 q^{70} +(-1.03568 - 0.304104i) q^{71} +(0.838715 - 0.967929i) q^{72} +(-1.97436 - 1.26884i) q^{73} +(0.136316 - 0.948096i) q^{74} +(1.10305 - 0.708888i) q^{75} +(-0.482533 - 1.05660i) q^{76} +(-7.45825 - 8.60728i) q^{77} +(-0.657248 - 4.57126i) q^{78} +(3.03627 - 6.64851i) q^{79} +(0.959493 - 0.281733i) q^{80} +(3.37493 - 0.990969i) q^{81} +(0.914650 - 2.00280i) q^{82} +(2.08646 + 14.5117i) q^{83} +(3.10501 + 3.58338i) q^{84} +(-2.06360 - 4.51865i) q^{85} +(7.10903 - 4.56870i) q^{86} +(-0.941433 + 6.54781i) q^{87} +(-2.64953 - 1.70275i) q^{88} +(-1.03857 + 1.19857i) q^{89} +(-1.22887 - 0.360830i) q^{90} -12.7367 q^{91} +(4.24581 + 2.23005i) q^{92} +8.07430 q^{93} +(5.91073 + 1.73555i) q^{94} +(-0.760665 + 0.877854i) q^{95} +(1.10305 + 0.708888i) q^{96} +(0.0192305 - 0.133751i) q^{97} +(5.11187 - 3.28520i) q^{98} +(1.67568 + 3.66922i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{2} - q^{3} - 3 q^{4} + 3 q^{5} - q^{6} + 8 q^{7} - 3 q^{8} + 12 q^{9}+O(q^{10}) \) 30 * q - 3 * q^2 - q^3 - 3 * q^4 + 3 * q^5 - q^6 + 8 * q^7 - 3 * q^8 + 12 * q^9	\( 30 q - 3 q^{2} - q^{3} - 3 q^{4} + 3 q^{5} - q^{6} + 8 q^{7} - 3 q^{8} + 12 q^{9} + 3 q^{10} - 3 q^{11} - q^{12} + 12 q^{13} - 3 q^{14} + q^{15} - 3 q^{16} - 26 q^{17} + 12 q^{18} - 25 q^{19} + 3 q^{20} - 11 q^{21} - 14 q^{22} + 14 q^{23} + 10 q^{24} - 3 q^{25} - 10 q^{26} - 52 q^{27} - 3 q^{28} + 4 q^{29} + q^{30} + 5 q^{31} - 3 q^{32} + 9 q^{33} + 7 q^{34} + 3 q^{35} + 12 q^{36} - 20 q^{37} + 19 q^{38} + 41 q^{39} + 3 q^{40} + 32 q^{41} + 22 q^{42} - 46 q^{43} - 3 q^{44} - 56 q^{45} + 3 q^{46} + 80 q^{47} - q^{48} - 41 q^{49} - 3 q^{50} - 34 q^{51} - 21 q^{52} + 29 q^{53} + 47 q^{54} + 3 q^{55} + 8 q^{56} - 33 q^{57} - 7 q^{58} - 3 q^{59} + q^{60} - q^{61} - 28 q^{62} - 8 q^{63} - 3 q^{64} + 21 q^{65} - 46 q^{66} - 63 q^{67} - 4 q^{68} + 78 q^{69} - 8 q^{70} + 55 q^{71} - 32 q^{72} - 36 q^{73} - 20 q^{74} - q^{75} - 3 q^{76} - 9 q^{77} - 80 q^{78} - 29 q^{79} + 3 q^{80} + 15 q^{81} - 23 q^{82} - 63 q^{83} + 4 q^{85} + 31 q^{86} + 63 q^{87} - 3 q^{88} - 95 q^{89} + 10 q^{90} - 12 q^{91} + 14 q^{92} + 126 q^{93} + 3 q^{94} - 19 q^{95} - q^{96} + 11 q^{97} + 58 q^{98} + 97 q^{99}+O(q^{100}) \) 30 * q - 3 * q^2 - q^3 - 3 * q^4 + 3 * q^5 - q^6 + 8 * q^7 - 3 * q^8 + 12 * q^9 + 3 * q^10 - 3 * q^11 - q^12 + 12 * q^13 - 3 * q^14 + q^15 - 3 * q^16 - 26 * q^17 + 12 * q^18 - 25 * q^19 + 3 * q^20 - 11 * q^21 - 14 * q^22 + 14 * q^23 + 10 * q^24 - 3 * q^25 - 10 * q^26 - 52 * q^27 - 3 * q^28 + 4 * q^29 + q^30 + 5 * q^31 - 3 * q^32 + 9 * q^33 + 7 * q^34 + 3 * q^35 + 12 * q^36 - 20 * q^37 + 19 * q^38 + 41 * q^39 + 3 * q^40 + 32 * q^41 + 22 * q^42 - 46 * q^43 - 3 * q^44 - 56 * q^45 + 3 * q^46 + 80 * q^47 - q^48 - 41 * q^49 - 3 * q^50 - 34 * q^51 - 21 * q^52 + 29 * q^53 + 47 * q^54 + 3 * q^55 + 8 * q^56 - 33 * q^57 - 7 * q^58 - 3 * q^59 + q^60 - q^61 - 28 * q^62 - 8 * q^63 - 3 * q^64 + 21 * q^65 - 46 * q^66 - 63 * q^67 - 4 * q^68 + 78 * q^69 - 8 * q^70 + 55 * q^71 - 32 * q^72 - 36 * q^73 - 20 * q^74 - q^75 - 3 * q^76 - 9 * q^77 - 80 * q^78 - 29 * q^79 + 3 * q^80 + 15 * q^81 - 23 * q^82 - 63 * q^83 + 4 * q^85 + 31 * q^86 + 63 * q^87 - 3 * q^88 - 95 * q^89 + 10 * q^90 - 12 * q^91 + 14 * q^92 + 126 * q^93 + 3 * q^94 - 19 * q^95 - q^96 + 11 * q^97 + 58 * q^98 + 97 * q^99

Introduction

L-functions

Modular forms

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