LMFDB - Embedded newform 224.2.be.a.59.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(3,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 9, 4]))

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

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

chi := DirichletCharacter("224.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.be (of order $24$, degree $8$, 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:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			59.9
Character	$\chi$	$=$	224.59
Dual form			224.2.be.a.19.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.936244 - 1.05993i) q^{2} +(0.164372 + 0.0216400i) q^{3} +(-0.246896 + 1.98470i) q^{4} +(-0.755608 + 0.0994777i) q^{5} +(-0.130955 - 0.194483i) q^{6} +(-0.876446 - 2.49637i) q^{7} +(2.33480 - 1.59647i) q^{8} +(-2.87123 - 0.769343i) q^{9} +(0.812872 + 0.707755i) q^{10} +(2.95339 - 2.26622i) q^{11} +(-0.0835318 + 0.320887i) q^{12} +(-1.74960 - 4.22391i) q^{13} +(-1.82540 + 3.26618i) q^{14} -0.126354 q^{15} +(-3.87808 - 0.980031i) q^{16} +(3.44670 - 5.96986i) q^{17} +(1.87272 + 3.76359i) q^{18} +(1.01793 + 0.781087i) q^{19} +(-0.0108768 - 1.52422i) q^{20} +(-0.0900419 - 0.429299i) q^{21} +(-5.16712 - 1.00865i) q^{22} +(-1.63213 + 6.09119i) q^{23} +(0.418323 - 0.211890i) q^{24} +(-4.26858 + 1.14376i) q^{25} +(-2.83899 + 5.80906i) q^{26} +(-0.914812 - 0.378928i) q^{27} +(5.17093 - 1.12314i) q^{28} +(-0.478719 - 1.15573i) q^{29} +(0.118298 + 0.133926i) q^{30} +(-1.64276 + 2.84535i) q^{31} +(2.59207 + 5.02804i) q^{32} +(0.534496 - 0.308592i) q^{33} +(-9.55457 + 1.93599i) q^{34} +(0.910582 + 1.79909i) q^{35} +(2.23581 - 5.50858i) q^{36} +(-1.24039 - 9.42166i) q^{37} +(-0.125136 - 1.81022i) q^{38} +(-0.196180 - 0.732154i) q^{39} +(-1.60538 + 1.43857i) q^{40} +(7.52016 + 7.52016i) q^{41} +(-0.370725 + 0.497366i) q^{42} +(5.35637 + 2.21868i) q^{43} +(3.76859 + 6.42113i) q^{44} +(2.24606 + 0.295699i) q^{45} +(7.98430 - 3.97290i) q^{46} +(4.87523 - 2.81471i) q^{47} +(-0.616241 - 0.245011i) q^{48} +(-5.46368 + 4.37586i) q^{49} +(5.20874 + 3.45355i) q^{50} +(0.695729 - 0.906691i) q^{51} +(8.81517 - 2.42957i) q^{52} +(1.62230 + 2.11422i) q^{53} +(0.454851 + 1.32440i) q^{54} +(-2.00617 + 2.00617i) q^{55} +(-6.03170 - 4.42929i) q^{56} +(0.150417 + 0.150417i) q^{57} +(-0.776794 + 1.58945i) q^{58} +(10.5628 - 8.10514i) q^{59} +(0.0311962 - 0.250774i) q^{60} +(-8.78360 - 6.73989i) q^{61} +(4.55390 - 0.922729i) q^{62} +(0.595914 + 7.84192i) q^{63} +(2.90255 - 7.45488i) q^{64} +(1.74220 + 3.01757i) q^{65} +(-0.827504 - 0.277611i) q^{66} +(-1.21395 + 9.22085i) q^{67} +(10.9974 + 8.31461i) q^{68} +(-0.400090 + 0.965903i) q^{69} +(1.05438 - 2.64954i) q^{70} +(-5.31630 + 5.31630i) q^{71} +(-7.93197 + 2.78758i) q^{72} +(4.98088 - 1.33462i) q^{73} +(-8.82498 + 10.1357i) q^{74} +(-0.726387 + 0.0956306i) q^{75} +(-1.80155 + 1.82744i) q^{76} +(-8.24580 - 5.38653i) q^{77} +(-0.592359 + 0.893411i) q^{78} +(3.13677 + 5.43304i) q^{79} +(3.02780 + 0.354736i) q^{80} +(7.58065 + 4.37669i) q^{81} +(0.930130 - 15.0115i) q^{82} +(6.31332 - 2.61506i) q^{83} +(0.874262 - 0.0727140i) q^{84} +(-2.01049 + 4.85374i) q^{85} +(-2.66323 - 7.75460i) q^{86} +(-0.0536781 - 0.200329i) q^{87} +(3.27762 - 10.0062i) q^{88} +(-11.2573 - 3.01639i) q^{89} +(-1.78944 - 2.65750i) q^{90} +(-9.01099 + 8.06967i) q^{91} +(-11.6862 - 4.74319i) q^{92} +(-0.331598 + 0.432147i) q^{93} +(-7.54780 - 2.53213i) q^{94} +(-0.846859 - 0.488934i) q^{95} +(0.317257 + 0.882562i) q^{96} -0.918957i q^{97} +(9.75344 + 1.69424i) q^{98} +(-10.2234 + 4.23466i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{2} - 12 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 12 q^{10} - 4 q^{11} - 12 q^{12} - 40 q^{14} - 32 q^{15} - 24 q^{16} + 16 q^{18} - 12 q^{19} - 8 q^{21} - 8 q^{22} + 4 q^{23}+ \cdots - 40 q^{99}+O(q^{100}) $ 240 * q - 4 * q^2 - 12 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 12 * q^10 - 4 * q^11 - 12 * q^12 - 40 * q^14 - 32 * q^15 - 24 * q^16 + 16 * q^18 - 12 * q^19 - 8 * q^21 - 8 * q^22 + 4 * q^23 - 12 * q^24 - 4 * q^25 - 12 * q^26 + 12 * q^28 - 16 * q^29 - 52 * q^30 - 4 * q^32 - 24 * q^33 - 32 * q^35 + 64 * q^36 - 4 * q^37 - 12 * q^38 - 4 * q^39 - 12 * q^40 - 28 * q^42 - 32 * q^43 - 52 * q^44 - 48 * q^45 - 4 * q^46 - 24 * q^47 - 40 * q^50 + 20 * q^51 + 60 * q^52 - 20 * q^53 - 12 * q^54 - 48 * q^56 - 16 * q^57 - 36 * q^58 + 84 * q^59 + 28 * q^60 - 12 * q^61 - 136 * q^64 - 8 * q^65 + 132 * q^66 + 36 * q^67 - 12 * q^68 + 28 * q^70 - 80 * q^71 - 4 * q^72 - 12 * q^73 - 20 * q^74 - 72 * q^75 - 8 * q^77 - 216 * q^78 - 8 * q^79 + 24 * q^80 + 108 * q^82 + 12 * q^84 + 24 * q^85 - 4 * q^86 - 12 * q^87 - 48 * q^88 - 12 * q^89 + 40 * q^91 - 80 * q^92 + 20 * q^93 + 60 * q^94 + 312 * q^96 - 16 * q^98 - 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{8}\right)$

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 $

$2$	−0.936244	−	1.05993i	−0.662024	−	0.749483i
$2$	−0.936244	−	1.05993i	−0.662024	−	0.749483i
$3$	0.164372	+	0.0216400i	0.0949003	+	0.0124939i	0.177827	−	0.984062i	$-0.443093\pi$
$3$	0.164372	+	0.0216400i	0.0949003	+	0.0124939i	−0.0829265	+	0.996556i	$0.526427\pi$
$4$	−0.246896	+	1.98470i	−0.123448	+	0.992351i
$5$	−0.755608	+	0.0994777i	−0.337918	+	0.0444878i	−0.297576	−	0.954698i	$-0.596178\pi$
$5$	−0.755608	+	0.0994777i	−0.337918	+	0.0444878i	−0.0403422	+	0.999186i	$0.512845\pi$
$6$	−0.130955	−	0.194483i	−0.0534623	−	0.0793973i
$7$	−0.876446	−	2.49637i	−0.331265	−	0.943538i
$7$	−0.876446	−	2.49637i	−0.331265	−	0.943538i
$8$	2.33480	−	1.59647i	0.825475	−	0.564438i
$9$	−2.87123	−	0.769343i	−0.957076	−	0.256448i
$10$	0.812872	+	0.707755i	0.257053	+	0.223812i
$11$	2.95339	−	2.26622i	0.890481	−	0.683290i	−0.0586134	−	0.998281i	$-0.518668\pi$
$11$	2.95339	−	2.26622i	0.890481	−	0.683290i	0.949095	+	0.314990i	$0.102001\pi$
$12$	−0.0835318	+	0.320887i	−0.0241135	+	0.0926320i
$13$	−1.74960	−	4.22391i	−0.485252	−	1.17150i	−0.957083	−	0.289813i	$-0.906407\pi$
$13$	−1.74960	−	4.22391i	−0.485252	−	1.17150i	0.471831	−	0.881689i	$-0.343593\pi$
$14$	−1.82540	+	3.26618i	−0.487859	+	0.872922i
$15$	−0.126354			−0.0326243
$16$	−3.87808	−	0.980031i	−0.969521	−	0.245008i
$17$	3.44670	−	5.96986i	0.835947	−	1.44790i	−0.0573094	−	0.998356i	$-0.518252\pi$
$17$	3.44670	−	5.96986i	0.835947	−	1.44790i	0.893257	−	0.449547i	$-0.148415\pi$
$18$	1.87272	+	3.76359i	0.441404	+	0.887086i
$19$	1.01793	+	0.781087i	0.233530	+	0.179194i	0.718897	−	0.695117i	$-0.244647\pi$
$19$	1.01793	+	0.781087i	0.233530	+	0.179194i	−0.485367	+	0.874310i	$0.661314\pi$
$20$	−0.0108768	−	1.52422i	−0.00243213	−	0.340825i
$21$	−0.0900419	−	0.429299i	−0.0196488	−	0.0936807i
$22$	−5.16712	−	1.00865i	−1.10163	−	0.215046i
$23$	−1.63213	+	6.09119i	−0.340323	+	1.27010i	0.557659	+	0.830070i	$0.311700\pi$
$23$	−1.63213	+	6.09119i	−0.340323	+	1.27010i	−0.897982	+	0.440032i	$0.854967\pi$
$24$	0.418323	−	0.211890i	0.0853898	−	0.0432520i
$25$	−4.26858	+	1.14376i	−0.853716	+	0.228753i
$26$	−2.83899	+	5.80906i	−0.556772	+	1.13925i
$27$	−0.914812	−	0.378928i	−0.176056	−	0.0729246i
$28$	5.17093	−	1.12314i	0.977215	−	0.212254i
$29$	−0.478719	−	1.15573i	−0.0888959	−	0.214614i	0.873179	−	0.487400i	$-0.162055\pi$
$29$	−0.478719	−	1.15573i	−0.0888959	−	0.214614i	−0.962075	+	0.272787i	$0.912055\pi$
$30$	0.118298	+	0.133926i	0.0215981	+	0.0244514i
$31$	−1.64276	+	2.84535i	−0.295049	+	0.511040i	−0.974996	−	0.222221i	$-0.928669\pi$
$31$	−1.64276	+	2.84535i	−0.295049	+	0.511040i	0.679947	+	0.733261i	$0.262003\pi$
$32$	2.59207	+	5.02804i	0.458217	+	0.888840i
$33$	0.534496	−	0.308592i	0.0930439	−	0.0537189i
$34$	−9.55457	+	1.93599i	−1.63860	+	0.332019i
$35$	0.910582	+	1.79909i	0.153917	+	0.304101i
$36$	2.23581	−	5.50858i	0.372635	−	0.918097i
$37$	−1.24039	−	9.42166i	−0.203918	−	1.54891i	−0.720975	−	0.692961i	$-0.756306\pi$
$37$	−1.24039	−	9.42166i	−0.203918	−	1.54891i	0.517057	−	0.855951i	$-0.327027\pi$
$38$	−0.125136	−	1.81022i	−0.0202998	−	0.293657i
$39$	−0.196180	−	0.732154i	−0.0314140	−	0.117238i
$40$	−1.60538	+	1.43857i	−0.253833	+	0.227457i
$41$	7.52016	+	7.52016i	1.17445	+	1.17445i	0.981137	+	0.193315i	$0.0619240\pi$
$41$	7.52016	+	7.52016i	1.17445	+	1.17445i	0.193315	+	0.981137i	$0.438076\pi$
$42$	−0.370725	+	0.497366i	−0.0572041	+	0.0767453i
$43$	5.35637	+	2.21868i	0.816839	+	0.338346i	0.751679	−	0.659529i	$-0.229244\pi$
$43$	5.35637	+	2.21868i	0.816839	+	0.338346i	0.0651601	+	0.997875i	$0.479244\pi$
$44$	3.76859	+	6.42113i	0.568136	+	0.968021i
$45$	2.24606	+	0.295699i	0.334822	+	0.0440802i
$46$	7.98430	−	3.97290i	1.17722	−	0.585772i
$47$	4.87523	−	2.81471i	0.711125	−	0.410568i	−0.100352	−	0.994952i	$-0.531997\pi$
$47$	4.87523	−	2.81471i	0.711125	−	0.410568i	0.811478	+	0.584384i	$0.198664\pi$
$48$	−0.616241	−	0.245011i	−0.0889467	−	0.0353643i
$49$	−5.46368	+	4.37586i	−0.780526	+	0.625123i
$50$	5.20874	+	3.45355i	0.736627	+	0.488406i
$51$	0.695729	−	0.906691i	0.0974215	−	0.126962i
$52$	8.81517	−	2.42957i	1.22244	−	0.336921i
$53$	1.62230	+	2.11422i	0.222840	+	0.290411i	0.891372	−	0.453273i	$-0.149744\pi$
$53$	1.62230	+	2.11422i	0.222840	+	0.290411i	−0.668532	+	0.743684i	$0.733077\pi$
$54$	0.454851	+	1.32440i	0.0618974	+	0.180229i
$55$	−2.00617	+	2.00617i	−0.270512	+	0.270512i
$56$	−6.03170	−	4.42929i	−0.806020	−	0.591888i
$57$	0.150417	+	0.150417i	0.0199232	+	0.0199232i
$58$	−0.776794	+	1.58945i	−0.101998	+	0.208705i
$59$	10.5628	−	8.10514i	1.37516	−	1.05520i	0.383889	−	0.923379i	$-0.374585\pi$
$59$	10.5628	−	8.10514i	1.37516	−	1.05520i	0.991274	−	0.131820i	$-0.0420821\pi$
$60$	0.0311962	−	0.250774i	0.00402741	−	0.0323748i
$61$	−8.78360	−	6.73989i	−1.12462	−	0.862955i	−0.132873	−	0.991133i	$-0.542420\pi$
$61$	−8.78360	−	6.73989i	−1.12462	−	0.862955i	−0.991751	+	0.128178i	$0.959087\pi$
$62$	4.55390	−	0.922729i	0.578345	−	0.117187i
$63$	0.595914	+	7.84192i	0.0750781	+	0.987989i
$64$	2.90255	−	7.45488i	0.362819	−	0.931860i
$65$	1.74220	+	3.01757i	0.216093	+	0.374284i
$66$	−0.827504	−	0.277611i	−0.101859	−	0.0341715i
$67$	−1.21395	+	9.22085i	−0.148307	+	1.12651i	0.741756	+	0.670670i	$0.233993\pi$
$67$	−1.21395	+	9.22085i	−0.148307	+	1.12651i	−0.890063	+	0.455837i	$0.849340\pi$
$68$	10.9974	+	8.31461i	1.33363	+	1.00829i
$69$	−0.400090	+	0.965903i	−0.0481652	+	0.116281i
$70$	1.05438	−	2.64954i	0.126022	−	0.316680i
$71$	−5.31630	+	5.31630i	−0.630929	+	0.630929i	−0.948301	−	0.317372i	$-0.897200\pi$
$71$	−5.31630	+	5.31630i	−0.630929	+	0.630929i	0.317372	+	0.948301i	$0.397200\pi$
$72$	−7.93197	+	2.78758i	−0.934791	+	0.328519i
$73$	4.98088	−	1.33462i	0.582968	−	0.156206i	0.0447307	−	0.998999i	$-0.485757\pi$
$73$	4.98088	−	1.33462i	0.582968	−	0.156206i	0.538237	+	0.842793i	$0.319090\pi$
$74$	−8.82498	+	10.1357i	−1.02588	+	1.17825i
$75$	−0.726387	+	0.0956306i	−0.0838759	+	0.0110425i
$76$	−1.80155	+	1.82744i	−0.206652	+	0.209622i
$77$	−8.24580	−	5.38653i	−0.939696	−	0.613852i
$78$	−0.592359	+	0.893411i	−0.0670714	+	0.101159i
$79$	3.13677	+	5.43304i	0.352914	+	0.611265i	0.986759	−	0.162195i	$-0.0518575\pi$
$79$	3.13677	+	5.43304i	0.352914	+	0.611265i	−0.633845	+	0.773460i	$0.718524\pi$
$80$	3.02780	+	0.354736i	0.338519	+	0.0396607i
$81$	7.58065	+	4.37669i	0.842294	+	0.486299i
$82$	0.930130	−	15.0115i	0.102716	−	1.65775i
$83$	6.31332	−	2.61506i	0.692977	−	0.287040i	−0.00826298	−	0.999966i	$-0.502630\pi$
$83$	6.31332	−	2.61506i	0.692977	−	0.287040i	0.701240	+	0.712925i	$0.252630\pi$
$84$	0.874262	−	0.0727140i	0.0953898	−	0.00793375i
$85$	−2.01049	+	4.85374i	−0.218068	+	0.526462i
$86$	−2.66323	−	7.75460i	−0.287183	−	0.836200i
$87$	−0.0536781	−	0.200329i	−0.00575489	−	0.0214775i
$88$	3.27762	−	10.0062i	0.349395	−	1.06666i
$89$	−11.2573	−	3.01639i	−1.19327	−	0.319736i	−0.393094	−	0.919498i	$-0.628595\pi$
$89$	−11.2573	−	3.01639i	−1.19327	−	0.319736i	−0.800178	+	0.599762i	$0.795262\pi$
$90$	−1.78944	−	2.65750i	−0.188623	−	0.280125i
$91$	−9.01099	+	8.06967i	−0.944609	+	0.845931i
$92$	−11.6862	−	4.74319i	−1.21837	−	0.494511i
$93$	−0.331598	+	0.432147i	−0.0343851	+	0.0448115i
$94$	−7.54780	−	2.53213i	−0.778496	−	0.261170i
$95$	−0.846859	−	0.488934i	−0.0868859	−	0.0501636i
$96$	0.317257	+	0.882562i	0.0323799	+	0.0900761i
$97$		−	0.918957i		−	0.0933060i	−0.998911	−	0.0466530i	$-0.985145\pi$
$97$		−	0.918957i		−	0.0933060i	0.998911	−	0.0466530i	$-0.0148555\pi$
$98$	9.75344	+	1.69424i	0.985246	+	0.171145i
$99$	−10.2234	+	4.23466i	−1.02749	+	0.425599i
$100$	−1.21613	−	8.75425i	−0.121613	−	0.875425i
$101$	3.16043	+	4.11875i	0.314474	+	0.409831i	0.923670	−	0.383189i	$-0.125174\pi$
$101$	3.16043	+	4.11875i	0.314474	+	0.409831i	−0.609196	+	0.793020i	$0.708508\pi$
$102$	−1.61240	+	0.111461i	−0.159651	+	0.0110363i
$103$	3.13918	−	11.7156i	0.309312	−	1.15437i	−0.619857	−	0.784715i	$-0.712809\pi$
$103$	3.13918	−	11.7156i	0.309312	−	1.15437i	0.929169	−	0.369654i	$-0.120524\pi$
$104$	−10.8283	−	7.06878i	−1.06180	−	0.693151i
$105$	0.110742	+	0.315425i	0.0108073	+	0.0307823i
$106$	0.722057	−	3.69895i	0.0701324	−	0.359274i
$107$	−0.874024	−	6.63887i	−0.0844951	−	0.641804i	−0.980323	−	0.197402i	$-0.936750\pi$
$107$	−0.874024	−	6.63887i	−0.0844951	−	0.641804i	0.895827	−	0.444402i	$-0.146584\pi$
$108$	0.977922	−	1.72207i	0.0941006	−	0.165707i
$109$	0.499545	−	3.79442i	0.0478477	−	0.363440i	−0.950725	−	0.310035i	$-0.899659\pi$
$109$	0.499545	−	3.79442i	0.0478477	−	0.363440i	0.998573	−	0.0534048i	$-0.0170074\pi$
$110$	4.00466	+	0.248133i	0.381829	+	0.0236585i
$111$		−	1.57550i		−	0.149540i
$112$	0.952416	+	10.5401i	0.0899949	+	0.995942i
$113$			5.43512i			0.511293i	0.966770	+	0.255647i	$0.0822884\pi$
$113$			5.43512i			0.511293i	−0.966770	+	0.255647i	$0.917712\pi$
$114$	0.0186043	−	0.300258i	0.00174245	−	0.0281217i
$115$	0.627313	−	4.76492i	0.0584973	−	0.444331i
$116$	2.41197	−	0.664770i	0.223946	−	0.0617223i
$117$	1.77387	+	13.4738i	0.163994	+	1.24566i
$118$	−18.4802	−	3.60745i	−1.70124	−	0.332093i
$119$	−17.9238	−	3.37196i	−1.64307	−	0.309107i
$120$	−0.295010	+	0.201720i	−0.0269306	+	0.0184144i
$121$	0.739776	−	2.76088i	0.0672524	−	0.250989i
$122$	1.07978	+	15.6202i	0.0977591	+	1.41418i
$123$	1.07337	+	1.39884i	0.0967823	+	0.126129i
$124$	−5.24158	−	3.96290i	−0.470708	−	0.355879i
$125$	6.63217	−	2.74713i	0.593199	−	0.245711i
$126$	7.75395	−	7.97357i	0.690777	−	0.710343i
$127$			8.82945i			0.783487i	0.920074	+	0.391744i	$0.128128\pi$
$127$			8.82945i			0.783487i	−0.920074	+	0.391744i	$0.871872\pi$
$128$	−10.6191	+	3.90308i	−0.938607	+	0.344987i
$129$	0.832426	+	0.480601i	0.0732910	+	0.0423146i
$130$	1.56729	−	4.67179i	0.137461	−	0.409743i
$131$	2.86212	−	3.72998i	0.250064	−	0.325890i	−0.651407	−	0.758728i	$-0.725821\pi$
$131$	2.86212	−	3.72998i	0.250064	−	0.325890i	0.901472	+	0.432838i	$0.142488\pi$
$132$	0.480497	+	1.13701i	0.0418219	+	0.0989637i
$133$	1.05772	−	3.22571i	0.0917156	−	0.279705i
$134$	10.9100	−	7.34627i	0.942480	−	0.634621i
$135$	0.728934	+	0.195317i	0.0627367	+	0.0168102i
$136$	−1.48337	−	19.4410i	−0.127198	−	1.66705i
$137$	0.565209	+	2.10939i	0.0482891	+	0.180217i	0.985858	−	0.167582i	$-0.0535958\pi$
$137$	0.565209	+	2.10939i	0.0482891	+	0.180217i	−0.937569	+	0.347799i	$0.886929\pi$
$138$	1.39837	−	0.480254i	0.119037	−	0.0408819i
$139$	4.95117	−	11.9532i	0.419953	−	1.01386i	−0.562407	−	0.826860i	$-0.690125\pi$
$139$	4.95117	−	11.9532i	0.419953	−	1.01386i	0.982361	−	0.186996i	$-0.0598753\pi$
$140$	−3.79547	+	1.36305i	−0.320776	+	0.115198i
$141$	0.862262	−	0.357161i	0.0726155	−	0.0300783i
$142$	10.6123	+	0.657546i	0.890560	+	0.0551800i
$143$	−14.7396	−	8.50989i	−1.23258	−	0.711633i
$144$	10.3809	+	5.79747i	0.865074	+	0.483122i
$145$	0.476693	+	0.825657i	0.0395872	+	0.0685671i
$146$	−6.07792	−	4.02985i	−0.503013	−	0.333512i
$147$	−0.992771	+	0.601035i	−0.0818823	+	0.0495725i
$148$	19.0054	−	0.135623i	1.56224	−	0.0111481i
$149$	−3.78459	+	0.498251i	−0.310046	+	0.0408183i	−0.283944	−	0.958841i	$-0.591643\pi$
$149$	−3.78459	+	0.498251i	−0.310046	+	0.0408183i	−0.0261020	+	0.999659i	$0.508309\pi$
$150$	0.781436	+	0.680384i	0.0638040	+	0.0555531i
$151$	−9.72187	+	2.60497i	−0.791154	+	0.211989i	−0.631697	−	0.775216i	$-0.717641\pi$
$151$	−9.72187	+	2.60497i	−0.791154	+	0.211989i	−0.159458	+	0.987205i	$0.550975\pi$
$152$	3.62365	+	0.198579i	0.293917	+	0.0161069i
$153$	−14.4891	+	14.4891i	−1.17138	+	1.17138i
$154$	2.01074	+	13.7831i	0.162030	+	1.11067i
$155$	0.958237	−	2.31339i	0.0769675	−	0.185816i
$156$	1.50154	−	0.208593i	0.120220	−	0.0167008i
$157$	−0.711396	+	5.40359i	−0.0567756	+	0.431254i	0.939325	+	0.343029i	$0.111453\pi$
$157$	−0.711396	+	5.40359i	−0.0567756	+	0.431254i	−0.996101	+	0.0882250i	$0.971881\pi$
$158$	2.82186	−	8.41140i	0.224495	−	0.669175i
$159$	0.220909	+	0.382626i	0.0175192	+	0.0303442i
$160$	−2.45877	−	3.54137i	−0.194383	−	0.279970i
$161$	16.6363	−	1.26421i	1.31113	−	0.0996335i
$162$	−2.45836	−	12.1326i	−0.193147	−	0.953226i
$163$	17.6114	+	13.5137i	1.37943	+	1.05847i	0.990545	+	0.137187i	$0.0438060\pi$
$163$	17.6114	+	13.5137i	1.37943	+	1.05847i	0.388884	+	0.921287i	$0.372861\pi$
$164$	−16.7820	+	13.0686i	−1.31045	+	1.02048i
$165$	−0.373172	+	0.286345i	−0.0290514	+	0.0222919i
$166$	−8.68258	−	4.24333i	−0.673899	−	0.329346i
$167$	2.28366	+	2.28366i	0.176715	+	0.176715i	0.789922	−	0.613207i	$-0.210121\pi$
$167$	2.28366	+	2.28366i	0.176715	+	0.176715i	−0.613207	+	0.789922i	$0.710121\pi$
$168$	−0.895594	−	0.858577i	−0.0690965	−	0.0662406i
$169$	−5.58792	+	5.58792i	−0.429840	+	0.429840i
$170$	7.02692	−	2.41331i	0.538940	−	0.185093i
$171$	−2.32179	−	3.02582i	−0.177552	−	0.231390i
$172$	−5.72589	+	10.0830i	−0.436595	+	0.768823i
$173$	10.9379	−	14.2545i	0.831591	−	1.08375i	−0.163671	−	0.986515i	$-0.552333\pi$
$173$	10.9379	−	14.2545i	0.831591	−	1.08375i	0.995261	−	0.0972351i	$-0.0309999\pi$
$174$	−0.162079	+	0.244452i	−0.0122872	+	0.0185318i
$175$	6.59643	+	9.65349i	0.498643	+	0.729736i
$176$	−13.6745	+	5.89417i	−1.03075	+	0.444290i
$177$	1.91163	−	1.10368i	0.143687	−	0.0829576i
$178$	7.34243	+	14.7560i	0.550338	+	1.10601i
$179$	5.00207	+	0.658535i	0.373872	+	0.0492212i	0.315121	−	0.949051i	$-0.397955\pi$
$179$	5.00207	+	0.658535i	0.373872	+	0.0492212i	0.0587510	+	0.998273i	$0.481288\pi$
$180$	−1.14142	+	4.38474i	−0.0850762	+	0.326819i
$181$	10.4866	+	4.34370i	0.779465	+	0.322865i	0.736699	−	0.676220i	$-0.236383\pi$
$181$	10.4866	+	4.34370i	0.779465	+	0.322865i	0.0427652	+	0.999085i	$0.486383\pi$
$182$	16.9898	+	1.99583i	1.25936	+	0.147941i
$183$	−1.29793	−	1.29793i	−0.0959455	−	0.0959455i
$184$	5.91373	+	16.8274i	0.435966	+	1.24053i
$185$	1.87449	+	6.99569i	0.137815	+	0.514334i
$186$	0.768501	−	0.0531246i	0.0563492	−	0.00389529i
$187$	−3.34954	−	25.4423i	−0.244943	−	1.86053i
$188$	4.38269	+	10.3708i	0.319641	+	0.756370i
$189$	−0.144158	+	2.61582i	−0.0104860	+	0.190273i
$190$	0.274631	+	1.35537i	0.0199238	+	0.0983289i
$191$	5.30380	−	3.06215i	0.383769	−	0.221569i	−0.295688	−	0.955285i	$-0.595549\pi$
$191$	5.30380	−	3.06215i	0.383769	−	0.221569i	0.679457	+	0.733715i	$0.262215\pi$
$192$	0.638422	−	1.16256i	0.0460741	−	0.0839007i
$193$	8.12985	−	14.0813i	0.585199	−	1.01359i	−0.409651	−	0.912242i	$-0.634350\pi$
$193$	8.12985	−	14.0813i	0.585199	−	1.01359i	0.994851	−	0.101353i	$-0.0323171\pi$
$194$	−0.974029	+	0.860368i	−0.0699312	+	0.0617708i
$195$	0.221068	+	0.533706i	0.0158310	+	0.0382195i
$196$	−7.33581	−	11.9242i	−0.523987	−	0.851726i
$197$	7.20307	+	2.98361i	0.513197	+	0.212573i	0.624226	−	0.781244i	$-0.285415\pi$
$197$	7.20307	+	2.98361i	0.513197	+	0.212573i	−0.111029	+	0.993817i	$0.535415\pi$
$198$	14.0600	+	6.87136i	0.999200	+	0.488327i
$199$	−3.34125	+	0.895286i	−0.236855	+	0.0634651i	−0.375294	−	0.926906i	$-0.622458\pi$
$199$	−3.34125	+	0.895286i	−0.236855	+	0.0634651i	0.138439	+	0.990371i	$0.455792\pi$
$200$	−8.14028	+	9.48513i	−0.575605	+	0.670700i
$201$	−0.399078	+	1.48938i	−0.0281488	+	0.105053i
$202$	1.40665	−	7.20598i	0.0989715	−	0.507011i
$203$	−2.46555	+	2.20799i	−0.173048	+	0.154971i
$204$	1.62774	+	1.60467i	0.113965	+	0.112350i
$205$	−6.43038	−	4.93421i	−0.449117	−	0.344620i
$206$	−15.3567	+	7.64132i	−1.06995	+	0.532396i
$207$	9.37244	−	16.2335i	0.651429	−	1.12831i
$208$	2.64554	+	18.0953i	0.183435	+	1.25469i
$209$	4.77647			0.330395
$210$	0.230646	−	0.412693i	0.0159161	−	0.0284785i
$211$	−5.19732	−	12.5474i	−0.357798	−	0.863801i	−0.995609	−	0.0936084i	$-0.970160\pi$
$211$	−5.19732	−	12.5474i	−0.357798	−	0.863801i	0.637811	−	0.770193i	$-0.279840\pi$
$212$	−4.59664	+	2.69779i	−0.315699	+	0.185285i
$213$	−0.988896	+	0.758807i	−0.0677581	+	0.0519926i
$214$	−6.21843	+	7.14201i	−0.425083	+	0.488217i
$215$	−4.26803	−	1.14361i	−0.291077	−	0.0779939i
$216$	−2.74085	+	0.575753i	−0.186491	+	0.0391750i
$217$	8.54283	+	1.60714i	0.579925	+	0.109100i
$218$	−4.48951	+	3.02302i	−0.304068	+	0.204745i
$219$	0.847599	−	0.111589i	0.0572754	−	0.00754045i
$220$	−3.48633	−	4.47696i	−0.235049	−	0.301837i
$221$	−31.2465	−	4.11368i	−2.10187	−	0.276716i
$222$	−1.66992	+	1.47505i	−0.112077	+	0.0989990i
$223$	18.0910			1.21146			0.605731	−	0.795669i	$-0.292881\pi$
$223$	18.0910			1.21146			0.605731	+	0.795669i	$0.292881\pi$
$224$	10.2800	−	10.8776i	0.686862	−	0.726787i
$225$	13.1360			0.875734
$226$	5.76084	−	5.08860i	0.383205	−	0.338489i
$227$	−17.1298	−	2.25519i	−1.13695	−	0.149682i	−0.461535	−	0.887122i	$-0.652701\pi$
$227$	−17.1298	−	2.25519i	−1.13695	−	0.149682i	−0.675413	+	0.737440i	$0.736034\pi$
$228$	−0.335670	+	0.261395i	−0.0222303	+	0.0173113i
$229$	−9.14503	+	1.20397i	−0.604320	+	0.0795603i	−0.426477	−	0.904498i	$-0.640245\pi$
$229$	−9.14503	+	1.20397i	−0.604320	+	0.0795603i	−0.177844	+	0.984059i	$0.556912\pi$
$230$	−5.63779	+	3.79622i	−0.371745	+	0.250315i
$231$	−1.23881	−	1.06383i	−0.0815080	−	0.0699952i
$232$	−2.96280	−	1.93413i	−0.194518	−	0.126982i
$233$	3.10637	+	0.832350i	0.203505	+	0.0545291i	0.359132	−	0.933287i	$-0.383073\pi$
$233$	3.10637	+	0.832350i	0.203505	+	0.0545291i	−0.155626	+	0.987816i	$0.549740\pi$
$234$	12.6205	−	14.4950i	0.825031	−	0.947566i
$235$	−3.40376	+	2.61180i	−0.222037	+	0.170375i
$236$	13.4784	+	22.9652i	0.877367	+	1.49491i
$237$	0.398026	+	0.960920i	0.0258546	+	0.0624184i
$238$	13.2070	+	22.1549i	0.856082	+	1.43609i
$239$	9.57247			0.619192			0.309596	−	0.950868i	$-0.399806\pi$
$239$	9.57247			0.619192			0.309596	+	0.950868i	$0.399806\pi$
$240$	0.490010	+	0.123830i	0.0316300	+	0.00799322i
$241$	−2.51104	+	4.34925i	−0.161750	+	0.280160i	−0.935497	−	0.353336i	$-0.885047\pi$
$241$	−2.51104	+	4.34925i	−0.161750	+	0.280160i	0.773746	+	0.633496i	$0.218381\pi$
$242$	−3.61895	+	1.80075i	−0.232635	+	0.115756i
$243$	3.50804	+	2.69181i	0.225041	+	0.172680i
$244$	15.5453	−	15.7688i	0.995187	−	1.00949i
$245$	3.69310	−	3.84995i	0.235944	−	0.245964i
$246$	0.477737	−	2.44735i	0.0304594	−	0.156037i
$247$	1.51827	−	5.66624i	0.0966049	−	0.360534i
$248$	0.707003	+	9.26595i	0.0448947	+	0.588388i
$249$	1.09432	−	0.293223i	0.0693499	−	0.0185823i
$250$	−9.12109	−	4.45764i	−0.576868	−	0.281926i
$251$	−3.85388	−	1.59633i	−0.243255	−	0.100759i	0.257725	−	0.966218i	$-0.417027\pi$
$251$	−3.85388	−	1.59633i	−0.243255	−	0.100759i	−0.500980	+	0.865459i	$0.667027\pi$
$252$	−15.7110	−	0.753429i	−0.989700	−	0.0474616i
$253$	8.98365	+	21.6885i	0.564797	+	1.36354i
$254$	9.35859	−	8.26652i	0.587210	−	0.518688i
$255$	−0.435503	+	0.754313i	−0.0272722	+	0.0472369i
$256$	14.0791	+	7.60128i	0.879942	+	0.475080i
$257$	−8.95509	+	5.17022i	−0.558603	+	0.322510i	−0.752585	−	0.658495i	$-0.771193\pi$
$257$	−8.95509	+	5.17022i	−0.558603	+	0.322510i	0.193981	+	0.981005i	$0.437860\pi$
$258$	−0.269950	−	1.33227i	−0.0168064	−	0.0829436i
$259$	−22.4328	+	11.3540i	−1.39391	+	0.705505i
$260$	−6.41913	+	2.71271i	−0.398097	+	0.168235i
$261$	0.485359	+	3.68666i	0.0300429	+	0.228199i
$262$	−6.63315	+	0.458534i	−0.409798	+	0.0283283i
$263$	−6.35310	−	23.7101i	−0.391749	−	1.46203i	−0.827248	−	0.561837i	$-0.810095\pi$
$263$	−6.35310	−	23.7101i	−0.391749	−	1.46203i	0.435499	−	0.900189i	$-0.356572\pi$
$264$	0.755282	−	1.57381i	0.0464844	−	0.0968611i
$265$	−1.43614	−	1.43614i	−0.0882215	−	0.0882215i
$266$	−4.40930	+	1.89895i	−0.270352	+	0.116432i
$267$	−1.78511	−	0.739418i	−0.109247	−	0.0452516i
$268$	−18.0009	−	4.68592i	−1.09958	−	0.286238i
$269$	27.9949	+	3.68560i	1.70688	+	0.224715i	0.919869	−	0.392225i	$-0.128295\pi$
$269$	27.9949	+	3.68560i	1.70688	+	0.224715i	0.787010	+	0.616940i	$0.211628\pi$
$270$	−0.475438	−	0.955483i	−0.0289342	−	0.0581488i
$271$	−13.7220	+	7.92238i	−0.833550	+	0.481250i	−0.855066	−	0.518518i	$-0.826484\pi$
$271$	−13.7220	+	7.92238i	−0.833550	+	0.481250i	0.0215168	+	0.999768i	$0.493150\pi$
$272$	−19.2172	+	19.7737i	−1.16522	+	1.19896i
$273$	−1.65578	+	1.13143i	−0.100213	+	0.0684773i
$274$	1.70663	−	2.57398i	0.103101	−	0.155500i
$275$	−10.0148	+	13.0515i	−0.603914	+	0.787036i
$276$	−1.81825	−	1.03254i	−0.109446	−	0.0621514i
$277$	1.71019	+	2.22877i	0.102756	+	0.133914i	0.841901	−	0.539633i	$-0.181437\pi$
$277$	1.71019	+	2.22877i	0.102756	+	0.133914i	−0.739145	+	0.673546i	$0.764770\pi$
$278$	−17.3050	+	5.94321i	−1.03789	+	0.356450i
$279$	6.90580	−	6.90580i	0.413440	−	0.413440i
$280$	4.99822	+	2.74678i	0.298701	+	0.164152i
$281$	−13.2850	−	13.2850i	−0.792516	−	0.792516i	0.189387	−	0.981903i	$-0.439350\pi$
$281$	−13.2850	−	13.2850i	−0.792516	−	0.792516i	−0.981903	+	0.189387i	$0.939350\pi$
$282$	−1.18585	−	0.579546i	−0.0706164	−	0.0345115i
$283$	−0.240509	+	0.184549i	−0.0142968	+	0.0109703i	−0.615885	−	0.787836i	$-0.711201\pi$
$283$	−0.240509	+	0.184549i	−0.0142968	+	0.0109703i	0.601588	+	0.798806i	$0.294535\pi$
$284$	−9.23870	−	11.8639i	−0.548216	−	0.703990i
$285$	−0.128619	−	0.0986931i	−0.00761875	−	0.00584608i
$286$	4.77994	+	23.5902i	0.282644	+	1.39492i
$287$	12.1821	−	25.3641i	0.719084	−	1.49719i
$288$	−3.57413	−	16.4308i	−0.210608	−	0.968196i
$289$	−15.2595	−	26.4302i	−0.897616	−	1.55472i
$290$	0.428836	−	1.27828i	0.0251821	−	0.0750630i
$291$	0.0198862	−	0.151051i	0.00116575	−	0.00885476i
$292$	1.41907	+	10.2151i	0.0830447	+	0.597792i
$293$	2.40867	−	5.81504i	0.140716	−	0.339718i	−0.837773	−	0.546019i	$-0.816143\pi$
$293$	2.40867	−	5.81504i	0.140716	−	0.339718i	0.978489	+	0.206301i	$0.0661426\pi$
$294$	1.56653	+	0.489551i	0.0913618	+	0.0285512i
$295$	−7.17507	+	7.17507i	−0.417749	+	0.417749i
$296$	−17.9375	−	20.0174i	−1.04259	−	1.16349i
$297$	−3.56053	+	0.954042i	−0.206603	+	0.0553591i
$298$	4.07141	+	3.54491i	0.235850	+	0.205351i
$299$	28.5842	−	3.76319i	1.65307	−	0.217631i
$300$	−0.0104562	−	1.46527i	−0.000603689	−	0.0845975i
$301$	0.844071	−	15.3160i	0.0486515	−	0.882801i
$302$	11.8631	+	7.86560i	0.682645	+	0.452614i
$303$	0.430356	+	0.745399i	0.0247233	+	0.0428221i
$304$	−3.18214	−	4.02673i	−0.182508	−	0.230949i
$305$	7.30743	+	4.21894i	0.418422	+	0.241576i
$306$	28.9228	+	1.79209i	1.65341	+	0.102447i
$307$	−23.6025	+	9.77646i	−1.34706	+	0.557972i	−0.935474	−	0.353397i	$-0.885027\pi$
$307$	−23.6025	+	9.77646i	−1.34706	+	0.557972i	−0.411590	+	0.911369i	$0.635027\pi$
$308$	12.7265	−	15.0355i	0.725161	−	0.856729i
$309$	0.769518	−	1.85778i	0.0437763	−	0.105685i
$310$	−3.34917	+	1.15023i	−0.190220	+	0.0653288i
$311$	0.184071	+	0.686962i	0.0104377	+	0.0389540i	0.970948	−	0.239289i	$-0.0769145\pi$
$311$	0.184071	+	0.686962i	0.0104377	+	0.0389540i	−0.960511	+	0.278243i	$0.910248\pi$
$312$	−1.62690	−	1.39624i	−0.0921053	−	0.0790462i
$313$	6.54934	+	1.75489i	0.370191	+	0.0991923i	0.439118	−	0.898429i	$-0.355291\pi$
$313$	6.54934	+	1.75489i	0.370191	+	0.0991923i	−0.0689272	+	0.997622i	$0.521958\pi$
$314$	6.39346	−	4.30505i	0.360804	−	0.242948i
$315$	−1.23037	−	5.86614i	−0.0693237	−	0.330520i
$316$	−11.5574	+	4.88415i	−0.650156	+	0.274755i
$317$	10.0933	−	13.1539i	0.566897	−	0.738794i	−0.418659	−	0.908143i	$-0.637500\pi$
$317$	10.0933	−	13.1539i	0.566897	−	0.738794i	0.985556	+	0.169349i	$0.0541665\pi$
$318$	0.198731	−	0.592379i	0.0111443	−	0.0332190i
$319$	−4.03298	−	2.32844i	−0.225804	−	0.130368i
$320$	−1.45160	+	5.92170i	−0.0811468	+	0.331033i
$321$		−	1.11016i		−	0.0619630i
$322$	−16.9156	−	16.4497i	−0.942671	−	0.916706i
$323$	8.17148	−	3.38474i	0.454674	−	0.188332i
$324$	−10.5581	+	13.9647i	−0.586559	+	0.775819i
$325$	12.2995	+	16.0290i	0.682252	+	0.889128i
$326$	−2.16500	−	31.3189i	−0.119908	−	1.73459i
$327$	0.164222	−	0.612887i	0.00908152	−	0.0338927i
$328$	29.5638	+	5.55232i	1.63239	+	0.306576i
$329$	−11.2994	−	9.70341i	−0.622958	−	0.534966i
$330$	0.652884	+	0.127447i	0.0359401	+	0.00701572i
$331$	2.94098	+	22.3390i	0.161651	+	1.22786i	0.859319	+	0.511440i	$0.170888\pi$
$331$	2.94098	+	22.3390i	0.161651	+	1.22786i	−0.697668	+	0.716421i	$0.745779\pi$
$332$	3.63139	+	13.1757i	0.199298	+	0.723111i
$333$	−3.68706	+	28.0060i	−0.202050	+	1.53472i
$334$	0.282453	−	4.55857i	0.0154552	−	0.249434i
$335$		−	7.08811i		−	0.387265i
$336$	−0.0715362	+	1.75310i	−0.00390262	+	0.0956396i
$337$			0.915967i			0.0498959i	0.999689	+	0.0249479i	$0.00794200\pi$
$337$			0.915967i			0.0498959i	−0.999689	+	0.0249479i	$0.992058\pi$
$338$	11.1545	+	0.691141i	0.606722	+	0.0375931i
$339$	−0.117616	+	0.893382i	−0.00638802	+	0.0485219i
$340$	−9.13685	−	5.18859i	−0.495515	−	0.281391i
$341$	1.59646	+	12.1263i	0.0864531	+	0.656676i
$342$	−1.03339	+	5.29383i	−0.0558792	+	0.286258i
$343$	15.7124	+	9.80415i	0.848388	+	0.529374i
$344$	16.0481	−	3.37113i	0.865256	−	0.181759i
$345$	0.206226	−	0.769644i	0.0111028	−	0.0414362i
$346$	−25.3493	+	1.75233i	−1.36278	+	0.0942060i
$347$	−5.88778	−	7.67310i	−0.316072	−	0.411914i	0.608117	−	0.793847i	$-0.291925\pi$
$347$	−5.88778	−	7.67310i	−0.316072	−	0.411914i	−0.924190	+	0.381934i	$0.875258\pi$
$348$	0.410847	−	0.0570744i	0.0220237	−	0.00305951i
$349$	11.5729	−	4.79365i	0.619482	−	0.256598i	−0.0507946	−	0.998709i	$-0.516175\pi$
$349$	11.5729	−	4.79365i	0.619482	−	0.256598i	0.670277	+	0.742111i	$0.266175\pi$
$350$	4.05615	−	16.0298i	0.216810	−	0.856827i
$351$			4.52706i			0.241636i
$352$	19.0500	+	8.97558i	1.01537	+	0.478400i
$353$	−11.5041	−	6.64190i	−0.612302	−	0.353513i	0.161564	−	0.986862i	$-0.448346\pi$
$353$	−11.5041	−	6.64190i	−0.612302	−	0.353513i	−0.773866	+	0.633350i	$0.781680\pi$
$354$	−2.95957	−	0.992877i	−0.157299	−	0.0527708i
$355$	3.48819	−	4.54589i	0.185134	−	0.241271i
$356$	8.76601	−	21.5977i	0.464598	−	1.14467i
$357$	−2.87320	−	0.942127i	−0.152066	−	0.0498627i
$358$	−3.98515	−	5.91838i	−0.210622	−	0.312796i
$359$	20.5191	+	5.49807i	1.08296	+	0.290177i	0.755806	−	0.654796i	$-0.227245\pi$
$359$	20.5191	+	5.49807i	1.08296	+	0.290177i	0.327149	+	0.944973i	$0.393912\pi$
$360$	5.71616	−	2.89537i	0.301268	−	0.152599i
$361$	−4.49147	−	16.7624i	−0.236393	−	0.882232i
$362$	−5.21402	−	15.1818i	−0.274043	−	0.797939i
$363$	0.181344	−	0.437803i	0.00951809	−	0.0229787i
$364$	−13.7911	−	19.8765i	−0.722851	−	1.04181i
$365$	−3.63083	+	1.50394i	−0.190046	+	0.0787198i
$366$	−0.160534	+	2.59089i	−0.00839124	+	0.135428i
$367$	−11.2214	−	6.47865i	−0.585750	−	0.338183i	0.177665	−	0.984091i	$-0.443146\pi$
$367$	−11.2214	−	6.47865i	−0.585750	−	0.338183i	−0.763415	+	0.645908i	$0.776479\pi$
$368$	12.2991	−	22.0226i	0.641135	−	1.14801i
$369$	−15.8065	−	27.3777i	−0.822854	−	1.42523i
$370$	5.65995	−	8.53650i	0.294247	−	0.443791i
$371$	3.85602	−	5.90286i	0.200194	−	0.306461i
$372$	−0.775813	−	0.764819i	−0.0402240	−	0.0396540i
$373$	3.05321	−	0.401963i	0.158089	−	0.0208129i	−0.0510660	−	0.998695i	$-0.516262\pi$
$373$	3.05321	−	0.401963i	0.158089	−	0.0208129i	0.209155	+	0.977882i	$0.432929\pi$
$374$	−23.8310	+	27.3705i	−1.23227	+	1.41529i
$375$	1.14959	−	0.308032i	0.0593646	−	0.0159067i
$376$	6.88906	−	14.3550i	0.355276	−	0.740300i
$377$	−4.04413	+	4.04413i	−0.208283	+	0.208283i
$378$	2.90754	−	2.29624i	0.149548	−	0.118106i
$379$	−13.4966	+	32.5837i	−0.693275	+	1.67371i	0.0448006	+	0.998996i	$0.485735\pi$
$379$	−13.4966	+	32.5837i	−0.693275	+	1.67371i	−0.738076	+	0.674718i	$0.764265\pi$
$380$	1.17947	−	1.56005i	0.0605058	−	0.0800287i
$381$	−0.191069	+	1.45132i	−0.00978878	+	0.0743532i
$382$	−8.21130	−	2.75473i	−0.420127	−	0.140944i
$383$	15.8005	+	27.3673i	0.807370	+	1.39841i	0.914680	+	0.404179i	$0.132443\pi$
$383$	15.8005	+	27.3673i	0.807370	+	1.39841i	−0.107310	+	0.994226i	$0.534224\pi$
$384$	−1.82995	+	0.411760i	−0.0933843	+	0.0210125i
$385$	6.76643	+	3.24983i	0.344849	+	0.165627i
$386$	−22.5367	+	4.56648i	−1.14709	+	0.232428i
$387$	−13.6724	−	10.4912i	−0.695009	−	0.533299i
$388$	1.82386	+	0.226887i	0.0925923	+	0.0115184i
$389$	−14.9420	+	11.4654i	−0.757589	+	0.581318i	−0.913685	−	0.406424i	$-0.866776\pi$
$389$	−14.9420	+	11.4654i	−0.757589	+	0.581318i	0.156096	+	0.987742i	$0.450109\pi$
$390$	0.358716	−	0.733995i	0.0181643	−	0.0371673i
$391$	30.7381	+	30.7381i	1.55449	+	1.55449i
$392$	−5.77066	+	18.9394i	−0.291462	+	0.956582i
$393$	0.551169	−	0.551169i	0.0278028	−	0.0278028i
$394$	−3.58141	−	10.4281i	−0.180429	−	0.525361i
$395$	−2.91063	−	3.79321i	−0.146450	−	0.190857i
$396$	−5.88042	−	21.3358i	−0.295502	−	1.07217i
$397$	−16.0021	+	20.8544i	−0.803124	+	1.04665i	0.194710	+	0.980861i	$0.437624\pi$
$397$	−16.0021	+	20.8544i	−0.803124	+	1.04665i	−0.997833	+	0.0657904i	$0.979043\pi$
$398$	4.07716	+	2.70328i	0.204370	+	0.135503i
$399$	0.243663	−	0.507328i	0.0121984	−	0.0253982i
$400$	17.6748	−	0.252269i	0.883742	−	0.0126134i
$401$	−12.2322	+	7.06227i	−0.610847	+	0.352673i	−0.773297	−	0.634044i	$-0.781394\pi$
$401$	−12.2322	+	7.06227i	−0.610847	+	0.352673i	0.162450	+	0.986717i	$0.448060\pi$
$402$	1.95227	−	0.971429i	0.0973704	−	0.0484505i
$403$	14.8927	+	1.96066i	0.741858	+	0.0976674i
$404$	−8.95479	+	5.25560i	−0.445517	+	0.261476i
$405$	−6.16338	−	2.55296i	−0.306261	−	0.126857i
$406$	4.64867	+	0.546091i	0.230710	+	0.0271021i
$407$	−25.0149	−	25.0149i	−1.23994	−	1.23994i
$408$	0.176878	−	3.22765i	0.00875676	−	0.159793i
$409$	−7.90351	−	29.4963i	−0.390803	−	1.45850i	−0.828812	−	0.559527i	$-0.810983\pi$
$409$	−7.90351	−	29.4963i	−0.390803	−	1.45850i	0.438009	−	0.898971i	$-0.355684\pi$
$410$	0.790499	+	11.4354i	0.0390400	+	0.564752i
$411$	0.0472574	+	0.358956i	0.00233104	+	0.0177060i
$412$	22.4769	+	9.12286i	1.10736	+	0.449451i
$413$	−29.4911	−	19.2650i	−1.45116	−	0.947967i
$414$	−25.9813	+	5.26443i	−1.27691	+	0.258733i
$415$	−4.51025	+	2.60400i	−0.221400	+	0.127825i
$416$	16.7029	−	19.7457i	0.818927	−	0.968114i
$417$	1.07250	−	1.85763i	0.0525206	−	0.0909684i
$418$	−4.47194	−	5.06271i	−0.218730	−	0.247625i
$419$	−1.09590	−	2.64573i	−0.0535381	−	0.129252i	0.894847	−	0.446372i	$-0.147284\pi$
$419$	−1.09590	−	2.64573i	−0.0535381	−	0.129252i	−0.948385	+	0.317120i	$0.897284\pi$
$420$	−0.653366	+	0.141913i	−0.0318810	+	0.00692464i
$421$	−10.0359	−	4.15701i	−0.489120	−	0.202600i	0.124473	−	0.992223i	$-0.460276\pi$
$421$	−10.0359	−	4.15701i	−0.489120	−	0.202600i	−0.613592	+	0.789623i	$0.710276\pi$
$422$	−8.43343	+	17.2562i	−0.410533	+	0.840021i
$423$	−16.1634	+	4.33096i	−0.785890	+	0.210579i
$424$	7.16304	+	2.34632i	0.347868	+	0.113948i
$425$	−7.88441	+	29.4250i	−0.382450	+	1.42732i
$426$	1.73013	+	0.337731i	0.0838250	+	0.0163631i
$427$	−9.12689	+	27.8342i	−0.441681	+	1.34699i
$428$	13.3920	−	0.0955653i	0.647326	−	0.00461932i
$429$	−2.23862	−	1.71775i	−0.108081	−	0.0829338i
$430$	2.78376	+	5.59451i	0.134245	+	0.269791i
$431$	−8.83029	+	15.2945i	−0.425340	+	0.736711i	−0.996452	−	0.0841614i	$-0.973179\pi$
$431$	−8.83029	+	15.2945i	−0.425340	+	0.736711i	0.571112	+	0.820872i	$0.306512\pi$
$432$	3.17636	+	2.36606i	0.152823	+	0.113837i
$433$	5.56633			0.267501			0.133750	−	0.991015i	$-0.457298\pi$
$433$	5.56633			0.267501			0.133750	+	0.991015i	$0.457298\pi$
$434$	−6.29471	−	10.5595i	−0.302156	−	0.506871i
$435$	0.0604879	+	0.146031i	0.00290017	+	0.00700163i
$436$	7.40746	+	1.92828i	0.354753	+	0.0923477i
$437$	−6.41915	+	4.92559i	−0.307070	+	0.235623i
$438$	−0.911835	−	0.793920i	−0.0435692	−	0.0379350i
$439$	30.9188	+	8.28467i	1.47567	+	0.395406i	0.904873	−	0.425683i	$-0.139966\pi$
$439$	30.9188	+	8.28467i	1.47567	+	0.395406i	0.570801	+	0.821088i	$0.306633\pi$
$440$	−1.48120	+	7.88679i	−0.0706137	+	0.375988i
$441$	19.0540	−	8.36064i	0.907334	−	0.398126i
$442$	24.8941	+	36.9704i	1.18409	+	1.75850i
$443$	−10.1562	+	1.33709i	−0.482537	+	0.0635272i	−0.367871	−	0.929877i	$-0.619913\pi$
$443$	−10.1562	+	1.33709i	−0.482537	+	0.0635272i	−0.114666	+	0.993404i	$0.536580\pi$
$444$	3.12690	+	0.388985i	0.148396	+	0.0184604i
$445$	8.80617	+	1.15935i	0.417453	+	0.0549587i
$446$	−16.9376	−	19.1752i	−0.802018	−	0.907970i
$447$	−0.632863			−0.0299334
$448$	−21.1540	−	0.712038i	−0.999434	−	0.0336406i
$449$	14.2000			0.670138			0.335069	−	0.942194i	$-0.391240\pi$
$449$	14.2000			0.670138			0.335069	+	0.942194i	$0.391240\pi$
$450$	−12.2985	−	13.9232i	−0.579757	−	0.656348i
$451$	39.2523	+	5.16767i	1.84832	+	0.243336i
$452$	−10.7871	−	1.34191i	−0.507382	−	0.0631182i
$453$	−1.65437	+	0.217803i	−0.0777293	+	0.0102333i
$454$	13.6474	+	20.2678i	0.640503	+	0.951215i
$455$	6.00603	−	6.99390i	0.281567	−	0.327879i
$456$	0.591329	+	0.111057i	0.0276915	+	0.00520070i
$457$	−4.32849	−	1.15982i	−0.202478	−	0.0542539i	0.156154	−	0.987733i	$-0.450090\pi$
$457$	−4.32849	−	1.15982i	−0.202478	−	0.0542539i	−0.358633	+	0.933479i	$0.616757\pi$
$458$	9.83809	+	8.56587i	0.459704	+	0.400257i
$459$	−5.41523	+	4.15525i	−0.252761	+	0.193950i
$460$	9.30206	+	2.42147i	0.433711	+	0.112902i
$461$	15.0926	+	36.4369i	0.702934	+	1.69703i	0.716943	+	0.697131i	$0.245541\pi$
$461$	15.0926	+	36.4369i	0.702934	+	1.69703i	−0.0140091	+	0.999902i	$0.504459\pi$
$462$	0.0322439	+	2.30906i	0.00150012	+	0.107427i
$463$	14.3306			0.666001			0.333001	−	0.942927i	$-0.391939\pi$
$463$	14.3306			0.666001			0.333001	+	0.942927i	$0.391939\pi$
$464$	0.723862	+	4.95118i	0.0336045	+	0.229853i
$465$	0.207569	−	0.359520i	0.00962579	−	0.0166724i
$466$	−2.02609	−	4.07181i	−0.0938568	−	0.188623i
$467$	11.2826	+	8.65746i	0.522097	+	0.400619i	0.835911	−	0.548865i	$-0.184940\pi$
$467$	11.2826	+	8.65746i	0.522097	+	0.400619i	−0.313813	+	0.949485i	$0.601607\pi$
$468$	−27.1795	+	0.193953i	−1.25637	+	0.00896550i
$469$	24.0826	−	5.05112i	1.11203	−	0.233239i
$470$	5.95507	+	1.16246i	0.274687	+	0.0536205i
$471$	−0.233867	+	0.872805i	−0.0107760	+	0.0402167i
$472$	11.7224	−	35.7871i	0.539568	−	1.64724i
$473$	20.8475	−	5.58607i	0.958569	−	0.256848i
$474$	0.645857	−	1.32153i	0.0296652	−	0.0607001i
$475$	−5.23851	−	2.16986i	−0.240359	−	0.0995600i
$476$	11.1177	−	34.7409i	0.509577	−	1.59235i
$477$	−3.03143	−	7.31852i	−0.138800	−	0.335092i
$478$	−8.96217	−	10.1461i	−0.409920	−	0.464073i
$479$	−11.1648	+	19.3380i	−0.510133	+	0.883576i	0.489798	+	0.871836i	$0.337070\pi$
$479$	−11.1648	+	19.3380i	−0.510133	+	0.883576i	−0.999931	+	0.0117402i	$0.996263\pi$
$480$	−0.327517	−	0.635311i	−0.0149490	−	0.0289978i
$481$	−37.6261	+	21.7234i	−1.71560	+	0.990503i
$482$	6.96084	−	1.41043i	0.317058	−	0.0642435i
$483$	2.76190	+	0.152210i	0.125671	+	0.00692577i
$484$	5.29688	+	2.14989i	0.240767	+	0.0977221i
$485$	0.0914157	+	0.694371i	0.00415097	+	0.0315298i
$486$	−0.431249	−	6.23846i	−0.0195619	−	0.282982i
$487$	−2.14340	−	7.99926i	−0.0971266	−	0.362481i	0.900207	−	0.435463i	$-0.143415\pi$
$487$	−2.14340	−	7.99926i	−0.0971266	−	0.362481i	−0.997333	+	0.0729815i	$0.976749\pi$
$488$	−31.2680	−	1.71351i	−1.41543	−	0.0775669i
$489$	2.60238	+	2.60238i	0.117684	+	0.117684i
$490$	−7.53832	−	0.309935i	−0.340546	−	0.0140014i
$491$	3.23599	+	1.34039i	0.146038	+	0.0604910i	0.454505	−	0.890744i	$-0.349816\pi$
$491$	3.23599	+	1.34039i	0.146038	+	0.0604910i	−0.308467	+	0.951235i	$0.599816\pi$
$492$	−3.04129	+	1.78495i	−0.137112	+	0.0804717i
$493$	−8.54955	−	1.12557i	−0.385052	−	0.0506931i
$494$	−7.42728	+	3.69573i	−0.334169	+	0.166279i
$495$	7.30360	−	4.21674i	0.328272	−	0.189528i
$496$	9.15931	−	9.42456i	0.411265	−	0.423175i
$497$	17.9309	+	8.61198i	0.804310	+	0.386300i
$498$	−1.33535	−	0.885376i	−0.0598384	−	0.0396747i
$499$	−1.59756	+	2.08198i	−0.0715165	+	0.0932021i	−0.827742	−	0.561109i	$-0.810375\pi$
$499$	−1.59756	+	2.08198i	−0.0715165	+	0.0932021i	0.756225	+	0.654311i	$0.227041\pi$
$500$	3.81479	+	13.8411i	0.170602	+	0.618994i
$501$	0.325951	+	0.424787i	0.0145624	+	0.0189781i
$502$	1.91618	+	5.57939i	0.0855231	+	0.249021i
$503$	−6.94204	+	6.94204i	−0.309530	+	0.309530i	−0.844727	−	0.535197i	$-0.820237\pi$
$503$	−6.94204	+	6.94204i	−0.309530	+	0.309530i	0.535197	+	0.844727i	$0.320237\pi$
$504$	13.9107	+	17.3579i	0.619634	+	0.773184i
$505$	−2.79777	−	2.79777i	−0.124499	−	0.124499i
$506$	14.5773	−	29.8277i	0.648041	−	1.32600i
$507$	−1.03942	+	0.797576i	−0.0461623	+	0.0354216i
$508$	−17.5238	−	2.17996i	−0.777495	−	0.0967200i
$509$	14.7887	+	11.3478i	0.655499	+	0.502982i	0.882134	−	0.470998i	$-0.156106\pi$
$509$	14.7887	+	11.3478i	0.655499	+	0.502982i	−0.226636	+	0.973980i	$0.572773\pi$
$510$	1.20725	−	0.244619i	0.0534581	−	0.0108319i
$511$	−7.69718	−	11.2644i	−0.340503	−	0.498307i
$512$	−5.12463	−	22.0395i	−0.226479	−	0.974016i
$513$	−0.635241	−	1.10027i	−0.0280466	−	0.0485781i
$514$	13.8642	+	4.65117i	0.611524	+	0.205154i
$515$	−1.20655	+	9.16465i	−0.0531669	+	0.403843i
$516$	−1.15937	+	1.53346i	−0.0510386	+	0.0675068i
$517$	8.01971	−	19.3613i	0.352706	−	0.851509i
$518$	33.0370	+	13.1470i	1.45156	+	0.577646i
$519$	2.10635	−	2.10635i	0.0924584	−	0.0924584i
$520$	8.88515	+	4.26405i	0.389640	+	0.186991i
$521$	7.55554	−	2.02450i	0.331014	−	0.0886950i	−0.0894842	−	0.995988i	$-0.528522\pi$
$521$	7.55554	−	2.02450i	0.331014	−	0.0886950i	0.420499	+	0.907293i	$0.361855\pi$
$522$	3.45319	−	3.96606i	0.151142	−	0.173590i
$523$	−31.4402	+	4.13918i	−1.37479	+	0.180994i	−0.781453	−	0.623964i	$-0.785521\pi$
$523$	−31.4402	+	4.13918i	−1.37479	+	0.180994i	−0.593332	+	0.804958i	$0.702188\pi$
$524$	6.69626	+	6.60137i	0.292527	+	0.288382i
$525$	0.875368	+	1.72951i	0.0382042	+	0.0754821i
$526$	−19.1829	+	28.9322i	−0.836416	+	1.26151i
$527$	11.3242	+	19.6141i	0.493291	+	0.854406i
$528$	−2.37525	+	0.672921i	−0.103370	+	0.0292851i
$529$	−14.5202	−	8.38325i	−0.631314	−	0.364489i
$530$	−0.177629	+	2.86679i	−0.00771571	+	0.124525i
$531$	−36.5639	+	15.1453i	−1.58674	+	0.657249i
$532$	6.14093	+	2.89567i	0.266243	+	0.125543i
$533$	18.6072	−	44.9218i	0.805967	−	1.94578i
$534$	0.887570	+	2.58437i	0.0384089	+	0.111836i
$535$	1.32084	+	4.92944i	0.0571049	+	0.213118i
$536$	11.8865	+	23.4669i	0.513419	+	1.01361i
$537$	0.807949	+	0.216489i	0.0348656	+	0.00934221i
$538$	−22.3036	−	33.1232i	−0.961575	−	1.42804i
$539$	−6.21976	+	25.3055i	−0.267904	+	1.08999i
$540$	−0.567618	+	1.39849i	−0.0244264	+	0.0601816i
$541$	−2.09316	+	2.72786i	−0.0899921	+	0.117280i	−0.836179	−	0.548456i	$-0.815216\pi$
$541$	−2.09316	+	2.72786i	−0.0899921	+	0.117280i	0.746187	+	0.665736i	$0.231882\pi$
$542$	21.2442	+	7.12702i	0.912519	+	0.306132i
$543$	1.62971	+	0.940914i	0.0699376	+	0.0403785i
$544$	38.9508	+	1.85585i	1.67000	+	0.0795691i
$545$			2.91679i			0.124942i
$546$	2.74945	+	0.695717i	0.117666	+	0.0297739i
$547$	21.7445	−	9.00687i	0.929728	−	0.385106i	0.134153	−	0.990961i	$-0.457169\pi$
$547$	21.7445	−	9.00687i	0.929728	−	0.385106i	0.795575	+	0.605855i	$0.207169\pi$
$548$	−4.32606	+	0.600972i	−0.184800	+	0.0256722i
$549$	20.0344	+	26.1094i	0.855048	+	1.11432i
$550$	23.2099	−	1.60445i	0.989676	−	0.0684139i
$551$	0.415422	−	1.55038i	0.0176976	−	0.0660483i
$552$	0.607908	+	2.89392i	0.0258743	+	0.123173i
$553$	10.8136	−	12.5923i	0.459843	−	0.535478i
$554$	0.761176	−	3.89935i	0.0323393	−	0.165668i
$555$	0.156727	+	1.19046i	0.00665269	+	0.0505322i
$556$	22.5011	+	12.7778i	0.954259	+	0.541900i
$557$	4.26845	−	32.4221i	0.180860	−	1.37377i	−0.624520	−	0.781009i	$-0.714705\pi$
$557$	4.26845	−	32.4221i	0.180860	−	1.37377i	0.805380	−	0.592759i	$-0.201961\pi$
$558$	−13.7852	−	0.854143i	−0.583573	−	0.0361588i
$559$		−	26.5066i		−	1.12111i
$560$	−1.76815	−	7.86941i	−0.0747182	−	0.332543i
$561$		−	4.25449i		−	0.179625i
$562$	−1.64315	+	26.5191i	−0.0693121	+	1.11864i
$563$	−2.81747	+	21.4008i	−0.118742	+	0.901936i	0.823573	+	0.567210i	$0.191977\pi$
$563$	−2.81747	+	21.4008i	−0.118742	+	0.901936i	−0.942315	+	0.334726i	$0.891356\pi$
$564$	0.495968	+	1.79951i	0.0208840	+	0.0757732i
$565$	−0.540673	−	4.10682i	−0.0227463	−	0.172775i
$566$	0.420783	+	0.0821393i	0.0176868	+	0.00345257i
$567$	4.28179	−	22.7600i	0.179818	−	0.955830i
$568$	−3.92516	+	20.8998i	−0.164696	+	0.876937i
$569$	−0.929263	+	3.46806i	−0.0389567	+	0.145389i	−0.982665	−	0.185391i	$-0.940645\pi$
$569$	−0.929263	+	3.46806i	−0.0389567	+	0.145389i	0.943708	+	0.330779i	$0.107312\pi$
$570$	0.0158114	+	0.228728i	0.000662268	+	0.00958037i
$571$	21.4934	+	28.0107i	0.899469	+	1.17221i	0.984421	+	0.175826i	$0.0562596\pi$
$571$	21.4934	+	28.0107i	0.899469	+	1.17221i	−0.0849520	+	0.996385i	$0.527074\pi$
$572$	20.5287	−	27.1526i	0.858349	−	1.13531i
$573$	0.938061	−	0.388557i	0.0391880	−	0.0162322i
$574$	−38.2895	+	10.8349i	−1.59817	+	0.452238i
$575$		−	27.8675i		−	1.16216i
$576$	−14.0692	+	19.1716i	−0.586219	+	0.798816i
$577$	−27.3948	−	15.8164i	−1.14046	−	0.658444i	−0.193915	−	0.981018i	$-0.562119\pi$
$577$	−27.3948	−	15.8164i	−1.14046	−	0.658444i	−0.946544	+	0.322574i	$0.895452\pi$
$578$	−13.7275	+	40.9190i	−0.570989	+	1.70201i
$579$	1.64104	−	2.13864i	0.0681993	−	0.0888790i
$580$	−1.75638	+	0.742243i	−0.0729296	+	0.0308200i
$581$	−12.0614	−	13.4684i	−0.500393	−	0.558763i
$582$	−0.178721	+	0.120342i	−0.00740824	+	0.00498835i
$583$	9.58258	+	2.56765i	0.396870	+	0.106341i
$584$	9.49866	−	11.0679i	0.393057	−	0.457994i
$585$	−2.68069	−	10.0045i	−0.110833	−	0.413635i
$586$	−8.41862	+	2.89128i	−0.347770	+	0.119438i
$587$	17.2902	−	41.7421i	0.713641	−	1.72288i	0.0229454	−	0.999737i	$-0.492696\pi$
$587$	17.2902	−	41.7421i	0.713641	−	1.72288i	0.690696	−	0.723145i	$-0.257304\pi$
$588$	−0.947764	−	2.11875i	−0.0390851	−	0.0873757i
$589$	−3.89469	+	1.61323i	−0.160478	+	0.0664721i
$590$	14.3227	+	0.887448i	0.589656	+	0.0365357i
$591$	1.11942	+	0.646296i	0.0460467	+	0.0265851i
$592$	−4.42320	+	37.7536i	−0.181792	+	1.55166i
$593$	7.13623	+	12.3603i	0.293050	+	0.507577i	0.974529	−	0.224260i	$-0.0719965\pi$
$593$	7.13623	+	12.3603i	0.293050	+	0.507577i	−0.681480	+	0.731837i	$0.738663\pi$
$594$	4.34474	+	2.88069i	0.178267	+	0.118196i
$595$	13.8788	+	0.764865i	0.568975	+	0.0313564i
$596$	−0.0544784	−	7.63430i	−0.00223152	−	0.312713i
$597$	−0.568582	+	0.0748553i	−0.0232705	+	0.00306362i
$598$	−30.7505	−	26.7740i	−1.25748	−	1.09487i
$599$	35.1380	−	9.41520i	1.43570	−	0.384695i	0.544675	−	0.838647i	$-0.316653\pi$
$599$	35.1380	−	9.41520i	1.43570	−	0.384695i	0.891026	+	0.453953i	$0.149986\pi$
$600$	−1.54329	+	1.38293i	−0.0630047	+	0.0564580i
$601$	−28.1564	+	28.1564i	−1.14852	+	1.14852i	−0.161678	+	0.986844i	$0.551691\pi$
$601$	−28.1564	+	28.1564i	−1.14852	+	1.14852i	−0.986844	+	0.161678i	$0.948309\pi$
$602$	−17.0241	+	13.4449i	−0.693852	+	0.547972i
$603$	10.5795	−	25.5412i	0.430831	−	1.04012i
$604$	−2.76979	−	19.9382i	−0.112701	−	0.811272i
$605$	−0.284335	+	2.15974i	−0.0115598	+	0.0878057i
$606$	0.387151	−	1.15402i	0.0157269	−	0.0468789i
$607$	−1.97544	−	3.42156i	−0.0801806	−	0.138877i	0.823147	−	0.567829i	$-0.192216\pi$
$607$	−1.97544	−	3.42156i	−0.0801806	−	0.138877i	−0.903327	+	0.428952i	$0.858883\pi$
$608$	−1.28878	+	7.14283i	−0.0522671	+	0.289680i
$609$	−0.453049	+	0.309578i	−0.0183585	+	0.0125447i
$610$	−2.36975	−	11.6953i	−0.0959484	−	0.473529i
$611$	−20.4188	−	15.6679i	−0.826056	−	0.633855i
$612$	−25.1793	−	32.3339i	−1.01781	−	1.30702i
$613$	−32.0836	+	24.6186i	−1.29584	+	0.994336i	−0.296618	+	0.954996i	$0.595859\pi$
$613$	−32.0836	+	24.6186i	−1.29584	+	0.994336i	−0.999226	+	0.0393399i	$0.987474\pi$
$614$	32.4600	+	15.8638i	1.30998	+	0.640210i
$615$	−0.950199	−	0.950199i	−0.0383157	−	0.0383157i
$616$	−27.8517	+	0.587731i	−1.12218	+	0.0236804i
$617$	−11.3927	+	11.3927i	−0.458653	+	0.458653i	−0.898213	−	0.439560i	$-0.855134\pi$
$617$	−11.3927	+	11.3927i	−0.458653	+	0.458653i	0.439560	+	0.898213i	$0.355134\pi$
$618$	−2.68957	+	0.923701i	−0.108190	+	0.0371567i
$619$	−5.26335	−	6.85933i	−0.211552	−	0.275700i	0.675510	−	0.737351i	$-0.263924\pi$
$619$	−5.26335	−	6.85933i	−0.211552	−	0.275700i	−0.887061	+	0.461652i	$0.847257\pi$
$620$	4.35480	+	2.47298i	0.174893	+	0.0993174i
$621$	3.80121	−	4.95384i	0.152537	−	0.198791i
$622$	0.555795	−	0.838266i	0.0222854	−	0.0336114i
$623$	2.33642	+	30.7461i	0.0936066	+	1.23181i
$624$	0.0432695	+	3.03162i	0.00173217	+	0.121362i
$625$	14.3975	−	8.31239i	0.575899	−	0.332496i
$626$	−4.27172	−	8.58484i	−0.170732	−	0.343119i
$627$	0.785118	+	0.103363i	0.0313546	+	0.00412791i
$628$	−10.5489	−	2.74604i	−0.420946	−	0.109579i
$629$	−60.5212	−	25.0687i	−2.41314	−	0.999555i
$630$	−5.06576	+	6.79624i	−0.201825	+	0.270769i
$631$	22.3250	+	22.3250i	0.888745	+	0.888745i	0.994403	−	0.105657i	$-0.0336947\pi$
$631$	22.3250	+	22.3250i	0.888745	+	0.888745i	−0.105657	+	0.994403i	$0.533695\pi$
$632$	15.9974	+	7.67728i	0.636343	+	0.305386i
$633$	−0.582768	−	2.17492i	−0.0231629	−	0.0864453i
$634$	−23.3919	+	1.61703i	−0.929013	+	0.0642204i
$635$	−0.878334	−	6.67161i	−0.0348556	−	0.264755i
$636$	−0.813940	+	0.343970i	−0.0322748	+	0.0136393i
$637$	28.0425	+	15.4221i	1.11108	+	0.611046i
$638$	1.30787	+	6.45466i	0.0517791	+	0.255543i
$639$	19.3544	−	11.1743i	0.765647	−	0.442047i
$640$	7.63563	−	4.00557i	0.301825	−	0.158334i
$641$	−8.31636	+	14.4044i	−0.328477	+	0.568938i	−0.982210	−	0.187787i	$-0.939869\pi$
$641$	−8.31636	+	14.4044i	−0.328477	+	0.568938i	0.653733	+	0.756725i	$0.273202\pi$
$642$	−1.17669	+	1.03938i	−0.0464402	+	0.0410210i
$643$	−18.4617	−	44.5706i	−0.728060	−	1.75769i	−0.648958	−	0.760825i	$-0.724795\pi$
$643$	−18.4617	−	44.5706i	−0.728060	−	1.75769i	−0.0791019	−	0.996867i	$-0.525205\pi$
$644$	−1.59837	+	33.3303i	−0.0629846	+	1.31340i
$645$	−0.676797	−	0.280338i	−0.0266489	−	0.0110383i
$646$	−11.2381	−	5.49225i	−0.442156	−	0.216090i
$647$	−33.0501	+	8.85575i	−1.29933	+	0.348155i	−0.841198	−	0.540727i	$-0.818149\pi$
$647$	−33.0501	+	8.85575i	−1.29933	+	0.348155i	−0.458135	+	0.888883i	$0.651482\pi$
$648$	24.6865	−	1.88361i	0.969779	−	0.0739953i
$649$	12.8282	−	47.8753i	0.503549	−	1.87927i
$650$	5.47427	−	28.0436i	0.214719	−	1.09996i
$651$	1.36942	+	0.449036i	0.0536720	+	0.0175991i
$652$	−31.1688	+	31.6169i	−1.22067	+	1.23821i
$653$	−11.2089	−	8.60087i	−0.438637	−	0.336578i	0.365719	−	0.930725i	$-0.380823\pi$
$653$	−11.2089	−	8.60087i	−0.438637	−	0.336578i	−0.804356	+	0.594147i	$0.797490\pi$
$654$	−0.803368	+	0.399747i	−0.0314142	+	0.0156313i
$655$	−1.79159	+	3.10312i	−0.0700032	+	0.121249i
$656$	−21.7938	−	36.5338i	−0.850906	−	1.42641i
$657$	−15.3280			−0.598003
$658$	0.294102	+	21.0613i	0.0114653	+	0.821057i
$659$	−9.75158	−	23.5424i	−0.379868	−	0.917081i	−0.991990	−	0.126318i	$-0.959684\pi$
$659$	−9.75158	−	23.5424i	−0.379868	−	0.917081i	0.612122	−	0.790763i	$-0.290316\pi$
$660$	−0.476174	−	0.811332i	−0.0185351	−	0.0315811i
$661$	−15.5565	+	11.9369i	−0.605076	+	0.464291i	−0.865298	−	0.501258i	$-0.832871\pi$
$661$	−15.5565	+	11.9369i	−0.605076	+	0.464291i	0.260222	+	0.965549i	$0.416204\pi$
$662$	20.9242	−	24.0319i	0.813243	−	0.934028i
$663$	−5.04703	−	1.35235i	−0.196010	−	0.0525208i
$664$	10.5654	−	16.1847i	0.410019	−	0.628087i
$665$	−0.478332	+	2.54259i	−0.0185489	+	0.0985975i
$666$	33.1364	−	22.3124i	1.28401	−	0.864589i
$667$	7.82111	−	1.02967i	0.302835	−	0.0398689i
$668$	−5.09620	+	3.96855i	−0.197178	+	0.153548i
$669$	2.97365	+	0.391489i	0.114968	+	0.0151358i
$670$	−7.51289	+	6.63620i	−0.290248	+	0.256379i
$671$	−41.2155			−1.59111
$672$	1.92514	−	1.56551i	0.0742638	−	0.0603907i
$673$	4.92340			0.189783			0.0948915	−	0.995488i	$-0.469750\pi$
$673$	4.92340			0.189783			0.0948915	+	0.995488i	$0.469750\pi$
$674$	0.970859	−	0.857568i	0.0373961	−	0.0330323i
$675$	4.33835	+	0.571155i	0.166983	+	0.0219838i
$676$	−9.71072	−	12.4700i	−0.373489	−	0.479615i
$677$	38.4690	−	5.06454i	1.47848	−	0.194646i	0.652263	−	0.757993i	$-0.273820\pi$
$677$	38.4690	−	5.06454i	1.47848	−	0.194646i	0.826220	+	0.563347i	$0.190487\pi$
$678$	1.05704	−	0.711759i	0.0405953	−	0.0273349i
$679$	−2.29405	+	0.805416i	−0.0880377	+	0.0309090i
$680$	3.05479	+	14.5422i	0.117146	+	0.557667i
$681$	−2.76687	−	0.741379i	−0.106026	−	0.0284097i
$682$	11.3583	−	13.0453i	0.434933	−	0.499531i
$683$	−6.76158	+	5.18834i	−0.258725	+	0.198526i	−0.729976	−	0.683472i	$-0.760469\pi$
$683$	−6.76158	+	5.18834i	−0.258725	+	0.198526i	0.471252	+	0.881999i	$0.343802\pi$
$684$	6.57859	−	3.86100i	0.251539	−	0.147629i
$685$	−0.636914	−	1.53765i	−0.0243352	−	0.0587504i
$686$	−4.31891	−	25.8331i	−0.164897	−	0.986311i
$687$	−1.52924			−0.0583442
$688$	−18.5981	−	13.8537i	−0.709046	−	0.528165i
$689$	6.09191	−	10.5515i	0.232083	−	0.401980i
$690$	−1.00884	+	0.501990i	−0.0384061	+	0.0191104i
$691$	−2.82843	−	2.17033i	−0.107599	−	0.0825633i	0.553561	−	0.832809i	$-0.313269\pi$
$691$	−2.82843	−	2.17033i	−0.107599	−	0.0825633i	−0.661159	+	0.750245i	$0.729935\pi$
$692$	25.5904	+	25.2278i	0.972802	+	0.959017i
$693$	19.5315	+	21.8098i	0.741939	+	0.828486i
$694$	−2.62054	+	13.4245i	−0.0994744	+	0.509587i
$695$	−2.55207	+	9.52446i	−0.0968056	+	0.361283i
$696$	−0.445147	−	0.382033i	−0.0168733	−	0.0144809i
$697$	70.8140	−	18.9746i	2.68227	−	0.718713i
$698$	−15.9160	−	7.77841i	−0.602428	−	0.294417i
$699$	0.492589	+	0.204037i	0.0186314	+	0.00771739i
$700$	−20.7879	+	10.7085i	−0.785710	+	0.404745i
$701$	4.49496	+	10.8518i	0.169772	+	0.409867i	0.985750	−	0.168217i	$-0.0538009\pi$
$701$	4.49496	+	10.8518i	0.169772	+	0.409867i	−0.815978	+	0.578083i	$0.803801\pi$
$702$	4.79835	−	4.23843i	0.181102	−	0.159969i
$703$	6.09651	−	10.5595i	0.229934	−	0.398258i
$704$	−8.32200	−	28.5950i	−0.313647	−	1.07771i
$705$	−0.616002	+	0.355649i	−0.0232000	+	0.0133945i
$706$	3.73071	+	18.4120i	0.140407	+	0.692944i
$707$	7.51196	−	11.4994i	0.282516	−	0.432481i
$708$	1.71850	+	4.06651i	0.0645852	+	0.152829i
$709$	−5.25490	−	39.9150i	−0.197352	−	1.49904i	−0.747663	−	0.664078i	$-0.768824\pi$
$709$	−5.25490	−	39.9150i	−0.197352	−	1.49904i	0.550311	−	0.834960i	$-0.314509\pi$
$710$	−8.08411	+	0.558835i	−0.303391	+	0.0209727i
$711$	−4.82650	−	18.0127i	−0.181008	−	0.675531i
$712$	−31.0991	+	10.9293i	−1.16549	+	0.409594i
$713$	−14.6504	−	14.6504i	−0.548661	−	0.548661i
$714$	1.69143	+	3.92745i	0.0633001	+	0.146981i
$715$	11.9839	+	4.96388i	0.448171	+	0.185639i
$716$	−2.54199	+	9.76502i	−0.0949985	+	0.364936i
$717$	1.57345	+	0.207148i	0.0587615	+	0.00773609i
$718$	−13.3833	−	26.8963i	−0.499460	−	1.00376i
$719$	−11.2169	+	6.47606i	−0.418319	+	0.241516i	−0.694358	−	0.719630i	$-0.744311\pi$
$719$	−11.2169	+	6.47606i	−0.418319	+	0.241516i	0.276039	+	0.961146i	$0.410978\pi$
$720$	−8.42060	−	3.34795i	−0.313817	−	0.124771i
$721$	−31.9977	+	2.43153i	−1.19165	+	0.0905548i
$722$	−13.5618	+	20.4543i	−0.504719	+	0.761231i
$723$	−0.506863	+	0.660556i	−0.0188504	+	0.0245664i
$724$	−11.2101	+	19.7404i	−0.416619	+	0.733646i
$725$	3.36533	+	4.38579i	0.124985	+	0.162884i
$726$	−0.633822	+	0.217679i	−0.0235233	+	0.00807881i
$727$	−9.58470	+	9.58470i	−0.355477	+	0.355477i	−0.862143	−	0.506666i	$-0.830878\pi$
$727$	−9.58470	+	9.58470i	−0.355477	+	0.355477i	0.506666	+	0.862143i	$0.330878\pi$
$728$	−8.15583	+	33.2268i	−0.302275	+	1.23147i
$729$	−18.0503	−	18.0503i	−0.668531	−	0.668531i
$730$	4.99341	+	2.44037i	0.184814	+	0.0903220i
$731$	31.7070	−	24.3297i	1.17273	−	0.899865i
$732$	2.89645	−	2.25554i	0.107056	−	0.0833673i
$733$	−13.1024	−	10.0538i	−0.483947	−	0.371346i	0.337782	−	0.941224i	$-0.390323\pi$
$733$	−13.1024	−	10.0538i	−0.483947	−	0.371346i	−0.821729	+	0.569879i	$0.806990\pi$
$734$	3.63901	+	17.9594i	0.134318	+	0.662895i
$735$	0.690356	−	0.552905i	0.0254642	−	0.0203942i
$736$	−34.8574	+	7.58238i	−1.28486	+	0.279490i
$737$	17.3112	+	29.9839i	0.637666	+	1.10447i
$738$	−14.2196	+	42.3859i	−0.523432	+	1.56025i
$739$	−1.75267	+	13.3128i	−0.0644729	+	0.489720i	0.928496	+	0.371343i	$0.121103\pi$
$739$	−1.75267	+	13.3128i	−0.0644729	+	0.489720i	−0.992969	+	0.118377i	$0.962231\pi$
$740$	−14.3472	+	1.99309i	−0.527412	+	0.0732676i
$741$	0.372178	−	0.898517i	0.0136723	−	0.0330078i
$742$	−9.86678	+	1.43941i	−0.362221	+	0.0528425i
$743$	−37.8565	+	37.8565i	−1.38882	+	1.38882i	−0.561018	+	0.827803i	$0.689590\pi$
$743$	−37.8565	+	37.8565i	−1.38882	+	1.38882i	−0.827803	+	0.561018i	$0.810410\pi$
$744$	−0.0843034	+	1.53836i	−0.00309071	+	0.0563991i
$745$	2.81010	−	0.752964i	0.102954	−	0.0275865i
$746$	−3.28460	−	2.85985i	−0.120258	−	0.104707i
$747$	−20.1389	+	2.65133i	−0.736842	+	0.0970071i
$748$	51.3224	−	0.366237i	1.87653	−	0.0133910i
$749$	−15.8070	+	8.00050i	−0.577576	+	0.292332i
$750$	−1.40279	−	0.930091i	−0.0512226	−	0.0339621i
$751$	−17.6776	−	30.6185i	−0.645064	−	1.11728i	−0.984287	−	0.176578i	$-0.943497\pi$
$751$	−17.6776	−	30.6185i	−0.645064	−	1.11728i	0.339222	−	0.940706i	$-0.389836\pi$
$752$	−21.6651	+	6.13783i	−0.790043	+	0.223824i
$753$	−0.598926	−	0.345790i	−0.0218261	−	0.0126013i
$754$	8.07278	+	0.500198i	0.293993	+	0.0182161i
$755$	7.08679	−	2.93544i	0.257915	−	0.106832i
$756$	−5.15602	−	0.931946i	−0.187523	−	0.0338946i
$757$	13.5015	−	32.5954i	0.490719	−	1.18470i	−0.463635	−	0.886026i	$-0.653455\pi$
$757$	13.5015	−	32.5954i	0.490719	−	1.18470i	0.954355	−	0.298675i	$-0.0965447\pi$
$758$	47.1725	−	16.2009i	1.71338	−	0.588442i
$759$	1.00732	+	3.75938i	0.0365635	+	0.136457i
$760$	−2.75781	+	0.210424i	−0.100036	+	0.00763290i
$761$	52.1715	+	13.9793i	1.89122	+	0.506750i	0.998414	+	0.0562987i	$0.0179299\pi$
$761$	52.1715	+	13.9793i	1.89122	+	0.506750i	0.892801	+	0.450451i	$0.148737\pi$
$762$	1.71718	−	1.15627i	0.0622068	−	0.0418871i
$763$	−9.91009	+	2.07856i	−0.358769	+	0.0752489i
$764$	4.76796	+	11.2825i	0.172499	+	0.408186i
$765$	9.50676	−	12.3894i	0.343718	−	0.447941i
$766$	14.2143	−	42.3699i	0.513582	−	1.53089i
$767$	−52.7161	−	30.4357i	−1.90347	−	1.09897i
$768$	2.14972	+	1.55411i	0.0775712	+	0.0560791i
$769$		−	12.5480i		−	0.452494i	−0.974070	−	0.226247i	$-0.927354\pi$
$769$		−	12.5480i		−	0.452494i	0.974070	−	0.226247i	$-0.0726457\pi$
$770$	−2.89044	−	10.2146i	−0.104164	−	0.368108i
$771$	−1.58385	+	0.656052i	−0.0570410	+	0.0236271i
$772$	25.9400	+	19.6119i	0.933600	+	0.705849i
$773$	−3.57043	−	4.65308i	−0.128420	−	0.167360i	0.724718	−	0.689045i	$-0.241970\pi$
$773$	−3.57043	−	4.65308i	−0.128420	−	0.167360i	−0.853138	+	0.521686i	$0.825303\pi$
$774$	1.68078	+	24.3142i	0.0604144	+	0.873954i
$775$	3.75787	−	14.0245i	0.134987	−	0.503777i
$776$	−1.46709	−	2.14558i	−0.0526654	−	0.0770218i
$777$	−3.93302	+	1.38084i	−0.141096	+	0.0495374i
$778$	26.1418	+	5.10304i	0.937230	+	0.182953i
$779$	1.78112	+	13.5289i	0.0638151	+	0.484724i
$780$	−1.11383	+	0.306985i	−0.0398815	+	0.0109918i
$781$	−3.65323	+	27.7490i	−0.130723	+	0.992938i
$782$	3.80184	−	61.3585i	0.135953	−	2.19418i
$783$			1.23868i			0.0442667i
$784$	25.4771	−	11.6154i	0.909897	−	0.414835i
$785$		−	4.15377i		−	0.148254i
$786$	−1.10023	−	0.0681712i	−0.0392438	−	0.00243159i
$787$	4.48023	−	34.0307i	0.159703	−	1.21306i	−0.704420	−	0.709783i	$-0.748793\pi$
$787$	4.48023	−	34.0307i	0.159703	−	1.21306i	0.864123	−	0.503280i	$-0.167874\pi$
$788$	−7.69998	+	13.5593i	−0.274301	+	0.483030i
$789$	−0.531186	−	4.03476i	−0.0189107	−	0.143641i
$790$	−1.29547	+	6.63643i	−0.0460908	+	0.236114i
$791$	13.5681	−	4.76359i	0.482424	−	0.169374i
$792$	−17.1090	+	26.2084i	−0.607941	+	0.931274i
$793$	−13.1009	+	48.8932i	−0.465227	+	1.73625i
$794$	37.0860	−	2.56367i	1.31613	−	0.0909812i
$795$	−0.204983	−	0.267140i	−0.00727001	−	0.00947447i
$796$	−0.951933	−	6.85243i	−0.0337404	−	0.242878i
$797$	24.9001	−	10.3139i	0.882006	−	0.365339i	0.104731	−	0.994501i	$-0.466602\pi$
$797$	24.9001	−	10.3139i	0.882006	−	0.365339i	0.777274	+	0.629162i	$0.216602\pi$
$798$	−0.765859	+	0.216717i	−0.0271111	+	0.00767169i
$799$		−	38.8059i		−	1.37285i
$800$	−16.8153	−	18.4979i	−0.594512	−	0.653999i
$801$	30.0017	+	17.3215i	1.06006	+	0.612024i
$802$	18.9378	+	6.35326i	0.668718	+	0.224341i
$803$	11.6860	−	15.2294i	0.412388	−	0.537435i
$804$	−2.85745	−	1.15977i	−0.100774	−	0.0409021i
$805$	−12.4448	+	2.61019i	−0.438621	+	0.0919971i
$806$	−11.8650	−	17.6208i	−0.417928	−	0.620668i
$807$	4.52182	+	1.21162i	0.159176	+	0.0426510i
$808$	13.9544	+	4.57091i	0.490915	+	0.160804i
$809$	13.8695	+	51.7619i	0.487627	+	1.81985i	0.567926	+	0.823079i	$0.307746\pi$
$809$	13.8695	+	51.7619i	0.487627	+	1.81985i	−0.0802991	+	0.996771i	$0.525588\pi$
$810$	3.06448	+	8.92293i	0.107675	+	0.313520i
$811$	−12.0724	+	29.1453i	−0.423919	+	1.02343i	0.557262	+	0.830337i	$0.311852\pi$
$811$	−12.0724	+	29.1453i	−0.423919	+	1.02343i	−0.981180	+	0.193093i	$0.938148\pi$
$812$	−3.77347	−	5.43854i	−0.132423	−	0.190855i
$813$	−2.42695	+	1.00527i	−0.0851167	+	0.0352565i
$814$	−3.09396	+	49.9340i	−0.108443	+	1.75019i
$815$	−14.6516	−	8.45911i	−0.513223	−	0.296310i
$816$	−3.58668	+	2.83439i	−0.125559	+	0.0992235i
$817$	3.71944	+	6.44226i	0.130127	+	0.225386i
$818$	−23.8643	+	35.9929i	−0.834397	+	1.25846i
$819$	32.0810	−	16.2373i	1.12100	−	0.567378i
$820$	11.3806	−	11.5442i	0.397427	−	0.403139i
$821$	−24.5651	+	3.23405i	−0.857327	+	0.112869i	−0.546359	−	0.837551i	$-0.683987\pi$
$821$	−24.5651	+	3.23405i	−0.857327	+	0.112869i	−0.310968	+	0.950420i	$0.600653\pi$
$822$	0.336223	−	0.386160i	0.0117271	−	0.0134689i
$823$	−2.05683	+	0.551127i	−0.0716967	+	0.0192111i	−0.294489	−	0.955655i	$-0.595149\pi$
$823$	−2.05683	+	0.551127i	−0.0716967	+	0.0192111i	0.222792	+	0.974866i	$0.428483\pi$
$824$	−11.3742	−	32.3651i	−0.396240	−	1.12749i
$825$	−1.92859	+	1.92859i	−0.0671447	+	0.0671447i
$826$	7.19142	+	49.2952i	0.250221	+	1.71520i
$827$	−11.4984	+	27.7596i	−0.399839	+	0.965297i	0.587865	+	0.808959i	$0.299969\pi$
$827$	−11.4984	+	27.7596i	−0.399839	+	0.965297i	−0.987704	+	0.156338i	$0.950031\pi$
$828$	29.9047	+	22.6095i	1.03926	+	0.785734i
$829$	−5.69948	+	43.2919i	−0.197951	+	1.50359i	0.547374	+	0.836888i	$0.315628\pi$
$829$	−5.69948	+	43.2919i	−0.197951	+	1.50359i	−0.745325	+	0.666701i	$0.767706\pi$
$830$	6.98275	+	2.34257i	0.242375	+	0.0813119i
$831$	0.232878	+	0.403356i	0.00807843	+	0.0139923i
$832$	−36.5670	+	0.782934i	−1.26773	+	0.0271434i
$833$	7.29158	+	47.6997i	0.252638	+	1.65270i
$834$	−2.97307	+	0.602417i	−0.102949	+	0.0208600i
$835$	−1.95272	−	1.49838i	−0.0675767	−	0.0518534i
$836$	−1.17929	+	9.47986i	−0.0407867	+	0.327868i
$837$	2.58100	−	1.98047i	0.0892125	−	0.0684552i
$838$	−1.77826	+	3.63862i	−0.0614289	+	0.125694i
$839$	24.7653	+	24.7653i	0.854993	+	0.854993i	0.990743	−	0.135750i	$-0.0433445\pi$
$839$	24.7653	+	24.7653i	0.854993	+	0.854993i	−0.135750	+	0.990743i	$0.543345\pi$
$840$	0.762127	+	0.559656i	0.0262959	+	0.0193100i
$841$	19.3996	−	19.3996i	0.668950	−	0.668950i
$842$	4.98992	+	14.5293i	0.171964	+	0.500713i
$843$	−1.89619	−	2.47117i	−0.0653084	−	0.0851115i
$844$	26.1861	−	7.21722i	0.901364	−	0.248427i
$845$	3.66641	−	4.77815i	0.126128	−	0.164373i
$846$	19.7234	+	13.0772i	0.678103	+	0.449603i
$847$	−7.54054	+	0.573012i	−0.259096	+	0.0196889i
$848$	−4.21942	−	9.78904i	−0.144895	−	0.336157i
$849$	−0.0435265	+	0.0251301i	−0.00149383	+	0.000862461i
$850$	38.5702	−	19.1921i	1.32295	−	0.658283i
$851$	59.4136	+	7.82195i	2.03667	+	0.268133i
$852$	−1.26185	−	2.15001i	−0.0432303	−	0.0736582i
$853$	−28.4368	−	11.7789i	−0.973656	−	0.403302i	−0.161584	−	0.986859i	$-0.551660\pi$
$853$	−28.4368	−	11.7789i	−0.973656	−	0.403302i	−0.812072	+	0.583557i	$0.801660\pi$
$854$	38.0473	−	16.3858i	1.30195	−	0.560709i
$855$	2.05537	+	2.05537i	0.0702920	+	0.0702920i
$856$	−12.6394	−	14.1051i	−0.432007	−	0.482101i
$857$	2.98648	+	11.1457i	0.102016	+	0.380730i	0.997990	−	0.0633778i	$-0.0201873\pi$
$857$	2.98648	+	11.1457i	0.102016	+	0.380730i	−0.895973	+	0.444108i	$0.853521\pi$
$858$	0.275198	+	3.98101i	0.00939509	+	0.135909i
$859$	2.75125	+	20.8978i	0.0938715	+	0.713025i	0.972064	+	0.234717i	$0.0754163\pi$
$859$	2.75125	+	20.8978i	0.0938715	+	0.713025i	−0.878192	+	0.478308i	$0.841250\pi$
$860$	3.32349	−	8.18841i	0.113330	−	0.279223i
$861$	2.55127	−	3.90553i	0.0869470	−	0.133100i
$862$	24.4784	−	4.95991i	0.833737	−	0.168935i
$863$	−25.2885	+	14.6003i	−0.860830	+	0.497000i	−0.864290	−	0.502994i	$-0.832232\pi$
$863$	−25.2885	+	14.6003i	−0.860830	+	0.497000i	0.00346028	+	0.999994i	$0.498899\pi$
$864$	−0.465994	−	5.58192i	−0.0158534	−	0.189901i
$865$	−6.84674	+	11.8589i	−0.232796	+	0.403214i
$866$	−5.21144	−	5.89992i	−0.177092	−	0.200487i
$867$	−1.93628	−	4.67460i	−0.0657596	−	0.158758i
$868$	−5.29890	+	16.5582i	−0.179856	+	0.562021i
$869$	21.5766	+	8.93730i	0.731935	+	0.303177i
$870$	0.0981506	−	0.200833i	0.00332762	−	0.00680888i
$871$	41.0720	−	11.0052i	1.39167	−	0.372897i
$872$	−4.89135	−	9.65671i	−0.165642	−	0.327018i
$873$	−0.706993	+	2.63854i	−0.0239281	+	0.0893009i
$874$	11.2307	+	2.19229i	0.379883	+	0.0741553i
$875$	−12.6706	−	14.1486i	−0.428344	−	0.478310i
$876$	0.0122010	+	1.70978i	0.000412234	+	0.0577682i
$877$	33.8885	+	26.0036i	1.14433	+	0.878078i	0.993872	−	0.110538i	$-0.0352574\pi$
$877$	33.8885	+	26.0036i	1.14433	+	0.878078i	0.150461	+	0.988616i	$0.451924\pi$
$878$	−20.1664	−	40.5282i	−0.680582	−	1.36776i
$879$	0.521755	−	0.903706i	0.0175984	−	0.0304812i
$880$	9.74620	−	5.81399i	0.328544	−	0.195989i
$881$	−21.7004			−0.731104			−0.365552	−	0.930791i	$-0.619120\pi$
$881$	−21.7004			−0.731104			−0.365552	+	0.930791i	$0.619120\pi$
$882$	−26.7009	−	12.3683i	−0.899065	−	0.416462i
$883$	−20.5104	−	49.5165i	−0.690230	−	1.66636i	−0.744317	−	0.667827i	$-0.767225\pi$
$883$	−20.5104	−	49.5165i	−0.690230	−	1.66636i	0.0540868	−	0.998536i	$-0.482775\pi$
$884$	15.8791	−	60.9993i	0.534071	−	2.05163i
$885$	−1.33465	+	1.02411i	−0.0448638	+	0.0344252i
$886$	10.9259	+	9.51303i	0.367064	+	0.319597i
$887$	1.58433	+	0.424519i	0.0531965	+	0.0142539i	0.285319	−	0.958433i	$-0.407900\pi$
$887$	1.58433	+	0.424519i	0.0531965	+	0.0142539i	−0.232123	+	0.972687i	$0.574567\pi$
$888$	−2.51524	−	3.67847i	−0.0844060	−	0.123441i
$889$	22.0415	−	7.73854i	0.739250	−	0.259542i
$890$	−7.01589	−	10.4194i	−0.235173	−	0.349258i
$891$	32.3072	−	4.25332i	1.08233	−	0.142492i
$892$	−4.46660	+	35.9052i	−0.149553	+	1.20220i
$893$	7.16119	+	0.942788i	0.239640	+	0.0315492i
$894$	0.592514	+	0.670789i	0.0198166	+	0.0224345i
$895$	−3.84511			−0.128528
$896$	19.0506	+	23.0884i	0.636436	+	0.771329i
$897$	4.77988			0.159596
$898$	−13.2946	−	15.0509i	−0.443647	−	0.502257i
$899$	4.07488	+	0.536468i	0.135905	+	0.0178922i
$900$	−3.24323	+	26.0711i	−0.108108	+	0.869036i
$901$	18.2132	−	2.39781i	0.606770	−	0.0798827i
$902$	−31.2724	−	46.4428i	−1.04126	−	1.54638i
$903$	0.470180	−	2.49926i	0.0156466	−	0.0831702i
$904$	8.67702	+	12.6899i	0.288593	+	0.422060i
$905$	−8.35588	−	2.23895i	−0.277759	−	0.0744253i
$906$	1.77975	+	1.54960i	0.0591283	+	0.0514821i
$907$	−17.6175	+	13.5184i	−0.584979	+	0.448870i	−0.858369	−	0.513033i	$-0.828522\pi$
$907$	−17.6175	+	13.5184i	−0.584979	+	0.448870i	0.273390	+	0.961903i	$0.411855\pi$
$908$	8.70517	−	33.4408i	0.288891	−	1.10977i
$909$	−5.90558	−	14.2573i	−0.195876	−	0.472886i
$910$	−13.0361	+	0.182037i	−0.432144	+	0.00603448i
$911$	19.3134			0.639882			0.319941	−	0.947438i	$-0.396337\pi$
$911$	19.3134			0.639882			0.319941	+	0.947438i	$0.396337\pi$
$912$	−0.435916	−	0.730743i	−0.0144346	−	0.0241973i
$913$	12.7194	−	22.0307i	0.420951	−	0.729109i
$914$	2.82320	+	5.67376i	0.0933832	+	0.187671i
$915$	1.10984	+	0.851609i	0.0366901	+	0.0281533i
$916$	−0.131641	−	18.4474i	−0.00434954	−	0.609520i
$917$	−11.8199	−	3.87576i	−0.390327	−	0.127989i
$918$	9.47424	+	1.84943i	0.312696	+	0.0610402i
$919$	−2.63372	+	9.82917i	−0.0868784	+	0.324235i	−0.995663	−	0.0930304i	$-0.970345\pi$
$919$	−2.63372	+	9.82917i	−0.0868784	+	0.324235i	0.908785	+	0.417265i	$0.137011\pi$
$920$	−6.14241	−	12.1266i	−0.202509	−	0.399802i
$921$	−4.09115	+	1.09622i	−0.134808	+	0.0361217i
$922$	24.4901	−	50.1109i	0.806537	−	1.65031i
$923$	31.7570	+	13.1542i	1.04529	+	0.432975i
$924$	2.41725	−	2.19602i	0.0795218	−	0.0722438i
$925$	16.0708	+	38.7984i	0.528406	+	1.27568i
$926$	−13.4170	−	15.1895i	−0.440909	−	0.499156i
$927$	−18.0266	+	31.2229i	−0.592070	+	1.02550i
$928$	4.57018	−	5.40275i	0.150024	−	0.177354i
$929$	−33.6366	+	19.4201i	−1.10358	+	0.637153i	−0.937159	−	0.348901i	$-0.886555\pi$
$929$	−33.6366	+	19.4201i	−1.10358	+	0.637153i	−0.166422	+	0.986055i	$0.553221\pi$
$930$	−0.575401	+	0.116590i	−0.0188681	+	0.00382314i
$931$	−8.97959	+	0.186716i	−0.294294	+	0.00611937i
$932$	−2.41892	+	5.95972i	−0.0792343	+	0.195217i
$933$	0.0153903	+	0.116901i	0.000503855	+	0.00382716i
$934$	−1.38699	−	20.0643i	−0.0453838	−	0.656523i
$935$	5.06188	+	18.8912i	0.165541	+	0.617809i
$936$	25.6522	+	28.6268i	0.838470	+	0.935695i
$937$	31.5427	+	31.5427i	1.03045	+	1.03045i	0.999521	+	0.0309321i	$0.00984755\pi$
$937$	31.5427	+	31.5427i	1.03045	+	1.03045i	0.0309321	+	0.999521i	$0.490152\pi$
$938$	−27.9010	−	20.7967i	−0.910999	−	0.679037i
$939$	1.03855	+	0.430183i	0.0338919	+	0.0140385i
$940$	−4.34326	−	7.40029i	−0.141662	−	0.241371i
$941$	13.3561	+	1.75837i	0.435398	+	0.0573212i	0.345040	−	0.938588i	$-0.387865\pi$
$941$	13.3561	+	1.75837i	0.435398	+	0.0573212i	0.0903582	+	0.995909i	$0.471199\pi$
$942$	1.14407	−	0.569275i	0.0372757	−	0.0185480i
$943$	−58.0807	+	33.5329i	−1.89137	+	1.09198i
$944$	−48.9068	+	21.0805i	−1.59178	+	0.686113i
$945$	−0.151288	−	1.99087i	−0.00492140	−	0.0647631i
$946$	−25.4392	−	16.8669i	−0.827099	−	0.548391i
$947$	−3.58091	+	4.66673i	−0.116364	+	0.151648i	−0.847904	−	0.530150i	$-0.822135\pi$
$947$	−3.58091	+	4.66673i	−0.116364	+	0.151648i	0.731540	+	0.681799i	$0.238802\pi$
$948$	−2.00541	+	0.552716i	−0.0651327	+	0.0179514i
$949$	−14.3519	−	18.7037i	−0.465882	−	0.607149i
$950$	2.60462	+	7.58396i	0.0845050	+	0.246056i
$951$	1.94371	−	1.94371i	0.0630290	−	0.0630290i
$952$	−47.2317	+	20.7420i	−1.53079	+	0.672252i
$953$	−7.07749	−	7.07749i	−0.229263	−	0.229263i	0.583122	−	0.812385i	$-0.301831\pi$
$953$	−7.07749	−	7.07749i	−0.229263	−	0.229263i	−0.812385	+	0.583122i	$0.801831\pi$
$954$	−4.91895	+	10.0650i	−0.159257	+	0.325867i
$955$	−3.70298	+	2.84139i	−0.119825	+	0.0919453i
$956$	−2.36341	+	18.9985i	−0.0764380	+	0.614456i
$957$	−0.612522	−	0.470005i	−0.0198000	−	0.0151931i
$958$	30.9499	−	6.27119i	0.999945	−	0.202613i
$959$	4.77043	−	3.25973i	0.154045	−	0.105262i
$960$	−0.366748	+	0.941950i	−0.0118367	+	0.0304013i
$961$	10.1026	+	17.4983i	0.325892	+	0.564461i
$962$	58.2524	+	19.5425i	1.87813	+	0.630076i
$963$	−2.59805	+	19.7341i	−0.0837210	+	0.635924i
$964$	−8.01200	−	6.05748i	−0.258049	−	0.195098i
$965$	−4.74220	+	11.4487i	−0.152657	+	0.368546i
$966$	−2.42448	−	3.06993i	−0.0780065	−	0.0987733i
$967$	−2.01214	+	2.01214i	−0.0647061	+	0.0647061i	−0.738719	−	0.674013i	$-0.764569\pi$
$967$	−2.01214	+	2.01214i	−0.0647061	+	0.0647061i	0.674013	+	0.738719i	$0.264569\pi$
$968$	−2.68044	−	7.62713i	−0.0861527	−	0.245145i
$969$	1.41641	−	0.379526i	0.0455016	−	0.0121921i
$970$	0.650397	−	0.746995i	0.0208830	−	0.0239846i
$971$	−31.7990	+	4.18642i	−1.02048	+	0.134349i	−0.622153	−	0.782896i	$-0.713742\pi$
$971$	−31.7990	+	4.18642i	−1.02048	+	0.134349i	−0.398325	+	0.917244i	$0.630409\pi$
$972$	−6.20856	+	6.29781i	−0.199140	+	0.202002i
$973$	−34.1790	−	1.88362i	−1.09573	−	0.0603859i
$974$	−6.47191	+	9.76111i	−0.207373	+	0.312766i
$975$	1.67482	+	2.90088i	0.0536372	+	0.0929024i
$976$	27.4582	+	34.7461i	0.878917	+	1.11219i
$977$	20.5849	+	11.8847i	0.658570	+	0.380225i	0.791732	−	0.610869i	$-0.209180\pi$
$977$	20.5849	+	11.8847i	0.658570	+	0.380225i	−0.133162	+	0.991094i	$0.542513\pi$
$978$	0.321875	−	5.19480i	0.0102924	−	0.166111i
$979$	−40.0830	+	16.6029i	−1.28106	+	0.530632i
$980$	6.72919	+	8.28025i	0.214956	+	0.264503i
$981$	−4.35352	+	10.5103i	−0.138997	+	0.335569i
$982$	−1.60896	−	4.68485i	−0.0513439	−	0.149500i
$983$	−3.40257	−	12.6986i	−0.108525	−	0.405022i	0.890196	−	0.455578i	$-0.150567\pi$
$983$	−3.40257	−	12.6986i	−0.108525	−	0.405022i	−0.998721	+	0.0505560i	$0.983901\pi$
$984$	4.73931	+	1.55241i	0.151084	+	0.0494889i
$985$	−5.73950	−	1.53789i	−0.182876	−	0.0490014i
$986$	6.81144	+	10.1157i	0.216920	+	0.322150i
$987$	−1.64733	−	1.83949i	−0.0524351	−	0.0585516i
$988$	10.8710	+	4.41228i	0.345851	+	0.140373i
$989$	−22.2567	+	29.0055i	−0.707723	+	0.922322i
$990$	−11.3074	−	3.79340i	−0.359372	−	0.120562i
$991$	7.99556	+	4.61624i	0.253987	+	0.146640i	0.621589	−	0.783344i	$-0.286488\pi$
$991$	7.99556	+	4.61624i	0.253987	+	0.146640i	−0.367601	+	0.929984i	$0.619821\pi$
$992$	−18.5647	−	0.884536i	−0.589430	−	0.0280841i
$993$			3.73554i			0.118544i
$994$	−7.65959	−	27.0684i	−0.242947	−	0.858556i
$995$	2.43562	−	1.00886i	0.0772142	−	0.0319832i
$996$	0.311776	+	2.24430i	0.00987900	+	0.0711134i
$997$	−30.2927	−	39.4782i	−0.959380	−	1.25029i	−0.968161	−	0.250327i	$-0.919462\pi$
$997$	−30.2927	−	39.4782i	−0.959380	−	1.25029i	0.00878113	−	0.999961i	$-0.497205\pi$
$998$	3.70245	−	0.255941i	0.117199	−	0.00810168i
$999$	−2.43541	+	9.08907i	−0.0770529	+	0.287565i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.be.a.59.9	yes	240
4.3	odd	2		896.2.bi.a.143.15		240
7.5	odd	6	inner	224.2.be.a.187.12	yes	240
28.19	even	6		896.2.bi.a.271.15		240
32.13	even	8		896.2.bi.a.367.15		240
32.19	odd	8	inner	224.2.be.a.115.12	yes	240
224.19	even	24	inner	224.2.be.a.19.9	✓	240
224.173	odd	24		896.2.bi.a.495.15		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.be.a.19.9	✓	240	224.19	even	24	inner
224.2.be.a.59.9	yes	240	1.1	even	1	trivial
224.2.be.a.115.12	yes	240	32.19	odd	8	inner
224.2.be.a.187.12	yes	240	7.5	odd	6	inner
896.2.bi.a.143.15		240	4.3	odd	2
896.2.bi.a.271.15		240	28.19	even	6
896.2.bi.a.367.15		240	32.13	even	8
896.2.bi.a.495.15		240	224.173	odd	24

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.be (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.936244 - 1.05993i) q^{2} +(0.164372 + 0.0216400i) q^{3} +(-0.246896 + 1.98470i) q^{4} +(-0.755608 + 0.0994777i) q^{5} +(-0.130955 - 0.194483i) q^{6} +(-0.876446 - 2.49637i) q^{7} +(2.33480 - 1.59647i) q^{8} +(-2.87123 - 0.769343i) q^{9} +(0.812872 + 0.707755i) q^{10} +(2.95339 - 2.26622i) q^{11} +(-0.0835318 + 0.320887i) q^{12} +(-1.74960 - 4.22391i) q^{13} +(-1.82540 + 3.26618i) q^{14} -0.126354 q^{15} +(-3.87808 - 0.980031i) q^{16} +(3.44670 - 5.96986i) q^{17} +(1.87272 + 3.76359i) q^{18} +(1.01793 + 0.781087i) q^{19} +(-0.0108768 - 1.52422i) q^{20} +(-0.0900419 - 0.429299i) q^{21} +(-5.16712 - 1.00865i) q^{22} +(-1.63213 + 6.09119i) q^{23} +(0.418323 - 0.211890i) q^{24} +(-4.26858 + 1.14376i) q^{25} +(-2.83899 + 5.80906i) q^{26} +(-0.914812 - 0.378928i) q^{27} +(5.17093 - 1.12314i) q^{28} +(-0.478719 - 1.15573i) q^{29} +(0.118298 + 0.133926i) q^{30} +(-1.64276 + 2.84535i) q^{31} +(2.59207 + 5.02804i) q^{32} +(0.534496 - 0.308592i) q^{33} +(-9.55457 + 1.93599i) q^{34} +(0.910582 + 1.79909i) q^{35} +(2.23581 - 5.50858i) q^{36} +(-1.24039 - 9.42166i) q^{37} +(-0.125136 - 1.81022i) q^{38} +(-0.196180 - 0.732154i) q^{39} +(-1.60538 + 1.43857i) q^{40} +(7.52016 + 7.52016i) q^{41} +(-0.370725 + 0.497366i) q^{42} +(5.35637 + 2.21868i) q^{43} +(3.76859 + 6.42113i) q^{44} +(2.24606 + 0.295699i) q^{45} +(7.98430 - 3.97290i) q^{46} +(4.87523 - 2.81471i) q^{47} +(-0.616241 - 0.245011i) q^{48} +(-5.46368 + 4.37586i) q^{49} +(5.20874 + 3.45355i) q^{50} +(0.695729 - 0.906691i) q^{51} +(8.81517 - 2.42957i) q^{52} +(1.62230 + 2.11422i) q^{53} +(0.454851 + 1.32440i) q^{54} +(-2.00617 + 2.00617i) q^{55} +(-6.03170 - 4.42929i) q^{56} +(0.150417 + 0.150417i) q^{57} +(-0.776794 + 1.58945i) q^{58} +(10.5628 - 8.10514i) q^{59} +(0.0311962 - 0.250774i) q^{60} +(-8.78360 - 6.73989i) q^{61} +(4.55390 - 0.922729i) q^{62} +(0.595914 + 7.84192i) q^{63} +(2.90255 - 7.45488i) q^{64} +(1.74220 + 3.01757i) q^{65} +(-0.827504 - 0.277611i) q^{66} +(-1.21395 + 9.22085i) q^{67} +(10.9974 + 8.31461i) q^{68} +(-0.400090 + 0.965903i) q^{69} +(1.05438 - 2.64954i) q^{70} +(-5.31630 + 5.31630i) q^{71} +(-7.93197 + 2.78758i) q^{72} +(4.98088 - 1.33462i) q^{73} +(-8.82498 + 10.1357i) q^{74} +(-0.726387 + 0.0956306i) q^{75} +(-1.80155 + 1.82744i) q^{76} +(-8.24580 - 5.38653i) q^{77} +(-0.592359 + 0.893411i) q^{78} +(3.13677 + 5.43304i) q^{79} +(3.02780 + 0.354736i) q^{80} +(7.58065 + 4.37669i) q^{81} +(0.930130 - 15.0115i) q^{82} +(6.31332 - 2.61506i) q^{83} +(0.874262 - 0.0727140i) q^{84} +(-2.01049 + 4.85374i) q^{85} +(-2.66323 - 7.75460i) q^{86} +(-0.0536781 - 0.200329i) q^{87} +(3.27762 - 10.0062i) q^{88} +(-11.2573 - 3.01639i) q^{89} +(-1.78944 - 2.65750i) q^{90} +(-9.01099 + 8.06967i) q^{91} +(-11.6862 - 4.74319i) q^{92} +(-0.331598 + 0.432147i) q^{93} +(-7.54780 - 2.53213i) q^{94} +(-0.846859 - 0.488934i) q^{95} +(0.317257 + 0.882562i) q^{96} -0.918957i q^{97} +(9.75344 + 1.69424i) q^{98} +(-10.2234 + 4.23466i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{2} - 12 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 12 q^{10} - 4 q^{11} - 12 q^{12} - 40 q^{14} - 32 q^{15} - 24 q^{16} + 16 q^{18} - 12 q^{19} - 8 q^{21} - 8 q^{22} + 4 q^{23}+ \cdots - 40 q^{99}+O(q^{100}) \) 240 * q - 4 * q^2 - 12 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 12 * q^10 - 4 * q^11 - 12 * q^12 - 40 * q^14 - 32 * q^15 - 24 * q^16 + 16 * q^18 - 12 * q^19 - 8 * q^21 - 8 * q^22 + 4 * q^23 - 12 * q^24 - 4 * q^25 - 12 * q^26 + 12 * q^28 - 16 * q^29 - 52 * q^30 - 4 * q^32 - 24 * q^33 - 32 * q^35 + 64 * q^36 - 4 * q^37 - 12 * q^38 - 4 * q^39 - 12 * q^40 - 28 * q^42 - 32 * q^43 - 52 * q^44 - 48 * q^45 - 4 * q^46 - 24 * q^47 - 40 * q^50 + 20 * q^51 + 60 * q^52 - 20 * q^53 - 12 * q^54 - 48 * q^56 - 16 * q^57 - 36 * q^58 + 84 * q^59 + 28 * q^60 - 12 * q^61 - 136 * q^64 - 8 * q^65 + 132 * q^66 + 36 * q^67 - 12 * q^68 + 28 * q^70 - 80 * q^71 - 4 * q^72 - 12 * q^73 - 20 * q^74 - 72 * q^75 - 8 * q^77 - 216 * q^78 - 8 * q^79 + 24 * q^80 + 108 * q^82 + 12 * q^84 + 24 * q^85 - 4 * q^86 - 12 * q^87 - 48 * q^88 - 12 * q^89 + 40 * q^91 - 80 * q^92 + 20 * q^93 + 60 * q^94 + 312 * q^96 - 16 * q^98 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more