LMFDB - Embedded newform 228.2.c.a.191.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [228,2,Mod(191,228)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(228, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("228.191"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	228.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.82058916609$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			191.13
Character	$\chi$	$=$	228.191
Dual form			228.2.c.a.191.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.557018 - 1.29990i) q^{2} +(1.17516 + 1.27240i) q^{3} +(-1.37946 + 1.44813i) q^{4} -3.63294i q^{5} +(0.999396 - 2.23634i) q^{6} -2.62764i q^{7} +(2.65081 + 0.986525i) q^{8} +(-0.237980 + 2.99055i) q^{9} +(-4.72245 + 2.02361i) q^{10} -0.651652 q^{11} +(-3.46369 - 0.0534317i) q^{12} +2.40746 q^{13} +(-3.41567 + 1.46364i) q^{14} +(4.62254 - 4.26930i) q^{15} +(-0.194164 - 3.99528i) q^{16} -6.69682i q^{17} +(4.01996 - 1.35644i) q^{18} +1.00000i q^{19} +(5.26097 + 5.01151i) q^{20} +(3.34340 - 3.08791i) q^{21} +(0.362981 + 0.847080i) q^{22} +4.11930 q^{23} +(1.85988 + 4.53220i) q^{24} -8.19827 q^{25} +(-1.34099 - 3.12944i) q^{26} +(-4.08482 + 3.21158i) q^{27} +(3.80517 + 3.62474i) q^{28} -0.639739i q^{29} +(-8.12449 - 3.63075i) q^{30} +9.21261i q^{31} +(-5.08530 + 2.47784i) q^{32} +(-0.765797 - 0.829159i) q^{33} +(-8.70517 + 3.73024i) q^{34} -9.54608 q^{35} +(-4.00242 - 4.46997i) q^{36} +4.79722 q^{37} +(1.29990 - 0.557018i) q^{38} +(2.82915 + 3.06324i) q^{39} +(3.58399 - 9.63022i) q^{40} +10.7118i q^{41} +(-5.87630 - 2.62606i) q^{42} +1.99033i q^{43} +(0.898929 - 0.943677i) q^{44} +(10.8645 + 0.864569i) q^{45} +(-2.29452 - 5.35466i) q^{46} -5.91398 q^{47} +(4.85541 - 4.94217i) q^{48} +0.0954894 q^{49} +(4.56658 + 10.6569i) q^{50} +(8.52100 - 7.86986i) q^{51} +(-3.32100 + 3.48631i) q^{52} +3.35009i q^{53} +(6.45004 + 3.52094i) q^{54} +2.36741i q^{55} +(2.59224 - 6.96537i) q^{56} +(-1.27240 + 1.17516i) q^{57} +(-0.831595 + 0.356346i) q^{58} -3.51525 q^{59} +(-0.194114 + 12.5834i) q^{60} +3.79587 q^{61} +(11.9754 - 5.13159i) q^{62} +(7.85809 + 0.625328i) q^{63} +(6.05354 + 5.23017i) q^{64} -8.74615i q^{65} +(-0.651258 + 1.45731i) q^{66} +11.0209i q^{67} +(9.69787 + 9.23801i) q^{68} +(4.84085 + 5.24138i) q^{69} +(5.31733 + 12.4089i) q^{70} -6.24757 q^{71} +(-3.58109 + 7.69258i) q^{72} -3.88513 q^{73} +(-2.67214 - 6.23589i) q^{74} +(-9.63431 - 10.4314i) q^{75} +(-1.44813 - 1.37946i) q^{76} +1.71231i q^{77} +(2.40600 - 5.38388i) q^{78} -13.6600i q^{79} +(-14.5146 + 0.705388i) q^{80} +(-8.88673 - 1.42338i) q^{81} +(13.9243 - 5.96669i) q^{82} +10.0360 q^{83} +(-0.140400 + 9.10134i) q^{84} -24.3291 q^{85} +(2.58722 - 1.10865i) q^{86} +(0.814002 - 0.751799i) q^{87} +(-1.72740 - 0.642871i) q^{88} +2.37053i q^{89} +(-4.92786 - 14.6043i) q^{90} -6.32593i q^{91} +(-5.68242 + 5.96528i) q^{92} +(-11.7221 + 10.8263i) q^{93} +(3.29419 + 7.68756i) q^{94} +3.63294 q^{95} +(-9.12885 - 3.55865i) q^{96} +15.2205 q^{97} +(-0.0531893 - 0.124126i) q^{98} +(0.155080 - 1.94879i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 6 q^{6} + 8 q^{10} + 4 q^{12} - 8 q^{16} + 16 q^{18} + 8 q^{21} - 12 q^{22} - 2 q^{24} - 28 q^{25} + 12 q^{28} - 12 q^{30} - 28 q^{34} - 22 q^{36} - 16 q^{37} - 12 q^{40} + 10 q^{42} + 16 q^{45}+ \cdots + 40 q^{97}+O(q^{100}) $ 36 * q - 6 * q^6 + 8 * q^10 + 4 * q^12 - 8 * q^16 + 16 * q^18 + 8 * q^21 - 12 * q^22 - 2 * q^24 - 28 * q^25 + 12 * q^28 - 12 * q^30 - 28 * q^34 - 22 * q^36 - 16 * q^37 - 12 * q^40 + 10 * q^42 + 16 * q^45 - 4 * q^46 + 32 * q^48 - 44 * q^49 - 36 * q^52 - 20 * q^54 - 4 * q^58 - 4 * q^60 + 16 * q^61 + 24 * q^64 + 24 * q^66 - 16 * q^69 + 36 * q^70 - 36 * q^72 - 8 * q^73 - 32 * q^78 - 40 * q^81 + 72 * q^82 - 20 * q^84 + 16 * q^85 - 16 * q^88 - 56 * q^90 + 8 * q^93 - 56 * q^94 + 2 * q^96 + 40 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−0.557018	−	1.29990i	−0.393871	−	0.919166i
$2$	−0.557018	−	1.29990i	−0.393871	−	0.919166i
$3$	1.17516	+	1.27240i	0.678481	+	0.734618i
$3$	1.17516	+	1.27240i	0.678481	+	0.734618i
$4$	−1.37946	+	1.44813i	−0.689731	+	0.724065i
$5$		−	3.63294i		−	1.62470i	−0.583169	−	0.812351i	$-0.698188\pi$
$5$		−	3.63294i		−	1.62470i	0.583169	−	0.812351i	$-0.301812\pi$
$6$	0.999396	−	2.23634i	0.408002	−	0.912981i
$7$		−	2.62764i		−	0.993156i	−0.867992	−	0.496578i	$-0.834590\pi$
$7$		−	2.62764i		−	0.993156i	0.867992	−	0.496578i	$-0.165410\pi$
$8$	2.65081	+	0.986525i	0.937201	+	0.348789i
$9$	−0.237980	+	2.99055i	−0.0793268	+	0.996849i
$10$	−4.72245	+	2.02361i	−1.49337	+	0.639922i
$11$	−0.651652			−0.196480			−0.0982402	−	0.995163i	$-0.531321\pi$
$11$	−0.651652			−0.196480			−0.0982402	+	0.995163i	$0.531321\pi$
$12$	−3.46369	−	0.0534317i	−0.999881	−	0.0154244i
$13$	2.40746			0.667708			0.333854	−	0.942625i	$-0.391651\pi$
$13$	2.40746			0.667708			0.333854	+	0.942625i	$0.391651\pi$
$14$	−3.41567	+	1.46364i	−0.912875	+	0.391175i
$15$	4.62254	−	4.26930i	1.19353	−	1.10233i
$16$	−0.194164	−	3.99528i	−0.0485411	−	0.998821i
$17$		−	6.69682i		−	1.62422i	−0.583507	−	0.812108i	$-0.698320\pi$
$17$		−	6.69682i		−	1.62422i	0.583507	−	0.812108i	$-0.301680\pi$
$18$	4.01996	−	1.35644i	0.947514	−	0.319715i
$19$			1.00000i			0.229416i
$19$			1.00000i			0.229416i
$20$	5.26097	+	5.01151i	1.17639	+	1.12061i
$21$	3.34340	−	3.08791i	0.729590	−	0.673838i
$22$	0.362981	+	0.847080i	0.0773879	+	0.180598i
$23$	4.11930			0.858933			0.429467	−	0.903083i	$-0.358702\pi$
$23$	4.11930			0.858933			0.429467	+	0.903083i	$0.358702\pi$
$24$	1.85988	+	4.53220i	0.379646	+	0.925132i
$25$	−8.19827			−1.63965
$26$	−1.34099	−	3.12944i	−0.262991	−	0.613734i
$27$	−4.08482	+	3.21158i	−0.786125	+	0.618068i
$28$	3.80517	+	3.62474i	0.719110	+	0.685011i
$29$		−	0.639739i		−	0.118797i	−0.998234	−	0.0593983i	$-0.981082\pi$
$29$		−	0.639739i		−	0.118797i	0.998234	−	0.0593983i	$-0.0189182\pi$
$30$	−8.12449	−	3.63075i	−1.48332	−	0.662881i
$31$			9.21261i			1.65463i	0.561735	+	0.827317i	$0.310134\pi$
$31$			9.21261i			1.65463i	−0.561735	+	0.827317i	$0.689866\pi$
$32$	−5.08530	+	2.47784i	−0.898963	+	0.438024i
$33$	−0.765797	−	0.829159i	−0.133308	−	0.144338i
$34$	−8.70517	+	3.73024i	−1.49292	+	0.639732i
$35$	−9.54608			−1.61358
$36$	−4.00242	−	4.46997i	−0.667069	−	0.744996i
$37$	4.79722			0.788658			0.394329	−	0.918969i	$-0.370977\pi$
$37$	4.79722			0.788658			0.394329	+	0.918969i	$0.370977\pi$
$38$	1.29990	−	0.557018i	0.210871	−	0.0903602i
$39$	2.82915	+	3.06324i	0.453027	+	0.490510i
$40$	3.58399	−	9.63022i	0.566678	−	1.52267i
$41$			10.7118i			1.67291i	0.548036	+	0.836455i	$0.315376\pi$
$41$			10.7118i			1.67291i	−0.548036	+	0.836455i	$0.684624\pi$
$42$	−5.87630	−	2.62606i	−0.906733	−	0.405209i
$43$			1.99033i			0.303522i	0.988417	+	0.151761i	$0.0484945\pi$
$43$			1.99033i			0.303522i	−0.988417	+	0.151761i	$0.951506\pi$
$44$	0.898929	−	0.943677i	0.135519	−	0.142265i
$45$	10.8645	+	0.864569i	1.61958	+	0.128882i
$46$	−2.29452	−	5.35466i	−0.338309	−	0.789502i
$47$	−5.91398			−0.862642			−0.431321	−	0.902198i	$-0.641952\pi$
$47$	−5.91398			−0.862642			−0.431321	+	0.902198i	$0.641952\pi$
$48$	4.85541	−	4.94217i	0.700818	−	0.713340i
$49$	0.0954894			0.0136413
$50$	4.56658	+	10.6569i	0.645812	+	1.50711i
$51$	8.52100	−	7.86986i	1.19318	−	1.10200i
$52$	−3.32100	+	3.48631i	−0.460539	+	0.483464i
$53$			3.35009i			0.460171i	0.973170	+	0.230085i	$0.0739005\pi$
$53$			3.35009i			0.460171i	−0.973170	+	0.230085i	$0.926099\pi$
$54$	6.45004	+	3.52094i	0.877739	+	0.479140i
$55$			2.36741i			0.319222i
$56$	2.59224	−	6.96537i	0.346402	−	0.930787i
$57$	−1.27240	+	1.17516i	−0.168533	+	0.155654i
$58$	−0.831595	+	0.356346i	−0.109194	+	0.0467905i
$59$	−3.51525			−0.457647			−0.228824	−	0.973468i	$-0.573488\pi$
$59$	−3.51525			−0.457647			−0.228824	+	0.973468i	$0.573488\pi$
$60$	−0.194114	+	12.5834i	−0.0250601	+	1.62451i
$61$	3.79587			0.486011			0.243006	−	0.970025i	$-0.421867\pi$
$61$	3.79587			0.486011			0.243006	+	0.970025i	$0.421867\pi$
$62$	11.9754	−	5.13159i	1.52088	−	0.651712i
$63$	7.85809	+	0.625328i	0.990026	+	0.0787839i
$64$	6.05354	+	5.23017i	0.756692	+	0.653771i
$65$		−	8.74615i		−	1.08483i
$66$	−0.651258	+	1.45731i	−0.0801643	+	0.179383i
$67$			11.0209i			1.34642i	0.739453	+	0.673208i	$0.235084\pi$
$67$			11.0209i			1.34642i	−0.739453	+	0.673208i	$0.764916\pi$
$68$	9.69787	+	9.23801i	1.17604	+	1.12027i
$69$	4.84085	+	5.24138i	0.582770	+	0.630988i
$70$	5.31733	+	12.4089i	0.635543	+	1.48315i
$71$	−6.24757			−0.741450			−0.370725	−	0.928743i	$-0.620891\pi$
$71$	−6.24757			−0.741450			−0.370725	+	0.928743i	$0.620891\pi$
$72$	−3.58109	+	7.69258i	−0.422035	+	0.906579i
$73$	−3.88513			−0.454720			−0.227360	−	0.973811i	$-0.573009\pi$
$73$	−3.88513			−0.454720			−0.227360	+	0.973811i	$0.573009\pi$
$74$	−2.67214	−	6.23589i	−0.310629	−	0.724907i
$75$	−9.63431	−	10.4314i	−1.11247	−	1.20452i
$76$	−1.44813	−	1.37946i	−0.166112	−	0.158235i
$77$			1.71231i			0.195136i
$78$	2.40600	−	5.38388i	0.272426	−	0.609605i
$79$		−	13.6600i		−	1.53687i	−0.639927	−	0.768436i	$-0.721035\pi$
$79$		−	13.6600i		−	1.53687i	0.639927	−	0.768436i	$-0.278965\pi$
$80$	−14.5146	+	0.705388i	−1.62279	+	0.0788648i
$81$	−8.88673	−	1.42338i	−0.987415	−	0.158154i
$82$	13.9243	−	5.96669i	1.53768	−	0.658910i
$83$	10.0360			1.10159			0.550795	−	0.834641i	$-0.314325\pi$
$83$	10.0360			1.10159			0.550795	+	0.834641i	$0.314325\pi$
$84$	−0.140400	+	9.10134i	−0.0153188	+	0.993038i
$85$	−24.3291			−2.63887
$86$	2.58722	−	1.10865i	0.278987	−	0.119549i
$87$	0.814002	−	0.751799i	0.0872701	−	0.0806013i
$88$	−1.72740	−	0.642871i	−0.184142	−	0.0685302i
$89$			2.37053i			0.251276i	0.992076	+	0.125638i	$0.0400977\pi$
$89$			2.37053i			0.251276i	−0.992076	+	0.125638i	$0.959902\pi$
$90$	−4.92786	−	14.6043i	−0.519442	−	1.53943i
$91$		−	6.32593i		−	0.663138i
$92$	−5.68242	+	5.96528i	−0.592433	+	0.621924i
$93$	−11.7221	+	10.8263i	−1.21552	+	1.12264i
$94$	3.29419	+	7.68756i	0.339770	+	0.792911i
$95$	3.63294			0.372732
$96$	−9.12885	−	3.55865i	−0.931710	−	0.363204i
$97$	15.2205			1.54541			0.772706	−	0.634764i	$-0.218903\pi$
$97$	15.2205			1.54541			0.772706	+	0.634764i	$0.218903\pi$
$98$	−0.0531893	−	0.124126i	−0.00537293	−	0.0125387i
$99$	0.155080	−	1.94879i	0.0155862	−	0.195861i
$100$	11.3092	−	11.8722i	1.13092	−	1.18722i
$101$			7.28728i			0.725112i	0.931962	+	0.362556i	$0.118096\pi$
$101$			7.28728i			0.725112i	−0.931962	+	0.362556i	$0.881904\pi$
$102$	−14.9763	−	6.69277i	−1.48288	−	0.662683i
$103$		−	5.07353i		−	0.499909i	−0.968258	−	0.249955i	$-0.919584\pi$
$103$		−	5.07353i		−	0.499909i	0.968258	−	0.249955i	$-0.0804157\pi$
$104$	6.38170	+	2.37502i	0.625777	+	0.232889i
$105$	−11.2182	−	12.1464i	−1.09478	−	1.18537i
$106$	4.35477	−	1.86606i	0.422973	−	0.181248i
$107$	−8.95261			−0.865481			−0.432741	−	0.901518i	$-0.642453\pi$
$107$	−8.95261			−0.865481			−0.432741	+	0.901518i	$0.642453\pi$
$108$	0.984080	−	10.3456i	0.0946932	−	0.995507i
$109$	11.4954			1.10106			0.550530	−	0.834815i	$-0.314426\pi$
$109$	11.4954			1.10106			0.550530	+	0.834815i	$0.314426\pi$
$110$	3.07739	−	1.31869i	0.293418	−	0.125732i
$111$	5.63752	+	6.10396i	0.535089	+	0.579362i
$112$	−10.4982	+	0.510195i	−0.991985	+	0.0482089i
$113$		−	11.2989i		−	1.06291i	−0.847087	−	0.531454i	$-0.821646\pi$
$113$		−	11.2989i		−	1.06291i	0.847087	−	0.531454i	$-0.178354\pi$
$114$	2.23634	+	0.999396i	0.209452	+	0.0936020i
$115$		−	14.9652i		−	1.39551i
$116$	0.926426	+	0.882497i	0.0860165	+	0.0819378i
$117$	−0.572927	+	7.19961i	−0.0529672	+	0.665604i
$118$	1.95806	+	4.56947i	0.180254	+	0.420654i
$119$	−17.5968			−1.61310
$120$	16.4652	−	6.75684i	1.50306	−	0.616812i
$121$	−10.5754			−0.961395
$122$	−2.11436	−	4.93424i	−0.191426	−	0.446725i
$123$	−13.6297	+	12.5882i	−1.22895	+	1.13504i
$124$	−13.3411	−	12.7085i	−1.19806	−	1.14125i
$125$			11.6191i			1.03925i
$126$	−3.56423	−	10.5630i	−0.317527	−	0.941029i
$127$		−	8.49379i		−	0.753702i	−0.926274	−	0.376851i	$-0.877007\pi$
$127$		−	8.49379i		−	0.753702i	0.926274	−	0.376851i	$-0.122993\pi$
$128$	3.42676	−	10.7823i	0.302885	−	0.953027i
$129$	−2.53249	+	2.33896i	−0.222973	+	0.205934i
$130$	−11.3691	+	4.87176i	−0.997135	+	0.427281i
$131$	10.0106			0.874632			0.437316	−	0.899308i	$-0.355929\pi$
$131$	10.0106			0.874632			0.437316	+	0.899308i	$0.355929\pi$
$132$	2.25712	+	0.0348189i	0.196457	+	0.00303059i
$133$	2.62764			0.227846
$134$	14.3260	−	6.13883i	1.23758	−	0.530314i
$135$	11.6675	+	14.8399i	1.00418	+	1.27722i
$136$	6.60658	−	17.7520i	0.566509	−	1.52222i
$137$		−	3.36105i		−	0.287154i	−0.989639	−	0.143577i	$-0.954140\pi$
$137$		−	3.36105i		−	0.287154i	0.989639	−	0.143577i	$-0.0458605\pi$
$138$	4.11681	−	9.21215i	0.350446	−	0.784190i
$139$			3.01614i			0.255826i	0.991785	+	0.127913i	$0.0408278\pi$
$139$			3.01614i			0.255826i	−0.991785	+	0.127913i	$0.959172\pi$
$140$	13.1685	−	13.8240i	1.11294	−	1.16834i
$141$	−6.94989	−	7.52492i	−0.585286	−	0.633712i
$142$	3.48001	+	8.12119i	0.292036	+	0.681516i
$143$	−1.56882			−0.131192
$144$	11.9943	+	0.370142i	0.999524	+	0.0308452i
$145$	−2.32414			−0.193009
$146$	2.16408	+	5.05026i	0.179101	+	0.417963i
$147$	0.112216	+	0.121500i	0.00925539	+	0.0100212i
$148$	−6.61758	+	6.94700i	−0.543962	+	0.571040i
$149$			12.3639i			1.01289i	0.862272	+	0.506445i	$0.169041\pi$
$149$			12.3639i			1.01289i	−0.862272	+	0.506445i	$0.830959\pi$
$150$	−8.19331	+	18.3341i	−0.668981	+	1.49697i
$151$		−	15.9684i		−	1.29949i	−0.760151	−	0.649747i	$-0.774875\pi$
$151$		−	15.9684i		−	1.29949i	0.760151	−	0.649747i	$-0.225125\pi$
$152$	−0.986525	+	2.65081i	−0.0800177	+	0.215009i
$153$	20.0271	+	1.59371i	1.61910	+	0.128844i
$154$	2.22582	−	0.953786i	0.179362	−	0.0768582i
$155$	33.4689			2.68829
$156$	−8.33868	−	0.128635i	−0.667629	−	0.0102990i
$157$	2.70288			0.215713			0.107857	−	0.994166i	$-0.465601\pi$
$157$	2.70288			0.215713			0.107857	+	0.994166i	$0.465601\pi$
$158$	−17.7566	+	7.60887i	−1.41264	+	0.605329i
$159$	−4.26264	+	3.93691i	−0.338049	+	0.312217i
$160$	9.00184	+	18.4746i	0.711658	+	1.46055i
$161$		−	10.8241i		−	0.853055i
$162$	3.09981	+	12.3447i	0.243544	+	0.969890i
$163$			18.8821i			1.47896i	0.673178	+	0.739480i	$0.264929\pi$
$163$			18.8821i			1.47896i	−0.673178	+	0.739480i	$0.735071\pi$
$164$	−15.5122	−	14.7766i	−1.21130	−	1.15386i
$165$	−3.01229	+	2.78210i	−0.234506	+	0.216586i
$166$	−5.59020	−	13.0457i	−0.433884	−	1.01254i
$167$	−11.3696			−0.879807			−0.439903	−	0.898045i	$-0.644987\pi$
$167$	−11.3696			−0.879807			−0.439903	+	0.898045i	$0.644987\pi$
$168$	11.9090	−	4.88710i	0.918800	−	0.377048i
$169$	−7.20416			−0.554166
$170$	13.5518	+	31.6254i	1.03937	+	2.42556i
$171$	−2.99055	−	0.237980i	−0.228693	−	0.0181988i
$172$	−2.88226	−	2.74559i	−0.219770	−	0.209349i
$173$			2.60748i			0.198243i	0.995075	+	0.0991215i	$0.0316032\pi$
$173$			2.60748i			0.198243i	−0.995075	+	0.0991215i	$0.968397\pi$
$174$	−1.43067	−	0.639353i	−0.108459	−	0.0484692i
$175$			21.5421i			1.62843i
$176$	0.126528	+	2.60353i	0.00953738	+	0.196249i
$177$	−4.13100	−	4.47279i	−0.310505	−	0.336196i
$178$	3.08144	−	1.32043i	0.230964	−	0.0989702i
$179$	−3.65952			−0.273525			−0.136763	−	0.990604i	$-0.543670\pi$
$179$	−3.65952			−0.273525			−0.136763	+	0.990604i	$0.543670\pi$
$180$	−16.2392	+	14.5405i	−1.21040	+	1.08379i
$181$	3.06413			0.227755			0.113878	−	0.993495i	$-0.463673\pi$
$181$	3.06413			0.227755			0.113878	+	0.993495i	$0.463673\pi$
$182$	−8.22306	+	3.52366i	−0.609534	+	0.261191i
$183$	4.46077	+	4.82984i	0.329749	+	0.357032i
$184$	10.9195	+	4.06379i	0.804993	+	0.299587i
$185$		−	17.4280i		−	1.28133i
$186$	20.6025	+	9.20705i	1.51065	+	0.675094i
$187$			4.36399i			0.319127i
$188$	8.15811	−	8.56421i	0.594991	−	0.624609i
$189$	8.43888	+	10.7335i	0.613838	+	0.780744i
$190$	−2.02361	−	4.72245i	−0.146808	−	0.342602i
$191$	−11.6763			−0.844866			−0.422433	−	0.906394i	$-0.638824\pi$
$191$	−11.6763			−0.844866			−0.422433	+	0.906394i	$0.638824\pi$
$192$	0.459050	+	13.8488i	0.0331291	+	0.999451i
$193$	−1.91907			−0.138138			−0.0690688	−	0.997612i	$-0.522003\pi$
$193$	−1.91907			−0.138138			−0.0690688	+	0.997612i	$0.522003\pi$
$194$	−8.47811	−	19.7851i	−0.608693	−	1.42049i
$195$	11.1286	−	10.2782i	0.796932	−	0.736034i
$196$	−0.131724	+	0.138281i	−0.00940886	+	0.00987722i
$197$		−	4.48798i		−	0.319755i	−0.987137	−	0.159878i	$-0.948890\pi$
$197$		−	4.48798i		−	0.319755i	0.987137	−	0.159878i	$-0.0511100\pi$
$198$	−2.61961	+	0.883924i	−0.186168	+	0.0628178i
$199$		−	20.3699i		−	1.44398i	−0.691901	−	0.721992i	$-0.743227\pi$
$199$		−	20.3699i		−	1.44398i	0.691901	−	0.721992i	$-0.256773\pi$
$200$	−21.7320	−	8.08780i	−1.53669	−	0.571894i
$201$	−14.0229	+	12.9513i	−0.989101	+	0.913518i
$202$	9.47272	−	4.05914i	0.666498	−	0.285600i
$203$	−1.68101			−0.117984
$204$	−0.357823	+	23.1957i	−0.0250526	+	1.62402i
$205$	38.9155			2.71798
$206$	−6.59506	+	2.82604i	−0.459500	+	0.196900i
$207$	−0.980313	+	12.3190i	−0.0681364	+	0.856227i
$208$	−0.467442	−	9.61847i	−0.0324113	−	0.666921i
$209$		−	0.651652i		−	0.0450757i
$210$	−9.54031	+	21.3483i	−0.658344	+	1.47317i
$211$		−	16.7861i		−	1.15560i	−0.816178	−	0.577801i	$-0.803911\pi$
$211$		−	16.7861i		−	1.15560i	0.816178	−	0.577801i	$-0.196089\pi$
$212$	−4.85137	−	4.62133i	−0.333193	−	0.317394i
$213$	−7.34192	−	7.94938i	−0.503060	−	0.544682i
$214$	4.98676	+	11.6375i	0.340888	+	0.795521i
$215$	7.23075			0.493133
$216$	−13.9964	+	4.48348i	−0.952332	+	0.305062i
$217$	24.2075			1.64331
$218$	−6.40314	−	14.9428i	−0.433675	−	1.01206i
$219$	−4.56566	−	4.94342i	−0.308519	−	0.334045i
$220$	−3.42832	−	3.26576i	−0.231137	−	0.220177i
$221$		−	16.1223i		−	1.08450i
$222$	4.79432	−	10.7282i	0.321774	−	0.720030i
$223$			13.7561i			0.921177i	0.887614	+	0.460588i	$0.152362\pi$
$223$			13.7561i			0.921177i	−0.887614	+	0.460588i	$0.847638\pi$
$224$	6.51087	+	13.3624i	0.435026	+	0.892811i
$225$	1.95103	−	24.5173i	0.130068	−	1.63449i
$226$	−14.6874	+	6.29367i	−0.976990	+	0.418649i
$227$	1.13538			0.0753575			0.0376787	−	0.999290i	$-0.488004\pi$
$227$	1.13538			0.0753575			0.0376787	+	0.999290i	$0.488004\pi$
$228$	0.0534317	−	3.46369i	0.00353860	−	0.229388i
$229$	−7.56542			−0.499937			−0.249968	−	0.968254i	$-0.580420\pi$
$229$	−7.56542			−0.499937			−0.249968	+	0.968254i	$0.580420\pi$
$230$	−19.4532	+	8.33587i	−1.28270	+	0.549651i
$231$	−2.17873	+	2.01224i	−0.143350	+	0.132396i
$232$	0.631119	−	1.69582i	0.0414350	−	0.111336i
$233$			8.23593i			0.539553i	0.962923	+	0.269777i	$0.0869499\pi$
$233$			8.23593i			0.539553i	−0.962923	+	0.269777i	$0.913050\pi$
$234$	9.67787	−	3.26556i	0.632662	−	0.213476i
$235$			21.4851i			1.40154i
$236$	4.84916	−	5.09055i	0.315654	−	0.331366i
$237$	17.3809	−	16.0528i	1.12901	−	1.04274i
$238$	9.80175	+	22.8741i	0.635353	+	1.48271i
$239$	25.9625			1.67937			0.839687	−	0.543070i	$-0.182738\pi$
$239$	25.9625			1.67937			0.839687	+	0.543070i	$0.182738\pi$
$240$	−17.9546	−	17.6394i	−1.15896	−	1.13862i
$241$	−18.1294			−1.16782			−0.583909	−	0.811819i	$-0.698477\pi$
$241$	−18.1294			−1.16782			−0.583909	+	0.811819i	$0.698477\pi$
$242$	5.89066	+	13.7469i	0.378666	+	0.883682i
$243$	−8.63226	−	12.9801i	−0.553760	−	0.832677i
$244$	−5.23626	+	5.49691i	−0.335217	+	0.351904i
$245$		−	0.346907i		−	0.0221631i
$246$	23.9553	+	10.7054i	1.52733	+	0.682550i
$247$			2.40746i			0.153183i
$248$	−9.08847	+	24.4208i	−0.577119	+	1.55073i
$249$	11.7939	+	12.7697i	0.747407	+	0.809247i
$250$	15.1037	−	6.47205i	0.955239	−	0.409329i
$251$	−13.9985			−0.883579			−0.441789	−	0.897119i	$-0.645656\pi$
$251$	−13.9985			−0.883579			−0.441789	+	0.897119i	$0.645656\pi$
$252$	−11.7455	+	10.5169i	−0.739897	+	0.662504i
$253$	−2.68435			−0.168764
$254$	−11.0411	+	4.73119i	−0.692777	+	0.296861i
$255$	−28.5907	−	30.9563i	−1.79042	−	1.93856i
$256$	−15.9246	+	1.55148i	−0.995288	+	0.0969678i
$257$			20.2463i			1.26293i	0.775405	+	0.631464i	$0.217546\pi$
$257$			20.2463i			1.26293i	−0.775405	+	0.631464i	$0.782454\pi$
$258$	4.45105	+	1.98913i	0.277110	+	0.123838i
$259$		−	12.6054i		−	0.783260i
$260$	12.6656	+	12.0650i	0.785485	+	0.748239i
$261$	1.91317	+	0.152245i	0.118422	+	0.00942376i
$262$	−5.57609	−	13.0128i	−0.344492	−	0.803932i
$263$	−9.35379			−0.576779			−0.288390	−	0.957513i	$-0.593120\pi$
$263$	−9.35379			−0.576779			−0.288390	+	0.957513i	$0.593120\pi$
$264$	−1.21199	−	2.95342i	−0.0745931	−	0.181770i
$265$	12.1707			0.747640
$266$	−1.46364	−	3.41567i	−0.0897417	−	0.209428i
$267$	−3.01625	+	2.78576i	−0.184592	+	0.170486i
$268$	−15.9597	−	15.2029i	−0.974893	−	0.928665i
$269$			3.50865i			0.213926i	0.994263	+	0.106963i	$0.0341126\pi$
$269$			3.50865i			0.213926i	−0.994263	+	0.106963i	$0.965887\pi$
$270$	12.7914	−	23.4326i	0.778459	−	1.42606i
$271$		−	9.74570i		−	0.592009i	−0.955187	−	0.296005i	$-0.904346\pi$
$271$		−	9.74570i		−	0.592009i	0.955187	−	0.296005i	$-0.0956544\pi$
$272$	−26.7557	+	1.30028i	−1.62230	+	0.0788413i
$273$	8.04909	−	7.43401i	0.487153	−	0.449927i
$274$	−4.36902	+	1.87216i	−0.263942	+	0.113102i
$275$	5.34241			0.322160
$276$	−14.2680	−	0.220101i	−0.858831	−	0.0132485i
$277$	23.0773			1.38658			0.693290	−	0.720659i	$-0.256161\pi$
$277$	23.0773			1.38658			0.693290	+	0.720659i	$0.256161\pi$
$278$	3.92067	−	1.68004i	0.235146	−	0.100762i
$279$	−27.5507	−	2.19242i	−1.64942	−	0.131257i
$280$	−25.3048	−	9.41744i	−1.51225	−	0.562800i
$281$		−	8.82611i		−	0.526522i	−0.964725	−	0.263261i	$-0.915202\pi$
$281$		−	8.82611i		−	0.526522i	0.964725	−	0.263261i	$-0.0847980\pi$
$282$	−5.91040	+	13.2257i	−0.351959	+	0.787576i
$283$			28.0105i			1.66505i	0.553984	+	0.832527i	$0.313107\pi$
$283$			28.0105i			1.66505i	−0.553984	+	0.832527i	$0.686893\pi$
$284$	8.61829	−	9.04730i	0.511401	−	0.536858i
$285$	4.26930	+	4.62254i	0.252892	+	0.273816i
$286$	0.873862	+	2.03931i	0.0516725	+	0.120587i
$287$	28.1469			1.66146
$288$	−6.19988	−	15.7975i	−0.365332	−	0.930877i
$289$	−27.8474			−1.63808
$290$	1.29458	+	3.02114i	0.0760206	+	0.177407i
$291$	17.8866	+	19.3665i	1.04853	+	1.13529i
$292$	5.35939	−	5.62617i	0.313634	−	0.329247i
$293$			27.7246i			1.61969i	0.586646	+	0.809844i	$0.300448\pi$
$293$			27.7246i			1.61969i	−0.586646	+	0.809844i	$0.699552\pi$
$294$	0.0954317	−	0.213547i	0.00556569	−	0.0124543i
$295$			12.7707i			0.743540i
$296$	12.7165	+	4.73258i	0.739131	+	0.275075i
$297$	2.66188	−	2.09283i	0.154458	−	0.121438i
$298$	16.0718	−	6.88691i	0.931014	−	0.398948i
$299$	9.91703			0.573517
$300$	28.3963	+	0.438048i	1.63946	+	0.0252907i
$301$	5.22988			0.301445
$302$	−20.7573	+	8.89470i	−1.19445	+	0.511833i
$303$	−9.27231	+	8.56375i	−0.532680	+	0.491975i
$304$	3.99528	−	0.194164i	0.229145	−	0.0111361i
$305$		−	13.7902i		−	0.789623i
$306$	−9.08381	−	26.9209i	−0.519287	−	1.53897i
$307$			16.2927i			0.929873i	0.885344	+	0.464936i	$0.153923\pi$
$307$			16.2927i			0.929873i	−0.885344	+	0.464936i	$0.846077\pi$
$308$	−2.47965	−	2.36207i	−0.141291	−	0.134591i
$309$	6.45553	−	5.96222i	0.367242	−	0.339179i
$310$	−18.6428	−	43.5061i	−1.05884	−	2.47098i
$311$	2.92046			0.165604			0.0828022	−	0.996566i	$-0.473613\pi$
$311$	2.92046			0.165604			0.0828022	+	0.996566i	$0.473613\pi$
$312$	4.47758	+	10.9111i	0.253493	+	0.617718i
$313$	−18.3578			−1.03765			−0.518823	−	0.854882i	$-0.673629\pi$
$313$	−18.3578			−1.03765			−0.518823	+	0.854882i	$0.673629\pi$
$314$	−1.50555	−	3.51346i	−0.0849632	−	0.198276i
$315$	2.27178	−	28.5480i	0.128000	−	1.60850i
$316$	19.7815	+	18.8435i	1.11280	+	1.06003i
$317$		−	4.14920i		−	0.233042i	−0.993188	−	0.116521i	$-0.962826\pi$
$317$		−	4.14920i		−	0.233042i	0.993188	−	0.116521i	$-0.0371743\pi$
$318$	7.49194	+	3.34807i	0.420127	+	0.187750i
$319$			0.416887i			0.0233412i
$320$	19.0009	−	21.9921i	1.06218	−	1.22940i
$321$	−10.5208	−	11.3913i	−0.587213	−	0.635798i
$322$	−14.0701	+	6.02919i	−0.784099	+	0.335993i
$323$	6.69682			0.372621
$324$	14.3202	−	10.9056i	0.795564	−	0.605869i
$325$	−19.7370			−1.09481
$326$	24.5448	−	10.5177i	1.35941	−	0.582520i
$327$	13.5090	+	14.6267i	0.747048	+	0.808858i
$328$	−10.5675	+	28.3950i	−0.583493	+	1.56785i
$329$			15.5398i			0.856738i
$330$	5.29433	+	2.36598i	0.291444	+	0.130243i
$331$			6.70165i			0.368356i	0.982893	+	0.184178i	$0.0589622\pi$
$331$			6.70165i			0.368356i	−0.982893	+	0.184178i	$0.941038\pi$
$332$	−13.8442	+	14.5334i	−0.759801	+	0.797623i
$333$	−1.14164	+	14.3463i	−0.0625617	+	0.786173i
$334$	6.33307	+	14.7793i	0.346530	+	0.808688i
$335$	40.0383			2.18752
$336$	−12.9863	−	12.7583i	−0.708458	−	0.696021i
$337$	−14.0836			−0.767181			−0.383591	−	0.923503i	$-0.625313\pi$
$337$	−14.0836			−0.767181			−0.383591	+	0.923503i	$0.625313\pi$
$338$	4.01284	+	9.36466i	0.218270	+	0.509370i
$339$	14.3766	−	13.2780i	0.780832	−	0.721164i
$340$	33.5612	−	35.2318i	1.82011	−	1.91071i
$341$		−	6.00342i		−	0.325103i
$342$	1.35644	+	4.01996i	0.0733477	+	0.217375i
$343$		−	18.6444i		−	1.00670i
$344$	−1.96351	+	5.27598i	−0.105865	+	0.284462i
$345$	19.0416	−	17.5865i	1.02517	−	0.946827i
$346$	3.38945	−	1.45241i	0.182218	−	0.0780821i
$347$	26.1978			1.40637			0.703186	−	0.711005i	$-0.251760\pi$
$347$	26.1978			1.40637			0.703186	+	0.711005i	$0.251760\pi$
$348$	−0.0341824	+	2.21586i	−0.00183237	+	0.118782i
$349$	−16.9299			−0.906236			−0.453118	−	0.891451i	$-0.649688\pi$
$349$	−16.9299			−0.906236			−0.453118	+	0.891451i	$0.649688\pi$
$350$	28.0025	−	11.9993i	1.49680	−	0.641392i
$351$	−9.83403	+	7.73173i	−0.524902	+	0.412689i
$352$	3.31385	−	1.61469i	0.176629	−	0.0860631i
$353$		−	16.6106i		−	0.884094i	−0.896992	−	0.442047i	$-0.854252\pi$
$353$		−	16.6106i		−	0.884094i	0.896992	−	0.442047i	$-0.145748\pi$
$354$	−3.51313	+	7.86130i	−0.186721	+	0.417823i
$355$			22.6971i			1.20463i
$356$	−3.43284	−	3.27006i	−0.181940	−	0.173313i
$357$	−20.6792	−	22.3902i	−1.09446	−	1.18501i
$358$	2.03842	+	4.75700i	0.107734	+	0.251415i
$359$	−10.2165			−0.539208			−0.269604	−	0.962971i	$-0.586893\pi$
$359$	−10.2165			−0.539208			−0.269604	+	0.962971i	$0.586893\pi$
$360$	27.9467	+	13.0099i	1.47292	+	0.685681i
$361$	−1.00000			−0.0526316
$362$	−1.70678	−	3.98306i	−0.0897062	−	0.209345i
$363$	−12.4278	−	13.4560i	−0.652289	−	0.706258i
$364$	9.16078	+	8.72639i	0.480155	+	0.457387i
$365$			14.1144i			0.738784i
$366$	3.79357	−	8.48884i	0.198293	−	0.443719i
$367$		−	5.21790i		−	0.272372i	−0.990683	−	0.136186i	$-0.956515\pi$
$367$		−	5.21790i		−	0.272372i	0.990683	−	0.136186i	$-0.0434845\pi$
$368$	−0.799822	−	16.4578i	−0.0416936	−	0.857921i
$369$	−32.0343	−	2.54921i	−1.66764	−	0.132707i
$370$	−22.6546	+	9.70771i	−1.17776	+	0.504680i
$371$	8.80285			0.457021
$372$	0.492246	−	31.9096i	0.0255218	−	1.65444i
$373$	−14.0586			−0.727929			−0.363964	−	0.931413i	$-0.618577\pi$
$373$	−14.0586			−0.727929			−0.363964	+	0.931413i	$0.618577\pi$
$374$	5.67274	−	2.43082i	0.293330	−	0.125695i
$375$	−14.7841	+	13.6544i	−0.763448	+	0.705109i
$376$	−15.6768	−	5.83429i	−0.808469	−	0.300880i
$377$		−	1.54014i		−	0.0793215i
$378$	9.25179	−	16.9484i	0.475861	−	0.871731i
$379$		−	34.5756i		−	1.77603i	−0.459814	−	0.888016i	$-0.652084\pi$
$379$		−	34.5756i		−	1.77603i	0.459814	−	0.888016i	$-0.347916\pi$
$380$	−5.01151	+	5.26097i	−0.257085	+	0.269882i
$381$	10.8075	−	9.98159i	0.553683	−	0.511373i
$382$	6.50390	+	15.1780i	0.332768	+	0.776572i
$383$	−12.7713			−0.652583			−0.326292	−	0.945269i	$-0.605799\pi$
$383$	−12.7713			−0.652583			−0.326292	+	0.945269i	$0.605799\pi$
$384$	17.7463	−	8.31074i	0.905613	−	0.424106i
$385$	6.22072			0.317037
$386$	1.06896	+	2.49459i	0.0544084	+	0.126971i
$387$	−5.95217	−	0.473660i	−0.302566	−	0.0240775i
$388$	−20.9962	+	22.0413i	−1.06592	+	1.11898i
$389$		−	36.9945i		−	1.87570i	−0.347044	−	0.937849i	$-0.612814\pi$
$389$		−	36.9945i		−	1.87570i	0.347044	−	0.937849i	$-0.387186\pi$
$390$	−19.5593	−	8.74086i	−0.990426	−	0.442611i
$391$		−	27.5862i		−	1.39509i
$392$	0.253124	+	0.0942027i	0.0127847	+	0.00475795i
$393$	11.7641	+	12.7375i	0.593422	+	0.642521i
$394$	−5.83391	+	2.49988i	−0.293908	+	0.125942i
$395$	−49.6261			−2.49696
$396$	2.60818	+	2.91287i	0.131066	+	0.146377i
$397$	9.81733			0.492718			0.246359	−	0.969179i	$-0.420766\pi$
$397$	9.81733			0.492718			0.246359	+	0.969179i	$0.420766\pi$
$398$	−26.4788	+	11.3464i	−1.32726	+	0.568744i
$399$	3.08791	+	3.34340i	0.154589	+	0.167379i
$400$	1.59181	+	32.7544i	0.0795906	+	1.63772i
$401$			15.6435i			0.781197i	0.920561	+	0.390598i	$0.127732\pi$
$401$			15.6435i			0.781197i	−0.920561	+	0.390598i	$0.872268\pi$
$402$	24.6464	+	11.0142i	1.22925	+	0.549340i
$403$			22.1790i			1.10481i
$404$	−10.5529	−	10.0525i	−0.525028	−	0.500132i
$405$	−5.17107	+	32.2850i	−0.256952	+	1.60425i
$406$	0.936351	+	2.18514i	0.0464703	+	0.108446i
$407$	−3.12612			−0.154956
$408$	30.3513	−	12.4553i	1.50261	−	0.616628i
$409$	4.46179			0.220621			0.110311	−	0.993897i	$-0.464815\pi$
$409$	4.46179			0.220621			0.110311	+	0.993897i	$0.464815\pi$
$410$	−21.6766	−	50.5861i	−1.07053	−	2.49827i
$411$	4.27659	−	3.94979i	0.210948	−	0.194829i
$412$	7.34713	+	6.99874i	0.361967	+	0.344803i
$413$			9.23683i			0.454515i
$414$	16.5594	−	5.58757i	0.813851	−	0.274614i
$415$		−	36.4600i		−	1.78975i
$416$	−12.2426	+	5.96528i	−0.600245	+	0.292472i
$417$	−3.83772	+	3.54446i	−0.187934	+	0.173573i
$418$	−0.847080	+	0.362981i	−0.0414320	+	0.0177540i
$419$	−38.4525			−1.87853			−0.939263	−	0.343198i	$-0.888490\pi$
$419$	−38.4525			−1.87853			−0.939263	+	0.343198i	$0.888490\pi$
$420$	33.0646	+	0.510063i	1.61339	+	0.0248885i
$421$	−15.6016			−0.760375			−0.380187	−	0.924909i	$-0.624141\pi$
$421$	−15.6016			−0.760375			−0.380187	+	0.924909i	$0.624141\pi$
$422$	−21.8202	+	9.35014i	−1.06219	+	0.455158i
$423$	1.40741	−	17.6860i	0.0684307	−	0.859924i
$424$	−3.30495	+	8.88044i	−0.160503	+	0.431272i
$425$			54.9023i			2.66315i
$426$	−6.24379	+	13.9717i	−0.302513	+	0.676930i
$427$		−	9.97419i		−	0.482685i
$428$	12.3498	−	12.9645i	0.596950	−	0.626665i
$429$	−1.84362	−	1.99616i	−0.0890110	−	0.0963756i
$430$	−4.02766	−	9.39923i	−0.194231	−	0.453271i
$431$	4.29686			0.206973			0.103486	−	0.994631i	$-0.467000\pi$
$431$	4.29686			0.206973			0.103486	+	0.994631i	$0.467000\pi$
$432$	13.6243	+	15.6965i	0.655499	+	0.755196i
$433$	−22.4778			−1.08021			−0.540107	−	0.841596i	$-0.681616\pi$
$433$	−22.4778			−1.08021			−0.540107	+	0.841596i	$0.681616\pi$
$434$	−13.4840	−	31.4672i	−0.647252	−	1.51047i
$435$	−2.73124	−	2.95722i	−0.130953	−	0.141788i
$436$	−15.8575	+	16.6468i	−0.759435	+	0.797239i
$437$			4.11930i			0.197053i
$438$	−3.88278	+	8.68846i	−0.185526	+	0.415151i
$439$			32.7558i			1.56335i	0.623688	+	0.781673i	$0.285634\pi$
$439$			32.7558i			1.56335i	−0.623688	+	0.781673i	$0.714366\pi$
$440$	−2.33551	+	6.27555i	−0.111341	+	0.299175i
$441$	−0.0227246	+	0.285565i	−0.00108212	+	0.0135984i
$442$	−20.9573	+	8.98040i	−0.996838	+	0.427154i
$443$	31.4632			1.49486			0.747430	−	0.664341i	$-0.231288\pi$
$443$	31.4632			1.49486			0.747430	+	0.664341i	$0.231288\pi$
$444$	−16.6161	−	0.256324i	−0.788564	−	0.0121646i
$445$	8.61200			0.408248
$446$	17.8815	−	7.66239i	0.846714	−	0.362825i
$447$	−15.7318	+	14.5296i	−0.744087	+	0.687227i
$448$	13.7430	−	15.9065i	0.649297	−	0.751513i
$449$			28.8351i			1.36081i	0.732836	+	0.680406i	$0.238196\pi$
$449$			28.8351i			1.36081i	−0.732836	+	0.680406i	$0.761804\pi$
$450$	−32.9567	+	11.1204i	−1.55359	+	0.524222i
$451$		−	6.98039i		−	0.328694i
$452$	16.3622	+	15.5864i	0.769615	+	0.733122i
$453$	20.3182	−	18.7655i	0.954631	−	0.881682i
$454$	−0.632424	−	1.47587i	−0.0296811	−	0.0692660i
$455$	−22.9818			−1.07740
$456$	−4.53220	+	1.85988i	−0.212240	+	0.0870969i
$457$	−0.236640			−0.0110696			−0.00553479	−	0.999985i	$-0.501762\pi$
$457$	−0.236640			−0.0110696			−0.00553479	+	0.999985i	$0.501762\pi$
$458$	4.21407	+	9.83426i	0.196911	+	0.459525i
$459$	21.5073	+	27.3553i	1.00388	+	1.27684i
$460$	21.6715	+	20.6439i	1.01044	+	0.962527i
$461$			38.9708i			1.81505i	0.419996	+	0.907526i	$0.362031\pi$
$461$			38.9708i			1.81505i	−0.419996	+	0.907526i	$0.637969\pi$
$462$	3.82930	+	1.71127i	0.178155	+	0.0796157i
$463$		−	32.2200i		−	1.49739i	−0.662916	−	0.748694i	$-0.730681\pi$
$463$		−	32.2200i		−	1.49739i	0.662916	−	0.748694i	$-0.269319\pi$
$464$	−2.55594	+	0.124215i	−0.118657	+	0.00576652i
$465$	39.3314	+	42.5857i	1.82395	+	1.97486i
$466$	10.7059	−	4.58755i	0.495939	−	0.212514i
$467$	−13.4664			−0.623150			−0.311575	−	0.950222i	$-0.600857\pi$
$467$	−13.4664			−0.623150			−0.311575	+	0.950222i	$0.600857\pi$
$468$	−9.63564	−	10.7613i	−0.445408	−	0.497440i
$469$	28.9590			1.33720
$470$	27.9285	−	11.9676i	1.28824	−	0.552024i
$471$	3.17633	+	3.43913i	0.146357	+	0.158467i
$472$	−9.31825	−	3.46789i	−0.428907	−	0.159622i
$473$		−	1.29700i		−	0.0596362i
$474$	−30.5484	−	13.6518i	−1.40314	−	0.627046i
$475$		−	8.19827i		−	0.376162i
$476$	24.2742	−	25.4825i	1.11261	−	1.16799i
$477$	−10.0186	−	0.797256i	−0.458720	−	0.0365039i
$478$	−14.4616	−	33.7486i	−0.661457	−	1.54362i
$479$	−1.06420			−0.0486246			−0.0243123	−	0.999704i	$-0.507740\pi$
$479$	−1.06420			−0.0486246			−0.0243123	+	0.999704i	$0.507740\pi$
$480$	−12.9284	+	33.1646i	−0.590097	+	1.51375i
$481$	11.5491			0.526593
$482$	10.0984	+	23.5664i	0.459969	+	1.07342i
$483$	13.7725	−	12.7200i	0.626669	−	0.578781i
$484$	14.5883	−	15.3145i	0.663105	−	0.696113i
$485$		−	55.2953i		−	2.51083i
$486$	−12.0645	+	18.4512i	−0.547258	+	0.836964i
$487$			23.2945i			1.05557i	0.849377	+	0.527787i	$0.176978\pi$
$487$			23.2945i			1.05557i	−0.849377	+	0.527787i	$0.823022\pi$
$488$	10.0621	+	3.74472i	0.455490	+	0.169515i
$489$	−24.0255	+	22.1896i	−1.08647	+	1.00345i
$490$	−0.450944	+	0.193234i	−0.0203716	+	0.00872940i
$491$	−0.176960			−0.00798608			−0.00399304	−	0.999992i	$-0.501271\pi$
$491$	−0.176960			−0.00798608			−0.00399304	+	0.999992i	$0.501271\pi$
$492$	0.572352	−	37.1025i	0.0258036	−	1.67271i
$493$	−4.28422			−0.192951
$494$	3.12944	−	1.34099i	0.140800	−	0.0603342i
$495$	−7.07986	−	0.563398i	−0.318216	−	0.0253229i
$496$	36.8070	−	1.78876i	1.65268	−	0.0803178i
$497$			16.4164i			0.736375i
$498$	10.0299	−	22.4438i	0.449450	−	1.00573i
$499$			21.6262i			0.968124i	0.875034	+	0.484062i	$0.160839\pi$
$499$			21.6262i			0.968124i	−0.875034	+	0.484062i	$0.839161\pi$
$500$	−16.8260	−	16.0281i	−0.752482	−	0.716800i
$501$	−13.3612	−	14.4666i	−0.596932	−	0.646322i
$502$	7.79742	+	18.1966i	0.348016	+	0.812155i
$503$	−15.2473			−0.679845			−0.339923	−	0.940453i	$-0.610401\pi$
$503$	−15.2473			−0.679845			−0.339923	+	0.940453i	$0.610401\pi$
$504$	20.2134	+	9.40982i	0.900375	+	0.419147i
$505$	26.4743			1.17809
$506$	1.49523	+	3.48938i	0.0664710	+	0.155122i
$507$	−8.46607	−	9.16654i	−0.375991	−	0.407100i
$508$	12.3001	+	11.7169i	0.545729	+	0.519852i
$509$		−	4.76798i		−	0.211337i	−0.994401	−	0.105669i	$-0.966302\pi$
$509$		−	4.76798i		−	0.211337i	0.994401	−	0.105669i	$-0.0336983\pi$
$510$	−24.3144	+	54.4082i	−1.07666	+	2.40924i
$511$			10.2087i			0.451608i
$512$	10.8871	+	19.8361i	0.481144	+	0.876641i
$513$	−3.21158	−	4.08482i	−0.141795	−	0.180349i
$514$	26.3181	−	11.2775i	1.16084	−	0.497431i
$515$	−18.4318			−0.812203
$516$	0.106347	−	6.89388i	0.00468166	−	0.303486i
$517$	3.85385			0.169492
$518$	−16.3857	+	7.02142i	−0.719946	+	0.308503i
$519$	−3.31775	+	3.06422i	−0.145633	+	0.134504i
$520$	8.62829	−	23.1843i	0.378376	−	1.01670i
$521$		−	34.7570i		−	1.52273i	−0.648323	−	0.761365i	$-0.724529\pi$
$521$		−	34.7570i		−	1.52273i	0.648323	−	0.761365i	$-0.275471\pi$
$522$	−0.867766	−	2.57173i	−0.0379811	−	0.112561i
$523$		−	23.1541i		−	1.01246i	−0.862399	−	0.506228i	$-0.831039\pi$
$523$		−	23.1541i		−	1.01246i	0.862399	−	0.506228i	$-0.168961\pi$
$524$	−13.8093	+	14.4967i	−0.603261	+	0.633291i
$525$	−27.4101	+	25.3155i	−1.19627	+	1.10486i
$526$	5.21022	+	12.1590i	0.227177	+	0.530156i
$527$	61.6952			2.68748
$528$	−3.16403	+	3.22057i	−0.137697	+	0.140157i
$529$	−6.03137			−0.262234
$530$	−6.77929	−	15.8206i	−0.294473	−	0.687205i
$531$	0.836562	−	10.5125i	0.0363037	−	0.456205i
$532$	−3.62474	+	3.80517i	−0.157152	+	0.164975i
$533$			25.7883i			1.11701i
$534$	5.30131	+	2.36910i	0.229410	+	0.102521i
$535$			32.5243i			1.40615i
$536$	−10.8724	+	29.2142i	−0.469615	+	1.26186i
$537$	−4.30054	−	4.65636i	−0.185582	−	0.200937i
$538$	4.56088	−	1.95438i	0.196633	−	0.0842592i
$539$	−0.0622258			−0.00268026
$540$	−37.5850	−	3.57511i	−1.61740	−	0.153848i
$541$	22.6295			0.972920			0.486460	−	0.873703i	$-0.338288\pi$
$541$	22.6295			0.972920			0.486460	+	0.873703i	$0.338288\pi$
$542$	−12.6684	+	5.42853i	−0.544155	+	0.233175i
$543$	3.60086	+	3.89879i	0.154528	+	0.167313i
$544$	16.5936	+	34.0554i	0.711446	+	1.46011i
$545$		−	41.7621i		−	1.78889i
$546$	−14.1469	−	6.32211i	−0.605433	−	0.270561i
$547$		−	9.61465i		−	0.411093i	−0.978647	−	0.205546i	$-0.934103\pi$
$547$		−	9.61465i		−	0.411093i	0.978647	−	0.205546i	$-0.0658971\pi$
$548$	4.86724	+	4.63645i	0.207918	+	0.198059i
$549$	−0.903342	+	11.3517i	−0.0385537	+	0.484479i
$550$	−2.97582	−	6.94459i	−0.126889	−	0.296118i
$551$	0.639739			0.0272538
$552$	7.66140	+	18.6695i	0.326091	+	0.794626i
$553$	−35.8937			−1.52635
$554$	−12.8545	−	29.9981i	−0.546133	−	1.27450i
$555$	22.1753	−	20.4808i	0.941290	−	0.869360i
$556$	−4.36776	−	4.16065i	−0.185234	−	0.176451i
$557$		−	20.6980i		−	0.877003i	−0.898730	−	0.438502i	$-0.855509\pi$
$557$		−	20.6980i		−	0.877003i	0.898730	−	0.438502i	$-0.144491\pi$
$558$	12.4963	+	37.0343i	0.529012	+	1.56779i
$559$			4.79163i			0.202664i
$560$	1.85351	+	38.1393i	0.0783251	+	1.61168i
$561$	−5.55272	+	5.12840i	−0.234436	+	0.216521i
$562$	−11.4730	+	4.91630i	−0.483961	+	0.207382i
$563$	−17.0790			−0.719796			−0.359898	−	0.932992i	$-0.617188\pi$
$563$	−17.0790			−0.719796			−0.359898	+	0.932992i	$0.617188\pi$
$564$	20.4842	+	0.315994i	0.862540	+	0.0133058i
$565$	−41.0482			−1.72691
$566$	36.4108	−	15.6024i	1.53046	−	0.655816i
$567$	−3.74014	+	23.3512i	−0.157071	+	0.980657i
$568$	−16.5611	−	6.16338i	−0.694888	−	0.258610i
$569$		−	16.0479i		−	0.672763i	−0.941726	−	0.336382i	$-0.890797\pi$
$569$		−	16.0479i		−	0.672763i	0.941726	−	0.336382i	$-0.109203\pi$
$570$	3.63075	−	8.12449i	0.152075	−	0.340297i
$571$		−	20.9044i		−	0.874822i	−0.899262	−	0.437411i	$-0.855895\pi$
$571$		−	20.9044i		−	0.874822i	0.899262	−	0.437411i	$-0.144105\pi$
$572$	2.16413	−	2.27186i	0.0904869	−	0.0949912i
$573$	−13.7215	−	14.8569i	−0.573226	−	0.620654i
$574$	−15.6783	−	36.5881i	−0.654401	−	1.52716i
$575$	−33.7711			−1.40835
$576$	−17.0817	+	16.8587i	−0.711737	+	0.702446i
$577$	11.4856			0.478150			0.239075	−	0.971001i	$-0.423156\pi$
$577$	11.4856			0.478150			0.239075	+	0.971001i	$0.423156\pi$
$578$	15.5115	+	36.1987i	0.645192	+	1.50567i
$579$	−2.25522	−	2.44181i	−0.0937237	−	0.101478i
$580$	3.20606	−	3.36565i	0.133124	−	0.139751i
$581$		−	26.3709i		−	1.09405i
$582$	15.2113	−	34.0383i	0.630531	−	1.41093i
$583$		−	2.18309i		−	0.0904145i
$584$	−10.2987	−	3.83277i	−0.426164	−	0.158601i
$585$	26.1558	+	2.08141i	1.08141	+	0.0860558i
$586$	36.0391	−	15.4431i	1.48876	−	0.637948i
$587$	4.15088			0.171325			0.0856625	−	0.996324i	$-0.472699\pi$
$587$	4.15088			0.171325			0.0856625	+	0.996324i	$0.472699\pi$
$588$	−0.330746	−	0.00510216i	−0.0136397	−	0.000210410i
$589$	−9.21261			−0.379599
$590$	16.6006	−	7.11351i	0.683436	−	0.292859i
$591$	5.71048	−	5.27411i	0.234898	−	0.216948i
$592$	−0.931449	−	19.1663i	−0.0382823	−	0.787728i
$593$		−	1.67494i		−	0.0687817i	−0.999408	−	0.0343908i	$-0.989051\pi$
$593$		−	1.67494i		−	0.0687817i	0.999408	−	0.0343908i	$-0.0109491\pi$
$594$	−4.20318	−	2.29443i	−0.172458	−	0.0941416i
$595$			63.9283i			2.62081i
$596$	−17.9045	−	17.0555i	−0.733399	−	0.698622i
$597$	25.9186	−	23.9380i	1.06078	−	0.979716i
$598$	−5.52396	−	12.8911i	−0.225892	−	0.527157i
$599$	16.9799			0.693782			0.346891	−	0.937906i	$-0.387237\pi$
$599$	16.9799			0.693782			0.346891	+	0.937906i	$0.387237\pi$
$600$	−15.2478	−	37.1562i	−0.622489	−	1.51690i
$601$	43.8536			1.78883			0.894413	−	0.447241i	$-0.147593\pi$
$601$	43.8536			1.78883			0.894413	+	0.447241i	$0.147593\pi$
$602$	−2.91313	−	6.79830i	−0.118730	−	0.277078i
$603$	−32.9585	−	2.62276i	−1.34217	−	0.106807i
$604$	23.1244	+	22.0279i	0.940918	+	0.896301i
$605$			38.4196i			1.56198i
$606$	16.2968	+	7.28288i	0.662013	+	0.295847i
$607$			5.06681i			0.205655i	0.994699	+	0.102828i	$0.0327890\pi$
$607$			5.06681i			0.205655i	−0.994699	+	0.102828i	$0.967211\pi$
$608$	−2.47784	−	5.08530i	−0.100490	−	0.206236i
$609$	−1.97546	−	2.13891i	−0.0800496	−	0.0866728i
$610$	−17.9258	+	7.68137i	−0.725794	+	0.311009i
$611$	−14.2376			−0.575993
$612$	−29.9346	+	26.8034i	−1.21003	+	1.08347i
$613$	10.6328			0.429456			0.214728	−	0.976674i	$-0.431113\pi$
$613$	10.6328			0.429456			0.214728	+	0.976674i	$0.431113\pi$
$614$	21.1788	−	9.07531i	0.854707	−	0.366250i
$615$	45.7321	+	49.5159i	1.84410	+	1.99667i
$616$	−1.68923	+	4.53900i	−0.0680612	+	0.182881i
$617$			3.96322i			0.159553i	0.996813	+	0.0797766i	$0.0254207\pi$
$617$			3.96322i			0.159553i	−0.996813	+	0.0797766i	$0.974579\pi$
$618$	−11.3461	−	5.07046i	−0.456408	−	0.203964i
$619$			41.0229i			1.64885i	0.565970	+	0.824426i	$0.308502\pi$
$619$			41.0229i			1.64885i	−0.565970	+	0.824426i	$0.691498\pi$
$620$	−46.1691	+	48.4673i	−1.85420	+	1.94649i
$621$	−16.8266	+	13.2294i	−0.675229	+	0.530879i
$622$	−1.62675	−	3.79630i	−0.0652267	−	0.152218i
$623$	6.22891			0.249556
$624$	11.6892	−	11.8980i	0.467942	−	0.476303i
$625$	1.22025			0.0488101
$626$	10.2256	+	23.8633i	0.408698	+	0.953768i
$627$	0.829159	−	0.765797i	0.0331134	−	0.0305830i
$628$	−3.72852	+	3.91412i	−0.148784	+	0.156191i
$629$		−	32.1261i		−	1.28095i
$630$	−38.3748	+	12.9486i	−1.52889	+	0.515886i
$631$		−	5.60276i		−	0.223042i	−0.993762	−	0.111521i	$-0.964428\pi$
$631$		−	5.60276i		−	0.223042i	0.993762	−	0.111521i	$-0.0355723\pi$
$632$	13.4760	−	36.2100i	0.536045	−	1.44036i
$633$	21.3585	−	19.7264i	0.848926	−	0.784054i
$634$	−5.39353	+	2.31118i	−0.214204	+	0.0917885i
$635$	−30.8574			−1.22454
$636$	0.179001	−	11.6037i	0.00709786	−	0.460116i
$637$	0.229886			0.00910843
$638$	0.541910	−	0.232214i	0.0214544	−	0.00919342i
$639$	1.48680	−	18.6836i	0.0588169	−	0.739113i
$640$	−39.1714	−	12.4492i	−1.54838	−	0.492098i
$641$		−	8.01996i		−	0.316769i	−0.987377	−	0.158385i	$-0.949371\pi$
$641$		−	8.01996i		−	0.316769i	0.987377	−	0.158385i	$-0.0506286\pi$
$642$	−8.94720	+	20.0211i	−0.353118	+	0.790168i
$643$		−	15.6530i		−	0.617294i	−0.951177	−	0.308647i	$-0.900124\pi$
$643$		−	15.6530i		−	0.617294i	0.951177	−	0.308647i	$-0.0998761\pi$
$644$	15.6746	+	14.9314i	0.617667	+	0.588379i
$645$	8.49732	+	9.20038i	0.334582	+	0.362265i
$646$	−3.73024	−	8.70517i	−0.146765	−	0.342500i
$647$	29.2256			1.14898			0.574489	−	0.818513i	$-0.305201\pi$
$647$	29.2256			1.14898			0.574489	+	0.818513i	$0.305201\pi$
$648$	−22.1528	−	12.5401i	−0.870244	−	0.492621i
$649$	2.29072			0.0899187
$650$	10.9938	+	25.6560i	0.431214	+	1.00631i
$651$	28.4477	+	30.8015i	1.11495	+	1.20720i
$652$	−27.3438	−	26.0472i	−1.07086	−	1.02009i
$653$		−	1.40570i		−	0.0550093i	−0.999622	−	0.0275047i	$-0.991244\pi$
$653$		−	1.40570i		−	0.0550093i	0.999622	−	0.0275047i	$-0.00875611\pi$
$654$	11.4885	−	25.7076i	0.449234	−	1.00525i
$655$		−	36.3680i		−	1.42102i
$656$	42.7969	−	2.07986i	1.67094	−	0.0812049i
$657$	0.924584	−	11.6187i	0.0360715	−	0.453287i
$658$	20.2002	−	8.65596i	0.787484	−	0.337444i
$659$	22.3588			0.870976			0.435488	−	0.900194i	$-0.356576\pi$
$659$	22.3588			0.870976			0.435488	+	0.900194i	$0.356576\pi$
$660$	0.126495	−	8.19998i	0.00492381	−	0.319184i
$661$	−2.98455			−0.116086			−0.0580428	−	0.998314i	$-0.518486\pi$
$661$	−2.98455			−0.116086			−0.0580428	+	0.998314i	$0.518486\pi$
$662$	8.71145	−	3.73293i	0.338580	−	0.145085i
$663$	20.5139	−	18.9463i	0.796695	−	0.735814i
$664$	26.6034	+	9.90072i	1.03241	+	0.384222i
$665$		−	9.54608i		−	0.370181i
$666$	19.2846	−	6.50712i	0.747264	−	0.252146i
$667$		−	2.63528i		−	0.102038i
$668$	15.6840	−	16.4647i	0.606831	−	0.637038i
$669$	−17.5032	+	16.1657i	−0.676713	+	0.625001i
$670$	−22.3020	−	52.0456i	−0.861602	−	2.01070i
$671$	−2.47358			−0.0954916
$672$	−9.35087	+	23.9874i	−0.360718	+	0.925333i
$673$	8.93595			0.344456			0.172228	−	0.985057i	$-0.444903\pi$
$673$	8.93595			0.344456			0.172228	+	0.985057i	$0.444903\pi$
$674$	7.84480	+	18.3072i	0.302170	+	0.705167i
$675$	33.4885	−	26.3294i	1.28897	−	1.01342i
$676$	9.93787	−	10.4326i	0.382226	−	0.401252i
$677$		−	37.8884i		−	1.45617i	−0.685487	−	0.728085i	$-0.740411\pi$
$677$		−	37.8884i		−	1.45617i	0.685487	−	0.728085i	$-0.259589\pi$
$678$	−25.2681	−	11.2921i	−0.970416	−	0.433669i
$679$		−	39.9942i		−	1.53483i
$680$	−64.4918	−	24.0013i	−2.47315	−	0.920408i
$681$	1.33425	+	1.44465i	0.0511286	+	0.0553590i
$682$	−7.80382	+	3.34401i	−0.298824	+	0.128049i
$683$	−20.0990			−0.769066			−0.384533	−	0.923111i	$-0.625637\pi$
$683$	−20.0990			−0.769066			−0.384533	+	0.923111i	$0.625637\pi$
$684$	4.46997	−	4.00242i	0.170914	−	0.153036i
$685$	−12.2105			−0.466539
$686$	−24.2358	+	10.3853i	−0.925328	+	0.396511i
$687$	−8.89061	−	9.62620i	−0.339198	−	0.367263i
$688$	7.95193	−	0.386451i	0.303165	−	0.0147333i
$689$			8.06520i			0.307260i
$690$	−33.4672	−	14.9561i	−1.27407	−	0.569370i
$691$		−	6.63959i		−	0.252582i	−0.991993	−	0.126291i	$-0.959693\pi$
$691$		−	6.63959i		−	0.252582i	0.991993	−	0.126291i	$-0.0403073\pi$
$692$	−3.77597	−	3.59692i	−0.143541	−	0.136734i
$693$	−5.12074	−	0.407496i	−0.194521	−	0.0154795i
$694$	−14.5926	−	34.0545i	−0.553929	−	1.29269i
$695$	10.9575			0.415640
$696$	2.89943	−	1.18984i	0.109903	−	0.0451007i
$697$	71.7353			2.71717
$698$	9.43024	+	22.0071i	0.356940	+	0.832981i
$699$	−10.4794	+	9.67856i	−0.396366	+	0.366077i
$700$	−31.1958	−	29.7166i	−1.17909	−	1.12318i
$701$			2.22311i			0.0839656i	0.999118	+	0.0419828i	$0.0133675\pi$
$701$			2.22311i			0.0839656i	−0.999118	+	0.0419828i	$0.986633\pi$
$702$	15.5282	+	8.47652i	0.586073	+	0.319925i
$703$			4.79722i			0.180931i
$704$	−3.94480	−	3.40825i	−0.148675	−	0.128453i
$705$	−27.3376	+	25.2486i	−1.02959	+	0.950916i
$706$	−21.5921	+	9.25241i	−0.812629	+	0.348219i
$707$	19.1484			0.720149
$708$	12.1757	+	0.187826i	0.457593	+	0.00705894i
$709$	−22.6774			−0.851668			−0.425834	−	0.904801i	$-0.640019\pi$
$709$	−22.6774			−0.851668			−0.425834	+	0.904801i	$0.640019\pi$
$710$	29.5038	−	12.6427i	1.10726	−	0.474471i
$711$	40.8509	+	3.25082i	1.53203	+	0.121915i
$712$	−2.33859	+	6.28381i	−0.0876423	+	0.235496i
$713$			37.9495i			1.42122i
$714$	−17.5862	+	39.3525i	−0.658148	+	1.47273i
$715$			5.69944i			0.213147i
$716$	5.04817	−	5.29946i	0.188659	−	0.198050i
$717$	30.5102	+	33.0346i	1.13942	+	1.23370i
$718$	5.69079	+	13.2804i	0.212378	+	0.495622i
$719$	−47.5667			−1.77394			−0.886970	−	0.461827i	$-0.847194\pi$
$719$	−47.5667			−1.77394			−0.886970	+	0.461827i	$0.847194\pi$
$720$	1.34470	−	43.5746i	0.0501142	−	1.62393i
$721$	−13.3314			−0.496488
$722$	0.557018	+	1.29990i	0.0207300	+	0.0483771i
$723$	−21.3050	−	23.0678i	−0.792342	−	0.857900i
$724$	−4.22686	+	4.43727i	−0.157090	+	0.164910i
$725$			5.24476i			0.194785i
$726$	−10.5690	+	23.6501i	−0.392251	+	0.877736i
$727$		−	24.3087i		−	0.901560i	−0.892635	−	0.450780i	$-0.851146\pi$
$727$		−	24.3087i		−	0.901560i	0.892635	−	0.450780i	$-0.148854\pi$
$728$	6.24069	−	16.7688i	0.231295	−	0.621494i
$729$	6.37156	−	26.2374i	0.235984	−	0.971757i
$730$	18.3473	−	7.86199i	0.679065	−	0.290985i
$731$	13.3289			0.492986
$732$	−13.1477	−	0.202820i	−0.485953	−	0.00749643i
$733$	−34.3170			−1.26753			−0.633764	−	0.773527i	$-0.718491\pi$
$733$	−34.3170			−1.26753			−0.633764	+	0.773527i	$0.718491\pi$
$734$	−6.78274	+	2.90646i	−0.250355	+	0.107280i
$735$	0.441403	−	0.407673i	0.0162814	−	0.0150372i
$736$	−20.9479	+	10.2070i	−0.772150	+	0.376233i
$737$		−	7.18178i		−	0.264544i
$738$	14.5299	+	43.0612i	0.534854	+	1.58510i
$739$			2.84086i			0.104503i	0.998634	+	0.0522513i	$0.0166397\pi$
$739$			2.84086i			0.104503i	−0.998634	+	0.0522513i	$0.983360\pi$
$740$	25.2380	+	24.0413i	0.927769	+	0.883776i
$741$	−3.06324	+	2.82915i	−0.112531	+	0.103932i
$742$	−4.90334	−	11.4428i	−0.180007	−	0.420078i
$743$	10.1141			0.371050			0.185525	−	0.982640i	$-0.440601\pi$
$743$	10.1141			0.371050			0.185525	+	0.982640i	$0.440601\pi$
$744$	−41.7534	+	17.1344i	−1.53075	+	0.628176i
$745$	44.9173			1.64564
$746$	7.83091	+	18.2748i	0.286710	+	0.669087i
$747$	−2.38836	+	30.0130i	−0.0873856	+	1.09812i
$748$	−6.31963	−	6.01996i	−0.231069	−	0.220112i
$749$			23.5243i			0.859558i
$750$	25.9843	+	11.6121i	0.948812	+	0.424014i
$751$			7.24573i			0.264400i	0.991223	+	0.132200i	$0.0422042\pi$
$751$			7.24573i			0.264400i	−0.991223	+	0.132200i	$0.957796\pi$
$752$	1.14828	+	23.6280i	0.0418736	+	0.861625i
$753$	−16.4505	−	17.8117i	−0.599491	−	0.649093i
$754$	−2.00203	+	0.857887i	−0.0729096	+	0.0312424i
$755$	−58.0124			−2.11129
$756$	−27.1846	−	2.58581i	−0.988693	−	0.0940451i
$757$	−29.0364			−1.05534			−0.527672	−	0.849448i	$-0.676935\pi$
$757$	−29.0364			−1.05534			−0.527672	+	0.849448i	$0.676935\pi$
$758$	−44.9448	+	19.2592i	−1.63247	+	0.699527i
$759$	−3.15455	−	3.41555i	−0.114503	−	0.123977i
$760$	9.63022	+	3.58399i	0.349325	+	0.130005i
$761$		−	31.1933i		−	1.13076i	−0.824832	−	0.565378i	$-0.808730\pi$
$761$		−	31.1933i		−	1.13076i	0.824832	−	0.565378i	$-0.191270\pi$
$762$	−18.9950	−	8.48866i	−0.688116	−	0.307512i
$763$		−	30.2058i		−	1.09352i
$764$	16.1070	−	16.9088i	0.582731	−	0.611738i
$765$	5.78986	−	72.7574i	0.209333	−	2.63055i
$766$	7.11384	+	16.6014i	0.257033	+	0.599832i
$767$	−8.46282			−0.305575
$768$	−20.6881	−	18.4391i	−0.746518	−	0.665365i
$769$	48.8770			1.76255			0.881274	−	0.472605i	$-0.156686\pi$
$769$	48.8770			1.76255			0.881274	+	0.472605i	$0.156686\pi$
$770$	−3.46505	−	8.08629i	−0.124872	−	0.291410i
$771$	−25.7613	+	23.7927i	−0.927769	+	0.856873i
$772$	2.64728	−	2.77906i	0.0952778	−	0.100021i
$773$		−	29.3574i		−	1.05591i	−0.849272	−	0.527956i	$-0.822959\pi$
$773$		−	29.3574i		−	1.05591i	0.849272	−	0.527956i	$-0.177041\pi$
$774$	2.69976	+	8.00105i	0.0970407	+	0.287592i
$775$		−	75.5275i		−	2.71303i
$776$	40.3467	+	15.0154i	1.44836	+	0.539023i
$777$	16.0390	−	14.8134i	0.575397	−	0.531427i
$778$	−48.0891	+	20.6066i	−1.72408	+	0.738783i
$779$	−10.7118			−0.383792
$780$	−0.467322	+	30.2939i	−0.0167328	+	1.08470i
$781$	4.07124			0.145680
$782$	−35.8592	+	15.3660i	−1.28232	+	0.549487i
$783$	2.05457	+	2.61322i	0.0734244	+	0.0933890i
$784$	−0.0185406	−	0.381507i	−0.000662166	−	0.0136253i
$785$		−	9.81941i		−	0.350470i
$786$	10.0046	−	22.3871i	0.356851	−	0.798523i
$787$			8.60877i			0.306870i	0.988159	+	0.153435i	$0.0490335\pi$
$787$			8.60877i			0.306870i	−0.988159	+	0.153435i	$0.950967\pi$
$788$	6.49918	+	6.19100i	0.231524	+	0.220545i
$789$	−10.9922	−	11.9017i	−0.391334	−	0.423712i
$790$	27.6426	+	64.5087i	0.983479	+	2.29512i
$791$	−29.6894			−1.05563
$792$	2.33362	−	5.01288i	0.0829216	−	0.178125i
$793$	9.13838			0.324513
$794$	−5.46842	−	12.7615i	−0.194067	−	0.452889i
$795$	14.3026	+	15.4859i	0.507259	+	0.549229i
$796$	29.4983	+	28.0995i	1.04554	+	0.995962i
$797$		−	21.5215i		−	0.762332i	−0.924507	−	0.381166i	$-0.875523\pi$
$797$		−	21.5215i		−	0.762332i	0.924507	−	0.381166i	$-0.124477\pi$
$798$	2.62606	−	5.87630i	0.0929614	−	0.208019i
$799$			39.6048i			1.40112i
$800$	41.6907	−	20.3140i	1.47399	−	0.718207i
$801$	−7.08918	−	0.564140i	−0.250484	−	0.0199329i
$802$	20.3349	−	8.71368i	0.718049	−	0.307691i
$803$	2.53175			0.0893435
$804$	0.588865	−	38.1729i	0.0207677	−	1.34626i
$805$	−39.3231			−1.38596
$806$	28.8304	−	12.3541i	1.01551	−	0.435154i
$807$	−4.46439	+	4.12323i	−0.157154	+	0.145145i
$808$	−7.18909	+	19.3172i	−0.252911	+	0.679576i
$809$			32.7020i			1.14974i	0.818245	+	0.574870i	$0.194947\pi$
$809$			32.7020i			1.14974i	−0.818245	+	0.574870i	$0.805053\pi$
$810$	44.8475	−	11.2614i	1.57578	−	0.395687i
$811$			10.6159i			0.372774i	0.982476	+	0.186387i	$0.0596779\pi$
$811$			10.6159i			0.372774i	−0.982476	+	0.186387i	$0.940322\pi$
$812$	2.31889	−	2.43432i	0.0813770	−	0.0854278i
$813$	12.4004	−	11.4528i	0.434901	−	0.401667i
$814$	1.74130	+	4.06363i	0.0610326	+	0.142430i
$815$	68.5976			2.40287
$816$	−33.0968	−	32.5158i	−1.15862	−	1.13828i
$817$	−1.99033			−0.0696328
$818$	−2.48529	−	5.79986i	−0.0868963	−	0.202787i
$819$	18.9180	+	1.50545i	0.661048	+	0.0526046i
$820$	−53.6825	+	56.3547i	−1.87467	+	1.96799i
$821$			8.06932i			0.281621i	0.990037	+	0.140811i	$0.0449708\pi$
$821$			8.06932i			0.281621i	−0.990037	+	0.140811i	$0.955029\pi$
$822$	−7.51645	−	3.35902i	−0.262166	−	0.117159i
$823$		−	48.2742i		−	1.68273i	−0.540464	−	0.841367i	$-0.681751\pi$
$823$		−	48.2742i		−	1.68273i	0.540464	−	0.841367i	$-0.318249\pi$
$824$	5.00516	−	13.4489i	0.174363	−	0.468516i
$825$	6.27821	+	6.79766i	0.218579	+	0.236664i
$826$	12.0069	−	5.14508i	0.417775	−	0.179020i
$827$	4.15986			0.144653			0.0723263	−	0.997381i	$-0.476958\pi$
$827$	4.15986			0.144653			0.0723263	+	0.997381i	$0.476958\pi$
$828$	−16.4871	−	18.4132i	−0.572968	−	0.639902i
$829$	−1.89646			−0.0658668			−0.0329334	−	0.999458i	$-0.510485\pi$
$829$	−1.89646			−0.0658668			−0.0329334	+	0.999458i	$0.510485\pi$
$830$	−47.3943	+	20.3089i	−1.64508	+	0.704932i
$831$	27.1196	+	29.3634i	0.940768	+	1.01861i
$832$	14.5736	+	12.5914i	0.505249	+	0.436528i
$833$		−	0.639475i		−	0.0221565i
$834$	6.74511	+	3.01432i	0.233564	+	0.104377i
$835$			41.3051i			1.42942i
$836$	0.943677	+	0.898929i	0.0326377	+	0.0310901i
$837$	−29.5870	−	37.6319i	−1.02268	−	1.30075i
$838$	21.4187	+	49.9842i	0.739897	+	1.72668i
$839$	−11.9752			−0.413429			−0.206715	−	0.978401i	$-0.566277\pi$
$839$	−11.9752			−0.413429			−0.206715	+	0.978401i	$0.566277\pi$
$840$	−17.7546	−	43.2647i	−0.612590	−	1.49278i
$841$	28.5907			0.985887
$842$	8.69036	+	20.2805i	0.299490	+	0.698911i
$843$	11.2303	−	10.3721i	0.386792	−	0.357235i
$844$	24.3084	+	23.1558i	0.836731	+	0.797055i
$845$			26.1723i			0.900354i
$846$	−23.7740	+	8.02194i	−0.817365	+	0.275800i
$847$			27.7883i			0.954816i
$848$	13.3846	−	0.650469i	0.459628	−	0.0223372i
$849$	−35.6405	+	32.9170i	−1.22318	+	1.12971i
$850$	71.3673	−	30.5815i	2.44788	−	1.04894i
$851$	19.7612			0.677405
$852$	21.6396	+	0.333818i	0.741362	+	0.0114364i
$853$	11.7731			0.403105			0.201552	−	0.979478i	$-0.435401\pi$
$853$	11.7731			0.403105			0.201552	+	0.979478i	$0.435401\pi$
$854$	−12.9654	+	5.55580i	−0.443667	+	0.190115i
$855$	−0.864569	+	10.8645i	−0.0295676	+	0.371557i
$856$	−23.7316	−	8.83197i	−0.811130	−	0.301871i
$857$			7.50907i			0.256505i	0.991742	+	0.128253i	$0.0409368\pi$
$857$			7.50907i			0.256505i	−0.991742	+	0.128253i	$0.959063\pi$
$858$	−1.56787	+	3.50842i	−0.0535264	+	0.119775i
$859$		−	23.3754i		−	0.797559i	−0.917047	−	0.398779i	$-0.869434\pi$
$859$		−	23.3754i		−	0.797559i	0.917047	−	0.398779i	$-0.130566\pi$
$860$	−9.97456	+	10.4711i	−0.340130	+	0.357061i
$861$	33.0772	+	35.8140i	1.12727	+	1.22054i
$862$	−2.39343	−	5.58548i	−0.0815204	−	0.190242i
$863$	−34.9859			−1.19094			−0.595468	−	0.803379i	$-0.703033\pi$
$863$	−34.9859			−1.19094			−0.595468	+	0.803379i	$0.703033\pi$
$864$	12.8148	−	26.4534i	0.435969	−	0.899962i
$865$	9.47282			0.322086
$866$	12.5205	+	29.2188i	0.425465	+	0.992896i
$867$	−32.7252	−	35.4329i	−1.11141	−	1.20336i
$868$	−33.3933	+	35.0556i	−1.13344	+	1.18986i
$869$			8.90157i			0.301965i
$870$	−2.32273	+	5.19755i	−0.0787480	+	0.176214i
$871$			26.5323i			0.899013i
$872$	30.4721	+	11.3405i	1.03191	+	0.384038i
$873$	−3.62219	+	45.5177i	−0.122593	+	1.54054i
$874$	5.35466	−	2.29452i	0.181124	−	0.0776134i
$875$	30.5309			1.03213
$876$	13.4569	+	0.207589i	0.454666	+	0.00701378i
$877$	30.4765			1.02912			0.514559	−	0.857455i	$-0.327956\pi$
$877$	30.4765			1.02912			0.514559	+	0.857455i	$0.327956\pi$
$878$	42.5791	−	18.2455i	1.43698	−	0.615757i
$879$	−35.2766	+	32.5809i	−1.18985	+	1.09893i
$880$	9.45849	−	0.459667i	0.318846	−	0.0154954i
$881$			17.5489i			0.591238i	0.955306	+	0.295619i	$0.0955258\pi$
$881$			17.5489i			0.591238i	−0.955306	+	0.295619i	$0.904474\pi$
$882$	0.383864	−	0.129525i	0.0129254	−	0.00436134i
$883$			27.3259i			0.919591i	0.888025	+	0.459795i	$0.152077\pi$
$883$			27.3259i			0.919591i	−0.888025	+	0.459795i	$0.847923\pi$
$884$	23.3472	+	22.2401i	0.785251	+	0.748015i
$885$	−16.2494	+	15.0077i	−0.546218	+	0.504478i
$886$	−17.5255	−	40.8989i	−0.588782	−	1.37402i
$887$	−16.4131			−0.551096			−0.275548	−	0.961287i	$-0.588859\pi$
$887$	−16.4131			−0.551096			−0.275548	+	0.961287i	$0.588859\pi$
$888$	8.92225	+	21.7420i	0.299411	+	0.729612i
$889$	−22.3187			−0.748544
$890$	−4.79703	−	11.1947i	−0.160797	−	0.375247i
$891$	5.79105	+	0.927550i	0.194008	+	0.0310741i
$892$	−19.9206	−	18.9760i	−0.666992	−	0.635365i
$893$		−	5.91398i		−	0.197904i
$894$	27.6499	+	12.3564i	0.924750	+	0.413261i
$895$			13.2948i			0.444397i
$896$	−28.3320	−	9.00429i	−0.946504	−	0.300812i
$897$	11.6541	+	12.6184i	0.389120	+	0.421316i
$898$	37.4826	−	16.0616i	1.25081	−	0.535984i
$899$	5.89367			0.196565
$900$	32.8129	+	36.6460i	1.09376	+	1.22153i
$901$	22.4350			0.747417
$902$	−9.07379	+	3.88820i	−0.302124	+	0.129463i
$903$	6.14596	+	6.65447i	0.204525	+	0.221447i
$904$	11.1466	−	29.9511i	0.370731	−	0.996160i
$905$		−	11.1318i		−	0.370034i
$906$	−35.7108	−	15.9588i	−1.18641	−	0.530195i
$907$		−	19.5954i		−	0.650653i	−0.945602	−	0.325327i	$-0.894526\pi$
$907$		−	19.5954i		−	0.650653i	0.945602	−	0.325327i	$-0.105474\pi$
$908$	−1.56621	+	1.64417i	−0.0519764	+	0.0545637i
$909$	−21.7930	−	1.73423i	−0.722827	−	0.0575208i
$910$	12.8012	+	29.8739i	0.424357	+	0.990310i
$911$	−12.1428			−0.402308			−0.201154	−	0.979560i	$-0.564469\pi$
$911$	−12.1428			−0.402308			−0.201154	+	0.979560i	$0.564469\pi$
$912$	4.94217	+	4.85541i	0.163652	+	0.160779i
$913$	−6.53995			−0.216441
$914$	0.131813	+	0.307608i	0.00435998	+	0.0101748i
$915$	17.5465	−	16.2057i	0.580071	−	0.535744i
$916$	10.4362	−	10.9557i	0.344822	−	0.361987i
$917$		−	26.3044i		−	0.868646i
$918$	23.5791	−	43.1947i	0.778227	−	1.42564i
$919$			1.48763i			0.0490725i	0.999699	+	0.0245363i	$0.00781092\pi$
$919$			1.48763i			0.0490725i	−0.999699	+	0.0245363i	$0.992189\pi$
$920$	14.7635	−	39.6698i	0.486739	−	1.30787i
$921$	−20.7307	+	19.1466i	−0.683101	+	0.630901i
$922$	50.6580	−	21.7074i	1.66833	−	0.714896i
$923$	−15.0407			−0.495072
$924$	0.0914916	−	5.93090i	0.00300985	−	0.195112i
$925$	−39.3289			−1.29313
$926$	−41.8826	+	17.9471i	−1.37635	+	0.589778i
$927$	15.1726	+	1.20740i	0.498334	+	0.0396562i
$928$	1.58517	+	3.25327i	0.0520358	+	0.106794i
$929$			42.9003i			1.40751i	0.710441	+	0.703757i	$0.248496\pi$
$929$			42.9003i			1.40751i	−0.710441	+	0.703757i	$0.751504\pi$
$930$	33.4487	−	74.8478i	1.09683	−	2.45435i
$931$			0.0954894i			0.00312954i
$932$	−11.9267	−	11.3612i	−0.390672	−	0.372147i
$933$	3.43202	+	3.71599i	0.112359	+	0.121656i
$934$	7.50101	+	17.5049i	0.245441	+	0.572778i
$935$	15.8541			0.518485
$936$	−8.62131	+	18.5195i	−0.281796	+	0.605330i
$937$	−28.3048			−0.924676			−0.462338	−	0.886704i	$-0.652989\pi$
$937$	−28.3048			−0.924676			−0.462338	+	0.886704i	$0.652989\pi$
$938$	−16.1307	−	37.6437i	−0.526685	−	1.22911i
$939$	−21.5734	−	23.3584i	−0.704023	−	0.762273i
$940$	−31.1133	−	29.6379i	−1.01480	−	0.966683i
$941$			35.1506i			1.14588i	0.819599	+	0.572938i	$0.194196\pi$
$941$			35.1506i			1.14588i	−0.819599	+	0.572938i	$0.805804\pi$
$942$	2.70125	−	6.04455i	0.0880114	−	0.196942i
$943$			44.1253i			1.43692i
$944$	0.682537	+	14.0444i	0.0222147	+	0.457108i
$945$	38.9940	−	30.6579i	1.26848	−	0.997303i
$946$	−1.68597	+	0.722453i	−0.0548156	+	0.0234890i
$947$	−3.19828			−0.103930			−0.0519651	−	0.998649i	$-0.516548\pi$
$947$	−3.19828			−0.103930			−0.0519651	+	0.998649i	$0.516548\pi$
$948$	−0.729878	+	47.3141i	−0.0237054	+	1.53669i
$949$	−9.35327			−0.303620
$950$	−10.6569	+	4.56658i	−0.345756	+	0.148159i
$951$	5.27942	−	4.87599i	0.171197	−	0.158115i
$952$	−46.6458	−	17.3597i	−1.51180	−	0.562632i
$953$			49.6292i			1.60765i	0.594868	+	0.803823i	$0.297204\pi$
$953$			49.6292i			1.60765i	−0.594868	+	0.803823i	$0.702796\pi$
$954$	4.54419	+	13.4672i	0.147123	+	0.436018i
$955$			42.4193i			1.37266i
$956$	−35.8143	+	37.5971i	−1.15832	+	1.21598i
$957$	−0.530445	+	0.489911i	−0.0171469	+	0.0158366i
$958$	0.592778	+	1.38335i	0.0191518	+	0.0446940i
$959$	−8.83165			−0.285189
$960$	50.3119	−	1.66770i	1.62381	−	0.0538249i
$961$	−53.8723			−1.73782
$962$	−6.43305	−	15.0126i	−0.207410	−	0.484026i
$963$	2.13055	−	26.7732i	0.0686559	−	0.862754i
$964$	25.0088	−	26.2537i	0.805481	−	0.845576i
$965$			6.97187i			0.224432i
$966$	−24.2062	−	10.8175i	−0.778823	−	0.348048i
$967$		−	24.1473i		−	0.776524i	−0.921549	−	0.388262i	$-0.873076\pi$
$967$		−	24.1473i		−	0.776524i	0.921549	−	0.388262i	$-0.126924\pi$
$968$	−28.0332	−	10.4328i	−0.901021	−	0.335324i
$969$	7.86986	+	8.52100i	0.252816	+	0.273734i
$970$	−71.8782	+	30.8005i	−2.30787	+	0.988944i
$971$	−15.5601			−0.499346			−0.249673	−	0.968330i	$-0.580323\pi$
$971$	−15.5601			−0.499346			−0.249673	+	0.968330i	$0.580323\pi$
$972$	30.7048	+	5.40499i	0.984858	+	0.173365i
$973$	7.92534			0.254075
$974$	30.2804	−	12.9754i	0.970248	−	0.415760i
$975$	−23.1942	−	25.1132i	−0.742808	−	0.804267i
$976$	−0.737023	−	15.1656i	−0.0235915	−	0.485438i
$977$			1.85014i			0.0591913i	0.999562	+	0.0295957i	$0.00942197\pi$
$977$			1.85014i			0.0591913i	−0.999562	+	0.0295957i	$0.990578\pi$
$978$	42.2268	+	18.8707i	1.35026	+	0.603418i
$979$		−	1.54476i		−	0.0493707i
$980$	0.502367	+	0.478546i	0.0160475	+	0.0152866i
$981$	−2.73568	+	34.3775i	−0.0873436	+	1.09759i
$982$	0.0985697	+	0.230029i	0.00314549	+	0.00734053i
$983$	18.1075			0.577541			0.288770	−	0.957398i	$-0.406754\pi$
$983$	18.1075			0.577541			0.288770	+	0.957398i	$0.406754\pi$
$984$	−48.5482	+	19.9227i	−1.54766	+	0.635114i
$985$	−16.3046			−0.519507
$986$	2.38638	+	5.56904i	0.0759980	+	0.177354i
$987$	−19.7728	+	18.2618i	−0.629375	+	0.581281i
$988$	−3.48631	−	3.32100i	−0.110914	−	0.105655i
$989$			8.19876i			0.260706i
$990$	3.21125	+	9.51690i	0.102060	+	0.302467i
$991$			21.2947i			0.676448i	0.941066	+	0.338224i	$0.109826\pi$
$991$			21.2947i			0.676448i	−0.941066	+	0.338224i	$0.890174\pi$
$992$	−22.8274	−	46.8489i	−0.724769	−	1.48746i
$993$	−8.52714	+	7.87553i	−0.270601	+	0.249922i
$994$	21.3396	−	9.14421i	0.676851	−	0.290037i
$995$	−74.0027			−2.34604
$996$	−34.7614	−	0.536238i	−1.10146	−	0.0169914i
$997$	−28.8259			−0.912925			−0.456462	−	0.889743i	$-0.650884\pi$
$997$	−28.8259			−0.912925			−0.456462	+	0.889743i	$0.650884\pi$
$998$	28.1119	−	12.0462i	0.889866	−	0.381316i
$999$	−19.5958	+	15.4066i	−0.619983	+	0.487444i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.2.c.a.191.13	✓	36
3.2	odd	2	inner	228.2.c.a.191.24	yes	36
4.3	odd	2	inner	228.2.c.a.191.23	yes	36
12.11	even	2	inner	228.2.c.a.191.14	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.c.a.191.13	✓	36	1.1	even	1	trivial
228.2.c.a.191.14	yes	36	12.11	even	2	inner
228.2.c.a.191.23	yes	36	4.3	odd	2	inner
228.2.c.a.191.24	yes	36	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	228.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.557018 - 1.29990i) q^{2} +(1.17516 + 1.27240i) q^{3} +(-1.37946 + 1.44813i) q^{4} -3.63294i q^{5} +(0.999396 - 2.23634i) q^{6} -2.62764i q^{7} +(2.65081 + 0.986525i) q^{8} +(-0.237980 + 2.99055i) q^{9} +(-4.72245 + 2.02361i) q^{10} -0.651652 q^{11} +(-3.46369 - 0.0534317i) q^{12} +2.40746 q^{13} +(-3.41567 + 1.46364i) q^{14} +(4.62254 - 4.26930i) q^{15} +(-0.194164 - 3.99528i) q^{16} -6.69682i q^{17} +(4.01996 - 1.35644i) q^{18} +1.00000i q^{19} +(5.26097 + 5.01151i) q^{20} +(3.34340 - 3.08791i) q^{21} +(0.362981 + 0.847080i) q^{22} +4.11930 q^{23} +(1.85988 + 4.53220i) q^{24} -8.19827 q^{25} +(-1.34099 - 3.12944i) q^{26} +(-4.08482 + 3.21158i) q^{27} +(3.80517 + 3.62474i) q^{28} -0.639739i q^{29} +(-8.12449 - 3.63075i) q^{30} +9.21261i q^{31} +(-5.08530 + 2.47784i) q^{32} +(-0.765797 - 0.829159i) q^{33} +(-8.70517 + 3.73024i) q^{34} -9.54608 q^{35} +(-4.00242 - 4.46997i) q^{36} +4.79722 q^{37} +(1.29990 - 0.557018i) q^{38} +(2.82915 + 3.06324i) q^{39} +(3.58399 - 9.63022i) q^{40} +10.7118i q^{41} +(-5.87630 - 2.62606i) q^{42} +1.99033i q^{43} +(0.898929 - 0.943677i) q^{44} +(10.8645 + 0.864569i) q^{45} +(-2.29452 - 5.35466i) q^{46} -5.91398 q^{47} +(4.85541 - 4.94217i) q^{48} +0.0954894 q^{49} +(4.56658 + 10.6569i) q^{50} +(8.52100 - 7.86986i) q^{51} +(-3.32100 + 3.48631i) q^{52} +3.35009i q^{53} +(6.45004 + 3.52094i) q^{54} +2.36741i q^{55} +(2.59224 - 6.96537i) q^{56} +(-1.27240 + 1.17516i) q^{57} +(-0.831595 + 0.356346i) q^{58} -3.51525 q^{59} +(-0.194114 + 12.5834i) q^{60} +3.79587 q^{61} +(11.9754 - 5.13159i) q^{62} +(7.85809 + 0.625328i) q^{63} +(6.05354 + 5.23017i) q^{64} -8.74615i q^{65} +(-0.651258 + 1.45731i) q^{66} +11.0209i q^{67} +(9.69787 + 9.23801i) q^{68} +(4.84085 + 5.24138i) q^{69} +(5.31733 + 12.4089i) q^{70} -6.24757 q^{71} +(-3.58109 + 7.69258i) q^{72} -3.88513 q^{73} +(-2.67214 - 6.23589i) q^{74} +(-9.63431 - 10.4314i) q^{75} +(-1.44813 - 1.37946i) q^{76} +1.71231i q^{77} +(2.40600 - 5.38388i) q^{78} -13.6600i q^{79} +(-14.5146 + 0.705388i) q^{80} +(-8.88673 - 1.42338i) q^{81} +(13.9243 - 5.96669i) q^{82} +10.0360 q^{83} +(-0.140400 + 9.10134i) q^{84} -24.3291 q^{85} +(2.58722 - 1.10865i) q^{86} +(0.814002 - 0.751799i) q^{87} +(-1.72740 - 0.642871i) q^{88} +2.37053i q^{89} +(-4.92786 - 14.6043i) q^{90} -6.32593i q^{91} +(-5.68242 + 5.96528i) q^{92} +(-11.7221 + 10.8263i) q^{93} +(3.29419 + 7.68756i) q^{94} +3.63294 q^{95} +(-9.12885 - 3.55865i) q^{96} +15.2205 q^{97} +(-0.0531893 - 0.124126i) q^{98} +(0.155080 - 1.94879i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 6 q^{6} + 8 q^{10} + 4 q^{12} - 8 q^{16} + 16 q^{18} + 8 q^{21} - 12 q^{22} - 2 q^{24} - 28 q^{25} + 12 q^{28} - 12 q^{30} - 28 q^{34} - 22 q^{36} - 16 q^{37} - 12 q^{40} + 10 q^{42} + 16 q^{45}+ \cdots + 40 q^{97}+O(q^{100}) \) 36 * q - 6 * q^6 + 8 * q^10 + 4 * q^12 - 8 * q^16 + 16 * q^18 + 8 * q^21 - 12 * q^22 - 2 * q^24 - 28 * q^25 + 12 * q^28 - 12 * q^30 - 28 * q^34 - 22 * q^36 - 16 * q^37 - 12 * q^40 + 10 * q^42 + 16 * q^45 - 4 * q^46 + 32 * q^48 - 44 * q^49 - 36 * q^52 - 20 * q^54 - 4 * q^58 - 4 * q^60 + 16 * q^61 + 24 * q^64 + 24 * q^66 - 16 * q^69 + 36 * q^70 - 36 * q^72 - 8 * q^73 - 32 * q^78 - 40 * q^81 + 72 * q^82 - 20 * q^84 + 16 * q^85 - 16 * q^88 - 56 * q^90 + 8 * q^93 - 56 * q^94 + 2 * q^96 + 40 * q^97

Introduction

L-functions

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