LMFDB - Embedded newform 228.3.b.e.227.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [228,3,Mod(227,228)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(228, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("228.227");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	228.b (of order $2$, degree $1$, 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:	$6.21255002741$
Analytic rank:	$0$
Dimension:	$72$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			227.11
Character	$\chi$	$=$	228.227
Dual form			228.3.b.e.227.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.76755 + 0.935824i) q^{2} +(-1.44490 + 2.62912i) q^{3} +(2.24847 - 3.30823i) q^{4} +0.614363i q^{5} +(0.0935298 - 5.99927i) q^{6} -2.53686i q^{7} +(-0.878356 + 7.95163i) q^{8} +(-4.82456 - 7.59761i) q^{9} +O(q^{10})$	\(q+(-1.76755 + 0.935824i) q^{2} +(-1.44490 + 2.62912i) q^{3} +(2.24847 - 3.30823i) q^{4} +0.614363i q^{5} +(0.0935298 - 5.99927i) q^{6} -2.53686i q^{7} +(-0.878356 + 7.95163i) q^{8} +(-4.82456 - 7.59761i) q^{9} +(-0.574935 - 1.08592i) q^{10} -1.05328 q^{11} +(5.44894 + 10.6915i) q^{12} -20.8318i q^{13} +(2.37406 + 4.48404i) q^{14} +(-1.61523 - 0.887689i) q^{15} +(-5.88879 - 14.8769i) q^{16} -14.1484i q^{17} +(15.6377 + 8.91422i) q^{18} +(-14.0156 + 12.8282i) q^{19} +(2.03245 + 1.38137i) q^{20} +(6.66972 + 3.66550i) q^{21} +(1.86173 - 0.985687i) q^{22} +19.4635 q^{23} +(-19.6367 - 13.7986i) q^{24} +24.6226 q^{25} +(19.4949 + 36.8213i) q^{26} +(26.9460 - 1.70660i) q^{27} +(-8.39254 - 5.70406i) q^{28} +0.245501 q^{29} +(3.68573 + 0.0574612i) q^{30} +45.8339 q^{31} +(24.3309 + 20.7848i) q^{32} +(1.52188 - 2.76921i) q^{33} +(13.2404 + 25.0080i) q^{34} +1.55855 q^{35} +(-35.9825 - 1.12222i) q^{36} -46.8458i q^{37} +(12.7683 - 35.7907i) q^{38} +(54.7693 + 30.0998i) q^{39} +(-4.88519 - 0.539629i) q^{40} -25.2928 q^{41} +(-15.2193 - 0.237272i) q^{42} -23.2285i q^{43} +(-2.36827 + 3.48450i) q^{44} +(4.66769 - 2.96403i) q^{45} +(-34.4027 + 18.2144i) q^{46} -35.1820 q^{47} +(47.6219 + 6.01321i) q^{48} +42.5643 q^{49} +(-43.5216 + 23.0424i) q^{50} +(37.1978 + 20.4429i) q^{51} +(-68.9164 - 46.8396i) q^{52} -42.4438 q^{53} +(-46.0314 + 28.2332i) q^{54} -0.647097i q^{55} +(20.1722 + 2.22827i) q^{56} +(-13.4759 - 55.3841i) q^{57} +(-0.433935 + 0.229745i) q^{58} -38.7419i q^{59} +(-6.56848 + 3.34763i) q^{60} +61.8868 q^{61} +(-81.0138 + 42.8925i) q^{62} +(-19.2741 + 12.2392i) q^{63} +(-62.4570 - 13.9687i) q^{64} +12.7983 q^{65} +(-0.0985133 + 6.31893i) q^{66} -54.8238 q^{67} +(-46.8061 - 31.8121i) q^{68} +(-28.1227 + 51.1720i) q^{69} +(-2.75482 + 1.45853i) q^{70} -101.146i q^{71} +(64.6511 - 31.6897i) q^{72} -36.6423 q^{73} +(43.8394 + 82.8023i) q^{74} +(-35.5770 + 64.7357i) q^{75} +(10.9252 + 75.2106i) q^{76} +2.67204i q^{77} +(-124.976 - 1.94839i) q^{78} -19.0101 q^{79} +(9.13981 - 3.61785i) q^{80} +(-34.4473 + 73.3102i) q^{81} +(44.7064 - 23.6697i) q^{82} -135.020 q^{83} +(27.1230 - 13.8232i) q^{84} +8.69223 q^{85} +(21.7378 + 41.0575i) q^{86} +(-0.354723 + 0.645451i) q^{87} +(0.925157 - 8.37532i) q^{88} +96.7299 q^{89} +(-5.47656 + 9.60720i) q^{90} -52.8475 q^{91} +(43.7631 - 64.3898i) q^{92} +(-66.2252 + 120.503i) q^{93} +(62.1860 - 32.9242i) q^{94} +(-7.88118 - 8.61065i) q^{95} +(-89.8013 + 33.9370i) q^{96} -85.3270i q^{97} +(-75.2346 + 39.8327i) q^{98} +(5.08162 + 8.00243i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 16 q^{4} + 6 q^{6} - 48 q^{9}+O(q^{10}) $ 72 * q - 16 * q^4 + 6 * q^6 - 48 * q^9	$ 72 q - 16 q^{4} + 6 q^{6} - 48 q^{9} - 40 q^{16} + 94 q^{24} - 408 q^{25} + 60 q^{28} + 176 q^{30} - 214 q^{36} + 2 q^{42} + 96 q^{45} - 616 q^{49} + 72 q^{54} + 320 q^{57} + 564 q^{58} + 592 q^{61} - 424 q^{64} + 608 q^{66} + 128 q^{73} - 292 q^{76} - 208 q^{81} + 472 q^{82} - 160 q^{85} + 128 q^{93} + 166 q^{96}+O(q^{100}) $ 72 * q - 16 * q^4 + 6 * q^6 - 48 * q^9 - 40 * q^16 + 94 * q^24 - 408 * q^25 + 60 * q^28 + 176 * q^30 - 214 * q^36 + 2 * q^42 + 96 * q^45 - 616 * q^49 + 72 * q^54 + 320 * q^57 + 564 * q^58 + 592 * q^61 - 424 * q^64 + 608 * q^66 + 128 * q^73 - 292 * q^76 - 208 * q^81 + 472 * q^82 - 160 * q^85 + 128 * q^93 + 166 * q^96

Display 100 coefficients 10 coefficients

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 $

$2$	−1.76755	+	0.935824i	−0.883775	+	0.467912i
$2$	−1.76755	+	0.935824i	−0.883775	+	0.467912i
$3$	−1.44490	+	2.62912i	−0.481632	+	0.876374i
$3$	−1.44490	+	2.62912i	−0.481632	+	0.876374i
$4$	2.24847	−	3.30823i	0.562117	−	0.827058i
$5$			0.614363i			0.122873i	0.998111	+	0.0614363i	$0.0195681\pi$
$5$			0.614363i			0.122873i	−0.998111	+	0.0614363i	$0.980432\pi$
$6$	0.0935298	−	5.99927i	0.0155883	−	0.999878i
$7$		−	2.53686i		−	0.362409i	−0.983445	−	0.181205i	$-0.942000\pi$
$7$		−	2.53686i		−	0.362409i	0.983445	−	0.181205i	$-0.0579996\pi$
$8$	−0.878356	+	7.95163i	−0.109794	+	0.993954i
$9$	−4.82456	−	7.59761i	−0.536062	−	0.844179i
$10$	−0.574935	−	1.08592i	−0.0574935	−	0.108592i
$11$	−1.05328			−0.0957530			−0.0478765	−	0.998853i	$-0.515245\pi$
$11$	−1.05328			−0.0957530			−0.0478765	+	0.998853i	$0.515245\pi$
$12$	5.44894	+	10.6915i	0.454079	+	0.890962i
$13$		−	20.8318i		−	1.60245i	−0.598365	−	0.801223i	$-0.704183\pi$
$13$		−	20.8318i		−	1.60245i	0.598365	−	0.801223i	$-0.295817\pi$
$14$	2.37406	+	4.48404i	0.169576	+	0.320288i
$15$	−1.61523	−	0.887689i	−0.107682	−	0.0591793i
$16$	−5.88879	−	14.8769i	−0.368050	−	0.929806i
$17$		−	14.1484i		−	0.832257i	−0.909306	−	0.416128i	$-0.863387\pi$
$17$		−	14.1484i		−	0.832257i	0.909306	−	0.416128i	$-0.136613\pi$
$18$	15.6377	+	8.91422i	0.868759	+	0.495234i
$19$	−14.0156	+	12.8282i	−0.737662	+	0.675170i
$19$	−14.0156	+	12.8282i	−0.737662	+	0.675170i
$20$	2.03245	+	1.38137i	0.101623	+	0.0690687i
$21$	6.66972	+	3.66550i	0.317606	+	0.174548i
$22$	1.86173	−	0.985687i	0.0846241	−	0.0448040i
$23$	19.4635			0.846240			0.423120	−	0.906074i	$-0.360935\pi$
$23$	19.4635			0.846240			0.423120	+	0.906074i	$0.360935\pi$
$24$	−19.6367	−	13.7986i	−0.818195	−	0.574941i
$25$	24.6226			0.984902
$26$	19.4949	+	36.8213i	0.749804	+	1.41620i
$27$	26.9460	−	1.70660i	0.998000	−	0.0632073i
$28$	−8.39254	−	5.70406i	−0.299733	−	0.203716i
$29$	0.245501			0.00846554			0.00423277	−	0.999991i	$-0.498653\pi$
$29$	0.245501			0.00846554			0.00423277	+	0.999991i	$0.498653\pi$
$30$	3.68573	+	0.0574612i	0.122858	+	0.00191537i
$31$	45.8339			1.47851			0.739257	−	0.673424i	$-0.235177\pi$
$31$	45.8339			1.47851			0.739257	+	0.673424i	$0.235177\pi$
$32$	24.3309	+	20.7848i	0.760340	+	0.649525i
$33$	1.52188	−	2.76921i	0.0461177	−	0.0839154i
$34$	13.2404	+	25.0080i	0.389423	+	0.735528i
$35$	1.55855			0.0445301
$36$	−35.9825	−	1.12222i	−0.999514	−	0.0311728i
$37$		−	46.8458i		−	1.26610i	−0.774110	−	0.633051i	$-0.781802\pi$
$37$		−	46.8458i		−	1.26610i	0.774110	−	0.633051i	$-0.218198\pi$
$38$	12.7683	−	35.7907i	0.336007	−	0.941859i
$39$	54.7693	+	30.0998i	1.40434	+	0.771789i
$40$	−4.88519	−	0.539629i	−0.122130	−	0.0134907i
$41$	−25.2928			−0.616899			−0.308449	−	0.951241i	$-0.599810\pi$
$41$	−25.2928			−0.616899			−0.308449	+	0.951241i	$0.599810\pi$
$42$	−15.2193	−	0.237272i	−0.362365	−	0.00564934i
$43$		−	23.2285i		−	0.540198i	−0.962833	−	0.270099i	$-0.912944\pi$
$43$		−	23.2285i		−	0.540198i	0.962833	−	0.270099i	$-0.0870564\pi$
$44$	−2.36827	+	3.48450i	−0.0538244	+	0.0791933i
$45$	4.66769	−	2.96403i	0.103726	−	0.0658673i
$46$	−34.4027	+	18.2144i	−0.747886	+	0.395966i
$47$	−35.1820			−0.748554			−0.374277	−	0.927317i	$-0.622109\pi$
$47$	−35.1820			−0.748554			−0.374277	+	0.927317i	$0.622109\pi$
$48$	47.6219	+	6.01321i	0.992122	+	0.125275i
$49$	42.5643			0.868660
$50$	−43.5216	+	23.0424i	−0.870432	+	0.460848i
$51$	37.1978	+	20.4429i	0.729368	+	0.400841i
$52$	−68.9164	−	46.8396i	−1.32532	−	0.900762i
$53$	−42.4438			−0.800826			−0.400413	−	0.916335i	$-0.631133\pi$
$53$	−42.4438			−0.800826			−0.400413	+	0.916335i	$0.631133\pi$
$54$	−46.0314	+	28.2332i	−0.852432	+	0.522837i
$55$		−	0.647097i		−	0.0117654i
$56$	20.1722	+	2.22827i	0.360218	+	0.0397905i
$57$	−13.4759	−	55.3841i	−0.236420	−	0.971651i
$58$	−0.433935	+	0.229745i	−0.00748163	+	0.00396113i
$59$		−	38.7419i		−	0.656642i	−0.944566	−	0.328321i	$-0.893517\pi$
$59$		−	38.7419i		−	0.656642i	0.944566	−	0.328321i	$-0.106483\pi$
$60$	−6.56848	+	3.34763i	−0.109475	+	0.0557938i
$61$	61.8868			1.01454			0.507269	−	0.861788i	$-0.330655\pi$
$61$	61.8868			1.01454			0.507269	+	0.861788i	$0.330655\pi$
$62$	−81.0138	+	42.8925i	−1.30667	+	0.691814i
$63$	−19.2741	+	12.2392i	−0.305938	+	0.194274i
$64$	−62.4570	−	13.9687i	−0.975890	−	0.218261i
$65$	12.7983			0.196897
$66$	−0.0985133	+	6.31893i	−0.00149263	+	0.0957413i
$67$	−54.8238			−0.818266			−0.409133	−	0.912475i	$-0.634169\pi$
$67$	−54.8238			−0.818266			−0.409133	+	0.912475i	$0.634169\pi$
$68$	−46.8061	−	31.8121i	−0.688325	−	0.467826i
$69$	−28.1227	+	51.1720i	−0.407576	+	0.741622i
$70$	−2.75482	+	1.45853i	−0.0393546	+	0.0208362i
$71$		−	101.146i		−	1.42460i	−0.701876	−	0.712299i	$-0.747654\pi$
$71$		−	101.146i		−	1.42460i	0.701876	−	0.712299i	$-0.252346\pi$
$72$	64.6511	−	31.6897i	0.897932	−	0.440135i
$73$	−36.6423			−0.501950			−0.250975	−	0.967994i	$-0.580751\pi$
$73$	−36.6423			−0.501950			−0.250975	+	0.967994i	$0.580751\pi$
$74$	43.8394	+	82.8023i	0.592424	+	1.11895i
$75$	−35.5770	+	64.7357i	−0.474360	+	0.863143i
$76$	10.9252	+	75.2106i	0.143752	+	0.989614i
$77$			2.67204i			0.0347018i
$78$	−124.976	−	1.94839i	−1.60225	−	0.0249794i
$79$	−19.0101			−0.240635			−0.120317	−	0.992735i	$-0.538391\pi$
$79$	−19.0101			−0.240635			−0.120317	+	0.992735i	$0.538391\pi$
$80$	9.13981	−	3.61785i	0.114248	−	0.0452232i
$81$	−34.4473	+	73.3102i	−0.425275	+	0.905064i
$82$	44.7064	−	23.6697i	0.545200	−	0.288654i
$83$	−135.020			−1.62675			−0.813373	−	0.581743i	$-0.802371\pi$
$83$	−135.020			−1.62675			−0.813373	+	0.581743i	$0.802371\pi$
$84$	27.1230	−	13.8232i	0.322893	−	0.164562i
$85$	8.69223			0.102262
$86$	21.7378	+	41.0575i	0.252765	+	0.477413i
$87$	−0.354723	+	0.645451i	−0.00407727	+	0.00741898i
$88$	0.925157	−	8.37532i	0.0105131	−	0.0951741i
$89$	96.7299			1.08685			0.543426	−	0.839457i	$-0.317127\pi$
$89$	96.7299			1.08685			0.543426	+	0.839457i	$0.317127\pi$
$90$	−5.47656	+	9.60720i	−0.0608507	+	0.106747i
$91$	−52.8475			−0.580741
$92$	43.7631	−	64.3898i	0.475686	−	0.699889i
$93$	−66.2252	+	120.503i	−0.712099	+	1.29573i
$94$	62.1860	−	32.9242i	0.661553	−	0.350257i
$95$	−7.88118	−	8.61065i	−0.0829598	−	0.0906384i
$96$	−89.8013	+	33.9370i	−0.935430	+	0.353511i
$97$		−	85.3270i		−	0.879660i	−0.898081	−	0.439830i	$-0.855039\pi$
$97$		−	85.3270i		−	0.879660i	0.898081	−	0.439830i	$-0.144961\pi$
$98$	−75.2346	+	39.8327i	−0.767700	+	0.406456i
$99$	5.08162	+	8.00243i	0.0513295	+	0.0808326i
$100$	55.3630	−	81.4571i	0.553630	−	0.814571i
$101$		−	95.8311i		−	0.948823i	−0.880303	−	0.474412i	$-0.842661\pi$
$101$		−	95.8311i		−	0.948823i	0.880303	−	0.474412i	$-0.157339\pi$
$102$	−84.8799	−	1.32329i	−0.832156	−	0.0129735i
$103$	11.1758			0.108503			0.0542514	−	0.998527i	$-0.482723\pi$
$103$	11.1758			0.108503			0.0542514	+	0.998527i	$0.482723\pi$
$104$	165.647	+	18.2977i	1.59276	+	0.175940i
$105$	−2.25195	+	4.09763i	−0.0214471	+	0.0390250i
$106$	75.0215	−	39.7199i	0.707750	−	0.374716i
$107$		−	8.03908i		−	0.0751316i	−0.999294	−	0.0375658i	$-0.988040\pi$
$107$		−	8.03908i		−	0.0751316i	0.999294	−	0.0375658i	$-0.0119604\pi$
$108$	54.9414	−	92.9809i	0.508717	−	0.860934i
$109$			95.5631i			0.876725i	0.898798	+	0.438363i	$0.144441\pi$
$109$			95.5631i			0.876725i	−0.898798	+	0.438363i	$0.855559\pi$
$110$	0.605569	+	1.14378i	0.00550518	+	0.0103980i
$111$	123.163	+	67.6872i	1.10958	+	0.609795i
$112$	−37.7407	+	14.9391i	−0.336970	+	0.133385i
$113$	135.634			1.20030			0.600151	−	0.799887i	$-0.295107\pi$
$113$	135.634			1.20030			0.600151	+	0.799887i	$0.295107\pi$
$114$	75.6492	+	85.2831i	0.663589	+	0.748097i
$115$			11.9577i			0.103980i
$116$	0.552000	−	0.812173i	0.00475862	−	0.00700149i
$117$	−158.272	+	100.504i	−1.35275	+	0.859011i
$118$	36.2556	+	68.4782i	0.307251	+	0.580324i
$119$	−35.8925			−0.301618
$120$	8.47733	−	12.0640i	0.0706444	−	0.100534i
$121$	−119.891			−0.990831
$122$	−109.388	+	57.9151i	−0.896623	+	0.474714i
$123$	36.5455	−	66.4980i	0.297118	−	0.540634i
$124$	103.056	−	151.629i	0.831097	−	1.22282i
$125$			30.4862i			0.243890i
$126$	22.6142	−	39.6706i	0.179477	−	0.314846i
$127$	−24.4645			−0.192634			−0.0963168	−	0.995351i	$-0.530706\pi$
$127$	−24.4645			−0.192634			−0.0963168	+	0.995351i	$0.530706\pi$
$128$	123.468	−	33.7583i	0.964595	−	0.263737i
$129$	61.0705	+	33.5627i	0.473415	+	0.260176i
$130$	−22.6216	+	11.9769i	−0.174012	+	0.0921303i
$131$	−67.4165			−0.514630			−0.257315	−	0.966328i	$-0.582838\pi$
$131$	−67.4165			−0.514630			−0.257315	+	0.966328i	$0.582838\pi$
$132$	−5.73928	−	11.2612i	−0.0434794	−	0.0853122i
$133$	32.5435	+	35.5556i	0.244688	+	0.267336i
$134$	96.9038	−	51.3054i	0.723163	−	0.382876i
$135$	1.04847	+	16.5546i	0.00776645	+	0.122627i
$136$	112.503	+	12.4273i	0.827225	+	0.0913772i
$137$		−	238.670i		−	1.74212i	−0.491180	−	0.871058i	$-0.663434\pi$
$137$		−	238.670i		−	1.74212i	0.491180	−	0.871058i	$-0.336566\pi$
$138$	1.82042	−	116.767i	0.0131914	−	0.846137i
$139$			71.7384i			0.516104i	0.966131	+	0.258052i	$0.0830805\pi$
$139$			71.7384i			0.516104i	−0.966131	+	0.258052i	$0.916919\pi$
$140$	3.50436	−	5.15606i	0.0250311	−	0.0368290i
$141$	50.8343	−	92.4978i	0.360527	−	0.656013i
$142$	94.6553	+	178.781i	0.666587	+	1.25902i
$143$			21.9418i			0.153439i
$144$	−84.6180	+	116.515i	−0.587625	+	0.809133i
$145$			0.150826i			0.00104018i
$146$	64.7672	−	34.2908i	0.443611	−	0.234868i
$147$	−61.5010	+	111.907i	−0.418374	+	0.761270i
$148$	−154.977	−	105.331i	−1.04714	−	0.711697i
$149$			155.869i			1.04610i	0.852303	+	0.523049i	$0.175205\pi$
$149$			155.869i			1.04610i	−0.852303	+	0.523049i	$0.824795\pi$
$150$	2.30294	−	147.717i	0.0153529	−	0.984783i
$151$	140.319			0.929265			0.464632	−	0.885504i	$-0.346186\pi$
$151$	140.319			0.929265			0.464632	+	0.885504i	$0.346186\pi$
$152$	−89.6947	−	122.715i	−0.590097	−	0.807332i
$153$	−107.494	+	68.2596i	−0.702574	+	0.446141i
$154$	−2.50055	−	4.72296i	−0.0162374	−	0.0306685i
$155$			28.1586i			0.181669i
$156$	222.724	−	113.511i	1.42772	−	0.727637i
$157$	−12.8449			−0.0818143			−0.0409072	−	0.999163i	$-0.513025\pi$
$157$	−12.8449			−0.0818143			−0.0409072	+	0.999163i	$0.513025\pi$
$158$	33.6014	−	17.7901i	0.212667	−	0.112596i
$159$	61.3268	−	111.590i	0.385703	−	0.701823i
$160$	−12.7694	+	14.9480i	−0.0798087	+	0.0934249i
$161$		−	49.3763i		−	0.306685i
$162$	−7.71809	−	161.816i	−0.0476425	−	0.998864i
$163$		−	282.827i		−	1.73514i	−0.497318	−	0.867568i	$-0.665682\pi$
$163$		−	282.827i		−	1.73514i	0.497318	−	0.867568i	$-0.334318\pi$
$164$	−56.8701	+	83.6746i	−0.346769	+	0.510211i
$165$	1.70130	+	0.934988i	0.0103109	+	0.00566659i
$166$	238.654	−	126.355i	1.43768	−	0.761174i
$167$		−	161.639i		−	0.967898i	−0.875096	−	0.483949i	$-0.839202\pi$
$167$		−	161.639i		−	0.967898i	0.875096	−	0.483949i	$-0.160798\pi$
$168$	−35.0051	+	49.8156i	−0.208364	+	0.296521i
$169$	−264.964			−1.56784
$170$	−15.3639	+	8.13440i	−0.0903762	+	0.0478494i
$171$	165.083	+	44.5944i	0.965397	+	0.260786i
$172$	−76.8453	−	52.2285i	−0.446775	−	0.303654i
$173$	231.702			1.33932			0.669659	−	0.742669i	$-0.266440\pi$
$173$	231.702			1.33932			0.669659	+	0.742669i	$0.266440\pi$
$174$	0.0229616	−	1.47282i	0.000131963	−	0.00846451i
$175$		−	62.4641i		−	0.356938i
$176$	6.20256	+	15.6696i	0.0352418	+	0.0890317i
$177$	101.857	+	55.9779i	0.575464	+	0.316259i
$178$	−170.975	+	90.5221i	−0.960533	+	0.508551i
$179$			212.421i			1.18671i	0.804941	+	0.593355i	$0.202197\pi$
$179$			212.421i			1.18671i	−0.804941	+	0.593355i	$0.797803\pi$
$180$	0.689450	−	22.1063i	0.00383028	−	0.122813i
$181$			263.835i			1.45765i	0.684698	+	0.728827i	$0.259934\pi$
$181$			263.835i			1.45765i	−0.684698	+	0.728827i	$0.740066\pi$
$182$	93.4106	−	49.4559i	0.513245	−	0.271736i
$183$	−89.4199	+	162.708i	−0.488633	+	0.889114i
$184$	−17.0959	+	154.767i	−0.0929125	+	0.841124i
$185$	28.7803			0.155569
$186$	4.28684	−	274.970i	0.0230475	−	1.47833i
$187$			14.9022i			0.0796911i
$188$	−79.1056	+	116.390i	−0.420775	+	0.619097i
$189$	−4.32941	−	68.3584i	−0.0229069	−	0.361685i
$190$	21.9884	+	7.84435i	0.115729	+	0.0412861i
$191$	188.192			0.985296			0.492648	−	0.870229i	$-0.336029\pi$
$191$	188.192			0.985296			0.492648	+	0.870229i	$0.336029\pi$
$192$	126.969	−	144.024i	0.661298	−	0.750123i
$193$			276.161i			1.43088i	0.698672	+	0.715442i	$0.253775\pi$
$193$			276.161i			1.43088i	−0.698672	+	0.715442i	$0.746225\pi$
$194$	79.8511	+	150.820i	0.411603	+	0.777422i
$195$	−18.4922	+	33.6482i	−0.0948317	+	0.172555i
$196$	95.7045	−	140.813i	0.488288	−	0.718432i
$197$			267.688i			1.35882i	0.733757	+	0.679412i	$0.237765\pi$
$197$			267.688i			1.35882i	−0.733757	+	0.679412i	$0.762235\pi$
$198$	−16.4709	−	9.38919i	−0.0831863	−	0.0474202i
$199$			93.4486i			0.469591i	0.972045	+	0.234796i	$0.0754421\pi$
$199$			93.4486i			0.469591i	−0.972045	+	0.234796i	$0.924558\pi$
$200$	−21.6274	+	195.790i	−0.108137	+	0.978948i
$201$	79.2146	−	144.138i	0.394103	−	0.717107i
$202$	89.6811	+	169.386i	0.443966	+	0.838546i
$203$		−	0.622802i		−	0.00306799i
$204$	151.268	−	77.0937i	0.741509	−	0.377910i
$205$		−	15.5390i		−	0.0757999i
$206$	−19.7538	+	10.4586i	−0.0958921	+	0.0507698i
$207$	−93.9029	−	147.876i	−0.453637	−	0.714378i
$208$	−309.913	+	122.674i	−1.48996	+	0.589780i
$209$	14.7624	−	13.5118i	0.0706333	−	0.0646495i
$210$	0.145771	−	9.35019i	0.000694149	−	0.0445247i
$211$	37.3532			0.177029			0.0885146	−	0.996075i	$-0.471788\pi$
$211$	37.3532			0.177029			0.0885146	+	0.996075i	$0.471788\pi$
$212$	−95.4334	+	140.414i	−0.450158	+	0.662329i
$213$	265.926	+	146.146i	1.24848	+	0.686132i
$214$	7.52317	+	14.2095i	0.0351550	+	0.0663994i
$215$	14.2707			0.0663755
$216$	−10.0979	+	215.764i	−0.0467497	+	0.998907i
$217$		−	116.274i		−	0.535827i
$218$	−89.4302	−	168.913i	−0.410230	−	0.774828i
$219$	52.9443	−	96.3371i	0.241755	−	0.439896i
$220$	−2.14075	−	1.45498i	−0.00973067	−	0.00661353i
$221$	−294.736			−1.33365
$222$	−281.041	−	4.38147i	−1.26595	−	0.0197364i
$223$	−226.283			−1.01472			−0.507361	−	0.861733i	$-0.669379\pi$
$223$	−226.283			−1.01472			−0.507361	+	0.861733i	$0.669379\pi$
$224$	52.7282	−	61.7242i	0.235394	−	0.275554i
$225$	−118.793	−	187.073i	−0.527969	−	0.831434i
$226$	−239.740	+	126.930i	−1.06080	+	0.561636i
$227$		−	201.415i		−	0.887290i	−0.896203	−	0.443645i	$-0.853685\pi$
$227$		−	201.415i		−	0.887290i	0.896203	−	0.443645i	$-0.146315\pi$
$228$	−213.524	−	79.9478i	−0.936507	−	0.350648i
$229$	−179.177			−0.782432			−0.391216	−	0.920299i	$-0.627945\pi$
$229$	−179.177			−0.782432			−0.391216	+	0.920299i	$0.627945\pi$
$230$	−11.1903	−	21.1358i	−0.0486533	−	0.0918946i
$231$	−7.02511	−	3.86081i	−0.0304117	−	0.0167135i
$232$	−0.215637	+	1.95213i	−0.000929469	+	0.00841436i
$233$		−	47.8619i		−	0.205416i	−0.994712	−	0.102708i	$-0.967249\pi$
$233$		−	47.8619i		−	0.205416i	0.994712	−	0.102708i	$-0.0327507\pi$
$234$	185.699	−	325.761i	0.793587	−	1.39214i
$235$		−	21.6145i		−	0.0919767i
$236$	−128.167	−	87.1098i	−0.543081	−	0.369109i
$237$	27.4676	−	49.9799i	0.115897	−	0.210886i
$238$	63.4418	−	33.5891i	0.266562	−	0.141130i
$239$	−403.764			−1.68939			−0.844694	−	0.535250i	$-0.820217\pi$
$239$	−403.764			−1.68939			−0.844694	+	0.535250i	$0.820217\pi$
$240$	−3.69429	+	29.2571i	−0.0153929	+	0.121905i
$241$		−	151.061i		−	0.626811i	−0.949619	−	0.313405i	$-0.898530\pi$
$241$		−	151.061i		−	0.626811i	0.949619	−	0.313405i	$-0.101470\pi$
$242$	211.913	−	112.196i	0.875672	−	0.463622i
$243$	−142.969	−	196.492i	−0.588348	−	0.808608i
$244$	139.150	−	204.736i	0.570288	−	0.839081i
$245$			26.1499i			0.106734i
$246$	−2.36563	+	151.739i	−0.00961640	+	0.616824i
$247$	267.235	+	291.970i	1.08192	+	1.18206i
$248$	−40.2585	+	364.455i	−0.162333	+	1.46958i
$249$	195.090	−	354.984i	0.783492	−	1.42564i
$250$	−28.5298	−	53.8860i	−0.114119	−	0.215544i
$251$	−10.6103			−0.0422722			−0.0211361	−	0.999777i	$-0.506728\pi$
$251$	−10.6103			−0.0422722			−0.0211361	+	0.999777i	$0.506728\pi$
$252$	−2.84692	+	91.2827i	−0.0112973	+	0.362233i
$253$	−20.5006			−0.0810300
$254$	43.2422	−	22.8944i	0.170245	−	0.0901356i
$255$	−12.5594	+	22.8529i	−0.0492524	+	0.0896193i
$256$	−186.644	+	175.214i	−0.729079	+	0.684429i
$257$	−304.107			−1.18330			−0.591649	−	0.806196i	$-0.701523\pi$
$257$	−304.107			−1.18330			−0.591649	+	0.806196i	$0.701523\pi$
$258$	−139.354	−	2.17256i	−0.540132	−	0.00842076i
$259$	−118.841			−0.458847
$260$	28.7765	−	42.3397i	0.110679	−	0.162845i
$261$	−1.18443	−	1.86522i	−0.00453805	−	0.00714643i
$262$	119.162	−	63.0900i	0.454817	−	0.240801i
$263$	−124.165			−0.472111			−0.236055	−	0.971740i	$-0.575855\pi$
$263$	−124.165			−0.472111			−0.236055	+	0.971740i	$0.575855\pi$
$264$	20.6830	+	14.5338i	0.0783446	+	0.0550523i
$265$		−	26.0759i		−	0.0983995i
$266$	−90.7960	−	32.3914i	−0.341339	−	0.121772i
$267$	−139.765	+	254.315i	−0.523463	+	0.952489i
$268$	−123.270	+	181.370i	−0.459961	+	0.676753i
$269$	−349.961			−1.30097			−0.650484	−	0.759520i	$-0.725434\pi$
$269$	−349.961			−1.30097			−0.650484	+	0.759520i	$0.725434\pi$
$270$	−17.3454	−	28.2799i	−0.0642424	−	0.104741i
$271$			227.793i			0.840564i	0.907394	+	0.420282i	$0.138069\pi$
$271$			227.793i			0.840564i	−0.907394	+	0.420282i	$0.861931\pi$
$272$	−210.484	+	83.3168i	−0.773838	+	0.306312i
$273$	76.3591	−	138.942i	0.279703	−	0.508947i
$274$	223.353	+	421.861i	0.815157	+	1.53964i
$275$	−25.9345			−0.0943073
$276$	106.056	+	208.095i	0.384259	+	0.753967i
$277$	524.413			1.89319			0.946594	−	0.322427i	$-0.104499\pi$
$277$	524.413			1.89319			0.946594	+	0.322427i	$0.104499\pi$
$278$	−67.1345	−	126.801i	−0.241491	−	0.456119i
$279$	−221.128	−	348.228i	−0.792575	−	1.24813i
$280$	−1.36897	+	12.3931i	−0.00488916	+	0.0442609i
$281$	491.723			1.74990			0.874951	−	0.484211i	$-0.160893\pi$
$281$	491.723			1.74990			0.874951	+	0.484211i	$0.160893\pi$
$282$	−3.29057	+	211.067i	−0.0116687	+	0.748463i
$283$			224.463i			0.793157i	0.918001	+	0.396579i	$0.129803\pi$
$283$			224.463i			0.793157i	−0.918001	+	0.396579i	$0.870197\pi$
$284$	−334.616	−	227.425i	−1.17823	−	0.800791i
$285$	34.0259	−	8.27911i	0.119389	−	0.0290495i
$286$	−20.5336	−	38.7832i	−0.0717960	−	0.135606i
$287$			64.1645i			0.223570i
$288$	40.5289	−	285.134i	0.140725	−	0.990049i
$289$	88.8237			0.307348
$290$	−0.141147	−	0.266593i	−0.000486714	−	0.000919287i
$291$	224.335	+	123.289i	0.770911	+	0.423672i
$292$	−82.3891	+	121.221i	−0.282154	+	0.415141i
$293$	−323.122			−1.10281			−0.551403	−	0.834239i	$-0.685907\pi$
$293$	−323.122			−1.10281			−0.551403	+	0.834239i	$0.685907\pi$
$294$	3.98103	−	255.355i	0.0135409	−	0.868554i
$295$	23.8016			0.0806832
$296$	372.501	+	41.1473i	1.25845	+	0.139011i
$297$	−28.3818	+	1.79753i	−0.0955615	+	0.00605229i
$298$	−145.866	−	275.505i	−0.489482	−	0.924515i
$299$		−	405.460i		−	1.35605i
$300$	134.167	+	263.253i	0.447223	+	0.877510i
$301$	−58.9276			−0.195773
$302$	−248.021	+	131.314i	−0.821261	+	0.434814i
$303$	251.952	+	138.466i	0.831524	+	0.456983i
$304$	273.379	+	132.966i	0.899273	+	0.437387i
$305$			38.0209i			0.124659i
$306$	126.122	−	221.248i	0.412162	−	0.723031i
$307$	144.672			0.471244			0.235622	−	0.971845i	$-0.424287\pi$
$307$	144.672			0.471244			0.235622	+	0.971845i	$0.424287\pi$
$308$	8.83971	+	6.00798i	0.0287004	+	0.0195064i
$309$	−16.1479	+	29.3825i	−0.0522584	+	0.0950891i
$310$	−26.3515	−	49.7718i	−0.0850050	−	0.160554i
$311$	238.327			0.766324			0.383162	−	0.923681i	$-0.374835\pi$
$311$	238.327			0.766324			0.383162	+	0.923681i	$0.374835\pi$
$312$	−287.449	+	409.068i	−0.921312	+	1.31111i
$313$	179.693			0.574099			0.287050	−	0.957916i	$-0.407326\pi$
$313$	179.693			0.574099			0.287050	+	0.957916i	$0.407326\pi$
$314$	22.7039	−	12.0205i	0.0723055	−	0.0382819i
$315$	−7.51934	−	11.8413i	−0.0238709	−	0.0375914i
$316$	−42.7437	+	62.8899i	−0.135265	+	0.199019i
$317$	45.4076			0.143242			0.0716208	−	0.997432i	$-0.477183\pi$
$317$	45.4076			0.143242			0.0716208	+	0.997432i	$0.477183\pi$
$318$	−3.96975	+	254.632i	−0.0124835	+	0.800728i
$319$	−0.258582			−0.000810601
$320$	8.58186	−	38.3712i	0.0268183	−	0.119910i
$321$	21.1357	+	11.6156i	0.0658434	+	0.0361858i
$322$	46.2075	+	87.2751i	0.143502	+	0.271041i
$323$	181.499	+	198.298i	0.561915	+	0.613924i
$324$	165.073	+	278.795i	0.509486	+	0.860479i
$325$		−	512.932i		−	1.57825i
$326$	264.677	+	499.911i	0.811891	+	1.53347i
$327$	−251.247	−	138.079i	−0.768339	−	0.422259i
$328$	22.2161	−	201.119i	0.0677321	−	0.613169i
$329$			89.2520i			0.271283i
$330$	−3.88211	−	0.0605229i	−0.0117640	−	0.000183403i
$331$	443.252			1.33913			0.669565	−	0.742754i	$-0.266481\pi$
$331$	443.252			1.33913			0.669565	+	0.742754i	$0.266481\pi$
$332$	−303.588	+	446.677i	−0.914421	+	1.34541i
$333$	−355.916	+	226.010i	−1.06882	+	0.678709i
$334$	151.266	+	285.705i	0.452891	+	0.855404i
$335$		−	33.6817i		−	0.100542i
$336$	15.2547	−	120.810i	0.0454009	−	0.359554i
$337$		−	77.5130i		−	0.230009i	−0.993365	−	0.115004i	$-0.963312\pi$
$337$		−	77.5130i		−	0.230009i	0.993365	−	0.115004i	$-0.0366882\pi$
$338$	468.338	−	247.960i	1.38561	−	0.733609i
$339$	−195.977	+	356.599i	−0.578104	+	1.05191i
$340$	19.5442	−	28.7559i	0.0574829	−	0.0845762i
$341$	−48.2761			−0.141572
$342$	−333.525	+	75.6657i	−0.975218	+	0.221245i
$343$		−	232.286i		−	0.677219i
$344$	184.705	+	20.4029i	0.536932	+	0.0593107i
$345$	−31.4381	−	17.2776i	−0.0911250	−	0.0500799i
$346$	−409.545	+	216.832i	−1.18366	+	0.626683i
$347$	362.339			1.04421			0.522103	−	0.852883i	$-0.325148\pi$
$347$	362.339			1.04421			0.522103	+	0.852883i	$0.325148\pi$
$348$	1.33772	+	2.62478i	0.00384402	+	0.00754247i
$349$	−188.930			−0.541346			−0.270673	−	0.962671i	$-0.587246\pi$
$349$	−188.930			−0.541346			−0.270673	+	0.962671i	$0.587246\pi$
$350$	58.4554	+	110.408i	0.167015	+	0.315453i
$351$	−35.5515	−	561.334i	−0.101286	−	1.59924i
$352$	−25.6273	−	21.8923i	−0.0728049	−	0.0621939i
$353$		−	490.791i		−	1.39034i	−0.718844	−	0.695172i	$-0.755328\pi$
$353$		−	490.791i		−	1.39034i	0.718844	−	0.695172i	$-0.244672\pi$
$354$	−232.423	−	3.62352i	−0.656562	−	0.0102359i
$355$	62.1406			0.175044
$356$	217.494	−	320.005i	0.610938	−	0.898890i
$357$	51.8609	−	94.3657i	0.145269	−	0.264330i
$358$	−198.789	−	375.465i	−0.555275	−	1.04878i
$359$	555.286			1.54676			0.773380	−	0.633943i	$-0.218565\pi$
$359$	555.286			1.54676			0.773380	+	0.633943i	$0.218565\pi$
$360$	19.4690	+	39.7192i	0.0540805	+	0.110331i
$361$	31.8730	−	359.590i	0.0882909	−	0.996095i
$362$	−246.904	−	466.342i	−0.682054	−	1.28824i
$363$	173.229	−	315.207i	0.477216	−	0.868339i
$364$	−118.826	+	174.832i	−0.326445	+	0.480307i
$365$		−	22.5117i		−	0.0616758i
$366$	5.78826	−	371.276i	0.0158149	−	1.01441i
$367$			428.266i			1.16694i	0.812136	+	0.583469i	$0.198305\pi$
$367$			428.266i			1.16694i	−0.812136	+	0.583469i	$0.801695\pi$
$368$	−114.617	−	289.557i	−0.311458	−	0.786839i
$369$	122.027	+	192.165i	0.330696	+	0.520773i
$370$	−50.8706	+	26.9333i	−0.137488	+	0.0727927i
$371$			107.674i			0.290227i
$372$	249.746	+	490.035i	0.671361	+	1.31730i
$373$			354.262i			0.949765i	0.880049	+	0.474882i	$0.157509\pi$
$373$			354.262i			0.949765i	−0.880049	+	0.474882i	$0.842491\pi$
$374$	−13.9459	−	26.3404i	−0.0372884	−	0.0704290i
$375$	−80.1520	−	44.0494i	−0.213739	−	0.117465i
$376$	30.9023	−	279.755i	0.0821871	−	0.744028i
$377$		−	5.11422i		−	0.0135656i
$378$	71.6239	+	116.775i	0.189481	+	0.308929i
$379$	−491.206			−1.29606			−0.648029	−	0.761616i	$-0.724406\pi$
$379$	−491.206			−1.29606			−0.648029	+	0.761616i	$0.724406\pi$
$380$	−46.2066	+	6.71202i	−0.121596	+	0.0176632i
$381$	35.3486	−	64.3200i	0.0927784	−	0.168819i
$382$	−332.638	+	176.114i	−0.870780	+	0.461032i
$383$			713.617i			1.86323i	0.363446	+	0.931615i	$0.381600\pi$
$383$			713.617i			1.86323i	−0.363446	+	0.931615i	$0.618400\pi$
$384$	−89.6438	+	373.390i	−0.233447	+	0.972369i
$385$	−1.64160			−0.00426389
$386$	−258.438	−	488.128i	−0.669528	−	1.26458i
$387$	−176.481	+	112.067i	−0.456023	+	0.289579i
$388$	−282.282	−	191.855i	−0.727530	−	0.494472i
$389$			221.340i			0.568998i	0.958676	+	0.284499i	$0.0918272\pi$
$389$			221.340i			0.568998i	−0.958676	+	0.284499i	$0.908173\pi$
$390$	1.19702	−	76.7804i	0.00306928	−	0.196873i
$391$		−	275.377i		−	0.704289i
$392$	−37.3866	+	338.456i	−0.0953740	+	0.863408i
$393$	97.4097	−	177.246i	0.247862	−	0.451008i
$394$	−250.509	−	473.152i	−0.635810	−	1.20089i
$395$		−	11.6791i		−	0.0295674i
$396$	37.8997	+	1.18202i	0.0957064	+	0.00298489i
$397$	503.939			1.26937			0.634684	−	0.772772i	$-0.281130\pi$
$397$	503.939			1.26937			0.634684	+	0.772772i	$0.281130\pi$
$398$	−87.4515	−	165.175i	−0.219727	−	0.415013i
$399$	−140.502	+	34.1866i	−0.352135	+	0.0856807i
$400$	−144.997	−	366.307i	−0.362493	−	0.915768i
$401$	762.374			1.90118			0.950590	−	0.310448i	$-0.100479\pi$
$401$	762.374			1.90118			0.950590	+	0.310448i	$0.100479\pi$
$402$	−5.12766	+	328.903i	−0.0127554	+	0.818166i
$403$		−	954.804i		−	2.36924i
$404$	−317.032	−	215.473i	−0.784732	−	0.533349i
$405$	−45.0390	−	21.1631i	−0.111207	−	0.0522547i
$406$	0.582833	+	1.10083i	0.00143555	+	0.00271141i
$407$			49.3419i			0.121233i
$408$	−195.227	+	277.827i	−0.478499	+	0.680948i
$409$			284.887i			0.696545i	0.937393	+	0.348273i	$0.113232\pi$
$409$			284.887i			0.696545i	−0.937393	+	0.348273i	$0.886768\pi$
$410$	14.5417	+	27.4659i	0.0354677	+	0.0669901i
$411$	627.492	+	344.853i	1.52674	+	0.839058i
$412$	25.1284	−	36.9721i	0.0609913	−	0.0897382i
$413$	−98.2829			−0.237973
$414$	304.364	+	173.502i	0.735179	+	0.419087i
$415$		−	82.9512i		−	0.199882i
$416$	432.985	−	506.857i	1.04083	−	1.21841i
$417$	−188.609	−	103.654i	−0.452300	−	0.248572i
$418$	−13.4486	+	37.6977i	−0.0321737	+	0.0901858i
$419$	−485.175			−1.15794			−0.578968	−	0.815350i	$-0.696544\pi$
$419$	−485.175			−1.15794			−0.578968	+	0.815350i	$0.696544\pi$
$420$	8.49248	+	16.6633i	0.0202202	+	0.0396746i
$421$			140.305i			0.333266i	0.986019	+	0.166633i	$0.0532896\pi$
$421$			140.305i			0.333266i	−0.986019	+	0.166633i	$0.946710\pi$
$422$	−66.0236	+	34.9560i	−0.156454	+	0.0828341i
$423$	169.738	+	267.299i	0.401271	+	0.631913i
$424$	37.2807	−	337.497i	0.0879262	−	0.795984i
$425$		−	348.369i		−	0.819692i
$426$	−606.805	−	9.46021i	−1.42443	−	0.0222071i
$427$		−	156.998i		−	0.367678i
$428$	−26.5951	−	18.0756i	−0.0621382	−	0.0422327i
$429$	−57.6876	−	31.7036i	−0.134470	−	0.0739011i
$430$	−25.2242	+	13.3549i	−0.0586610	+	0.0310579i
$431$			679.526i			1.57663i	0.615274	+	0.788314i	$0.289045\pi$
$431$			679.526i			1.57663i	−0.615274	+	0.788314i	$0.710955\pi$
$432$	−184.068	−	390.823i	−0.426084	−	0.904684i
$433$		−	510.460i		−	1.17889i	−0.807808	−	0.589446i	$-0.799346\pi$
$433$		−	510.460i		−	1.17889i	0.807808	−	0.589446i	$-0.200654\pi$
$434$	108.812	+	205.521i	0.250720	+	0.473551i
$435$	−0.396541	−	0.217928i	−0.000911588	−	0.000500985i
$436$	316.145	+	214.870i	0.725103	+	0.492822i
$437$	−272.793	+	249.683i	−0.624239	+	0.571356i
$438$	−3.42715	+	219.827i	−0.00782454	+	0.501889i
$439$	−108.632			−0.247454			−0.123727	−	0.992316i	$-0.539485\pi$
$439$	−108.632			−0.247454			−0.123727	+	0.992316i	$0.539485\pi$
$440$	5.14548	+	0.568382i	0.0116943	+	0.00129178i
$441$	−205.354	−	323.387i	−0.465655	−	0.733304i
$442$	520.961	−	275.821i	1.17864	−	0.624030i
$443$	722.458			1.63083			0.815415	−	0.578877i	$-0.196509\pi$
$443$	722.458			1.63083			0.815415	+	0.578877i	$0.196509\pi$
$444$	500.854	−	255.260i	1.12805	−	0.574910i
$445$			59.4272i			0.133544i
$446$	399.967	−	211.761i	0.896787	−	0.474801i
$447$	−409.797	−	225.214i	−0.916772	−	0.503834i
$448$	−35.4368	+	158.445i	−0.0790999	+	0.353672i
$449$	−348.240			−0.775590			−0.387795	−	0.921746i	$-0.626763\pi$
$449$	−348.240			−0.775590			−0.387795	+	0.921746i	$0.626763\pi$
$450$	385.039	+	219.491i	0.855643	+	0.487757i
$451$	26.6405			0.0590699
$452$	304.969	−	448.709i	0.674710	−	0.992720i
$453$	−202.746	+	368.916i	−0.447563	+	0.814383i
$454$	188.489	+	356.011i	0.415173	+	0.784164i
$455$		−	32.4675i		−	0.0713572i
$456$	452.231	−	58.5087i	0.991734	−	0.128309i
$457$	−63.2068			−0.138308			−0.0691541	−	0.997606i	$-0.522030\pi$
$457$	−63.2068			−0.138308			−0.0691541	+	0.997606i	$0.522030\pi$
$458$	316.704	−	167.678i	0.691494	−	0.366109i
$459$	−24.1456	−	381.242i	−0.0526047	−	0.830593i
$460$	39.5587	+	26.8864i	0.0859972	+	0.0584487i
$461$			54.9910i			0.119286i	0.998220	+	0.0596432i	$0.0189963\pi$
$461$			54.9910i			0.119286i	−0.998220	+	0.0596432i	$0.981004\pi$
$462$	16.0303	+	0.249915i	0.0346975	+	0.000540941i
$463$		−	280.716i		−	0.606297i	−0.952943	−	0.303149i	$-0.901962\pi$
$463$		−	280.716i		−	0.606297i	0.952943	−	0.303149i	$-0.0980379\pi$
$464$	−1.44570	−	3.65229i	−0.00311574	−	0.00787131i
$465$	−74.0325	−	40.6863i	−0.159210	−	0.0874974i
$466$	44.7903	+	84.5983i	0.0961165	+	0.181541i
$467$	410.634			0.879302			0.439651	−	0.898169i	$-0.355102\pi$
$467$	410.634			0.879302			0.439651	+	0.898169i	$0.355102\pi$
$468$	−23.3779	+	749.581i	−0.0499527	+	1.60167i
$469$			139.081i			0.296547i
$470$	20.2274	+	38.2048i	0.0430370	+	0.0812867i
$471$	18.5595	−	33.7707i	0.0394044	−	0.0716999i
$472$	308.061	+	34.0291i	0.652672	+	0.0720956i
$473$			24.4662i			0.0517255i
$474$	−1.77801	+	114.047i	−0.00375108	+	0.240605i
$475$	−345.099	+	315.864i	−0.726525	+	0.664977i
$476$	−80.7031	+	118.741i	−0.169544	+	0.249455i
$477$	204.772	+	322.471i	0.429292	+	0.676040i
$478$	713.673	−	377.852i	1.49304	−	0.790485i
$479$	−744.185			−1.55362			−0.776811	−	0.629733i	$-0.783164\pi$
$479$	−744.185			−1.55362			−0.776811	+	0.629733i	$0.783164\pi$
$480$	−20.8496	−	55.1706i	−0.0434367	−	0.114939i
$481$	−975.882			−2.02886
$482$	141.367	+	267.009i	0.293292	+	0.553960i
$483$	129.816	+	71.3436i	0.268771	+	0.147709i
$484$	−269.570	+	396.626i	−0.556963	+	0.819475i
$485$	52.4217			0.108086
$486$	436.586	+	213.515i	0.898325	+	0.439332i
$487$	396.240			0.813634			0.406817	−	0.913510i	$-0.366639\pi$
$487$	396.240			0.813634			0.406817	+	0.913510i	$0.366639\pi$
$488$	−54.3586	+	492.101i	−0.111391	+	1.00840i
$489$	743.587	+	408.656i	1.52063	+	0.835697i
$490$	−24.4717	−	46.2213i	−0.0499423	−	0.0943292i
$491$	497.509			1.01326			0.506628	−	0.862165i	$-0.330892\pi$
$491$	497.509			1.01326			0.506628	+	0.862165i	$0.330892\pi$
$492$	−137.819	−	270.419i	−0.280120	−	0.549633i
$493$		−	3.47343i		−	0.00704550i
$494$	−745.584	−	265.986i	−1.50928	−	0.538434i
$495$	−4.91639	+	3.12196i	−0.00993211	+	0.00630699i
$496$	−269.906	−	681.867i	−0.544166	−	1.37473i
$497$	−256.595			−0.516288
$498$	−12.6284	+	810.021i	−0.0253582	+	1.62655i
$499$			749.433i			1.50187i	0.660377	+	0.750935i	$0.270397\pi$
$499$			749.433i			1.50187i	−0.660377	+	0.750935i	$0.729603\pi$
$500$	100.856	+	68.5473i	0.201711	+	0.137095i
$501$	424.968	+	233.551i	0.848240	+	0.466170i
$502$	18.7543	−	9.92939i	0.0373591	−	0.0197797i
$503$	−308.721			−0.613760			−0.306880	−	0.951748i	$-0.599285\pi$
$503$	−308.721			−0.613760			−0.306880	+	0.951748i	$0.599285\pi$
$504$	−80.3925	−	164.011i	−0.159509	−	0.325419i
$505$	58.8751			0.116584
$506$	36.2358	−	19.1849i	0.0716123	−	0.0379149i
$507$	382.845	−	696.623i	0.755119	−	1.37401i
$508$	−55.0075	+	80.9341i	−0.108283	+	0.159319i
$509$	502.767			0.987754			0.493877	−	0.869532i	$-0.335579\pi$
$509$	502.767			0.987754			0.493877	+	0.869532i	$0.335579\pi$
$510$	0.812982	−	52.1470i	0.00159408	−	0.102249i
$511$			92.9566i			0.181911i
$512$	165.934	−	484.366i	0.324089	−	0.946027i
$513$	−355.771	+	369.589i	−0.693511	+	0.720446i
$514$	537.525	−	284.591i	1.04577	−	0.553679i
$515$			6.86599i			0.0133320i
$516$	248.348	−	126.571i	0.481295	−	0.245292i
$517$	37.0566			0.0716763
$518$	210.058	−	111.215i	0.405518	−	0.214700i
$519$	−334.785	+	609.172i	−0.645058	+	1.17374i
$520$	−11.2414	+	101.767i	−0.0216182	+	0.195706i
$521$	−108.596			−0.208437			−0.104219	−	0.994554i	$-0.533234\pi$
$521$	−108.596			−0.208437			−0.104219	+	0.994554i	$0.533234\pi$
$522$	3.83906	+	2.18845i	0.00735452	+	0.00419243i
$523$	−476.876			−0.911809			−0.455905	−	0.890029i	$-0.650684\pi$
$523$	−476.876			−0.911809			−0.455905	+	0.890029i	$0.650684\pi$
$524$	−151.584	+	223.029i	−0.289282	+	0.425629i
$525$	164.226	+	90.2541i	0.312811	+	0.171912i
$526$	219.468	−	116.197i	0.417240	−	0.220906i
$527$		−	648.475i		−	1.23050i
$528$	−50.1593	−	6.33361i	−0.0949986	−	0.0119955i
$529$	−150.171			−0.283878
$530$	24.4024	+	46.0904i	0.0460423	+	0.0869630i
$531$	−294.346	+	186.912i	−0.554323	+	0.352001i
$532$	190.799	−	27.7157i	0.358645	−	0.0520972i
$533$			526.896i			0.988547i
$534$	9.04712	−	580.309i	0.0169422	−	1.08672i
$535$	4.93891			0.00923161
$536$	48.1548	−	435.939i	0.0898411	−	0.813319i
$537$	−558.480	−	306.926i	−1.04000	−	0.571557i
$538$	618.573	−	327.502i	1.14976	−	0.608739i
$539$	−44.8323			−0.0831767
$540$	57.1240	+	33.7539i	0.105785	+	0.0625073i
$541$	433.700			0.801664			0.400832	−	0.916151i	$-0.368721\pi$
$541$	433.700			0.801664			0.400832	+	0.916151i	$0.368721\pi$
$542$	−213.174	−	402.635i	−0.393310	−	0.742869i
$543$	−693.655	−	381.214i	−1.27745	−	0.702052i
$544$	294.071	−	344.242i	0.540572	−	0.632799i
$545$	−58.7104			−0.107725
$546$	−4.94281	+	317.046i	−0.00905277	+	0.580671i
$547$	−677.328			−1.23826			−0.619130	−	0.785289i	$-0.712514\pi$
$547$	−677.328			−1.23826			−0.619130	+	0.785289i	$0.712514\pi$
$548$	−789.575	−	536.641i	−1.44083	−	0.979273i
$549$	−298.576	−	470.191i	−0.543855	−	0.856451i
$550$	45.8406	−	24.2701i	0.0833465	−	0.0441275i
$551$	−3.44083	+	3.14934i	−0.00624471	+	0.00571568i
$552$	−382.199	−	268.569i	−0.692389	−	0.486538i
$553$			48.2261i			0.0872082i
$554$	−926.927	+	490.758i	−1.67315	+	0.885846i
$555$	−41.5845	+	75.6669i	−0.0749270	+	0.136337i
$556$	237.327	+	161.301i	0.426848	+	0.290110i
$557$			771.550i			1.38519i	0.721328	+	0.692594i	$0.243532\pi$
$557$			771.550i			1.38519i	−0.721328	+	0.692594i	$0.756468\pi$
$558$	716.736	+	408.574i	1.28447	+	0.732211i
$559$	−483.892			−0.865638
$560$	−9.17800	−	23.1865i	−0.0163893	−	0.0414044i
$561$	−39.1798	−	21.5322i	−0.0698392	−	0.0383817i
$562$	−869.144	+	460.166i	−1.54652	+	0.818800i
$563$		−	172.755i		−	0.306848i	−0.988160	−	0.153424i	$-0.950970\pi$
$563$		−	172.755i		−	0.306848i	0.988160	−	0.153424i	$-0.0490300\pi$
$564$	−191.705	−	376.150i	−0.339902	−	0.666933i
$565$			83.3286i			0.147484i
$566$	−210.058	−	396.750i	−0.371128	−	0.700973i
$567$	185.978	+	87.3881i	0.328004	+	0.154124i
$568$	804.280	+	88.8426i	1.41599	+	0.156413i
$569$	226.161			0.397471			0.198735	−	0.980053i	$-0.436317\pi$
$569$	226.161			0.397471			0.198735	+	0.980053i	$0.436317\pi$
$570$	−52.3947	+	46.4760i	−0.0919206	+	0.0815369i
$571$		−	4.73060i		−	0.00828477i	−0.999991	−	0.00414239i	$-0.998681\pi$
$571$		−	4.73060i		−	0.00828477i	0.999991	−	0.00414239i	$-0.00131857\pi$
$572$	72.5885	+	49.3354i	0.126903	+	0.0862507i
$573$	−271.917	+	494.778i	−0.474550	+	0.863487i
$574$	−60.0467	−	113.414i	−0.104611	−	0.197585i
$575$	479.242			0.833464
$576$	195.198	+	541.917i	0.338886	+	0.940827i
$577$	441.556			0.765262			0.382631	−	0.923901i	$-0.375018\pi$
$577$	441.556			0.765262			0.382631	+	0.923901i	$0.375018\pi$
$578$	−157.000	+	83.1233i	−0.271627	+	0.143812i
$579$	−726.060	−	399.023i	−1.25399	−	0.689159i
$580$	0.498969	+	0.339128i	0.000860291	+	0.000584704i
$581$			342.527i			0.589548i
$582$	−511.900	−	7.98062i	−0.879553	−	0.0137124i
$583$	44.7053			0.0766814
$584$	32.1850	−	291.366i	0.0551113	−	0.498915i
$585$	−61.7460	−	97.2363i	−0.105549	−	0.166216i
$586$	571.135	−	302.386i	0.974633	−	0.516016i
$587$	−1079.72			−1.83939			−0.919695	−	0.392633i	$-0.871564\pi$
$587$	−1079.72			−1.83939			−0.919695	+	0.392633i	$0.871564\pi$
$588$	231.931	+	455.078i	0.394440	+	0.773942i
$589$	−642.389	+	587.968i	−1.09064	+	0.998248i
$590$	−42.0704	+	22.2741i	−0.0713058	+	0.0377526i
$591$	−703.785	−	386.781i	−1.19084	−	0.654452i
$592$	−696.920	+	275.865i	−1.17723	+	0.465988i
$593$			1106.24i			1.86550i	0.360521	+	0.932751i	$0.382599\pi$
$593$			1106.24i			1.86550i	−0.360521	+	0.932751i	$0.617401\pi$
$594$	48.4840	−	29.7376i	0.0816229	−	0.0500632i
$595$		−	22.0510i		−	0.0370605i
$596$	515.649	+	350.465i	0.865183	+	0.588029i
$597$	−245.688	−	135.023i	−0.411537	−	0.226170i
$598$	379.439	+	716.671i	0.634514	+	1.19845i
$599$			318.933i			0.532443i	0.963912	+	0.266221i	$0.0857753\pi$
$599$			318.933i			0.532443i	−0.963912	+	0.266221i	$0.914225\pi$
$600$	−483.505	−	339.756i	−0.805842	−	0.566261i
$601$			78.1306i			0.130001i	0.997885	+	0.0650005i	$0.0207049\pi$
$601$			78.1306i			0.130001i	−0.997885	+	0.0650005i	$0.979295\pi$
$602$	104.157	−	55.1458i	0.173019	−	0.0916044i
$603$	264.501	+	416.530i	0.438641	+	0.690762i
$604$	315.503	−	464.208i	0.522355	−	0.768556i
$605$		−	73.6563i		−	0.121746i
$606$	−574.917	−	8.96306i	−0.948708	−	0.0147905i
$607$	624.194			1.02833			0.514163	−	0.857692i	$-0.328103\pi$
$607$	624.194			1.02833			0.514163	+	0.857692i	$0.328103\pi$
$608$	−607.644	+	20.8114i	−0.999414	+	0.0342292i
$609$	1.63742	+	0.899883i	0.00268871	+	0.00147764i
$610$	−35.5809	−	67.2039i	−0.0583293	−	0.110170i
$611$			732.905i			1.19952i
$612$	−15.8776	+	509.094i	−0.0259438	+	0.831852i
$613$	−65.4906			−0.106836			−0.0534181	−	0.998572i	$-0.517012\pi$
$613$	−65.4906			−0.106836			−0.0534181	+	0.998572i	$0.517012\pi$
$614$	−255.715	+	135.387i	−0.416474	+	0.220501i
$615$	40.8539	+	22.4522i	0.0664290	+	0.0365076i
$616$	−21.2470	−	2.34700i	−0.0344920	−	0.00381006i
$617$		−	719.594i		−	1.16628i	−0.812372	−	0.583140i	$-0.801824\pi$
$617$		−	719.594i		−	1.16628i	0.812372	−	0.583140i	$-0.198176\pi$
$618$	1.04527	−	67.0466i	0.00169137	−	0.108490i
$619$		−	932.726i		−	1.50683i	−0.657547	−	0.753413i	$-0.728406\pi$
$619$		−	932.726i		−	1.50683i	0.657547	−	0.753413i	$-0.271594\pi$
$620$	93.1553	+	63.3138i	0.150251	+	0.102119i
$621$	524.464	−	33.2164i	0.844548	−	0.0534886i
$622$	−421.254	+	223.032i	−0.677258	+	0.358572i
$623$		−	245.391i		−	0.393885i
$624$	125.266	−	992.049i	0.200747	−	1.58982i
$625$	596.834			0.954935
$626$	−317.616	+	168.161i	−0.507374	+	0.268628i
$627$	14.1940	+	58.3351i	0.0226379	+	0.0930385i
$628$	−28.8812	+	42.4937i	−0.0459892	+	0.0676652i
$629$	−662.791			−1.05372
$630$	24.3722	+	13.8933i	0.0386860	+	0.0220528i
$631$		−	623.222i		−	0.987673i	−0.869555	−	0.493837i	$-0.835594\pi$
$631$		−	623.222i		−	0.987673i	0.869555	−	0.493837i	$-0.164406\pi$
$632$	16.6977	−	151.162i	0.0264203	−	0.239180i
$633$	−53.9714	+	98.2060i	−0.0852629	+	0.155144i
$634$	−80.2602	+	42.4935i	−0.126593	+	0.0670245i
$635$		−	15.0301i		−	0.0236694i
$636$	−231.274	−	453.789i	−0.363638	−	0.713505i
$637$		−	886.692i		−	1.39198i
$638$	0.457056	−	0.241987i	0.000716389	−	0.000379290i
$639$	−768.471	+	487.987i	−1.20262	+	0.763673i
$640$	20.7398	+	75.8542i	0.0324060	+	0.118522i
$641$	−386.368			−0.602758			−0.301379	−	0.953504i	$-0.597447\pi$
$641$	−386.368			−0.602758			−0.301379	+	0.953504i	$0.597447\pi$
$642$	−48.2286	−	0.751893i	−0.0751225	−	0.00117117i
$643$			581.708i			0.904678i	0.891846	+	0.452339i	$0.149410\pi$
$643$			581.708i			0.904678i	−0.891846	+	0.452339i	$0.850590\pi$
$644$	−163.348	−	111.021i	−0.253646	−	0.172393i
$645$	−20.6197	+	37.5195i	−0.0319685	+	0.0581697i
$646$	−506.379	−	180.650i	−0.783869	−	0.279644i
$647$	553.170			0.854976			0.427488	−	0.904021i	$-0.359399\pi$
$647$	553.170			0.854976			0.427488	+	0.904021i	$0.359399\pi$
$648$	−552.679	−	338.305i	−0.852899	−	0.522075i
$649$			40.8061i			0.0628754i
$650$	480.014	+	906.634i	0.738484	+	1.39482i
$651$	305.700	+	168.004i	0.469585	+	0.258071i
$652$	−935.658	−	635.928i	−1.43506	−	0.975349i
$653$		−	976.920i		−	1.49605i	−0.663671	−	0.748024i	$-0.731003\pi$
$653$		−	976.920i		−	1.49605i	0.663671	−	0.748024i	$-0.268997\pi$
$654$	573.309	+	8.93799i	0.876619	+	0.0136667i
$655$		−	41.4182i		−	0.0632338i
$656$	148.944	+	376.279i	0.227049	+	0.573596i
$657$	176.783	+	278.394i	0.269076	+	0.423735i
$658$	−83.5242	−	157.757i	−0.126936	−	0.239753i
$659$			247.333i			0.375316i	0.982234	+	0.187658i	$0.0600896\pi$
$659$			247.333i			0.375316i	−0.982234	+	0.187658i	$0.939910\pi$
$660$	6.91847	−	3.52600i	0.0104825	−	0.00534242i
$661$			473.618i			0.716518i	0.933622	+	0.358259i	$0.116629\pi$
$661$			473.618i			0.716518i	−0.933622	+	0.358259i	$0.883371\pi$
$662$	−783.470	+	414.806i	−1.18349	+	0.626595i
$663$	425.863	−	774.897i	0.642327	−	1.16877i
$664$	118.596	−	1073.63i	0.178608	−	1.61691i
$665$	−21.8440	+	19.9935i	−0.0328482	+	0.0300654i
$666$	417.593	−	732.559i	0.627017	−	1.09994i
$667$	4.77831			0.00716388
$668$	−534.739	−	363.440i	−0.800507	−	0.544072i
$669$	326.955	−	594.926i	0.488723	−	0.889276i
$670$	31.5201	+	59.5341i	0.0470450	+	0.0888568i
$671$	−65.1843			−0.0971450
$672$	86.0936	+	227.814i	0.128116	+	0.339009i
$673$			328.180i			0.487637i	0.969821	+	0.243819i	$0.0784002\pi$
$673$			328.180i			0.487637i	−0.969821	+	0.243819i	$0.921600\pi$
$674$	72.5385	+	137.008i	0.107624	+	0.203276i
$675$	663.480	−	42.0208i	0.982933	−	0.0622531i
$676$	−595.763	+	876.563i	−0.881307	+	1.29669i
$677$	−456.594			−0.674437			−0.337219	−	0.941426i	$-0.609486\pi$
$677$	−456.594			−0.674437			−0.337219	+	0.941426i	$0.609486\pi$
$678$	12.6858	−	813.706i	0.0187107	−	1.20016i
$679$	−216.463			−0.318797
$680$	−7.63487	+	69.1174i	−0.0112277	+	0.101643i
$681$	529.544	+	291.023i	0.777597	+	0.427347i
$682$	85.3304	−	45.1779i	0.125118	−	0.0662433i
$683$		−	34.2971i		−	0.0502154i	−0.999685	−	0.0251077i	$-0.992007\pi$
$683$		−	34.2971i		−	0.0502154i	0.999685	−	0.0251077i	$-0.00799287\pi$
$684$	518.712	−	445.863i	0.758351	−	0.651847i
$685$	146.630			0.214058
$686$	217.379	+	410.578i	0.316879	+	0.598510i
$687$	258.892	−	471.078i	0.376844	−	0.685703i
$688$	−345.568	+	136.788i	−0.502279	+	0.198820i
$689$			884.180i			1.28328i
$690$	71.7372	+	1.11840i	0.103967	+	0.00162087i
$691$		−	1111.03i		−	1.60786i	−0.594726	−	0.803929i	$-0.702739\pi$
$691$		−	1111.03i		−	1.60786i	0.594726	−	0.803929i	$-0.297261\pi$
$692$	520.974	−	766.524i	0.752853	−	1.10769i
$693$	20.3011	−	12.8914i	0.0292945	−	0.0186023i
$694$	−640.453	+	339.086i	−0.922843	+	0.488596i
$695$	−44.0734			−0.0634149
$696$	−4.82082	−	3.38756i	−0.00692646	−	0.00486718i
$697$			357.852i			0.513418i
$698$	333.943	−	176.805i	0.478428	−	0.253302i
$699$	125.835	+	69.1554i	0.180021	+	0.0989347i
$700$	−206.646	−	140.448i	−0.295208	−	0.200641i
$701$		−	466.944i		−	0.666111i	−0.942907	−	0.333055i	$-0.891920\pi$
$701$		−	466.944i		−	0.666111i	0.942907	−	0.333055i	$-0.108080\pi$
$702$	588.149	+	958.916i	0.837819	+	1.36598i
$703$	600.948	+	656.571i	0.854834	+	0.933956i
$704$	65.7849	+	14.7130i	0.0934444	+	0.0208992i
$705$	56.8272	+	31.2307i	0.0806060	+	0.0442989i
$706$	459.294	+	867.498i	0.650558	+	1.22875i
$707$	−243.111			−0.343862
$708$	414.210	−	211.102i	0.585043	−	0.298167i
$709$	−675.121			−0.952215			−0.476108	−	0.879387i	$-0.657953\pi$
$709$	−675.121			−0.952215			−0.476108	+	0.879387i	$0.657953\pi$
$710$	−109.837	+	58.1527i	−0.154700	+	0.0819052i
$711$	91.7155	+	144.432i	0.128995	+	0.203139i
$712$	−84.9632	+	769.161i	−0.119330	+	1.08028i
$713$	892.089			1.25118
$714$	−3.35702	+	215.329i	−0.00470170	+	0.301581i
$715$	−13.4802			−0.0188534
$716$	702.738	+	477.622i	0.981477	+	0.667069i
$717$	583.396	−	1061.54i	0.813663	−	1.48054i
$718$	−981.497	+	519.650i	−1.36699	+	0.723747i
$719$	1003.31			1.39543			0.697715	−	0.716376i	$-0.254200\pi$
$719$	1003.31			1.39543			0.697715	+	0.716376i	$0.254200\pi$
$720$	−71.5826	−	51.9862i	−0.0994202	−	0.0722030i
$721$		−	28.3515i		−	0.0393224i
$722$	280.176	+	665.421i	0.388055	+	0.921636i
$723$	397.159	+	218.268i	0.549321	+	0.301892i
$724$	872.829	+	593.225i	1.20556	+	0.819372i
$725$	6.04485			0.00833773
$726$	−11.2133	+	719.256i	−0.0154454	+	0.990711i
$727$			1353.04i			1.86113i	0.366133	+	0.930563i	$0.380682\pi$
$727$			1353.04i			1.86113i	−0.366133	+	0.930563i	$0.619318\pi$
$728$	46.4189	−	420.224i	0.0637622	−	0.577230i
$729$	723.175	−	91.9720i	0.992010	−	0.126162i
$730$	21.0670	+	39.7905i	0.0288589	+	0.0545076i
$731$	−328.645			−0.449583
$732$	337.218	+	661.665i	0.460680	+	0.903914i
$733$	−607.098			−0.828238			−0.414119	−	0.910223i	$-0.635910\pi$
$733$	−607.098			−0.828238			−0.414119	+	0.910223i	$0.635910\pi$
$734$	−400.782	−	756.981i	−0.546024	−	1.03131i
$735$	−68.7513	−	37.7839i	−0.0935392	−	0.0514067i
$736$	473.565	+	404.545i	0.643430	+	0.549654i
$737$	57.7450			0.0783514
$738$	−395.521	−	225.466i	−0.535937	−	0.305509i
$739$			80.5158i			0.108952i	0.998515	+	0.0544762i	$0.0173489\pi$
$739$			80.5158i			0.108952i	−0.998515	+	0.0544762i	$0.982651\pi$
$740$	64.7115	−	95.2119i	0.0874480	−	0.128665i
$741$	−1153.75	+	280.728i	−1.55702	+	0.378850i
$742$	−100.764	−	190.319i	−0.135800	−	0.256495i
$743$		−	545.838i		−	0.734640i	−0.930095	−	0.367320i	$-0.880275\pi$
$743$		−	545.838i		−	0.734640i	0.930095	−	0.367320i	$-0.119725\pi$
$744$	−900.026	−	632.443i	−1.20971	−	0.850058i
$745$	−95.7598			−0.128537
$746$	−331.527	−	626.176i	−0.444406	−	0.839379i
$747$	651.411	+	1025.83i	0.872036	+	1.37326i
$748$	49.3000	+	33.5072i	0.0659091	+	0.0447957i
$749$	−20.3941			−0.0272284
$750$	182.895	+	2.85137i	0.243860	+	0.00380183i
$751$	1401.36			1.86600			0.932999	−	0.359879i	$-0.117182\pi$
$751$	1401.36			1.86600			0.932999	+	0.359879i	$0.117182\pi$
$752$	207.180	+	523.400i	0.275505	+	0.696010i
$753$	15.3308	−	27.8958i	0.0203596	−	0.0370462i
$754$	4.78601	+	9.03964i	0.00634750	+	0.0119889i
$755$			86.2067i			0.114181i
$756$	−235.880	−	139.379i	−0.312010	−	0.184364i
$757$	24.4598			0.0323115			0.0161558	−	0.999869i	$-0.494857\pi$
$757$	24.4598			0.0323115			0.0161558	+	0.999869i	$0.494857\pi$
$758$	868.231	−	459.682i	1.14542	−	0.606441i
$759$	29.6212	−	53.8985i	0.0390266	−	0.0710126i
$760$	75.3912	−	55.1051i	0.0991990	−	0.0725067i
$761$		−	1020.41i		−	1.34087i	−0.741966	−	0.670437i	$-0.766107\pi$
$761$		−	1020.41i		−	1.34087i	0.741966	−	0.670437i	$-0.233893\pi$
$762$	−2.28816	+	146.769i	−0.00300283	+	0.192610i
$763$	242.431			0.317733
$764$	423.142	−	622.581i	0.553851	−	0.814897i
$765$	−41.9361	−	66.0401i	−0.0548185	−	0.0863270i
$766$	−667.820	−	1261.35i	−0.871828	−	1.64668i
$767$	−807.063			−1.05223
$768$	−190.977	−	743.876i	−0.248668	−	0.968589i
$769$	614.747			0.799411			0.399705	−	0.916644i	$-0.369112\pi$
$769$	614.747			0.799411			0.399705	+	0.916644i	$0.369112\pi$
$770$	2.90161	−	1.53625i	0.00376832	−	0.00199513i
$771$	439.403	−	799.535i	0.569913	−	1.03701i
$772$	913.604	+	620.938i	1.18342	+	0.804324i
$773$	166.524			0.215426			0.107713	−	0.994182i	$-0.465647\pi$
$773$	166.524			0.215426			0.107713	+	0.994182i	$0.465647\pi$
$774$	207.064	−	363.240i	0.267524	−	0.469302i
$775$	1128.55			1.45619
$776$	678.489	+	74.9475i	0.874342	+	0.0965818i
$777$	171.713	−	312.448i	0.220995	−	0.402122i
$778$	−207.135	−	391.230i	−0.266241	−	0.502866i
$779$	354.494	−	324.462i	0.455063	−	0.416511i
$780$	69.7371	+	136.833i	0.0894066	+	0.175427i
$781$			106.536i			0.136410i
$782$	257.704	+	486.743i	0.329545	+	0.622433i
$783$	6.61526	−	0.418971i	0.00844861	−	0.000535084i
$784$	−250.652	−	633.225i	−0.319710	−	0.807685i
$785$		−	7.89140i		−	0.0100527i
$786$	−6.30545	+	404.450i	−0.00802220	+	0.514567i
$787$	−253.484			−0.322089			−0.161044	−	0.986947i	$-0.551486\pi$
$787$	−253.484			−0.322089			−0.161044	+	0.986947i	$0.551486\pi$
$788$	885.574	+	601.888i	1.12383	+	0.763817i
$789$	179.406	−	326.445i	0.227384	−	0.413746i
$790$	10.9296	+	20.6434i	0.0138349	+	0.0261309i
$791$		−	344.086i		−	0.435001i
$792$	−68.0959	+	33.3782i	−0.0859796	+	0.0421442i
$793$		−	1289.21i		−	1.62574i
$794$	−890.737	+	471.598i	−1.12184	+	0.593952i
$795$	68.5566	+	37.6769i	0.0862347	+	0.0473923i
$796$	309.150	+	210.116i	0.388379	+	0.263965i
$797$	1079.90			1.35495			0.677475	−	0.735546i	$-0.263074\pi$
$797$	1079.90			1.35495			0.677475	+	0.735546i	$0.263074\pi$
$798$	216.352	−	191.912i	0.271117	−	0.240491i
$799$			497.768i			0.622989i
$800$	599.089	+	511.775i	0.748861	+	0.639718i
$801$	−466.679	−	734.916i	−0.582620	−	0.917498i
$802$	−1347.53	+	713.447i	−1.68022	+	0.889585i
$803$	38.5947			0.0480632
$804$	−298.732	−	586.151i	−0.371557	−	0.729043i
$805$	30.3350			0.0376832
$806$	893.528	+	1687.66i	1.10860	+	2.09387i
$807$	505.656	−	920.089i	0.626588	−	1.14013i
$808$	762.014	+	84.1738i	0.943087	+	0.104176i
$809$		−	52.8618i		−	0.0653421i	−0.999466	−	0.0326711i	$-0.989599\pi$
$809$		−	52.8618i		−	0.0653421i	0.999466	−	0.0326711i	$-0.0104014\pi$
$810$	99.4137	−	4.74171i	0.122733	−	0.00585396i
$811$	−1297.43			−1.59979			−0.799893	−	0.600142i	$-0.795111\pi$
$811$	−1297.43			−1.59979			−0.799893	+	0.600142i	$0.795111\pi$
$812$	−2.06037	−	1.40035i	−0.00253740	−	0.00172457i
$813$	−598.895	−	329.137i	−0.736648	−	0.404842i
$814$	−46.1753	−	87.2142i	−0.0567264	−	0.107143i
$815$	173.758			0.213201
$816$	85.0771	−	673.772i	0.104261	−	0.825700i
$817$	297.981	+	325.561i	0.364725	+	0.398483i
$818$	−266.604	−	503.552i	−0.325922	−	0.615589i
$819$	254.966	+	401.514i	0.311313	+	0.490250i
$820$	−51.4065	−	34.9389i	−0.0626909	−	0.0426084i
$821$		−	1617.84i		−	1.97057i	−0.170915	−	0.985286i	$-0.554672\pi$
$821$		−	1617.84i		−	1.97057i	0.170915	−	0.985286i	$-0.445328\pi$
$822$	−1431.85	−	22.3227i	−1.74190	−	0.0271566i
$823$			952.502i			1.15735i	0.815557	+	0.578677i	$0.196431\pi$
$823$			952.502i			1.15735i	−0.815557	+	0.578677i	$0.803569\pi$
$824$	−9.81633	+	88.8658i	−0.0119130	+	0.107847i
$825$	37.4727	−	68.1850i	0.0454214	−	0.0826485i
$826$	173.720	−	91.9755i	0.210315	−	0.111350i
$827$			686.266i			0.829826i	0.909861	+	0.414913i	$0.136188\pi$
$827$			686.266i			0.829826i	−0.909861	+	0.414913i	$0.863812\pi$
$828$	−700.346	−	21.8424i	−0.845829	−	0.0263797i
$829$		−	371.643i		−	0.448303i	−0.974554	−	0.224151i	$-0.928039\pi$
$829$		−	371.643i		−	0.448303i	0.974554	−	0.224151i	$-0.0719610\pi$
$830$	77.6277	+	146.620i	0.0935274	+	0.176651i
$831$	−757.722	+	1378.75i	−0.911820	+	1.65914i
$832$	−290.994	+	1301.09i	−0.349752	+	1.56381i
$833$		−	602.216i		−	0.722948i
$834$	430.378	+	6.70967i	0.516041	+	0.00804517i
$835$	99.3049			0.118928
$836$	−11.5073	−	79.2181i	−0.0137647	−	0.0947585i
$837$	1235.04	−	78.2201i	1.47556	−	0.0934529i
$838$	857.572	−	454.039i	1.02336	−	0.541812i
$839$		−	435.430i		−	0.518987i	−0.965745	−	0.259494i	$-0.916444\pi$
$839$		−	435.430i		−	0.518987i	0.965745	−	0.259494i	$-0.0835556\pi$
$840$	−30.6048	−	21.5058i	−0.0364343	−	0.0256022i
$841$	−840.940			−0.999928
$842$	−131.301	−	247.996i	−0.155939	−	0.294533i
$843$	−710.487	+	1292.80i	−0.842808	+	1.53357i
$844$	83.9874	−	123.573i	0.0995111	−	0.146413i
$845$		−	162.784i		−	0.192644i
$846$	−550.165	−	313.620i	−0.650313	−	0.370710i
$847$			304.146i			0.359086i
$848$	249.942	+	631.432i	0.294743	+	0.744613i
$849$	−590.142	−	324.326i	−0.695102	−	0.382010i
$850$	326.012	+	615.760i	0.383544	+	0.724423i
$851$		−	911.784i		−	1.07143i
$852$	1081.41	−	551.141i	1.26926	−	0.646880i
$853$	840.335			0.985152			0.492576	−	0.870269i	$-0.336055\pi$
$853$	840.335			0.985152			0.492576	+	0.870269i	$0.336055\pi$
$854$	146.923	+	277.502i	0.172041	+	0.324944i
$855$	−27.3971	+	101.421i	−0.0320434	+	0.118621i
$856$	63.9238	+	7.06117i	0.0746774	+	0.00824904i
$857$	−1201.97			−1.40254			−0.701268	−	0.712898i	$-0.747382\pi$
$857$	−1201.97			−1.40254			−0.701268	+	0.712898i	$0.747382\pi$
$858$	131.635	+	2.05221i	0.153420	+	0.00239185i
$859$		−	1144.95i		−	1.33289i	−0.745556	−	0.666443i	$-0.767816\pi$
$859$		−	1144.95i		−	1.33289i	0.745556	−	0.666443i	$-0.232184\pi$
$860$	32.0872	−	47.2109i	0.0373108	−	0.0548963i
$861$	−168.696	−	92.7110i	−0.195931	−	0.107678i
$862$	−635.917	−	1201.10i	−0.737723	−	1.39338i
$863$		−	230.736i		−	0.267365i	−0.991024	−	0.133683i	$-0.957320\pi$
$863$		−	230.736i		−	0.267365i	0.991024	−	0.133683i	$-0.0426803\pi$
$864$	691.092	+	518.544i	0.799875	+	0.600167i
$865$			142.349i			0.164565i
$866$	477.701	+	902.264i	0.551618	+	1.04188i
$867$	−128.341	+	233.528i	−0.148029	+	0.269352i
$868$	−384.663	−	261.439i	−0.443160	−	0.301197i
$869$	20.0230			0.0230415
$870$	0.904848	+	0.0141068i	0.00104006	+	1.62147e-5i
$871$			1142.08i			1.31123i
$872$	−759.883	−	83.9384i	−0.871425	−	0.0962596i
$873$	−648.281	+	411.665i	−0.742590	+	0.471552i
$874$	248.516	−	696.612i	0.284343	−	0.797039i
$875$	77.3395			0.0883880
$876$	−199.662	−	391.763i	−0.227925	−	0.447218i
$877$		−	985.032i		−	1.12318i	−0.827414	−	0.561592i	$-0.810189\pi$
$877$		−	985.032i		−	1.12318i	0.827414	−	0.561592i	$-0.189811\pi$
$878$	192.013	−	101.661i	0.218693	−	0.115786i
$879$	466.878	−	849.528i	0.531147	−	0.966471i
$880$	−9.62680	+	3.81062i	−0.0109396	+	0.00433025i
$881$		−	140.799i		−	0.159817i	−0.996802	−	0.0799084i	$-0.974537\pi$
$881$		−	140.799i		−	0.159817i	0.996802	−	0.0799084i	$-0.0254628\pi$
$882$	665.607	+	379.428i	0.754656	+	0.430190i
$883$		−	502.318i		−	0.568877i	−0.958694	−	0.284438i	$-0.908193\pi$
$883$		−	502.318i		−	0.568877i	0.958694	−	0.284438i	$-0.0918071\pi$
$884$	−662.704	+	975.055i	−0.749666	+	1.10300i
$885$	−34.3907	+	62.5772i	−0.0388596	+	0.0707087i
$886$	−1276.98	+	676.093i	−1.44129	+	0.763085i
$887$		−	402.702i		−	0.454004i	−0.973894	−	0.227002i	$-0.927108\pi$
$887$		−	402.702i		−	0.454004i	0.973894	−	0.227002i	$-0.0728924\pi$
$888$	−646.405	+	919.896i	−0.727934	+	1.03592i
$889$			62.0630i			0.0698122i
$890$	−55.6134	−	105.041i	−0.0624870	−	0.118023i
$891$	36.2827	−	77.2163i	0.0407214	−	0.0866626i
$892$	−508.790	+	748.597i	−0.570393	+	0.839234i
$893$	493.097	−	451.323i	0.552180	−	0.505401i
$894$	935.098	+	14.5783i	1.04597	+	0.0163069i
$895$	−130.503			−0.145814
$896$	−85.6403	−	313.222i	−0.0955806	−	0.349578i
$897$	1066.00	+	585.848i	1.18841	+	0.653119i
$898$	615.532	−	325.891i	0.685447	−	0.362908i
$899$	11.2523			0.0125164
$900$	−885.981	−	27.6319i	−0.984424	−	0.0307022i
$901$			600.510i			0.666493i
$902$	−47.0884	+	24.9308i	−0.0522045	+	0.0276395i
$903$	85.1441	−	154.928i	0.0942903	−	0.171570i
$904$	−119.135	+	1078.51i	−0.131787	+	1.19305i
$905$	−162.091			−0.179106
$906$	13.1240	−	841.812i	0.0144857	−	0.929152i
$907$	1069.32			1.17896			0.589480	−	0.807783i	$-0.299333\pi$
$907$	1069.32			1.17896			0.589480	+	0.807783i	$0.299333\pi$
$908$	−666.327	−	452.874i	−0.733840	−	0.498760i
$909$	−728.087	+	462.343i	−0.800976	+	0.508628i
$910$	30.3839	+	57.3880i	0.0333889	+	0.0630637i
$911$		−	677.538i		−	0.743730i	−0.928287	−	0.371865i	$-0.878719\pi$
$911$		−	677.538i		−	0.743730i	0.928287	−	0.371865i	$-0.121281\pi$
$912$	−744.587	+	526.626i	−0.816433	+	0.577440i
$913$	142.214			0.155766
$914$	111.721	−	59.1505i	0.122233	−	0.0647161i
$915$	−99.9616	−	54.9362i	−0.109248	−	0.0600396i
$916$	−402.873	+	592.759i	−0.439818	+	0.647116i
$917$			171.026i			0.186507i
$918$	399.454	+	651.269i	0.435135	+	0.709443i
$919$		−	1235.92i		−	1.34486i	−0.740163	−	0.672428i	$-0.765252\pi$
$919$		−	1235.92i		−	1.34486i	0.740163	−	0.672428i	$-0.234748\pi$
$920$	−95.0829	−	10.5031i	−0.103351	−	0.0114164i
$921$	−209.036	+	380.360i	−0.226966	+	0.412986i
$922$	−51.4619	−	97.1994i	−0.0558155	−	0.105422i
$923$	−2107.06			−2.28284
$924$	−28.5682	+	14.5598i	−0.0309179	+	0.0157573i
$925$		−	1153.46i		−	1.24699i
$926$	262.700	+	496.179i	0.283694	+	0.535830i
$927$	−53.9183	−	84.9093i	−0.0581643	−	0.0915958i
$928$	5.97325	+	5.10268i	0.00643669	+	0.00549858i
$929$			1546.36i			1.66454i	0.554371	+	0.832270i	$0.312959\pi$
$929$			1546.36i			1.66454i	−0.554371	+	0.832270i	$0.687041\pi$
$930$	168.931	+	2.63367i	0.181647	+	0.00283190i
$931$	−596.564	+	546.025i	−0.640777	+	0.586493i
$932$	−158.338	−	107.616i	−0.169891	−	0.115468i
$933$	−344.357	+	626.590i	−0.369086	+	0.671586i
$934$	−725.816	+	384.281i	−0.777105	+	0.411436i
$935$	−9.15537			−0.00979184
$936$	−660.154	−	1346.80i	−0.705293	−	1.43889i
$937$	−1064.83			−1.13643			−0.568214	−	0.822881i	$-0.692365\pi$
$937$	−1064.83			−1.13643			−0.568214	+	0.822881i	$0.692365\pi$
$938$	−130.155	−	245.832i	−0.138758	−	0.262081i
$939$	−259.638	+	472.435i	−0.276504	+	0.503125i
$940$	−71.5059	−	48.5995i	−0.0760701	−	0.0517016i
$941$	1240.97			1.31878			0.659390	−	0.751801i	$-0.270815\pi$
$941$	1240.97			1.31878			0.659390	+	0.751801i	$0.270815\pi$
$942$	−1.20138	+	77.0598i	−0.00127535	+	0.0818044i
$943$	−492.288			−0.522044
$944$	−576.359	+	228.143i	−0.610550	+	0.241677i
$945$	41.9968	−	2.65983i	0.0444411	−	0.00281463i
$946$	−22.8960	−	43.2452i	−0.0242030	−	0.0457137i
$947$	−789.498			−0.833683			−0.416841	−	0.908979i	$-0.636863\pi$
$947$	−789.498			−0.833683			−0.416841	+	0.908979i	$0.636863\pi$
$948$	−103.585	−	203.248i	−0.109267	−	0.214396i
$949$			763.326i			0.804348i
$950$	314.388	−	881.258i	0.330934	−	0.927640i
$951$	−65.6092	+	119.382i	−0.0689897	+	0.125533i
$952$	31.5264	−	285.404i	0.0331159	−	0.299794i
$953$	1284.61			1.34797			0.673983	−	0.738747i	$-0.264582\pi$
$953$	1284.61			1.34797			0.673983	+	0.738747i	$0.264582\pi$
$954$	−663.721	−	378.353i	−0.695725	−	0.396596i
$955$			115.618i			0.121066i
$956$	−907.849	+	1335.74i	−0.949633	+	1.39722i
$957$	0.373623	−	0.679842i	0.000390411	−	0.000710389i
$958$	1315.39	−	696.427i	1.37305	−	0.726959i
$959$	−605.473			−0.631359
$960$	88.4827	+	78.0052i	0.0921695	+	0.0812554i
$961$	1139.75			1.18600
$962$	1724.92	−	913.254i	1.79306	−	0.949329i
$963$	−61.0778	+	38.7850i	−0.0634245	+	0.0402752i
$964$	−499.746	−	339.657i	−0.518409	−	0.352341i
$965$	−169.663			−0.175816
$966$	−296.222	−	4.61815i	−0.306648	−	0.00478070i
$967$			577.553i			0.597263i	0.954368	+	0.298632i	$0.0965302\pi$
$967$			577.553i			0.597263i	−0.954368	+	0.298632i	$0.903470\pi$
$968$	105.307	−	953.326i	0.108788	−	0.984841i
$969$	−783.595	+	190.662i	−0.808663	+	0.196762i
$970$	−92.6580	+	49.0575i	−0.0955238	+	0.0505748i
$971$			1037.72i			1.06872i	0.845259	+	0.534358i	$0.179446\pi$
$971$			1037.72i			1.06872i	−0.845259	+	0.534358i	$0.820554\pi$
$972$	−971.500	+	31.1683i	−0.999486	+	0.0320662i
$973$	181.991			0.187041
$974$	−700.374	+	370.811i	−0.719070	+	0.380709i
$975$	1348.56	+	741.133i	1.38314	+	0.760137i
$976$	−364.438	−	920.683i	−0.373400	−	0.943323i
$977$	−1409.62			−1.44280			−0.721400	−	0.692518i	$-0.756501\pi$
$977$	−1409.62			−1.44280			−0.721400	+	0.692518i	$0.756501\pi$
$978$	−1696.76	−	26.4528i	−1.73493	−	0.0270478i
$979$	−101.884			−0.104069
$980$	86.5100	+	58.7972i	0.0882755	+	0.0599972i
$981$	726.051	−	461.049i	0.740113	−	0.469979i
$982$	−879.372	+	465.581i	−0.895490	+	0.474115i
$983$		−	854.082i		−	0.868852i	−0.900707	−	0.434426i	$-0.856951\pi$
$983$		−	854.082i		−	0.868852i	0.900707	−	0.434426i	$-0.143049\pi$
$984$	496.667	+	349.005i	0.504743	+	0.354680i
$985$	−164.458			−0.166962
$986$	3.25052	+	6.13947i	0.00329668	+	0.00622664i
$987$	−234.654	−	128.960i	−0.237745	−	0.130658i
$988$	1566.77	−	227.591i	1.58580	−	0.230356i
$989$		−	452.108i		−	0.457137i
$990$	5.76837	−	10.1191i	0.00582663	−	0.0102213i
$991$	−2.66847			−0.00269270			−0.00134635	−	0.999999i	$-0.500429\pi$
$991$	−2.66847			−0.00269270			−0.00134635	+	0.999999i	$0.500429\pi$
$992$	1115.18	+	952.649i	1.12417	+	0.960331i
$993$	−640.453	+	1165.36i	−0.644967	+	1.17358i
$994$	453.544	−	240.128i	0.456282	−	0.241577i
$995$	−57.4114			−0.0576999
$996$	−735.716	−	1443.57i	−0.738671	−	1.44937i
$997$	786.093			0.788458			0.394229	−	0.919012i	$-0.371012\pi$
$997$	786.093			0.788458			0.394229	+	0.919012i	$0.371012\pi$
$998$	−701.337	−	1324.66i	−0.702743	−	1.32731i
$999$	−79.9469	−	1262.31i	−0.0800270	−	1.26357i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.3.b.e.227.11	yes	72
3.2	odd	2	inner	228.3.b.e.227.61	yes	72
4.3	odd	2	inner	228.3.b.e.227.10	yes	72
12.11	even	2	inner	228.3.b.e.227.64	yes	72
19.18	odd	2	inner	228.3.b.e.227.62	yes	72
57.56	even	2	inner	228.3.b.e.227.12	yes	72
76.75	even	2	inner	228.3.b.e.227.63	yes	72
228.227	odd	2	inner	228.3.b.e.227.9	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.3.b.e.227.9	✓	72	228.227	odd	2	inner
228.3.b.e.227.10	yes	72	4.3	odd	2	inner
228.3.b.e.227.11	yes	72	1.1	even	1	trivial
228.3.b.e.227.12	yes	72	57.56	even	2	inner
228.3.b.e.227.61	yes	72	3.2	odd	2	inner
228.3.b.e.227.62	yes	72	19.18	odd	2	inner
228.3.b.e.227.63	yes	72	76.75	even	2	inner
228.3.b.e.227.64	yes	72	12.11	even	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.76755 + 0.935824i) q^{2} +(-1.44490 + 2.62912i) q^{3} +(2.24847 - 3.30823i) q^{4} +0.614363i q^{5} +(0.0935298 - 5.99927i) q^{6} -2.53686i q^{7} +(-0.878356 + 7.95163i) q^{8} +(-4.82456 - 7.59761i) q^{9} +O(q^{10})\)	\(q+(-1.76755 + 0.935824i) q^{2} +(-1.44490 + 2.62912i) q^{3} +(2.24847 - 3.30823i) q^{4} +0.614363i q^{5} +(0.0935298 - 5.99927i) q^{6} -2.53686i q^{7} +(-0.878356 + 7.95163i) q^{8} +(-4.82456 - 7.59761i) q^{9} +(-0.574935 - 1.08592i) q^{10} -1.05328 q^{11} +(5.44894 + 10.6915i) q^{12} -20.8318i q^{13} +(2.37406 + 4.48404i) q^{14} +(-1.61523 - 0.887689i) q^{15} +(-5.88879 - 14.8769i) q^{16} -14.1484i q^{17} +(15.6377 + 8.91422i) q^{18} +(-14.0156 + 12.8282i) q^{19} +(2.03245 + 1.38137i) q^{20} +(6.66972 + 3.66550i) q^{21} +(1.86173 - 0.985687i) q^{22} +19.4635 q^{23} +(-19.6367 - 13.7986i) q^{24} +24.6226 q^{25} +(19.4949 + 36.8213i) q^{26} +(26.9460 - 1.70660i) q^{27} +(-8.39254 - 5.70406i) q^{28} +0.245501 q^{29} +(3.68573 + 0.0574612i) q^{30} +45.8339 q^{31} +(24.3309 + 20.7848i) q^{32} +(1.52188 - 2.76921i) q^{33} +(13.2404 + 25.0080i) q^{34} +1.55855 q^{35} +(-35.9825 - 1.12222i) q^{36} -46.8458i q^{37} +(12.7683 - 35.7907i) q^{38} +(54.7693 + 30.0998i) q^{39} +(-4.88519 - 0.539629i) q^{40} -25.2928 q^{41} +(-15.2193 - 0.237272i) q^{42} -23.2285i q^{43} +(-2.36827 + 3.48450i) q^{44} +(4.66769 - 2.96403i) q^{45} +(-34.4027 + 18.2144i) q^{46} -35.1820 q^{47} +(47.6219 + 6.01321i) q^{48} +42.5643 q^{49} +(-43.5216 + 23.0424i) q^{50} +(37.1978 + 20.4429i) q^{51} +(-68.9164 - 46.8396i) q^{52} -42.4438 q^{53} +(-46.0314 + 28.2332i) q^{54} -0.647097i q^{55} +(20.1722 + 2.22827i) q^{56} +(-13.4759 - 55.3841i) q^{57} +(-0.433935 + 0.229745i) q^{58} -38.7419i q^{59} +(-6.56848 + 3.34763i) q^{60} +61.8868 q^{61} +(-81.0138 + 42.8925i) q^{62} +(-19.2741 + 12.2392i) q^{63} +(-62.4570 - 13.9687i) q^{64} +12.7983 q^{65} +(-0.0985133 + 6.31893i) q^{66} -54.8238 q^{67} +(-46.8061 - 31.8121i) q^{68} +(-28.1227 + 51.1720i) q^{69} +(-2.75482 + 1.45853i) q^{70} -101.146i q^{71} +(64.6511 - 31.6897i) q^{72} -36.6423 q^{73} +(43.8394 + 82.8023i) q^{74} +(-35.5770 + 64.7357i) q^{75} +(10.9252 + 75.2106i) q^{76} +2.67204i q^{77} +(-124.976 - 1.94839i) q^{78} -19.0101 q^{79} +(9.13981 - 3.61785i) q^{80} +(-34.4473 + 73.3102i) q^{81} +(44.7064 - 23.6697i) q^{82} -135.020 q^{83} +(27.1230 - 13.8232i) q^{84} +8.69223 q^{85} +(21.7378 + 41.0575i) q^{86} +(-0.354723 + 0.645451i) q^{87} +(0.925157 - 8.37532i) q^{88} +96.7299 q^{89} +(-5.47656 + 9.60720i) q^{90} -52.8475 q^{91} +(43.7631 - 64.3898i) q^{92} +(-66.2252 + 120.503i) q^{93} +(62.1860 - 32.9242i) q^{94} +(-7.88118 - 8.61065i) q^{95} +(-89.8013 + 33.9370i) q^{96} -85.3270i q^{97} +(-75.2346 + 39.8327i) q^{98} +(5.08162 + 8.00243i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 16 q^{4} + 6 q^{6} - 48 q^{9}+O(q^{10}) \) 72 * q - 16 * q^4 + 6 * q^6 - 48 * q^9	\( 72 q - 16 q^{4} + 6 q^{6} - 48 q^{9} - 40 q^{16} + 94 q^{24} - 408 q^{25} + 60 q^{28} + 176 q^{30} - 214 q^{36} + 2 q^{42} + 96 q^{45} - 616 q^{49} + 72 q^{54} + 320 q^{57} + 564 q^{58} + 592 q^{61} - 424 q^{64} + 608 q^{66} + 128 q^{73} - 292 q^{76} - 208 q^{81} + 472 q^{82} - 160 q^{85} + 128 q^{93} + 166 q^{96}+O(q^{100}) \) 72 * q - 16 * q^4 + 6 * q^6 - 48 * q^9 - 40 * q^16 + 94 * q^24 - 408 * q^25 + 60 * q^28 + 176 * q^30 - 214 * q^36 + 2 * q^42 + 96 * q^45 - 616 * q^49 + 72 * q^54 + 320 * q^57 + 564 * q^58 + 592 * q^61 - 424 * q^64 + 608 * q^66 + 128 * q^73 - 292 * q^76 - 208 * q^81 + 472 * q^82 - 160 * q^85 + 128 * q^93 + 166 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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