LMFDB - Embedded newform 228.3.b.e.227.63

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			227.63
Character	$\chi$	$=$	228.227
Dual form			228.3.b.e.227.61

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.76755 + 0.935824i) q^{2} +(-1.44490 + 2.62912i) q^{3} +(2.24847 + 3.30823i) q^{4} +0.614363i q^{5} +(-5.01432 + 3.29494i) q^{6} +2.53686i q^{7} +(0.878356 + 7.95163i) q^{8} +(-4.82456 - 7.59761i) q^{9} +O(q^{10})$	\(q+(1.76755 + 0.935824i) q^{2} +(-1.44490 + 2.62912i) q^{3} +(2.24847 + 3.30823i) q^{4} +0.614363i q^{5} +(-5.01432 + 3.29494i) 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} +(-11.9465 + 1.13145i) 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} +(-1.41762 - 17.9441i) 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} +(-22.1749 - 9.17997i) 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} +(-2.02429 - 3.08061i) 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} +(14.2868 - 33.0437i) 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} +(-8.35881 - 12.7206i) 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} +(-30.6045 - 36.9779i) 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} +(49.2255 + 22.2002i) q^{54} +0.647097i q^{55} +(-20.1722 + 2.22827i) q^{56} +(53.9780 - 18.3132i) q^{57} +(-0.433935 - 0.229745i) q^{58} -38.7419i q^{59} +(-0.695118 - 7.33951i) 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} +(-5.28150 + 3.47050i) 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} +(56.1757 - 45.0365i) 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} +(-68.6395 - 104.457i) 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} +(-2.87032 - 30.3068i) 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} +(11.0242 - 0.870934i) 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} +(-19.4902 - 94.0007i) 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	$0.980432\pi$
$6$	−5.01432	+	3.29494i	−0.835720	+	0.549156i
$7$			2.53686i			0.362409i	0.983445	+	0.181205i	$0.0579996\pi$
$7$			2.53686i			0.362409i	−0.983445	+	0.181205i	$0.942000\pi$
$8$	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	$-0.484755\pi$
$11$	1.05328			0.0957530			0.0478765	+	0.998853i	$0.484755\pi$
$12$	−11.9465	+	1.13145i	−0.995545	+	0.0942871i
$13$			20.8318i			1.60245i	0.598365	+	0.801223i	$0.295817\pi$
$13$			20.8318i			1.60245i	−0.598365	+	0.801223i	$0.704183\pi$
$14$	−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	$-0.136613\pi$
$18$	−1.41762	−	17.9441i	−0.0787568	−	0.996894i
$19$	−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	$-0.639065\pi$
$23$	−19.4635			−0.846240			−0.423120	+	0.906074i	$0.639065\pi$
$24$	−22.1749	−	9.17997i	−0.923956	−	0.382499i
$25$	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	$-0.501347\pi$
$29$	−0.245501			−0.00846554			−0.00423277	+	0.999991i	$0.501347\pi$
$30$	−2.02429	−	3.08061i	−0.0674762	−	0.102687i
$31$	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
$36$	14.2868	−	33.0437i	0.396855	−	0.917881i
$37$			46.8458i			1.26610i	0.774110	+	0.633051i	$0.218198\pi$
$37$			46.8458i			1.26610i	−0.774110	+	0.633051i	$0.781802\pi$
$38$	−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	$-0.400190\pi$
$41$	25.2928			0.616899			0.308449	+	0.951241i	$0.400190\pi$
$42$	−8.35881	−	12.7206i	−0.199019	−	0.302873i
$43$			23.2285i			0.540198i	0.962833	+	0.270099i	$0.0870564\pi$
$43$			23.2285i			0.540198i	−0.962833	+	0.270099i	$0.912944\pi$
$44$	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	$-0.377891\pi$
$47$	35.1820			0.748554			0.374277	+	0.927317i	$0.377891\pi$
$48$	−30.6045	−	36.9779i	−0.637593	−	0.770373i
$49$	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	$-0.368867\pi$
$53$	42.4438			0.800826			0.400413	+	0.916335i	$0.368867\pi$
$54$	49.2255	+	22.2002i	0.911583	+	0.411115i
$55$			0.647097i			0.0117654i
$56$	−20.1722	+	2.22827i	−0.360218	+	0.0397905i
$57$	53.9780	−	18.3132i	0.946983	−	0.321284i
$58$	−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	$-0.106483\pi$
$60$	−0.695118	−	7.33951i	−0.0115853	−	0.122325i
$61$	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
$66$	−5.28150	+	3.47050i	−0.0800227	+	0.0525833i
$67$	−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	$-0.252346\pi$
$72$	56.1757	−	45.0365i	0.780218	−	0.625507i
$73$	−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
$78$	−68.6395	−	104.457i	−0.879993	−	1.33920i
$79$	−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	$-0.197629\pi$
$83$	135.020			1.62675			0.813373	+	0.581743i	$0.197629\pi$
$84$	−2.87032	−	30.3068i	−0.0341705	−	0.360795i
$85$	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	$-0.682873\pi$
$89$	−96.7299			−1.08685			−0.543426	+	0.839457i	$0.682873\pi$
$90$	11.0242	−	0.870934i	0.122491	−	0.00967704i
$91$	−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
$96$	−19.4902	−	94.0007i	−0.203022	−	0.979174i
$97$			85.3270i			0.879660i	0.898081	+	0.439830i	$0.144961\pi$
$97$			85.3270i			0.879660i	−0.898081	+	0.439830i	$0.855039\pi$
$98$	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	$-0.157339\pi$
$102$	46.6180	+	70.9444i	0.457039	+	0.695534i
$103$	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	$-0.0119604\pi$
$108$	66.2330	+	85.3064i	0.613269	+	0.789874i
$109$		−	95.5631i		−	0.876725i	−0.898798	−	0.438363i	$-0.855559\pi$
$109$		−	95.5631i		−	0.876725i	0.898798	−	0.438363i	$-0.144441\pi$
$110$	−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	$-0.704893\pi$
$113$	−135.634			−1.20030			−0.600151	+	0.799887i	$0.704893\pi$
$114$	112.547	+	18.1444i	0.987253	+	0.159161i
$115$		−	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
$120$	5.63983	−	13.6235i	0.0469986	−	0.113529i
$121$	−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
$126$	45.5217	−	3.59632i	0.361284	−	0.0285422i
$127$	−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	$-0.417162\pi$
$131$	67.4165			0.514630			0.257315	+	0.966328i	$0.417162\pi$
$132$	−12.5831	+	1.19173i	−0.0953264	+	0.00902827i
$133$	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	$-0.336566\pi$
$138$	97.5963	−	64.1311i	0.707220	−	0.464718i
$139$		−	71.7384i		−	0.516104i	−0.966131	−	0.258052i	$-0.916919\pi$
$139$		−	71.7384i		−	0.516104i	0.966131	−	0.258052i	$-0.0830805\pi$
$140$	−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
$144$	141.440	−	27.0337i	0.982220	−	0.187734i
$145$		−	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	$0.824795\pi$
$150$	−123.465	+	81.1298i	−0.823102	+	0.540865i
$151$	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
$156$	−23.5700	−	248.868i	−0.151090	−	1.59531i
$157$	−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
$162$	−129.493	+	97.3428i	−0.799338	+	0.600882i
$163$			282.827i			1.73514i	0.497318	+	0.867568i	$0.334318\pi$
$163$			282.827i			1.73514i	−0.497318	+	0.867568i	$0.665682\pi$
$164$	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	$-0.160798\pi$
$168$	23.2883	−	56.2548i	0.138621	−	0.334850i
$169$	−264.964			−1.56784
$170$	15.3639	+	8.13440i	0.0903762	+	0.0478494i
$171$	−29.8449	+	168.375i	−0.174532	+	0.984652i
$172$	−76.8453	+	52.2285i	−0.446775	+	0.303654i
$173$	−231.702			−1.33932			−0.669659	−	0.742669i	$-0.733560\pi$
$173$	−231.702			−1.33932			−0.669659	+	0.742669i	$0.733560\pi$
$174$	1.23102	−	0.808909i	0.00707482	−	0.00464890i
$175$			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	$0.797803\pi$
$180$	20.3008	+	8.77727i	0.112782	+	0.0487626i
$181$		−	263.835i		−	1.45765i	−0.684698	−	0.728827i	$-0.740066\pi$
$181$		−	263.835i		−	1.45765i	0.684698	−	0.728827i	$-0.259934\pi$
$182$	−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
$186$	−229.826	+	151.020i	−1.23562	+	0.811935i
$187$		−	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	$-0.663971\pi$
$191$	−188.192			−0.985296			−0.492648	+	0.870229i	$0.663971\pi$
$192$	53.5183	−	184.390i	0.278741	−	0.960366i
$193$		−	276.161i		−	1.43088i	−0.698672	−	0.715442i	$-0.746225\pi$
$193$		−	276.161i		−	1.43088i	0.698672	−	0.715442i	$-0.253775\pi$
$194$	−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	$0.762235\pi$
$198$	−1.49316	−	18.9002i	−0.00754120	−	0.0954556i
$199$		−	93.4486i		−	0.469591i	−0.972045	−	0.234796i	$-0.924558\pi$
$199$		−	93.4486i		−	0.469591i	0.972045	−	0.234796i	$-0.0754421\pi$
$200$	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
$204$	16.0081	+	169.024i	0.0784711	+	0.828549i
$205$			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
$210$	7.81509	−	5.13534i	0.0372147	−	0.0244540i
$211$	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
$216$	37.2384	+	212.766i	0.172400	+	0.985027i
$217$			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
$222$	−154.354	−	234.900i	−0.695288	−	1.05811i
$223$	−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	$-0.146315\pi$
$228$	181.952	+	137.395i	0.798036	+	0.602610i
$229$	−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	$-0.0327507\pi$
$234$	373.808	−	29.5316i	1.59747	−	0.126204i
$235$			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	$-0.179783\pi$
$239$	403.764			1.68939			0.844694	+	0.535250i	$0.179783\pi$
$240$	22.7178	−	18.8023i	0.0946577	−	0.0783427i
$241$			151.061i			0.626811i	0.949619	+	0.313405i	$0.101470\pi$
$241$			151.061i			0.626811i	−0.949619	+	0.313405i	$0.898530\pi$
$242$	−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
$246$	−126.826	+	83.3383i	−0.515554	+	0.338774i
$247$	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	$-0.493272\pi$
$251$	10.6103			0.0422722			0.0211361	+	0.999777i	$0.493272\pi$
$252$	83.8274	+	36.2437i	0.332649	+	0.143824i
$253$	−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	$-0.298477\pi$
$257$	304.107			1.18330			0.591649	+	0.806196i	$0.298477\pi$
$258$	−76.5364	−	116.475i	−0.296653	−	0.451454i
$259$	−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	$-0.424145\pi$
$263$	124.165			0.472111			0.236055	+	0.971740i	$0.424145\pi$
$264$	−23.3565	−	9.66911i	−0.0884715	−	0.0366254i
$265$			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	$-0.274566\pi$
$269$	349.961			1.30097			0.650484	+	0.759520i	$0.274566\pi$
$270$	−13.6390	+	30.2423i	−0.0505148	+	0.112009i
$271$		−	227.793i		−	0.840564i	−0.907394	−	0.420282i	$-0.861931\pi$
$271$		−	227.793i		−	0.840564i	0.907394	−	0.420282i	$-0.138069\pi$
$272$	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
$276$	232.522	−	22.0219i	0.842470	−	0.0797895i
$277$	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	$-0.839107\pi$
$281$	−491.723			−1.74990			−0.874951	+	0.484211i	$0.839107\pi$
$282$	−176.414	+	115.923i	−0.625581	+	0.411073i
$283$		−	224.463i		−	0.793157i	−0.918001	−	0.396579i	$-0.870197\pi$
$283$		−	224.463i		−	0.793157i	0.918001	−	0.396579i	$-0.129803\pi$
$284$	334.616	−	227.425i	1.17823	−	0.800791i
$285$	11.2510	+	33.1621i	0.0394770	+	0.116358i
$286$	−20.5336	+	38.7832i	−0.0717960	+	0.135606i
$287$			64.1645i			0.223570i
$288$	275.300	+	84.5792i	0.955904	+	0.293678i
$289$	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	$-0.314093\pi$
$293$	323.122			1.10281			0.551403	+	0.834239i	$0.314093\pi$
$294$	−213.431	+	140.247i	−0.725956	+	0.477030i
$295$	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
$300$	−294.154	+	27.8591i	−0.980515	+	0.0928636i
$301$	−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
$306$	−253.880	+	20.0570i	−0.829672	+	0.0655459i
$307$	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	$-0.625165\pi$
$311$	−238.327			−0.766324			−0.383162	+	0.923681i	$0.625165\pi$
$312$	191.235	−	461.944i	0.612934	−	1.48059i
$313$	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	$-0.522817\pi$
$317$	−45.4076			−0.143242			−0.0716208	+	0.997432i	$0.522817\pi$
$318$	−212.827	+	139.849i	−0.669266	+	0.439778i
$319$	−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
$324$	−319.981	+	50.8759i	−0.987595	+	0.157024i
$325$			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
$330$	−2.13214	−	3.24475i	−0.00646105	−	0.00983259i
$331$	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
$336$	93.8079	−	77.6394i	0.279190	−	0.231070i
$337$			77.5130i			0.230009i	0.993365	+	0.115004i	$0.0366882\pi$
$337$			77.5130i			0.230009i	−0.993365	+	0.115004i	$0.963312\pi$
$338$	−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
$342$	−210.322	+	269.682i	−0.614977	+	0.788545i
$343$			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	$-0.674852\pi$
$347$	−362.339			−1.04421			−0.522103	+	0.852883i	$0.674852\pi$
$348$	2.93288	−	0.277770i	0.00842783	−	0.000798191i
$349$	−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	$-0.244672\pi$
$354$	127.652	+	194.264i	0.360599	+	0.548769i
$355$	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	$-0.781435\pi$
$359$	−555.286			−1.54676			−0.773380	+	0.633943i	$0.781435\pi$
$360$	27.6688	+	34.5123i	0.0768576	+	0.0958674i
$361$	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
$366$	−310.320	+	203.913i	−0.847869	+	0.557139i
$367$		−	428.266i		−	1.16694i	−0.812136	−	0.583469i	$-0.801695\pi$
$367$		−	428.266i		−	1.16694i	0.812136	−	0.583469i	$-0.198305\pi$
$368$	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
$372$	−547.557	+	51.8586i	−1.47193	+	0.139405i
$373$		−	354.262i		−	0.949765i	−0.880049	−	0.474882i	$-0.842491\pi$
$373$		−	354.262i		−	0.949765i	0.880049	−	0.474882i	$-0.157509\pi$
$374$	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
$378$	−56.3190	+	124.878i	−0.148992	+	0.330366i
$379$	−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	$0.618400\pi$
$384$	267.153	−	275.835i	0.695711	−	0.718321i
$385$	−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	$0.908173\pi$
$390$	64.1747	−	42.1695i	0.164550	−	0.108127i
$391$			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
$396$	15.0480	−	34.8044i	0.0380001	−	0.0878899i
$397$	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
$399$	46.4581	+	136.935i	0.116436	+	0.343195i
$400$	−144.997	+	366.307i	−0.362493	+	0.915768i
$401$	−762.374			−1.90118			−0.950590	−	0.310448i	$-0.899521\pi$
$401$	−762.374			−1.90118			−0.950590	+	0.310448i	$0.899521\pi$
$402$	274.904	−	180.641i	0.683841	−	0.449356i
$403$			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
$408$	−129.882	+	313.739i	−0.318337	+	0.768969i
$409$		−	284.887i		−	0.696545i	−0.937393	−	0.348273i	$-0.886768\pi$
$409$		−	284.887i		−	0.696545i	0.937393	−	0.348273i	$-0.113232\pi$
$410$	−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
$414$	27.5919	+	349.255i	0.0666471	+	0.843611i
$415$			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	$-0.303456\pi$
$419$	485.175			1.15794			0.578968	+	0.815350i	$0.303456\pi$
$420$	18.6193	−	1.76342i	0.0443318	−	0.00419862i
$421$		−	140.305i		−	0.333266i	−0.986019	−	0.166633i	$-0.946710\pi$
$421$		−	140.305i		−	0.333266i	0.986019	−	0.166633i	$-0.0532896\pi$
$422$	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
$426$	333.271	+	507.181i	0.782327	+	1.19057i
$427$			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	$0.710955\pi$
$432$	−133.291	+	410.923i	−0.308543	+	0.951210i
$433$			510.460i			1.17889i	0.807808	+	0.589446i	$0.200654\pi$
$433$			510.460i			1.17889i	−0.807808	+	0.589446i	$0.799346\pi$
$434$	−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
$438$	183.736	−	120.734i	0.419489	−	0.275649i
$439$	−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	$-0.803491\pi$
$443$	−722.458			−1.63083			−0.815415	+	0.578877i	$0.803491\pi$
$444$	−53.0034	−	559.645i	−0.119377	−	1.26046i
$445$		−	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	$-0.373237\pi$
$449$	348.240			0.775590			0.387795	+	0.921746i	$0.373237\pi$
$450$	−34.9055	−	441.829i	−0.0775677	−	0.981843i
$451$	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
$456$	193.032	+	413.128i	0.423316	+	0.905982i
$457$	−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	$0.981004\pi$
$462$	−8.80419	−	13.3984i	−0.0190567	−	0.0290009i
$463$			280.716i			0.606297i	0.952943	+	0.303149i	$0.0980379\pi$
$463$			280.716i			0.606297i	−0.952943	+	0.303149i	$0.901962\pi$
$464$	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	$-0.644898\pi$
$467$	−410.634			−0.879302			−0.439651	+	0.898169i	$0.644898\pi$
$468$	688.360	+	297.620i	1.47086	+	0.635939i
$469$		−	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
$474$	95.3229	−	62.6372i	0.201103	−	0.132146i
$475$	−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	$-0.216836\pi$
$479$	744.185			1.55362			0.776811	+	0.629733i	$0.216836\pi$
$480$	57.7505	−	11.9740i	0.120314	−	0.0249459i
$481$	−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
$486$	−68.8226	−	481.102i	−0.141610	−	0.989922i
$487$	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	$-0.669108\pi$
$491$	−497.509			−1.01326			−0.506628	+	0.862165i	$0.669108\pi$
$492$	−302.162	+	28.6175i	−0.614150	+	0.0581656i
$493$			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
$498$	−677.033	+	444.882i	−1.35950	+	0.893337i
$499$		−	749.433i		−	1.50187i	−0.660377	−	0.750935i	$-0.729603\pi$
$499$		−	749.433i		−	1.50187i	0.660377	−	0.750935i	$-0.270397\pi$
$500$	−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	$-0.400715\pi$
$503$	308.721			0.613760			0.306880	+	0.951748i	$0.400715\pi$
$504$	114.252	+	142.510i	0.226690	+	0.282758i
$505$	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	$-0.664421\pi$
$509$	−502.767			−0.987754			−0.493877	+	0.869532i	$0.664421\pi$
$510$	−43.5856	+	28.6403i	−0.0854620	+	0.0561575i
$511$		−	92.9566i		−	0.181911i
$512$	−165.934	−	484.366i	−0.324089	−	0.946027i
$513$	−399.557	−	321.751i	−0.778863	−	0.627194i
$514$	537.525	+	284.591i	1.04577	+	0.553679i
$515$			6.86599i			0.0133320i
$516$	−26.2818	−	277.500i	−0.0509337	−	0.537791i
$517$	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	$-0.466766\pi$
$521$	108.596			0.208437			0.104219	+	0.994554i	$0.466766\pi$
$522$	0.348027	+	4.40529i	0.000666719	+	0.00843924i
$523$	−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
$528$	−32.2352	−	38.9482i	−0.0610515	−	0.0737655i
$529$	−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
$534$	485.034	−	318.719i	0.908304	−	0.596852i
$535$	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
$540$	−52.4091	+	40.6911i	−0.0970538	+	0.0753539i
$541$	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
$546$	264.994	−	174.129i	0.485337	−	0.318918i
$547$	−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
$552$	431.602	+	178.675i	0.781888	+	0.323686i
$553$		−	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	$0.756468\pi$
$558$	−64.9752	−	822.448i	−0.116443	−	1.47392i
$559$	−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	$-0.0490300\pi$
$564$	−420.304	+	39.8065i	−0.745219	+	0.0705790i
$565$		−	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	$-0.563683\pi$
$569$	−226.161			−0.397471			−0.198735	+	0.980053i	$0.563683\pi$
$570$	−11.1472	+	69.1445i	−0.0195566	+	0.121306i
$571$			4.73060i			0.00828477i	0.999991	+	0.00414239i	$0.00131857\pi$
$571$			4.73060i			0.00828477i	−0.999991	+	0.00414239i	$0.998681\pi$
$572$	−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
$576$	407.456	+	407.131i	0.707389	+	0.706824i
$577$	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
$582$	−281.147	−	427.857i	−0.483071	−	0.735149i
$583$	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	$-0.128436\pi$
$587$	1079.72			1.83939			0.919695	+	0.392633i	$0.128436\pi$
$588$	−508.496	+	48.1592i	−0.864790	+	0.0819034i
$589$	−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	$0.617401\pi$
$594$	51.8484	+	23.3831i	0.0872868	+	0.0393655i
$595$			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	$0.914225\pi$
$600$	−546.004	−	226.034i	−0.910006	−	0.376724i
$601$		−	78.1306i		−	0.130001i	−0.997885	−	0.0650005i	$-0.979295\pi$
$601$		−	78.1306i		−	0.130001i	0.997885	−	0.0650005i	$-0.0207049\pi$
$602$	−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
$606$	315.757	+	480.528i	0.521052	+	0.792950i
$607$	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
$612$	−467.515	−	202.135i	−0.763913	−	0.330286i
$613$	−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	$-0.198176\pi$
$618$	−56.0390	+	36.8235i	−0.0906780	+	0.0595850i
$619$			932.726i			1.50683i	0.657547	+	0.753413i	$0.271594\pi$
$619$			932.726i			1.50683i	−0.657547	+	0.753413i	$0.728406\pi$
$620$	−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
$624$	770.317	−	637.547i	1.23448	−	1.02171i
$625$	596.834			0.954935
$626$	317.616	+	168.161i	0.507374	+	0.268628i
$627$	56.8541	−	19.2890i	0.0906764	−	0.0307639i
$628$	−28.8812	−	42.4937i	−0.0459892	−	0.0676652i
$629$	662.791			1.05372
$630$	2.20944	+	27.9668i	0.00350705	+	0.0443918i
$631$			623.222i			0.987673i	0.869555	+	0.493837i	$0.164406\pi$
$631$			623.222i			0.987673i	−0.869555	+	0.493837i	$0.835594\pi$
$632$	−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
$636$	−507.056	+	48.0228i	−0.797258	+	0.0755075i
$637$			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	$-0.402553\pi$
$641$	386.368			0.602758			0.301379	+	0.953504i	$0.402553\pi$
$642$	26.4883	+	40.3105i	0.0412590	+	0.0627890i
$643$		−	581.708i		−	0.904678i	−0.891846	−	0.452339i	$-0.850590\pi$
$643$		−	581.708i		−	0.904678i	0.891846	−	0.452339i	$-0.149410\pi$
$644$	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	$-0.640601\pi$
$647$	−553.170			−0.854976			−0.427488	+	0.904021i	$0.640601\pi$
$648$	−613.193	−	209.520i	−0.946285	−	0.323333i
$649$		−	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	$-0.268997\pi$
$654$	314.874	+	479.184i	0.481459	+	0.732697i
$655$			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	$0.939910\pi$
$660$	−0.732155	−	7.73058i	−0.00110933	−	0.0117130i
$661$		−	473.618i		−	0.716518i	−0.933622	−	0.358259i	$-0.883371\pi$
$661$		−	473.618i		−	0.716518i	0.933622	−	0.358259i	$-0.116629\pi$
$662$	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
$666$	840.605	−	66.4096i	1.26217	−	0.0997141i
$667$	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
$672$	238.467	−	49.4439i	0.354862	−	0.0735772i
$673$		−	328.180i		−	0.487637i	−0.969821	−	0.243819i	$-0.921600\pi$
$673$		−	328.180i		−	0.487637i	0.969821	−	0.243819i	$-0.0784002\pi$
$674$	−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	$-0.390514\pi$
$677$	456.594			0.674437			0.337219	+	0.941426i	$0.390514\pi$
$678$	680.113	−	446.906i	1.00312	−	0.659153i
$679$	−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	$-0.00799287\pi$
$684$	−624.130	+	279.853i	−0.912471	+	0.409141i
$685$	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
$690$	39.3997	+	59.9595i	0.0571010	+	0.0868978i
$691$			1111.03i			1.60786i	0.594726	+	0.803929i	$0.297261\pi$
$691$			1111.03i			1.60786i	−0.594726	+	0.803929i	$0.702739\pi$
$692$	−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
$696$	5.44396	+	2.25369i	0.00782179	+	0.00323806i
$697$		−	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	$-0.108080\pi$
$702$	−462.471	+	1025.46i	−0.658790	+	1.46076i
$703$	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
$708$	43.8343	+	462.831i	0.0619128	+	0.653716i
$709$	−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
$714$	−179.976	+	118.263i	−0.252068	+	0.165635i
$715$	−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	$-0.745800\pi$
$719$	−1003.31			−1.39543			−0.697715	+	0.716376i	$0.745800\pi$
$720$	16.6085	+	86.8952i	0.0230674	+	0.120688i
$721$			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
$726$	601.170	−	395.032i	0.828057	−	0.544121i
$727$		−	1353.04i		−	1.86113i	−0.366133	−	0.930563i	$-0.619318\pi$
$727$		−	1353.04i		−	1.86113i	0.366133	−	0.930563i	$-0.380682\pi$
$728$	−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
$732$	−739.333	+	70.0215i	−1.01002	+	0.0956578i
$733$	−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
$738$	−35.8557	−	453.857i	−0.0485850	−	0.614982i
$739$		−	80.5158i		−	0.108952i	−0.998515	−	0.0544762i	$-0.982651\pi$
$739$		−	80.5158i		−	0.108952i	0.998515	−	0.0544762i	$-0.0173489\pi$
$740$	−64.7115	−	95.2119i	−0.0874480	−	0.128665i
$741$	381.497	+	1124.46i	0.514841	+	1.51749i
$742$	−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	$-0.119725\pi$
$744$	−1016.36	−	420.754i	−1.36608	−	0.565530i
$745$	−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
$750$	−100.450	−	152.868i	−0.133934	−	0.203824i
$751$	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
$756$	−216.411	+	168.024i	−0.286258	+	0.222254i
$757$	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	$-0.233893\pi$
$762$	122.673	−	80.6089i	0.160988	−	0.105786i
$763$	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
$768$	730.340	−	237.545i	0.950964	−	0.309303i
$769$	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	$-0.534353\pi$
$773$	−166.524			−0.215426			−0.107713	+	0.994182i	$0.534353\pi$
$774$	416.814	−	32.9292i	0.538520	−	0.0425442i
$775$	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
$780$	152.895	−	14.4806i	0.196020	−	0.0185648i
$781$		−	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
$786$	−338.048	+	222.133i	−0.430086	+	0.282612i
$787$	−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
$792$	59.1689	−	47.4362i	0.0747082	−	0.0598942i
$793$			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	$-0.736926\pi$
$797$	−1079.90			−1.35495			−0.677475	+	0.735546i	$0.736926\pi$
$798$	−46.0299	+	285.516i	−0.0576815	+	0.357789i
$799$		−	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
$804$	654.955	−	62.0301i	0.814620	−	0.0771519i
$805$	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	$-0.0104014\pi$
$810$	−59.8038	−	79.5555i	−0.0738318	−	0.0982167i
$811$	−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
$816$	−523.177	+	433.004i	−0.641148	+	0.530642i
$817$	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	$-0.445328\pi$
$822$	786.402	+	1196.77i	0.956694	+	1.45592i
$823$		−	952.502i		−	1.15735i	−0.815557	−	0.578677i	$-0.803569\pi$
$823$		−	952.502i		−	1.15735i	0.815557	−	0.578677i	$-0.196431\pi$
$824$	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	$0.863812\pi$
$828$	−278.071	+	643.147i	−0.335835	+	0.776748i
$829$			371.643i			0.448303i	0.974554	+	0.224151i	$0.0719610\pi$
$829$			371.643i			0.448303i	−0.974554	+	0.224151i	$0.928039\pi$
$830$	−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
$834$	236.373	+	359.719i	0.283421	+	0.431318i
$835$	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	$-0.0835556\pi$
$840$	34.5609	+	14.3075i	0.0411439	+	0.0170327i
$841$	−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
$846$	−49.8748	−	631.310i	−0.0589537	−	0.746229i
$847$		−	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
$852$	114.442	+	1208.35i	0.134321	+	1.41825i
$853$	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
$855$	−103.444	−	18.3356i	−0.120987	−	0.0214451i
$856$	63.9238	−	7.06117i	0.0746774	−	0.00824904i
$857$	1201.97			1.40254			0.701268	−	0.712898i	$-0.252618\pi$
$857$	1201.97			1.40254			0.701268	+	0.712898i	$0.252618\pi$
$858$	−72.2968	−	110.023i	−0.0842620	−	0.128232i
$859$			1144.95i			1.33289i	0.745556	+	0.666443i	$0.232184\pi$
$859$			1144.95i			1.33289i	−0.745556	+	0.666443i	$0.767816\pi$
$860$	−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	$-0.0426803\pi$
$864$	−620.149	+	601.590i	−0.717765	+	0.696285i
$865$		−	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
$870$	0.496963	+	0.756292i	0.000571222	+	0.000869301i
$871$		−	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
$876$	437.749	−	41.4588i	0.499714	−	0.0473274i
$877$			985.032i			1.12318i	0.827414	+	0.561592i	$0.189811\pi$
$877$			985.032i			1.12318i	−0.827414	+	0.561592i	$0.810189\pi$
$878$	−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	$-0.0254628\pi$
$882$	−60.3401	−	763.778i	−0.0684128	−	0.865961i
$883$			502.318i			0.568877i	0.958694	+	0.284438i	$0.0918071\pi$
$883$			502.318i			0.568877i	−0.958694	+	0.284438i	$0.908193\pi$
$884$	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	$-0.0728924\pi$
$888$	430.043	−	1038.80i	0.484283	−	1.16982i
$889$		−	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
$894$	−513.577	−	781.575i	−0.574471	−	0.874245i
$895$	−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
$900$	351.777	−	813.621i	0.390864	−	0.904023i
$901$		−	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
$906$	−703.604	+	462.342i	−0.776605	+	0.510311i
$907$	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	$-0.121281\pi$
$912$	−45.4214	+	910.868i	−0.0498042	+	0.998759i
$913$	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
$918$	314.097	−	696.461i	0.342154	−	0.758672i
$919$			1235.92i			1.34486i	0.740163	+	0.672428i	$0.234748\pi$
$919$			1235.92i			1.34486i	−0.740163	+	0.672428i	$0.765252\pi$
$920$	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
$924$	−3.02326	−	31.9216i	−0.00327193	−	0.0345472i
$925$			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	$0.687041\pi$
$930$	−92.7810	−	141.196i	−0.0997645	−	0.151824i
$931$	−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
$936$	938.192	+	1170.24i	1.00234	+	1.25026i
$937$	−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	$-0.729185\pi$
$941$	−1240.97			−1.31878			−0.659390	+	0.751801i	$0.729185\pi$
$942$	64.4082	−	42.3230i	0.0683739	−	0.0449288i
$943$	−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	$-0.363137\pi$
$947$	789.498			0.833683			0.416841	+	0.908979i	$0.363137\pi$
$948$	227.105	−	21.5089i	0.239563	−	0.0226887i
$949$		−	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	$-0.735418\pi$
$953$	−1284.61			−1.34797			−0.673983	+	0.738747i	$0.735418\pi$
$954$	−60.1692	−	761.615i	−0.0630705	−	0.798338i
$955$		−	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
$960$	113.283	+	32.8796i	0.118003	+	0.0342496i
$961$	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
$966$	162.692	+	247.589i	0.168418	+	0.256303i
$967$		−	577.553i		−	0.597263i	−0.954368	−	0.298632i	$-0.903470\pi$
$967$		−	577.553i		−	0.597263i	0.954368	−	0.298632i	$-0.0965302\pi$
$968$	−105.307	−	953.326i	−0.108788	−	0.984841i
$969$	−259.102	−	763.701i	−0.267391	−	0.788133i
$970$	−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	$0.820554\pi$
$972$	328.580	−	914.778i	0.338045	−	0.941130i
$973$	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	$-0.243499\pi$
$977$	1409.62			1.44280			0.721400	+	0.692518i	$0.243499\pi$
$978$	−931.898	−	1418.19i	−0.952861	−	1.45009i
$979$	−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	$-0.143049\pi$
$984$	−560.867	−	232.188i	−0.569987	−	0.235963i
$985$	−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
$990$	11.6116	−	0.917340i	0.0117289	−	0.000926606i
$991$	−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
$996$	−1613.02	+	152.768i	−1.61950	+	0.153381i
$997$	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.227.63	yes	72
3.2	odd	2	inner	228.3.b.e.227.9	✓	72
4.3	odd	2	inner	228.3.b.e.227.62	yes	72
12.11	even	2	inner	228.3.b.e.227.12	yes	72
19.18	odd	2	inner	228.3.b.e.227.10	yes	72
57.56	even	2	inner	228.3.b.e.227.64	yes	72
76.75	even	2	inner	228.3.b.e.227.11	yes	72
228.227	odd	2	inner	228.3.b.e.227.61	yes	72

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

\(f(q)\)	\(=\)	\(q+(1.76755 + 0.935824i) q^{2} +(-1.44490 + 2.62912i) q^{3} +(2.24847 + 3.30823i) q^{4} +0.614363i q^{5} +(-5.01432 + 3.29494i) q^{6} +2.53686i q^{7} +(0.878356 + 7.95163i) q^{8} +(-4.82456 - 7.59761i) q^{9} +O(q^{10})\)	\(q+(1.76755 + 0.935824i) q^{2} +(-1.44490 + 2.62912i) q^{3} +(2.24847 + 3.30823i) q^{4} +0.614363i q^{5} +(-5.01432 + 3.29494i) 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} +(-11.9465 + 1.13145i) 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} +(-1.41762 - 17.9441i) 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} +(-22.1749 - 9.17997i) 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} +(-2.02429 - 3.08061i) 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} +(14.2868 - 33.0437i) 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} +(-8.35881 - 12.7206i) 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} +(-30.6045 - 36.9779i) 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} +(49.2255 + 22.2002i) q^{54} +0.647097i q^{55} +(-20.1722 + 2.22827i) q^{56} +(53.9780 - 18.3132i) q^{57} +(-0.433935 - 0.229745i) q^{58} -38.7419i q^{59} +(-0.695118 - 7.33951i) 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} +(-5.28150 + 3.47050i) 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} +(56.1757 - 45.0365i) 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} +(-68.6395 - 104.457i) 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} +(-2.87032 - 30.3068i) 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} +(11.0242 - 0.870934i) 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} +(-19.4902 - 94.0007i) 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

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