LMFDB - Embedded newform 228.3.b.e.227.12

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			227.12
Character	$\chi$	$=$	228.227
Dual form			228.3.b.e.227.10

$q$-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} +(-36.7782 - 9.55842i) 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} +(-13.4759 + 55.3841i) 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} +(73.9523 - 17.5229i) 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	$-0.980432\pi$
$5$		−	0.614363i		−	0.122873i	0.998111	−	0.0614363i	$-0.0195681\pi$
$6$	−5.01432	−	3.29494i	−0.835720	−	0.549156i
$7$		−	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	$-0.484755\pi$
$11$	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	$0.136613\pi$
$17$			14.1484i			0.832257i	−0.909306	+	0.416128i	$0.863387\pi$
$18$	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	$-0.498653\pi$
$29$	0.245501			0.00846554			0.00423277	+	0.999991i	$0.498653\pi$
$30$	−2.02429	+	3.08061i	−0.0674762	+	0.102687i
$31$	−45.8339			−1.47851			−0.739257	−	0.673424i	$-0.764823\pi$
$31$	−45.8339			−1.47851			−0.739257	+	0.673424i	$0.764823\pi$
$32$	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	$0.781802\pi$
$38$	−36.7782	−	9.55842i	−0.967848	−	0.251537i
$39$	−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	$0.599810\pi$
$42$	−8.35881	+	12.7206i	−0.199019	+	0.302873i
$43$		−	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	$-0.377891\pi$
$47$	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	$-0.631133\pi$
$53$	−42.4438			−0.800826			−0.400413	+	0.916335i	$0.631133\pi$
$54$	49.2255	−	22.2002i	0.911583	−	0.411115i
$55$		−	0.647097i		−	0.0117654i
$56$	20.1722	+	2.22827i	0.360218	+	0.0397905i
$57$	−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	$-0.106483\pi$
$60$	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	$-0.365831\pi$
$67$	54.8238			0.818266			0.409133	+	0.912475i	$0.365831\pi$
$68$	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
$76$	73.9523	−	17.5229i	0.973057	−	0.230565i
$77$		−	2.67204i		−	0.0347018i
$78$	68.6395	−	104.457i	0.879993	−	1.33920i
$79$	19.0101			0.240635			0.120317	−	0.992735i	$-0.461609\pi$
$79$	19.0101			0.240635			0.120317	+	0.992735i	$0.461609\pi$
$80$	−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	$-0.317127\pi$
$89$	96.7299			1.08685			0.543426	+	0.839457i	$0.317127\pi$
$90$	−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	$0.157339\pi$
$101$			95.8311i			0.948823i	−0.880303	+	0.474412i	$0.842661\pi$
$102$	46.6180	−	70.9444i	0.457039	−	0.695534i
$103$	−11.1758			−0.108503			−0.0542514	−	0.998527i	$-0.517277\pi$
$103$	−11.1758			−0.108503			−0.0542514	+	0.998527i	$0.517277\pi$
$104$	−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	$-0.295107\pi$
$113$	135.634			1.20030			0.600151	+	0.799887i	$0.295107\pi$
$114$	−28.0104	−	110.505i	−0.245705	−	0.969345i
$115$			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	$-0.469294\pi$
$127$	24.4645			0.192634			0.0963168	+	0.995351i	$0.469294\pi$
$128$	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	$0.336566\pi$
$137$			238.670i			1.74212i	−0.491180	+	0.871058i	$0.663434\pi$
$138$	97.5963	+	64.1311i	0.707220	+	0.464718i
$139$			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
$144$	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	$-0.824795\pi$
$149$		−	155.869i		−	1.04610i	0.852303	−	0.523049i	$-0.175205\pi$
$150$	−123.465	−	81.1298i	−0.823102	−	0.540865i
$151$	−140.319			−0.929265			−0.464632	−	0.885504i	$-0.653814\pi$
$151$	−140.319			−0.929265			−0.464632	+	0.885504i	$0.653814\pi$
$152$	−114.316	+	100.179i	−0.752079	+	0.659073i
$153$	−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	$-0.665682\pi$
$163$		−	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	$-0.160798\pi$
$168$	23.2883	+	56.2548i	0.138621	+	0.334850i
$169$	−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	$0.266440\pi$
$174$	−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
$190$	−5.87234	+	22.5952i	−0.0309070	+	0.118922i
$191$	−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	$-0.762235\pi$
$197$		−	267.688i		−	1.35882i	0.733757	−	0.679412i	$-0.237765\pi$
$198$	1.49316	−	18.9002i	0.00754120	−	0.0954556i
$199$			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
$204$	−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	$-0.528212\pi$
$211$	−37.3532			−0.177029			−0.0885146	+	0.996075i	$0.528212\pi$
$212$	−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	$-0.330621\pi$
$223$	226.283			1.01472			0.507361	+	0.861733i	$0.330621\pi$
$224$	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	$-0.146315\pi$
$228$	152.923	+	169.111i	0.670716	+	0.741714i
$229$	−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	$0.0327507\pi$
$233$			47.8619i			0.205416i	−0.994712	+	0.102708i	$0.967249\pi$
$234$	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	$-0.701523\pi$
$257$	−304.107			−1.18330			−0.591649	+	0.806196i	$0.701523\pi$
$258$	−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
$266$	−24.2484	+	93.3013i	−0.0911595	+	0.350757i
$267$	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	$0.725434\pi$
$270$	−13.6390	−	30.2423i	−0.0505148	−	0.112009i
$271$			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
$276$	−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	$-0.160893\pi$
$281$	491.723			1.74990			0.874951	+	0.484211i	$0.160893\pi$
$282$	−176.414	−	115.923i	−0.625581	−	0.411073i
$283$			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
$288$	−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	$-0.685907\pi$
$293$	−323.122			−1.10281			−0.551403	+	0.834239i	$0.685907\pi$
$294$	−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
$304$	108.309	−	284.051i	0.356281	−	0.934379i
$305$		−	38.0209i		−	0.124659i
$306$	253.880	+	20.0570i	0.829672	+	0.0655459i
$307$	−144.672			−0.471244			−0.235622	−	0.971845i	$-0.575713\pi$
$307$	−144.672			−0.471244			−0.235622	+	0.971845i	$0.575713\pi$
$308$	−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	$-0.477183\pi$
$317$	45.4076			0.143242			0.0716208	+	0.997432i	$0.477183\pi$
$318$	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	$-0.733519\pi$
$331$	−443.252			−1.33913			−0.669565	+	0.742754i	$0.733519\pi$
$332$	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
$342$	250.060	−	233.311i	0.731169	−	0.682197i
$343$		−	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	$0.244672\pi$
$353$			490.791i			1.39034i	−0.718844	+	0.695172i	$0.755328\pi$
$354$	−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	$0.198305\pi$
$367$			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
$372$	−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	$-0.275594\pi$
$379$	491.206			1.29606			0.648029	+	0.761616i	$0.275594\pi$
$380$	−10.7654	−	45.4335i	−0.0283301	−	0.119562i
$381$	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	$-0.908173\pi$
$389$		−	221.340i		−	0.568998i	0.958676	−	0.284499i	$-0.0918272\pi$
$390$	−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
$399$	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	$0.100479\pi$
$402$	−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
$418$	−38.7378	−	10.0677i	−0.0926743	−	0.0240855i
$419$	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	$-0.460515\pi$
$439$	108.632			0.247454			0.123727	+	0.992316i	$0.460515\pi$
$440$	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	$-0.626763\pi$
$449$	−348.240			−0.775590			−0.387795	+	0.921746i	$0.626763\pi$
$450$	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
$456$	−428.558	−	155.803i	−0.939819	−	0.341672i
$457$	−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	$-0.981004\pi$
$461$		−	54.9910i		−	0.119286i	0.998220	−	0.0596432i	$-0.0189963\pi$
$462$	−8.80419	+	13.3984i	−0.0190567	+	0.0290009i
$463$		−	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	$-0.644898\pi$
$467$	−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	$-0.633361\pi$
$487$	−396.240			−0.813634			−0.406817	+	0.913510i	$0.633361\pi$
$488$	−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
$494$	199.119	−	766.157i	0.403075	−	1.55092i
$495$	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	$0.270397\pi$
$499$			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	$-0.400715\pi$
$503$	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	$-0.335579\pi$
$509$	502.767			0.987754			0.493877	+	0.869532i	$0.335579\pi$
$510$	−43.5856	−	28.6403i	−0.0854620	−	0.0561575i
$511$			92.9566i			0.181911i
$512$	165.934	−	484.366i	0.324089	−	0.946027i
$513$	−355.771	−	369.589i	−0.693511	−	0.720446i
$514$	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	$-0.533234\pi$
$521$	−108.596			−0.208437			−0.104219	+	0.994554i	$0.533234\pi$
$522$	0.348027	−	4.40529i	0.000666719	−	0.00843924i
$523$	476.876			0.911809			0.455905	−	0.890029i	$-0.349316\pi$
$523$	476.876			0.911809			0.455905	+	0.890029i	$0.349316\pi$
$524$	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
$532$	−44.4533	−	187.607i	−0.0835589	−	0.352645i
$533$		−	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	$-0.287486\pi$
$547$	677.328			1.23826			0.619130	+	0.785289i	$0.287486\pi$
$548$	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	$-0.756468\pi$
$557$		−	771.550i		−	1.38519i	0.721328	−	0.692594i	$-0.243532\pi$
$558$	−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	$-0.436317\pi$
$569$	226.161			0.397471			0.198735	+	0.980053i	$0.436317\pi$
$570$	−67.8903	+	17.2085i	−0.119106	+	0.0301904i
$571$		−	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
$576$	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	$-0.617401\pi$
$593$		−	1106.24i		−	1.86550i	0.360521	−	0.932751i	$-0.382599\pi$
$594$	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	$-0.671897\pi$
$607$	−624.194			−1.02833			−0.514163	+	0.857692i	$0.671897\pi$
$608$	74.3795	+	603.433i	0.122335	+	0.992489i
$609$	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	$0.198176\pi$
$617$			719.594i			1.16628i	−0.812372	+	0.583140i	$0.801824\pi$
$618$	56.0390	+	36.8235i	0.0906780	+	0.0595850i
$619$		−	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
$624$	770.317	+	637.547i	1.23448	+	1.02171i
$625$	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
$630$	−2.20944	+	27.9668i	−0.00350705	+	0.0443918i
$631$		−	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
$636$	−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	$-0.597447\pi$
$641$	−386.368			−0.602758			−0.301379	+	0.953504i	$0.597447\pi$
$642$	−26.4883	+	40.3105i	−0.0412590	+	0.0627890i
$643$			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
$646$	135.236	−	520.352i	0.209344	−	0.805498i
$647$	−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	$0.268997\pi$
$653$			976.920i			1.49605i	−0.663671	+	0.748024i	$0.731003\pi$
$654$	−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	$-0.609486\pi$
$677$	−456.594			−0.674437			−0.337219	+	0.941426i	$0.609486\pi$
$678$	−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	$-0.00799287\pi$
$684$	−223.655	+	646.401i	−0.326981	+	0.945031i
$685$	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	$-0.702739\pi$
$691$		−	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
$696$	−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	$0.108080\pi$
$701$			466.944i			0.666111i	−0.942907	+	0.333055i	$0.891920\pi$
$702$	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
$722$	−392.850	−	605.766i	−0.544114	−	0.839011i
$723$	−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	$0.380682\pi$
$727$			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
$732$	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	$0.0173489\pi$
$739$			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	$-0.119725\pi$
$744$	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	$-0.882818\pi$
$751$	−1401.36			−1.86600			−0.932999	+	0.359879i	$0.882818\pi$
$752$	−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
$760$	61.5462	+	70.2315i	0.0809819	+	0.0924099i
$761$			1020.41i			1.34087i	0.741966	+	0.670437i	$0.233893\pi$
$761$			1020.41i			1.34087i	−0.741966	+	0.670437i	$0.766107\pi$
$762$	−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	$-0.465647\pi$
$773$	166.524			0.215426			0.107713	+	0.994182i	$0.465647\pi$
$774$	−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	$-0.448514\pi$
$787$	253.484			0.322089			0.161044	+	0.986947i	$0.448514\pi$
$788$	−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	$-0.263074\pi$
$797$	1079.90			1.35495			0.677475	+	0.735546i	$0.263074\pi$
$798$	−280.337	+	71.0586i	−0.351299	+	0.0890458i
$799$			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	$0.0104014\pi$
$809$			52.8618i			0.0653421i	−0.999466	+	0.0326711i	$0.989599\pi$
$810$	59.8038	−	79.5555i	0.0738318	−	0.0982167i
$811$	1297.43			1.59979			0.799893	−	0.600142i	$-0.204889\pi$
$811$	1297.43			1.59979			0.799893	+	0.600142i	$0.204889\pi$
$812$	−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	$0.445328\pi$
$821$			1617.84i			1.97057i	−0.170915	+	0.985286i	$0.554672\pi$
$822$	786.402	−	1196.77i	0.956694	−	1.45592i
$823$			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	$0.863812\pi$
$828$	−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
$836$	77.8927	−	18.4566i	0.0931731	−	0.0220773i
$837$	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
$855$	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	$0.747382\pi$
$858$	72.2968	−	110.023i	0.0842620	−	0.128232i
$859$		−	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	$-0.0426803\pi$
$864$	−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
$874$	715.833	+	186.041i	0.819031	+	0.212861i
$875$	−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	$0.0254628\pi$
$881$			140.799i			0.159817i	−0.996802	+	0.0799084i	$0.974537\pi$
$882$	60.3401	−	763.778i	0.0684128	−	0.865961i
$883$		−	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	$-0.0728924\pi$
$888$	−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	$-0.700667\pi$
$907$	−1069.32			−1.17896			−0.589480	+	0.807783i	$0.700667\pi$
$908$	−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	$-0.121281\pi$
$912$	903.301	−	125.665i	0.990461	−	0.137791i
$913$	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	$-0.765252\pi$
$919$		−	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
$924$	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	$-0.687041\pi$
$929$		−	1546.36i		−	1.66454i	0.554371	−	0.832270i	$-0.312959\pi$
$930$	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	$-0.270815\pi$
$941$	1240.97			1.31878			0.659390	+	0.751801i	$0.270815\pi$
$942$	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
$950$	−905.574	−	235.353i	−0.953235	−	0.247740i
$951$	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	$0.264582\pi$
$954$	−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	$0.0965302\pi$
$967$			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	$0.820554\pi$
$972$	−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	$-0.756501\pi$
$977$	−1409.62			−1.44280			−0.721400	+	0.692518i	$0.756501\pi$
$978$	−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
$988$	365.034	+	1540.56i	0.369468	+	1.55927i
$989$			452.108i			0.457137i
$990$	−11.6116	−	0.917340i	−0.0117289	−	0.000926606i
$991$	2.66847			0.00269270			0.00134635	−	0.999999i	$-0.499571\pi$
$991$	2.66847			0.00269270			0.00134635	+	0.999999i	$0.499571\pi$
$992$	−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.227.12	yes	72
3.2	odd	2	inner	228.3.b.e.227.62	yes	72
4.3	odd	2	inner	228.3.b.e.227.9	✓	72
12.11	even	2	inner	228.3.b.e.227.63	yes	72
19.18	odd	2	inner	228.3.b.e.227.61	yes	72
57.56	even	2	inner	228.3.b.e.227.11	yes	72
76.75	even	2	inner	228.3.b.e.227.64	yes	72
228.227	odd	2	inner	228.3.b.e.227.10	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.3.b.e.227.9	✓	72	4.3	odd	2	inner
228.3.b.e.227.10	yes	72	228.227	odd	2	inner
228.3.b.e.227.11	yes	72	57.56	even	2	inner
228.3.b.e.227.12	yes	72	1.1	even	1	trivial
228.3.b.e.227.61	yes	72	19.18	odd	2	inner
228.3.b.e.227.62	yes	72	3.2	odd	2	inner
228.3.b.e.227.63	yes	72	12.11	even	2	inner
228.3.b.e.227.64	yes	72	76.75	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} +(-36.7782 - 9.55842i) 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} +(-13.4759 + 55.3841i) 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} +(73.9523 - 17.5229i) 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

Varieties

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Representations

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Database

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