LMFDB - Embedded newform 228.2.c.a.191.27

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			191.27
Character	$\chi$	$=$	228.191
Dual form			228.2.c.a.191.28

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.08992 - 0.901156i) q^{2} +(1.45940 + 0.932823i) q^{3} +(0.375835 - 1.96437i) q^{4} -2.01739i q^{5} +(2.43124 - 0.298447i) q^{6} +2.54076i q^{7} +(-1.36058 - 2.47968i) q^{8} +(1.25968 + 2.72272i) q^{9} +(-1.81798 - 2.19879i) q^{10} +0.727096 q^{11} +(2.38090 - 2.51621i) q^{12} -6.54605 q^{13} +(2.28962 + 2.76921i) q^{14} +(1.88187 - 2.94418i) q^{15} +(-3.71750 - 1.47656i) q^{16} +1.39772i q^{17} +(3.82654 + 1.83236i) q^{18} -1.00000i q^{19} +(-3.96290 - 0.758206i) q^{20} +(-2.37007 + 3.70797i) q^{21} +(0.792473 - 0.655227i) q^{22} +5.80077 q^{23} +(0.327485 - 4.88802i) q^{24} +0.930133 q^{25} +(-7.13465 + 5.89902i) q^{26} +(-0.701433 + 5.14859i) q^{27} +(4.99098 + 0.954905i) q^{28} +2.06391i q^{29} +(-0.602084 - 4.90476i) q^{30} +1.55042i q^{31} +(-5.38237 + 1.74072i) q^{32} +(1.06112 + 0.678251i) q^{33} +(1.25957 + 1.52340i) q^{34} +5.12570 q^{35} +(5.82186 - 1.45119i) q^{36} -9.59638 q^{37} +(-0.901156 - 1.08992i) q^{38} +(-9.55330 - 6.10631i) q^{39} +(-5.00249 + 2.74481i) q^{40} -7.32942i q^{41} +(0.758281 + 6.17719i) q^{42} +7.93463i q^{43} +(0.273268 - 1.42828i) q^{44} +(5.49279 - 2.54128i) q^{45} +(6.32235 - 5.22740i) q^{46} -10.3890 q^{47} +(-4.04794 - 5.62265i) q^{48} +0.544559 q^{49} +(1.01377 - 0.838195i) q^{50} +(-1.30383 + 2.03983i) q^{51} +(-2.46024 + 12.8589i) q^{52} -9.29883i q^{53} +(3.87518 + 6.24363i) q^{54} -1.46684i q^{55} +(6.30027 - 3.45689i) q^{56} +(0.932823 - 1.45940i) q^{57} +(1.85990 + 2.24949i) q^{58} -1.87656 q^{59} +(-5.07618 - 4.80321i) q^{60} +3.98204 q^{61} +(1.39717 + 1.68983i) q^{62} +(-6.91776 + 3.20055i) q^{63} +(-4.29767 + 6.74760i) q^{64} +13.2060i q^{65} +(1.76774 - 0.217000i) q^{66} -5.40235i q^{67} +(2.74564 + 0.525313i) q^{68} +(8.46563 + 5.41109i) q^{69} +(5.58658 - 4.61906i) q^{70} +14.6425 q^{71} +(5.03759 - 6.82808i) q^{72} +5.82387 q^{73} +(-10.4593 + 8.64784i) q^{74} +(1.35743 + 0.867649i) q^{75} +(-1.96437 - 0.375835i) q^{76} +1.84737i q^{77} +(-15.9150 + 1.95365i) q^{78} +4.95815i q^{79} +(-2.97879 + 7.49964i) q^{80} +(-5.82639 + 6.85953i) q^{81} +(-6.60496 - 7.98846i) q^{82} -1.92329 q^{83} +(6.39307 + 6.04929i) q^{84} +2.81975 q^{85} +(7.15034 + 8.64808i) q^{86} +(-1.92526 + 3.01206i) q^{87} +(-0.989269 - 1.80297i) q^{88} -9.00334i q^{89} +(3.69659 - 7.71964i) q^{90} -16.6319i q^{91} +(2.18013 - 11.3949i) q^{92} +(-1.44626 + 2.26268i) q^{93} +(-11.3232 + 9.36216i) q^{94} -2.01739 q^{95} +(-9.47880 - 2.48039i) q^{96} +10.0867 q^{97} +(0.593524 - 0.490733i) q^{98} +(0.915911 + 1.97968i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 6 q^{6} + 8 q^{10} + 4 q^{12} - 8 q^{16} + 16 q^{18} + 8 q^{21} - 12 q^{22} - 2 q^{24} - 28 q^{25} + 12 q^{28} - 12 q^{30} - 28 q^{34} - 22 q^{36} - 16 q^{37} - 12 q^{40} + 10 q^{42} + 16 q^{45}+ \cdots + 40 q^{97}+O(q^{100}) $ 36 * q - 6 * q^6 + 8 * q^10 + 4 * q^12 - 8 * q^16 + 16 * q^18 + 8 * q^21 - 12 * q^22 - 2 * q^24 - 28 * q^25 + 12 * q^28 - 12 * q^30 - 28 * q^34 - 22 * q^36 - 16 * q^37 - 12 * q^40 + 10 * q^42 + 16 * q^45 - 4 * q^46 + 32 * q^48 - 44 * q^49 - 36 * q^52 - 20 * q^54 - 4 * q^58 - 4 * q^60 + 16 * q^61 + 24 * q^64 + 24 * q^66 - 16 * q^69 + 36 * q^70 - 36 * q^72 - 8 * q^73 - 32 * q^78 - 40 * q^81 + 72 * q^82 - 20 * q^84 + 16 * q^85 - 16 * q^88 - 56 * q^90 + 8 * q^93 - 56 * q^94 + 2 * q^96 + 40 * q^97

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.08992	−	0.901156i	0.770687	−	0.637214i
$2$	1.08992	−	0.901156i	0.770687	−	0.637214i
$3$	1.45940	+	0.932823i	0.842584	+	0.538565i
$3$	1.45940	+	0.932823i	0.842584	+	0.538565i
$4$	0.375835	−	1.96437i	0.187917	−	0.982185i
$5$		−	2.01739i		−	0.902205i	−0.892472	−	0.451102i	$-0.851031\pi$
$5$		−	2.01739i		−	0.902205i	0.892472	−	0.451102i	$-0.148969\pi$
$6$	2.43124	−	0.298447i	0.992550	−	0.121840i
$7$			2.54076i			0.960315i	0.877182	+	0.480158i	$0.159421\pi$
$7$			2.54076i			0.960315i	−0.877182	+	0.480158i	$0.840579\pi$
$8$	−1.36058	−	2.47968i	−0.481036	−	0.876701i
$9$	1.25968	+	2.72272i	0.419895	+	0.907573i
$10$	−1.81798	−	2.19879i	−0.574897	−	0.695318i
$11$	0.727096			0.219228			0.109614	−	0.993974i	$-0.465039\pi$
$11$	0.727096			0.219228			0.109614	+	0.993974i	$0.465039\pi$
$12$	2.38090	−	2.51621i	0.687307	−	0.726367i
$13$	−6.54605			−1.81555			−0.907774	−	0.419459i	$-0.862220\pi$
$13$	−6.54605			−1.81555			−0.907774	+	0.419459i	$0.862220\pi$
$14$	2.28962	+	2.76921i	0.611926	+	0.740103i
$15$	1.88187	−	2.94418i	0.485896	−	0.760183i
$16$	−3.71750	−	1.47656i	−0.929374	−	0.369139i
$17$			1.39772i			0.338997i	0.985530	+	0.169499i	$0.0542148\pi$
$17$			1.39772i			0.338997i	−0.985530	+	0.169499i	$0.945785\pi$
$18$	3.82654	+	1.83236i	0.901925	+	0.431892i
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	−3.96290	−	0.758206i	−0.886132	−	0.169540i
$21$	−2.37007	+	3.70797i	−0.517193	+	0.809146i
$22$	0.792473	−	0.655227i	0.168956	−	0.139695i
$23$	5.80077			1.20954			0.604772	−	0.796399i	$-0.293264\pi$
$23$	5.80077			1.20954			0.604772	+	0.796399i	$0.293264\pi$
$24$	0.327485	−	4.88802i	0.0668475	−	0.997763i
$25$	0.930133			0.186027
$26$	−7.13465	+	5.89902i	−1.39922	+	1.15689i
$27$	−0.701433	+	5.14859i	−0.134991	+	0.990847i
$28$	4.99098	+	0.954905i	0.943207	+	0.180460i
$29$			2.06391i			0.383258i	0.981467	+	0.191629i	$0.0613771\pi$
$29$			2.06391i			0.383258i	−0.981467	+	0.191629i	$0.938623\pi$
$30$	−0.602084	−	4.90476i	−0.109925	−	0.895483i
$31$			1.55042i			0.278463i	0.990260	+	0.139232i	$0.0444632\pi$
$31$			1.55042i			0.278463i	−0.990260	+	0.139232i	$0.955537\pi$
$32$	−5.38237	+	1.74072i	−0.951477	+	0.307719i
$33$	1.06112	+	0.678251i	0.184718	+	0.118068i
$34$	1.25957	+	1.52340i	0.216014	+	0.261261i
$35$	5.12570			0.866401
$36$	5.82186	−	1.45119i	0.970310	−	0.241865i
$37$	−9.59638			−1.57764			−0.788818	−	0.614627i	$-0.789306\pi$
$37$	−9.59638			−1.57764			−0.788818	+	0.614627i	$0.789306\pi$
$38$	−0.901156	−	1.08992i	−0.146187	−	0.176808i
$39$	−9.55330	−	6.10631i	−1.52975	−	0.977792i
$40$	−5.00249	+	2.74481i	−0.790964	+	0.433993i
$41$		−	7.32942i		−	1.14466i	−0.820022	−	0.572332i	$-0.806039\pi$
$41$		−	7.32942i		−	1.14466i	0.820022	−	0.572332i	$-0.193961\pi$
$42$	0.758281	+	6.17719i	0.117005	+	0.953161i
$43$			7.93463i			1.21002i	0.796218	+	0.605010i	$0.206831\pi$
$43$			7.93463i			1.21002i	−0.796218	+	0.605010i	$0.793169\pi$
$44$	0.273268	−	1.42828i	0.0411967	−	0.215322i
$45$	5.49279	−	2.54128i	0.818817	−	0.378831i
$46$	6.32235	−	5.22740i	0.932180	−	0.770738i
$47$	−10.3890			−1.51540			−0.757699	−	0.652604i	$-0.773677\pi$
$47$	−10.3890			−1.51540			−0.757699	+	0.652604i	$0.773677\pi$
$48$	−4.04794	−	5.62265i	−0.584270	−	0.811559i
$49$	0.544559			0.0777942
$50$	1.01377	−	0.838195i	0.143368	−	0.118539i
$51$	−1.30383	+	2.03983i	−0.182572	+	0.285634i
$52$	−2.46024	+	12.8589i	−0.341173	+	1.78320i
$53$		−	9.29883i		−	1.27729i	−0.769500	−	0.638646i	$-0.779495\pi$
$53$		−	9.29883i		−	1.27729i	0.769500	−	0.638646i	$-0.220505\pi$
$54$	3.87518	+	6.24363i	0.527345	+	0.849651i
$55$		−	1.46684i		−	0.197788i
$56$	6.30027	−	3.45689i	0.841909	−	0.461946i
$57$	0.932823	−	1.45940i	0.123555	−	0.193302i
$58$	1.85990	+	2.24949i	0.244217	+	0.295372i
$59$	−1.87656			−0.244307			−0.122154	−	0.992511i	$-0.538980\pi$
$59$	−1.87656			−0.244307			−0.122154	+	0.992511i	$0.538980\pi$
$60$	−5.07618	−	4.80321i	−0.655332	−	0.620092i
$61$	3.98204			0.509848			0.254924	−	0.966961i	$-0.417950\pi$
$61$	3.98204			0.509848			0.254924	+	0.966961i	$0.417950\pi$
$62$	1.39717	+	1.68983i	0.177441	+	0.214608i
$63$	−6.91776	+	3.20055i	−0.871556	+	0.403231i
$64$	−4.29767	+	6.74760i	−0.537209	+	0.843449i
$65$			13.2060i			1.63800i
$66$	1.76774	−	0.217000i	0.217594	−	0.0267108i
$67$		−	5.40235i		−	0.660002i	−0.943981	−	0.330001i	$-0.892951\pi$
$67$		−	5.40235i		−	0.660002i	0.943981	−	0.330001i	$-0.107049\pi$
$68$	2.74564	+	0.525313i	0.332958	+	0.0637035i
$69$	8.46563	+	5.41109i	1.01914	+	0.651419i
$70$	5.58658	−	4.61906i	0.667724	−	0.552083i
$71$	14.6425			1.73774			0.868872	−	0.495038i	$-0.164846\pi$
$71$	14.6425			1.73774			0.868872	+	0.495038i	$0.164846\pi$
$72$	5.03759	−	6.82808i	0.593685	−	0.804697i
$73$	5.82387			0.681632			0.340816	−	0.940130i	$-0.389297\pi$
$73$	5.82387			0.681632			0.340816	+	0.940130i	$0.389297\pi$
$74$	−10.4593	+	8.64784i	−1.21586	+	1.00529i
$75$	1.35743	+	0.867649i	0.156743	+	0.100187i
$76$	−1.96437	−	0.375835i	−0.225329	−	0.0431112i
$77$			1.84737i			0.210528i
$78$	−15.9150	+	1.95365i	−1.80202	+	0.221207i
$79$			4.95815i			0.557835i	0.960315	+	0.278918i	$0.0899756\pi$
$79$			4.95815i			0.557835i	−0.960315	+	0.278918i	$0.910024\pi$
$80$	−2.97879	+	7.49964i	−0.333039	+	0.838486i
$81$	−5.82639	+	6.85953i	−0.647377	+	0.762170i
$82$	−6.60496	−	7.98846i	−0.729395	−	0.882178i
$83$	−1.92329			−0.211108			−0.105554	−	0.994414i	$-0.533662\pi$
$83$	−1.92329			−0.211108			−0.105554	+	0.994414i	$0.533662\pi$
$84$	6.39307	+	6.04929i	0.697542	+	0.660031i
$85$	2.81975			0.305845
$86$	7.15034	+	8.64808i	0.771041	+	0.932546i
$87$	−1.92526	+	3.01206i	−0.206410	+	0.322927i
$88$	−0.989269	−	1.80297i	−0.105456	−	0.192197i
$89$		−	9.00334i		−	0.954352i	−0.878808	−	0.477176i	$-0.841660\pi$
$89$		−	9.00334i		−	0.954352i	0.878808	−	0.477176i	$-0.158340\pi$
$90$	3.69659	−	7.71964i	0.389655	−	0.813721i
$91$		−	16.6319i		−	1.74350i
$92$	2.18013	−	11.3949i	0.227294	−	1.18800i
$93$	−1.44626	+	2.26268i	−0.149971	+	0.234629i
$94$	−11.3232	+	9.36216i	−1.16790	+	0.965633i
$95$	−2.01739			−0.206980
$96$	−9.47880	−	2.48039i	−0.967426	−	0.253154i
$97$	10.0867			1.02415			0.512076	−	0.858940i	$-0.328876\pi$
$97$	10.0867			1.02415			0.512076	+	0.858940i	$0.328876\pi$
$98$	0.593524	−	0.490733i	0.0599550	−	0.0495715i
$99$	0.915911	+	1.97968i	0.0920525	+	0.198965i
$100$	0.349576	−	1.82712i	0.0349576	−	0.182712i
$101$		−	14.0676i		−	1.39977i	−0.714254	−	0.699887i	$-0.753234\pi$
$101$		−	14.0676i		−	1.39977i	0.714254	−	0.699887i	$-0.246766\pi$
$102$	0.417146	+	3.39820i	0.0413036	+	0.336472i
$103$		−	12.8001i		−	1.26123i	−0.776094	−	0.630617i	$-0.782802\pi$
$103$		−	12.8001i		−	1.26123i	0.776094	−	0.630617i	$-0.217198\pi$
$104$	8.90640	+	16.2321i	0.873344	+	1.59169i
$105$	7.48043	+	4.78137i	0.730016	+	0.466614i
$106$	−8.37970	−	10.1349i	−0.813909	−	0.984393i
$107$	4.69040			0.453438			0.226719	−	0.973960i	$-0.427200\pi$
$107$	4.69040			0.453438			0.226719	+	0.973960i	$0.427200\pi$
$108$	9.85011	+	3.31289i	0.947828	+	0.318783i
$109$	6.28723			0.602207			0.301104	−	0.953591i	$-0.402645\pi$
$109$	6.28723			0.602207			0.301104	+	0.953591i	$0.402645\pi$
$110$	−1.32185	−	1.59873i	−0.126033	−	0.152433i
$111$	−14.0049	−	8.95172i	−1.32929	−	0.849660i
$112$	3.75157	−	9.44525i	0.354490	−	0.892492i
$113$		−	0.642554i		−	0.0604464i	−0.999543	−	0.0302232i	$-0.990378\pi$
$113$		−	0.642554i		−	0.0604464i	0.999543	−	0.0302232i	$-0.00962181\pi$
$114$	−0.298447	−	2.43124i	−0.0279521	−	0.227707i
$115$		−	11.7024i		−	1.09126i
$116$	4.05428	+	0.775689i	0.376430	+	0.0720209i
$117$	−8.24596	−	17.8231i	−0.762339	−	1.64774i
$118$	−2.04529	+	1.69107i	−0.188285	+	0.155676i
$119$	−3.55127			−0.325544
$120$	−9.86105	−	0.660665i	−0.900187	−	0.0603102i
$121$	−10.4713			−0.951939
$122$	4.34009	−	3.58844i	0.392933	−	0.324882i
$123$	6.83705	−	10.6965i	0.616476	−	0.964475i
$124$	3.04559	+	0.582701i	0.273502	+	0.0523281i
$125$		−	11.9634i		−	1.07004i
$126$	−4.65559	+	9.72232i	−0.414753	+	0.866133i
$127$			3.77227i			0.334735i	0.985895	+	0.167367i	$0.0535266\pi$
$127$			3.77227i			0.334735i	−0.985895	+	0.167367i	$0.946473\pi$
$128$	1.39654	+	11.2272i	0.123438	+	0.992352i
$129$	−7.40160	+	11.5798i	−0.651675	+	1.01954i
$130$	11.9006	+	14.3934i	1.04375	+	1.26238i
$131$	4.63074			0.404589			0.202295	−	0.979325i	$-0.435160\pi$
$131$	4.63074			0.404589			0.202295	+	0.979325i	$0.435160\pi$
$132$	1.73114	−	1.82953i	0.150677	−	0.159240i
$133$	2.54076			0.220311
$134$	−4.86836	−	5.88811i	−0.420562	−	0.508655i
$135$	10.3867	+	1.41506i	0.893947	+	0.121789i
$136$	3.46591	−	1.90171i	0.297199	−	0.163070i
$137$			3.87335i			0.330922i	0.986216	+	0.165461i	$0.0529113\pi$
$137$			3.87335i			0.330922i	−0.986216	+	0.165461i	$0.947089\pi$
$138$	14.1031	−	1.73122i	1.20053	−	0.147371i
$139$			22.4011i			1.90004i	0.312194	+	0.950018i	$0.398936\pi$
$139$			22.4011i			1.90004i	−0.312194	+	0.950018i	$0.601064\pi$
$140$	1.92642	−	10.0688i	0.162812	−	0.850966i
$141$	−15.1618	−	9.69114i	−1.27685	−	0.816141i
$142$	15.9591	−	13.1952i	1.33926	−	1.10731i
$143$	−4.75961			−0.398018
$144$	−0.662621	−	11.9817i	−0.0552184	−	0.998474i
$145$	4.16371			0.345777
$146$	6.34753	−	5.24821i	0.525325	−	0.434345i
$147$	0.794728	+	0.507977i	0.0655481	+	0.0418972i
$148$	−3.60665	+	18.8508i	−0.296465	+	1.54953i
$149$			11.4359i			0.936863i	0.883500	+	0.468432i	$0.155181\pi$
$149$			11.4359i			0.936863i	−0.883500	+	0.468432i	$0.844819\pi$
$150$	2.26138	−	0.277595i	0.184641	−	0.0226656i
$151$			4.99693i			0.406645i	0.979112	+	0.203322i	$0.0651740\pi$
$151$			4.99693i			0.406645i	−0.979112	+	0.203322i	$0.934826\pi$
$152$	−2.47968	+	1.36058i	−0.201129	+	0.110357i
$153$	−3.80560	+	1.76069i	−0.307665	+	0.142343i
$154$	1.66477	+	2.01348i	0.134151	+	0.162251i
$155$	3.12780			0.251231
$156$	−15.5855	+	16.4712i	−1.24784	+	1.31875i
$157$	−13.0178			−1.03894			−0.519468	−	0.854490i	$-0.673870\pi$
$157$	−13.0178			−1.03894			−0.519468	+	0.854490i	$0.673870\pi$
$158$	4.46806	+	5.40396i	0.355460	+	0.429916i
$159$	8.67416	−	13.5707i	0.687906	−	1.07623i
$160$	3.51172	+	10.8583i	0.277626	+	0.858427i
$161$			14.7383i			1.16154i
$162$	−0.168771	+	12.7268i	−0.0132599	+	0.999912i
$163$		−	12.1262i		−	0.949796i	−0.880041	−	0.474898i	$-0.842485\pi$
$163$		−	12.1262i		−	0.949796i	0.880041	−	0.474898i	$-0.157515\pi$
$164$	−14.3977	−	2.75465i	−1.12427	−	0.215102i
$165$	1.36830	−	2.14070i	0.106522	−	0.166653i
$166$	−2.09622	+	1.73318i	−0.162698	+	0.134521i
$167$	−8.92206			−0.690409			−0.345205	−	0.938527i	$-0.612191\pi$
$167$	−8.92206			−0.690409			−0.345205	+	0.938527i	$0.612191\pi$
$168$	12.4193	+	0.832059i	0.958167	+	0.0641947i
$169$	29.8508			2.29622
$170$	3.07329	−	2.54104i	0.235711	−	0.194889i
$171$	2.72272	−	1.25968i	0.208211	−	0.0963304i
$172$	15.5865	+	2.98211i	1.18846	+	0.227384i
$173$		−	21.4936i		−	1.63413i	−0.576549	−	0.817063i	$-0.695601\pi$
$173$		−	21.4936i		−	1.63413i	0.576549	−	0.817063i	$-0.304399\pi$
$174$	0.615967	+	5.01786i	0.0466964	+	0.380403i
$175$			2.36324i			0.178644i
$176$	−2.70298	−	1.07360i	−0.203744	−	0.0809255i
$177$	−2.73865	−	1.75050i	−0.205849	−	0.131575i
$178$	−8.11341	−	9.81288i	−0.608126	−	0.735507i
$179$	−9.32665			−0.697107			−0.348553	−	0.937289i	$-0.613327\pi$
$179$	−9.32665			−0.697107			−0.348553	+	0.937289i	$0.613327\pi$
$180$	−2.92762	−	11.7450i	−0.218212	−	0.875418i
$181$	18.1076			1.34593			0.672963	−	0.739676i	$-0.265021\pi$
$181$	18.1076			1.34593			0.672963	+	0.739676i	$0.265021\pi$
$182$	−14.9880	−	18.1274i	−1.11098	−	1.34369i
$183$	5.81138	+	3.71453i	0.429589	+	0.274586i
$184$	−7.89238	−	14.3841i	−0.581834	−	1.06041i
$185$			19.3597i			1.42335i
$186$	0.462717	+	3.76944i	0.0339281	+	0.276389i
$187$			1.01628i			0.0743176i
$188$	−3.90457	+	20.4079i	−0.284770	+	1.48840i
$189$	−13.0813	−	1.78217i	−0.951526	−	0.129634i
$190$	−2.19879	+	1.81798i	−0.159517	+	0.131890i
$191$	7.97618			0.577136			0.288568	−	0.957459i	$-0.406821\pi$
$191$	7.97618			0.577136			0.288568	+	0.957459i	$0.406821\pi$
$192$	−12.5663	+	5.83846i	−0.906896	+	0.421355i
$193$	−1.53606			−0.110568			−0.0552840	−	0.998471i	$-0.517606\pi$
$193$	−1.53606			−0.110568			−0.0552840	+	0.998471i	$0.517606\pi$
$194$	10.9937	−	9.08973i	0.789302	−	0.652604i
$195$	−12.3188	+	19.2727i	−0.882168	+	1.38015i
$196$	0.204664	−	1.06972i	0.0146189	−	0.0764083i
$197$			13.4918i			0.961253i	0.876925	+	0.480627i	$0.159591\pi$
$197$			13.4918i			0.961253i	−0.876925	+	0.480627i	$0.840409\pi$
$198$	2.78226	+	1.33230i	0.197727	+	0.0946827i
$199$			15.9943i			1.13380i	0.823786	+	0.566902i	$0.191858\pi$
$199$			15.9943i			1.13380i	−0.823786	+	0.566902i	$0.808142\pi$
$200$	−1.26552	−	2.30644i	−0.0894855	−	0.163090i
$201$	5.03943	−	7.88418i	0.355454	−	0.556107i
$202$	−12.6771	−	15.3325i	−0.891955	−	1.07879i
$203$	−5.24389			−0.368049
$204$	3.51696	+	3.32784i	0.246237	+	0.232995i
$205$	−14.7863			−1.03272
$206$	−11.5349	−	13.9511i	−0.803676	−	0.972018i
$207$	7.30714	+	15.7939i	0.507881	+	1.09775i
$208$	24.3349	+	9.66562i	1.68732	+	0.670190i
$209$		−	0.727096i		−	0.0502943i
$210$	12.4618	−	1.52975i	0.859946	−	0.105563i
$211$		−	0.163922i		−	0.0112849i	−0.999984	−	0.00564243i	$-0.998204\pi$
$211$		−	0.163922i		−	0.0112849i	0.999984	−	0.00564243i	$-0.00179605\pi$
$212$	−18.2663	−	3.49483i	−1.25454	−	0.240026i
$213$	21.3692	+	13.6588i	1.46419	+	0.935888i
$214$	5.11214	−	4.22678i	0.349459	−	0.288937i
$215$	16.0072			1.09169
$216$	13.7212	−	5.26571i	0.933612	−	0.358286i
$217$	−3.93923			−0.267413
$218$	6.85255	−	5.66578i	0.464113	−	0.383735i
$219$	8.49934	+	5.43263i	0.574332	+	0.367103i
$220$	−2.88141	−	0.551288i	−0.194265	−	0.0371678i
$221$		−	9.14956i		−	0.615466i
$222$	−23.3311	+	2.86401i	−1.56588	+	0.192220i
$223$			6.81128i			0.456117i	0.973647	+	0.228058i	$0.0732377\pi$
$223$			6.81128i			0.456117i	−0.973647	+	0.228058i	$0.926762\pi$
$224$	−4.42275	−	13.6753i	−0.295507	−	0.913718i
$225$	1.17167	+	2.53249i	0.0781115	+	0.168833i
$226$	−0.579041	−	0.700330i	−0.0385173	−	0.0465853i
$227$	−27.7694			−1.84312			−0.921561	−	0.388234i	$-0.873085\pi$
$227$	−27.7694			−1.84312			−0.921561	+	0.388234i	$0.873085\pi$
$228$	−2.51621	−	2.38090i	−0.166640	−	0.157679i
$229$	−15.8094			−1.04472			−0.522358	−	0.852726i	$-0.674948\pi$
$229$	−15.8094			−1.04472			−0.522358	+	0.852726i	$0.674948\pi$
$230$	−10.5457	−	12.7547i	−0.695364	−	0.841017i
$231$	−1.72327	+	2.69605i	−0.113383	+	0.177387i
$232$	5.11784	−	2.80810i	0.336003	−	0.184361i
$233$		−	3.87729i		−	0.254010i	−0.991902	−	0.127005i	$-0.959464\pi$
$233$		−	3.87729i		−	0.254010i	0.991902	−	0.127005i	$-0.0405364\pi$
$234$	−25.0488	−	11.9947i	−1.63749	−	0.784121i
$235$			20.9588i			1.36720i
$236$	−0.705277	+	3.68626i	−0.0459096	+	0.239955i
$237$	−4.62507	+	7.23591i	−0.300431	+	0.470023i
$238$	−3.87059	+	3.20025i	−0.250893	+	0.207441i
$239$	−14.6126			−0.945213			−0.472606	−	0.881274i	$-0.656687\pi$
$239$	−14.6126			−0.945213			−0.472606	+	0.881274i	$0.656687\pi$
$240$	−11.3431	+	8.16628i	−0.732193	+	0.527131i
$241$	−17.6532			−1.13714			−0.568571	−	0.822634i	$-0.692504\pi$
$241$	−17.6532			−1.13714			−0.568571	+	0.822634i	$0.692504\pi$
$242$	−11.4129	+	9.43631i	−0.733647	+	0.606589i
$243$	−14.9017	+	4.57579i	−0.955948	+	0.293537i
$244$	1.49659	−	7.82219i	0.0958092	−	0.500765i
$245$		−	1.09859i		−	0.0701863i
$246$	−2.18744	−	17.8196i	−0.139466	−	1.13614i
$247$			6.54605i			0.416515i
$248$	3.84455	−	2.10946i	0.244129	−	0.133951i
$249$	−2.80684	−	1.79409i	−0.177876	−	0.113696i
$250$	−10.7809	−	13.0391i	−0.681843	−	0.824665i
$251$	1.59930			0.100947			0.0504733	−	0.998725i	$-0.483927\pi$
$251$	1.59930			0.100947			0.0504733	+	0.998725i	$0.483927\pi$
$252$	3.68713	+	14.7919i	0.232267	+	0.931804i
$253$	4.21771			0.265165
$254$	3.39940	+	4.11146i	0.213297	+	0.257976i
$255$	4.11514	+	2.63033i	0.257700	+	0.164718i
$256$	11.6396	+	10.9782i	0.727472	+	0.686137i
$257$			27.6838i			1.72687i	0.504460	+	0.863435i	$0.331692\pi$
$257$			27.6838i			1.72687i	−0.504460	+	0.863435i	$0.668308\pi$
$258$	2.36807	+	19.2910i	0.147429	+	1.20100i
$259$		−	24.3821i		−	1.51503i
$260$	25.9414	+	4.96326i	1.60882	+	0.307808i
$261$	−5.61944	+	2.59987i	−0.347835	+	0.160928i
$262$	5.04712	−	4.17302i	0.311812	−	0.257810i
$263$	10.0901			0.622179			0.311090	−	0.950381i	$-0.399306\pi$
$263$	10.0901			0.622179			0.311090	+	0.950381i	$0.399306\pi$
$264$	0.238113	−	3.55406i	0.0146548	−	0.218737i
$265$	−18.7594			−1.15238
$266$	2.76921	−	2.28962i	0.169791	−	0.140385i
$267$	8.39851	−	13.1394i	0.513981	−	0.804121i
$268$	−10.6122	−	2.03039i	−0.648244	−	0.124026i
$269$		−	5.76248i		−	0.351344i	−0.984449	−	0.175672i	$-0.943790\pi$
$269$		−	5.76248i		−	0.351344i	0.984449	−	0.175672i	$-0.0562099\pi$
$270$	12.5959	−	7.81776i	0.766559	−	0.475774i
$271$		−	18.6669i		−	1.13393i	−0.823742	−	0.566965i	$-0.808117\pi$
$271$		−	18.6669i		−	1.13393i	0.823742	−	0.566965i	$-0.191883\pi$
$272$	2.06382	−	5.19603i	0.125137	−	0.315055i
$273$	15.5146	−	24.2726i	0.938989	−	1.46904i
$274$	3.49049	+	4.22162i	0.210868	+	0.255038i
$275$	0.676295			0.0407821
$276$	13.8111	−	14.5960i	0.831328	−	0.878573i
$277$	0.581850			0.0349600			0.0174800	−	0.999847i	$-0.494436\pi$
$277$	0.581850			0.0349600			0.0174800	+	0.999847i	$0.494436\pi$
$278$	20.1869	+	24.4153i	1.21073	+	1.46433i
$279$	−4.22135	+	1.95304i	−0.252726	+	0.116925i
$280$	−6.97390	−	12.7101i	−0.416770	−	0.759575i
$281$			22.6275i			1.34985i	0.737889	+	0.674923i	$0.235823\pi$
$281$			22.6275i			1.34985i	−0.737889	+	0.674923i	$0.764177\pi$
$282$	−25.2583	+	3.10058i	−1.50411	+	0.184637i
$283$			2.77447i			0.164925i	0.996594	+	0.0824626i	$0.0262785\pi$
$283$			2.77447i			0.164925i	−0.996594	+	0.0824626i	$0.973721\pi$
$284$	5.50316	−	28.7633i	0.326552	−	1.70679i
$285$	−2.94418	−	1.88187i	−0.174398	−	0.111472i
$286$	−5.18757	+	4.28915i	−0.306748	+	0.253623i
$287$	18.6223			1.09924
$288$	−11.5196	−	12.4619i	−0.678798	−	0.734325i
$289$	15.0464			0.885081
$290$	4.53810	−	3.75216i	0.266486	−	0.220334i
$291$	14.7206	+	9.40914i	0.862935	+	0.551573i
$292$	2.18881	−	11.4402i	0.128091	−	0.669489i
$293$			25.4795i			1.48853i	0.667884	+	0.744266i	$0.267200\pi$
$293$			25.4795i			1.48853i	−0.667884	+	0.744266i	$0.732800\pi$
$294$	1.32395	−	0.162522i	0.0772146	−	0.00947848i
$295$			3.78576i			0.220415i
$296$	13.0566	+	23.7960i	0.758900	+	1.38311i
$297$	−0.510009	+	3.74352i	−0.0295937	+	0.217221i
$298$	10.3055	+	12.4641i	0.596982	+	0.722028i
$299$	−37.9722			−2.19599
$300$	2.21455	−	2.34041i	0.127857	−	0.135124i
$301$	−20.1600			−1.16200
$302$	4.50302	+	5.44624i	0.259120	+	0.313396i
$303$	13.1225	−	20.5302i	0.753870	−	1.17943i
$304$	−1.47656	+	3.71750i	−0.0846864	+	0.213213i
$305$		−	8.03333i		−	0.459987i
$306$	−2.56113	+	5.34845i	−0.146410	+	0.305750i
$307$			25.9786i			1.48268i	0.671130	+	0.741340i	$0.265809\pi$
$307$			25.9786i			1.48268i	−0.671130	+	0.741340i	$0.734191\pi$
$308$	3.62892	+	0.694307i	0.206777	+	0.0395618i
$309$	11.9403	−	18.6805i	0.679257	−	1.06270i
$310$	3.40904	−	2.81864i	0.193620	−	0.160088i
$311$	23.0143			1.30502			0.652512	−	0.757779i	$-0.273715\pi$
$311$	23.0143			1.30502			0.652512	+	0.757779i	$0.273715\pi$
$312$	−2.14373	+	31.9973i	−0.121365	+	1.81149i
$313$	−24.8085			−1.40226			−0.701129	−	0.713035i	$-0.747320\pi$
$313$	−24.8085			−1.40226			−0.701129	+	0.713035i	$0.747320\pi$
$314$	−14.1883	+	11.7311i	−0.800694	+	0.662024i
$315$	6.45676	+	13.9558i	0.363797	+	0.786322i
$316$	9.73963	+	1.86344i	0.547897	+	0.104827i
$317$			10.4192i			0.585198i	0.956235	+	0.292599i	$0.0945201\pi$
$317$			10.4192i			0.585198i	−0.956235	+	0.292599i	$0.905480\pi$
$318$	−2.77521	−	22.6077i	−0.155626	−	1.26778i
$319$			1.50066i			0.0840208i
$320$	13.6125	+	8.67008i	0.760964	+	0.484672i
$321$	6.84516	+	4.37531i	0.382059	+	0.244206i
$322$	13.2815	+	16.0636i	0.740152	+	0.895187i
$323$	1.39772			0.0777713
$324$	11.2849	+	14.0232i	0.626938	+	0.779069i
$325$	−6.08870			−0.337740
$326$	−10.9276	−	13.2165i	−0.605223	−	0.731996i
$327$	9.17557	+	5.86487i	0.507410	+	0.324328i
$328$	−18.1747	+	9.97223i	−1.00353	+	0.550624i
$329$		−	26.3960i		−	1.45526i
$330$	−0.437773	−	3.56623i	−0.0240986	−	0.196315i
$331$		−	26.3290i		−	1.44717i	−0.690234	−	0.723587i	$-0.742492\pi$
$331$		−	26.3290i		−	1.44717i	0.690234	−	0.723587i	$-0.257508\pi$
$332$	−0.722838	+	3.77805i	−0.0396709	+	0.207347i
$333$	−12.0884	−	26.1282i	−0.662441	−	1.43182i
$334$	−9.72429	+	8.04017i	−0.532090	+	0.439938i
$335$	−10.8987			−0.595457
$336$	14.2858	−	10.2848i	0.779353	−	0.561083i
$337$	13.5566			0.738474			0.369237	−	0.929335i	$-0.379619\pi$
$337$	13.5566			0.738474			0.369237	+	0.929335i	$0.379619\pi$
$338$	32.5349	−	26.9003i	1.76967	−	1.46318i
$339$	0.599389	−	0.937742i	0.0325543	−	0.0509311i
$340$	1.05976	−	5.53903i	0.0574736	−	0.300396i
$341$			1.12730i			0.0610468i
$342$	1.83236	−	3.82654i	0.0990828	−	0.206916i
$343$			19.1689i			1.03502i
$344$	19.6754	−	10.7957i	1.06083	−	0.582063i
$345$	10.9163	−	17.0785i	0.587713	−	0.919475i
$346$	−19.3691	−	23.4262i	−1.04129	−	1.25940i
$347$	31.9662			1.71604			0.858018	−	0.513620i	$-0.171696\pi$
$347$	31.9662			1.71604			0.858018	+	0.513620i	$0.171696\pi$
$348$	5.19323	+	4.91396i	0.278386	+	0.263416i
$349$	21.7785			1.16578			0.582888	−	0.812553i	$-0.301923\pi$
$349$	21.7785			1.16578			0.582888	+	0.812553i	$0.301923\pi$
$350$	2.12965	+	2.57573i	0.113834	+	0.137679i
$351$	4.59162	−	33.7030i	0.245082	−	1.79893i
$352$	−3.91350	+	1.26567i	−0.208590	+	0.0674605i
$353$			2.69656i			0.143523i	0.997422	+	0.0717617i	$0.0228621\pi$
$353$			2.69656i			0.143523i	−0.997422	+	0.0717617i	$0.977138\pi$
$354$	−4.56237	+	0.560054i	−0.242487	+	0.0297665i
$355$		−	29.5396i		−	1.56780i
$356$	−17.6859	−	3.38377i	−0.937350	−	0.179339i
$357$	−5.18272	−	3.31270i	−0.274298	−	0.175327i
$358$	−10.1653	+	8.40477i	−0.537251	+	0.444206i
$359$	−5.31406			−0.280466			−0.140233	−	0.990119i	$-0.544785\pi$
$359$	−5.31406			−0.280466			−0.140233	+	0.990119i	$0.544785\pi$
$360$	−13.7749	−	10.1628i	−0.726002	−	0.535626i
$361$	−1.00000			−0.0526316
$362$	19.7357	−	16.3178i	1.03729	−	0.857642i
$363$	−15.2818	−	9.76789i	−0.802089	−	0.512682i
$364$	−32.6713	−	6.25086i	−1.71244	−	0.327634i
$365$		−	11.7490i		−	0.614972i
$366$	9.68129	−	1.18843i	0.506049	−	0.0621201i
$367$			13.7547i			0.717988i	0.933340	+	0.358994i	$0.116880\pi$
$367$			13.7547i			0.717988i	−0.933340	+	0.358994i	$0.883120\pi$
$368$	−21.5643	−	8.56517i	−1.12412	−	0.446490i
$369$	19.9560	−	9.23276i	1.03887	−	0.480638i
$370$	17.4461	+	21.1004i	0.906978	+	1.09696i
$371$	23.6261			1.22660
$372$	3.90118	+	3.69139i	0.202267	+	0.191390i
$373$	1.33858			0.0693089			0.0346545	−	0.999399i	$-0.488967\pi$
$373$	1.33858			0.0693089			0.0346545	+	0.999399i	$0.488967\pi$
$374$	0.915825	+	1.10766i	0.0473562	+	0.0572756i
$375$	11.1597	−	17.4594i	0.576286	−	0.901597i
$376$	14.1351	+	25.7616i	0.728961	+	1.32855i
$377$		−	13.5105i		−	0.695824i
$378$	−15.8636	+	9.84589i	−0.815933	+	0.506418i
$379$		−	36.0193i		−	1.85019i	−0.379741	−	0.925093i	$-0.623987\pi$
$379$		−	36.0193i		−	1.85019i	0.379741	−	0.925093i	$-0.376013\pi$
$380$	−0.758206	+	3.96290i	−0.0388951	+	0.203293i
$381$	−3.51886	+	5.50524i	−0.180276	+	0.282042i
$382$	8.69336	−	7.18778i	0.444791	−	0.367759i
$383$	−15.6128			−0.797775			−0.398887	−	0.917000i	$-0.630604\pi$
$383$	−15.6128			−0.797775			−0.398887	+	0.917000i	$0.630604\pi$
$384$	−8.43487	+	17.6877i	−0.430440	+	0.902619i
$385$	3.72687			0.189939
$386$	−1.67418	+	1.38423i	−0.0852134	+	0.0704555i
$387$	−21.6038	+	9.99512i	−1.09818	+	0.508081i
$388$	3.79095	−	19.8141i	0.192456	−	1.00591i
$389$			21.4397i			1.08703i	0.839398	+	0.543517i	$0.182908\pi$
$389$			21.4397i			1.08703i	−0.839398	+	0.543517i	$0.817092\pi$
$390$	3.94128	+	32.1068i	0.199574	+	1.62579i
$391$			8.10786i			0.410032i
$392$	−0.740914	−	1.35033i	−0.0374218	−	0.0682022i
$393$	6.75809	+	4.31966i	0.340900	+	0.217898i
$394$	12.1582	+	14.7050i	0.612524	+	0.740826i
$395$	10.0025			0.503281
$396$	4.23305	−	1.05516i	0.212719	−	0.0530236i
$397$	2.81788			0.141425			0.0707127	−	0.997497i	$-0.477473\pi$
$397$	2.81788			0.141425			0.0707127	+	0.997497i	$0.477473\pi$
$398$	14.4133	+	17.4324i	0.722475	+	0.873808i
$399$	3.70797	+	2.37007i	0.185631	+	0.118652i
$400$	−3.45776	−	1.37339i	−0.172888	−	0.0686697i
$401$			6.75130i			0.337144i	0.985689	+	0.168572i	$0.0539156\pi$
$401$			6.75130i			0.337144i	−0.985689	+	0.168572i	$0.946084\pi$
$402$	−1.61231	−	13.1344i	−0.0804149	−	0.655085i
$403$		−	10.1491i		−	0.505564i
$404$	−27.6339	−	5.28708i	−1.37484	−	0.263042i
$405$	13.8384	+	11.7541i	0.687633	+	0.584067i
$406$	−5.71540	+	4.72556i	−0.283651	+	0.234526i
$407$	−6.97749			−0.345861
$408$	6.83209	+	0.457733i	0.338239	+	0.0226611i
$409$	−2.09657			−0.103669			−0.0518343	−	0.998656i	$-0.516507\pi$
$409$	−2.09657			−0.103669			−0.0518343	+	0.998656i	$0.516507\pi$
$410$	−16.1158	+	13.3248i	−0.795905	+	0.658064i
$411$	−3.61315	+	5.65275i	−0.178223	+	0.278830i
$412$	−25.1442	−	4.81074i	−1.23877	−	0.237008i
$413$		−	4.76788i		−	0.234612i
$414$	22.1969	+	10.6291i	1.09092	+	0.522393i
$415$			3.88002i			0.190463i
$416$	35.2333	−	11.3949i	1.72745	−	0.558679i
$417$	−20.8963	+	32.6921i	−1.02329	+	1.60094i
$418$	−0.655227	−	0.792473i	−0.0320482	−	0.0387611i
$419$	−15.3243			−0.748640			−0.374320	−	0.927300i	$-0.622124\pi$
$419$	−15.3243			−0.748640			−0.374320	+	0.927300i	$0.622124\pi$
$420$	12.2038	−	12.8973i	0.595484	−	0.629325i
$421$	22.5292			1.09801			0.549004	−	0.835820i	$-0.315007\pi$
$421$	22.5292			1.09801			0.549004	+	0.835820i	$0.315007\pi$
$422$	−0.147719	−	0.178661i	−0.00719086	−	0.00869709i
$423$	−13.0869	−	28.2865i	−0.636308	−	1.37533i
$424$	−23.0582	+	12.6518i	−1.11980	+	0.614424i
$425$			1.30007i			0.0630625i
$426$	35.5994	−	4.37001i	1.72480	−	0.211727i
$427$			10.1174i			0.489614i
$428$	1.76281	−	9.21367i	0.0852089	−	0.445360i
$429$	−6.94616	−	4.43987i	−0.335364	−	0.214359i
$430$	17.4466	−	14.4250i	0.841348	−	0.695637i
$431$	−25.0323			−1.20576			−0.602882	−	0.797831i	$-0.705981\pi$
$431$	−25.0323			−1.20576			−0.602882	+	0.797831i	$0.705981\pi$
$432$	10.2098	−	18.1042i	0.491218	−	0.871037i
$433$	3.91908			0.188339			0.0941695	−	0.995556i	$-0.469980\pi$
$433$	3.91908			0.188339			0.0941695	+	0.995556i	$0.469980\pi$
$434$	−4.29343	+	3.54986i	−0.206091	+	0.170399i
$435$	6.07651	+	3.88400i	0.291346	+	0.186224i
$436$	2.36296	−	12.3504i	0.113165	−	0.591479i
$437$		−	5.80077i		−	0.277488i
$438$	14.1592	−	1.73811i	0.676554	−	0.0830503i
$439$			13.6187i			0.649984i	0.945717	+	0.324992i	$0.105362\pi$
$439$			13.6187i			0.649984i	−0.945717	+	0.324992i	$0.894638\pi$
$440$	−3.63729	+	1.99574i	−0.173401	+	0.0951432i
$441$	0.685973	+	1.48268i	0.0326654	+	0.0706039i
$442$	−8.24519	−	9.97226i	−0.392183	−	0.474332i
$443$	−9.43157			−0.448108			−0.224054	−	0.974577i	$-0.571929\pi$
$443$	−9.43157			−0.448108			−0.224054	+	0.974577i	$0.571929\pi$
$444$	−22.8480	+	24.1465i	−1.08432	+	1.14594i
$445$	−18.1633			−0.861021
$446$	6.13802	+	7.42372i	0.290644	+	0.351523i
$447$	−10.6676	+	16.6895i	−0.504562	+	0.789386i
$448$	−17.1440	−	10.9193i	−0.809978	−	0.515890i
$449$		−	26.2107i		−	1.23696i	−0.785801	−	0.618480i	$-0.787749\pi$
$449$		−	26.2107i		−	1.23696i	0.785801	−	0.618480i	$-0.212251\pi$
$450$	3.55919	+	1.70434i	0.167782	+	0.0803434i
$451$		−	5.32919i		−	0.250942i
$452$	−1.26221	−	0.241494i	−0.0593695	−	0.0113589i
$453$	−4.66125	+	7.29252i	−0.219005	+	0.342632i
$454$	−30.2664	+	25.0246i	−1.42047	+	1.17446i
$455$	−33.5531			−1.57299
$456$	−4.88802	−	0.327485i	−0.228903	−	0.0153359i
$457$	−26.8025			−1.25377			−0.626883	−	0.779113i	$-0.715670\pi$
$457$	−26.8025			−1.25377			−0.626883	+	0.779113i	$0.715670\pi$
$458$	−17.2310	+	14.2468i	−0.805150	+	0.665708i
$459$	−7.19630	−	0.980408i	−0.335894	−	0.0457615i
$460$	−22.9879	−	4.39818i	−1.07182	−	0.205066i
$461$		−	1.52855i		−	0.0711917i	−0.999366	−	0.0355959i	$-0.988667\pi$
$461$		−	1.52855i		−	0.0711917i	0.999366	−	0.0355959i	$-0.0113329\pi$
$462$	0.551343	+	4.49141i	0.0256508	+	0.208959i
$463$			4.87005i			0.226330i	0.993576	+	0.113165i	$0.0360989\pi$
$463$			4.87005i			0.226330i	−0.993576	+	0.113165i	$0.963901\pi$
$464$	3.04748	−	7.67257i	0.141476	−	0.356190i
$465$	4.56470	+	2.91768i	0.211683	+	0.135304i
$466$	−3.49404	−	4.22592i	−0.161859	−	0.195762i
$467$	13.3761			0.618974			0.309487	−	0.950904i	$-0.399843\pi$
$467$	13.3761			0.618974			0.309487	+	0.950904i	$0.399843\pi$
$468$	−38.1102	+	9.49959i	−1.76164	+	0.439118i
$469$	13.7261			0.633810
$470$	18.8871	+	22.8433i	0.871198	+	1.05368i
$471$	−18.9982	−	12.1433i	−0.875390	−	0.559535i
$472$	2.55320	+	4.65328i	0.117521	+	0.214184i
$473$			5.76923i			0.265270i
$474$	1.47974	+	12.0544i	0.0679669	+	0.553679i
$475$		−	0.930133i		−	0.0426774i
$476$	−1.33469	+	6.97601i	−0.0611755	+	0.319745i
$477$	25.3181	−	11.7136i	1.15924	−	0.536329i
$478$	−15.9265	+	13.1683i	−0.728463	+	0.602302i
$479$	−8.65866			−0.395624			−0.197812	−	0.980240i	$-0.563384\pi$
$479$	−8.65866			−0.395624			−0.197812	+	0.980240i	$0.563384\pi$
$480$	−5.00392	+	19.1224i	−0.228397	+	0.872816i
$481$	62.8184			2.86427
$482$	−19.2405	+	15.9083i	−0.876382	+	0.724603i
$483$	−13.7483	+	21.5091i	−0.625567	+	0.978698i
$484$	−3.93549	+	20.5696i	−0.178886	+	0.934980i
$485$		−	20.3489i		−	0.923996i
$486$	−12.1182	+	18.4160i	−0.549691	+	0.835368i
$487$			29.1490i			1.32087i	0.750884	+	0.660434i	$0.229628\pi$
$487$			29.1490i			1.32087i	−0.750884	+	0.660434i	$0.770372\pi$
$488$	−5.41786	−	9.87419i	−0.245255	−	0.446984i
$489$	11.3116	−	17.6969i	0.511527	−	0.800283i
$490$	−0.990000	−	1.19737i	−0.0447237	−	0.0540917i
$491$	2.66853			0.120429			0.0602146	−	0.998185i	$-0.480821\pi$
$491$	2.66853			0.120429			0.0602146	+	0.998185i	$0.480821\pi$
$492$	−18.4424	−	17.4506i	−0.831446	−	0.786735i
$493$	−2.88477			−0.129924
$494$	5.89902	+	7.13465i	0.265409	+	0.321003i
$495$	3.99378	−	1.84775i	0.179507	−	0.0830502i
$496$	2.28928	−	5.76367i	0.102792	−	0.258796i
$497$			37.2030i			1.66878i
$498$	−4.67597	+	0.573999i	−0.209535	+	0.0257215i
$499$		−	15.8891i		−	0.711293i	−0.934621	−	0.355646i	$-0.884261\pi$
$499$		−	15.8891i		−	0.711293i	0.934621	−	0.355646i	$-0.115739\pi$
$500$	−23.5005	−	4.49626i	−1.05098	−	0.201079i
$501$	−13.0208	−	8.32270i	−0.581728	−	0.371831i
$502$	1.74310	−	1.44122i	0.0777983	−	0.0643246i
$503$	−6.56501			−0.292719			−0.146360	−	0.989231i	$-0.546756\pi$
$503$	−6.56501			−0.292719			−0.146360	+	0.989231i	$0.546756\pi$
$504$	17.3485	+	12.7993i	0.772763	+	0.570125i
$505$	−28.3798			−1.26288
$506$	4.59696	−	3.80082i	0.204360	−	0.168967i
$507$	43.5642	+	27.8455i	1.93476	+	1.23666i
$508$	7.41013	+	1.41775i	0.328771	+	0.0629025i
$509$			3.24604i			0.143878i	0.997409	+	0.0719391i	$0.0229187\pi$
$509$			3.24604i			0.143878i	−0.997409	+	0.0719391i	$0.977081\pi$
$510$	6.85549	−	0.841546i	0.303566	−	0.0372643i
$511$			14.7970i			0.654582i
$512$	22.5792	+	1.47625i	0.997869	+	0.0652417i
$513$	5.14859	+	0.701433i	0.227316	+	0.0309690i
$514$	24.9475	+	30.1731i	1.10039	+	1.33088i
$515$	−25.8229			−1.13789
$516$	19.9652	+	18.8916i	0.878918	+	0.831655i
$517$	−7.55383			−0.332217
$518$	−21.9720	−	26.5744i	−0.965396	−	1.16761i
$519$	20.0497	−	31.3677i	0.880083	−	1.37689i
$520$	32.7466	−	17.9677i	1.43603	−	0.787936i
$521$		−	8.82115i		−	0.386462i	−0.981153	−	0.193231i	$-0.938103\pi$
$521$		−	8.82115i		−	0.386462i	0.981153	−	0.193231i	$-0.0618966\pi$
$522$	−3.78183	+	7.89764i	−0.165526	+	0.345670i
$523$		−	15.8016i		−	0.690954i	−0.938427	−	0.345477i	$-0.887717\pi$
$523$		−	15.8016i		−	0.690954i	0.938427	−	0.345477i	$-0.112283\pi$
$524$	1.74039	−	9.09648i	0.0760294	−	0.397382i
$525$	−2.20448	+	3.44891i	−0.0962115	+	0.150523i
$526$	10.9973	−	9.09271i	0.479505	−	0.396461i
$527$	−2.16705			−0.0943983
$528$	−2.94324	−	4.08820i	−0.128088	−	0.177916i
$529$	10.6489			0.462997
$530$	−20.4462	+	16.9051i	−0.888124	+	0.734312i
$531$	−2.36387	−	5.10935i	−0.102583	−	0.221727i
$532$	0.954905	−	4.99098i	0.0414004	−	0.216387i
$533$			47.9788i			2.07819i
$534$	−2.68702	−	21.8893i	−0.116279	−	0.947241i
$535$		−	9.46237i		−	0.409094i
$536$	−13.3961	+	7.35030i	−0.578624	+	0.317485i
$537$	−13.6113	−	8.70011i	−0.587371	−	0.375438i
$538$	−5.19289	−	6.28062i	−0.223881	−	0.270777i
$539$	0.395947			0.0170546
$540$	6.68340	−	19.8715i	0.287608	−	0.855135i
$541$	20.7315			0.891317			0.445658	−	0.895203i	$-0.352970\pi$
$541$	20.7315			0.891317			0.445658	+	0.895203i	$0.352970\pi$
$542$	−16.8218	−	20.3453i	−0.722556	−	0.873906i
$543$	26.4262	+	16.8912i	1.13406	+	0.724869i
$544$	−2.43304	−	7.52305i	−0.104316	−	0.322548i
$545$		−	12.6838i		−	0.543314i
$546$	−4.96375	−	40.4362i	−0.212429	−	1.73051i
$547$			2.58790i			0.110651i	0.998468	+	0.0553254i	$0.0176196\pi$
$547$			2.58790i			0.110651i	−0.998468	+	0.0553254i	$0.982380\pi$
$548$	7.60868	+	1.45574i	0.325027	+	0.0621861i
$549$	5.01611	+	10.8420i	0.214082	+	0.462724i
$550$	0.737105	−	0.609448i	0.0314303	−	0.0259869i
$551$	2.06391			0.0879255
$552$	1.89966	−	28.3543i	0.0808550	−	1.20684i
$553$	−12.5974			−0.535698
$554$	0.634168	−	0.524338i	0.0269432	−	0.0222770i
$555$	−18.0591	+	28.2534i	−0.766567	+	1.19929i
$556$	44.0040	+	8.41912i	1.86619	+	0.357050i
$557$		−	14.5437i		−	0.616236i	−0.951348	−	0.308118i	$-0.900301\pi$
$557$		−	14.5437i		−	0.616236i	0.951348	−	0.308118i	$-0.0996992\pi$
$558$	−2.84093	+	5.93274i	−0.120266	+	0.251153i
$559$		−	51.9405i		−	2.19685i
$560$	−19.0548	−	7.56839i	−0.805211	−	0.319823i
$561$	−0.948007	+	1.48315i	−0.0400249	+	0.0626188i
$562$	20.3909	+	24.6621i	0.860140	+	1.04031i
$563$	1.19729			0.0504597			0.0252299	−	0.999682i	$-0.491968\pi$
$563$	1.19729			0.0504597			0.0252299	+	0.999682i	$0.491968\pi$
$564$	−24.7353	+	26.1410i	−1.04154	+	1.10074i
$565$	−1.29628			−0.0545350
$566$	2.50023	+	3.02394i	0.105093	+	0.127106i
$567$	−17.4284	−	14.8034i	−0.731924	−	0.621686i
$568$	−19.9222	−	36.3087i	−0.835917	−	1.52348i
$569$		−	38.7847i		−	1.62594i	−0.582306	−	0.812970i	$-0.697849\pi$
$569$		−	38.7847i		−	1.62594i	0.582306	−	0.812970i	$-0.302151\pi$
$570$	−4.90476	+	0.602084i	−0.205438	+	0.0252185i
$571$			14.5644i			0.609503i	0.952432	+	0.304752i	$0.0985734\pi$
$571$			14.5644i			0.609503i	−0.952432	+	0.304752i	$0.901427\pi$
$572$	−1.78883	+	9.34963i	−0.0747946	+	0.390928i
$573$	11.6404	+	7.44036i	0.486285	+	0.310825i
$574$	20.2967	−	16.7816i	0.847169	−	0.700450i
$575$	5.39548			0.225007
$576$	−23.7855	−	3.20150i	−0.991063	−	0.133396i
$577$	−3.29239			−0.137064			−0.0685319	−	0.997649i	$-0.521831\pi$
$577$	−3.29239			−0.137064			−0.0685319	+	0.997649i	$0.521831\pi$
$578$	16.3993	−	13.5591i	0.682120	−	0.563986i
$579$	−2.24172	−	1.43287i	−0.0931628	−	0.0595481i
$580$	1.56487	−	8.17907i	0.0649776	−	0.339617i
$581$		−	4.88660i		−	0.202730i
$582$	24.5233	−	3.01036i	1.01652	−	0.124783i
$583$		−	6.76114i		−	0.280018i
$584$	−7.92381	−	14.4413i	−0.327890	−	0.597587i
$585$	−35.9561	+	16.6353i	−1.48660	+	0.687786i
$586$	22.9611	+	27.7706i	0.948512	+	1.14719i
$587$	19.8625			0.819813			0.409906	−	0.912128i	$-0.365561\pi$
$587$	19.8625			0.819813			0.409906	+	0.912128i	$0.365561\pi$
$588$	1.29654	−	1.37023i	0.0534685	−	0.0565071i
$589$	1.55042			0.0638838
$590$	3.41156	+	4.12616i	0.140452	+	0.169871i
$591$	−12.5855	+	19.6900i	−0.517698	+	0.809936i
$592$	35.6745	+	14.1696i	1.46621	+	0.582367i
$593$		−	34.5843i		−	1.42021i	−0.704097	−	0.710104i	$-0.748648\pi$
$593$		−	34.5843i		−	1.42021i	0.704097	−	0.710104i	$-0.251352\pi$
$594$	2.81763	+	4.53972i	0.115609	+	0.186267i
$595$			7.16430i			0.293708i
$596$	22.4643	+	4.29800i	0.920173	+	0.176053i
$597$	−14.9198	+	23.3420i	−0.610627	+	0.955324i
$598$	−41.3865	+	34.2188i	−1.69242	+	1.39931i
$599$	3.98842			0.162963			0.0814813	−	0.996675i	$-0.474035\pi$
$599$	3.98842			0.162963			0.0814813	+	0.996675i	$0.474035\pi$
$600$	0.304604	−	4.54651i	0.0124354	−	0.185610i
$601$	−3.71725			−0.151630			−0.0758149	−	0.997122i	$-0.524156\pi$
$601$	−3.71725			−0.151630			−0.0758149	+	0.997122i	$0.524156\pi$
$602$	−21.9727	+	18.1673i	−0.895539	+	0.740443i
$603$	14.7091	−	6.80525i	0.599000	−	0.277131i
$604$	9.81583	+	1.87802i	0.399400	+	0.0764156i
$605$			21.1248i			0.858844i
$606$	−4.19842	−	34.2016i	−0.170549	−	1.38935i
$607$		−	13.5369i		−	0.549446i	−0.961523	−	0.274723i	$-0.911414\pi$
$607$		−	13.5369i		−	0.549446i	0.961523	−	0.274723i	$-0.0885861\pi$
$608$	1.74072	+	5.38237i	0.0705956	+	0.218284i
$609$	−7.65292	−	4.89162i	−0.310112	−	0.198218i
$610$	−7.23928	−	8.75565i	−0.293110	−	0.354506i
$611$	68.0073			2.75128
$612$	2.02836	+	8.13734i	0.0819917	+	0.328932i
$613$	20.0068			0.808068			0.404034	−	0.914744i	$-0.367608\pi$
$613$	20.0068			0.808068			0.404034	+	0.914744i	$0.367608\pi$
$614$	23.4108	+	28.3145i	0.944783	+	1.14268i
$615$	−21.5791	−	13.7930i	−0.870154	−	0.556188i
$616$	4.58090	−	2.51349i	0.184570	−	0.101271i
$617$		−	28.1107i		−	1.13169i	−0.824511	−	0.565846i	$-0.808549\pi$
$617$		−	28.1107i		−	1.13169i	0.824511	−	0.565846i	$-0.191451\pi$
$618$	−3.82016	−	31.1202i	−0.153669	−	1.25184i
$619$		−	5.86592i		−	0.235771i	−0.993027	−	0.117886i	$-0.962388\pi$
$619$		−	5.86592i		−	0.235771i	0.993027	−	0.117886i	$-0.0376116\pi$
$620$	1.17554	−	6.14415i	0.0472107	−	0.246755i
$621$	−4.06885	+	29.8658i	−0.163277	+	1.19847i
$622$	25.0837	−	20.7395i	1.00577	−	0.831579i
$623$	22.8753			0.916479
$624$	26.4980	+	36.8062i	1.06077	+	1.47343i
$625$	−19.4842			−0.779368
$626$	−27.0392	+	22.3563i	−1.08070	+	0.893538i
$627$	0.678251	−	1.06112i	0.0270867	−	0.0423771i
$628$	−4.89255	+	25.5718i	−0.195234	+	1.02043i
$629$		−	13.4131i		−	0.534814i
$630$	19.6137	+	9.39214i	0.781429	+	0.374192i
$631$			28.9629i			1.15300i	0.817099	+	0.576498i	$0.195581\pi$
$631$			28.9629i			1.15300i	−0.817099	+	0.576498i	$0.804419\pi$
$632$	12.2946	−	6.74593i	0.489054	−	0.268339i
$633$	0.152910	−	0.239227i	0.00607763	−	0.00950843i
$634$	9.38929	+	11.3560i	0.372896	+	0.451005i
$635$	7.61014			0.301999
$636$	−23.3978	−	22.1396i	−0.927784	−	0.877892i
$637$	−3.56471			−0.141239
$638$	1.35233	+	1.63559i	0.0535392	+	0.0647538i
$639$	18.4449	+	39.8674i	0.729669	+	1.57713i
$640$	22.6496	−	2.81736i	0.895305	−	0.111366i
$641$		−	27.1139i		−	1.07093i	−0.844556	−	0.535467i	$-0.820136\pi$
$641$		−	27.1139i		−	1.07093i	0.844556	−	0.535467i	$-0.179864\pi$
$642$	11.4035	−	1.39983i	0.450060	−	0.0552471i
$643$			15.5077i			0.611563i	0.952102	+	0.305782i	$0.0989178\pi$
$643$			15.5077i			0.611563i	−0.952102	+	0.305782i	$0.901082\pi$
$644$	28.9515	+	5.53918i	1.14085	+	0.218274i
$645$	23.3609	+	14.9319i	0.919836	+	0.587944i
$646$	1.52340	−	1.25957i	0.0599374	−	0.0495570i
$647$	−38.8465			−1.52721			−0.763606	−	0.645682i	$-0.776573\pi$
$647$	−38.8465			−1.52721			−0.763606	+	0.645682i	$0.776573\pi$
$648$	24.9367	+	5.11470i	0.979607	+	0.200925i
$649$	−1.36444			−0.0535589
$650$	−6.63617	+	5.48687i	−0.260292	+	0.215213i
$651$	−5.74891	−	3.67461i	−0.225317	−	0.144019i
$652$	−23.8203	−	4.55744i	−0.932876	−	0.178483i
$653$			4.91558i			0.192361i	0.995364	+	0.0961807i	$0.0306627\pi$
$653$			4.91558i			0.192361i	−0.995364	+	0.0961807i	$0.969337\pi$
$654$	15.2858	−	1.87640i	0.597721	−	0.0733732i
$655$		−	9.34201i		−	0.365023i
$656$	−10.8223	+	27.2471i	−0.422540	+	1.06382i
$657$	7.33623	+	15.8567i	0.286214	+	0.618631i
$658$	−23.7870	−	28.7695i	−0.927312	−	1.12155i
$659$	−3.75738			−0.146367			−0.0731834	−	0.997318i	$-0.523316\pi$
$659$	−3.75738			−0.146367			−0.0731834	+	0.997318i	$0.523316\pi$
$660$	−3.69087	−	3.49239i	−0.143667	−	0.135941i
$661$	−25.2722			−0.982974			−0.491487	−	0.870885i	$-0.663547\pi$
$661$	−25.2722			−0.982974			−0.491487	+	0.870885i	$0.663547\pi$
$662$	−23.7265	−	28.6964i	−0.922159	−	1.11532i
$663$	8.53492	−	13.3529i	0.331469	−	0.518582i
$664$	2.61678	+	4.76914i	0.101551	+	0.185079i
$665$		−	5.12570i		−	0.198766i
$666$	−36.7210	−	17.5841i	−1.42291	−	0.681368i
$667$			11.9723i			0.463568i
$668$	−3.35322	+	17.5262i	−0.129740	+	0.678110i
$669$	−6.35371	+	9.94036i	−0.245649	+	0.384317i
$670$	−11.8786	+	9.82139i	−0.458911	+	0.379433i
$671$	2.89532			0.111773
$672$	6.30207	−	24.0833i	0.243107	−	0.929034i
$673$	−44.1413			−1.70152			−0.850762	−	0.525552i	$-0.823859\pi$
$673$	−44.1413			−1.70152			−0.850762	+	0.525552i	$0.823859\pi$
$674$	14.7755	−	12.2166i	0.569133	−	0.470566i
$675$	−0.652426	+	4.78887i	−0.0251119	+	0.184324i
$676$	11.2190	−	58.6381i	0.431499	−	2.25531i
$677$			25.6758i			0.986802i	0.869802	+	0.493401i	$0.164246\pi$
$677$			25.6758i			0.986802i	−0.869802	+	0.493401i	$0.835754\pi$
$678$	−0.191768	−	1.56220i	−0.00736482	−	0.0599960i
$679$			25.6279i			0.983510i
$680$	−3.83648	−	6.99209i	−0.147122	−	0.268135i
$681$	−40.5266	−	25.9040i	−1.55298	−	0.992642i
$682$	1.01588	+	1.22866i	0.0388999	+	0.0470480i
$683$	29.7802			1.13951			0.569754	−	0.821815i	$-0.307038\pi$
$683$	29.7802			1.13951			0.569754	+	0.821815i	$0.307038\pi$
$684$	−1.45119	−	5.82186i	−0.0554877	−	0.222604i
$685$	7.81406			0.298560
$686$	17.2742	+	20.8925i	0.659530	+	0.797679i
$687$	−23.0723	−	14.7474i	−0.880261	−	0.562648i
$688$	11.7159	−	29.4970i	0.446666	−	1.12456i
$689$			60.8707i			2.31899i
$690$	−3.49255	−	28.4514i	−0.132959	−	1.08313i
$691$		−	25.0122i		−	0.951510i	−0.879578	−	0.475755i	$-0.842175\pi$
$691$		−	25.0122i		−	0.951510i	0.879578	−	0.475755i	$-0.157825\pi$
$692$	−42.2213	−	8.07803i	−1.60501	−	0.307081i
$693$	−5.02988	+	2.32711i	−0.191069	+	0.0883994i
$694$	34.8405	−	28.8065i	1.32253	−	1.09348i
$695$	45.1918			1.71422
$696$	10.0884	+	0.675899i	0.382401	+	0.0256199i
$697$	10.2445			0.388038
$698$	23.7367	−	19.6258i	0.898448	−	0.742848i
$699$	3.61682	−	5.65851i	0.136801	−	0.214025i
$700$	4.64228	+	0.888188i	0.175462	+	0.0335703i
$701$		−	39.1020i		−	1.47686i	−0.674329	−	0.738431i	$-0.735567\pi$
$701$		−	39.1020i		−	1.47686i	0.674329	−	0.738431i	$-0.264433\pi$
$702$	−25.3672	−	40.8712i	−0.957421	−	1.54258i
$703$			9.59638i			0.361934i
$704$	−3.12482	+	4.90615i	−0.117771	+	0.184907i
$705$	−19.5508	+	30.5872i	−0.736327	+	1.15198i
$706$	2.43002	+	2.93902i	0.0914550	+	0.110612i
$707$	35.7422			1.34422
$708$	−4.46790	+	4.72182i	−0.167914	+	0.177457i
$709$	−14.1929			−0.533027			−0.266513	−	0.963831i	$-0.585872\pi$
$709$	−14.1929			−0.533027			−0.266513	+	0.963831i	$0.585872\pi$
$710$	−26.6198	−	32.1957i	−0.999024	−	1.20828i
$711$	−13.4996	+	6.24570i	−0.506276	+	0.234232i
$712$	−22.3254	+	12.2497i	−0.836681	+	0.459078i
$713$			8.99361i			0.336814i
$714$	−8.63399	+	1.05987i	−0.323119	+	0.0396645i
$715$			9.60199i			0.359094i
$716$	−3.50528	+	18.3210i	−0.130999	+	0.684688i
$717$	−21.3256	−	13.6310i	−0.796421	−	0.509059i
$718$	−5.79188	+	4.78880i	−0.216151	+	0.178716i
$719$	16.8705			0.629163			0.314581	−	0.949231i	$-0.398136\pi$
$719$	16.8705			0.629163			0.314581	+	0.949231i	$0.398136\pi$
$720$	−24.1718	+	1.33677i	−0.900828	+	0.0498183i
$721$	32.5220			1.21118
$722$	−1.08992	+	0.901156i	−0.0405625	+	0.0335376i
$723$	−25.7631	−	16.4673i	−0.958138	−	0.612426i
$724$	6.80546	−	35.5700i	0.252923	−	1.32195i
$725$			1.91971i			0.0712962i
$726$	−25.4583	+	3.12514i	−0.944847	+	0.115985i
$727$		−	7.36061i		−	0.272990i	−0.990641	−	0.136495i	$-0.956416\pi$
$727$		−	7.36061i		−	0.272990i	0.990641	−	0.136495i	$-0.0435837\pi$
$728$	−41.2419	+	22.6290i	−1.52853	+	0.838686i
$729$	−26.0160	−	7.22278i	−0.963555	−	0.267511i
$730$	−10.5877	−	12.8054i	−0.391868	−	0.473951i
$731$	−11.0904			−0.410193
$732$	9.48083	−	10.0196i	0.350422	−	0.370336i
$733$	38.7249			1.43034			0.715168	−	0.698952i	$-0.246350\pi$
$733$	38.7249			1.43034			0.715168	+	0.698952i	$0.246350\pi$
$734$	12.3951	+	14.9914i	0.457512	+	0.553344i
$735$	1.02479	−	1.60328i	0.0377999	−	0.0591378i
$736$	−31.2219	+	10.0975i	−1.15085	+	0.372200i
$737$		−	3.92802i		−	0.144691i
$738$	13.4302	−	28.0464i	0.494371	−	1.03240i
$739$			6.85149i			0.252036i	0.992028	+	0.126018i	$0.0402197\pi$
$739$			6.85149i			0.252036i	−0.992028	+	0.126018i	$0.959780\pi$
$740$	38.0295	+	7.27603i	1.39799	+	0.267472i
$741$	−6.10631	+	9.55330i	−0.224321	+	0.350949i
$742$	25.7504	−	21.2908i	0.945328	−	0.781609i
$743$	−9.48809			−0.348084			−0.174042	−	0.984738i	$-0.555683\pi$
$743$	−9.48809			−0.348084			−0.174042	+	0.984738i	$0.555683\pi$
$744$	7.57847	+	0.507738i	0.277840	+	0.0186146i
$745$	23.0706			0.845242
$746$	1.45894	−	1.20627i	0.0534155	−	0.0441646i
$747$	−2.42273	−	5.23657i	−0.0886432	−	0.191596i
$748$	1.99634	+	0.381953i	0.0729936	+	0.0139656i
$749$			11.9172i			0.435443i
$750$	−3.57044	−	29.0859i	−0.130374	−	1.06207i
$751$			28.0866i			1.02489i	0.858719	+	0.512447i	$0.171261\pi$
$751$			28.0866i			1.02489i	−0.858719	+	0.512447i	$0.828739\pi$
$752$	38.6213	+	15.3400i	1.40837	+	0.559393i
$753$	2.33401	+	1.49186i	0.0850560	+	0.0543664i
$754$	−12.1750	−	14.7253i	−0.443389	−	0.536263i
$755$	10.0808			0.366877
$756$	−8.41726	+	25.0267i	−0.306133	+	0.910214i
$757$	3.10549			0.112871			0.0564355	−	0.998406i	$-0.482026\pi$
$757$	3.10549			0.112871			0.0564355	+	0.998406i	$0.482026\pi$
$758$	−32.4590	−	39.2580i	−1.17896	−	1.42591i
$759$	6.15532	+	3.93438i	0.223424	+	0.142809i
$760$	2.74481	+	5.00249i	0.0995648	+	0.181460i
$761$		−	31.6202i		−	1.14623i	−0.819475	−	0.573115i	$-0.805735\pi$
$761$		−	31.6202i		−	1.14623i	0.819475	−	0.573115i	$-0.194265\pi$
$762$	1.12582	+	9.17129i	0.0407842	+	0.332241i
$763$			15.9743i			0.578309i
$764$	2.99773	−	15.6682i	0.108454	−	0.566854i
$765$	3.55200	+	7.67739i	0.128423	+	0.277577i
$766$	−17.0166	+	14.0695i	−0.614835	+	0.508353i
$767$	12.2841			0.443552
$768$	6.74604	+	26.8792i	0.243427	+	0.969919i
$769$	−14.8426			−0.535238			−0.267619	−	0.963525i	$-0.586237\pi$
$769$	−14.8426			−0.535238			−0.267619	+	0.963525i	$0.586237\pi$
$770$	4.06198	−	3.35850i	0.146384	−	0.121032i
$771$	−25.8241	+	40.4017i	−0.930033	+	1.45503i
$772$	−0.577305	+	3.01739i	−0.0207777	+	0.108598i
$773$			13.0831i			0.470565i	0.971927	+	0.235282i	$0.0756015\pi$
$773$			13.0831i			0.470565i	−0.971927	+	0.235282i	$0.924398\pi$
$774$	−14.5391	+	30.3622i	−0.522598	+	1.09135i
$775$			1.44209i			0.0518015i
$776$	−13.7238	−	25.0119i	−0.492654	−	0.897876i
$777$	22.7441	−	35.5831i	0.815941	−	1.27654i
$778$	19.3205	+	23.3674i	0.692673	+	0.837764i
$779$	−7.32942			−0.262604
$780$	33.2289	+	31.4421i	1.18979	+	1.12581i
$781$	10.6465			0.380961
$782$	7.30645	+	8.83689i	0.261278	+	0.316007i
$783$	−10.6262	−	1.44769i	−0.379750	−	0.0517364i
$784$	−2.02440	−	0.804073i	−0.0722999	−	0.0287169i
$785$			26.2620i			0.937333i
$786$	11.2584	−	1.38203i	0.401575	−	0.0492954i
$787$			40.1253i			1.43031i	0.698964	+	0.715157i	$0.253645\pi$
$787$			40.1253i			1.43031i	−0.698964	+	0.715157i	$0.746355\pi$
$788$	26.5029	+	5.07070i	0.944128	+	0.180636i
$789$	14.7254	+	9.41223i	0.524238	+	0.335084i
$790$	10.9019	−	9.01383i	0.387873	−	0.320698i
$791$	1.63257			0.0580476
$792$	3.66281	−	4.96467i	0.130152	−	0.176412i
$793$	−26.0666			−0.925653
$794$	3.07125	−	2.53935i	0.108995	−	0.0901182i
$795$	−27.3774	−	17.4992i	−0.970976	−	0.620632i
$796$	31.4186	+	6.01120i	1.11360	+	0.213061i
$797$			41.3973i			1.46637i	0.680030	+	0.733185i	$0.261967\pi$
$797$			41.3973i			1.46637i	−0.680030	+	0.733185i	$0.738033\pi$
$798$	6.17719	−	0.758281i	0.218670	−	0.0268429i
$799$		−	14.5210i		−	0.513716i
$800$	−5.00632	+	1.61910i	−0.177000	+	0.0572439i
$801$	24.5135	−	11.3414i	0.866144	−	0.400727i
$802$	6.08398	+	7.35836i	0.214833	+	0.259833i
$803$	4.23451			0.149433
$804$	−13.5934	−	12.8625i	−0.479404	−	0.453624i
$805$	29.7330			1.04795
$806$	−9.14594	−	11.0617i	−0.322152	−	0.389631i
$807$	5.37537	−	8.40975i	0.189222	−	0.296037i
$808$	−34.8831	+	19.1400i	−1.22718	+	0.673342i
$809$			25.6754i			0.902699i	0.892347	+	0.451349i	$0.149057\pi$
$809$			25.6754i			0.902699i	−0.892347	+	0.451349i	$0.850943\pi$
$810$	25.6749	+	0.340477i	0.902125	+	0.0119631i
$811$		−	31.2201i		−	1.09629i	−0.836385	−	0.548143i	$-0.815335\pi$
$811$		−	31.2201i		−	1.09629i	0.836385	−	0.548143i	$-0.184665\pi$
$812$	−1.97084	+	10.3009i	−0.0691628	+	0.361492i
$813$	17.4129	−	27.2424i	0.610696	−	0.955432i
$814$	−7.60488	+	6.28781i	−0.266551	+	0.220387i
$815$	−24.4633			−0.856911
$816$	7.85890	−	5.65789i	0.275116	−	0.198066i
$817$	7.93463			0.277597
$818$	−2.28509	+	1.88934i	−0.0798961	+	0.0660591i
$819$	45.2841	−	20.9510i	1.58235	−	0.732086i
$820$	−5.55721	+	29.0458i	−0.194066	+	1.01432i
$821$		−	15.0797i		−	0.526285i	−0.964757	−	0.263143i	$-0.915241\pi$
$821$		−	15.0797i		−	0.526285i	0.964757	−	0.263143i	$-0.0847590\pi$
$822$	1.15599	+	9.41704i	0.0403197	+	0.328457i
$823$		−	31.1286i		−	1.08507i	−0.840032	−	0.542537i	$-0.817464\pi$
$823$		−	31.1286i		−	1.08507i	0.840032	−	0.542537i	$-0.182536\pi$
$824$	−31.7403	+	17.4156i	−1.10573	+	0.606699i
$825$	0.986984	+	0.630864i	0.0343624	+	0.0219639i
$826$	−4.29661	−	5.19659i	−0.149498	−	0.180813i
$827$	−28.7116			−0.998399			−0.499199	−	0.866487i	$-0.666372\pi$
$827$	−28.7116			−0.998399			−0.499199	+	0.866487i	$0.666372\pi$
$828$	33.7713	−	8.41803i	1.17363	−	0.292547i
$829$	−20.9197			−0.726572			−0.363286	−	0.931678i	$-0.618345\pi$
$829$	−20.9197			−0.726572			−0.363286	+	0.931678i	$0.618345\pi$
$830$	3.49651	+	4.22890i	0.121366	+	0.146787i
$831$	0.849151	+	0.542763i	0.0294567	+	0.0188282i
$832$	28.1328	−	44.1701i	0.975328	−	1.53132i
$833$			0.761142i			0.0263720i
$834$	6.68554	+	54.4625i	0.231501	+	1.88588i
$835$			17.9993i			0.622891i
$836$	−1.42828	−	0.273268i	−0.0493983	−	0.00945117i
$837$	−7.98247	−	1.08751i	−0.275914	−	0.0375900i
$838$	−16.7022	+	13.8096i	−0.576967	+	0.477044i
$839$	36.2840			1.25266			0.626332	−	0.779557i	$-0.284556\pi$
$839$	36.2840			1.25266			0.626332	+	0.779557i	$0.284556\pi$
$840$	1.67859	−	25.0545i	0.0579168	−	0.864463i
$841$	24.7403			0.853113
$842$	24.5550	−	20.3024i	0.846221	−	0.699666i
$843$	−21.1075	+	33.0226i	−0.726980	+	1.13736i
$844$	−0.322003	−	0.0616076i	−0.0110838	−	0.00212062i
$845$		−	60.2208i		−	2.07166i
$846$	−39.7542	−	19.0365i	−1.36678	−	0.654489i
$847$		−	26.6051i		−	0.914162i
$848$	−13.7303	+	34.5684i	−0.471499	+	1.18708i
$849$	−2.58809	+	4.04906i	−0.0888230	+	0.138963i
$850$	1.17156	+	1.41696i	0.0401843	+	0.0486015i
$851$	−55.6664			−1.90822
$852$	34.8623	−	36.8436i	1.19436	−	1.26224i
$853$	2.43892			0.0835071			0.0417535	−	0.999128i	$-0.486706\pi$
$853$	2.43892			0.0835071			0.0417535	+	0.999128i	$0.486706\pi$
$854$	9.11734	+	11.0271i	0.311989	+	0.377340i
$855$	−2.54128	−	5.49279i	−0.0869098	−	0.187849i
$856$	−6.38164	−	11.6307i	−0.218120	−	0.397529i
$857$		−	18.0974i		−	0.618196i	−0.951030	−	0.309098i	$-0.899973\pi$
$857$		−	18.0974i		−	0.618196i	0.951030	−	0.309098i	$-0.100027\pi$
$858$	−11.5718	+	1.42049i	−0.395053	+	0.0484947i
$859$		−	37.6257i		−	1.28377i	−0.766799	−	0.641887i	$-0.778152\pi$
$859$		−	37.6257i		−	1.28377i	0.766799	−	0.641887i	$-0.221848\pi$
$860$	6.01608	−	31.4442i	0.205147	−	1.07224i
$861$	27.1773	+	17.3713i	0.926200	+	0.592012i
$862$	−27.2831	+	22.5580i	−0.929267	+	0.768329i
$863$	54.7768			1.86462			0.932312	−	0.361655i	$-0.117788\pi$
$863$	54.7768			1.86462			0.932312	+	0.361655i	$0.117788\pi$
$864$	−5.18689	−	28.9326i	−0.176462	−	0.984308i
$865$	−43.3609			−1.47432
$866$	4.27147	−	3.53171i	0.145150	−	0.120012i
$867$	21.9586	+	14.0356i	0.745755	+	0.476674i
$868$	−1.48050	+	7.73811i	−0.0502515	+	0.262649i
$869$			3.60505i			0.122293i
$870$	10.1230	−	1.24265i	0.343201	−	0.0421297i
$871$			35.3641i			1.19827i
$872$	−8.55425	−	15.5903i	−0.289683	−	0.527956i
$873$	12.7061	+	27.4633i	0.430036	+	0.929493i
$874$	−5.22740	−	6.32235i	−0.176819	−	0.213857i
$875$	30.3961			1.02757
$876$	13.8660	−	14.6541i	0.468490	−	0.495115i
$877$	30.5097			1.03024			0.515120	−	0.857118i	$-0.327747\pi$
$877$	30.5097			1.03024			0.515120	+	0.857118i	$0.327747\pi$
$878$	12.2725	+	14.8432i	0.414178	+	0.500934i
$879$	−23.7679	+	37.1848i	−0.801671	+	1.25421i
$880$	−2.16587	+	5.45296i	−0.0730114	+	0.183819i
$881$			15.7689i			0.531268i	0.964074	+	0.265634i	$0.0855812\pi$
$881$			15.7689i			0.531268i	−0.964074	+	0.265634i	$0.914419\pi$
$882$	2.08378	+	0.997830i	0.0701645	+	0.0335987i
$883$			0.131483i			0.00442475i	0.999998	+	0.00221237i	$0.000704221\pi$
$883$			0.131483i			0.00442475i	−0.999998	+	0.00221237i	$0.999296\pi$
$884$	−17.9731	−	3.43872i	−0.604502	−	0.115657i
$885$	−3.53144	+	5.52493i	−0.118708	+	0.185718i
$886$	−10.2796	+	8.49932i	−0.345351	+	0.285540i
$887$	−12.9309			−0.434177			−0.217088	−	0.976152i	$-0.569656\pi$
$887$	−12.9309			−0.434177			−0.217088	+	0.976152i	$0.569656\pi$
$888$	−3.14267	+	46.9073i	−0.105461	+	1.57411i
$889$	−9.58441			−0.321451
$890$	−19.7964	+	16.3679i	−0.663578	+	0.548654i
$891$	−4.23634	+	4.98753i	−0.141923	+	0.167089i
$892$	13.3799	+	2.55992i	0.447991	+	0.0857123i
$893$			10.3890i			0.347656i
$894$	3.41300	+	27.8034i	0.114148	+	0.929883i
$895$			18.8155i			0.628933i
$896$	−28.5255	+	3.54826i	−0.952971	+	0.118539i
$897$	−55.4165	−	35.4213i	−1.85030	−	1.18268i
$898$	−23.6199	−	28.5675i	−0.788208	−	0.953309i
$899$	−3.19992			−0.106723
$900$	5.41510	−	1.34980i	0.180503	−	0.0449934i
$901$	12.9972			0.432999
$902$	−4.80243	−	5.80837i	−0.159904	−	0.193398i
$903$	−29.4214	−	18.8057i	−0.979083	−	0.625813i
$904$	−1.59333	+	0.874243i	−0.0529934	+	0.0290769i
$905$		−	36.5301i		−	1.21430i
$906$	1.49132	+	12.1487i	0.0495458	+	0.403615i
$907$			14.5231i			0.482232i	0.970496	+	0.241116i	$0.0775134\pi$
$907$			14.5231i			0.482232i	−0.970496	+	0.241116i	$0.922487\pi$
$908$	−10.4367	+	54.5494i	−0.346355	+	1.81029i
$909$	38.3020	−	17.7207i	1.27040	−	0.587758i
$910$	−36.5701	+	30.2366i	−1.21229	+	1.00233i
$911$	−24.6410			−0.816393			−0.408197	−	0.912894i	$-0.633842\pi$
$911$	−24.6410			−0.816393			−0.408197	+	0.912894i	$0.633842\pi$
$912$	−5.62265	+	4.04794i	−0.186185	+	0.134041i
$913$	−1.39841			−0.0462807
$914$	−29.2124	+	24.1532i	−0.966262	+	0.798917i
$915$	7.49367	−	11.7238i	0.247733	−	0.387577i
$916$	−5.94174	+	31.0556i	−0.196320	+	1.02610i
$917$			11.7656i			0.388533i
$918$	−8.72686	+	5.41643i	−0.288029	+	0.178769i
$919$			22.6906i			0.748494i	0.927329	+	0.374247i	$0.122099\pi$
$919$			22.6906i			0.748494i	−0.927329	+	0.374247i	$0.877901\pi$
$920$	−29.0183	+	15.9220i	−0.956705	+	0.524934i
$921$	−24.2335	+	37.9132i	−0.798520	+	1.24928i
$922$	−1.37746	−	1.66599i	−0.0453644	−	0.0548666i
$923$	−95.8505			−3.15496
$924$	4.64838	+	4.39841i	0.152920	+	0.144697i
$925$	−8.92591			−0.293482
$926$	4.38867	+	5.30794i	0.144221	+	0.174430i
$927$	34.8512	−	16.1241i	1.14466	−	0.529586i
$928$	−3.59269	−	11.1087i	−0.117936	−	0.364662i
$929$		−	48.7913i		−	1.60079i	−0.599473	−	0.800395i	$-0.704623\pi$
$929$		−	48.7913i		−	1.60079i	0.599473	−	0.800395i	$-0.295377\pi$
$930$	7.60443	−	0.933482i	0.249359	−	0.0306101i
$931$		−	0.544559i		−	0.0178472i
$932$	−7.61643	−	1.45722i	−0.249485	−	0.0477329i
$933$	33.5871	+	21.4683i	1.09959	+	0.702841i
$934$	14.5789	−	12.0540i	0.477036	−	0.394419i
$935$	2.05023			0.0670497
$936$	−32.9763	+	44.6970i	−1.07786	+	1.46097i
$937$	−15.5138			−0.506813			−0.253406	−	0.967360i	$-0.581551\pi$
$937$	−15.5138			−0.506813			−0.253406	+	0.967360i	$0.581551\pi$
$938$	14.9602	−	12.3693i	0.488469	−	0.403872i
$939$	−36.2054	−	23.1419i	−1.18152	−	0.755207i
$940$	41.1708	+	7.87704i	1.34284	+	0.256921i
$941$		−	51.3089i		−	1.67262i	−0.548255	−	0.836311i	$-0.684708\pi$
$941$		−	51.3089i		−	1.67262i	0.548255	−	0.836311i	$-0.315292\pi$
$942$	−31.6495	+	3.88513i	−1.03120	+	0.126584i
$943$		−	42.5163i		−	1.38452i
$944$	6.97611	+	2.77085i	0.227053	+	0.0901835i
$945$	−3.59533	+	26.3901i	−0.116956	+	0.858471i
$946$	5.19898	+	6.28798i	0.169033	+	0.204440i
$947$	40.8390			1.32709			0.663544	−	0.748137i	$-0.269051\pi$
$947$	40.8390			1.32709			0.663544	+	0.748137i	$0.269051\pi$
$948$	12.4757	+	11.8049i	0.405193	+	0.383404i
$949$	−38.1233			−1.23754
$950$	−0.838195	−	1.01377i	−0.0271946	−	0.0328909i
$951$	−9.71922	+	15.2057i	−0.315167	+	0.493078i
$952$	4.83177	+	8.80603i	0.156599	+	0.285405i
$953$		−	6.58132i		−	0.213190i	−0.994303	−	0.106595i	$-0.966005\pi$
$953$		−	6.58132i		−	0.213190i	0.994303	−	0.106595i	$-0.0339948\pi$
$954$	17.0388	−	35.5824i	0.551653	−	1.15202i
$955$		−	16.0911i		−	0.520695i
$956$	−5.49194	+	28.7046i	−0.177622	+	0.928374i
$957$	−1.39985	+	2.19006i	−0.0452507	+	0.0707946i
$958$	−9.43721	+	7.80280i	−0.304902	+	0.252097i
$959$	−9.84123			−0.317790
$960$	11.7785	+	25.3512i	0.380148	+	0.818206i
$961$	28.5962			0.922458
$962$	68.4668	−	56.6092i	2.20746	−	1.82515i
$963$	5.90842	+	12.7706i	0.190396	+	0.411528i
$964$	−6.63469	+	34.6774i	−0.213689	+	1.11688i
$965$			3.09883i			0.0997550i
$966$	4.39861	+	35.8324i	0.141523	+	1.15289i
$967$		−	37.5634i		−	1.20796i	−0.797000	−	0.603980i	$-0.793581\pi$
$967$		−	37.5634i		−	1.20796i	0.797000	−	0.603980i	$-0.206419\pi$
$968$	14.2470	+	25.9656i	0.457917	+	0.834566i
$969$	2.03983	+	1.30383i	0.0655288	+	0.0418849i
$970$	−18.3375	−	22.1786i	−0.588783	−	0.712112i
$971$	−18.9158			−0.607036			−0.303518	−	0.952826i	$-0.598161\pi$
$971$	−18.9158			−0.607036			−0.303518	+	0.952826i	$0.598161\pi$
$972$	3.38795	+	30.9923i	0.108669	+	0.994078i
$973$	−56.9157			−1.82463
$974$	26.2678	+	31.7700i	0.841675	+	1.01798i
$975$	−8.88583	−	5.67968i	−0.284574	−	0.181895i
$976$	−14.8032	−	5.87971i	−0.473839	−	0.188205i
$977$		−	33.1592i		−	1.06086i	−0.847730	−	0.530428i	$-0.822031\pi$
$977$		−	33.1592i		−	1.06086i	0.847730	−	0.530428i	$-0.177969\pi$
$978$	−3.61902	−	29.4817i	−0.115724	−	0.942720i
$979$		−	6.54629i		−	0.209220i
$980$	−2.15803	−	0.412888i	−0.0689359	−	0.0131892i
$981$	7.91992	+	17.1184i	0.252864	+	0.546547i
$982$	2.90848	−	2.40477i	0.0928133	−	0.0767391i
$983$	−40.4924			−1.29151			−0.645753	−	0.763546i	$-0.723457\pi$
$983$	−40.4924			−1.29151			−0.645753	+	0.763546i	$0.723457\pi$
$984$	−35.8264	−	2.40027i	−1.14210	−	0.0765179i
$985$	27.2183			0.867247
$986$	−3.14416	+	2.59963i	−0.100130	+	0.0827891i
$987$	24.6228	−	38.5223i	0.783753	−	1.22618i
$988$	12.8589	+	2.46024i	0.409095	+	0.0782705i
$989$			46.0269i			1.46357i
$990$	2.68778	−	5.61292i	0.0854232	−	0.178390i
$991$			5.51298i			0.175126i	0.996159	+	0.0875629i	$0.0279079\pi$
$991$			5.51298i			0.175126i	−0.996159	+	0.0875629i	$0.972092\pi$
$992$	−2.69884	−	8.34492i	−0.0856884	−	0.264951i
$993$	24.5603	−	38.4245i	0.779397	−	1.21936i
$994$	33.5257	+	40.5481i	1.06337	+	1.28611i
$995$	32.2667			1.02292
$996$	−4.57916	+	4.83939i	−0.145096	+	0.153342i
$997$	11.3549			0.359614			0.179807	−	0.983702i	$-0.442453\pi$
$997$	11.3549			0.359614			0.179807	+	0.983702i	$0.442453\pi$
$998$	−14.3185	−	17.3178i	−0.453245	−	0.548184i
$999$	6.73122	−	49.4078i	0.212966	−	1.56320i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.2.c.a.191.27	yes	36
3.2	odd	2	inner	228.2.c.a.191.10	yes	36
4.3	odd	2	inner	228.2.c.a.191.9	✓	36
12.11	even	2	inner	228.2.c.a.191.28	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.c.a.191.9	✓	36	4.3	odd	2	inner
228.2.c.a.191.10	yes	36	3.2	odd	2	inner
228.2.c.a.191.27	yes	36	1.1	even	1	trivial
228.2.c.a.191.28	yes	36	12.11	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.08992 - 0.901156i) q^{2} +(1.45940 + 0.932823i) q^{3} +(0.375835 - 1.96437i) q^{4} -2.01739i q^{5} +(2.43124 - 0.298447i) q^{6} +2.54076i q^{7} +(-1.36058 - 2.47968i) q^{8} +(1.25968 + 2.72272i) q^{9} +(-1.81798 - 2.19879i) q^{10} +0.727096 q^{11} +(2.38090 - 2.51621i) q^{12} -6.54605 q^{13} +(2.28962 + 2.76921i) q^{14} +(1.88187 - 2.94418i) q^{15} +(-3.71750 - 1.47656i) q^{16} +1.39772i q^{17} +(3.82654 + 1.83236i) q^{18} -1.00000i q^{19} +(-3.96290 - 0.758206i) q^{20} +(-2.37007 + 3.70797i) q^{21} +(0.792473 - 0.655227i) q^{22} +5.80077 q^{23} +(0.327485 - 4.88802i) q^{24} +0.930133 q^{25} +(-7.13465 + 5.89902i) q^{26} +(-0.701433 + 5.14859i) q^{27} +(4.99098 + 0.954905i) q^{28} +2.06391i q^{29} +(-0.602084 - 4.90476i) q^{30} +1.55042i q^{31} +(-5.38237 + 1.74072i) q^{32} +(1.06112 + 0.678251i) q^{33} +(1.25957 + 1.52340i) q^{34} +5.12570 q^{35} +(5.82186 - 1.45119i) q^{36} -9.59638 q^{37} +(-0.901156 - 1.08992i) q^{38} +(-9.55330 - 6.10631i) q^{39} +(-5.00249 + 2.74481i) q^{40} -7.32942i q^{41} +(0.758281 + 6.17719i) q^{42} +7.93463i q^{43} +(0.273268 - 1.42828i) q^{44} +(5.49279 - 2.54128i) q^{45} +(6.32235 - 5.22740i) q^{46} -10.3890 q^{47} +(-4.04794 - 5.62265i) q^{48} +0.544559 q^{49} +(1.01377 - 0.838195i) q^{50} +(-1.30383 + 2.03983i) q^{51} +(-2.46024 + 12.8589i) q^{52} -9.29883i q^{53} +(3.87518 + 6.24363i) q^{54} -1.46684i q^{55} +(6.30027 - 3.45689i) q^{56} +(0.932823 - 1.45940i) q^{57} +(1.85990 + 2.24949i) q^{58} -1.87656 q^{59} +(-5.07618 - 4.80321i) q^{60} +3.98204 q^{61} +(1.39717 + 1.68983i) q^{62} +(-6.91776 + 3.20055i) q^{63} +(-4.29767 + 6.74760i) q^{64} +13.2060i q^{65} +(1.76774 - 0.217000i) q^{66} -5.40235i q^{67} +(2.74564 + 0.525313i) q^{68} +(8.46563 + 5.41109i) q^{69} +(5.58658 - 4.61906i) q^{70} +14.6425 q^{71} +(5.03759 - 6.82808i) q^{72} +5.82387 q^{73} +(-10.4593 + 8.64784i) q^{74} +(1.35743 + 0.867649i) q^{75} +(-1.96437 - 0.375835i) q^{76} +1.84737i q^{77} +(-15.9150 + 1.95365i) q^{78} +4.95815i q^{79} +(-2.97879 + 7.49964i) q^{80} +(-5.82639 + 6.85953i) q^{81} +(-6.60496 - 7.98846i) q^{82} -1.92329 q^{83} +(6.39307 + 6.04929i) q^{84} +2.81975 q^{85} +(7.15034 + 8.64808i) q^{86} +(-1.92526 + 3.01206i) q^{87} +(-0.989269 - 1.80297i) q^{88} -9.00334i q^{89} +(3.69659 - 7.71964i) q^{90} -16.6319i q^{91} +(2.18013 - 11.3949i) q^{92} +(-1.44626 + 2.26268i) q^{93} +(-11.3232 + 9.36216i) q^{94} -2.01739 q^{95} +(-9.47880 - 2.48039i) q^{96} +10.0867 q^{97} +(0.593524 - 0.490733i) q^{98} +(0.915911 + 1.97968i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 6 q^{6} + 8 q^{10} + 4 q^{12} - 8 q^{16} + 16 q^{18} + 8 q^{21} - 12 q^{22} - 2 q^{24} - 28 q^{25} + 12 q^{28} - 12 q^{30} - 28 q^{34} - 22 q^{36} - 16 q^{37} - 12 q^{40} + 10 q^{42} + 16 q^{45}+ \cdots + 40 q^{97}+O(q^{100}) \) 36 * q - 6 * q^6 + 8 * q^10 + 4 * q^12 - 8 * q^16 + 16 * q^18 + 8 * q^21 - 12 * q^22 - 2 * q^24 - 28 * q^25 + 12 * q^28 - 12 * q^30 - 28 * q^34 - 22 * q^36 - 16 * q^37 - 12 * q^40 + 10 * q^42 + 16 * q^45 - 4 * q^46 + 32 * q^48 - 44 * q^49 - 36 * q^52 - 20 * q^54 - 4 * q^58 - 4 * q^60 + 16 * q^61 + 24 * q^64 + 24 * q^66 - 16 * q^69 + 36 * q^70 - 36 * q^72 - 8 * q^73 - 32 * q^78 - 40 * q^81 + 72 * q^82 - 20 * q^84 + 16 * q^85 - 16 * q^88 - 56 * q^90 + 8 * q^93 - 56 * q^94 + 2 * q^96 + 40 * q^97

Introduction

L-functions

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