LMFDB - Embedded newform 228.2.c.a.191.20

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			191.20
Character	$\chi$	$=$	228.191
Dual form			228.2.c.a.191.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.221733 + 1.39672i) q^{2} +(0.958759 - 1.44249i) q^{3} +(-1.90167 + 0.619399i) q^{4} -3.67393i q^{5} +(2.22735 + 1.01927i) q^{6} +1.73008i q^{7} +(-1.28679 - 2.51876i) q^{8} +(-1.16156 - 2.76600i) q^{9} +(5.13146 - 0.814631i) q^{10} +5.81266 q^{11} +(-0.929763 + 3.33700i) q^{12} -0.320444 q^{13} +(-2.41645 + 0.383617i) q^{14} +(-5.29961 - 3.52241i) q^{15} +(3.23269 - 2.35579i) q^{16} -1.14820i q^{17} +(3.60578 - 2.23570i) q^{18} +1.00000i q^{19} +(2.27563 + 6.98659i) q^{20} +(2.49563 + 1.65873i) q^{21} +(1.28886 + 8.11867i) q^{22} -2.06567 q^{23} +(-4.86702 - 0.558699i) q^{24} -8.49773 q^{25} +(-0.0710531 - 0.447572i) q^{26} +(-5.10359 - 0.976385i) q^{27} +(-1.07161 - 3.29005i) q^{28} +7.38989i q^{29} +(3.74473 - 8.18312i) q^{30} +6.00906i q^{31} +(4.00717 + 3.99281i) q^{32} +(5.57294 - 8.38471i) q^{33} +(1.60372 - 0.254595i) q^{34} +6.35620 q^{35} +(3.92217 + 4.54055i) q^{36} -5.56327 q^{37} +(-1.39672 + 0.221733i) q^{38} +(-0.307229 + 0.462238i) q^{39} +(-9.25375 + 4.72758i) q^{40} -4.66894i q^{41} +(-1.76343 + 3.85350i) q^{42} +11.9295i q^{43} +(-11.0538 + 3.60036i) q^{44} +(-10.1621 + 4.26750i) q^{45} +(-0.458027 - 2.88517i) q^{46} +2.44325 q^{47} +(-0.298831 - 6.92176i) q^{48} +4.00681 q^{49} +(-1.88423 - 11.8690i) q^{50} +(-1.65627 - 1.10085i) q^{51} +(0.609379 - 0.198483i) q^{52} -3.33090i q^{53} +(0.232103 - 7.34480i) q^{54} -21.3553i q^{55} +(4.35767 - 2.22626i) q^{56} +(1.44249 + 0.958759i) q^{57} +(-10.3216 + 1.63858i) q^{58} +3.98210 q^{59} +(12.2599 + 3.41588i) q^{60} +8.88865 q^{61} +(-8.39299 + 1.33241i) q^{62} +(4.78542 - 2.00960i) q^{63} +(-4.68833 + 6.48225i) q^{64} +1.17729i q^{65} +(12.9468 + 5.92468i) q^{66} -6.97256i q^{67} +(0.711197 + 2.18350i) q^{68} +(-1.98048 + 2.97971i) q^{69} +(1.40938 + 8.87786i) q^{70} -13.3687 q^{71} +(-5.47221 + 6.48497i) q^{72} +3.33790 q^{73} +(-1.23356 - 7.77034i) q^{74} +(-8.14728 + 12.2579i) q^{75} +(-0.619399 - 1.90167i) q^{76} +10.0564i q^{77} +(-0.713741 - 0.326620i) q^{78} -4.89883i q^{79} +(-8.65498 - 11.8767i) q^{80} +(-6.30154 + 6.42577i) q^{81} +(6.52121 - 1.03526i) q^{82} +1.65281 q^{83} +(-5.77329 - 1.60857i) q^{84} -4.21842 q^{85} +(-16.6621 + 2.64516i) q^{86} +(10.6599 + 7.08513i) q^{87} +(-7.47968 - 14.6407i) q^{88} +8.78961i q^{89} +(-8.21378 - 13.2474i) q^{90} -0.554395i q^{91} +(3.92822 - 1.27947i) q^{92} +(8.66802 + 5.76124i) q^{93} +(0.541749 + 3.41254i) q^{94} +3.67393 q^{95} +(9.60151 - 1.95217i) q^{96} +3.03627 q^{97} +(0.888442 + 5.59640i) q^{98} +(-6.75177 - 16.0778i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 6 q^{6} + 8 q^{10} + 4 q^{12} - 8 q^{16} + 16 q^{18} + 8 q^{21} - 12 q^{22} - 2 q^{24} - 28 q^{25} + 12 q^{28} - 12 q^{30} - 28 q^{34} - 22 q^{36} - 16 q^{37} - 12 q^{40} + 10 q^{42} + 16 q^{45}+ \cdots + 40 q^{97}+O(q^{100}) $ 36 * q - 6 * q^6 + 8 * q^10 + 4 * q^12 - 8 * q^16 + 16 * q^18 + 8 * q^21 - 12 * q^22 - 2 * q^24 - 28 * q^25 + 12 * q^28 - 12 * q^30 - 28 * q^34 - 22 * q^36 - 16 * q^37 - 12 * q^40 + 10 * q^42 + 16 * q^45 - 4 * q^46 + 32 * q^48 - 44 * q^49 - 36 * q^52 - 20 * q^54 - 4 * q^58 - 4 * q^60 + 16 * q^61 + 24 * q^64 + 24 * q^66 - 16 * q^69 + 36 * q^70 - 36 * q^72 - 8 * q^73 - 32 * q^78 - 40 * q^81 + 72 * q^82 - 20 * q^84 + 16 * q^85 - 16 * q^88 - 56 * q^90 + 8 * q^93 - 56 * q^94 + 2 * q^96 + 40 * q^97

Character values

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

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

Coefficient data

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

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

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

$2$	0.221733	+	1.39672i	0.156789	+	0.987632i
$2$	0.221733	+	1.39672i	0.156789	+	0.987632i
$3$	0.958759	−	1.44249i	0.553540	−	0.832823i
$3$	0.958759	−	1.44249i	0.553540	−	0.832823i
$4$	−1.90167	+	0.619399i	−0.950834	+	0.309700i
$5$		−	3.67393i		−	1.64303i	−0.570187	−	0.821515i	$-0.693129\pi$
$5$		−	3.67393i		−	1.64303i	0.570187	−	0.821515i	$-0.306871\pi$
$6$	2.22735	+	1.01927i	0.909311	+	0.416116i
$7$			1.73008i			0.653911i	0.945040	+	0.326955i	$0.106023\pi$
$7$			1.73008i			0.653911i	−0.945040	+	0.326955i	$0.893977\pi$
$8$	−1.28679	−	2.51876i	−0.454950	−	0.890517i
$9$	−1.16156	−	2.76600i	−0.387188	−	0.922001i
$10$	5.13146	−	0.814631i	1.62271	−	0.257609i
$11$	5.81266			1.75258			0.876291	−	0.481782i	$-0.160010\pi$
$11$	5.81266			1.75258			0.876291	+	0.481782i	$0.160010\pi$
$12$	−0.929763	+	3.33700i	−0.268400	+	0.963308i
$13$	−0.320444			−0.0888752			−0.0444376	−	0.999012i	$-0.514150\pi$
$13$	−0.320444			−0.0888752			−0.0444376	+	0.999012i	$0.514150\pi$
$14$	−2.41645	+	0.383617i	−0.645823	+	0.102526i
$15$	−5.29961	−	3.52241i	−1.36835	−	0.909482i
$16$	3.23269	−	2.35579i	0.808172	−	0.588946i
$17$		−	1.14820i		−	0.278480i	−0.990259	−	0.139240i	$-0.955534\pi$
$17$		−	1.14820i		−	0.278480i	0.990259	−	0.139240i	$-0.0444660\pi$
$18$	3.60578	−	2.23570i	0.849891	−	0.526959i
$19$			1.00000i			0.229416i
$19$			1.00000i			0.229416i
$20$	2.27563	+	6.98659i	0.508846	+	1.56225i
$21$	2.49563	+	1.65873i	0.544592	+	0.361965i
$22$	1.28886	+	8.11867i	0.274786	+	1.73091i
$23$	−2.06567			−0.430722			−0.215361	−	0.976535i	$-0.569093\pi$
$23$	−2.06567			−0.430722			−0.215361	+	0.976535i	$0.569093\pi$
$24$	−4.86702	−	0.558699i	−0.993476	−	0.114044i
$25$	−8.49773			−1.69955
$26$	−0.0710531	−	0.447572i	−0.0139347	−	0.0877760i
$27$	−5.10359	−	0.976385i	−0.982187	−	0.187905i
$28$	−1.07161	−	3.29005i	−0.202516	−	0.621761i
$29$			7.38989i			1.37227i	0.727475	+	0.686135i	$0.240694\pi$
$29$			7.38989i			1.37227i	−0.727475	+	0.686135i	$0.759306\pi$
$30$	3.74473	−	8.18312i	0.683691	−	1.49403i
$31$			6.00906i			1.07926i	0.841902	+	0.539630i	$0.181436\pi$
$31$			6.00906i			1.07926i	−0.841902	+	0.539630i	$0.818564\pi$
$32$	4.00717	+	3.99281i	0.708375	+	0.705836i
$33$	5.57294	−	8.38471i	0.970124	−	1.45959i
$34$	1.60372	−	0.254595i	0.275036	−	0.0436627i
$35$	6.35620			1.07439
$36$	3.92217	+	4.54055i	0.653695	+	0.756758i
$37$	−5.56327			−0.914595			−0.457298	−	0.889314i	$-0.651183\pi$
$37$	−5.56327			−0.914595			−0.457298	+	0.889314i	$0.651183\pi$
$38$	−1.39672	+	0.221733i	−0.226578	+	0.0359699i
$39$	−0.307229	+	0.462238i	−0.0491959	+	0.0740173i
$40$	−9.25375	+	4.72758i	−1.46315	+	0.747496i
$41$		−	4.66894i		−	0.729165i	−0.931171	−	0.364583i	$-0.881212\pi$
$41$		−	4.66894i		−	0.729165i	0.931171	−	0.364583i	$-0.118788\pi$
$42$	−1.76343	+	3.85350i	−0.272103	+	0.594608i
$43$			11.9295i			1.81923i	0.415457	+	0.909613i	$0.363622\pi$
$43$			11.9295i			1.81923i	−0.415457	+	0.909613i	$0.636378\pi$
$44$	−11.0538	+	3.60036i	−1.66642	+	0.542774i
$45$	−10.1621	+	4.26750i	−1.51487	+	0.636161i
$46$	−0.458027	−	2.88517i	−0.0675324	−	0.425394i
$47$	2.44325			0.356385			0.178192	−	0.983996i	$-0.442975\pi$
$47$	2.44325			0.356385			0.178192	+	0.983996i	$0.442975\pi$
$48$	−0.298831	−	6.92176i	−0.0431326	−	0.999069i
$49$	4.00681			0.572401
$50$	−1.88423	−	11.8690i	−0.266470	−	1.67853i
$51$	−1.65627	−	1.10085i	−0.231925	−	0.154150i
$52$	0.609379	−	0.198483i	0.0845056	−	0.0275246i
$53$		−	3.33090i		−	0.457535i	−0.973481	−	0.228767i	$-0.926530\pi$
$53$		−	3.33090i		−	0.457535i	0.973481	−	0.228767i	$-0.0734695\pi$
$54$	0.232103	−	7.34480i	0.0315852	−	0.999501i
$55$		−	21.3553i		−	2.87955i
$56$	4.35767	−	2.22626i	0.582319	−	0.297496i
$57$	1.44249	+	0.958759i	0.191063	+	0.126991i
$58$	−10.3216	+	1.63858i	−1.35530	+	0.215157i
$59$	3.98210			0.518425			0.259212	−	0.965820i	$-0.416537\pi$
$59$	3.98210			0.518425			0.259212	+	0.965820i	$0.416537\pi$
$60$	12.2599	+	3.41588i	1.58274	+	0.440988i
$61$	8.88865			1.13807			0.569037	−	0.822312i	$-0.307316\pi$
$61$	8.88865			1.13807			0.569037	+	0.822312i	$0.307316\pi$
$62$	−8.39299	+	1.33241i	−1.06591	+	0.169216i
$63$	4.78542	−	2.00960i	0.602906	−	0.253186i
$64$	−4.68833	+	6.48225i	−0.586041	+	0.810281i
$65$			1.17729i			0.146025i
$66$	12.9468	+	5.92468i	1.59364	+	0.729278i
$67$		−	6.97256i		−	0.851834i	−0.904762	−	0.425917i	$-0.859952\pi$
$67$		−	6.97256i		−	0.851834i	0.904762	−	0.425917i	$-0.140048\pi$
$68$	0.711197	+	2.18350i	0.0862453	+	0.264789i
$69$	−1.98048	+	2.97971i	−0.238421	+	0.358715i
$70$	1.40938	+	8.87786i	0.168453	+	1.06111i
$71$	−13.3687			−1.58657			−0.793286	−	0.608849i	$-0.791631\pi$
$71$	−13.3687			−1.58657			−0.793286	+	0.608849i	$0.791631\pi$
$72$	−5.47221	+	6.48497i	−0.644907	+	0.764261i
$73$	3.33790			0.390671			0.195336	−	0.980736i	$-0.437420\pi$
$73$	3.33790			0.390671			0.195336	+	0.980736i	$0.437420\pi$
$74$	−1.23356	−	7.77034i	−0.143398	−	0.903284i
$75$	−8.14728	+	12.2579i	−0.940767	+	1.41542i
$76$	−0.619399	−	1.90167i	−0.0710500	−	0.218136i
$77$			10.0564i			1.14603i
$78$	−0.713741	−	0.326620i	−0.0808152	−	0.0369824i
$79$		−	4.89883i		−	0.551161i	−0.961278	−	0.275580i	$-0.911130\pi$
$79$		−	4.89883i		−	0.551161i	0.961278	−	0.275580i	$-0.0888700\pi$
$80$	−8.65498	−	11.8767i	−0.967656	−	1.32785i
$81$	−6.30154	+	6.42577i	−0.700171	+	0.713975i
$82$	6.52121	−	1.03526i	0.720147	−	0.114325i
$83$	1.65281			0.181420			0.0907099	−	0.995877i	$-0.471086\pi$
$83$	1.65281			0.181420			0.0907099	+	0.995877i	$0.471086\pi$
$84$	−5.77329	−	1.60857i	−0.629917	−	0.175509i
$85$	−4.21842			−0.457552
$86$	−16.6621	+	2.64516i	−1.79673	+	0.285235i
$87$	10.6599	+	7.08513i	1.14286	+	0.759605i
$88$	−7.47968	−	14.6407i	−0.797337	−	1.56070i
$89$			8.78961i			0.931697i	0.884864	+	0.465849i	$0.154251\pi$
$89$			8.78961i			0.931697i	−0.884864	+	0.465849i	$0.845749\pi$
$90$	−8.21378	−	13.2474i	−0.865809	−	1.39640i
$91$		−	0.554395i		−	0.0581164i
$92$	3.92822	−	1.27947i	0.409545	−	0.133394i
$93$	8.66802	+	5.76124i	0.898832	+	0.597413i
$94$	0.541749	+	3.41254i	0.0558772	+	0.351977i
$95$	3.67393			0.376937
$96$	9.60151	−	1.95217i	0.979950	−	0.199242i
$97$	3.03627			0.308286			0.154143	−	0.988049i	$-0.450738\pi$
$97$	3.03627			0.308286			0.154143	+	0.988049i	$0.450738\pi$
$98$	0.888442	+	5.59640i	0.0897462	+	0.565322i
$99$	−6.75177	−	16.0778i	−0.678578	−	1.61588i
$100$	16.1599	−	5.26349i	1.61599	−	0.526349i
$101$			0.974881i			0.0970043i	0.998823	+	0.0485022i	$0.0154448\pi$
$101$			0.974881i			0.0970043i	−0.998823	+	0.0485022i	$0.984555\pi$
$102$	1.17033	−	2.55745i	0.115880	−	0.253225i
$103$			9.24897i			0.911328i	0.890152	+	0.455664i	$0.150598\pi$
$103$			9.24897i			0.911328i	−0.890152	+	0.455664i	$0.849402\pi$
$104$	0.412345	+	0.807123i	0.0404338	+	0.0791449i
$105$	6.09407	−	9.16877i	0.594720	−	0.894780i
$106$	4.65235	−	0.738572i	0.451876	−	0.0717365i
$107$	10.2320			0.989161			0.494581	−	0.869132i	$-0.335322\pi$
$107$	10.2320			0.989161			0.494581	+	0.869132i	$0.335322\pi$
$108$	10.3101	−	1.30440i	0.992092	−	0.125516i
$109$	−3.53378			−0.338475			−0.169237	−	0.985575i	$-0.554130\pi$
$109$	−3.53378			−0.338475			−0.169237	+	0.985575i	$0.554130\pi$
$110$	29.8274	−	4.73517i	2.84393	−	0.451481i
$111$	−5.33383	+	8.02496i	−0.506265	+	0.761696i
$112$	4.07571	+	5.59283i	0.385118	+	0.528472i
$113$		−	7.14806i		−	0.672433i	−0.941785	−	0.336216i	$-0.890853\pi$
$113$		−	7.14806i		−	0.672433i	0.941785	−	0.336216i	$-0.109147\pi$
$114$	−1.01927	+	2.22735i	−0.0954636	+	0.208610i
$115$			7.58911i			0.707688i
$116$	−4.57730	−	14.0531i	−0.424991	−	1.30480i
$117$	0.372216	+	0.886349i	0.0344114	+	0.0819430i
$118$	0.882962	+	5.56188i	0.0812833	+	0.512013i
$119$	1.98649			0.182101
$120$	−2.05262	+	17.8811i	−0.187378	+	1.63231i
$121$	22.7870			2.07155
$122$	1.97091	+	12.4150i	0.178438	+	1.12400i
$123$	−6.73490	−	4.47638i	−0.607265	−	0.403622i
$124$	−3.72201	−	11.4272i	−0.334246	−	1.02620i
$125$			12.8504i			1.14938i
$126$	3.86794	+	6.23831i	0.344584	+	0.555753i
$127$		−	0.834796i		−	0.0740762i	−0.999314	−	0.0370381i	$-0.988208\pi$
$127$		−	0.834796i		−	0.0740762i	0.999314	−	0.0370381i	$-0.0117923\pi$
$128$	−10.0935	−	5.11097i	−0.892145	−	0.451750i
$129$	17.2081	+	11.4375i	1.51509	+	1.00701i
$130$	−1.64434	+	0.261044i	−0.144219	+	0.0228951i
$131$	−3.82897			−0.334539			−0.167269	−	0.985911i	$-0.553495\pi$
$131$	−3.82897			−0.334539			−0.167269	+	0.985911i	$0.553495\pi$
$132$	−5.40440	+	19.3968i	−0.470392	+	1.68828i
$133$	−1.73008			−0.150017
$134$	9.73874	−	1.54605i	0.841299	−	0.133558i
$135$	−3.58717	+	18.7502i	−0.308734	+	1.61376i
$136$	−2.89205	+	1.47750i	−0.247992	+	0.126695i
$137$		−	9.03709i		−	0.772091i	−0.922480	−	0.386045i	$-0.873841\pi$
$137$		−	9.03709i		−	0.772091i	0.922480	−	0.386045i	$-0.126159\pi$
$138$	−4.60096	−	2.10548i	−0.391660	−	0.179230i
$139$		−	1.87019i		−	0.158627i	−0.996850	−	0.0793136i	$-0.974727\pi$
$139$		−	1.87019i		−	0.158627i	0.996850	−	0.0793136i	$-0.0252729\pi$
$140$	−12.0874	+	3.93703i	−1.02157	+	0.332740i
$141$	2.34249	−	3.52437i	0.197273	−	0.296805i
$142$	−2.96428	−	18.6724i	−0.248757	−	1.56695i
$143$	−1.86263			−0.155761
$144$	−10.2711	−	6.20523i	−0.855923	−	0.517103i
$145$	27.1499			2.25468
$146$	0.740123	+	4.66212i	0.0612530	+	0.385840i
$147$	3.84156	−	5.77978i	0.316847	−	0.476709i
$148$	10.5795	−	3.44588i	0.869629	−	0.283250i
$149$		−	14.4252i		−	1.18176i	−0.806760	−	0.590880i	$-0.798781\pi$
$149$		−	14.4252i		−	1.18176i	0.806760	−	0.590880i	$-0.201219\pi$
$150$	−18.9274	−	8.66150i	−1.54542	−	0.707209i
$151$			16.4454i			1.33831i	0.743124	+	0.669153i	$0.233343\pi$
$151$			16.4454i			1.33831i	−0.743124	+	0.669153i	$0.766657\pi$
$152$	2.51876	−	1.28679i	0.204299	−	0.104373i
$153$	−3.17594	+	1.33371i	−0.256759	+	0.107824i
$154$	−14.0460	+	2.22984i	−1.13186	+	0.179685i
$155$	22.0769			1.77326
$156$	0.297937	−	1.06932i	0.0238541	−	0.0856142i
$157$	−22.3196			−1.78130			−0.890650	−	0.454689i	$-0.849751\pi$
$157$	−22.3196			−1.78130			−0.890650	+	0.454689i	$0.849751\pi$
$158$	6.84230	−	1.08623i	0.544344	−	0.0864160i
$159$	−4.80480	−	3.19353i	−0.381046	−	0.253264i
$160$	14.6693	−	14.7221i	1.15971	−	1.16388i
$161$		−	3.57378i		−	0.281653i
$162$	−10.3723	−	7.37670i	−0.814924	−	0.579568i
$163$			4.70763i			0.368730i	0.982858	+	0.184365i	$0.0590229\pi$
$163$			4.70763i			0.368730i	−0.982858	+	0.184365i	$0.940977\pi$
$164$	2.89194	+	8.87877i	0.225822	+	0.693315i
$165$	−30.8048	−	20.4746i	−2.39815	−	1.59394i
$166$	0.366483	+	2.30852i	0.0284446	+	0.179176i
$167$	−9.20995			−0.712688			−0.356344	−	0.934355i	$-0.615977\pi$
$167$	−9.20995			−0.712688			−0.356344	+	0.934355i	$0.615977\pi$
$168$	0.966597	−	8.42035i	0.0745746	−	0.649644i
$169$	−12.8973			−0.992101
$170$	−0.935363	−	5.89196i	−0.0717391	−	0.451893i
$171$	2.76600	−	1.16156i	0.211522	−	0.0888269i
$172$	−7.38910	−	22.6859i	−0.563414	−	1.72978i
$173$			8.98041i			0.682768i	0.939924	+	0.341384i	$0.110896\pi$
$173$			8.98041i			0.682768i	−0.939924	+	0.341384i	$0.889104\pi$
$174$	−7.53231	+	16.4599i	−0.571023	+	1.24782i
$175$		−	14.7018i		−	1.11135i
$176$	18.7905	−	13.6934i	1.41639	−	1.03218i
$177$	3.81787	−	5.74414i	0.286969	−	0.431756i
$178$	−12.2767	+	1.94895i	−0.920174	+	0.146080i
$179$	−12.4735			−0.932312			−0.466156	−	0.884702i	$-0.654361\pi$
$179$	−12.4735			−0.932312			−0.466156	+	0.884702i	$0.654361\pi$
$180$	16.6816	−	14.4098i	1.24338	−	1.07404i
$181$	2.83275			0.210557			0.105278	−	0.994443i	$-0.466427\pi$
$181$	2.83275			0.210557			0.105278	+	0.994443i	$0.466427\pi$
$182$	0.774337	−	0.122928i	0.0573977	−	0.00911202i
$183$	8.52207	−	12.8218i	0.629969	−	0.947815i
$184$	2.65809	+	5.20293i	0.195957	+	0.383565i
$185$			20.4390i			1.50271i
$186$	−6.12487	+	13.3843i	−0.449097	+	0.981383i
$187$		−	6.67412i		−	0.488060i
$188$	−4.64625	+	1.51335i	−0.338863	+	0.110372i
$189$	1.68923	−	8.82965i	0.122873	−	0.642263i
$190$	0.814631	+	5.13146i	0.0590996	+	0.372275i
$191$	−19.3693			−1.40151			−0.700755	−	0.713402i	$-0.747153\pi$
$191$	−19.3693			−1.40151			−0.700755	+	0.713402i	$0.747153\pi$
$192$	4.85561	+	12.9778i	0.350423	+	0.936591i
$193$	−21.9760			−1.58187			−0.790933	−	0.611902i	$-0.790405\pi$
$193$	−21.9760			−1.58187			−0.790933	+	0.611902i	$0.790405\pi$
$194$	0.673241	+	4.24083i	0.0483359	+	0.304474i
$195$	1.69823	+	1.12874i	0.121613	+	0.0808304i
$196$	−7.61962	+	2.48181i	−0.544258	+	0.177272i
$197$		−	9.14745i		−	0.651729i	−0.945417	−	0.325864i	$-0.894345\pi$
$197$		−	9.14745i		−	0.651729i	0.945417	−	0.325864i	$-0.105655\pi$
$198$	20.9592	−	12.9953i	1.48950	−	0.923538i
$199$		−	17.4353i		−	1.23596i	−0.786195	−	0.617978i	$-0.787952\pi$
$199$		−	17.4353i		−	1.23596i	0.786195	−	0.617978i	$-0.212048\pi$
$200$	10.9348	+	21.4038i	0.773208	+	1.51348i
$201$	−10.0579	−	6.68501i	−0.709427	−	0.471524i
$202$	−1.36164	+	0.216163i	−0.0958046	+	0.0152092i
$203$	−12.7851			−0.897341
$204$	3.83155	+	1.06756i	0.268262	+	0.0747440i
$205$	−17.1533			−1.19804
$206$	−12.9182	+	2.05080i	−0.900057	+	0.142886i
$207$	2.39940	+	5.71364i	0.166770	+	0.397126i
$208$	−1.03590	+	0.754897i	−0.0718265	+	0.0523427i
$209$			5.81266i			0.402070i
$210$	14.1575	+	6.47870i	0.976959	+	0.447073i
$211$			4.41057i			0.303636i	0.988408	+	0.151818i	$0.0485128\pi$
$211$			4.41057i			0.303636i	−0.988408	+	0.151818i	$0.951487\pi$
$212$	2.06316	+	6.33428i	0.141698	+	0.435040i
$213$	−12.8174	+	19.2842i	−0.878231	+	1.32133i
$214$	2.26877	+	14.2912i	0.155090	+	0.976927i
$215$	43.8280			2.98904
$216$	4.10798	+	14.1111i	0.279513	+	0.960142i
$217$	−10.3962			−0.705739
$218$	−0.783556	−	4.93571i	−0.0530691	−	0.334289i
$219$	3.20024	−	4.81489i	0.216252	−	0.325360i
$220$	13.2274	+	40.6107i	0.891794	+	2.73797i
$221$			0.367935i			0.0247500i
$222$	−12.3913	−	5.67048i	−0.831652	−	0.380578i
$223$		−	4.91633i		−	0.329222i	−0.986359	−	0.164611i	$-0.947363\pi$
$223$		−	4.91633i		−	0.329222i	0.986359	−	0.164611i	$-0.0526368\pi$
$224$	−6.90791	+	6.93275i	−0.461554	+	0.463214i
$225$	9.87065	+	23.5048i	0.658044	+	1.56698i
$226$	9.98386	−	1.58496i	0.664116	−	0.105430i
$227$	−24.0751			−1.59792			−0.798961	−	0.601383i	$-0.794617\pi$
$227$	−24.0751			−1.59792			−0.798961	+	0.601383i	$0.794617\pi$
$228$	−3.33700	−	0.929763i	−0.220998	−	0.0615751i
$229$	17.8367			1.17868			0.589341	−	0.807884i	$-0.299387\pi$
$229$	17.8367			1.17868			0.589341	+	0.807884i	$0.299387\pi$
$230$	−10.5999	+	1.68276i	−0.698936	+	0.110958i
$231$	14.5063	+	9.64166i	0.954442	+	0.634374i
$232$	18.6134	−	9.50926i	1.22203	−	0.624313i
$233$		−	22.3249i		−	1.46255i	−0.682080	−	0.731277i	$-0.738925\pi$
$233$		−	22.3249i		−	1.46255i	0.682080	−	0.731277i	$-0.261075\pi$
$234$	−1.15545	+	0.716416i	−0.0755342	+	0.0468336i
$235$		−	8.97632i		−	0.585550i
$236$	−7.57263	+	2.46651i	−0.492936	+	0.160556i
$237$	−7.06651	−	4.69679i	−0.459019	−	0.305089i
$238$	0.440471	+	2.77458i	0.0285515	+	0.179849i
$239$	2.61489			0.169143			0.0845715	−	0.996417i	$-0.473048\pi$
$239$	2.61489			0.169143			0.0845715	+	0.996417i	$0.473048\pi$
$240$	−25.4300	+	1.09788i	−1.64150	+	0.0708681i
$241$	24.5271			1.57993			0.789963	−	0.613154i	$-0.210099\pi$
$241$	24.5271			1.57993			0.789963	+	0.613154i	$0.210099\pi$
$242$	5.05263	+	31.8271i	0.324796	+	2.04593i
$243$	3.22746	+	15.2507i	0.207042	+	0.978332i
$244$	−16.9033	+	5.50562i	−1.08212	+	0.352461i
$245$		−	14.7207i		−	0.940472i
$246$	4.75892	−	10.3994i	0.303417	−	0.663038i
$247$		−	0.320444i		−	0.0203894i
$248$	15.1354	−	7.73241i	0.961099	−	0.491009i
$249$	1.58465	−	2.38417i	0.100423	−	0.151091i
$250$	−17.9485	+	2.84936i	−1.13516	+	0.180210i
$251$	24.8409			1.56794			0.783971	−	0.620798i	$-0.213191\pi$
$251$	24.8409			1.56794			0.783971	+	0.620798i	$0.213191\pi$
$252$	−7.85554	+	6.78568i	−0.494852	+	0.427458i
$253$	−12.0070			−0.754875
$254$	1.16598	−	0.185102i	0.0731600	−	0.0116143i
$255$	−4.04445	+	6.08503i	−0.253273	+	0.381059i
$256$	4.90055	−	15.2310i	0.306284	−	0.951940i
$257$		−	9.42139i		−	0.587690i	−0.955853	−	0.293845i	$-0.905065\pi$
$257$		−	9.42139i		−	0.587690i	0.955853	−	0.293845i	$-0.0949350\pi$
$258$	−12.1594	+	26.5711i	−0.757009	+	1.65424i
$259$		−	9.62492i		−	0.598064i
$260$	−0.729212	−	2.23881i	−0.0452238	−	0.138845i
$261$	20.4405	−	8.58383i	1.26523	−	0.531326i
$262$	−0.849010	−	5.34801i	−0.0524520	−	0.330401i
$263$	−23.7957			−1.46731			−0.733654	−	0.679524i	$-0.762187\pi$
$263$	−23.7957			−1.46731			−0.733654	+	0.679524i	$0.762187\pi$
$264$	−28.2903	−	3.24753i	−1.74115	−	0.199872i
$265$	−12.2375			−0.751744
$266$	−0.383617	−	2.41645i	−0.0235211	−	0.148162i
$267$	12.6789	+	8.42712i	0.775939	+	0.515731i
$268$	4.31880	+	13.2595i	0.263813	+	0.809953i
$269$			23.0117i			1.40305i	0.712645	+	0.701525i	$0.247497\pi$
$269$			23.0117i			1.40305i	−0.712645	+	0.701525i	$0.752503\pi$
$270$	−26.9843	−	0.852729i	−1.64221	−	0.0518955i
$271$		−	15.9375i		−	0.968137i	−0.875030	−	0.484068i	$-0.839159\pi$
$271$		−	15.9375i		−	0.968137i	0.875030	−	0.484068i	$-0.160841\pi$
$272$	−2.70492	−	3.71179i	−0.164010	−	0.225060i
$273$	−0.799711	−	0.531532i	−0.0484007	−	0.0321698i
$274$	12.6223	−	2.00382i	0.762542	−	0.121055i
$275$	−49.3944			−2.97860
$276$	1.92058	−	6.89313i	0.115605	−	0.414917i
$277$	−1.00257			−0.0602388			−0.0301194	−	0.999546i	$-0.509589\pi$
$277$	−1.00257			−0.0602388			−0.0301194	+	0.999546i	$0.509589\pi$
$278$	2.61213	−	0.414683i	0.156665	−	0.0248710i
$279$	16.6211	−	6.97990i	0.995078	−	0.417876i
$280$	−8.17911	−	16.0098i	−0.488796	−	0.956767i
$281$		−	11.4958i		−	0.685779i	−0.939376	−	0.342890i	$-0.888594\pi$
$281$		−	11.4958i		−	0.685779i	0.939376	−	0.342890i	$-0.111406\pi$
$282$	5.44197	+	2.49034i	0.324065	+	0.148297i
$283$		−	0.305221i		−	0.0181435i	−0.999959	−	0.00907174i	$-0.997112\pi$
$283$		−	0.305221i		−	0.0181435i	0.999959	−	0.00907174i	$-0.00288767\pi$
$284$	25.4228	−	8.28056i	1.50857	−	0.491361i
$285$	3.52241	−	5.29961i	0.208650	−	0.313922i
$286$	−0.413007	−	2.60158i	−0.0244216	−	0.153835i
$287$	8.07766			0.476809
$288$	6.38955	−	15.7218i	0.376508	−	0.926413i
$289$	15.6816			0.922449
$290$	6.02004	+	37.9209i	0.353509	+	2.22679i
$291$	2.91105	−	4.37979i	0.170649	−	0.256748i
$292$	−6.34758	+	2.06749i	−0.371464	+	0.120991i
$293$		−	12.9953i		−	0.759193i	−0.925152	−	0.379597i	$-0.876063\pi$
$293$		−	12.9953i		−	0.759193i	0.925152	−	0.379597i	$-0.123937\pi$
$294$	8.92456	+	4.08403i	0.520491	+	0.238185i
$295$		−	14.6299i		−	0.851787i
$296$	7.15877	+	14.0125i	0.416095	+	0.814463i
$297$	−29.6655	−	5.67539i	−1.72136	−	0.329320i
$298$	20.1480	−	3.19855i	1.16714	−	0.185287i
$299$	0.661931			0.0382805
$300$	7.90088	−	28.3569i	0.456158	−	1.63719i
$301$	−20.6390			−1.18961
$302$	−22.9696	+	3.64649i	−1.32175	+	0.209832i
$303$	1.40626	+	0.934676i	0.0807874	+	0.0536957i
$304$	2.35579	+	3.23269i	0.135114	+	0.185407i
$305$		−	32.6562i		−	1.86989i
$306$	−2.56704	−	4.14017i	−0.146748	−	0.236678i
$307$			22.9049i			1.30725i	0.756818	+	0.653626i	$0.226753\pi$
$307$			22.9049i			1.30725i	−0.756818	+	0.653626i	$0.773247\pi$
$308$	−6.22892	−	19.1239i	−0.354926	−	1.08969i
$309$	13.3416	+	8.86753i	0.758975	+	0.504456i
$310$	4.89517	+	30.8352i	0.278027	+	1.75132i
$311$	8.47275			0.480446			0.240223	−	0.970718i	$-0.422779\pi$
$311$	8.47275			0.480446			0.240223	+	0.970718i	$0.422779\pi$
$312$	1.55961	+	0.179032i	0.0882954	+	0.0101357i
$313$	19.5449			1.10474			0.552371	−	0.833598i	$-0.313723\pi$
$313$	19.5449			1.10474			0.552371	+	0.833598i	$0.313723\pi$
$314$	−4.94900	−	31.1743i	−0.279288	−	1.75927i
$315$	−7.38313	−	17.5813i	−0.415992	−	0.990593i
$316$	3.03433	+	9.31594i	0.170694	+	0.524063i
$317$			1.43545i			0.0806231i	0.999187	+	0.0403116i	$0.0128350\pi$
$317$			1.43545i			0.0806231i	−0.999187	+	0.0403116i	$0.987165\pi$
$318$	3.39510	−	7.41909i	0.190388	−	0.416042i
$319$			42.9549i			2.40501i
$320$	23.8153	+	17.2246i	1.33132	+	0.962883i
$321$	9.80999	−	14.7595i	0.547540	−	0.823796i
$322$	4.99158	−	0.792426i	0.278170	−	0.0441602i
$323$	1.14820			0.0638878
$324$	8.00333	−	16.1229i	0.444629	−	0.895715i
$325$	2.72305			0.151048
$326$	−6.57526	+	1.04384i	−0.364170	+	0.0578128i
$327$	−3.38804	+	5.09745i	−0.187359	+	0.281890i
$328$	−11.7599	+	6.00795i	−0.649334	+	0.331734i
$329$			4.22703i			0.233044i
$330$	21.7668	−	47.5657i	1.19823	−	2.61840i
$331$			0.779123i			0.0428245i	0.999771	+	0.0214122i	$0.00681624\pi$
$331$			0.779123i			0.0428245i	−0.999771	+	0.0214122i	$0.993184\pi$
$332$	−3.14310	+	1.02375i	−0.172500	+	0.0561856i
$333$	6.46208	+	15.3880i	0.354120	+	0.843258i
$334$	−2.04215	−	12.8638i	−0.111742	−	0.703873i
$335$	−25.6167			−1.39959
$336$	11.9752	−	0.517003i	0.653302	−	0.0282048i
$337$	−15.9391			−0.868260			−0.434130	−	0.900850i	$-0.642944\pi$
$337$	−15.9391			−0.868260			−0.434130	+	0.900850i	$0.642944\pi$
$338$	−2.85976	−	18.0140i	−0.155551	−	0.979831i
$339$	−10.3110	−	6.85327i	−0.560017	−	0.372218i
$340$	8.02203	−	2.61289i	0.435056	−	0.141704i
$341$			34.9286i			1.89149i
$342$	2.23570	+	3.60578i	0.120893	+	0.194978i
$343$			19.0427i			1.02821i
$344$	30.0475	−	15.3507i	1.62005	−	0.827656i
$345$	10.9472	+	7.27613i	0.589379	+	0.391734i
$346$	−12.5431	+	1.99125i	−0.674323	+	0.107050i
$347$	−16.6470			−0.893660			−0.446830	−	0.894619i	$-0.647447\pi$
$347$	−16.6470			−0.893660			−0.446830	+	0.894619i	$0.647447\pi$
$348$	−24.6600	−	6.87085i	−1.32192	−	0.368316i
$349$	−8.39076			−0.449147			−0.224574	−	0.974457i	$-0.572099\pi$
$349$	−8.39076			−0.449147			−0.224574	+	0.974457i	$0.572099\pi$
$350$	20.5343	−	3.25988i	1.09761	−	0.174248i
$351$	1.63542	+	0.312877i	0.0872921	+	0.0167001i
$352$	23.2923	+	23.2089i	1.24149	+	1.23704i
$353$		−	8.61810i		−	0.458695i	−0.973345	−	0.229348i	$-0.926341\pi$
$353$		−	8.61810i		−	0.458695i	0.973345	−	0.229348i	$-0.0736592\pi$
$354$	8.86952	+	4.05884i	0.471409	+	0.215725i
$355$			49.1156i			2.60679i
$356$	−5.44428	−	16.7149i	−0.288546	−	0.885890i
$357$	1.90457	−	2.86550i	0.100800	−	0.151658i
$358$	−2.76579	−	17.4220i	−0.146176	−	0.920781i
$359$	24.4848			1.29226			0.646128	−	0.763229i	$-0.276387\pi$
$359$	24.4848			1.29226			0.646128	+	0.763229i	$0.276387\pi$
$360$	23.8253	+	20.1045i	1.25570	+	1.05960i
$361$	−1.00000			−0.0526316
$362$	0.628116	+	3.95657i	0.0330130	+	0.207953i
$363$	21.8472	−	32.8701i	1.14668	−	1.72523i
$364$	0.343392	+	1.05428i	0.0179986	+	0.0552591i
$365$		−	12.2632i		−	0.641885i
$366$	19.7981	+	9.05995i	1.03486	+	0.473571i
$367$		−	33.6485i		−	1.75644i	−0.478261	−	0.878218i	$-0.658733\pi$
$367$		−	33.6485i		−	1.75644i	0.478261	−	0.878218i	$-0.341267\pi$
$368$	−6.67766	+	4.86627i	−0.348097	+	0.253672i
$369$	−12.9143	+	5.42326i	−0.672291	+	0.282324i
$370$	−28.5477	+	4.53201i	−1.48412	+	0.235608i
$371$	5.76275			0.299187
$372$	−20.0522	−	5.58701i	−1.03966	−	0.289673i
$373$	3.12634			0.161876			0.0809378	−	0.996719i	$-0.474208\pi$
$373$	3.12634			0.161876			0.0809378	+	0.996719i	$0.474208\pi$
$374$	9.32190	−	1.47987i	0.482024	−	0.0765224i
$375$	18.5366	+	12.3205i	0.957227	+	0.636225i
$376$	−3.14395	−	6.15397i	−0.162137	−	0.317367i
$377$		−	2.36805i		−	0.121961i
$378$	12.7071	+	0.401558i	0.653584	+	0.0206539i
$379$			26.1996i			1.34579i	0.739740	+	0.672893i	$0.234948\pi$
$379$			26.1996i			1.34579i	−0.739740	+	0.672893i	$0.765052\pi$
$380$	−6.98659	+	2.27563i	−0.358405	+	0.116737i
$381$	−1.20419	−	0.800368i	−0.0616923	−	0.0410041i
$382$	−4.29481	−	27.0535i	−0.219741	−	1.38418i
$383$	13.6398			0.696963			0.348481	−	0.937316i	$-0.386697\pi$
$383$	13.6398			0.696963			0.348481	+	0.937316i	$0.386697\pi$
$384$	−17.0497	+	9.65955i	−0.870065	+	0.492937i
$385$	36.9464			1.88297
$386$	−4.87281	−	30.6944i	−0.248019	−	1.56230i
$387$	32.9969	−	13.8568i	1.67733	−	0.704382i
$388$	−5.77398	+	1.88066i	−0.293129	+	0.0954762i
$389$			24.3790i			1.23606i	0.786153	+	0.618031i	$0.212070\pi$
$389$			24.3790i			1.23606i	−0.786153	+	0.618031i	$0.787930\pi$
$390$	−1.19998	+	2.62223i	−0.0607632	+	0.132782i
$391$			2.37181i			0.119948i
$392$	−5.15593	−	10.0922i	−0.260414	−	0.509733i
$393$	−3.67106	+	5.52326i	−0.185181	+	0.278612i
$394$	12.7764	−	2.02829i	0.643668	−	0.102184i
$395$	−17.9979			−0.905574
$396$	22.7982	+	26.3927i	1.14565	+	1.32628i
$397$	11.5743			0.580897			0.290449	−	0.956891i	$-0.406195\pi$
$397$	11.5743			0.580897			0.290449	+	0.956891i	$0.406195\pi$
$398$	24.3523	−	3.86599i	1.22067	−	0.193784i
$399$	−1.65873	+	2.49563i	−0.0830406	+	0.124938i
$400$	−27.4705	+	20.0188i	−1.37353	+	1.00094i
$401$		−	9.02182i		−	0.450528i	−0.974298	−	0.225264i	$-0.927675\pi$
$401$		−	9.02182i		−	0.450528i	0.974298	−	0.225264i	$-0.0723245\pi$
$402$	7.10694	−	15.5303i	0.354462	−	0.774583i
$403$		−	1.92557i		−	0.0959194i
$404$	−0.603841	−	1.85390i	−0.0300422	−	0.0922350i
$405$	23.6078	+	23.1514i	1.17308	+	1.15040i
$406$	−2.83489	−	17.8573i	−0.140693	−	0.886243i
$407$	−32.3374			−1.60290
$408$	−0.641501	+	5.58833i	−0.0317590	+	0.276664i
$409$	−9.52160			−0.470813			−0.235406	−	0.971897i	$-0.575642\pi$
$409$	−9.52160			−0.470813			−0.235406	+	0.971897i	$0.575642\pi$
$410$	−3.80346	−	23.9584i	−0.187840	−	1.18322i
$411$	−13.0359	−	8.66439i	−0.643015	−	0.427383i
$412$	−5.72881	−	17.5885i	−0.282238	−	0.866522i
$413$			6.88936i			0.339003i
$414$	−7.44835	+	4.61821i	−0.366066	+	0.226972i
$415$		−	6.07231i		−	0.298078i
$416$	−1.28407	−	1.27947i	−0.0629570	−	0.0627314i
$417$	−2.69773	−	1.79306i	−0.132108	−	0.0878065i
$418$	−8.11867	+	1.28886i	−0.397097	+	0.0630402i
$419$	−11.6215			−0.567747			−0.283874	−	0.958862i	$-0.591620\pi$
$419$	−11.6215			−0.567747			−0.283874	+	0.958862i	$0.591620\pi$
$420$	−5.90977	+	21.2106i	−0.288367	+	1.03497i
$421$	14.5668			0.709943			0.354972	−	0.934877i	$-0.384491\pi$
$421$	14.5668			0.709943			0.354972	+	0.934877i	$0.384491\pi$
$422$	−6.16034	+	0.977970i	−0.299881	+	0.0476068i
$423$	−2.83799	−	6.75803i	−0.137988	−	0.328587i
$424$	−8.38976	+	4.28618i	−0.407443	+	0.208155i
$425$			9.75713i			0.473291i
$426$	−29.7767	−	13.6263i	−1.44269	−	0.660198i
$427$			15.3781i			0.744199i
$428$	−19.4578	+	6.33767i	−0.940529	+	0.306343i
$429$	−1.78582	+	2.68683i	−0.0862200	+	0.129721i
$430$	9.71811	+	61.2155i	0.468649	+	2.95207i
$431$	17.3949			0.837885			0.418943	−	0.908013i	$-0.362401\pi$
$431$	17.3949			0.837885			0.418943	+	0.908013i	$0.362401\pi$
$432$	−18.7985	+	8.86662i	−0.904442	+	0.426596i
$433$	−35.1008			−1.68684			−0.843419	−	0.537256i	$-0.819461\pi$
$433$	−35.1008			−1.68684			−0.843419	+	0.537256i	$0.819461\pi$
$434$	−2.30518	−	14.5206i	−0.110652	−	0.697011i
$435$	26.0302	−	39.1635i	1.24805	−	1.87775i
$436$	6.72008	−	2.18882i	0.321833	−	0.104826i
$437$		−	2.06567i		−	0.0988143i
$438$	7.43467	+	3.40223i	0.355242	+	0.162565i
$439$		−	13.3382i		−	0.636598i	−0.947990	−	0.318299i	$-0.896888\pi$
$439$		−	13.3382i		−	0.636598i	0.947990	−	0.318299i	$-0.103112\pi$
$440$	−53.7889	+	27.4798i	−2.56428	+	1.31005i
$441$	−4.65416	−	11.0828i	−0.221627	−	0.527754i
$442$	−0.513904	+	0.0815834i	−0.0244439	+	0.00388053i
$443$	−20.0242			−0.951379			−0.475690	−	0.879613i	$-0.657801\pi$
$443$	−20.0242			−0.951379			−0.475690	+	0.879613i	$0.657801\pi$
$444$	5.17252	−	18.5646i	0.245477	−	0.881037i
$445$	32.2924			1.53081
$446$	6.86675	−	1.09011i	0.325150	−	0.0516183i
$447$	−20.8082	−	13.8303i	−0.984196	−	0.654151i
$448$	−11.2148	−	8.11121i	−0.529851	−	0.383219i
$449$			29.6569i			1.39960i	0.714341	+	0.699798i	$0.246727\pi$
$449$			29.6569i			1.39960i	−0.714341	+	0.699798i	$0.753273\pi$
$450$	−30.6410	+	18.9983i	−1.44443	+	0.895591i
$451$		−	27.1389i		−	1.27792i
$452$	4.42750	+	13.5932i	0.208252	+	0.639372i
$453$	23.7223	+	15.7672i	1.11457	+	0.740806i
$454$	−5.33825	−	33.6263i	−0.250537	−	1.57816i
$455$	−2.03681			−0.0954870
$456$	0.558699	−	4.86702i	0.0261635	−	0.227919i
$457$	−26.0395			−1.21808			−0.609039	−	0.793140i	$-0.708445\pi$
$457$	−26.0395			−1.21808			−0.609039	+	0.793140i	$0.708445\pi$
$458$	3.95499	+	24.9129i	0.184804	+	1.16410i
$459$	−1.12109	+	5.85997i	−0.0523280	+	0.273520i
$460$	−4.70069	−	14.4320i	−0.219171	−	0.672894i
$461$			8.06603i			0.375672i	0.982200	+	0.187836i	$0.0601474\pi$
$461$			8.06603i			0.375672i	−0.982200	+	0.187836i	$0.939853\pi$
$462$	−10.2502	+	22.3991i	−0.476883	+	1.04210i
$463$			19.0704i			0.886275i	0.896454	+	0.443137i	$0.146135\pi$
$463$			19.0704i			0.886275i	−0.896454	+	0.443137i	$0.853865\pi$
$464$	17.4090	+	23.8892i	0.808193	+	1.10903i
$465$	21.1664	−	31.8457i	0.981567	−	1.47681i
$466$	31.1817	−	4.95018i	1.44447	−	0.229312i
$467$	−8.42828			−0.390014			−0.195007	−	0.980802i	$-0.562473\pi$
$467$	−8.42828			−0.390014			−0.195007	+	0.980802i	$0.562473\pi$
$468$	−1.25684	−	1.45499i	−0.0580973	−	0.0672570i
$469$	12.0631			0.557023
$470$	12.5374	−	1.99035i	0.578308	−	0.0918079i
$471$	−21.3991	+	32.1959i	−0.986021	+	1.48351i
$472$	−5.12413	−	10.0300i	−0.235857	−	0.461666i
$473$			69.3419i			3.18834i
$474$	4.99324	−	10.9114i	0.229347	−	0.501177i
$475$		−	8.49773i		−	0.389903i
$476$	−3.77765	+	1.23043i	−0.173148	+	0.0563967i
$477$	−9.21329	+	3.86906i	−0.421848	+	0.177152i
$478$	0.579807	+	3.65227i	0.0265197	+	0.167051i
$479$	14.4989			0.662472			0.331236	−	0.943548i	$-0.392534\pi$
$479$	14.4989			0.662472			0.331236	+	0.943548i	$0.392534\pi$
$480$	−7.17212	−	35.2752i	−0.327361	−	1.61009i
$481$	1.78272			0.0812848
$482$	5.43846	+	34.2575i	0.247715	+	1.56039i
$483$	−5.15515	−	3.42639i	−0.234567	−	0.155906i
$484$	−43.3333	+	14.1143i	−1.96970	+	0.641557i
$485$		−	11.1550i		−	0.506524i
$486$	−20.5853	+	7.88945i	−0.933770	+	0.357873i
$487$		−	12.0624i		−	0.546598i	−0.961929	−	0.273299i	$-0.911885\pi$
$487$		−	12.0624i		−	0.546598i	0.961929	−	0.273299i	$-0.0881149\pi$
$488$	−11.4378	−	22.3884i	−0.517767	−	1.01347i
$489$	6.79072	+	4.51348i	0.307087	+	0.204107i
$490$	20.5608	−	3.26407i	0.928840	−	0.147456i
$491$	23.8990			1.07855			0.539273	−	0.842131i	$-0.318699\pi$
$491$	23.8990			1.07855			0.539273	+	0.842131i	$0.318699\pi$
$492$	15.5802	+	4.34101i	0.702411	+	0.195708i
$493$	8.48511			0.382150
$494$	0.447572	−	0.0710531i	0.0201372	−	0.00319683i
$495$	−59.0688	+	24.8055i	−2.65494	+	1.11492i
$496$	14.1561	+	19.4254i	0.635626	+	0.872227i
$497$		−	23.1290i		−	1.03748i
$498$	3.68139	+	1.68467i	0.164967	+	0.0754917i
$499$		−	10.1336i		−	0.453642i	−0.973936	−	0.226821i	$-0.927167\pi$
$499$		−	10.1336i		−	0.453642i	0.973936	−	0.226821i	$-0.0728333\pi$
$500$	−7.95954	−	24.4372i	−0.355962	−	1.09287i
$501$	−8.83012	+	13.2853i	−0.394501	+	0.593543i
$502$	5.50804	+	34.6958i	0.245836	+	1.54855i
$503$	8.58793			0.382917			0.191458	−	0.981501i	$-0.438678\pi$
$503$	8.58793			0.382917			0.191458	+	0.981501i	$0.438678\pi$
$504$	−11.2196	−	9.46740i	−0.499759	−	0.421711i
$505$	3.58164			0.159381
$506$	−2.66236	−	16.7705i	−0.118356	−	0.745539i
$507$	−12.3654	+	18.6043i	−0.549167	+	0.826245i
$508$	0.517072	+	1.58751i	0.0229414	+	0.0704342i
$509$		−	0.684898i		−	0.0303576i	−0.999885	−	0.0151788i	$-0.995168\pi$
$509$		−	0.684898i		−	0.0303576i	0.999885	−	0.0151788i	$-0.00483174\pi$
$510$	−9.39589	−	4.29972i	−0.416057	−	0.190395i
$511$			5.77485i			0.255464i
$512$	22.3602	+	3.46749i	0.988189	+	0.153243i
$513$	0.976385	−	5.10359i	0.0431084	−	0.225329i
$514$	13.1591	−	2.08904i	0.580422	−	0.0921434i
$515$	33.9800			1.49734
$516$	−39.8086	−	11.0916i	−1.75247	−	0.488279i
$517$	14.2018			0.624593
$518$	13.4433	−	2.13416i	0.590667	−	0.0937698i
$519$	12.9542	+	8.61005i	0.568625	+	0.377939i
$520$	2.96531	−	1.51493i	0.130037	−	0.0664339i
$521$		−	1.04205i		−	0.0456531i	−0.999739	−	0.0228266i	$-0.992733\pi$
$521$		−	1.04205i		−	0.0456531i	0.999739	−	0.0228266i	$-0.00726655\pi$
$522$	16.5216	+	26.6463i	0.723129	+	1.16628i
$523$			24.3770i			1.06593i	0.846137	+	0.532966i	$0.178923\pi$
$523$			24.3770i			1.06593i	−0.846137	+	0.532966i	$0.821077\pi$
$524$	7.28144	−	2.37166i	0.318091	−	0.103607i
$525$	−21.2072	−	14.0955i	−0.925559	−	0.615177i
$526$	−5.27630	−	33.2360i	−0.230058	−	1.44916i
$527$	6.89963			0.300553
$528$	−1.73700	−	40.2338i	−0.0755934	−	1.75095i
$529$	−18.7330			−0.814479
$530$	−2.71346	−	17.0924i	−0.117865	−	0.742446i
$531$	−4.62545	−	11.0145i	−0.200728	−	0.477988i
$532$	3.29005	−	1.07161i	0.142642	−	0.0464603i
$533$			1.49613i			0.0648047i
$534$	−8.95901	+	19.5775i	−0.387694	+	0.847203i
$535$		−	37.5915i		−	1.62522i
$536$	−17.5622	+	8.97224i	−0.758573	+	0.387542i
$537$	−11.9591	+	17.9929i	−0.516072	+	0.776451i
$538$	−32.1410	+	5.10246i	−1.38570	+	0.219983i
$539$	23.2902			1.00318
$540$	−4.79228	−	37.8786i	−0.206227	−	1.63004i
$541$	−31.4017			−1.35007			−0.675033	−	0.737788i	$-0.735871\pi$
$541$	−31.4017			−1.35007			−0.675033	+	0.737788i	$0.735871\pi$
$542$	22.2603	−	3.53388i	0.956163	−	0.151793i
$543$	2.71593	−	4.08622i	0.116552	−	0.175357i
$544$	4.58457	−	4.60105i	0.196562	−	0.197269i
$545$			12.9828i			0.556124i
$546$	0.565080	−	1.23483i	0.0241832	−	0.0528459i
$547$		−	10.6554i		−	0.455590i	−0.973709	−	0.227795i	$-0.926848\pi$
$547$		−	10.6554i		−	0.455590i	0.973709	−	0.227795i	$-0.0731517\pi$
$548$	5.59757	+	17.1856i	0.239116	+	0.734131i
$549$	−10.3247	−	24.5860i	−0.440648	−	1.04931i
$550$	−10.9524	−	68.9903i	−0.467011	−	2.94176i
$551$	−7.38989			−0.314820
$552$	10.0536	+	1.15409i	0.427911	+	0.0491212i
$553$	8.47538			0.360410
$554$	−0.222304	−	1.40032i	−0.00944478	−	0.0594938i
$555$	29.4831	+	19.5961i	1.25149	+	0.831808i
$556$	1.15839	+	3.55648i	0.0491268	+	0.150828i
$557$		−	35.3132i		−	1.49627i	−0.663548	−	0.748133i	$-0.730950\pi$
$557$		−	35.3132i		−	1.49627i	0.663548	−	0.748133i	$-0.269050\pi$
$558$	13.4344	+	21.6674i	0.568725	+	0.917253i
$559$		−	3.82272i		−	0.161684i
$560$	20.5476	−	14.9739i	0.868296	−	0.632761i
$561$	−9.62736	−	6.39887i	−0.406467	−	0.270161i
$562$	16.0564	−	2.54899i	0.677298	−	0.107523i
$563$	27.1086			1.14249			0.571246	−	0.820779i	$-0.306460\pi$
$563$	27.1086			1.14249			0.571246	+	0.820779i	$0.306460\pi$
$564$	−2.27164	+	8.15311i	−0.0956535	+	0.343308i
$565$	−26.2614			−1.10483
$566$	0.426309	−	0.0676775i	0.0179191	−	0.00284470i
$567$	−11.1171	−	10.9022i	−0.466876	−	0.457850i
$568$	17.2027	+	33.6726i	0.721811	+	1.41287i
$569$			6.20354i			0.260066i	0.991510	+	0.130033i	$0.0415083\pi$
$569$			6.20354i			0.260066i	−0.991510	+	0.130033i	$0.958492\pi$
$570$	8.18312	+	3.74473i	0.342753	+	0.156850i
$571$		−	8.36244i		−	0.349957i	−0.984572	−	0.174979i	$-0.944014\pi$
$571$		−	8.36244i		−	0.349957i	0.984572	−	0.174979i	$-0.0559856\pi$
$572$	3.54211	−	1.15371i	0.148103	−	0.0482392i
$573$	−18.5704	+	27.9400i	−0.775791	+	1.16721i
$574$	1.79108	+	11.2822i	0.0747584	+	0.470912i
$575$	17.5535			0.732031
$576$	23.3757	+	5.43840i	0.973988	+	0.226600i
$577$	−15.6919			−0.653262			−0.326631	−	0.945152i	$-0.605913\pi$
$577$	−15.6919			−0.653262			−0.326631	+	0.945152i	$0.605913\pi$
$578$	3.47714	+	21.9029i	0.144630	+	0.911040i
$579$	−21.0697	+	31.7002i	−0.875626	+	1.31741i
$580$	−51.6302	+	16.8167i	−2.14383	+	0.698273i
$581$			2.85951i			0.118632i
$582$	6.76283	+	3.09478i	0.280328	+	0.128283i
$583$		−	19.3614i		−	0.801868i
$584$	−4.29518	−	8.40737i	−0.177736	−	0.347900i
$585$	3.25638	−	1.36749i	0.134635	−	0.0565389i
$586$	18.1508	−	2.88149i	0.749804	−	0.119033i
$587$	−12.3495			−0.509717			−0.254858	−	0.966978i	$-0.582029\pi$
$587$	−12.3495			−0.509717			−0.254858	+	0.966978i	$0.582029\pi$
$588$	−3.72538	+	13.3707i	−0.153632	+	0.551398i
$589$	−6.00906			−0.247599
$590$	20.4339	−	3.24394i	0.841252	−	0.133551i
$591$	−13.1951	−	8.77020i	−0.542774	−	0.360758i
$592$	−17.9843	+	13.1059i	−0.739150	+	0.538647i
$593$			28.4632i			1.16884i	0.811450	+	0.584421i	$0.198678\pi$
$593$			28.4632i			1.16884i	−0.811450	+	0.584421i	$0.801322\pi$
$594$	1.34914	−	42.6928i	0.0553557	−	1.75171i
$595$		−	7.29822i		−	0.299198i
$596$	8.93497	+	27.4320i	0.365991	+	1.12366i
$597$	−25.1503	−	16.7163i	−1.02933	−	0.684151i
$598$	0.146772	+	0.924534i	0.00600196	+	0.0378070i
$599$	−12.0609			−0.492796			−0.246398	−	0.969169i	$-0.579247\pi$
$599$	−12.0609			−0.492796			−0.246398	+	0.969169i	$0.579247\pi$
$600$	41.3586	+	4.74768i	1.68846	+	0.193823i
$601$	−3.46288			−0.141254			−0.0706270	−	0.997503i	$-0.522500\pi$
$601$	−3.46288			−0.141254			−0.0706270	+	0.997503i	$0.522500\pi$
$602$	−4.57635	−	28.8269i	−0.186518	−	1.17490i
$603$	−19.2861	+	8.09907i	−0.785392	+	0.329820i
$604$	−10.1863	−	31.2737i	−0.414473	−	1.27251i
$605$		−	83.7178i		−	3.40361i
$606$	−0.993669	+	2.17140i	−0.0403651	+	0.0882071i
$607$		−	36.1262i		−	1.46632i	−0.680057	−	0.733159i	$-0.738045\pi$
$607$		−	36.1262i		−	1.46632i	0.680057	−	0.733159i	$-0.261955\pi$
$608$	−3.99281	+	4.00717i	−0.161930	+	0.162512i
$609$	−12.2579	+	18.4425i	−0.496714	+	0.747326i
$610$	45.6117	−	7.24097i	1.84676	−	0.293178i
$611$	−0.782925			−0.0316737
$612$	5.21348	−	4.50345i	0.210742	−	0.182041i
$613$	19.0155			0.768029			0.384015	−	0.923327i	$-0.374541\pi$
$613$	19.0155			0.768029			0.384015	+	0.923327i	$0.374541\pi$
$614$	−31.9918	+	5.07878i	−1.29108	+	0.204963i
$615$	−16.4459	+	24.7435i	−0.663163	+	0.997755i
$616$	25.3297	−	12.9405i	1.02056	−	0.521387i
$617$			6.01745i			0.242253i	0.992637	+	0.121127i	$0.0386507\pi$
$617$			6.01745i			0.242253i	−0.992637	+	0.121127i	$0.961349\pi$
$618$	−9.42722	+	20.6007i	−0.379218	+	0.828681i
$619$		−	0.966961i		−	0.0388654i	−0.999811	−	0.0194327i	$-0.993814\pi$
$619$		−	0.966961i		−	0.0388654i	0.999811	−	0.0194327i	$-0.00618602\pi$
$620$	−41.9829	+	13.6744i	−1.68607	+	0.549177i
$621$	10.5423	+	2.01689i	0.423049	+	0.0809349i
$622$	1.87869	+	11.8341i	0.0753286	+	0.474504i
$623$	−15.2068			−0.609247
$624$	0.0957587	+	2.21804i	0.00383342	+	0.0887925i
$625$	4.72282			0.188913
$626$	4.33375	+	27.2988i	0.173211	+	1.09108i
$627$	8.38471	+	5.57294i	0.334853	+	0.222562i
$628$	42.4446	−	13.8248i	1.69372	−	0.551668i
$629$			6.38777i			0.254697i
$630$	22.9191	−	14.2105i	0.913118	−	0.566161i
$631$			17.4022i			0.692770i	0.938092	+	0.346385i	$0.112591\pi$
$631$			17.4022i			0.692770i	−0.938092	+	0.346385i	$0.887409\pi$
$632$	−12.3390	+	6.30377i	−0.490818	+	0.250751i
$633$	6.36221	+	4.22867i	0.252875	+	0.168075i
$634$	−2.00493	+	0.318288i	−0.0796260	+	0.0126408i
$635$	−3.06698			−0.121709
$636$	11.1152	+	3.09695i	0.440747	+	0.122802i
$637$	−1.28396			−0.0508722
$638$	−59.9961	+	9.52453i	−2.37527	+	0.377080i
$639$	15.5286	+	36.9778i	0.614301	+	1.46282i
$640$	−18.7773	+	37.0826i	−0.742239	+	1.46582i
$641$		−	17.4478i		−	0.689148i	−0.938759	−	0.344574i	$-0.888023\pi$
$641$		−	17.4478i		−	0.689148i	0.938759	−	0.344574i	$-0.111977\pi$
$642$	22.7902	+	10.4292i	0.899456	+	0.411606i
$643$			41.4106i			1.63307i	0.577293	+	0.816537i	$0.304109\pi$
$643$			41.4106i			1.63307i	−0.577293	+	0.816537i	$0.695891\pi$
$644$	2.21360	+	6.79615i	0.0872280	+	0.267806i
$645$	42.0204	−	63.2214i	1.65455	−	2.48934i
$646$	0.254595	+	1.60372i	0.0100169	+	0.0630976i
$647$	16.9254			0.665407			0.332704	−	0.943031i	$-0.392039\pi$
$647$	16.9254			0.665407			0.332704	+	0.943031i	$0.392039\pi$
$648$	24.2938	+	7.60346i	0.954350	+	0.298692i
$649$	23.1466			0.908582
$650$	0.603790	+	3.80334i	0.0236826	+	0.149179i
$651$	−9.96744	+	14.9964i	−0.390655	+	0.587756i
$652$	−2.91590	−	8.95236i	−0.114196	−	0.350601i
$653$		−	8.60694i		−	0.336816i	−0.985717	−	0.168408i	$-0.946137\pi$
$653$		−	8.60694i		−	0.336816i	0.985717	−	0.168408i	$-0.0538626\pi$
$654$	−7.87096	−	3.60188i	−0.307779	−	0.140845i
$655$			14.0674i			0.549657i
$656$	−10.9990	−	15.0932i	−0.429439	−	0.589291i
$657$	−3.87718	−	9.23264i	−0.151263	−	0.360199i
$658$	−5.90399	+	0.937272i	−0.230161	+	0.0365387i
$659$	−23.0444			−0.897683			−0.448841	−	0.893611i	$-0.648163\pi$
$659$	−23.0444			−0.897683			−0.448841	+	0.893611i	$0.648163\pi$
$660$	71.2625	+	19.8554i	2.77389	+	0.772869i
$661$	38.8606			1.51150			0.755750	−	0.654860i	$-0.227272\pi$
$661$	38.8606			1.51150			0.755750	+	0.654860i	$0.227272\pi$
$662$	−1.08822	+	0.172757i	−0.0422948	+	0.00671440i
$663$	0.530743	+	0.352761i	0.0206124	+	0.0137001i
$664$	−2.12683	−	4.16304i	−0.0825369	−	0.161557i
$665$			6.35620i			0.246483i
$666$	−20.0599	+	12.4378i	−0.777306	+	0.481954i
$667$		−	15.2651i		−	0.591066i
$668$	17.5143	−	5.70464i	0.677648	−	0.220719i
$669$	−7.09176	−	4.71357i	−0.274183	−	0.182237i
$670$	−5.68007	−	35.7794i	−0.219440	−	1.38228i
$671$	51.6667			1.99457
$672$	3.37741	+	16.6114i	0.130287	+	0.640800i
$673$	45.6737			1.76059			0.880295	−	0.474426i	$-0.157344\pi$
$673$	45.6737			1.76059			0.880295	+	0.474426i	$0.157344\pi$
$674$	−3.53424	−	22.2626i	−0.136134	−	0.857522i
$675$	43.3690	+	8.29706i	1.66927	+	0.319354i
$676$	24.5264	−	7.98859i	0.943324	−	0.307253i
$677$		−	10.0169i		−	0.384981i	−0.981299	−	0.192490i	$-0.938344\pi$
$677$		−	10.0169i		−	0.384981i	0.981299	−	0.192490i	$-0.0616564\pi$
$678$	7.28582	−	15.9212i	0.279810	−	0.611451i
$679$			5.25300i			0.201592i
$680$	5.42823	+	10.6252i	0.208163	+	0.407458i
$681$	−23.0822	+	34.7282i	−0.884513	+	1.33079i
$682$	−48.7856	+	7.74483i	−1.86810	+	0.296565i
$683$	−17.5621			−0.671996			−0.335998	−	0.941863i	$-0.609074\pi$
$683$	−17.5621			−0.671996			−0.335998	+	0.941863i	$0.609074\pi$
$684$	−4.54055	+	3.92217i	−0.173612	+	0.149968i
$685$	−33.2016			−1.26857
$686$	−26.5974	+	4.22240i	−1.01549	+	0.161212i
$687$	17.1011	−	25.7293i	0.652448	−	0.981634i
$688$	28.1032	+	38.5642i	1.07143	+	1.47025i
$689$			1.06737i			0.0406635i
$690$	−7.73537	+	16.9036i	−0.294481	+	0.643509i
$691$		−	32.1872i		−	1.22446i	−0.790681	−	0.612229i	$-0.790273\pi$
$691$		−	32.1872i		−	1.22446i	0.790681	−	0.612229i	$-0.209727\pi$
$692$	−5.56246	−	17.0778i	−0.211453	−	0.649199i
$693$	27.8160	−	11.6811i	1.05664	−	0.443730i
$694$	−3.69120	−	23.2513i	−0.140116	−	0.882607i
$695$	−6.87093			−0.260629
$696$	4.12873	−	35.9667i	0.156499	−	1.36332i
$697$	−5.36089			−0.203058
$698$	−1.86051	−	11.7196i	−0.0704214	−	0.443592i
$699$	−32.2035	−	21.4042i	−1.21805	−	0.809582i
$700$	9.10629	+	27.9580i	0.344185	+	1.05671i
$701$		−	16.9473i		−	0.640091i	−0.947402	−	0.320045i	$-0.896302\pi$
$701$		−	16.9473i		−	0.640091i	0.947402	−	0.320045i	$-0.103698\pi$
$702$	−0.0743760	+	2.35360i	−0.00280714	+	0.0888309i
$703$		−	5.56327i		−	0.209823i
$704$	−27.2517	+	37.6791i	−1.02709	+	1.42008i
$705$	−12.9483	−	8.60612i	−0.487660	−	0.324125i
$706$	12.0371	−	1.91092i	0.453022	−	0.0719184i
$707$	−1.68663			−0.0634321
$708$	−3.70241	+	13.2882i	−0.139145	+	0.499402i
$709$	42.7497			1.60550			0.802749	−	0.596317i	$-0.203370\pi$
$709$	42.7497			1.60550			0.802749	+	0.596317i	$0.203370\pi$
$710$	−68.6009	+	10.8906i	−2.57454	+	0.408715i
$711$	−13.5502	+	5.69029i	−0.508171	+	0.213403i
$712$	22.1390	−	11.3104i	0.829692	−	0.423875i
$713$		−	12.4127i		−	0.464860i
$714$	4.42461	+	2.02477i	0.165587	+	0.0757753i
$715$			6.84317i			0.255920i
$716$	23.7204	−	7.72607i	0.886475	−	0.288737i
$717$	2.50704	−	3.77195i	0.0936273	−	0.140866i
$718$	5.42909	+	34.1984i	0.202612	+	1.27627i
$719$	−13.4036			−0.499870			−0.249935	−	0.968263i	$-0.580409\pi$
$719$	−13.4036			−0.499870			−0.249935	+	0.968263i	$0.580409\pi$
$720$	−22.7976	+	37.7352i	−0.849615	+	1.40631i
$721$	−16.0015			−0.595927
$722$	−0.221733	−	1.39672i	−0.00825205	−	0.0519806i
$723$	23.5155	−	35.3801i	0.874552	−	1.31580i
$724$	−5.38696	+	1.75461i	−0.200205	+	0.0652094i
$725$		−	62.7974i		−	2.33224i
$726$	50.7546	+	23.2262i	1.88368	+	0.862004i
$727$		−	0.887307i		−	0.0329084i	−0.999865	−	0.0164542i	$-0.994762\pi$
$727$		−	0.887307i		−	0.0329084i	0.999865	−	0.0164542i	$-0.00523777\pi$
$728$	−1.39639	+	0.713392i	−0.0517537	+	0.0264401i
$729$	25.0933	+	9.96614i	0.929383	+	0.369116i
$730$	17.1283	−	2.71916i	0.633946	−	0.100640i
$731$	13.6975			0.506619
$732$	−8.26434	+	29.6614i	−0.305459	+	1.09632i
$733$	29.1958			1.07837			0.539185	−	0.842187i	$-0.318732\pi$
$733$	29.1958			1.07837			0.539185	+	0.842187i	$0.318732\pi$
$734$	46.9976	−	7.46098i	1.73471	−	0.275390i
$735$	−21.2345	−	14.1136i	−0.783246	−	0.520588i
$736$	−8.27749	−	8.24783i	−0.305112	−	0.304019i
$737$		−	40.5291i		−	1.49291i
$738$	−10.4383	−	16.8352i	−0.384240	−	0.619711i
$739$			34.9682i			1.28633i	0.765729	+	0.643164i	$0.222379\pi$
$739$			34.9682i			1.28633i	−0.765729	+	0.643164i	$0.777621\pi$
$740$	−12.6599	−	38.8683i	−0.465388	−	1.42883i
$741$	−0.462238	−	0.307229i	−0.0169807	−	0.0112863i
$742$	1.27779	+	8.04896i	0.0469092	+	0.295487i
$743$	−37.6871			−1.38261			−0.691303	−	0.722565i	$-0.742963\pi$
$743$	−37.6871			−1.38261			−0.691303	+	0.722565i	$0.742963\pi$
$744$	3.35726	−	29.2462i	0.123083	−	1.07222i
$745$	−52.9972			−1.94167
$746$	0.693213	+	4.36663i	0.0253803	+	0.159874i
$747$	−1.91985	−	4.57168i	−0.0702435	−	0.167269i
$748$	4.13395	+	12.6920i	0.151152	+	0.464064i
$749$			17.7022i			0.646823i
$750$	−13.0981	+	28.6224i	−0.478274	+	1.04514i
$751$		−	16.7896i		−	0.612661i	−0.951925	−	0.306330i	$-0.900899\pi$
$751$		−	16.7896i		−	0.612661i	0.951925	−	0.306330i	$-0.0991012\pi$
$752$	7.89826	−	5.75577i	0.288020	−	0.209891i
$753$	23.8164	−	35.8327i	0.867918	−	1.30582i
$754$	3.30751	−	0.525075i	0.120452	−	0.0191221i
$755$	60.4191			2.19888
$756$	2.25673	+	17.8374i	0.0820764	+	0.648739i
$757$	17.5329			0.637244			0.318622	−	0.947882i	$-0.396780\pi$
$757$	17.5329			0.637244			0.318622	+	0.947882i	$0.396780\pi$
$758$	−36.5936	+	5.80933i	−1.32914	+	0.211004i
$759$	−11.5118	+	17.3200i	−0.417853	+	0.628677i
$760$	−4.72758	−	9.25375i	−0.171487	−	0.335669i
$761$			12.5185i			0.453794i	0.973919	+	0.226897i	$0.0728581\pi$
$761$			12.5185i			0.453794i	−0.973919	+	0.226897i	$0.927142\pi$
$762$	0.850884	−	1.85938i	0.0308243	−	0.0673583i
$763$		−	6.11374i		−	0.221332i
$764$	36.8339	−	11.9973i	1.33260	−	0.434047i
$765$	4.89996	+	11.6682i	0.177158	+	0.421863i
$766$	3.02440	+	19.0511i	0.109276	+	0.688343i
$767$	−1.27604			−0.0460751
$768$	−17.2722	−	21.6719i	−0.623257	−	0.782017i
$769$	−44.7999			−1.61553			−0.807763	−	0.589508i	$-0.799322\pi$
$769$	−44.7999			−1.61553			−0.807763	+	0.589508i	$0.799322\pi$
$770$	8.19225	+	51.6039i	0.295228	+	1.85968i
$771$	−13.5903	−	9.03284i	−0.489442	−	0.325310i
$772$	41.7911	−	13.6119i	1.50409	−	0.489904i
$773$			14.2736i			0.513384i	0.966493	+	0.256692i	$0.0826326\pi$
$773$			14.2736i			0.513384i	−0.966493	+	0.256692i	$0.917367\pi$
$774$	26.6706	+	43.0150i	0.958656	+	1.54614i
$775$		−	51.0634i		−	1.83425i
$776$	−3.90705	−	7.64764i	−0.140255	−	0.274534i
$777$	−13.8839	−	9.22798i	−0.498081	−	0.331052i
$778$	−34.0507	+	5.40563i	−1.22078	+	0.193801i
$779$	4.66894			0.167282
$780$	−3.92860	−	1.09460i	−0.140667	−	0.0391929i
$781$	−77.7077			−2.78060
$782$	−3.31276	+	0.525909i	−0.118464	+	0.0188065i
$783$	7.21538	−	37.7150i	0.257857	−	1.34782i
$784$	12.9528	−	9.43917i	0.462598	−	0.337113i
$785$			82.0007i			2.92673i
$786$	−8.52846	−	3.90276i	−0.304200	−	0.139207i
$787$			48.8692i			1.74200i	0.491285	+	0.870999i	$0.336527\pi$
$787$			48.8692i			1.74200i	−0.491285	+	0.870999i	$0.663473\pi$
$788$	5.66592	+	17.3954i	0.201840	+	0.619686i
$789$	−22.8144	+	34.3251i	−0.812213	+	1.22201i
$790$	−3.99074	−	25.1381i	−0.141984	−	0.894374i
$791$	12.3668			0.439711
$792$	−31.8081	+	37.6949i	−1.13025	+	1.33943i
$793$	−2.84831			−0.101147
$794$	2.56641	+	16.1661i	0.0910783	+	0.573713i
$795$	−11.7328	+	17.6525i	−0.416120	+	0.626069i
$796$	10.7994	+	33.1562i	0.382775	+	1.17519i
$797$			25.7601i			0.912471i	0.889859	+	0.456236i	$0.150803\pi$
$797$			25.7601i			0.912471i	−0.889859	+	0.456236i	$0.849197\pi$
$798$	−3.85350	−	1.76343i	−0.136413	−	0.0624246i
$799$		−	2.80535i		−	0.0992461i
$800$	−34.0519	−	33.9299i	−1.20392	−	1.19960i
$801$	24.3121	−	10.2097i	0.859026	−	0.360742i
$802$	12.6010	−	2.00044i	0.444956	−	0.0706379i
$803$	19.4021			0.684684
$804$	23.2674	+	6.48283i	0.820578	+	0.228632i
$805$	−13.1298			−0.462765
$806$	2.68949	−	0.426962i	0.0947331	−	0.0150391i
$807$	33.1942	+	22.0627i	1.16849	+	0.776644i
$808$	2.45549	−	1.25447i	0.0863840	−	0.0441321i
$809$			10.8052i			0.379889i	0.981795	+	0.189945i	$0.0608309\pi$
$809$			10.8052i			0.379889i	−0.981795	+	0.189945i	$0.939169\pi$
$810$	−27.1015	+	38.1070i	−0.952248	+	1.33894i
$811$		−	38.4645i		−	1.35067i	−0.737510	−	0.675336i	$-0.763999\pi$
$811$		−	38.4645i		−	1.35067i	0.737510	−	0.675336i	$-0.236001\pi$
$812$	24.3131	−	7.91911i	0.853223	−	0.277906i
$813$	−22.9898	−	15.2803i	−0.806286	−	0.535902i
$814$	−7.17027	−	45.1663i	−0.251318	−	1.58308i
$815$	17.2955			0.605835
$816$	−7.94759	+	0.343119i	−0.278221	+	0.0120116i
$817$	−11.9295			−0.417359
$818$	−2.11125	−	13.2990i	−0.0738182	−	0.464990i
$819$	−1.53346	+	0.643965i	−0.0535834	+	0.0225020i
$820$	32.6199	−	10.6248i	1.13914	−	0.371033i
$821$			10.2823i			0.358853i	0.983771	+	0.179427i	$0.0574243\pi$
$821$			10.2823i			0.358853i	−0.983771	+	0.179427i	$0.942576\pi$
$822$	9.21126	−	20.1288i	0.321279	−	0.702071i
$823$		−	8.11105i		−	0.282733i	−0.989957	−	0.141367i	$-0.954850\pi$
$823$		−	8.11105i		−	0.282733i	0.989957	−	0.141367i	$-0.0451496\pi$
$824$	23.2960	−	11.9015i	0.811553	−	0.414609i
$825$	−47.3573	+	71.2510i	−1.64877	+	2.48064i
$826$	−9.62253	+	1.52760i	−0.334811	+	0.0531520i
$827$	33.2385			1.15581			0.577907	−	0.816102i	$-0.303869\pi$
$827$	33.2385			1.15581			0.577907	+	0.816102i	$0.303869\pi$
$828$	−8.10190	−	9.37927i	−0.281560	−	0.325952i
$829$	15.1546			0.526340			0.263170	−	0.964749i	$-0.415232\pi$
$829$	15.1546			0.526340			0.263170	+	0.964749i	$0.415232\pi$
$830$	8.48134	−	1.34643i	0.294391	−	0.0467354i
$831$	−0.961226	+	1.44620i	−0.0333446	+	0.0501682i
$832$	1.50235	−	2.07720i	0.0520845	−	0.0720139i
$833$		−	4.60063i		−	0.159402i
$834$	1.90623	−	4.16556i	0.0660074	−	0.144242i
$835$			33.8367i			1.17097i
$836$	−3.60036	−	11.0538i	−0.124521	−	0.382302i
$837$	5.86716	−	30.6678i	0.202799	−	1.06003i
$838$	−2.57687	−	16.2320i	−0.0890165	−	0.560725i
$839$	−40.6940			−1.40491			−0.702457	−	0.711726i	$-0.747914\pi$
$839$	−40.6940			−1.40491			−0.702457	+	0.711726i	$0.747914\pi$
$840$	−30.9358	−	3.55121i	−1.06738	−	0.122528i
$841$	−25.6105			−0.883122
$842$	3.22995	+	20.3458i	0.111311	+	0.701163i
$843$	−16.5825	−	11.0217i	−0.571133	−	0.379606i
$844$	−2.73191	−	8.38745i	−0.0940361	−	0.288708i
$845$			47.3838i			1.63005i
$846$	8.80982	−	5.46236i	0.302888	−	0.187800i
$847$			39.4235i			1.35461i
$848$	−7.84690	−	10.7678i	−0.269464	−	0.369767i
$849$	−0.440278	−	0.292633i	−0.0151103	−	0.0100431i
$850$	−13.6280	+	2.16348i	−0.467437	+	0.0742068i
$851$	11.4919			0.393936
$852$	12.4297	−	44.6113i	0.425835	−	1.52836i
$853$	21.7094			0.743316			0.371658	−	0.928370i	$-0.378789\pi$
$853$	21.7094			0.743316			0.371658	+	0.928370i	$0.378789\pi$
$854$	−21.4790	+	3.40984i	−0.734995	+	0.116682i
$855$	−4.26750	−	10.1621i	−0.145945	−	0.347536i
$856$	−13.1664	−	25.7719i	−0.450019	−	0.880865i
$857$		−	3.52329i		−	0.120353i	−0.998188	−	0.0601766i	$-0.980834\pi$
$857$		−	3.52329i		−	0.120353i	0.998188	−	0.0601766i	$-0.0191664\pi$
$858$	−4.14873	−	1.89853i	−0.141635	−	0.0648147i
$859$		−	42.9804i		−	1.46647i	−0.679974	−	0.733236i	$-0.738009\pi$
$859$		−	42.9804i		−	1.46647i	0.679974	−	0.733236i	$-0.261991\pi$
$860$	−83.3463	+	27.1470i	−2.84208	+	0.925705i
$861$	7.74452	−	11.6519i	0.263933	−	0.397097i
$862$	3.85704	+	24.2959i	0.131371	+	0.827522i
$863$	52.1673			1.77580			0.887898	−	0.460041i	$-0.152165\pi$
$863$	52.1673			1.77580			0.887898	+	0.460041i	$0.152165\pi$
$864$	−16.5525	−	24.2902i	−0.563126	−	0.826371i
$865$	32.9934			1.12181
$866$	−7.78302	−	49.0261i	−0.264478	−	1.66598i
$867$	15.0349	−	22.6206i	0.510612	−	0.768236i
$868$	19.7701	−	6.43939i	0.671041	−	0.218567i
$869$		−	28.4752i		−	0.965955i
$870$	60.4724	+	27.6732i	2.05021	+	0.938208i
$871$			2.23432i			0.0757069i
$872$	4.54724	+	8.90075i	0.153989	+	0.301418i
$873$	−3.52682	−	8.39833i	−0.119365	−	0.284240i
$874$	2.88517	−	0.458027i	0.0975922	−	0.0154930i
$875$	−22.2323			−0.751589
$876$	−3.10346	+	11.1386i	−0.104856	+	0.376337i
$877$	7.79733			0.263297			0.131649	−	0.991296i	$-0.457973\pi$
$877$	7.79733			0.263297			0.131649	+	0.991296i	$0.457973\pi$
$878$	18.6298	−	2.95752i	0.628724	−	0.0998115i
$879$	−18.7456	−	12.4594i	−0.632273	−	0.420244i
$880$	−50.3085	−	69.0350i	−1.69590	−	2.32717i
$881$		−	57.1545i		−	1.92558i	−0.270245	−	0.962791i	$-0.587105\pi$
$881$		−	57.1545i		−	1.92558i	0.270245	−	0.962791i	$-0.412895\pi$
$882$	14.4477	−	8.95800i	0.486478	−	0.301632i
$883$			18.5092i			0.622883i	0.950265	+	0.311442i	$0.100812\pi$
$883$			18.5092i			0.622883i	−0.950265	+	0.311442i	$0.899188\pi$
$884$	−0.227899	−	0.699691i	−0.00766507	−	0.0235332i
$885$	−21.1035	−	14.0266i	−0.709388	−	0.471498i
$886$	−4.44003	−	27.9683i	−0.149166	−	0.939613i
$887$	−2.05663			−0.0690549			−0.0345275	−	0.999404i	$-0.510993\pi$
$887$	−2.05663			−0.0690549			−0.0345275	+	0.999404i	$0.510993\pi$
$888$	27.0765	+	3.10819i	0.908628	+	0.104304i
$889$	1.44427			0.0484392
$890$	7.16029	+	45.1035i	0.240014	+	1.51187i
$891$	−36.6287	+	37.3508i	−1.22711	+	1.25130i
$892$	3.04517	+	9.34923i	0.101960	+	0.313035i
$893$			2.44325i			0.0817602i
$894$	14.7032	−	32.1300i	0.491749	−	1.07459i
$895$			45.8267i			1.53182i
$896$	8.84241	−	17.4625i	0.295404	−	0.583383i
$897$	0.634632	−	0.954830i	0.0211898	−	0.0318808i
$898$	−41.4225	+	6.57592i	−1.38229	+	0.219441i
$899$	−44.4063			−1.48103
$900$	−33.3295	−	38.5844i	−1.11098	−	1.28615i
$901$	−3.82456			−0.127415
$902$	37.9056	−	6.01760i	1.26212	−	0.200364i
$903$	−19.7878	+	29.7715i	−0.658497	+	0.990735i
$904$	−18.0043	+	9.19807i	−0.598813	+	0.305923i
$905$		−	10.4073i		−	0.345951i
$906$	−16.7623	+	36.6296i	−0.556891	+	1.21694i
$907$		−	3.79582i		−	0.126038i	−0.998012	−	0.0630191i	$-0.979927\pi$
$907$		−	3.79582i		−	0.126038i	0.998012	−	0.0630191i	$-0.0200729\pi$
$908$	45.7829	−	14.9121i	1.51936	−	0.494876i
$909$	2.69652	−	1.13239i	0.0894381	−	0.0375589i
$910$	−0.451628	−	2.84486i	−0.0149713	−	0.0943061i
$911$	−40.5320			−1.34288			−0.671442	−	0.741057i	$-0.734325\pi$
$911$	−40.5320			−1.34288			−0.671442	+	0.741057i	$0.734325\pi$
$912$	6.92176	−	0.298831i	0.229202	−	0.00989529i
$913$	9.60724			0.317953
$914$	−5.77383	−	36.3700i	−0.190981	−	1.20301i
$915$	−47.1063	−	31.3095i	−1.55729	−	1.03506i
$916$	−33.9195	+	11.0480i	−1.12073	+	0.365038i
$917$		−	6.62445i		−	0.218759i
$918$	−8.43333	−	0.266502i	−0.278341	−	0.00879587i
$919$		−	22.9784i		−	0.757988i	−0.925399	−	0.378994i	$-0.876270\pi$
$919$		−	22.9784i		−	0.757988i	0.925399	−	0.378994i	$-0.123730\pi$
$920$	19.1152	−	9.76561i	0.630209	−	0.321963i
$921$	33.0401	+	21.9603i	1.08871	+	0.723616i
$922$	−11.2660	+	1.78851i	−0.371026	+	0.0589013i
$923$	4.28392			0.141007
$924$	−33.5581	−	9.35007i	−1.10398	−	0.307595i
$925$	47.2752			1.55440
$926$	−26.6360	+	4.22853i	−0.875314	+	0.138958i
$927$	25.5827	−	10.7433i	0.840246	−	0.352855i
$928$	−29.5065	+	29.6126i	−0.968598	+	0.972081i
$929$		−	0.758618i		−	0.0248895i	−0.999923	−	0.0124447i	$-0.996039\pi$
$929$		−	0.758618i		−	0.0248895i	0.999923	−	0.0124447i	$-0.00396138\pi$
$930$	49.1729	+	22.5023i	1.61244	+	0.737880i
$931$			4.00681i			0.131318i
$932$	13.8280	+	42.4546i	0.452953	+	1.39065i
$933$	8.12333	−	12.2219i	0.265946	−	0.400126i
$934$	−1.86883	−	11.7720i	−0.0611499	−	0.385190i
$935$	−24.5202			−0.801897
$936$	1.75354	−	2.07807i	0.0573162	−	0.0679239i
$937$	−0.0489880			−0.00160037			−0.000800184	−	1.00000i	$-0.500255\pi$
$937$	−0.0489880			−0.00160037			−0.000800184		1.00000i	$0.500255\pi$
$938$	2.67480	+	16.8488i	0.0873352	+	0.550134i
$939$	18.7388	−	28.1933i	0.611519	−	0.920055i
$940$	5.55993	+	17.0700i	0.181345	+	0.556761i
$941$			22.7131i			0.740425i	0.928947	+	0.370212i	$0.120715\pi$
$941$			22.7131i			0.740425i	−0.928947	+	0.370212i	$0.879285\pi$
$942$	−49.7136	−	22.7498i	−1.61976	−	0.741228i
$943$			9.64447i			0.314067i
$944$	12.8729	−	9.38096i	0.418976	−	0.305324i
$945$	−32.4395	−	6.20610i	−1.05526	−	0.201885i
$946$	−96.8514	+	15.3754i	−3.14891	+	0.499897i
$947$	43.1702			1.40284			0.701421	−	0.712747i	$-0.252549\pi$
$947$	43.1702			1.40284			0.701421	+	0.712747i	$0.252549\pi$
$948$	16.3474	+	4.55475i	0.530938	+	0.147931i
$949$	−1.06961			−0.0347210
$950$	11.8690	−	1.88423i	0.385081	−	0.0611325i
$951$	2.07063	+	1.37625i	0.0671448	+	0.0446281i
$952$	−2.55620	−	5.00350i	−0.0828470	−	0.162164i
$953$			50.9827i			1.65149i	0.564041	+	0.825747i	$0.309246\pi$
$953$			50.9827i			1.65149i	−0.564041	+	0.825747i	$0.690754\pi$
$954$	−7.44689	−	12.0105i	−0.241102	−	0.388855i
$955$			71.1612i			2.30272i
$956$	−4.97265	+	1.61966i	−0.160827	+	0.0523835i
$957$	61.9621	+	41.1834i	2.00295	+	1.33127i
$958$	3.21489	+	20.2510i	0.103868	+	0.654279i
$959$	15.6349			0.504878
$960$	47.6794	−	17.8392i	1.53885	−	0.575756i
$961$	−5.10883			−0.164801
$962$	0.395287	+	2.48996i	0.0127446	+	0.0802795i
$963$	−11.8851	−	28.3016i	−0.382991	−	0.912008i
$964$	−46.6423	+	15.1920i	−1.50225	+	0.489303i
$965$			80.7382i			2.59905i
$966$	3.64266	−	7.96006i	0.117201	−	0.256111i
$967$		−	0.829652i		−	0.0266798i	−0.999911	−	0.0133399i	$-0.995754\pi$
$967$		−	0.829652i		−	0.0266798i	0.999911	−	0.0133399i	$-0.00424635\pi$
$968$	−29.3221	−	57.3951i	−0.942449	−	1.84475i
$969$	1.10085	−	1.65627i	0.0353644	−	0.0532072i
$970$	15.5805	−	2.47344i	0.500259	−	0.0794174i
$971$	−15.5337			−0.498499			−0.249249	−	0.968439i	$-0.580184\pi$
$971$	−15.5337			−0.498499			−0.249249	+	0.968439i	$0.580184\pi$
$972$	−15.5838	−	27.0027i	−0.499852	−	0.866111i
$973$	3.23558			0.103728
$974$	16.8478	−	2.67463i	0.539838	−	0.0857006i
$975$	2.61075	−	3.92797i	0.0836108	−	0.125796i
$976$	28.7342	−	20.9397i	0.919760	−	0.670265i
$977$		−	42.2978i		−	1.35323i	−0.736338	−	0.676614i	$-0.763447\pi$
$977$		−	42.2978i		−	1.35323i	0.736338	−	0.676614i	$-0.236553\pi$
$978$	−4.79836	+	10.4855i	−0.153435	+	0.335291i
$979$			51.0910i			1.63288i
$980$	9.11800	+	27.9939i	0.291264	+	0.894233i
$981$	4.10471	+	9.77445i	0.131053	+	0.312074i
$982$	5.29920	+	33.3803i	0.169104	+	1.06521i
$983$	−44.2459			−1.41123			−0.705613	−	0.708598i	$-0.749328\pi$
$983$	−44.2459			−1.41123			−0.705613	+	0.708598i	$0.749328\pi$
$984$	−2.60853	+	22.7238i	−0.0831569	+	0.724408i
$985$	−33.6070			−1.07081
$986$	1.88143	+	11.8513i	0.0599169	+	0.377424i
$987$	6.09745	+	4.05270i	0.194084	+	0.128999i
$988$	0.198483	+	0.609379i	0.00631458	+	0.0193869i
$989$		−	24.6423i		−	0.783580i
$990$	−47.7439	−	77.0025i	−1.51740	−	2.44730i
$991$		−	47.5875i		−	1.51167i	−0.654763	−	0.755834i	$-0.727232\pi$
$991$		−	47.5875i		−	1.51167i	0.654763	−	0.755834i	$-0.272768\pi$
$992$	−23.9931	+	24.0794i	−0.761781	+	0.764520i
$993$	1.12388	+	0.746991i	0.0356652	+	0.0237050i
$994$	32.3048	−	5.12846i	1.02464	−	0.162665i
$995$	−64.0560			−2.03071
$996$	−1.53672	+	5.51543i	−0.0486930	+	0.174763i
$997$	8.42001			0.266665			0.133332	−	0.991071i	$-0.457432\pi$
$997$	8.42001			0.266665			0.133332	+	0.991071i	$0.457432\pi$
$998$	14.1538	−	2.24696i	0.448032	−	0.0711262i
$999$	28.3926	+	5.43189i	0.898304	+	0.171857i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.2.c.a.191.20	yes	36
3.2	odd	2	inner	228.2.c.a.191.17	✓	36
4.3	odd	2	inner	228.2.c.a.191.18	yes	36
12.11	even	2	inner	228.2.c.a.191.19	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.c.a.191.17	✓	36	3.2	odd	2	inner
228.2.c.a.191.18	yes	36	4.3	odd	2	inner
228.2.c.a.191.19	yes	36	12.11	even	2	inner
228.2.c.a.191.20	yes	36	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.221733 + 1.39672i) q^{2} +(0.958759 - 1.44249i) q^{3} +(-1.90167 + 0.619399i) q^{4} -3.67393i q^{5} +(2.22735 + 1.01927i) q^{6} +1.73008i q^{7} +(-1.28679 - 2.51876i) q^{8} +(-1.16156 - 2.76600i) q^{9} +(5.13146 - 0.814631i) q^{10} +5.81266 q^{11} +(-0.929763 + 3.33700i) q^{12} -0.320444 q^{13} +(-2.41645 + 0.383617i) q^{14} +(-5.29961 - 3.52241i) q^{15} +(3.23269 - 2.35579i) q^{16} -1.14820i q^{17} +(3.60578 - 2.23570i) q^{18} +1.00000i q^{19} +(2.27563 + 6.98659i) q^{20} +(2.49563 + 1.65873i) q^{21} +(1.28886 + 8.11867i) q^{22} -2.06567 q^{23} +(-4.86702 - 0.558699i) q^{24} -8.49773 q^{25} +(-0.0710531 - 0.447572i) q^{26} +(-5.10359 - 0.976385i) q^{27} +(-1.07161 - 3.29005i) q^{28} +7.38989i q^{29} +(3.74473 - 8.18312i) q^{30} +6.00906i q^{31} +(4.00717 + 3.99281i) q^{32} +(5.57294 - 8.38471i) q^{33} +(1.60372 - 0.254595i) q^{34} +6.35620 q^{35} +(3.92217 + 4.54055i) q^{36} -5.56327 q^{37} +(-1.39672 + 0.221733i) q^{38} +(-0.307229 + 0.462238i) q^{39} +(-9.25375 + 4.72758i) q^{40} -4.66894i q^{41} +(-1.76343 + 3.85350i) q^{42} +11.9295i q^{43} +(-11.0538 + 3.60036i) q^{44} +(-10.1621 + 4.26750i) q^{45} +(-0.458027 - 2.88517i) q^{46} +2.44325 q^{47} +(-0.298831 - 6.92176i) q^{48} +4.00681 q^{49} +(-1.88423 - 11.8690i) q^{50} +(-1.65627 - 1.10085i) q^{51} +(0.609379 - 0.198483i) q^{52} -3.33090i q^{53} +(0.232103 - 7.34480i) q^{54} -21.3553i q^{55} +(4.35767 - 2.22626i) q^{56} +(1.44249 + 0.958759i) q^{57} +(-10.3216 + 1.63858i) q^{58} +3.98210 q^{59} +(12.2599 + 3.41588i) q^{60} +8.88865 q^{61} +(-8.39299 + 1.33241i) q^{62} +(4.78542 - 2.00960i) q^{63} +(-4.68833 + 6.48225i) q^{64} +1.17729i q^{65} +(12.9468 + 5.92468i) q^{66} -6.97256i q^{67} +(0.711197 + 2.18350i) q^{68} +(-1.98048 + 2.97971i) q^{69} +(1.40938 + 8.87786i) q^{70} -13.3687 q^{71} +(-5.47221 + 6.48497i) q^{72} +3.33790 q^{73} +(-1.23356 - 7.77034i) q^{74} +(-8.14728 + 12.2579i) q^{75} +(-0.619399 - 1.90167i) q^{76} +10.0564i q^{77} +(-0.713741 - 0.326620i) q^{78} -4.89883i q^{79} +(-8.65498 - 11.8767i) q^{80} +(-6.30154 + 6.42577i) q^{81} +(6.52121 - 1.03526i) q^{82} +1.65281 q^{83} +(-5.77329 - 1.60857i) q^{84} -4.21842 q^{85} +(-16.6621 + 2.64516i) q^{86} +(10.6599 + 7.08513i) q^{87} +(-7.47968 - 14.6407i) q^{88} +8.78961i q^{89} +(-8.21378 - 13.2474i) q^{90} -0.554395i q^{91} +(3.92822 - 1.27947i) q^{92} +(8.66802 + 5.76124i) q^{93} +(0.541749 + 3.41254i) q^{94} +3.67393 q^{95} +(9.60151 - 1.95217i) q^{96} +3.03627 q^{97} +(0.888442 + 5.59640i) q^{98} +(-6.75177 - 16.0778i) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more