LMFDB - Embedded newform 380.2.f.a.151.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(151,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("380.151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.f (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{18} + x^{16} - 9x^{14} + 20x^{12} - 24x^{10} + 80x^{8} - 144x^{6} + 64x^{4} - 256x^{2} + 1024 $ x^20 - x^18 + x^16 - 9x^14 + 20x^12 - 24x^10 + 80x^8 - 144x^6 + 64x^4 - 256*x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			151.5
Root			$0.976481 - 1.02298i$ of defining polynomial
Character	$\chi$	$=$	380.151
Dual form			380.2.f.a.151.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.976481 - 1.02298i) q^{2} -0.502080 q^{3} +(-0.0929701 + 1.99784i) q^{4} -1.00000 q^{5} +(0.490271 + 0.513617i) q^{6} +3.57756i q^{7} +(2.13453 - 1.85574i) q^{8} -2.74792 q^{9} +O(q^{10})$	\(q+(-0.976481 - 1.02298i) q^{2} -0.502080 q^{3} +(-0.0929701 + 1.99784i) q^{4} -1.00000 q^{5} +(0.490271 + 0.513617i) q^{6} +3.57756i q^{7} +(2.13453 - 1.85574i) q^{8} -2.74792 q^{9} +(0.976481 + 1.02298i) q^{10} -3.89395i q^{11} +(0.0466784 - 1.00307i) q^{12} -7.12548i q^{13} +(3.65977 - 3.49342i) q^{14} +0.502080 q^{15} +(-3.98271 - 0.371479i) q^{16} +6.79894 q^{17} +(2.68329 + 2.81106i) q^{18} +(-3.48135 - 2.62301i) q^{19} +(0.0929701 - 1.99784i) q^{20} -1.79622i q^{21} +(-3.98343 + 3.80237i) q^{22} -3.22874i q^{23} +(-1.07170 + 0.931732i) q^{24} +1.00000 q^{25} +(-7.28921 + 6.95790i) q^{26} +2.88591 q^{27} +(-7.14739 - 0.332606i) q^{28} -2.89493i q^{29} +(-0.490271 - 0.513617i) q^{30} -6.29953 q^{31} +(3.50903 + 4.43697i) q^{32} +1.95508i q^{33} +(-6.63904 - 6.95517i) q^{34} -3.57756i q^{35} +(0.255474 - 5.48989i) q^{36} -1.99820i q^{37} +(0.716184 + 6.12267i) q^{38} +3.57756i q^{39} +(-2.13453 + 1.85574i) q^{40} +1.95508i q^{41} +(-1.83750 + 1.75398i) q^{42} -1.00325i q^{43} +(7.77949 + 0.362021i) q^{44} +2.74792 q^{45} +(-3.30293 + 3.15280i) q^{46} -5.80305i q^{47} +(1.99964 + 0.186512i) q^{48} -5.79894 q^{49} +(-0.976481 - 1.02298i) q^{50} -3.41361 q^{51} +(14.2356 + 0.662457i) q^{52} +1.75310i q^{53} +(-2.81804 - 2.95223i) q^{54} +3.89395i q^{55} +(6.63904 + 7.63641i) q^{56} +(1.74792 + 1.31696i) q^{57} +(-2.96145 + 2.82684i) q^{58} +4.07679 q^{59} +(-0.0466784 + 1.00307i) q^{60} -7.38399 q^{61} +(6.15137 + 6.44428i) q^{62} -9.83084i q^{63} +(1.11243 - 7.92228i) q^{64} +7.12548i q^{65} +(2.00000 - 1.90909i) q^{66} -6.64659 q^{67} +(-0.632099 + 13.5832i) q^{68} +1.62109i q^{69} +(-3.65977 + 3.49342i) q^{70} -15.3022 q^{71} +(-5.86551 + 5.09943i) q^{72} +6.38815 q^{73} +(-2.04411 + 1.95120i) q^{74} -0.502080 q^{75} +(5.56402 - 6.71131i) q^{76} +13.9309 q^{77} +(3.65977 - 3.49342i) q^{78} +12.9717 q^{79} +(3.98271 + 0.371479i) q^{80} +6.79479 q^{81} +(2.00000 - 1.90909i) q^{82} +3.02454i q^{83} +(3.58856 + 0.166995i) q^{84} -6.79894 q^{85} +(-1.02631 + 0.979659i) q^{86} +1.45348i q^{87} +(-7.22618 - 8.31175i) q^{88} -12.1961i q^{89} +(-2.68329 - 2.81106i) q^{90} +25.4918 q^{91} +(6.45050 + 0.300176i) q^{92} +3.16287 q^{93} +(-5.93639 + 5.66656i) q^{94} +(3.48135 + 2.62301i) q^{95} +(-1.76181 - 2.22771i) q^{96} +9.60294i q^{97} +(5.66256 + 5.93219i) q^{98} +10.7003i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{4} - 20 q^{5} - 6 q^{6} + 16 q^{9}+O(q^{10}) $ 20 * q + 2 * q^4 - 20 * q^5 - 6 * q^6 + 16 * q^9	$ 20 q + 2 q^{4} - 20 q^{5} - 6 q^{6} + 16 q^{9} - 2 q^{16} + 20 q^{17} - 2 q^{20} + 26 q^{24} + 20 q^{25} - 14 q^{26} - 14 q^{28} + 6 q^{30} - 4 q^{36} + 10 q^{38} - 42 q^{42} + 8 q^{44} - 16 q^{45} - 30 q^{54} - 36 q^{57} + 62 q^{58} - 24 q^{61} - 40 q^{62} + 50 q^{64} + 40 q^{66} + 6 q^{68} - 36 q^{73} - 36 q^{74} - 28 q^{76} - 32 q^{77} + 2 q^{80} + 60 q^{81} + 40 q^{82} - 20 q^{85} + 26 q^{92} - 122 q^{96}+O(q^{100}) $ 20 * q + 2 * q^4 - 20 * q^5 - 6 * q^6 + 16 * q^9 - 2 * q^16 + 20 * q^17 - 2 * q^20 + 26 * q^24 + 20 * q^25 - 14 * q^26 - 14 * q^28 + 6 * q^30 - 4 * q^36 + 10 * q^38 - 42 * q^42 + 8 * q^44 - 16 * q^45 - 30 * q^54 - 36 * q^57 + 62 * q^58 - 24 * q^61 - 40 * q^62 + 50 * q^64 + 40 * q^66 + 6 * q^68 - 36 * q^73 - 36 * q^74 - 28 * q^76 - 32 * q^77 + 2 * q^80 + 60 * q^81 + 40 * q^82 - 20 * q^85 + 26 * q^92 - 122 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−0.976481	−	1.02298i	−0.690476	−	0.723355i
$2$	−0.976481	−	1.02298i	−0.690476	−	0.723355i
$3$	−0.502080			−0.289876			−0.144938	−	0.989441i	$-0.546298\pi$
$3$	−0.502080			−0.289876			−0.144938	+	0.989441i	$0.546298\pi$
$4$	−0.0929701	+	1.99784i	−0.0464851	+	0.998919i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	0.490271	+	0.513617i	0.200152	+	0.209683i
$7$			3.57756i			1.35219i	0.736814	+	0.676095i	$0.236329\pi$
$7$			3.57756i			1.35219i	−0.736814	+	0.676095i	$0.763671\pi$
$8$	2.13453	−	1.85574i	0.754670	−	0.656105i
$9$	−2.74792			−0.915972
$10$	0.976481	+	1.02298i	0.308790	+	0.323494i
$11$		−	3.89395i		−	1.17407i	−0.809561	−	0.587035i	$-0.800295\pi$
$11$		−	3.89395i		−	1.17407i	0.809561	−	0.587035i	$-0.199705\pi$
$12$	0.0466784	−	1.00307i	0.0134749	−	0.289563i
$13$		−	7.12548i		−	1.97625i	−0.153643	−	0.988126i	$-0.549100\pi$
$13$		−	7.12548i		−	1.97625i	0.153643	−	0.988126i	$-0.450900\pi$
$14$	3.65977	−	3.49342i	0.978114	−	0.933656i
$15$	0.502080			0.129636
$16$	−3.98271	−	0.371479i	−0.995678	−	0.0928696i
$17$	6.79894			1.64899			0.824493	−	0.565872i	$-0.191460\pi$
$17$	6.79894			1.64899			0.824493	+	0.565872i	$0.191460\pi$
$18$	2.68329	+	2.81106i	0.632457	+	0.662573i
$19$	−3.48135	−	2.62301i	−0.798676	−	0.601761i
$19$	−3.48135	−	2.62301i	−0.798676	−	0.601761i
$20$	0.0929701	−	1.99784i	0.0207888	−	0.446730i
$21$		−	1.79622i		−	0.391968i
$22$	−3.98343	+	3.80237i	−0.849270	+	0.810668i
$23$		−	3.22874i		−	0.673239i	−0.941641	−	0.336619i	$-0.890716\pi$
$23$		−	3.22874i		−	0.673239i	0.941641	−	0.336619i	$-0.109284\pi$
$24$	−1.07170	+	0.931732i	−0.218761	+	0.190189i
$25$	1.00000			0.200000
$26$	−7.28921	+	6.95790i	−1.42953	+	1.36456i
$27$	2.88591			0.555394
$28$	−7.14739	−	0.332606i	−1.35073	−	0.0628567i
$29$		−	2.89493i		−	0.537574i	−0.963200	−	0.268787i	$-0.913377\pi$
$29$		−	2.89493i		−	0.537574i	0.963200	−	0.268787i	$-0.0866228\pi$
$30$	−0.490271	−	0.513617i	−0.0895109	−	0.0937732i
$31$	−6.29953			−1.13143			−0.565714	−	0.824601i	$-0.691399\pi$
$31$	−6.29953			−1.13143			−0.565714	+	0.824601i	$0.691399\pi$
$32$	3.50903	+	4.43697i	0.620314	+	0.784353i
$33$			1.95508i			0.340335i
$34$	−6.63904	−	6.95517i	−1.13859	−	1.19280i
$35$		−	3.57756i		−	0.604718i
$36$	0.255474	−	5.48989i	0.0425790	−	0.914982i
$37$		−	1.99820i		−	0.328502i	−0.986419	−	0.164251i	$-0.947479\pi$
$37$		−	1.99820i		−	0.328502i	0.986419	−	0.164251i	$-0.0525206\pi$
$38$	0.716184	+	6.12267i	0.116180	+	0.993228i
$39$			3.57756i			0.572868i
$40$	−2.13453	+	1.85574i	−0.337499	+	0.293419i
$41$			1.95508i			0.305331i	0.988278	+	0.152666i	$0.0487858\pi$
$41$			1.95508i			0.305331i	−0.988278	+	0.152666i	$0.951214\pi$
$42$	−1.83750	+	1.75398i	−0.283532	+	0.270644i
$43$		−	1.00325i		−	0.152995i	−0.997070	−	0.0764975i	$-0.975626\pi$
$43$		−	1.00325i		−	0.152995i	0.997070	−	0.0764975i	$-0.0243737\pi$
$44$	7.77949	+	0.362021i	1.17280	+	0.0545768i
$45$	2.74792			0.409635
$46$	−3.30293	+	3.15280i	−0.486991	+	0.464855i
$47$		−	5.80305i		−	0.846461i	−0.906022	−	0.423231i	$-0.860896\pi$
$47$		−	5.80305i		−	0.846461i	0.906022	−	0.423231i	$-0.139104\pi$
$48$	1.99964	+	0.186512i	0.288623	+	0.0269207i
$49$	−5.79894			−0.828420
$50$	−0.976481	−	1.02298i	−0.138095	−	0.144671i
$51$	−3.41361			−0.478001
$52$	14.2356	+	0.662457i	1.97412	+	0.0918663i
$53$			1.75310i			0.240807i	0.992725	+	0.120403i	$0.0384188\pi$
$53$			1.75310i			0.240807i	−0.992725	+	0.120403i	$0.961581\pi$
$54$	−2.81804	−	2.95223i	−0.383487	−	0.401747i
$55$			3.89395i			0.525060i
$56$	6.63904	+	7.63641i	0.887179	+	1.02046i
$57$	1.74792	+	1.31696i	0.231517	+	0.174436i
$58$	−2.96145	+	2.82684i	−0.388857	+	0.371182i
$59$	4.07679			0.530752			0.265376	−	0.964145i	$-0.414504\pi$
$59$	4.07679			0.530752			0.265376	+	0.964145i	$0.414504\pi$
$60$	−0.0466784	+	1.00307i	−0.00602616	+	0.129496i
$61$	−7.38399			−0.945423			−0.472712	−	0.881217i	$-0.656725\pi$
$61$	−7.38399			−0.945423			−0.472712	+	0.881217i	$0.656725\pi$
$62$	6.15137	+	6.44428i	0.781224	+	0.818424i
$63$		−	9.83084i		−	1.23857i
$64$	1.11243	−	7.92228i	0.139053	−	0.990285i
$65$			7.12548i			0.883807i
$66$	2.00000	−	1.90909i	0.246183	−	0.234993i
$67$	−6.64659			−0.812011			−0.406005	−	0.913871i	$-0.633079\pi$
$67$	−6.64659			−0.812011			−0.406005	+	0.913871i	$0.633079\pi$
$68$	−0.632099	+	13.5832i	−0.0766532	+	1.64720i
$69$			1.62109i			0.195156i
$70$	−3.65977	+	3.49342i	−0.437426	+	0.417544i
$71$	−15.3022			−1.81604			−0.908021	−	0.418924i	$-0.862407\pi$
$71$	−15.3022			−1.81604			−0.908021	+	0.418924i	$0.862407\pi$
$72$	−5.86551	+	5.09943i	−0.691256	+	0.600973i
$73$	6.38815			0.747676			0.373838	−	0.927494i	$-0.378042\pi$
$73$	6.38815			0.747676			0.373838	+	0.927494i	$0.378042\pi$
$74$	−2.04411	+	1.95120i	−0.237623	+	0.226823i
$75$	−0.502080			−0.0579752
$76$	5.56402	−	6.71131i	0.638237	−	0.769840i
$77$	13.9309			1.58757
$78$	3.65977	−	3.49342i	0.414387	−	0.395552i
$79$	12.9717			1.45943			0.729717	−	0.683749i	$-0.239652\pi$
$79$	12.9717			1.45943			0.729717	+	0.683749i	$0.239652\pi$
$80$	3.98271	+	0.371479i	0.445281	+	0.0415326i
$81$	6.79479			0.754976
$82$	2.00000	−	1.90909i	0.220863	−	0.210824i
$83$			3.02454i			0.331986i	0.986127	+	0.165993i	$0.0530829\pi$
$83$			3.02454i			0.331986i	−0.986127	+	0.165993i	$0.946917\pi$
$84$	3.58856	+	0.166995i	0.391544	+	0.0182206i
$85$	−6.79894			−0.737449
$86$	−1.02631	+	0.979659i	−0.110670	+	0.105639i
$87$			1.45348i			0.155830i
$88$	−7.22618	−	8.31175i	−0.770313	−	0.886036i
$89$		−	12.1961i		−	1.29279i	−0.763004	−	0.646393i	$-0.776277\pi$
$89$		−	12.1961i		−	1.29279i	0.763004	−	0.646393i	$-0.223723\pi$
$90$	−2.68329	−	2.81106i	−0.282843	−	0.296312i
$91$	25.4918			2.67227
$92$	6.45050	+	0.300176i	0.672511	+	0.0312955i
$93$	3.16287			0.327974
$94$	−5.93639	+	5.66656i	−0.612292	+	0.584461i
$95$	3.48135	+	2.62301i	0.357179	+	0.269116i
$96$	−1.76181	−	2.22771i	−0.179814	−	0.227365i
$97$			9.60294i			0.975031i	0.873114	+	0.487515i	$0.162097\pi$
$97$			9.60294i			0.975031i	−0.873114	+	0.487515i	$0.837903\pi$
$98$	5.66256	+	5.93219i	0.572005	+	0.599242i
$99$			10.7003i			1.07542i
$100$	−0.0929701	+	1.99784i	−0.00929701	+	0.199784i
$101$	3.05103			0.303589			0.151794	−	0.988412i	$-0.451495\pi$
$101$	3.05103			0.303589			0.151794	+	0.988412i	$0.451495\pi$
$102$	3.33333	+	3.49205i	0.330049	+	0.345765i
$103$	−3.57471			−0.352226			−0.176113	−	0.984370i	$-0.556352\pi$
$103$	−3.57471			−0.352226			−0.176113	+	0.984370i	$0.556352\pi$
$104$	−13.2231	−	15.2095i	−1.29663	−	1.49142i
$105$			1.79622i			0.175293i
$106$	1.79338	−	1.71187i	0.174189	−	0.166271i
$107$	8.12795			0.785759			0.392879	−	0.919590i	$-0.371479\pi$
$107$	8.12795			0.785759			0.392879	+	0.919590i	$0.371479\pi$
$108$	−0.268304	+	5.76559i	−0.0258175	+	0.554794i
$109$			9.80491i			0.939140i	0.882895	+	0.469570i	$0.155591\pi$
$109$			9.80491i			0.939140i	−0.882895	+	0.469570i	$0.844409\pi$
$110$	3.98343	−	3.80237i	0.379805	−	0.362542i
$111$			1.00325i			0.0952247i
$112$	1.32899	−	14.2484i	0.125577	−	1.34635i
$113$		−	14.0168i		−	1.31859i	−0.751884	−	0.659295i	$-0.770855\pi$
$113$		−	14.0168i		−	1.31859i	0.751884	−	0.659295i	$-0.229145\pi$
$114$	−0.359582	−	3.07407i	−0.0336779	−	0.287913i
$115$			3.22874i			0.301082i
$116$	5.78359	+	0.269142i	0.536993	+	0.0249892i
$117$			19.5802i			1.81019i
$118$	−3.98090	−	4.17047i	−0.366472	−	0.383922i
$119$			24.3236i			2.22974i
$120$	1.07170	−	0.931732i	0.0978327	−	0.0850551i
$121$	−4.16287			−0.378442
$122$	7.21033	+	7.55367i	0.652792	+	0.683877i
$123$		−	0.981604i		−	0.0885083i
$124$	0.585668	−	12.5854i	0.0525945	−	1.13021i
$125$	−1.00000			−0.0894427
$126$	−10.0567	+	9.59962i	−0.895925	+	0.855202i
$127$	−8.87007			−0.787092			−0.393546	−	0.919305i	$-0.628752\pi$
$127$	−8.87007			−0.787092			−0.393546	+	0.919305i	$0.628752\pi$
$128$	−9.19059	+	6.59796i	−0.812341	+	0.583183i
$129$			0.503714i			0.0443496i
$130$	7.28921	−	6.95790i	0.639306	−	0.610248i
$131$		−	13.7248i		−	1.19914i	−0.800322	−	0.599570i	$-0.795338\pi$
$131$		−	13.7248i		−	1.19914i	0.800322	−	0.599570i	$-0.204662\pi$
$132$	−3.90592	−	0.181764i	−0.339967	−	0.0158205i
$133$	9.38399	−	12.4547i	0.813695	−	1.07996i
$134$	6.49027	+	6.79932i	0.560674	+	0.587372i
$135$	−2.88591			−0.248380
$136$	14.5125	−	12.6171i	1.24444	−	1.08191i
$137$	−10.7211			−0.915967			−0.457983	−	0.888961i	$-0.651428\pi$
$137$	−10.7211			−0.915967			−0.457983	+	0.888961i	$0.651428\pi$
$138$	1.65834	−	1.58296i	0.141167	−	0.134750i
$139$		−	7.63778i		−	0.647828i	−0.946087	−	0.323914i	$-0.895001\pi$
$139$		−	7.63778i		−	0.647828i	0.946087	−	0.323914i	$-0.104999\pi$
$140$	7.14739	+	0.332606i	0.604064	+	0.0281104i
$141$			2.91359i			0.245369i
$142$	14.9424	+	15.6539i	1.25393	+	1.31364i
$143$	−27.7463			−2.32026
$144$	10.9442	+	1.02079i	0.912013	+	0.0850660i
$145$			2.89493i			0.240411i
$146$	−6.23790	−	6.53494i	−0.516253	−	0.540835i
$147$	2.91153			0.240139
$148$	3.99207	+	0.185773i	0.328147	+	0.0152704i
$149$	0.538178			0.0440893			0.0220446	−	0.999757i	$-0.492982\pi$
$149$	0.538178			0.0440893			0.0220446	+	0.999757i	$0.492982\pi$
$150$	0.490271	+	0.513617i	0.0400305	+	0.0419366i
$151$	4.66389			0.379542			0.189771	−	0.981828i	$-0.439225\pi$
$151$	4.66389			0.379542			0.189771	+	0.981828i	$0.439225\pi$
$152$	−12.2987	+	0.861595i	−0.997555	+	0.0698846i
$153$	−18.6829			−1.51042
$154$	−13.6032	−	14.2510i	−1.09618	−	1.14838i
$155$	6.29953			0.505990
$156$	−7.14739	−	0.332606i	−0.572249	−	0.0266298i
$157$	−15.1871			−1.21206			−0.606031	−	0.795441i	$-0.707239\pi$
$157$	−15.1871			−1.21206			−0.606031	+	0.795441i	$0.707239\pi$
$158$	−12.6667	−	13.2698i	−1.00770	−	1.05569i
$159$		−	0.880196i		−	0.0698041i
$160$	−3.50903	−	4.43697i	−0.277413	−	0.350773i
$161$	11.5510			0.910347
$162$	−6.63498	−	6.95092i	−0.521293	−	0.546116i
$163$			6.15187i			0.481851i	0.970544	+	0.240926i	$0.0774510\pi$
$163$			6.15187i			0.481851i	−0.970544	+	0.240926i	$0.922549\pi$
$164$	−3.90592	−	0.181764i	−0.305001	−	0.0141934i
$165$		−	1.95508i		−	0.152202i
$166$	3.09404	−	2.95340i	0.240144	−	0.229228i
$167$	−5.21034			−0.403188			−0.201594	−	0.979469i	$-0.564612\pi$
$167$	−5.21034			−0.403188			−0.201594	+	0.979469i	$0.564612\pi$
$168$	−3.33333	−	3.83409i	−0.257172	−	0.295806i
$169$	−37.7725			−2.90558
$170$	6.63904	+	6.95517i	0.509191	+	0.533437i
$171$	9.56646	+	7.20782i	0.731565	+	0.551196i
$172$	2.00434	+	0.0932727i	0.152830	+	0.00711198i
$173$			14.6118i			1.11091i	0.831545	+	0.555457i	$0.187457\pi$
$173$			14.6118i			1.11091i	−0.831545	+	0.555457i	$0.812543\pi$
$174$	1.48688	−	1.41930i	0.112720	−	0.107597i
$175$			3.57756i			0.270438i
$176$	−1.44652	+	15.5085i	−0.109036	+	1.16900i
$177$	−2.04687			−0.153852
$178$	−12.4764	+	11.9093i	−0.935144	+	0.892639i
$179$	11.7809			0.880543			0.440272	−	0.897865i	$-0.354882\pi$
$179$	11.7809			0.880543			0.440272	+	0.897865i	$0.354882\pi$
$180$	−0.255474	+	5.48989i	−0.0190419	+	0.409192i
$181$		−	0.0159023i		−	0.00118201i	−1.00000		0.000591006i	$-0.999812\pi$
$181$		−	0.0159023i		−	0.00118201i	1.00000		0.000591006i	$-0.000188123\pi$
$182$	−24.8923	−	26.0776i	−1.84514	−	1.93300i
$183$	3.70735			0.274056
$184$	−5.99171	−	6.89184i	−0.441715	−	0.508073i
$185$			1.99820i			0.146910i
$186$	−3.08848	−	3.23554i	−0.226458	−	0.237242i
$187$		−	26.4748i		−	1.93603i
$188$	11.5935	+	0.539510i	0.845546	+	0.0393478i
$189$			10.3245i			0.750999i
$190$	−0.716184	−	6.12267i	−0.0519575	−	0.444185i
$191$			9.84162i			0.712114i	0.934464	+	0.356057i	$0.115879\pi$
$191$			9.84162i			0.712114i	−0.934464	+	0.356057i	$0.884121\pi$
$192$	−0.558527	+	3.97762i	−0.0403082	+	0.287060i
$193$		−	8.24047i		−	0.593162i	−0.955008	−	0.296581i	$-0.904154\pi$
$193$		−	8.24047i		−	0.593162i	0.955008	−	0.296581i	$-0.0958465\pi$
$194$	9.82360	−	9.37709i	0.705293	−	0.673235i
$195$		−	3.57756i		−	0.256194i
$196$	0.539129	−	11.5853i	0.0385092	−	0.827525i
$197$	6.33297			0.451205			0.225603	−	0.974219i	$-0.427565\pi$
$197$	6.33297			0.451205			0.225603	+	0.974219i	$0.427565\pi$
$198$	10.9461	−	10.4486i	0.777908	−	0.742549i
$199$			8.10430i			0.574498i	0.957856	+	0.287249i	$0.0927408\pi$
$199$			8.10430i			0.574498i	−0.957856	+	0.287249i	$0.907259\pi$
$200$	2.13453	−	1.85574i	0.150934	−	0.131221i
$201$	3.33712			0.235382
$202$	−2.97927	−	3.12114i	−0.209621	−	0.219602i
$203$	10.3568			0.726903
$204$	0.317364	−	6.81985i	0.0222199	−	0.477485i
$205$		−	1.95508i		−	0.136548i
$206$	3.49063	+	3.65685i	0.243204	+	0.254785i
$207$			8.87230i			0.616668i
$208$	−2.64696	+	28.3787i	−0.183534	+	1.96771i
$209$	−10.2139	+	13.5562i	−0.706510	+	0.937703i
$210$	1.83750	−	1.75398i	0.126799	−	0.121036i
$211$	−19.0056			−1.30840			−0.654200	−	0.756322i	$-0.726995\pi$
$211$	−19.0056			−1.30840			−0.654200	+	0.756322i	$0.726995\pi$
$212$	−3.50241	−	0.162986i	−0.240546	−	0.0111939i
$213$	7.68295			0.526427
$214$	−7.93679	−	8.31472i	−0.542548	−	0.568383i
$215$			1.00325i			0.0684214i
$216$	6.16006	−	5.35552i	0.419139	−	0.364397i
$217$		−	22.5369i		−	1.52991i
$218$	10.0302	−	9.57431i	0.679332	−	0.648454i
$219$	−3.20736			−0.216733
$220$	−7.77949	−	0.362021i	−0.524493	−	0.0244075i
$221$		−	48.4457i		−	3.25881i
$222$	1.02631	−	0.979659i	0.0688813	−	0.0657504i
$223$	29.1455			1.95173			0.975863	−	0.218382i	$-0.0700778\pi$
$223$	29.1455			1.95173			0.975863	+	0.218382i	$0.0700778\pi$
$224$	−15.8735	+	12.5538i	−1.06060	+	0.838784i
$225$	−2.74792			−0.183194
$226$	−14.3389	+	13.6871i	−0.953809	+	0.910455i
$227$	23.5845			1.56536			0.782678	−	0.622427i	$-0.213853\pi$
$227$	23.5845			1.56536			0.782678	+	0.622427i	$0.213853\pi$
$228$	−2.79358	+	3.36961i	−0.185009	+	0.223158i
$229$	−17.0753			−1.12836			−0.564182	−	0.825650i	$-0.690808\pi$
$229$	−17.0753			−1.12836			−0.564182	+	0.825650i	$0.690808\pi$
$230$	3.30293	−	3.15280i	0.217789	−	0.207890i
$231$	−6.99440			−0.460198
$232$	−5.37224	−	6.17930i	−0.352705	−	0.405691i
$233$	22.2566			1.45808			0.729039	−	0.684473i	$-0.239967\pi$
$233$	22.2566			1.45808			0.729039	+	0.684473i	$0.239967\pi$
$234$	20.0301	−	19.1197i	1.30941	−	1.24989i
$235$			5.80305i			0.378549i
$236$	−0.379019	+	8.14476i	−0.0246721	+	0.530179i
$237$	−6.51285			−0.423055
$238$	24.8826	−	23.7516i	1.61290	−	1.53959i
$239$		−	3.71140i		−	0.240070i	−0.992770	−	0.120035i	$-0.961699\pi$
$239$		−	3.71140i		−	0.240070i	0.992770	−	0.120035i	$-0.0383008\pi$
$240$	−1.99964	−	0.186512i	−0.129076	−	0.0120393i
$241$			11.7168i			0.754745i	0.926061	+	0.377373i	$0.123172\pi$
$241$			11.7168i			0.754745i	−0.926061	+	0.377373i	$0.876828\pi$
$242$	4.06496	+	4.25852i	0.261305	+	0.273748i
$243$	−12.0693			−0.774244
$244$	0.686491	−	14.7520i	0.0439481	−	0.944401i
$245$	5.79894			0.370481
$246$	−1.00416	+	0.958518i	−0.0640229	+	0.0611128i
$247$	−18.6902	+	24.8063i	−1.18923	+	1.57839i
$248$	−13.4465	+	11.6903i	−0.853855	+	0.742335i
$249$		−	1.51856i		−	0.0962347i
$250$	0.976481	+	1.02298i	0.0617581	+	0.0646988i
$251$		−	1.13709i		−	0.0717727i	−0.999356	−	0.0358863i	$-0.988575\pi$
$251$		−	1.13709i		−	0.0717727i	0.999356	−	0.0358863i	$-0.0114254\pi$
$252$	19.6404	+	0.913974i	1.23723	+	0.0575750i
$253$	−12.5726			−0.790430
$254$	8.66146	+	9.07389i	0.543468	+	0.569347i
$255$	3.41361			0.213769
$256$	15.7240	+	2.95898i	0.982750	+	0.184937i
$257$			11.4583i			0.714746i	0.933962	+	0.357373i	$0.116328\pi$
$257$			11.4583i			0.714746i	−0.933962	+	0.357373i	$0.883672\pi$
$258$	0.515289	−	0.491867i	0.0320805	−	0.0306223i
$259$	7.14867			0.444197
$260$	−14.2356	−	0.662457i	−0.882852	−	0.0410838i
$261$			7.95501i			0.492403i
$262$	−14.0402	+	13.4020i	−0.867404	+	0.827978i
$263$		−	18.3907i		−	1.13402i	−0.823710	−	0.567011i	$-0.808100\pi$
$263$		−	18.3907i		−	1.13402i	0.823710	−	0.567011i	$-0.191900\pi$
$264$	3.62812	+	4.17316i	0.223295	+	0.256841i
$265$		−	1.75310i		−	0.107692i
$266$	−21.9042	+	2.56219i	−1.34303	+	0.157098i
$267$			6.12343i			0.374748i
$268$	0.617935	−	13.2788i	0.0377464	−	0.811133i
$269$			12.4869i			0.761341i	0.924711	+	0.380671i	$0.124307\pi$
$269$			12.4869i			0.761341i	−0.924711	+	0.380671i	$0.875693\pi$
$270$	2.81804	+	2.95223i	0.171500	+	0.179667i
$271$			24.8063i			1.50688i	0.657520	+	0.753438i	$0.271606\pi$
$271$			24.8063i			1.50688i	−0.657520	+	0.753438i	$0.728394\pi$
$272$	−27.0782	−	2.52566i	−1.64186	−	0.153141i
$273$	−12.7989			−0.774627
$274$	10.4690	+	10.9675i	0.632453	+	0.662569i
$275$		−	3.89395i		−	0.234814i
$276$	−3.23867	−	0.150713i	−0.194945	−	0.00907183i
$277$	4.19543			0.252079			0.126039	−	0.992025i	$-0.459773\pi$
$277$	4.19543			0.252079			0.126039	+	0.992025i	$0.459773\pi$
$278$	−7.81329	+	7.45815i	−0.468610	+	0.447310i
$279$	17.3106			1.03636
$280$	−6.63904	−	7.63641i	−0.396758	−	0.456363i
$281$		−	8.96483i		−	0.534797i	−0.963586	−	0.267398i	$-0.913836\pi$
$281$		−	8.96483i		−	0.534797i	0.963586	−	0.267398i	$-0.0861639\pi$
$282$	2.98054	−	2.84507i	0.177489	−	0.169421i
$283$		−	20.7461i		−	1.23323i	−0.787266	−	0.616613i	$-0.788504\pi$
$283$		−	20.7461i		−	1.23323i	0.787266	−	0.616613i	$-0.211496\pi$
$284$	1.42265	−	30.5714i	0.0844189	−	1.81408i
$285$	−1.74792	−	1.31696i	−0.103538	−	0.0780101i
$286$	27.0937	+	28.3839i	1.60209	+	1.67837i
$287$	−6.99440			−0.412866
$288$	−9.64252	−	12.1924i	−0.568191	−	0.718445i
$289$	29.2256			1.71915
$290$	2.96145	−	2.82684i	0.173902	−	0.165998i
$291$		−	4.82144i		−	0.282638i
$292$	−0.593907	+	12.7625i	−0.0347558	+	0.746868i
$293$			22.3730i			1.30704i	0.756907	+	0.653522i	$0.226709\pi$
$293$			22.3730i			1.30704i	−0.756907	+	0.653522i	$0.773291\pi$
$294$	−2.84306	−	2.97844i	−0.165810	−	0.173706i
$295$	−4.07679			−0.237360
$296$	−3.70814	−	4.26521i	−0.215531	−	0.247910i
$297$		−	11.2376i		−	0.652072i
$298$	−0.525520	−	0.550544i	−0.0304426	−	0.0318922i
$299$	−23.0063			−1.33049
$300$	0.0466784	−	1.00307i	0.00269498	−	0.0579125i
$301$	3.58921			0.206878
$302$	−4.55420	−	4.77106i	−0.262065	−	0.274544i
$303$	−1.53186			−0.0880030
$304$	12.8908	+	11.7400i	0.739339	+	0.673333i
$305$	7.38399			0.422806
$306$	18.2435	+	19.1122i	1.04291	+	1.09257i
$307$	9.37823			0.535244			0.267622	−	0.963524i	$-0.413762\pi$
$307$	9.37823			0.535244			0.267622	+	0.963524i	$0.413762\pi$
$308$	−1.29515	+	27.8316i	−0.0737982	+	1.58585i
$309$	1.79479			0.102102
$310$	−6.15137	−	6.44428i	−0.349374	−	0.366010i
$311$		−	13.9073i		−	0.788613i	−0.918979	−	0.394307i	$-0.870985\pi$
$311$		−	13.9073i		−	0.788613i	0.918979	−	0.394307i	$-0.129015\pi$
$312$	6.63904	+	7.63641i	0.375862	+	0.432326i
$313$	25.1406			1.42103			0.710515	−	0.703682i	$-0.248462\pi$
$313$	25.1406			1.42103			0.710515	+	0.703682i	$0.248462\pi$
$314$	14.8299	+	15.5361i	0.836900	+	0.876751i
$315$			9.83084i			0.553905i
$316$	−1.20598	+	25.9154i	−0.0678419	+	1.45786i
$317$		−	22.9140i		−	1.28698i	−0.765454	−	0.643491i	$-0.777486\pi$
$317$		−	22.9140i		−	1.28698i	0.765454	−	0.643491i	$-0.222514\pi$
$318$	−0.900422	+	0.859495i	−0.0504931	+	0.0481981i
$319$	−11.2727			−0.631150
$320$	−1.11243	+	7.92228i	−0.0621866	+	0.442869i
$321$	−4.08088			−0.227773
$322$	−11.2793	−	11.8164i	−0.628573	−	0.658504i
$323$	−23.6695	−	17.8337i	−1.31701	−	0.992295i
$324$	−0.631712	+	13.5749i	−0.0350951	+	0.754160i
$325$		−	7.12548i		−	0.395251i
$326$	6.29323	−	6.00718i	0.348550	−	0.332707i
$327$		−	4.92285i		−	0.272234i
$328$	3.62812	+	4.17316i	0.200329	+	0.230424i
$329$	20.7608			1.14458
$330$	−2.00000	+	1.90909i	−0.110096	+	0.105092i
$331$	−5.92935			−0.325907			−0.162953	−	0.986634i	$-0.552102\pi$
$331$	−5.92935			−0.325907			−0.162953	+	0.986634i	$0.552102\pi$
$332$	−6.04253	−	0.281191i	−0.331627	−	0.0154324i
$333$			5.49088i			0.300898i
$334$	5.08780	+	5.33006i	0.278392	+	0.291648i
$335$	6.64659			0.363142
$336$	−0.667258	+	7.15383i	−0.0364019	+	0.390274i
$337$		−	1.82068i		−	0.0991786i	−0.998770	−	0.0495893i	$-0.984209\pi$
$337$		−	1.82068i		−	0.0991786i	0.998770	−	0.0495893i	$-0.0157912\pi$
$338$	36.8841	+	38.6404i	2.00623	+	2.10176i
$339$			7.03755i			0.382228i
$340$	0.632099	−	13.5832i	0.0342804	−	0.736652i
$341$			24.5301i			1.32838i
$342$	−1.96801	−	16.8246i	−0.106418	−	0.909769i
$343$			4.29685i			0.232008i
$344$	−1.86178	−	2.14148i	−0.100381	−	0.115461i
$345$		−	1.62109i		−	0.0872763i
$346$	14.9476	−	14.2681i	0.803585	−	0.767060i
$347$		−	7.75148i		−	0.416121i	−0.978116	−	0.208061i	$-0.933285\pi$
$347$		−	7.75148i		−	0.416121i	0.978116	−	0.208061i	$-0.0667152\pi$
$348$	−2.90383	−	0.135131i	−0.155661	−	0.00724376i
$349$	9.82880			0.526123			0.263062	−	0.964779i	$-0.415268\pi$
$349$	9.82880			0.526123			0.263062	+	0.964779i	$0.415268\pi$
$350$	3.65977	−	3.49342i	0.195623	−	0.186731i
$351$		−	20.5635i		−	1.09760i
$352$	17.2774	−	13.6640i	0.920886	−	0.728293i
$353$	18.5344			0.986485			0.493242	−	0.869892i	$-0.335812\pi$
$353$	18.5344			0.986485			0.493242	+	0.869892i	$0.335812\pi$
$354$	1.99873	+	2.09391i	0.106231	+	0.111290i
$355$	15.3022			0.812159
$356$	24.3659	+	1.13388i	1.29139	+	0.0600953i
$357$		−	12.2124i		−	0.646349i
$358$	−11.5038	−	12.0516i	−0.607994	−	0.636945i
$359$		−	32.0358i		−	1.69078i	−0.534147	−	0.845392i	$-0.679367\pi$
$359$		−	32.0358i		−	1.69078i	0.534147	−	0.845392i	$-0.320633\pi$
$360$	5.86551	−	5.09943i	0.309139	−	0.268763i
$361$	5.23959	+	18.2633i	0.275768	+	0.961224i
$362$	−0.0162678	+	0.0155283i	−0.000855014	+	0.000816151i
$363$	2.09009			0.109701
$364$	−2.36998	+	50.9286i	−0.124221	+	2.66938i
$365$	−6.38815			−0.334371
$366$	−3.62016	−	3.79254i	−0.189229	−	0.198239i
$367$			0.296114i			0.0154570i	0.999970	+	0.00772851i	$0.00246009\pi$
$367$			0.296114i			0.0154570i	−0.999970	+	0.00772851i	$0.997540\pi$
$368$	−1.19941	+	12.8591i	−0.0625234	+	0.670329i
$369$		−	5.37238i		−	0.279675i
$370$	2.04411	−	1.95120i	0.106268	−	0.101438i
$371$	−6.27182			−0.325617
$372$	−0.294052	+	6.31889i	−0.0152459	+	0.327619i
$373$		−	15.3117i		−	0.792809i	−0.918076	−	0.396405i	$-0.870258\pi$
$373$		−	15.3117i		−	0.792809i	0.918076	−	0.396405i	$-0.129742\pi$
$374$	−27.0831	+	25.8521i	−1.40043	+	1.33678i
$375$	0.502080			0.0259273
$376$	−10.7690	−	12.3868i	−0.555367	−	0.638799i
$377$	−20.6277			−1.06238
$378$	10.5618	−	10.0817i	0.543239	−	0.518547i
$379$	13.1825			0.677142			0.338571	−	0.940941i	$-0.390057\pi$
$379$	13.1825			0.677142			0.338571	+	0.940941i	$0.390057\pi$
$380$	−5.56402	+	6.71131i	−0.285428	+	0.344283i
$381$	4.45349			0.228159
$382$	10.0678	−	9.61015i	0.515111	−	0.491698i
$383$	−20.5155			−1.04829			−0.524146	−	0.851629i	$-0.675615\pi$
$383$	−20.5155			−1.04829			−0.524146	+	0.851629i	$0.675615\pi$
$384$	4.61441	−	3.31271i	0.235478	−	0.169051i
$385$	−13.9309			−0.709982
$386$	−8.42982	+	8.04666i	−0.429067	+	0.409564i
$387$			2.75686i			0.140139i
$388$	−19.1851	−	0.892786i	−0.973977	−	0.0453244i
$389$	−0.230912			−0.0117077			−0.00585384	−	0.999983i	$-0.501863\pi$
$389$	−0.230912			−0.0117077			−0.00585384	+	0.999983i	$0.501863\pi$
$390$	−3.65977	+	3.49342i	−0.185320	+	0.176896i
$391$		−	21.9520i		−	1.11016i
$392$	−12.3780	+	10.7614i	−0.625184	+	0.543530i
$393$			6.89094i			0.347602i
$394$	−6.18402	−	6.47849i	−0.311546	−	0.326382i
$395$	−12.9717			−0.652679
$396$	−21.3774	−	0.994804i	−1.07425	−	0.0499908i
$397$	29.1958			1.46529			0.732647	−	0.680609i	$-0.238285\pi$
$397$	29.1958			1.46529			0.732647	+	0.680609i	$0.238285\pi$
$398$	8.29052	−	7.91369i	0.415566	−	0.396677i
$399$	−4.71151	+	6.25328i	−0.235871	+	0.313055i
$400$	−3.98271	−	0.371479i	−0.199136	−	0.0185739i
$401$		−	9.06459i		−	0.452664i	−0.974050	−	0.226332i	$-0.927327\pi$
$401$		−	9.06459i		−	0.452664i	0.974050	−	0.226332i	$-0.0726734\pi$
$402$	−3.25863	−	3.41380i	−0.162526	−	0.170265i
$403$			44.8872i			2.23599i
$404$	−0.283654	+	6.09546i	−0.0141123	+	0.303260i
$405$	−6.79479			−0.337636
$406$	−10.1132	−	10.5948i	−0.501909	−	0.525809i
$407$	−7.78089			−0.385684
$408$	−7.28645	+	6.33479i	−0.360733	+	0.313619i
$409$			38.3635i			1.89696i	0.316844	+	0.948478i	$0.397377\pi$
$409$			38.3635i			1.89696i	−0.316844	+	0.948478i	$0.602623\pi$
$410$	−2.00000	+	1.90909i	−0.0987730	+	0.0942834i
$411$	5.38286			0.265517
$412$	0.332341	−	7.14168i	0.0163733	−	0.351846i
$413$			14.5850i			0.717679i
$414$	9.07618	−	8.66364i	0.446070	−	0.425794i
$415$		−	3.02454i		−	0.148469i
$416$	31.6156	−	25.0035i	1.55008	−	1.22590i
$417$			3.83478i			0.187790i
$418$	23.8414	−	2.78879i	1.16612	−	0.136404i
$419$			21.5776i			1.05413i	0.849824	+	0.527066i	$0.176708\pi$
$419$			21.5776i			1.05413i	−0.849824	+	0.527066i	$0.823292\pi$
$420$	−3.58856	−	0.166995i	−0.175104	−	0.00814852i
$421$		−	5.14319i		−	0.250664i	−0.992115	−	0.125332i	$-0.960000\pi$
$421$		−	5.14319i		−	0.250664i	0.992115	−	0.125332i	$-0.0399995\pi$
$422$	18.5586	+	19.4423i	0.903419	+	0.946438i
$423$			15.9463i			0.775335i
$424$	3.25330	+	3.74204i	0.157994	+	0.181730i
$425$	6.79894			0.329797
$426$	−7.50225	−	7.85949i	−0.363485	−	0.380794i
$427$		−	26.4167i		−	1.27839i
$428$	−0.755657	+	16.2383i	−0.0365261	+	0.784909i
$429$	13.9309			0.672588
$430$	1.02631	−	0.979659i	0.0494930	−	0.0472434i
$431$	25.6306			1.23458			0.617291	−	0.786735i	$-0.288230\pi$
$431$	25.6306			1.23458			0.617291	+	0.786735i	$0.288230\pi$
$432$	−11.4938	−	1.07205i	−0.552994	−	0.0515793i
$433$		−	18.7674i		−	0.901905i	−0.892548	−	0.450952i	$-0.851084\pi$
$433$		−	18.7674i		−	0.901905i	0.892548	−	0.450952i	$-0.148916\pi$
$434$	−23.0548	+	22.0069i	−1.10667	+	1.05636i
$435$		−	1.45348i		−	0.0696892i
$436$	−19.5886	−	0.911564i	−0.938125	−	0.0436560i
$437$	−8.46903	+	11.2404i	−0.405129	+	0.537700i
$438$	3.13193	+	3.28106i	0.149649	+	0.156775i
$439$	−24.5788			−1.17308			−0.586541	−	0.809920i	$-0.699511\pi$
$439$	−24.5788			−1.17308			−0.586541	+	0.809920i	$0.699511\pi$
$440$	7.22618	+	8.31175i	0.344495	+	0.396247i
$441$	15.9350			0.758810
$442$	−49.5590	+	47.3063i	−2.35728	+	2.25013i
$443$		−	32.3359i		−	1.53632i	−0.640256	−	0.768162i	$-0.721172\pi$
$443$		−	32.3359i		−	1.53632i	0.640256	−	0.768162i	$-0.278828\pi$
$444$	−2.00434	−	0.0932727i	−0.0951218	−	0.00442653i
$445$			12.1961i			0.578152i
$446$	−28.4600	−	29.8152i	−1.34762	−	1.41179i
$447$	−0.270208			−0.0127804
$448$	28.3424	+	3.97978i	1.33905	+	0.188027i
$449$			15.5407i			0.733411i	0.930337	+	0.366706i	$0.119514\pi$
$449$			15.5407i			0.733411i	−0.930337	+	0.366706i	$0.880486\pi$
$450$	2.68329	+	2.81106i	0.126491	+	0.132515i
$451$	7.61297			0.358481
$452$	28.0033	+	1.30314i	1.31716	+	0.0612947i
$453$	−2.34165			−0.110020
$454$	−23.0298	−	24.1264i	−1.08084	−	1.13231i
$455$	−25.4918			−1.19508
$456$	6.17492	−	0.432589i	0.289167	−	0.0202579i
$457$	19.0541			0.891312			0.445656	−	0.895204i	$-0.352970\pi$
$457$	19.0541			0.891312			0.445656	+	0.895204i	$0.352970\pi$
$458$	16.6737	+	17.4676i	0.779109	+	0.816208i
$459$	19.6212			0.915837
$460$	−6.45050	−	0.300176i	−0.300756	−	0.0139958i
$461$	−18.3500			−0.854643			−0.427321	−	0.904100i	$-0.640543\pi$
$461$	−18.3500			−0.854643			−0.427321	+	0.904100i	$0.640543\pi$
$462$	6.82990	+	7.15512i	0.317756	+	0.332886i
$463$			14.9794i			0.696154i	0.937466	+	0.348077i	$0.113165\pi$
$463$			14.9794i			0.696154i	−0.937466	+	0.348077i	$0.886835\pi$
$464$	−1.07540	+	11.5297i	−0.0499243	+	0.535251i
$465$	−3.16287			−0.146674
$466$	−21.7331	−	22.7680i	−1.00677	−	1.05471i
$467$		−	7.41743i		−	0.343238i	−0.985163	−	0.171619i	$-0.945100\pi$
$467$		−	7.41743i		−	0.343238i	0.985163	−	0.171619i	$-0.0548998\pi$
$468$	−39.1181	−	1.82038i	−1.80824	−	0.0841469i
$469$		−	23.7786i		−	1.09799i
$470$	5.93639	−	5.66656i	0.273825	−	0.261379i
$471$	7.62513			0.351348
$472$	8.70202	−	7.56547i	0.400543	−	0.348229i
$473$	−3.90663			−0.179627
$474$	6.35967	+	6.66251i	0.292109	+	0.306019i
$475$	−3.48135	−	2.62301i	−0.159735	−	0.120352i
$476$	−48.5947	−	2.26137i	−2.22733	−	0.103650i
$477$		−	4.81737i		−	0.220572i
$478$	−3.79668	+	3.62411i	−0.173656	+	0.165763i
$479$		−	21.5411i		−	0.984239i	−0.870528	−	0.492120i	$-0.836222\pi$
$479$		−	21.5411i		−	0.984239i	0.870528	−	0.492120i	$-0.163778\pi$
$480$	1.76181	+	2.22771i	0.0804154	+	0.101681i
$481$	−14.2381			−0.649202
$482$	11.9860	−	11.4412i	0.545949	−	0.521134i
$483$	−5.79953			−0.263888
$484$	0.387022	−	8.31673i	0.0175919	−	0.378033i
$485$		−	9.60294i		−	0.436047i
$486$	11.7854	+	12.3466i	0.534597	+	0.560053i
$487$	−18.5043			−0.838508			−0.419254	−	0.907869i	$-0.637708\pi$
$487$	−18.5043			−0.838508			−0.419254	+	0.907869i	$0.637708\pi$
$488$	−15.7613	+	13.7028i	−0.713483	+	0.620297i
$489$		−	3.08873i		−	0.139677i
$490$	−5.66256	−	5.93219i	−0.255808	−	0.267989i
$491$		−	17.8190i		−	0.804158i	−0.915605	−	0.402079i	$-0.868288\pi$
$491$		−	17.8190i		−	0.804158i	0.915605	−	0.402079i	$-0.131712\pi$
$492$	1.96109	+	0.0912599i	0.0884126	+	0.00411431i
$493$		−	19.6824i		−	0.886452i
$494$	43.6270	−	5.10316i	1.96287	−	0.229602i
$495$		−	10.7003i		−	0.480941i
$496$	25.0892	+	2.34014i	1.12654	+	0.105075i
$497$		−	54.7447i		−	2.45564i
$498$	−1.55345	+	1.48284i	−0.0696119	+	0.0664478i
$499$		−	12.4972i		−	0.559450i	−0.960080	−	0.279725i	$-0.909757\pi$
$499$		−	12.4972i		−	0.559450i	0.960080	−	0.279725i	$-0.0902432\pi$
$500$	0.0929701	−	1.99784i	0.00415775	−	0.0893460i
$501$	2.61601			0.116875
$502$	−1.16322	+	1.11035i	−0.0519171	+	0.0495573i
$503$			20.1350i			0.897774i	0.893588	+	0.448887i	$0.148179\pi$
$503$			20.1350i			0.897774i	−0.893588	+	0.448887i	$0.851821\pi$
$504$	−18.2435	−	20.9842i	−0.812631	−	0.934711i
$505$	−3.05103			−0.135769
$506$	12.2769	+	12.8615i	0.545773	+	0.571762i
$507$	18.9648			0.842257
$508$	0.824652	−	17.7210i	0.0365880	−	0.786241i
$509$		−	35.7272i		−	1.58358i	−0.610792	−	0.791791i	$-0.709149\pi$
$509$		−	35.7272i		−	1.58358i	0.610792	−	0.791791i	$-0.290851\pi$
$510$	−3.33333	−	3.49205i	−0.147602	−	0.154631i
$511$			22.8540i			1.01100i
$512$	−12.3272	−	18.9747i	−0.544791	−	0.838572i
$513$	−10.0469	−	7.56979i	−0.443580	−	0.334214i
$514$	11.7215	−	11.1888i	0.517015	−	0.493515i
$515$	3.57471			0.157520
$516$	−1.00634	−	0.0468304i	−0.0443016	−	0.00206159i
$517$	−22.5968			−0.993805
$518$	−6.98054	−	7.31294i	−0.306707	−	0.321312i
$519$		−	7.33629i		−	0.322027i
$520$	13.2231	+	15.2095i	0.579870	+	0.666983i
$521$			22.0197i			0.964701i	0.875978	+	0.482350i	$0.160217\pi$
$521$			22.0197i			0.964701i	−0.875978	+	0.482350i	$0.839783\pi$
$522$	8.13781	−	7.76792i	0.356182	−	0.339993i
$523$	−1.35123			−0.0590851			−0.0295425	−	0.999564i	$-0.509405\pi$
$523$	−1.35123			−0.0590851			−0.0295425	+	0.999564i	$0.509405\pi$
$524$	27.4199	+	1.27600i	1.19784	+	0.0557421i
$525$		−	1.79622i		−	0.0783935i
$526$	−18.8133	+	17.9582i	−0.820300	+	0.783015i
$527$	−42.8301			−1.86571
$528$	0.726268	−	7.78650i	0.0316068	−	0.338864i
$529$	12.5752			0.546750
$530$	−1.79338	+	1.71187i	−0.0778996	+	0.0743588i
$531$	−11.2027			−0.486154
$532$	24.0101	+	19.9056i	1.04097	+	0.863018i
$533$	13.9309			0.603412
$534$	6.26414	−	5.97941i	0.271076	−	0.258754i
$535$	−8.12795			−0.351402
$536$	−14.1873	+	12.3344i	−0.612800	+	0.532764i
$537$	−5.91494			−0.255248
$538$	12.7739	−	12.1932i	0.550720	−	0.525688i
$539$			22.5808i			0.972624i
$540$	0.268304	−	5.76559i	0.0115460	−	0.248111i
$541$	−14.5469			−0.625418			−0.312709	−	0.949849i	$-0.601237\pi$
$541$	−14.5469			−0.625418			−0.312709	+	0.949849i	$0.601237\pi$
$542$	25.3763	−	24.2229i	1.09001	−	1.04046i
$543$			0.00798425i			0.000342637i
$544$	23.8577	+	30.1667i	1.02289	+	1.29339i
$545$		−	9.80491i		−	0.419996i
$546$	12.4979	+	13.0930i	0.534862	+	0.560331i
$547$	42.6225			1.82241			0.911204	−	0.411956i	$-0.135154\pi$
$547$	42.6225			1.82241			0.911204	+	0.411956i	$0.135154\pi$
$548$	0.996743	−	21.4190i	0.0425788	−	0.914976i
$549$	20.2906			0.865981
$550$	−3.98343	+	3.80237i	−0.169854	+	0.162134i
$551$	−7.59343	+	10.0782i	−0.323491	+	0.429348i
$552$	3.00832	+	3.46025i	0.128043	+	0.147278i
$553$			46.4072i			1.97343i
$554$	−4.09676	−	4.29183i	−0.174054	−	0.182343i
$555$		−	1.00325i		−	0.0425858i
$556$	15.2590	+	0.710086i	0.647128	+	0.0301143i
$557$	−29.7524			−1.26065			−0.630325	−	0.776331i	$-0.717078\pi$
$557$	−29.7524			−1.26065			−0.630325	+	0.776331i	$0.717078\pi$
$558$	−16.9034	−	17.7083i	−0.715580	−	0.749654i
$559$	−7.14867			−0.302357
$560$	−1.32899	+	14.2484i	−0.0561600	+	0.602105i
$561$			13.2924i			0.561207i
$562$	−9.17082	+	8.75398i	−0.386848	+	0.369264i
$563$	34.1468			1.43911			0.719557	−	0.694433i	$-0.244345\pi$
$563$	34.1468			1.43911			0.719557	+	0.694433i	$0.244345\pi$
$564$	−5.82089	−	0.270877i	−0.245104	−	0.0114060i
$565$			14.0168i			0.589691i
$566$	−21.2228	+	20.2581i	−0.892060	+	0.851513i
$567$			24.3088i			1.02087i
$568$	−32.6631	+	28.3971i	−1.37051	+	1.19151i
$569$		−	12.9930i		−	0.544696i	−0.962199	−	0.272348i	$-0.912200\pi$
$569$		−	12.9930i		−	0.544696i	0.962199	−	0.272348i	$-0.0878002\pi$
$570$	0.359582	+	3.07407i	0.0150612	+	0.128759i
$571$			9.02101i			0.377517i	0.982024	+	0.188759i	$0.0604464\pi$
$571$			9.02101i			0.377517i	−0.982024	+	0.188759i	$0.939554\pi$
$572$	2.57958	−	55.4326i	0.107857	−	2.31775i
$573$		−	4.94128i		−	0.206425i
$574$	6.82990	+	7.15512i	0.285074	+	0.298649i
$575$		−	3.22874i		−	0.134648i
$576$	−3.05686	+	21.7698i	−0.127369	+	0.907073i
$577$	5.64476			0.234994			0.117497	−	0.993073i	$-0.462513\pi$
$577$	5.64476			0.234994			0.117497	+	0.993073i	$0.462513\pi$
$578$	−28.5383	−	29.8972i	−1.18704	−	1.24356i
$579$			4.13737i			0.171943i
$580$	−5.78359	−	0.269142i	−0.240151	−	0.0111755i
$581$	−10.8205			−0.448908
$582$	−4.93223	+	4.70805i	−0.204448	+	0.195155i
$583$	6.82649			0.282724
$584$	13.6357	−	11.8548i	0.564249	−	0.490554i
$585$		−	19.5802i		−	0.809543i
$586$	22.8871	−	21.8468i	0.945457	−	0.902483i
$587$		−	1.27772i		−	0.0527371i	−0.999652	−	0.0263685i	$-0.991606\pi$
$587$		−	1.27772i		−	0.0527371i	0.999652	−	0.0263685i	$-0.00839434\pi$
$588$	−0.270686	+	5.81677i	−0.0111629	+	0.239880i
$589$	21.9309	+	16.5237i	0.903645	+	0.680849i
$590$	3.98090	+	4.17047i	0.163891	+	0.171695i
$591$	−3.17966			−0.130794
$592$	−0.742287	+	7.95825i	−0.0305078	+	0.327082i
$593$	−21.4603			−0.881271			−0.440635	−	0.897686i	$-0.645247\pi$
$593$	−21.4603			−0.881271			−0.440635	+	0.897686i	$0.645247\pi$
$594$	−11.4958	+	10.9733i	−0.471680	+	0.450240i
$595$		−	24.3236i		−	0.997172i
$596$	−0.0500345	+	1.07519i	−0.00204949	+	0.0440416i
$597$		−	4.06900i		−	0.166533i
$598$	22.4652	+	23.5350i	0.918672	+	0.962417i
$599$	8.89170			0.363305			0.181652	−	0.983363i	$-0.441855\pi$
$599$	8.89170			0.363305			0.181652	+	0.983363i	$0.441855\pi$
$600$	−1.07170	+	0.931732i	−0.0437521	+	0.0380378i
$601$		−	20.1780i		−	0.823080i	−0.911392	−	0.411540i	$-0.864991\pi$
$601$		−	20.1780i		−	0.823080i	0.911392	−	0.411540i	$-0.135009\pi$
$602$	−3.50479	−	3.67168i	−0.142845	−	0.149646i
$603$	18.2643			0.743779
$604$	−0.433603	+	9.31770i	−0.0176430	+	0.379132i
$605$	4.16287			0.169245
$606$	1.49583	+	1.56706i	0.0607640	+	0.0636574i
$607$	24.4930			0.994141			0.497071	−	0.867710i	$-0.334409\pi$
$607$	24.4930			0.994141			0.497071	+	0.867710i	$0.334409\pi$
$608$	−0.577916	−	24.6509i	−0.0234376	−	0.999725i
$609$	−5.19993			−0.210712
$610$	−7.21033	−	7.55367i	−0.291938	−	0.305839i
$611$	−41.3495			−1.67282
$612$	1.73695	−	37.3255i	0.0702122	−	1.50879i
$613$	−27.8375			−1.12435			−0.562173	−	0.827020i	$-0.690034\pi$
$613$	−27.8375			−1.12435			−0.562173	+	0.827020i	$0.690034\pi$
$614$	−9.15767	−	9.59373i	−0.369573	−	0.387172i
$615$			0.981604i			0.0395821i
$616$	29.7358	−	25.8521i	1.19809	−	1.04161i
$617$	−1.81325			−0.0729988			−0.0364994	−	0.999334i	$-0.511621\pi$
$617$	−1.81325			−0.0729988			−0.0364994	+	0.999334i	$0.511621\pi$
$618$	−1.75258	−	1.83603i	−0.0704990	−	0.0738560i
$619$		−	11.3168i		−	0.454859i	−0.973795	−	0.227429i	$-0.926968\pi$
$619$		−	11.3168i		−	0.454859i	0.973795	−	0.227429i	$-0.0730321\pi$
$620$	−0.585668	+	12.5854i	−0.0235210	+	0.505443i
$621$		−	9.31786i		−	0.373913i
$622$	−14.2269	+	13.5803i	−0.570447	+	0.544519i
$623$	43.6324			1.74809
$624$	1.32899	−	14.2484i	0.0532021	−	0.570392i
$625$	1.00000			0.0400000
$626$	−24.5493	−	25.7183i	−0.981188	−	1.02791i
$627$	5.12819	−	6.80630i	0.204800	−	0.271817i
$628$	1.41195	−	30.3413i	0.0563428	−	1.21075i
$629$		−	13.5856i		−	0.541695i
$630$	10.0567	−	9.59962i	0.400670	−	0.382458i
$631$		−	34.9589i		−	1.39169i	−0.718191	−	0.695846i	$-0.755030\pi$
$631$		−	34.9589i		−	1.39169i	0.718191	−	0.695846i	$-0.244970\pi$
$632$	27.6886	−	24.0722i	1.10139	−	0.957542i
$633$	9.54233			0.379274
$634$	−23.4406	+	22.3751i	−0.930944	+	0.888630i
$635$	8.87007			0.351998
$636$	1.75849	+	0.0818319i	0.0697286	+	0.00324485i
$637$			41.3203i			1.63717i
$638$	11.0076	+	11.5317i	0.435794	+	0.456546i
$639$	42.0493			1.66344
$640$	9.19059	−	6.59796i	0.363290	−	0.260807i
$641$		−	35.5815i		−	1.40539i	−0.711493	−	0.702693i	$-0.751981\pi$
$641$		−	35.5815i		−	1.40539i	0.711493	−	0.702693i	$-0.248019\pi$
$642$	3.98490	+	4.17465i	0.157272	+	0.164760i
$643$		−	18.0905i		−	0.713419i	−0.934215	−	0.356710i	$-0.883899\pi$
$643$		−	18.0905i		−	0.713419i	0.934215	−	0.356710i	$-0.116101\pi$
$644$	−1.07390	+	23.0771i	−0.0423176	+	0.909363i
$645$		−	0.503714i		−	0.0198337i
$646$	4.86930	+	41.6277i	0.191580	+	1.63782i
$647$			37.1859i			1.46193i	0.682416	+	0.730964i	$0.260929\pi$
$647$			37.1859i			1.46193i	−0.682416	+	0.730964i	$0.739071\pi$
$648$	14.5037	−	12.6094i	0.569758	−	0.495344i
$649$		−	15.8748i		−	0.623141i
$650$	−7.28921	+	6.95790i	−0.285907	+	0.272911i
$651$			11.3153i			0.443483i
$652$	−12.2904	−	0.571940i	−0.481331	−	0.0223989i
$653$	23.8375			0.932833			0.466416	−	0.884565i	$-0.345545\pi$
$653$	23.8375			0.932833			0.466416	+	0.884565i	$0.345545\pi$
$654$	−5.03597	+	4.80707i	−0.196922	+	0.187971i
$655$			13.7248i			0.536272i
$656$	0.726268	−	7.78650i	0.0283560	−	0.304012i
$657$	−17.5541			−0.684850
$658$	−20.2725	−	21.2378i	−0.790303	−	0.827936i
$659$	−25.6152			−0.997825			−0.498912	−	0.866652i	$-0.666267\pi$
$659$	−25.6152			−0.997825			−0.498912	+	0.866652i	$0.666267\pi$
$660$	3.90592	+	0.181764i	0.152038	+	0.00707514i
$661$			38.2450i			1.48756i	0.668426	+	0.743779i	$0.266968\pi$
$661$			38.2450i			1.48756i	−0.668426	+	0.743779i	$0.733032\pi$
$662$	5.78990	+	6.06560i	0.225031	+	0.235746i
$663$			24.3236i			0.944652i
$664$	5.61276	+	6.45596i	0.217817	+	0.250540i
$665$	−9.38399	+	12.4547i	−0.363896	+	0.482974i
$666$	5.61705	−	5.36174i	0.217656	−	0.207763i
$667$	−9.34696			−0.361916
$668$	0.484406	−	10.4094i	0.0187422	−	0.402752i
$669$	−14.6334			−0.565759
$670$	−6.49027	−	6.79932i	−0.250741	−	0.262681i
$671$			28.7529i			1.10999i
$672$	7.96978	−	6.30299i	0.307441	−	0.243143i
$673$		−	16.7714i		−	0.646491i	−0.946315	−	0.323245i	$-0.895226\pi$
$673$		−	16.7714i		−	0.646491i	0.946315	−	0.323245i	$-0.104774\pi$
$674$	−1.86251	+	1.77786i	−0.0717413	+	0.0684805i
$675$	2.88591			0.111079
$676$	3.51171	−	75.4633i	0.135066	−	2.90243i
$677$			6.44663i			0.247764i	0.992297	+	0.123882i	$0.0395345\pi$
$677$			6.44663i			0.247764i	−0.992297	+	0.123882i	$0.960466\pi$
$678$	7.19927	−	6.87204i	0.276486	−	0.263919i
$679$	−34.3551			−1.31843
$680$	−14.5125	+	12.6171i	−0.556531	+	0.483844i
$681$	−11.8413			−0.453759
$682$	25.0937	−	23.9531i	0.960888	−	0.917213i
$683$	7.93233			0.303522			0.151761	−	0.988417i	$-0.451506\pi$
$683$	7.93233			0.303522			0.151761	+	0.988417i	$0.451506\pi$
$684$	−15.2895	+	18.4421i	−0.584607	+	0.705152i
$685$	10.7211			0.409633
$686$	4.39559	−	4.19580i	0.167824	−	0.160196i
$687$	8.57314			0.327086
$688$	−0.372688	+	3.99568i	−0.0142086	+	0.152334i
$689$	12.4917			0.475895
$690$	−1.65834	+	1.58296i	−0.0631318	+	0.0602622i
$691$			44.5492i			1.69473i	0.531009	+	0.847366i	$0.321813\pi$
$691$			44.5492i			1.69473i	−0.531009	+	0.847366i	$0.678187\pi$
$692$	−29.1920	−	1.35846i	−1.10971	−	0.0516409i
$693$	−38.2808			−1.45417
$694$	−7.92960	+	7.56917i	−0.301004	+	0.287322i
$695$			7.63778i			0.289718i
$696$	2.69729	+	3.10250i	0.102241	+	0.117600i
$697$			13.2924i			0.503487i
$698$	−9.59763	−	10.0546i	−0.363276	−	0.380574i
$699$	−11.1746			−0.422662
$700$	−7.14739	−	0.332606i	−0.270146	−	0.0125713i
$701$	8.03401			0.303440			0.151720	−	0.988423i	$-0.451519\pi$
$701$	8.03401			0.303440			0.151720	+	0.988423i	$0.451519\pi$
$702$	−21.0360	+	20.0799i	−0.793954	+	0.757866i
$703$	−5.24130	+	6.95642i	−0.197679	+	0.262367i
$704$	−30.8490	−	4.33174i	−1.16266	−	0.163259i
$705$		−	2.91359i		−	0.109732i
$706$	−18.0985	−	18.9603i	−0.681144	−	0.713579i
$707$			10.9152i			0.410510i
$708$	0.190298	−	4.08932i	0.00715184	−	0.153686i
$709$	−13.5892			−0.510353			−0.255177	−	0.966894i	$-0.582134\pi$
$709$	−13.5892			−0.510353			−0.255177	+	0.966894i	$0.582134\pi$
$710$	−14.9424	−	15.6539i	−0.560776	−	0.587479i
$711$	−35.6452			−1.33680
$712$	−22.6329	−	26.0330i	−0.848203	−	0.975627i
$713$			20.3395i			0.761721i
$714$	−12.4930	+	11.9252i	−0.467540	+	0.446289i
$715$	27.7463			1.03765
$716$	−1.09527	+	23.5363i	−0.0409321	+	0.879591i
$717$			1.86342i			0.0695907i
$718$	−32.7719	+	31.2823i	−1.22304	+	1.16745i
$719$		−	15.5718i		−	0.580731i	−0.956916	−	0.290365i	$-0.906223\pi$
$719$		−	15.5718i		−	0.580731i	0.956916	−	0.290365i	$-0.0937769\pi$
$720$	−10.9442	−	1.02079i	−0.407865	−	0.0380427i
$721$		−	12.7887i		−	0.476277i
$722$	13.5666	−	23.1937i	0.504895	−	0.863181i
$723$		−	5.88277i		−	0.218783i
$724$	0.0317703	+	0.00147844i	0.00118073	+	5.49459e-5i
$725$		−	2.89493i		−	0.107515i
$726$	−2.04093	−	2.13812i	−0.0757462	−	0.0793530i
$727$			46.6530i			1.73027i	0.501543	+	0.865133i	$0.332766\pi$
$727$			46.6530i			1.73027i	−0.501543	+	0.865133i	$0.667234\pi$
$728$	54.4131	−	47.3063i	2.01668	−	1.75329i
$729$	−14.3246			−0.530542
$730$	6.23790	+	6.53494i	0.230875	+	0.241869i
$731$		−	6.82107i		−	0.252286i
$732$	−0.344673	+	7.40669i	−0.0127395	+	0.273759i
$733$	−25.9392			−0.958085			−0.479042	−	0.877792i	$-0.659016\pi$
$733$	−25.9392			−0.958085			−0.479042	+	0.877792i	$0.659016\pi$
$734$	0.302918	−	0.289150i	0.0111809	−	0.0106727i
$735$	−2.91153			−0.107394
$736$	14.3258	−	11.3297i	0.528057	−	0.417620i
$737$			25.8815i			0.953358i
$738$	−5.49583	+	5.24603i	−0.202304	+	0.193109i
$739$			25.0159i			0.920223i	0.887861	+	0.460112i	$0.152191\pi$
$739$			25.0159i			0.920223i	−0.887861	+	0.460112i	$0.847809\pi$
$740$	−3.99207	−	0.185773i	−0.146752	−	0.00682914i
$741$	9.38399	−	12.4547i	0.344730	−	0.457536i
$742$	6.12431	+	6.41594i	0.224831	+	0.235536i
$743$	3.30302			0.121176			0.0605880	−	0.998163i	$-0.480702\pi$
$743$	3.30302			0.121176			0.0605880	+	0.998163i	$0.480702\pi$
$744$	6.75123	−	5.86947i	0.247512	−	0.215185i
$745$	−0.538178			−0.0197173
$746$	−15.6635	+	14.9516i	−0.573483	+	0.547416i
$747$		−	8.31117i		−	0.304090i
$748$	52.8923	+	2.46136i	1.93393	+	0.0899963i
$749$			29.0782i			1.06250i
$750$	−0.490271	−	0.513617i	−0.0179022	−	0.0187546i
$751$	20.4773			0.747228			0.373614	−	0.927584i	$-0.378118\pi$
$751$	20.4773			0.747228			0.373614	+	0.927584i	$0.378118\pi$
$752$	−2.15571	+	23.1119i	−0.0786105	+	0.842803i
$753$			0.570911i			0.0208052i
$754$	20.1426	+	21.1017i	0.733550	+	0.768480i
$755$	−4.66389			−0.169736
$756$	−20.6267	−	0.959873i	−0.750187	−	0.0349102i
$757$	42.5740			1.54738			0.773689	−	0.633565i	$-0.218409\pi$
$757$	42.5740			1.54738			0.773689	+	0.633565i	$0.218409\pi$
$758$	−12.8725	−	13.4855i	−0.467550	−	0.489814i
$759$	6.31243			0.229127
$760$	12.2987	−	0.861595i	0.446120	−	0.0312533i
$761$	−24.0287			−0.871041			−0.435520	−	0.900179i	$-0.643436\pi$
$761$	−24.0287			−0.871041			−0.435520	+	0.900179i	$0.643436\pi$
$762$	−4.34874	−	4.55582i	−0.157538	−	0.165040i
$763$	−35.0777			−1.26990
$764$	−19.6620	−	0.914976i	−0.711345	−	0.0331027i
$765$	18.6829			0.675483
$766$	20.0330	+	20.9869i	0.723820	+	0.758287i
$767$		−	29.0491i		−	1.04890i
$768$	−7.89471	−	1.48565i	−0.284876	−	0.0536087i
$769$	−3.21550			−0.115954			−0.0579769	−	0.998318i	$-0.518465\pi$
$769$	−3.21550			−0.115954			−0.0579769	+	0.998318i	$0.518465\pi$
$770$	13.6032	+	14.2510i	0.490226	+	0.513569i
$771$		−	5.75296i		−	0.207188i
$772$	16.4631	+	0.766117i	0.592521	+	0.0275732i
$773$			21.4008i			0.769734i	0.922972	+	0.384867i	$0.125753\pi$
$773$			21.4008i			0.769734i	−0.922972	+	0.384867i	$0.874247\pi$
$774$	2.82021	−	2.69202i	0.101370	−	0.0967627i
$775$	−6.29953			−0.226286
$776$	17.8206	+	20.4977i	0.639722	+	0.735826i
$777$	−3.58921			−0.128762
$778$	0.225481	+	0.236218i	0.00808388	+	0.00846881i
$779$	5.12819	−	6.80630i	0.183736	−	0.243861i
$780$	7.14739	+	0.332606i	0.255918	+	0.0119092i
$781$			59.5862i			2.13216i
$782$	−22.4564	+	21.4357i	−0.803041	+	0.766540i
$783$		−	8.35450i		−	0.298566i
$784$	23.0955	+	2.15418i	0.824840	+	0.0769351i
$785$	15.1871			0.542051
$786$	7.04928	−	6.72887i	0.251440	−	0.240011i
$787$	−22.5839			−0.805030			−0.402515	−	0.915413i	$-0.631864\pi$
$787$	−22.5839			−0.805030			−0.402515	+	0.915413i	$0.631864\pi$
$788$	−0.588777	+	12.6522i	−0.0209743	+	0.450717i
$789$			9.23362i			0.328726i
$790$	12.6667	+	13.2698i	0.450659	+	0.472119i
$791$	50.1460			1.78299
$792$	19.8569	+	22.8400i	0.705585	+	0.811584i
$793$			52.6145i			1.86840i
$794$	−28.5091	−	29.8666i	−1.01175	−	1.05993i
$795$			0.880196i			0.0312173i
$796$	−16.1911	−	0.753457i	−0.573877	−	0.0267056i
$797$		−	17.5980i		−	0.623353i	−0.950188	−	0.311676i	$-0.899109\pi$
$797$		−	17.5980i		−	0.623353i	0.950188	−	0.311676i	$-0.100891\pi$
$798$	10.9977	−	1.28643i	0.389313	−	0.0455390i
$799$		−	39.4546i		−	1.39580i
$800$	3.50903	+	4.43697i	0.124063	+	0.156871i
$801$			33.5139i			1.18416i
$802$	−9.27288	+	8.85140i	−0.327437	+	0.312554i
$803$		−	24.8751i		−	0.877825i
$804$	−0.310253	+	6.66703i	−0.0109418	+	0.235128i
$805$	−11.5510			−0.407120
$806$	45.9186	−	43.8314i	1.61741	−	1.54390i
$807$		−	6.26943i		−	0.220695i
$808$	6.51251	−	5.66193i	0.229109	−	0.199186i
$809$	8.97883			0.315679			0.157839	−	0.987465i	$-0.449547\pi$
$809$	8.97883			0.315679			0.157839	+	0.987465i	$0.449547\pi$
$810$	6.63498	+	6.95092i	0.233129	+	0.244231i
$811$	55.3343			1.94305			0.971525	−	0.236937i	$-0.0761434\pi$
$811$	55.3343			1.94305			0.971525	+	0.236937i	$0.0761434\pi$
$812$	−0.962871	+	20.6912i	−0.0337901	+	0.726117i
$813$		−	12.4547i		−	0.436807i
$814$	7.59789	+	7.95968i	0.266306	+	0.278987i
$815$		−	6.15187i		−	0.215491i
$816$	13.5954	+	1.26808i	0.475936	+	0.0443918i
$817$	−2.63155	+	3.49268i	−0.0920663	+	0.122193i
$818$	39.2451	−	37.4613i	1.37217	−	1.30980i
$819$	−70.0494			−2.44773
$820$	3.90592	+	0.181764i	0.136401	+	0.00634746i
$821$	18.2197			0.635870			0.317935	−	0.948112i	$-0.397011\pi$
$821$	18.2197			0.635870			0.317935	+	0.948112i	$0.397011\pi$
$822$	−5.25626	−	5.50655i	−0.183333	−	0.192063i
$823$		−	12.1212i		−	0.422518i	−0.977430	−	0.211259i	$-0.932244\pi$
$823$		−	12.1212i		−	0.422518i	0.977430	−	0.211259i	$-0.0677563\pi$
$824$	−7.63031	+	6.63374i	−0.265815	+	0.231097i
$825$			1.95508i			0.0680670i
$826$	14.9201	−	14.2419i	0.519136	−	0.495540i
$827$	−6.53920			−0.227390			−0.113695	−	0.993516i	$-0.536269\pi$
$827$	−6.53920			−0.227390			−0.113695	+	0.993516i	$0.536269\pi$
$828$	−17.7254	−	0.824859i	−0.616001	−	0.0286658i
$829$			0.250130i			0.00868737i	0.999991	+	0.00434369i	$0.00138264\pi$
$829$			0.250130i			0.00868737i	−0.999991	+	0.00434369i	$0.998617\pi$
$830$	−3.09404	+	2.95340i	−0.107396	+	0.102514i
$831$	−2.10644			−0.0730716
$832$	−56.4501	−	7.92658i	−1.95705	−	0.274805i
$833$	−39.4267			−1.36605
$834$	3.92289	−	3.74459i	0.135839	−	0.129664i
$835$	5.21034			0.180311
$836$	−26.1335	−	21.6660i	−0.903847	−	0.749335i
$837$	−18.1799			−0.628389
$838$	22.0734	−	21.0701i	0.762512	−	0.727853i
$839$	35.0976			1.21170			0.605852	−	0.795578i	$-0.292832\pi$
$839$	35.0976			1.21170			0.605852	+	0.795578i	$0.292832\pi$
$840$	3.33333	+	3.83409i	0.115011	+	0.132289i
$841$	20.6194			0.711014
$842$	−5.26137	+	5.02222i	−0.181319	+	0.173077i
$843$			4.50106i			0.155025i
$844$	1.76695	−	37.9701i	0.0608211	−	1.30699i
$845$	37.7725			1.29941
$846$	16.3127	−	15.5712i	0.560842	−	0.535350i
$847$		−	14.8929i		−	0.511726i
$848$	0.651239	−	6.98209i	0.0223636	−	0.239766i
$849$			10.4162i			0.357483i
$850$	−6.63904	−	6.95517i	−0.227717	−	0.238560i
$851$	−6.45166			−0.221160
$852$	−0.714285	+	15.3493i	−0.0244710	+	0.525858i
$853$	−38.1277			−1.30547			−0.652734	−	0.757587i	$-0.726378\pi$
$853$	−38.1277			−1.30547			−0.652734	+	0.757587i	$0.726378\pi$
$854$	−27.0237	+	25.7954i	−0.924732	+	0.882700i
$855$	−9.56646	−	7.20782i	−0.327166	−	0.246502i
$856$	17.3494	−	15.0834i	0.592989	−	0.515540i
$857$			49.3051i			1.68423i	0.539297	+	0.842116i	$0.318690\pi$
$857$			49.3051i			1.68423i	−0.539297	+	0.842116i	$0.681310\pi$
$858$	−13.6032	−	14.2510i	−0.464406	−	0.486520i
$859$		−	13.5315i		−	0.461688i	−0.972991	−	0.230844i	$-0.925851\pi$
$859$		−	13.5315i		−	0.461688i	0.972991	−	0.230844i	$-0.0741487\pi$
$860$	−2.00434	−	0.0932727i	−0.0683474	−	0.00318057i
$861$	3.51175			0.119680
$862$	−25.0278	−	26.2195i	−0.852449	−	0.893041i
$863$	44.5010			1.51483			0.757416	−	0.652932i	$-0.226461\pi$
$863$	44.5010			1.51483			0.757416	+	0.652932i	$0.226461\pi$
$864$	10.1268	+	12.8047i	0.344519	+	0.435625i
$865$		−	14.6118i		−	0.496816i
$866$	−19.1987	+	18.3260i	−0.652397	+	0.622744i
$867$	−14.6736			−0.498342
$868$	45.0252	+	2.09526i	1.52825	+	0.0711178i
$869$		−	50.5113i		−	1.71348i
$870$	−1.48688	+	1.41930i	−0.0504101	+	0.0481188i
$871$			47.3602i			1.60474i
$872$	18.1954	+	20.9289i	0.616174	+	0.708741i
$873$		−	26.3881i		−	0.893101i
$874$	19.7685	−	2.31237i	0.668680	−	0.0782172i
$875$		−	3.57756i		−	0.120944i
$876$	0.298189	−	6.40779i	0.0100749	−	0.216499i
$877$		−	1.58349i		−	0.0534707i	−0.999643	−	0.0267354i	$-0.991489\pi$
$877$		−	1.58349i		−	0.0534707i	0.999643	−	0.0267354i	$-0.00851115\pi$
$878$	24.0007	+	25.1436i	0.809985	+	0.848555i
$879$		−	11.2330i		−	0.378881i
$880$	1.44652	−	15.5085i	0.0487622	−	0.522791i
$881$	−24.1278			−0.812885			−0.406442	−	0.913676i	$-0.633231\pi$
$881$	−24.1278			−0.812885			−0.406442	+	0.913676i	$0.633231\pi$
$882$	−15.5602	−	16.3012i	−0.523940	−	0.548889i
$883$			46.3189i			1.55875i	0.626555	+	0.779377i	$0.284464\pi$
$883$			46.3189i			1.55875i	−0.626555	+	0.779377i	$0.715536\pi$
$884$	96.7867	+	4.50401i	3.25529	+	0.151486i
$885$	2.04687			0.0688049
$886$	−33.0789	+	31.5754i	−1.11131	+	1.06080i
$887$	2.29524			0.0770666			0.0385333	−	0.999257i	$-0.487731\pi$
$887$	2.29524			0.0770666			0.0385333	+	0.999257i	$0.487731\pi$
$888$	1.86178	+	2.14148i	0.0624774	+	0.0718632i
$889$		−	31.7332i		−	1.06430i
$890$	12.4764	−	11.9093i	0.418209	−	0.399200i
$891$		−	26.4586i		−	0.886396i
$892$	−2.70966	+	58.2280i	−0.0907262	+	1.94962i
$893$	−15.2215	+	20.2024i	−0.509367	+	0.676049i
$894$	0.263853	+	0.276417i	0.00882457	+	0.00924478i
$895$	−11.7809			−0.393791
$896$	−23.6046	−	32.8799i	−0.788575	−	1.09844i
$897$	11.5510			0.385677
$898$	15.8978	−	15.1752i	0.530517	−	0.506403i
$899$			18.2367i			0.608227i
$900$	0.255474	−	5.48989i	0.00851580	−	0.182996i
$901$			11.9192i			0.397087i
$902$	−7.43392	−	7.78790i	−0.247522	−	0.259309i
$903$	−1.80207			−0.0599691
$904$	−26.0116	−	29.9193i	−0.865133	−	0.995100i
$905$			0.0159023i			0.000528612i
$906$	2.28657	+	2.39545i	0.0759663	+	0.0795837i
$907$	22.0534			0.732270			0.366135	−	0.930562i	$-0.380681\pi$
$907$	22.0534			0.732270			0.366135	+	0.930562i	$0.380681\pi$
$908$	−2.19265	+	47.1180i	−0.0727657	+	1.56366i
$909$	−8.38397			−0.278079
$910$	24.8923	+	26.0776i	0.825172	+	0.864464i
$911$	12.3821			0.410238			0.205119	−	0.978737i	$-0.434242\pi$
$911$	12.3821			0.410238			0.205119	+	0.978737i	$0.434242\pi$
$912$	−6.47222	−	5.89440i	−0.214317	−	0.195183i
$913$	11.7774			0.389775
$914$	−18.6059	−	19.4919i	−0.615430	−	0.644735i
$915$	−3.70735			−0.122561
$916$	1.58749	−	34.1136i	0.0524521	−	1.12714i
$917$	49.1013			1.62147
$918$	−19.1597	−	20.0720i	−0.632364	−	0.662475i
$919$		−	41.3638i		−	1.36447i	−0.731135	−	0.682233i	$-0.761009\pi$
$919$		−	41.3638i		−	1.36447i	0.731135	−	0.682233i	$-0.238991\pi$
$920$	5.99171	+	6.89184i	0.197541	+	0.227217i
$921$	−4.70862			−0.155154
$922$	17.9184	+	18.7716i	0.590110	+	0.618210i
$923$			109.036i			3.58896i
$924$	0.650270	−	13.9737i	0.0213923	−	0.459700i
$925$		−	1.99820i		−	0.0657003i
$926$	15.3237	−	14.6271i	0.503567	−	0.480678i
$927$	9.82299			0.322629
$928$	12.8447	−	10.1584i	0.421648	−	0.333465i
$929$	18.0866			0.593404			0.296702	−	0.954970i	$-0.404113\pi$
$929$	18.0866			0.593404			0.296702	+	0.954970i	$0.404113\pi$
$930$	3.08848	+	3.23554i	0.101275	+	0.106098i
$931$	20.1881	+	15.2107i	0.661640	+	0.498511i
$932$	−2.06920	+	44.4650i	−0.0677788	+	1.45650i
$933$			6.98260i			0.228600i
$934$	−7.58787	+	7.24298i	−0.248283	+	0.236998i
$935$			26.4748i			0.865817i
$936$	36.3359	+	41.7946i	1.18768	+	1.36610i
$937$	45.6353			1.49084			0.745420	−	0.666595i	$-0.232249\pi$
$937$	45.6353			1.49084			0.745420	+	0.666595i	$0.232249\pi$
$938$	−24.3250	+	23.2193i	−0.794239	+	0.758138i
$939$	−12.6226			−0.411923
$940$	−11.5935	−	0.539510i	−0.378140	−	0.0175969i
$941$		−	15.5812i		−	0.507934i	−0.967213	−	0.253967i	$-0.918265\pi$
$941$		−	15.5812i		−	0.507934i	0.967213	−	0.253967i	$-0.0817355\pi$
$942$	−7.44580	−	7.80035i	−0.242597	−	0.254149i
$943$	6.31243			0.205561
$944$	−16.2367	−	1.51444i	−0.528459	−	0.0492908i
$945$		−	10.3245i		−	0.335857i
$946$	3.81475	+	3.99639i	0.124028	+	0.129934i
$947$			53.7595i			1.74695i	0.486871	+	0.873474i	$0.338138\pi$
$947$			53.7595i			1.74695i	−0.486871	+	0.873474i	$0.661862\pi$
$948$	0.605500	−	13.0116i	0.0196657	−	0.422598i
$949$		−	45.5186i		−	1.47760i
$950$	0.716184	+	6.12267i	0.0232361	+	0.198646i
$951$			11.5047i			0.373065i
$952$	45.1384	+	51.9195i	1.46295	+	1.68272i
$953$		−	27.1606i		−	0.879817i	−0.898043	−	0.439909i	$-0.855011\pi$
$953$		−	27.1606i		−	0.879817i	0.898043	−	0.439909i	$-0.144989\pi$
$954$	−4.92807	+	4.70407i	−0.159552	+	0.152300i
$955$		−	9.84162i		−	0.318467i
$956$	7.41477	+	0.345049i	0.239811	+	0.0111597i
$957$	5.65980			0.182955
$958$	−22.0361	+	21.0345i	−0.711955	+	0.679594i
$959$		−	38.3554i		−	1.23856i
$960$	0.558527	−	3.97762i	0.0180264	−	0.128377i
$961$	8.68402			0.280130
$962$	13.9033	+	14.5653i	0.448259	+	0.469604i
$963$	−22.3349			−0.719733
$964$	−23.4083	−	1.08931i	−0.753930	−	0.0350844i
$965$			8.24047i			0.265270i
$966$	5.66313	+	5.93280i	0.182208	+	0.190885i
$967$		−	36.4395i		−	1.17182i	−0.810377	−	0.585908i	$-0.800738\pi$
$967$		−	36.4395i		−	1.17182i	0.810377	−	0.585908i	$-0.199262\pi$
$968$	−8.88576	+	7.72521i	−0.285599	+	0.248298i
$969$	11.8840	+	8.95395i	0.381768	+	0.287642i
$970$	−9.82360	+	9.37709i	−0.315417	+	0.301080i
$971$	23.9164			0.767513			0.383756	−	0.923434i	$-0.374630\pi$
$971$	23.9164			0.767513			0.383756	+	0.923434i	$0.374630\pi$
$972$	1.12208	−	24.1124i	0.0359908	−	0.773407i
$973$	27.3246			0.875987
$974$	18.0691	+	18.9295i	0.578970	+	0.606539i
$975$			3.57756i			0.114574i
$976$	29.4083	+	2.74300i	0.941338	+	0.0878011i
$977$		−	9.67831i		−	0.309637i	−0.987943	−	0.154818i	$-0.950521\pi$
$977$		−	9.67831i		−	0.309637i	0.987943	−	0.154818i	$-0.0494792\pi$
$978$	−3.15970	+	3.01608i	−0.101036	+	0.0964438i
$979$	−47.4911			−1.51782
$980$	−0.539129	+	11.5853i	−0.0172218	+	0.370080i
$981$		−	26.9431i		−	0.860226i
$982$	−18.2284	+	17.3999i	−0.581692	+	0.555252i
$983$	−28.0339			−0.894144			−0.447072	−	0.894498i	$-0.647533\pi$
$983$	−28.0339			−0.894144			−0.447072	+	0.894498i	$0.647533\pi$
$984$	−1.82161	−	2.09526i	−0.0580707	−	0.0667945i
$985$	−6.33297			−0.201785
$986$	−20.1347	+	19.2195i	−0.641220	+	0.612074i
$987$	−10.4236			−0.331785
$988$	−47.8213	−	39.6463i	−1.52140	−	1.26132i
$989$	−3.23925			−0.103002
$990$	−10.9461	+	10.4486i	−0.347891	+	0.332078i
$991$	−7.31511			−0.232372			−0.116186	−	0.993227i	$-0.537067\pi$
$991$	−7.31511			−0.232372			−0.116186	+	0.993227i	$0.537067\pi$
$992$	−22.1052	−	27.9508i	−0.701841	−	0.887439i
$993$	2.97701			0.0944725
$994$	−56.0027	+	53.4572i	−1.77630	+	1.69556i
$995$		−	8.10430i		−	0.256923i
$996$	3.03383	+	0.141181i	0.0961307	+	0.00447348i
$997$	24.4426			0.774104			0.387052	−	0.922058i	$-0.373493\pi$
$997$	24.4426			0.774104			0.387052	+	0.922058i	$0.373493\pi$
$998$	−12.7843	+	12.2032i	−0.404681	+	0.386287i
$999$		−	5.76662i		−	0.182448i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.f.a.151.5	✓	20
4.3	odd	2	inner	380.2.f.a.151.15	yes	20
19.18	odd	2	inner	380.2.f.a.151.16	yes	20
76.75	even	2	inner	380.2.f.a.151.6	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.f.a.151.5	✓	20	1.1	even	1	trivial
380.2.f.a.151.6	yes	20	76.75	even	2	inner
380.2.f.a.151.15	yes	20	4.3	odd	2	inner
380.2.f.a.151.16	yes	20	19.18	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.976481 - 1.02298i) q^{2} -0.502080 q^{3} +(-0.0929701 + 1.99784i) q^{4} -1.00000 q^{5} +(0.490271 + 0.513617i) q^{6} +3.57756i q^{7} +(2.13453 - 1.85574i) q^{8} -2.74792 q^{9} +O(q^{10})\)	\(q+(-0.976481 - 1.02298i) q^{2} -0.502080 q^{3} +(-0.0929701 + 1.99784i) q^{4} -1.00000 q^{5} +(0.490271 + 0.513617i) q^{6} +3.57756i q^{7} +(2.13453 - 1.85574i) q^{8} -2.74792 q^{9} +(0.976481 + 1.02298i) q^{10} -3.89395i q^{11} +(0.0466784 - 1.00307i) q^{12} -7.12548i q^{13} +(3.65977 - 3.49342i) q^{14} +0.502080 q^{15} +(-3.98271 - 0.371479i) q^{16} +6.79894 q^{17} +(2.68329 + 2.81106i) q^{18} +(-3.48135 - 2.62301i) q^{19} +(0.0929701 - 1.99784i) q^{20} -1.79622i q^{21} +(-3.98343 + 3.80237i) q^{22} -3.22874i q^{23} +(-1.07170 + 0.931732i) q^{24} +1.00000 q^{25} +(-7.28921 + 6.95790i) q^{26} +2.88591 q^{27} +(-7.14739 - 0.332606i) q^{28} -2.89493i q^{29} +(-0.490271 - 0.513617i) q^{30} -6.29953 q^{31} +(3.50903 + 4.43697i) q^{32} +1.95508i q^{33} +(-6.63904 - 6.95517i) q^{34} -3.57756i q^{35} +(0.255474 - 5.48989i) q^{36} -1.99820i q^{37} +(0.716184 + 6.12267i) q^{38} +3.57756i q^{39} +(-2.13453 + 1.85574i) q^{40} +1.95508i q^{41} +(-1.83750 + 1.75398i) q^{42} -1.00325i q^{43} +(7.77949 + 0.362021i) q^{44} +2.74792 q^{45} +(-3.30293 + 3.15280i) q^{46} -5.80305i q^{47} +(1.99964 + 0.186512i) q^{48} -5.79894 q^{49} +(-0.976481 - 1.02298i) q^{50} -3.41361 q^{51} +(14.2356 + 0.662457i) q^{52} +1.75310i q^{53} +(-2.81804 - 2.95223i) q^{54} +3.89395i q^{55} +(6.63904 + 7.63641i) q^{56} +(1.74792 + 1.31696i) q^{57} +(-2.96145 + 2.82684i) q^{58} +4.07679 q^{59} +(-0.0466784 + 1.00307i) q^{60} -7.38399 q^{61} +(6.15137 + 6.44428i) q^{62} -9.83084i q^{63} +(1.11243 - 7.92228i) q^{64} +7.12548i q^{65} +(2.00000 - 1.90909i) q^{66} -6.64659 q^{67} +(-0.632099 + 13.5832i) q^{68} +1.62109i q^{69} +(-3.65977 + 3.49342i) q^{70} -15.3022 q^{71} +(-5.86551 + 5.09943i) q^{72} +6.38815 q^{73} +(-2.04411 + 1.95120i) q^{74} -0.502080 q^{75} +(5.56402 - 6.71131i) q^{76} +13.9309 q^{77} +(3.65977 - 3.49342i) q^{78} +12.9717 q^{79} +(3.98271 + 0.371479i) q^{80} +6.79479 q^{81} +(2.00000 - 1.90909i) q^{82} +3.02454i q^{83} +(3.58856 + 0.166995i) q^{84} -6.79894 q^{85} +(-1.02631 + 0.979659i) q^{86} +1.45348i q^{87} +(-7.22618 - 8.31175i) q^{88} -12.1961i q^{89} +(-2.68329 - 2.81106i) q^{90} +25.4918 q^{91} +(6.45050 + 0.300176i) q^{92} +3.16287 q^{93} +(-5.93639 + 5.66656i) q^{94} +(3.48135 + 2.62301i) q^{95} +(-1.76181 - 2.22771i) q^{96} +9.60294i q^{97} +(5.66256 + 5.93219i) q^{98} +10.7003i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{4} - 20 q^{5} - 6 q^{6} + 16 q^{9}+O(q^{10}) \) 20 * q + 2 * q^4 - 20 * q^5 - 6 * q^6 + 16 * q^9	\( 20 q + 2 q^{4} - 20 q^{5} - 6 q^{6} + 16 q^{9} - 2 q^{16} + 20 q^{17} - 2 q^{20} + 26 q^{24} + 20 q^{25} - 14 q^{26} - 14 q^{28} + 6 q^{30} - 4 q^{36} + 10 q^{38} - 42 q^{42} + 8 q^{44} - 16 q^{45} - 30 q^{54} - 36 q^{57} + 62 q^{58} - 24 q^{61} - 40 q^{62} + 50 q^{64} + 40 q^{66} + 6 q^{68} - 36 q^{73} - 36 q^{74} - 28 q^{76} - 32 q^{77} + 2 q^{80} + 60 q^{81} + 40 q^{82} - 20 q^{85} + 26 q^{92} - 122 q^{96}+O(q^{100}) \) 20 * q + 2 * q^4 - 20 * q^5 - 6 * q^6 + 16 * q^9 - 2 * q^16 + 20 * q^17 - 2 * q^20 + 26 * q^24 + 20 * q^25 - 14 * q^26 - 14 * q^28 + 6 * q^30 - 4 * q^36 + 10 * q^38 - 42 * q^42 + 8 * q^44 - 16 * q^45 - 30 * q^54 - 36 * q^57 + 62 * q^58 - 24 * q^61 - 40 * q^62 + 50 * q^64 + 40 * q^66 + 6 * q^68 - 36 * q^73 - 36 * q^74 - 28 * q^76 - 32 * q^77 + 2 * q^80 + 60 * q^81 + 40 * q^82 - 20 * q^85 + 26 * q^92 - 122 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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