LMFDB - Embedded newform 380.2.f.a.151.20

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			151.20
Root			$-1.40065 + 0.195405i$ of defining polynomial
Character	$\chi$	$=$	380.151
Dual form			380.2.f.a.151.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40065 + 0.195405i) q^{2} -1.89649 q^{3} +(1.92363 + 0.547388i) q^{4} -1.00000 q^{5} +(-2.65631 - 0.370584i) q^{6} +2.89109i q^{7} +(2.58737 + 1.14259i) q^{8} +0.596662 q^{9} +O(q^{10})$	\(q+(1.40065 + 0.195405i) q^{2} -1.89649 q^{3} +(1.92363 + 0.547388i) q^{4} -1.00000 q^{5} +(-2.65631 - 0.370584i) q^{6} +2.89109i q^{7} +(2.58737 + 1.14259i) q^{8} +0.596662 q^{9} +(-1.40065 - 0.195405i) q^{10} +5.39689i q^{11} +(-3.64815 - 1.03811i) q^{12} -1.52445i q^{13} +(-0.564935 + 4.04941i) q^{14} +1.89649 q^{15} +(3.40073 + 2.10595i) q^{16} +2.35843 q^{17} +(0.835714 + 0.116591i) q^{18} +(0.841905 + 4.27682i) q^{19} +(-1.92363 - 0.547388i) q^{20} -5.48292i q^{21} +(-1.05458 + 7.55915i) q^{22} -5.72592i q^{23} +(-4.90692 - 2.16690i) q^{24} +1.00000 q^{25} +(0.297885 - 2.13522i) q^{26} +4.55790 q^{27} +(-1.58255 + 5.56141i) q^{28} +7.31719i q^{29} +(2.65631 + 0.370584i) q^{30} -9.03062 q^{31} +(4.35172 + 3.61422i) q^{32} -10.2351i q^{33} +(3.30333 + 0.460849i) q^{34} -2.89109i q^{35} +(1.14776 + 0.326606i) q^{36} +0.169748i q^{37} +(0.343500 + 6.15484i) q^{38} +2.89109i q^{39} +(-2.58737 - 1.14259i) q^{40} -10.2351i q^{41} +(1.07139 - 7.67965i) q^{42} +0.321924i q^{43} +(-2.95420 + 10.3816i) q^{44} -0.596662 q^{45} +(1.11887 - 8.02000i) q^{46} -8.93894i q^{47} +(-6.44944 - 3.99390i) q^{48} -1.35843 q^{49} +(1.40065 + 0.195405i) q^{50} -4.47272 q^{51} +(0.834465 - 2.93248i) q^{52} -4.58247i q^{53} +(6.38402 + 0.890638i) q^{54} -5.39689i q^{55} +(-3.30333 + 7.48034i) q^{56} +(-1.59666 - 8.11093i) q^{57} +(-1.42982 + 10.2488i) q^{58} -6.24171 q^{59} +(3.64815 + 1.03811i) q^{60} +14.3647 q^{61} +(-12.6487 - 1.76463i) q^{62} +1.72501i q^{63} +(5.38899 + 5.91260i) q^{64} +1.52445i q^{65} +(2.00000 - 14.3358i) q^{66} +2.38724 q^{67} +(4.53675 + 1.29098i) q^{68} +10.8591i q^{69} +(0.564935 - 4.04941i) q^{70} +12.9742 q^{71} +(1.54379 + 0.681738i) q^{72} -2.57229 q^{73} +(-0.0331696 + 0.237757i) q^{74} -1.89649 q^{75} +(-0.721565 + 8.68788i) q^{76} -15.6029 q^{77} +(-0.564935 + 4.04941i) q^{78} +4.66172 q^{79} +(-3.40073 - 2.10595i) q^{80} -10.4340 q^{81} +(2.00000 - 14.3358i) q^{82} -10.3420i q^{83} +(3.00129 - 10.5471i) q^{84} -2.35843 q^{85} +(-0.0629056 + 0.450902i) q^{86} -13.8770i q^{87} +(-6.16642 + 13.9638i) q^{88} -2.58922i q^{89} +(-0.835714 - 0.116591i) q^{90} +4.40732 q^{91} +(3.13430 - 11.0146i) q^{92} +17.1265 q^{93} +(1.74672 - 12.5203i) q^{94} +(-0.841905 - 4.27682i) q^{95} +(-8.25297 - 6.85431i) q^{96} +14.9486i q^{97} +(-1.90268 - 0.265444i) q^{98} +3.22012i 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 $

$2$	1.40065	+	0.195405i	0.990408	+	0.138172i
$2$	1.40065	+	0.195405i	0.990408	+	0.138172i
$3$	−1.89649			−1.09494			−0.547469	−	0.836826i	$-0.684408\pi$
$3$	−1.89649			−1.09494			−0.547469	+	0.836826i	$0.684408\pi$
$4$	1.92363	+	0.547388i	0.961817	+	0.273694i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−2.65631	−	0.370584i	−1.08443	−	0.151290i
$7$			2.89109i			1.09273i	0.837547	+	0.546365i	$0.183989\pi$
$7$			2.89109i			1.09273i	−0.837547	+	0.546365i	$0.816011\pi$
$8$	2.58737	+	1.14259i	0.914774	+	0.403966i
$9$	0.596662			0.198887
$10$	−1.40065	−	0.195405i	−0.442924	−	0.0617926i
$11$			5.39689i			1.62722i	0.581408	+	0.813612i	$0.302502\pi$
$11$			5.39689i			1.62722i	−0.581408	+	0.813612i	$0.697498\pi$
$12$	−3.64815	−	1.03811i	−1.05313	−	0.299678i
$13$		−	1.52445i		−	0.422806i	−0.977399	−	0.211403i	$-0.932197\pi$
$13$		−	1.52445i		−	0.422806i	0.977399	−	0.211403i	$-0.0678032\pi$
$14$	−0.564935	+	4.04941i	−0.150985	+	1.08225i
$15$	1.89649			0.489671
$16$	3.40073	+	2.10595i	0.850183	+	0.526487i
$17$	2.35843			0.572002			0.286001	−	0.958229i	$-0.407674\pi$
$17$	2.35843			0.572002			0.286001	+	0.958229i	$0.407674\pi$
$18$	0.835714	+	0.116591i	0.196980	+	0.0274807i
$19$	0.841905	+	4.27682i	0.193146	+	0.981170i
$19$	0.841905	+	4.27682i	0.193146	+	0.981170i
$20$	−1.92363	−	0.547388i	−0.430138	−	0.122400i
$21$		−	5.48292i		−	1.19647i
$22$	−1.05458	+	7.55915i	−0.224838	+	1.61162i
$23$		−	5.72592i		−	1.19394i	−0.802265	−	0.596968i	$-0.796372\pi$
$23$		−	5.72592i		−	1.19394i	0.802265	−	0.596968i	$-0.203628\pi$
$24$	−4.90692	−	2.16690i	−1.00162	−	0.442317i
$25$	1.00000			0.200000
$26$	0.297885	−	2.13522i	0.0584201	−	0.418750i
$27$	4.55790			0.877168
$28$	−1.58255	+	5.56141i	−0.299074	+	1.05101i
$29$			7.31719i			1.35877i	0.733783	+	0.679384i	$0.237753\pi$
$29$			7.31719i			1.35877i	−0.733783	+	0.679384i	$0.762247\pi$
$30$	2.65631	+	0.370584i	0.484974	+	0.0676590i
$31$	−9.03062			−1.62195			−0.810974	−	0.585082i	$-0.801062\pi$
$31$	−9.03062			−1.62195			−0.810974	+	0.585082i	$0.801062\pi$
$32$	4.35172	+	3.61422i	0.769282	+	0.638909i
$33$		−	10.2351i		−	1.78171i
$34$	3.30333	+	0.460849i	0.566516	+	0.0790350i
$35$		−	2.89109i		−	0.488684i
$36$	1.14776	+	0.326606i	0.191293	+	0.0544343i
$37$			0.169748i			0.0279063i	0.999903	+	0.0139532i	$0.00444157\pi$
$37$			0.169748i			0.0279063i	−0.999903	+	0.0139532i	$0.995558\pi$
$38$	0.343500	+	6.15484i	0.0557230	+	0.998446i
$39$			2.89109i			0.462946i
$40$	−2.58737	−	1.14259i	−0.409099	−	0.180659i
$41$		−	10.2351i		−	1.59846i	−0.601025	−	0.799230i	$-0.705241\pi$
$41$		−	10.2351i		−	1.59846i	0.601025	−	0.799230i	$-0.294759\pi$
$42$	1.07139	−	7.67965i	0.165319	−	1.18500i
$43$			0.321924i			0.0490929i	0.999699	+	0.0245465i	$0.00781417\pi$
$43$			0.321924i			0.0490929i	−0.999699	+	0.0245465i	$0.992186\pi$
$44$	−2.95420	+	10.3816i	−0.445362	+	1.56509i
$45$	−0.596662			−0.0889451
$46$	1.11887	−	8.02000i	0.164969	−	1.18248i
$47$		−	8.93894i		−	1.30388i	−0.758271	−	0.651939i	$-0.773956\pi$
$47$		−	8.93894i		−	1.30388i	0.758271	−	0.651939i	$-0.226044\pi$
$48$	−6.44944	−	3.99390i	−0.930897	−	0.576471i
$49$	−1.35843			−0.194061
$50$	1.40065	+	0.195405i	0.198082	+	0.0276345i
$51$	−4.47272			−0.626307
$52$	0.834465	−	2.93248i	0.115719	−	0.406662i
$53$		−	4.58247i		−	0.629450i	−0.949183	−	0.314725i	$-0.898088\pi$
$53$		−	4.58247i		−	0.629450i	0.949183	−	0.314725i	$-0.101912\pi$
$54$	6.38402	+	0.890638i	0.868754	+	0.121200i
$55$		−	5.39689i		−	0.727717i
$56$	−3.30333	+	7.48034i	−0.441426	+	0.999602i
$57$	−1.59666	−	8.11093i	−0.211483	−	1.07432i
$58$	−1.42982	+	10.2488i	−0.187744	+	1.34574i
$59$	−6.24171			−0.812601			−0.406301	−	0.913739i	$-0.633181\pi$
$59$	−6.24171			−0.812601			−0.406301	+	0.913739i	$0.633181\pi$
$60$	3.64815	+	1.03811i	0.470974	+	0.134020i
$61$	14.3647			1.83921			0.919605	−	0.392844i	$-0.128509\pi$
$61$	14.3647			1.83921			0.919605	+	0.392844i	$0.128509\pi$
$62$	−12.6487	−	1.76463i	−1.60639	−	0.224108i
$63$			1.72501i			0.217330i
$64$	5.38899	+	5.91260i	0.673624	+	0.739074i
$65$			1.52445i			0.189084i
$66$	2.00000	−	14.3358i	0.246183	−	1.76462i
$67$	2.38724			0.291648			0.145824	−	0.989311i	$-0.453417\pi$
$67$	2.38724			0.291648			0.145824	+	0.989311i	$0.453417\pi$
$68$	4.53675	+	1.29098i	0.550162	+	0.156554i
$69$			10.8591i			1.30729i
$70$	0.564935	−	4.04941i	0.0675227	−	0.483997i
$71$	12.9742			1.53975			0.769876	−	0.638194i	$-0.220318\pi$
$71$	12.9742			1.53975			0.769876	+	0.638194i	$0.220318\pi$
$72$	1.54379	+	0.681738i	0.181937	+	0.0803436i
$73$	−2.57229			−0.301063			−0.150532	−	0.988605i	$-0.548099\pi$
$73$	−2.57229			−0.301063			−0.150532	+	0.988605i	$0.548099\pi$
$74$	−0.0331696	+	0.237757i	−0.00385588	+	0.0276386i
$75$	−1.89649			−0.218987
$76$	−0.721565	+	8.68788i	−0.0827692	+	0.996569i
$77$	−15.6029			−1.77812
$78$	−0.564935	+	4.04941i	−0.0639663	+	0.458505i
$79$	4.66172			0.524484			0.262242	−	0.965002i	$-0.415538\pi$
$79$	4.66172			0.524484			0.262242	+	0.965002i	$0.415538\pi$
$80$	−3.40073	−	2.10595i	−0.380213	−	0.235452i
$81$	−10.4340			−1.15933
$82$	2.00000	−	14.3358i	0.220863	−	1.58313i
$83$		−	10.3420i		−	1.13518i	−0.823310	−	0.567592i	$-0.807875\pi$
$83$		−	10.3420i		−	1.13518i	0.823310	−	0.567592i	$-0.192125\pi$
$84$	3.00129	−	10.5471i	0.327467	−	1.15079i
$85$	−2.35843			−0.255807
$86$	−0.0629056	+	0.450902i	−0.00678329	+	0.0486220i
$87$		−	13.8770i		−	1.48777i
$88$	−6.16642	+	13.9638i	−0.657343	+	1.48854i
$89$		−	2.58922i		−	0.274456i	−0.990539	−	0.137228i	$-0.956181\pi$
$89$		−	2.58922i		−	0.274456i	0.990539	−	0.137228i	$-0.0438194\pi$
$90$	−0.835714	−	0.116591i	−0.0880919	−	0.0122898i
$91$	4.40732			0.462013
$92$	3.13430	−	11.0146i	0.326774	−	1.14835i
$93$	17.1265			1.77593
$94$	1.74672	−	12.5203i	0.180160	−	1.29137i
$95$	−0.841905	−	4.27682i	−0.0863776	−	0.438793i
$96$	−8.25297	−	6.85431i	−0.842316	−	0.699565i
$97$			14.9486i			1.51780i	0.651210	+	0.758898i	$0.274262\pi$
$97$			14.9486i			1.51780i	−0.651210	+	0.758898i	$0.725738\pi$
$98$	−1.90268	−	0.265444i	−0.192200	−	0.0268139i
$99$			3.22012i			0.323634i
$100$	1.92363	+	0.547388i	0.192363	+	0.0547388i
$101$	1.95509			0.194539			0.0972693	−	0.995258i	$-0.468989\pi$
$101$	1.95509			0.194539			0.0972693	+	0.995258i	$0.468989\pi$
$102$	−6.26472	−	0.873994i	−0.620299	−	0.0865383i
$103$	8.13820			0.801880			0.400940	−	0.916104i	$-0.368684\pi$
$103$	8.13820			0.801880			0.400940	+	0.916104i	$0.368684\pi$
$104$	1.74181	−	3.94431i	0.170799	−	0.386772i
$105$			5.48292i			0.535078i
$106$	0.895438	−	6.41843i	0.0869727	−	0.623413i
$107$	−10.5018			−1.01524			−0.507622	−	0.861580i	$-0.669475\pi$
$107$	−10.5018			−1.01524			−0.507622	+	0.861580i	$0.669475\pi$
$108$	8.76773	+	2.49494i	0.843675	+	0.240076i
$109$			9.29589i			0.890384i	0.895435	+	0.445192i	$0.146865\pi$
$109$			9.29589i			0.890384i	−0.895435	+	0.445192i	$0.853135\pi$
$110$	1.05458	−	7.55915i	0.100550	−	0.720737i
$111$		−	0.321924i		−	0.0305557i
$112$	−6.08850	+	9.83184i	−0.575309	+	0.929021i
$113$			6.13224i			0.576873i	0.957499	+	0.288436i	$0.0931354\pi$
$113$			6.13224i			0.576873i	−0.957499	+	0.288436i	$0.906865\pi$
$114$	−0.651443	−	11.6726i	−0.0610132	−	1.09324i
$115$			5.72592i			0.533945i
$116$	−4.00535	+	14.0756i	−0.371887	+	1.30689i
$117$		−	0.909579i		−	0.0840907i
$118$	−8.74244	−	1.21966i	−0.804807	−	0.112279i
$119$			6.81843i			0.625045i
$120$	4.90692	+	2.16690i	0.447938	+	0.197810i
$121$	−18.1265			−1.64786
$122$	20.1199	+	2.80694i	1.82157	+	0.254128i
$123$			19.4108i			1.75021i
$124$	−17.3716	−	4.94326i	−1.56002	−	0.443918i
$125$	−1.00000			−0.0894427
$126$	−0.337075	+	2.41613i	−0.0300290	+	0.215246i
$127$	2.90055			0.257382			0.128691	−	0.991685i	$-0.458922\pi$
$127$	2.90055			0.257382			0.128691	+	0.991685i	$0.458922\pi$
$128$	6.39273	+	9.33451i	0.565043	+	0.825062i
$129$		−	0.610524i		−	0.0537537i
$130$	−0.297885	+	2.13522i	−0.0261263	+	0.187271i
$131$			7.12190i			0.622243i	0.950370	+	0.311122i	$0.100705\pi$
$131$			7.12190i			0.622243i	−0.950370	+	0.311122i	$0.899295\pi$
$132$	5.60259	−	19.6887i	0.487643	−	1.71368i
$133$	−12.3647	+	2.43403i	−1.07215	+	0.211057i
$134$	3.34369	+	0.466480i	0.288851	+	0.0402977i
$135$	−4.55790			−0.392281
$136$	6.10213	+	2.69471i	0.523253	+	0.231069i
$137$	18.8921			1.61406			0.807029	−	0.590512i	$-0.201074\pi$
$137$	18.8921			1.61406			0.807029	+	0.590512i	$0.201074\pi$
$138$	−2.12193	+	15.2098i	−0.180631	+	1.29475i
$139$			2.31968i			0.196753i	0.995149	+	0.0983765i	$0.0313650\pi$
$139$			2.31968i			0.196753i	−0.995149	+	0.0983765i	$0.968635\pi$
$140$	1.58255	−	5.56141i	0.133750	−	0.470025i
$141$			16.9526i			1.42766i
$142$	18.1723	+	2.53522i	1.52498	+	0.212751i
$143$	8.22728			0.688000
$144$	2.02909	+	1.25654i	0.169091	+	0.104712i
$145$		−	7.31719i		−	0.607660i
$146$	−3.60287	−	0.502638i	−0.298176	−	0.0415986i
$147$	2.57624			0.212485
$148$	−0.0929178	+	0.326532i	−0.00763780	+	0.0268408i
$149$	−2.88580			−0.236414			−0.118207	−	0.992989i	$-0.537715\pi$
$149$	−2.88580			−0.236414			−0.118207	+	0.992989i	$0.537715\pi$
$150$	−2.65631	−	0.370584i	−0.216887	−	0.0302580i
$151$	−11.9549			−0.972872			−0.486436	−	0.873716i	$-0.661703\pi$
$151$	−11.9549			−0.972872			−0.486436	+	0.873716i	$0.661703\pi$
$152$	−2.70832	+	12.0277i	−0.219674	+	0.975573i
$153$	1.40718			0.113764
$154$	−21.8542	−	3.04889i	−1.76106	−	0.245687i
$155$	9.03062			0.725357
$156$	−1.58255	+	5.56141i	−0.126706	+	0.445269i
$157$	−1.78614			−0.142550			−0.0712748	−	0.997457i	$-0.522707\pi$
$157$	−1.78614			−0.142550			−0.0712748	+	0.997457i	$0.522707\pi$
$158$	6.52943	+	0.910925i	0.519454	+	0.0724693i
$159$			8.69059i			0.689208i
$160$	−4.35172	−	3.61422i	−0.344033	−	0.285729i
$161$	16.5542			1.30465
$162$	−14.6143	−	2.03886i	−1.14821	−	0.160188i
$163$			6.10411i			0.478111i	0.971006	+	0.239055i	$0.0768378\pi$
$163$			6.10411i			0.478111i	−0.971006	+	0.239055i	$0.923162\pi$
$164$	5.60259	−	19.6887i	0.437489	−	1.53743i
$165$			10.2351i			0.796804i
$166$	2.02089	−	14.4855i	0.156851	−	1.12430i
$167$	−12.8473			−0.994152			−0.497076	−	0.867707i	$-0.665593\pi$
$167$	−12.8473			−0.994152			−0.497076	+	0.867707i	$0.665593\pi$
$168$	6.26472	−	14.1864i	0.483333	−	1.09450i
$169$	10.6761			0.821235
$170$	−3.30333	−	0.460849i	−0.253354	−	0.0353455i
$171$	0.502333	+	2.55182i	0.0384143	+	0.195142i
$172$	−0.176217	+	0.619264i	−0.0134365	+	0.0472184i
$173$		−	18.3218i		−	1.39298i	−0.717565	−	0.696492i	$-0.754743\pi$
$173$		−	18.3218i		−	1.39298i	0.717565	−	0.696492i	$-0.245257\pi$
$174$	2.71163	−	19.4367i	0.205568	−	1.47350i
$175$			2.89109i			0.218546i
$176$	−11.3656	+	18.3534i	−0.856713	+	1.38344i
$177$	11.8373			0.889747
$178$	0.505947	−	3.62658i	0.0379223	−	0.271824i
$179$	15.4613			1.15563			0.577817	−	0.816166i	$-0.303905\pi$
$179$	15.4613			1.15563			0.577817	+	0.816166i	$0.303905\pi$
$180$	−1.14776	−	0.326606i	−0.0855489	−	0.0243438i
$181$		−	4.49195i		−	0.333884i	−0.985967	−	0.166942i	$-0.946611\pi$
$181$		−	4.49195i		−	0.333884i	0.985967	−	0.166942i	$-0.0533893\pi$
$182$	6.17311	+	0.861214i	0.457581	+	0.0638374i
$183$	−27.2424			−2.01382
$184$	6.54236	−	14.8151i	0.482309	−	1.09218i
$185$		−	0.169748i		−	0.0124801i
$186$	23.9881	+	3.34660i	1.75890	+	0.245385i
$187$			12.7282i			0.930776i
$188$	4.89307	−	17.1952i	0.356864	−	1.25409i
$189$			13.1773i			0.958509i
$190$	−0.343500	−	6.15484i	−0.0249201	−	0.446519i
$191$		−	15.3607i		−	1.11146i	−0.831362	−	0.555731i	$-0.812438\pi$
$191$		−	15.3607i		−	1.11146i	0.831362	−	0.555731i	$-0.187562\pi$
$192$	−10.2201	−	11.2132i	−0.737576	−	0.809240i
$193$			0.933817i			0.0672176i	0.999435	+	0.0336088i	$0.0107000\pi$
$193$			0.933817i			0.0672176i	−0.999435	+	0.0336088i	$0.989300\pi$
$194$	−2.92103	+	20.9377i	−0.209718	+	1.50324i
$195$		−	2.89109i		−	0.207036i
$196$	−2.61311	−	0.743587i	−0.186651	−	0.0531133i
$197$	−14.3198			−1.02024			−0.510121	−	0.860103i	$-0.670399\pi$
$197$	−14.3198			−1.02024			−0.510121	+	0.860103i	$0.670399\pi$
$198$	−0.629229	+	4.51026i	−0.0447173	+	0.320530i
$199$		−	19.0818i		−	1.35267i	−0.736594	−	0.676336i	$-0.763567\pi$
$199$		−	19.0818i		−	1.35267i	0.736594	−	0.676336i	$-0.236433\pi$
$200$	2.58737	+	1.14259i	0.182955	+	0.0807931i
$201$	−4.52737			−0.319336
$202$	2.73839	+	0.382035i	0.192673	+	0.0268799i
$203$	−21.1547			−1.48477
$204$	−8.60388	−	2.44832i	−0.602392	−	0.171417i
$205$			10.2351i			0.714853i
$206$	11.3988	+	1.59025i	0.794189	+	0.110798i
$207$		−	3.41644i		−	0.237459i
$208$	3.21041	−	5.18424i	0.222602	−	0.359462i
$209$	−23.0815	+	4.54367i	−1.59658	+	0.314292i
$210$	−1.07139	+	7.67965i	−0.0739331	+	0.529946i
$211$	−9.96928			−0.686314			−0.343157	−	0.939278i	$-0.611496\pi$
$211$	−9.96928			−0.686314			−0.343157	+	0.939278i	$0.611496\pi$
$212$	2.50839	−	8.81499i	0.172277	−	0.605416i
$213$	−24.6053			−1.68593
$214$	−14.7093	−	2.05210i	−1.00551	−	0.140279i
$215$		−	0.321924i		−	0.0219550i
$216$	11.7930	+	5.20780i	0.802411	+	0.354346i
$217$		−	26.1084i		−	1.77235i
$218$	−1.81647	+	13.0203i	−0.123027	+	0.881844i
$219$	4.87831			0.329645
$220$	2.95420	−	10.3816i	0.199172	−	0.699930i
$221$		−	3.59530i		−	0.241846i
$222$	0.0629056	−	0.450902i	0.00422195	−	0.0302626i
$223$	14.5848			0.976668			0.488334	−	0.872657i	$-0.337605\pi$
$223$	14.5848			0.976668			0.488334	+	0.872657i	$0.337605\pi$
$224$	−10.4490	+	12.5812i	−0.698156	+	0.840618i
$225$	0.596662			0.0397774
$226$	−1.19827	+	8.58912i	−0.0797079	+	0.571339i
$227$	5.62406			0.373282			0.186641	−	0.982428i	$-0.440240\pi$
$227$	5.62406			0.373282			0.186641	+	0.982428i	$0.440240\pi$
$228$	1.36844	−	16.4765i	0.0906271	−	1.09118i
$229$	11.3852			0.752357			0.376179	−	0.926547i	$-0.377238\pi$
$229$	11.3852			0.752357			0.376179	+	0.926547i	$0.377238\pi$
$230$	−1.11887	+	8.02000i	−0.0737764	+	0.528823i
$231$	29.5907			1.94693
$232$	−8.36053	+	18.9323i	−0.548896	+	1.24297i
$233$	20.6500			1.35283			0.676413	−	0.736523i	$-0.263534\pi$
$233$	20.6500			1.35283			0.676413	+	0.736523i	$0.263534\pi$
$234$	0.177737	−	1.27400i	0.0116190	−	0.0832841i
$235$			8.93894i			0.583112i
$236$	−12.0068	−	3.41664i	−0.781574	−	0.222404i
$237$	−8.84089			−0.574277
$238$	−1.33236	+	9.55023i	−0.0863639	+	0.619049i
$239$			2.37595i			0.153688i	0.997043	+	0.0768439i	$0.0244843\pi$
$239$			2.37595i			0.153688i	−0.997043	+	0.0768439i	$0.975516\pi$
$240$	6.44944	+	3.99390i	0.416310	+	0.257805i
$241$			29.9656i			1.93025i	0.261785	+	0.965126i	$0.415689\pi$
$241$			29.9656i			1.93025i	−0.261785	+	0.965126i	$0.584311\pi$
$242$	−25.3888	−	3.54201i	−1.63205	−	0.227689i
$243$	6.11421			0.392227
$244$	27.6324	+	7.86307i	1.76898	+	0.503381i
$245$	1.35843			0.0867867
$246$	−3.79297	+	27.1877i	−0.241831	+	1.73343i
$247$	6.51979	−	1.28344i	0.414844	−	0.0816633i
$248$	−23.3656	−	10.3183i	−1.48372	−	0.655211i
$249$			19.6135i			1.24296i
$250$	−1.40065	−	0.195405i	−0.0885848	−	0.0123585i
$251$			5.58897i			0.352773i	0.984321	+	0.176386i	$0.0564408\pi$
$251$			5.58897i			0.352773i	−0.984321	+	0.176386i	$0.943559\pi$
$252$	−0.944248	+	3.31828i	−0.0594820	+	0.209032i
$253$	30.9022			1.94280
$254$	4.06265	+	0.566782i	0.254913	+	0.0355631i
$255$	4.47272			0.280093
$256$	7.12995	+	14.3235i	0.445622	+	0.895221i
$257$		−	5.98140i		−	0.373109i	−0.982445	−	0.186555i	$-0.940268\pi$
$257$		−	5.98140i		−	0.373109i	0.982445	−	0.186555i	$-0.0597321\pi$
$258$	0.119300	−	0.855130i	0.00742727	−	0.0532381i
$259$	−0.490756			−0.0304941
$260$	−0.834465	+	2.93248i	−0.0517513	+	0.181865i
$261$			4.36589i			0.270242i
$262$	−1.39166	+	9.97528i	−0.0859768	+	0.616275i
$263$		−	7.40601i		−	0.456674i	−0.973582	−	0.228337i	$-0.926671\pi$
$263$		−	7.40601i		−	0.456674i	0.973582	−	0.228337i	$-0.0733288\pi$
$264$	11.6945	−	26.4821i	0.719749	−	1.62986i
$265$			4.58247i			0.281499i
$266$	−17.7942	+	0.993090i	−1.09103	+	0.0608903i
$267$			4.91041i			0.300513i
$268$	4.59218	+	1.30675i	0.280512	+	0.0798224i
$269$			12.3998i			0.756028i	0.925800	+	0.378014i	$0.123393\pi$
$269$			12.3998i			0.756028i	−0.925800	+	0.378014i	$0.876607\pi$
$270$	−6.38402	−	0.890638i	−0.388519	−	0.0542025i
$271$		−	1.28344i		−	0.0779634i	−0.999240	−	0.0389817i	$-0.987589\pi$
$271$		−	1.28344i		−	0.0779634i	0.999240	−	0.0389817i	$-0.0124114\pi$
$272$	8.02038	+	4.96673i	0.486307	+	0.301152i
$273$	−8.35843			−0.505875
$274$	26.4611	+	3.69161i	1.59858	+	0.223018i
$275$			5.39689i			0.325445i
$276$	−5.94416	+	20.8890i	−0.357796	+	1.25737i
$277$	4.17279			0.250719			0.125359	−	0.992111i	$-0.459992\pi$
$277$	4.17279			0.250719			0.125359	+	0.992111i	$0.459992\pi$
$278$	−0.453279	+	3.24906i	−0.0271859	+	0.194866i
$279$	−5.38823			−0.322585
$280$	3.30333	−	7.48034i	0.197412	−	0.447036i
$281$		−	17.0728i		−	1.01848i	−0.860626	−	0.509238i	$-0.829927\pi$
$281$		−	17.0728i		−	1.01848i	0.860626	−	0.509238i	$-0.170073\pi$
$282$	−3.31262	+	23.7446i	−0.197264	+	1.41397i
$283$		−	3.92734i		−	0.233456i	−0.993164	−	0.116728i	$-0.962759\pi$
$283$		−	3.92734i		−	0.233456i	0.993164	−	0.116728i	$-0.0372406\pi$
$284$	24.9576	+	7.10191i	1.48096	+	0.421421i
$285$	1.59666	+	8.11093i	0.0945781	+	0.480450i
$286$	11.5235	+	1.60765i	0.681401	+	0.0950626i
$287$	29.5907			1.74669
$288$	2.59650	+	2.15646i	0.153000	+	0.127071i
$289$	−11.4378			−0.672813
$290$	1.42982	−	10.2488i	0.0839618	−	0.601831i
$291$		−	28.3497i		−	1.66189i
$292$	−4.94814	−	1.40804i	−0.289568	−	0.0823993i
$293$		−	32.8495i		−	1.91909i	−0.281558	−	0.959544i	$-0.590851\pi$
$293$		−	32.8495i		−	1.91909i	0.281558	−	0.959544i	$-0.409149\pi$
$294$	3.60840	+	0.503411i	0.210446	+	0.0293595i
$295$	6.24171			0.363406
$296$	−0.193951	+	0.439200i	−0.0112732	+	0.0255280i
$297$			24.5985i			1.42735i
$298$	−4.04199	−	0.563901i	−0.234146	−	0.0326659i
$299$	−8.72886			−0.504803
$300$	−3.64815	−	1.03811i	−0.210626	−	0.0599356i
$301$	−0.930712			−0.0536454
$302$	−16.7445	−	2.33604i	−0.963540	−	0.134424i
$303$	−3.70780			−0.213007
$304$	−6.14367	+	16.3173i	−0.352364	+	0.935863i
$305$	−14.3647			−0.822520
$306$	1.97097	+	0.274971i	0.112673	+	0.0157190i
$307$	−26.9293			−1.53694			−0.768469	−	0.639887i	$-0.778981\pi$
$307$	−26.9293			−1.53694			−0.768469	+	0.639887i	$0.778981\pi$
$308$	−30.0143	−	8.54086i	−1.71022	−	0.486661i
$309$	−15.4340			−0.878008
$310$	12.6487	+	1.76463i	0.718400	+	0.100224i
$311$			10.1428i			0.575148i	0.957758	+	0.287574i	$0.0928486\pi$
$311$			10.1428i			0.575148i	−0.957758	+	0.287574i	$0.907151\pi$
$312$	−3.30333	+	7.48034i	−0.187014	+	0.423491i
$313$	−4.31379			−0.243830			−0.121915	−	0.992541i	$-0.538903\pi$
$313$	−4.31379			−0.243830			−0.121915	+	0.992541i	$0.538903\pi$
$314$	−2.50176	−	0.349021i	−0.141182	−	0.0196964i
$315$		−	1.72501i		−	0.0971930i
$316$	8.96744	+	2.55177i	0.504458	+	0.143548i
$317$		−	15.0795i		−	0.846950i	−0.905908	−	0.423475i	$-0.860810\pi$
$317$		−	15.0795i		−	0.846950i	0.905908	−	0.423475i	$-0.139190\pi$
$318$	−1.69819	+	12.1725i	−0.0952296	+	0.682598i
$319$	−39.4901			−2.21102
$320$	−5.38899	−	5.91260i	−0.301254	−	0.330524i
$321$	19.9164			1.11163
$322$	23.1866	+	3.23477i	1.29214	+	0.180267i
$323$	1.98557	+	10.0866i	0.110480	+	0.561232i
$324$	−20.0712	−	5.71144i	−1.11506	−	0.317302i
$325$		−	1.52445i		−	0.0845611i
$326$	−1.19278	+	8.54972i	−0.0660618	+	0.473525i
$327$		−	17.6295i		−	0.974915i
$328$	11.6945	−	26.4821i	0.645723	−	1.46223i
$329$	25.8433			1.42479
$330$	−2.00000	+	14.3358i	−0.110096	+	0.789161i
$331$	−3.81552			−0.209720			−0.104860	−	0.994487i	$-0.533439\pi$
$331$	−3.81552			−0.209720			−0.104860	+	0.994487i	$0.533439\pi$
$332$	5.66110	−	19.8943i	0.310693	−	1.09184i
$333$			0.101282i			0.00555021i
$334$	−17.9945	−	2.51043i	−0.984617	−	0.137364i
$335$	−2.38724			−0.130429
$336$	11.5468	−	18.6459i	0.629927	−	1.01722i
$337$			8.72146i			0.475088i	0.971377	+	0.237544i	$0.0763424\pi$
$337$			8.72146i			0.475088i	−0.971377	+	0.237544i	$0.923658\pi$
$338$	14.9534	+	2.08616i	0.813358	+	0.113472i
$339$		−	11.6297i		−	0.631639i
$340$	−4.53675	−	1.29098i	−0.246040	−	0.0700130i
$341$		−	48.7373i		−	2.63927i
$342$	0.204953	+	3.67236i	0.0110826	+	0.198578i
$343$			16.3103i			0.880675i
$344$	−0.367826	+	0.832937i	−0.0198319	+	0.0449089i
$345$		−	10.8591i		−	0.584636i
$346$	3.58018	−	25.6625i	0.192472	−	1.37962i
$347$			20.5064i			1.10084i	0.834887	+	0.550421i	$0.185533\pi$
$347$			20.5064i			1.10084i	−0.834887	+	0.550421i	$0.814467\pi$
$348$	7.59609	−	26.6942i	0.407193	−	1.43096i
$349$	−17.5131			−0.937455			−0.468727	−	0.883343i	$-0.655287\pi$
$349$	−17.5131			−0.937455			−0.468727	+	0.883343i	$0.655287\pi$
$350$	−0.564935	+	4.04941i	−0.0301971	+	0.216450i
$351$		−	6.94828i		−	0.370872i
$352$	−19.5055	+	23.4858i	−1.03965	+	1.25179i
$353$	−15.4173			−0.820579			−0.410290	−	0.911955i	$-0.634572\pi$
$353$	−15.4173			−0.820579			−0.410290	+	0.911955i	$0.634572\pi$
$354$	16.5799	+	2.31307i	0.881213	+	0.122939i
$355$	−12.9742			−0.688598
$356$	1.41731	−	4.98070i	0.0751171	−	0.263977i
$357$		−	12.9311i		−	0.684385i
$358$	21.6559	+	3.02123i	1.14455	+	0.159677i
$359$		−	30.0932i		−	1.58826i	−0.607749	−	0.794129i	$-0.707927\pi$
$359$		−	30.0932i		−	1.58826i	0.607749	−	0.794129i	$-0.292073\pi$
$360$	−1.54379	−	0.681738i	−0.0813647	−	0.0359307i
$361$	−17.5824	+	7.20135i	−0.925389	+	0.379019i
$362$	0.877752	−	6.29165i	0.0461336	−	0.330682i
$363$	34.3766			1.80430
$364$	8.47807	+	2.41252i	0.444372	+	0.126450i
$365$	2.57229			0.134640
$366$	−38.1571	−	5.32332i	−1.99450	−	0.278254i
$367$		−	9.34040i		−	0.487565i	−0.969830	−	0.243782i	$-0.921612\pi$
$367$		−	9.34040i		−	0.487565i	0.969830	−	0.243782i	$-0.0783883\pi$
$368$	12.0585	−	19.4723i	0.628592	−	1.01506i
$369$		−	6.10691i		−	0.317913i
$370$	0.0331696	−	0.237757i	0.00172440	−	0.0123604i
$371$	13.2483			0.687820
$372$	32.9450	+	9.37482i	1.70812	+	0.486062i
$373$		−	13.8891i		−	0.719151i	−0.933116	−	0.359576i	$-0.882921\pi$
$373$		−	13.8891i		−	0.719151i	0.933116	−	0.359576i	$-0.117079\pi$
$374$	−2.48715	+	17.8277i	−0.128608	+	0.921849i
$375$	1.89649			0.0979342
$376$	10.2135	−	23.1284i	0.526722	−	1.19275i
$377$	11.1547			0.574495
$378$	−2.57492	+	18.4568i	−0.132439	+	0.949315i
$379$	4.81680			0.247423			0.123711	−	0.992318i	$-0.460520\pi$
$379$	4.81680			0.247423			0.123711	+	0.992318i	$0.460520\pi$
$380$	0.721565	−	8.68788i	0.0370155	−	0.445679i
$381$	−5.50085			−0.281817
$382$	3.00157	−	21.5150i	0.153573	−	1.10080i
$383$	−23.1900			−1.18496			−0.592478	−	0.805587i	$-0.701850\pi$
$383$	−23.1900			−1.18496			−0.592478	+	0.805587i	$0.701850\pi$
$384$	−12.1237	−	17.7028i	−0.618686	−	0.903391i
$385$	15.6029			0.795199
$386$	−0.182473	+	1.30795i	−0.00928762	+	0.0665729i
$387$			0.192080i			0.00976396i
$388$	−8.18267	+	28.7555i	−0.415412	+	1.45984i
$389$	18.2300			0.924296			0.462148	−	0.886803i	$-0.347079\pi$
$389$	18.2300			0.924296			0.462148	+	0.886803i	$0.347079\pi$
$390$	0.564935	−	4.04941i	0.0286066	−	0.205050i
$391$		−	13.5042i		−	0.682935i
$392$	−3.51475	−	1.55212i	−0.177522	−	0.0783939i
$393$		−	13.5066i		−	0.681317i
$394$	−20.0570	−	2.79816i	−1.01046	−	0.140969i
$395$	−4.66172			−0.234557
$396$	−1.76266	+	6.19433i	−0.0885768	+	0.311277i
$397$	11.4337			0.573841			0.286921	−	0.957954i	$-0.407368\pi$
$397$	11.4337			0.573841			0.286921	+	0.957954i	$0.407368\pi$
$398$	3.72868	−	26.7269i	0.186902	−	1.33970i
$399$	23.4495	−	4.61610i	1.17394	−	0.231094i
$400$	3.40073	+	2.10595i	0.170037	+	0.105297i
$401$		−	27.7676i		−	1.38665i	−0.720627	−	0.693323i	$-0.756146\pi$
$401$		−	27.7676i		−	1.38665i	0.720627	−	0.693323i	$-0.243854\pi$
$402$	−6.34126	−	0.884673i	−0.316273	−	0.0441235i
$403$			13.7667i			0.685769i
$404$	3.76087	+	1.07019i	0.187110	+	0.0532441i
$405$	10.4340			0.518469
$406$	−29.6303	−	4.13374i	−1.47053	−	0.205154i
$407$	−0.916109			−0.0454098
$408$	−11.5726	−	5.11048i	−0.572929	−	0.253006i
$409$		−	24.9471i		−	1.23356i	−0.787137	−	0.616778i	$-0.788438\pi$
$409$		−	24.9471i		−	1.23356i	0.787137	−	0.616778i	$-0.211562\pi$
$410$	−2.00000	+	14.3358i	−0.0987730	+	0.707996i
$411$	−35.8286			−1.76729
$412$	15.6549	+	4.45475i	0.771262	+	0.219470i
$413$		−	18.0454i		−	0.887955i
$414$	0.667590	−	4.78523i	0.0328103	−	0.235181i
$415$			10.3420i			0.507670i
$416$	5.50968	−	6.63396i	0.270134	−	0.325257i
$417$		−	4.39925i		−	0.215432i
$418$	−33.2170	+	1.85383i	−1.62470	+	0.0906739i
$419$		−	7.00936i		−	0.342430i	−0.985234	−	0.171215i	$-0.945231\pi$
$419$		−	7.00936i		−	0.342430i	0.985234	−	0.171215i	$-0.0547692\pi$
$420$	−3.00129	+	10.5471i	−0.146448	+	0.514647i
$421$		−	6.18615i		−	0.301494i	−0.988572	−	0.150747i	$-0.951832\pi$
$421$		−	6.18615i		−	0.301494i	0.988572	−	0.150747i	$-0.0481680\pi$
$422$	−13.9635	−	1.94805i	−0.679731	−	0.0948296i
$423$		−	5.33352i		−	0.259325i
$424$	5.23587	−	11.8565i	0.254276	−	0.575805i
$425$	2.35843			0.114400
$426$	−34.4634	−	4.80802i	−1.66976	−	0.232949i
$427$			41.5297i			2.00976i
$428$	−20.2015	−	5.74854i	−0.976478	−	0.277866i
$429$	−15.6029			−0.753316
$430$	0.0629056	−	0.450902i	0.00303358	−	0.0217444i
$431$	−40.6222			−1.95670			−0.978351	−	0.206951i	$-0.933646\pi$
$431$	−40.6222			−1.95670			−0.978351	+	0.206951i	$0.933646\pi$
$432$	15.5002	+	9.59870i	0.745753	+	0.461818i
$433$			28.5295i			1.37104i	0.728054	+	0.685520i	$0.240425\pi$
$433$			28.5295i			1.37104i	−0.728054	+	0.685520i	$0.759575\pi$
$434$	5.10172	−	36.5687i	0.244890	−	1.75535i
$435$			13.8770i			0.665349i
$436$	−5.08846	+	17.8819i	−0.243693	+	0.856387i
$437$	24.4887	−	4.82068i	1.17145	−	0.230604i
$438$	6.83279	+	0.953247i	0.326483	+	0.0455479i
$439$	32.9206			1.57121			0.785606	−	0.618727i	$-0.212351\pi$
$439$	32.9206			1.57121			0.785606	+	0.618727i	$0.212351\pi$
$440$	6.16642	−	13.9638i	0.293973	−	0.665697i
$441$	−0.810521			−0.0385962
$442$	0.702540	−	5.03575i	0.0334164	−	0.239526i
$443$		−	25.0123i		−	1.18837i	−0.804329	−	0.594184i	$-0.797475\pi$
$443$		−	25.0123i		−	1.18837i	0.804329	−	0.594184i	$-0.202525\pi$
$444$	0.176217	−	0.619264i	0.00836291	−	0.0293889i
$445$			2.58922i			0.122741i
$446$	20.4281	+	2.84994i	0.967300	+	0.134949i
$447$	5.47288			0.258858
$448$	−17.0939	+	15.5801i	−0.807610	+	0.736089i
$449$		−	10.6355i		−	0.501919i	−0.967998	−	0.250960i	$-0.919254\pi$
$449$		−	10.6355i		−	0.501919i	0.967998	−	0.250960i	$-0.0807461\pi$
$450$	0.835714	+	0.116591i	0.0393959	+	0.00549615i
$451$	55.2379			2.60105
$452$	−3.35672	+	11.7962i	−0.157887	+	0.554846i
$453$	22.6722			1.06523
$454$	7.87733	+	1.09897i	0.369701	+	0.0515772i
$455$	−4.40732			−0.206618
$456$	5.13629	−	22.8103i	0.240529	−	1.06819i
$457$	−31.2118			−1.46003			−0.730014	−	0.683432i	$-0.760487\pi$
$457$	−31.2118			−1.46003			−0.730014	+	0.683432i	$0.760487\pi$
$458$	15.9467	+	2.22473i	0.745141	+	0.103955i
$459$	10.7495			0.501742
$460$	−3.13430	+	11.0146i	−0.146138	+	0.513557i
$461$	−18.9126			−0.880847			−0.440424	−	0.897790i	$-0.645172\pi$
$461$	−18.9126			−0.880847			−0.440424	+	0.897790i	$0.645172\pi$
$462$	41.4462	+	5.78219i	1.92825	+	0.269012i
$463$			4.70103i			0.218475i	0.994016	+	0.109238i	$0.0348410\pi$
$463$			4.70103i			0.218475i	−0.994016	+	0.109238i	$0.965159\pi$
$464$	−15.4096	+	24.8838i	−0.715375	+	1.15520i
$465$	−17.1265			−0.794220
$466$	28.9234	+	4.03512i	1.33985	+	0.186923i
$467$			27.0478i			1.25162i	0.779974	+	0.625812i	$0.215232\pi$
$467$			27.0478i			1.25162i	−0.779974	+	0.625812i	$0.784768\pi$
$468$	0.497893	−	1.74970i	0.0230151	−	0.0808798i
$469$			6.90174i			0.318693i
$470$	−1.74672	+	12.5203i	−0.0805700	+	0.577519i
$471$	3.38739			0.156083
$472$	−16.1496	−	7.13170i	−0.743347	−	0.328263i
$473$	−1.73739			−0.0798852
$474$	−12.3830	−	1.72756i	−0.568769	−	0.0793493i
$475$	0.841905	+	4.27682i	0.0386293	+	0.196234i
$476$	−3.73233	+	13.1162i	−0.171071	+	0.601179i
$477$		−	2.73418i		−	0.125190i
$478$	−0.464274	+	3.32788i	−0.0212354	+	0.152214i
$479$			16.7220i			0.764047i	0.924153	+	0.382024i	$0.124773\pi$
$479$			16.7220i			0.764047i	−0.924153	+	0.382024i	$0.875227\pi$
$480$	8.25297	+	6.85431i	0.376695	+	0.312855i
$481$	0.258771			0.0117989
$482$	−5.85543	+	41.9712i	−0.266708	+	1.91174i
$483$	−31.3948			−1.42851
$484$	−34.8687	−	9.92221i	−1.58494	−	0.451010i
$485$		−	14.9486i		−	0.678779i
$486$	8.56386	+	1.19475i	0.388464	+	0.0541949i
$487$	7.71284			0.349502			0.174751	−	0.984613i	$-0.444088\pi$
$487$	7.71284			0.349502			0.174751	+	0.984613i	$0.444088\pi$
$488$	37.1668	+	16.4129i	1.68246	+	0.742978i
$489$		−	11.5764i		−	0.523501i
$490$	1.90268	+	0.265444i	0.0859542	+	0.0119915i
$491$			0.710320i			0.0320563i	0.999872	+	0.0160282i	$0.00510214\pi$
$491$			0.710320i			0.0320563i	−0.999872	+	0.0160282i	$0.994898\pi$
$492$	−10.6252	+	37.3393i	−0.479023	+	1.68338i
$493$			17.2571i			0.777219i
$494$	9.38272	−	0.523647i	0.422149	−	0.0235600i
$495$		−	3.22012i		−	0.144734i
$496$	−30.7107	−	19.0180i	−1.37895	−	0.853935i
$497$			37.5096i			1.68253i
$498$	−3.83258	+	27.4716i	−0.171742	+	1.23103i
$499$		−	41.9119i		−	1.87623i	−0.346320	−	0.938117i	$-0.612569\pi$
$499$		−	41.9119i		−	1.87623i	0.346320	−	0.938117i	$-0.387431\pi$
$500$	−1.92363	−	0.547388i	−0.0860275	−	0.0244800i
$501$	24.3647			1.08853
$502$	−1.09212	+	7.82819i	−0.0487435	+	0.349389i
$503$		−	38.1073i		−	1.69912i	−0.527492	−	0.849560i	$-0.676868\pi$
$503$		−	38.1073i		−	1.69912i	0.527492	−	0.849560i	$-0.323132\pi$
$504$	−1.97097	+	4.46323i	−0.0877939	+	0.198808i
$505$	−1.95509			−0.0870003
$506$	43.2831	+	6.03845i	1.92417	+	0.268442i
$507$	−20.2470			−0.899201
$508$	5.57959	+	1.58773i	0.247554	+	0.0704439i
$509$			22.6532i			1.00408i	0.864843	+	0.502042i	$0.167418\pi$
$509$			22.6532i			1.00408i	−0.864843	+	0.502042i	$0.832582\pi$
$510$	6.26472	+	0.873994i	0.277406	+	0.0387011i
$511$		−	7.43672i		−	0.328981i
$512$	7.18767	+	21.4555i	0.317653	+	0.948207i
$513$	3.83732	+	19.4933i	0.169422	+	0.860651i
$514$	1.16880	−	8.37783i	0.0515534	−	0.369530i
$515$	−8.13820			−0.358612
$516$	0.334194	−	1.17443i	0.0147121	−	0.0517012i
$517$	48.2425			2.12170
$518$	−0.687377	−	0.0958963i	−0.0302016	−	0.00421344i
$519$			34.7471i			1.52523i
$520$	−1.74181	+	3.94431i	−0.0763836	+	0.172970i
$521$			36.1549i			1.58397i	0.610538	+	0.791987i	$0.290953\pi$
$521$			36.1549i			1.58397i	−0.610538	+	0.791987i	$0.709047\pi$
$522$	−0.853118	+	6.11508i	−0.0373400	+	0.267650i
$523$	7.62489			0.333413			0.166707	−	0.986007i	$-0.446687\pi$
$523$	7.62489			0.333413			0.166707	+	0.986007i	$0.446687\pi$
$524$	−3.89844	+	13.6999i	−0.170304	+	0.598484i
$525$		−	5.48292i		−	0.239294i
$526$	1.44717	−	10.3732i	0.0630998	−	0.452294i
$527$	−21.2981			−0.927758
$528$	21.5547	−	34.8070i	0.938047	−	1.51478i
$529$	−9.78615			−0.425485
$530$	−0.895438	+	6.41843i	−0.0388954	+	0.278799i
$531$	−3.72419			−0.161616
$532$	−25.1175	−	2.08611i	−1.08898	−	0.0904445i
$533$	−15.6029			−0.675838
$534$	−0.959521	+	6.87777i	−0.0415225	+	0.297630i
$535$	10.5018			0.454031
$536$	6.17669	+	2.72763i	0.266792	+	0.117816i
$537$	−29.3222			−1.26535
$538$	−2.42298	+	17.3677i	−0.104462	+	0.748776i
$539$		−	7.33128i		−	0.315781i
$540$	−8.76773	−	2.49494i	−0.377303	−	0.107365i
$541$	−6.76176			−0.290711			−0.145355	−	0.989379i	$-0.546433\pi$
$541$	−6.76176			−0.290711			−0.145355	+	0.989379i	$0.546433\pi$
$542$	0.250791	−	1.79765i	0.0107724	−	0.0772156i
$543$			8.51893i			0.365582i
$544$	10.2632	+	8.52386i	0.440031	+	0.365458i
$545$		−	9.29589i		−	0.398192i
$546$	−11.7072	−	1.63328i	−0.501023	−	0.0698980i
$547$	−28.0992			−1.20144			−0.600718	−	0.799461i	$-0.705119\pi$
$547$	−28.0992			−1.20144			−0.600718	+	0.799461i	$0.705119\pi$
$548$	36.3414	+	10.3413i	1.55243	+	0.441758i
$549$	8.57086			0.365795
$550$	−1.05458	+	7.55915i	−0.0449675	+	0.322323i
$551$	−31.2943	+	6.16038i	−1.33318	+	0.262441i
$552$	−12.4075	+	28.0966i	−0.528098	+	1.19587i
$553$			13.4775i			0.573120i
$554$	5.84461	+	0.815385i	0.248314	+	0.0346424i
$555$			0.321924i			0.0136649i
$556$	−1.26977	+	4.46222i	−0.0538502	+	0.189240i
$557$	−21.4567			−0.909148			−0.454574	−	0.890709i	$-0.650208\pi$
$557$	−21.4567			−0.909148			−0.454574	+	0.890709i	$0.650208\pi$
$558$	−7.54701	−	1.05289i	−0.319491	−	0.0445723i
$559$	0.490756			0.0207568
$560$	6.08850	−	9.83184i	0.257286	−	0.415471i
$561$		−	24.1388i		−	1.01914i
$562$	3.33611	−	23.9129i	0.140725	−	1.00871i
$563$	9.60603			0.404846			0.202423	−	0.979298i	$-0.435118\pi$
$563$	9.60603			0.404846			0.202423	+	0.979298i	$0.435118\pi$
$564$	−9.27964	+	32.6105i	−0.390743	+	1.37315i
$565$		−	6.13224i		−	0.257985i
$566$	0.767423	−	5.50082i	0.0322572	−	0.231217i
$567$		−	30.1656i		−	1.26684i
$568$	33.5690	+	14.8241i	1.40852	+	0.622006i
$569$		−	25.7172i		−	1.07812i	−0.842267	−	0.539060i	$-0.818780\pi$
$569$		−	25.7172i		−	1.07812i	0.842267	−	0.539060i	$-0.181220\pi$
$570$	0.651443	+	11.6726i	0.0272859	+	0.488910i
$571$			28.3006i			1.18434i	0.805812	+	0.592171i	$0.201729\pi$
$571$			28.3006i			1.18434i	−0.805812	+	0.592171i	$0.798271\pi$
$572$	15.8263	+	4.50352i	0.661730	+	0.188302i
$573$			29.1314i			1.21698i
$574$	41.4462	+	5.78219i	1.72993	+	0.241344i
$575$		−	5.72592i		−	0.238787i
$576$	3.21540	+	3.52782i	0.133975	+	0.146992i
$577$	−17.1205			−0.712734			−0.356367	−	0.934346i	$-0.615985\pi$
$577$	−17.1205			−0.712734			−0.356367	+	0.934346i	$0.615985\pi$
$578$	−16.0204	−	2.23501i	−0.666360	−	0.0929642i
$579$		−	1.77097i		−	0.0735990i
$580$	4.00535	−	14.0756i	0.166313	−	0.584457i
$581$	29.8998			1.24045
$582$	5.53969	−	39.7080i	0.229628	−	1.64595i
$583$	24.7311			1.02426
$584$	−6.65546	−	2.93906i	−0.275405	−	0.121619i
$585$			0.909579i			0.0376065i
$586$	6.41897	−	46.0106i	0.265165	−	1.90068i
$587$			28.7512i			1.18669i	0.804949	+	0.593345i	$0.202193\pi$
$587$			28.7512i			1.18669i	−0.804949	+	0.593345i	$0.797807\pi$
$588$	4.95574	+	1.41020i	0.204371	+	0.0581558i
$589$	−7.60293	−	38.6224i	−0.313273	−	1.59141i
$590$	8.74244	+	1.21966i	0.359921	+	0.0502127i
$591$	27.1573			1.11710
$592$	−0.357480	+	0.577266i	−0.0146923	+	0.0237255i
$593$	−33.2094			−1.36375			−0.681874	−	0.731470i	$-0.738835\pi$
$593$	−33.2094			−1.36375			−0.681874	+	0.731470i	$0.738835\pi$
$594$	−4.80668	+	34.4538i	−0.197220	+	1.41366i
$595$		−	6.81843i		−	0.279529i
$596$	−5.55122	−	1.57965i	−0.227387	−	0.0647051i
$597$			36.1883i			1.48109i
$598$	−12.2261	−	1.70567i	−0.499961	−	0.0697499i
$599$	45.3037			1.85106			0.925529	−	0.378676i	$-0.123620\pi$
$599$	45.3037			1.85106			0.925529	+	0.378676i	$0.123620\pi$
$600$	−4.90692	−	2.16690i	−0.200324	−	0.0884634i
$601$			34.2916i			1.39878i	0.714739	+	0.699391i	$0.246545\pi$
$601$			34.2916i			1.39878i	−0.714739	+	0.699391i	$0.753455\pi$
$602$	−1.30360	−	0.181866i	−0.0531308	−	0.00741231i
$603$	1.42438			0.0580051
$604$	−22.9968	−	6.54395i	−0.935725	−	0.266269i
$605$	18.1265			0.736945
$606$	−5.19332	−	0.724524i	−0.210964	−	0.0294318i
$607$	−9.52529			−0.386620			−0.193310	−	0.981138i	$-0.561922\pi$
$607$	−9.52529			−0.386620			−0.193310	+	0.981138i	$0.561922\pi$
$608$	−11.7936	+	21.6543i	−0.478295	+	0.878199i
$609$	40.1196			1.62573
$610$	−20.1199	−	2.80694i	−0.814630	−	0.113650i
$611$	−13.6269			−0.551287
$612$	2.70690	+	0.770276i	0.109420	+	0.0311365i
$613$	3.86554			0.156128			0.0780638	−	0.996948i	$-0.475126\pi$
$613$	3.86554			0.156128			0.0780638	+	0.996948i	$0.475126\pi$
$614$	−37.7185	−	5.26213i	−1.52220	−	0.212362i
$615$		−	19.4108i		−	0.782719i
$616$	−40.3706	−	17.8277i	−1.62658	−	0.718299i
$617$	2.52522			0.101662			0.0508308	−	0.998707i	$-0.483813\pi$
$617$	2.52522			0.101662			0.0508308	+	0.998707i	$0.483813\pi$
$618$	−21.6176	−	3.01588i	−0.869587	−	0.121317i
$619$			10.1488i			0.407915i	0.978980	+	0.203957i	$0.0653804\pi$
$619$			10.1488i			0.407915i	−0.978980	+	0.203957i	$0.934620\pi$
$620$	17.3716	+	4.94326i	0.697661	+	0.198526i
$621$		−	26.0982i		−	1.04728i
$622$	−1.98196	+	14.2066i	−0.0794695	+	0.569631i
$623$	7.48567			0.299907
$624$	−6.08850	+	9.83184i	−0.243735	+	0.393588i
$625$	1.00000			0.0400000
$626$	−6.04210	−	0.842937i	−0.241491	−	0.0336905i
$627$	43.7738	−	8.61701i	1.74816	−	0.344130i
$628$	−3.43588	−	0.977713i	−0.137107	−	0.0390150i
$629$			0.400337i			0.0159625i
$630$	0.337075	−	2.41613i	0.0134294	−	0.0962608i
$631$		−	30.4714i		−	1.21305i	−0.795066	−	0.606524i	$-0.792564\pi$
$631$		−	30.4714i		−	1.21305i	0.795066	−	0.606524i	$-0.207436\pi$
$632$	12.0616	+	5.32642i	0.479785	+	0.211874i
$633$	18.9066			0.751470
$634$	2.94662	−	21.1211i	0.117025	−	0.838826i
$635$	−2.90055			−0.115105
$636$	−4.75713	+	16.7175i	−0.188632	+	0.662892i
$637$			2.07085i			0.0820501i
$638$	−55.3118	−	7.71658i	−2.18981	−	0.305502i
$639$	7.74119			0.306237
$640$	−6.39273	−	9.33451i	−0.252695	−	0.368979i
$641$			22.2210i			0.877675i	0.898566	+	0.438838i	$0.144610\pi$
$641$			22.2210i			0.877675i	−0.898566	+	0.438838i	$0.855390\pi$
$642$	27.8959	+	3.89178i	1.10096	+	0.153596i
$643$		−	24.3542i		−	0.960436i	−0.877149	−	0.480218i	$-0.840557\pi$
$643$		−	24.3542i		−	0.960436i	0.877149	−	0.480218i	$-0.159443\pi$
$644$	31.8442	+	9.06156i	1.25484	+	0.357076i
$645$			0.610524i			0.0240394i
$646$	0.810119	+	14.5157i	0.0318737	+	0.571114i
$647$			23.2165i			0.912736i	0.889791	+	0.456368i	$0.150850\pi$
$647$			23.2165i			0.912736i	−0.889791	+	0.456368i	$0.849150\pi$
$648$	−26.9966	−	11.9217i	−1.06053	−	0.468330i
$649$		−	33.6858i		−	1.32228i
$650$	0.297885	−	2.13522i	0.0116840	−	0.0837500i
$651$			49.5142i			1.94061i
$652$	−3.34132	+	11.7421i	−0.130856	+	0.459855i
$653$	−7.86554			−0.307802			−0.153901	−	0.988086i	$-0.549184\pi$
$653$	−7.86554			−0.307802			−0.153901	+	0.988086i	$0.549184\pi$
$654$	3.44490	−	24.6928i	0.134706	−	0.965564i
$655$		−	7.12190i		−	0.278276i
$656$	21.5547	−	34.8070i	0.841569	−	1.35898i
$657$	−1.53478			−0.0598776
$658$	36.1974	+	5.04992i	1.41112	+	0.196866i
$659$	−45.6286			−1.77744			−0.888719	−	0.458452i	$-0.848404\pi$
$659$	−45.6286			−1.77744			−0.888719	+	0.458452i	$0.848404\pi$
$660$	−5.60259	+	19.6887i	−0.218081	+	0.766380i
$661$			22.0287i			0.856818i	0.903585	+	0.428409i	$0.140926\pi$
$661$			22.0287i			0.856818i	−0.903585	+	0.428409i	$0.859074\pi$
$662$	−5.34420	−	0.745573i	−0.207708	−	0.0289775i
$663$			6.81843i			0.264806i
$664$	11.8167	−	26.7587i	0.458575	−	1.03844i
$665$	12.3647	−	2.43403i	0.479482	−	0.0943875i
$666$	−0.0197910	+	0.141860i	−0.000766886	+	0.00549697i
$667$	41.8977			1.62228
$668$	−24.7135	−	7.03245i	−0.956192	−	0.272094i
$669$	−27.6598			−1.06939
$670$	−3.34369	−	0.466480i	−0.129178	−	0.0180217i
$671$			77.5247i			2.99281i
$672$	19.8165	−	23.8601i	0.764437	−	0.920424i
$673$			38.8772i			1.49861i	0.662228	+	0.749303i	$0.269611\pi$
$673$			38.8772i			1.49861i	−0.662228	+	0.749303i	$0.730389\pi$
$674$	−1.70422	+	12.2157i	−0.0656441	+	0.470531i
$675$	4.55790			0.175434
$676$	20.5368	+	5.84395i	0.789878	+	0.224767i
$677$			7.51118i			0.288678i	0.989528	+	0.144339i	$0.0461056\pi$
$677$			7.51118i			0.288678i	−0.989528	+	0.144339i	$0.953894\pi$
$678$	2.27251	−	16.2891i	0.0872751	−	0.625581i
$679$	−43.2177			−1.65854
$680$	−6.10213	−	2.69471i	−0.234006	−	0.103337i
$681$	−10.6659			−0.408720
$682$	9.52353	−	68.2639i	0.364675	−	2.61396i
$683$	21.5411			0.824247			0.412124	−	0.911128i	$-0.364787\pi$
$683$	21.5411			0.824247			0.412124	+	0.911128i	$0.364787\pi$
$684$	−0.430530	+	5.18373i	−0.0164617	+	0.198205i
$685$	−18.8921			−0.721829
$686$	−3.18712	+	22.8450i	−0.121685	+	0.872227i
$687$	−21.5919			−0.823784
$688$	−0.677955	+	1.09478i	−0.0258468	+	0.0417380i
$689$	−6.98573			−0.266135
$690$	2.12193	−	15.2098i	0.0807805	−	0.579028i
$691$		−	28.3733i		−	1.07937i	−0.841866	−	0.539686i	$-0.818543\pi$
$691$		−	28.3733i		−	1.07937i	0.841866	−	0.539686i	$-0.181457\pi$
$692$	10.0292	−	35.2445i	0.381251	−	1.33979i
$693$	−9.30967			−0.353645
$694$	−4.00706	+	28.7223i	−0.152106	+	1.09028i
$695$		−	2.31968i		−	0.0879907i
$696$	15.8556	−	35.9049i	0.601006	−	1.36097i
$697$		−	24.1388i		−	0.914323i
$698$	−24.5297	−	3.42215i	−0.928463	−	0.129530i
$699$	−39.1624			−1.48126
$700$	−1.58255	+	5.56141i	−0.0598148	+	0.210201i
$701$	−2.07912			−0.0785274			−0.0392637	−	0.999229i	$-0.512501\pi$
$701$	−2.07912			−0.0785274			−0.0392637	+	0.999229i	$0.512501\pi$
$702$	1.35773	−	9.73210i	0.0512442	−	0.367314i
$703$	−0.725980	+	0.142911i	−0.0273808	+	0.00539000i
$704$	−31.9096	+	29.0838i	−1.20264	+	1.09614i
$705$		−	16.9526i		−	0.638471i
$706$	−21.5942	−	3.01262i	−0.812709	−	0.113381i
$707$			5.65234i			0.212578i
$708$	22.7707	+	6.47961i	0.855774	+	0.243519i
$709$	−9.06929			−0.340604			−0.170302	−	0.985392i	$-0.554474\pi$
$709$	−9.06929			−0.340604			−0.170302	+	0.985392i	$0.554474\pi$
$710$	−18.1723	−	2.53522i	−0.681993	−	0.0951452i
$711$	2.78147			0.104313
$712$	2.95841	−	6.69927i	0.110871	−	0.251066i
$713$			51.7086i			1.93650i
$714$	2.52680	−	18.1119i	0.0945631	−	0.677820i
$715$	−8.22728			−0.307683
$716$	29.7419	+	8.46335i	1.11151	+	0.316290i
$717$		−	4.50597i		−	0.168278i
$718$	5.88037	−	42.1500i	0.219454	−	1.57302i
$719$			25.8470i			0.963932i	0.876190	+	0.481966i	$0.160077\pi$
$719$			25.8470i			0.963932i	−0.876190	+	0.481966i	$0.839923\pi$
$720$	−2.02909	−	1.25654i	−0.0756196	−	0.0468285i
$721$			23.5283i			0.876239i
$722$	−26.0339	+	6.65087i	−0.968883	+	0.247520i
$723$		−	56.8293i		−	2.11351i
$724$	2.45884	−	8.64087i	0.0913822	−	0.321136i
$725$			7.31719i			0.271754i
$726$	48.1495	+	6.71737i	1.78700	+	0.249305i
$727$		−	12.6577i		−	0.469448i	−0.972062	−	0.234724i	$-0.924581\pi$
$727$		−	12.6577i		−	0.469448i	0.972062	−	0.234724i	$-0.0754187\pi$
$728$	11.4034	+	5.03575i	0.422637	+	0.186637i
$729$	19.7064			0.729868
$730$	3.60287	+	0.502638i	0.133348	+	0.0186035i
$731$			0.759234i			0.0280813i
$732$	−52.4045	−	14.9122i	−1.93693	−	0.551171i
$733$	−21.9819			−0.811919			−0.405960	−	0.913891i	$-0.633063\pi$
$733$	−21.9819			−0.811919			−0.405960	+	0.913891i	$0.633063\pi$
$734$	1.82516	−	13.0826i	0.0673680	−	0.482888i
$735$	−2.57624			−0.0950260
$736$	20.6947	−	24.9176i	0.762817	−	0.918474i
$737$			12.8837i			0.474577i
$738$	1.19332	−	8.55364i	0.0439268	−	0.314864i
$739$			37.0804i			1.36403i	0.731340	+	0.682013i	$0.238895\pi$
$739$			37.0804i			1.36403i	−0.731340	+	0.682013i	$0.761105\pi$
$740$	0.0929178	−	0.326532i	0.00341573	−	0.0120036i
$741$	−12.3647	+	2.43403i	−0.454228	+	0.0894162i
$742$	18.5563	+	2.58880i	0.681222	+	0.0950377i
$743$	28.9060			1.06046			0.530228	−	0.847855i	$-0.322106\pi$
$743$	28.9060			1.06046			0.530228	+	0.847855i	$0.322106\pi$
$744$	44.3125	+	19.5685i	1.62458	+	0.717415i
$745$	2.88580			0.105728
$746$	2.71401	−	19.4538i	0.0993669	−	0.712254i
$747$		−	6.17069i		−	0.225774i
$748$	−6.96726	+	24.4843i	−0.254748	+	0.895236i
$749$		−	30.3616i		−	1.10939i
$750$	2.65631	+	0.370584i	0.0969948	+	0.0135318i
$751$	35.0907			1.28048			0.640239	−	0.768176i	$-0.278835\pi$
$751$	35.0907			1.28048			0.640239	+	0.768176i	$0.278835\pi$
$752$	18.8249	−	30.3989i	0.686475	−	1.10853i
$753$		−	10.5994i		−	0.386264i
$754$	15.6238	+	2.17968i	0.568985	+	0.0793794i
$755$	11.9549			0.435082
$756$	−7.21311	+	25.3483i	−0.262338	+	0.921910i
$757$	43.3181			1.57442			0.787211	−	0.616683i	$-0.211524\pi$
$757$	43.3181			1.57442			0.787211	+	0.616683i	$0.211524\pi$
$758$	6.74665	+	0.941229i	0.245049	+	0.0341870i
$759$	−58.6056			−2.12725
$760$	2.70832	−	12.0277i	0.0982410	−	0.436290i
$761$	8.28699			0.300403			0.150202	−	0.988655i	$-0.452008\pi$
$761$	8.28699			0.300403			0.150202	+	0.988655i	$0.452008\pi$
$762$	−7.70475	−	1.07489i	−0.279114	−	0.0389393i
$763$	−26.8753			−0.972951
$764$	8.40828	−	29.5484i	0.304201	−	1.06902i
$765$	−1.40718			−0.0508768
$766$	−32.4811	−	4.53146i	−1.17359	−	0.163728i
$767$			9.51516i			0.343572i
$768$	−13.5219	−	27.1644i	−0.487928	−	0.980211i
$769$	36.9599			1.33281			0.666405	−	0.745590i	$-0.267832\pi$
$769$	36.9599			1.33281			0.666405	+	0.745590i	$0.267832\pi$
$770$	21.8542	+	3.04889i	0.787571	+	0.109875i
$771$			11.3436i			0.408531i
$772$	−0.511160	+	1.79632i	−0.0183971	+	0.0646510i
$773$			31.3392i			1.12719i	0.826051	+	0.563596i	$0.190582\pi$
$773$			31.3392i			1.12719i	−0.826051	+	0.563596i	$0.809418\pi$
$774$	−0.0375334	+	0.269036i	−0.00134911	+	0.00967030i
$775$	−9.03062			−0.324390
$776$	−17.0800	+	38.6775i	−0.613137	+	1.38844i
$777$	0.930712			0.0333891
$778$	25.5338	+	3.56223i	0.915430	+	0.127712i
$779$	43.7738	−	8.61701i	1.56836	−	0.308737i
$780$	1.58255	−	5.56141i	0.0566644	−	0.199130i
$781$			70.0202i			2.50552i
$782$	2.63878	−	18.9146i	0.0943627	−	0.676384i
$783$			33.3510i			1.19187i
$784$	−4.61964	−	2.86078i	−0.164987	−	0.102171i
$785$	1.78614			0.0637501
$786$	2.63926	−	18.9180i	0.0941392	−	0.674782i
$787$	−9.36238			−0.333733			−0.166866	−	0.985980i	$-0.553365\pi$
$787$	−9.36238			−0.333733			−0.166866	+	0.985980i	$0.553365\pi$
$788$	−27.5460	−	7.83848i	−0.981286	−	0.279234i
$789$			14.0454i			0.500030i
$790$	−6.52943	−	0.910925i	−0.232307	−	0.0324092i
$791$	−17.7289			−0.630367
$792$	−3.67927	+	8.33165i	−0.130737	+	0.296052i
$793$		−	21.8982i		−	0.777629i
$794$	16.0146	+	2.23421i	0.568337	+	0.0792890i
$795$		−	8.69059i		−	0.308223i
$796$	10.4451	−	36.7063i	0.370218	−	1.30102i
$797$			37.2181i			1.31833i	0.751997	+	0.659166i	$0.229091\pi$
$797$			37.2181i			1.31833i	−0.751997	+	0.659166i	$0.770909\pi$
$798$	33.7465	−	1.88338i	1.19461	−	0.0666710i
$799$		−	21.0818i		−	0.745821i
$800$	4.35172	+	3.61422i	0.153856	+	0.127782i
$801$		−	1.54489i		−	0.0545859i
$802$	5.42593	−	38.8926i	0.191596	−	1.37335i
$803$		−	13.8824i		−	0.489898i
$804$	−8.70901	−	2.47823i	−0.307143	−	0.0874005i
$805$	−16.5542			−0.583458
$806$	−2.69009	+	19.2823i	−0.0947543	+	0.679191i
$807$		−	23.5160i		−	0.827803i
$808$	5.05854	+	2.23386i	0.177959	+	0.0785869i
$809$	27.5191			0.967520			0.483760	−	0.875201i	$-0.339271\pi$
$809$	27.5191			0.967520			0.483760	+	0.875201i	$0.339271\pi$
$810$	14.6143	+	2.03886i	0.513496	+	0.0716381i
$811$	4.63135			0.162629			0.0813144	−	0.996689i	$-0.474088\pi$
$811$	4.63135			0.162629			0.0813144	+	0.996689i	$0.474088\pi$
$812$	−40.6939	−	11.5798i	−1.42808	−	0.406373i
$813$			2.43403i			0.0853651i
$814$	−1.28315	−	0.179013i	−0.0449743	−	0.00627439i
$815$		−	6.10411i		−	0.213818i
$816$	−15.2105	−	9.41933i	−0.532475	−	0.329743i
$817$	−1.37681	+	0.271029i	−0.0481685	+	0.00948212i
$818$	4.87480	−	34.9421i	0.170443	−	1.22172i
$819$	2.62968			0.0918885
$820$	−5.60259	+	19.6887i	−0.195651	+	0.687558i
$821$	−9.16753			−0.319949			−0.159974	−	0.987121i	$-0.551141\pi$
$821$	−9.16753			−0.319949			−0.159974	+	0.987121i	$0.551141\pi$
$822$	−50.1832	−	7.00109i	−1.75034	−	0.244191i
$823$		−	15.2292i		−	0.530855i	−0.964131	−	0.265428i	$-0.914487\pi$
$823$		−	15.2292i		−	0.530855i	0.964131	−	0.265428i	$-0.0855131\pi$
$824$	21.0565	+	9.29860i	0.733539	+	0.323932i
$825$		−	10.2351i		−	0.356342i
$826$	3.52616	−	25.2752i	0.122691	−	0.879438i
$827$	27.1962			0.945705			0.472853	−	0.881142i	$-0.343224\pi$
$827$	27.1962			0.945705			0.472853	+	0.881142i	$0.343224\pi$
$828$	1.87012	−	6.57197i	0.0649911	−	0.228392i
$829$		−	27.2971i		−	0.948068i	−0.880506	−	0.474034i	$-0.842797\pi$
$829$		−	27.2971i		−	0.948068i	0.880506	−	0.474034i	$-0.157203\pi$
$830$	−2.02089	+	14.4855i	−0.0701460	+	0.502800i
$831$	−7.91364			−0.274521
$832$	9.01344	−	8.21523i	0.312485	−	0.284812i
$833$	−3.20375			−0.111003
$834$	0.859637	−	6.16181i	0.0297668	−	0.213366i
$835$	12.8473			0.444598
$836$	−46.8876	−	3.89421i	−1.62164	−	0.134684i
$837$	−41.1607			−1.42272
$838$	1.36967	−	9.81765i	0.0473143	−	0.339145i
$839$	−6.89831			−0.238156			−0.119078	−	0.992885i	$-0.537994\pi$
$839$	−6.89831			−0.238156			−0.119078	+	0.992885i	$0.537994\pi$
$840$	−6.26472	+	14.1864i	−0.216153	+	0.489476i
$841$	−24.5413			−0.846253
$842$	1.20881	−	8.66462i	0.0416582	−	0.298603i
$843$			32.3783i			1.11517i
$844$	−19.1772	−	5.45707i	−0.660108	−	0.187840i
$845$	−10.6761			−0.367268
$846$	1.04220	−	7.47039i	0.0358315	−	0.256837i
$847$		−	52.4053i		−	1.80067i
$848$	9.65044	−	15.5837i	0.331398	−	0.535148i
$849$			7.44815i			0.255620i
$850$	3.30333	+	0.460849i	0.113303	+	0.0158070i
$851$	0.971960			0.0333184
$852$	−47.3317	−	13.4687i	−1.62156	−	0.461429i
$853$	−52.7901			−1.80750			−0.903750	−	0.428061i	$-0.859197\pi$
$853$	−52.7901			−1.80750			−0.903750	+	0.428061i	$0.859197\pi$
$854$	−8.11512	+	58.1685i	−0.277694	+	1.99048i
$855$	−0.502333	−	2.55182i	−0.0171794	−	0.0872702i
$856$	−27.1720	−	11.9992i	−0.928718	−	0.410123i
$857$		−	52.0917i		−	1.77942i	−0.456528	−	0.889709i	$-0.650907\pi$
$857$		−	52.0917i		−	1.77942i	0.456528	−	0.889709i	$-0.349093\pi$
$858$	−21.8542	−	3.04889i	−0.746091	−	0.104088i
$859$		−	29.0067i		−	0.989694i	−0.868980	−	0.494847i	$-0.835224\pi$
$859$		−	29.0067i		−	0.989694i	0.868980	−	0.494847i	$-0.164776\pi$
$860$	0.176217	−	0.619264i	0.00600896	−	0.0211167i
$861$	−56.1185			−1.91251
$862$	−56.8974	−	7.93779i	−1.93793	−	0.270362i
$863$	7.06596			0.240528			0.120264	−	0.992742i	$-0.461626\pi$
$863$	7.06596			0.240528			0.120264	+	0.992742i	$0.461626\pi$
$864$	19.8347	+	16.4732i	0.674790	+	0.560431i
$865$			18.3218i			0.622961i
$866$	−5.57481	+	39.9598i	−0.189440	+	1.35789i
$867$	21.6917			0.736688
$868$	14.2914	−	50.2230i	0.485083	−	1.70468i
$869$			25.1588i			0.853454i
$870$	−2.71163	+	19.4367i	−0.0919329	+	0.658967i
$871$		−	3.63923i		−	0.123310i
$872$	−10.6214	+	24.0519i	−0.359685	+	0.814501i
$873$			8.91923i			0.301870i
$874$	35.2421	−	1.96685i	1.19208	−	0.0665297i
$875$		−	2.89109i		−	0.0977368i
$876$	9.38407	+	2.67033i	0.317058	+	0.0902220i
$877$		−	40.3494i		−	1.36250i	−0.732050	−	0.681251i	$-0.761436\pi$
$877$		−	40.3494i		−	1.36250i	0.732050	−	0.681251i	$-0.238564\pi$
$878$	46.1101	+	6.43285i	1.55614	+	0.217098i
$879$			62.2986i			2.10128i
$880$	11.3656	−	18.3534i	0.383134	−	0.618693i
$881$	13.7538			0.463376			0.231688	−	0.972790i	$-0.425575\pi$
$881$	13.7538			0.463376			0.231688	+	0.972790i	$0.425575\pi$
$882$	−1.13526	−	0.158380i	−0.0382260	−	0.00533294i
$883$			12.1400i			0.408545i	0.978914	+	0.204272i	$0.0654829\pi$
$883$			12.1400i			0.408545i	−0.978914	+	0.204272i	$0.934517\pi$
$884$	1.96802	−	6.91603i	0.0661918	−	0.232611i
$885$	−11.8373			−0.397907
$886$	4.88753	−	35.0334i	0.164200	−	1.17697i
$887$	17.5817			0.590335			0.295168	−	0.955445i	$-0.404625\pi$
$887$	17.5817			0.590335			0.295168	+	0.955445i	$0.404625\pi$
$888$	0.367826	−	0.832937i	0.0123434	−	0.0279515i
$889$			8.38575i			0.281249i
$890$	−0.505947	+	3.62658i	−0.0169594	+	0.121563i
$891$		−	56.3111i		−	1.88649i
$892$	28.0558	+	7.98353i	0.939376	+	0.267308i
$893$	38.2302	−	7.52574i	1.27933	−	0.251839i
$894$	7.66559	+	1.06943i	0.256376	+	0.0357671i
$895$	−15.4613			−0.516815
$896$	−26.9869	+	18.4820i	−0.901570	+	0.617440i
$897$	16.5542			0.552728
$898$	2.07823	−	14.8966i	0.0693514	−	0.497105i
$899$		−	66.0788i		−	2.20385i
$900$	1.14776	+	0.326606i	0.0382586	+	0.0108869i
$901$		−	10.8074i		−	0.360047i
$902$	77.3689	+	10.7938i	2.57610	+	0.359394i
$903$	1.76508			0.0587383
$904$	−7.00662	+	15.8664i	−0.233037	+	0.527708i
$905$			4.49195i			0.149318i
$906$	31.7558	+	4.43027i	1.05502	+	0.147186i
$907$	−13.8694			−0.460525			−0.230263	−	0.973129i	$-0.573959\pi$
$907$	−13.8694			−0.460525			−0.230263	+	0.973129i	$0.573959\pi$
$908$	10.8186	+	3.07854i	0.359029	+	0.102165i
$909$	1.16653			0.0386912
$910$	−6.17311	−	0.861214i	−0.204637	−	0.0285490i
$911$	28.9895			0.960465			0.480232	−	0.877141i	$-0.340552\pi$
$911$	28.9895			0.960465			0.480232	+	0.877141i	$0.340552\pi$
$912$	11.6514	−	30.9456i	0.385816	−	1.02471i
$913$	55.8148			1.84720
$914$	−43.7168	−	6.09896i	−1.44602	−	0.201736i
$915$	27.2424			0.900608
$916$	21.9010	+	6.23214i	0.723630	+	0.205916i
$917$	−20.5901			−0.679944
$918$	15.0562	+	2.10050i	0.496930	+	0.0693269i
$919$		−	4.07849i		−	0.134537i	−0.997735	−	0.0672685i	$-0.978572\pi$
$919$		−	4.07849i		−	0.134537i	0.997735	−	0.0672685i	$-0.0214284\pi$
$920$	−6.54236	+	14.8151i	−0.215695	+	0.488439i
$921$	51.0711			1.68285
$922$	−26.4899	−	3.69562i	−0.872399	−	0.121709i
$923$		−	19.7784i		−	0.651016i
$924$	56.9217	+	16.1976i	1.87259	+	0.532863i
$925$			0.169748i			0.00558126i
$926$	−0.918606	+	6.58449i	−0.0301873	+	0.216380i
$927$	4.85575			0.159484
$928$	−26.4459	+	31.8424i	−0.868130	+	1.04528i
$929$	−46.1655			−1.51464			−0.757321	−	0.653043i	$-0.773492\pi$
$929$	−46.1655			−1.51464			−0.757321	+	0.653043i	$0.773492\pi$
$930$	−23.9881	−	3.34660i	−0.786602	−	0.109739i
$931$	−1.14367	−	5.80975i	−0.0374821	−	0.190407i
$932$	39.7230	+	11.3036i	1.30117	+	0.370261i
$933$		−	19.2358i		−	0.629750i
$934$	−5.28529	+	37.8845i	−0.172940	+	1.23962i
$935$		−	12.7282i		−	0.416256i
$936$	1.03927	−	2.35342i	0.0339697	−	0.0769240i
$937$	−52.4665			−1.71400			−0.857002	−	0.515313i	$-0.827676\pi$
$937$	−52.4665			−1.71400			−0.857002	+	0.515313i	$0.827676\pi$
$938$	−1.34864	+	9.66692i	−0.0440346	+	0.315636i
$939$	8.18104			0.266978
$940$	−4.89307	+	17.1952i	−0.159594	+	0.560847i
$941$		−	4.09746i		−	0.133573i	−0.997767	−	0.0667867i	$-0.978725\pi$
$941$		−	4.09746i		−	0.133573i	0.997767	−	0.0667867i	$-0.0212747\pi$
$942$	4.74455	+	0.661914i	0.154586	+	0.0215663i
$943$	−58.6056			−1.90846
$944$	−21.2264	−	13.1447i	−0.690860	−	0.427824i
$945$		−	13.1773i		−	0.428658i
$946$	−2.43347	−	0.339495i	−0.0791190	−	0.0110379i
$947$			10.3503i			0.336339i	0.985758	+	0.168169i	$0.0537855\pi$
$947$			10.3503i			0.336339i	−0.985758	+	0.168169i	$0.946214\pi$
$948$	−17.0066	−	4.83940i	−0.552350	−	0.157176i
$949$			3.92131i			0.127291i
$950$	0.343500	+	6.15484i	0.0111446	+	0.199689i
$951$			28.5981i			0.927356i
$952$	−7.79065	+	17.6418i	−0.252497	+	0.571775i
$953$			12.5571i			0.406765i	0.979099	+	0.203382i	$0.0651935\pi$
$953$			12.5571i			0.406765i	−0.979099	+	0.203382i	$0.934807\pi$
$954$	0.534274	−	3.82963i	0.0172978	−	0.123989i
$955$			15.3607i			0.497061i
$956$	−1.30057	+	4.57047i	−0.0420634	+	0.147819i
$957$	74.8925			2.42093
$958$	−3.26757	+	23.4216i	−0.105570	+	0.756719i
$959$			54.6187i			1.76373i
$960$	10.2201	+	11.2132i	0.329854	+	0.361903i
$961$	50.5522			1.63071
$962$	0.362447	+	0.0505653i	0.0116858	+	0.00163029i
$963$	−6.26600			−0.201919
$964$	−16.4028	+	57.6428i	−0.528299	+	1.85655i
$965$		−	0.933817i		−	0.0300606i
$966$	−43.9730	−	6.13470i	−1.41481	−	0.197381i
$967$		−	46.1120i		−	1.48286i	−0.671030	−	0.741430i	$-0.734148\pi$
$967$		−	46.1120i		−	1.48286i	0.671030	−	0.741430i	$-0.265852\pi$
$968$	−46.8999	−	20.7111i	−1.50742	−	0.665679i
$969$	−3.76561	−	19.1290i	−0.120969	−	0.614513i
$970$	2.92103	−	20.9377i	0.0937885	−	0.672268i
$971$	−37.9918			−1.21921			−0.609607	−	0.792704i	$-0.708673\pi$
$971$	−37.9918			−1.21921			−0.609607	+	0.792704i	$0.708673\pi$
$972$	11.7615	+	3.34685i	0.377250	+	0.107350i
$973$	−6.70643			−0.214998
$974$	10.8030	+	1.50713i	0.346150	+	0.0482916i
$975$			2.89109i			0.0925891i
$976$	48.8505	+	30.2513i	1.56367	+	0.968321i
$977$			1.12247i			0.0359109i	0.999839	+	0.0179554i	$0.00571570\pi$
$977$			1.12247i			0.0359109i	−0.999839	+	0.0179554i	$0.994284\pi$
$978$	2.26208	−	16.2144i	0.0723335	−	0.518480i
$979$	13.9737			0.446602
$980$	2.61311	+	0.743587i	0.0834729	+	0.0237530i
$981$			5.54650i			0.177086i
$982$	−0.138800	+	0.994909i	−0.00442930	+	0.0317488i
$983$	14.0172			0.447079			0.223539	−	0.974695i	$-0.428239\pi$
$983$	14.0172			0.447079			0.223539	+	0.974695i	$0.428239\pi$
$984$	−22.1785	+	50.2230i	−0.707026	+	1.60105i
$985$	14.3198			0.456266
$986$	−3.37212	+	24.1711i	−0.107390	+	0.769764i
$987$	−49.0115			−1.56005
$988$	13.2442	+	1.09999i	0.421355	+	0.0349953i
$989$	1.84331			0.0586138
$990$	0.629229	−	4.51026i	0.0199982	−	0.143345i
$991$	23.2413			0.738285			0.369142	−	0.929373i	$-0.379651\pi$
$991$	23.2413			0.738285			0.369142	+	0.929373i	$0.379651\pi$
$992$	−39.2987	−	32.6386i	−1.24774	−	1.03628i
$993$	7.23608			0.229630
$994$	−7.32957	+	52.5377i	−0.232480	+	1.66640i
$995$			19.0818i			0.604933i
$996$	−10.7362	+	37.7292i	−0.340190	+	1.19550i
$997$	−52.5232			−1.66343			−0.831713	−	0.555205i	$-0.812640\pi$
$997$	−52.5232			−1.66343			−0.831713	+	0.555205i	$0.812640\pi$
$998$	8.18980	−	58.7038i	0.259244	−	1.85824i
$999$			0.773692i			0.0244785i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.f.a.151.20	yes	20
4.3	odd	2	inner	380.2.f.a.151.2	yes	20
19.18	odd	2	inner	380.2.f.a.151.1	✓	20
76.75	even	2	inner	380.2.f.a.151.19	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.f.a.151.1	✓	20	19.18	odd	2	inner
380.2.f.a.151.2	yes	20	4.3	odd	2	inner
380.2.f.a.151.19	yes	20	76.75	even	2	inner
380.2.f.a.151.20	yes	20	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.40065 + 0.195405i) q^{2} -1.89649 q^{3} +(1.92363 + 0.547388i) q^{4} -1.00000 q^{5} +(-2.65631 - 0.370584i) q^{6} +2.89109i q^{7} +(2.58737 + 1.14259i) q^{8} +0.596662 q^{9} +O(q^{10})\)	\(q+(1.40065 + 0.195405i) q^{2} -1.89649 q^{3} +(1.92363 + 0.547388i) q^{4} -1.00000 q^{5} +(-2.65631 - 0.370584i) q^{6} +2.89109i q^{7} +(2.58737 + 1.14259i) q^{8} +0.596662 q^{9} +(-1.40065 - 0.195405i) q^{10} +5.39689i q^{11} +(-3.64815 - 1.03811i) q^{12} -1.52445i q^{13} +(-0.564935 + 4.04941i) q^{14} +1.89649 q^{15} +(3.40073 + 2.10595i) q^{16} +2.35843 q^{17} +(0.835714 + 0.116591i) q^{18} +(0.841905 + 4.27682i) q^{19} +(-1.92363 - 0.547388i) q^{20} -5.48292i q^{21} +(-1.05458 + 7.55915i) q^{22} -5.72592i q^{23} +(-4.90692 - 2.16690i) q^{24} +1.00000 q^{25} +(0.297885 - 2.13522i) q^{26} +4.55790 q^{27} +(-1.58255 + 5.56141i) q^{28} +7.31719i q^{29} +(2.65631 + 0.370584i) q^{30} -9.03062 q^{31} +(4.35172 + 3.61422i) q^{32} -10.2351i q^{33} +(3.30333 + 0.460849i) q^{34} -2.89109i q^{35} +(1.14776 + 0.326606i) q^{36} +0.169748i q^{37} +(0.343500 + 6.15484i) q^{38} +2.89109i q^{39} +(-2.58737 - 1.14259i) q^{40} -10.2351i q^{41} +(1.07139 - 7.67965i) q^{42} +0.321924i q^{43} +(-2.95420 + 10.3816i) q^{44} -0.596662 q^{45} +(1.11887 - 8.02000i) q^{46} -8.93894i q^{47} +(-6.44944 - 3.99390i) q^{48} -1.35843 q^{49} +(1.40065 + 0.195405i) q^{50} -4.47272 q^{51} +(0.834465 - 2.93248i) q^{52} -4.58247i q^{53} +(6.38402 + 0.890638i) q^{54} -5.39689i q^{55} +(-3.30333 + 7.48034i) q^{56} +(-1.59666 - 8.11093i) q^{57} +(-1.42982 + 10.2488i) q^{58} -6.24171 q^{59} +(3.64815 + 1.03811i) q^{60} +14.3647 q^{61} +(-12.6487 - 1.76463i) q^{62} +1.72501i q^{63} +(5.38899 + 5.91260i) q^{64} +1.52445i q^{65} +(2.00000 - 14.3358i) q^{66} +2.38724 q^{67} +(4.53675 + 1.29098i) q^{68} +10.8591i q^{69} +(0.564935 - 4.04941i) q^{70} +12.9742 q^{71} +(1.54379 + 0.681738i) q^{72} -2.57229 q^{73} +(-0.0331696 + 0.237757i) q^{74} -1.89649 q^{75} +(-0.721565 + 8.68788i) q^{76} -15.6029 q^{77} +(-0.564935 + 4.04941i) q^{78} +4.66172 q^{79} +(-3.40073 - 2.10595i) q^{80} -10.4340 q^{81} +(2.00000 - 14.3358i) q^{82} -10.3420i q^{83} +(3.00129 - 10.5471i) q^{84} -2.35843 q^{85} +(-0.0629056 + 0.450902i) q^{86} -13.8770i q^{87} +(-6.16642 + 13.9638i) q^{88} -2.58922i q^{89} +(-0.835714 - 0.116591i) q^{90} +4.40732 q^{91} +(3.13430 - 11.0146i) q^{92} +17.1265 q^{93} +(1.74672 - 12.5203i) q^{94} +(-0.841905 - 4.27682i) q^{95} +(-8.25297 - 6.85431i) q^{96} +14.9486i q^{97} +(-1.90268 - 0.265444i) q^{98} +3.22012i 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

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Database

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