LMFDB - Embedded newform 1620.2.e.a.971.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1620,2,Mod(971,1620)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1620, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1620.971");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1620 = 2^{2} \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1620.e (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:	$12.9357651274$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			971.11
Character	$\chi$	$=$	1620.971
Dual form			1620.2.e.a.971.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.03403 - 0.964765i) q^{2} +(0.138457 + 1.99520i) q^{4} -1.00000i q^{5} +3.54880i q^{7} +(1.78173 - 2.19669i) q^{8} +O(q^{10})$	\(q+(-1.03403 - 0.964765i) q^{2} +(0.138457 + 1.99520i) q^{4} -1.00000i q^{5} +3.54880i q^{7} +(1.78173 - 2.19669i) q^{8} +(-0.964765 + 1.03403i) q^{10} +4.36571 q^{11} +4.76047 q^{13} +(3.42376 - 3.66958i) q^{14} +(-3.96166 + 0.552498i) q^{16} -3.02111i q^{17} +1.16321i q^{19} +(1.99520 - 0.138457i) q^{20} +(-4.51430 - 4.21189i) q^{22} -3.11010 q^{23} -1.00000 q^{25} +(-4.92249 - 4.59273i) q^{26} +(-7.08057 + 0.491355i) q^{28} +8.14117i q^{29} -4.79418i q^{31} +(4.62953 + 3.25077i) q^{32} +(-2.91466 + 3.12393i) q^{34} +3.54880 q^{35} -7.83140 q^{37} +(1.12222 - 1.20280i) q^{38} +(-2.19669 - 1.78173i) q^{40} +4.61999i q^{41} +8.70155i q^{43} +(0.604462 + 8.71048i) q^{44} +(3.21595 + 3.00052i) q^{46} +8.13862 q^{47} -5.59396 q^{49} +(1.03403 + 0.964765i) q^{50} +(0.659119 + 9.49810i) q^{52} -11.9836i q^{53} -4.36571i q^{55} +(7.79559 + 6.32300i) q^{56} +(7.85431 - 8.41825i) q^{58} -0.684441 q^{59} +10.5876 q^{61} +(-4.62526 + 4.95735i) q^{62} +(-1.65086 - 7.82781i) q^{64} -4.76047i q^{65} +7.95024i q^{67} +(6.02772 - 0.418292i) q^{68} +(-3.66958 - 3.42376i) q^{70} +10.6669 q^{71} +9.41743 q^{73} +(8.09794 + 7.55546i) q^{74} +(-2.32083 + 0.161054i) q^{76} +15.4930i q^{77} +8.75803i q^{79} +(0.552498 + 3.96166i) q^{80} +(4.45720 - 4.77723i) q^{82} -13.3807 q^{83} -3.02111 q^{85} +(8.39496 - 8.99771i) q^{86} +(7.77853 - 9.59010i) q^{88} +4.93294i q^{89} +16.8939i q^{91} +(-0.430614 - 6.20528i) q^{92} +(-8.41561 - 7.85185i) q^{94} +1.16321 q^{95} -6.64201 q^{97} +(5.78435 + 5.39686i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 24 q^{16} - 24 q^{22} - 48 q^{25} + 24 q^{28} - 24 q^{34} - 24 q^{40} + 48 q^{46} - 48 q^{49} + 24 q^{58} + 24 q^{64} + 24 q^{76} + 24 q^{88}+O(q^{100}) $ 48 * q - 24 * q^16 - 24 * q^22 - 48 * q^25 + 24 * q^28 - 24 * q^34 - 24 * q^40 + 48 * q^46 - 48 * q^49 + 24 * q^58 + 24 * q^64 + 24 * q^76 + 24 * q^88

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times$.

$n$	$811$	$1297$	$1541$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−1.03403	−	0.964765i	−0.731173	−	0.682192i
$2$	−1.03403	−	0.964765i	−0.731173	−	0.682192i
$3$		0			0
$3$		0			0
$4$	0.138457	+	1.99520i	0.0692283	+	0.997601i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$			3.54880i			1.34132i	0.741765	+	0.670660i	$0.233989\pi$
$7$			3.54880i			1.34132i	−0.741765	+	0.670660i	$0.766011\pi$
$8$	1.78173	−	2.19669i	0.629937	−	0.776646i
$9$		0			0
$10$	−0.964765	+	1.03403i	−0.305086	+	0.326991i
$11$	4.36571			1.31631			0.658156	−	0.752882i	$-0.271337\pi$
$11$	4.36571			1.31631			0.658156	+	0.752882i	$0.271337\pi$
$12$		0			0
$13$	4.76047			1.32032			0.660158	−	0.751127i	$-0.270489\pi$
$13$	4.76047			1.32032			0.660158	+	0.751127i	$0.270489\pi$
$14$	3.42376	−	3.66958i	0.915037	−	0.980737i
$15$		0			0
$16$	−3.96166	+	0.552498i	−0.990415	+	0.138124i
$17$		−	3.02111i		−	0.732726i	−0.930472	−	0.366363i	$-0.880603\pi$
$17$		−	3.02111i		−	0.732726i	0.930472	−	0.366363i	$-0.119397\pi$
$18$		0			0
$19$			1.16321i			0.266858i	0.991058	+	0.133429i	$0.0425988\pi$
$19$			1.16321i			0.266858i	−0.991058	+	0.133429i	$0.957401\pi$
$20$	1.99520	−	0.138457i	0.446141	−	0.0309599i
$21$		0			0
$22$	−4.51430	−	4.21189i	−0.962452	−	0.897977i
$23$	−3.11010			−0.648501			−0.324251	−	0.945971i	$-0.605112\pi$
$23$	−3.11010			−0.648501			−0.324251	+	0.945971i	$0.605112\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−4.92249	−	4.59273i	−0.965380	−	0.900709i
$27$		0			0
$28$	−7.08057	+	0.491355i	−1.33810	+	0.0928573i
$29$			8.14117i			1.51178i	0.654701	+	0.755888i	$0.272795\pi$
$29$			8.14117i			1.51178i	−0.654701	+	0.755888i	$0.727205\pi$
$30$		0			0
$31$		−	4.79418i		−	0.861061i	−0.902576	−	0.430530i	$-0.858327\pi$
$31$		−	4.79418i		−	0.861061i	0.902576	−	0.430530i	$-0.141673\pi$
$32$	4.62953	+	3.25077i	0.818392	+	0.574660i
$33$		0			0
$34$	−2.91466	+	3.12393i	−0.499860	+	0.535750i
$35$	3.54880			0.599856
$36$		0			0
$37$	−7.83140			−1.28747			−0.643737	−	0.765247i	$-0.722617\pi$
$37$	−7.83140			−1.28747			−0.643737	+	0.765247i	$0.722617\pi$
$38$	1.12222	−	1.20280i	0.182048	−	0.195119i
$39$		0			0
$40$	−2.19669	−	1.78173i	−0.347327	−	0.281717i
$41$			4.61999i			0.721521i	0.932658	+	0.360761i	$0.117483\pi$
$41$			4.61999i			0.721521i	−0.932658	+	0.360761i	$0.882517\pi$
$42$		0			0
$43$			8.70155i			1.32697i	0.748188	+	0.663487i	$0.230924\pi$
$43$			8.70155i			1.32697i	−0.748188	+	0.663487i	$0.769076\pi$
$44$	0.604462	+	8.71048i	0.0911261	+	1.31315i
$45$		0			0
$46$	3.21595	+	3.00052i	0.474167	+	0.442402i
$47$	8.13862			1.18714			0.593570	−	0.804783i	$-0.297718\pi$
$47$	8.13862			1.18714			0.593570	+	0.804783i	$0.297718\pi$
$48$		0			0
$49$	−5.59396			−0.799137
$50$	1.03403	+	0.964765i	0.146235	+	0.136438i
$51$		0			0
$52$	0.659119	+	9.49810i	0.0914033	+	1.31715i
$53$		−	11.9836i		−	1.64607i	−0.567991	−	0.823035i	$-0.692279\pi$
$53$		−	11.9836i		−	1.64607i	0.567991	−	0.823035i	$-0.307721\pi$
$54$		0			0
$55$		−	4.36571i		−	0.588672i
$56$	7.79559	+	6.32300i	1.04173	+	0.844947i
$57$		0			0
$58$	7.85431	−	8.41825i	1.03132	−	1.10537i
$59$	−0.684441			−0.0891066			−0.0445533	−	0.999007i	$-0.514186\pi$
$59$	−0.684441			−0.0891066			−0.0445533	+	0.999007i	$0.514186\pi$
$60$		0			0
$61$	10.5876			1.35560			0.677801	−	0.735245i	$-0.262933\pi$
$61$	10.5876			1.35560			0.677801	+	0.735245i	$0.262933\pi$
$62$	−4.62526	+	4.95735i	−0.587409	+	0.629585i
$63$		0			0
$64$	−1.65086	−	7.82781i	−0.206358	−	0.978477i
$65$		−	4.76047i		−	0.590463i
$66$		0			0
$67$			7.95024i			0.971276i	0.874160	+	0.485638i	$0.161413\pi$
$67$			7.95024i			0.971276i	−0.874160	+	0.485638i	$0.838587\pi$
$68$	6.02772	−	0.418292i	0.730968	−	0.0507254i
$69$		0			0
$70$	−3.66958	−	3.42376i	−0.438599	−	0.409217i
$71$	10.6669			1.26593			0.632964	−	0.774181i	$-0.281838\pi$
$71$	10.6669			1.26593			0.632964	+	0.774181i	$0.281838\pi$
$72$		0			0
$73$	9.41743			1.10223			0.551114	−	0.834430i	$-0.314203\pi$
$73$	9.41743			1.10223			0.551114	+	0.834430i	$0.314203\pi$
$74$	8.09794	+	7.55546i	0.941367	+	0.878305i
$75$		0			0
$76$	−2.32083	+	0.161054i	−0.266217	+	0.0184741i
$77$			15.4930i			1.76559i
$78$		0			0
$79$			8.75803i			0.985356i	0.870212	+	0.492678i	$0.163982\pi$
$79$			8.75803i			0.985356i	−0.870212	+	0.492678i	$0.836018\pi$
$80$	0.552498	+	3.96166i	0.0617712	+	0.442927i
$81$		0			0
$82$	4.45720	−	4.77723i	0.492216	−	0.527557i
$83$	−13.3807			−1.46872			−0.734361	−	0.678759i	$-0.762518\pi$
$83$	−13.3807			−1.46872			−0.734361	+	0.678759i	$0.762518\pi$
$84$		0			0
$85$	−3.02111			−0.327685
$86$	8.39496	−	8.99771i	0.905251	−	0.970248i
$87$		0			0
$88$	7.77853	−	9.59010i	0.829194	−	1.02231i
$89$			4.93294i			0.522891i	0.965218	+	0.261445i	$0.0841991\pi$
$89$			4.93294i			0.522891i	−0.965218	+	0.261445i	$0.915801\pi$
$90$		0			0
$91$			16.8939i			1.77097i
$92$	−0.430614	−	6.20528i	−0.0448947	−	0.646945i
$93$		0			0
$94$	−8.41561	−	7.85185i	−0.868004	−	0.809857i
$95$	1.16321			0.119342
$96$		0			0
$97$	−6.64201			−0.674394			−0.337197	−	0.941434i	$-0.609479\pi$
$97$	−6.64201			−0.674394			−0.337197	+	0.941434i	$0.609479\pi$
$98$	5.78435	+	5.39686i	0.584308	+	0.545165i
$99$		0			0
$100$	−0.138457	−	1.99520i	−0.0138457	−	0.199520i
$101$		−	6.85118i		−	0.681718i	−0.940115	−	0.340859i	$-0.889282\pi$
$101$		−	6.85118i		−	0.681718i	0.940115	−	0.340859i	$-0.110718\pi$
$102$		0			0
$103$		−	14.3805i		−	1.41695i	−0.705735	−	0.708476i	$-0.749383\pi$
$103$		−	14.3805i		−	1.41695i	0.705735	−	0.708476i	$-0.250617\pi$
$104$	8.48188	−	10.4573i	0.831717	−	1.02542i
$105$		0			0
$106$	−11.5613	+	12.3914i	−1.12294	+	1.20356i
$107$	0.485829			0.0469669			0.0234835	−	0.999724i	$-0.492524\pi$
$107$	0.485829			0.0469669			0.0234835	+	0.999724i	$0.492524\pi$
$108$		0			0
$109$	15.6731			1.50121			0.750607	−	0.660749i	$-0.229761\pi$
$109$	15.6731			1.50121			0.750607	+	0.660749i	$0.229761\pi$
$110$	−4.21189	+	4.51430i	−0.401588	+	0.430422i
$111$		0			0
$112$	−1.96070	−	14.0591i	−0.185269	−	1.32846i
$113$		−	1.16042i		−	0.109163i	−0.998509	−	0.0545817i	$-0.982617\pi$
$113$		−	1.16042i		−	0.109163i	0.998509	−	0.0545817i	$-0.0173825\pi$
$114$		0			0
$115$			3.11010i			0.290019i
$116$	−16.2433	+	1.12720i	−1.50815	+	0.104658i
$117$		0			0
$118$	0.707736	+	0.660325i	0.0651523	+	0.0607878i
$119$	10.7213			0.982820
$120$		0			0
$121$	8.05944			0.732676
$122$	−10.9479	−	10.2145i	−0.991180	−	0.924781i
$123$		0			0
$124$	9.56536	−	0.663787i	0.858995	−	0.0596098i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$			10.0882i			0.895180i	0.894239	+	0.447590i	$0.147718\pi$
$127$			10.0882i			0.895180i	−0.894239	+	0.447590i	$0.852282\pi$
$128$	−5.84495	+	9.68693i	−0.516625	+	0.856211i
$129$		0			0
$130$	−4.59273	+	4.92249i	−0.402809	+	0.431731i
$131$	4.79010			0.418513			0.209256	−	0.977861i	$-0.432896\pi$
$131$	4.79010			0.418513			0.209256	+	0.977861i	$0.432896\pi$
$132$		0			0
$133$	−4.12798			−0.357941
$134$	7.67011	−	8.22083i	0.662597	−	0.710171i
$135$		0			0
$136$	−6.63642	−	5.38280i	−0.569069	−	0.461572i
$137$		−	2.91386i		−	0.248948i	−0.992223	−	0.124474i	$-0.960276\pi$
$137$		−	2.91386i		−	0.248948i	0.992223	−	0.124474i	$-0.0397243\pi$
$138$		0			0
$139$			13.7267i			1.16428i	0.813087	+	0.582142i	$0.197785\pi$
$139$			13.7267i			1.16428i	−0.813087	+	0.582142i	$0.802215\pi$
$140$	0.491355	+	7.08057i	0.0415270	+	0.598417i
$141$		0			0
$142$	−11.0300	−	10.2911i	−0.925613	−	0.863606i
$143$	20.7828			1.73795
$144$		0			0
$145$	8.14117			0.676087
$146$	−9.73795	−	9.08561i	−0.805919	−	0.751930i
$147$		0			0
$148$	−1.08431	−	15.6252i	−0.0891297	−	1.28439i
$149$			10.4866i			0.859094i	0.903045	+	0.429547i	$0.141327\pi$
$149$			10.4866i			0.859094i	−0.903045	+	0.429547i	$0.858673\pi$
$150$		0			0
$151$			23.0452i			1.87539i	0.347455	+	0.937697i	$0.387046\pi$
$151$			23.0452i			1.87539i	−0.347455	+	0.937697i	$0.612954\pi$
$152$	2.55520	+	2.07252i	0.207254	+	0.168104i
$153$		0			0
$154$	14.9471	−	16.0203i	1.20447	−	1.29096i
$155$	−4.79418			−0.385078
$156$		0			0
$157$	14.5160			1.15851			0.579253	−	0.815148i	$-0.303344\pi$
$157$	14.5160			1.15851			0.579253	+	0.815148i	$0.303344\pi$
$158$	8.44944	−	9.05611i	0.672202	−	0.720466i
$159$		0			0
$160$	3.25077	−	4.62953i	0.256996	−	0.365996i
$161$		−	11.0371i		−	0.869847i
$162$		0			0
$163$		−	9.73510i		−	0.762512i	−0.924469	−	0.381256i	$-0.875492\pi$
$163$		−	9.73510i		−	0.762512i	0.924469	−	0.381256i	$-0.124508\pi$
$164$	−9.21781	+	0.639668i	−0.719790	+	0.0499497i
$165$		0			0
$166$	13.8361	+	12.9092i	1.07389	+	1.00195i
$167$	−13.5625			−1.04950			−0.524751	−	0.851256i	$-0.675841\pi$
$167$	−13.5625			−1.04950			−0.524751	+	0.851256i	$0.675841\pi$
$168$		0			0
$169$	9.66206			0.743236
$170$	3.12393	+	2.91466i	0.239595	+	0.223544i
$171$		0			0
$172$	−17.3614	+	1.20479i	−1.32379	+	0.0918642i
$173$		−	13.4117i		−	1.01967i	−0.860271	−	0.509837i	$-0.829706\pi$
$173$		−	13.4117i		−	1.01967i	0.860271	−	0.509837i	$-0.170294\pi$
$174$		0			0
$175$		−	3.54880i		−	0.268264i
$176$	−17.2955	+	2.41205i	−1.30369	+	0.181815i
$177$		0			0
$178$	4.75913	−	5.10083i	0.356712	−	0.382324i
$179$	19.9570			1.49166			0.745830	−	0.666137i	$-0.232053\pi$
$179$	19.9570			1.49166			0.745830	+	0.666137i	$0.232053\pi$
$180$		0			0
$181$	−17.6204			−1.30971			−0.654857	−	0.755753i	$-0.727271\pi$
$181$	−17.6204			−1.30971			−0.654857	+	0.755753i	$0.727271\pi$
$182$	16.2987	−	17.4689i	1.20814	−	1.29488i
$183$		0			0
$184$	−5.54137	+	6.83192i	−0.408515	+	0.503656i
$185$			7.83140i			0.575776i
$186$		0			0
$187$		−	13.1893i		−	0.964496i
$188$	1.12685	+	16.2382i	0.0821837	+	1.18429i
$189$		0			0
$190$	−1.20280	−	1.12222i	−0.0872600	−	0.0814144i
$191$	17.0170			1.23131			0.615654	−	0.788016i	$-0.288892\pi$
$191$	17.0170			1.23131			0.615654	+	0.788016i	$0.288892\pi$
$192$		0			0
$193$	10.7707			0.775292			0.387646	−	0.921808i	$-0.373288\pi$
$193$	10.7707			0.775292			0.387646	+	0.921808i	$0.373288\pi$
$194$	6.86807	+	6.40798i	0.493099	+	0.460066i
$195$		0			0
$196$	−0.774521	−	11.1611i	−0.0553229	−	0.797220i
$197$		−	0.458004i		−	0.0326314i	−0.999867	−	0.0163157i	$-0.994806\pi$
$197$		−	0.458004i		−	0.0326314i	0.999867	−	0.0163157i	$-0.00519369\pi$
$198$		0			0
$199$		−	2.14750i		−	0.152232i	−0.997099	−	0.0761162i	$-0.975748\pi$
$199$		−	2.14750i		−	0.152232i	0.997099	−	0.0761162i	$-0.0242520\pi$
$200$	−1.78173	+	2.19669i	−0.125987	+	0.155329i
$201$		0			0
$202$	−6.60978	+	7.08436i	−0.465062	+	0.498454i
$203$	−28.8913			−2.02777
$204$		0			0
$205$	4.61999			0.322674
$206$	−13.8738	+	14.8699i	−0.966633	+	1.03604i
$207$		0			0
$208$	−18.8594	+	2.63015i	−1.30766	+	0.182368i
$209$			5.07822i			0.351268i
$210$		0			0
$211$			2.17455i			0.149702i	0.997195	+	0.0748510i	$0.0238481\pi$
$211$			2.17455i			0.149702i	−0.997195	+	0.0748510i	$0.976152\pi$
$212$	23.9096	−	1.65920i	1.64212	−	0.113955i
$213$		0			0
$214$	−0.502365	−	0.468711i	−0.0343409	−	0.0320404i
$215$	8.70155			0.593441
$216$		0			0
$217$	17.0136			1.15496
$218$	−16.2066	−	15.1209i	−1.09765	−	1.02412i
$219$		0			0
$220$	8.71048	−	0.604462i	0.587260	−	0.0407528i
$221$		−	14.3819i		−	0.967430i
$222$		0			0
$223$		−	21.4295i		−	1.43503i	−0.696545	−	0.717513i	$-0.745280\pi$
$223$		−	21.4295i		−	1.43503i	0.696545	−	0.717513i	$-0.254720\pi$
$224$	−11.5363	+	16.4292i	−0.770803	+	1.09773i
$225$		0			0
$226$	−1.11954	+	1.19992i	−0.0744704	+	0.0798174i
$227$	−8.83418			−0.586345			−0.293172	−	0.956060i	$-0.594711\pi$
$227$	−8.83418			−0.586345			−0.293172	+	0.956060i	$0.594711\pi$
$228$		0			0
$229$	20.0779			1.32678			0.663392	−	0.748272i	$-0.269116\pi$
$229$	20.0779			1.32678			0.663392	+	0.748272i	$0.269116\pi$
$230$	3.00052	−	3.21595i	0.197848	−	0.212054i
$231$		0			0
$232$	17.8836	+	14.5054i	1.17412	+	0.952324i
$233$			8.52014i			0.558173i	0.960266	+	0.279086i	$0.0900316\pi$
$233$			8.52014i			0.558173i	−0.960266	+	0.279086i	$0.909968\pi$
$234$		0			0
$235$		−	8.13862i		−	0.530905i
$236$	−0.0947654	−	1.36560i	−0.00616870	−	0.0888928i
$237$		0			0
$238$	−11.0862	−	10.3435i	−0.718611	−	0.670472i
$239$	−2.93361			−0.189760			−0.0948798	−	0.995489i	$-0.530247\pi$
$239$	−2.93361			−0.189760			−0.0948798	+	0.995489i	$0.530247\pi$
$240$		0			0
$241$	25.8849			1.66739			0.833695	−	0.552225i	$-0.186221\pi$
$241$	25.8849			1.66739			0.833695	+	0.552225i	$0.186221\pi$
$242$	−8.33374	−	7.77547i	−0.535713	−	0.499826i
$243$		0			0
$244$	1.46592	+	21.1244i	0.0938461	+	1.35235i
$245$			5.59396i			0.357385i
$246$		0			0
$247$			5.53740i			0.352337i
$248$	−10.5313	−	8.54195i	−0.668739	−	0.542414i
$249$		0			0
$250$	0.964765	−	1.03403i	0.0610171	−	0.0653981i
$251$	−26.6272			−1.68070			−0.840348	−	0.542047i	$-0.817650\pi$
$251$	−26.6272			−1.68070			−0.840348	+	0.542047i	$0.817650\pi$
$252$		0			0
$253$	−13.5778			−0.853630
$254$	9.73271	−	10.4315i	0.610685	−	0.654532i
$255$		0			0
$256$	15.3895	−	4.37762i	0.961843	−	0.273601i
$257$		−	1.52448i		−	0.0950946i	−0.998869	−	0.0475473i	$-0.984860\pi$
$257$		−	1.52448i		−	0.0950946i	0.998869	−	0.0475473i	$-0.0151405\pi$
$258$		0			0
$259$		−	27.7921i		−	1.72691i
$260$	9.49810	−	0.659119i	0.589047	−	0.0408768i
$261$		0			0
$262$	−4.95313	−	4.62132i	−0.306005	−	0.285506i
$263$	−25.9018			−1.59718			−0.798588	−	0.601878i	$-0.794419\pi$
$263$	−25.9018			−1.59718			−0.798588	+	0.601878i	$0.794419\pi$
$264$		0			0
$265$	−11.9836			−0.736145
$266$	4.26848	+	3.98253i	0.261717	+	0.244185i
$267$		0			0
$268$	−15.8623	+	1.10076i	−0.968946	+	0.0672398i
$269$		−	15.0345i		−	0.916667i	−0.888780	−	0.458334i	$-0.848446\pi$
$269$		−	15.0345i		−	0.916667i	0.888780	−	0.458334i	$-0.151554\pi$
$270$		0			0
$271$		−	2.18871i		−	0.132955i	−0.997788	−	0.0664773i	$-0.978824\pi$
$271$		−	2.18871i		−	0.132955i	0.997788	−	0.0664773i	$-0.0211760\pi$
$272$	1.66916	+	11.9686i	0.101207	+	0.725703i
$273$		0			0
$274$	−2.81119	+	3.01303i	−0.169830	+	0.182024i
$275$	−4.36571			−0.263262
$276$		0			0
$277$	3.05505			0.183560			0.0917800	−	0.995779i	$-0.470744\pi$
$277$	3.05505			0.183560			0.0917800	+	0.995779i	$0.470744\pi$
$278$	13.2431	−	14.1939i	0.794266	−	0.851294i
$279$		0			0
$280$	6.32300	−	7.79559i	0.377872	−	0.465876i
$281$			6.76617i			0.403636i	0.979423	+	0.201818i	$0.0646849\pi$
$281$			6.76617i			0.403636i	−0.979423	+	0.201818i	$0.935315\pi$
$282$		0			0
$283$			5.92694i			0.352320i	0.984362	+	0.176160i	$0.0563676\pi$
$283$			5.92694i			0.352320i	−0.984362	+	0.176160i	$0.943632\pi$
$284$	1.47690	+	21.2826i	0.0876381	+	1.26289i
$285$		0			0
$286$	−21.4902	−	20.0506i	−1.27074	−	1.18561i
$287$	−16.3954			−0.967790
$288$		0			0
$289$	7.87291			0.463113
$290$	−8.41825	−	7.85431i	−0.494337	−	0.461221i
$291$		0			0
$292$	1.30391	+	18.7897i	0.0763053	+	1.09958i
$293$		−	13.5069i		−	0.789082i	−0.918878	−	0.394541i	$-0.870904\pi$
$293$		−	13.5069i		−	0.789082i	0.918878	−	0.394541i	$-0.129096\pi$
$294$		0			0
$295$			0.684441i			0.0398497i
$296$	−13.9535	+	17.2031i	−0.811028	+	0.999912i
$297$		0			0
$298$	10.1171	−	10.8435i	0.586067	−	0.628146i
$299$	−14.8055			−0.856227
$300$		0			0
$301$	−30.8801			−1.77990
$302$	22.2332	−	23.8296i	1.27938	−	1.37124i
$303$		0			0
$304$	−0.642669	−	4.60823i	−0.0368596	−	0.264300i
$305$		−	10.5876i		−	0.606244i
$306$		0			0
$307$			21.6606i			1.23623i	0.786086	+	0.618117i	$0.212104\pi$
$307$			21.6606i			1.23623i	−0.786086	+	0.618117i	$0.787896\pi$
$308$	−30.9117	+	2.14511i	−1.76136	+	0.122229i
$309$		0			0
$310$	4.95735	+	4.62526i	0.281559	+	0.262697i
$311$	−6.40381			−0.363127			−0.181563	−	0.983379i	$-0.558116\pi$
$311$	−6.40381			−0.363127			−0.181563	+	0.983379i	$0.558116\pi$
$312$		0			0
$313$	−2.85521			−0.161386			−0.0806930	−	0.996739i	$-0.525713\pi$
$313$	−2.85521			−0.161386			−0.0806930	+	0.996739i	$0.525713\pi$
$314$	−15.0101	−	14.0046i	−0.847068	−	0.790323i
$315$		0			0
$316$	−17.4740	+	1.21261i	−0.982992	+	0.0682145i
$317$			13.6790i			0.768290i	0.923273	+	0.384145i	$0.125504\pi$
$317$			13.6790i			0.768290i	−0.923273	+	0.384145i	$0.874496\pi$
$318$		0			0
$319$			35.5420i			1.98997i
$320$	−7.82781	+	1.65086i	−0.437588	+	0.0922861i
$321$		0			0
$322$	−10.6482	+	11.4128i	−0.593403	+	0.636009i
$323$	3.51417			0.195534
$324$		0			0
$325$	−4.76047			−0.264063
$326$	−9.39209	+	10.0664i	−0.520180	+	0.557528i
$327$		0			0
$328$	10.1487	+	8.23158i	0.560366	+	0.454513i
$329$			28.8823i			1.59233i
$330$		0			0
$331$			26.9698i			1.48239i	0.671289	+	0.741196i	$0.265741\pi$
$331$			26.9698i			1.48239i	−0.671289	+	0.741196i	$0.734259\pi$
$332$	−1.85265	−	26.6972i	−0.101677	−	1.46520i
$333$		0			0
$334$	14.0241	+	13.0847i	0.767367	+	0.715961i
$335$	7.95024			0.434368
$336$		0			0
$337$	0.591145			0.0322017			0.0161009	−	0.999870i	$-0.494875\pi$
$337$	0.591145			0.0322017			0.0161009	+	0.999870i	$0.494875\pi$
$338$	−9.99091	−	9.32162i	−0.543434	−	0.507029i
$339$		0			0
$340$	−0.418292	−	6.02772i	−0.0226851	−	0.326899i
$341$		−	20.9300i		−	1.13342i
$342$		0			0
$343$			4.98975i			0.269421i
$344$	19.1146	+	15.5038i	1.03059	+	0.835911i
$345$		0			0
$346$	−12.9391	+	13.8682i	−0.695613	+	0.745558i
$347$	−9.47925			−0.508873			−0.254436	−	0.967090i	$-0.581890\pi$
$347$	−9.47925			−0.508873			−0.254436	+	0.967090i	$0.581890\pi$
$348$		0			0
$349$	−22.0924			−1.18258			−0.591289	−	0.806460i	$-0.701381\pi$
$349$	−22.0924			−1.18258			−0.591289	+	0.806460i	$0.701381\pi$
$350$	−3.42376	+	3.66958i	−0.183007	+	0.196147i
$351$		0			0
$352$	20.2112	+	14.1919i	1.07726	+	0.756432i
$353$			0.355858i			0.0189404i	0.999955	+	0.00947020i	$0.00301450\pi$
$353$			0.355858i			0.0189404i	−0.999955	+	0.00947020i	$0.996985\pi$
$354$		0			0
$355$		−	10.6669i		−	0.566141i
$356$	−9.84221	+	0.682999i	−0.521636	+	0.0361989i
$357$		0			0
$358$	−20.6363	−	19.2539i	−1.09066	−	1.01760i
$359$	−26.7105			−1.40973			−0.704864	−	0.709342i	$-0.748992\pi$
$359$	−26.7105			−1.40973			−0.704864	+	0.709342i	$0.748992\pi$
$360$		0			0
$361$	17.6470			0.928787
$362$	18.2201	+	16.9996i	0.957628	+	0.893477i
$363$		0			0
$364$	−33.7068	+	2.33908i	−1.76672	+	0.122601i
$365$		−	9.41743i		−	0.492931i
$366$		0			0
$367$		−	9.41093i		−	0.491247i	−0.969365	−	0.245623i	$-0.921007\pi$
$367$		−	9.41093i		−	0.491247i	0.969365	−	0.245623i	$-0.0789926\pi$
$368$	12.3212	−	1.71833i	0.642285	−	0.0895739i
$369$		0			0
$370$	7.55546	−	8.09794i	0.392790	−	0.420992i
$371$	42.5273			2.20790
$372$		0			0
$373$	12.8467			0.665179			0.332590	−	0.943072i	$-0.392078\pi$
$373$	12.8467			0.665179			0.332590	+	0.943072i	$0.392078\pi$
$374$	−12.7246	+	13.6382i	−0.657971	+	0.705213i
$375$		0			0
$376$	14.5008	−	17.8780i	0.747823	−	0.921987i
$377$			38.7558i			1.99602i
$378$		0			0
$379$		−	22.5515i		−	1.15839i	−0.815188	−	0.579196i	$-0.803366\pi$
$379$		−	22.5515i		−	1.15839i	0.815188	−	0.579196i	$-0.196634\pi$
$380$	0.161054	+	2.32083i	0.00826188	+	0.119056i
$381$		0			0
$382$	−17.5962	−	16.4174i	−0.900300	−	0.839989i
$383$	25.8689			1.32184			0.660920	−	0.750456i	$-0.270166\pi$
$383$	25.8689			1.32184			0.660920	+	0.750456i	$0.270166\pi$
$384$		0			0
$385$	15.4930			0.789598
$386$	−11.1373	−	10.3912i	−0.566873	−	0.528898i
$387$		0			0
$388$	−0.919630	−	13.2521i	−0.0466872	−	0.672776i
$389$		−	16.2154i		−	0.822155i	−0.911600	−	0.411077i	$-0.865153\pi$
$389$		−	16.2154i		−	0.822155i	0.911600	−	0.411077i	$-0.134847\pi$
$390$		0			0
$391$			9.39595i			0.475174i
$392$	−9.96694	+	12.2882i	−0.503406	+	0.620647i
$393$		0			0
$394$	−0.441866	+	0.473592i	−0.0222609	+	0.0238592i
$395$	8.75803			0.440664
$396$		0			0
$397$	10.4591			0.524925			0.262463	−	0.964942i	$-0.415465\pi$
$397$	10.4591			0.524925			0.262463	+	0.964942i	$0.415465\pi$
$398$	−2.07184	+	2.22059i	−0.103852	+	0.111308i
$399$		0			0
$400$	3.96166	−	0.552498i	0.198083	−	0.0276249i
$401$			2.17980i			0.108854i	0.998518	+	0.0544269i	$0.0173332\pi$
$401$			2.17980i			0.108854i	−0.998518	+	0.0544269i	$0.982667\pi$
$402$		0			0
$403$		−	22.8226i		−	1.13687i
$404$	13.6695	−	0.948591i	0.680082	−	0.0471942i
$405$		0			0
$406$	29.8747	+	27.8734i	1.48265	+	1.38333i
$407$	−34.1896			−1.69472
$408$		0			0
$409$	−25.6245			−1.26705			−0.633525	−	0.773722i	$-0.718393\pi$
$409$	−25.6245			−1.26705			−0.633525	+	0.773722i	$0.718393\pi$
$410$	−4.77723	−	4.45720i	−0.235931	−	0.220126i
$411$		0			0
$412$	28.6920	−	1.99107i	1.41355	−	0.0980932i
$413$		−	2.42894i		−	0.119520i
$414$		0			0
$415$			13.3807i			0.656833i
$416$	22.0387	+	15.4752i	1.08054	+	0.758733i
$417$		0			0
$418$	4.89929	−	5.25106i	0.239632	−	0.256838i
$419$	−8.97928			−0.438666			−0.219333	−	0.975650i	$-0.570388\pi$
$419$	−8.97928			−0.438666			−0.219333	+	0.975650i	$0.570388\pi$
$420$		0			0
$421$	−33.7085			−1.64285			−0.821426	−	0.570315i	$-0.806821\pi$
$421$	−33.7085			−1.64285			−0.821426	+	0.570315i	$0.806821\pi$
$422$	2.09793	−	2.24856i	0.102126	−	0.109458i
$423$		0			0
$424$	−26.3241	−	21.3515i	−1.27841	−	1.03692i
$425$			3.02111i			0.146545i
$426$		0			0
$427$			37.5732i			1.81830i
$428$	0.0672663	+	0.969328i	0.00325144	+	0.0468542i
$429$		0			0
$430$	−8.99771	−	8.39496i	−0.433908	−	0.404841i
$431$	−31.0229			−1.49432			−0.747160	−	0.664645i	$-0.768583\pi$
$431$	−31.0229			−1.49432			−0.747160	+	0.664645i	$0.768583\pi$
$432$		0			0
$433$	−34.5070			−1.65830			−0.829150	−	0.559026i	$-0.811175\pi$
$433$	−34.5070			−1.65830			−0.829150	+	0.559026i	$0.811175\pi$
$434$	−17.5926	−	16.4141i	−0.844474	−	0.787903i
$435$		0			0
$436$	2.17005	+	31.2711i	0.103927	+	1.49761i
$437$		−	3.61769i		−	0.173058i
$438$		0			0
$439$			2.45314i			0.117082i	0.998285	+	0.0585411i	$0.0186449\pi$
$439$			2.45314i			0.117082i	−0.998285	+	0.0585411i	$0.981355\pi$
$440$	−9.59010	−	7.77853i	−0.457190	−	0.370827i
$441$		0			0
$442$	−13.8751	+	14.8714i	−0.659973	+	0.707359i
$443$	−7.51153			−0.356883			−0.178442	−	0.983950i	$-0.557106\pi$
$443$	−7.51153			−0.356883			−0.178442	+	0.983950i	$0.557106\pi$
$444$		0			0
$445$	4.93294			0.233844
$446$	−20.6744	+	22.1589i	−0.978963	+	1.04925i
$447$		0			0
$448$	27.7793	−	5.85858i	1.31245	−	0.276792i
$449$			29.2553i			1.38064i	0.723504	+	0.690321i	$0.242531\pi$
$449$			29.2553i			1.38064i	−0.723504	+	0.690321i	$0.757469\pi$
$450$		0			0
$451$			20.1695i			0.949747i
$452$	2.31528	−	0.160668i	0.108902	−	0.00755720i
$453$		0			0
$454$	9.13485	+	8.52290i	0.428720	+	0.400000i
$455$	16.8939			0.792000
$456$		0			0
$457$	−30.9220			−1.44647			−0.723235	−	0.690602i	$-0.757346\pi$
$457$	−30.9220			−1.44647			−0.723235	+	0.690602i	$0.757346\pi$
$458$	−20.7612	−	19.3704i	−0.970109	−	0.905121i
$459$		0			0
$460$	−6.20528	+	0.430614i	−0.289323	+	0.0200775i
$461$		−	24.4816i		−	1.14022i	−0.821567	−	0.570112i	$-0.806900\pi$
$461$		−	24.4816i		−	1.14022i	0.821567	−	0.570112i	$-0.193100\pi$
$462$		0			0
$463$		−	19.0943i		−	0.887387i	−0.896179	−	0.443694i	$-0.853668\pi$
$463$		−	19.0943i		−	0.887387i	0.896179	−	0.443694i	$-0.146332\pi$
$464$	−4.49798	−	32.2525i	−0.208813	−	1.49729i
$465$		0			0
$466$	8.21993	−	8.81012i	0.380781	−	0.408121i
$467$	−33.8471			−1.56626			−0.783129	−	0.621859i	$-0.786378\pi$
$467$	−33.8471			−1.56626			−0.783129	+	0.621859i	$0.786378\pi$
$468$		0			0
$469$	−28.2138			−1.30279
$470$	−7.85185	+	8.41561i	−0.362179	+	0.388183i
$471$		0			0
$472$	−1.21949	+	1.50350i	−0.0561316	+	0.0692043i
$473$			37.9885i			1.74671i
$474$		0			0
$475$		−	1.16321i		−	0.0533715i
$476$	1.48443	+	21.3911i	0.0680390	+	0.980462i
$477$		0			0
$478$	3.03346	+	2.83025i	0.138747	+	0.129452i
$479$	3.07957			0.140709			0.0703547	−	0.997522i	$-0.477587\pi$
$479$	3.07957			0.140709			0.0703547	+	0.997522i	$0.477587\pi$
$480$		0			0
$481$	−37.2811			−1.69987
$482$	−26.7659	−	24.9728i	−1.21915	−	1.13748i
$483$		0			0
$484$	1.11588	+	16.0802i	0.0507220	+	0.730919i
$485$			6.64201i			0.301598i
$486$		0			0
$487$		−	32.0600i		−	1.45278i	−0.687285	−	0.726388i	$-0.741198\pi$
$487$		−	32.0600i		−	1.45278i	0.687285	−	0.726388i	$-0.258802\pi$
$488$	18.8642	−	23.2576i	0.853944	−	1.05282i
$489$		0			0
$490$	5.39686	−	5.78435i	0.243805	−	0.261310i
$491$	20.8359			0.940313			0.470157	−	0.882583i	$-0.344197\pi$
$491$	20.8359			0.940313			0.470157	+	0.882583i	$0.344197\pi$
$492$		0			0
$493$	24.5953			1.10772
$494$	5.34229	−	5.72587i	0.240361	−	0.257619i
$495$		0			0
$496$	2.64878	+	18.9929i	0.118934	+	0.852807i
$497$			37.8547i			1.69801i
$498$		0			0
$499$		−	21.0503i		−	0.942340i	−0.882043	−	0.471170i	$-0.843832\pi$
$499$		−	21.0503i		−	0.942340i	0.882043	−	0.471170i	$-0.156168\pi$
$500$	−1.99520	+	0.138457i	−0.0892281	+	0.00619197i
$501$		0			0
$502$	27.5335	+	25.6890i	1.22888	+	1.14656i
$503$	42.5778			1.89845			0.949225	−	0.314597i	$-0.101869\pi$
$503$	42.5778			1.89845			0.949225	+	0.314597i	$0.101869\pi$
$504$		0			0
$505$	−6.85118			−0.304873
$506$	14.0399	+	13.0994i	0.624151	+	0.582339i
$507$		0			0
$508$	−20.1279	+	1.39677i	−0.893033	+	0.0619718i
$509$		−	19.2768i		−	0.854431i	−0.904150	−	0.427216i	$-0.859495\pi$
$509$		−	19.2768i		−	0.854431i	0.904150	−	0.427216i	$-0.140505\pi$
$510$		0			0
$511$			33.4206i			1.47844i
$512$	−20.1366	−	10.3206i	−0.889922	−	0.456112i
$513$		0			0
$514$	−1.47077	+	1.57637i	−0.0648728	+	0.0695306i
$515$	−14.3805			−0.633680
$516$		0			0
$517$	35.5309			1.56265
$518$	−26.8128	+	28.7380i	−1.17809	+	1.26267i
$519$		0			0
$520$	−10.4573	−	8.48188i	−0.458581	−	0.371955i
$521$		−	26.9346i		−	1.18002i	−0.807394	−	0.590012i	$-0.799123\pi$
$521$		−	26.9346i		−	1.18002i	0.807394	−	0.590012i	$-0.200877\pi$
$522$		0			0
$523$		−	6.75789i		−	0.295502i	−0.989025	−	0.147751i	$-0.952797\pi$
$523$		−	6.75789i		−	0.295502i	0.989025	−	0.147751i	$-0.0472034\pi$
$524$	0.663221	+	9.55721i	0.0289729	+	0.417509i
$525$		0			0
$526$	26.7834	+	24.9892i	1.16781	+	1.08958i
$527$	−14.4837			−0.630922
$528$		0			0
$529$	−13.3273			−0.579446
$530$	12.3914	+	11.5613i	0.538249	+	0.502192i
$531$		0			0
$532$	−0.571547	−	8.23616i	−0.0247797	−	0.357083i
$533$			21.9933i			0.952636i
$534$		0			0
$535$		−	0.485829i		−	0.0210042i
$536$	17.4642	+	14.1652i	0.754338	+	0.611843i
$537$		0			0
$538$	−14.5047	+	15.5462i	−0.625343	+	0.670243i
$539$	−24.4216			−1.05191
$540$		0			0
$541$	−15.3714			−0.660869			−0.330435	−	0.943829i	$-0.607195\pi$
$541$	−15.3714			−0.660869			−0.330435	+	0.943829i	$0.607195\pi$
$542$	−2.11159	+	2.26320i	−0.0907005	+	0.0972128i
$543$		0			0
$544$	9.82092	−	13.9863i	0.421068	−	0.599657i
$545$		−	15.6731i		−	0.671363i
$546$		0			0
$547$		−	18.7918i		−	0.803478i	−0.915754	−	0.401739i	$-0.868406\pi$
$547$		−	18.7918i		−	0.803478i	0.915754	−	0.401739i	$-0.131594\pi$
$548$	5.81373	−	0.403443i	0.248350	−	0.0172342i
$549$		0			0
$550$	4.51430	+	4.21189i	0.192490	+	0.179595i
$551$	−9.46985			−0.403429
$552$		0			0
$553$	−31.0805			−1.32168
$554$	−3.15903	−	2.94740i	−0.134214	−	0.125223i
$555$		0			0
$556$	−27.3876	+	1.90056i	−1.16149	+	0.0806015i
$557$		−	36.4336i		−	1.54374i	−0.635779	−	0.771871i	$-0.719321\pi$
$557$		−	36.4336i		−	1.54374i	0.635779	−	0.771871i	$-0.280679\pi$
$558$		0			0
$559$			41.4235i			1.75203i
$560$	−14.0591	+	1.96070i	−0.594106	+	0.0828548i
$561$		0			0
$562$	6.52776	−	6.99646i	0.275357	−	0.295128i
$563$	18.5365			0.781219			0.390610	−	0.920556i	$-0.372264\pi$
$563$	18.5365			0.781219			0.390610	+	0.920556i	$0.372264\pi$
$564$		0			0
$565$	−1.16042			−0.0488194
$566$	5.71811	−	6.12867i	0.240350	−	0.257607i
$567$		0			0
$568$	19.0056	−	23.4318i	0.797456	−	0.983178i
$569$			5.79139i			0.242788i	0.992604	+	0.121394i	$0.0387364\pi$
$569$			5.79139i			0.242788i	−0.992604	+	0.121394i	$0.961264\pi$
$570$		0			0
$571$		−	40.0776i		−	1.67720i	−0.544751	−	0.838598i	$-0.683376\pi$
$571$		−	40.0776i		−	1.67720i	0.544751	−	0.838598i	$-0.316624\pi$
$572$	2.87752	+	41.4659i	0.120315	+	1.73378i
$573$		0			0
$574$	16.9534	+	15.8177i	0.707622	+	0.660219i
$575$	3.11010			0.129700
$576$		0			0
$577$	−9.44022			−0.393001			−0.196501	−	0.980504i	$-0.562958\pi$
$577$	−9.44022			−0.393001			−0.196501	+	0.980504i	$0.562958\pi$
$578$	−8.14087	−	7.59551i	−0.338615	−	0.315932i
$579$		0			0
$580$	1.12720	+	16.2433i	0.0468044	+	0.674465i
$581$		−	47.4854i		−	1.97003i
$582$		0			0
$583$		−	52.3168i		−	2.16674i
$584$	16.7793	−	20.6871i	0.694334	−	0.856040i
$585$		0			0
$586$	−13.0310	+	13.9666i	−0.538306	+	0.576956i
$587$	40.0701			1.65387			0.826934	−	0.562299i	$-0.190083\pi$
$587$	40.0701			1.65387			0.826934	+	0.562299i	$0.190083\pi$
$588$		0			0
$589$	5.57662			0.229781
$590$	0.660325	−	0.707736i	0.0271851	−	0.0291370i
$591$		0			0
$592$	31.0254	−	4.32683i	1.27513	−	0.177832i
$593$			21.8552i			0.897486i	0.893661	+	0.448743i	$0.148128\pi$
$593$			21.8552i			0.897486i	−0.893661	+	0.448743i	$0.851872\pi$
$594$		0			0
$595$		−	10.7213i		−	0.439530i
$596$	−20.9228	+	1.45194i	−0.857033	+	0.0594736i
$597$		0			0
$598$	15.3094	+	14.2839i	0.626050	+	0.584111i
$599$	3.02327			0.123528			0.0617638	−	0.998091i	$-0.480327\pi$
$599$	3.02327			0.123528			0.0617638	+	0.998091i	$0.480327\pi$
$600$		0			0
$601$	33.9064			1.38307			0.691536	−	0.722342i	$-0.256934\pi$
$601$	33.9064			1.38307			0.691536	+	0.722342i	$0.256934\pi$
$602$	31.9311	+	29.7920i	1.30141	+	1.21423i
$603$		0			0
$604$	−45.9799	+	3.19076i	−1.87089	+	0.129830i
$605$		−	8.05944i		−	0.327663i
$606$		0			0
$607$			30.4571i			1.23622i	0.786093	+	0.618108i	$0.212101\pi$
$607$			30.4571i			1.23622i	−0.786093	+	0.618108i	$0.787899\pi$
$608$	−3.78131	+	5.38509i	−0.153352	+	0.218394i
$609$		0			0
$610$	−10.2145	+	10.9479i	−0.413575	+	0.443269i
$611$	38.7436			1.56740
$612$		0			0
$613$	26.4631			1.06883			0.534417	−	0.845221i	$-0.320531\pi$
$613$	26.4631			1.06883			0.534417	+	0.845221i	$0.320531\pi$
$614$	20.8973	−	22.3978i	0.843348	−	0.903900i
$615$		0			0
$616$	34.0333	+	27.6044i	1.37124	+	1.11221i
$617$		−	15.7692i		−	0.634843i	−0.948285	−	0.317421i	$-0.897183\pi$
$617$		−	15.7692i		−	0.634843i	0.948285	−	0.317421i	$-0.102817\pi$
$618$		0			0
$619$		−	2.68614i		−	0.107965i	−0.998542	−	0.0539825i	$-0.982808\pi$
$619$		−	2.68614i		−	0.107965i	0.998542	−	0.0539825i	$-0.0171915\pi$
$620$	−0.663787	−	9.56536i	−0.0266583	−	0.384154i
$621$		0			0
$622$	6.62176	+	6.17817i	0.265508	+	0.247722i
$623$	−17.5060			−0.701363
$624$		0			0
$625$	1.00000			0.0400000
$626$	2.95239	+	2.75461i	0.118001	+	0.110096i
$627$		0			0
$628$	2.00984	+	28.9624i	0.0802014	+	1.15573i
$629$			23.6595i			0.943366i
$630$		0			0
$631$		−	39.2086i		−	1.56087i	−0.625238	−	0.780434i	$-0.714998\pi$
$631$		−	39.2086i		−	1.56087i	0.625238	−	0.780434i	$-0.285002\pi$
$632$	19.2387	+	15.6045i	0.765273	+	0.620712i
$633$		0			0
$634$	13.1970	−	14.1446i	0.524122	−	0.561753i
$635$	10.0882			0.400337
$636$		0			0
$637$	−26.6299			−1.05511
$638$	34.2897	−	36.7517i	1.35754	−	1.45501i
$639$		0			0
$640$	9.68693	+	5.84495i	0.382909	+	0.231042i
$641$		−	31.5443i		−	1.24592i	−0.782252	−	0.622962i	$-0.785929\pi$
$641$		−	31.5443i		−	1.24592i	0.782252	−	0.622962i	$-0.214071\pi$
$642$		0			0
$643$		−	9.18421i		−	0.362190i	−0.983466	−	0.181095i	$-0.942036\pi$
$643$		−	9.18421i		−	0.362190i	0.983466	−	0.181095i	$-0.0579641\pi$
$644$	22.0213	−	1.52816i	0.867760	−	0.0602181i
$645$		0			0
$646$	−3.63377	−	3.39035i	−0.142969	−	0.133391i
$647$	−25.5421			−1.00416			−0.502081	−	0.864821i	$-0.667432\pi$
$647$	−25.5421			−1.00416			−0.502081	+	0.864821i	$0.667432\pi$
$648$		0			0
$649$	−2.98807			−0.117292
$650$	4.92249	+	4.59273i	0.193076	+	0.180142i
$651$		0			0
$652$	19.4235	−	1.34789i	0.760683	−	0.0527874i
$653$		−	10.4334i		−	0.408289i	−0.978941	−	0.204145i	$-0.934559\pi$
$653$		−	10.4334i		−	0.408289i	0.978941	−	0.204145i	$-0.0654413\pi$
$654$		0			0
$655$		−	4.79010i		−	0.187165i
$656$	−2.55253	−	18.3028i	−0.0996597	−	0.714605i
$657$		0			0
$658$	27.8646	−	29.8653i	1.08628	−	1.16427i
$659$	−8.12696			−0.316581			−0.158291	−	0.987393i	$-0.550598\pi$
$659$	−8.12696			−0.316581			−0.158291	+	0.987393i	$0.550598\pi$
$660$		0			0
$661$	8.66356			0.336974			0.168487	−	0.985704i	$-0.446112\pi$
$661$	8.66356			0.336974			0.168487	+	0.985704i	$0.446112\pi$
$662$	26.0195	−	27.8877i	1.01128	−	1.08389i
$663$		0			0
$664$	−23.8408	+	29.3932i	−0.925203	+	1.14068i
$665$			4.12798i			0.160076i
$666$		0			0
$667$		−	25.3199i		−	0.980389i
$668$	−1.87783	−	27.0600i	−0.0726552	−	1.04698i
$669$		0			0
$670$	−8.22083	−	7.67011i	−0.317598	−	0.296322i
$671$	46.2224			1.78440
$672$		0			0
$673$	−15.7922			−0.608746			−0.304373	−	0.952553i	$-0.598447\pi$
$673$	−15.7922			−0.608746			−0.304373	+	0.952553i	$0.598447\pi$
$674$	−0.611265	−	0.570316i	−0.0235450	−	0.0219678i
$675$		0			0
$676$	1.33778	+	19.2778i	0.0514530	+	0.741452i
$677$		−	29.2086i		−	1.12258i	−0.827620	−	0.561289i	$-0.810305\pi$
$677$		−	29.2086i		−	1.12258i	0.827620	−	0.561289i	$-0.189695\pi$
$678$		0			0
$679$		−	23.5711i		−	0.904577i
$680$	−5.38280	+	6.63642i	−0.206421	+	0.254495i
$681$		0			0
$682$	−20.1926	+	21.6424i	−0.773213	+	0.828730i
$683$	−29.1095			−1.11385			−0.556923	−	0.830564i	$-0.688018\pi$
$683$	−29.1095			−1.11385			−0.556923	+	0.830564i	$0.688018\pi$
$684$		0			0
$685$	−2.91386			−0.111333
$686$	4.81393	−	5.15957i	0.183797	−	0.196993i
$687$		0			0
$688$	−4.80759	−	34.4726i	−0.183288	−	1.31426i
$689$		−	57.0474i		−	2.17333i
$690$		0			0
$691$			5.36149i			0.203961i	0.994786	+	0.101980i	$0.0325179\pi$
$691$			5.36149i			0.203961i	−0.994786	+	0.101980i	$0.967482\pi$
$692$	26.7591	−	1.85694i	1.01723	−	0.0705903i
$693$		0			0
$694$	9.80188	+	9.14525i	0.372074	+	0.347149i
$695$	13.7267			0.520684
$696$		0			0
$697$	13.9575			0.528677
$698$	22.8443	+	21.3140i	0.864669	+	0.806745i
$699$		0			0
$700$	7.08057	−	0.491355i	0.267620	−	0.0185715i
$701$			26.2574i			0.991728i	0.868400	+	0.495864i	$0.165148\pi$
$701$			26.2574i			0.991728i	−0.868400	+	0.495864i	$0.834852\pi$
$702$		0			0
$703$		−	9.10953i		−	0.343573i
$704$	−7.20719	−	34.1740i	−0.271631	−	1.28798i
$705$		0			0
$706$	0.343319	−	0.367969i	0.0129210	−	0.0138487i
$707$	24.3134			0.914401
$708$		0			0
$709$	−22.6687			−0.851342			−0.425671	−	0.904878i	$-0.639962\pi$
$709$	−22.6687			−0.851342			−0.425671	+	0.904878i	$0.639962\pi$
$710$	−10.2911	+	11.0300i	−0.386217	+	0.413947i
$711$		0			0
$712$	10.8361	+	8.78918i	0.406101	+	0.329388i
$713$			14.9104i			0.558399i
$714$		0			0
$715$		−	20.7828i		−	0.777234i
$716$	2.76318	+	39.8183i	0.103265	+	1.48808i
$717$		0			0
$718$	27.6196	+	25.7694i	1.03076	+	0.961705i
$719$	−29.1172			−1.08589			−0.542945	−	0.839768i	$-0.682691\pi$
$719$	−29.1172			−1.08589			−0.542945	+	0.839768i	$0.682691\pi$
$720$		0			0
$721$	51.0334			1.90058
$722$	−18.2476	−	17.0252i	−0.679104	−	0.633611i
$723$		0			0
$724$	−2.43966	−	35.1563i	−0.0906694	−	1.30657i
$725$		−	8.14117i		−	0.302355i
$726$		0			0
$727$		−	22.7265i		−	0.842879i	−0.906856	−	0.421440i	$-0.861525\pi$
$727$		−	22.7265i		−	0.842879i	0.906856	−	0.421440i	$-0.138475\pi$
$728$	37.1107	+	30.1005i	1.37541	+	1.11560i
$729$		0			0
$730$	−9.08561	+	9.73795i	−0.336274	+	0.360418i
$731$	26.2883			0.972309
$732$		0			0
$733$	6.03204			0.222799			0.111399	−	0.993776i	$-0.464467\pi$
$733$	6.03204			0.222799			0.111399	+	0.993776i	$0.464467\pi$
$734$	−9.07934	+	9.73123i	−0.335124	+	0.359186i
$735$		0			0
$736$	−14.3983	−	10.1102i	−0.530728	−	0.372668i
$737$			34.7085i			1.27850i
$738$		0			0
$739$		−	11.1343i		−	0.409582i	−0.978806	−	0.204791i	$-0.934349\pi$
$739$		−	11.1343i		−	0.409582i	0.978806	−	0.204791i	$-0.0656514\pi$
$740$	−15.6252	+	1.08431i	−0.574395	+	0.0398600i
$741$		0			0
$742$	−43.9747	−	41.0288i	−1.61436	−	1.50621i
$743$	−17.4343			−0.639601			−0.319801	−	0.947485i	$-0.603616\pi$
$743$	−17.4343			−0.639601			−0.319801	+	0.947485i	$0.603616\pi$
$744$		0			0
$745$	10.4866			0.384198
$746$	−13.2840	−	12.3941i	−0.486361	−	0.453780i
$747$		0			0
$748$	26.3153	−	1.82614i	0.962182	−	0.0667704i
$749$			1.72411i			0.0629976i
$750$		0			0
$751$		−	43.7231i		−	1.59548i	−0.603002	−	0.797740i	$-0.706029\pi$
$751$		−	43.7231i		−	1.59548i	0.603002	−	0.797740i	$-0.293971\pi$
$752$	−32.2424	+	4.49657i	−1.17576	+	0.163973i
$753$		0			0
$754$	37.3902	−	40.0748i	1.36167	−	1.45944i
$755$	23.0452			0.838701
$756$		0			0
$757$	−28.7104			−1.04350			−0.521749	−	0.853099i	$-0.674720\pi$
$757$	−28.7104			−1.04350			−0.521749	+	0.853099i	$0.674720\pi$
$758$	−21.7569	+	23.3190i	−0.790246	+	0.846985i
$759$		0			0
$760$	2.07252	−	2.55520i	0.0751782	−	0.0926868i
$761$		−	14.3521i		−	0.520265i	−0.965573	−	0.260132i	$-0.916234\pi$
$761$		−	14.3521i		−	0.520265i	0.965573	−	0.260132i	$-0.0837662\pi$
$762$		0			0
$763$			55.6208i			2.01361i
$764$	2.35612	+	33.9524i	0.0852414	+	1.22835i
$765$		0			0
$766$	−26.7494	−	24.9574i	−0.966494	−	0.901748i
$767$	−3.25826			−0.117649
$768$		0			0
$769$	20.7832			0.749463			0.374732	−	0.927133i	$-0.377735\pi$
$769$	20.7832			0.749463			0.374732	+	0.927133i	$0.377735\pi$
$770$	−16.0203	−	14.9471i	−0.577333	−	0.538657i
$771$		0			0
$772$	1.49128	+	21.4897i	0.0536722	+	0.773432i
$773$			33.9470i			1.22099i	0.792020	+	0.610495i	$0.209029\pi$
$773$			33.9470i			1.22099i	−0.792020	+	0.610495i	$0.790971\pi$
$774$		0			0
$775$			4.79418i			0.172212i
$776$	−11.8343	+	14.5904i	−0.424826	+	0.523765i
$777$		0			0
$778$	−15.6441	+	16.7673i	−0.560867	+	0.601138i
$779$	−5.37400			−0.192543
$780$		0			0
$781$	46.5686			1.66636
$782$	9.06489	−	9.71574i	0.324160	−	0.347434i
$783$		0			0
$784$	22.1614	−	3.09065i	0.791477	−	0.110380i
$785$		−	14.5160i		−	0.518099i
$786$		0			0
$787$		−	35.8401i		−	1.27756i	−0.769388	−	0.638782i	$-0.779439\pi$
$787$		−	35.8401i		−	1.27756i	0.769388	−	0.638782i	$-0.220561\pi$
$788$	0.913811	−	0.0634137i	0.0325532	−	0.00225902i
$789$		0			0
$790$	−9.05611	−	8.44944i	−0.322202	−	0.300618i
$791$	4.11811			0.146423
$792$		0			0
$793$	50.4019			1.78982
$794$	−10.8150	−	10.0905i	−0.383811	−	0.358100i
$795$		0			0
$796$	4.28470	−	0.297336i	0.151867	−	0.0105388i
$797$			8.52002i			0.301795i	0.988549	+	0.150897i	$0.0482163\pi$
$797$			8.52002i			0.301795i	−0.988549	+	0.150897i	$0.951784\pi$
$798$		0			0
$799$		−	24.5876i		−	0.869848i
$800$	−4.62953	−	3.25077i	−0.163678	−	0.114932i
$801$		0			0
$802$	2.10299	−	2.25399i	0.0742592	−	0.0795910i
$803$	41.1138			1.45087
$804$		0			0
$805$	−11.0371			−0.389007
$806$	−22.0184	+	23.5993i	−0.775565	+	0.831251i
$807$		0			0
$808$	−15.0499	−	12.2070i	−0.529453	−	0.429439i
$809$		−	6.70486i		−	0.235730i	−0.993030	−	0.117865i	$-0.962395\pi$
$809$		−	6.70486i		−	0.235730i	0.993030	−	0.117865i	$-0.0376051\pi$
$810$		0			0
$811$		−	24.0578i		−	0.844784i	−0.906413	−	0.422392i	$-0.861191\pi$
$811$		−	24.0578i		−	0.844784i	0.906413	−	0.422392i	$-0.138809\pi$
$812$	−4.00020	−	57.6441i	−0.140379	−	2.02291i
$813$		0			0
$814$	35.3533	+	32.9850i	1.23913	+	1.15612i
$815$	−9.73510			−0.341006
$816$		0			0
$817$	−10.1217			−0.354113
$818$	26.4966	+	24.7216i	0.926433	+	0.864371i
$819$		0			0
$820$	0.639668	+	9.21781i	0.0223382	+	0.321900i
$821$		−	25.7881i		−	0.900013i	−0.893025	−	0.450006i	$-0.851422\pi$
$821$		−	25.7881i		−	0.900013i	0.893025	−	0.450006i	$-0.148578\pi$
$822$		0			0
$823$			11.6163i			0.404920i	0.979291	+	0.202460i	$0.0648936\pi$
$823$			11.6163i			0.404920i	−0.979291	+	0.202460i	$0.935106\pi$
$824$	−31.5894	−	25.6222i	−1.10047	−	0.892590i
$825$		0			0
$826$	−2.34336	+	2.51161i	−0.0815358	+	0.0873901i
$827$	−2.17283			−0.0755567			−0.0377783	−	0.999286i	$-0.512028\pi$
$827$	−2.17283			−0.0755567			−0.0377783	+	0.999286i	$0.512028\pi$
$828$		0			0
$829$	−37.9307			−1.31739			−0.658693	−	0.752412i	$-0.728891\pi$
$829$	−37.9307			−1.31739			−0.658693	+	0.752412i	$0.728891\pi$
$830$	12.9092	−	13.8361i	0.448086	−	0.480258i
$831$		0			0
$832$	−7.85888	−	37.2641i	−0.272458	−	1.29190i
$833$			16.9000i			0.585549i
$834$		0			0
$835$			13.5625i			0.469351i
$836$	−10.1321	+	0.703114i	−0.350425	+	0.0243177i
$837$		0			0
$838$	9.28489	+	8.66289i	0.320741	+	0.299255i
$839$	−8.91430			−0.307756			−0.153878	−	0.988090i	$-0.549176\pi$
$839$	−8.91430			−0.307756			−0.153878	+	0.988090i	$0.549176\pi$
$840$		0			0
$841$	−37.2786			−1.28547
$842$	34.8558	+	32.5208i	1.20121	+	1.12074i
$843$		0			0
$844$	−4.33866	+	0.301081i	−0.149343	+	0.0103636i
$845$		−	9.66206i		−	0.332385i
$846$		0			0
$847$			28.6013i			0.982753i
$848$	6.62090	+	47.4748i	0.227363	+	1.63029i
$849$		0			0
$850$	2.91466	−	3.12393i	0.0999720	−	0.107150i
$851$	24.3565			0.834929
$852$		0			0
$853$	8.49722			0.290939			0.145470	−	0.989363i	$-0.453531\pi$
$853$	8.49722			0.290939			0.145470	+	0.989363i	$0.453531\pi$
$854$	36.2493	−	38.8520i	1.24043	−	1.32949i
$855$		0			0
$856$	0.865618	−	1.06722i	0.0295862	−	0.0364767i
$857$			40.8364i			1.39495i	0.716611	+	0.697473i	$0.245692\pi$
$857$			40.8364i			1.39495i	−0.716611	+	0.697473i	$0.754308\pi$
$858$		0			0
$859$		−	44.5472i		−	1.51993i	−0.649964	−	0.759965i	$-0.725216\pi$
$859$		−	44.5472i		−	1.51993i	0.649964	−	0.759965i	$-0.274784\pi$
$860$	1.20479	+	17.3614i	0.0410829	+	0.592017i
$861$		0			0
$862$	32.0787	+	29.9298i	1.09261	+	1.01941i
$863$	22.6193			0.769971			0.384985	−	0.922923i	$-0.374206\pi$
$863$	22.6193			0.769971			0.384985	+	0.922923i	$0.374206\pi$
$864$		0			0
$865$	−13.4117			−0.456012
$866$	35.6814	+	33.2911i	1.21250	+	1.13128i
$867$		0			0
$868$	2.35564	+	33.9455i	0.0799558	+	1.15219i
$869$			38.2350i			1.29704i
$870$		0			0
$871$			37.8469i			1.28239i
$872$	27.9253	−	34.4290i	0.945670	−	1.16591i
$873$		0			0
$874$	−3.49022	+	3.74082i	−0.118058	+	0.126535i
$875$	−3.54880			−0.119971
$876$		0			0
$877$	7.37149			0.248917			0.124459	−	0.992225i	$-0.460281\pi$
$877$	7.37149			0.248917			0.124459	+	0.992225i	$0.460281\pi$
$878$	2.36671	−	2.53664i	0.0798725	−	0.0856073i
$879$		0			0
$880$	2.41205	+	17.2955i	0.0813101	+	0.583030i
$881$			41.0770i			1.38392i	0.721937	+	0.691959i	$0.243252\pi$
$881$			41.0770i			1.38392i	−0.721937	+	0.691959i	$0.756748\pi$
$882$		0			0
$883$		−	23.9030i		−	0.804401i	−0.915552	−	0.402201i	$-0.868245\pi$
$883$		−	23.9030i		−	0.804401i	0.915552	−	0.402201i	$-0.131755\pi$
$884$	28.6948	−	1.99127i	0.965109	−	0.0669736i
$885$		0			0
$886$	7.76718	+	7.24686i	0.260944	+	0.243463i
$887$	37.8953			1.27240			0.636200	−	0.771524i	$-0.280505\pi$
$887$	37.8953			1.27240			0.636200	+	0.771524i	$0.280505\pi$
$888$		0			0
$889$	−35.8009			−1.20072
$890$	−5.10083	−	4.75913i	−0.170980	−	0.159526i
$891$		0			0
$892$	42.7562	−	2.96706i	1.43158	−	0.0993444i
$893$			9.46689i			0.316797i
$894$		0			0
$895$		−	19.9570i		−	0.667090i
$896$	−34.3769	−	20.7425i	−1.14845	−	0.692960i
$897$		0			0
$898$	28.2245	−	30.2510i	0.941862	−	1.00949i
$899$	39.0302			1.30173
$900$		0			0
$901$	−36.2036			−1.20612
$902$	19.4589	−	20.8560i	0.647910	−	0.694429i
$903$		0			0
$904$	−2.54909	−	2.06756i	−0.0847813	−	0.0687661i
$905$			17.6204i			0.585722i
$906$		0			0
$907$			22.5057i			0.747291i	0.927572	+	0.373646i	$0.121892\pi$
$907$			22.5057i			0.747291i	−0.927572	+	0.373646i	$0.878108\pi$
$908$	−1.22315	−	17.6260i	−0.0405917	−	0.584938i
$909$		0			0
$910$	−17.4689	−	16.2987i	−0.579089	−	0.540296i
$911$	−7.91542			−0.262250			−0.131125	−	0.991366i	$-0.541859\pi$
$911$	−7.91542			−0.262250			−0.131125	+	0.991366i	$0.541859\pi$
$912$		0			0
$913$	−58.4163			−1.93330
$914$	31.9744	+	29.8325i	1.05762	+	0.986770i
$915$		0			0
$916$	2.77992	+	40.0594i	0.0918511	+	1.32360i
$917$			16.9991i			0.561359i
$918$		0			0
$919$		−	1.24778i		−	0.0411605i	−0.999788	−	0.0205802i	$-0.993449\pi$
$919$		−	1.24778i		−	0.0411605i	0.999788	−	0.0205802i	$-0.00655136\pi$
$920$	6.83192	+	5.54137i	0.225242	+	0.182693i
$921$		0			0
$922$	−23.6190	+	25.3149i	−0.777852	+	0.833701i
$923$	50.7795			1.67143
$924$		0			0
$925$	7.83140			0.257495
$926$	−18.4215	+	19.7442i	−0.605368	+	0.648834i
$927$		0			0
$928$	−26.4650	+	37.6897i	−0.868758	+	1.23723i
$929$			36.0809i			1.18378i	0.806021	+	0.591888i	$0.201617\pi$
$929$			36.0809i			1.18378i	−0.806021	+	0.591888i	$0.798383\pi$
$930$		0			0
$931$		−	6.50693i		−	0.213256i
$932$	−16.9994	+	1.17967i	−0.556834	+	0.0386414i
$933$		0			0
$934$	34.9991	+	32.6545i	1.14521	+	1.06849i
$935$	−13.1893			−0.431336
$936$		0			0
$937$	9.59638			0.313500			0.156750	−	0.987638i	$-0.449898\pi$
$937$	9.59638			0.313500			0.156750	+	0.987638i	$0.449898\pi$
$938$	29.1740	+	27.2197i	0.952566	+	0.888754i
$939$		0			0
$940$	16.2382	−	1.12685i	0.529631	−	0.0367537i
$941$			10.8397i			0.353365i	0.984268	+	0.176683i	$0.0565366\pi$
$941$			10.8397i			0.353365i	−0.984268	+	0.176683i	$0.943463\pi$
$942$		0			0
$943$		−	14.3686i		−	0.467907i
$944$	2.71152	−	0.378152i	0.0882525	−	0.0123078i
$945$		0			0
$946$	36.6500	−	39.2814i	1.19159	−	1.27715i
$947$	−35.1208			−1.14127			−0.570636	−	0.821203i	$-0.693303\pi$
$947$	−35.1208			−1.14127			−0.570636	+	0.821203i	$0.693303\pi$
$948$		0			0
$949$	44.8314			1.45529
$950$	−1.12222	+	1.20280i	−0.0364096	+	0.0390238i
$951$		0			0
$952$	19.1025	−	23.5513i	0.619115	−	0.763303i
$953$			23.5204i			0.761900i	0.924596	+	0.380950i	$0.124403\pi$
$953$			23.5204i			0.761900i	−0.924596	+	0.380950i	$0.875597\pi$
$954$		0			0
$955$		−	17.0170i		−	0.550658i
$956$	−0.406178	−	5.85315i	−0.0131367	−	0.189304i
$957$		0			0
$958$	−3.18439	−	2.97107i	−0.102883	−	0.0959908i
$959$	10.3407			0.333918
$960$		0			0
$961$	8.01580			0.258574
$962$	38.5500	+	35.9675i	1.24290	+	1.15964i
$963$		0			0
$964$	3.58393	+	51.6455i	0.115431	+	1.66339i
$965$		−	10.7707i		−	0.346721i
$966$		0			0
$967$			20.2517i			0.651252i	0.945499	+	0.325626i	$0.105575\pi$
$967$			20.2517i			0.651252i	−0.945499	+	0.325626i	$0.894425\pi$
$968$	14.3598	−	17.7041i	0.461540	−	0.569030i
$969$		0			0
$970$	6.40798	−	6.86807i	0.205748	−	0.220520i
$971$	29.6220			0.950616			0.475308	−	0.879819i	$-0.342337\pi$
$971$	29.6220			0.950616			0.475308	+	0.879819i	$0.342337\pi$
$972$		0			0
$973$	−48.7133			−1.56168
$974$	−30.9303	+	33.1511i	−0.991072	+	1.06223i
$975$		0			0
$976$	−41.9444	+	5.84962i	−1.34261	+	0.187242i
$977$			35.3726i			1.13167i	0.824518	+	0.565835i	$0.191446\pi$
$977$			35.3726i			1.13167i	−0.824518	+	0.565835i	$0.808554\pi$
$978$		0			0
$979$			21.5358i			0.688287i
$980$	−11.1611	+	0.774521i	−0.356528	+	0.0247412i
$981$		0			0
$982$	−21.5451	−	20.1018i	−0.687532	−	0.641474i
$983$	−0.0488705			−0.00155873			−0.000779364	−	1.00000i	$-0.500248\pi$
$983$	−0.0488705			−0.00155873			−0.000779364		1.00000i	$0.500248\pi$
$984$		0			0
$985$	−0.458004			−0.0145932
$986$	−25.4324	−	23.7287i	−0.809934	−	0.755676i
$987$		0			0
$988$	−11.0482	+	0.766691i	−0.351491	+	0.0243917i
$989$		−	27.0627i		−	0.860545i
$990$		0			0
$991$		−	12.0395i		−	0.382446i	−0.981547	−	0.191223i	$-0.938755\pi$
$991$		−	12.0395i		−	0.382446i	0.981547	−	0.191223i	$-0.0612454\pi$
$992$	15.5848	−	22.1948i	0.494817	−	0.704685i
$993$		0			0
$994$	36.5209	−	39.1431i	1.15837	−	1.24154i
$995$	−2.14750			−0.0680804
$996$		0			0
$997$	−48.8679			−1.54766			−0.773831	−	0.633392i	$-0.781662\pi$
$997$	−48.8679			−1.54766			−0.773831	+	0.633392i	$0.781662\pi$
$998$	−20.3086	+	21.7667i	−0.642856	+	0.689013i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1620.2.e.a.971.11	✓	48
3.2	odd	2	inner	1620.2.e.a.971.38	yes	48
4.3	odd	2	inner	1620.2.e.a.971.37	yes	48
12.11	even	2	inner	1620.2.e.a.971.12	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1620.2.e.a.971.11	✓	48	1.1	even	1	trivial
1620.2.e.a.971.12	yes	48	12.11	even	2	inner
1620.2.e.a.971.37	yes	48	4.3	odd	2	inner
1620.2.e.a.971.38	yes	48	3.2	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:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1620.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.03403 - 0.964765i) q^{2} +(0.138457 + 1.99520i) q^{4} -1.00000i q^{5} +3.54880i q^{7} +(1.78173 - 2.19669i) q^{8} +O(q^{10})\)	\(q+(-1.03403 - 0.964765i) q^{2} +(0.138457 + 1.99520i) q^{4} -1.00000i q^{5} +3.54880i q^{7} +(1.78173 - 2.19669i) q^{8} +(-0.964765 + 1.03403i) q^{10} +4.36571 q^{11} +4.76047 q^{13} +(3.42376 - 3.66958i) q^{14} +(-3.96166 + 0.552498i) q^{16} -3.02111i q^{17} +1.16321i q^{19} +(1.99520 - 0.138457i) q^{20} +(-4.51430 - 4.21189i) q^{22} -3.11010 q^{23} -1.00000 q^{25} +(-4.92249 - 4.59273i) q^{26} +(-7.08057 + 0.491355i) q^{28} +8.14117i q^{29} -4.79418i q^{31} +(4.62953 + 3.25077i) q^{32} +(-2.91466 + 3.12393i) q^{34} +3.54880 q^{35} -7.83140 q^{37} +(1.12222 - 1.20280i) q^{38} +(-2.19669 - 1.78173i) q^{40} +4.61999i q^{41} +8.70155i q^{43} +(0.604462 + 8.71048i) q^{44} +(3.21595 + 3.00052i) q^{46} +8.13862 q^{47} -5.59396 q^{49} +(1.03403 + 0.964765i) q^{50} +(0.659119 + 9.49810i) q^{52} -11.9836i q^{53} -4.36571i q^{55} +(7.79559 + 6.32300i) q^{56} +(7.85431 - 8.41825i) q^{58} -0.684441 q^{59} +10.5876 q^{61} +(-4.62526 + 4.95735i) q^{62} +(-1.65086 - 7.82781i) q^{64} -4.76047i q^{65} +7.95024i q^{67} +(6.02772 - 0.418292i) q^{68} +(-3.66958 - 3.42376i) q^{70} +10.6669 q^{71} +9.41743 q^{73} +(8.09794 + 7.55546i) q^{74} +(-2.32083 + 0.161054i) q^{76} +15.4930i q^{77} +8.75803i q^{79} +(0.552498 + 3.96166i) q^{80} +(4.45720 - 4.77723i) q^{82} -13.3807 q^{83} -3.02111 q^{85} +(8.39496 - 8.99771i) q^{86} +(7.77853 - 9.59010i) q^{88} +4.93294i q^{89} +16.8939i q^{91} +(-0.430614 - 6.20528i) q^{92} +(-8.41561 - 7.85185i) q^{94} +1.16321 q^{95} -6.64201 q^{97} +(5.78435 + 5.39686i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 24 q^{16} - 24 q^{22} - 48 q^{25} + 24 q^{28} - 24 q^{34} - 24 q^{40} + 48 q^{46} - 48 q^{49} + 24 q^{58} + 24 q^{64} + 24 q^{76} + 24 q^{88}+O(q^{100}) \) 48 * q - 24 * q^16 - 24 * q^22 - 48 * q^25 + 24 * q^28 - 24 * q^34 - 24 * q^40 + 48 * q^46 - 48 * q^49 + 24 * q^58 + 24 * q^64 + 24 * q^76 + 24 * q^88

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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