LMFDB - Embedded newform 966.2.g.b.643.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(643,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("966.643");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.g (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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{14})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 49 $ x^4 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			643.1
Root			$1.87083 - 1.87083i$ of defining polynomial
Character	$\chi$	$=$	966.643
Dual form			966.2.g.b.643.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} -3.74166 q^{5} +1.00000i q^{6} +(1.87083 - 1.87083i) q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} -3.74166 q^{5} +1.00000i q^{6} +(1.87083 - 1.87083i) q^{7} -1.00000 q^{8} -1.00000 q^{9} +3.74166 q^{10} -1.00000i q^{12} +2.00000i q^{13} +(-1.87083 + 1.87083i) q^{14} +3.74166i q^{15} +1.00000 q^{16} -3.74166 q^{17} +1.00000 q^{18} -3.74166 q^{19} -3.74166 q^{20} +(-1.87083 - 1.87083i) q^{21} +(-3.00000 - 3.74166i) q^{23} +1.00000i q^{24} +9.00000 q^{25} -2.00000i q^{26} +1.00000i q^{27} +(1.87083 - 1.87083i) q^{28} +6.00000 q^{29} -3.74166i q^{30} +4.00000i q^{31} -1.00000 q^{32} +3.74166 q^{34} +(-7.00000 + 7.00000i) q^{35} -1.00000 q^{36} +3.74166 q^{38} +2.00000 q^{39} +3.74166 q^{40} +2.00000i q^{41} +(1.87083 + 1.87083i) q^{42} +11.2250i q^{43} +3.74166 q^{45} +(3.00000 + 3.74166i) q^{46} +6.00000i q^{47} -1.00000i q^{48} -7.00000i q^{49} -9.00000 q^{50} +3.74166i q^{51} +2.00000i q^{52} +3.74166i q^{53} -1.00000i q^{54} +(-1.87083 + 1.87083i) q^{56} +3.74166i q^{57} -6.00000 q^{58} +14.0000i q^{59} +3.74166i q^{60} -4.00000i q^{62} +(-1.87083 + 1.87083i) q^{63} +1.00000 q^{64} -7.48331i q^{65} +3.74166i q^{67} -3.74166 q^{68} +(-3.74166 + 3.00000i) q^{69} +(7.00000 - 7.00000i) q^{70} +6.00000 q^{71} +1.00000 q^{72} -4.00000i q^{73} -9.00000i q^{75} -3.74166 q^{76} -2.00000 q^{78} +3.74166i q^{79} -3.74166 q^{80} +1.00000 q^{81} -2.00000i q^{82} +7.48331 q^{83} +(-1.87083 - 1.87083i) q^{84} +14.0000 q^{85} -11.2250i q^{86} -6.00000i q^{87} -3.74166 q^{89} -3.74166 q^{90} +(3.74166 + 3.74166i) q^{91} +(-3.00000 - 3.74166i) q^{92} +4.00000 q^{93} -6.00000i q^{94} +14.0000 q^{95} +1.00000i q^{96} -7.48331 q^{97} +7.00000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 4 q^{4} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 - 4 * q^9	$ 4 q - 4 q^{2} + 4 q^{4} - 4 q^{8} - 4 q^{9} + 4 q^{16} + 4 q^{18} - 12 q^{23} + 36 q^{25} + 24 q^{29} - 4 q^{32} - 28 q^{35} - 4 q^{36} + 8 q^{39} + 12 q^{46} - 36 q^{50} - 24 q^{58} + 4 q^{64} + 28 q^{70} + 24 q^{71} + 4 q^{72} - 8 q^{78} + 4 q^{81} + 56 q^{85} - 12 q^{92} + 16 q^{93} + 56 q^{95}+O(q^{100}) $ 4 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 - 4 * q^9 + 4 * q^16 + 4 * q^18 - 12 * q^23 + 36 * q^25 + 24 * q^29 - 4 * q^32 - 28 * q^35 - 4 * q^36 + 8 * q^39 + 12 * q^46 - 36 * q^50 - 24 * q^58 + 4 * q^64 + 28 * q^70 + 24 * q^71 + 4 * q^72 - 8 * q^78 + 4 * q^81 + 56 * q^85 - 12 * q^92 + 16 * q^93 + 56 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.00000			0.500000
$5$	−3.74166			−1.67332			−0.836660	−	0.547723i	$-0.815495\pi$
$5$	−3.74166			−1.67332			−0.836660	+	0.547723i	$0.815495\pi$
$6$			1.00000i			0.408248i
$7$	1.87083	−	1.87083i	0.707107	−	0.707107i
$7$	1.87083	−	1.87083i	0.707107	−	0.707107i
$8$	−1.00000			−0.353553
$9$	−1.00000			−0.333333
$10$	3.74166			1.18322
$11$		0			0		1.00000			$0$
$11$		0			0		−1.00000			$\pi$
$12$		−	1.00000i		−	0.288675i
$13$			2.00000i			0.554700i	0.960769	+	0.277350i	$0.0894562\pi$
$13$			2.00000i			0.554700i	−0.960769	+	0.277350i	$0.910544\pi$
$14$	−1.87083	+	1.87083i	−0.500000	+	0.500000i
$15$			3.74166i			0.966092i
$16$	1.00000			0.250000
$17$	−3.74166			−0.907485			−0.453743	−	0.891133i	$-0.649911\pi$
$17$	−3.74166			−0.907485			−0.453743	+	0.891133i	$0.649911\pi$
$18$	1.00000			0.235702
$19$	−3.74166			−0.858395			−0.429198	−	0.903211i	$-0.641204\pi$
$19$	−3.74166			−0.858395			−0.429198	+	0.903211i	$0.641204\pi$
$20$	−3.74166			−0.836660
$21$	−1.87083	−	1.87083i	−0.408248	−	0.408248i
$22$		0			0
$23$	−3.00000	−	3.74166i	−0.625543	−	0.780189i
$23$	−3.00000	−	3.74166i	−0.625543	−	0.780189i
$24$			1.00000i			0.204124i
$25$	9.00000			1.80000
$26$		−	2.00000i		−	0.392232i
$27$			1.00000i			0.192450i
$28$	1.87083	−	1.87083i	0.353553	−	0.353553i
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$		−	3.74166i		−	0.683130i
$31$			4.00000i			0.718421i	0.933257	+	0.359211i	$0.116954\pi$
$31$			4.00000i			0.718421i	−0.933257	+	0.359211i	$0.883046\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	3.74166			0.641689
$35$	−7.00000	+	7.00000i	−1.18322	+	1.18322i
$36$	−1.00000			−0.166667
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	3.74166			0.606977
$39$	2.00000			0.320256
$40$	3.74166			0.591608
$41$			2.00000i			0.312348i	0.987730	+	0.156174i	$0.0499160\pi$
$41$			2.00000i			0.312348i	−0.987730	+	0.156174i	$0.950084\pi$
$42$	1.87083	+	1.87083i	0.288675	+	0.288675i
$43$			11.2250i			1.71179i	0.517148	+	0.855896i	$0.326994\pi$
$43$			11.2250i			1.71179i	−0.517148	+	0.855896i	$0.673006\pi$
$44$		0			0
$45$	3.74166			0.557773
$46$	3.00000	+	3.74166i	0.442326	+	0.551677i
$47$			6.00000i			0.875190i	0.899172	+	0.437595i	$0.144170\pi$
$47$			6.00000i			0.875190i	−0.899172	+	0.437595i	$0.855830\pi$
$48$		−	1.00000i		−	0.144338i
$49$		−	7.00000i		−	1.00000i
$50$	−9.00000			−1.27279
$51$			3.74166i			0.523937i
$52$			2.00000i			0.277350i
$53$			3.74166i			0.513956i	0.966417	+	0.256978i	$0.0827268\pi$
$53$			3.74166i			0.513956i	−0.966417	+	0.256978i	$0.917273\pi$
$54$		−	1.00000i		−	0.136083i
$55$		0			0
$56$	−1.87083	+	1.87083i	−0.250000	+	0.250000i
$57$			3.74166i			0.495595i
$58$	−6.00000			−0.787839
$59$			14.0000i			1.82264i	0.411693	+	0.911322i	$0.364937\pi$
$59$			14.0000i			1.82264i	−0.411693	+	0.911322i	$0.635063\pi$
$60$			3.74166i			0.483046i
$61$		0			0			−	1.00000i	$-0.5\pi$
$61$		0			0				1.00000i	$0.5\pi$
$62$		−	4.00000i		−	0.508001i
$63$	−1.87083	+	1.87083i	−0.235702	+	0.235702i
$64$	1.00000			0.125000
$65$		−	7.48331i		−	0.928191i
$66$		0			0
$67$			3.74166i			0.457116i	0.973530	+	0.228558i	$0.0734011\pi$
$67$			3.74166i			0.457116i	−0.973530	+	0.228558i	$0.926599\pi$
$68$	−3.74166			−0.453743
$69$	−3.74166	+	3.00000i	−0.450443	+	0.361158i
$70$	7.00000	−	7.00000i	0.836660	−	0.836660i
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$	1.00000			0.117851
$73$		−	4.00000i		−	0.468165i	−0.972217	−	0.234082i	$-0.924791\pi$
$73$		−	4.00000i		−	0.468165i	0.972217	−	0.234082i	$-0.0752085\pi$
$74$		0			0
$75$		−	9.00000i		−	1.03923i
$76$	−3.74166			−0.429198
$77$		0			0
$78$	−2.00000			−0.226455
$79$			3.74166i			0.420969i	0.977597	+	0.210485i	$0.0675042\pi$
$79$			3.74166i			0.420969i	−0.977597	+	0.210485i	$0.932496\pi$
$80$	−3.74166			−0.418330
$81$	1.00000			0.111111
$82$		−	2.00000i		−	0.220863i
$83$	7.48331			0.821401			0.410700	−	0.911770i	$-0.365284\pi$
$83$	7.48331			0.821401			0.410700	+	0.911770i	$0.365284\pi$
$84$	−1.87083	−	1.87083i	−0.204124	−	0.204124i
$85$	14.0000			1.51851
$86$		−	11.2250i		−	1.21042i
$87$		−	6.00000i		−	0.643268i
$88$		0			0
$89$	−3.74166			−0.396615			−0.198307	−	0.980140i	$-0.563544\pi$
$89$	−3.74166			−0.396615			−0.198307	+	0.980140i	$0.563544\pi$
$90$	−3.74166			−0.394405
$91$	3.74166	+	3.74166i	0.392232	+	0.392232i
$92$	−3.00000	−	3.74166i	−0.312772	−	0.390095i
$93$	4.00000			0.414781
$94$		−	6.00000i		−	0.618853i
$95$	14.0000			1.43637
$96$			1.00000i			0.102062i
$97$	−7.48331			−0.759815			−0.379908	−	0.925024i	$-0.624044\pi$
$97$	−7.48331			−0.759815			−0.379908	+	0.925024i	$0.624044\pi$
$98$			7.00000i			0.707107i
$99$		0			0
$100$	9.00000			0.900000
$101$			14.0000i			1.39305i	0.717532	+	0.696526i	$0.245272\pi$
$101$			14.0000i			1.39305i	−0.717532	+	0.696526i	$0.754728\pi$
$102$		−	3.74166i		−	0.370479i
$103$	−18.7083			−1.84338			−0.921691	−	0.387925i	$-0.873192\pi$
$103$	−18.7083			−1.84338			−0.921691	+	0.387925i	$0.873192\pi$
$104$		−	2.00000i		−	0.196116i
$105$	7.00000	+	7.00000i	0.683130	+	0.683130i
$106$		−	3.74166i		−	0.363422i
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$			1.00000i			0.0962250i
$109$			7.48331i			0.716772i	0.933574	+	0.358386i	$0.116673\pi$
$109$			7.48331i			0.716772i	−0.933574	+	0.358386i	$0.883327\pi$
$110$		0			0
$111$		0			0
$112$	1.87083	−	1.87083i	0.176777	−	0.176777i
$113$			11.2250i			1.05596i	0.849258	+	0.527978i	$0.177050\pi$
$113$			11.2250i			1.05596i	−0.849258	+	0.527978i	$0.822950\pi$
$114$		−	3.74166i		−	0.350438i
$115$	11.2250	+	14.0000i	1.04673	+	1.30551i
$116$	6.00000			0.557086
$117$		−	2.00000i		−	0.184900i
$118$		−	14.0000i		−	1.28880i
$119$	−7.00000	+	7.00000i	−0.641689	+	0.641689i
$120$		−	3.74166i		−	0.341565i
$121$	11.0000			1.00000
$122$		0			0
$123$	2.00000			0.180334
$124$			4.00000i			0.359211i
$125$	−14.9666			−1.33866
$126$	1.87083	−	1.87083i	0.166667	−	0.166667i
$127$	−20.0000			−1.77471			−0.887357	−	0.461084i	$-0.847461\pi$
$127$	−20.0000			−1.77471			−0.887357	+	0.461084i	$0.847461\pi$
$128$	−1.00000			−0.0883883
$129$	11.2250			0.988304
$130$			7.48331i			0.656330i
$131$		−	20.0000i		−	1.74741i	−0.486458	−	0.873704i	$-0.661711\pi$
$131$		−	20.0000i		−	1.74741i	0.486458	−	0.873704i	$-0.338289\pi$
$132$		0			0
$133$	−7.00000	+	7.00000i	−0.606977	+	0.606977i
$134$		−	3.74166i		−	0.323230i
$135$		−	3.74166i		−	0.322031i
$136$	3.74166			0.320844
$137$		−	18.7083i		−	1.59836i	−0.601094	−	0.799178i	$-0.705268\pi$
$137$		−	18.7083i		−	1.59836i	0.601094	−	0.799178i	$-0.294732\pi$
$138$	3.74166	−	3.00000i	0.318511	−	0.255377i
$139$		−	16.0000i		−	1.35710i	−0.734553	−	0.678551i	$-0.762608\pi$
$139$		−	16.0000i		−	1.35710i	0.734553	−	0.678551i	$-0.237392\pi$
$140$	−7.00000	+	7.00000i	−0.591608	+	0.591608i
$141$	6.00000			0.505291
$142$	−6.00000			−0.503509
$143$		0			0
$144$	−1.00000			−0.0833333
$145$	−22.4499			−1.86437
$146$			4.00000i			0.331042i
$147$	−7.00000			−0.577350
$148$		0			0
$149$			18.7083i			1.53264i	0.642458	+	0.766321i	$0.277915\pi$
$149$			18.7083i			1.53264i	−0.642458	+	0.766321i	$0.722085\pi$
$150$			9.00000i			0.734847i
$151$	−12.0000			−0.976546			−0.488273	−	0.872691i	$-0.662373\pi$
$151$	−12.0000			−0.976546			−0.488273	+	0.872691i	$0.662373\pi$
$152$	3.74166			0.303488
$153$	3.74166			0.302495
$154$		0			0
$155$		−	14.9666i		−	1.20215i
$156$	2.00000			0.160128
$157$	14.9666			1.19447			0.597234	−	0.802067i	$-0.296267\pi$
$157$	14.9666			1.19447			0.597234	+	0.802067i	$0.296267\pi$
$158$		−	3.74166i		−	0.297670i
$159$	3.74166			0.296733
$160$	3.74166			0.295804
$161$	−12.6125	−	1.38751i	−0.994003	−	0.109351i
$162$	−1.00000			−0.0785674
$163$	−4.00000			−0.313304			−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000			−0.313304			−0.156652	+	0.987654i	$0.550070\pi$
$164$			2.00000i			0.156174i
$165$		0			0
$166$	−7.48331			−0.580818
$167$		0			0		1.00000			$0$
$167$		0			0		−1.00000			$\pi$
$168$	1.87083	+	1.87083i	0.144338	+	0.144338i
$169$	9.00000			0.692308
$170$	−14.0000			−1.07375
$171$	3.74166			0.286132
$172$			11.2250i			0.855896i
$173$			14.0000i			1.06440i	0.846619	+	0.532200i	$0.178635\pi$
$173$			14.0000i			1.06440i	−0.846619	+	0.532200i	$0.821365\pi$
$174$			6.00000i			0.454859i
$175$	16.8375	−	16.8375i	1.27279	−	1.27279i
$176$		0			0
$177$	14.0000			1.05230
$178$	3.74166			0.280449
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$	3.74166			0.278887
$181$	7.48331			0.556230			0.278115	−	0.960548i	$-0.410290\pi$
$181$	7.48331			0.556230			0.278115	+	0.960548i	$0.410290\pi$
$182$	−3.74166	−	3.74166i	−0.277350	−	0.277350i
$183$		0			0
$184$	3.00000	+	3.74166i	0.221163	+	0.275839i
$185$		0			0
$186$	−4.00000			−0.293294
$187$		0			0
$188$			6.00000i			0.437595i
$189$	1.87083	+	1.87083i	0.136083	+	0.136083i
$190$	−14.0000			−1.01567
$191$		0			0		1.00000			$0$
$191$		0			0		−1.00000			$\pi$
$192$		−	1.00000i		−	0.0721688i
$193$	−16.0000			−1.15171			−0.575853	−	0.817554i	$-0.695330\pi$
$193$	−16.0000			−1.15171			−0.575853	+	0.817554i	$0.695330\pi$
$194$	7.48331			0.537271
$195$	−7.48331			−0.535891
$196$		−	7.00000i		−	0.500000i
$197$	−22.0000			−1.56744			−0.783718	−	0.621117i	$-0.786679\pi$
$197$	−22.0000			−1.56744			−0.783718	+	0.621117i	$0.786679\pi$
$198$		0			0
$199$	−3.74166			−0.265239			−0.132620	−	0.991167i	$-0.542339\pi$
$199$	−3.74166			−0.265239			−0.132620	+	0.991167i	$0.542339\pi$
$200$	−9.00000			−0.636396
$201$	3.74166			0.263916
$202$		−	14.0000i		−	0.985037i
$203$	11.2250	−	11.2250i	0.787839	−	0.787839i
$204$			3.74166i			0.261968i
$205$		−	7.48331i		−	0.522657i
$206$	18.7083			1.30347
$207$	3.00000	+	3.74166i	0.208514	+	0.260063i
$208$			2.00000i			0.138675i
$209$		0			0
$210$	−7.00000	−	7.00000i	−0.483046	−	0.483046i
$211$	12.0000			0.826114			0.413057	−	0.910705i	$-0.364461\pi$
$211$	12.0000			0.826114			0.413057	+	0.910705i	$0.364461\pi$
$212$			3.74166i			0.256978i
$213$		−	6.00000i		−	0.411113i
$214$		0			0
$215$		−	42.0000i		−	2.86438i
$216$		−	1.00000i		−	0.0680414i
$217$	7.48331	+	7.48331i	0.508001	+	0.508001i
$218$		−	7.48331i		−	0.506834i
$219$	−4.00000			−0.270295
$220$		0			0
$221$		−	7.48331i		−	0.503382i
$222$		0			0
$223$		0			0		1.00000			$0$
$223$		0			0		−1.00000			$\pi$
$224$	−1.87083	+	1.87083i	−0.125000	+	0.125000i
$225$	−9.00000			−0.600000
$226$		−	11.2250i		−	0.746674i
$227$	14.9666			0.993370			0.496685	−	0.867931i	$-0.334550\pi$
$227$	14.9666			0.993370			0.496685	+	0.867931i	$0.334550\pi$
$228$			3.74166i			0.247797i
$229$	7.48331			0.494511			0.247256	−	0.968950i	$-0.420471\pi$
$229$	7.48331			0.494511			0.247256	+	0.968950i	$0.420471\pi$
$230$	−11.2250	−	14.0000i	−0.740153	−	0.923133i
$231$		0			0
$232$	−6.00000			−0.393919
$233$	10.0000			0.655122			0.327561	−	0.944830i	$-0.393773\pi$
$233$	10.0000			0.655122			0.327561	+	0.944830i	$0.393773\pi$
$234$			2.00000i			0.130744i
$235$		−	22.4499i		−	1.46447i
$236$			14.0000i			0.911322i
$237$	3.74166			0.243047
$238$	7.00000	−	7.00000i	0.453743	−	0.453743i
$239$	−6.00000			−0.388108			−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000			−0.388108			−0.194054	+	0.980991i	$0.562164\pi$
$240$			3.74166i			0.241523i
$241$	−7.48331			−0.482043			−0.241021	−	0.970520i	$-0.577482\pi$
$241$	−7.48331			−0.482043			−0.241021	+	0.970520i	$0.577482\pi$
$242$	−11.0000			−0.707107
$243$		−	1.00000i		−	0.0641500i
$244$		0			0
$245$			26.1916i			1.67332i
$246$	−2.00000			−0.127515
$247$		−	7.48331i		−	0.476152i
$248$		−	4.00000i		−	0.254000i
$249$		−	7.48331i		−	0.474236i
$250$	14.9666			0.946573
$251$	−29.9333			−1.88937			−0.944685	−	0.327978i	$-0.893633\pi$
$251$	−29.9333			−1.88937			−0.944685	+	0.327978i	$0.893633\pi$
$252$	−1.87083	+	1.87083i	−0.117851	+	0.117851i
$253$		0			0
$254$	20.0000			1.25491
$255$		−	14.0000i		−	0.876714i
$256$	1.00000			0.0625000
$257$		−	22.0000i		−	1.37232i	−0.727450	−	0.686161i	$-0.759294\pi$
$257$		−	22.0000i		−	1.37232i	0.727450	−	0.686161i	$-0.240706\pi$
$258$	−11.2250			−0.698836
$259$		0			0
$260$		−	7.48331i		−	0.464095i
$261$	−6.00000			−0.371391
$262$			20.0000i			1.23560i
$263$		−	29.9333i		−	1.84576i	−0.385083	−	0.922882i	$-0.625827\pi$
$263$		−	29.9333i		−	1.84576i	0.385083	−	0.922882i	$-0.374173\pi$
$264$		0			0
$265$		−	14.0000i		−	0.860013i
$266$	7.00000	−	7.00000i	0.429198	−	0.429198i
$267$			3.74166i			0.228986i
$268$			3.74166i			0.228558i
$269$		−	18.0000i		−	1.09748i	−0.835993	−	0.548740i	$-0.815108\pi$
$269$		−	18.0000i		−	1.09748i	0.835993	−	0.548740i	$-0.184892\pi$
$270$			3.74166i			0.227710i
$271$			28.0000i			1.70088i	0.526073	+	0.850439i	$0.323664\pi$
$271$			28.0000i			1.70088i	−0.526073	+	0.850439i	$0.676336\pi$
$272$	−3.74166			−0.226871
$273$	3.74166	−	3.74166i	0.226455	−	0.226455i
$274$			18.7083i			1.13021i
$275$		0			0
$276$	−3.74166	+	3.00000i	−0.225221	+	0.180579i
$277$	−26.0000			−1.56219			−0.781094	−	0.624413i	$-0.785338\pi$
$277$	−26.0000			−1.56219			−0.781094	+	0.624413i	$0.785338\pi$
$278$			16.0000i			0.959616i
$279$		−	4.00000i		−	0.239474i
$280$	7.00000	−	7.00000i	0.418330	−	0.418330i
$281$		−	3.74166i		−	0.223209i	−0.993753	−	0.111604i	$-0.964401\pi$
$281$		−	3.74166i		−	0.223209i	0.993753	−	0.111604i	$-0.0355989\pi$
$282$	−6.00000			−0.357295
$283$	18.7083			1.11209			0.556046	−	0.831151i	$-0.312318\pi$
$283$	18.7083			1.11209			0.556046	+	0.831151i	$0.312318\pi$
$284$	6.00000			0.356034
$285$		−	14.0000i		−	0.829288i
$286$		0			0
$287$	3.74166	+	3.74166i	0.220863	+	0.220863i
$288$	1.00000			0.0589256
$289$	−3.00000			−0.176471
$290$	22.4499			1.31831
$291$			7.48331i			0.438680i
$292$		−	4.00000i		−	0.234082i
$293$	−3.74166			−0.218590			−0.109295	−	0.994009i	$-0.534859\pi$
$293$	−3.74166			−0.218590			−0.109295	+	0.994009i	$0.534859\pi$
$294$	7.00000			0.408248
$295$		−	52.3832i		−	3.04987i
$296$		0			0
$297$		0			0
$298$		−	18.7083i		−	1.08374i
$299$	7.48331	−	6.00000i	0.432771	−	0.346989i
$300$		−	9.00000i		−	0.519615i
$301$	21.0000	+	21.0000i	1.21042	+	1.21042i
$302$	12.0000			0.690522
$303$	14.0000			0.804279
$304$	−3.74166			−0.214599
$305$		0			0
$306$	−3.74166			−0.213896
$307$		−	28.0000i		−	1.59804i	−0.601302	−	0.799022i	$-0.705351\pi$
$307$		−	28.0000i		−	1.59804i	0.601302	−	0.799022i	$-0.294649\pi$
$308$		0			0
$309$			18.7083i			1.06428i
$310$			14.9666i			0.850047i
$311$			18.0000i			1.02069i	0.859971	+	0.510343i	$0.170482\pi$
$311$			18.0000i			1.02069i	−0.859971	+	0.510343i	$0.829518\pi$
$312$	−2.00000			−0.113228
$313$		0			0			−	1.00000i	$-0.5\pi$
$313$		0			0				1.00000i	$0.5\pi$
$314$	−14.9666			−0.844616
$315$	7.00000	−	7.00000i	0.394405	−	0.394405i
$316$			3.74166i			0.210485i
$317$	−22.0000			−1.23564			−0.617822	−	0.786318i	$-0.711985\pi$
$317$	−22.0000			−1.23564			−0.617822	+	0.786318i	$0.711985\pi$
$318$	−3.74166			−0.209822
$319$		0			0
$320$	−3.74166			−0.209165
$321$		0			0
$322$	12.6125	+	1.38751i	0.702866	+	0.0773231i
$323$	14.0000			0.778981
$324$	1.00000			0.0555556
$325$			18.0000i			0.998460i
$326$	4.00000			0.221540
$327$	7.48331			0.413828
$328$		−	2.00000i		−	0.110432i
$329$	11.2250	+	11.2250i	0.618853	+	0.618853i
$330$		0			0
$331$	−24.0000			−1.31916			−0.659580	−	0.751635i	$-0.729266\pi$
$331$	−24.0000			−1.31916			−0.659580	+	0.751635i	$0.729266\pi$
$332$	7.48331			0.410700
$333$		0			0
$334$		0			0
$335$		−	14.0000i		−	0.764902i
$336$	−1.87083	−	1.87083i	−0.102062	−	0.102062i
$337$		−	22.4499i		−	1.22293i	−0.791273	−	0.611463i	$-0.790581\pi$
$337$		−	22.4499i		−	1.22293i	0.791273	−	0.611463i	$-0.209419\pi$
$338$	−9.00000			−0.489535
$339$	11.2250			0.609657
$340$	14.0000			0.759257
$341$		0			0
$342$	−3.74166			−0.202326
$343$	−13.0958	−	13.0958i	−0.707107	−	0.707107i
$344$		−	11.2250i		−	0.605210i
$345$	14.0000	−	11.2250i	0.753735	−	0.604332i
$346$		−	14.0000i		−	0.752645i
$347$	−4.00000			−0.214731			−0.107366	−	0.994220i	$-0.534242\pi$
$347$	−4.00000			−0.214731			−0.107366	+	0.994220i	$0.534242\pi$
$348$		−	6.00000i		−	0.321634i
$349$			2.00000i			0.107058i	0.998566	+	0.0535288i	$0.0170469\pi$
$349$			2.00000i			0.107058i	−0.998566	+	0.0535288i	$0.982953\pi$
$350$	−16.8375	+	16.8375i	−0.900000	+	0.900000i
$351$	−2.00000			−0.106752
$352$		0			0
$353$			18.0000i			0.958043i	0.877803	+	0.479022i	$0.159008\pi$
$353$			18.0000i			0.958043i	−0.877803	+	0.479022i	$0.840992\pi$
$354$	−14.0000			−0.744092
$355$	−22.4499			−1.19152
$356$	−3.74166			−0.198307
$357$	7.00000	+	7.00000i	0.370479	+	0.370479i
$358$	12.0000			0.634220
$359$			14.9666i			0.789908i	0.918701	+	0.394954i	$0.129240\pi$
$359$			14.9666i			0.789908i	−0.918701	+	0.394954i	$0.870760\pi$
$360$	−3.74166			−0.197203
$361$	−5.00000			−0.263158
$362$	−7.48331			−0.393314
$363$		−	11.0000i		−	0.577350i
$364$	3.74166	+	3.74166i	0.196116	+	0.196116i
$365$			14.9666i			0.783389i
$366$		0			0
$367$	−3.74166			−0.195313			−0.0976565	−	0.995220i	$-0.531135\pi$
$367$	−3.74166			−0.195313			−0.0976565	+	0.995220i	$0.531135\pi$
$368$	−3.00000	−	3.74166i	−0.156386	−	0.195047i
$369$		−	2.00000i		−	0.104116i
$370$		0			0
$371$	7.00000	+	7.00000i	0.363422	+	0.363422i
$372$	4.00000			0.207390
$373$			29.9333i			1.54989i	0.632031	+	0.774943i	$0.282221\pi$
$373$			29.9333i			1.54989i	−0.632031	+	0.774943i	$0.717779\pi$
$374$		0			0
$375$			14.9666i			0.772873i
$376$		−	6.00000i		−	0.309426i
$377$			12.0000i			0.618031i
$378$	−1.87083	−	1.87083i	−0.0962250	−	0.0962250i
$379$			18.7083i			0.960980i	0.877000	+	0.480490i	$0.159541\pi$
$379$			18.7083i			0.960980i	−0.877000	+	0.480490i	$0.840459\pi$
$380$	14.0000			0.718185
$381$			20.0000i			1.02463i
$382$		0			0
$383$	7.48331			0.382380			0.191190	−	0.981553i	$-0.438765\pi$
$383$	7.48331			0.382380			0.191190	+	0.981553i	$0.438765\pi$
$384$			1.00000i			0.0510310i
$385$		0			0
$386$	16.0000			0.814379
$387$		−	11.2250i		−	0.570597i
$388$	−7.48331			−0.379908
$389$		−	18.7083i		−	0.948548i	−0.880377	−	0.474274i	$-0.842711\pi$
$389$		−	18.7083i		−	0.948548i	0.880377	−	0.474274i	$-0.157289\pi$
$390$	7.48331			0.378932
$391$	11.2250	+	14.0000i	0.567671	+	0.708010i
$392$			7.00000i			0.353553i
$393$	−20.0000			−1.00887
$394$	22.0000			1.10834
$395$		−	14.0000i		−	0.704416i
$396$		0			0
$397$			20.0000i			1.00377i	0.864934	+	0.501886i	$0.167360\pi$
$397$			20.0000i			1.00377i	−0.864934	+	0.501886i	$0.832640\pi$
$398$	3.74166			0.187552
$399$	7.00000	+	7.00000i	0.350438	+	0.350438i
$400$	9.00000			0.450000
$401$			11.2250i			0.560548i	0.959920	+	0.280274i	$0.0904254\pi$
$401$			11.2250i			0.560548i	−0.959920	+	0.280274i	$0.909575\pi$
$402$	−3.74166			−0.186617
$403$	−8.00000			−0.398508
$404$			14.0000i			0.696526i
$405$	−3.74166			−0.185924
$406$	−11.2250	+	11.2250i	−0.557086	+	0.557086i
$407$		0			0
$408$		−	3.74166i		−	0.185240i
$409$			10.0000i			0.494468i	0.968956	+	0.247234i	$0.0795217\pi$
$409$			10.0000i			0.494468i	−0.968956	+	0.247234i	$0.920478\pi$
$410$			7.48331i			0.369575i
$411$	−18.7083			−0.922812
$412$	−18.7083			−0.921691
$413$	26.1916	+	26.1916i	1.28880	+	1.28880i
$414$	−3.00000	−	3.74166i	−0.147442	−	0.183892i
$415$	−28.0000			−1.37447
$416$		−	2.00000i		−	0.0980581i
$417$	−16.0000			−0.783523
$418$		0			0
$419$	7.48331			0.365584			0.182792	−	0.983152i	$-0.441487\pi$
$419$	7.48331			0.365584			0.182792	+	0.983152i	$0.441487\pi$
$420$	7.00000	+	7.00000i	0.341565	+	0.341565i
$421$			22.4499i			1.09414i	0.837086	+	0.547072i	$0.184257\pi$
$421$			22.4499i			1.09414i	−0.837086	+	0.547072i	$0.815743\pi$
$422$	−12.0000			−0.584151
$423$		−	6.00000i		−	0.291730i
$424$		−	3.74166i		−	0.181711i
$425$	−33.6749			−1.63347
$426$			6.00000i			0.290701i
$427$		0			0
$428$		0			0
$429$		0			0
$430$			42.0000i			2.02542i
$431$			37.4166i			1.80229i	0.433515	+	0.901146i	$0.357273\pi$
$431$			37.4166i			1.80229i	−0.433515	+	0.901146i	$0.642727\pi$
$432$			1.00000i			0.0481125i
$433$		0			0			−	1.00000i	$-0.5\pi$
$433$		0			0				1.00000i	$0.5\pi$
$434$	−7.48331	−	7.48331i	−0.359211	−	0.359211i
$435$			22.4499i			1.07639i
$436$			7.48331i			0.358386i
$437$	11.2250	+	14.0000i	0.536963	+	0.669711i
$438$	4.00000			0.191127
$439$		−	8.00000i		−	0.381819i	−0.981608	−	0.190910i	$-0.938856\pi$
$439$		−	8.00000i		−	0.381819i	0.981608	−	0.190910i	$-0.0611437\pi$
$440$		0			0
$441$			7.00000i			0.333333i
$442$			7.48331i			0.355945i
$443$	−18.0000			−0.855206			−0.427603	−	0.903967i	$-0.640642\pi$
$443$	−18.0000			−0.855206			−0.427603	+	0.903967i	$0.640642\pi$
$444$		0			0
$445$	14.0000			0.663664
$446$		0			0
$447$	18.7083			0.884872
$448$	1.87083	−	1.87083i	0.0883883	−	0.0883883i
$449$	26.0000			1.22702			0.613508	−	0.789689i	$-0.289758\pi$
$449$	26.0000			1.22702			0.613508	+	0.789689i	$0.289758\pi$
$450$	9.00000			0.424264
$451$		0			0
$452$			11.2250i			0.527978i
$453$			12.0000i			0.563809i
$454$	−14.9666			−0.702419
$455$	−14.0000	−	14.0000i	−0.656330	−	0.656330i
$456$		−	3.74166i		−	0.175219i
$457$			22.4499i			1.05016i	0.851052	+	0.525082i	$0.175965\pi$
$457$			22.4499i			1.05016i	−0.851052	+	0.525082i	$0.824035\pi$
$458$	−7.48331			−0.349672
$459$		−	3.74166i		−	0.174646i
$460$	11.2250	+	14.0000i	0.523367	+	0.652753i
$461$			26.0000i			1.21094i	0.795868	+	0.605470i	$0.207015\pi$
$461$			26.0000i			1.21094i	−0.795868	+	0.605470i	$0.792985\pi$
$462$		0			0
$463$	−16.0000			−0.743583			−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000			−0.743583			−0.371792	+	0.928316i	$0.621256\pi$
$464$	6.00000			0.278543
$465$	−14.9666			−0.694061
$466$	−10.0000			−0.463241
$467$	14.9666			0.692573			0.346287	−	0.938129i	$-0.387443\pi$
$467$	14.9666			0.692573			0.346287	+	0.938129i	$0.387443\pi$
$468$		−	2.00000i		−	0.0924500i
$469$	7.00000	+	7.00000i	0.323230	+	0.323230i
$470$			22.4499i			1.03554i
$471$		−	14.9666i		−	0.689626i
$472$		−	14.0000i		−	0.644402i
$473$		0			0
$474$	−3.74166			−0.171860
$475$	−33.6749			−1.54511
$476$	−7.00000	+	7.00000i	−0.320844	+	0.320844i
$477$		−	3.74166i		−	0.171319i
$478$	6.00000			0.274434
$479$	29.9333			1.36769			0.683843	−	0.729629i	$-0.260307\pi$
$479$	29.9333			1.36769			0.683843	+	0.729629i	$0.260307\pi$
$480$		−	3.74166i		−	0.170783i
$481$		0			0
$482$	7.48331			0.340856
$483$	−1.38751	+	12.6125i	−0.0631341	+	0.573888i
$484$	11.0000			0.500000
$485$	28.0000			1.27141
$486$			1.00000i			0.0453609i
$487$	12.0000			0.543772			0.271886	−	0.962329i	$-0.412353\pi$
$487$	12.0000			0.543772			0.271886	+	0.962329i	$0.412353\pi$
$488$		0			0
$489$			4.00000i			0.180886i
$490$		−	26.1916i		−	1.18322i
$491$	20.0000			0.902587			0.451294	−	0.892375i	$-0.350963\pi$
$491$	20.0000			0.902587			0.451294	+	0.892375i	$0.350963\pi$
$492$	2.00000			0.0901670
$493$	−22.4499			−1.01109
$494$			7.48331i			0.336690i
$495$		0			0
$496$			4.00000i			0.179605i
$497$	11.2250	−	11.2250i	0.503509	−	0.503509i
$498$			7.48331i			0.335335i
$499$	−24.0000			−1.07439			−0.537194	−	0.843459i	$-0.680516\pi$
$499$	−24.0000			−1.07439			−0.537194	+	0.843459i	$0.680516\pi$
$500$	−14.9666			−0.669328
$501$		0			0
$502$	29.9333			1.33599
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$	1.87083	−	1.87083i	0.0833333	−	0.0833333i
$505$		−	52.3832i		−	2.33102i
$506$		0			0
$507$		−	9.00000i		−	0.399704i
$508$	−20.0000			−0.887357
$509$			6.00000i			0.265945i	0.991120	+	0.132973i	$0.0424523\pi$
$509$			6.00000i			0.265945i	−0.991120	+	0.132973i	$0.957548\pi$
$510$			14.0000i			0.619930i
$511$	−7.48331	−	7.48331i	−0.331042	−	0.331042i
$512$	−1.00000			−0.0441942
$513$		−	3.74166i		−	0.165198i
$514$			22.0000i			0.970378i
$515$	70.0000			3.08457
$516$	11.2250			0.494152
$517$		0			0
$518$		0			0
$519$	14.0000			0.614532
$520$			7.48331i			0.328165i
$521$	−3.74166			−0.163925			−0.0819625	−	0.996635i	$-0.526119\pi$
$521$	−3.74166			−0.163925			−0.0819625	+	0.996635i	$0.526119\pi$
$522$	6.00000			0.262613
$523$	−33.6749			−1.47250			−0.736251	−	0.676709i	$-0.763406\pi$
$523$	−33.6749			−1.47250			−0.736251	+	0.676709i	$0.763406\pi$
$524$		−	20.0000i		−	0.873704i
$525$	−16.8375	−	16.8375i	−0.734847	−	0.734847i
$526$			29.9333i			1.30515i
$527$		−	14.9666i		−	0.651957i
$528$		0			0
$529$	−5.00000	+	22.4499i	−0.217391	+	0.976085i
$530$			14.0000i			0.608121i
$531$		−	14.0000i		−	0.607548i
$532$	−7.00000	+	7.00000i	−0.303488	+	0.303488i
$533$	−4.00000			−0.173259
$534$		−	3.74166i		−	0.161917i
$535$		0			0
$536$		−	3.74166i		−	0.161615i
$537$			12.0000i			0.517838i
$538$			18.0000i			0.776035i
$539$		0			0
$540$		−	3.74166i		−	0.161015i
$541$	32.0000			1.37579			0.687894	−	0.725811i	$-0.258536\pi$
$541$	32.0000			1.37579			0.687894	+	0.725811i	$0.258536\pi$
$542$		−	28.0000i		−	1.20270i
$543$		−	7.48331i		−	0.321140i
$544$	3.74166			0.160422
$545$		−	28.0000i		−	1.19939i
$546$	−3.74166	+	3.74166i	−0.160128	+	0.160128i
$547$	8.00000			0.342055			0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000			0.342055			0.171028	+	0.985266i	$0.445291\pi$
$548$		−	18.7083i		−	0.799178i
$549$		0			0
$550$		0			0
$551$	−22.4499			−0.956400
$552$	3.74166	−	3.00000i	0.159256	−	0.127688i
$553$	7.00000	+	7.00000i	0.297670	+	0.297670i
$554$	26.0000			1.10463
$555$		0			0
$556$		−	16.0000i		−	0.678551i
$557$		−	26.1916i		−	1.10977i	−0.831926	−	0.554887i	$-0.812762\pi$
$557$		−	26.1916i		−	1.10977i	0.831926	−	0.554887i	$-0.187238\pi$
$558$			4.00000i			0.169334i
$559$	−22.4499			−0.949531
$560$	−7.00000	+	7.00000i	−0.295804	+	0.295804i
$561$		0			0
$562$			3.74166i			0.157832i
$563$	−14.9666			−0.630768			−0.315384	−	0.948964i	$-0.602133\pi$
$563$	−14.9666			−0.630768			−0.315384	+	0.948964i	$0.602133\pi$
$564$	6.00000			0.252646
$565$		−	42.0000i		−	1.76695i
$566$	−18.7083			−0.786368
$567$	1.87083	−	1.87083i	0.0785674	−	0.0785674i
$568$	−6.00000			−0.251754
$569$			3.74166i			0.156858i	0.996920	+	0.0784292i	$0.0249905\pi$
$569$			3.74166i			0.156858i	−0.996920	+	0.0784292i	$0.975010\pi$
$570$			14.0000i			0.586395i
$571$			33.6749i			1.40925i	0.709579	+	0.704626i	$0.248885\pi$
$571$			33.6749i			1.40925i	−0.709579	+	0.704626i	$0.751115\pi$
$572$		0			0
$573$		0			0
$574$	−3.74166	−	3.74166i	−0.156174	−	0.156174i
$575$	−27.0000	−	33.6749i	−1.12598	−	1.40434i
$576$	−1.00000			−0.0416667
$577$		−	38.0000i		−	1.58196i	−0.611842	−	0.790980i	$-0.709571\pi$
$577$		−	38.0000i		−	1.58196i	0.611842	−	0.790980i	$-0.290429\pi$
$578$	3.00000			0.124784
$579$			16.0000i			0.664937i
$580$	−22.4499			−0.932183
$581$	14.0000	−	14.0000i	0.580818	−	0.580818i
$582$		−	7.48331i		−	0.310193i
$583$		0			0
$584$			4.00000i			0.165521i
$585$			7.48331i			0.309397i
$586$	3.74166			0.154566
$587$		−	12.0000i		−	0.495293i	−0.968850	−	0.247647i	$-0.920343\pi$
$587$		−	12.0000i		−	0.495293i	0.968850	−	0.247647i	$-0.0796572\pi$
$588$	−7.00000			−0.288675
$589$		−	14.9666i		−	0.616689i
$590$			52.3832i			2.15658i
$591$			22.0000i			0.904959i
$592$		0			0
$593$			14.0000i			0.574911i	0.957794	+	0.287456i	$0.0928094\pi$
$593$			14.0000i			0.574911i	−0.957794	+	0.287456i	$0.907191\pi$
$594$		0			0
$595$	26.1916	−	26.1916i	1.07375	−	1.07375i
$596$			18.7083i			0.766321i
$597$			3.74166i			0.153136i
$598$	−7.48331	+	6.00000i	−0.306015	+	0.245358i
$599$	38.0000			1.55264			0.776319	−	0.630340i	$-0.217085\pi$
$599$	38.0000			1.55264			0.776319	+	0.630340i	$0.217085\pi$
$600$			9.00000i			0.367423i
$601$		−	2.00000i		−	0.0815817i	−0.999168	−	0.0407909i	$-0.987012\pi$
$601$		−	2.00000i		−	0.0815817i	0.999168	−	0.0407909i	$-0.0129877\pi$
$602$	−21.0000	−	21.0000i	−0.855896	−	0.855896i
$603$		−	3.74166i		−	0.152372i
$604$	−12.0000			−0.488273
$605$	−41.1582			−1.67332
$606$	−14.0000			−0.568711
$607$		−	28.0000i		−	1.13648i	−0.822861	−	0.568242i	$-0.807624\pi$
$607$		−	28.0000i		−	1.13648i	0.822861	−	0.568242i	$-0.192376\pi$
$608$	3.74166			0.151744
$609$	−11.2250	−	11.2250i	−0.454859	−	0.454859i
$610$		0			0
$611$	−12.0000			−0.485468
$612$	3.74166			0.151248
$613$			29.9333i			1.20899i	0.796608	+	0.604496i	$0.206626\pi$
$613$			29.9333i			1.20899i	−0.796608	+	0.604496i	$0.793374\pi$
$614$			28.0000i			1.12999i
$615$	−7.48331			−0.301756
$616$		0			0
$617$		−	41.1582i		−	1.65697i	−0.560013	−	0.828484i	$-0.689204\pi$
$617$		−	41.1582i		−	1.65697i	0.560013	−	0.828484i	$-0.310796\pi$
$618$		−	18.7083i		−	0.752558i
$619$	11.2250			0.451170			0.225585	−	0.974224i	$-0.427571\pi$
$619$	11.2250			0.451170			0.225585	+	0.974224i	$0.427571\pi$
$620$		−	14.9666i		−	0.601074i
$621$	3.74166	−	3.00000i	0.150148	−	0.120386i
$622$		−	18.0000i		−	0.721734i
$623$	−7.00000	+	7.00000i	−0.280449	+	0.280449i
$624$	2.00000			0.0800641
$625$	11.0000			0.440000
$626$		0			0
$627$		0			0
$628$	14.9666			0.597234
$629$		0			0
$630$	−7.00000	+	7.00000i	−0.278887	+	0.278887i
$631$		−	3.74166i		−	0.148953i	−0.997223	−	0.0744765i	$-0.976271\pi$
$631$		−	3.74166i		−	0.148953i	0.997223	−	0.0744765i	$-0.0237286\pi$
$632$		−	3.74166i		−	0.148835i
$633$		−	12.0000i		−	0.476957i
$634$	22.0000			0.873732
$635$	74.8331			2.96966
$636$	3.74166			0.148366
$637$	14.0000			0.554700
$638$		0			0
$639$	−6.00000			−0.237356
$640$	3.74166			0.147902
$641$		−	18.7083i		−	0.738933i	−0.929244	−	0.369466i	$-0.879540\pi$
$641$		−	18.7083i		−	0.738933i	0.929244	−	0.369466i	$-0.120460\pi$
$642$		0			0
$643$	−11.2250			−0.442670			−0.221335	−	0.975198i	$-0.571041\pi$
$643$	−11.2250			−0.442670			−0.221335	+	0.975198i	$0.571041\pi$
$644$	−12.6125	−	1.38751i	−0.497002	−	0.0546757i
$645$	−42.0000			−1.65375
$646$	−14.0000			−0.550823
$647$		−	10.0000i		−	0.393141i	−0.980490	−	0.196570i	$-0.937020\pi$
$647$		−	10.0000i		−	0.393141i	0.980490	−	0.196570i	$-0.0629804\pi$
$648$	−1.00000			−0.0392837
$649$		0			0
$650$		−	18.0000i		−	0.706018i
$651$	7.48331	−	7.48331i	0.293294	−	0.293294i
$652$	−4.00000			−0.156652
$653$	18.0000			0.704394			0.352197	−	0.935926i	$-0.385435\pi$
$653$	18.0000			0.704394			0.352197	+	0.935926i	$0.385435\pi$
$654$	−7.48331			−0.292621
$655$			74.8331i			2.92397i
$656$			2.00000i			0.0780869i
$657$			4.00000i			0.156055i
$658$	−11.2250	−	11.2250i	−0.437595	−	0.437595i
$659$			22.4499i			0.874526i	0.899334	+	0.437263i	$0.144052\pi$
$659$			22.4499i			0.874526i	−0.899334	+	0.437263i	$0.855948\pi$
$660$		0			0
$661$	−14.9666			−0.582134			−0.291067	−	0.956703i	$-0.594010\pi$
$661$	−14.9666			−0.582134			−0.291067	+	0.956703i	$0.594010\pi$
$662$	24.0000			0.932786
$663$	−7.48331			−0.290628
$664$	−7.48331			−0.290409
$665$	26.1916	−	26.1916i	1.01567	−	1.01567i
$666$		0			0
$667$	−18.0000	−	22.4499i	−0.696963	−	0.869265i
$668$		0			0
$669$		0			0
$670$			14.0000i			0.540867i
$671$		0			0
$672$	1.87083	+	1.87083i	0.0721688	+	0.0721688i
$673$	−8.00000			−0.308377			−0.154189	−	0.988041i	$-0.549276\pi$
$673$	−8.00000			−0.308377			−0.154189	+	0.988041i	$0.549276\pi$
$674$			22.4499i			0.864740i
$675$			9.00000i			0.346410i
$676$	9.00000			0.346154
$677$	−18.7083			−0.719018			−0.359509	−	0.933142i	$-0.617056\pi$
$677$	−18.7083			−0.719018			−0.359509	+	0.933142i	$0.617056\pi$
$678$	−11.2250			−0.431092
$679$	−14.0000	+	14.0000i	−0.537271	+	0.537271i
$680$	−14.0000			−0.536875
$681$		−	14.9666i		−	0.573522i
$682$		0			0
$683$	26.0000			0.994862			0.497431	−	0.867503i	$-0.334277\pi$
$683$	26.0000			0.994862			0.497431	+	0.867503i	$0.334277\pi$
$684$	3.74166			0.143066
$685$			70.0000i			2.67456i
$686$	13.0958	+	13.0958i	0.500000	+	0.500000i
$687$		−	7.48331i		−	0.285506i
$688$			11.2250i			0.427948i
$689$	−7.48331			−0.285092
$690$	−14.0000	+	11.2250i	−0.532971	+	0.427327i
$691$		0			0		1.00000			$0$
$691$		0			0		−1.00000			$\pi$
$692$			14.0000i			0.532200i
$693$		0			0
$694$	4.00000			0.151838
$695$			59.8665i			2.27087i
$696$			6.00000i			0.227429i
$697$		−	7.48331i		−	0.283451i
$698$		−	2.00000i		−	0.0757011i
$699$		−	10.0000i		−	0.378235i
$700$	16.8375	−	16.8375i	0.636396	−	0.636396i
$701$			41.1582i			1.55452i	0.629176	+	0.777262i	$0.283392\pi$
$701$			41.1582i			1.55452i	−0.629176	+	0.777262i	$0.716608\pi$
$702$	2.00000			0.0754851
$703$		0			0
$704$		0			0
$705$	−22.4499			−0.845514
$706$		−	18.0000i		−	0.677439i
$707$	26.1916	+	26.1916i	0.985037	+	0.985037i
$708$	14.0000			0.526152
$709$		−	22.4499i		−	0.843125i	−0.906799	−	0.421563i	$-0.861482\pi$
$709$		−	22.4499i		−	0.843125i	0.906799	−	0.421563i	$-0.138518\pi$
$710$	22.4499			0.842531
$711$		−	3.74166i		−	0.140323i
$712$	3.74166			0.140225
$713$	14.9666	−	12.0000i	0.560505	−	0.449404i
$714$	−7.00000	−	7.00000i	−0.261968	−	0.261968i
$715$		0			0
$716$	−12.0000			−0.448461
$717$			6.00000i			0.224074i
$718$		−	14.9666i		−	0.558550i
$719$		−	14.0000i		−	0.522112i	−0.965324	−	0.261056i	$-0.915929\pi$
$719$		−	14.0000i		−	0.522112i	0.965324	−	0.261056i	$-0.0840707\pi$
$720$	3.74166			0.139443
$721$	−35.0000	+	35.0000i	−1.30347	+	1.30347i
$722$	5.00000			0.186081
$723$			7.48331i			0.278307i
$724$	7.48331			0.278115
$725$	54.0000			2.00551
$726$			11.0000i			0.408248i
$727$	18.7083			0.693852			0.346926	−	0.937893i	$-0.387226\pi$
$727$	18.7083			0.693852			0.346926	+	0.937893i	$0.387226\pi$
$728$	−3.74166	−	3.74166i	−0.138675	−	0.138675i
$729$	−1.00000			−0.0370370
$730$		−	14.9666i		−	0.553940i
$731$		−	42.0000i		−	1.55343i
$732$		0			0
$733$	52.3832			1.93482			0.967409	−	0.253219i	$-0.0814894\pi$
$733$	52.3832			1.93482			0.967409	+	0.253219i	$0.0814894\pi$
$734$	3.74166			0.138107
$735$	26.1916			0.966092
$736$	3.00000	+	3.74166i	0.110581	+	0.137919i
$737$		0			0
$738$			2.00000i			0.0736210i
$739$	−44.0000			−1.61857			−0.809283	−	0.587419i	$-0.800144\pi$
$739$	−44.0000			−1.61857			−0.809283	+	0.587419i	$0.800144\pi$
$740$		0			0
$741$	−7.48331			−0.274906
$742$	−7.00000	−	7.00000i	−0.256978	−	0.256978i
$743$			44.8999i			1.64722i	0.567159	+	0.823609i	$0.308043\pi$
$743$			44.8999i			1.64722i	−0.567159	+	0.823609i	$0.691957\pi$
$744$	−4.00000			−0.146647
$745$		−	70.0000i		−	2.56460i
$746$		−	29.9333i		−	1.09593i
$747$	−7.48331			−0.273800
$748$		0			0
$749$		0			0
$750$		−	14.9666i		−	0.546504i
$751$		−	11.2250i		−	0.409605i	−0.978803	−	0.204803i	$-0.934345\pi$
$751$		−	11.2250i		−	0.409605i	0.978803	−	0.204803i	$-0.0656552\pi$
$752$			6.00000i			0.218797i
$753$			29.9333i			1.09083i
$754$		−	12.0000i		−	0.437014i
$755$	44.8999			1.63407
$756$	1.87083	+	1.87083i	0.0680414	+	0.0680414i
$757$			22.4499i			0.815957i	0.912992	+	0.407979i	$0.133766\pi$
$757$			22.4499i			0.815957i	−0.912992	+	0.407979i	$0.866234\pi$
$758$		−	18.7083i		−	0.679516i
$759$		0			0
$760$	−14.0000			−0.507833
$761$		−	22.0000i		−	0.797499i	−0.917060	−	0.398750i	$-0.869444\pi$
$761$		−	22.0000i		−	0.797499i	0.917060	−	0.398750i	$-0.130556\pi$
$762$		−	20.0000i		−	0.724524i
$763$	14.0000	+	14.0000i	0.506834	+	0.506834i
$764$		0			0
$765$	−14.0000			−0.506171
$766$	−7.48331			−0.270383
$767$	−28.0000			−1.01102
$768$		−	1.00000i		−	0.0360844i
$769$	29.9333			1.07942			0.539710	−	0.841851i	$-0.318534\pi$
$769$	29.9333			1.07942			0.539710	+	0.841851i	$0.318534\pi$
$770$		0			0
$771$	−22.0000			−0.792311
$772$	−16.0000			−0.575853
$773$	3.74166			0.134578			0.0672890	−	0.997734i	$-0.478565\pi$
$773$	3.74166			0.134578			0.0672890	+	0.997734i	$0.478565\pi$
$774$			11.2250i			0.403473i
$775$			36.0000i			1.29316i
$776$	7.48331			0.268635
$777$		0			0
$778$			18.7083i			0.670725i
$779$		−	7.48331i		−	0.268118i
$780$	−7.48331			−0.267946
$781$		0			0
$782$	−11.2250	−	14.0000i	−0.401404	−	0.500639i
$783$			6.00000i			0.214423i
$784$		−	7.00000i		−	0.250000i
$785$	−56.0000			−1.99873
$786$	20.0000			0.713376
$787$	3.74166			0.133376			0.0666878	−	0.997774i	$-0.478757\pi$
$787$	3.74166			0.133376			0.0666878	+	0.997774i	$0.478757\pi$
$788$	−22.0000			−0.783718
$789$	−29.9333			−1.06565
$790$			14.0000i			0.498098i
$791$	21.0000	+	21.0000i	0.746674	+	0.746674i
$792$		0			0
$793$		0			0
$794$		−	20.0000i		−	0.709773i
$795$	−14.0000			−0.496529
$796$	−3.74166			−0.132620
$797$	−18.7083			−0.662682			−0.331341	−	0.943511i	$-0.607501\pi$
$797$	−18.7083			−0.662682			−0.331341	+	0.943511i	$0.607501\pi$
$798$	−7.00000	−	7.00000i	−0.247797	−	0.247797i
$799$		−	22.4499i		−	0.794222i
$800$	−9.00000			−0.318198
$801$	3.74166			0.132205
$802$		−	11.2250i		−	0.396368i
$803$		0			0
$804$	3.74166			0.131958
$805$	47.1916	+	5.19160i	1.66329	+	0.182980i
$806$	8.00000			0.281788
$807$	−18.0000			−0.633630
$808$		−	14.0000i		−	0.492518i
$809$	−10.0000			−0.351581			−0.175791	−	0.984428i	$-0.556248\pi$
$809$	−10.0000			−0.351581			−0.175791	+	0.984428i	$0.556248\pi$
$810$	3.74166			0.131468
$811$			16.0000i			0.561836i	0.959732	+	0.280918i	$0.0906389\pi$
$811$			16.0000i			0.561836i	−0.959732	+	0.280918i	$0.909361\pi$
$812$	11.2250	−	11.2250i	0.393919	−	0.393919i
$813$	28.0000			0.982003
$814$		0			0
$815$	14.9666			0.524258
$816$			3.74166i			0.130984i
$817$		−	42.0000i		−	1.46939i
$818$		−	10.0000i		−	0.349642i
$819$	−3.74166	−	3.74166i	−0.130744	−	0.130744i
$820$		−	7.48331i		−	0.261329i
$821$	−22.0000			−0.767805			−0.383903	−	0.923374i	$-0.625420\pi$
$821$	−22.0000			−0.767805			−0.383903	+	0.923374i	$0.625420\pi$
$822$	18.7083			0.652526
$823$	40.0000			1.39431			0.697156	−	0.716919i	$-0.254448\pi$
$823$	40.0000			1.39431			0.697156	+	0.716919i	$0.254448\pi$
$824$	18.7083			0.651734
$825$		0			0
$826$	−26.1916	−	26.1916i	−0.911322	−	0.911322i
$827$		−	37.4166i		−	1.30110i	−0.759463	−	0.650551i	$-0.774538\pi$
$827$		−	37.4166i		−	1.30110i	0.759463	−	0.650551i	$-0.225462\pi$
$828$	3.00000	+	3.74166i	0.104257	+	0.130032i
$829$			14.0000i			0.486240i	0.969996	+	0.243120i	$0.0781709\pi$
$829$			14.0000i			0.486240i	−0.969996	+	0.243120i	$0.921829\pi$
$830$	28.0000			0.971894
$831$			26.0000i			0.901930i
$832$			2.00000i			0.0693375i
$833$			26.1916i			0.907485i
$834$	16.0000			0.554035
$835$		0			0
$836$		0			0
$837$	−4.00000			−0.138260
$838$	−7.48331			−0.258507
$839$	−52.3832			−1.80847			−0.904235	−	0.427036i	$-0.859558\pi$
$839$	−52.3832			−1.80847			−0.904235	+	0.427036i	$0.859558\pi$
$840$	−7.00000	−	7.00000i	−0.241523	−	0.241523i
$841$	7.00000			0.241379
$842$		−	22.4499i		−	0.773676i
$843$	−3.74166			−0.128870
$844$	12.0000			0.413057
$845$	−33.6749			−1.15845
$846$			6.00000i			0.206284i
$847$	20.5791	−	20.5791i	0.707107	−	0.707107i
$848$			3.74166i			0.128489i
$849$		−	18.7083i		−	0.642067i
$850$	33.6749			1.15504
$851$		0			0
$852$		−	6.00000i		−	0.205557i
$853$			28.0000i			0.958702i	0.877623	+	0.479351i	$0.159128\pi$
$853$			28.0000i			0.958702i	−0.877623	+	0.479351i	$0.840872\pi$
$854$		0			0
$855$	−14.0000			−0.478790
$856$		0			0
$857$		−	18.0000i		−	0.614868i	−0.951569	−	0.307434i	$-0.900530\pi$
$857$		−	18.0000i		−	0.614868i	0.951569	−	0.307434i	$-0.0994704\pi$
$858$		0			0
$859$		−	20.0000i		−	0.682391i	−0.939992	−	0.341196i	$-0.889168\pi$
$859$		−	20.0000i		−	0.682391i	0.939992	−	0.341196i	$-0.110832\pi$
$860$		−	42.0000i		−	1.43219i
$861$	3.74166	−	3.74166i	0.127515	−	0.127515i
$862$		−	37.4166i		−	1.27441i
$863$	−32.0000			−1.08929			−0.544646	−	0.838666i	$-0.683336\pi$
$863$	−32.0000			−1.08929			−0.544646	+	0.838666i	$0.683336\pi$
$864$		−	1.00000i		−	0.0340207i
$865$		−	52.3832i		−	1.78108i
$866$		0			0
$867$			3.00000i			0.101885i
$868$	7.48331	+	7.48331i	0.254000	+	0.254000i
$869$		0			0
$870$		−	22.4499i		−	0.761124i
$871$	−7.48331			−0.253562
$872$		−	7.48331i		−	0.253417i
$873$	7.48331			0.253272
$874$	−11.2250	−	14.0000i	−0.379690	−	0.473557i
$875$	−28.0000	+	28.0000i	−0.946573	+	0.946573i
$876$	−4.00000			−0.135147
$877$	22.0000			0.742887			0.371444	−	0.928456i	$-0.378863\pi$
$877$	22.0000			0.742887			0.371444	+	0.928456i	$0.378863\pi$
$878$			8.00000i			0.269987i
$879$			3.74166i			0.126203i
$880$		0			0
$881$	56.1249			1.89089			0.945447	−	0.325775i	$-0.105625\pi$
$881$	56.1249			1.89089			0.945447	+	0.325775i	$0.105625\pi$
$882$		−	7.00000i		−	0.235702i
$883$	40.0000			1.34611			0.673054	−	0.739594i	$-0.264982\pi$
$883$	40.0000			1.34611			0.673054	+	0.739594i	$0.264982\pi$
$884$		−	7.48331i		−	0.251691i
$885$	−52.3832			−1.76084
$886$	18.0000			0.604722
$887$		−	34.0000i		−	1.14161i	−0.821086	−	0.570804i	$-0.806632\pi$
$887$		−	34.0000i		−	1.14161i	0.821086	−	0.570804i	$-0.193368\pi$
$888$		0			0
$889$	−37.4166	+	37.4166i	−1.25491	+	1.25491i
$890$	−14.0000			−0.469281
$891$		0			0
$892$		0			0
$893$		−	22.4499i		−	0.751259i
$894$	−18.7083			−0.625699
$895$	44.8999			1.50084
$896$	−1.87083	+	1.87083i	−0.0625000	+	0.0625000i
$897$	−6.00000	−	7.48331i	−0.200334	−	0.249861i
$898$	−26.0000			−0.867631
$899$			24.0000i			0.800445i
$900$	−9.00000			−0.300000
$901$		−	14.0000i		−	0.466408i
$902$		0			0
$903$	21.0000	−	21.0000i	0.698836	−	0.698836i
$904$		−	11.2250i		−	0.373337i
$905$	−28.0000			−0.930751
$906$		−	12.0000i		−	0.398673i
$907$		−	26.1916i		−	0.869678i	−0.900508	−	0.434839i	$-0.856805\pi$
$907$		−	26.1916i		−	0.869678i	0.900508	−	0.434839i	$-0.143195\pi$
$908$	14.9666			0.496685
$909$		−	14.0000i		−	0.464351i
$910$	14.0000	+	14.0000i	0.464095	+	0.464095i
$911$			7.48331i			0.247933i	0.992286	+	0.123967i	$0.0395616\pi$
$911$			7.48331i			0.247933i	−0.992286	+	0.123967i	$0.960438\pi$
$912$			3.74166i			0.123899i
$913$		0			0
$914$		−	22.4499i		−	0.742578i
$915$		0			0
$916$	7.48331			0.247256
$917$	−37.4166	−	37.4166i	−1.23560	−	1.23560i
$918$			3.74166i			0.123493i
$919$		−	26.1916i		−	0.863981i	−0.901878	−	0.431991i	$-0.857811\pi$
$919$		−	26.1916i		−	0.863981i	0.901878	−	0.431991i	$-0.142189\pi$
$920$	−11.2250	−	14.0000i	−0.370076	−	0.461566i
$921$	−28.0000			−0.922631
$922$		−	26.0000i		−	0.856264i
$923$			12.0000i			0.394985i
$924$		0			0
$925$		0			0
$926$	16.0000			0.525793
$927$	18.7083			0.614461
$928$	−6.00000			−0.196960
$929$			50.0000i			1.64045i	0.572043	+	0.820223i	$0.306151\pi$
$929$			50.0000i			1.64045i	−0.572043	+	0.820223i	$0.693849\pi$
$930$	14.9666			0.490775
$931$			26.1916i			0.858395i
$932$	10.0000			0.327561
$933$	18.0000			0.589294
$934$	−14.9666			−0.489723
$935$		0			0
$936$			2.00000i			0.0653720i
$937$	14.9666			0.488938			0.244469	−	0.969657i	$-0.421386\pi$
$937$	14.9666			0.488938			0.244469	+	0.969657i	$0.421386\pi$
$938$	−7.00000	−	7.00000i	−0.228558	−	0.228558i
$939$		0			0
$940$		−	22.4499i		−	0.732236i
$941$	−56.1249			−1.82962			−0.914809	−	0.403887i	$-0.867659\pi$
$941$	−56.1249			−1.82962			−0.914809	+	0.403887i	$0.867659\pi$
$942$			14.9666i			0.487639i
$943$	7.48331	−	6.00000i	0.243690	−	0.195387i
$944$			14.0000i			0.455661i
$945$	−7.00000	−	7.00000i	−0.227710	−	0.227710i
$946$		0			0
$947$	−52.0000			−1.68977			−0.844886	−	0.534946i	$-0.820332\pi$
$947$	−52.0000			−1.68977			−0.844886	+	0.534946i	$0.820332\pi$
$948$	3.74166			0.121523
$949$	8.00000			0.259691
$950$	33.6749			1.09256
$951$			22.0000i			0.713399i
$952$	7.00000	−	7.00000i	0.226871	−	0.226871i
$953$			33.6749i			1.09084i	0.838164	+	0.545419i	$0.183629\pi$
$953$			33.6749i			1.09084i	−0.838164	+	0.545419i	$0.816371\pi$
$954$			3.74166i			0.121141i
$955$		0			0
$956$	−6.00000			−0.194054
$957$		0			0
$958$	−29.9333			−0.967100
$959$	−35.0000	−	35.0000i	−1.13021	−	1.13021i
$960$			3.74166i			0.120761i
$961$	15.0000			0.483871
$962$		0			0
$963$		0			0
$964$	−7.48331			−0.241021
$965$	59.8665			1.92717
$966$	1.38751	−	12.6125i	0.0446425	−	0.405800i
$967$	20.0000			0.643157			0.321578	−	0.946883i	$-0.395787\pi$
$967$	20.0000			0.643157			0.321578	+	0.946883i	$0.395787\pi$
$968$	−11.0000			−0.353553
$969$		−	14.0000i		−	0.449745i
$970$	−28.0000			−0.899026
$971$	−14.9666			−0.480302			−0.240151	−	0.970736i	$-0.577197\pi$
$971$	−14.9666			−0.480302			−0.240151	+	0.970736i	$0.577197\pi$
$972$		−	1.00000i		−	0.0320750i
$973$	−29.9333	−	29.9333i	−0.959616	−	0.959616i
$974$	−12.0000			−0.384505
$975$	18.0000			0.576461
$976$		0			0
$977$			26.1916i			0.837944i	0.907999	+	0.418972i	$0.137609\pi$
$977$			26.1916i			0.837944i	−0.907999	+	0.418972i	$0.862391\pi$
$978$		−	4.00000i		−	0.127906i
$979$		0			0
$980$			26.1916i			0.836660i
$981$		−	7.48331i		−	0.238924i
$982$	−20.0000			−0.638226
$983$	−59.8665			−1.90945			−0.954723	−	0.297497i	$-0.903848\pi$
$983$	−59.8665			−1.90945			−0.954723	+	0.297497i	$0.903848\pi$
$984$	−2.00000			−0.0637577
$985$	82.3165			2.62282
$986$	22.4499			0.714952
$987$	11.2250	−	11.2250i	0.357295	−	0.357295i
$988$		−	7.48331i		−	0.238076i
$989$	42.0000	−	33.6749i	1.33552	−	1.07080i
$990$		0			0
$991$	−52.0000			−1.65183			−0.825917	−	0.563791i	$-0.809342\pi$
$991$	−52.0000			−1.65183			−0.825917	+	0.563791i	$0.809342\pi$
$992$		−	4.00000i		−	0.127000i
$993$			24.0000i			0.761617i
$994$	−11.2250	+	11.2250i	−0.356034	+	0.356034i
$995$	14.0000			0.443830
$996$		−	7.48331i		−	0.237118i
$997$		−	14.0000i		−	0.443384i	−0.975117	−	0.221692i	$-0.928842\pi$
$997$		−	14.0000i		−	0.443384i	0.975117	−	0.221692i	$-0.0711580\pi$
$998$	24.0000			0.759707
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.g.b.643.1	✓	4
3.2	odd	2		2898.2.g.h.2575.3		4
7.6	odd	2	inner	966.2.g.b.643.4	yes	4
21.20	even	2		2898.2.g.h.2575.1		4
23.22	odd	2	inner	966.2.g.b.643.2	yes	4
69.68	even	2		2898.2.g.h.2575.2		4
161.160	even	2	inner	966.2.g.b.643.3	yes	4
483.482	odd	2		2898.2.g.h.2575.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.g.b.643.1	✓	4	1.1	even	1	trivial
966.2.g.b.643.2	yes	4	23.22	odd	2	inner
966.2.g.b.643.3	yes	4	161.160	even	2	inner
966.2.g.b.643.4	yes	4	7.6	odd	2	inner
2898.2.g.h.2575.1		4	21.20	even	2
2898.2.g.h.2575.2		4	69.68	even	2
2898.2.g.h.2575.3		4	3.2	odd	2
2898.2.g.h.2575.4		4	483.482	odd	2

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} -3.74166 q^{5} +1.00000i q^{6} +(1.87083 - 1.87083i) q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} -3.74166 q^{5} +1.00000i q^{6} +(1.87083 - 1.87083i) q^{7} -1.00000 q^{8} -1.00000 q^{9} +3.74166 q^{10} -1.00000i q^{12} +2.00000i q^{13} +(-1.87083 + 1.87083i) q^{14} +3.74166i q^{15} +1.00000 q^{16} -3.74166 q^{17} +1.00000 q^{18} -3.74166 q^{19} -3.74166 q^{20} +(-1.87083 - 1.87083i) q^{21} +(-3.00000 - 3.74166i) q^{23} +1.00000i q^{24} +9.00000 q^{25} -2.00000i q^{26} +1.00000i q^{27} +(1.87083 - 1.87083i) q^{28} +6.00000 q^{29} -3.74166i q^{30} +4.00000i q^{31} -1.00000 q^{32} +3.74166 q^{34} +(-7.00000 + 7.00000i) q^{35} -1.00000 q^{36} +3.74166 q^{38} +2.00000 q^{39} +3.74166 q^{40} +2.00000i q^{41} +(1.87083 + 1.87083i) q^{42} +11.2250i q^{43} +3.74166 q^{45} +(3.00000 + 3.74166i) q^{46} +6.00000i q^{47} -1.00000i q^{48} -7.00000i q^{49} -9.00000 q^{50} +3.74166i q^{51} +2.00000i q^{52} +3.74166i q^{53} -1.00000i q^{54} +(-1.87083 + 1.87083i) q^{56} +3.74166i q^{57} -6.00000 q^{58} +14.0000i q^{59} +3.74166i q^{60} -4.00000i q^{62} +(-1.87083 + 1.87083i) q^{63} +1.00000 q^{64} -7.48331i q^{65} +3.74166i q^{67} -3.74166 q^{68} +(-3.74166 + 3.00000i) q^{69} +(7.00000 - 7.00000i) q^{70} +6.00000 q^{71} +1.00000 q^{72} -4.00000i q^{73} -9.00000i q^{75} -3.74166 q^{76} -2.00000 q^{78} +3.74166i q^{79} -3.74166 q^{80} +1.00000 q^{81} -2.00000i q^{82} +7.48331 q^{83} +(-1.87083 - 1.87083i) q^{84} +14.0000 q^{85} -11.2250i q^{86} -6.00000i q^{87} -3.74166 q^{89} -3.74166 q^{90} +(3.74166 + 3.74166i) q^{91} +(-3.00000 - 3.74166i) q^{92} +4.00000 q^{93} -6.00000i q^{94} +14.0000 q^{95} +1.00000i q^{96} -7.48331 q^{97} +7.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{4} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 - 4 * q^9	\( 4 q - 4 q^{2} + 4 q^{4} - 4 q^{8} - 4 q^{9} + 4 q^{16} + 4 q^{18} - 12 q^{23} + 36 q^{25} + 24 q^{29} - 4 q^{32} - 28 q^{35} - 4 q^{36} + 8 q^{39} + 12 q^{46} - 36 q^{50} - 24 q^{58} + 4 q^{64} + 28 q^{70} + 24 q^{71} + 4 q^{72} - 8 q^{78} + 4 q^{81} + 56 q^{85} - 12 q^{92} + 16 q^{93} + 56 q^{95}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 - 4 * q^9 + 4 * q^16 + 4 * q^18 - 12 * q^23 + 36 * q^25 + 24 * q^29 - 4 * q^32 - 28 * q^35 - 4 * q^36 + 8 * q^39 + 12 * q^46 - 36 * q^50 - 24 * q^58 + 4 * q^64 + 28 * q^70 + 24 * q^71 + 4 * q^72 - 8 * q^78 + 4 * q^81 + 56 * q^85 - 12 * q^92 + 16 * q^93 + 56 * q^95

Introduction

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