LMFDB - Embedded newform 468.2.c.c.287.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [468,2,Mod(287,468)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(468, 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("468.287");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 468 = 2^{2} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	468.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.73699881460$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.1279179096064000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 5x^{8} - 4x^{6} + 20x^{4} + 64 $ x^12 + 5x^8 - 4x^6 + 20*x^4 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			287.11
Root			$1.31293 - 0.525570i$ of defining polynomial
Character	$\chi$	$=$	468.287
Dual form			468.2.c.c.287.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.31293 - 0.525570i) q^{2} +(1.44755 - 1.38007i) q^{4} -4.09430i q^{5} +3.71352i q^{7} +(1.17521 - 2.57272i) q^{8} +O(q^{10})$	\(q+(1.31293 - 0.525570i) q^{2} +(1.44755 - 1.38007i) q^{4} -4.09430i q^{5} +3.71352i q^{7} +(1.17521 - 2.57272i) q^{8} +(-2.15184 - 5.37551i) q^{10} +2.08943 q^{11} -1.00000 q^{13} +(1.95171 + 4.87558i) q^{14} +(0.190821 - 3.99545i) q^{16} +0.688065i q^{17} -6.27889i q^{19} +(-5.65041 - 5.92672i) q^{20} +(2.74327 - 1.09814i) q^{22} -1.07285 q^{23} -11.7633 q^{25} +(-1.31293 + 0.525570i) q^{26} +(5.12491 + 5.37551i) q^{28} +4.24264i q^{29} +8.18565i q^{31} +(-1.84935 - 5.34602i) q^{32} +(0.361626 + 0.903379i) q^{34} +15.2043 q^{35} +4.81714 q^{37} +(-3.30000 - 8.24373i) q^{38} +(-10.5335 - 4.81166i) q^{40} +1.26587i q^{41} +7.03751i q^{43} +(3.02456 - 2.88356i) q^{44} +(-1.40857 + 0.563856i) q^{46} +4.23513 q^{47} -6.79021 q^{49} +(-15.4443 + 6.18242i) q^{50} +(-1.44755 + 1.38007i) q^{52} +0.688065i q^{53} -8.55475i q^{55} +(9.55384 + 4.36416i) q^{56} +(2.22980 + 5.57028i) q^{58} +3.16228 q^{59} +13.7902 q^{61} +(4.30213 + 10.7472i) q^{62} +(-5.23777 - 6.04697i) q^{64} +4.09430i q^{65} +10.7510i q^{67} +(0.949577 + 0.996010i) q^{68} +(19.9621 - 7.99089i) q^{70} +10.9691 q^{71} -10.7633 q^{73} +(6.32456 - 2.53174i) q^{74} +(-8.66530 - 9.08903i) q^{76} +7.75913i q^{77} +12.5578i q^{79} +(-16.3585 - 0.781278i) q^{80} +(0.665304 + 1.66200i) q^{82} -16.7428 q^{83} +2.81714 q^{85} +(3.69870 + 9.23974i) q^{86} +(2.45552 - 5.37551i) q^{88} -1.56256i q^{89} -3.71352i q^{91} +(-1.55301 + 1.48060i) q^{92} +(5.56041 - 2.22585i) q^{94} -25.7077 q^{95} +2.76328 q^{97} +(-8.91505 + 3.56873i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q+O(q^{10}) $ 12 * q	$ 12 q + 4 q^{10} - 12 q^{13} - 20 q^{16} + 28 q^{22} - 52 q^{25} + 12 q^{28} + 44 q^{34} + 8 q^{37} - 52 q^{40} + 8 q^{46} - 12 q^{49} + 12 q^{58} + 96 q^{61} + 24 q^{64} + 56 q^{70} - 40 q^{73} - 84 q^{76} - 12 q^{82} - 16 q^{85} - 60 q^{88} + 12 q^{94} - 56 q^{97}+O(q^{100}) $ 12 * q + 4 * q^10 - 12 * q^13 - 20 * q^16 + 28 * q^22 - 52 * q^25 + 12 * q^28 + 44 * q^34 + 8 * q^37 - 52 * q^40 + 8 * q^46 - 12 * q^49 + 12 * q^58 + 96 * q^61 + 24 * q^64 + 56 * q^70 - 40 * q^73 - 84 * q^76 - 12 * q^82 - 16 * q^85 - 60 * q^88 + 12 * q^94 - 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/468\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$235$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	1.31293	−	0.525570i	0.928379	−	0.371634i
$2$	1.31293	−	0.525570i	0.928379	−	0.371634i
$3$		0			0
$3$		0			0
$4$	1.44755	−	1.38007i	0.723777	−	0.690034i
$5$		−	4.09430i		−	1.83103i	−0.402288	−	0.915513i	$-0.631785\pi$
$5$		−	4.09430i		−	1.83103i	0.402288	−	0.915513i	$-0.368215\pi$
$6$		0			0
$7$			3.71352i			1.40358i	0.712385	+	0.701789i	$0.247615\pi$
$7$			3.71352i			1.40358i	−0.712385	+	0.701789i	$0.752385\pi$
$8$	1.17521	−	2.57272i	0.415499	−	0.909594i
$9$		0			0
$10$	−2.15184	−	5.37551i	−0.680471	−	1.69989i
$11$	2.08943			0.629987			0.314993	−	0.949094i	$-0.397998\pi$
$11$	2.08943			0.629987			0.314993	+	0.949094i	$0.397998\pi$
$12$		0			0
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	1.95171	+	4.87558i	0.521617	+	1.30305i
$15$		0			0
$16$	0.190821	−	3.99545i	0.0477052	−	0.998861i
$17$			0.688065i			0.166880i	0.996513	+	0.0834401i	$0.0265907\pi$
$17$			0.688065i			0.166880i	−0.996513	+	0.0834401i	$0.973409\pi$
$18$		0			0
$19$		−	6.27889i		−	1.44048i	−0.693727	−	0.720238i	$-0.744032\pi$
$19$		−	6.27889i		−	1.44048i	0.693727	−	0.720238i	$-0.255968\pi$
$20$	−5.65041	−	5.92672i	−1.26347	−	1.32525i
$21$		0			0
$22$	2.74327	−	1.09814i	0.584867	−	0.234124i
$23$	−1.07285			−0.223704			−0.111852	−	0.993725i	$-0.535678\pi$
$23$	−1.07285			−0.223704			−0.111852	+	0.993725i	$0.535678\pi$
$24$		0			0
$25$	−11.7633			−2.35266
$26$	−1.31293	+	0.525570i	−0.257486	+	0.103073i
$27$		0			0
$28$	5.12491	+	5.37551i	0.968517	+	1.01588i
$29$			4.24264i			0.787839i	0.919145	+	0.393919i	$0.128881\pi$
$29$			4.24264i			0.787839i	−0.919145	+	0.393919i	$0.871119\pi$
$30$		0			0
$31$			8.18565i			1.47019i	0.677966	+	0.735093i	$0.262862\pi$
$31$			8.18565i			1.47019i	−0.677966	+	0.735093i	$0.737138\pi$
$32$	−1.84935	−	5.34602i	−0.326922	−	0.945051i
$33$		0			0
$34$	0.361626	+	0.903379i	0.0620183	+	0.154928i
$35$	15.2043			2.56999
$36$		0			0
$37$	4.81714			0.791933			0.395967	−	0.918265i	$-0.370410\pi$
$37$	4.81714			0.791933			0.395967	+	0.918265i	$0.370410\pi$
$38$	−3.30000	−	8.24373i	−0.535330	−	1.33731i
$39$		0			0
$40$	−10.5335	−	4.81166i	−1.66549	−	0.760790i
$41$			1.26587i			0.197696i	0.995103	+	0.0988480i	$0.0315158\pi$
$41$			1.26587i			0.197696i	−0.995103	+	0.0988480i	$0.968484\pi$
$42$		0			0
$43$			7.03751i			1.07321i	0.843833	+	0.536605i	$0.180294\pi$
$43$			7.03751i			1.07321i	−0.843833	+	0.536605i	$0.819706\pi$
$44$	3.02456	−	2.88356i	0.455970	−	0.434712i
$45$		0			0
$46$	−1.40857	+	0.563856i	−0.207683	+	0.0831361i
$47$	4.23513			0.617757			0.308878	−	0.951102i	$-0.400046\pi$
$47$	4.23513			0.617757			0.308878	+	0.951102i	$0.400046\pi$
$48$		0			0
$49$	−6.79021			−0.970030
$50$	−15.4443	+	6.18242i	−2.18416	+	0.874327i
$51$		0			0
$52$	−1.44755	+	1.38007i	−0.200740	+	0.191381i
$53$			0.688065i			0.0945130i	0.998883	+	0.0472565i	$0.0150478\pi$
$53$			0.688065i			0.0945130i	−0.998883	+	0.0472565i	$0.984952\pi$
$54$		0			0
$55$		−	8.55475i		−	1.15352i
$56$	9.55384	+	4.36416i	1.27669	+	0.583185i
$57$		0			0
$58$	2.22980	+	5.57028i	0.292787	+	0.731413i
$59$	3.16228			0.411693			0.205847	−	0.978584i	$-0.434005\pi$
$59$	3.16228			0.411693			0.205847	+	0.978584i	$0.434005\pi$
$60$		0			0
$61$	13.7902			1.76566			0.882828	−	0.469697i	$-0.155637\pi$
$61$	13.7902			1.76566			0.882828	+	0.469697i	$0.155637\pi$
$62$	4.30213	+	10.7472i	0.546371	+	1.36489i
$63$		0			0
$64$	−5.23777	−	6.04697i	−0.654721	−	0.755871i
$65$			4.09430i			0.507835i
$66$		0			0
$67$			10.7510i			1.31345i	0.754131	+	0.656724i	$0.228058\pi$
$67$			10.7510i			1.31345i	−0.754131	+	0.656724i	$0.771942\pi$
$68$	0.949577	+	0.996010i	0.115153	+	0.120784i
$69$		0			0
$70$	19.9621	−	7.99089i	2.38592	−	0.955094i
$71$	10.9691			1.30180			0.650898	−	0.759165i	$-0.274393\pi$
$71$	10.9691			1.30180			0.650898	+	0.759165i	$0.274393\pi$
$72$		0			0
$73$	−10.7633			−1.25975			−0.629874	−	0.776698i	$-0.716893\pi$
$73$	−10.7633			−1.25975			−0.629874	+	0.776698i	$0.716893\pi$
$74$	6.32456	−	2.53174i	0.735215	−	0.294309i
$75$		0			0
$76$	−8.66530	−	9.08903i	−0.993979	−	1.04258i
$77$			7.75913i			0.884235i
$78$		0			0
$79$			12.5578i			1.41286i	0.707782	+	0.706431i	$0.249696\pi$
$79$			12.5578i			1.41286i	−0.707782	+	0.706431i	$0.750304\pi$
$80$	−16.3585	−	0.781278i	−1.82894	−	0.0873495i
$81$		0			0
$82$	0.665304	+	1.66200i	0.0734705	+	0.183537i
$83$	−16.7428			−1.83776			−0.918881	−	0.394535i	$-0.870906\pi$
$83$	−16.7428			−1.83776			−0.918881	+	0.394535i	$0.870906\pi$
$84$		0			0
$85$	2.81714			0.305562
$86$	3.69870	+	9.23974i	0.398841	+	0.996346i
$87$		0			0
$88$	2.45552	−	5.37551i	0.261759	−	0.573032i
$89$		−	1.56256i		−	0.165631i	−0.996565	−	0.0828153i	$-0.973609\pi$
$89$		−	1.56256i		−	0.165631i	0.996565	−	0.0828153i	$-0.0263911\pi$
$90$		0			0
$91$		−	3.71352i		−	0.389282i
$92$	−1.55301	+	1.48060i	−0.161912	+	0.154364i
$93$		0			0
$94$	5.56041	−	2.22585i	0.573513	−	0.229579i
$95$	−25.7077			−2.63755
$96$		0			0
$97$	2.76328			0.280569			0.140284	−	0.990111i	$-0.455198\pi$
$97$	2.76328			0.280569			0.140284	+	0.990111i	$0.455198\pi$
$98$	−8.91505	+	3.56873i	−0.900556	+	0.360496i
$99$		0			0
$100$	−17.0280	+	16.2341i	−1.70280	+	1.62341i
$101$		−	15.6891i		−	1.56113i	−0.625077	−	0.780563i	$-0.714932\pi$
$101$		−	15.6891i		−	1.56113i	0.625077	−	0.780563i	$-0.285068\pi$
$102$		0			0
$103$			1.90676i			0.187879i	0.995578	+	0.0939393i	$0.0299460\pi$
$103$			1.90676i			0.187879i	−0.995578	+	0.0939393i	$0.970054\pi$
$104$	−1.17521	+	2.57272i	−0.115239	+	0.252276i
$105$		0			0
$106$	0.361626	+	0.903379i	0.0351242	+	0.0877439i
$107$	−16.6865			−1.61315			−0.806575	−	0.591132i	$-0.798681\pi$
$107$	−16.6865			−1.61315			−0.806575	+	0.591132i	$0.798681\pi$
$108$		0			0
$109$	0.973070			0.0932032			0.0466016	−	0.998914i	$-0.485161\pi$
$109$	0.973070			0.0932032			0.0466016	+	0.998914i	$0.485161\pi$
$110$	−4.49612	−	11.2318i	−0.428688	−	1.07091i
$111$		0			0
$112$	14.8372	+	0.708617i	1.40198	+	0.0669580i
$113$		−	10.5495i		−	0.992411i	−0.868205	−	0.496206i	$-0.834726\pi$
$113$		−	10.5495i		−	0.992411i	0.868205	−	0.496206i	$-0.165274\pi$
$114$		0			0
$115$			4.39256i			0.409609i
$116$	5.85514	+	6.14145i	0.543636	+	0.570219i
$117$		0			0
$118$	4.15184	−	1.66200i	0.382208	−	0.152999i
$119$	−2.55514			−0.234229
$120$		0			0
$121$	−6.63429			−0.603117
$122$	18.1055	−	7.24772i	1.63920	−	0.656177i
$123$		0			0
$124$	11.2968	+	11.8492i	1.01448	+	1.06409i
$125$			27.6909i			2.47675i
$126$		0			0
$127$			1.51724i			0.134633i	0.997732	+	0.0673165i	$0.0214437\pi$
$127$			1.51724i			0.134633i	−0.997732	+	0.0673165i	$0.978556\pi$
$128$	−10.0549	−	5.18641i	−0.888736	−	0.458419i
$129$		0			0
$130$	2.15184	+	5.37551i	0.188729	+	0.471464i
$131$	−1.62372			−0.141865			−0.0709325	−	0.997481i	$-0.522597\pi$
$131$	−1.62372			−0.141865			−0.0709325	+	0.997481i	$0.522597\pi$
$132$		0			0
$133$	23.3168			2.02182
$134$	5.65041	+	14.1153i	0.488121	+	1.21938i
$135$		0			0
$136$	1.77020	+	0.808620i	0.151793	+	0.0693386i
$137$			13.6590i			1.16697i	0.812124	+	0.583485i	$0.198311\pi$
$137$			13.6590i			1.16697i	−0.812124	+	0.583485i	$0.801689\pi$
$138$		0			0
$139$		−	21.8916i		−	1.85682i	−0.371558	−	0.928410i	$-0.621176\pi$
$139$		−	21.8916i		−	1.85682i	0.371558	−	0.928410i	$-0.378824\pi$
$140$	22.0090	−	20.9829i	1.86010	−	1.77338i
$141$		0			0
$142$	14.4017	−	5.76504i	1.20856	−	0.483791i
$143$	−2.08943			−0.174727
$144$		0			0
$145$	17.3706			1.44255
$146$	−14.1314	+	5.65685i	−1.16952	+	0.468165i
$147$		0			0
$148$	6.97307	−	6.64799i	0.573183	−	0.546461i
$149$		−	9.67498i		−	0.792606i	−0.918120	−	0.396303i	$-0.870293\pi$
$149$		−	9.67498i		−	0.792606i	0.918120	−	0.396303i	$-0.129707\pi$
$150$		0			0
$151$		−	1.53767i		−	0.125133i	−0.998041	−	0.0625667i	$-0.980071\pi$
$151$		−	1.53767i		−	0.125133i	0.998041	−	0.0625667i	$-0.0199286\pi$
$152$	−16.1538	−	7.37901i	−1.31025	−	0.598517i
$153$		0			0
$154$	4.07796	+	10.1872i	0.328612	+	0.820906i
$155$	33.5145			2.69195
$156$		0			0
$157$	−14.3437			−1.14475			−0.572376	−	0.819991i	$-0.693978\pi$
$157$	−14.3437			−1.14475			−0.572376	+	0.819991i	$0.693978\pi$
$158$	6.59999	+	16.4875i	0.525067	+	1.31167i
$159$		0			0
$160$	−21.8882	+	7.57180i	−1.73041	+	0.598603i
$161$		−	3.98404i		−	0.313986i
$162$		0			0
$163$			1.14814i			0.0899294i	0.998989	+	0.0449647i	$0.0143175\pi$
$163$			1.14814i			0.0899294i	−0.998989	+	0.0449647i	$0.985682\pi$
$164$	1.74699	+	1.83242i	0.136417	+	0.143088i
$165$		0			0
$166$	−21.9821	+	8.79951i	−1.70614	+	0.682975i
$167$	10.5597			0.817133			0.408566	−	0.912729i	$-0.366029\pi$
$167$	10.5597			0.817133			0.408566	+	0.912729i	$0.366029\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	3.69870	−	1.48060i	0.283677	−	0.113557i
$171$		0			0
$172$	9.71225	+	10.1872i	0.740552	+	0.776765i
$173$		−	13.0812i		−	0.994547i	−0.867594	−	0.497273i	$-0.834335\pi$
$173$		−	13.0812i		−	0.994547i	0.867594	−	0.497273i	$-0.165665\pi$
$174$		0			0
$175$		−	43.6832i		−	3.30214i
$176$	0.398707	−	8.34820i	0.0300536	−	0.629269i
$177$		0			0
$178$	−0.821232	−	2.05152i	−0.0615539	−	0.153768i
$179$	−7.94827			−0.594082			−0.297041	−	0.954865i	$-0.596000\pi$
$179$	−7.94827			−0.594082			−0.297041	+	0.954865i	$0.596000\pi$
$180$		0			0
$181$	−4.76328			−0.354052			−0.177026	−	0.984206i	$-0.556648\pi$
$181$	−4.76328			−0.354052			−0.177026	+	0.984206i	$0.556648\pi$
$182$	−1.95171	−	4.87558i	−0.144671	−	0.361402i
$183$		0			0
$184$	−1.26082	+	2.76014i	−0.0929490	+	0.203480i
$185$		−	19.7228i		−	1.45005i
$186$		0			0
$187$			1.43766i			0.105132i
$188$	6.13057	−	5.84476i	0.447118	−	0.426273i
$189$		0			0
$190$	−33.7523	+	13.5112i	−2.44865	+	0.980203i
$191$	−7.94827			−0.575117			−0.287558	−	0.957763i	$-0.592844\pi$
$191$	−7.94827			−0.575117			−0.287558	+	0.957763i	$0.592844\pi$
$192$		0			0
$193$	12.5535			0.903620			0.451810	−	0.892114i	$-0.350778\pi$
$193$	12.5535			0.903620			0.451810	+	0.892114i	$0.350778\pi$
$194$	3.62799	−	1.45230i	0.260474	−	0.104269i
$195$		0			0
$196$	−9.82919	+	9.37096i	−0.702085	+	0.669354i
$197$			17.9398i			1.27815i	0.769143	+	0.639077i	$0.220684\pi$
$197$			17.9398i			1.27815i	−0.769143	+	0.639077i	$0.779316\pi$
$198$		0			0
$199$		−	8.20608i		−	0.581714i	−0.956767	−	0.290857i	$-0.906060\pi$
$199$		−	8.20608i		−	0.581714i	0.956767	−	0.290857i	$-0.0939404\pi$
$200$	−13.8243	+	30.2636i	−0.977527	+	2.13996i
$201$		0			0
$202$	−8.24573	−	20.5987i	−0.580168	−	1.44932i
$203$	−15.7551			−1.10579
$204$		0			0
$205$	5.18286			0.361986
$206$	1.00214	+	2.50344i	0.0698221	+	0.174423i
$207$		0			0
$208$	−0.190821	+	3.99545i	−0.0132310	+	0.277034i
$209$		−	13.1193i		−	0.907481i
$210$		0			0
$211$			6.64799i			0.457666i	0.973466	+	0.228833i	$0.0734910\pi$
$211$			6.64799i			0.457666i	−0.973466	+	0.228833i	$0.926509\pi$
$212$	0.949577	+	0.996010i	0.0652172	+	0.0684063i
$213$		0			0
$214$	−21.9082	+	8.76994i	−1.49761	+	0.599501i
$215$	28.8137			1.96508
$216$		0			0
$217$	−30.3976			−2.06352
$218$	1.27757	−	0.511416i	0.0865280	−	0.0346375i
$219$		0			0
$220$	−11.8061	−	12.3835i	−0.795970	−	0.834892i
$221$		−	0.688065i		−	0.0462842i
$222$		0			0
$223$		−	11.2201i		−	0.751355i	−0.926750	−	0.375678i	$-0.877410\pi$
$223$		−	11.2201i		−	0.751355i	0.926750	−	0.375678i	$-0.122590\pi$
$224$	19.8525	−	6.86760i	1.32645	−	0.458861i
$225$		0			0
$226$	−5.54448	−	13.8507i	−0.368814	−	0.921334i
$227$	−6.93169			−0.460073			−0.230036	−	0.973182i	$-0.573884\pi$
$227$	−6.93169			−0.460073			−0.230036	+	0.973182i	$0.573884\pi$
$228$		0			0
$229$	7.94614			0.525096			0.262548	−	0.964919i	$-0.415437\pi$
$229$	7.94614			0.525096			0.262548	+	0.964919i	$0.415437\pi$
$230$	2.30860	+	5.76711i	0.152224	+	0.380272i
$231$		0			0
$232$	10.9151	+	4.98599i	0.716613	+	0.327346i
$233$		−	9.67898i		−	0.634091i	−0.948410	−	0.317046i	$-0.897309\pi$
$233$		−	9.67898i		−	0.634091i	0.948410	−	0.317046i	$-0.102691\pi$
$234$		0			0
$235$		−	17.3399i		−	1.13113i
$236$	4.57757	−	4.36416i	0.297974	−	0.284083i
$237$		0			0
$238$	−3.35471	+	1.34290i	−0.217454	+	0.0870475i
$239$	−7.34114			−0.474859			−0.237429	−	0.971405i	$-0.576305\pi$
$239$	−7.34114			−0.474859			−0.237429	+	0.971405i	$0.576305\pi$
$240$		0			0
$241$	−17.7364			−1.14250			−0.571249	−	0.820776i	$-0.693541\pi$
$241$	−17.7364			−1.14250			−0.571249	+	0.820776i	$0.693541\pi$
$242$	−8.71033	+	3.48678i	−0.559921	+	0.224139i
$243$		0			0
$244$	19.9621	−	19.0314i	1.27794	−	1.21836i
$245$			27.8012i			1.77615i
$246$		0			0
$247$			6.27889i			0.399516i
$248$	21.0594	+	9.61986i	1.33727	+	0.610861i
$249$		0			0
$250$	14.5535	+	36.3561i	0.920444	+	2.29936i
$251$	3.62799			0.228997			0.114498	−	0.993423i	$-0.463474\pi$
$251$	3.62799			0.228997			0.114498	+	0.993423i	$0.463474\pi$
$252$		0			0
$253$	−2.24164			−0.140931
$254$	0.797413	+	1.99202i	0.0500342	+	0.124990i
$255$		0			0
$256$	−15.9272	−	1.52483i	−0.995448	−	0.0953018i
$257$		−	10.9789i		−	0.684848i	−0.939546	−	0.342424i	$-0.888752\pi$
$257$		−	10.9789i		−	0.684848i	0.939546	−	0.342424i	$-0.111248\pi$
$258$		0			0
$259$			17.8885i			1.11154i
$260$	5.65041	+	5.92672i	0.350424	+	0.367559i
$261$		0			0
$262$	−2.13182	+	0.853377i	−0.131704	+	0.0527218i
$263$	−16.2771			−1.00369			−0.501844	−	0.864958i	$-0.667345\pi$
$263$	−16.2771			−1.00369			−0.501844	+	0.864958i	$0.667345\pi$
$264$		0			0
$265$	2.81714			0.173056
$266$	30.6132	−	12.2546i	1.87702	−	0.751377i
$267$		0			0
$268$	14.8372	+	15.5627i	0.906324	+	0.950642i
$269$			19.7609i			1.20484i	0.798178	+	0.602422i	$0.205797\pi$
$269$			19.7609i			1.20484i	−0.798178	+	0.602422i	$0.794203\pi$
$270$		0			0
$271$			14.1750i			0.861072i	0.902574	+	0.430536i	$0.141675\pi$
$271$			14.1750i			0.861072i	−0.902574	+	0.430536i	$0.858325\pi$
$272$	2.74913	+	0.131297i	0.166690	+	0.00796106i
$273$		0			0
$274$	7.17877	+	17.9333i	0.433685	+	1.08339i
$275$	−24.5785			−1.48214
$276$		0			0
$277$	2.97307			0.178634			0.0893172	−	0.996003i	$-0.471532\pi$
$277$	2.97307			0.178634			0.0893172	+	0.996003i	$0.471532\pi$
$278$	−11.5055	−	28.7420i	−0.690057	−	1.72383i
$279$		0			0
$280$	17.8682	−	39.1163i	1.06783	−	2.33764i
$281$		−	29.5501i		−	1.76281i	−0.472358	−	0.881407i	$-0.656597\pi$
$281$		−	29.5501i		−	1.76281i	0.472358	−	0.881407i	$-0.343403\pi$
$282$		0			0
$283$		−	11.0405i		−	0.656293i	−0.944627	−	0.328146i	$-0.893576\pi$
$283$		−	11.0405i		−	0.656293i	0.944627	−	0.328146i	$-0.106424\pi$
$284$	15.8784	−	15.1381i	0.942209	−	0.898284i
$285$		0			0
$286$	−2.74327	+	1.09814i	−0.162213	+	0.0649344i
$287$	−4.70084			−0.277482
$288$		0			0
$289$	16.5266			0.972151
$290$	22.8064	−	9.12948i	1.33924	−	0.536101i
$291$		0			0
$292$	−15.5804	+	14.8541i	−0.911775	+	0.869269i
$293$		−	11.9862i		−	0.700242i	−0.936704	−	0.350121i	$-0.886140\pi$
$293$		−	11.9862i		−	0.700242i	0.936704	−	0.350121i	$-0.113860\pi$
$294$		0			0
$295$		−	12.9473i		−	0.753822i
$296$	5.66115	−	12.3932i	0.329048	−	0.720337i
$297$		0			0
$298$	−5.08488	−	12.7025i	−0.294559	−	0.735839i
$299$	1.07285			0.0620444
$300$		0			0
$301$	−26.1339			−1.50633
$302$	−0.808150	−	2.01884i	−0.0465038	−	0.116171i
$303$		0			0
$304$	−25.0870	−	1.19814i	−1.43884	−	0.0687183i
$305$		−	56.4613i		−	3.23296i
$306$		0			0
$307$			22.5706i			1.28817i	0.764952	+	0.644087i	$0.222762\pi$
$307$			22.5706i			1.28817i	−0.764952	+	0.644087i	$0.777238\pi$
$308$	10.7081	+	11.2318i	0.610153	+	0.639989i
$309$		0			0
$310$	44.0021	−	17.6142i	2.49915	−	1.00042i
$311$	6.73400			0.381850			0.190925	−	0.981605i	$-0.438851\pi$
$311$	6.73400			0.381850			0.190925	+	0.981605i	$0.438851\pi$
$312$		0			0
$313$	13.1070			0.740851			0.370426	−	0.928862i	$-0.379212\pi$
$313$	13.1070			0.740851			0.370426	+	0.928862i	$0.379212\pi$
$314$	−18.8322	+	7.53862i	−1.06276	+	0.425429i
$315$		0			0
$316$	17.3306	+	18.1781i	0.974923	+	1.02260i
$317$			9.75115i			0.547679i	0.961775	+	0.273840i	$0.0882938\pi$
$317$			9.75115i			0.547679i	−0.961775	+	0.273840i	$0.911706\pi$
$318$		0			0
$319$			8.86470i			0.496328i
$320$	−24.7581	+	21.4450i	−1.38402	+	1.19881i
$321$		0			0
$322$	−2.09389	−	5.23075i	−0.116688	−	0.291499i
$323$	4.32028			0.240387
$324$		0			0
$325$	11.7633			0.652510
$326$	0.603429	+	1.50743i	0.0334208	+	0.0834886i
$327$		0			0
$328$	3.25673	+	1.48766i	0.179823	+	0.0821425i
$329$			15.7272i			0.867069i
$330$		0			0
$331$		−	4.10304i		−	0.225524i	−0.993622	−	0.112762i	$-0.964030\pi$
$331$		−	4.10304i		−	0.225524i	0.993622	−	0.112762i	$-0.0359697\pi$
$332$	−24.2361	+	23.1062i	−1.33013	+	1.26812i
$333$		0			0
$334$	13.8641	−	5.54985i	0.758609	−	0.303674i
$335$	44.0179			2.40496
$336$		0			0
$337$	−12.8654			−0.700820			−0.350410	−	0.936596i	$-0.613958\pi$
$337$	−12.8654			−0.700820			−0.350410	+	0.936596i	$0.613958\pi$
$338$	1.31293	−	0.525570i	0.0714138	−	0.0285872i
$339$		0			0
$340$	4.07796	−	3.88785i	0.221159	−	0.210848i
$341$			17.1033i			0.926198i
$342$		0			0
$343$			0.779048i			0.0420646i
$344$	18.1055	+	8.27055i	0.976185	+	0.445918i
$345$		0			0
$346$	−6.87509	−	17.1747i	−0.369607	−	0.923317i
$347$	−32.5542			−1.74760			−0.873800	−	0.486285i	$-0.838352\pi$
$347$	−32.5542			−1.74760			−0.873800	+	0.486285i	$0.838352\pi$
$348$		0			0
$349$	−7.68249			−0.411235			−0.205617	−	0.978632i	$-0.565920\pi$
$349$	−7.68249			−0.411235			−0.205617	+	0.978632i	$0.565920\pi$
$350$	−22.9585	−	57.3528i	−1.22719	−	3.06564i
$351$		0			0
$352$	−3.86409	−	11.1701i	−0.205957	−	0.595370i
$353$			11.1273i			0.592245i	0.955150	+	0.296123i	$0.0956937\pi$
$353$			11.1273i			0.592245i	−0.955150	+	0.296123i	$0.904306\pi$
$354$		0			0
$355$		−	44.9109i		−	2.38362i
$356$	−2.15643	−	2.26188i	−0.114291	−	0.119880i
$357$		0			0
$358$	−10.4355	+	4.17737i	−0.551533	+	0.220781i
$359$	−19.2980			−1.01851			−0.509253	−	0.860617i	$-0.670078\pi$
$359$	−19.2980			−1.01851			−0.509253	+	0.860617i	$0.670078\pi$
$360$		0			0
$361$	−20.4245			−1.07497
$362$	−6.25384	+	2.50344i	−0.328695	+	0.131578i
$363$		0			0
$364$	−5.12491	−	5.37551i	−0.268618	−	0.281754i
$365$			44.0681i			2.30663i
$366$		0			0
$367$		−	0.389524i		−	0.0203330i	−0.999948	−	0.0101665i	$-0.996764\pi$
$367$		−	0.389524i		−	0.0203330i	0.999948	−	0.0101665i	$-0.00323615\pi$
$368$	−0.204722	+	4.28651i	−0.0106719	+	0.223450i
$369$		0			0
$370$	−10.3657	−	25.8946i	−0.538888	−	1.34620i
$371$	−2.55514			−0.132656
$372$		0			0
$373$	13.5266			0.700379			0.350190	−	0.936679i	$-0.386117\pi$
$373$	13.5266			0.700379			0.350190	+	0.936679i	$0.386117\pi$
$374$	0.755592	+	1.88755i	0.0390707	+	0.0976027i
$375$		0			0
$376$	4.97716	−	10.8958i	0.256677	−	0.561907i
$377$		−	4.24264i		−	0.218507i
$378$		0			0
$379$		−	4.18262i		−	0.214847i	−0.994213	−	0.107423i	$-0.965740\pi$
$379$		−	4.18262i		−	0.214847i	0.994213	−	0.107423i	$-0.0342600\pi$
$380$	−37.2132	+	35.4783i	−1.90900	+	1.82000i
$381$		0			0
$382$	−10.4355	+	4.17737i	−0.533927	+	0.213733i
$383$	8.79454			0.449380			0.224690	−	0.974430i	$-0.427863\pi$
$383$	8.79454			0.449380			0.224690	+	0.974430i	$0.427863\pi$
$384$		0			0
$385$	31.7682			1.61906
$386$	16.4818	−	6.59774i	0.838903	−	0.335816i
$387$		0			0
$388$	4.00000	−	3.81352i	0.203069	−	0.193602i
$389$		−	19.2437i		−	0.975695i	−0.872929	−	0.487847i	$-0.837782\pi$
$389$		−	19.2437i		−	0.975695i	0.872929	−	0.487847i	$-0.162218\pi$
$390$		0			0
$391$		−	0.738189i		−	0.0373318i
$392$	−7.97992	+	17.4693i	−0.403047	+	0.882333i
$393$		0			0
$394$	9.42859	+	23.5536i	0.475005	+	1.18661i
$395$	51.4153			2.58699
$396$		0			0
$397$	7.89793			0.396386			0.198193	−	0.980163i	$-0.436493\pi$
$397$	7.89793			0.396386			0.198193	+	0.980163i	$0.436493\pi$
$398$	−4.31287	−	10.7740i	−0.216185	−	0.540051i
$399$		0			0
$400$	−2.24468	+	46.9996i	−0.112234	+	2.34998i
$401$			0.110258i			0.00550600i	0.999996	+	0.00275300i	$0.000876309\pi$
$401$			0.110258i			0.00550600i	−0.999996	+	0.00275300i	$0.999124\pi$
$402$		0			0
$403$		−	8.18565i		−	0.407756i
$404$	−21.6521	−	22.7109i	−1.07723	−	1.12991i
$405$		0			0
$406$	−20.6853	+	8.28041i	−1.02660	+	0.410950i
$407$	10.0651			0.498907
$408$		0			0
$409$	22.3437			1.10483			0.552413	−	0.833571i	$-0.313707\pi$
$409$	22.3437			1.10483			0.552413	+	0.833571i	$0.313707\pi$
$410$	6.80471	−	2.72395i	0.336061	−	0.134526i
$411$		0			0
$412$	2.63146	+	2.76014i	0.129643	+	0.135982i
$413$			11.7432i			0.577844i
$414$		0			0
$415$			68.5501i			3.36499i
$416$	1.84935	+	5.34602i	0.0906719	+	0.262110i
$417$		0			0
$418$	−6.89511	−	17.2247i	−0.337251	−	0.842487i
$419$	−17.7883			−0.869014			−0.434507	−	0.900668i	$-0.643077\pi$
$419$	−17.7883			−0.869014			−0.434507	+	0.900668i	$0.643077\pi$
$420$		0			0
$421$	5.68814			0.277223			0.138612	−	0.990347i	$-0.455736\pi$
$421$	5.68814			0.277223			0.138612	+	0.990347i	$0.455736\pi$
$422$	3.49398	+	8.72832i	0.170084	+	0.424888i
$423$		0			0
$424$	1.77020	+	0.808620i	0.0859684	+	0.0392701i
$425$		−	8.09390i		−	0.392612i
$426$		0			0
$427$			51.2102i			2.47824i
$428$	−24.1547	+	23.0286i	−1.16756	+	1.11313i
$429$		0			0
$430$	37.8302	−	15.1436i	1.82434	−	0.730289i
$431$	13.1437			0.633110			0.316555	−	0.948574i	$-0.397474\pi$
$431$	13.1437			0.633110			0.316555	+	0.948574i	$0.397474\pi$
$432$		0			0
$433$	28.3437			1.36211			0.681056	−	0.732231i	$-0.261521\pi$
$433$	28.3437			1.36211			0.681056	+	0.732231i	$0.261521\pi$
$434$	−39.9098	+	15.9760i	−1.91573	+	0.766874i
$435$		0			0
$436$	1.40857	−	1.34290i	0.0674583	−	0.0643134i
$437$			6.73630i			0.322241i
$438$		0			0
$439$		−	35.9666i		−	1.71659i	−0.513155	−	0.858296i	$-0.671523\pi$
$439$		−	35.9666i		−	1.71659i	0.513155	−	0.858296i	$-0.328477\pi$
$440$	−22.0090	−	10.0536i	−1.04924	−	0.479287i
$441$		0			0
$442$	−0.361626	−	0.903379i	−0.0172008	−	0.0429693i
$443$	34.7288			1.65001			0.825007	−	0.565122i	$-0.191171\pi$
$443$	34.7288			1.65001			0.825007	+	0.565122i	$0.191171\pi$
$444$		0			0
$445$	−6.39757			−0.303274
$446$	−5.89696	−	14.7312i	−0.279229	−	0.697543i
$447$		0			0
$448$	22.4555	−	19.4505i	1.06092	−	0.918952i
$449$			1.18970i			0.0561456i	0.999606	+	0.0280728i	$0.00893702\pi$
$449$			1.18970i			0.0561456i	−0.999606	+	0.0280728i	$0.991063\pi$
$450$		0			0
$451$			2.64495i			0.124546i
$452$	−14.5590	−	15.2709i	−0.684798	−	0.718284i
$453$		0			0
$454$	−9.10080	+	3.64309i	−0.427122	+	0.170979i
$455$	−15.2043			−0.712786
$456$		0			0
$457$	8.39757			0.392822			0.196411	−	0.980522i	$-0.437071\pi$
$457$	8.39757			0.392822			0.196411	+	0.980522i	$0.437071\pi$
$458$	10.4327	−	4.17625i	0.487488	−	0.195143i
$459$		0			0
$460$	6.06204	+	6.35847i	0.282644	+	0.296465i
$461$			30.9263i			1.44038i	0.693777	+	0.720190i	$0.255945\pi$
$461$			30.9263i			1.44038i	−0.693777	+	0.720190i	$0.744055\pi$
$462$		0			0
$463$			10.3615i			0.481540i	0.970582	+	0.240770i	$0.0773999\pi$
$463$			10.3615i			0.481540i	−0.970582	+	0.240770i	$0.922600\pi$
$464$	16.9512	+	0.809584i	0.786942	+	0.0375840i
$465$		0			0
$466$	−5.08698	−	12.7078i	−0.235650	−	0.588677i
$467$	25.7366			1.19095			0.595473	−	0.803375i	$-0.296965\pi$
$467$	25.7366			1.19095			0.595473	+	0.803375i	$0.296965\pi$
$468$		0			0
$469$	−39.9241			−1.84353
$470$	−9.11331	−	22.7660i	−0.420366	−	1.05012i
$471$		0			0
$472$	3.71634	−	8.13565i	0.171058	−	0.374474i
$473$			14.7044i			0.676108i
$474$		0			0
$475$			73.8604i			3.38895i
$476$	−3.69870	+	3.52627i	−0.169530	+	0.161626i
$477$		0			0
$478$	−9.63837	+	3.85828i	−0.440849	+	0.176474i
$479$	−31.4251			−1.43585			−0.717924	−	0.696121i	$-0.754908\pi$
$479$	−31.4251			−1.43585			−0.717924	+	0.696121i	$0.754908\pi$
$480$		0			0
$481$	−4.81714			−0.219643
$482$	−23.2865	+	9.32169i	−1.06067	+	0.424591i
$483$		0			0
$484$	−9.60348	+	9.15577i	−0.436522	+	0.416171i
$485$		−	11.3137i		−	0.513729i
$486$		0			0
$487$			21.4816i			0.973426i	0.873562	+	0.486713i	$0.161804\pi$
$487$			21.4816i			0.973426i	−0.873562	+	0.486713i	$0.838196\pi$
$488$	16.2064	−	35.4783i	0.733629	−	1.60603i
$489$		0			0
$490$	14.6114	+	36.5009i	0.660078	+	1.64894i
$491$	−17.3788			−0.784296			−0.392148	−	0.919902i	$-0.628268\pi$
$491$	−17.3788			−0.784296			−0.392148	+	0.919902i	$0.628268\pi$
$492$		0			0
$493$	−2.91921			−0.131475
$494$	3.30000	+	8.24373i	0.148474	+	0.370903i
$495$		0			0
$496$	32.7053	+	1.56199i	1.46851	+	0.0701356i
$497$			40.7340i			1.82717i
$498$		0			0
$499$			9.97198i			0.446407i	0.974772	+	0.223204i	$0.0716515\pi$
$499$			9.97198i			0.446407i	−0.974772	+	0.223204i	$0.928349\pi$
$500$	38.2153	+	40.0841i	1.70904	+	1.79261i
$501$		0			0
$502$	4.76328	−	1.90676i	0.212596	−	0.0851029i
$503$	−32.4417			−1.44650			−0.723251	−	0.690585i	$-0.757353\pi$
$503$	−32.4417			−1.44650			−0.723251	+	0.690585i	$0.757353\pi$
$504$		0			0
$505$	−64.2360			−2.85846
$506$	−2.94311	+	1.17814i	−0.130837	+	0.0523746i
$507$		0			0
$508$	2.09389	+	2.19628i	0.0929014	+	0.0974442i
$509$			21.9238i			0.971755i	0.874027	+	0.485878i	$0.161500\pi$
$509$			21.9238i			0.971755i	−0.874027	+	0.485878i	$0.838500\pi$
$510$		0			0
$511$		−	39.9696i		−	1.76815i
$512$	−21.7126	+	6.36885i	−0.959571	+	0.281466i
$513$		0			0
$514$	−5.77020	−	14.4145i	−0.254512	−	0.635798i
$515$	7.80685			0.344011
$516$		0			0
$517$	8.84900			0.389178
$518$	9.40167	+	23.4863i	0.413086	+	1.03193i
$519$		0			0
$520$	10.5335	+	4.81166i	0.461924	+	0.211005i
$521$		−	30.6140i		−	1.34122i	−0.741808	−	0.670612i	$-0.766031\pi$
$521$		−	30.6140i		−	1.34122i	0.741808	−	0.670612i	$-0.233969\pi$
$522$		0			0
$523$		−	27.2223i		−	1.19035i	−0.803596	−	0.595175i	$-0.797083\pi$
$523$		−	27.2223i		−	1.19035i	0.803596	−	0.595175i	$-0.202917\pi$
$524$	−2.35042	+	2.24084i	−0.102679	+	0.0978917i
$525$		0			0
$526$	−21.3706	+	8.55475i	−0.931804	+	0.373005i
$527$	−5.63226			−0.245345
$528$		0			0
$529$	−21.8490			−0.949956
$530$	3.69870	−	1.48060i	0.160661	−	0.0643133i
$531$		0			0
$532$	33.7523	−	32.1788i	1.46335	−	1.39513i
$533$		−	1.26587i		−	0.0548310i
$534$		0			0
$535$			68.3197i			2.95372i
$536$	27.6594	+	12.6347i	1.19470	+	0.545736i
$537$		0			0
$538$	10.3857	+	25.9446i	0.447761	+	1.11855i
$539$	−14.1877			−0.611106
$540$		0			0
$541$	10.0000			0.429934			0.214967	−	0.976621i	$-0.431036\pi$
$541$	10.0000			0.429934			0.214967	+	0.976621i	$0.431036\pi$
$542$	7.44996	+	18.6108i	0.320003	+	0.799401i
$543$		0			0
$544$	3.67841	−	1.27247i	0.157710	−	0.0545568i
$545$		−	3.98404i		−	0.170658i
$546$		0			0
$547$		−	2.64495i		−	0.113090i	−0.998400	−	0.0565449i	$-0.981992\pi$
$547$		−	2.64495i		−	0.113090i	0.998400	−	0.0565449i	$-0.0180084\pi$
$548$	18.8504	+	19.7722i	0.805249	+	0.844625i
$549$		0			0
$550$	−32.2698	+	12.9177i	−1.37599	+	0.550814i
$551$	26.6391			1.13486
$552$		0			0
$553$	−46.6336			−1.98306
$554$	3.90342	−	1.56256i	0.165841	−	0.0663866i
$555$		0			0
$556$	−30.2119	−	31.6892i	−1.28127	−	1.34392i
$557$			3.15920i			0.133860i	0.997758	+	0.0669298i	$0.0213204\pi$
$557$			3.15920i			0.133860i	−0.997758	+	0.0669298i	$0.978680\pi$
$558$		0			0
$559$		−	7.03751i		−	0.297655i
$560$	2.90129	−	60.7478i	0.122602	−	2.56706i
$561$		0			0
$562$	−15.5307	−	38.7972i	−0.655121	−	1.63656i
$563$	13.6094			0.573569			0.286784	−	0.957995i	$-0.407414\pi$
$563$	13.6094			0.573569			0.286784	+	0.957995i	$0.407414\pi$
$564$		0			0
$565$	−43.1927			−1.81713
$566$	−5.80258	−	14.4954i	−0.243900	−	0.609288i
$567$		0			0
$568$	12.8910	−	28.2205i	0.540895	−	1.18410i
$569$			16.3391i			0.684971i	0.939523	+	0.342486i	$0.111269\pi$
$569$			16.3391i			0.684971i	−0.939523	+	0.342486i	$0.888731\pi$
$570$		0			0
$571$		−	33.2808i		−	1.39276i	−0.717674	−	0.696379i	$-0.754793\pi$
$571$		−	33.2808i		−	1.39276i	0.717674	−	0.696379i	$-0.245207\pi$
$572$	−3.02456	+	2.88356i	−0.126463	+	0.120568i
$573$		0			0
$574$	−6.17185	+	2.47062i	−0.257608	+	0.103122i
$575$	12.6202			0.526300
$576$		0			0
$577$	−9.47271			−0.394354			−0.197177	−	0.980368i	$-0.563177\pi$
$577$	−9.47271			−0.394354			−0.197177	+	0.980368i	$0.563177\pi$
$578$	21.6982	−	8.68586i	0.902525	−	0.361284i
$579$		0			0
$580$	25.1449	−	23.9727i	1.04409	−	0.995411i
$581$		−	62.1747i		−	2.57944i
$582$		0			0
$583$			1.43766i			0.0595419i
$584$	−12.6491	+	27.6909i	−0.523424	+	1.14586i
$585$		0			0
$586$	−6.29959	−	15.7370i	−0.260234	−	0.650090i
$587$	10.0377			0.414300			0.207150	−	0.978309i	$-0.433581\pi$
$587$	10.0377			0.414300			0.207150	+	0.978309i	$0.433581\pi$
$588$		0			0
$589$	51.3968			2.11777
$590$	−6.80471	−	16.9989i	−0.280146	−	0.699832i
$591$		0			0
$592$	0.919211	−	19.2466i	0.0377794	−	0.791032i
$593$			24.1900i			0.993363i	0.867933	+	0.496682i	$0.165448\pi$
$593$			24.1900i			0.993363i	−0.867933	+	0.496682i	$0.834552\pi$
$594$		0			0
$595$			10.4615i			0.428880i
$596$	−13.3521	−	14.0051i	−0.546925	−	0.573669i
$597$		0			0
$598$	1.40857	−	0.563856i	0.0576008	−	0.0230578i
$599$	−38.3857			−1.56840			−0.784198	−	0.620511i	$-0.786925\pi$
$599$	−38.3857			−1.56840			−0.784198	+	0.620511i	$0.786925\pi$
$600$		0			0
$601$	−27.5804			−1.12503			−0.562515	−	0.826787i	$-0.690166\pi$
$601$	−27.5804			−1.12503			−0.562515	+	0.826787i	$0.690166\pi$
$602$	−34.3119	+	13.7352i	−1.39845	+	0.559805i
$603$		0			0
$604$	−2.12208	−	2.22585i	−0.0863464	−	0.0905687i
$605$			27.1627i			1.10432i
$606$		0			0
$607$			21.8916i			0.888552i	0.895890	+	0.444276i	$0.146539\pi$
$607$			21.8916i			0.888552i	−0.895890	+	0.444276i	$0.853461\pi$
$608$	−33.5671	+	11.6119i	−1.36132	+	0.470924i
$609$		0			0
$610$	−29.6743	−	74.1295i	−1.20148	−	3.00142i
$611$	−4.23513			−0.171335
$612$		0			0
$613$	45.9241			1.85486			0.927429	−	0.373999i	$-0.122014\pi$
$613$	45.9241			1.85486			0.927429	+	0.373999i	$0.122014\pi$
$614$	11.8624	+	29.6336i	0.478729	+	1.19591i
$615$		0			0
$616$	19.9621	+	9.11860i	0.804295	+	0.367399i
$617$		−	17.1570i		−	0.690714i	−0.938471	−	0.345357i	$-0.887758\pi$
$617$		−	17.1570i		−	0.690714i	0.938471	−	0.345357i	$-0.112242\pi$
$618$		0			0
$619$		−	9.97198i		−	0.400808i	−0.979713	−	0.200404i	$-0.935775\pi$
$619$		−	9.97198i		−	0.400808i	0.979713	−	0.200404i	$-0.0642254\pi$
$620$	48.5140	−	46.2523i	1.94837	−	1.85754i
$621$		0			0
$622$	8.84125	−	3.53918i	0.354502	−	0.141908i
$623$	5.80258			0.232475
$624$		0			0
$625$	54.5584			2.18234
$626$	17.2085	−	6.88864i	0.687791	−	0.275325i
$627$		0			0
$628$	−20.7633	+	19.7953i	−0.828545	+	0.789919i
$629$			3.31451i			0.132158i
$630$		0			0
$631$			8.18565i			0.325866i	0.986637	+	0.162933i	$0.0520954\pi$
$631$			8.18565i			0.325866i	−0.986637	+	0.162933i	$0.947905\pi$
$632$	32.3077	+	14.7580i	1.28513	+	0.587043i
$633$		0			0
$634$	5.12491	+	12.8025i	0.203536	+	0.508454i
$635$	6.21202			0.246517
$636$		0			0
$637$	6.79021			0.269038
$638$	4.65902	+	11.6387i	0.184452	+	0.460780i
$639$		0			0
$640$	−21.2347	+	41.1678i	−0.839376	+	1.62730i
$641$			10.1846i			0.402268i	0.979564	+	0.201134i	$0.0644627\pi$
$641$			10.1846i			0.402268i	−0.979564	+	0.201134i	$0.935537\pi$
$642$		0			0
$643$		−	40.4592i		−	1.59555i	−0.602953	−	0.797777i	$-0.706009\pi$
$643$		−	40.4592i		−	1.59555i	0.602953	−	0.797777i	$-0.293991\pi$
$644$	−5.49825	−	5.76711i	−0.216661	−	0.227256i
$645$		0			0
$646$	5.67222	−	2.27061i	0.223170	−	0.0893360i
$647$	39.3171			1.54571			0.772857	−	0.634580i	$-0.218827\pi$
$647$	39.3171			1.54571			0.772857	+	0.634580i	$0.218827\pi$
$648$		0			0
$649$	6.60736			0.259361
$650$	15.4443	−	6.18242i	0.605776	−	0.242495i
$651$		0			0
$652$	1.58452	+	1.66200i	0.0620544	+	0.0650888i
$653$		−	15.1835i		−	0.594176i	−0.954850	−	0.297088i	$-0.903984\pi$
$653$		−	15.1835i		−	0.594176i	0.954850	−	0.297088i	$-0.0960155\pi$
$654$		0			0
$655$			6.64799i			0.259758i
$656$	5.05772	+	0.241555i	0.197471	+	0.00943113i
$657$		0			0
$658$	8.26575	+	20.6487i	0.322232	+	0.804969i
$659$	30.4085			1.18455			0.592274	−	0.805737i	$-0.298230\pi$
$659$	30.4085			1.18455			0.592274	+	0.805737i	$0.298230\pi$
$660$		0			0
$661$	−27.9780			−1.08822			−0.544109	−	0.839015i	$-0.683132\pi$
$661$	−27.9780			−1.08822			−0.544109	+	0.839015i	$0.683132\pi$
$662$	−2.15643	−	5.38699i	−0.0838122	−	0.209371i
$663$		0			0
$664$	−19.6763	+	43.0745i	−0.763589	+	1.67162i
$665$		−	95.4659i		−	3.70201i
$666$		0			0
$667$		−	4.55171i		−	0.176243i
$668$	15.2857	−	14.5731i	0.591422	−	0.563850i
$669$		0			0
$670$	57.7923	−	23.1345i	2.23271	−	0.893763i
$671$	28.8137			1.11234
$672$		0			0
$673$	−16.8972			−0.651339			−0.325670	−	0.945484i	$-0.605590\pi$
$673$	−16.8972			−0.651339			−0.325670	+	0.945484i	$0.605590\pi$
$674$	−16.8913	+	6.76164i	−0.650627	+	0.260449i
$675$		0			0
$676$	1.44755	−	1.38007i	0.0556751	−	0.0530796i
$677$		−	14.8302i		−	0.569971i	−0.958532	−	0.284985i	$-0.908011\pi$
$677$		−	14.8302i		−	0.569971i	0.958532	−	0.284985i	$-0.0919888\pi$
$678$		0			0
$679$			10.2615i			0.393800i
$680$	3.31073	−	7.24772i	0.126961	−	0.277937i
$681$		0			0
$682$	8.98900	+	22.4554i	0.344206	+	0.859863i
$683$	2.46998			0.0945112			0.0472556	−	0.998883i	$-0.484952\pi$
$683$	2.46998			0.0945112			0.0472556	+	0.998883i	$0.484952\pi$
$684$		0			0
$685$	55.9241			2.13675
$686$	0.409444	+	1.02283i	0.0156326	+	0.0390519i
$687$		0			0
$688$	28.1180	+	1.34290i	1.07199	+	0.0511977i
$689$		−	0.688065i		−	0.0262132i
$690$		0			0
$691$		−	22.3706i		−	0.851018i	−0.904954	−	0.425509i	$-0.860095\pi$
$691$		−	22.3706i		−	0.851018i	0.904954	−	0.425509i	$-0.139905\pi$
$692$	−18.0530	−	18.9358i	−0.686271	−	0.719830i
$693$		0			0
$694$	−42.7413	+	17.1095i	−1.62244	+	0.649468i
$695$	−89.6307			−3.39989
$696$		0			0
$697$	−0.871002			−0.0329915
$698$	−10.0866	+	4.03769i	−0.381782	+	0.152829i
$699$		0			0
$700$	−60.2858	−	63.2337i	−2.27859	−	2.39001i
$701$			49.1246i			1.85541i	0.373312	+	0.927706i	$0.378222\pi$
$701$			49.1246i			1.85541i	−0.373312	+	0.927706i	$0.621778\pi$
$702$		0			0
$703$		−	30.2463i		−	1.14076i
$704$	−10.9439	−	12.6347i	−0.412465	−	0.476189i
$705$		0			0
$706$	5.84816	+	14.6093i	0.220098	+	0.549829i
$707$	58.2619			2.19116
$708$		0			0
$709$	46.2678			1.73763			0.868813	−	0.495141i	$-0.164884\pi$
$709$	46.2678			1.73763			0.868813	+	0.495141i	$0.164884\pi$
$710$	−23.6038	−	58.9647i	−0.885834	−	2.21291i
$711$		0			0
$712$	−4.02002	−	1.83633i	−0.150656	−	0.0688194i
$713$		−	8.78196i		−	0.328887i
$714$		0			0
$715$			8.55475i			0.319929i
$716$	−11.5055	+	10.9692i	−0.429983	+	0.409937i
$717$		0			0
$718$	−25.3368	+	10.1424i	−0.945561	+	0.378512i
$719$	−6.46598			−0.241140			−0.120570	−	0.992705i	$-0.538472\pi$
$719$	−6.46598			−0.241140			−0.120570	+	0.992705i	$0.538472\pi$
$720$		0			0
$721$	−7.08079			−0.263702
$722$	−26.8159	+	10.7345i	−0.997983	+	0.399497i
$723$		0			0
$724$	−6.89511	+	6.57366i	−0.256255	+	0.244308i
$725$		−	49.9074i		−	1.85351i
$726$		0			0
$727$			7.62704i			0.282871i	0.989947	+	0.141436i	$0.0451718\pi$
$727$			7.62704i			0.282871i	−0.989947	+	0.141436i	$0.954828\pi$
$728$	−9.55384	−	4.36416i	−0.354089	−	0.161747i
$729$		0			0
$730$	23.1609	+	57.8582i	0.857222	+	2.14143i
$731$	−4.84226			−0.179098
$732$		0			0
$733$	−23.0269			−0.850519			−0.425260	−	0.905071i	$-0.639817\pi$
$733$	−23.0269			−0.850519			−0.425260	+	0.905071i	$0.639817\pi$
$734$	−0.204722	−	0.511416i	−0.00755642	−	0.0188767i
$735$		0			0
$736$	1.98407	+	5.73547i	0.0731339	+	0.211412i
$737$			22.4635i			0.827454i
$738$		0			0
$739$		−	4.10304i		−	0.150933i	−0.997148	−	0.0754664i	$-0.975955\pi$
$739$		−	4.10304i		−	0.150933i	0.997148	−	0.0754664i	$-0.0240446\pi$
$740$	−27.2188	−	28.5498i	−1.00058	−	1.04951i
$741$		0			0
$742$	−3.35471	+	1.34290i	−0.123155	+	0.0492996i
$743$	3.54283			0.129974			0.0649869	−	0.997886i	$-0.479299\pi$
$743$	3.54283			0.129974			0.0649869	+	0.997886i	$0.479299\pi$
$744$		0			0
$745$	−39.6123			−1.45128
$746$	17.7594	−	7.10915i	0.650218	−	0.260285i
$747$		0			0
$748$	1.98407	+	2.08109i	0.0725449	+	0.0760923i
$749$		−	61.9658i		−	2.26418i
$750$		0			0
$751$		−	41.2974i		−	1.50696i	−0.657470	−	0.753481i	$-0.728373\pi$
$751$		−	41.2974i		−	1.50696i	0.657470	−	0.753481i	$-0.271627\pi$
$752$	0.808150	−	16.9212i	0.0294702	−	0.617053i
$753$		0			0
$754$	−2.22980	−	5.57028i	−0.0812046	−	0.202858i
$755$	−6.29566			−0.229123
$756$		0			0
$757$	−1.12900			−0.0410341			−0.0205171	−	0.999790i	$-0.506531\pi$
$757$	−1.12900			−0.0410341			−0.0205171	+	0.999790i	$0.506531\pi$
$758$	−2.19826	−	5.49147i	−0.0798442	−	0.199459i
$759$		0			0
$760$	−30.2119	+	66.1386i	−1.09590	+	2.39910i
$761$		−	7.51609i		−	0.272458i	−0.990677	−	0.136229i	$-0.956502\pi$
$761$		−	7.51609i		−	0.272458i	0.990677	−	0.136229i	$-0.0434983\pi$
$762$		0			0
$763$			3.61351i			0.130818i
$764$	−11.5055	+	10.9692i	−0.416256	+	0.396850i
$765$		0			0
$766$	11.5466	−	4.62214i	0.417195	−	0.167005i
$767$	−3.16228			−0.114183
$768$		0			0
$769$	−4.66121			−0.168088			−0.0840439	−	0.996462i	$-0.526784\pi$
$769$	−4.66121			−0.168088			−0.0840439	+	0.996462i	$0.526784\pi$
$770$	41.7093	−	16.6964i	1.50310	−	0.601697i
$771$		0			0
$772$	18.1719	−	17.3247i	0.654019	−	0.623529i
$773$			23.0794i			0.830109i	0.909797	+	0.415054i	$0.136237\pi$
$773$			23.0794i			0.830109i	−0.909797	+	0.415054i	$0.863763\pi$
$774$		0			0
$775$		−	96.2902i		−	3.45884i
$776$	3.24744	−	7.10915i	0.116576	−	0.255204i
$777$		0			0
$778$	−10.1139	−	25.2656i	−0.362601	−	0.905815i
$779$	7.94827			0.284776
$780$		0			0
$781$	22.9192			0.820114
$782$	−0.387970	−	0.969188i	−0.0138738	−	0.0346581i
$783$		0			0
$784$	−1.29571	+	27.1299i	−0.0462755	+	0.968926i
$785$			58.7274i			2.09607i
$786$		0			0
$787$			22.5706i			0.804556i	0.915518	+	0.402278i	$0.131781\pi$
$787$			22.5706i			0.804556i	−0.915518	+	0.402278i	$0.868219\pi$
$788$	24.7581	+	25.9687i	0.881970	+	0.925098i
$789$		0			0
$790$	67.5046	−	27.0223i	2.40170	−	0.961411i
$791$	39.1757			1.39293
$792$		0			0
$793$	−13.7902			−0.489705
$794$	10.3694	−	4.15091i	0.367996	−	0.147310i
$795$		0			0
$796$	−11.3250	−	11.8787i	−0.401402	−	0.421031i
$797$		−	27.3561i		−	0.969004i	−0.874790	−	0.484502i	$-0.839001\pi$
$797$		−	27.3561i		−	0.969004i	0.874790	−	0.484502i	$-0.160999\pi$
$798$		0			0
$799$			2.91404i			0.103091i
$800$	21.7544	+	62.8867i	0.769136	+	2.22338i
$801$		0			0
$802$	0.0579481	+	0.144760i	0.00204622	+	0.00511166i
$803$	−22.4891			−0.793624
$804$		0			0
$805$	−16.3119			−0.574917
$806$	−4.30213	−	10.7472i	−0.151536	−	0.378553i
$807$		0			0
$808$	−40.3637	−	18.4380i	−1.41999	−	0.648647i
$809$			9.24951i			0.325196i	0.986692	+	0.162598i	$0.0519873\pi$
$809$			9.24951i			0.325196i	−0.986692	+	0.162598i	$0.948013\pi$
$810$		0			0
$811$		−	14.2850i		−	0.501613i	−0.968037	−	0.250807i	$-0.919304\pi$
$811$		−	14.2850i		−	0.501613i	0.968037	−	0.250807i	$-0.0806958\pi$
$812$	−22.8064	+	21.7431i	−0.800347	+	0.763035i
$813$		0			0
$814$	13.2147	−	5.28990i	0.463175	−	0.185411i
$815$	4.70084			0.164663
$816$		0			0
$817$	44.1878			1.54593
$818$	29.3357	−	11.7432i	1.02570	−	0.410590i
$819$		0			0
$820$	7.50246	−	7.15270i	0.261997	−	0.249783i
$821$			27.7250i			0.967609i	0.875176	+	0.483804i	$0.160745\pi$
$821$			27.7250i			0.967609i	−0.875176	+	0.483804i	$0.839255\pi$
$822$		0			0
$823$		−	12.2091i		−	0.425583i	−0.977098	−	0.212792i	$-0.931744\pi$
$823$		−	12.2091i		−	0.425583i	0.977098	−	0.212792i	$-0.0682555\pi$
$824$	4.90556	+	2.24084i	0.170893	+	0.0780635i
$825$		0			0
$826$	6.17185	+	15.4179i	0.214746	+	0.536458i
$827$	−31.8345			−1.10699			−0.553497	−	0.832851i	$-0.686707\pi$
$827$	−31.8345			−1.10699			−0.553497	+	0.832851i	$0.686707\pi$
$828$		0			0
$829$	26.2360			0.911214			0.455607	−	0.890181i	$-0.349422\pi$
$829$	26.2360			0.911214			0.455607	+	0.890181i	$0.349422\pi$
$830$	36.0278	+	90.0012i	1.25054	+	3.12399i
$831$		0			0
$832$	5.23777	+	6.04697i	0.181587	+	0.209641i
$833$		−	4.67211i		−	0.161879i
$834$		0			0
$835$		−	43.2345i		−	1.49619i
$836$	−18.1055	−	18.9909i	−0.626193	−	0.656814i
$837$		0			0
$838$	−23.3547	+	9.34898i	−0.806775	+	0.322955i
$839$	44.6251			1.54063			0.770314	−	0.637665i	$-0.220099\pi$
$839$	44.6251			1.54063			0.770314	+	0.637665i	$0.220099\pi$
$840$		0			0
$841$	11.0000			0.379310
$842$	7.46812	−	2.98952i	0.257368	−	0.103026i
$843$		0			0
$844$	9.17468	+	9.62332i	0.315805	+	0.331248i
$845$		−	4.09430i		−	0.140848i
$846$		0			0
$847$		−	24.6365i		−	0.846521i
$848$	2.74913	+	0.131297i	0.0944053	+	0.00450876i
$849$		0			0
$850$	−4.25391	−	10.6267i	−0.145908	−	0.364493i
$851$	−5.16806			−0.177159
$852$		0			0
$853$	−53.5046			−1.83196			−0.915981	−	0.401222i	$-0.868585\pi$
$853$	−53.5046			−1.83196			−0.915981	+	0.401222i	$0.868585\pi$
$854$	26.9145	+	67.2352i	0.920996	+	2.30074i
$855$		0			0
$856$	−19.6102	+	42.9298i	−0.670262	+	1.46731i
$857$			20.5437i			0.701758i	0.936421	+	0.350879i	$0.114117\pi$
$857$			20.5437i			0.701758i	−0.936421	+	0.350879i	$0.885883\pi$
$858$		0			0
$859$		−	13.5368i		−	0.461871i	−0.972969	−	0.230936i	$-0.925821\pi$
$859$		−	13.5368i		−	0.461871i	0.972969	−	0.230936i	$-0.0741786\pi$
$860$	41.7093	−	39.7649i	1.42228	−	1.35597i
$861$		0			0
$862$	17.2567	−	6.90794i	0.587767	−	0.235285i
$863$	−52.8414			−1.79874			−0.899370	−	0.437188i	$-0.855975\pi$
$863$	−52.8414			−1.79874			−0.899370	+	0.437188i	$0.855975\pi$
$864$		0			0
$865$	−53.5584			−1.82104
$866$	37.2132	−	14.8966i	1.26456	−	0.506207i
$867$		0			0
$868$	−44.0021	+	41.9507i	−1.49353	+	1.42390i
$869$			26.2386i			0.890084i
$870$		0			0
$871$		−	10.7510i		−	0.364285i
$872$	1.14356	−	2.50344i	0.0387259	−	0.0847771i
$873$		0			0
$874$	3.54039	+	8.84427i	0.119756	+	0.299162i
$875$	−102.831			−3.47631
$876$		0			0
$877$	12.3976			0.418636			0.209318	−	0.977848i	$-0.432876\pi$
$877$	12.3976			0.418636			0.209318	+	0.977848i	$0.432876\pi$
$878$	−18.9030	−	47.2215i	−0.637944	−	1.59365i
$879$		0			0
$880$	−34.1800	−	1.63242i	−1.15221	−	0.0550290i
$881$			51.1392i			1.72292i	0.507823	+	0.861461i	$0.330450\pi$
$881$			51.1392i			1.72292i	−0.507823	+	0.861461i	$0.669550\pi$
$882$		0			0
$883$			33.1216i			1.11463i	0.830300	+	0.557316i	$0.188169\pi$
$883$			33.1216i			1.11463i	−0.830300	+	0.557316i	$0.811831\pi$
$884$	−0.949577	−	0.996010i	−0.0319377	−	0.0334995i
$885$		0			0
$886$	45.5964	−	18.2524i	1.53184	−	0.613201i
$887$	−5.25171			−0.176335			−0.0881675	−	0.996106i	$-0.528101\pi$
$887$	−5.25171			−0.176335			−0.0881675	+	0.996106i	$0.528101\pi$
$888$		0			0
$889$	−5.63429			−0.188968
$890$	−8.39954	+	3.36237i	−0.281553	+	0.112707i
$891$		0			0
$892$	−15.4845	−	16.2417i	−0.518461	−	0.543813i
$893$		−	26.5919i		−	0.889864i
$894$		0			0
$895$			32.5426i			1.08778i
$896$	19.2598	−	37.3391i	0.643426	−	1.24741i
$897$		0			0
$898$	0.625272	+	1.56199i	0.0208656	+	0.0521244i
$899$	−34.7288			−1.15827
$900$		0			0
$901$	−0.473433			−0.0157723
$902$	1.39011	+	3.47263i	0.0462854	+	0.115626i
$903$		0			0
$904$	−27.1408	−	12.3978i	−0.902691	−	0.412346i
$905$			19.5023i			0.648279i
$906$		0			0
$907$			38.4524i			1.27679i	0.769708	+	0.638396i	$0.220402\pi$
$907$			38.4524i			1.27679i	−0.769708	+	0.638396i	$0.779598\pi$
$908$	−10.0340	+	9.56621i	−0.332990	+	0.317466i
$909$		0			0
$910$	−19.9621	+	7.99089i	−0.661736	+	0.264895i
$911$	34.6163			1.14689			0.573444	−	0.819245i	$-0.305607\pi$
$911$	34.6163			1.14689			0.573444	+	0.819245i	$0.305607\pi$
$912$		0			0
$913$	−34.9829			−1.15777
$914$	11.0254	−	4.41351i	0.364688	−	0.145986i
$915$		0			0
$916$	11.5025	−	10.9662i	0.380052	−	0.362334i
$917$		−	6.02971i		−	0.199118i
$918$		0			0
$919$		−	27.6119i		−	0.910831i	−0.890279	−	0.455416i	$-0.849491\pi$
$919$		−	27.6119i		−	0.910831i	0.890279	−	0.455416i	$-0.150509\pi$
$920$	11.3008	+	5.16218i	0.372577	+	0.170192i
$921$		0			0
$922$	16.2539	+	40.6039i	0.535294	+	1.33722i
$923$	−10.9691			−0.361053
$924$		0			0
$925$	−56.6654			−1.86315
$926$	5.44569	+	13.6039i	0.178957	+	0.447052i
$927$		0			0
$928$	22.6812	−	7.84613i	0.744548	−	0.257562i
$929$		−	34.6818i		−	1.13787i	−0.822381	−	0.568937i	$-0.807355\pi$
$929$		−	34.6818i		−	1.13787i	0.822381	−	0.568937i	$-0.192645\pi$
$930$		0			0
$931$			42.6350i			1.39731i
$932$	−13.3577	−	14.0108i	−0.437545	−	0.458940i
$933$		0			0
$934$	33.7902	−	13.5264i	1.10565	−	0.442596i
$935$	5.88622			0.192500
$936$		0			0
$937$	55.5046			1.81325			0.906627	−	0.421932i	$-0.138648\pi$
$937$	55.5046			1.81325			0.906627	+	0.421932i	$0.138648\pi$
$938$	−52.4175	+	20.9829i	−1.71149	+	0.685116i
$939$		0			0
$940$	−23.9302	−	25.1004i	−0.780518	−	0.818684i
$941$		−	50.9908i		−	1.66225i	−0.556083	−	0.831127i	$-0.687696\pi$
$941$		−	50.9908i		−	1.66225i	0.556083	−	0.831127i	$-0.312304\pi$
$942$		0			0
$943$		−	1.35809i		−	0.0442254i
$944$	0.603429	−	12.6347i	0.0196399	−	0.411225i
$945$		0			0
$946$	7.72818	+	19.3058i	0.251265	+	0.627685i
$947$	16.1919			0.526167			0.263084	−	0.964773i	$-0.415260\pi$
$947$	16.1919			0.526167			0.263084	+	0.964773i	$0.415260\pi$
$948$		0			0
$949$	10.7633			0.349391
$950$	38.8188	+	96.9733i	1.25945	+	3.14623i
$951$		0			0
$952$	−3.00282	+	6.57366i	−0.0973221	+	0.213053i
$953$		−	12.7279i		−	0.412298i	−0.978521	−	0.206149i	$-0.933907\pi$
$953$		−	12.7279i		−	0.412298i	0.978521	−	0.206149i	$-0.0660931\pi$
$954$		0			0
$955$			32.5426i			1.05305i
$956$	−10.6267	+	10.1313i	−0.343692	+	0.327669i
$957$		0			0
$958$	−41.2588	+	16.5161i	−1.33301	+	0.533610i
$959$	−50.7230			−1.63793
$960$		0			0
$961$	−36.0049			−1.16145
$962$	−6.32456	+	2.53174i	−0.203912	+	0.0816267i
$963$		0			0
$964$	−25.6743	+	24.4774i	−0.826914	+	0.788364i
$965$		−	51.3978i		−	1.65455i
$966$		0			0
$967$			38.4728i			1.23720i	0.785705	+	0.618601i	$0.212300\pi$
$967$			38.4728i			1.23720i	−0.785705	+	0.618601i	$0.787700\pi$
$968$	−7.79667	+	17.0682i	−0.250595	+	0.548591i
$969$		0			0
$970$	−5.94614	−	14.8541i	−0.190919	−	0.476935i
$971$	−26.6680			−0.855816			−0.427908	−	0.903822i	$-0.640749\pi$
$971$	−26.6680			−0.855816			−0.427908	+	0.903822i	$0.640749\pi$
$972$		0			0
$973$	81.2948			2.60619
$974$	11.2901	+	28.2038i	0.361758	+	0.903708i
$975$		0			0
$976$	2.63146	−	55.0980i	0.0842310	−	1.76365i
$977$			48.7558i			1.55984i	0.625882	+	0.779918i	$0.284739\pi$
$977$			48.7558i			1.55984i	−0.625882	+	0.779918i	$0.715261\pi$
$978$		0			0
$979$		−	3.26485i		−	0.104345i
$980$	38.3675	+	40.2437i	1.22561	+	1.28554i
$981$		0			0
$982$	−22.8171	+	9.13379i	−0.728124	+	0.291471i
$983$	16.1919			0.516443			0.258221	−	0.966086i	$-0.416864\pi$
$983$	16.1919			0.516443			0.258221	+	0.966086i	$0.416864\pi$
$984$		0			0
$985$	73.4507			2.34033
$986$	−3.83271	+	1.53425i	−0.122058	+	0.0488604i
$987$		0			0
$988$	8.66530	+	9.08903i	0.275680	+	0.289161i
$989$		−	7.55018i		−	0.240082i
$990$		0			0
$991$		−	32.1939i		−	1.02267i	−0.859380	−	0.511337i	$-0.829150\pi$
$991$		−	32.1939i		−	1.02267i	0.859380	−	0.511337i	$-0.170850\pi$
$992$	43.7606	−	15.1381i	1.38940	−	0.480637i
$993$		0			0
$994$	21.4086	+	53.4808i	0.679039	+	1.69631i
$995$	−33.5982			−1.06513
$996$		0			0
$997$	17.1609			0.543490			0.271745	−	0.962369i	$-0.412399\pi$
$997$	17.1609			0.543490			0.271745	+	0.962369i	$0.412399\pi$
$998$	5.24097	+	13.0925i	0.165900	+	0.414435i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	468.2.c.c.287.11	yes	12
3.2	odd	2	inner	468.2.c.c.287.2	yes	12
4.3	odd	2	inner	468.2.c.c.287.1	✓	12
8.3	odd	2		7488.2.d.m.4031.11		12
8.5	even	2		7488.2.d.m.4031.12		12
12.11	even	2	inner	468.2.c.c.287.12	yes	12
24.5	odd	2		7488.2.d.m.4031.2		12
24.11	even	2		7488.2.d.m.4031.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
468.2.c.c.287.1	✓	12	4.3	odd	2	inner
468.2.c.c.287.2	yes	12	3.2	odd	2	inner
468.2.c.c.287.11	yes	12	1.1	even	1	trivial
468.2.c.c.287.12	yes	12	12.11	even	2	inner
7488.2.d.m.4031.1		12	24.11	even	2
7488.2.d.m.4031.2		12	24.5	odd	2
7488.2.d.m.4031.11		12	8.3	odd	2
7488.2.d.m.4031.12		12	8.5	even	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:	\( N \)	\(=\)	\( 468 = 2^{2} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	468.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.31293 - 0.525570i) q^{2} +(1.44755 - 1.38007i) q^{4} -4.09430i q^{5} +3.71352i q^{7} +(1.17521 - 2.57272i) q^{8} +O(q^{10})\)	\(q+(1.31293 - 0.525570i) q^{2} +(1.44755 - 1.38007i) q^{4} -4.09430i q^{5} +3.71352i q^{7} +(1.17521 - 2.57272i) q^{8} +(-2.15184 - 5.37551i) q^{10} +2.08943 q^{11} -1.00000 q^{13} +(1.95171 + 4.87558i) q^{14} +(0.190821 - 3.99545i) q^{16} +0.688065i q^{17} -6.27889i q^{19} +(-5.65041 - 5.92672i) q^{20} +(2.74327 - 1.09814i) q^{22} -1.07285 q^{23} -11.7633 q^{25} +(-1.31293 + 0.525570i) q^{26} +(5.12491 + 5.37551i) q^{28} +4.24264i q^{29} +8.18565i q^{31} +(-1.84935 - 5.34602i) q^{32} +(0.361626 + 0.903379i) q^{34} +15.2043 q^{35} +4.81714 q^{37} +(-3.30000 - 8.24373i) q^{38} +(-10.5335 - 4.81166i) q^{40} +1.26587i q^{41} +7.03751i q^{43} +(3.02456 - 2.88356i) q^{44} +(-1.40857 + 0.563856i) q^{46} +4.23513 q^{47} -6.79021 q^{49} +(-15.4443 + 6.18242i) q^{50} +(-1.44755 + 1.38007i) q^{52} +0.688065i q^{53} -8.55475i q^{55} +(9.55384 + 4.36416i) q^{56} +(2.22980 + 5.57028i) q^{58} +3.16228 q^{59} +13.7902 q^{61} +(4.30213 + 10.7472i) q^{62} +(-5.23777 - 6.04697i) q^{64} +4.09430i q^{65} +10.7510i q^{67} +(0.949577 + 0.996010i) q^{68} +(19.9621 - 7.99089i) q^{70} +10.9691 q^{71} -10.7633 q^{73} +(6.32456 - 2.53174i) q^{74} +(-8.66530 - 9.08903i) q^{76} +7.75913i q^{77} +12.5578i q^{79} +(-16.3585 - 0.781278i) q^{80} +(0.665304 + 1.66200i) q^{82} -16.7428 q^{83} +2.81714 q^{85} +(3.69870 + 9.23974i) q^{86} +(2.45552 - 5.37551i) q^{88} -1.56256i q^{89} -3.71352i q^{91} +(-1.55301 + 1.48060i) q^{92} +(5.56041 - 2.22585i) q^{94} -25.7077 q^{95} +2.76328 q^{97} +(-8.91505 + 3.56873i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q+O(q^{10}) \) 12 * q	\( 12 q + 4 q^{10} - 12 q^{13} - 20 q^{16} + 28 q^{22} - 52 q^{25} + 12 q^{28} + 44 q^{34} + 8 q^{37} - 52 q^{40} + 8 q^{46} - 12 q^{49} + 12 q^{58} + 96 q^{61} + 24 q^{64} + 56 q^{70} - 40 q^{73} - 84 q^{76} - 12 q^{82} - 16 q^{85} - 60 q^{88} + 12 q^{94} - 56 q^{97}+O(q^{100}) \) 12 * q + 4 * q^10 - 12 * q^13 - 20 * q^16 + 28 * q^22 - 52 * q^25 + 12 * q^28 + 44 * q^34 + 8 * q^37 - 52 * q^40 + 8 * q^46 - 12 * q^49 + 12 * q^58 + 96 * q^61 + 24 * q^64 + 56 * q^70 - 40 * q^73 - 84 * q^76 - 12 * q^82 - 16 * q^85 - 60 * q^88 + 12 * q^94 - 56 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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