LMFDB - Embedded newform 1248.2.bb.f.463.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1248,2,Mod(463,1248)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1248, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 0, 1]))

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

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

chi := DirichletCharacter("1248.463");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1248 = 2^{5} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1248.bb (of order $4$, degree $2$, not 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:	$9.96533017226$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			463.11
Character	$\chi$	$=$	1248.463
Dual form			1248.2.bb.f.655.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{3} +(1.98058 - 1.98058i) q^{5} +(3.05943 + 3.05943i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{3} +(1.98058 - 1.98058i) q^{5} +(3.05943 + 3.05943i) q^{7} +1.00000 q^{9} +(1.08518 - 1.08518i) q^{11} +(-3.57990 + 0.429300i) q^{13} +(1.98058 - 1.98058i) q^{15} +5.70052i q^{17} +(4.39498 + 4.39498i) q^{19} +(3.05943 + 3.05943i) q^{21} +2.95135 q^{23} -2.84537i q^{25} +1.00000 q^{27} -6.96062i q^{29} +(-3.05943 + 3.05943i) q^{31} +(1.08518 - 1.08518i) q^{33} +12.1189 q^{35} +(-5.14026 - 5.14026i) q^{37} +(-3.57990 + 0.429300i) q^{39} +(-2.77963 - 2.77963i) q^{41} +3.00392i q^{43} +(1.98058 - 1.98058i) q^{45} +(-6.40146 - 6.40146i) q^{47} +11.7202i q^{49} +5.70052i q^{51} -4.28172i q^{53} -4.29856i q^{55} +(4.39498 + 4.39498i) q^{57} +(-3.00033 + 3.00033i) q^{59} +1.13106i q^{61} +(3.05943 + 3.05943i) q^{63} +(-6.24001 + 7.94053i) q^{65} +(-7.39889 - 7.39889i) q^{67} +2.95135 q^{69} +(3.20281 - 3.20281i) q^{71} +(7.87480 - 7.87480i) q^{73} -2.84537i q^{75} +6.64004 q^{77} -4.46803i q^{79} +1.00000 q^{81} +(9.78962 + 9.78962i) q^{83} +(11.2903 + 11.2903i) q^{85} -6.96062i q^{87} +(4.24001 - 4.24001i) q^{89} +(-12.2659 - 9.63903i) q^{91} +(-3.05943 + 3.05943i) q^{93} +17.4092 q^{95} +(-11.5753 - 11.5753i) q^{97} +(1.08518 - 1.08518i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{3} + 24 q^{9}+O(q^{10}) $ 24 * q + 24 * q^3 + 24 * q^9	$ 24 q + 24 q^{3} + 24 q^{9} - 8 q^{11} - 20 q^{19} + 24 q^{27} - 8 q^{33} - 16 q^{35} - 12 q^{41} - 20 q^{57} + 16 q^{59} - 76 q^{65} - 28 q^{67} - 8 q^{73} + 24 q^{81} + 72 q^{83} + 28 q^{89} + 4 q^{91} + 24 q^{97} - 8 q^{99}+O(q^{100}) $ 24 * q + 24 * q^3 + 24 * q^9 - 8 * q^11 - 20 * q^19 + 24 * q^27 - 8 * q^33 - 16 * q^35 - 12 * q^41 - 20 * q^57 + 16 * q^59 - 76 * q^65 - 28 * q^67 - 8 * q^73 + 24 * q^81 + 72 * q^83 + 28 * q^89 + 4 * q^91 + 24 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1248\mathbb{Z}\right)^\times$.

$n$	$703$	$769$	$833$	$1093$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$		0			0
$5$	1.98058	−	1.98058i	0.885741	−	0.885741i	−0.108370	−	0.994111i	$-0.534563\pi$
$5$	1.98058	−	1.98058i	0.885741	−	0.885741i	0.994111	+	0.108370i	$0.0345630\pi$
$6$		0			0
$7$	3.05943	+	3.05943i	1.15635	+	1.15635i	0.985254	+	0.171100i	$0.0547323\pi$
$7$	3.05943	+	3.05943i	1.15635	+	1.15635i	0.171100	+	0.985254i	$0.445268\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	1.08518	−	1.08518i	0.327194	−	0.327194i	−0.524325	−	0.851518i	$-0.675682\pi$
$11$	1.08518	−	1.08518i	0.327194	−	0.327194i	0.851518	+	0.524325i	$0.175682\pi$
$12$		0			0
$13$	−3.57990	+	0.429300i	−0.992886	+	0.119066i
$13$	−3.57990	+	0.429300i	−0.992886	+	0.119066i
$14$		0			0
$15$	1.98058	−	1.98058i	0.511383	−	0.511383i
$16$		0			0
$17$			5.70052i			1.38258i	0.722578	+	0.691290i	$0.242957\pi$
$17$			5.70052i			1.38258i	−0.722578	+	0.691290i	$0.757043\pi$
$18$		0			0
$19$	4.39498	+	4.39498i	1.00828	+	1.00828i	0.999965	+	0.00831097i	$0.00264550\pi$
$19$	4.39498	+	4.39498i	1.00828	+	1.00828i	0.00831097	+	0.999965i	$0.497355\pi$
$20$		0			0
$21$	3.05943	+	3.05943i	0.667621	+	0.667621i
$22$		0			0
$23$	2.95135			0.615398			0.307699	−	0.951484i	$-0.400441\pi$
$23$	2.95135			0.615398			0.307699	+	0.951484i	$0.400441\pi$
$24$		0			0
$25$		−	2.84537i		−	0.569074i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$		−	6.96062i		−	1.29255i	−0.763103	−	0.646277i	$-0.776325\pi$
$29$		−	6.96062i		−	1.29255i	0.763103	−	0.646277i	$-0.223675\pi$
$30$		0			0
$31$	−3.05943	+	3.05943i	−0.549489	+	0.549489i	−0.926293	−	0.376804i	$-0.877023\pi$
$31$	−3.05943	+	3.05943i	−0.549489	+	0.549489i	0.376804	+	0.926293i	$0.377023\pi$
$32$		0			0
$33$	1.08518	−	1.08518i	0.188905	−	0.188905i
$34$		0			0
$35$	12.1189			2.04846
$36$		0			0
$37$	−5.14026	−	5.14026i	−0.845053	−	0.845053i	0.144458	−	0.989511i	$-0.453856\pi$
$37$	−5.14026	−	5.14026i	−0.845053	−	0.845053i	−0.989511	+	0.144458i	$0.953856\pi$
$38$		0			0
$39$	−3.57990	+	0.429300i	−0.573243	+	0.0687430i
$40$		0			0
$41$	−2.77963	−	2.77963i	−0.434106	−	0.434106i	0.455917	−	0.890022i	$-0.349311\pi$
$41$	−2.77963	−	2.77963i	−0.434106	−	0.434106i	−0.890022	+	0.455917i	$0.849311\pi$
$42$		0			0
$43$			3.00392i			0.458093i	0.973415	+	0.229046i	$0.0735608\pi$
$43$			3.00392i			0.458093i	−0.973415	+	0.229046i	$0.926439\pi$
$44$		0			0
$45$	1.98058	−	1.98058i	0.295247	−	0.295247i
$46$		0			0
$47$	−6.40146	−	6.40146i	−0.933749	−	0.933749i	0.0641887	−	0.997938i	$-0.479554\pi$
$47$	−6.40146	−	6.40146i	−0.933749	−	0.933749i	−0.997938	+	0.0641887i	$0.979554\pi$
$48$		0			0
$49$			11.7202i			1.67431i
$50$		0			0
$51$			5.70052i			0.798233i
$52$		0			0
$53$		−	4.28172i		−	0.588140i	−0.955784	−	0.294070i	$-0.904990\pi$
$53$		−	4.28172i		−	0.588140i	0.955784	−	0.294070i	$-0.0950099\pi$
$54$		0			0
$55$		−	4.29856i		−	0.579618i
$56$		0			0
$57$	4.39498	+	4.39498i	0.582129	+	0.582129i
$58$		0			0
$59$	−3.00033	+	3.00033i	−0.390610	+	0.390610i	−0.874905	−	0.484295i	$-0.839076\pi$
$59$	−3.00033	+	3.00033i	−0.390610	+	0.390610i	0.484295	+	0.874905i	$0.339076\pi$
$60$		0			0
$61$			1.13106i			0.144817i	0.997375	+	0.0724084i	$0.0230685\pi$
$61$			1.13106i			0.144817i	−0.997375	+	0.0724084i	$0.976932\pi$
$62$		0			0
$63$	3.05943	+	3.05943i	0.385451	+	0.385451i
$64$		0			0
$65$	−6.24001	+	7.94053i	−0.773978	+	0.984902i
$66$		0			0
$67$	−7.39889	−	7.39889i	−0.903918	−	0.903918i	0.0918540	−	0.995772i	$-0.470721\pi$
$67$	−7.39889	−	7.39889i	−0.903918	−	0.903918i	−0.995772	+	0.0918540i	$0.970721\pi$
$68$		0			0
$69$	2.95135			0.355300
$70$		0			0
$71$	3.20281	−	3.20281i	0.380104	−	0.380104i	−0.491036	−	0.871139i	$-0.663382\pi$
$71$	3.20281	−	3.20281i	0.380104	−	0.380104i	0.871139	+	0.491036i	$0.163382\pi$
$72$		0			0
$73$	7.87480	−	7.87480i	0.921675	−	0.921675i	−0.0754728	−	0.997148i	$-0.524047\pi$
$73$	7.87480	−	7.87480i	0.921675	−	0.921675i	0.997148	+	0.0754728i	$0.0240466\pi$
$74$		0			0
$75$		−	2.84537i		−	0.328555i
$76$		0			0
$77$	6.64004			0.756703
$78$		0			0
$79$		−	4.46803i		−	0.502693i	−0.967897	−	0.251347i	$-0.919127\pi$
$79$		−	4.46803i		−	0.502693i	0.967897	−	0.251347i	$-0.0808734\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	9.78962	+	9.78962i	1.07455	+	1.07455i	0.996987	+	0.0775625i	$0.0247137\pi$
$83$	9.78962	+	9.78962i	1.07455	+	1.07455i	0.0775625	+	0.996987i	$0.475286\pi$
$84$		0			0
$85$	11.2903	+	11.2903i	1.22461	+	1.22461i
$86$		0			0
$87$		−	6.96062i		−	0.746256i
$88$		0			0
$89$	4.24001	−	4.24001i	0.449440	−	0.449440i	−0.445728	−	0.895168i	$-0.647055\pi$
$89$	4.24001	−	4.24001i	0.449440	−	0.449440i	0.895168	+	0.445728i	$0.147055\pi$
$90$		0			0
$91$	−12.2659	−	9.63903i	−1.28581	−	1.01045i
$92$		0			0
$93$	−3.05943	+	3.05943i	−0.317248	+	0.317248i
$94$		0			0
$95$	17.4092			1.78614
$96$		0			0
$97$	−11.5753	−	11.5753i	−1.17530	−	1.17530i	−0.980929	−	0.194366i	$-0.937735\pi$
$97$	−11.5753	−	11.5753i	−1.17530	−	1.17530i	−0.194366	−	0.980929i	$-0.562265\pi$
$98$		0			0
$99$	1.08518	−	1.08518i	0.109065	−	0.109065i
$100$		0			0
$101$	−5.67835			−0.565017			−0.282509	−	0.959265i	$-0.591167\pi$
$101$	−5.67835			−0.565017			−0.282509	+	0.959265i	$0.591167\pi$
$102$		0			0
$103$	1.20900			0.119126			0.0595630	−	0.998225i	$-0.481029\pi$
$103$	1.20900			0.119126			0.0595630	+	0.998225i	$0.481029\pi$
$104$		0			0
$105$	12.1189			1.18268
$106$		0			0
$107$	11.6314			1.12445			0.562225	−	0.826984i	$-0.309945\pi$
$107$	11.6314			1.12445			0.562225	+	0.826984i	$0.309945\pi$
$108$		0			0
$109$	7.32910	−	7.32910i	0.702001	−	0.702001i	−0.262839	−	0.964840i	$-0.584659\pi$
$109$	7.32910	−	7.32910i	0.702001	−	0.702001i	0.964840	+	0.262839i	$0.0846588\pi$
$110$		0			0
$111$	−5.14026	−	5.14026i	−0.487892	−	0.487892i
$112$		0			0
$113$	15.2598			1.43552			0.717760	−	0.696291i	$-0.245168\pi$
$113$	15.2598			1.43552			0.717760	+	0.696291i	$0.245168\pi$
$114$		0			0
$115$	5.84537	−	5.84537i	0.545084	−	0.545084i
$116$		0			0
$117$	−3.57990	+	0.429300i	−0.330962	+	0.0396888i
$118$		0			0
$119$	−17.4403	+	17.4403i	−1.59875	+	1.59875i
$120$		0			0
$121$			8.64478i			0.785889i
$122$		0			0
$123$	−2.77963	−	2.77963i	−0.250631	−	0.250631i
$124$		0			0
$125$	4.26741	+	4.26741i	0.381689	+	0.381689i
$126$		0			0
$127$	−5.22910			−0.464008			−0.232004	−	0.972715i	$-0.574528\pi$
$127$	−5.22910			−0.464008			−0.232004	+	0.972715i	$0.574528\pi$
$128$		0			0
$129$			3.00392i			0.264480i
$130$		0			0
$131$	−17.2100			−1.50364			−0.751821	−	0.659367i	$-0.770824\pi$
$131$	−17.2100			−1.50364			−0.751821	+	0.659367i	$0.770824\pi$
$132$		0			0
$133$			26.8922i			2.33185i
$134$		0			0
$135$	1.98058	−	1.98058i	0.170461	−	0.170461i
$136$		0			0
$137$	2.23218	−	2.23218i	0.190708	−	0.190708i	−0.605294	−	0.796002i	$-0.706944\pi$
$137$	2.23218	−	2.23218i	0.190708	−	0.190708i	0.796002	+	0.605294i	$0.206944\pi$
$138$		0			0
$139$	−16.1346			−1.36852			−0.684259	−	0.729239i	$-0.739874\pi$
$139$	−16.1346			−1.36852			−0.684259	+	0.729239i	$0.739874\pi$
$140$		0			0
$141$	−6.40146	−	6.40146i	−0.539100	−	0.539100i
$142$		0			0
$143$	−3.41897	+	4.35070i	−0.285908	+	0.363824i
$144$		0			0
$145$	−13.7860	−	13.7860i	−1.14487	−	1.14487i
$146$		0			0
$147$			11.7202i			0.966663i
$148$		0			0
$149$	−9.30975	+	9.30975i	−0.762684	+	0.762684i	−0.976807	−	0.214123i	$-0.931311\pi$
$149$	−9.30975	+	9.30975i	−0.762684	+	0.762684i	0.214123	+	0.976807i	$0.431311\pi$
$150$		0			0
$151$	6.21009	+	6.21009i	0.505370	+	0.505370i	0.913102	−	0.407732i	$-0.133680\pi$
$151$	6.21009	+	6.21009i	0.505370	+	0.505370i	−0.407732	+	0.913102i	$0.633680\pi$
$152$		0			0
$153$			5.70052i			0.460860i
$154$		0			0
$155$			12.1189i			0.973410i
$156$		0			0
$157$		−	13.0048i		−	1.03789i	−0.854807	−	0.518947i	$-0.826324\pi$
$157$		−	13.0048i		−	1.03789i	0.854807	−	0.518947i	$-0.173676\pi$
$158$		0			0
$159$		−	4.28172i		−	0.339563i
$160$		0			0
$161$	9.02943	+	9.02943i	0.711618	+	0.711618i
$162$		0			0
$163$	−4.16037	+	4.16037i	−0.325865	+	0.325865i	−0.851012	−	0.525146i	$-0.824011\pi$
$163$	−4.16037	+	4.16037i	−0.325865	+	0.325865i	0.525146	+	0.851012i	$0.324011\pi$
$164$		0			0
$165$		−	4.29856i		−	0.334642i
$166$		0			0
$167$	9.56896	+	9.56896i	0.740469	+	0.740469i	0.972668	−	0.232199i	$-0.0745922\pi$
$167$	9.56896	+	9.56896i	0.740469	+	0.740469i	−0.232199	+	0.972668i	$0.574592\pi$
$168$		0			0
$169$	12.6314	−	3.07370i	0.971646	−	0.236439i
$170$		0			0
$171$	4.39498	+	4.39498i	0.336092	+	0.336092i
$172$		0			0
$173$	−10.9034			−0.828968			−0.414484	−	0.910057i	$-0.636038\pi$
$173$	−10.9034			−0.828968			−0.414484	+	0.910057i	$0.636038\pi$
$174$		0			0
$175$	8.70520	−	8.70520i	0.658051	−	0.658051i
$176$		0			0
$177$	−3.00033	+	3.00033i	−0.225519	+	0.225519i
$178$		0			0
$179$		−	6.70998i		−	0.501527i	−0.968048	−	0.250764i	$-0.919318\pi$
$179$		−	6.70998i		−	0.501527i	0.968048	−	0.250764i	$-0.0806817\pi$
$180$		0			0
$181$	−15.8485			−1.17801			−0.589003	−	0.808131i	$-0.700479\pi$
$181$	−15.8485			−1.17801			−0.589003	+	0.808131i	$0.700479\pi$
$182$		0			0
$183$			1.13106i			0.0836100i
$184$		0			0
$185$	−20.3614			−1.49700
$186$		0			0
$187$	6.18608	+	6.18608i	0.452371	+	0.452371i
$188$		0			0
$189$	3.05943	+	3.05943i	0.222540	+	0.222540i
$190$		0			0
$191$		−	17.4715i		−	1.26419i	−0.774890	−	0.632096i	$-0.782195\pi$
$191$		−	17.4715i		−	1.26419i	0.774890	−	0.632096i	$-0.217805\pi$
$192$		0			0
$193$	12.6490	−	12.6490i	0.910496	−	0.910496i	−0.0858148	−	0.996311i	$-0.527349\pi$
$193$	12.6490	−	12.6490i	0.910496	−	0.910496i	0.996311	+	0.0858148i	$0.0273493\pi$
$194$		0			0
$195$	−6.24001	+	7.94053i	−0.446856	+	0.568633i
$196$		0			0
$197$	4.24269	−	4.24269i	0.302279	−	0.302279i	−0.539626	−	0.841905i	$-0.681434\pi$
$197$	4.24269	−	4.24269i	0.302279	−	0.302279i	0.841905	+	0.539626i	$0.181434\pi$
$198$		0			0
$199$	−8.86969			−0.628755			−0.314378	−	0.949298i	$-0.601796\pi$
$199$	−8.86969			−0.628755			−0.314378	+	0.949298i	$0.601796\pi$
$200$		0			0
$201$	−7.39889	−	7.39889i	−0.521878	−	0.521878i
$202$		0			0
$203$	21.2955	−	21.2955i	1.49465	−	1.49465i
$204$		0			0
$205$	−11.0105			−0.769010
$206$		0			0
$207$	2.95135			0.205133
$208$		0			0
$209$	9.53866			0.659803
$210$		0			0
$211$	−8.48028			−0.583807			−0.291903	−	0.956448i	$-0.594289\pi$
$211$	−8.48028			−0.583807			−0.291903	+	0.956448i	$0.594289\pi$
$212$		0			0
$213$	3.20281	−	3.20281i	0.219453	−	0.219453i
$214$		0			0
$215$	5.94949	+	5.94949i	0.405752	+	0.405752i
$216$		0			0
$217$	−18.7202			−1.27081
$218$		0			0
$219$	7.87480	−	7.87480i	0.532129	−	0.532129i
$220$		0			0
$221$	−2.44723	−	20.4073i	−0.164619	−	1.37274i
$222$		0			0
$223$	−16.9807	+	16.9807i	−1.13711	+	1.13711i	−0.148143	+	0.988966i	$0.547330\pi$
$223$	−16.9807	+	16.9807i	−1.13711	+	1.13711i	−0.988966	+	0.148143i	$0.952670\pi$
$224$		0			0
$225$		−	2.84537i		−	0.189691i
$226$		0			0
$227$	−8.63107	−	8.63107i	−0.572864	−	0.572864i	0.360064	−	0.932928i	$-0.382755\pi$
$227$	−8.63107	−	8.63107i	−0.572864	−	0.572864i	−0.932928	+	0.360064i	$0.882755\pi$
$228$		0			0
$229$	4.16041	+	4.16041i	0.274928	+	0.274928i	0.831080	−	0.556153i	$-0.187723\pi$
$229$	4.16041	+	4.16041i	0.274928	+	0.274928i	−0.556153	+	0.831080i	$0.687723\pi$
$230$		0			0
$231$	6.64004			0.436883
$232$		0			0
$233$		−	2.78928i		−	0.182732i	−0.995817	−	0.0913660i	$-0.970877\pi$
$233$		−	2.78928i		−	0.182732i	0.995817	−	0.0913660i	$-0.0291233\pi$
$234$		0			0
$235$	−25.3572			−1.65412
$236$		0			0
$237$		−	4.46803i		−	0.290230i
$238$		0			0
$239$	−3.17166	+	3.17166i	−0.205158	+	0.205158i	−0.802206	−	0.597048i	$-0.796340\pi$
$239$	−3.17166	+	3.17166i	−0.205158	+	0.205158i	0.597048	+	0.802206i	$0.296340\pi$
$240$		0			0
$241$	−19.8233	+	19.8233i	−1.27693	+	1.27693i	−0.334554	+	0.942377i	$0.608586\pi$
$241$	−19.8233	+	19.8233i	−1.27693	+	1.27693i	−0.942377	+	0.334554i	$0.891414\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	23.2127	+	23.2127i	1.48300	+	1.48300i
$246$		0			0
$247$	−17.6203	−	13.8468i	−1.12116	−	0.881052i
$248$		0			0
$249$	9.78962	+	9.78962i	0.620392	+	0.620392i
$250$		0			0
$251$			5.23069i			0.330158i	0.986280	+	0.165079i	$0.0527879\pi$
$251$			5.23069i			0.330158i	−0.986280	+	0.165079i	$0.947212\pi$
$252$		0			0
$253$	3.20274	−	3.20274i	0.201354	−	0.201354i
$254$		0			0
$255$	11.2903	+	11.2903i	0.707027	+	0.707027i
$256$		0			0
$257$		−	8.93669i		−	0.557455i	−0.960370	−	0.278728i	$-0.910087\pi$
$257$		−	8.93669i		−	0.557455i	0.960370	−	0.278728i	$-0.0899127\pi$
$258$		0			0
$259$		−	31.4525i		−	1.95436i
$260$		0			0
$261$		−	6.96062i		−	0.430851i
$262$		0			0
$263$		−	6.37699i		−	0.393222i	−0.980482	−	0.196611i	$-0.937006\pi$
$263$		−	6.37699i		−	0.393222i	0.980482	−	0.196611i	$-0.0629936\pi$
$264$		0			0
$265$	−8.48028	−	8.48028i	−0.520940	−	0.520940i
$266$		0			0
$267$	4.24001	−	4.24001i	0.259484	−	0.259484i
$268$		0			0
$269$		−	15.2813i		−	0.931717i	−0.884859	−	0.465859i	$-0.845745\pi$
$269$		−	15.2813i		−	0.931717i	0.884859	−	0.465859i	$-0.154255\pi$
$270$		0			0
$271$	−1.94520	−	1.94520i	−0.118163	−	0.118163i	0.645553	−	0.763716i	$-0.276627\pi$
$271$	−1.94520	−	1.94520i	−0.118163	−	0.118163i	−0.763716	+	0.645553i	$0.776627\pi$
$272$		0			0
$273$	−12.2659	−	9.63903i	−0.742363	−	0.583381i
$274$		0			0
$275$	−3.08773	−	3.08773i	−0.186197	−	0.186197i
$276$		0			0
$277$	6.63729			0.398796			0.199398	−	0.979919i	$-0.436101\pi$
$277$	6.63729			0.398796			0.199398	+	0.979919i	$0.436101\pi$
$278$		0			0
$279$	−3.05943	+	3.05943i	−0.183163	+	0.183163i
$280$		0			0
$281$	−13.3992	+	13.3992i	−0.799331	+	0.799331i	−0.982990	−	0.183659i	$-0.941206\pi$
$281$	−13.3992	+	13.3992i	−0.799331	+	0.799331i	0.183659	+	0.982990i	$0.441206\pi$
$282$		0			0
$283$			8.82007i			0.524299i	0.965027	+	0.262149i	$0.0844313\pi$
$283$			8.82007i			0.524299i	−0.965027	+	0.262149i	$0.915569\pi$
$284$		0			0
$285$	17.4092			1.03123
$286$		0			0
$287$		−	17.0082i		−	1.00396i
$288$		0			0
$289$	−15.4959			−0.911526
$290$		0			0
$291$	−11.5753	−	11.5753i	−0.678557	−	0.678557i
$292$		0			0
$293$	12.6596	+	12.6596i	0.739582	+	0.739582i	0.972497	−	0.232915i	$-0.0748264\pi$
$293$	12.6596	+	12.6596i	0.739582	+	0.739582i	−0.232915	+	0.972497i	$0.574826\pi$
$294$		0			0
$295$			11.8848i			0.691959i
$296$		0			0
$297$	1.08518	−	1.08518i	0.0629684	−	0.0629684i
$298$		0			0
$299$	−10.5655	+	1.26701i	−0.611021	+	0.0732732i
$300$		0			0
$301$	−9.19026	+	9.19026i	−0.529718	+	0.529718i
$302$		0			0
$303$	−5.67835			−0.326213
$304$		0			0
$305$	2.24014	+	2.24014i	0.128270	+	0.128270i
$306$		0			0
$307$	11.6407	−	11.6407i	0.664371	−	0.664371i	−0.292036	−	0.956407i	$-0.594333\pi$
$307$	11.6407	−	11.6407i	0.664371	−	0.664371i	0.956407	+	0.292036i	$0.0943328\pi$
$308$		0			0
$309$	1.20900			0.0687774
$310$		0			0
$311$	14.2715			0.809263			0.404632	−	0.914480i	$-0.367400\pi$
$311$	14.2715			0.809263			0.404632	+	0.914480i	$0.367400\pi$
$312$		0			0
$313$	−20.4770			−1.15743			−0.578714	−	0.815531i	$-0.696445\pi$
$313$	−20.4770			−1.15743			−0.578714	+	0.815531i	$0.696445\pi$
$314$		0			0
$315$	12.1189			0.682820
$316$		0			0
$317$	−18.4519	+	18.4519i	−1.03636	+	1.03636i	−0.0370478	+	0.999313i	$0.511795\pi$
$317$	−18.4519	+	18.4519i	−1.03636	+	1.03636i	−0.999313	+	0.0370478i	$0.988205\pi$
$318$		0			0
$319$	−7.55351	−	7.55351i	−0.422915	−	0.422915i
$320$		0			0
$321$	11.6314			0.649202
$322$		0			0
$323$	−25.0537	+	25.0537i	−1.39402	+	1.39402i
$324$		0			0
$325$	1.22152	+	10.1861i	0.0677575	+	0.565026i
$326$		0			0
$327$	7.32910	−	7.32910i	0.405300	−	0.405300i
$328$		0			0
$329$		−	39.1696i		−	2.15949i
$330$		0			0
$331$	9.99851	+	9.99851i	0.549568	+	0.549568i	0.926316	−	0.376748i	$-0.122958\pi$
$331$	9.99851	+	9.99851i	0.549568	+	0.549568i	−0.376748	+	0.926316i	$0.622958\pi$
$332$		0			0
$333$	−5.14026	−	5.14026i	−0.281684	−	0.281684i
$334$		0			0
$335$	−29.3081			−1.60128
$336$		0			0
$337$		−	13.7956i		−	0.751492i	−0.926723	−	0.375746i	$-0.877387\pi$
$337$		−	13.7956i		−	0.751492i	0.926723	−	0.375746i	$-0.122613\pi$
$338$		0			0
$339$	15.2598			0.828798
$340$		0			0
$341$			6.64004i			0.359579i
$342$		0			0
$343$	−14.4410	+	14.4410i	−0.779740	+	0.779740i
$344$		0			0
$345$	5.84537	−	5.84537i	0.314704	−	0.314704i
$346$		0			0
$347$	−2.33288			−0.125236			−0.0626178	−	0.998038i	$-0.519945\pi$
$347$	−2.33288			−0.125236			−0.0626178	+	0.998038i	$0.519945\pi$
$348$		0			0
$349$	−14.8829	−	14.8829i	−0.796661	−	0.796661i	0.185906	−	0.982567i	$-0.440478\pi$
$349$	−14.8829	−	14.8829i	−0.796661	−	0.796661i	−0.982567	+	0.185906i	$0.940478\pi$
$350$		0			0
$351$	−3.57990	+	0.429300i	−0.191081	+	0.0229143i
$352$		0			0
$353$	−3.75999	−	3.75999i	−0.200124	−	0.200124i	0.599929	−	0.800053i	$-0.295195\pi$
$353$	−3.75999	−	3.75999i	−0.200124	−	0.200124i	−0.800053	+	0.599929i	$0.795195\pi$
$354$		0			0
$355$		−	12.6868i		−	0.673347i
$356$		0			0
$357$	−17.4403	+	17.4403i	−0.923040	+	0.923040i
$358$		0			0
$359$	17.6464	+	17.6464i	0.931343	+	0.931343i	0.997790	−	0.0664468i	$-0.0211663\pi$
$359$	17.6464	+	17.6464i	0.931343	+	0.931343i	−0.0664468	+	0.997790i	$0.521166\pi$
$360$		0			0
$361$			19.6316i			1.03324i
$362$		0			0
$363$			8.64478i			0.453733i
$364$		0			0
$365$		−	31.1933i		−	1.63273i
$366$		0			0
$367$			37.0651i			1.93478i	0.253290	+	0.967390i	$0.418487\pi$
$367$			37.0651i			1.93478i	−0.253290	+	0.967390i	$0.581513\pi$
$368$		0			0
$369$	−2.77963	−	2.77963i	−0.144702	−	0.144702i
$370$		0			0
$371$	13.0996	−	13.0996i	0.680098	−	0.680098i
$372$		0			0
$373$			17.1978i			0.890470i	0.895414	+	0.445235i	$0.146880\pi$
$373$			17.1978i			0.890470i	−0.895414	+	0.445235i	$0.853120\pi$
$374$		0			0
$375$	4.26741	+	4.26741i	0.220368	+	0.220368i
$376$		0			0
$377$	2.98819	+	24.9183i	0.153900	+	1.28336i
$378$		0			0
$379$	20.6610	+	20.6610i	1.06129	+	1.06129i	0.997995	+	0.0632908i	$0.0201596\pi$
$379$	20.6610	+	20.6610i	1.06129	+	1.06129i	0.0632908	+	0.997995i	$0.479840\pi$
$380$		0			0
$381$	−5.22910			−0.267895
$382$		0			0
$383$	14.2843	−	14.2843i	0.729894	−	0.729894i	−0.240705	−	0.970598i	$-0.577379\pi$
$383$	14.2843	−	14.2843i	0.729894	−	0.729894i	0.970598	+	0.240705i	$0.0773785\pi$
$384$		0			0
$385$	13.1511	−	13.1511i	0.670243	−	0.670243i
$386$		0			0
$387$			3.00392i			0.152698i
$388$		0			0
$389$	−3.02809			−0.153530			−0.0767651	−	0.997049i	$-0.524459\pi$
$389$	−3.02809			−0.153530			−0.0767651	+	0.997049i	$0.524459\pi$
$390$		0			0
$391$			16.8242i			0.850837i
$392$		0			0
$393$	−17.2100			−0.868128
$394$		0			0
$395$	−8.84929	−	8.84929i	−0.445256	−	0.445256i
$396$		0			0
$397$	5.46083	+	5.46083i	0.274071	+	0.274071i	0.830737	−	0.556666i	$-0.187920\pi$
$397$	5.46083	+	5.46083i	0.274071	+	0.274071i	−0.556666	+	0.830737i	$0.687920\pi$
$398$		0			0
$399$			26.8922i			1.34629i
$400$		0			0
$401$	−14.1868	+	14.1868i	−0.708456	+	0.708456i	−0.966210	−	0.257754i	$-0.917017\pi$
$401$	−14.1868	+	14.1868i	−0.708456	+	0.708456i	0.257754	+	0.966210i	$0.417017\pi$
$402$		0			0
$403$	9.63903	−	12.2659i	0.480154	−	0.611006i
$404$		0			0
$405$	1.98058	−	1.98058i	0.0984157	−	0.0984157i
$406$		0			0
$407$	−11.1562			−0.552992
$408$		0			0
$409$	−9.80736	−	9.80736i	−0.484943	−	0.484943i	0.421763	−	0.906706i	$-0.361411\pi$
$409$	−9.80736	−	9.80736i	−0.484943	−	0.484943i	−0.906706	+	0.421763i	$0.861411\pi$
$410$		0			0
$411$	2.23218	−	2.23218i	0.110105	−	0.110105i
$412$		0			0
$413$	−18.3586			−0.903367
$414$		0			0
$415$	38.7782			1.90355
$416$		0			0
$417$	−16.1346			−0.790114
$418$		0			0
$419$	−17.4997			−0.854915			−0.427457	−	0.904036i	$-0.640591\pi$
$419$	−17.4997			−0.854915			−0.427457	+	0.904036i	$0.640591\pi$
$420$		0			0
$421$	−11.9652	+	11.9652i	−0.583147	+	0.583147i	−0.935767	−	0.352620i	$-0.885291\pi$
$421$	−11.9652	+	11.9652i	−0.583147	+	0.583147i	0.352620	+	0.935767i	$0.385291\pi$
$422$		0			0
$423$	−6.40146	−	6.40146i	−0.311250	−	0.311250i
$424$		0			0
$425$	16.2201			0.786790
$426$		0			0
$427$	−3.46038	+	3.46038i	−0.167460	+	0.167460i
$428$		0			0
$429$	−3.41897	+	4.35070i	−0.165069	+	0.210054i
$430$		0			0
$431$	0.239905	−	0.239905i	0.0115558	−	0.0115558i	−0.701305	−	0.712861i	$-0.747399\pi$
$431$	0.239905	−	0.239905i	0.0115558	−	0.0115558i	0.712861	+	0.701305i	$0.247399\pi$
$432$		0			0
$433$		−	20.0909i		−	0.965507i	−0.875756	−	0.482754i	$-0.839637\pi$
$433$		−	20.0909i		−	0.965507i	0.875756	−	0.482754i	$-0.160363\pi$
$434$		0			0
$435$	−13.7860	−	13.7860i	−0.660990	−	0.660990i
$436$		0			0
$437$	12.9711	+	12.9711i	0.620492	+	0.620492i
$438$		0			0
$439$	−2.49150			−0.118913			−0.0594565	−	0.998231i	$-0.518937\pi$
$439$	−2.49150			−0.118913			−0.0594565	+	0.998231i	$0.518937\pi$
$440$		0			0
$441$			11.7202i			0.558103i
$442$		0			0
$443$	−13.5192			−0.642318			−0.321159	−	0.947025i	$-0.604072\pi$
$443$	−13.5192			−0.642318			−0.321159	+	0.947025i	$0.604072\pi$
$444$		0			0
$445$		−	16.7953i		−	0.796175i
$446$		0			0
$447$	−9.30975	+	9.30975i	−0.440336	+	0.440336i
$448$		0			0
$449$	12.8287	−	12.8287i	0.605424	−	0.605424i	−0.336323	−	0.941747i	$-0.609183\pi$
$449$	12.8287	−	12.8287i	0.605424	−	0.605424i	0.941747	+	0.336323i	$0.109183\pi$
$450$		0			0
$451$	−6.03279			−0.284073
$452$		0			0
$453$	6.21009	+	6.21009i	0.291776	+	0.291776i
$454$		0			0
$455$	−43.3843	+	5.20262i	−2.03389	+	0.243903i
$456$		0			0
$457$	21.9620	+	21.9620i	1.02734	+	1.02734i	0.999616	+	0.0277231i	$0.00882568\pi$
$457$	21.9620	+	21.9620i	1.02734	+	1.02734i	0.0277231	+	0.999616i	$0.491174\pi$
$458$		0			0
$459$			5.70052i			0.266078i
$460$		0			0
$461$	20.6299	−	20.6299i	0.960830	−	0.960830i	−0.0384313	−	0.999261i	$-0.512236\pi$
$461$	20.6299	−	20.6299i	0.960830	−	0.960830i	0.999261	+	0.0384313i	$0.0122361\pi$
$462$		0			0
$463$	−0.0796856	−	0.0796856i	−0.00370330	−	0.00370330i	0.705253	−	0.708956i	$-0.250834\pi$
$463$	−0.0796856	−	0.0796856i	−0.00370330	−	0.00370330i	−0.708956	+	0.705253i	$0.750834\pi$
$464$		0			0
$465$			12.1189i			0.561998i
$466$		0			0
$467$			21.9896i			1.01756i	0.860898	+	0.508778i	$0.169903\pi$
$467$			21.9896i			1.01756i	−0.860898	+	0.508778i	$0.830097\pi$
$468$		0			0
$469$		−	45.2727i		−	2.09050i
$470$		0			0
$471$		−	13.0048i		−	0.599228i
$472$		0			0
$473$	3.25979	+	3.25979i	0.149885	+	0.149885i
$474$		0			0
$475$	12.5053	−	12.5053i	0.573784	−	0.573784i
$476$		0			0
$477$		−	4.28172i		−	0.196047i
$478$		0			0
$479$	−4.31955	−	4.31955i	−0.197365	−	0.197365i	0.601504	−	0.798870i	$-0.294568\pi$
$479$	−4.31955	−	4.31955i	−0.197365	−	0.197365i	−0.798870	+	0.601504i	$0.794568\pi$
$480$		0			0
$481$	20.6083	+	16.1949i	0.939659	+	0.738424i
$482$		0			0
$483$	9.02943	+	9.02943i	0.410853	+	0.410853i
$484$		0			0
$485$	−45.8516			−2.08201
$486$		0			0
$487$	28.5902	−	28.5902i	1.29555	−	1.29555i	0.364243	−	0.931304i	$-0.381328\pi$
$487$	28.5902	−	28.5902i	1.29555	−	1.29555i	0.931304	−	0.364243i	$-0.118672\pi$
$488$		0			0
$489$	−4.16037	+	4.16037i	−0.188139	+	0.188139i
$490$		0			0
$491$		−	12.4888i		−	0.563611i	−0.959472	−	0.281805i	$-0.909067\pi$
$491$		−	12.4888i		−	0.563611i	0.959472	−	0.281805i	$-0.0909333\pi$
$492$		0			0
$493$	39.6791			1.78706
$494$		0			0
$495$		−	4.29856i		−	0.193206i
$496$		0			0
$497$	19.5975			0.879069
$498$		0			0
$499$	−10.2871	−	10.2871i	−0.460512	−	0.460512i	0.438311	−	0.898823i	$-0.355577\pi$
$499$	−10.2871	−	10.2871i	−0.460512	−	0.460512i	−0.898823	+	0.438311i	$0.855577\pi$
$500$		0			0
$501$	9.56896	+	9.56896i	0.427510	+	0.427510i
$502$		0			0
$503$		−	20.3269i		−	0.906329i	−0.891427	−	0.453165i	$-0.850295\pi$
$503$		−	20.3269i		−	0.906329i	0.891427	−	0.453165i	$-0.149705\pi$
$504$		0			0
$505$	−11.2464	+	11.2464i	−0.500459	+	0.500459i
$506$		0			0
$507$	12.6314	−	3.07370i	0.560980	−	0.136508i
$508$		0			0
$509$	2.36729	−	2.36729i	0.104928	−	0.104928i	−0.652694	−	0.757622i	$-0.726361\pi$
$509$	2.36729	−	2.36729i	0.104928	−	0.104928i	0.757622	+	0.652694i	$0.226361\pi$
$510$		0			0
$511$	48.1847			2.13157
$512$		0			0
$513$	4.39498	+	4.39498i	0.194043	+	0.194043i
$514$		0			0
$515$	2.39451	−	2.39451i	0.105515	−	0.105515i
$516$		0			0
$517$	−13.8935			−0.611033
$518$		0			0
$519$	−10.9034			−0.478605
$520$		0			0
$521$	−25.2723			−1.10720			−0.553600	−	0.832782i	$-0.686746\pi$
$521$	−25.2723			−1.10720			−0.553600	+	0.832782i	$0.686746\pi$
$522$		0			0
$523$	14.5946			0.638178			0.319089	−	0.947725i	$-0.396623\pi$
$523$	14.5946			0.638178			0.319089	+	0.947725i	$0.396623\pi$
$524$		0			0
$525$	8.70520	−	8.70520i	0.379926	−	0.379926i
$526$		0			0
$527$	−17.4403	−	17.4403i	−0.759712	−	0.759712i
$528$		0			0
$529$	−14.2896			−0.621285
$530$		0			0
$531$	−3.00033	+	3.00033i	−0.130203	+	0.130203i
$532$		0			0
$533$	11.1441	+	8.75752i	0.482705	+	0.379330i
$534$		0			0
$535$	23.0369	−	23.0369i	0.995972	−	0.995972i
$536$		0			0
$537$		−	6.70998i		−	0.289557i
$538$		0			0
$539$	12.7185	+	12.7185i	0.547823	+	0.547823i
$540$		0			0
$541$	−0.0297801	−	0.0297801i	−0.00128035	−	0.00128035i	0.706466	−	0.707747i	$-0.250288\pi$
$541$	−0.0297801	−	0.0297801i	−0.00128035	−	0.00128035i	−0.707747	+	0.706466i	$0.750288\pi$
$542$		0			0
$543$	−15.8485			−0.680122
$544$		0			0
$545$		−	29.0317i		−	1.24358i
$546$		0			0
$547$	−8.90794			−0.380876			−0.190438	−	0.981699i	$-0.560991\pi$
$547$	−8.90794			−0.380876			−0.190438	+	0.981699i	$0.560991\pi$
$548$		0			0
$549$			1.13106i			0.0482723i
$550$		0			0
$551$	30.5917	−	30.5917i	1.30325	−	1.30325i
$552$		0			0
$553$	13.6696	−	13.6696i	0.581291	−	0.581291i
$554$		0			0
$555$	−20.3614			−0.864291
$556$		0			0
$557$	3.04221	+	3.04221i	0.128902	+	0.128902i	0.768615	−	0.639712i	$-0.220946\pi$
$557$	3.04221	+	3.04221i	0.128902	+	0.128902i	−0.639712	+	0.768615i	$0.720946\pi$
$558$		0			0
$559$	−1.28958	−	10.7537i	−0.0545434	−	0.454834i
$560$		0			0
$561$	6.18608	+	6.18608i	0.261177	+	0.261177i
$562$		0			0
$563$			19.1221i			0.805900i	0.915222	+	0.402950i	$0.132015\pi$
$563$			19.1221i			0.805900i	−0.915222	+	0.402950i	$0.867985\pi$
$564$		0			0
$565$	30.2232	−	30.2232i	1.27150	−	1.27150i
$566$		0			0
$567$	3.05943	+	3.05943i	0.128484	+	0.128484i
$568$		0			0
$569$		−	17.6181i		−	0.738590i	−0.929312	−	0.369295i	$-0.879599\pi$
$569$		−	17.6181i		−	0.738590i	0.929312	−	0.369295i	$-0.120401\pi$
$570$		0			0
$571$		−	3.59788i		−	0.150567i	−0.997162	−	0.0752833i	$-0.976014\pi$
$571$		−	3.59788i		−	0.150567i	0.997162	−	0.0752833i	$-0.0239861\pi$
$572$		0			0
$573$		−	17.4715i		−	0.729881i
$574$		0			0
$575$		−	8.39767i		−	0.350207i
$576$		0			0
$577$	26.9842	+	26.9842i	1.12337	+	1.12337i	0.991232	+	0.132135i	$0.0421832\pi$
$577$	26.9842	+	26.9842i	1.12337	+	1.12337i	0.132135	+	0.991232i	$0.457817\pi$
$578$		0			0
$579$	12.6490	−	12.6490i	0.525675	−	0.525675i
$580$		0			0
$581$			59.9012i			2.48512i
$582$		0			0
$583$	−4.64644	−	4.64644i	−0.192436	−	0.192436i
$584$		0			0
$585$	−6.24001	+	7.94053i	−0.257993	+	0.328301i
$586$		0			0
$587$	−15.2640	−	15.2640i	−0.630014	−	0.630014i	0.318057	−	0.948071i	$-0.396970\pi$
$587$	−15.2640	−	15.2640i	−0.630014	−	0.630014i	−0.948071	+	0.318057i	$0.896970\pi$
$588$		0			0
$589$	−26.8922			−1.10807
$590$		0			0
$591$	4.24269	−	4.24269i	0.174521	−	0.174521i
$592$		0			0
$593$	17.5925	−	17.5925i	0.722439	−	0.722439i	−0.246663	−	0.969101i	$-0.579334\pi$
$593$	17.5925	−	17.5925i	0.722439	−	0.722439i	0.969101	+	0.246663i	$0.0793339\pi$
$594$		0			0
$595$			69.0838i			2.83216i
$596$		0			0
$597$	−8.86969			−0.363012
$598$		0			0
$599$			12.8652i			0.525659i	0.964842	+	0.262829i	$0.0846556\pi$
$599$			12.8652i			0.525659i	−0.964842	+	0.262829i	$0.915344\pi$
$600$		0			0
$601$	25.5562			1.04246			0.521230	−	0.853416i	$-0.325473\pi$
$601$	25.5562			1.04246			0.521230	+	0.853416i	$0.325473\pi$
$602$		0			0
$603$	−7.39889	−	7.39889i	−0.301306	−	0.301306i
$604$		0			0
$605$	17.1216	+	17.1216i	0.696094	+	0.696094i
$606$		0			0
$607$			31.7217i			1.28754i	0.765218	+	0.643771i	$0.222631\pi$
$607$			31.7217i			1.28754i	−0.765218	+	0.643771i	$0.777369\pi$
$608$		0			0
$609$	21.2955	−	21.2955i	0.862936	−	0.862936i
$610$		0			0
$611$	25.6648	+	20.1685i	1.03828	+	0.815929i
$612$		0			0
$613$	−11.2028	+	11.2028i	−0.452477	+	0.452477i	−0.896176	−	0.443699i	$-0.853666\pi$
$613$	−11.2028	+	11.2028i	−0.452477	+	0.452477i	0.443699	+	0.896176i	$0.353666\pi$
$614$		0			0
$615$	−11.0105			−0.443988
$616$		0			0
$617$	13.6394	+	13.6394i	0.549100	+	0.549100i	0.926181	−	0.377080i	$-0.123072\pi$
$617$	13.6394	+	13.6394i	0.549100	+	0.549100i	−0.377080	+	0.926181i	$0.623072\pi$
$618$		0			0
$619$	−24.5702	+	24.5702i	−0.987561	+	0.987561i	−0.999924	−	0.0123622i	$-0.996065\pi$
$619$	−24.5702	+	24.5702i	−0.987561	+	0.987561i	0.0123622	+	0.999924i	$0.496065\pi$
$620$		0			0
$621$	2.95135			0.118433
$622$		0			0
$623$	25.9440			1.03942
$624$		0			0
$625$	31.1307			1.24523
$626$		0			0
$627$	9.53866			0.380938
$628$		0			0
$629$	29.3022	−	29.3022i	1.16835	−	1.16835i
$630$		0			0
$631$	−14.4587	−	14.4587i	−0.575593	−	0.575593i	0.358093	−	0.933686i	$-0.383427\pi$
$631$	−14.4587	−	14.4587i	−0.575593	−	0.575593i	−0.933686	+	0.358093i	$0.883427\pi$
$632$		0			0
$633$	−8.48028			−0.337061
$634$		0			0
$635$	−10.3566	+	10.3566i	−0.410991	+	0.410991i
$636$		0			0
$637$	−5.03146	−	41.9570i	−0.199354	−	1.66240i
$638$		0			0
$639$	3.20281	−	3.20281i	0.126701	−	0.126701i
$640$		0			0
$641$			29.9697i			1.18373i	0.806037	+	0.591866i	$0.201608\pi$
$641$			29.9697i			1.18373i	−0.806037	+	0.591866i	$0.798392\pi$
$642$		0			0
$643$	19.9356	+	19.9356i	0.786183	+	0.786183i	0.980866	−	0.194683i	$-0.0623679\pi$
$643$	19.9356	+	19.9356i	0.786183	+	0.786183i	−0.194683	+	0.980866i	$0.562368\pi$
$644$		0			0
$645$	5.94949	+	5.94949i	0.234261	+	0.234261i
$646$		0			0
$647$	27.3423			1.07494			0.537469	−	0.843283i	$-0.319380\pi$
$647$	27.3423			1.07494			0.537469	+	0.843283i	$0.319380\pi$
$648$		0			0
$649$			6.51179i			0.255610i
$650$		0			0
$651$	−18.7202			−0.733701
$652$		0			0
$653$		−	9.37861i		−	0.367013i	−0.983018	−	0.183507i	$-0.941255\pi$
$653$		−	9.37861i		−	0.367013i	0.983018	−	0.183507i	$-0.0587449\pi$
$654$		0			0
$655$	−34.0857	+	34.0857i	−1.33184	+	1.33184i
$656$		0			0
$657$	7.87480	−	7.87480i	0.307225	−	0.307225i
$658$		0			0
$659$	16.9639			0.660821			0.330411	−	0.943837i	$-0.392813\pi$
$659$	16.9639			0.660821			0.330411	+	0.943837i	$0.392813\pi$
$660$		0			0
$661$	29.9758	+	29.9758i	1.16592	+	1.16592i	0.983156	+	0.182768i	$0.0585056\pi$
$661$	29.9758	+	29.9758i	1.16592	+	1.16592i	0.182768	+	0.983156i	$0.441494\pi$
$662$		0			0
$663$	−2.44723	−	20.4073i	−0.0950426	−	0.792554i
$664$		0			0
$665$	53.2621	+	53.2621i	2.06541	+	2.06541i
$666$		0			0
$667$		−	20.5432i		−	0.795436i
$668$		0			0
$669$	−16.9807	+	16.9807i	−0.656510	+	0.656510i
$670$		0			0
$671$	1.22740	+	1.22740i	0.0473831	+	0.0473831i
$672$		0			0
$673$		−	6.87865i		−	0.265152i	−0.991173	−	0.132576i	$-0.957675\pi$
$673$		−	6.87865i		−	0.265152i	0.991173	−	0.132576i	$-0.0423249\pi$
$674$		0			0
$675$		−	2.84537i		−	0.109518i
$676$		0			0
$677$			13.0371i			0.501057i	0.968109	+	0.250528i	$0.0806043\pi$
$677$			13.0371i			0.501057i	−0.968109	+	0.250528i	$0.919396\pi$
$678$		0			0
$679$		−	70.8276i		−	2.71812i
$680$		0			0
$681$	−8.63107	−	8.63107i	−0.330743	−	0.330743i
$682$		0			0
$683$	20.9718	−	20.9718i	0.802463	−	0.802463i	−0.181017	−	0.983480i	$-0.557939\pi$
$683$	20.9718	−	20.9718i	0.802463	−	0.802463i	0.983480	+	0.181017i	$0.0579389\pi$
$684$		0			0
$685$		−	8.84200i		−	0.337836i
$686$		0			0
$687$	4.16041	+	4.16041i	0.158730	+	0.158730i
$688$		0			0
$689$	1.83814	+	15.3282i	0.0700277	+	0.583956i
$690$		0			0
$691$	33.4370	+	33.4370i	1.27200	+	1.27200i	0.945035	+	0.326969i	$0.106027\pi$
$691$	33.4370	+	33.4370i	1.27200	+	1.27200i	0.326969	+	0.945035i	$0.393973\pi$
$692$		0			0
$693$	6.64004			0.252234
$694$		0			0
$695$	−31.9558	+	31.9558i	−1.21215	+	1.21215i
$696$		0			0
$697$	15.8454	−	15.8454i	0.600185	−	0.600185i
$698$		0			0
$699$		−	2.78928i		−	0.105500i
$700$		0			0
$701$	−15.0565			−0.568675			−0.284338	−	0.958724i	$-0.591774\pi$
$701$	−15.0565			−0.568675			−0.284338	+	0.958724i	$0.591774\pi$
$702$		0			0
$703$		−	45.1826i		−	1.70409i
$704$		0			0
$705$	−25.3572			−0.955006
$706$		0			0
$707$	−17.3725	−	17.3725i	−0.653360	−	0.653360i
$708$		0			0
$709$	−14.4736	−	14.4736i	−0.543569	−	0.543569i	0.381004	−	0.924573i	$-0.375578\pi$
$709$	−14.4736	−	14.4736i	−0.543569	−	0.543569i	−0.924573	+	0.381004i	$0.875578\pi$
$710$		0			0
$711$		−	4.46803i		−	0.167564i
$712$		0			0
$713$	−9.02943	+	9.02943i	−0.338155	+	0.338155i
$714$		0			0
$715$	1.84537	+	15.3884i	0.0690129	+	0.575494i
$716$		0			0
$717$	−3.17166	+	3.17166i	−0.118448	+	0.118448i
$718$		0			0
$719$	−30.9497			−1.15423			−0.577114	−	0.816663i	$-0.695821\pi$
$719$	−30.9497			−1.15423			−0.577114	+	0.816663i	$0.695821\pi$
$720$		0			0
$721$	3.69883	+	3.69883i	0.137752	+	0.137752i
$722$		0			0
$723$	−19.8233	+	19.8233i	−0.737236	+	0.737236i
$724$		0			0
$725$	−19.8055			−0.735559
$726$		0			0
$727$	−34.8766			−1.29350			−0.646750	−	0.762702i	$-0.723872\pi$
$727$	−34.8766			−1.29350			−0.646750	+	0.762702i	$0.723872\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−17.1239			−0.633350
$732$		0			0
$733$	−2.70878	+	2.70878i	−0.100051	+	0.100051i	−0.755361	−	0.655309i	$-0.772538\pi$
$733$	−2.70878	+	2.70878i	−0.100051	+	0.100051i	0.655309	+	0.755361i	$0.272538\pi$
$734$		0			0
$735$	23.2127	+	23.2127i	0.856213	+	0.856213i
$736$		0			0
$737$	−16.0582			−0.591513
$738$		0			0
$739$	36.0138	−	36.0138i	1.32479	−	1.32479i	0.414938	−	0.909850i	$-0.363803\pi$
$739$	36.0138	−	36.0138i	1.32479	−	1.32479i	0.909850	−	0.414938i	$-0.136197\pi$
$740$		0			0
$741$	−17.6203	−	13.8468i	−0.647299	−	0.508676i
$742$		0			0
$743$	−34.5489	+	34.5489i	−1.26747	+	1.26747i	−0.320086	+	0.947388i	$0.603712\pi$
$743$	−34.5489	+	34.5489i	−1.26747	+	1.26747i	−0.947388	+	0.320086i	$0.896288\pi$
$744$		0			0
$745$			36.8773i			1.35108i
$746$		0			0
$747$	9.78962	+	9.78962i	0.358183	+	0.358183i
$748$		0			0
$749$	35.5854	+	35.5854i	1.30026	+	1.30026i
$750$		0			0
$751$	−33.5927			−1.22582			−0.612908	−	0.790154i	$-0.710000\pi$
$751$	−33.5927			−1.22582			−0.612908	+	0.790154i	$0.710000\pi$
$752$		0			0
$753$			5.23069i			0.190617i
$754$		0			0
$755$	24.5991			0.895254
$756$		0			0
$757$			43.6629i			1.58695i	0.608600	+	0.793477i	$0.291731\pi$
$757$			43.6629i			1.58695i	−0.608600	+	0.793477i	$0.708269\pi$
$758$		0			0
$759$	3.20274	−	3.20274i	0.116252	−	0.116252i
$760$		0			0
$761$	−8.82087	+	8.82087i	−0.319756	+	0.319756i	−0.848673	−	0.528917i	$-0.822598\pi$
$761$	−8.82087	+	8.82087i	−0.319756	+	0.319756i	0.528917	+	0.848673i	$0.322598\pi$
$762$		0			0
$763$	44.8457			1.62352
$764$		0			0
$765$	11.2903	+	11.2903i	0.408202	+	0.408202i
$766$		0			0
$767$	9.45286	−	12.0289i	0.341323	−	0.434340i
$768$		0			0
$769$	34.6156	+	34.6156i	1.24827	+	1.24827i	0.956483	+	0.291787i	$0.0942499\pi$
$769$	34.6156	+	34.6156i	1.24827	+	1.24827i	0.291787	+	0.956483i	$0.405750\pi$
$770$		0			0
$771$		−	8.93669i		−	0.321847i
$772$		0			0
$773$	29.1933	−	29.1933i	1.05001	−	1.05001i	0.0513298	−	0.998682i	$-0.483654\pi$
$773$	29.1933	−	29.1933i	1.05001	−	1.05001i	0.998682	−	0.0513298i	$-0.0163460\pi$
$774$		0			0
$775$	8.70520	+	8.70520i	0.312700	+	0.312700i
$776$		0			0
$777$		−	31.4525i		−	1.12835i
$778$		0			0
$779$		−	24.4328i		−	0.875397i
$780$		0			0
$781$		−	6.95124i		−	0.248735i
$782$		0			0
$783$		−	6.96062i		−	0.248752i
$784$		0			0
$785$	−25.7569	−	25.7569i	−0.919305	−	0.919305i
$786$		0			0
$787$	−7.46253	+	7.46253i	−0.266011	+	0.266011i	−0.827490	−	0.561480i	$-0.810232\pi$
$787$	−7.46253	+	7.46253i	−0.266011	+	0.266011i	0.561480	+	0.827490i	$0.310232\pi$
$788$		0			0
$789$		−	6.37699i		−	0.227027i
$790$		0			0
$791$	46.6862	+	46.6862i	1.65997	+	1.65997i
$792$		0			0
$793$	−0.485562	−	4.04907i	−0.0172428	−	0.143787i
$794$		0			0
$795$	−8.48028	−	8.48028i	−0.300765	−	0.300765i
$796$		0			0
$797$	−22.8833			−0.810568			−0.405284	−	0.914191i	$-0.632827\pi$
$797$	−22.8833			−0.810568			−0.405284	+	0.914191i	$0.632827\pi$
$798$		0			0
$799$	36.4917	−	36.4917i	1.29098	−	1.29098i
$800$		0			0
$801$	4.24001	−	4.24001i	0.149813	−	0.149813i
$802$		0			0
$803$		−	17.0911i		−	0.603132i
$804$		0			0
$805$	35.7669			1.26062
$806$		0			0
$807$		−	15.2813i		−	0.537927i
$808$		0			0
$809$	44.2093			1.55432			0.777158	−	0.629306i	$-0.216661\pi$
$809$	44.2093			1.55432			0.777158	+	0.629306i	$0.216661\pi$
$810$		0			0
$811$	2.94966	+	2.94966i	0.103576	+	0.103576i	0.756996	−	0.653420i	$-0.226666\pi$
$811$	2.94966	+	2.94966i	0.103576	+	0.103576i	−0.653420	+	0.756996i	$0.726666\pi$
$812$		0			0
$813$	−1.94520	−	1.94520i	−0.0682213	−	0.0682213i
$814$		0			0
$815$			16.4799i			0.577265i
$816$		0			0
$817$	−13.2021	+	13.2021i	−0.461884	+	0.461884i
$818$		0			0
$819$	−12.2659	−	9.63903i	−0.428604	−	0.336815i
$820$		0			0
$821$	−21.8863	+	21.8863i	−0.763837	+	0.763837i	−0.977014	−	0.213177i	$-0.931619\pi$
$821$	−21.8863	+	21.8863i	−0.763837	+	0.763837i	0.213177	+	0.977014i	$0.431619\pi$
$822$		0			0
$823$	4.14879			0.144618			0.0723088	−	0.997382i	$-0.476963\pi$
$823$	4.14879			0.144618			0.0723088	+	0.997382i	$0.476963\pi$
$824$		0			0
$825$	−3.08773	−	3.08773i	−0.107501	−	0.107501i
$826$		0			0
$827$	10.6504	−	10.6504i	0.370350	−	0.370350i	−0.497255	−	0.867605i	$-0.665659\pi$
$827$	10.6504	−	10.6504i	0.370350	−	0.370350i	0.867605	+	0.497255i	$0.165659\pi$
$828$		0			0
$829$	0.216258			0.00751097			0.00375548	−	0.999993i	$-0.498805\pi$
$829$	0.216258			0.00751097			0.00375548	+	0.999993i	$0.498805\pi$
$830$		0			0
$831$	6.63729			0.230245
$832$		0			0
$833$	−66.8111			−2.31487
$834$		0			0
$835$	37.9041			1.31173
$836$		0			0
$837$	−3.05943	+	3.05943i	−0.105749	+	0.105749i
$838$		0			0
$839$	25.0859	+	25.0859i	0.866061	+	0.866061i	0.992034	−	0.125972i	$-0.0402050\pi$
$839$	25.0859	+	25.0859i	0.866061	+	0.866061i	−0.125972	+	0.992034i	$0.540205\pi$
$840$		0			0
$841$	−19.4502			−0.670695
$842$		0			0
$843$	−13.3992	+	13.3992i	−0.461494	+	0.461494i
$844$		0			0
$845$	18.9298	−	31.1052i	0.651204	−	1.07005i
$846$		0			0
$847$	−26.4480	+	26.4480i	−0.908766	+	0.908766i
$848$		0			0
$849$			8.82007i			0.302704i
$850$		0			0
$851$	−15.1707	−	15.1707i	−0.520044	−	0.520044i
$852$		0			0
$853$	11.0517	+	11.0517i	0.378403	+	0.378403i	0.870526	−	0.492123i	$-0.163779\pi$
$853$	11.0517	+	11.0517i	0.378403	+	0.378403i	−0.492123	+	0.870526i	$0.663779\pi$
$854$		0			0
$855$	17.4092			0.595381
$856$		0			0
$857$		−	51.1359i		−	1.74677i	−0.487031	−	0.873385i	$-0.661920\pi$
$857$		−	51.1359i		−	1.74677i	0.487031	−	0.873385i	$-0.338080\pi$
$858$		0			0
$859$	−7.91145			−0.269935			−0.134968	−	0.990850i	$-0.543093\pi$
$859$	−7.91145			−0.269935			−0.134968	+	0.990850i	$0.543093\pi$
$860$		0			0
$861$		−	17.0082i		−	0.579636i
$862$		0			0
$863$	12.9345	−	12.9345i	0.440294	−	0.440294i	−0.451817	−	0.892111i	$-0.649224\pi$
$863$	12.9345	−	12.9345i	0.440294	−	0.440294i	0.892111	+	0.451817i	$0.149224\pi$
$864$		0			0
$865$	−21.5950	+	21.5950i	−0.734251	+	0.734251i
$866$		0			0
$867$	−15.4959			−0.526270
$868$		0			0
$869$	−4.84861	−	4.84861i	−0.164478	−	0.164478i
$870$		0			0
$871$	29.6637	+	23.3110i	1.00511	+	0.789862i
$872$		0			0
$873$	−11.5753	−	11.5753i	−0.391765	−	0.391765i
$874$		0			0
$875$			26.1116i			0.882735i
$876$		0			0
$877$	14.4085	−	14.4085i	0.486539	−	0.486539i	−0.420673	−	0.907212i	$-0.638206\pi$
$877$	14.4085	−	14.4085i	0.486539	−	0.486539i	0.907212	+	0.420673i	$0.138206\pi$
$878$		0			0
$879$	12.6596	+	12.6596i	0.426998	+	0.426998i
$880$		0			0
$881$		−	22.8221i		−	0.768895i	−0.923147	−	0.384448i	$-0.874392\pi$
$881$		−	22.8221i		−	0.768895i	0.923147	−	0.384448i	$-0.125608\pi$
$882$		0			0
$883$		−	16.8248i		−	0.566199i	−0.959091	−	0.283099i	$-0.908637\pi$
$883$		−	16.8248i		−	0.566199i	0.959091	−	0.283099i	$-0.0913626\pi$
$884$		0			0
$885$			11.8848i			0.399503i
$886$		0			0
$887$			13.8258i			0.464226i	0.972689	+	0.232113i	$0.0745640\pi$
$887$			13.8258i			0.464226i	−0.972689	+	0.232113i	$0.925436\pi$
$888$		0			0
$889$	−15.9981	−	15.9981i	−0.536557	−	0.536557i
$890$		0			0
$891$	1.08518	−	1.08518i	0.0363548	−	0.0363548i
$892$		0			0
$893$		−	56.2685i		−	1.88295i
$894$		0			0
$895$	−13.2896	−	13.2896i	−0.444223	−	0.444223i
$896$		0			0
$897$	−10.5655	+	1.26701i	−0.352773	+	0.0423043i
$898$		0			0
$899$	21.2955	+	21.2955i	0.710244	+	0.710244i
$900$		0			0
$901$	24.4081			0.813151
$902$		0			0
$903$	−9.19026	+	9.19026i	−0.305833	+	0.305833i
$904$		0			0
$905$	−31.3891	+	31.3891i	−1.04341	+	1.04341i
$906$		0			0
$907$			0.155764i			0.00517206i	0.999997	+	0.00258603i	$0.000823160\pi$
$907$			0.155764i			0.00517206i	−0.999997	+	0.00258603i	$0.999177\pi$
$908$		0			0
$909$	−5.67835			−0.188339
$910$		0			0
$911$		−	3.37534i		−	0.111830i	−0.998436	−	0.0559150i	$-0.982192\pi$
$911$		−	3.37534i		−	0.111830i	0.998436	−	0.0559150i	$-0.0178076\pi$
$912$		0			0
$913$	21.2470			0.703172
$914$		0			0
$915$	2.24014	+	2.24014i	0.0740568	+	0.0740568i
$916$		0			0
$917$	−52.6526	−	52.6526i	−1.73874	−	1.73874i
$918$		0			0
$919$			25.7638i			0.849869i	0.905224	+	0.424935i	$0.139703\pi$
$919$			25.7638i			0.849869i	−0.905224	+	0.424935i	$0.860297\pi$
$920$		0			0
$921$	11.6407	−	11.6407i	0.383575	−	0.383575i
$922$		0			0
$923$	−10.0908	+	12.8407i	−0.332142	+	0.422657i
$924$		0			0
$925$	−14.6259	+	14.6259i	−0.480898	+	0.480898i
$926$		0			0
$927$	1.20900			0.0397087
$928$		0			0
$929$	−28.3002	−	28.3002i	−0.928499	−	0.928499i	0.0691097	−	0.997609i	$-0.477984\pi$
$929$	−28.3002	−	28.3002i	−0.928499	−	0.928499i	−0.997609	+	0.0691097i	$0.977984\pi$
$930$		0			0
$931$	−51.5098	+	51.5098i	−1.68817	+	1.68817i
$932$		0			0
$933$	14.2715			0.467228
$934$		0			0
$935$	24.5040			0.801367
$936$		0			0
$937$	42.3237			1.38266			0.691328	−	0.722541i	$-0.257026\pi$
$937$	42.3237			1.38266			0.691328	+	0.722541i	$0.257026\pi$
$938$		0			0
$939$	−20.4770			−0.668241
$940$		0			0
$941$	−21.0672	+	21.0672i	−0.686769	+	0.686769i	−0.961517	−	0.274747i	$-0.911406\pi$
$941$	−21.0672	+	21.0672i	−0.686769	+	0.686769i	0.274747	+	0.961517i	$0.411406\pi$
$942$		0			0
$943$	−8.20366	−	8.20366i	−0.267148	−	0.267148i
$944$		0			0
$945$	12.1189			0.394226
$946$		0			0
$947$	37.8829	−	37.8829i	1.23103	−	1.23103i	0.267459	−	0.963569i	$-0.413816\pi$
$947$	37.8829	−	37.8829i	1.23103	−	1.23103i	0.963569	−	0.267459i	$-0.0861840\pi$
$948$		0			0
$949$	−24.8104	+	31.5716i	−0.805378	+	1.02486i
$950$		0			0
$951$	−18.4519	+	18.4519i	−0.598343	+	0.598343i
$952$		0			0
$953$		−	35.9170i		−	1.16346i	−0.813380	−	0.581732i	$-0.802375\pi$
$953$		−	35.9170i		−	1.16346i	0.813380	−	0.581732i	$-0.197625\pi$
$954$		0			0
$955$	−34.6036	−	34.6036i	−1.11975	−	1.11975i
$956$		0			0
$957$	−7.55351	−	7.55351i	−0.244170	−	0.244170i
$958$		0			0
$959$	13.6584			0.441052
$960$		0			0
$961$			12.2798i			0.396124i
$962$		0			0
$963$	11.6314			0.374817
$964$		0			0
$965$		−	50.1047i		−	1.61293i
$966$		0			0
$967$	24.7361	−	24.7361i	0.795460	−	0.795460i	−0.186916	−	0.982376i	$-0.559849\pi$
$967$	24.7361	−	24.7361i	0.795460	−	0.795460i	0.982376	+	0.186916i	$0.0598492\pi$
$968$		0			0
$969$	−25.0537	+	25.0537i	−0.804839	+	0.804839i
$970$		0			0
$971$	19.1899			0.615834			0.307917	−	0.951413i	$-0.400368\pi$
$971$	19.1899			0.615834			0.307917	+	0.951413i	$0.400368\pi$
$972$		0			0
$973$	−49.3625	−	49.3625i	−1.58249	−	1.58249i
$974$		0			0
$975$	1.22152	+	10.1861i	0.0391198	+	0.326218i
$976$		0			0
$977$	−22.9975	−	22.9975i	−0.735755	−	0.735755i	0.235999	−	0.971753i	$-0.424164\pi$
$977$	−22.9975	−	22.9975i	−0.735755	−	0.735755i	−0.971753	+	0.235999i	$0.924164\pi$
$978$		0			0
$979$		−	9.20234i		−	0.294108i
$980$		0			0
$981$	7.32910	−	7.32910i	0.234000	−	0.234000i
$982$		0			0
$983$	1.02696	+	1.02696i	0.0327549	+	0.0327549i	0.723295	−	0.690540i	$-0.242627\pi$
$983$	1.02696	+	1.02696i	0.0327549	+	0.0327549i	−0.690540	+	0.723295i	$0.742627\pi$
$984$		0			0
$985$		−	16.8059i		−	0.535482i
$986$		0			0
$987$		−	39.1696i		−	1.24678i
$988$		0			0
$989$			8.86560i			0.281910i
$990$		0			0
$991$			57.0449i			1.81209i	0.423181	+	0.906045i	$0.360913\pi$
$991$			57.0449i			1.81209i	−0.423181	+	0.906045i	$0.639087\pi$
$992$		0			0
$993$	9.99851	+	9.99851i	0.317293	+	0.317293i
$994$		0			0
$995$	−17.5671	+	17.5671i	−0.556914	+	0.556914i
$996$		0			0
$997$		−	12.0315i		−	0.381042i	−0.981683	−	0.190521i	$-0.938982\pi$
$997$		−	12.0315i		−	0.381042i	0.981683	−	0.190521i	$-0.0610177\pi$
$998$		0			0
$999$	−5.14026	−	5.14026i	−0.162631	−	0.162631i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1248.2.bb.f.463.11		24
4.3	odd	2		312.2.t.e.307.3	yes	24
8.3	odd	2	inner	1248.2.bb.f.463.2		24
8.5	even	2		312.2.t.e.307.8	yes	24
12.11	even	2		936.2.w.j.307.10		24
13.5	odd	4	inner	1248.2.bb.f.655.2		24
24.5	odd	2		936.2.w.j.307.5		24
52.31	even	4		312.2.t.e.187.8	yes	24
104.5	odd	4		312.2.t.e.187.3	✓	24
104.83	even	4	inner	1248.2.bb.f.655.11		24
156.83	odd	4		936.2.w.j.811.5		24
312.5	even	4		936.2.w.j.811.10		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.t.e.187.3	✓	24	104.5	odd	4
312.2.t.e.187.8	yes	24	52.31	even	4
312.2.t.e.307.3	yes	24	4.3	odd	2
312.2.t.e.307.8	yes	24	8.5	even	2
936.2.w.j.307.5		24	24.5	odd	2
936.2.w.j.307.10		24	12.11	even	2
936.2.w.j.811.5		24	156.83	odd	4
936.2.w.j.811.10		24	312.5	even	4
1248.2.bb.f.463.2		24	8.3	odd	2	inner
1248.2.bb.f.463.11		24	1.1	even	1	trivial
1248.2.bb.f.655.2		24	13.5	odd	4	inner
1248.2.bb.f.655.11		24	104.83	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1248 = 2^{5} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1248.bb (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{3} +(1.98058 - 1.98058i) q^{5} +(3.05943 + 3.05943i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{3} +(1.98058 - 1.98058i) q^{5} +(3.05943 + 3.05943i) q^{7} +1.00000 q^{9} +(1.08518 - 1.08518i) q^{11} +(-3.57990 + 0.429300i) q^{13} +(1.98058 - 1.98058i) q^{15} +5.70052i q^{17} +(4.39498 + 4.39498i) q^{19} +(3.05943 + 3.05943i) q^{21} +2.95135 q^{23} -2.84537i q^{25} +1.00000 q^{27} -6.96062i q^{29} +(-3.05943 + 3.05943i) q^{31} +(1.08518 - 1.08518i) q^{33} +12.1189 q^{35} +(-5.14026 - 5.14026i) q^{37} +(-3.57990 + 0.429300i) q^{39} +(-2.77963 - 2.77963i) q^{41} +3.00392i q^{43} +(1.98058 - 1.98058i) q^{45} +(-6.40146 - 6.40146i) q^{47} +11.7202i q^{49} +5.70052i q^{51} -4.28172i q^{53} -4.29856i q^{55} +(4.39498 + 4.39498i) q^{57} +(-3.00033 + 3.00033i) q^{59} +1.13106i q^{61} +(3.05943 + 3.05943i) q^{63} +(-6.24001 + 7.94053i) q^{65} +(-7.39889 - 7.39889i) q^{67} +2.95135 q^{69} +(3.20281 - 3.20281i) q^{71} +(7.87480 - 7.87480i) q^{73} -2.84537i q^{75} +6.64004 q^{77} -4.46803i q^{79} +1.00000 q^{81} +(9.78962 + 9.78962i) q^{83} +(11.2903 + 11.2903i) q^{85} -6.96062i q^{87} +(4.24001 - 4.24001i) q^{89} +(-12.2659 - 9.63903i) q^{91} +(-3.05943 + 3.05943i) q^{93} +17.4092 q^{95} +(-11.5753 - 11.5753i) q^{97} +(1.08518 - 1.08518i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{3} + 24 q^{9}+O(q^{10}) \) 24 * q + 24 * q^3 + 24 * q^9	\( 24 q + 24 q^{3} + 24 q^{9} - 8 q^{11} - 20 q^{19} + 24 q^{27} - 8 q^{33} - 16 q^{35} - 12 q^{41} - 20 q^{57} + 16 q^{59} - 76 q^{65} - 28 q^{67} - 8 q^{73} + 24 q^{81} + 72 q^{83} + 28 q^{89} + 4 q^{91} + 24 q^{97} - 8 q^{99}+O(q^{100}) \) 24 * q + 24 * q^3 + 24 * q^9 - 8 * q^11 - 20 * q^19 + 24 * q^27 - 8 * q^33 - 16 * q^35 - 12 * q^41 - 20 * q^57 + 16 * q^59 - 76 * q^65 - 28 * q^67 - 8 * q^73 + 24 * q^81 + 72 * q^83 + 28 * q^89 + 4 * q^91 + 24 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

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