LMFDB - Embedded newform 464.3.l.c.17.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [464,3,Mod(17,464)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(464, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("464.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 464 = 2^{4} \cdot 29 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	464.l (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:	$12.6430842663$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 18x^{6} + 91x^{4} + 126x^{2} + 25 $ x^8 + 18x^6 + 91x^4 + 126*x^2 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.3
Root			$-3.22189i$ of defining polynomial
Character	$\chi$	$=$	464.17
Dual form			464.3.l.c.273.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.14254 - 2.14254i) q^{3} +0.488689i q^{5} -8.09117 q^{7} -0.180982i q^{9} +O(q^{10})$	\(q+(2.14254 - 2.14254i) q^{3} +0.488689i q^{5} -8.09117 q^{7} -0.180982i q^{9} +(-11.3195 + 11.3195i) q^{11} +10.0463i q^{13} +(1.04704 + 1.04704i) q^{15} +(-9.69799 + 9.69799i) q^{17} +(-8.58453 + 8.58453i) q^{19} +(-17.3357 + 17.3357i) q^{21} +14.4215 q^{23} +24.7612 q^{25} +(18.8951 + 18.8951i) q^{27} +(-11.8706 - 26.4592i) q^{29} +(-31.2221 + 31.2221i) q^{31} +48.5052i q^{33} -3.95407i q^{35} +(-31.2631 - 31.2631i) q^{37} +(21.5246 + 21.5246i) q^{39} +(19.6337 + 19.6337i) q^{41} +(50.2394 - 50.2394i) q^{43} +0.0884438 q^{45} +(-42.2268 - 42.2268i) q^{47} +16.4671 q^{49} +41.5567i q^{51} +16.5613 q^{53} +(-5.53173 - 5.53173i) q^{55} +36.7855i q^{57} +14.5041 q^{59} +(-45.3849 + 45.3849i) q^{61} +1.46435i q^{63} -4.90950 q^{65} +133.589i q^{67} +(30.8987 - 30.8987i) q^{69} +33.9204i q^{71} +(-22.1752 - 22.1752i) q^{73} +(53.0519 - 53.0519i) q^{75} +(91.5883 - 91.5883i) q^{77} +(-9.72981 + 9.72981i) q^{79} +82.5961 q^{81} -64.2570 q^{83} +(-4.73930 - 4.73930i) q^{85} +(-82.1233 - 31.2565i) q^{87} +(-119.740 + 119.740i) q^{89} -81.2861i q^{91} +133.790i q^{93} +(-4.19517 - 4.19517i) q^{95} +(-33.5755 - 33.5755i) q^{97} +(2.04863 + 2.04863i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} + 4 q^{7}+O(q^{10}) $ 8 * q + 2 * q^3 + 4 * q^7	$ 8 q + 2 q^{3} + 4 q^{7} + 6 q^{11} + 10 q^{15} + 12 q^{17} + 16 q^{19} - 36 q^{21} + 104 q^{25} + 98 q^{27} + 128 q^{29} + 10 q^{31} - 84 q^{37} + 90 q^{39} + 20 q^{41} + 190 q^{43} + 292 q^{45} - 58 q^{47} - 72 q^{49} + 252 q^{53} + 74 q^{55} + 40 q^{59} - 208 q^{61} + 36 q^{65} + 120 q^{69} - 188 q^{73} + 12 q^{75} + 180 q^{77} + 382 q^{79} - 124 q^{81} - 280 q^{83} + 32 q^{85} - 34 q^{87} - 64 q^{89} + 380 q^{95} - 44 q^{97} - 552 q^{99}+O(q^{100}) $ 8 * q + 2 * q^3 + 4 * q^7 + 6 * q^11 + 10 * q^15 + 12 * q^17 + 16 * q^19 - 36 * q^21 + 104 * q^25 + 98 * q^27 + 128 * q^29 + 10 * q^31 - 84 * q^37 + 90 * q^39 + 20 * q^41 + 190 * q^43 + 292 * q^45 - 58 * q^47 - 72 * q^49 + 252 * q^53 + 74 * q^55 + 40 * q^59 - 208 * q^61 + 36 * q^65 + 120 * q^69 - 188 * q^73 + 12 * q^75 + 180 * q^77 + 382 * q^79 - 124 * q^81 - 280 * q^83 + 32 * q^85 - 34 * q^87 - 64 * q^89 + 380 * q^95 - 44 * q^97 - 552 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/464\mathbb{Z}\right)^\times$.

$n$	$117$	$175$	$321$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	2.14254	−	2.14254i	0.714181	−	0.714181i	−0.253226	−	0.967407i	$-0.581492\pi$
$3$	2.14254	−	2.14254i	0.714181	−	0.714181i	0.967407	+	0.253226i	$0.0814917\pi$
$4$		0			0
$5$			0.488689i			0.0977379i	0.998805	+	0.0488689i	$0.0155617\pi$
$5$			0.488689i			0.0977379i	−0.998805	+	0.0488689i	$0.984438\pi$
$6$		0			0
$7$	−8.09117			−1.15588			−0.577941	−	0.816079i	$-0.696144\pi$
$7$	−8.09117			−1.15588			−0.577941	+	0.816079i	$0.696144\pi$
$8$		0			0
$9$		−	0.180982i		−	0.0201091i
$10$		0			0
$11$	−11.3195	+	11.3195i	−1.02905	+	1.02905i	−0.0294830	+	0.999565i	$0.509386\pi$
$11$	−11.3195	+	11.3195i	−1.02905	+	1.02905i	−0.999565	+	0.0294830i	$0.990614\pi$
$12$		0			0
$13$			10.0463i			0.772790i	0.922333	+	0.386395i	$0.126280\pi$
$13$			10.0463i			0.772790i	−0.922333	+	0.386395i	$0.873720\pi$
$14$		0			0
$15$	1.04704	+	1.04704i	0.0698025	+	0.0698025i
$16$		0			0
$17$	−9.69799	+	9.69799i	−0.570470	+	0.570470i	−0.932260	−	0.361790i	$-0.882166\pi$
$17$	−9.69799	+	9.69799i	−0.570470	+	0.570470i	0.361790	+	0.932260i	$0.382166\pi$
$18$		0			0
$19$	−8.58453	+	8.58453i	−0.451818	+	0.451818i	−0.895957	−	0.444140i	$-0.853509\pi$
$19$	−8.58453	+	8.58453i	−0.451818	+	0.451818i	0.444140	+	0.895957i	$0.353509\pi$
$20$		0			0
$21$	−17.3357	+	17.3357i	−0.825509	+	0.825509i
$22$		0			0
$23$	14.4215			0.627022			0.313511	−	0.949585i	$-0.398495\pi$
$23$	14.4215			0.627022			0.313511	+	0.949585i	$0.398495\pi$
$24$		0			0
$25$	24.7612			0.990447
$26$		0			0
$27$	18.8951	+	18.8951i	0.699820	+	0.699820i
$28$		0			0
$29$	−11.8706	−	26.4592i	−0.409333	−	0.912385i
$29$	−11.8706	−	26.4592i	−0.409333	−	0.912385i
$30$		0			0
$31$	−31.2221	+	31.2221i	−1.00717	+	1.00717i	−0.00719198	+	0.999974i	$0.502289\pi$
$31$	−31.2221	+	31.2221i	−1.00717	+	1.00717i	−0.999974	+	0.00719198i	$0.997711\pi$
$32$		0			0
$33$			48.5052i			1.46985i
$34$		0			0
$35$		−	3.95407i		−	0.112973i
$36$		0			0
$37$	−31.2631	−	31.2631i	−0.844950	−	0.844950i	0.144548	−	0.989498i	$-0.453827\pi$
$37$	−31.2631	−	31.2631i	−0.844950	−	0.844950i	−0.989498	+	0.144548i	$0.953827\pi$
$38$		0			0
$39$	21.5246	+	21.5246i	0.551912	+	0.551912i
$40$		0			0
$41$	19.6337	+	19.6337i	0.478871	+	0.478871i	0.904770	−	0.425900i	$-0.140042\pi$
$41$	19.6337	+	19.6337i	0.478871	+	0.478871i	−0.425900	+	0.904770i	$0.640042\pi$
$42$		0			0
$43$	50.2394	−	50.2394i	1.16836	−	1.16836i	0.185764	−	0.982594i	$-0.440524\pi$
$43$	50.2394	−	50.2394i	1.16836	−	1.16836i	0.982594	−	0.185764i	$-0.0594760\pi$
$44$		0			0
$45$	0.0884438			0.00196542
$46$		0			0
$47$	−42.2268	−	42.2268i	−0.898443	−	0.898443i	0.0968555	−	0.995298i	$-0.469122\pi$
$47$	−42.2268	−	42.2268i	−0.898443	−	0.898443i	−0.995298	+	0.0968555i	$0.969122\pi$
$48$		0			0
$49$	16.4671			0.336063
$50$		0			0
$51$			41.5567i			0.814838i
$52$		0			0
$53$	16.5613			0.312477			0.156239	−	0.987719i	$-0.450063\pi$
$53$	16.5613			0.312477			0.156239	+	0.987719i	$0.450063\pi$
$54$		0			0
$55$	−5.53173	−	5.53173i	−0.100577	−	0.100577i
$56$		0			0
$57$			36.7855i			0.645359i
$58$		0			0
$59$	14.5041			0.245833			0.122916	−	0.992417i	$-0.460775\pi$
$59$	14.5041			0.245833			0.122916	+	0.992417i	$0.460775\pi$
$60$		0			0
$61$	−45.3849	+	45.3849i	−0.744014	+	0.744014i	−0.973348	−	0.229334i	$-0.926345\pi$
$61$	−45.3849	+	45.3849i	−0.744014	+	0.744014i	0.229334	+	0.973348i	$0.426345\pi$
$62$		0			0
$63$			1.46435i			0.0232437i
$64$		0			0
$65$	−4.90950			−0.0755308
$66$		0			0
$67$			133.589i			1.99386i	0.0782703	+	0.996932i	$0.475060\pi$
$67$			133.589i			1.99386i	−0.0782703	+	0.996932i	$0.524940\pi$
$68$		0			0
$69$	30.8987	−	30.8987i	0.447807	−	0.447807i
$70$		0			0
$71$			33.9204i			0.477752i	0.971050	+	0.238876i	$0.0767790\pi$
$71$			33.9204i			0.477752i	−0.971050	+	0.238876i	$0.923221\pi$
$72$		0			0
$73$	−22.1752	−	22.1752i	−0.303770	−	0.303770i	0.538717	−	0.842487i	$-0.318909\pi$
$73$	−22.1752	−	22.1752i	−0.303770	−	0.303770i	−0.842487	+	0.538717i	$0.818909\pi$
$74$		0			0
$75$	53.0519	−	53.0519i	0.707359	−	0.707359i
$76$		0			0
$77$	91.5883	−	91.5883i	1.18946	−	1.18946i
$78$		0			0
$79$	−9.72981	+	9.72981i	−0.123162	+	0.123162i	−0.766001	−	0.642839i	$-0.777756\pi$
$79$	−9.72981	+	9.72981i	−0.123162	+	0.123162i	0.642839	+	0.766001i	$0.277756\pi$
$80$		0			0
$81$	82.5961			1.01970
$82$		0			0
$83$	−64.2570			−0.774181			−0.387091	−	0.922042i	$-0.626520\pi$
$83$	−64.2570			−0.774181			−0.387091	+	0.922042i	$0.626520\pi$
$84$		0			0
$85$	−4.73930	−	4.73930i	−0.0557565	−	0.0557565i
$86$		0			0
$87$	−82.1233	−	31.2565i	−0.943946	−	0.359271i
$88$		0			0
$89$	−119.740	+	119.740i	−1.34540	+	1.34540i	−0.454808	+	0.890590i	$0.650292\pi$
$89$	−119.740	+	119.740i	−1.34540	+	1.34540i	−0.890590	+	0.454808i	$0.849708\pi$
$90$		0			0
$91$		−	81.2861i		−	0.893254i
$92$		0			0
$93$			133.790i			1.43860i
$94$		0			0
$95$	−4.19517	−	4.19517i	−0.0441597	−	0.0441597i
$96$		0			0
$97$	−33.5755	−	33.5755i	−0.346139	−	0.346139i	0.512530	−	0.858669i	$-0.328708\pi$
$97$	−33.5755	−	33.5755i	−0.346139	−	0.346139i	−0.858669	+	0.512530i	$0.828708\pi$
$98$		0			0
$99$	2.04863	+	2.04863i	0.0206932	+	0.0206932i
$100$		0			0
$101$	−38.2463	+	38.2463i	−0.378676	+	0.378676i	−0.870624	−	0.491948i	$-0.836285\pi$
$101$	−38.2463	+	38.2463i	−0.378676	+	0.378676i	0.491948	+	0.870624i	$0.336285\pi$
$102$		0			0
$103$	−61.6568			−0.598609			−0.299305	−	0.954158i	$-0.596755\pi$
$103$	−61.6568			−0.598609			−0.299305	+	0.954158i	$0.596755\pi$
$104$		0			0
$105$	−8.47176	−	8.47176i	−0.0806835	−	0.0806835i
$106$		0			0
$107$	48.5836			0.454052			0.227026	−	0.973889i	$-0.427100\pi$
$107$	48.5836			0.454052			0.227026	+	0.973889i	$0.427100\pi$
$108$		0			0
$109$		−	82.0131i		−	0.752414i	−0.926536	−	0.376207i	$-0.877228\pi$
$109$		−	82.0131i		−	0.752414i	0.926536	−	0.376207i	$-0.122772\pi$
$110$		0			0
$111$	−133.965			−1.20689
$112$		0			0
$113$	0.444855	+	0.444855i	0.00393677	+	0.00393677i	0.709072	−	0.705136i	$-0.249114\pi$
$113$	0.444855	+	0.444855i	0.00393677	+	0.00393677i	−0.705136	+	0.709072i	$0.749114\pi$
$114$		0			0
$115$			7.04763i			0.0612838i
$116$		0			0
$117$	1.81819			0.0155401
$118$		0			0
$119$	78.4681	−	78.4681i	0.659396	−	0.659396i
$120$		0			0
$121$		−	135.264i		−	1.11788i
$122$		0			0
$123$	84.1321			0.684001
$124$		0			0
$125$			24.3178i			0.194542i
$126$		0			0
$127$	21.4010	−	21.4010i	0.168512	−	0.168512i	−0.617813	−	0.786325i	$-0.711981\pi$
$127$	21.4010	−	21.4010i	0.168512	−	0.168512i	0.786325	+	0.617813i	$0.211981\pi$
$128$		0			0
$129$		−	215.280i		−	1.66884i
$130$		0			0
$131$	46.6907	+	46.6907i	0.356417	+	0.356417i	0.862491	−	0.506073i	$-0.168903\pi$
$131$	46.6907	+	46.6907i	0.356417	+	0.356417i	−0.506073	+	0.862491i	$0.668903\pi$
$132$		0			0
$133$	69.4589	−	69.4589i	0.522248	−	0.522248i
$134$		0			0
$135$	−9.23385	+	9.23385i	−0.0683989	+	0.0683989i
$136$		0			0
$137$	5.76576	−	5.76576i	0.0420858	−	0.0420858i	−0.685751	−	0.727837i	$-0.740526\pi$
$137$	5.76576	−	5.76576i	0.0420858	−	0.0420858i	0.727837	+	0.685751i	$0.240526\pi$
$138$		0			0
$139$	223.985			1.61140			0.805701	−	0.592322i	$-0.201789\pi$
$139$	223.985			1.61140			0.805701	+	0.592322i	$0.201789\pi$
$140$		0			0
$141$	−180.946			−1.28330
$142$		0			0
$143$	−113.719	−	113.719i	−0.795238	−	0.795238i
$144$		0			0
$145$	12.9303	−	5.80106i	0.0891746	−	0.0400073i
$146$		0			0
$147$	35.2814	−	35.2814i	0.240010	−	0.240010i
$148$		0			0
$149$		−	129.230i		−	0.867316i	−0.901078	−	0.433658i	$-0.857223\pi$
$149$		−	129.230i		−	0.867316i	0.901078	−	0.433658i	$-0.142777\pi$
$150$		0			0
$151$		−	59.3971i		−	0.393359i	−0.980468	−	0.196679i	$-0.936984\pi$
$151$		−	59.3971i		−	0.393359i	0.980468	−	0.196679i	$-0.0630158\pi$
$152$		0			0
$153$	1.75516	+	1.75516i	0.0114716	+	0.0114716i
$154$		0			0
$155$	−15.2579	−	15.2579i	−0.0984383	−	0.0984383i
$156$		0			0
$157$	210.885	+	210.885i	1.34321	+	1.34321i	0.892840	+	0.450374i	$0.148709\pi$
$157$	210.885	+	210.885i	1.34321	+	1.34321i	0.450374	+	0.892840i	$0.351291\pi$
$158$		0			0
$159$	35.4833	−	35.4833i	0.223165	−	0.223165i
$160$		0			0
$161$	−116.687			−0.724763
$162$		0			0
$163$	151.656	+	151.656i	0.930405	+	0.930405i	0.997731	−	0.0673260i	$-0.0214467\pi$
$163$	151.656	+	151.656i	0.930405	+	0.930405i	−0.0673260	+	0.997731i	$0.521447\pi$
$164$		0			0
$165$	−23.7040			−0.143660
$166$		0			0
$167$		−	117.024i		−	0.700743i	−0.936611	−	0.350371i	$-0.886055\pi$
$167$		−	117.024i		−	0.700743i	0.936611	−	0.350371i	$-0.113945\pi$
$168$		0			0
$169$	68.0725			0.402796
$170$		0			0
$171$	1.55364	+	1.55364i	0.00908563	+	0.00908563i
$172$		0			0
$173$		−	51.3836i		−	0.297015i	−0.988911	−	0.148508i	$-0.952553\pi$
$173$		−	51.3836i		−	0.297015i	0.988911	−	0.148508i	$-0.0474469\pi$
$174$		0			0
$175$	−200.347			−1.14484
$176$		0			0
$177$	31.0757	−	31.0757i	0.175569	−	0.175569i
$178$		0			0
$179$		−	292.744i		−	1.63544i	−0.575615	−	0.817721i	$-0.695237\pi$
$179$		−	292.744i		−	1.63544i	0.575615	−	0.817721i	$-0.304763\pi$
$180$		0			0
$181$	175.159			0.967728			0.483864	−	0.875143i	$-0.339233\pi$
$181$	175.159			0.967728			0.483864	+	0.875143i	$0.339233\pi$
$182$		0			0
$183$			194.478i			1.06272i
$184$		0			0
$185$	15.2780	−	15.2780i	0.0825836	−	0.0825836i
$186$		0			0
$187$		−	219.553i		−	1.17408i
$188$		0			0
$189$	−152.884	−	152.884i	−0.808909	−	0.808909i
$190$		0			0
$191$	−46.8745	+	46.8745i	−0.245416	+	0.245416i	−0.819086	−	0.573670i	$-0.805519\pi$
$191$	−46.8745	+	46.8745i	−0.245416	+	0.245416i	0.573670	+	0.819086i	$0.305519\pi$
$192$		0			0
$193$	49.8678	−	49.8678i	0.258382	−	0.258382i	−0.566014	−	0.824396i	$-0.691515\pi$
$193$	49.8678	−	49.8678i	0.258382	−	0.258382i	0.824396	+	0.566014i	$0.191515\pi$
$194$		0			0
$195$	−10.5188	+	10.5188i	−0.0539427	+	0.0539427i
$196$		0			0
$197$	−59.7514			−0.303307			−0.151653	−	0.988434i	$-0.548460\pi$
$197$	−59.7514			−0.303307			−0.151653	+	0.988434i	$0.548460\pi$
$198$		0			0
$199$	10.7830			0.0541859			0.0270929	−	0.999633i	$-0.491375\pi$
$199$	10.7830			0.0541859			0.0270929	+	0.999633i	$0.491375\pi$
$200$		0			0
$201$	286.220	+	286.220i	1.42398	+	1.42398i
$202$		0			0
$203$	96.0474	+	214.086i	0.473140	+	1.05461i
$204$		0			0
$205$	−9.59478	+	9.59478i	−0.0468038	+	0.0468038i
$206$		0			0
$207$		−	2.61003i		−	0.0126088i
$208$		0			0
$209$		−	194.346i		−	0.929884i
$210$		0			0
$211$	−71.2119	−	71.2119i	−0.337497	−	0.337497i	0.517928	−	0.855424i	$-0.326704\pi$
$211$	−71.2119	−	71.2119i	−0.337497	−	0.337497i	−0.855424	+	0.517928i	$0.826704\pi$
$212$		0			0
$213$	72.6759	+	72.6759i	0.341201	+	0.341201i
$214$		0			0
$215$	24.5515	+	24.5515i	0.114193	+	0.114193i
$216$		0			0
$217$	252.624	−	252.624i	1.16417	−	1.16417i
$218$		0			0
$219$	−95.0227			−0.433894
$220$		0			0
$221$	−97.4286	−	97.4286i	−0.440853	−	0.440853i
$222$		0			0
$223$	166.943			0.748625			0.374312	−	0.927303i	$-0.377879\pi$
$223$	166.943			0.748625			0.374312	+	0.927303i	$0.377879\pi$
$224$		0			0
$225$		−	4.48132i		−	0.0199170i
$226$		0			0
$227$	120.332			0.530095			0.265048	−	0.964235i	$-0.414612\pi$
$227$	120.332			0.530095			0.265048	+	0.964235i	$0.414612\pi$
$228$		0			0
$229$	9.30072	+	9.30072i	0.0406145	+	0.0406145i	0.727122	−	0.686508i	$-0.240857\pi$
$229$	9.30072	+	9.30072i	0.0406145	+	0.0406145i	−0.686508	+	0.727122i	$0.740857\pi$
$230$		0			0
$231$		−	392.464i		−	1.69898i
$232$		0			0
$233$	−235.895			−1.01243			−0.506213	−	0.862408i	$-0.668955\pi$
$233$	−235.895			−1.01243			−0.506213	+	0.862408i	$0.668955\pi$
$234$		0			0
$235$	20.6358	−	20.6358i	0.0878119	−	0.0878119i
$236$		0			0
$237$			41.6931i			0.175920i
$238$		0			0
$239$	−389.332			−1.62900			−0.814501	−	0.580162i	$-0.802989\pi$
$239$	−389.332			−1.62900			−0.814501	+	0.580162i	$0.802989\pi$
$240$		0			0
$241$			163.689i			0.679206i	0.940569	+	0.339603i	$0.110293\pi$
$241$			163.689i			0.679206i	−0.940569	+	0.339603i	$0.889707\pi$
$242$		0			0
$243$	6.90952	−	6.90952i	0.0284342	−	0.0284342i
$244$		0			0
$245$			8.04729i			0.0328461i
$246$		0			0
$247$	−86.2425	−	86.2425i	−0.349160	−	0.349160i
$248$		0			0
$249$	−137.673	+	137.673i	−0.552905	+	0.552905i
$250$		0			0
$251$	132.018	−	132.018i	0.525968	−	0.525968i	−0.393399	−	0.919368i	$-0.628701\pi$
$251$	132.018	−	132.018i	0.525968	−	0.525968i	0.919368	+	0.393399i	$0.128701\pi$
$252$		0			0
$253$	−163.245	+	163.245i	−0.645236	+	0.645236i
$254$		0			0
$255$	−20.3083			−0.0796405
$256$		0			0
$257$	−113.634			−0.442155			−0.221078	−	0.975256i	$-0.570957\pi$
$257$	−113.634			−0.442155			−0.221078	+	0.975256i	$0.570957\pi$
$258$		0			0
$259$	252.955	+	252.955i	0.976662	+	0.976662i
$260$		0			0
$261$	−4.78863	+	2.14837i	−0.0183472	+	0.00823130i
$262$		0			0
$263$	−279.851	+	279.851i	−1.06407	+	1.06407i	−0.0662687	+	0.997802i	$0.521109\pi$
$263$	−279.851	+	279.851i	−1.06407	+	1.06407i	−0.997802	+	0.0662687i	$0.978891\pi$
$264$		0			0
$265$			8.09332i			0.0305408i
$266$		0			0
$267$			513.098i			1.92171i
$268$		0			0
$269$	302.867	+	302.867i	1.12590	+	1.12590i	0.990837	+	0.135061i	$0.0431231\pi$
$269$	302.867	+	302.867i	1.12590	+	1.12590i	0.135061	+	0.990837i	$0.456877\pi$
$270$		0			0
$271$	222.952	+	222.952i	0.822702	+	0.822702i	0.986495	−	0.163793i	$-0.0523728\pi$
$271$	222.952	+	222.952i	0.822702	+	0.822702i	−0.163793	+	0.986495i	$0.552373\pi$
$272$		0			0
$273$	−174.159	−	174.159i	−0.637945	−	0.637945i
$274$		0			0
$275$	−280.285	+	280.285i	−1.01922	+	1.01922i
$276$		0			0
$277$	290.196			1.04764			0.523820	−	0.851829i	$-0.324507\pi$
$277$	290.196			1.04764			0.523820	+	0.851829i	$0.324507\pi$
$278$		0			0
$279$	5.65064	+	5.65064i	0.0202532	+	0.0202532i
$280$		0			0
$281$	−486.000			−1.72954			−0.864768	−	0.502171i	$-0.832535\pi$
$281$	−486.000			−1.72954			−0.864768	+	0.502171i	$0.832535\pi$
$282$		0			0
$283$			95.1009i			0.336046i	0.985783	+	0.168023i	$0.0537382\pi$
$283$			95.1009i			0.336046i	−0.985783	+	0.168023i	$0.946262\pi$
$284$		0			0
$285$	−17.9767			−0.0630760
$286$		0			0
$287$	−158.860	−	158.860i	−0.553518	−	0.553518i
$288$		0			0
$289$			100.898i			0.349128i
$290$		0			0
$291$	−143.874			−0.494412
$292$		0			0
$293$	21.2589	−	21.2589i	0.0725559	−	0.0725559i	−0.669898	−	0.742454i	$-0.733662\pi$
$293$	21.2589	−	21.2589i	0.0725559	−	0.0725559i	0.742454	+	0.669898i	$0.233662\pi$
$294$		0			0
$295$			7.08801i			0.0240272i
$296$		0			0
$297$	−427.768			−1.44030
$298$		0			0
$299$			144.882i			0.484556i
$300$		0			0
$301$	−406.496	+	406.496i	−1.35048	+	1.35048i
$302$		0			0
$303$			163.889i			0.540887i
$304$		0			0
$305$	−22.1791	−	22.1791i	−0.0727183	−	0.0727183i
$306$		0			0
$307$	193.144	−	193.144i	0.629135	−	0.629135i	−0.318715	−	0.947850i	$-0.603251\pi$
$307$	193.144	−	193.144i	0.629135	−	0.629135i	0.947850	+	0.318715i	$0.103251\pi$
$308$		0			0
$309$	−132.102	+	132.102i	−0.427516	+	0.427516i
$310$		0			0
$311$	−112.842	+	112.842i	−0.362835	+	0.362835i	−0.864856	−	0.502021i	$-0.832590\pi$
$311$	−112.842	+	112.842i	−0.362835	+	0.362835i	0.502021	+	0.864856i	$0.332590\pi$
$312$		0			0
$313$	119.788			0.382710			0.191355	−	0.981521i	$-0.438712\pi$
$313$	119.788			0.382710			0.191355	+	0.981521i	$0.438712\pi$
$314$		0			0
$315$	−0.715614			−0.00227179
$316$		0			0
$317$	270.382	+	270.382i	0.852942	+	0.852942i	0.990494	−	0.137553i	$-0.0439237\pi$
$317$	270.382	+	270.382i	0.852942	+	0.852942i	−0.137553	+	0.990494i	$0.543924\pi$
$318$		0			0
$319$	433.876	+	165.135i	1.36011	+	0.517665i
$320$		0			0
$321$	104.092	−	104.092i	0.324276	−	0.324276i
$322$		0			0
$323$		−	166.505i		−	0.515497i
$324$		0			0
$325$			248.758i			0.765408i
$326$		0			0
$327$	−175.717	−	175.717i	−0.537360	−	0.537360i
$328$		0			0
$329$	341.665	+	341.665i	1.03849	+	1.03849i
$330$		0			0
$331$	64.5326	+	64.5326i	0.194962	+	0.194962i	0.797836	−	0.602874i	$-0.205978\pi$
$331$	64.5326	+	64.5326i	0.194962	+	0.194962i	−0.602874	+	0.797836i	$0.705978\pi$
$332$		0			0
$333$	−5.65806	+	5.65806i	−0.0169912	+	0.0169912i
$334$		0			0
$335$	−65.2835			−0.194876
$336$		0			0
$337$	−49.1921	−	49.1921i	−0.145971	−	0.145971i	0.630345	−	0.776315i	$-0.282914\pi$
$337$	−49.1921	−	49.1921i	−0.145971	−	0.145971i	−0.776315	+	0.630345i	$0.782914\pi$
$338$		0			0
$339$	1.90624			0.00562313
$340$		0			0
$341$		−	706.840i		−	2.07285i
$342$		0			0
$343$	263.229			0.767433
$344$		0			0
$345$	15.0999	+	15.0999i	0.0437677	+	0.0437677i
$346$		0			0
$347$		−	75.0323i		−	0.216231i	−0.994138	−	0.108116i	$-0.965518\pi$
$347$		−	75.0323i		−	0.216231i	0.994138	−	0.108116i	$-0.0344817\pi$
$348$		0			0
$349$	284.109			0.814067			0.407033	−	0.913413i	$-0.366563\pi$
$349$	284.109			0.814067			0.407033	+	0.913413i	$0.366563\pi$
$350$		0			0
$351$	−189.826	+	189.826i	−0.540813	+	0.540813i
$352$		0			0
$353$			157.587i			0.446422i	0.974770	+	0.223211i	$0.0716538\pi$
$353$			157.587i			0.446422i	−0.974770	+	0.223211i	$0.928346\pi$
$354$		0			0
$355$	−16.5765			−0.0466945
$356$		0			0
$357$		−	336.243i		−	0.941856i
$358$		0			0
$359$	327.012	−	327.012i	0.910896	−	0.910896i	−0.0854467	−	0.996343i	$-0.527232\pi$
$359$	327.012	−	327.012i	0.910896	−	0.910896i	0.996343	+	0.0854467i	$0.0272317\pi$
$360$		0			0
$361$			213.612i			0.591722i
$362$		0			0
$363$	−289.808	−	289.808i	−0.798369	−	0.798369i
$364$		0			0
$365$	10.8368	−	10.8368i	0.0296898	−	0.0296898i
$366$		0			0
$367$	−243.021	+	243.021i	−0.662182	+	0.662182i	−0.955894	−	0.293712i	$-0.905109\pi$
$367$	−243.021	+	243.021i	−0.662182	+	0.662182i	0.293712	+	0.955894i	$0.405109\pi$
$368$		0			0
$369$	3.55334	−	3.55334i	0.00962965	−	0.00962965i
$370$		0			0
$371$	−134.000			−0.361187
$372$		0			0
$373$	−503.790			−1.35064			−0.675322	−	0.737523i	$-0.735995\pi$
$373$	−503.790			−1.35064			−0.675322	+	0.737523i	$0.735995\pi$
$374$		0			0
$375$	52.1018	+	52.1018i	0.138938	+	0.138938i
$376$		0			0
$377$	265.816	−	119.256i	0.705082	−	0.316328i
$378$		0			0
$379$	74.1929	−	74.1929i	0.195760	−	0.195760i	−0.602420	−	0.798179i	$-0.705797\pi$
$379$	74.1929	−	74.1929i	0.195760	−	0.195760i	0.798179	+	0.602420i	$0.205797\pi$
$380$		0			0
$381$		−	91.7051i		−	0.240696i
$382$		0			0
$383$			561.592i			1.46630i	0.680068	+	0.733149i	$0.261950\pi$
$383$			561.592i			1.46630i	−0.680068	+	0.733149i	$0.738050\pi$
$384$		0			0
$385$	44.7582	+	44.7582i	0.116255	+	0.116255i
$386$		0			0
$387$	−9.09241	−	9.09241i	−0.0234946	−	0.0234946i
$388$		0			0
$389$	−111.236	−	111.236i	−0.285953	−	0.285953i	0.549525	−	0.835478i	$-0.314809\pi$
$389$	−111.236	−	111.236i	−0.285953	−	0.285953i	−0.835478	+	0.549525i	$0.814809\pi$
$390$		0			0
$391$	−139.860	+	139.860i	−0.357697	+	0.357697i
$392$		0			0
$393$	200.074			0.509093
$394$		0			0
$395$	−4.75485	−	4.75485i	−0.0120376	−	0.0120376i
$396$		0			0
$397$	695.905			1.75291			0.876455	−	0.481484i	$-0.159902\pi$
$397$	695.905			1.75291			0.876455	+	0.481484i	$0.159902\pi$
$398$		0			0
$399$		−	297.638i		−	0.745959i
$400$		0			0
$401$	450.193			1.12268			0.561338	−	0.827587i	$-0.310287\pi$
$401$	450.193			1.12268			0.561338	+	0.827587i	$0.310287\pi$
$402$		0			0
$403$	−313.666	−	313.666i	−0.778328	−	0.778328i
$404$		0			0
$405$			40.3638i			0.0996638i
$406$		0			0
$407$	707.768			1.73899
$408$		0			0
$409$	−449.447	+	449.447i	−1.09889	+	1.09889i	−0.104353	+	0.994540i	$0.533277\pi$
$409$	−449.447	+	449.447i	−1.09889	+	1.09889i	−0.994540	+	0.104353i	$0.966723\pi$
$410$		0			0
$411$		−	24.7068i		−	0.0601138i
$412$		0			0
$413$	−117.355			−0.284154
$414$		0			0
$415$		−	31.4017i		−	0.0756668i
$416$		0			0
$417$	479.898	−	479.898i	1.15083	−	1.15083i
$418$		0			0
$419$			585.961i			1.39848i	0.714889	+	0.699238i	$0.246477\pi$
$419$			585.961i			1.39848i	−0.714889	+	0.699238i	$0.753523\pi$
$420$		0			0
$421$	−37.5863	−	37.5863i	−0.0892786	−	0.0892786i	0.661057	−	0.750336i	$-0.270108\pi$
$421$	−37.5863	−	37.5863i	−0.0892786	−	0.0892786i	−0.750336	+	0.661057i	$0.770108\pi$
$422$		0			0
$423$	−7.64228	+	7.64228i	−0.0180669	+	0.0180669i
$424$		0			0
$425$	−240.134	+	240.134i	−0.565020	+	0.565020i
$426$		0			0
$427$	367.217	−	367.217i	0.859992	−	0.859992i
$428$		0			0
$429$	−487.296			−1.13589
$430$		0			0
$431$	−270.174			−0.626853			−0.313427	−	0.949612i	$-0.601477\pi$
$431$	−270.174			−0.626853			−0.313427	+	0.949612i	$0.601477\pi$
$432$		0			0
$433$	214.672	+	214.672i	0.495779	+	0.495779i	0.910121	−	0.414342i	$-0.135988\pi$
$433$	214.672	+	214.672i	0.495779	+	0.495779i	−0.414342	+	0.910121i	$0.635988\pi$
$434$		0			0
$435$	15.2747	−	40.1328i	0.0351143	−	0.0922592i
$436$		0			0
$437$	−123.802	+	123.802i	−0.283299	+	0.283299i
$438$		0			0
$439$		−	380.066i		−	0.865753i	−0.901453	−	0.432877i	$-0.857499\pi$
$439$		−	380.066i		−	0.865753i	0.901453	−	0.432877i	$-0.142501\pi$
$440$		0			0
$441$		−	2.98024i		−	0.00675792i
$442$		0			0
$443$	248.852	+	248.852i	0.561743	+	0.561743i	0.929802	−	0.368059i	$-0.119978\pi$
$443$	248.852	+	248.852i	0.561743	+	0.561743i	−0.368059	+	0.929802i	$0.619978\pi$
$444$		0			0
$445$	−58.5158	−	58.5158i	−0.131496	−	0.131496i
$446$		0			0
$447$	−276.881	−	276.881i	−0.619420	−	0.619420i
$448$		0			0
$449$	133.874	−	133.874i	0.298159	−	0.298159i	−0.542133	−	0.840293i	$-0.682383\pi$
$449$	133.874	−	133.874i	0.298159	−	0.298159i	0.840293	+	0.542133i	$0.182383\pi$
$450$		0			0
$451$	−444.489			−0.985562
$452$		0			0
$453$	−127.261	−	127.261i	−0.280929	−	0.280929i
$454$		0			0
$455$	39.7236			0.0873047
$456$		0			0
$457$			476.374i			1.04239i	0.853436	+	0.521197i	$0.174514\pi$
$457$			476.374i			1.04239i	−0.853436	+	0.521197i	$0.825486\pi$
$458$		0			0
$459$	−366.489			−0.798452
$460$		0			0
$461$	−478.069	−	478.069i	−1.03703	−	1.03703i	−0.999288	−	0.0377379i	$-0.987985\pi$
$461$	−478.069	−	478.069i	−1.03703	−	1.03703i	−0.0377379	−	0.999288i	$-0.512015\pi$
$462$		0			0
$463$			144.158i			0.311357i	0.987808	+	0.155678i	$0.0497564\pi$
$463$			144.158i			0.311357i	−0.987808	+	0.155678i	$0.950244\pi$
$464$		0			0
$465$	−65.3815			−0.140605
$466$		0			0
$467$	63.5129	−	63.5129i	0.136002	−	0.136002i	−0.635828	−	0.771830i	$-0.719341\pi$
$467$	63.5129	−	63.5129i	0.136002	−	0.136002i	0.771830	+	0.635828i	$0.219341\pi$
$468$		0			0
$469$		−	1080.89i		−	2.30467i
$470$		0			0
$471$	903.659			1.91860
$472$		0			0
$473$			1137.37i			2.40459i
$474$		0			0
$475$	−212.563	+	212.563i	−0.447501	+	0.447501i
$476$		0			0
$477$		−	2.99729i		−	0.00628363i
$478$		0			0
$479$	25.8901	+	25.8901i	0.0540503	+	0.0540503i	0.733615	−	0.679565i	$-0.237831\pi$
$479$	25.8901	+	25.8901i	0.0540503	+	0.0540503i	−0.679565	+	0.733615i	$0.737831\pi$
$480$		0			0
$481$	314.078	−	314.078i	0.652969	−	0.652969i
$482$		0			0
$483$	−250.007	+	250.007i	−0.517612	+	0.517612i
$484$		0			0
$485$	16.4080	−	16.4080i	0.0338309	−	0.0338309i
$486$		0			0
$487$	383.625			0.787730			0.393865	−	0.919168i	$-0.371138\pi$
$487$	383.625			0.787730			0.393865	+	0.919168i	$0.371138\pi$
$488$		0			0
$489$	649.859			1.32896
$490$		0			0
$491$	−196.364	−	196.364i	−0.399927	−	0.399927i	0.478280	−	0.878207i	$-0.341260\pi$
$491$	−196.364	−	196.364i	−0.399927	−	0.399927i	−0.878207	+	0.478280i	$0.841260\pi$
$492$		0			0
$493$	371.722	+	141.479i	0.754000	+	0.286976i
$494$		0			0
$495$	−1.00114	+	1.00114i	−0.00202251	+	0.00202251i
$496$		0			0
$497$		−	274.456i		−	0.552225i
$498$		0			0
$499$		−	513.725i		−	1.02951i	−0.857337	−	0.514755i	$-0.827883\pi$
$499$		−	513.725i		−	1.02951i	0.857337	−	0.514755i	$-0.172117\pi$
$500$		0			0
$501$	−250.729	−	250.729i	−0.500457	−	0.500457i
$502$		0			0
$503$	−195.929	−	195.929i	−0.389522	−	0.389522i	0.484995	−	0.874517i	$-0.338821\pi$
$503$	−195.929	−	195.929i	−0.389522	−	0.389522i	−0.874517	+	0.484995i	$0.838821\pi$
$504$		0			0
$505$	−18.6905	−	18.6905i	−0.0370110	−	0.0370110i
$506$		0			0
$507$	145.848	−	145.848i	0.287669	−	0.287669i
$508$		0			0
$509$	−802.720			−1.57705			−0.788526	−	0.615001i	$-0.789155\pi$
$509$	−802.720			−1.57705			−0.788526	+	0.615001i	$0.789155\pi$
$510$		0			0
$511$	179.424	+	179.424i	0.351122	+	0.351122i
$512$		0			0
$513$	−324.412			−0.632381
$514$		0			0
$515$		−	30.1310i		−	0.0585068i
$516$		0			0
$517$	955.976			1.84908
$518$		0			0
$519$	−110.092	−	110.092i	−0.212123	−	0.212123i
$520$		0			0
$521$		−	913.769i		−	1.75388i	−0.480604	−	0.876938i	$-0.659583\pi$
$521$		−	913.769i		−	1.75388i	0.480604	−	0.876938i	$-0.340417\pi$
$522$		0			0
$523$	280.930			0.537151			0.268575	−	0.963259i	$-0.413447\pi$
$523$	280.930			0.537151			0.268575	+	0.963259i	$0.413447\pi$
$524$		0			0
$525$	−429.252	+	429.252i	−0.817623	+	0.817623i
$526$		0			0
$527$		−	605.584i		−	1.14912i
$528$		0			0
$529$	−321.020			−0.606844
$530$		0			0
$531$		−	2.62498i		−	0.00494347i
$532$		0			0
$533$	−197.245	+	197.245i	−0.370067	+	0.370067i
$534$		0			0
$535$			23.7423i			0.0443781i
$536$		0			0
$537$	−627.217	−	627.217i	−1.16800	−	1.16800i
$538$		0			0
$539$	−186.400	+	186.400i	−0.345825	+	0.345825i
$540$		0			0
$541$	−17.1635	+	17.1635i	−0.0317255	+	0.0317255i	−0.722792	−	0.691066i	$-0.757141\pi$
$541$	−17.1635	+	17.1635i	−0.0317255	+	0.0317255i	0.691066	+	0.722792i	$0.257141\pi$
$542$		0			0
$543$	375.285	−	375.285i	0.691133	−	0.691133i
$544$		0			0
$545$	40.0789			0.0735393
$546$		0			0
$547$	−116.845			−0.213610			−0.106805	−	0.994280i	$-0.534062\pi$
$547$	−116.845			−0.213610			−0.106805	+	0.994280i	$0.534062\pi$
$548$		0			0
$549$	8.21383	+	8.21383i	0.0149614	+	0.0149614i
$550$		0			0
$551$	329.044	+	125.236i	0.597175	+	0.227288i
$552$		0			0
$553$	78.7255	−	78.7255i	0.142361	−	0.142361i
$554$		0			0
$555$		−	65.4674i		−	0.117959i
$556$		0			0
$557$			575.508i			1.03323i	0.856218	+	0.516614i	$0.172808\pi$
$557$			575.508i			1.03323i	−0.856218	+	0.516614i	$0.827192\pi$
$558$		0			0
$559$	504.719	+	504.719i	0.902896	+	0.902896i
$560$		0			0
$561$	−470.403	−	470.403i	−0.838507	−	0.838507i
$562$		0			0
$563$	−465.411	−	465.411i	−0.826662	−	0.826662i	0.160391	−	0.987054i	$-0.448724\pi$
$563$	−465.411	−	465.411i	−0.826662	−	0.826662i	−0.987054	+	0.160391i	$0.948724\pi$
$564$		0			0
$565$	−0.217396	+	0.217396i	−0.000384771	+	0.000384771i
$566$		0			0
$567$	−668.299			−1.17866
$568$		0			0
$569$	417.363	+	417.363i	0.733503	+	0.733503i	0.971312	−	0.237809i	$-0.0764292\pi$
$569$	417.363	+	417.363i	0.733503	+	0.733503i	−0.237809	+	0.971312i	$0.576429\pi$
$570$		0			0
$571$	−24.6693			−0.0432037			−0.0216019	−	0.999767i	$-0.506877\pi$
$571$	−24.6693			−0.0432037			−0.0216019	+	0.999767i	$0.506877\pi$
$572$		0			0
$573$			200.861i			0.350543i
$574$		0			0
$575$	357.093			0.621032
$576$		0			0
$577$	−152.708	−	152.708i	−0.264659	−	0.264659i	0.562285	−	0.826944i	$-0.309922\pi$
$577$	−152.708	−	152.708i	−0.264659	−	0.264659i	−0.826944	+	0.562285i	$0.809922\pi$
$578$		0			0
$579$		−	213.688i		−	0.369063i
$580$		0			0
$581$	519.915			0.894862
$582$		0			0
$583$	−187.466	+	187.466i	−0.321554	+	0.321554i
$584$		0			0
$585$			0.888530i			0.00151886i
$586$		0			0
$587$	−891.866			−1.51936			−0.759681	−	0.650295i	$-0.774645\pi$
$587$	−891.866			−1.51936			−0.759681	+	0.650295i	$0.774645\pi$
$588$		0			0
$589$		−	536.055i		−	0.910111i
$590$		0			0
$591$	−128.020	+	128.020i	−0.216616	+	0.216616i
$592$		0			0
$593$		−	1124.61i		−	1.89647i	−0.317563	−	0.948237i	$-0.602864\pi$
$593$		−	1124.61i		−	1.89647i	0.317563	−	0.948237i	$-0.397136\pi$
$594$		0			0
$595$	38.3465	+	38.3465i	0.0644479	+	0.0644479i
$596$		0			0
$597$	23.1030	−	23.1030i	0.0386985	−	0.0386985i
$598$		0			0
$599$	−222.555	+	222.555i	−0.371544	+	0.371544i	−0.868040	−	0.496495i	$-0.834620\pi$
$599$	−222.555	+	222.555i	−0.371544	+	0.371544i	0.496495	+	0.868040i	$0.334620\pi$
$600$		0			0
$601$	−196.657	+	196.657i	−0.327216	+	0.327216i	−0.851527	−	0.524311i	$-0.824323\pi$
$601$	−196.657	+	196.657i	−0.327216	+	0.327216i	0.524311	+	0.851527i	$0.324323\pi$
$602$		0			0
$603$	24.1771			0.0400948
$604$		0			0
$605$	66.1019			0.109259
$606$		0			0
$607$	660.823	+	660.823i	1.08867	+	1.08867i	0.995666	+	0.0930047i	$0.0296471\pi$
$607$	660.823	+	660.823i	1.08867	+	1.08867i	0.0930047	+	0.995666i	$0.470353\pi$
$608$		0			0
$609$	664.474	+	252.902i	1.09109	+	0.415274i
$610$		0			0
$611$	424.222	−	424.222i	0.694308	−	0.694308i
$612$		0			0
$613$		−	299.378i		−	0.488382i	−0.969727	−	0.244191i	$-0.921478\pi$
$613$		−	299.378i		−	0.488382i	0.969727	−	0.244191i	$-0.0785224\pi$
$614$		0			0
$615$			41.1145i			0.0668528i
$616$		0			0
$617$	−419.542	−	419.542i	−0.679972	−	0.679972i	0.280022	−	0.959994i	$-0.409658\pi$
$617$	−419.542	−	419.542i	−0.679972	−	0.679972i	−0.959994	+	0.280022i	$0.909658\pi$
$618$		0			0
$619$	−243.311	−	243.311i	−0.393072	−	0.393072i	0.482709	−	0.875781i	$-0.339653\pi$
$619$	−243.311	−	243.311i	−0.393072	−	0.393072i	−0.875781	+	0.482709i	$0.839653\pi$
$620$		0			0
$621$	272.496	+	272.496i	0.438802	+	0.438802i
$622$		0			0
$623$	968.840	−	968.840i	1.55512	−	1.55512i
$624$		0			0
$625$	607.146			0.971433
$626$		0			0
$627$	−416.394	−	416.394i	−0.664106	−	0.664106i
$628$		0			0
$629$	606.379			0.964037
$630$		0			0
$631$			96.3199i			0.152647i	0.997083	+	0.0763233i	$0.0243181\pi$
$631$			96.3199i			0.152647i	−0.997083	+	0.0763233i	$0.975682\pi$
$632$		0			0
$633$	−305.149			−0.482068
$634$		0			0
$635$	10.4584	+	10.4584i	0.0164700	+	0.0164700i
$636$		0			0
$637$			165.433i			0.259706i
$638$		0			0
$639$	6.13897			0.00960715
$640$		0			0
$641$	−378.246	+	378.246i	−0.590088	+	0.590088i	−0.937655	−	0.347567i	$-0.887008\pi$
$641$	−378.246	+	378.246i	−0.590088	+	0.590088i	0.347567	+	0.937655i	$0.387008\pi$
$642$		0			0
$643$			258.453i			0.401949i	0.979597	+	0.200974i	$0.0644108\pi$
$643$			258.453i			0.401949i	−0.979597	+	0.200974i	$0.935589\pi$
$644$		0			0
$645$	105.205			0.163109
$646$		0			0
$647$			568.930i			0.879336i	0.898160	+	0.439668i	$0.144904\pi$
$647$			568.930i			0.879336i	−0.898160	+	0.439668i	$0.855096\pi$
$648$		0			0
$649$	−164.180	+	164.180i	−0.252974	+	0.252974i
$650$		0			0
$651$		−	1082.51i		−	1.66285i
$652$		0			0
$653$	810.018	+	810.018i	1.24046	+	1.24046i	0.959812	+	0.280645i	$0.0905485\pi$
$653$	810.018	+	810.018i	1.24046	+	1.24046i	0.280645	+	0.959812i	$0.409452\pi$
$654$		0			0
$655$	−22.8172	+	22.8172i	−0.0348355	+	0.0348355i
$656$		0			0
$657$	−4.01331	+	4.01331i	−0.00610854	+	0.00610854i
$658$		0			0
$659$	−573.095	+	573.095i	−0.869644	+	0.869644i	−0.992433	−	0.122789i	$-0.960816\pi$
$659$	−573.095	+	573.095i	−0.869644	+	0.869644i	0.122789	+	0.992433i	$0.460816\pi$
$660$		0			0
$661$	654.922			0.990804			0.495402	−	0.868664i	$-0.335021\pi$
$661$	654.922			0.990804			0.495402	+	0.868664i	$0.335021\pi$
$662$		0			0
$663$	−417.490			−0.629698
$664$		0			0
$665$	33.9438	+	33.9438i	0.0510434	+	0.0510434i
$666$		0			0
$667$	−171.193	−	381.581i	−0.256660	−	0.572085i
$668$		0			0
$669$	357.683	−	357.683i	0.534653	−	0.534653i
$670$		0			0
$671$		−	1027.47i		−	1.53125i
$672$		0			0
$673$			395.630i			0.587861i	0.955827	+	0.293930i	$0.0949633\pi$
$673$			395.630i			0.587861i	−0.955827	+	0.293930i	$0.905037\pi$
$674$		0			0
$675$	467.866	+	467.866i	0.693134	+	0.693134i
$676$		0			0
$677$	−161.375	−	161.375i	−0.238368	−	0.238368i	0.577806	−	0.816174i	$-0.303909\pi$
$677$	−161.375	−	161.375i	−0.238368	−	0.238368i	−0.816174	+	0.577806i	$0.803909\pi$
$678$		0			0
$679$	271.665	+	271.665i	0.400096	+	0.400096i
$680$		0			0
$681$	257.816	−	257.816i	0.378584	−	0.378584i
$682$		0			0
$683$	−635.971			−0.931143			−0.465572	−	0.885010i	$-0.654151\pi$
$683$	−635.971			−0.931143			−0.465572	+	0.885010i	$0.654151\pi$
$684$		0			0
$685$	2.81766	+	2.81766i	0.00411338	+	0.00411338i
$686$		0			0
$687$	39.8544			0.0580122
$688$		0			0
$689$			166.379i			0.241479i
$690$		0			0
$691$	440.160			0.636990			0.318495	−	0.947925i	$-0.396823\pi$
$691$	440.160			0.636990			0.318495	+	0.947925i	$0.396823\pi$
$692$		0			0
$693$	−16.5758	−	16.5758i	−0.0239189	−	0.0239189i
$694$		0			0
$695$			109.459i			0.157495i
$696$		0			0
$697$	−380.815			−0.546363
$698$		0			0
$699$	−505.416	+	505.416i	−0.723056	+	0.723056i
$700$		0			0
$701$			330.622i			0.471643i	0.971796	+	0.235822i	$0.0757781\pi$
$701$			330.622i			0.471643i	−0.971796	+	0.235822i	$0.924222\pi$
$702$		0			0
$703$	536.759			0.763526
$704$		0			0
$705$		−	88.4262i		−	0.125427i
$706$		0			0
$707$	309.457	−	309.457i	0.437705	−	0.437705i
$708$		0			0
$709$		−	740.213i		−	1.04402i	−0.852938	−	0.522012i	$-0.825182\pi$
$709$		−	740.213i		−	1.04402i	0.852938	−	0.522012i	$-0.174818\pi$
$710$		0			0
$711$	1.76092	+	1.76092i	0.00247668	+	0.00247668i
$712$		0			0
$713$	−450.270	+	450.270i	−0.631515	+	0.631515i
$714$		0			0
$715$	55.5733	−	55.5733i	0.0777249	−	0.0777249i
$716$		0			0
$717$	−834.160	+	834.160i	−1.16340	+	1.16340i
$718$		0			0
$719$	177.916			0.247449			0.123725	−	0.992317i	$-0.460516\pi$
$719$	177.916			0.247449			0.123725	+	0.992317i	$0.460516\pi$
$720$		0			0
$721$	498.876			0.691922
$722$		0			0
$723$	350.710	+	350.710i	0.485076	+	0.485076i
$724$		0			0
$725$	−293.931	−	655.160i	−0.405422	−	0.903670i
$726$		0			0
$727$	322.555	−	322.555i	0.443680	−	0.443680i	−0.449567	−	0.893247i	$-0.648422\pi$
$727$	322.555	−	322.555i	0.443680	−	0.443680i	0.893247	+	0.449567i	$0.148422\pi$
$728$		0			0
$729$			713.757i			0.979090i
$730$		0			0
$731$			974.443i			1.33303i
$732$		0			0
$733$	691.012	+	691.012i	0.942718	+	0.942718i	0.998446	−	0.0557278i	$-0.0177479\pi$
$733$	691.012	+	691.012i	0.942718	+	0.942718i	−0.0557278	+	0.998446i	$0.517748\pi$
$734$		0			0
$735$	17.2417	+	17.2417i	0.0234580	+	0.0234580i
$736$		0			0
$737$	−1512.16	−	1512.16i	−2.05178	−	2.05178i
$738$		0			0
$739$	80.9996	−	80.9996i	0.109607	−	0.109607i	−0.650176	−	0.759783i	$-0.725305\pi$
$739$	80.9996	−	80.9996i	0.109607	−	0.109607i	0.759783	+	0.650176i	$0.225305\pi$
$740$		0			0
$741$	−369.557			−0.498727
$742$		0			0
$743$	27.4691	+	27.4691i	0.0369705	+	0.0369705i	0.725350	−	0.688380i	$-0.241678\pi$
$743$	27.4691	+	27.4691i	0.0369705	+	0.0369705i	−0.688380	+	0.725350i	$0.741678\pi$
$744$		0			0
$745$	63.1533			0.0847696
$746$		0			0
$747$			11.6293i			0.0155681i
$748$		0			0
$749$	−393.098			−0.524831
$750$		0			0
$751$	−370.129	−	370.129i	−0.492849	−	0.492849i	0.416354	−	0.909203i	$-0.363308\pi$
$751$	−370.129	−	370.129i	−0.492849	−	0.492849i	−0.909203	+	0.416354i	$0.863308\pi$
$752$		0			0
$753$		−	565.709i		−	0.751273i
$754$		0			0
$755$	29.0267			0.0384460
$756$		0			0
$757$	361.762	−	361.762i	0.477889	−	0.477889i	−0.426567	−	0.904456i	$-0.640277\pi$
$757$	361.762	−	361.762i	0.477889	−	0.477889i	0.904456	+	0.426567i	$0.140277\pi$
$758$		0			0
$759$			699.517i			0.921630i
$760$		0			0
$761$	955.440			1.25551			0.627753	−	0.778413i	$-0.283975\pi$
$761$	955.440			1.25551			0.627753	+	0.778413i	$0.283975\pi$
$762$		0			0
$763$			663.582i			0.869702i
$764$		0			0
$765$	−0.857727	+	0.857727i	−0.00112121	+	0.00112121i
$766$		0			0
$767$			145.712i			0.189977i
$768$		0			0
$769$	−881.047	−	881.047i	−1.14570	−	1.14570i	−0.987388	−	0.158316i	$-0.949393\pi$
$769$	−881.047	−	881.047i	−1.14570	−	1.14570i	−0.158316	−	0.987388i	$-0.550607\pi$
$770$		0			0
$771$	−243.466	+	243.466i	−0.315779	+	0.315779i
$772$		0			0
$773$	−46.5963	+	46.5963i	−0.0602799	+	0.0602799i	−0.736604	−	0.676324i	$-0.763572\pi$
$773$	−46.5963	+	46.5963i	−0.0602799	+	0.0602799i	0.676324	+	0.736604i	$0.263572\pi$
$774$		0			0
$775$	−773.097	+	773.097i	−0.997545	+	0.997545i
$776$		0			0
$777$	1083.94			1.39503
$778$		0			0
$779$	−337.092			−0.432724
$780$		0			0
$781$	−383.963	−	383.963i	−0.491630	−	0.491630i
$782$		0			0
$783$	275.652	−	724.247i	0.352046	−	0.924964i
$784$		0			0
$785$	−103.057	+	103.057i	−0.131283	+	0.131283i
$786$		0			0
$787$			201.018i			0.255424i	0.991811	+	0.127712i	$0.0407633\pi$
$787$			201.018i			0.255424i	−0.991811	+	0.127712i	$0.959237\pi$
$788$		0			0
$789$			1199.18i			1.51988i
$790$		0			0
$791$	−3.59940	−	3.59940i	−0.00455044	−	0.00455044i
$792$		0			0
$793$	−455.948	−	455.948i	−0.574967	−	0.574967i
$794$		0			0
$795$	17.3403	+	17.3403i	0.0218117	+	0.0218117i
$796$		0			0
$797$	−463.705	+	463.705i	−0.581813	+	0.581813i	−0.935401	−	0.353588i	$-0.884962\pi$
$797$	−463.705	+	463.705i	−0.581813	+	0.581813i	0.353588	+	0.935401i	$0.384962\pi$
$798$		0			0
$799$	819.030			1.02507
$800$		0			0
$801$	21.6708	+	21.6708i	0.0270547	+	0.0270547i
$802$		0			0
$803$	502.026			0.625188
$804$		0			0
$805$		−	57.0236i		−	0.0708368i
$806$		0			0
$807$	1297.81			1.60819
$808$		0			0
$809$	775.202	+	775.202i	0.958222	+	0.958222i	0.999162	−	0.0409393i	$-0.0130350\pi$
$809$	775.202	+	775.202i	0.958222	+	0.958222i	−0.0409393	+	0.999162i	$0.513035\pi$
$810$		0			0
$811$		−	612.179i		−	0.754845i	−0.926041	−	0.377423i	$-0.876810\pi$
$811$		−	612.179i		−	0.754845i	0.926041	−	0.377423i	$-0.123190\pi$
$812$		0			0
$813$	955.370			1.17512
$814$		0			0
$815$	−74.1127	+	74.1127i	−0.0909358	+	0.0909358i
$816$		0			0
$817$			862.564i			1.05577i
$818$		0			0
$819$	−14.7113			−0.0179625
$820$		0			0
$821$			436.309i			0.531436i	0.964051	+	0.265718i	$0.0856091\pi$
$821$			436.309i			0.531436i	−0.964051	+	0.265718i	$0.914391\pi$
$822$		0			0
$823$	−1065.70	+	1065.70i	−1.29489	+	1.29489i	−0.363168	+	0.931724i	$0.618305\pi$
$823$	−1065.70	+	1065.70i	−1.29489	+	1.29489i	−0.931724	+	0.363168i	$0.881695\pi$
$824$		0			0
$825$			1201.05i			1.45581i
$826$		0			0
$827$	−348.391	−	348.391i	−0.421271	−	0.421271i	0.464370	−	0.885641i	$-0.346281\pi$
$827$	−348.391	−	348.391i	−0.421271	−	0.421271i	−0.885641	+	0.464370i	$0.846281\pi$
$828$		0			0
$829$	−973.035	+	973.035i	−1.17375	+	1.17375i	−0.192436	+	0.981310i	$0.561639\pi$
$829$	−973.035	+	973.035i	−1.17375	+	1.17375i	−0.981310	+	0.192436i	$0.938361\pi$
$830$		0			0
$831$	621.758	−	621.758i	0.748204	−	0.748204i
$832$		0			0
$833$	−159.698	+	159.698i	−0.191714	+	0.191714i
$834$		0			0
$835$	57.1884			0.0684891
$836$		0			0
$837$	−1179.89			−1.40967
$838$		0			0
$839$	−356.180	−	356.180i	−0.424530	−	0.424530i	0.462230	−	0.886760i	$-0.347049\pi$
$839$	−356.180	−	356.180i	−0.424530	−	0.424530i	−0.886760	+	0.462230i	$0.847049\pi$
$840$		0			0
$841$	−559.176	+	628.175i	−0.664894	+	0.746938i
$842$		0			0
$843$	−1041.28	+	1041.28i	−1.23520	+	1.23520i
$844$		0			0
$845$			33.2663i			0.0393684i
$846$		0			0
$847$			1094.44i			1.29214i
$848$		0			0
$849$	203.758	+	203.758i	0.239997	+	0.239997i
$850$		0			0
$851$	−450.861	−	450.861i	−0.529802	−	0.529802i
$852$		0			0
$853$	386.118	+	386.118i	0.452658	+	0.452658i	0.896236	−	0.443578i	$-0.146291\pi$
$853$	386.118	+	386.118i	0.452658	+	0.452658i	−0.443578	+	0.896236i	$0.646291\pi$
$854$		0			0
$855$	−0.759249	+	0.759249i	−0.000888010	+	0.000888010i
$856$		0			0
$857$	−1215.88			−1.41876			−0.709379	−	0.704827i	$-0.751025\pi$
$857$	−1215.88			−1.41876			−0.709379	+	0.704827i	$0.751025\pi$
$858$		0			0
$859$	−255.287	−	255.287i	−0.297191	−	0.297191i	0.542721	−	0.839913i	$-0.317394\pi$
$859$	−255.287	−	255.287i	−0.297191	−	0.297191i	−0.839913	+	0.542721i	$0.817394\pi$
$860$		0			0
$861$	−680.728			−0.790624
$862$		0			0
$863$			785.434i			0.910120i	0.890461	+	0.455060i	$0.150382\pi$
$863$			785.434i			0.910120i	−0.890461	+	0.455060i	$0.849618\pi$
$864$		0			0
$865$	25.1106			0.0290296
$866$		0			0
$867$	216.178	+	216.178i	0.249341	+	0.249341i
$868$		0			0
$869$		−	220.274i		−	0.253479i
$870$		0			0
$871$	−1342.07			−1.54084
$872$		0			0
$873$	−6.07655	+	6.07655i	−0.00696054	+	0.00696054i
$874$		0			0
$875$		−	196.759i		−	0.224868i
$876$		0			0
$877$	928.813			1.05908			0.529540	−	0.848285i	$-0.322365\pi$
$877$	928.813			1.05908			0.529540	+	0.848285i	$0.322365\pi$
$878$		0			0
$879$		−	91.0962i		−	0.103636i
$880$		0			0
$881$	254.765	−	254.765i	0.289177	−	0.289177i	−0.547578	−	0.836755i	$-0.684450\pi$
$881$	254.765	−	254.765i	0.289177	−	0.289177i	0.836755	+	0.547578i	$0.184450\pi$
$882$		0			0
$883$		−	3.93324i		−	0.00445441i	−0.999998	−	0.00222720i	$-0.999291\pi$
$883$		−	3.93324i		−	0.00445441i	0.999998	−	0.00222720i	$-0.000708941\pi$
$884$		0			0
$885$	15.1864	+	15.1864i	0.0171597	+	0.0171597i
$886$		0			0
$887$	−59.1814	+	59.1814i	−0.0667208	+	0.0667208i	−0.739680	−	0.672959i	$-0.765023\pi$
$887$	−59.1814	+	59.1814i	−0.0667208	+	0.0667208i	0.672959	+	0.739680i	$0.265023\pi$
$888$		0			0
$889$	−173.159	+	173.159i	−0.194780	+	0.194780i
$890$		0			0
$891$	−934.949	+	934.949i	−1.04933	+	1.04933i
$892$		0			0
$893$	724.995			0.811865
$894$		0			0
$895$	143.061			0.159845
$896$		0			0
$897$	310.417	+	310.417i	0.346061	+	0.346061i
$898$		0			0
$899$	1196.74	+	455.485i	1.33119	+	0.506658i
$900$		0			0
$901$	−160.611	+	160.611i	−0.178259	+	0.178259i
$902$		0			0
$903$			1741.87i			1.92898i
$904$		0			0
$905$			85.5982i			0.0945837i
$906$		0			0
$907$	106.097	+	106.097i	0.116976	+	0.116976i	0.763172	−	0.646196i	$-0.223641\pi$
$907$	106.097	+	106.097i	0.116976	+	0.116976i	−0.646196	+	0.763172i	$0.723641\pi$
$908$		0			0
$909$	6.92188	+	6.92188i	0.00761483	+	0.00761483i
$910$		0			0
$911$	−844.949	−	844.949i	−0.927496	−	0.927496i	0.0700474	−	0.997544i	$-0.477685\pi$
$911$	−844.949	−	844.949i	−0.927496	−	0.927496i	−0.997544	+	0.0700474i	$0.977685\pi$
$912$		0			0
$913$	727.359	−	727.359i	0.796670	−	0.796670i
$914$		0			0
$915$	−95.0393			−0.103868
$916$		0			0
$917$	−377.782	−	377.782i	−0.411977	−	0.411977i
$918$		0			0
$919$	−1137.34			−1.23759			−0.618793	−	0.785554i	$-0.712378\pi$
$919$	−1137.34			−1.23759			−0.618793	+	0.785554i	$0.712378\pi$
$920$		0			0
$921$		−	827.641i		−	0.898633i
$922$		0			0
$923$	−340.773			−0.369202
$924$		0			0
$925$	−774.112	−	774.112i	−0.836878	−	0.836878i
$926$		0			0
$927$			11.1587i			0.0120375i
$928$		0			0
$929$	−50.8383			−0.0547237			−0.0273619	−	0.999626i	$-0.508711\pi$
$929$	−50.8383			−0.0547237			−0.0273619	+	0.999626i	$0.508711\pi$
$930$		0			0
$931$	−141.362	+	141.362i	−0.151839	+	0.151839i
$932$		0			0
$933$			483.536i			0.518259i
$934$		0			0
$935$	107.293			0.114752
$936$		0			0
$937$			1022.04i			1.09076i	0.838189	+	0.545380i	$0.183615\pi$
$937$			1022.04i			1.09076i	−0.838189	+	0.545380i	$0.816385\pi$
$938$		0			0
$939$	256.652	−	256.652i	0.273325	−	0.273325i
$940$		0			0
$941$			1171.17i			1.24460i	0.782779	+	0.622300i	$0.213802\pi$
$941$			1171.17i			1.24460i	−0.782779	+	0.622300i	$0.786198\pi$
$942$		0			0
$943$	283.148	+	283.148i	0.300262	+	0.300262i
$944$		0			0
$945$	74.7126	−	74.7126i	0.0790610	−	0.0790610i
$946$		0			0
$947$	−32.8294	+	32.8294i	−0.0346668	+	0.0346668i	−0.724228	−	0.689561i	$-0.757804\pi$
$947$	−32.8294	+	32.8294i	−0.0346668	+	0.0346668i	0.689561	+	0.724228i	$0.257804\pi$
$948$		0			0
$949$	222.778	−	222.778i	0.234751	−	0.234751i
$950$		0			0
$951$	1158.61			1.21831
$952$		0			0
$953$	−532.758			−0.559032			−0.279516	−	0.960141i	$-0.590174\pi$
$953$	−532.758			−0.559032			−0.279516	+	0.960141i	$0.590174\pi$
$954$		0			0
$955$	−22.9071	−	22.9071i	−0.0239865	−	0.0239865i
$956$		0			0
$957$	1283.41	−	575.788i	1.34107	−	0.601659i
$958$		0			0
$959$	−46.6517	+	46.6517i	−0.0486462	+	0.0486462i
$960$		0			0
$961$		−	988.645i		−	1.02877i
$962$		0			0
$963$		−	8.79274i		−	0.00913058i
$964$		0			0
$965$	24.3698	+	24.3698i	0.0252537	+	0.0252537i
$966$		0			0
$967$	−1050.69	−	1050.69i	−1.08655	−	1.08655i	−0.995881	−	0.0906692i	$-0.971099\pi$
$967$	−1050.69	−	1050.69i	−1.08655	−	1.08655i	−0.0906692	−	0.995881i	$-0.528901\pi$
$968$		0			0
$969$	−356.745	−	356.745i	−0.368158	−	0.368158i
$970$		0			0
$971$	645.432	−	645.432i	0.664709	−	0.664709i	−0.291777	−	0.956486i	$-0.594247\pi$
$971$	645.432	−	645.432i	0.664709	−	0.664709i	0.956486	+	0.291777i	$0.0942466\pi$
$972$		0			0
$973$	−1812.30			−1.86259
$974$		0			0
$975$	532.974	+	532.974i	0.546640	+	0.546640i
$976$		0			0
$977$	1341.58			1.37317			0.686583	−	0.727052i	$-0.259110\pi$
$977$	1341.58			1.37317			0.686583	+	0.727052i	$0.259110\pi$
$978$		0			0
$979$		−	2710.81i		−	2.76896i
$980$		0			0
$981$	−14.8429			−0.0151303
$982$		0			0
$983$	717.569	+	717.569i	0.729979	+	0.729979i	0.970615	−	0.240636i	$-0.0773562\pi$
$983$	717.569	+	717.569i	0.729979	+	0.729979i	−0.240636	+	0.970615i	$0.577356\pi$
$984$		0			0
$985$		−	29.1999i		−	0.0296445i
$986$		0			0
$987$	1464.06			1.48335
$988$		0			0
$989$	724.528	−	724.528i	0.732586	−	0.732586i
$990$		0			0
$991$		−	1257.05i		−	1.26846i	−0.773142	−	0.634232i	$-0.781316\pi$
$991$		−	1257.05i		−	1.26846i	0.773142	−	0.634232i	$-0.218684\pi$
$992$		0			0
$993$	276.528			0.278477
$994$		0			0
$995$			5.26953i			0.00529601i
$996$		0			0
$997$	19.5297	−	19.5297i	0.0195885	−	0.0195885i	−0.697245	−	0.716833i	$-0.745591\pi$
$997$	19.5297	−	19.5297i	0.0195885	−	0.0195885i	0.716833	+	0.697245i	$0.245591\pi$
$998$		0			0
$999$		−	1181.44i		−	1.18262i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	464.3.l.c.17.3		8
4.3	odd	2		29.3.c.a.17.2	yes	8
12.11	even	2		261.3.f.a.46.3		8
29.12	odd	4	inner	464.3.l.c.273.3		8
116.99	even	4		29.3.c.a.12.2	✓	8
348.215	odd	4		261.3.f.a.244.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.3.c.a.12.2	✓	8	116.99	even	4
29.3.c.a.17.2	yes	8	4.3	odd	2
261.3.f.a.46.3		8	12.11	even	2
261.3.f.a.244.3		8	348.215	odd	4
464.3.l.c.17.3		8	1.1	even	1	trivial
464.3.l.c.273.3		8	29.12	odd	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:	\( N \)	\(=\)	\( 464 = 2^{4} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	464.l (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.14254 - 2.14254i) q^{3} +0.488689i q^{5} -8.09117 q^{7} -0.180982i q^{9} +O(q^{10})\)	\(q+(2.14254 - 2.14254i) q^{3} +0.488689i q^{5} -8.09117 q^{7} -0.180982i q^{9} +(-11.3195 + 11.3195i) q^{11} +10.0463i q^{13} +(1.04704 + 1.04704i) q^{15} +(-9.69799 + 9.69799i) q^{17} +(-8.58453 + 8.58453i) q^{19} +(-17.3357 + 17.3357i) q^{21} +14.4215 q^{23} +24.7612 q^{25} +(18.8951 + 18.8951i) q^{27} +(-11.8706 - 26.4592i) q^{29} +(-31.2221 + 31.2221i) q^{31} +48.5052i q^{33} -3.95407i q^{35} +(-31.2631 - 31.2631i) q^{37} +(21.5246 + 21.5246i) q^{39} +(19.6337 + 19.6337i) q^{41} +(50.2394 - 50.2394i) q^{43} +0.0884438 q^{45} +(-42.2268 - 42.2268i) q^{47} +16.4671 q^{49} +41.5567i q^{51} +16.5613 q^{53} +(-5.53173 - 5.53173i) q^{55} +36.7855i q^{57} +14.5041 q^{59} +(-45.3849 + 45.3849i) q^{61} +1.46435i q^{63} -4.90950 q^{65} +133.589i q^{67} +(30.8987 - 30.8987i) q^{69} +33.9204i q^{71} +(-22.1752 - 22.1752i) q^{73} +(53.0519 - 53.0519i) q^{75} +(91.5883 - 91.5883i) q^{77} +(-9.72981 + 9.72981i) q^{79} +82.5961 q^{81} -64.2570 q^{83} +(-4.73930 - 4.73930i) q^{85} +(-82.1233 - 31.2565i) q^{87} +(-119.740 + 119.740i) q^{89} -81.2861i q^{91} +133.790i q^{93} +(-4.19517 - 4.19517i) q^{95} +(-33.5755 - 33.5755i) q^{97} +(2.04863 + 2.04863i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} + 4 q^{7}+O(q^{10}) \) 8 * q + 2 * q^3 + 4 * q^7	\( 8 q + 2 q^{3} + 4 q^{7} + 6 q^{11} + 10 q^{15} + 12 q^{17} + 16 q^{19} - 36 q^{21} + 104 q^{25} + 98 q^{27} + 128 q^{29} + 10 q^{31} - 84 q^{37} + 90 q^{39} + 20 q^{41} + 190 q^{43} + 292 q^{45} - 58 q^{47} - 72 q^{49} + 252 q^{53} + 74 q^{55} + 40 q^{59} - 208 q^{61} + 36 q^{65} + 120 q^{69} - 188 q^{73} + 12 q^{75} + 180 q^{77} + 382 q^{79} - 124 q^{81} - 280 q^{83} + 32 q^{85} - 34 q^{87} - 64 q^{89} + 380 q^{95} - 44 q^{97} - 552 q^{99}+O(q^{100}) \) 8 * q + 2 * q^3 + 4 * q^7 + 6 * q^11 + 10 * q^15 + 12 * q^17 + 16 * q^19 - 36 * q^21 + 104 * q^25 + 98 * q^27 + 128 * q^29 + 10 * q^31 - 84 * q^37 + 90 * q^39 + 20 * q^41 + 190 * q^43 + 292 * q^45 - 58 * q^47 - 72 * q^49 + 252 * q^53 + 74 * q^55 + 40 * q^59 - 208 * q^61 + 36 * q^65 + 120 * q^69 - 188 * q^73 + 12 * q^75 + 180 * q^77 + 382 * q^79 - 124 * q^81 - 280 * q^83 + 32 * q^85 - 34 * q^87 - 64 * q^89 + 380 * q^95 - 44 * q^97 - 552 * q^99

Introduction

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