LMFDB - Embedded newform 464.3.l.c.17.2

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			17.2
Root			$1.35225i$ of defining polynomial
Character	$\chi$	$=$	464.17
Dual form			464.3.l.c.273.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.442660 + 0.442660i) q^{3} -4.16447i q^{5} +9.68815 q^{7} +8.60810i q^{9} +O(q^{10})$	\(q+(-0.442660 + 0.442660i) q^{3} -4.16447i q^{5} +9.68815 q^{7} +8.60810i q^{9} +(0.334930 - 0.334930i) q^{11} -12.2282i q^{13} +(1.84345 + 1.84345i) q^{15} +(6.80978 - 6.80978i) q^{17} +(-14.6673 + 14.6673i) q^{19} +(-4.28855 + 4.28855i) q^{21} +10.0844 q^{23} +7.65715 q^{25} +(-7.79440 - 7.79440i) q^{27} +(28.1041 + 7.15263i) q^{29} +(37.3099 - 37.3099i) q^{31} +0.296520i q^{33} -40.3460i q^{35} +(-45.0215 - 45.0215i) q^{37} +(5.41292 + 5.41292i) q^{39} +(22.8142 + 22.8142i) q^{41} +(17.5030 - 17.5030i) q^{43} +35.8482 q^{45} +(-2.20999 - 2.20999i) q^{47} +44.8602 q^{49} +6.02883i q^{51} +90.1375 q^{53} +(-1.39481 - 1.39481i) q^{55} -12.9852i q^{57} +90.4223 q^{59} +(-29.4354 + 29.4354i) q^{61} +83.3966i q^{63} -50.9239 q^{65} -31.5543i q^{67} +(-4.46397 + 4.46397i) q^{69} +99.8673i q^{71} +(-3.96285 - 3.96285i) q^{73} +(-3.38951 + 3.38951i) q^{75} +(3.24485 - 3.24485i) q^{77} +(40.3117 - 40.3117i) q^{79} -70.5724 q^{81} -137.714 q^{83} +(-28.3592 - 28.3592i) q^{85} +(-15.6067 + 9.27437i) q^{87} +(83.1506 - 83.1506i) q^{89} -118.468i q^{91} +33.0312i q^{93} +(61.0816 + 61.0816i) q^{95} +(-79.9850 - 79.9850i) q^{97} +(2.88311 + 2.88311i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.442660	+	0.442660i	−0.147553	+	0.147553i	−0.777024	−	0.629471i	$-0.783272\pi$
$3$	−0.442660	+	0.442660i	−0.147553	+	0.147553i	0.629471	+	0.777024i	$0.283272\pi$
$4$		0			0
$5$		−	4.16447i		−	0.832895i	−0.909160	−	0.416447i	$-0.863275\pi$
$5$		−	4.16447i		−	0.832895i	0.909160	−	0.416447i	$-0.136725\pi$
$6$		0			0
$7$	9.68815			1.38402			0.692011	−	0.721887i	$-0.256725\pi$
$7$	9.68815			1.38402			0.692011	+	0.721887i	$0.256725\pi$
$8$		0			0
$9$			8.60810i			0.956456i
$10$		0			0
$11$	0.334930	−	0.334930i	0.0304481	−	0.0304481i	−0.691719	−	0.722167i	$-0.743146\pi$
$11$	0.334930	−	0.334930i	0.0304481	−	0.0304481i	0.722167	+	0.691719i	$0.243146\pi$
$12$		0			0
$13$		−	12.2282i		−	0.940628i	−0.882499	−	0.470314i	$-0.844141\pi$
$13$		−	12.2282i		−	0.940628i	0.882499	−	0.470314i	$-0.155859\pi$
$14$		0			0
$15$	1.84345	+	1.84345i	0.122896	+	0.122896i
$16$		0			0
$17$	6.80978	−	6.80978i	0.400575	−	0.400575i	−0.477861	−	0.878436i	$-0.658588\pi$
$17$	6.80978	−	6.80978i	0.400575	−	0.400575i	0.878436	+	0.477861i	$0.158588\pi$
$18$		0			0
$19$	−14.6673	+	14.6673i	−0.771963	+	0.771963i	−0.978449	−	0.206486i	$-0.933797\pi$
$19$	−14.6673	+	14.6673i	−0.771963	+	0.771963i	0.206486	+	0.978449i	$0.433797\pi$
$20$		0			0
$21$	−4.28855	+	4.28855i	−0.204217	+	0.204217i
$22$		0			0
$23$	10.0844			0.438454			0.219227	−	0.975674i	$-0.429647\pi$
$23$	10.0844			0.438454			0.219227	+	0.975674i	$0.429647\pi$
$24$		0			0
$25$	7.65715			0.306286
$26$		0			0
$27$	−7.79440	−	7.79440i	−0.288681	−	0.288681i
$28$		0			0
$29$	28.1041	+	7.15263i	0.969107	+	0.246642i
$29$	28.1041	+	7.15263i	0.969107	+	0.246642i
$30$		0			0
$31$	37.3099	−	37.3099i	1.20355	−	1.20355i	0.230466	−	0.973080i	$-0.425975\pi$
$31$	37.3099	−	37.3099i	1.20355	−	1.20355i	0.973080	−	0.230466i	$-0.0740250\pi$
$32$		0			0
$33$			0.296520i			0.00898545i
$34$		0			0
$35$		−	40.3460i		−	1.15274i
$36$		0			0
$37$	−45.0215	−	45.0215i	−1.21680	−	1.21680i	−0.968747	−	0.248050i	$-0.920210\pi$
$37$	−45.0215	−	45.0215i	−1.21680	−	1.21680i	−0.248050	−	0.968747i	$-0.579790\pi$
$38$		0			0
$39$	5.41292	+	5.41292i	0.138793	+	0.138793i
$40$		0			0
$41$	22.8142	+	22.8142i	0.556443	+	0.556443i	0.928293	−	0.371850i	$-0.121276\pi$
$41$	22.8142	+	22.8142i	0.556443	+	0.556443i	−0.371850	+	0.928293i	$0.621276\pi$
$42$		0			0
$43$	17.5030	−	17.5030i	0.407048	−	0.407048i	−0.473660	−	0.880708i	$-0.657067\pi$
$43$	17.5030	−	17.5030i	0.407048	−	0.407048i	0.880708	+	0.473660i	$0.157067\pi$
$44$		0			0
$45$	35.8482			0.796627
$46$		0			0
$47$	−2.20999	−	2.20999i	−0.0470210	−	0.0470210i	0.683205	−	0.730226i	$-0.260585\pi$
$47$	−2.20999	−	2.20999i	−0.0470210	−	0.0470210i	−0.730226	+	0.683205i	$0.760585\pi$
$48$		0			0
$49$	44.8602			0.915514
$50$		0			0
$51$			6.02883i			0.118212i
$52$		0			0
$53$	90.1375			1.70071			0.850354	−	0.526212i	$-0.176388\pi$
$53$	90.1375			1.70071			0.850354	+	0.526212i	$0.176388\pi$
$54$		0			0
$55$	−1.39481	−	1.39481i	−0.0253601	−	0.0253601i
$56$		0			0
$57$		−	12.9852i		−	0.227811i
$58$		0			0
$59$	90.4223			1.53258			0.766291	−	0.642494i	$-0.222100\pi$
$59$	90.4223			1.53258			0.766291	+	0.642494i	$0.222100\pi$
$60$		0			0
$61$	−29.4354	+	29.4354i	−0.482548	+	0.482548i	−0.905944	−	0.423397i	$-0.860838\pi$
$61$	−29.4354	+	29.4354i	−0.482548	+	0.482548i	0.423397	+	0.905944i	$0.360838\pi$
$62$		0			0
$63$			83.3966i			1.32376i
$64$		0			0
$65$	−50.9239			−0.783445
$66$		0			0
$67$		−	31.5543i		−	0.470960i	−0.971879	−	0.235480i	$-0.924334\pi$
$67$		−	31.5543i		−	0.470960i	0.971879	−	0.235480i	$-0.0756662\pi$
$68$		0			0
$69$	−4.46397	+	4.46397i	−0.0646953	+	0.0646953i
$70$		0			0
$71$			99.8673i			1.40658i	0.710902	+	0.703291i	$0.248287\pi$
$71$			99.8673i			1.40658i	−0.710902	+	0.703291i	$0.751713\pi$
$72$		0			0
$73$	−3.96285	−	3.96285i	−0.0542856	−	0.0542856i	0.679443	−	0.733728i	$-0.262222\pi$
$73$	−3.96285	−	3.96285i	−0.0542856	−	0.0542856i	−0.733728	+	0.679443i	$0.762222\pi$
$74$		0			0
$75$	−3.38951	+	3.38951i	−0.0451935	+	0.0451935i
$76$		0			0
$77$	3.24485	−	3.24485i	0.0421409	−	0.0421409i
$78$		0			0
$79$	40.3117	−	40.3117i	0.510275	−	0.510275i	−0.404335	−	0.914611i	$-0.632497\pi$
$79$	40.3117	−	40.3117i	0.510275	−	0.510275i	0.914611	+	0.404335i	$0.132497\pi$
$80$		0			0
$81$	−70.5724			−0.871264
$82$		0			0
$83$	−137.714			−1.65921			−0.829604	−	0.558352i	$-0.811434\pi$
$83$	−137.714			−1.65921			−0.829604	+	0.558352i	$0.811434\pi$
$84$		0			0
$85$	−28.3592	−	28.3592i	−0.333637	−	0.333637i
$86$		0			0
$87$	−15.6067	+	9.27437i	−0.179388	+	0.106602i
$88$		0			0
$89$	83.1506	−	83.1506i	0.934276	−	0.934276i	−0.0636936	−	0.997969i	$-0.520288\pi$
$89$	83.1506	−	83.1506i	0.934276	−	0.934276i	0.997969	+	0.0636936i	$0.0202880\pi$
$90$		0			0
$91$		−	118.468i		−	1.30185i
$92$		0			0
$93$			33.0312i			0.355174i
$94$		0			0
$95$	61.0816	+	61.0816i	0.642964	+	0.642964i
$96$		0			0
$97$	−79.9850	−	79.9850i	−0.824588	−	0.824588i	0.162174	−	0.986762i	$-0.448149\pi$
$97$	−79.9850	−	79.9850i	−0.824588	−	0.824588i	−0.986762	+	0.162174i	$0.948149\pi$
$98$		0			0
$99$	2.88311	+	2.88311i	0.0291223	+	0.0291223i
$100$		0			0
$101$	−52.1216	+	52.1216i	−0.516055	+	0.516055i	−0.916375	−	0.400320i	$-0.868899\pi$
$101$	−52.1216	+	52.1216i	−0.516055	+	0.516055i	0.400320	+	0.916375i	$0.368899\pi$
$102$		0			0
$103$	−139.377			−1.35318			−0.676588	−	0.736361i	$-0.736542\pi$
$103$	−139.377			−1.35318			−0.676588	+	0.736361i	$0.736542\pi$
$104$		0			0
$105$	17.8596	+	17.8596i	0.170091	+	0.170091i
$106$		0			0
$107$	14.9646			0.139856			0.0699282	−	0.997552i	$-0.477723\pi$
$107$	14.9646			0.139856			0.0699282	+	0.997552i	$0.477723\pi$
$108$		0			0
$109$			38.6223i			0.354333i	0.984181	+	0.177167i	$0.0566931\pi$
$109$			38.6223i			0.354333i	−0.984181	+	0.177167i	$0.943307\pi$
$110$		0			0
$111$	39.8584			0.359085
$112$		0			0
$113$	−20.2695	−	20.2695i	−0.179376	−	0.179376i	0.611708	−	0.791084i	$-0.290483\pi$
$113$	−20.2695	−	20.2695i	−0.179376	−	0.179376i	−0.791084	+	0.611708i	$0.790483\pi$
$114$		0			0
$115$		−	41.9964i		−	0.365186i
$116$		0			0
$117$	105.261			0.899670
$118$		0			0
$119$	65.9741	−	65.9741i	0.554405	−	0.554405i
$120$		0			0
$121$			120.776i			0.998146i
$122$		0			0
$123$	−20.1978			−0.164210
$124$		0			0
$125$		−	136.000i		−	1.08800i
$126$		0			0
$127$	−52.2215	+	52.2215i	−0.411193	+	0.411193i	−0.882154	−	0.470961i	$-0.843907\pi$
$127$	−52.2215	+	52.2215i	−0.411193	+	0.411193i	0.470961	+	0.882154i	$0.343907\pi$
$128$		0			0
$129$			15.4958i			0.120122i
$130$		0			0
$131$	−25.3821	−	25.3821i	−0.193756	−	0.193756i	0.603561	−	0.797317i	$-0.293748\pi$
$131$	−25.3821	−	25.3821i	−0.193756	−	0.193756i	−0.797317	+	0.603561i	$0.793748\pi$
$132$		0			0
$133$	−142.099	+	142.099i	−1.06841	+	1.06841i
$134$		0			0
$135$	−32.4596	+	32.4596i	−0.240441	+	0.240441i
$136$		0			0
$137$	−117.179	+	117.179i	−0.855320	+	0.855320i	−0.990782	−	0.135462i	$-0.956748\pi$
$137$	−117.179	+	117.179i	−0.855320	+	0.855320i	0.135462	+	0.990782i	$0.456748\pi$
$138$		0			0
$139$	−62.2884			−0.448118			−0.224059	−	0.974576i	$-0.571931\pi$
$139$	−62.2884			−0.448118			−0.224059	+	0.974576i	$0.571931\pi$
$140$		0			0
$141$	1.95655			0.0138762
$142$		0			0
$143$	−4.09558	−	4.09558i	−0.0286404	−	0.0286404i
$144$		0			0
$145$	29.7869	−	117.039i	0.205427	−	0.807164i
$146$		0			0
$147$	−19.8578	+	19.8578i	−0.135087	+	0.135087i
$148$		0			0
$149$			140.996i			0.946284i	0.880986	+	0.473142i	$0.156880\pi$
$149$			140.996i			0.946284i	−0.880986	+	0.473142i	$0.843120\pi$
$150$		0			0
$151$			269.100i			1.78212i	0.453889	+	0.891058i	$0.350036\pi$
$151$			269.100i			1.78212i	−0.453889	+	0.891058i	$0.649964\pi$
$152$		0			0
$153$	58.6193	+	58.6193i	0.383133	+	0.383133i
$154$		0			0
$155$	−155.376	−	155.376i	−1.00243	−	1.00243i
$156$		0			0
$157$	−82.6681	−	82.6681i	−0.526549	−	0.526549i	0.392993	−	0.919541i	$-0.371440\pi$
$157$	−82.6681	−	82.6681i	−0.526549	−	0.526549i	−0.919541	+	0.392993i	$0.871440\pi$
$158$		0			0
$159$	−39.9002	+	39.9002i	−0.250945	+	0.250945i
$160$		0			0
$161$	97.6995			0.606829
$162$		0			0
$163$	−16.1649	−	16.1649i	−0.0991711	−	0.0991711i	0.655780	−	0.754952i	$-0.272340\pi$
$163$	−16.1649	−	16.1649i	−0.0991711	−	0.0991711i	−0.754952	+	0.655780i	$0.772340\pi$
$164$		0			0
$165$	1.23485			0.00748393
$166$		0			0
$167$			134.528i			0.805558i	0.915297	+	0.402779i	$0.131956\pi$
$167$			134.528i			0.805558i	−0.915297	+	0.402779i	$0.868044\pi$
$168$		0			0
$169$	19.4719			0.115218
$170$		0			0
$171$	−126.258	−	126.258i	−0.738349	−	0.738349i
$172$		0			0
$173$		−	94.1756i		−	0.544368i	−0.962245	−	0.272184i	$-0.912254\pi$
$173$		−	94.1756i		−	0.544368i	0.962245	−	0.272184i	$-0.0877459\pi$
$174$		0			0
$175$	74.1836			0.423906
$176$		0			0
$177$	−40.0263	+	40.0263i	−0.226137	+	0.226137i
$178$		0			0
$179$			55.6892i			0.311113i	0.987827	+	0.155557i	$0.0497171\pi$
$179$			55.6892i			0.311113i	−0.987827	+	0.155557i	$0.950283\pi$
$180$		0			0
$181$	−131.878			−0.728610			−0.364305	−	0.931280i	$-0.618693\pi$
$181$	−131.878			−0.728610			−0.364305	+	0.931280i	$0.618693\pi$
$182$		0			0
$183$		−	26.0598i		−	0.142403i
$184$		0			0
$185$	−187.491	+	187.491i	−1.01346	+	1.01346i
$186$		0			0
$187$		−	4.56159i		−	0.0243935i
$188$		0			0
$189$	−75.5133	−	75.5133i	−0.399541	−	0.399541i
$190$		0			0
$191$	−122.543	+	122.543i	−0.641588	+	0.641588i	−0.950946	−	0.309358i	$-0.899886\pi$
$191$	−122.543	+	122.543i	−0.641588	+	0.641588i	0.309358	+	0.950946i	$0.399886\pi$
$192$		0			0
$193$	−175.959	+	175.959i	−0.911702	+	0.911702i	−0.996406	−	0.0847039i	$-0.973006\pi$
$193$	−175.959	+	175.959i	−0.911702	+	0.911702i	0.0847039	+	0.996406i	$0.473006\pi$
$194$		0			0
$195$	22.5420	−	22.5420i	0.115600	−	0.115600i
$196$		0			0
$197$	42.7699			0.217106			0.108553	−	0.994091i	$-0.465378\pi$
$197$	42.7699			0.217106			0.108553	+	0.994091i	$0.465378\pi$
$198$		0			0
$199$	101.732			0.511216			0.255608	−	0.966781i	$-0.417724\pi$
$199$	101.732			0.511216			0.255608	+	0.966781i	$0.417724\pi$
$200$		0			0
$201$	13.9678	+	13.9678i	0.0694916	+	0.0694916i
$202$		0			0
$203$	272.277	+	69.2957i	1.34126	+	0.341358i
$204$		0			0
$205$	95.0090	−	95.0090i	0.463459	−	0.463459i
$206$		0			0
$207$			86.8078i			0.419362i
$208$		0			0
$209$			9.82502i			0.0470097i
$210$		0			0
$211$	−84.0454	−	84.0454i	−0.398319	−	0.398319i	0.479321	−	0.877640i	$-0.340883\pi$
$211$	−84.0454	−	84.0454i	−0.398319	−	0.398319i	−0.877640	+	0.479321i	$0.840883\pi$
$212$		0			0
$213$	−44.2072	−	44.2072i	−0.207546	−	0.207546i
$214$		0			0
$215$	−72.8910	−	72.8910i	−0.339028	−	0.339028i
$216$		0			0
$217$	361.464	−	361.464i	1.66573	−	1.66573i
$218$		0			0
$219$	3.50839			0.0160200
$220$		0			0
$221$	−83.2711	−	83.2711i	−0.376792	−	0.376792i
$222$		0			0
$223$	306.140			1.37283			0.686413	−	0.727212i	$-0.259184\pi$
$223$	306.140			1.37283			0.686413	+	0.727212i	$0.259184\pi$
$224$		0			0
$225$			65.9135i			0.292949i
$226$		0			0
$227$	−19.8257			−0.0873379			−0.0436689	−	0.999046i	$-0.513905\pi$
$227$	−19.8257			−0.0873379			−0.0436689	+	0.999046i	$0.513905\pi$
$228$		0			0
$229$	150.087	+	150.087i	0.655402	+	0.655402i	0.954289	−	0.298887i	$-0.0966153\pi$
$229$	150.087	+	150.087i	0.655402	+	0.655402i	−0.298887	+	0.954289i	$0.596615\pi$
$230$		0			0
$231$			2.87273i			0.0124360i
$232$		0			0
$233$	132.431			0.568375			0.284187	−	0.958769i	$-0.408276\pi$
$233$	132.431			0.568375			0.284187	+	0.958769i	$0.408276\pi$
$234$		0			0
$235$	−9.20344	+	9.20344i	−0.0391636	+	0.0391636i
$236$		0			0
$237$			35.6888i			0.150586i
$238$		0			0
$239$	−176.690			−0.739288			−0.369644	−	0.929173i	$-0.620520\pi$
$239$	−176.690			−0.739288			−0.369644	+	0.929173i	$0.620520\pi$
$240$		0			0
$241$		−	161.010i		−	0.668093i	−0.942557	−	0.334046i	$-0.891586\pi$
$241$		−	161.010i		−	0.668093i	0.942557	−	0.334046i	$-0.108414\pi$
$242$		0			0
$243$	101.389	−	101.389i	0.417239	−	0.417239i
$244$		0			0
$245$		−	186.819i		−	0.762527i
$246$		0			0
$247$	179.354	+	179.354i	0.726130	+	0.726130i
$248$		0			0
$249$	60.9606	−	60.9606i	0.244822	−	0.244822i
$250$		0			0
$251$	−136.621	+	136.621i	−0.544306	+	0.544306i	−0.924788	−	0.380482i	$-0.875758\pi$
$251$	−136.621	+	136.621i	−0.544306	+	0.544306i	0.380482	+	0.924788i	$0.375758\pi$
$252$		0			0
$253$	3.37757	−	3.37757i	0.0133501	−	0.0133501i
$254$		0			0
$255$	25.1069			0.0984585
$256$		0			0
$257$	−275.616			−1.07244			−0.536218	−	0.844079i	$-0.680148\pi$
$257$	−275.616			−1.07244			−0.536218	+	0.844079i	$0.680148\pi$
$258$		0			0
$259$	−436.175	−	436.175i	−1.68407	−	1.68407i
$260$		0			0
$261$	−61.5706	+	241.923i	−0.235903	+	0.926908i
$262$		0			0
$263$	242.820	−	242.820i	0.923269	−	0.923269i	−0.0739900	−	0.997259i	$-0.523573\pi$
$263$	242.820	−	242.820i	0.923269	−	0.923269i	0.997259	+	0.0739900i	$0.0235733\pi$
$264$		0			0
$265$		−	375.375i		−	1.41651i
$266$		0			0
$267$			73.6148i			0.275711i
$268$		0			0
$269$	167.754	+	167.754i	0.623620	+	0.623620i	0.946455	−	0.322836i	$-0.104636\pi$
$269$	167.754	+	167.754i	0.623620	+	0.623620i	−0.322836	+	0.946455i	$0.604636\pi$
$270$		0			0
$271$	−282.361	−	282.361i	−1.04192	−	1.04192i	−0.999082	−	0.0428420i	$-0.986359\pi$
$271$	−282.361	−	282.361i	−1.04192	−	1.04192i	−0.0428420	−	0.999082i	$-0.513641\pi$
$272$		0			0
$273$	52.4412	+	52.4412i	0.192092	+	0.192092i
$274$		0			0
$275$	2.56461	−	2.56461i	0.00932584	−	0.00932584i
$276$		0			0
$277$	30.5322			0.110224			0.0551122	−	0.998480i	$-0.482448\pi$
$277$	30.5322			0.110224			0.0551122	+	0.998480i	$0.482448\pi$
$278$		0			0
$279$	321.168	+	321.168i	1.15114	+	1.15114i
$280$		0			0
$281$	−2.92201			−0.0103986			−0.00519931	−	0.999986i	$-0.501655\pi$
$281$	−2.92201			−0.0103986			−0.00519931	+	0.999986i	$0.501655\pi$
$282$		0			0
$283$			26.9414i			0.0951993i	0.998866	+	0.0475997i	$0.0151572\pi$
$283$			26.9414i			0.0951993i	−0.998866	+	0.0475997i	$0.984843\pi$
$284$		0			0
$285$	−54.0767			−0.189743
$286$		0			0
$287$	221.027	+	221.027i	0.770129	+	0.770129i
$288$		0			0
$289$			196.254i			0.679079i
$290$		0			0
$291$	70.8123			0.243341
$292$		0			0
$293$	−255.770	+	255.770i	−0.872934	+	0.872934i	−0.992791	−	0.119857i	$-0.961756\pi$
$293$	−255.770	+	255.770i	−0.872934	+	0.872934i	0.119857	+	0.992791i	$0.461756\pi$
$294$		0			0
$295$		−	376.561i		−	1.27648i
$296$		0			0
$297$	−5.22115			−0.0175796
$298$		0			0
$299$		−	123.314i		−	0.412422i
$300$		0			0
$301$	169.572	−	169.572i	0.563362	−	0.563362i
$302$		0			0
$303$		−	46.1443i		−	0.152291i
$304$		0			0
$305$	122.583	+	122.583i	0.401912	+	0.401912i
$306$		0			0
$307$	9.20371	−	9.20371i	0.0299795	−	0.0299795i	−0.691958	−	0.721938i	$-0.743252\pi$
$307$	9.20371	−	9.20371i	0.0299795	−	0.0299795i	0.721938	+	0.691958i	$0.243252\pi$
$308$		0			0
$309$	61.6967	−	61.6967i	0.199666	−	0.199666i
$310$		0			0
$311$	−94.0902	+	94.0902i	−0.302541	+	0.302541i	−0.842007	−	0.539466i	$-0.818626\pi$
$311$	−94.0902	+	94.0902i	−0.302541	+	0.302541i	0.539466	+	0.842007i	$0.318626\pi$
$312$		0			0
$313$	133.762			0.427356			0.213678	−	0.976904i	$-0.431456\pi$
$313$	133.762			0.427356			0.213678	+	0.976904i	$0.431456\pi$
$314$		0			0
$315$	347.303			1.10255
$316$		0			0
$317$	405.329	+	405.329i	1.27864	+	1.27864i	0.941428	+	0.337213i	$0.109484\pi$
$317$	405.329	+	405.329i	1.27864	+	1.27864i	0.337213	+	0.941428i	$0.390516\pi$
$318$		0			0
$319$	11.8085	−	7.01726i	0.0370173	−	0.0219977i
$320$		0			0
$321$	−6.62424	+	6.62424i	−0.0206363	+	0.0206363i
$322$		0			0
$323$			199.762i			0.618458i
$324$		0			0
$325$		−	93.6329i		−	0.288101i
$326$		0			0
$327$	−17.0965	−	17.0965i	−0.0522830	−	0.0522830i
$328$		0			0
$329$	−21.4107	−	21.4107i	−0.0650781	−	0.0650781i
$330$		0			0
$331$	−185.108	−	185.108i	−0.559238	−	0.559238i	0.369853	−	0.929090i	$-0.379408\pi$
$331$	−185.108	−	185.108i	−0.559238	−	0.559238i	−0.929090	+	0.369853i	$0.879408\pi$
$332$		0			0
$333$	387.550	−	387.550i	1.16381	−	1.16381i
$334$		0			0
$335$	−131.407			−0.392260
$336$		0			0
$337$	−71.8022	−	71.8022i	−0.213063	−	0.213063i	0.592504	−	0.805567i	$-0.298139\pi$
$337$	−71.8022	−	71.8022i	−0.213063	−	0.213063i	−0.805567	+	0.592504i	$0.798139\pi$
$338$		0			0
$339$	17.9450			0.0529351
$340$		0			0
$341$		−	24.9924i		−	0.0732915i
$342$		0			0
$343$	−40.1069			−0.116930
$344$		0			0
$345$	18.5901	+	18.5901i	0.0538843	+	0.0538843i
$346$		0			0
$347$			181.565i			0.523241i	0.965171	+	0.261621i	$0.0842569\pi$
$347$			181.565i			0.523241i	−0.965171	+	0.261621i	$0.915743\pi$
$348$		0			0
$349$	205.399			0.588536			0.294268	−	0.955723i	$-0.404924\pi$
$349$	205.399			0.588536			0.294268	+	0.955723i	$0.404924\pi$
$350$		0			0
$351$	−95.3112	+	95.3112i	−0.271542	+	0.271542i
$352$		0			0
$353$		−	150.904i		−	0.427489i	−0.976890	−	0.213745i	$-0.931434\pi$
$353$		−	150.904i		−	0.427489i	0.976890	−	0.213745i	$-0.0685660\pi$
$354$		0			0
$355$	415.895			1.17153
$356$		0			0
$357$			58.4082i			0.163608i
$358$		0			0
$359$	366.501	−	366.501i	1.02089	−	1.02089i	0.0211170	−	0.999777i	$-0.493278\pi$
$359$	366.501	−	366.501i	1.02089	−	1.02089i	0.999777	−	0.0211170i	$-0.00672225\pi$
$360$		0			0
$361$		−	69.2592i		−	0.191854i
$362$		0			0
$363$	−53.4625	−	53.4625i	−0.147280	−	0.147280i
$364$		0			0
$365$	−16.5032	+	16.5032i	−0.0452142	+	0.0452142i
$366$		0			0
$367$	84.3213	−	84.3213i	0.229758	−	0.229758i	−0.582833	−	0.812592i	$-0.698056\pi$
$367$	84.3213	−	84.3213i	0.229758	−	0.229758i	0.812592	+	0.582833i	$0.198056\pi$
$368$		0			0
$369$	−196.387	+	196.387i	−0.532213	+	0.532213i
$370$		0			0
$371$	873.265			2.35381
$372$		0			0
$373$	91.4080			0.245062			0.122531	−	0.992465i	$-0.460899\pi$
$373$	91.4080			0.245062			0.122531	+	0.992465i	$0.460899\pi$
$374$		0			0
$375$	60.2017	+	60.2017i	0.160538	+	0.160538i
$376$		0			0
$377$	87.4635	−	343.662i	0.231999	−	0.911569i
$378$		0			0
$379$	−178.021	+	178.021i	−0.469713	+	0.469713i	−0.901822	−	0.432108i	$-0.857770\pi$
$379$	−178.021	+	178.021i	−0.469713	+	0.469713i	0.432108	+	0.901822i	$0.357770\pi$
$380$		0			0
$381$		−	46.2327i		−	0.121346i
$382$		0			0
$383$			142.083i			0.370973i	0.982647	+	0.185486i	$0.0593860\pi$
$383$			142.083i			0.370973i	−0.982647	+	0.185486i	$0.940614\pi$
$384$		0			0
$385$	−13.5131	−	13.5131i	−0.0350989	−	0.0350989i
$386$		0			0
$387$	150.668	+	150.668i	0.389323	+	0.389323i
$388$		0			0
$389$	−339.694	−	339.694i	−0.873250	−	0.873250i	0.119575	−	0.992825i	$-0.461847\pi$
$389$	−339.694	−	339.694i	−0.873250	−	0.873250i	−0.992825	+	0.119575i	$0.961847\pi$
$390$		0			0
$391$	68.6727	−	68.6727i	0.175634	−	0.175634i
$392$		0			0
$393$	22.4712			0.0571787
$394$		0			0
$395$	−167.877	−	167.877i	−0.425006	−	0.425006i
$396$		0			0
$397$	−657.787			−1.65689			−0.828447	−	0.560068i	$-0.810775\pi$
$397$	−657.787			−1.65689			−0.828447	+	0.560068i	$0.810775\pi$
$398$		0			0
$399$		−	125.803i		−	0.315296i
$400$		0			0
$401$	343.872			0.857537			0.428768	−	0.903414i	$-0.358948\pi$
$401$	343.872			0.857537			0.428768	+	0.903414i	$0.358948\pi$
$402$		0			0
$403$	−456.232	−	456.232i	−1.13209	−	1.13209i
$404$		0			0
$405$			293.897i			0.725672i
$406$		0			0
$407$	−30.1581			−0.0740984
$408$		0			0
$409$	219.662	−	219.662i	0.537072	−	0.537072i	−0.385596	−	0.922668i	$-0.626004\pi$
$409$	219.662	−	219.662i	0.537072	−	0.537072i	0.922668	+	0.385596i	$0.126004\pi$
$410$		0			0
$411$		−	103.741i		−	0.252411i
$412$		0			0
$413$	876.024			2.12112
$414$		0			0
$415$			573.508i			1.38195i
$416$		0			0
$417$	27.5726	−	27.5726i	0.0661213	−	0.0661213i
$418$		0			0
$419$			512.017i			1.22200i	0.791631	+	0.610999i	$0.209232\pi$
$419$			512.017i			1.22200i	−0.791631	+	0.610999i	$0.790768\pi$
$420$		0			0
$421$	−426.710	−	426.710i	−1.01356	−	1.01356i	−0.999907	−	0.0136572i	$-0.995653\pi$
$421$	−426.710	−	426.710i	−1.01356	−	1.01356i	−0.0136572	−	0.999907i	$-0.504347\pi$
$422$		0			0
$423$	19.0238	−	19.0238i	0.0449735	−	0.0449735i
$424$		0			0
$425$	52.1435	−	52.1435i	0.122691	−	0.122691i
$426$		0			0
$427$	−285.175	+	285.175i	−0.667857	+	0.667857i
$428$		0			0
$429$	3.62589			0.00845197
$430$		0			0
$431$	−596.638			−1.38431			−0.692156	−	0.721748i	$-0.743339\pi$
$431$	−596.638			−1.38431			−0.692156	+	0.721748i	$0.743339\pi$
$432$		0			0
$433$	−41.8737	−	41.8737i	−0.0967059	−	0.0967059i	0.657099	−	0.753805i	$-0.271783\pi$
$433$	−41.8737	−	41.8737i	−0.0967059	−	0.0967059i	−0.753805	+	0.657099i	$0.771783\pi$
$434$		0			0
$435$	38.6229	+	64.9938i	0.0887882	+	0.149411i
$436$		0			0
$437$	−147.911	+	147.911i	−0.338470	+	0.338470i
$438$		0			0
$439$		−	344.567i		−	0.784891i	−0.919775	−	0.392445i	$-0.871629\pi$
$439$		−	344.567i		−	0.784891i	0.919775	−	0.392445i	$-0.128371\pi$
$440$		0			0
$441$			386.161i			0.875649i
$442$		0			0
$443$	124.564	+	124.564i	0.281184	+	0.281184i	0.833581	−	0.552397i	$-0.186287\pi$
$443$	124.564	+	124.564i	0.281184	+	0.281184i	−0.552397	+	0.833581i	$0.686287\pi$
$444$		0			0
$445$	−346.278	−	346.278i	−0.778154	−	0.778154i
$446$		0			0
$447$	−62.4134	−	62.4134i	−0.139627	−	0.139627i
$448$		0			0
$449$	−562.904	+	562.904i	−1.25368	+	1.25368i	−0.299628	+	0.954056i	$0.596863\pi$
$449$	−562.904	+	562.904i	−1.25368	+	1.25368i	−0.954056	+	0.299628i	$0.903137\pi$
$450$		0			0
$451$	15.2823			0.0338853
$452$		0			0
$453$	−119.120	−	119.120i	−0.262957	−	0.262957i
$454$		0			0
$455$	−493.358			−1.08430
$456$		0			0
$457$		−	377.138i		−	0.825247i	−0.910902	−	0.412623i	$-0.864613\pi$
$457$		−	377.138i		−	0.825247i	0.910902	−	0.412623i	$-0.135387\pi$
$458$		0			0
$459$	−106.156			−0.231277
$460$		0			0
$461$	−40.0863	−	40.0863i	−0.0869552	−	0.0869552i	0.662291	−	0.749246i	$-0.269584\pi$
$461$	−40.0863	−	40.0863i	−0.0869552	−	0.0869552i	−0.749246	+	0.662291i	$0.769584\pi$
$462$		0			0
$463$		−	410.934i		−	0.887546i	−0.896139	−	0.443773i	$-0.853640\pi$
$463$		−	410.934i		−	0.887546i	0.896139	−	0.443773i	$-0.146360\pi$
$464$		0			0
$465$	137.558			0.295823
$466$		0			0
$467$	427.051	−	427.051i	0.914455	−	0.914455i	−0.0821634	−	0.996619i	$-0.526183\pi$
$467$	427.051	−	427.051i	0.914455	−	0.914455i	0.996619	+	0.0821634i	$0.0261829\pi$
$468$		0			0
$469$		−	305.703i		−	0.651818i
$470$		0			0
$471$	73.1877			0.155388
$472$		0			0
$473$		−	11.7246i		−	0.0247877i
$474$		0			0
$475$	−112.310	+	112.310i	−0.236441	+	0.236441i
$476$		0			0
$477$			775.913i			1.62665i
$478$		0			0
$479$	−223.602	−	223.602i	−0.466811	−	0.466811i	0.434069	−	0.900880i	$-0.357077\pi$
$479$	−223.602	−	223.602i	−0.466811	−	0.466811i	−0.900880	+	0.434069i	$0.857077\pi$
$480$		0			0
$481$	−550.530	+	550.530i	−1.14455	+	1.14455i
$482$		0			0
$483$	−43.2476	+	43.2476i	−0.0895396	+	0.0895396i
$484$		0			0
$485$	−333.096	+	333.096i	−0.686795	+	0.686795i
$486$		0			0
$487$	−397.009			−0.815214			−0.407607	−	0.913157i	$-0.633637\pi$
$487$	−397.009			−0.815214			−0.407607	+	0.913157i	$0.633637\pi$
$488$		0			0
$489$	14.3111			0.0292661
$490$		0			0
$491$	441.208	+	441.208i	0.898591	+	0.898591i	0.995312	−	0.0967208i	$-0.0308354\pi$
$491$	441.208	+	441.208i	0.898591	+	0.898591i	−0.0967208	+	0.995312i	$0.530835\pi$
$492$		0			0
$493$	240.090	−	142.675i	0.486999	−	0.289401i
$494$		0			0
$495$	12.0066	−	12.0066i	0.0242558	−	0.0242558i
$496$		0			0
$497$			967.529i			1.94674i
$498$		0			0
$499$			94.9470i			0.190275i	0.995464	+	0.0951373i	$0.0303290\pi$
$499$			94.9470i			0.190275i	−0.995464	+	0.0951373i	$0.969671\pi$
$500$		0			0
$501$	−59.5502	−	59.5502i	−0.118863	−	0.118863i
$502$		0			0
$503$	35.4061	+	35.4061i	0.0703899	+	0.0703899i	0.741425	−	0.671035i	$-0.234150\pi$
$503$	35.4061	+	35.4061i	0.0703899	+	0.0703899i	−0.671035	+	0.741425i	$0.734150\pi$
$504$		0			0
$505$	217.059	+	217.059i	0.429820	+	0.429820i
$506$		0			0
$507$	−8.61942	+	8.61942i	−0.0170008	+	0.0170008i
$508$		0			0
$509$	215.741			0.423852			0.211926	−	0.977286i	$-0.432026\pi$
$509$	215.741			0.423852			0.211926	+	0.977286i	$0.432026\pi$
$510$		0			0
$511$	−38.3927	−	38.3927i	−0.0751324	−	0.0751324i
$512$		0			0
$513$	228.646			0.445703
$514$		0			0
$515$			580.433i			1.12705i
$516$		0			0
$517$	−1.48038			−0.00286341
$518$		0			0
$519$	41.6878	+	41.6878i	0.0803232	+	0.0803232i
$520$		0			0
$521$			279.099i			0.535700i	0.963461	+	0.267850i	$0.0863131\pi$
$521$			279.099i			0.535700i	−0.963461	+	0.267850i	$0.913687\pi$
$522$		0			0
$523$	135.622			0.259316			0.129658	−	0.991559i	$-0.458612\pi$
$523$	135.622			0.259316			0.129658	+	0.991559i	$0.458612\pi$
$524$		0			0
$525$	−32.8381	+	32.8381i	−0.0625488	+	0.0625488i
$526$		0			0
$527$		−	508.145i		−	0.964221i
$528$		0			0
$529$	−427.304			−0.807758
$530$		0			0
$531$			778.365i			1.46585i
$532$		0			0
$533$	278.975	−	278.975i	0.523406	−	0.523406i
$534$		0			0
$535$		−	62.3198i		−	0.116486i
$536$		0			0
$537$	−24.6514	−	24.6514i	−0.0459057	−	0.0459057i
$538$		0			0
$539$	15.0250	−	15.0250i	0.0278757	−	0.0278757i
$540$		0			0
$541$	381.445	−	381.445i	0.705074	−	0.705074i	−0.260421	−	0.965495i	$-0.583861\pi$
$541$	381.445	−	381.445i	0.705074	−	0.705074i	0.965495	+	0.260421i	$0.0838614\pi$
$542$		0			0
$543$	58.3773	−	58.3773i	0.107509	−	0.107509i
$544$		0			0
$545$	160.842			0.295122
$546$		0			0
$547$	−104.335			−0.190739			−0.0953697	−	0.995442i	$-0.530403\pi$
$547$	−104.335			−0.190739			−0.0953697	+	0.995442i	$0.530403\pi$
$548$		0			0
$549$	−253.383	−	253.383i	−0.461536	−	0.461536i
$550$		0			0
$551$	−517.121	+	307.301i	−0.938513	+	0.557716i
$552$		0			0
$553$	390.546	−	390.546i	0.706232	−	0.706232i
$554$		0			0
$555$		−	165.989i		−	0.299080i
$556$		0			0
$557$			132.616i			0.238090i	0.992889	+	0.119045i	$0.0379833\pi$
$557$			132.616i			0.238090i	−0.992889	+	0.119045i	$0.962017\pi$
$558$		0			0
$559$	−214.030	−	214.030i	−0.382880	−	0.382880i
$560$		0			0
$561$	2.01923	+	2.01923i	0.00359935	+	0.00359935i
$562$		0			0
$563$	−253.583	−	253.583i	−0.450413	−	0.450413i	0.445078	−	0.895492i	$-0.353176\pi$
$563$	−253.583	−	253.583i	−0.450413	−	0.450413i	−0.895492	+	0.445078i	$0.853176\pi$
$564$		0			0
$565$	−84.4120	+	84.4120i	−0.149402	+	0.149402i
$566$		0			0
$567$	−683.716			−1.20585
$568$		0			0
$569$	216.864	+	216.864i	0.381133	+	0.381133i	0.871510	−	0.490377i	$-0.163141\pi$
$569$	216.864	+	216.864i	0.381133	+	0.381133i	−0.490377	+	0.871510i	$0.663141\pi$
$570$		0			0
$571$	−398.256			−0.697472			−0.348736	−	0.937221i	$-0.613389\pi$
$571$	−398.256			−0.697472			−0.348736	+	0.937221i	$0.613389\pi$
$572$		0			0
$573$		−	108.490i		−	0.189337i
$574$		0			0
$575$	77.2180			0.134292
$576$		0			0
$577$	−504.599	−	504.599i	−0.874521	−	0.874521i	0.118440	−	0.992961i	$-0.462211\pi$
$577$	−504.599	−	504.599i	−0.874521	−	0.874521i	−0.992961	+	0.118440i	$0.962211\pi$
$578$		0			0
$579$		−	155.780i		−	0.269049i
$580$		0			0
$581$	−1334.20			−2.29638
$582$		0			0
$583$	30.1897	−	30.1897i	0.0517834	−	0.0517834i
$584$		0			0
$585$		−	438.358i		−	0.749330i
$586$		0			0
$587$	−110.932			−0.188982			−0.0944911	−	0.995526i	$-0.530122\pi$
$587$	−110.932			−0.188982			−0.0944911	+	0.995526i	$0.530122\pi$
$588$		0			0
$589$			1094.47i			1.85819i
$590$		0			0
$591$	−18.9325	+	18.9325i	−0.0320347	+	0.0320347i
$592$		0			0
$593$		−	988.969i		−	1.66774i	−0.551962	−	0.833870i	$-0.686121\pi$
$593$		−	988.969i		−	1.66774i	0.551962	−	0.833870i	$-0.313879\pi$
$594$		0			0
$595$	−274.748	−	274.748i	−0.461761	−	0.461761i
$596$		0			0
$597$	−45.0326	+	45.0326i	−0.0754315	+	0.0754315i
$598$		0			0
$599$	−262.125	+	262.125i	−0.437604	+	0.437604i	−0.891205	−	0.453601i	$-0.850139\pi$
$599$	−262.125	+	262.125i	−0.437604	+	0.437604i	0.453601	+	0.891205i	$0.350139\pi$
$600$		0			0
$601$	−496.848	+	496.848i	−0.826702	+	0.826702i	−0.987059	−	0.160357i	$-0.948735\pi$
$601$	−496.848	+	496.848i	−0.826702	+	0.826702i	0.160357	+	0.987059i	$0.448735\pi$
$602$		0			0
$603$	271.623			0.450452
$604$		0			0
$605$	502.967			0.831351
$606$		0			0
$607$	466.144	+	466.144i	0.767947	+	0.767947i	0.977745	−	0.209798i	$-0.0672806\pi$
$607$	466.144	+	466.144i	0.767947	+	0.767947i	−0.209798	+	0.977745i	$0.567281\pi$
$608$		0			0
$609$	−151.200	+	89.8515i	−0.248276	+	0.147539i
$610$		0			0
$611$	−27.0241	+	27.0241i	−0.0442293	+	0.0442293i
$612$		0			0
$613$			581.681i			0.948908i	0.880280	+	0.474454i	$0.157355\pi$
$613$			581.681i			0.948908i	−0.880280	+	0.474454i	$0.842645\pi$
$614$		0			0
$615$			84.1133i			0.136770i
$616$		0			0
$617$	−546.898	−	546.898i	−0.886383	−	0.886383i	0.107791	−	0.994174i	$-0.465622\pi$
$617$	−546.898	−	546.898i	−0.886383	−	0.886383i	−0.994174	+	0.107791i	$0.965622\pi$
$618$		0			0
$619$	650.477	+	650.477i	1.05085	+	1.05085i	0.998636	+	0.0522157i	$0.0166283\pi$
$619$	650.477	+	650.477i	1.05085	+	1.05085i	0.0522157	+	0.998636i	$0.483372\pi$
$620$		0			0
$621$	−78.6021	−	78.6021i	−0.126573	−	0.126573i
$622$		0			0
$623$	805.575	−	805.575i	1.29306	−	1.29306i
$624$		0			0
$625$	−374.939			−0.599903
$626$		0			0
$627$	−4.34914	−	4.34914i	−0.00693643	−	0.00693643i
$628$		0			0
$629$	−613.173			−0.974837
$630$		0			0
$631$		−	1020.55i		−	1.61735i	−0.588253	−	0.808677i	$-0.700184\pi$
$631$		−	1020.55i		−	1.61735i	0.588253	−	0.808677i	$-0.299816\pi$
$632$		0			0
$633$	74.4070			0.117547
$634$		0			0
$635$	217.475	+	217.475i	0.342480	+	0.342480i
$636$		0			0
$637$		−	548.558i		−	0.861159i
$638$		0			0
$639$	−859.668			−1.34533
$640$		0			0
$641$	65.0163	−	65.0163i	0.101430	−	0.101430i	−0.654571	−	0.756001i	$-0.727151\pi$
$641$	65.0163	−	65.0163i	0.101430	−	0.101430i	0.756001	+	0.654571i	$0.227151\pi$
$642$		0			0
$643$			590.198i			0.917882i	0.888467	+	0.458941i	$0.151771\pi$
$643$			590.198i			0.917882i	−0.888467	+	0.458941i	$0.848229\pi$
$644$		0			0
$645$	64.5318			0.100049
$646$		0			0
$647$			96.4448i			0.149065i	0.997219	+	0.0745323i	$0.0237464\pi$
$647$			96.4448i			0.149065i	−0.997219	+	0.0745323i	$0.976254\pi$
$648$		0			0
$649$	30.2851	−	30.2851i	0.0466642	−	0.0466642i
$650$		0			0
$651$			320.011i			0.491569i
$652$		0			0
$653$	−185.978	−	185.978i	−0.284806	−	0.284806i	0.550216	−	0.835022i	$-0.314545\pi$
$653$	−185.978	−	185.978i	−0.284806	−	0.284806i	−0.835022	+	0.550216i	$0.814545\pi$
$654$		0			0
$655$	−105.703	+	105.703i	−0.161379	+	0.161379i
$656$		0			0
$657$	34.1126	−	34.1126i	0.0519218	−	0.0519218i
$658$		0			0
$659$	−811.110	+	811.110i	−1.23082	+	1.23082i	−0.267170	+	0.963649i	$0.586089\pi$
$659$	−811.110	+	811.110i	−1.23082	+	1.23082i	−0.963649	+	0.267170i	$0.913911\pi$
$660$		0			0
$661$	442.227			0.669027			0.334513	−	0.942391i	$-0.391428\pi$
$661$	442.227			0.669027			0.334513	+	0.942391i	$0.391428\pi$
$662$		0			0
$663$	73.7216			0.111194
$664$		0			0
$665$	591.767	+	591.767i	0.889876	+	0.889876i
$666$		0			0
$667$	283.414	+	72.1302i	0.424908	+	0.108141i
$668$		0			0
$669$	−135.516	+	135.516i	−0.202565	+	0.202565i
$670$		0			0
$671$			19.7176i			0.0293854i
$672$		0			0
$673$			725.102i			1.07742i	0.842492	+	0.538708i	$0.181088\pi$
$673$			725.102i			1.07742i	−0.842492	+	0.538708i	$0.818912\pi$
$674$		0			0
$675$	−59.6829	−	59.6829i	−0.0884191	−	0.0884191i
$676$		0			0
$677$	650.790	+	650.790i	0.961285	+	0.961285i	0.999278	−	0.0379933i	$-0.0120965\pi$
$677$	650.790	+	650.790i	0.961285	+	0.961285i	−0.0379933	+	0.999278i	$0.512097\pi$
$678$		0			0
$679$	−774.907	−	774.907i	−1.14125	−	1.14125i
$680$		0			0
$681$	8.77604	−	8.77604i	0.0128870	−	0.0128870i
$682$		0			0
$683$	791.357			1.15865			0.579324	−	0.815097i	$-0.303317\pi$
$683$	791.357			1.15865			0.579324	+	0.815097i	$0.303317\pi$
$684$		0			0
$685$	487.988	+	487.988i	0.712392	+	0.712392i
$686$		0			0
$687$	−132.875			−0.193413
$688$		0			0
$689$		−	1102.22i		−	1.59973i
$690$		0			0
$691$	−646.166			−0.935118			−0.467559	−	0.883962i	$-0.654866\pi$
$691$	−646.166			−0.935118			−0.467559	+	0.883962i	$0.654866\pi$
$692$		0			0
$693$	27.9320	+	27.9320i	0.0403059	+	0.0403059i
$694$		0			0
$695$			259.399i			0.373235i
$696$		0			0
$697$	310.719			0.445795
$698$		0			0
$699$	−58.6220	+	58.6220i	−0.0838656	+	0.0838656i
$700$		0			0
$701$		−	738.399i		−	1.05335i	−0.850066	−	0.526676i	$-0.823438\pi$
$701$		−	738.399i		−	1.05335i	0.850066	−	0.526676i	$-0.176562\pi$
$702$		0			0
$703$	1320.69			1.87864
$704$		0			0
$705$		−	8.14799i		−	0.0115574i
$706$		0			0
$707$	−504.962	+	504.962i	−0.714231	+	0.714231i
$708$		0			0
$709$			211.506i			0.298316i	0.988813	+	0.149158i	$0.0476564\pi$
$709$			211.506i			0.298316i	−0.988813	+	0.149158i	$0.952344\pi$
$710$		0			0
$711$	347.008	+	347.008i	0.488056	+	0.488056i
$712$		0			0
$713$	376.249	−	376.249i	0.527699	−	0.527699i
$714$		0			0
$715$	−17.0559	+	17.0559i	−0.0238544	+	0.0238544i
$716$		0			0
$717$	78.2135	−	78.2135i	0.109084	−	0.109084i
$718$		0			0
$719$	479.844			0.667376			0.333688	−	0.942684i	$-0.391707\pi$
$719$	479.844			0.667376			0.333688	+	0.942684i	$0.391707\pi$
$720$		0			0
$721$	−1350.31			−1.87283
$722$		0			0
$723$	71.2728	+	71.2728i	0.0985792	+	0.0985792i
$724$		0			0
$725$	215.197	+	54.7687i	0.296824	+	0.0755431i
$726$		0			0
$727$	943.499	−	943.499i	1.29780	−	1.29780i	0.367953	−	0.929844i	$-0.380059\pi$
$727$	943.499	−	943.499i	1.29780	−	1.29780i	0.929844	−	0.367953i	$-0.119941\pi$
$728$		0			0
$729$		−	545.390i		−	0.748134i
$730$		0			0
$731$		−	238.384i		−	0.326106i
$732$		0			0
$733$	256.074	+	256.074i	0.349350	+	0.349350i	0.859868	−	0.510517i	$-0.170546\pi$
$733$	256.074	+	256.074i	0.349350	+	0.349350i	−0.510517	+	0.859868i	$0.670546\pi$
$734$		0			0
$735$	82.6973	+	82.6973i	0.112513	+	0.112513i
$736$		0			0
$737$	−10.5685	−	10.5685i	−0.0143398	−	0.0143398i
$738$		0			0
$739$	−9.12101	+	9.12101i	−0.0123424	+	0.0123424i	−0.713251	−	0.700909i	$-0.752778\pi$
$739$	−9.12101	+	9.12101i	−0.0123424	+	0.0123424i	0.700909	+	0.713251i	$0.252778\pi$
$740$		0			0
$741$	−158.786			−0.214286
$742$		0			0
$743$	343.894	+	343.894i	0.462845	+	0.462845i	0.899587	−	0.436742i	$-0.143868\pi$
$743$	343.894	+	343.894i	0.462845	+	0.462845i	−0.436742	+	0.899587i	$0.643868\pi$
$744$		0			0
$745$	587.175			0.788155
$746$		0			0
$747$		−	1185.46i		−	1.58696i
$748$		0			0
$749$	144.980			0.193564
$750$		0			0
$751$	−485.159	−	485.159i	−0.646017	−	0.646017i	0.306011	−	0.952028i	$-0.401006\pi$
$751$	−485.159	−	485.159i	−0.646017	−	0.646017i	−0.952028	+	0.306011i	$0.901006\pi$
$752$		0			0
$753$		−	120.953i		−	0.160628i
$754$		0			0
$755$	1120.66			1.48432
$756$		0			0
$757$	−158.090	+	158.090i	−0.208838	+	0.208838i	−0.803773	−	0.594936i	$-0.797178\pi$
$757$	−158.090	+	158.090i	−0.208838	+	0.208838i	0.594936	+	0.803773i	$0.297178\pi$
$758$		0			0
$759$			2.99023i			0.00393970i
$760$		0			0
$761$	1412.54			1.85617			0.928084	−	0.372371i	$-0.121455\pi$
$761$	1412.54			1.85617			0.928084	+	0.372371i	$0.121455\pi$
$762$		0			0
$763$			374.179i			0.490405i
$764$		0			0
$765$	244.119	−	244.119i	0.319109	−	0.319109i
$766$		0			0
$767$		−	1105.70i		−	1.44159i
$768$		0			0
$769$	−137.717	−	137.717i	−0.179086	−	0.179086i	0.611871	−	0.790957i	$-0.290417\pi$
$769$	−137.717	−	137.717i	−0.179086	−	0.179086i	−0.790957	+	0.611871i	$0.790417\pi$
$770$		0			0
$771$	122.004	−	122.004i	0.158242	−	0.158242i
$772$		0			0
$773$	−349.001	+	349.001i	−0.451489	+	0.451489i	−0.895848	−	0.444360i	$-0.853431\pi$
$773$	−349.001	+	349.001i	−0.451489	+	0.451489i	0.444360	+	0.895848i	$0.353431\pi$
$774$		0			0
$775$	285.688	−	285.688i	0.368629	−	0.368629i
$776$		0			0
$777$	386.154			0.496981
$778$		0			0
$779$	−669.244			−0.859107
$780$		0			0
$781$	33.4485	+	33.4485i	0.0428278	+	0.0428278i
$782$		0			0
$783$	−163.304	−	274.805i	−0.208562	−	0.350964i
$784$		0			0
$785$	−344.269	+	344.269i	−0.438560	+	0.438560i
$786$		0			0
$787$			880.918i			1.11934i	0.828717	+	0.559668i	$0.189071\pi$
$787$			880.918i			1.11934i	−0.828717	+	0.559668i	$0.810929\pi$
$788$		0			0
$789$			214.973i			0.272463i
$790$		0			0
$791$	−196.374	−	196.374i	−0.248261	−	0.248261i
$792$		0			0
$793$	359.941	+	359.941i	0.453898	+	0.453898i
$794$		0			0
$795$	166.164	+	166.164i	0.209011	+	0.209011i
$796$		0			0
$797$	634.695	−	634.695i	0.796356	−	0.796356i	−0.186163	−	0.982519i	$-0.559605\pi$
$797$	634.695	−	634.695i	0.796356	−	0.796356i	0.982519	+	0.186163i	$0.0596053\pi$
$798$		0			0
$799$	−30.0991			−0.0376709
$800$		0			0
$801$	715.769	+	715.769i	0.893594	+	0.893594i
$802$		0			0
$803$	−2.65455			−0.00330579
$804$		0			0
$805$		−	406.867i		−	0.505425i
$806$		0			0
$807$	−148.516			−0.184034
$808$		0			0
$809$	−768.799	−	768.799i	−0.950308	−	0.950308i	0.0485143	−	0.998822i	$-0.484551\pi$
$809$	−768.799	−	768.799i	−0.950308	−	0.950308i	−0.998822	+	0.0485143i	$0.984551\pi$
$810$		0			0
$811$			615.818i			0.759332i	0.925124	+	0.379666i	$0.123961\pi$
$811$			615.818i			0.759332i	−0.925124	+	0.379666i	$0.876039\pi$
$812$		0			0
$813$	249.980			0.307479
$814$		0			0
$815$	−67.3183	+	67.3183i	−0.0825991	+	0.0825991i
$816$		0			0
$817$			513.445i			0.628451i
$818$		0			0
$819$	1019.79			1.24516
$820$		0			0
$821$			998.934i			1.21673i	0.793658	+	0.608364i	$0.208174\pi$
$821$			998.934i			1.21673i	−0.793658	+	0.608364i	$0.791826\pi$
$822$		0			0
$823$	117.268	−	117.268i	0.142489	−	0.142489i	−0.632264	−	0.774753i	$-0.717874\pi$
$823$	117.268	−	117.268i	0.142489	−	0.142489i	0.774753	+	0.632264i	$0.217874\pi$
$824$		0			0
$825$			2.27050i			0.00275212i
$826$		0			0
$827$	−1079.32	−	1079.32i	−1.30510	−	1.30510i	−0.924906	−	0.380195i	$-0.875857\pi$
$827$	−1079.32	−	1079.32i	−1.30510	−	1.30510i	−0.380195	−	0.924906i	$-0.624143\pi$
$828$		0			0
$829$	671.650	−	671.650i	0.810192	−	0.810192i	−0.174470	−	0.984662i	$-0.555821\pi$
$829$	671.650	−	671.650i	0.810192	−	0.810192i	0.984662	+	0.174470i	$0.0558212\pi$
$830$		0			0
$831$	−13.5154	+	13.5154i	−0.0162640	+	0.0162640i
$832$		0			0
$833$	305.488	−	305.488i	0.366732	−	0.366732i
$834$		0			0
$835$	560.239			0.670945
$836$		0			0
$837$	−581.617			−0.694883
$838$		0			0
$839$	100.846	+	100.846i	0.120197	+	0.120197i	0.764647	−	0.644449i	$-0.222913\pi$
$839$	100.846	+	100.846i	0.120197	+	0.120197i	−0.644449	+	0.764647i	$0.722913\pi$
$840$		0			0
$841$	738.680	+	402.036i	0.878335	+	0.478045i
$842$		0			0
$843$	1.29346	−	1.29346i	0.00153435	−	0.00153435i
$844$		0			0
$845$		−	81.0901i		−	0.0959646i
$846$		0			0
$847$			1170.09i			1.38145i
$848$		0			0
$849$	−11.9259	−	11.9259i	−0.0140470	−	0.0140470i
$850$		0			0
$851$	−454.016	−	454.016i	−0.533509	−	0.533509i
$852$		0			0
$853$	−922.579	−	922.579i	−1.08157	−	1.08157i	−0.996363	−	0.0852066i	$-0.972845\pi$
$853$	−922.579	−	922.579i	−1.08157	−	1.08157i	−0.0852066	−	0.996363i	$-0.527155\pi$
$854$		0			0
$855$	−525.797	+	525.797i	−0.614967	+	0.614967i
$856$		0			0
$857$	−633.774			−0.739527			−0.369763	−	0.929126i	$-0.620561\pi$
$857$	−633.774			−0.739527			−0.369763	+	0.929126i	$0.620561\pi$
$858$		0			0
$859$	834.541	+	834.541i	0.971526	+	0.971526i	0.999606	−	0.0280796i	$-0.00893918\pi$
$859$	834.541	+	834.541i	0.971526	+	0.971526i	−0.0280796	+	0.999606i	$0.508939\pi$
$860$		0			0
$861$	−195.680			−0.227270
$862$		0			0
$863$		−	805.408i		−	0.933265i	−0.884451	−	0.466632i	$-0.845467\pi$
$863$		−	805.408i		−	0.933265i	0.884451	−	0.466632i	$-0.154533\pi$
$864$		0			0
$865$	−392.192			−0.453401
$866$		0			0
$867$	−86.8737	−	86.8737i	−0.100200	−	0.100200i
$868$		0			0
$869$		−	27.0032i		−	0.0310739i
$870$		0			0
$871$	−385.851			−0.442998
$872$		0			0
$873$	688.520	−	688.520i	0.788682	−	0.788682i
$874$		0			0
$875$		−	1317.59i		−	1.50581i
$876$		0			0
$877$	427.725			0.487714			0.243857	−	0.969811i	$-0.421587\pi$
$877$	427.725			0.487714			0.243857	+	0.969811i	$0.421587\pi$
$878$		0			0
$879$		−	226.438i		−	0.257609i
$880$		0			0
$881$	−977.952	+	977.952i	−1.11005	+	1.11005i	−0.116905	+	0.993143i	$0.537297\pi$
$881$	−977.952	+	977.952i	−1.11005	+	1.11005i	−0.993143	+	0.116905i	$0.962703\pi$
$882$		0			0
$883$		−	1215.83i		−	1.37693i	−0.725270	−	0.688464i	$-0.758285\pi$
$883$		−	1215.83i		−	1.37693i	0.725270	−	0.688464i	$-0.241715\pi$
$884$		0			0
$885$	166.689	+	166.689i	0.188349	+	0.188349i
$886$		0			0
$887$	−1221.32	+	1221.32i	−1.37691	+	1.37691i	−0.527122	+	0.849790i	$0.676729\pi$
$887$	−1221.32	+	1221.32i	−1.37691	+	1.37691i	−0.849790	+	0.527122i	$0.823271\pi$
$888$		0			0
$889$	−505.929	+	505.929i	−0.569099	+	0.569099i
$890$		0			0
$891$	−23.6368	+	23.6368i	−0.0265284	+	0.0265284i
$892$		0			0
$893$	64.8291			0.0725970
$894$		0			0
$895$	231.916			0.259124
$896$		0			0
$897$	54.5862	+	54.5862i	0.0608542	+	0.0608542i
$898$		0			0
$899$	1315.43	−	781.698i	1.46321	−	0.869519i
$900$		0			0
$901$	613.816	−	613.816i	0.681261	−	0.681261i
$902$		0			0
$903$			150.125i			0.166252i
$904$		0			0
$905$			549.204i			0.606856i
$906$		0			0
$907$	236.820	+	236.820i	0.261103	+	0.261103i	0.825502	−	0.564399i	$-0.190892\pi$
$907$	236.820	+	236.820i	0.261103	+	0.261103i	−0.564399	+	0.825502i	$0.690892\pi$
$908$		0			0
$909$	−448.668	−	448.668i	−0.493584	−	0.493584i
$910$		0			0
$911$	807.445	+	807.445i	0.886328	+	0.886328i	0.994168	−	0.107840i	$-0.0343936\pi$
$911$	807.445	+	807.445i	0.886328	+	0.886328i	−0.107840	+	0.994168i	$0.534394\pi$
$912$		0			0
$913$	−46.1246	+	46.1246i	−0.0505198	+	0.0505198i
$914$		0			0
$915$	−108.525			−0.118607
$916$		0			0
$917$	−245.905	−	245.905i	−0.268163	−	0.268163i
$918$		0			0
$919$	791.267			0.861009			0.430504	−	0.902589i	$-0.358336\pi$
$919$	791.267			0.861009			0.430504	+	0.902589i	$0.358336\pi$
$920$		0			0
$921$			8.14823i			0.00884715i
$922$		0			0
$923$	1221.19			1.32307
$924$		0			0
$925$	−344.736	−	344.736i	−0.372688	−	0.372688i
$926$		0			0
$927$		−	1199.77i		−	1.29425i
$928$		0			0
$929$	1491.46			1.60545			0.802724	−	0.596351i	$-0.203383\pi$
$929$	1491.46			1.60545			0.802724	+	0.596351i	$0.203383\pi$
$930$		0			0
$931$	−657.978	+	657.978i	−0.706743	+	0.706743i
$932$		0			0
$933$		−	83.2999i		−	0.0892818i
$934$		0			0
$935$	−18.9966			−0.0203173
$936$		0			0
$937$		−	910.587i		−	0.971811i	−0.874011	−	0.485905i	$-0.838490\pi$
$937$		−	910.587i		−	0.971811i	0.874011	−	0.485905i	$-0.161510\pi$
$938$		0			0
$939$	−59.2113	+	59.2113i	−0.0630578	+	0.0630578i
$940$		0			0
$941$		−	1302.28i		−	1.38393i	−0.721929	−	0.691967i	$-0.756744\pi$
$941$		−	1302.28i		−	1.38393i	0.721929	−	0.691967i	$-0.243256\pi$
$942$		0			0
$943$	230.068	+	230.068i	0.243974	+	0.243974i
$944$		0			0
$945$	−314.473	+	314.473i	−0.332776	+	0.332776i
$946$		0			0
$947$	455.078	−	455.078i	0.480547	−	0.480547i	−0.424759	−	0.905306i	$-0.639641\pi$
$947$	455.078	−	455.078i	0.480547	−	0.480547i	0.905306	+	0.424759i	$0.139641\pi$
$948$		0			0
$949$	−48.4584	+	48.4584i	−0.0510626	+	0.0510626i
$950$		0			0
$951$	−358.846			−0.377335
$952$		0			0
$953$	299.880			0.314670			0.157335	−	0.987545i	$-0.449710\pi$
$953$	299.880			0.314670			0.157335	+	0.987545i	$0.449710\pi$
$954$		0			0
$955$	510.328	+	510.328i	0.534375	+	0.534375i
$956$		0			0
$957$	−2.12090	+	8.33342i	−0.00221619	+	0.00870785i
$958$		0			0
$959$	−1135.25	+	1135.25i	−1.18378	+	1.18378i
$960$		0			0
$961$		−	1823.06i		−	1.89705i
$962$		0			0
$963$			128.817i			0.133766i
$964$		0			0
$965$	732.775	+	732.775i	0.759352	+	0.759352i
$966$		0			0
$967$	−136.707	−	136.707i	−0.141372	−	0.141372i	0.632879	−	0.774251i	$-0.281873\pi$
$967$	−136.707	−	136.707i	−0.141372	−	0.141372i	−0.774251	+	0.632879i	$0.781873\pi$
$968$		0			0
$969$	−88.4266	−	88.4266i	−0.0912556	−	0.0912556i
$970$		0			0
$971$	−225.421	+	225.421i	−0.232153	+	0.232153i	−0.813591	−	0.581438i	$-0.802490\pi$
$971$	−225.421	+	225.421i	−0.232153	+	0.232153i	0.581438	+	0.813591i	$0.302490\pi$
$972$		0			0
$973$	−603.459			−0.620205
$974$		0			0
$975$	41.4475	+	41.4475i	0.0425103	+	0.0425103i
$976$		0			0
$977$	119.816			0.122637			0.0613186	−	0.998118i	$-0.480469\pi$
$977$	119.816			0.122637			0.0613186	+	0.998118i	$0.480469\pi$
$978$		0			0
$979$		−	55.6992i		−	0.0568939i
$980$		0			0
$981$	−332.465			−0.338904
$982$		0			0
$983$	−727.465	−	727.465i	−0.740046	−	0.740046i	0.232540	−	0.972587i	$-0.425296\pi$
$983$	−727.465	−	727.465i	−0.740046	−	0.740046i	−0.972587	+	0.232540i	$0.925296\pi$
$984$		0			0
$985$		−	178.114i		−	0.180827i
$986$		0			0
$987$	18.9553			0.0192050
$988$		0			0
$989$	176.508	−	176.508i	0.178471	−	0.178471i
$990$		0			0
$991$			76.7646i			0.0774617i	0.999250	+	0.0387309i	$0.0123315\pi$
$991$			76.7646i			0.0774617i	−0.999250	+	0.0387309i	$0.987669\pi$
$992$		0			0
$993$	163.879			0.165035
$994$		0			0
$995$		−	423.660i		−	0.425789i
$996$		0			0
$997$	−352.075	+	352.075i	−0.353135	+	0.353135i	−0.861275	−	0.508140i	$-0.830333\pi$
$997$	−352.075	+	352.075i	−0.353135	+	0.353135i	0.508140	+	0.861275i	$0.330333\pi$
$998$		0			0
$999$			701.831i			0.702533i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	464.3.l.c.17.2		8
4.3	odd	2		29.3.c.a.17.3	yes	8
12.11	even	2		261.3.f.a.46.2		8
29.12	odd	4	inner	464.3.l.c.273.2		8
116.99	even	4		29.3.c.a.12.3	✓	8
348.215	odd	4		261.3.f.a.244.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.3.c.a.12.3	✓	8	116.99	even	4
29.3.c.a.17.3	yes	8	4.3	odd	2
261.3.f.a.46.2		8	12.11	even	2
261.3.f.a.244.2		8	348.215	odd	4
464.3.l.c.17.2		8	1.1	even	1	trivial
464.3.l.c.273.2		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)

\(f(q)\)	\(=\)	\(q+(-0.442660 + 0.442660i) q^{3} -4.16447i q^{5} +9.68815 q^{7} +8.60810i q^{9} +O(q^{10})\)	\(q+(-0.442660 + 0.442660i) q^{3} -4.16447i q^{5} +9.68815 q^{7} +8.60810i q^{9} +(0.334930 - 0.334930i) q^{11} -12.2282i q^{13} +(1.84345 + 1.84345i) q^{15} +(6.80978 - 6.80978i) q^{17} +(-14.6673 + 14.6673i) q^{19} +(-4.28855 + 4.28855i) q^{21} +10.0844 q^{23} +7.65715 q^{25} +(-7.79440 - 7.79440i) q^{27} +(28.1041 + 7.15263i) q^{29} +(37.3099 - 37.3099i) q^{31} +0.296520i q^{33} -40.3460i q^{35} +(-45.0215 - 45.0215i) q^{37} +(5.41292 + 5.41292i) q^{39} +(22.8142 + 22.8142i) q^{41} +(17.5030 - 17.5030i) q^{43} +35.8482 q^{45} +(-2.20999 - 2.20999i) q^{47} +44.8602 q^{49} +6.02883i q^{51} +90.1375 q^{53} +(-1.39481 - 1.39481i) q^{55} -12.9852i q^{57} +90.4223 q^{59} +(-29.4354 + 29.4354i) q^{61} +83.3966i q^{63} -50.9239 q^{65} -31.5543i q^{67} +(-4.46397 + 4.46397i) q^{69} +99.8673i q^{71} +(-3.96285 - 3.96285i) q^{73} +(-3.38951 + 3.38951i) q^{75} +(3.24485 - 3.24485i) q^{77} +(40.3117 - 40.3117i) q^{79} -70.5724 q^{81} -137.714 q^{83} +(-28.3592 - 28.3592i) q^{85} +(-15.6067 + 9.27437i) q^{87} +(83.1506 - 83.1506i) q^{89} -118.468i q^{91} +33.0312i q^{93} +(61.0816 + 61.0816i) q^{95} +(-79.9850 - 79.9850i) q^{97} +(2.88311 + 2.88311i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} + 4 q^{7}+O(q^{10}) \) 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

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