LMFDB - Embedded newform 1815.2.c.g.364.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1815,2,Mod(364,1815)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1815, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1815.364");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1815 = 3 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1815.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.4928479669$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			364.6
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1815.364
Dual form			1815.2.c.g.364.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} -1.00000i q^{3} +(0.224745 + 2.22474i) q^{5} +1.41421 q^{6} +1.73205i q^{7} +2.82843i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.41421i q^{2} -1.00000i q^{3} +(0.224745 + 2.22474i) q^{5} +1.41421 q^{6} +1.73205i q^{7} +2.82843i q^{8} -1.00000 q^{9} +(-3.14626 + 0.317837i) q^{10} +6.29253i q^{13} -2.44949 q^{14} +(2.22474 - 0.224745i) q^{15} -4.00000 q^{16} -2.04989i q^{17} -1.41421i q^{18} -1.73205 q^{19} +1.73205 q^{21} -2.00000i q^{23} +2.82843 q^{24} +(-4.89898 + 1.00000i) q^{25} -8.89898 q^{26} +1.00000i q^{27} -5.51399 q^{29} +(0.317837 + 3.14626i) q^{30} +1.89898 q^{31} +2.89898 q^{34} +(-3.85337 + 0.389270i) q^{35} -3.89898i q^{37} -2.44949i q^{38} +6.29253 q^{39} +(-6.29253 + 0.635674i) q^{40} +2.19275 q^{41} +2.44949i q^{42} -5.65685i q^{43} +(-0.224745 - 2.22474i) q^{45} +2.82843 q^{46} -7.34847i q^{47} +4.00000i q^{48} +4.00000 q^{49} +(-1.41421 - 6.92820i) q^{50} -2.04989 q^{51} +10.0000i q^{53} -1.41421 q^{54} -4.89898 q^{56} +1.73205i q^{57} -7.79796i q^{58} -12.2474 q^{59} +13.6814 q^{61} +2.68556i q^{62} -1.73205i q^{63} -8.00000 q^{64} +(-13.9993 + 1.41421i) q^{65} -13.8990i q^{67} -2.00000 q^{69} +(-0.550510 - 5.44949i) q^{70} -8.44949 q^{71} -2.82843i q^{72} +13.6814i q^{73} +5.51399 q^{74} +(1.00000 + 4.89898i) q^{75} +8.89898i q^{78} +10.2173 q^{79} +(-0.898979 - 8.89898i) q^{80} +1.00000 q^{81} +3.10102i q^{82} +12.7279i q^{83} +(4.56048 - 0.460702i) q^{85} +8.00000 q^{86} +5.51399i q^{87} +13.3485 q^{89} +(3.14626 - 0.317837i) q^{90} -10.8990 q^{91} -1.89898i q^{93} +10.3923 q^{94} +(-0.389270 - 3.85337i) q^{95} -5.00000i q^{97} +5.65685i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{5} - 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^5 - 8 * q^9	$ 8 q - 8 q^{5} - 8 q^{9} + 8 q^{15} - 32 q^{16} - 32 q^{26} - 24 q^{31} - 16 q^{34} + 8 q^{45} + 32 q^{49} - 64 q^{64} - 16 q^{69} - 24 q^{70} - 48 q^{71} + 8 q^{75} + 32 q^{80} + 8 q^{81} + 64 q^{86} + 48 q^{89} - 48 q^{91}+O(q^{100}) $ 8 * q - 8 * q^5 - 8 * q^9 + 8 * q^15 - 32 * q^16 - 32 * q^26 - 24 * q^31 - 16 * q^34 + 8 * q^45 + 32 * q^49 - 64 * q^64 - 16 * q^69 - 24 * q^70 - 48 * q^71 + 8 * q^75 + 32 * q^80 + 8 * q^81 + 64 * q^86 + 48 * q^89 - 48 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1815\mathbb{Z}\right)^\times$.

$n$	$727$	$1211$	$1696$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$			1.41421i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$2$			1.41421i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$		0			0
$5$	0.224745	+	2.22474i	0.100509	+	0.994936i
$5$	0.224745	+	2.22474i	0.100509	+	0.994936i
$6$	1.41421			0.577350
$7$			1.73205i			0.654654i	0.944911	+	0.327327i	$0.106148\pi$
$7$			1.73205i			0.654654i	−0.944911	+	0.327327i	$0.893852\pi$
$8$			2.82843i			1.00000i
$9$	−1.00000			−0.333333
$10$	−3.14626	+	0.317837i	−0.994936	+	0.100509i
$11$		0			0
$11$		0			0
$12$		0			0
$13$			6.29253i			1.74523i	0.488406	+	0.872617i	$0.337579\pi$
$13$			6.29253i			1.74523i	−0.488406	+	0.872617i	$0.662421\pi$
$14$	−2.44949			−0.654654
$15$	2.22474	−	0.224745i	0.574427	−	0.0580289i
$16$	−4.00000			−1.00000
$17$		−	2.04989i		−	0.497171i	−0.968610	−	0.248585i	$-0.920034\pi$
$17$		−	2.04989i		−	0.497171i	0.968610	−	0.248585i	$-0.0799657\pi$
$18$		−	1.41421i		−	0.333333i
$19$	−1.73205			−0.397360			−0.198680	−	0.980064i	$-0.563665\pi$
$19$	−1.73205			−0.397360			−0.198680	+	0.980064i	$0.563665\pi$
$20$		0			0
$21$	1.73205			0.377964
$22$		0			0
$23$		−	2.00000i		−	0.417029i	−0.978019	−	0.208514i	$-0.933137\pi$
$23$		−	2.00000i		−	0.417029i	0.978019	−	0.208514i	$-0.0668628\pi$
$24$	2.82843			0.577350
$25$	−4.89898	+	1.00000i	−0.979796	+	0.200000i
$26$	−8.89898			−1.74523
$27$			1.00000i			0.192450i
$28$		0			0
$29$	−5.51399			−1.02392			−0.511961	−	0.859009i	$-0.671081\pi$
$29$	−5.51399			−1.02392			−0.511961	+	0.859009i	$0.671081\pi$
$30$	0.317837	+	3.14626i	0.0580289	+	0.574427i
$31$	1.89898			0.341067			0.170533	−	0.985352i	$-0.445451\pi$
$31$	1.89898			0.341067			0.170533	+	0.985352i	$0.445451\pi$
$32$		0			0
$33$		0			0
$34$	2.89898			0.497171
$35$	−3.85337	+	0.389270i	−0.651339	+	0.0657986i
$36$		0			0
$37$		−	3.89898i		−	0.640988i	−0.947250	−	0.320494i	$-0.896151\pi$
$37$		−	3.89898i		−	0.640988i	0.947250	−	0.320494i	$-0.103849\pi$
$38$		−	2.44949i		−	0.397360i
$39$	6.29253			1.00761
$40$	−6.29253	+	0.635674i	−0.994936	+	0.100509i
$41$	2.19275			0.342450			0.171225	−	0.985232i	$-0.445227\pi$
$41$	2.19275			0.342450			0.171225	+	0.985232i	$0.445227\pi$
$42$			2.44949i			0.377964i
$43$		−	5.65685i		−	0.862662i	−0.902194	−	0.431331i	$-0.858044\pi$
$43$		−	5.65685i		−	0.862662i	0.902194	−	0.431331i	$-0.141956\pi$
$44$		0			0
$45$	−0.224745	−	2.22474i	−0.0335030	−	0.331645i
$46$	2.82843			0.417029
$47$		−	7.34847i		−	1.07188i	−0.844255	−	0.535942i	$-0.819956\pi$
$47$		−	7.34847i		−	1.07188i	0.844255	−	0.535942i	$-0.180044\pi$
$48$			4.00000i			0.577350i
$49$	4.00000			0.571429
$50$	−1.41421	−	6.92820i	−0.200000	−	0.979796i
$51$	−2.04989			−0.287042
$52$		0			0
$53$			10.0000i			1.37361i	0.726844	+	0.686803i	$0.240986\pi$
$53$			10.0000i			1.37361i	−0.726844	+	0.686803i	$0.759014\pi$
$54$	−1.41421			−0.192450
$55$		0			0
$56$	−4.89898			−0.654654
$57$			1.73205i			0.229416i
$58$		−	7.79796i		−	1.02392i
$59$	−12.2474			−1.59448			−0.797241	−	0.603661i	$-0.793708\pi$
$59$	−12.2474			−1.59448			−0.797241	+	0.603661i	$0.793708\pi$
$60$		0			0
$61$	13.6814			1.75173			0.875864	−	0.482558i	$-0.160292\pi$
$61$	13.6814			1.75173			0.875864	+	0.482558i	$0.160292\pi$
$62$			2.68556i			0.341067i
$63$		−	1.73205i		−	0.218218i
$64$	−8.00000			−1.00000
$65$	−13.9993	+	1.41421i	−1.73640	+	0.175412i
$66$		0			0
$67$		−	13.8990i		−	1.69803i	−0.528368	−	0.849015i	$-0.677196\pi$
$67$		−	13.8990i		−	1.69803i	0.528368	−	0.849015i	$-0.322804\pi$
$68$		0			0
$69$	−2.00000			−0.240772
$70$	−0.550510	−	5.44949i	−0.0657986	−	0.651339i
$71$	−8.44949			−1.00277			−0.501385	−	0.865224i	$-0.667176\pi$
$71$	−8.44949			−1.00277			−0.501385	+	0.865224i	$0.667176\pi$
$72$		−	2.82843i		−	0.333333i
$73$			13.6814i			1.60129i	0.599139	+	0.800645i	$0.295510\pi$
$73$			13.6814i			1.60129i	−0.599139	+	0.800645i	$0.704490\pi$
$74$	5.51399			0.640988
$75$	1.00000	+	4.89898i	0.115470	+	0.565685i
$76$		0			0
$77$		0			0
$78$			8.89898i			1.00761i
$79$	10.2173			1.14954			0.574770	−	0.818315i	$-0.305092\pi$
$79$	10.2173			1.14954			0.574770	+	0.818315i	$0.305092\pi$
$80$	−0.898979	−	8.89898i	−0.100509	−	0.994936i
$81$	1.00000			0.111111
$82$			3.10102i			0.342450i
$83$			12.7279i			1.39707i	0.715575	+	0.698535i	$0.246165\pi$
$83$			12.7279i			1.39707i	−0.715575	+	0.698535i	$0.753835\pi$
$84$		0			0
$85$	4.56048	−	0.460702i	0.494653	−	0.0499701i
$86$	8.00000			0.862662
$87$			5.51399i			0.591162i
$88$		0			0
$89$	13.3485			1.41493			0.707467	−	0.706746i	$-0.249838\pi$
$89$	13.3485			1.41493			0.707467	+	0.706746i	$0.249838\pi$
$90$	3.14626	−	0.317837i	0.331645	−	0.0335030i
$91$	−10.8990			−1.14252
$92$		0			0
$93$		−	1.89898i		−	0.196915i
$94$	10.3923			1.07188
$95$	−0.389270	−	3.85337i	−0.0399382	−	0.395348i
$96$		0			0
$97$		−	5.00000i		−	0.507673i	−0.967247	−	0.253837i	$-0.918307\pi$
$97$		−	5.00000i		−	0.507673i	0.967247	−	0.253837i	$-0.0816925\pi$
$98$			5.65685i			0.571429i
$99$		0			0
$100$		0			0
$101$	−13.9993			−1.39298			−0.696490	−	0.717567i	$-0.745256\pi$
$101$	−13.9993			−1.39298			−0.696490	+	0.717567i	$0.745256\pi$
$102$		−	2.89898i		−	0.287042i
$103$			8.10102i			0.798217i	0.916904	+	0.399109i	$0.130680\pi$
$103$			8.10102i			0.798217i	−0.916904	+	0.399109i	$0.869320\pi$
$104$	−17.7980			−1.74523
$105$	0.389270	+	3.85337i	0.0379888	+	0.376051i
$106$	−14.1421			−1.37361
$107$			5.51399i			0.533058i	0.963827	+	0.266529i	$0.0858767\pi$
$107$			5.51399i			0.533058i	−0.963827	+	0.266529i	$0.914123\pi$
$108$		0			0
$109$	8.94598			0.856870			0.428435	−	0.903573i	$-0.359065\pi$
$109$	8.94598			0.856870			0.428435	+	0.903573i	$0.359065\pi$
$110$		0			0
$111$	−3.89898			−0.370075
$112$		−	6.92820i		−	0.654654i
$113$			18.4495i			1.73558i	0.496929	+	0.867791i	$0.334461\pi$
$113$			18.4495i			1.73558i	−0.496929	+	0.867791i	$0.665539\pi$
$114$	−2.44949			−0.229416
$115$	4.44949	−	0.449490i	0.414917	−	0.0419151i
$116$		0			0
$117$		−	6.29253i		−	0.581744i
$118$		−	17.3205i		−	1.59448i
$119$	3.55051			0.325475
$120$	0.635674	+	6.29253i	0.0580289	+	0.574427i
$121$		0			0
$122$			19.3485i			1.75173i
$123$		−	2.19275i		−	0.197714i
$124$		0			0
$125$	−3.32577	−	10.6742i	−0.297465	−	0.954733i
$126$	2.44949			0.218218
$127$			15.2385i			1.35220i	0.736810	+	0.676100i	$0.236331\pi$
$127$			15.2385i			1.35220i	−0.736810	+	0.676100i	$0.763669\pi$
$128$		−	11.3137i		−	1.00000i
$129$	−5.65685			−0.498058
$130$	−2.00000	−	19.7980i	−0.175412	−	1.73640i
$131$	−17.6062			−1.53826			−0.769132	−	0.639090i	$-0.779311\pi$
$131$	−17.6062			−1.53826			−0.769132	+	0.639090i	$0.779311\pi$
$132$		0			0
$133$		−	3.00000i		−	0.260133i
$134$	19.6561			1.69803
$135$	−2.22474	+	0.224745i	−0.191476	+	0.0193430i
$136$	5.79796			0.497171
$137$		−	2.20204i		−	0.188133i	−0.995566	−	0.0940665i	$-0.970013\pi$
$137$		−	2.20204i		−	0.188133i	0.995566	−	0.0940665i	$-0.0299866\pi$
$138$		−	2.82843i		−	0.240772i
$139$	1.27135			0.107834			0.0539172	−	0.998545i	$-0.482829\pi$
$139$	1.27135			0.107834			0.0539172	+	0.998545i	$0.482829\pi$
$140$		0			0
$141$	−7.34847			−0.618853
$142$		−	11.9494i		−	1.00277i
$143$		0			0
$144$	4.00000			0.333333
$145$	−1.23924	−	12.2672i	−0.102913	−	1.01874i
$146$	−19.3485			−1.60129
$147$		−	4.00000i		−	0.329914i
$148$		0			0
$149$	−8.97809			−0.735514			−0.367757	−	0.929922i	$-0.619874\pi$
$149$	−8.97809			−0.735514			−0.367757	+	0.929922i	$0.619874\pi$
$150$	−6.92820	+	1.41421i	−0.565685	+	0.115470i
$151$	−4.73545			−0.385366			−0.192683	−	0.981261i	$-0.561719\pi$
$151$	−4.73545			−0.385366			−0.192683	+	0.981261i	$0.561719\pi$
$152$		−	4.89898i		−	0.397360i
$153$			2.04989i			0.165724i
$154$		0			0
$155$	0.426786	+	4.22474i	0.0342803	+	0.339340i
$156$		0			0
$157$			20.5959i			1.64373i	0.569680	+	0.821867i	$0.307067\pi$
$157$			20.5959i			1.64373i	−0.569680	+	0.821867i	$0.692933\pi$
$158$			14.4495i			1.14954i
$159$	10.0000			0.793052
$160$		0			0
$161$	3.46410			0.273009
$162$			1.41421i			0.111111i
$163$		−	1.00000i		−	0.0783260i	−0.999233	−	0.0391630i	$-0.987531\pi$
$163$		−	1.00000i		−	0.0783260i	0.999233	−	0.0391630i	$-0.0124692\pi$
$164$		0			0
$165$		0			0
$166$	−18.0000			−1.39707
$167$		−	7.56388i		−	0.585310i	−0.956218	−	0.292655i	$-0.905461\pi$
$167$		−	7.56388i		−	0.585310i	0.956218	−	0.292655i	$-0.0945388\pi$
$168$			4.89898i			0.377964i
$169$	−26.5959			−2.04584
$170$	0.651531	+	6.44949i	0.0499701	+	0.494653i
$171$	1.73205			0.132453
$172$		0			0
$173$		−	6.14966i		−	0.467550i	−0.972291	−	0.233775i	$-0.924892\pi$
$173$		−	6.14966i		−	0.467550i	0.972291	−	0.233775i	$-0.0751080\pi$
$174$	−7.79796			−0.591162
$175$	−1.73205	−	8.48528i	−0.130931	−	0.641427i
$176$		0			0
$177$			12.2474i			0.920575i
$178$			18.8776i			1.41493i
$179$	18.0454			1.34878			0.674389	−	0.738377i	$-0.264407\pi$
$179$	18.0454			1.34878			0.674389	+	0.738377i	$0.264407\pi$
$180$		0			0
$181$	5.00000			0.371647			0.185824	−	0.982583i	$-0.440505\pi$
$181$	5.00000			0.371647			0.185824	+	0.982583i	$0.440505\pi$
$182$		−	15.4135i		−	1.14252i
$183$		−	13.6814i		−	1.01136i
$184$	5.65685			0.417029
$185$	8.67423	−	0.876276i	0.637742	−	0.0644251i
$186$	2.68556			0.196915
$187$		0			0
$188$		0			0
$189$	−1.73205			−0.125988
$190$	5.44949	−	0.550510i	0.395348	−	0.0399382i
$191$	13.7980			0.998385			0.499193	−	0.866491i	$-0.333630\pi$
$191$	13.7980			0.998385			0.499193	+	0.866491i	$0.333630\pi$
$192$			8.00000i			0.577350i
$193$			6.46750i			0.465541i	0.972532	+	0.232770i	$0.0747791\pi$
$193$			6.46750i			0.465541i	−0.972532	+	0.232770i	$0.925221\pi$
$194$	7.07107			0.507673
$195$	1.41421	+	13.9993i	0.101274	+	1.00251i
$196$		0			0
$197$			2.82843i			0.201517i	0.994911	+	0.100759i	$0.0321270\pi$
$197$			2.82843i			0.201517i	−0.994911	+	0.100759i	$0.967873\pi$
$198$		0			0
$199$	22.5959			1.60178			0.800891	−	0.598810i	$-0.204360\pi$
$199$	22.5959			1.60178			0.800891	+	0.598810i	$0.204360\pi$
$200$	−2.82843	−	13.8564i	−0.200000	−	0.979796i
$201$	−13.8990			−0.980358
$202$		−	19.7980i		−	1.39298i
$203$		−	9.55051i		−	0.670314i
$204$		0			0
$205$	0.492810	+	4.87832i	0.0344193	+	0.340716i
$206$	−11.4566			−0.798217
$207$			2.00000i			0.139010i
$208$		−	25.1701i		−	1.74523i
$209$		0			0
$210$	−5.44949	+	0.550510i	−0.376051	+	0.0379888i
$211$	−15.8742			−1.09282			−0.546412	−	0.837517i	$-0.684007\pi$
$211$	−15.8742			−1.09282			−0.546412	+	0.837517i	$0.684007\pi$
$212$		0			0
$213$			8.44949i			0.578949i
$214$	−7.79796			−0.533058
$215$	12.5851	−	1.27135i	0.858294	−	0.0867053i
$216$	−2.82843			−0.192450
$217$			3.28913i			0.223281i
$218$			12.6515i			0.856870i
$219$	13.6814			0.924506
$220$		0			0
$221$	12.8990			0.867679
$222$		−	5.51399i		−	0.370075i
$223$			11.0000i			0.736614i	0.929704	+	0.368307i	$0.120063\pi$
$223$			11.0000i			0.736614i	−0.929704	+	0.368307i	$0.879937\pi$
$224$		0			0
$225$	4.89898	−	1.00000i	0.326599	−	0.0666667i
$226$	−26.0915			−1.73558
$227$		−	9.75663i		−	0.647570i	−0.946131	−	0.323785i	$-0.895045\pi$
$227$		−	9.75663i		−	0.647570i	0.946131	−	0.323785i	$-0.104955\pi$
$228$		0			0
$229$	12.8990			0.852389			0.426194	−	0.904632i	$-0.359854\pi$
$229$	12.8990			0.852389			0.426194	+	0.904632i	$0.359854\pi$
$230$	0.635674	+	6.29253i	0.0419151	+	0.414917i
$231$		0			0
$232$		−	15.5959i		−	1.02392i
$233$			3.95691i			0.259226i	0.991565	+	0.129613i	$0.0413735\pi$
$233$			3.95691i			0.259226i	−0.991565	+	0.129613i	$0.958627\pi$
$234$	8.89898			0.581744
$235$	16.3485	−	1.65153i	1.06646	−	0.107734i
$236$		0			0
$237$		−	10.2173i		−	0.663687i
$238$			5.02118i			0.325475i
$239$	−9.89949			−0.640345			−0.320173	−	0.947359i	$-0.603741\pi$
$239$	−9.89949			−0.640345			−0.320173	+	0.947359i	$0.603741\pi$
$240$	−8.89898	+	0.898979i	−0.574427	+	0.0580289i
$241$	6.29253			0.405337			0.202669	−	0.979247i	$-0.435039\pi$
$241$	6.29253			0.405337			0.202669	+	0.979247i	$0.435039\pi$
$242$		0			0
$243$		−	1.00000i		−	0.0641500i
$244$		0			0
$245$	0.898979	+	8.89898i	0.0574337	+	0.568535i
$246$	3.10102			0.197714
$247$		−	10.8990i		−	0.693485i
$248$			5.37113i			0.341067i
$249$	12.7279			0.806599
$250$	15.0956	−	4.70334i	0.954733	−	0.297465i
$251$	2.00000			0.126239			0.0631194	−	0.998006i	$-0.479895\pi$
$251$	2.00000			0.126239			0.0631194	+	0.998006i	$0.479895\pi$
$252$		0			0
$253$		0			0
$254$	−21.5505			−1.35220
$255$	−0.460702	−	4.56048i	−0.0288503	−	0.285588i
$256$		0			0
$257$			20.6969i			1.29104i	0.763744	+	0.645520i	$0.223359\pi$
$257$			20.6969i			1.29104i	−0.763744	+	0.645520i	$0.776641\pi$
$258$		−	8.00000i		−	0.498058i
$259$	6.75323			0.419625
$260$		0			0
$261$	5.51399			0.341307
$262$		−	24.8990i		−	1.53826i
$263$		−	4.73545i		−	0.292000i	−0.989285	−	0.146000i	$-0.953360\pi$
$263$		−	4.73545i		−	0.292000i	0.989285	−	0.146000i	$-0.0466400\pi$
$264$		0			0
$265$	−22.2474	+	2.24745i	−1.36665	+	0.138060i
$266$	4.24264			0.260133
$267$		−	13.3485i		−	0.816913i
$268$		0			0
$269$	−5.55051			−0.338421			−0.169210	−	0.985580i	$-0.554122\pi$
$269$	−5.55051			−0.338421			−0.169210	+	0.985580i	$0.554122\pi$
$270$	−0.317837	−	3.14626i	−0.0193430	−	0.191476i
$271$	19.5133			1.18535			0.592673	−	0.805443i	$-0.298073\pi$
$271$	19.5133			1.18535			0.592673	+	0.805443i	$0.298073\pi$
$272$			8.19955i			0.497171i
$273$			10.8990i			0.659636i
$274$	3.11416			0.188133
$275$		0			0
$276$		0			0
$277$		−	11.7744i		−	0.707456i	−0.935348	−	0.353728i	$-0.884914\pi$
$277$		−	11.7744i		−	0.707456i	0.935348	−	0.353728i	$-0.115086\pi$
$278$			1.79796i			0.107834i
$279$	−1.89898			−0.113689
$280$	−1.10102	−	10.8990i	−0.0657986	−	0.651339i
$281$	4.87832			0.291016			0.145508	−	0.989357i	$-0.453518\pi$
$281$	4.87832			0.291016			0.145508	+	0.989357i	$0.453518\pi$
$282$		−	10.3923i		−	0.618853i
$283$		−	28.4592i		−	1.69173i	−0.533400	−	0.845863i	$-0.679086\pi$
$283$		−	28.4592i		−	1.69173i	0.533400	−	0.845863i	$-0.320914\pi$
$284$		0			0
$285$	−3.85337	+	0.389270i	−0.228254	+	0.0230583i
$286$		0			0
$287$			3.79796i			0.224186i
$288$		0			0
$289$	12.7980			0.752821
$290$	17.3485	−	1.75255i	1.01874	−	0.102913i
$291$	−5.00000			−0.293105
$292$		0			0
$293$		−	25.6629i		−	1.49924i	−0.661866	−	0.749622i	$-0.730235\pi$
$293$		−	25.6629i		−	1.49924i	0.661866	−	0.749622i	$-0.269765\pi$
$294$	5.65685			0.329914
$295$	−2.75255	−	27.2474i	−0.160260	−	1.58641i
$296$	11.0280			0.640988
$297$		0			0
$298$		−	12.6969i		−	0.735514i
$299$	12.5851			0.727813
$300$		0			0
$301$	9.79796			0.564745
$302$		−	6.69694i		−	0.385366i
$303$			13.9993i			0.804237i
$304$	6.92820			0.397360
$305$	3.07483	+	30.4377i	0.176064	+	1.74286i
$306$	−2.89898			−0.165724
$307$			29.7306i			1.69681i	0.529344	+	0.848407i	$0.322438\pi$
$307$			29.7306i			1.69681i	−0.529344	+	0.848407i	$0.677562\pi$
$308$		0			0
$309$	8.10102			0.460851
$310$	−5.97469	+	0.603566i	−0.339340	+	0.0342803i
$311$	30.2474			1.71518			0.857588	−	0.514338i	$-0.171962\pi$
$311$	30.2474			1.71518			0.857588	+	0.514338i	$0.171962\pi$
$312$			17.7980i			1.00761i
$313$			6.69694i			0.378533i	0.981926	+	0.189267i	$0.0606111\pi$
$313$			6.69694i			0.378533i	−0.981926	+	0.189267i	$0.939389\pi$
$314$	−29.1270			−1.64373
$315$	3.85337	−	0.389270i	0.217113	−	0.0219329i
$316$		0			0
$317$		−	3.55051i		−	0.199417i	−0.995017	−	0.0997083i	$-0.968209\pi$
$317$		−	3.55051i		−	0.199417i	0.995017	−	0.0997083i	$-0.0317910\pi$
$318$			14.1421i			0.793052i
$319$		0			0
$320$	−1.79796	−	17.7980i	−0.100509	−	0.994936i
$321$	5.51399			0.307761
$322$			4.89898i			0.273009i
$323$			3.55051i			0.197556i
$324$		0			0
$325$	−6.29253	−	30.8270i	−0.349047	−	1.70997i
$326$	1.41421			0.0783260
$327$		−	8.94598i		−	0.494714i
$328$			6.20204i			0.342450i
$329$	12.7279			0.701713
$330$		0			0
$331$	20.5959			1.13205			0.566027	−	0.824387i	$-0.308480\pi$
$331$	20.5959			1.13205			0.566027	+	0.824387i	$0.308480\pi$
$332$		0			0
$333$			3.89898i			0.213663i
$334$	10.6969			0.585310
$335$	30.9217	−	3.12372i	1.68943	−	0.170667i
$336$	−6.92820			−0.377964
$337$			28.4592i			1.55027i	0.631793	+	0.775137i	$0.282319\pi$
$337$			28.4592i			1.55027i	−0.631793	+	0.775137i	$0.717681\pi$
$338$		−	37.6123i		−	2.04584i
$339$	18.4495			1.00204
$340$		0			0
$341$		0			0
$342$			2.44949i			0.132453i
$343$			19.0526i			1.02874i
$344$	16.0000			0.862662
$345$	−0.449490	−	4.44949i	−0.0241997	−	0.239552i
$346$	8.69694			0.467550
$347$			7.56388i			0.406050i	0.979174	+	0.203025i	$0.0650773\pi$
$347$			7.56388i			0.406050i	−0.979174	+	0.203025i	$0.934923\pi$
$348$		0			0
$349$	−5.19615			−0.278144			−0.139072	−	0.990282i	$-0.544412\pi$
$349$	−5.19615			−0.278144			−0.139072	+	0.990282i	$0.544412\pi$
$350$	12.0000	−	2.44949i	0.641427	−	0.130931i
$351$	−6.29253			−0.335870
$352$		0			0
$353$			12.4495i			0.662619i	0.943522	+	0.331310i	$0.107491\pi$
$353$			12.4495i			0.662619i	−0.943522	+	0.331310i	$0.892509\pi$
$354$	−17.3205			−0.920575
$355$	−1.89898	−	18.7980i	−0.100787	−	0.997692i
$356$		0			0
$357$		−	3.55051i		−	0.187913i
$358$			25.5201i			1.34878i
$359$	5.16404			0.272548			0.136274	−	0.990671i	$-0.456487\pi$
$359$	5.16404			0.272548			0.136274	+	0.990671i	$0.456487\pi$
$360$	6.29253	−	0.635674i	0.331645	−	0.0335030i
$361$	−16.0000			−0.842105
$362$			7.07107i			0.371647i
$363$		0			0
$364$		0			0
$365$	−30.4377	+	3.07483i	−1.59318	+	0.160944i
$366$	19.3485			1.01136
$367$		−	16.2020i		−	0.845740i	−0.906190	−	0.422870i	$-0.861023\pi$
$367$		−	16.2020i		−	0.845740i	0.906190	−	0.422870i	$-0.138977\pi$
$368$			8.00000i			0.417029i
$369$	−2.19275			−0.114150
$370$	1.23924	+	12.2672i	0.0644251	+	0.637742i
$371$	−17.3205			−0.899236
$372$		0			0
$373$		−	4.27475i		−	0.221338i	−0.993857	−	0.110669i	$-0.964701\pi$
$373$		−	4.27475i		−	0.221338i	0.993857	−	0.110669i	$-0.0352994\pi$
$374$		0			0
$375$	−10.6742	+	3.32577i	−0.551215	+	0.171742i
$376$	20.7846			1.07188
$377$		−	34.6969i		−	1.78698i
$378$		−	2.44949i		−	0.125988i
$379$	17.7980			0.914220			0.457110	−	0.889410i	$-0.348885\pi$
$379$	17.7980			0.914220			0.457110	+	0.889410i	$0.348885\pi$
$380$		0			0
$381$	15.2385			0.780693
$382$			19.5133i			0.998385i
$383$			26.4949i			1.35383i	0.736063	+	0.676913i	$0.236683\pi$
$383$			26.4949i			1.35383i	−0.736063	+	0.676913i	$0.763317\pi$
$384$	−11.3137			−0.577350
$385$		0			0
$386$	−9.14643			−0.465541
$387$			5.65685i			0.287554i
$388$		0			0
$389$	1.10102			0.0558240			0.0279120	−	0.999610i	$-0.491114\pi$
$389$	1.10102			0.0558240			0.0279120	+	0.999610i	$0.491114\pi$
$390$	−19.7980	+	2.00000i	−1.00251	+	0.101274i
$391$	−4.09978			−0.207335
$392$			11.3137i			0.571429i
$393$			17.6062i			0.888117i
$394$	−4.00000			−0.201517
$395$	2.29629	+	22.7310i	0.115539	+	1.14372i
$396$		0			0
$397$		−	34.3939i		−	1.72618i	−0.505051	−	0.863090i	$-0.668526\pi$
$397$		−	34.3939i		−	1.72618i	0.505051	−	0.863090i	$-0.331474\pi$
$398$			31.9555i			1.60178i
$399$	−3.00000			−0.150188
$400$	19.5959	−	4.00000i	0.979796	−	0.200000i
$401$	25.3485			1.26584			0.632921	−	0.774216i	$-0.281856\pi$
$401$	25.3485			1.26584			0.632921	+	0.774216i	$0.281856\pi$
$402$		−	19.6561i		−	0.980358i
$403$			11.9494i			0.595241i
$404$		0			0
$405$	0.224745	+	2.22474i	0.0111677	+	0.110548i
$406$	13.5065			0.670314
$407$		0			0
$408$		−	5.79796i		−	0.287042i
$409$	−23.1523			−1.14481			−0.572405	−	0.819971i	$-0.693989\pi$
$409$	−23.1523			−1.14481			−0.572405	+	0.819971i	$0.693989\pi$
$410$	−6.89898	+	0.696938i	−0.340716	+	0.0344193i
$411$	−2.20204			−0.108619
$412$		0			0
$413$		−	21.2132i		−	1.04383i
$414$	−2.82843			−0.139010
$415$	−28.3164	+	2.86054i	−1.39000	+	0.140418i
$416$		0			0
$417$		−	1.27135i		−	0.0622582i
$418$		0			0
$419$	−14.4495			−0.705904			−0.352952	−	0.935641i	$-0.614822\pi$
$419$	−14.4495			−0.705904			−0.352952	+	0.935641i	$0.614822\pi$
$420$		0			0
$421$	5.30306			0.258455			0.129228	−	0.991615i	$-0.458750\pi$
$421$	5.30306			0.258455			0.129228	+	0.991615i	$0.458750\pi$
$422$		−	22.4495i		−	1.09282i
$423$			7.34847i			0.357295i
$424$	−28.2843			−1.37361
$425$	2.04989	+	10.0424i	0.0994342	+	0.487126i
$426$	−11.9494			−0.578949
$427$			23.6969i			1.14678i
$428$		0			0
$429$		0			0
$430$	1.79796	+	17.7980i	0.0867053	+	0.858294i
$431$	−11.6637			−0.561818			−0.280909	−	0.959734i	$-0.590636\pi$
$431$	−11.6637			−0.561818			−0.280909	+	0.959734i	$0.590636\pi$
$432$		−	4.00000i		−	0.192450i
$433$			19.0000i			0.913082i	0.889702	+	0.456541i	$0.150912\pi$
$433$			19.0000i			0.913082i	−0.889702	+	0.456541i	$0.849088\pi$
$434$	−4.65153			−0.223281
$435$	−12.2672	+	1.23924i	−0.588168	+	0.0594171i
$436$		0			0
$437$			3.46410i			0.165710i
$438$			19.3485i			0.924506i
$439$	9.93160			0.474010			0.237005	−	0.971508i	$-0.423834\pi$
$439$	9.93160			0.474010			0.237005	+	0.971508i	$0.423834\pi$
$440$		0			0
$441$	−4.00000			−0.190476
$442$			18.2419i			0.867679i
$443$		−	13.3485i		−	0.634205i	−0.948391	−	0.317102i	$-0.897290\pi$
$443$		−	13.3485i		−	0.634205i	0.948391	−	0.317102i	$-0.102710\pi$
$444$		0			0
$445$	3.00000	+	29.6969i	0.142214	+	1.40777i
$446$	−15.5563			−0.736614
$447$			8.97809i			0.424649i
$448$		−	13.8564i		−	0.654654i
$449$	−36.4495			−1.72016			−0.860079	−	0.510161i	$-0.829586\pi$
$449$	−36.4495			−1.72016			−0.860079	+	0.510161i	$0.829586\pi$
$450$	1.41421	+	6.92820i	0.0666667	+	0.326599i
$451$		0			0
$452$		0			0
$453$			4.73545i			0.222491i
$454$	13.7980			0.647570
$455$	−2.44949	−	24.2474i	−0.114834	−	1.13674i
$456$	−4.89898			−0.229416
$457$			10.0424i			0.469762i	0.972024	+	0.234881i	$0.0754700\pi$
$457$			10.0424i			0.469762i	−0.972024	+	0.234881i	$0.924530\pi$
$458$			18.2419i			0.852389i
$459$	2.04989			0.0956806
$460$		0			0
$461$	27.3629			1.27442			0.637208	−	0.770692i	$-0.280089\pi$
$461$	27.3629			1.27442			0.637208	+	0.770692i	$0.280089\pi$
$462$		0			0
$463$		−	7.30306i		−	0.339402i	−0.985496	−	0.169701i	$-0.945720\pi$
$463$		−	7.30306i		−	0.339402i	0.985496	−	0.169701i	$-0.0542802\pi$
$464$	22.0560			1.02392
$465$	4.22474	−	0.426786i	0.195918	−	0.0197917i
$466$	−5.59592			−0.259226
$467$			14.2474i			0.659293i	0.944104	+	0.329647i	$0.106930\pi$
$467$			14.2474i			0.659293i	−0.944104	+	0.329647i	$0.893070\pi$
$468$		0			0
$469$	24.0737			1.11162
$470$	2.33562	+	23.1202i	0.107734	+	1.06646i
$471$	20.5959			0.949010
$472$		−	34.6410i		−	1.59448i
$473$		0			0
$474$	14.4495			0.663687
$475$	8.48528	−	1.73205i	0.389331	−	0.0794719i
$476$		0			0
$477$		−	10.0000i		−	0.457869i
$478$		−	14.0000i		−	0.640345i
$479$	5.51399			0.251941			0.125970	−	0.992034i	$-0.459796\pi$
$479$	5.51399			0.251941			0.125970	+	0.992034i	$0.459796\pi$
$480$		0			0
$481$	24.5344			1.11867
$482$			8.89898i			0.405337i
$483$		−	3.46410i		−	0.157622i
$484$		0			0
$485$	11.1237	−	1.12372i	0.505102	−	0.0510257i
$486$	1.41421			0.0641500
$487$			10.4949i			0.475569i	0.971318	+	0.237785i	$0.0764212\pi$
$487$			10.4949i			0.475569i	−0.971318	+	0.237785i	$0.923579\pi$
$488$			38.6969i			1.75173i
$489$	−1.00000			−0.0452216
$490$	−12.5851	+	1.27135i	−0.568535	+	0.0574337i
$491$	9.40669			0.424518			0.212259	−	0.977213i	$-0.431918\pi$
$491$	9.40669			0.424518			0.212259	+	0.977213i	$0.431918\pi$
$492$		0			0
$493$			11.3031i			0.509064i
$494$	15.4135			0.693485
$495$		0			0
$496$	−7.59592			−0.341067
$497$		−	14.6349i		−	0.656467i
$498$			18.0000i			0.806599i
$499$	39.6969			1.77708			0.888540	−	0.458800i	$-0.151721\pi$
$499$	39.6969			1.77708			0.888540	+	0.458800i	$0.151721\pi$
$500$		0			0
$501$	−7.56388			−0.337929
$502$			2.82843i			0.126239i
$503$			1.55708i			0.0694267i	0.999397	+	0.0347133i	$0.0110518\pi$
$503$			1.55708i			0.0694267i	−0.999397	+	0.0347133i	$0.988948\pi$
$504$	4.89898			0.218218
$505$	−3.14626	−	31.1448i	−0.140007	−	1.38593i
$506$		0			0
$507$			26.5959i			1.18117i
$508$		0			0
$509$	−21.1464			−0.937299			−0.468649	−	0.883384i	$-0.655259\pi$
$509$	−21.1464			−0.937299			−0.468649	+	0.883384i	$0.655259\pi$
$510$	6.44949	−	0.651531i	0.285588	−	0.0288503i
$511$	−23.6969			−1.04829
$512$		−	22.6274i		−	1.00000i
$513$		−	1.73205i		−	0.0764719i
$514$	−29.2699			−1.29104
$515$	−18.0227	+	1.82066i	−0.794175	+	0.0802280i
$516$		0			0
$517$		0			0
$518$			9.55051i			0.419625i
$519$	−6.14966			−0.269940
$520$	−4.00000	−	39.5959i	−0.175412	−	1.73640i
$521$	25.1464			1.10169			0.550843	−	0.834609i	$-0.314306\pi$
$521$	25.1464			1.10169			0.550843	+	0.834609i	$0.314306\pi$
$522$			7.79796i			0.341307i
$523$		−	23.4381i		−	1.02487i	−0.858725	−	0.512437i	$-0.828743\pi$
$523$		−	23.4381i		−	1.02487i	0.858725	−	0.512437i	$-0.171257\pi$
$524$		0			0
$525$	−8.48528	+	1.73205i	−0.370328	+	0.0755929i
$526$	6.69694			0.292000
$527$		−	3.89270i		−	0.169568i
$528$		0			0
$529$	19.0000			0.826087
$530$	−3.17837	−	31.4626i	−0.138060	−	1.36665i
$531$	12.2474			0.531494
$532$		0			0
$533$			13.7980i			0.597656i
$534$	18.8776			0.816913
$535$	−12.2672	+	1.23924i	−0.530358	+	0.0535771i
$536$	39.3123			1.69803
$537$		−	18.0454i		−	0.778717i
$538$		−	7.84961i		−	0.338421i
$539$		0			0
$540$		0			0
$541$	−14.4921			−0.623063			−0.311532	−	0.950236i	$-0.600842\pi$
$541$	−14.4921			−0.623063			−0.311532	+	0.950236i	$0.600842\pi$
$542$			27.5959i			1.18535i
$543$		−	5.00000i		−	0.214571i
$544$		0			0
$545$	2.01056	+	19.9025i	0.0861231	+	0.852531i
$546$	−15.4135			−0.659636
$547$			15.6992i			0.671250i	0.941996	+	0.335625i	$0.108947\pi$
$547$			15.6992i			0.671250i	−0.941996	+	0.335625i	$0.891053\pi$
$548$		0			0
$549$	−13.6814			−0.583909
$550$		0			0
$551$	9.55051			0.406865
$552$		−	5.65685i		−	0.240772i
$553$			17.6969i			0.752550i
$554$	16.6515			0.707456
$555$	−0.876276	−	8.67423i	−0.0371958	−	0.368201i
$556$		0			0
$557$			0.778539i			0.0329878i	0.999864	+	0.0164939i	$0.00525040\pi$
$557$			0.778539i			0.0329878i	−0.999864	+	0.0164939i	$0.994750\pi$
$558$		−	2.68556i		−	0.113689i
$559$	35.5959			1.50555
$560$	15.4135	−	1.55708i	0.651339	−	0.0657986i
$561$		0			0
$562$			6.89898i			0.291016i
$563$			25.1701i			1.06079i	0.847749	+	0.530397i	$0.177957\pi$
$563$			25.1701i			1.06079i	−0.847749	+	0.530397i	$0.822043\pi$
$564$		0			0
$565$	−41.0454	+	4.14643i	−1.72679	+	0.174442i
$566$	40.2474			1.69173
$567$			1.73205i			0.0727393i
$568$		−	23.8988i		−	1.00277i
$569$	23.6130			0.989910			0.494955	−	0.868919i	$-0.335185\pi$
$569$	23.6130			0.989910			0.494955	+	0.868919i	$0.335185\pi$
$570$	−0.550510	−	5.44949i	−0.0230583	−	0.228254i
$571$	−43.5870			−1.82406			−0.912030	−	0.410124i	$-0.865485\pi$
$571$	−43.5870			−1.82406			−0.912030	+	0.410124i	$0.865485\pi$
$572$		0			0
$573$		−	13.7980i		−	0.576418i
$574$	−5.37113			−0.224186
$575$	2.00000	+	9.79796i	0.0834058	+	0.408603i
$576$	8.00000			0.333333
$577$			25.4949i			1.06137i	0.847570	+	0.530683i	$0.178065\pi$
$577$			25.4949i			1.06137i	−0.847570	+	0.530683i	$0.821935\pi$
$578$			18.0990i			0.752821i
$579$	6.46750			0.268780
$580$		0			0
$581$	−22.0454			−0.914598
$582$		−	7.07107i		−	0.293105i
$583$		0			0
$584$	−38.6969			−1.60129
$585$	13.9993	−	1.41421i	0.578799	−	0.0584705i
$586$	36.2929			1.49924
$587$		−	18.6969i		−	0.771705i	−0.922560	−	0.385853i	$-0.873907\pi$
$587$		−	18.6969i		−	0.771705i	0.922560	−	0.385853i	$-0.126093\pi$
$588$		0			0
$589$	−3.28913			−0.135526
$590$	38.5337	−	3.89270i	1.58641	−	0.160260i
$591$	2.82843			0.116346
$592$			15.5959i			0.640988i
$593$		−	17.6062i		−	0.723002i	−0.932372	−	0.361501i	$-0.882264\pi$
$593$		−	17.6062i		−	0.723002i	0.932372	−	0.361501i	$-0.117736\pi$
$594$		0			0
$595$	0.797959	+	7.89898i	0.0327131	+	0.323827i
$596$		0			0
$597$		−	22.5959i		−	0.924789i
$598$			17.7980i			0.727813i
$599$	−14.6515			−0.598645			−0.299323	−	0.954152i	$-0.596761\pi$
$599$	−14.6515			−0.598645			−0.299323	+	0.954152i	$0.596761\pi$
$600$	−13.8564	+	2.82843i	−0.565685	+	0.115470i
$601$	1.09638			0.0447221			0.0223611	−	0.999750i	$-0.492882\pi$
$601$	1.09638			0.0447221			0.0223611	+	0.999750i	$0.492882\pi$
$602$			13.8564i			0.564745i
$603$			13.8990i			0.566010i
$604$		0			0
$605$		0			0
$606$	−19.7980			−0.804237
$607$		−	24.8844i		−	1.01003i	−0.863112	−	0.505013i	$-0.831488\pi$
$607$		−	24.8844i		−	1.01003i	0.863112	−	0.505013i	$-0.168512\pi$
$608$		0			0
$609$	−9.55051			−0.387006
$610$	−43.0454	+	4.34847i	−1.74286	+	0.176064i
$611$	46.2405			1.87069
$612$		0			0
$613$		−	17.1455i		−	0.692502i	−0.938142	−	0.346251i	$-0.887455\pi$
$613$		−	17.1455i		−	0.692502i	0.938142	−	0.346251i	$-0.112545\pi$
$614$	−42.0454			−1.69681
$615$	4.87832	−	0.492810i	0.196713	−	0.0198720i
$616$		0			0
$617$			4.04541i			0.162862i	0.996679	+	0.0814310i	$0.0259490\pi$
$617$			4.04541i			0.162862i	−0.996679	+	0.0814310i	$0.974051\pi$
$618$			11.4566i			0.460851i
$619$	−0.696938			−0.0280123			−0.0140062	−	0.999902i	$-0.504458\pi$
$619$	−0.696938			−0.0280123			−0.0140062	+	0.999902i	$0.504458\pi$
$620$		0			0
$621$	2.00000			0.0802572
$622$			42.7764i			1.71518i
$623$			23.1202i			0.926292i
$624$	−25.1701			−1.00761
$625$	23.0000	−	9.79796i	0.920000	−	0.391918i
$626$	−9.47090			−0.378533
$627$		0			0
$628$		0			0
$629$	−7.99247			−0.318681
$630$	0.550510	+	5.44949i	0.0219329	+	0.217113i
$631$	−9.10102			−0.362306			−0.181153	−	0.983455i	$-0.557983\pi$
$631$	−9.10102			−0.362306			−0.181153	+	0.983455i	$0.557983\pi$
$632$			28.8990i			1.14954i
$633$			15.8742i			0.630942i
$634$	5.02118			0.199417
$635$	−33.9018	+	3.42478i	−1.34535	+	0.135908i
$636$		0			0
$637$			25.1701i			0.997276i
$638$		0			0
$639$	8.44949			0.334257
$640$	25.1701	−	2.54270i	0.994936	−	0.100509i
$641$	3.55051			0.140237			0.0701184	−	0.997539i	$-0.477662\pi$
$641$	3.55051			0.140237			0.0701184	+	0.997539i	$0.477662\pi$
$642$			7.79796i			0.307761i
$643$			0.303062i			0.0119516i	0.999982	+	0.00597579i	$0.00190216\pi$
$643$			0.303062i			0.0119516i	−0.999982	+	0.00597579i	$0.998098\pi$
$644$		0			0
$645$	−1.27135	−	12.5851i	−0.0500593	−	0.495536i
$646$	−5.02118			−0.197556
$647$		−	41.7980i		−	1.64325i	−0.570030	−	0.821624i	$-0.693069\pi$
$647$		−	41.7980i		−	1.64325i	0.570030	−	0.821624i	$-0.306931\pi$
$648$			2.82843i			0.111111i
$649$		0			0
$650$	43.5959	−	8.89898i	1.70997	−	0.349047i
$651$	3.28913			0.128911
$652$		0			0
$653$			7.30306i			0.285791i	0.989738	+	0.142895i	$0.0456413\pi$
$653$			7.30306i			0.285791i	−0.989738	+	0.142895i	$0.954359\pi$
$654$	12.6515			0.494714
$655$	−3.95691	−	39.1694i	−0.154609	−	1.53047i
$656$	−8.77101			−0.342450
$657$		−	13.6814i		−	0.533764i
$658$			18.0000i			0.701713i
$659$	25.5201			0.994120			0.497060	−	0.867716i	$-0.334413\pi$
$659$	25.5201			0.994120			0.497060	+	0.867716i	$0.334413\pi$
$660$		0			0
$661$	−34.7980			−1.35348			−0.676742	−	0.736220i	$-0.736609\pi$
$661$	−34.7980			−1.35348			−0.676742	+	0.736220i	$0.736609\pi$
$662$			29.1270i			1.13205i
$663$		−	12.8990i		−	0.500955i
$664$	−36.0000			−1.39707
$665$	6.67423	−	0.674235i	0.258816	−	0.0261457i
$666$	−5.51399			−0.213663
$667$			11.0280i			0.427005i
$668$		0			0
$669$	11.0000			0.425285
$670$	4.41761	+	43.7299i	0.170667	+	1.68943i
$671$		0			0
$672$		0			0
$673$		−	0.110756i		−	0.00426935i	−0.999998	−	0.00213467i	$-0.999321\pi$
$673$		−	0.110756i		−	0.00426935i	0.999998	−	0.00213467i	$-0.000679489\pi$
$674$	−40.2474			−1.55027
$675$	−1.00000	−	4.89898i	−0.0384900	−	0.188562i
$676$		0			0
$677$		−	15.6992i		−	0.603370i	−0.953408	−	0.301685i	$-0.902451\pi$
$677$		−	15.6992i		−	0.603370i	0.953408	−	0.301685i	$-0.0975491\pi$
$678$			26.0915i			1.00204i
$679$	8.66025			0.332350
$680$	1.30306	+	12.8990i	0.0499701	+	0.494653i
$681$	−9.75663			−0.373875
$682$		0			0
$683$			6.00000i			0.229584i	0.993390	+	0.114792i	$0.0366201\pi$
$683$			6.00000i			0.229584i	−0.993390	+	0.114792i	$0.963380\pi$
$684$		0			0
$685$	4.89898	−	0.494897i	0.187180	−	0.0189091i
$686$	−26.9444			−1.02874
$687$		−	12.8990i		−	0.492127i
$688$			22.6274i			0.862662i
$689$	−62.9253			−2.39726
$690$	6.29253	−	0.635674i	0.239552	−	0.0241997i
$691$	37.8990			1.44175			0.720873	−	0.693068i	$-0.243741\pi$
$691$	37.8990			1.44175			0.720873	+	0.693068i	$0.243741\pi$
$692$		0			0
$693$		0			0
$694$	−10.6969			−0.406050
$695$	0.285729	+	2.82843i	0.0108383	+	0.107288i
$696$	−15.5959			−0.591162
$697$		−	4.49490i		−	0.170256i
$698$		−	7.34847i		−	0.278144i
$699$	3.95691			0.149664
$700$		0			0
$701$	16.0492			0.606168			0.303084	−	0.952964i	$-0.401984\pi$
$701$	16.0492			0.606168			0.303084	+	0.952964i	$0.401984\pi$
$702$		−	8.89898i		−	0.335870i
$703$			6.75323i			0.254703i
$704$		0			0
$705$	−1.65153	−	16.3485i	−0.0622002	−	0.615719i
$706$	−17.6062			−0.662619
$707$		−	24.2474i		−	0.911919i
$708$		0			0
$709$	24.0000			0.901339			0.450669	−	0.892691i	$-0.351185\pi$
$709$	24.0000			0.901339			0.450669	+	0.892691i	$0.351185\pi$
$710$	26.5843	−	2.68556i	0.997692	−	0.100787i
$711$	−10.2173			−0.383180
$712$			37.7552i			1.41493i
$713$		−	3.79796i		−	0.142235i
$714$	5.02118			0.187913
$715$		0			0
$716$		0			0
$717$			9.89949i			0.369703i
$718$			7.30306i			0.272548i
$719$	46.5403			1.73566			0.867830	−	0.496861i	$-0.165514\pi$
$719$	46.5403			1.73566			0.867830	+	0.496861i	$0.165514\pi$
$720$	0.898979	+	8.89898i	0.0335030	+	0.331645i
$721$	−14.0314			−0.522556
$722$		−	22.6274i		−	0.842105i
$723$		−	6.29253i		−	0.234022i
$724$		0			0
$725$	27.0129	−	5.51399i	1.00323	−	0.204784i
$726$		0			0
$727$		−	15.3939i		−	0.570927i	−0.958390	−	0.285464i	$-0.907852\pi$
$727$		−	15.3939i		−	0.570927i	0.958390	−	0.285464i	$-0.0921476\pi$
$728$		−	30.8270i		−	1.14252i
$729$	−1.00000			−0.0370370
$730$	−4.34847	−	43.0454i	−0.160944	−	1.59318i
$731$	−11.5959			−0.428891
$732$		0			0
$733$		−	16.0492i		−	0.592789i	−0.955066	−	0.296395i	$-0.904216\pi$
$733$		−	16.0492i		−	0.592789i	0.955066	−	0.296395i	$-0.0957844\pi$
$734$	22.9131			0.845740
$735$	8.89898	−	0.898979i	0.328244	−	0.0331594i
$736$		0			0
$737$		0			0
$738$		−	3.10102i		−	0.114150i
$739$	−14.6028			−0.537174			−0.268587	−	0.963255i	$-0.586557\pi$
$739$	−14.6028			−0.537174			−0.268587	+	0.963255i	$0.586557\pi$
$740$		0			0
$741$	−10.8990			−0.400384
$742$		−	24.4949i		−	0.899236i
$743$			37.7552i			1.38510i	0.721368	+	0.692551i	$0.243513\pi$
$743$			37.7552i			1.38510i	−0.721368	+	0.692551i	$0.756487\pi$
$744$	5.37113			0.196915
$745$	−2.01778	−	19.9740i	−0.0739257	−	0.731789i
$746$	6.04541			0.221338
$747$		−	12.7279i		−	0.465690i
$748$		0			0
$749$	−9.55051			−0.348968
$750$	−4.70334	−	15.0956i	−0.171742	−	0.551215i
$751$	−13.8990			−0.507181			−0.253590	−	0.967312i	$-0.581612\pi$
$751$	−13.8990			−0.507181			−0.253590	+	0.967312i	$0.581612\pi$
$752$			29.3939i			1.07188i
$753$		−	2.00000i		−	0.0728841i
$754$	49.0689			1.78698
$755$	−1.06427	−	10.5352i	−0.0387327	−	0.383414i
$756$		0			0
$757$		−	4.10102i		−	0.149054i	−0.997219	−	0.0745271i	$-0.976255\pi$
$757$		−	4.10102i		−	0.149054i	0.997219	−	0.0745271i	$-0.0237447\pi$
$758$			25.1701i			0.914220i
$759$		0			0
$760$	10.8990	−	1.10102i	0.395348	−	0.0399382i
$761$	0.207081			0.00750667			0.00375334	−	0.999993i	$-0.498805\pi$
$761$	0.207081			0.00750667			0.00375334	+	0.999993i	$0.498805\pi$
$762$			21.5505i			0.780693i
$763$			15.4949i			0.560953i
$764$		0			0
$765$	−4.56048	+	0.460702i	−0.164884	+	0.0166567i
$766$	−37.4694			−1.35383
$767$		−	77.0674i		−	2.78274i
$768$		0			0
$769$	−46.3512			−1.67147			−0.835734	−	0.549135i	$-0.814957\pi$
$769$	−46.3512			−1.67147			−0.835734	+	0.549135i	$0.814957\pi$
$770$		0			0
$771$	20.6969			0.745382
$772$		0			0
$773$		−	7.59592i		−	0.273206i	−0.990626	−	0.136603i	$-0.956382\pi$
$773$		−	7.59592i		−	0.273206i	0.990626	−	0.136603i	$-0.0436185\pi$
$774$	−8.00000			−0.287554
$775$	−9.30306	+	1.89898i	−0.334176	+	0.0682134i
$776$	14.1421			0.507673
$777$		−	6.75323i		−	0.242271i
$778$			1.55708i			0.0558240i
$779$	−3.79796			−0.136076
$780$		0			0
$781$		0			0
$782$		−	5.79796i		−	0.207335i
$783$		−	5.51399i		−	0.197054i
$784$	−16.0000			−0.571429
$785$	−45.8207	+	4.62883i	−1.63541	+	0.165210i
$786$	−24.8990			−0.888117
$787$		−	33.0839i		−	1.17932i	−0.807653	−	0.589658i	$-0.799263\pi$
$787$		−	33.0839i		−	1.17932i	0.807653	−	0.589658i	$-0.200737\pi$
$788$		0			0
$789$	−4.73545			−0.168587
$790$	−32.1464	+	3.24745i	−1.14372	+	0.115539i
$791$	−31.9555			−1.13621
$792$		0			0
$793$			86.0908i			3.05717i
$794$	48.6403			1.72618
$795$	2.24745	+	22.2474i	0.0797088	+	0.789036i
$796$		0			0
$797$		−	35.3939i		−	1.25372i	−0.779134	−	0.626858i	$-0.784341\pi$
$797$		−	35.3939i		−	1.25372i	0.779134	−	0.626858i	$-0.215659\pi$
$798$		−	4.24264i		−	0.150188i
$799$	−15.0635			−0.532910
$800$		0			0
$801$	−13.3485			−0.471645
$802$			35.8481i			1.26584i
$803$		0			0
$804$		0			0
$805$	0.778539	+	7.70674i	0.0274399	+	0.271627i
$806$	−16.8990			−0.595241
$807$			5.55051i			0.195387i
$808$		−	39.5959i		−	1.39298i
$809$	−26.9343			−0.946959			−0.473479	−	0.880805i	$-0.657002\pi$
$809$	−26.9343			−0.946959			−0.473479	+	0.880805i	$0.657002\pi$
$810$	−3.14626	+	0.317837i	−0.110548	+	0.0111677i
$811$	29.4449			1.03395			0.516975	−	0.856001i	$-0.327058\pi$
$811$	29.4449			1.03395			0.516975	+	0.856001i	$0.327058\pi$
$812$		0			0
$813$		−	19.5133i		−	0.684360i
$814$		0			0
$815$	2.22474	−	0.224745i	0.0779294	−	0.00787247i
$816$	8.19955			0.287042
$817$			9.79796i			0.342787i
$818$		−	32.7423i		−	1.14481i
$819$	10.8990			0.380841
$820$		0			0
$821$	28.6342			0.999341			0.499671	−	0.866216i	$-0.333454\pi$
$821$	28.6342			0.999341			0.499671	+	0.866216i	$0.333454\pi$
$822$		−	3.11416i		−	0.108619i
$823$		−	47.4949i		−	1.65557i	−0.561047	−	0.827784i	$-0.689601\pi$
$823$		−	47.4949i		−	1.65557i	0.561047	−	0.827784i	$-0.310399\pi$
$824$	−22.9131			−0.798217
$825$		0			0
$826$	30.0000			1.04383
$827$		−	41.7121i		−	1.45047i	−0.688501	−	0.725236i	$-0.741731\pi$
$827$		−	41.7121i		−	1.45047i	0.688501	−	0.725236i	$-0.258269\pi$
$828$		0			0
$829$	−8.79796			−0.305566			−0.152783	−	0.988260i	$-0.548824\pi$
$829$	−8.79796			−0.305566			−0.152783	+	0.988260i	$0.548824\pi$
$830$	−4.04541	−	40.0454i	−0.140418	−	1.39000i
$831$	−11.7744			−0.408450
$832$		−	50.3402i		−	1.74523i
$833$		−	8.19955i		−	0.284098i
$834$	1.79796			0.0622582
$835$	16.8277	−	1.69994i	0.582347	−	0.0588289i
$836$		0			0
$837$			1.89898i			0.0656383i
$838$		−	20.4347i		−	0.705904i
$839$	−8.89898			−0.307227			−0.153613	−	0.988131i	$-0.549091\pi$
$839$	−8.89898			−0.307227			−0.153613	+	0.988131i	$0.549091\pi$
$840$	−10.8990	+	1.10102i	−0.376051	+	0.0379888i
$841$	1.40408			0.0484166
$842$			7.49966i			0.258455i
$843$		−	4.87832i		−	0.168018i
$844$		0			0
$845$	−5.97730	−	59.1691i	−0.205625	−	2.03548i
$846$	−10.3923			−0.357295
$847$		0			0
$848$		−	40.0000i		−	1.37361i
$849$	−28.4592			−0.976719
$850$	−14.2020	+	2.89898i	−0.487126	+	0.0994342i
$851$	−7.79796			−0.267311
$852$		0			0
$853$		−	4.56048i		−	0.156148i	−0.996948	−	0.0780739i	$-0.975123\pi$
$853$		−	4.56048i		−	0.156148i	0.996948	−	0.0780739i	$-0.0248770\pi$
$854$	−33.5125			−1.14678
$855$	0.389270	+	3.85337i	0.0133127	+	0.131783i
$856$	−15.5959			−0.533058
$857$		−	3.89270i		−	0.132972i	−0.997787	−	0.0664860i	$-0.978821\pi$
$857$		−	3.89270i		−	0.132972i	0.997787	−	0.0664860i	$-0.0211788\pi$
$858$		0			0
$859$	−33.2929			−1.13594			−0.567969	−	0.823050i	$-0.692271\pi$
$859$	−33.2929			−1.13594			−0.567969	+	0.823050i	$0.692271\pi$
$860$		0			0
$861$	3.79796			0.129434
$862$		−	16.4949i		−	0.561818i
$863$		−	47.8434i		−	1.62861i	−0.580439	−	0.814304i	$-0.697119\pi$
$863$		−	47.8434i		−	1.62861i	0.580439	−	0.814304i	$-0.302881\pi$
$864$		0			0
$865$	13.6814	−	1.38211i	0.465183	−	0.0469930i
$866$	−26.8701			−0.913082
$867$		−	12.7980i		−	0.434641i
$868$		0			0
$869$		0			0
$870$	−1.75255	−	17.3485i	−0.0594171	−	0.588168i
$871$	87.4597			2.96346
$872$			25.3031i			0.856870i
$873$			5.00000i			0.169224i
$874$	−4.89898			−0.165710
$875$	18.4883	−	5.76039i	0.625019	−	0.194737i
$876$		0			0
$877$			13.9672i			0.471638i	0.971797	+	0.235819i	$0.0757772\pi$
$877$			13.9672i			0.471638i	−0.971797	+	0.235819i	$0.924223\pi$
$878$			14.0454i			0.474010i
$879$	−25.6629			−0.865589
$880$		0			0
$881$	37.6413			1.26817			0.634084	−	0.773264i	$-0.281377\pi$
$881$	37.6413			1.26817			0.634084	+	0.773264i	$0.281377\pi$
$882$		−	5.65685i		−	0.190476i
$883$			15.8990i			0.535043i	0.963552	+	0.267522i	$0.0862047\pi$
$883$			15.8990i			0.535043i	−0.963552	+	0.267522i	$0.913795\pi$
$884$		0			0
$885$	−27.2474	+	2.75255i	−0.915913	+	0.0925260i
$886$	18.8776			0.634205
$887$		−	7.56388i		−	0.253970i	−0.991905	−	0.126985i	$-0.959470\pi$
$887$		−	7.56388i		−	0.253970i	0.991905	−	0.126985i	$-0.0405300\pi$
$888$		−	11.0280i		−	0.370075i
$889$	−26.3939			−0.885222
$890$	−41.9978	+	4.24264i	−1.40777	+	0.142214i
$891$		0			0
$892$		0			0
$893$			12.7279i			0.425924i
$894$	−12.6969			−0.424649
$895$	4.05561	+	40.1464i	0.135564	+	1.34195i
$896$	19.5959			0.654654
$897$		−	12.5851i		−	0.420203i
$898$		−	51.5474i		−	1.72016i
$899$	−10.4710			−0.349226
$900$		0			0
$901$	20.4989			0.682917
$902$		0			0
$903$		−	9.79796i		−	0.326056i
$904$	−52.1830			−1.73558
$905$	1.12372	+	11.1237i	0.0373539	+	0.369765i
$906$	−6.69694			−0.222491
$907$		−	41.6969i		−	1.38452i	−0.721646	−	0.692262i	$-0.756614\pi$
$907$		−	41.6969i		−	1.38452i	0.721646	−	0.692262i	$-0.243386\pi$
$908$		0			0
$909$	13.9993			0.464327
$910$	34.2911	−	3.46410i	1.13674	−	0.114834i
$911$	6.20204			0.205483			0.102741	−	0.994708i	$-0.467239\pi$
$911$	6.20204			0.205483			0.102741	+	0.994708i	$0.467239\pi$
$912$		−	6.92820i		−	0.229416i
$913$		0			0
$914$	−14.2020			−0.469762
$915$	30.4377	−	3.07483i	1.00624	−	0.101651i
$916$		0			0
$917$		−	30.4949i		−	1.00703i
$918$			2.89898i			0.0956806i
$919$	58.3648			1.92528			0.962639	−	0.270789i	$-0.0872846\pi$
$919$	58.3648			1.92528			0.962639	+	0.270789i	$0.0872846\pi$
$920$	1.27135	+	12.5851i	0.0419151	+	0.414917i
$921$	29.7306			0.979656
$922$			38.6969i			1.27442i
$923$		−	53.1687i		−	1.75007i
$924$		0			0
$925$	3.89898	+	19.1010i	0.128198	+	0.628038i
$926$	10.3281			0.339402
$927$		−	8.10102i		−	0.266072i
$928$		0			0
$929$	−29.1010			−0.954774			−0.477387	−	0.878693i	$-0.658416\pi$
$929$	−29.1010			−0.954774			−0.477387	+	0.878693i	$0.658416\pi$
$930$	0.603566	+	5.97469i	0.0197917	+	0.195918i
$931$	−6.92820			−0.227063
$932$		0			0
$933$		−	30.2474i		−	0.990257i
$934$	−20.1489			−0.659293
$935$		0			0
$936$	17.7980			0.581744
$937$		−	31.9233i		−	1.04289i	−0.853285	−	0.521445i	$-0.825393\pi$
$937$		−	31.9233i		−	1.04289i	0.853285	−	0.521445i	$-0.174607\pi$
$938$			34.0454i			1.11162i
$939$	6.69694			0.218546
$940$		0			0
$941$	26.7914			0.873375			0.436687	−	0.899613i	$-0.356152\pi$
$941$	26.7914			0.873375			0.436687	+	0.899613i	$0.356152\pi$
$942$			29.1270i			0.949010i
$943$		−	4.38551i		−	0.142812i
$944$	48.9898			1.59448
$945$	−0.389270	−	3.85337i	−0.0126629	−	0.125350i
$946$		0			0
$947$			10.4495i			0.339563i	0.985482	+	0.169781i	$0.0543062\pi$
$947$			10.4495i			0.339563i	−0.985482	+	0.169781i	$0.945694\pi$
$948$		0			0
$949$	−86.0908			−2.79463
$950$	2.44949	+	12.0000i	0.0794719	+	0.389331i
$951$	−3.55051			−0.115133
$952$			10.0424i			0.325475i
$953$		−	25.8058i		−	0.835932i	−0.908463	−	0.417966i	$-0.862743\pi$
$953$		−	25.8058i		−	0.835932i	0.908463	−	0.417966i	$-0.137257\pi$
$954$	14.1421			0.457869
$955$	3.10102	+	30.6969i	0.100347	+	0.993330i
$956$		0			0
$957$		0			0
$958$			7.79796i			0.251941i
$959$	3.81405			0.123162
$960$	−17.7980	+	1.79796i	−0.574427	+	0.0580289i
$961$	−27.3939			−0.883673
$962$			34.6969i			1.11867i
$963$		−	5.51399i		−	0.177686i
$964$		0			0
$965$	−14.3885	+	1.45354i	−0.463184	+	0.0467910i
$966$	4.89898			0.157622
$967$			16.5099i			0.530921i	0.964122	+	0.265461i	$0.0855240\pi$
$967$			16.5099i			0.530921i	−0.964122	+	0.265461i	$0.914476\pi$
$968$		0			0
$969$	3.55051			0.114059
$970$	1.58919	+	15.7313i	0.0510257	+	0.505102i
$971$	−22.8990			−0.734863			−0.367432	−	0.930051i	$-0.619763\pi$
$971$	−22.8990			−0.734863			−0.367432	+	0.930051i	$0.619763\pi$
$972$		0			0
$973$			2.20204i			0.0705942i
$974$	−14.8420			−0.475569
$975$	−30.8270	+	6.29253i	−0.987253	+	0.201522i
$976$	−54.7257			−1.75173
$977$			5.50510i			0.176124i	0.996115	+	0.0880619i	$0.0280673\pi$
$977$			5.50510i			0.176124i	−0.996115	+	0.0880619i	$0.971933\pi$
$978$		−	1.41421i		−	0.0452216i
$979$		0			0
$980$		0			0
$981$	−8.94598			−0.285623
$982$			13.3031i			0.424518i
$983$			16.2929i			0.519661i	0.965654	+	0.259831i	$0.0836668\pi$
$983$			16.2929i			0.519661i	−0.965654	+	0.259831i	$0.916333\pi$
$984$	6.20204			0.197714
$985$	−6.29253	+	0.635674i	−0.200497	+	0.0202543i
$986$	−15.9849			−0.509064
$987$		−	12.7279i		−	0.405134i
$988$		0			0
$989$	−11.3137			−0.359755
$990$		0			0
$991$	29.1918			0.927309			0.463655	−	0.886016i	$-0.346538\pi$
$991$	29.1918			0.927309			0.463655	+	0.886016i	$0.346538\pi$
$992$		0			0
$993$		−	20.5959i		−	0.653592i
$994$	20.6969			0.656467
$995$	5.07832	+	50.2702i	0.160993	+	1.59367i
$996$		0			0
$997$		−	1.38211i		−	0.0437717i	−0.999760	−	0.0218859i	$-0.993033\pi$
$997$		−	1.38211i		−	0.0437717i	0.999760	−	0.0218859i	$-0.00696704\pi$
$998$			56.1399i			1.77708i
$999$	3.89898			0.123358

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.2.c.g.364.6	yes	8
5.2	odd	4		9075.2.a.cr.1.1		4
5.3	odd	4		9075.2.a.cy.1.4		4
5.4	even	2	inner	1815.2.c.g.364.4	yes	8
11.10	odd	2	inner	1815.2.c.g.364.2	✓	8
55.32	even	4		9075.2.a.cr.1.4		4
55.43	even	4		9075.2.a.cy.1.1		4
55.54	odd	2	inner	1815.2.c.g.364.8	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1815.2.c.g.364.2	✓	8	11.10	odd	2	inner
1815.2.c.g.364.4	yes	8	5.4	even	2	inner
1815.2.c.g.364.6	yes	8	1.1	even	1	trivial
1815.2.c.g.364.8	yes	8	55.54	odd	2	inner
9075.2.a.cr.1.1		4	5.2	odd	4
9075.2.a.cr.1.4		4	55.32	even	4
9075.2.a.cy.1.1		4	55.43	even	4
9075.2.a.cy.1.4		4	5.3	odd	4

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:	\( N \)	\(=\)	\( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1815.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} -1.00000i q^{3} +(0.224745 + 2.22474i) q^{5} +1.41421 q^{6} +1.73205i q^{7} +2.82843i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.41421i q^{2} -1.00000i q^{3} +(0.224745 + 2.22474i) q^{5} +1.41421 q^{6} +1.73205i q^{7} +2.82843i q^{8} -1.00000 q^{9} +(-3.14626 + 0.317837i) q^{10} +6.29253i q^{13} -2.44949 q^{14} +(2.22474 - 0.224745i) q^{15} -4.00000 q^{16} -2.04989i q^{17} -1.41421i q^{18} -1.73205 q^{19} +1.73205 q^{21} -2.00000i q^{23} +2.82843 q^{24} +(-4.89898 + 1.00000i) q^{25} -8.89898 q^{26} +1.00000i q^{27} -5.51399 q^{29} +(0.317837 + 3.14626i) q^{30} +1.89898 q^{31} +2.89898 q^{34} +(-3.85337 + 0.389270i) q^{35} -3.89898i q^{37} -2.44949i q^{38} +6.29253 q^{39} +(-6.29253 + 0.635674i) q^{40} +2.19275 q^{41} +2.44949i q^{42} -5.65685i q^{43} +(-0.224745 - 2.22474i) q^{45} +2.82843 q^{46} -7.34847i q^{47} +4.00000i q^{48} +4.00000 q^{49} +(-1.41421 - 6.92820i) q^{50} -2.04989 q^{51} +10.0000i q^{53} -1.41421 q^{54} -4.89898 q^{56} +1.73205i q^{57} -7.79796i q^{58} -12.2474 q^{59} +13.6814 q^{61} +2.68556i q^{62} -1.73205i q^{63} -8.00000 q^{64} +(-13.9993 + 1.41421i) q^{65} -13.8990i q^{67} -2.00000 q^{69} +(-0.550510 - 5.44949i) q^{70} -8.44949 q^{71} -2.82843i q^{72} +13.6814i q^{73} +5.51399 q^{74} +(1.00000 + 4.89898i) q^{75} +8.89898i q^{78} +10.2173 q^{79} +(-0.898979 - 8.89898i) q^{80} +1.00000 q^{81} +3.10102i q^{82} +12.7279i q^{83} +(4.56048 - 0.460702i) q^{85} +8.00000 q^{86} +5.51399i q^{87} +13.3485 q^{89} +(3.14626 - 0.317837i) q^{90} -10.8990 q^{91} -1.89898i q^{93} +10.3923 q^{94} +(-0.389270 - 3.85337i) q^{95} -5.00000i q^{97} +5.65685i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{5} - 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^5 - 8 * q^9	\( 8 q - 8 q^{5} - 8 q^{9} + 8 q^{15} - 32 q^{16} - 32 q^{26} - 24 q^{31} - 16 q^{34} + 8 q^{45} + 32 q^{49} - 64 q^{64} - 16 q^{69} - 24 q^{70} - 48 q^{71} + 8 q^{75} + 32 q^{80} + 8 q^{81} + 64 q^{86} + 48 q^{89} - 48 q^{91}+O(q^{100}) \) 8 * q - 8 * q^5 - 8 * q^9 + 8 * q^15 - 32 * q^16 - 32 * q^26 - 24 * q^31 - 16 * q^34 + 8 * q^45 + 32 * q^49 - 64 * q^64 - 16 * q^69 - 24 * q^70 - 48 * q^71 + 8 * q^75 + 32 * q^80 + 8 * q^81 + 64 * q^86 + 48 * q^89 - 48 * q^91

Introduction

L-functions

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