LMFDB - Embedded newform 1800.2.d.r.1549.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1800,2,Mod(1549,1800)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1800, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1800.1549");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1800.d (of order $2$, degree $1$, 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:	$14.3730723638$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.399424.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 $ x^6 - 2x^5 + 3x^4 - 6x^3 + 6x^2 - 8*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1549.4
Root			$1.40680 - 0.144584i$ of defining polynomial
Character	$\chi$	$=$	1800.1549
Dual form			1800.2.d.r.1549.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.144584 + 1.40680i) q^{2} +(-1.95819 - 0.406803i) q^{4} +3.62721i q^{7} +(0.855416 - 2.69597i) q^{8} +O(q^{10})$	\(q+(-0.144584 + 1.40680i) q^{2} +(-1.95819 - 0.406803i) q^{4} +3.62721i q^{7} +(0.855416 - 2.69597i) q^{8} -6.20555i q^{11} +0.578337 q^{13} +(-5.10278 - 0.524438i) q^{14} +(3.66902 + 1.59320i) q^{16} +1.42166i q^{17} +5.62721i q^{19} +(8.72999 + 0.897225i) q^{22} +5.62721i q^{23} +(-0.0836184 + 0.813607i) q^{26} +(1.47556 - 7.10278i) q^{28} +2.00000i q^{29} -2.57834 q^{31} +(-2.77180 + 4.93124i) q^{32} +(-2.00000 - 0.205550i) q^{34} -7.83276 q^{37} +(-7.91638 - 0.813607i) q^{38} -5.25443 q^{41} +7.25443 q^{43} +(-2.52444 + 12.1517i) q^{44} +(-7.91638 - 0.813607i) q^{46} +6.78389i q^{47} -6.15667 q^{49} +(-1.13249 - 0.235269i) q^{52} -2.00000 q^{53} +(9.77886 + 3.10278i) q^{56} +(-2.81361 - 0.289169i) q^{58} -2.20555i q^{59} +12.4111i q^{61} +(0.372787 - 3.62721i) q^{62} +(-6.53653 - 4.61235i) q^{64} +4.00000 q^{67} +(0.578337 - 2.78389i) q^{68} -8.41110 q^{71} -6.00000i q^{73} +(1.13249 - 11.0192i) q^{74} +(2.28917 - 11.0192i) q^{76} +22.5089 q^{77} -5.42166 q^{79} +(0.759707 - 7.39194i) q^{82} +3.25443 q^{83} +(-1.04888 + 10.2056i) q^{86} +(-16.7300 - 5.30833i) q^{88} -13.2544 q^{89} +2.09775i q^{91} +(2.28917 - 11.0192i) q^{92} +(-9.54359 - 0.980843i) q^{94} -4.84333i q^{97} +(0.890158 - 8.66123i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{4} + 6 q^{8}+O(q^{10}) $ 6 * q + 2 * q^4 + 6 * q^8	$ 6 q + 2 q^{4} + 6 q^{8} - 16 q^{14} + 10 q^{16} + 12 q^{22} - 28 q^{26} + 20 q^{28} - 12 q^{31} + 10 q^{32} - 12 q^{34} + 8 q^{37} - 20 q^{38} + 20 q^{41} - 8 q^{43} - 4 q^{44} - 20 q^{46} - 30 q^{49} - 12 q^{52} - 12 q^{53} - 4 q^{56} - 4 q^{58} + 28 q^{62} - 22 q^{64} + 24 q^{67} + 8 q^{71} + 12 q^{74} + 12 q^{76} + 32 q^{77} - 36 q^{79} - 16 q^{82} - 32 q^{83} + 16 q^{86} - 60 q^{88} - 28 q^{89} + 12 q^{92} - 4 q^{94} + 56 q^{98}+O(q^{100}) $ 6 * q + 2 * q^4 + 6 * q^8 - 16 * q^14 + 10 * q^16 + 12 * q^22 - 28 * q^26 + 20 * q^28 - 12 * q^31 + 10 * q^32 - 12 * q^34 + 8 * q^37 - 20 * q^38 + 20 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 - 30 * q^49 - 12 * q^52 - 12 * q^53 - 4 * q^56 - 4 * q^58 + 28 * q^62 - 22 * q^64 + 24 * q^67 + 8 * q^71 + 12 * q^74 + 12 * q^76 + 32 * q^77 - 36 * q^79 - 16 * q^82 - 32 * q^83 + 16 * q^86 - 60 * q^88 - 28 * q^89 + 12 * q^92 - 4 * q^94 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1001$	$1351$
$\chi(n)$	$-1$	$-1$	$1$	$1$

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 $

$2$	−0.144584	+	1.40680i	−0.102237	+	0.994760i
$2$	−0.144584	+	1.40680i	−0.102237	+	0.994760i
$3$		0			0
$3$		0			0
$4$	−1.95819	−	0.406803i	−0.979095	−	0.203402i
$5$		0			0
$5$		0			0
$6$		0			0
$7$			3.62721i			1.37096i	0.728093	+	0.685479i	$0.240407\pi$
$7$			3.62721i			1.37096i	−0.728093	+	0.685479i	$0.759593\pi$
$8$	0.855416	−	2.69597i	0.302435	−	0.953170i
$9$		0			0
$10$		0			0
$11$		−	6.20555i		−	1.87104i	−0.353269	−	0.935522i	$-0.614930\pi$
$11$		−	6.20555i		−	1.87104i	0.353269	−	0.935522i	$-0.385070\pi$
$12$		0			0
$13$	0.578337			0.160402			0.0802009	−	0.996779i	$-0.474444\pi$
$13$	0.578337			0.160402			0.0802009	+	0.996779i	$0.474444\pi$
$14$	−5.10278	−	0.524438i	−1.36377	−	0.140162i
$15$		0			0
$16$	3.66902	+	1.59320i	0.917256	+	0.398299i
$17$			1.42166i			0.344804i	0.985027	+	0.172402i	$0.0551528\pi$
$17$			1.42166i			0.344804i	−0.985027	+	0.172402i	$0.944847\pi$
$18$		0			0
$19$			5.62721i			1.29097i	0.763772	+	0.645486i	$0.223345\pi$
$19$			5.62721i			1.29097i	−0.763772	+	0.645486i	$0.776655\pi$
$20$		0			0
$21$		0			0
$22$	8.72999	+	0.897225i	1.86124	+	0.191289i
$23$			5.62721i			1.17336i	0.809821	+	0.586678i	$0.199564\pi$
$23$			5.62721i			1.17336i	−0.809821	+	0.586678i	$0.800436\pi$
$24$		0			0
$25$		0			0
$26$	−0.0836184	+	0.813607i	−0.0163989	+	0.159561i
$27$		0			0
$28$	1.47556	−	7.10278i	0.278855	−	1.34230i
$29$			2.00000i			0.371391i	0.982607	+	0.185695i	$0.0594537\pi$
$29$			2.00000i			0.371391i	−0.982607	+	0.185695i	$0.940546\pi$
$30$		0			0
$31$	−2.57834			−0.463083			−0.231542	−	0.972825i	$-0.574377\pi$
$31$	−2.57834			−0.463083			−0.231542	+	0.972825i	$0.574377\pi$
$32$	−2.77180	+	4.93124i	−0.489989	+	0.871729i
$33$		0			0
$34$	−2.00000	−	0.205550i	−0.342997	−	0.0352516i
$35$		0			0
$36$		0			0
$37$	−7.83276			−1.28770			−0.643849	−	0.765152i	$-0.722664\pi$
$37$	−7.83276			−1.28770			−0.643849	+	0.765152i	$0.722664\pi$
$38$	−7.91638	−	0.813607i	−1.28421	−	0.131984i
$39$		0			0
$40$		0			0
$41$	−5.25443			−0.820603			−0.410302	−	0.911950i	$-0.634577\pi$
$41$	−5.25443			−0.820603			−0.410302	+	0.911950i	$0.634577\pi$
$42$		0			0
$43$	7.25443			1.10629			0.553145	−	0.833085i	$-0.313428\pi$
$43$	7.25443			1.10629			0.553145	+	0.833085i	$0.313428\pi$
$44$	−2.52444	+	12.1517i	−0.380573	+	1.83193i
$45$		0			0
$46$	−7.91638	−	0.813607i	−1.16721	−	0.119960i
$47$			6.78389i			0.989532i	0.869026	+	0.494766i	$0.164746\pi$
$47$			6.78389i			0.989532i	−0.869026	+	0.494766i	$0.835254\pi$
$48$		0			0
$49$	−6.15667			−0.879525
$50$		0			0
$51$		0			0
$52$	−1.13249	−	0.235269i	−0.157049	−	0.0326260i
$53$	−2.00000			−0.274721			−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000			−0.274721			−0.137361	+	0.990521i	$0.543862\pi$
$54$		0			0
$55$		0			0
$56$	9.77886	+	3.10278i	1.30676	+	0.414626i
$57$		0			0
$58$	−2.81361	−	0.289169i	−0.369445	−	0.0379697i
$59$		−	2.20555i		−	0.287138i	−0.989640	−	0.143569i	$-0.954142\pi$
$59$		−	2.20555i		−	0.287138i	0.989640	−	0.143569i	$-0.0458579\pi$
$60$		0			0
$61$			12.4111i			1.58908i	0.607213	+	0.794539i	$0.292288\pi$
$61$			12.4111i			1.58908i	−0.607213	+	0.794539i	$0.707712\pi$
$62$	0.372787	−	3.62721i	0.0473440	−	0.460657i
$63$		0			0
$64$	−6.53653	−	4.61235i	−0.817066	−	0.576544i
$65$		0			0
$66$		0			0
$67$	4.00000			0.488678			0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000			0.488678			0.244339	+	0.969690i	$0.421429\pi$
$68$	0.578337	−	2.78389i	0.0701337	−	0.337596i
$69$		0			0
$70$		0			0
$71$	−8.41110			−0.998214			−0.499107	−	0.866540i	$-0.666339\pi$
$71$	−8.41110			−0.998214			−0.499107	+	0.866540i	$0.666339\pi$
$72$		0			0
$73$		−	6.00000i		−	0.702247i	−0.936329	−	0.351123i	$-0.885800\pi$
$73$		−	6.00000i		−	0.702247i	0.936329	−	0.351123i	$-0.114200\pi$
$74$	1.13249	−	11.0192i	0.131650	−	1.28095i
$75$		0			0
$76$	2.28917	−	11.0192i	0.262586	−	1.26398i
$77$	22.5089			2.56512
$78$		0			0
$79$	−5.42166			−0.609985			−0.304992	−	0.952355i	$-0.598654\pi$
$79$	−5.42166			−0.609985			−0.304992	+	0.952355i	$0.598654\pi$
$80$		0			0
$81$		0			0
$82$	0.759707	−	7.39194i	0.0838956	−	0.816304i
$83$	3.25443			0.357220			0.178610	−	0.983920i	$-0.442840\pi$
$83$	3.25443			0.357220			0.178610	+	0.983920i	$0.442840\pi$
$84$		0			0
$85$		0			0
$86$	−1.04888	+	10.2056i	−0.113103	+	1.10049i
$87$		0			0
$88$	−16.7300	−	5.30833i	−1.78342	−	0.565869i
$89$	−13.2544			−1.40497			−0.702483	−	0.711700i	$-0.747925\pi$
$89$	−13.2544			−1.40497			−0.702483	+	0.711700i	$0.747925\pi$
$90$		0			0
$91$			2.09775i			0.219904i
$92$	2.28917	−	11.0192i	0.238662	−	1.14883i
$93$		0			0
$94$	−9.54359	−	0.980843i	−0.984347	−	0.101166i
$95$		0			0
$96$		0			0
$97$		−	4.84333i		−	0.491765i	−0.969300	−	0.245883i	$-0.920922\pi$
$97$		−	4.84333i		−	0.491765i	0.969300	−	0.245883i	$-0.0790778\pi$
$98$	0.890158	−	8.66123i	0.0899196	−	0.874916i
$99$		0			0
$100$		0			0
$101$			2.00000i			0.199007i	0.995037	+	0.0995037i	$0.0317255\pi$
$101$			2.00000i			0.199007i	−0.995037	+	0.0995037i	$0.968274\pi$
$102$		0			0
$103$			2.47054i			0.243429i	0.992565	+	0.121715i	$0.0388393\pi$
$103$			2.47054i			0.243429i	−0.992565	+	0.121715i	$0.961161\pi$
$104$	0.494719	−	1.55918i	0.0485112	−	0.152890i
$105$		0			0
$106$	0.289169	−	2.81361i	0.0280865	−	0.273282i
$107$	−14.0978			−1.36288			−0.681441	−	0.731873i	$-0.738646\pi$
$107$	−14.0978			−1.36288			−0.681441	+	0.731873i	$0.738646\pi$
$108$		0			0
$109$		−	7.25443i		−	0.694848i	−0.937708	−	0.347424i	$-0.887056\pi$
$109$		−	7.25443i		−	0.694848i	0.937708	−	0.347424i	$-0.112944\pi$
$110$		0			0
$111$		0			0
$112$	−5.77886	+	13.3083i	−0.546051	+	1.25752i
$113$			9.08719i			0.854851i	0.904051	+	0.427425i	$0.140579\pi$
$113$			9.08719i			0.854851i	−0.904051	+	0.427425i	$0.859421\pi$
$114$		0			0
$115$		0			0
$116$	0.813607	−	3.91638i	0.0755415	−	0.363627i
$117$		0			0
$118$	3.10278	+	0.318888i	0.285634	+	0.0293560i
$119$	−5.15667			−0.472712
$120$		0			0
$121$	−27.5089			−2.50080
$122$	−17.4600	−	1.79445i	−1.58075	−	0.162462i
$123$		0			0
$124$	5.04888	+	1.04888i	0.453402	+	0.0941918i
$125$		0			0
$126$		0			0
$127$			10.4705i			0.929110i	0.885544	+	0.464555i	$0.153786\pi$
$127$			10.4705i			0.929110i	−0.885544	+	0.464555i	$0.846214\pi$
$128$	7.43375	−	8.52873i	0.657057	−	0.753841i
$129$		0			0
$130$		0			0
$131$			13.4600i			1.17600i	0.808860	+	0.588002i	$0.200085\pi$
$131$			13.4600i			1.17600i	−0.808860	+	0.588002i	$0.799915\pi$
$132$		0			0
$133$	−20.4111			−1.76987
$134$	−0.578337	+	5.62721i	−0.0499607	+	0.486117i
$135$		0			0
$136$	3.83276	+	1.21611i	0.328657	+	0.104281i
$137$		−	10.5783i		−	0.903768i	−0.892077	−	0.451884i	$-0.850752\pi$
$137$		−	10.5783i		−	0.903768i	0.892077	−	0.451884i	$-0.149248\pi$
$138$		0			0
$139$			12.4705i			1.05774i	0.848704	+	0.528869i	$0.177384\pi$
$139$			12.4705i			1.05774i	−0.848704	+	0.528869i	$0.822616\pi$
$140$		0			0
$141$		0			0
$142$	1.21611	−	11.8328i	0.102054	−	0.992983i
$143$		−	3.58890i		−	0.300119i
$144$		0			0
$145$		0			0
$146$	8.44082	+	0.867506i	0.698567	+	0.0717953i
$147$		0			0
$148$	15.3380	+	3.18639i	1.26078	+	0.261920i
$149$			2.00000i			0.163846i	0.996639	+	0.0819232i	$0.0261062\pi$
$149$			2.00000i			0.163846i	−0.996639	+	0.0819232i	$0.973894\pi$
$150$		0			0
$151$	12.6761			1.03157			0.515783	−	0.856719i	$-0.327501\pi$
$151$	12.6761			1.03157			0.515783	+	0.856719i	$0.327501\pi$
$152$	15.1708	+	4.81361i	1.23051	+	0.390435i
$153$		0			0
$154$	−3.25443	+	31.6655i	−0.262249	+	2.55168i
$155$		0			0
$156$		0			0
$157$	−1.32391			−0.105660			−0.0528298	−	0.998604i	$-0.516824\pi$
$157$	−1.32391			−0.105660			−0.0528298	+	0.998604i	$0.516824\pi$
$158$	0.783887	−	7.62721i	0.0623627	−	0.606788i
$159$		0			0
$160$		0			0
$161$	−20.4111			−1.60862
$162$		0			0
$163$	−15.2544			−1.19482			−0.597409	−	0.801936i	$-0.703803\pi$
$163$	−15.2544			−1.19482			−0.597409	+	0.801936i	$0.703803\pi$
$164$	10.2892	+	2.13752i	0.803449	+	0.166912i
$165$		0			0
$166$	−0.470539	+	4.57834i	−0.0365209	+	0.355348i
$167$			10.7839i			0.834482i	0.908796	+	0.417241i	$0.137003\pi$
$167$			10.7839i			0.834482i	−0.908796	+	0.417241i	$0.862997\pi$
$168$		0			0
$169$	−12.6655			−0.974271
$170$		0			0
$171$		0			0
$172$	−14.2056	−	2.95112i	−1.08316	−	0.225021i
$173$	13.6655			1.03897			0.519485	−	0.854479i	$-0.326124\pi$
$173$	13.6655			1.03897			0.519485	+	0.854479i	$0.326124\pi$
$174$		0			0
$175$		0			0
$176$	9.88666	−	22.7683i	0.745235	−	1.71623i
$177$		0			0
$178$	1.91638	−	18.6464i	0.143639	−	1.39760i
$179$		−	9.04888i		−	0.676345i	−0.941084	−	0.338172i	$-0.890191\pi$
$179$		−	9.04888i		−	0.676345i	0.941084	−	0.338172i	$-0.109809\pi$
$180$		0			0
$181$		−	23.2544i		−	1.72849i	−0.503073	−	0.864244i	$-0.667797\pi$
$181$		−	23.2544i		−	1.72849i	0.503073	−	0.864244i	$-0.332203\pi$
$182$	−2.95112	−	0.303302i	−0.218752	−	0.0224822i
$183$		0			0
$184$	15.1708	+	4.81361i	1.11841	+	0.354864i
$185$		0			0
$186$		0			0
$187$	8.82220			0.645143
$188$	2.75971	−	13.2841i	0.201272	−	0.968846i
$189$		0			0
$190$		0			0
$191$	8.00000			0.578860			0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000			0.578860			0.289430	+	0.957199i	$0.406534\pi$
$192$		0			0
$193$			25.6655i			1.84745i	0.383062	+	0.923723i	$0.374869\pi$
$193$			25.6655i			1.84745i	−0.383062	+	0.923723i	$0.625131\pi$
$194$	6.81361	+	0.700269i	0.489188	+	0.0502764i
$195$		0			0
$196$	12.0559	+	2.50456i	0.861139	+	0.178897i
$197$	−15.1567			−1.07987			−0.539934	−	0.841707i	$-0.681551\pi$
$197$	−15.1567			−1.07987			−0.539934	+	0.841707i	$0.681551\pi$
$198$		0			0
$199$	20.6761			1.46569			0.732845	−	0.680396i	$-0.238192\pi$
$199$	20.6761			1.46569			0.732845	+	0.680396i	$0.238192\pi$
$200$		0			0
$201$		0			0
$202$	−2.81361	−	0.289169i	−0.197965	−	0.0203458i
$203$	−7.25443			−0.509161
$204$		0			0
$205$		0			0
$206$	−3.47556	−	0.357201i	−0.242154	−	0.0248874i
$207$		0			0
$208$	2.12193	+	0.921405i	0.147129	+	0.0638879i
$209$	34.9200			2.41546
$210$		0			0
$211$		−	2.03831i		−	0.140323i	−0.997536	−	0.0701616i	$-0.977648\pi$
$211$		−	2.03831i		−	0.140323i	0.997536	−	0.0701616i	$-0.0223515\pi$
$212$	3.91638	+	0.813607i	0.268978	+	0.0558787i
$213$		0			0
$214$	2.03831	−	19.8328i	0.139336	−	1.35574i
$215$		0			0
$216$		0			0
$217$		−	9.35218i		−	0.634867i
$218$	10.2056	+	1.04888i	0.691207	+	0.0710388i
$219$		0			0
$220$		0			0
$221$			0.822200i			0.0553072i
$222$		0			0
$223$		−	7.21611i		−	0.483227i	−0.970373	−	0.241613i	$-0.922323\pi$
$223$		−	7.21611i		−	0.483227i	0.970373	−	0.241613i	$-0.0776766\pi$
$224$	−17.8867	−	10.0539i	−1.19510	−	0.671754i
$225$		0			0
$226$	−12.7839	−	1.31386i	−0.850372	−	0.0873970i
$227$	−1.15667			−0.0767712			−0.0383856	−	0.999263i	$-0.512222\pi$
$227$	−1.15667			−0.0767712			−0.0383856	+	0.999263i	$0.512222\pi$
$228$		0			0
$229$		−	14.0978i		−	0.931606i	−0.884889	−	0.465803i	$-0.845766\pi$
$229$		−	14.0978i		−	0.931606i	0.884889	−	0.465803i	$-0.154234\pi$
$230$		0			0
$231$		0			0
$232$	5.39194	+	1.71083i	0.353998	+	0.112322i
$233$			14.5783i			0.955059i	0.878616	+	0.477529i	$0.158468\pi$
$233$			14.5783i			0.955059i	−0.878616	+	0.477529i	$0.841532\pi$
$234$		0			0
$235$		0			0
$236$	−0.897225	+	4.31889i	−0.0584044	+	0.281136i
$237$		0			0
$238$	0.745574	−	7.25443i	0.0483284	−	0.470235i
$239$	19.2544			1.24547			0.622733	−	0.782435i	$-0.286022\pi$
$239$	19.2544			1.24547			0.622733	+	0.782435i	$0.286022\pi$
$240$		0			0
$241$	−13.6655			−0.880274			−0.440137	−	0.897931i	$-0.645070\pi$
$241$	−13.6655			−0.880274			−0.440137	+	0.897931i	$0.645070\pi$
$242$	3.97735	−	38.6995i	0.255674	−	2.48770i
$243$		0			0
$244$	5.04888	−	24.3033i	0.323221	−	1.55586i
$245$		0			0
$246$		0			0
$247$			3.25443i			0.207074i
$248$	−2.20555	+	6.95112i	−0.140053	+	0.441397i
$249$		0			0
$250$		0			0
$251$			7.14663i			0.451091i	0.974233	+	0.225546i	$0.0724165\pi$
$251$			7.14663i			0.451091i	−0.974233	+	0.225546i	$0.927584\pi$
$252$		0			0
$253$	34.9200			2.19540
$254$	−14.7300	−	1.51388i	−0.924242	−	0.0949890i
$255$		0			0
$256$	10.9234	+	11.6909i	0.682716	+	0.730684i
$257$			7.73501i			0.482497i	0.970463	+	0.241248i	$0.0775568\pi$
$257$			7.73501i			0.482497i	−0.970463	+	0.241248i	$0.922443\pi$
$258$		0			0
$259$		−	28.4111i		−	1.76538i
$260$		0			0
$261$		0			0
$262$	−18.9355	−	1.94610i	−1.16984	−	0.120231i
$263$			18.7839i			1.15826i	0.815234	+	0.579132i	$0.196608\pi$
$263$			18.7839i			1.15826i	−0.815234	+	0.579132i	$0.803392\pi$
$264$		0			0
$265$		0			0
$266$	2.95112	−	28.7144i	0.180945	−	1.76059i
$267$		0			0
$268$	−7.83276	−	1.62721i	−0.478462	−	0.0993979i
$269$			8.50885i			0.518794i	0.965771	+	0.259397i	$0.0835238\pi$
$269$			8.50885i			0.518794i	−0.965771	+	0.259397i	$0.916476\pi$
$270$		0			0
$271$	30.9894			1.88247			0.941237	−	0.337746i	$-0.109665\pi$
$271$	30.9894			1.88247			0.941237	+	0.337746i	$0.109665\pi$
$272$	−2.26499	+	5.21611i	−0.137335	+	0.316273i
$273$		0			0
$274$	14.8816	+	1.52946i	0.899033	+	0.0923981i
$275$		0			0
$276$		0			0
$277$	9.51941			0.571966			0.285983	−	0.958235i	$-0.407680\pi$
$277$	9.51941			0.571966			0.285983	+	0.958235i	$0.407680\pi$
$278$	−17.5436	−	1.80304i	−1.05219	−	0.108139i
$279$		0			0
$280$		0			0
$281$	−13.6655			−0.815217			−0.407608	−	0.913157i	$-0.633637\pi$
$281$	−13.6655			−0.815217			−0.407608	+	0.913157i	$0.633637\pi$
$282$		0			0
$283$	20.0000			1.18888			0.594438	−	0.804141i	$-0.297374\pi$
$283$	20.0000			1.18888			0.594438	+	0.804141i	$0.297374\pi$
$284$	16.4705	+	3.42166i	0.977347	+	0.203038i
$285$		0			0
$286$	5.04888	+	0.518898i	0.298546	+	0.0306831i
$287$		−	19.0589i		−	1.12501i
$288$		0			0
$289$	14.9789			0.881110
$290$		0			0
$291$		0			0
$292$	−2.44082	+	11.7491i	−0.142838	+	0.687567i
$293$	−4.31335			−0.251989			−0.125994	−	0.992031i	$-0.540212\pi$
$293$	−4.31335			−0.251989			−0.125994	+	0.992031i	$0.540212\pi$
$294$		0			0
$295$		0			0
$296$	−6.70027	+	21.1169i	−0.389445	+	1.22740i
$297$		0			0
$298$	−2.81361	−	0.289169i	−0.162988	−	0.0167511i
$299$			3.25443i			0.188208i
$300$		0			0
$301$			26.3133i			1.51668i
$302$	−1.83276	+	17.8328i	−0.105464	+	1.02616i
$303$		0			0
$304$	−8.96526	+	20.6464i	−0.514193	+	1.18415i
$305$		0			0
$306$		0			0
$307$	25.5678			1.45923			0.729615	−	0.683858i	$-0.239699\pi$
$307$	25.5678			1.45923			0.729615	+	0.683858i	$0.239699\pi$
$308$	−44.0766	−	9.15667i	−2.51150	−	0.521750i
$309$		0			0
$310$		0			0
$311$	20.0766			1.13844			0.569221	−	0.822185i	$-0.307245\pi$
$311$	20.0766			1.13844			0.569221	+	0.822185i	$0.307245\pi$
$312$		0			0
$313$			7.15667i			0.404519i	0.979332	+	0.202260i	$0.0648285\pi$
$313$			7.15667i			0.404519i	−0.979332	+	0.202260i	$0.935172\pi$
$314$	0.191417	−	1.86248i	0.0108023	−	0.105106i
$315$		0			0
$316$	10.6167	+	2.20555i	0.597233	+	0.124072i
$317$	−24.1744			−1.35777			−0.678884	−	0.734245i	$-0.737536\pi$
$317$	−24.1744			−1.35777			−0.678884	+	0.734245i	$0.737536\pi$
$318$		0			0
$319$	12.4111			0.694888
$320$		0			0
$321$		0			0
$322$	2.95112	−	28.7144i	0.164460	−	1.60019i
$323$	−8.00000			−0.445132
$324$		0			0
$325$		0			0
$326$	2.20555	−	21.4600i	0.122154	−	1.18856i
$327$		0			0
$328$	−4.49472	+	14.1658i	−0.248179	+	0.782175i
$329$	−24.6066			−1.35661
$330$		0			0
$331$		−	27.1950i		−	1.49477i	−0.664390	−	0.747386i	$-0.731309\pi$
$331$		−	27.1950i		−	1.49477i	0.664390	−	0.747386i	$-0.268691\pi$
$332$	−6.37279	−	1.32391i	−0.349752	−	0.0726591i
$333$		0			0
$334$	−15.1708	−	1.55918i	−0.830110	−	0.0853146i
$335$		0			0
$336$		0			0
$337$		−	22.8222i		−	1.24320i	−0.783333	−	0.621602i	$-0.786482\pi$
$337$		−	22.8222i		−	1.24320i	0.783333	−	0.621602i	$-0.213518\pi$
$338$	1.83124	−	17.8179i	0.0996061	−	0.969166i
$339$		0			0
$340$		0			0
$341$			16.0000i			0.866449i
$342$		0			0
$343$			3.05892i			0.165166i
$344$	6.20555	−	19.5577i	0.334581	−	1.05448i
$345$		0			0
$346$	−1.97582	+	19.2247i	−0.106221	+	1.03353i
$347$	23.6655			1.27043			0.635216	−	0.772335i	$-0.280911\pi$
$347$	23.6655			1.27043			0.635216	+	0.772335i	$0.280911\pi$
$348$		0			0
$349$			34.9200i			1.86922i	0.355671	+	0.934611i	$0.384252\pi$
$349$			34.9200i			1.86922i	−0.355671	+	0.934611i	$0.615748\pi$
$350$		0			0
$351$		0			0
$352$	30.6011	+	17.2005i	1.63104	+	0.916791i
$353$			15.9305i			0.847896i	0.905687	+	0.423948i	$0.139356\pi$
$353$			15.9305i			0.847896i	−0.905687	+	0.423948i	$0.860644\pi$
$354$		0			0
$355$		0			0
$356$	25.9547	+	5.39194i	1.37560	+	0.285772i
$357$		0			0
$358$	12.7300	+	1.30833i	0.672801	+	0.0691471i
$359$	8.41110			0.443921			0.221960	−	0.975056i	$-0.428754\pi$
$359$	8.41110			0.443921			0.221960	+	0.975056i	$0.428754\pi$
$360$		0			0
$361$	−12.6655			−0.666607
$362$	32.7144	+	3.36222i	1.71943	+	0.176715i
$363$		0			0
$364$	0.853372	−	4.10780i	0.0447289	−	0.215307i
$365$		0			0
$366$		0			0
$367$			24.4494i			1.27625i	0.769933	+	0.638124i	$0.220289\pi$
$367$			24.4494i			1.27625i	−0.769933	+	0.638124i	$0.779711\pi$
$368$	−8.96526	+	20.6464i	−0.467346	+	1.07627i
$369$		0			0
$370$		0			0
$371$		−	7.25443i		−	0.376631i
$372$		0			0
$373$	0.167237			0.00865920			0.00432960	−	0.999991i	$-0.498622\pi$
$373$	0.167237			0.00865920			0.00432960	+	0.999991i	$0.498622\pi$
$374$	−1.27555	+	12.4111i	−0.0659572	+	0.641763i
$375$		0			0
$376$	18.2892	+	5.80304i	0.943192	+	0.299269i
$377$			1.15667i			0.0595718i
$378$		0			0
$379$		−	7.72496i		−	0.396805i	−0.980121	−	0.198402i	$-0.936425\pi$
$379$		−	7.72496i		−	0.396805i	0.980121	−	0.198402i	$-0.0635753\pi$
$380$		0			0
$381$		0			0
$382$	−1.15667	+	11.2544i	−0.0591806	+	0.575827i
$383$			1.62721i			0.0831467i	0.999135	+	0.0415734i	$0.0132370\pi$
$383$			1.62721i			0.0831467i	−0.999135	+	0.0415734i	$0.986763\pi$
$384$		0			0
$385$		0			0
$386$	−36.1063	−	3.71083i	−1.83776	−	0.188876i
$387$		0			0
$388$	−1.97028	+	9.48416i	−0.100026	+	0.481485i
$389$			12.3133i			0.624312i	0.950031	+	0.312156i	$0.101051\pi$
$389$			12.3133i			0.624312i	−0.950031	+	0.312156i	$0.898949\pi$
$390$		0			0
$391$	−8.00000			−0.404577
$392$	−5.26652	+	16.5982i	−0.265999	+	0.838337i
$393$		0			0
$394$	2.19142	−	21.3225i	0.110402	−	1.07421i
$395$		0			0
$396$		0			0
$397$	−19.0872			−0.957959			−0.478979	−	0.877826i	$-0.658993\pi$
$397$	−19.0872			−0.957959			−0.478979	+	0.877826i	$0.658993\pi$
$398$	−2.98944	+	29.0872i	−0.149847	+	1.45801i
$399$		0			0
$400$		0			0
$401$	14.4111			0.719656			0.359828	−	0.933019i	$-0.382835\pi$
$401$	14.4111			0.719656			0.359828	+	0.933019i	$0.382835\pi$
$402$		0			0
$403$	−1.49115			−0.0742794
$404$	0.813607	−	3.91638i	0.0404784	−	0.194847i
$405$		0			0
$406$	1.04888	−	10.2056i	0.0520548	−	0.506493i
$407$			48.6066i			2.40934i
$408$		0			0
$409$	8.31335			0.411069			0.205534	−	0.978650i	$-0.434107\pi$
$409$	8.31335			0.411069			0.205534	+	0.978650i	$0.434107\pi$
$410$		0			0
$411$		0			0
$412$	1.00502	−	4.83779i	0.0495139	−	0.238341i
$413$	8.00000			0.393654
$414$		0			0
$415$		0			0
$416$	−1.60303	+	2.85192i	−0.0785952	+	0.139827i
$417$		0			0
$418$	−5.04888	+	49.1255i	−0.246949	+	2.40281i
$419$		−	7.36222i		−	0.359668i	−0.983697	−	0.179834i	$-0.942444\pi$
$419$		−	7.36222i		−	0.359668i	0.983697	−	0.179834i	$-0.0575561\pi$
$420$		0			0
$421$		−	30.0978i		−	1.46687i	−0.679757	−	0.733437i	$-0.737915\pi$
$421$		−	30.0978i		−	1.46687i	0.679757	−	0.733437i	$-0.262085\pi$
$422$	2.86751	+	0.294708i	0.139588	+	0.0143462i
$423$		0			0
$424$	−1.71083	+	5.39194i	−0.0830853	+	0.261856i
$425$		0			0
$426$		0			0
$427$	−45.0177			−2.17856
$428$	27.6061	+	5.73501i	1.33439	+	0.277212i
$429$		0			0
$430$		0			0
$431$	−8.41110			−0.405148			−0.202574	−	0.979267i	$-0.564931\pi$
$431$	−8.41110			−0.405148			−0.202574	+	0.979267i	$0.564931\pi$
$432$		0			0
$433$		−	4.31335i		−	0.207286i	−0.994615	−	0.103643i	$-0.966950\pi$
$433$		−	4.31335i		−	0.207286i	0.994615	−	0.103643i	$-0.0330500\pi$
$434$	13.1567	+	1.35218i	0.631541	+	0.0649066i
$435$		0			0
$436$	−2.95112	+	14.2056i	−0.141333	+	0.680322i
$437$	−31.6655			−1.51477
$438$		0			0
$439$	−9.83276			−0.469292			−0.234646	−	0.972081i	$-0.575393\pi$
$439$	−9.83276			−0.469292			−0.234646	+	0.972081i	$0.575393\pi$
$440$		0			0
$441$		0			0
$442$	−1.15667	−	0.118877i	−0.0550174	−	0.00565441i
$443$	21.3522			1.01447			0.507236	−	0.861807i	$-0.330667\pi$
$443$	21.3522			1.01447			0.507236	+	0.861807i	$0.330667\pi$
$444$		0			0
$445$		0			0
$446$	10.1517	+	1.04334i	0.480695	+	0.0494034i
$447$		0			0
$448$	16.7300	−	23.7094i	0.790418	−	1.12016i
$449$	−20.3133			−0.958646			−0.479323	−	0.877639i	$-0.659118\pi$
$449$	−20.3133			−0.958646			−0.479323	+	0.877639i	$0.659118\pi$
$450$		0			0
$451$			32.6066i			1.53539i
$452$	3.69670	−	17.7944i	0.173878	−	0.836981i
$453$		0			0
$454$	0.167237	−	1.62721i	0.00784882	−	0.0763689i
$455$		0			0
$456$		0			0
$457$			3.35218i			0.156808i	0.996922	+	0.0784041i	$0.0249825\pi$
$457$			3.35218i			0.156808i	−0.996922	+	0.0784041i	$0.975018\pi$
$458$	19.8328	+	2.03831i	0.926724	+	0.0952441i
$459$		0			0
$460$		0			0
$461$		−	28.5089i		−	1.32779i	−0.747826	−	0.663895i	$-0.768902\pi$
$461$		−	28.5089i		−	1.32779i	0.747826	−	0.663895i	$-0.231098\pi$
$462$		0			0
$463$			23.6272i			1.09805i	0.835806	+	0.549025i	$0.185001\pi$
$463$			23.6272i			1.09805i	−0.835806	+	0.549025i	$0.814999\pi$
$464$	−3.18639	+	7.33804i	−0.147925	+	0.340660i
$465$		0			0
$466$	−20.5089	−	2.10780i	−0.950054	−	0.0976419i
$467$	29.5678			1.36823			0.684117	−	0.729373i	$-0.260188\pi$
$467$	29.5678			1.36823			0.684117	+	0.729373i	$0.260188\pi$
$468$		0			0
$469$			14.5089i			0.669957i
$470$		0			0
$471$		0			0
$472$	−5.94610	−	1.88666i	−0.273691	−	0.0868407i
$473$		−	45.0177i		−	2.06992i
$474$		0			0
$475$		0			0
$476$	10.0978	+	2.09775i	0.462830	+	0.0961503i
$477$		0			0
$478$	−2.78389	+	27.0872i	−0.127332	+	1.23894i
$479$	−22.0978			−1.00967			−0.504836	−	0.863215i	$-0.668447\pi$
$479$	−22.0978			−1.00967			−0.504836	+	0.863215i	$0.668447\pi$
$480$		0			0
$481$	−4.52998			−0.206549
$482$	1.97582	−	19.2247i	0.0899961	−	0.875661i
$483$		0			0
$484$	53.8676	+	11.1907i	2.44853	+	0.508668i
$485$		0			0
$486$		0			0
$487$		−	4.03831i		−	0.182993i	−0.995805	−	0.0914967i	$-0.970835\pi$
$487$		−	4.03831i		−	0.182993i	0.995805	−	0.0914967i	$-0.0291651\pi$
$488$	33.4600	+	10.6167i	1.51466	+	0.480593i
$489$		0			0
$490$		0			0
$491$		−	18.2056i		−	0.821605i	−0.911724	−	0.410802i	$-0.865249\pi$
$491$		−	18.2056i		−	0.821605i	0.911724	−	0.410802i	$-0.134751\pi$
$492$		0			0
$493$	−2.84333			−0.128057
$494$	−4.57834	−	0.470539i	−0.205989	−	0.0211705i
$495$		0			0
$496$	−9.45998	−	4.10780i	−0.424765	−	0.184446i
$497$		−	30.5089i		−	1.36851i
$498$		0			0
$499$		−	0.0594386i		−	0.00266084i	−0.999999	−	0.00133042i	$-0.999577\pi$
$499$		−	0.0594386i		−	0.00266084i	0.999999	−	0.00133042i	$-0.000423486\pi$
$500$		0			0
$501$		0			0
$502$	−10.0539	−	1.03329i	−0.448727	−	0.0461180i
$503$		−	2.03831i		−	0.0908839i	−0.998967	−	0.0454419i	$-0.985530\pi$
$503$		−	2.03831i		−	0.0908839i	0.998967	−	0.0454419i	$-0.0144696\pi$
$504$		0			0
$505$		0			0
$506$	−5.04888	+	49.1255i	−0.224450	+	2.18389i
$507$		0			0
$508$	4.25945	−	20.5033i	0.188983	−	0.909687i
$509$		−	40.7044i		−	1.80419i	−0.431539	−	0.902094i	$-0.642029\pi$
$509$		−	40.7044i		−	1.80419i	0.431539	−	0.902094i	$-0.357971\pi$
$510$		0			0
$511$	21.7633			0.962751
$512$	−18.0262	+	13.6768i	−0.796654	+	0.604436i
$513$		0			0
$514$	−10.8816	−	1.11836i	−0.479969	−	0.0493288i
$515$		0			0
$516$		0			0
$517$	42.0978			1.85146
$518$	39.9688	+	4.10780i	1.75613	+	0.180486i
$519$		0			0
$520$		0			0
$521$	−10.0000			−0.438108			−0.219054	−	0.975713i	$-0.570297\pi$
$521$	−10.0000			−0.438108			−0.219054	+	0.975713i	$0.570297\pi$
$522$		0			0
$523$	−35.3311			−1.54492			−0.772460	−	0.635064i	$-0.780974\pi$
$523$	−35.3311			−1.54492			−0.772460	+	0.635064i	$0.780974\pi$
$524$	5.47556	−	26.3572i	0.239201	−	1.15142i
$525$		0			0
$526$	−26.4252	−	2.71585i	−1.15219	−	0.118417i
$527$		−	3.66553i		−	0.159673i
$528$		0			0
$529$	−8.66553			−0.376762
$530$		0			0
$531$		0			0
$532$	39.9688	+	8.30330i	1.73287	+	0.359994i
$533$	−3.03883			−0.131626
$534$		0			0
$535$		0			0
$536$	3.42166	−	10.7839i	0.147793	−	0.465793i
$537$		0			0
$538$	−11.9703	−	1.23025i	−0.516075	−	0.0530397i
$539$			38.2056i			1.64563i
$540$		0			0
$541$			3.05892i			0.131513i	0.997836	+	0.0657567i	$0.0209461\pi$
$541$			3.05892i			0.131513i	−0.997836	+	0.0657567i	$0.979054\pi$
$542$	−4.48059	+	43.5960i	−0.192458	+	1.87261i
$543$		0			0
$544$	−7.01056	−	3.94056i	−0.300575	−	0.168950i
$545$		0			0
$546$		0			0
$547$	−32.0766			−1.37150			−0.685749	−	0.727838i	$-0.740525\pi$
$547$	−32.0766			−1.37150			−0.685749	+	0.727838i	$0.740525\pi$
$548$	−4.30330	+	20.7144i	−0.183828	+	0.884875i
$549$		0			0
$550$		0			0
$551$	−11.2544			−0.479455
$552$		0			0
$553$		−	19.6655i		−	0.836263i
$554$	−1.37636	+	13.3919i	−0.0584758	+	0.568969i
$555$		0			0
$556$	5.07306	−	24.4197i	0.215145	−	1.03563i
$557$	33.6655			1.42645			0.713227	−	0.700933i	$-0.247233\pi$
$557$	33.6655			1.42645			0.713227	+	0.700933i	$0.247233\pi$
$558$		0			0
$559$	4.19550			0.177451
$560$		0			0
$561$		0			0
$562$	1.97582	−	19.2247i	0.0833449	−	0.810945i
$563$	−5.35218			−0.225567			−0.112784	−	0.993620i	$-0.535977\pi$
$563$	−5.35218			−0.225567			−0.112784	+	0.993620i	$0.535977\pi$
$564$		0			0
$565$		0			0
$566$	−2.89169	+	28.1361i	−0.121547	+	1.18265i
$567$		0			0
$568$	−7.19499	+	22.6761i	−0.301895	+	0.951468i
$569$	5.58890			0.234299			0.117149	−	0.993114i	$-0.462624\pi$
$569$	5.58890			0.234299			0.117149	+	0.993114i	$0.462624\pi$
$570$		0			0
$571$		−	10.3728i		−	0.434088i	−0.976162	−	0.217044i	$-0.930359\pi$
$571$		−	10.3728i		−	0.434088i	0.976162	−	0.217044i	$-0.0696414\pi$
$572$	−1.45998	+	7.02775i	−0.0610447	+	0.293845i
$573$		0			0
$574$	26.8122	+	2.75562i	1.11912	+	0.115017i
$575$		0			0
$576$		0			0
$577$		−	21.6655i		−	0.901948i	−0.892537	−	0.450974i	$-0.851077\pi$
$577$		−	21.6655i		−	0.901948i	0.892537	−	0.450974i	$-0.148923\pi$
$578$	−2.16571	+	21.0723i	−0.0900816	+	0.876493i
$579$		0			0
$580$		0			0
$581$			11.8045i			0.489733i
$582$		0			0
$583$			12.4111i			0.514015i
$584$	−16.1758	−	5.13249i	−0.669361	−	0.212384i
$585$		0			0
$586$	0.623642	−	6.06803i	0.0257624	−	0.250668i
$587$	−1.90225			−0.0785142			−0.0392571	−	0.999229i	$-0.512499\pi$
$587$	−1.90225			−0.0785142			−0.0392571	+	0.999229i	$0.512499\pi$
$588$		0			0
$589$		−	14.5089i		−	0.597827i
$590$		0			0
$591$		0			0
$592$	−28.7386	−	12.4791i	−1.18115	−	0.512889i
$593$			2.57834i			0.105880i	0.998598	+	0.0529398i	$0.0168591\pi$
$593$			2.57834i			0.105880i	−0.998598	+	0.0529398i	$0.983141\pi$
$594$		0			0
$595$		0			0
$596$	0.813607	−	3.91638i	0.0333266	−	0.160421i
$597$		0			0
$598$	−4.57834	−	0.470539i	−0.187222	−	0.0192418i
$599$	26.7244			1.09193			0.545966	−	0.837808i	$-0.316163\pi$
$599$	26.7244			1.09193			0.545966	+	0.837808i	$0.316163\pi$
$600$		0			0
$601$	33.3311			1.35960			0.679801	−	0.733397i	$-0.262066\pi$
$601$	33.3311			1.35960			0.679801	+	0.733397i	$0.262066\pi$
$602$	−37.0177	−	3.80450i	−1.50873	−	0.155060i
$603$		0			0
$604$	−24.8222	−	5.15667i	−1.01000	−	0.209822i
$605$		0			0
$606$		0			0
$607$			21.9406i			0.890540i	0.895396	+	0.445270i	$0.146892\pi$
$607$			21.9406i			0.890540i	−0.895396	+	0.445270i	$0.853108\pi$
$608$	−27.7491	−	15.5975i	−1.12538	−	0.632562i
$609$		0			0
$610$		0			0
$611$			3.92337i			0.158723i
$612$		0			0
$613$	3.42166			0.138200			0.0690998	−	0.997610i	$-0.477987\pi$
$613$	3.42166			0.138200			0.0690998	+	0.997610i	$0.477987\pi$
$614$	−3.69670	+	35.9688i	−0.149187	+	1.45158i
$615$		0			0
$616$	19.2544	−	60.6832i	0.775783	−	2.44500i
$617$			19.7350i			0.794502i	0.917710	+	0.397251i	$0.130036\pi$
$617$			19.7350i			0.794502i	−0.917710	+	0.397251i	$0.869964\pi$
$618$		0			0
$619$			20.4705i			0.822780i	0.911459	+	0.411390i	$0.134957\pi$
$619$			20.4705i			0.822780i	−0.911459	+	0.411390i	$0.865043\pi$
$620$		0			0
$621$		0			0
$622$	−2.90276	+	28.2439i	−0.116390	+	1.13248i
$623$		−	48.0766i		−	1.92615i
$624$		0			0
$625$		0			0
$626$	−10.0680	−	1.03474i	−0.402400	−	0.0413566i
$627$		0			0
$628$	2.59247	+	0.538571i	0.103451	+	0.0214913i
$629$		−	11.1355i		−	0.444003i
$630$		0			0
$631$	1.08719			0.0432803			0.0216402	−	0.999766i	$-0.493111\pi$
$631$	1.08719			0.0432803			0.0216402	+	0.999766i	$0.493111\pi$
$632$	−4.63778	+	14.6167i	−0.184481	+	0.581419i
$633$		0			0
$634$	3.49523	−	34.0086i	0.138814	−	1.35065i
$635$		0			0
$636$		0			0
$637$	−3.56063			−0.141077
$638$	−1.79445	+	17.4600i	−0.0710430	+	0.691247i
$639$		0			0
$640$		0			0
$641$	27.9789			1.10510			0.552550	−	0.833480i	$-0.313655\pi$
$641$	27.9789			1.10510			0.552550	+	0.833480i	$0.313655\pi$
$642$		0			0
$643$	4.94108			0.194857			0.0974285	−	0.995243i	$-0.468938\pi$
$643$	4.94108			0.194857			0.0974285	+	0.995243i	$0.468938\pi$
$644$	39.9688	+	8.30330i	1.57499	+	0.327196i
$645$		0			0
$646$	1.15667	−	11.2544i	0.0455087	−	0.442799i
$647$		−	49.3694i		−	1.94091i	−0.241282	−	0.970455i	$-0.577568\pi$
$647$		−	49.3694i		−	1.94091i	0.241282	−	0.970455i	$-0.422432\pi$
$648$		0			0
$649$	−13.6867			−0.537248
$650$		0			0
$651$		0			0
$652$	29.8711	+	6.20555i	1.16984	+	0.243028i
$653$	−40.1744			−1.57214			−0.786072	−	0.618134i	$-0.787889\pi$
$653$	−40.1744			−1.57214			−0.786072	+	0.618134i	$0.787889\pi$
$654$		0			0
$655$		0			0
$656$	−19.2786	−	8.37133i	−0.752703	−	0.326846i
$657$		0			0
$658$	3.55773	−	34.6167i	0.138695	−	1.34950i
$659$			21.1255i			0.822933i	0.911425	+	0.411466i	$0.134983\pi$
$659$			21.1255i			0.822933i	−0.911425	+	0.411466i	$0.865017\pi$
$660$		0			0
$661$			10.9200i			0.424737i	0.977190	+	0.212368i	$0.0681177\pi$
$661$			10.9200i			0.424737i	−0.977190	+	0.212368i	$0.931882\pi$
$662$	38.2580	+	3.93197i	1.48694	+	0.152820i
$663$		0			0
$664$	2.78389	−	8.77384i	0.108036	−	0.340491i
$665$		0			0
$666$		0			0
$667$	−11.2544			−0.435773
$668$	4.38692	−	21.1169i	0.169735	−	0.817038i
$669$		0			0
$670$		0			0
$671$	77.0177			2.97324
$672$		0			0
$673$		−	18.0000i		−	0.693849i	−0.937893	−	0.346925i	$-0.887226\pi$
$673$		−	18.0000i		−	0.693849i	0.937893	−	0.346925i	$-0.112774\pi$
$674$	32.1063	+	3.29973i	1.23669	+	0.127101i
$675$		0			0
$676$	24.8015	+	5.15238i	0.953904	+	0.198168i
$677$	30.4877			1.17174			0.585869	−	0.810406i	$-0.300753\pi$
$677$	30.4877			1.17174			0.585869	+	0.810406i	$0.300753\pi$
$678$		0			0
$679$	17.5678			0.674189
$680$		0			0
$681$		0			0
$682$	−22.5089	−	2.31335i	−0.861908	−	0.0885827i
$683$	35.2544			1.34897			0.674487	−	0.738287i	$-0.264365\pi$
$683$	35.2544			1.34897			0.674487	+	0.738287i	$0.264365\pi$
$684$		0			0
$685$		0			0
$686$	−4.30330	−	0.442272i	−0.164301	−	0.0168860i
$687$		0			0
$688$	26.6167	+	11.5577i	1.01475	+	0.440634i
$689$	−1.15667			−0.0440658
$690$		0			0
$691$			28.1361i			1.07035i	0.844742	+	0.535173i	$0.179754\pi$
$691$			28.1361i			1.07035i	−0.844742	+	0.535173i	$0.820246\pi$
$692$	−26.7597	−	5.55918i	−1.01725	−	0.211328i
$693$		0			0
$694$	−3.42166	+	33.2927i	−0.129885	+	1.26378i
$695$		0			0
$696$		0			0
$697$		−	7.47002i		−	0.282947i
$698$	−49.1255	−	5.04888i	−1.85943	−	0.191103i
$699$		0			0
$700$		0			0
$701$		−	34.8222i		−	1.31522i	−0.753360	−	0.657608i	$-0.771568\pi$
$701$		−	34.8222i		−	1.31522i	0.753360	−	0.657608i	$-0.228432\pi$
$702$		0			0
$703$		−	44.0766i		−	1.66238i
$704$	−28.6222	+	40.5628i	−1.07874	+	1.52877i
$705$		0			0
$706$	−22.4111	−	2.30330i	−0.843453	−	0.0866859i
$707$	−7.25443			−0.272831
$708$		0			0
$709$		−	7.58890i		−	0.285007i	−0.989794	−	0.142504i	$-0.954485\pi$
$709$		−	7.58890i		−	0.285007i	0.989794	−	0.142504i	$-0.0455152\pi$
$710$		0			0
$711$		0			0
$712$	−11.3380	+	35.7336i	−0.424911	+	1.33917i
$713$		−	14.5089i		−	0.543361i
$714$		0			0
$715$		0			0
$716$	−3.68111	+	17.7194i	−0.137570	+	0.662206i
$717$		0			0
$718$	−1.21611	+	11.8328i	−0.0453849	+	0.441595i
$719$	−3.66553			−0.136701			−0.0683505	−	0.997661i	$-0.521774\pi$
$719$	−3.66553			−0.136701			−0.0683505	+	0.997661i	$0.521774\pi$
$720$		0			0
$721$	−8.96117			−0.333731
$722$	1.83124	−	17.8179i	0.0681515	−	0.663114i
$723$		0			0
$724$	−9.45998	+	45.5366i	−0.351577	+	1.69235i
$725$		0			0
$726$		0			0
$727$			36.1149i			1.33943i	0.742619	+	0.669714i	$0.233584\pi$
$727$			36.1149i			1.33943i	−0.742619	+	0.669714i	$0.766416\pi$
$728$	5.65548	+	1.79445i	0.209606	+	0.0665067i
$729$		0			0
$730$		0			0
$731$			10.3133i			0.381453i
$732$		0			0
$733$	−34.0071			−1.25608			−0.628041	−	0.778180i	$-0.716143\pi$
$733$	−34.0071			−1.25608			−0.628041	+	0.778180i	$0.716143\pi$
$734$	−34.3955	−	3.53500i	−1.26956	−	0.130479i
$735$		0			0
$736$	−27.7491	−	15.5975i	−1.02285	−	0.574931i
$737$		−	24.8222i		−	0.914338i
$738$		0			0
$739$		−	52.0172i		−	1.91348i	−0.290939	−	0.956742i	$-0.593968\pi$
$739$		−	52.0172i		−	1.91348i	0.290939	−	0.956742i	$-0.406032\pi$
$740$		0			0
$741$		0			0
$742$	10.2056	+	1.04888i	0.374658	+	0.0385054i
$743$			23.3139i			0.855303i	0.903944	+	0.427651i	$0.140659\pi$
$743$			23.3139i			0.855303i	−0.903944	+	0.427651i	$0.859341\pi$
$744$		0			0
$745$		0			0
$746$	−0.0241798	+	0.235269i	−0.000885286	+	0.00861383i
$747$		0			0
$748$	−17.2756	−	3.58890i	−0.631657	−	0.131223i
$749$		−	51.1355i		−	1.86845i
$750$		0			0
$751$	11.1083			0.405348			0.202674	−	0.979246i	$-0.435037\pi$
$751$	11.1083			0.405348			0.202674	+	0.979246i	$0.435037\pi$
$752$	−10.8081	+	24.8902i	−0.394130	+	0.907653i
$753$		0			0
$754$	−1.62721	−	0.167237i	−0.0592596	−	0.00609041i
$755$		0			0
$756$		0			0
$757$	13.3239			0.484266			0.242133	−	0.970243i	$-0.422153\pi$
$757$	13.3239			0.484266			0.242133	+	0.970243i	$0.422153\pi$
$758$	10.8675	+	1.11691i	0.394726	+	0.0405679i
$759$		0			0
$760$		0			0
$761$	17.1355			0.621163			0.310582	−	0.950547i	$-0.399476\pi$
$761$	17.1355			0.621163			0.310582	+	0.950547i	$0.399476\pi$
$762$		0			0
$763$	26.3133			0.952607
$764$	−15.6655	−	3.25443i	−0.566759	−	0.117741i
$765$		0			0
$766$	−2.28917	−	0.235269i	−0.0827110	−	0.00850063i
$767$		−	1.27555i		−	0.0460575i
$768$		0			0
$769$	−5.47002			−0.197254			−0.0986270	−	0.995124i	$-0.531445\pi$
$769$	−5.47002			−0.197254			−0.0986270	+	0.995124i	$0.531445\pi$
$770$		0			0
$771$		0			0
$772$	10.4408	−	50.2580i	0.375773	−	1.80882i
$773$	−3.15667			−0.113538			−0.0567688	−	0.998387i	$-0.518080\pi$
$773$	−3.15667			−0.113538			−0.0567688	+	0.998387i	$0.518080\pi$
$774$		0			0
$775$		0			0
$776$	−13.0575	−	4.14306i	−0.468736	−	0.148727i
$777$		0			0
$778$	−17.3225	−	1.78032i	−0.621040	−	0.0638274i
$779$		−	29.5678i		−	1.05938i
$780$		0			0
$781$			52.1955i			1.86770i
$782$	1.15667	−	11.2544i	0.0413626	−	0.402457i
$783$		0			0
$784$	−22.5890	−	9.80879i	−0.806749	−	0.350314i
$785$		0			0
$786$		0			0
$787$	31.1355			1.10986			0.554931	−	0.831896i	$-0.312745\pi$
$787$	31.1355			1.10986			0.554931	+	0.831896i	$0.312745\pi$
$788$	29.6797	+	6.16578i	1.05729	+	0.219647i
$789$		0			0
$790$		0			0
$791$	−32.9612			−1.17196
$792$		0			0
$793$			7.17780i			0.254891i
$794$	2.75971	−	26.8519i	0.0979383	−	0.952939i
$795$		0			0
$796$	−40.4877	−	8.41110i	−1.43505	−	0.298124i
$797$	10.0000			0.354218			0.177109	−	0.984191i	$-0.443325\pi$
$797$	10.0000			0.354218			0.177109	+	0.984191i	$0.443325\pi$
$798$		0			0
$799$	−9.64440			−0.341194
$800$		0			0
$801$		0			0
$802$	−2.08362	+	20.2736i	−0.0735751	+	0.715885i
$803$	−37.2333			−1.31393
$804$		0			0
$805$		0			0
$806$	0.215597	−	2.09775i	0.00759406	−	0.0738902i
$807$		0			0
$808$	5.39194	+	1.71083i	0.189688	+	0.0601868i
$809$	29.0388			1.02095			0.510475	−	0.859892i	$-0.329469\pi$
$809$	29.0388			1.02095			0.510475	+	0.859892i	$0.329469\pi$
$810$		0			0
$811$			2.58838i			0.0908904i	0.998967	+	0.0454452i	$0.0144706\pi$
$811$			2.58838i			0.0908904i	−0.998967	+	0.0454452i	$0.985529\pi$
$812$	14.2056	+	2.95112i	0.498517	+	0.103564i
$813$		0			0
$814$	−68.3799	−	7.02775i	−2.39672	−	0.246323i
$815$		0			0
$816$		0			0
$817$			40.8222i			1.42819i
$818$	−1.20198	+	11.6952i	−0.0420262	+	0.408915i
$819$		0			0
$820$		0			0
$821$			38.1955i			1.33303i	0.745491	+	0.666516i	$0.232215\pi$
$821$			38.1955i			1.33303i	−0.745491	+	0.666516i	$0.767785\pi$
$822$		0			0
$823$		−	18.3517i		−	0.639699i	−0.947468	−	0.319849i	$-0.896368\pi$
$823$		−	18.3517i		−	0.639699i	0.947468	−	0.319849i	$-0.103632\pi$
$824$	6.66050	+	2.11334i	0.232030	+	0.0736216i
$825$		0			0
$826$	−1.15667	+	11.2544i	−0.0402458	+	0.391592i
$827$	−20.0000			−0.695468			−0.347734	−	0.937593i	$-0.613049\pi$
$827$	−20.0000			−0.695468			−0.347734	+	0.937593i	$0.613049\pi$
$828$		0			0
$829$			24.7456i			0.859449i	0.902960	+	0.429725i	$0.141389\pi$
$829$			24.7456i			0.859449i	−0.902960	+	0.429725i	$0.858611\pi$
$830$		0			0
$831$		0			0
$832$	−3.78032	−	2.66750i	−0.131059	−	0.0924788i
$833$		−	8.75272i		−	0.303264i
$834$		0			0
$835$		0			0
$836$	−68.3799	−	14.2056i	−2.36497	−	0.491309i
$837$		0			0
$838$	10.3572	+	1.06446i	0.357784	+	0.0367712i
$839$	−53.4288			−1.84457			−0.922284	−	0.386514i	$-0.873679\pi$
$839$	−53.4288			−1.84457			−0.922284	+	0.386514i	$0.873679\pi$
$840$		0			0
$841$	25.0000			0.862069
$842$	42.3416	+	4.35166i	1.45919	+	0.149968i
$843$		0			0
$844$	−0.829192	+	3.99141i	−0.0285420	+	0.137390i
$845$		0			0
$846$		0			0
$847$		−	99.7805i		−	3.42850i
$848$	−7.33804	−	3.18639i	−0.251989	−	0.109421i
$849$		0			0
$850$		0			0
$851$		−	44.0766i		−	1.51093i
$852$		0			0
$853$	29.0661			0.995203			0.497602	−	0.867406i	$-0.334214\pi$
$853$	29.0661			0.995203			0.497602	+	0.867406i	$0.334214\pi$
$854$	6.50885	−	63.3311i	0.222728	−	2.16714i
$855$		0			0
$856$	−12.0594	+	38.0071i	−0.412183	+	1.29906i
$857$		−	10.2439i		−	0.349924i	−0.984575	−	0.174962i	$-0.944020\pi$
$857$		−	10.2439i		−	0.349924i	0.984575	−	0.174962i	$-0.0559802\pi$
$858$		0			0
$859$			10.9794i			0.374612i	0.982302	+	0.187306i	$0.0599756\pi$
$859$			10.9794i			0.374612i	−0.982302	+	0.187306i	$0.940024\pi$
$860$		0			0
$861$		0			0
$862$	1.21611	−	11.8328i	0.0414210	−	0.403026i
$863$		−	38.8605i		−	1.32283i	−0.750021	−	0.661414i	$-0.769957\pi$
$863$		−	38.8605i		−	1.32283i	0.750021	−	0.661414i	$-0.230043\pi$
$864$		0			0
$865$		0			0
$866$	6.06803	+	0.623642i	0.206200	+	0.0211922i
$867$		0			0
$868$	−3.80450	+	18.3133i	−0.129133	+	0.621596i
$869$			33.6444i			1.14131i
$870$		0			0
$871$	2.31335			0.0783848
$872$	−19.5577	−	6.20555i	−0.662308	−	0.210146i
$873$		0			0
$874$	4.57834	−	44.5472i	0.154865	−	1.50683i
$875$		0			0
$876$		0			0
$877$	−22.3416			−0.754423			−0.377211	−	0.926127i	$-0.623117\pi$
$877$	−22.3416			−0.754423			−0.377211	+	0.926127i	$0.623117\pi$
$878$	1.42166	−	13.8328i	0.0479788	−	0.466833i
$879$		0			0
$880$		0			0
$881$	−9.88112			−0.332903			−0.166452	−	0.986050i	$-0.553231\pi$
$881$	−9.88112			−0.332903			−0.166452	+	0.986050i	$0.553231\pi$
$882$		0			0
$883$	−10.6277			−0.357652			−0.178826	−	0.983881i	$-0.557230\pi$
$883$	−10.6277			−0.357652			−0.178826	+	0.983881i	$0.557230\pi$
$884$	0.334474	−	1.61003i	0.0112496	−	0.0541510i
$885$		0			0
$886$	−3.08719	+	30.0383i	−0.103716	+	1.00916i
$887$			11.6061i			0.389694i	0.980834	+	0.194847i	$0.0624211\pi$
$887$			11.6061i			0.389694i	−0.980834	+	0.194847i	$0.937579\pi$
$888$		0			0
$889$	−37.9789			−1.27377
$890$		0			0
$891$		0			0
$892$	−2.93554	+	14.1305i	−0.0982891	+	0.473125i
$893$	−38.1744			−1.27746
$894$		0			0
$895$		0			0
$896$	30.9355	+	26.9638i	1.03348	+	0.900797i
$897$		0			0
$898$	2.93699	−	28.5769i	0.0980086	−	0.953623i
$899$		−	5.15667i		−	0.171985i
$900$		0			0
$901$		−	2.84333i		−	0.0947249i
$902$	−45.8711	−	4.71440i	−1.52734	−	0.156972i
$903$		0			0
$904$	24.4988	+	7.77332i	0.814818	+	0.258537i
$905$		0			0
$906$		0			0
$907$	0.195504			0.00649159			0.00324580	−	0.999995i	$-0.498967\pi$
$907$	0.195504			0.00649159			0.00324580	+	0.999995i	$0.498967\pi$
$908$	2.26499	+	0.470539i	0.0751663	+	0.0156154i
$909$		0			0
$910$		0			0
$911$	7.88112			0.261113			0.130557	−	0.991441i	$-0.458324\pi$
$911$	7.88112			0.261113			0.130557	+	0.991441i	$0.458324\pi$
$912$		0			0
$913$		−	20.1955i		−	0.668374i
$914$	−4.71585	−	0.484672i	−0.155987	−	0.0160315i
$915$		0			0
$916$	−5.73501	+	27.6061i	−0.189490	+	0.912131i
$917$	−48.8222			−1.61225
$918$		0			0
$919$	−9.75614			−0.321825			−0.160913	−	0.986969i	$-0.551444\pi$
$919$	−9.75614			−0.321825			−0.160913	+	0.986969i	$0.551444\pi$
$920$		0			0
$921$		0			0
$922$	40.1063	+	4.12193i	1.32083	+	0.135749i
$923$	−4.86445			−0.160115
$924$		0			0
$925$		0			0
$926$	−33.2388	−	3.41612i	−1.09230	−	0.112261i
$927$		0			0
$928$	−9.86248	−	5.54359i	−0.323752	−	0.181977i
$929$	6.82220			0.223829			0.111915	−	0.993718i	$-0.464302\pi$
$929$	6.82220			0.223829			0.111915	+	0.993718i	$0.464302\pi$
$930$		0			0
$931$		−	34.6449i		−	1.13544i
$932$	5.93051	−	28.5472i	0.194260	−	0.935093i
$933$		0			0
$934$	−4.27504	+	41.5960i	−0.139883	+	1.36106i
$935$		0			0
$936$		0			0
$937$		−	57.5266i		−	1.87931i	−0.342123	−	0.939655i	$-0.611146\pi$
$937$		−	57.5266i		−	1.87931i	0.342123	−	0.939655i	$-0.388854\pi$
$938$	−20.4111	−	2.09775i	−0.666446	−	0.0684940i
$939$		0			0
$940$		0			0
$941$			0.508852i			0.0165881i	0.999966	+	0.00829405i	$0.00264011\pi$
$941$			0.508852i			0.0165881i	−0.999966	+	0.00829405i	$0.997360\pi$
$942$		0			0
$943$		−	29.5678i		−	0.962859i
$944$	3.51388	−	8.09221i	0.114367	−	0.263379i
$945$		0			0
$946$	63.3311	+	6.50885i	2.05907	+	0.211621i
$947$	−1.68665			−0.0548088			−0.0274044	−	0.999624i	$-0.508724\pi$
$947$	−1.68665			−0.0548088			−0.0274044	+	0.999624i	$0.508724\pi$
$948$		0			0
$949$		−	3.47002i		−	0.112642i
$950$		0			0
$951$		0			0
$952$	−4.41110	+	13.9022i	−0.142965	+	0.450574i
$953$		−	9.22616i		−	0.298865i	−0.988772	−	0.149432i	$-0.952255\pi$
$953$		−	9.22616i		−	0.298865i	0.988772	−	0.149432i	$-0.0477446\pi$
$954$		0			0
$955$		0			0
$956$	−37.7038	−	7.83276i	−1.21943	−	0.253330i
$957$		0			0
$958$	3.19499	−	31.0872i	0.103225	−	1.00438i
$959$	38.3699			1.23903
$960$		0			0
$961$	−24.3522			−0.785554
$962$	0.654963	−	6.37279i	0.0211169	−	0.205467i
$963$		0			0
$964$	26.7597	+	5.55918i	0.861872	+	0.179049i
$965$		0			0
$966$		0			0
$967$		−	12.2338i		−	0.393413i	−0.980462	−	0.196707i	$-0.936975\pi$
$967$		−	12.2338i		−	0.393413i	0.980462	−	0.196707i	$-0.0630246\pi$
$968$	−23.5315	+	74.1631i	−0.756331	+	2.38369i
$969$		0			0
$970$		0			0
$971$		−	33.2444i		−	1.06686i	−0.845843	−	0.533431i	$-0.820902\pi$
$971$		−	33.2444i		−	1.06686i	0.845843	−	0.533431i	$-0.179098\pi$
$972$		0			0
$973$	−45.2333			−1.45011
$974$	5.68111	+	0.583877i	0.182035	+	0.0187086i
$975$		0			0
$976$	−19.7733	+	45.5366i	−0.632929	+	1.45759i
$977$			7.93051i			0.253720i	0.991921	+	0.126860i	$0.0404898\pi$
$977$			7.93051i			0.253720i	−0.991921	+	0.126860i	$0.959510\pi$
$978$		0			0
$979$			82.2510i			2.62875i
$980$		0			0
$981$		0			0
$982$	25.6116	+	2.63224i	0.817300	+	0.0839980i
$983$		−	41.8993i		−	1.33638i	−0.743990	−	0.668191i	$-0.767069\pi$
$983$		−	41.8993i		−	1.33638i	0.743990	−	0.668191i	$-0.232931\pi$
$984$		0			0
$985$		0			0
$986$	0.411100	−	4.00000i	0.0130921	−	0.127386i
$987$		0			0
$988$	1.32391	−	6.37279i	0.0421192	−	0.202745i
$989$			40.8222i			1.29807i
$990$		0			0
$991$	−35.1849			−1.11769			−0.558843	−	0.829273i	$-0.688755\pi$
$991$	−35.1849			−1.11769			−0.558843	+	0.829273i	$0.688755\pi$
$992$	7.14663	−	12.7144i	0.226906	−	0.403683i
$993$		0			0
$994$	42.9200	+	4.41110i	1.36134	+	0.139912i
$995$		0			0
$996$		0			0
$997$	8.04836			0.254894			0.127447	−	0.991845i	$-0.459322\pi$
$997$	8.04836			0.254894			0.127447	+	0.991845i	$0.459322\pi$
$998$	0.0836184	+	0.00859389i	0.00264690	+	0.000272035i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1800.2.d.r.1549.4		6
3.2	odd	2		600.2.d.f.349.3		6
4.3	odd	2		7200.2.d.r.2449.2		6
5.2	odd	4		360.2.k.f.181.1		6
5.3	odd	4		1800.2.k.p.901.6		6
5.4	even	2		1800.2.d.q.1549.3		6
8.3	odd	2		7200.2.d.q.2449.2		6
8.5	even	2		1800.2.d.q.1549.4		6
12.11	even	2		2400.2.d.e.49.2		6
15.2	even	4		120.2.k.b.61.6	yes	6
15.8	even	4		600.2.k.c.301.1		6
15.14	odd	2		600.2.d.e.349.4		6
20.3	even	4		7200.2.k.p.3601.2		6
20.7	even	4		1440.2.k.f.721.6		6
20.19	odd	2		7200.2.d.q.2449.5		6
24.5	odd	2		600.2.d.e.349.3		6
24.11	even	2		2400.2.d.f.49.2		6
40.3	even	4		7200.2.k.p.3601.1		6
40.13	odd	4		1800.2.k.p.901.5		6
40.19	odd	2		7200.2.d.r.2449.5		6
40.27	even	4		1440.2.k.f.721.3		6
40.29	even	2	inner	1800.2.d.r.1549.3		6
40.37	odd	4		360.2.k.f.181.2		6
60.23	odd	4		2400.2.k.c.1201.1		6
60.47	odd	4		480.2.k.b.241.6		6
60.59	even	2		2400.2.d.f.49.5		6
120.29	odd	2		600.2.d.f.349.4		6
120.53	even	4		600.2.k.c.301.2		6
120.59	even	2		2400.2.d.e.49.5		6
120.77	even	4		120.2.k.b.61.5	✓	6
120.83	odd	4		2400.2.k.c.1201.4		6
120.107	odd	4		480.2.k.b.241.3		6
240.77	even	4		3840.2.a.bq.1.3		3
240.107	odd	4		3840.2.a.br.1.1		3
240.197	even	4		3840.2.a.bp.1.3		3
240.227	odd	4		3840.2.a.bo.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.k.b.61.5	✓	6	120.77	even	4
120.2.k.b.61.6	yes	6	15.2	even	4
360.2.k.f.181.1		6	5.2	odd	4
360.2.k.f.181.2		6	40.37	odd	4
480.2.k.b.241.3		6	120.107	odd	4
480.2.k.b.241.6		6	60.47	odd	4
600.2.d.e.349.3		6	24.5	odd	2
600.2.d.e.349.4		6	15.14	odd	2
600.2.d.f.349.3		6	3.2	odd	2
600.2.d.f.349.4		6	120.29	odd	2
600.2.k.c.301.1		6	15.8	even	4
600.2.k.c.301.2		6	120.53	even	4
1440.2.k.f.721.3		6	40.27	even	4
1440.2.k.f.721.6		6	20.7	even	4
1800.2.d.q.1549.3		6	5.4	even	2
1800.2.d.q.1549.4		6	8.5	even	2
1800.2.d.r.1549.3		6	40.29	even	2	inner
1800.2.d.r.1549.4		6	1.1	even	1	trivial
1800.2.k.p.901.5		6	40.13	odd	4
1800.2.k.p.901.6		6	5.3	odd	4
2400.2.d.e.49.2		6	12.11	even	2
2400.2.d.e.49.5		6	120.59	even	2
2400.2.d.f.49.2		6	24.11	even	2
2400.2.d.f.49.5		6	60.59	even	2
2400.2.k.c.1201.1		6	60.23	odd	4
2400.2.k.c.1201.4		6	120.83	odd	4
3840.2.a.bo.1.1		3	240.227	odd	4
3840.2.a.bp.1.3		3	240.197	even	4
3840.2.a.bq.1.3		3	240.77	even	4
3840.2.a.br.1.1		3	240.107	odd	4
7200.2.d.q.2449.2		6	8.3	odd	2
7200.2.d.q.2449.5		6	20.19	odd	2
7200.2.d.r.2449.2		6	4.3	odd	2
7200.2.d.r.2449.5		6	40.19	odd	2
7200.2.k.p.3601.1		6	40.3	even	4
7200.2.k.p.3601.2		6	20.3	even	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:	\( N \)	\(=\)	\( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1800.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.144584 + 1.40680i) q^{2} +(-1.95819 - 0.406803i) q^{4} +3.62721i q^{7} +(0.855416 - 2.69597i) q^{8} +O(q^{10})\)	\(q+(-0.144584 + 1.40680i) q^{2} +(-1.95819 - 0.406803i) q^{4} +3.62721i q^{7} +(0.855416 - 2.69597i) q^{8} -6.20555i q^{11} +0.578337 q^{13} +(-5.10278 - 0.524438i) q^{14} +(3.66902 + 1.59320i) q^{16} +1.42166i q^{17} +5.62721i q^{19} +(8.72999 + 0.897225i) q^{22} +5.62721i q^{23} +(-0.0836184 + 0.813607i) q^{26} +(1.47556 - 7.10278i) q^{28} +2.00000i q^{29} -2.57834 q^{31} +(-2.77180 + 4.93124i) q^{32} +(-2.00000 - 0.205550i) q^{34} -7.83276 q^{37} +(-7.91638 - 0.813607i) q^{38} -5.25443 q^{41} +7.25443 q^{43} +(-2.52444 + 12.1517i) q^{44} +(-7.91638 - 0.813607i) q^{46} +6.78389i q^{47} -6.15667 q^{49} +(-1.13249 - 0.235269i) q^{52} -2.00000 q^{53} +(9.77886 + 3.10278i) q^{56} +(-2.81361 - 0.289169i) q^{58} -2.20555i q^{59} +12.4111i q^{61} +(0.372787 - 3.62721i) q^{62} +(-6.53653 - 4.61235i) q^{64} +4.00000 q^{67} +(0.578337 - 2.78389i) q^{68} -8.41110 q^{71} -6.00000i q^{73} +(1.13249 - 11.0192i) q^{74} +(2.28917 - 11.0192i) q^{76} +22.5089 q^{77} -5.42166 q^{79} +(0.759707 - 7.39194i) q^{82} +3.25443 q^{83} +(-1.04888 + 10.2056i) q^{86} +(-16.7300 - 5.30833i) q^{88} -13.2544 q^{89} +2.09775i q^{91} +(2.28917 - 11.0192i) q^{92} +(-9.54359 - 0.980843i) q^{94} -4.84333i q^{97} +(0.890158 - 8.66123i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{4} + 6 q^{8}+O(q^{10}) \) 6 * q + 2 * q^4 + 6 * q^8	\( 6 q + 2 q^{4} + 6 q^{8} - 16 q^{14} + 10 q^{16} + 12 q^{22} - 28 q^{26} + 20 q^{28} - 12 q^{31} + 10 q^{32} - 12 q^{34} + 8 q^{37} - 20 q^{38} + 20 q^{41} - 8 q^{43} - 4 q^{44} - 20 q^{46} - 30 q^{49} - 12 q^{52} - 12 q^{53} - 4 q^{56} - 4 q^{58} + 28 q^{62} - 22 q^{64} + 24 q^{67} + 8 q^{71} + 12 q^{74} + 12 q^{76} + 32 q^{77} - 36 q^{79} - 16 q^{82} - 32 q^{83} + 16 q^{86} - 60 q^{88} - 28 q^{89} + 12 q^{92} - 4 q^{94} + 56 q^{98}+O(q^{100}) \) 6 * q + 2 * q^4 + 6 * q^8 - 16 * q^14 + 10 * q^16 + 12 * q^22 - 28 * q^26 + 20 * q^28 - 12 * q^31 + 10 * q^32 - 12 * q^34 + 8 * q^37 - 20 * q^38 + 20 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 - 30 * q^49 - 12 * q^52 - 12 * q^53 - 4 * q^56 - 4 * q^58 + 28 * q^62 - 22 * q^64 + 24 * q^67 + 8 * q^71 + 12 * q^74 + 12 * q^76 + 32 * q^77 - 36 * q^79 - 16 * q^82 - 32 * q^83 + 16 * q^86 - 60 * q^88 - 28 * q^89 + 12 * q^92 - 4 * q^94 + 56 * q^98

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