LMFDB - Embedded newform 1800.2.d.q.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.q.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	$0.385070\pi$
$11$			6.20555i			1.87104i	−0.353269	+	0.935522i	$0.614930\pi$
$12$		0			0
$13$	−0.578337			−0.160402			−0.0802009	−	0.996779i	$-0.525556\pi$
$13$	−0.578337			−0.160402			−0.0802009	+	0.996779i	$0.525556\pi$
$14$	−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	$-0.776655\pi$
$19$		−	5.62721i		−	1.29097i	0.763772	−	0.645486i	$-0.223345\pi$
$20$		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	$-0.940546\pi$
$29$		−	2.00000i		−	0.371391i	0.982607	−	0.185695i	$-0.0594537\pi$
$30$		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	$-0.277336\pi$
$37$	7.83276			1.28770			0.643849	+	0.765152i	$0.277336\pi$
$38$	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	$-0.686572\pi$
$43$	−7.25443			−1.10629			−0.553145	+	0.833085i	$0.686572\pi$
$44$	−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	$-0.456138\pi$
$53$	2.00000			0.274721			0.137361	+	0.990521i	$0.456138\pi$
$54$		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	$0.0458579\pi$
$59$			2.20555i			0.287138i	−0.989640	+	0.143569i	$0.954142\pi$
$60$		0			0
$61$		−	12.4111i		−	1.58908i	−0.607213	−	0.794539i	$-0.707712\pi$
$61$		−	12.4111i		−	1.58908i	0.607213	−	0.794539i	$-0.292288\pi$
$62$	−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	$-0.578571\pi$
$67$	−4.00000			−0.488678			−0.244339	+	0.969690i	$0.578571\pi$
$68$	−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	$-0.557160\pi$
$83$	−3.25443			−0.357220			−0.178610	+	0.983920i	$0.557160\pi$
$84$		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	$-0.968274\pi$
$101$		−	2.00000i		−	0.199007i	0.995037	−	0.0995037i	$-0.0317255\pi$
$102$		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	$-0.261354\pi$
$107$	14.0978			1.36288			0.681441	+	0.731873i	$0.261354\pi$
$108$		0			0
$109$			7.25443i			0.694848i	0.937708	+	0.347424i	$0.112944\pi$
$109$			7.25443i			0.694848i	−0.937708	+	0.347424i	$0.887056\pi$
$110$		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	$-0.799915\pi$
$131$		−	13.4600i		−	1.17600i	0.808860	−	0.588002i	$-0.200085\pi$
$132$		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	$-0.822616\pi$
$139$		−	12.4705i		−	1.05774i	0.848704	−	0.528869i	$-0.177384\pi$
$140$		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	$-0.973894\pi$
$149$		−	2.00000i		−	0.163846i	0.996639	−	0.0819232i	$-0.0261062\pi$
$150$		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	$-0.483176\pi$
$157$	1.32391			0.105660			0.0528298	+	0.998604i	$0.483176\pi$
$158$	−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	$-0.296197\pi$
$163$	15.2544			1.19482			0.597409	+	0.801936i	$0.296197\pi$
$164$	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	$-0.673876\pi$
$173$	−13.6655			−1.03897			−0.519485	+	0.854479i	$0.673876\pi$
$174$		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	$0.109809\pi$
$179$			9.04888i			0.676345i	−0.941084	+	0.338172i	$0.890191\pi$
$180$		0			0
$181$			23.2544i			1.72849i	0.503073	+	0.864244i	$0.332203\pi$
$181$			23.2544i			1.72849i	−0.503073	+	0.864244i	$0.667797\pi$
$182$	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	$-0.318449\pi$
$197$	15.1567			1.07987			0.539934	+	0.841707i	$0.318449\pi$
$198$		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	$0.0223515\pi$
$211$			2.03831i			0.140323i	−0.997536	+	0.0701616i	$0.977648\pi$
$212$	−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	$-0.487778\pi$
$227$	1.15667			0.0767712			0.0383856	+	0.999263i	$0.487778\pi$
$228$		0			0
$229$			14.0978i			0.931606i	0.884889	+	0.465803i	$0.154234\pi$
$229$			14.0978i			0.931606i	−0.884889	+	0.465803i	$0.845766\pi$
$230$		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	$-0.927584\pi$
$251$		−	7.14663i		−	0.451091i	0.974233	−	0.225546i	$-0.0724165\pi$
$252$		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	$-0.916476\pi$
$269$		−	8.50885i		−	0.518794i	0.965771	−	0.259397i	$-0.0835238\pi$
$270$		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	$-0.592320\pi$
$277$	−9.51941			−0.571966			−0.285983	+	0.958235i	$0.592320\pi$
$278$	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	$-0.702626\pi$
$283$	−20.0000			−1.18888			−0.594438	+	0.804141i	$0.702626\pi$
$284$	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	$-0.459788\pi$
$293$	4.31335			0.251989			0.125994	+	0.992031i	$0.459788\pi$
$294$		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	$-0.760301\pi$
$307$	−25.5678			−1.45923			−0.729615	+	0.683858i	$0.760301\pi$
$308$	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	$-0.262464\pi$
$317$	24.1744			1.35777			0.678884	+	0.734245i	$0.262464\pi$
$318$		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	$0.268691\pi$
$331$			27.1950i			1.49477i	−0.664390	+	0.747386i	$0.731309\pi$
$332$	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	$-0.719089\pi$
$347$	−23.6655			−1.27043			−0.635216	+	0.772335i	$0.719089\pi$
$348$		0			0
$349$		−	34.9200i		−	1.86922i	−0.355671	−	0.934611i	$-0.615748\pi$
$349$		−	34.9200i		−	1.86922i	0.355671	−	0.934611i	$-0.384252\pi$
$350$		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	$-0.501378\pi$
$373$	−0.167237			−0.00865920			−0.00432960	+	0.999991i	$0.501378\pi$
$374$	−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	$0.0635753\pi$
$379$			7.72496i			0.396805i	−0.980121	+	0.198402i	$0.936425\pi$
$380$		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	$-0.898949\pi$
$389$		−	12.3133i		−	0.624312i	0.950031	−	0.312156i	$-0.101051\pi$
$390$		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	$-0.341007\pi$
$397$	19.0872			0.957959			0.478979	+	0.877826i	$0.341007\pi$
$398$	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	$0.0575561\pi$
$419$			7.36222i			0.359668i	−0.983697	+	0.179834i	$0.942444\pi$
$420$		0			0
$421$			30.0978i			1.46687i	0.679757	+	0.733437i	$0.262085\pi$
$421$			30.0978i			1.46687i	−0.679757	+	0.733437i	$0.737915\pi$
$422$	−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	$-0.669333\pi$
$443$	−21.3522			−1.01447			−0.507236	+	0.861807i	$0.669333\pi$
$444$		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	$0.231098\pi$
$461$			28.5089i			1.32779i	−0.747826	+	0.663895i	$0.768902\pi$
$462$		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	$-0.739812\pi$
$467$	−29.5678			−1.36823			−0.684117	+	0.729373i	$0.739812\pi$
$468$		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	$0.134751\pi$
$491$			18.2056i			0.821605i	−0.911724	+	0.410802i	$0.865249\pi$
$492$		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	$0.000423486\pi$
$499$			0.0594386i			0.00266084i	−0.999999	+	0.00133042i	$0.999577\pi$
$500$		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	$0.357971\pi$
$509$			40.7044i			1.80419i	−0.431539	+	0.902094i	$0.642029\pi$
$510$		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	$-0.219026\pi$
$523$	35.3311			1.54492			0.772460	+	0.635064i	$0.219026\pi$
$524$	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	$-0.979054\pi$
$541$		−	3.05892i		−	0.131513i	0.997836	−	0.0657567i	$-0.0209461\pi$
$542$	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	$-0.259475\pi$
$547$	32.0766			1.37150			0.685749	+	0.727838i	$0.259475\pi$
$548$	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	$-0.752767\pi$
$557$	−33.6655			−1.42645			−0.713227	+	0.700933i	$0.752767\pi$
$558$		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	$-0.464023\pi$
$563$	5.35218			0.225567			0.112784	+	0.993620i	$0.464023\pi$
$564$		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	$0.0696414\pi$
$571$			10.3728i			0.434088i	−0.976162	+	0.217044i	$0.930359\pi$
$572$	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	$-0.487501\pi$
$587$	1.90225			0.0785142			0.0392571	+	0.999229i	$0.487501\pi$
$588$		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	$-0.522013\pi$
$613$	−3.42166			−0.138200			−0.0690998	+	0.997610i	$0.522013\pi$
$614$	−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	$-0.865043\pi$
$619$		−	20.4705i		−	0.822780i	0.911459	−	0.411390i	$-0.134957\pi$
$620$		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	$-0.531062\pi$
$643$	−4.94108			−0.194857			−0.0974285	+	0.995243i	$0.531062\pi$
$644$	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	$-0.212111\pi$
$653$	40.1744			1.57214			0.786072	+	0.618134i	$0.212111\pi$
$654$		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	$-0.865017\pi$
$659$		−	21.1255i		−	0.822933i	0.911425	−	0.411466i	$-0.134983\pi$
$660$		0			0
$661$		−	10.9200i		−	0.424737i	−0.977190	−	0.212368i	$-0.931882\pi$
$661$		−	10.9200i		−	0.424737i	0.977190	−	0.212368i	$-0.0681177\pi$
$662$	−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	$-0.699247\pi$
$677$	−30.4877			−1.17174			−0.585869	+	0.810406i	$0.699247\pi$
$678$		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	$-0.735635\pi$
$683$	−35.2544			−1.34897			−0.674487	+	0.738287i	$0.735635\pi$
$684$		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	$-0.820246\pi$
$691$		−	28.1361i		−	1.07035i	0.844742	−	0.535173i	$-0.179754\pi$
$692$	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	$0.228432\pi$
$701$			34.8222i			1.31522i	−0.753360	+	0.657608i	$0.771568\pi$
$702$		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	$0.0455152\pi$
$709$			7.58890i			0.285007i	−0.989794	+	0.142504i	$0.954485\pi$
$710$		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	$-0.283857\pi$
$733$	34.0071			1.25608			0.628041	+	0.778180i	$0.283857\pi$
$734$	−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	$0.406032\pi$
$739$			52.0172i			1.91348i	−0.290939	+	0.956742i	$0.593968\pi$
$740$		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	$-0.577847\pi$
$757$	−13.3239			−0.484266			−0.242133	+	0.970243i	$0.577847\pi$
$758$	−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	$-0.481920\pi$
$773$	3.15667			0.113538			0.0567688	+	0.998387i	$0.481920\pi$
$774$		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	$-0.687255\pi$
$787$	−31.1355			−1.10986			−0.554931	+	0.831896i	$0.687255\pi$
$788$	−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	$-0.556675\pi$
$797$	−10.0000			−0.354218			−0.177109	+	0.984191i	$0.556675\pi$
$798$		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	$-0.985529\pi$
$811$		−	2.58838i		−	0.0908904i	0.998967	−	0.0454452i	$-0.0144706\pi$
$812$	−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	$-0.767785\pi$
$821$		−	38.1955i		−	1.33303i	0.745491	−	0.666516i	$-0.232215\pi$
$822$		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	$-0.386951\pi$
$827$	20.0000			0.695468			0.347734	+	0.937593i	$0.386951\pi$
$828$		0			0
$829$		−	24.7456i		−	0.859449i	−0.902960	−	0.429725i	$-0.858611\pi$
$829$		−	24.7456i		−	0.859449i	0.902960	−	0.429725i	$-0.141389\pi$
$830$		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	$-0.665786\pi$
$853$	−29.0661			−0.995203			−0.497602	+	0.867406i	$0.665786\pi$
$854$	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	$-0.940024\pi$
$859$		−	10.9794i		−	0.374612i	0.982302	−	0.187306i	$-0.0599756\pi$
$860$		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	$-0.376883\pi$
$877$	22.3416			0.754423			0.377211	+	0.926127i	$0.376883\pi$
$878$	−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	$-0.442770\pi$
$883$	10.6277			0.357652			0.178826	+	0.983881i	$0.442770\pi$
$884$	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	$-0.501033\pi$
$907$	−0.195504			−0.00649159			−0.00324580	+	0.999995i	$0.501033\pi$
$908$	−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	$-0.997360\pi$
$941$		−	0.508852i		−	0.0165881i	0.999966	−	0.00829405i	$-0.00264011\pi$
$942$		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	$-0.491276\pi$
$947$	1.68665			0.0548088			0.0274044	+	0.999624i	$0.491276\pi$
$948$		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	$0.179098\pi$
$971$			33.2444i			1.06686i	−0.845843	+	0.533431i	$0.820902\pi$
$972$		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	$-0.540678\pi$
$997$	−8.04836			−0.254894			−0.127447	+	0.991845i	$0.540678\pi$
$998$	−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.q.1549.4		6
3.2	odd	2		600.2.d.e.349.3		6
4.3	odd	2		7200.2.d.q.2449.2		6
5.2	odd	4		360.2.k.f.181.2		6
5.3	odd	4		1800.2.k.p.901.5		6
5.4	even	2		1800.2.d.r.1549.3		6
8.3	odd	2		7200.2.d.r.2449.2		6
8.5	even	2		1800.2.d.r.1549.4		6
12.11	even	2		2400.2.d.f.49.2		6
15.2	even	4		120.2.k.b.61.5	✓	6
15.8	even	4		600.2.k.c.301.2		6
15.14	odd	2		600.2.d.f.349.4		6
20.3	even	4		7200.2.k.p.3601.1		6
20.7	even	4		1440.2.k.f.721.3		6
20.19	odd	2		7200.2.d.r.2449.5		6
24.5	odd	2		600.2.d.f.349.3		6
24.11	even	2		2400.2.d.e.49.2		6
40.3	even	4		7200.2.k.p.3601.2		6
40.13	odd	4		1800.2.k.p.901.6		6
40.19	odd	2		7200.2.d.q.2449.5		6
40.27	even	4		1440.2.k.f.721.6		6
40.29	even	2	inner	1800.2.d.q.1549.3		6
40.37	odd	4		360.2.k.f.181.1		6
60.23	odd	4		2400.2.k.c.1201.4		6
60.47	odd	4		480.2.k.b.241.3		6
60.59	even	2		2400.2.d.e.49.5		6
120.29	odd	2		600.2.d.e.349.4		6
120.53	even	4		600.2.k.c.301.1		6
120.59	even	2		2400.2.d.f.49.5		6
120.77	even	4		120.2.k.b.61.6	yes	6
120.83	odd	4		2400.2.k.c.1201.1		6
120.107	odd	4		480.2.k.b.241.6		6
240.77	even	4		3840.2.a.bp.1.3		3
240.107	odd	4		3840.2.a.bo.1.1		3
240.197	even	4		3840.2.a.bq.1.3		3
240.227	odd	4		3840.2.a.br.1.1		3

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