LMFDB - Embedded newform 1800.2.k.p.901.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1800,2,Mod(901,1800)]

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, 0]))

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

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

chi := DirichletCharacter("1800.901");

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.k (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.3730723638$
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^{2} $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			901.5
Root			$1.40680 + 0.144584i$ of defining polynomial
Character	$\chi$	$=$	1800.901
Dual form			1800.2.k.p.901.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

$2$	1.40680	−	0.144584i	0.994760	−	0.102237i
$2$	1.40680	−	0.144584i	0.994760	−	0.102237i
$3$		0			0
$3$		0			0
$4$	1.95819	−	0.406803i	0.979095	−	0.203402i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	3.62721			1.37096			0.685479	−	0.728093i	$-0.259593\pi$
$7$	3.62721			1.37096			0.685479	+	0.728093i	$0.259593\pi$
$8$	2.69597	−	0.855416i	0.953170	−	0.302435i
$9$		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
$13$		−	0.578337i		−	0.160402i	−0.996779	−	0.0802009i	$-0.974444\pi$
$13$		−	0.578337i		−	0.160402i	0.996779	−	0.0802009i	$-0.0255562\pi$
$14$	5.10278	−	0.524438i	1.36377	−	0.140162i
$15$		0			0
$16$	3.66902	−	1.59320i	0.917256	−	0.398299i
$17$	1.42166			0.344804			0.172402	−	0.985027i	$-0.444847\pi$
$17$	1.42166			0.344804			0.172402	+	0.985027i	$0.444847\pi$
$18$		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
$22$	0.897225	+	8.72999i	0.191289	+	1.86124i
$23$	−5.62721			−1.17336			−0.586678	−	0.809821i	$-0.699564\pi$
$23$	−5.62721			−1.17336			−0.586678	+	0.809821i	$0.699564\pi$
$24$		0			0
$25$		0			0
$26$	−0.0836184	−	0.813607i	−0.0163989	−	0.159561i
$27$		0			0
$28$	7.10278	−	1.47556i	1.34230	−	0.278855i
$29$			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	$0.574377\pi$
$32$	4.93124	−	2.77180i	0.871729	−	0.489989i
$33$		0			0
$34$	2.00000	−	0.205550i	0.342997	−	0.0352516i
$35$		0			0
$36$		0			0
$37$		−	7.83276i		−	1.28770i	−0.765152	−	0.643849i	$-0.777336\pi$
$37$		−	7.83276i		−	1.28770i	0.765152	−	0.643849i	$-0.222664\pi$
$38$	0.813607	+	7.91638i	0.131984	+	1.28421i
$39$		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
$43$		−	7.25443i		−	1.10629i	−0.833085	−	0.553145i	$-0.813428\pi$
$43$		−	7.25443i		−	1.10629i	0.833085	−	0.553145i	$-0.186572\pi$
$44$	2.52444	+	12.1517i	0.380573	+	1.83193i
$45$		0			0
$46$	−7.91638	+	0.813607i	−1.16721	+	0.119960i
$47$	6.78389			0.989532			0.494766	−	0.869026i	$-0.335254\pi$
$47$	6.78389			0.989532			0.494766	+	0.869026i	$0.335254\pi$
$48$		0			0
$49$	6.15667			0.879525
$50$		0			0
$51$		0			0
$52$	−0.235269	−	1.13249i	−0.0326260	−	0.157049i
$53$			2.00000i			0.274721i	0.990521	+	0.137361i	$0.0438619\pi$
$53$			2.00000i			0.274721i	−0.990521	+	0.137361i	$0.956138\pi$
$54$		0			0
$55$		0			0
$56$	9.77886	−	3.10278i	1.30676	−	0.414626i
$57$		0			0
$58$	0.289169	+	2.81361i	0.0379697	+	0.369445i
$59$		−	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	$-0.707712\pi$
$61$		−	12.4111i		−	1.58908i	0.607213	−	0.794539i	$-0.292288\pi$
$62$	−3.62721	+	0.372787i	−0.460657	+	0.0473440i
$63$		0			0
$64$	6.53653	−	4.61235i	0.817066	−	0.576544i
$65$		0			0
$66$		0			0
$67$			4.00000i			0.488678i	0.969690	+	0.244339i	$0.0785709\pi$
$67$			4.00000i			0.488678i	−0.969690	+	0.244339i	$0.921429\pi$
$68$	2.78389	−	0.578337i	0.337596	−	0.0701337i
$69$		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
$73$	6.00000			0.702247			0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000			0.702247			0.351123	+	0.936329i	$0.385800\pi$
$74$	−1.13249	−	11.0192i	−0.131650	−	1.28095i
$75$		0			0
$76$	2.28917	+	11.0192i	0.262586	+	1.26398i
$77$			22.5089i			2.56512i
$78$		0			0
$79$	5.42166			0.609985			0.304992	−	0.952355i	$-0.401346\pi$
$79$	5.42166			0.609985			0.304992	+	0.952355i	$0.401346\pi$
$80$		0			0
$81$		0			0
$82$	−7.39194	+	0.759707i	−0.816304	+	0.0838956i
$83$		−	3.25443i		−	0.357220i	−0.983920	−	0.178610i	$-0.942840\pi$
$83$		−	3.25443i		−	0.357220i	0.983920	−	0.178610i	$-0.0571600\pi$
$84$		0			0
$85$		0			0
$86$	−1.04888	−	10.2056i	−0.113103	−	1.10049i
$87$		0			0
$88$	5.30833	+	16.7300i	0.565869	+	1.78342i
$89$	13.2544			1.40497			0.702483	−	0.711700i	$-0.252075\pi$
$89$	13.2544			1.40497			0.702483	+	0.711700i	$0.252075\pi$
$90$		0			0
$91$		−	2.09775i		−	0.219904i
$92$	−11.0192	+	2.28917i	−1.14883	+	0.238662i
$93$		0			0
$94$	9.54359	−	0.980843i	0.984347	−	0.101166i
$95$		0			0
$96$		0			0
$97$	−4.84333			−0.491765			−0.245883	−	0.969300i	$-0.579078\pi$
$97$	−4.84333			−0.491765			−0.245883	+	0.969300i	$0.579078\pi$
$98$	8.66123	−	0.890158i	0.874916	−	0.0899196i
$99$		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
$103$	−2.47054			−0.243429			−0.121715	−	0.992565i	$-0.538839\pi$
$103$	−2.47054			−0.243429			−0.121715	+	0.992565i	$0.538839\pi$
$104$	−0.494719	−	1.55918i	−0.0485112	−	0.152890i
$105$		0			0
$106$	0.289169	+	2.81361i	0.0280865	+	0.273282i
$107$		−	14.0978i		−	1.36288i	−0.731873	−	0.681441i	$-0.761354\pi$
$107$		−	14.0978i		−	1.36288i	0.731873	−	0.681441i	$-0.238646\pi$
$108$		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
$112$	13.3083	−	5.77886i	1.25752	−	0.546051i
$113$	−9.08719			−0.854851			−0.427425	−	0.904051i	$-0.640579\pi$
$113$	−9.08719			−0.854851			−0.427425	+	0.904051i	$0.640579\pi$
$114$		0			0
$115$		0			0
$116$	0.813607	+	3.91638i	0.0755415	+	0.363627i
$117$		0			0
$118$	−0.318888	−	3.10278i	−0.0293560	−	0.285634i
$119$	5.15667			0.472712
$120$		0			0
$121$	−27.5089			−2.50080
$122$	−1.79445	−	17.4600i	−0.162462	−	1.58075i
$123$		0			0
$124$	−5.04888	+	1.04888i	−0.453402	+	0.0941918i
$125$		0			0
$126$		0			0
$127$	10.4705			0.929110			0.464555	−	0.885544i	$-0.346214\pi$
$127$	10.4705			0.929110			0.464555	+	0.885544i	$0.346214\pi$
$128$	8.52873	−	7.43375i	0.753841	−	0.657057i
$129$		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
$133$			20.4111i			1.76987i
$134$	0.578337	+	5.62721i	0.0499607	+	0.486117i
$135$		0			0
$136$	3.83276	−	1.21611i	0.328657	−	0.104281i
$137$	−10.5783			−0.903768			−0.451884	−	0.892077i	$-0.649248\pi$
$137$	−10.5783			−0.903768			−0.451884	+	0.892077i	$0.649248\pi$
$138$		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
$142$	−11.8328	+	1.21611i	−0.992983	+	0.102054i
$143$	3.58890			0.300119
$144$		0			0
$145$		0			0
$146$	8.44082	−	0.867506i	0.698567	−	0.0717953i
$147$		0			0
$148$	−3.18639	−	15.3380i	−0.261920	−	1.26078i
$149$			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	$0.327501\pi$
$152$	4.81361	+	15.1708i	0.390435	+	1.23051i
$153$		0			0
$154$	3.25443	+	31.6655i	0.262249	+	2.55168i
$155$		0			0
$156$		0			0
$157$		−	1.32391i		−	0.105660i	−0.998604	−	0.0528298i	$-0.983176\pi$
$157$		−	1.32391i		−	0.105660i	0.998604	−	0.0528298i	$-0.0168241\pi$
$158$	7.62721	−	0.783887i	0.606788	−	0.0623627i
$159$		0			0
$160$		0			0
$161$	−20.4111			−1.60862
$162$		0			0
$163$			15.2544i			1.19482i	0.801936	+	0.597409i	$0.203803\pi$
$163$			15.2544i			1.19482i	−0.801936	+	0.597409i	$0.796197\pi$
$164$	−10.2892	+	2.13752i	−0.803449	+	0.166912i
$165$		0			0
$166$	−0.470539	−	4.57834i	−0.0365209	−	0.355348i
$167$	10.7839			0.834482			0.417241	−	0.908796i	$-0.362997\pi$
$167$	10.7839			0.834482			0.417241	+	0.908796i	$0.362997\pi$
$168$		0			0
$169$	12.6655			0.974271
$170$		0			0
$171$		0			0
$172$	−2.95112	−	14.2056i	−0.225021	−	1.08316i
$173$		−	13.6655i		−	1.03897i	−0.854479	−	0.519485i	$-0.826124\pi$
$173$		−	13.6655i		−	1.03897i	0.854479	−	0.519485i	$-0.173876\pi$
$174$		0			0
$175$		0			0
$176$	9.88666	+	22.7683i	0.745235	+	1.71623i
$177$		0			0
$178$	18.6464	−	1.91638i	1.39760	−	0.143639i
$179$		−	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	$0.332203\pi$
$181$			23.2544i			1.72849i	−0.503073	+	0.864244i	$0.667797\pi$
$182$	−0.303302	−	2.95112i	−0.0224822	−	0.218752i
$183$		0			0
$184$	−15.1708	+	4.81361i	−1.11841	+	0.354864i
$185$		0			0
$186$		0			0
$187$			8.82220i			0.645143i
$188$	13.2841	−	2.75971i	0.968846	−	0.201272i
$189$		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
$193$	−25.6655			−1.84745			−0.923723	−	0.383062i	$-0.874869\pi$
$193$	−25.6655			−1.84745			−0.923723	+	0.383062i	$0.874869\pi$
$194$	−6.81361	+	0.700269i	−0.489188	+	0.0502764i
$195$		0			0
$196$	12.0559	−	2.50456i	0.861139	−	0.178897i
$197$		−	15.1567i		−	1.07987i	−0.841707	−	0.539934i	$-0.818449\pi$
$197$		−	15.1567i		−	1.07987i	0.841707	−	0.539934i	$-0.181551\pi$
$198$		0			0
$199$	−20.6761			−1.46569			−0.732845	−	0.680396i	$-0.761808\pi$
$199$	−20.6761			−1.46569			−0.732845	+	0.680396i	$0.761808\pi$
$200$		0			0
$201$		0			0
$202$	−0.289169	−	2.81361i	−0.0203458	−	0.197965i
$203$			7.25443i			0.509161i
$204$		0			0
$205$		0			0
$206$	−3.47556	+	0.357201i	−0.242154	+	0.0248874i
$207$		0			0
$208$	−0.921405	−	2.12193i	−0.0638879	−	0.147129i
$209$	−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	$0.977648\pi$
$212$	0.813607	+	3.91638i	0.0558787	+	0.268978i
$213$		0			0
$214$	−2.03831	−	19.8328i	−0.139336	−	1.35574i
$215$		0			0
$216$		0			0
$217$	−9.35218			−0.634867
$218$	−1.04888	−	10.2056i	−0.0710388	−	0.691207i
$219$		0			0
$220$		0			0
$221$		−	0.822200i		−	0.0553072i
$222$		0			0
$223$	7.21611			0.483227			0.241613	−	0.970373i	$-0.422323\pi$
$223$	7.21611			0.483227			0.241613	+	0.970373i	$0.422323\pi$
$224$	17.8867	−	10.0539i	1.19510	−	0.671754i
$225$		0			0
$226$	−12.7839	+	1.31386i	−0.850372	+	0.0873970i
$227$		−	1.15667i		−	0.0767712i	−0.999263	−	0.0383856i	$-0.987778\pi$
$227$		−	1.15667i		−	0.0767712i	0.999263	−	0.0383856i	$-0.0122215\pi$
$228$		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
$232$	1.71083	+	5.39194i	0.112322	+	0.353998i
$233$	−14.5783			−0.955059			−0.477529	−	0.878616i	$-0.658468\pi$
$233$	−14.5783			−0.955059			−0.477529	+	0.878616i	$0.658468\pi$
$234$		0			0
$235$		0			0
$236$	−0.897225	−	4.31889i	−0.0584044	−	0.281136i
$237$		0			0
$238$	7.25443	−	0.745574i	0.470235	−	0.0483284i
$239$	−19.2544			−1.24547			−0.622733	−	0.782435i	$-0.713978\pi$
$239$	−19.2544			−1.24547			−0.622733	+	0.782435i	$0.713978\pi$
$240$		0			0
$241$	−13.6655			−0.880274			−0.440137	−	0.897931i	$-0.645070\pi$
$241$	−13.6655			−0.880274			−0.440137	+	0.897931i	$0.645070\pi$
$242$	−38.6995	+	3.97735i	−2.48770	+	0.255674i
$243$		0			0
$244$	−5.04888	−	24.3033i	−0.323221	−	1.55586i
$245$		0			0
$246$		0			0
$247$	3.25443			0.207074
$248$	−6.95112	+	2.20555i	−0.441397	+	0.140053i
$249$		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
$253$		−	34.9200i		−	2.19540i
$254$	14.7300	−	1.51388i	0.924242	−	0.0949890i
$255$		0			0
$256$	10.9234	−	11.6909i	0.682716	−	0.730684i
$257$	7.73501			0.482497			0.241248	−	0.970463i	$-0.422443\pi$
$257$	7.73501			0.482497			0.241248	+	0.970463i	$0.422443\pi$
$258$		0			0
$259$		−	28.4111i		−	1.76538i
$260$		0			0
$261$		0			0
$262$	−1.94610	−	18.9355i	−0.120231	−	1.16984i
$263$	−18.7839			−1.15826			−0.579132	−	0.815234i	$-0.696608\pi$
$263$	−18.7839			−1.15826			−0.579132	+	0.815234i	$0.696608\pi$
$264$		0			0
$265$		0			0
$266$	2.95112	+	28.7144i	0.180945	+	1.76059i
$267$		0			0
$268$	1.62721	+	7.83276i	0.0993979	+	0.478462i
$269$			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	$0.109665\pi$
$272$	5.21611	−	2.26499i	0.316273	−	0.137335i
$273$		0			0
$274$	−14.8816	+	1.52946i	−0.899033	+	0.0923981i
$275$		0			0
$276$		0			0
$277$			9.51941i			0.571966i	0.958235	+	0.285983i	$0.0923201\pi$
$277$			9.51941i			0.571966i	−0.958235	+	0.285983i	$0.907680\pi$
$278$	1.80304	+	17.5436i	0.108139	+	1.05219i
$279$		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
$283$		−	20.0000i		−	1.18888i	−0.804141	−	0.594438i	$-0.797374\pi$
$283$		−	20.0000i		−	1.18888i	0.804141	−	0.594438i	$-0.202626\pi$
$284$	−16.4705	+	3.42166i	−0.977347	+	0.203038i
$285$		0			0
$286$	5.04888	−	0.518898i	0.298546	−	0.0306831i
$287$	−19.0589			−1.12501
$288$		0			0
$289$	−14.9789			−0.881110
$290$		0			0
$291$		0			0
$292$	11.7491	−	2.44082i	0.687567	−	0.142838i
$293$			4.31335i			0.251989i	0.992031	+	0.125994i	$0.0402121\pi$
$293$			4.31335i			0.251989i	−0.992031	+	0.125994i	$0.959788\pi$
$294$		0			0
$295$		0			0
$296$	−6.70027	−	21.1169i	−0.389445	−	1.22740i
$297$		0			0
$298$	0.289169	+	2.81361i	0.0167511	+	0.162988i
$299$			3.25443i			0.188208i
$300$		0			0
$301$		−	26.3133i		−	1.51668i
$302$	17.8328	−	1.83276i	1.02616	−	0.105464i
$303$		0			0
$304$	8.96526	+	20.6464i	0.514193	+	1.18415i
$305$		0			0
$306$		0			0
$307$			25.5678i			1.45923i	0.683858	+	0.729615i	$0.260301\pi$
$307$			25.5678i			1.45923i	−0.683858	+	0.729615i	$0.739699\pi$
$308$	9.15667	+	44.0766i	0.521750	+	2.51150i
$309$		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
$313$	−7.15667			−0.404519			−0.202260	−	0.979332i	$-0.564828\pi$
$313$	−7.15667			−0.404519			−0.202260	+	0.979332i	$0.564828\pi$
$314$	−0.191417	−	1.86248i	−0.0108023	−	0.105106i
$315$		0			0
$316$	10.6167	−	2.20555i	0.597233	−	0.124072i
$317$		−	24.1744i		−	1.35777i	−0.734245	−	0.678884i	$-0.762464\pi$
$317$		−	24.1744i		−	1.35777i	0.734245	−	0.678884i	$-0.237536\pi$
$318$		0			0
$319$	−12.4111			−0.694888
$320$		0			0
$321$		0			0
$322$	−28.7144	+	2.95112i	−1.60019	+	0.164460i
$323$			8.00000i			0.445132i
$324$		0			0
$325$		0			0
$326$	2.20555	+	21.4600i	0.122154	+	1.18856i
$327$		0			0
$328$	−14.1658	+	4.49472i	−0.782175	+	0.248179i
$329$	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	$0.731309\pi$
$332$	−1.32391	−	6.37279i	−0.0726591	−	0.349752i
$333$		0			0
$334$	15.1708	−	1.55918i	0.830110	−	0.0853146i
$335$		0			0
$336$		0			0
$337$	−22.8222			−1.24320			−0.621602	−	0.783333i	$-0.713518\pi$
$337$	−22.8222			−1.24320			−0.621602	+	0.783333i	$0.713518\pi$
$338$	17.8179	−	1.83124i	0.969166	−	0.0996061i
$339$		0			0
$340$		0			0
$341$		−	16.0000i		−	0.866449i
$342$		0			0
$343$	−3.05892			−0.165166
$344$	−6.20555	−	19.5577i	−0.334581	−	1.05448i
$345$		0			0
$346$	−1.97582	−	19.2247i	−0.106221	−	1.03353i
$347$			23.6655i			1.27043i	0.772335	+	0.635216i	$0.219089\pi$
$347$			23.6655i			1.27043i	−0.772335	+	0.635216i	$0.780911\pi$
$348$		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
$352$	17.2005	+	30.6011i	0.916791	+	1.63104i
$353$	−15.9305			−0.847896			−0.423948	−	0.905687i	$-0.639356\pi$
$353$	−15.9305			−0.847896			−0.423948	+	0.905687i	$0.639356\pi$
$354$		0			0
$355$		0			0
$356$	25.9547	−	5.39194i	1.37560	−	0.285772i
$357$		0			0
$358$	−1.30833	−	12.7300i	−0.0691471	−	0.672801i
$359$	−8.41110			−0.443921			−0.221960	−	0.975056i	$-0.571246\pi$
$359$	−8.41110			−0.443921			−0.221960	+	0.975056i	$0.571246\pi$
$360$		0			0
$361$	−12.6655			−0.666607
$362$	3.36222	+	32.7144i	0.176715	+	1.71943i
$363$		0			0
$364$	−0.853372	−	4.10780i	−0.0447289	−	0.215307i
$365$		0			0
$366$		0			0
$367$	24.4494			1.27625			0.638124	−	0.769933i	$-0.279711\pi$
$367$	24.4494			1.27625			0.638124	+	0.769933i	$0.279711\pi$
$368$	−20.6464	+	8.96526i	−1.07627	+	0.467346i
$369$		0			0
$370$		0			0
$371$			7.25443i			0.376631i
$372$		0			0
$373$		−	0.167237i		−	0.00865920i	−0.999991	−	0.00432960i	$-0.998622\pi$
$373$		−	0.167237i		−	0.00865920i	0.999991	−	0.00432960i	$-0.00137816\pi$
$374$	1.27555	+	12.4111i	0.0659572	+	0.641763i
$375$		0			0
$376$	18.2892	−	5.80304i	0.943192	−	0.299269i
$377$	1.15667			0.0595718
$378$		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
$382$	11.2544	−	1.15667i	0.575827	−	0.0591806i
$383$	−1.62721			−0.0831467			−0.0415734	−	0.999135i	$-0.513237\pi$
$383$	−1.62721			−0.0831467			−0.0415734	+	0.999135i	$0.513237\pi$
$384$		0			0
$385$		0			0
$386$	−36.1063	+	3.71083i	−1.83776	+	0.188876i
$387$		0			0
$388$	−9.48416	+	1.97028i	−0.481485	+	0.100026i
$389$			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
$392$	16.5982	−	5.26652i	0.838337	−	0.265999i
$393$		0			0
$394$	−2.19142	−	21.3225i	−0.110402	−	1.07421i
$395$		0			0
$396$		0			0
$397$		−	19.0872i		−	0.957959i	−0.877826	−	0.478979i	$-0.841007\pi$
$397$		−	19.0872i		−	0.957959i	0.877826	−	0.478979i	$-0.158993\pi$
$398$	−29.0872	+	2.98944i	−1.45801	+	0.149847i
$399$		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
$403$			1.49115i			0.0742794i
$404$	−0.813607	−	3.91638i	−0.0404784	−	0.194847i
$405$		0			0
$406$	1.04888	+	10.2056i	0.0520548	+	0.506493i
$407$	48.6066			2.40934
$408$		0			0
$409$	−8.31335			−0.411069			−0.205534	−	0.978650i	$-0.565893\pi$
$409$	−8.31335			−0.411069			−0.205534	+	0.978650i	$0.565893\pi$
$410$		0			0
$411$		0			0
$412$	−4.83779	+	1.00502i	−0.238341	+	0.0495139i
$413$		−	8.00000i		−	0.393654i
$414$		0			0
$415$		0			0
$416$	−1.60303	−	2.85192i	−0.0785952	−	0.139827i
$417$		0			0
$418$	−49.1255	+	5.04888i	−2.40281	+	0.246949i
$419$		−	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	$0.262085\pi$
$421$			30.0978i			1.46687i	−0.679757	+	0.733437i	$0.737915\pi$
$422$	0.294708	+	2.86751i	0.0143462	+	0.139588i
$423$		0			0
$424$	1.71083	+	5.39194i	0.0830853	+	0.261856i
$425$		0			0
$426$		0			0
$427$		−	45.0177i		−	2.17856i
$428$	−5.73501	−	27.6061i	−0.277212	−	1.33439i
$429$		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
$433$	4.31335			0.207286			0.103643	−	0.994615i	$-0.466950\pi$
$433$	4.31335			0.207286			0.103643	+	0.994615i	$0.466950\pi$
$434$	−13.1567	+	1.35218i	−0.631541	+	0.0649066i
$435$		0			0
$436$	−2.95112	−	14.2056i	−0.141333	−	0.680322i
$437$		−	31.6655i		−	1.51477i
$438$		0			0
$439$	9.83276			0.469292			0.234646	−	0.972081i	$-0.424607\pi$
$439$	9.83276			0.469292			0.234646	+	0.972081i	$0.424607\pi$
$440$		0			0
$441$		0			0
$442$	−0.118877	−	1.15667i	−0.00565441	−	0.0550174i
$443$		−	21.3522i		−	1.01447i	−0.861807	−	0.507236i	$-0.830667\pi$
$443$		−	21.3522i		−	1.01447i	0.861807	−	0.507236i	$-0.169333\pi$
$444$		0			0
$445$		0			0
$446$	10.1517	−	1.04334i	0.480695	−	0.0494034i
$447$		0			0
$448$	23.7094	−	16.7300i	1.12016	−	0.790418i
$449$	20.3133			0.958646			0.479323	−	0.877639i	$-0.340882\pi$
$449$	20.3133			0.958646			0.479323	+	0.877639i	$0.340882\pi$
$450$		0			0
$451$		−	32.6066i		−	1.53539i
$452$	−17.7944	+	3.69670i	−0.836981	+	0.173878i
$453$		0			0
$454$	−0.167237	−	1.62721i	−0.00784882	−	0.0763689i
$455$		0			0
$456$		0			0
$457$	3.35218			0.156808			0.0784041	−	0.996922i	$-0.475018\pi$
$457$	3.35218			0.156808			0.0784041	+	0.996922i	$0.475018\pi$
$458$	−2.03831	−	19.8328i	−0.0952441	−	0.926724i
$459$		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
$463$	−23.6272			−1.09805			−0.549025	−	0.835806i	$-0.685001\pi$
$463$	−23.6272			−1.09805			−0.549025	+	0.835806i	$0.685001\pi$
$464$	3.18639	+	7.33804i	0.147925	+	0.340660i
$465$		0			0
$466$	−20.5089	+	2.10780i	−0.950054	+	0.0976419i
$467$			29.5678i			1.36823i	0.729373	+	0.684117i	$0.239812\pi$
$467$			29.5678i			1.36823i	−0.729373	+	0.684117i	$0.760188\pi$
$468$		0			0
$469$			14.5089i			0.669957i
$470$		0			0
$471$		0			0
$472$	−1.88666	−	5.94610i	−0.0868407	−	0.273691i
$473$	45.0177			2.06992
$474$		0			0
$475$		0			0
$476$	10.0978	−	2.09775i	0.462830	−	0.0961503i
$477$		0			0
$478$	−27.0872	+	2.78389i	−1.23894	+	0.127332i
$479$	22.0978			1.00967			0.504836	−	0.863215i	$-0.331553\pi$
$479$	22.0978			1.00967			0.504836	+	0.863215i	$0.331553\pi$
$480$		0			0
$481$	−4.52998			−0.206549
$482$	−19.2247	+	1.97582i	−0.875661	+	0.0899961i
$483$		0			0
$484$	−53.8676	+	11.1907i	−2.44853	+	0.508668i
$485$		0			0
$486$		0			0
$487$	−4.03831			−0.182993			−0.0914967	−	0.995805i	$-0.529165\pi$
$487$	−4.03831			−0.182993			−0.0914967	+	0.995805i	$0.529165\pi$
$488$	−10.6167	−	33.4600i	−0.480593	−	1.51466i
$489$		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
$493$			2.84333i			0.128057i
$494$	4.57834	−	0.470539i	0.205989	−	0.0211705i
$495$		0			0
$496$	−9.45998	+	4.10780i	−0.424765	+	0.184446i
$497$	−30.5089			−1.36851
$498$		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
$502$	−1.03329	−	10.0539i	−0.0461180	−	0.448727i
$503$	2.03831			0.0908839			0.0454419	−	0.998967i	$-0.485530\pi$
$503$	2.03831			0.0908839			0.0454419	+	0.998967i	$0.485530\pi$
$504$		0			0
$505$		0			0
$506$	−5.04888	−	49.1255i	−0.224450	−	2.18389i
$507$		0			0
$508$	20.5033	−	4.25945i	0.909687	−	0.188983i
$509$		−	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
$512$	13.6768	−	18.0262i	0.604436	−	0.796654i
$513$		0			0
$514$	10.8816	−	1.11836i	0.479969	−	0.0493288i
$515$		0			0
$516$		0			0
$517$			42.0978i			1.85146i
$518$	−4.10780	−	39.9688i	−0.180486	−	1.75613i
$519$		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
$523$			35.3311i			1.54492i	0.635064	+	0.772460i	$0.280974\pi$
$523$			35.3311i			1.54492i	−0.635064	+	0.772460i	$0.719026\pi$
$524$	−5.47556	−	26.3572i	−0.239201	−	1.15142i
$525$		0			0
$526$	−26.4252	+	2.71585i	−1.15219	+	0.118417i
$527$	−3.66553			−0.159673
$528$		0			0
$529$	8.66553			0.376762
$530$		0			0
$531$		0			0
$532$	8.30330	+	39.9688i	0.359994	+	1.73287i
$533$			3.03883i			0.131626i
$534$		0			0
$535$		0			0
$536$	3.42166	+	10.7839i	0.147793	+	0.465793i
$537$		0			0
$538$	1.23025	+	11.9703i	0.0530397	+	0.516075i
$539$			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	$-0.0209461\pi$
$542$	43.5960	−	4.48059i	1.87261	−	0.192458i
$543$		0			0
$544$	7.01056	−	3.94056i	0.300575	−	0.168950i
$545$		0			0
$546$		0			0
$547$		−	32.0766i		−	1.37150i	−0.727838	−	0.685749i	$-0.759475\pi$
$547$		−	32.0766i		−	1.37150i	0.727838	−	0.685749i	$-0.240525\pi$
$548$	−20.7144	+	4.30330i	−0.884875	+	0.183828i
$549$		0			0
$550$		0			0
$551$	−11.2544			−0.479455
$552$		0			0
$553$	19.6655			0.836263
$554$	1.37636	+	13.3919i	0.0584758	+	0.568969i
$555$		0			0
$556$	5.07306	+	24.4197i	0.215145	+	1.03563i
$557$			33.6655i			1.42645i	0.700933	+	0.713227i	$0.252767\pi$
$557$			33.6655i			1.42645i	−0.700933	+	0.713227i	$0.747233\pi$
$558$		0			0
$559$	−4.19550			−0.177451
$560$		0			0
$561$		0			0
$562$	−19.2247	+	1.97582i	−0.810945	+	0.0833449i
$563$			5.35218i			0.225567i	0.993620	+	0.112784i	$0.0359767\pi$
$563$			5.35218i			0.225567i	−0.993620	+	0.112784i	$0.964023\pi$
$564$		0			0
$565$		0			0
$566$	−2.89169	−	28.1361i	−0.121547	−	1.18265i
$567$		0			0
$568$	−22.6761	+	7.19499i	−0.951468	+	0.301895i
$569$	−5.58890			−0.234299			−0.117149	−	0.993114i	$-0.537376\pi$
$569$	−5.58890			−0.234299			−0.117149	+	0.993114i	$0.537376\pi$
$570$		0			0
$571$			10.3728i			0.434088i	0.976162	+	0.217044i	$0.0696414\pi$
$571$			10.3728i			0.434088i	−0.976162	+	0.217044i	$0.930359\pi$
$572$	7.02775	−	1.45998i	0.293845	−	0.0610447i
$573$		0			0
$574$	−26.8122	+	2.75562i	−1.11912	+	0.115017i
$575$		0			0
$576$		0			0
$577$	−21.6655			−0.901948			−0.450974	−	0.892537i	$-0.648923\pi$
$577$	−21.6655			−0.901948			−0.450974	+	0.892537i	$0.648923\pi$
$578$	−21.0723	+	2.16571i	−0.876493	+	0.0900816i
$579$		0			0
$580$		0			0
$581$		−	11.8045i		−	0.489733i
$582$		0			0
$583$	−12.4111			−0.514015
$584$	16.1758	−	5.13249i	0.669361	−	0.212384i
$585$		0			0
$586$	0.623642	+	6.06803i	0.0257624	+	0.250668i
$587$		−	1.90225i		−	0.0785142i	−0.999229	−	0.0392571i	$-0.987501\pi$
$587$		−	1.90225i		−	0.0785142i	0.999229	−	0.0392571i	$-0.0124991\pi$
$588$		0			0
$589$		−	14.5089i		−	0.597827i
$590$		0			0
$591$		0			0
$592$	−12.4791	−	28.7386i	−0.512889	−	1.18115i
$593$	−2.57834			−0.105880			−0.0529398	−	0.998598i	$-0.516859\pi$
$593$	−2.57834			−0.105880			−0.0529398	+	0.998598i	$0.516859\pi$
$594$		0			0
$595$		0			0
$596$	0.813607	+	3.91638i	0.0333266	+	0.160421i
$597$		0			0
$598$	0.470539	+	4.57834i	0.0192418	+	0.187222i
$599$	−26.7244			−1.09193			−0.545966	−	0.837808i	$-0.683837\pi$
$599$	−26.7244			−1.09193			−0.545966	+	0.837808i	$0.683837\pi$
$600$		0			0
$601$	33.3311			1.35960			0.679801	−	0.733397i	$-0.262066\pi$
$601$	33.3311			1.35960			0.679801	+	0.733397i	$0.262066\pi$
$602$	−3.80450	−	37.0177i	−0.155060	−	1.50873i
$603$		0			0
$604$	24.8222	−	5.15667i	1.01000	−	0.209822i
$605$		0			0
$606$		0			0
$607$	21.9406			0.890540			0.445270	−	0.895396i	$-0.353108\pi$
$607$	21.9406			0.890540			0.445270	+	0.895396i	$0.353108\pi$
$608$	15.5975	+	27.7491i	0.632562	+	1.12538i
$609$		0			0
$610$		0			0
$611$		−	3.92337i		−	0.158723i
$612$		0			0
$613$		−	3.42166i		−	0.138200i	−0.997610	−	0.0690998i	$-0.977987\pi$
$613$		−	3.42166i		−	0.138200i	0.997610	−	0.0690998i	$-0.0220127\pi$
$614$	3.69670	+	35.9688i	0.149187	+	1.45158i
$615$		0			0
$616$	19.2544	+	60.6832i	0.775783	+	2.44500i
$617$	19.7350			0.794502			0.397251	−	0.917710i	$-0.369964\pi$
$617$	19.7350			0.794502			0.397251	+	0.917710i	$0.369964\pi$
$618$		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
$622$	28.2439	−	2.90276i	1.13248	−	0.116390i
$623$	48.0766			1.92615
$624$		0			0
$625$		0			0
$626$	−10.0680	+	1.03474i	−0.402400	+	0.0413566i
$627$		0			0
$628$	−0.538571	−	2.59247i	−0.0214913	−	0.103451i
$629$		−	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	$0.493111\pi$
$632$	14.6167	−	4.63778i	0.581419	−	0.184481i
$633$		0			0
$634$	−3.49523	−	34.0086i	−0.138814	−	1.35065i
$635$		0			0
$636$		0			0
$637$		−	3.56063i		−	0.141077i
$638$	−17.4600	+	1.79445i	−0.691247	+	0.0710430i
$639$		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
$643$		−	4.94108i		−	0.194857i	−0.995243	−	0.0974285i	$-0.968938\pi$
$643$		−	4.94108i		−	0.194857i	0.995243	−	0.0974285i	$-0.0310617\pi$
$644$	−39.9688	+	8.30330i	−1.57499	+	0.327196i
$645$		0			0
$646$	1.15667	+	11.2544i	0.0455087	+	0.442799i
$647$	−49.3694			−1.94091			−0.970455	−	0.241282i	$-0.922432\pi$
$647$	−49.3694			−1.94091			−0.970455	+	0.241282i	$0.922432\pi$
$648$		0			0
$649$	13.6867			0.537248
$650$		0			0
$651$		0			0
$652$	6.20555	+	29.8711i	0.243028	+	1.16984i
$653$			40.1744i			1.57214i	0.618134	+	0.786072i	$0.287889\pi$
$653$			40.1744i			1.57214i	−0.618134	+	0.786072i	$0.712111\pi$
$654$		0			0
$655$		0			0
$656$	−19.2786	+	8.37133i	−0.752703	+	0.326846i
$657$		0			0
$658$	34.6167	−	3.55773i	1.34950	−	0.138695i
$659$			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	$-0.931882\pi$
$661$		−	10.9200i		−	0.424737i	0.977190	−	0.212368i	$-0.0681177\pi$
$662$	3.93197	+	38.2580i	0.152820	+	1.48694i
$663$		0			0
$664$	−2.78389	−	8.77384i	−0.108036	−	0.340491i
$665$		0			0
$666$		0			0
$667$		−	11.2544i		−	0.435773i
$668$	21.1169	−	4.38692i	0.817038	−	0.169735i
$669$		0			0
$670$		0			0
$671$	77.0177			2.97324
$672$		0			0
$673$	18.0000			0.693849			0.346925	−	0.937893i	$-0.387226\pi$
$673$	18.0000			0.693849			0.346925	+	0.937893i	$0.387226\pi$
$674$	−32.1063	+	3.29973i	−1.23669	+	0.127101i
$675$		0			0
$676$	24.8015	−	5.15238i	0.953904	−	0.198168i
$677$			30.4877i			1.17174i	0.810406	+	0.585869i	$0.199247\pi$
$677$			30.4877i			1.17174i	−0.810406	+	0.585869i	$0.800753\pi$
$678$		0			0
$679$	−17.5678			−0.674189
$680$		0			0
$681$		0			0
$682$	−2.31335	−	22.5089i	−0.0885827	−	0.861908i
$683$		−	35.2544i		−	1.34897i	−0.738287	−	0.674487i	$-0.764365\pi$
$683$		−	35.2544i		−	1.34897i	0.738287	−	0.674487i	$-0.235635\pi$
$684$		0			0
$685$		0			0
$686$	−4.30330	+	0.442272i	−0.164301	+	0.0168860i
$687$		0			0
$688$	−11.5577	−	26.6167i	−0.440634	−	1.01475i
$689$	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	$-0.179754\pi$
$692$	−5.55918	−	26.7597i	−0.211328	−	1.01725i
$693$		0			0
$694$	3.42166	+	33.2927i	0.129885	+	1.26378i
$695$		0			0
$696$		0			0
$697$	−7.47002			−0.282947
$698$	5.04888	+	49.1255i	0.191103	+	1.85943i
$699$		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
$703$	44.0766			1.66238
$704$	28.6222	+	40.5628i	1.07874	+	1.52877i
$705$		0			0
$706$	−22.4111	+	2.30330i	−0.843453	+	0.0866859i
$707$		−	7.25443i		−	0.272831i
$708$		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
$712$	35.7336	−	11.3380i	1.33917	−	0.424911i
$713$	14.5089			0.543361
$714$		0			0
$715$		0			0
$716$	−3.68111	−	17.7194i	−0.137570	−	0.662206i
$717$		0			0
$718$	−11.8328	+	1.21611i	−0.441595	+	0.0453849i
$719$	3.66553			0.136701			0.0683505	−	0.997661i	$-0.478226\pi$
$719$	3.66553			0.136701			0.0683505	+	0.997661i	$0.478226\pi$
$720$		0			0
$721$	−8.96117			−0.333731
$722$	−17.8179	+	1.83124i	−0.663114	+	0.0681515i
$723$		0			0
$724$	9.45998	+	45.5366i	0.351577	+	1.69235i
$725$		0			0
$726$		0			0
$727$	36.1149			1.33943			0.669714	−	0.742619i	$-0.266416\pi$
$727$	36.1149			1.33943			0.669714	+	0.742619i	$0.266416\pi$
$728$	−1.79445	−	5.65548i	−0.0665067	−	0.209606i
$729$		0			0
$730$		0			0
$731$		−	10.3133i		−	0.381453i
$732$		0			0
$733$			34.0071i			1.25608i	0.778180	+	0.628041i	$0.216143\pi$
$733$			34.0071i			1.25608i	−0.778180	+	0.628041i	$0.783857\pi$
$734$	34.3955	−	3.53500i	1.26956	−	0.130479i
$735$		0			0
$736$	−27.7491	+	15.5975i	−1.02285	+	0.574931i
$737$	−24.8222			−0.914338
$738$		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
$742$	1.04888	+	10.2056i	0.0385054	+	0.374658i
$743$	−23.3139			−0.855303			−0.427651	−	0.903944i	$-0.640659\pi$
$743$	−23.3139			−0.855303			−0.427651	+	0.903944i	$0.640659\pi$
$744$		0			0
$745$		0			0
$746$	−0.0241798	−	0.235269i	−0.000885286	−	0.00861383i
$747$		0			0
$748$	3.58890	+	17.2756i	0.131223	+	0.631657i
$749$		−	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	$0.435037\pi$
$752$	24.8902	−	10.8081i	0.907653	−	0.394130i
$753$		0			0
$754$	1.62721	−	0.167237i	0.0592596	−	0.00609041i
$755$		0			0
$756$		0			0
$757$			13.3239i			0.484266i	0.970243	+	0.242133i	$0.0778470\pi$
$757$			13.3239i			0.484266i	−0.970243	+	0.242133i	$0.922153\pi$
$758$	−1.11691	−	10.8675i	−0.0405679	−	0.394726i
$759$		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
$763$		−	26.3133i		−	0.952607i
$764$	15.6655	−	3.25443i	0.566759	−	0.117741i
$765$		0			0
$766$	−2.28917	+	0.235269i	−0.0827110	+	0.00850063i
$767$	−1.27555			−0.0460575
$768$		0			0
$769$	5.47002			0.197254			0.0986270	−	0.995124i	$-0.468555\pi$
$769$	5.47002			0.197254			0.0986270	+	0.995124i	$0.468555\pi$
$770$		0			0
$771$		0			0
$772$	−50.2580	+	10.4408i	−1.80882	+	0.375773i
$773$			3.15667i			0.113538i	0.998387	+	0.0567688i	$0.0180798\pi$
$773$			3.15667i			0.113538i	−0.998387	+	0.0567688i	$0.981920\pi$
$774$		0			0
$775$		0			0
$776$	−13.0575	+	4.14306i	−0.468736	+	0.148727i
$777$		0			0
$778$	1.78032	+	17.3225i	0.0638274	+	0.621040i
$779$		−	29.5678i		−	1.05938i
$780$		0			0
$781$		−	52.1955i		−	1.86770i
$782$	−11.2544	+	1.15667i	−0.402457	+	0.0413626i
$783$		0			0
$784$	22.5890	−	9.80879i	0.806749	−	0.350314i
$785$		0			0
$786$		0			0
$787$			31.1355i			1.10986i	0.831896	+	0.554931i	$0.187255\pi$
$787$			31.1355i			1.10986i	−0.831896	+	0.554931i	$0.812745\pi$
$788$	−6.16578	−	29.6797i	−0.219647	−	1.05729i
$789$		0			0
$790$		0			0
$791$	−32.9612			−1.17196
$792$		0			0
$793$	−7.17780			−0.254891
$794$	−2.75971	−	26.8519i	−0.0979383	−	0.952939i
$795$		0			0
$796$	−40.4877	+	8.41110i	−1.43505	+	0.298124i
$797$			10.0000i			0.354218i	0.984191	+	0.177109i	$0.0566745\pi$
$797$			10.0000i			0.354218i	−0.984191	+	0.177109i	$0.943325\pi$
$798$		0			0
$799$	9.64440			0.341194
$800$		0			0
$801$		0			0
$802$	20.2736	−	2.08362i	0.715885	−	0.0735751i
$803$			37.2333i			1.31393i
$804$		0			0
$805$		0			0
$806$	0.215597	+	2.09775i	0.00759406	+	0.0738902i
$807$		0			0
$808$	−1.71083	−	5.39194i	−0.0601868	−	0.189688i
$809$	−29.0388			−1.02095			−0.510475	−	0.859892i	$-0.670531\pi$
$809$	−29.0388			−1.02095			−0.510475	+	0.859892i	$0.670531\pi$
$810$		0			0
$811$		−	2.58838i		−	0.0908904i	−0.998967	−	0.0454452i	$-0.985529\pi$
$811$		−	2.58838i		−	0.0908904i	0.998967	−	0.0454452i	$-0.0144706\pi$
$812$	2.95112	+	14.2056i	0.103564	+	0.498517i
$813$		0			0
$814$	68.3799	−	7.02775i	2.39672	−	0.246323i
$815$		0			0
$816$		0			0
$817$	40.8222			1.42819
$818$	−11.6952	+	1.20198i	−0.408915	+	0.0420262i
$819$		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
$823$	18.3517			0.639699			0.319849	−	0.947468i	$-0.396368\pi$
$823$	18.3517			0.639699			0.319849	+	0.947468i	$0.396368\pi$
$824$	−6.66050	+	2.11334i	−0.232030	+	0.0736216i
$825$		0			0
$826$	−1.15667	−	11.2544i	−0.0402458	−	0.391592i
$827$		−	20.0000i		−	0.695468i	−0.937593	−	0.347734i	$-0.886951\pi$
$827$		−	20.0000i		−	0.695468i	0.937593	−	0.347734i	$-0.113049\pi$
$828$		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
$832$	−2.66750	−	3.78032i	−0.0924788	−	0.131059i
$833$	8.75272			0.303264
$834$		0			0
$835$		0			0
$836$	−68.3799	+	14.2056i	−2.36497	+	0.491309i
$837$		0			0
$838$	−1.06446	−	10.3572i	−0.0367712	−	0.357784i
$839$	53.4288			1.84457			0.922284	−	0.386514i	$-0.126321\pi$
$839$	53.4288			1.84457			0.922284	+	0.386514i	$0.126321\pi$
$840$		0			0
$841$	25.0000			0.862069
$842$	4.35166	+	42.3416i	0.149968	+	1.45919i
$843$		0			0
$844$	0.829192	+	3.99141i	0.0285420	+	0.137390i
$845$		0			0
$846$		0			0
$847$	−99.7805			−3.42850
$848$	3.18639	+	7.33804i	0.109421	+	0.251989i
$849$		0			0
$850$		0			0
$851$			44.0766i			1.51093i
$852$		0			0
$853$		−	29.0661i		−	0.995203i	−0.867406	−	0.497602i	$-0.834214\pi$
$853$		−	29.0661i		−	0.995203i	0.867406	−	0.497602i	$-0.165786\pi$
$854$	−6.50885	−	63.3311i	−0.222728	−	2.16714i
$855$		0			0
$856$	−12.0594	−	38.0071i	−0.412183	−	1.29906i
$857$	−10.2439			−0.349924			−0.174962	−	0.984575i	$-0.555980\pi$
$857$	−10.2439			−0.349924			−0.174962	+	0.984575i	$0.555980\pi$
$858$		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
$862$	−11.8328	+	1.21611i	−0.403026	+	0.0414210i
$863$	38.8605			1.32283			0.661414	−	0.750021i	$-0.269957\pi$
$863$	38.8605			1.32283			0.661414	+	0.750021i	$0.269957\pi$
$864$		0			0
$865$		0			0
$866$	6.06803	−	0.623642i	0.206200	−	0.0211922i
$867$		0			0
$868$	−18.3133	+	3.80450i	−0.621596	+	0.129133i
$869$			33.6444i			1.14131i
$870$		0			0
$871$	2.31335			0.0783848
$872$	−6.20555	−	19.5577i	−0.210146	−	0.662308i
$873$		0			0
$874$	−4.57834	−	44.5472i	−0.154865	−	1.50683i
$875$		0			0
$876$		0			0
$877$		−	22.3416i		−	0.754423i	−0.926127	−	0.377211i	$-0.876883\pi$
$877$		−	22.3416i		−	0.754423i	0.926127	−	0.377211i	$-0.123117\pi$
$878$	13.8328	−	1.42166i	0.466833	−	0.0479788i
$879$		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
$883$			10.6277i			0.357652i	0.983881	+	0.178826i	$0.0572298\pi$
$883$			10.6277i			0.357652i	−0.983881	+	0.178826i	$0.942770\pi$
$884$	−0.334474	−	1.61003i	−0.0112496	−	0.0541510i
$885$		0			0
$886$	−3.08719	−	30.0383i	−0.103716	−	1.00916i
$887$	11.6061			0.389694			0.194847	−	0.980834i	$-0.437579\pi$
$887$	11.6061			0.389694			0.194847	+	0.980834i	$0.437579\pi$
$888$		0			0
$889$	37.9789			1.27377
$890$		0			0
$891$		0			0
$892$	14.1305	−	2.93554i	0.473125	−	0.0982891i
$893$			38.1744i			1.27746i
$894$		0			0
$895$		0			0
$896$	30.9355	−	26.9638i	1.03348	−	0.900797i
$897$		0			0
$898$	28.5769	−	2.93699i	0.953623	−	0.0980086i
$899$		−	5.15667i		−	0.171985i
$900$		0			0
$901$			2.84333i			0.0947249i
$902$	−4.71440	−	45.8711i	−0.156972	−	1.52734i
$903$		0			0
$904$	−24.4988	+	7.77332i	−0.814818	+	0.258537i
$905$		0			0
$906$		0			0
$907$			0.195504i			0.00649159i	0.999995	+	0.00324580i	$0.00103317\pi$
$907$			0.195504i			0.00649159i	−0.999995	+	0.00324580i	$0.998967\pi$
$908$	−0.470539	−	2.26499i	−0.0156154	−	0.0751663i
$909$		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
$913$	20.1955			0.668374
$914$	4.71585	−	0.484672i	0.155987	−	0.0160315i
$915$		0			0
$916$	−5.73501	−	27.6061i	−0.189490	−	0.912131i
$917$		−	48.8222i		−	1.61225i
$918$		0			0
$919$	9.75614			0.321825			0.160913	−	0.986969i	$-0.448556\pi$
$919$	9.75614			0.321825			0.160913	+	0.986969i	$0.448556\pi$
$920$		0			0
$921$		0			0
$922$	4.12193	+	40.1063i	0.135749	+	1.32083i
$923$			4.86445i			0.160115i
$924$		0			0
$925$		0			0
$926$	−33.2388	+	3.41612i	−1.09230	+	0.112261i
$927$		0			0
$928$	5.54359	+	9.86248i	0.181977	+	0.323752i
$929$	−6.82220			−0.223829			−0.111915	−	0.993718i	$-0.535698\pi$
$929$	−6.82220			−0.223829			−0.111915	+	0.993718i	$0.535698\pi$
$930$		0			0
$931$			34.6449i			1.13544i
$932$	−28.5472	+	5.93051i	−0.935093	+	0.194260i
$933$		0			0
$934$	4.27504	+	41.5960i	0.139883	+	1.36106i
$935$		0			0
$936$		0			0
$937$	−57.5266			−1.87931			−0.939655	−	0.342123i	$-0.888854\pi$
$937$	−57.5266			−1.87931			−0.939655	+	0.342123i	$0.888854\pi$
$938$	2.09775	+	20.4111i	0.0684940	+	0.666446i
$939$		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
$943$	29.5678			0.962859
$944$	−3.51388	−	8.09221i	−0.114367	−	0.263379i
$945$		0			0
$946$	63.3311	−	6.50885i	2.05907	−	0.211621i
$947$		−	1.68665i		−	0.0548088i	−0.999624	−	0.0274044i	$-0.991276\pi$
$947$		−	1.68665i		−	0.0548088i	0.999624	−	0.0274044i	$-0.00872419\pi$
$948$		0			0
$949$		−	3.47002i		−	0.112642i
$950$		0			0
$951$		0			0
$952$	13.9022	−	4.41110i	0.450574	−	0.142965i
$953$	9.22616			0.298865			0.149432	−	0.988772i	$-0.452255\pi$
$953$	9.22616			0.298865			0.149432	+	0.988772i	$0.452255\pi$
$954$		0			0
$955$		0			0
$956$	−37.7038	+	7.83276i	−1.21943	+	0.253330i
$957$		0			0
$958$	31.0872	−	3.19499i	1.00438	−	0.103225i
$959$	−38.3699			−1.23903
$960$		0			0
$961$	−24.3522			−0.785554
$962$	−6.37279	+	0.654963i	−0.205467	+	0.0211169i
$963$		0			0
$964$	−26.7597	+	5.55918i	−0.861872	+	0.179049i
$965$		0			0
$966$		0			0
$967$	−12.2338			−0.393413			−0.196707	−	0.980462i	$-0.563025\pi$
$967$	−12.2338			−0.393413			−0.196707	+	0.980462i	$0.563025\pi$
$968$	−74.1631	+	23.5315i	−2.38369	+	0.756331i
$969$		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
$973$			45.2333i			1.45011i
$974$	−5.68111	+	0.583877i	−0.182035	+	0.0187086i
$975$		0			0
$976$	−19.7733	−	45.5366i	−0.632929	−	1.45759i
$977$	7.93051			0.253720			0.126860	−	0.991921i	$-0.459510\pi$
$977$	7.93051			0.253720			0.126860	+	0.991921i	$0.459510\pi$
$978$		0			0
$979$			82.2510i			2.62875i
$980$		0			0
$981$		0			0
$982$	2.63224	+	25.6116i	0.0839980	+	0.817300i
$983$	41.8993			1.33638			0.668191	−	0.743990i	$-0.267069\pi$
$983$	41.8993			1.33638			0.668191	+	0.743990i	$0.267069\pi$
$984$		0			0
$985$		0			0
$986$	0.411100	+	4.00000i	0.0130921	+	0.127386i
$987$		0			0
$988$	6.37279	−	1.32391i	0.202745	−	0.0421192i
$989$			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	$0.688755\pi$
$992$	−12.7144	+	7.14663i	−0.403683	+	0.226906i
$993$		0			0
$994$	−42.9200	+	4.41110i	−1.36134	+	0.139912i
$995$		0			0
$996$		0			0
$997$			8.04836i			0.254894i	0.991845	+	0.127447i	$0.0406783\pi$
$997$			8.04836i			0.254894i	−0.991845	+	0.127447i	$0.959322\pi$
$998$	−0.00859389	−	0.0836184i	−0.000272035	−	0.00264690i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1800.2.k.p.901.5		6
3.2	odd	2		600.2.k.c.301.2		6
4.3	odd	2		7200.2.k.p.3601.1		6
5.2	odd	4		1800.2.d.q.1549.4		6
5.3	odd	4		1800.2.d.r.1549.3		6
5.4	even	2		360.2.k.f.181.2		6
8.3	odd	2		7200.2.k.p.3601.2		6
8.5	even	2	inner	1800.2.k.p.901.6		6
12.11	even	2		2400.2.k.c.1201.4		6
15.2	even	4		600.2.d.e.349.3		6
15.8	even	4		600.2.d.f.349.4		6
15.14	odd	2		120.2.k.b.61.5	✓	6
20.3	even	4		7200.2.d.r.2449.5		6
20.7	even	4		7200.2.d.q.2449.2		6
20.19	odd	2		1440.2.k.f.721.3		6
24.5	odd	2		600.2.k.c.301.1		6
24.11	even	2		2400.2.k.c.1201.1		6
40.3	even	4		7200.2.d.q.2449.5		6
40.13	odd	4		1800.2.d.q.1549.3		6
40.19	odd	2		1440.2.k.f.721.6		6
40.27	even	4		7200.2.d.r.2449.2		6
40.29	even	2		360.2.k.f.181.1		6
40.37	odd	4		1800.2.d.r.1549.4		6
60.23	odd	4		2400.2.d.e.49.5		6
60.47	odd	4		2400.2.d.f.49.2		6
60.59	even	2		480.2.k.b.241.3		6
120.29	odd	2		120.2.k.b.61.6	yes	6
120.53	even	4		600.2.d.e.349.4		6
120.59	even	2		480.2.k.b.241.6		6
120.77	even	4		600.2.d.f.349.3		6
120.83	odd	4		2400.2.d.f.49.5		6
120.107	odd	4		2400.2.d.e.49.2		6
240.29	odd	4		3840.2.a.bp.1.3		3
240.59	even	4		3840.2.a.bo.1.1		3
240.149	odd	4		3840.2.a.bq.1.3		3
240.179	even	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	15.14	odd	2
120.2.k.b.61.6	yes	6	120.29	odd	2
360.2.k.f.181.1		6	40.29	even	2
360.2.k.f.181.2		6	5.4	even	2
480.2.k.b.241.3		6	60.59	even	2
480.2.k.b.241.6		6	120.59	even	2
600.2.d.e.349.3		6	15.2	even	4
600.2.d.e.349.4		6	120.53	even	4
600.2.d.f.349.3		6	120.77	even	4
600.2.d.f.349.4		6	15.8	even	4
600.2.k.c.301.1		6	24.5	odd	2
600.2.k.c.301.2		6	3.2	odd	2
1440.2.k.f.721.3		6	20.19	odd	2
1440.2.k.f.721.6		6	40.19	odd	2
1800.2.d.q.1549.3		6	40.13	odd	4
1800.2.d.q.1549.4		6	5.2	odd	4
1800.2.d.r.1549.3		6	5.3	odd	4
1800.2.d.r.1549.4		6	40.37	odd	4
1800.2.k.p.901.5		6	1.1	even	1	trivial
1800.2.k.p.901.6		6	8.5	even	2	inner
2400.2.d.e.49.2		6	120.107	odd	4
2400.2.d.e.49.5		6	60.23	odd	4
2400.2.d.f.49.2		6	60.47	odd	4
2400.2.d.f.49.5		6	120.83	odd	4
2400.2.k.c.1201.1		6	24.11	even	2
2400.2.k.c.1201.4		6	12.11	even	2
3840.2.a.bo.1.1		3	240.59	even	4
3840.2.a.bp.1.3		3	240.29	odd	4
3840.2.a.bq.1.3		3	240.149	odd	4
3840.2.a.br.1.1		3	240.179	even	4
7200.2.d.q.2449.2		6	20.7	even	4
7200.2.d.q.2449.5		6	40.3	even	4
7200.2.d.r.2449.2		6	40.27	even	4
7200.2.d.r.2449.5		6	20.3	even	4
7200.2.k.p.3601.1		6	4.3	odd	2
7200.2.k.p.3601.2		6	8.3	odd	2

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.k (of order \(2\), degree \(1\), minimal)

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

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