LMFDB - Embedded newform 1900.2.i.d.201.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1900,2,Mod(201,1900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1900, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("1900.201");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1900 = 2^{2} \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1900.i (of order $3$, degree $2$, 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:	$15.1715763840$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 9x^{6} + 2x^{5} + 65x^{4} - 20x^{3} + 25x^{2} + 6x + 4 $ x^8 - x^7 + 9x^6 + 2x^5 + 65x^4 - 20x^3 + 25x^2 + 6x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 380)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			201.4
Root			$1.58253 - 2.74101i$ of defining polynomial
Character	$\chi$	$=$	1900.201
Dual form			1900.2.i.d.501.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.58253 - 2.74101i) q^{3} +1.53315 q^{7} +(-3.50877 - 6.07738i) q^{9} +O(q^{10})$	$q+(1.58253 - 2.74101i) q^{3} +1.53315 q^{7} +(-3.50877 - 6.07738i) q^{9} -3.79695 q^{11} +(-3.34910 - 5.80081i) q^{13} +(-3.00877 + 5.21135i) q^{17} +(-3.93502 - 1.87499i) q^{19} +(2.42625 - 4.20239i) q^{21} +(2.19282 + 3.79808i) q^{23} -12.7158 q^{27} +(0.549376 + 0.951547i) q^{29} -1.05555 q^{31} +(-6.00877 + 10.4075i) q^{33} +10.7970 q^{37} -21.2002 q^{39} +(-1.76658 + 3.05980i) q^{41} +(2.77535 - 4.80705i) q^{43} +(-5.61907 - 9.73252i) q^{47} -4.64945 q^{49} +(9.52293 + 16.4942i) q^{51} +(0.788178 + 1.36516i) q^{53} +(-11.3667 + 7.81874i) q^{57} +(-1.61568 + 2.79843i) q^{59} +(-0.0331500 - 0.0574175i) q^{61} +(-5.37948 - 9.31753i) q^{63} +(-2.85250 - 4.94067i) q^{67} +13.8808 q^{69} +(3.23880 - 5.60977i) q^{71} +(6.98978 - 12.1066i) q^{73} -5.82130 q^{77} +(0.996602 - 1.72617i) q^{79} +(-9.59668 + 16.6219i) q^{81} +10.3477 q^{83} +3.47760 q^{87} +(-1.53655 - 2.66138i) q^{89} +(-5.13467 - 8.89352i) q^{91} +(-1.67043 + 2.89327i) q^{93} +(4.43502 - 7.68169i) q^{97} +(13.3227 + 23.0755i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{3} - 5 q^{9}+O(q^{10}) $ 8 * q + q^3 - 5 * q^9	$ 8 q + q^{3} - 5 q^{9} + 4 q^{11} - 9 q^{13} - q^{17} + 3 q^{19} + 8 q^{21} - 20 q^{27} + 5 q^{29} - 20 q^{31} - 25 q^{33} + 52 q^{37} - 54 q^{39} - 8 q^{41} - 7 q^{43} - 16 q^{47} + 20 q^{49} + 12 q^{51} - 5 q^{53} - 27 q^{57} + 11 q^{59} + 12 q^{61} + 3 q^{63} + 6 q^{69} + 14 q^{71} + 4 q^{73} + 44 q^{77} + 13 q^{79} - 24 q^{81} - 10 q^{83} + 4 q^{87} + 5 q^{89} - 46 q^{91} + 28 q^{93} + q^{97} + 24 q^{99}+O(q^{100}) $ 8 * q + q^3 - 5 * q^9 + 4 * q^11 - 9 * q^13 - q^17 + 3 * q^19 + 8 * q^21 - 20 * q^27 + 5 * q^29 - 20 * q^31 - 25 * q^33 + 52 * q^37 - 54 * q^39 - 8 * q^41 - 7 * q^43 - 16 * q^47 + 20 * q^49 + 12 * q^51 - 5 * q^53 - 27 * q^57 + 11 * q^59 + 12 * q^61 + 3 * q^63 + 6 * q^69 + 14 * q^71 + 4 * q^73 + 44 * q^77 + 13 * q^79 - 24 * q^81 - 10 * q^83 + 4 * q^87 + 5 * q^89 - 46 * q^91 + 28 * q^93 + q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times$.

$n$	$77$	$401$	$951$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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			0
$2$		0			0
$3$	1.58253	−	2.74101i	0.913672	−	1.58253i	0.104837	−	0.994489i	$-0.466568\pi$
$3$	1.58253	−	2.74101i	0.913672	−	1.58253i	0.808835	−	0.588036i	$-0.200099\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.53315			0.579476			0.289738	−	0.957106i	$-0.406432\pi$
$7$	1.53315			0.579476			0.289738	+	0.957106i	$0.406432\pi$
$8$		0			0
$9$	−3.50877	−	6.07738i	−1.16959	−	2.02579i
$10$		0			0
$11$	−3.79695			−1.14482			−0.572412	−	0.819966i	$-0.693992\pi$
$11$	−3.79695			−1.14482			−0.572412	+	0.819966i	$0.693992\pi$
$12$		0			0
$13$	−3.34910	−	5.80081i	−0.928873	−	1.60886i	−0.785210	−	0.619229i	$-0.787445\pi$
$13$	−3.34910	−	5.80081i	−0.928873	−	1.60886i	−0.143663	−	0.989627i	$-0.545888\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.00877	+	5.21135i	−0.729735	+	1.26394i	0.227260	+	0.973834i	$0.427023\pi$
$17$	−3.00877	+	5.21135i	−0.729735	+	1.26394i	−0.956995	+	0.290104i	$0.906310\pi$
$18$		0			0
$19$	−3.93502	−	1.87499i	−0.902756	−	0.430152i
$19$	−3.93502	−	1.87499i	−0.902756	−	0.430152i
$20$		0			0
$21$	2.42625	−	4.20239i	0.529451	−	0.917036i
$22$		0			0
$23$	2.19282	+	3.79808i	0.457235	+	0.791955i	0.998814	−	0.0486953i	$-0.0155063\pi$
$23$	2.19282	+	3.79808i	0.457235	+	0.791955i	−0.541578	+	0.840650i	$0.682173\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−12.7158			−2.44715
$28$		0			0
$29$	0.549376	+	0.951547i	0.102016	+	0.176698i	0.912515	−	0.409042i	$-0.134137\pi$
$29$	0.549376	+	0.951547i	0.102016	+	0.176698i	−0.810499	+	0.585740i	$0.800804\pi$
$30$		0			0
$31$	−1.05555			−0.189582			−0.0947908	−	0.995497i	$-0.530218\pi$
$31$	−1.05555			−0.189582			−0.0947908	+	0.995497i	$0.530218\pi$
$32$		0			0
$33$	−6.00877	+	10.4075i	−1.04599	+	1.81171i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	10.7970			1.77501			0.887504	−	0.460800i	$-0.152437\pi$
$37$	10.7970			1.77501			0.887504	+	0.460800i	$0.152437\pi$
$38$		0			0
$39$	−21.2002			−3.39474
$40$		0			0
$41$	−1.76658	+	3.05980i	−0.275893	+	0.477860i	−0.970360	−	0.241664i	$-0.922307\pi$
$41$	−1.76658	+	3.05980i	−0.275893	+	0.477860i	0.694467	+	0.719524i	$0.255640\pi$
$42$		0			0
$43$	2.77535	−	4.80705i	0.423237	−	0.733068i	−0.573017	−	0.819543i	$-0.694227\pi$
$43$	2.77535	−	4.80705i	0.423237	−	0.733068i	0.996254	+	0.0864756i	$0.0275605\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.61907	−	9.73252i	−0.819626	−	1.41963i	−0.905958	−	0.423368i	$-0.860848\pi$
$47$	−5.61907	−	9.73252i	−0.819626	−	1.41963i	0.0863319	−	0.996266i	$-0.472485\pi$
$48$		0			0
$49$	−4.64945			−0.664207
$50$		0			0
$51$	9.52293	+	16.4942i	1.33348	+	2.30965i
$52$		0			0
$53$	0.788178	+	1.36516i	0.108265	+	0.187520i	0.915067	−	0.403301i	$-0.132137\pi$
$53$	0.788178	+	1.36516i	0.108265	+	0.187520i	−0.806803	+	0.590821i	$0.798804\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−11.3667	+	7.81874i	−1.50555	+	1.03562i
$58$		0			0
$59$	−1.61568	+	2.79843i	−0.210343	+	0.364325i	−0.951822	−	0.306651i	$-0.900791\pi$
$59$	−1.61568	+	2.79843i	−0.210343	+	0.364325i	0.741479	+	0.670976i	$0.234125\pi$
$60$		0			0
$61$	−0.0331500	−	0.0574175i	−0.00424442	−	0.00735156i	0.863895	−	0.503671i	$-0.168018\pi$
$61$	−0.0331500	−	0.0574175i	−0.00424442	−	0.00735156i	−0.868140	+	0.496320i	$0.834684\pi$
$62$		0			0
$63$	−5.37948	−	9.31753i	−0.677751	−	1.17390i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−2.85250	−	4.94067i	−0.348488	−	0.603599i	0.637493	−	0.770456i	$-0.279972\pi$
$67$	−2.85250	−	4.94067i	−0.348488	−	0.603599i	−0.985981	+	0.166857i	$0.946638\pi$
$68$		0			0
$69$	13.8808			1.67105
$70$		0			0
$71$	3.23880	−	5.60977i	0.384375	−	0.665757i	−0.607307	−	0.794467i	$-0.707750\pi$
$71$	3.23880	−	5.60977i	0.384375	−	0.665757i	0.991682	+	0.128710i	$0.0410836\pi$
$72$		0			0
$73$	6.98978	−	12.1066i	0.818091	−	1.41698i	−0.0889951	−	0.996032i	$-0.528366\pi$
$73$	6.98978	−	12.1066i	0.818091	−	1.41698i	0.907087	−	0.420944i	$-0.138301\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−5.82130			−0.663398
$78$		0			0
$79$	0.996602	−	1.72617i	0.112127	−	0.194209i	−0.804501	−	0.593951i	$-0.797567\pi$
$79$	0.996602	−	1.72617i	0.112127	−	0.194209i	0.916627	+	0.399743i	$0.130900\pi$
$80$		0			0
$81$	−9.59668	+	16.6219i	−1.06630	+	1.84688i
$82$		0			0
$83$	10.3477			1.13580			0.567901	−	0.823097i	$-0.307756\pi$
$83$	10.3477			1.13580			0.567901	+	0.823097i	$0.307756\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	3.47760			0.372838
$88$		0			0
$89$	−1.53655	−	2.66138i	−0.162874	−	0.282106i	0.773024	−	0.634376i	$-0.218743\pi$
$89$	−1.53655	−	2.66138i	−0.162874	−	0.282106i	−0.935898	+	0.352271i	$0.885410\pi$
$90$		0			0
$91$	−5.13467	−	8.89352i	−0.538260	−	0.932294i
$92$		0			0
$93$	−1.67043	+	2.89327i	−0.173215	+	0.300018i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	4.43502	−	7.68169i	0.450308	−	0.779957i	−0.548097	−	0.836415i	$-0.684647\pi$
$97$	4.43502	−	7.68169i	0.450308	−	0.779957i	0.998405	+	0.0564579i	$0.0179807\pi$
$98$		0			0
$99$	13.3227	+	23.0755i	1.33898	+	2.31918i
$100$		0			0
$101$	−3.10413	−	5.37651i	−0.308872	−	0.534983i	0.669244	−	0.743043i	$-0.266618\pi$
$101$	−3.10413	−	5.37651i	−0.308872	−	0.534983i	−0.978116	+	0.208060i	$0.933285\pi$
$102$		0			0
$103$	0.253048			0.0249336			0.0124668	−	0.999922i	$-0.496032\pi$
$103$	0.253048			0.0249336			0.0124668	+	0.999922i	$0.496032\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.05555			0.585412			0.292706	−	0.956203i	$-0.405444\pi$
$107$	6.05555			0.585412			0.292706	+	0.956203i	$0.405444\pi$
$108$		0			0
$109$	−2.62445	+	4.54568i	−0.251377	+	0.435397i	−0.963905	−	0.266246i	$-0.914217\pi$
$109$	−2.62445	+	4.54568i	−0.251377	+	0.435397i	0.712528	+	0.701643i	$0.247550\pi$
$110$		0			0
$111$	17.0865	−	29.5946i	1.62177	−	2.80900i
$112$		0			0
$113$	−2.42885			−0.228487			−0.114244	−	0.993453i	$-0.536444\pi$
$113$	−2.42885			−0.228487			−0.114244	+	0.993453i	$0.536444\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−23.5025	+	40.7075i	−2.17281	+	3.76341i
$118$		0			0
$119$	−4.61290	+	7.98978i	−0.422864	+	0.732422i
$120$		0			0
$121$	3.41685			0.310623
$122$		0			0
$123$	5.59130	+	9.68442i	0.504151	+	0.873214i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−9.64945	−	16.7133i	−0.856250	−	1.48307i	−0.875480	−	0.483254i	$-0.839455\pi$
$127$	−9.64945	−	16.7133i	−0.856250	−	1.48307i	0.0192299	−	0.999815i	$-0.493879\pi$
$128$		0			0
$129$	−8.78412	−	15.2146i	−0.773399	−	1.33957i
$130$		0			0
$131$	6.62983	−	11.4832i	0.579251	−	1.00329i	−0.416315	−	0.909221i	$-0.636679\pi$
$131$	6.62983	−	11.4832i	0.579251	−	1.00329i	0.995565	−	0.0940711i	$-0.0299881\pi$
$132$		0			0
$133$	−6.03298	−	2.87464i	−0.523126	−	0.249263i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−7.77535	−	13.4673i	−0.664293	−	1.15059i	−0.979476	−	0.201558i	$-0.935399\pi$
$137$	−7.77535	−	13.4673i	−0.664293	−	1.15059i	0.315184	−	0.949031i	$-0.397934\pi$
$138$		0			0
$139$	9.31110	+	16.1273i	0.789758	+	1.36790i	0.926115	+	0.377241i	$0.123127\pi$
$139$	9.31110	+	16.1273i	0.789758	+	1.36790i	−0.136358	+	0.990660i	$0.543540\pi$
$140$		0			0
$141$	−35.5693			−2.99548
$142$		0			0
$143$	12.7164	+	22.0254i	1.06340	+	1.84186i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−7.35788	+	12.7442i	−0.606867	+	1.05113i
$148$		0			0
$149$	2.34372	−	4.05945i	0.192005	−	0.332563i	−0.753909	−	0.656978i	$-0.771834\pi$
$149$	2.34372	−	4.05945i	0.192005	−	0.332563i	0.945915	+	0.324415i	$0.105168\pi$
$150$		0			0
$151$	−5.93370			−0.482878			−0.241439	−	0.970416i	$-0.577619\pi$
$151$	−5.93370			−0.482878			−0.241439	+	0.970416i	$0.577619\pi$
$152$		0			0
$153$	42.2285			3.41397
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−4.64685	+	8.04857i	−0.370859	+	0.642346i	−0.989698	−	0.143172i	$-0.954270\pi$
$157$	−4.64685	+	8.04857i	−0.370859	+	0.642346i	0.618839	+	0.785518i	$0.287603\pi$
$158$		0			0
$159$	4.98925			0.395673
$160$		0			0
$161$	3.36193	+	5.82303i	0.264957	+	0.458919i
$162$		0			0
$163$	−5.88495			−0.460945			−0.230472	−	0.973079i	$-0.574027\pi$
$163$	−5.88495			−0.460945			−0.230472	+	0.973079i	$0.574027\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	6.39848	+	11.0825i	0.495129	+	0.857589i	0.999984	−	0.00561549i	$-0.00178747\pi$
$167$	6.39848	+	11.0825i	0.495129	+	0.857589i	−0.504855	+	0.863204i	$0.668454\pi$
$168$		0			0
$169$	−15.9330	+	27.5967i	−1.22561	+	2.12282i
$170$		0			0
$171$	2.41210	+	30.4935i	0.184458	+	2.33190i
$172$		0			0
$173$	−7.52032	+	13.0256i	−0.571760	+	0.990317i	0.424626	+	0.905369i	$0.360406\pi$
$173$	−7.52032	+	13.0256i	−0.571760	+	0.990317i	−0.996385	+	0.0849476i	$0.972928\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	5.11370	+	8.85718i	0.384369	+	0.665747i
$178$		0			0
$179$	21.5452			1.61036			0.805180	−	0.593030i	$-0.202069\pi$
$179$	21.5452			1.61036			0.805180	+	0.593030i	$0.202069\pi$
$180$		0			0
$181$	−2.13530	−	3.69845i	−0.158716	−	0.274903i	0.775690	−	0.631114i	$-0.217402\pi$
$181$	−2.13530	−	3.69845i	−0.158716	−	0.274903i	−0.934406	+	0.356210i	$0.884069\pi$
$182$		0			0
$183$	−0.209843			−0.0155120
$184$		0			0
$185$		0			0
$186$		0			0
$187$	11.4242	−	19.7873i	0.835418	−	1.44699i
$188$		0			0
$189$	−19.4952			−1.41806
$190$		0			0
$191$	−6.30180			−0.455982			−0.227991	−	0.973663i	$-0.573216\pi$
$191$	−6.30180			−0.455982			−0.227991	+	0.973663i	$0.573216\pi$
$192$		0			0
$193$	−7.68943	+	13.3185i	−0.553497	+	0.958685i	0.444522	+	0.895768i	$0.353374\pi$
$193$	−7.68943	+	13.3185i	−0.553497	+	0.958685i	−0.998019	+	0.0629169i	$0.979960\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	12.7210			0.906331			0.453165	−	0.891426i	$-0.350295\pi$
$197$	12.7210			0.906331			0.453165	+	0.891426i	$0.350295\pi$
$198$		0			0
$199$	−5.10885	−	8.84879i	−0.362157	−	0.627274i	0.626159	−	0.779696i	$-0.284626\pi$
$199$	−5.10885	−	8.84879i	−0.362157	−	0.627274i	−0.988316	+	0.152422i	$0.951293\pi$
$200$		0			0
$201$	−18.0566			−1.27361
$202$		0			0
$203$	0.842275	+	1.45886i	0.0591161	+	0.102392i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	15.3883	−	26.6532i	1.06956	−	1.85253i
$208$		0			0
$209$	14.9411	+	7.11925i	1.03350	+	0.492449i
$210$		0			0
$211$	−2.53655	+	4.39343i	−0.174623	+	0.302456i	−0.940031	−	0.341090i	$-0.889204\pi$
$211$	−2.53655	+	4.39343i	−0.174623	+	0.302456i	0.765408	+	0.643546i	$0.222537\pi$
$212$		0			0
$213$	−10.2510	−	17.7552i	−0.702385	−	1.21657i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−1.61831			−0.109858
$218$		0			0
$219$	−22.1230	−	38.3182i	−1.49493	−	2.58930i
$220$		0			0
$221$	40.3068			2.71133
$222$		0			0
$223$	−4.26318	+	7.38404i	−0.285483	+	0.494472i	−0.972726	−	0.231956i	$-0.925487\pi$
$223$	−4.26318	+	7.38404i	−0.285483	+	0.494472i	0.687243	+	0.726428i	$0.258821\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	20.0566			1.33120			0.665602	−	0.746307i	$-0.268175\pi$
$227$	20.0566			1.33120			0.665602	+	0.746307i	$0.268175\pi$
$228$		0			0
$229$	7.92955			0.524000			0.262000	−	0.965068i	$-0.415618\pi$
$229$	7.92955			0.524000			0.262000	+	0.965068i	$0.415618\pi$
$230$		0			0
$231$	−9.21235	+	15.9563i	−0.606128	+	1.04985i
$232$		0			0
$233$	5.28950	−	9.16169i	0.346527	−	0.600202i	−0.639103	−	0.769121i	$-0.720694\pi$
$233$	5.28950	−	9.16169i	0.346527	−	0.600202i	0.985630	+	0.168919i	$0.0540276\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−3.15430	−	5.46340i	−0.204894	−	0.354886i
$238$		0			0
$239$	−5.68065			−0.367451			−0.183725	−	0.982978i	$-0.558816\pi$
$239$	−5.68065			−0.367451			−0.183725	+	0.982978i	$0.558816\pi$
$240$		0			0
$241$	−4.75714	−	8.23962i	−0.306435	−	0.530760i	0.671145	−	0.741326i	$-0.265803\pi$
$241$	−4.75714	−	8.23962i	−0.306435	−	0.530760i	−0.977580	+	0.210566i	$0.932469\pi$
$242$		0			0
$243$	11.3004	+	19.5728i	0.724918	+	1.25559i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	2.30233	+	29.1059i	0.146494	+	1.85196i
$248$		0			0
$249$	16.3754	−	28.3631i	1.03775	−	1.79744i
$250$		0			0
$251$	−6.26658	−	10.8540i	−0.395543	−	0.685100i	0.597628	−	0.801774i	$-0.296110\pi$
$251$	−6.26658	−	10.8540i	−0.395543	−	0.685100i	−0.993170	+	0.116674i	$0.962777\pi$
$252$		0			0
$253$	−8.32605	−	14.4211i	−0.523454	−	0.906649i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−8.54453	−	14.7996i	−0.532993	−	0.923171i	−0.999258	−	0.0385258i	$-0.987734\pi$
$257$	−8.54453	−	14.7996i	−0.532993	−	0.923171i	0.466264	−	0.884645i	$-0.345600\pi$
$258$		0			0
$259$	16.5533			1.02857
$260$		0			0
$261$	3.85527	−	6.67753i	0.238635	−	0.413328i
$262$		0			0
$263$	0.460054	−	0.796838i	0.0283682	−	0.0491351i	−0.851493	−	0.524366i	$-0.824302\pi$
$263$	0.460054	−	0.796838i	0.0283682	−	0.0491351i	0.879861	+	0.475231i	$0.157636\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−9.72651			−0.595252
$268$		0			0
$269$	−12.6826	+	21.9669i	−0.773272	+	1.33935i	0.162489	+	0.986710i	$0.448048\pi$
$269$	−12.6826	+	21.9669i	−0.773272	+	1.33935i	−0.935761	+	0.352636i	$0.885285\pi$
$270$		0			0
$271$	5.61828	−	9.73115i	0.341286	−	0.591125i	−0.643386	−	0.765542i	$-0.722471\pi$
$271$	5.61828	−	9.73115i	0.341286	−	0.591125i	0.984672	+	0.174417i	$0.0558041\pi$
$272$		0			0
$273$	−32.5030			−1.96717
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−16.5491			−0.994340			−0.497170	−	0.867653i	$-0.665627\pi$
$277$	−16.5491			−0.994340			−0.497170	+	0.867653i	$0.665627\pi$
$278$		0			0
$279$	3.70367	+	6.41495i	0.221733	+	0.384053i
$280$		0			0
$281$	5.28950	+	9.16169i	0.315545	+	0.546540i	0.979553	−	0.201185i	$-0.0644793\pi$
$281$	5.28950	+	9.16169i	0.315545	+	0.546540i	−0.664008	+	0.747725i	$0.731146\pi$
$282$		0			0
$283$	10.3707	−	17.9626i	0.616474	−	1.06776i	−0.373650	−	0.927570i	$-0.621894\pi$
$283$	10.3707	−	17.9626i	0.616474	−	1.06776i	0.990124	−	0.140195i	$-0.0447729\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−2.70842	+	4.69113i	−0.159873	+	0.276909i
$288$		0			0
$289$	−9.60545	−	16.6371i	−0.565027	−	0.978655i
$290$		0			0
$291$	−14.0371	−	24.3129i	−0.822868	−	1.42525i
$292$		0			0
$293$	−13.6846			−0.799460			−0.399730	−	0.916633i	$-0.630896\pi$
$293$	−13.6846			−0.799460			−0.399730	+	0.916633i	$0.630896\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	48.2811			2.80155
$298$		0			0
$299$	14.6880	−	25.4403i	0.849428	−	1.47125i
$300$		0			0
$301$	4.25503	−	7.36992i	0.245256	−	0.424795i
$302$		0			0
$303$	−19.6495			−1.12883
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−4.31872	+	7.48025i	−0.246483	+	0.426920i	−0.962547	−	0.271113i	$-0.912608\pi$
$307$	−4.31872	+	7.48025i	−0.246483	+	0.426920i	0.716065	+	0.698034i	$0.245941\pi$
$308$		0			0
$309$	0.400456	−	0.693609i	0.0227811	−	0.0394581i
$310$		0			0
$311$	29.7658			1.68786			0.843930	−	0.536453i	$-0.180236\pi$
$311$	29.7658			1.68786			0.843930	+	0.536453i	$0.180236\pi$
$312$		0			0
$313$	5.60413	+	9.70664i	0.316764	+	0.548651i	0.979811	−	0.199926i	$-0.0640703\pi$
$313$	5.60413	+	9.70664i	0.316764	+	0.548651i	−0.663047	+	0.748578i	$0.730737\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.34650	−	4.06425i	−0.131792	−	0.228271i	0.792575	−	0.609774i	$-0.208740\pi$
$317$	−2.34650	−	4.06425i	−0.131792	−	0.228271i	−0.924368	+	0.381503i	$0.875407\pi$
$318$		0			0
$319$	−2.08595	−	3.61298i	−0.116791	−	0.202288i
$320$		0			0
$321$	9.58306	−	16.5983i	0.534874	−	0.926429i
$322$		0			0
$323$	21.6108	−	14.8654i	1.20246	−	0.827131i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	8.30652	+	14.3873i	0.459352	+	0.795620i
$328$		0			0
$329$	−8.61488	−	14.9214i	−0.474954	−	0.822644i
$330$		0			0
$331$	29.1137			1.60024			0.800118	−	0.599843i	$-0.204770\pi$
$331$	29.1137			1.60024			0.800118	+	0.599843i	$0.204770\pi$
$332$		0			0
$333$	−37.8841	−	65.6171i	−2.07603	−	3.59580i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	11.5790	−	20.0554i	0.630749	−	1.09249i	−0.356650	−	0.934238i	$-0.616081\pi$
$337$	11.5790	−	20.0554i	0.630749	−	1.09249i	0.987399	−	0.158251i	$-0.0505854\pi$
$338$		0			0
$339$	−3.84372	+	6.65752i	−0.208762	+	0.361587i
$340$		0			0
$341$	4.00786			0.217038
$342$		0			0
$343$	−17.8604			−0.964369
$344$		0			0
$345$		0			0
$346$		0			0
$347$	7.83090	−	13.5635i	0.420385	−	0.728127i	−0.575592	−	0.817737i	$-0.695229\pi$
$347$	7.83090	−	13.5635i	0.420385	−	0.728127i	0.995977	+	0.0896094i	$0.0285619\pi$
$348$		0			0
$349$	−9.72130			−0.520369			−0.260185	−	0.965559i	$-0.583783\pi$
$349$	−9.72130			−0.520369			−0.260185	+	0.965559i	$0.583783\pi$
$350$		0			0
$351$	42.5863	+	73.7617i	2.27309	+	3.93711i
$352$		0			0
$353$	−11.3789			−0.605635			−0.302818	−	0.953049i	$-0.597927\pi$
$353$	−11.3789			−0.605635			−0.302818	+	0.953049i	$0.597927\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	14.6001	+	25.2881i	0.772718	+	1.33839i
$358$		0			0
$359$	−14.3876	+	24.9201i	−0.759350	+	1.31523i	0.183833	+	0.982958i	$0.441150\pi$
$359$	−14.3876	+	24.9201i	−0.759350	+	1.31523i	−0.943183	+	0.332275i	$0.892184\pi$
$360$		0			0
$361$	11.9688	+	14.7563i	0.629938	+	0.776645i
$362$		0			0
$363$	5.40725	−	9.36563i	0.283807	−	0.491568i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−12.0649	−	20.8969i	−0.629780	−	1.09081i	−0.987596	−	0.157019i	$-0.949812\pi$
$367$	−12.0649	−	20.8969i	−0.629780	−	1.09081i	0.357815	−	0.933792i	$-0.383522\pi$
$368$		0			0
$369$	24.7941			1.29073
$370$		0			0
$371$	1.20839	+	2.09300i	0.0627367	+	0.108663i
$372$		0			0
$373$	26.7281			1.38393			0.691964	−	0.721932i	$-0.256746\pi$
$373$	26.7281			1.38393			0.691964	+	0.721932i	$0.256746\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	3.67983	−	6.37365i	0.189521	−	0.328260i
$378$		0			0
$379$	4.29369			0.220552			0.110276	−	0.993901i	$-0.464826\pi$
$379$	4.29369			0.220552			0.110276	+	0.993901i	$0.464826\pi$
$380$		0			0
$381$	−61.0820			−3.12933
$382$		0			0
$383$	2.78610	−	4.82567i	0.142363	−	0.246580i	−0.786023	−	0.618197i	$-0.787863\pi$
$383$	2.78610	−	4.82567i	0.142363	−	0.246580i	0.928386	+	0.371617i	$0.121197\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−38.9523			−1.98006
$388$		0			0
$389$	−14.0743	−	24.3774i	−0.713594	−	1.23598i	−0.963499	−	0.267711i	$-0.913733\pi$
$389$	−14.0743	−	24.3774i	−0.713594	−	1.23598i	0.249905	−	0.968270i	$-0.419601\pi$
$390$		0			0
$391$	−26.3909			−1.33464
$392$		0			0
$393$	−20.9837	−	36.3449i	−1.05849	−	1.83336i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	17.3712	−	30.0879i	0.871837	−	1.51007i	0.0117431	−	0.999931i	$-0.496262\pi$
$397$	17.3712	−	30.0879i	0.871837	−	1.51007i	0.860094	−	0.510135i	$-0.170405\pi$
$398$		0			0
$399$	−17.4268	+	11.9873i	−0.872430	+	0.600116i
$400$		0			0
$401$	11.9370	−	20.6755i	0.596106	−	1.03249i	−0.397284	−	0.917696i	$-0.630047\pi$
$401$	11.9370	−	20.6755i	0.596106	−	1.03249i	0.993390	−	0.114789i	$-0.0366193\pi$
$402$		0			0
$403$	3.53513	+	6.12302i	0.176097	+	0.305010i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−40.9955			−2.03207
$408$		0			0
$409$	18.7346	+	32.4492i	0.926365	+	1.60451i	0.789350	+	0.613943i	$0.210418\pi$
$409$	18.7346	+	32.4492i	0.926365	+	1.60451i	0.137015	+	0.990569i	$0.456249\pi$
$410$		0			0
$411$	−49.2188			−2.42778
$412$		0			0
$413$	−2.47707	+	4.29042i	−0.121889	+	0.211118i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	58.9402			2.88632
$418$		0			0
$419$	−0.360241			−0.0175989			−0.00879947	−	0.999961i	$-0.502801\pi$
$419$	−0.360241			−0.0175989			−0.00879947	+	0.999961i	$0.502801\pi$
$420$		0			0
$421$	−12.1243	+	20.9999i	−0.590901	+	1.02347i	0.403210	+	0.915108i	$0.367894\pi$
$421$	−12.1243	+	20.9999i	−0.590901	+	1.02347i	−0.994111	+	0.108364i	$0.965439\pi$
$422$		0			0
$423$	−39.4321	+	68.2984i	−1.91726	+	3.32078i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−0.0508239	−	0.0880297i	−0.00245954	−	0.00426005i
$428$		0			0
$429$	80.4960			3.88638
$430$		0			0
$431$	6.32067	+	10.9477i	0.304456	+	0.527333i	0.977140	−	0.212596i	$-0.0681920\pi$
$431$	6.32067	+	10.9477i	0.304456	+	0.527333i	−0.672684	+	0.739930i	$0.734859\pi$
$432$		0			0
$433$	−12.2320	−	21.1864i	−0.587831	−	1.01815i	−0.994516	−	0.104585i	$-0.966649\pi$
$433$	−12.2320	−	21.1864i	−0.587831	−	1.01815i	0.406685	−	0.913569i	$-0.366685\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.50745	−	19.0571i	−0.0721111	−	0.911623i
$438$		0			0
$439$	12.4004	−	21.4782i	0.591840	−	1.02510i	−0.402144	−	0.915576i	$-0.631735\pi$
$439$	12.4004	−	21.4782i	0.591840	−	1.02510i	0.993985	−	0.109521i	$-0.0349316\pi$
$440$		0			0
$441$	16.3139	+	28.2565i	0.776851	+	1.34555i
$442$		0			0
$443$	15.1318	+	26.2090i	0.718932	+	1.24523i	0.961423	+	0.275074i	$0.0887023\pi$
$443$	15.1318	+	26.2090i	0.718932	+	1.24523i	−0.242491	+	0.970154i	$0.577964\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−7.41801	−	12.8484i	−0.350860	−	0.607707i
$448$		0			0
$449$	−29.0742			−1.37209			−0.686047	−	0.727557i	$-0.740656\pi$
$449$	−29.0742			−1.37209			−0.686047	+	0.727557i	$0.740656\pi$
$450$		0			0
$451$	6.70760	−	11.6179i	0.315849	−	0.547066i
$452$		0			0
$453$	−9.39023	+	16.2644i	−0.441192	+	0.764166i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	3.06234			0.143250			0.0716251	−	0.997432i	$-0.477181\pi$
$457$	3.06234			0.143250			0.0716251	+	0.997432i	$0.477181\pi$
$458$		0			0
$459$	38.2588	−	66.2662i	1.78577	−	3.09304i
$460$		0			0
$461$	13.2934	−	23.0249i	0.619137	−	1.07238i	−0.370507	−	0.928830i	$-0.620816\pi$
$461$	13.2934	−	23.0249i	0.619137	−	1.07238i	0.989644	−	0.143547i	$-0.0458507\pi$
$462$		0			0
$463$	−4.82684			−0.224322			−0.112161	−	0.993690i	$-0.535777\pi$
$463$	−4.82684			−0.224322			−0.112161	+	0.993690i	$0.535777\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	1.31539			0.0608690			0.0304345	−	0.999537i	$-0.490311\pi$
$467$	1.31539			0.0608690			0.0304345	+	0.999537i	$0.490311\pi$
$468$		0			0
$469$	−4.37331	−	7.57479i	−0.201941	−	0.349771i
$470$		0			0
$471$	14.7075	+	25.4741i	0.677686	+	1.17379i
$472$		0			0
$473$	−10.5379	+	18.2521i	−0.484532	+	0.839234i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	5.53108	−	9.58011i	0.253251	−	0.438643i
$478$		0			0
$479$	−9.53915	−	16.5223i	−0.435855	−	0.754923i	0.561510	−	0.827470i	$-0.310221\pi$
$479$	−9.53915	−	16.5223i	−0.435855	−	0.754923i	−0.997365	+	0.0725469i	$0.976887\pi$
$480$		0			0
$481$	−36.1601	−	62.6311i	−1.64876	−	2.85573i
$482$		0			0
$483$	21.2814			0.968335
$484$		0			0
$485$		0			0
$486$		0			0
$487$	8.23656			0.373234			0.186617	−	0.982433i	$-0.440248\pi$
$487$	8.23656			0.373234			0.186617	+	0.982433i	$0.440248\pi$
$488$		0			0
$489$	−9.31308	+	16.1307i	−0.421152	+	0.729457i
$490$		0			0
$491$	−15.4776	+	26.8079i	−0.698493	+	1.20983i	0.270496	+	0.962721i	$0.412812\pi$
$491$	−15.4776	+	26.8079i	−0.698493	+	1.20983i	−0.968989	+	0.247104i	$0.920521\pi$
$492$		0			0
$493$	−6.61179			−0.297780
$494$		0			0
$495$		0			0
$496$		0			0
$497$	4.96557	−	8.60062i	0.222736	−	0.385790i
$498$		0			0
$499$	−0.554753	+	0.960860i	−0.0248341	+	0.0430140i	−0.878175	−	0.478339i	$-0.841239\pi$
$499$	−0.554753	+	0.960860i	−0.0248341	+	0.0430140i	0.853341	+	0.521353i	$0.174572\pi$
$500$		0			0
$501$	40.5030			1.80954
$502$		0			0
$503$	4.32552	+	7.49202i	0.192865	+	0.334053i	0.946199	−	0.323586i	$-0.104889\pi$
$503$	4.32552	+	7.49202i	0.192865	+	0.334053i	−0.753333	+	0.657639i	$0.771555\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	50.4286	+	87.3449i	2.23961	+	3.87912i
$508$		0			0
$509$	10.3944	+	18.0037i	0.460725	+	0.797999i	0.998997	−	0.0447722i	$-0.0142562\pi$
$509$	10.3944	+	18.0037i	0.460725	+	0.797999i	−0.538273	+	0.842771i	$0.680923\pi$
$510$		0			0
$511$	10.7164	−	18.5613i	0.474065	−	0.821104i
$512$		0			0
$513$	50.0368	+	23.8419i	2.20918	+	1.05265i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	21.3354	+	36.9539i	0.938328	+	1.62523i
$518$		0			0
$519$	23.8022	+	41.2266i	1.04480	+	1.80965i
$520$		0			0
$521$	−24.5098			−1.07379			−0.536897	−	0.843648i	$-0.680404\pi$
$521$	−24.5098			−1.07379			−0.536897	+	0.843648i	$0.680404\pi$
$522$		0			0
$523$	9.03447	+	15.6482i	0.395050	+	0.684247i	0.993108	−	0.117207i	$-0.0373939\pi$
$523$	9.03447	+	15.6482i	0.395050	+	0.684247i	−0.598058	+	0.801453i	$0.704061\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	3.17590	−	5.50082i	0.138344	−	0.239619i
$528$		0			0
$529$	1.88304	−	3.26153i	0.0818715	−	0.141806i
$530$		0			0
$531$	22.6762			0.984062
$532$		0			0
$533$	23.6658			1.02508
$534$		0			0
$535$		0			0
$536$		0			0
$537$	34.0958	−	59.0556i	1.47134	−	2.54844i
$538$		0			0
$539$	17.6537			0.760401
$540$		0			0
$541$	8.75440	+	15.1631i	0.376381	+	0.651911i	0.990533	−	0.137277i	$-0.0438350\pi$
$541$	8.75440	+	15.1631i	0.376381	+	0.651911i	−0.614152	+	0.789188i	$0.710502\pi$
$542$		0			0
$543$	−13.5167			−0.580055
$544$		0			0
$545$		0			0
$546$		0			0
$547$	13.4864	+	23.3591i	0.576636	+	0.998763i	0.995862	+	0.0908807i	$0.0289682\pi$
$547$	13.4864	+	23.3591i	0.576636	+	0.998763i	−0.419226	+	0.907882i	$0.637698\pi$
$548$		0			0
$549$	−0.232632	+	0.402930i	−0.00992849	+	0.0171966i
$550$		0			0
$551$	−0.377667	−	4.77443i	−0.0160891	−	0.203398i
$552$		0			0
$553$	1.52794	−	2.64647i	0.0649746	−	0.112539i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−7.98361	−	13.8280i	−0.338276	−	0.585912i	0.645832	−	0.763479i	$-0.276510\pi$
$557$	−7.98361	−	13.8280i	−0.338276	−	0.585912i	−0.984109	+	0.177568i	$0.943177\pi$
$558$		0			0
$559$	−37.1797			−1.57253
$560$		0			0
$561$	−36.1581	−	62.6277i	−1.52660	−	2.64414i
$562$		0			0
$563$	8.58711			0.361904			0.180952	−	0.983492i	$-0.442082\pi$
$563$	8.58711			0.361904			0.180952	+	0.983492i	$0.442082\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−14.7131	+	25.4839i	−0.617894	+	1.07022i
$568$		0			0
$569$	22.5910			0.947064			0.473532	−	0.880777i	$-0.342979\pi$
$569$	22.5910			0.947064			0.473532	+	0.880777i	$0.342979\pi$
$570$		0			0
$571$	17.1000			0.715613			0.357806	−	0.933796i	$-0.383525\pi$
$571$	17.1000			0.715613			0.357806	+	0.933796i	$0.383525\pi$
$572$		0			0
$573$	−9.97276	+	17.2733i	−0.416618	+	0.721603i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	0.677755			0.0282153			0.0141077	−	0.999900i	$-0.495509\pi$
$577$	0.677755			0.0282153			0.0141077	+	0.999900i	$0.495509\pi$
$578$		0			0
$579$	24.3374	+	42.1537i	1.01143	+	1.75185i
$580$		0			0
$581$	15.8645			0.658171
$582$		0			0
$583$	−2.99267	−	5.18346i	−0.123944	−	0.214677i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	13.6859	−	23.7047i	0.564878	−	0.978397i	−0.432183	−	0.901786i	$-0.642257\pi$
$587$	13.6859	−	23.7047i	0.564878	−	0.978397i	0.997061	−	0.0766112i	$-0.0244100\pi$
$588$		0			0
$589$	4.15360	+	1.97914i	0.171146	+	0.0815489i
$590$		0			0
$591$	20.1312	−	34.8683i	0.828089	−	1.43429i
$592$		0			0
$593$	4.18940	+	7.25625i	0.172038	+	0.297978i	0.939132	−	0.343556i	$-0.111632\pi$
$593$	4.18940	+	7.25625i	0.172038	+	0.297978i	−0.767094	+	0.641534i	$0.778298\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−32.3395			−1.32357
$598$		0			0
$599$	16.9553	+	29.3675i	0.692777	+	1.19992i	0.970924	+	0.239386i	$0.0769462\pi$
$599$	16.9553	+	29.3675i	0.692777	+	1.19992i	−0.278148	+	0.960538i	$0.589720\pi$
$600$		0			0
$601$	−5.74951			−0.234528			−0.117264	−	0.993101i	$-0.537412\pi$
$601$	−5.74951			−0.234528			−0.117264	+	0.993101i	$0.537412\pi$
$602$		0			0
$603$	−20.0175	+	34.6714i	−0.815178	+	1.41193i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	8.87815			0.360353			0.180177	−	0.983634i	$-0.442333\pi$
$607$	8.87815			0.360353			0.180177	+	0.983634i	$0.442333\pi$
$608$		0			0
$609$	5.33169			0.216051
$610$		0			0
$611$	−37.6377	+	65.1904i	−1.52266	+	2.63732i
$612$		0			0
$613$	−6.02098	+	10.4286i	−0.243185	+	0.421209i	−0.961620	−	0.274386i	$-0.911526\pi$
$613$	−6.02098	+	10.4286i	−0.243185	+	0.421209i	0.718435	+	0.695594i	$0.244859\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	23.4362	+	40.5927i	0.943505	+	1.63420i	0.758717	+	0.651420i	$0.225827\pi$
$617$	23.4362	+	40.5927i	0.943505	+	1.63420i	0.184788	+	0.982778i	$0.440840\pi$
$618$		0			0
$619$	14.8700			0.597678			0.298839	−	0.954304i	$-0.403401\pi$
$619$	14.8700			0.597678			0.298839	+	0.954304i	$0.403401\pi$
$620$		0			0
$621$	−27.8834	−	48.2955i	−1.11892	−	1.93803i
$622$		0			0
$623$	−2.35576	−	4.08029i	−0.0943815	−	0.163473i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	43.1586	−	29.6874i	1.72359	−	1.18560i
$628$		0			0
$629$	−32.4856	+	56.2667i	−1.29529	+	2.24350i
$630$		0			0
$631$	−8.71235	−	15.0902i	−0.346833	−	0.600733i	0.638852	−	0.769330i	$-0.279410\pi$
$631$	−8.71235	−	15.0902i	−0.346833	−	0.600733i	−0.985685	+	0.168597i	$0.946076\pi$
$632$		0			0
$633$	8.02830	+	13.9054i	0.319096	+	0.552691i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	15.5715	+	26.9706i	0.616964	+	1.06861i
$638$		0			0
$639$	−45.4569			−1.79825
$640$		0			0
$641$	−15.9973	+	27.7081i	−0.631854	+	1.09440i	0.355318	+	0.934745i	$0.384373\pi$
$641$	−15.9973	+	27.7081i	−0.631854	+	1.09440i	−0.987172	+	0.159658i	$0.948961\pi$
$642$		0			0
$643$	17.5203	−	30.3461i	0.690934	−	1.19673i	−0.280598	−	0.959825i	$-0.590533\pi$
$643$	17.5203	−	30.3461i	0.690934	−	1.19673i	0.971532	−	0.236908i	$-0.0761339\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−17.4260			−0.685087			−0.342544	−	0.939502i	$-0.611288\pi$
$647$	−17.4260			−0.685087			−0.342544	+	0.939502i	$0.611288\pi$
$648$		0			0
$649$	6.13464	−	10.6255i	0.240806	−	0.417088i
$650$		0			0
$651$	−2.56102	+	4.43581i	−0.100374	+	0.173853i
$652$		0			0
$653$	49.1457			1.92322			0.961609	−	0.274422i	$-0.0884866\pi$
$653$	49.1457			1.92322			0.961609	+	0.274422i	$0.0884866\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−98.1022			−3.82733
$658$		0			0
$659$	−0.862722	−	1.49428i	−0.0336069	−	0.0582088i	0.848733	−	0.528822i	$-0.177366\pi$
$659$	−0.862722	−	1.49428i	−0.0336069	−	0.0582088i	−0.882340	+	0.470613i	$0.844033\pi$
$660$		0			0
$661$	−10.9594	−	18.9822i	−0.426270	−	0.738321i	0.570268	−	0.821459i	$-0.306839\pi$
$661$	−10.9594	−	18.9822i	−0.426270	−	0.738321i	−0.996538	+	0.0831373i	$0.973506\pi$
$662$		0			0
$663$	63.7865	−	110.481i	2.47726	−	4.29074i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−2.40937	+	4.17315i	−0.0932911	+	0.161585i
$668$		0			0
$669$	13.4932	+	23.3709i	0.521676	+	0.903570i
$670$		0			0
$671$	0.125869	+	0.218012i	0.00485912	+	0.00841624i
$672$		0			0
$673$	−6.63165			−0.255631			−0.127816	−	0.991798i	$-0.540797\pi$
$673$	−6.63165			−0.255631			−0.127816	+	0.991798i	$0.540797\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−32.7008			−1.25679			−0.628397	−	0.777893i	$-0.716289\pi$
$677$	−32.7008			−1.25679			−0.628397	+	0.777893i	$0.716289\pi$
$678$		0			0
$679$	6.79956	−	11.7772i	0.260943	−	0.451967i
$680$		0			0
$681$	31.7401	−	54.9755i	1.21628	−	2.10666i
$682$		0			0
$683$	51.9872			1.98923			0.994617	−	0.103622i	$-0.0330432\pi$
$683$	51.9872			1.98923			0.994617	+	0.103622i	$0.0330432\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	12.5487	−	21.7350i	0.478764	−	0.829243i
$688$		0			0
$689$	5.27937	−	9.14414i	0.201128	−	0.348364i
$690$		0			0
$691$	−8.93635			−0.339955			−0.169977	−	0.985448i	$-0.554369\pi$
$691$	−8.93635			−0.339955			−0.169977	+	0.985448i	$0.554369\pi$
$692$		0			0
$693$	20.4256	+	35.3782i	0.775905	+	1.34391i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−10.6305	−	18.4125i	−0.402657	−	0.697423i
$698$		0			0
$699$	−16.7415	−	28.9972i	−0.633223	−	1.09678i
$700$		0			0
$701$	−1.12927	+	1.95595i	−0.0426518	+	0.0738751i	−0.886563	−	0.462607i	$-0.846914\pi$
$701$	−1.12927	+	1.95595i	−0.0426518	+	0.0738751i	0.843911	+	0.536483i	$0.180247\pi$
$702$		0			0
$703$	−42.4863	−	20.2442i	−1.60240	−	0.763523i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−4.75909	−	8.24299i	−0.178984	−	0.310010i
$708$		0			0
$709$	−23.4045	−	40.5378i	−0.878975	−	1.52243i	−0.852467	−	0.522781i	$-0.824894\pi$
$709$	−23.4045	−	40.5378i	−0.878975	−	1.52243i	−0.0265084	−	0.999649i	$-0.508439\pi$
$710$		0			0
$711$	−13.9874			−0.524569
$712$		0			0
$713$	−2.31463	−	4.00905i	−0.0866834	−	0.150140i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−8.98978	+	15.5708i	−0.335729	+	0.581500i
$718$		0			0
$719$	11.7570	−	20.3637i	0.438462	−	0.759439i	−0.559109	−	0.829094i	$-0.688857\pi$
$719$	11.7570	−	20.3637i	0.438462	−	0.759439i	0.997571	+	0.0696552i	$0.0221899\pi$
$720$		0			0
$721$	0.387961			0.0144484
$722$		0			0
$723$	−30.1132			−1.11992
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−12.7374	+	22.0617i	−0.472402	+	0.818225i	−0.999501	−	0.0315791i	$-0.989946\pi$
$727$	−12.7374	+	22.0617i	−0.472402	+	0.818225i	0.527099	+	0.849804i	$0.323280\pi$
$728$		0			0
$729$	13.9523			0.516752
$730$		0			0
$731$	16.7008	+	28.9266i	0.617702	+	1.06989i
$732$		0			0
$733$	1.41916			0.0524179			0.0262090	−	0.999656i	$-0.491656\pi$
$733$	1.41916			0.0524179			0.0262090	+	0.999656i	$0.491656\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	10.8308	+	18.7595i	0.398958	+	0.691015i
$738$		0			0
$739$	10.7699	−	18.6540i	0.396176	−	0.686198i	−0.597074	−	0.802186i	$-0.703670\pi$
$739$	10.7699	−	18.6540i	0.396176	−	0.686198i	0.993251	+	0.115988i	$0.0370035\pi$
$740$		0			0
$741$	83.4231	+	39.7501i	3.06462	+	1.46025i
$742$		0			0
$743$	−21.2813	+	36.8602i	−0.780734	+	1.35227i	0.150781	+	0.988567i	$0.451821\pi$
$743$	−21.2813	+	36.8602i	−0.780734	+	1.35227i	−0.931515	+	0.363703i	$0.881512\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−36.3076	−	62.8866i	−1.32842	−	2.30090i
$748$		0			0
$749$	9.28406			0.339232
$750$		0			0
$751$	−9.30708	−	16.1203i	−0.339620	−	0.588239i	0.644741	−	0.764401i	$-0.276965\pi$
$751$	−9.30708	−	16.1203i	−0.339620	−	0.588239i	−0.984361	+	0.176162i	$0.943632\pi$
$752$		0			0
$753$	−39.6681			−1.44558
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−15.3842	+	26.6462i	−0.559148	+	0.968473i	0.438420	+	0.898770i	$0.355538\pi$
$757$	−15.3842	+	26.6462i	−0.559148	+	0.968473i	−0.997568	+	0.0697028i	$0.977795\pi$
$758$		0			0
$759$	−52.7047			−1.91306
$760$		0			0
$761$	13.9270			0.504853			0.252427	−	0.967616i	$-0.418771\pi$
$761$	13.9270			0.504853			0.252427	+	0.967616i	$0.418771\pi$
$762$		0			0
$763$	−4.02368	+	6.96921i	−0.145667	+	0.252302i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	21.6442			0.781528
$768$		0			0
$769$	24.3166	+	42.1176i	0.876880	+	1.51880i	0.854747	+	0.519045i	$0.173712\pi$
$769$	24.3166	+	42.1176i	0.876880	+	1.51880i	0.0221329	+	0.999755i	$0.492954\pi$
$770$		0			0
$771$	−54.0877			−1.94792
$772$		0			0
$773$	−9.79276	−	16.9616i	−0.352221	−	0.610065i	0.634417	−	0.772991i	$-0.281240\pi$
$773$	−9.79276	−	16.9616i	−0.352221	−	0.610065i	−0.986638	+	0.162926i	$0.947907\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	26.1961	−	45.3730i	0.939780	−	1.62775i
$778$		0			0
$779$	12.6886	−	8.72807i	0.454616	−	0.312715i
$780$		0			0
$781$	−12.2976	+	21.3000i	−0.440042	+	0.762175i
$782$		0			0
$783$	−6.98572	−	12.0996i	−0.249649	−	0.432405i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−13.4029			−0.477760			−0.238880	−	0.971049i	$-0.576780\pi$
$787$	−13.4029			−0.477760			−0.238880	+	0.971049i	$0.576780\pi$
$788$		0			0
$789$	−1.45610	−	2.52203i	−0.0518384	−	0.0897867i
$790$		0			0
$791$	−3.72380			−0.132403
$792$		0			0
$793$	−0.222045	+	0.384594i	−0.00788507	+	0.0136573i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−30.0201			−1.06337			−0.531684	−	0.846943i	$-0.678441\pi$
$797$	−30.0201			−1.06337			−0.531684	+	0.846943i	$0.678441\pi$
$798$		0			0
$799$	67.6261			2.39244
$800$		0			0
$801$	−10.7828	+	18.6764i	−0.380992	+	0.659897i
$802$		0			0
$803$	−26.5399	+	45.9684i	−0.936571	+	1.62219i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	40.1411	+	69.5264i	1.41303	+	2.44745i
$808$		0			0
$809$	−13.4967			−0.474520			−0.237260	−	0.971446i	$-0.576249\pi$
$809$	−13.4967			−0.474520			−0.237260	+	0.971446i	$0.576249\pi$
$810$		0			0
$811$	2.63260	+	4.55980i	0.0924431	+	0.160116i	0.908539	−	0.417801i	$-0.137199\pi$
$811$	2.63260	+	4.55980i	0.0924431	+	0.160116i	−0.816096	+	0.577917i	$0.803866\pi$
$812$		0			0
$813$	−17.7821	−	30.7996i	−0.623647	−	1.08019i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−19.9342	+	13.7121i	−0.697410	+	0.479725i
$818$		0			0
$819$	−36.0328	+	62.4107i	−1.25909	+	2.18081i
$820$		0			0
$821$	16.4147	+	28.4312i	0.572879	+	0.992255i	0.996269	+	0.0863073i	$0.0275067\pi$
$821$	16.4147	+	28.4312i	0.572879	+	0.992255i	−0.423390	+	0.905948i	$0.639160\pi$
$822$		0			0
$823$	20.8577	+	36.1266i	0.727054	+	1.25929i	0.958123	+	0.286357i	$0.0924444\pi$
$823$	20.8577	+	36.1266i	0.727054	+	1.25929i	−0.231069	+	0.972937i	$0.574222\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−6.09523	−	10.5572i	−0.211952	−	0.367111i	0.740373	−	0.672196i	$-0.234649\pi$
$827$	−6.09523	−	10.5572i	−0.211952	−	0.367111i	−0.952325	+	0.305084i	$0.901315\pi$
$828$		0			0
$829$	−52.9958			−1.84062			−0.920310	−	0.391190i	$-0.872064\pi$
$829$	−52.9958			−1.84062			−0.920310	+	0.391190i	$0.872064\pi$
$830$		0			0
$831$	−26.1894	+	45.3614i	−0.908500	+	1.57357i
$832$		0			0
$833$	13.9892	−	24.2299i	0.484695	−	0.839517i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	13.4221			0.463934
$838$		0			0
$839$	7.60822	−	13.1778i	0.262665	−	0.454949i	−0.704284	−	0.709918i	$-0.748732\pi$
$839$	7.60822	−	13.1778i	0.262665	−	0.454949i	0.966949	+	0.254969i	$0.0820652\pi$
$840$		0			0
$841$	13.8964	−	24.0692i	0.479185	−	0.829973i
$842$		0			0
$843$	33.4831			1.15322
$844$		0			0
$845$		0			0
$846$		0			0
$847$	5.23854			0.179998
$848$		0			0
$849$	−32.8238	−	56.8525i	−1.12651	−	1.95117i
$850$		0			0
$851$	23.6758	+	41.0077i	0.811597	+	1.40573i
$852$		0			0
$853$	−23.5729	+	40.8295i	−0.807122	+	1.39798i	0.107728	+	0.994180i	$0.465643\pi$
$853$	−23.5729	+	40.8295i	−0.807122	+	1.39798i	−0.914849	+	0.403795i	$0.867691\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−25.6906	+	44.4974i	−0.877574	+	1.52000i	−0.0235779	+	0.999722i	$0.507506\pi$
$857$	−25.6906	+	44.4974i	−0.877574	+	1.52000i	−0.853996	+	0.520280i	$0.825828\pi$
$858$		0			0
$859$	−1.03055	−	1.78496i	−0.0351618	−	0.0609019i	0.847909	−	0.530142i	$-0.177861\pi$
$859$	−1.03055	−	1.78496i	−0.0351618	−	0.0609019i	−0.883071	+	0.469240i	$0.844528\pi$
$860$		0			0
$861$	8.57230	+	14.8477i	0.292143	+	0.506007i
$862$		0			0
$863$	35.8646			1.22084			0.610422	−	0.792076i	$-0.291000\pi$
$863$	35.8646			1.22084			0.610422	+	0.792076i	$0.291000\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−60.8035			−2.06500
$868$		0			0
$869$	−3.78405	+	6.55417i	−0.128365	+	0.222335i
$870$		0			0
$871$	−19.1066	+	33.0936i	−0.647403	+	1.12133i
$872$		0			0
$873$	−62.2460			−2.10671
$874$		0			0
$875$		0			0
$876$		0			0
$877$	6.54598	−	11.3380i	0.221042	−	0.382856i	−0.734083	−	0.679060i	$-0.762388\pi$
$877$	6.54598	−	11.3380i	0.221042	−	0.382856i	0.955125	+	0.296204i	$0.0957209\pi$
$878$		0			0
$879$	−21.6562	+	37.5096i	−0.730444	+	1.26517i
$880$		0			0
$881$	−26.9322			−0.907369			−0.453684	−	0.891162i	$-0.649891\pi$
$881$	−26.9322			−0.907369			−0.453684	+	0.891162i	$0.649891\pi$
$882$		0			0
$883$	−14.8172	−	25.6642i	−0.498640	−	0.863670i	0.501359	−	0.865239i	$-0.332834\pi$
$883$	−14.8172	−	25.6642i	−0.498640	−	0.863670i	−0.999999	+	0.00156969i	$0.999500\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−15.2151	−	26.3533i	−0.510873	−	0.884858i	−0.999921	−	0.0126008i	$-0.995989\pi$
$887$	−15.2151	−	26.3533i	−0.510873	−	0.884858i	0.489048	−	0.872257i	$-0.337344\pi$
$888$		0			0
$889$	−14.7941	−	25.6241i	−0.496177	−	0.859403i
$890$		0			0
$891$	36.4381	−	63.1127i	1.22072	−	2.11435i
$892$		0			0
$893$	3.86282	+	48.8334i	0.129264	+	1.63415i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−46.4882	−	80.5199i	−1.55220	−	2.68848i
$898$		0			0
$899$	−0.579891	−	1.00440i	−0.0193405	−	0.0334986i
$900$		0			0
$901$	−9.48580			−0.316018
$902$		0			0
$903$	−13.4674	−	23.3262i	−0.448166	−	0.776247i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	5.59680	−	9.69395i	0.185839	−	0.321882i	−0.758020	−	0.652231i	$-0.773833\pi$
$907$	5.59680	−	9.69395i	0.185839	−	0.321882i	0.943859	+	0.330349i	$0.107166\pi$
$908$		0			0
$909$	−21.7834	+	37.7299i	−0.722509	+	1.25142i
$910$		0			0
$911$	−0.339795			−0.0112579			−0.00562895	−	0.999984i	$-0.501792\pi$
$911$	−0.339795			−0.0112579			−0.00562895	+	0.999984i	$0.501792\pi$
$912$		0			0
$913$	−39.2895			−1.30029
$914$		0			0
$915$		0			0
$916$		0			0
$917$	10.1645	−	17.6055i	0.335662	−	0.581384i
$918$		0			0
$919$	−15.0715			−0.497163			−0.248582	−	0.968611i	$-0.579964\pi$
$919$	−15.0715			−0.497163			−0.248582	+	0.968611i	$0.579964\pi$
$920$		0			0
$921$	13.6690	+	23.6754i	0.450408	+	0.780130i
$922$		0			0
$923$	−43.3883			−1.42814
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−0.887890	−	1.53787i	−0.0291621	−	0.0505103i
$928$		0			0
$929$	−11.3279	+	19.6204i	−0.371655	+	0.643725i	−0.989820	−	0.142323i	$-0.954543\pi$
$929$	−11.3279	+	19.6204i	−0.371655	+	0.643725i	0.618165	+	0.786048i	$0.287876\pi$
$930$		0			0
$931$	18.2957	+	8.71767i	0.599617	+	0.285710i
$932$		0			0
$933$	47.1051	−	81.5884i	1.54215	−	2.67108i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	9.41266	+	16.3032i	0.307498	+	0.532602i	0.977814	−	0.209473i	$-0.0671749\pi$
$937$	9.41266	+	16.3032i	0.307498	+	0.532602i	−0.670316	+	0.742076i	$0.733842\pi$
$938$		0			0
$939$	35.4747			1.15767
$940$		0			0
$941$	6.91540	+	11.9778i	0.225436	+	0.390466i	0.956450	−	0.291896i	$-0.0942861\pi$
$941$	6.91540	+	11.9778i	0.225436	+	0.390466i	−0.731014	+	0.682362i	$0.760953\pi$
$942$		0			0
$943$	−15.4952			−0.504592
$944$		0			0
$945$		0			0
$946$		0			0
$947$	23.0053	−	39.8463i	0.747570	−	1.29483i	−0.201414	−	0.979506i	$-0.564554\pi$
$947$	23.0053	−	39.8463i	0.747570	−	1.29483i	0.948984	−	0.315323i	$-0.102113\pi$
$948$		0			0
$949$	−93.6379			−3.03961
$950$		0			0
$951$	−14.8536			−0.481660
$952$		0			0
$953$	−3.72192	+	6.44656i	−0.120565	+	0.208824i	−0.919991	−	0.391940i	$-0.871804\pi$
$953$	−3.72192	+	6.44656i	−0.120565	+	0.208824i	0.799426	+	0.600765i	$0.205137\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−13.2043			−0.426834
$958$		0			0
$959$	−11.9208	−	20.6474i	−0.384942	−	0.666739i
$960$		0			0
$961$	−29.8858			−0.964059
$962$		0			0
$963$	−21.2475	−	36.8018i	−0.684693	−	1.18592i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−20.8376	+	36.0918i	−0.670092	+	1.16063i	0.307786	+	0.951456i	$0.400412\pi$
$967$	−20.8376	+	36.0918i	−0.670092	+	1.16063i	−0.977878	+	0.209178i	$0.932921\pi$
$968$		0			0
$969$	−6.54651	−	82.7604i	−0.210304	−	2.65865i
$970$		0			0
$971$	9.63451	−	16.6875i	0.309186	−	0.535526i	−0.668999	−	0.743264i	$-0.733277\pi$
$971$	9.63451	−	16.6875i	0.309186	−	0.535526i	0.978185	+	0.207738i	$0.0666101\pi$
$972$		0			0
$973$	14.2753	+	24.7256i	0.457646	+	0.792666i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−19.7307			−0.631242			−0.315621	−	0.948885i	$-0.602213\pi$
$977$	−19.7307			−0.631242			−0.315621	+	0.948885i	$0.602213\pi$
$978$		0			0
$979$	5.83420	+	10.1051i	0.186462	+	0.322961i
$980$		0			0
$981$	36.8344			1.17603
$982$		0			0
$983$	16.6318	−	28.8071i	0.530472	−	0.918805i	−0.468896	−	0.883254i	$-0.655348\pi$
$983$	16.6318	−	28.8071i	0.530472	−	0.918805i	0.999368	−	0.0355513i	$-0.0113187\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−54.5331			−1.73581
$988$		0			0
$989$	24.3434			0.774076
$990$		0			0
$991$	8.90804	−	15.4292i	0.282973	−	0.490124i	−0.689142	−	0.724626i	$-0.742013\pi$
$991$	8.90804	−	15.4292i	0.282973	−	0.490124i	0.972116	+	0.234502i	$0.0753459\pi$
$992$		0			0
$993$	46.0732	−	79.8012i	1.46209	−	2.53241i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	10.6048	+	18.3680i	0.335857	+	0.581722i	0.983649	−	0.180095i	$-0.0576407\pi$
$997$	10.6048	+	18.3680i	0.335857	+	0.581722i	−0.647792	+	0.761817i	$0.724307\pi$
$998$		0			0
$999$	−137.291			−4.34371

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1900.2.i.d.201.4		8
5.2	odd	4		1900.2.s.d.49.1		16
5.3	odd	4		1900.2.s.d.49.8		16
5.4	even	2		380.2.i.c.201.1	yes	8
15.14	odd	2		3420.2.t.w.3241.2		8
19.7	even	3	inner	1900.2.i.d.501.4		8
20.19	odd	2		1520.2.q.m.961.4		8
95.7	odd	12		1900.2.s.d.349.8		16
95.49	even	6		7220.2.a.r.1.4		4
95.64	even	6		380.2.i.c.121.1	✓	8
95.83	odd	12		1900.2.s.d.349.1		16
95.84	odd	6		7220.2.a.p.1.1		4
285.254	odd	6		3420.2.t.w.1261.2		8
380.159	odd	6		1520.2.q.m.881.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.i.c.121.1	✓	8	95.64	even	6
380.2.i.c.201.1	yes	8	5.4	even	2
1520.2.q.m.881.4		8	380.159	odd	6
1520.2.q.m.961.4		8	20.19	odd	2
1900.2.i.d.201.4		8	1.1	even	1	trivial
1900.2.i.d.501.4		8	19.7	even	3	inner
1900.2.s.d.49.1		16	5.2	odd	4
1900.2.s.d.49.8		16	5.3	odd	4
1900.2.s.d.349.1		16	95.83	odd	12
1900.2.s.d.349.8		16	95.7	odd	12
3420.2.t.w.1261.2		8	285.254	odd	6
3420.2.t.w.3241.2		8	15.14	odd	2
7220.2.a.p.1.1		4	95.84	odd	6
7220.2.a.r.1.4		4	95.49	even	6

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:	\( N \)	\(=\)	\( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1900.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.58253 - 2.74101i) q^{3} +1.53315 q^{7} +(-3.50877 - 6.07738i) q^{9} +O(q^{10})\)	\(q+(1.58253 - 2.74101i) q^{3} +1.53315 q^{7} +(-3.50877 - 6.07738i) q^{9} -3.79695 q^{11} +(-3.34910 - 5.80081i) q^{13} +(-3.00877 + 5.21135i) q^{17} +(-3.93502 - 1.87499i) q^{19} +(2.42625 - 4.20239i) q^{21} +(2.19282 + 3.79808i) q^{23} -12.7158 q^{27} +(0.549376 + 0.951547i) q^{29} -1.05555 q^{31} +(-6.00877 + 10.4075i) q^{33} +10.7970 q^{37} -21.2002 q^{39} +(-1.76658 + 3.05980i) q^{41} +(2.77535 - 4.80705i) q^{43} +(-5.61907 - 9.73252i) q^{47} -4.64945 q^{49} +(9.52293 + 16.4942i) q^{51} +(0.788178 + 1.36516i) q^{53} +(-11.3667 + 7.81874i) q^{57} +(-1.61568 + 2.79843i) q^{59} +(-0.0331500 - 0.0574175i) q^{61} +(-5.37948 - 9.31753i) q^{63} +(-2.85250 - 4.94067i) q^{67} +13.8808 q^{69} +(3.23880 - 5.60977i) q^{71} +(6.98978 - 12.1066i) q^{73} -5.82130 q^{77} +(0.996602 - 1.72617i) q^{79} +(-9.59668 + 16.6219i) q^{81} +10.3477 q^{83} +3.47760 q^{87} +(-1.53655 - 2.66138i) q^{89} +(-5.13467 - 8.89352i) q^{91} +(-1.67043 + 2.89327i) q^{93} +(4.43502 - 7.68169i) q^{97} +(13.3227 + 23.0755i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{3} - 5 q^{9}+O(q^{10}) \) 8 * q + q^3 - 5 * q^9	\( 8 q + q^{3} - 5 q^{9} + 4 q^{11} - 9 q^{13} - q^{17} + 3 q^{19} + 8 q^{21} - 20 q^{27} + 5 q^{29} - 20 q^{31} - 25 q^{33} + 52 q^{37} - 54 q^{39} - 8 q^{41} - 7 q^{43} - 16 q^{47} + 20 q^{49} + 12 q^{51} - 5 q^{53} - 27 q^{57} + 11 q^{59} + 12 q^{61} + 3 q^{63} + 6 q^{69} + 14 q^{71} + 4 q^{73} + 44 q^{77} + 13 q^{79} - 24 q^{81} - 10 q^{83} + 4 q^{87} + 5 q^{89} - 46 q^{91} + 28 q^{93} + q^{97} + 24 q^{99}+O(q^{100}) \) 8 * q + q^3 - 5 * q^9 + 4 * q^11 - 9 * q^13 - q^17 + 3 * q^19 + 8 * q^21 - 20 * q^27 + 5 * q^29 - 20 * q^31 - 25 * q^33 + 52 * q^37 - 54 * q^39 - 8 * q^41 - 7 * q^43 - 16 * q^47 + 20 * q^49 + 12 * q^51 - 5 * q^53 - 27 * q^57 + 11 * q^59 + 12 * q^61 + 3 * q^63 + 6 * q^69 + 14 * q^71 + 4 * q^73 + 44 * q^77 + 13 * q^79 - 24 * q^81 - 10 * q^83 + 4 * q^87 + 5 * q^89 - 46 * q^91 + 28 * q^93 + q^97 + 24 * q^99

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