LMFDB - Embedded newform 1900.2.s.d.349.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1900,2,Mod(49,1900)]

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, 3, 4]))

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

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

chi := DirichletCharacter("1900.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1900 = 2^{2} \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1900.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.1715763840$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 17x^{14} + 215x^{12} - 1176x^{10} + 4775x^{8} - 2898x^{6} + 1385x^{4} - 164x^{2} + 16 $ x^16 - 17x^14 + 215x^12 - 1176x^10 + 4775x^8 - 2898x^6 + 1385x^4 - 164*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 380)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			349.1
Root			$-2.74101 - 1.58253i$ of defining polynomial
Character	$\chi$	$=$	1900.349
Dual form			1900.2.s.d.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.74101 + 1.58253i) q^{3} -1.53315i q^{7} +(3.50877 - 6.07738i) q^{9} +O(q^{10})$	\(q+(-2.74101 + 1.58253i) q^{3} -1.53315i q^{7} +(3.50877 - 6.07738i) q^{9} -3.79695 q^{11} +(-5.80081 - 3.34910i) q^{13} +(-5.21135 + 3.00877i) q^{17} +(3.93502 - 1.87499i) q^{19} +(2.42625 + 4.20239i) q^{21} +(3.79808 + 2.19282i) q^{23} +12.7158i q^{27} +(-0.549376 + 0.951547i) q^{29} -1.05555 q^{31} +(10.4075 - 6.00877i) q^{33} -10.7970i q^{37} +21.2002 q^{39} +(-1.76658 - 3.05980i) q^{41} +(-4.80705 + 2.77535i) q^{43} +(9.73252 + 5.61907i) q^{47} +4.64945 q^{49} +(9.52293 - 16.4942i) q^{51} +(1.36516 + 0.788178i) q^{53} +(-7.81874 + 11.3667i) q^{57} +(1.61568 + 2.79843i) q^{59} +(-0.0331500 + 0.0574175i) q^{61} +(-9.31753 - 5.37948i) q^{63} +(4.94067 + 2.85250i) q^{67} -13.8808 q^{69} +(3.23880 + 5.60977i) q^{71} +(-12.1066 + 6.98978i) q^{73} +5.82130i q^{77} +(-0.996602 - 1.72617i) q^{79} +(-9.59668 - 16.6219i) q^{81} +10.3477i q^{83} -3.47760i q^{87} +(1.53655 - 2.66138i) q^{89} +(-5.13467 + 8.89352i) q^{91} +(2.89327 - 1.67043i) q^{93} +(7.68169 - 4.43502i) q^{97} +(-13.3227 + 23.0755i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 10 q^{9}+O(q^{10}) $ 16 * q + 10 * q^9	$ 16 q + 10 q^{9} + 8 q^{11} - 6 q^{19} + 16 q^{21} - 10 q^{29} - 40 q^{31} + 108 q^{39} - 16 q^{41} - 40 q^{49} + 24 q^{51} - 22 q^{59} + 24 q^{61} - 12 q^{69} + 28 q^{71} - 26 q^{79} - 48 q^{81} - 10 q^{89} - 92 q^{91} - 48 q^{99}+O(q^{100}) $ 16 * q + 10 * q^9 + 8 * q^11 - 6 * q^19 + 16 * q^21 - 10 * q^29 - 40 * q^31 + 108 * q^39 - 16 * q^41 - 40 * q^49 + 24 * q^51 - 22 * q^59 + 24 * q^61 - 12 * q^69 + 28 * q^71 - 26 * q^79 - 48 * q^81 - 10 * q^89 - 92 * q^91 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−2.74101	+	1.58253i	−1.58253	+	0.913672i	−0.588036	+	0.808835i	$0.700099\pi$
$3$	−2.74101	+	1.58253i	−1.58253	+	0.913672i	−0.994489	+	0.104837i	$0.966568\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$		−	1.53315i		−	0.579476i	−0.957106	−	0.289738i	$-0.906432\pi$
$7$		−	1.53315i		−	0.579476i	0.957106	−	0.289738i	$-0.0935682\pi$
$8$		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
$13$	−5.80081	−	3.34910i	−1.60886	−	0.928873i	−0.989627	−	0.143663i	$-0.954112\pi$
$13$	−5.80081	−	3.34910i	−1.60886	−	0.928873i	−0.619229	−	0.785210i	$-0.712555\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−5.21135	+	3.00877i	−1.26394	+	0.729735i	−0.973834	−	0.227260i	$-0.927023\pi$
$17$	−5.21135	+	3.00877i	−1.26394	+	0.729735i	−0.290104	+	0.956995i	$0.593690\pi$
$18$		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
$23$	3.79808	+	2.19282i	0.791955	+	0.457235i	0.840650	−	0.541578i	$-0.182173\pi$
$23$	3.79808	+	2.19282i	0.791955	+	0.457235i	−0.0486953	+	0.998814i	$0.515506\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$			12.7158i			2.44715i
$28$		0			0
$29$	−0.549376	+	0.951547i	−0.102016	+	0.176698i	−0.912515	−	0.409042i	$-0.865863\pi$
$29$	−0.549376	+	0.951547i	−0.102016	+	0.176698i	0.810499	+	0.585740i	$0.199196\pi$
$30$		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
$33$	10.4075	−	6.00877i	1.81171	−	1.04599i
$34$		0			0
$35$		0			0
$36$		0			0
$37$		−	10.7970i		−	1.77501i	−0.460800	−	0.887504i	$-0.652437\pi$
$37$		−	10.7970i		−	1.77501i	0.460800	−	0.887504i	$-0.347563\pi$
$38$		0			0
$39$	21.2002			3.39474
$40$		0			0
$41$	−1.76658	−	3.05980i	−0.275893	−	0.477860i	0.694467	−	0.719524i	$-0.255640\pi$
$41$	−1.76658	−	3.05980i	−0.275893	−	0.477860i	−0.970360	+	0.241664i	$0.922307\pi$
$42$		0			0
$43$	−4.80705	+	2.77535i	−0.733068	+	0.423237i	−0.819543	−	0.573017i	$-0.805773\pi$
$43$	−4.80705	+	2.77535i	−0.733068	+	0.423237i	0.0864756	+	0.996254i	$0.472440\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	9.73252	+	5.61907i	1.41963	+	0.819626i	0.996266	−	0.0863319i	$-0.0275145\pi$
$47$	9.73252	+	5.61907i	1.41963	+	0.819626i	0.423368	+	0.905958i	$0.360848\pi$
$48$		0			0
$49$	4.64945			0.664207
$50$		0			0
$51$	9.52293	−	16.4942i	1.33348	−	2.30965i
$52$		0			0
$53$	1.36516	+	0.788178i	0.187520	+	0.108265i	0.590821	−	0.806803i	$-0.298804\pi$
$53$	1.36516	+	0.788178i	0.187520	+	0.108265i	−0.403301	+	0.915067i	$0.632137\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−7.81874	+	11.3667i	−1.03562	+	1.50555i
$58$		0			0
$59$	1.61568	+	2.79843i	0.210343	+	0.364325i	0.951822	−	0.306651i	$-0.0992086\pi$
$59$	1.61568	+	2.79843i	0.210343	+	0.364325i	−0.741479	+	0.670976i	$0.765875\pi$
$60$		0			0
$61$	−0.0331500	+	0.0574175i	−0.00424442	+	0.00735156i	−0.868140	−	0.496320i	$-0.834684\pi$
$61$	−0.0331500	+	0.0574175i	−0.00424442	+	0.00735156i	0.863895	+	0.503671i	$0.168018\pi$
$62$		0			0
$63$	−9.31753	−	5.37948i	−1.17390	−	0.677751i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	4.94067	+	2.85250i	0.603599	+	0.348488i	0.770456	−	0.637493i	$-0.220028\pi$
$67$	4.94067	+	2.85250i	0.603599	+	0.348488i	−0.166857	+	0.985981i	$0.553362\pi$
$68$		0			0
$69$	−13.8808			−1.67105
$70$		0			0
$71$	3.23880	+	5.60977i	0.384375	+	0.665757i	0.991682	−	0.128710i	$-0.0410836\pi$
$71$	3.23880	+	5.60977i	0.384375	+	0.665757i	−0.607307	+	0.794467i	$0.707750\pi$
$72$		0			0
$73$	−12.1066	+	6.98978i	−1.41698	+	0.818091i	−0.996032	−	0.0889951i	$-0.971634\pi$
$73$	−12.1066	+	6.98978i	−1.41698	+	0.818091i	−0.420944	+	0.907087i	$0.638301\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$			5.82130i			0.663398i
$78$		0			0
$79$	−0.996602	−	1.72617i	−0.112127	−	0.194209i	0.804501	−	0.593951i	$-0.202433\pi$
$79$	−0.996602	−	1.72617i	−0.112127	−	0.194209i	−0.916627	+	0.399743i	$0.869100\pi$
$80$		0			0
$81$	−9.59668	−	16.6219i	−1.06630	−	1.84688i
$82$		0			0
$83$			10.3477i			1.13580i	0.823097	+	0.567901i	$0.192244\pi$
$83$			10.3477i			1.13580i	−0.823097	+	0.567901i	$0.807756\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		−	3.47760i		−	0.372838i
$88$		0			0
$89$	1.53655	−	2.66138i	0.162874	−	0.282106i	−0.773024	−	0.634376i	$-0.781257\pi$
$89$	1.53655	−	2.66138i	0.162874	−	0.282106i	0.935898	+	0.352271i	$0.114590\pi$
$90$		0			0
$91$	−5.13467	+	8.89352i	−0.538260	+	0.932294i
$92$		0			0
$93$	2.89327	−	1.67043i	0.300018	−	0.173215i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	7.68169	−	4.43502i	0.779957	−	0.450308i	−0.0564579	−	0.998405i	$-0.517981\pi$
$97$	7.68169	−	4.43502i	0.779957	−	0.450308i	0.836415	+	0.548097i	$0.184647\pi$
$98$		0			0
$99$	−13.3227	+	23.0755i	−1.33898	+	2.31918i
$100$		0			0
$101$	−3.10413	+	5.37651i	−0.308872	+	0.534983i	−0.978116	−	0.208060i	$-0.933285\pi$
$101$	−3.10413	+	5.37651i	−0.308872	+	0.534983i	0.669244	+	0.743043i	$0.266618\pi$
$102$		0			0
$103$			0.253048i			0.0249336i	0.999922	+	0.0124668i	$0.00396841\pi$
$103$			0.253048i			0.0249336i	−0.999922	+	0.0124668i	$0.996032\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	6.05555i		−	0.585412i	−0.956203	−	0.292706i	$-0.905444\pi$
$107$		−	6.05555i		−	0.585412i	0.956203	−	0.292706i	$-0.0945557\pi$
$108$		0			0
$109$	2.62445	+	4.54568i	0.251377	+	0.435397i	0.963905	−	0.266246i	$-0.0857833\pi$
$109$	2.62445	+	4.54568i	0.251377	+	0.435397i	−0.712528	+	0.701643i	$0.752450\pi$
$110$		0			0
$111$	17.0865	+	29.5946i	1.62177	+	2.80900i
$112$		0			0
$113$		−	2.42885i		−	0.228487i	−0.993453	−	0.114244i	$-0.963556\pi$
$113$		−	2.42885i		−	0.228487i	0.993453	−	0.114244i	$-0.0364445\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−40.7075	+	23.5025i	−3.76341	+	2.17281i
$118$		0			0
$119$	4.61290	+	7.98978i	0.422864	+	0.732422i
$120$		0			0
$121$	3.41685			0.310623
$122$		0			0
$123$	9.68442	+	5.59130i	0.873214	+	0.504151i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	16.7133	+	9.64945i	1.48307	+	0.856250i	0.999815	−	0.0192299i	$-0.00612144\pi$
$127$	16.7133	+	9.64945i	1.48307	+	0.856250i	0.483254	+	0.875480i	$0.339455\pi$
$128$		0			0
$129$	8.78412	−	15.2146i	0.773399	−	1.33957i
$130$		0			0
$131$	6.62983	+	11.4832i	0.579251	+	1.00329i	0.995565	+	0.0940711i	$0.0299881\pi$
$131$	6.62983	+	11.4832i	0.579251	+	1.00329i	−0.416315	+	0.909221i	$0.636679\pi$
$132$		0			0
$133$	−2.87464	−	6.03298i	−0.249263	−	0.523126i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	13.4673	+	7.77535i	1.15059	+	0.664293i	0.949031	−	0.315184i	$-0.102066\pi$
$137$	13.4673	+	7.77535i	1.15059	+	0.664293i	0.201558	+	0.979476i	$0.435399\pi$
$138$		0			0
$139$	−9.31110	+	16.1273i	−0.789758	+	1.36790i	0.136358	+	0.990660i	$0.456460\pi$
$139$	−9.31110	+	16.1273i	−0.789758	+	1.36790i	−0.926115	+	0.377241i	$0.876873\pi$
$140$		0			0
$141$	−35.5693			−2.99548
$142$		0			0
$143$	22.0254	+	12.7164i	1.84186	+	1.06340i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−12.7442	+	7.35788i	−1.05113	+	0.606867i
$148$		0			0
$149$	−2.34372	−	4.05945i	−0.192005	−	0.332563i	0.753909	−	0.656978i	$-0.228166\pi$
$149$	−2.34372	−	4.05945i	−0.192005	−	0.332563i	−0.945915	+	0.324415i	$0.894832\pi$
$150$		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
$153$			42.2285i			3.41397i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−8.04857	+	4.64685i	−0.642346	+	0.370859i	−0.785518	−	0.618839i	$-0.787603\pi$
$157$	−8.04857	+	4.64685i	−0.642346	+	0.370859i	0.143172	+	0.989698i	$0.454270\pi$
$158$		0			0
$159$	−4.98925			−0.395673
$160$		0			0
$161$	3.36193	−	5.82303i	0.264957	−	0.458919i
$162$		0			0
$163$		−	5.88495i		−	0.460945i	−0.973079	−	0.230472i	$-0.925973\pi$
$163$		−	5.88495i		−	0.460945i	0.973079	−	0.230472i	$-0.0740271\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−11.0825	−	6.39848i	−0.857589	−	0.495129i	0.00561549	−	0.999984i	$-0.498213\pi$
$167$	−11.0825	−	6.39848i	−0.857589	−	0.495129i	−0.863204	+	0.504855i	$0.831546\pi$
$168$		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
$173$	13.0256	−	7.52032i	0.990317	−	0.571760i	0.0849476	−	0.996385i	$-0.472928\pi$
$173$	13.0256	−	7.52032i	0.990317	−	0.571760i	0.905369	+	0.424626i	$0.139594\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−8.85718	−	5.11370i	−0.665747	−	0.384369i
$178$		0			0
$179$	−21.5452			−1.61036			−0.805180	−	0.593030i	$-0.797931\pi$
$179$	−21.5452			−1.61036			−0.805180	+	0.593030i	$0.797931\pi$
$180$		0			0
$181$	−2.13530	+	3.69845i	−0.158716	+	0.274903i	−0.934406	−	0.356210i	$-0.884069\pi$
$181$	−2.13530	+	3.69845i	−0.158716	+	0.274903i	0.775690	+	0.631114i	$0.217402\pi$
$182$		0			0
$183$		−	0.209843i		−	0.0155120i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	19.7873	−	11.4242i	1.44699	−	0.835418i
$188$		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
$193$	13.3185	−	7.68943i	0.958685	−	0.553497i	0.0629169	−	0.998019i	$-0.479960\pi$
$193$	13.3185	−	7.68943i	0.958685	−	0.553497i	0.895768	+	0.444522i	$0.146626\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	12.7210i		−	0.906331i	−0.891426	−	0.453165i	$-0.850295\pi$
$197$		−	12.7210i		−	0.906331i	0.891426	−	0.453165i	$-0.149705\pi$
$198$		0			0
$199$	5.10885	−	8.84879i	0.362157	−	0.627274i	−0.626159	−	0.779696i	$-0.715374\pi$
$199$	5.10885	−	8.84879i	0.362157	−	0.627274i	0.988316	+	0.152422i	$0.0487072\pi$
$200$		0			0
$201$	−18.0566			−1.27361
$202$		0			0
$203$	1.45886	+	0.842275i	0.102392	+	0.0591161i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	26.6532	−	15.3883i	1.85253	−	1.06956i
$208$		0			0
$209$	−14.9411	+	7.11925i	−1.03350	+	0.492449i
$210$		0			0
$211$	−2.53655	−	4.39343i	−0.174623	−	0.302456i	0.765408	−	0.643546i	$-0.222537\pi$
$211$	−2.53655	−	4.39343i	−0.174623	−	0.302456i	−0.940031	+	0.341090i	$0.889204\pi$
$212$		0			0
$213$	−17.7552	−	10.2510i	−1.21657	−	0.702385i
$214$		0			0
$215$		0			0
$216$		0			0
$217$			1.61831i			0.109858i
$218$		0			0
$219$	22.1230	−	38.3182i	1.49493	−	2.58930i
$220$		0			0
$221$	40.3068			2.71133
$222$		0			0
$223$	7.38404	−	4.26318i	0.494472	−	0.285483i	−0.231956	−	0.972726i	$-0.574513\pi$
$223$	7.38404	−	4.26318i	0.494472	−	0.285483i	0.726428	+	0.687243i	$0.241179\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$		−	20.0566i		−	1.33120i	−0.746307	−	0.665602i	$-0.768175\pi$
$227$		−	20.0566i		−	1.33120i	0.746307	−	0.665602i	$-0.231825\pi$
$228$		0			0
$229$	−7.92955			−0.524000			−0.262000	−	0.965068i	$-0.584382\pi$
$229$	−7.92955			−0.524000			−0.262000	+	0.965068i	$0.584382\pi$
$230$		0			0
$231$	−9.21235	−	15.9563i	−0.606128	−	1.04985i
$232$		0			0
$233$	−9.16169	+	5.28950i	−0.600202	+	0.346527i	−0.769121	−	0.639103i	$-0.779306\pi$
$233$	−9.16169	+	5.28950i	−0.600202	+	0.346527i	0.168919	+	0.985630i	$0.445972\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	5.46340	+	3.15430i	0.354886	+	0.204894i
$238$		0			0
$239$	5.68065			0.367451			0.183725	−	0.982978i	$-0.441184\pi$
$239$	5.68065			0.367451			0.183725	+	0.982978i	$0.441184\pi$
$240$		0			0
$241$	−4.75714	+	8.23962i	−0.306435	+	0.530760i	−0.977580	−	0.210566i	$-0.932469\pi$
$241$	−4.75714	+	8.23962i	−0.306435	+	0.530760i	0.671145	+	0.741326i	$0.265803\pi$
$242$		0			0
$243$	19.5728	+	11.3004i	1.25559	+	0.724918i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−29.1059	−	2.30233i	−1.85196	−	0.146494i
$248$		0			0
$249$	−16.3754	−	28.3631i	−1.03775	−	1.79744i
$250$		0			0
$251$	−6.26658	+	10.8540i	−0.395543	+	0.685100i	−0.993170	−	0.116674i	$-0.962777\pi$
$251$	−6.26658	+	10.8540i	−0.395543	+	0.685100i	0.597628	+	0.801774i	$0.296110\pi$
$252$		0			0
$253$	−14.4211	−	8.32605i	−0.906649	−	0.523454i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	14.7996	+	8.54453i	0.923171	+	0.532993i	0.884645	−	0.466264i	$-0.154400\pi$
$257$	14.7996	+	8.54453i	0.923171	+	0.532993i	0.0385258	+	0.999258i	$0.487734\pi$
$258$		0			0
$259$	−16.5533			−1.02857
$260$		0			0
$261$	3.85527	+	6.67753i	0.238635	+	0.413328i
$262$		0			0
$263$	−0.796838	+	0.460054i	−0.0491351	+	0.0283682i	−0.524366	−	0.851493i	$-0.675698\pi$
$263$	−0.796838	+	0.460054i	−0.0491351	+	0.0283682i	0.475231	+	0.879861i	$0.342364\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$			9.72651i			0.595252i
$268$		0			0
$269$	12.6826	+	21.9669i	0.773272	+	1.33935i	0.935761	+	0.352636i	$0.114715\pi$
$269$	12.6826	+	21.9669i	0.773272	+	1.33935i	−0.162489	+	0.986710i	$0.551952\pi$
$270$		0			0
$271$	5.61828	+	9.73115i	0.341286	+	0.591125i	0.984672	−	0.174417i	$-0.0558041\pi$
$271$	5.61828	+	9.73115i	0.341286	+	0.591125i	−0.643386	+	0.765542i	$0.722471\pi$
$272$		0			0
$273$		−	32.5030i		−	1.96717i
$274$		0			0
$275$		0			0
$276$		0			0
$277$			16.5491i			0.994340i	0.867653	+	0.497170i	$0.165627\pi$
$277$			16.5491i			0.994340i	−0.867653	+	0.497170i	$0.834373\pi$
$278$		0			0
$279$	−3.70367	+	6.41495i	−0.221733	+	0.384053i
$280$		0			0
$281$	5.28950	−	9.16169i	0.315545	−	0.546540i	−0.664008	−	0.747725i	$-0.731146\pi$
$281$	5.28950	−	9.16169i	0.315545	−	0.546540i	0.979553	+	0.201185i	$0.0644793\pi$
$282$		0			0
$283$	−17.9626	+	10.3707i	−1.06776	+	0.616474i	−0.927570	−	0.373650i	$-0.878106\pi$
$283$	−17.9626	+	10.3707i	−1.06776	+	0.616474i	−0.140195	+	0.990124i	$0.544773\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−4.69113	+	2.70842i	−0.276909	+	0.159873i
$288$		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
$293$		−	13.6846i		−	0.799460i	−0.916633	−	0.399730i	$-0.869104\pi$
$293$		−	13.6846i		−	0.799460i	0.916633	−	0.399730i	$-0.130896\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		−	48.2811i		−	2.80155i
$298$		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
$303$		−	19.6495i		−	1.12883i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−7.48025	+	4.31872i	−0.426920	+	0.246483i	−0.698034	−	0.716065i	$-0.745941\pi$
$307$	−7.48025	+	4.31872i	−0.426920	+	0.246483i	0.271113	+	0.962547i	$0.412608\pi$
$308$		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
$313$	9.70664	+	5.60413i	0.548651	+	0.316764i	0.748578	−	0.663047i	$-0.230737\pi$
$313$	9.70664	+	5.60413i	0.548651	+	0.316764i	−0.199926	+	0.979811i	$0.564070\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	4.06425	+	2.34650i	0.228271	+	0.131792i	0.609774	−	0.792575i	$-0.291260\pi$
$317$	4.06425	+	2.34650i	0.228271	+	0.131792i	−0.381503	+	0.924368i	$0.624593\pi$
$318$		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
$323$	−14.8654	+	21.6108i	−0.827131	+	1.20246i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−14.3873	−	8.30652i	−0.795620	−	0.459352i
$328$		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
$333$	−65.6171	−	37.8841i	−3.59580	−	2.07603i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	20.0554	−	11.5790i	1.09249	−	0.630749i	0.158251	−	0.987399i	$-0.449415\pi$
$337$	20.0554	−	11.5790i	1.09249	−	0.630749i	0.934238	+	0.356650i	$0.116081\pi$
$338$		0			0
$339$	3.84372	+	6.65752i	0.208762	+	0.361587i
$340$		0			0
$341$	4.00786			0.217038
$342$		0			0
$343$		−	17.8604i		−	0.964369i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	13.5635	−	7.83090i	0.728127	−	0.420385i	−0.0896094	−	0.995977i	$-0.528562\pi$
$347$	13.5635	−	7.83090i	0.728127	−	0.420385i	0.817737	+	0.575592i	$0.195229\pi$
$348$		0			0
$349$	9.72130			0.520369			0.260185	−	0.965559i	$-0.416217\pi$
$349$	9.72130			0.520369			0.260185	+	0.965559i	$0.416217\pi$
$350$		0			0
$351$	42.5863	−	73.7617i	2.27309	−	3.93711i
$352$		0			0
$353$		−	11.3789i		−	0.605635i	−0.953049	−	0.302818i	$-0.902073\pi$
$353$		−	11.3789i		−	0.605635i	0.953049	−	0.302818i	$-0.0979273\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−25.2881	−	14.6001i	−1.33839	−	0.772718i
$358$		0			0
$359$	14.3876	+	24.9201i	0.759350	+	1.31523i	0.943183	+	0.332275i	$0.107816\pi$
$359$	14.3876	+	24.9201i	0.759350	+	1.31523i	−0.183833	+	0.982958i	$0.558850\pi$
$360$		0			0
$361$	11.9688	−	14.7563i	0.629938	−	0.776645i
$362$		0			0
$363$	−9.36563	+	5.40725i	−0.491568	+	0.283807i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	20.8969	+	12.0649i	1.09081	+	0.629780i	0.933792	−	0.357815i	$-0.116478\pi$
$367$	20.8969	+	12.0649i	1.09081	+	0.629780i	0.157019	+	0.987596i	$0.449812\pi$
$368$		0			0
$369$	−24.7941			−1.29073
$370$		0			0
$371$	1.20839	−	2.09300i	0.0627367	−	0.108663i
$372$		0			0
$373$			26.7281i			1.38393i	0.721932	+	0.691964i	$0.243254\pi$
$373$			26.7281i			1.38393i	−0.721932	+	0.691964i	$0.756746\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	6.37365	−	3.67983i	0.328260	−	0.189521i
$378$		0			0
$379$	−4.29369			−0.220552			−0.110276	−	0.993901i	$-0.535174\pi$
$379$	−4.29369			−0.220552			−0.110276	+	0.993901i	$0.535174\pi$
$380$		0			0
$381$	−61.0820			−3.12933
$382$		0			0
$383$	−4.82567	+	2.78610i	−0.246580	+	0.142363i	−0.618197	−	0.786023i	$-0.712137\pi$
$383$	−4.82567	+	2.78610i	−0.246580	+	0.142363i	0.371617	+	0.928386i	$0.378803\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$			38.9523i			1.98006i
$388$		0			0
$389$	14.0743	−	24.3774i	0.713594	−	1.23598i	−0.249905	−	0.968270i	$-0.580399\pi$
$389$	14.0743	−	24.3774i	0.713594	−	1.23598i	0.963499	−	0.267711i	$-0.0862674\pi$
$390$		0			0
$391$	−26.3909			−1.33464
$392$		0			0
$393$	−36.3449	−	20.9837i	−1.83336	−	1.05849i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	30.0879	−	17.3712i	1.51007	−	0.871837i	0.510135	−	0.860094i	$-0.329595\pi$
$397$	30.0879	−	17.3712i	1.51007	−	0.871837i	0.999931	−	0.0117431i	$-0.00373805\pi$
$398$		0			0
$399$	17.4268	+	11.9873i	0.872430	+	0.600116i
$400$		0			0
$401$	11.9370	+	20.6755i	0.596106	+	1.03249i	0.993390	+	0.114789i	$0.0366193\pi$
$401$	11.9370	+	20.6755i	0.596106	+	1.03249i	−0.397284	+	0.917696i	$0.630047\pi$
$402$		0			0
$403$	6.12302	+	3.53513i	0.305010	+	0.176097i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			40.9955i			2.03207i
$408$		0			0
$409$	−18.7346	+	32.4492i	−0.926365	+	1.60451i	−0.137015	+	0.990569i	$0.543751\pi$
$409$	−18.7346	+	32.4492i	−0.926365	+	1.60451i	−0.789350	+	0.613943i	$0.789582\pi$
$410$		0			0
$411$	−49.2188			−2.42778
$412$		0			0
$413$	4.29042	−	2.47707i	0.211118	−	0.121889i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		−	58.9402i		−	2.88632i
$418$		0			0
$419$	0.360241			0.0175989			0.00879947	−	0.999961i	$-0.497199\pi$
$419$	0.360241			0.0175989			0.00879947	+	0.999961i	$0.497199\pi$
$420$		0			0
$421$	−12.1243	−	20.9999i	−0.590901	−	1.02347i	−0.994111	−	0.108364i	$-0.965439\pi$
$421$	−12.1243	−	20.9999i	−0.590901	−	1.02347i	0.403210	−	0.915108i	$-0.367894\pi$
$422$		0			0
$423$	68.2984	−	39.4321i	3.32078	−	1.91726i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	0.0880297	+	0.0508239i	0.00426005	+	0.00245954i
$428$		0			0
$429$	−80.4960			−3.88638
$430$		0			0
$431$	6.32067	−	10.9477i	0.304456	−	0.527333i	−0.672684	−	0.739930i	$-0.734859\pi$
$431$	6.32067	−	10.9477i	0.304456	−	0.527333i	0.977140	+	0.212596i	$0.0681920\pi$
$432$		0			0
$433$	−21.1864	−	12.2320i	−1.01815	−	0.587831i	−0.104585	−	0.994516i	$-0.533351\pi$
$433$	−21.1864	−	12.2320i	−1.01815	−	0.587831i	−0.913569	+	0.406685i	$0.866685\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	19.0571	+	1.50745i	0.911623	+	0.0721111i
$438$		0			0
$439$	−12.4004	−	21.4782i	−0.591840	−	1.02510i	−0.993985	−	0.109521i	$-0.965068\pi$
$439$	−12.4004	−	21.4782i	−0.591840	−	1.02510i	0.402144	−	0.915576i	$-0.368265\pi$
$440$		0			0
$441$	16.3139	−	28.2565i	0.776851	−	1.34555i
$442$		0			0
$443$	26.2090	+	15.1318i	1.24523	+	0.718932i	0.970154	−	0.242491i	$-0.0779644\pi$
$443$	26.2090	+	15.1318i	1.24523	+	0.718932i	0.275074	+	0.961423i	$0.411298\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	12.8484	+	7.41801i	0.607707	+	0.350860i
$448$		0			0
$449$	29.0742			1.37209			0.686047	−	0.727557i	$-0.259344\pi$
$449$	29.0742			1.37209			0.686047	+	0.727557i	$0.259344\pi$
$450$		0			0
$451$	6.70760	+	11.6179i	0.315849	+	0.547066i
$452$		0			0
$453$	16.2644	−	9.39023i	0.764166	−	0.441192i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		−	3.06234i		−	0.143250i	−0.997432	−	0.0716251i	$-0.977181\pi$
$457$		−	3.06234i		−	0.143250i	0.997432	−	0.0716251i	$-0.0228185\pi$
$458$		0			0
$459$	−38.2588	−	66.2662i	−1.78577	−	3.09304i
$460$		0			0
$461$	13.2934	+	23.0249i	0.619137	+	1.07238i	0.989644	+	0.143547i	$0.0458507\pi$
$461$	13.2934	+	23.0249i	0.619137	+	1.07238i	−0.370507	+	0.928830i	$0.620816\pi$
$462$		0			0
$463$		−	4.82684i		−	0.224322i	−0.993690	−	0.112161i	$-0.964223\pi$
$463$		−	4.82684i		−	0.224322i	0.993690	−	0.112161i	$-0.0357773\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	1.31539i		−	0.0608690i	−0.999537	−	0.0304345i	$-0.990311\pi$
$467$		−	1.31539i		−	0.0608690i	0.999537	−	0.0304345i	$-0.00968910\pi$
$468$		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
$473$	18.2521	−	10.5379i	0.839234	−	0.484532i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	9.58011	−	5.53108i	0.438643	−	0.253251i
$478$		0			0
$479$	9.53915	−	16.5223i	0.435855	−	0.754923i	−0.561510	−	0.827470i	$-0.689779\pi$
$479$	9.53915	−	16.5223i	0.435855	−	0.754923i	0.997365	+	0.0725469i	$0.0231127\pi$
$480$		0			0
$481$	−36.1601	+	62.6311i	−1.64876	+	2.85573i
$482$		0			0
$483$			21.2814i			0.968335i
$484$		0			0
$485$		0			0
$486$		0			0
$487$		−	8.23656i		−	0.373234i	−0.982433	−	0.186617i	$-0.940248\pi$
$487$		−	8.23656i		−	0.373234i	0.982433	−	0.186617i	$-0.0597524\pi$
$488$		0			0
$489$	9.31308	+	16.1307i	0.421152	+	0.729457i
$490$		0			0
$491$	−15.4776	−	26.8079i	−0.698493	−	1.20983i	−0.968989	−	0.247104i	$-0.920521\pi$
$491$	−15.4776	−	26.8079i	−0.698493	−	1.20983i	0.270496	−	0.962721i	$-0.412812\pi$
$492$		0			0
$493$		−	6.61179i		−	0.297780i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	8.60062	−	4.96557i	0.385790	−	0.222736i
$498$		0			0
$499$	0.554753	+	0.960860i	0.0248341	+	0.0430140i	0.878175	−	0.478339i	$-0.158761\pi$
$499$	0.554753	+	0.960860i	0.0248341	+	0.0430140i	−0.853341	+	0.521353i	$0.825428\pi$
$500$		0			0
$501$	40.5030			1.80954
$502$		0			0
$503$	7.49202	+	4.32552i	0.334053	+	0.192865i	0.657639	−	0.753333i	$-0.271555\pi$
$503$	7.49202	+	4.32552i	0.334053	+	0.192865i	−0.323586	+	0.946199i	$0.604889\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−87.3449	−	50.4286i	−3.87912	−	2.23961i
$508$		0			0
$509$	−10.3944	+	18.0037i	−0.460725	+	0.797999i	−0.998997	−	0.0447722i	$-0.985744\pi$
$509$	−10.3944	+	18.0037i	−0.460725	+	0.797999i	0.538273	+	0.842771i	$0.319077\pi$
$510$		0			0
$511$	10.7164	+	18.5613i	0.474065	+	0.821104i
$512$		0			0
$513$	23.8419	+	50.0368i	1.05265	+	2.20918i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−36.9539	−	21.3354i	−1.62523	−	0.938328i
$518$		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
$523$	15.6482	+	9.03447i	0.684247	+	0.395050i	0.801453	−	0.598058i	$-0.204061\pi$
$523$	15.6482	+	9.03447i	0.684247	+	0.395050i	−0.117207	+	0.993108i	$0.537394\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	5.50082	−	3.17590i	0.239619	−	0.138344i
$528$		0			0
$529$	−1.88304	−	3.26153i	−0.0818715	−	0.141806i
$530$		0			0
$531$	22.6762			0.984062
$532$		0			0
$533$			23.6658i			1.02508i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	59.0556	−	34.0958i	2.54844	−	1.47134i
$538$		0			0
$539$	−17.6537			−0.760401
$540$		0			0
$541$	8.75440	−	15.1631i	0.376381	−	0.651911i	−0.614152	−	0.789188i	$-0.710502\pi$
$541$	8.75440	−	15.1631i	0.376381	−	0.651911i	0.990533	+	0.137277i	$0.0438350\pi$
$542$		0			0
$543$		−	13.5167i		−	0.580055i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−23.3591	−	13.4864i	−0.998763	−	0.576636i	−0.0908807	−	0.995862i	$-0.528968\pi$
$547$	−23.3591	−	13.4864i	−0.998763	−	0.576636i	−0.907882	+	0.419226i	$0.862302\pi$
$548$		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
$553$	−2.64647	+	1.52794i	−0.112539	+	0.0649746i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	13.8280	+	7.98361i	0.585912	+	0.338276i	0.763479	−	0.645832i	$-0.223490\pi$
$557$	13.8280	+	7.98361i	0.585912	+	0.338276i	−0.177568	+	0.984109i	$0.556823\pi$
$558$		0			0
$559$	37.1797			1.57253
$560$		0			0
$561$	−36.1581	+	62.6277i	−1.52660	+	2.64414i
$562$		0			0
$563$			8.58711i			0.361904i	0.983492	+	0.180952i	$0.0579178\pi$
$563$			8.58711i			0.361904i	−0.983492	+	0.180952i	$0.942082\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−25.4839	+	14.7131i	−1.07022	+	0.617894i
$568$		0			0
$569$	−22.5910			−0.947064			−0.473532	−	0.880777i	$-0.657021\pi$
$569$	−22.5910			−0.947064			−0.473532	+	0.880777i	$0.657021\pi$
$570$		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
$573$	17.2733	−	9.97276i	0.721603	−	0.416618i
$574$		0			0
$575$		0			0
$576$		0			0
$577$		−	0.677755i		−	0.0282153i	−0.999900	−	0.0141077i	$-0.995509\pi$
$577$		−	0.677755i		−	0.0282153i	0.999900	−	0.0141077i	$-0.00449075\pi$
$578$		0			0
$579$	−24.3374	+	42.1537i	−1.01143	+	1.75185i
$580$		0			0
$581$	15.8645			0.658171
$582$		0			0
$583$	−5.18346	−	2.99267i	−0.214677	−	0.123944i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	23.7047	−	13.6859i	0.978397	−	0.564878i	0.0766112	−	0.997061i	$-0.475590\pi$
$587$	23.7047	−	13.6859i	0.978397	−	0.564878i	0.901786	+	0.432183i	$0.142257\pi$
$588$		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
$593$	7.25625	+	4.18940i	0.297978	+	0.172038i	0.641534	−	0.767094i	$-0.278298\pi$
$593$	7.25625	+	4.18940i	0.297978	+	0.172038i	−0.343556	+	0.939132i	$0.611632\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$			32.3395i			1.32357i
$598$		0			0
$599$	−16.9553	+	29.3675i	−0.692777	+	1.19992i	0.278148	+	0.960538i	$0.410280\pi$
$599$	−16.9553	+	29.3675i	−0.692777	+	1.19992i	−0.970924	+	0.239386i	$0.923054\pi$
$600$		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
$603$	34.6714	−	20.0175i	1.41193	−	0.815178i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		−	8.87815i		−	0.360353i	−0.983634	−	0.180177i	$-0.942333\pi$
$607$		−	8.87815i		−	0.360353i	0.983634	−	0.180177i	$-0.0576669\pi$
$608$		0			0
$609$	−5.33169			−0.216051
$610$		0			0
$611$	−37.6377	−	65.1904i	−1.52266	−	2.63732i
$612$		0			0
$613$	10.4286	−	6.02098i	0.421209	−	0.243185i	−0.274386	−	0.961620i	$-0.588474\pi$
$613$	10.4286	−	6.02098i	0.421209	−	0.243185i	0.695594	+	0.718435i	$0.255141\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−40.5927	−	23.4362i	−1.63420	−	0.943505i	−0.982778	−	0.184788i	$-0.940840\pi$
$617$	−40.5927	−	23.4362i	−1.63420	−	0.943505i	−0.651420	−	0.758717i	$-0.725827\pi$
$618$		0			0
$619$	−14.8700			−0.597678			−0.298839	−	0.954304i	$-0.596599\pi$
$619$	−14.8700			−0.597678			−0.298839	+	0.954304i	$0.596599\pi$
$620$		0			0
$621$	−27.8834	+	48.2955i	−1.11892	+	1.93803i
$622$		0			0
$623$	−4.08029	−	2.35576i	−0.163473	−	0.0943815i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	29.6874	−	43.1586i	1.18560	−	1.72359i
$628$		0			0
$629$	32.4856	+	56.2667i	1.29529	+	2.24350i
$630$		0			0
$631$	−8.71235	+	15.0902i	−0.346833	+	0.600733i	−0.985685	−	0.168597i	$-0.946076\pi$
$631$	−8.71235	+	15.0902i	−0.346833	+	0.600733i	0.638852	+	0.769330i	$0.279410\pi$
$632$		0			0
$633$	13.9054	+	8.02830i	0.552691	+	0.319096i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−26.9706	−	15.5715i	−1.06861	−	0.616964i
$638$		0			0
$639$	45.4569			1.79825
$640$		0			0
$641$	−15.9973	−	27.7081i	−0.631854	−	1.09440i	−0.987172	−	0.159658i	$-0.948961\pi$
$641$	−15.9973	−	27.7081i	−0.631854	−	1.09440i	0.355318	−	0.934745i	$-0.384373\pi$
$642$		0			0
$643$	−30.3461	+	17.5203i	−1.19673	+	0.690934i	−0.959825	−	0.280598i	$-0.909467\pi$
$643$	−30.3461	+	17.5203i	−1.19673	+	0.690934i	−0.236908	+	0.971532i	$0.576134\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			17.4260i			0.685087i	0.939502	+	0.342544i	$0.111288\pi$
$647$			17.4260i			0.685087i	−0.939502	+	0.342544i	$0.888712\pi$
$648$		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
$653$			49.1457i			1.92322i	0.274422	+	0.961609i	$0.411513\pi$
$653$			49.1457i			1.92322i	−0.274422	+	0.961609i	$0.588487\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$			98.1022i			3.82733i
$658$		0			0
$659$	0.862722	−	1.49428i	0.0336069	−	0.0582088i	−0.848733	−	0.528822i	$-0.822634\pi$
$659$	0.862722	−	1.49428i	0.0336069	−	0.0582088i	0.882340	+	0.470613i	$0.155967\pi$
$660$		0			0
$661$	−10.9594	+	18.9822i	−0.426270	+	0.738321i	−0.996538	−	0.0831373i	$-0.973506\pi$
$661$	−10.9594	+	18.9822i	−0.426270	+	0.738321i	0.570268	+	0.821459i	$0.306839\pi$
$662$		0			0
$663$	−110.481	+	63.7865i	−4.29074	+	2.47726i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−4.17315	+	2.40937i	−0.161585	+	0.0932911i
$668$		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
$673$		−	6.63165i		−	0.255631i	−0.991798	−	0.127816i	$-0.959203\pi$
$673$		−	6.63165i		−	0.255631i	0.991798	−	0.127816i	$-0.0407966\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			32.7008i			1.25679i	0.777893	+	0.628397i	$0.216289\pi$
$677$			32.7008i			1.25679i	−0.777893	+	0.628397i	$0.783711\pi$
$678$		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
$683$			51.9872i			1.98923i	0.103622	+	0.994617i	$0.466957\pi$
$683$			51.9872i			1.98923i	−0.103622	+	0.994617i	$0.533043\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	21.7350	−	12.5487i	0.829243	−	0.478764i
$688$		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
$693$	35.3782	+	20.4256i	1.34391	+	0.775905i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	18.4125	+	10.6305i	0.697423	+	0.402657i
$698$		0			0
$699$	16.7415	−	28.9972i	0.633223	−	1.09678i
$700$		0			0
$701$	−1.12927	−	1.95595i	−0.0426518	−	0.0738751i	0.843911	−	0.536483i	$-0.180247\pi$
$701$	−1.12927	−	1.95595i	−0.0426518	−	0.0738751i	−0.886563	+	0.462607i	$0.846914\pi$
$702$		0			0
$703$	−20.2442	−	42.4863i	−0.763523	−	1.60240i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	8.24299	+	4.75909i	0.310010	+	0.178984i
$708$		0			0
$709$	23.4045	−	40.5378i	0.878975	−	1.52243i	0.0265084	−	0.999649i	$-0.491561\pi$
$709$	23.4045	−	40.5378i	0.878975	−	1.52243i	0.852467	−	0.522781i	$-0.175106\pi$
$710$		0			0
$711$	−13.9874			−0.524569
$712$		0			0
$713$	−4.00905	−	2.31463i	−0.150140	−	0.0866834i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−15.5708	+	8.98978i	−0.581500	+	0.335729i
$718$		0			0
$719$	−11.7570	−	20.3637i	−0.438462	−	0.759439i	0.559109	−	0.829094i	$-0.311143\pi$
$719$	−11.7570	−	20.3637i	−0.438462	−	0.759439i	−0.997571	+	0.0696552i	$0.977810\pi$
$720$		0			0
$721$	0.387961			0.0144484
$722$		0			0
$723$		−	30.1132i		−	1.11992i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−22.0617	+	12.7374i	−0.818225	+	0.472402i	−0.849804	−	0.527099i	$-0.823280\pi$
$727$	−22.0617	+	12.7374i	−0.818225	+	0.472402i	0.0315791	+	0.999501i	$0.489946\pi$
$728$		0			0
$729$	−13.9523			−0.516752
$730$		0			0
$731$	16.7008	−	28.9266i	0.617702	−	1.06989i
$732$		0			0
$733$			1.41916i			0.0524179i	0.999656	+	0.0262090i	$0.00834353\pi$
$733$			1.41916i			0.0524179i	−0.999656	+	0.0262090i	$0.991656\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−18.7595	−	10.8308i	−0.691015	−	0.398958i
$738$		0			0
$739$	−10.7699	−	18.6540i	−0.396176	−	0.686198i	0.597074	−	0.802186i	$-0.296330\pi$
$739$	−10.7699	−	18.6540i	−0.396176	−	0.686198i	−0.993251	+	0.115988i	$0.962996\pi$
$740$		0			0
$741$	83.4231	−	39.7501i	3.06462	−	1.46025i
$742$		0			0
$743$	36.8602	−	21.2813i	1.35227	−	0.780734i	0.363703	−	0.931515i	$-0.381512\pi$
$743$	36.8602	−	21.2813i	1.35227	−	0.780734i	0.988567	+	0.150781i	$0.0481789\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	62.8866	+	36.3076i	2.30090	+	1.32842i
$748$		0			0
$749$	−9.28406			−0.339232
$750$		0			0
$751$	−9.30708	+	16.1203i	−0.339620	+	0.588239i	−0.984361	−	0.176162i	$-0.943632\pi$
$751$	−9.30708	+	16.1203i	−0.339620	+	0.588239i	0.644741	+	0.764401i	$0.276965\pi$
$752$		0			0
$753$		−	39.6681i		−	1.44558i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−26.6462	+	15.3842i	−0.968473	+	0.559148i	−0.898770	−	0.438420i	$-0.855538\pi$
$757$	−26.6462	+	15.3842i	−0.968473	+	0.559148i	−0.0697028	+	0.997568i	$0.522205\pi$
$758$		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
$763$	6.96921	−	4.02368i	0.252302	−	0.145667i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	21.6442i		−	0.781528i
$768$		0			0
$769$	−24.3166	+	42.1176i	−0.876880	+	1.51880i	−0.0221329	+	0.999755i	$0.507046\pi$
$769$	−24.3166	+	42.1176i	−0.876880	+	1.51880i	−0.854747	+	0.519045i	$0.826288\pi$
$770$		0			0
$771$	−54.0877			−1.94792
$772$		0			0
$773$	−16.9616	−	9.79276i	−0.610065	−	0.352221i	0.162926	−	0.986638i	$-0.447907\pi$
$773$	−16.9616	−	9.79276i	−0.610065	−	0.352221i	−0.772991	+	0.634417i	$0.781240\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	45.3730	−	26.1961i	1.62775	−	0.939780i
$778$		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
$783$	−12.0996	−	6.98572i	−0.432405	−	0.249649i
$784$		0			0
$785$		0			0
$786$		0			0
$787$			13.4029i			0.477760i	0.971049	+	0.238880i	$0.0767803\pi$
$787$			13.4029i			0.477760i	−0.971049	+	0.238880i	$0.923220\pi$
$788$		0			0
$789$	1.45610	−	2.52203i	0.0518384	−	0.0897867i
$790$		0			0
$791$	−3.72380			−0.132403
$792$		0			0
$793$	0.384594	−	0.222045i	0.0136573	−	0.00788507i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			30.0201i			1.06337i	0.846943	+	0.531684i	$0.178441\pi$
$797$			30.0201i			1.06337i	−0.846943	+	0.531684i	$0.821559\pi$
$798$		0			0
$799$	−67.6261			−2.39244
$800$		0			0
$801$	−10.7828	−	18.6764i	−0.380992	−	0.659897i
$802$		0			0
$803$	45.9684	−	26.5399i	1.62219	−	0.936571i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−69.5264	−	40.1411i	−2.44745	−	1.41303i
$808$		0			0
$809$	13.4967			0.474520			0.237260	−	0.971446i	$-0.423751\pi$
$809$	13.4967			0.474520			0.237260	+	0.971446i	$0.423751\pi$
$810$		0			0
$811$	2.63260	−	4.55980i	0.0924431	−	0.160116i	−0.816096	−	0.577917i	$-0.803866\pi$
$811$	2.63260	−	4.55980i	0.0924431	−	0.160116i	0.908539	+	0.417801i	$0.137199\pi$
$812$		0			0
$813$	−30.7996	−	17.7821i	−1.08019	−	0.623647i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−13.7121	+	19.9342i	−0.479725	+	0.697410i
$818$		0			0
$819$	36.0328	+	62.4107i	1.25909	+	2.18081i
$820$		0			0
$821$	16.4147	−	28.4312i	0.572879	−	0.992255i	−0.423390	−	0.905948i	$-0.639160\pi$
$821$	16.4147	−	28.4312i	0.572879	−	0.992255i	0.996269	−	0.0863073i	$-0.0275067\pi$
$822$		0			0
$823$	36.1266	+	20.8577i	1.25929	+	0.727054i	0.972937	−	0.231069i	$-0.0742223\pi$
$823$	36.1266	+	20.8577i	1.25929	+	0.727054i	0.286357	+	0.958123i	$0.407556\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	10.5572	+	6.09523i	0.367111	+	0.211952i	0.672196	−	0.740373i	$-0.265351\pi$
$827$	10.5572	+	6.09523i	0.367111	+	0.211952i	−0.305084	+	0.952325i	$0.598685\pi$
$828$		0			0
$829$	52.9958			1.84062			0.920310	−	0.391190i	$-0.127936\pi$
$829$	52.9958			1.84062			0.920310	+	0.391190i	$0.127936\pi$
$830$		0			0
$831$	−26.1894	−	45.3614i	−0.908500	−	1.57357i
$832$		0			0
$833$	−24.2299	+	13.9892i	−0.839517	+	0.484695i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		−	13.4221i		−	0.463934i
$838$		0			0
$839$	−7.60822	−	13.1778i	−0.262665	−	0.454949i	0.704284	−	0.709918i	$-0.251268\pi$
$839$	−7.60822	−	13.1778i	−0.262665	−	0.454949i	−0.966949	+	0.254969i	$0.917935\pi$
$840$		0			0
$841$	13.8964	+	24.0692i	0.479185	+	0.829973i
$842$		0			0
$843$			33.4831i			1.15322i
$844$		0			0
$845$		0			0
$846$		0			0
$847$		−	5.23854i		−	0.179998i
$848$		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
$853$	40.8295	−	23.5729i	1.39798	−	0.807122i	0.403795	−	0.914849i	$-0.367691\pi$
$853$	40.8295	−	23.5729i	1.39798	−	0.807122i	0.994180	+	0.107728i	$0.0343575\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−44.4974	+	25.6906i	−1.52000	+	0.877574i	−0.520280	+	0.853996i	$0.674172\pi$
$857$	−44.4974	+	25.6906i	−1.52000	+	0.877574i	−0.999722	+	0.0235779i	$0.992494\pi$
$858$		0			0
$859$	1.03055	−	1.78496i	0.0351618	−	0.0609019i	−0.847909	−	0.530142i	$-0.822139\pi$
$859$	1.03055	−	1.78496i	0.0351618	−	0.0609019i	0.883071	+	0.469240i	$0.155472\pi$
$860$		0			0
$861$	8.57230	−	14.8477i	0.292143	−	0.506007i
$862$		0			0
$863$			35.8646i			1.22084i	0.792076	+	0.610422i	$0.209000\pi$
$863$			35.8646i			1.22084i	−0.792076	+	0.610422i	$0.791000\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$			60.8035i			2.06500i
$868$		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
$873$		−	62.2460i		−	2.10671i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	11.3380	−	6.54598i	0.382856	−	0.221042i	−0.296204	−	0.955125i	$-0.595721\pi$
$877$	11.3380	−	6.54598i	0.382856	−	0.221042i	0.679060	+	0.734083i	$0.262388\pi$
$878$		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
$883$	−25.6642	−	14.8172i	−0.863670	−	0.498640i	0.00156969	−	0.999999i	$-0.499500\pi$
$883$	−25.6642	−	14.8172i	−0.863670	−	0.498640i	−0.865239	+	0.501359i	$0.832834\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	26.3533	+	15.2151i	0.884858	+	0.510873i	0.872257	−	0.489048i	$-0.162656\pi$
$887$	26.3533	+	15.2151i	0.884858	+	0.510873i	0.0126008	+	0.999921i	$0.495989\pi$
$888$		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
$893$	48.8334	+	3.86282i	1.63415	+	0.129264i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	80.5199	+	46.4882i	2.68848	+	1.55220i
$898$		0			0
$899$	0.579891	−	1.00440i	0.0193405	−	0.0334986i
$900$		0			0
$901$	−9.48580			−0.316018
$902$		0			0
$903$	−23.3262	−	13.4674i	−0.776247	−	0.448166i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	9.69395	−	5.59680i	0.321882	−	0.185839i	−0.330349	−	0.943859i	$-0.607166\pi$
$907$	9.69395	−	5.59680i	0.321882	−	0.185839i	0.652231	+	0.758020i	$0.273833\pi$
$908$		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
$913$		−	39.2895i		−	1.30029i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	17.6055	−	10.1645i	0.581384	−	0.335662i
$918$		0			0
$919$	15.0715			0.497163			0.248582	−	0.968611i	$-0.420036\pi$
$919$	15.0715			0.497163			0.248582	+	0.968611i	$0.420036\pi$
$920$		0			0
$921$	13.6690	−	23.6754i	0.450408	−	0.780130i
$922$		0			0
$923$		−	43.3883i		−	1.42814i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	1.53787	+	0.887890i	0.0505103	+	0.0291621i
$928$		0			0
$929$	11.3279	+	19.6204i	0.371655	+	0.643725i	0.989820	−	0.142323i	$-0.0454571\pi$
$929$	11.3279	+	19.6204i	0.371655	+	0.643725i	−0.618165	+	0.786048i	$0.712124\pi$
$930$		0			0
$931$	18.2957	−	8.71767i	0.599617	−	0.285710i
$932$		0			0
$933$	−81.5884	+	47.1051i	−2.67108	+	1.54215i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−16.3032	−	9.41266i	−0.532602	−	0.307498i	0.209473	−	0.977814i	$-0.432825\pi$
$937$	−16.3032	−	9.41266i	−0.532602	−	0.307498i	−0.742076	+	0.670316i	$0.766158\pi$
$938$		0			0
$939$	−35.4747			−1.15767
$940$		0			0
$941$	6.91540	−	11.9778i	0.225436	−	0.390466i	−0.731014	−	0.682362i	$-0.760953\pi$
$941$	6.91540	−	11.9778i	0.225436	−	0.390466i	0.956450	+	0.291896i	$0.0942861\pi$
$942$		0			0
$943$		−	15.4952i		−	0.504592i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	39.8463	−	23.0053i	1.29483	−	0.747570i	0.315323	−	0.948984i	$-0.397887\pi$
$947$	39.8463	−	23.0053i	1.29483	−	0.747570i	0.979506	+	0.201414i	$0.0645536\pi$
$948$		0			0
$949$	93.6379			3.03961
$950$		0			0
$951$	−14.8536			−0.481660
$952$		0			0
$953$	6.44656	−	3.72192i	0.208824	−	0.120565i	−0.391940	−	0.919991i	$-0.628196\pi$
$953$	6.44656	−	3.72192i	0.208824	−	0.120565i	0.600765	+	0.799426i	$0.294863\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$			13.2043i			0.426834i
$958$		0			0
$959$	11.9208	−	20.6474i	0.384942	−	0.666739i
$960$		0			0
$961$	−29.8858			−0.964059
$962$		0			0
$963$	−36.8018	−	21.2475i	−1.18592	−	0.684693i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−36.0918	+	20.8376i	−1.16063	+	0.670092i	−0.951456	−	0.307786i	$-0.900412\pi$
$967$	−36.0918	+	20.8376i	−1.16063	+	0.670092i	−0.209178	+	0.977878i	$0.567079\pi$
$968$		0			0
$969$	6.54651	−	82.7604i	0.210304	−	2.65865i
$970$		0			0
$971$	9.63451	+	16.6875i	0.309186	+	0.535526i	0.978185	−	0.207738i	$-0.0666101\pi$
$971$	9.63451	+	16.6875i	0.309186	+	0.535526i	−0.668999	+	0.743264i	$0.733277\pi$
$972$		0			0
$973$	24.7256	+	14.2753i	0.792666	+	0.457646i
$974$		0			0
$975$		0			0
$976$		0			0
$977$			19.7307i			0.631242i	0.948885	+	0.315621i	$0.102213\pi$
$977$			19.7307i			0.631242i	−0.948885	+	0.315621i	$0.897787\pi$
$978$		0			0
$979$	−5.83420	+	10.1051i	−0.186462	+	0.322961i
$980$		0			0
$981$	36.8344			1.17603
$982$		0			0
$983$	−28.8071	+	16.6318i	−0.918805	+	0.530472i	−0.883254	−	0.468896i	$-0.844652\pi$
$983$	−28.8071	+	16.6318i	−0.918805	+	0.530472i	−0.0355513	+	0.999368i	$0.511319\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$			54.5331i			1.73581i
$988$		0			0
$989$	−24.3434			−0.774076
$990$		0			0
$991$	8.90804	+	15.4292i	0.282973	+	0.490124i	0.972116	−	0.234502i	$-0.0753459\pi$
$991$	8.90804	+	15.4292i	0.282973	+	0.490124i	−0.689142	+	0.724626i	$0.742013\pi$
$992$		0			0
$993$	−79.8012	+	46.0732i	−2.53241	+	1.46209i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−18.3680	−	10.6048i	−0.581722	−	0.335857i	0.180095	−	0.983649i	$-0.442359\pi$
$997$	−18.3680	−	10.6048i	−0.581722	−	0.335857i	−0.761817	+	0.647792i	$0.775693\pi$
$998$		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.s.d.349.1		16
5.2	odd	4		1900.2.i.d.501.4		8
5.3	odd	4		380.2.i.c.121.1	✓	8
5.4	even	2	inner	1900.2.s.d.349.8		16
15.8	even	4		3420.2.t.w.1261.2		8
19.11	even	3	inner	1900.2.s.d.49.8		16
20.3	even	4		1520.2.q.m.881.4		8
95.49	even	6	inner	1900.2.s.d.49.1		16
95.68	odd	12		380.2.i.c.201.1	yes	8
95.83	odd	12		7220.2.a.r.1.4		4
95.87	odd	12		1900.2.i.d.201.4		8
95.88	even	12		7220.2.a.p.1.1		4
285.68	even	12		3420.2.t.w.3241.2		8
380.163	even	12		1520.2.q.m.961.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.i.c.121.1	✓	8	5.3	odd	4
380.2.i.c.201.1	yes	8	95.68	odd	12
1520.2.q.m.881.4		8	20.3	even	4
1520.2.q.m.961.4		8	380.163	even	12
1900.2.i.d.201.4		8	95.87	odd	12
1900.2.i.d.501.4		8	5.2	odd	4
1900.2.s.d.49.1		16	95.49	even	6	inner
1900.2.s.d.49.8		16	19.11	even	3	inner
1900.2.s.d.349.1		16	1.1	even	1	trivial
1900.2.s.d.349.8		16	5.4	even	2	inner
3420.2.t.w.1261.2		8	15.8	even	4
3420.2.t.w.3241.2		8	285.68	even	12
7220.2.a.p.1.1		4	95.88	even	12
7220.2.a.r.1.4		4	95.83	odd	12

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.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.74101 + 1.58253i) q^{3} -1.53315i q^{7} +(3.50877 - 6.07738i) q^{9} +O(q^{10})\)	\(q+(-2.74101 + 1.58253i) q^{3} -1.53315i q^{7} +(3.50877 - 6.07738i) q^{9} -3.79695 q^{11} +(-5.80081 - 3.34910i) q^{13} +(-5.21135 + 3.00877i) q^{17} +(3.93502 - 1.87499i) q^{19} +(2.42625 + 4.20239i) q^{21} +(3.79808 + 2.19282i) q^{23} +12.7158i q^{27} +(-0.549376 + 0.951547i) q^{29} -1.05555 q^{31} +(10.4075 - 6.00877i) q^{33} -10.7970i q^{37} +21.2002 q^{39} +(-1.76658 - 3.05980i) q^{41} +(-4.80705 + 2.77535i) q^{43} +(9.73252 + 5.61907i) q^{47} +4.64945 q^{49} +(9.52293 - 16.4942i) q^{51} +(1.36516 + 0.788178i) q^{53} +(-7.81874 + 11.3667i) q^{57} +(1.61568 + 2.79843i) q^{59} +(-0.0331500 + 0.0574175i) q^{61} +(-9.31753 - 5.37948i) q^{63} +(4.94067 + 2.85250i) q^{67} -13.8808 q^{69} +(3.23880 + 5.60977i) q^{71} +(-12.1066 + 6.98978i) q^{73} +5.82130i q^{77} +(-0.996602 - 1.72617i) q^{79} +(-9.59668 - 16.6219i) q^{81} +10.3477i q^{83} -3.47760i q^{87} +(1.53655 - 2.66138i) q^{89} +(-5.13467 + 8.89352i) q^{91} +(2.89327 - 1.67043i) q^{93} +(7.68169 - 4.43502i) q^{97} +(-13.3227 + 23.0755i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 10 q^{9}+O(q^{10}) \) 16 * q + 10 * q^9	\( 16 q + 10 q^{9} + 8 q^{11} - 6 q^{19} + 16 q^{21} - 10 q^{29} - 40 q^{31} + 108 q^{39} - 16 q^{41} - 40 q^{49} + 24 q^{51} - 22 q^{59} + 24 q^{61} - 12 q^{69} + 28 q^{71} - 26 q^{79} - 48 q^{81} - 10 q^{89} - 92 q^{91} - 48 q^{99}+O(q^{100}) \) 16 * q + 10 * q^9 + 8 * q^11 - 6 * q^19 + 16 * q^21 - 10 * q^29 - 40 * q^31 + 108 * q^39 - 16 * q^41 - 40 * q^49 + 24 * q^51 - 22 * q^59 + 24 * q^61 - 12 * q^69 + 28 * q^71 - 26 * q^79 - 48 * q^81 - 10 * q^89 - 92 * q^91 - 48 * q^99

Introduction

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