LMFDB - Embedded newform 1900.2.i.e.501.1

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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 15 x^{10} - 16 x^{9} + 79 x^{8} - 65 x^{7} + 298 x^{6} + 13 x^{5} + 233 x^{4} + \cdots + 9 $ x^12 - 3x^11 + 15x^10 - 16x^9 + 79x^8 - 65x^7 + 298x^6 + 13x^5 + 233x^4 + 14x^3 + 145x^2 + 33*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			501.1
Root			$-1.08347 - 1.87662i$ of defining polynomial
Character	$\chi$	$=$	1900.501
Dual form			1900.2.i.e.201.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.58347 - 2.74265i) q^{3} -3.03607 q^{7} +(-3.51475 + 6.08773i) q^{9} +O(q^{10})$	$q+(-1.58347 - 2.74265i) q^{3} -3.03607 q^{7} +(-3.51475 + 6.08773i) q^{9} +2.71642 q^{11} +(-1.95668 + 3.38907i) q^{13} +(0.944962 + 1.63672i) q^{17} +(1.83281 + 3.95485i) q^{19} +(4.80753 + 8.32689i) q^{21} +(3.57611 - 6.19400i) q^{23} +12.7612 q^{27} +(1.45668 - 2.52305i) q^{29} +7.40548 q^{31} +(-4.30137 - 7.45019i) q^{33} +3.43284 q^{37} +12.3934 q^{39} +(-5.16090 - 8.93895i) q^{41} +(-5.37852 - 9.31587i) q^{43} +(-2.63731 + 4.56795i) q^{47} +2.21774 q^{49} +(2.99264 - 5.18340i) q^{51} +(-0.843574 + 1.46111i) q^{53} +(7.94456 - 11.2891i) q^{57} +(0.347967 + 0.602697i) q^{59} +(-6.28553 + 10.8869i) q^{61} +(10.6710 - 18.4828i) q^{63} +(-0.365572 + 0.633189i) q^{67} -22.6506 q^{69} +(1.75274 + 3.03584i) q^{71} +(5.55396 + 9.61973i) q^{73} -8.24725 q^{77} +(6.03374 + 10.4507i) q^{79} +(-9.66273 - 16.7363i) q^{81} +11.4181 q^{83} -9.22645 q^{87} +(4.34057 - 7.51809i) q^{89} +(5.94063 - 10.2895i) q^{91} +(-11.7264 - 20.3106i) q^{93} +(3.43468 + 5.94905i) q^{97} +(-9.54754 + 16.5368i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} - 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^3 - 3 * q^9	$ 12 q - 3 q^{3} - 3 q^{9} + 2 q^{11} - 7 q^{13} + q^{17} + q^{21} + 2 q^{23} + 24 q^{27} + q^{29} + 2 q^{31} - 10 q^{33} - 20 q^{37} + 36 q^{39} - 7 q^{41} - 19 q^{43} + 14 q^{47} + 8 q^{49} + 11 q^{51} - 6 q^{53} + 28 q^{57} - 5 q^{61} + 11 q^{63} - 14 q^{67} - 14 q^{69} + 8 q^{71} + 9 q^{73} - 2 q^{77} + q^{79} + 2 q^{81} + 26 q^{83} - 30 q^{87} - 8 q^{89} + 3 q^{91} - 9 q^{93} + 11 q^{97} - 18 q^{99}+O(q^{100}) $ 12 * q - 3 * q^3 - 3 * q^9 + 2 * q^11 - 7 * q^13 + q^17 + q^21 + 2 * q^23 + 24 * q^27 + q^29 + 2 * q^31 - 10 * q^33 - 20 * q^37 + 36 * q^39 - 7 * q^41 - 19 * q^43 + 14 * q^47 + 8 * q^49 + 11 * q^51 - 6 * q^53 + 28 * q^57 - 5 * q^61 + 11 * q^63 - 14 * q^67 - 14 * q^69 + 8 * q^71 + 9 * q^73 - 2 * q^77 + q^79 + 2 * q^81 + 26 * q^83 - 30 * q^87 - 8 * q^89 + 3 * q^91 - 9 * q^93 + 11 * q^97 - 18 * 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
$3$	−1.58347	−	2.74265i	−0.914217	−	1.58347i	−0.808044	−	0.589122i	$-0.799474\pi$
$3$	−1.58347	−	2.74265i	−0.914217	−	1.58347i	−0.106173	−	0.994348i	$-0.533860\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−3.03607			−1.14753			−0.573764	−	0.819021i	$-0.694517\pi$
$7$	−3.03607			−1.14753			−0.573764	+	0.819021i	$0.694517\pi$
$8$		0			0
$9$	−3.51475	+	6.08773i	−1.17158	+	2.02924i
$10$		0			0
$11$	2.71642			0.819031			0.409516	−	0.912303i	$-0.365698\pi$
$11$	2.71642			0.819031			0.409516	+	0.912303i	$0.365698\pi$
$12$		0			0
$13$	−1.95668	+	3.38907i	−0.542686	+	0.939960i	0.456062	+	0.889948i	$0.349259\pi$
$13$	−1.95668	+	3.38907i	−0.542686	+	0.939960i	−0.998749	+	0.0500123i	$0.984074\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.944962	+	1.63672i	0.229187	+	0.396963i	0.957567	−	0.288210i	$-0.0930600\pi$
$17$	0.944962	+	1.63672i	0.229187	+	0.396963i	−0.728380	+	0.685173i	$0.759727\pi$
$18$		0			0
$19$	1.83281	+	3.95485i	0.420476	+	0.907304i
$19$	1.83281	+	3.95485i	0.420476	+	0.907304i
$20$		0			0
$21$	4.80753	+	8.32689i	1.04909	+	1.81708i
$22$		0			0
$23$	3.57611	−	6.19400i	0.745670	−	1.29154i	−0.204211	−	0.978927i	$-0.565463\pi$
$23$	3.57611	−	6.19400i	0.745670	−	1.29154i	0.949881	−	0.312611i	$-0.101204\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	12.7612			2.45590
$28$		0			0
$29$	1.45668	−	2.52305i	0.270499	−	0.468518i	−0.698491	−	0.715619i	$-0.746145\pi$
$29$	1.45668	−	2.52305i	0.270499	−	0.468518i	0.968990	+	0.247101i	$0.0794779\pi$
$30$		0			0
$31$	7.40548			1.33006			0.665032	−	0.746815i	$-0.268418\pi$
$31$	7.40548			1.33006			0.665032	+	0.746815i	$0.268418\pi$
$32$		0			0
$33$	−4.30137	−	7.45019i	−0.748772	−	1.29691i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.43284			0.564355			0.282178	−	0.959362i	$-0.408943\pi$
$37$	3.43284			0.564355			0.282178	+	0.959362i	$0.408943\pi$
$38$		0			0
$39$	12.3934			1.98453
$40$		0			0
$41$	−5.16090	−	8.93895i	−0.805998	−	1.39603i	−0.915616	−	0.402055i	$-0.868296\pi$
$41$	−5.16090	−	8.93895i	−0.805998	−	1.39603i	0.109618	−	0.993974i	$-0.465037\pi$
$42$		0			0
$43$	−5.37852	−	9.31587i	−0.820217	−	1.42066i	−0.905521	−	0.424302i	$-0.860519\pi$
$43$	−5.37852	−	9.31587i	−0.820217	−	1.42066i	0.0853036	−	0.996355i	$-0.472814\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.63731	+	4.56795i	−0.384691	+	0.666304i	−0.991726	−	0.128371i	$-0.959025\pi$
$47$	−2.63731	+	4.56795i	−0.384691	+	0.666304i	0.607035	+	0.794675i	$0.292359\pi$
$48$		0			0
$49$	2.21774			0.316820
$50$		0			0
$51$	2.99264	−	5.18340i	0.419053	−	0.725821i
$52$		0			0
$53$	−0.843574	+	1.46111i	−0.115874	+	0.200699i	−0.918129	−	0.396282i	$-0.870300\pi$
$53$	−0.843574	+	1.46111i	−0.115874	+	0.200699i	0.802255	+	0.596982i	$0.203633\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	7.94456	−	11.2891i	1.05228	−	1.49528i
$58$		0			0
$59$	0.347967	+	0.602697i	0.0453015	+	0.0784644i	0.887787	−	0.460254i	$-0.152242\pi$
$59$	0.347967	+	0.602697i	0.0453015	+	0.0784644i	−0.842486	+	0.538719i	$0.818908\pi$
$60$		0			0
$61$	−6.28553	+	10.8869i	−0.804780	+	1.39392i	0.111660	+	0.993747i	$0.464383\pi$
$61$	−6.28553	+	10.8869i	−0.804780	+	1.39392i	−0.916440	+	0.400173i	$0.868950\pi$
$62$		0			0
$63$	10.6710	−	18.4828i	1.34443	−	2.32861i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−0.365572	+	0.633189i	−0.0446617	+	0.0773564i	−0.887492	−	0.460823i	$-0.847554\pi$
$67$	−0.365572	+	0.633189i	−0.0446617	+	0.0773564i	0.842830	+	0.538179i	$0.180888\pi$
$68$		0			0
$69$	−22.6506			−2.72682
$70$		0			0
$71$	1.75274	+	3.03584i	0.208012	+	0.360288i	0.951088	−	0.308919i	$-0.0999673\pi$
$71$	1.75274	+	3.03584i	0.208012	+	0.360288i	−0.743076	+	0.669207i	$0.766634\pi$
$72$		0			0
$73$	5.55396	+	9.61973i	0.650041	+	1.12590i	0.983112	+	0.183003i	$0.0585818\pi$
$73$	5.55396	+	9.61973i	0.650041	+	1.12590i	−0.333071	+	0.942902i	$0.608085\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−8.24725			−0.939861
$78$		0			0
$79$	6.03374	+	10.4507i	0.678849	+	1.17580i	0.975328	+	0.220761i	$0.0708542\pi$
$79$	6.03374	+	10.4507i	0.678849	+	1.17580i	−0.296479	+	0.955039i	$0.595812\pi$
$80$		0			0
$81$	−9.66273	−	16.7363i	−1.07364	−	1.85959i
$82$		0			0
$83$	11.4181			1.25330			0.626650	−	0.779301i	$-0.284425\pi$
$83$	11.4181			1.25330			0.626650	+	0.779301i	$0.284425\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−9.22645			−0.989180
$88$		0			0
$89$	4.34057	−	7.51809i	0.460099	−	0.796916i	−0.538866	−	0.842392i	$-0.681147\pi$
$89$	4.34057	−	7.51809i	0.460099	−	0.796916i	0.998965	+	0.0454758i	$0.0144804\pi$
$90$		0			0
$91$	5.94063	−	10.2895i	0.622747	−	1.07863i
$92$		0			0
$93$	−11.7264	−	20.3106i	−1.21597	−	2.10612i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	3.43468	+	5.94905i	0.348739	+	0.604034i	0.986026	−	0.166593i	$-0.0532765\pi$
$97$	3.43468	+	5.94905i	0.348739	+	0.604034i	−0.637286	+	0.770627i	$0.719943\pi$
$98$		0			0
$99$	−9.54754	+	16.5368i	−0.959564	+	1.66201i
$100$		0			0
$101$	6.96831	−	12.0695i	0.693373	−	1.20096i	−0.277354	−	0.960768i	$-0.589457\pi$
$101$	6.96831	−	12.0695i	0.693373	−	1.20096i	0.970726	−	0.240189i	$-0.0772093\pi$
$102$		0			0
$103$	9.81071			0.966678			0.483339	−	0.875433i	$-0.339424\pi$
$103$	9.81071			0.966678			0.483339	+	0.875433i	$0.339424\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−12.6908			−1.22687			−0.613434	−	0.789746i	$-0.710212\pi$
$107$	−12.6908			−1.22687			−0.613434	+	0.789746i	$0.710212\pi$
$108$		0			0
$109$	−3.85085	−	6.66986i	−0.368844	−	0.638857i	0.620541	−	0.784174i	$-0.286913\pi$
$109$	−3.85085	−	6.66986i	−0.368844	−	0.638857i	−0.989385	+	0.145317i	$0.953580\pi$
$110$		0			0
$111$	−5.43580	−	9.41507i	−0.515943	−	0.893639i
$112$		0			0
$113$	12.8536			1.20917			0.604583	−	0.796542i	$-0.293340\pi$
$113$	12.8536			1.20917			0.604583	+	0.796542i	$0.293340\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−13.7545	−	23.8235i	−1.27161	−	2.20249i
$118$		0			0
$119$	−2.86897	−	4.96921i	−0.262998	−	0.455526i
$120$		0			0
$121$	−3.62107			−0.329188
$122$		0			0
$123$	−16.3443	+	28.3091i	−1.47371	+	2.55255i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	0.735934	−	1.27468i	0.0653036	−	0.113109i	−0.831525	−	0.555487i	$-0.812532\pi$
$127$	0.735934	−	1.27468i	0.0653036	−	0.113109i	0.896829	+	0.442378i	$0.145865\pi$
$128$		0			0
$129$	−17.0335	+	29.5028i	−1.49971	+	2.59758i
$130$		0			0
$131$	−8.76584	−	15.1829i	−0.765875	−	1.32653i	−0.939783	−	0.341773i	$-0.888973\pi$
$131$	−8.76584	−	15.1829i	−0.765875	−	1.32653i	0.173907	−	0.984762i	$-0.444361\pi$
$132$		0			0
$133$	−5.56455	−	12.0072i	−0.482507	−	1.04116i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.49344	−	6.05081i	0.298464	−	0.516955i	−0.677321	−	0.735688i	$-0.736859\pi$
$137$	3.49344	−	6.05081i	0.298464	−	0.516955i	0.975785	+	0.218733i	$0.0701923\pi$
$138$		0			0
$139$	7.52394	−	13.0318i	0.638172	−	1.10535i	−0.347661	−	0.937620i	$-0.613024\pi$
$139$	7.52394	−	13.0318i	0.638172	−	1.10535i	0.985834	−	0.167727i	$-0.0536426\pi$
$140$		0			0
$141$	16.7044			1.40676
$142$		0			0
$143$	−5.31517	+	9.20615i	−0.444477	+	0.769857i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−3.51172	−	6.08248i	−0.289642	−	0.501674i
$148$		0			0
$149$	0.664435	+	1.15084i	0.0544326	+	0.0942801i	0.891958	−	0.452119i	$-0.149332\pi$
$149$	0.664435	+	1.15084i	0.0544326	+	0.0942801i	−0.837525	+	0.546399i	$0.815998\pi$
$150$		0			0
$151$	−1.88336			−0.153266			−0.0766328	−	0.997059i	$-0.524417\pi$
$151$	−1.88336			−0.153266			−0.0766328	+	0.997059i	$0.524417\pi$
$152$		0			0
$153$	−13.2852			−1.07405
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−4.40932	−	7.63717i	−0.351902	−	0.609512i	0.634681	−	0.772775i	$-0.281132\pi$
$157$	−4.40932	−	7.63717i	−0.351902	−	0.609512i	−0.986583	+	0.163262i	$0.947798\pi$
$158$		0			0
$159$	5.34310			0.423735
$160$		0			0
$161$	−10.8573	+	18.8054i	−0.855677	+	1.48208i
$162$		0			0
$163$	19.9424			1.56201			0.781004	−	0.624526i	$-0.214708\pi$
$163$	19.9424			1.56201			0.781004	+	0.624526i	$0.214708\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	7.43395	−	12.8760i	0.575256	−	0.996373i	−0.420757	−	0.907173i	$-0.638236\pi$
$167$	7.43395	−	12.8760i	0.575256	−	0.996373i	0.996014	−	0.0892000i	$-0.0284310\pi$
$168$		0			0
$169$	−1.15722	−	2.00436i	−0.0890167	−	0.154181i
$170$		0			0
$171$	−30.5179	−	2.74265i	−2.33376	−	0.209736i
$172$		0			0
$173$	5.61271	+	9.72149i	0.426726	+	0.739111i	0.996580	−	0.0826348i	$-0.0263335\pi$
$173$	5.61271	+	9.72149i	0.426726	+	0.739111i	−0.569854	+	0.821746i	$0.693000\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	1.10199	−	1.90870i	0.0828307	−	0.143467i
$178$		0			0
$179$	17.2702			1.29084			0.645419	−	0.763828i	$-0.276683\pi$
$179$	17.2702			1.29084			0.645419	+	0.763828i	$0.276683\pi$
$180$		0			0
$181$	8.87048	−	15.3641i	0.659338	−	1.14201i	−0.321450	−	0.946927i	$-0.604170\pi$
$181$	8.87048	−	15.3641i	0.659338	−	1.14201i	0.980787	−	0.195080i	$-0.0624965\pi$
$182$		0			0
$183$	39.8118			2.94297
$184$		0			0
$185$		0			0
$186$		0			0
$187$	2.56691	+	4.44602i	0.187711	+	0.325125i
$188$		0			0
$189$	−38.7440			−2.81821
$190$		0			0
$191$	−25.1341			−1.81864			−0.909321	−	0.416096i	$-0.863398\pi$
$191$	−25.1341			−1.81864			−0.909321	+	0.416096i	$0.863398\pi$
$192$		0			0
$193$	−7.61627	−	13.1918i	−0.548231	−	0.949564i	−0.998396	−	0.0566184i	$-0.981968\pi$
$193$	−7.61627	−	13.1918i	−0.548231	−	0.949564i	0.450165	−	0.892945i	$-0.351365\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	8.15878			0.581289			0.290644	−	0.956831i	$-0.406130\pi$
$197$	8.15878			0.581289			0.290644	+	0.956831i	$0.406130\pi$
$198$		0			0
$199$	6.96105	−	12.0569i	0.493456	−	0.854690i	−0.506516	−	0.862231i	$-0.669067\pi$
$199$	6.96105	−	12.0569i	0.493456	−	0.854690i	0.999972	+	0.00754036i	$0.00240020\pi$
$200$		0			0
$201$	2.31549			0.163322
$202$		0			0
$203$	−4.42260	+	7.66016i	−0.310405	+	0.537638i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	25.1383	+	43.5408i	1.74723	+	3.02629i
$208$		0			0
$209$	4.97868	+	10.7430i	0.344383	+	0.743110i
$210$		0			0
$211$	2.79305	+	4.83770i	0.192281	+	0.333041i	0.946006	−	0.324149i	$-0.105078\pi$
$211$	2.79305	+	4.83770i	0.192281	+	0.333041i	−0.753725	+	0.657190i	$0.771745\pi$
$212$		0			0
$213$	5.55083	−	9.61431i	0.380336	−	0.658762i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−22.4836			−1.52629
$218$		0			0
$219$	17.5890	−	30.4651i	1.18856	−	2.05864i
$220$		0			0
$221$	−7.39596			−0.497506
$222$		0			0
$223$	2.43684	+	4.22074i	0.163183	+	0.282641i	0.936009	−	0.351977i	$-0.114491\pi$
$223$	2.43684	+	4.22074i	0.163183	+	0.282641i	−0.772825	+	0.634619i	$0.781157\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	26.7800			1.77745			0.888727	−	0.458438i	$-0.151591\pi$
$227$	26.7800			1.77745			0.888727	+	0.458438i	$0.151591\pi$
$228$		0			0
$229$	21.4407			1.41684			0.708422	−	0.705789i	$-0.249407\pi$
$229$	21.4407			1.41684			0.708422	+	0.705789i	$0.249407\pi$
$230$		0			0
$231$	13.0593	+	22.6193i	0.859237	+	1.48824i
$232$		0			0
$233$	−0.0459183	−	0.0795329i	−0.00300821	−	0.00521037i	0.864517	−	0.502603i	$-0.167624\pi$
$233$	−0.0459183	−	0.0795329i	−0.00300821	−	0.00521037i	−0.867526	+	0.497393i	$0.834291\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	19.1085	−	33.0969i	1.24123	−	2.14987i
$238$		0			0
$239$	20.9290			1.35378			0.676892	−	0.736082i	$-0.263326\pi$
$239$	20.9290			1.35378			0.676892	+	0.736082i	$0.263326\pi$
$240$		0			0
$241$	0.937689	−	1.62412i	0.0604019	−	0.104619i	−0.834243	−	0.551397i	$-0.814095\pi$
$241$	0.937689	−	1.62412i	0.0604019	−	0.104619i	0.894645	+	0.446778i	$0.147428\pi$
$242$		0			0
$243$	−11.4595	+	19.8484i	−0.735125	+	1.27327i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−16.9895	−	1.52685i	−1.08102	−	0.0971511i
$248$		0			0
$249$	−18.0802	−	31.3159i	−1.14579	−	1.98456i
$250$		0			0
$251$	8.93088	−	15.4687i	0.563712	−	0.976378i	−0.433456	−	0.901175i	$-0.642706\pi$
$251$	8.93088	−	15.4687i	0.563712	−	0.976378i	0.997168	−	0.0752035i	$-0.0239606\pi$
$252$		0			0
$253$	9.71421	−	16.8255i	0.610727	−	1.05781i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−15.0988	+	26.1518i	−0.941836	+	1.63131i	−0.179869	+	0.983691i	$0.557567\pi$
$257$	−15.0988	+	26.1518i	−0.941836	+	1.63131i	−0.761967	+	0.647616i	$0.775766\pi$
$258$		0			0
$259$	−10.4223			−0.647613
$260$		0			0
$261$	10.2398	+	17.7358i	0.633826	+	1.09782i
$262$		0			0
$263$	−10.6687	−	18.4788i	−0.657863	−	1.13945i	−0.981168	−	0.193157i	$-0.938127\pi$
$263$	−10.6687	−	18.4788i	−0.657863	−	1.13945i	0.323305	−	0.946295i	$-0.395206\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−27.4926			−1.68252
$268$		0			0
$269$	15.1825	+	26.2969i	0.925694	+	1.60335i	0.790441	+	0.612538i	$0.209851\pi$
$269$	15.1825	+	26.2969i	0.925694	+	1.60335i	0.135253	+	0.990811i	$0.456815\pi$
$270$		0			0
$271$	5.20262	+	9.01119i	0.316036	+	0.547391i	0.979657	−	0.200678i	$-0.0643145\pi$
$271$	5.20262	+	9.01119i	0.316036	+	0.547391i	−0.663621	+	0.748069i	$0.730981\pi$
$272$		0			0
$273$	−37.6272			−2.27730
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−13.5757			−0.815683			−0.407842	−	0.913053i	$-0.633718\pi$
$277$	−13.5757			−0.815683			−0.407842	+	0.913053i	$0.633718\pi$
$278$		0			0
$279$	−26.0284	+	45.0826i	−1.55828	+	2.69902i
$280$		0			0
$281$	2.30763	−	3.99693i	0.137661	−	0.238437i	−0.788950	−	0.614458i	$-0.789375\pi$
$281$	2.30763	−	3.99693i	0.137661	−	0.238437i	0.926611	+	0.376021i	$0.122708\pi$
$282$		0			0
$283$	−7.38676	−	12.7942i	−0.439097	−	0.760539i	0.558523	−	0.829489i	$-0.311368\pi$
$283$	−7.38676	−	12.7942i	−0.439097	−	0.760539i	−0.997620	+	0.0689504i	$0.978035\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	15.6689	+	27.1393i	0.924905	+	1.60198i
$288$		0			0
$289$	6.71409	−	11.6292i	0.394947	−	0.684068i
$290$		0			0
$291$	10.8774	−	18.8403i	0.637647	−	1.10444i
$292$		0			0
$293$	16.5565			0.967240			0.483620	−	0.875278i	$-0.339322\pi$
$293$	16.5565			0.967240			0.483620	+	0.875278i	$0.339322\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	34.6648			2.01146
$298$		0			0
$299$	13.9946	+	24.2394i	0.809330	+	1.40180i
$300$		0			0
$301$	16.3296	+	28.2837i	0.941222	+	1.63024i
$302$		0			0
$303$	−44.1364			−2.53557
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−7.07134	−	12.2479i	−0.403583	−	0.699026i	0.590573	−	0.806984i	$-0.298902\pi$
$307$	−7.07134	−	12.2479i	−0.403583	−	0.699026i	−0.994155	+	0.107959i	$0.965569\pi$
$308$		0			0
$309$	−15.5350	−	26.9074i	−0.883754	−	1.53071i
$310$		0			0
$311$	23.1773			1.31427			0.657133	−	0.753775i	$-0.271769\pi$
$311$	23.1773			1.31427			0.657133	+	0.753775i	$0.271769\pi$
$312$		0			0
$313$	−12.4209	+	21.5136i	−0.702068	+	1.21602i	0.265671	+	0.964064i	$0.414407\pi$
$313$	−12.4209	+	21.5136i	−0.702068	+	1.21602i	−0.967739	+	0.251954i	$0.918927\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−13.9737	+	24.2031i	−0.784840	+	1.35938i	0.144255	+	0.989541i	$0.453922\pi$
$317$	−13.9737	+	24.2031i	−0.784840	+	1.35938i	−0.929095	+	0.369842i	$0.879412\pi$
$318$		0			0
$319$	3.95696	−	6.85366i	0.221547	−	0.383731i
$320$		0			0
$321$	20.0955	+	34.8065i	1.12162	+	1.94271i
$322$		0			0
$323$	−4.74105	+	6.73698i	−0.263799	+	0.374856i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−12.1954	+	21.1231i	−0.674407	+	1.16811i
$328$		0			0
$329$	8.00706	−	13.8686i	0.441443	−	0.764602i
$330$		0			0
$331$	15.3670			0.844649			0.422324	−	0.906445i	$-0.361214\pi$
$331$	15.3670			0.844649			0.422324	+	0.906445i	$0.361214\pi$
$332$		0			0
$333$	−12.0656	+	20.8982i	−0.661190	+	1.14521i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	2.85108	+	4.93822i	0.155308	+	0.269002i	0.933171	−	0.359432i	$-0.117030\pi$
$337$	2.85108	+	4.93822i	0.155308	+	0.269002i	−0.777863	+	0.628434i	$0.783696\pi$
$338$		0			0
$339$	−20.3533	−	35.2529i	−1.10544	−	1.91468i
$340$		0			0
$341$	20.1164			1.08936
$342$		0			0
$343$	14.5193			0.783968
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−3.48887	−	6.04290i	−0.187292	−	0.324400i	0.757054	−	0.653352i	$-0.226638\pi$
$347$	−3.48887	−	6.04290i	−0.187292	−	0.324400i	−0.944347	+	0.328952i	$0.893304\pi$
$348$		0			0
$349$	−16.9017			−0.904729			−0.452364	−	0.891833i	$-0.649419\pi$
$349$	−16.9017			−0.904729			−0.452364	+	0.891833i	$0.649419\pi$
$350$		0			0
$351$	−24.9696	+	43.2487i	−1.33278	+	2.30844i
$352$		0			0
$353$	30.5814			1.62768			0.813842	−	0.581086i	$-0.197372\pi$
$353$	30.5814			1.62768			0.813842	+	0.581086i	$0.197372\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−9.08586	+	15.7372i	−0.480875	+	0.832900i
$358$		0			0
$359$	−7.95750	−	13.7828i	−0.419981	−	0.727428i	0.575956	−	0.817480i	$-0.304630\pi$
$359$	−7.95750	−	13.7828i	−0.419981	−	0.727428i	−0.995937	+	0.0900527i	$0.971296\pi$
$360$		0			0
$361$	−12.2816	+	14.4970i	−0.646401	+	0.762998i
$362$		0			0
$363$	5.73385	+	9.93132i	0.300949	+	0.521259i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−8.91470	+	15.4407i	−0.465343	+	0.805998i	−0.999217	−	0.0395659i	$-0.987403\pi$
$367$	−8.91470	+	15.4407i	−0.465343	+	0.805998i	0.533874	+	0.845564i	$0.320736\pi$
$368$		0			0
$369$	72.5572			3.77718
$370$		0			0
$371$	2.56115	−	4.43605i	0.132968	−	0.230308i
$372$		0			0
$373$	−10.3643			−0.536645			−0.268323	−	0.963329i	$-0.586469\pi$
$373$	−10.3643			−0.536645			−0.268323	+	0.963329i	$0.586469\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	5.70053	+	9.87361i	0.293592	+	0.508517i
$378$		0			0
$379$	−13.1604			−0.676002			−0.338001	−	0.941146i	$-0.609751\pi$
$379$	−13.1604			−0.676002			−0.338001	+	0.941146i	$0.609751\pi$
$380$		0			0
$381$	−4.66132			−0.238807
$382$		0			0
$383$	10.1227	+	17.5330i	0.517244	+	0.895894i	0.999799	+	0.0200280i	$0.00637553\pi$
$383$	10.1227	+	17.5330i	0.517244	+	0.895894i	−0.482555	+	0.875866i	$0.660291\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	75.6167			3.84381
$388$		0			0
$389$	−0.347599	+	0.602059i	−0.0176240	+	0.0305256i	−0.874703	−	0.484660i	$-0.838944\pi$
$389$	−0.347599	+	0.602059i	−0.0176240	+	0.0305256i	0.857079	+	0.515185i	$0.172277\pi$
$390$		0			0
$391$	13.5171			0.683591
$392$		0			0
$393$	−27.7609	+	48.0833i	−1.40035	+	2.42548i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−8.16274	−	14.1383i	−0.409676	−	0.709580i	0.585177	−	0.810906i	$-0.301025\pi$
$397$	−8.16274	−	14.1383i	−0.409676	−	0.709580i	−0.994853	+	0.101325i	$0.967692\pi$
$398$		0			0
$399$	−24.1203	+	34.2746i	−1.20752	+	1.71588i
$400$		0			0
$401$	4.19765	+	7.27055i	0.209621	+	0.363074i	0.951595	−	0.307354i	$-0.0994437\pi$
$401$	4.19765	+	7.27055i	0.209621	+	0.363074i	−0.741974	+	0.670428i	$0.766110\pi$
$402$		0			0
$403$	−14.4902	+	25.0977i	−0.721807	+	1.25021i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	9.32503			0.462224
$408$		0			0
$409$	−2.21536	+	3.83711i	−0.109542	+	0.189733i	−0.915585	−	0.402125i	$-0.868272\pi$
$409$	−2.21536	+	3.83711i	−0.109542	+	0.189733i	0.806043	+	0.591858i	$0.201605\pi$
$410$		0			0
$411$	−22.1270			−1.09144
$412$		0			0
$413$	−1.05645	−	1.82983i	−0.0519847	−	0.0900401i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−47.6557			−2.33371
$418$		0			0
$419$	−2.05906			−0.100592			−0.0502958	−	0.998734i	$-0.516016\pi$
$419$	−2.05906			−0.100592			−0.0502958	+	0.998734i	$0.516016\pi$
$420$		0			0
$421$	6.71640	+	11.6331i	0.327337	+	0.566965i	0.981983	−	0.188971i	$-0.0605154\pi$
$421$	6.71640	+	11.6331i	0.327337	+	0.566965i	−0.654645	+	0.755936i	$0.727182\pi$
$422$		0			0
$423$	−18.5390	−	32.1104i	−0.901396	−	1.56126i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	19.0833	−	33.0533i	0.923507	−	1.59956i
$428$		0			0
$429$	33.6657			1.62539
$430$		0			0
$431$	−19.4194	+	33.6353i	−0.935398	+	1.62016i	−0.161475	+	0.986877i	$0.551625\pi$
$431$	−19.4194	+	33.6353i	−0.935398	+	1.62016i	−0.773923	+	0.633280i	$0.781708\pi$
$432$		0			0
$433$	−1.51526	+	2.62451i	−0.0728188	+	0.126126i	−0.900136	−	0.435610i	$-0.856533\pi$
$433$	−1.51526	+	2.62451i	−0.0728188	+	0.126126i	0.827317	+	0.561736i	$0.189866\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	31.0506	+	2.79053i	1.48535	+	0.133489i
$438$		0			0
$439$	12.6233	+	21.8642i	0.602477	+	1.04352i	0.992445	+	0.122692i	$0.0391529\pi$
$439$	12.6233	+	21.8642i	0.602477	+	1.04352i	−0.389968	+	0.920829i	$0.627514\pi$
$440$		0			0
$441$	−7.79480	+	13.5010i	−0.371181	+	0.642904i
$442$		0			0
$443$	−10.7494	+	18.6185i	−0.510718	+	0.884590i	0.489205	+	0.872169i	$0.337287\pi$
$443$	−10.7494	+	18.6185i	−0.510718	+	0.884590i	−0.999923	+	0.0124209i	$0.996046\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	2.10423	−	3.64463i	0.0995265	−	0.172385i
$448$		0			0
$449$	24.7928			1.17004			0.585022	−	0.811018i	$-0.301086\pi$
$449$	24.7928			1.17004			0.585022	+	0.811018i	$0.301086\pi$
$450$		0			0
$451$	−14.0192	−	24.2819i	−0.660137	−	1.14339i
$452$		0			0
$453$	2.98224	+	5.16539i	0.140118	+	0.242691i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	3.55913			0.166489			0.0832444	−	0.996529i	$-0.473472\pi$
$457$	3.55913			0.166489			0.0832444	+	0.996529i	$0.473472\pi$
$458$		0			0
$459$	12.0589	+	20.8866i	0.562859	+	0.974901i
$460$		0			0
$461$	−4.73320	−	8.19814i	−0.220447	−	0.381826i	0.734497	−	0.678612i	$-0.237418\pi$
$461$	−4.73320	−	8.19814i	−0.220447	−	0.381826i	−0.954944	+	0.296787i	$0.904085\pi$
$462$		0			0
$463$	20.7465			0.964171			0.482085	−	0.876124i	$-0.339879\pi$
$463$	20.7465			0.964171			0.482085	+	0.876124i	$0.339879\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−1.36791			−0.0632992			−0.0316496	−	0.999499i	$-0.510076\pi$
$467$	−1.36791			−0.0632992			−0.0316496	+	0.999499i	$0.510076\pi$
$468$		0			0
$469$	1.10990	−	1.92241i	0.0512506	−	0.0887686i
$470$		0			0
$471$	−13.9641	+	24.1864i	−0.643430	+	1.11445i
$472$		0			0
$473$	−14.6103	−	25.3058i	−0.671783	−	1.16356i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−5.92991	−	10.2709i	−0.271512	−	0.470272i
$478$		0			0
$479$	−2.40085	+	4.15840i	−0.109698	+	0.190002i	−0.915648	−	0.401981i	$-0.868322\pi$
$479$	−2.40085	+	4.15840i	−0.109698	+	0.190002i	0.805950	+	0.591984i	$0.201655\pi$
$480$		0			0
$481$	−6.71698	+	11.6341i	−0.306268	+	0.530471i
$482$		0			0
$483$	68.7690			3.12910
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−15.1236			−0.685315			−0.342657	−	0.939460i	$-0.611327\pi$
$487$	−15.1236			−0.685315			−0.342657	+	0.939460i	$0.611327\pi$
$488$		0			0
$489$	−31.5781	−	54.6950i	−1.42801	−	2.47339i
$490$		0			0
$491$	−20.0731	−	34.7676i	−0.905885	−	1.56904i	−0.819724	−	0.572759i	$-0.805873\pi$
$491$	−20.0731	−	34.7676i	−0.905885	−	1.56904i	−0.0861613	−	0.996281i	$-0.527460\pi$
$492$		0			0
$493$	5.50604			0.247980
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−5.32145	−	9.21702i	−0.238700	−	0.413440i
$498$		0			0
$499$	−18.2320	−	31.5788i	−0.816178	−	1.41366i	−0.908479	−	0.417930i	$-0.862756\pi$
$499$	−18.2320	−	31.5788i	−0.816178	−	1.41366i	0.0923011	−	0.995731i	$-0.470578\pi$
$500$		0			0
$501$	−47.0857			−2.10364
$502$		0			0
$503$	6.09897	−	10.5637i	0.271939	−	0.471013i	−0.697419	−	0.716664i	$-0.745668\pi$
$503$	6.09897	−	10.5637i	0.271939	−	0.471013i	0.969358	+	0.245651i	$0.0790016\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−3.66484	+	6.34768i	−0.162761	+	0.281910i
$508$		0			0
$509$	−4.94830	+	8.57071i	−0.219330	+	0.379890i	−0.954603	−	0.297880i	$-0.903720\pi$
$509$	−4.94830	+	8.57071i	−0.219330	+	0.379890i	0.735274	+	0.677770i	$0.237054\pi$
$510$		0			0
$511$	−16.8622	−	29.2062i	−0.745940	−	1.29201i
$512$		0			0
$513$	23.3889	+	50.4686i	1.03264	+	2.22824i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−7.16403	+	12.4085i	−0.315074	+	0.545724i
$518$		0			0
$519$	17.7751	−	30.7874i	0.780240	−	1.35142i
$520$		0			0
$521$	37.7004			1.65169			0.825843	−	0.563900i	$-0.190700\pi$
$521$	37.7004			1.65169			0.825843	+	0.563900i	$0.190700\pi$
$522$		0			0
$523$	−4.49459	+	7.78487i	−0.196535	+	0.340408i	−0.947403	−	0.320044i	$-0.896302\pi$
$523$	−4.49459	+	7.78487i	−0.196535	+	0.340408i	0.750868	+	0.660453i	$0.229636\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	6.99790	+	12.1207i	0.304833	+	0.527987i
$528$		0			0
$529$	−14.0771	−	24.3822i	−0.612047	−	1.06010i
$530$		0			0
$531$	−4.89208			−0.212298
$532$		0			0
$533$	40.3930			1.74962
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−27.3469	−	47.3662i	−1.18011	−	2.04400i
$538$		0			0
$539$	6.02431			0.259485
$540$		0			0
$541$	7.49491	−	12.9816i	0.322231	−	0.558121i	−0.658717	−	0.752391i	$-0.728900\pi$
$541$	7.49491	−	12.9816i	0.322231	−	0.558121i	0.980948	+	0.194270i	$0.0622338\pi$
$542$		0			0
$543$	−56.1846			−2.41111
$544$		0			0
$545$		0			0
$546$		0			0
$547$	13.9344	−	24.1350i	0.595790	−	1.03194i	−0.397644	−	0.917540i	$-0.630172\pi$
$547$	13.9344	−	24.1350i	0.595790	−	1.03194i	0.993435	−	0.114400i	$-0.0364945\pi$
$548$		0			0
$549$	−44.1842	−	76.5293i	−1.88574	−	3.26619i
$550$		0			0
$551$	12.6481	+	1.13669i	0.538827	+	0.0484245i
$552$		0			0
$553$	−18.3189	−	31.7292i	−0.778998	−	1.34926i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−11.9869	+	20.7620i	−0.507903	+	0.879714i	0.492055	+	0.870564i	$0.336246\pi$
$557$	−11.9869	+	20.7620i	−0.507903	+	0.879714i	−0.999958	+	0.00914996i	$0.997087\pi$
$558$		0			0
$559$	42.0963			1.78048
$560$		0			0
$561$	8.12926	−	14.0803i	0.343217	−	0.594470i
$562$		0			0
$563$	−28.6346			−1.20681			−0.603403	−	0.797436i	$-0.706189\pi$
$563$	−28.6346			−1.20681			−0.603403	+	0.797436i	$0.706189\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	29.3367	+	50.8127i	1.23203	+	2.13393i
$568$		0			0
$569$	−14.5588			−0.610338			−0.305169	−	0.952298i	$-0.598713\pi$
$569$	−14.5588			−0.610338			−0.305169	+	0.952298i	$0.598713\pi$
$570$		0			0
$571$	21.5089			0.900121			0.450061	−	0.892998i	$-0.351402\pi$
$571$	21.5089			0.900121			0.450061	+	0.892998i	$0.351402\pi$
$572$		0			0
$573$	39.7991	+	68.9341i	1.66263	+	2.87976i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−42.3885			−1.76466			−0.882329	−	0.470634i	$-0.844025\pi$
$577$	−42.3885			−1.76466			−0.882329	+	0.470634i	$0.844025\pi$
$578$		0			0
$579$	−24.1203	+	41.7775i	−1.00240	+	1.73621i
$580$		0			0
$581$	−34.6662			−1.43820
$582$		0			0
$583$	−2.29150	+	3.96900i	−0.0949042	+	0.164379i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	14.2971	+	24.7634i	0.590106	+	1.02209i	0.994218	+	0.107384i	$0.0342474\pi$
$587$	14.2971	+	24.7634i	0.590106	+	1.02209i	−0.404112	+	0.914710i	$0.632419\pi$
$588$		0			0
$589$	13.5728	+	29.2875i	0.559259	+	1.20677i
$590$		0			0
$591$	−12.9192	−	22.3767i	−0.531424	−	0.920454i
$592$		0			0
$593$	3.33107	−	5.76958i	0.136791	−	0.236928i	−0.789489	−	0.613764i	$-0.789655\pi$
$593$	3.33107	−	5.76958i	0.136791	−	0.236928i	0.926280	+	0.376836i	$0.122988\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−44.0904			−1.80450
$598$		0			0
$599$	−2.78523	+	4.82416i	−0.113801	+	0.197110i	−0.917300	−	0.398197i	$-0.869636\pi$
$599$	−2.78523	+	4.82416i	−0.113801	+	0.197110i	0.803499	+	0.595307i	$0.202969\pi$
$600$		0			0
$601$	2.78840			0.113741			0.0568706	−	0.998382i	$-0.481888\pi$
$601$	2.78840			0.113741			0.0568706	+	0.998382i	$0.481888\pi$
$602$		0			0
$603$	−2.56979	−	4.45101i	−0.104650	−	0.181259i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−31.6698			−1.28544			−0.642718	−	0.766102i	$-0.722193\pi$
$607$	−31.6698			−1.28544			−0.642718	+	0.766102i	$0.722193\pi$
$608$		0			0
$609$	28.0122			1.13511
$610$		0			0
$611$	−10.3207	−	17.8761i	−0.417533	−	0.723188i
$612$		0			0
$613$	2.75765	+	4.77639i	0.111380	+	0.192916i	0.916327	−	0.400431i	$-0.131139\pi$
$613$	2.75765	+	4.77639i	0.111380	+	0.192916i	−0.804947	+	0.593347i	$0.797806\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−3.21546	+	5.56934i	−0.129450	+	0.224213i	−0.923463	−	0.383686i	$-0.874654\pi$
$617$	−3.21546	+	5.56934i	−0.129450	+	0.224213i	0.794014	+	0.607900i	$0.207988\pi$
$618$		0			0
$619$	−40.7761			−1.63893			−0.819465	−	0.573130i	$-0.805729\pi$
$619$	−40.7761			−1.63893			−0.819465	+	0.573130i	$0.805729\pi$
$620$		0			0
$621$	45.6355	−	79.0429i	1.83129	−	3.17188i
$622$		0			0
$623$	−13.1783	+	22.8255i	−0.527977	+	0.914483i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	21.5808	−	30.6660i	0.861852	−	1.22468i
$628$		0			0
$629$	3.24390	+	5.61860i	0.129343	+	0.224028i
$630$		0			0
$631$	3.83753	−	6.64680i	0.152770	−	0.264605i	−0.779475	−	0.626433i	$-0.784514\pi$
$631$	3.83753	−	6.64680i	0.152770	−	0.264605i	0.932245	+	0.361828i	$0.117847\pi$
$632$		0			0
$633$	8.84541	−	15.3207i	0.351574	−	0.608943i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−4.33941	+	7.51608i	−0.171934	+	0.297798i
$638$		0			0
$639$	−24.6418			−0.974815
$640$		0			0
$641$	8.21362	+	14.2264i	0.324419	+	0.561910i	0.981395	−	0.192002i	$-0.0614980\pi$
$641$	8.21362	+	14.2264i	0.324419	+	0.561910i	−0.656976	+	0.753912i	$0.728165\pi$
$642$		0			0
$643$	1.14488	+	1.98298i	0.0451495	+	0.0782013i	0.887717	−	0.460389i	$-0.152290\pi$
$643$	1.14488	+	1.98298i	0.0451495	+	0.0782013i	−0.842568	+	0.538591i	$0.818957\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	37.0509			1.45662			0.728311	−	0.685247i	$-0.240306\pi$
$647$	37.0509			1.45662			0.728311	+	0.685247i	$0.240306\pi$
$648$		0			0
$649$	0.945225	+	1.63718i	0.0371033	+	0.0642648i
$650$		0			0
$651$	35.6021	+	61.6646i	1.39536	+	2.41683i
$652$		0			0
$653$	11.6500			0.455900			0.227950	−	0.973673i	$-0.426798\pi$
$653$	11.6500			0.455900			0.227950	+	0.973673i	$0.426798\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−78.0832			−3.04631
$658$		0			0
$659$	−6.74906	+	11.6897i	−0.262906	+	0.455366i	−0.967013	−	0.254728i	$-0.918014\pi$
$659$	−6.74906	+	11.6897i	−0.262906	+	0.455366i	0.704107	+	0.710094i	$0.251348\pi$
$660$		0			0
$661$	−5.57990	+	9.66468i	−0.217033	+	0.375912i	−0.953900	−	0.300126i	$-0.902971\pi$
$661$	−5.57990	+	9.66468i	−0.217033	+	0.375912i	0.736867	+	0.676038i	$0.236305\pi$
$662$		0			0
$663$	11.7113	+	20.2845i	0.454829	+	0.787786i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−10.4185	−	18.0454i	−0.403406	−	0.698720i
$668$		0			0
$669$	7.71734	−	13.3668i	0.298369	−	0.516791i
$670$		0			0
$671$	−17.0741	+	29.5733i	−0.659140	+	1.14166i
$672$		0			0
$673$	−24.4257			−0.941541			−0.470770	−	0.882256i	$-0.656024\pi$
$673$	−24.4257			−0.941541			−0.470770	+	0.882256i	$0.656024\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	40.4552			1.55482			0.777409	−	0.628995i	$-0.216534\pi$
$677$	40.4552			1.55482			0.777409	+	0.628995i	$0.216534\pi$
$678$		0			0
$679$	−10.4280	−	18.0617i	−0.400188	−	0.693146i
$680$		0			0
$681$	−42.4054	−	73.4483i	−1.62498	−	2.81454i
$682$		0			0
$683$	−43.7736			−1.67495			−0.837474	−	0.546477i	$-0.815969\pi$
$683$	−43.7736			−1.67495			−0.837474	+	0.546477i	$0.815969\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−33.9508	−	58.8044i	−1.29530	−	2.24353i
$688$		0			0
$689$	−3.30121	−	5.71787i	−0.125766	−	0.217833i
$690$		0			0
$691$	−24.3966			−0.928091			−0.464045	−	0.885811i	$-0.653603\pi$
$691$	−24.3966			−0.928091			−0.464045	+	0.885811i	$0.653603\pi$
$692$		0			0
$693$	28.9870	−	50.2070i	1.10113	−	1.90721i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	9.75371	−	16.8939i	0.369448	−	0.639903i
$698$		0			0
$699$	−0.145421	+	0.251876i	−0.00550031	+	0.00952682i
$700$		0			0
$701$	−17.0204	−	29.4802i	−0.642853	−	1.11345i	−0.984793	−	0.173732i	$-0.944417\pi$
$701$	−17.0204	−	29.4802i	−0.642853	−	1.11345i	0.341940	−	0.939722i	$-0.388916\pi$
$702$		0			0
$703$	6.29174	+	13.5763i	0.237298	+	0.512042i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−21.1563	+	36.6438i	−0.795664	+	1.37813i
$708$		0			0
$709$	7.29226	−	12.6306i	0.273867	−	0.474351i	−0.695982	−	0.718059i	$-0.745031\pi$
$709$	7.29226	−	12.6306i	0.273867	−	0.474351i	0.969849	+	0.243708i	$0.0783640\pi$
$710$		0			0
$711$	−84.8285			−3.18132
$712$		0			0
$713$	26.4828	−	45.8696i	0.991789	−	1.71783i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−33.1404	−	57.4009i	−1.23765	−	2.14368i
$718$		0			0
$719$	12.8694	+	22.2904i	0.479946	+	0.831291i	0.999735	−	0.0230037i	$-0.00732294\pi$
$719$	12.8694	+	22.2904i	0.479946	+	0.831291i	−0.519789	+	0.854294i	$0.673990\pi$
$720$		0			0
$721$	−29.7860			−1.10929
$722$		0			0
$723$	−5.93921			−0.220882
$724$		0			0
$725$		0			0
$726$		0			0
$727$	7.54728	+	13.0723i	0.279913	+	0.484824i	0.971363	−	0.237601i	$-0.0763610\pi$
$727$	7.54728	+	13.0723i	0.279913	+	0.484824i	−0.691450	+	0.722425i	$0.743028\pi$
$728$		0			0
$729$	14.6065			0.540982
$730$		0			0
$731$	10.1650	−	17.6063i	0.375966	−	0.651192i
$732$		0			0
$733$	47.3268			1.74806			0.874028	−	0.485875i	$-0.161499\pi$
$733$	47.3268			1.74806			0.874028	+	0.485875i	$0.161499\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.993047	+	1.72001i	−0.0365794	+	0.0633573i
$738$		0			0
$739$	−6.80350	−	11.7840i	−0.250271	−	0.433482i	0.713330	−	0.700829i	$-0.247186\pi$
$739$	−6.80350	−	11.7840i	−0.250271	−	0.433482i	−0.963600	+	0.267347i	$0.913853\pi$
$740$		0			0
$741$	22.7147	+	49.0140i	0.834447	+	1.80057i
$742$		0			0
$743$	18.7359	+	32.4514i	0.687352	+	1.19053i	0.972692	+	0.232102i	$0.0745602\pi$
$743$	18.7359	+	32.4514i	0.687352	+	1.19053i	−0.285340	+	0.958426i	$0.592106\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−40.1319	+	69.5104i	−1.46835	+	2.54325i
$748$		0			0
$749$	38.5302			1.40786
$750$		0			0
$751$	6.17270	−	10.6914i	0.225245	−	0.390136i	−0.731148	−	0.682219i	$-0.761015\pi$
$751$	6.17270	−	10.6914i	0.225245	−	0.390136i	0.956393	+	0.292083i	$0.0943484\pi$
$752$		0			0
$753$	−56.5671			−2.06142
$754$		0			0
$755$		0			0
$756$		0			0
$757$	15.1799	+	26.2923i	0.551722	+	0.955610i	0.998151	+	0.0607908i	$0.0193623\pi$
$757$	15.1799	+	26.2923i	0.551722	+	0.955610i	−0.446429	+	0.894819i	$0.647304\pi$
$758$		0			0
$759$	−61.5286			−2.23335
$760$		0			0
$761$	7.80837			0.283053			0.141527	−	0.989934i	$-0.454799\pi$
$761$	7.80837			0.283053			0.141527	+	0.989934i	$0.454799\pi$
$762$		0			0
$763$	11.6915	+	20.2502i	0.423259	+	0.733106i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−2.72345			−0.0983379
$768$		0			0
$769$	−21.5971	+	37.4073i	−0.778811	+	1.34894i	0.153816	+	0.988099i	$0.450844\pi$
$769$	−21.5971	+	37.4073i	−0.778811	+	1.34894i	−0.932627	+	0.360841i	$0.882490\pi$
$770$		0			0
$771$	95.6338			3.44417
$772$		0			0
$773$	9.12048	−	15.7971i	0.328041	−	0.568183i	−0.654082	−	0.756423i	$-0.726945\pi$
$773$	9.12048	−	15.7971i	0.328041	−	0.568183i	0.982123	+	0.188240i	$0.0602783\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	16.5035	+	28.5849i	0.592059	+	1.02548i
$778$		0			0
$779$	25.8932	−	36.7940i	0.927720	−	1.31828i
$780$		0			0
$781$	4.76118	+	8.24661i	0.170368	+	0.295087i
$782$		0			0
$783$	18.5890	−	32.1972i	0.664318	−	1.15063i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	42.8266			1.52660			0.763302	−	0.646042i	$-0.223577\pi$
$787$	42.8266			1.52660			0.763302	+	0.646042i	$0.223577\pi$
$788$		0			0
$789$	−33.7872	+	58.5212i	−1.20286	+	2.08341i
$790$		0			0
$791$	−39.0245			−1.38755
$792$		0			0
$793$	−24.5976	−	42.6043i	−0.873486	−	1.51292i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	51.5064			1.82445			0.912225	−	0.409689i	$-0.134363\pi$
$797$	51.5064			1.82445			0.912225	+	0.409689i	$0.134363\pi$
$798$		0			0
$799$	−9.96862			−0.352664
$800$		0			0
$801$	30.5121	+	52.8485i	1.07809	+	1.86731i
$802$		0			0
$803$	15.0869	+	26.1312i	0.532404	+	0.922151i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	48.0821	−	83.2806i	1.69257	−	2.93162i
$808$		0			0
$809$	22.4328			0.788694			0.394347	−	0.918962i	$-0.370971\pi$
$809$	22.4328			0.788694			0.394347	+	0.918962i	$0.370971\pi$
$810$		0			0
$811$	−3.76975	+	6.52940i	−0.132374	+	0.229278i	−0.924591	−	0.380961i	$-0.875593\pi$
$811$	−3.76975	+	6.52940i	−0.132374	+	0.229278i	0.792217	+	0.610239i	$0.208927\pi$
$812$		0			0
$813$	16.4764	−	28.5379i	0.577852	−	1.00087i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	26.9850	−	38.3455i	0.944087	−	1.34154i
$818$		0			0
$819$	41.7597	+	72.3300i	1.45920	+	2.52741i
$820$		0			0
$821$	−11.6808	+	20.2318i	−0.407664	+	0.706095i	−0.994628	−	0.103519i	$-0.966990\pi$
$821$	−11.6808	+	20.2318i	−0.407664	+	0.706095i	0.586964	+	0.809613i	$0.300323\pi$
$822$		0			0
$823$	7.59991	−	13.1634i	0.264916	−	0.458848i	−0.702625	−	0.711560i	$-0.747989\pi$
$823$	7.59991	−	13.1634i	0.264916	−	0.458848i	0.967542	+	0.252711i	$0.0813223\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	16.6367	−	28.8156i	0.578515	−	1.00202i	−0.417135	−	0.908845i	$-0.636966\pi$
$827$	16.6367	−	28.8156i	0.578515	−	1.00202i	0.995650	−	0.0931733i	$-0.0297011\pi$
$828$		0			0
$829$	27.7210			0.962789			0.481394	−	0.876504i	$-0.340130\pi$
$829$	27.7210			0.962789			0.481394	+	0.876504i	$0.340130\pi$
$830$		0			0
$831$	21.4967	+	37.2333i	0.745711	+	1.29161i
$832$		0			0
$833$	2.09568	+	3.62982i	0.0726109	+	0.125766i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	94.5029			3.26650
$838$		0			0
$839$	8.67328	+	15.0226i	0.299435	+	0.518636i	0.976007	−	0.217740i	$-0.0698686\pi$
$839$	8.67328	+	15.0226i	0.299435	+	0.518636i	−0.676572	+	0.736377i	$0.736535\pi$
$840$		0			0
$841$	10.2561	+	17.7642i	0.353660	+	0.612558i
$842$		0			0
$843$	−14.6162			−0.503410
$844$		0			0
$845$		0			0
$846$		0			0
$847$	10.9938			0.377752
$848$		0			0
$849$	−23.3934	+	40.5186i	−0.802860	+	1.39059i
$850$		0			0
$851$	12.2762	−	21.2630i	0.420823	−	0.728886i
$852$		0			0
$853$	−1.51813	−	2.62947i	−0.0519796	−	0.0900314i	0.838865	−	0.544340i	$-0.183220\pi$
$853$	−1.51813	−	2.62947i	−0.0519796	−	0.0900314i	−0.890844	+	0.454308i	$0.849886\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−10.9217	−	18.9170i	−0.373079	−	0.646191i	0.616959	−	0.786996i	$-0.288365\pi$
$857$	−10.9217	−	18.9170i	−0.373079	−	0.646191i	−0.990037	+	0.140804i	$0.955031\pi$
$858$		0			0
$859$	6.57180	−	11.3827i	0.224227	−	0.388373i	−0.731860	−	0.681455i	$-0.761348\pi$
$859$	6.57180	−	11.3827i	0.224227	−	0.388373i	0.956087	+	0.293082i	$0.0946809\pi$
$860$		0			0
$861$	49.6224	−	85.9485i	1.69113	−	2.92912i
$862$		0			0
$863$	−19.5725			−0.666255			−0.333128	−	0.942882i	$-0.608104\pi$
$863$	−19.5725			−0.666255			−0.333128	+	0.942882i	$0.608104\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−42.5263			−1.44427
$868$		0			0
$869$	16.3902	+	28.3886i	0.555998	+	0.963017i
$870$		0			0
$871$	−1.43062	−	2.47790i	−0.0484746	−	0.0839605i
$872$		0			0
$873$	−48.2883			−1.63431
$874$		0			0
$875$		0			0
$876$		0			0
$877$	12.7783	+	22.1326i	0.431491	+	0.747365i	0.997002	−	0.0773760i	$-0.0246542\pi$
$877$	12.7783	+	22.1326i	0.431491	+	0.747365i	−0.565511	+	0.824741i	$0.691321\pi$
$878$		0			0
$879$	−26.2167	−	45.4086i	−0.884267	−	1.53159i
$880$		0			0
$881$	−7.49566			−0.252535			−0.126268	−	0.991996i	$-0.540300\pi$
$881$	−7.49566			−0.252535			−0.126268	+	0.991996i	$0.540300\pi$
$882$		0			0
$883$	12.4848	−	21.6244i	0.420148	−	0.727718i	−0.575805	−	0.817587i	$-0.695311\pi$
$883$	12.4848	−	21.6244i	0.420148	−	0.727718i	0.995954	+	0.0898687i	$0.0286448\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−0.530770	+	0.919320i	−0.0178215	+	0.0308677i	−0.874799	−	0.484487i	$-0.839006\pi$
$887$	−0.530770	+	0.919320i	−0.0178215	+	0.0308677i	0.856977	+	0.515354i	$0.172340\pi$
$888$		0			0
$889$	−2.23435	+	3.87001i	−0.0749377	+	0.129796i
$890$		0			0
$891$	−26.2480	−	45.4629i	−0.879342	−	1.52306i
$892$		0			0
$893$	−22.8992	−	2.05796i	−0.766293	−	0.0688669i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	44.3201	−	76.7647i	1.47981	−	2.56310i
$898$		0			0
$899$	10.7874	−	18.6844i	0.359781	−	0.623159i
$900$		0			0
$901$	−3.18858			−0.106227
$902$		0			0
$903$	51.7148	−	89.5727i	1.72096	−	2.98079i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−4.43661	−	7.68443i	−0.147315	−	0.255157i	0.782919	−	0.622123i	$-0.213730\pi$
$907$	−4.43661	−	7.68443i	−0.147315	−	0.255157i	−0.930234	+	0.366966i	$0.880396\pi$
$908$		0			0
$909$	48.9838	+	84.8424i	1.62469	+	2.81404i
$910$		0			0
$911$	6.13587			0.203291			0.101645	−	0.994821i	$-0.467589\pi$
$911$	6.13587			0.203291			0.101645	+	0.994821i	$0.467589\pi$
$912$		0			0
$913$	31.0164			1.02649
$914$		0			0
$915$		0			0
$916$		0			0
$917$	26.6137	+	46.0963i	0.878863	+	1.52224i
$918$		0			0
$919$	−10.0840			−0.332640			−0.166320	−	0.986072i	$-0.553188\pi$
$919$	−10.0840			−0.332640			−0.166320	+	0.986072i	$0.553188\pi$
$920$		0			0
$921$	−22.3945	+	38.7884i	−0.737924	+	1.27812i
$922$		0			0
$923$	−13.7182			−0.451541
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−34.4822	+	59.7250i	−1.13255	+	1.96163i
$928$		0			0
$929$	−0.618121	−	1.07062i	−0.0202799	−	0.0351258i	0.855707	−	0.517460i	$-0.173122\pi$
$929$	−0.618121	−	1.07062i	−0.0202799	−	0.0351258i	−0.875987	+	0.482334i	$0.839789\pi$
$930$		0			0
$931$	4.06469	+	8.77081i	0.133215	+	0.287452i
$932$		0			0
$933$	−36.7006	−	63.5673i	−1.20152	−	2.08110i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−9.35919	+	16.2106i	−0.305751	+	0.529577i	−0.977428	−	0.211267i	$-0.932241\pi$
$937$	−9.35919	+	16.2106i	−0.305751	+	0.529577i	0.671677	+	0.740844i	$0.265574\pi$
$938$		0			0
$939$	78.6722			2.56737
$940$		0			0
$941$	−7.90050	+	13.6841i	−0.257549	+	0.446088i	−0.965585	−	0.260089i	$-0.916248\pi$
$941$	−7.90050	+	13.6841i	−0.257549	+	0.446088i	0.708036	+	0.706177i	$0.249582\pi$
$942$		0			0
$943$	−73.8238			−2.40403
$944$		0			0
$945$		0			0
$946$		0			0
$947$	15.4891	+	26.8278i	0.503327	+	0.871788i	0.999993	+	0.00384589i	$0.00122419\pi$
$947$	15.4891	+	26.8278i	0.503327	+	0.871788i	−0.496666	+	0.867942i	$0.665442\pi$
$948$		0			0
$949$	−43.4693			−1.41107
$950$		0			0
$951$	88.5076			2.87006
$952$		0			0
$953$	−2.89629	−	5.01652i	−0.0938200	−	0.162501i	0.815296	−	0.579045i	$-0.196574\pi$
$953$	−2.89629	−	5.01652i	−0.0938200	−	0.162501i	−0.909116	+	0.416544i	$0.863241\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−25.0629			−0.810169
$958$		0			0
$959$	−10.6063	+	18.3707i	−0.342496	+	0.593221i
$960$		0			0
$961$	23.8412			0.769070
$962$		0			0
$963$	44.6051	−	77.2583i	1.43738	−	2.48961i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	0.560463	+	0.970750i	0.0180233	+	0.0312172i	0.874896	−	0.484310i	$-0.160929\pi$
$967$	0.560463	+	0.970750i	0.0180233	+	0.0312172i	−0.856873	+	0.515527i	$0.827596\pi$
$968$		0			0
$969$	25.9845	+	2.33523i	0.834742	+	0.0750184i
$970$		0			0
$971$	−28.2567	−	48.9420i	−0.906800	−	1.57062i	−0.818483	−	0.574531i	$-0.805184\pi$
$971$	−28.2567	−	48.9420i	−0.906800	−	1.57062i	−0.0883174	−	0.996092i	$-0.528149\pi$
$972$		0			0
$973$	−22.8432	+	39.5656i	−0.732321	+	1.26842i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	14.2112			0.454657			0.227328	−	0.973818i	$-0.427001\pi$
$977$	14.2112			0.454657			0.227328	+	0.973818i	$0.427001\pi$
$978$		0			0
$979$	11.7908	−	20.4223i	0.376836	−	0.652699i
$980$		0			0
$981$	54.1391			1.72853
$982$		0			0
$983$	8.52459	+	14.7650i	0.271892	+	0.470931i	0.969346	−	0.245698i	$-0.0790173\pi$
$983$	8.52459	+	14.7650i	0.271892	+	0.470931i	−0.697454	+	0.716629i	$0.745684\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−50.7157			−1.61430
$988$		0			0
$989$	−76.9367			−2.44644
$990$		0			0
$991$	16.4730	+	28.5321i	0.523282	+	0.906351i	0.999633	+	0.0270956i	$0.00862584\pi$
$991$	16.4730	+	28.5321i	0.523282	+	0.906351i	−0.476351	+	0.879255i	$0.658041\pi$
$992$		0			0
$993$	−24.3332	−	42.1464i	−0.772192	−	1.33748i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	13.1143	−	22.7146i	0.415333	−	0.719378i	−0.580130	−	0.814524i	$-0.696998\pi$
$997$	13.1143	−	22.7146i	0.415333	−	0.719378i	0.995463	+	0.0951458i	$0.0303317\pi$
$998$		0			0
$999$	43.8072			1.38600

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1900.2.i.e.501.1	yes	12
5.2	odd	4		1900.2.s.e.349.1		24
5.3	odd	4		1900.2.s.e.349.12		24
5.4	even	2		1900.2.i.f.501.6	yes	12
19.11	even	3	inner	1900.2.i.e.201.1	✓	12
95.49	even	6		1900.2.i.f.201.6	yes	12
95.68	odd	12		1900.2.s.e.49.1		24
95.87	odd	12		1900.2.s.e.49.12		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1900.2.i.e.201.1	✓	12	19.11	even	3	inner
1900.2.i.e.501.1	yes	12	1.1	even	1	trivial
1900.2.i.f.201.6	yes	12	95.49	even	6
1900.2.i.f.501.6	yes	12	5.4	even	2
1900.2.s.e.49.1		24	95.68	odd	12
1900.2.s.e.49.12		24	95.87	odd	12
1900.2.s.e.349.1		24	5.2	odd	4
1900.2.s.e.349.12		24	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.58347 - 2.74265i) q^{3} -3.03607 q^{7} +(-3.51475 + 6.08773i) q^{9} +O(q^{10})\)	\(q+(-1.58347 - 2.74265i) q^{3} -3.03607 q^{7} +(-3.51475 + 6.08773i) q^{9} +2.71642 q^{11} +(-1.95668 + 3.38907i) q^{13} +(0.944962 + 1.63672i) q^{17} +(1.83281 + 3.95485i) q^{19} +(4.80753 + 8.32689i) q^{21} +(3.57611 - 6.19400i) q^{23} +12.7612 q^{27} +(1.45668 - 2.52305i) q^{29} +7.40548 q^{31} +(-4.30137 - 7.45019i) q^{33} +3.43284 q^{37} +12.3934 q^{39} +(-5.16090 - 8.93895i) q^{41} +(-5.37852 - 9.31587i) q^{43} +(-2.63731 + 4.56795i) q^{47} +2.21774 q^{49} +(2.99264 - 5.18340i) q^{51} +(-0.843574 + 1.46111i) q^{53} +(7.94456 - 11.2891i) q^{57} +(0.347967 + 0.602697i) q^{59} +(-6.28553 + 10.8869i) q^{61} +(10.6710 - 18.4828i) q^{63} +(-0.365572 + 0.633189i) q^{67} -22.6506 q^{69} +(1.75274 + 3.03584i) q^{71} +(5.55396 + 9.61973i) q^{73} -8.24725 q^{77} +(6.03374 + 10.4507i) q^{79} +(-9.66273 - 16.7363i) q^{81} +11.4181 q^{83} -9.22645 q^{87} +(4.34057 - 7.51809i) q^{89} +(5.94063 - 10.2895i) q^{91} +(-11.7264 - 20.3106i) q^{93} +(3.43468 + 5.94905i) q^{97} +(-9.54754 + 16.5368i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} - 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^3 - 3 * q^9	\( 12 q - 3 q^{3} - 3 q^{9} + 2 q^{11} - 7 q^{13} + q^{17} + q^{21} + 2 q^{23} + 24 q^{27} + q^{29} + 2 q^{31} - 10 q^{33} - 20 q^{37} + 36 q^{39} - 7 q^{41} - 19 q^{43} + 14 q^{47} + 8 q^{49} + 11 q^{51} - 6 q^{53} + 28 q^{57} - 5 q^{61} + 11 q^{63} - 14 q^{67} - 14 q^{69} + 8 q^{71} + 9 q^{73} - 2 q^{77} + q^{79} + 2 q^{81} + 26 q^{83} - 30 q^{87} - 8 q^{89} + 3 q^{91} - 9 q^{93} + 11 q^{97} - 18 q^{99}+O(q^{100}) \) 12 * q - 3 * q^3 - 3 * q^9 + 2 * q^11 - 7 * q^13 + q^17 + q^21 + 2 * q^23 + 24 * q^27 + q^29 + 2 * q^31 - 10 * q^33 - 20 * q^37 + 36 * q^39 - 7 * q^41 - 19 * q^43 + 14 * q^47 + 8 * q^49 + 11 * q^51 - 6 * q^53 + 28 * q^57 - 5 * q^61 + 11 * q^63 - 14 * q^67 - 14 * q^69 + 8 * q^71 + 9 * q^73 - 2 * q^77 + q^79 + 2 * q^81 + 26 * q^83 - 30 * q^87 - 8 * q^89 + 3 * q^91 - 9 * q^93 + 11 * q^97 - 18 * q^99

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