LMFDB - Embedded newform 1900.2.i.e.201.2

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			201.2
Root			$-0.432807 + 0.749643i$ of defining polynomial
Character	$\chi$	$=$	1900.201
Dual form			1900.2.i.e.501.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.932807 + 1.61567i) q^{3} +3.93019 q^{7} +(-0.240257 - 0.416137i) q^{9} +O(q^{10})$	\(q+(-0.932807 + 1.61567i) q^{3} +3.93019 q^{7} +(-0.240257 - 0.416137i) q^{9} -2.01692 q^{11} +(-3.09783 - 5.36560i) q^{13} +(-2.28101 + 3.95082i) q^{17} +(-4.29884 + 0.721064i) q^{19} +(-3.66611 + 6.34988i) q^{21} +(-4.32267 - 7.48708i) q^{23} -4.70039 q^{27} +(2.59783 + 4.49958i) q^{29} -0.856936 q^{31} +(1.88140 - 3.25868i) q^{33} -6.03385 q^{37} +11.5587 q^{39} +(-1.37208 + 2.37652i) q^{41} +(-6.39534 + 11.0771i) q^{43} +(4.32637 + 7.49349i) q^{47} +8.44638 q^{49} +(-4.25548 - 7.37070i) q^{51} +(-3.17440 - 5.49823i) q^{53} +(2.84499 - 7.61812i) q^{57} +(-7.18458 + 12.4441i) q^{59} +(4.73872 + 8.20770i) q^{61} +(-0.944255 - 1.63550i) q^{63} +(-5.24701 - 9.08810i) q^{67} +16.1289 q^{69} +(-2.51388 + 4.35417i) q^{71} +(0.663946 - 1.14999i) q^{73} -7.92689 q^{77} +(1.38211 - 2.39389i) q^{79} +(5.10532 - 8.84268i) q^{81} -12.5448 q^{83} -9.69310 q^{87} +(-3.45771 - 5.98893i) q^{89} +(-12.1751 - 21.0878i) q^{91} +(0.799355 - 1.38452i) q^{93} +(2.02522 - 3.50778i) q^{97} +(0.484580 + 0.839317i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.932807	+	1.61567i	−0.538556	+	0.932807i	0.460426	+	0.887698i	$0.347697\pi$
$3$	−0.932807	+	1.61567i	−0.538556	+	0.932807i	−0.998982	+	0.0451086i	$0.985637\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	3.93019			1.48547			0.742736	−	0.669585i	$-0.233528\pi$
$7$	3.93019			1.48547			0.742736	+	0.669585i	$0.233528\pi$
$8$		0			0
$9$	−0.240257	−	0.416137i	−0.0800857	−	0.138712i
$10$		0			0
$11$	−2.01692			−0.608126			−0.304063	−	0.952652i	$-0.598343\pi$
$11$	−2.01692			−0.608126			−0.304063	+	0.952652i	$0.598343\pi$
$12$		0			0
$13$	−3.09783	−	5.36560i	−0.859184	−	1.48815i	−0.872708	−	0.488242i	$-0.837638\pi$
$13$	−3.09783	−	5.36560i	−0.859184	−	1.48815i	0.0135240	−	0.999909i	$-0.495695\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.28101	+	3.95082i	−0.553225	+	0.958214i	0.444814	+	0.895623i	$0.353270\pi$
$17$	−2.28101	+	3.95082i	−0.553225	+	0.958214i	−0.998039	+	0.0625914i	$0.980064\pi$
$18$		0			0
$19$	−4.29884	+	0.721064i	−0.986223	+	0.165424i
$19$	−4.29884	+	0.721064i	−0.986223	+	0.165424i
$20$		0			0
$21$	−3.66611	+	6.34988i	−0.800010	+	1.38566i
$22$		0			0
$23$	−4.32267	−	7.48708i	−0.901339	−	1.56116i	−0.825758	−	0.564025i	$-0.809252\pi$
$23$	−4.32267	−	7.48708i	−0.901339	−	1.56116i	−0.0755814	−	0.997140i	$-0.524081\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−4.70039			−0.904590
$28$		0			0
$29$	2.59783	+	4.49958i	0.482405	+	0.835551i	0.999796	−	0.0201987i	$-0.00642988\pi$
$29$	2.59783	+	4.49958i	0.482405	+	0.835551i	−0.517391	+	0.855749i	$0.673097\pi$
$30$		0			0
$31$	−0.856936			−0.153910			−0.0769551	−	0.997035i	$-0.524520\pi$
$31$	−0.856936			−0.153910			−0.0769551	+	0.997035i	$0.524520\pi$
$32$		0			0
$33$	1.88140	−	3.25868i	0.327510	−	0.567264i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−6.03385			−0.991959			−0.495979	−	0.868334i	$-0.665191\pi$
$37$	−6.03385			−0.991959			−0.495979	+	0.868334i	$0.665191\pi$
$38$		0			0
$39$	11.5587			1.85088
$40$		0			0
$41$	−1.37208	+	2.37652i	−0.214283	+	0.371149i	−0.953051	−	0.302811i	$-0.902075\pi$
$41$	−1.37208	+	2.37652i	−0.214283	+	0.371149i	0.738767	+	0.673960i	$0.235408\pi$
$42$		0			0
$43$	−6.39534	+	11.0771i	−0.975280	+	1.68923i	−0.296272	+	0.955103i	$0.595744\pi$
$43$	−6.39534	+	11.0771i	−0.975280	+	1.68923i	−0.679008	+	0.734131i	$0.737590\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.32637	+	7.49349i	0.631066	+	1.09304i	0.987334	+	0.158654i	$0.0507155\pi$
$47$	4.32637	+	7.49349i	0.631066	+	1.09304i	−0.356268	+	0.934384i	$0.615951\pi$
$48$		0			0
$49$	8.44638			1.20663
$50$		0			0
$51$	−4.25548	−	7.37070i	−0.595886	−	1.03210i
$52$		0			0
$53$	−3.17440	−	5.49823i	−0.436038	−	0.755239i	0.561342	−	0.827584i	$-0.310285\pi$
$53$	−3.17440	−	5.49823i	−0.436038	−	0.755239i	−0.997380	+	0.0723445i	$0.976952\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	2.84499	−	7.61812i	0.376828	−	1.00905i
$58$		0			0
$59$	−7.18458	+	12.4441i	−0.935353	+	1.62008i	−0.161350	+	0.986897i	$0.551585\pi$
$59$	−7.18458	+	12.4441i	−0.935353	+	1.62008i	−0.774003	+	0.633182i	$0.781748\pi$
$60$		0			0
$61$	4.73872	+	8.20770i	0.606731	+	1.05089i	0.991775	+	0.127991i	$0.0408527\pi$
$61$	4.73872	+	8.20770i	0.606731	+	1.05089i	−0.385045	+	0.922898i	$0.625814\pi$
$62$		0			0
$63$	−0.944255	−	1.63550i	−0.118965	−	0.206053i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−5.24701	−	9.08810i	−0.641025	−	1.11029i	−0.985204	−	0.171384i	$-0.945176\pi$
$67$	−5.24701	−	9.08810i	−0.641025	−	1.11029i	0.344180	−	0.938904i	$-0.388157\pi$
$68$		0			0
$69$	16.1289			1.94169
$70$		0			0
$71$	−2.51388	+	4.35417i	−0.298343	+	0.516745i	−0.975757	−	0.218857i	$-0.929767\pi$
$71$	−2.51388	+	4.35417i	−0.298343	+	0.516745i	0.677414	+	0.735602i	$0.263101\pi$
$72$		0			0
$73$	0.663946	−	1.14999i	0.0777090	−	0.134596i	−0.824552	−	0.565786i	$-0.808573\pi$
$73$	0.663946	−	1.14999i	0.0777090	−	0.134596i	0.902261	+	0.431190i	$0.141906\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−7.92689			−0.903353
$78$		0			0
$79$	1.38211	−	2.39389i	0.155500	−	0.269334i	−0.777741	−	0.628585i	$-0.783634\pi$
$79$	1.38211	−	2.39389i	0.155500	−	0.269334i	0.933241	+	0.359251i	$0.116968\pi$
$80$		0			0
$81$	5.10532	−	8.84268i	0.567258	−	0.982520i
$82$		0			0
$83$	−12.5448			−1.37697			−0.688485	−	0.725250i	$-0.741724\pi$
$83$	−12.5448			−1.37697			−0.688485	+	0.725250i	$0.741724\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−9.69310			−1.03921
$88$		0			0
$89$	−3.45771	−	5.98893i	−0.366517	−	0.634826i	0.622502	−	0.782619i	$-0.286116\pi$
$89$	−3.45771	−	5.98893i	−0.366517	−	0.634826i	−0.989018	+	0.147793i	$0.952783\pi$
$90$		0			0
$91$	−12.1751	−	21.0878i	−1.27629	−	2.21061i
$92$		0			0
$93$	0.799355	−	1.38452i	0.0828893	−	0.143568i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	2.02522	−	3.50778i	0.205630	−	0.356162i	−0.744703	−	0.667396i	$-0.767409\pi$
$97$	2.02522	−	3.50778i	0.205630	−	0.356162i	0.950333	+	0.311234i	$0.100742\pi$
$98$		0			0
$99$	0.484580	+	0.839317i	0.0487021	+	0.0843546i
$100$		0			0
$101$	−0.515787	−	0.893370i	−0.0513227	−	0.0888936i	0.839223	−	0.543788i	$-0.183010\pi$
$101$	−0.515787	−	0.893370i	−0.0513227	−	0.0888936i	−0.890545	+	0.454894i	$0.849677\pi$
$102$		0			0
$103$	2.84260			0.280090			0.140045	−	0.990145i	$-0.455275\pi$
$103$	2.84260			0.280090			0.140045	+	0.990145i	$0.455275\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	17.0087			1.64430			0.822148	−	0.569274i	$-0.192776\pi$
$107$	17.0087			1.64430			0.822148	+	0.569274i	$0.192776\pi$
$108$		0			0
$109$	5.76394	−	9.98343i	0.552085	−	0.956240i	−0.446039	−	0.895014i	$-0.647166\pi$
$109$	5.76394	−	9.98343i	0.552085	−	0.956240i	0.998124	−	0.0612260i	$-0.0195010\pi$
$110$		0			0
$111$	5.62842	−	9.74870i	0.534226	−	0.925306i
$112$		0			0
$113$	−11.0548			−1.03994			−0.519972	−	0.854183i	$-0.674058\pi$
$113$	−11.0548			−1.03994			−0.519972	+	0.854183i	$0.674058\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−1.48855	+	2.57825i	−0.137617	+	0.238359i
$118$		0			0
$119$	−8.96478	+	15.5275i	−0.821800	+	1.42340i
$120$		0			0
$121$	−6.93202			−0.630183
$122$		0			0
$123$	−2.55977	−	4.43366i	−0.230807	−	0.399770i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−8.27930	−	14.3402i	−0.734669	−	1.27248i	−0.954868	−	0.297029i	$-0.904004\pi$
$127$	−8.27930	−	14.3402i	−0.734669	−	1.27248i	0.220199	−	0.975455i	$-0.429329\pi$
$128$		0			0
$129$	−11.9312	−	20.6655i	−1.05049	−	1.81950i
$130$		0			0
$131$	−9.78173	+	16.9425i	−0.854634	+	1.48027i	0.0223499	+	0.999750i	$0.492885\pi$
$131$	−9.78173	+	16.9425i	−0.854634	+	1.48027i	−0.876984	+	0.480520i	$0.840448\pi$
$132$		0			0
$133$	−16.8953	+	2.83392i	−1.46501	+	0.245732i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.91070	+	6.77353i	0.334114	+	0.578702i	0.983314	−	0.181915i	$-0.0582297\pi$
$137$	3.91070	+	6.77353i	0.334114	+	0.578702i	−0.649200	+	0.760617i	$0.724896\pi$
$138$		0			0
$139$	0.518328	+	0.897770i	0.0439640	+	0.0761478i	0.887170	−	0.461443i	$-0.152668\pi$
$139$	0.518328	+	0.897770i	0.0439640	+	0.0761478i	−0.843206	+	0.537590i	$0.819335\pi$
$140$		0			0
$141$	−16.1427			−1.35946
$142$		0			0
$143$	6.24809	+	10.8220i	0.522492	+	0.904983i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−7.87884	+	13.6465i	−0.649836	+	1.12555i
$148$		0			0
$149$	4.09996	−	7.10134i	0.335882	−	0.581765i	−0.647772	−	0.761834i	$-0.724299\pi$
$149$	4.09996	−	7.10134i	0.335882	−	0.581765i	0.983654	+	0.180070i	$0.0576323\pi$
$150$		0			0
$151$	4.15131			0.337829			0.168914	−	0.985631i	$-0.445974\pi$
$151$	4.15131			0.337829			0.168914	+	0.985631i	$0.445974\pi$
$152$		0			0
$153$	2.19211			0.177222
$154$		0			0
$155$		0			0
$156$		0			0
$157$	7.74751	−	13.4191i	0.618319	−	1.07096i	−0.371474	−	0.928443i	$-0.621147\pi$
$157$	7.74751	−	13.4191i	0.618319	−	1.07096i	0.989793	−	0.142516i	$-0.0455192\pi$
$158$		0			0
$159$	11.8444			0.939323
$160$		0			0
$161$	−16.9889	−	29.4256i	−1.33891	−	2.31907i
$162$		0			0
$163$	0.809717			0.0634219			0.0317110	−	0.999497i	$-0.489904\pi$
$163$	0.809717			0.0634219			0.0317110	+	0.999497i	$0.489904\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	8.96336	+	15.5250i	0.693606	+	1.20136i	0.970648	+	0.240503i	$0.0773123\pi$
$167$	8.96336	+	15.5250i	0.693606	+	1.20136i	−0.277043	+	0.960858i	$0.589354\pi$
$168$		0			0
$169$	−12.6931	+	21.9852i	−0.976395	+	1.69117i
$170$		0			0
$171$	1.33289	+	1.61567i	0.101929	+	0.123553i
$172$		0			0
$173$	2.54943	−	4.41574i	0.193829	−	0.335722i	−0.752687	−	0.658379i	$-0.771243\pi$
$173$	2.54943	−	4.41574i	0.193829	−	0.335722i	0.946516	+	0.322656i	$0.104576\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−13.4037	−	23.2158i	−1.00748	−	1.74501i
$178$		0			0
$179$	9.25613			0.691835			0.345918	−	0.938265i	$-0.387568\pi$
$179$	9.25613			0.691835			0.345918	+	0.938265i	$0.387568\pi$
$180$		0			0
$181$	−3.60319	−	6.24092i	−0.267823	−	0.463884i	0.700476	−	0.713676i	$-0.252971\pi$
$181$	−3.60319	−	6.24092i	−0.267823	−	0.463884i	−0.968299	+	0.249792i	$0.919638\pi$
$182$		0			0
$183$	−17.6812			−1.30703
$184$		0			0
$185$		0			0
$186$		0			0
$187$	4.60062	−	7.96850i	0.336430	−	0.582715i
$188$		0			0
$189$	−18.4734			−1.34374
$190$		0			0
$191$	3.49391			0.252811			0.126405	−	0.991979i	$-0.459656\pi$
$191$	3.49391			0.252811			0.126405	+	0.991979i	$0.459656\pi$
$192$		0			0
$193$	5.99339	−	10.3809i	0.431414	−	0.747230i	−0.565582	−	0.824692i	$-0.691348\pi$
$193$	5.99339	−	10.3809i	0.431414	−	0.747230i	0.996995	+	0.0774620i	$0.0246817\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−8.05604			−0.573969			−0.286985	−	0.957935i	$-0.592653\pi$
$197$	−8.05604			−0.573969			−0.286985	+	0.957935i	$0.592653\pi$
$198$		0			0
$199$	−0.980163	−	1.69769i	−0.0694819	−	0.120346i	0.829191	−	0.558965i	$-0.188801\pi$
$199$	−0.980163	−	1.69769i	−0.0694819	−	0.120346i	−0.898673	+	0.438619i	$0.855468\pi$
$200$		0			0
$201$	19.5778			1.38091
$202$		0			0
$203$	10.2100	+	17.6842i	0.716599	+	1.24119i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−2.07710	+	3.59765i	−0.144369	+	0.250054i
$208$		0			0
$209$	8.67045	−	1.45433i	0.599747	−	0.100598i
$210$		0			0
$211$	−6.54247	+	11.3319i	−0.450402	+	0.780119i	−0.998411	−	0.0563531i	$-0.982053\pi$
$211$	−6.54247	+	11.3319i	−0.450402	+	0.780119i	0.548009	+	0.836473i	$0.315386\pi$
$212$		0			0
$213$	−4.68993	−	8.12320i	−0.321349	−	0.556592i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−3.36792			−0.228629
$218$		0			0
$219$	1.23867	+	2.14543i	0.0837013	+	0.144975i
$220$		0			0
$221$	28.2647			1.90129
$222$		0			0
$223$	6.47099	−	11.2081i	0.433330	−	0.750549i	−0.563828	−	0.825892i	$-0.690672\pi$
$223$	6.47099	−	11.2081i	0.433330	−	0.750549i	0.997158	+	0.0753430i	$0.0240052\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−0.456782			−0.0303177			−0.0151588	−	0.999885i	$-0.504825\pi$
$227$	−0.456782			−0.0303177			−0.0151588	+	0.999885i	$0.504825\pi$
$228$		0			0
$229$	14.8676			0.982478			0.491239	−	0.871025i	$-0.336544\pi$
$229$	14.8676			0.982478			0.491239	+	0.871025i	$0.336544\pi$
$230$		0			0
$231$	7.39426	−	12.8072i	0.486507	−	0.842654i
$232$		0			0
$233$	−7.16028	+	12.4020i	−0.469085	+	0.812480i	−0.999375	−	0.0353365i	$-0.988750\pi$
$233$	−7.16028	+	12.4020i	−0.469085	+	0.812480i	0.530290	+	0.847816i	$0.322083\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	2.57849	+	4.46608i	0.167491	+	0.290103i
$238$		0			0
$239$	12.1876			0.788350			0.394175	−	0.919035i	$-0.371030\pi$
$239$	12.1876			0.788350			0.394175	+	0.919035i	$0.371030\pi$
$240$		0			0
$241$	9.65733	+	16.7270i	0.622084	+	1.07748i	0.989097	+	0.147265i	$0.0470469\pi$
$241$	9.65733	+	16.7270i	0.622084	+	1.07748i	−0.367014	+	0.930216i	$0.619620\pi$
$242$		0			0
$243$	2.47398	+	4.28506i	0.158706	+	0.274887i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	17.1860	+	20.8322i	1.09352	+	1.32552i
$248$		0			0
$249$	11.7019	−	20.2682i	0.741576	−	1.28445i
$250$		0			0
$251$	4.43345	+	7.67896i	0.279837	+	0.484691i	0.971344	−	0.237678i	$-0.0763863\pi$
$251$	4.43345	+	7.67896i	0.279837	+	0.484691i	−0.691507	+	0.722369i	$0.743053\pi$
$252$		0			0
$253$	8.71850	+	15.1009i	0.548127	+	0.949384i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−11.4060	−	19.7558i	−0.711487	−	1.23233i	−0.964299	−	0.264817i	$-0.914689\pi$
$257$	−11.4060	−	19.7558i	−0.711487	−	1.23233i	0.252811	−	0.967516i	$-0.418645\pi$
$258$		0			0
$259$	−23.7142			−1.47353
$260$		0			0
$261$	1.24829	−	2.16211i	0.0772675	−	0.133831i
$262$		0			0
$263$	0.830801	−	1.43899i	0.0512294	−	0.0887319i	−0.839274	−	0.543709i	$-0.817019\pi$
$263$	0.830801	−	1.43899i	0.0512294	−	0.0887319i	0.890503	+	0.454977i	$0.150353\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	12.9015			0.789560
$268$		0			0
$269$	6.70271	−	11.6094i	0.408672	−	0.707840i	−0.586070	−	0.810261i	$-0.699326\pi$
$269$	6.70271	−	11.6094i	0.408672	−	0.707840i	0.994741	+	0.102421i	$0.0326588\pi$
$270$		0			0
$271$	5.84977	−	10.1321i	0.355348	−	0.615481i	−0.631829	−	0.775108i	$-0.717696\pi$
$271$	5.84977	−	10.1321i	0.355348	−	0.615481i	0.987177	+	0.159626i	$0.0510290\pi$
$272$		0			0
$273$	45.4279			2.74942
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−3.69837			−0.222214			−0.111107	−	0.993808i	$-0.535440\pi$
$277$	−3.69837			−0.222214			−0.111107	+	0.993808i	$0.535440\pi$
$278$		0			0
$279$	0.205885	+	0.356603i	0.0123260	+	0.0213493i
$280$		0			0
$281$	6.82635	+	11.8236i	0.407226	+	0.705336i	0.994578	−	0.103996i	$-0.0331628\pi$
$281$	6.82635	+	11.8236i	0.407226	+	0.705336i	−0.587352	+	0.809332i	$0.699829\pi$
$282$		0			0
$283$	−2.56646	+	4.44524i	−0.152560	+	0.264242i	−0.932168	−	0.362026i	$-0.882085\pi$
$283$	−2.56646	+	4.44524i	−0.152560	+	0.264242i	0.779608	+	0.626268i	$0.215418\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−5.39254	+	9.34015i	−0.318312	+	0.551332i
$288$		0			0
$289$	−1.90598	−	3.30126i	−0.112117	−	0.194192i
$290$		0			0
$291$	3.77828	+	6.54417i	0.221487	+	0.383626i
$292$		0			0
$293$	22.7969			1.33181			0.665906	−	0.746036i	$-0.268045\pi$
$293$	22.7969			1.33181			0.665906	+	0.746036i	$0.268045\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	9.48033			0.550104
$298$		0			0
$299$	−26.7818	+	46.3875i	−1.54883	+	2.68266i
$300$		0			0
$301$	−25.1349	+	43.5349i	−1.44875	+	2.50931i
$302$		0			0
$303$	1.92452			0.110561
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−6.38132	+	11.0528i	−0.364201	+	0.630815i	−0.988648	−	0.150253i	$-0.951991\pi$
$307$	−6.38132	+	11.0528i	−0.364201	+	0.630815i	0.624446	+	0.781068i	$0.285325\pi$
$308$		0			0
$309$	−2.65160	+	4.59270i	−0.150844	+	0.261270i
$310$		0			0
$311$	3.90832			0.221621			0.110810	−	0.993842i	$-0.464655\pi$
$311$	3.90832			0.221621			0.110810	+	0.993842i	$0.464655\pi$
$312$		0			0
$313$	−7.80242	−	13.5142i	−0.441019	−	0.763867i	0.556747	−	0.830682i	$-0.312049\pi$
$313$	−7.80242	−	13.5142i	−0.441019	−	0.763867i	−0.997765	+	0.0668157i	$0.978716\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	9.66803	+	16.7455i	0.543011	+	0.940522i	0.998729	+	0.0503981i	$0.0160490\pi$
$317$	9.66803	+	16.7455i	0.543011	+	0.940522i	−0.455719	+	0.890124i	$0.650618\pi$
$318$		0			0
$319$	−5.23963	−	9.07531i	−0.293363	−	0.508120i
$320$		0			0
$321$	−15.8659	+	27.4805i	−0.885546	+	1.53381i
$322$		0			0
$323$	6.95690	−	18.6287i	0.387092	−	1.03653i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	10.7533	+	18.6252i	0.594658	+	1.02998i
$328$		0			0
$329$	17.0034	+	29.4508i	0.937430	+	1.62368i
$330$		0			0
$331$	−15.7431			−0.865317			−0.432659	−	0.901558i	$-0.642424\pi$
$331$	−15.7431			−0.865317			−0.432659	+	0.901558i	$0.642424\pi$
$332$		0			0
$333$	1.44967	+	2.51091i	0.0794417	+	0.137597i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−3.91770	+	6.78565i	−0.213411	+	0.369638i	−0.952780	−	0.303662i	$-0.901791\pi$
$337$	−3.91770	+	6.78565i	−0.213411	+	0.369638i	0.739369	+	0.673300i	$0.235124\pi$
$338$		0			0
$339$	10.3120	−	17.8608i	0.560069	−	0.970067i
$340$		0			0
$341$	1.72837			0.0935967
$342$		0			0
$343$	5.68454			0.306936
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−16.1917	+	28.0449i	−0.869218	+	1.50553i	−0.00642067	+	0.999979i	$0.502044\pi$
$347$	−16.1917	+	28.0449i	−0.869218	+	1.50553i	−0.862797	+	0.505550i	$0.831290\pi$
$348$		0			0
$349$	−24.2988			−1.30068			−0.650342	−	0.759642i	$-0.725374\pi$
$349$	−24.2988			−1.30068			−0.650342	+	0.759642i	$0.725374\pi$
$350$		0			0
$351$	14.5610	+	25.2204i	0.777209	+	1.34617i
$352$		0			0
$353$	7.36569			0.392036			0.196018	−	0.980600i	$-0.437199\pi$
$353$	7.36569			0.392036			0.196018	+	0.980600i	$0.437199\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−16.7248	−	28.9682i	−0.885172	−	1.53316i
$358$		0			0
$359$	−11.3960	+	19.7385i	−0.601460	+	1.04176i	0.391141	+	0.920331i	$0.372081\pi$
$359$	−11.3960	+	19.7385i	−0.601460	+	1.04176i	−0.992600	+	0.121428i	$0.961253\pi$
$360$		0			0
$361$	17.9601	−	6.19949i	0.945270	−	0.326289i
$362$		0			0
$363$	6.46623	−	11.1998i	0.339389	−	0.587839i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	3.85986	+	6.68547i	0.201483	+	0.348978i	0.949006	−	0.315257i	$-0.102091\pi$
$367$	3.85986	+	6.68547i	0.201483	+	0.348978i	−0.747524	+	0.664235i	$0.768757\pi$
$368$		0			0
$369$	1.31861			0.0686440
$370$		0			0
$371$	−12.4760	−	21.6091i	−0.647721	−	1.12189i
$372$		0			0
$373$	7.12828			0.369089			0.184544	−	0.982824i	$-0.440919\pi$
$373$	7.12828			0.369089			0.184544	+	0.982824i	$0.440919\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	16.0953	−	27.8779i	0.828950	−	1.43578i
$378$		0			0
$379$	−24.6790			−1.26768			−0.633838	−	0.773466i	$-0.718522\pi$
$379$	−24.6790			−1.26768			−0.633838	+	0.773466i	$0.718522\pi$
$380$		0			0
$381$	30.8920			1.58264
$382$		0			0
$383$	−1.51399	+	2.62232i	−0.0773615	+	0.133994i	−0.902111	−	0.431505i	$-0.857983\pi$
$383$	−1.51399	+	2.62232i	−0.0773615	+	0.133994i	0.824749	+	0.565499i	$0.191316\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	6.14610			0.312424
$388$		0			0
$389$	−19.3164	−	33.4570i	−0.979382	−	1.69634i	−0.664644	−	0.747160i	$-0.731417\pi$
$389$	−19.3164	−	33.4570i	−0.979382	−	1.69634i	−0.314738	−	0.949179i	$-0.601917\pi$
$390$		0			0
$391$	39.4402			1.99457
$392$		0			0
$393$	−18.2489	−	31.6081i	−0.920537	−	1.59442i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	19.0080	−	32.9229i	0.953986	−	1.65235i	0.217315	−	0.976102i	$-0.430270\pi$
$397$	19.0080	−	32.9229i	0.953986	−	1.65235i	0.736671	−	0.676251i	$-0.236397\pi$
$398$		0			0
$399$	11.1813	−	29.9407i	0.559767	−	1.49891i
$400$		0			0
$401$	−0.315049	+	0.545681i	−0.0157328	+	0.0272500i	−0.873785	−	0.486313i	$-0.838341\pi$
$401$	−0.315049	+	0.545681i	−0.0157328	+	0.0272500i	0.858052	+	0.513563i	$0.171675\pi$
$402$		0			0
$403$	2.65464	+	4.59798i	0.132237	+	0.229042i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	12.1698			0.603235
$408$		0			0
$409$	−8.40249	−	14.5535i	−0.415476	−	0.719626i	0.580002	−	0.814615i	$-0.303052\pi$
$409$	−8.40249	−	14.5535i	−0.415476	−	0.719626i	−0.995478	+	0.0949889i	$0.969718\pi$
$410$		0			0
$411$	−14.5917			−0.719756
$412$		0			0
$413$	−28.2368	+	48.9075i	−1.38944	+	2.40658i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−1.93400			−0.0947083
$418$		0			0
$419$	15.4367			0.754131			0.377065	−	0.926187i	$-0.376933\pi$
$419$	15.4367			0.754131			0.377065	+	0.926187i	$0.376933\pi$
$420$		0			0
$421$	4.18192	−	7.24330i	0.203814	−	0.353017i	−0.745940	−	0.666013i	$-0.767999\pi$
$421$	4.18192	−	7.24330i	0.203814	−	0.353017i	0.949754	+	0.312996i	$0.101333\pi$
$422$		0			0
$423$	2.07888	−	3.60073i	0.101079	−	0.175073i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	18.6241	+	32.2578i	0.901281	+	1.56106i
$428$		0			0
$429$	−23.3131			−1.12557
$430$		0			0
$431$	−11.0127	−	19.0746i	−0.530464	−	0.918790i	−0.999368	−	0.0355410i	$-0.988685\pi$
$431$	−11.0127	−	19.0746i	−0.530464	−	0.918790i	0.468905	−	0.883249i	$-0.344649\pi$
$432$		0			0
$433$	2.46513	+	4.26973i	0.118467	+	0.205190i	0.919160	−	0.393884i	$-0.128869\pi$
$433$	2.46513	+	4.26973i	0.118467	+	0.205190i	−0.800694	+	0.599074i	$0.795536\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	23.9812	+	29.0689i	1.14717	+	1.39055i
$438$		0			0
$439$	−10.1611	+	17.5995i	−0.484962	+	0.839980i	−0.999851	−	0.0172777i	$-0.994500\pi$
$439$	−10.1611	+	17.5995i	−0.484962	+	0.839980i	0.514888	+	0.857257i	$0.327833\pi$
$440$		0			0
$441$	−2.02930	−	3.51485i	−0.0966334	−	0.167374i
$442$		0			0
$443$	18.7037	+	32.3958i	0.888640	+	1.53917i	0.841484	+	0.540282i	$0.181682\pi$
$443$	18.7037	+	32.3958i	0.888640	+	1.53917i	0.0471558	+	0.998888i	$0.484984\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	7.64894	+	13.2484i	0.361783	+	0.626626i
$448$		0			0
$449$	−19.4967			−0.920107			−0.460054	−	0.887891i	$-0.652170\pi$
$449$	−19.4967			−0.920107			−0.460054	+	0.887891i	$0.652170\pi$
$450$		0			0
$451$	2.76739	−	4.79325i	0.130311	−	0.225705i
$452$		0			0
$453$	−3.87237	+	6.70714i	−0.181940	+	0.315129i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	38.0618			1.78046			0.890228	−	0.455515i	$-0.150545\pi$
$457$	38.0618			1.78046			0.890228	+	0.455515i	$0.150545\pi$
$458$		0			0
$459$	10.7216	−	18.5704i	0.500442	−	0.866791i
$460$		0			0
$461$	3.84100	−	6.65281i	0.178893	−	0.309852i	−0.762608	−	0.646860i	$-0.776082\pi$
$461$	3.84100	−	6.65281i	0.178893	−	0.309852i	0.941502	+	0.337008i	$0.109415\pi$
$462$		0			0
$463$	−11.2113			−0.521035			−0.260518	−	0.965469i	$-0.583893\pi$
$463$	−11.2113			−0.521035			−0.260518	+	0.965469i	$0.583893\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−8.19426			−0.379185			−0.189592	−	0.981863i	$-0.560717\pi$
$467$	−8.19426			−0.379185			−0.189592	+	0.981863i	$0.560717\pi$
$468$		0			0
$469$	−20.6218	−	35.7179i	−0.952224	−	1.64930i
$470$		0			0
$471$	14.4539	+	25.0348i	0.665999	+	1.15354i
$472$		0			0
$473$	12.8989	−	22.3416i	0.593093	−	1.02727i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−1.52534	+	2.64197i	−0.0698407	+	0.120968i
$478$		0			0
$479$	−1.15581	−	2.00192i	−0.0528102	−	0.0914700i	0.838412	−	0.545037i	$-0.183485\pi$
$479$	−1.15581	−	2.00192i	−0.0528102	−	0.0914700i	−0.891222	+	0.453567i	$0.850151\pi$
$480$		0			0
$481$	18.6919	+	32.3752i	0.852275	+	1.47618i
$482$		0			0
$483$	63.3895			2.88432
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−32.3928			−1.46786			−0.733928	−	0.679227i	$-0.762315\pi$
$487$	−32.3928			−1.46786			−0.733928	+	0.679227i	$0.762315\pi$
$488$		0			0
$489$	−0.755309	+	1.30823i	−0.0341563	+	0.0591604i
$490$		0			0
$491$	16.9913	−	29.4297i	0.766805	−	1.32814i	−0.172482	−	0.985013i	$-0.555179\pi$
$491$	16.9913	−	29.4297i	0.766805	−	1.32814i	0.939287	−	0.343132i	$-0.111488\pi$
$492$		0			0
$493$	−23.7027			−1.06752
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−9.88003	+	17.1127i	−0.443180	+	0.767610i
$498$		0			0
$499$	6.86353	−	11.8880i	0.307254	−	0.532180i	−0.670507	−	0.741904i	$-0.733923\pi$
$499$	6.86353	−	11.8880i	0.307254	−	0.532180i	0.977761	+	0.209724i	$0.0672566\pi$
$500$		0			0
$501$	−33.4443			−1.49418
$502$		0			0
$503$	13.6844	+	23.7021i	0.610158	+	1.05682i	0.991213	+	0.132272i	$0.0422273\pi$
$503$	13.6844	+	23.7021i	0.610158	+	1.05682i	−0.381056	+	0.924552i	$0.624439\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−23.6805	−	41.0158i	−1.05169	−	1.82158i
$508$		0			0
$509$	17.0380	+	29.5108i	0.755198	+	1.30804i	0.945276	+	0.326272i	$0.105793\pi$
$509$	17.0380	+	29.5108i	0.755198	+	1.30804i	−0.190078	+	0.981769i	$0.560874\pi$
$510$		0			0
$511$	2.60943	−	4.51967i	0.115434	−	0.199938i
$512$		0			0
$513$	20.2062	−	3.38928i	0.892127	−	0.149640i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−8.72596	−	15.1138i	−0.383767	−	0.664704i
$518$		0			0
$519$	4.75625	+	8.23806i	0.208776	+	0.361611i
$520$		0			0
$521$	18.0207			0.789500			0.394750	−	0.918789i	$-0.370831\pi$
$521$	18.0207			0.789500			0.394750	+	0.918789i	$0.370831\pi$
$522$		0			0
$523$	7.72277	+	13.3762i	0.337693	+	0.584902i	0.983998	−	0.178177i	$-0.0570200\pi$
$523$	7.72277	+	13.3762i	0.337693	+	0.584902i	−0.646305	+	0.763079i	$0.723687\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.95468	−	3.38560i	0.0851470	−	0.147479i
$528$		0			0
$529$	−25.8709	+	44.8098i	−1.12482	+	1.94825i
$530$		0			0
$531$	6.90459			0.299633
$532$		0			0
$533$	17.0019			0.736435
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−8.63418	+	14.9548i	−0.372592	+	0.645349i
$538$		0			0
$539$	−17.0357			−0.733780
$540$		0			0
$541$	−3.67493	−	6.36516i	−0.157998	−	0.273660i	0.776149	−	0.630550i	$-0.217170\pi$
$541$	−3.67493	−	6.36516i	−0.157998	−	0.273660i	−0.934146	+	0.356890i	$0.883837\pi$
$542$		0			0
$543$	13.4443			0.576952
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−10.9646	−	18.9913i	−0.468814	−	0.812010i	0.530550	−	0.847654i	$-0.321985\pi$
$547$	−10.9646	−	18.9913i	−0.468814	−	0.812010i	−0.999365	+	0.0356431i	$0.988652\pi$
$548$		0			0
$549$	2.27702	−	3.94391i	0.0971809	−	0.168322i
$550$		0			0
$551$	−14.4122	−	17.4698i	−0.613979	−	0.744238i
$552$		0			0
$553$	5.43197	−	9.40844i	0.230991	−	0.400088i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−6.77739	−	11.7388i	−0.287167	−	0.497388i	0.685965	−	0.727634i	$-0.259380\pi$
$557$	−6.77739	−	11.7388i	−0.287167	−	0.497388i	−0.973132	+	0.230246i	$0.926047\pi$
$558$		0			0
$559$	79.2468			3.35178
$560$		0			0
$561$	8.58297	+	14.8661i	0.362373	+	0.627649i
$562$		0			0
$563$	5.18133			0.218367			0.109184	−	0.994022i	$-0.465176\pi$
$563$	5.18133			0.218367			0.109184	+	0.994022i	$0.465176\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	20.0649	−	34.7534i	0.842646	−	1.45951i
$568$		0			0
$569$	−20.5453			−0.861305			−0.430653	−	0.902518i	$-0.641717\pi$
$569$	−20.5453			−0.861305			−0.430653	+	0.902518i	$0.641717\pi$
$570$		0			0
$571$	−26.4763			−1.10800			−0.553998	−	0.832518i	$-0.686899\pi$
$571$	−26.4763			−1.10800			−0.553998	+	0.832518i	$0.686899\pi$
$572$		0			0
$573$	−3.25915	+	5.64501i	−0.136153	+	0.235824i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	1.37829			0.0573790			0.0286895	−	0.999588i	$-0.490867\pi$
$577$	1.37829			0.0573790			0.0286895	+	0.999588i	$0.490867\pi$
$578$		0			0
$579$	11.1813	+	19.3667i	0.464681	+	0.804851i
$580$		0			0
$581$	−49.3034			−2.04545
$582$		0			0
$583$	6.40253	+	11.0895i	0.265166	+	0.459280i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−3.15349	+	5.46201i	−0.130158	+	0.225441i	−0.923738	−	0.383026i	$-0.874882\pi$
$587$	−3.15349	+	5.46201i	−0.130158	+	0.225441i	0.793579	+	0.608467i	$0.208215\pi$
$588$		0			0
$589$	3.68383	−	0.617906i	0.151790	−	0.0254604i
$590$		0			0
$591$	7.51473	−	13.0159i	0.309115	−	0.535402i
$592$		0			0
$593$	16.5840	+	28.7244i	0.681025	+	1.17957i	0.974669	+	0.223654i	$0.0717986\pi$
$593$	16.5840	+	28.7244i	0.681025	+	1.17957i	−0.293644	+	0.955915i	$0.594868\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	3.65721			0.149680
$598$		0			0
$599$	−13.6681	−	23.6738i	−0.558463	−	0.967286i	−0.997625	−	0.0688782i	$-0.978058\pi$
$599$	−13.6681	−	23.6738i	−0.558463	−	0.967286i	0.439162	−	0.898408i	$-0.355275\pi$
$600$		0			0
$601$	8.61345			0.351350			0.175675	−	0.984448i	$-0.443789\pi$
$601$	8.61345			0.351350			0.175675	+	0.984448i	$0.443789\pi$
$602$		0			0
$603$	−2.52126	+	4.36696i	−0.102674	+	0.177836i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	0.0887553			0.00360246			0.00180123	−	0.999998i	$-0.499427\pi$
$607$	0.0887553			0.00360246			0.00180123	+	0.999998i	$0.499427\pi$
$608$		0			0
$609$	−38.0957			−1.54372
$610$		0			0
$611$	26.8047	−	46.4272i	1.08440	−	1.87824i
$612$		0			0
$613$	−4.15757	+	7.20112i	−0.167923	+	0.290851i	−0.937689	−	0.347475i	$-0.887039\pi$
$613$	−4.15757	+	7.20112i	−0.167923	+	0.290851i	0.769767	+	0.638325i	$0.220373\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	14.4122	+	24.9627i	0.580214	+	1.00496i	0.995454	+	0.0952483i	$0.0303645\pi$
$617$	14.4122	+	24.9627i	0.580214	+	1.00496i	−0.415239	+	0.909712i	$0.636302\pi$
$618$		0			0
$619$	37.6699			1.51408			0.757041	−	0.653368i	$-0.226644\pi$
$619$	37.6699			1.51408			0.757041	+	0.653368i	$0.226644\pi$
$620$		0			0
$621$	20.3182	+	35.1922i	0.815342	+	1.41221i
$622$		0			0
$623$	−13.5895	−	23.5376i	−0.544450	−	0.943015i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−5.73813	+	15.3652i	−0.229159	+	0.613626i
$628$		0			0
$629$	13.7632	−	23.8386i	0.548777	−	0.950509i
$630$		0			0
$631$	9.88223	+	17.1165i	0.393405	+	0.681398i	0.992896	−	0.118984i	$-0.0379636\pi$
$631$	9.88223	+	17.1165i	0.393405	+	0.681398i	−0.599491	+	0.800382i	$0.704630\pi$
$632$		0			0
$633$	−12.2057	−	21.1409i	−0.485134	−	0.840276i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−26.1655	−	45.3199i	−1.03671	−	1.79564i
$638$		0			0
$639$	2.41591			0.0955719
$640$		0			0
$641$	13.9679	−	24.1931i	0.551699	−	0.955570i	−0.446453	−	0.894807i	$-0.647313\pi$
$641$	13.9679	−	24.1931i	0.551699	−	0.955570i	0.998152	−	0.0607636i	$-0.0193536\pi$
$642$		0			0
$643$	1.39520	−	2.41656i	0.0550214	−	0.0952999i	−0.837203	−	0.546893i	$-0.815811\pi$
$643$	1.39520	−	2.41656i	0.0550214	−	0.0952999i	0.892224	+	0.451593i	$0.149144\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−26.5020			−1.04190			−0.520951	−	0.853587i	$-0.674423\pi$
$647$	−26.5020			−1.04190			−0.520951	+	0.853587i	$0.674423\pi$
$648$		0			0
$649$	14.4908	−	25.0987i	0.568812	−	0.985212i
$650$		0			0
$651$	3.14162	−	5.44144i	0.123130	−	0.213267i
$652$		0			0
$653$	−20.7333			−0.811357			−0.405679	−	0.914016i	$-0.632965\pi$
$653$	−20.7333			−0.811357			−0.405679	+	0.914016i	$0.632965\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−0.638070			−0.0248935
$658$		0			0
$659$	−17.8072	−	30.8429i	−0.693669	−	1.20147i	−0.970627	−	0.240588i	$-0.922660\pi$
$659$	−17.8072	−	30.8429i	−0.693669	−	1.20147i	0.276958	−	0.960882i	$-0.410674\pi$
$660$		0			0
$661$	−4.68728	−	8.11860i	−0.182314	−	0.315777i	0.760354	−	0.649509i	$-0.225025\pi$
$661$	−4.68728	−	8.11860i	−0.182314	−	0.315777i	−0.942668	+	0.333732i	$0.891692\pi$
$662$		0			0
$663$	−26.3655	+	45.6664i	−1.02395	+	1.77354i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	22.4591	−	38.9004i	0.869622	−	1.50623i
$668$		0			0
$669$	12.0724	+	20.9100i	0.466745	+	0.808426i
$670$		0			0
$671$	−9.55764	−	16.5543i	−0.368968	−	0.639072i
$672$		0			0
$673$	22.9430			0.884386			0.442193	−	0.896920i	$-0.354201\pi$
$673$	22.9430			0.884386			0.442193	+	0.896920i	$0.354201\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	11.3430			0.435946			0.217973	−	0.975955i	$-0.430056\pi$
$677$	11.3430			0.435946			0.217973	+	0.975955i	$0.430056\pi$
$678$		0			0
$679$	7.95950	−	13.7863i	0.305457	−	0.529068i
$680$		0			0
$681$	0.426089	−	0.738008i	0.0163278	−	0.0282805i
$682$		0			0
$683$	−10.9942			−0.420683			−0.210342	−	0.977628i	$-0.567458\pi$
$683$	−10.9942			−0.420683			−0.210342	+	0.977628i	$0.567458\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−13.8686	+	24.0211i	−0.529120	+	0.916462i
$688$		0			0
$689$	−19.6675	+	34.0652i	−0.749273	+	1.29778i
$690$		0			0
$691$	−12.4077			−0.472010			−0.236005	−	0.971752i	$-0.575838\pi$
$691$	−12.4077			−0.472010			−0.236005	+	0.971752i	$0.575838\pi$
$692$		0			0
$693$	1.90449	+	3.29868i	0.0723456	+	0.125306i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−6.25945	−	10.8417i	−0.237094	−	0.410658i
$698$		0			0
$699$	−13.3583	−	23.1373i	−0.505258	−	0.875132i
$700$		0			0
$701$	3.66794	−	6.35306i	0.138536	−	0.239952i	−0.788406	−	0.615155i	$-0.789094\pi$
$701$	3.66794	−	6.35306i	0.138536	−	0.239952i	0.926943	+	0.375203i	$0.122427\pi$
$702$		0			0
$703$	25.9386	−	4.35079i	0.978292	−	0.164093i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−2.02714	−	3.51111i	−0.0762385	−	0.132049i
$708$		0			0
$709$	−0.370109	−	0.641048i	−0.0138997	−	0.0240750i	0.858992	−	0.511989i	$-0.171091\pi$
$709$	−0.370109	−	0.641048i	−0.0138997	−	0.0240750i	−0.872892	+	0.487914i	$0.837758\pi$
$710$		0			0
$711$	−1.32825			−0.0498133
$712$		0			0
$713$	3.70425	+	6.41595i	0.138725	+	0.240279i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−11.3687	+	19.6911i	−0.424571	+	0.735378i
$718$		0			0
$719$	−14.6029	+	25.2930i	−0.544597	+	0.943269i	0.454035	+	0.890984i	$0.349984\pi$
$719$	−14.6029	+	25.2930i	−0.544597	+	0.943269i	−0.998632	+	0.0522857i	$0.983349\pi$
$720$		0			0
$721$	11.1720			0.416066
$722$		0			0
$723$	−36.0337			−1.34011
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−14.5048	+	25.1231i	−0.537953	+	0.931762i	0.461061	+	0.887369i	$0.347469\pi$
$727$	−14.5048	+	25.1231i	−0.537953	+	0.931762i	−0.999014	+	0.0443939i	$0.985864\pi$
$728$		0			0
$729$	21.4010			0.792628
$730$		0			0
$731$	−29.1756	−	50.5337i	−1.07910	−	1.86905i
$732$		0			0
$733$	−43.3389			−1.60076			−0.800379	−	0.599494i	$-0.795368\pi$
$733$	−43.3389			−1.60076			−0.800379	+	0.599494i	$0.795368\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	10.5828	+	18.3300i	0.389824	+	0.675194i
$738$		0			0
$739$	6.77074	−	11.7273i	0.249066	−	0.431395i	−0.714201	−	0.699941i	$-0.753210\pi$
$739$	6.77074	−	11.7273i	0.249066	−	0.431395i	0.963267	+	0.268546i	$0.0865431\pi$
$740$		0			0
$741$	−49.6891	+	8.33458i	−1.82538	+	0.306178i
$742$		0			0
$743$	−16.2590	+	28.1613i	−0.596483	+	1.03314i	0.396852	+	0.917882i	$0.370102\pi$
$743$	−16.2590	+	28.1613i	−0.596483	+	1.03314i	−0.993336	+	0.115257i	$0.963231\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	3.01398	+	5.22036i	0.110276	+	0.191003i
$748$		0			0
$749$	66.8475			2.44255
$750$		0			0
$751$	21.9422	+	38.0051i	0.800683	+	1.38682i	0.919167	+	0.393868i	$0.128863\pi$
$751$	21.9422	+	38.0051i	0.800683	+	1.38682i	−0.118484	+	0.992956i	$0.537803\pi$
$752$		0			0
$753$	−16.5422			−0.602831
$754$		0			0
$755$		0			0
$756$		0			0
$757$	0.347953	−	0.602673i	0.0126466	−	0.0219045i	−0.859633	−	0.510912i	$-0.829308\pi$
$757$	0.347953	−	0.602673i	0.0126466	−	0.0219045i	0.872279	+	0.489008i	$0.162641\pi$
$758$		0			0
$759$	−32.5307			−1.18079
$760$		0			0
$761$	−35.0382			−1.27013			−0.635066	−	0.772458i	$-0.719027\pi$
$761$	−35.0382			−1.27013			−0.635066	+	0.772458i	$0.719027\pi$
$762$		0			0
$763$	22.6534	−	39.2368i	0.820107	−	1.42047i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	89.0266			3.21456
$768$		0			0
$769$	18.0700	+	31.2981i	0.651620	+	1.12864i	0.982730	+	0.185046i	$0.0592436\pi$
$769$	18.0700	+	31.2981i	0.651620	+	1.12864i	−0.331110	+	0.943592i	$0.607423\pi$
$770$		0			0
$771$	42.5584			1.53270
$772$		0			0
$773$	−25.8878	−	44.8390i	−0.931120	−	1.61275i	−0.781411	−	0.624016i	$-0.785500\pi$
$773$	−25.8878	−	44.8390i	−0.931120	−	1.61275i	−0.149708	−	0.988730i	$-0.547834\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	22.1207	−	38.3142i	0.793577	−	1.37452i
$778$		0			0
$779$	4.18475	−	11.2056i	0.149934	−	0.401483i
$780$		0			0
$781$	5.07031	−	8.78203i	0.181430	−	0.314246i
$782$		0			0
$783$	−12.2108	−	21.1498i	−0.436379	−	0.755831i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−47.4316			−1.69076			−0.845378	−	0.534169i	$-0.820625\pi$
$787$	−47.4316			−1.69076			−0.845378	+	0.534169i	$0.820625\pi$
$788$		0			0
$789$	1.54995	+	2.68460i	0.0551798	+	0.0955743i
$790$		0			0
$791$	−43.4473			−1.54481
$792$		0			0
$793$	29.3595	−	50.8522i	1.04259	−	1.80581i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−6.36820			−0.225573			−0.112787	−	0.993619i	$-0.535978\pi$
$797$	−6.36820			−0.225573			−0.112787	+	0.993619i	$0.535978\pi$
$798$		0			0
$799$	−39.4739			−1.39649
$800$		0			0
$801$	−1.66148	+	2.87777i	−0.0587055	+	0.101681i
$802$		0			0
$803$	−1.33913	+	2.31944i	−0.0472568	+	0.0818512i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	12.5047	+	21.6587i	0.440185	+	0.762423i
$808$		0			0
$809$	−21.2232			−0.746167			−0.373083	−	0.927798i	$-0.621699\pi$
$809$	−21.2232			−0.746167			−0.373083	+	0.927798i	$0.621699\pi$
$810$		0			0
$811$	−4.70964	−	8.15734i	−0.165378	−	0.286443i	0.771412	−	0.636337i	$-0.219551\pi$
$811$	−4.70964	−	8.15734i	−0.165378	−	0.286443i	−0.936789	+	0.349894i	$0.886218\pi$
$812$		0			0
$813$	10.9134	+	18.9026i	0.382750	+	0.662942i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	19.5053	−	52.2300i	0.682404	−	1.82730i
$818$		0			0
$819$	−5.85029	+	10.1330i	−0.204426	+	0.354076i
$820$		0			0
$821$	−7.20303	−	12.4760i	−0.251388	−	0.435416i	0.712521	−	0.701651i	$-0.247554\pi$
$821$	−7.20303	−	12.4760i	−0.251388	−	0.435416i	−0.963908	+	0.266235i	$0.914220\pi$
$822$		0			0
$823$	−21.2351	−	36.7803i	−0.740210	−	1.28208i	−0.952399	−	0.304853i	$-0.901393\pi$
$823$	−21.2351	−	36.7803i	−0.740210	−	1.28208i	0.212189	−	0.977229i	$-0.431941\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	10.9707	+	19.0018i	0.381489	+	0.660759i	0.991275	−	0.131807i	$-0.0420780\pi$
$827$	10.9707	+	19.0018i	0.381489	+	0.660759i	−0.609786	+	0.792566i	$0.708745\pi$
$828$		0			0
$829$	15.1442			0.525979			0.262989	−	0.964799i	$-0.415292\pi$
$829$	15.1442			0.525979			0.262989	+	0.964799i	$0.415292\pi$
$830$		0			0
$831$	3.44987	−	5.97534i	0.119675	−	0.207282i
$832$		0			0
$833$	−19.2662	+	33.3701i	−0.667536	+	1.15621i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	4.02793			0.139226
$838$		0			0
$839$	−12.0477	+	20.8672i	−0.415931	+	0.720414i	−0.995526	−	0.0944909i	$-0.969878\pi$
$839$	−12.0477	+	20.8672i	−0.415931	+	0.720414i	0.579594	+	0.814905i	$0.303211\pi$
$840$		0			0
$841$	1.00253	−	1.73643i	0.0345700	−	0.0598770i
$842$		0			0
$843$	−25.4707			−0.877257
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−27.2441			−0.936119
$848$		0			0
$849$	−4.78802	−	8.29310i	−0.164324	−	0.284618i
$850$		0			0
$851$	26.0823	+	45.1759i	0.894091	+	1.54861i
$852$		0			0
$853$	−22.5648	+	39.0833i	−0.772602	+	1.33819i	0.163530	+	0.986538i	$0.447712\pi$
$853$	−22.5648	+	39.0833i	−0.772602	+	1.33819i	−0.936132	+	0.351648i	$0.885621\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−19.2369	+	33.3193i	−0.657119	+	1.13816i	0.324239	+	0.945975i	$0.394892\pi$
$857$	−19.2369	+	33.3193i	−0.657119	+	1.13816i	−0.981358	+	0.192189i	$0.938441\pi$
$858$		0			0
$859$	10.7404	+	18.6030i	0.366459	+	0.634725i	0.989009	−	0.147855i	$-0.0472368\pi$
$859$	10.7404	+	18.6030i	0.366459	+	0.634725i	−0.622550	+	0.782580i	$0.713903\pi$
$860$		0			0
$861$	−10.0604	−	17.4251i	−0.342857	−	0.593846i
$862$		0			0
$863$	−32.7793			−1.11582			−0.557910	−	0.829901i	$-0.688397\pi$
$863$	−32.7793			−1.11582			−0.557910	+	0.829901i	$0.688397\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	7.11165			0.241524
$868$		0			0
$869$	−2.78762	+	4.82830i	−0.0945635	+	0.163789i
$870$		0			0
$871$	−32.5087	+	56.3068i	−1.10152	+	1.90788i
$872$		0			0
$873$	−1.94629			−0.0658720
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−23.1075	+	40.0234i	−0.780286	+	1.35150i	0.151488	+	0.988459i	$0.451593\pi$
$877$	−23.1075	+	40.0234i	−0.780286	+	1.35150i	−0.931775	+	0.363037i	$0.881740\pi$
$878$		0			0
$879$	−21.2651	+	36.8323i	−0.717255	+	1.24232i
$880$		0			0
$881$	2.07865			0.0700314			0.0350157	−	0.999387i	$-0.488852\pi$
$881$	2.07865			0.0700314			0.0350157	+	0.999387i	$0.488852\pi$
$882$		0			0
$883$	3.68187	+	6.37719i	0.123905	+	0.214609i	0.921304	−	0.388842i	$-0.127125\pi$
$883$	3.68187	+	6.37719i	0.123905	+	0.214609i	−0.797399	+	0.603452i	$0.793792\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−5.12785	−	8.88169i	−0.172176	−	0.298218i	0.767004	−	0.641642i	$-0.221747\pi$
$887$	−5.12785	−	8.88169i	−0.172176	−	0.298218i	−0.939180	+	0.343424i	$0.888413\pi$
$888$		0			0
$889$	−32.5392	−	56.3596i	−1.09133	−	1.89024i
$890$		0			0
$891$	−10.2971	+	17.8350i	−0.344964	+	0.597496i
$892$		0			0
$893$	−24.0017	−	29.0938i	−0.803185	−	0.973586i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−49.9645	−	86.5411i	−1.66827	−	2.88952i
$898$		0			0
$899$	−2.22618	−	3.85585i	−0.0742471	−	0.128600i
$900$		0			0
$901$	28.9633			0.964908
$902$		0			0
$903$	−46.8920	−	81.2193i	−1.56047	−	2.70281i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−5.62475	+	9.74236i	−0.186767	+	0.323490i	−0.944170	−	0.329457i	$-0.893134\pi$
$907$	−5.62475	+	9.74236i	−0.186767	+	0.323490i	0.757404	+	0.652947i	$0.226468\pi$
$908$		0			0
$909$	−0.247843	+	0.429277i	−0.00822043	+	0.0142382i
$910$		0			0
$911$	21.0681			0.698017			0.349008	−	0.937120i	$-0.386518\pi$
$911$	21.0681			0.698017			0.349008	+	0.937120i	$0.386518\pi$
$912$		0			0
$913$	25.3019			0.837371
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−38.4441	+	66.5871i	−1.26953	+	2.19890i
$918$		0			0
$919$	35.6990			1.17760			0.588800	−	0.808279i	$-0.299601\pi$
$919$	35.6990			1.17760			0.588800	+	0.808279i	$0.299601\pi$
$920$		0			0
$921$	−11.9051	−	20.6202i	−0.392286	−	0.679459i
$922$		0			0
$923$	31.1503			1.02533
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−0.682955	−	1.18291i	−0.0224312	−	0.0388520i
$928$		0			0
$929$	−5.26955	+	9.12713i	−0.172888	+	0.299451i	−0.939428	−	0.342745i	$-0.888643\pi$
$929$	−5.26955	+	9.12713i	−0.172888	+	0.299451i	0.766540	+	0.642196i	$0.221977\pi$
$930$		0			0
$931$	−36.3097	+	6.09038i	−1.19000	+	0.199604i
$932$		0			0
$933$	−3.64571	+	6.31456i	−0.119355	+	0.206729i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	23.3787	+	40.4931i	0.763750	+	1.32285i	0.940905	+	0.338670i	$0.109977\pi$
$937$	23.3787	+	40.4931i	0.763750	+	1.32285i	−0.177155	+	0.984183i	$0.556690\pi$
$938$		0			0
$939$	29.1126			0.950053
$940$		0			0
$941$	22.8595	+	39.5939i	0.745199	+	1.29072i	0.950102	+	0.311940i	$0.100979\pi$
$941$	22.8595	+	39.5939i	0.745199	+	1.29072i	−0.204903	+	0.978782i	$0.565688\pi$
$942$		0			0
$943$	23.7242			0.772567
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−21.1570	+	36.6450i	−0.687511	+	1.19080i	0.285130	+	0.958489i	$0.407963\pi$
$947$	−21.1570	+	36.6450i	−0.687511	+	1.19080i	−0.972641	+	0.232314i	$0.925370\pi$
$948$		0			0
$949$	−8.22717			−0.267065
$950$		0			0
$951$	−36.0736			−1.16977
$952$		0			0
$953$	−6.84954	+	11.8637i	−0.221878	+	0.384304i	−0.955378	−	0.295385i	$-0.904552\pi$
$953$	−6.84954	+	11.8637i	−0.221878	+	0.384304i	0.733500	+	0.679689i	$0.237885\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	19.5503			0.631970
$958$		0			0
$959$	15.3698	+	26.6213i	0.496317	+	0.859645i
$960$		0			0
$961$	−30.2657			−0.976312
$962$		0			0
$963$	−4.08646	−	7.07796i	−0.131684	−	0.228084i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	28.5114	−	49.3833i	0.916866	−	1.58806i	0.112721	−	0.993627i	$-0.464043\pi$
$967$	28.5114	−	49.3833i	0.916866	−	1.58806i	0.804145	−	0.594433i	$-0.202623\pi$
$968$		0			0
$969$	23.6084	+	28.6170i	0.758411	+	0.919311i
$970$		0			0
$971$	−25.0955	+	43.4666i	−0.805352	+	1.39491i	0.110702	+	0.993854i	$0.464690\pi$
$971$	−25.0955	+	43.4666i	−0.805352	+	1.39491i	−0.916053	+	0.401057i	$0.868643\pi$
$972$		0			0
$973$	2.03713	+	3.52840i	0.0653072	+	0.113115i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	30.0311			0.960779			0.480389	−	0.877055i	$-0.340495\pi$
$977$	30.0311			0.960779			0.480389	+	0.877055i	$0.340495\pi$
$978$		0			0
$979$	6.97394	+	12.0792i	0.222888	+	0.386054i
$980$		0			0
$981$	−5.53931			−0.176856
$982$		0			0
$983$	0.0372150	−	0.0644583i	0.00118698	−	0.00205590i	−0.865431	−	0.501028i	$-0.832956\pi$
$983$	0.0372150	−	0.0644583i	0.00118698	−	0.00205590i	0.866618	+	0.498972i	$0.166289\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−63.4437			−2.01944
$988$		0			0
$989$	110.580			3.51623
$990$		0			0
$991$	−7.20973	+	12.4876i	−0.229025	+	0.396682i	−0.957519	−	0.288369i	$-0.906887\pi$
$991$	−7.20973	+	12.4876i	−0.229025	+	0.396682i	0.728495	+	0.685051i	$0.240220\pi$
$992$		0			0
$993$	14.6852	−	25.4356i	0.466022	−	0.807174i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	13.9965	+	24.2426i	0.443273	+	0.767771i	0.997930	−	0.0643078i	$-0.0204840\pi$
$997$	13.9965	+	24.2426i	0.443273	+	0.767771i	−0.554657	+	0.832079i	$0.687151\pi$
$998$		0			0
$999$	28.3614			0.897316

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1900.2.i.e.201.2	✓	12
5.2	odd	4		1900.2.s.e.49.11		24
5.3	odd	4		1900.2.s.e.49.2		24
5.4	even	2		1900.2.i.f.201.5	yes	12
19.7	even	3	inner	1900.2.i.e.501.2	yes	12
95.7	odd	12		1900.2.s.e.349.2		24
95.64	even	6		1900.2.i.f.501.5	yes	12
95.83	odd	12		1900.2.s.e.349.11		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1900.2.i.e.201.2	✓	12	1.1	even	1	trivial
1900.2.i.e.501.2	yes	12	19.7	even	3	inner
1900.2.i.f.201.5	yes	12	5.4	even	2
1900.2.i.f.501.5	yes	12	95.64	even	6
1900.2.s.e.49.2		24	5.3	odd	4
1900.2.s.e.49.11		24	5.2	odd	4
1900.2.s.e.349.2		24	95.7	odd	12
1900.2.s.e.349.11		24	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.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.932807 + 1.61567i) q^{3} +3.93019 q^{7} +(-0.240257 - 0.416137i) q^{9} +O(q^{10})\)	\(q+(-0.932807 + 1.61567i) q^{3} +3.93019 q^{7} +(-0.240257 - 0.416137i) q^{9} -2.01692 q^{11} +(-3.09783 - 5.36560i) q^{13} +(-2.28101 + 3.95082i) q^{17} +(-4.29884 + 0.721064i) q^{19} +(-3.66611 + 6.34988i) q^{21} +(-4.32267 - 7.48708i) q^{23} -4.70039 q^{27} +(2.59783 + 4.49958i) q^{29} -0.856936 q^{31} +(1.88140 - 3.25868i) q^{33} -6.03385 q^{37} +11.5587 q^{39} +(-1.37208 + 2.37652i) q^{41} +(-6.39534 + 11.0771i) q^{43} +(4.32637 + 7.49349i) q^{47} +8.44638 q^{49} +(-4.25548 - 7.37070i) q^{51} +(-3.17440 - 5.49823i) q^{53} +(2.84499 - 7.61812i) q^{57} +(-7.18458 + 12.4441i) q^{59} +(4.73872 + 8.20770i) q^{61} +(-0.944255 - 1.63550i) q^{63} +(-5.24701 - 9.08810i) q^{67} +16.1289 q^{69} +(-2.51388 + 4.35417i) q^{71} +(0.663946 - 1.14999i) q^{73} -7.92689 q^{77} +(1.38211 - 2.39389i) q^{79} +(5.10532 - 8.84268i) q^{81} -12.5448 q^{83} -9.69310 q^{87} +(-3.45771 - 5.98893i) q^{89} +(-12.1751 - 21.0878i) q^{91} +(0.799355 - 1.38452i) q^{93} +(2.02522 - 3.50778i) q^{97} +(0.484580 + 0.839317i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} - 3 q^{9}+O(q^{10}) \) 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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