LMFDB - Embedded newform 1900.3.g.d.949.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1900,3,Mod(949,1900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1900, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1900.949");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1900 = 2^{2} \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1900.g (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$51.7712502285$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			949.11
Character	$\chi$	$=$	1900.949
Dual form			1900.3.g.d.949.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.84332 q^{3} +10.5375i q^{7} -5.60216 q^{9} +O(q^{10})$	$q-1.84332 q^{3} +10.5375i q^{7} -5.60216 q^{9} +12.7272 q^{11} -23.0282 q^{13} -4.77411i q^{17} +(-1.66986 + 18.9265i) q^{19} -19.4239i q^{21} +35.7018i q^{23} +26.9165 q^{27} +13.7704i q^{29} -30.5166i q^{31} -23.4603 q^{33} -54.8524 q^{37} +42.4484 q^{39} +18.6001i q^{41} -29.0112i q^{43} +11.3148i q^{47} -62.0382 q^{49} +8.80023i q^{51} -10.7760 q^{53} +(3.07808 - 34.8876i) q^{57} -54.5728i q^{59} +17.7698 q^{61} -59.0326i q^{63} +60.2136 q^{67} -65.8100i q^{69} +39.9041i q^{71} +24.6243i q^{73} +134.112i q^{77} +6.95992i q^{79} +0.803679 q^{81} +130.188i q^{83} -25.3833i q^{87} -160.576i q^{89} -242.659i q^{91} +56.2519i q^{93} +71.2997 q^{97} -71.2998 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 104 q^{9}+O(q^{10}) $ 28 * q + 104 * q^9	$ 28 q + 104 q^{9} + 8 q^{11} + 58 q^{19} + 112 q^{39} - 276 q^{49} - 100 q^{61} + 132 q^{81} - 184 q^{99}+O(q^{100}) $ 28 * q + 104 * q^9 + 8 * q^11 + 58 * q^19 + 112 * q^39 - 276 * q^49 - 100 * q^61 + 132 * q^81 - 184 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$	$951$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.84332			−0.614441			−0.307220	−	0.951638i	$-0.599399\pi$
$3$	−1.84332			−0.614441			−0.307220	+	0.951638i	$0.599399\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$			10.5375i			1.50535i	0.658391	+	0.752676i	$0.271237\pi$
$7$			10.5375i			1.50535i	−0.658391	+	0.752676i	$0.728763\pi$
$8$		0			0
$9$	−5.60216			−0.622462
$10$		0			0
$11$	12.7272			1.15702			0.578509	−	0.815676i	$-0.303635\pi$
$11$	12.7272			1.15702			0.578509	+	0.815676i	$0.303635\pi$
$12$		0			0
$13$	−23.0282			−1.77140			−0.885700	−	0.464258i	$-0.846321\pi$
$13$	−23.0282			−1.77140			−0.885700	+	0.464258i	$0.846321\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	4.77411i		−	0.280830i	−0.990093	−	0.140415i	$-0.955156\pi$
$17$		−	4.77411i		−	0.280830i	0.990093	−	0.140415i	$-0.0448437\pi$
$18$		0			0
$19$	−1.66986	+	18.9265i	−0.0878871	+	0.996130i
$19$	−1.66986	+	18.9265i	−0.0878871	+	0.996130i
$20$		0			0
$21$		−	19.4239i		−	0.924950i
$22$		0			0
$23$			35.7018i			1.55225i	0.630576	+	0.776127i	$0.282819\pi$
$23$			35.7018i			1.55225i	−0.630576	+	0.776127i	$0.717181\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	26.9165			0.996907
$28$		0			0
$29$			13.7704i			0.474842i	0.971407	+	0.237421i	$0.0763020\pi$
$29$			13.7704i			0.474842i	−0.971407	+	0.237421i	$0.923698\pi$
$30$		0			0
$31$		−	30.5166i		−	0.984405i	−0.870481	−	0.492203i	$-0.836192\pi$
$31$		−	30.5166i		−	0.984405i	0.870481	−	0.492203i	$-0.163808\pi$
$32$		0			0
$33$	−23.4603			−0.710919
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−54.8524			−1.48250			−0.741249	−	0.671230i	$-0.765766\pi$
$37$	−54.8524			−1.48250			−0.741249	+	0.671230i	$0.765766\pi$
$38$		0			0
$39$	42.4484			1.08842
$40$		0			0
$41$			18.6001i			0.453660i	0.973934	+	0.226830i	$0.0728362\pi$
$41$			18.6001i			0.453660i	−0.973934	+	0.226830i	$0.927164\pi$
$42$		0			0
$43$		−	29.0112i		−	0.674679i	−0.941383	−	0.337340i	$-0.890473\pi$
$43$		−	29.0112i		−	0.674679i	0.941383	−	0.337340i	$-0.109527\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			11.3148i			0.240740i	0.992729	+	0.120370i	$0.0384080\pi$
$47$			11.3148i			0.240740i	−0.992729	+	0.120370i	$0.961592\pi$
$48$		0			0
$49$	−62.0382			−1.26609
$50$		0			0
$51$			8.80023i			0.172553i
$52$		0			0
$53$	−10.7760			−0.203321			−0.101660	−	0.994819i	$-0.532415\pi$
$53$	−10.7760			−0.203321			−0.101660	+	0.994819i	$0.532415\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	3.07808	−	34.8876i	0.0540014	−	0.612063i
$58$		0			0
$59$		−	54.5728i		−	0.924963i	−0.886629	−	0.462482i	$-0.846959\pi$
$59$		−	54.5728i		−	0.924963i	0.886629	−	0.462482i	$-0.153041\pi$
$60$		0			0
$61$	17.7698			0.291308			0.145654	−	0.989336i	$-0.453471\pi$
$61$	17.7698			0.291308			0.145654	+	0.989336i	$0.453471\pi$
$62$		0			0
$63$		−	59.0326i		−	0.937025i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	60.2136			0.898710			0.449355	−	0.893353i	$-0.351654\pi$
$67$	60.2136			0.898710			0.449355	+	0.893353i	$0.351654\pi$
$68$		0			0
$69$		−	65.8100i		−	0.953768i
$70$		0			0
$71$			39.9041i			0.562030i	0.959703	+	0.281015i	$0.0906710\pi$
$71$			39.9041i			0.562030i	−0.959703	+	0.281015i	$0.909329\pi$
$72$		0			0
$73$			24.6243i			0.337319i	0.985674	+	0.168660i	$0.0539439\pi$
$73$			24.6243i			0.337319i	−0.985674	+	0.168660i	$0.946056\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$			134.112i			1.74172i
$78$		0			0
$79$			6.95992i			0.0881003i	0.999029	+	0.0440502i	$0.0140261\pi$
$79$			6.95992i			0.0881003i	−0.999029	+	0.0440502i	$0.985974\pi$
$80$		0			0
$81$	0.803679			0.00992196
$82$		0			0
$83$			130.188i			1.56853i	0.620429	+	0.784263i	$0.286959\pi$
$83$			130.188i			1.56853i	−0.620429	+	0.784263i	$0.713041\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		−	25.3833i		−	0.291762i
$88$		0			0
$89$		−	160.576i		−	1.80423i	−0.431498	−	0.902114i	$-0.642015\pi$
$89$		−	160.576i		−	1.80423i	0.431498	−	0.902114i	$-0.357985\pi$
$90$		0			0
$91$		−	242.659i		−	2.66658i
$92$		0			0
$93$			56.2519i			0.604859i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	71.2997			0.735049			0.367524	−	0.930014i	$-0.380205\pi$
$97$	71.2997			0.735049			0.367524	+	0.930014i	$0.380205\pi$
$98$		0			0
$99$	−71.2998			−0.720200
$100$		0			0
$101$	107.366			1.06303			0.531514	−	0.847049i	$-0.321623\pi$
$101$	107.366			1.06303			0.531514	+	0.847049i	$0.321623\pi$
$102$		0			0
$103$	16.6106			0.161268			0.0806341	−	0.996744i	$-0.474305\pi$
$103$	16.6106			0.161268			0.0806341	+	0.996744i	$0.474305\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	133.725			1.24977			0.624884	−	0.780718i	$-0.285146\pi$
$107$	133.725			1.24977			0.624884	+	0.780718i	$0.285146\pi$
$108$		0			0
$109$		−	176.340i		−	1.61780i	−0.587947	−	0.808899i	$-0.700064\pi$
$109$		−	176.340i		−	1.61780i	0.587947	−	0.808899i	$-0.299936\pi$
$110$		0			0
$111$	101.111			0.910908
$112$		0			0
$113$	−224.945			−1.99066			−0.995330	−	0.0965339i	$-0.969224\pi$
$113$	−224.945			−1.99066			−0.995330	+	0.0965339i	$0.969224\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	129.008			1.10263
$118$		0			0
$119$	50.3070			0.422748
$120$		0			0
$121$	40.9815			0.338690
$122$		0			0
$123$		−	34.2859i		−	0.278747i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−125.867			−0.991076			−0.495538	−	0.868586i	$-0.665029\pi$
$127$	−125.867			−0.991076			−0.495538	+	0.868586i	$0.665029\pi$
$128$		0			0
$129$			53.4770i			0.414551i
$130$		0			0
$131$	−169.986			−1.29760			−0.648800	−	0.760959i	$-0.724729\pi$
$131$	−169.986			−1.29760			−0.648800	+	0.760959i	$0.724729\pi$
$132$		0			0
$133$	−199.437	−	17.5960i	−1.49953	−	0.132301i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	169.636i		−	1.23822i	−0.785305	−	0.619109i	$-0.787494\pi$
$137$		−	169.636i		−	1.23822i	0.785305	−	0.619109i	$-0.212506\pi$
$138$		0			0
$139$	−250.882			−1.80491			−0.902455	−	0.430784i	$-0.858237\pi$
$139$	−250.882			−1.80491			−0.902455	+	0.430784i	$0.858237\pi$
$140$		0			0
$141$		−	20.8568i		−	0.147920i
$142$		0			0
$143$	−293.084			−2.04954
$144$		0			0
$145$		0			0
$146$		0			0
$147$	114.356			0.777935
$148$		0			0
$149$	156.146			1.04796			0.523979	−	0.851731i	$-0.324447\pi$
$149$	156.146			1.04796			0.523979	+	0.851731i	$0.324447\pi$
$150$		0			0
$151$		−	86.4696i		−	0.572646i	−0.958133	−	0.286323i	$-0.907567\pi$
$151$		−	86.4696i		−	0.572646i	0.958133	−	0.286323i	$-0.0924331\pi$
$152$		0			0
$153$			26.7453i			0.174806i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		−	59.9932i		−	0.382122i	−0.981578	−	0.191061i	$-0.938807\pi$
$157$		−	59.9932i		−	0.382122i	0.981578	−	0.191061i	$-0.0611929\pi$
$158$		0			0
$159$	19.8636			0.124929
$160$		0			0
$161$	−376.207			−2.33669
$162$		0			0
$163$		−	206.566i		−	1.26727i	−0.773630	−	0.633637i	$-0.781561\pi$
$163$		−	206.566i		−	1.26727i	0.773630	−	0.633637i	$-0.218439\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−175.728			−1.05227			−0.526133	−	0.850403i	$-0.676358\pi$
$167$	−175.728			−1.05227			−0.526133	+	0.850403i	$0.676358\pi$
$168$		0			0
$169$	361.298			2.13786
$170$		0			0
$171$	9.35480	−	106.029i	0.0547064	−	0.620054i
$172$		0			0
$173$	−36.0672			−0.208481			−0.104241	−	0.994552i	$-0.533241\pi$
$173$	−36.0672			−0.208481			−0.104241	+	0.994552i	$0.533241\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$			100.595i			0.568335i
$178$		0			0
$179$		−	219.282i		−	1.22504i	−0.790456	−	0.612518i	$-0.790157\pi$
$179$		−	219.282i		−	1.22504i	0.790456	−	0.612518i	$-0.209843\pi$
$180$		0			0
$181$		−	40.5089i		−	0.223806i	−0.993719	−	0.111903i	$-0.964305\pi$
$181$		−	40.5089i		−	0.223806i	0.993719	−	0.111903i	$-0.0356946\pi$
$182$		0			0
$183$	−32.7555			−0.178992
$184$		0			0
$185$		0			0
$186$		0			0
$187$		−	60.7611i		−	0.324925i
$188$		0			0
$189$			283.632i			1.50070i
$190$		0			0
$191$	−83.0565			−0.434851			−0.217425	−	0.976077i	$-0.569766\pi$
$191$	−83.0565			−0.434851			−0.217425	+	0.976077i	$0.569766\pi$
$192$		0			0
$193$	−187.911			−0.973630			−0.486815	−	0.873505i	$-0.661841\pi$
$193$	−187.911			−0.973630			−0.486815	+	0.873505i	$0.661841\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			170.319i			0.864562i	0.901739	+	0.432281i	$0.142291\pi$
$197$			170.319i			0.864562i	−0.901739	+	0.432281i	$0.857709\pi$
$198$		0			0
$199$	−121.271			−0.609400			−0.304700	−	0.952448i	$-0.598556\pi$
$199$	−121.271			−0.609400			−0.304700	+	0.952448i	$0.598556\pi$
$200$		0			0
$201$	−110.993			−0.552204
$202$		0			0
$203$	−145.105			−0.714804
$204$		0			0
$205$		0			0
$206$		0			0
$207$		−	200.008i		−	0.966220i
$208$		0			0
$209$	−21.2526	+	240.881i	−0.101687	+	1.15254i
$210$		0			0
$211$		−	182.151i		−	0.863276i	−0.902047	−	0.431638i	$-0.857936\pi$
$211$		−	182.151i		−	0.863276i	0.902047	−	0.431638i	$-0.142064\pi$
$212$		0			0
$213$		−	73.5561i		−	0.345334i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	321.567			1.48188
$218$		0			0
$219$		−	45.3906i		−	0.207263i
$220$		0			0
$221$			109.939i			0.497462i
$222$		0			0
$223$	215.134			0.964727			0.482363	−	0.875971i	$-0.339778\pi$
$223$	215.134			0.964727			0.482363	+	0.875971i	$0.339778\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−265.837			−1.17109			−0.585545	−	0.810640i	$-0.699119\pi$
$227$	−265.837			−1.17109			−0.585545	+	0.810640i	$0.699119\pi$
$228$		0			0
$229$	−115.365			−0.503777			−0.251889	−	0.967756i	$-0.581052\pi$
$229$	−115.365			−0.503777			−0.251889	+	0.967756i	$0.581052\pi$
$230$		0			0
$231$		−	247.212i		−	1.07018i
$232$		0			0
$233$		−	189.784i		−	0.814524i	−0.913311	−	0.407262i	$-0.866484\pi$
$233$		−	189.784i		−	0.814524i	0.913311	−	0.407262i	$-0.133516\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		−	12.8294i		−	0.0541324i
$238$		0			0
$239$	−99.3829			−0.415828			−0.207914	−	0.978147i	$-0.566667\pi$
$239$	−99.3829			−0.415828			−0.207914	+	0.978147i	$0.566667\pi$
$240$		0			0
$241$		−	130.340i		−	0.540829i	−0.962744	−	0.270414i	$-0.912839\pi$
$241$		−	130.340i		−	0.540829i	0.962744	−	0.270414i	$-0.0871607\pi$
$242$		0			0
$243$	−243.730			−1.00300
$244$		0			0
$245$		0			0
$246$		0			0
$247$	38.4538	−	435.843i	0.155683	−	1.76455i
$248$		0			0
$249$		−	239.978i		−	0.963766i
$250$		0			0
$251$	501.184			1.99675			0.998374	−	0.0569953i	$-0.0181520\pi$
$251$	501.184			1.99675			0.998374	+	0.0569953i	$0.0181520\pi$
$252$		0			0
$253$			454.384i			1.79599i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−162.791			−0.633428			−0.316714	−	0.948521i	$-0.602580\pi$
$257$	−162.791			−0.633428			−0.316714	+	0.948521i	$0.602580\pi$
$258$		0			0
$259$		−	578.006i		−	2.23168i
$260$		0			0
$261$		−	77.1440i		−	0.295571i
$262$		0			0
$263$		−	50.4816i		−	0.191945i	−0.995384	−	0.0959727i	$-0.969404\pi$
$263$		−	50.4816i		−	0.191945i	0.995384	−	0.0959727i	$-0.0305961\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$			295.994i			1.10859i
$268$		0			0
$269$			28.7859i			0.107011i	0.998568	+	0.0535053i	$0.0170394\pi$
$269$			28.7859i			0.107011i	−0.998568	+	0.0535053i	$0.982961\pi$
$270$		0			0
$271$	−400.882			−1.47927			−0.739634	−	0.673009i	$-0.765001\pi$
$271$	−400.882			−1.47927			−0.739634	+	0.673009i	$0.765001\pi$
$272$		0			0
$273$			447.299i			1.63846i
$274$		0			0
$275$		0			0
$276$		0			0
$277$			213.844i			0.772001i	0.922499	+	0.386000i	$0.126144\pi$
$277$			213.844i			0.772001i	−0.922499	+	0.386000i	$0.873856\pi$
$278$		0			0
$279$			170.959i			0.612755i
$280$		0			0
$281$			229.607i			0.817108i	0.912734	+	0.408554i	$0.133967\pi$
$281$			229.607i			0.817108i	−0.912734	+	0.408554i	$0.866033\pi$
$282$		0			0
$283$		−	201.356i		−	0.711506i	−0.934580	−	0.355753i	$-0.884224\pi$
$283$		−	201.356i		−	0.711506i	0.934580	−	0.355753i	$-0.115776\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−195.998			−0.682919
$288$		0			0
$289$	266.208			0.921134
$290$		0			0
$291$	−131.428			−0.451644
$292$		0			0
$293$	−285.899			−0.975765			−0.487883	−	0.872909i	$-0.662231\pi$
$293$	−285.899			−0.975765			−0.487883	+	0.872909i	$0.662231\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	342.572			1.15344
$298$		0			0
$299$		−	822.149i		−	2.74966i
$300$		0			0
$301$	305.705			1.01563
$302$		0			0
$303$	−197.910			−0.653168
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−38.7426			−0.126197			−0.0630986	−	0.998007i	$-0.520098\pi$
$307$	−38.7426			−0.126197			−0.0630986	+	0.998007i	$0.520098\pi$
$308$		0			0
$309$	−30.6187			−0.0990898
$310$		0			0
$311$	607.655			1.95387			0.976937	−	0.213526i	$-0.0684949\pi$
$311$	607.655			1.95387			0.976937	+	0.213526i	$0.0684949\pi$
$312$		0			0
$313$		−	293.775i		−	0.938577i	−0.883045	−	0.469289i	$-0.844510\pi$
$313$		−	293.775i		−	0.938577i	0.883045	−	0.469289i	$-0.155490\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	558.422			1.76158			0.880792	−	0.473503i	$-0.157011\pi$
$317$	558.422			1.76158			0.880792	+	0.473503i	$0.157011\pi$
$318$		0			0
$319$			175.259i			0.549400i
$320$		0			0
$321$	−246.498			−0.767908
$322$		0			0
$323$	90.3571	+	7.97208i	0.279743	+	0.0246814i
$324$		0			0
$325$		0			0
$326$		0			0
$327$			325.052i			0.994041i
$328$		0			0
$329$	−119.229			−0.362398
$330$		0			0
$331$			366.890i			1.10843i	0.832374	+	0.554214i	$0.186981\pi$
$331$			366.890i			1.10843i	−0.832374	+	0.554214i	$0.813019\pi$
$332$		0			0
$333$	307.292			0.922800
$334$		0			0
$335$		0			0
$336$		0			0
$337$	466.486			1.38423			0.692115	−	0.721787i	$-0.256679\pi$
$337$	466.486			1.38423			0.692115	+	0.721787i	$0.256679\pi$
$338$		0			0
$339$	414.645			1.22314
$340$		0			0
$341$		−	388.390i		−	1.13897i
$342$		0			0
$343$		−	137.389i		−	0.400552i
$344$		0			0
$345$		0			0
$346$		0			0
$347$		−	490.615i		−	1.41388i	−0.707275	−	0.706938i	$-0.750076\pi$
$347$		−	490.615i		−	1.41388i	0.707275	−	0.706938i	$-0.249924\pi$
$348$		0			0
$349$	−503.588			−1.44295			−0.721473	−	0.692443i	$-0.756535\pi$
$349$	−503.588			−1.44295			−0.721473	+	0.692443i	$0.756535\pi$
$350$		0			0
$351$	−619.838			−1.76592
$352$		0			0
$353$		−	353.912i		−	1.00258i	−0.865278	−	0.501292i	$-0.832858\pi$
$353$		−	353.912i		−	1.00258i	0.865278	−	0.501292i	$-0.167142\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−92.7321			−0.259754
$358$		0			0
$359$	−226.398			−0.630634			−0.315317	−	0.948986i	$-0.602111\pi$
$359$	−226.398			−0.630634			−0.315317	+	0.948986i	$0.602111\pi$
$360$		0			0
$361$	−355.423	−	63.2090i	−0.984552	−	0.175094i
$362$		0			0
$363$	−75.5422			−0.208105
$364$		0			0
$365$		0			0
$366$		0			0
$367$			427.998i			1.16621i	0.812398	+	0.583104i	$0.198162\pi$
$367$			427.998i			1.16621i	−0.812398	+	0.583104i	$0.801838\pi$
$368$		0			0
$369$		−	104.201i		−	0.282387i
$370$		0			0
$371$		−	113.552i		−	0.306069i
$372$		0			0
$373$	275.474			0.738537			0.369268	−	0.929323i	$-0.379608\pi$
$373$	275.474			0.738537			0.369268	+	0.929323i	$0.379608\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	317.108i		−	0.841134i
$378$		0			0
$379$			250.621i			0.661268i	0.943759	+	0.330634i	$0.107263\pi$
$379$			250.621i			0.661268i	−0.943759	+	0.330634i	$0.892737\pi$
$380$		0			0
$381$	232.013			0.608957
$382$		0			0
$383$	148.912			0.388805			0.194403	−	0.980922i	$-0.437723\pi$
$383$	148.912			0.388805			0.194403	+	0.980922i	$0.437723\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$			162.526i			0.419963i
$388$		0			0
$389$	−57.2486			−0.147169			−0.0735843	−	0.997289i	$-0.523444\pi$
$389$	−57.2486			−0.147169			−0.0735843	+	0.997289i	$0.523444\pi$
$390$		0			0
$391$	170.445			0.435920
$392$		0			0
$393$	313.338			0.797298
$394$		0			0
$395$		0			0
$396$		0			0
$397$		−	597.128i		−	1.50410i	−0.659106	−	0.752050i	$-0.729065\pi$
$397$		−	597.128i		−	1.50410i	0.659106	−	0.752050i	$-0.270935\pi$
$398$		0			0
$399$	367.627	+	32.4352i	0.921371	+	0.0812912i
$400$		0			0
$401$			422.141i			1.05272i	0.850262	+	0.526360i	$0.176444\pi$
$401$			422.141i			1.05272i	−0.850262	+	0.526360i	$0.823556\pi$
$402$		0			0
$403$			702.741i			1.74378i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−698.118			−1.71528
$408$		0			0
$409$			244.086i			0.596786i	0.954443	+	0.298393i	$0.0964506\pi$
$409$			244.086i			0.596786i	−0.954443	+	0.298393i	$0.903549\pi$
$410$		0			0
$411$			312.693i			0.760811i
$412$		0			0
$413$	575.059			1.39240
$414$		0			0
$415$		0			0
$416$		0			0
$417$	462.457			1.10901
$418$		0			0
$419$	−499.432			−1.19196			−0.595980	−	0.802999i	$-0.703236\pi$
$419$	−499.432			−1.19196			−0.595980	+	0.802999i	$0.703236\pi$
$420$		0			0
$421$			521.240i			1.23810i	0.785351	+	0.619050i	$0.212482\pi$
$421$			521.240i			1.23810i	−0.785351	+	0.619050i	$0.787518\pi$
$422$		0			0
$423$		−	63.3872i		−	0.149851i
$424$		0			0
$425$		0			0
$426$		0			0
$427$			187.249i			0.438522i
$428$		0			0
$429$	540.249			1.25932
$430$		0			0
$431$		−	252.375i		−	0.585557i	−0.956180	−	0.292778i	$-0.905420\pi$
$431$		−	252.375i		−	0.585557i	0.956180	−	0.292778i	$-0.0945798\pi$
$432$		0			0
$433$	−516.782			−1.19349			−0.596746	−	0.802430i	$-0.703540\pi$
$433$	−516.782			−1.19349			−0.596746	+	0.802430i	$0.703540\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−675.710	−	59.6169i	−1.54625	−	0.136423i
$438$		0			0
$439$			706.635i			1.60965i	0.593514	+	0.804823i	$0.297740\pi$
$439$			706.635i			1.60965i	−0.593514	+	0.804823i	$0.702260\pi$
$440$		0			0
$441$	347.548			0.788091
$442$		0			0
$443$			405.631i			0.915645i	0.889044	+	0.457823i	$0.151370\pi$
$443$			405.631i			0.915645i	−0.889044	+	0.457823i	$0.848630\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−287.827			−0.643908
$448$		0			0
$449$			585.708i			1.30447i	0.758015	+	0.652237i	$0.226169\pi$
$449$			585.708i			1.30447i	−0.758015	+	0.652237i	$0.773831\pi$
$450$		0			0
$451$			236.727i			0.524893i
$452$		0			0
$453$			159.391i			0.351857i
$454$		0			0
$455$		0			0
$456$		0			0
$457$			445.652i			0.975169i	0.873076	+	0.487585i	$0.162122\pi$
$457$			445.652i			0.975169i	−0.873076	+	0.487585i	$0.837878\pi$
$458$		0			0
$459$		−	128.502i		−	0.279962i
$460$		0			0
$461$	334.203			0.724953			0.362476	−	0.931993i	$-0.381931\pi$
$461$	334.203			0.724953			0.362476	+	0.931993i	$0.381931\pi$
$462$		0			0
$463$			180.792i			0.390479i	0.980756	+	0.195240i	$0.0625485\pi$
$463$			180.792i			0.390479i	−0.980756	+	0.195240i	$0.937452\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			629.520i			1.34801i	0.738727	+	0.674004i	$0.235427\pi$
$467$			629.520i			1.34801i	−0.738727	+	0.674004i	$0.764573\pi$
$468$		0			0
$469$			634.498i			1.35287i
$470$		0			0
$471$			110.587i			0.234792i
$472$		0			0
$473$		−	369.231i		−	0.780616i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	60.3689			0.126559
$478$		0			0
$479$	−304.093			−0.634849			−0.317425	−	0.948284i	$-0.602818\pi$
$479$	−304.093			−0.634849			−0.317425	+	0.948284i	$0.602818\pi$
$480$		0			0
$481$	1263.15			2.62610
$482$		0			0
$483$	693.471			1.43576
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−235.191			−0.482938			−0.241469	−	0.970409i	$-0.577629\pi$
$487$	−235.191			−0.482938			−0.241469	+	0.970409i	$0.577629\pi$
$488$		0			0
$489$			380.767i			0.778665i
$490$		0			0
$491$	289.350			0.589308			0.294654	−	0.955604i	$-0.404796\pi$
$491$	289.350			0.589308			0.294654	+	0.955604i	$0.404796\pi$
$492$		0			0
$493$	65.7415			0.133350
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−420.488			−0.846053
$498$		0			0
$499$	754.978			1.51298			0.756491	−	0.654004i	$-0.226912\pi$
$499$	754.978			1.51298			0.756491	+	0.654004i	$0.226912\pi$
$500$		0			0
$501$	323.924			0.646555
$502$		0			0
$503$		−	347.663i		−	0.691180i	−0.938386	−	0.345590i	$-0.887679\pi$
$503$		−	347.663i		−	0.691180i	0.938386	−	0.345590i	$-0.112321\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−665.989			−1.31359
$508$		0			0
$509$		−	117.878i		−	0.231587i	−0.993273	−	0.115794i	$-0.963059\pi$
$509$		−	117.878i		−	0.231587i	0.993273	−	0.115794i	$-0.0369411\pi$
$510$		0			0
$511$	−259.478			−0.507784
$512$		0			0
$513$	−44.9467	+	509.434i	−0.0876153	+	0.993050i
$514$		0			0
$515$		0			0
$516$		0			0
$517$			144.005i			0.278540i
$518$		0			0
$519$	66.4836			0.128099
$520$		0			0
$521$		−	844.507i		−	1.62093i	−0.585784	−	0.810467i	$-0.699213\pi$
$521$		−	844.507i		−	1.62093i	0.585784	−	0.810467i	$-0.300787\pi$
$522$		0			0
$523$	482.142			0.921879			0.460939	−	0.887432i	$-0.347513\pi$
$523$	482.142			0.921879			0.460939	+	0.887432i	$0.347513\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−145.689			−0.276451
$528$		0			0
$529$	−745.622			−1.40949
$530$		0			0
$531$			305.726i			0.575755i
$532$		0			0
$533$		−	428.326i		−	0.803614i
$534$		0			0
$535$		0			0
$536$		0			0
$537$			404.207i			0.752713i
$538$		0			0
$539$	−789.572			−1.46488
$540$		0			0
$541$	−973.284			−1.79905			−0.899524	−	0.436872i	$-0.856086\pi$
$541$	−973.284			−1.79905			−0.899524	+	0.436872i	$0.856086\pi$
$542$		0			0
$543$			74.6709i			0.137516i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	425.904			0.778618			0.389309	−	0.921107i	$-0.372714\pi$
$547$	425.904			0.778618			0.389309	+	0.921107i	$0.372714\pi$
$548$		0			0
$549$	−99.5493			−0.181328
$550$		0			0
$551$	−260.625	−	22.9946i	−0.473004	−	0.0417325i
$552$		0			0
$553$	−73.3400			−0.132622
$554$		0			0
$555$		0			0
$556$		0			0
$557$			401.955i			0.721643i	0.932635	+	0.360822i	$0.117504\pi$
$557$			401.955i			0.721643i	−0.932635	+	0.360822i	$0.882496\pi$
$558$		0			0
$559$			668.076i			1.19513i
$560$		0			0
$561$			112.002i			0.199647i
$562$		0			0
$563$	655.640			1.16455			0.582274	−	0.812993i	$-0.302163\pi$
$563$	655.640			1.16455			0.582274	+	0.812993i	$0.302163\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$			8.46874i			0.0149361i
$568$		0			0
$569$			485.171i			0.852674i	0.904564	+	0.426337i	$0.140196\pi$
$569$			485.171i			0.852674i	−0.904564	+	0.426337i	$0.859804\pi$
$570$		0			0
$571$	1001.50			1.75395			0.876974	−	0.480537i	$-0.159558\pi$
$571$	1001.50			1.75395			0.876974	+	0.480537i	$0.159558\pi$
$572$		0			0
$573$	153.100			0.267190
$574$		0			0
$575$		0			0
$576$		0			0
$577$		−	33.1105i		−	0.0573838i	−0.999588	−	0.0286919i	$-0.990866\pi$
$577$		−	33.1105i		−	0.0573838i	0.999588	−	0.0286919i	$-0.00913417\pi$
$578$		0			0
$579$	346.380			0.598238
$580$		0			0
$581$	−1371.85			−2.36118
$582$		0			0
$583$	−137.148			−0.235246
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	635.756i		−	1.08306i	−0.840681	−	0.541530i	$-0.817845\pi$
$587$		−	635.756i		−	1.08306i	0.840681	−	0.541530i	$-0.182155\pi$
$588$		0			0
$589$	577.571	+	50.9582i	0.980596	+	0.0865165i
$590$		0			0
$591$		−	313.952i		−	0.531222i
$592$		0			0
$593$			59.1677i			0.0997770i	0.998755	+	0.0498885i	$0.0158866\pi$
$593$			59.1677i			0.0997770i	−0.998755	+	0.0498885i	$0.984113\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	223.541			0.374440
$598$		0			0
$599$		−	941.332i		−	1.57151i	−0.618540	−	0.785753i	$-0.712276\pi$
$599$		−	941.332i		−	1.57151i	0.618540	−	0.785753i	$-0.287724\pi$
$600$		0			0
$601$			333.283i			0.554547i	0.960791	+	0.277274i	$0.0894308\pi$
$601$			333.283i			0.554547i	−0.960791	+	0.277274i	$0.910569\pi$
$602$		0			0
$603$	−337.326			−0.559413
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−747.914			−1.23215			−0.616074	−	0.787688i	$-0.711278\pi$
$607$	−747.914			−1.23215			−0.616074	+	0.787688i	$0.711278\pi$
$608$		0			0
$609$	267.476			0.439205
$610$		0			0
$611$		−	260.559i		−	0.426446i
$612$		0			0
$613$		−	226.642i		−	0.369726i	−0.982764	−	0.184863i	$-0.940816\pi$
$613$		−	226.642i		−	0.369726i	0.982764	−	0.184863i	$-0.0591841\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	796.334i		−	1.29065i	−0.763906	−	0.645327i	$-0.776721\pi$
$617$		−	796.334i		−	1.29065i	0.763906	−	0.645327i	$-0.223279\pi$
$618$		0			0
$619$	31.3780			0.0506914			0.0253457	−	0.999679i	$-0.491931\pi$
$619$	31.3780			0.0506914			0.0253457	+	0.999679i	$0.491931\pi$
$620$		0			0
$621$			960.969i			1.54745i
$622$		0			0
$623$	1692.07			2.71600
$624$		0			0
$625$		0			0
$626$		0			0
$627$	39.1754	−	444.021i	0.0624806	−	0.708168i
$628$		0			0
$629$			261.872i			0.416330i
$630$		0			0
$631$	−493.470			−0.782045			−0.391022	−	0.920381i	$-0.627878\pi$
$631$	−493.470			−0.782045			−0.391022	+	0.920381i	$0.627878\pi$
$632$		0			0
$633$			335.763i			0.530432i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	1428.63			2.24274
$638$		0			0
$639$		−	223.549i		−	0.349842i
$640$		0			0
$641$			946.351i			1.47637i	0.674600	+	0.738183i	$0.264316\pi$
$641$			946.351i			1.47637i	−0.674600	+	0.738183i	$0.735684\pi$
$642$		0			0
$643$		−	816.065i		−	1.26915i	−0.772860	−	0.634576i	$-0.781175\pi$
$643$		−	816.065i		−	1.26915i	0.772860	−	0.634576i	$-0.218825\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	573.382i		−	0.886217i	−0.896468	−	0.443108i	$-0.853876\pi$
$647$		−	573.382i		−	0.886217i	0.896468	−	0.443108i	$-0.146124\pi$
$648$		0			0
$649$		−	694.559i		−	1.07020i
$650$		0			0
$651$	−592.752			−0.910525
$652$		0			0
$653$			443.988i			0.679920i	0.940440	+	0.339960i	$0.110414\pi$
$653$			443.988i			0.679920i	−0.940440	+	0.339960i	$0.889586\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	137.949i		−	0.209969i
$658$		0			0
$659$		−	571.755i		−	0.867609i	−0.901007	−	0.433805i	$-0.857171\pi$
$659$		−	571.755i		−	0.867609i	0.901007	−	0.433805i	$-0.142829\pi$
$660$		0			0
$661$			1244.42i			1.88264i	0.337519	+	0.941319i	$0.390412\pi$
$661$			1244.42i			1.88264i	−0.337519	+	0.941319i	$0.609588\pi$
$662$		0			0
$663$		−	202.653i		−	0.305661i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−491.629			−0.737075
$668$		0			0
$669$	−396.562			−0.592768
$670$		0			0
$671$	226.160			0.337049
$672$		0			0
$673$	−236.320			−0.351144			−0.175572	−	0.984467i	$-0.556177\pi$
$673$	−236.320			−0.351144			−0.175572	+	0.984467i	$0.556177\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−1066.35			−1.57512			−0.787559	−	0.616239i	$-0.788655\pi$
$677$	−1066.35			−1.57512			−0.787559	+	0.616239i	$0.788655\pi$
$678$		0			0
$679$			751.318i			1.10651i
$680$		0			0
$681$	490.024			0.719566
$682$		0			0
$683$	1176.02			1.72184			0.860921	−	0.508739i	$-0.169888\pi$
$683$	1176.02			1.72184			0.860921	+	0.508739i	$0.169888\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	212.655			0.309541
$688$		0			0
$689$	248.152			0.360162
$690$		0			0
$691$	18.1811			0.0263113			0.0131557	−	0.999913i	$-0.495812\pi$
$691$	18.1811			0.0263113			0.0131557	+	0.999913i	$0.495812\pi$
$692$		0			0
$693$		−	751.319i		−	1.08415i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	88.7988			0.127401
$698$		0			0
$699$			349.833i			0.500477i
$700$		0			0
$701$	−438.306			−0.625258			−0.312629	−	0.949875i	$-0.601210\pi$
$701$	−438.306			−0.625258			−0.312629	+	0.949875i	$0.601210\pi$
$702$		0			0
$703$	91.5957	−	1038.16i	0.130293	−	1.47676i
$704$		0			0
$705$		0			0
$706$		0			0
$707$			1131.36i			1.60023i
$708$		0			0
$709$	629.057			0.887245			0.443622	−	0.896214i	$-0.353693\pi$
$709$	629.057			0.887245			0.443622	+	0.896214i	$0.353693\pi$
$710$		0			0
$711$		−	38.9906i		−	0.0548391i
$712$		0			0
$713$	1089.50			1.52805
$714$		0			0
$715$		0			0
$716$		0			0
$717$	183.195			0.255502
$718$		0			0
$719$	1112.31			1.54702			0.773509	−	0.633786i	$-0.218500\pi$
$719$	1112.31			1.54702			0.773509	+	0.633786i	$0.218500\pi$
$720$		0			0
$721$			175.034i			0.242765i
$722$		0			0
$723$			240.258i			0.332307i
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	684.037i		−	0.940904i	−0.882426	−	0.470452i	$-0.844091\pi$
$727$		−	684.037i		−	0.940904i	0.882426	−	0.470452i	$-0.155909\pi$
$728$		0			0
$729$	442.040			0.606364
$730$		0			0
$731$	−138.503			−0.189470
$732$		0			0
$733$			171.268i			0.233653i	0.993152	+	0.116826i	$0.0372721\pi$
$733$			171.268i			0.233653i	−0.993152	+	0.116826i	$0.962728\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	766.350			1.03982
$738$		0			0
$739$	−317.424			−0.429532			−0.214766	−	0.976665i	$-0.568899\pi$
$739$	−317.424			−0.429532			−0.214766	+	0.976665i	$0.568899\pi$
$740$		0			0
$741$	−70.8827	+	803.399i	−0.0956582	+	1.08421i
$742$		0			0
$743$	140.619			0.189258			0.0946289	−	0.995513i	$-0.469834\pi$
$743$	140.619			0.189258			0.0946289	+	0.995513i	$0.469834\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		−	729.332i		−	0.976348i
$748$		0			0
$749$			1409.12i			1.88134i
$750$		0			0
$751$			825.612i			1.09935i	0.835378	+	0.549675i	$0.185249\pi$
$751$			825.612i			1.09935i	−0.835378	+	0.549675i	$0.814751\pi$
$752$		0			0
$753$	−923.844			−1.22688
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	693.756i		−	0.916454i	−0.888835	−	0.458227i	$-0.848485\pi$
$757$		−	693.756i		−	0.916454i	0.888835	−	0.458227i	$-0.151515\pi$
$758$		0			0
$759$		−	837.577i		−	1.10353i
$760$		0			0
$761$	−148.006			−0.194489			−0.0972447	−	0.995261i	$-0.531003\pi$
$761$	−148.006			−0.194489			−0.0972447	+	0.995261i	$0.531003\pi$
$762$		0			0
$763$	1858.18			2.43536
$764$		0			0
$765$		0			0
$766$		0			0
$767$			1256.71i			1.63848i
$768$		0			0
$769$	−1090.86			−1.41854			−0.709270	−	0.704937i	$-0.750975\pi$
$769$	−1090.86			−1.41854			−0.709270	+	0.704937i	$0.750975\pi$
$770$		0			0
$771$	300.076			0.389204
$772$		0			0
$773$	498.925			0.645440			0.322720	−	0.946494i	$-0.395403\pi$
$773$	498.925			0.645440			0.322720	+	0.946494i	$0.395403\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$			1065.45i			1.37124i
$778$		0			0
$779$	−352.034	−	31.0594i	−0.451905	−	0.0398709i
$780$		0			0
$781$			507.867i			0.650278i
$782$		0			0
$783$			370.651i			0.473373i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−703.635			−0.894072			−0.447036	−	0.894516i	$-0.647520\pi$
$787$	−703.635			−0.894072			−0.447036	+	0.894516i	$0.647520\pi$
$788$		0			0
$789$			93.0539i			0.117939i
$790$		0			0
$791$		−	2370.35i		−	2.99664i
$792$		0			0
$793$	−409.207			−0.516023
$794$		0			0
$795$		0			0
$796$		0			0
$797$	28.1611			0.0353339			0.0176669	−	0.999844i	$-0.494376\pi$
$797$	28.1611			0.0353339			0.0176669	+	0.999844i	$0.494376\pi$
$798$		0			0
$799$	54.0180			0.0676070
$800$		0			0
$801$			899.574i			1.12306i
$802$		0			0
$803$			313.399i			0.390285i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		−	53.0616i		−	0.0657517i
$808$		0			0
$809$	−666.095			−0.823356			−0.411678	−	0.911329i	$-0.635057\pi$
$809$	−666.095			−0.823356			−0.411678	+	0.911329i	$0.635057\pi$
$810$		0			0
$811$			803.237i			0.990428i	0.868771	+	0.495214i	$0.164910\pi$
$811$			803.237i			0.990428i	−0.868771	+	0.495214i	$0.835090\pi$
$812$		0			0
$813$	738.954			0.908923
$814$		0			0
$815$		0			0
$816$		0			0
$817$	549.080	+	48.4445i	0.672069	+	0.0592956i
$818$		0			0
$819$			1359.41i			1.65985i
$820$		0			0
$821$	433.616			0.528157			0.264078	−	0.964501i	$-0.414932\pi$
$821$	433.616			0.528157			0.264078	+	0.964501i	$0.414932\pi$
$822$		0			0
$823$			69.2993i			0.0842033i	0.999113	+	0.0421016i	$0.0134053\pi$
$823$			69.2993i			0.0842033i	−0.999113	+	0.0421016i	$0.986595\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−282.525			−0.341626			−0.170813	−	0.985303i	$-0.554639\pi$
$827$	−282.525			−0.341626			−0.170813	+	0.985303i	$0.554639\pi$
$828$		0			0
$829$			1136.04i			1.37037i	0.728369	+	0.685185i	$0.240278\pi$
$829$			1136.04i			1.37037i	−0.728369	+	0.685185i	$0.759722\pi$
$830$		0			0
$831$		−	394.184i		−	0.474349i
$832$		0			0
$833$			296.177i			0.355555i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		−	821.399i		−	0.981361i
$838$		0			0
$839$		−	474.238i		−	0.565242i	−0.959232	−	0.282621i	$-0.908796\pi$
$839$		−	474.238i		−	0.565242i	0.959232	−	0.282621i	$-0.0912039\pi$
$840$		0			0
$841$	651.376			0.774526
$842$		0			0
$843$		−	423.240i		−	0.502065i
$844$		0			0
$845$		0			0
$846$		0			0
$847$			431.842i			0.509848i
$848$		0			0
$849$			371.164i			0.437178i
$850$		0			0
$851$		−	1958.33i		−	2.30121i
$852$		0			0
$853$		−	843.815i		−	0.989232i	−0.869112	−	0.494616i	$-0.835309\pi$
$853$		−	843.815i		−	0.989232i	0.869112	−	0.494616i	$-0.164691\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−435.275			−0.507906			−0.253953	−	0.967217i	$-0.581731\pi$
$857$	−435.275			−0.507906			−0.253953	+	0.967217i	$0.581731\pi$
$858$		0			0
$859$	−715.550			−0.833003			−0.416502	−	0.909135i	$-0.636744\pi$
$859$	−715.550			−0.833003			−0.416502	+	0.909135i	$0.636744\pi$
$860$		0			0
$861$	361.287			0.419613
$862$		0			0
$863$	−1083.60			−1.25562			−0.627811	−	0.778366i	$-0.716049\pi$
$863$	−1083.60			−1.25562			−0.627811	+	0.778366i	$0.716049\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−490.707			−0.565983
$868$		0			0
$869$			88.5803i			0.101934i
$870$		0			0
$871$	−1386.61			−1.59197
$872$		0			0
$873$	−399.433			−0.457540
$874$		0			0
$875$		0			0
$876$		0			0
$877$	737.245			0.840644			0.420322	−	0.907375i	$-0.361917\pi$
$877$	737.245			0.840644			0.420322	+	0.907375i	$0.361917\pi$
$878$		0			0
$879$	527.005			0.599550
$880$		0			0
$881$	−64.9086			−0.0736761			−0.0368380	−	0.999321i	$-0.511729\pi$
$881$	−64.9086			−0.0736761			−0.0368380	+	0.999321i	$0.511729\pi$
$882$		0			0
$883$			1325.97i			1.50166i	0.660495	+	0.750830i	$0.270346\pi$
$883$			1325.97i			1.50166i	−0.660495	+	0.750830i	$0.729654\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−842.262			−0.949563			−0.474781	−	0.880104i	$-0.657473\pi$
$887$	−842.262			−0.949563			−0.474781	+	0.880104i	$0.657473\pi$
$888$		0			0
$889$		−	1326.32i		−	1.49192i
$890$		0			0
$891$	10.2286			0.0114799
$892$		0			0
$893$	−214.149	−	18.8940i	−0.239808	−	0.0211579i
$894$		0			0
$895$		0			0
$896$		0			0
$897$			1515.49i			1.68951i
$898$		0			0
$899$	420.225			0.467436
$900$		0			0
$901$			51.4458i			0.0570986i
$902$		0			0
$903$	−563.512			−0.624045
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−1212.41			−1.33673			−0.668364	−	0.743834i	$-0.733005\pi$
$907$	−1212.41			−1.33673			−0.668364	+	0.743834i	$0.733005\pi$
$908$		0			0
$909$	−601.481			−0.661695
$910$		0			0
$911$			1204.26i			1.32191i	0.750427	+	0.660954i	$0.229848\pi$
$911$			1204.26i			1.32191i	−0.750427	+	0.660954i	$0.770152\pi$
$912$		0			0
$913$			1656.92i			1.81481i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	1791.22i		−	1.95334i
$918$		0			0
$919$	117.855			0.128243			0.0641214	−	0.997942i	$-0.479576\pi$
$919$	117.855			0.128243			0.0641214	+	0.997942i	$0.479576\pi$
$920$		0			0
$921$	71.4150			0.0775408
$922$		0			0
$923$		−	918.920i		−	0.995579i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−93.0554			−0.100383
$928$		0			0
$929$	1171.59			1.26113			0.630566	−	0.776136i	$-0.282823\pi$
$929$	1171.59			1.26113			0.630566	+	0.776136i	$0.282823\pi$
$930$		0			0
$931$	103.595	−	1174.16i	0.111273	−	1.26119i
$932$		0			0
$933$	−1120.10			−1.20054
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	1657.08i		−	1.76849i	−0.467020	−	0.884247i	$-0.654672\pi$
$937$		−	1657.08i		−	1.76849i	0.467020	−	0.884247i	$-0.345328\pi$
$938$		0			0
$939$			541.522i			0.576700i
$940$		0			0
$941$			897.326i			0.953588i	0.879015	+	0.476794i	$0.158201\pi$
$941$			897.326i			0.953588i	−0.879015	+	0.476794i	$0.841799\pi$
$942$		0			0
$943$	−664.057			−0.704196
$944$		0			0
$945$		0			0
$946$		0			0
$947$			1458.19i			1.53980i	0.638163	+	0.769901i	$0.279695\pi$
$947$			1458.19i			1.53980i	−0.638163	+	0.769901i	$0.720305\pi$
$948$		0			0
$949$		−	567.054i		−	0.597528i
$950$		0			0
$951$	−1029.35			−1.08239
$952$		0			0
$953$	−1049.86			−1.10164			−0.550820	−	0.834624i	$-0.685685\pi$
$953$	−1049.86			−1.10164			−0.550820	+	0.834624i	$0.685685\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		−	323.058i		−	0.337574i
$958$		0			0
$959$	1787.53			1.86395
$960$		0			0
$961$	29.7397			0.0309466
$962$		0			0
$963$	−749.150			−0.777933
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	236.232i		−	0.244293i	−0.992512	−	0.122147i	$-0.961022\pi$
$967$		−	236.232i		−	0.244293i	0.992512	−	0.122147i	$-0.0389778\pi$
$968$		0			0
$969$	−166.557	−	14.6951i	−0.171886	−	0.0151652i
$970$		0			0
$971$		−	1281.82i		−	1.32010i	−0.751220	−	0.660052i	$-0.770534\pi$
$971$		−	1281.82i		−	1.32010i	0.751220	−	0.660052i	$-0.229466\pi$
$972$		0			0
$973$		−	2643.67i		−	2.71702i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1475.99			−1.51074			−0.755369	−	0.655300i	$-0.772542\pi$
$977$	−1475.99			−1.51074			−0.755369	+	0.655300i	$0.772542\pi$
$978$		0			0
$979$		−	2043.69i		−	2.08752i
$980$		0			0
$981$			987.885i			1.00702i
$982$		0			0
$983$	574.909			0.584851			0.292426	−	0.956288i	$-0.405538\pi$
$983$	574.909			0.584851			0.292426	+	0.956288i	$0.405538\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	219.777			0.222672
$988$		0			0
$989$	1035.75			1.04727
$990$		0			0
$991$		−	47.2482i		−	0.0476773i	−0.999716	−	0.0238387i	$-0.992411\pi$
$991$		−	47.2482i		−	0.0476773i	0.999716	−	0.0238387i	$-0.00758880\pi$
$992$		0			0
$993$		−	676.296i		−	0.681064i
$994$		0			0
$995$		0			0
$996$		0			0
$997$			671.475i			0.673495i	0.941595	+	0.336748i	$0.109327\pi$
$997$			671.475i			0.673495i	−0.941595	+	0.336748i	$0.890673\pi$
$998$		0			0
$999$	−1476.44			−1.47791

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1900.3.g.d.949.11		28
5.2	odd	4		1900.3.e.g.1101.9	yes	14
5.3	odd	4		1900.3.e.h.1101.6	yes	14
5.4	even	2	inner	1900.3.g.d.949.18		28
19.18	odd	2	inner	1900.3.g.d.949.17		28
95.18	even	4		1900.3.e.h.1101.9	yes	14
95.37	even	4		1900.3.e.g.1101.6	✓	14
95.94	odd	2	inner	1900.3.g.d.949.12		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1900.3.e.g.1101.6	✓	14	95.37	even	4
1900.3.e.g.1101.9	yes	14	5.2	odd	4
1900.3.e.h.1101.6	yes	14	5.3	odd	4
1900.3.e.h.1101.9	yes	14	95.18	even	4
1900.3.g.d.949.11		28	1.1	even	1	trivial
1900.3.g.d.949.12		28	95.94	odd	2	inner
1900.3.g.d.949.17		28	19.18	odd	2	inner
1900.3.g.d.949.18		28	5.4	even	2	inner

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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1900.g (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.84332 q^{3} +10.5375i q^{7} -5.60216 q^{9} +O(q^{10})\)	\(q-1.84332 q^{3} +10.5375i q^{7} -5.60216 q^{9} +12.7272 q^{11} -23.0282 q^{13} -4.77411i q^{17} +(-1.66986 + 18.9265i) q^{19} -19.4239i q^{21} +35.7018i q^{23} +26.9165 q^{27} +13.7704i q^{29} -30.5166i q^{31} -23.4603 q^{33} -54.8524 q^{37} +42.4484 q^{39} +18.6001i q^{41} -29.0112i q^{43} +11.3148i q^{47} -62.0382 q^{49} +8.80023i q^{51} -10.7760 q^{53} +(3.07808 - 34.8876i) q^{57} -54.5728i q^{59} +17.7698 q^{61} -59.0326i q^{63} +60.2136 q^{67} -65.8100i q^{69} +39.9041i q^{71} +24.6243i q^{73} +134.112i q^{77} +6.95992i q^{79} +0.803679 q^{81} +130.188i q^{83} -25.3833i q^{87} -160.576i q^{89} -242.659i q^{91} +56.2519i q^{93} +71.2997 q^{97} -71.2998 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 104 q^{9}+O(q^{10}) \) 28 * q + 104 * q^9	\( 28 q + 104 q^{9} + 8 q^{11} + 58 q^{19} + 112 q^{39} - 276 q^{49} - 100 q^{61} + 132 q^{81} - 184 q^{99}+O(q^{100}) \) 28 * q + 104 * q^9 + 8 * q^11 + 58 * q^19 + 112 * q^39 - 276 * q^49 - 100 * q^61 + 132 * q^81 - 184 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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