LMFDB - Embedded newform 1900.3.g.d.949.2

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			949.2
Character	$\chi$	$=$	1900.949
Dual form			1900.3.g.d.949.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.26531 q^{3} -12.1735i q^{7} +18.7235 q^{9} +O(q^{10})$	$q-5.26531 q^{3} -12.1735i q^{7} +18.7235 q^{9} -4.59727 q^{11} -19.9019 q^{13} +4.10564i q^{17} +(17.9241 - 6.30286i) q^{19} +64.0972i q^{21} +35.2013i q^{23} -51.1972 q^{27} +16.4948i q^{29} -4.01062i q^{31} +24.2060 q^{33} +10.6049 q^{37} +104.790 q^{39} +22.4270i q^{41} -51.8177i q^{43} +23.7025i q^{47} -99.1940 q^{49} -21.6174i q^{51} -97.3018 q^{53} +(-94.3760 + 33.1865i) q^{57} +33.1216i q^{59} -75.1967 q^{61} -227.930i q^{63} +6.31874 q^{67} -185.346i q^{69} +118.291i q^{71} +7.02357i q^{73} +55.9648i q^{77} -76.0473i q^{79} +101.058 q^{81} -100.198i q^{83} -86.8500i q^{87} +123.299i q^{89} +242.276i q^{91} +21.1171i q^{93} +101.202 q^{97} -86.0769 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−5.26531			−1.75510			−0.877552	−	0.479482i	$-0.840825\pi$
$3$	−5.26531			−1.75510			−0.877552	+	0.479482i	$0.840825\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$		−	12.1735i		−	1.73907i	−0.493871	−	0.869535i	$-0.664418\pi$
$7$		−	12.1735i		−	1.73907i	0.493871	−	0.869535i	$-0.335582\pi$
$8$		0			0
$9$	18.7235			2.08039
$10$		0			0
$11$	−4.59727			−0.417933			−0.208967	−	0.977923i	$-0.567010\pi$
$11$	−4.59727			−0.417933			−0.208967	+	0.977923i	$0.567010\pi$
$12$		0			0
$13$	−19.9019			−1.53092			−0.765458	−	0.643486i	$-0.777488\pi$
$13$	−19.9019			−1.53092			−0.765458	+	0.643486i	$0.777488\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			4.10564i			0.241508i	0.992682	+	0.120754i	$0.0385312\pi$
$17$			4.10564i			0.241508i	−0.992682	+	0.120754i	$0.961469\pi$
$18$		0			0
$19$	17.9241	−	6.30286i	0.943375	−	0.331729i
$19$	17.9241	−	6.30286i	0.943375	−	0.331729i
$20$		0			0
$21$			64.0972i			3.05225i
$22$		0			0
$23$			35.2013i			1.53049i	0.643738	+	0.765246i	$0.277383\pi$
$23$			35.2013i			1.53049i	−0.643738	+	0.765246i	$0.722617\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−51.1972			−1.89619
$28$		0			0
$29$			16.4948i			0.568785i	0.958708	+	0.284392i	$0.0917919\pi$
$29$			16.4948i			0.568785i	−0.958708	+	0.284392i	$0.908208\pi$
$30$		0			0
$31$		−	4.01062i		−	0.129375i	−0.997906	−	0.0646873i	$-0.979395\pi$
$31$		−	4.01062i		−	0.129375i	0.997906	−	0.0646873i	$-0.0206050\pi$
$32$		0			0
$33$	24.2060			0.733516
$34$		0			0
$35$		0			0
$36$		0			0
$37$	10.6049			0.286620			0.143310	−	0.989678i	$-0.454225\pi$
$37$	10.6049			0.286620			0.143310	+	0.989678i	$0.454225\pi$
$38$		0			0
$39$	104.790			2.68692
$40$		0			0
$41$			22.4270i			0.546999i	0.961872	+	0.273500i	$0.0881812\pi$
$41$			22.4270i			0.546999i	−0.961872	+	0.273500i	$0.911819\pi$
$42$		0			0
$43$		−	51.8177i		−	1.20506i	−0.798095	−	0.602531i	$-0.794159\pi$
$43$		−	51.8177i		−	1.20506i	0.798095	−	0.602531i	$-0.205841\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			23.7025i			0.504308i	0.967687	+	0.252154i	$0.0811389\pi$
$47$			23.7025i			0.504308i	−0.967687	+	0.252154i	$0.918861\pi$
$48$		0			0
$49$	−99.1940			−2.02437
$50$		0			0
$51$		−	21.6174i		−	0.423871i
$52$		0			0
$53$	−97.3018			−1.83588			−0.917942	−	0.396715i	$-0.870150\pi$
$53$	−97.3018			−1.83588			−0.917942	+	0.396715i	$0.870150\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−94.3760	+	33.1865i	−1.65572	+	0.582219i
$58$		0			0
$59$			33.1216i			0.561384i	0.959798	+	0.280692i	$0.0905639\pi$
$59$			33.1216i			0.561384i	−0.959798	+	0.280692i	$0.909436\pi$
$60$		0			0
$61$	−75.1967			−1.23273			−0.616366	−	0.787460i	$-0.711396\pi$
$61$	−75.1967			−1.23273			−0.616366	+	0.787460i	$0.711396\pi$
$62$		0			0
$63$		−	227.930i		−	3.61794i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	6.31874			0.0943095			0.0471548	−	0.998888i	$-0.484985\pi$
$67$	6.31874			0.0943095			0.0471548	+	0.998888i	$0.484985\pi$
$68$		0			0
$69$		−	185.346i		−	2.68617i
$70$		0			0
$71$			118.291i			1.66607i	0.553224	+	0.833033i	$0.313397\pi$
$71$			118.291i			1.66607i	−0.553224	+	0.833033i	$0.686603\pi$
$72$		0			0
$73$			7.02357i			0.0962133i	0.998842	+	0.0481067i	$0.0153187\pi$
$73$			7.02357i			0.0962133i	−0.998842	+	0.0481067i	$0.984681\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$			55.9648i			0.726815i
$78$		0			0
$79$		−	76.0473i		−	0.962624i	−0.876549	−	0.481312i	$-0.840160\pi$
$79$		−	76.0473i		−	0.962624i	0.876549	−	0.481312i	$-0.159840\pi$
$80$		0			0
$81$	101.058			1.24763
$82$		0			0
$83$		−	100.198i		−	1.20720i	−0.797287	−	0.603600i	$-0.793732\pi$
$83$		−	100.198i		−	1.20720i	0.797287	−	0.603600i	$-0.206268\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		−	86.8500i		−	0.998276i
$88$		0			0
$89$			123.299i			1.38538i	0.721233	+	0.692692i	$0.243576\pi$
$89$			123.299i			1.38538i	−0.721233	+	0.692692i	$0.756424\pi$
$90$		0			0
$91$			242.276i			2.66237i
$92$		0			0
$93$			21.1171i			0.227066i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	101.202			1.04332			0.521659	−	0.853154i	$-0.325313\pi$
$97$	101.202			1.04332			0.521659	+	0.853154i	$0.325313\pi$
$98$		0			0
$99$	−86.0769			−0.869463
$100$		0			0
$101$	150.478			1.48988			0.744939	−	0.667133i	$-0.232479\pi$
$101$	150.478			1.48988			0.744939	+	0.667133i	$0.232479\pi$
$102$		0			0
$103$	112.271			1.09001			0.545003	−	0.838434i	$-0.316529\pi$
$103$	112.271			1.09001			0.545003	+	0.838434i	$0.316529\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−144.877			−1.35399			−0.676996	−	0.735987i	$-0.736718\pi$
$107$	−144.877			−1.35399			−0.676996	+	0.735987i	$0.736718\pi$
$108$		0			0
$109$		−	50.7929i		−	0.465990i	−0.972478	−	0.232995i	$-0.925147\pi$
$109$		−	50.7929i		−	0.465990i	0.972478	−	0.232995i	$-0.0748526\pi$
$110$		0			0
$111$	−55.8382			−0.503047
$112$		0			0
$113$	84.1325			0.744536			0.372268	−	0.928125i	$-0.378580\pi$
$113$	84.1325			0.744536			0.372268	+	0.928125i	$0.378580\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−372.633			−3.18490
$118$		0			0
$119$	49.9799			0.419999
$120$		0			0
$121$	−99.8651			−0.825332
$122$		0			0
$123$		−	118.085i		−	0.960040i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	129.368			1.01864			0.509322	−	0.860576i	$-0.329896\pi$
$127$	129.368			1.01864			0.509322	+	0.860576i	$0.329896\pi$
$128$		0			0
$129$			272.836i			2.11501i
$130$		0			0
$131$	139.421			1.06428			0.532141	−	0.846656i	$-0.321388\pi$
$131$	139.421			1.06428			0.532141	+	0.846656i	$0.321388\pi$
$132$		0			0
$133$	−76.7278	−	218.199i	−0.576901	−	1.64060i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	64.8931i		−	0.473672i	−0.971550	−	0.236836i	$-0.923890\pi$
$137$		−	64.8931i		−	0.473672i	0.971550	−	0.236836i	$-0.0761104\pi$
$138$		0			0
$139$	164.632			1.18440			0.592200	−	0.805791i	$-0.298259\pi$
$139$	164.632			1.18440			0.592200	+	0.805791i	$0.298259\pi$
$140$		0			0
$141$		−	124.801i		−	0.885112i
$142$		0			0
$143$	91.4944			0.639821
$144$		0			0
$145$		0			0
$146$		0			0
$147$	522.287			3.55297
$148$		0			0
$149$	−13.8027			−0.0926354			−0.0463177	−	0.998927i	$-0.514749\pi$
$149$	−13.8027			−0.0926354			−0.0463177	+	0.998927i	$0.514749\pi$
$150$		0			0
$151$		−	214.161i		−	1.41829i	−0.705064	−	0.709144i	$-0.749082\pi$
$151$		−	214.161i		−	1.41829i	0.705064	−	0.709144i	$-0.250918\pi$
$152$		0			0
$153$			76.8718i			0.502430i
$154$		0			0
$155$		0			0
$156$		0			0
$157$			145.383i			0.926009i	0.886356	+	0.463004i	$0.153229\pi$
$157$			145.383i			0.926009i	−0.886356	+	0.463004i	$0.846771\pi$
$158$		0			0
$159$	512.324			3.22217
$160$		0			0
$161$	428.523			2.66163
$162$		0			0
$163$			172.709i			1.05956i	0.848135	+	0.529781i	$0.177726\pi$
$163$			172.709i			1.05956i	−0.848135	+	0.529781i	$0.822274\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	232.500			1.39222			0.696108	−	0.717937i	$-0.254914\pi$
$167$	232.500			1.39222			0.696108	+	0.717937i	$0.254914\pi$
$168$		0			0
$169$	227.086			1.34370
$170$		0			0
$171$	335.602	−	118.012i	1.96259	−	0.690126i
$172$		0			0
$173$	−290.870			−1.68133			−0.840665	−	0.541556i	$-0.817835\pi$
$173$	−290.870			−1.68133			−0.840665	+	0.541556i	$0.817835\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		−	174.396i		−	0.985286i
$178$		0			0
$179$		−	172.255i		−	0.962319i	−0.876633	−	0.481159i	$-0.840216\pi$
$179$		−	172.255i		−	0.962319i	0.876633	−	0.481159i	$-0.159784\pi$
$180$		0			0
$181$		−	343.036i		−	1.89523i	−0.319420	−	0.947613i	$-0.603488\pi$
$181$		−	343.036i		−	1.89523i	0.319420	−	0.947613i	$-0.396512\pi$
$182$		0			0
$183$	395.934			2.16357
$184$		0			0
$185$		0			0
$186$		0			0
$187$		−	18.8747i		−	0.100934i
$188$		0			0
$189$			623.249i			3.29761i
$190$		0			0
$191$	−184.283			−0.964832			−0.482416	−	0.875942i	$-0.660241\pi$
$191$	−184.283			−0.964832			−0.482416	+	0.875942i	$0.660241\pi$
$192$		0			0
$193$	304.518			1.57781			0.788907	−	0.614513i	$-0.210647\pi$
$193$	304.518			1.57781			0.788907	+	0.614513i	$0.210647\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			306.839i			1.55756i	0.627299	+	0.778778i	$0.284160\pi$
$197$			306.839i			1.55756i	−0.627299	+	0.778778i	$0.715840\pi$
$198$		0			0
$199$	89.0393			0.447434			0.223717	−	0.974654i	$-0.428181\pi$
$199$	89.0393			0.447434			0.223717	+	0.974654i	$0.428181\pi$
$200$		0			0
$201$	−33.2701			−0.165523
$202$		0			0
$203$	200.799			0.989157
$204$		0			0
$205$		0			0
$206$		0			0
$207$			659.091i			3.18402i
$208$		0			0
$209$	−82.4019	+	28.9759i	−0.394268	+	0.138641i
$210$		0			0
$211$			156.363i			0.741056i	0.928821	+	0.370528i	$0.120823\pi$
$211$			156.363i			0.741056i	−0.928821	+	0.370528i	$0.879177\pi$
$212$		0			0
$213$		−	622.837i		−	2.92412i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−48.8232			−0.224992
$218$		0			0
$219$		−	36.9813i		−	0.168864i
$220$		0			0
$221$		−	81.7100i		−	0.369728i
$222$		0			0
$223$	312.945			1.40334			0.701671	−	0.712501i	$-0.252437\pi$
$223$	312.945			1.40334			0.701671	+	0.712501i	$0.252437\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−199.435			−0.878570			−0.439285	−	0.898348i	$-0.644768\pi$
$227$	−199.435			−0.878570			−0.439285	+	0.898348i	$0.644768\pi$
$228$		0			0
$229$	−251.971			−1.10031			−0.550155	−	0.835063i	$-0.685431\pi$
$229$	−251.971			−1.10031			−0.550155	+	0.835063i	$0.685431\pi$
$230$		0			0
$231$		−	294.672i		−	1.27564i
$232$		0			0
$233$			452.694i			1.94289i	0.237259	+	0.971446i	$0.423751\pi$
$233$			452.694i			1.94289i	−0.237259	+	0.971446i	$0.576249\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$			400.413i			1.68950i
$238$		0			0
$239$	−143.219			−0.599245			−0.299622	−	0.954058i	$-0.596861\pi$
$239$	−143.219			−0.599245			−0.299622	+	0.954058i	$0.596861\pi$
$240$		0			0
$241$		−	6.63375i		−	0.0275259i	−0.999905	−	0.0137630i	$-0.995619\pi$
$241$		−	6.63375i		−	0.0275259i	0.999905	−	0.0137630i	$-0.00438103\pi$
$242$		0			0
$243$	−71.3257			−0.293521
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−356.724	+	125.439i	−1.44423	+	0.507850i
$248$		0			0
$249$			527.571i			2.11876i
$250$		0			0
$251$	180.383			0.718658			0.359329	−	0.933211i	$-0.383006\pi$
$251$	180.383			0.718658			0.359329	+	0.933211i	$0.383006\pi$
$252$		0			0
$253$		−	161.830i		−	0.639643i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−14.9645			−0.0582275			−0.0291137	−	0.999576i	$-0.509268\pi$
$257$	−14.9645			−0.0582275			−0.0291137	+	0.999576i	$0.509268\pi$
$258$		0			0
$259$		−	129.099i		−	0.498452i
$260$		0			0
$261$			308.840i			1.18329i
$262$		0			0
$263$			439.986i			1.67295i	0.548005	+	0.836475i	$0.315387\pi$
$263$			439.986i			1.67295i	−0.548005	+	0.836475i	$0.684613\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		−	649.209i		−	2.43149i
$268$		0			0
$269$		−	253.894i		−	0.943843i	−0.881641	−	0.471922i	$-0.843561\pi$
$269$		−	253.894i		−	0.943843i	0.881641	−	0.471922i	$-0.156439\pi$
$270$		0			0
$271$	107.372			0.396208			0.198104	−	0.980181i	$-0.436522\pi$
$271$	107.372			0.396208			0.198104	+	0.980181i	$0.436522\pi$
$272$		0			0
$273$		−	1275.66i		−	4.67274i
$274$		0			0
$275$		0			0
$276$		0			0
$277$			21.9808i			0.0793531i	0.999213	+	0.0396765i	$0.0126327\pi$
$277$			21.9808i			0.0793531i	−0.999213	+	0.0396765i	$0.987367\pi$
$278$		0			0
$279$		−	75.0927i		−	0.269150i
$280$		0			0
$281$		−	223.590i		−	0.795694i	−0.917452	−	0.397847i	$-0.869757\pi$
$281$		−	223.590i		−	0.795694i	0.917452	−	0.397847i	$-0.130243\pi$
$282$		0			0
$283$		−	52.7660i		−	0.186452i	−0.995645	−	0.0932261i	$-0.970282\pi$
$283$		−	52.7660i		−	0.186452i	0.995645	−	0.0932261i	$-0.0297179\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	273.015			0.951270
$288$		0			0
$289$	272.144			0.941674
$290$		0			0
$291$	−532.859			−1.83113
$292$		0			0
$293$	293.865			1.00295			0.501476	−	0.865172i	$-0.332791\pi$
$293$	293.865			1.00295			0.501476	+	0.865172i	$0.332791\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	235.367			0.792482
$298$		0			0
$299$		−	700.573i		−	2.34305i
$300$		0			0
$301$	−630.802			−2.09569
$302$		0			0
$303$	−792.311			−2.61489
$304$		0			0
$305$		0			0
$306$		0			0
$307$	392.330			1.27795			0.638975	−	0.769228i	$-0.279359\pi$
$307$	392.330			1.27795			0.638975	+	0.769228i	$0.279359\pi$
$308$		0			0
$309$	−591.139			−1.91307
$310$		0			0
$311$	223.375			0.718249			0.359124	−	0.933290i	$-0.383075\pi$
$311$	223.375			0.718249			0.359124	+	0.933290i	$0.383075\pi$
$312$		0			0
$313$		−	254.194i		−	0.812123i	−0.913846	−	0.406062i	$-0.866902\pi$
$313$		−	254.194i		−	0.812123i	0.913846	−	0.406062i	$-0.133098\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	40.8360			0.128820			0.0644101	−	0.997924i	$-0.479483\pi$
$317$	40.8360			0.128820			0.0644101	+	0.997924i	$0.479483\pi$
$318$		0			0
$319$		−	75.8308i		−	0.237714i
$320$		0			0
$321$	762.823			2.37640
$322$		0			0
$323$	25.8772	+	73.5899i	0.0801153	+	0.227832i
$324$		0			0
$325$		0			0
$326$		0			0
$327$			267.440i			0.817861i
$328$		0			0
$329$	288.542			0.877027
$330$		0			0
$331$			108.046i			0.326423i	0.986591	+	0.163211i	$0.0521852\pi$
$331$			108.046i			0.326423i	−0.986591	+	0.163211i	$0.947815\pi$
$332$		0			0
$333$	198.561			0.596280
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−185.597			−0.550732			−0.275366	−	0.961339i	$-0.588799\pi$
$337$	−185.597			−0.550732			−0.275366	+	0.961339i	$0.588799\pi$
$338$		0			0
$339$	−442.984			−1.30674
$340$		0			0
$341$			18.4379i			0.0540700i
$342$		0			0
$343$			611.036i			1.78145i
$344$		0			0
$345$		0			0
$346$		0			0
$347$		−	590.178i		−	1.70080i	−0.526136	−	0.850400i	$-0.676360\pi$
$347$		−	590.178i		−	1.70080i	0.526136	−	0.850400i	$-0.323640\pi$
$348$		0			0
$349$	71.3361			0.204401			0.102201	−	0.994764i	$-0.467412\pi$
$349$	71.3361			0.204401			0.102201	+	0.994764i	$0.467412\pi$
$350$		0			0
$351$	1018.92			2.90291
$352$		0			0
$353$			174.929i			0.495550i	0.968818	+	0.247775i	$0.0796993\pi$
$353$			174.929i			0.495550i	−0.968818	+	0.247775i	$0.920301\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−263.160			−0.737142
$358$		0			0
$359$	−339.112			−0.944600			−0.472300	−	0.881438i	$-0.656576\pi$
$359$	−339.112			−0.944600			−0.472300	+	0.881438i	$0.656576\pi$
$360$		0			0
$361$	281.548	−	225.946i	0.779911	−	0.625890i
$362$		0			0
$363$	525.821			1.44854
$364$		0			0
$365$		0			0
$366$		0			0
$367$		−	407.386i		−	1.11004i	−0.831836	−	0.555022i	$-0.812710\pi$
$367$		−	407.386i		−	1.11004i	0.831836	−	0.555022i	$-0.187290\pi$
$368$		0			0
$369$			419.911i			1.13797i
$370$		0			0
$371$			1184.50i			3.19273i
$372$		0			0
$373$	−369.020			−0.989330			−0.494665	−	0.869084i	$-0.664709\pi$
$373$	−369.020			−0.989330			−0.494665	+	0.869084i	$0.664709\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	328.277i		−	0.870762i
$378$		0			0
$379$		−	67.5519i		−	0.178237i	−0.996021	−	0.0891187i	$-0.971595\pi$
$379$		−	67.5519i		−	0.178237i	0.996021	−	0.0891187i	$-0.0284050\pi$
$380$		0			0
$381$	−681.161			−1.78782
$382$		0			0
$383$	−352.331			−0.919923			−0.459962	−	0.887939i	$-0.652137\pi$
$383$	−352.331			−0.919923			−0.459962	+	0.887939i	$0.652137\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		−	970.208i		−	2.50700i
$388$		0			0
$389$	628.198			1.61491			0.807453	−	0.589932i	$-0.200846\pi$
$389$	628.198			1.61491			0.807453	+	0.589932i	$0.200846\pi$
$390$		0			0
$391$	−144.524			−0.369626
$392$		0			0
$393$	−734.094			−1.86792
$394$		0			0
$395$		0			0
$396$		0			0
$397$		−	407.340i		−	1.02604i	−0.858375	−	0.513022i	$-0.828526\pi$
$397$		−	407.340i		−	1.02604i	0.858375	−	0.513022i	$-0.171474\pi$
$398$		0			0
$399$	403.996	+	1148.89i	1.01252	+	2.87941i
$400$		0			0
$401$		−	433.712i		−	1.08158i	−0.841159	−	0.540788i	$-0.818126\pi$
$401$		−	433.712i		−	1.08158i	0.841159	−	0.540788i	$-0.181874\pi$
$402$		0			0
$403$			79.8189i			0.198062i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−48.7537			−0.119788
$408$		0			0
$409$		−	744.375i		−	1.81999i	−0.414622	−	0.909994i	$-0.636086\pi$
$409$		−	744.375i		−	1.81999i	0.414622	−	0.909994i	$-0.363914\pi$
$410$		0			0
$411$			341.682i			0.831343i
$412$		0			0
$413$	403.206			0.976286
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−866.837			−2.07875
$418$		0			0
$419$	271.530			0.648042			0.324021	−	0.946050i	$-0.394965\pi$
$419$	271.530			0.648042			0.324021	+	0.946050i	$0.394965\pi$
$420$		0			0
$421$			819.454i			1.94645i	0.229860	+	0.973224i	$0.426173\pi$
$421$			819.454i			1.94645i	−0.229860	+	0.973224i	$0.573827\pi$
$422$		0			0
$423$			443.793i			1.04916i
$424$		0			0
$425$		0			0
$426$		0			0
$427$			915.406i			2.14381i
$428$		0			0
$429$	−481.746			−1.12295
$430$		0			0
$431$			723.199i			1.67796i	0.544166	+	0.838978i	$0.316846\pi$
$431$			723.199i			1.67796i	−0.544166	+	0.838978i	$0.683154\pi$
$432$		0			0
$433$	228.589			0.527920			0.263960	−	0.964534i	$-0.414971\pi$
$433$	228.589			0.527920			0.263960	+	0.964534i	$0.414971\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	221.869	+	630.952i	0.507709	+	1.44383i
$438$		0			0
$439$		−	207.651i		−	0.473009i	−0.971630	−	0.236504i	$-0.923998\pi$
$439$		−	207.651i		−	0.473009i	0.971630	−	0.236504i	$-0.0760018\pi$
$440$		0			0
$441$	−1857.26			−4.21147
$442$		0			0
$443$		−	573.475i		−	1.29453i	−0.762267	−	0.647263i	$-0.775914\pi$
$443$		−	573.475i		−	1.29453i	0.762267	−	0.647263i	$-0.224086\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	72.6753			0.162585
$448$		0			0
$449$		−	479.112i		−	1.06707i	−0.845779	−	0.533533i	$-0.820864\pi$
$449$		−	479.112i		−	1.06707i	0.845779	−	0.533533i	$-0.179136\pi$
$450$		0			0
$451$		−	103.103i		−	0.228609i
$452$		0			0
$453$			1127.63i			2.48924i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		−	88.4835i		−	0.193618i	−0.995303	−	0.0968090i	$-0.969136\pi$
$457$		−	88.4835i		−	0.193618i	0.995303	−	0.0968090i	$-0.0308636\pi$
$458$		0			0
$459$		−	210.197i		−	0.457946i
$460$		0			0
$461$	241.330			0.523493			0.261746	−	0.965137i	$-0.415702\pi$
$461$	241.330			0.523493			0.261746	+	0.965137i	$0.415702\pi$
$462$		0			0
$463$		−	661.506i		−	1.42874i	−0.699769	−	0.714370i	$-0.746714\pi$
$463$		−	661.506i		−	1.42874i	0.699769	−	0.714370i	$-0.253286\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			286.229i			0.612910i	0.951885	+	0.306455i	$0.0991429\pi$
$467$			286.229i			0.612910i	−0.951885	+	0.306455i	$0.900857\pi$
$468$		0			0
$469$		−	76.9211i		−	0.164011i
$470$		0			0
$471$		−	765.489i		−	1.62524i
$472$		0			0
$473$			238.220i			0.503636i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−1821.83			−3.81935
$478$		0			0
$479$	239.881			0.500796			0.250398	−	0.968143i	$-0.419438\pi$
$479$	239.881			0.500796			0.250398	+	0.968143i	$0.419438\pi$
$480$		0			0
$481$	−211.058			−0.438791
$482$		0			0
$483$	−2256.31			−4.67144
$484$		0			0
$485$		0			0
$486$		0			0
$487$	566.043			1.16231			0.581153	−	0.813795i	$-0.302602\pi$
$487$	566.043			1.16231			0.581153	+	0.813795i	$0.302602\pi$
$488$		0			0
$489$		−	909.364i		−	1.85964i
$490$		0			0
$491$	−390.830			−0.795988			−0.397994	−	0.917388i	$-0.630294\pi$
$491$	−390.830			−0.795988			−0.397994	+	0.917388i	$0.630294\pi$
$492$		0			0
$493$	−67.7215			−0.137366
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1440.01			2.89740
$498$		0			0
$499$	−163.998			−0.328652			−0.164326	−	0.986406i	$-0.552545\pi$
$499$	−163.998			−0.328652			−0.164326	+	0.986406i	$0.552545\pi$
$500$		0			0
$501$	−1224.18			−2.44348
$502$		0			0
$503$		−	35.1241i		−	0.0698291i	−0.999390	−	0.0349146i	$-0.988884\pi$
$503$		−	35.1241i		−	0.0698291i	0.999390	−	0.0349146i	$-0.0111159\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−1195.68			−2.35834
$508$		0			0
$509$		−	306.832i		−	0.602813i	−0.953496	−	0.301406i	$-0.902544\pi$
$509$		−	306.832i		−	0.602813i	0.953496	−	0.301406i	$-0.0974561\pi$
$510$		0			0
$511$	85.5014			0.167322
$512$		0			0
$513$	−917.665	+	322.689i	−1.78882	+	0.629023i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		−	108.966i		−	0.210767i
$518$		0			0
$519$	1531.52			2.95091
$520$		0			0
$521$			283.389i			0.543932i	0.962307	+	0.271966i	$0.0876739\pi$
$521$			283.389i			0.543932i	−0.962307	+	0.271966i	$0.912326\pi$
$522$		0			0
$523$	187.427			0.358368			0.179184	−	0.983816i	$-0.442654\pi$
$523$	187.427			0.358368			0.179184	+	0.983816i	$0.442654\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	16.4661			0.0312450
$528$		0			0
$529$	−710.132			−1.34240
$530$		0			0
$531$			620.153i			1.16790i
$532$		0			0
$533$		−	446.340i		−	0.837410i
$534$		0			0
$535$		0			0
$536$		0			0
$537$			906.976i			1.68897i
$538$		0			0
$539$	456.021			0.846050
$540$		0			0
$541$	282.159			0.521552			0.260776	−	0.965399i	$-0.416022\pi$
$541$	282.159			0.521552			0.260776	+	0.965399i	$0.416022\pi$
$542$		0			0
$543$			1806.19i			3.32632i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−342.502			−0.626146			−0.313073	−	0.949729i	$-0.601358\pi$
$547$	−342.502			−0.626146			−0.313073	+	0.949729i	$0.601358\pi$
$548$		0			0
$549$	−1407.94			−2.56456
$550$		0			0
$551$	103.964	+	295.654i	0.188683	+	0.536577i
$552$		0			0
$553$	−925.761			−1.67407
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	27.8687i		−	0.0500336i	−0.999687	−	0.0250168i	$-0.992036\pi$
$557$		−	27.8687i		−	0.0500336i	0.999687	−	0.0250168i	$-0.00796392\pi$
$558$		0			0
$559$			1031.27i			1.84485i
$560$		0			0
$561$			99.3811i			0.177150i
$562$		0			0
$563$	359.430			0.638420			0.319210	−	0.947684i	$-0.396583\pi$
$563$	359.430			0.638420			0.319210	+	0.947684i	$0.396583\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		−	1230.23i		−	2.16971i
$568$		0			0
$569$			137.757i			0.242103i	0.992646	+	0.121051i	$0.0386266\pi$
$569$			137.757i			0.242103i	−0.992646	+	0.121051i	$0.961373\pi$
$570$		0			0
$571$	383.100			0.670929			0.335464	−	0.942053i	$-0.391107\pi$
$571$	383.100			0.670929			0.335464	+	0.942053i	$0.391107\pi$
$572$		0			0
$573$	970.307			1.69338
$574$		0			0
$575$		0			0
$576$		0			0
$577$			655.282i			1.13567i	0.823142	+	0.567836i	$0.192219\pi$
$577$			655.282i			1.13567i	−0.823142	+	0.567836i	$0.807781\pi$
$578$		0			0
$579$	−1603.38			−2.76923
$580$		0			0
$581$	−1219.75			−2.09941
$582$		0			0
$583$	447.322			0.767277
$584$		0			0
$585$		0			0
$586$		0			0
$587$			229.615i			0.391167i	0.980687	+	0.195583i	$0.0626600\pi$
$587$			229.615i			0.391167i	−0.980687	+	0.195583i	$0.937340\pi$
$588$		0			0
$589$	−25.2783	−	71.8867i	−0.0429174	−	0.122049i
$590$		0			0
$591$		−	1615.60i		−	2.73367i
$592$		0			0
$593$			1014.80i			1.71129i	0.517562	+	0.855645i	$0.326840\pi$
$593$			1014.80i			1.71129i	−0.517562	+	0.855645i	$0.673160\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−468.819			−0.785292
$598$		0			0
$599$		−	848.378i		−	1.41632i	−0.706050	−	0.708162i	$-0.749525\pi$
$599$		−	848.378i		−	1.41632i	0.706050	−	0.708162i	$-0.250475\pi$
$600$		0			0
$601$			712.920i			1.18622i	0.805121	+	0.593111i	$0.202101\pi$
$601$			712.920i			1.18622i	−0.805121	+	0.593111i	$0.797899\pi$
$602$		0			0
$603$	118.309			0.196200
$604$		0			0
$605$		0			0
$606$		0			0
$607$	291.033			0.479462			0.239731	−	0.970839i	$-0.422941\pi$
$607$	291.033			0.479462			0.239731	+	0.970839i	$0.422941\pi$
$608$		0			0
$609$	−1057.27			−1.73607
$610$		0			0
$611$		−	471.724i		−	0.772053i
$612$		0			0
$613$			872.135i			1.42273i	0.702822	+	0.711366i	$0.251923\pi$
$613$			872.135i			1.42273i	−0.702822	+	0.711366i	$0.748077\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	587.897i		−	0.952832i	−0.879220	−	0.476416i	$-0.841936\pi$
$617$		−	587.897i		−	0.952832i	0.879220	−	0.476416i	$-0.158064\pi$
$618$		0			0
$619$	−312.874			−0.505450			−0.252725	−	0.967538i	$-0.581327\pi$
$619$	−312.874			−0.505450			−0.252725	+	0.967538i	$0.581327\pi$
$620$		0			0
$621$		−	1802.21i		−	2.90211i
$622$		0			0
$623$	1500.98			2.40928
$624$		0			0
$625$		0			0
$626$		0			0
$627$	433.872	−	152.567i	0.691980	−	0.243329i
$628$		0			0
$629$			43.5400i			0.0692209i
$630$		0			0
$631$	−445.242			−0.705614			−0.352807	−	0.935696i	$-0.614773\pi$
$631$	−445.242			−0.705614			−0.352807	+	0.935696i	$0.614773\pi$
$632$		0			0
$633$		−	823.299i		−	1.30063i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	1974.15			3.09914
$638$		0			0
$639$			2214.81i			3.46606i
$640$		0			0
$641$		−	111.139i		−	0.173384i	−0.996235	−	0.0866920i	$-0.972370\pi$
$641$		−	111.139i		−	0.173384i	0.996235	−	0.0866920i	$-0.0276296\pi$
$642$		0			0
$643$		−	434.676i		−	0.676012i	−0.941144	−	0.338006i	$-0.890248\pi$
$643$		−	434.676i		−	0.676012i	0.941144	−	0.338006i	$-0.109752\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	902.589i		−	1.39504i	−0.716567	−	0.697518i	$-0.754288\pi$
$647$		−	902.589i		−	1.39504i	0.716567	−	0.697518i	$-0.245712\pi$
$648$		0			0
$649$		−	152.269i		−	0.234621i
$650$		0			0
$651$	257.069			0.394884
$652$		0			0
$653$			190.902i			0.292346i	0.989259	+	0.146173i	$0.0466957\pi$
$653$			190.902i			0.292346i	−0.989259	+	0.146173i	$0.953304\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$			131.506i			0.200161i
$658$		0			0
$659$			412.242i			0.625558i	0.949826	+	0.312779i	$0.101260\pi$
$659$			412.242i			0.625558i	−0.949826	+	0.312779i	$0.898740\pi$
$660$		0			0
$661$			384.455i			0.581626i	0.956780	+	0.290813i	$0.0939257\pi$
$661$			384.455i			0.581626i	−0.956780	+	0.290813i	$0.906074\pi$
$662$		0			0
$663$			430.228i			0.648912i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−580.637			−0.870520
$668$		0			0
$669$	−1647.76			−2.46301
$670$		0			0
$671$	345.699			0.515200
$672$		0			0
$673$	1051.54			1.56247			0.781235	−	0.624237i	$-0.214590\pi$
$673$	1051.54			1.56247			0.781235	+	0.624237i	$0.214590\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	954.223			1.40949			0.704744	−	0.709462i	$-0.251062\pi$
$677$	954.223			1.40949			0.704744	+	0.709462i	$0.251062\pi$
$678$		0			0
$679$		−	1231.98i		−	1.81440i
$680$		0			0
$681$	1050.09			1.54198
$682$		0			0
$683$	−564.386			−0.826334			−0.413167	−	0.910655i	$-0.635577\pi$
$683$	−564.386			−0.826334			−0.413167	+	0.910655i	$0.635577\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	1326.70			1.93116
$688$		0			0
$689$	1936.49			2.81058
$690$		0			0
$691$	−566.388			−0.819664			−0.409832	−	0.912161i	$-0.634413\pi$
$691$	−566.388			−0.819664			−0.409832	+	0.912161i	$0.634413\pi$
$692$		0			0
$693$			1047.86i			1.51206i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−92.0770			−0.132105
$698$		0			0
$699$		−	2383.57i		−	3.40998i
$700$		0			0
$701$	534.434			0.762388			0.381194	−	0.924495i	$-0.375513\pi$
$701$	534.434			0.762388			0.381194	+	0.924495i	$0.375513\pi$
$702$		0			0
$703$	190.084	−	66.8414i	0.270390	−	0.0950802i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	1831.84i		−	2.59100i
$708$		0			0
$709$	−574.352			−0.810087			−0.405044	−	0.914297i	$-0.632744\pi$
$709$	−574.352			−0.810087			−0.405044	+	0.914297i	$0.632744\pi$
$710$		0			0
$711$		−	1423.87i		−	2.00263i
$712$		0			0
$713$	141.179			0.198007
$714$		0			0
$715$		0			0
$716$		0			0
$717$	754.095			1.05174
$718$		0			0
$719$	−334.794			−0.465638			−0.232819	−	0.972520i	$-0.574795\pi$
$719$	−334.794			−0.465638			−0.232819	+	0.972520i	$0.574795\pi$
$720$		0			0
$721$		−	1366.72i		−	1.89560i
$722$		0			0
$723$			34.9287i			0.0483108i
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	269.044i		−	0.370075i	−0.982731	−	0.185037i	$-0.940759\pi$
$727$		−	269.044i		−	0.370075i	0.982731	−	0.185037i	$-0.0592407\pi$
$728$		0			0
$729$	−533.968			−0.732467
$730$		0			0
$731$	212.744			0.291032
$732$		0			0
$733$			677.757i			0.924634i	0.886715	+	0.462317i	$0.152982\pi$
$733$			677.757i			0.924634i	−0.886715	+	0.462317i	$0.847018\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−29.0489			−0.0394151
$738$		0			0
$739$	848.152			1.14770			0.573851	−	0.818959i	$-0.305449\pi$
$739$	848.152			1.14770			0.573851	+	0.818959i	$0.305449\pi$
$740$		0			0
$741$	1878.26	−	660.475i	2.53477	−	0.891329i
$742$		0			0
$743$	−1211.81			−1.63097			−0.815485	−	0.578778i	$-0.803530\pi$
$743$	−1211.81			−1.63097			−0.815485	+	0.578778i	$0.803530\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		−	1876.05i		−	2.51144i
$748$		0			0
$749$			1763.66i			2.35469i
$750$		0			0
$751$			146.559i			0.195152i	0.995228	+	0.0975758i	$0.0311088\pi$
$751$			146.559i			0.195152i	−0.995228	+	0.0975758i	$0.968891\pi$
$752$		0			0
$753$	−949.773			−1.26132
$754$		0			0
$755$		0			0
$756$		0			0
$757$			1421.26i			1.87748i	0.344621	+	0.938742i	$0.388008\pi$
$757$			1421.26i			1.87748i	−0.344621	+	0.938742i	$0.611992\pi$
$758$		0			0
$759$			852.084i			1.12264i
$760$		0			0
$761$	−879.279			−1.15543			−0.577713	−	0.816240i	$-0.696055\pi$
$761$	−879.279			−1.15543			−0.577713	+	0.816240i	$0.696055\pi$
$762$		0			0
$763$	−618.327			−0.810390
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	659.184i		−	0.859431i
$768$		0			0
$769$	−412.091			−0.535879			−0.267940	−	0.963436i	$-0.586343\pi$
$769$	−412.091			−0.535879			−0.267940	+	0.963436i	$0.586343\pi$
$770$		0			0
$771$	78.7925			0.102195
$772$		0			0
$773$	526.855			0.681572			0.340786	−	0.940141i	$-0.389307\pi$
$773$	526.855			0.681572			0.340786	+	0.940141i	$0.389307\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$			679.747i			0.874835i
$778$		0			0
$779$	141.354	+	401.984i	0.181456	+	0.516025i
$780$		0			0
$781$		−	543.813i		−	0.696304i
$782$		0			0
$783$		−	844.486i		−	1.07853i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−306.426			−0.389359			−0.194680	−	0.980867i	$-0.562367\pi$
$787$	−306.426			−0.389359			−0.194680	+	0.980867i	$0.562367\pi$
$788$		0			0
$789$		−	2316.66i		−	2.93620i
$790$		0			0
$791$		−	1024.19i		−	1.29480i
$792$		0			0
$793$	1496.56			1.88721
$794$		0			0
$795$		0			0
$796$		0			0
$797$	797.902			1.00113			0.500566	−	0.865698i	$-0.333125\pi$
$797$	797.902			1.00113			0.500566	+	0.865698i	$0.333125\pi$
$798$		0			0
$799$	−97.3137			−0.121794
$800$		0			0
$801$			2308.59i			2.88214i
$802$		0			0
$803$		−	32.2892i		−	0.0402107i
$804$		0			0
$805$		0			0
$806$		0			0
$807$			1336.83i			1.65654i
$808$		0			0
$809$	−432.577			−0.534706			−0.267353	−	0.963599i	$-0.586149\pi$
$809$	−432.577			−0.534706			−0.267353	+	0.963599i	$0.586149\pi$
$810$		0			0
$811$			356.906i			0.440081i	0.975491	+	0.220041i	$0.0706190\pi$
$811$			356.906i			0.440081i	−0.975491	+	0.220041i	$0.929381\pi$
$812$		0			0
$813$	−565.349			−0.695387
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−326.599	−	928.786i	−0.399755	−	1.13683i
$818$		0			0
$819$			4536.25i			5.53877i
$820$		0			0
$821$	72.1659			0.0879000			0.0439500	−	0.999034i	$-0.486006\pi$
$821$	72.1659			0.0879000			0.0439500	+	0.999034i	$0.486006\pi$
$822$		0			0
$823$			1322.13i			1.60647i	0.595662	+	0.803236i	$0.296890\pi$
$823$			1322.13i			1.60647i	−0.595662	+	0.803236i	$0.703110\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	799.247			0.966441			0.483220	−	0.875499i	$-0.339467\pi$
$827$	799.247			0.966441			0.483220	+	0.875499i	$0.339467\pi$
$828$		0			0
$829$		−	1131.58i		−	1.36499i	−0.730890	−	0.682496i	$-0.760895\pi$
$829$		−	1131.58i		−	1.36499i	0.730890	−	0.682496i	$-0.239105\pi$
$830$		0			0
$831$		−	115.736i		−	0.139273i
$832$		0			0
$833$		−	407.254i		−	0.488901i
$834$		0			0
$835$		0			0
$836$		0			0
$837$			205.332i			0.245319i
$838$		0			0
$839$		−	770.869i		−	0.918795i	−0.888231	−	0.459398i	$-0.848065\pi$
$839$		−	770.869i		−	0.918795i	0.888231	−	0.459398i	$-0.151935\pi$
$840$		0			0
$841$	568.923			0.676484
$842$		0			0
$843$			1177.27i			1.39653i
$844$		0			0
$845$		0			0
$846$		0			0
$847$			1215.71i			1.43531i
$848$		0			0
$849$			277.829i			0.327243i
$850$		0			0
$851$			373.307i			0.438669i
$852$		0			0
$853$			426.548i			0.500056i	0.968239	+	0.250028i	$0.0804398\pi$
$853$			426.548i			0.500056i	−0.968239	+	0.250028i	$0.919560\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−1400.33			−1.63400			−0.816998	−	0.576641i	$-0.804363\pi$
$857$	−1400.33			−1.63400			−0.816998	+	0.576641i	$0.804363\pi$
$858$		0			0
$859$	870.240			1.01308			0.506542	−	0.862215i	$-0.330923\pi$
$859$	870.240			1.01308			0.506542	+	0.862215i	$0.330923\pi$
$860$		0			0
$861$	−1437.51			−1.66958
$862$		0			0
$863$	−929.692			−1.07728			−0.538640	−	0.842536i	$-0.681062\pi$
$863$	−929.692			−1.07728			−0.538640	+	0.842536i	$0.681062\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−1432.92			−1.65274
$868$		0			0
$869$			349.610i			0.402312i
$870$		0			0
$871$	−125.755			−0.144380
$872$		0			0
$873$	1894.85			2.17051
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1223.42			−1.39501			−0.697505	−	0.716580i	$-0.745706\pi$
$877$	−1223.42			−1.39501			−0.697505	+	0.716580i	$0.745706\pi$
$878$		0			0
$879$	−1547.29			−1.76028
$880$		0			0
$881$	−146.489			−0.166276			−0.0831378	−	0.996538i	$-0.526494\pi$
$881$	−146.489			−0.166276			−0.0831378	+	0.996538i	$0.526494\pi$
$882$		0			0
$883$			794.391i			0.899650i	0.893117	+	0.449825i	$0.148514\pi$
$883$			794.391i			0.899650i	−0.893117	+	0.449825i	$0.851486\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	944.311			1.06461			0.532306	−	0.846552i	$-0.321326\pi$
$887$	944.311			1.06461			0.532306	+	0.846552i	$0.321326\pi$
$888$		0			0
$889$		−	1574.86i		−	1.77149i
$890$		0			0
$891$	−464.590			−0.521425
$892$		0			0
$893$	149.393	+	424.846i	0.167294	+	0.475751i
$894$		0			0
$895$		0			0
$896$		0			0
$897$			3688.74i			4.11230i
$898$		0			0
$899$	66.1541			0.0735864
$900$		0			0
$901$		−	399.486i		−	0.443381i
$902$		0			0
$903$	3321.37			3.67815
$904$		0			0
$905$		0			0
$906$		0			0
$907$	449.939			0.496074			0.248037	−	0.968751i	$-0.420215\pi$
$907$	449.939			0.496074			0.248037	+	0.968751i	$0.420215\pi$
$908$		0			0
$909$	2817.47			3.09952
$910$		0			0
$911$		−	1423.86i		−	1.56297i	−0.623926	−	0.781484i	$-0.714463\pi$
$911$		−	1423.86i		−	1.56297i	0.623926	−	0.781484i	$-0.285537\pi$
$912$		0			0
$913$			460.635i			0.504529i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	1697.24i		−	1.85086i
$918$		0			0
$919$	−441.636			−0.480562			−0.240281	−	0.970703i	$-0.577240\pi$
$919$	−441.636			−0.480562			−0.240281	+	0.970703i	$0.577240\pi$
$920$		0			0
$921$	−2065.74			−2.24293
$922$		0			0
$923$		−	2354.21i		−	2.55061i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	2102.10			2.26763
$928$		0			0
$929$	109.177			0.117521			0.0587605	−	0.998272i	$-0.481285\pi$
$929$	109.177			0.117521			0.0587605	+	0.998272i	$0.481285\pi$
$930$		0			0
$931$	−1777.96	+	625.206i	−1.90974	+	0.671542i
$932$		0			0
$933$	−1176.14			−1.26060
$934$		0			0
$935$		0			0
$936$		0			0
$937$			1319.18i			1.40787i	0.710262	+	0.703937i	$0.248576\pi$
$937$			1319.18i			1.40787i	−0.710262	+	0.703937i	$0.751424\pi$
$938$		0			0
$939$			1338.41i			1.42536i
$940$		0			0
$941$		−	459.707i		−	0.488530i	−0.969708	−	0.244265i	$-0.921453\pi$
$941$		−	459.707i		−	0.488530i	0.969708	−	0.244265i	$-0.0785467\pi$
$942$		0			0
$943$	−789.459			−0.837178
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	1310.81i		−	1.38418i	−0.721813	−	0.692088i	$-0.756691\pi$
$947$		−	1310.81i		−	1.38418i	0.721813	−	0.692088i	$-0.243309\pi$
$948$		0			0
$949$		−	139.782i		−	0.147295i
$950$		0			0
$951$	−215.014			−0.226093
$952$		0			0
$953$	1302.16			1.36638			0.683192	−	0.730238i	$-0.260591\pi$
$953$	1302.16			1.36638			0.683192	+	0.730238i	$0.260591\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$			399.273i			0.417213i
$958$		0			0
$959$	−789.975			−0.823749
$960$		0			0
$961$	944.915			0.983262
$962$		0			0
$963$	−2712.61			−2.81683
$964$		0			0
$965$		0			0
$966$		0			0
$967$			167.641i			0.173362i	0.996236	+	0.0866809i	$0.0276261\pi$
$967$			167.641i			0.173362i	−0.996236	+	0.0866809i	$0.972374\pi$
$968$		0			0
$969$	−136.252	−	387.474i	−0.140611	−	0.399870i
$970$		0			0
$971$			866.411i			0.892288i	0.894961	+	0.446144i	$0.147203\pi$
$971$			866.411i			0.892288i	−0.894961	+	0.446144i	$0.852797\pi$
$972$		0			0
$973$		−	2004.14i		−	2.05976i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1247.03			−1.27639			−0.638195	−	0.769874i	$-0.720319\pi$
$977$	−1247.03			−1.27639			−0.638195	+	0.769874i	$0.720319\pi$
$978$		0			0
$979$		−	566.839i		−	0.578998i
$980$		0			0
$981$		−	951.021i		−	0.969440i
$982$		0			0
$983$	−657.563			−0.668934			−0.334467	−	0.942407i	$-0.608556\pi$
$983$	−657.563			−0.668934			−0.334467	+	0.942407i	$0.608556\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−1519.26			−1.53927
$988$		0			0
$989$	1824.05			1.84434
$990$		0			0
$991$		−	1045.43i		−	1.05492i	−0.849579	−	0.527461i	$-0.823144\pi$
$991$		−	1045.43i		−	1.05492i	0.849579	−	0.527461i	$-0.176856\pi$
$992$		0			0
$993$		−	568.895i		−	0.572906i
$994$		0			0
$995$		0			0
$996$		0			0
$997$			1131.50i			1.13491i	0.823405	+	0.567455i	$0.192072\pi$
$997$			1131.50i			1.13491i	−0.823405	+	0.567455i	$0.807928\pi$
$998$		0			0
$999$	−542.943			−0.543486

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1900.3.g.d.949.2		28
5.2	odd	4		1900.3.e.g.1101.14	yes	14
5.3	odd	4		1900.3.e.h.1101.1	yes	14
5.4	even	2	inner	1900.3.g.d.949.27		28
19.18	odd	2	inner	1900.3.g.d.949.28		28
95.18	even	4		1900.3.e.h.1101.14	yes	14
95.37	even	4		1900.3.e.g.1101.1	✓	14
95.94	odd	2	inner	1900.3.g.d.949.1		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1900.3.e.g.1101.1	✓	14	95.37	even	4
1900.3.e.g.1101.14	yes	14	5.2	odd	4
1900.3.e.h.1101.1	yes	14	5.3	odd	4
1900.3.e.h.1101.14	yes	14	95.18	even	4
1900.3.g.d.949.1		28	95.94	odd	2	inner
1900.3.g.d.949.2		28	1.1	even	1	trivial
1900.3.g.d.949.27		28	5.4	even	2	inner
1900.3.g.d.949.28		28	19.18	odd	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)

\(f(q)\)	\(=\)	\(q-5.26531 q^{3} -12.1735i q^{7} +18.7235 q^{9} +O(q^{10})\)	\(q-5.26531 q^{3} -12.1735i q^{7} +18.7235 q^{9} -4.59727 q^{11} -19.9019 q^{13} +4.10564i q^{17} +(17.9241 - 6.30286i) q^{19} +64.0972i q^{21} +35.2013i q^{23} -51.1972 q^{27} +16.4948i q^{29} -4.01062i q^{31} +24.2060 q^{33} +10.6049 q^{37} +104.790 q^{39} +22.4270i q^{41} -51.8177i q^{43} +23.7025i q^{47} -99.1940 q^{49} -21.6174i q^{51} -97.3018 q^{53} +(-94.3760 + 33.1865i) q^{57} +33.1216i q^{59} -75.1967 q^{61} -227.930i q^{63} +6.31874 q^{67} -185.346i q^{69} +118.291i q^{71} +7.02357i q^{73} +55.9648i q^{77} -76.0473i q^{79} +101.058 q^{81} -100.198i q^{83} -86.8500i q^{87} +123.299i q^{89} +242.276i q^{91} +21.1171i q^{93} +101.202 q^{97} -86.0769 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 104 q^{9}+O(q^{10}) \) 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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