LMFDB - Embedded newform 9450.2.a.bb.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9450,2,Mod(1,9450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9450, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("9450.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9450 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9450.a (trivial)

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:	yes
Analytic conductor:	$75.4586299101$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1890)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	9450.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{7} -1.00000 q^{8} +O(q^{10})$

$q-1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{7} -1.00000 q^{8} -5.00000 q^{11} +5.00000 q^{13} -1.00000 q^{14} +1.00000 q^{16} +3.00000 q^{17} -6.00000 q^{19} +5.00000 q^{22} +1.00000 q^{23} -5.00000 q^{26} +1.00000 q^{28} -1.00000 q^{29} +1.00000 q^{31} -1.00000 q^{32} -3.00000 q^{34} +10.0000 q^{37} +6.00000 q^{38} -4.00000 q^{41} -5.00000 q^{43} -5.00000 q^{44} -1.00000 q^{46} -11.0000 q^{47} +1.00000 q^{49} +5.00000 q^{52} -2.00000 q^{53} -1.00000 q^{56} +1.00000 q^{58} -4.00000 q^{59} -1.00000 q^{62} +1.00000 q^{64} -12.0000 q^{67} +3.00000 q^{68} +12.0000 q^{71} +12.0000 q^{73} -10.0000 q^{74} -6.00000 q^{76} -5.00000 q^{77} +1.00000 q^{79} +4.00000 q^{82} -16.0000 q^{83} +5.00000 q^{86} +5.00000 q^{88} +16.0000 q^{89} +5.00000 q^{91} +1.00000 q^{92} +11.0000 q^{94} +4.00000 q^{97} -1.00000 q^{98} +O(q^{100})$

Display 100 coefficients 10 coefficients

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0	0
$3$	0	0
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	0	0
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	0	0
$10$	0	0
$11$	−5.00000	−1.50756	−0.753778	−	0.657129i	$-0.771771\pi$
$11$	−5.00000	−1.50756	−0.753778	+	0.657129i	$0.771771\pi$
$12$	0	0
$13$	5.00000	1.38675	0.693375	−	0.720577i	$-0.256123\pi$
$13$	5.00000	1.38675	0.693375	+	0.720577i	$0.256123\pi$
$14$	−1.00000	−0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	3.00000	0.727607	0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000	0.727607	0.363803	+	0.931476i	$0.381478\pi$
$18$	0	0
$19$	−6.00000	−1.37649	−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−6.00000	−1.37649	−0.688247	+	0.725476i	$0.741620\pi$
$20$	0	0
$21$	0	0
$22$	5.00000	1.06600
$23$	1.00000	0.208514	0.104257	−	0.994550i	$-0.466753\pi$
$23$	1.00000	0.208514	0.104257	+	0.994550i	$0.466753\pi$
$24$	0	0
$25$	0	0
$26$	−5.00000	−0.980581
$27$	0	0
$28$	1.00000	0.188982
$29$	−1.00000	−0.185695	−0.0928477	−	0.995680i	$-0.529597\pi$
$29$	−1.00000	−0.185695	−0.0928477	+	0.995680i	$0.529597\pi$
$30$	0	0
$31$	1.00000	0.179605	0.0898027	−	0.995960i	$-0.471376\pi$
$31$	1.00000	0.179605	0.0898027	+	0.995960i	$0.471376\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−3.00000	−0.514496
$35$	0	0
$36$	0	0
$37$	10.0000	1.64399	0.821995	−	0.569495i	$-0.192861\pi$
$37$	10.0000	1.64399	0.821995	+	0.569495i	$0.192861\pi$
$38$	6.00000	0.973329
$39$	0	0
$40$	0	0
$41$	−4.00000	−0.624695	−0.312348	−	0.949968i	$-0.601115\pi$
$41$	−4.00000	−0.624695	−0.312348	+	0.949968i	$0.601115\pi$
$42$	0	0
$43$	−5.00000	−0.762493	−0.381246	−	0.924473i	$-0.624505\pi$
$43$	−5.00000	−0.762493	−0.381246	+	0.924473i	$0.624505\pi$
$44$	−5.00000	−0.753778
$45$	0	0
$46$	−1.00000	−0.147442
$47$	−11.0000	−1.60451	−0.802257	−	0.596978i	$-0.796368\pi$
$47$	−11.0000	−1.60451	−0.802257	+	0.596978i	$0.796368\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	0	0
$51$	0	0
$52$	5.00000	0.693375
$53$	−2.00000	−0.274721	−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000	−0.274721	−0.137361	+	0.990521i	$0.543862\pi$
$54$	0	0
$55$	0	0
$56$	−1.00000	−0.133631
$57$	0	0
$58$	1.00000	0.131306
$59$	−4.00000	−0.520756	−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000	−0.520756	−0.260378	+	0.965507i	$0.583847\pi$
$60$	0	0
$61$	0	0		−	1.00000i	$-0.5\pi$
$61$	0	0			1.00000i	$0.5\pi$
$62$	−1.00000	−0.127000
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	−12.0000	−1.46603	−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000	−1.46603	−0.733017	+	0.680211i	$0.761888\pi$
$68$	3.00000	0.363803
$69$	0	0
$70$	0	0
$71$	12.0000	1.42414	0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000	1.42414	0.712069	+	0.702109i	$0.247758\pi$
$72$	0	0
$73$	12.0000	1.40449	0.702247	−	0.711934i	$-0.252180\pi$
$73$	12.0000	1.40449	0.702247	+	0.711934i	$0.252180\pi$
$74$	−10.0000	−1.16248
$75$	0	0
$76$	−6.00000	−0.688247
$77$	−5.00000	−0.569803
$78$	0	0
$79$	1.00000	0.112509	0.0562544	−	0.998416i	$-0.482084\pi$
$79$	1.00000	0.112509	0.0562544	+	0.998416i	$0.482084\pi$
$80$	0	0
$81$	0	0
$82$	4.00000	0.441726
$83$	−16.0000	−1.75623	−0.878114	−	0.478451i	$-0.841198\pi$
$83$	−16.0000	−1.75623	−0.878114	+	0.478451i	$0.841198\pi$
$84$	0	0
$85$	0	0
$86$	5.00000	0.539164
$87$	0	0
$88$	5.00000	0.533002
$89$	16.0000	1.69600	0.847998	−	0.529999i	$-0.177808\pi$
$89$	16.0000	1.69600	0.847998	+	0.529999i	$0.177808\pi$
$90$	0	0
$91$	5.00000	0.524142
$92$	1.00000	0.104257
$93$	0	0
$94$	11.0000	1.13456
$95$	0	0
$96$	0	0
$97$	4.00000	0.406138	0.203069	−	0.979164i	$-0.434908\pi$
$97$	4.00000	0.406138	0.203069	+	0.979164i	$0.434908\pi$
$98$	−1.00000	−0.101015
$99$	0	0
$100$	0	0
$101$	−9.00000	−0.895533	−0.447767	−	0.894150i	$-0.647781\pi$
$101$	−9.00000	−0.895533	−0.447767	+	0.894150i	$0.647781\pi$
$102$	0	0
$103$	16.0000	1.57653	0.788263	−	0.615338i	$-0.210980\pi$
$103$	16.0000	1.57653	0.788263	+	0.615338i	$0.210980\pi$
$104$	−5.00000	−0.490290
$105$	0	0
$106$	2.00000	0.194257
$107$	8.00000	0.773389	0.386695	−	0.922208i	$-0.373617\pi$
$107$	8.00000	0.773389	0.386695	+	0.922208i	$0.373617\pi$
$108$	0	0
$109$	−18.0000	−1.72409	−0.862044	−	0.506834i	$-0.830816\pi$
$109$	−18.0000	−1.72409	−0.862044	+	0.506834i	$0.830816\pi$
$110$	0	0
$111$	0	0
$112$	1.00000	0.0944911
$113$	−3.00000	−0.282216	−0.141108	−	0.989994i	$-0.545067\pi$
$113$	−3.00000	−0.282216	−0.141108	+	0.989994i	$0.545067\pi$
$114$	0	0
$115$	0	0
$116$	−1.00000	−0.0928477
$117$	0	0
$118$	4.00000	0.368230
$119$	3.00000	0.275010
$120$	0	0
$121$	14.0000	1.27273
$122$	0	0
$123$	0	0
$124$	1.00000	0.0898027
$125$	0	0
$126$	0	0
$127$	−10.0000	−0.887357	−0.443678	−	0.896186i	$-0.646327\pi$
$127$	−10.0000	−0.887357	−0.443678	+	0.896186i	$0.646327\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	0	0
$131$	−13.0000	−1.13582	−0.567908	−	0.823092i	$-0.692247\pi$
$131$	−13.0000	−1.13582	−0.567908	+	0.823092i	$0.692247\pi$
$132$	0	0
$133$	−6.00000	−0.520266
$134$	12.0000	1.03664
$135$	0	0
$136$	−3.00000	−0.257248
$137$	−6.00000	−0.512615	−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000	−0.512615	−0.256307	+	0.966595i	$0.582506\pi$
$138$	0	0
$139$	−10.0000	−0.848189	−0.424094	−	0.905618i	$-0.639408\pi$
$139$	−10.0000	−0.848189	−0.424094	+	0.905618i	$0.639408\pi$
$140$	0	0
$141$	0	0
$142$	−12.0000	−1.00702
$143$	−25.0000	−2.09061
$144$	0	0
$145$	0	0
$146$	−12.0000	−0.993127
$147$	0	0
$148$	10.0000	0.821995
$149$	−9.00000	−0.737309	−0.368654	−	0.929567i	$-0.620181\pi$
$149$	−9.00000	−0.737309	−0.368654	+	0.929567i	$0.620181\pi$
$150$	0	0
$151$	−15.0000	−1.22068	−0.610341	−	0.792139i	$-0.708968\pi$
$151$	−15.0000	−1.22068	−0.610341	+	0.792139i	$0.708968\pi$
$152$	6.00000	0.486664
$153$	0	0
$154$	5.00000	0.402911
$155$	0	0
$156$	0	0
$157$	7.00000	0.558661	0.279330	−	0.960195i	$-0.409888\pi$
$157$	7.00000	0.558661	0.279330	+	0.960195i	$0.409888\pi$
$158$	−1.00000	−0.0795557
$159$	0	0
$160$	0	0
$161$	1.00000	0.0788110
$162$	0	0
$163$	−1.00000	−0.0783260	−0.0391630	−	0.999233i	$-0.512469\pi$
$163$	−1.00000	−0.0783260	−0.0391630	+	0.999233i	$0.512469\pi$
$164$	−4.00000	−0.312348
$165$	0	0
$166$	16.0000	1.24184
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	0	0
$169$	12.0000	0.923077
$170$	0	0
$171$	0	0
$172$	−5.00000	−0.381246
$173$	18.0000	1.36851	0.684257	−	0.729241i	$-0.260127\pi$
$173$	18.0000	1.36851	0.684257	+	0.729241i	$0.260127\pi$
$174$	0	0
$175$	0	0
$176$	−5.00000	−0.376889
$177$	0	0
$178$	−16.0000	−1.19925
$179$	4.00000	0.298974	0.149487	−	0.988764i	$-0.452238\pi$
$179$	4.00000	0.298974	0.149487	+	0.988764i	$0.452238\pi$
$180$	0	0
$181$	−12.0000	−0.891953	−0.445976	−	0.895045i	$-0.647144\pi$
$181$	−12.0000	−0.891953	−0.445976	+	0.895045i	$0.647144\pi$
$182$	−5.00000	−0.370625
$183$	0	0
$184$	−1.00000	−0.0737210
$185$	0	0
$186$	0	0
$187$	−15.0000	−1.09691
$188$	−11.0000	−0.802257
$189$	0	0
$190$	0	0
$191$	12.0000	0.868290	0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000	0.868290	0.434145	+	0.900843i	$0.357051\pi$
$192$	0	0
$193$	20.0000	1.43963	0.719816	−	0.694165i	$-0.244226\pi$
$193$	20.0000	1.43963	0.719816	+	0.694165i	$0.244226\pi$
$194$	−4.00000	−0.287183
$195$	0	0
$196$	1.00000	0.0714286
$197$	−10.0000	−0.712470	−0.356235	−	0.934396i	$-0.615940\pi$
$197$	−10.0000	−0.712470	−0.356235	+	0.934396i	$0.615940\pi$
$198$	0	0
$199$	−3.00000	−0.212664	−0.106332	−	0.994331i	$-0.533911\pi$
$199$	−3.00000	−0.212664	−0.106332	+	0.994331i	$0.533911\pi$
$200$	0	0
$201$	0	0
$202$	9.00000	0.633238
$203$	−1.00000	−0.0701862
$204$	0	0
$205$	0	0
$206$	−16.0000	−1.11477
$207$	0	0
$208$	5.00000	0.346688
$209$	30.0000	2.07514
$210$	0	0
$211$	−22.0000	−1.51454	−0.757271	−	0.653101i	$-0.773468\pi$
$211$	−22.0000	−1.51454	−0.757271	+	0.653101i	$0.773468\pi$
$212$	−2.00000	−0.137361
$213$	0	0
$214$	−8.00000	−0.546869
$215$	0	0
$216$	0	0
$217$	1.00000	0.0678844
$218$	18.0000	1.21911
$219$	0	0
$220$	0	0
$221$	15.0000	1.00901
$222$	0	0
$223$	0	0		−	1.00000i	$-0.5\pi$
$223$	0	0			1.00000i	$0.5\pi$
$224$	−1.00000	−0.0668153
$225$	0	0
$226$	3.00000	0.199557
$227$	−16.0000	−1.06196	−0.530979	−	0.847385i	$-0.678176\pi$
$227$	−16.0000	−1.06196	−0.530979	+	0.847385i	$0.678176\pi$
$228$	0	0
$229$	8.00000	0.528655	0.264327	−	0.964433i	$-0.414850\pi$
$229$	8.00000	0.528655	0.264327	+	0.964433i	$0.414850\pi$
$230$	0	0
$231$	0	0
$232$	1.00000	0.0656532
$233$	6.00000	0.393073	0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000	0.393073	0.196537	+	0.980497i	$0.437031\pi$
$234$	0	0
$235$	0	0
$236$	−4.00000	−0.260378
$237$	0	0
$238$	−3.00000	−0.194461
$239$	24.0000	1.55243	0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000	1.55243	0.776215	+	0.630468i	$0.217137\pi$
$240$	0	0
$241$	19.0000	1.22390	0.611949	−	0.790897i	$-0.290386\pi$
$241$	19.0000	1.22390	0.611949	+	0.790897i	$0.290386\pi$
$242$	−14.0000	−0.899954
$243$	0	0
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−30.0000	−1.90885
$248$	−1.00000	−0.0635001
$249$	0	0
$250$	0	0
$251$	−19.0000	−1.19927	−0.599635	−	0.800274i	$-0.704687\pi$
$251$	−19.0000	−1.19927	−0.599635	+	0.800274i	$0.704687\pi$
$252$	0	0
$253$	−5.00000	−0.314347
$254$	10.0000	0.627456
$255$	0	0
$256$	1.00000	0.0625000
$257$	−17.0000	−1.06043	−0.530215	−	0.847863i	$-0.677889\pi$
$257$	−17.0000	−1.06043	−0.530215	+	0.847863i	$0.677889\pi$
$258$	0	0
$259$	10.0000	0.621370
$260$	0	0
$261$	0	0
$262$	13.0000	0.803143
$263$	−24.0000	−1.47990	−0.739952	−	0.672660i	$-0.765152\pi$
$263$	−24.0000	−1.47990	−0.739952	+	0.672660i	$0.765152\pi$
$264$	0	0
$265$	0	0
$266$	6.00000	0.367884
$267$	0	0
$268$	−12.0000	−0.733017
$269$	−17.0000	−1.03651	−0.518254	−	0.855227i	$-0.673418\pi$
$269$	−17.0000	−1.03651	−0.518254	+	0.855227i	$0.673418\pi$
$270$	0	0
$271$	−16.0000	−0.971931	−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000	−0.971931	−0.485965	+	0.873978i	$0.661532\pi$
$272$	3.00000	0.181902
$273$	0	0
$274$	6.00000	0.362473
$275$	0	0
$276$	0	0
$277$	−26.0000	−1.56219	−0.781094	−	0.624413i	$-0.785338\pi$
$277$	−26.0000	−1.56219	−0.781094	+	0.624413i	$0.785338\pi$
$278$	10.0000	0.599760
$279$	0	0
$280$	0	0
$281$	−20.0000	−1.19310	−0.596550	−	0.802576i	$-0.703462\pi$
$281$	−20.0000	−1.19310	−0.596550	+	0.802576i	$0.703462\pi$
$282$	0	0
$283$	20.0000	1.18888	0.594438	−	0.804141i	$-0.297374\pi$
$283$	20.0000	1.18888	0.594438	+	0.804141i	$0.297374\pi$
$284$	12.0000	0.712069
$285$	0	0
$286$	25.0000	1.47828
$287$	−4.00000	−0.236113
$288$	0	0
$289$	−8.00000	−0.470588
$290$	0	0
$291$	0	0
$292$	12.0000	0.702247
$293$	12.0000	0.701047	0.350524	−	0.936554i	$-0.386004\pi$
$293$	12.0000	0.701047	0.350524	+	0.936554i	$0.386004\pi$
$294$	0	0
$295$	0	0
$296$	−10.0000	−0.581238
$297$	0	0
$298$	9.00000	0.521356
$299$	5.00000	0.289157
$300$	0	0
$301$	−5.00000	−0.288195
$302$	15.0000	0.863153
$303$	0	0
$304$	−6.00000	−0.344124
$305$	0	0
$306$	0	0
$307$	25.0000	1.42683	0.713413	−	0.700744i	$-0.247149\pi$
$307$	25.0000	1.42683	0.713413	+	0.700744i	$0.247149\pi$
$308$	−5.00000	−0.284901
$309$	0	0
$310$	0	0
$311$	−18.0000	−1.02069	−0.510343	−	0.859971i	$-0.670482\pi$
$311$	−18.0000	−1.02069	−0.510343	+	0.859971i	$0.670482\pi$
$312$	0	0
$313$	−12.0000	−0.678280	−0.339140	−	0.940736i	$-0.610136\pi$
$313$	−12.0000	−0.678280	−0.339140	+	0.940736i	$0.610136\pi$
$314$	−7.00000	−0.395033
$315$	0	0
$316$	1.00000	0.0562544
$317$	−12.0000	−0.673987	−0.336994	−	0.941507i	$-0.609410\pi$
$317$	−12.0000	−0.673987	−0.336994	+	0.941507i	$0.609410\pi$
$318$	0	0
$319$	5.00000	0.279946
$320$	0	0
$321$	0	0
$322$	−1.00000	−0.0557278
$323$	−18.0000	−1.00155
$324$	0	0
$325$	0	0
$326$	1.00000	0.0553849
$327$	0	0
$328$	4.00000	0.220863
$329$	−11.0000	−0.606450
$330$	0	0
$331$	26.0000	1.42909	0.714545	−	0.699590i	$-0.246634\pi$
$331$	26.0000	1.42909	0.714545	+	0.699590i	$0.246634\pi$
$332$	−16.0000	−0.878114
$333$	0	0
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−12.0000	−0.653682	−0.326841	−	0.945079i	$-0.605984\pi$
$337$	−12.0000	−0.653682	−0.326841	+	0.945079i	$0.605984\pi$
$338$	−12.0000	−0.652714
$339$	0	0
$340$	0	0
$341$	−5.00000	−0.270765
$342$	0	0
$343$	1.00000	0.0539949
$344$	5.00000	0.269582
$345$	0	0
$346$	−18.0000	−0.967686
$347$	−22.0000	−1.18102	−0.590511	−	0.807030i	$-0.701074\pi$
$347$	−22.0000	−1.18102	−0.590511	+	0.807030i	$0.701074\pi$
$348$	0	0
$349$	−6.00000	−0.321173	−0.160586	−	0.987022i	$-0.551338\pi$
$349$	−6.00000	−0.321173	−0.160586	+	0.987022i	$0.551338\pi$
$350$	0	0
$351$	0	0
$352$	5.00000	0.266501
$353$	33.0000	1.75641	0.878206	−	0.478282i	$-0.158740\pi$
$353$	33.0000	1.75641	0.878206	+	0.478282i	$0.158740\pi$
$354$	0	0
$355$	0	0
$356$	16.0000	0.847998
$357$	0	0
$358$	−4.00000	−0.211407
$359$	14.0000	0.738892	0.369446	−	0.929252i	$-0.379548\pi$
$359$	14.0000	0.738892	0.369446	+	0.929252i	$0.379548\pi$
$360$	0	0
$361$	17.0000	0.894737
$362$	12.0000	0.630706
$363$	0	0
$364$	5.00000	0.262071
$365$	0	0
$366$	0	0
$367$	−10.0000	−0.521996	−0.260998	−	0.965339i	$-0.584052\pi$
$367$	−10.0000	−0.521996	−0.260998	+	0.965339i	$0.584052\pi$
$368$	1.00000	0.0521286
$369$	0	0
$370$	0	0
$371$	−2.00000	−0.103835
$372$	0	0
$373$	−3.00000	−0.155334	−0.0776671	−	0.996979i	$-0.524747\pi$
$373$	−3.00000	−0.155334	−0.0776671	+	0.996979i	$0.524747\pi$
$374$	15.0000	0.775632
$375$	0	0
$376$	11.0000	0.567282
$377$	−5.00000	−0.257513
$378$	0	0
$379$	26.0000	1.33553	0.667765	−	0.744372i	$-0.267251\pi$
$379$	26.0000	1.33553	0.667765	+	0.744372i	$0.267251\pi$
$380$	0	0
$381$	0	0
$382$	−12.0000	−0.613973
$383$	35.0000	1.78842	0.894208	−	0.447651i	$-0.147739\pi$
$383$	35.0000	1.78842	0.894208	+	0.447651i	$0.147739\pi$
$384$	0	0
$385$	0	0
$386$	−20.0000	−1.01797
$387$	0	0
$388$	4.00000	0.203069
$389$	−25.0000	−1.26755	−0.633775	−	0.773517i	$-0.718496\pi$
$389$	−25.0000	−1.26755	−0.633775	+	0.773517i	$0.718496\pi$
$390$	0	0
$391$	3.00000	0.151717
$392$	−1.00000	−0.0505076
$393$	0	0
$394$	10.0000	0.503793
$395$	0	0
$396$	0	0
$397$	−35.0000	−1.75660	−0.878300	−	0.478110i	$-0.841322\pi$
$397$	−35.0000	−1.75660	−0.878300	+	0.478110i	$0.841322\pi$
$398$	3.00000	0.150376
$399$	0	0
$400$	0	0
$401$	−22.0000	−1.09863	−0.549314	−	0.835616i	$-0.685111\pi$
$401$	−22.0000	−1.09863	−0.549314	+	0.835616i	$0.685111\pi$
$402$	0	0
$403$	5.00000	0.249068
$404$	−9.00000	−0.447767
$405$	0	0
$406$	1.00000	0.0496292
$407$	−50.0000	−2.47841
$408$	0	0
$409$	5.00000	0.247234	0.123617	−	0.992330i	$-0.460551\pi$
$409$	5.00000	0.247234	0.123617	+	0.992330i	$0.460551\pi$
$410$	0	0
$411$	0	0
$412$	16.0000	0.788263
$413$	−4.00000	−0.196827
$414$	0	0
$415$	0	0
$416$	−5.00000	−0.245145
$417$	0	0
$418$	−30.0000	−1.46735
$419$	11.0000	0.537385	0.268693	−	0.963226i	$-0.413408\pi$
$419$	11.0000	0.537385	0.268693	+	0.963226i	$0.413408\pi$
$420$	0	0
$421$	28.0000	1.36464	0.682318	−	0.731055i	$-0.260972\pi$
$421$	28.0000	1.36464	0.682318	+	0.731055i	$0.260972\pi$
$422$	22.0000	1.07094
$423$	0	0
$424$	2.00000	0.0971286
$425$	0	0
$426$	0	0
$427$	0	0
$428$	8.00000	0.386695
$429$	0	0
$430$	0	0
$431$	−30.0000	−1.44505	−0.722525	−	0.691345i	$-0.757018\pi$
$431$	−30.0000	−1.44505	−0.722525	+	0.691345i	$0.757018\pi$
$432$	0	0
$433$	14.0000	0.672797	0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000	0.672797	0.336399	+	0.941720i	$0.390791\pi$
$434$	−1.00000	−0.0480015
$435$	0	0
$436$	−18.0000	−0.862044
$437$	−6.00000	−0.287019
$438$	0	0
$439$	−16.0000	−0.763638	−0.381819	−	0.924237i	$-0.624702\pi$
$439$	−16.0000	−0.763638	−0.381819	+	0.924237i	$0.624702\pi$
$440$	0	0
$441$	0	0
$442$	−15.0000	−0.713477
$443$	4.00000	0.190046	0.0950229	−	0.995475i	$-0.469708\pi$
$443$	4.00000	0.190046	0.0950229	+	0.995475i	$0.469708\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	0	0
$448$	1.00000	0.0472456
$449$	−20.0000	−0.943858	−0.471929	−	0.881636i	$-0.656442\pi$
$449$	−20.0000	−0.943858	−0.471929	+	0.881636i	$0.656442\pi$
$450$	0	0
$451$	20.0000	0.941763
$452$	−3.00000	−0.141108
$453$	0	0
$454$	16.0000	0.750917
$455$	0	0
$456$	0	0
$457$	−18.0000	−0.842004	−0.421002	−	0.907060i	$-0.638322\pi$
$457$	−18.0000	−0.842004	−0.421002	+	0.907060i	$0.638322\pi$
$458$	−8.00000	−0.373815
$459$	0	0
$460$	0	0
$461$	6.00000	0.279448	0.139724	−	0.990190i	$-0.455378\pi$
$461$	6.00000	0.279448	0.139724	+	0.990190i	$0.455378\pi$
$462$	0	0
$463$	−26.0000	−1.20832	−0.604161	−	0.796862i	$-0.706492\pi$
$463$	−26.0000	−1.20832	−0.604161	+	0.796862i	$0.706492\pi$
$464$	−1.00000	−0.0464238
$465$	0	0
$466$	−6.00000	−0.277945
$467$	−24.0000	−1.11059	−0.555294	−	0.831654i	$-0.687394\pi$
$467$	−24.0000	−1.11059	−0.555294	+	0.831654i	$0.687394\pi$
$468$	0	0
$469$	−12.0000	−0.554109
$470$	0	0
$471$	0	0
$472$	4.00000	0.184115
$473$	25.0000	1.14950
$474$	0	0
$475$	0	0
$476$	3.00000	0.137505
$477$	0	0
$478$	−24.0000	−1.09773
$479$	−28.0000	−1.27935	−0.639676	−	0.768644i	$-0.720932\pi$
$479$	−28.0000	−1.27935	−0.639676	+	0.768644i	$0.720932\pi$
$480$	0	0
$481$	50.0000	2.27980
$482$	−19.0000	−0.865426
$483$	0	0
$484$	14.0000	0.636364
$485$	0	0
$486$	0	0
$487$	34.0000	1.54069	0.770344	−	0.637629i	$-0.220085\pi$
$487$	34.0000	1.54069	0.770344	+	0.637629i	$0.220085\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	4.00000	0.180517	0.0902587	−	0.995918i	$-0.471231\pi$
$491$	4.00000	0.180517	0.0902587	+	0.995918i	$0.471231\pi$
$492$	0	0
$493$	−3.00000	−0.135113
$494$	30.0000	1.34976
$495$	0	0
$496$	1.00000	0.0449013
$497$	12.0000	0.538274
$498$	0	0
$499$	10.0000	0.447661	0.223831	−	0.974628i	$-0.428144\pi$
$499$	10.0000	0.447661	0.223831	+	0.974628i	$0.428144\pi$
$500$	0	0
$501$	0	0
$502$	19.0000	0.848012
$503$	−21.0000	−0.936344	−0.468172	−	0.883637i	$-0.655087\pi$
$503$	−21.0000	−0.936344	−0.468172	+	0.883637i	$0.655087\pi$
$504$	0	0
$505$	0	0
$506$	5.00000	0.222277
$507$	0	0
$508$	−10.0000	−0.443678
$509$	13.0000	0.576215	0.288107	−	0.957598i	$-0.406974\pi$
$509$	13.0000	0.576215	0.288107	+	0.957598i	$0.406974\pi$
$510$	0	0
$511$	12.0000	0.530849
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	17.0000	0.749838
$515$	0	0
$516$	0	0
$517$	55.0000	2.41890
$518$	−10.0000	−0.439375
$519$	0	0
$520$	0	0
$521$	−30.0000	−1.31432	−0.657162	−	0.753749i	$-0.728243\pi$
$521$	−30.0000	−1.31432	−0.657162	+	0.753749i	$0.728243\pi$
$522$	0	0
$523$	19.0000	0.830812	0.415406	−	0.909636i	$-0.363640\pi$
$523$	19.0000	0.830812	0.415406	+	0.909636i	$0.363640\pi$
$524$	−13.0000	−0.567908
$525$	0	0
$526$	24.0000	1.04645
$527$	3.00000	0.130682
$528$	0	0
$529$	−22.0000	−0.956522
$530$	0	0
$531$	0	0
$532$	−6.00000	−0.260133
$533$	−20.0000	−0.866296
$534$	0	0
$535$	0	0
$536$	12.0000	0.518321
$537$	0	0
$538$	17.0000	0.732922
$539$	−5.00000	−0.215365
$540$	0	0
$541$	32.0000	1.37579	0.687894	−	0.725811i	$-0.258536\pi$
$541$	32.0000	1.37579	0.687894	+	0.725811i	$0.258536\pi$
$542$	16.0000	0.687259
$543$	0	0
$544$	−3.00000	−0.128624
$545$	0	0
$546$	0	0
$547$	−37.0000	−1.58201	−0.791003	−	0.611812i	$-0.790441\pi$
$547$	−37.0000	−1.58201	−0.791003	+	0.611812i	$0.790441\pi$
$548$	−6.00000	−0.256307
$549$	0	0
$550$	0	0
$551$	6.00000	0.255609
$552$	0	0
$553$	1.00000	0.0425243
$554$	26.0000	1.10463
$555$	0	0
$556$	−10.0000	−0.424094
$557$	−12.0000	−0.508456	−0.254228	−	0.967144i	$-0.581821\pi$
$557$	−12.0000	−0.508456	−0.254228	+	0.967144i	$0.581821\pi$
$558$	0	0
$559$	−25.0000	−1.05739
$560$	0	0
$561$	0	0
$562$	20.0000	0.843649
$563$	4.00000	0.168580	0.0842900	−	0.996441i	$-0.473138\pi$
$563$	4.00000	0.168580	0.0842900	+	0.996441i	$0.473138\pi$
$564$	0	0
$565$	0	0
$566$	−20.0000	−0.840663
$567$	0	0
$568$	−12.0000	−0.503509
$569$	30.0000	1.25767	0.628833	−	0.777541i	$-0.283533\pi$
$569$	30.0000	1.25767	0.628833	+	0.777541i	$0.283533\pi$
$570$	0	0
$571$	−32.0000	−1.33916	−0.669579	−	0.742741i	$-0.733526\pi$
$571$	−32.0000	−1.33916	−0.669579	+	0.742741i	$0.733526\pi$
$572$	−25.0000	−1.04530
$573$	0	0
$574$	4.00000	0.166957
$575$	0	0
$576$	0	0
$577$	−16.0000	−0.666089	−0.333044	−	0.942911i	$-0.608076\pi$
$577$	−16.0000	−0.666089	−0.333044	+	0.942911i	$0.608076\pi$
$578$	8.00000	0.332756
$579$	0	0
$580$	0	0
$581$	−16.0000	−0.663792
$582$	0	0
$583$	10.0000	0.414158
$584$	−12.0000	−0.496564
$585$	0	0
$586$	−12.0000	−0.495715
$587$	36.0000	1.48588	0.742940	−	0.669359i	$-0.233431\pi$
$587$	36.0000	1.48588	0.742940	+	0.669359i	$0.233431\pi$
$588$	0	0
$589$	−6.00000	−0.247226
$590$	0	0
$591$	0	0
$592$	10.0000	0.410997
$593$	−29.0000	−1.19089	−0.595444	−	0.803397i	$-0.703024\pi$
$593$	−29.0000	−1.19089	−0.595444	+	0.803397i	$0.703024\pi$
$594$	0	0
$595$	0	0
$596$	−9.00000	−0.368654
$597$	0	0
$598$	−5.00000	−0.204465
$599$	−2.00000	−0.0817178	−0.0408589	−	0.999165i	$-0.513009\pi$
$599$	−2.00000	−0.0817178	−0.0408589	+	0.999165i	$0.513009\pi$
$600$	0	0
$601$	−17.0000	−0.693444	−0.346722	−	0.937968i	$-0.612705\pi$
$601$	−17.0000	−0.693444	−0.346722	+	0.937968i	$0.612705\pi$
$602$	5.00000	0.203785
$603$	0	0
$604$	−15.0000	−0.610341
$605$	0	0
$606$	0	0
$607$	−2.00000	−0.0811775	−0.0405887	−	0.999176i	$-0.512923\pi$
$607$	−2.00000	−0.0811775	−0.0405887	+	0.999176i	$0.512923\pi$
$608$	6.00000	0.243332
$609$	0	0
$610$	0	0
$611$	−55.0000	−2.22506
$612$	0	0
$613$	35.0000	1.41364	0.706818	−	0.707395i	$-0.250130\pi$
$613$	35.0000	1.41364	0.706818	+	0.707395i	$0.250130\pi$
$614$	−25.0000	−1.00892
$615$	0	0
$616$	5.00000	0.201456
$617$	31.0000	1.24801	0.624007	−	0.781419i	$-0.285504\pi$
$617$	31.0000	1.24801	0.624007	+	0.781419i	$0.285504\pi$
$618$	0	0
$619$	14.0000	0.562708	0.281354	−	0.959604i	$-0.409217\pi$
$619$	14.0000	0.562708	0.281354	+	0.959604i	$0.409217\pi$
$620$	0	0
$621$	0	0
$622$	18.0000	0.721734
$623$	16.0000	0.641026
$624$	0	0
$625$	0	0
$626$	12.0000	0.479616
$627$	0	0
$628$	7.00000	0.279330
$629$	30.0000	1.19618
$630$	0	0
$631$	−32.0000	−1.27390	−0.636950	−	0.770905i	$-0.719804\pi$
$631$	−32.0000	−1.27390	−0.636950	+	0.770905i	$0.719804\pi$
$632$	−1.00000	−0.0397779
$633$	0	0
$634$	12.0000	0.476581
$635$	0	0
$636$	0	0
$637$	5.00000	0.198107
$638$	−5.00000	−0.197952
$639$	0	0
$640$	0	0
$641$	18.0000	0.710957	0.355479	−	0.934684i	$-0.384318\pi$
$641$	18.0000	0.710957	0.355479	+	0.934684i	$0.384318\pi$
$642$	0	0
$643$	13.0000	0.512670	0.256335	−	0.966588i	$-0.417485\pi$
$643$	13.0000	0.512670	0.256335	+	0.966588i	$0.417485\pi$
$644$	1.00000	0.0394055
$645$	0	0
$646$	18.0000	0.708201
$647$	28.0000	1.10079	0.550397	−	0.834903i	$-0.314476\pi$
$647$	28.0000	1.10079	0.550397	+	0.834903i	$0.314476\pi$
$648$	0	0
$649$	20.0000	0.785069
$650$	0	0
$651$	0	0
$652$	−1.00000	−0.0391630
$653$	10.0000	0.391330	0.195665	−	0.980671i	$-0.437313\pi$
$653$	10.0000	0.391330	0.195665	+	0.980671i	$0.437313\pi$
$654$	0	0
$655$	0	0
$656$	−4.00000	−0.156174
$657$	0	0
$658$	11.0000	0.428825
$659$	12.0000	0.467454	0.233727	−	0.972302i	$-0.424908\pi$
$659$	12.0000	0.467454	0.233727	+	0.972302i	$0.424908\pi$
$660$	0	0
$661$	−42.0000	−1.63361	−0.816805	−	0.576913i	$-0.804257\pi$
$661$	−42.0000	−1.63361	−0.816805	+	0.576913i	$0.804257\pi$
$662$	−26.0000	−1.01052
$663$	0	0
$664$	16.0000	0.620920
$665$	0	0
$666$	0	0
$667$	−1.00000	−0.0387202
$668$	0	0
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	−16.0000	−0.616755	−0.308377	−	0.951264i	$-0.599786\pi$
$673$	−16.0000	−0.616755	−0.308377	+	0.951264i	$0.599786\pi$
$674$	12.0000	0.462223
$675$	0	0
$676$	12.0000	0.461538
$677$	8.00000	0.307465	0.153732	−	0.988113i	$-0.450871\pi$
$677$	8.00000	0.307465	0.153732	+	0.988113i	$0.450871\pi$
$678$	0	0
$679$	4.00000	0.153506
$680$	0	0
$681$	0	0
$682$	5.00000	0.191460
$683$	34.0000	1.30097	0.650487	−	0.759517i	$-0.274565\pi$
$683$	34.0000	1.30097	0.650487	+	0.759517i	$0.274565\pi$
$684$	0	0
$685$	0	0
$686$	−1.00000	−0.0381802
$687$	0	0
$688$	−5.00000	−0.190623
$689$	−10.0000	−0.380970
$690$	0	0
$691$	6.00000	0.228251	0.114125	−	0.993466i	$-0.463593\pi$
$691$	6.00000	0.228251	0.114125	+	0.993466i	$0.463593\pi$
$692$	18.0000	0.684257
$693$	0	0
$694$	22.0000	0.835109
$695$	0	0
$696$	0	0
$697$	−12.0000	−0.454532
$698$	6.00000	0.227103
$699$	0	0
$700$	0	0
$701$	−45.0000	−1.69963	−0.849813	−	0.527084i	$-0.823285\pi$
$701$	−45.0000	−1.69963	−0.849813	+	0.527084i	$0.823285\pi$
$702$	0	0
$703$	−60.0000	−2.26294
$704$	−5.00000	−0.188445
$705$	0	0
$706$	−33.0000	−1.24197
$707$	−9.00000	−0.338480
$708$	0	0
$709$	−40.0000	−1.50223	−0.751116	−	0.660171i	$-0.770484\pi$
$709$	−40.0000	−1.50223	−0.751116	+	0.660171i	$0.770484\pi$
$710$	0	0
$711$	0	0
$712$	−16.0000	−0.599625
$713$	1.00000	0.0374503
$714$	0	0
$715$	0	0
$716$	4.00000	0.149487
$717$	0	0
$718$	−14.0000	−0.522475
$719$	40.0000	1.49175	0.745874	−	0.666087i	$-0.232032\pi$
$719$	40.0000	1.49175	0.745874	+	0.666087i	$0.232032\pi$
$720$	0	0
$721$	16.0000	0.595871
$722$	−17.0000	−0.632674
$723$	0	0
$724$	−12.0000	−0.445976
$725$	0	0
$726$	0	0
$727$	−38.0000	−1.40934	−0.704671	−	0.709534i	$-0.748905\pi$
$727$	−38.0000	−1.40934	−0.704671	+	0.709534i	$0.748905\pi$
$728$	−5.00000	−0.185312
$729$	0	0
$730$	0	0
$731$	−15.0000	−0.554795
$732$	0	0
$733$	−2.00000	−0.0738717	−0.0369358	−	0.999318i	$-0.511760\pi$
$733$	−2.00000	−0.0738717	−0.0369358	+	0.999318i	$0.511760\pi$
$734$	10.0000	0.369107
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	60.0000	2.21013
$738$	0	0
$739$	−22.0000	−0.809283	−0.404642	−	0.914475i	$-0.632604\pi$
$739$	−22.0000	−0.809283	−0.404642	+	0.914475i	$0.632604\pi$
$740$	0	0
$741$	0	0
$742$	2.00000	0.0734223
$743$	−29.0000	−1.06391	−0.531953	−	0.846774i	$-0.678542\pi$
$743$	−29.0000	−1.06391	−0.531953	+	0.846774i	$0.678542\pi$
$744$	0	0
$745$	0	0
$746$	3.00000	0.109838
$747$	0	0
$748$	−15.0000	−0.548454
$749$	8.00000	0.292314
$750$	0	0
$751$	−7.00000	−0.255434	−0.127717	−	0.991811i	$-0.540765\pi$
$751$	−7.00000	−0.255434	−0.127717	+	0.991811i	$0.540765\pi$
$752$	−11.0000	−0.401129
$753$	0	0
$754$	5.00000	0.182089
$755$	0	0
$756$	0	0
$757$	−47.0000	−1.70824	−0.854122	−	0.520073i	$-0.825905\pi$
$757$	−47.0000	−1.70824	−0.854122	+	0.520073i	$0.825905\pi$
$758$	−26.0000	−0.944363
$759$	0	0
$760$	0	0
$761$	18.0000	0.652499	0.326250	−	0.945284i	$-0.394215\pi$
$761$	18.0000	0.652499	0.326250	+	0.945284i	$0.394215\pi$
$762$	0	0
$763$	−18.0000	−0.651644
$764$	12.0000	0.434145
$765$	0	0
$766$	−35.0000	−1.26460
$767$	−20.0000	−0.722158
$768$	0	0
$769$	−35.0000	−1.26213	−0.631066	−	0.775729i	$-0.717382\pi$
$769$	−35.0000	−1.26213	−0.631066	+	0.775729i	$0.717382\pi$
$770$	0	0
$771$	0	0
$772$	20.0000	0.719816
$773$	6.00000	0.215805	0.107903	−	0.994161i	$-0.465587\pi$
$773$	6.00000	0.215805	0.107903	+	0.994161i	$0.465587\pi$
$774$	0	0
$775$	0	0
$776$	−4.00000	−0.143592
$777$	0	0
$778$	25.0000	0.896293
$779$	24.0000	0.859889
$780$	0	0
$781$	−60.0000	−2.14697
$782$	−3.00000	−0.107280
$783$	0	0
$784$	1.00000	0.0357143
$785$	0	0
$786$	0	0
$787$	5.00000	0.178231	0.0891154	−	0.996021i	$-0.471596\pi$
$787$	5.00000	0.178231	0.0891154	+	0.996021i	$0.471596\pi$
$788$	−10.0000	−0.356235
$789$	0	0
$790$	0	0
$791$	−3.00000	−0.106668
$792$	0	0
$793$	0	0
$794$	35.0000	1.24210
$795$	0	0
$796$	−3.00000	−0.106332
$797$	−42.0000	−1.48772	−0.743858	−	0.668338i	$-0.767006\pi$
$797$	−42.0000	−1.48772	−0.743858	+	0.668338i	$0.767006\pi$
$798$	0	0
$799$	−33.0000	−1.16746
$800$	0	0
$801$	0	0
$802$	22.0000	0.776847
$803$	−60.0000	−2.11735
$804$	0	0
$805$	0	0
$806$	−5.00000	−0.176117
$807$	0	0
$808$	9.00000	0.316619
$809$	0	0		−	1.00000i	$-0.5\pi$
$809$	0	0			1.00000i	$0.5\pi$
$810$	0	0
$811$	−24.0000	−0.842754	−0.421377	−	0.906886i	$-0.638453\pi$
$811$	−24.0000	−0.842754	−0.421377	+	0.906886i	$0.638453\pi$
$812$	−1.00000	−0.0350931
$813$	0	0
$814$	50.0000	1.75250
$815$	0	0
$816$	0	0
$817$	30.0000	1.04957
$818$	−5.00000	−0.174821
$819$	0	0
$820$	0	0
$821$	−30.0000	−1.04701	−0.523504	−	0.852023i	$-0.675375\pi$
$821$	−30.0000	−1.04701	−0.523504	+	0.852023i	$0.675375\pi$
$822$	0	0
$823$	−54.0000	−1.88232	−0.941161	−	0.337959i	$-0.890263\pi$
$823$	−54.0000	−1.88232	−0.941161	+	0.337959i	$0.890263\pi$
$824$	−16.0000	−0.557386
$825$	0	0
$826$	4.00000	0.139178
$827$	38.0000	1.32139	0.660695	−	0.750655i	$-0.270262\pi$
$827$	38.0000	1.32139	0.660695	+	0.750655i	$0.270262\pi$
$828$	0	0
$829$	−20.0000	−0.694629	−0.347314	−	0.937749i	$-0.612906\pi$
$829$	−20.0000	−0.694629	−0.347314	+	0.937749i	$0.612906\pi$
$830$	0	0
$831$	0	0
$832$	5.00000	0.173344
$833$	3.00000	0.103944
$834$	0	0
$835$	0	0
$836$	30.0000	1.03757
$837$	0	0
$838$	−11.0000	−0.379989
$839$	16.0000	0.552381	0.276191	−	0.961103i	$-0.410928\pi$
$839$	16.0000	0.552381	0.276191	+	0.961103i	$0.410928\pi$
$840$	0	0
$841$	−28.0000	−0.965517
$842$	−28.0000	−0.964944
$843$	0	0
$844$	−22.0000	−0.757271
$845$	0	0
$846$	0	0
$847$	14.0000	0.481046
$848$	−2.00000	−0.0686803
$849$	0	0
$850$	0	0
$851$	10.0000	0.342796
$852$	0	0
$853$	−19.0000	−0.650548	−0.325274	−	0.945620i	$-0.605456\pi$
$853$	−19.0000	−0.650548	−0.325274	+	0.945620i	$0.605456\pi$
$854$	0	0
$855$	0	0
$856$	−8.00000	−0.273434
$857$	−38.0000	−1.29806	−0.649028	−	0.760765i	$-0.724824\pi$
$857$	−38.0000	−1.29806	−0.649028	+	0.760765i	$0.724824\pi$
$858$	0	0
$859$	30.0000	1.02359	0.511793	−	0.859109i	$-0.328981\pi$
$859$	30.0000	1.02359	0.511793	+	0.859109i	$0.328981\pi$
$860$	0	0
$861$	0	0
$862$	30.0000	1.02180
$863$	−41.0000	−1.39566	−0.697828	−	0.716265i	$-0.745850\pi$
$863$	−41.0000	−1.39566	−0.697828	+	0.716265i	$0.745850\pi$
$864$	0	0
$865$	0	0
$866$	−14.0000	−0.475739
$867$	0	0
$868$	1.00000	0.0339422
$869$	−5.00000	−0.169613
$870$	0	0
$871$	−60.0000	−2.03302
$872$	18.0000	0.609557
$873$	0	0
$874$	6.00000	0.202953
$875$	0	0
$876$	0	0
$877$	−35.0000	−1.18187	−0.590933	−	0.806721i	$-0.701240\pi$
$877$	−35.0000	−1.18187	−0.590933	+	0.806721i	$0.701240\pi$
$878$	16.0000	0.539974
$879$	0	0
$880$	0	0
$881$	−40.0000	−1.34763	−0.673817	−	0.738898i	$-0.735346\pi$
$881$	−40.0000	−1.34763	−0.673817	+	0.738898i	$0.735346\pi$
$882$	0	0
$883$	−12.0000	−0.403832	−0.201916	−	0.979403i	$-0.564717\pi$
$883$	−12.0000	−0.403832	−0.201916	+	0.979403i	$0.564717\pi$
$884$	15.0000	0.504505
$885$	0	0
$886$	−4.00000	−0.134383
$887$	−31.0000	−1.04088	−0.520439	−	0.853899i	$-0.674232\pi$
$887$	−31.0000	−1.04088	−0.520439	+	0.853899i	$0.674232\pi$
$888$	0	0
$889$	−10.0000	−0.335389
$890$	0	0
$891$	0	0
$892$	0	0
$893$	66.0000	2.20861
$894$	0	0
$895$	0	0
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	20.0000	0.667409
$899$	−1.00000	−0.0333519
$900$	0	0
$901$	−6.00000	−0.199889
$902$	−20.0000	−0.665927
$903$	0	0
$904$	3.00000	0.0997785
$905$	0	0
$906$	0	0
$907$	55.0000	1.82625	0.913123	−	0.407685i	$-0.133664\pi$
$907$	55.0000	1.82625	0.913123	+	0.407685i	$0.133664\pi$
$908$	−16.0000	−0.530979
$909$	0	0
$910$	0	0
$911$	56.0000	1.85536	0.927681	−	0.373373i	$-0.121799\pi$
$911$	56.0000	1.85536	0.927681	+	0.373373i	$0.121799\pi$
$912$	0	0
$913$	80.0000	2.64761
$914$	18.0000	0.595387
$915$	0	0
$916$	8.00000	0.264327
$917$	−13.0000	−0.429298
$918$	0	0
$919$	9.00000	0.296883	0.148441	−	0.988921i	$-0.452574\pi$
$919$	9.00000	0.296883	0.148441	+	0.988921i	$0.452574\pi$
$920$	0	0
$921$	0	0
$922$	−6.00000	−0.197599
$923$	60.0000	1.97492
$924$	0	0
$925$	0	0
$926$	26.0000	0.854413
$927$	0	0
$928$	1.00000	0.0328266
$929$	−42.0000	−1.37798	−0.688988	−	0.724773i	$-0.741945\pi$
$929$	−42.0000	−1.37798	−0.688988	+	0.724773i	$0.741945\pi$
$930$	0	0
$931$	−6.00000	−0.196642
$932$	6.00000	0.196537
$933$	0	0
$934$	24.0000	0.785304
$935$	0	0
$936$	0	0
$937$	−12.0000	−0.392023	−0.196011	−	0.980602i	$-0.562799\pi$
$937$	−12.0000	−0.392023	−0.196011	+	0.980602i	$0.562799\pi$
$938$	12.0000	0.391814
$939$	0	0
$940$	0	0
$941$	33.0000	1.07577	0.537885	−	0.843018i	$-0.319224\pi$
$941$	33.0000	1.07577	0.537885	+	0.843018i	$0.319224\pi$
$942$	0	0
$943$	−4.00000	−0.130258
$944$	−4.00000	−0.130189
$945$	0	0
$946$	−25.0000	−0.812820
$947$	−8.00000	−0.259965	−0.129983	−	0.991516i	$-0.541492\pi$
$947$	−8.00000	−0.259965	−0.129983	+	0.991516i	$0.541492\pi$
$948$	0	0
$949$	60.0000	1.94768
$950$	0	0
$951$	0	0
$952$	−3.00000	−0.0972306
$953$	−29.0000	−0.939402	−0.469701	−	0.882826i	$-0.655638\pi$
$953$	−29.0000	−0.939402	−0.469701	+	0.882826i	$0.655638\pi$
$954$	0	0
$955$	0	0
$956$	24.0000	0.776215
$957$	0	0
$958$	28.0000	0.904639
$959$	−6.00000	−0.193750
$960$	0	0
$961$	−30.0000	−0.967742
$962$	−50.0000	−1.61206
$963$	0	0
$964$	19.0000	0.611949
$965$	0	0
$966$	0	0
$967$	38.0000	1.22200	0.610999	−	0.791632i	$-0.290768\pi$
$967$	38.0000	1.22200	0.610999	+	0.791632i	$0.290768\pi$
$968$	−14.0000	−0.449977
$969$	0	0
$970$	0	0
$971$	21.0000	0.673922	0.336961	−	0.941519i	$-0.390601\pi$
$971$	21.0000	0.673922	0.336961	+	0.941519i	$0.390601\pi$
$972$	0	0
$973$	−10.0000	−0.320585
$974$	−34.0000	−1.08943
$975$	0	0
$976$	0	0
$977$	45.0000	1.43968	0.719839	−	0.694141i	$-0.244216\pi$
$977$	45.0000	1.43968	0.719839	+	0.694141i	$0.244216\pi$
$978$	0	0
$979$	−80.0000	−2.55681
$980$	0	0
$981$	0	0
$982$	−4.00000	−0.127645
$983$	−5.00000	−0.159475	−0.0797376	−	0.996816i	$-0.525408\pi$
$983$	−5.00000	−0.159475	−0.0797376	+	0.996816i	$0.525408\pi$
$984$	0	0
$985$	0	0
$986$	3.00000	0.0955395
$987$	0	0
$988$	−30.0000	−0.954427
$989$	−5.00000	−0.158991
$990$	0	0
$991$	31.0000	0.984747	0.492374	−	0.870384i	$-0.336129\pi$
$991$	31.0000	0.984747	0.492374	+	0.870384i	$0.336129\pi$
$992$	−1.00000	−0.0317500
$993$	0	0
$994$	−12.0000	−0.380617
$995$	0	0
$996$	0	0
$997$	−53.0000	−1.67853	−0.839263	−	0.543725i	$-0.817013\pi$
$997$	−53.0000	−1.67853	−0.839263	+	0.543725i	$0.817013\pi$
$998$	−10.0000	−0.316544
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9450.2.a.bb.1.1		1
3.2	odd	2		9450.2.a.dy.1.1		1
5.4	even	2		1890.2.a.u.1.1	yes	1
15.14	odd	2		1890.2.a.b.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1890.2.a.b.1.1	✓	1	15.14	odd	2
1890.2.a.u.1.1	yes	1	5.4	even	2
9450.2.a.bb.1.1		1	1.1	even	1	trivial
9450.2.a.dy.1.1		1	3.2	odd	2

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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:	\( N \)	\(=\)	\( 9450 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9450.a (trivial)

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