LMFDB - Embedded newform 9450.2.a.dv.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 378)
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)

$f(q)$

$=$

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

$q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{7} +1.00000 q^{8} +4.00000 q^{11} -3.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} -7.00000 q^{17} +2.00000 q^{19} +4.00000 q^{22} -1.00000 q^{23} -3.00000 q^{26} +1.00000 q^{28} -1.00000 q^{29} -9.00000 q^{31} +1.00000 q^{32} -7.00000 q^{34} -2.00000 q^{37} +2.00000 q^{38} -6.00000 q^{41} -11.0000 q^{43} +4.00000 q^{44} -1.00000 q^{46} -6.00000 q^{47} +1.00000 q^{49} -3.00000 q^{52} -9.00000 q^{53} +1.00000 q^{56} -1.00000 q^{58} +5.00000 q^{59} -6.00000 q^{61} -9.00000 q^{62} +1.00000 q^{64} -7.00000 q^{67} -7.00000 q^{68} +7.00000 q^{71} +14.0000 q^{73} -2.00000 q^{74} +2.00000 q^{76} +4.00000 q^{77} -6.00000 q^{79} -6.00000 q^{82} -4.00000 q^{83} -11.0000 q^{86} +4.00000 q^{88} +3.00000 q^{89} -3.00000 q^{91} -1.00000 q^{92} -6.00000 q^{94} +8.00000 q^{97} +1.00000 q^{98} +O(q^{100})$

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
$11$	4.00000	1.20605	0.603023	−	0.797724i	$-0.293963\pi$
$11$	4.00000	1.20605	0.603023	+	0.797724i	$0.293963\pi$
$12$	0	0
$13$	−3.00000	−0.832050	−0.416025	−	0.909353i	$-0.636577\pi$
$13$	−3.00000	−0.832050	−0.416025	+	0.909353i	$0.636577\pi$
$14$	1.00000	0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	−7.00000	−1.69775	−0.848875	−	0.528594i	$-0.822719\pi$
$17$	−7.00000	−1.69775	−0.848875	+	0.528594i	$0.822719\pi$
$18$	0	0
$19$	2.00000	0.458831	0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000	0.458831	0.229416	+	0.973329i	$0.426318\pi$
$20$	0	0
$21$	0	0
$22$	4.00000	0.852803
$23$	−1.00000	−0.208514	−0.104257	−	0.994550i	$-0.533247\pi$
$23$	−1.00000	−0.208514	−0.104257	+	0.994550i	$0.533247\pi$
$24$	0	0
$25$	0	0
$26$	−3.00000	−0.588348
$27$	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
$31$	−9.00000	−1.61645	−0.808224	−	0.588875i	$-0.799571\pi$
$31$	−9.00000	−1.61645	−0.808224	+	0.588875i	$0.799571\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−7.00000	−1.20049
$35$	0	0
$36$	0	0
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	2.00000	0.324443
$39$	0	0
$40$	0	0
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	0	0
$43$	−11.0000	−1.67748	−0.838742	−	0.544529i	$-0.816708\pi$
$43$	−11.0000	−1.67748	−0.838742	+	0.544529i	$0.816708\pi$
$44$	4.00000	0.603023
$45$	0	0
$46$	−1.00000	−0.147442
$47$	−6.00000	−0.875190	−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000	−0.875190	−0.437595	+	0.899172i	$0.644170\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	0	0
$51$	0	0
$52$	−3.00000	−0.416025
$53$	−9.00000	−1.23625	−0.618123	−	0.786082i	$-0.712106\pi$
$53$	−9.00000	−1.23625	−0.618123	+	0.786082i	$0.712106\pi$
$54$	0	0
$55$	0	0
$56$	1.00000	0.133631
$57$	0	0
$58$	−1.00000	−0.131306
$59$	5.00000	0.650945	0.325472	−	0.945552i	$-0.394477\pi$
$59$	5.00000	0.650945	0.325472	+	0.945552i	$0.394477\pi$
$60$	0	0
$61$	−6.00000	−0.768221	−0.384111	−	0.923287i	$-0.625492\pi$
$61$	−6.00000	−0.768221	−0.384111	+	0.923287i	$0.625492\pi$
$62$	−9.00000	−1.14300
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	−7.00000	−0.855186	−0.427593	−	0.903971i	$-0.640638\pi$
$67$	−7.00000	−0.855186	−0.427593	+	0.903971i	$0.640638\pi$
$68$	−7.00000	−0.848875
$69$	0	0
$70$	0	0
$71$	7.00000	0.830747	0.415374	−	0.909651i	$-0.363651\pi$
$71$	7.00000	0.830747	0.415374	+	0.909651i	$0.363651\pi$
$72$	0	0
$73$	14.0000	1.63858	0.819288	−	0.573382i	$-0.194369\pi$
$73$	14.0000	1.63858	0.819288	+	0.573382i	$0.194369\pi$
$74$	−2.00000	−0.232495
$75$	0	0
$76$	2.00000	0.229416
$77$	4.00000	0.455842
$78$	0	0
$79$	−6.00000	−0.675053	−0.337526	−	0.941316i	$-0.609590\pi$
$79$	−6.00000	−0.675053	−0.337526	+	0.941316i	$0.609590\pi$
$80$	0	0
$81$	0	0
$82$	−6.00000	−0.662589
$83$	−4.00000	−0.439057	−0.219529	−	0.975606i	$-0.570452\pi$
$83$	−4.00000	−0.439057	−0.219529	+	0.975606i	$0.570452\pi$
$84$	0	0
$85$	0	0
$86$	−11.0000	−1.18616
$87$	0	0
$88$	4.00000	0.426401
$89$	3.00000	0.317999	0.159000	−	0.987279i	$-0.449173\pi$
$89$	3.00000	0.317999	0.159000	+	0.987279i	$0.449173\pi$
$90$	0	0
$91$	−3.00000	−0.314485
$92$	−1.00000	−0.104257
$93$	0	0
$94$	−6.00000	−0.618853
$95$	0	0
$96$	0	0
$97$	8.00000	0.812277	0.406138	−	0.913812i	$-0.366875\pi$
$97$	8.00000	0.812277	0.406138	+	0.913812i	$0.366875\pi$
$98$	1.00000	0.101015
$99$	0	0
$100$	0	0
$101$	−10.0000	−0.995037	−0.497519	−	0.867453i	$-0.665755\pi$
$101$	−10.0000	−0.995037	−0.497519	+	0.867453i	$0.665755\pi$
$102$	0	0
$103$	−17.0000	−1.67506	−0.837530	−	0.546392i	$-0.816001\pi$
$103$	−17.0000	−1.67506	−0.837530	+	0.546392i	$0.816001\pi$
$104$	−3.00000	−0.294174
$105$	0	0
$106$	−9.00000	−0.874157
$107$	12.0000	1.16008	0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000	1.16008	0.580042	+	0.814587i	$0.303036\pi$
$108$	0	0
$109$	16.0000	1.53252	0.766261	−	0.642529i	$-0.222115\pi$
$109$	16.0000	1.53252	0.766261	+	0.642529i	$0.222115\pi$
$110$	0	0
$111$	0	0
$112$	1.00000	0.0944911
$113$	−8.00000	−0.752577	−0.376288	−	0.926503i	$-0.622800\pi$
$113$	−8.00000	−0.752577	−0.376288	+	0.926503i	$0.622800\pi$
$114$	0	0
$115$	0	0
$116$	−1.00000	−0.0928477
$117$	0	0
$118$	5.00000	0.460287
$119$	−7.00000	−0.641689
$120$	0	0
$121$	5.00000	0.454545
$122$	−6.00000	−0.543214
$123$	0	0
$124$	−9.00000	−0.808224
$125$	0	0
$126$	0	0
$127$	0	0		−	1.00000i	$-0.5\pi$
$127$	0	0			1.00000i	$0.5\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	0	0
$131$	−1.00000	−0.0873704	−0.0436852	−	0.999045i	$-0.513910\pi$
$131$	−1.00000	−0.0873704	−0.0436852	+	0.999045i	$0.513910\pi$
$132$	0	0
$133$	2.00000	0.173422
$134$	−7.00000	−0.604708
$135$	0	0
$136$	−7.00000	−0.600245
$137$	22.0000	1.87959	0.939793	−	0.341743i	$-0.111017\pi$
$137$	22.0000	1.87959	0.939793	+	0.341743i	$0.111017\pi$
$138$	0	0
$139$	10.0000	0.848189	0.424094	−	0.905618i	$-0.360592\pi$
$139$	10.0000	0.848189	0.424094	+	0.905618i	$0.360592\pi$
$140$	0	0
$141$	0	0
$142$	7.00000	0.587427
$143$	−12.0000	−1.00349
$144$	0	0
$145$	0	0
$146$	14.0000	1.15865
$147$	0	0
$148$	−2.00000	−0.164399
$149$	3.00000	0.245770	0.122885	−	0.992421i	$-0.460785\pi$
$149$	3.00000	0.245770	0.122885	+	0.992421i	$0.460785\pi$
$150$	0	0
$151$	10.0000	0.813788	0.406894	−	0.913475i	$-0.366612\pi$
$151$	10.0000	0.813788	0.406894	+	0.913475i	$0.366612\pi$
$152$	2.00000	0.162221
$153$	0	0
$154$	4.00000	0.322329
$155$	0	0
$156$	0	0
$157$	−17.0000	−1.35675	−0.678374	−	0.734717i	$-0.737315\pi$
$157$	−17.0000	−1.35675	−0.678374	+	0.734717i	$0.737315\pi$
$158$	−6.00000	−0.477334
$159$	0	0
$160$	0	0
$161$	−1.00000	−0.0788110
$162$	0	0
$163$	1.00000	0.0783260	0.0391630	−	0.999233i	$-0.487531\pi$
$163$	1.00000	0.0783260	0.0391630	+	0.999233i	$0.487531\pi$
$164$	−6.00000	−0.468521
$165$	0	0
$166$	−4.00000	−0.310460
$167$	−8.00000	−0.619059	−0.309529	−	0.950890i	$-0.600171\pi$
$167$	−8.00000	−0.619059	−0.309529	+	0.950890i	$0.600171\pi$
$168$	0	0
$169$	−4.00000	−0.307692
$170$	0	0
$171$	0	0
$172$	−11.0000	−0.838742
$173$	−8.00000	−0.608229	−0.304114	−	0.952636i	$-0.598361\pi$
$173$	−8.00000	−0.608229	−0.304114	+	0.952636i	$0.598361\pi$
$174$	0	0
$175$	0	0
$176$	4.00000	0.301511
$177$	0	0
$178$	3.00000	0.224860
$179$	12.0000	0.896922	0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000	0.896922	0.448461	+	0.893802i	$0.351972\pi$
$180$	0	0
$181$	−9.00000	−0.668965	−0.334482	−	0.942402i	$-0.608561\pi$
$181$	−9.00000	−0.668965	−0.334482	+	0.942402i	$0.608561\pi$
$182$	−3.00000	−0.222375
$183$	0	0
$184$	−1.00000	−0.0737210
$185$	0	0
$186$	0	0
$187$	−28.0000	−2.04756
$188$	−6.00000	−0.437595
$189$	0	0
$190$	0	0
$191$	−12.0000	−0.868290	−0.434145	−	0.900843i	$-0.642949\pi$
$191$	−12.0000	−0.868290	−0.434145	+	0.900843i	$0.642949\pi$
$192$	0	0
$193$	−5.00000	−0.359908	−0.179954	−	0.983675i	$-0.557595\pi$
$193$	−5.00000	−0.359908	−0.179954	+	0.983675i	$0.557595\pi$
$194$	8.00000	0.574367
$195$	0	0
$196$	1.00000	0.0714286
$197$	26.0000	1.85242	0.926212	−	0.377004i	$-0.123046\pi$
$197$	26.0000	1.85242	0.926212	+	0.377004i	$0.123046\pi$
$198$	0	0
$199$	−7.00000	−0.496217	−0.248108	−	0.968732i	$-0.579809\pi$
$199$	−7.00000	−0.496217	−0.248108	+	0.968732i	$0.579809\pi$
$200$	0	0
$201$	0	0
$202$	−10.0000	−0.703598
$203$	−1.00000	−0.0701862
$204$	0	0
$205$	0	0
$206$	−17.0000	−1.18445
$207$	0	0
$208$	−3.00000	−0.208013
$209$	8.00000	0.553372
$210$	0	0
$211$	−1.00000	−0.0688428	−0.0344214	−	0.999407i	$-0.510959\pi$
$211$	−1.00000	−0.0688428	−0.0344214	+	0.999407i	$0.510959\pi$
$212$	−9.00000	−0.618123
$213$	0	0
$214$	12.0000	0.820303
$215$	0	0
$216$	0	0
$217$	−9.00000	−0.610960
$218$	16.0000	1.08366
$219$	0	0
$220$	0	0
$221$	21.0000	1.41261
$222$	0	0
$223$	−8.00000	−0.535720	−0.267860	−	0.963458i	$-0.586316\pi$
$223$	−8.00000	−0.535720	−0.267860	+	0.963458i	$0.586316\pi$
$224$	1.00000	0.0668153
$225$	0	0
$226$	−8.00000	−0.532152
$227$	−9.00000	−0.597351	−0.298675	−	0.954355i	$-0.596545\pi$
$227$	−9.00000	−0.597351	−0.298675	+	0.954355i	$0.596545\pi$
$228$	0	0
$229$	−14.0000	−0.925146	−0.462573	−	0.886581i	$-0.653074\pi$
$229$	−14.0000	−0.925146	−0.462573	+	0.886581i	$0.653074\pi$
$230$	0	0
$231$	0	0
$232$	−1.00000	−0.0656532
$233$	−4.00000	−0.262049	−0.131024	−	0.991379i	$-0.541827\pi$
$233$	−4.00000	−0.262049	−0.131024	+	0.991379i	$0.541827\pi$
$234$	0	0
$235$	0	0
$236$	5.00000	0.325472
$237$	0	0
$238$	−7.00000	−0.453743
$239$	−12.0000	−0.776215	−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000	−0.776215	−0.388108	+	0.921614i	$0.626871\pi$
$240$	0	0
$241$	−10.0000	−0.644157	−0.322078	−	0.946713i	$-0.604381\pi$
$241$	−10.0000	−0.644157	−0.322078	+	0.946713i	$0.604381\pi$
$242$	5.00000	0.321412
$243$	0	0
$244$	−6.00000	−0.384111
$245$	0	0
$246$	0	0
$247$	−6.00000	−0.381771
$248$	−9.00000	−0.571501
$249$	0	0
$250$	0	0
$251$	0	0		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	0	0
$253$	−4.00000	−0.251478
$254$	0	0
$255$	0	0
$256$	1.00000	0.0625000
$257$	30.0000	1.87135	0.935674	−	0.352865i	$-0.114792\pi$
$257$	30.0000	1.87135	0.935674	+	0.352865i	$0.114792\pi$
$258$	0	0
$259$	−2.00000	−0.124274
$260$	0	0
$261$	0	0
$262$	−1.00000	−0.0617802
$263$	9.00000	0.554964	0.277482	−	0.960731i	$-0.410500\pi$
$263$	9.00000	0.554964	0.277482	+	0.960731i	$0.410500\pi$
$264$	0	0
$265$	0	0
$266$	2.00000	0.122628
$267$	0	0
$268$	−7.00000	−0.427593
$269$	−4.00000	−0.243884	−0.121942	−	0.992537i	$-0.538912\pi$
$269$	−4.00000	−0.243884	−0.121942	+	0.992537i	$0.538912\pi$
$270$	0	0
$271$	3.00000	0.182237	0.0911185	−	0.995840i	$-0.470956\pi$
$271$	3.00000	0.182237	0.0911185	+	0.995840i	$0.470956\pi$
$272$	−7.00000	−0.424437
$273$	0	0
$274$	22.0000	1.32907
$275$	0	0
$276$	0	0
$277$	−8.00000	−0.480673	−0.240337	−	0.970690i	$-0.577258\pi$
$277$	−8.00000	−0.480673	−0.240337	+	0.970690i	$0.577258\pi$
$278$	10.0000	0.599760
$279$	0	0
$280$	0	0
$281$	10.0000	0.596550	0.298275	−	0.954480i	$-0.403589\pi$
$281$	10.0000	0.596550	0.298275	+	0.954480i	$0.403589\pi$
$282$	0	0
$283$	−28.0000	−1.66443	−0.832214	−	0.554455i	$-0.812927\pi$
$283$	−28.0000	−1.66443	−0.832214	+	0.554455i	$0.812927\pi$
$284$	7.00000	0.415374
$285$	0	0
$286$	−12.0000	−0.709575
$287$	−6.00000	−0.354169
$288$	0	0
$289$	32.0000	1.88235
$290$	0	0
$291$	0	0
$292$	14.0000	0.819288
$293$	6.00000	0.350524	0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000	0.350524	0.175262	+	0.984522i	$0.443923\pi$
$294$	0	0
$295$	0	0
$296$	−2.00000	−0.116248
$297$	0	0
$298$	3.00000	0.173785
$299$	3.00000	0.173494
$300$	0	0
$301$	−11.0000	−0.634029
$302$	10.0000	0.575435
$303$	0	0
$304$	2.00000	0.114708
$305$	0	0
$306$	0	0
$307$	2.00000	0.114146	0.0570730	−	0.998370i	$-0.481823\pi$
$307$	2.00000	0.114146	0.0570730	+	0.998370i	$0.481823\pi$
$308$	4.00000	0.227921
$309$	0	0
$310$	0	0
$311$	8.00000	0.453638	0.226819	−	0.973937i	$-0.427167\pi$
$311$	8.00000	0.453638	0.226819	+	0.973937i	$0.427167\pi$
$312$	0	0
$313$	26.0000	1.46961	0.734803	−	0.678280i	$-0.237274\pi$
$313$	26.0000	1.46961	0.734803	+	0.678280i	$0.237274\pi$
$314$	−17.0000	−0.959366
$315$	0	0
$316$	−6.00000	−0.337526
$317$	−18.0000	−1.01098	−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000	−1.01098	−0.505490	+	0.862832i	$0.668688\pi$
$318$	0	0
$319$	−4.00000	−0.223957
$320$	0	0
$321$	0	0
$322$	−1.00000	−0.0557278
$323$	−14.0000	−0.778981
$324$	0	0
$325$	0	0
$326$	1.00000	0.0553849
$327$	0	0
$328$	−6.00000	−0.331295
$329$	−6.00000	−0.330791
$330$	0	0
$331$	−31.0000	−1.70391	−0.851957	−	0.523612i	$-0.824584\pi$
$331$	−31.0000	−1.70391	−0.851957	+	0.523612i	$0.824584\pi$
$332$	−4.00000	−0.219529
$333$	0	0
$334$	−8.00000	−0.437741
$335$	0	0
$336$	0	0
$337$	−27.0000	−1.47078	−0.735392	−	0.677642i	$-0.763002\pi$
$337$	−27.0000	−1.47078	−0.735392	+	0.677642i	$0.763002\pi$
$338$	−4.00000	−0.217571
$339$	0	0
$340$	0	0
$341$	−36.0000	−1.94951
$342$	0	0
$343$	1.00000	0.0539949
$344$	−11.0000	−0.593080
$345$	0	0
$346$	−8.00000	−0.430083
$347$	18.0000	0.966291	0.483145	−	0.875540i	$-0.339494\pi$
$347$	18.0000	0.966291	0.483145	+	0.875540i	$0.339494\pi$
$348$	0	0
$349$	25.0000	1.33822	0.669110	−	0.743164i	$-0.266676\pi$
$349$	25.0000	1.33822	0.669110	+	0.743164i	$0.266676\pi$
$350$	0	0
$351$	0	0
$352$	4.00000	0.213201
$353$	15.0000	0.798369	0.399185	−	0.916871i	$-0.369293\pi$
$353$	15.0000	0.798369	0.399185	+	0.916871i	$0.369293\pi$
$354$	0	0
$355$	0	0
$356$	3.00000	0.159000
$357$	0	0
$358$	12.0000	0.634220
$359$	11.0000	0.580558	0.290279	−	0.956942i	$-0.406252\pi$
$359$	11.0000	0.580558	0.290279	+	0.956942i	$0.406252\pi$
$360$	0	0
$361$	−15.0000	−0.789474
$362$	−9.00000	−0.473029
$363$	0	0
$364$	−3.00000	−0.157243
$365$	0	0
$366$	0	0
$367$	25.0000	1.30499	0.652495	−	0.757793i	$-0.273722\pi$
$367$	25.0000	1.30499	0.652495	+	0.757793i	$0.273722\pi$
$368$	−1.00000	−0.0521286
$369$	0	0
$370$	0	0
$371$	−9.00000	−0.467257
$372$	0	0
$373$	38.0000	1.96757	0.983783	−	0.179364i	$-0.0574041\pi$
$373$	38.0000	1.96757	0.983783	+	0.179364i	$0.0574041\pi$
$374$	−28.0000	−1.44785
$375$	0	0
$376$	−6.00000	−0.309426
$377$	3.00000	0.154508
$378$	0	0
$379$	−8.00000	−0.410932	−0.205466	−	0.978664i	$-0.565871\pi$
$379$	−8.00000	−0.410932	−0.205466	+	0.978664i	$0.565871\pi$
$380$	0	0
$381$	0	0
$382$	−12.0000	−0.613973
$383$	−4.00000	−0.204390	−0.102195	−	0.994764i	$-0.532587\pi$
$383$	−4.00000	−0.204390	−0.102195	+	0.994764i	$0.532587\pi$
$384$	0	0
$385$	0	0
$386$	−5.00000	−0.254493
$387$	0	0
$388$	8.00000	0.406138
$389$	14.0000	0.709828	0.354914	−	0.934899i	$-0.384510\pi$
$389$	14.0000	0.709828	0.354914	+	0.934899i	$0.384510\pi$
$390$	0	0
$391$	7.00000	0.354005
$392$	1.00000	0.0505076
$393$	0	0
$394$	26.0000	1.30986
$395$	0	0
$396$	0	0
$397$	−6.00000	−0.301131	−0.150566	−	0.988600i	$-0.548110\pi$
$397$	−6.00000	−0.301131	−0.150566	+	0.988600i	$0.548110\pi$
$398$	−7.00000	−0.350878
$399$	0	0
$400$	0	0
$401$	−30.0000	−1.49813	−0.749064	−	0.662497i	$-0.769497\pi$
$401$	−30.0000	−1.49813	−0.749064	+	0.662497i	$0.769497\pi$
$402$	0	0
$403$	27.0000	1.34497
$404$	−10.0000	−0.497519
$405$	0	0
$406$	−1.00000	−0.0496292
$407$	−8.00000	−0.396545
$408$	0	0
$409$	2.00000	0.0988936	0.0494468	−	0.998777i	$-0.484254\pi$
$409$	2.00000	0.0988936	0.0494468	+	0.998777i	$0.484254\pi$
$410$	0	0
$411$	0	0
$412$	−17.0000	−0.837530
$413$	5.00000	0.246034
$414$	0	0
$415$	0	0
$416$	−3.00000	−0.147087
$417$	0	0
$418$	8.00000	0.391293
$419$	33.0000	1.61216	0.806078	−	0.591810i	$-0.201586\pi$
$419$	33.0000	1.61216	0.806078	+	0.591810i	$0.201586\pi$
$420$	0	0
$421$	−6.00000	−0.292422	−0.146211	−	0.989253i	$-0.546708\pi$
$421$	−6.00000	−0.292422	−0.146211	+	0.989253i	$0.546708\pi$
$422$	−1.00000	−0.0486792
$423$	0	0
$424$	−9.00000	−0.437079
$425$	0	0
$426$	0	0
$427$	−6.00000	−0.290360
$428$	12.0000	0.580042
$429$	0	0
$430$	0	0
$431$	−24.0000	−1.15604	−0.578020	−	0.816023i	$-0.696174\pi$
$431$	−24.0000	−1.15604	−0.578020	+	0.816023i	$0.696174\pi$
$432$	0	0
$433$	−8.00000	−0.384455	−0.192228	−	0.981350i	$-0.561571\pi$
$433$	−8.00000	−0.384455	−0.192228	+	0.981350i	$0.561571\pi$
$434$	−9.00000	−0.432014
$435$	0	0
$436$	16.0000	0.766261
$437$	−2.00000	−0.0956730
$438$	0	0
$439$	9.00000	0.429547	0.214773	−	0.976664i	$-0.431099\pi$
$439$	9.00000	0.429547	0.214773	+	0.976664i	$0.431099\pi$
$440$	0	0
$441$	0	0
$442$	21.0000	0.998868
$443$	26.0000	1.23530	0.617649	−	0.786454i	$-0.288085\pi$
$443$	26.0000	1.23530	0.617649	+	0.786454i	$0.288085\pi$
$444$	0	0
$445$	0	0
$446$	−8.00000	−0.378811
$447$	0	0
$448$	1.00000	0.0472456
$449$	−4.00000	−0.188772	−0.0943858	−	0.995536i	$-0.530089\pi$
$449$	−4.00000	−0.188772	−0.0943858	+	0.995536i	$0.530089\pi$
$450$	0	0
$451$	−24.0000	−1.13012
$452$	−8.00000	−0.376288
$453$	0	0
$454$	−9.00000	−0.422391
$455$	0	0
$456$	0	0
$457$	29.0000	1.35656	0.678281	−	0.734802i	$-0.262725\pi$
$457$	29.0000	1.35656	0.678281	+	0.734802i	$0.262725\pi$
$458$	−14.0000	−0.654177
$459$	0	0
$460$	0	0
$461$	14.0000	0.652045	0.326023	−	0.945362i	$-0.394291\pi$
$461$	14.0000	0.652045	0.326023	+	0.945362i	$0.394291\pi$
$462$	0	0
$463$	−22.0000	−1.02243	−0.511213	−	0.859454i	$-0.670804\pi$
$463$	−22.0000	−1.02243	−0.511213	+	0.859454i	$0.670804\pi$
$464$	−1.00000	−0.0464238
$465$	0	0
$466$	−4.00000	−0.185296
$467$	−8.00000	−0.370196	−0.185098	−	0.982720i	$-0.559260\pi$
$467$	−8.00000	−0.370196	−0.185098	+	0.982720i	$0.559260\pi$
$468$	0	0
$469$	−7.00000	−0.323230
$470$	0	0
$471$	0	0
$472$	5.00000	0.230144
$473$	−44.0000	−2.02312
$474$	0	0
$475$	0	0
$476$	−7.00000	−0.320844
$477$	0	0
$478$	−12.0000	−0.548867
$479$	−8.00000	−0.365529	−0.182765	−	0.983157i	$-0.558505\pi$
$479$	−8.00000	−0.365529	−0.182765	+	0.983157i	$0.558505\pi$
$480$	0	0
$481$	6.00000	0.273576
$482$	−10.0000	−0.455488
$483$	0	0
$484$	5.00000	0.227273
$485$	0	0
$486$	0	0
$487$	−26.0000	−1.17817	−0.589086	−	0.808070i	$-0.700512\pi$
$487$	−26.0000	−1.17817	−0.589086	+	0.808070i	$0.700512\pi$
$488$	−6.00000	−0.271607
$489$	0	0
$490$	0	0
$491$	−24.0000	−1.08310	−0.541552	−	0.840667i	$-0.682163\pi$
$491$	−24.0000	−1.08310	−0.541552	+	0.840667i	$0.682163\pi$
$492$	0	0
$493$	7.00000	0.315264
$494$	−6.00000	−0.269953
$495$	0	0
$496$	−9.00000	−0.404112
$497$	7.00000	0.313993
$498$	0	0
$499$	28.0000	1.25345	0.626726	−	0.779240i	$-0.284395\pi$
$499$	28.0000	1.25345	0.626726	+	0.779240i	$0.284395\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	−24.0000	−1.07011	−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000	−1.07011	−0.535054	+	0.844818i	$0.679709\pi$
$504$	0	0
$505$	0	0
$506$	−4.00000	−0.177822
$507$	0	0
$508$	0	0
$509$	6.00000	0.265945	0.132973	−	0.991120i	$-0.457548\pi$
$509$	6.00000	0.265945	0.132973	+	0.991120i	$0.457548\pi$
$510$	0	0
$511$	14.0000	0.619324
$512$	1.00000	0.0441942
$513$	0	0
$514$	30.0000	1.32324
$515$	0	0
$516$	0	0
$517$	−24.0000	−1.05552
$518$	−2.00000	−0.0878750
$519$	0	0
$520$	0	0
$521$	15.0000	0.657162	0.328581	−	0.944476i	$-0.393430\pi$
$521$	15.0000	0.657162	0.328581	+	0.944476i	$0.393430\pi$
$522$	0	0
$523$	16.0000	0.699631	0.349816	−	0.936819i	$-0.386244\pi$
$523$	16.0000	0.699631	0.349816	+	0.936819i	$0.386244\pi$
$524$	−1.00000	−0.0436852
$525$	0	0
$526$	9.00000	0.392419
$527$	63.0000	2.74432
$528$	0	0
$529$	−22.0000	−0.956522
$530$	0	0
$531$	0	0
$532$	2.00000	0.0867110
$533$	18.0000	0.779667
$534$	0	0
$535$	0	0
$536$	−7.00000	−0.302354
$537$	0	0
$538$	−4.00000	−0.172452
$539$	4.00000	0.172292
$540$	0	0
$541$	−36.0000	−1.54776	−0.773880	−	0.633332i	$-0.781687\pi$
$541$	−36.0000	−1.54776	−0.773880	+	0.633332i	$0.781687\pi$
$542$	3.00000	0.128861
$543$	0	0
$544$	−7.00000	−0.300123
$545$	0	0
$546$	0	0
$547$	−36.0000	−1.53925	−0.769624	−	0.638497i	$-0.779557\pi$
$547$	−36.0000	−1.53925	−0.769624	+	0.638497i	$0.779557\pi$
$548$	22.0000	0.939793
$549$	0	0
$550$	0	0
$551$	−2.00000	−0.0852029
$552$	0	0
$553$	−6.00000	−0.255146
$554$	−8.00000	−0.339887
$555$	0	0
$556$	10.0000	0.424094
$557$	1.00000	0.0423714	0.0211857	−	0.999776i	$-0.493256\pi$
$557$	1.00000	0.0423714	0.0211857	+	0.999776i	$0.493256\pi$
$558$	0	0
$559$	33.0000	1.39575
$560$	0	0
$561$	0	0
$562$	10.0000	0.421825
$563$	11.0000	0.463595	0.231797	−	0.972764i	$-0.425539\pi$
$563$	11.0000	0.463595	0.231797	+	0.972764i	$0.425539\pi$
$564$	0	0
$565$	0	0
$566$	−28.0000	−1.17693
$567$	0	0
$568$	7.00000	0.293713
$569$	−12.0000	−0.503066	−0.251533	−	0.967849i	$-0.580935\pi$
$569$	−12.0000	−0.503066	−0.251533	+	0.967849i	$0.580935\pi$
$570$	0	0
$571$	−39.0000	−1.63210	−0.816050	−	0.577982i	$-0.803840\pi$
$571$	−39.0000	−1.63210	−0.816050	+	0.577982i	$0.803840\pi$
$572$	−12.0000	−0.501745
$573$	0	0
$574$	−6.00000	−0.250435
$575$	0	0
$576$	0	0
$577$	−10.0000	−0.416305	−0.208153	−	0.978096i	$-0.566745\pi$
$577$	−10.0000	−0.416305	−0.208153	+	0.978096i	$0.566745\pi$
$578$	32.0000	1.33102
$579$	0	0
$580$	0	0
$581$	−4.00000	−0.165948
$582$	0	0
$583$	−36.0000	−1.49097
$584$	14.0000	0.579324
$585$	0	0
$586$	6.00000	0.247858
$587$	−25.0000	−1.03186	−0.515930	−	0.856631i	$-0.672554\pi$
$587$	−25.0000	−1.03186	−0.515930	+	0.856631i	$0.672554\pi$
$588$	0	0
$589$	−18.0000	−0.741677
$590$	0	0
$591$	0	0
$592$	−2.00000	−0.0821995
$593$	−18.0000	−0.739171	−0.369586	−	0.929197i	$-0.620500\pi$
$593$	−18.0000	−0.739171	−0.369586	+	0.929197i	$0.620500\pi$
$594$	0	0
$595$	0	0
$596$	3.00000	0.122885
$597$	0	0
$598$	3.00000	0.122679
$599$	−21.0000	−0.858037	−0.429018	−	0.903296i	$-0.641140\pi$
$599$	−21.0000	−0.858037	−0.429018	+	0.903296i	$0.641140\pi$
$600$	0	0
$601$	−28.0000	−1.14214	−0.571072	−	0.820900i	$-0.693472\pi$
$601$	−28.0000	−1.14214	−0.571072	+	0.820900i	$0.693472\pi$
$602$	−11.0000	−0.448327
$603$	0	0
$604$	10.0000	0.406894
$605$	0	0
$606$	0	0
$607$	−39.0000	−1.58296	−0.791481	−	0.611194i	$-0.790689\pi$
$607$	−39.0000	−1.58296	−0.791481	+	0.611194i	$0.790689\pi$
$608$	2.00000	0.0811107
$609$	0	0
$610$	0	0
$611$	18.0000	0.728202
$612$	0	0
$613$	6.00000	0.242338	0.121169	−	0.992632i	$-0.461336\pi$
$613$	6.00000	0.242338	0.121169	+	0.992632i	$0.461336\pi$
$614$	2.00000	0.0807134
$615$	0	0
$616$	4.00000	0.161165
$617$	14.0000	0.563619	0.281809	−	0.959470i	$-0.409065\pi$
$617$	14.0000	0.563619	0.281809	+	0.959470i	$0.409065\pi$
$618$	0	0
$619$	−14.0000	−0.562708	−0.281354	−	0.959604i	$-0.590783\pi$
$619$	−14.0000	−0.562708	−0.281354	+	0.959604i	$0.590783\pi$
$620$	0	0
$621$	0	0
$622$	8.00000	0.320771
$623$	3.00000	0.120192
$624$	0	0
$625$	0	0
$626$	26.0000	1.03917
$627$	0	0
$628$	−17.0000	−0.678374
$629$	14.0000	0.558217
$630$	0	0
$631$	−4.00000	−0.159237	−0.0796187	−	0.996825i	$-0.525370\pi$
$631$	−4.00000	−0.159237	−0.0796187	+	0.996825i	$0.525370\pi$
$632$	−6.00000	−0.238667
$633$	0	0
$634$	−18.0000	−0.714871
$635$	0	0
$636$	0	0
$637$	−3.00000	−0.118864
$638$	−4.00000	−0.158362
$639$	0	0
$640$	0	0
$641$	28.0000	1.10593	0.552967	−	0.833203i	$-0.313496\pi$
$641$	28.0000	1.10593	0.552967	+	0.833203i	$0.313496\pi$
$642$	0	0
$643$	4.00000	0.157745	0.0788723	−	0.996885i	$-0.474868\pi$
$643$	4.00000	0.157745	0.0788723	+	0.996885i	$0.474868\pi$
$644$	−1.00000	−0.0394055
$645$	0	0
$646$	−14.0000	−0.550823
$647$	42.0000	1.65119	0.825595	−	0.564263i	$-0.190840\pi$
$647$	42.0000	1.65119	0.825595	+	0.564263i	$0.190840\pi$
$648$	0	0
$649$	20.0000	0.785069
$650$	0	0
$651$	0	0
$652$	1.00000	0.0391630
$653$	3.00000	0.117399	0.0586995	−	0.998276i	$-0.481305\pi$
$653$	3.00000	0.117399	0.0586995	+	0.998276i	$0.481305\pi$
$654$	0	0
$655$	0	0
$656$	−6.00000	−0.234261
$657$	0	0
$658$	−6.00000	−0.233904
$659$	28.0000	1.09073	0.545363	−	0.838200i	$-0.316392\pi$
$659$	28.0000	1.09073	0.545363	+	0.838200i	$0.316392\pi$
$660$	0	0
$661$	−14.0000	−0.544537	−0.272268	−	0.962221i	$-0.587774\pi$
$661$	−14.0000	−0.544537	−0.272268	+	0.962221i	$0.587774\pi$
$662$	−31.0000	−1.20485
$663$	0	0
$664$	−4.00000	−0.155230
$665$	0	0
$666$	0	0
$667$	1.00000	0.0387202
$668$	−8.00000	−0.309529
$669$	0	0
$670$	0	0
$671$	−24.0000	−0.926510
$672$	0	0
$673$	−23.0000	−0.886585	−0.443292	−	0.896377i	$-0.646190\pi$
$673$	−23.0000	−0.886585	−0.443292	+	0.896377i	$0.646190\pi$
$674$	−27.0000	−1.04000
$675$	0	0
$676$	−4.00000	−0.153846
$677$	0	0		−	1.00000i	$-0.5\pi$
$677$	0	0			1.00000i	$0.5\pi$
$678$	0	0
$679$	8.00000	0.307012
$680$	0	0
$681$	0	0
$682$	−36.0000	−1.37851
$683$	−48.0000	−1.83667	−0.918334	−	0.395805i	$-0.870466\pi$
$683$	−48.0000	−1.83667	−0.918334	+	0.395805i	$0.870466\pi$
$684$	0	0
$685$	0	0
$686$	1.00000	0.0381802
$687$	0	0
$688$	−11.0000	−0.419371
$689$	27.0000	1.02862
$690$	0	0
$691$	−40.0000	−1.52167	−0.760836	−	0.648944i	$-0.775211\pi$
$691$	−40.0000	−1.52167	−0.760836	+	0.648944i	$0.775211\pi$
$692$	−8.00000	−0.304114
$693$	0	0
$694$	18.0000	0.683271
$695$	0	0
$696$	0	0
$697$	42.0000	1.59086
$698$	25.0000	0.946264
$699$	0	0
$700$	0	0
$701$	2.00000	0.0755390	0.0377695	−	0.999286i	$-0.487975\pi$
$701$	2.00000	0.0755390	0.0377695	+	0.999286i	$0.487975\pi$
$702$	0	0
$703$	−4.00000	−0.150863
$704$	4.00000	0.150756
$705$	0	0
$706$	15.0000	0.564532
$707$	−10.0000	−0.376089
$708$	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
$712$	3.00000	0.112430
$713$	9.00000	0.337053
$714$	0	0
$715$	0	0
$716$	12.0000	0.448461
$717$	0	0
$718$	11.0000	0.410516
$719$	−48.0000	−1.79010	−0.895049	−	0.445968i	$-0.852860\pi$
$719$	−48.0000	−1.79010	−0.895049	+	0.445968i	$0.852860\pi$
$720$	0	0
$721$	−17.0000	−0.633113
$722$	−15.0000	−0.558242
$723$	0	0
$724$	−9.00000	−0.334482
$725$	0	0
$726$	0	0
$727$	29.0000	1.07555	0.537775	−	0.843088i	$-0.319265\pi$
$727$	29.0000	1.07555	0.537775	+	0.843088i	$0.319265\pi$
$728$	−3.00000	−0.111187
$729$	0	0
$730$	0	0
$731$	77.0000	2.84795
$732$	0	0
$733$	15.0000	0.554038	0.277019	−	0.960864i	$-0.410654\pi$
$733$	15.0000	0.554038	0.277019	+	0.960864i	$0.410654\pi$
$734$	25.0000	0.922767
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	−28.0000	−1.03139
$738$	0	0
$739$	12.0000	0.441427	0.220714	−	0.975339i	$-0.429161\pi$
$739$	12.0000	0.441427	0.220714	+	0.975339i	$0.429161\pi$
$740$	0	0
$741$	0	0
$742$	−9.00000	−0.330400
$743$	51.0000	1.87101	0.935504	−	0.353315i	$-0.114946\pi$
$743$	51.0000	1.87101	0.935504	+	0.353315i	$0.114946\pi$
$744$	0	0
$745$	0	0
$746$	38.0000	1.39128
$747$	0	0
$748$	−28.0000	−1.02378
$749$	12.0000	0.438470
$750$	0	0
$751$	6.00000	0.218943	0.109472	−	0.993990i	$-0.465084\pi$
$751$	6.00000	0.218943	0.109472	+	0.993990i	$0.465084\pi$
$752$	−6.00000	−0.218797
$753$	0	0
$754$	3.00000	0.109254
$755$	0	0
$756$	0	0
$757$	12.0000	0.436147	0.218074	−	0.975932i	$-0.430023\pi$
$757$	12.0000	0.436147	0.218074	+	0.975932i	$0.430023\pi$
$758$	−8.00000	−0.290573
$759$	0	0
$760$	0	0
$761$	13.0000	0.471250	0.235625	−	0.971844i	$-0.424286\pi$
$761$	13.0000	0.471250	0.235625	+	0.971844i	$0.424286\pi$
$762$	0	0
$763$	16.0000	0.579239
$764$	−12.0000	−0.434145
$765$	0	0
$766$	−4.00000	−0.144526
$767$	−15.0000	−0.541619
$768$	0	0
$769$	4.00000	0.144244	0.0721218	−	0.997396i	$-0.477023\pi$
$769$	4.00000	0.144244	0.0721218	+	0.997396i	$0.477023\pi$
$770$	0	0
$771$	0	0
$772$	−5.00000	−0.179954
$773$	4.00000	0.143870	0.0719350	−	0.997409i	$-0.477083\pi$
$773$	4.00000	0.143870	0.0719350	+	0.997409i	$0.477083\pi$
$774$	0	0
$775$	0	0
$776$	8.00000	0.287183
$777$	0	0
$778$	14.0000	0.501924
$779$	−12.0000	−0.429945
$780$	0	0
$781$	28.0000	1.00192
$782$	7.00000	0.250319
$783$	0	0
$784$	1.00000	0.0357143
$785$	0	0
$786$	0	0
$787$	−18.0000	−0.641631	−0.320815	−	0.947142i	$-0.603957\pi$
$787$	−18.0000	−0.641631	−0.320815	+	0.947142i	$0.603957\pi$
$788$	26.0000	0.926212
$789$	0	0
$790$	0	0
$791$	−8.00000	−0.284447
$792$	0	0
$793$	18.0000	0.639199
$794$	−6.00000	−0.212932
$795$	0	0
$796$	−7.00000	−0.248108
$797$	−18.0000	−0.637593	−0.318796	−	0.947823i	$-0.603279\pi$
$797$	−18.0000	−0.637593	−0.318796	+	0.947823i	$0.603279\pi$
$798$	0	0
$799$	42.0000	1.48585
$800$	0	0
$801$	0	0
$802$	−30.0000	−1.05934
$803$	56.0000	1.97620
$804$	0	0
$805$	0	0
$806$	27.0000	0.951034
$807$	0	0
$808$	−10.0000	−0.351799
$809$	32.0000	1.12506	0.562530	−	0.826777i	$-0.309828\pi$
$809$	32.0000	1.12506	0.562530	+	0.826777i	$0.309828\pi$
$810$	0	0
$811$	−26.0000	−0.912983	−0.456492	−	0.889728i	$-0.650894\pi$
$811$	−26.0000	−0.912983	−0.456492	+	0.889728i	$0.650894\pi$
$812$	−1.00000	−0.0350931
$813$	0	0
$814$	−8.00000	−0.280400
$815$	0	0
$816$	0	0
$817$	−22.0000	−0.769683
$818$	2.00000	0.0699284
$819$	0	0
$820$	0	0
$821$	13.0000	0.453703	0.226852	−	0.973929i	$-0.427157\pi$
$821$	13.0000	0.453703	0.226852	+	0.973929i	$0.427157\pi$
$822$	0	0
$823$	38.0000	1.32460	0.662298	−	0.749240i	$-0.269581\pi$
$823$	38.0000	1.32460	0.662298	+	0.749240i	$0.269581\pi$
$824$	−17.0000	−0.592223
$825$	0	0
$826$	5.00000	0.173972
$827$	42.0000	1.46048	0.730242	−	0.683189i	$-0.239408\pi$
$827$	42.0000	1.46048	0.730242	+	0.683189i	$0.239408\pi$
$828$	0	0
$829$	−26.0000	−0.903017	−0.451509	−	0.892267i	$-0.649114\pi$
$829$	−26.0000	−0.903017	−0.451509	+	0.892267i	$0.649114\pi$
$830$	0	0
$831$	0	0
$832$	−3.00000	−0.104006
$833$	−7.00000	−0.242536
$834$	0	0
$835$	0	0
$836$	8.00000	0.276686
$837$	0	0
$838$	33.0000	1.13997
$839$	10.0000	0.345238	0.172619	−	0.984989i	$-0.444777\pi$
$839$	10.0000	0.345238	0.172619	+	0.984989i	$0.444777\pi$
$840$	0	0
$841$	−28.0000	−0.965517
$842$	−6.00000	−0.206774
$843$	0	0
$844$	−1.00000	−0.0344214
$845$	0	0
$846$	0	0
$847$	5.00000	0.171802
$848$	−9.00000	−0.309061
$849$	0	0
$850$	0	0
$851$	2.00000	0.0685591
$852$	0	0
$853$	−53.0000	−1.81469	−0.907343	−	0.420392i	$-0.861893\pi$
$853$	−53.0000	−1.81469	−0.907343	+	0.420392i	$0.861893\pi$
$854$	−6.00000	−0.205316
$855$	0	0
$856$	12.0000	0.410152
$857$	27.0000	0.922302	0.461151	−	0.887322i	$-0.347437\pi$
$857$	27.0000	0.922302	0.461151	+	0.887322i	$0.347437\pi$
$858$	0	0
$859$	2.00000	0.0682391	0.0341196	−	0.999418i	$-0.489137\pi$
$859$	2.00000	0.0682391	0.0341196	+	0.999418i	$0.489137\pi$
$860$	0	0
$861$	0	0
$862$	−24.0000	−0.817443
$863$	1.00000	0.0340404	0.0170202	−	0.999855i	$-0.494582\pi$
$863$	1.00000	0.0340404	0.0170202	+	0.999855i	$0.494582\pi$
$864$	0	0
$865$	0	0
$866$	−8.00000	−0.271851
$867$	0	0
$868$	−9.00000	−0.305480
$869$	−24.0000	−0.814144
$870$	0	0
$871$	21.0000	0.711558
$872$	16.0000	0.541828
$873$	0	0
$874$	−2.00000	−0.0676510
$875$	0	0
$876$	0	0
$877$	8.00000	0.270141	0.135070	−	0.990836i	$-0.456874\pi$
$877$	8.00000	0.270141	0.135070	+	0.990836i	$0.456874\pi$
$878$	9.00000	0.303735
$879$	0	0
$880$	0	0
$881$	−15.0000	−0.505363	−0.252681	−	0.967550i	$-0.581312\pi$
$881$	−15.0000	−0.505363	−0.252681	+	0.967550i	$0.581312\pi$
$882$	0	0
$883$	19.0000	0.639401	0.319700	−	0.947519i	$-0.396418\pi$
$883$	19.0000	0.639401	0.319700	+	0.947519i	$0.396418\pi$
$884$	21.0000	0.706306
$885$	0	0
$886$	26.0000	0.873487
$887$	−12.0000	−0.402921	−0.201460	−	0.979497i	$-0.564569\pi$
$887$	−12.0000	−0.402921	−0.201460	+	0.979497i	$0.564569\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	0	0
$892$	−8.00000	−0.267860
$893$	−12.0000	−0.401565
$894$	0	0
$895$	0	0
$896$	1.00000	0.0334077
$897$	0	0
$898$	−4.00000	−0.133482
$899$	9.00000	0.300167
$900$	0	0
$901$	63.0000	2.09883
$902$	−24.0000	−0.799113
$903$	0	0
$904$	−8.00000	−0.266076
$905$	0	0
$906$	0	0
$907$	−12.0000	−0.398453	−0.199227	−	0.979953i	$-0.563843\pi$
$907$	−12.0000	−0.398453	−0.199227	+	0.979953i	$0.563843\pi$
$908$	−9.00000	−0.298675
$909$	0	0
$910$	0	0
$911$	48.0000	1.59031	0.795155	−	0.606406i	$-0.207389\pi$
$911$	48.0000	1.59031	0.795155	+	0.606406i	$0.207389\pi$
$912$	0	0
$913$	−16.0000	−0.529523
$914$	29.0000	0.959235
$915$	0	0
$916$	−14.0000	−0.462573
$917$	−1.00000	−0.0330229
$918$	0	0
$919$	22.0000	0.725713	0.362857	−	0.931845i	$-0.381802\pi$
$919$	22.0000	0.725713	0.362857	+	0.931845i	$0.381802\pi$
$920$	0	0
$921$	0	0
$922$	14.0000	0.461065
$923$	−21.0000	−0.691223
$924$	0	0
$925$	0	0
$926$	−22.0000	−0.722965
$927$	0	0
$928$	−1.00000	−0.0328266
$929$	30.0000	0.984268	0.492134	−	0.870519i	$-0.336217\pi$
$929$	30.0000	0.984268	0.492134	+	0.870519i	$0.336217\pi$
$930$	0	0
$931$	2.00000	0.0655474
$932$	−4.00000	−0.131024
$933$	0	0
$934$	−8.00000	−0.261768
$935$	0	0
$936$	0	0
$937$	52.0000	1.69877	0.849383	−	0.527777i	$-0.176974\pi$
$937$	52.0000	1.69877	0.849383	+	0.527777i	$0.176974\pi$
$938$	−7.00000	−0.228558
$939$	0	0
$940$	0	0
$941$	2.00000	0.0651981	0.0325991	−	0.999469i	$-0.489622\pi$
$941$	2.00000	0.0651981	0.0325991	+	0.999469i	$0.489622\pi$
$942$	0	0
$943$	6.00000	0.195387
$944$	5.00000	0.162736
$945$	0	0
$946$	−44.0000	−1.43056
$947$	−2.00000	−0.0649913	−0.0324956	−	0.999472i	$-0.510346\pi$
$947$	−2.00000	−0.0649913	−0.0324956	+	0.999472i	$0.510346\pi$
$948$	0	0
$949$	−42.0000	−1.36338
$950$	0	0
$951$	0	0
$952$	−7.00000	−0.226871
$953$	8.00000	0.259145	0.129573	−	0.991570i	$-0.458639\pi$
$953$	8.00000	0.259145	0.129573	+	0.991570i	$0.458639\pi$
$954$	0	0
$955$	0	0
$956$	−12.0000	−0.388108
$957$	0	0
$958$	−8.00000	−0.258468
$959$	22.0000	0.710417
$960$	0	0
$961$	50.0000	1.61290
$962$	6.00000	0.193448
$963$	0	0
$964$	−10.0000	−0.322078
$965$	0	0
$966$	0	0
$967$	40.0000	1.28631	0.643157	−	0.765735i	$-0.277624\pi$
$967$	40.0000	1.28631	0.643157	+	0.765735i	$0.277624\pi$
$968$	5.00000	0.160706
$969$	0	0
$970$	0	0
$971$	15.0000	0.481373	0.240686	−	0.970603i	$-0.422627\pi$
$971$	15.0000	0.481373	0.240686	+	0.970603i	$0.422627\pi$
$972$	0	0
$973$	10.0000	0.320585
$974$	−26.0000	−0.833094
$975$	0	0
$976$	−6.00000	−0.192055
$977$	−42.0000	−1.34370	−0.671850	−	0.740688i	$-0.734500\pi$
$977$	−42.0000	−1.34370	−0.671850	+	0.740688i	$0.734500\pi$
$978$	0	0
$979$	12.0000	0.383522
$980$	0	0
$981$	0	0
$982$	−24.0000	−0.765871
$983$	36.0000	1.14822	0.574111	−	0.818778i	$-0.305348\pi$
$983$	36.0000	1.14822	0.574111	+	0.818778i	$0.305348\pi$
$984$	0	0
$985$	0	0
$986$	7.00000	0.222925
$987$	0	0
$988$	−6.00000	−0.190885
$989$	11.0000	0.349780
$990$	0	0
$991$	26.0000	0.825917	0.412959	−	0.910750i	$-0.364495\pi$
$991$	26.0000	0.825917	0.412959	+	0.910750i	$0.364495\pi$
$992$	−9.00000	−0.285750
$993$	0	0
$994$	7.00000	0.222027
$995$	0	0
$996$	0	0
$997$	−35.0000	−1.10846	−0.554231	−	0.832363i	$-0.686987\pi$
$997$	−35.0000	−1.10846	−0.554231	+	0.832363i	$0.686987\pi$
$998$	28.0000	0.886325
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9450.2.a.dv.1.1		1
3.2	odd	2		9450.2.a.bc.1.1		1
5.4	even	2		378.2.a.a.1.1	✓	1
15.14	odd	2		378.2.a.h.1.1	yes	1
20.19	odd	2		3024.2.a.a.1.1		1
35.34	odd	2		2646.2.a.o.1.1		1
45.4	even	6		1134.2.f.p.379.1		2
45.14	odd	6		1134.2.f.a.379.1		2
45.29	odd	6		1134.2.f.a.757.1		2
45.34	even	6		1134.2.f.p.757.1		2
60.59	even	2		3024.2.a.bd.1.1		1
105.104	even	2		2646.2.a.p.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.a.a.1.1	✓	1	5.4	even	2
378.2.a.h.1.1	yes	1	15.14	odd	2
1134.2.f.a.379.1		2	45.14	odd	6
1134.2.f.a.757.1		2	45.29	odd	6
1134.2.f.p.379.1		2	45.4	even	6
1134.2.f.p.757.1		2	45.34	even	6
2646.2.a.o.1.1		1	35.34	odd	2
2646.2.a.p.1.1		1	105.104	even	2
3024.2.a.a.1.1		1	20.19	odd	2
3024.2.a.bd.1.1		1	60.59	even	2
9450.2.a.bc.1.1		1	3.2	odd	2
9450.2.a.dv.1.1		1	1.1	even	1	trivial

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

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