LMFDB - Embedded newform 9450.2.a.bw.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)

$f(q)$

$=$

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

$q-1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{7} -1.00000 q^{8} +5.00000 q^{11} -1.00000 q^{13} -1.00000 q^{14} +1.00000 q^{16} +7.00000 q^{17} -2.00000 q^{19} -5.00000 q^{22} -9.00000 q^{23} +1.00000 q^{26} +1.00000 q^{28} -3.00000 q^{29} +3.00000 q^{31} -1.00000 q^{32} -7.00000 q^{34} +2.00000 q^{37} +2.00000 q^{38} -6.00000 q^{41} -13.0000 q^{43} +5.00000 q^{44} +9.00000 q^{46} -7.00000 q^{47} +1.00000 q^{49} -1.00000 q^{52} -4.00000 q^{53} -1.00000 q^{56} +3.00000 q^{58} -4.00000 q^{59} +4.00000 q^{61} -3.00000 q^{62} +1.00000 q^{64} -12.0000 q^{67} +7.00000 q^{68} -10.0000 q^{71} +14.0000 q^{73} -2.00000 q^{74} -2.00000 q^{76} +5.00000 q^{77} -11.0000 q^{79} +6.00000 q^{82} -16.0000 q^{83} +13.0000 q^{86} -5.00000 q^{88} -10.0000 q^{89} -1.00000 q^{91} -9.00000 q^{92} +7.00000 q^{94} -2.00000 q^{97} -1.00000 q^{98} +O(q^{100})$

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	$-0.228229\pi$
$11$	5.00000	1.50756	0.753778	+	0.657129i	$0.228229\pi$
$12$	0	0
$13$	−1.00000	−0.277350	−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000	−0.277350	−0.138675	+	0.990338i	$0.544284\pi$
$14$	−1.00000	−0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	7.00000	1.69775	0.848875	−	0.528594i	$-0.177281\pi$
$17$	7.00000	1.69775	0.848875	+	0.528594i	$0.177281\pi$
$18$	0	0
$19$	−2.00000	−0.458831	−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000	−0.458831	−0.229416	+	0.973329i	$0.573682\pi$
$20$	0	0
$21$	0	0
$22$	−5.00000	−1.06600
$23$	−9.00000	−1.87663	−0.938315	−	0.345782i	$-0.887614\pi$
$23$	−9.00000	−1.87663	−0.938315	+	0.345782i	$0.887614\pi$
$24$	0	0
$25$	0	0
$26$	1.00000	0.196116
$27$	0	0
$28$	1.00000	0.188982
$29$	−3.00000	−0.557086	−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000	−0.557086	−0.278543	+	0.960424i	$0.589851\pi$
$30$	0	0
$31$	3.00000	0.538816	0.269408	−	0.963026i	$-0.413172\pi$
$31$	3.00000	0.538816	0.269408	+	0.963026i	$0.413172\pi$
$32$	−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	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	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
$43$	−13.0000	−1.98248	−0.991241	−	0.132068i	$-0.957838\pi$
$43$	−13.0000	−1.98248	−0.991241	+	0.132068i	$0.957838\pi$
$44$	5.00000	0.753778
$45$	0	0
$46$	9.00000	1.32698
$47$	−7.00000	−1.02105	−0.510527	−	0.859861i	$-0.670550\pi$
$47$	−7.00000	−1.02105	−0.510527	+	0.859861i	$0.670550\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	0	0
$51$	0	0
$52$	−1.00000	−0.138675
$53$	−4.00000	−0.549442	−0.274721	−	0.961524i	$-0.588586\pi$
$53$	−4.00000	−0.549442	−0.274721	+	0.961524i	$0.588586\pi$
$54$	0	0
$55$	0	0
$56$	−1.00000	−0.133631
$57$	0	0
$58$	3.00000	0.393919
$59$	−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
$61$	4.00000	0.512148	0.256074	−	0.966657i	$-0.417571\pi$
$61$	4.00000	0.512148	0.256074	+	0.966657i	$0.417571\pi$
$62$	−3.00000	−0.381000
$63$	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	$0.761888\pi$
$68$	7.00000	0.848875
$69$	0	0
$70$	0	0
$71$	−10.0000	−1.18678	−0.593391	−	0.804914i	$-0.702211\pi$
$71$	−10.0000	−1.18678	−0.593391	+	0.804914i	$0.702211\pi$
$72$	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
$77$	5.00000	0.569803
$78$	0	0
$79$	−11.0000	−1.23760	−0.618798	−	0.785550i	$-0.712380\pi$
$79$	−11.0000	−1.23760	−0.618798	+	0.785550i	$0.712380\pi$
$80$	0	0
$81$	0	0
$82$	6.00000	0.662589
$83$	−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
$86$	13.0000	1.40183
$87$	0	0
$88$	−5.00000	−0.533002
$89$	−10.0000	−1.06000	−0.529999	−	0.847998i	$-0.677808\pi$
$89$	−10.0000	−1.06000	−0.529999	+	0.847998i	$0.677808\pi$
$90$	0	0
$91$	−1.00000	−0.104828
$92$	−9.00000	−0.938315
$93$	0	0
$94$	7.00000	0.721995
$95$	0	0
$96$	0	0
$97$	−2.00000	−0.203069	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000	−0.203069	−0.101535	+	0.994832i	$0.532375\pi$
$98$	−1.00000	−0.101015
$99$	0	0
$100$	0	0
$101$	7.00000	0.696526	0.348263	−	0.937397i	$-0.386772\pi$
$101$	7.00000	0.696526	0.348263	+	0.937397i	$0.386772\pi$
$102$	0	0
$103$	6.00000	0.591198	0.295599	−	0.955312i	$-0.404481\pi$
$103$	6.00000	0.591198	0.295599	+	0.955312i	$0.404481\pi$
$104$	1.00000	0.0980581
$105$	0	0
$106$	4.00000	0.388514
$107$	−18.0000	−1.74013	−0.870063	−	0.492941i	$-0.835922\pi$
$107$	−18.0000	−1.74013	−0.870063	+	0.492941i	$0.835922\pi$
$108$	0	0
$109$	12.0000	1.14939	0.574696	−	0.818367i	$-0.305120\pi$
$109$	12.0000	1.14939	0.574696	+	0.818367i	$0.305120\pi$
$110$	0	0
$111$	0	0
$112$	1.00000	0.0944911
$113$	−9.00000	−0.846649	−0.423324	−	0.905978i	$-0.639137\pi$
$113$	−9.00000	−0.846649	−0.423324	+	0.905978i	$0.639137\pi$
$114$	0	0
$115$	0	0
$116$	−3.00000	−0.278543
$117$	0	0
$118$	4.00000	0.368230
$119$	7.00000	0.641689
$120$	0	0
$121$	14.0000	1.27273
$122$	−4.00000	−0.362143
$123$	0	0
$124$	3.00000	0.269408
$125$	0	0
$126$	0	0
$127$	−12.0000	−1.06483	−0.532414	−	0.846484i	$-0.678715\pi$
$127$	−12.0000	−1.06483	−0.532414	+	0.846484i	$0.678715\pi$
$128$	−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
$134$	12.0000	1.03664
$135$	0	0
$136$	−7.00000	−0.600245
$137$	2.00000	0.170872	0.0854358	−	0.996344i	$-0.472772\pi$
$137$	2.00000	0.170872	0.0854358	+	0.996344i	$0.472772\pi$
$138$	0	0
$139$	16.0000	1.35710	0.678551	−	0.734553i	$-0.262608\pi$
$139$	16.0000	1.35710	0.678551	+	0.734553i	$0.262608\pi$
$140$	0	0
$141$	0	0
$142$	10.0000	0.839181
$143$	−5.00000	−0.418121
$144$	0	0
$145$	0	0
$146$	−14.0000	−1.15865
$147$	0	0
$148$	2.00000	0.164399
$149$	−15.0000	−1.22885	−0.614424	−	0.788976i	$-0.710612\pi$
$149$	−15.0000	−1.22885	−0.614424	+	0.788976i	$0.710612\pi$
$150$	0	0
$151$	17.0000	1.38344	0.691720	−	0.722166i	$-0.256853\pi$
$151$	17.0000	1.38344	0.691720	+	0.722166i	$0.256853\pi$
$152$	2.00000	0.162221
$153$	0	0
$154$	−5.00000	−0.402911
$155$	0	0
$156$	0	0
$157$	−7.00000	−0.558661	−0.279330	−	0.960195i	$-0.590112\pi$
$157$	−7.00000	−0.558661	−0.279330	+	0.960195i	$0.590112\pi$
$158$	11.0000	0.875113
$159$	0	0
$160$	0	0
$161$	−9.00000	−0.709299
$162$	0	0
$163$	15.0000	1.17489	0.587445	−	0.809264i	$-0.300134\pi$
$163$	15.0000	1.17489	0.587445	+	0.809264i	$0.300134\pi$
$164$	−6.00000	−0.468521
$165$	0	0
$166$	16.0000	1.24184
$167$	−4.00000	−0.309529	−0.154765	−	0.987951i	$-0.549462\pi$
$167$	−4.00000	−0.309529	−0.154765	+	0.987951i	$0.549462\pi$
$168$	0	0
$169$	−12.0000	−0.923077
$170$	0	0
$171$	0	0
$172$	−13.0000	−0.991241
$173$	−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
$176$	5.00000	0.376889
$177$	0	0
$178$	10.0000	0.749532
$179$	20.0000	1.49487	0.747435	−	0.664335i	$-0.231285\pi$
$179$	20.0000	1.49487	0.747435	+	0.664335i	$0.231285\pi$
$180$	0	0
$181$	−14.0000	−1.04061	−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000	−1.04061	−0.520306	+	0.853980i	$0.674182\pi$
$182$	1.00000	0.0741249
$183$	0	0
$184$	9.00000	0.663489
$185$	0	0
$186$	0	0
$187$	35.0000	2.55945
$188$	−7.00000	−0.510527
$189$	0	0
$190$	0	0
$191$	10.0000	0.723575	0.361787	−	0.932261i	$-0.382167\pi$
$191$	10.0000	0.723575	0.361787	+	0.932261i	$0.382167\pi$
$192$	0	0
$193$	0	0		−	1.00000i	$-0.5\pi$
$193$	0	0			1.00000i	$0.5\pi$
$194$	2.00000	0.143592
$195$	0	0
$196$	1.00000	0.0714286
$197$	18.0000	1.28245	0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000	1.28245	0.641223	+	0.767354i	$0.278427\pi$
$198$	0	0
$199$	−5.00000	−0.354441	−0.177220	−	0.984171i	$-0.556711\pi$
$199$	−5.00000	−0.354441	−0.177220	+	0.984171i	$0.556711\pi$
$200$	0	0
$201$	0	0
$202$	−7.00000	−0.492518
$203$	−3.00000	−0.210559
$204$	0	0
$205$	0	0
$206$	−6.00000	−0.418040
$207$	0	0
$208$	−1.00000	−0.0693375
$209$	−10.0000	−0.691714
$210$	0	0
$211$	−8.00000	−0.550743	−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000	−0.550743	−0.275371	+	0.961338i	$0.588801\pi$
$212$	−4.00000	−0.274721
$213$	0	0
$214$	18.0000	1.23045
$215$	0	0
$216$	0	0
$217$	3.00000	0.203653
$218$	−12.0000	−0.812743
$219$	0	0
$220$	0	0
$221$	−7.00000	−0.470871
$222$	0	0
$223$	26.0000	1.74109	0.870544	−	0.492090i	$-0.163767\pi$
$223$	26.0000	1.74109	0.870544	+	0.492090i	$0.163767\pi$
$224$	−1.00000	−0.0668153
$225$	0	0
$226$	9.00000	0.598671
$227$	−22.0000	−1.46019	−0.730096	−	0.683345i	$-0.760525\pi$
$227$	−22.0000	−1.46019	−0.730096	+	0.683345i	$0.760525\pi$
$228$	0	0
$229$	2.00000	0.132164	0.0660819	−	0.997814i	$-0.478950\pi$
$229$	2.00000	0.132164	0.0660819	+	0.997814i	$0.478950\pi$
$230$	0	0
$231$	0	0
$232$	3.00000	0.196960
$233$	−6.00000	−0.393073	−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000	−0.393073	−0.196537	+	0.980497i	$0.562969\pi$
$234$	0	0
$235$	0	0
$236$	−4.00000	−0.260378
$237$	0	0
$238$	−7.00000	−0.453743
$239$	4.00000	0.258738	0.129369	−	0.991596i	$-0.458705\pi$
$239$	4.00000	0.258738	0.129369	+	0.991596i	$0.458705\pi$
$240$	0	0
$241$	−19.0000	−1.22390	−0.611949	−	0.790897i	$-0.709614\pi$
$241$	−19.0000	−1.22390	−0.611949	+	0.790897i	$0.709614\pi$
$242$	−14.0000	−0.899954
$243$	0	0
$244$	4.00000	0.256074
$245$	0	0
$246$	0	0
$247$	2.00000	0.127257
$248$	−3.00000	−0.190500
$249$	0	0
$250$	0	0
$251$	21.0000	1.32551	0.662754	−	0.748837i	$-0.269387\pi$
$251$	21.0000	1.32551	0.662754	+	0.748837i	$0.269387\pi$
$252$	0	0
$253$	−45.0000	−2.82913
$254$	12.0000	0.752947
$255$	0	0
$256$	1.00000	0.0625000
$257$	−13.0000	−0.810918	−0.405459	−	0.914113i	$-0.632888\pi$
$257$	−13.0000	−0.810918	−0.405459	+	0.914113i	$0.632888\pi$
$258$	0	0
$259$	2.00000	0.124274
$260$	0	0
$261$	0	0
$262$	1.00000	0.0617802
$263$	0	0		−	1.00000i	$-0.5\pi$
$263$	0	0			1.00000i	$0.5\pi$
$264$	0	0
$265$	0	0
$266$	2.00000	0.122628
$267$	0	0
$268$	−12.0000	−0.733017
$269$	7.00000	0.426798	0.213399	−	0.976965i	$-0.431547\pi$
$269$	7.00000	0.426798	0.213399	+	0.976965i	$0.431547\pi$
$270$	0	0
$271$	8.00000	0.485965	0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000	0.485965	0.242983	+	0.970031i	$0.421874\pi$
$272$	7.00000	0.424437
$273$	0	0
$274$	−2.00000	−0.120824
$275$	0	0
$276$	0	0
$277$	10.0000	0.600842	0.300421	−	0.953807i	$-0.402873\pi$
$277$	10.0000	0.600842	0.300421	+	0.953807i	$0.402873\pi$
$278$	−16.0000	−0.959616
$279$	0	0
$280$	0	0
$281$	14.0000	0.835170	0.417585	−	0.908638i	$-0.362877\pi$
$281$	14.0000	0.835170	0.417585	+	0.908638i	$0.362877\pi$
$282$	0	0
$283$	4.00000	0.237775	0.118888	−	0.992908i	$-0.462067\pi$
$283$	4.00000	0.237775	0.118888	+	0.992908i	$0.462067\pi$
$284$	−10.0000	−0.593391
$285$	0	0
$286$	5.00000	0.295656
$287$	−6.00000	−0.354169
$288$	0	0
$289$	32.0000	1.88235
$290$	0	0
$291$	0	0
$292$	14.0000	0.819288
$293$	−14.0000	−0.817889	−0.408944	−	0.912559i	$-0.634103\pi$
$293$	−14.0000	−0.817889	−0.408944	+	0.912559i	$0.634103\pi$
$294$	0	0
$295$	0	0
$296$	−2.00000	−0.116248
$297$	0	0
$298$	15.0000	0.868927
$299$	9.00000	0.520483
$300$	0	0
$301$	−13.0000	−0.749308
$302$	−17.0000	−0.978240
$303$	0	0
$304$	−2.00000	−0.114708
$305$	0	0
$306$	0	0
$307$	−29.0000	−1.65512	−0.827559	−	0.561379i	$-0.810271\pi$
$307$	−29.0000	−1.65512	−0.827559	+	0.561379i	$0.810271\pi$
$308$	5.00000	0.284901
$309$	0	0
$310$	0	0
$311$	2.00000	0.113410	0.0567048	−	0.998391i	$-0.481941\pi$
$311$	2.00000	0.113410	0.0567048	+	0.998391i	$0.481941\pi$
$312$	0	0
$313$	−2.00000	−0.113047	−0.0565233	−	0.998401i	$-0.518002\pi$
$313$	−2.00000	−0.113047	−0.0565233	+	0.998401i	$0.518002\pi$
$314$	7.00000	0.395033
$315$	0	0
$316$	−11.0000	−0.618798
$317$	20.0000	1.12331	0.561656	−	0.827371i	$-0.310164\pi$
$317$	20.0000	1.12331	0.561656	+	0.827371i	$0.310164\pi$
$318$	0	0
$319$	−15.0000	−0.839839
$320$	0	0
$321$	0	0
$322$	9.00000	0.501550
$323$	−14.0000	−0.778981
$324$	0	0
$325$	0	0
$326$	−15.0000	−0.830773
$327$	0	0
$328$	6.00000	0.331295
$329$	−7.00000	−0.385922
$330$	0	0
$331$	−30.0000	−1.64895	−0.824475	−	0.565899i	$-0.808529\pi$
$331$	−30.0000	−1.64895	−0.824475	+	0.565899i	$0.808529\pi$
$332$	−16.0000	−0.878114
$333$	0	0
$334$	4.00000	0.218870
$335$	0	0
$336$	0	0
$337$	8.00000	0.435788	0.217894	−	0.975972i	$-0.430081\pi$
$337$	8.00000	0.435788	0.217894	+	0.975972i	$0.430081\pi$
$338$	12.0000	0.652714
$339$	0	0
$340$	0	0
$341$	15.0000	0.812296
$342$	0	0
$343$	1.00000	0.0539949
$344$	13.0000	0.700913
$345$	0	0
$346$	8.00000	0.430083
$347$	2.00000	0.107366	0.0536828	−	0.998558i	$-0.482904\pi$
$347$	2.00000	0.107366	0.0536828	+	0.998558i	$0.482904\pi$
$348$	0	0
$349$	0	0		−	1.00000i	$-0.5\pi$
$349$	0	0			1.00000i	$0.5\pi$
$350$	0	0
$351$	0	0
$352$	−5.00000	−0.266501
$353$	−3.00000	−0.159674	−0.0798369	−	0.996808i	$-0.525440\pi$
$353$	−3.00000	−0.159674	−0.0798369	+	0.996808i	$0.525440\pi$
$354$	0	0
$355$	0	0
$356$	−10.0000	−0.529999
$357$	0	0
$358$	−20.0000	−1.05703
$359$	22.0000	1.16112	0.580558	−	0.814219i	$-0.302835\pi$
$359$	22.0000	1.16112	0.580558	+	0.814219i	$0.302835\pi$
$360$	0	0
$361$	−15.0000	−0.789474
$362$	14.0000	0.735824
$363$	0	0
$364$	−1.00000	−0.0524142
$365$	0	0
$366$	0	0
$367$	10.0000	0.521996	0.260998	−	0.965339i	$-0.415948\pi$
$367$	10.0000	0.521996	0.260998	+	0.965339i	$0.415948\pi$
$368$	−9.00000	−0.469157
$369$	0	0
$370$	0	0
$371$	−4.00000	−0.207670
$372$	0	0
$373$	−27.0000	−1.39801	−0.699004	−	0.715118i	$-0.746373\pi$
$373$	−27.0000	−1.39801	−0.699004	+	0.715118i	$0.746373\pi$
$374$	−35.0000	−1.80981
$375$	0	0
$376$	7.00000	0.360997
$377$	3.00000	0.154508
$378$	0	0
$379$	8.00000	0.410932	0.205466	−	0.978664i	$-0.434129\pi$
$379$	8.00000	0.410932	0.205466	+	0.978664i	$0.434129\pi$
$380$	0	0
$381$	0	0
$382$	−10.0000	−0.511645
$383$	−9.00000	−0.459879	−0.229939	−	0.973205i	$-0.573853\pi$
$383$	−9.00000	−0.459879	−0.229939	+	0.973205i	$0.573853\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	0	0
$388$	−2.00000	−0.101535
$389$	9.00000	0.456318	0.228159	−	0.973624i	$-0.426729\pi$
$389$	9.00000	0.456318	0.228159	+	0.973624i	$0.426729\pi$
$390$	0	0
$391$	−63.0000	−3.18605
$392$	−1.00000	−0.0505076
$393$	0	0
$394$	−18.0000	−0.906827
$395$	0	0
$396$	0	0
$397$	−25.0000	−1.25471	−0.627357	−	0.778732i	$-0.715863\pi$
$397$	−25.0000	−1.25471	−0.627357	+	0.778732i	$0.715863\pi$
$398$	5.00000	0.250627
$399$	0	0
$400$	0	0
$401$	−12.0000	−0.599251	−0.299626	−	0.954057i	$-0.596862\pi$
$401$	−12.0000	−0.599251	−0.299626	+	0.954057i	$0.596862\pi$
$402$	0	0
$403$	−3.00000	−0.149441
$404$	7.00000	0.348263
$405$	0	0
$406$	3.00000	0.148888
$407$	10.0000	0.495682
$408$	0	0
$409$	7.00000	0.346128	0.173064	−	0.984911i	$-0.444633\pi$
$409$	7.00000	0.346128	0.173064	+	0.984911i	$0.444633\pi$
$410$	0	0
$411$	0	0
$412$	6.00000	0.295599
$413$	−4.00000	−0.196827
$414$	0	0
$415$	0	0
$416$	1.00000	0.0490290
$417$	0	0
$418$	10.0000	0.489116
$419$	3.00000	0.146560	0.0732798	−	0.997311i	$-0.476653\pi$
$419$	3.00000	0.146560	0.0732798	+	0.997311i	$0.476653\pi$
$420$	0	0
$421$	22.0000	1.07221	0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000	1.07221	0.536107	+	0.844150i	$0.319894\pi$
$422$	8.00000	0.389434
$423$	0	0
$424$	4.00000	0.194257
$425$	0	0
$426$	0	0
$427$	4.00000	0.193574
$428$	−18.0000	−0.870063
$429$	0	0
$430$	0	0
$431$	−12.0000	−0.578020	−0.289010	−	0.957326i	$-0.593326\pi$
$431$	−12.0000	−0.578020	−0.289010	+	0.957326i	$0.593326\pi$
$432$	0	0
$433$	26.0000	1.24948	0.624740	−	0.780833i	$-0.285205\pi$
$433$	26.0000	1.24948	0.624740	+	0.780833i	$0.285205\pi$
$434$	−3.00000	−0.144005
$435$	0	0
$436$	12.0000	0.574696
$437$	18.0000	0.861057
$438$	0	0
$439$	24.0000	1.14546	0.572729	−	0.819745i	$-0.305885\pi$
$439$	24.0000	1.14546	0.572729	+	0.819745i	$0.305885\pi$
$440$	0	0
$441$	0	0
$442$	7.00000	0.332956
$443$	−18.0000	−0.855206	−0.427603	−	0.903967i	$-0.640642\pi$
$443$	−18.0000	−0.855206	−0.427603	+	0.903967i	$0.640642\pi$
$444$	0	0
$445$	0	0
$446$	−26.0000	−1.23114
$447$	0	0
$448$	1.00000	0.0472456
$449$	−12.0000	−0.566315	−0.283158	−	0.959073i	$-0.591382\pi$
$449$	−12.0000	−0.566315	−0.283158	+	0.959073i	$0.591382\pi$
$450$	0	0
$451$	−30.0000	−1.41264
$452$	−9.00000	−0.423324
$453$	0	0
$454$	22.0000	1.03251
$455$	0	0
$456$	0	0
$457$	20.0000	0.935561	0.467780	−	0.883845i	$-0.345054\pi$
$457$	20.0000	0.935561	0.467780	+	0.883845i	$0.345054\pi$
$458$	−2.00000	−0.0934539
$459$	0	0
$460$	0	0
$461$	30.0000	1.39724	0.698620	−	0.715493i	$-0.253798\pi$
$461$	30.0000	1.39724	0.698620	+	0.715493i	$0.253798\pi$
$462$	0	0
$463$	−18.0000	−0.836531	−0.418265	−	0.908325i	$-0.637362\pi$
$463$	−18.0000	−0.836531	−0.418265	+	0.908325i	$0.637362\pi$
$464$	−3.00000	−0.139272
$465$	0	0
$466$	6.00000	0.277945
$467$	−22.0000	−1.01804	−0.509019	−	0.860755i	$-0.669992\pi$
$467$	−22.0000	−1.01804	−0.509019	+	0.860755i	$0.669992\pi$
$468$	0	0
$469$	−12.0000	−0.554109
$470$	0	0
$471$	0	0
$472$	4.00000	0.184115
$473$	−65.0000	−2.98870
$474$	0	0
$475$	0	0
$476$	7.00000	0.320844
$477$	0	0
$478$	−4.00000	−0.182956
$479$	−38.0000	−1.73626	−0.868132	−	0.496333i	$-0.834679\pi$
$479$	−38.0000	−1.73626	−0.868132	+	0.496333i	$0.834679\pi$
$480$	0	0
$481$	−2.00000	−0.0911922
$482$	19.0000	0.865426
$483$	0	0
$484$	14.0000	0.636364
$485$	0	0
$486$	0	0
$487$	24.0000	1.08754	0.543772	−	0.839233i	$-0.316996\pi$
$487$	24.0000	1.08754	0.543772	+	0.839233i	$0.316996\pi$
$488$	−4.00000	−0.181071
$489$	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
$493$	−21.0000	−0.945792
$494$	−2.00000	−0.0899843
$495$	0	0
$496$	3.00000	0.134704
$497$	−10.0000	−0.448561
$498$	0	0
$499$	−16.0000	−0.716258	−0.358129	−	0.933672i	$-0.616585\pi$
$499$	−16.0000	−0.716258	−0.358129	+	0.933672i	$0.616585\pi$
$500$	0	0
$501$	0	0
$502$	−21.0000	−0.937276
$503$	27.0000	1.20387	0.601935	−	0.798545i	$-0.294397\pi$
$503$	27.0000	1.20387	0.601935	+	0.798545i	$0.294397\pi$
$504$	0	0
$505$	0	0
$506$	45.0000	2.00049
$507$	0	0
$508$	−12.0000	−0.532414
$509$	−11.0000	−0.487566	−0.243783	−	0.969830i	$-0.578389\pi$
$509$	−11.0000	−0.487566	−0.243783	+	0.969830i	$0.578389\pi$
$510$	0	0
$511$	14.0000	0.619324
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	13.0000	0.573405
$515$	0	0
$516$	0	0
$517$	−35.0000	−1.53930
$518$	−2.00000	−0.0878750
$519$	0	0
$520$	0	0
$521$	18.0000	0.788594	0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000	0.788594	0.394297	+	0.918983i	$0.370988\pi$
$522$	0	0
$523$	−39.0000	−1.70535	−0.852675	−	0.522441i	$-0.825022\pi$
$523$	−39.0000	−1.70535	−0.852675	+	0.522441i	$0.825022\pi$
$524$	−1.00000	−0.0436852
$525$	0	0
$526$	0	0
$527$	21.0000	0.914774
$528$	0	0
$529$	58.0000	2.52174
$530$	0	0
$531$	0	0
$532$	−2.00000	−0.0867110
$533$	6.00000	0.259889
$534$	0	0
$535$	0	0
$536$	12.0000	0.518321
$537$	0	0
$538$	−7.00000	−0.301791
$539$	5.00000	0.215365
$540$	0	0
$541$	22.0000	0.945854	0.472927	−	0.881102i	$-0.343197\pi$
$541$	22.0000	0.945854	0.472927	+	0.881102i	$0.343197\pi$
$542$	−8.00000	−0.343629
$543$	0	0
$544$	−7.00000	−0.300123
$545$	0	0
$546$	0	0
$547$	35.0000	1.49649	0.748246	−	0.663421i	$-0.230896\pi$
$547$	35.0000	1.49649	0.748246	+	0.663421i	$0.230896\pi$
$548$	2.00000	0.0854358
$549$	0	0
$550$	0	0
$551$	6.00000	0.255609
$552$	0	0
$553$	−11.0000	−0.467768
$554$	−10.0000	−0.424859
$555$	0	0
$556$	16.0000	0.678551
$557$	30.0000	1.27114	0.635570	−	0.772043i	$-0.280765\pi$
$557$	30.0000	1.27114	0.635570	+	0.772043i	$0.280765\pi$
$558$	0	0
$559$	13.0000	0.549841
$560$	0	0
$561$	0	0
$562$	−14.0000	−0.590554
$563$	0	0		−	1.00000i	$-0.5\pi$
$563$	0	0			1.00000i	$0.5\pi$
$564$	0	0
$565$	0	0
$566$	−4.00000	−0.168133
$567$	0	0
$568$	10.0000	0.419591
$569$	−24.0000	−1.00613	−0.503066	−	0.864248i	$-0.667795\pi$
$569$	−24.0000	−1.00613	−0.503066	+	0.864248i	$0.667795\pi$
$570$	0	0
$571$	28.0000	1.17176	0.585882	−	0.810397i	$-0.300748\pi$
$571$	28.0000	1.17176	0.585882	+	0.810397i	$0.300748\pi$
$572$	−5.00000	−0.209061
$573$	0	0
$574$	6.00000	0.250435
$575$	0	0
$576$	0	0
$577$	0	0		−	1.00000i	$-0.5\pi$
$577$	0	0			1.00000i	$0.5\pi$
$578$	−32.0000	−1.33102
$579$	0	0
$580$	0	0
$581$	−16.0000	−0.663792
$582$	0	0
$583$	−20.0000	−0.828315
$584$	−14.0000	−0.579324
$585$	0	0
$586$	14.0000	0.578335
$587$	−40.0000	−1.65098	−0.825488	−	0.564419i	$-0.809100\pi$
$587$	−40.0000	−1.65098	−0.825488	+	0.564419i	$0.809100\pi$
$588$	0	0
$589$	−6.00000	−0.247226
$590$	0	0
$591$	0	0
$592$	2.00000	0.0821995
$593$	−37.0000	−1.51941	−0.759704	−	0.650269i	$-0.774656\pi$
$593$	−37.0000	−1.51941	−0.759704	+	0.650269i	$0.774656\pi$
$594$	0	0
$595$	0	0
$596$	−15.0000	−0.614424
$597$	0	0
$598$	−9.00000	−0.368037
$599$	34.0000	1.38920	0.694601	−	0.719395i	$-0.255581\pi$
$599$	34.0000	1.38920	0.694601	+	0.719395i	$0.255581\pi$
$600$	0	0
$601$	9.00000	0.367118	0.183559	−	0.983009i	$-0.441238\pi$
$601$	9.00000	0.367118	0.183559	+	0.983009i	$0.441238\pi$
$602$	13.0000	0.529840
$603$	0	0
$604$	17.0000	0.691720
$605$	0	0
$606$	0	0
$607$	2.00000	0.0811775	0.0405887	−	0.999176i	$-0.487077\pi$
$607$	2.00000	0.0811775	0.0405887	+	0.999176i	$0.487077\pi$
$608$	2.00000	0.0811107
$609$	0	0
$610$	0	0
$611$	7.00000	0.283190
$612$	0	0
$613$	47.0000	1.89831	0.949156	−	0.314806i	$-0.101939\pi$
$613$	47.0000	1.89831	0.949156	+	0.314806i	$0.101939\pi$
$614$	29.0000	1.17034
$615$	0	0
$616$	−5.00000	−0.201456
$617$	−15.0000	−0.603877	−0.301939	−	0.953327i	$-0.597634\pi$
$617$	−15.0000	−0.603877	−0.301939	+	0.953327i	$0.597634\pi$
$618$	0	0
$619$	−6.00000	−0.241160	−0.120580	−	0.992704i	$-0.538475\pi$
$619$	−6.00000	−0.241160	−0.120580	+	0.992704i	$0.538475\pi$
$620$	0	0
$621$	0	0
$622$	−2.00000	−0.0801927
$623$	−10.0000	−0.400642
$624$	0	0
$625$	0	0
$626$	2.00000	0.0799361
$627$	0	0
$628$	−7.00000	−0.279330
$629$	14.0000	0.558217
$630$	0	0
$631$	−12.0000	−0.477712	−0.238856	−	0.971055i	$-0.576772\pi$
$631$	−12.0000	−0.477712	−0.238856	+	0.971055i	$0.576772\pi$
$632$	11.0000	0.437557
$633$	0	0
$634$	−20.0000	−0.794301
$635$	0	0
$636$	0	0
$637$	−1.00000	−0.0396214
$638$	15.0000	0.593856
$639$	0	0
$640$	0	0
$641$	−12.0000	−0.473972	−0.236986	−	0.971513i	$-0.576159\pi$
$641$	−12.0000	−0.473972	−0.236986	+	0.971513i	$0.576159\pi$
$642$	0	0
$643$	19.0000	0.749287	0.374643	−	0.927169i	$-0.377765\pi$
$643$	19.0000	0.749287	0.374643	+	0.927169i	$0.377765\pi$
$644$	−9.00000	−0.354650
$645$	0	0
$646$	14.0000	0.550823
$647$	8.00000	0.314512	0.157256	−	0.987558i	$-0.449735\pi$
$647$	8.00000	0.314512	0.157256	+	0.987558i	$0.449735\pi$
$648$	0	0
$649$	−20.0000	−0.785069
$650$	0	0
$651$	0	0
$652$	15.0000	0.587445
$653$	−10.0000	−0.391330	−0.195665	−	0.980671i	$-0.562687\pi$
$653$	−10.0000	−0.391330	−0.195665	+	0.980671i	$0.562687\pi$
$654$	0	0
$655$	0	0
$656$	−6.00000	−0.234261
$657$	0	0
$658$	7.00000	0.272888
$659$	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
$661$	−20.0000	−0.777910	−0.388955	−	0.921257i	$-0.627164\pi$
$661$	−20.0000	−0.777910	−0.388955	+	0.921257i	$0.627164\pi$
$662$	30.0000	1.16598
$663$	0	0
$664$	16.0000	0.620920
$665$	0	0
$666$	0	0
$667$	27.0000	1.04544
$668$	−4.00000	−0.154765
$669$	0	0
$670$	0	0
$671$	20.0000	0.772091
$672$	0	0
$673$	36.0000	1.38770	0.693849	−	0.720121i	$-0.255914\pi$
$673$	36.0000	1.38770	0.693849	+	0.720121i	$0.255914\pi$
$674$	−8.00000	−0.308148
$675$	0	0
$676$	−12.0000	−0.461538
$677$	−12.0000	−0.461197	−0.230599	−	0.973049i	$-0.574068\pi$
$677$	−12.0000	−0.461197	−0.230599	+	0.973049i	$0.574068\pi$
$678$	0	0
$679$	−2.00000	−0.0767530
$680$	0	0
$681$	0	0
$682$	−15.0000	−0.574380
$683$	8.00000	0.306111	0.153056	−	0.988218i	$-0.451089\pi$
$683$	8.00000	0.306111	0.153056	+	0.988218i	$0.451089\pi$
$684$	0	0
$685$	0	0
$686$	−1.00000	−0.0381802
$687$	0	0
$688$	−13.0000	−0.495620
$689$	4.00000	0.152388
$690$	0	0
$691$	−26.0000	−0.989087	−0.494543	−	0.869153i	$-0.664665\pi$
$691$	−26.0000	−0.989087	−0.494543	+	0.869153i	$0.664665\pi$
$692$	−8.00000	−0.304114
$693$	0	0
$694$	−2.00000	−0.0759190
$695$	0	0
$696$	0	0
$697$	−42.0000	−1.59086
$698$	0	0
$699$	0	0
$700$	0	0
$701$	45.0000	1.69963	0.849813	−	0.527084i	$-0.176715\pi$
$701$	45.0000	1.69963	0.849813	+	0.527084i	$0.176715\pi$
$702$	0	0
$703$	−4.00000	−0.150863
$704$	5.00000	0.188445
$705$	0	0
$706$	3.00000	0.112906
$707$	7.00000	0.263262
$708$	0	0
$709$	−32.0000	−1.20179	−0.600893	−	0.799330i	$-0.705188\pi$
$709$	−32.0000	−1.20179	−0.600893	+	0.799330i	$0.705188\pi$
$710$	0	0
$711$	0	0
$712$	10.0000	0.374766
$713$	−27.0000	−1.01116
$714$	0	0
$715$	0	0
$716$	20.0000	0.747435
$717$	0	0
$718$	−22.0000	−0.821033
$719$	8.00000	0.298350	0.149175	−	0.988811i	$-0.452338\pi$
$719$	8.00000	0.298350	0.149175	+	0.988811i	$0.452338\pi$
$720$	0	0
$721$	6.00000	0.223452
$722$	15.0000	0.558242
$723$	0	0
$724$	−14.0000	−0.520306
$725$	0	0
$726$	0	0
$727$	−44.0000	−1.63187	−0.815935	−	0.578144i	$-0.803777\pi$
$727$	−44.0000	−1.63187	−0.815935	+	0.578144i	$0.803777\pi$
$728$	1.00000	0.0370625
$729$	0	0
$730$	0	0
$731$	−91.0000	−3.36576
$732$	0	0
$733$	54.0000	1.99454	0.997268	−	0.0738717i	$-0.0235355\pi$
$733$	54.0000	1.99454	0.997268	+	0.0738717i	$0.0235355\pi$
$734$	−10.0000	−0.369107
$735$	0	0
$736$	9.00000	0.331744
$737$	−60.0000	−2.21013
$738$	0	0
$739$	−34.0000	−1.25071	−0.625355	−	0.780340i	$-0.715046\pi$
$739$	−34.0000	−1.25071	−0.625355	+	0.780340i	$0.715046\pi$
$740$	0	0
$741$	0	0
$742$	4.00000	0.146845
$743$	41.0000	1.50414	0.752072	−	0.659081i	$-0.229055\pi$
$743$	41.0000	1.50414	0.752072	+	0.659081i	$0.229055\pi$
$744$	0	0
$745$	0	0
$746$	27.0000	0.988540
$747$	0	0
$748$	35.0000	1.27973
$749$	−18.0000	−0.657706
$750$	0	0
$751$	13.0000	0.474377	0.237188	−	0.971464i	$-0.423774\pi$
$751$	13.0000	0.474377	0.237188	+	0.971464i	$0.423774\pi$
$752$	−7.00000	−0.255264
$753$	0	0
$754$	−3.00000	−0.109254
$755$	0	0
$756$	0	0
$757$	29.0000	1.05402	0.527011	−	0.849858i	$-0.323312\pi$
$757$	29.0000	1.05402	0.527011	+	0.849858i	$0.323312\pi$
$758$	−8.00000	−0.290573
$759$	0	0
$760$	0	0
$761$	−36.0000	−1.30500	−0.652499	−	0.757789i	$-0.726280\pi$
$761$	−36.0000	−1.30500	−0.652499	+	0.757789i	$0.726280\pi$
$762$	0	0
$763$	12.0000	0.434429
$764$	10.0000	0.361787
$765$	0	0
$766$	9.00000	0.325183
$767$	4.00000	0.144432
$768$	0	0
$769$	−9.00000	−0.324548	−0.162274	−	0.986746i	$-0.551883\pi$
$769$	−9.00000	−0.324548	−0.162274	+	0.986746i	$0.551883\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	−22.0000	−0.791285	−0.395643	−	0.918405i	$-0.629478\pi$
$773$	−22.0000	−0.791285	−0.395643	+	0.918405i	$0.629478\pi$
$774$	0	0
$775$	0	0
$776$	2.00000	0.0717958
$777$	0	0
$778$	−9.00000	−0.322666
$779$	12.0000	0.429945
$780$	0	0
$781$	−50.0000	−1.78914
$782$	63.0000	2.25288
$783$	0	0
$784$	1.00000	0.0357143
$785$	0	0
$786$	0	0
$787$	−29.0000	−1.03374	−0.516869	−	0.856064i	$-0.672903\pi$
$787$	−29.0000	−1.03374	−0.516869	+	0.856064i	$0.672903\pi$
$788$	18.0000	0.641223
$789$	0	0
$790$	0	0
$791$	−9.00000	−0.320003
$792$	0	0
$793$	−4.00000	−0.142044
$794$	25.0000	0.887217
$795$	0	0
$796$	−5.00000	−0.177220
$797$	−30.0000	−1.06265	−0.531327	−	0.847167i	$-0.678307\pi$
$797$	−30.0000	−1.06265	−0.531327	+	0.847167i	$0.678307\pi$
$798$	0	0
$799$	−49.0000	−1.73350
$800$	0	0
$801$	0	0
$802$	12.0000	0.423735
$803$	70.0000	2.47025
$804$	0	0
$805$	0	0
$806$	3.00000	0.105670
$807$	0	0
$808$	−7.00000	−0.246259
$809$	36.0000	1.26569	0.632846	−	0.774277i	$-0.281886\pi$
$809$	36.0000	1.26569	0.632846	+	0.774277i	$0.281886\pi$
$810$	0	0
$811$	2.00000	0.0702295	0.0351147	−	0.999383i	$-0.488820\pi$
$811$	2.00000	0.0702295	0.0351147	+	0.999383i	$0.488820\pi$
$812$	−3.00000	−0.105279
$813$	0	0
$814$	−10.0000	−0.350500
$815$	0	0
$816$	0	0
$817$	26.0000	0.909625
$818$	−7.00000	−0.244749
$819$	0	0
$820$	0	0
$821$	30.0000	1.04701	0.523504	−	0.852023i	$-0.324625\pi$
$821$	30.0000	1.04701	0.523504	+	0.852023i	$0.324625\pi$
$822$	0	0
$823$	20.0000	0.697156	0.348578	−	0.937280i	$-0.386665\pi$
$823$	20.0000	0.697156	0.348578	+	0.937280i	$0.386665\pi$
$824$	−6.00000	−0.209020
$825$	0	0
$826$	4.00000	0.139178
$827$	−30.0000	−1.04320	−0.521601	−	0.853189i	$-0.674665\pi$
$827$	−30.0000	−1.04320	−0.521601	+	0.853189i	$0.674665\pi$
$828$	0	0
$829$	−16.0000	−0.555703	−0.277851	−	0.960624i	$-0.589622\pi$
$829$	−16.0000	−0.555703	−0.277851	+	0.960624i	$0.589622\pi$
$830$	0	0
$831$	0	0
$832$	−1.00000	−0.0346688
$833$	7.00000	0.242536
$834$	0	0
$835$	0	0
$836$	−10.0000	−0.345857
$837$	0	0
$838$	−3.00000	−0.103633
$839$	−26.0000	−0.897620	−0.448810	−	0.893627i	$-0.648152\pi$
$839$	−26.0000	−0.897620	−0.448810	+	0.893627i	$0.648152\pi$
$840$	0	0
$841$	−20.0000	−0.689655
$842$	−22.0000	−0.758170
$843$	0	0
$844$	−8.00000	−0.275371
$845$	0	0
$846$	0	0
$847$	14.0000	0.481046
$848$	−4.00000	−0.137361
$849$	0	0
$850$	0	0
$851$	−18.0000	−0.617032
$852$	0	0
$853$	55.0000	1.88316	0.941582	−	0.336784i	$-0.109339\pi$
$853$	55.0000	1.88316	0.941582	+	0.336784i	$0.109339\pi$
$854$	−4.00000	−0.136877
$855$	0	0
$856$	18.0000	0.615227
$857$	−2.00000	−0.0683187	−0.0341593	−	0.999416i	$-0.510875\pi$
$857$	−2.00000	−0.0683187	−0.0341593	+	0.999416i	$0.510875\pi$
$858$	0	0
$859$	−54.0000	−1.84246	−0.921228	−	0.389023i	$-0.872813\pi$
$859$	−54.0000	−1.84246	−0.921228	+	0.389023i	$0.872813\pi$
$860$	0	0
$861$	0	0
$862$	12.0000	0.408722
$863$	33.0000	1.12333	0.561667	−	0.827364i	$-0.310160\pi$
$863$	33.0000	1.12333	0.561667	+	0.827364i	$0.310160\pi$
$864$	0	0
$865$	0	0
$866$	−26.0000	−0.883516
$867$	0	0
$868$	3.00000	0.101827
$869$	−55.0000	−1.86575
$870$	0	0
$871$	12.0000	0.406604
$872$	−12.0000	−0.406371
$873$	0	0
$874$	−18.0000	−0.608859
$875$	0	0
$876$	0	0
$877$	−15.0000	−0.506514	−0.253257	−	0.967399i	$-0.581502\pi$
$877$	−15.0000	−0.506514	−0.253257	+	0.967399i	$0.581502\pi$
$878$	−24.0000	−0.809961
$879$	0	0
$880$	0	0
$881$	−42.0000	−1.41502	−0.707508	−	0.706705i	$-0.750181\pi$
$881$	−42.0000	−1.41502	−0.707508	+	0.706705i	$0.750181\pi$
$882$	0	0
$883$	−20.0000	−0.673054	−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000	−0.673054	−0.336527	+	0.941674i	$0.609252\pi$
$884$	−7.00000	−0.235435
$885$	0	0
$886$	18.0000	0.604722
$887$	−15.0000	−0.503651	−0.251825	−	0.967773i	$-0.581031\pi$
$887$	−15.0000	−0.503651	−0.251825	+	0.967773i	$0.581031\pi$
$888$	0	0
$889$	−12.0000	−0.402467
$890$	0	0
$891$	0	0
$892$	26.0000	0.870544
$893$	14.0000	0.468492
$894$	0	0
$895$	0	0
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	12.0000	0.400445
$899$	−9.00000	−0.300167
$900$	0	0
$901$	−28.0000	−0.932815
$902$	30.0000	0.998891
$903$	0	0
$904$	9.00000	0.299336
$905$	0	0
$906$	0	0
$907$	7.00000	0.232431	0.116216	−	0.993224i	$-0.462924\pi$
$907$	7.00000	0.232431	0.116216	+	0.993224i	$0.462924\pi$
$908$	−22.0000	−0.730096
$909$	0	0
$910$	0	0
$911$	−12.0000	−0.397578	−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000	−0.397578	−0.198789	+	0.980042i	$0.563701\pi$
$912$	0	0
$913$	−80.0000	−2.64761
$914$	−20.0000	−0.661541
$915$	0	0
$916$	2.00000	0.0660819
$917$	−1.00000	−0.0330229
$918$	0	0
$919$	−43.0000	−1.41844	−0.709220	−	0.704988i	$-0.750953\pi$
$919$	−43.0000	−1.41844	−0.709220	+	0.704988i	$0.750953\pi$
$920$	0	0
$921$	0	0
$922$	−30.0000	−0.987997
$923$	10.0000	0.329154
$924$	0	0
$925$	0	0
$926$	18.0000	0.591517
$927$	0	0
$928$	3.00000	0.0984798
$929$	−54.0000	−1.77168	−0.885841	−	0.463988i	$-0.846418\pi$
$929$	−54.0000	−1.77168	−0.885841	+	0.463988i	$0.846418\pi$
$930$	0	0
$931$	−2.00000	−0.0655474
$932$	−6.00000	−0.196537
$933$	0	0
$934$	22.0000	0.719862
$935$	0	0
$936$	0	0
$937$	4.00000	0.130674	0.0653372	−	0.997863i	$-0.479188\pi$
$937$	4.00000	0.130674	0.0653372	+	0.997863i	$0.479188\pi$
$938$	12.0000	0.391814
$939$	0	0
$940$	0	0
$941$	−39.0000	−1.27136	−0.635682	−	0.771951i	$-0.719281\pi$
$941$	−39.0000	−1.27136	−0.635682	+	0.771951i	$0.719281\pi$
$942$	0	0
$943$	54.0000	1.75848
$944$	−4.00000	−0.130189
$945$	0	0
$946$	65.0000	2.11333
$947$	−12.0000	−0.389948	−0.194974	−	0.980808i	$-0.562462\pi$
$947$	−12.0000	−0.389948	−0.194974	+	0.980808i	$0.562462\pi$
$948$	0	0
$949$	−14.0000	−0.454459
$950$	0	0
$951$	0	0
$952$	−7.00000	−0.226871
$953$	−15.0000	−0.485898	−0.242949	−	0.970039i	$-0.578115\pi$
$953$	−15.0000	−0.485898	−0.242949	+	0.970039i	$0.578115\pi$
$954$	0	0
$955$	0	0
$956$	4.00000	0.129369
$957$	0	0
$958$	38.0000	1.22772
$959$	2.00000	0.0645834
$960$	0	0
$961$	−22.0000	−0.709677
$962$	2.00000	0.0644826
$963$	0	0
$964$	−19.0000	−0.611949
$965$	0	0
$966$	0	0
$967$	−18.0000	−0.578841	−0.289420	−	0.957202i	$-0.593463\pi$
$967$	−18.0000	−0.578841	−0.289420	+	0.957202i	$0.593463\pi$
$968$	−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
$973$	16.0000	0.512936
$974$	−24.0000	−0.769010
$975$	0	0
$976$	4.00000	0.128037
$977$	−21.0000	−0.671850	−0.335925	−	0.941889i	$-0.609049\pi$
$977$	−21.0000	−0.671850	−0.335925	+	0.941889i	$0.609049\pi$
$978$	0	0
$979$	−50.0000	−1.59801
$980$	0	0
$981$	0	0
$982$	24.0000	0.765871
$983$	−9.00000	−0.287055	−0.143528	−	0.989646i	$-0.545845\pi$
$983$	−9.00000	−0.287055	−0.143528	+	0.989646i	$0.545845\pi$
$984$	0	0
$985$	0	0
$986$	21.0000	0.668776
$987$	0	0
$988$	2.00000	0.0636285
$989$	117.000	3.72038
$990$	0	0
$991$	−45.0000	−1.42947	−0.714736	−	0.699394i	$-0.753453\pi$
$991$	−45.0000	−1.42947	−0.714736	+	0.699394i	$0.753453\pi$
$992$	−3.00000	−0.0952501
$993$	0	0
$994$	10.0000	0.317181
$995$	0	0
$996$	0	0
$997$	−11.0000	−0.348373	−0.174187	−	0.984713i	$-0.555730\pi$
$997$	−11.0000	−0.348373	−0.174187	+	0.984713i	$0.555730\pi$
$998$	16.0000	0.506471
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9450.2.a.bw.1.1		1
3.2	odd	2		9450.2.a.db.1.1		1
5.2	odd	4		1890.2.g.j.379.1	yes	2
5.3	odd	4		1890.2.g.j.379.2	yes	2
5.4	even	2		9450.2.a.cx.1.1		1
15.2	even	4		1890.2.g.c.379.2	yes	2
15.8	even	4		1890.2.g.c.379.1	✓	2
15.14	odd	2		9450.2.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1890.2.g.c.379.1	✓	2	15.8	even	4
1890.2.g.c.379.2	yes	2	15.2	even	4
1890.2.g.j.379.1	yes	2	5.2	odd	4
1890.2.g.j.379.2	yes	2	5.3	odd	4
9450.2.a.d.1.1		1	15.14	odd	2
9450.2.a.bw.1.1		1	1.1	even	1	trivial
9450.2.a.cx.1.1		1	5.4	even	2
9450.2.a.db.1.1		1	3.2	odd	2

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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