LMFDB - Embedded newform 9450.2.a.f.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:	$0$
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)

$f(q)$

$=$

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

$q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{7} -1.00000 q^{8} -3.00000 q^{11} -1.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} -1.00000 q^{17} -2.00000 q^{19} +3.00000 q^{22} +7.00000 q^{23} +1.00000 q^{26} -1.00000 q^{28} +5.00000 q^{29} -5.00000 q^{31} -1.00000 q^{32} +1.00000 q^{34} +2.00000 q^{37} +2.00000 q^{38} -6.00000 q^{41} -5.00000 q^{43} -3.00000 q^{44} -7.00000 q^{46} +1.00000 q^{47} +1.00000 q^{49} -1.00000 q^{52} +12.0000 q^{53} +1.00000 q^{56} -5.00000 q^{58} -4.00000 q^{59} -12.0000 q^{61} +5.00000 q^{62} +1.00000 q^{64} +4.00000 q^{67} -1.00000 q^{68} +6.00000 q^{71} -2.00000 q^{73} -2.00000 q^{74} -2.00000 q^{76} +3.00000 q^{77} +5.00000 q^{79} +6.00000 q^{82} +5.00000 q^{86} +3.00000 q^{88} -10.0000 q^{89} +1.00000 q^{91} +7.00000 q^{92} -1.00000 q^{94} -18.0000 q^{97} -1.00000 q^{98} +O(q^{100})$

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
$11$	−3.00000	−0.904534	−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000	−0.904534	−0.452267	+	0.891883i	$0.649385\pi$
$12$	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
$17$	−1.00000	−0.242536	−0.121268	−	0.992620i	$-0.538696\pi$
$17$	−1.00000	−0.242536	−0.121268	+	0.992620i	$0.538696\pi$
$18$	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
$22$	3.00000	0.639602
$23$	7.00000	1.45960	0.729800	−	0.683660i	$-0.239613\pi$
$23$	7.00000	1.45960	0.729800	+	0.683660i	$0.239613\pi$
$24$	0	0
$25$	0	0
$26$	1.00000	0.196116
$27$	0	0
$28$	−1.00000	−0.188982
$29$	5.00000	0.928477	0.464238	−	0.885710i	$-0.346328\pi$
$29$	5.00000	0.928477	0.464238	+	0.885710i	$0.346328\pi$
$30$	0	0
$31$	−5.00000	−0.898027	−0.449013	−	0.893525i	$-0.648224\pi$
$31$	−5.00000	−0.898027	−0.449013	+	0.893525i	$0.648224\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	1.00000	0.171499
$35$	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
$43$	−5.00000	−0.762493	−0.381246	−	0.924473i	$-0.624505\pi$
$43$	−5.00000	−0.762493	−0.381246	+	0.924473i	$0.624505\pi$
$44$	−3.00000	−0.452267
$45$	0	0
$46$	−7.00000	−1.03209
$47$	1.00000	0.145865	0.0729325	−	0.997337i	$-0.476764\pi$
$47$	1.00000	0.145865	0.0729325	+	0.997337i	$0.476764\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	0	0
$51$	0	0
$52$	−1.00000	−0.138675
$53$	12.0000	1.64833	0.824163	−	0.566352i	$-0.191646\pi$
$53$	12.0000	1.64833	0.824163	+	0.566352i	$0.191646\pi$
$54$	0	0
$55$	0	0
$56$	1.00000	0.133631
$57$	0	0
$58$	−5.00000	−0.656532
$59$	−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
$61$	−12.0000	−1.53644	−0.768221	−	0.640184i	$-0.778858\pi$
$61$	−12.0000	−1.53644	−0.768221	+	0.640184i	$0.778858\pi$
$62$	5.00000	0.635001
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	4.00000	0.488678	0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000	0.488678	0.244339	+	0.969690i	$0.421429\pi$
$68$	−1.00000	−0.121268
$69$	0	0
$70$	0	0
$71$	6.00000	0.712069	0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000	0.712069	0.356034	+	0.934473i	$0.384129\pi$
$72$	0	0
$73$	−2.00000	−0.234082	−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000	−0.234082	−0.117041	+	0.993127i	$0.537341\pi$
$74$	−2.00000	−0.232495
$75$	0	0
$76$	−2.00000	−0.229416
$77$	3.00000	0.341882
$78$	0	0
$79$	5.00000	0.562544	0.281272	−	0.959628i	$-0.409244\pi$
$79$	5.00000	0.562544	0.281272	+	0.959628i	$0.409244\pi$
$80$	0	0
$81$	0	0
$82$	6.00000	0.662589
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	0	0
$85$	0	0
$86$	5.00000	0.539164
$87$	0	0
$88$	3.00000	0.319801
$89$	−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
$92$	7.00000	0.729800
$93$	0	0
$94$	−1.00000	−0.103142
$95$	0	0
$96$	0	0
$97$	−18.0000	−1.82762	−0.913812	−	0.406138i	$-0.866875\pi$
$97$	−18.0000	−1.82762	−0.913812	+	0.406138i	$0.866875\pi$
$98$	−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
$103$	−10.0000	−0.985329	−0.492665	−	0.870219i	$-0.663977\pi$
$103$	−10.0000	−0.985329	−0.492665	+	0.870219i	$0.663977\pi$
$104$	1.00000	0.0980581
$105$	0	0
$106$	−12.0000	−1.16554
$107$	−2.00000	−0.193347	−0.0966736	−	0.995316i	$-0.530820\pi$
$107$	−2.00000	−0.193347	−0.0966736	+	0.995316i	$0.530820\pi$
$108$	0	0
$109$	−4.00000	−0.383131	−0.191565	−	0.981480i	$-0.561356\pi$
$109$	−4.00000	−0.383131	−0.191565	+	0.981480i	$0.561356\pi$
$110$	0	0
$111$	0	0
$112$	−1.00000	−0.0944911
$113$	7.00000	0.658505	0.329252	−	0.944242i	$-0.393203\pi$
$113$	7.00000	0.658505	0.329252	+	0.944242i	$0.393203\pi$
$114$	0	0
$115$	0	0
$116$	5.00000	0.464238
$117$	0	0
$118$	4.00000	0.368230
$119$	1.00000	0.0916698
$120$	0	0
$121$	−2.00000	−0.181818
$122$	12.0000	1.08643
$123$	0	0
$124$	−5.00000	−0.449013
$125$	0	0
$126$	0	0
$127$	20.0000	1.77471	0.887357	−	0.461084i	$-0.152539\pi$
$127$	20.0000	1.77471	0.887357	+	0.461084i	$0.152539\pi$
$128$	−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
$134$	−4.00000	−0.345547
$135$	0	0
$136$	1.00000	0.0857493
$137$	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
$142$	−6.00000	−0.503509
$143$	3.00000	0.250873
$144$	0	0
$145$	0	0
$146$	2.00000	0.165521
$147$	0	0
$148$	2.00000	0.164399
$149$	9.00000	0.737309	0.368654	−	0.929567i	$-0.379819\pi$
$149$	9.00000	0.737309	0.368654	+	0.929567i	$0.379819\pi$
$150$	0	0
$151$	−15.0000	−1.22068	−0.610341	−	0.792139i	$-0.708968\pi$
$151$	−15.0000	−1.22068	−0.610341	+	0.792139i	$0.708968\pi$
$152$	2.00000	0.162221
$153$	0	0
$154$	−3.00000	−0.241747
$155$	0	0
$156$	0	0
$157$	9.00000	0.718278	0.359139	−	0.933284i	$-0.383070\pi$
$157$	9.00000	0.718278	0.359139	+	0.933284i	$0.383070\pi$
$158$	−5.00000	−0.397779
$159$	0	0
$160$	0	0
$161$	−7.00000	−0.551677
$162$	0	0
$163$	−9.00000	−0.704934	−0.352467	−	0.935824i	$-0.614657\pi$
$163$	−9.00000	−0.704934	−0.352467	+	0.935824i	$0.614657\pi$
$164$	−6.00000	−0.468521
$165$	0	0
$166$	0	0
$167$	12.0000	0.928588	0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000	0.928588	0.464294	+	0.885681i	$0.346308\pi$
$168$	0	0
$169$	−12.0000	−0.923077
$170$	0	0
$171$	0	0
$172$	−5.00000	−0.381246
$173$	24.0000	1.82469	0.912343	−	0.409426i	$-0.134271\pi$
$173$	24.0000	1.82469	0.912343	+	0.409426i	$0.134271\pi$
$174$	0	0
$175$	0	0
$176$	−3.00000	−0.226134
$177$	0	0
$178$	10.0000	0.749532
$179$	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
$181$	2.00000	0.148659	0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000	0.148659	0.0743294	+	0.997234i	$0.476318\pi$
$182$	−1.00000	−0.0741249
$183$	0	0
$184$	−7.00000	−0.516047
$185$	0	0
$186$	0	0
$187$	3.00000	0.219382
$188$	1.00000	0.0729325
$189$	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
$193$	16.0000	1.15171	0.575853	−	0.817554i	$-0.304670\pi$
$193$	16.0000	1.15171	0.575853	+	0.817554i	$0.304670\pi$
$194$	18.0000	1.29232
$195$	0	0
$196$	1.00000	0.0714286
$197$	2.00000	0.142494	0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000	0.142494	0.0712470	+	0.997459i	$0.477302\pi$
$198$	0	0
$199$	3.00000	0.212664	0.106332	−	0.994331i	$-0.466089\pi$
$199$	3.00000	0.212664	0.106332	+	0.994331i	$0.466089\pi$
$200$	0	0
$201$	0	0
$202$	9.00000	0.633238
$203$	−5.00000	−0.350931
$204$	0	0
$205$	0	0
$206$	10.0000	0.696733
$207$	0	0
$208$	−1.00000	−0.0693375
$209$	6.00000	0.415029
$210$	0	0
$211$	24.0000	1.65223	0.826114	−	0.563503i	$-0.190547\pi$
$211$	24.0000	1.65223	0.826114	+	0.563503i	$0.190547\pi$
$212$	12.0000	0.824163
$213$	0	0
$214$	2.00000	0.136717
$215$	0	0
$216$	0	0
$217$	5.00000	0.339422
$218$	4.00000	0.270914
$219$	0	0
$220$	0	0
$221$	1.00000	0.0672673
$222$	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
$226$	−7.00000	−0.465633
$227$	−6.00000	−0.398234	−0.199117	−	0.979976i	$-0.563807\pi$
$227$	−6.00000	−0.398234	−0.199117	+	0.979976i	$0.563807\pi$
$228$	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
$232$	−5.00000	−0.328266
$233$	26.0000	1.70332	0.851658	−	0.524097i	$-0.175597\pi$
$233$	26.0000	1.70332	0.851658	+	0.524097i	$0.175597\pi$
$234$	0	0
$235$	0	0
$236$	−4.00000	−0.260378
$237$	0	0
$238$	−1.00000	−0.0648204
$239$	20.0000	1.29369	0.646846	−	0.762620i	$-0.276088\pi$
$239$	20.0000	1.29369	0.646846	+	0.762620i	$0.276088\pi$
$240$	0	0
$241$	21.0000	1.35273	0.676364	−	0.736567i	$-0.263554\pi$
$241$	21.0000	1.35273	0.676364	+	0.736567i	$0.263554\pi$
$242$	2.00000	0.128565
$243$	0	0
$244$	−12.0000	−0.768221
$245$	0	0
$246$	0	0
$247$	2.00000	0.127257
$248$	5.00000	0.317500
$249$	0	0
$250$	0	0
$251$	5.00000	0.315597	0.157799	−	0.987471i	$-0.449560\pi$
$251$	5.00000	0.315597	0.157799	+	0.987471i	$0.449560\pi$
$252$	0	0
$253$	−21.0000	−1.32026
$254$	−20.0000	−1.25491
$255$	0	0
$256$	1.00000	0.0625000
$257$	−21.0000	−1.30994	−0.654972	−	0.755653i	$-0.727320\pi$
$257$	−21.0000	−1.30994	−0.654972	+	0.755653i	$0.727320\pi$
$258$	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
$268$	4.00000	0.244339
$269$	−25.0000	−1.52428	−0.762138	−	0.647414i	$-0.775850\pi$
$269$	−25.0000	−1.52428	−0.762138	+	0.647414i	$0.775850\pi$
$270$	0	0
$271$	24.0000	1.45790	0.728948	−	0.684569i	$-0.240010\pi$
$271$	24.0000	1.45790	0.728948	+	0.684569i	$0.240010\pi$
$272$	−1.00000	−0.0606339
$273$	0	0
$274$	−2.00000	−0.120824
$275$	0	0
$276$	0	0
$277$	−22.0000	−1.32185	−0.660926	−	0.750451i	$-0.729836\pi$
$277$	−22.0000	−1.32185	−0.660926	+	0.750451i	$0.729836\pi$
$278$	−16.0000	−0.959616
$279$	0	0
$280$	0	0
$281$	−18.0000	−1.07379	−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000	−1.07379	−0.536895	+	0.843649i	$0.680403\pi$
$282$	0	0
$283$	4.00000	0.237775	0.118888	−	0.992908i	$-0.462067\pi$
$283$	4.00000	0.237775	0.118888	+	0.992908i	$0.462067\pi$
$284$	6.00000	0.356034
$285$	0	0
$286$	−3.00000	−0.177394
$287$	6.00000	0.354169
$288$	0	0
$289$	−16.0000	−0.941176
$290$	0	0
$291$	0	0
$292$	−2.00000	−0.117041
$293$	18.0000	1.05157	0.525786	−	0.850617i	$-0.323771\pi$
$293$	18.0000	1.05157	0.525786	+	0.850617i	$0.323771\pi$
$294$	0	0
$295$	0	0
$296$	−2.00000	−0.116248
$297$	0	0
$298$	−9.00000	−0.521356
$299$	−7.00000	−0.404820
$300$	0	0
$301$	5.00000	0.288195
$302$	15.0000	0.863153
$303$	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	$0.810271\pi$
$308$	3.00000	0.170941
$309$	0	0
$310$	0	0
$311$	18.0000	1.02069	0.510343	−	0.859971i	$-0.329518\pi$
$311$	18.0000	1.02069	0.510343	+	0.859971i	$0.329518\pi$
$312$	0	0
$313$	−2.00000	−0.113047	−0.0565233	−	0.998401i	$-0.518002\pi$
$313$	−2.00000	−0.113047	−0.0565233	+	0.998401i	$0.518002\pi$
$314$	−9.00000	−0.507899
$315$	0	0
$316$	5.00000	0.281272
$317$	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
$322$	7.00000	0.390095
$323$	2.00000	0.111283
$324$	0	0
$325$	0	0
$326$	9.00000	0.498464
$327$	0	0
$328$	6.00000	0.331295
$329$	−1.00000	−0.0551318
$330$	0	0
$331$	2.00000	0.109930	0.0549650	−	0.998488i	$-0.482495\pi$
$331$	2.00000	0.109930	0.0549650	+	0.998488i	$0.482495\pi$
$332$	0	0
$333$	0	0
$334$	−12.0000	−0.656611
$335$	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
$344$	5.00000	0.269582
$345$	0	0
$346$	−24.0000	−1.29025
$347$	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
$349$	0	0		−	1.00000i	$-0.5\pi$
$349$	0	0			1.00000i	$0.5\pi$
$350$	0	0
$351$	0	0
$352$	3.00000	0.159901
$353$	21.0000	1.11772	0.558859	−	0.829263i	$-0.311239\pi$
$353$	21.0000	1.11772	0.558859	+	0.829263i	$0.311239\pi$
$354$	0	0
$355$	0	0
$356$	−10.0000	−0.529999
$357$	0	0
$358$	−4.00000	−0.211407
$359$	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
$362$	−2.00000	−0.105118
$363$	0	0
$364$	1.00000	0.0524142
$365$	0	0
$366$	0	0
$367$	−22.0000	−1.14839	−0.574195	−	0.818718i	$-0.694685\pi$
$367$	−22.0000	−1.14839	−0.574195	+	0.818718i	$0.694685\pi$
$368$	7.00000	0.364900
$369$	0	0
$370$	0	0
$371$	−12.0000	−0.623009
$372$	0	0
$373$	13.0000	0.673114	0.336557	−	0.941663i	$-0.390737\pi$
$373$	13.0000	0.673114	0.336557	+	0.941663i	$0.390737\pi$
$374$	−3.00000	−0.155126
$375$	0	0
$376$	−1.00000	−0.0515711
$377$	−5.00000	−0.257513
$378$	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
$382$	−10.0000	−0.511645
$383$	15.0000	0.766464	0.383232	−	0.923652i	$-0.374811\pi$
$383$	15.0000	0.766464	0.383232	+	0.923652i	$0.374811\pi$
$384$	0	0
$385$	0	0
$386$	−16.0000	−0.814379
$387$	0	0
$388$	−18.0000	−0.913812
$389$	33.0000	1.67317	0.836583	−	0.547840i	$-0.184550\pi$
$389$	33.0000	1.67317	0.836583	+	0.547840i	$0.184550\pi$
$390$	0	0
$391$	−7.00000	−0.354005
$392$	−1.00000	−0.0505076
$393$	0	0
$394$	−2.00000	−0.100759
$395$	0	0
$396$	0	0
$397$	23.0000	1.15434	0.577168	−	0.816625i	$-0.304158\pi$
$397$	23.0000	1.15434	0.577168	+	0.816625i	$0.304158\pi$
$398$	−3.00000	−0.150376
$399$	0	0
$400$	0	0
$401$	36.0000	1.79775	0.898877	−	0.438201i	$-0.144384\pi$
$401$	36.0000	1.79775	0.898877	+	0.438201i	$0.144384\pi$
$402$	0	0
$403$	5.00000	0.249068
$404$	−9.00000	−0.447767
$405$	0	0
$406$	5.00000	0.248146
$407$	−6.00000	−0.297409
$408$	0	0
$409$	−17.0000	−0.840596	−0.420298	−	0.907386i	$-0.638074\pi$
$409$	−17.0000	−0.840596	−0.420298	+	0.907386i	$0.638074\pi$
$410$	0	0
$411$	0	0
$412$	−10.0000	−0.492665
$413$	4.00000	0.196827
$414$	0	0
$415$	0	0
$416$	1.00000	0.0490290
$417$	0	0
$418$	−6.00000	−0.293470
$419$	−13.0000	−0.635092	−0.317546	−	0.948243i	$-0.602859\pi$
$419$	−13.0000	−0.635092	−0.317546	+	0.948243i	$0.602859\pi$
$420$	0	0
$421$	22.0000	1.07221	0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000	1.07221	0.536107	+	0.844150i	$0.319894\pi$
$422$	−24.0000	−1.16830
$423$	0	0
$424$	−12.0000	−0.582772
$425$	0	0
$426$	0	0
$427$	12.0000	0.580721
$428$	−2.00000	−0.0966736
$429$	0	0
$430$	0	0
$431$	−28.0000	−1.34871	−0.674356	−	0.738406i	$-0.735579\pi$
$431$	−28.0000	−1.34871	−0.674356	+	0.738406i	$0.735579\pi$
$432$	0	0
$433$	26.0000	1.24948	0.624740	−	0.780833i	$-0.285205\pi$
$433$	26.0000	1.24948	0.624740	+	0.780833i	$0.285205\pi$
$434$	−5.00000	−0.240008
$435$	0	0
$436$	−4.00000	−0.191565
$437$	−14.0000	−0.669711
$438$	0	0
$439$	8.00000	0.381819	0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000	0.381819	0.190910	+	0.981608i	$0.438856\pi$
$440$	0	0
$441$	0	0
$442$	−1.00000	−0.0475651
$443$	−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
$449$	−28.0000	−1.32140	−0.660701	−	0.750649i	$-0.729741\pi$
$449$	−28.0000	−1.32140	−0.660701	+	0.750649i	$0.729741\pi$
$450$	0	0
$451$	18.0000	0.847587
$452$	7.00000	0.329252
$453$	0	0
$454$	6.00000	0.281594
$455$	0	0
$456$	0	0
$457$	4.00000	0.187112	0.0935561	−	0.995614i	$-0.470177\pi$
$457$	4.00000	0.187112	0.0935561	+	0.995614i	$0.470177\pi$
$458$	14.0000	0.654177
$459$	0	0
$460$	0	0
$461$	−2.00000	−0.0931493	−0.0465746	−	0.998915i	$-0.514831\pi$
$461$	−2.00000	−0.0931493	−0.0465746	+	0.998915i	$0.514831\pi$
$462$	0	0
$463$	−34.0000	−1.58011	−0.790057	−	0.613033i	$-0.789949\pi$
$463$	−34.0000	−1.58011	−0.790057	+	0.613033i	$0.789949\pi$
$464$	5.00000	0.232119
$465$	0	0
$466$	−26.0000	−1.20443
$467$	26.0000	1.20314	0.601568	−	0.798821i	$-0.294543\pi$
$467$	26.0000	1.20314	0.601568	+	0.798821i	$0.294543\pi$
$468$	0	0
$469$	−4.00000	−0.184703
$470$	0	0
$471$	0	0
$472$	4.00000	0.184115
$473$	15.0000	0.689701
$474$	0	0
$475$	0	0
$476$	1.00000	0.0458349
$477$	0	0
$478$	−20.0000	−0.914779
$479$	−6.00000	−0.274147	−0.137073	−	0.990561i	$-0.543770\pi$
$479$	−6.00000	−0.274147	−0.137073	+	0.990561i	$0.543770\pi$
$480$	0	0
$481$	−2.00000	−0.0911922
$482$	−21.0000	−0.956524
$483$	0	0
$484$	−2.00000	−0.0909091
$485$	0	0
$486$	0	0
$487$	8.00000	0.362515	0.181257	−	0.983436i	$-0.441983\pi$
$487$	8.00000	0.362515	0.181257	+	0.983436i	$0.441983\pi$
$488$	12.0000	0.543214
$489$	0	0
$490$	0	0
$491$	24.0000	1.08310	0.541552	−	0.840667i	$-0.317837\pi$
$491$	24.0000	1.08310	0.541552	+	0.840667i	$0.317837\pi$
$492$	0	0
$493$	−5.00000	−0.225189
$494$	−2.00000	−0.0899843
$495$	0	0
$496$	−5.00000	−0.224507
$497$	−6.00000	−0.269137
$498$	0	0
$499$	−32.0000	−1.43252	−0.716258	−	0.697835i	$-0.754147\pi$
$499$	−32.0000	−1.43252	−0.716258	+	0.697835i	$0.754147\pi$
$500$	0	0
$501$	0	0
$502$	−5.00000	−0.223161
$503$	35.0000	1.56057	0.780286	−	0.625422i	$-0.215073\pi$
$503$	35.0000	1.56057	0.780286	+	0.625422i	$0.215073\pi$
$504$	0	0
$505$	0	0
$506$	21.0000	0.933564
$507$	0	0
$508$	20.0000	0.887357
$509$	5.00000	0.221621	0.110811	−	0.993842i	$-0.464655\pi$
$509$	5.00000	0.221621	0.110811	+	0.993842i	$0.464655\pi$
$510$	0	0
$511$	2.00000	0.0884748
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	21.0000	0.926270
$515$	0	0
$516$	0	0
$517$	−3.00000	−0.131940
$518$	2.00000	0.0878750
$519$	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
$523$	41.0000	1.79280	0.896402	−	0.443241i	$-0.146171\pi$
$523$	41.0000	1.79280	0.896402	+	0.443241i	$0.146171\pi$
$524$	−1.00000	−0.0436852
$525$	0	0
$526$	0	0
$527$	5.00000	0.217803
$528$	0	0
$529$	26.0000	1.13043
$530$	0	0
$531$	0	0
$532$	2.00000	0.0867110
$533$	6.00000	0.259889
$534$	0	0
$535$	0	0
$536$	−4.00000	−0.172774
$537$	0	0
$538$	25.0000	1.07783
$539$	−3.00000	−0.129219
$540$	0	0
$541$	38.0000	1.63375	0.816874	−	0.576816i	$-0.195705\pi$
$541$	38.0000	1.63375	0.816874	+	0.576816i	$0.195705\pi$
$542$	−24.0000	−1.03089
$543$	0	0
$544$	1.00000	0.0428746
$545$	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	$0.790441\pi$
$548$	2.00000	0.0854358
$549$	0	0
$550$	0	0
$551$	−10.0000	−0.426014
$552$	0	0
$553$	−5.00000	−0.212622
$554$	22.0000	0.934690
$555$	0	0
$556$	16.0000	0.678551
$557$	−2.00000	−0.0847427	−0.0423714	−	0.999102i	$-0.513491\pi$
$557$	−2.00000	−0.0847427	−0.0423714	+	0.999102i	$0.513491\pi$
$558$	0	0
$559$	5.00000	0.211477
$560$	0	0
$561$	0	0
$562$	18.0000	0.759284
$563$	16.0000	0.674320	0.337160	−	0.941447i	$-0.390534\pi$
$563$	16.0000	0.674320	0.337160	+	0.941447i	$0.390534\pi$
$564$	0	0
$565$	0	0
$566$	−4.00000	−0.168133
$567$	0	0
$568$	−6.00000	−0.251754
$569$	24.0000	1.00613	0.503066	−	0.864248i	$-0.332205\pi$
$569$	24.0000	1.00613	0.503066	+	0.864248i	$0.332205\pi$
$570$	0	0
$571$	44.0000	1.84134	0.920671	−	0.390339i	$-0.127642\pi$
$571$	44.0000	1.84134	0.920671	+	0.390339i	$0.127642\pi$
$572$	3.00000	0.125436
$573$	0	0
$574$	−6.00000	−0.250435
$575$	0	0
$576$	0	0
$577$	−32.0000	−1.33218	−0.666089	−	0.745873i	$-0.732033\pi$
$577$	−32.0000	−1.33218	−0.666089	+	0.745873i	$0.732033\pi$
$578$	16.0000	0.665512
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	−36.0000	−1.49097
$584$	2.00000	0.0827606
$585$	0	0
$586$	−18.0000	−0.743573
$587$	8.00000	0.330195	0.165098	−	0.986277i	$-0.447206\pi$
$587$	8.00000	0.330195	0.165098	+	0.986277i	$0.447206\pi$
$588$	0	0
$589$	10.0000	0.412043
$590$	0	0
$591$	0	0
$592$	2.00000	0.0821995
$593$	3.00000	0.123195	0.0615976	−	0.998101i	$-0.480380\pi$
$593$	3.00000	0.123195	0.0615976	+	0.998101i	$0.480380\pi$
$594$	0	0
$595$	0	0
$596$	9.00000	0.368654
$597$	0	0
$598$	7.00000	0.286251
$599$	18.0000	0.735460	0.367730	−	0.929933i	$-0.380135\pi$
$599$	18.0000	0.735460	0.367730	+	0.929933i	$0.380135\pi$
$600$	0	0
$601$	17.0000	0.693444	0.346722	−	0.937968i	$-0.387295\pi$
$601$	17.0000	0.693444	0.346722	+	0.937968i	$0.387295\pi$
$602$	−5.00000	−0.203785
$603$	0	0
$604$	−15.0000	−0.610341
$605$	0	0
$606$	0	0
$607$	34.0000	1.38002	0.690009	−	0.723801i	$-0.257607\pi$
$607$	34.0000	1.38002	0.690009	+	0.723801i	$0.257607\pi$
$608$	2.00000	0.0811107
$609$	0	0
$610$	0	0
$611$	−1.00000	−0.0404557
$612$	0	0
$613$	−9.00000	−0.363507	−0.181753	−	0.983344i	$-0.558177\pi$
$613$	−9.00000	−0.363507	−0.181753	+	0.983344i	$0.558177\pi$
$614$	29.0000	1.17034
$615$	0	0
$616$	−3.00000	−0.120873
$617$	−47.0000	−1.89215	−0.946074	−	0.323949i	$-0.894989\pi$
$617$	−47.0000	−1.89215	−0.946074	+	0.323949i	$0.894989\pi$
$618$	0	0
$619$	10.0000	0.401934	0.200967	−	0.979598i	$-0.435592\pi$
$619$	10.0000	0.401934	0.200967	+	0.979598i	$0.435592\pi$
$620$	0	0
$621$	0	0
$622$	−18.0000	−0.721734
$623$	10.0000	0.400642
$624$	0	0
$625$	0	0
$626$	2.00000	0.0799361
$627$	0	0
$628$	9.00000	0.359139
$629$	−2.00000	−0.0797452
$630$	0	0
$631$	−12.0000	−0.477712	−0.238856	−	0.971055i	$-0.576772\pi$
$631$	−12.0000	−0.477712	−0.238856	+	0.971055i	$0.576772\pi$
$632$	−5.00000	−0.198889
$633$	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
$641$	−44.0000	−1.73790	−0.868948	−	0.494904i	$-0.835203\pi$
$641$	−44.0000	−1.73790	−0.868948	+	0.494904i	$0.835203\pi$
$642$	0	0
$643$	35.0000	1.38027	0.690133	−	0.723683i	$-0.257552\pi$
$643$	35.0000	1.38027	0.690133	+	0.723683i	$0.257552\pi$
$644$	−7.00000	−0.275839
$645$	0	0
$646$	−2.00000	−0.0786889
$647$	24.0000	0.943537	0.471769	−	0.881722i	$-0.343616\pi$
$647$	24.0000	0.943537	0.471769	+	0.881722i	$0.343616\pi$
$648$	0	0
$649$	12.0000	0.471041
$650$	0	0
$651$	0	0
$652$	−9.00000	−0.352467
$653$	6.00000	0.234798	0.117399	−	0.993085i	$-0.462544\pi$
$653$	6.00000	0.234798	0.117399	+	0.993085i	$0.462544\pi$
$654$	0	0
$655$	0	0
$656$	−6.00000	−0.234261
$657$	0	0
$658$	1.00000	0.0389841
$659$	−36.0000	−1.40236	−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000	−1.40236	−0.701180	+	0.712984i	$0.747343\pi$
$660$	0	0
$661$	−20.0000	−0.777910	−0.388955	−	0.921257i	$-0.627164\pi$
$661$	−20.0000	−0.777910	−0.388955	+	0.921257i	$0.627164\pi$
$662$	−2.00000	−0.0777322
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	35.0000	1.35521
$668$	12.0000	0.464294
$669$	0	0
$670$	0	0
$671$	36.0000	1.38976
$672$	0	0
$673$	−44.0000	−1.69608	−0.848038	−	0.529936i	$-0.822216\pi$
$673$	−44.0000	−1.69608	−0.848038	+	0.529936i	$0.822216\pi$
$674$	−8.00000	−0.308148
$675$	0	0
$676$	−12.0000	−0.461538
$677$	20.0000	0.768662	0.384331	−	0.923195i	$-0.374432\pi$
$677$	20.0000	0.768662	0.384331	+	0.923195i	$0.374432\pi$
$678$	0	0
$679$	18.0000	0.690777
$680$	0	0
$681$	0	0
$682$	−15.0000	−0.574380
$683$	−40.0000	−1.53056	−0.765279	−	0.643699i	$-0.777399\pi$
$683$	−40.0000	−1.53056	−0.765279	+	0.643699i	$0.777399\pi$
$684$	0	0
$685$	0	0
$686$	1.00000	0.0381802
$687$	0	0
$688$	−5.00000	−0.190623
$689$	−12.0000	−0.457164
$690$	0	0
$691$	22.0000	0.836919	0.418460	−	0.908235i	$-0.362570\pi$
$691$	22.0000	0.836919	0.418460	+	0.908235i	$0.362570\pi$
$692$	24.0000	0.912343
$693$	0	0
$694$	−18.0000	−0.683271
$695$	0	0
$696$	0	0
$697$	6.00000	0.227266
$698$	0	0
$699$	0	0
$700$	0	0
$701$	5.00000	0.188847	0.0944237	−	0.995532i	$-0.469899\pi$
$701$	5.00000	0.188847	0.0944237	+	0.995532i	$0.469899\pi$
$702$	0	0
$703$	−4.00000	−0.150863
$704$	−3.00000	−0.113067
$705$	0	0
$706$	−21.0000	−0.790345
$707$	9.00000	0.338480
$708$	0	0
$709$	0	0		−	1.00000i	$-0.5\pi$
$709$	0	0			1.00000i	$0.5\pi$
$710$	0	0
$711$	0	0
$712$	10.0000	0.374766
$713$	−35.0000	−1.31076
$714$	0	0
$715$	0	0
$716$	4.00000	0.149487
$717$	0	0
$718$	−22.0000	−0.821033
$719$	−40.0000	−1.49175	−0.745874	−	0.666087i	$-0.767968\pi$
$719$	−40.0000	−1.49175	−0.745874	+	0.666087i	$0.767968\pi$
$720$	0	0
$721$	10.0000	0.372419
$722$	15.0000	0.558242
$723$	0	0
$724$	2.00000	0.0743294
$725$	0	0
$726$	0	0
$727$	−28.0000	−1.03846	−0.519231	−	0.854634i	$-0.673782\pi$
$727$	−28.0000	−1.03846	−0.519231	+	0.854634i	$0.673782\pi$
$728$	−1.00000	−0.0370625
$729$	0	0
$730$	0	0
$731$	5.00000	0.184932
$732$	0	0
$733$	22.0000	0.812589	0.406294	−	0.913742i	$-0.366821\pi$
$733$	22.0000	0.812589	0.406294	+	0.913742i	$0.366821\pi$
$734$	22.0000	0.812035
$735$	0	0
$736$	−7.00000	−0.258023
$737$	−12.0000	−0.442026
$738$	0	0
$739$	46.0000	1.69214	0.846069	−	0.533074i	$-0.178963\pi$
$739$	46.0000	1.69214	0.846069	+	0.533074i	$0.178963\pi$
$740$	0	0
$741$	0	0
$742$	12.0000	0.440534
$743$	9.00000	0.330178	0.165089	−	0.986279i	$-0.447209\pi$
$743$	9.00000	0.330178	0.165089	+	0.986279i	$0.447209\pi$
$744$	0	0
$745$	0	0
$746$	−13.0000	−0.475964
$747$	0	0
$748$	3.00000	0.109691
$749$	2.00000	0.0730784
$750$	0	0
$751$	13.0000	0.474377	0.237188	−	0.971464i	$-0.423774\pi$
$751$	13.0000	0.474377	0.237188	+	0.971464i	$0.423774\pi$
$752$	1.00000	0.0364662
$753$	0	0
$754$	5.00000	0.182089
$755$	0	0
$756$	0	0
$757$	−27.0000	−0.981332	−0.490666	−	0.871348i	$-0.663246\pi$
$757$	−27.0000	−0.981332	−0.490666	+	0.871348i	$0.663246\pi$
$758$	8.00000	0.290573
$759$	0	0
$760$	0	0
$761$	28.0000	1.01500	0.507500	−	0.861652i	$-0.330570\pi$
$761$	28.0000	1.01500	0.507500	+	0.861652i	$0.330570\pi$
$762$	0	0
$763$	4.00000	0.144810
$764$	10.0000	0.361787
$765$	0	0
$766$	−15.0000	−0.541972
$767$	4.00000	0.144432
$768$	0	0
$769$	31.0000	1.11789	0.558944	−	0.829205i	$-0.311207\pi$
$769$	31.0000	1.11789	0.558944	+	0.829205i	$0.311207\pi$
$770$	0	0
$771$	0	0
$772$	16.0000	0.575853
$773$	−6.00000	−0.215805	−0.107903	−	0.994161i	$-0.534413\pi$
$773$	−6.00000	−0.215805	−0.107903	+	0.994161i	$0.534413\pi$
$774$	0	0
$775$	0	0
$776$	18.0000	0.646162
$777$	0	0
$778$	−33.0000	−1.18311
$779$	12.0000	0.429945
$780$	0	0
$781$	−18.0000	−0.644091
$782$	7.00000	0.250319
$783$	0	0
$784$	1.00000	0.0357143
$785$	0	0
$786$	0	0
$787$	3.00000	0.106938	0.0534692	−	0.998569i	$-0.482972\pi$
$787$	3.00000	0.106938	0.0534692	+	0.998569i	$0.482972\pi$
$788$	2.00000	0.0712470
$789$	0	0
$790$	0	0
$791$	−7.00000	−0.248891
$792$	0	0
$793$	12.0000	0.426132
$794$	−23.0000	−0.816239
$795$	0	0
$796$	3.00000	0.106332
$797$	2.00000	0.0708436	0.0354218	−	0.999372i	$-0.488723\pi$
$797$	2.00000	0.0708436	0.0354218	+	0.999372i	$0.488723\pi$
$798$	0	0
$799$	−1.00000	−0.0353775
$800$	0	0
$801$	0	0
$802$	−36.0000	−1.27120
$803$	6.00000	0.211735
$804$	0	0
$805$	0	0
$806$	−5.00000	−0.176117
$807$	0	0
$808$	9.00000	0.316619
$809$	4.00000	0.140633	0.0703163	−	0.997525i	$-0.477599\pi$
$809$	4.00000	0.140633	0.0703163	+	0.997525i	$0.477599\pi$
$810$	0	0
$811$	−30.0000	−1.05344	−0.526721	−	0.850038i	$-0.676579\pi$
$811$	−30.0000	−1.05344	−0.526721	+	0.850038i	$0.676579\pi$
$812$	−5.00000	−0.175466
$813$	0	0
$814$	6.00000	0.210300
$815$	0	0
$816$	0	0
$817$	10.0000	0.349856
$818$	17.0000	0.594391
$819$	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
$823$	36.0000	1.25488	0.627441	−	0.778664i	$-0.284103\pi$
$823$	36.0000	1.25488	0.627441	+	0.778664i	$0.284103\pi$
$824$	10.0000	0.348367
$825$	0	0
$826$	−4.00000	−0.139178
$827$	34.0000	1.18230	0.591148	−	0.806563i	$-0.298675\pi$
$827$	34.0000	1.18230	0.591148	+	0.806563i	$0.298675\pi$
$828$	0	0
$829$	16.0000	0.555703	0.277851	−	0.960624i	$-0.410378\pi$
$829$	16.0000	0.555703	0.277851	+	0.960624i	$0.410378\pi$
$830$	0	0
$831$	0	0
$832$	−1.00000	−0.0346688
$833$	−1.00000	−0.0346479
$834$	0	0
$835$	0	0
$836$	6.00000	0.207514
$837$	0	0
$838$	13.0000	0.449078
$839$	−10.0000	−0.345238	−0.172619	−	0.984989i	$-0.555223\pi$
$839$	−10.0000	−0.345238	−0.172619	+	0.984989i	$0.555223\pi$
$840$	0	0
$841$	−4.00000	−0.137931
$842$	−22.0000	−0.758170
$843$	0	0
$844$	24.0000	0.826114
$845$	0	0
$846$	0	0
$847$	2.00000	0.0687208
$848$	12.0000	0.412082
$849$	0	0
$850$	0	0
$851$	14.0000	0.479914
$852$	0	0
$853$	7.00000	0.239675	0.119838	−	0.992793i	$-0.461763\pi$
$853$	7.00000	0.239675	0.119838	+	0.992793i	$0.461763\pi$
$854$	−12.0000	−0.410632
$855$	0	0
$856$	2.00000	0.0683586
$857$	−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
$859$	−6.00000	−0.204717	−0.102359	−	0.994748i	$-0.532639\pi$
$859$	−6.00000	−0.204717	−0.102359	+	0.994748i	$0.532639\pi$
$860$	0	0
$861$	0	0
$862$	28.0000	0.953684
$863$	−31.0000	−1.05525	−0.527626	−	0.849477i	$-0.676918\pi$
$863$	−31.0000	−1.05525	−0.527626	+	0.849477i	$0.676918\pi$
$864$	0	0
$865$	0	0
$866$	−26.0000	−0.883516
$867$	0	0
$868$	5.00000	0.169711
$869$	−15.0000	−0.508840
$870$	0	0
$871$	−4.00000	−0.135535
$872$	4.00000	0.135457
$873$	0	0
$874$	14.0000	0.473557
$875$	0	0
$876$	0	0
$877$	41.0000	1.38447	0.692236	−	0.721671i	$-0.256626\pi$
$877$	41.0000	1.38447	0.692236	+	0.721671i	$0.256626\pi$
$878$	−8.00000	−0.269987
$879$	0	0
$880$	0	0
$881$	6.00000	0.202145	0.101073	−	0.994879i	$-0.467773\pi$
$881$	6.00000	0.202145	0.101073	+	0.994879i	$0.467773\pi$
$882$	0	0
$883$	−4.00000	−0.134611	−0.0673054	−	0.997732i	$-0.521440\pi$
$883$	−4.00000	−0.134611	−0.0673054	+	0.997732i	$0.521440\pi$
$884$	1.00000	0.0336336
$885$	0	0
$886$	18.0000	0.604722
$887$	9.00000	0.302190	0.151095	−	0.988519i	$-0.451720\pi$
$887$	9.00000	0.302190	0.151095	+	0.988519i	$0.451720\pi$
$888$	0	0
$889$	−20.0000	−0.670778
$890$	0	0
$891$	0	0
$892$	26.0000	0.870544
$893$	−2.00000	−0.0669274
$894$	0	0
$895$	0	0
$896$	1.00000	0.0334077
$897$	0	0
$898$	28.0000	0.934372
$899$	−25.0000	−0.833797
$900$	0	0
$901$	−12.0000	−0.399778
$902$	−18.0000	−0.599334
$903$	0	0
$904$	−7.00000	−0.232817
$905$	0	0
$906$	0	0
$907$	31.0000	1.02934	0.514669	−	0.857389i	$-0.327915\pi$
$907$	31.0000	1.02934	0.514669	+	0.857389i	$0.327915\pi$
$908$	−6.00000	−0.199117
$909$	0	0
$910$	0	0
$911$	20.0000	0.662630	0.331315	−	0.943520i	$-0.392508\pi$
$911$	20.0000	0.662630	0.331315	+	0.943520i	$0.392508\pi$
$912$	0	0
$913$	0	0
$914$	−4.00000	−0.132308
$915$	0	0
$916$	−14.0000	−0.462573
$917$	1.00000	0.0330229
$918$	0	0
$919$	53.0000	1.74831	0.874154	−	0.485648i	$-0.161416\pi$
$919$	53.0000	1.74831	0.874154	+	0.485648i	$0.161416\pi$
$920$	0	0
$921$	0	0
$922$	2.00000	0.0658665
$923$	−6.00000	−0.197492
$924$	0	0
$925$	0	0
$926$	34.0000	1.11731
$927$	0	0
$928$	−5.00000	−0.164133
$929$	−6.00000	−0.196854	−0.0984268	−	0.995144i	$-0.531381\pi$
$929$	−6.00000	−0.196854	−0.0984268	+	0.995144i	$0.531381\pi$
$930$	0	0
$931$	−2.00000	−0.0655474
$932$	26.0000	0.851658
$933$	0	0
$934$	−26.0000	−0.850746
$935$	0	0
$936$	0	0
$937$	20.0000	0.653372	0.326686	−	0.945133i	$-0.394068\pi$
$937$	20.0000	0.653372	0.326686	+	0.945133i	$0.394068\pi$
$938$	4.00000	0.130605
$939$	0	0
$940$	0	0
$941$	−55.0000	−1.79295	−0.896474	−	0.443096i	$-0.853880\pi$
$941$	−55.0000	−1.79295	−0.896474	+	0.443096i	$0.853880\pi$
$942$	0	0
$943$	−42.0000	−1.36771
$944$	−4.00000	−0.130189
$945$	0	0
$946$	−15.0000	−0.487692
$947$	36.0000	1.16984	0.584921	−	0.811090i	$-0.301125\pi$
$947$	36.0000	1.16984	0.584921	+	0.811090i	$0.301125\pi$
$948$	0	0
$949$	2.00000	0.0649227
$950$	0	0
$951$	0	0
$952$	−1.00000	−0.0324102
$953$	−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
$956$	20.0000	0.646846
$957$	0	0
$958$	6.00000	0.193851
$959$	−2.00000	−0.0645834
$960$	0	0
$961$	−6.00000	−0.193548
$962$	2.00000	0.0644826
$963$	0	0
$964$	21.0000	0.676364
$965$	0	0
$966$	0	0
$967$	−2.00000	−0.0643157	−0.0321578	−	0.999483i	$-0.510238\pi$
$967$	−2.00000	−0.0643157	−0.0321578	+	0.999483i	$0.510238\pi$
$968$	2.00000	0.0642824
$969$	0	0
$970$	0	0
$971$	−27.0000	−0.866471	−0.433236	−	0.901281i	$-0.642628\pi$
$971$	−27.0000	−0.866471	−0.433236	+	0.901281i	$0.642628\pi$
$972$	0	0
$973$	−16.0000	−0.512936
$974$	−8.00000	−0.256337
$975$	0	0
$976$	−12.0000	−0.384111
$977$	27.0000	0.863807	0.431903	−	0.901920i	$-0.357842\pi$
$977$	27.0000	0.863807	0.431903	+	0.901920i	$0.357842\pi$
$978$	0	0
$979$	30.0000	0.958804
$980$	0	0
$981$	0	0
$982$	−24.0000	−0.765871
$983$	−1.00000	−0.0318950	−0.0159475	−	0.999873i	$-0.505076\pi$
$983$	−1.00000	−0.0318950	−0.0159475	+	0.999873i	$0.505076\pi$
$984$	0	0
$985$	0	0
$986$	5.00000	0.159232
$987$	0	0
$988$	2.00000	0.0636285
$989$	−35.0000	−1.11294
$990$	0	0
$991$	19.0000	0.603555	0.301777	−	0.953378i	$-0.402420\pi$
$991$	19.0000	0.603555	0.301777	+	0.953378i	$0.402420\pi$
$992$	5.00000	0.158750
$993$	0	0
$994$	6.00000	0.190308
$995$	0	0
$996$	0	0
$997$	5.00000	0.158352	0.0791758	−	0.996861i	$-0.474771\pi$
$997$	5.00000	0.158352	0.0791758	+	0.996861i	$0.474771\pi$
$998$	32.0000	1.01294
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9450.2.a.f.1.1		1
3.2	odd	2		9450.2.a.cs.1.1		1
5.2	odd	4		1890.2.g.h.379.1	yes	2
5.3	odd	4		1890.2.g.h.379.2	yes	2
5.4	even	2		9450.2.a.dg.1.1		1
15.2	even	4		1890.2.g.f.379.2	yes	2
15.8	even	4		1890.2.g.f.379.1	✓	2
15.14	odd	2		9450.2.a.bv.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1890.2.g.f.379.1	✓	2	15.8	even	4
1890.2.g.f.379.2	yes	2	15.2	even	4
1890.2.g.h.379.1	yes	2	5.2	odd	4
1890.2.g.h.379.2	yes	2	5.3	odd	4
9450.2.a.f.1.1		1	1.1	even	1	trivial
9450.2.a.bv.1.1		1	15.14	odd	2
9450.2.a.cs.1.1		1	3.2	odd	2
9450.2.a.dg.1.1		1	5.4	even	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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