LMFDB - Embedded newform 4544.2.a.n.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4544,2,Mod(1,4544)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4544, 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("4544.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4544 = 2^{6} \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4544.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:	$36.2840226785$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 142)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4544.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+3.00000 q^{3} -2.00000 q^{5} +3.00000 q^{7} +6.00000 q^{9} +O(q^{10})$

$q+3.00000 q^{3} -2.00000 q^{5} +3.00000 q^{7} +6.00000 q^{9} -6.00000 q^{11} +5.00000 q^{13} -6.00000 q^{15} +6.00000 q^{17} +1.00000 q^{19} +9.00000 q^{21} -5.00000 q^{23} -1.00000 q^{25} +9.00000 q^{27} +2.00000 q^{29} +5.00000 q^{31} -18.0000 q^{33} -6.00000 q^{35} +2.00000 q^{37} +15.0000 q^{39} +10.0000 q^{41} +1.00000 q^{43} -12.0000 q^{45} +1.00000 q^{47} +2.00000 q^{49} +18.0000 q^{51} -6.00000 q^{53} +12.0000 q^{55} +3.00000 q^{57} -2.00000 q^{59} +2.00000 q^{61} +18.0000 q^{63} -10.0000 q^{65} +2.00000 q^{67} -15.0000 q^{69} -1.00000 q^{71} +7.00000 q^{73} -3.00000 q^{75} -18.0000 q^{77} +6.00000 q^{79} +9.00000 q^{81} -4.00000 q^{83} -12.0000 q^{85} +6.00000 q^{87} +9.00000 q^{89} +15.0000 q^{91} +15.0000 q^{93} -2.00000 q^{95} +2.00000 q^{97} -36.0000 q^{99} +O(q^{100})$

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 $

$2$	0	0
$2$	0	0
$3$	3.00000	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$3$	3.00000	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$4$	0	0
$5$	−2.00000	−0.894427	−0.447214	−	0.894427i	$-0.647584\pi$
$5$	−2.00000	−0.894427	−0.447214	+	0.894427i	$0.647584\pi$
$6$	0	0
$7$	3.00000	1.13389	0.566947	−	0.823754i	$-0.308125\pi$
$7$	3.00000	1.13389	0.566947	+	0.823754i	$0.308125\pi$
$8$	0	0
$9$	6.00000	2.00000
$10$	0	0
$11$	−6.00000	−1.80907	−0.904534	−	0.426401i	$-0.859781\pi$
$11$	−6.00000	−1.80907	−0.904534	+	0.426401i	$0.859781\pi$
$12$	0	0
$13$	5.00000	1.38675	0.693375	−	0.720577i	$-0.256123\pi$
$13$	5.00000	1.38675	0.693375	+	0.720577i	$0.256123\pi$
$14$	0	0
$15$	−6.00000	−1.54919
$16$	0	0
$17$	6.00000	1.45521	0.727607	−	0.685994i	$-0.240633\pi$
$17$	6.00000	1.45521	0.727607	+	0.685994i	$0.240633\pi$
$18$	0	0
$19$	1.00000	0.229416	0.114708	−	0.993399i	$-0.463407\pi$
$19$	1.00000	0.229416	0.114708	+	0.993399i	$0.463407\pi$
$20$	0	0
$21$	9.00000	1.96396
$22$	0	0
$23$	−5.00000	−1.04257	−0.521286	−	0.853382i	$-0.674548\pi$
$23$	−5.00000	−1.04257	−0.521286	+	0.853382i	$0.674548\pi$
$24$	0	0
$25$	−1.00000	−0.200000
$26$	0	0
$27$	9.00000	1.73205
$28$	0	0
$29$	2.00000	0.371391	0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000	0.371391	0.185695	+	0.982607i	$0.440546\pi$
$30$	0	0
$31$	5.00000	0.898027	0.449013	−	0.893525i	$-0.351776\pi$
$31$	5.00000	0.898027	0.449013	+	0.893525i	$0.351776\pi$
$32$	0	0
$33$	−18.0000	−3.13340
$34$	0	0
$35$	−6.00000	−1.01419
$36$	0	0
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	0	0
$39$	15.0000	2.40192
$40$	0	0
$41$	10.0000	1.56174	0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000	1.56174	0.780869	+	0.624695i	$0.214777\pi$
$42$	0	0
$43$	1.00000	0.152499	0.0762493	−	0.997089i	$-0.475706\pi$
$43$	1.00000	0.152499	0.0762493	+	0.997089i	$0.475706\pi$
$44$	0	0
$45$	−12.0000	−1.78885
$46$	0	0
$47$	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
$49$	2.00000	0.285714
$50$	0	0
$51$	18.0000	2.52050
$52$	0	0
$53$	−6.00000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	0	0
$55$	12.0000	1.61808
$56$	0	0
$57$	3.00000	0.397360
$58$	0	0
$59$	−2.00000	−0.260378	−0.130189	−	0.991489i	$-0.541558\pi$
$59$	−2.00000	−0.260378	−0.130189	+	0.991489i	$0.541558\pi$
$60$	0	0
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	0	0
$63$	18.0000	2.26779
$64$	0	0
$65$	−10.0000	−1.24035
$66$	0	0
$67$	2.00000	0.244339	0.122169	−	0.992509i	$-0.461015\pi$
$67$	2.00000	0.244339	0.122169	+	0.992509i	$0.461015\pi$
$68$	0	0
$69$	−15.0000	−1.80579
$70$	0	0
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	0	0
$73$	7.00000	0.819288	0.409644	−	0.912245i	$-0.365653\pi$
$73$	7.00000	0.819288	0.409644	+	0.912245i	$0.365653\pi$
$74$	0	0
$75$	−3.00000	−0.346410
$76$	0	0
$77$	−18.0000	−2.05129
$78$	0	0
$79$	6.00000	0.675053	0.337526	−	0.941316i	$-0.390410\pi$
$79$	6.00000	0.675053	0.337526	+	0.941316i	$0.390410\pi$
$80$	0	0
$81$	9.00000	1.00000
$82$	0	0
$83$	−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
$85$	−12.0000	−1.30158
$86$	0	0
$87$	6.00000	0.643268
$88$	0	0
$89$	9.00000	0.953998	0.476999	−	0.878904i	$-0.341725\pi$
$89$	9.00000	0.953998	0.476999	+	0.878904i	$0.341725\pi$
$90$	0	0
$91$	15.0000	1.57243
$92$	0	0
$93$	15.0000	1.55543
$94$	0	0
$95$	−2.00000	−0.205196
$96$	0	0
$97$	2.00000	0.203069	0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000	0.203069	0.101535	+	0.994832i	$0.467625\pi$
$98$	0	0
$99$	−36.0000	−3.61814
$100$	0	0
$101$	12.0000	1.19404	0.597022	−	0.802225i	$-0.296350\pi$
$101$	12.0000	1.19404	0.597022	+	0.802225i	$0.296350\pi$
$102$	0	0
$103$	4.00000	0.394132	0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000	0.394132	0.197066	+	0.980390i	$0.436859\pi$
$104$	0	0
$105$	−18.0000	−1.75662
$106$	0	0
$107$	11.0000	1.06341	0.531705	−	0.846930i	$-0.321551\pi$
$107$	11.0000	1.06341	0.531705	+	0.846930i	$0.321551\pi$
$108$	0	0
$109$	−12.0000	−1.14939	−0.574696	−	0.818367i	$-0.694880\pi$
$109$	−12.0000	−1.14939	−0.574696	+	0.818367i	$0.694880\pi$
$110$	0	0
$111$	6.00000	0.569495
$112$	0	0
$113$	−14.0000	−1.31701	−0.658505	−	0.752577i	$-0.728811\pi$
$113$	−14.0000	−1.31701	−0.658505	+	0.752577i	$0.728811\pi$
$114$	0	0
$115$	10.0000	0.932505
$116$	0	0
$117$	30.0000	2.77350
$118$	0	0
$119$	18.0000	1.65006
$120$	0	0
$121$	25.0000	2.27273
$122$	0	0
$123$	30.0000	2.70501
$124$	0	0
$125$	12.0000	1.07331
$126$	0	0
$127$	−8.00000	−0.709885	−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000	−0.709885	−0.354943	+	0.934888i	$0.615500\pi$
$128$	0	0
$129$	3.00000	0.264135
$130$	0	0
$131$	−17.0000	−1.48530	−0.742648	−	0.669681i	$-0.766431\pi$
$131$	−17.0000	−1.48530	−0.742648	+	0.669681i	$0.766431\pi$
$132$	0	0
$133$	3.00000	0.260133
$134$	0	0
$135$	−18.0000	−1.54919
$136$	0	0
$137$	16.0000	1.36697	0.683486	−	0.729964i	$-0.260463\pi$
$137$	16.0000	1.36697	0.683486	+	0.729964i	$0.260463\pi$
$138$	0	0
$139$	−16.0000	−1.35710	−0.678551	−	0.734553i	$-0.737392\pi$
$139$	−16.0000	−1.35710	−0.678551	+	0.734553i	$0.737392\pi$
$140$	0	0
$141$	3.00000	0.252646
$142$	0	0
$143$	−30.0000	−2.50873
$144$	0	0
$145$	−4.00000	−0.332182
$146$	0	0
$147$	6.00000	0.494872
$148$	0	0
$149$	11.0000	0.901155	0.450578	−	0.892737i	$-0.351218\pi$
$149$	11.0000	0.901155	0.450578	+	0.892737i	$0.351218\pi$
$150$	0	0
$151$	−4.00000	−0.325515	−0.162758	−	0.986666i	$-0.552039\pi$
$151$	−4.00000	−0.325515	−0.162758	+	0.986666i	$0.552039\pi$
$152$	0	0
$153$	36.0000	2.91043
$154$	0	0
$155$	−10.0000	−0.803219
$156$	0	0
$157$	−22.0000	−1.75579	−0.877896	−	0.478852i	$-0.841053\pi$
$157$	−22.0000	−1.75579	−0.877896	+	0.478852i	$0.841053\pi$
$158$	0	0
$159$	−18.0000	−1.42749
$160$	0	0
$161$	−15.0000	−1.18217
$162$	0	0
$163$	10.0000	0.783260	0.391630	−	0.920123i	$-0.371911\pi$
$163$	10.0000	0.783260	0.391630	+	0.920123i	$0.371911\pi$
$164$	0	0
$165$	36.0000	2.80260
$166$	0	0
$167$	−16.0000	−1.23812	−0.619059	−	0.785345i	$-0.712486\pi$
$167$	−16.0000	−1.23812	−0.619059	+	0.785345i	$0.712486\pi$
$168$	0	0
$169$	12.0000	0.923077
$170$	0	0
$171$	6.00000	0.458831
$172$	0	0
$173$	−9.00000	−0.684257	−0.342129	−	0.939653i	$-0.611148\pi$
$173$	−9.00000	−0.684257	−0.342129	+	0.939653i	$0.611148\pi$
$174$	0	0
$175$	−3.00000	−0.226779
$176$	0	0
$177$	−6.00000	−0.450988
$178$	0	0
$179$	9.00000	0.672692	0.336346	−	0.941739i	$-0.390809\pi$
$179$	9.00000	0.672692	0.336346	+	0.941739i	$0.390809\pi$
$180$	0	0
$181$	21.0000	1.56092	0.780459	−	0.625207i	$-0.214986\pi$
$181$	21.0000	1.56092	0.780459	+	0.625207i	$0.214986\pi$
$182$	0	0
$183$	6.00000	0.443533
$184$	0	0
$185$	−4.00000	−0.294086
$186$	0	0
$187$	−36.0000	−2.63258
$188$	0	0
$189$	27.0000	1.96396
$190$	0	0
$191$	8.00000	0.578860	0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000	0.578860	0.289430	+	0.957199i	$0.406534\pi$
$192$	0	0
$193$	−14.0000	−1.00774	−0.503871	−	0.863779i	$-0.668091\pi$
$193$	−14.0000	−1.00774	−0.503871	+	0.863779i	$0.668091\pi$
$194$	0	0
$195$	−30.0000	−2.14834
$196$	0	0
$197$	−21.0000	−1.49619	−0.748094	−	0.663593i	$-0.769031\pi$
$197$	−21.0000	−1.49619	−0.748094	+	0.663593i	$0.769031\pi$
$198$	0	0
$199$	14.0000	0.992434	0.496217	−	0.868199i	$-0.334722\pi$
$199$	14.0000	0.992434	0.496217	+	0.868199i	$0.334722\pi$
$200$	0	0
$201$	6.00000	0.423207
$202$	0	0
$203$	6.00000	0.421117
$204$	0	0
$205$	−20.0000	−1.39686
$206$	0	0
$207$	−30.0000	−2.08514
$208$	0	0
$209$	−6.00000	−0.415029
$210$	0	0
$211$	18.0000	1.23917	0.619586	−	0.784929i	$-0.287301\pi$
$211$	18.0000	1.23917	0.619586	+	0.784929i	$0.287301\pi$
$212$	0	0
$213$	−3.00000	−0.205557
$214$	0	0
$215$	−2.00000	−0.136399
$216$	0	0
$217$	15.0000	1.01827
$218$	0	0
$219$	21.0000	1.41905
$220$	0	0
$221$	30.0000	2.01802
$222$	0	0
$223$	14.0000	0.937509	0.468755	−	0.883328i	$-0.344703\pi$
$223$	14.0000	0.937509	0.468755	+	0.883328i	$0.344703\pi$
$224$	0	0
$225$	−6.00000	−0.400000
$226$	0	0
$227$	10.0000	0.663723	0.331862	−	0.943328i	$-0.392323\pi$
$227$	10.0000	0.663723	0.331862	+	0.943328i	$0.392323\pi$
$228$	0	0
$229$	10.0000	0.660819	0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000	0.660819	0.330409	+	0.943838i	$0.392813\pi$
$230$	0	0
$231$	−54.0000	−3.55294
$232$	0	0
$233$	−25.0000	−1.63780	−0.818902	−	0.573933i	$-0.805417\pi$
$233$	−25.0000	−1.63780	−0.818902	+	0.573933i	$0.805417\pi$
$234$	0	0
$235$	−2.00000	−0.130466
$236$	0	0
$237$	18.0000	1.16923
$238$	0	0
$239$	−11.0000	−0.711531	−0.355765	−	0.934575i	$-0.615780\pi$
$239$	−11.0000	−0.711531	−0.355765	+	0.934575i	$0.615780\pi$
$240$	0	0
$241$	14.0000	0.901819	0.450910	−	0.892570i	$-0.351100\pi$
$241$	14.0000	0.901819	0.450910	+	0.892570i	$0.351100\pi$
$242$	0	0
$243$	0	0
$244$	0	0
$245$	−4.00000	−0.255551
$246$	0	0
$247$	5.00000	0.318142
$248$	0	0
$249$	−12.0000	−0.760469
$250$	0	0
$251$	−17.0000	−1.07303	−0.536515	−	0.843891i	$-0.680260\pi$
$251$	−17.0000	−1.07303	−0.536515	+	0.843891i	$0.680260\pi$
$252$	0	0
$253$	30.0000	1.88608
$254$	0	0
$255$	−36.0000	−2.25441
$256$	0	0
$257$	−8.00000	−0.499026	−0.249513	−	0.968371i	$-0.580271\pi$
$257$	−8.00000	−0.499026	−0.249513	+	0.968371i	$0.580271\pi$
$258$	0	0
$259$	6.00000	0.372822
$260$	0	0
$261$	12.0000	0.742781
$262$	0	0
$263$	−6.00000	−0.369976	−0.184988	−	0.982741i	$-0.559225\pi$
$263$	−6.00000	−0.369976	−0.184988	+	0.982741i	$0.559225\pi$
$264$	0	0
$265$	12.0000	0.737154
$266$	0	0
$267$	27.0000	1.65237
$268$	0	0
$269$	15.0000	0.914566	0.457283	−	0.889321i	$-0.348823\pi$
$269$	15.0000	0.914566	0.457283	+	0.889321i	$0.348823\pi$
$270$	0	0
$271$	16.0000	0.971931	0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000	0.971931	0.485965	+	0.873978i	$0.338468\pi$
$272$	0	0
$273$	45.0000	2.72352
$274$	0	0
$275$	6.00000	0.361814
$276$	0	0
$277$	10.0000	0.600842	0.300421	−	0.953807i	$-0.402873\pi$
$277$	10.0000	0.600842	0.300421	+	0.953807i	$0.402873\pi$
$278$	0	0
$279$	30.0000	1.79605
$280$	0	0
$281$	−4.00000	−0.238620	−0.119310	−	0.992857i	$-0.538068\pi$
$281$	−4.00000	−0.238620	−0.119310	+	0.992857i	$0.538068\pi$
$282$	0	0
$283$	18.0000	1.06999	0.534994	−	0.844856i	$-0.320314\pi$
$283$	18.0000	1.06999	0.534994	+	0.844856i	$0.320314\pi$
$284$	0	0
$285$	−6.00000	−0.355409
$286$	0	0
$287$	30.0000	1.77084
$288$	0	0
$289$	19.0000	1.11765
$290$	0	0
$291$	6.00000	0.351726
$292$	0	0
$293$	−12.0000	−0.701047	−0.350524	−	0.936554i	$-0.613996\pi$
$293$	−12.0000	−0.701047	−0.350524	+	0.936554i	$0.613996\pi$
$294$	0	0
$295$	4.00000	0.232889
$296$	0	0
$297$	−54.0000	−3.13340
$298$	0	0
$299$	−25.0000	−1.44579
$300$	0	0
$301$	3.00000	0.172917
$302$	0	0
$303$	36.0000	2.06815
$304$	0	0
$305$	−4.00000	−0.229039
$306$	0	0
$307$	−34.0000	−1.94048	−0.970241	−	0.242140i	$-0.922151\pi$
$307$	−34.0000	−1.94048	−0.970241	+	0.242140i	$0.922151\pi$
$308$	0	0
$309$	12.0000	0.682656
$310$	0	0
$311$	−8.00000	−0.453638	−0.226819	−	0.973937i	$-0.572833\pi$
$311$	−8.00000	−0.453638	−0.226819	+	0.973937i	$0.572833\pi$
$312$	0	0
$313$	27.0000	1.52613	0.763065	−	0.646322i	$-0.223694\pi$
$313$	27.0000	1.52613	0.763065	+	0.646322i	$0.223694\pi$
$314$	0	0
$315$	−36.0000	−2.02837
$316$	0	0
$317$	−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
$319$	−12.0000	−0.671871
$320$	0	0
$321$	33.0000	1.84188
$322$	0	0
$323$	6.00000	0.333849
$324$	0	0
$325$	−5.00000	−0.277350
$326$	0	0
$327$	−36.0000	−1.99080
$328$	0	0
$329$	3.00000	0.165395
$330$	0	0
$331$	−8.00000	−0.439720	−0.219860	−	0.975531i	$-0.570560\pi$
$331$	−8.00000	−0.439720	−0.219860	+	0.975531i	$0.570560\pi$
$332$	0	0
$333$	12.0000	0.657596
$334$	0	0
$335$	−4.00000	−0.218543
$336$	0	0
$337$	−22.0000	−1.19842	−0.599208	−	0.800593i	$-0.704518\pi$
$337$	−22.0000	−1.19842	−0.599208	+	0.800593i	$0.704518\pi$
$338$	0	0
$339$	−42.0000	−2.28113
$340$	0	0
$341$	−30.0000	−1.62459
$342$	0	0
$343$	−15.0000	−0.809924
$344$	0	0
$345$	30.0000	1.61515
$346$	0	0
$347$	−22.0000	−1.18102	−0.590511	−	0.807030i	$-0.701074\pi$
$347$	−22.0000	−1.18102	−0.590511	+	0.807030i	$0.701074\pi$
$348$	0	0
$349$	−19.0000	−1.01705	−0.508523	−	0.861048i	$-0.669808\pi$
$349$	−19.0000	−1.01705	−0.508523	+	0.861048i	$0.669808\pi$
$350$	0	0
$351$	45.0000	2.40192
$352$	0	0
$353$	−18.0000	−0.958043	−0.479022	−	0.877803i	$-0.659008\pi$
$353$	−18.0000	−0.958043	−0.479022	+	0.877803i	$0.659008\pi$
$354$	0	0
$355$	2.00000	0.106149
$356$	0	0
$357$	54.0000	2.85798
$358$	0	0
$359$	12.0000	0.633336	0.316668	−	0.948536i	$-0.397436\pi$
$359$	12.0000	0.633336	0.316668	+	0.948536i	$0.397436\pi$
$360$	0	0
$361$	−18.0000	−0.947368
$362$	0	0
$363$	75.0000	3.93648
$364$	0	0
$365$	−14.0000	−0.732793
$366$	0	0
$367$	−14.0000	−0.730794	−0.365397	−	0.930852i	$-0.619067\pi$
$367$	−14.0000	−0.730794	−0.365397	+	0.930852i	$0.619067\pi$
$368$	0	0
$369$	60.0000	3.12348
$370$	0	0
$371$	−18.0000	−0.934513
$372$	0	0
$373$	28.0000	1.44979	0.724893	−	0.688862i	$-0.241889\pi$
$373$	28.0000	1.44979	0.724893	+	0.688862i	$0.241889\pi$
$374$	0	0
$375$	36.0000	1.85903
$376$	0	0
$377$	10.0000	0.515026
$378$	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
$381$	−24.0000	−1.22956
$382$	0	0
$383$	1.00000	0.0510976	0.0255488	−	0.999674i	$-0.491867\pi$
$383$	1.00000	0.0510976	0.0255488	+	0.999674i	$0.491867\pi$
$384$	0	0
$385$	36.0000	1.83473
$386$	0	0
$387$	6.00000	0.304997
$388$	0	0
$389$	−13.0000	−0.659126	−0.329563	−	0.944134i	$-0.606901\pi$
$389$	−13.0000	−0.659126	−0.329563	+	0.944134i	$0.606901\pi$
$390$	0	0
$391$	−30.0000	−1.51717
$392$	0	0
$393$	−51.0000	−2.57261
$394$	0	0
$395$	−12.0000	−0.603786
$396$	0	0
$397$	18.0000	0.903394	0.451697	−	0.892171i	$-0.350819\pi$
$397$	18.0000	0.903394	0.451697	+	0.892171i	$0.350819\pi$
$398$	0	0
$399$	9.00000	0.450564
$400$	0	0
$401$	0	0		−	1.00000i	$-0.5\pi$
$401$	0	0			1.00000i	$0.5\pi$
$402$	0	0
$403$	25.0000	1.24534
$404$	0	0
$405$	−18.0000	−0.894427
$406$	0	0
$407$	−12.0000	−0.594818
$408$	0	0
$409$	−19.0000	−0.939490	−0.469745	−	0.882802i	$-0.655654\pi$
$409$	−19.0000	−0.939490	−0.469745	+	0.882802i	$0.655654\pi$
$410$	0	0
$411$	48.0000	2.36767
$412$	0	0
$413$	−6.00000	−0.295241
$414$	0	0
$415$	8.00000	0.392705
$416$	0	0
$417$	−48.0000	−2.35057
$418$	0	0
$419$	12.0000	0.586238	0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000	0.586238	0.293119	+	0.956076i	$0.405307\pi$
$420$	0	0
$421$	1.00000	0.0487370	0.0243685	−	0.999703i	$-0.492242\pi$
$421$	1.00000	0.0487370	0.0243685	+	0.999703i	$0.492242\pi$
$422$	0	0
$423$	6.00000	0.291730
$424$	0	0
$425$	−6.00000	−0.291043
$426$	0	0
$427$	6.00000	0.290360
$428$	0	0
$429$	−90.0000	−4.34524
$430$	0	0
$431$	−20.0000	−0.963366	−0.481683	−	0.876346i	$-0.659974\pi$
$431$	−20.0000	−0.963366	−0.481683	+	0.876346i	$0.659974\pi$
$432$	0	0
$433$	2.00000	0.0961139	0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000	0.0961139	0.0480569	+	0.998845i	$0.484697\pi$
$434$	0	0
$435$	−12.0000	−0.575356
$436$	0	0
$437$	−5.00000	−0.239182
$438$	0	0
$439$	−28.0000	−1.33637	−0.668184	−	0.743996i	$-0.732928\pi$
$439$	−28.0000	−1.33637	−0.668184	+	0.743996i	$0.732928\pi$
$440$	0	0
$441$	12.0000	0.571429
$442$	0	0
$443$	−36.0000	−1.71041	−0.855206	−	0.518289i	$-0.826569\pi$
$443$	−36.0000	−1.71041	−0.855206	+	0.518289i	$0.826569\pi$
$444$	0	0
$445$	−18.0000	−0.853282
$446$	0	0
$447$	33.0000	1.56085
$448$	0	0
$449$	−6.00000	−0.283158	−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000	−0.283158	−0.141579	+	0.989927i	$0.545218\pi$
$450$	0	0
$451$	−60.0000	−2.82529
$452$	0	0
$453$	−12.0000	−0.563809
$454$	0	0
$455$	−30.0000	−1.40642
$456$	0	0
$457$	8.00000	0.374224	0.187112	−	0.982339i	$-0.440087\pi$
$457$	8.00000	0.374224	0.187112	+	0.982339i	$0.440087\pi$
$458$	0	0
$459$	54.0000	2.52050
$460$	0	0
$461$	13.0000	0.605470	0.302735	−	0.953075i	$-0.402100\pi$
$461$	13.0000	0.605470	0.302735	+	0.953075i	$0.402100\pi$
$462$	0	0
$463$	6.00000	0.278844	0.139422	−	0.990233i	$-0.455476\pi$
$463$	6.00000	0.278844	0.139422	+	0.990233i	$0.455476\pi$
$464$	0	0
$465$	−30.0000	−1.39122
$466$	0	0
$467$	28.0000	1.29569	0.647843	−	0.761774i	$-0.275671\pi$
$467$	28.0000	1.29569	0.647843	+	0.761774i	$0.275671\pi$
$468$	0	0
$469$	6.00000	0.277054
$470$	0	0
$471$	−66.0000	−3.04112
$472$	0	0
$473$	−6.00000	−0.275880
$474$	0	0
$475$	−1.00000	−0.0458831
$476$	0	0
$477$	−36.0000	−1.64833
$478$	0	0
$479$	−21.0000	−0.959514	−0.479757	−	0.877401i	$-0.659275\pi$
$479$	−21.0000	−0.959514	−0.479757	+	0.877401i	$0.659275\pi$
$480$	0	0
$481$	10.0000	0.455961
$482$	0	0
$483$	−45.0000	−2.04757
$484$	0	0
$485$	−4.00000	−0.181631
$486$	0	0
$487$	16.0000	0.725029	0.362515	−	0.931978i	$-0.381918\pi$
$487$	16.0000	0.725029	0.362515	+	0.931978i	$0.381918\pi$
$488$	0	0
$489$	30.0000	1.35665
$490$	0	0
$491$	12.0000	0.541552	0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000	0.541552	0.270776	+	0.962642i	$0.412720\pi$
$492$	0	0
$493$	12.0000	0.540453
$494$	0	0
$495$	72.0000	3.23616
$496$	0	0
$497$	−3.00000	−0.134568
$498$	0	0
$499$	−29.0000	−1.29822	−0.649109	−	0.760695i	$-0.724858\pi$
$499$	−29.0000	−1.29822	−0.649109	+	0.760695i	$0.724858\pi$
$500$	0	0
$501$	−48.0000	−2.14448
$502$	0	0
$503$	−36.0000	−1.60516	−0.802580	−	0.596544i	$-0.796540\pi$
$503$	−36.0000	−1.60516	−0.802580	+	0.596544i	$0.796540\pi$
$504$	0	0
$505$	−24.0000	−1.06799
$506$	0	0
$507$	36.0000	1.59882
$508$	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
$511$	21.0000	0.928985
$512$	0	0
$513$	9.00000	0.397360
$514$	0	0
$515$	−8.00000	−0.352522
$516$	0	0
$517$	−6.00000	−0.263880
$518$	0	0
$519$	−27.0000	−1.18517
$520$	0	0
$521$	−22.0000	−0.963837	−0.481919	−	0.876216i	$-0.660060\pi$
$521$	−22.0000	−0.963837	−0.481919	+	0.876216i	$0.660060\pi$
$522$	0	0
$523$	−20.0000	−0.874539	−0.437269	−	0.899331i	$-0.644054\pi$
$523$	−20.0000	−0.874539	−0.437269	+	0.899331i	$0.644054\pi$
$524$	0	0
$525$	−9.00000	−0.392792
$526$	0	0
$527$	30.0000	1.30682
$528$	0	0
$529$	2.00000	0.0869565
$530$	0	0
$531$	−12.0000	−0.520756
$532$	0	0
$533$	50.0000	2.16574
$534$	0	0
$535$	−22.0000	−0.951143
$536$	0	0
$537$	27.0000	1.16514
$538$	0	0
$539$	−12.0000	−0.516877
$540$	0	0
$541$	30.0000	1.28980	0.644900	−	0.764267i	$-0.276899\pi$
$541$	30.0000	1.28980	0.644900	+	0.764267i	$0.276899\pi$
$542$	0	0
$543$	63.0000	2.70359
$544$	0	0
$545$	24.0000	1.02805
$546$	0	0
$547$	23.0000	0.983409	0.491704	−	0.870762i	$-0.336374\pi$
$547$	23.0000	0.983409	0.491704	+	0.870762i	$0.336374\pi$
$548$	0	0
$549$	12.0000	0.512148
$550$	0	0
$551$	2.00000	0.0852029
$552$	0	0
$553$	18.0000	0.765438
$554$	0	0
$555$	−12.0000	−0.509372
$556$	0	0
$557$	26.0000	1.10166	0.550828	−	0.834619i	$-0.314312\pi$
$557$	26.0000	1.10166	0.550828	+	0.834619i	$0.314312\pi$
$558$	0	0
$559$	5.00000	0.211477
$560$	0	0
$561$	−108.000	−4.55976
$562$	0	0
$563$	26.0000	1.09577	0.547885	−	0.836554i	$-0.315433\pi$
$563$	26.0000	1.09577	0.547885	+	0.836554i	$0.315433\pi$
$564$	0	0
$565$	28.0000	1.17797
$566$	0	0
$567$	27.0000	1.13389
$568$	0	0
$569$	27.0000	1.13190	0.565949	−	0.824440i	$-0.308510\pi$
$569$	27.0000	1.13190	0.565949	+	0.824440i	$0.308510\pi$
$570$	0	0
$571$	−40.0000	−1.67395	−0.836974	−	0.547243i	$-0.815677\pi$
$571$	−40.0000	−1.67395	−0.836974	+	0.547243i	$0.815677\pi$
$572$	0	0
$573$	24.0000	1.00261
$574$	0	0
$575$	5.00000	0.208514
$576$	0	0
$577$	−18.0000	−0.749350	−0.374675	−	0.927156i	$-0.622246\pi$
$577$	−18.0000	−0.749350	−0.374675	+	0.927156i	$0.622246\pi$
$578$	0	0
$579$	−42.0000	−1.74546
$580$	0	0
$581$	−12.0000	−0.497844
$582$	0	0
$583$	36.0000	1.49097
$584$	0	0
$585$	−60.0000	−2.48069
$586$	0	0
$587$	36.0000	1.48588	0.742940	−	0.669359i	$-0.233431\pi$
$587$	36.0000	1.48588	0.742940	+	0.669359i	$0.233431\pi$
$588$	0	0
$589$	5.00000	0.206021
$590$	0	0
$591$	−63.0000	−2.59147
$592$	0	0
$593$	−39.0000	−1.60154	−0.800769	−	0.598973i	$-0.795576\pi$
$593$	−39.0000	−1.60154	−0.800769	+	0.598973i	$0.795576\pi$
$594$	0	0
$595$	−36.0000	−1.47586
$596$	0	0
$597$	42.0000	1.71895
$598$	0	0
$599$	−35.0000	−1.43006	−0.715031	−	0.699093i	$-0.753587\pi$
$599$	−35.0000	−1.43006	−0.715031	+	0.699093i	$0.753587\pi$
$600$	0	0
$601$	4.00000	0.163163	0.0815817	−	0.996667i	$-0.474003\pi$
$601$	4.00000	0.163163	0.0815817	+	0.996667i	$0.474003\pi$
$602$	0	0
$603$	12.0000	0.488678
$604$	0	0
$605$	−50.0000	−2.03279
$606$	0	0
$607$	−20.0000	−0.811775	−0.405887	−	0.913923i	$-0.633038\pi$
$607$	−20.0000	−0.811775	−0.405887	+	0.913923i	$0.633038\pi$
$608$	0	0
$609$	18.0000	0.729397
$610$	0	0
$611$	5.00000	0.202278
$612$	0	0
$613$	−40.0000	−1.61558	−0.807792	−	0.589467i	$-0.799338\pi$
$613$	−40.0000	−1.61558	−0.807792	+	0.589467i	$0.799338\pi$
$614$	0	0
$615$	−60.0000	−2.41943
$616$	0	0
$617$	3.00000	0.120775	0.0603877	−	0.998175i	$-0.480766\pi$
$617$	3.00000	0.120775	0.0603877	+	0.998175i	$0.480766\pi$
$618$	0	0
$619$	0	0		−	1.00000i	$-0.5\pi$
$619$	0	0			1.00000i	$0.5\pi$
$620$	0	0
$621$	−45.0000	−1.80579
$622$	0	0
$623$	27.0000	1.08173
$624$	0	0
$625$	−19.0000	−0.760000
$626$	0	0
$627$	−18.0000	−0.718851
$628$	0	0
$629$	12.0000	0.478471
$630$	0	0
$631$	−32.0000	−1.27390	−0.636950	−	0.770905i	$-0.719804\pi$
$631$	−32.0000	−1.27390	−0.636950	+	0.770905i	$0.719804\pi$
$632$	0	0
$633$	54.0000	2.14631
$634$	0	0
$635$	16.0000	0.634941
$636$	0	0
$637$	10.0000	0.396214
$638$	0	0
$639$	−6.00000	−0.237356
$640$	0	0
$641$	37.0000	1.46141	0.730706	−	0.682692i	$-0.239191\pi$
$641$	37.0000	1.46141	0.730706	+	0.682692i	$0.239191\pi$
$642$	0	0
$643$	−21.0000	−0.828159	−0.414080	−	0.910241i	$-0.635896\pi$
$643$	−21.0000	−0.828159	−0.414080	+	0.910241i	$0.635896\pi$
$644$	0	0
$645$	−6.00000	−0.236250
$646$	0	0
$647$	−32.0000	−1.25805	−0.629025	−	0.777385i	$-0.716546\pi$
$647$	−32.0000	−1.25805	−0.629025	+	0.777385i	$0.716546\pi$
$648$	0	0
$649$	12.0000	0.471041
$650$	0	0
$651$	45.0000	1.76369
$652$	0	0
$653$	46.0000	1.80012	0.900060	−	0.435767i	$-0.143523\pi$
$653$	46.0000	1.80012	0.900060	+	0.435767i	$0.143523\pi$
$654$	0	0
$655$	34.0000	1.32849
$656$	0	0
$657$	42.0000	1.63858
$658$	0	0
$659$	−15.0000	−0.584317	−0.292159	−	0.956370i	$-0.594373\pi$
$659$	−15.0000	−0.584317	−0.292159	+	0.956370i	$0.594373\pi$
$660$	0	0
$661$	−45.0000	−1.75030	−0.875149	−	0.483854i	$-0.839236\pi$
$661$	−45.0000	−1.75030	−0.875149	+	0.483854i	$0.839236\pi$
$662$	0	0
$663$	90.0000	3.49531
$664$	0	0
$665$	−6.00000	−0.232670
$666$	0	0
$667$	−10.0000	−0.387202
$668$	0	0
$669$	42.0000	1.62381
$670$	0	0
$671$	−12.0000	−0.463255
$672$	0	0
$673$	−12.0000	−0.462566	−0.231283	−	0.972887i	$-0.574292\pi$
$673$	−12.0000	−0.462566	−0.231283	+	0.972887i	$0.574292\pi$
$674$	0	0
$675$	−9.00000	−0.346410
$676$	0	0
$677$	−8.00000	−0.307465	−0.153732	−	0.988113i	$-0.549129\pi$
$677$	−8.00000	−0.307465	−0.153732	+	0.988113i	$0.549129\pi$
$678$	0	0
$679$	6.00000	0.230259
$680$	0	0
$681$	30.0000	1.14960
$682$	0	0
$683$	16.0000	0.612223	0.306111	−	0.951996i	$-0.400972\pi$
$683$	16.0000	0.612223	0.306111	+	0.951996i	$0.400972\pi$
$684$	0	0
$685$	−32.0000	−1.22266
$686$	0	0
$687$	30.0000	1.14457
$688$	0	0
$689$	−30.0000	−1.14291
$690$	0	0
$691$	0	0		−	1.00000i	$-0.5\pi$
$691$	0	0			1.00000i	$0.5\pi$
$692$	0	0
$693$	−108.000	−4.10258
$694$	0	0
$695$	32.0000	1.21383
$696$	0	0
$697$	60.0000	2.27266
$698$	0	0
$699$	−75.0000	−2.83676
$700$	0	0
$701$	3.00000	0.113308	0.0566542	−	0.998394i	$-0.481957\pi$
$701$	3.00000	0.113308	0.0566542	+	0.998394i	$0.481957\pi$
$702$	0	0
$703$	2.00000	0.0754314
$704$	0	0
$705$	−6.00000	−0.225973
$706$	0	0
$707$	36.0000	1.35392
$708$	0	0
$709$	25.0000	0.938895	0.469447	−	0.882960i	$-0.344453\pi$
$709$	25.0000	0.938895	0.469447	+	0.882960i	$0.344453\pi$
$710$	0	0
$711$	36.0000	1.35011
$712$	0	0
$713$	−25.0000	−0.936257
$714$	0	0
$715$	60.0000	2.24387
$716$	0	0
$717$	−33.0000	−1.23241
$718$	0	0
$719$	−36.0000	−1.34257	−0.671287	−	0.741198i	$-0.734258\pi$
$719$	−36.0000	−1.34257	−0.671287	+	0.741198i	$0.734258\pi$
$720$	0	0
$721$	12.0000	0.446903
$722$	0	0
$723$	42.0000	1.56200
$724$	0	0
$725$	−2.00000	−0.0742781
$726$	0	0
$727$	−33.0000	−1.22390	−0.611951	−	0.790896i	$-0.709615\pi$
$727$	−33.0000	−1.22390	−0.611951	+	0.790896i	$0.709615\pi$
$728$	0	0
$729$	−27.0000	−1.00000
$730$	0	0
$731$	6.00000	0.221918
$732$	0	0
$733$	5.00000	0.184679	0.0923396	−	0.995728i	$-0.470565\pi$
$733$	5.00000	0.184679	0.0923396	+	0.995728i	$0.470565\pi$
$734$	0	0
$735$	−12.0000	−0.442627
$736$	0	0
$737$	−12.0000	−0.442026
$738$	0	0
$739$	41.0000	1.50821	0.754105	−	0.656754i	$-0.228071\pi$
$739$	41.0000	1.50821	0.754105	+	0.656754i	$0.228071\pi$
$740$	0	0
$741$	15.0000	0.551039
$742$	0	0
$743$	17.0000	0.623670	0.311835	−	0.950136i	$-0.399056\pi$
$743$	17.0000	0.623670	0.311835	+	0.950136i	$0.399056\pi$
$744$	0	0
$745$	−22.0000	−0.806018
$746$	0	0
$747$	−24.0000	−0.878114
$748$	0	0
$749$	33.0000	1.20579
$750$	0	0
$751$	12.0000	0.437886	0.218943	−	0.975738i	$-0.429739\pi$
$751$	12.0000	0.437886	0.218943	+	0.975738i	$0.429739\pi$
$752$	0	0
$753$	−51.0000	−1.85854
$754$	0	0
$755$	8.00000	0.291150
$756$	0	0
$757$	35.0000	1.27210	0.636048	−	0.771649i	$-0.280568\pi$
$757$	35.0000	1.27210	0.636048	+	0.771649i	$0.280568\pi$
$758$	0	0
$759$	90.0000	3.26679
$760$	0	0
$761$	−24.0000	−0.869999	−0.435000	−	0.900431i	$-0.643252\pi$
$761$	−24.0000	−0.869999	−0.435000	+	0.900431i	$0.643252\pi$
$762$	0	0
$763$	−36.0000	−1.30329
$764$	0	0
$765$	−72.0000	−2.60317
$766$	0	0
$767$	−10.0000	−0.361079
$768$	0	0
$769$	20.0000	0.721218	0.360609	−	0.932717i	$-0.382569\pi$
$769$	20.0000	0.721218	0.360609	+	0.932717i	$0.382569\pi$
$770$	0	0
$771$	−24.0000	−0.864339
$772$	0	0
$773$	1.00000	0.0359675	0.0179838	−	0.999838i	$-0.494275\pi$
$773$	1.00000	0.0359675	0.0179838	+	0.999838i	$0.494275\pi$
$774$	0	0
$775$	−5.00000	−0.179605
$776$	0	0
$777$	18.0000	0.645746
$778$	0	0
$779$	10.0000	0.358287
$780$	0	0
$781$	6.00000	0.214697
$782$	0	0
$783$	18.0000	0.643268
$784$	0	0
$785$	44.0000	1.57043
$786$	0	0
$787$	−5.00000	−0.178231	−0.0891154	−	0.996021i	$-0.528404\pi$
$787$	−5.00000	−0.178231	−0.0891154	+	0.996021i	$0.528404\pi$
$788$	0	0
$789$	−18.0000	−0.640817
$790$	0	0
$791$	−42.0000	−1.49335
$792$	0	0
$793$	10.0000	0.355110
$794$	0	0
$795$	36.0000	1.27679
$796$	0	0
$797$	−26.0000	−0.920967	−0.460484	−	0.887668i	$-0.652324\pi$
$797$	−26.0000	−0.920967	−0.460484	+	0.887668i	$0.652324\pi$
$798$	0	0
$799$	6.00000	0.212265
$800$	0	0
$801$	54.0000	1.90800
$802$	0	0
$803$	−42.0000	−1.48215
$804$	0	0
$805$	30.0000	1.05736
$806$	0	0
$807$	45.0000	1.58408
$808$	0	0
$809$	12.0000	0.421898	0.210949	−	0.977497i	$-0.432345\pi$
$809$	12.0000	0.421898	0.210949	+	0.977497i	$0.432345\pi$
$810$	0	0
$811$	−28.0000	−0.983213	−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000	−0.983213	−0.491606	+	0.870817i	$0.663590\pi$
$812$	0	0
$813$	48.0000	1.68343
$814$	0	0
$815$	−20.0000	−0.700569
$816$	0	0
$817$	1.00000	0.0349856
$818$	0	0
$819$	90.0000	3.14485
$820$	0	0
$821$	−8.00000	−0.279202	−0.139601	−	0.990208i	$-0.544582\pi$
$821$	−8.00000	−0.279202	−0.139601	+	0.990208i	$0.544582\pi$
$822$	0	0
$823$	5.00000	0.174289	0.0871445	−	0.996196i	$-0.472226\pi$
$823$	5.00000	0.174289	0.0871445	+	0.996196i	$0.472226\pi$
$824$	0	0
$825$	18.0000	0.626680
$826$	0	0
$827$	30.0000	1.04320	0.521601	−	0.853189i	$-0.325335\pi$
$827$	30.0000	1.04320	0.521601	+	0.853189i	$0.325335\pi$
$828$	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
$831$	30.0000	1.04069
$832$	0	0
$833$	12.0000	0.415775
$834$	0	0
$835$	32.0000	1.10741
$836$	0	0
$837$	45.0000	1.55543
$838$	0	0
$839$	36.0000	1.24286	0.621429	−	0.783470i	$-0.286552\pi$
$839$	36.0000	1.24286	0.621429	+	0.783470i	$0.286552\pi$
$840$	0	0
$841$	−25.0000	−0.862069
$842$	0	0
$843$	−12.0000	−0.413302
$844$	0	0
$845$	−24.0000	−0.825625
$846$	0	0
$847$	75.0000	2.57703
$848$	0	0
$849$	54.0000	1.85328
$850$	0	0
$851$	−10.0000	−0.342796
$852$	0	0
$853$	28.0000	0.958702	0.479351	−	0.877623i	$-0.340872\pi$
$853$	28.0000	0.958702	0.479351	+	0.877623i	$0.340872\pi$
$854$	0	0
$855$	−12.0000	−0.410391
$856$	0	0
$857$	29.0000	0.990621	0.495311	−	0.868716i	$-0.335054\pi$
$857$	29.0000	0.990621	0.495311	+	0.868716i	$0.335054\pi$
$858$	0	0
$859$	40.0000	1.36478	0.682391	−	0.730987i	$-0.260940\pi$
$859$	40.0000	1.36478	0.682391	+	0.730987i	$0.260940\pi$
$860$	0	0
$861$	90.0000	3.06719
$862$	0	0
$863$	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
$865$	18.0000	0.612018
$866$	0	0
$867$	57.0000	1.93582
$868$	0	0
$869$	−36.0000	−1.22122
$870$	0	0
$871$	10.0000	0.338837
$872$	0	0
$873$	12.0000	0.406138
$874$	0	0
$875$	36.0000	1.21702
$876$	0	0
$877$	−40.0000	−1.35070	−0.675352	−	0.737496i	$-0.736008\pi$
$877$	−40.0000	−1.35070	−0.675352	+	0.737496i	$0.736008\pi$
$878$	0	0
$879$	−36.0000	−1.21425
$880$	0	0
$881$	1.00000	0.0336909	0.0168454	−	0.999858i	$-0.494638\pi$
$881$	1.00000	0.0336909	0.0168454	+	0.999858i	$0.494638\pi$
$882$	0	0
$883$	−42.0000	−1.41341	−0.706706	−	0.707507i	$-0.749820\pi$
$883$	−42.0000	−1.41341	−0.706706	+	0.707507i	$0.749820\pi$
$884$	0	0
$885$	12.0000	0.403376
$886$	0	0
$887$	36.0000	1.20876	0.604381	−	0.796696i	$-0.293421\pi$
$887$	36.0000	1.20876	0.604381	+	0.796696i	$0.293421\pi$
$888$	0	0
$889$	−24.0000	−0.804934
$890$	0	0
$891$	−54.0000	−1.80907
$892$	0	0
$893$	1.00000	0.0334637
$894$	0	0
$895$	−18.0000	−0.601674
$896$	0	0
$897$	−75.0000	−2.50418
$898$	0	0
$899$	10.0000	0.333519
$900$	0	0
$901$	−36.0000	−1.19933
$902$	0	0
$903$	9.00000	0.299501
$904$	0	0
$905$	−42.0000	−1.39613
$906$	0	0
$907$	−8.00000	−0.265636	−0.132818	−	0.991140i	$-0.542403\pi$
$907$	−8.00000	−0.265636	−0.132818	+	0.991140i	$0.542403\pi$
$908$	0	0
$909$	72.0000	2.38809
$910$	0	0
$911$	−51.0000	−1.68971	−0.844853	−	0.534999i	$-0.820312\pi$
$911$	−51.0000	−1.68971	−0.844853	+	0.534999i	$0.820312\pi$
$912$	0	0
$913$	24.0000	0.794284
$914$	0	0
$915$	−12.0000	−0.396708
$916$	0	0
$917$	−51.0000	−1.68417
$918$	0	0
$919$	39.0000	1.28649	0.643246	−	0.765660i	$-0.277587\pi$
$919$	39.0000	1.28649	0.643246	+	0.765660i	$0.277587\pi$
$920$	0	0
$921$	−102.000	−3.36101
$922$	0	0
$923$	−5.00000	−0.164577
$924$	0	0
$925$	−2.00000	−0.0657596
$926$	0	0
$927$	24.0000	0.788263
$928$	0	0
$929$	6.00000	0.196854	0.0984268	−	0.995144i	$-0.468619\pi$
$929$	6.00000	0.196854	0.0984268	+	0.995144i	$0.468619\pi$
$930$	0	0
$931$	2.00000	0.0655474
$932$	0	0
$933$	−24.0000	−0.785725
$934$	0	0
$935$	72.0000	2.35465
$936$	0	0
$937$	−16.0000	−0.522697	−0.261349	−	0.965244i	$-0.584167\pi$
$937$	−16.0000	−0.522697	−0.261349	+	0.965244i	$0.584167\pi$
$938$	0	0
$939$	81.0000	2.64334
$940$	0	0
$941$	0	0		−	1.00000i	$-0.5\pi$
$941$	0	0			1.00000i	$0.5\pi$
$942$	0	0
$943$	−50.0000	−1.62822
$944$	0	0
$945$	−54.0000	−1.75662
$946$	0	0
$947$	0	0		−	1.00000i	$-0.5\pi$
$947$	0	0			1.00000i	$0.5\pi$
$948$	0	0
$949$	35.0000	1.13615
$950$	0	0
$951$	−54.0000	−1.75107
$952$	0	0
$953$	−10.0000	−0.323932	−0.161966	−	0.986796i	$-0.551783\pi$
$953$	−10.0000	−0.323932	−0.161966	+	0.986796i	$0.551783\pi$
$954$	0	0
$955$	−16.0000	−0.517748
$956$	0	0
$957$	−36.0000	−1.16371
$958$	0	0
$959$	48.0000	1.55000
$960$	0	0
$961$	−6.00000	−0.193548
$962$	0	0
$963$	66.0000	2.12682
$964$	0	0
$965$	28.0000	0.901352
$966$	0	0
$967$	−9.00000	−0.289420	−0.144710	−	0.989474i	$-0.546225\pi$
$967$	−9.00000	−0.289420	−0.144710	+	0.989474i	$0.546225\pi$
$968$	0	0
$969$	18.0000	0.578243
$970$	0	0
$971$	13.0000	0.417190	0.208595	−	0.978002i	$-0.433111\pi$
$971$	13.0000	0.417190	0.208595	+	0.978002i	$0.433111\pi$
$972$	0	0
$973$	−48.0000	−1.53881
$974$	0	0
$975$	−15.0000	−0.480384
$976$	0	0
$977$	18.0000	0.575871	0.287936	−	0.957650i	$-0.407031\pi$
$977$	18.0000	0.575871	0.287936	+	0.957650i	$0.407031\pi$
$978$	0	0
$979$	−54.0000	−1.72585
$980$	0	0
$981$	−72.0000	−2.29878
$982$	0	0
$983$	−18.0000	−0.574111	−0.287055	−	0.957914i	$-0.592676\pi$
$983$	−18.0000	−0.574111	−0.287055	+	0.957914i	$0.592676\pi$
$984$	0	0
$985$	42.0000	1.33823
$986$	0	0
$987$	9.00000	0.286473
$988$	0	0
$989$	−5.00000	−0.158991
$990$	0	0
$991$	−47.0000	−1.49300	−0.746502	−	0.665383i	$-0.768268\pi$
$991$	−47.0000	−1.49300	−0.746502	+	0.665383i	$0.768268\pi$
$992$	0	0
$993$	−24.0000	−0.761617
$994$	0	0
$995$	−28.0000	−0.887660
$996$	0	0
$997$	28.0000	0.886769	0.443384	−	0.896332i	$-0.353778\pi$
$997$	28.0000	0.886769	0.443384	+	0.896332i	$0.353778\pi$
$998$	0	0
$999$	18.0000	0.569495

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4544.2.a.n.1.1		1
4.3	odd	2		4544.2.a.a.1.1		1
8.3	odd	2		142.2.a.c.1.1	✓	1
8.5	even	2		1136.2.a.a.1.1		1
24.11	even	2		1278.2.a.g.1.1		1
40.19	odd	2		3550.2.a.j.1.1		1
56.27	even	2		6958.2.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
142.2.a.c.1.1	✓	1	8.3	odd	2
1136.2.a.a.1.1		1	8.5	even	2
1278.2.a.g.1.1		1	24.11	even	2
3550.2.a.j.1.1		1	40.19	odd	2
4544.2.a.a.1.1		1	4.3	odd	2
4544.2.a.n.1.1		1	1.1	even	1	trivial
6958.2.a.a.1.1		1	56.27	even	2

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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:	\( N \)	\(=\)	\( 4544 = 2^{6} \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4544.a (trivial)

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