LMFDB - Embedded newform 5824.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5824,2,Mod(1,5824)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5824, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("5824.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5824 = 2^{6} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5824.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:	$46.5048741372$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 364)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	5824.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{3} -1.00000 q^{5} +1.00000 q^{7} +1.00000 q^{9} +O(q^{10})$

$q-2.00000 q^{3} -1.00000 q^{5} +1.00000 q^{7} +1.00000 q^{9} -4.00000 q^{11} -1.00000 q^{13} +2.00000 q^{15} -2.00000 q^{17} -1.00000 q^{19} -2.00000 q^{21} +7.00000 q^{23} -4.00000 q^{25} +4.00000 q^{27} +5.00000 q^{29} +9.00000 q^{31} +8.00000 q^{33} -1.00000 q^{35} +2.00000 q^{37} +2.00000 q^{39} +2.00000 q^{41} +1.00000 q^{43} -1.00000 q^{45} -9.00000 q^{47} +1.00000 q^{49} +4.00000 q^{51} -3.00000 q^{53} +4.00000 q^{55} +2.00000 q^{57} -14.0000 q^{61} +1.00000 q^{63} +1.00000 q^{65} +10.0000 q^{67} -14.0000 q^{69} +14.0000 q^{71} +3.00000 q^{73} +8.00000 q^{75} -4.00000 q^{77} -5.00000 q^{79} -11.0000 q^{81} +5.00000 q^{83} +2.00000 q^{85} -10.0000 q^{87} -9.00000 q^{89} -1.00000 q^{91} -18.0000 q^{93} +1.00000 q^{95} -1.00000 q^{97} -4.00000 q^{99} +O(q^{100})$

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
$3$	−2.00000	−1.15470	−0.577350	−	0.816497i	$-0.695913\pi$
$3$	−2.00000	−1.15470	−0.577350	+	0.816497i	$0.695913\pi$
$4$	0	0
$5$	−1.00000	−0.447214	−0.223607	−	0.974679i	$-0.571783\pi$
$5$	−1.00000	−0.447214	−0.223607	+	0.974679i	$0.571783\pi$
$6$	0	0
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	0	0
$9$	1.00000	0.333333
$10$	0	0
$11$	−4.00000	−1.20605	−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000	−1.20605	−0.603023	+	0.797724i	$0.706037\pi$
$12$	0	0
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	2.00000	0.516398
$16$	0	0
$17$	−2.00000	−0.485071	−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000	−0.485071	−0.242536	+	0.970143i	$0.577979\pi$
$18$	0	0
$19$	−1.00000	−0.229416	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	−1.00000	−0.229416	−0.114708	+	0.993399i	$0.536593\pi$
$20$	0	0
$21$	−2.00000	−0.436436
$22$	0	0
$23$	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
$25$	−4.00000	−0.800000
$26$	0	0
$27$	4.00000	0.769800
$28$	0	0
$29$	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
$31$	9.00000	1.61645	0.808224	−	0.588875i	$-0.200429\pi$
$31$	9.00000	1.61645	0.808224	+	0.588875i	$0.200429\pi$
$32$	0	0
$33$	8.00000	1.39262
$34$	0	0
$35$	−1.00000	−0.169031
$36$	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
$39$	2.00000	0.320256
$40$	0	0
$41$	2.00000	0.312348	0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000	0.312348	0.156174	+	0.987730i	$0.450084\pi$
$42$	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
$45$	−1.00000	−0.149071
$46$	0	0
$47$	−9.00000	−1.31278	−0.656392	−	0.754420i	$-0.727918\pi$
$47$	−9.00000	−1.31278	−0.656392	+	0.754420i	$0.727918\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	0	0
$51$	4.00000	0.560112
$52$	0	0
$53$	−3.00000	−0.412082	−0.206041	−	0.978543i	$-0.566058\pi$
$53$	−3.00000	−0.412082	−0.206041	+	0.978543i	$0.566058\pi$
$54$	0	0
$55$	4.00000	0.539360
$56$	0	0
$57$	2.00000	0.264906
$58$	0	0
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	0	0
$61$	−14.0000	−1.79252	−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−14.0000	−1.79252	−0.896258	+	0.443533i	$0.853725\pi$
$62$	0	0
$63$	1.00000	0.125988
$64$	0	0
$65$	1.00000	0.124035
$66$	0	0
$67$	10.0000	1.22169	0.610847	−	0.791748i	$-0.290829\pi$
$67$	10.0000	1.22169	0.610847	+	0.791748i	$0.290829\pi$
$68$	0	0
$69$	−14.0000	−1.68540
$70$	0	0
$71$	14.0000	1.66149	0.830747	−	0.556650i	$-0.187914\pi$
$71$	14.0000	1.66149	0.830747	+	0.556650i	$0.187914\pi$
$72$	0	0
$73$	3.00000	0.351123	0.175562	−	0.984468i	$-0.443826\pi$
$73$	3.00000	0.351123	0.175562	+	0.984468i	$0.443826\pi$
$74$	0	0
$75$	8.00000	0.923760
$76$	0	0
$77$	−4.00000	−0.455842
$78$	0	0
$79$	−5.00000	−0.562544	−0.281272	−	0.959628i	$-0.590756\pi$
$79$	−5.00000	−0.562544	−0.281272	+	0.959628i	$0.590756\pi$
$80$	0	0
$81$	−11.0000	−1.22222
$82$	0	0
$83$	5.00000	0.548821	0.274411	−	0.961613i	$-0.411517\pi$
$83$	5.00000	0.548821	0.274411	+	0.961613i	$0.411517\pi$
$84$	0	0
$85$	2.00000	0.216930
$86$	0	0
$87$	−10.0000	−1.07211
$88$	0	0
$89$	−9.00000	−0.953998	−0.476999	−	0.878904i	$-0.658275\pi$
$89$	−9.00000	−0.953998	−0.476999	+	0.878904i	$0.658275\pi$
$90$	0	0
$91$	−1.00000	−0.104828
$92$	0	0
$93$	−18.0000	−1.86651
$94$	0	0
$95$	1.00000	0.102598
$96$	0	0
$97$	−1.00000	−0.101535	−0.0507673	−	0.998711i	$-0.516167\pi$
$97$	−1.00000	−0.101535	−0.0507673	+	0.998711i	$0.516167\pi$
$98$	0	0
$99$	−4.00000	−0.402015
$100$	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	$-0.563141\pi$
$103$	−4.00000	−0.394132	−0.197066	+	0.980390i	$0.563141\pi$
$104$	0	0
$105$	2.00000	0.195180
$106$	0	0
$107$	−12.0000	−1.16008	−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000	−1.16008	−0.580042	+	0.814587i	$0.696964\pi$
$108$	0	0
$109$	4.00000	0.383131	0.191565	−	0.981480i	$-0.438644\pi$
$109$	4.00000	0.383131	0.191565	+	0.981480i	$0.438644\pi$
$110$	0	0
$111$	−4.00000	−0.379663
$112$	0	0
$113$	1.00000	0.0940721	0.0470360	−	0.998893i	$-0.485022\pi$
$113$	1.00000	0.0940721	0.0470360	+	0.998893i	$0.485022\pi$
$114$	0	0
$115$	−7.00000	−0.652753
$116$	0	0
$117$	−1.00000	−0.0924500
$118$	0	0
$119$	−2.00000	−0.183340
$120$	0	0
$121$	5.00000	0.454545
$122$	0	0
$123$	−4.00000	−0.360668
$124$	0	0
$125$	9.00000	0.804984
$126$	0	0
$127$	8.00000	0.709885	0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000	0.709885	0.354943	+	0.934888i	$0.384500\pi$
$128$	0	0
$129$	−2.00000	−0.176090
$130$	0	0
$131$	−12.0000	−1.04844	−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000	−1.04844	−0.524222	+	0.851581i	$0.675644\pi$
$132$	0	0
$133$	−1.00000	−0.0867110
$134$	0	0
$135$	−4.00000	−0.344265
$136$	0	0
$137$	−14.0000	−1.19610	−0.598050	−	0.801459i	$-0.704058\pi$
$137$	−14.0000	−1.19610	−0.598050	+	0.801459i	$0.704058\pi$
$138$	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
$141$	18.0000	1.51587
$142$	0	0
$143$	4.00000	0.334497
$144$	0	0
$145$	−5.00000	−0.415227
$146$	0	0
$147$	−2.00000	−0.164957
$148$	0	0
$149$	−12.0000	−0.983078	−0.491539	−	0.870855i	$-0.663566\pi$
$149$	−12.0000	−0.983078	−0.491539	+	0.870855i	$0.663566\pi$
$150$	0	0
$151$	−14.0000	−1.13930	−0.569652	−	0.821886i	$-0.692922\pi$
$151$	−14.0000	−1.13930	−0.569652	+	0.821886i	$0.692922\pi$
$152$	0	0
$153$	−2.00000	−0.161690
$154$	0	0
$155$	−9.00000	−0.722897
$156$	0	0
$157$	−10.0000	−0.798087	−0.399043	−	0.916932i	$-0.630658\pi$
$157$	−10.0000	−0.798087	−0.399043	+	0.916932i	$0.630658\pi$
$158$	0	0
$159$	6.00000	0.475831
$160$	0	0
$161$	7.00000	0.551677
$162$	0	0
$163$	24.0000	1.87983	0.939913	−	0.341415i	$-0.110906\pi$
$163$	24.0000	1.87983	0.939913	+	0.341415i	$0.110906\pi$
$164$	0	0
$165$	−8.00000	−0.622799
$166$	0	0
$167$	−3.00000	−0.232147	−0.116073	−	0.993241i	$-0.537031\pi$
$167$	−3.00000	−0.232147	−0.116073	+	0.993241i	$0.537031\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	0	0
$171$	−1.00000	−0.0764719
$172$	0	0
$173$	−2.00000	−0.152057	−0.0760286	−	0.997106i	$-0.524224\pi$
$173$	−2.00000	−0.152057	−0.0760286	+	0.997106i	$0.524224\pi$
$174$	0	0
$175$	−4.00000	−0.302372
$176$	0	0
$177$	0	0
$178$	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
$181$	20.0000	1.48659	0.743294	−	0.668965i	$-0.233262\pi$
$181$	20.0000	1.48659	0.743294	+	0.668965i	$0.233262\pi$
$182$	0	0
$183$	28.0000	2.06982
$184$	0	0
$185$	−2.00000	−0.147043
$186$	0	0
$187$	8.00000	0.585018
$188$	0	0
$189$	4.00000	0.290957
$190$	0	0
$191$	24.0000	1.73658	0.868290	−	0.496058i	$-0.165220\pi$
$191$	24.0000	1.73658	0.868290	+	0.496058i	$0.165220\pi$
$192$	0	0
$193$	2.00000	0.143963	0.0719816	−	0.997406i	$-0.477068\pi$
$193$	2.00000	0.143963	0.0719816	+	0.997406i	$0.477068\pi$
$194$	0	0
$195$	−2.00000	−0.143223
$196$	0	0
$197$	−6.00000	−0.427482	−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000	−0.427482	−0.213741	+	0.976890i	$0.568565\pi$
$198$	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
$201$	−20.0000	−1.41069
$202$	0	0
$203$	5.00000	0.350931
$204$	0	0
$205$	−2.00000	−0.139686
$206$	0	0
$207$	7.00000	0.486534
$208$	0	0
$209$	4.00000	0.276686
$210$	0	0
$211$	−23.0000	−1.58339	−0.791693	−	0.610920i	$-0.790800\pi$
$211$	−23.0000	−1.58339	−0.791693	+	0.610920i	$0.790800\pi$
$212$	0	0
$213$	−28.0000	−1.91853
$214$	0	0
$215$	−1.00000	−0.0681994
$216$	0	0
$217$	9.00000	0.610960
$218$	0	0
$219$	−6.00000	−0.405442
$220$	0	0
$221$	2.00000	0.134535
$222$	0	0
$223$	−21.0000	−1.40626	−0.703132	−	0.711059i	$-0.748216\pi$
$223$	−21.0000	−1.40626	−0.703132	+	0.711059i	$0.748216\pi$
$224$	0	0
$225$	−4.00000	−0.266667
$226$	0	0
$227$	−8.00000	−0.530979	−0.265489	−	0.964114i	$-0.585534\pi$
$227$	−8.00000	−0.530979	−0.265489	+	0.964114i	$0.585534\pi$
$228$	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
$231$	8.00000	0.526361
$232$	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
$235$	9.00000	0.587095
$236$	0	0
$237$	10.0000	0.649570
$238$	0	0
$239$	−12.0000	−0.776215	−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000	−0.776215	−0.388108	+	0.921614i	$0.626871\pi$
$240$	0	0
$241$	−25.0000	−1.61039	−0.805196	−	0.593009i	$-0.797940\pi$
$241$	−25.0000	−1.61039	−0.805196	+	0.593009i	$0.797940\pi$
$242$	0	0
$243$	10.0000	0.641500
$244$	0	0
$245$	−1.00000	−0.0638877
$246$	0	0
$247$	1.00000	0.0636285
$248$	0	0
$249$	−10.0000	−0.633724
$250$	0	0
$251$	−16.0000	−1.00991	−0.504956	−	0.863145i	$-0.668491\pi$
$251$	−16.0000	−1.00991	−0.504956	+	0.863145i	$0.668491\pi$
$252$	0	0
$253$	−28.0000	−1.76034
$254$	0	0
$255$	−4.00000	−0.250490
$256$	0	0
$257$	−12.0000	−0.748539	−0.374270	−	0.927320i	$-0.622107\pi$
$257$	−12.0000	−0.748539	−0.374270	+	0.927320i	$0.622107\pi$
$258$	0	0
$259$	2.00000	0.124274
$260$	0	0
$261$	5.00000	0.309492
$262$	0	0
$263$	−19.0000	−1.17159	−0.585795	−	0.810459i	$-0.699218\pi$
$263$	−19.0000	−1.17159	−0.585795	+	0.810459i	$0.699218\pi$
$264$	0	0
$265$	3.00000	0.184289
$266$	0	0
$267$	18.0000	1.10158
$268$	0	0
$269$	−24.0000	−1.46331	−0.731653	−	0.681677i	$-0.761251\pi$
$269$	−24.0000	−1.46331	−0.731653	+	0.681677i	$0.761251\pi$
$270$	0	0
$271$	0	0		−	1.00000i	$-0.5\pi$
$271$	0	0			1.00000i	$0.5\pi$
$272$	0	0
$273$	2.00000	0.121046
$274$	0	0
$275$	16.0000	0.964836
$276$	0	0
$277$	23.0000	1.38194	0.690968	−	0.722885i	$-0.257185\pi$
$277$	23.0000	1.38194	0.690968	+	0.722885i	$0.257185\pi$
$278$	0	0
$279$	9.00000	0.538816
$280$	0	0
$281$	−8.00000	−0.477240	−0.238620	−	0.971113i	$-0.576695\pi$
$281$	−8.00000	−0.477240	−0.238620	+	0.971113i	$0.576695\pi$
$282$	0	0
$283$	−4.00000	−0.237775	−0.118888	−	0.992908i	$-0.537933\pi$
$283$	−4.00000	−0.237775	−0.118888	+	0.992908i	$0.537933\pi$
$284$	0	0
$285$	−2.00000	−0.118470
$286$	0	0
$287$	2.00000	0.118056
$288$	0	0
$289$	−13.0000	−0.764706
$290$	0	0
$291$	2.00000	0.117242
$292$	0	0
$293$	−5.00000	−0.292103	−0.146052	−	0.989277i	$-0.546657\pi$
$293$	−5.00000	−0.292103	−0.146052	+	0.989277i	$0.546657\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	−16.0000	−0.928414
$298$	0	0
$299$	−7.00000	−0.404820
$300$	0	0
$301$	1.00000	0.0576390
$302$	0	0
$303$	−24.0000	−1.37876
$304$	0	0
$305$	14.0000	0.801638
$306$	0	0
$307$	−27.0000	−1.54097	−0.770486	−	0.637457i	$-0.779986\pi$
$307$	−27.0000	−1.54097	−0.770486	+	0.637457i	$0.779986\pi$
$308$	0	0
$309$	8.00000	0.455104
$310$	0	0
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	0	0
$313$	−12.0000	−0.678280	−0.339140	−	0.940736i	$-0.610136\pi$
$313$	−12.0000	−0.678280	−0.339140	+	0.940736i	$0.610136\pi$
$314$	0	0
$315$	−1.00000	−0.0563436
$316$	0	0
$317$	−20.0000	−1.12331	−0.561656	−	0.827371i	$-0.689836\pi$
$317$	−20.0000	−1.12331	−0.561656	+	0.827371i	$0.689836\pi$
$318$	0	0
$319$	−20.0000	−1.11979
$320$	0	0
$321$	24.0000	1.33955
$322$	0	0
$323$	2.00000	0.111283
$324$	0	0
$325$	4.00000	0.221880
$326$	0	0
$327$	−8.00000	−0.442401
$328$	0	0
$329$	−9.00000	−0.496186
$330$	0	0
$331$	30.0000	1.64895	0.824475	−	0.565899i	$-0.191471\pi$
$331$	30.0000	1.64895	0.824475	+	0.565899i	$0.191471\pi$
$332$	0	0
$333$	2.00000	0.109599
$334$	0	0
$335$	−10.0000	−0.546358
$336$	0	0
$337$	21.0000	1.14394	0.571971	−	0.820274i	$-0.306179\pi$
$337$	21.0000	1.14394	0.571971	+	0.820274i	$0.306179\pi$
$338$	0	0
$339$	−2.00000	−0.108625
$340$	0	0
$341$	−36.0000	−1.94951
$342$	0	0
$343$	1.00000	0.0539949
$344$	0	0
$345$	14.0000	0.753735
$346$	0	0
$347$	16.0000	0.858925	0.429463	−	0.903085i	$-0.358703\pi$
$347$	16.0000	0.858925	0.429463	+	0.903085i	$0.358703\pi$
$348$	0	0
$349$	−35.0000	−1.87351	−0.936754	−	0.349990i	$-0.886185\pi$
$349$	−35.0000	−1.87351	−0.936754	+	0.349990i	$0.886185\pi$
$350$	0	0
$351$	−4.00000	−0.213504
$352$	0	0
$353$	−2.00000	−0.106449	−0.0532246	−	0.998583i	$-0.516950\pi$
$353$	−2.00000	−0.106449	−0.0532246	+	0.998583i	$0.516950\pi$
$354$	0	0
$355$	−14.0000	−0.743043
$356$	0	0
$357$	4.00000	0.211702
$358$	0	0
$359$	30.0000	1.58334	0.791670	−	0.610949i	$-0.209212\pi$
$359$	30.0000	1.58334	0.791670	+	0.610949i	$0.209212\pi$
$360$	0	0
$361$	−18.0000	−0.947368
$362$	0	0
$363$	−10.0000	−0.524864
$364$	0	0
$365$	−3.00000	−0.157027
$366$	0	0
$367$	−24.0000	−1.25279	−0.626395	−	0.779506i	$-0.715470\pi$
$367$	−24.0000	−1.25279	−0.626395	+	0.779506i	$0.715470\pi$
$368$	0	0
$369$	2.00000	0.104116
$370$	0	0
$371$	−3.00000	−0.155752
$372$	0	0
$373$	26.0000	1.34623	0.673114	−	0.739538i	$-0.264956\pi$
$373$	26.0000	1.34623	0.673114	+	0.739538i	$0.264956\pi$
$374$	0	0
$375$	−18.0000	−0.929516
$376$	0	0
$377$	−5.00000	−0.257513
$378$	0	0
$379$	28.0000	1.43826	0.719132	−	0.694874i	$-0.244540\pi$
$379$	28.0000	1.43826	0.719132	+	0.694874i	$0.244540\pi$
$380$	0	0
$381$	−16.0000	−0.819705
$382$	0	0
$383$	−24.0000	−1.22634	−0.613171	−	0.789950i	$-0.710106\pi$
$383$	−24.0000	−1.22634	−0.613171	+	0.789950i	$0.710106\pi$
$384$	0	0
$385$	4.00000	0.203859
$386$	0	0
$387$	1.00000	0.0508329
$388$	0	0
$389$	22.0000	1.11544	0.557722	−	0.830028i	$-0.311675\pi$
$389$	22.0000	1.11544	0.557722	+	0.830028i	$0.311675\pi$
$390$	0	0
$391$	−14.0000	−0.708010
$392$	0	0
$393$	24.0000	1.21064
$394$	0	0
$395$	5.00000	0.251577
$396$	0	0
$397$	25.0000	1.25471	0.627357	−	0.778732i	$-0.284137\pi$
$397$	25.0000	1.25471	0.627357	+	0.778732i	$0.284137\pi$
$398$	0	0
$399$	2.00000	0.100125
$400$	0	0
$401$	−28.0000	−1.39825	−0.699127	−	0.714998i	$-0.746428\pi$
$401$	−28.0000	−1.39825	−0.699127	+	0.714998i	$0.746428\pi$
$402$	0	0
$403$	−9.00000	−0.448322
$404$	0	0
$405$	11.0000	0.546594
$406$	0	0
$407$	−8.00000	−0.396545
$408$	0	0
$409$	−25.0000	−1.23617	−0.618085	−	0.786111i	$-0.712091\pi$
$409$	−25.0000	−1.23617	−0.618085	+	0.786111i	$0.712091\pi$
$410$	0	0
$411$	28.0000	1.38114
$412$	0	0
$413$	0	0
$414$	0	0
$415$	−5.00000	−0.245440
$416$	0	0
$417$	−32.0000	−1.56705
$418$	0	0
$419$	−16.0000	−0.781651	−0.390826	−	0.920465i	$-0.627810\pi$
$419$	−16.0000	−0.781651	−0.390826	+	0.920465i	$0.627810\pi$
$420$	0	0
$421$	−10.0000	−0.487370	−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000	−0.487370	−0.243685	+	0.969854i	$0.578356\pi$
$422$	0	0
$423$	−9.00000	−0.437595
$424$	0	0
$425$	8.00000	0.388057
$426$	0	0
$427$	−14.0000	−0.677507
$428$	0	0
$429$	−8.00000	−0.386244
$430$	0	0
$431$	−14.0000	−0.674356	−0.337178	−	0.941441i	$-0.609472\pi$
$431$	−14.0000	−0.674356	−0.337178	+	0.941441i	$0.609472\pi$
$432$	0	0
$433$	24.0000	1.15337	0.576683	−	0.816968i	$-0.304347\pi$
$433$	24.0000	1.15337	0.576683	+	0.816968i	$0.304347\pi$
$434$	0	0
$435$	10.0000	0.479463
$436$	0	0
$437$	−7.00000	−0.334855
$438$	0	0
$439$	−10.0000	−0.477274	−0.238637	−	0.971109i	$-0.576701\pi$
$439$	−10.0000	−0.477274	−0.238637	+	0.971109i	$0.576701\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	0	0
$443$	−39.0000	−1.85295	−0.926473	−	0.376361i	$-0.877175\pi$
$443$	−39.0000	−1.85295	−0.926473	+	0.376361i	$0.877175\pi$
$444$	0	0
$445$	9.00000	0.426641
$446$	0	0
$447$	24.0000	1.13516
$448$	0	0
$449$	0	0		−	1.00000i	$-0.5\pi$
$449$	0	0			1.00000i	$0.5\pi$
$450$	0	0
$451$	−8.00000	−0.376705
$452$	0	0
$453$	28.0000	1.31555
$454$	0	0
$455$	1.00000	0.0468807
$456$	0	0
$457$	−6.00000	−0.280668	−0.140334	−	0.990104i	$-0.544818\pi$
$457$	−6.00000	−0.280668	−0.140334	+	0.990104i	$0.544818\pi$
$458$	0	0
$459$	−8.00000	−0.373408
$460$	0	0
$461$	−10.0000	−0.465746	−0.232873	−	0.972507i	$-0.574813\pi$
$461$	−10.0000	−0.465746	−0.232873	+	0.972507i	$0.574813\pi$
$462$	0	0
$463$	−24.0000	−1.11537	−0.557687	−	0.830051i	$-0.688311\pi$
$463$	−24.0000	−1.11537	−0.557687	+	0.830051i	$0.688311\pi$
$464$	0	0
$465$	18.0000	0.834730
$466$	0	0
$467$	−8.00000	−0.370196	−0.185098	−	0.982720i	$-0.559260\pi$
$467$	−8.00000	−0.370196	−0.185098	+	0.982720i	$0.559260\pi$
$468$	0	0
$469$	10.0000	0.461757
$470$	0	0
$471$	20.0000	0.921551
$472$	0	0
$473$	−4.00000	−0.183920
$474$	0	0
$475$	4.00000	0.183533
$476$	0	0
$477$	−3.00000	−0.137361
$478$	0	0
$479$	−27.0000	−1.23366	−0.616831	−	0.787096i	$-0.711584\pi$
$479$	−27.0000	−1.23366	−0.616831	+	0.787096i	$0.711584\pi$
$480$	0	0
$481$	−2.00000	−0.0911922
$482$	0	0
$483$	−14.0000	−0.637022
$484$	0	0
$485$	1.00000	0.0454077
$486$	0	0
$487$	34.0000	1.54069	0.770344	−	0.637629i	$-0.220085\pi$
$487$	34.0000	1.54069	0.770344	+	0.637629i	$0.220085\pi$
$488$	0	0
$489$	−48.0000	−2.17064
$490$	0	0
$491$	−8.00000	−0.361035	−0.180517	−	0.983572i	$-0.557777\pi$
$491$	−8.00000	−0.361035	−0.180517	+	0.983572i	$0.557777\pi$
$492$	0	0
$493$	−10.0000	−0.450377
$494$	0	0
$495$	4.00000	0.179787
$496$	0	0
$497$	14.0000	0.627986
$498$	0	0
$499$	−2.00000	−0.0895323	−0.0447661	−	0.998997i	$-0.514254\pi$
$499$	−2.00000	−0.0895323	−0.0447661	+	0.998997i	$0.514254\pi$
$500$	0	0
$501$	6.00000	0.268060
$502$	0	0
$503$	34.0000	1.51599	0.757993	−	0.652263i	$-0.226180\pi$
$503$	34.0000	1.51599	0.757993	+	0.652263i	$0.226180\pi$
$504$	0	0
$505$	−12.0000	−0.533993
$506$	0	0
$507$	−2.00000	−0.0888231
$508$	0	0
$509$	−9.00000	−0.398918	−0.199459	−	0.979906i	$-0.563918\pi$
$509$	−9.00000	−0.398918	−0.199459	+	0.979906i	$0.563918\pi$
$510$	0	0
$511$	3.00000	0.132712
$512$	0	0
$513$	−4.00000	−0.176604
$514$	0	0
$515$	4.00000	0.176261
$516$	0	0
$517$	36.0000	1.58328
$518$	0	0
$519$	4.00000	0.175581
$520$	0	0
$521$	0	0		−	1.00000i	$-0.5\pi$
$521$	0	0			1.00000i	$0.5\pi$
$522$	0	0
$523$	−18.0000	−0.787085	−0.393543	−	0.919306i	$-0.628751\pi$
$523$	−18.0000	−0.787085	−0.393543	+	0.919306i	$0.628751\pi$
$524$	0	0
$525$	8.00000	0.349149
$526$	0	0
$527$	−18.0000	−0.784092
$528$	0	0
$529$	26.0000	1.13043
$530$	0	0
$531$	0	0
$532$	0	0
$533$	−2.00000	−0.0866296
$534$	0	0
$535$	12.0000	0.518805
$536$	0	0
$537$	−18.0000	−0.776757
$538$	0	0
$539$	−4.00000	−0.172292
$540$	0	0
$541$	38.0000	1.63375	0.816874	−	0.576816i	$-0.195705\pi$
$541$	38.0000	1.63375	0.816874	+	0.576816i	$0.195705\pi$
$542$	0	0
$543$	−40.0000	−1.71656
$544$	0	0
$545$	−4.00000	−0.171341
$546$	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
$549$	−14.0000	−0.597505
$550$	0	0
$551$	−5.00000	−0.213007
$552$	0	0
$553$	−5.00000	−0.212622
$554$	0	0
$555$	4.00000	0.169791
$556$	0	0
$557$	−4.00000	−0.169485	−0.0847427	−	0.996403i	$-0.527007\pi$
$557$	−4.00000	−0.169485	−0.0847427	+	0.996403i	$0.527007\pi$
$558$	0	0
$559$	−1.00000	−0.0422955
$560$	0	0
$561$	−16.0000	−0.675521
$562$	0	0
$563$	−40.0000	−1.68580	−0.842900	−	0.538071i	$-0.819153\pi$
$563$	−40.0000	−1.68580	−0.842900	+	0.538071i	$0.819153\pi$
$564$	0	0
$565$	−1.00000	−0.0420703
$566$	0	0
$567$	−11.0000	−0.461957
$568$	0	0
$569$	−37.0000	−1.55112	−0.775560	−	0.631273i	$-0.782533\pi$
$569$	−37.0000	−1.55112	−0.775560	+	0.631273i	$0.782533\pi$
$570$	0	0
$571$	−7.00000	−0.292941	−0.146470	−	0.989215i	$-0.546791\pi$
$571$	−7.00000	−0.292941	−0.146470	+	0.989215i	$0.546791\pi$
$572$	0	0
$573$	−48.0000	−2.00523
$574$	0	0
$575$	−28.0000	−1.16768
$576$	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
$579$	−4.00000	−0.166234
$580$	0	0
$581$	5.00000	0.207435
$582$	0	0
$583$	12.0000	0.496989
$584$	0	0
$585$	1.00000	0.0413449
$586$	0	0
$587$	−15.0000	−0.619116	−0.309558	−	0.950881i	$-0.600181\pi$
$587$	−15.0000	−0.619116	−0.309558	+	0.950881i	$0.600181\pi$
$588$	0	0
$589$	−9.00000	−0.370839
$590$	0	0
$591$	12.0000	0.493614
$592$	0	0
$593$	41.0000	1.68367	0.841834	−	0.539736i	$-0.181476\pi$
$593$	41.0000	1.68367	0.841834	+	0.539736i	$0.181476\pi$
$594$	0	0
$595$	2.00000	0.0819920
$596$	0	0
$597$	−28.0000	−1.14596
$598$	0	0
$599$	−21.0000	−0.858037	−0.429018	−	0.903296i	$-0.641140\pi$
$599$	−21.0000	−0.858037	−0.429018	+	0.903296i	$0.641140\pi$
$600$	0	0
$601$	2.00000	0.0815817	0.0407909	−	0.999168i	$-0.487012\pi$
$601$	2.00000	0.0815817	0.0407909	+	0.999168i	$0.487012\pi$
$602$	0	0
$603$	10.0000	0.407231
$604$	0	0
$605$	−5.00000	−0.203279
$606$	0	0
$607$	40.0000	1.62355	0.811775	−	0.583970i	$-0.198502\pi$
$607$	40.0000	1.62355	0.811775	+	0.583970i	$0.198502\pi$
$608$	0	0
$609$	−10.0000	−0.405220
$610$	0	0
$611$	9.00000	0.364101
$612$	0	0
$613$	16.0000	0.646234	0.323117	−	0.946359i	$-0.395269\pi$
$613$	16.0000	0.646234	0.323117	+	0.946359i	$0.395269\pi$
$614$	0	0
$615$	4.00000	0.161296
$616$	0	0
$617$	34.0000	1.36879	0.684394	−	0.729112i	$-0.260067\pi$
$617$	34.0000	1.36879	0.684394	+	0.729112i	$0.260067\pi$
$618$	0	0
$619$	20.0000	0.803868	0.401934	−	0.915669i	$-0.368338\pi$
$619$	20.0000	0.803868	0.401934	+	0.915669i	$0.368338\pi$
$620$	0	0
$621$	28.0000	1.12360
$622$	0	0
$623$	−9.00000	−0.360577
$624$	0	0
$625$	11.0000	0.440000
$626$	0	0
$627$	−8.00000	−0.319489
$628$	0	0
$629$	−4.00000	−0.159490
$630$	0	0
$631$	2.00000	0.0796187	0.0398094	−	0.999207i	$-0.487325\pi$
$631$	2.00000	0.0796187	0.0398094	+	0.999207i	$0.487325\pi$
$632$	0	0
$633$	46.0000	1.82834
$634$	0	0
$635$	−8.00000	−0.317470
$636$	0	0
$637$	−1.00000	−0.0396214
$638$	0	0
$639$	14.0000	0.553831
$640$	0	0
$641$	41.0000	1.61940	0.809701	−	0.586842i	$-0.199629\pi$
$641$	41.0000	1.61940	0.809701	+	0.586842i	$0.199629\pi$
$642$	0	0
$643$	−28.0000	−1.10421	−0.552106	−	0.833774i	$-0.686176\pi$
$643$	−28.0000	−1.10421	−0.552106	+	0.833774i	$0.686176\pi$
$644$	0	0
$645$	2.00000	0.0787499
$646$	0	0
$647$	−12.0000	−0.471769	−0.235884	−	0.971781i	$-0.575799\pi$
$647$	−12.0000	−0.471769	−0.235884	+	0.971781i	$0.575799\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	−18.0000	−0.705476
$652$	0	0
$653$	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
$655$	12.0000	0.468879
$656$	0	0
$657$	3.00000	0.117041
$658$	0	0
$659$	−45.0000	−1.75295	−0.876476	−	0.481446i	$-0.840112\pi$
$659$	−45.0000	−1.75295	−0.876476	+	0.481446i	$0.840112\pi$
$660$	0	0
$661$	−31.0000	−1.20576	−0.602880	−	0.797832i	$-0.705980\pi$
$661$	−31.0000	−1.20576	−0.602880	+	0.797832i	$0.705980\pi$
$662$	0	0
$663$	−4.00000	−0.155347
$664$	0	0
$665$	1.00000	0.0387783
$666$	0	0
$667$	35.0000	1.35521
$668$	0	0
$669$	42.0000	1.62381
$670$	0	0
$671$	56.0000	2.16186
$672$	0	0
$673$	21.0000	0.809491	0.404745	−	0.914429i	$-0.367360\pi$
$673$	21.0000	0.809491	0.404745	+	0.914429i	$0.367360\pi$
$674$	0	0
$675$	−16.0000	−0.615840
$676$	0	0
$677$	−16.0000	−0.614930	−0.307465	−	0.951559i	$-0.599481\pi$
$677$	−16.0000	−0.614930	−0.307465	+	0.951559i	$0.599481\pi$
$678$	0	0
$679$	−1.00000	−0.0383765
$680$	0	0
$681$	16.0000	0.613121
$682$	0	0
$683$	4.00000	0.153056	0.0765279	−	0.997067i	$-0.475617\pi$
$683$	4.00000	0.153056	0.0765279	+	0.997067i	$0.475617\pi$
$684$	0	0
$685$	14.0000	0.534913
$686$	0	0
$687$	−4.00000	−0.152610
$688$	0	0
$689$	3.00000	0.114291
$690$	0	0
$691$	−35.0000	−1.33146	−0.665731	−	0.746191i	$-0.731880\pi$
$691$	−35.0000	−1.33146	−0.665731	+	0.746191i	$0.731880\pi$
$692$	0	0
$693$	−4.00000	−0.151947
$694$	0	0
$695$	−16.0000	−0.606915
$696$	0	0
$697$	−4.00000	−0.151511
$698$	0	0
$699$	50.0000	1.89117
$700$	0	0
$701$	−45.0000	−1.69963	−0.849813	−	0.527084i	$-0.823285\pi$
$701$	−45.0000	−1.69963	−0.849813	+	0.527084i	$0.823285\pi$
$702$	0	0
$703$	−2.00000	−0.0754314
$704$	0	0
$705$	−18.0000	−0.677919
$706$	0	0
$707$	12.0000	0.451306
$708$	0	0
$709$	12.0000	0.450669	0.225335	−	0.974281i	$-0.427652\pi$
$709$	12.0000	0.450669	0.225335	+	0.974281i	$0.427652\pi$
$710$	0	0
$711$	−5.00000	−0.187515
$712$	0	0
$713$	63.0000	2.35937
$714$	0	0
$715$	−4.00000	−0.149592
$716$	0	0
$717$	24.0000	0.896296
$718$	0	0
$719$	40.0000	1.49175	0.745874	−	0.666087i	$-0.232032\pi$
$719$	40.0000	1.49175	0.745874	+	0.666087i	$0.232032\pi$
$720$	0	0
$721$	−4.00000	−0.148968
$722$	0	0
$723$	50.0000	1.85952
$724$	0	0
$725$	−20.0000	−0.742781
$726$	0	0
$727$	42.0000	1.55769	0.778847	−	0.627214i	$-0.215805\pi$
$727$	42.0000	1.55769	0.778847	+	0.627214i	$0.215805\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	0	0
$731$	−2.00000	−0.0739727
$732$	0	0
$733$	21.0000	0.775653	0.387826	−	0.921732i	$-0.373226\pi$
$733$	21.0000	0.775653	0.387826	+	0.921732i	$0.373226\pi$
$734$	0	0
$735$	2.00000	0.0737711
$736$	0	0
$737$	−40.0000	−1.47342
$738$	0	0
$739$	−8.00000	−0.294285	−0.147142	−	0.989115i	$-0.547008\pi$
$739$	−8.00000	−0.294285	−0.147142	+	0.989115i	$0.547008\pi$
$740$	0	0
$741$	−2.00000	−0.0734718
$742$	0	0
$743$	8.00000	0.293492	0.146746	−	0.989174i	$-0.453120\pi$
$743$	8.00000	0.293492	0.146746	+	0.989174i	$0.453120\pi$
$744$	0	0
$745$	12.0000	0.439646
$746$	0	0
$747$	5.00000	0.182940
$748$	0	0
$749$	−12.0000	−0.438470
$750$	0	0
$751$	−25.0000	−0.912263	−0.456131	−	0.889912i	$-0.650765\pi$
$751$	−25.0000	−0.912263	−0.456131	+	0.889912i	$0.650765\pi$
$752$	0	0
$753$	32.0000	1.16614
$754$	0	0
$755$	14.0000	0.509512
$756$	0	0
$757$	47.0000	1.70824	0.854122	−	0.520073i	$-0.174095\pi$
$757$	47.0000	1.70824	0.854122	+	0.520073i	$0.174095\pi$
$758$	0	0
$759$	56.0000	2.03267
$760$	0	0
$761$	−35.0000	−1.26875	−0.634375	−	0.773026i	$-0.718742\pi$
$761$	−35.0000	−1.26875	−0.634375	+	0.773026i	$0.718742\pi$
$762$	0	0
$763$	4.00000	0.144810
$764$	0	0
$765$	2.00000	0.0723102
$766$	0	0
$767$	0	0
$768$	0	0
$769$	37.0000	1.33425	0.667127	−	0.744944i	$-0.267524\pi$
$769$	37.0000	1.33425	0.667127	+	0.744944i	$0.267524\pi$
$770$	0	0
$771$	24.0000	0.864339
$772$	0	0
$773$	−38.0000	−1.36677	−0.683383	−	0.730061i	$-0.739492\pi$
$773$	−38.0000	−1.36677	−0.683383	+	0.730061i	$0.739492\pi$
$774$	0	0
$775$	−36.0000	−1.29316
$776$	0	0
$777$	−4.00000	−0.143499
$778$	0	0
$779$	−2.00000	−0.0716574
$780$	0	0
$781$	−56.0000	−2.00384
$782$	0	0
$783$	20.0000	0.714742
$784$	0	0
$785$	10.0000	0.356915
$786$	0	0
$787$	−37.0000	−1.31891	−0.659454	−	0.751745i	$-0.729212\pi$
$787$	−37.0000	−1.31891	−0.659454	+	0.751745i	$0.729212\pi$
$788$	0	0
$789$	38.0000	1.35284
$790$	0	0
$791$	1.00000	0.0355559
$792$	0	0
$793$	14.0000	0.497155
$794$	0	0
$795$	−6.00000	−0.212798
$796$	0	0
$797$	−6.00000	−0.212531	−0.106265	−	0.994338i	$-0.533889\pi$
$797$	−6.00000	−0.212531	−0.106265	+	0.994338i	$0.533889\pi$
$798$	0	0
$799$	18.0000	0.636794
$800$	0	0
$801$	−9.00000	−0.317999
$802$	0	0
$803$	−12.0000	−0.423471
$804$	0	0
$805$	−7.00000	−0.246718
$806$	0	0
$807$	48.0000	1.68968
$808$	0	0
$809$	45.0000	1.58212	0.791058	−	0.611741i	$-0.209531\pi$
$809$	45.0000	1.58212	0.791058	+	0.611741i	$0.209531\pi$
$810$	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
$813$	0	0
$814$	0	0
$815$	−24.0000	−0.840683
$816$	0	0
$817$	−1.00000	−0.0349856
$818$	0	0
$819$	−1.00000	−0.0349428
$820$	0	0
$821$	−34.0000	−1.18661	−0.593304	−	0.804978i	$-0.702177\pi$
$821$	−34.0000	−1.18661	−0.593304	+	0.804978i	$0.702177\pi$
$822$	0	0
$823$	−16.0000	−0.557725	−0.278862	−	0.960331i	$-0.589957\pi$
$823$	−16.0000	−0.557725	−0.278862	+	0.960331i	$0.589957\pi$
$824$	0	0
$825$	−32.0000	−1.11410
$826$	0	0
$827$	40.0000	1.39094	0.695468	−	0.718557i	$-0.255197\pi$
$827$	40.0000	1.39094	0.695468	+	0.718557i	$0.255197\pi$
$828$	0	0
$829$	−24.0000	−0.833554	−0.416777	−	0.909009i	$-0.636840\pi$
$829$	−24.0000	−0.833554	−0.416777	+	0.909009i	$0.636840\pi$
$830$	0	0
$831$	−46.0000	−1.59572
$832$	0	0
$833$	−2.00000	−0.0692959
$834$	0	0
$835$	3.00000	0.103819
$836$	0	0
$837$	36.0000	1.24434
$838$	0	0
$839$	12.0000	0.414286	0.207143	−	0.978311i	$-0.433583\pi$
$839$	12.0000	0.414286	0.207143	+	0.978311i	$0.433583\pi$
$840$	0	0
$841$	−4.00000	−0.137931
$842$	0	0
$843$	16.0000	0.551069
$844$	0	0
$845$	−1.00000	−0.0344010
$846$	0	0
$847$	5.00000	0.171802
$848$	0	0
$849$	8.00000	0.274559
$850$	0	0
$851$	14.0000	0.479914
$852$	0	0
$853$	−37.0000	−1.26686	−0.633428	−	0.773802i	$-0.718353\pi$
$853$	−37.0000	−1.26686	−0.633428	+	0.773802i	$0.718353\pi$
$854$	0	0
$855$	1.00000	0.0341993
$856$	0	0
$857$	30.0000	1.02478	0.512390	−	0.858753i	$-0.328760\pi$
$857$	30.0000	1.02478	0.512390	+	0.858753i	$0.328760\pi$
$858$	0	0
$859$	22.0000	0.750630	0.375315	−	0.926897i	$-0.377534\pi$
$859$	22.0000	0.750630	0.375315	+	0.926897i	$0.377534\pi$
$860$	0	0
$861$	−4.00000	−0.136320
$862$	0	0
$863$	48.0000	1.63394	0.816970	−	0.576681i	$-0.195652\pi$
$863$	48.0000	1.63394	0.816970	+	0.576681i	$0.195652\pi$
$864$	0	0
$865$	2.00000	0.0680020
$866$	0	0
$867$	26.0000	0.883006
$868$	0	0
$869$	20.0000	0.678454
$870$	0	0
$871$	−10.0000	−0.338837
$872$	0	0
$873$	−1.00000	−0.0338449
$874$	0	0
$875$	9.00000	0.304256
$876$	0	0
$877$	−14.0000	−0.472746	−0.236373	−	0.971662i	$-0.575959\pi$
$877$	−14.0000	−0.472746	−0.236373	+	0.971662i	$0.575959\pi$
$878$	0	0
$879$	10.0000	0.337292
$880$	0	0
$881$	−2.00000	−0.0673817	−0.0336909	−	0.999432i	$-0.510726\pi$
$881$	−2.00000	−0.0673817	−0.0336909	+	0.999432i	$0.510726\pi$
$882$	0	0
$883$	−16.0000	−0.538443	−0.269221	−	0.963078i	$-0.586766\pi$
$883$	−16.0000	−0.538443	−0.269221	+	0.963078i	$0.586766\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	−32.0000	−1.07445	−0.537227	−	0.843437i	$-0.680528\pi$
$887$	−32.0000	−1.07445	−0.537227	+	0.843437i	$0.680528\pi$
$888$	0	0
$889$	8.00000	0.268311
$890$	0	0
$891$	44.0000	1.47406
$892$	0	0
$893$	9.00000	0.301174
$894$	0	0
$895$	−9.00000	−0.300837
$896$	0	0
$897$	14.0000	0.467446
$898$	0	0
$899$	45.0000	1.50083
$900$	0	0
$901$	6.00000	0.199889
$902$	0	0
$903$	−2.00000	−0.0665558
$904$	0	0
$905$	−20.0000	−0.664822
$906$	0	0
$907$	−3.00000	−0.0996134	−0.0498067	−	0.998759i	$-0.515861\pi$
$907$	−3.00000	−0.0996134	−0.0498067	+	0.998759i	$0.515861\pi$
$908$	0	0
$909$	12.0000	0.398015
$910$	0	0
$911$	21.0000	0.695761	0.347881	−	0.937539i	$-0.386901\pi$
$911$	21.0000	0.695761	0.347881	+	0.937539i	$0.386901\pi$
$912$	0	0
$913$	−20.0000	−0.661903
$914$	0	0
$915$	−28.0000	−0.925651
$916$	0	0
$917$	−12.0000	−0.396275
$918$	0	0
$919$	40.0000	1.31948	0.659739	−	0.751495i	$-0.270667\pi$
$919$	40.0000	1.31948	0.659739	+	0.751495i	$0.270667\pi$
$920$	0	0
$921$	54.0000	1.77936
$922$	0	0
$923$	−14.0000	−0.460816
$924$	0	0
$925$	−8.00000	−0.263038
$926$	0	0
$927$	−4.00000	−0.131377
$928$	0	0
$929$	−3.00000	−0.0984268	−0.0492134	−	0.998788i	$-0.515671\pi$
$929$	−3.00000	−0.0984268	−0.0492134	+	0.998788i	$0.515671\pi$
$930$	0	0
$931$	−1.00000	−0.0327737
$932$	0	0
$933$	0	0
$934$	0	0
$935$	−8.00000	−0.261628
$936$	0	0
$937$	30.0000	0.980057	0.490029	−	0.871706i	$-0.336986\pi$
$937$	30.0000	0.980057	0.490029	+	0.871706i	$0.336986\pi$
$938$	0	0
$939$	24.0000	0.783210
$940$	0	0
$941$	−35.0000	−1.14097	−0.570484	−	0.821309i	$-0.693244\pi$
$941$	−35.0000	−1.14097	−0.570484	+	0.821309i	$0.693244\pi$
$942$	0	0
$943$	14.0000	0.455903
$944$	0	0
$945$	−4.00000	−0.130120
$946$	0	0
$947$	10.0000	0.324956	0.162478	−	0.986712i	$-0.448051\pi$
$947$	10.0000	0.324956	0.162478	+	0.986712i	$0.448051\pi$
$948$	0	0
$949$	−3.00000	−0.0973841
$950$	0	0
$951$	40.0000	1.29709
$952$	0	0
$953$	−19.0000	−0.615470	−0.307735	−	0.951472i	$-0.599571\pi$
$953$	−19.0000	−0.615470	−0.307735	+	0.951472i	$0.599571\pi$
$954$	0	0
$955$	−24.0000	−0.776622
$956$	0	0
$957$	40.0000	1.29302
$958$	0	0
$959$	−14.0000	−0.452084
$960$	0	0
$961$	50.0000	1.61290
$962$	0	0
$963$	−12.0000	−0.386695
$964$	0	0
$965$	−2.00000	−0.0643823
$966$	0	0
$967$	12.0000	0.385894	0.192947	−	0.981209i	$-0.438195\pi$
$967$	12.0000	0.385894	0.192947	+	0.981209i	$0.438195\pi$
$968$	0	0
$969$	−4.00000	−0.128499
$970$	0	0
$971$	30.0000	0.962746	0.481373	−	0.876516i	$-0.340138\pi$
$971$	30.0000	0.962746	0.481373	+	0.876516i	$0.340138\pi$
$972$	0	0
$973$	16.0000	0.512936
$974$	0	0
$975$	−8.00000	−0.256205
$976$	0	0
$977$	−60.0000	−1.91957	−0.959785	−	0.280736i	$-0.909421\pi$
$977$	−60.0000	−1.91957	−0.959785	+	0.280736i	$0.909421\pi$
$978$	0	0
$979$	36.0000	1.15056
$980$	0	0
$981$	4.00000	0.127710
$982$	0	0
$983$	−11.0000	−0.350846	−0.175423	−	0.984493i	$-0.556129\pi$
$983$	−11.0000	−0.350846	−0.175423	+	0.984493i	$0.556129\pi$
$984$	0	0
$985$	6.00000	0.191176
$986$	0	0
$987$	18.0000	0.572946
$988$	0	0
$989$	7.00000	0.222587
$990$	0	0
$991$	−24.0000	−0.762385	−0.381193	−	0.924496i	$-0.624487\pi$
$991$	−24.0000	−0.762385	−0.381193	+	0.924496i	$0.624487\pi$
$992$	0	0
$993$	−60.0000	−1.90404
$994$	0	0
$995$	−14.0000	−0.443830
$996$	0	0
$997$	32.0000	1.01345	0.506725	−	0.862108i	$-0.330856\pi$
$997$	32.0000	1.01345	0.506725	+	0.862108i	$0.330856\pi$
$998$	0	0
$999$	8.00000	0.253109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5824.2.a.d.1.1		1
4.3	odd	2		5824.2.a.bb.1.1		1
8.3	odd	2		364.2.a.a.1.1	✓	1
8.5	even	2		1456.2.a.m.1.1		1
24.11	even	2		3276.2.a.b.1.1		1
40.19	odd	2		9100.2.a.l.1.1		1
56.3	even	6		2548.2.j.c.1353.1		2
56.11	odd	6		2548.2.j.j.1353.1		2
56.19	even	6		2548.2.j.c.1145.1		2
56.27	even	2		2548.2.a.i.1.1		1
56.51	odd	6		2548.2.j.j.1145.1		2
104.51	odd	2		4732.2.a.a.1.1		1
104.83	even	4		4732.2.g.a.337.1		2
104.99	even	4		4732.2.g.a.337.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
364.2.a.a.1.1	✓	1	8.3	odd	2
1456.2.a.m.1.1		1	8.5	even	2
2548.2.a.i.1.1		1	56.27	even	2
2548.2.j.c.1145.1		2	56.19	even	6
2548.2.j.c.1353.1		2	56.3	even	6
2548.2.j.j.1145.1		2	56.51	odd	6
2548.2.j.j.1353.1		2	56.11	odd	6
3276.2.a.b.1.1		1	24.11	even	2
4732.2.a.a.1.1		1	104.51	odd	2
4732.2.g.a.337.1		2	104.83	even	4
4732.2.g.a.337.2		2	104.99	even	4
5824.2.a.d.1.1		1	1.1	even	1	trivial
5824.2.a.bb.1.1		1	4.3	odd	2
9100.2.a.l.1.1		1	40.19	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:	\( N \)	\(=\)	\( 5824 = 2^{6} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5824.a (trivial)

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