LMFDB - Embedded newform 935.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [935,2,Mod(1,935)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(935, 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("935.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 935 = 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	935.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:	$7.46601258899$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	935.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{3} -2.00000 q^{4} -1.00000 q^{5} +3.00000 q^{7} +1.00000 q^{9} +O(q^{10})$

$q-2.00000 q^{3} -2.00000 q^{4} -1.00000 q^{5} +3.00000 q^{7} +1.00000 q^{9} +1.00000 q^{11} +4.00000 q^{12} +2.00000 q^{15} +4.00000 q^{16} +1.00000 q^{17} +2.00000 q^{20} -6.00000 q^{21} -2.00000 q^{23} +1.00000 q^{25} +4.00000 q^{27} -6.00000 q^{28} +3.00000 q^{29} -10.0000 q^{31} -2.00000 q^{33} -3.00000 q^{35} -2.00000 q^{36} -4.00000 q^{37} -1.00000 q^{41} -8.00000 q^{43} -2.00000 q^{44} -1.00000 q^{45} -3.00000 q^{47} -8.00000 q^{48} +2.00000 q^{49} -2.00000 q^{51} -9.00000 q^{53} -1.00000 q^{55} +1.00000 q^{59} -4.00000 q^{60} +2.00000 q^{61} +3.00000 q^{63} -8.00000 q^{64} -3.00000 q^{67} -2.00000 q^{68} +4.00000 q^{69} +2.00000 q^{71} -11.0000 q^{73} -2.00000 q^{75} +3.00000 q^{77} -4.00000 q^{80} -11.0000 q^{81} +6.00000 q^{83} +12.0000 q^{84} -1.00000 q^{85} -6.00000 q^{87} -7.00000 q^{89} +4.00000 q^{92} +20.0000 q^{93} -12.0000 q^{97} +1.00000 q^{99} +O(q^{100})$

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		−	1.00000i	$-0.5\pi$
$2$	0	0			1.00000i	$0.5\pi$
$3$	−2.00000	−1.15470	−0.577350	−	0.816497i	$-0.695913\pi$
$3$	−2.00000	−1.15470	−0.577350	+	0.816497i	$0.695913\pi$
$4$	−2.00000	−1.00000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	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
$9$	1.00000	0.333333
$10$	0	0
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	4.00000	1.15470
$13$	0	0		−	1.00000i	$-0.5\pi$
$13$	0	0			1.00000i	$0.5\pi$
$14$	0	0
$15$	2.00000	0.516398
$16$	4.00000	1.00000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	0	0
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	2.00000	0.447214
$21$	−6.00000	−1.30931
$22$	0	0
$23$	−2.00000	−0.417029	−0.208514	−	0.978019i	$-0.566863\pi$
$23$	−2.00000	−0.417029	−0.208514	+	0.978019i	$0.566863\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	4.00000	0.769800
$28$	−6.00000	−1.13389
$29$	3.00000	0.557086	0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000	0.557086	0.278543	+	0.960424i	$0.410149\pi$
$30$	0	0
$31$	−10.0000	−1.79605	−0.898027	−	0.439941i	$-0.854999\pi$
$31$	−10.0000	−1.79605	−0.898027	+	0.439941i	$0.854999\pi$
$32$	0	0
$33$	−2.00000	−0.348155
$34$	0	0
$35$	−3.00000	−0.507093
$36$	−2.00000	−0.333333
$37$	−4.00000	−0.657596	−0.328798	−	0.944400i	$-0.606644\pi$
$37$	−4.00000	−0.657596	−0.328798	+	0.944400i	$0.606644\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	−1.00000	−0.156174	−0.0780869	−	0.996947i	$-0.524881\pi$
$41$	−1.00000	−0.156174	−0.0780869	+	0.996947i	$0.524881\pi$
$42$	0	0
$43$	−8.00000	−1.21999	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	−2.00000	−0.301511
$45$	−1.00000	−0.149071
$46$	0	0
$47$	−3.00000	−0.437595	−0.218797	−	0.975770i	$-0.570213\pi$
$47$	−3.00000	−0.437595	−0.218797	+	0.975770i	$0.570213\pi$
$48$	−8.00000	−1.15470
$49$	2.00000	0.285714
$50$	0	0
$51$	−2.00000	−0.280056
$52$	0	0
$53$	−9.00000	−1.23625	−0.618123	−	0.786082i	$-0.712106\pi$
$53$	−9.00000	−1.23625	−0.618123	+	0.786082i	$0.712106\pi$
$54$	0	0
$55$	−1.00000	−0.134840
$56$	0	0
$57$	0	0
$58$	0	0
$59$	1.00000	0.130189	0.0650945	−	0.997879i	$-0.479265\pi$
$59$	1.00000	0.130189	0.0650945	+	0.997879i	$0.479265\pi$
$60$	−4.00000	−0.516398
$61$	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
$63$	3.00000	0.377964
$64$	−8.00000	−1.00000
$65$	0	0
$66$	0	0
$67$	−3.00000	−0.366508	−0.183254	−	0.983066i	$-0.558663\pi$
$67$	−3.00000	−0.366508	−0.183254	+	0.983066i	$0.558663\pi$
$68$	−2.00000	−0.242536
$69$	4.00000	0.481543
$70$	0	0
$71$	2.00000	0.237356	0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000	0.237356	0.118678	+	0.992933i	$0.462134\pi$
$72$	0	0
$73$	−11.0000	−1.28745	−0.643726	−	0.765256i	$-0.722612\pi$
$73$	−11.0000	−1.28745	−0.643726	+	0.765256i	$0.722612\pi$
$74$	0	0
$75$	−2.00000	−0.230940
$76$	0	0
$77$	3.00000	0.341882
$78$	0	0
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	−4.00000	−0.447214
$81$	−11.0000	−1.22222
$82$	0	0
$83$	6.00000	0.658586	0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000	0.658586	0.329293	+	0.944228i	$0.393190\pi$
$84$	12.0000	1.30931
$85$	−1.00000	−0.108465
$86$	0	0
$87$	−6.00000	−0.643268
$88$	0	0
$89$	−7.00000	−0.741999	−0.370999	−	0.928633i	$-0.620985\pi$
$89$	−7.00000	−0.741999	−0.370999	+	0.928633i	$0.620985\pi$
$90$	0	0
$91$	0	0
$92$	4.00000	0.417029
$93$	20.0000	2.07390
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−12.0000	−1.21842	−0.609208	−	0.793011i	$-0.708512\pi$
$97$	−12.0000	−1.21842	−0.609208	+	0.793011i	$0.708512\pi$
$98$	0	0
$99$	1.00000	0.100504
$100$	−2.00000	−0.200000
$101$	16.0000	1.59206	0.796030	−	0.605257i	$-0.206930\pi$
$101$	16.0000	1.59206	0.796030	+	0.605257i	$0.206930\pi$
$102$	0	0
$103$	−17.0000	−1.67506	−0.837530	−	0.546392i	$-0.816001\pi$
$103$	−17.0000	−1.67506	−0.837530	+	0.546392i	$0.816001\pi$
$104$	0	0
$105$	6.00000	0.585540
$106$	0	0
$107$	3.00000	0.290021	0.145010	−	0.989430i	$-0.453678\pi$
$107$	3.00000	0.290021	0.145010	+	0.989430i	$0.453678\pi$
$108$	−8.00000	−0.769800
$109$	5.00000	0.478913	0.239457	−	0.970907i	$-0.423031\pi$
$109$	5.00000	0.478913	0.239457	+	0.970907i	$0.423031\pi$
$110$	0	0
$111$	8.00000	0.759326
$112$	12.0000	1.13389
$113$	−4.00000	−0.376288	−0.188144	−	0.982141i	$-0.560247\pi$
$113$	−4.00000	−0.376288	−0.188144	+	0.982141i	$0.560247\pi$
$114$	0	0
$115$	2.00000	0.186501
$116$	−6.00000	−0.557086
$117$	0	0
$118$	0	0
$119$	3.00000	0.275010
$120$	0	0
$121$	1.00000	0.0909091
$122$	0	0
$123$	2.00000	0.180334
$124$	20.0000	1.79605
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	20.0000	1.77471	0.887357	−	0.461084i	$-0.152539\pi$
$127$	20.0000	1.77471	0.887357	+	0.461084i	$0.152539\pi$
$128$	0	0
$129$	16.0000	1.40872
$130$	0	0
$131$	−5.00000	−0.436852	−0.218426	−	0.975854i	$-0.570092\pi$
$131$	−5.00000	−0.436852	−0.218426	+	0.975854i	$0.570092\pi$
$132$	4.00000	0.348155
$133$	0	0
$134$	0	0
$135$	−4.00000	−0.344265
$136$	0	0
$137$	−7.00000	−0.598050	−0.299025	−	0.954245i	$-0.596661\pi$
$137$	−7.00000	−0.598050	−0.299025	+	0.954245i	$0.596661\pi$
$138$	0	0
$139$	19.0000	1.61156	0.805779	−	0.592216i	$-0.201747\pi$
$139$	19.0000	1.61156	0.805779	+	0.592216i	$0.201747\pi$
$140$	6.00000	0.507093
$141$	6.00000	0.505291
$142$	0	0
$143$	0	0
$144$	4.00000	0.333333
$145$	−3.00000	−0.249136
$146$	0	0
$147$	−4.00000	−0.329914
$148$	8.00000	0.657596
$149$	10.0000	0.819232	0.409616	−	0.912258i	$-0.365663\pi$
$149$	10.0000	0.819232	0.409616	+	0.912258i	$0.365663\pi$
$150$	0	0
$151$	10.0000	0.813788	0.406894	−	0.913475i	$-0.366612\pi$
$151$	10.0000	0.813788	0.406894	+	0.913475i	$0.366612\pi$
$152$	0	0
$153$	1.00000	0.0808452
$154$	0	0
$155$	10.0000	0.803219
$156$	0	0
$157$	−17.0000	−1.35675	−0.678374	−	0.734717i	$-0.737315\pi$
$157$	−17.0000	−1.35675	−0.678374	+	0.734717i	$0.737315\pi$
$158$	0	0
$159$	18.0000	1.42749
$160$	0	0
$161$	−6.00000	−0.472866
$162$	0	0
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	2.00000	0.156174
$165$	2.00000	0.155700
$166$	0	0
$167$	−20.0000	−1.54765	−0.773823	−	0.633402i	$-0.781658\pi$
$167$	−20.0000	−1.54765	−0.773823	+	0.633402i	$0.781658\pi$
$168$	0	0
$169$	−13.0000	−1.00000
$170$	0	0
$171$	0	0
$172$	16.0000	1.21999
$173$	−1.00000	−0.0760286	−0.0380143	−	0.999277i	$-0.512103\pi$
$173$	−1.00000	−0.0760286	−0.0380143	+	0.999277i	$0.512103\pi$
$174$	0	0
$175$	3.00000	0.226779
$176$	4.00000	0.301511
$177$	−2.00000	−0.150329
$178$	0	0
$179$	−9.00000	−0.672692	−0.336346	−	0.941739i	$-0.609191\pi$
$179$	−9.00000	−0.672692	−0.336346	+	0.941739i	$0.609191\pi$
$180$	2.00000	0.149071
$181$	−12.0000	−0.891953	−0.445976	−	0.895045i	$-0.647144\pi$
$181$	−12.0000	−0.891953	−0.445976	+	0.895045i	$0.647144\pi$
$182$	0	0
$183$	−4.00000	−0.295689
$184$	0	0
$185$	4.00000	0.294086
$186$	0	0
$187$	1.00000	0.0731272
$188$	6.00000	0.437595
$189$	12.0000	0.872872
$190$	0	0
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	16.0000	1.15470
$193$	−18.0000	−1.29567	−0.647834	−	0.761781i	$-0.724325\pi$
$193$	−18.0000	−1.29567	−0.647834	+	0.761781i	$0.724325\pi$
$194$	0	0
$195$	0	0
$196$	−4.00000	−0.285714
$197$	−10.0000	−0.712470	−0.356235	−	0.934396i	$-0.615940\pi$
$197$	−10.0000	−0.712470	−0.356235	+	0.934396i	$0.615940\pi$
$198$	0	0
$199$	−12.0000	−0.850657	−0.425329	−	0.905039i	$-0.639842\pi$
$199$	−12.0000	−0.850657	−0.425329	+	0.905039i	$0.639842\pi$
$200$	0	0
$201$	6.00000	0.423207
$202$	0	0
$203$	9.00000	0.631676
$204$	4.00000	0.280056
$205$	1.00000	0.0698430
$206$	0	0
$207$	−2.00000	−0.139010
$208$	0	0
$209$	0	0
$210$	0	0
$211$	13.0000	0.894957	0.447478	−	0.894295i	$-0.352322\pi$
$211$	13.0000	0.894957	0.447478	+	0.894295i	$0.352322\pi$
$212$	18.0000	1.23625
$213$	−4.00000	−0.274075
$214$	0	0
$215$	8.00000	0.545595
$216$	0	0
$217$	−30.0000	−2.03653
$218$	0	0
$219$	22.0000	1.48662
$220$	2.00000	0.134840
$221$	0	0
$222$	0	0
$223$	0	0		−	1.00000i	$-0.5\pi$
$223$	0	0			1.00000i	$0.5\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	0	0
$227$	3.00000	0.199117	0.0995585	−	0.995032i	$-0.468257\pi$
$227$	3.00000	0.199117	0.0995585	+	0.995032i	$0.468257\pi$
$228$	0	0
$229$	7.00000	0.462573	0.231287	−	0.972886i	$-0.425707\pi$
$229$	7.00000	0.462573	0.231287	+	0.972886i	$0.425707\pi$
$230$	0	0
$231$	−6.00000	−0.394771
$232$	0	0
$233$	−15.0000	−0.982683	−0.491341	−	0.870967i	$-0.663493\pi$
$233$	−15.0000	−0.982683	−0.491341	+	0.870967i	$0.663493\pi$
$234$	0	0
$235$	3.00000	0.195698
$236$	−2.00000	−0.130189
$237$	0	0
$238$	0	0
$239$	6.00000	0.388108	0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000	0.388108	0.194054	+	0.980991i	$0.437836\pi$
$240$	8.00000	0.516398
$241$	−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
$244$	−4.00000	−0.256074
$245$	−2.00000	−0.127775
$246$	0	0
$247$	0	0
$248$	0	0
$249$	−12.0000	−0.760469
$250$	0	0
$251$	4.00000	0.252478	0.126239	−	0.992000i	$-0.459709\pi$
$251$	4.00000	0.252478	0.126239	+	0.992000i	$0.459709\pi$
$252$	−6.00000	−0.377964
$253$	−2.00000	−0.125739
$254$	0	0
$255$	2.00000	0.125245
$256$	16.0000	1.00000
$257$	−15.0000	−0.935674	−0.467837	−	0.883815i	$-0.654967\pi$
$257$	−15.0000	−0.935674	−0.467837	+	0.883815i	$0.654967\pi$
$258$	0	0
$259$	−12.0000	−0.745644
$260$	0	0
$261$	3.00000	0.185695
$262$	0	0
$263$	16.0000	0.986602	0.493301	−	0.869859i	$-0.335790\pi$
$263$	16.0000	0.986602	0.493301	+	0.869859i	$0.335790\pi$
$264$	0	0
$265$	9.00000	0.552866
$266$	0	0
$267$	14.0000	0.856786
$268$	6.00000	0.366508
$269$	−30.0000	−1.82913	−0.914566	−	0.404436i	$-0.867468\pi$
$269$	−30.0000	−1.82913	−0.914566	+	0.404436i	$0.867468\pi$
$270$	0	0
$271$	−10.0000	−0.607457	−0.303728	−	0.952759i	$-0.598232\pi$
$271$	−10.0000	−0.607457	−0.303728	+	0.952759i	$0.598232\pi$
$272$	4.00000	0.242536
$273$	0	0
$274$	0	0
$275$	1.00000	0.0603023
$276$	−8.00000	−0.481543
$277$	−19.0000	−1.14160	−0.570800	−	0.821089i	$-0.693367\pi$
$277$	−19.0000	−1.14160	−0.570800	+	0.821089i	$0.693367\pi$
$278$	0	0
$279$	−10.0000	−0.598684
$280$	0	0
$281$	32.0000	1.90896	0.954480	−	0.298275i	$-0.0964112\pi$
$281$	32.0000	1.90896	0.954480	+	0.298275i	$0.0964112\pi$
$282$	0	0
$283$	−28.0000	−1.66443	−0.832214	−	0.554455i	$-0.812927\pi$
$283$	−28.0000	−1.66443	−0.832214	+	0.554455i	$0.812927\pi$
$284$	−4.00000	−0.237356
$285$	0	0
$286$	0	0
$287$	−3.00000	−0.177084
$288$	0	0
$289$	1.00000	0.0588235
$290$	0	0
$291$	24.0000	1.40690
$292$	22.0000	1.28745
$293$	22.0000	1.28525	0.642627	−	0.766179i	$-0.277845\pi$
$293$	22.0000	1.28525	0.642627	+	0.766179i	$0.277845\pi$
$294$	0	0
$295$	−1.00000	−0.0582223
$296$	0	0
$297$	4.00000	0.232104
$298$	0	0
$299$	0	0
$300$	4.00000	0.230940
$301$	−24.0000	−1.38334
$302$	0	0
$303$	−32.0000	−1.83835
$304$	0	0
$305$	−2.00000	−0.114520
$306$	0	0
$307$	6.00000	0.342438	0.171219	−	0.985233i	$-0.445229\pi$
$307$	6.00000	0.342438	0.171219	+	0.985233i	$0.445229\pi$
$308$	−6.00000	−0.341882
$309$	34.0000	1.93419
$310$	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
$313$	28.0000	1.58265	0.791327	−	0.611393i	$-0.209391\pi$
$313$	28.0000	1.58265	0.791327	+	0.611393i	$0.209391\pi$
$314$	0	0
$315$	−3.00000	−0.169031
$316$	0	0
$317$	−6.00000	−0.336994	−0.168497	−	0.985702i	$-0.553891\pi$
$317$	−6.00000	−0.336994	−0.168497	+	0.985702i	$0.553891\pi$
$318$	0	0
$319$	3.00000	0.167968
$320$	8.00000	0.447214
$321$	−6.00000	−0.334887
$322$	0	0
$323$	0	0
$324$	22.0000	1.22222
$325$	0	0
$326$	0	0
$327$	−10.0000	−0.553001
$328$	0	0
$329$	−9.00000	−0.496186
$330$	0	0
$331$	4.00000	0.219860	0.109930	−	0.993939i	$-0.464937\pi$
$331$	4.00000	0.219860	0.109930	+	0.993939i	$0.464937\pi$
$332$	−12.0000	−0.658586
$333$	−4.00000	−0.219199
$334$	0	0
$335$	3.00000	0.163908
$336$	−24.0000	−1.30931
$337$	−3.00000	−0.163420	−0.0817102	−	0.996656i	$-0.526038\pi$
$337$	−3.00000	−0.163420	−0.0817102	+	0.996656i	$0.526038\pi$
$338$	0	0
$339$	8.00000	0.434500
$340$	2.00000	0.108465
$341$	−10.0000	−0.541530
$342$	0	0
$343$	−15.0000	−0.809924
$344$	0	0
$345$	−4.00000	−0.215353
$346$	0	0
$347$	23.0000	1.23470	0.617352	−	0.786687i	$-0.288205\pi$
$347$	23.0000	1.23470	0.617352	+	0.786687i	$0.288205\pi$
$348$	12.0000	0.643268
$349$	−10.0000	−0.535288	−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000	−0.535288	−0.267644	+	0.963518i	$0.586245\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	25.0000	1.33062	0.665308	−	0.746569i	$-0.268300\pi$
$353$	25.0000	1.33062	0.665308	+	0.746569i	$0.268300\pi$
$354$	0	0
$355$	−2.00000	−0.106149
$356$	14.0000	0.741999
$357$	−6.00000	−0.317554
$358$	0	0
$359$	0	0		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	0	0
$361$	−19.0000	−1.00000
$362$	0	0
$363$	−2.00000	−0.104973
$364$	0	0
$365$	11.0000	0.575766
$366$	0	0
$367$	2.00000	0.104399	0.0521996	−	0.998637i	$-0.483377\pi$
$367$	2.00000	0.104399	0.0521996	+	0.998637i	$0.483377\pi$
$368$	−8.00000	−0.417029
$369$	−1.00000	−0.0520579
$370$	0	0
$371$	−27.0000	−1.40177
$372$	−40.0000	−2.07390
$373$	−8.00000	−0.414224	−0.207112	−	0.978317i	$-0.566407\pi$
$373$	−8.00000	−0.414224	−0.207112	+	0.978317i	$0.566407\pi$
$374$	0	0
$375$	2.00000	0.103280
$376$	0	0
$377$	0	0
$378$	0	0
$379$	20.0000	1.02733	0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000	1.02733	0.513665	+	0.857991i	$0.328287\pi$
$380$	0	0
$381$	−40.0000	−2.04926
$382$	0	0
$383$	32.0000	1.63512	0.817562	−	0.575841i	$-0.195325\pi$
$383$	32.0000	1.63512	0.817562	+	0.575841i	$0.195325\pi$
$384$	0	0
$385$	−3.00000	−0.152894
$386$	0	0
$387$	−8.00000	−0.406663
$388$	24.0000	1.21842
$389$	−31.0000	−1.57176	−0.785881	−	0.618378i	$-0.787790\pi$
$389$	−31.0000	−1.57176	−0.785881	+	0.618378i	$0.787790\pi$
$390$	0	0
$391$	−2.00000	−0.101144
$392$	0	0
$393$	10.0000	0.504433
$394$	0	0
$395$	0	0
$396$	−2.00000	−0.100504
$397$	−20.0000	−1.00377	−0.501886	−	0.864934i	$-0.667360\pi$
$397$	−20.0000	−1.00377	−0.501886	+	0.864934i	$0.667360\pi$
$398$	0	0
$399$	0	0
$400$	4.00000	0.200000
$401$	−26.0000	−1.29838	−0.649189	−	0.760627i	$-0.724892\pi$
$401$	−26.0000	−1.29838	−0.649189	+	0.760627i	$0.724892\pi$
$402$	0	0
$403$	0	0
$404$	−32.0000	−1.59206
$405$	11.0000	0.546594
$406$	0	0
$407$	−4.00000	−0.198273
$408$	0	0
$409$	28.0000	1.38451	0.692255	−	0.721653i	$-0.256617\pi$
$409$	28.0000	1.38451	0.692255	+	0.721653i	$0.256617\pi$
$410$	0	0
$411$	14.0000	0.690569
$412$	34.0000	1.67506
$413$	3.00000	0.147620
$414$	0	0
$415$	−6.00000	−0.294528
$416$	0	0
$417$	−38.0000	−1.86087
$418$	0	0
$419$	−10.0000	−0.488532	−0.244266	−	0.969708i	$-0.578547\pi$
$419$	−10.0000	−0.488532	−0.244266	+	0.969708i	$0.578547\pi$
$420$	−12.0000	−0.585540
$421$	15.0000	0.731055	0.365528	−	0.930800i	$-0.380889\pi$
$421$	15.0000	0.731055	0.365528	+	0.930800i	$0.380889\pi$
$422$	0	0
$423$	−3.00000	−0.145865
$424$	0	0
$425$	1.00000	0.0485071
$426$	0	0
$427$	6.00000	0.290360
$428$	−6.00000	−0.290021
$429$	0	0
$430$	0	0
$431$	1.00000	0.0481683	0.0240842	−	0.999710i	$-0.492333\pi$
$431$	1.00000	0.0481683	0.0240842	+	0.999710i	$0.492333\pi$
$432$	16.0000	0.769800
$433$	−25.0000	−1.20142	−0.600712	−	0.799466i	$-0.705116\pi$
$433$	−25.0000	−1.20142	−0.600712	+	0.799466i	$0.705116\pi$
$434$	0	0
$435$	6.00000	0.287678
$436$	−10.0000	−0.478913
$437$	0	0
$438$	0	0
$439$	−25.0000	−1.19318	−0.596592	−	0.802544i	$-0.703479\pi$
$439$	−25.0000	−1.19318	−0.596592	+	0.802544i	$0.703479\pi$
$440$	0	0
$441$	2.00000	0.0952381
$442$	0	0
$443$	12.0000	0.570137	0.285069	−	0.958507i	$-0.407984\pi$
$443$	12.0000	0.570137	0.285069	+	0.958507i	$0.407984\pi$
$444$	−16.0000	−0.759326
$445$	7.00000	0.331832
$446$	0	0
$447$	−20.0000	−0.945968
$448$	−24.0000	−1.13389
$449$	22.0000	1.03824	0.519122	−	0.854700i	$-0.326259\pi$
$449$	22.0000	1.03824	0.519122	+	0.854700i	$0.326259\pi$
$450$	0	0
$451$	−1.00000	−0.0470882
$452$	8.00000	0.376288
$453$	−20.0000	−0.939682
$454$	0	0
$455$	0	0
$456$	0	0
$457$	28.0000	1.30978	0.654892	−	0.755722i	$-0.272714\pi$
$457$	28.0000	1.30978	0.654892	+	0.755722i	$0.272714\pi$
$458$	0	0
$459$	4.00000	0.186704
$460$	−4.00000	−0.186501
$461$	2.00000	0.0931493	0.0465746	−	0.998915i	$-0.485169\pi$
$461$	2.00000	0.0931493	0.0465746	+	0.998915i	$0.485169\pi$
$462$	0	0
$463$	−13.0000	−0.604161	−0.302081	−	0.953282i	$-0.597681\pi$
$463$	−13.0000	−0.604161	−0.302081	+	0.953282i	$0.597681\pi$
$464$	12.0000	0.557086
$465$	−20.0000	−0.927478
$466$	0	0
$467$	37.0000	1.71216	0.856078	−	0.516847i	$-0.172894\pi$
$467$	37.0000	1.71216	0.856078	+	0.516847i	$0.172894\pi$
$468$	0	0
$469$	−9.00000	−0.415581
$470$	0	0
$471$	34.0000	1.56664
$472$	0	0
$473$	−8.00000	−0.367840
$474$	0	0
$475$	0	0
$476$	−6.00000	−0.275010
$477$	−9.00000	−0.412082
$478$	0	0
$479$	27.0000	1.23366	0.616831	−	0.787096i	$-0.288416\pi$
$479$	27.0000	1.23366	0.616831	+	0.787096i	$0.288416\pi$
$480$	0	0
$481$	0	0
$482$	0	0
$483$	12.0000	0.546019
$484$	−2.00000	−0.0909091
$485$	12.0000	0.544892
$486$	0	0
$487$	−24.0000	−1.08754	−0.543772	−	0.839233i	$-0.683004\pi$
$487$	−24.0000	−1.08754	−0.543772	+	0.839233i	$0.683004\pi$
$488$	0	0
$489$	8.00000	0.361773
$490$	0	0
$491$	6.00000	0.270776	0.135388	−	0.990793i	$-0.456772\pi$
$491$	6.00000	0.270776	0.135388	+	0.990793i	$0.456772\pi$
$492$	−4.00000	−0.180334
$493$	3.00000	0.135113
$494$	0	0
$495$	−1.00000	−0.0449467
$496$	−40.0000	−1.79605
$497$	6.00000	0.269137
$498$	0	0
$499$	8.00000	0.358129	0.179065	−	0.983837i	$-0.442693\pi$
$499$	8.00000	0.358129	0.179065	+	0.983837i	$0.442693\pi$
$500$	2.00000	0.0894427
$501$	40.0000	1.78707
$502$	0	0
$503$	−11.0000	−0.490466	−0.245233	−	0.969464i	$-0.578864\pi$
$503$	−11.0000	−0.490466	−0.245233	+	0.969464i	$0.578864\pi$
$504$	0	0
$505$	−16.0000	−0.711991
$506$	0	0
$507$	26.0000	1.15470
$508$	−40.0000	−1.77471
$509$	−1.00000	−0.0443242	−0.0221621	−	0.999754i	$-0.507055\pi$
$509$	−1.00000	−0.0443242	−0.0221621	+	0.999754i	$0.507055\pi$
$510$	0	0
$511$	−33.0000	−1.45983
$512$	0	0
$513$	0	0
$514$	0	0
$515$	17.0000	0.749110
$516$	−32.0000	−1.40872
$517$	−3.00000	−0.131940
$518$	0	0
$519$	2.00000	0.0877903
$520$	0	0
$521$	−18.0000	−0.788594	−0.394297	−	0.918983i	$-0.629012\pi$
$521$	−18.0000	−0.788594	−0.394297	+	0.918983i	$0.629012\pi$
$522$	0	0
$523$	28.0000	1.22435	0.612177	−	0.790721i	$-0.290294\pi$
$523$	28.0000	1.22435	0.612177	+	0.790721i	$0.290294\pi$
$524$	10.0000	0.436852
$525$	−6.00000	−0.261861
$526$	0	0
$527$	−10.0000	−0.435607
$528$	−8.00000	−0.348155
$529$	−19.0000	−0.826087
$530$	0	0
$531$	1.00000	0.0433963
$532$	0	0
$533$	0	0
$534$	0	0
$535$	−3.00000	−0.129701
$536$	0	0
$537$	18.0000	0.776757
$538$	0	0
$539$	2.00000	0.0861461
$540$	8.00000	0.344265
$541$	39.0000	1.67674	0.838370	−	0.545101i	$-0.183509\pi$
$541$	39.0000	1.67674	0.838370	+	0.545101i	$0.183509\pi$
$542$	0	0
$543$	24.0000	1.02994
$544$	0	0
$545$	−5.00000	−0.214176
$546$	0	0
$547$	12.0000	0.513083	0.256541	−	0.966533i	$-0.417417\pi$
$547$	12.0000	0.513083	0.256541	+	0.966533i	$0.417417\pi$
$548$	14.0000	0.598050
$549$	2.00000	0.0853579
$550$	0	0
$551$	0	0
$552$	0	0
$553$	0	0
$554$	0	0
$555$	−8.00000	−0.339581
$556$	−38.0000	−1.61156
$557$	2.00000	0.0847427	0.0423714	−	0.999102i	$-0.486509\pi$
$557$	2.00000	0.0847427	0.0423714	+	0.999102i	$0.486509\pi$
$558$	0	0
$559$	0	0
$560$	−12.0000	−0.507093
$561$	−2.00000	−0.0844401
$562$	0	0
$563$	8.00000	0.337160	0.168580	−	0.985688i	$-0.446082\pi$
$563$	8.00000	0.337160	0.168580	+	0.985688i	$0.446082\pi$
$564$	−12.0000	−0.505291
$565$	4.00000	0.168281
$566$	0	0
$567$	−33.0000	−1.38587
$568$	0	0
$569$	−22.0000	−0.922288	−0.461144	−	0.887325i	$-0.652561\pi$
$569$	−22.0000	−0.922288	−0.461144	+	0.887325i	$0.652561\pi$
$570$	0	0
$571$	−23.0000	−0.962520	−0.481260	−	0.876578i	$-0.659821\pi$
$571$	−23.0000	−0.962520	−0.481260	+	0.876578i	$0.659821\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	−2.00000	−0.0834058
$576$	−8.00000	−0.333333
$577$	−3.00000	−0.124892	−0.0624458	−	0.998048i	$-0.519890\pi$
$577$	−3.00000	−0.124892	−0.0624458	+	0.998048i	$0.519890\pi$
$578$	0	0
$579$	36.0000	1.49611
$580$	6.00000	0.249136
$581$	18.0000	0.746766
$582$	0	0
$583$	−9.00000	−0.372742
$584$	0	0
$585$	0	0
$586$	0	0
$587$	28.0000	1.15568	0.577842	−	0.816149i	$-0.303895\pi$
$587$	28.0000	1.15568	0.577842	+	0.816149i	$0.303895\pi$
$588$	8.00000	0.329914
$589$	0	0
$590$	0	0
$591$	20.0000	0.822690
$592$	−16.0000	−0.657596
$593$	−24.0000	−0.985562	−0.492781	−	0.870153i	$-0.664020\pi$
$593$	−24.0000	−0.985562	−0.492781	+	0.870153i	$0.664020\pi$
$594$	0	0
$595$	−3.00000	−0.122988
$596$	−20.0000	−0.819232
$597$	24.0000	0.982255
$598$	0	0
$599$	9.00000	0.367730	0.183865	−	0.982952i	$-0.441139\pi$
$599$	9.00000	0.367730	0.183865	+	0.982952i	$0.441139\pi$
$600$	0	0
$601$	−26.0000	−1.06056	−0.530281	−	0.847822i	$-0.677914\pi$
$601$	−26.0000	−1.06056	−0.530281	+	0.847822i	$0.677914\pi$
$602$	0	0
$603$	−3.00000	−0.122169
$604$	−20.0000	−0.813788
$605$	−1.00000	−0.0406558
$606$	0	0
$607$	4.00000	0.162355	0.0811775	−	0.996700i	$-0.474132\pi$
$607$	4.00000	0.162355	0.0811775	+	0.996700i	$0.474132\pi$
$608$	0	0
$609$	−18.0000	−0.729397
$610$	0	0
$611$	0	0
$612$	−2.00000	−0.0808452
$613$	4.00000	0.161558	0.0807792	−	0.996732i	$-0.474259\pi$
$613$	4.00000	0.161558	0.0807792	+	0.996732i	$0.474259\pi$
$614$	0	0
$615$	−2.00000	−0.0806478
$616$	0	0
$617$	−12.0000	−0.483102	−0.241551	−	0.970388i	$-0.577656\pi$
$617$	−12.0000	−0.483102	−0.241551	+	0.970388i	$0.577656\pi$
$618$	0	0
$619$	−30.0000	−1.20580	−0.602901	−	0.797816i	$-0.705989\pi$
$619$	−30.0000	−1.20580	−0.602901	+	0.797816i	$0.705989\pi$
$620$	−20.0000	−0.803219
$621$	−8.00000	−0.321029
$622$	0	0
$623$	−21.0000	−0.841347
$624$	0	0
$625$	1.00000	0.0400000
$626$	0	0
$627$	0	0
$628$	34.0000	1.35675
$629$	−4.00000	−0.159490
$630$	0	0
$631$	39.0000	1.55257	0.776283	−	0.630385i	$-0.217103\pi$
$631$	39.0000	1.55257	0.776283	+	0.630385i	$0.217103\pi$
$632$	0	0
$633$	−26.0000	−1.03341
$634$	0	0
$635$	−20.0000	−0.793676
$636$	−36.0000	−1.42749
$637$	0	0
$638$	0	0
$639$	2.00000	0.0791188
$640$	0	0
$641$	12.0000	0.473972	0.236986	−	0.971513i	$-0.423841\pi$
$641$	12.0000	0.473972	0.236986	+	0.971513i	$0.423841\pi$
$642$	0	0
$643$	−26.0000	−1.02534	−0.512670	−	0.858586i	$-0.671344\pi$
$643$	−26.0000	−1.02534	−0.512670	+	0.858586i	$0.671344\pi$
$644$	12.0000	0.472866
$645$	−16.0000	−0.629999
$646$	0	0
$647$	−19.0000	−0.746967	−0.373484	−	0.927637i	$-0.621837\pi$
$647$	−19.0000	−0.746967	−0.373484	+	0.927637i	$0.621837\pi$
$648$	0	0
$649$	1.00000	0.0392534
$650$	0	0
$651$	60.0000	2.35159
$652$	8.00000	0.313304
$653$	30.0000	1.17399	0.586995	−	0.809590i	$-0.300311\pi$
$653$	30.0000	1.17399	0.586995	+	0.809590i	$0.300311\pi$
$654$	0	0
$655$	5.00000	0.195366
$656$	−4.00000	−0.156174
$657$	−11.0000	−0.429151
$658$	0	0
$659$	−10.0000	−0.389545	−0.194772	−	0.980848i	$-0.562397\pi$
$659$	−10.0000	−0.389545	−0.194772	+	0.980848i	$0.562397\pi$
$660$	−4.00000	−0.155700
$661$	−13.0000	−0.505641	−0.252821	−	0.967513i	$-0.581358\pi$
$661$	−13.0000	−0.505641	−0.252821	+	0.967513i	$0.581358\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−6.00000	−0.232321
$668$	40.0000	1.54765
$669$	0	0
$670$	0	0
$671$	2.00000	0.0772091
$672$	0	0
$673$	−17.0000	−0.655302	−0.327651	−	0.944799i	$-0.606257\pi$
$673$	−17.0000	−0.655302	−0.327651	+	0.944799i	$0.606257\pi$
$674$	0	0
$675$	4.00000	0.153960
$676$	26.0000	1.00000
$677$	−3.00000	−0.115299	−0.0576497	−	0.998337i	$-0.518361\pi$
$677$	−3.00000	−0.115299	−0.0576497	+	0.998337i	$0.518361\pi$
$678$	0	0
$679$	−36.0000	−1.38155
$680$	0	0
$681$	−6.00000	−0.229920
$682$	0	0
$683$	36.0000	1.37750	0.688751	−	0.724998i	$-0.258159\pi$
$683$	36.0000	1.37750	0.688751	+	0.724998i	$0.258159\pi$
$684$	0	0
$685$	7.00000	0.267456
$686$	0	0
$687$	−14.0000	−0.534133
$688$	−32.0000	−1.21999
$689$	0	0
$690$	0	0
$691$	−4.00000	−0.152167	−0.0760836	−	0.997101i	$-0.524242\pi$
$691$	−4.00000	−0.152167	−0.0760836	+	0.997101i	$0.524242\pi$
$692$	2.00000	0.0760286
$693$	3.00000	0.113961
$694$	0	0
$695$	−19.0000	−0.720711
$696$	0	0
$697$	−1.00000	−0.0378777
$698$	0	0
$699$	30.0000	1.13470
$700$	−6.00000	−0.226779
$701$	36.0000	1.35970	0.679851	−	0.733351i	$-0.262045\pi$
$701$	36.0000	1.35970	0.679851	+	0.733351i	$0.262045\pi$
$702$	0	0
$703$	0	0
$704$	−8.00000	−0.301511
$705$	−6.00000	−0.225973
$706$	0	0
$707$	48.0000	1.80523
$708$	4.00000	0.150329
$709$	−10.0000	−0.375558	−0.187779	−	0.982211i	$-0.560129\pi$
$709$	−10.0000	−0.375558	−0.187779	+	0.982211i	$0.560129\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	20.0000	0.749006
$714$	0	0
$715$	0	0
$716$	18.0000	0.672692
$717$	−12.0000	−0.448148
$718$	0	0
$719$	−14.0000	−0.522112	−0.261056	−	0.965324i	$-0.584071\pi$
$719$	−14.0000	−0.522112	−0.261056	+	0.965324i	$0.584071\pi$
$720$	−4.00000	−0.149071
$721$	−51.0000	−1.89934
$722$	0	0
$723$	50.0000	1.85952
$724$	24.0000	0.891953
$725$	3.00000	0.111417
$726$	0	0
$727$	−3.00000	−0.111264	−0.0556319	−	0.998451i	$-0.517717\pi$
$727$	−3.00000	−0.111264	−0.0556319	+	0.998451i	$0.517717\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	0	0
$731$	−8.00000	−0.295891
$732$	8.00000	0.295689
$733$	14.0000	0.517102	0.258551	−	0.965998i	$-0.416755\pi$
$733$	14.0000	0.517102	0.258551	+	0.965998i	$0.416755\pi$
$734$	0	0
$735$	4.00000	0.147542
$736$	0	0
$737$	−3.00000	−0.110506
$738$	0	0
$739$	−14.0000	−0.514998	−0.257499	−	0.966279i	$-0.582898\pi$
$739$	−14.0000	−0.514998	−0.257499	+	0.966279i	$0.582898\pi$
$740$	−8.00000	−0.294086
$741$	0	0
$742$	0	0
$743$	−9.00000	−0.330178	−0.165089	−	0.986279i	$-0.552791\pi$
$743$	−9.00000	−0.330178	−0.165089	+	0.986279i	$0.552791\pi$
$744$	0	0
$745$	−10.0000	−0.366372
$746$	0	0
$747$	6.00000	0.219529
$748$	−2.00000	−0.0731272
$749$	9.00000	0.328853
$750$	0	0
$751$	46.0000	1.67856	0.839282	−	0.543696i	$-0.182976\pi$
$751$	46.0000	1.67856	0.839282	+	0.543696i	$0.182976\pi$
$752$	−12.0000	−0.437595
$753$	−8.00000	−0.291536
$754$	0	0
$755$	−10.0000	−0.363937
$756$	−24.0000	−0.872872
$757$	2.00000	0.0726912	0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000	0.0726912	0.0363456	+	0.999339i	$0.488428\pi$
$758$	0	0
$759$	4.00000	0.145191
$760$	0	0
$761$	48.0000	1.74000	0.869999	−	0.493053i	$-0.164119\pi$
$761$	48.0000	1.74000	0.869999	+	0.493053i	$0.164119\pi$
$762$	0	0
$763$	15.0000	0.543036
$764$	0	0
$765$	−1.00000	−0.0361551
$766$	0	0
$767$	0	0
$768$	−32.0000	−1.15470
$769$	−26.0000	−0.937584	−0.468792	−	0.883309i	$-0.655311\pi$
$769$	−26.0000	−0.937584	−0.468792	+	0.883309i	$0.655311\pi$
$770$	0	0
$771$	30.0000	1.08042
$772$	36.0000	1.29567
$773$	−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
$775$	−10.0000	−0.359211
$776$	0	0
$777$	24.0000	0.860995
$778$	0	0
$779$	0	0
$780$	0	0
$781$	2.00000	0.0715656
$782$	0	0
$783$	12.0000	0.428845
$784$	8.00000	0.285714
$785$	17.0000	0.606756
$786$	0	0
$787$	−25.0000	−0.891154	−0.445577	−	0.895244i	$-0.647001\pi$
$787$	−25.0000	−0.891154	−0.445577	+	0.895244i	$0.647001\pi$
$788$	20.0000	0.712470
$789$	−32.0000	−1.13923
$790$	0	0
$791$	−12.0000	−0.426671
$792$	0	0
$793$	0	0
$794$	0	0
$795$	−18.0000	−0.638394
$796$	24.0000	0.850657
$797$	−18.0000	−0.637593	−0.318796	−	0.947823i	$-0.603279\pi$
$797$	−18.0000	−0.637593	−0.318796	+	0.947823i	$0.603279\pi$
$798$	0	0
$799$	−3.00000	−0.106132
$800$	0	0
$801$	−7.00000	−0.247333
$802$	0	0
$803$	−11.0000	−0.388182
$804$	−12.0000	−0.423207
$805$	6.00000	0.211472
$806$	0	0
$807$	60.0000	2.11210
$808$	0	0
$809$	17.0000	0.597688	0.298844	−	0.954302i	$-0.403399\pi$
$809$	17.0000	0.597688	0.298844	+	0.954302i	$0.403399\pi$
$810$	0	0
$811$	24.0000	0.842754	0.421377	−	0.906886i	$-0.361547\pi$
$811$	24.0000	0.842754	0.421377	+	0.906886i	$0.361547\pi$
$812$	−18.0000	−0.631676
$813$	20.0000	0.701431
$814$	0	0
$815$	4.00000	0.140114
$816$	−8.00000	−0.280056
$817$	0	0
$818$	0	0
$819$	0	0
$820$	−2.00000	−0.0698430
$821$	42.0000	1.46581	0.732905	−	0.680331i	$-0.238164\pi$
$821$	42.0000	1.46581	0.732905	+	0.680331i	$0.238164\pi$
$822$	0	0
$823$	−2.00000	−0.0697156	−0.0348578	−	0.999392i	$-0.511098\pi$
$823$	−2.00000	−0.0697156	−0.0348578	+	0.999392i	$0.511098\pi$
$824$	0	0
$825$	−2.00000	−0.0696311
$826$	0	0
$827$	19.0000	0.660695	0.330347	−	0.943859i	$-0.392834\pi$
$827$	19.0000	0.660695	0.330347	+	0.943859i	$0.392834\pi$
$828$	4.00000	0.139010
$829$	34.0000	1.18087	0.590434	−	0.807086i	$-0.298956\pi$
$829$	34.0000	1.18087	0.590434	+	0.807086i	$0.298956\pi$
$830$	0	0
$831$	38.0000	1.31821
$832$	0	0
$833$	2.00000	0.0692959
$834$	0	0
$835$	20.0000	0.692129
$836$	0	0
$837$	−40.0000	−1.38260
$838$	0	0
$839$	−26.0000	−0.897620	−0.448810	−	0.893627i	$-0.648152\pi$
$839$	−26.0000	−0.897620	−0.448810	+	0.893627i	$0.648152\pi$
$840$	0	0
$841$	−20.0000	−0.689655
$842$	0	0
$843$	−64.0000	−2.20428
$844$	−26.0000	−0.894957
$845$	13.0000	0.447214
$846$	0	0
$847$	3.00000	0.103081
$848$	−36.0000	−1.23625
$849$	56.0000	1.92192
$850$	0	0
$851$	8.00000	0.274236
$852$	8.00000	0.274075
$853$	−1.00000	−0.0342393	−0.0171197	−	0.999853i	$-0.505450\pi$
$853$	−1.00000	−0.0342393	−0.0171197	+	0.999853i	$0.505450\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−14.0000	−0.478231	−0.239115	−	0.970991i	$-0.576857\pi$
$857$	−14.0000	−0.478231	−0.239115	+	0.970991i	$0.576857\pi$
$858$	0	0
$859$	23.0000	0.784750	0.392375	−	0.919805i	$-0.371654\pi$
$859$	23.0000	0.784750	0.392375	+	0.919805i	$0.371654\pi$
$860$	−16.0000	−0.545595
$861$	6.00000	0.204479
$862$	0	0
$863$	16.0000	0.544646	0.272323	−	0.962206i	$-0.412208\pi$
$863$	16.0000	0.544646	0.272323	+	0.962206i	$0.412208\pi$
$864$	0	0
$865$	1.00000	0.0340010
$866$	0	0
$867$	−2.00000	−0.0679236
$868$	60.0000	2.03653
$869$	0	0
$870$	0	0
$871$	0	0
$872$	0	0
$873$	−12.0000	−0.406138
$874$	0	0
$875$	−3.00000	−0.101419
$876$	−44.0000	−1.48662
$877$	38.0000	1.28317	0.641584	−	0.767052i	$-0.278277\pi$
$877$	38.0000	1.28317	0.641584	+	0.767052i	$0.278277\pi$
$878$	0	0
$879$	−44.0000	−1.48408
$880$	−4.00000	−0.134840
$881$	42.0000	1.41502	0.707508	−	0.706705i	$-0.249819\pi$
$881$	42.0000	1.41502	0.707508	+	0.706705i	$0.249819\pi$
$882$	0	0
$883$	−19.0000	−0.639401	−0.319700	−	0.947519i	$-0.603582\pi$
$883$	−19.0000	−0.639401	−0.319700	+	0.947519i	$0.603582\pi$
$884$	0	0
$885$	2.00000	0.0672293
$886$	0	0
$887$	32.0000	1.07445	0.537227	−	0.843437i	$-0.319472\pi$
$887$	32.0000	1.07445	0.537227	+	0.843437i	$0.319472\pi$
$888$	0	0
$889$	60.0000	2.01234
$890$	0	0
$891$	−11.0000	−0.368514
$892$	0	0
$893$	0	0
$894$	0	0
$895$	9.00000	0.300837
$896$	0	0
$897$	0	0
$898$	0	0
$899$	−30.0000	−1.00056
$900$	−2.00000	−0.0666667
$901$	−9.00000	−0.299833
$902$	0	0
$903$	48.0000	1.59734
$904$	0	0
$905$	12.0000	0.398893
$906$	0	0
$907$	30.0000	0.996134	0.498067	−	0.867139i	$-0.334043\pi$
$907$	30.0000	0.996134	0.498067	+	0.867139i	$0.334043\pi$
$908$	−6.00000	−0.199117
$909$	16.0000	0.530687
$910$	0	0
$911$	52.0000	1.72284	0.861418	−	0.507896i	$-0.169577\pi$
$911$	52.0000	1.72284	0.861418	+	0.507896i	$0.169577\pi$
$912$	0	0
$913$	6.00000	0.198571
$914$	0	0
$915$	4.00000	0.132236
$916$	−14.0000	−0.462573
$917$	−15.0000	−0.495344
$918$	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
$921$	−12.0000	−0.395413
$922$	0	0
$923$	0	0
$924$	12.0000	0.394771
$925$	−4.00000	−0.131519
$926$	0	0
$927$	−17.0000	−0.558353
$928$	0	0
$929$	−34.0000	−1.11550	−0.557752	−	0.830008i	$-0.688336\pi$
$929$	−34.0000	−1.11550	−0.557752	+	0.830008i	$0.688336\pi$
$930$	0	0
$931$	0	0
$932$	30.0000	0.982683
$933$	−36.0000	−1.17859
$934$	0	0
$935$	−1.00000	−0.0327035
$936$	0	0
$937$	10.0000	0.326686	0.163343	−	0.986569i	$-0.447772\pi$
$937$	10.0000	0.326686	0.163343	+	0.986569i	$0.447772\pi$
$938$	0	0
$939$	−56.0000	−1.82749
$940$	−6.00000	−0.195698
$941$	39.0000	1.27136	0.635682	−	0.771951i	$-0.280719\pi$
$941$	39.0000	1.27136	0.635682	+	0.771951i	$0.280719\pi$
$942$	0	0
$943$	2.00000	0.0651290
$944$	4.00000	0.130189
$945$	−12.0000	−0.390360
$946$	0	0
$947$	−24.0000	−0.779895	−0.389948	−	0.920837i	$-0.627507\pi$
$947$	−24.0000	−0.779895	−0.389948	+	0.920837i	$0.627507\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	12.0000	0.389127
$952$	0	0
$953$	20.0000	0.647864	0.323932	−	0.946080i	$-0.394995\pi$
$953$	20.0000	0.647864	0.323932	+	0.946080i	$0.394995\pi$
$954$	0	0
$955$	0	0
$956$	−12.0000	−0.388108
$957$	−6.00000	−0.193952
$958$	0	0
$959$	−21.0000	−0.678125
$960$	−16.0000	−0.516398
$961$	69.0000	2.22581
$962$	0	0
$963$	3.00000	0.0966736
$964$	50.0000	1.61039
$965$	18.0000	0.579441
$966$	0	0
$967$	14.0000	0.450210	0.225105	−	0.974335i	$-0.427728\pi$
$967$	14.0000	0.450210	0.225105	+	0.974335i	$0.427728\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	28.0000	0.898563	0.449281	−	0.893390i	$-0.351680\pi$
$971$	28.0000	0.898563	0.449281	+	0.893390i	$0.351680\pi$
$972$	−20.0000	−0.641500
$973$	57.0000	1.82734
$974$	0	0
$975$	0	0
$976$	8.00000	0.256074
$977$	25.0000	0.799821	0.399910	−	0.916554i	$-0.369041\pi$
$977$	25.0000	0.799821	0.399910	+	0.916554i	$0.369041\pi$
$978$	0	0
$979$	−7.00000	−0.223721
$980$	4.00000	0.127775
$981$	5.00000	0.159638
$982$	0	0
$983$	−42.0000	−1.33959	−0.669796	−	0.742545i	$-0.733618\pi$
$983$	−42.0000	−1.33959	−0.669796	+	0.742545i	$0.733618\pi$
$984$	0	0
$985$	10.0000	0.318626
$986$	0	0
$987$	18.0000	0.572946
$988$	0	0
$989$	16.0000	0.508770
$990$	0	0
$991$	−20.0000	−0.635321	−0.317660	−	0.948205i	$-0.602897\pi$
$991$	−20.0000	−0.635321	−0.317660	+	0.948205i	$0.602897\pi$
$992$	0	0
$993$	−8.00000	−0.253872
$994$	0	0
$995$	12.0000	0.380426
$996$	24.0000	0.760469
$997$	−9.00000	−0.285033	−0.142516	−	0.989792i	$-0.545519\pi$
$997$	−9.00000	−0.285033	−0.142516	+	0.989792i	$0.545519\pi$
$998$	0	0
$999$	−16.0000	−0.506218

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	935.2.a.a.1.1	✓	1
3.2	odd	2		8415.2.a.k.1.1		1
5.4	even	2		4675.2.a.l.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
935.2.a.a.1.1	✓	1	1.1	even	1	trivial
4675.2.a.l.1.1		1	5.4	even	2
8415.2.a.k.1.1		1	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 935 = 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	935.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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