LMFDB - Embedded newform 570.2.a.k.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(1,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, 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("570.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.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:	$4.55147291521$
Analytic rank:	$0$
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	$\chi$	$=$	570.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +6.00000 q^{11} +1.00000 q^{12} -4.00000 q^{13} +2.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -6.00000 q^{17} +1.00000 q^{18} +1.00000 q^{19} -1.00000 q^{20} +2.00000 q^{21} +6.00000 q^{22} +1.00000 q^{24} +1.00000 q^{25} -4.00000 q^{26} +1.00000 q^{27} +2.00000 q^{28} -1.00000 q^{30} +8.00000 q^{31} +1.00000 q^{32} +6.00000 q^{33} -6.00000 q^{34} -2.00000 q^{35} +1.00000 q^{36} +8.00000 q^{37} +1.00000 q^{38} -4.00000 q^{39} -1.00000 q^{40} -12.0000 q^{41} +2.00000 q^{42} +2.00000 q^{43} +6.00000 q^{44} -1.00000 q^{45} +1.00000 q^{48} -3.00000 q^{49} +1.00000 q^{50} -6.00000 q^{51} -4.00000 q^{52} -6.00000 q^{53} +1.00000 q^{54} -6.00000 q^{55} +2.00000 q^{56} +1.00000 q^{57} -12.0000 q^{59} -1.00000 q^{60} +2.00000 q^{61} +8.00000 q^{62} +2.00000 q^{63} +1.00000 q^{64} +4.00000 q^{65} +6.00000 q^{66} -16.0000 q^{67} -6.00000 q^{68} -2.00000 q^{70} +1.00000 q^{72} -10.0000 q^{73} +8.00000 q^{74} +1.00000 q^{75} +1.00000 q^{76} +12.0000 q^{77} -4.00000 q^{78} +8.00000 q^{79} -1.00000 q^{80} +1.00000 q^{81} -12.0000 q^{82} +2.00000 q^{84} +6.00000 q^{85} +2.00000 q^{86} +6.00000 q^{88} -12.0000 q^{89} -1.00000 q^{90} -8.00000 q^{91} +8.00000 q^{93} -1.00000 q^{95} +1.00000 q^{96} +8.00000 q^{97} -3.00000 q^{98} +6.00000 q^{99} +O(q^{100})\)

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.00000	0.408248
$7$	2.00000	0.755929	0.377964	−	0.925820i	$-0.376624\pi$
$7$	2.00000	0.755929	0.377964	+	0.925820i	$0.376624\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	6.00000	1.80907	0.904534	−	0.426401i	$-0.140219\pi$
$11$	6.00000	1.80907	0.904534	+	0.426401i	$0.140219\pi$
$12$	1.00000	0.288675
$13$	−4.00000	−1.10940	−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000	−1.10940	−0.554700	+	0.832050i	$0.687167\pi$
$14$	2.00000	0.534522
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−6.00000	−1.45521	−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000	−1.45521	−0.727607	+	0.685994i	$0.759367\pi$
$18$	1.00000	0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−1.00000	−0.223607
$21$	2.00000	0.436436
$22$	6.00000	1.27920
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	−4.00000	−0.784465
$27$	1.00000	0.192450
$28$	2.00000	0.377964
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	−1.00000	−0.182574
$31$	8.00000	1.43684	0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000	1.43684	0.718421	+	0.695608i	$0.244865\pi$
$32$	1.00000	0.176777
$33$	6.00000	1.04447
$34$	−6.00000	−1.02899
$35$	−2.00000	−0.338062
$36$	1.00000	0.166667
$37$	8.00000	1.31519	0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000	1.31519	0.657596	+	0.753371i	$0.271573\pi$
$38$	1.00000	0.162221
$39$	−4.00000	−0.640513
$40$	−1.00000	−0.158114
$41$	−12.0000	−1.87409	−0.937043	−	0.349215i	$-0.886448\pi$
$41$	−12.0000	−1.87409	−0.937043	+	0.349215i	$0.886448\pi$
$42$	2.00000	0.308607
$43$	2.00000	0.304997	0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000	0.304997	0.152499	+	0.988304i	$0.451268\pi$
$44$	6.00000	0.904534
$45$	−1.00000	−0.149071
$46$	0	0
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	1.00000	0.144338
$49$	−3.00000	−0.428571
$50$	1.00000	0.141421
$51$	−6.00000	−0.840168
$52$	−4.00000	−0.554700
$53$	−6.00000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	1.00000	0.136083
$55$	−6.00000	−0.809040
$56$	2.00000	0.267261
$57$	1.00000	0.132453
$58$	0	0
$59$	−12.0000	−1.56227	−0.781133	−	0.624364i	$-0.785358\pi$
$59$	−12.0000	−1.56227	−0.781133	+	0.624364i	$0.785358\pi$
$60$	−1.00000	−0.129099
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	8.00000	1.01600
$63$	2.00000	0.251976
$64$	1.00000	0.125000
$65$	4.00000	0.496139
$66$	6.00000	0.738549
$67$	−16.0000	−1.95471	−0.977356	−	0.211604i	$-0.932131\pi$
$67$	−16.0000	−1.95471	−0.977356	+	0.211604i	$0.932131\pi$
$68$	−6.00000	−0.727607
$69$	0	0
$70$	−2.00000	−0.239046
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	1.00000	0.117851
$73$	−10.0000	−1.17041	−0.585206	−	0.810885i	$-0.698986\pi$
$73$	−10.0000	−1.17041	−0.585206	+	0.810885i	$0.698986\pi$
$74$	8.00000	0.929981
$75$	1.00000	0.115470
$76$	1.00000	0.114708
$77$	12.0000	1.36753
$78$	−4.00000	−0.452911
$79$	8.00000	0.900070	0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000	0.900070	0.450035	+	0.893011i	$0.351411\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−12.0000	−1.32518
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	2.00000	0.218218
$85$	6.00000	0.650791
$86$	2.00000	0.215666
$87$	0	0
$88$	6.00000	0.639602
$89$	−12.0000	−1.27200	−0.635999	−	0.771690i	$-0.719412\pi$
$89$	−12.0000	−1.27200	−0.635999	+	0.771690i	$0.719412\pi$
$90$	−1.00000	−0.105409
$91$	−8.00000	−0.838628
$92$	0	0
$93$	8.00000	0.829561
$94$	0	0
$95$	−1.00000	−0.102598
$96$	1.00000	0.102062
$97$	8.00000	0.812277	0.406138	−	0.913812i	$-0.366875\pi$
$97$	8.00000	0.812277	0.406138	+	0.913812i	$0.366875\pi$
$98$	−3.00000	−0.303046
$99$	6.00000	0.603023
$100$	1.00000	0.100000
$101$	6.00000	0.597022	0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000	0.597022	0.298511	+	0.954406i	$0.403510\pi$
$102$	−6.00000	−0.594089
$103$	−16.0000	−1.57653	−0.788263	−	0.615338i	$-0.789020\pi$
$103$	−16.0000	−1.57653	−0.788263	+	0.615338i	$0.789020\pi$
$104$	−4.00000	−0.392232
$105$	−2.00000	−0.195180
$106$	−6.00000	−0.582772
$107$	−12.0000	−1.16008	−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000	−1.16008	−0.580042	+	0.814587i	$0.696964\pi$
$108$	1.00000	0.0962250
$109$	2.00000	0.191565	0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000	0.191565	0.0957826	+	0.995402i	$0.469465\pi$
$110$	−6.00000	−0.572078
$111$	8.00000	0.759326
$112$	2.00000	0.188982
$113$	−6.00000	−0.564433	−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000	−0.564433	−0.282216	+	0.959351i	$0.591070\pi$
$114$	1.00000	0.0936586
$115$	0	0
$116$	0	0
$117$	−4.00000	−0.369800
$118$	−12.0000	−1.10469
$119$	−12.0000	−1.10004
$120$	−1.00000	−0.0912871
$121$	25.0000	2.27273
$122$	2.00000	0.181071
$123$	−12.0000	−1.08200
$124$	8.00000	0.718421
$125$	−1.00000	−0.0894427
$126$	2.00000	0.178174
$127$	20.0000	1.77471	0.887357	−	0.461084i	$-0.152539\pi$
$127$	20.0000	1.77471	0.887357	+	0.461084i	$0.152539\pi$
$128$	1.00000	0.0883883
$129$	2.00000	0.176090
$130$	4.00000	0.350823
$131$	18.0000	1.57267	0.786334	−	0.617802i	$-0.211977\pi$
$131$	18.0000	1.57267	0.786334	+	0.617802i	$0.211977\pi$
$132$	6.00000	0.522233
$133$	2.00000	0.173422
$134$	−16.0000	−1.38219
$135$	−1.00000	−0.0860663
$136$	−6.00000	−0.514496
$137$	6.00000	0.512615	0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000	0.512615	0.256307	+	0.966595i	$0.417494\pi$
$138$	0	0
$139$	8.00000	0.678551	0.339276	−	0.940687i	$-0.389818\pi$
$139$	8.00000	0.678551	0.339276	+	0.940687i	$0.389818\pi$
$140$	−2.00000	−0.169031
$141$	0	0
$142$	0	0
$143$	−24.0000	−2.00698
$144$	1.00000	0.0833333
$145$	0	0
$146$	−10.0000	−0.827606
$147$	−3.00000	−0.247436
$148$	8.00000	0.657596
$149$	−18.0000	−1.47462	−0.737309	−	0.675556i	$-0.763904\pi$
$149$	−18.0000	−1.47462	−0.737309	+	0.675556i	$0.763904\pi$
$150$	1.00000	0.0816497
$151$	8.00000	0.651031	0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000	0.651031	0.325515	+	0.945537i	$0.394462\pi$
$152$	1.00000	0.0811107
$153$	−6.00000	−0.485071
$154$	12.0000	0.966988
$155$	−8.00000	−0.642575
$156$	−4.00000	−0.320256
$157$	−10.0000	−0.798087	−0.399043	−	0.916932i	$-0.630658\pi$
$157$	−10.0000	−0.798087	−0.399043	+	0.916932i	$0.630658\pi$
$158$	8.00000	0.636446
$159$	−6.00000	−0.475831
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	1.00000	0.0785674
$163$	−10.0000	−0.783260	−0.391630	−	0.920123i	$-0.628089\pi$
$163$	−10.0000	−0.783260	−0.391630	+	0.920123i	$0.628089\pi$
$164$	−12.0000	−0.937043
$165$	−6.00000	−0.467099
$166$	0	0
$167$	24.0000	1.85718	0.928588	−	0.371113i	$-0.121024\pi$
$167$	24.0000	1.85718	0.928588	+	0.371113i	$0.121024\pi$
$168$	2.00000	0.154303
$169$	3.00000	0.230769
$170$	6.00000	0.460179
$171$	1.00000	0.0764719
$172$	2.00000	0.152499
$173$	6.00000	0.456172	0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000	0.456172	0.228086	+	0.973641i	$0.426753\pi$
$174$	0	0
$175$	2.00000	0.151186
$176$	6.00000	0.452267
$177$	−12.0000	−0.901975
$178$	−12.0000	−0.899438
$179$	−12.0000	−0.896922	−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000	−0.896922	−0.448461	+	0.893802i	$0.648028\pi$
$180$	−1.00000	−0.0745356
$181$	2.00000	0.148659	0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000	0.148659	0.0743294	+	0.997234i	$0.476318\pi$
$182$	−8.00000	−0.592999
$183$	2.00000	0.147844
$184$	0	0
$185$	−8.00000	−0.588172
$186$	8.00000	0.586588
$187$	−36.0000	−2.63258
$188$	0	0
$189$	2.00000	0.145479
$190$	−1.00000	−0.0725476
$191$	6.00000	0.434145	0.217072	−	0.976156i	$-0.430349\pi$
$191$	6.00000	0.434145	0.217072	+	0.976156i	$0.430349\pi$
$192$	1.00000	0.0721688
$193$	20.0000	1.43963	0.719816	−	0.694165i	$-0.244226\pi$
$193$	20.0000	1.43963	0.719816	+	0.694165i	$0.244226\pi$
$194$	8.00000	0.574367
$195$	4.00000	0.286446
$196$	−3.00000	−0.214286
$197$	6.00000	0.427482	0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000	0.427482	0.213741	+	0.976890i	$0.431435\pi$
$198$	6.00000	0.426401
$199$	20.0000	1.41776	0.708881	−	0.705328i	$-0.249200\pi$
$199$	20.0000	1.41776	0.708881	+	0.705328i	$0.249200\pi$
$200$	1.00000	0.0707107
$201$	−16.0000	−1.12855
$202$	6.00000	0.422159
$203$	0	0
$204$	−6.00000	−0.420084
$205$	12.0000	0.838116
$206$	−16.0000	−1.11477
$207$	0	0
$208$	−4.00000	−0.277350
$209$	6.00000	0.415029
$210$	−2.00000	−0.138013
$211$	−4.00000	−0.275371	−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000	−0.275371	−0.137686	+	0.990476i	$0.543966\pi$
$212$	−6.00000	−0.412082
$213$	0	0
$214$	−12.0000	−0.820303
$215$	−2.00000	−0.136399
$216$	1.00000	0.0680414
$217$	16.0000	1.08615
$218$	2.00000	0.135457
$219$	−10.0000	−0.675737
$220$	−6.00000	−0.404520
$221$	24.0000	1.61441
$222$	8.00000	0.536925
$223$	−16.0000	−1.07144	−0.535720	−	0.844396i	$-0.679960\pi$
$223$	−16.0000	−1.07144	−0.535720	+	0.844396i	$0.679960\pi$
$224$	2.00000	0.133631
$225$	1.00000	0.0666667
$226$	−6.00000	−0.399114
$227$	12.0000	0.796468	0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000	0.796468	0.398234	+	0.917284i	$0.369623\pi$
$228$	1.00000	0.0662266
$229$	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
$231$	12.0000	0.789542
$232$	0	0
$233$	6.00000	0.393073	0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000	0.393073	0.196537	+	0.980497i	$0.437031\pi$
$234$	−4.00000	−0.261488
$235$	0	0
$236$	−12.0000	−0.781133
$237$	8.00000	0.519656
$238$	−12.0000	−0.777844
$239$	−6.00000	−0.388108	−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000	−0.388108	−0.194054	+	0.980991i	$0.562164\pi$
$240$	−1.00000	−0.0645497
$241$	2.00000	0.128831	0.0644157	−	0.997923i	$-0.479482\pi$
$241$	2.00000	0.128831	0.0644157	+	0.997923i	$0.479482\pi$
$242$	25.0000	1.60706
$243$	1.00000	0.0641500
$244$	2.00000	0.128037
$245$	3.00000	0.191663
$246$	−12.0000	−0.765092
$247$	−4.00000	−0.254514
$248$	8.00000	0.508001
$249$	0	0
$250$	−1.00000	−0.0632456
$251$	6.00000	0.378717	0.189358	−	0.981908i	$-0.439359\pi$
$251$	6.00000	0.378717	0.189358	+	0.981908i	$0.439359\pi$
$252$	2.00000	0.125988
$253$	0	0
$254$	20.0000	1.25491
$255$	6.00000	0.375735
$256$	1.00000	0.0625000
$257$	−6.00000	−0.374270	−0.187135	−	0.982334i	$-0.559920\pi$
$257$	−6.00000	−0.374270	−0.187135	+	0.982334i	$0.559920\pi$
$258$	2.00000	0.124515
$259$	16.0000	0.994192
$260$	4.00000	0.248069
$261$	0	0
$262$	18.0000	1.11204
$263$	−12.0000	−0.739952	−0.369976	−	0.929041i	$-0.620634\pi$
$263$	−12.0000	−0.739952	−0.369976	+	0.929041i	$0.620634\pi$
$264$	6.00000	0.369274
$265$	6.00000	0.368577
$266$	2.00000	0.122628
$267$	−12.0000	−0.734388
$268$	−16.0000	−0.977356
$269$	24.0000	1.46331	0.731653	−	0.681677i	$-0.238749\pi$
$269$	24.0000	1.46331	0.731653	+	0.681677i	$0.238749\pi$
$270$	−1.00000	−0.0608581
$271$	20.0000	1.21491	0.607457	−	0.794353i	$-0.292190\pi$
$271$	20.0000	1.21491	0.607457	+	0.794353i	$0.292190\pi$
$272$	−6.00000	−0.363803
$273$	−8.00000	−0.484182
$274$	6.00000	0.362473
$275$	6.00000	0.361814
$276$	0	0
$277$	−10.0000	−0.600842	−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000	−0.600842	−0.300421	+	0.953807i	$0.597127\pi$
$278$	8.00000	0.479808
$279$	8.00000	0.478947
$280$	−2.00000	−0.119523
$281$	24.0000	1.43172	0.715860	−	0.698244i	$-0.246035\pi$
$281$	24.0000	1.43172	0.715860	+	0.698244i	$0.246035\pi$
$282$	0	0
$283$	14.0000	0.832214	0.416107	−	0.909316i	$-0.363394\pi$
$283$	14.0000	0.832214	0.416107	+	0.909316i	$0.363394\pi$
$284$	0	0
$285$	−1.00000	−0.0592349
$286$	−24.0000	−1.41915
$287$	−24.0000	−1.41668
$288$	1.00000	0.0589256
$289$	19.0000	1.11765
$290$	0	0
$291$	8.00000	0.468968
$292$	−10.0000	−0.585206
$293$	−18.0000	−1.05157	−0.525786	−	0.850617i	$-0.676229\pi$
$293$	−18.0000	−1.05157	−0.525786	+	0.850617i	$0.676229\pi$
$294$	−3.00000	−0.174964
$295$	12.0000	0.698667
$296$	8.00000	0.464991
$297$	6.00000	0.348155
$298$	−18.0000	−1.04271
$299$	0	0
$300$	1.00000	0.0577350
$301$	4.00000	0.230556
$302$	8.00000	0.460348
$303$	6.00000	0.344691
$304$	1.00000	0.0573539
$305$	−2.00000	−0.114520
$306$	−6.00000	−0.342997
$307$	−16.0000	−0.913168	−0.456584	−	0.889680i	$-0.650927\pi$
$307$	−16.0000	−0.913168	−0.456584	+	0.889680i	$0.650927\pi$
$308$	12.0000	0.683763
$309$	−16.0000	−0.910208
$310$	−8.00000	−0.454369
$311$	−18.0000	−1.02069	−0.510343	−	0.859971i	$-0.670482\pi$
$311$	−18.0000	−1.02069	−0.510343	+	0.859971i	$0.670482\pi$
$312$	−4.00000	−0.226455
$313$	26.0000	1.46961	0.734803	−	0.678280i	$-0.237274\pi$
$313$	26.0000	1.46961	0.734803	+	0.678280i	$0.237274\pi$
$314$	−10.0000	−0.564333
$315$	−2.00000	−0.112687
$316$	8.00000	0.450035
$317$	−30.0000	−1.68497	−0.842484	−	0.538721i	$-0.818908\pi$
$317$	−30.0000	−1.68497	−0.842484	+	0.538721i	$0.818908\pi$
$318$	−6.00000	−0.336463
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	−12.0000	−0.669775
$322$	0	0
$323$	−6.00000	−0.333849
$324$	1.00000	0.0555556
$325$	−4.00000	−0.221880
$326$	−10.0000	−0.553849
$327$	2.00000	0.110600
$328$	−12.0000	−0.662589
$329$	0	0
$330$	−6.00000	−0.330289
$331$	−28.0000	−1.53902	−0.769510	−	0.638635i	$-0.779499\pi$
$331$	−28.0000	−1.53902	−0.769510	+	0.638635i	$0.779499\pi$
$332$	0	0
$333$	8.00000	0.438397
$334$	24.0000	1.31322
$335$	16.0000	0.874173
$336$	2.00000	0.109109
$337$	8.00000	0.435788	0.217894	−	0.975972i	$-0.430081\pi$
$337$	8.00000	0.435788	0.217894	+	0.975972i	$0.430081\pi$
$338$	3.00000	0.163178
$339$	−6.00000	−0.325875
$340$	6.00000	0.325396
$341$	48.0000	2.59935
$342$	1.00000	0.0540738
$343$	−20.0000	−1.07990
$344$	2.00000	0.107833
$345$	0	0
$346$	6.00000	0.322562
$347$	24.0000	1.28839	0.644194	−	0.764862i	$-0.277193\pi$
$347$	24.0000	1.28839	0.644194	+	0.764862i	$0.277193\pi$
$348$	0	0
$349$	14.0000	0.749403	0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000	0.749403	0.374701	+	0.927146i	$0.377745\pi$
$350$	2.00000	0.106904
$351$	−4.00000	−0.213504
$352$	6.00000	0.319801
$353$	30.0000	1.59674	0.798369	−	0.602168i	$-0.205696\pi$
$353$	30.0000	1.59674	0.798369	+	0.602168i	$0.205696\pi$
$354$	−12.0000	−0.637793
$355$	0	0
$356$	−12.0000	−0.635999
$357$	−12.0000	−0.635107
$358$	−12.0000	−0.634220
$359$	6.00000	0.316668	0.158334	−	0.987386i	$-0.449388\pi$
$359$	6.00000	0.316668	0.158334	+	0.987386i	$0.449388\pi$
$360$	−1.00000	−0.0527046
$361$	1.00000	0.0526316
$362$	2.00000	0.105118
$363$	25.0000	1.31216
$364$	−8.00000	−0.419314
$365$	10.0000	0.523424
$366$	2.00000	0.104542
$367$	−34.0000	−1.77479	−0.887393	−	0.461014i	$-0.847486\pi$
$367$	−34.0000	−1.77479	−0.887393	+	0.461014i	$0.847486\pi$
$368$	0	0
$369$	−12.0000	−0.624695
$370$	−8.00000	−0.415900
$371$	−12.0000	−0.623009
$372$	8.00000	0.414781
$373$	−4.00000	−0.207112	−0.103556	−	0.994624i	$-0.533022\pi$
$373$	−4.00000	−0.207112	−0.103556	+	0.994624i	$0.533022\pi$
$374$	−36.0000	−1.86152
$375$	−1.00000	−0.0516398
$376$	0	0
$377$	0	0
$378$	2.00000	0.102869
$379$	−4.00000	−0.205466	−0.102733	−	0.994709i	$-0.532759\pi$
$379$	−4.00000	−0.205466	−0.102733	+	0.994709i	$0.532759\pi$
$380$	−1.00000	−0.0512989
$381$	20.0000	1.02463
$382$	6.00000	0.306987
$383$	24.0000	1.22634	0.613171	−	0.789950i	$-0.289894\pi$
$383$	24.0000	1.22634	0.613171	+	0.789950i	$0.289894\pi$
$384$	1.00000	0.0510310
$385$	−12.0000	−0.611577
$386$	20.0000	1.01797
$387$	2.00000	0.101666
$388$	8.00000	0.406138
$389$	18.0000	0.912636	0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000	0.912636	0.456318	+	0.889817i	$0.349168\pi$
$390$	4.00000	0.202548
$391$	0	0
$392$	−3.00000	−0.151523
$393$	18.0000	0.907980
$394$	6.00000	0.302276
$395$	−8.00000	−0.402524
$396$	6.00000	0.301511
$397$	14.0000	0.702640	0.351320	−	0.936255i	$-0.385733\pi$
$397$	14.0000	0.702640	0.351320	+	0.936255i	$0.385733\pi$
$398$	20.0000	1.00251
$399$	2.00000	0.100125
$400$	1.00000	0.0500000
$401$	0	0		−	1.00000i	$-0.5\pi$
$401$	0	0			1.00000i	$0.5\pi$
$402$	−16.0000	−0.798007
$403$	−32.0000	−1.59403
$404$	6.00000	0.298511
$405$	−1.00000	−0.0496904
$406$	0	0
$407$	48.0000	2.37927
$408$	−6.00000	−0.297044
$409$	14.0000	0.692255	0.346128	−	0.938187i	$-0.387496\pi$
$409$	14.0000	0.692255	0.346128	+	0.938187i	$0.387496\pi$
$410$	12.0000	0.592638
$411$	6.00000	0.295958
$412$	−16.0000	−0.788263
$413$	−24.0000	−1.18096
$414$	0	0
$415$	0	0
$416$	−4.00000	−0.196116
$417$	8.00000	0.391762
$418$	6.00000	0.293470
$419$	30.0000	1.46560	0.732798	−	0.680446i	$-0.238214\pi$
$419$	30.0000	1.46560	0.732798	+	0.680446i	$0.238214\pi$
$420$	−2.00000	−0.0975900
$421$	−10.0000	−0.487370	−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000	−0.487370	−0.243685	+	0.969854i	$0.578356\pi$
$422$	−4.00000	−0.194717
$423$	0	0
$424$	−6.00000	−0.291386
$425$	−6.00000	−0.291043
$426$	0	0
$427$	4.00000	0.193574
$428$	−12.0000	−0.580042
$429$	−24.0000	−1.15873
$430$	−2.00000	−0.0964486
$431$	12.0000	0.578020	0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000	0.578020	0.289010	+	0.957326i	$0.406674\pi$
$432$	1.00000	0.0481125
$433$	−4.00000	−0.192228	−0.0961139	−	0.995370i	$-0.530641\pi$
$433$	−4.00000	−0.192228	−0.0961139	+	0.995370i	$0.530641\pi$
$434$	16.0000	0.768025
$435$	0	0
$436$	2.00000	0.0957826
$437$	0	0
$438$	−10.0000	−0.477818
$439$	8.00000	0.381819	0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000	0.381819	0.190910	+	0.981608i	$0.438856\pi$
$440$	−6.00000	−0.286039
$441$	−3.00000	−0.142857
$442$	24.0000	1.14156
$443$	−36.0000	−1.71041	−0.855206	−	0.518289i	$-0.826569\pi$
$443$	−36.0000	−1.71041	−0.855206	+	0.518289i	$0.826569\pi$
$444$	8.00000	0.379663
$445$	12.0000	0.568855
$446$	−16.0000	−0.757622
$447$	−18.0000	−0.851371
$448$	2.00000	0.0944911
$449$	12.0000	0.566315	0.283158	−	0.959073i	$-0.408618\pi$
$449$	12.0000	0.566315	0.283158	+	0.959073i	$0.408618\pi$
$450$	1.00000	0.0471405
$451$	−72.0000	−3.39035
$452$	−6.00000	−0.282216
$453$	8.00000	0.375873
$454$	12.0000	0.563188
$455$	8.00000	0.375046
$456$	1.00000	0.0468293
$457$	−22.0000	−1.02912	−0.514558	−	0.857455i	$-0.672044\pi$
$457$	−22.0000	−1.02912	−0.514558	+	0.857455i	$0.672044\pi$
$458$	2.00000	0.0934539
$459$	−6.00000	−0.280056
$460$	0	0
$461$	−42.0000	−1.95614	−0.978068	−	0.208288i	$-0.933211\pi$
$461$	−42.0000	−1.95614	−0.978068	+	0.208288i	$0.933211\pi$
$462$	12.0000	0.558291
$463$	14.0000	0.650635	0.325318	−	0.945605i	$-0.394529\pi$
$463$	14.0000	0.650635	0.325318	+	0.945605i	$0.394529\pi$
$464$	0	0
$465$	−8.00000	−0.370991
$466$	6.00000	0.277945
$467$	36.0000	1.66588	0.832941	−	0.553362i	$-0.186655\pi$
$467$	36.0000	1.66588	0.832941	+	0.553362i	$0.186655\pi$
$468$	−4.00000	−0.184900
$469$	−32.0000	−1.47762
$470$	0	0
$471$	−10.0000	−0.460776
$472$	−12.0000	−0.552345
$473$	12.0000	0.551761
$474$	8.00000	0.367452
$475$	1.00000	0.0458831
$476$	−12.0000	−0.550019
$477$	−6.00000	−0.274721
$478$	−6.00000	−0.274434
$479$	30.0000	1.37073	0.685367	−	0.728197i	$-0.259642\pi$
$479$	30.0000	1.37073	0.685367	+	0.728197i	$0.259642\pi$
$480$	−1.00000	−0.0456435
$481$	−32.0000	−1.45907
$482$	2.00000	0.0910975
$483$	0	0
$484$	25.0000	1.13636
$485$	−8.00000	−0.363261
$486$	1.00000	0.0453609
$487$	−16.0000	−0.725029	−0.362515	−	0.931978i	$-0.618082\pi$
$487$	−16.0000	−0.725029	−0.362515	+	0.931978i	$0.618082\pi$
$488$	2.00000	0.0905357
$489$	−10.0000	−0.452216
$490$	3.00000	0.135526
$491$	−6.00000	−0.270776	−0.135388	−	0.990793i	$-0.543228\pi$
$491$	−6.00000	−0.270776	−0.135388	+	0.990793i	$0.543228\pi$
$492$	−12.0000	−0.541002
$493$	0	0
$494$	−4.00000	−0.179969
$495$	−6.00000	−0.269680
$496$	8.00000	0.359211
$497$	0	0
$498$	0	0
$499$	32.0000	1.43252	0.716258	−	0.697835i	$-0.245853\pi$
$499$	32.0000	1.43252	0.716258	+	0.697835i	$0.245853\pi$
$500$	−1.00000	−0.0447214
$501$	24.0000	1.07224
$502$	6.00000	0.267793
$503$	12.0000	0.535054	0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000	0.535054	0.267527	+	0.963550i	$0.413794\pi$
$504$	2.00000	0.0890871
$505$	−6.00000	−0.266996
$506$	0	0
$507$	3.00000	0.133235
$508$	20.0000	0.887357
$509$	−36.0000	−1.59567	−0.797836	−	0.602875i	$-0.794022\pi$
$509$	−36.0000	−1.59567	−0.797836	+	0.602875i	$0.794022\pi$
$510$	6.00000	0.265684
$511$	−20.0000	−0.884748
$512$	1.00000	0.0441942
$513$	1.00000	0.0441511
$514$	−6.00000	−0.264649
$515$	16.0000	0.705044
$516$	2.00000	0.0880451
$517$	0	0
$518$	16.0000	0.703000
$519$	6.00000	0.263371
$520$	4.00000	0.175412
$521$	−24.0000	−1.05146	−0.525730	−	0.850652i	$-0.676208\pi$
$521$	−24.0000	−1.05146	−0.525730	+	0.850652i	$0.676208\pi$
$522$	0	0
$523$	−4.00000	−0.174908	−0.0874539	−	0.996169i	$-0.527873\pi$
$523$	−4.00000	−0.174908	−0.0874539	+	0.996169i	$0.527873\pi$
$524$	18.0000	0.786334
$525$	2.00000	0.0872872
$526$	−12.0000	−0.523225
$527$	−48.0000	−2.09091
$528$	6.00000	0.261116
$529$	−23.0000	−1.00000
$530$	6.00000	0.260623
$531$	−12.0000	−0.520756
$532$	2.00000	0.0867110
$533$	48.0000	2.07911
$534$	−12.0000	−0.519291
$535$	12.0000	0.518805
$536$	−16.0000	−0.691095
$537$	−12.0000	−0.517838
$538$	24.0000	1.03471
$539$	−18.0000	−0.775315
$540$	−1.00000	−0.0430331
$541$	−10.0000	−0.429934	−0.214967	−	0.976621i	$-0.568964\pi$
$541$	−10.0000	−0.429934	−0.214967	+	0.976621i	$0.568964\pi$
$542$	20.0000	0.859074
$543$	2.00000	0.0858282
$544$	−6.00000	−0.257248
$545$	−2.00000	−0.0856706
$546$	−8.00000	−0.342368
$547$	−16.0000	−0.684111	−0.342055	−	0.939680i	$-0.611123\pi$
$547$	−16.0000	−0.684111	−0.342055	+	0.939680i	$0.611123\pi$
$548$	6.00000	0.256307
$549$	2.00000	0.0853579
$550$	6.00000	0.255841
$551$	0	0
$552$	0	0
$553$	16.0000	0.680389
$554$	−10.0000	−0.424859
$555$	−8.00000	−0.339581
$556$	8.00000	0.339276
$557$	−30.0000	−1.27114	−0.635570	−	0.772043i	$-0.719235\pi$
$557$	−30.0000	−1.27114	−0.635570	+	0.772043i	$0.719235\pi$
$558$	8.00000	0.338667
$559$	−8.00000	−0.338364
$560$	−2.00000	−0.0845154
$561$	−36.0000	−1.51992
$562$	24.0000	1.01238
$563$	12.0000	0.505740	0.252870	−	0.967500i	$-0.418626\pi$
$563$	12.0000	0.505740	0.252870	+	0.967500i	$0.418626\pi$
$564$	0	0
$565$	6.00000	0.252422
$566$	14.0000	0.588464
$567$	2.00000	0.0839921
$568$	0	0
$569$	−36.0000	−1.50920	−0.754599	−	0.656186i	$-0.772169\pi$
$569$	−36.0000	−1.50920	−0.754599	+	0.656186i	$0.772169\pi$
$570$	−1.00000	−0.0418854
$571$	−16.0000	−0.669579	−0.334790	−	0.942293i	$-0.608665\pi$
$571$	−16.0000	−0.669579	−0.334790	+	0.942293i	$0.608665\pi$
$572$	−24.0000	−1.00349
$573$	6.00000	0.250654
$574$	−24.0000	−1.00174
$575$	0	0
$576$	1.00000	0.0416667
$577$	2.00000	0.0832611	0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000	0.0832611	0.0416305	+	0.999133i	$0.486745\pi$
$578$	19.0000	0.790296
$579$	20.0000	0.831172
$580$	0	0
$581$	0	0
$582$	8.00000	0.331611
$583$	−36.0000	−1.49097
$584$	−10.0000	−0.413803
$585$	4.00000	0.165380
$586$	−18.0000	−0.743573
$587$	−12.0000	−0.495293	−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000	−0.495293	−0.247647	+	0.968850i	$0.579657\pi$
$588$	−3.00000	−0.123718
$589$	8.00000	0.329634
$590$	12.0000	0.494032
$591$	6.00000	0.246807
$592$	8.00000	0.328798
$593$	6.00000	0.246390	0.123195	−	0.992382i	$-0.460686\pi$
$593$	6.00000	0.246390	0.123195	+	0.992382i	$0.460686\pi$
$594$	6.00000	0.246183
$595$	12.0000	0.491952
$596$	−18.0000	−0.737309
$597$	20.0000	0.818546
$598$	0	0
$599$	−12.0000	−0.490307	−0.245153	−	0.969484i	$-0.578838\pi$
$599$	−12.0000	−0.490307	−0.245153	+	0.969484i	$0.578838\pi$
$600$	1.00000	0.0408248
$601$	−34.0000	−1.38689	−0.693444	−	0.720510i	$-0.743908\pi$
$601$	−34.0000	−1.38689	−0.693444	+	0.720510i	$0.743908\pi$
$602$	4.00000	0.163028
$603$	−16.0000	−0.651570
$604$	8.00000	0.325515
$605$	−25.0000	−1.01639
$606$	6.00000	0.243733
$607$	8.00000	0.324710	0.162355	−	0.986732i	$-0.448091\pi$
$607$	8.00000	0.324710	0.162355	+	0.986732i	$0.448091\pi$
$608$	1.00000	0.0405554
$609$	0	0
$610$	−2.00000	−0.0809776
$611$	0	0
$612$	−6.00000	−0.242536
$613$	38.0000	1.53481	0.767403	−	0.641165i	$-0.221549\pi$
$613$	38.0000	1.53481	0.767403	+	0.641165i	$0.221549\pi$
$614$	−16.0000	−0.645707
$615$	12.0000	0.483887
$616$	12.0000	0.483494
$617$	−30.0000	−1.20775	−0.603877	−	0.797077i	$-0.706378\pi$
$617$	−30.0000	−1.20775	−0.603877	+	0.797077i	$0.706378\pi$
$618$	−16.0000	−0.643614
$619$	−16.0000	−0.643094	−0.321547	−	0.946894i	$-0.604203\pi$
$619$	−16.0000	−0.643094	−0.321547	+	0.946894i	$0.604203\pi$
$620$	−8.00000	−0.321288
$621$	0	0
$622$	−18.0000	−0.721734
$623$	−24.0000	−0.961540
$624$	−4.00000	−0.160128
$625$	1.00000	0.0400000
$626$	26.0000	1.03917
$627$	6.00000	0.239617
$628$	−10.0000	−0.399043
$629$	−48.0000	−1.91389
$630$	−2.00000	−0.0796819
$631$	8.00000	0.318475	0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000	0.318475	0.159237	+	0.987240i	$0.449096\pi$
$632$	8.00000	0.318223
$633$	−4.00000	−0.158986
$634$	−30.0000	−1.19145
$635$	−20.0000	−0.793676
$636$	−6.00000	−0.237915
$637$	12.0000	0.475457
$638$	0	0
$639$	0	0
$640$	−1.00000	−0.0395285
$641$	12.0000	0.473972	0.236986	−	0.971513i	$-0.423841\pi$
$641$	12.0000	0.473972	0.236986	+	0.971513i	$0.423841\pi$
$642$	−12.0000	−0.473602
$643$	14.0000	0.552106	0.276053	−	0.961142i	$-0.410973\pi$
$643$	14.0000	0.552106	0.276053	+	0.961142i	$0.410973\pi$
$644$	0	0
$645$	−2.00000	−0.0787499
$646$	−6.00000	−0.236067
$647$	−12.0000	−0.471769	−0.235884	−	0.971781i	$-0.575799\pi$
$647$	−12.0000	−0.471769	−0.235884	+	0.971781i	$0.575799\pi$
$648$	1.00000	0.0392837
$649$	−72.0000	−2.82625
$650$	−4.00000	−0.156893
$651$	16.0000	0.627089
$652$	−10.0000	−0.391630
$653$	30.0000	1.17399	0.586995	−	0.809590i	$-0.300311\pi$
$653$	30.0000	1.17399	0.586995	+	0.809590i	$0.300311\pi$
$654$	2.00000	0.0782062
$655$	−18.0000	−0.703318
$656$	−12.0000	−0.468521
$657$	−10.0000	−0.390137
$658$	0	0
$659$	0	0		−	1.00000i	$-0.5\pi$
$659$	0	0			1.00000i	$0.5\pi$
$660$	−6.00000	−0.233550
$661$	50.0000	1.94477	0.972387	−	0.233373i	$-0.0749763\pi$
$661$	50.0000	1.94477	0.972387	+	0.233373i	$0.0749763\pi$
$662$	−28.0000	−1.08825
$663$	24.0000	0.932083
$664$	0	0
$665$	−2.00000	−0.0775567
$666$	8.00000	0.309994
$667$	0	0
$668$	24.0000	0.928588
$669$	−16.0000	−0.618596
$670$	16.0000	0.618134
$671$	12.0000	0.463255
$672$	2.00000	0.0771517
$673$	8.00000	0.308377	0.154189	−	0.988041i	$-0.450724\pi$
$673$	8.00000	0.308377	0.154189	+	0.988041i	$0.450724\pi$
$674$	8.00000	0.308148
$675$	1.00000	0.0384900
$676$	3.00000	0.115385
$677$	42.0000	1.61419	0.807096	−	0.590421i	$-0.201038\pi$
$677$	42.0000	1.61419	0.807096	+	0.590421i	$0.201038\pi$
$678$	−6.00000	−0.230429
$679$	16.0000	0.614024
$680$	6.00000	0.230089
$681$	12.0000	0.459841
$682$	48.0000	1.83801
$683$	12.0000	0.459167	0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000	0.459167	0.229584	+	0.973289i	$0.426264\pi$
$684$	1.00000	0.0382360
$685$	−6.00000	−0.229248
$686$	−20.0000	−0.763604
$687$	2.00000	0.0763048
$688$	2.00000	0.0762493
$689$	24.0000	0.914327
$690$	0	0
$691$	8.00000	0.304334	0.152167	−	0.988355i	$-0.451375\pi$
$691$	8.00000	0.304334	0.152167	+	0.988355i	$0.451375\pi$
$692$	6.00000	0.228086
$693$	12.0000	0.455842
$694$	24.0000	0.911028
$695$	−8.00000	−0.303457
$696$	0	0
$697$	72.0000	2.72719
$698$	14.0000	0.529908
$699$	6.00000	0.226941
$700$	2.00000	0.0755929
$701$	30.0000	1.13308	0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000	1.13308	0.566542	+	0.824033i	$0.308281\pi$
$702$	−4.00000	−0.150970
$703$	8.00000	0.301726
$704$	6.00000	0.226134
$705$	0	0
$706$	30.0000	1.12906
$707$	12.0000	0.451306
$708$	−12.0000	−0.450988
$709$	−46.0000	−1.72757	−0.863783	−	0.503864i	$-0.831911\pi$
$709$	−46.0000	−1.72757	−0.863783	+	0.503864i	$0.831911\pi$
$710$	0	0
$711$	8.00000	0.300023
$712$	−12.0000	−0.449719
$713$	0	0
$714$	−12.0000	−0.449089
$715$	24.0000	0.897549
$716$	−12.0000	−0.448461
$717$	−6.00000	−0.224074
$718$	6.00000	0.223918
$719$	18.0000	0.671287	0.335643	−	0.941989i	$-0.391046\pi$
$719$	18.0000	0.671287	0.335643	+	0.941989i	$0.391046\pi$
$720$	−1.00000	−0.0372678
$721$	−32.0000	−1.19174
$722$	1.00000	0.0372161
$723$	2.00000	0.0743808
$724$	2.00000	0.0743294
$725$	0	0
$726$	25.0000	0.927837
$727$	−10.0000	−0.370879	−0.185440	−	0.982656i	$-0.559371\pi$
$727$	−10.0000	−0.370879	−0.185440	+	0.982656i	$0.559371\pi$
$728$	−8.00000	−0.296500
$729$	1.00000	0.0370370
$730$	10.0000	0.370117
$731$	−12.0000	−0.443836
$732$	2.00000	0.0739221
$733$	−22.0000	−0.812589	−0.406294	−	0.913742i	$-0.633179\pi$
$733$	−22.0000	−0.812589	−0.406294	+	0.913742i	$0.633179\pi$
$734$	−34.0000	−1.25496
$735$	3.00000	0.110657
$736$	0	0
$737$	−96.0000	−3.53621
$738$	−12.0000	−0.441726
$739$	44.0000	1.61857	0.809283	−	0.587419i	$-0.199856\pi$
$739$	44.0000	1.61857	0.809283	+	0.587419i	$0.199856\pi$
$740$	−8.00000	−0.294086
$741$	−4.00000	−0.146944
$742$	−12.0000	−0.440534
$743$	24.0000	0.880475	0.440237	−	0.897881i	$-0.354894\pi$
$743$	24.0000	0.880475	0.440237	+	0.897881i	$0.354894\pi$
$744$	8.00000	0.293294
$745$	18.0000	0.659469
$746$	−4.00000	−0.146450
$747$	0	0
$748$	−36.0000	−1.31629
$749$	−24.0000	−0.876941
$750$	−1.00000	−0.0365148
$751$	−16.0000	−0.583848	−0.291924	−	0.956441i	$-0.594295\pi$
$751$	−16.0000	−0.583848	−0.291924	+	0.956441i	$0.594295\pi$
$752$	0	0
$753$	6.00000	0.218652
$754$	0	0
$755$	−8.00000	−0.291150
$756$	2.00000	0.0727393
$757$	−22.0000	−0.799604	−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000	−0.799604	−0.399802	+	0.916602i	$0.630921\pi$
$758$	−4.00000	−0.145287
$759$	0	0
$760$	−1.00000	−0.0362738
$761$	6.00000	0.217500	0.108750	−	0.994069i	$-0.465315\pi$
$761$	6.00000	0.217500	0.108750	+	0.994069i	$0.465315\pi$
$762$	20.0000	0.724524
$763$	4.00000	0.144810
$764$	6.00000	0.217072
$765$	6.00000	0.216930
$766$	24.0000	0.867155
$767$	48.0000	1.73318
$768$	1.00000	0.0360844
$769$	50.0000	1.80305	0.901523	−	0.432731i	$-0.142450\pi$
$769$	50.0000	1.80305	0.901523	+	0.432731i	$0.142450\pi$
$770$	−12.0000	−0.432450
$771$	−6.00000	−0.216085
$772$	20.0000	0.719816
$773$	−30.0000	−1.07903	−0.539513	−	0.841978i	$-0.681391\pi$
$773$	−30.0000	−1.07903	−0.539513	+	0.841978i	$0.681391\pi$
$774$	2.00000	0.0718885
$775$	8.00000	0.287368
$776$	8.00000	0.287183
$777$	16.0000	0.573997
$778$	18.0000	0.645331
$779$	−12.0000	−0.429945
$780$	4.00000	0.143223
$781$	0	0
$782$	0	0
$783$	0	0
$784$	−3.00000	−0.107143
$785$	10.0000	0.356915
$786$	18.0000	0.642039
$787$	−28.0000	−0.998092	−0.499046	−	0.866575i	$-0.666316\pi$
$787$	−28.0000	−0.998092	−0.499046	+	0.866575i	$0.666316\pi$
$788$	6.00000	0.213741
$789$	−12.0000	−0.427211
$790$	−8.00000	−0.284627
$791$	−12.0000	−0.426671
$792$	6.00000	0.213201
$793$	−8.00000	−0.284088
$794$	14.0000	0.496841
$795$	6.00000	0.212798
$796$	20.0000	0.708881
$797$	−42.0000	−1.48772	−0.743858	−	0.668338i	$-0.767006\pi$
$797$	−42.0000	−1.48772	−0.743858	+	0.668338i	$0.767006\pi$
$798$	2.00000	0.0707992
$799$	0	0
$800$	1.00000	0.0353553
$801$	−12.0000	−0.423999
$802$	0	0
$803$	−60.0000	−2.11735
$804$	−16.0000	−0.564276
$805$	0	0
$806$	−32.0000	−1.12715
$807$	24.0000	0.844840
$808$	6.00000	0.211079
$809$	−30.0000	−1.05474	−0.527372	−	0.849635i	$-0.676823\pi$
$809$	−30.0000	−1.05474	−0.527372	+	0.849635i	$0.676823\pi$
$810$	−1.00000	−0.0351364
$811$	20.0000	0.702295	0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000	0.702295	0.351147	+	0.936320i	$0.385792\pi$
$812$	0	0
$813$	20.0000	0.701431
$814$	48.0000	1.68240
$815$	10.0000	0.350285
$816$	−6.00000	−0.210042
$817$	2.00000	0.0699711
$818$	14.0000	0.489499
$819$	−8.00000	−0.279543
$820$	12.0000	0.419058
$821$	30.0000	1.04701	0.523504	−	0.852023i	$-0.324625\pi$
$821$	30.0000	1.04701	0.523504	+	0.852023i	$0.324625\pi$
$822$	6.00000	0.209274
$823$	14.0000	0.488009	0.244005	−	0.969774i	$-0.421539\pi$
$823$	14.0000	0.488009	0.244005	+	0.969774i	$0.421539\pi$
$824$	−16.0000	−0.557386
$825$	6.00000	0.208893
$826$	−24.0000	−0.835067
$827$	12.0000	0.417281	0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000	0.417281	0.208640	+	0.977992i	$0.433096\pi$
$828$	0	0
$829$	2.00000	0.0694629	0.0347314	−	0.999397i	$-0.488942\pi$
$829$	2.00000	0.0694629	0.0347314	+	0.999397i	$0.488942\pi$
$830$	0	0
$831$	−10.0000	−0.346896
$832$	−4.00000	−0.138675
$833$	18.0000	0.623663
$834$	8.00000	0.277017
$835$	−24.0000	−0.830554
$836$	6.00000	0.207514
$837$	8.00000	0.276520
$838$	30.0000	1.03633
$839$	24.0000	0.828572	0.414286	−	0.910147i	$-0.364031\pi$
$839$	24.0000	0.828572	0.414286	+	0.910147i	$0.364031\pi$
$840$	−2.00000	−0.0690066
$841$	−29.0000	−1.00000
$842$	−10.0000	−0.344623
$843$	24.0000	0.826604
$844$	−4.00000	−0.137686
$845$	−3.00000	−0.103203
$846$	0	0
$847$	50.0000	1.71802
$848$	−6.00000	−0.206041
$849$	14.0000	0.480479
$850$	−6.00000	−0.205798
$851$	0	0
$852$	0	0
$853$	−22.0000	−0.753266	−0.376633	−	0.926363i	$-0.622918\pi$
$853$	−22.0000	−0.753266	−0.376633	+	0.926363i	$0.622918\pi$
$854$	4.00000	0.136877
$855$	−1.00000	−0.0341993
$856$	−12.0000	−0.410152
$857$	6.00000	0.204956	0.102478	−	0.994735i	$-0.467323\pi$
$857$	6.00000	0.204956	0.102478	+	0.994735i	$0.467323\pi$
$858$	−24.0000	−0.819346
$859$	−52.0000	−1.77422	−0.887109	−	0.461561i	$-0.847290\pi$
$859$	−52.0000	−1.77422	−0.887109	+	0.461561i	$0.847290\pi$
$860$	−2.00000	−0.0681994
$861$	−24.0000	−0.817918
$862$	12.0000	0.408722
$863$	24.0000	0.816970	0.408485	−	0.912765i	$-0.366057\pi$
$863$	24.0000	0.816970	0.408485	+	0.912765i	$0.366057\pi$
$864$	1.00000	0.0340207
$865$	−6.00000	−0.204006
$866$	−4.00000	−0.135926
$867$	19.0000	0.645274
$868$	16.0000	0.543075
$869$	48.0000	1.62829
$870$	0	0
$871$	64.0000	2.16856
$872$	2.00000	0.0677285
$873$	8.00000	0.270759
$874$	0	0
$875$	−2.00000	−0.0676123
$876$	−10.0000	−0.337869
$877$	20.0000	0.675352	0.337676	−	0.941262i	$-0.390359\pi$
$877$	20.0000	0.675352	0.337676	+	0.941262i	$0.390359\pi$
$878$	8.00000	0.269987
$879$	−18.0000	−0.607125
$880$	−6.00000	−0.202260
$881$	30.0000	1.01073	0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000	1.01073	0.505363	+	0.862907i	$0.331359\pi$
$882$	−3.00000	−0.101015
$883$	−34.0000	−1.14419	−0.572096	−	0.820187i	$-0.693869\pi$
$883$	−34.0000	−1.14419	−0.572096	+	0.820187i	$0.693869\pi$
$884$	24.0000	0.807207
$885$	12.0000	0.403376
$886$	−36.0000	−1.20944
$887$	0	0		−	1.00000i	$-0.5\pi$
$887$	0	0			1.00000i	$0.5\pi$
$888$	8.00000	0.268462
$889$	40.0000	1.34156
$890$	12.0000	0.402241
$891$	6.00000	0.201008
$892$	−16.0000	−0.535720
$893$	0	0
$894$	−18.0000	−0.602010
$895$	12.0000	0.401116
$896$	2.00000	0.0668153
$897$	0	0
$898$	12.0000	0.400445
$899$	0	0
$900$	1.00000	0.0333333
$901$	36.0000	1.19933
$902$	−72.0000	−2.39734
$903$	4.00000	0.133112
$904$	−6.00000	−0.199557
$905$	−2.00000	−0.0664822
$906$	8.00000	0.265782
$907$	44.0000	1.46100	0.730498	−	0.682915i	$-0.239288\pi$
$907$	44.0000	1.46100	0.730498	+	0.682915i	$0.239288\pi$
$908$	12.0000	0.398234
$909$	6.00000	0.199007
$910$	8.00000	0.265197
$911$	48.0000	1.59031	0.795155	−	0.606406i	$-0.207389\pi$
$911$	48.0000	1.59031	0.795155	+	0.606406i	$0.207389\pi$
$912$	1.00000	0.0331133
$913$	0	0
$914$	−22.0000	−0.727695
$915$	−2.00000	−0.0661180
$916$	2.00000	0.0660819
$917$	36.0000	1.18882
$918$	−6.00000	−0.198030
$919$	56.0000	1.84727	0.923635	−	0.383274i	$-0.125203\pi$
$919$	56.0000	1.84727	0.923635	+	0.383274i	$0.125203\pi$
$920$	0	0
$921$	−16.0000	−0.527218
$922$	−42.0000	−1.38320
$923$	0	0
$924$	12.0000	0.394771
$925$	8.00000	0.263038
$926$	14.0000	0.460069
$927$	−16.0000	−0.525509
$928$	0	0
$929$	18.0000	0.590561	0.295280	−	0.955411i	$-0.404587\pi$
$929$	18.0000	0.590561	0.295280	+	0.955411i	$0.404587\pi$
$930$	−8.00000	−0.262330
$931$	−3.00000	−0.0983210
$932$	6.00000	0.196537
$933$	−18.0000	−0.589294
$934$	36.0000	1.17796
$935$	36.0000	1.17733
$936$	−4.00000	−0.130744
$937$	−10.0000	−0.326686	−0.163343	−	0.986569i	$-0.552228\pi$
$937$	−10.0000	−0.326686	−0.163343	+	0.986569i	$0.552228\pi$
$938$	−32.0000	−1.04484
$939$	26.0000	0.848478
$940$	0	0
$941$	−24.0000	−0.782378	−0.391189	−	0.920310i	$-0.627936\pi$
$941$	−24.0000	−0.782378	−0.391189	+	0.920310i	$0.627936\pi$
$942$	−10.0000	−0.325818
$943$	0	0
$944$	−12.0000	−0.390567
$945$	−2.00000	−0.0650600
$946$	12.0000	0.390154
$947$	0	0		−	1.00000i	$-0.5\pi$
$947$	0	0			1.00000i	$0.5\pi$
$948$	8.00000	0.259828
$949$	40.0000	1.29845
$950$	1.00000	0.0324443
$951$	−30.0000	−0.972817
$952$	−12.0000	−0.388922
$953$	18.0000	0.583077	0.291539	−	0.956559i	$-0.405833\pi$
$953$	18.0000	0.583077	0.291539	+	0.956559i	$0.405833\pi$
$954$	−6.00000	−0.194257
$955$	−6.00000	−0.194155
$956$	−6.00000	−0.194054
$957$	0	0
$958$	30.0000	0.969256
$959$	12.0000	0.387500
$960$	−1.00000	−0.0322749
$961$	33.0000	1.06452
$962$	−32.0000	−1.03172
$963$	−12.0000	−0.386695
$964$	2.00000	0.0644157
$965$	−20.0000	−0.643823
$966$	0	0
$967$	−34.0000	−1.09337	−0.546683	−	0.837340i	$-0.684110\pi$
$967$	−34.0000	−1.09337	−0.546683	+	0.837340i	$0.684110\pi$
$968$	25.0000	0.803530
$969$	−6.00000	−0.192748
$970$	−8.00000	−0.256865
$971$	−24.0000	−0.770197	−0.385098	−	0.922876i	$-0.625832\pi$
$971$	−24.0000	−0.770197	−0.385098	+	0.922876i	$0.625832\pi$
$972$	1.00000	0.0320750
$973$	16.0000	0.512936
$974$	−16.0000	−0.512673
$975$	−4.00000	−0.128103
$976$	2.00000	0.0640184
$977$	30.0000	0.959785	0.479893	−	0.877327i	$-0.340676\pi$
$977$	30.0000	0.959785	0.479893	+	0.877327i	$0.340676\pi$
$978$	−10.0000	−0.319765
$979$	−72.0000	−2.30113
$980$	3.00000	0.0958315
$981$	2.00000	0.0638551
$982$	−6.00000	−0.191468
$983$	0	0		−	1.00000i	$-0.5\pi$
$983$	0	0			1.00000i	$0.5\pi$
$984$	−12.0000	−0.382546
$985$	−6.00000	−0.191176
$986$	0	0
$987$	0	0
$988$	−4.00000	−0.127257
$989$	0	0
$990$	−6.00000	−0.190693
$991$	32.0000	1.01651	0.508257	−	0.861206i	$-0.330290\pi$
$991$	32.0000	1.01651	0.508257	+	0.861206i	$0.330290\pi$
$992$	8.00000	0.254000
$993$	−28.0000	−0.888553
$994$	0	0
$995$	−20.0000	−0.634043
$996$	0	0
$997$	−10.0000	−0.316703	−0.158352	−	0.987383i	$-0.550618\pi$
$997$	−10.0000	−0.316703	−0.158352	+	0.987383i	$0.550618\pi$
$998$	32.0000	1.01294
$999$	8.00000	0.253109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.a.k.1.1	✓	1
3.2	odd	2		1710.2.a.j.1.1		1
4.3	odd	2		4560.2.a.b.1.1		1
5.2	odd	4		2850.2.d.t.799.2		2
5.3	odd	4		2850.2.d.t.799.1		2
5.4	even	2		2850.2.a.c.1.1		1
15.14	odd	2		8550.2.a.v.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.a.k.1.1	✓	1	1.1	even	1	trivial
1710.2.a.j.1.1		1	3.2	odd	2
2850.2.a.c.1.1		1	5.4	even	2
2850.2.d.t.799.1		2	5.3	odd	4
2850.2.d.t.799.2		2	5.2	odd	4
4560.2.a.b.1.1		1	4.3	odd	2
8550.2.a.v.1.1		1	15.14	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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