LMFDB - Embedded newform 570.2.a.j.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)

$f(q)$

$=$

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

\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -4.00000 q^{11} +1.00000 q^{12} +6.00000 q^{13} +2.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} +4.00000 q^{17} +1.00000 q^{18} +1.00000 q^{19} -1.00000 q^{20} +2.00000 q^{21} -4.00000 q^{22} +1.00000 q^{24} +1.00000 q^{25} +6.00000 q^{26} +1.00000 q^{27} +2.00000 q^{28} -10.0000 q^{29} -1.00000 q^{30} -2.00000 q^{31} +1.00000 q^{32} -4.00000 q^{33} +4.00000 q^{34} -2.00000 q^{35} +1.00000 q^{36} -2.00000 q^{37} +1.00000 q^{38} +6.00000 q^{39} -1.00000 q^{40} +8.00000 q^{41} +2.00000 q^{42} -8.00000 q^{43} -4.00000 q^{44} -1.00000 q^{45} +1.00000 q^{48} -3.00000 q^{49} +1.00000 q^{50} +4.00000 q^{51} +6.00000 q^{52} -6.00000 q^{53} +1.00000 q^{54} +4.00000 q^{55} +2.00000 q^{56} +1.00000 q^{57} -10.0000 q^{58} -2.00000 q^{59} -1.00000 q^{60} +2.00000 q^{61} -2.00000 q^{62} +2.00000 q^{63} +1.00000 q^{64} -6.00000 q^{65} -4.00000 q^{66} +4.00000 q^{67} +4.00000 q^{68} -2.00000 q^{70} +1.00000 q^{72} -10.0000 q^{73} -2.00000 q^{74} +1.00000 q^{75} +1.00000 q^{76} -8.00000 q^{77} +6.00000 q^{78} -2.00000 q^{79} -1.00000 q^{80} +1.00000 q^{81} +8.00000 q^{82} -10.0000 q^{83} +2.00000 q^{84} -4.00000 q^{85} -8.00000 q^{86} -10.0000 q^{87} -4.00000 q^{88} -12.0000 q^{89} -1.00000 q^{90} +12.0000 q^{91} -2.00000 q^{93} -1.00000 q^{95} +1.00000 q^{96} -2.00000 q^{97} -3.00000 q^{98} -4.00000 q^{99} +O(q^{100})\)

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 $

$2$	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
$11$	−4.00000	−1.20605	−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000	−1.20605	−0.603023	+	0.797724i	$0.706037\pi$
$12$	1.00000	0.288675
$13$	6.00000	1.66410	0.832050	−	0.554700i	$-0.187167\pi$
$13$	6.00000	1.66410	0.832050	+	0.554700i	$0.187167\pi$
$14$	2.00000	0.534522
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	4.00000	0.970143	0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000	0.970143	0.485071	+	0.874475i	$0.338794\pi$
$18$	1.00000	0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−1.00000	−0.223607
$21$	2.00000	0.436436
$22$	−4.00000	−0.852803
$23$	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
$26$	6.00000	1.17670
$27$	1.00000	0.192450
$28$	2.00000	0.377964
$29$	−10.0000	−1.85695	−0.928477	−	0.371391i	$-0.878881\pi$
$29$	−10.0000	−1.85695	−0.928477	+	0.371391i	$0.878881\pi$
$30$	−1.00000	−0.182574
$31$	−2.00000	−0.359211	−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000	−0.359211	−0.179605	+	0.983739i	$0.557482\pi$
$32$	1.00000	0.176777
$33$	−4.00000	−0.696311
$34$	4.00000	0.685994
$35$	−2.00000	−0.338062
$36$	1.00000	0.166667
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	1.00000	0.162221
$39$	6.00000	0.960769
$40$	−1.00000	−0.158114
$41$	8.00000	1.24939	0.624695	−	0.780869i	$-0.285223\pi$
$41$	8.00000	1.24939	0.624695	+	0.780869i	$0.285223\pi$
$42$	2.00000	0.308607
$43$	−8.00000	−1.21999	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	−4.00000	−0.603023
$45$	−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
$51$	4.00000	0.560112
$52$	6.00000	0.832050
$53$	−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
$55$	4.00000	0.539360
$56$	2.00000	0.267261
$57$	1.00000	0.132453
$58$	−10.0000	−1.31306
$59$	−2.00000	−0.260378	−0.130189	−	0.991489i	$-0.541558\pi$
$59$	−2.00000	−0.260378	−0.130189	+	0.991489i	$0.541558\pi$
$60$	−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	$0.459132\pi$
$62$	−2.00000	−0.254000
$63$	2.00000	0.251976
$64$	1.00000	0.125000
$65$	−6.00000	−0.744208
$66$	−4.00000	−0.492366
$67$	4.00000	0.488678	0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000	0.488678	0.244339	+	0.969690i	$0.421429\pi$
$68$	4.00000	0.485071
$69$	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	$0.698986\pi$
$74$	−2.00000	−0.232495
$75$	1.00000	0.115470
$76$	1.00000	0.114708
$77$	−8.00000	−0.911685
$78$	6.00000	0.679366
$79$	−2.00000	−0.225018	−0.112509	−	0.993651i	$-0.535889\pi$
$79$	−2.00000	−0.225018	−0.112509	+	0.993651i	$0.535889\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	8.00000	0.883452
$83$	−10.0000	−1.09764	−0.548821	−	0.835940i	$-0.684923\pi$
$83$	−10.0000	−1.09764	−0.548821	+	0.835940i	$0.684923\pi$
$84$	2.00000	0.218218
$85$	−4.00000	−0.433861
$86$	−8.00000	−0.862662
$87$	−10.0000	−1.07211
$88$	−4.00000	−0.426401
$89$	−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
$91$	12.0000	1.25794
$92$	0	0
$93$	−2.00000	−0.207390
$94$	0	0
$95$	−1.00000	−0.102598
$96$	1.00000	0.102062
$97$	−2.00000	−0.203069	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000	−0.203069	−0.101535	+	0.994832i	$0.532375\pi$
$98$	−3.00000	−0.303046
$99$	−4.00000	−0.402015
$100$	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	$0.403510\pi$
$102$	4.00000	0.396059
$103$	4.00000	0.394132	0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000	0.394132	0.197066	+	0.980390i	$0.436859\pi$
$104$	6.00000	0.588348
$105$	−2.00000	−0.195180
$106$	−6.00000	−0.582772
$107$	8.00000	0.773389	0.386695	−	0.922208i	$-0.373617\pi$
$107$	8.00000	0.773389	0.386695	+	0.922208i	$0.373617\pi$
$108$	1.00000	0.0962250
$109$	12.0000	1.14939	0.574696	−	0.818367i	$-0.305120\pi$
$109$	12.0000	1.14939	0.574696	+	0.818367i	$0.305120\pi$
$110$	4.00000	0.381385
$111$	−2.00000	−0.189832
$112$	2.00000	0.188982
$113$	14.0000	1.31701	0.658505	−	0.752577i	$-0.271189\pi$
$113$	14.0000	1.31701	0.658505	+	0.752577i	$0.271189\pi$
$114$	1.00000	0.0936586
$115$	0	0
$116$	−10.0000	−0.928477
$117$	6.00000	0.554700
$118$	−2.00000	−0.184115
$119$	8.00000	0.733359
$120$	−1.00000	−0.0912871
$121$	5.00000	0.454545
$122$	2.00000	0.181071
$123$	8.00000	0.721336
$124$	−2.00000	−0.179605
$125$	−1.00000	−0.0894427
$126$	2.00000	0.178174
$127$	−20.0000	−1.77471	−0.887357	−	0.461084i	$-0.847461\pi$
$127$	−20.0000	−1.77471	−0.887357	+	0.461084i	$0.847461\pi$
$128$	1.00000	0.0883883
$129$	−8.00000	−0.704361
$130$	−6.00000	−0.526235
$131$	−12.0000	−1.04844	−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000	−1.04844	−0.524222	+	0.851581i	$0.675644\pi$
$132$	−4.00000	−0.348155
$133$	2.00000	0.173422
$134$	4.00000	0.345547
$135$	−1.00000	−0.0860663
$136$	4.00000	0.342997
$137$	16.0000	1.36697	0.683486	−	0.729964i	$-0.260463\pi$
$137$	16.0000	1.36697	0.683486	+	0.729964i	$0.260463\pi$
$138$	0	0
$139$	−12.0000	−1.01783	−0.508913	−	0.860818i	$-0.669953\pi$
$139$	−12.0000	−1.01783	−0.508913	+	0.860818i	$0.669953\pi$
$140$	−2.00000	−0.169031
$141$	0	0
$142$	0	0
$143$	−24.0000	−2.00698
$144$	1.00000	0.0833333
$145$	10.0000	0.830455
$146$	−10.0000	−0.827606
$147$	−3.00000	−0.247436
$148$	−2.00000	−0.164399
$149$	−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
$151$	18.0000	1.46482	0.732410	−	0.680864i	$-0.238396\pi$
$151$	18.0000	1.46482	0.732410	+	0.680864i	$0.238396\pi$
$152$	1.00000	0.0811107
$153$	4.00000	0.323381
$154$	−8.00000	−0.644658
$155$	2.00000	0.160644
$156$	6.00000	0.480384
$157$	20.0000	1.59617	0.798087	−	0.602542i	$-0.205846\pi$
$157$	20.0000	1.59617	0.798087	+	0.602542i	$0.205846\pi$
$158$	−2.00000	−0.159111
$159$	−6.00000	−0.475831
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	1.00000	0.0785674
$163$	−20.0000	−1.56652	−0.783260	−	0.621694i	$-0.786445\pi$
$163$	−20.0000	−1.56652	−0.783260	+	0.621694i	$0.786445\pi$
$164$	8.00000	0.624695
$165$	4.00000	0.311400
$166$	−10.0000	−0.776151
$167$	−16.0000	−1.23812	−0.619059	−	0.785345i	$-0.712486\pi$
$167$	−16.0000	−1.23812	−0.619059	+	0.785345i	$0.712486\pi$
$168$	2.00000	0.154303
$169$	23.0000	1.76923
$170$	−4.00000	−0.306786
$171$	1.00000	0.0764719
$172$	−8.00000	−0.609994
$173$	−14.0000	−1.06440	−0.532200	−	0.846619i	$-0.678635\pi$
$173$	−14.0000	−1.06440	−0.532200	+	0.846619i	$0.678635\pi$
$174$	−10.0000	−0.758098
$175$	2.00000	0.151186
$176$	−4.00000	−0.301511
$177$	−2.00000	−0.150329
$178$	−12.0000	−0.899438
$179$	−22.0000	−1.64436	−0.822179	−	0.569230i	$-0.807242\pi$
$179$	−22.0000	−1.64436	−0.822179	+	0.569230i	$0.807242\pi$
$180$	−1.00000	−0.0745356
$181$	12.0000	0.891953	0.445976	−	0.895045i	$-0.352856\pi$
$181$	12.0000	0.891953	0.445976	+	0.895045i	$0.352856\pi$
$182$	12.0000	0.889499
$183$	2.00000	0.147844
$184$	0	0
$185$	2.00000	0.147043
$186$	−2.00000	−0.146647
$187$	−16.0000	−1.17004
$188$	0	0
$189$	2.00000	0.145479
$190$	−1.00000	−0.0725476
$191$	16.0000	1.15772	0.578860	−	0.815427i	$-0.303498\pi$
$191$	16.0000	1.15772	0.578860	+	0.815427i	$0.303498\pi$
$192$	1.00000	0.0721688
$193$	10.0000	0.719816	0.359908	−	0.932988i	$-0.382808\pi$
$193$	10.0000	0.719816	0.359908	+	0.932988i	$0.382808\pi$
$194$	−2.00000	−0.143592
$195$	−6.00000	−0.429669
$196$	−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	$0.431435\pi$
$198$	−4.00000	−0.284268
$199$	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
$201$	4.00000	0.282138
$202$	6.00000	0.422159
$203$	−20.0000	−1.40372
$204$	4.00000	0.280056
$205$	−8.00000	−0.558744
$206$	4.00000	0.278693
$207$	0	0
$208$	6.00000	0.416025
$209$	−4.00000	−0.276686
$210$	−2.00000	−0.138013
$211$	16.0000	1.10149	0.550743	−	0.834675i	$-0.314345\pi$
$211$	16.0000	1.10149	0.550743	+	0.834675i	$0.314345\pi$
$212$	−6.00000	−0.412082
$213$	0	0
$214$	8.00000	0.546869
$215$	8.00000	0.545595
$216$	1.00000	0.0680414
$217$	−4.00000	−0.271538
$218$	12.0000	0.812743
$219$	−10.0000	−0.675737
$220$	4.00000	0.269680
$221$	24.0000	1.61441
$222$	−2.00000	−0.134231
$223$	−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
$226$	14.0000	0.931266
$227$	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
$229$	22.0000	1.45380	0.726900	−	0.686743i	$-0.240960\pi$
$229$	22.0000	1.45380	0.726900	+	0.686743i	$0.240960\pi$
$230$	0	0
$231$	−8.00000	−0.526361
$232$	−10.0000	−0.656532
$233$	−4.00000	−0.262049	−0.131024	−	0.991379i	$-0.541827\pi$
$233$	−4.00000	−0.262049	−0.131024	+	0.991379i	$0.541827\pi$
$234$	6.00000	0.392232
$235$	0	0
$236$	−2.00000	−0.130189
$237$	−2.00000	−0.129914
$238$	8.00000	0.518563
$239$	24.0000	1.55243	0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000	1.55243	0.776215	+	0.630468i	$0.217137\pi$
$240$	−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	$0.479482\pi$
$242$	5.00000	0.321412
$243$	1.00000	0.0641500
$244$	2.00000	0.128037
$245$	3.00000	0.191663
$246$	8.00000	0.510061
$247$	6.00000	0.381771
$248$	−2.00000	−0.127000
$249$	−10.0000	−0.633724
$250$	−1.00000	−0.0632456
$251$	16.0000	1.00991	0.504956	−	0.863145i	$-0.331509\pi$
$251$	16.0000	1.00991	0.504956	+	0.863145i	$0.331509\pi$
$252$	2.00000	0.125988
$253$	0	0
$254$	−20.0000	−1.25491
$255$	−4.00000	−0.250490
$256$	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	$0.559920\pi$
$258$	−8.00000	−0.498058
$259$	−4.00000	−0.248548
$260$	−6.00000	−0.372104
$261$	−10.0000	−0.618984
$262$	−12.0000	−0.741362
$263$	8.00000	0.493301	0.246651	−	0.969104i	$-0.420670\pi$
$263$	8.00000	0.493301	0.246651	+	0.969104i	$0.420670\pi$
$264$	−4.00000	−0.246183
$265$	6.00000	0.368577
$266$	2.00000	0.122628
$267$	−12.0000	−0.734388
$268$	4.00000	0.244339
$269$	−26.0000	−1.58525	−0.792624	−	0.609711i	$-0.791286\pi$
$269$	−26.0000	−1.58525	−0.792624	+	0.609711i	$0.791286\pi$
$270$	−1.00000	−0.0608581
$271$	−20.0000	−1.21491	−0.607457	−	0.794353i	$-0.707810\pi$
$271$	−20.0000	−1.21491	−0.607457	+	0.794353i	$0.707810\pi$
$272$	4.00000	0.242536
$273$	12.0000	0.726273
$274$	16.0000	0.966595
$275$	−4.00000	−0.241209
$276$	0	0
$277$	20.0000	1.20168	0.600842	−	0.799368i	$-0.294832\pi$
$277$	20.0000	1.20168	0.600842	+	0.799368i	$0.294832\pi$
$278$	−12.0000	−0.719712
$279$	−2.00000	−0.119737
$280$	−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
$283$	−16.0000	−0.951101	−0.475551	−	0.879688i	$-0.657751\pi$
$283$	−16.0000	−0.951101	−0.475551	+	0.879688i	$0.657751\pi$
$284$	0	0
$285$	−1.00000	−0.0592349
$286$	−24.0000	−1.41915
$287$	16.0000	0.944450
$288$	1.00000	0.0589256
$289$	−1.00000	−0.0588235
$290$	10.0000	0.587220
$291$	−2.00000	−0.117242
$292$	−10.0000	−0.585206
$293$	22.0000	1.28525	0.642627	−	0.766179i	$-0.277845\pi$
$293$	22.0000	1.28525	0.642627	+	0.766179i	$0.277845\pi$
$294$	−3.00000	−0.174964
$295$	2.00000	0.116445
$296$	−2.00000	−0.116248
$297$	−4.00000	−0.232104
$298$	−18.0000	−1.04271
$299$	0	0
$300$	1.00000	0.0577350
$301$	−16.0000	−0.922225
$302$	18.0000	1.03578
$303$	6.00000	0.344691
$304$	1.00000	0.0573539
$305$	−2.00000	−0.114520
$306$	4.00000	0.228665
$307$	4.00000	0.228292	0.114146	−	0.993464i	$-0.463587\pi$
$307$	4.00000	0.228292	0.114146	+	0.993464i	$0.463587\pi$
$308$	−8.00000	−0.455842
$309$	4.00000	0.227552
$310$	2.00000	0.113592
$311$	32.0000	1.81455	0.907277	−	0.420534i	$-0.138157\pi$
$311$	32.0000	1.81455	0.907277	+	0.420534i	$0.138157\pi$
$312$	6.00000	0.339683
$313$	6.00000	0.339140	0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000	0.339140	0.169570	+	0.985518i	$0.445762\pi$
$314$	20.0000	1.12867
$315$	−2.00000	−0.112687
$316$	−2.00000	−0.112509
$317$	30.0000	1.68497	0.842484	−	0.538721i	$-0.181092\pi$
$317$	30.0000	1.68497	0.842484	+	0.538721i	$0.181092\pi$
$318$	−6.00000	−0.336463
$319$	40.0000	2.23957
$320$	−1.00000	−0.0559017
$321$	8.00000	0.446516
$322$	0	0
$323$	4.00000	0.222566
$324$	1.00000	0.0555556
$325$	6.00000	0.332820
$326$	−20.0000	−1.10770
$327$	12.0000	0.663602
$328$	8.00000	0.441726
$329$	0	0
$330$	4.00000	0.220193
$331$	−28.0000	−1.53902	−0.769510	−	0.638635i	$-0.779499\pi$
$331$	−28.0000	−1.53902	−0.769510	+	0.638635i	$0.779499\pi$
$332$	−10.0000	−0.548821
$333$	−2.00000	−0.109599
$334$	−16.0000	−0.875481
$335$	−4.00000	−0.218543
$336$	2.00000	0.109109
$337$	−22.0000	−1.19842	−0.599208	−	0.800593i	$-0.704518\pi$
$337$	−22.0000	−1.19842	−0.599208	+	0.800593i	$0.704518\pi$
$338$	23.0000	1.25104
$339$	14.0000	0.760376
$340$	−4.00000	−0.216930
$341$	8.00000	0.433224
$342$	1.00000	0.0540738
$343$	−20.0000	−1.07990
$344$	−8.00000	−0.431331
$345$	0	0
$346$	−14.0000	−0.752645
$347$	−6.00000	−0.322097	−0.161048	−	0.986947i	$-0.551488\pi$
$347$	−6.00000	−0.322097	−0.161048	+	0.986947i	$0.551488\pi$
$348$	−10.0000	−0.536056
$349$	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
$351$	6.00000	0.320256
$352$	−4.00000	−0.213201
$353$	0	0		−	1.00000i	$-0.5\pi$
$353$	0	0			1.00000i	$0.5\pi$
$354$	−2.00000	−0.106299
$355$	0	0
$356$	−12.0000	−0.635999
$357$	8.00000	0.423405
$358$	−22.0000	−1.16274
$359$	16.0000	0.844448	0.422224	−	0.906492i	$-0.361250\pi$
$359$	16.0000	0.844448	0.422224	+	0.906492i	$0.361250\pi$
$360$	−1.00000	−0.0527046
$361$	1.00000	0.0526316
$362$	12.0000	0.630706
$363$	5.00000	0.262432
$364$	12.0000	0.628971
$365$	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
$369$	8.00000	0.416463
$370$	2.00000	0.103975
$371$	−12.0000	−0.623009
$372$	−2.00000	−0.103695
$373$	26.0000	1.34623	0.673114	−	0.739538i	$-0.264956\pi$
$373$	26.0000	1.34623	0.673114	+	0.739538i	$0.264956\pi$
$374$	−16.0000	−0.827340
$375$	−1.00000	−0.0516398
$376$	0	0
$377$	−60.0000	−3.09016
$378$	2.00000	0.102869
$379$	16.0000	0.821865	0.410932	−	0.911666i	$-0.365203\pi$
$379$	16.0000	0.821865	0.410932	+	0.911666i	$0.365203\pi$
$380$	−1.00000	−0.0512989
$381$	−20.0000	−1.02463
$382$	16.0000	0.818631
$383$	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
$385$	8.00000	0.407718
$386$	10.0000	0.508987
$387$	−8.00000	−0.406663
$388$	−2.00000	−0.101535
$389$	38.0000	1.92668	0.963338	−	0.268290i	$-0.0864585\pi$
$389$	38.0000	1.92668	0.963338	+	0.268290i	$0.0864585\pi$
$390$	−6.00000	−0.303822
$391$	0	0
$392$	−3.00000	−0.151523
$393$	−12.0000	−0.605320
$394$	6.00000	0.302276
$395$	2.00000	0.100631
$396$	−4.00000	−0.201008
$397$	−16.0000	−0.803017	−0.401508	−	0.915855i	$-0.631514\pi$
$397$	−16.0000	−0.803017	−0.401508	+	0.915855i	$0.631514\pi$
$398$	20.0000	1.00251
$399$	2.00000	0.100125
$400$	1.00000	0.0500000
$401$	−20.0000	−0.998752	−0.499376	−	0.866385i	$-0.666437\pi$
$401$	−20.0000	−0.998752	−0.499376	+	0.866385i	$0.666437\pi$
$402$	4.00000	0.199502
$403$	−12.0000	−0.597763
$404$	6.00000	0.298511
$405$	−1.00000	−0.0496904
$406$	−20.0000	−0.992583
$407$	8.00000	0.396545
$408$	4.00000	0.198030
$409$	−6.00000	−0.296681	−0.148340	−	0.988936i	$-0.547393\pi$
$409$	−6.00000	−0.296681	−0.148340	+	0.988936i	$0.547393\pi$
$410$	−8.00000	−0.395092
$411$	16.0000	0.789222
$412$	4.00000	0.197066
$413$	−4.00000	−0.196827
$414$	0	0
$415$	10.0000	0.490881
$416$	6.00000	0.294174
$417$	−12.0000	−0.587643
$418$	−4.00000	−0.195646
$419$	0	0		−	1.00000i	$-0.5\pi$
$419$	0	0			1.00000i	$0.5\pi$
$420$	−2.00000	−0.0975900
$421$	−20.0000	−0.974740	−0.487370	−	0.873195i	$-0.662044\pi$
$421$	−20.0000	−0.974740	−0.487370	+	0.873195i	$0.662044\pi$
$422$	16.0000	0.778868
$423$	0	0
$424$	−6.00000	−0.291386
$425$	4.00000	0.194029
$426$	0	0
$427$	4.00000	0.193574
$428$	8.00000	0.386695
$429$	−24.0000	−1.15873
$430$	8.00000	0.385794
$431$	−8.00000	−0.385346	−0.192673	−	0.981263i	$-0.561716\pi$
$431$	−8.00000	−0.385346	−0.192673	+	0.981263i	$0.561716\pi$
$432$	1.00000	0.0481125
$433$	26.0000	1.24948	0.624740	−	0.780833i	$-0.285205\pi$
$433$	26.0000	1.24948	0.624740	+	0.780833i	$0.285205\pi$
$434$	−4.00000	−0.192006
$435$	10.0000	0.479463
$436$	12.0000	0.574696
$437$	0	0
$438$	−10.0000	−0.477818
$439$	−2.00000	−0.0954548	−0.0477274	−	0.998860i	$-0.515198\pi$
$439$	−2.00000	−0.0954548	−0.0477274	+	0.998860i	$0.515198\pi$
$440$	4.00000	0.190693
$441$	−3.00000	−0.142857
$442$	24.0000	1.14156
$443$	−6.00000	−0.285069	−0.142534	−	0.989790i	$-0.545525\pi$
$443$	−6.00000	−0.285069	−0.142534	+	0.989790i	$0.545525\pi$
$444$	−2.00000	−0.0949158
$445$	12.0000	0.568855
$446$	−16.0000	−0.757622
$447$	−18.0000	−0.851371
$448$	2.00000	0.0944911
$449$	−8.00000	−0.377543	−0.188772	−	0.982021i	$-0.560451\pi$
$449$	−8.00000	−0.377543	−0.188772	+	0.982021i	$0.560451\pi$
$450$	1.00000	0.0471405
$451$	−32.0000	−1.50682
$452$	14.0000	0.658505
$453$	18.0000	0.845714
$454$	12.0000	0.563188
$455$	−12.0000	−0.562569
$456$	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	$0.672044\pi$
$458$	22.0000	1.02799
$459$	4.00000	0.186704
$460$	0	0
$461$	18.0000	0.838344	0.419172	−	0.907907i	$-0.362320\pi$
$461$	18.0000	0.838344	0.419172	+	0.907907i	$0.362320\pi$
$462$	−8.00000	−0.372194
$463$	34.0000	1.58011	0.790057	−	0.613033i	$-0.210051\pi$
$463$	34.0000	1.58011	0.790057	+	0.613033i	$0.210051\pi$
$464$	−10.0000	−0.464238
$465$	2.00000	0.0927478
$466$	−4.00000	−0.185296
$467$	6.00000	0.277647	0.138823	−	0.990317i	$-0.455668\pi$
$467$	6.00000	0.277647	0.138823	+	0.990317i	$0.455668\pi$
$468$	6.00000	0.277350
$469$	8.00000	0.369406
$470$	0	0
$471$	20.0000	0.921551
$472$	−2.00000	−0.0920575
$473$	32.0000	1.47136
$474$	−2.00000	−0.0918630
$475$	1.00000	0.0458831
$476$	8.00000	0.366679
$477$	−6.00000	−0.274721
$478$	24.0000	1.09773
$479$	0	0		−	1.00000i	$-0.5\pi$
$479$	0	0			1.00000i	$0.5\pi$
$480$	−1.00000	−0.0456435
$481$	−12.0000	−0.547153
$482$	2.00000	0.0910975
$483$	0	0
$484$	5.00000	0.227273
$485$	2.00000	0.0908153
$486$	1.00000	0.0453609
$487$	4.00000	0.181257	0.0906287	−	0.995885i	$-0.471112\pi$
$487$	4.00000	0.181257	0.0906287	+	0.995885i	$0.471112\pi$
$488$	2.00000	0.0905357
$489$	−20.0000	−0.904431
$490$	3.00000	0.135526
$491$	4.00000	0.180517	0.0902587	−	0.995918i	$-0.471231\pi$
$491$	4.00000	0.180517	0.0902587	+	0.995918i	$0.471231\pi$
$492$	8.00000	0.360668
$493$	−40.0000	−1.80151
$494$	6.00000	0.269953
$495$	4.00000	0.179787
$496$	−2.00000	−0.0898027
$497$	0	0
$498$	−10.0000	−0.448111
$499$	−28.0000	−1.25345	−0.626726	−	0.779240i	$-0.715605\pi$
$499$	−28.0000	−1.25345	−0.626726	+	0.779240i	$0.715605\pi$
$500$	−1.00000	−0.0447214
$501$	−16.0000	−0.714827
$502$	16.0000	0.714115
$503$	−28.0000	−1.24846	−0.624229	−	0.781241i	$-0.714587\pi$
$503$	−28.0000	−1.24846	−0.624229	+	0.781241i	$0.714587\pi$
$504$	2.00000	0.0890871
$505$	−6.00000	−0.266996
$506$	0	0
$507$	23.0000	1.02147
$508$	−20.0000	−0.887357
$509$	−26.0000	−1.15243	−0.576215	−	0.817298i	$-0.695471\pi$
$509$	−26.0000	−1.15243	−0.576215	+	0.817298i	$0.695471\pi$
$510$	−4.00000	−0.177123
$511$	−20.0000	−0.884748
$512$	1.00000	0.0441942
$513$	1.00000	0.0441511
$514$	−6.00000	−0.264649
$515$	−4.00000	−0.176261
$516$	−8.00000	−0.352180
$517$	0	0
$518$	−4.00000	−0.175750
$519$	−14.0000	−0.614532
$520$	−6.00000	−0.263117
$521$	−4.00000	−0.175243	−0.0876216	−	0.996154i	$-0.527927\pi$
$521$	−4.00000	−0.175243	−0.0876216	+	0.996154i	$0.527927\pi$
$522$	−10.0000	−0.437688
$523$	−44.0000	−1.92399	−0.961993	−	0.273075i	$-0.911959\pi$
$523$	−44.0000	−1.92399	−0.961993	+	0.273075i	$0.911959\pi$
$524$	−12.0000	−0.524222
$525$	2.00000	0.0872872
$526$	8.00000	0.348817
$527$	−8.00000	−0.348485
$528$	−4.00000	−0.174078
$529$	−23.0000	−1.00000
$530$	6.00000	0.260623
$531$	−2.00000	−0.0867926
$532$	2.00000	0.0867110
$533$	48.0000	2.07911
$534$	−12.0000	−0.519291
$535$	−8.00000	−0.345870
$536$	4.00000	0.172774
$537$	−22.0000	−0.949370
$538$	−26.0000	−1.12094
$539$	12.0000	0.516877
$540$	−1.00000	−0.0430331
$541$	30.0000	1.28980	0.644900	−	0.764267i	$-0.276899\pi$
$541$	30.0000	1.28980	0.644900	+	0.764267i	$0.276899\pi$
$542$	−20.0000	−0.859074
$543$	12.0000	0.514969
$544$	4.00000	0.171499
$545$	−12.0000	−0.514024
$546$	12.0000	0.513553
$547$	−36.0000	−1.53925	−0.769624	−	0.638497i	$-0.779557\pi$
$547$	−36.0000	−1.53925	−0.769624	+	0.638497i	$0.779557\pi$
$548$	16.0000	0.683486
$549$	2.00000	0.0853579
$550$	−4.00000	−0.170561
$551$	−10.0000	−0.426014
$552$	0	0
$553$	−4.00000	−0.170097
$554$	20.0000	0.849719
$555$	2.00000	0.0848953
$556$	−12.0000	−0.508913
$557$	−30.0000	−1.27114	−0.635570	−	0.772043i	$-0.719235\pi$
$557$	−30.0000	−1.27114	−0.635570	+	0.772043i	$0.719235\pi$
$558$	−2.00000	−0.0846668
$559$	−48.0000	−2.03018
$560$	−2.00000	−0.0845154
$561$	−16.0000	−0.675521
$562$	24.0000	1.01238
$563$	−8.00000	−0.337160	−0.168580	−	0.985688i	$-0.553918\pi$
$563$	−8.00000	−0.337160	−0.168580	+	0.985688i	$0.553918\pi$
$564$	0	0
$565$	−14.0000	−0.588984
$566$	−16.0000	−0.672530
$567$	2.00000	0.0839921
$568$	0	0
$569$	24.0000	1.00613	0.503066	−	0.864248i	$-0.332205\pi$
$569$	24.0000	1.00613	0.503066	+	0.864248i	$0.332205\pi$
$570$	−1.00000	−0.0418854
$571$	−36.0000	−1.50655	−0.753277	−	0.657704i	$-0.771528\pi$
$571$	−36.0000	−1.50655	−0.753277	+	0.657704i	$0.771528\pi$
$572$	−24.0000	−1.00349
$573$	16.0000	0.668410
$574$	16.0000	0.667827
$575$	0	0
$576$	1.00000	0.0416667
$577$	42.0000	1.74848	0.874241	−	0.485491i	$-0.161359\pi$
$577$	42.0000	1.74848	0.874241	+	0.485491i	$0.161359\pi$
$578$	−1.00000	−0.0415945
$579$	10.0000	0.415586
$580$	10.0000	0.415227
$581$	−20.0000	−0.829740
$582$	−2.00000	−0.0829027
$583$	24.0000	0.993978
$584$	−10.0000	−0.413803
$585$	−6.00000	−0.248069
$586$	22.0000	0.908812
$587$	18.0000	0.742940	0.371470	−	0.928445i	$-0.378854\pi$
$587$	18.0000	0.742940	0.371470	+	0.928445i	$0.378854\pi$
$588$	−3.00000	−0.123718
$589$	−2.00000	−0.0824086
$590$	2.00000	0.0823387
$591$	6.00000	0.246807
$592$	−2.00000	−0.0821995
$593$	16.0000	0.657041	0.328521	−	0.944497i	$-0.393450\pi$
$593$	16.0000	0.657041	0.328521	+	0.944497i	$0.393450\pi$
$594$	−4.00000	−0.164122
$595$	−8.00000	−0.327968
$596$	−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
$601$	−14.0000	−0.571072	−0.285536	−	0.958368i	$-0.592172\pi$
$601$	−14.0000	−0.571072	−0.285536	+	0.958368i	$0.592172\pi$
$602$	−16.0000	−0.652111
$603$	4.00000	0.162893
$604$	18.0000	0.732410
$605$	−5.00000	−0.203279
$606$	6.00000	0.243733
$607$	−12.0000	−0.487065	−0.243532	−	0.969893i	$-0.578306\pi$
$607$	−12.0000	−0.487065	−0.243532	+	0.969893i	$0.578306\pi$
$608$	1.00000	0.0405554
$609$	−20.0000	−0.810441
$610$	−2.00000	−0.0809776
$611$	0	0
$612$	4.00000	0.161690
$613$	8.00000	0.323117	0.161558	−	0.986863i	$-0.448348\pi$
$613$	8.00000	0.323117	0.161558	+	0.986863i	$0.448348\pi$
$614$	4.00000	0.161427
$615$	−8.00000	−0.322591
$616$	−8.00000	−0.322329
$617$	0	0		−	1.00000i	$-0.5\pi$
$617$	0	0			1.00000i	$0.5\pi$
$618$	4.00000	0.160904
$619$	4.00000	0.160774	0.0803868	−	0.996764i	$-0.474384\pi$
$619$	4.00000	0.160774	0.0803868	+	0.996764i	$0.474384\pi$
$620$	2.00000	0.0803219
$621$	0	0
$622$	32.0000	1.28308
$623$	−24.0000	−0.961540
$624$	6.00000	0.240192
$625$	1.00000	0.0400000
$626$	6.00000	0.239808
$627$	−4.00000	−0.159745
$628$	20.0000	0.798087
$629$	−8.00000	−0.318981
$630$	−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	$0.449096\pi$
$632$	−2.00000	−0.0795557
$633$	16.0000	0.635943
$634$	30.0000	1.19145
$635$	20.0000	0.793676
$636$	−6.00000	−0.237915
$637$	−18.0000	−0.713186
$638$	40.0000	1.58362
$639$	0	0
$640$	−1.00000	−0.0395285
$641$	−48.0000	−1.89589	−0.947943	−	0.318440i	$-0.896841\pi$
$641$	−48.0000	−1.89589	−0.947943	+	0.318440i	$0.896841\pi$
$642$	8.00000	0.315735
$643$	−16.0000	−0.630978	−0.315489	−	0.948929i	$-0.602169\pi$
$643$	−16.0000	−0.630978	−0.315489	+	0.948929i	$0.602169\pi$
$644$	0	0
$645$	8.00000	0.315000
$646$	4.00000	0.157378
$647$	28.0000	1.10079	0.550397	−	0.834903i	$-0.314476\pi$
$647$	28.0000	1.10079	0.550397	+	0.834903i	$0.314476\pi$
$648$	1.00000	0.0392837
$649$	8.00000	0.314027
$650$	6.00000	0.235339
$651$	−4.00000	−0.156772
$652$	−20.0000	−0.783260
$653$	−30.0000	−1.17399	−0.586995	−	0.809590i	$-0.699689\pi$
$653$	−30.0000	−1.17399	−0.586995	+	0.809590i	$0.699689\pi$
$654$	12.0000	0.469237
$655$	12.0000	0.468879
$656$	8.00000	0.312348
$657$	−10.0000	−0.390137
$658$	0	0
$659$	−30.0000	−1.16863	−0.584317	−	0.811525i	$-0.698638\pi$
$659$	−30.0000	−1.16863	−0.584317	+	0.811525i	$0.698638\pi$
$660$	4.00000	0.155700
$661$	−20.0000	−0.777910	−0.388955	−	0.921257i	$-0.627164\pi$
$661$	−20.0000	−0.777910	−0.388955	+	0.921257i	$0.627164\pi$
$662$	−28.0000	−1.08825
$663$	24.0000	0.932083
$664$	−10.0000	−0.388075
$665$	−2.00000	−0.0775567
$666$	−2.00000	−0.0774984
$667$	0	0
$668$	−16.0000	−0.619059
$669$	−16.0000	−0.618596
$670$	−4.00000	−0.154533
$671$	−8.00000	−0.308837
$672$	2.00000	0.0771517
$673$	−2.00000	−0.0770943	−0.0385472	−	0.999257i	$-0.512273\pi$
$673$	−2.00000	−0.0770943	−0.0385472	+	0.999257i	$0.512273\pi$
$674$	−22.0000	−0.847408
$675$	1.00000	0.0384900
$676$	23.0000	0.884615
$677$	−18.0000	−0.691796	−0.345898	−	0.938272i	$-0.612426\pi$
$677$	−18.0000	−0.691796	−0.345898	+	0.938272i	$0.612426\pi$
$678$	14.0000	0.537667
$679$	−4.00000	−0.153506
$680$	−4.00000	−0.153393
$681$	12.0000	0.459841
$682$	8.00000	0.306336
$683$	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
$685$	−16.0000	−0.611329
$686$	−20.0000	−0.763604
$687$	22.0000	0.839352
$688$	−8.00000	−0.304997
$689$	−36.0000	−1.37149
$690$	0	0
$691$	28.0000	1.06517	0.532585	−	0.846376i	$-0.321221\pi$
$691$	28.0000	1.06517	0.532585	+	0.846376i	$0.321221\pi$
$692$	−14.0000	−0.532200
$693$	−8.00000	−0.303895
$694$	−6.00000	−0.227757
$695$	12.0000	0.455186
$696$	−10.0000	−0.379049
$697$	32.0000	1.21209
$698$	14.0000	0.529908
$699$	−4.00000	−0.151294
$700$	2.00000	0.0755929
$701$	10.0000	0.377695	0.188847	−	0.982006i	$-0.439525\pi$
$701$	10.0000	0.377695	0.188847	+	0.982006i	$0.439525\pi$
$702$	6.00000	0.226455
$703$	−2.00000	−0.0754314
$704$	−4.00000	−0.150756
$705$	0	0
$706$	0	0
$707$	12.0000	0.451306
$708$	−2.00000	−0.0751646
$709$	−26.0000	−0.976450	−0.488225	−	0.872718i	$-0.662356\pi$
$709$	−26.0000	−0.976450	−0.488225	+	0.872718i	$0.662356\pi$
$710$	0	0
$711$	−2.00000	−0.0750059
$712$	−12.0000	−0.449719
$713$	0	0
$714$	8.00000	0.299392
$715$	24.0000	0.897549
$716$	−22.0000	−0.822179
$717$	24.0000	0.896296
$718$	16.0000	0.597115
$719$	8.00000	0.298350	0.149175	−	0.988811i	$-0.452338\pi$
$719$	8.00000	0.298350	0.149175	+	0.988811i	$0.452338\pi$
$720$	−1.00000	−0.0372678
$721$	8.00000	0.297936
$722$	1.00000	0.0372161
$723$	2.00000	0.0743808
$724$	12.0000	0.445976
$725$	−10.0000	−0.371391
$726$	5.00000	0.185567
$727$	30.0000	1.11264	0.556319	−	0.830969i	$-0.312213\pi$
$727$	30.0000	1.11264	0.556319	+	0.830969i	$0.312213\pi$
$728$	12.0000	0.444750
$729$	1.00000	0.0370370
$730$	10.0000	0.370117
$731$	−32.0000	−1.18356
$732$	2.00000	0.0739221
$733$	8.00000	0.295487	0.147743	−	0.989026i	$-0.452799\pi$
$733$	8.00000	0.295487	0.147743	+	0.989026i	$0.452799\pi$
$734$	−34.0000	−1.25496
$735$	3.00000	0.110657
$736$	0	0
$737$	−16.0000	−0.589368
$738$	8.00000	0.294484
$739$	4.00000	0.147142	0.0735712	−	0.997290i	$-0.476560\pi$
$739$	4.00000	0.147142	0.0735712	+	0.997290i	$0.476560\pi$
$740$	2.00000	0.0735215
$741$	6.00000	0.220416
$742$	−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	$0.354894\pi$
$744$	−2.00000	−0.0733236
$745$	18.0000	0.659469
$746$	26.0000	0.951928
$747$	−10.0000	−0.365881
$748$	−16.0000	−0.585018
$749$	16.0000	0.584627
$750$	−1.00000	−0.0365148
$751$	−26.0000	−0.948753	−0.474377	−	0.880322i	$-0.657327\pi$
$751$	−26.0000	−0.948753	−0.474377	+	0.880322i	$0.657327\pi$
$752$	0	0
$753$	16.0000	0.583072
$754$	−60.0000	−2.18507
$755$	−18.0000	−0.655087
$756$	2.00000	0.0727393
$757$	8.00000	0.290765	0.145382	−	0.989376i	$-0.453559\pi$
$757$	8.00000	0.290765	0.145382	+	0.989376i	$0.453559\pi$
$758$	16.0000	0.581146
$759$	0	0
$760$	−1.00000	−0.0362738
$761$	46.0000	1.66750	0.833749	−	0.552143i	$-0.186190\pi$
$761$	46.0000	1.66750	0.833749	+	0.552143i	$0.186190\pi$
$762$	−20.0000	−0.724524
$763$	24.0000	0.868858
$764$	16.0000	0.578860
$765$	−4.00000	−0.144620
$766$	24.0000	0.867155
$767$	−12.0000	−0.433295
$768$	1.00000	0.0360844
$769$	30.0000	1.08183	0.540914	−	0.841078i	$-0.318079\pi$
$769$	30.0000	1.08183	0.540914	+	0.841078i	$0.318079\pi$
$770$	8.00000	0.288300
$771$	−6.00000	−0.216085
$772$	10.0000	0.359908
$773$	−30.0000	−1.07903	−0.539513	−	0.841978i	$-0.681391\pi$
$773$	−30.0000	−1.07903	−0.539513	+	0.841978i	$0.681391\pi$
$774$	−8.00000	−0.287554
$775$	−2.00000	−0.0718421
$776$	−2.00000	−0.0717958
$777$	−4.00000	−0.143499
$778$	38.0000	1.36237
$779$	8.00000	0.286630
$780$	−6.00000	−0.214834
$781$	0	0
$782$	0	0
$783$	−10.0000	−0.357371
$784$	−3.00000	−0.107143
$785$	−20.0000	−0.713831
$786$	−12.0000	−0.428026
$787$	52.0000	1.85360	0.926800	−	0.375555i	$-0.122548\pi$
$787$	52.0000	1.85360	0.926800	+	0.375555i	$0.122548\pi$
$788$	6.00000	0.213741
$789$	8.00000	0.284808
$790$	2.00000	0.0711568
$791$	28.0000	0.995565
$792$	−4.00000	−0.142134
$793$	12.0000	0.426132
$794$	−16.0000	−0.567819
$795$	6.00000	0.212798
$796$	20.0000	0.708881
$797$	38.0000	1.34603	0.673015	−	0.739629i	$-0.264999\pi$
$797$	38.0000	1.34603	0.673015	+	0.739629i	$0.264999\pi$
$798$	2.00000	0.0707992
$799$	0	0
$800$	1.00000	0.0353553
$801$	−12.0000	−0.423999
$802$	−20.0000	−0.706225
$803$	40.0000	1.41157
$804$	4.00000	0.141069
$805$	0	0
$806$	−12.0000	−0.422682
$807$	−26.0000	−0.915243
$808$	6.00000	0.211079
$809$	−10.0000	−0.351581	−0.175791	−	0.984428i	$-0.556248\pi$
$809$	−10.0000	−0.351581	−0.175791	+	0.984428i	$0.556248\pi$
$810$	−1.00000	−0.0351364
$811$	−40.0000	−1.40459	−0.702295	−	0.711886i	$-0.747841\pi$
$811$	−40.0000	−1.40459	−0.702295	+	0.711886i	$0.747841\pi$
$812$	−20.0000	−0.701862
$813$	−20.0000	−0.701431
$814$	8.00000	0.280400
$815$	20.0000	0.700569
$816$	4.00000	0.140028
$817$	−8.00000	−0.279885
$818$	−6.00000	−0.209785
$819$	12.0000	0.419314
$820$	−8.00000	−0.279372
$821$	−10.0000	−0.349002	−0.174501	−	0.984657i	$-0.555831\pi$
$821$	−10.0000	−0.349002	−0.174501	+	0.984657i	$0.555831\pi$
$822$	16.0000	0.558064
$823$	34.0000	1.18517	0.592583	−	0.805510i	$-0.298108\pi$
$823$	34.0000	1.18517	0.592583	+	0.805510i	$0.298108\pi$
$824$	4.00000	0.139347
$825$	−4.00000	−0.139262
$826$	−4.00000	−0.139178
$827$	32.0000	1.11275	0.556375	−	0.830932i	$-0.312192\pi$
$827$	32.0000	1.11275	0.556375	+	0.830932i	$0.312192\pi$
$828$	0	0
$829$	−28.0000	−0.972480	−0.486240	−	0.873825i	$-0.661632\pi$
$829$	−28.0000	−0.972480	−0.486240	+	0.873825i	$0.661632\pi$
$830$	10.0000	0.347105
$831$	20.0000	0.693792
$832$	6.00000	0.208013
$833$	−12.0000	−0.415775
$834$	−12.0000	−0.415526
$835$	16.0000	0.553703
$836$	−4.00000	−0.138343
$837$	−2.00000	−0.0691301
$838$	0	0
$839$	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
$841$	71.0000	2.44828
$842$	−20.0000	−0.689246
$843$	24.0000	0.826604
$844$	16.0000	0.550743
$845$	−23.0000	−0.791224
$846$	0	0
$847$	10.0000	0.343604
$848$	−6.00000	−0.206041
$849$	−16.0000	−0.549119
$850$	4.00000	0.137199
$851$	0	0
$852$	0	0
$853$	28.0000	0.958702	0.479351	−	0.877623i	$-0.340872\pi$
$853$	28.0000	0.958702	0.479351	+	0.877623i	$0.340872\pi$
$854$	4.00000	0.136877
$855$	−1.00000	−0.0341993
$856$	8.00000	0.273434
$857$	−54.0000	−1.84460	−0.922302	−	0.386469i	$-0.873695\pi$
$857$	−54.0000	−1.84460	−0.922302	+	0.386469i	$0.873695\pi$
$858$	−24.0000	−0.819346
$859$	28.0000	0.955348	0.477674	−	0.878537i	$-0.341480\pi$
$859$	28.0000	0.955348	0.477674	+	0.878537i	$0.341480\pi$
$860$	8.00000	0.272798
$861$	16.0000	0.545279
$862$	−8.00000	−0.272481
$863$	−56.0000	−1.90626	−0.953131	−	0.302558i	$-0.902160\pi$
$863$	−56.0000	−1.90626	−0.953131	+	0.302558i	$0.902160\pi$
$864$	1.00000	0.0340207
$865$	14.0000	0.476014
$866$	26.0000	0.883516
$867$	−1.00000	−0.0339618
$868$	−4.00000	−0.135769
$869$	8.00000	0.271381
$870$	10.0000	0.339032
$871$	24.0000	0.813209
$872$	12.0000	0.406371
$873$	−2.00000	−0.0676897
$874$	0	0
$875$	−2.00000	−0.0676123
$876$	−10.0000	−0.337869
$877$	−30.0000	−1.01303	−0.506514	−	0.862232i	$-0.669066\pi$
$877$	−30.0000	−1.01303	−0.506514	+	0.862232i	$0.669066\pi$
$878$	−2.00000	−0.0674967
$879$	22.0000	0.742042
$880$	4.00000	0.134840
$881$	10.0000	0.336909	0.168454	−	0.985709i	$-0.446122\pi$
$881$	10.0000	0.336909	0.168454	+	0.985709i	$0.446122\pi$
$882$	−3.00000	−0.101015
$883$	16.0000	0.538443	0.269221	−	0.963078i	$-0.413234\pi$
$883$	16.0000	0.538443	0.269221	+	0.963078i	$0.413234\pi$
$884$	24.0000	0.807207
$885$	2.00000	0.0672293
$886$	−6.00000	−0.201574
$887$	0	0		−	1.00000i	$-0.5\pi$
$887$	0	0			1.00000i	$0.5\pi$
$888$	−2.00000	−0.0671156
$889$	−40.0000	−1.34156
$890$	12.0000	0.402241
$891$	−4.00000	−0.134005
$892$	−16.0000	−0.535720
$893$	0	0
$894$	−18.0000	−0.602010
$895$	22.0000	0.735379
$896$	2.00000	0.0668153
$897$	0	0
$898$	−8.00000	−0.266963
$899$	20.0000	0.667037
$900$	1.00000	0.0333333
$901$	−24.0000	−0.799556
$902$	−32.0000	−1.06548
$903$	−16.0000	−0.532447
$904$	14.0000	0.465633
$905$	−12.0000	−0.398893
$906$	18.0000	0.598010
$907$	−36.0000	−1.19536	−0.597680	−	0.801735i	$-0.703911\pi$
$907$	−36.0000	−1.19536	−0.597680	+	0.801735i	$0.703911\pi$
$908$	12.0000	0.398234
$909$	6.00000	0.199007
$910$	−12.0000	−0.397796
$911$	−12.0000	−0.397578	−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000	−0.397578	−0.198789	+	0.980042i	$0.563701\pi$
$912$	1.00000	0.0331133
$913$	40.0000	1.32381
$914$	−22.0000	−0.727695
$915$	−2.00000	−0.0661180
$916$	22.0000	0.726900
$917$	−24.0000	−0.792550
$918$	4.00000	0.132020
$919$	16.0000	0.527791	0.263896	−	0.964551i	$-0.414993\pi$
$919$	16.0000	0.527791	0.263896	+	0.964551i	$0.414993\pi$
$920$	0	0
$921$	4.00000	0.131804
$922$	18.0000	0.592798
$923$	0	0
$924$	−8.00000	−0.263181
$925$	−2.00000	−0.0657596
$926$	34.0000	1.11731
$927$	4.00000	0.131377
$928$	−10.0000	−0.328266
$929$	18.0000	0.590561	0.295280	−	0.955411i	$-0.404587\pi$
$929$	18.0000	0.590561	0.295280	+	0.955411i	$0.404587\pi$
$930$	2.00000	0.0655826
$931$	−3.00000	−0.0983210
$932$	−4.00000	−0.131024
$933$	32.0000	1.04763
$934$	6.00000	0.196326
$935$	16.0000	0.523256
$936$	6.00000	0.196116
$937$	−30.0000	−0.980057	−0.490029	−	0.871706i	$-0.663014\pi$
$937$	−30.0000	−0.980057	−0.490029	+	0.871706i	$0.663014\pi$
$938$	8.00000	0.261209
$939$	6.00000	0.195803
$940$	0	0
$941$	26.0000	0.847576	0.423788	−	0.905761i	$-0.360700\pi$
$941$	26.0000	0.847576	0.423788	+	0.905761i	$0.360700\pi$
$942$	20.0000	0.651635
$943$	0	0
$944$	−2.00000	−0.0650945
$945$	−2.00000	−0.0650600
$946$	32.0000	1.04041
$947$	−10.0000	−0.324956	−0.162478	−	0.986712i	$-0.551949\pi$
$947$	−10.0000	−0.324956	−0.162478	+	0.986712i	$0.551949\pi$
$948$	−2.00000	−0.0649570
$949$	−60.0000	−1.94768
$950$	1.00000	0.0324443
$951$	30.0000	0.972817
$952$	8.00000	0.259281
$953$	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
$955$	−16.0000	−0.517748
$956$	24.0000	0.776215
$957$	40.0000	1.29302
$958$	0	0
$959$	32.0000	1.03333
$960$	−1.00000	−0.0322749
$961$	−27.0000	−0.870968
$962$	−12.0000	−0.386896
$963$	8.00000	0.257796
$964$	2.00000	0.0644157
$965$	−10.0000	−0.321911
$966$	0	0
$967$	26.0000	0.836104	0.418052	−	0.908423i	$-0.362713\pi$
$967$	26.0000	0.836104	0.418052	+	0.908423i	$0.362713\pi$
$968$	5.00000	0.160706
$969$	4.00000	0.128499
$970$	2.00000	0.0642161
$971$	−14.0000	−0.449281	−0.224641	−	0.974442i	$-0.572121\pi$
$971$	−14.0000	−0.449281	−0.224641	+	0.974442i	$0.572121\pi$
$972$	1.00000	0.0320750
$973$	−24.0000	−0.769405
$974$	4.00000	0.128168
$975$	6.00000	0.192154
$976$	2.00000	0.0640184
$977$	50.0000	1.59964	0.799821	−	0.600239i	$-0.204928\pi$
$977$	50.0000	1.59964	0.799821	+	0.600239i	$0.204928\pi$
$978$	−20.0000	−0.639529
$979$	48.0000	1.53409
$980$	3.00000	0.0958315
$981$	12.0000	0.383131
$982$	4.00000	0.127645
$983$	0	0		−	1.00000i	$-0.5\pi$
$983$	0	0			1.00000i	$0.5\pi$
$984$	8.00000	0.255031
$985$	−6.00000	−0.191176
$986$	−40.0000	−1.27386
$987$	0	0
$988$	6.00000	0.190885
$989$	0	0
$990$	4.00000	0.127128
$991$	2.00000	0.0635321	0.0317660	−	0.999495i	$-0.489887\pi$
$991$	2.00000	0.0635321	0.0317660	+	0.999495i	$0.489887\pi$
$992$	−2.00000	−0.0635001
$993$	−28.0000	−0.888553
$994$	0	0
$995$	−20.0000	−0.634043
$996$	−10.0000	−0.316862
$997$	20.0000	0.633406	0.316703	−	0.948525i	$-0.397424\pi$
$997$	20.0000	0.633406	0.316703	+	0.948525i	$0.397424\pi$
$998$	−28.0000	−0.886325
$999$	−2.00000	−0.0632772

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.a.j.1.1	✓	1	1.1	even	1	trivial
1710.2.a.k.1.1		1	3.2	odd	2
2850.2.a.b.1.1		1	5.4	even	2
2850.2.d.l.799.1		2	5.3	odd	4
2850.2.d.l.799.2		2	5.2	odd	4
4560.2.a.d.1.1		1	4.3	odd	2
8550.2.a.w.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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