LMFDB - Embedded newform 4650.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4650,2,Mod(1,4650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4650, 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("4650.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4650 = 2 \cdot 3 \cdot 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4650.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:	$37.1304369399$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 930)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4650.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -6.00000 q^{11} -1.00000 q^{12} +2.00000 q^{13} +2.00000 q^{14} +1.00000 q^{16} -6.00000 q^{17} -1.00000 q^{18} +8.00000 q^{19} +2.00000 q^{21} +6.00000 q^{22} -4.00000 q^{23} +1.00000 q^{24} -2.00000 q^{26} -1.00000 q^{27} -2.00000 q^{28} -4.00000 q^{29} -1.00000 q^{31} -1.00000 q^{32} +6.00000 q^{33} +6.00000 q^{34} +1.00000 q^{36} -2.00000 q^{37} -8.00000 q^{38} -2.00000 q^{39} +2.00000 q^{41} -2.00000 q^{42} +4.00000 q^{43} -6.00000 q^{44} +4.00000 q^{46} -8.00000 q^{47} -1.00000 q^{48} -3.00000 q^{49} +6.00000 q^{51} +2.00000 q^{52} -10.0000 q^{53} +1.00000 q^{54} +2.00000 q^{56} -8.00000 q^{57} +4.00000 q^{58} +6.00000 q^{59} -14.0000 q^{61} +1.00000 q^{62} -2.00000 q^{63} +1.00000 q^{64} -6.00000 q^{66} -4.00000 q^{67} -6.00000 q^{68} +4.00000 q^{69} +16.0000 q^{71} -1.00000 q^{72} +8.00000 q^{73} +2.00000 q^{74} +8.00000 q^{76} +12.0000 q^{77} +2.00000 q^{78} +1.00000 q^{81} -2.00000 q^{82} +4.00000 q^{83} +2.00000 q^{84} -4.00000 q^{86} +4.00000 q^{87} +6.00000 q^{88} +10.0000 q^{89} -4.00000 q^{91} -4.00000 q^{92} +1.00000 q^{93} +8.00000 q^{94} +1.00000 q^{96} -16.0000 q^{97} +3.00000 q^{98} -6.00000 q^{99} +O(q^{100})\)

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
$5$	0	0
$5$	0	0
$6$	1.00000	0.408248
$7$	−2.00000	−0.755929	−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000	−0.755929	−0.377964	+	0.925820i	$0.623376\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	−6.00000	−1.80907	−0.904534	−	0.426401i	$-0.859781\pi$
$11$	−6.00000	−1.80907	−0.904534	+	0.426401i	$0.859781\pi$
$12$	−1.00000	−0.288675
$13$	2.00000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	2.00000	0.534522
$15$	0	0
$16$	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
$19$	8.00000	1.83533	0.917663	−	0.397360i	$-0.130073\pi$
$19$	8.00000	1.83533	0.917663	+	0.397360i	$0.130073\pi$
$20$	0	0
$21$	2.00000	0.436436
$22$	6.00000	1.27920
$23$	−4.00000	−0.834058	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000	−0.834058	−0.417029	+	0.908893i	$0.636929\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	−2.00000	−0.392232
$27$	−1.00000	−0.192450
$28$	−2.00000	−0.377964
$29$	−4.00000	−0.742781	−0.371391	−	0.928477i	$-0.621119\pi$
$29$	−4.00000	−0.742781	−0.371391	+	0.928477i	$0.621119\pi$
$30$	0	0
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−1.00000	−0.176777
$33$	6.00000	1.04447
$34$	6.00000	1.02899
$35$	0	0
$36$	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	$0.552568\pi$
$38$	−8.00000	−1.29777
$39$	−2.00000	−0.320256
$40$	0	0
$41$	2.00000	0.312348	0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000	0.312348	0.156174	+	0.987730i	$0.450084\pi$
$42$	−2.00000	−0.308607
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	−6.00000	−0.904534
$45$	0	0
$46$	4.00000	0.589768
$47$	−8.00000	−1.16692	−0.583460	−	0.812142i	$-0.698301\pi$
$47$	−8.00000	−1.16692	−0.583460	+	0.812142i	$0.698301\pi$
$48$	−1.00000	−0.144338
$49$	−3.00000	−0.428571
$50$	0	0
$51$	6.00000	0.840168
$52$	2.00000	0.277350
$53$	−10.0000	−1.37361	−0.686803	−	0.726844i	$-0.740986\pi$
$53$	−10.0000	−1.37361	−0.686803	+	0.726844i	$0.740986\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	2.00000	0.267261
$57$	−8.00000	−1.05963
$58$	4.00000	0.525226
$59$	6.00000	0.781133	0.390567	−	0.920575i	$-0.372279\pi$
$59$	6.00000	0.781133	0.390567	+	0.920575i	$0.372279\pi$
$60$	0	0
$61$	−14.0000	−1.79252	−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−14.0000	−1.79252	−0.896258	+	0.443533i	$0.853725\pi$
$62$	1.00000	0.127000
$63$	−2.00000	−0.251976
$64$	1.00000	0.125000
$65$	0	0
$66$	−6.00000	−0.738549
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	−6.00000	−0.727607
$69$	4.00000	0.481543
$70$	0	0
$71$	16.0000	1.89885	0.949425	−	0.313993i	$-0.101667\pi$
$71$	16.0000	1.89885	0.949425	+	0.313993i	$0.101667\pi$
$72$	−1.00000	−0.117851
$73$	8.00000	0.936329	0.468165	−	0.883641i	$-0.344915\pi$
$73$	8.00000	0.936329	0.468165	+	0.883641i	$0.344915\pi$
$74$	2.00000	0.232495
$75$	0	0
$76$	8.00000	0.917663
$77$	12.0000	1.36753
$78$	2.00000	0.226455
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−2.00000	−0.220863
$83$	4.00000	0.439057	0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000	0.439057	0.219529	+	0.975606i	$0.429548\pi$
$84$	2.00000	0.218218
$85$	0	0
$86$	−4.00000	−0.431331
$87$	4.00000	0.428845
$88$	6.00000	0.639602
$89$	10.0000	1.06000	0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000	1.06000	0.529999	+	0.847998i	$0.322192\pi$
$90$	0	0
$91$	−4.00000	−0.419314
$92$	−4.00000	−0.417029
$93$	1.00000	0.103695
$94$	8.00000	0.825137
$95$	0	0
$96$	1.00000	0.102062
$97$	−16.0000	−1.62455	−0.812277	−	0.583272i	$-0.801772\pi$
$97$	−16.0000	−1.62455	−0.812277	+	0.583272i	$0.801772\pi$
$98$	3.00000	0.303046
$99$	−6.00000	−0.603023
$100$	0	0
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	−6.00000	−0.594089
$103$	6.00000	0.591198	0.295599	−	0.955312i	$-0.404481\pi$
$103$	6.00000	0.591198	0.295599	+	0.955312i	$0.404481\pi$
$104$	−2.00000	−0.196116
$105$	0	0
$106$	10.0000	0.971286
$107$	4.00000	0.386695	0.193347	−	0.981130i	$-0.438066\pi$
$107$	4.00000	0.386695	0.193347	+	0.981130i	$0.438066\pi$
$108$	−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	$0.469465\pi$
$110$	0	0
$111$	2.00000	0.189832
$112$	−2.00000	−0.188982
$113$	−18.0000	−1.69330	−0.846649	−	0.532152i	$-0.821383\pi$
$113$	−18.0000	−1.69330	−0.846649	+	0.532152i	$0.821383\pi$
$114$	8.00000	0.749269
$115$	0	0
$116$	−4.00000	−0.371391
$117$	2.00000	0.184900
$118$	−6.00000	−0.552345
$119$	12.0000	1.10004
$120$	0	0
$121$	25.0000	2.27273
$122$	14.0000	1.26750
$123$	−2.00000	−0.180334
$124$	−1.00000	−0.0898027
$125$	0	0
$126$	2.00000	0.178174
$127$	2.00000	0.177471	0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000	0.177471	0.0887357	+	0.996055i	$0.471717\pi$
$128$	−1.00000	−0.0883883
$129$	−4.00000	−0.352180
$130$	0	0
$131$	10.0000	0.873704	0.436852	−	0.899533i	$-0.356093\pi$
$131$	10.0000	0.873704	0.436852	+	0.899533i	$0.356093\pi$
$132$	6.00000	0.522233
$133$	−16.0000	−1.38738
$134$	4.00000	0.345547
$135$	0	0
$136$	6.00000	0.514496
$137$	14.0000	1.19610	0.598050	−	0.801459i	$-0.295942\pi$
$137$	14.0000	1.19610	0.598050	+	0.801459i	$0.295942\pi$
$138$	−4.00000	−0.340503
$139$	−20.0000	−1.69638	−0.848189	−	0.529694i	$-0.822307\pi$
$139$	−20.0000	−1.69638	−0.848189	+	0.529694i	$0.822307\pi$
$140$	0	0
$141$	8.00000	0.673722
$142$	−16.0000	−1.34269
$143$	−12.0000	−1.00349
$144$	1.00000	0.0833333
$145$	0	0
$146$	−8.00000	−0.662085
$147$	3.00000	0.247436
$148$	−2.00000	−0.164399
$149$	−12.0000	−0.983078	−0.491539	−	0.870855i	$-0.663566\pi$
$149$	−12.0000	−0.983078	−0.491539	+	0.870855i	$0.663566\pi$
$150$	0	0
$151$	8.00000	0.651031	0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000	0.651031	0.325515	+	0.945537i	$0.394462\pi$
$152$	−8.00000	−0.648886
$153$	−6.00000	−0.485071
$154$	−12.0000	−0.966988
$155$	0	0
$156$	−2.00000	−0.160128
$157$	6.00000	0.478852	0.239426	−	0.970915i	$-0.423041\pi$
$157$	6.00000	0.478852	0.239426	+	0.970915i	$0.423041\pi$
$158$	0	0
$159$	10.0000	0.793052
$160$	0	0
$161$	8.00000	0.630488
$162$	−1.00000	−0.0785674
$163$	20.0000	1.56652	0.783260	−	0.621694i	$-0.213555\pi$
$163$	20.0000	1.56652	0.783260	+	0.621694i	$0.213555\pi$
$164$	2.00000	0.156174
$165$	0	0
$166$	−4.00000	−0.310460
$167$	12.0000	0.928588	0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000	0.928588	0.464294	+	0.885681i	$0.346308\pi$
$168$	−2.00000	−0.154303
$169$	−9.00000	−0.692308
$170$	0	0
$171$	8.00000	0.611775
$172$	4.00000	0.304997
$173$	−14.0000	−1.06440	−0.532200	−	0.846619i	$-0.678635\pi$
$173$	−14.0000	−1.06440	−0.532200	+	0.846619i	$0.678635\pi$
$174$	−4.00000	−0.303239
$175$	0	0
$176$	−6.00000	−0.452267
$177$	−6.00000	−0.450988
$178$	−10.0000	−0.749532
$179$	18.0000	1.34538	0.672692	−	0.739923i	$-0.265138\pi$
$179$	18.0000	1.34538	0.672692	+	0.739923i	$0.265138\pi$
$180$	0	0
$181$	10.0000	0.743294	0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000	0.743294	0.371647	+	0.928374i	$0.378793\pi$
$182$	4.00000	0.296500
$183$	14.0000	1.03491
$184$	4.00000	0.294884
$185$	0	0
$186$	−1.00000	−0.0733236
$187$	36.0000	2.63258
$188$	−8.00000	−0.583460
$189$	2.00000	0.145479
$190$	0	0
$191$	8.00000	0.578860	0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000	0.578860	0.289430	+	0.957199i	$0.406534\pi$
$192$	−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	$0.244226\pi$
$194$	16.0000	1.14873
$195$	0	0
$196$	−3.00000	−0.214286
$197$	−18.0000	−1.28245	−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000	−1.28245	−0.641223	+	0.767354i	$0.721573\pi$
$198$	6.00000	0.426401
$199$	0	0		−	1.00000i	$-0.5\pi$
$199$	0	0			1.00000i	$0.5\pi$
$200$	0	0
$201$	4.00000	0.282138
$202$	0	0
$203$	8.00000	0.561490
$204$	6.00000	0.420084
$205$	0	0
$206$	−6.00000	−0.418040
$207$	−4.00000	−0.278019
$208$	2.00000	0.138675
$209$	−48.0000	−3.32023
$210$	0	0
$211$	−20.0000	−1.37686	−0.688428	−	0.725304i	$-0.741699\pi$
$211$	−20.0000	−1.37686	−0.688428	+	0.725304i	$0.741699\pi$
$212$	−10.0000	−0.686803
$213$	−16.0000	−1.09630
$214$	−4.00000	−0.273434
$215$	0	0
$216$	1.00000	0.0680414
$217$	2.00000	0.135769
$218$	−2.00000	−0.135457
$219$	−8.00000	−0.540590
$220$	0	0
$221$	−12.0000	−0.807207
$222$	−2.00000	−0.134231
$223$	−14.0000	−0.937509	−0.468755	−	0.883328i	$-0.655297\pi$
$223$	−14.0000	−0.937509	−0.468755	+	0.883328i	$0.655297\pi$
$224$	2.00000	0.133631
$225$	0	0
$226$	18.0000	1.19734
$227$	12.0000	0.796468	0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000	0.796468	0.398234	+	0.917284i	$0.369623\pi$
$228$	−8.00000	−0.529813
$229$	6.00000	0.396491	0.198246	−	0.980152i	$-0.436476\pi$
$229$	6.00000	0.396491	0.198246	+	0.980152i	$0.436476\pi$
$230$	0	0
$231$	−12.0000	−0.789542
$232$	4.00000	0.262613
$233$	18.0000	1.17922	0.589610	−	0.807688i	$-0.299282\pi$
$233$	18.0000	1.17922	0.589610	+	0.807688i	$0.299282\pi$
$234$	−2.00000	−0.130744
$235$	0	0
$236$	6.00000	0.390567
$237$	0	0
$238$	−12.0000	−0.777844
$239$	−20.0000	−1.29369	−0.646846	−	0.762620i	$-0.723912\pi$
$239$	−20.0000	−1.29369	−0.646846	+	0.762620i	$0.723912\pi$
$240$	0	0
$241$	−18.0000	−1.15948	−0.579741	−	0.814801i	$-0.696846\pi$
$241$	−18.0000	−1.15948	−0.579741	+	0.814801i	$0.696846\pi$
$242$	−25.0000	−1.60706
$243$	−1.00000	−0.0641500
$244$	−14.0000	−0.896258
$245$	0	0
$246$	2.00000	0.127515
$247$	16.0000	1.01806
$248$	1.00000	0.0635001
$249$	−4.00000	−0.253490
$250$	0	0
$251$	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
$253$	24.0000	1.50887
$254$	−2.00000	−0.125491
$255$	0	0
$256$	1.00000	0.0625000
$257$	14.0000	0.873296	0.436648	−	0.899632i	$-0.356166\pi$
$257$	14.0000	0.873296	0.436648	+	0.899632i	$0.356166\pi$
$258$	4.00000	0.249029
$259$	4.00000	0.248548
$260$	0	0
$261$	−4.00000	−0.247594
$262$	−10.0000	−0.617802
$263$	12.0000	0.739952	0.369976	−	0.929041i	$-0.379366\pi$
$263$	12.0000	0.739952	0.369976	+	0.929041i	$0.379366\pi$
$264$	−6.00000	−0.369274
$265$	0	0
$266$	16.0000	0.981023
$267$	−10.0000	−0.611990
$268$	−4.00000	−0.244339
$269$	−4.00000	−0.243884	−0.121942	−	0.992537i	$-0.538912\pi$
$269$	−4.00000	−0.243884	−0.121942	+	0.992537i	$0.538912\pi$
$270$	0	0
$271$	0	0		−	1.00000i	$-0.5\pi$
$271$	0	0			1.00000i	$0.5\pi$
$272$	−6.00000	−0.363803
$273$	4.00000	0.242091
$274$	−14.0000	−0.845771
$275$	0	0
$276$	4.00000	0.240772
$277$	−10.0000	−0.600842	−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000	−0.600842	−0.300421	+	0.953807i	$0.597127\pi$
$278$	20.0000	1.19952
$279$	−1.00000	−0.0598684
$280$	0	0
$281$	22.0000	1.31241	0.656205	−	0.754583i	$-0.272161\pi$
$281$	22.0000	1.31241	0.656205	+	0.754583i	$0.272161\pi$
$282$	−8.00000	−0.476393
$283$	20.0000	1.18888	0.594438	−	0.804141i	$-0.297374\pi$
$283$	20.0000	1.18888	0.594438	+	0.804141i	$0.297374\pi$
$284$	16.0000	0.949425
$285$	0	0
$286$	12.0000	0.709575
$287$	−4.00000	−0.236113
$288$	−1.00000	−0.0589256
$289$	19.0000	1.11765
$290$	0	0
$291$	16.0000	0.937937
$292$	8.00000	0.468165
$293$	6.00000	0.350524	0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000	0.350524	0.175262	+	0.984522i	$0.443923\pi$
$294$	−3.00000	−0.174964
$295$	0	0
$296$	2.00000	0.116248
$297$	6.00000	0.348155
$298$	12.0000	0.695141
$299$	−8.00000	−0.462652
$300$	0	0
$301$	−8.00000	−0.461112
$302$	−8.00000	−0.460348
$303$	0	0
$304$	8.00000	0.458831
$305$	0	0
$306$	6.00000	0.342997
$307$	8.00000	0.456584	0.228292	−	0.973593i	$-0.426686\pi$
$307$	8.00000	0.456584	0.228292	+	0.973593i	$0.426686\pi$
$308$	12.0000	0.683763
$309$	−6.00000	−0.341328
$310$	0	0
$311$	−8.00000	−0.453638	−0.226819	−	0.973937i	$-0.572833\pi$
$311$	−8.00000	−0.453638	−0.226819	+	0.973937i	$0.572833\pi$
$312$	2.00000	0.113228
$313$	−24.0000	−1.35656	−0.678280	−	0.734803i	$-0.737274\pi$
$313$	−24.0000	−1.35656	−0.678280	+	0.734803i	$0.737274\pi$
$314$	−6.00000	−0.338600
$315$	0	0
$316$	0	0
$317$	18.0000	1.01098	0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000	1.01098	0.505490	+	0.862832i	$0.331312\pi$
$318$	−10.0000	−0.560772
$319$	24.0000	1.34374
$320$	0	0
$321$	−4.00000	−0.223258
$322$	−8.00000	−0.445823
$323$	−48.0000	−2.67079
$324$	1.00000	0.0555556
$325$	0	0
$326$	−20.0000	−1.10770
$327$	−2.00000	−0.110600
$328$	−2.00000	−0.110432
$329$	16.0000	0.882109
$330$	0	0
$331$	8.00000	0.439720	0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000	0.439720	0.219860	+	0.975531i	$0.429440\pi$
$332$	4.00000	0.219529
$333$	−2.00000	−0.109599
$334$	−12.0000	−0.656611
$335$	0	0
$336$	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	$0.430081\pi$
$338$	9.00000	0.489535
$339$	18.0000	0.977626
$340$	0	0
$341$	6.00000	0.324918
$342$	−8.00000	−0.432590
$343$	20.0000	1.07990
$344$	−4.00000	−0.215666
$345$	0	0
$346$	14.0000	0.752645
$347$	−4.00000	−0.214731	−0.107366	−	0.994220i	$-0.534242\pi$
$347$	−4.00000	−0.214731	−0.107366	+	0.994220i	$0.534242\pi$
$348$	4.00000	0.214423
$349$	2.00000	0.107058	0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000	0.107058	0.0535288	+	0.998566i	$0.482953\pi$
$350$	0	0
$351$	−2.00000	−0.106752
$352$	6.00000	0.319801
$353$	18.0000	0.958043	0.479022	−	0.877803i	$-0.340992\pi$
$353$	18.0000	0.958043	0.479022	+	0.877803i	$0.340992\pi$
$354$	6.00000	0.318896
$355$	0	0
$356$	10.0000	0.529999
$357$	−12.0000	−0.635107
$358$	−18.0000	−0.951330
$359$	12.0000	0.633336	0.316668	−	0.948536i	$-0.397436\pi$
$359$	12.0000	0.633336	0.316668	+	0.948536i	$0.397436\pi$
$360$	0	0
$361$	45.0000	2.36842
$362$	−10.0000	−0.525588
$363$	−25.0000	−1.31216
$364$	−4.00000	−0.209657
$365$	0	0
$366$	−14.0000	−0.731792
$367$	26.0000	1.35719	0.678594	−	0.734513i	$-0.262589\pi$
$367$	26.0000	1.35719	0.678594	+	0.734513i	$0.262589\pi$
$368$	−4.00000	−0.208514
$369$	2.00000	0.104116
$370$	0	0
$371$	20.0000	1.03835
$372$	1.00000	0.0518476
$373$	22.0000	1.13912	0.569558	−	0.821951i	$-0.307114\pi$
$373$	22.0000	1.13912	0.569558	+	0.821951i	$0.307114\pi$
$374$	−36.0000	−1.86152
$375$	0	0
$376$	8.00000	0.412568
$377$	−8.00000	−0.412021
$378$	−2.00000	−0.102869
$379$	36.0000	1.84920	0.924598	−	0.380945i	$-0.124401\pi$
$379$	36.0000	1.84920	0.924598	+	0.380945i	$0.124401\pi$
$380$	0	0
$381$	−2.00000	−0.102463
$382$	−8.00000	−0.409316
$383$	16.0000	0.817562	0.408781	−	0.912633i	$-0.365954\pi$
$383$	16.0000	0.817562	0.408781	+	0.912633i	$0.365954\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−20.0000	−1.01797
$387$	4.00000	0.203331
$388$	−16.0000	−0.812277
$389$	−16.0000	−0.811232	−0.405616	−	0.914044i	$-0.632943\pi$
$389$	−16.0000	−0.811232	−0.405616	+	0.914044i	$0.632943\pi$
$390$	0	0
$391$	24.0000	1.21373
$392$	3.00000	0.151523
$393$	−10.0000	−0.504433
$394$	18.0000	0.906827
$395$	0	0
$396$	−6.00000	−0.301511
$397$	−22.0000	−1.10415	−0.552074	−	0.833795i	$-0.686163\pi$
$397$	−22.0000	−1.10415	−0.552074	+	0.833795i	$0.686163\pi$
$398$	0	0
$399$	16.0000	0.801002
$400$	0	0
$401$	2.00000	0.0998752	0.0499376	−	0.998752i	$-0.484098\pi$
$401$	2.00000	0.0998752	0.0499376	+	0.998752i	$0.484098\pi$
$402$	−4.00000	−0.199502
$403$	−2.00000	−0.0996271
$404$	0	0
$405$	0	0
$406$	−8.00000	−0.397033
$407$	12.0000	0.594818
$408$	−6.00000	−0.297044
$409$	22.0000	1.08783	0.543915	−	0.839140i	$-0.316941\pi$
$409$	22.0000	1.08783	0.543915	+	0.839140i	$0.316941\pi$
$410$	0	0
$411$	−14.0000	−0.690569
$412$	6.00000	0.295599
$413$	−12.0000	−0.590481
$414$	4.00000	0.196589
$415$	0	0
$416$	−2.00000	−0.0980581
$417$	20.0000	0.979404
$418$	48.0000	2.34776
$419$	−6.00000	−0.293119	−0.146560	−	0.989202i	$-0.546820\pi$
$419$	−6.00000	−0.293119	−0.146560	+	0.989202i	$0.546820\pi$
$420$	0	0
$421$	−2.00000	−0.0974740	−0.0487370	−	0.998812i	$-0.515520\pi$
$421$	−2.00000	−0.0974740	−0.0487370	+	0.998812i	$0.515520\pi$
$422$	20.0000	0.973585
$423$	−8.00000	−0.388973
$424$	10.0000	0.485643
$425$	0	0
$426$	16.0000	0.775203
$427$	28.0000	1.35501
$428$	4.00000	0.193347
$429$	12.0000	0.579365
$430$	0	0
$431$	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
$433$	−8.00000	−0.384455	−0.192228	−	0.981350i	$-0.561571\pi$
$433$	−8.00000	−0.384455	−0.192228	+	0.981350i	$0.561571\pi$
$434$	−2.00000	−0.0960031
$435$	0	0
$436$	2.00000	0.0957826
$437$	−32.0000	−1.53077
$438$	8.00000	0.382255
$439$	32.0000	1.52728	0.763638	−	0.645644i	$-0.223411\pi$
$439$	32.0000	1.52728	0.763638	+	0.645644i	$0.223411\pi$
$440$	0	0
$441$	−3.00000	−0.142857
$442$	12.0000	0.570782
$443$	−4.00000	−0.190046	−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000	−0.190046	−0.0950229	+	0.995475i	$0.530292\pi$
$444$	2.00000	0.0949158
$445$	0	0
$446$	14.0000	0.662919
$447$	12.0000	0.567581
$448$	−2.00000	−0.0944911
$449$	26.0000	1.22702	0.613508	−	0.789689i	$-0.289758\pi$
$449$	26.0000	1.22702	0.613508	+	0.789689i	$0.289758\pi$
$450$	0	0
$451$	−12.0000	−0.565058
$452$	−18.0000	−0.846649
$453$	−8.00000	−0.375873
$454$	−12.0000	−0.563188
$455$	0	0
$456$	8.00000	0.374634
$457$	12.0000	0.561336	0.280668	−	0.959805i	$-0.409444\pi$
$457$	12.0000	0.561336	0.280668	+	0.959805i	$0.409444\pi$
$458$	−6.00000	−0.280362
$459$	6.00000	0.280056
$460$	0	0
$461$	−32.0000	−1.49039	−0.745194	−	0.666847i	$-0.767643\pi$
$461$	−32.0000	−1.49039	−0.745194	+	0.666847i	$0.767643\pi$
$462$	12.0000	0.558291
$463$	−26.0000	−1.20832	−0.604161	−	0.796862i	$-0.706492\pi$
$463$	−26.0000	−1.20832	−0.604161	+	0.796862i	$0.706492\pi$
$464$	−4.00000	−0.185695
$465$	0	0
$466$	−18.0000	−0.833834
$467$	4.00000	0.185098	0.0925490	−	0.995708i	$-0.470499\pi$
$467$	4.00000	0.185098	0.0925490	+	0.995708i	$0.470499\pi$
$468$	2.00000	0.0924500
$469$	8.00000	0.369406
$470$	0	0
$471$	−6.00000	−0.276465
$472$	−6.00000	−0.276172
$473$	−24.0000	−1.10352
$474$	0	0
$475$	0	0
$476$	12.0000	0.550019
$477$	−10.0000	−0.457869
$478$	20.0000	0.914779
$479$	−40.0000	−1.82765	−0.913823	−	0.406112i	$-0.866884\pi$
$479$	−40.0000	−1.82765	−0.913823	+	0.406112i	$0.866884\pi$
$480$	0	0
$481$	−4.00000	−0.182384
$482$	18.0000	0.819878
$483$	−8.00000	−0.364013
$484$	25.0000	1.13636
$485$	0	0
$486$	1.00000	0.0453609
$487$	14.0000	0.634401	0.317200	−	0.948359i	$-0.397257\pi$
$487$	14.0000	0.634401	0.317200	+	0.948359i	$0.397257\pi$
$488$	14.0000	0.633750
$489$	−20.0000	−0.904431
$490$	0	0
$491$	30.0000	1.35388	0.676941	−	0.736038i	$-0.263305\pi$
$491$	30.0000	1.35388	0.676941	+	0.736038i	$0.263305\pi$
$492$	−2.00000	−0.0901670
$493$	24.0000	1.08091
$494$	−16.0000	−0.719874
$495$	0	0
$496$	−1.00000	−0.0449013
$497$	−32.0000	−1.43540
$498$	4.00000	0.179244
$499$	−32.0000	−1.43252	−0.716258	−	0.697835i	$-0.754147\pi$
$499$	−32.0000	−1.43252	−0.716258	+	0.697835i	$0.754147\pi$
$500$	0	0
$501$	−12.0000	−0.536120
$502$	−6.00000	−0.267793
$503$	8.00000	0.356702	0.178351	−	0.983967i	$-0.442924\pi$
$503$	8.00000	0.356702	0.178351	+	0.983967i	$0.442924\pi$
$504$	2.00000	0.0890871
$505$	0	0
$506$	−24.0000	−1.06693
$507$	9.00000	0.399704
$508$	2.00000	0.0887357
$509$	20.0000	0.886484	0.443242	−	0.896402i	$-0.353828\pi$
$509$	20.0000	0.886484	0.443242	+	0.896402i	$0.353828\pi$
$510$	0	0
$511$	−16.0000	−0.707798
$512$	−1.00000	−0.0441942
$513$	−8.00000	−0.353209
$514$	−14.0000	−0.617514
$515$	0	0
$516$	−4.00000	−0.176090
$517$	48.0000	2.11104
$518$	−4.00000	−0.175750
$519$	14.0000	0.614532
$520$	0	0
$521$	−42.0000	−1.84005	−0.920027	−	0.391856i	$-0.871833\pi$
$521$	−42.0000	−1.84005	−0.920027	+	0.391856i	$0.871833\pi$
$522$	4.00000	0.175075
$523$	40.0000	1.74908	0.874539	−	0.484955i	$-0.161164\pi$
$523$	40.0000	1.74908	0.874539	+	0.484955i	$0.161164\pi$
$524$	10.0000	0.436852
$525$	0	0
$526$	−12.0000	−0.523225
$527$	6.00000	0.261364
$528$	6.00000	0.261116
$529$	−7.00000	−0.304348
$530$	0	0
$531$	6.00000	0.260378
$532$	−16.0000	−0.693688
$533$	4.00000	0.173259
$534$	10.0000	0.432742
$535$	0	0
$536$	4.00000	0.172774
$537$	−18.0000	−0.776757
$538$	4.00000	0.172452
$539$	18.0000	0.775315
$540$	0	0
$541$	18.0000	0.773880	0.386940	−	0.922105i	$-0.373532\pi$
$541$	18.0000	0.773880	0.386940	+	0.922105i	$0.373532\pi$
$542$	0	0
$543$	−10.0000	−0.429141
$544$	6.00000	0.257248
$545$	0	0
$546$	−4.00000	−0.171184
$547$	−8.00000	−0.342055	−0.171028	−	0.985266i	$-0.554709\pi$
$547$	−8.00000	−0.342055	−0.171028	+	0.985266i	$0.554709\pi$
$548$	14.0000	0.598050
$549$	−14.0000	−0.597505
$550$	0	0
$551$	−32.0000	−1.36325
$552$	−4.00000	−0.170251
$553$	0	0
$554$	10.0000	0.424859
$555$	0	0
$556$	−20.0000	−0.848189
$557$	30.0000	1.27114	0.635570	−	0.772043i	$-0.280765\pi$
$557$	30.0000	1.27114	0.635570	+	0.772043i	$0.280765\pi$
$558$	1.00000	0.0423334
$559$	8.00000	0.338364
$560$	0	0
$561$	−36.0000	−1.51992
$562$	−22.0000	−0.928014
$563$	36.0000	1.51722	0.758610	−	0.651546i	$-0.225879\pi$
$563$	36.0000	1.51722	0.758610	+	0.651546i	$0.225879\pi$
$564$	8.00000	0.336861
$565$	0	0
$566$	−20.0000	−0.840663
$567$	−2.00000	−0.0839921
$568$	−16.0000	−0.671345
$569$	18.0000	0.754599	0.377300	−	0.926091i	$-0.376853\pi$
$569$	18.0000	0.754599	0.377300	+	0.926091i	$0.376853\pi$
$570$	0	0
$571$	−40.0000	−1.67395	−0.836974	−	0.547243i	$-0.815677\pi$
$571$	−40.0000	−1.67395	−0.836974	+	0.547243i	$0.815677\pi$
$572$	−12.0000	−0.501745
$573$	−8.00000	−0.334205
$574$	4.00000	0.166957
$575$	0	0
$576$	1.00000	0.0416667
$577$	−16.0000	−0.666089	−0.333044	−	0.942911i	$-0.608076\pi$
$577$	−16.0000	−0.666089	−0.333044	+	0.942911i	$0.608076\pi$
$578$	−19.0000	−0.790296
$579$	−20.0000	−0.831172
$580$	0	0
$581$	−8.00000	−0.331896
$582$	−16.0000	−0.663221
$583$	60.0000	2.48495
$584$	−8.00000	−0.331042
$585$	0	0
$586$	−6.00000	−0.247858
$587$	12.0000	0.495293	0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000	0.495293	0.247647	+	0.968850i	$0.420343\pi$
$588$	3.00000	0.123718
$589$	−8.00000	−0.329634
$590$	0	0
$591$	18.0000	0.740421
$592$	−2.00000	−0.0821995
$593$	30.0000	1.23195	0.615976	−	0.787765i	$-0.288762\pi$
$593$	30.0000	1.23195	0.615976	+	0.787765i	$0.288762\pi$
$594$	−6.00000	−0.246183
$595$	0	0
$596$	−12.0000	−0.491539
$597$	0	0
$598$	8.00000	0.327144
$599$	−20.0000	−0.817178	−0.408589	−	0.912719i	$-0.633979\pi$
$599$	−20.0000	−0.817178	−0.408589	+	0.912719i	$0.633979\pi$
$600$	0	0
$601$	10.0000	0.407909	0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000	0.407909	0.203954	+	0.978980i	$0.434621\pi$
$602$	8.00000	0.326056
$603$	−4.00000	−0.162893
$604$	8.00000	0.325515
$605$	0	0
$606$	0	0
$607$	−6.00000	−0.243532	−0.121766	−	0.992559i	$-0.538856\pi$
$607$	−6.00000	−0.243532	−0.121766	+	0.992559i	$0.538856\pi$
$608$	−8.00000	−0.324443
$609$	−8.00000	−0.324176
$610$	0	0
$611$	−16.0000	−0.647291
$612$	−6.00000	−0.242536
$613$	30.0000	1.21169	0.605844	−	0.795583i	$-0.292835\pi$
$613$	30.0000	1.21169	0.605844	+	0.795583i	$0.292835\pi$
$614$	−8.00000	−0.322854
$615$	0	0
$616$	−12.0000	−0.483494
$617$	−22.0000	−0.885687	−0.442843	−	0.896599i	$-0.646030\pi$
$617$	−22.0000	−0.885687	−0.442843	+	0.896599i	$0.646030\pi$
$618$	6.00000	0.241355
$619$	−12.0000	−0.482321	−0.241160	−	0.970485i	$-0.577528\pi$
$619$	−12.0000	−0.482321	−0.241160	+	0.970485i	$0.577528\pi$
$620$	0	0
$621$	4.00000	0.160514
$622$	8.00000	0.320771
$623$	−20.0000	−0.801283
$624$	−2.00000	−0.0800641
$625$	0	0
$626$	24.0000	0.959233
$627$	48.0000	1.91694
$628$	6.00000	0.239426
$629$	12.0000	0.478471
$630$	0	0
$631$	−8.00000	−0.318475	−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000	−0.318475	−0.159237	+	0.987240i	$0.550904\pi$
$632$	0	0
$633$	20.0000	0.794929
$634$	−18.0000	−0.714871
$635$	0	0
$636$	10.0000	0.396526
$637$	−6.00000	−0.237729
$638$	−24.0000	−0.950169
$639$	16.0000	0.632950
$640$	0	0
$641$	14.0000	0.552967	0.276483	−	0.961019i	$-0.410831\pi$
$641$	14.0000	0.552967	0.276483	+	0.961019i	$0.410831\pi$
$642$	4.00000	0.157867
$643$	32.0000	1.26196	0.630978	−	0.775800i	$-0.282654\pi$
$643$	32.0000	1.26196	0.630978	+	0.775800i	$0.282654\pi$
$644$	8.00000	0.315244
$645$	0	0
$646$	48.0000	1.88853
$647$	−32.0000	−1.25805	−0.629025	−	0.777385i	$-0.716546\pi$
$647$	−32.0000	−1.25805	−0.629025	+	0.777385i	$0.716546\pi$
$648$	−1.00000	−0.0392837
$649$	−36.0000	−1.41312
$650$	0	0
$651$	−2.00000	−0.0783862
$652$	20.0000	0.783260
$653$	42.0000	1.64359	0.821794	−	0.569785i	$-0.192974\pi$
$653$	42.0000	1.64359	0.821794	+	0.569785i	$0.192974\pi$
$654$	2.00000	0.0782062
$655$	0	0
$656$	2.00000	0.0780869
$657$	8.00000	0.312110
$658$	−16.0000	−0.623745
$659$	18.0000	0.701180	0.350590	−	0.936529i	$-0.385981\pi$
$659$	18.0000	0.701180	0.350590	+	0.936529i	$0.385981\pi$
$660$	0	0
$661$	18.0000	0.700119	0.350059	−	0.936727i	$-0.386161\pi$
$661$	18.0000	0.700119	0.350059	+	0.936727i	$0.386161\pi$
$662$	−8.00000	−0.310929
$663$	12.0000	0.466041
$664$	−4.00000	−0.155230
$665$	0	0
$666$	2.00000	0.0774984
$667$	16.0000	0.619522
$668$	12.0000	0.464294
$669$	14.0000	0.541271
$670$	0	0
$671$	84.0000	3.24278
$672$	−2.00000	−0.0771517
$673$	−24.0000	−0.925132	−0.462566	−	0.886585i	$-0.653071\pi$
$673$	−24.0000	−0.925132	−0.462566	+	0.886585i	$0.653071\pi$
$674$	−8.00000	−0.308148
$675$	0	0
$676$	−9.00000	−0.346154
$677$	10.0000	0.384331	0.192166	−	0.981363i	$-0.438449\pi$
$677$	10.0000	0.384331	0.192166	+	0.981363i	$0.438449\pi$
$678$	−18.0000	−0.691286
$679$	32.0000	1.22805
$680$	0	0
$681$	−12.0000	−0.459841
$682$	−6.00000	−0.229752
$683$	−4.00000	−0.153056	−0.0765279	−	0.997067i	$-0.524383\pi$
$683$	−4.00000	−0.153056	−0.0765279	+	0.997067i	$0.524383\pi$
$684$	8.00000	0.305888
$685$	0	0
$686$	−20.0000	−0.763604
$687$	−6.00000	−0.228914
$688$	4.00000	0.152499
$689$	−20.0000	−0.761939
$690$	0	0
$691$	−32.0000	−1.21734	−0.608669	−	0.793424i	$-0.708296\pi$
$691$	−32.0000	−1.21734	−0.608669	+	0.793424i	$0.708296\pi$
$692$	−14.0000	−0.532200
$693$	12.0000	0.455842
$694$	4.00000	0.151838
$695$	0	0
$696$	−4.00000	−0.151620
$697$	−12.0000	−0.454532
$698$	−2.00000	−0.0757011
$699$	−18.0000	−0.680823
$700$	0	0
$701$	16.0000	0.604312	0.302156	−	0.953259i	$-0.402294\pi$
$701$	16.0000	0.604312	0.302156	+	0.953259i	$0.402294\pi$
$702$	2.00000	0.0754851
$703$	−16.0000	−0.603451
$704$	−6.00000	−0.226134
$705$	0	0
$706$	−18.0000	−0.677439
$707$	0	0
$708$	−6.00000	−0.225494
$709$	−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
$712$	−10.0000	−0.374766
$713$	4.00000	0.149801
$714$	12.0000	0.449089
$715$	0	0
$716$	18.0000	0.672692
$717$	20.0000	0.746914
$718$	−12.0000	−0.447836
$719$	−8.00000	−0.298350	−0.149175	−	0.988811i	$-0.547662\pi$
$719$	−8.00000	−0.298350	−0.149175	+	0.988811i	$0.547662\pi$
$720$	0	0
$721$	−12.0000	−0.446903
$722$	−45.0000	−1.67473
$723$	18.0000	0.669427
$724$	10.0000	0.371647
$725$	0	0
$726$	25.0000	0.927837
$727$	−38.0000	−1.40934	−0.704671	−	0.709534i	$-0.748905\pi$
$727$	−38.0000	−1.40934	−0.704671	+	0.709534i	$0.748905\pi$
$728$	4.00000	0.148250
$729$	1.00000	0.0370370
$730$	0	0
$731$	−24.0000	−0.887672
$732$	14.0000	0.517455
$733$	−22.0000	−0.812589	−0.406294	−	0.913742i	$-0.633179\pi$
$733$	−22.0000	−0.812589	−0.406294	+	0.913742i	$0.633179\pi$
$734$	−26.0000	−0.959678
$735$	0	0
$736$	4.00000	0.147442
$737$	24.0000	0.884051
$738$	−2.00000	−0.0736210
$739$	−24.0000	−0.882854	−0.441427	−	0.897297i	$-0.645528\pi$
$739$	−24.0000	−0.882854	−0.441427	+	0.897297i	$0.645528\pi$
$740$	0	0
$741$	−16.0000	−0.587775
$742$	−20.0000	−0.734223
$743$	−24.0000	−0.880475	−0.440237	−	0.897881i	$-0.645106\pi$
$743$	−24.0000	−0.880475	−0.440237	+	0.897881i	$0.645106\pi$
$744$	−1.00000	−0.0366618
$745$	0	0
$746$	−22.0000	−0.805477
$747$	4.00000	0.146352
$748$	36.0000	1.31629
$749$	−8.00000	−0.292314
$750$	0	0
$751$	40.0000	1.45962	0.729810	−	0.683650i	$-0.239608\pi$
$751$	40.0000	1.45962	0.729810	+	0.683650i	$0.239608\pi$
$752$	−8.00000	−0.291730
$753$	−6.00000	−0.218652
$754$	8.00000	0.291343
$755$	0	0
$756$	2.00000	0.0727393
$757$	−34.0000	−1.23575	−0.617876	−	0.786276i	$-0.712006\pi$
$757$	−34.0000	−1.23575	−0.617876	+	0.786276i	$0.712006\pi$
$758$	−36.0000	−1.30758
$759$	−24.0000	−0.871145
$760$	0	0
$761$	−54.0000	−1.95750	−0.978749	−	0.205061i	$-0.934261\pi$
$761$	−54.0000	−1.95750	−0.978749	+	0.205061i	$0.934261\pi$
$762$	2.00000	0.0724524
$763$	−4.00000	−0.144810
$764$	8.00000	0.289430
$765$	0	0
$766$	−16.0000	−0.578103
$767$	12.0000	0.433295
$768$	−1.00000	−0.0360844
$769$	−30.0000	−1.08183	−0.540914	−	0.841078i	$-0.681921\pi$
$769$	−30.0000	−1.08183	−0.540914	+	0.841078i	$0.681921\pi$
$770$	0	0
$771$	−14.0000	−0.504198
$772$	20.0000	0.719816
$773$	34.0000	1.22290	0.611448	−	0.791285i	$-0.290588\pi$
$773$	34.0000	1.22290	0.611448	+	0.791285i	$0.290588\pi$
$774$	−4.00000	−0.143777
$775$	0	0
$776$	16.0000	0.574367
$777$	−4.00000	−0.143499
$778$	16.0000	0.573628
$779$	16.0000	0.573259
$780$	0	0
$781$	−96.0000	−3.43515
$782$	−24.0000	−0.858238
$783$	4.00000	0.142948
$784$	−3.00000	−0.107143
$785$	0	0
$786$	10.0000	0.356688
$787$	0	0		−	1.00000i	$-0.5\pi$
$787$	0	0			1.00000i	$0.5\pi$
$788$	−18.0000	−0.641223
$789$	−12.0000	−0.427211
$790$	0	0
$791$	36.0000	1.28001
$792$	6.00000	0.213201
$793$	−28.0000	−0.994309
$794$	22.0000	0.780751
$795$	0	0
$796$	0	0
$797$	50.0000	1.77109	0.885545	−	0.464553i	$-0.153785\pi$
$797$	50.0000	1.77109	0.885545	+	0.464553i	$0.153785\pi$
$798$	−16.0000	−0.566394
$799$	48.0000	1.69812
$800$	0	0
$801$	10.0000	0.353333
$802$	−2.00000	−0.0706225
$803$	−48.0000	−1.69388
$804$	4.00000	0.141069
$805$	0	0
$806$	2.00000	0.0704470
$807$	4.00000	0.140807
$808$	0	0
$809$	−18.0000	−0.632846	−0.316423	−	0.948618i	$-0.602482\pi$
$809$	−18.0000	−0.632846	−0.316423	+	0.948618i	$0.602482\pi$
$810$	0	0
$811$	−28.0000	−0.983213	−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000	−0.983213	−0.491606	+	0.870817i	$0.663590\pi$
$812$	8.00000	0.280745
$813$	0	0
$814$	−12.0000	−0.420600
$815$	0	0
$816$	6.00000	0.210042
$817$	32.0000	1.11954
$818$	−22.0000	−0.769212
$819$	−4.00000	−0.139771
$820$	0	0
$821$	36.0000	1.25641	0.628204	−	0.778048i	$-0.283790\pi$
$821$	36.0000	1.25641	0.628204	+	0.778048i	$0.283790\pi$
$822$	14.0000	0.488306
$823$	54.0000	1.88232	0.941161	−	0.337959i	$-0.109737\pi$
$823$	54.0000	1.88232	0.941161	+	0.337959i	$0.109737\pi$
$824$	−6.00000	−0.209020
$825$	0	0
$826$	12.0000	0.417533
$827$	−4.00000	−0.139094	−0.0695468	−	0.997579i	$-0.522155\pi$
$827$	−4.00000	−0.139094	−0.0695468	+	0.997579i	$0.522155\pi$
$828$	−4.00000	−0.139010
$829$	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
$832$	2.00000	0.0693375
$833$	18.0000	0.623663
$834$	−20.0000	−0.692543
$835$	0	0
$836$	−48.0000	−1.66011
$837$	1.00000	0.0345651
$838$	6.00000	0.207267
$839$	−12.0000	−0.414286	−0.207143	−	0.978311i	$-0.566417\pi$
$839$	−12.0000	−0.414286	−0.207143	+	0.978311i	$0.566417\pi$
$840$	0	0
$841$	−13.0000	−0.448276
$842$	2.00000	0.0689246
$843$	−22.0000	−0.757720
$844$	−20.0000	−0.688428
$845$	0	0
$846$	8.00000	0.275046
$847$	−50.0000	−1.71802
$848$	−10.0000	−0.343401
$849$	−20.0000	−0.686398
$850$	0	0
$851$	8.00000	0.274236
$852$	−16.0000	−0.548151
$853$	−22.0000	−0.753266	−0.376633	−	0.926363i	$-0.622918\pi$
$853$	−22.0000	−0.753266	−0.376633	+	0.926363i	$0.622918\pi$
$854$	−28.0000	−0.958140
$855$	0	0
$856$	−4.00000	−0.136717
$857$	−46.0000	−1.57133	−0.785665	−	0.618652i	$-0.787679\pi$
$857$	−46.0000	−1.57133	−0.785665	+	0.618652i	$0.787679\pi$
$858$	−12.0000	−0.409673
$859$	4.00000	0.136478	0.0682391	−	0.997669i	$-0.478262\pi$
$859$	4.00000	0.136478	0.0682391	+	0.997669i	$0.478262\pi$
$860$	0	0
$861$	4.00000	0.136320
$862$	−12.0000	−0.408722
$863$	−44.0000	−1.49778	−0.748889	−	0.662696i	$-0.769412\pi$
$863$	−44.0000	−1.49778	−0.748889	+	0.662696i	$0.769412\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	8.00000	0.271851
$867$	−19.0000	−0.645274
$868$	2.00000	0.0678844
$869$	0	0
$870$	0	0
$871$	−8.00000	−0.271070
$872$	−2.00000	−0.0677285
$873$	−16.0000	−0.541518
$874$	32.0000	1.08242
$875$	0	0
$876$	−8.00000	−0.270295
$877$	30.0000	1.01303	0.506514	−	0.862232i	$-0.330934\pi$
$877$	30.0000	1.01303	0.506514	+	0.862232i	$0.330934\pi$
$878$	−32.0000	−1.07995
$879$	−6.00000	−0.202375
$880$	0	0
$881$	18.0000	0.606435	0.303218	−	0.952921i	$-0.401939\pi$
$881$	18.0000	0.606435	0.303218	+	0.952921i	$0.401939\pi$
$882$	3.00000	0.101015
$883$	−56.0000	−1.88455	−0.942275	−	0.334840i	$-0.891318\pi$
$883$	−56.0000	−1.88455	−0.942275	+	0.334840i	$0.891318\pi$
$884$	−12.0000	−0.403604
$885$	0	0
$886$	4.00000	0.134383
$887$	−12.0000	−0.402921	−0.201460	−	0.979497i	$-0.564569\pi$
$887$	−12.0000	−0.402921	−0.201460	+	0.979497i	$0.564569\pi$
$888$	−2.00000	−0.0671156
$889$	−4.00000	−0.134156
$890$	0	0
$891$	−6.00000	−0.201008
$892$	−14.0000	−0.468755
$893$	−64.0000	−2.14168
$894$	−12.0000	−0.401340
$895$	0	0
$896$	2.00000	0.0668153
$897$	8.00000	0.267112
$898$	−26.0000	−0.867631
$899$	4.00000	0.133407
$900$	0	0
$901$	60.0000	1.99889
$902$	12.0000	0.399556
$903$	8.00000	0.266223
$904$	18.0000	0.598671
$905$	0	0
$906$	8.00000	0.265782
$907$	24.0000	0.796907	0.398453	−	0.917189i	$-0.369547\pi$
$907$	24.0000	0.796907	0.398453	+	0.917189i	$0.369547\pi$
$908$	12.0000	0.398234
$909$	0	0
$910$	0	0
$911$	−16.0000	−0.530104	−0.265052	−	0.964234i	$-0.585389\pi$
$911$	−16.0000	−0.530104	−0.265052	+	0.964234i	$0.585389\pi$
$912$	−8.00000	−0.264906
$913$	−24.0000	−0.794284
$914$	−12.0000	−0.396925
$915$	0	0
$916$	6.00000	0.198246
$917$	−20.0000	−0.660458
$918$	−6.00000	−0.198030
$919$	−16.0000	−0.527791	−0.263896	−	0.964551i	$-0.585007\pi$
$919$	−16.0000	−0.527791	−0.263896	+	0.964551i	$0.585007\pi$
$920$	0	0
$921$	−8.00000	−0.263609
$922$	32.0000	1.05386
$923$	32.0000	1.05329
$924$	−12.0000	−0.394771
$925$	0	0
$926$	26.0000	0.854413
$927$	6.00000	0.197066
$928$	4.00000	0.131306
$929$	50.0000	1.64045	0.820223	−	0.572043i	$-0.193849\pi$
$929$	50.0000	1.64045	0.820223	+	0.572043i	$0.193849\pi$
$930$	0	0
$931$	−24.0000	−0.786568
$932$	18.0000	0.589610
$933$	8.00000	0.261908
$934$	−4.00000	−0.130884
$935$	0	0
$936$	−2.00000	−0.0653720
$937$	16.0000	0.522697	0.261349	−	0.965244i	$-0.415833\pi$
$937$	16.0000	0.522697	0.261349	+	0.965244i	$0.415833\pi$
$938$	−8.00000	−0.261209
$939$	24.0000	0.783210
$940$	0	0
$941$	16.0000	0.521585	0.260793	−	0.965395i	$-0.416016\pi$
$941$	16.0000	0.521585	0.260793	+	0.965395i	$0.416016\pi$
$942$	6.00000	0.195491
$943$	−8.00000	−0.260516
$944$	6.00000	0.195283
$945$	0	0
$946$	24.0000	0.780307
$947$	−44.0000	−1.42981	−0.714904	−	0.699223i	$-0.753530\pi$
$947$	−44.0000	−1.42981	−0.714904	+	0.699223i	$0.753530\pi$
$948$	0	0
$949$	16.0000	0.519382
$950$	0	0
$951$	−18.0000	−0.583690
$952$	−12.0000	−0.388922
$953$	38.0000	1.23094	0.615470	−	0.788160i	$-0.288966\pi$
$953$	38.0000	1.23094	0.615470	+	0.788160i	$0.288966\pi$
$954$	10.0000	0.323762
$955$	0	0
$956$	−20.0000	−0.646846
$957$	−24.0000	−0.775810
$958$	40.0000	1.29234
$959$	−28.0000	−0.904167
$960$	0	0
$961$	1.00000	0.0322581
$962$	4.00000	0.128965
$963$	4.00000	0.128898
$964$	−18.0000	−0.579741
$965$	0	0
$966$	8.00000	0.257396
$967$	−14.0000	−0.450210	−0.225105	−	0.974335i	$-0.572272\pi$
$967$	−14.0000	−0.450210	−0.225105	+	0.974335i	$0.572272\pi$
$968$	−25.0000	−0.803530
$969$	48.0000	1.54198
$970$	0	0
$971$	−30.0000	−0.962746	−0.481373	−	0.876516i	$-0.659862\pi$
$971$	−30.0000	−0.962746	−0.481373	+	0.876516i	$0.659862\pi$
$972$	−1.00000	−0.0320750
$973$	40.0000	1.28234
$974$	−14.0000	−0.448589
$975$	0	0
$976$	−14.0000	−0.448129
$977$	−30.0000	−0.959785	−0.479893	−	0.877327i	$-0.659324\pi$
$977$	−30.0000	−0.959785	−0.479893	+	0.877327i	$0.659324\pi$
$978$	20.0000	0.639529
$979$	−60.0000	−1.91761
$980$	0	0
$981$	2.00000	0.0638551
$982$	−30.0000	−0.957338
$983$	0	0		−	1.00000i	$-0.5\pi$
$983$	0	0			1.00000i	$0.5\pi$
$984$	2.00000	0.0637577
$985$	0	0
$986$	−24.0000	−0.764316
$987$	−16.0000	−0.509286
$988$	16.0000	0.509028
$989$	−16.0000	−0.508770
$990$	0	0
$991$	16.0000	0.508257	0.254128	−	0.967170i	$-0.418211\pi$
$991$	16.0000	0.508257	0.254128	+	0.967170i	$0.418211\pi$
$992$	1.00000	0.0317500
$993$	−8.00000	−0.253872
$994$	32.0000	1.01498
$995$	0	0
$996$	−4.00000	−0.126745
$997$	30.0000	0.950110	0.475055	−	0.879956i	$-0.342428\pi$
$997$	30.0000	0.950110	0.475055	+	0.879956i	$0.342428\pi$
$998$	32.0000	1.01294
$999$	2.00000	0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4650.2.a.c.1.1		1
5.2	odd	4		930.2.d.e.559.1	✓	2
5.3	odd	4		930.2.d.e.559.2	yes	2
5.4	even	2		4650.2.a.bs.1.1		1
15.2	even	4		2790.2.d.c.559.2		2
15.8	even	4		2790.2.d.c.559.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.d.e.559.1	✓	2	5.2	odd	4
930.2.d.e.559.2	yes	2	5.3	odd	4
2790.2.d.c.559.1		2	15.8	even	4
2790.2.d.c.559.2		2	15.2	even	4
4650.2.a.c.1.1		1	1.1	even	1	trivial
4650.2.a.bs.1.1		1	5.4	even	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:	\( N \)	\(=\)	\( 4650 = 2 \cdot 3 \cdot 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4650.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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