LMFDB - Embedded newform 4290.2.a.bb.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4290,2,Mod(1,4290)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4290, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4290.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4290 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4290.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:	$34.2558224671$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4290.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -4.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -4.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} +1.00000 q^{13} -4.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} -6.00000 q^{17} +1.00000 q^{18} -4.00000 q^{19} +1.00000 q^{20} -4.00000 q^{21} -1.00000 q^{22} +1.00000 q^{24} +1.00000 q^{25} +1.00000 q^{26} +1.00000 q^{27} -4.00000 q^{28} -6.00000 q^{29} +1.00000 q^{30} -4.00000 q^{31} +1.00000 q^{32} -1.00000 q^{33} -6.00000 q^{34} -4.00000 q^{35} +1.00000 q^{36} +2.00000 q^{37} -4.00000 q^{38} +1.00000 q^{39} +1.00000 q^{40} -6.00000 q^{41} -4.00000 q^{42} -4.00000 q^{43} -1.00000 q^{44} +1.00000 q^{45} +1.00000 q^{48} +9.00000 q^{49} +1.00000 q^{50} -6.00000 q^{51} +1.00000 q^{52} -6.00000 q^{53} +1.00000 q^{54} -1.00000 q^{55} -4.00000 q^{56} -4.00000 q^{57} -6.00000 q^{58} +12.0000 q^{59} +1.00000 q^{60} -10.0000 q^{61} -4.00000 q^{62} -4.00000 q^{63} +1.00000 q^{64} +1.00000 q^{65} -1.00000 q^{66} -4.00000 q^{67} -6.00000 q^{68} -4.00000 q^{70} +1.00000 q^{72} +2.00000 q^{73} +2.00000 q^{74} +1.00000 q^{75} -4.00000 q^{76} +4.00000 q^{77} +1.00000 q^{78} +8.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} -6.00000 q^{82} +12.0000 q^{83} -4.00000 q^{84} -6.00000 q^{85} -4.00000 q^{86} -6.00000 q^{87} -1.00000 q^{88} -6.00000 q^{89} +1.00000 q^{90} -4.00000 q^{91} -4.00000 q^{93} -4.00000 q^{95} +1.00000 q^{96} -10.0000 q^{97} +9.00000 q^{98} -1.00000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	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
$7$	−4.00000	−1.51186	−0.755929	−	0.654654i	$-0.772814\pi$
$7$	−4.00000	−1.51186	−0.755929	+	0.654654i	$0.772814\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.00000	0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−4.00000	−1.06904
$15$	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
$19$	−4.00000	−0.917663	−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000	−0.917663	−0.458831	+	0.888523i	$0.651732\pi$
$20$	1.00000	0.223607
$21$	−4.00000	−0.872872
$22$	−1.00000	−0.213201
$23$	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
$26$	1.00000	0.196116
$27$	1.00000	0.192450
$28$	−4.00000	−0.755929
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	1.00000	0.182574
$31$	−4.00000	−0.718421	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000	−0.718421	−0.359211	+	0.933257i	$0.616954\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	−6.00000	−1.02899
$35$	−4.00000	−0.676123
$36$	1.00000	0.166667
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	−4.00000	−0.648886
$39$	1.00000	0.160128
$40$	1.00000	0.158114
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	−4.00000	−0.617213
$43$	−4.00000	−0.609994	−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000	−0.609994	−0.304997	+	0.952353i	$0.598656\pi$
$44$	−1.00000	−0.150756
$45$	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
$49$	9.00000	1.28571
$50$	1.00000	0.141421
$51$	−6.00000	−0.840168
$52$	1.00000	0.138675
$53$	−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
$55$	−1.00000	−0.134840
$56$	−4.00000	−0.534522
$57$	−4.00000	−0.529813
$58$	−6.00000	−0.787839
$59$	12.0000	1.56227	0.781133	−	0.624364i	$-0.214642\pi$
$59$	12.0000	1.56227	0.781133	+	0.624364i	$0.214642\pi$
$60$	1.00000	0.129099
$61$	−10.0000	−1.28037	−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000	−1.28037	−0.640184	+	0.768221i	$0.721142\pi$
$62$	−4.00000	−0.508001
$63$	−4.00000	−0.503953
$64$	1.00000	0.125000
$65$	1.00000	0.124035
$66$	−1.00000	−0.123091
$67$	−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
$69$	0	0
$70$	−4.00000	−0.478091
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	1.00000	0.117851
$73$	2.00000	0.234082	0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000	0.234082	0.117041	+	0.993127i	$0.462659\pi$
$74$	2.00000	0.232495
$75$	1.00000	0.115470
$76$	−4.00000	−0.458831
$77$	4.00000	0.455842
$78$	1.00000	0.113228
$79$	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
$82$	−6.00000	−0.662589
$83$	12.0000	1.31717	0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000	1.31717	0.658586	+	0.752506i	$0.271155\pi$
$84$	−4.00000	−0.436436
$85$	−6.00000	−0.650791
$86$	−4.00000	−0.431331
$87$	−6.00000	−0.643268
$88$	−1.00000	−0.106600
$89$	−6.00000	−0.635999	−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000	−0.635999	−0.317999	+	0.948091i	$0.603011\pi$
$90$	1.00000	0.105409
$91$	−4.00000	−0.419314
$92$	0	0
$93$	−4.00000	−0.414781
$94$	0	0
$95$	−4.00000	−0.410391
$96$	1.00000	0.102062
$97$	−10.0000	−1.01535	−0.507673	−	0.861550i	$-0.669494\pi$
$97$	−10.0000	−1.01535	−0.507673	+	0.861550i	$0.669494\pi$
$98$	9.00000	0.909137
$99$	−1.00000	−0.100504
$100$	1.00000	0.100000
$101$	−6.00000	−0.597022	−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000	−0.597022	−0.298511	+	0.954406i	$0.596490\pi$
$102$	−6.00000	−0.594089
$103$	8.00000	0.788263	0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000	0.788263	0.394132	+	0.919054i	$0.371045\pi$
$104$	1.00000	0.0980581
$105$	−4.00000	−0.390360
$106$	−6.00000	−0.582772
$107$	0	0		−	1.00000i	$-0.5\pi$
$107$	0	0			1.00000i	$0.5\pi$
$108$	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	$0.469465\pi$
$110$	−1.00000	−0.0953463
$111$	2.00000	0.189832
$112$	−4.00000	−0.377964
$113$	6.00000	0.564433	0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000	0.564433	0.282216	+	0.959351i	$0.408930\pi$
$114$	−4.00000	−0.374634
$115$	0	0
$116$	−6.00000	−0.557086
$117$	1.00000	0.0924500
$118$	12.0000	1.10469
$119$	24.0000	2.20008
$120$	1.00000	0.0912871
$121$	1.00000	0.0909091
$122$	−10.0000	−0.905357
$123$	−6.00000	−0.541002
$124$	−4.00000	−0.359211
$125$	1.00000	0.0894427
$126$	−4.00000	−0.356348
$127$	−16.0000	−1.41977	−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000	−1.41977	−0.709885	+	0.704317i	$0.751253\pi$
$128$	1.00000	0.0883883
$129$	−4.00000	−0.352180
$130$	1.00000	0.0877058
$131$	−12.0000	−1.04844	−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000	−1.04844	−0.524222	+	0.851581i	$0.675644\pi$
$132$	−1.00000	−0.0870388
$133$	16.0000	1.38738
$134$	−4.00000	−0.345547
$135$	1.00000	0.0860663
$136$	−6.00000	−0.514496
$137$	−6.00000	−0.512615	−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000	−0.512615	−0.256307	+	0.966595i	$0.582506\pi$
$138$	0	0
$139$	−4.00000	−0.339276	−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000	−0.339276	−0.169638	+	0.985506i	$0.554260\pi$
$140$	−4.00000	−0.338062
$141$	0	0
$142$	0	0
$143$	−1.00000	−0.0836242
$144$	1.00000	0.0833333
$145$	−6.00000	−0.498273
$146$	2.00000	0.165521
$147$	9.00000	0.742307
$148$	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
$151$	8.00000	0.651031	0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000	0.651031	0.325515	+	0.945537i	$0.394462\pi$
$152$	−4.00000	−0.324443
$153$	−6.00000	−0.485071
$154$	4.00000	0.322329
$155$	−4.00000	−0.321288
$156$	1.00000	0.0800641
$157$	14.0000	1.11732	0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000	1.11732	0.558661	+	0.829396i	$0.311315\pi$
$158$	8.00000	0.636446
$159$	−6.00000	−0.475831
$160$	1.00000	0.0790569
$161$	0	0
$162$	1.00000	0.0785674
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	−6.00000	−0.468521
$165$	−1.00000	−0.0778499
$166$	12.0000	0.931381
$167$	24.0000	1.85718	0.928588	−	0.371113i	$-0.121024\pi$
$167$	24.0000	1.85718	0.928588	+	0.371113i	$0.121024\pi$
$168$	−4.00000	−0.308607
$169$	1.00000	0.0769231
$170$	−6.00000	−0.460179
$171$	−4.00000	−0.305888
$172$	−4.00000	−0.304997
$173$	6.00000	0.456172	0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000	0.456172	0.228086	+	0.973641i	$0.426753\pi$
$174$	−6.00000	−0.454859
$175$	−4.00000	−0.302372
$176$	−1.00000	−0.0753778
$177$	12.0000	0.901975
$178$	−6.00000	−0.449719
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	1.00000	0.0745356
$181$	−10.0000	−0.743294	−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000	−0.743294	−0.371647	+	0.928374i	$0.621207\pi$
$182$	−4.00000	−0.296500
$183$	−10.0000	−0.739221
$184$	0	0
$185$	2.00000	0.147043
$186$	−4.00000	−0.293294
$187$	6.00000	0.438763
$188$	0	0
$189$	−4.00000	−0.290957
$190$	−4.00000	−0.290191
$191$	12.0000	0.868290	0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000	0.868290	0.434145	+	0.900843i	$0.357051\pi$
$192$	1.00000	0.0721688
$193$	−22.0000	−1.58359	−0.791797	−	0.610784i	$-0.790854\pi$
$193$	−22.0000	−1.58359	−0.791797	+	0.610784i	$0.790854\pi$
$194$	−10.0000	−0.717958
$195$	1.00000	0.0716115
$196$	9.00000	0.642857
$197$	6.00000	0.427482	0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000	0.427482	0.213741	+	0.976890i	$0.431435\pi$
$198$	−1.00000	−0.0710669
$199$	−16.0000	−1.13421	−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000	−1.13421	−0.567105	+	0.823646i	$0.691937\pi$
$200$	1.00000	0.0707107
$201$	−4.00000	−0.282138
$202$	−6.00000	−0.422159
$203$	24.0000	1.68447
$204$	−6.00000	−0.420084
$205$	−6.00000	−0.419058
$206$	8.00000	0.557386
$207$	0	0
$208$	1.00000	0.0693375
$209$	4.00000	0.276686
$210$	−4.00000	−0.276026
$211$	−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
$214$	0	0
$215$	−4.00000	−0.272798
$216$	1.00000	0.0680414
$217$	16.0000	1.08615
$218$	2.00000	0.135457
$219$	2.00000	0.135147
$220$	−1.00000	−0.0674200
$221$	−6.00000	−0.403604
$222$	2.00000	0.134231
$223$	8.00000	0.535720	0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000	0.535720	0.267860	+	0.963458i	$0.413684\pi$
$224$	−4.00000	−0.267261
$225$	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	$0.369623\pi$
$228$	−4.00000	−0.264906
$229$	14.0000	0.925146	0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000	0.925146	0.462573	+	0.886581i	$0.346926\pi$
$230$	0	0
$231$	4.00000	0.263181
$232$	−6.00000	−0.393919
$233$	−6.00000	−0.393073	−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000	−0.393073	−0.196537	+	0.980497i	$0.562969\pi$
$234$	1.00000	0.0653720
$235$	0	0
$236$	12.0000	0.781133
$237$	8.00000	0.519656
$238$	24.0000	1.55569
$239$	0	0		−	1.00000i	$-0.5\pi$
$239$	0	0			1.00000i	$0.5\pi$
$240$	1.00000	0.0645497
$241$	−10.0000	−0.644157	−0.322078	−	0.946713i	$-0.604381\pi$
$241$	−10.0000	−0.644157	−0.322078	+	0.946713i	$0.604381\pi$
$242$	1.00000	0.0642824
$243$	1.00000	0.0641500
$244$	−10.0000	−0.640184
$245$	9.00000	0.574989
$246$	−6.00000	−0.382546
$247$	−4.00000	−0.254514
$248$	−4.00000	−0.254000
$249$	12.0000	0.760469
$250$	1.00000	0.0632456
$251$	−24.0000	−1.51487	−0.757433	−	0.652913i	$-0.773547\pi$
$251$	−24.0000	−1.51487	−0.757433	+	0.652913i	$0.773547\pi$
$252$	−4.00000	−0.251976
$253$	0	0
$254$	−16.0000	−1.00393
$255$	−6.00000	−0.375735
$256$	1.00000	0.0625000
$257$	−18.0000	−1.12281	−0.561405	−	0.827541i	$-0.689739\pi$
$257$	−18.0000	−1.12281	−0.561405	+	0.827541i	$0.689739\pi$
$258$	−4.00000	−0.249029
$259$	−8.00000	−0.497096
$260$	1.00000	0.0620174
$261$	−6.00000	−0.371391
$262$	−12.0000	−0.741362
$263$	12.0000	0.739952	0.369976	−	0.929041i	$-0.379366\pi$
$263$	12.0000	0.739952	0.369976	+	0.929041i	$0.379366\pi$
$264$	−1.00000	−0.0615457
$265$	−6.00000	−0.368577
$266$	16.0000	0.981023
$267$	−6.00000	−0.367194
$268$	−4.00000	−0.244339
$269$	−18.0000	−1.09748	−0.548740	−	0.835993i	$-0.684892\pi$
$269$	−18.0000	−1.09748	−0.548740	+	0.835993i	$0.684892\pi$
$270$	1.00000	0.0608581
$271$	8.00000	0.485965	0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000	0.485965	0.242983	+	0.970031i	$0.421874\pi$
$272$	−6.00000	−0.363803
$273$	−4.00000	−0.242091
$274$	−6.00000	−0.362473
$275$	−1.00000	−0.0603023
$276$	0	0
$277$	−10.0000	−0.600842	−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000	−0.600842	−0.300421	+	0.953807i	$0.597127\pi$
$278$	−4.00000	−0.239904
$279$	−4.00000	−0.239474
$280$	−4.00000	−0.239046
$281$	−6.00000	−0.357930	−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000	−0.357930	−0.178965	+	0.983855i	$0.557275\pi$
$282$	0	0
$283$	−4.00000	−0.237775	−0.118888	−	0.992908i	$-0.537933\pi$
$283$	−4.00000	−0.237775	−0.118888	+	0.992908i	$0.537933\pi$
$284$	0	0
$285$	−4.00000	−0.236940
$286$	−1.00000	−0.0591312
$287$	24.0000	1.41668
$288$	1.00000	0.0589256
$289$	19.0000	1.11765
$290$	−6.00000	−0.352332
$291$	−10.0000	−0.586210
$292$	2.00000	0.117041
$293$	6.00000	0.350524	0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000	0.350524	0.175262	+	0.984522i	$0.443923\pi$
$294$	9.00000	0.524891
$295$	12.0000	0.698667
$296$	2.00000	0.116248
$297$	−1.00000	−0.0580259
$298$	−18.0000	−1.04271
$299$	0	0
$300$	1.00000	0.0577350
$301$	16.0000	0.922225
$302$	8.00000	0.460348
$303$	−6.00000	−0.344691
$304$	−4.00000	−0.229416
$305$	−10.0000	−0.572598
$306$	−6.00000	−0.342997
$307$	32.0000	1.82634	0.913168	−	0.407583i	$-0.133628\pi$
$307$	32.0000	1.82634	0.913168	+	0.407583i	$0.133628\pi$
$308$	4.00000	0.227921
$309$	8.00000	0.455104
$310$	−4.00000	−0.227185
$311$	12.0000	0.680458	0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000	0.680458	0.340229	+	0.940343i	$0.389495\pi$
$312$	1.00000	0.0566139
$313$	2.00000	0.113047	0.0565233	−	0.998401i	$-0.481998\pi$
$313$	2.00000	0.113047	0.0565233	+	0.998401i	$0.481998\pi$
$314$	14.0000	0.790066
$315$	−4.00000	−0.225374
$316$	8.00000	0.450035
$317$	−18.0000	−1.01098	−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000	−1.01098	−0.505490	+	0.862832i	$0.668688\pi$
$318$	−6.00000	−0.336463
$319$	6.00000	0.335936
$320$	1.00000	0.0559017
$321$	0	0
$322$	0	0
$323$	24.0000	1.33540
$324$	1.00000	0.0555556
$325$	1.00000	0.0554700
$326$	−4.00000	−0.221540
$327$	2.00000	0.110600
$328$	−6.00000	−0.331295
$329$	0	0
$330$	−1.00000	−0.0550482
$331$	8.00000	0.439720	0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000	0.439720	0.219860	+	0.975531i	$0.429440\pi$
$332$	12.0000	0.658586
$333$	2.00000	0.109599
$334$	24.0000	1.31322
$335$	−4.00000	−0.218543
$336$	−4.00000	−0.218218
$337$	2.00000	0.108947	0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000	0.108947	0.0544735	+	0.998515i	$0.482652\pi$
$338$	1.00000	0.0543928
$339$	6.00000	0.325875
$340$	−6.00000	−0.325396
$341$	4.00000	0.216612
$342$	−4.00000	−0.216295
$343$	−8.00000	−0.431959
$344$	−4.00000	−0.215666
$345$	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	$0.277193\pi$
$348$	−6.00000	−0.321634
$349$	26.0000	1.39175	0.695874	−	0.718164i	$-0.255017\pi$
$349$	26.0000	1.39175	0.695874	+	0.718164i	$0.255017\pi$
$350$	−4.00000	−0.213809
$351$	1.00000	0.0533761
$352$	−1.00000	−0.0533002
$353$	18.0000	0.958043	0.479022	−	0.877803i	$-0.340992\pi$
$353$	18.0000	0.958043	0.479022	+	0.877803i	$0.340992\pi$
$354$	12.0000	0.637793
$355$	0	0
$356$	−6.00000	−0.317999
$357$	24.0000	1.27021
$358$	0	0
$359$	0	0		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	1.00000	0.0527046
$361$	−3.00000	−0.157895
$362$	−10.0000	−0.525588
$363$	1.00000	0.0524864
$364$	−4.00000	−0.209657
$365$	2.00000	0.104685
$366$	−10.0000	−0.522708
$367$	32.0000	1.67039	0.835193	−	0.549957i	$-0.185356\pi$
$367$	32.0000	1.67039	0.835193	+	0.549957i	$0.185356\pi$
$368$	0	0
$369$	−6.00000	−0.312348
$370$	2.00000	0.103975
$371$	24.0000	1.24602
$372$	−4.00000	−0.207390
$373$	−10.0000	−0.517780	−0.258890	−	0.965907i	$-0.583357\pi$
$373$	−10.0000	−0.517780	−0.258890	+	0.965907i	$0.583357\pi$
$374$	6.00000	0.310253
$375$	1.00000	0.0516398
$376$	0	0
$377$	−6.00000	−0.309016
$378$	−4.00000	−0.205738
$379$	32.0000	1.64373	0.821865	−	0.569683i	$-0.192934\pi$
$379$	32.0000	1.64373	0.821865	+	0.569683i	$0.192934\pi$
$380$	−4.00000	−0.205196
$381$	−16.0000	−0.819705
$382$	12.0000	0.613973
$383$	−24.0000	−1.22634	−0.613171	−	0.789950i	$-0.710106\pi$
$383$	−24.0000	−1.22634	−0.613171	+	0.789950i	$0.710106\pi$
$384$	1.00000	0.0510310
$385$	4.00000	0.203859
$386$	−22.0000	−1.11977
$387$	−4.00000	−0.203331
$388$	−10.0000	−0.507673
$389$	−18.0000	−0.912636	−0.456318	−	0.889817i	$-0.650832\pi$
$389$	−18.0000	−0.912636	−0.456318	+	0.889817i	$0.650832\pi$
$390$	1.00000	0.0506370
$391$	0	0
$392$	9.00000	0.454569
$393$	−12.0000	−0.605320
$394$	6.00000	0.302276
$395$	8.00000	0.402524
$396$	−1.00000	−0.0502519
$397$	2.00000	0.100377	0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000	0.100377	0.0501886	+	0.998740i	$0.484018\pi$
$398$	−16.0000	−0.802008
$399$	16.0000	0.801002
$400$	1.00000	0.0500000
$401$	18.0000	0.898877	0.449439	−	0.893311i	$-0.351624\pi$
$401$	18.0000	0.898877	0.449439	+	0.893311i	$0.351624\pi$
$402$	−4.00000	−0.199502
$403$	−4.00000	−0.199254
$404$	−6.00000	−0.298511
$405$	1.00000	0.0496904
$406$	24.0000	1.19110
$407$	−2.00000	−0.0991363
$408$	−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	$0.387496\pi$
$410$	−6.00000	−0.296319
$411$	−6.00000	−0.295958
$412$	8.00000	0.394132
$413$	−48.0000	−2.36193
$414$	0	0
$415$	12.0000	0.589057
$416$	1.00000	0.0490290
$417$	−4.00000	−0.195881
$418$	4.00000	0.195646
$419$	−24.0000	−1.17248	−0.586238	−	0.810139i	$-0.699392\pi$
$419$	−24.0000	−1.17248	−0.586238	+	0.810139i	$0.699392\pi$
$420$	−4.00000	−0.195180
$421$	−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
$427$	40.0000	1.93574
$428$	0	0
$429$	−1.00000	−0.0482805
$430$	−4.00000	−0.192897
$431$	−24.0000	−1.15604	−0.578020	−	0.816023i	$-0.696174\pi$
$431$	−24.0000	−1.15604	−0.578020	+	0.816023i	$0.696174\pi$
$432$	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	$0.285205\pi$
$434$	16.0000	0.768025
$435$	−6.00000	−0.287678
$436$	2.00000	0.0957826
$437$	0	0
$438$	2.00000	0.0955637
$439$	32.0000	1.52728	0.763638	−	0.645644i	$-0.223411\pi$
$439$	32.0000	1.52728	0.763638	+	0.645644i	$0.223411\pi$
$440$	−1.00000	−0.0476731
$441$	9.00000	0.428571
$442$	−6.00000	−0.285391
$443$	12.0000	0.570137	0.285069	−	0.958507i	$-0.407984\pi$
$443$	12.0000	0.570137	0.285069	+	0.958507i	$0.407984\pi$
$444$	2.00000	0.0949158
$445$	−6.00000	−0.284427
$446$	8.00000	0.378811
$447$	−18.0000	−0.851371
$448$	−4.00000	−0.188982
$449$	−30.0000	−1.41579	−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000	−1.41579	−0.707894	+	0.706319i	$0.750354\pi$
$450$	1.00000	0.0471405
$451$	6.00000	0.282529
$452$	6.00000	0.282216
$453$	8.00000	0.375873
$454$	12.0000	0.563188
$455$	−4.00000	−0.187523
$456$	−4.00000	−0.187317
$457$	−22.0000	−1.02912	−0.514558	−	0.857455i	$-0.672044\pi$
$457$	−22.0000	−1.02912	−0.514558	+	0.857455i	$0.672044\pi$
$458$	14.0000	0.654177
$459$	−6.00000	−0.280056
$460$	0	0
$461$	−18.0000	−0.838344	−0.419172	−	0.907907i	$-0.637680\pi$
$461$	−18.0000	−0.838344	−0.419172	+	0.907907i	$0.637680\pi$
$462$	4.00000	0.186097
$463$	−16.0000	−0.743583	−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000	−0.743583	−0.371792	+	0.928316i	$0.621256\pi$
$464$	−6.00000	−0.278543
$465$	−4.00000	−0.185496
$466$	−6.00000	−0.277945
$467$	12.0000	0.555294	0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000	0.555294	0.277647	+	0.960683i	$0.410445\pi$
$468$	1.00000	0.0462250
$469$	16.0000	0.738811
$470$	0	0
$471$	14.0000	0.645086
$472$	12.0000	0.552345
$473$	4.00000	0.183920
$474$	8.00000	0.367452
$475$	−4.00000	−0.183533
$476$	24.0000	1.10004
$477$	−6.00000	−0.274721
$478$	0	0
$479$	−24.0000	−1.09659	−0.548294	−	0.836286i	$-0.684723\pi$
$479$	−24.0000	−1.09659	−0.548294	+	0.836286i	$0.684723\pi$
$480$	1.00000	0.0456435
$481$	2.00000	0.0911922
$482$	−10.0000	−0.455488
$483$	0	0
$484$	1.00000	0.0454545
$485$	−10.0000	−0.454077
$486$	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	$0.618082\pi$
$488$	−10.0000	−0.452679
$489$	−4.00000	−0.180886
$490$	9.00000	0.406579
$491$	−36.0000	−1.62466	−0.812329	−	0.583200i	$-0.801800\pi$
$491$	−36.0000	−1.62466	−0.812329	+	0.583200i	$0.801800\pi$
$492$	−6.00000	−0.270501
$493$	36.0000	1.62136
$494$	−4.00000	−0.179969
$495$	−1.00000	−0.0449467
$496$	−4.00000	−0.179605
$497$	0	0
$498$	12.0000	0.537733
$499$	8.00000	0.358129	0.179065	−	0.983837i	$-0.442693\pi$
$499$	8.00000	0.358129	0.179065	+	0.983837i	$0.442693\pi$
$500$	1.00000	0.0447214
$501$	24.0000	1.07224
$502$	−24.0000	−1.07117
$503$	12.0000	0.535054	0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000	0.535054	0.267527	+	0.963550i	$0.413794\pi$
$504$	−4.00000	−0.178174
$505$	−6.00000	−0.266996
$506$	0	0
$507$	1.00000	0.0444116
$508$	−16.0000	−0.709885
$509$	30.0000	1.32973	0.664863	−	0.746965i	$-0.268490\pi$
$509$	30.0000	1.32973	0.664863	+	0.746965i	$0.268490\pi$
$510$	−6.00000	−0.265684
$511$	−8.00000	−0.353899
$512$	1.00000	0.0441942
$513$	−4.00000	−0.176604
$514$	−18.0000	−0.793946
$515$	8.00000	0.352522
$516$	−4.00000	−0.176090
$517$	0	0
$518$	−8.00000	−0.351500
$519$	6.00000	0.263371
$520$	1.00000	0.0438529
$521$	−30.0000	−1.31432	−0.657162	−	0.753749i	$-0.728243\pi$
$521$	−30.0000	−1.31432	−0.657162	+	0.753749i	$0.728243\pi$
$522$	−6.00000	−0.262613
$523$	20.0000	0.874539	0.437269	−	0.899331i	$-0.355946\pi$
$523$	20.0000	0.874539	0.437269	+	0.899331i	$0.355946\pi$
$524$	−12.0000	−0.524222
$525$	−4.00000	−0.174574
$526$	12.0000	0.523225
$527$	24.0000	1.04546
$528$	−1.00000	−0.0435194
$529$	−23.0000	−1.00000
$530$	−6.00000	−0.260623
$531$	12.0000	0.520756
$532$	16.0000	0.693688
$533$	−6.00000	−0.259889
$534$	−6.00000	−0.259645
$535$	0	0
$536$	−4.00000	−0.172774
$537$	0	0
$538$	−18.0000	−0.776035
$539$	−9.00000	−0.387657
$540$	1.00000	0.0430331
$541$	26.0000	1.11783	0.558914	−	0.829226i	$-0.311218\pi$
$541$	26.0000	1.11783	0.558914	+	0.829226i	$0.311218\pi$
$542$	8.00000	0.343629
$543$	−10.0000	−0.429141
$544$	−6.00000	−0.257248
$545$	2.00000	0.0856706
$546$	−4.00000	−0.171184
$547$	20.0000	0.855138	0.427569	−	0.903983i	$-0.359370\pi$
$547$	20.0000	0.855138	0.427569	+	0.903983i	$0.359370\pi$
$548$	−6.00000	−0.256307
$549$	−10.0000	−0.426790
$550$	−1.00000	−0.0426401
$551$	24.0000	1.02243
$552$	0	0
$553$	−32.0000	−1.36078
$554$	−10.0000	−0.424859
$555$	2.00000	0.0848953
$556$	−4.00000	−0.169638
$557$	30.0000	1.27114	0.635570	−	0.772043i	$-0.280765\pi$
$557$	30.0000	1.27114	0.635570	+	0.772043i	$0.280765\pi$
$558$	−4.00000	−0.169334
$559$	−4.00000	−0.169182
$560$	−4.00000	−0.169031
$561$	6.00000	0.253320
$562$	−6.00000	−0.253095
$563$	−24.0000	−1.01148	−0.505740	−	0.862686i	$-0.668780\pi$
$563$	−24.0000	−1.01148	−0.505740	+	0.862686i	$0.668780\pi$
$564$	0	0
$565$	6.00000	0.252422
$566$	−4.00000	−0.168133
$567$	−4.00000	−0.167984
$568$	0	0
$569$	−18.0000	−0.754599	−0.377300	−	0.926091i	$-0.623147\pi$
$569$	−18.0000	−0.754599	−0.377300	+	0.926091i	$0.623147\pi$
$570$	−4.00000	−0.167542
$571$	−28.0000	−1.17176	−0.585882	−	0.810397i	$-0.699252\pi$
$571$	−28.0000	−1.17176	−0.585882	+	0.810397i	$0.699252\pi$
$572$	−1.00000	−0.0418121
$573$	12.0000	0.501307
$574$	24.0000	1.00174
$575$	0	0
$576$	1.00000	0.0416667
$577$	38.0000	1.58196	0.790980	−	0.611842i	$-0.209571\pi$
$577$	38.0000	1.58196	0.790980	+	0.611842i	$0.209571\pi$
$578$	19.0000	0.790296
$579$	−22.0000	−0.914289
$580$	−6.00000	−0.249136
$581$	−48.0000	−1.99138
$582$	−10.0000	−0.414513
$583$	6.00000	0.248495
$584$	2.00000	0.0827606
$585$	1.00000	0.0413449
$586$	6.00000	0.247858
$587$	−36.0000	−1.48588	−0.742940	−	0.669359i	$-0.766569\pi$
$587$	−36.0000	−1.48588	−0.742940	+	0.669359i	$0.766569\pi$
$588$	9.00000	0.371154
$589$	16.0000	0.659269
$590$	12.0000	0.494032
$591$	6.00000	0.246807
$592$	2.00000	0.0821995
$593$	18.0000	0.739171	0.369586	−	0.929197i	$-0.379500\pi$
$593$	18.0000	0.739171	0.369586	+	0.929197i	$0.379500\pi$
$594$	−1.00000	−0.0410305
$595$	24.0000	0.983904
$596$	−18.0000	−0.737309
$597$	−16.0000	−0.654836
$598$	0	0
$599$	−36.0000	−1.47092	−0.735460	−	0.677568i	$-0.763034\pi$
$599$	−36.0000	−1.47092	−0.735460	+	0.677568i	$0.763034\pi$
$600$	1.00000	0.0408248
$601$	2.00000	0.0815817	0.0407909	−	0.999168i	$-0.487012\pi$
$601$	2.00000	0.0815817	0.0407909	+	0.999168i	$0.487012\pi$
$602$	16.0000	0.652111
$603$	−4.00000	−0.162893
$604$	8.00000	0.325515
$605$	1.00000	0.0406558
$606$	−6.00000	−0.243733
$607$	−40.0000	−1.62355	−0.811775	−	0.583970i	$-0.801498\pi$
$607$	−40.0000	−1.62355	−0.811775	+	0.583970i	$0.801498\pi$
$608$	−4.00000	−0.162221
$609$	24.0000	0.972529
$610$	−10.0000	−0.404888
$611$	0	0
$612$	−6.00000	−0.242536
$613$	−34.0000	−1.37325	−0.686624	−	0.727013i	$-0.740908\pi$
$613$	−34.0000	−1.37325	−0.686624	+	0.727013i	$0.740908\pi$
$614$	32.0000	1.29141
$615$	−6.00000	−0.241943
$616$	4.00000	0.161165
$617$	−6.00000	−0.241551	−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000	−0.241551	−0.120775	+	0.992680i	$0.538538\pi$
$618$	8.00000	0.321807
$619$	8.00000	0.321547	0.160774	−	0.986991i	$-0.448601\pi$
$619$	8.00000	0.321547	0.160774	+	0.986991i	$0.448601\pi$
$620$	−4.00000	−0.160644
$621$	0	0
$622$	12.0000	0.481156
$623$	24.0000	0.961540
$624$	1.00000	0.0400320
$625$	1.00000	0.0400000
$626$	2.00000	0.0799361
$627$	4.00000	0.159745
$628$	14.0000	0.558661
$629$	−12.0000	−0.478471
$630$	−4.00000	−0.159364
$631$	−4.00000	−0.159237	−0.0796187	−	0.996825i	$-0.525370\pi$
$631$	−4.00000	−0.159237	−0.0796187	+	0.996825i	$0.525370\pi$
$632$	8.00000	0.318223
$633$	−4.00000	−0.158986
$634$	−18.0000	−0.714871
$635$	−16.0000	−0.634941
$636$	−6.00000	−0.237915
$637$	9.00000	0.356593
$638$	6.00000	0.237542
$639$	0	0
$640$	1.00000	0.0395285
$641$	42.0000	1.65890	0.829450	−	0.558581i	$-0.188654\pi$
$641$	42.0000	1.65890	0.829450	+	0.558581i	$0.188654\pi$
$642$	0	0
$643$	−4.00000	−0.157745	−0.0788723	−	0.996885i	$-0.525132\pi$
$643$	−4.00000	−0.157745	−0.0788723	+	0.996885i	$0.525132\pi$
$644$	0	0
$645$	−4.00000	−0.157500
$646$	24.0000	0.944267
$647$	−24.0000	−0.943537	−0.471769	−	0.881722i	$-0.656384\pi$
$647$	−24.0000	−0.943537	−0.471769	+	0.881722i	$0.656384\pi$
$648$	1.00000	0.0392837
$649$	−12.0000	−0.471041
$650$	1.00000	0.0392232
$651$	16.0000	0.627089
$652$	−4.00000	−0.156652
$653$	−6.00000	−0.234798	−0.117399	−	0.993085i	$-0.537456\pi$
$653$	−6.00000	−0.234798	−0.117399	+	0.993085i	$0.537456\pi$
$654$	2.00000	0.0782062
$655$	−12.0000	−0.468879
$656$	−6.00000	−0.234261
$657$	2.00000	0.0780274
$658$	0	0
$659$	36.0000	1.40236	0.701180	−	0.712984i	$-0.252657\pi$
$659$	36.0000	1.40236	0.701180	+	0.712984i	$0.252657\pi$
$660$	−1.00000	−0.0389249
$661$	−10.0000	−0.388955	−0.194477	−	0.980907i	$-0.562301\pi$
$661$	−10.0000	−0.388955	−0.194477	+	0.980907i	$0.562301\pi$
$662$	8.00000	0.310929
$663$	−6.00000	−0.233021
$664$	12.0000	0.465690
$665$	16.0000	0.620453
$666$	2.00000	0.0774984
$667$	0	0
$668$	24.0000	0.928588
$669$	8.00000	0.309298
$670$	−4.00000	−0.154533
$671$	10.0000	0.386046
$672$	−4.00000	−0.154303
$673$	−46.0000	−1.77317	−0.886585	−	0.462566i	$-0.846929\pi$
$673$	−46.0000	−1.77317	−0.886585	+	0.462566i	$0.846929\pi$
$674$	2.00000	0.0770371
$675$	1.00000	0.0384900
$676$	1.00000	0.0384615
$677$	6.00000	0.230599	0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000	0.230599	0.115299	+	0.993331i	$0.463217\pi$
$678$	6.00000	0.230429
$679$	40.0000	1.53506
$680$	−6.00000	−0.230089
$681$	12.0000	0.459841
$682$	4.00000	0.153168
$683$	−36.0000	−1.37750	−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000	−1.37750	−0.688751	+	0.724998i	$0.741841\pi$
$684$	−4.00000	−0.152944
$685$	−6.00000	−0.229248
$686$	−8.00000	−0.305441
$687$	14.0000	0.534133
$688$	−4.00000	−0.152499
$689$	−6.00000	−0.228582
$690$	0	0
$691$	−40.0000	−1.52167	−0.760836	−	0.648944i	$-0.775211\pi$
$691$	−40.0000	−1.52167	−0.760836	+	0.648944i	$0.775211\pi$
$692$	6.00000	0.228086
$693$	4.00000	0.151947
$694$	24.0000	0.911028
$695$	−4.00000	−0.151729
$696$	−6.00000	−0.227429
$697$	36.0000	1.36360
$698$	26.0000	0.984115
$699$	−6.00000	−0.226941
$700$	−4.00000	−0.151186
$701$	−6.00000	−0.226617	−0.113308	−	0.993560i	$-0.536145\pi$
$701$	−6.00000	−0.226617	−0.113308	+	0.993560i	$0.536145\pi$
$702$	1.00000	0.0377426
$703$	−8.00000	−0.301726
$704$	−1.00000	−0.0376889
$705$	0	0
$706$	18.0000	0.677439
$707$	24.0000	0.902613
$708$	12.0000	0.450988
$709$	14.0000	0.525781	0.262891	−	0.964826i	$-0.415324\pi$
$709$	14.0000	0.525781	0.262891	+	0.964826i	$0.415324\pi$
$710$	0	0
$711$	8.00000	0.300023
$712$	−6.00000	−0.224860
$713$	0	0
$714$	24.0000	0.898177
$715$	−1.00000	−0.0373979
$716$	0	0
$717$	0	0
$718$	0	0
$719$	−36.0000	−1.34257	−0.671287	−	0.741198i	$-0.734258\pi$
$719$	−36.0000	−1.34257	−0.671287	+	0.741198i	$0.734258\pi$
$720$	1.00000	0.0372678
$721$	−32.0000	−1.19174
$722$	−3.00000	−0.111648
$723$	−10.0000	−0.371904
$724$	−10.0000	−0.371647
$725$	−6.00000	−0.222834
$726$	1.00000	0.0371135
$727$	−16.0000	−0.593407	−0.296704	−	0.954970i	$-0.595887\pi$
$727$	−16.0000	−0.593407	−0.296704	+	0.954970i	$0.595887\pi$
$728$	−4.00000	−0.148250
$729$	1.00000	0.0370370
$730$	2.00000	0.0740233
$731$	24.0000	0.887672
$732$	−10.0000	−0.369611
$733$	−10.0000	−0.369358	−0.184679	−	0.982799i	$-0.559125\pi$
$733$	−10.0000	−0.369358	−0.184679	+	0.982799i	$0.559125\pi$
$734$	32.0000	1.18114
$735$	9.00000	0.331970
$736$	0	0
$737$	4.00000	0.147342
$738$	−6.00000	−0.220863
$739$	44.0000	1.61857	0.809283	−	0.587419i	$-0.199856\pi$
$739$	44.0000	1.61857	0.809283	+	0.587419i	$0.199856\pi$
$740$	2.00000	0.0735215
$741$	−4.00000	−0.146944
$742$	24.0000	0.881068
$743$	−24.0000	−0.880475	−0.440237	−	0.897881i	$-0.645106\pi$
$743$	−24.0000	−0.880475	−0.440237	+	0.897881i	$0.645106\pi$
$744$	−4.00000	−0.146647
$745$	−18.0000	−0.659469
$746$	−10.0000	−0.366126
$747$	12.0000	0.439057
$748$	6.00000	0.219382
$749$	0	0
$750$	1.00000	0.0365148
$751$	32.0000	1.16770	0.583848	−	0.811863i	$-0.301546\pi$
$751$	32.0000	1.16770	0.583848	+	0.811863i	$0.301546\pi$
$752$	0	0
$753$	−24.0000	−0.874609
$754$	−6.00000	−0.218507
$755$	8.00000	0.291150
$756$	−4.00000	−0.145479
$757$	38.0000	1.38113	0.690567	−	0.723269i	$-0.257361\pi$
$757$	38.0000	1.38113	0.690567	+	0.723269i	$0.257361\pi$
$758$	32.0000	1.16229
$759$	0	0
$760$	−4.00000	−0.145095
$761$	42.0000	1.52250	0.761249	−	0.648459i	$-0.224586\pi$
$761$	42.0000	1.52250	0.761249	+	0.648459i	$0.224586\pi$
$762$	−16.0000	−0.579619
$763$	−8.00000	−0.289619
$764$	12.0000	0.434145
$765$	−6.00000	−0.216930
$766$	−24.0000	−0.867155
$767$	12.0000	0.433295
$768$	1.00000	0.0360844
$769$	14.0000	0.504853	0.252426	−	0.967616i	$-0.418771\pi$
$769$	14.0000	0.504853	0.252426	+	0.967616i	$0.418771\pi$
$770$	4.00000	0.144150
$771$	−18.0000	−0.648254
$772$	−22.0000	−0.791797
$773$	30.0000	1.07903	0.539513	−	0.841978i	$-0.318609\pi$
$773$	30.0000	1.07903	0.539513	+	0.841978i	$0.318609\pi$
$774$	−4.00000	−0.143777
$775$	−4.00000	−0.143684
$776$	−10.0000	−0.358979
$777$	−8.00000	−0.286998
$778$	−18.0000	−0.645331
$779$	24.0000	0.859889
$780$	1.00000	0.0358057
$781$	0	0
$782$	0	0
$783$	−6.00000	−0.214423
$784$	9.00000	0.321429
$785$	14.0000	0.499681
$786$	−12.0000	−0.428026
$787$	32.0000	1.14068	0.570338	−	0.821410i	$-0.306812\pi$
$787$	32.0000	1.14068	0.570338	+	0.821410i	$0.306812\pi$
$788$	6.00000	0.213741
$789$	12.0000	0.427211
$790$	8.00000	0.284627
$791$	−24.0000	−0.853342
$792$	−1.00000	−0.0355335
$793$	−10.0000	−0.355110
$794$	2.00000	0.0709773
$795$	−6.00000	−0.212798
$796$	−16.0000	−0.567105
$797$	−30.0000	−1.06265	−0.531327	−	0.847167i	$-0.678307\pi$
$797$	−30.0000	−1.06265	−0.531327	+	0.847167i	$0.678307\pi$
$798$	16.0000	0.566394
$799$	0	0
$800$	1.00000	0.0353553
$801$	−6.00000	−0.212000
$802$	18.0000	0.635602
$803$	−2.00000	−0.0705785
$804$	−4.00000	−0.141069
$805$	0	0
$806$	−4.00000	−0.140894
$807$	−18.0000	−0.633630
$808$	−6.00000	−0.211079
$809$	6.00000	0.210949	0.105474	−	0.994422i	$-0.466364\pi$
$809$	6.00000	0.210949	0.105474	+	0.994422i	$0.466364\pi$
$810$	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	$0.385792\pi$
$812$	24.0000	0.842235
$813$	8.00000	0.280572
$814$	−2.00000	−0.0701000
$815$	−4.00000	−0.140114
$816$	−6.00000	−0.210042
$817$	16.0000	0.559769
$818$	14.0000	0.489499
$819$	−4.00000	−0.139771
$820$	−6.00000	−0.209529
$821$	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
$823$	32.0000	1.11545	0.557725	−	0.830026i	$-0.311674\pi$
$823$	32.0000	1.11545	0.557725	+	0.830026i	$0.311674\pi$
$824$	8.00000	0.278693
$825$	−1.00000	−0.0348155
$826$	−48.0000	−1.67013
$827$	−36.0000	−1.25184	−0.625921	−	0.779886i	$-0.715277\pi$
$827$	−36.0000	−1.25184	−0.625921	+	0.779886i	$0.715277\pi$
$828$	0	0
$829$	14.0000	0.486240	0.243120	−	0.969996i	$-0.421829\pi$
$829$	14.0000	0.486240	0.243120	+	0.969996i	$0.421829\pi$
$830$	12.0000	0.416526
$831$	−10.0000	−0.346896
$832$	1.00000	0.0346688
$833$	−54.0000	−1.87099
$834$	−4.00000	−0.138509
$835$	24.0000	0.830554
$836$	4.00000	0.138343
$837$	−4.00000	−0.138260
$838$	−24.0000	−0.829066
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	−4.00000	−0.138013
$841$	7.00000	0.241379
$842$	−10.0000	−0.344623
$843$	−6.00000	−0.206651
$844$	−4.00000	−0.137686
$845$	1.00000	0.0344010
$846$	0	0
$847$	−4.00000	−0.137442
$848$	−6.00000	−0.206041
$849$	−4.00000	−0.137280
$850$	−6.00000	−0.205798
$851$	0	0
$852$	0	0
$853$	14.0000	0.479351	0.239675	−	0.970853i	$-0.422959\pi$
$853$	14.0000	0.479351	0.239675	+	0.970853i	$0.422959\pi$
$854$	40.0000	1.36877
$855$	−4.00000	−0.136797
$856$	0	0
$857$	18.0000	0.614868	0.307434	−	0.951569i	$-0.400530\pi$
$857$	18.0000	0.614868	0.307434	+	0.951569i	$0.400530\pi$
$858$	−1.00000	−0.0341394
$859$	−4.00000	−0.136478	−0.0682391	−	0.997669i	$-0.521738\pi$
$859$	−4.00000	−0.136478	−0.0682391	+	0.997669i	$0.521738\pi$
$860$	−4.00000	−0.136399
$861$	24.0000	0.817918
$862$	−24.0000	−0.817443
$863$	0	0		−	1.00000i	$-0.5\pi$
$863$	0	0			1.00000i	$0.5\pi$
$864$	1.00000	0.0340207
$865$	6.00000	0.204006
$866$	26.0000	0.883516
$867$	19.0000	0.645274
$868$	16.0000	0.543075
$869$	−8.00000	−0.271381
$870$	−6.00000	−0.203419
$871$	−4.00000	−0.135535
$872$	2.00000	0.0677285
$873$	−10.0000	−0.338449
$874$	0	0
$875$	−4.00000	−0.135225
$876$	2.00000	0.0675737
$877$	38.0000	1.28317	0.641584	−	0.767052i	$-0.278277\pi$
$877$	38.0000	1.28317	0.641584	+	0.767052i	$0.278277\pi$
$878$	32.0000	1.07995
$879$	6.00000	0.202375
$880$	−1.00000	−0.0337100
$881$	−30.0000	−1.01073	−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000	−1.01073	−0.505363	+	0.862907i	$0.668641\pi$
$882$	9.00000	0.303046
$883$	−52.0000	−1.74994	−0.874970	−	0.484178i	$-0.839119\pi$
$883$	−52.0000	−1.74994	−0.874970	+	0.484178i	$0.839119\pi$
$884$	−6.00000	−0.201802
$885$	12.0000	0.403376
$886$	12.0000	0.403148
$887$	12.0000	0.402921	0.201460	−	0.979497i	$-0.435431\pi$
$887$	12.0000	0.402921	0.201460	+	0.979497i	$0.435431\pi$
$888$	2.00000	0.0671156
$889$	64.0000	2.14649
$890$	−6.00000	−0.201120
$891$	−1.00000	−0.0335013
$892$	8.00000	0.267860
$893$	0	0
$894$	−18.0000	−0.602010
$895$	0	0
$896$	−4.00000	−0.133631
$897$	0	0
$898$	−30.0000	−1.00111
$899$	24.0000	0.800445
$900$	1.00000	0.0333333
$901$	36.0000	1.19933
$902$	6.00000	0.199778
$903$	16.0000	0.532447
$904$	6.00000	0.199557
$905$	−10.0000	−0.332411
$906$	8.00000	0.265782
$907$	−4.00000	−0.132818	−0.0664089	−	0.997792i	$-0.521154\pi$
$907$	−4.00000	−0.132818	−0.0664089	+	0.997792i	$0.521154\pi$
$908$	12.0000	0.398234
$909$	−6.00000	−0.199007
$910$	−4.00000	−0.132599
$911$	−12.0000	−0.397578	−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000	−0.397578	−0.198789	+	0.980042i	$0.563701\pi$
$912$	−4.00000	−0.132453
$913$	−12.0000	−0.397142
$914$	−22.0000	−0.727695
$915$	−10.0000	−0.330590
$916$	14.0000	0.462573
$917$	48.0000	1.58510
$918$	−6.00000	−0.198030
$919$	−40.0000	−1.31948	−0.659739	−	0.751495i	$-0.729333\pi$
$919$	−40.0000	−1.31948	−0.659739	+	0.751495i	$0.729333\pi$
$920$	0	0
$921$	32.0000	1.05444
$922$	−18.0000	−0.592798
$923$	0	0
$924$	4.00000	0.131590
$925$	2.00000	0.0657596
$926$	−16.0000	−0.525793
$927$	8.00000	0.262754
$928$	−6.00000	−0.196960
$929$	−30.0000	−0.984268	−0.492134	−	0.870519i	$-0.663783\pi$
$929$	−30.0000	−0.984268	−0.492134	+	0.870519i	$0.663783\pi$
$930$	−4.00000	−0.131165
$931$	−36.0000	−1.17985
$932$	−6.00000	−0.196537
$933$	12.0000	0.392862
$934$	12.0000	0.392652
$935$	6.00000	0.196221
$936$	1.00000	0.0326860
$937$	−22.0000	−0.718709	−0.359354	−	0.933201i	$-0.617003\pi$
$937$	−22.0000	−0.718709	−0.359354	+	0.933201i	$0.617003\pi$
$938$	16.0000	0.522419
$939$	2.00000	0.0652675
$940$	0	0
$941$	6.00000	0.195594	0.0977972	−	0.995206i	$-0.468820\pi$
$941$	6.00000	0.195594	0.0977972	+	0.995206i	$0.468820\pi$
$942$	14.0000	0.456145
$943$	0	0
$944$	12.0000	0.390567
$945$	−4.00000	−0.130120
$946$	4.00000	0.130051
$947$	36.0000	1.16984	0.584921	−	0.811090i	$-0.301125\pi$
$947$	36.0000	1.16984	0.584921	+	0.811090i	$0.301125\pi$
$948$	8.00000	0.259828
$949$	2.00000	0.0649227
$950$	−4.00000	−0.129777
$951$	−18.0000	−0.583690
$952$	24.0000	0.777844
$953$	−6.00000	−0.194359	−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000	−0.194359	−0.0971795	+	0.995267i	$0.530982\pi$
$954$	−6.00000	−0.194257
$955$	12.0000	0.388311
$956$	0	0
$957$	6.00000	0.193952
$958$	−24.0000	−0.775405
$959$	24.0000	0.775000
$960$	1.00000	0.0322749
$961$	−15.0000	−0.483871
$962$	2.00000	0.0644826
$963$	0	0
$964$	−10.0000	−0.322078
$965$	−22.0000	−0.708205
$966$	0	0
$967$	44.0000	1.41494	0.707472	−	0.706741i	$-0.249835\pi$
$967$	44.0000	1.41494	0.707472	+	0.706741i	$0.249835\pi$
$968$	1.00000	0.0321412
$969$	24.0000	0.770991
$970$	−10.0000	−0.321081
$971$	−48.0000	−1.54039	−0.770197	−	0.637806i	$-0.779842\pi$
$971$	−48.0000	−1.54039	−0.770197	+	0.637806i	$0.779842\pi$
$972$	1.00000	0.0320750
$973$	16.0000	0.512936
$974$	−16.0000	−0.512673
$975$	1.00000	0.0320256
$976$	−10.0000	−0.320092
$977$	−6.00000	−0.191957	−0.0959785	−	0.995383i	$-0.530598\pi$
$977$	−6.00000	−0.191957	−0.0959785	+	0.995383i	$0.530598\pi$
$978$	−4.00000	−0.127906
$979$	6.00000	0.191761
$980$	9.00000	0.287494
$981$	2.00000	0.0638551
$982$	−36.0000	−1.14881
$983$	−24.0000	−0.765481	−0.382741	−	0.923856i	$-0.625020\pi$
$983$	−24.0000	−0.765481	−0.382741	+	0.923856i	$0.625020\pi$
$984$	−6.00000	−0.191273
$985$	6.00000	0.191176
$986$	36.0000	1.14647
$987$	0	0
$988$	−4.00000	−0.127257
$989$	0	0
$990$	−1.00000	−0.0317821
$991$	56.0000	1.77890	0.889449	−	0.457034i	$-0.151088\pi$
$991$	56.0000	1.77890	0.889449	+	0.457034i	$0.151088\pi$
$992$	−4.00000	−0.127000
$993$	8.00000	0.253872
$994$	0	0
$995$	−16.0000	−0.507234
$996$	12.0000	0.380235
$997$	−10.0000	−0.316703	−0.158352	−	0.987383i	$-0.550618\pi$
$997$	−10.0000	−0.316703	−0.158352	+	0.987383i	$0.550618\pi$
$998$	8.00000	0.253236
$999$	2.00000	0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4290.2.a.bb.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4290.2.a.bb.1.1	✓	1	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 4290 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4290.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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