LMFDB - Embedded newform 4018.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4018,2,Mod(1,4018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4018, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("4018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4018 = 2 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4018.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:	$32.0838915322$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 574)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} -3.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.00000 q^{6} -1.00000 q^{8} +6.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} -3.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.00000 q^{6} -1.00000 q^{8} +6.00000 q^{9} +1.00000 q^{10} -5.00000 q^{11} -3.00000 q^{12} +6.00000 q^{13} +3.00000 q^{15} +1.00000 q^{16} -6.00000 q^{18} +1.00000 q^{19} -1.00000 q^{20} +5.00000 q^{22} -4.00000 q^{23} +3.00000 q^{24} -4.00000 q^{25} -6.00000 q^{26} -9.00000 q^{27} -8.00000 q^{29} -3.00000 q^{30} +6.00000 q^{31} -1.00000 q^{32} +15.0000 q^{33} +6.00000 q^{36} -2.00000 q^{37} -1.00000 q^{38} -18.0000 q^{39} +1.00000 q^{40} -1.00000 q^{41} +4.00000 q^{43} -5.00000 q^{44} -6.00000 q^{45} +4.00000 q^{46} -3.00000 q^{48} +4.00000 q^{50} +6.00000 q^{52} +6.00000 q^{53} +9.00000 q^{54} +5.00000 q^{55} -3.00000 q^{57} +8.00000 q^{58} +2.00000 q^{59} +3.00000 q^{60} +13.0000 q^{61} -6.00000 q^{62} +1.00000 q^{64} -6.00000 q^{65} -15.0000 q^{66} +16.0000 q^{67} +12.0000 q^{69} -3.00000 q^{71} -6.00000 q^{72} -2.00000 q^{73} +2.00000 q^{74} +12.0000 q^{75} +1.00000 q^{76} +18.0000 q^{78} -11.0000 q^{79} -1.00000 q^{80} +9.00000 q^{81} +1.00000 q^{82} -14.0000 q^{83} -4.00000 q^{86} +24.0000 q^{87} +5.00000 q^{88} +14.0000 q^{89} +6.00000 q^{90} -4.00000 q^{92} -18.0000 q^{93} -1.00000 q^{95} +3.00000 q^{96} -8.00000 q^{97} -30.0000 q^{99} +O(q^{100})\)

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
$3$	−3.00000	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$3$	−3.00000	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214	−0.223607	−	0.974679i	$-0.571783\pi$
$5$	−1.00000	−0.447214	−0.223607	+	0.974679i	$0.571783\pi$
$6$	3.00000	1.22474
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	6.00000	2.00000
$10$	1.00000	0.316228
$11$	−5.00000	−1.50756	−0.753778	−	0.657129i	$-0.771771\pi$
$11$	−5.00000	−1.50756	−0.753778	+	0.657129i	$0.771771\pi$
$12$	−3.00000	−0.866025
$13$	6.00000	1.66410	0.832050	−	0.554700i	$-0.187167\pi$
$13$	6.00000	1.66410	0.832050	+	0.554700i	$0.187167\pi$
$14$	0	0
$15$	3.00000	0.774597
$16$	1.00000	0.250000
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	−6.00000	−1.41421
$19$	1.00000	0.229416	0.114708	−	0.993399i	$-0.463407\pi$
$19$	1.00000	0.229416	0.114708	+	0.993399i	$0.463407\pi$
$20$	−1.00000	−0.223607
$21$	0	0
$22$	5.00000	1.06600
$23$	−4.00000	−0.834058	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000	−0.834058	−0.417029	+	0.908893i	$0.636929\pi$
$24$	3.00000	0.612372
$25$	−4.00000	−0.800000
$26$	−6.00000	−1.17670
$27$	−9.00000	−1.73205
$28$	0	0
$29$	−8.00000	−1.48556	−0.742781	−	0.669534i	$-0.766494\pi$
$29$	−8.00000	−1.48556	−0.742781	+	0.669534i	$0.766494\pi$
$30$	−3.00000	−0.547723
$31$	6.00000	1.07763	0.538816	−	0.842424i	$-0.318872\pi$
$31$	6.00000	1.07763	0.538816	+	0.842424i	$0.318872\pi$
$32$	−1.00000	−0.176777
$33$	15.0000	2.61116
$34$	0	0
$35$	0	0
$36$	6.00000	1.00000
$37$	−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
$39$	−18.0000	−2.88231
$40$	1.00000	0.158114
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	−5.00000	−0.753778
$45$	−6.00000	−0.894427
$46$	4.00000	0.589768
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	−3.00000	−0.433013
$49$	0	0
$50$	4.00000	0.565685
$51$	0	0
$52$	6.00000	0.832050
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	9.00000	1.22474
$55$	5.00000	0.674200
$56$	0	0
$57$	−3.00000	−0.397360
$58$	8.00000	1.05045
$59$	2.00000	0.260378	0.130189	−	0.991489i	$-0.458442\pi$
$59$	2.00000	0.260378	0.130189	+	0.991489i	$0.458442\pi$
$60$	3.00000	0.387298
$61$	13.0000	1.66448	0.832240	−	0.554416i	$-0.187058\pi$
$61$	13.0000	1.66448	0.832240	+	0.554416i	$0.187058\pi$
$62$	−6.00000	−0.762001
$63$	0	0
$64$	1.00000	0.125000
$65$	−6.00000	−0.744208
$66$	−15.0000	−1.84637
$67$	16.0000	1.95471	0.977356	−	0.211604i	$-0.0678686\pi$
$67$	16.0000	1.95471	0.977356	+	0.211604i	$0.0678686\pi$
$68$	0	0
$69$	12.0000	1.44463
$70$	0	0
$71$	−3.00000	−0.356034	−0.178017	−	0.984027i	$-0.556968\pi$
$71$	−3.00000	−0.356034	−0.178017	+	0.984027i	$0.556968\pi$
$72$	−6.00000	−0.707107
$73$	−2.00000	−0.234082	−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000	−0.234082	−0.117041	+	0.993127i	$0.537341\pi$
$74$	2.00000	0.232495
$75$	12.0000	1.38564
$76$	1.00000	0.114708
$77$	0	0
$78$	18.0000	2.03810
$79$	−11.0000	−1.23760	−0.618798	−	0.785550i	$-0.712380\pi$
$79$	−11.0000	−1.23760	−0.618798	+	0.785550i	$0.712380\pi$
$80$	−1.00000	−0.111803
$81$	9.00000	1.00000
$82$	1.00000	0.110432
$83$	−14.0000	−1.53670	−0.768350	−	0.640030i	$-0.778922\pi$
$83$	−14.0000	−1.53670	−0.768350	+	0.640030i	$0.778922\pi$
$84$	0	0
$85$	0	0
$86$	−4.00000	−0.431331
$87$	24.0000	2.57307
$88$	5.00000	0.533002
$89$	14.0000	1.48400	0.741999	−	0.670402i	$-0.233878\pi$
$89$	14.0000	1.48400	0.741999	+	0.670402i	$0.233878\pi$
$90$	6.00000	0.632456
$91$	0	0
$92$	−4.00000	−0.417029
$93$	−18.0000	−1.86651
$94$	0	0
$95$	−1.00000	−0.102598
$96$	3.00000	0.306186
$97$	−8.00000	−0.812277	−0.406138	−	0.913812i	$-0.633125\pi$
$97$	−8.00000	−0.812277	−0.406138	+	0.913812i	$0.633125\pi$
$98$	0	0
$99$	−30.0000	−3.01511
$100$	−4.00000	−0.400000
$101$	8.00000	0.796030	0.398015	−	0.917379i	$-0.369699\pi$
$101$	8.00000	0.796030	0.398015	+	0.917379i	$0.369699\pi$
$102$	0	0
$103$	−14.0000	−1.37946	−0.689730	−	0.724066i	$-0.742271\pi$
$103$	−14.0000	−1.37946	−0.689730	+	0.724066i	$0.742271\pi$
$104$	−6.00000	−0.588348
$105$	0	0
$106$	−6.00000	−0.582772
$107$	−6.00000	−0.580042	−0.290021	−	0.957020i	$-0.593662\pi$
$107$	−6.00000	−0.580042	−0.290021	+	0.957020i	$0.593662\pi$
$108$	−9.00000	−0.866025
$109$	16.0000	1.53252	0.766261	−	0.642529i	$-0.222115\pi$
$109$	16.0000	1.53252	0.766261	+	0.642529i	$0.222115\pi$
$110$	−5.00000	−0.476731
$111$	6.00000	0.569495
$112$	0	0
$113$	21.0000	1.97551	0.987757	−	0.156001i	$-0.0498603\pi$
$113$	21.0000	1.97551	0.987757	+	0.156001i	$0.0498603\pi$
$114$	3.00000	0.280976
$115$	4.00000	0.373002
$116$	−8.00000	−0.742781
$117$	36.0000	3.32820
$118$	−2.00000	−0.184115
$119$	0	0
$120$	−3.00000	−0.273861
$121$	14.0000	1.27273
$122$	−13.0000	−1.17696
$123$	3.00000	0.270501
$124$	6.00000	0.538816
$125$	9.00000	0.804984
$126$	0	0
$127$	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
$129$	−12.0000	−1.05654
$130$	6.00000	0.526235
$131$	4.00000	0.349482	0.174741	−	0.984614i	$-0.444091\pi$
$131$	4.00000	0.349482	0.174741	+	0.984614i	$0.444091\pi$
$132$	15.0000	1.30558
$133$	0	0
$134$	−16.0000	−1.38219
$135$	9.00000	0.774597
$136$	0	0
$137$	−18.0000	−1.53784	−0.768922	−	0.639343i	$-0.779207\pi$
$137$	−18.0000	−1.53784	−0.768922	+	0.639343i	$0.779207\pi$
$138$	−12.0000	−1.02151
$139$	2.00000	0.169638	0.0848189	−	0.996396i	$-0.472969\pi$
$139$	2.00000	0.169638	0.0848189	+	0.996396i	$0.472969\pi$
$140$	0	0
$141$	0	0
$142$	3.00000	0.251754
$143$	−30.0000	−2.50873
$144$	6.00000	0.500000
$145$	8.00000	0.664364
$146$	2.00000	0.165521
$147$	0	0
$148$	−2.00000	−0.164399
$149$	18.0000	1.47462	0.737309	−	0.675556i	$-0.236096\pi$
$149$	18.0000	1.47462	0.737309	+	0.675556i	$0.236096\pi$
$150$	−12.0000	−0.979796
$151$	−8.00000	−0.651031	−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000	−0.651031	−0.325515	+	0.945537i	$0.605538\pi$
$152$	−1.00000	−0.0811107
$153$	0	0
$154$	0	0
$155$	−6.00000	−0.481932
$156$	−18.0000	−1.44115
$157$	4.00000	0.319235	0.159617	−	0.987179i	$-0.448974\pi$
$157$	4.00000	0.319235	0.159617	+	0.987179i	$0.448974\pi$
$158$	11.0000	0.875113
$159$	−18.0000	−1.42749
$160$	1.00000	0.0790569
$161$	0	0
$162$	−9.00000	−0.707107
$163$	−10.0000	−0.783260	−0.391630	−	0.920123i	$-0.628089\pi$
$163$	−10.0000	−0.783260	−0.391630	+	0.920123i	$0.628089\pi$
$164$	−1.00000	−0.0780869
$165$	−15.0000	−1.16775
$166$	14.0000	1.08661
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	0	0
$169$	23.0000	1.76923
$170$	0	0
$171$	6.00000	0.458831
$172$	4.00000	0.304997
$173$	5.00000	0.380143	0.190071	−	0.981770i	$-0.439128\pi$
$173$	5.00000	0.380143	0.190071	+	0.981770i	$0.439128\pi$
$174$	−24.0000	−1.81944
$175$	0	0
$176$	−5.00000	−0.376889
$177$	−6.00000	−0.450988
$178$	−14.0000	−1.04934
$179$	−1.00000	−0.0747435	−0.0373718	−	0.999301i	$-0.511899\pi$
$179$	−1.00000	−0.0747435	−0.0373718	+	0.999301i	$0.511899\pi$
$180$	−6.00000	−0.447214
$181$	−2.00000	−0.148659	−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000	−0.148659	−0.0743294	+	0.997234i	$0.523682\pi$
$182$	0	0
$183$	−39.0000	−2.88296
$184$	4.00000	0.294884
$185$	2.00000	0.147043
$186$	18.0000	1.31982
$187$	0	0
$188$	0	0
$189$	0	0
$190$	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	$0.303498\pi$
$192$	−3.00000	−0.216506
$193$	6.00000	0.431889	0.215945	−	0.976406i	$-0.430717\pi$
$193$	6.00000	0.431889	0.215945	+	0.976406i	$0.430717\pi$
$194$	8.00000	0.574367
$195$	18.0000	1.28901
$196$	0	0
$197$	−3.00000	−0.213741	−0.106871	−	0.994273i	$-0.534083\pi$
$197$	−3.00000	−0.213741	−0.106871	+	0.994273i	$0.534083\pi$
$198$	30.0000	2.13201
$199$	0	0		−	1.00000i	$-0.5\pi$
$199$	0	0			1.00000i	$0.5\pi$
$200$	4.00000	0.282843
$201$	−48.0000	−3.38566
$202$	−8.00000	−0.562878
$203$	0	0
$204$	0	0
$205$	1.00000	0.0698430
$206$	14.0000	0.975426
$207$	−24.0000	−1.66812
$208$	6.00000	0.416025
$209$	−5.00000	−0.345857
$210$	0	0
$211$	3.00000	0.206529	0.103264	−	0.994654i	$-0.467071\pi$
$211$	3.00000	0.206529	0.103264	+	0.994654i	$0.467071\pi$
$212$	6.00000	0.412082
$213$	9.00000	0.616670
$214$	6.00000	0.410152
$215$	−4.00000	−0.272798
$216$	9.00000	0.612372
$217$	0	0
$218$	−16.0000	−1.08366
$219$	6.00000	0.405442
$220$	5.00000	0.337100
$221$	0	0
$222$	−6.00000	−0.402694
$223$	−24.0000	−1.60716	−0.803579	−	0.595198i	$-0.797074\pi$
$223$	−24.0000	−1.60716	−0.803579	+	0.595198i	$0.797074\pi$
$224$	0	0
$225$	−24.0000	−1.60000
$226$	−21.0000	−1.39690
$227$	13.0000	0.862840	0.431420	−	0.902151i	$-0.358013\pi$
$227$	13.0000	0.862840	0.431420	+	0.902151i	$0.358013\pi$
$228$	−3.00000	−0.198680
$229$	−16.0000	−1.05731	−0.528655	−	0.848837i	$-0.677303\pi$
$229$	−16.0000	−1.05731	−0.528655	+	0.848837i	$0.677303\pi$
$230$	−4.00000	−0.263752
$231$	0	0
$232$	8.00000	0.525226
$233$	−14.0000	−0.917170	−0.458585	−	0.888650i	$-0.651644\pi$
$233$	−14.0000	−0.917170	−0.458585	+	0.888650i	$0.651644\pi$
$234$	−36.0000	−2.35339
$235$	0	0
$236$	2.00000	0.130189
$237$	33.0000	2.14358
$238$	0	0
$239$	−21.0000	−1.35838	−0.679189	−	0.733964i	$-0.737668\pi$
$239$	−21.0000	−1.35838	−0.679189	+	0.733964i	$0.737668\pi$
$240$	3.00000	0.193649
$241$	−22.0000	−1.41714	−0.708572	−	0.705638i	$-0.750660\pi$
$241$	−22.0000	−1.41714	−0.708572	+	0.705638i	$0.750660\pi$
$242$	−14.0000	−0.899954
$243$	0	0
$244$	13.0000	0.832240
$245$	0	0
$246$	−3.00000	−0.191273
$247$	6.00000	0.381771
$248$	−6.00000	−0.381000
$249$	42.0000	2.66164
$250$	−9.00000	−0.569210
$251$	18.0000	1.13615	0.568075	−	0.822977i	$-0.307688\pi$
$251$	18.0000	1.13615	0.568075	+	0.822977i	$0.307688\pi$
$252$	0	0
$253$	20.0000	1.25739
$254$	−2.00000	−0.125491
$255$	0	0
$256$	1.00000	0.0625000
$257$	0	0		−	1.00000i	$-0.5\pi$
$257$	0	0			1.00000i	$0.5\pi$
$258$	12.0000	0.747087
$259$	0	0
$260$	−6.00000	−0.372104
$261$	−48.0000	−2.97113
$262$	−4.00000	−0.247121
$263$	−16.0000	−0.986602	−0.493301	−	0.869859i	$-0.664210\pi$
$263$	−16.0000	−0.986602	−0.493301	+	0.869859i	$0.664210\pi$
$264$	−15.0000	−0.923186
$265$	−6.00000	−0.368577
$266$	0	0
$267$	−42.0000	−2.57036
$268$	16.0000	0.977356
$269$	−1.00000	−0.0609711	−0.0304855	−	0.999535i	$-0.509705\pi$
$269$	−1.00000	−0.0609711	−0.0304855	+	0.999535i	$0.509705\pi$
$270$	−9.00000	−0.547723
$271$	8.00000	0.485965	0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000	0.485965	0.242983	+	0.970031i	$0.421874\pi$
$272$	0	0
$273$	0	0
$274$	18.0000	1.08742
$275$	20.0000	1.20605
$276$	12.0000	0.722315
$277$	−31.0000	−1.86261	−0.931305	−	0.364241i	$-0.881328\pi$
$277$	−31.0000	−1.86261	−0.931305	+	0.364241i	$0.881328\pi$
$278$	−2.00000	−0.119952
$279$	36.0000	2.15526
$280$	0	0
$281$	20.0000	1.19310	0.596550	−	0.802576i	$-0.296538\pi$
$281$	20.0000	1.19310	0.596550	+	0.802576i	$0.296538\pi$
$282$	0	0
$283$	−6.00000	−0.356663	−0.178331	−	0.983970i	$-0.557070\pi$
$283$	−6.00000	−0.356663	−0.178331	+	0.983970i	$0.557070\pi$
$284$	−3.00000	−0.178017
$285$	3.00000	0.177705
$286$	30.0000	1.77394
$287$	0	0
$288$	−6.00000	−0.353553
$289$	−17.0000	−1.00000
$290$	−8.00000	−0.469776
$291$	24.0000	1.40690
$292$	−2.00000	−0.117041
$293$	−28.0000	−1.63578	−0.817889	−	0.575376i	$-0.804856\pi$
$293$	−28.0000	−1.63578	−0.817889	+	0.575376i	$0.804856\pi$
$294$	0	0
$295$	−2.00000	−0.116445
$296$	2.00000	0.116248
$297$	45.0000	2.61116
$298$	−18.0000	−1.04271
$299$	−24.0000	−1.38796
$300$	12.0000	0.692820
$301$	0	0
$302$	8.00000	0.460348
$303$	−24.0000	−1.37876
$304$	1.00000	0.0573539
$305$	−13.0000	−0.744378
$306$	0	0
$307$	−28.0000	−1.59804	−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000	−1.59804	−0.799022	+	0.601302i	$0.794649\pi$
$308$	0	0
$309$	42.0000	2.38930
$310$	6.00000	0.340777
$311$	−24.0000	−1.36092	−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000	−1.36092	−0.680458	+	0.732787i	$0.738219\pi$
$312$	18.0000	1.01905
$313$	−16.0000	−0.904373	−0.452187	−	0.891923i	$-0.649356\pi$
$313$	−16.0000	−0.904373	−0.452187	+	0.891923i	$0.649356\pi$
$314$	−4.00000	−0.225733
$315$	0	0
$316$	−11.0000	−0.618798
$317$	12.0000	0.673987	0.336994	−	0.941507i	$-0.390590\pi$
$317$	12.0000	0.673987	0.336994	+	0.941507i	$0.390590\pi$
$318$	18.0000	1.00939
$319$	40.0000	2.23957
$320$	−1.00000	−0.0559017
$321$	18.0000	1.00466
$322$	0	0
$323$	0	0
$324$	9.00000	0.500000
$325$	−24.0000	−1.33128
$326$	10.0000	0.553849
$327$	−48.0000	−2.65441
$328$	1.00000	0.0552158
$329$	0	0
$330$	15.0000	0.825723
$331$	−20.0000	−1.09930	−0.549650	−	0.835395i	$-0.685239\pi$
$331$	−20.0000	−1.09930	−0.549650	+	0.835395i	$0.685239\pi$
$332$	−14.0000	−0.768350
$333$	−12.0000	−0.657596
$334$	0	0
$335$	−16.0000	−0.874173
$336$	0	0
$337$	−13.0000	−0.708155	−0.354078	−	0.935216i	$-0.615205\pi$
$337$	−13.0000	−0.708155	−0.354078	+	0.935216i	$0.615205\pi$
$338$	−23.0000	−1.25104
$339$	−63.0000	−3.42169
$340$	0	0
$341$	−30.0000	−1.62459
$342$	−6.00000	−0.324443
$343$	0	0
$344$	−4.00000	−0.215666
$345$	−12.0000	−0.646058
$346$	−5.00000	−0.268802
$347$	−27.0000	−1.44944	−0.724718	−	0.689046i	$-0.758030\pi$
$347$	−27.0000	−1.44944	−0.724718	+	0.689046i	$0.758030\pi$
$348$	24.0000	1.28654
$349$	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
$351$	−54.0000	−2.88231
$352$	5.00000	0.266501
$353$	−27.0000	−1.43706	−0.718532	−	0.695493i	$-0.755186\pi$
$353$	−27.0000	−1.43706	−0.718532	+	0.695493i	$0.755186\pi$
$354$	6.00000	0.318896
$355$	3.00000	0.159223
$356$	14.0000	0.741999
$357$	0	0
$358$	1.00000	0.0528516
$359$	−30.0000	−1.58334	−0.791670	−	0.610949i	$-0.790788\pi$
$359$	−30.0000	−1.58334	−0.791670	+	0.610949i	$0.790788\pi$
$360$	6.00000	0.316228
$361$	−18.0000	−0.947368
$362$	2.00000	0.105118
$363$	−42.0000	−2.20443
$364$	0	0
$365$	2.00000	0.104685
$366$	39.0000	2.03856
$367$	−2.00000	−0.104399	−0.0521996	−	0.998637i	$-0.516623\pi$
$367$	−2.00000	−0.104399	−0.0521996	+	0.998637i	$0.516623\pi$
$368$	−4.00000	−0.208514
$369$	−6.00000	−0.312348
$370$	−2.00000	−0.103975
$371$	0	0
$372$	−18.0000	−0.933257
$373$	−9.00000	−0.466002	−0.233001	−	0.972476i	$-0.574855\pi$
$373$	−9.00000	−0.466002	−0.233001	+	0.972476i	$0.574855\pi$
$374$	0	0
$375$	−27.0000	−1.39427
$376$	0	0
$377$	−48.0000	−2.47213
$378$	0	0
$379$	22.0000	1.13006	0.565032	−	0.825069i	$-0.308864\pi$
$379$	22.0000	1.13006	0.565032	+	0.825069i	$0.308864\pi$
$380$	−1.00000	−0.0512989
$381$	−6.00000	−0.307389
$382$	−16.0000	−0.818631
$383$	35.0000	1.78842	0.894208	−	0.447651i	$-0.147739\pi$
$383$	35.0000	1.78842	0.894208	+	0.447651i	$0.147739\pi$
$384$	3.00000	0.153093
$385$	0	0
$386$	−6.00000	−0.305392
$387$	24.0000	1.21999
$388$	−8.00000	−0.406138
$389$	13.0000	0.659126	0.329563	−	0.944134i	$-0.393099\pi$
$389$	13.0000	0.659126	0.329563	+	0.944134i	$0.393099\pi$
$390$	−18.0000	−0.911465
$391$	0	0
$392$	0	0
$393$	−12.0000	−0.605320
$394$	3.00000	0.151138
$395$	11.0000	0.553470
$396$	−30.0000	−1.50756
$397$	2.00000	0.100377	0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000	0.100377	0.0501886	+	0.998740i	$0.484018\pi$
$398$	0	0
$399$	0	0
$400$	−4.00000	−0.200000
$401$	−1.00000	−0.0499376	−0.0249688	−	0.999688i	$-0.507949\pi$
$401$	−1.00000	−0.0499376	−0.0249688	+	0.999688i	$0.507949\pi$
$402$	48.0000	2.39402
$403$	36.0000	1.79329
$404$	8.00000	0.398015
$405$	−9.00000	−0.447214
$406$	0	0
$407$	10.0000	0.495682
$408$	0	0
$409$	29.0000	1.43396	0.716979	−	0.697095i	$-0.245524\pi$
$409$	29.0000	1.43396	0.716979	+	0.697095i	$0.245524\pi$
$410$	−1.00000	−0.0493865
$411$	54.0000	2.66362
$412$	−14.0000	−0.689730
$413$	0	0
$414$	24.0000	1.17954
$415$	14.0000	0.687233
$416$	−6.00000	−0.294174
$417$	−6.00000	−0.293821
$418$	5.00000	0.244558
$419$	4.00000	0.195413	0.0977064	−	0.995215i	$-0.468849\pi$
$419$	4.00000	0.195413	0.0977064	+	0.995215i	$0.468849\pi$
$420$	0	0
$421$	2.00000	0.0974740	0.0487370	−	0.998812i	$-0.484480\pi$
$421$	2.00000	0.0974740	0.0487370	+	0.998812i	$0.484480\pi$
$422$	−3.00000	−0.146038
$423$	0	0
$424$	−6.00000	−0.291386
$425$	0	0
$426$	−9.00000	−0.436051
$427$	0	0
$428$	−6.00000	−0.290021
$429$	90.0000	4.34524
$430$	4.00000	0.192897
$431$	−16.0000	−0.770693	−0.385346	−	0.922772i	$-0.625918\pi$
$431$	−16.0000	−0.770693	−0.385346	+	0.922772i	$0.625918\pi$
$432$	−9.00000	−0.433013
$433$	27.0000	1.29754	0.648769	−	0.760986i	$-0.275284\pi$
$433$	27.0000	1.29754	0.648769	+	0.760986i	$0.275284\pi$
$434$	0	0
$435$	−24.0000	−1.15071
$436$	16.0000	0.766261
$437$	−4.00000	−0.191346
$438$	−6.00000	−0.286691
$439$	−11.0000	−0.525001	−0.262501	−	0.964932i	$-0.584547\pi$
$439$	−11.0000	−0.525001	−0.262501	+	0.964932i	$0.584547\pi$
$440$	−5.00000	−0.238366
$441$	0	0
$442$	0	0
$443$	−28.0000	−1.33032	−0.665160	−	0.746701i	$-0.731637\pi$
$443$	−28.0000	−1.33032	−0.665160	+	0.746701i	$0.731637\pi$
$444$	6.00000	0.284747
$445$	−14.0000	−0.663664
$446$	24.0000	1.13643
$447$	−54.0000	−2.55411
$448$	0	0
$449$	9.00000	0.424736	0.212368	−	0.977190i	$-0.431882\pi$
$449$	9.00000	0.424736	0.212368	+	0.977190i	$0.431882\pi$
$450$	24.0000	1.13137
$451$	5.00000	0.235441
$452$	21.0000	0.987757
$453$	24.0000	1.12762
$454$	−13.0000	−0.610120
$455$	0	0
$456$	3.00000	0.140488
$457$	−36.0000	−1.68401	−0.842004	−	0.539471i	$-0.818624\pi$
$457$	−36.0000	−1.68401	−0.842004	+	0.539471i	$0.818624\pi$
$458$	16.0000	0.747631
$459$	0	0
$460$	4.00000	0.186501
$461$	−3.00000	−0.139724	−0.0698620	−	0.997557i	$-0.522256\pi$
$461$	−3.00000	−0.139724	−0.0698620	+	0.997557i	$0.522256\pi$
$462$	0	0
$463$	1.00000	0.0464739	0.0232370	−	0.999730i	$-0.492603\pi$
$463$	1.00000	0.0464739	0.0232370	+	0.999730i	$0.492603\pi$
$464$	−8.00000	−0.371391
$465$	18.0000	0.834730
$466$	14.0000	0.648537
$467$	12.0000	0.555294	0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000	0.555294	0.277647	+	0.960683i	$0.410445\pi$
$468$	36.0000	1.66410
$469$	0	0
$470$	0	0
$471$	−12.0000	−0.552931
$472$	−2.00000	−0.0920575
$473$	−20.0000	−0.919601
$474$	−33.0000	−1.51574
$475$	−4.00000	−0.183533
$476$	0	0
$477$	36.0000	1.64833
$478$	21.0000	0.960518
$479$	35.0000	1.59919	0.799595	−	0.600539i	$-0.205047\pi$
$479$	35.0000	1.59919	0.799595	+	0.600539i	$0.205047\pi$
$480$	−3.00000	−0.136931
$481$	−12.0000	−0.547153
$482$	22.0000	1.00207
$483$	0	0
$484$	14.0000	0.636364
$485$	8.00000	0.363261
$486$	0	0
$487$	6.00000	0.271886	0.135943	−	0.990717i	$-0.456594\pi$
$487$	6.00000	0.271886	0.135943	+	0.990717i	$0.456594\pi$
$488$	−13.0000	−0.588482
$489$	30.0000	1.35665
$490$	0	0
$491$	−26.0000	−1.17336	−0.586682	−	0.809818i	$-0.699566\pi$
$491$	−26.0000	−1.17336	−0.586682	+	0.809818i	$0.699566\pi$
$492$	3.00000	0.135250
$493$	0	0
$494$	−6.00000	−0.269953
$495$	30.0000	1.34840
$496$	6.00000	0.269408
$497$	0	0
$498$	−42.0000	−1.88207
$499$	−8.00000	−0.358129	−0.179065	−	0.983837i	$-0.557307\pi$
$499$	−8.00000	−0.358129	−0.179065	+	0.983837i	$0.557307\pi$
$500$	9.00000	0.402492
$501$	0	0
$502$	−18.0000	−0.803379
$503$	27.0000	1.20387	0.601935	−	0.798545i	$-0.294397\pi$
$503$	27.0000	1.20387	0.601935	+	0.798545i	$0.294397\pi$
$504$	0	0
$505$	−8.00000	−0.355995
$506$	−20.0000	−0.889108
$507$	−69.0000	−3.06440
$508$	2.00000	0.0887357
$509$	36.0000	1.59567	0.797836	−	0.602875i	$-0.205978\pi$
$509$	36.0000	1.59567	0.797836	+	0.602875i	$0.205978\pi$
$510$	0	0
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−9.00000	−0.397360
$514$	0	0
$515$	14.0000	0.616914
$516$	−12.0000	−0.528271
$517$	0	0
$518$	0	0
$519$	−15.0000	−0.658427
$520$	6.00000	0.263117
$521$	10.0000	0.438108	0.219054	−	0.975713i	$-0.429703\pi$
$521$	10.0000	0.438108	0.219054	+	0.975713i	$0.429703\pi$
$522$	48.0000	2.10090
$523$	−16.0000	−0.699631	−0.349816	−	0.936819i	$-0.613756\pi$
$523$	−16.0000	−0.699631	−0.349816	+	0.936819i	$0.613756\pi$
$524$	4.00000	0.174741
$525$	0	0
$526$	16.0000	0.697633
$527$	0	0
$528$	15.0000	0.652791
$529$	−7.00000	−0.304348
$530$	6.00000	0.260623
$531$	12.0000	0.520756
$532$	0	0
$533$	−6.00000	−0.259889
$534$	42.0000	1.81752
$535$	6.00000	0.259403
$536$	−16.0000	−0.691095
$537$	3.00000	0.129460
$538$	1.00000	0.0431131
$539$	0	0
$540$	9.00000	0.387298
$541$	10.0000	0.429934	0.214967	−	0.976621i	$-0.431036\pi$
$541$	10.0000	0.429934	0.214967	+	0.976621i	$0.431036\pi$
$542$	−8.00000	−0.343629
$543$	6.00000	0.257485
$544$	0	0
$545$	−16.0000	−0.685365
$546$	0	0
$547$	−28.0000	−1.19719	−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000	−1.19719	−0.598597	+	0.801050i	$0.704275\pi$
$548$	−18.0000	−0.768922
$549$	78.0000	3.32896
$550$	−20.0000	−0.852803
$551$	−8.00000	−0.340811
$552$	−12.0000	−0.510754
$553$	0	0
$554$	31.0000	1.31706
$555$	−6.00000	−0.254686
$556$	2.00000	0.0848189
$557$	−6.00000	−0.254228	−0.127114	−	0.991888i	$-0.540571\pi$
$557$	−6.00000	−0.254228	−0.127114	+	0.991888i	$0.540571\pi$
$558$	−36.0000	−1.52400
$559$	24.0000	1.01509
$560$	0	0
$561$	0	0
$562$	−20.0000	−0.843649
$563$	13.0000	0.547885	0.273942	−	0.961746i	$-0.411672\pi$
$563$	13.0000	0.547885	0.273942	+	0.961746i	$0.411672\pi$
$564$	0	0
$565$	−21.0000	−0.883477
$566$	6.00000	0.252199
$567$	0	0
$568$	3.00000	0.125877
$569$	−10.0000	−0.419222	−0.209611	−	0.977785i	$-0.567220\pi$
$569$	−10.0000	−0.419222	−0.209611	+	0.977785i	$0.567220\pi$
$570$	−3.00000	−0.125656
$571$	37.0000	1.54840	0.774201	−	0.632940i	$-0.218152\pi$
$571$	37.0000	1.54840	0.774201	+	0.632940i	$0.218152\pi$
$572$	−30.0000	−1.25436
$573$	−48.0000	−2.00523
$574$	0	0
$575$	16.0000	0.667246
$576$	6.00000	0.250000
$577$	−38.0000	−1.58196	−0.790980	−	0.611842i	$-0.790429\pi$
$577$	−38.0000	−1.58196	−0.790980	+	0.611842i	$0.790429\pi$
$578$	17.0000	0.707107
$579$	−18.0000	−0.748054
$580$	8.00000	0.332182
$581$	0	0
$582$	−24.0000	−0.994832
$583$	−30.0000	−1.24247
$584$	2.00000	0.0827606
$585$	−36.0000	−1.48842
$586$	28.0000	1.15667
$587$	15.0000	0.619116	0.309558	−	0.950881i	$-0.399819\pi$
$587$	15.0000	0.619116	0.309558	+	0.950881i	$0.399819\pi$
$588$	0	0
$589$	6.00000	0.247226
$590$	2.00000	0.0823387
$591$	9.00000	0.370211
$592$	−2.00000	−0.0821995
$593$	44.0000	1.80686	0.903432	−	0.428732i	$-0.141040\pi$
$593$	44.0000	1.80686	0.903432	+	0.428732i	$0.141040\pi$
$594$	−45.0000	−1.84637
$595$	0	0
$596$	18.0000	0.737309
$597$	0	0
$598$	24.0000	0.981433
$599$	16.0000	0.653742	0.326871	−	0.945069i	$-0.394006\pi$
$599$	16.0000	0.653742	0.326871	+	0.945069i	$0.394006\pi$
$600$	−12.0000	−0.489898
$601$	−6.00000	−0.244745	−0.122373	−	0.992484i	$-0.539050\pi$
$601$	−6.00000	−0.244745	−0.122373	+	0.992484i	$0.539050\pi$
$602$	0	0
$603$	96.0000	3.90942
$604$	−8.00000	−0.325515
$605$	−14.0000	−0.569181
$606$	24.0000	0.974933
$607$	−10.0000	−0.405887	−0.202944	−	0.979190i	$-0.565051\pi$
$607$	−10.0000	−0.405887	−0.202944	+	0.979190i	$0.565051\pi$
$608$	−1.00000	−0.0405554
$609$	0	0
$610$	13.0000	0.526355
$611$	0	0
$612$	0	0
$613$	−25.0000	−1.00974	−0.504870	−	0.863195i	$-0.668460\pi$
$613$	−25.0000	−1.00974	−0.504870	+	0.863195i	$0.668460\pi$
$614$	28.0000	1.12999
$615$	−3.00000	−0.120972
$616$	0	0
$617$	−3.00000	−0.120775	−0.0603877	−	0.998175i	$-0.519234\pi$
$617$	−3.00000	−0.120775	−0.0603877	+	0.998175i	$0.519234\pi$
$618$	−42.0000	−1.68949
$619$	−30.0000	−1.20580	−0.602901	−	0.797816i	$-0.705989\pi$
$619$	−30.0000	−1.20580	−0.602901	+	0.797816i	$0.705989\pi$
$620$	−6.00000	−0.240966
$621$	36.0000	1.44463
$622$	24.0000	0.962312
$623$	0	0
$624$	−18.0000	−0.720577
$625$	11.0000	0.440000
$626$	16.0000	0.639489
$627$	15.0000	0.599042
$628$	4.00000	0.159617
$629$	0	0
$630$	0	0
$631$	−42.0000	−1.67199	−0.835997	−	0.548734i	$-0.815110\pi$
$631$	−42.0000	−1.67199	−0.835997	+	0.548734i	$0.815110\pi$
$632$	11.0000	0.437557
$633$	−9.00000	−0.357718
$634$	−12.0000	−0.476581
$635$	−2.00000	−0.0793676
$636$	−18.0000	−0.713746
$637$	0	0
$638$	−40.0000	−1.58362
$639$	−18.0000	−0.712069
$640$	1.00000	0.0395285
$641$	−42.0000	−1.65890	−0.829450	−	0.558581i	$-0.811346\pi$
$641$	−42.0000	−1.65890	−0.829450	+	0.558581i	$0.811346\pi$
$642$	−18.0000	−0.710403
$643$	17.0000	0.670415	0.335207	−	0.942144i	$-0.391194\pi$
$643$	17.0000	0.670415	0.335207	+	0.942144i	$0.391194\pi$
$644$	0	0
$645$	12.0000	0.472500
$646$	0	0
$647$	18.0000	0.707653	0.353827	−	0.935311i	$-0.384880\pi$
$647$	18.0000	0.707653	0.353827	+	0.935311i	$0.384880\pi$
$648$	−9.00000	−0.353553
$649$	−10.0000	−0.392534
$650$	24.0000	0.941357
$651$	0	0
$652$	−10.0000	−0.391630
$653$	−48.0000	−1.87839	−0.939193	−	0.343391i	$-0.888424\pi$
$653$	−48.0000	−1.87839	−0.939193	+	0.343391i	$0.888424\pi$
$654$	48.0000	1.87695
$655$	−4.00000	−0.156293
$656$	−1.00000	−0.0390434
$657$	−12.0000	−0.468165
$658$	0	0
$659$	20.0000	0.779089	0.389545	−	0.921008i	$-0.372632\pi$
$659$	20.0000	0.779089	0.389545	+	0.921008i	$0.372632\pi$
$660$	−15.0000	−0.583874
$661$	43.0000	1.67251	0.836253	−	0.548344i	$-0.184741\pi$
$661$	43.0000	1.67251	0.836253	+	0.548344i	$0.184741\pi$
$662$	20.0000	0.777322
$663$	0	0
$664$	14.0000	0.543305
$665$	0	0
$666$	12.0000	0.464991
$667$	32.0000	1.23904
$668$	0	0
$669$	72.0000	2.78368
$670$	16.0000	0.618134
$671$	−65.0000	−2.50930
$672$	0	0
$673$	−18.0000	−0.693849	−0.346925	−	0.937893i	$-0.612774\pi$
$673$	−18.0000	−0.693849	−0.346925	+	0.937893i	$0.612774\pi$
$674$	13.0000	0.500741
$675$	36.0000	1.38564
$676$	23.0000	0.884615
$677$	27.0000	1.03769	0.518847	−	0.854867i	$-0.326361\pi$
$677$	27.0000	1.03769	0.518847	+	0.854867i	$0.326361\pi$
$678$	63.0000	2.41950
$679$	0	0
$680$	0	0
$681$	−39.0000	−1.49448
$682$	30.0000	1.14876
$683$	−8.00000	−0.306111	−0.153056	−	0.988218i	$-0.548911\pi$
$683$	−8.00000	−0.306111	−0.153056	+	0.988218i	$0.548911\pi$
$684$	6.00000	0.229416
$685$	18.0000	0.687745
$686$	0	0
$687$	48.0000	1.83131
$688$	4.00000	0.152499
$689$	36.0000	1.37149
$690$	12.0000	0.456832
$691$	−41.0000	−1.55971	−0.779857	−	0.625958i	$-0.784708\pi$
$691$	−41.0000	−1.55971	−0.779857	+	0.625958i	$0.784708\pi$
$692$	5.00000	0.190071
$693$	0	0
$694$	27.0000	1.02491
$695$	−2.00000	−0.0758643
$696$	−24.0000	−0.909718
$697$	0	0
$698$	−2.00000	−0.0757011
$699$	42.0000	1.58859
$700$	0	0
$701$	13.0000	0.491003	0.245502	−	0.969396i	$-0.421047\pi$
$701$	13.0000	0.491003	0.245502	+	0.969396i	$0.421047\pi$
$702$	54.0000	2.03810
$703$	−2.00000	−0.0754314
$704$	−5.00000	−0.188445
$705$	0	0
$706$	27.0000	1.01616
$707$	0	0
$708$	−6.00000	−0.225494
$709$	0	0		−	1.00000i	$-0.5\pi$
$709$	0	0			1.00000i	$0.5\pi$
$710$	−3.00000	−0.112588
$711$	−66.0000	−2.47519
$712$	−14.0000	−0.524672
$713$	−24.0000	−0.898807
$714$	0	0
$715$	30.0000	1.12194
$716$	−1.00000	−0.0373718
$717$	63.0000	2.35278
$718$	30.0000	1.11959
$719$	25.0000	0.932343	0.466171	−	0.884694i	$-0.345633\pi$
$719$	25.0000	0.932343	0.466171	+	0.884694i	$0.345633\pi$
$720$	−6.00000	−0.223607
$721$	0	0
$722$	18.0000	0.669891
$723$	66.0000	2.45457
$724$	−2.00000	−0.0743294
$725$	32.0000	1.18845
$726$	42.0000	1.55877
$727$	32.0000	1.18681	0.593407	−	0.804902i	$-0.297782\pi$
$727$	32.0000	1.18681	0.593407	+	0.804902i	$0.297782\pi$
$728$	0	0
$729$	−27.0000	−1.00000
$730$	−2.00000	−0.0740233
$731$	0	0
$732$	−39.0000	−1.44148
$733$	46.0000	1.69905	0.849524	−	0.527549i	$-0.176889\pi$
$733$	46.0000	1.69905	0.849524	+	0.527549i	$0.176889\pi$
$734$	2.00000	0.0738213
$735$	0	0
$736$	4.00000	0.147442
$737$	−80.0000	−2.94684
$738$	6.00000	0.220863
$739$	−2.00000	−0.0735712	−0.0367856	−	0.999323i	$-0.511712\pi$
$739$	−2.00000	−0.0735712	−0.0367856	+	0.999323i	$0.511712\pi$
$740$	2.00000	0.0735215
$741$	−18.0000	−0.661247
$742$	0	0
$743$	0	0		−	1.00000i	$-0.5\pi$
$743$	0	0			1.00000i	$0.5\pi$
$744$	18.0000	0.659912
$745$	−18.0000	−0.659469
$746$	9.00000	0.329513
$747$	−84.0000	−3.07340
$748$	0	0
$749$	0	0
$750$	27.0000	0.985901
$751$	39.0000	1.42313	0.711565	−	0.702620i	$-0.247987\pi$
$751$	39.0000	1.42313	0.711565	+	0.702620i	$0.247987\pi$
$752$	0	0
$753$	−54.0000	−1.96787
$754$	48.0000	1.74806
$755$	8.00000	0.291150
$756$	0	0
$757$	28.0000	1.01768	0.508839	−	0.860862i	$-0.330075\pi$
$757$	28.0000	1.01768	0.508839	+	0.860862i	$0.330075\pi$
$758$	−22.0000	−0.799076
$759$	−60.0000	−2.17786
$760$	1.00000	0.0362738
$761$	−30.0000	−1.08750	−0.543750	−	0.839248i	$-0.682996\pi$
$761$	−30.0000	−1.08750	−0.543750	+	0.839248i	$0.682996\pi$
$762$	6.00000	0.217357
$763$	0	0
$764$	16.0000	0.578860
$765$	0	0
$766$	−35.0000	−1.26460
$767$	12.0000	0.433295
$768$	−3.00000	−0.108253
$769$	−5.00000	−0.180305	−0.0901523	−	0.995928i	$-0.528735\pi$
$769$	−5.00000	−0.180305	−0.0901523	+	0.995928i	$0.528735\pi$
$770$	0	0
$771$	0	0
$772$	6.00000	0.215945
$773$	−2.00000	−0.0719350	−0.0359675	−	0.999353i	$-0.511451\pi$
$773$	−2.00000	−0.0719350	−0.0359675	+	0.999353i	$0.511451\pi$
$774$	−24.0000	−0.862662
$775$	−24.0000	−0.862105
$776$	8.00000	0.287183
$777$	0	0
$778$	−13.0000	−0.466073
$779$	−1.00000	−0.0358287
$780$	18.0000	0.644503
$781$	15.0000	0.536742
$782$	0	0
$783$	72.0000	2.57307
$784$	0	0
$785$	−4.00000	−0.142766
$786$	12.0000	0.428026
$787$	−28.0000	−0.998092	−0.499046	−	0.866575i	$-0.666316\pi$
$787$	−28.0000	−0.998092	−0.499046	+	0.866575i	$0.666316\pi$
$788$	−3.00000	−0.106871
$789$	48.0000	1.70885
$790$	−11.0000	−0.391362
$791$	0	0
$792$	30.0000	1.06600
$793$	78.0000	2.76986
$794$	−2.00000	−0.0709773
$795$	18.0000	0.638394
$796$	0	0
$797$	−30.0000	−1.06265	−0.531327	−	0.847167i	$-0.678307\pi$
$797$	−30.0000	−1.06265	−0.531327	+	0.847167i	$0.678307\pi$
$798$	0	0
$799$	0	0
$800$	4.00000	0.141421
$801$	84.0000	2.96799
$802$	1.00000	0.0353112
$803$	10.0000	0.352892
$804$	−48.0000	−1.69283
$805$	0	0
$806$	−36.0000	−1.26805
$807$	3.00000	0.105605
$808$	−8.00000	−0.281439
$809$	−24.0000	−0.843795	−0.421898	−	0.906644i	$-0.638636\pi$
$809$	−24.0000	−0.843795	−0.421898	+	0.906644i	$0.638636\pi$
$810$	9.00000	0.316228
$811$	−18.0000	−0.632065	−0.316033	−	0.948748i	$-0.602351\pi$
$811$	−18.0000	−0.632065	−0.316033	+	0.948748i	$0.602351\pi$
$812$	0	0
$813$	−24.0000	−0.841717
$814$	−10.0000	−0.350500
$815$	10.0000	0.350285
$816$	0	0
$817$	4.00000	0.139942
$818$	−29.0000	−1.01396
$819$	0	0
$820$	1.00000	0.0349215
$821$	5.00000	0.174501	0.0872506	−	0.996186i	$-0.472192\pi$
$821$	5.00000	0.174501	0.0872506	+	0.996186i	$0.472192\pi$
$822$	−54.0000	−1.88347
$823$	−9.00000	−0.313720	−0.156860	−	0.987621i	$-0.550137\pi$
$823$	−9.00000	−0.313720	−0.156860	+	0.987621i	$0.550137\pi$
$824$	14.0000	0.487713
$825$	−60.0000	−2.08893
$826$	0	0
$827$	24.0000	0.834562	0.417281	−	0.908778i	$-0.362983\pi$
$827$	24.0000	0.834562	0.417281	+	0.908778i	$0.362983\pi$
$828$	−24.0000	−0.834058
$829$	−22.0000	−0.764092	−0.382046	−	0.924143i	$-0.624780\pi$
$829$	−22.0000	−0.764092	−0.382046	+	0.924143i	$0.624780\pi$
$830$	−14.0000	−0.485947
$831$	93.0000	3.22613
$832$	6.00000	0.208013
$833$	0	0
$834$	6.00000	0.207763
$835$	0	0
$836$	−5.00000	−0.172929
$837$	−54.0000	−1.86651
$838$	−4.00000	−0.138178
$839$	−1.00000	−0.0345238	−0.0172619	−	0.999851i	$-0.505495\pi$
$839$	−1.00000	−0.0345238	−0.0172619	+	0.999851i	$0.505495\pi$
$840$	0	0
$841$	35.0000	1.20690
$842$	−2.00000	−0.0689246
$843$	−60.0000	−2.06651
$844$	3.00000	0.103264
$845$	−23.0000	−0.791224
$846$	0	0
$847$	0	0
$848$	6.00000	0.206041
$849$	18.0000	0.617758
$850$	0	0
$851$	8.00000	0.274236
$852$	9.00000	0.308335
$853$	−39.0000	−1.33533	−0.667667	−	0.744460i	$-0.732707\pi$
$853$	−39.0000	−1.33533	−0.667667	+	0.744460i	$0.732707\pi$
$854$	0	0
$855$	−6.00000	−0.205196
$856$	6.00000	0.205076
$857$	13.0000	0.444072	0.222036	−	0.975039i	$-0.428730\pi$
$857$	13.0000	0.444072	0.222036	+	0.975039i	$0.428730\pi$
$858$	−90.0000	−3.07255
$859$	−2.00000	−0.0682391	−0.0341196	−	0.999418i	$-0.510863\pi$
$859$	−2.00000	−0.0682391	−0.0341196	+	0.999418i	$0.510863\pi$
$860$	−4.00000	−0.136399
$861$	0	0
$862$	16.0000	0.544962
$863$	−50.0000	−1.70202	−0.851010	−	0.525150i	$-0.824009\pi$
$863$	−50.0000	−1.70202	−0.851010	+	0.525150i	$0.824009\pi$
$864$	9.00000	0.306186
$865$	−5.00000	−0.170005
$866$	−27.0000	−0.917497
$867$	51.0000	1.73205
$868$	0	0
$869$	55.0000	1.86575
$870$	24.0000	0.813676
$871$	96.0000	3.25284
$872$	−16.0000	−0.541828
$873$	−48.0000	−1.62455
$874$	4.00000	0.135302
$875$	0	0
$876$	6.00000	0.202721
$877$	−53.0000	−1.78968	−0.894841	−	0.446384i	$-0.852711\pi$
$877$	−53.0000	−1.78968	−0.894841	+	0.446384i	$0.852711\pi$
$878$	11.0000	0.371232
$879$	84.0000	2.83325
$880$	5.00000	0.168550
$881$	−15.0000	−0.505363	−0.252681	−	0.967550i	$-0.581312\pi$
$881$	−15.0000	−0.505363	−0.252681	+	0.967550i	$0.581312\pi$
$882$	0	0
$883$	4.00000	0.134611	0.0673054	−	0.997732i	$-0.478560\pi$
$883$	4.00000	0.134611	0.0673054	+	0.997732i	$0.478560\pi$
$884$	0	0
$885$	6.00000	0.201688
$886$	28.0000	0.940678
$887$	−19.0000	−0.637958	−0.318979	−	0.947762i	$-0.603340\pi$
$887$	−19.0000	−0.637958	−0.318979	+	0.947762i	$0.603340\pi$
$888$	−6.00000	−0.201347
$889$	0	0
$890$	14.0000	0.469281
$891$	−45.0000	−1.50756
$892$	−24.0000	−0.803579
$893$	0	0
$894$	54.0000	1.80603
$895$	1.00000	0.0334263
$896$	0	0
$897$	72.0000	2.40401
$898$	−9.00000	−0.300334
$899$	−48.0000	−1.60089
$900$	−24.0000	−0.800000
$901$	0	0
$902$	−5.00000	−0.166482
$903$	0	0
$904$	−21.0000	−0.698450
$905$	2.00000	0.0664822
$906$	−24.0000	−0.797347
$907$	10.0000	0.332045	0.166022	−	0.986122i	$-0.446908\pi$
$907$	10.0000	0.332045	0.166022	+	0.986122i	$0.446908\pi$
$908$	13.0000	0.431420
$909$	48.0000	1.59206
$910$	0	0
$911$	−4.00000	−0.132526	−0.0662630	−	0.997802i	$-0.521108\pi$
$911$	−4.00000	−0.132526	−0.0662630	+	0.997802i	$0.521108\pi$
$912$	−3.00000	−0.0993399
$913$	70.0000	2.31666
$914$	36.0000	1.19077
$915$	39.0000	1.28930
$916$	−16.0000	−0.528655
$917$	0	0
$918$	0	0
$919$	−51.0000	−1.68233	−0.841167	−	0.540775i	$-0.818131\pi$
$919$	−51.0000	−1.68233	−0.841167	+	0.540775i	$0.818131\pi$
$920$	−4.00000	−0.131876
$921$	84.0000	2.76789
$922$	3.00000	0.0987997
$923$	−18.0000	−0.592477
$924$	0	0
$925$	8.00000	0.263038
$926$	−1.00000	−0.0328620
$927$	−84.0000	−2.75892
$928$	8.00000	0.262613
$929$	−14.0000	−0.459325	−0.229663	−	0.973270i	$-0.573762\pi$
$929$	−14.0000	−0.459325	−0.229663	+	0.973270i	$0.573762\pi$
$930$	−18.0000	−0.590243
$931$	0	0
$932$	−14.0000	−0.458585
$933$	72.0000	2.35717
$934$	−12.0000	−0.392652
$935$	0	0
$936$	−36.0000	−1.17670
$937$	−44.0000	−1.43742	−0.718709	−	0.695311i	$-0.755266\pi$
$937$	−44.0000	−1.43742	−0.718709	+	0.695311i	$0.755266\pi$
$938$	0	0
$939$	48.0000	1.56642
$940$	0	0
$941$	−39.0000	−1.27136	−0.635682	−	0.771951i	$-0.719281\pi$
$941$	−39.0000	−1.27136	−0.635682	+	0.771951i	$0.719281\pi$
$942$	12.0000	0.390981
$943$	4.00000	0.130258
$944$	2.00000	0.0650945
$945$	0	0
$946$	20.0000	0.650256
$947$	−16.0000	−0.519930	−0.259965	−	0.965618i	$-0.583711\pi$
$947$	−16.0000	−0.519930	−0.259965	+	0.965618i	$0.583711\pi$
$948$	33.0000	1.07179
$949$	−12.0000	−0.389536
$950$	4.00000	0.129777
$951$	−36.0000	−1.16738
$952$	0	0
$953$	−6.00000	−0.194359	−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000	−0.194359	−0.0971795	+	0.995267i	$0.530982\pi$
$954$	−36.0000	−1.16554
$955$	−16.0000	−0.517748
$956$	−21.0000	−0.679189
$957$	−120.000	−3.87905
$958$	−35.0000	−1.13080
$959$	0	0
$960$	3.00000	0.0968246
$961$	5.00000	0.161290
$962$	12.0000	0.386896
$963$	−36.0000	−1.16008
$964$	−22.0000	−0.708572
$965$	−6.00000	−0.193147
$966$	0	0
$967$	37.0000	1.18984	0.594920	−	0.803785i	$-0.297184\pi$
$967$	37.0000	1.18984	0.594920	+	0.803785i	$0.297184\pi$
$968$	−14.0000	−0.449977
$969$	0	0
$970$	−8.00000	−0.256865
$971$	4.00000	0.128366	0.0641831	−	0.997938i	$-0.479556\pi$
$971$	4.00000	0.128366	0.0641831	+	0.997938i	$0.479556\pi$
$972$	0	0
$973$	0	0
$974$	−6.00000	−0.192252
$975$	72.0000	2.30585
$976$	13.0000	0.416120
$977$	−6.00000	−0.191957	−0.0959785	−	0.995383i	$-0.530598\pi$
$977$	−6.00000	−0.191957	−0.0959785	+	0.995383i	$0.530598\pi$
$978$	−30.0000	−0.959294
$979$	−70.0000	−2.23721
$980$	0	0
$981$	96.0000	3.06504
$982$	26.0000	0.829693
$983$	−36.0000	−1.14822	−0.574111	−	0.818778i	$-0.694652\pi$
$983$	−36.0000	−1.14822	−0.574111	+	0.818778i	$0.694652\pi$
$984$	−3.00000	−0.0956365
$985$	3.00000	0.0955879
$986$	0	0
$987$	0	0
$988$	6.00000	0.190885
$989$	−16.0000	−0.508770
$990$	−30.0000	−0.953463
$991$	−17.0000	−0.540023	−0.270011	−	0.962857i	$-0.587027\pi$
$991$	−17.0000	−0.540023	−0.270011	+	0.962857i	$0.587027\pi$
$992$	−6.00000	−0.190500
$993$	60.0000	1.90404
$994$	0	0
$995$	0	0
$996$	42.0000	1.33082
$997$	−14.0000	−0.443384	−0.221692	−	0.975117i	$-0.571158\pi$
$997$	−14.0000	−0.443384	−0.221692	+	0.975117i	$0.571158\pi$
$998$	8.00000	0.253236
$999$	18.0000	0.569495

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4018.2.a.a.1.1		1
7.2	even	3		574.2.e.c.165.1	✓	2
7.4	even	3		574.2.e.c.247.1	yes	2
7.6	odd	2		4018.2.a.k.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.e.c.165.1	✓	2	7.2	even	3
574.2.e.c.247.1	yes	2	7.4	even	3
4018.2.a.a.1.1		1	1.1	even	1	trivial
4018.2.a.k.1.1		1	7.6	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:	\( N \)	\(=\)	\( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4018.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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