LMFDB - Embedded newform 26.4.a.b.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [26,4,Mod(1,26)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("26.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(26, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 26 = 2 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	26.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,2,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$1.53404966015$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	26.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

\(q+2.00000 q^{2} -1.00000 q^{3} +4.00000 q^{4} +17.0000 q^{5} -2.00000 q^{6} -35.0000 q^{7} +8.00000 q^{8} -26.0000 q^{9} +34.0000 q^{10} +2.00000 q^{11} -4.00000 q^{12} +13.0000 q^{13} -70.0000 q^{14} -17.0000 q^{15} +16.0000 q^{16} -19.0000 q^{17} -52.0000 q^{18} +94.0000 q^{19} +68.0000 q^{20} +35.0000 q^{21} +4.00000 q^{22} -72.0000 q^{23} -8.00000 q^{24} +164.000 q^{25} +26.0000 q^{26} +53.0000 q^{27} -140.000 q^{28} +246.000 q^{29} -34.0000 q^{30} -100.000 q^{31} +32.0000 q^{32} -2.00000 q^{33} -38.0000 q^{34} -595.000 q^{35} -104.000 q^{36} -11.0000 q^{37} +188.000 q^{38} -13.0000 q^{39} +136.000 q^{40} -280.000 q^{41} +70.0000 q^{42} +241.000 q^{43} +8.00000 q^{44} -442.000 q^{45} -144.000 q^{46} +137.000 q^{47} -16.0000 q^{48} +882.000 q^{49} +328.000 q^{50} +19.0000 q^{51} +52.0000 q^{52} -232.000 q^{53} +106.000 q^{54} +34.0000 q^{55} -280.000 q^{56} -94.0000 q^{57} +492.000 q^{58} -386.000 q^{59} -68.0000 q^{60} +64.0000 q^{61} -200.000 q^{62} +910.000 q^{63} +64.0000 q^{64} +221.000 q^{65} -4.00000 q^{66} -670.000 q^{67} -76.0000 q^{68} +72.0000 q^{69} -1190.00 q^{70} +55.0000 q^{71} -208.000 q^{72} -838.000 q^{73} -22.0000 q^{74} -164.000 q^{75} +376.000 q^{76} -70.0000 q^{77} -26.0000 q^{78} +1016.00 q^{79} +272.000 q^{80} +649.000 q^{81} -560.000 q^{82} +420.000 q^{83} +140.000 q^{84} -323.000 q^{85} +482.000 q^{86} -246.000 q^{87} +16.0000 q^{88} -934.000 q^{89} -884.000 q^{90} -455.000 q^{91} -288.000 q^{92} +100.000 q^{93} +274.000 q^{94} +1598.00 q^{95} -32.0000 q^{96} -1154.00 q^{97} +1764.00 q^{98} -52.0000 q^{99} +O(q^{100})\)

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 $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	−1.00000	−0.192450	−0.0962250	−	0.995360i	$-0.530677\pi$
$3$	−1.00000	−0.192450	−0.0962250	+	0.995360i	$0.530677\pi$
$4$	4.00000	0.500000
$5$	17.0000	1.52053	0.760263	−	0.649615i	$-0.225070\pi$
$5$	17.0000	1.52053	0.760263	+	0.649615i	$0.225070\pi$
$6$	−2.00000	−0.136083
$7$	−35.0000	−1.88982	−0.944911	−	0.327327i	$-0.893852\pi$
$7$	−35.0000	−1.88982	−0.944911	+	0.327327i	$0.893852\pi$
$8$	8.00000	0.353553
$9$	−26.0000	−0.962963
$10$	34.0000	1.07517
$11$	2.00000	0.0548202	0.0274101	−	0.999624i	$-0.491274\pi$
$11$	2.00000	0.0548202	0.0274101	+	0.999624i	$0.491274\pi$
$12$	−4.00000	−0.0962250
$13$	13.0000	0.277350
$13$	13.0000	0.277350
$14$	−70.0000	−1.33631
$15$	−17.0000	−0.292625
$16$	16.0000	0.250000
$17$	−19.0000	−0.271069	−0.135535	−	0.990773i	$-0.543275\pi$
$17$	−19.0000	−0.271069	−0.135535	+	0.990773i	$0.543275\pi$
$18$	−52.0000	−0.680918
$19$	94.0000	1.13500	0.567502	−	0.823372i	$-0.307910\pi$
$19$	94.0000	1.13500	0.567502	+	0.823372i	$0.307910\pi$
$20$	68.0000	0.760263
$21$	35.0000	0.363696
$22$	4.00000	0.0387638
$23$	−72.0000	−0.652741	−0.326370	−	0.945242i	$-0.605826\pi$
$23$	−72.0000	−0.652741	−0.326370	+	0.945242i	$0.605826\pi$
$24$	−8.00000	−0.0680414
$25$	164.000	1.31200
$26$	26.0000	0.196116
$27$	53.0000	0.377772
$28$	−140.000	−0.944911
$29$	246.000	1.57521	0.787604	−	0.616181i	$-0.211321\pi$
$29$	246.000	1.57521	0.787604	+	0.616181i	$0.211321\pi$
$30$	−34.0000	−0.206917
$31$	−100.000	−0.579372	−0.289686	−	0.957122i	$-0.593551\pi$
$31$	−100.000	−0.579372	−0.289686	+	0.957122i	$0.593551\pi$
$32$	32.0000	0.176777
$33$	−2.00000	−0.0105502
$34$	−38.0000	−0.191675
$35$	−595.000	−2.87352
$36$	−104.000	−0.481481
$37$	−11.0000	−0.0488754	−0.0244377	−	0.999701i	$-0.507780\pi$
$37$	−11.0000	−0.0488754	−0.0244377	+	0.999701i	$0.507780\pi$
$38$	188.000	0.802569
$39$	−13.0000	−0.0533761
$40$	136.000	0.537587
$41$	−280.000	−1.06655	−0.533276	−	0.845941i	$-0.679039\pi$
$41$	−280.000	−1.06655	−0.533276	+	0.845941i	$0.679039\pi$
$42$	70.0000	0.257172
$43$	241.000	0.854701	0.427351	−	0.904086i	$-0.359447\pi$
$43$	241.000	0.854701	0.427351	+	0.904086i	$0.359447\pi$
$44$	8.00000	0.0274101
$45$	−442.000	−1.46421
$46$	−144.000	−0.461557
$47$	137.000	0.425181	0.212590	−	0.977141i	$-0.431810\pi$
$47$	137.000	0.425181	0.212590	+	0.977141i	$0.431810\pi$
$48$	−16.0000	−0.0481125
$49$	882.000	2.57143
$50$	328.000	0.927724
$51$	19.0000	0.0521673
$52$	52.0000	0.138675
$53$	−232.000	−0.601276	−0.300638	−	0.953738i	$-0.597200\pi$
$53$	−232.000	−0.601276	−0.300638	+	0.953738i	$0.597200\pi$
$54$	106.000	0.267125
$55$	34.0000	0.0833556
$56$	−280.000	−0.668153
$57$	−94.0000	−0.218432
$58$	492.000	1.11384
$59$	−386.000	−0.851744	−0.425872	−	0.904783i	$-0.640033\pi$
$59$	−386.000	−0.851744	−0.425872	+	0.904783i	$0.640033\pi$
$60$	−68.0000	−0.146313
$61$	64.0000	0.134334	0.0671669	−	0.997742i	$-0.478604\pi$
$61$	64.0000	0.134334	0.0671669	+	0.997742i	$0.478604\pi$
$62$	−200.000	−0.409678
$63$	910.000	1.81983
$64$	64.0000	0.125000
$65$	221.000	0.421718
$66$	−4.00000	−0.00746009
$67$	−670.000	−1.22169	−0.610847	−	0.791748i	$-0.709171\pi$
$67$	−670.000	−1.22169	−0.610847	+	0.791748i	$0.709171\pi$
$68$	−76.0000	−0.135535
$69$	72.0000	0.125620
$70$	−1190.00	−2.03189
$71$	55.0000	0.0919338	0.0459669	−	0.998943i	$-0.485363\pi$
$71$	55.0000	0.0919338	0.0459669	+	0.998943i	$0.485363\pi$
$72$	−208.000	−0.340459
$73$	−838.000	−1.34357	−0.671784	−	0.740747i	$-0.734472\pi$
$73$	−838.000	−1.34357	−0.671784	+	0.740747i	$0.734472\pi$
$74$	−22.0000	−0.0345601
$75$	−164.000	−0.252495
$76$	376.000	0.567502
$77$	−70.0000	−0.103601
$78$	−26.0000	−0.0377426
$79$	1016.00	1.44695	0.723474	−	0.690351i	$-0.242544\pi$
$79$	1016.00	1.44695	0.723474	+	0.690351i	$0.242544\pi$
$80$	272.000	0.380132
$81$	649.000	0.890261
$82$	−560.000	−0.754167
$83$	420.000	0.555434	0.277717	−	0.960663i	$-0.410422\pi$
$83$	420.000	0.555434	0.277717	+	0.960663i	$0.410422\pi$
$84$	140.000	0.181848
$85$	−323.000	−0.412168
$86$	482.000	0.604365
$87$	−246.000	−0.303149
$88$	16.0000	0.0193819
$89$	−934.000	−1.11240	−0.556201	−	0.831048i	$-0.687742\pi$
$89$	−934.000	−1.11240	−0.556201	+	0.831048i	$0.687742\pi$
$90$	−884.000	−1.03535
$91$	−455.000	−0.524142
$92$	−288.000	−0.326370
$93$	100.000	0.111500
$94$	274.000	0.300648
$95$	1598.00	1.72580
$96$	−32.0000	−0.0340207
$97$	−1154.00	−1.20795	−0.603974	−	0.797004i	$-0.706417\pi$
$97$	−1154.00	−1.20795	−0.603974	+	0.797004i	$0.706417\pi$
$98$	1764.00	1.81827
$99$	−52.0000	−0.0527899
$100$	656.000	0.656000
$101$	292.000	0.287674	0.143837	−	0.989601i	$-0.454056\pi$
$101$	292.000	0.287674	0.143837	+	0.989601i	$0.454056\pi$
$102$	38.0000	0.0368878
$103$	52.0000	0.0497448	0.0248724	−	0.999691i	$-0.492082\pi$
$103$	52.0000	0.0497448	0.0248724	+	0.999691i	$0.492082\pi$
$104$	104.000	0.0980581
$105$	595.000	0.553010
$106$	−464.000	−0.425167
$107$	12.0000	0.0108419	0.00542095	−	0.999985i	$-0.498274\pi$
$107$	12.0000	0.0108419	0.00542095	+	0.999985i	$0.498274\pi$
$108$	212.000	0.188886
$109$	1213.00	1.06591	0.532956	−	0.846143i	$-0.321081\pi$
$109$	1213.00	1.06591	0.532956	+	0.846143i	$0.321081\pi$
$110$	68.0000	0.0589413
$111$	11.0000	0.00940607
$112$	−560.000	−0.472456
$113$	−1158.00	−0.964031	−0.482015	−	0.876163i	$-0.660095\pi$
$113$	−1158.00	−0.964031	−0.482015	+	0.876163i	$0.660095\pi$
$114$	−188.000	−0.154455
$115$	−1224.00	−0.992509
$116$	984.000	0.787604
$117$	−338.000	−0.267078
$118$	−772.000	−0.602274
$119$	665.000	0.512273
$120$	−136.000	−0.103459
$121$	−1327.00	−0.996995
$122$	128.000	0.0949883
$123$	280.000	0.205258
$124$	−400.000	−0.289686
$125$	663.000	0.474404
$126$	1820.00	1.28681
$127$	−540.000	−0.377301	−0.188651	−	0.982044i	$-0.560411\pi$
$127$	−540.000	−0.377301	−0.188651	+	0.982044i	$0.560411\pi$
$128$	128.000	0.0883883
$129$	−241.000	−0.164487
$130$	442.000	0.298200
$131$	−1571.00	−1.04778	−0.523889	−	0.851787i	$-0.675519\pi$
$131$	−1571.00	−1.04778	−0.523889	+	0.851787i	$0.675519\pi$
$132$	−8.00000	−0.00527508
$133$	−3290.00	−2.14496
$134$	−1340.00	−0.863868
$135$	901.000	0.574413
$136$	−152.000	−0.0958374
$137$	−568.000	−0.354215	−0.177108	−	0.984191i	$-0.556674\pi$
$137$	−568.000	−0.354215	−0.177108	+	0.984191i	$0.556674\pi$
$138$	144.000	0.0888268
$139$	1845.00	1.12583	0.562917	−	0.826514i	$-0.309679\pi$
$139$	1845.00	1.12583	0.562917	+	0.826514i	$0.309679\pi$
$140$	−2380.00	−1.43676
$141$	−137.000	−0.0818261
$142$	110.000	0.0650070
$143$	26.0000	0.0152044
$144$	−416.000	−0.240741
$145$	4182.00	2.39515
$146$	−1676.00	−0.950046
$147$	−882.000	−0.494872
$148$	−44.0000	−0.0244377
$149$	2850.00	1.56699	0.783494	−	0.621400i	$-0.213436\pi$
$149$	2850.00	1.56699	0.783494	+	0.621400i	$0.213436\pi$
$150$	−328.000	−0.178541
$151$	2763.00	1.48907	0.744536	−	0.667583i	$-0.232671\pi$
$151$	2763.00	1.48907	0.744536	+	0.667583i	$0.232671\pi$
$152$	752.000	0.401285
$153$	494.000	0.261030
$154$	−140.000	−0.0732566
$155$	−1700.00	−0.880950
$156$	−52.0000	−0.0266880
$157$	−466.000	−0.236884	−0.118442	−	0.992961i	$-0.537790\pi$
$157$	−466.000	−0.236884	−0.118442	+	0.992961i	$0.537790\pi$
$158$	2032.00	1.02315
$159$	232.000	0.115716
$160$	544.000	0.268794
$161$	2520.00	1.23356
$162$	1298.00	0.629509
$163$	2552.00	1.22631	0.613154	−	0.789964i	$-0.289901\pi$
$163$	2552.00	1.22631	0.613154	+	0.789964i	$0.289901\pi$
$164$	−1120.00	−0.533276
$165$	−34.0000	−0.0160418
$166$	840.000	0.392751
$167$	−3768.00	−1.74597	−0.872984	−	0.487749i	$-0.837818\pi$
$167$	−3768.00	−1.74597	−0.872984	+	0.487749i	$0.837818\pi$
$168$	280.000	0.128586
$169$	169.000	0.0769231
$170$	−646.000	−0.291447
$171$	−2444.00	−1.09297
$172$	964.000	0.427351
$173$	3296.00	1.44850	0.724249	−	0.689538i	$-0.242187\pi$
$173$	3296.00	1.44850	0.724249	+	0.689538i	$0.242187\pi$
$174$	−492.000	−0.214359
$175$	−5740.00	−2.47945
$176$	32.0000	0.0137051
$177$	386.000	0.163918
$178$	−1868.00	−0.786587
$179$	45.0000	0.0187903	0.00939513	−	0.999956i	$-0.497009\pi$
$179$	45.0000	0.0187903	0.00939513	+	0.999956i	$0.497009\pi$
$180$	−1768.00	−0.732105
$181$	−364.000	−0.149480	−0.0747401	−	0.997203i	$-0.523813\pi$
$181$	−364.000	−0.149480	−0.0747401	+	0.997203i	$0.523813\pi$
$182$	−910.000	−0.370625
$183$	−64.0000	−0.0258525
$184$	−576.000	−0.230779
$185$	−187.000	−0.0743163
$186$	200.000	0.0788425
$187$	−38.0000	−0.0148601
$188$	548.000	0.212590
$189$	−1855.00	−0.713923
$190$	3196.00	1.22033
$191$	2482.00	0.940268	0.470134	−	0.882595i	$-0.344206\pi$
$191$	2482.00	0.940268	0.470134	+	0.882595i	$0.344206\pi$
$192$	−64.0000	−0.0240563
$193$	−1220.00	−0.455013	−0.227507	−	0.973777i	$-0.573057\pi$
$193$	−1220.00	−0.455013	−0.227507	+	0.973777i	$0.573057\pi$
$194$	−2308.00	−0.854148
$195$	−221.000	−0.0811597
$196$	3528.00	1.28571
$197$	−1593.00	−0.576125	−0.288062	−	0.957612i	$-0.593011\pi$
$197$	−1593.00	−0.576125	−0.288062	+	0.957612i	$0.593011\pi$
$198$	−104.000	−0.0373281
$199$	1606.00	0.572092	0.286046	−	0.958216i	$-0.407659\pi$
$199$	1606.00	0.572092	0.286046	+	0.958216i	$0.407659\pi$
$200$	1312.00	0.463862
$201$	670.000	0.235115
$202$	584.000	0.203416
$203$	−8610.00	−2.97686
$204$	76.0000	0.0260836
$205$	−4760.00	−1.62172
$206$	104.000	0.0351749
$207$	1872.00	0.628565
$208$	208.000	0.0693375
$209$	188.000	0.0622212
$210$	1190.00	0.391037
$211$	2469.00	0.805559	0.402780	−	0.915297i	$-0.368044\pi$
$211$	2469.00	0.805559	0.402780	+	0.915297i	$0.368044\pi$
$212$	−928.000	−0.300638
$213$	−55.0000	−0.0176927
$214$	24.0000	0.00766638
$215$	4097.00	1.29960
$216$	424.000	0.133563
$217$	3500.00	1.09491
$218$	2426.00	0.753713
$219$	838.000	0.258570
$220$	136.000	0.0416778
$221$	−247.000	−0.0751811
$222$	22.0000	0.00665110
$223$	1943.00	0.583466	0.291733	−	0.956500i	$-0.405768\pi$
$223$	1943.00	0.583466	0.291733	+	0.956500i	$0.405768\pi$
$224$	−1120.00	−0.334077
$225$	−4264.00	−1.26341
$226$	−2316.00	−0.681673
$227$	3032.00	0.886524	0.443262	−	0.896392i	$-0.353821\pi$
$227$	3032.00	0.886524	0.443262	+	0.896392i	$0.353821\pi$
$228$	−376.000	−0.109216
$229$	5311.00	1.53258	0.766290	−	0.642495i	$-0.222101\pi$
$229$	5311.00	1.53258	0.766290	+	0.642495i	$0.222101\pi$
$230$	−2448.00	−0.701810
$231$	70.0000	0.0199379
$232$	1968.00	0.556920
$233$	−507.000	−0.142552	−0.0712761	−	0.997457i	$-0.522707\pi$
$233$	−507.000	−0.142552	−0.0712761	+	0.997457i	$0.522707\pi$
$234$	−676.000	−0.188853
$235$	2329.00	0.646499
$236$	−1544.00	−0.425872
$237$	−1016.00	−0.278465
$238$	1330.00	0.362231
$239$	−6795.00	−1.83905	−0.919523	−	0.393036i	$-0.871425\pi$
$239$	−6795.00	−1.83905	−0.919523	+	0.393036i	$0.871425\pi$
$240$	−272.000	−0.0731564
$241$	−4442.00	−1.18728	−0.593640	−	0.804731i	$-0.702310\pi$
$241$	−4442.00	−1.18728	−0.593640	+	0.804731i	$0.702310\pi$
$242$	−2654.00	−0.704982
$243$	−2080.00	−0.549103
$244$	256.000	0.0671669
$245$	14994.0	3.90992
$246$	560.000	0.145139
$247$	1222.00	0.314794
$248$	−800.000	−0.204839
$249$	−420.000	−0.106893
$250$	1326.00	0.335454
$251$	−5024.00	−1.26339	−0.631697	−	0.775215i	$-0.717641\pi$
$251$	−5024.00	−1.26339	−0.631697	+	0.775215i	$0.717641\pi$
$252$	3640.00	0.909914
$253$	−144.000	−0.0357834
$254$	−1080.00	−0.266792
$255$	323.000	0.0793217
$256$	256.000	0.0625000
$257$	7065.00	1.71480	0.857398	−	0.514654i	$-0.172080\pi$
$257$	7065.00	1.71480	0.857398	+	0.514654i	$0.172080\pi$
$258$	−482.000	−0.116310
$259$	385.000	0.0923658
$260$	884.000	0.210859
$261$	−6396.00	−1.51687
$262$	−3142.00	−0.740891
$263$	1364.00	0.319802	0.159901	−	0.987133i	$-0.448883\pi$
$263$	1364.00	0.319802	0.159901	+	0.987133i	$0.448883\pi$
$264$	−16.0000	−0.00373005
$265$	−3944.00	−0.914257
$266$	−6580.00	−1.51671
$267$	934.000	0.214082
$268$	−2680.00	−0.610847
$269$	−4304.00	−0.975537	−0.487769	−	0.872973i	$-0.662189\pi$
$269$	−4304.00	−0.975537	−0.487769	+	0.872973i	$0.662189\pi$
$270$	1802.00	0.406171
$271$	−1519.00	−0.340490	−0.170245	−	0.985402i	$-0.554456\pi$
$271$	−1519.00	−0.340490	−0.170245	+	0.985402i	$0.554456\pi$
$272$	−304.000	−0.0677673
$273$	455.000	0.100871
$274$	−1136.00	−0.250468
$275$	328.000	0.0719242
$276$	288.000	0.0628100
$277$	1996.00	0.432953	0.216477	−	0.976288i	$-0.430544\pi$
$277$	1996.00	0.432953	0.216477	+	0.976288i	$0.430544\pi$
$278$	3690.00	0.796085
$279$	2600.00	0.557914
$280$	−4760.00	−1.01594
$281$	−2918.00	−0.619478	−0.309739	−	0.950822i	$-0.600242\pi$
$281$	−2918.00	−0.619478	−0.309739	+	0.950822i	$0.600242\pi$
$282$	−274.000	−0.0578598
$283$	812.000	0.170560	0.0852798	−	0.996357i	$-0.472822\pi$
$283$	812.000	0.170560	0.0852798	+	0.996357i	$0.472822\pi$
$284$	220.000	0.0459669
$285$	−1598.00	−0.332131
$286$	52.0000	0.0107511
$287$	9800.00	2.01559
$288$	−832.000	−0.170229
$289$	−4552.00	−0.926521
$290$	8364.00	1.69362
$291$	1154.00	0.232470
$292$	−3352.00	−0.671784
$293$	−1855.00	−0.369864	−0.184932	−	0.982751i	$-0.559207\pi$
$293$	−1855.00	−0.369864	−0.184932	+	0.982751i	$0.559207\pi$
$294$	−1764.00	−0.349927
$295$	−6562.00	−1.29510
$296$	−88.0000	−0.0172801
$297$	106.000	0.0207096
$298$	5700.00	1.10803
$299$	−936.000	−0.181038
$300$	−656.000	−0.126247
$301$	−8435.00	−1.61523
$302$	5526.00	1.05293
$303$	−292.000	−0.0553629
$304$	1504.00	0.283751
$305$	1088.00	0.204258
$306$	988.000	0.184576
$307$	5350.00	0.994595	0.497297	−	0.867580i	$-0.334326\pi$
$307$	5350.00	0.994595	0.497297	+	0.867580i	$0.334326\pi$
$308$	−280.000	−0.0518003
$309$	−52.0000	−0.00957339
$310$	−3400.00	−0.622926
$311$	2262.00	0.412432	0.206216	−	0.978507i	$-0.433885\pi$
$311$	2262.00	0.412432	0.206216	+	0.978507i	$0.433885\pi$
$312$	−104.000	−0.0188713
$313$	−1857.00	−0.335348	−0.167674	−	0.985843i	$-0.553626\pi$
$313$	−1857.00	−0.335348	−0.167674	+	0.985843i	$0.553626\pi$
$314$	−932.000	−0.167503
$315$	15470.0	2.76710
$316$	4064.00	0.723474
$317$	−3870.00	−0.685681	−0.342840	−	0.939394i	$-0.611389\pi$
$317$	−3870.00	−0.685681	−0.342840	+	0.939394i	$0.611389\pi$
$318$	464.000	0.0818234
$319$	492.000	0.0863533
$320$	1088.00	0.190066
$321$	−12.0000	−0.00208653
$322$	5040.00	0.872262
$323$	−1786.00	−0.307665
$324$	2596.00	0.445130
$325$	2132.00	0.363883
$326$	5104.00	0.867130
$327$	−1213.00	−0.205135
$328$	−2240.00	−0.377083
$329$	−4795.00	−0.803516
$330$	−68.0000	−0.0113433
$331$	10520.0	1.74692	0.873461	−	0.486893i	$-0.161870\pi$
$331$	10520.0	1.74692	0.873461	+	0.486893i	$0.161870\pi$
$332$	1680.00	0.277717
$333$	286.000	0.0470652
$334$	−7536.00	−1.23459
$335$	−11390.0	−1.85762
$336$	560.000	0.0909241
$337$	7839.00	1.26711	0.633557	−	0.773696i	$-0.281594\pi$
$337$	7839.00	1.26711	0.633557	+	0.773696i	$0.281594\pi$
$338$	338.000	0.0543928
$339$	1158.00	0.185528
$340$	−1292.00	−0.206084
$341$	−200.000	−0.0317613
$342$	−4888.00	−0.772844
$343$	−18865.0	−2.96972
$344$	1928.00	0.302183
$345$	1224.00	0.191009
$346$	6592.00	1.02424
$347$	−1275.00	−0.197250	−0.0986248	−	0.995125i	$-0.531444\pi$
$347$	−1275.00	−0.197250	−0.0986248	+	0.995125i	$0.531444\pi$
$348$	−984.000	−0.151575
$349$	−375.000	−0.0575166	−0.0287583	−	0.999586i	$-0.509155\pi$
$349$	−375.000	−0.0575166	−0.0287583	+	0.999586i	$0.509155\pi$
$350$	−11480.0	−1.75323
$351$	689.000	0.104775
$352$	64.0000	0.00969094
$353$	1592.00	0.240039	0.120019	−	0.992772i	$-0.461704\pi$
$353$	1592.00	0.240039	0.120019	+	0.992772i	$0.461704\pi$
$354$	772.000	0.115908
$355$	935.000	0.139788
$356$	−3736.00	−0.556201
$357$	−665.000	−0.0985869
$358$	90.0000	0.0132867
$359$	−2424.00	−0.356362	−0.178181	−	0.983998i	$-0.557021\pi$
$359$	−2424.00	−0.356362	−0.178181	+	0.983998i	$0.557021\pi$
$360$	−3536.00	−0.517677
$361$	1977.00	0.288234
$362$	−728.000	−0.105698
$363$	1327.00	0.191872
$364$	−1820.00	−0.262071
$365$	−14246.0	−2.04293
$366$	−128.000	−0.0182805
$367$	−7970.00	−1.13360	−0.566799	−	0.823856i	$-0.691818\pi$
$367$	−7970.00	−1.13360	−0.566799	+	0.823856i	$0.691818\pi$
$368$	−1152.00	−0.163185
$369$	7280.00	1.02705
$370$	−374.000	−0.0525496
$371$	8120.00	1.13631
$372$	400.000	0.0557501
$373$	12492.0	1.73408	0.867039	−	0.498240i	$-0.166020\pi$
$373$	12492.0	1.73408	0.867039	+	0.498240i	$0.166020\pi$
$374$	−76.0000	−0.0105077
$375$	−663.000	−0.0912991
$376$	1096.00	0.150324
$377$	3198.00	0.436884
$378$	−3710.00	−0.504820
$379$	−4284.00	−0.580618	−0.290309	−	0.956933i	$-0.593758\pi$
$379$	−4284.00	−0.580618	−0.290309	+	0.956933i	$0.593758\pi$
$380$	6392.00	0.862902
$381$	540.000	0.0726116
$382$	4964.00	0.664870
$383$	−2337.00	−0.311789	−0.155894	−	0.987774i	$-0.549826\pi$
$383$	−2337.00	−0.311789	−0.155894	+	0.987774i	$0.549826\pi$
$384$	−128.000	−0.0170103
$385$	−1190.00	−0.157527
$386$	−2440.00	−0.321743
$387$	−6266.00	−0.823046
$388$	−4616.00	−0.603974
$389$	3562.00	0.464269	0.232134	−	0.972684i	$-0.425429\pi$
$389$	3562.00	0.464269	0.232134	+	0.972684i	$0.425429\pi$
$390$	−442.000	−0.0573886
$391$	1368.00	0.176938
$392$	7056.00	0.909137
$393$	1571.00	0.201645
$394$	−3186.00	−0.407382
$395$	17272.0	2.20012
$396$	−208.000	−0.0263949
$397$	−5274.00	−0.666737	−0.333368	−	0.942797i	$-0.608185\pi$
$397$	−5274.00	−0.666737	−0.333368	+	0.942797i	$0.608185\pi$
$398$	3212.00	0.404530
$399$	3290.00	0.412797
$400$	2624.00	0.328000
$401$	4812.00	0.599251	0.299626	−	0.954057i	$-0.403138\pi$
$401$	4812.00	0.599251	0.299626	+	0.954057i	$0.403138\pi$
$402$	1340.00	0.166252
$403$	−1300.00	−0.160689
$404$	1168.00	0.143837
$405$	11033.0	1.35366
$406$	−17220.0	−2.10496
$407$	−22.0000	−0.00267936
$408$	152.000	0.0184439
$409$	−9448.00	−1.14223	−0.571117	−	0.820869i	$-0.693490\pi$
$409$	−9448.00	−1.14223	−0.571117	+	0.820869i	$0.693490\pi$
$410$	−9520.00	−1.14673
$411$	568.000	0.0681688
$412$	208.000	0.0248724
$413$	13510.0	1.60965
$414$	3744.00	0.444463
$415$	7140.00	0.844551
$416$	416.000	0.0490290
$417$	−1845.00	−0.216667
$418$	376.000	0.0439970
$419$	−521.000	−0.0607459	−0.0303729	−	0.999539i	$-0.509669\pi$
$419$	−521.000	−0.0607459	−0.0303729	+	0.999539i	$0.509669\pi$
$420$	2380.00	0.276505
$421$	7141.00	0.826677	0.413339	−	0.910577i	$-0.364363\pi$
$421$	7141.00	0.826677	0.413339	+	0.910577i	$0.364363\pi$
$422$	4938.00	0.569616
$423$	−3562.00	−0.409433
$424$	−1856.00	−0.212583
$425$	−3116.00	−0.355643
$426$	−110.000	−0.0125106
$427$	−2240.00	−0.253867
$428$	48.0000	0.00542095
$429$	−26.0000	−0.00292609
$430$	8194.00	0.918953
$431$	−6299.00	−0.703973	−0.351986	−	0.936005i	$-0.614494\pi$
$431$	−6299.00	−0.703973	−0.351986	+	0.936005i	$0.614494\pi$
$432$	848.000	0.0944431
$433$	3231.00	0.358596	0.179298	−	0.983795i	$-0.442617\pi$
$433$	3231.00	0.358596	0.179298	+	0.983795i	$0.442617\pi$
$434$	7000.00	0.774218
$435$	−4182.00	−0.460946
$436$	4852.00	0.532956
$437$	−6768.00	−0.740863
$438$	1676.00	0.182836
$439$	−410.000	−0.0445746	−0.0222873	−	0.999752i	$-0.507095\pi$
$439$	−410.000	−0.0445746	−0.0222873	+	0.999752i	$0.507095\pi$
$440$	272.000	0.0294707
$441$	−22932.0	−2.47619
$442$	−494.000	−0.0531610
$443$	−9397.00	−1.00782	−0.503911	−	0.863756i	$-0.668106\pi$
$443$	−9397.00	−1.00782	−0.503911	+	0.863756i	$0.668106\pi$
$444$	44.0000	0.00470304
$445$	−15878.0	−1.69144
$446$	3886.00	0.412573
$447$	−2850.00	−0.301567
$448$	−2240.00	−0.236228
$449$	654.000	0.0687398	0.0343699	−	0.999409i	$-0.489058\pi$
$449$	654.000	0.0687398	0.0343699	+	0.999409i	$0.489058\pi$
$450$	−8528.00	−0.893364
$451$	−560.000	−0.0584687
$452$	−4632.00	−0.482015
$453$	−2763.00	−0.286572
$454$	6064.00	0.626867
$455$	−7735.00	−0.796972
$456$	−752.000	−0.0772273
$457$	14982.0	1.53354	0.766771	−	0.641921i	$-0.221862\pi$
$457$	14982.0	1.53354	0.766771	+	0.641921i	$0.221862\pi$
$458$	10622.0	1.08370
$459$	−1007.00	−0.102402
$460$	−4896.00	−0.496255
$461$	10845.0	1.09567	0.547833	−	0.836588i	$-0.315453\pi$
$461$	10845.0	1.09567	0.547833	+	0.836588i	$0.315453\pi$
$462$	140.000	0.0140982
$463$	13072.0	1.31211	0.656055	−	0.754713i	$-0.272224\pi$
$463$	13072.0	1.31211	0.656055	+	0.754713i	$0.272224\pi$
$464$	3936.00	0.393802
$465$	1700.00	0.169539
$466$	−1014.00	−0.100800
$467$	−15340.0	−1.52002	−0.760011	−	0.649910i	$-0.774807\pi$
$467$	−15340.0	−1.52002	−0.760011	+	0.649910i	$0.774807\pi$
$468$	−1352.00	−0.133539
$469$	23450.0	2.30879
$470$	4658.00	0.457144
$471$	466.000	0.0455884
$472$	−3088.00	−0.301137
$473$	482.000	0.0468549
$474$	−2032.00	−0.196905
$475$	15416.0	1.48913
$476$	2660.00	0.256136
$477$	6032.00	0.579007
$478$	−13590.0	−1.30040
$479$	−19615.0	−1.87105	−0.935524	−	0.353262i	$-0.885072\pi$
$479$	−19615.0	−1.87105	−0.935524	+	0.353262i	$0.885072\pi$
$480$	−544.000	−0.0517294
$481$	−143.000	−0.0135556
$482$	−8884.00	−0.839533
$483$	−2520.00	−0.237400
$484$	−5308.00	−0.498497
$485$	−19618.0	−1.83672
$486$	−4160.00	−0.388275
$487$	−10904.0	−1.01459	−0.507297	−	0.861771i	$-0.669355\pi$
$487$	−10904.0	−1.01459	−0.507297	+	0.861771i	$0.669355\pi$
$488$	512.000	0.0474942
$489$	−2552.00	−0.236003
$490$	29988.0	2.76473
$491$	−18519.0	−1.70214	−0.851070	−	0.525052i	$-0.824046\pi$
$491$	−18519.0	−1.70214	−0.851070	+	0.525052i	$0.824046\pi$
$492$	1120.00	0.102629
$493$	−4674.00	−0.426991
$494$	2444.00	0.222593
$495$	−884.000	−0.0802684
$496$	−1600.00	−0.144843
$497$	−1925.00	−0.173739
$498$	−840.000	−0.0755849
$499$	−14400.0	−1.29185	−0.645924	−	0.763401i	$-0.723528\pi$
$499$	−14400.0	−1.29185	−0.645924	+	0.763401i	$0.723528\pi$
$500$	2652.00	0.237202
$501$	3768.00	0.336012
$502$	−10048.0	−0.893355
$503$	20422.0	1.81028	0.905141	−	0.425111i	$-0.139765\pi$
$503$	20422.0	1.81028	0.905141	+	0.425111i	$0.139765\pi$
$504$	7280.00	0.643407
$505$	4964.00	0.437416
$506$	−288.000	−0.0253027
$507$	−169.000	−0.0148039
$508$	−2160.00	−0.188651
$509$	15606.0	1.35899	0.679493	−	0.733682i	$-0.262200\pi$
$509$	15606.0	1.35899	0.679493	+	0.733682i	$0.262200\pi$
$510$	646.000	0.0560889
$511$	29330.0	2.53911
$512$	512.000	0.0441942
$513$	4982.00	0.428773
$514$	14130.0	1.21254
$515$	884.000	0.0756382
$516$	−964.000	−0.0822437
$517$	274.000	0.0233085
$518$	770.000	0.0653125
$519$	−3296.00	−0.278764
$520$	1768.00	0.149100
$521$	1783.00	0.149932	0.0749661	−	0.997186i	$-0.476115\pi$
$521$	1783.00	0.149932	0.0749661	+	0.997186i	$0.476115\pi$
$522$	−12792.0	−1.07259
$523$	11140.0	0.931392	0.465696	−	0.884945i	$-0.345804\pi$
$523$	11140.0	0.931392	0.465696	+	0.884945i	$0.345804\pi$
$524$	−6284.00	−0.523889
$525$	5740.00	0.477170
$526$	2728.00	0.226134
$527$	1900.00	0.157050
$528$	−32.0000	−0.00263754
$529$	−6983.00	−0.573929
$530$	−7888.00	−0.646477
$531$	10036.0	0.820198
$532$	−13160.0	−1.07248
$533$	−3640.00	−0.295808
$534$	1868.00	0.151379
$535$	204.000	0.0164854
$536$	−5360.00	−0.431934
$537$	−45.0000	−0.00361619
$538$	−8608.00	−0.689809
$539$	1764.00	0.140966
$540$	3604.00	0.287206
$541$	839.000	0.0666755	0.0333377	−	0.999444i	$-0.489386\pi$
$541$	839.000	0.0666755	0.0333377	+	0.999444i	$0.489386\pi$
$542$	−3038.00	−0.240762
$543$	364.000	0.0287675
$544$	−608.000	−0.0479187
$545$	20621.0	1.62075
$546$	910.000	0.0713267
$547$	17279.0	1.35063	0.675317	−	0.737528i	$-0.264007\pi$
$547$	17279.0	1.35063	0.675317	+	0.737528i	$0.264007\pi$
$548$	−2272.00	−0.177108
$549$	−1664.00	−0.129358
$550$	656.000	0.0508581
$551$	23124.0	1.78787
$552$	576.000	0.0444134
$553$	−35560.0	−2.73448
$554$	3992.00	0.306144
$555$	187.000	0.0143022
$556$	7380.00	0.562917
$557$	−20577.0	−1.56531	−0.782653	−	0.622458i	$-0.786134\pi$
$557$	−20577.0	−1.56531	−0.782653	+	0.622458i	$0.786134\pi$
$558$	5200.00	0.394505
$559$	3133.00	0.237051
$560$	−9520.00	−0.718381
$561$	38.0000	0.00285982
$562$	−5836.00	−0.438037
$563$	11785.0	0.882200	0.441100	−	0.897458i	$-0.354588\pi$
$563$	11785.0	0.882200	0.441100	+	0.897458i	$0.354588\pi$
$564$	−548.000	−0.0409131
$565$	−19686.0	−1.46583
$566$	1624.00	0.120604
$567$	−22715.0	−1.68243
$568$	440.000	0.0325035
$569$	10887.0	0.802121	0.401060	−	0.916052i	$-0.368642\pi$
$569$	10887.0	0.802121	0.401060	+	0.916052i	$0.368642\pi$
$570$	−3196.00	−0.234852
$571$	−11453.0	−0.839393	−0.419696	−	0.907665i	$-0.637863\pi$
$571$	−11453.0	−0.839393	−0.419696	+	0.907665i	$0.637863\pi$
$572$	104.000	0.00760220
$573$	−2482.00	−0.180955
$574$	19600.0	1.42524
$575$	−11808.0	−0.856396
$576$	−1664.00	−0.120370
$577$	14382.0	1.03766	0.518831	−	0.854877i	$-0.326368\pi$
$577$	14382.0	1.03766	0.518831	+	0.854877i	$0.326368\pi$
$578$	−9104.00	−0.655150
$579$	1220.00	0.0875673
$580$	16728.0	1.19757
$581$	−14700.0	−1.04967
$582$	2308.00	0.164381
$583$	−464.000	−0.0329621
$584$	−6704.00	−0.475023
$585$	−5746.00	−0.406099
$586$	−3710.00	−0.261534
$587$	−10160.0	−0.714392	−0.357196	−	0.934029i	$-0.616267\pi$
$587$	−10160.0	−0.714392	−0.357196	+	0.934029i	$0.616267\pi$
$588$	−3528.00	−0.247436
$589$	−9400.00	−0.657590
$590$	−13124.0	−0.915774
$591$	1593.00	0.110875
$592$	−176.000	−0.0122188
$593$	16842.0	1.16630	0.583152	−	0.812363i	$-0.301819\pi$
$593$	16842.0	1.16630	0.583152	+	0.812363i	$0.301819\pi$
$594$	212.000	0.0146439
$595$	11305.0	0.778924
$596$	11400.0	0.783494
$597$	−1606.00	−0.110099
$598$	−1872.00	−0.128013
$599$	−13830.0	−0.943370	−0.471685	−	0.881767i	$-0.656354\pi$
$599$	−13830.0	−0.943370	−0.471685	+	0.881767i	$0.656354\pi$
$600$	−1312.00	−0.0892703
$601$	−15835.0	−1.07475	−0.537374	−	0.843344i	$-0.680583\pi$
$601$	−15835.0	−1.07475	−0.537374	+	0.843344i	$0.680583\pi$
$602$	−16870.0	−1.14214
$603$	17420.0	1.17645
$604$	11052.0	0.744536
$605$	−22559.0	−1.51596
$606$	−584.000	−0.0391475
$607$	−22894.0	−1.53087	−0.765436	−	0.643513i	$-0.777476\pi$
$607$	−22894.0	−1.53087	−0.765436	+	0.643513i	$0.777476\pi$
$608$	3008.00	0.200642
$609$	8610.00	0.572898
$610$	2176.00	0.144432
$611$	1781.00	0.117924
$612$	1976.00	0.130515
$613$	9886.00	0.651373	0.325687	−	0.945478i	$-0.394405\pi$
$613$	9886.00	0.651373	0.325687	+	0.945478i	$0.394405\pi$
$614$	10700.0	0.703285
$615$	4760.00	0.312100
$616$	−560.000	−0.0366283
$617$	8856.00	0.577843	0.288922	−	0.957353i	$-0.406703\pi$
$617$	8856.00	0.577843	0.288922	+	0.957353i	$0.406703\pi$
$618$	−104.000	−0.00676941
$619$	3764.00	0.244407	0.122204	−	0.992505i	$-0.461004\pi$
$619$	3764.00	0.244407	0.122204	+	0.992505i	$0.461004\pi$
$620$	−6800.00	−0.440475
$621$	−3816.00	−0.246587
$622$	4524.00	0.291633
$623$	32690.0	2.10224
$624$	−208.000	−0.0133440
$625$	−9229.00	−0.590656
$626$	−3714.00	−0.237127
$627$	−188.000	−0.0119745
$628$	−1864.00	−0.118442
$629$	209.000	0.0132486
$630$	30940.0	1.95663
$631$	17775.0	1.12141	0.560706	−	0.828015i	$-0.310530\pi$
$631$	17775.0	1.12141	0.560706	+	0.828015i	$0.310530\pi$
$632$	8128.00	0.511574
$633$	−2469.00	−0.155030
$634$	−7740.00	−0.484850
$635$	−9180.00	−0.573696
$636$	928.000	0.0578579
$637$	11466.0	0.713186
$638$	984.000	0.0610610
$639$	−1430.00	−0.0885288
$640$	2176.00	0.134397
$641$	13358.0	0.823103	0.411552	−	0.911386i	$-0.364987\pi$
$641$	13358.0	0.823103	0.411552	+	0.911386i	$0.364987\pi$
$642$	−24.0000	−0.00147540
$643$	−26062.0	−1.59842	−0.799211	−	0.601051i	$-0.794749\pi$
$643$	−26062.0	−1.59842	−0.799211	+	0.601051i	$0.794749\pi$
$644$	10080.0	0.616782
$645$	−4097.00	−0.250107
$646$	−3572.00	−0.217552
$647$	20598.0	1.25161	0.625804	−	0.779980i	$-0.284771\pi$
$647$	20598.0	1.25161	0.625804	+	0.779980i	$0.284771\pi$
$648$	5192.00	0.314755
$649$	−772.000	−0.0466928
$650$	4264.00	0.257304
$651$	−3500.00	−0.210716
$652$	10208.0	0.613154
$653$	27104.0	1.62429	0.812145	−	0.583456i	$-0.198300\pi$
$653$	27104.0	1.62429	0.812145	+	0.583456i	$0.198300\pi$
$654$	−2426.00	−0.145052
$655$	−26707.0	−1.59317
$656$	−4480.00	−0.266638
$657$	21788.0	1.29381
$658$	−9590.00	−0.568172
$659$	7500.00	0.443336	0.221668	−	0.975122i	$-0.428850\pi$
$659$	7500.00	0.443336	0.221668	+	0.975122i	$0.428850\pi$
$660$	−136.000	−0.00802090
$661$	10402.0	0.612089	0.306045	−	0.952017i	$-0.400994\pi$
$661$	10402.0	0.612089	0.306045	+	0.952017i	$0.400994\pi$
$662$	21040.0	1.23526
$663$	247.000	0.0144686
$664$	3360.00	0.196375
$665$	−55930.0	−3.26146
$666$	572.000	0.0332801
$667$	−17712.0	−1.02820
$668$	−15072.0	−0.872984
$669$	−1943.00	−0.112288
$670$	−22780.0	−1.31353
$671$	128.000	0.00736421
$672$	1120.00	0.0642931
$673$	−19715.0	−1.12921	−0.564604	−	0.825362i	$-0.690971\pi$
$673$	−19715.0	−1.12921	−0.564604	+	0.825362i	$0.690971\pi$
$674$	15678.0	0.895985
$675$	8692.00	0.495637
$676$	676.000	0.0384615
$677$	−1168.00	−0.0663071	−0.0331535	−	0.999450i	$-0.510555\pi$
$677$	−1168.00	−0.0663071	−0.0331535	+	0.999450i	$0.510555\pi$
$678$	2316.00	0.131188
$679$	40390.0	2.28281
$680$	−2584.00	−0.145723
$681$	−3032.00	−0.170612
$682$	−400.000	−0.0224586
$683$	3800.00	0.212889	0.106444	−	0.994319i	$-0.466053\pi$
$683$	3800.00	0.212889	0.106444	+	0.994319i	$0.466053\pi$
$684$	−9776.00	−0.546483
$685$	−9656.00	−0.538594
$686$	−37730.0	−2.09991
$687$	−5311.00	−0.294945
$688$	3856.00	0.213675
$689$	−3016.00	−0.166764
$690$	2448.00	0.135063
$691$	−17336.0	−0.954403	−0.477202	−	0.878794i	$-0.658349\pi$
$691$	−17336.0	−0.954403	−0.477202	+	0.878794i	$0.658349\pi$
$692$	13184.0	0.724249
$693$	1820.00	0.0997635
$694$	−2550.00	−0.139476
$695$	31365.0	1.71186
$696$	−1968.00	−0.107179
$697$	5320.00	0.289110
$698$	−750.000	−0.0406704
$699$	507.000	0.0274342
$700$	−22960.0	−1.23972
$701$	−10088.0	−0.543536	−0.271768	−	0.962363i	$-0.587608\pi$
$701$	−10088.0	−0.543536	−0.271768	+	0.962363i	$0.587608\pi$
$702$	1378.00	0.0740873
$703$	−1034.00	−0.0554738
$704$	128.000	0.00685253
$705$	−2329.00	−0.124419
$706$	3184.00	0.169733
$707$	−10220.0	−0.543653
$708$	1544.00	0.0819591
$709$	11730.0	0.621339	0.310670	−	0.950518i	$-0.399447\pi$
$709$	11730.0	0.621339	0.310670	+	0.950518i	$0.399447\pi$
$710$	1870.00	0.0988449
$711$	−26416.0	−1.39336
$712$	−7472.00	−0.393294
$713$	7200.00	0.378180
$714$	−1330.00	−0.0697115
$715$	442.000	0.0231187
$716$	180.000	0.00939513
$717$	6795.00	0.353925
$718$	−4848.00	−0.251986
$719$	−2190.00	−0.113593	−0.0567964	−	0.998386i	$-0.518089\pi$
$719$	−2190.00	−0.113593	−0.0567964	+	0.998386i	$0.518089\pi$
$720$	−7072.00	−0.366053
$721$	−1820.00	−0.0940088
$722$	3954.00	0.203813
$723$	4442.00	0.228492
$724$	−1456.00	−0.0747401
$725$	40344.0	2.06667
$726$	2654.00	0.135674
$727$	−2470.00	−0.126007	−0.0630036	−	0.998013i	$-0.520068\pi$
$727$	−2470.00	−0.126007	−0.0630036	+	0.998013i	$0.520068\pi$
$728$	−3640.00	−0.185312
$729$	−15443.0	−0.784586
$730$	−28492.0	−1.44457
$731$	−4579.00	−0.231683
$732$	−256.000	−0.0129263
$733$	−8693.00	−0.438040	−0.219020	−	0.975720i	$-0.570286\pi$
$733$	−8693.00	−0.438040	−0.219020	+	0.975720i	$0.570286\pi$
$734$	−15940.0	−0.801575
$735$	−14994.0	−0.752465
$736$	−2304.00	−0.115389
$737$	−1340.00	−0.0669736
$738$	14560.0	0.726234
$739$	−14636.0	−0.728544	−0.364272	−	0.931293i	$-0.618682\pi$
$739$	−14636.0	−0.728544	−0.364272	+	0.931293i	$0.618682\pi$
$740$	−748.000	−0.0371581
$741$	−1222.00	−0.0605820
$742$	16240.0	0.803489
$743$	27501.0	1.35789	0.678946	−	0.734188i	$-0.262437\pi$
$743$	27501.0	1.35789	0.678946	+	0.734188i	$0.262437\pi$
$744$	800.000	0.0394213
$745$	48450.0	2.38265
$746$	24984.0	1.22618
$747$	−10920.0	−0.534862
$748$	−152.000	−0.00743004
$749$	−420.000	−0.0204893
$750$	−1326.00	−0.0645582
$751$	11888.0	0.577629	0.288814	−	0.957385i	$-0.406739\pi$
$751$	11888.0	0.577629	0.288814	+	0.957385i	$0.406739\pi$
$752$	2192.00	0.106295
$753$	5024.00	0.243140
$754$	6396.00	0.308924
$755$	46971.0	2.26417
$756$	−7420.00	−0.356961
$757$	10776.0	0.517385	0.258692	−	0.965960i	$-0.416708\pi$
$757$	10776.0	0.517385	0.258692	+	0.965960i	$0.416708\pi$
$758$	−8568.00	−0.410559
$759$	144.000	0.00688652
$760$	12784.0	0.610164
$761$	−21758.0	−1.03643	−0.518217	−	0.855249i	$-0.673404\pi$
$761$	−21758.0	−1.03643	−0.518217	+	0.855249i	$0.673404\pi$
$762$	1080.00	0.0513442
$763$	−42455.0	−2.01438
$764$	9928.00	0.470134
$765$	8398.00	0.396902
$766$	−4674.00	−0.220468
$767$	−5018.00	−0.236231
$768$	−256.000	−0.0120281
$769$	−8080.00	−0.378898	−0.189449	−	0.981891i	$-0.560670\pi$
$769$	−8080.00	−0.378898	−0.189449	+	0.981891i	$0.560670\pi$
$770$	−2380.00	−0.111389
$771$	−7065.00	−0.330013
$772$	−4880.00	−0.227507
$773$	3981.00	0.185235	0.0926175	−	0.995702i	$-0.470477\pi$
$773$	3981.00	0.185235	0.0926175	+	0.995702i	$0.470477\pi$
$774$	−12532.0	−0.581981
$775$	−16400.0	−0.760136
$776$	−9232.00	−0.427074
$777$	−385.000	−0.0177758
$778$	7124.00	0.328288
$779$	−26320.0	−1.21054
$780$	−884.000	−0.0405798
$781$	110.000	0.00503983
$782$	2736.00	0.125114
$783$	13038.0	0.595070
$784$	14112.0	0.642857
$785$	−7922.00	−0.360189
$786$	3142.00	0.142585
$787$	−26048.0	−1.17981	−0.589905	−	0.807472i	$-0.700835\pi$
$787$	−26048.0	−1.17981	−0.589905	+	0.807472i	$0.700835\pi$
$788$	−6372.00	−0.288062
$789$	−1364.00	−0.0615459
$790$	34544.0	1.55572
$791$	40530.0	1.82185
$792$	−416.000	−0.0186640
$793$	832.000	0.0372575
$794$	−10548.0	−0.471454
$795$	3944.00	0.175949
$796$	6424.00	0.286046
$797$	−12434.0	−0.552616	−0.276308	−	0.961069i	$-0.589111\pi$
$797$	−12434.0	−0.552616	−0.276308	+	0.961069i	$0.589111\pi$
$798$	6580.00	0.291892
$799$	−2603.00	−0.115253
$800$	5248.00	0.231931
$801$	24284.0	1.07120
$802$	9624.00	0.423735
$803$	−1676.00	−0.0736547
$804$	2680.00	0.117558
$805$	42840.0	1.87567
$806$	−2600.00	−0.113624
$807$	4304.00	0.187742
$808$	2336.00	0.101708
$809$	−8113.00	−0.352581	−0.176290	−	0.984338i	$-0.556410\pi$
$809$	−8113.00	−0.352581	−0.176290	+	0.984338i	$0.556410\pi$
$810$	22066.0	0.957185
$811$	732.000	0.0316942	0.0158471	−	0.999874i	$-0.494956\pi$
$811$	732.000	0.0316942	0.0158471	+	0.999874i	$0.494956\pi$
$812$	−34440.0	−1.48843
$813$	1519.00	0.0655273
$814$	−44.0000	−0.00189459
$815$	43384.0	1.86463
$816$	304.000	0.0130418
$817$	22654.0	0.970090
$818$	−18896.0	−0.807681
$819$	11830.0	0.504730
$820$	−19040.0	−0.810861
$821$	−32559.0	−1.38406	−0.692032	−	0.721867i	$-0.743284\pi$
$821$	−32559.0	−1.38406	−0.692032	+	0.721867i	$0.743284\pi$
$822$	1136.00	0.0482026
$823$	−43582.0	−1.84590	−0.922948	−	0.384924i	$-0.874228\pi$
$823$	−43582.0	−1.84590	−0.922948	+	0.384924i	$0.874228\pi$
$824$	416.000	0.0175874
$825$	−328.000	−0.0138418
$826$	27020.0	1.13819
$827$	−23042.0	−0.968862	−0.484431	−	0.874829i	$-0.660973\pi$
$827$	−23042.0	−0.968862	−0.484431	+	0.874829i	$0.660973\pi$
$828$	7488.00	0.314283
$829$	−20690.0	−0.866820	−0.433410	−	0.901197i	$-0.642690\pi$
$829$	−20690.0	−0.866820	−0.433410	+	0.901197i	$0.642690\pi$
$830$	14280.0	0.597188
$831$	−1996.00	−0.0833219
$832$	832.000	0.0346688
$833$	−16758.0	−0.697035
$834$	−3690.00	−0.153207
$835$	−64056.0	−2.65479
$836$	752.000	0.0311106
$837$	−5300.00	−0.218871
$838$	−1042.00	−0.0429538
$839$	−43000.0	−1.76940	−0.884699	−	0.466163i	$-0.845636\pi$
$839$	−43000.0	−1.76940	−0.884699	+	0.466163i	$0.845636\pi$
$840$	4760.00	0.195519
$841$	36127.0	1.48128
$842$	14282.0	0.584549
$843$	2918.00	0.119219
$844$	9876.00	0.402780
$845$	2873.00	0.116964
$846$	−7124.00	−0.289513
$847$	46445.0	1.88414
$848$	−3712.00	−0.150319
$849$	−812.000	−0.0328242
$850$	−6232.00	−0.251477
$851$	792.000	0.0319029
$852$	−220.000	−0.00884633
$853$	−33065.0	−1.32723	−0.663613	−	0.748076i	$-0.730978\pi$
$853$	−33065.0	−1.32723	−0.663613	+	0.748076i	$0.730978\pi$
$854$	−4480.00	−0.179511
$855$	−41548.0	−1.66188
$856$	96.0000	0.00383319
$857$	−28938.0	−1.15345	−0.576723	−	0.816940i	$-0.695669\pi$
$857$	−28938.0	−1.15345	−0.576723	+	0.816940i	$0.695669\pi$
$858$	−52.0000	−0.00206906
$859$	12508.0	0.496819	0.248409	−	0.968655i	$-0.420092\pi$
$859$	12508.0	0.496819	0.248409	+	0.968655i	$0.420092\pi$
$860$	16388.0	0.649798
$861$	−9800.00	−0.387901
$862$	−12598.0	−0.497784
$863$	−19535.0	−0.770544	−0.385272	−	0.922803i	$-0.625892\pi$
$863$	−19535.0	−0.770544	−0.385272	+	0.922803i	$0.625892\pi$
$864$	1696.00	0.0667814
$865$	56032.0	2.20248
$866$	6462.00	0.253565
$867$	4552.00	0.178309
$868$	14000.0	0.547455
$869$	2032.00	0.0793221
$870$	−8364.00	−0.325938
$871$	−8710.00	−0.338837
$872$	9704.00	0.376857
$873$	30004.0	1.16321
$874$	−13536.0	−0.523870
$875$	−23205.0	−0.896540
$876$	3352.00	0.129285
$877$	18775.0	0.722904	0.361452	−	0.932391i	$-0.382281\pi$
$877$	18775.0	0.722904	0.361452	+	0.932391i	$0.382281\pi$
$878$	−820.000	−0.0315190
$879$	1855.00	0.0711804
$880$	544.000	0.0208389
$881$	−43531.0	−1.66470	−0.832348	−	0.554254i	$-0.813004\pi$
$881$	−43531.0	−1.66470	−0.832348	+	0.554254i	$0.813004\pi$
$882$	−45864.0	−1.75093
$883$	6955.00	0.265067	0.132534	−	0.991179i	$-0.457689\pi$
$883$	6955.00	0.265067	0.132534	+	0.991179i	$0.457689\pi$
$884$	−988.000	−0.0375905
$885$	6562.00	0.249242
$886$	−18794.0	−0.712637
$887$	40728.0	1.54173	0.770864	−	0.637000i	$-0.219825\pi$
$887$	40728.0	1.54173	0.770864	+	0.637000i	$0.219825\pi$
$888$	88.0000	0.00332555
$889$	18900.0	0.713032
$890$	−31756.0	−1.19603
$891$	1298.00	0.0488043
$892$	7772.00	0.291733
$893$	12878.0	0.482582
$894$	−5700.00	−0.213240
$895$	765.000	0.0285711
$896$	−4480.00	−0.167038
$897$	936.000	0.0348407
$898$	1308.00	0.0486064
$899$	−24600.0	−0.912632
$900$	−17056.0	−0.631704
$901$	4408.00	0.162988
$902$	−1120.00	−0.0413436
$903$	8435.00	0.310852
$904$	−9264.00	−0.340836
$905$	−6188.00	−0.227288
$906$	−5526.00	−0.202637
$907$	23653.0	0.865915	0.432958	−	0.901414i	$-0.357470\pi$
$907$	23653.0	0.865915	0.432958	+	0.901414i	$0.357470\pi$
$908$	12128.0	0.443262
$909$	−7592.00	−0.277020
$910$	−15470.0	−0.563545
$911$	−206.000	−0.00749186	−0.00374593	−	0.999993i	$-0.501192\pi$
$911$	−206.000	−0.00749186	−0.00374593	+	0.999993i	$0.501192\pi$
$912$	−1504.00	−0.0546079
$913$	840.000	0.0304490
$914$	29964.0	1.08438
$915$	−1088.00	−0.0393095
$916$	21244.0	0.766290
$917$	54985.0	1.98011
$918$	−2014.00	−0.0724095
$919$	28352.0	1.01768	0.508839	−	0.860862i	$-0.330075\pi$
$919$	28352.0	1.01768	0.508839	+	0.860862i	$0.330075\pi$
$920$	−9792.00	−0.350905
$921$	−5350.00	−0.191410
$922$	21690.0	0.774753
$923$	715.000	0.0254978
$924$	280.000	0.00996897
$925$	−1804.00	−0.0641245
$926$	26144.0	0.927803
$927$	−1352.00	−0.0479024
$928$	7872.00	0.278460
$929$	−17612.0	−0.621992	−0.310996	−	0.950411i	$-0.600663\pi$
$929$	−17612.0	−0.621992	−0.310996	+	0.950411i	$0.600663\pi$
$930$	3400.00	0.119882
$931$	82908.0	2.91858
$932$	−2028.00	−0.0712761
$933$	−2262.00	−0.0793725
$934$	−30680.0	−1.07482
$935$	−646.000	−0.0225951
$936$	−2704.00	−0.0944263
$937$	12014.0	0.418869	0.209435	−	0.977823i	$-0.432838\pi$
$937$	12014.0	0.418869	0.209435	+	0.977823i	$0.432838\pi$
$938$	46900.0	1.63256
$939$	1857.00	0.0645377
$940$	9316.00	0.323249
$941$	−26737.0	−0.926250	−0.463125	−	0.886293i	$-0.653272\pi$
$941$	−26737.0	−0.926250	−0.463125	+	0.886293i	$0.653272\pi$
$942$	932.000	0.0322359
$943$	20160.0	0.696182
$944$	−6176.00	−0.212936
$945$	−31535.0	−1.08554
$946$	964.000	0.0331314
$947$	−35566.0	−1.22042	−0.610211	−	0.792239i	$-0.708915\pi$
$947$	−35566.0	−1.22042	−0.610211	+	0.792239i	$0.708915\pi$
$948$	−4064.00	−0.139233
$949$	−10894.0	−0.372639
$950$	30832.0	1.05297
$951$	3870.00	0.131959
$952$	5320.00	0.181116
$953$	12279.0	0.417372	0.208686	−	0.977983i	$-0.433081\pi$
$953$	12279.0	0.417372	0.208686	+	0.977983i	$0.433081\pi$
$954$	12064.0	0.409420
$955$	42194.0	1.42970
$956$	−27180.0	−0.919523
$957$	−492.000	−0.0166187
$958$	−39230.0	−1.32303
$959$	19880.0	0.669404
$960$	−1088.00	−0.0365782
$961$	−19791.0	−0.664328
$962$	−286.000	−0.00958525
$963$	−312.000	−0.0104404
$964$	−17768.0	−0.593640
$965$	−20740.0	−0.691859
$966$	−5040.00	−0.167867
$967$	51523.0	1.71341	0.856705	−	0.515806i	$-0.172508\pi$
$967$	51523.0	1.71341	0.856705	+	0.515806i	$0.172508\pi$
$968$	−10616.0	−0.352491
$969$	1786.00	0.0592101
$970$	−39236.0	−1.29875
$971$	41027.0	1.35594	0.677971	−	0.735089i	$-0.262860\pi$
$971$	41027.0	1.35594	0.677971	+	0.735089i	$0.262860\pi$
$972$	−8320.00	−0.274552
$973$	−64575.0	−2.12763
$974$	−21808.0	−0.717426
$975$	−2132.00	−0.0700294
$976$	1024.00	0.0335834
$977$	23562.0	0.771561	0.385781	−	0.922591i	$-0.373932\pi$
$977$	23562.0	0.771561	0.385781	+	0.922591i	$0.373932\pi$
$978$	−5104.00	−0.166879
$979$	−1868.00	−0.0609822
$980$	59976.0	1.95496
$981$	−31538.0	−1.02643
$982$	−37038.0	−1.20359
$983$	−41307.0	−1.34027	−0.670137	−	0.742238i	$-0.733765\pi$
$983$	−41307.0	−1.34027	−0.670137	+	0.742238i	$0.733765\pi$
$984$	2240.00	0.0725697
$985$	−27081.0	−0.876013
$986$	−9348.00	−0.301928
$987$	4795.00	0.154637
$988$	4888.00	0.157397
$989$	−17352.0	−0.557898
$990$	−1768.00	−0.0567583
$991$	−26586.0	−0.852202	−0.426101	−	0.904676i	$-0.640113\pi$
$991$	−26586.0	−0.852202	−0.426101	+	0.904676i	$0.640113\pi$
$992$	−3200.00	−0.102419
$993$	−10520.0	−0.336195
$994$	−3850.00	−0.122852
$995$	27302.0	0.869881
$996$	−1680.00	−0.0534466
$997$	39298.0	1.24833	0.624163	−	0.781295i	$-0.285440\pi$
$997$	39298.0	1.24833	0.624163	+	0.781295i	$0.285440\pi$
$998$	−28800.0	−0.913475
$999$	−583.000	−0.0184638

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	26.4.a.b.1.1	✓	1
3.2	odd	2		234.4.a.a.1.1		1
4.3	odd	2		208.4.a.e.1.1		1
5.2	odd	4		650.4.b.d.599.2		2
5.3	odd	4		650.4.b.d.599.1		2
5.4	even	2		650.4.a.c.1.1		1
7.6	odd	2		1274.4.a.f.1.1		1
8.3	odd	2		832.4.a.g.1.1		1
8.5	even	2		832.4.a.j.1.1		1
12.11	even	2		1872.4.a.b.1.1		1
13.2	odd	12		338.4.e.c.147.2		4
13.3	even	3		338.4.c.c.191.1		2
13.4	even	6		338.4.c.g.315.1		2
13.5	odd	4		338.4.b.b.337.1		2
13.6	odd	12		338.4.e.c.23.1		4
13.7	odd	12		338.4.e.c.23.2		4
13.8	odd	4		338.4.b.b.337.2		2
13.9	even	3		338.4.c.c.315.1		2
13.10	even	6		338.4.c.g.191.1		2
13.11	odd	12		338.4.e.c.147.1		4
13.12	even	2		338.4.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.4.a.b.1.1	✓	1	1.1	even	1	trivial
208.4.a.e.1.1		1	4.3	odd	2
234.4.a.a.1.1		1	3.2	odd	2
338.4.a.b.1.1		1	13.12	even	2
338.4.b.b.337.1		2	13.5	odd	4
338.4.b.b.337.2		2	13.8	odd	4
338.4.c.c.191.1		2	13.3	even	3
338.4.c.c.315.1		2	13.9	even	3
338.4.c.g.191.1		2	13.10	even	6
338.4.c.g.315.1		2	13.4	even	6
338.4.e.c.23.1		4	13.6	odd	12
338.4.e.c.23.2		4	13.7	odd	12
338.4.e.c.147.1		4	13.11	odd	12
338.4.e.c.147.2		4	13.2	odd	12
650.4.a.c.1.1		1	5.4	even	2
650.4.b.d.599.1		2	5.3	odd	4
650.4.b.d.599.2		2	5.2	odd	4
832.4.a.g.1.1		1	8.3	odd	2
832.4.a.j.1.1		1	8.5	even	2
1274.4.a.f.1.1		1	7.6	odd	2
1872.4.a.b.1.1		1	12.11	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	26.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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