LMFDB - Embedded newform 48.26.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,26,Mod(1,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 26, names="a")

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

chi := DirichletCharacter("48.1");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 26 $
Character orbit:	$[\chi]$	$=$	48.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:	$190.078454377$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 6)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	48.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+531441. q^{3} -2.92755e8 q^{5} -3.58064e9 q^{7} +2.82430e11 q^{9} +O(q^{10})$

$q+531441. q^{3} -2.92755e8 q^{5} -3.58064e9 q^{7} +2.82430e11 q^{9} -1.51116e13 q^{11} +1.22107e12 q^{13} -1.55582e14 q^{15} +2.51825e15 q^{17} +7.99269e15 q^{19} -1.90290e15 q^{21} +9.96456e16 q^{23} -2.12318e17 q^{25} +1.50095e17 q^{27} -2.08067e18 q^{29} +4.93767e18 q^{31} -8.03091e18 q^{33} +1.04825e18 q^{35} +1.98292e19 q^{37} +6.48928e17 q^{39} +2.24696e20 q^{41} +7.22210e19 q^{43} -8.26826e19 q^{45} -1.89872e20 q^{47} -1.32825e21 q^{49} +1.33830e21 q^{51} -2.64568e21 q^{53} +4.42399e21 q^{55} +4.24764e21 q^{57} +1.64546e22 q^{59} -3.55470e22 q^{61} -1.01128e21 q^{63} -3.57475e20 q^{65} -1.06704e23 q^{67} +5.29558e22 q^{69} -7.36720e22 q^{71} -2.62403e23 q^{73} -1.12834e23 q^{75} +5.41092e22 q^{77} +1.00264e24 q^{79} +7.97664e22 q^{81} -1.55859e24 q^{83} -7.37230e23 q^{85} -1.10575e24 q^{87} +2.18167e24 q^{89} -4.37222e21 q^{91} +2.62408e24 q^{93} -2.33990e24 q^{95} -4.40165e23 q^{97} -4.26795e24 q^{99} +O(q^{100})$

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 $

$2$	0	0
$2$	0	0
$3$	531441.	0.577350
$3$	531441.	0.577350
$4$	0	0
$5$	−2.92755e8	−0.536264	−0.268132	−	0.963382i	$-0.586406\pi$
$5$	−2.92755e8	−0.536264	−0.268132	+	0.963382i	$0.586406\pi$
$6$	0	0
$7$	−3.58064e9	−0.0977768	−0.0488884	−	0.998804i	$-0.515568\pi$
$7$	−3.58064e9	−0.0977768	−0.0488884	+	0.998804i	$0.515568\pi$
$8$	0	0
$9$	2.82430e11	0.333333
$10$	0	0
$11$	−1.51116e13	−1.45178	−0.725891	−	0.687810i	$-0.758572\pi$
$11$	−1.51116e13	−1.45178	−0.725891	+	0.687810i	$0.758572\pi$
$12$	0	0
$13$	1.22107e12	0.0145361	0.00726807	−	0.999974i	$-0.497686\pi$
$13$	1.22107e12	0.0145361	0.00726807	+	0.999974i	$0.497686\pi$
$14$	0	0
$15$	−1.55582e14	−0.309612
$16$	0	0
$17$	2.51825e15	1.04830	0.524152	−	0.851625i	$-0.324382\pi$
$17$	2.51825e15	1.04830	0.524152	+	0.851625i	$0.324382\pi$
$18$	0	0
$19$	7.99269e15	0.828463	0.414232	−	0.910172i	$-0.364050\pi$
$19$	7.99269e15	0.828463	0.414232	+	0.910172i	$0.364050\pi$
$20$	0	0
$21$	−1.90290e15	−0.0564514
$22$	0	0
$23$	9.96456e16	0.948114	0.474057	−	0.880494i	$-0.342789\pi$
$23$	9.96456e16	0.948114	0.474057	+	0.880494i	$0.342789\pi$
$24$	0	0
$25$	−2.12318e17	−0.712420
$26$	0	0
$27$	1.50095e17	0.192450
$28$	0	0
$29$	−2.08067e18	−1.09202	−0.546008	−	0.837780i	$-0.683853\pi$
$29$	−2.08067e18	−1.09202	−0.546008	+	0.837780i	$0.683853\pi$
$30$	0	0
$31$	4.93767e18	1.12590	0.562952	−	0.826490i	$-0.309666\pi$
$31$	4.93767e18	1.12590	0.562952	+	0.826490i	$0.309666\pi$
$32$	0	0
$33$	−8.03091e18	−0.838186
$34$	0	0
$35$	1.04825e18	0.0524342
$36$	0	0
$37$	1.98292e19	0.495202	0.247601	−	0.968862i	$-0.420358\pi$
$37$	1.98292e19	0.495202	0.247601	+	0.968862i	$0.420358\pi$
$38$	0	0
$39$	6.48928e17	0.00839245
$40$	0	0
$41$	2.24696e20	1.55524	0.777620	−	0.628735i	$-0.216427\pi$
$41$	2.24696e20	1.55524	0.777620	+	0.628735i	$0.216427\pi$
$42$	0	0
$43$	7.22210e19	0.275618	0.137809	−	0.990459i	$-0.455994\pi$
$43$	7.22210e19	0.275618	0.137809	+	0.990459i	$0.455994\pi$
$44$	0	0
$45$	−8.26826e19	−0.178755
$46$	0	0
$47$	−1.89872e20	−0.238363	−0.119181	−	0.992872i	$-0.538027\pi$
$47$	−1.89872e20	−0.238363	−0.119181	+	0.992872i	$0.538027\pi$
$48$	0	0
$49$	−1.32825e21	−0.990440
$50$	0	0
$51$	1.33830e21	0.605239
$52$	0	0
$53$	−2.64568e21	−0.739756	−0.369878	−	0.929080i	$-0.620600\pi$
$53$	−2.64568e21	−0.739756	−0.369878	+	0.929080i	$0.620600\pi$
$54$	0	0
$55$	4.42399e21	0.778539
$56$	0	0
$57$	4.24764e21	0.478313
$58$	0	0
$59$	1.64546e22	1.20403	0.602015	−	0.798485i	$-0.294365\pi$
$59$	1.64546e22	1.20403	0.602015	+	0.798485i	$0.294365\pi$
$60$	0	0
$61$	−3.55470e22	−1.71467	−0.857333	−	0.514762i	$-0.827880\pi$
$61$	−3.55470e22	−1.71467	−0.857333	+	0.514762i	$0.827880\pi$
$62$	0	0
$63$	−1.01128e21	−0.0325923
$64$	0	0
$65$	−3.57475e20	−0.00779522
$66$	0	0
$67$	−1.06704e23	−1.59311	−0.796553	−	0.604569i	$-0.793345\pi$
$67$	−1.06704e23	−1.59311	−0.796553	+	0.604569i	$0.793345\pi$
$68$	0	0
$69$	5.29558e22	0.547394
$70$	0	0
$71$	−7.36720e22	−0.532811	−0.266405	−	0.963861i	$-0.585836\pi$
$71$	−7.36720e22	−0.532811	−0.266405	+	0.963861i	$0.585836\pi$
$72$	0	0
$73$	−2.62403e23	−1.34101	−0.670506	−	0.741904i	$-0.733923\pi$
$73$	−2.62403e23	−1.34101	−0.670506	+	0.741904i	$0.733923\pi$
$74$	0	0
$75$	−1.12834e23	−0.411316
$76$	0	0
$77$	5.41092e22	0.141950
$78$	0	0
$79$	1.00264e24	1.90901	0.954503	−	0.298201i	$-0.0963866\pi$
$79$	1.00264e24	1.90901	0.954503	+	0.298201i	$0.0963866\pi$
$80$	0	0
$81$	7.97664e22	0.111111
$82$	0	0
$83$	−1.55859e24	−1.60050	−0.800249	−	0.599667i	$-0.795300\pi$
$83$	−1.55859e24	−1.60050	−0.800249	+	0.599667i	$0.795300\pi$
$84$	0	0
$85$	−7.37230e23	−0.562169
$86$	0	0
$87$	−1.10575e24	−0.630475
$88$	0	0
$89$	2.18167e24	0.936298	0.468149	−	0.883650i	$-0.344921\pi$
$89$	2.18167e24	0.936298	0.468149	+	0.883650i	$0.344921\pi$
$90$	0	0
$91$	−4.37222e21	−0.00142130
$92$	0	0
$93$	2.62408e24	0.650041
$94$	0	0
$95$	−2.33990e24	−0.444275
$96$	0	0
$97$	−4.40165e23	−0.0644123	−0.0322062	−	0.999481i	$-0.510253\pi$
$97$	−4.40165e23	−0.0644123	−0.0322062	+	0.999481i	$0.510253\pi$
$98$	0	0
$99$	−4.26795e24	−0.483927
$100$	0	0
$101$	−5.02582e24	−0.443802	−0.221901	−	0.975069i	$-0.571226\pi$
$101$	−5.02582e24	−0.443802	−0.221901	+	0.975069i	$0.571226\pi$
$102$	0	0
$103$	1.52311e25	1.05261	0.526304	−	0.850296i	$-0.323577\pi$
$103$	1.52311e25	1.05261	0.526304	+	0.850296i	$0.323577\pi$
$104$	0	0
$105$	5.57084e23	0.0302729
$106$	0	0
$107$	2.47232e25	1.06123	0.530613	−	0.847614i	$-0.321962\pi$
$107$	2.47232e25	1.06123	0.530613	+	0.847614i	$0.321962\pi$
$108$	0	0
$109$	−2.85771e25	−0.973166	−0.486583	−	0.873634i	$-0.661757\pi$
$109$	−2.85771e25	−0.973166	−0.486583	+	0.873634i	$0.661757\pi$
$110$	0	0
$111$	1.05380e25	0.285905
$112$	0	0
$113$	−1.73240e25	−0.375982	−0.187991	−	0.982171i	$-0.560198\pi$
$113$	−1.73240e25	−0.375982	−0.187991	+	0.982171i	$0.560198\pi$
$114$	0	0
$115$	−2.91717e25	−0.508440
$116$	0	0
$117$	3.44867e23	0.00484538
$118$	0	0
$119$	−9.01696e24	−0.102500
$120$	0	0
$121$	1.20013e26	1.10767
$122$	0	0
$123$	1.19413e26	0.897918
$124$	0	0
$125$	1.49405e26	0.918310
$126$	0	0
$127$	−3.23349e26	−1.62976	−0.814882	−	0.579627i	$-0.803198\pi$
$127$	−3.23349e26	−1.62976	−0.814882	+	0.579627i	$0.803198\pi$
$128$	0	0
$129$	3.83812e25	0.159128
$130$	0	0
$131$	3.63273e26	1.24263	0.621315	−	0.783561i	$-0.286599\pi$
$131$	3.63273e26	1.24263	0.621315	+	0.783561i	$0.286599\pi$
$132$	0	0
$133$	−2.86190e25	−0.0810044
$134$	0	0
$135$	−4.39409e25	−0.103204
$136$	0	0
$137$	−6.56742e26	−1.28348	−0.641738	−	0.766924i	$-0.721786\pi$
$137$	−6.56742e26	−1.28348	−0.641738	+	0.766924i	$0.721786\pi$
$138$	0	0
$139$	−6.72509e26	−1.09651	−0.548256	−	0.836311i	$-0.684708\pi$
$139$	−6.72509e26	−1.09651	−0.548256	+	0.836311i	$0.684708\pi$
$140$	0	0
$141$	−1.00906e26	−0.137619
$142$	0	0
$143$	−1.84523e25	−0.0211033
$144$	0	0
$145$	6.09127e26	0.585609
$146$	0	0
$147$	−7.05885e26	−0.571831
$148$	0	0
$149$	−7.98627e26	−0.546406	−0.273203	−	0.961956i	$-0.588083\pi$
$149$	−7.98627e26	−0.546406	−0.273203	+	0.961956i	$0.588083\pi$
$150$	0	0
$151$	1.03633e27	0.600187	0.300093	−	0.953910i	$-0.402982\pi$
$151$	1.03633e27	0.600187	0.300093	+	0.953910i	$0.402982\pi$
$152$	0	0
$153$	7.11228e26	0.349435
$154$	0	0
$155$	−1.44553e27	−0.603782
$156$	0	0
$157$	−3.36346e27	−1.19685	−0.598427	−	0.801178i	$-0.704207\pi$
$157$	−3.36346e27	−1.19685	−0.598427	+	0.801178i	$0.704207\pi$
$158$	0	0
$159$	−1.40602e27	−0.427098
$160$	0	0
$161$	−3.56796e26	−0.0927035
$162$	0	0
$163$	−8.00443e26	−0.178232	−0.0891159	−	0.996021i	$-0.528404\pi$
$163$	−8.00443e26	−0.178232	−0.0891159	+	0.996021i	$0.528404\pi$
$164$	0	0
$165$	2.35109e27	0.449489
$166$	0	0
$167$	5.17982e27	0.851842	0.425921	−	0.904760i	$-0.359950\pi$
$167$	5.17982e27	0.851842	0.425921	+	0.904760i	$0.359950\pi$
$168$	0	0
$169$	−7.05492e27	−0.999789
$170$	0	0
$171$	2.25737e27	0.276154
$172$	0	0
$173$	−3.40880e27	−0.360599	−0.180300	−	0.983612i	$-0.557707\pi$
$173$	−3.40880e27	−0.360599	−0.180300	+	0.983612i	$0.557707\pi$
$174$	0	0
$175$	7.60235e26	0.0696582
$176$	0	0
$177$	8.74465e27	0.695147
$178$	0	0
$179$	1.23610e28	0.853870	0.426935	−	0.904282i	$-0.359593\pi$
$179$	1.23610e28	0.853870	0.426935	+	0.904282i	$0.359593\pi$
$180$	0	0
$181$	3.38516e27	0.203516	0.101758	−	0.994809i	$-0.467553\pi$
$181$	3.38516e27	0.203516	0.101758	+	0.994809i	$0.467553\pi$
$182$	0	0
$183$	−1.88911e28	−0.989963
$184$	0	0
$185$	−5.80508e27	−0.265559
$186$	0	0
$187$	−3.80547e28	−1.52191
$188$	0	0
$189$	−5.37435e26	−0.0188171
$190$	0	0
$191$	−3.81140e28	−1.16995	−0.584975	−	0.811052i	$-0.698896\pi$
$191$	−3.81140e28	−1.16995	−0.584975	+	0.811052i	$0.698896\pi$
$192$	0	0
$193$	6.38842e28	1.72158	0.860790	−	0.508961i	$-0.169970\pi$
$193$	6.38842e28	1.72158	0.860790	+	0.508961i	$0.169970\pi$
$194$	0	0
$195$	−1.89977e26	−0.00450057
$196$	0	0
$197$	−8.73680e28	−1.82190	−0.910950	−	0.412517i	$-0.864650\pi$
$197$	−8.73680e28	−1.82190	−0.910950	+	0.412517i	$0.864650\pi$
$198$	0	0
$199$	−2.76766e28	−0.508686	−0.254343	−	0.967114i	$-0.581859\pi$
$199$	−2.76766e28	−0.508686	−0.254343	+	0.967114i	$0.581859\pi$
$200$	0	0
$201$	−5.67067e28	−0.919780
$202$	0	0
$203$	7.45015e27	0.106774
$204$	0	0
$205$	−6.57809e28	−0.834020
$206$	0	0
$207$	2.81429e28	0.316038
$208$	0	0
$209$	−1.20782e29	−1.20275
$210$	0	0
$211$	2.08479e28	0.184303	0.0921513	−	0.995745i	$-0.470626\pi$
$211$	2.08479e28	0.184303	0.0921513	+	0.995745i	$0.470626\pi$
$212$	0	0
$213$	−3.91523e28	−0.307619
$214$	0	0
$215$	−2.11431e28	−0.147804
$216$	0	0
$217$	−1.76800e28	−0.110087
$218$	0	0
$219$	−1.39452e29	−0.774234
$220$	0	0
$221$	3.07496e27	0.0152383
$222$	0	0
$223$	−2.90506e29	−1.28630	−0.643152	−	0.765739i	$-0.722374\pi$
$223$	−2.90506e29	−1.28630	−0.643152	+	0.765739i	$0.722374\pi$
$224$	0	0
$225$	−5.99648e28	−0.237473
$226$	0	0
$227$	−3.23765e29	−1.14791	−0.573954	−	0.818887i	$-0.694591\pi$
$227$	−3.23765e29	−1.14791	−0.573954	+	0.818887i	$0.694591\pi$
$228$	0	0
$229$	−5.11099e29	−1.62391	−0.811954	−	0.583721i	$-0.801596\pi$
$229$	−5.11099e29	−1.62391	−0.811954	+	0.583721i	$0.801596\pi$
$230$	0	0
$231$	2.87558e28	0.0819551
$232$	0	0
$233$	−1.20130e29	−0.307399	−0.153700	−	0.988118i	$-0.549119\pi$
$233$	−1.20130e29	−0.307399	−0.153700	+	0.988118i	$0.549119\pi$
$234$	0	0
$235$	5.55861e28	0.127826
$236$	0	0
$237$	5.32845e29	1.10217
$238$	0	0
$239$	−3.34916e29	−0.623681	−0.311840	−	0.950135i	$-0.600945\pi$
$239$	−3.34916e29	−0.623681	−0.311840	+	0.950135i	$0.600945\pi$
$240$	0	0
$241$	−3.53238e29	−0.592727	−0.296363	−	0.955075i	$-0.595774\pi$
$241$	−3.53238e29	−0.592727	−0.296363	+	0.955075i	$0.595774\pi$
$242$	0	0
$243$	4.23912e28	0.0641500
$244$	0	0
$245$	3.88851e29	0.531138
$246$	0	0
$247$	9.75965e27	0.0120427
$248$	0	0
$249$	−8.28298e29	−0.924048
$250$	0	0
$251$	−1.07603e30	−1.08619	−0.543093	−	0.839673i	$-0.682747\pi$
$251$	−1.07603e30	−1.08619	−0.543093	+	0.839673i	$0.682747\pi$
$252$	0	0
$253$	−1.50580e30	−1.37645
$254$	0	0
$255$	−3.91794e29	−0.324568
$256$	0	0
$257$	6.56258e27	0.00493073	0.00246536	−	0.999997i	$-0.499215\pi$
$257$	6.56258e27	0.00493073	0.00246536	+	0.999997i	$0.499215\pi$
$258$	0	0
$259$	−7.10011e28	−0.0484193
$260$	0	0
$261$	−5.87643e29	−0.364005
$262$	0	0
$263$	−2.03818e30	−1.14761	−0.573807	−	0.818990i	$-0.694534\pi$
$263$	−2.03818e30	−1.14761	−0.573807	+	0.818990i	$0.694534\pi$
$264$	0	0
$265$	7.74534e29	0.396705
$266$	0	0
$267$	1.15943e30	0.540572
$268$	0	0
$269$	1.30216e30	0.553046	0.276523	−	0.961007i	$-0.410818\pi$
$269$	1.30216e30	0.553046	0.276523	+	0.961007i	$0.410818\pi$
$270$	0	0
$271$	−2.73384e30	−1.05842	−0.529209	−	0.848492i	$-0.677511\pi$
$271$	−2.73384e30	−1.05842	−0.529209	+	0.848492i	$0.677511\pi$
$272$	0	0
$273$	−2.32358e27	−0.000820586 0
$274$	0	0
$275$	3.20846e30	1.03428
$276$	0	0
$277$	−4.83846e29	−0.142466	−0.0712329	−	0.997460i	$-0.522693\pi$
$277$	−4.83846e29	−0.142466	−0.0712329	+	0.997460i	$0.522693\pi$
$278$	0	0
$279$	1.39454e30	0.375301
$280$	0	0
$281$	−7.57818e30	−1.86525	−0.932623	−	0.360853i	$-0.882486\pi$
$281$	−7.57818e30	−1.86525	−0.932623	+	0.360853i	$0.882486\pi$
$282$	0	0
$283$	1.30443e30	0.293827	0.146914	−	0.989149i	$-0.453066\pi$
$283$	1.30443e30	0.293827	0.146914	+	0.989149i	$0.453066\pi$
$284$	0	0
$285$	−1.24352e30	−0.256502
$286$	0	0
$287$	−8.04557e29	−0.152066
$288$	0	0
$289$	5.70960e29	0.0989424
$290$	0	0
$291$	−2.33922e29	−0.0371885
$292$	0	0
$293$	−4.04021e29	−0.0589601	−0.0294800	−	0.999565i	$-0.509385\pi$
$293$	−4.04021e29	−0.0589601	−0.0294800	+	0.999565i	$0.509385\pi$
$294$	0	0
$295$	−4.81717e30	−0.645679
$296$	0	0
$297$	−2.26817e30	−0.279395
$298$	0	0
$299$	1.21674e29	0.0137819
$300$	0	0
$301$	−2.58598e29	−0.0269491
$302$	0	0
$303$	−2.67092e30	−0.256229
$304$	0	0
$305$	1.04065e31	0.919514
$306$	0	0
$307$	−6.95636e30	−0.566438	−0.283219	−	0.959055i	$-0.591402\pi$
$307$	−6.95636e30	−0.566438	−0.283219	+	0.959055i	$0.591402\pi$
$308$	0	0
$309$	8.09445e30	0.607724
$310$	0	0
$311$	−2.74913e30	−0.190410	−0.0952051	−	0.995458i	$-0.530351\pi$
$311$	−2.74913e30	−0.190410	−0.0952051	+	0.995458i	$0.530351\pi$
$312$	0	0
$313$	9.39383e30	0.600535	0.300267	−	0.953855i	$-0.402924\pi$
$313$	9.39383e30	0.600535	0.300267	+	0.953855i	$0.402924\pi$
$314$	0	0
$315$	2.96057e29	0.0174781
$316$	0	0
$317$	1.86543e31	1.01751	0.508755	−	0.860912i	$-0.330106\pi$
$317$	1.86543e31	1.01751	0.508755	+	0.860912i	$0.330106\pi$
$318$	0	0
$319$	3.14422e31	1.58537
$320$	0	0
$321$	1.31389e31	0.612699
$322$	0	0
$323$	2.01276e31	0.868482
$324$	0	0
$325$	−2.59255e29	−0.0103558
$326$	0	0
$327$	−1.51870e31	−0.561857
$328$	0	0
$329$	6.79866e29	0.0233064
$330$	0	0
$331$	4.71638e31	1.49885	0.749426	−	0.662088i	$-0.230330\pi$
$331$	4.71638e31	1.49885	0.749426	+	0.662088i	$0.230330\pi$
$332$	0	0
$333$	5.60034e30	0.165067
$334$	0	0
$335$	3.12380e31	0.854326
$336$	0	0
$337$	1.85792e31	0.471686	0.235843	−	0.971791i	$-0.424215\pi$
$337$	1.85792e31	0.471686	0.235843	+	0.971791i	$0.424215\pi$
$338$	0	0
$339$	−9.20668e30	−0.217074
$340$	0	0
$341$	−7.46160e31	−1.63456
$342$	0	0
$343$	9.55787e30	0.194619
$344$	0	0
$345$	−1.55031e31	−0.293548
$346$	0	0
$347$	7.27635e31	1.28173	0.640863	−	0.767655i	$-0.278577\pi$
$347$	7.27635e31	1.28173	0.640863	+	0.767655i	$0.278577\pi$
$348$	0	0
$349$	1.19713e32	1.96256	0.981282	−	0.192574i	$-0.0616835\pi$
$349$	1.19713e32	1.96256	0.981282	+	0.192574i	$0.0616835\pi$
$350$	0	0
$351$	1.83276e29	0.00279748
$352$	0	0
$353$	6.99722e31	0.994813	0.497407	−	0.867517i	$-0.334286\pi$
$353$	6.99722e31	0.994813	0.497407	+	0.867517i	$0.334286\pi$
$354$	0	0
$355$	2.15678e31	0.285728
$356$	0	0
$357$	−4.79198e30	−0.0591783
$358$	0	0
$359$	−6.06364e31	−0.698317	−0.349159	−	0.937064i	$-0.613533\pi$
$359$	−6.06364e31	−0.698317	−0.349159	+	0.937064i	$0.613533\pi$
$360$	0	0
$361$	−2.91933e31	−0.313649
$362$	0	0
$363$	6.37796e31	0.639513
$364$	0	0
$365$	7.68197e31	0.719137
$366$	0	0
$367$	−2.22539e32	−1.94572	−0.972860	−	0.231394i	$-0.925671\pi$
$367$	−2.22539e32	−1.94572	−0.972860	+	0.231394i	$0.925671\pi$
$368$	0	0
$369$	6.34608e31	0.518413
$370$	0	0
$371$	9.47322e30	0.0723309
$372$	0	0
$373$	−1.15379e32	−0.823695	−0.411848	−	0.911253i	$-0.635116\pi$
$373$	−1.15379e32	−0.823695	−0.411848	+	0.911253i	$0.635116\pi$
$374$	0	0
$375$	7.93998e31	0.530187
$376$	0	0
$377$	−2.54065e30	−0.0158737
$378$	0	0
$379$	−5.47213e31	−0.320012	−0.160006	−	0.987116i	$-0.551151\pi$
$379$	−5.47213e31	−0.320012	−0.160006	+	0.987116i	$0.551151\pi$
$380$	0	0
$381$	−1.71841e32	−0.940945
$382$	0	0
$383$	1.98130e32	1.01617	0.508085	−	0.861307i	$-0.330354\pi$
$383$	1.98130e32	1.01617	0.508085	+	0.861307i	$0.330354\pi$
$384$	0	0
$385$	−1.58407e31	−0.0761230
$386$	0	0
$387$	2.03973e31	0.0918727
$388$	0	0
$389$	4.19098e31	0.176989	0.0884945	−	0.996077i	$-0.471794\pi$
$389$	4.19098e31	0.176989	0.0884945	+	0.996077i	$0.471794\pi$
$390$	0	0
$391$	2.50933e32	0.993912
$392$	0	0
$393$	1.93058e32	0.717433
$394$	0	0
$395$	−2.93528e32	−1.02373
$396$	0	0
$397$	2.64500e32	0.866053	0.433027	−	0.901381i	$-0.357446\pi$
$397$	2.64500e32	0.866053	0.433027	+	0.901381i	$0.357446\pi$
$398$	0	0
$399$	−1.52093e31	−0.0467679
$400$	0	0
$401$	2.33767e32	0.675273	0.337636	−	0.941277i	$-0.390373\pi$
$401$	2.33767e32	0.675273	0.337636	+	0.941277i	$0.390373\pi$
$402$	0	0
$403$	6.02925e30	0.0163663
$404$	0	0
$405$	−2.33520e31	−0.0595849
$406$	0	0
$407$	−2.99650e32	−0.718925
$408$	0	0
$409$	−5.48497e32	−1.23775	−0.618875	−	0.785490i	$-0.712411\pi$
$409$	−5.48497e32	−1.23775	−0.618875	+	0.785490i	$0.712411\pi$
$410$	0	0
$411$	−3.49020e32	−0.741015
$412$	0	0
$413$	−5.89181e31	−0.117726
$414$	0	0
$415$	4.56284e32	0.858291
$416$	0	0
$417$	−3.57399e32	−0.633071
$418$	0	0
$419$	−3.41488e31	−0.0569771	−0.0284885	−	0.999594i	$-0.509069\pi$
$419$	−3.41488e31	−0.0569771	−0.0284885	+	0.999594i	$0.509069\pi$
$420$	0	0
$421$	−5.71127e32	−0.897856	−0.448928	−	0.893568i	$-0.648194\pi$
$421$	−5.71127e32	−0.897856	−0.448928	+	0.893568i	$0.648194\pi$
$422$	0	0
$423$	−5.36256e31	−0.0794543
$424$	0	0
$425$	−5.34670e32	−0.746834
$426$	0	0
$427$	1.27281e32	0.167654
$428$	0	0
$429$	−9.80632e30	−0.0121840
$430$	0	0
$431$	−5.26390e32	−0.617081	−0.308540	−	0.951211i	$-0.599840\pi$
$431$	−5.26390e32	−0.617081	−0.308540	+	0.951211i	$0.599840\pi$
$432$	0	0
$433$	−7.00633e32	−0.775160	−0.387580	−	0.921836i	$-0.626689\pi$
$433$	−7.00633e32	−0.775160	−0.387580	+	0.921836i	$0.626689\pi$
$434$	0	0
$435$	3.23715e32	0.338102
$436$	0	0
$437$	7.96437e32	0.785477
$438$	0	0
$439$	−5.29542e32	−0.493280	−0.246640	−	0.969107i	$-0.579327\pi$
$439$	−5.29542e32	−0.493280	−0.246640	+	0.969107i	$0.579327\pi$
$440$	0	0
$441$	−3.75136e32	−0.330147
$442$	0	0
$443$	−4.49792e32	−0.374080	−0.187040	−	0.982352i	$-0.559889\pi$
$443$	−4.49792e32	−0.374080	−0.187040	+	0.982352i	$0.559889\pi$
$444$	0	0
$445$	−6.38695e32	−0.502103
$446$	0	0
$447$	−4.24423e32	−0.315468
$448$	0	0
$449$	−9.88741e32	−0.695030	−0.347515	−	0.937674i	$-0.612974\pi$
$449$	−9.88741e32	−0.695030	−0.347515	+	0.937674i	$0.612974\pi$
$450$	0	0
$451$	−3.39551e33	−2.25787
$452$	0	0
$453$	5.50748e32	0.346518
$454$	0	0
$455$	1.27999e30	0.000762191 0
$456$	0	0
$457$	2.93791e33	1.65610	0.828050	−	0.560654i	$-0.189450\pi$
$457$	2.93791e33	1.65610	0.828050	+	0.560654i	$0.189450\pi$
$458$	0	0
$459$	3.77976e32	0.201746
$460$	0	0
$461$	−2.14053e33	−1.08208	−0.541039	−	0.840997i	$-0.681969\pi$
$461$	−2.14053e33	−1.08208	−0.541039	+	0.840997i	$0.681969\pi$
$462$	0	0
$463$	−8.71982e32	−0.417585	−0.208793	−	0.977960i	$-0.566953\pi$
$463$	−8.71982e32	−0.417585	−0.208793	+	0.977960i	$0.566953\pi$
$464$	0	0
$465$	−7.68213e32	−0.348594
$466$	0	0
$467$	6.01153e32	0.258538	0.129269	−	0.991610i	$-0.458737\pi$
$467$	6.01153e32	0.258538	0.129269	+	0.991610i	$0.458737\pi$
$468$	0	0
$469$	3.82068e32	0.155769
$470$	0	0
$471$	−1.78748e33	−0.691003
$472$	0	0
$473$	−1.09137e33	−0.400137
$474$	0	0
$475$	−1.69699e33	−0.590214
$476$	0	0
$477$	−7.47217e32	−0.246585
$478$	0	0
$479$	3.01870e33	0.945423	0.472711	−	0.881217i	$-0.343275\pi$
$479$	3.01870e33	0.945423	0.472711	+	0.881217i	$0.343275\pi$
$480$	0	0
$481$	2.42128e31	0.00719833
$482$	0	0
$483$	−1.89616e32	−0.0535224
$484$	0	0
$485$	1.28861e32	0.0345421
$486$	0	0
$487$	5.24137e33	1.33454	0.667272	−	0.744814i	$-0.267462\pi$
$487$	5.24137e33	1.33454	0.667272	+	0.744814i	$0.267462\pi$
$488$	0	0
$489$	−4.25388e32	−0.102902
$490$	0	0
$491$	3.08172e33	0.708393	0.354197	−	0.935171i	$-0.384754\pi$
$491$	3.08172e33	0.708393	0.354197	+	0.935171i	$0.384754\pi$
$492$	0	0
$493$	−5.23966e33	−1.14476
$494$	0	0
$495$	1.24946e33	0.259513
$496$	0	0
$497$	2.63793e32	0.0520965
$498$	0	0
$499$	1.64910e33	0.309734	0.154867	−	0.987935i	$-0.450505\pi$
$499$	1.64910e33	0.309734	0.154867	+	0.987935i	$0.450505\pi$
$500$	0	0
$501$	2.75277e33	0.491811
$502$	0	0
$503$	2.47162e32	0.0420128	0.0210064	−	0.999779i	$-0.493313\pi$
$503$	2.47162e32	0.0420128	0.0210064	+	0.999779i	$0.493313\pi$
$504$	0	0
$505$	1.47133e33	0.237995
$506$	0	0
$507$	−3.74927e33	−0.577228
$508$	0	0
$509$	6.26740e33	0.918577	0.459288	−	0.888287i	$-0.348105\pi$
$509$	6.26740e33	0.918577	0.459288	+	0.888287i	$0.348105\pi$
$510$	0	0
$511$	9.39571e32	0.131120
$512$	0	0
$513$	1.19966e33	0.159438
$514$	0	0
$515$	−4.45899e33	−0.564477
$516$	0	0
$517$	2.86927e33	0.346051
$518$	0	0
$519$	−1.81158e33	−0.208192
$520$	0	0
$521$	1.64678e34	1.80370	0.901850	−	0.432049i	$-0.142209\pi$
$521$	1.64678e34	1.80370	0.901850	+	0.432049i	$0.142209\pi$
$522$	0	0
$523$	3.45969e33	0.361216	0.180608	−	0.983555i	$-0.442194\pi$
$523$	3.45969e33	0.361216	0.180608	+	0.983555i	$0.442194\pi$
$524$	0	0
$525$	4.04020e32	0.0402172
$526$	0	0
$527$	1.24343e34	1.18029
$528$	0	0
$529$	−1.11651e33	−0.101081
$530$	0	0
$531$	4.64727e33	0.401343
$532$	0	0
$533$	2.74370e32	0.0226072
$534$	0	0
$535$	−7.23785e33	−0.569098
$536$	0	0
$537$	6.56916e33	0.492982
$538$	0	0
$539$	2.00719e34	1.43790
$540$	0	0
$541$	−2.31144e33	−0.158094	−0.0790472	−	0.996871i	$-0.525188\pi$
$541$	−2.31144e33	−0.158094	−0.0790472	+	0.996871i	$0.525188\pi$
$542$	0	0
$543$	1.79902e33	0.117500
$544$	0	0
$545$	8.36608e33	0.521874
$546$	0	0
$547$	4.04733e33	0.241172	0.120586	−	0.992703i	$-0.461523\pi$
$547$	4.04733e33	0.241172	0.120586	+	0.992703i	$0.461523\pi$
$548$	0	0
$549$	−1.00395e34	−0.571555
$550$	0	0
$551$	−1.66302e34	−0.904694
$552$	0	0
$553$	−3.59010e33	−0.186656
$554$	0	0
$555$	−3.08506e33	−0.153321
$556$	0	0
$557$	2.32181e34	1.10315	0.551577	−	0.834124i	$-0.314026\pi$
$557$	2.32181e34	1.10315	0.551577	+	0.834124i	$0.314026\pi$
$558$	0	0
$559$	8.81870e31	0.00400643
$560$	0	0
$561$	−2.02238e34	−0.878674
$562$	0	0
$563$	2.70103e34	1.12247	0.561235	−	0.827656i	$-0.310326\pi$
$563$	2.70103e34	1.12247	0.561235	+	0.827656i	$0.310326\pi$
$564$	0	0
$565$	5.07168e33	0.201626
$566$	0	0
$567$	−2.85615e32	−0.0108641
$568$	0	0
$569$	−2.32147e33	−0.0845007	−0.0422504	−	0.999107i	$-0.513453\pi$
$569$	−2.32147e33	−0.0845007	−0.0422504	+	0.999107i	$0.513453\pi$
$570$	0	0
$571$	−2.55837e34	−0.891276	−0.445638	−	0.895213i	$-0.647023\pi$
$571$	−2.55837e34	−0.891276	−0.445638	+	0.895213i	$0.647023\pi$
$572$	0	0
$573$	−2.02553e34	−0.675470
$574$	0	0
$575$	−2.11565e34	−0.675455
$576$	0	0
$577$	1.95952e34	0.599035	0.299517	−	0.954091i	$-0.403174\pi$
$577$	1.95952e34	0.599035	0.299517	+	0.954091i	$0.403174\pi$
$578$	0	0
$579$	3.39507e34	0.993954
$580$	0	0
$581$	5.58075e33	0.156492
$582$	0	0
$583$	3.99803e34	1.07396
$584$	0	0
$585$	−1.00961e32	−0.00259841
$586$	0	0
$587$	−5.98783e33	−0.147670	−0.0738352	−	0.997270i	$-0.523524\pi$
$587$	−5.98783e33	−0.147670	−0.0738352	+	0.997270i	$0.523524\pi$
$588$	0	0
$589$	3.94653e34	0.932769
$590$	0	0
$591$	−4.64309e34	−1.05187
$592$	0	0
$593$	1.57169e34	0.341338	0.170669	−	0.985328i	$-0.445407\pi$
$593$	1.57169e34	0.341338	0.170669	+	0.985328i	$0.445407\pi$
$594$	0	0
$595$	2.63976e33	0.0549670
$596$	0	0
$597$	−1.47085e34	−0.293690
$598$	0	0
$599$	7.90989e34	1.51473	0.757364	−	0.652992i	$-0.226487\pi$
$599$	7.90989e34	1.51473	0.757364	+	0.652992i	$0.226487\pi$
$600$	0	0
$601$	−9.50067e34	−1.74511	−0.872556	−	0.488514i	$-0.837539\pi$
$601$	−9.50067e34	−1.74511	−0.872556	+	0.488514i	$0.837539\pi$
$602$	0	0
$603$	−3.01363e34	−0.531035
$604$	0	0
$605$	−3.51343e34	−0.594003
$606$	0	0
$607$	3.98588e32	0.00646644	0.00323322	−	0.999995i	$-0.498971\pi$
$607$	3.98588e32	0.00646644	0.00323322	+	0.999995i	$0.498971\pi$
$608$	0	0
$609$	3.95931e33	0.0616458
$610$	0	0
$611$	−2.31848e32	−0.00346488
$612$	0	0
$613$	−6.82592e34	−0.979276	−0.489638	−	0.871926i	$-0.662871\pi$
$613$	−6.82592e34	−0.979276	−0.489638	+	0.871926i	$0.662871\pi$
$614$	0	0
$615$	−3.49586e34	−0.481521
$616$	0	0
$617$	1.15084e35	1.52212	0.761062	−	0.648679i	$-0.224678\pi$
$617$	1.15084e35	1.52212	0.761062	+	0.648679i	$0.224678\pi$
$618$	0	0
$619$	−4.34788e34	−0.552261	−0.276131	−	0.961120i	$-0.589052\pi$
$619$	−4.34788e34	−0.552261	−0.276131	+	0.961120i	$0.589052\pi$
$620$	0	0
$621$	1.49563e34	0.182465
$622$	0	0
$623$	−7.81178e33	−0.0915482
$624$	0	0
$625$	1.95367e34	0.219963
$626$	0	0
$627$	−6.41886e34	−0.694406
$628$	0	0
$629$	4.99348e34	0.519123
$630$	0	0
$631$	−1.27302e35	−1.27195	−0.635974	−	0.771711i	$-0.719401\pi$
$631$	−1.27302e35	−1.27195	−0.635974	+	0.771711i	$0.719401\pi$
$632$	0	0
$633$	1.10794e34	0.106407
$634$	0	0
$635$	9.46619e34	0.873985
$636$	0	0
$637$	−1.62189e33	−0.0143972
$638$	0	0
$639$	−2.08072e34	−0.177604
$640$	0	0
$641$	−9.45454e33	−0.0776096	−0.0388048	−	0.999247i	$-0.512355\pi$
$641$	−9.45454e33	−0.0776096	−0.0388048	+	0.999247i	$0.512355\pi$
$642$	0	0
$643$	−8.31941e34	−0.656834	−0.328417	−	0.944533i	$-0.606515\pi$
$643$	−8.31941e34	−0.656834	−0.328417	+	0.944533i	$0.606515\pi$
$644$	0	0
$645$	−1.12363e34	−0.0853348
$646$	0	0
$647$	−2.34992e35	−1.71692	−0.858460	−	0.512880i	$-0.828579\pi$
$647$	−2.34992e35	−1.71692	−0.858460	+	0.512880i	$0.828579\pi$
$648$	0	0
$649$	−2.48655e35	−1.74799
$650$	0	0
$651$	−9.39590e33	−0.0635589
$652$	0	0
$653$	−1.75276e35	−1.14106	−0.570530	−	0.821277i	$-0.693262\pi$
$653$	−1.75276e35	−1.14106	−0.570530	+	0.821277i	$0.693262\pi$
$654$	0	0
$655$	−1.06350e35	−0.666379
$656$	0	0
$657$	−7.41103e34	−0.447004
$658$	0	0
$659$	2.48211e35	1.44130	0.720648	−	0.693301i	$-0.243844\pi$
$659$	2.48211e35	1.44130	0.720648	+	0.693301i	$0.243844\pi$
$660$	0	0
$661$	−3.37345e35	−1.88606	−0.943030	−	0.332707i	$-0.892038\pi$
$661$	−3.37345e35	−1.88606	−0.943030	+	0.332707i	$0.892038\pi$
$662$	0	0
$663$	1.63416e33	0.00879784
$664$	0	0
$665$	8.37835e33	0.0434398
$666$	0	0
$667$	−2.07330e35	−1.03535
$668$	0	0
$669$	−1.54387e35	−0.742648
$670$	0	0
$671$	5.37170e35	2.48932
$672$	0	0
$673$	2.99045e35	1.33521	0.667604	−	0.744517i	$-0.267320\pi$
$673$	2.99045e35	1.33521	0.667604	+	0.744517i	$0.267320\pi$
$674$	0	0
$675$	−3.18678e34	−0.137105
$676$	0	0
$677$	5.69058e34	0.235938	0.117969	−	0.993017i	$-0.462362\pi$
$677$	5.69058e34	0.235938	0.117969	+	0.993017i	$0.462362\pi$
$678$	0	0
$679$	1.57608e33	0.00629803
$680$	0	0
$681$	−1.72062e35	−0.662745
$682$	0	0
$683$	−1.38059e35	−0.512633	−0.256317	−	0.966593i	$-0.582509\pi$
$683$	−1.38059e35	−0.512633	−0.256317	+	0.966593i	$0.582509\pi$
$684$	0	0
$685$	1.92264e35	0.688283
$686$	0	0
$687$	−2.71619e35	−0.937564
$688$	0	0
$689$	−3.23056e33	−0.0107532
$690$	0	0
$691$	−1.16343e35	−0.373479	−0.186739	−	0.982409i	$-0.559792\pi$
$691$	−1.16343e35	−0.373479	−0.186739	+	0.982409i	$0.559792\pi$
$692$	0	0
$693$	1.52820e34	0.0473168
$694$	0	0
$695$	1.96880e35	0.588020
$696$	0	0
$697$	5.65841e35	1.63036
$698$	0	0
$699$	−6.38421e34	−0.177477
$700$	0	0
$701$	6.30496e35	1.69125	0.845624	−	0.533779i	$-0.179229\pi$
$701$	6.30496e35	1.69125	0.845624	+	0.533779i	$0.179229\pi$
$702$	0	0
$703$	1.58488e35	0.410257
$704$	0	0
$705$	2.95407e34	0.0738001
$706$	0	0
$707$	1.79957e34	0.0433935
$708$	0	0
$709$	−7.52844e35	−1.75238	−0.876188	−	0.481970i	$-0.839921\pi$
$709$	−7.52844e35	−1.75238	−0.876188	+	0.481970i	$0.839921\pi$
$710$	0	0
$711$	2.83176e35	0.636335
$712$	0	0
$713$	4.92018e35	1.06748
$714$	0	0
$715$	5.40200e33	0.0113170
$716$	0	0
$717$	−1.77988e35	−0.360082
$718$	0	0
$719$	1.28708e35	0.251475	0.125738	−	0.992064i	$-0.459870\pi$
$719$	1.28708e35	0.251475	0.125738	+	0.992064i	$0.459870\pi$
$720$	0	0
$721$	−5.45373e34	−0.102921
$722$	0	0
$723$	−1.87725e35	−0.342211
$724$	0	0
$725$	4.41764e35	0.777974
$726$	0	0
$727$	−4.39640e35	−0.748027	−0.374014	−	0.927423i	$-0.622019\pi$
$727$	−4.39640e35	−0.748027	−0.374014	+	0.927423i	$0.622019\pi$
$728$	0	0
$729$	2.25284e34	0.0370370
$730$	0	0
$731$	1.81871e35	0.288932
$732$	0	0
$733$	−1.18297e36	−1.81625	−0.908124	−	0.418702i	$-0.862485\pi$
$733$	−1.18297e36	−1.81625	−0.908124	+	0.418702i	$0.862485\pi$
$734$	0	0
$735$	2.06651e35	0.306652
$736$	0	0
$737$	1.61246e36	2.31284
$738$	0	0
$739$	8.13836e35	1.12845	0.564224	−	0.825622i	$-0.309175\pi$
$739$	8.13836e35	1.12845	0.564224	+	0.825622i	$0.309175\pi$
$740$	0	0
$741$	5.18668e33	0.00695283
$742$	0	0
$743$	1.02640e36	1.33033	0.665164	−	0.746698i	$-0.268362\pi$
$743$	1.02640e36	1.33033	0.665164	+	0.746698i	$0.268362\pi$
$744$	0	0
$745$	2.33802e35	0.293018
$746$	0	0
$747$	−4.40191e35	−0.533500
$748$	0	0
$749$	−8.85251e34	−0.103763
$750$	0	0
$751$	1.43129e36	1.62266	0.811332	−	0.584586i	$-0.198743\pi$
$751$	1.43129e36	1.62266	0.811332	+	0.584586i	$0.198743\pi$
$752$	0	0
$753$	−5.71848e35	−0.627110
$754$	0	0
$755$	−3.03391e35	−0.321859
$756$	0	0
$757$	8.68697e35	0.891600	0.445800	−	0.895133i	$-0.352919\pi$
$757$	8.68697e35	0.891600	0.445800	+	0.895133i	$0.352919\pi$
$758$	0	0
$759$	−8.00245e35	−0.794696
$760$	0	0
$761$	5.51250e34	0.0529713	0.0264857	−	0.999649i	$-0.491568\pi$
$761$	5.51250e34	0.0529713	0.0264857	+	0.999649i	$0.491568\pi$
$762$	0	0
$763$	1.02324e35	0.0951530
$764$	0	0
$765$	−2.08216e35	−0.187390
$766$	0	0
$767$	2.00923e34	0.0175020
$768$	0	0
$769$	−4.98681e35	−0.420479	−0.210239	−	0.977650i	$-0.567424\pi$
$769$	−4.98681e35	−0.420479	−0.210239	+	0.977650i	$0.567424\pi$
$770$	0	0
$771$	3.48763e33	0.00284676
$772$	0	0
$773$	4.79467e35	0.378892	0.189446	−	0.981891i	$-0.439331\pi$
$773$	4.79467e35	0.378892	0.189446	+	0.981891i	$0.439331\pi$
$774$	0	0
$775$	−1.04836e36	−0.802116
$776$	0	0
$777$	−3.77329e34	−0.0279549
$778$	0	0
$779$	1.79593e36	1.28846
$780$	0	0
$781$	1.11330e36	0.773525
$782$	0	0
$783$	−3.12298e35	−0.210158
$784$	0	0
$785$	9.84670e35	0.641830
$786$	0	0
$787$	−1.22599e36	−0.774111	−0.387055	−	0.922056i	$-0.626508\pi$
$787$	−1.22599e36	−0.774111	−0.387055	+	0.922056i	$0.626508\pi$
$788$	0	0
$789$	−1.08317e36	−0.662576
$790$	0	0
$791$	6.20311e34	0.0367623
$792$	0	0
$793$	−4.34054e34	−0.0249246
$794$	0	0
$795$	4.11619e35	0.229038
$796$	0	0
$797$	−3.12403e36	−1.68456	−0.842278	−	0.539043i	$-0.818786\pi$
$797$	−3.12403e36	−1.68456	−0.842278	+	0.539043i	$0.818786\pi$
$798$	0	0
$799$	−4.78146e35	−0.249877
$800$	0	0
$801$	6.16168e35	0.312099
$802$	0	0
$803$	3.96532e36	1.94686
$804$	0	0
$805$	1.04454e35	0.0497136
$806$	0	0
$807$	6.92021e35	0.319301
$808$	0	0
$809$	4.16982e36	1.86535	0.932675	−	0.360717i	$-0.117468\pi$
$809$	4.16982e36	1.86535	0.932675	+	0.360717i	$0.117468\pi$
$810$	0	0
$811$	−7.93102e35	−0.344008	−0.172004	−	0.985096i	$-0.555024\pi$
$811$	−7.93102e35	−0.344008	−0.172004	+	0.985096i	$0.555024\pi$
$812$	0	0
$813$	−1.45287e36	−0.611078
$814$	0	0
$815$	2.34334e35	0.0955794
$816$	0	0
$817$	5.77240e35	0.228339
$818$	0	0
$819$	−1.23484e33	−0.000473766 0
$820$	0	0
$821$	2.22198e35	0.0826896	0.0413448	−	0.999145i	$-0.486836\pi$
$821$	2.22198e35	0.0826896	0.0413448	+	0.999145i	$0.486836\pi$
$822$	0	0
$823$	−4.63197e36	−1.67212	−0.836061	−	0.548637i	$-0.815147\pi$
$823$	−4.63197e36	−1.67212	−0.836061	+	0.548637i	$0.815147\pi$
$824$	0	0
$825$	1.70511e36	0.597141
$826$	0	0
$827$	−5.60825e36	−1.90550	−0.952748	−	0.303760i	$-0.901758\pi$
$827$	−5.60825e36	−1.90550	−0.952748	+	0.303760i	$0.901758\pi$
$828$	0	0
$829$	−3.61387e36	−1.19135	−0.595677	−	0.803224i	$-0.703116\pi$
$829$	−3.61387e36	−1.19135	−0.595677	+	0.803224i	$0.703116\pi$
$830$	0	0
$831$	−2.57136e35	−0.0822526
$832$	0	0
$833$	−3.34486e36	−1.03828
$834$	0	0
$835$	−1.51642e36	−0.456813
$836$	0	0
$837$	7.41118e35	0.216680
$838$	0	0
$839$	3.53738e36	1.00382	0.501911	−	0.864919i	$-0.332630\pi$
$839$	3.53738e36	1.00382	0.501911	+	0.864919i	$0.332630\pi$
$840$	0	0
$841$	6.98837e35	0.192498
$842$	0	0
$843$	−4.02736e36	−1.07690
$844$	0	0
$845$	2.06536e36	0.536151
$846$	0	0
$847$	−4.29722e35	−0.108304
$848$	0	0
$849$	6.93230e35	0.169641
$850$	0	0
$851$	1.97589e36	0.469508
$852$	0	0
$853$	−5.36485e36	−1.23792	−0.618962	−	0.785421i	$-0.712447\pi$
$853$	−5.36485e36	−1.23792	−0.618962	+	0.785421i	$0.712447\pi$
$854$	0	0
$855$	−6.60857e35	−0.148092
$856$	0	0
$857$	1.12850e36	0.245607	0.122803	−	0.992431i	$-0.460812\pi$
$857$	1.12850e36	0.245607	0.122803	+	0.992431i	$0.460812\pi$
$858$	0	0
$859$	6.05620e36	1.28022	0.640111	−	0.768282i	$-0.278888\pi$
$859$	6.05620e36	1.28022	0.640111	+	0.768282i	$0.278888\pi$
$860$	0	0
$861$	−4.27574e35	−0.0877955
$862$	0	0
$863$	−5.30956e35	−0.105907	−0.0529533	−	0.998597i	$-0.516863\pi$
$863$	−5.30956e35	−0.105907	−0.0529533	+	0.998597i	$0.516863\pi$
$864$	0	0
$865$	9.97942e35	0.193377
$866$	0	0
$867$	3.03432e35	0.0571244
$868$	0	0
$869$	−1.51515e37	−2.77146
$870$	0	0
$871$	−1.30293e35	−0.0231576
$872$	0	0
$873$	−1.24316e35	−0.0214708
$874$	0	0
$875$	−5.34965e35	−0.0897894
$876$	0	0
$877$	−5.83031e36	−0.951035	−0.475518	−	0.879706i	$-0.657739\pi$
$877$	−5.83031e36	−0.951035	−0.475518	+	0.879706i	$0.657739\pi$
$878$	0	0
$879$	−2.14713e35	−0.0340406
$880$	0	0
$881$	7.57293e36	1.16698	0.583492	−	0.812119i	$-0.301686\pi$
$881$	7.57293e36	1.16698	0.583492	+	0.812119i	$0.301686\pi$
$882$	0	0
$883$	2.59184e36	0.388239	0.194119	−	0.980978i	$-0.437815\pi$
$883$	2.59184e36	0.388239	0.194119	+	0.980978i	$0.437815\pi$
$884$	0	0
$885$	−2.56004e36	−0.372783
$886$	0	0
$887$	−7.96686e36	−1.12782	−0.563912	−	0.825835i	$-0.690704\pi$
$887$	−7.96686e36	−1.12782	−0.563912	+	0.825835i	$0.690704\pi$
$888$	0	0
$889$	1.15780e36	0.159353
$890$	0	0
$891$	−1.20540e36	−0.161309
$892$	0	0
$893$	−1.51759e36	−0.197475
$894$	0	0
$895$	−3.61875e36	−0.457900
$896$	0	0
$897$	6.46628e34	0.00795699
$898$	0	0
$899$	−1.02737e37	−1.22950
$900$	0	0
$901$	−6.66248e36	−0.775489
$902$	0	0
$903$	−1.37429e35	−0.0155590
$904$	0	0
$905$	−9.91023e35	−0.109138
$906$	0	0
$907$	4.86506e36	0.521191	0.260596	−	0.965448i	$-0.416081\pi$
$907$	4.86506e36	0.521191	0.260596	+	0.965448i	$0.416081\pi$
$908$	0	0
$909$	−1.41944e36	−0.147934
$910$	0	0
$911$	−1.10036e37	−1.11572	−0.557859	−	0.829936i	$-0.688377\pi$
$911$	−1.10036e37	−1.11572	−0.557859	+	0.829936i	$0.688377\pi$
$912$	0	0
$913$	2.35527e37	2.32357
$914$	0	0
$915$	5.53046e36	0.530882
$916$	0	0
$917$	−1.30075e36	−0.121500
$918$	0	0
$919$	−1.10577e37	−1.00513	−0.502564	−	0.864540i	$-0.667610\pi$
$919$	−1.10577e37	−1.00513	−0.502564	+	0.864540i	$0.667610\pi$
$920$	0	0
$921$	−3.69689e36	−0.327033
$922$	0	0
$923$	−8.99588e34	−0.00774502
$924$	0	0
$925$	−4.21008e36	−0.352792
$926$	0	0
$927$	4.30172e36	0.350870
$928$	0	0
$929$	1.82435e37	1.44848	0.724239	−	0.689549i	$-0.242191\pi$
$929$	1.82435e37	1.44848	0.724239	+	0.689549i	$0.242191\pi$
$930$	0	0
$931$	−1.06163e37	−0.820543
$932$	0	0
$933$	−1.46100e36	−0.109933
$934$	0	0
$935$	1.11407e37	0.816146
$936$	0	0
$937$	9.54074e36	0.680514	0.340257	−	0.940332i	$-0.389486\pi$
$937$	9.54074e36	0.680514	0.340257	+	0.940332i	$0.389486\pi$
$938$	0	0
$939$	4.99226e36	0.346719
$940$	0	0
$941$	−7.72127e36	−0.522178	−0.261089	−	0.965315i	$-0.584082\pi$
$941$	−7.72127e36	−0.522178	−0.261089	+	0.965315i	$0.584082\pi$
$942$	0	0
$943$	2.23900e37	1.47454
$944$	0	0
$945$	1.57337e35	0.0100910
$946$	0	0
$947$	1.89183e37	1.18170	0.590849	−	0.806782i	$-0.298793\pi$
$947$	1.89183e37	1.18170	0.590849	+	0.806782i	$0.298793\pi$
$948$	0	0
$949$	−3.20413e35	−0.0194932
$950$	0	0
$951$	9.91366e36	0.587459
$952$	0	0
$953$	−1.61494e37	−0.932172	−0.466086	−	0.884739i	$-0.654336\pi$
$953$	−1.61494e37	−0.932172	−0.466086	+	0.884739i	$0.654336\pi$
$954$	0	0
$955$	1.11580e37	0.627402
$956$	0	0
$957$	1.67097e37	0.915312
$958$	0	0
$959$	2.35156e36	0.125494
$960$	0	0
$961$	5.14781e36	0.267658
$962$	0	0
$963$	6.98257e36	0.353742
$964$	0	0
$965$	−1.87024e37	−0.923222
$966$	0	0
$967$	2.64645e37	1.27301	0.636507	−	0.771271i	$-0.280379\pi$
$967$	2.64645e37	1.27301	0.636507	+	0.771271i	$0.280379\pi$
$968$	0	0
$969$	1.06966e37	0.501418
$970$	0	0
$971$	−2.73601e37	−1.24990	−0.624952	−	0.780663i	$-0.714882\pi$
$971$	−2.73601e37	−1.24990	−0.624952	+	0.780663i	$0.714882\pi$
$972$	0	0
$973$	2.40802e36	0.107213
$974$	0	0
$975$	−1.37779e35	−0.00597895
$976$	0	0
$977$	3.04743e37	1.28900	0.644498	−	0.764606i	$-0.277066\pi$
$977$	3.04743e37	1.28900	0.644498	+	0.764606i	$0.277066\pi$
$978$	0	0
$979$	−3.29685e37	−1.35930
$980$	0	0
$981$	−8.07101e36	−0.324389
$982$	0	0
$983$	−3.84516e36	−0.150659	−0.0753296	−	0.997159i	$-0.524001\pi$
$983$	−3.84516e36	−0.150659	−0.0753296	+	0.997159i	$0.524001\pi$
$984$	0	0
$985$	2.55774e37	0.977020
$986$	0	0
$987$	3.61308e35	0.0134559
$988$	0	0
$989$	7.19651e36	0.261317
$990$	0	0
$991$	4.30043e37	1.52262	0.761309	−	0.648389i	$-0.224557\pi$
$991$	4.30043e37	1.52262	0.761309	+	0.648389i	$0.224557\pi$
$992$	0	0
$993$	2.50648e37	0.865363
$994$	0	0
$995$	8.10246e36	0.272790
$996$	0	0
$997$	−1.52317e37	−0.500103	−0.250051	−	0.968233i	$-0.580447\pi$
$997$	−1.52317e37	−0.500103	−0.250051	+	0.968233i	$0.580447\pi$
$998$	0	0
$999$	2.97625e36	0.0953017

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.26.a.c.1.1		1
4.3	odd	2		6.26.a.a.1.1	✓	1
12.11	even	2		18.26.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.26.a.a.1.1	✓	1	4.3	odd	2
18.26.a.d.1.1		1	12.11	even	2
48.26.a.c.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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	48.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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