LMFDB - Embedded newform 14.12.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [14,12,Mod(1,14)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(14, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("14.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	14.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:	$10.7568045278$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	14.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-32.0000 q^{2} -396.000 q^{3} +1024.00 q^{4} +7350.00 q^{5} +12672.0 q^{6} +16807.0 q^{7} -32768.0 q^{8} -20331.0 q^{9} +O(q^{10})$

\(q-32.0000 q^{2} -396.000 q^{3} +1024.00 q^{4} +7350.00 q^{5} +12672.0 q^{6} +16807.0 q^{7} -32768.0 q^{8} -20331.0 q^{9} -235200. q^{10} -108780. q^{11} -405504. q^{12} -635842. q^{13} -537824. q^{14} -2.91060e6 q^{15} +1.04858e6 q^{16} -9.22592e6 q^{17} +650592. q^{18} -7.55537e6 q^{19} +7.52640e6 q^{20} -6.65557e6 q^{21} +3.48096e6 q^{22} +2.64894e7 q^{23} +1.29761e7 q^{24} +5.19438e6 q^{25} +2.03469e7 q^{26} +7.82013e7 q^{27} +1.72104e7 q^{28} -1.69828e8 q^{29} +9.31392e7 q^{30} -5.13627e7 q^{31} -3.35544e7 q^{32} +4.30769e7 q^{33} +2.95229e8 q^{34} +1.23531e8 q^{35} -2.08189e7 q^{36} -2.51606e8 q^{37} +2.41772e8 q^{38} +2.51793e8 q^{39} -2.40845e8 q^{40} -9.28818e8 q^{41} +2.12978e8 q^{42} -1.81890e9 q^{43} -1.11391e8 q^{44} -1.49433e8 q^{45} -8.47661e8 q^{46} +5.23343e8 q^{47} -4.15236e8 q^{48} +2.82475e8 q^{49} -1.66220e8 q^{50} +3.65346e9 q^{51} -6.51102e8 q^{52} +4.19952e9 q^{53} -2.50244e9 q^{54} -7.99533e8 q^{55} -5.50732e8 q^{56} +2.99193e9 q^{57} +5.43448e9 q^{58} +9.14013e9 q^{59} -2.98045e9 q^{60} -6.63931e9 q^{61} +1.64361e9 q^{62} -3.41703e8 q^{63} +1.07374e9 q^{64} -4.67344e9 q^{65} -1.37846e9 q^{66} -2.87814e9 q^{67} -9.44734e9 q^{68} -1.04898e10 q^{69} -3.95301e9 q^{70} -4.34560e9 q^{71} +6.66206e8 q^{72} +2.34503e10 q^{73} +8.05139e9 q^{74} -2.05697e9 q^{75} -7.73670e9 q^{76} -1.82827e9 q^{77} -8.05739e9 q^{78} -2.87619e10 q^{79} +7.70703e9 q^{80} -2.73661e10 q^{81} +2.97222e10 q^{82} -5.57776e9 q^{83} -6.81531e9 q^{84} -6.78105e10 q^{85} +5.82047e10 q^{86} +6.72517e10 q^{87} +3.56450e9 q^{88} +7.80022e10 q^{89} +4.78185e9 q^{90} -1.06866e10 q^{91} +2.71251e10 q^{92} +2.03396e10 q^{93} -1.67470e10 q^{94} -5.55320e10 q^{95} +1.32876e10 q^{96} -2.66859e10 q^{97} -9.03921e9 q^{98} +2.21161e9 q^{99} +O(q^{100})\)

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 $

$2$	−32.0000	−0.707107
$2$	−32.0000	−0.707107
$3$	−396.000	−0.940867	−0.470434	−	0.882435i	$-0.655902\pi$
$3$	−396.000	−0.940867	−0.470434	+	0.882435i	$0.655902\pi$
$4$	1024.00	0.500000
$5$	7350.00	1.05185	0.525923	−	0.850532i	$-0.323720\pi$
$5$	7350.00	1.05185	0.525923	+	0.850532i	$0.323720\pi$
$6$	12672.0	0.665294
$7$	16807.0	0.377964
$7$	16807.0	0.377964
$8$	−32768.0	−0.353553
$9$	−20331.0	−0.114769
$10$	−235200.	−0.743768
$11$	−108780.	−0.203652	−0.101826	−	0.994802i	$-0.532469\pi$
$11$	−108780.	−0.203652	−0.101826	+	0.994802i	$0.532469\pi$
$12$	−405504.	−0.470434
$13$	−635842.	−0.474964	−0.237482	−	0.971392i	$-0.576322\pi$
$13$	−635842.	−0.474964	−0.237482	+	0.971392i	$0.576322\pi$
$14$	−537824.	−0.267261
$15$	−2.91060e6	−0.989648
$16$	1.04858e6	0.250000
$17$	−9.22592e6	−1.57594	−0.787972	−	0.615712i	$-0.788869\pi$
$17$	−9.22592e6	−1.57594	−0.787972	+	0.615712i	$0.788869\pi$
$18$	650592.	0.0811540
$19$	−7.55537e6	−0.700021	−0.350010	−	0.936746i	$-0.613822\pi$
$19$	−7.55537e6	−0.700021	−0.350010	+	0.936746i	$0.613822\pi$
$20$	7.52640e6	0.525923
$21$	−6.65557e6	−0.355614
$22$	3.48096e6	0.144004
$23$	2.64894e7	0.858161	0.429081	−	0.903266i	$-0.358838\pi$
$23$	2.64894e7	0.858161	0.429081	+	0.903266i	$0.358838\pi$
$24$	1.29761e7	0.332647
$25$	5.19438e6	0.106381
$26$	2.03469e7	0.335850
$27$	7.82013e7	1.04885
$28$	1.72104e7	0.188982
$29$	−1.69828e8	−1.53751	−0.768757	−	0.639541i	$-0.779125\pi$
$29$	−1.69828e8	−1.53751	−0.768757	+	0.639541i	$0.779125\pi$
$30$	9.31392e7	0.699787
$31$	−5.13627e7	−0.322225	−0.161112	−	0.986936i	$-0.551508\pi$
$31$	−5.13627e7	−0.322225	−0.161112	+	0.986936i	$0.551508\pi$
$32$	−3.35544e7	−0.176777
$33$	4.30769e7	0.191610
$34$	2.95229e8	1.11436
$35$	1.23531e8	0.397561
$36$	−2.08189e7	−0.0573845
$37$	−2.51606e8	−0.596501	−0.298251	−	0.954488i	$-0.596403\pi$
$37$	−2.51606e8	−0.596501	−0.298251	+	0.954488i	$0.596403\pi$
$38$	2.41772e8	0.494990
$39$	2.51793e8	0.446878
$40$	−2.40845e8	−0.371884
$41$	−9.28818e8	−1.25204	−0.626022	−	0.779806i	$-0.715318\pi$
$41$	−9.28818e8	−1.25204	−0.626022	+	0.779806i	$0.715318\pi$
$42$	2.12978e8	0.251457
$43$	−1.81890e9	−1.88682	−0.943412	−	0.331624i	$-0.892404\pi$
$43$	−1.81890e9	−1.88682	−0.943412	+	0.331624i	$0.892404\pi$
$44$	−1.11391e8	−0.101826
$45$	−1.49433e8	−0.120719
$46$	−8.47661e8	−0.606812
$47$	5.23343e8	0.332850	0.166425	−	0.986054i	$-0.446778\pi$
$47$	5.23343e8	0.332850	0.166425	+	0.986054i	$0.446778\pi$
$48$	−4.15236e8	−0.235217
$49$	2.82475e8	0.142857
$50$	−1.66220e8	−0.0752226
$51$	3.65346e9	1.48275
$52$	−6.51102e8	−0.237482
$53$	4.19952e9	1.37938	0.689688	−	0.724107i	$-0.257748\pi$
$53$	4.19952e9	1.37938	0.689688	+	0.724107i	$0.257748\pi$
$54$	−2.50244e9	−0.741649
$55$	−7.99533e8	−0.214211
$56$	−5.50732e8	−0.133631
$57$	2.99193e9	0.658627
$58$	5.43448e9	1.08719
$59$	9.14013e9	1.66443	0.832216	−	0.554451i	$-0.187072\pi$
$59$	9.14013e9	1.66443	0.832216	+	0.554451i	$0.187072\pi$
$60$	−2.98045e9	−0.494824
$61$	−6.63931e9	−1.00649	−0.503245	−	0.864144i	$-0.667860\pi$
$61$	−6.63931e9	−1.00649	−0.503245	+	0.864144i	$0.667860\pi$
$62$	1.64361e9	0.227847
$63$	−3.41703e8	−0.0433786
$64$	1.07374e9	0.125000
$65$	−4.67344e9	−0.499589
$66$	−1.37846e9	−0.135489
$67$	−2.87814e9	−0.260436	−0.130218	−	0.991485i	$-0.541568\pi$
$67$	−2.87814e9	−0.260436	−0.130218	+	0.991485i	$0.541568\pi$
$68$	−9.44734e9	−0.787972
$69$	−1.04898e10	−0.807416
$70$	−3.95301e9	−0.281118
$71$	−4.34560e9	−0.285844	−0.142922	−	0.989734i	$-0.545650\pi$
$71$	−4.34560e9	−0.285844	−0.142922	+	0.989734i	$0.545650\pi$
$72$	6.66206e8	0.0405770
$73$	2.34503e10	1.32396	0.661978	−	0.749524i	$-0.269717\pi$
$73$	2.34503e10	1.32396	0.661978	+	0.749524i	$0.269717\pi$
$74$	8.05139e9	0.421790
$75$	−2.05697e9	−0.100090
$76$	−7.73670e9	−0.350010
$77$	−1.82827e9	−0.0769733
$78$	−8.05739e9	−0.315991
$79$	−2.87619e10	−1.05164	−0.525821	−	0.850595i	$-0.676242\pi$
$79$	−2.87619e10	−1.05164	−0.525821	+	0.850595i	$0.676242\pi$
$80$	7.70703e9	0.262962
$81$	−2.73661e10	−0.872059
$82$	2.97222e10	0.885328
$83$	−5.57776e9	−0.155428	−0.0777142	−	0.996976i	$-0.524762\pi$
$83$	−5.57776e9	−0.155428	−0.0777142	+	0.996976i	$0.524762\pi$
$84$	−6.81531e9	−0.177807
$85$	−6.78105e10	−1.65765
$86$	5.82047e10	1.33419
$87$	6.72517e10	1.44660
$88$	3.56450e9	0.0720020
$89$	7.80022e10	1.48068	0.740341	−	0.672232i	$-0.234664\pi$
$89$	7.80022e10	1.48068	0.740341	+	0.672232i	$0.234664\pi$
$90$	4.78185e9	0.0853615
$91$	−1.06866e10	−0.179520
$92$	2.71251e10	0.429081
$93$	2.03396e10	0.303170
$94$	−1.67470e10	−0.235360
$95$	−5.55320e10	−0.736315
$96$	1.32876e10	0.166323
$97$	−2.66859e10	−0.315527	−0.157764	−	0.987477i	$-0.550428\pi$
$97$	−2.66859e10	−0.315527	−0.157764	+	0.987477i	$0.550428\pi$
$98$	−9.03921e9	−0.101015
$99$	2.21161e9	0.0233730
$100$	5.31904e9	0.0531904
$101$	1.78821e10	0.169298	0.0846490	−	0.996411i	$-0.473023\pi$
$101$	1.78821e10	0.169298	0.0846490	+	0.996411i	$0.473023\pi$
$102$	−1.16911e11	−1.04846
$103$	1.13608e11	0.965619	0.482810	−	0.875725i	$-0.339616\pi$
$103$	1.13608e11	0.965619	0.482810	+	0.875725i	$0.339616\pi$
$104$	2.08353e10	0.167925
$105$	−4.89185e10	−0.374052
$106$	−1.34385e11	−0.975365
$107$	2.84799e11	1.96304	0.981518	−	0.191370i	$-0.0612930\pi$
$107$	2.84799e11	1.96304	0.981518	+	0.191370i	$0.0612930\pi$
$108$	8.00781e10	0.524425
$109$	−2.87040e11	−1.78688	−0.893442	−	0.449179i	$-0.851717\pi$
$109$	−2.87040e11	−1.78688	−0.893442	+	0.449179i	$0.851717\pi$
$110$	2.55851e10	0.151470
$111$	9.96359e10	0.561228
$112$	1.76234e10	0.0944911
$113$	−2.68972e11	−1.37333	−0.686667	−	0.726972i	$-0.740927\pi$
$113$	−2.68972e11	−1.37333	−0.686667	+	0.726972i	$0.740927\pi$
$114$	−9.57417e10	−0.465719
$115$	1.94697e11	0.902654
$116$	−1.73903e11	−0.768757
$117$	1.29273e10	0.0545112
$118$	−2.92484e11	−1.17693
$119$	−1.55060e11	−0.595650
$120$	9.53745e10	0.349893
$121$	−2.73479e11	−0.958526
$122$	2.12458e11	0.711695
$123$	3.67812e11	1.17801
$124$	−5.25954e10	−0.161112
$125$	−3.20708e11	−0.939950
$126$	1.09345e10	0.0306733
$127$	7.86054e9	0.0211121	0.0105561	−	0.999944i	$-0.496640\pi$
$127$	7.86054e9	0.0211121	0.0105561	+	0.999944i	$0.496640\pi$
$128$	−3.43597e10	−0.0883883
$129$	7.20283e11	1.77525
$130$	1.49550e11	0.353263
$131$	−3.64669e10	−0.0825861	−0.0412930	−	0.999147i	$-0.513148\pi$
$131$	−3.64669e10	−0.0825861	−0.0412930	+	0.999147i	$0.513148\pi$
$132$	4.41107e10	0.0958049
$133$	−1.26983e11	−0.264583
$134$	9.21005e10	0.184156
$135$	5.74779e11	1.10323
$136$	3.02315e11	0.557180
$137$	3.73780e11	0.661687	0.330844	−	0.943686i	$-0.392667\pi$
$137$	3.73780e11	0.661687	0.330844	+	0.943686i	$0.392667\pi$
$138$	3.35674e11	0.570929
$139$	2.84074e11	0.464355	0.232178	−	0.972673i	$-0.425415\pi$
$139$	2.84074e11	0.464355	0.232178	+	0.972673i	$0.425415\pi$
$140$	1.26496e11	0.198780
$141$	−2.07244e11	−0.313167
$142$	1.39059e11	0.202122
$143$	6.91669e10	0.0967275
$144$	−2.13186e10	−0.0286923
$145$	−1.24823e12	−1.61723
$146$	−7.50411e11	−0.936178
$147$	−1.11860e11	−0.134410
$148$	−2.57644e11	−0.298251
$149$	−1.03402e11	−0.115346	−0.0576732	−	0.998336i	$-0.518368\pi$
$149$	−1.03402e11	−0.115346	−0.0576732	+	0.998336i	$0.518368\pi$
$150$	6.58231e10	0.0707745
$151$	−1.54608e12	−1.60273	−0.801364	−	0.598177i	$-0.795892\pi$
$151$	−1.54608e12	−1.60273	−0.801364	+	0.598177i	$0.795892\pi$
$152$	2.47574e11	0.247495
$153$	1.87572e11	0.180870
$154$	5.85045e10	0.0544284
$155$	−3.77516e11	−0.338931
$156$	2.57836e11	0.223439
$157$	−8.42897e11	−0.705223	−0.352611	−	0.935770i	$-0.614706\pi$
$157$	−8.42897e11	−0.705223	−0.352611	+	0.935770i	$0.614706\pi$
$158$	9.20379e11	0.743623
$159$	−1.66301e12	−1.29781
$160$	−2.46625e11	−0.185942
$161$	4.45207e11	0.324355
$162$	8.75716e11	0.616639
$163$	6.73322e11	0.458343	0.229172	−	0.973386i	$-0.426398\pi$
$163$	6.73322e11	0.458343	0.229172	+	0.973386i	$0.426398\pi$
$164$	−9.51109e11	−0.626022
$165$	3.16615e11	0.201544
$166$	1.78488e11	0.109904
$167$	1.75163e12	1.04352	0.521760	−	0.853092i	$-0.325276\pi$
$167$	1.75163e12	1.04352	0.521760	+	0.853092i	$0.325276\pi$
$168$	2.18090e11	0.125729
$169$	−1.38787e12	−0.774409
$170$	2.16994e12	1.17214
$171$	1.53608e11	0.0803408
$172$	−1.86255e12	−0.943412
$173$	3.10163e12	1.52172	0.760862	−	0.648914i	$-0.224777\pi$
$173$	3.10163e12	1.52172	0.760862	+	0.648914i	$0.224777\pi$
$174$	−2.15206e12	−1.02290
$175$	8.73019e10	0.0402082
$176$	−1.14064e11	−0.0509131
$177$	−3.61949e12	−1.56601
$178$	−2.49607e12	−1.04700
$179$	4.33769e12	1.76428	0.882138	−	0.470991i	$-0.156104\pi$
$179$	4.33769e12	1.76428	0.882138	+	0.470991i	$0.156104\pi$
$180$	−1.53019e11	−0.0603597
$181$	3.79736e12	1.45295	0.726474	−	0.687194i	$-0.241158\pi$
$181$	3.79736e12	1.45295	0.726474	+	0.687194i	$0.241158\pi$
$182$	3.41971e11	0.126939
$183$	2.62917e12	0.946972
$184$	−8.68005e11	−0.303406
$185$	−1.84930e12	−0.627428
$186$	−6.50868e11	−0.214374
$187$	1.00360e12	0.320944
$188$	5.35903e11	0.166425
$189$	1.31433e12	0.396428
$190$	1.77702e12	0.520653
$191$	−4.40391e12	−1.25359	−0.626795	−	0.779185i	$-0.715633\pi$
$191$	−4.40391e12	−1.25359	−0.626795	+	0.779185i	$0.715633\pi$
$192$	−4.25202e11	−0.117608
$193$	4.10216e12	1.10267	0.551337	−	0.834282i	$-0.314118\pi$
$193$	4.10216e12	1.10267	0.551337	+	0.834282i	$0.314118\pi$
$194$	8.53948e11	0.223111
$195$	1.85068e12	0.470047
$196$	2.89255e11	0.0714286
$197$	−1.81653e12	−0.436193	−0.218096	−	0.975927i	$-0.569985\pi$
$197$	−1.81653e12	−0.436193	−0.218096	+	0.975927i	$0.569985\pi$
$198$	−7.07714e10	−0.0165272
$199$	−4.43367e12	−1.00710	−0.503549	−	0.863967i	$-0.667973\pi$
$199$	−4.43367e12	−1.00710	−0.503549	+	0.863967i	$0.667973\pi$
$200$	−1.70209e11	−0.0376113
$201$	1.13974e12	0.245035
$202$	−5.72229e11	−0.119712
$203$	−2.85429e12	−0.581126
$204$	3.74115e12	0.741376
$205$	−6.82681e12	−1.31696
$206$	−3.63547e12	−0.682796
$207$	−5.38556e11	−0.0984904
$208$	−6.66729e11	−0.118741
$209$	8.21873e11	0.142561
$210$	1.56539e12	0.264494
$211$	7.55518e12	1.24363	0.621815	−	0.783164i	$-0.286396\pi$
$211$	7.55518e12	1.24363	0.621815	+	0.783164i	$0.286396\pi$
$212$	4.30031e12	0.689688
$213$	1.72086e12	0.268941
$214$	−9.11358e12	−1.38808
$215$	−1.33689e13	−1.98465
$216$	−2.56250e12	−0.370824
$217$	−8.63253e11	−0.121789
$218$	9.18527e12	1.26352
$219$	−9.28633e12	−1.24567
$220$	−8.18722e11	−0.107105
$221$	5.86623e12	0.748516
$222$	−3.18835e12	−0.396848
$223$	5.39596e12	0.655227	0.327613	−	0.944812i	$-0.393756\pi$
$223$	5.39596e12	0.655227	0.327613	+	0.944812i	$0.393756\pi$
$224$	−5.63949e11	−0.0668153
$225$	−1.05607e11	−0.0122092
$226$	8.60712e12	0.971094
$227$	−1.41713e13	−1.56052	−0.780259	−	0.625457i	$-0.784913\pi$
$227$	−1.41713e13	−1.56052	−0.780259	+	0.625457i	$0.784913\pi$
$228$	3.06373e12	0.329313
$229$	5.52026e12	0.579248	0.289624	−	0.957141i	$-0.406470\pi$
$229$	5.52026e12	0.579248	0.289624	+	0.957141i	$0.406470\pi$
$230$	−6.23031e12	−0.638273
$231$	7.23993e11	0.0724217
$232$	5.56491e12	0.543594
$233$	6.98852e12	0.666696	0.333348	−	0.942804i	$-0.391822\pi$
$233$	6.98852e12	0.666696	0.333348	+	0.942804i	$0.391822\pi$
$234$	−4.13674e11	−0.0385452
$235$	3.84657e12	0.350107
$236$	9.35949e12	0.832216
$237$	1.13897e13	0.989455
$238$	4.96192e12	0.421189
$239$	−9.35302e12	−0.775824	−0.387912	−	0.921696i	$-0.626804\pi$
$239$	−9.35302e12	−0.775824	−0.387912	+	0.921696i	$0.626804\pi$
$240$	−3.05199e12	−0.247412
$241$	7.22042e12	0.572096	0.286048	−	0.958215i	$-0.407658\pi$
$241$	7.22042e12	0.572096	0.286048	+	0.958215i	$0.407658\pi$
$242$	8.75131e12	0.677780
$243$	−3.01613e12	−0.228358
$244$	−6.79866e12	−0.503245
$245$	2.07619e12	0.150264
$246$	−1.17700e13	−0.832976
$247$	4.80402e12	0.332485
$248$	1.68305e12	0.113924
$249$	2.20879e12	0.146237
$250$	1.02627e13	0.664645
$251$	−7.61470e12	−0.482444	−0.241222	−	0.970470i	$-0.577548\pi$
$251$	−7.61470e12	−0.482444	−0.241222	+	0.970470i	$0.577548\pi$
$252$	−3.49904e11	−0.0216893
$253$	−2.88152e12	−0.174767
$254$	−2.51537e11	−0.0149285
$255$	2.68530e13	1.55963
$256$	1.09951e12	0.0625000
$257$	−1.52469e13	−0.848301	−0.424151	−	0.905592i	$-0.639427\pi$
$257$	−1.52469e13	−0.848301	−0.424151	+	0.905592i	$0.639427\pi$
$258$	−2.30490e13	−1.25529
$259$	−4.22874e12	−0.225456
$260$	−4.78560e12	−0.249795
$261$	3.45276e12	0.176459
$262$	1.16694e12	0.0583972
$263$	−6.34375e12	−0.310878	−0.155439	−	0.987846i	$-0.549679\pi$
$263$	−6.34375e12	−0.310878	−0.155439	+	0.987846i	$0.549679\pi$
$264$	−1.41154e12	−0.0677443
$265$	3.08665e13	1.45089
$266$	4.06346e12	0.187088
$267$	−3.08889e13	−1.39312
$268$	−2.94721e12	−0.130218
$269$	−1.09398e13	−0.473556	−0.236778	−	0.971564i	$-0.576091\pi$
$269$	−1.09398e13	−0.473556	−0.236778	+	0.971564i	$0.576091\pi$
$270$	−1.83929e13	−0.780100
$271$	−8.95501e12	−0.372164	−0.186082	−	0.982534i	$-0.559579\pi$
$271$	−8.95501e12	−0.372164	−0.186082	+	0.982534i	$0.559579\pi$
$272$	−9.67408e12	−0.393986
$273$	4.23189e12	0.168904
$274$	−1.19610e13	−0.467884
$275$	−5.65044e11	−0.0216647
$276$	−1.07416e13	−0.403708
$277$	−1.88381e13	−0.694063	−0.347031	−	0.937854i	$-0.612810\pi$
$277$	−1.88381e13	−0.694063	−0.347031	+	0.937854i	$0.612810\pi$
$278$	−9.09037e12	−0.328349
$279$	1.04426e12	0.0369814
$280$	−4.04788e12	−0.140559
$281$	−4.66247e13	−1.58756	−0.793782	−	0.608202i	$-0.791891\pi$
$281$	−4.66247e13	−1.58756	−0.793782	+	0.608202i	$0.791891\pi$
$282$	6.63180e12	0.221443
$283$	5.81912e13	1.90560	0.952800	−	0.303599i	$-0.0981884\pi$
$283$	5.81912e13	1.90560	0.952800	+	0.303599i	$0.0981884\pi$
$284$	−4.44989e12	−0.142922
$285$	2.19907e13	0.692774
$286$	−2.21334e12	−0.0683967
$287$	−1.56106e13	−0.473228
$288$	6.82195e11	0.0202885
$289$	5.08457e13	1.48360
$290$	3.99435e13	1.14355
$291$	1.05676e13	0.296869
$292$	2.40131e13	0.661978
$293$	2.50815e13	0.678548	0.339274	−	0.940688i	$-0.389819\pi$
$293$	2.50815e13	0.678548	0.339274	+	0.940688i	$0.389819\pi$
$294$	3.57953e12	0.0950419
$295$	6.71799e13	1.75073
$296$	8.24462e12	0.210895
$297$	−8.50674e12	−0.213601
$298$	3.30886e12	0.0815622
$299$	−1.68431e13	−0.407596
$300$	−2.10634e12	−0.0500451
$301$	−3.05702e13	−0.713152
$302$	4.94747e13	1.13330
$303$	−7.08133e12	−0.159287
$304$	−7.92238e12	−0.175005
$305$	−4.87989e13	−1.05867
$306$	−6.00231e12	−0.127894
$307$	−6.94186e13	−1.45283	−0.726415	−	0.687257i	$-0.758815\pi$
$307$	−6.94186e13	−1.45283	−0.726415	+	0.687257i	$0.758815\pi$
$308$	−1.87214e12	−0.0384867
$309$	−4.49889e13	−0.908519
$310$	1.20805e13	0.239660
$311$	1.60513e13	0.312844	0.156422	−	0.987690i	$-0.450004\pi$
$311$	1.60513e13	0.312844	0.156422	+	0.987690i	$0.450004\pi$
$312$	−8.25077e12	−0.157995
$313$	1.71739e13	0.323129	0.161564	−	0.986862i	$-0.448346\pi$
$313$	1.71739e13	0.323129	0.161564	+	0.986862i	$0.448346\pi$
$314$	2.69727e13	0.498668
$315$	−2.51152e12	−0.0456277
$316$	−2.94521e13	−0.525821
$317$	7.68224e12	0.134791	0.0673957	−	0.997726i	$-0.478531\pi$
$317$	7.68224e12	0.134791	0.0673957	+	0.997726i	$0.478531\pi$
$318$	5.32163e13	0.917689
$319$	1.84738e13	0.313118
$320$	7.89200e12	0.131481
$321$	−1.12781e14	−1.84696
$322$	−1.42466e13	−0.229353
$323$	6.97052e13	1.10319
$324$	−2.80229e13	−0.436029
$325$	−3.30280e12	−0.0505271
$326$	−2.15463e13	−0.324098
$327$	1.13668e14	1.68122
$328$	3.04355e13	0.442664
$329$	8.79583e12	0.125805
$330$	−1.01317e13	−0.142513
$331$	−9.90492e13	−1.37024	−0.685121	−	0.728429i	$-0.740251\pi$
$331$	−9.90492e13	−1.37024	−0.685121	+	0.728429i	$0.740251\pi$
$332$	−5.71162e12	−0.0777142
$333$	5.11540e12	0.0684599
$334$	−5.60520e13	−0.737880
$335$	−2.11543e13	−0.273938
$336$	−6.97887e12	−0.0889036
$337$	−7.25438e13	−0.909150	−0.454575	−	0.890708i	$-0.650209\pi$
$337$	−7.25438e13	−0.909150	−0.454575	+	0.890708i	$0.650209\pi$
$338$	4.44117e13	0.547590
$339$	1.06513e14	1.29213
$340$	−6.94379e13	−0.828825
$341$	5.58723e12	0.0656218
$342$	−4.91546e12	−0.0568095
$343$	4.74756e12	0.0539949
$344$	5.96016e13	0.667093
$345$	−7.71000e13	−0.849278
$346$	−9.92520e13	−1.07602
$347$	−4.22454e13	−0.450783	−0.225392	−	0.974268i	$-0.572366\pi$
$347$	−4.22454e13	−0.450783	−0.225392	+	0.974268i	$0.572366\pi$
$348$	6.88658e13	0.723298
$349$	5.11577e13	0.528897	0.264448	−	0.964400i	$-0.414810\pi$
$349$	5.11577e13	0.528897	0.264448	+	0.964400i	$0.414810\pi$
$350$	−2.79366e12	−0.0284315
$351$	−4.97237e13	−0.498166
$352$	3.65005e12	0.0360010
$353$	−1.16007e14	−1.12648	−0.563238	−	0.826295i	$-0.690444\pi$
$353$	−1.16007e14	−1.12648	−0.563238	+	0.826295i	$0.690444\pi$
$354$	1.15824e14	1.10734
$355$	−3.19401e13	−0.300664
$356$	7.98742e13	0.740341
$357$	6.14038e13	0.560428
$358$	−1.38806e14	−1.24753
$359$	7.25252e13	0.641903	0.320952	−	0.947096i	$-0.395997\pi$
$359$	7.25252e13	0.641903	0.320952	+	0.947096i	$0.395997\pi$
$360$	4.89662e12	0.0426808
$361$	−5.94066e13	−0.509971
$362$	−1.21516e14	−1.02739
$363$	1.08298e14	0.901845
$364$	−1.09431e13	−0.0897598
$365$	1.72360e14	1.39260
$366$	−8.41334e13	−0.669611
$367$	−9.10953e13	−0.714221	−0.357110	−	0.934062i	$-0.616238\pi$
$367$	−9.10953e13	−0.714221	−0.357110	+	0.934062i	$0.616238\pi$
$368$	2.77761e13	0.214540
$369$	1.88838e13	0.143696
$370$	5.91777e13	0.443658
$371$	7.05813e13	0.521355
$372$	2.08278e13	0.151585
$373$	2.50342e14	1.79529	0.897645	−	0.440719i	$-0.145276\pi$
$373$	2.50342e14	1.79529	0.897645	+	0.440719i	$0.145276\pi$
$374$	−3.21151e13	−0.226942
$375$	1.27000e14	0.884368
$376$	−1.71489e13	−0.117680
$377$	1.07984e14	0.730264
$378$	−4.20585e13	−0.280317
$379$	7.53223e13	0.494775	0.247388	−	0.968917i	$-0.420428\pi$
$379$	7.53223e13	0.494775	0.247388	+	0.968917i	$0.420428\pi$
$380$	−5.68648e13	−0.368157
$381$	−3.11278e12	−0.0198637
$382$	1.40925e14	0.886421
$383$	−2.45887e12	−0.0152455	−0.00762277	−	0.999971i	$-0.502426\pi$
$383$	−2.45887e12	−0.0152455	−0.00762277	+	0.999971i	$0.502426\pi$
$384$	1.36065e13	0.0831617
$385$	−1.34378e13	−0.0809641
$386$	−1.31269e14	−0.779709
$387$	3.69800e13	0.216549
$388$	−2.73263e13	−0.157764
$389$	7.45984e13	0.424626	0.212313	−	0.977202i	$-0.431900\pi$
$389$	7.45984e13	0.424626	0.212313	+	0.977202i	$0.431900\pi$
$390$	−5.92218e13	−0.332373
$391$	−2.44389e14	−1.35241
$392$	−9.25615e12	−0.0505076
$393$	1.44409e13	0.0777025
$394$	5.81290e13	0.308435
$395$	−2.11400e14	−1.10617
$396$	2.26468e12	0.0116865
$397$	−1.82483e14	−0.928698	−0.464349	−	0.885652i	$-0.653712\pi$
$397$	−1.82483e14	−0.928698	−0.464349	+	0.885652i	$0.653712\pi$
$398$	1.41878e14	0.712126
$399$	5.02853e13	0.248937
$400$	5.44670e12	0.0265952
$401$	−2.23181e14	−1.07489	−0.537444	−	0.843300i	$-0.680610\pi$
$401$	−2.23181e14	−1.07489	−0.537444	+	0.843300i	$0.680610\pi$
$402$	−3.64718e13	−0.173266
$403$	3.26586e13	0.153045
$404$	1.83113e13	0.0846490
$405$	−2.01141e14	−0.917272
$406$	9.13374e13	0.410918
$407$	2.73697e13	0.121479
$408$	−1.19717e14	−0.524232
$409$	−2.90743e14	−1.25612	−0.628060	−	0.778165i	$-0.716151\pi$
$409$	−2.90743e14	−1.25612	−0.628060	+	0.778165i	$0.716151\pi$
$410$	2.18458e14	0.931229
$411$	−1.48017e14	−0.622560
$412$	1.16335e14	0.482810
$413$	1.53618e14	0.629096
$414$	1.72338e13	0.0696432
$415$	−4.09965e13	−0.163487
$416$	2.13353e13	0.0839626
$417$	−1.12493e14	−0.436897
$418$	−2.62999e13	−0.100806
$419$	−9.66047e13	−0.365444	−0.182722	−	0.983165i	$-0.558491\pi$
$419$	−9.66047e13	−0.365444	−0.182722	+	0.983165i	$0.558491\pi$
$420$	−5.00925e13	−0.187026
$421$	2.51914e14	0.928326	0.464163	−	0.885750i	$-0.346355\pi$
$421$	2.51914e14	0.928326	0.464163	+	0.885750i	$0.346355\pi$
$422$	−2.41766e14	−0.879379
$423$	−1.06401e13	−0.0382009
$424$	−1.37610e14	−0.487683
$425$	−4.79229e13	−0.167650
$426$	−5.50674e13	−0.190170
$427$	−1.11587e14	−0.380417
$428$	2.91635e14	0.981518
$429$	−2.73901e13	−0.0910077
$430$	4.27804e14	1.40336
$431$	−8.35178e13	−0.270492	−0.135246	−	0.990812i	$-0.543182\pi$
$431$	−8.35178e13	−0.270492	−0.135246	+	0.990812i	$0.543182\pi$
$432$	8.20000e13	0.262212
$433$	−1.79811e14	−0.567717	−0.283859	−	0.958866i	$-0.591615\pi$
$433$	−1.79811e14	−0.567717	−0.283859	+	0.958866i	$0.591615\pi$
$434$	2.76241e13	0.0861181
$435$	4.94300e14	1.52160
$436$	−2.93929e14	−0.893442
$437$	−2.00137e14	−0.600731
$438$	2.97163e14	0.880819
$439$	−1.09961e14	−0.321874	−0.160937	−	0.986965i	$-0.551452\pi$
$439$	−1.09961e14	−0.321874	−0.160937	+	0.986965i	$0.551452\pi$
$440$	2.61991e13	0.0757350
$441$	−5.74300e12	−0.0163956
$442$	−1.87719e14	−0.529281
$443$	3.82052e14	1.06390	0.531951	−	0.846775i	$-0.321459\pi$
$443$	3.82052e14	1.06390	0.531951	+	0.846775i	$0.321459\pi$
$444$	1.02027e14	0.280614
$445$	5.73316e14	1.55745
$446$	−1.72671e14	−0.463315
$447$	4.09472e13	0.108526
$448$	1.80464e13	0.0472456
$449$	2.29943e14	0.594654	0.297327	−	0.954776i	$-0.403905\pi$
$449$	2.29943e14	0.594654	0.297327	+	0.954776i	$0.403905\pi$
$450$	3.37942e12	0.00863323
$451$	1.01037e14	0.254981
$452$	−2.75428e14	−0.686667
$453$	6.12249e14	1.50795
$454$	4.53483e14	1.10345
$455$	−7.85465e13	−0.188827
$456$	−9.80395e13	−0.232860
$457$	6.80630e13	0.159725	0.0798624	−	0.996806i	$-0.474552\pi$
$457$	6.80630e13	0.159725	0.0798624	+	0.996806i	$0.474552\pi$
$458$	−1.76648e14	−0.409590
$459$	−7.21479e14	−1.65293
$460$	1.99370e14	0.451327
$461$	3.80319e14	0.850732	0.425366	−	0.905021i	$-0.360145\pi$
$461$	3.80319e14	0.850732	0.425366	+	0.905021i	$0.360145\pi$
$462$	−2.31678e13	−0.0512099
$463$	−6.53296e14	−1.42697	−0.713484	−	0.700671i	$-0.752884\pi$
$463$	−6.53296e14	−1.42697	−0.713484	+	0.700671i	$0.752884\pi$
$464$	−1.78077e14	−0.384379
$465$	1.49496e14	0.318889
$466$	−2.23633e14	−0.471425
$467$	2.90414e14	0.605027	0.302513	−	0.953145i	$-0.402174\pi$
$467$	2.90414e14	0.605027	0.302513	+	0.953145i	$0.402174\pi$
$468$	1.32376e13	0.0272556
$469$	−4.83729e13	−0.0984354
$470$	−1.23090e14	−0.247563
$471$	3.33787e14	0.663521
$472$	−2.99504e14	−0.588466
$473$	1.97859e14	0.384256
$474$	−3.64470e14	−0.699651
$475$	−3.92454e13	−0.0744688
$476$	−1.58781e14	−0.297825
$477$	−8.53804e13	−0.158310
$478$	2.99297e14	0.548590
$479$	−8.15890e14	−1.47838	−0.739191	−	0.673496i	$-0.764792\pi$
$479$	−8.15890e14	−1.47838	−0.739191	+	0.673496i	$0.764792\pi$
$480$	9.76635e13	0.174947
$481$	1.59982e14	0.283317
$482$	−2.31053e14	−0.404533
$483$	−1.76302e14	−0.305175
$484$	−2.80042e14	−0.479263
$485$	−1.96141e14	−0.331886
$486$	9.65163e13	0.161473
$487$	−6.52014e14	−1.07857	−0.539284	−	0.842124i	$-0.681305\pi$
$487$	−6.52014e14	−1.07857	−0.539284	+	0.842124i	$0.681305\pi$
$488$	2.17557e14	0.355848
$489$	−2.66636e14	−0.431240
$490$	−6.64382e13	−0.106253
$491$	−6.53305e14	−1.03316	−0.516580	−	0.856239i	$-0.672795\pi$
$491$	−6.53305e14	−1.03316	−0.516580	+	0.856239i	$0.672795\pi$
$492$	3.76639e14	0.589003
$493$	1.56682e15	2.42304
$494$	−1.53729e14	−0.235102
$495$	1.62553e13	0.0245848
$496$	−5.38577e13	−0.0805561
$497$	−7.30364e13	−0.108039
$498$	−7.06813e13	−0.103405
$499$	−8.96816e13	−0.129763	−0.0648814	−	0.997893i	$-0.520667\pi$
$499$	−8.96816e13	−0.129763	−0.0648814	+	0.997893i	$0.520667\pi$
$500$	−3.28405e14	−0.469975
$501$	−6.93644e14	−0.981813
$502$	2.43670e14	0.341140
$503$	3.91572e14	0.542235	0.271117	−	0.962546i	$-0.412607\pi$
$503$	3.91572e14	0.542235	0.271117	+	0.962546i	$0.412607\pi$
$504$	1.11969e13	0.0153367
$505$	1.31434e14	0.178076
$506$	9.22085e13	0.123579
$507$	5.49595e14	0.728616
$508$	8.04920e12	0.0105561
$509$	3.95207e14	0.512716	0.256358	−	0.966582i	$-0.417477\pi$
$509$	3.95207e14	0.512716	0.256358	+	0.966582i	$0.417477\pi$
$510$	−8.59295e14	−1.10282
$511$	3.94130e14	0.500408
$512$	−3.51844e13	−0.0441942
$513$	−5.90840e14	−0.734217
$514$	4.87902e14	0.599840
$515$	8.35022e14	1.01568
$516$	7.37570e14	0.887625
$517$	−5.69293e13	−0.0677856
$518$	1.35320e14	0.159422
$519$	−1.22824e15	−1.43174
$520$	1.53139e14	0.176631
$521$	3.60802e14	0.411776	0.205888	−	0.978576i	$-0.433992\pi$
$521$	3.60802e14	0.411776	0.205888	+	0.978576i	$0.433992\pi$
$522$	−1.10488e14	−0.124775
$523$	1.75686e14	0.196327	0.0981633	−	0.995170i	$-0.468703\pi$
$523$	1.75686e14	0.196327	0.0981633	+	0.995170i	$0.468703\pi$
$524$	−3.73421e13	−0.0412930
$525$	−3.45715e13	−0.0378305
$526$	2.03000e14	0.219824
$527$	4.73868e14	0.507807
$528$	4.51694e13	0.0479024
$529$	−2.51121e14	−0.263559
$530$	−9.87727e14	−1.02593
$531$	−1.85828e14	−0.191025
$532$	−1.30031e14	−0.132292
$533$	5.90581e14	0.594676
$534$	9.88444e14	0.985088
$535$	2.09328e15	2.06481
$536$	9.43109e13	0.0920779
$537$	−1.71772e15	−1.65995
$538$	3.50073e14	0.334855
$539$	−3.07277e13	−0.0290932
$540$	5.88574e14	0.551614
$541$	−3.77999e14	−0.350676	−0.175338	−	0.984508i	$-0.556102\pi$
$541$	−3.77999e14	−0.350676	−0.175338	+	0.984508i	$0.556102\pi$
$542$	2.86560e14	0.263160
$543$	−1.50376e15	−1.36703
$544$	3.09570e14	0.278590
$545$	−2.10974e15	−1.87953
$546$	−1.35421e14	−0.119433
$547$	−9.07524e14	−0.792370	−0.396185	−	0.918171i	$-0.629666\pi$
$547$	−9.07524e14	−0.792370	−0.396185	+	0.918171i	$0.629666\pi$
$548$	3.82751e14	0.330844
$549$	1.34984e14	0.115514
$550$	1.80814e13	0.0153193
$551$	1.28311e15	1.07629
$552$	3.43730e14	0.285465
$553$	−4.83400e14	−0.397483
$554$	6.02820e14	0.490777
$555$	7.32324e14	0.590326
$556$	2.90892e14	0.232178
$557$	2.13629e15	1.68833	0.844164	−	0.536086i	$-0.180098\pi$
$557$	2.13629e15	1.68833	0.844164	+	0.536086i	$0.180098\pi$
$558$	−3.34162e13	−0.0261498
$559$	1.15653e15	0.896173
$560$	1.29532e14	0.0993901
$561$	−3.97424e14	−0.301966
$562$	1.49199e15	1.12258
$563$	4.39190e14	0.327232	0.163616	−	0.986524i	$-0.447684\pi$
$563$	4.39190e14	0.327232	0.163616	+	0.986524i	$0.447684\pi$
$564$	−2.12218e14	−0.156584
$565$	−1.97695e15	−1.44454
$566$	−1.86212e15	−1.34746
$567$	−4.59943e14	−0.329607
$568$	1.42397e14	0.101061
$569$	−1.40571e15	−0.988045	−0.494023	−	0.869449i	$-0.664474\pi$
$569$	−1.40571e15	−0.988045	−0.494023	+	0.869449i	$0.664474\pi$
$570$	−7.03701e14	−0.489865
$571$	1.59775e15	1.10157	0.550784	−	0.834648i	$-0.314329\pi$
$571$	1.59775e15	1.10157	0.550784	+	0.834648i	$0.314329\pi$
$572$	7.08269e13	0.0483638
$573$	1.74395e15	1.17946
$574$	4.99541e14	0.334623
$575$	1.37596e14	0.0912919
$576$	−2.18302e13	−0.0143461
$577$	−2.54900e15	−1.65922	−0.829609	−	0.558345i	$-0.811437\pi$
$577$	−2.54900e15	−1.65922	−0.829609	+	0.558345i	$0.811437\pi$
$578$	−1.62706e15	−1.04906
$579$	−1.62446e15	−1.03747
$580$	−1.27819e15	−0.808615
$581$	−9.37454e13	−0.0587464
$582$	−3.38163e14	−0.209918
$583$	−4.56824e14	−0.280913
$584$	−7.68421e14	−0.468089
$585$	9.50157e13	0.0573374
$586$	−8.02607e14	−0.479806
$587$	−6.31843e14	−0.374196	−0.187098	−	0.982341i	$-0.559908\pi$
$587$	−6.31843e14	−0.374196	−0.187098	+	0.982341i	$0.559908\pi$
$588$	−1.14545e14	−0.0672048
$589$	3.88064e14	0.225564
$590$	−2.14976e15	−1.23795
$591$	7.19346e14	0.410400
$592$	−2.63828e14	−0.149125
$593$	−1.12198e15	−0.628325	−0.314162	−	0.949369i	$-0.601724\pi$
$593$	−1.12198e15	−0.628325	−0.314162	+	0.949369i	$0.601724\pi$
$594$	2.72216e14	0.151038
$595$	−1.13969e15	−0.626533
$596$	−1.05884e14	−0.0576732
$597$	1.75574e15	0.947546
$598$	5.38978e14	0.288214
$599$	1.20395e15	0.637912	0.318956	−	0.947770i	$-0.396668\pi$
$599$	1.20395e15	0.637912	0.318956	+	0.947770i	$0.396668\pi$
$600$	6.74029e13	0.0353872
$601$	2.85268e15	1.48403	0.742017	−	0.670381i	$-0.233869\pi$
$601$	2.85268e15	1.48403	0.742017	+	0.670381i	$0.233869\pi$
$602$	9.78246e14	0.504275
$603$	5.85154e13	0.0298900
$604$	−1.58319e15	−0.801364
$605$	−2.01007e15	−1.00822
$606$	2.26603e14	0.112633
$607$	3.41662e15	1.68290	0.841450	−	0.540335i	$-0.181703\pi$
$607$	3.41662e15	1.68290	0.841450	+	0.540335i	$0.181703\pi$
$608$	2.53516e14	0.123747
$609$	1.13030e15	0.546762
$610$	1.56157e15	0.748594
$611$	−3.32764e14	−0.158092
$612$	1.92074e14	0.0904348
$613$	−2.35909e14	−0.110081	−0.0550403	−	0.998484i	$-0.517529\pi$
$613$	−2.35909e14	−0.110081	−0.0550403	+	0.998484i	$0.517529\pi$
$614$	2.22139e15	1.02731
$615$	2.70342e15	1.23908
$616$	5.99086e13	0.0272142
$617$	2.35156e14	0.105873	0.0529367	−	0.998598i	$-0.483142\pi$
$617$	2.35156e14	0.105873	0.0529367	+	0.998598i	$0.483142\pi$
$618$	1.43965e15	0.642420
$619$	7.01595e14	0.310305	0.155152	−	0.987891i	$-0.450413\pi$
$619$	7.01595e14	0.310305	0.155152	+	0.987891i	$0.450413\pi$
$620$	−3.86576e14	−0.169465
$621$	2.07151e15	0.900082
$622$	−5.13641e14	−0.221214
$623$	1.31098e15	0.559645
$624$	2.64025e14	0.111720
$625$	−2.61084e15	−1.09506
$626$	−5.49566e14	−0.228487
$627$	−3.25462e14	−0.134131
$628$	−8.63126e14	−0.352611
$629$	2.32130e15	0.940052
$630$	8.03686e13	0.0322636
$631$	−3.16919e15	−1.26121	−0.630604	−	0.776104i	$-0.717193\pi$
$631$	−3.16919e15	−1.26121	−0.630604	+	0.776104i	$0.717193\pi$
$632$	9.42468e14	0.371812
$633$	−2.99185e15	−1.17009
$634$	−2.45832e14	−0.0953118
$635$	5.77750e13	0.0222067
$636$	−1.70292e15	−0.648904
$637$	−1.79610e14	−0.0678520
$638$	−5.91163e14	−0.221408
$639$	8.83503e13	0.0328060
$640$	−2.52544e14	−0.0929710
$641$	8.56125e14	0.312477	0.156238	−	0.987719i	$-0.450063\pi$
$641$	8.56125e14	0.312477	0.156238	+	0.987719i	$0.450063\pi$
$642$	3.60898e15	1.30600
$643$	−1.00145e15	−0.359309	−0.179655	−	0.983730i	$-0.557498\pi$
$643$	−1.00145e15	−0.359309	−0.179655	+	0.983730i	$0.557498\pi$
$644$	4.55892e14	0.162177
$645$	5.29408e15	1.86729
$646$	−2.23057e15	−0.780075
$647$	−2.19290e15	−0.760405	−0.380202	−	0.924903i	$-0.624146\pi$
$647$	−2.19290e15	−0.760405	−0.380202	+	0.924903i	$0.624146\pi$
$648$	8.96733e14	0.308319
$649$	−9.94263e14	−0.338966
$650$	1.05690e14	0.0357280
$651$	3.41848e14	0.114588
$652$	6.89482e14	0.229172
$653$	−2.59040e15	−0.853777	−0.426889	−	0.904304i	$-0.640390\pi$
$653$	−2.59040e15	−0.853777	−0.426889	+	0.904304i	$0.640390\pi$
$654$	−3.63737e15	−1.18880
$655$	−2.68032e14	−0.0868679
$656$	−9.73936e14	−0.313011
$657$	−4.76769e14	−0.151949
$658$	−2.81466e14	−0.0889579
$659$	4.13777e15	1.29687	0.648436	−	0.761269i	$-0.275423\pi$
$659$	4.13777e15	1.29687	0.648436	+	0.761269i	$0.275423\pi$
$660$	3.24214e14	0.100772
$661$	−3.99704e15	−1.23206	−0.616028	−	0.787724i	$-0.711259\pi$
$661$	−3.99704e15	−1.23206	−0.616028	+	0.787724i	$0.711259\pi$
$662$	3.16958e15	0.968907
$663$	−2.32303e15	−0.704254
$664$	1.82772e14	0.0549522
$665$	−9.33326e14	−0.278301
$666$	−1.63693e14	−0.0484085
$667$	−4.49863e15	−1.31944
$668$	1.79366e15	0.521760
$669$	−2.13680e15	−0.616481
$670$	6.76938e14	0.193704
$671$	7.22224e14	0.204974
$672$	2.23324e14	0.0628643
$673$	−2.97888e15	−0.831707	−0.415854	−	0.909432i	$-0.636517\pi$
$673$	−2.97888e15	−0.831707	−0.415854	+	0.909432i	$0.636517\pi$
$674$	2.32140e15	0.642866
$675$	4.06207e14	0.111577
$676$	−1.42117e15	−0.387205
$677$	−3.51925e15	−0.951069	−0.475534	−	0.879697i	$-0.657745\pi$
$677$	−3.51925e15	−0.951069	−0.475534	+	0.879697i	$0.657745\pi$
$678$	−3.40842e15	−0.913670
$679$	−4.48509e14	−0.119258
$680$	2.22201e15	0.586068
$681$	5.61185e15	1.46824
$682$	−1.78792e14	−0.0464016
$683$	−3.86192e15	−0.994236	−0.497118	−	0.867683i	$-0.665608\pi$
$683$	−3.86192e15	−0.994236	−0.497118	+	0.867683i	$0.665608\pi$
$684$	1.57295e14	0.0401704
$685$	2.74728e15	0.695993
$686$	−1.51922e14	−0.0381802
$687$	−2.18602e15	−0.544995
$688$	−1.90725e15	−0.471706
$689$	−2.67023e15	−0.655154
$690$	2.46720e15	0.600530
$691$	−1.53785e14	−0.0371351	−0.0185676	−	0.999828i	$-0.505911\pi$
$691$	−1.53785e14	−0.0371351	−0.0185676	+	0.999828i	$0.505911\pi$
$692$	3.17606e15	0.760862
$693$	3.71705e13	0.00883416
$694$	1.35185e15	0.318752
$695$	2.08795e15	0.488430
$696$	−2.20370e15	−0.511449
$697$	8.56920e15	1.97315
$698$	−1.63704e15	−0.373986
$699$	−2.76745e15	−0.627272
$700$	8.93971e13	0.0201041
$701$	4.73254e15	1.05595	0.527977	−	0.849259i	$-0.322951\pi$
$701$	4.73254e15	1.05595	0.527977	+	0.849259i	$0.322951\pi$
$702$	1.59116e15	0.352256
$703$	1.90098e15	0.417563
$704$	−1.16802e14	−0.0254565
$705$	−1.52324e15	−0.329404
$706$	3.71221e15	0.796538
$707$	3.00545e14	0.0639887
$708$	−3.70636e15	−0.783005
$709$	−3.57763e15	−0.749965	−0.374983	−	0.927032i	$-0.622351\pi$
$709$	−3.57763e15	−0.749965	−0.374983	+	0.927032i	$0.622351\pi$
$710$	1.02208e15	0.212601
$711$	5.84757e14	0.120696
$712$	−2.55598e15	−0.523500
$713$	−1.36057e15	−0.276521
$714$	−1.96492e15	−0.396282
$715$	5.08377e14	0.101742
$716$	4.44179e15	0.882138
$717$	3.70379e15	0.729947
$718$	−2.32081e15	−0.453894
$719$	9.27430e14	0.180000	0.0899999	−	0.995942i	$-0.471313\pi$
$719$	9.27430e14	0.180000	0.0899999	+	0.995942i	$0.471313\pi$
$720$	−1.56692e14	−0.0301799
$721$	1.90942e15	0.364970
$722$	1.90101e15	0.360604
$723$	−2.85929e15	−0.538266
$724$	3.88850e15	0.726474
$725$	−8.82148e14	−0.163562
$726$	−3.46552e15	−0.637701
$727$	−5.15310e15	−0.941087	−0.470543	−	0.882377i	$-0.655942\pi$
$727$	−5.15310e15	−0.941087	−0.470543	+	0.882377i	$0.655942\pi$
$728$	3.50178e14	0.0634697
$729$	6.04222e15	1.08691
$730$	−5.51552e15	−0.984715
$731$	1.67810e16	2.97353
$732$	2.69227e15	0.473486
$733$	3.48423e15	0.608184	0.304092	−	0.952643i	$-0.401647\pi$
$733$	3.48423e15	0.608184	0.304092	+	0.952643i	$0.401647\pi$
$734$	2.91505e15	0.505030
$735$	−8.22172e14	−0.141378
$736$	−8.88837e14	−0.151703
$737$	3.13084e14	0.0530383
$738$	−6.04281e14	−0.101608
$739$	9.61035e14	0.160396	0.0801982	−	0.996779i	$-0.474445\pi$
$739$	9.61035e14	0.160396	0.0801982	+	0.996779i	$0.474445\pi$
$740$	−1.89369e15	−0.313714
$741$	−1.90239e15	−0.312824
$742$	−2.25860e15	−0.368653
$743$	−1.03646e16	−1.67925	−0.839623	−	0.543169i	$-0.817224\pi$
$743$	−1.03646e16	−1.67925	−0.839623	+	0.543169i	$0.817224\pi$
$744$	−6.66489e14	−0.107187
$745$	−7.60004e14	−0.121327
$746$	−8.01094e15	−1.26946
$747$	1.13401e14	0.0178384
$748$	1.02768e15	0.160472
$749$	4.78662e15	0.741958
$750$	−4.06401e15	−0.625343
$751$	9.38986e15	1.43430	0.717149	−	0.696920i	$-0.245447\pi$
$751$	9.38986e15	1.43430	0.717149	+	0.696920i	$0.245447\pi$
$752$	5.48765e14	0.0832125
$753$	3.01542e15	0.453916
$754$	−3.45547e15	−0.516375
$755$	−1.13637e16	−1.68582
$756$	1.34587e15	0.198214
$757$	−1.18986e16	−1.73968	−0.869838	−	0.493337i	$-0.835777\pi$
$757$	−1.18986e16	−1.73968	−0.869838	+	0.493337i	$0.835777\pi$
$758$	−2.41031e15	−0.349859
$759$	1.14108e15	0.164432
$760$	1.81967e15	0.260326
$761$	8.71686e15	1.23807	0.619034	−	0.785364i	$-0.287524\pi$
$761$	8.71686e15	1.23807	0.619034	+	0.785364i	$0.287524\pi$
$762$	9.96088e13	0.0140458
$763$	−4.82428e15	−0.675379
$764$	−4.50961e15	−0.626795
$765$	1.37866e15	0.190247
$766$	7.86840e13	0.0107802
$767$	−5.81168e15	−0.790546
$768$	−4.35407e14	−0.0588042
$769$	9.71386e15	1.30256	0.651279	−	0.758838i	$-0.274233\pi$
$769$	9.71386e15	1.30256	0.651279	+	0.758838i	$0.274233\pi$
$770$	4.30008e14	0.0572503
$771$	6.03778e15	0.798139
$772$	4.20061e15	0.551337
$773$	−8.46809e15	−1.10357	−0.551783	−	0.833988i	$-0.686052\pi$
$773$	−8.46809e15	−1.10357	−0.551783	+	0.833988i	$0.686052\pi$
$774$	−1.18336e15	−0.153123
$775$	−2.66797e14	−0.0342785
$776$	8.74442e14	0.111556
$777$	1.67458e15	0.212124
$778$	−2.38715e15	−0.300256
$779$	7.01756e15	0.876457
$780$	1.89510e15	0.235024
$781$	4.72714e14	0.0582127
$782$	7.82045e15	0.956301
$783$	−1.32807e16	−1.61262
$784$	2.96197e14	0.0357143
$785$	−6.19529e15	−0.741786
$786$	−4.62109e14	−0.0549440
$787$	7.87091e14	0.0929317	0.0464658	−	0.998920i	$-0.485204\pi$
$787$	7.87091e14	0.0929317	0.0464658	+	0.998920i	$0.485204\pi$
$788$	−1.86013e15	−0.218096
$789$	2.51213e15	0.292495
$790$	6.76479e15	0.782177
$791$	−4.52062e15	−0.519072
$792$	−7.24699e13	−0.00826360
$793$	4.22155e15	0.478046
$794$	5.83945e15	0.656689
$795$	−1.22231e16	−1.36510
$796$	−4.54008e15	−0.503549
$797$	−1.37130e16	−1.51047	−0.755234	−	0.655455i	$-0.772477\pi$
$797$	−1.37130e16	−1.51047	−0.755234	+	0.655455i	$0.772477\pi$
$798$	−1.60913e15	−0.176025
$799$	−4.82832e15	−0.524552
$800$	−1.74294e14	−0.0188056
$801$	−1.58586e15	−0.169936
$802$	7.14179e15	0.760060
$803$	−2.55093e15	−0.269626
$804$	1.16710e15	0.122518
$805$	3.27227e15	0.341171
$806$	−1.04507e15	−0.108219
$807$	4.33215e15	0.445553
$808$	−5.85962e14	−0.0598559
$809$	−1.26723e16	−1.28570	−0.642851	−	0.765991i	$-0.722248\pi$
$809$	−1.26723e16	−1.28570	−0.642851	+	0.765991i	$0.722248\pi$
$810$	6.43651e15	0.648609
$811$	9.14835e15	0.915647	0.457824	−	0.889043i	$-0.348629\pi$
$811$	9.14835e15	0.915647	0.457824	+	0.889043i	$0.348629\pi$
$812$	−2.92280e15	−0.290563
$813$	3.54618e15	0.350157
$814$	−8.75830e14	−0.0858985
$815$	4.94892e15	0.482107
$816$	3.83093e15	0.370688
$817$	1.37424e16	1.32082
$818$	9.30378e15	0.888211
$819$	2.17269e14	0.0206033
$820$	−6.99065e15	−0.658479
$821$	4.71261e15	0.440934	0.220467	−	0.975394i	$-0.429242\pi$
$821$	4.71261e15	0.440934	0.220467	+	0.975394i	$0.429242\pi$
$822$	4.73654e15	0.440216
$823$	−9.43675e15	−0.871211	−0.435606	−	0.900138i	$-0.643466\pi$
$823$	−9.43675e15	−0.871211	−0.435606	+	0.900138i	$0.643466\pi$
$824$	−3.72272e15	−0.341398
$825$	2.23757e14	0.0203836
$826$	−4.91578e15	−0.444838
$827$	7.74446e15	0.696163	0.348082	−	0.937464i	$-0.386833\pi$
$827$	7.74446e15	0.696163	0.348082	+	0.937464i	$0.386833\pi$
$828$	−5.51481e14	−0.0492452
$829$	5.29253e15	0.469476	0.234738	−	0.972059i	$-0.424577\pi$
$829$	5.29253e15	0.469476	0.234738	+	0.972059i	$0.424577\pi$
$830$	1.31189e15	0.115603
$831$	7.45989e15	0.653021
$832$	−6.82730e14	−0.0593705
$833$	−2.60609e15	−0.225135
$834$	3.59979e15	0.308933
$835$	1.28744e16	1.09762
$836$	8.41598e14	0.0712804
$837$	−4.01663e15	−0.337965
$838$	3.09135e15	0.258408
$839$	−1.10248e15	−0.0915545	−0.0457772	−	0.998952i	$-0.514576\pi$
$839$	−1.10248e15	−0.0915545	−0.0457772	+	0.998952i	$0.514576\pi$
$840$	1.60296e15	0.132247
$841$	1.66409e16	1.36395
$842$	−8.06125e15	−0.656426
$843$	1.84634e16	1.49369
$844$	7.73650e15	0.621815
$845$	−1.02008e16	−0.814559
$846$	3.40483e14	0.0270121
$847$	−4.59635e15	−0.362289
$848$	4.40352e15	0.344844
$849$	−2.30437e16	−1.79292
$850$	1.53353e15	0.118547
$851$	−6.66489e15	−0.511894
$852$	1.76216e15	0.134470
$853$	2.38420e16	1.80769	0.903843	−	0.427864i	$-0.140734\pi$
$853$	2.38420e16	1.80769	0.903843	+	0.427864i	$0.140734\pi$
$854$	3.57078e15	0.268996
$855$	1.12902e15	0.0845061
$856$	−9.33231e15	−0.694038
$857$	−2.26297e16	−1.67218	−0.836091	−	0.548591i	$-0.815164\pi$
$857$	−2.26297e16	−1.67218	−0.836091	+	0.548591i	$0.815164\pi$
$858$	8.76483e14	0.0643522
$859$	−2.09295e16	−1.52685	−0.763426	−	0.645896i	$-0.776484\pi$
$859$	−2.09295e16	−1.52685	−0.763426	+	0.645896i	$0.776484\pi$
$860$	−1.36897e16	−0.992324
$861$	6.18181e15	0.445245
$862$	2.67257e15	0.191267
$863$	6.25290e15	0.444654	0.222327	−	0.974972i	$-0.428635\pi$
$863$	6.25290e15	0.444654	0.222327	+	0.974972i	$0.428635\pi$
$864$	−2.62400e15	−0.185412
$865$	2.27969e16	1.60062
$866$	5.75394e15	0.401437
$867$	−2.01349e16	−1.39587
$868$	−8.83971e14	−0.0608947
$869$	3.12871e15	0.214169
$870$	−1.58176e16	−1.07593
$871$	1.83004e15	0.123698
$872$	9.40572e15	0.631759
$873$	5.42550e14	0.0362128
$874$	6.40439e15	0.424781
$875$	−5.39014e15	−0.355268
$876$	−9.50920e15	−0.622833
$877$	−2.61229e16	−1.70029	−0.850147	−	0.526545i	$-0.823487\pi$
$877$	−2.61229e16	−1.70029	−0.850147	+	0.526545i	$0.823487\pi$
$878$	3.51877e15	0.227599
$879$	−9.93226e15	−0.638424
$880$	−8.38371e14	−0.0535527
$881$	−2.85064e16	−1.80956	−0.904782	−	0.425874i	$-0.859967\pi$
$881$	−2.85064e16	−1.80956	−0.904782	+	0.425874i	$0.859967\pi$
$882$	1.83776e14	0.0115934
$883$	−2.17014e15	−0.136052	−0.0680259	−	0.997684i	$-0.521670\pi$
$883$	−2.17014e15	−0.136052	−0.0680259	+	0.997684i	$0.521670\pi$
$884$	6.00702e15	0.374258
$885$	−2.66033e16	−1.64720
$886$	−1.22257e16	−0.752293
$887$	2.78927e16	1.70573	0.852866	−	0.522130i	$-0.174862\pi$
$887$	2.78927e16	1.70573	0.852866	+	0.522130i	$0.174862\pi$
$888$	−3.26487e15	−0.198424
$889$	1.32112e14	0.00797964
$890$	−1.83461e16	−1.10128
$891$	2.97689e15	0.177597
$892$	5.52546e15	0.327613
$893$	−3.95405e15	−0.233002
$894$	−1.31031e15	−0.0767392
$895$	3.18820e16	1.85575
$896$	−5.77484e14	−0.0334077
$897$	6.66986e15	0.383494
$898$	−7.35816e15	−0.420484
$899$	8.72280e15	0.495425
$900$	−1.08141e14	−0.00610461
$901$	−3.87444e16	−2.17382
$902$	−3.23318e15	−0.180299
$903$	1.21058e16	0.670982
$904$	8.81369e15	0.485547
$905$	2.79106e16	1.52828
$906$	−1.95920e16	−1.06628
$907$	3.25257e16	1.75949	0.879743	−	0.475449i	$-0.157714\pi$
$907$	3.25257e16	1.75949	0.879743	+	0.475449i	$0.157714\pi$
$908$	−1.45115e16	−0.780259
$909$	−3.63562e14	−0.0194302
$910$	2.51349e15	0.133521
$911$	1.74456e16	0.921161	0.460580	−	0.887618i	$-0.347641\pi$
$911$	1.74456e16	0.921161	0.460580	+	0.887618i	$0.347641\pi$
$912$	3.13726e15	0.164657
$913$	6.06748e14	0.0316533
$914$	−2.17802e15	−0.112942
$915$	1.93244e16	0.996069
$916$	5.65274e15	0.289624
$917$	−6.12899e14	−0.0312146
$918$	2.30873e16	1.16880
$919$	−7.36463e15	−0.370609	−0.185304	−	0.982681i	$-0.559327\pi$
$919$	−7.36463e15	−0.370609	−0.185304	+	0.982681i	$0.559327\pi$
$920$	−6.37983e15	−0.319136
$921$	2.74898e16	1.36692
$922$	−1.21702e16	−0.601559
$923$	2.76311e15	0.135765
$924$	7.41369e14	0.0362108
$925$	−1.30694e15	−0.0634563
$926$	2.09055e16	1.00902
$927$	−2.30977e15	−0.110823
$928$	5.69847e15	0.271797
$929$	9.28906e15	0.440439	0.220219	−	0.975450i	$-0.429323\pi$
$929$	9.28906e15	0.440439	0.220219	+	0.975450i	$0.429323\pi$
$930$	−4.78388e15	−0.225488
$931$	−2.13421e15	−0.100003
$932$	7.15624e15	0.333348
$933$	−6.35630e15	−0.294344
$934$	−9.29325e15	−0.427819
$935$	7.37643e15	0.337584
$936$	−4.23602e14	−0.0192726
$937$	7.24601e15	0.327741	0.163871	−	0.986482i	$-0.447602\pi$
$937$	7.24601e15	0.327741	0.163871	+	0.986482i	$0.447602\pi$
$938$	1.54793e15	0.0696043
$939$	−6.80087e15	−0.304021
$940$	3.93889e15	0.175053
$941$	−2.74733e16	−1.21386	−0.606928	−	0.794757i	$-0.707598\pi$
$941$	−2.74733e16	−1.21386	−0.606928	+	0.794757i	$0.707598\pi$
$942$	−1.06812e16	−0.469180
$943$	−2.46038e16	−1.07446
$944$	9.58412e15	0.416108
$945$	9.66032e15	0.416981
$946$	−6.33150e15	−0.271710
$947$	2.63315e16	1.12344	0.561722	−	0.827326i	$-0.310139\pi$
$947$	2.63315e16	1.12344	0.561722	+	0.827326i	$0.310139\pi$
$948$	1.16630e16	0.494728
$949$	−1.49107e16	−0.628831
$950$	1.25585e15	0.0526574
$951$	−3.04217e15	−0.126821
$952$	5.08101e15	0.210594
$953$	9.83093e14	0.0405120	0.0202560	−	0.999795i	$-0.493552\pi$
$953$	9.83093e14	0.0405120	0.0202560	+	0.999795i	$0.493552\pi$
$954$	2.73217e15	0.111942
$955$	−3.23688e16	−1.31858
$956$	−9.57749e15	−0.387912
$957$	−7.31564e15	−0.294603
$958$	2.61085e16	1.04537
$959$	6.28212e15	0.250094
$960$	−3.12523e15	−0.123706
$961$	−2.27703e16	−0.896171
$962$	−5.11941e15	−0.200335
$963$	−5.79026e15	−0.225296
$964$	7.39371e15	0.286048
$965$	3.01509e16	1.15984
$966$	5.64167e15	0.215791
$967$	−5.05939e16	−1.92421	−0.962105	−	0.272679i	$-0.912090\pi$
$967$	−5.05939e16	−1.92421	−0.962105	+	0.272679i	$0.912090\pi$
$968$	8.96135e15	0.338890
$969$	−2.76033e16	−1.03796
$970$	6.27651e15	0.234679
$971$	6.01147e15	0.223499	0.111749	−	0.993736i	$-0.464355\pi$
$971$	6.01147e15	0.223499	0.111749	+	0.993736i	$0.464355\pi$
$972$	−3.08852e15	−0.114179
$973$	4.77443e15	0.175510
$974$	2.08644e16	0.762663
$975$	1.30791e15	0.0475392
$976$	−6.96182e15	−0.251622
$977$	3.98575e16	1.43248	0.716242	−	0.697852i	$-0.245861\pi$
$977$	3.98575e16	1.43248	0.716242	+	0.697852i	$0.245861\pi$
$978$	8.53234e15	0.304933
$979$	−8.48508e15	−0.301544
$980$	2.12602e15	0.0751319
$981$	5.83580e15	0.205079
$982$	2.09058e16	0.730555
$983$	5.37230e16	1.86688	0.933439	−	0.358735i	$-0.116792\pi$
$983$	5.37230e16	1.86688	0.933439	+	0.358735i	$0.116792\pi$
$984$	−1.20525e16	−0.416488
$985$	−1.33515e16	−0.458808
$986$	−5.01381e16	−1.71334
$987$	−3.48315e15	−0.118366
$988$	4.91932e15	0.166242
$989$	−4.81815e16	−1.61920
$990$	−5.20170e14	−0.0173841
$991$	−6.79892e15	−0.225962	−0.112981	−	0.993597i	$-0.536040\pi$
$991$	−6.79892e15	−0.225962	−0.112981	+	0.993597i	$0.536040\pi$
$992$	1.72345e15	0.0569618
$993$	3.92235e16	1.28922
$994$	2.33717e15	0.0763949
$995$	−3.25875e16	−1.05931
$996$	2.26180e15	0.0731187
$997$	−1.25580e16	−0.403736	−0.201868	−	0.979413i	$-0.564701\pi$
$997$	−1.25580e16	−0.403736	−0.201868	+	0.979413i	$0.564701\pi$
$998$	2.86981e15	0.0917562
$999$	−1.96759e16	−0.625640

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.12.a.a.1.1	✓	1
3.2	odd	2		126.12.a.d.1.1		1
4.3	odd	2		112.12.a.b.1.1		1
7.2	even	3		98.12.c.d.67.1		2
7.3	odd	6		98.12.c.c.79.1		2
7.4	even	3		98.12.c.d.79.1		2
7.5	odd	6		98.12.c.c.67.1		2
7.6	odd	2		98.12.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.12.a.a.1.1	✓	1	1.1	even	1	trivial
98.12.a.a.1.1		1	7.6	odd	2
98.12.c.c.67.1		2	7.5	odd	6
98.12.c.c.79.1		2	7.3	odd	6
98.12.c.d.67.1		2	7.2	even	3
98.12.c.d.79.1		2	7.4	even	3
112.12.a.b.1.1		1	4.3	odd	2
126.12.a.d.1.1		1	3.2	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:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	14.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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