LMFDB - Embedded newform 10.14.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,14,Mod(1,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 14, names="a")

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

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	10.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:	$10.7230928952$
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	$\chi$	$=$	10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-64.0000 q^{2} -26.0000 q^{3} +4096.00 q^{4} -15625.0 q^{5} +1664.00 q^{6} +538538. q^{7} -262144. q^{8} -1.59365e6 q^{9} +O(q^{10})$

\(q-64.0000 q^{2} -26.0000 q^{3} +4096.00 q^{4} -15625.0 q^{5} +1664.00 q^{6} +538538. q^{7} -262144. q^{8} -1.59365e6 q^{9} +1.00000e6 q^{10} -3.99485e6 q^{11} -106496. q^{12} -2.38344e7 q^{13} -3.44664e7 q^{14} +406250. q^{15} +1.67772e7 q^{16} -1.92273e8 q^{17} +1.01993e8 q^{18} +1.66486e8 q^{19} -6.40000e7 q^{20} -1.40020e7 q^{21} +2.55670e8 q^{22} -3.66867e8 q^{23} +6.81574e6 q^{24} +2.44141e8 q^{25} +1.52540e9 q^{26} +8.28872e7 q^{27} +2.20585e9 q^{28} +9.89856e8 q^{29} -2.60000e7 q^{30} -3.44505e9 q^{31} -1.07374e9 q^{32} +1.03866e8 q^{33} +1.23055e10 q^{34} -8.41466e9 q^{35} -6.52758e9 q^{36} -2.94299e10 q^{37} -1.06551e10 q^{38} +6.19696e8 q^{39} +4.09600e9 q^{40} +7.04371e9 q^{41} +8.96127e8 q^{42} +8.22801e9 q^{43} -1.63629e10 q^{44} +2.49007e10 q^{45} +2.34795e10 q^{46} +4.57419e10 q^{47} -4.36208e8 q^{48} +1.93134e11 q^{49} -1.56250e10 q^{50} +4.99910e9 q^{51} -9.76259e10 q^{52} -9.05920e10 q^{53} -5.30478e9 q^{54} +6.24195e10 q^{55} -1.41175e11 q^{56} -4.32863e9 q^{57} -6.33508e10 q^{58} +1.26033e11 q^{59} +1.66400e9 q^{60} -2.92124e11 q^{61} +2.20483e11 q^{62} -8.58239e11 q^{63} +6.87195e10 q^{64} +3.72413e11 q^{65} -6.64743e9 q^{66} +5.72402e11 q^{67} -7.87551e11 q^{68} +9.53854e9 q^{69} +5.38538e11 q^{70} -1.28433e12 q^{71} +4.17765e11 q^{72} +1.96495e11 q^{73} +1.88351e12 q^{74} -6.34766e9 q^{75} +6.81926e11 q^{76} -2.15138e12 q^{77} -3.96605e10 q^{78} +3.77680e12 q^{79} -2.62144e11 q^{80} +2.53863e12 q^{81} -4.50798e11 q^{82} -4.55684e12 q^{83} -5.73521e10 q^{84} +3.00427e12 q^{85} -5.26592e11 q^{86} -2.57362e10 q^{87} +1.04723e12 q^{88} +3.74839e12 q^{89} -1.59365e12 q^{90} -1.28358e13 q^{91} -1.50269e12 q^{92} +8.95713e10 q^{93} -2.92748e12 q^{94} -2.60134e12 q^{95} +2.79173e10 q^{96} -2.74398e12 q^{97} -1.23606e13 q^{98} +6.36638e12 q^{99} +O(q^{100})\)

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 $

$2$	−64.0000	−0.707107
$2$	−64.0000	−0.707107
$3$	−26.0000	−0.0205914	−0.0102957	−	0.999947i	$-0.503277\pi$
$3$	−26.0000	−0.0205914	−0.0102957	+	0.999947i	$0.503277\pi$
$4$	4096.00	0.500000
$5$	−15625.0	−0.447214
$5$	−15625.0	−0.447214
$6$	1664.00	0.0145603
$7$	538538.	1.73013	0.865066	−	0.501659i	$-0.167277\pi$
$7$	538538.	1.73013	0.865066	+	0.501659i	$0.167277\pi$
$8$	−262144.	−0.353553
$9$	−1.59365e6	−0.999576
$10$	1.00000e6	0.316228
$11$	−3.99485e6	−0.679904	−0.339952	−	0.940443i	$-0.610411\pi$
$11$	−3.99485e6	−0.679904	−0.339952	+	0.940443i	$0.610411\pi$
$12$	−106496.	−0.0102957
$13$	−2.38344e7	−1.36954	−0.684768	−	0.728761i	$-0.740096\pi$
$13$	−2.38344e7	−1.36954	−0.684768	+	0.728761i	$0.740096\pi$
$14$	−3.44664e7	−1.22339
$15$	406250.	0.00920874
$16$	1.67772e7	0.250000
$17$	−1.92273e8	−1.93197	−0.965986	−	0.258594i	$-0.916741\pi$
$17$	−1.92273e8	−1.93197	−0.965986	+	0.258594i	$0.916741\pi$
$18$	1.01993e8	0.706807
$19$	1.66486e8	0.811855	0.405928	−	0.913905i	$-0.366948\pi$
$19$	1.66486e8	0.811855	0.405928	+	0.913905i	$0.366948\pi$
$20$	−6.40000e7	−0.223607
$21$	−1.40020e7	−0.0356258
$22$	2.55670e8	0.480765
$23$	−3.66867e8	−0.516747	−0.258373	−	0.966045i	$-0.583186\pi$
$23$	−3.66867e8	−0.516747	−0.258373	+	0.966045i	$0.583186\pi$
$24$	6.81574e6	0.00728015
$25$	2.44141e8	0.200000
$26$	1.52540e9	0.968408
$27$	8.28872e7	0.0411740
$28$	2.20585e9	0.865066
$29$	9.89856e8	0.309019	0.154509	−	0.987991i	$-0.450620\pi$
$29$	9.89856e8	0.309019	0.154509	+	0.987991i	$0.450620\pi$
$30$	−2.60000e7	−0.00651156
$31$	−3.44505e9	−0.697179	−0.348590	−	0.937275i	$-0.613339\pi$
$31$	−3.44505e9	−0.697179	−0.348590	+	0.937275i	$0.613339\pi$
$32$	−1.07374e9	−0.176777
$33$	1.03866e8	0.0140002
$34$	1.23055e10	1.36611
$35$	−8.41466e9	−0.773738
$36$	−6.52758e9	−0.499788
$37$	−2.94299e10	−1.88572	−0.942859	−	0.333191i	$-0.891875\pi$
$37$	−2.94299e10	−1.88572	−0.942859	+	0.333191i	$0.891875\pi$
$38$	−1.06551e10	−0.574068
$39$	6.19696e8	0.0282006
$40$	4.09600e9	0.158114
$41$	7.04371e9	0.231583	0.115791	−	0.993274i	$-0.463060\pi$
$41$	7.04371e9	0.231583	0.115791	+	0.993274i	$0.463060\pi$
$42$	8.96127e8	0.0251912
$43$	8.22801e9	0.198495	0.0992475	−	0.995063i	$-0.468356\pi$
$43$	8.22801e9	0.198495	0.0992475	+	0.995063i	$0.468356\pi$
$44$	−1.63629e10	−0.339952
$45$	2.49007e10	0.447024
$46$	2.34795e10	0.365395
$47$	4.57419e10	0.618982	0.309491	−	0.950902i	$-0.399841\pi$
$47$	4.57419e10	0.618982	0.309491	+	0.950902i	$0.399841\pi$
$48$	−4.36208e8	−0.00514784
$49$	1.93134e11	1.99335
$50$	−1.56250e10	−0.141421
$51$	4.99910e9	0.0397819
$52$	−9.76259e10	−0.684768
$53$	−9.05920e10	−0.561431	−0.280716	−	0.959791i	$-0.590572\pi$
$53$	−9.05920e10	−0.561431	−0.280716	+	0.959791i	$0.590572\pi$
$54$	−5.30478e9	−0.0291144
$55$	6.24195e10	0.304062
$56$	−1.41175e11	−0.611694
$57$	−4.32863e9	−0.0167172
$58$	−6.33508e10	−0.218509
$59$	1.26033e11	0.388997	0.194499	−	0.980903i	$-0.437692\pi$
$59$	1.26033e11	0.388997	0.194499	+	0.980903i	$0.437692\pi$
$60$	1.66400e9	0.00460437
$61$	−2.92124e11	−0.725977	−0.362988	−	0.931794i	$-0.618244\pi$
$61$	−2.92124e11	−0.725977	−0.362988	+	0.931794i	$0.618244\pi$
$62$	2.20483e11	0.492980
$63$	−8.58239e11	−1.72940
$64$	6.87195e10	0.125000
$65$	3.72413e11	0.612475
$66$	−6.64743e9	−0.00989961
$67$	5.72402e11	0.773063	0.386532	−	0.922276i	$-0.373673\pi$
$67$	5.72402e11	0.773063	0.386532	+	0.922276i	$0.373673\pi$
$68$	−7.87551e11	−0.965986
$69$	9.53854e9	0.0106405
$70$	5.38538e11	0.547116
$71$	−1.28433e12	−1.18986	−0.594932	−	0.803776i	$-0.702821\pi$
$71$	−1.28433e12	−1.18986	−0.594932	+	0.803776i	$0.702821\pi$
$72$	4.17765e11	0.353403
$73$	1.96495e11	0.151968	0.0759841	−	0.997109i	$-0.475790\pi$
$73$	1.96495e11	0.151968	0.0759841	+	0.997109i	$0.475790\pi$
$74$	1.88351e12	1.33340
$75$	−6.34766e9	−0.00411827
$76$	6.81926e11	0.405928
$77$	−2.15138e12	−1.17632
$78$	−3.96605e10	−0.0199408
$79$	3.77680e12	1.74802	0.874012	−	0.485904i	$-0.161509\pi$
$79$	3.77680e12	1.74802	0.874012	+	0.485904i	$0.161509\pi$
$80$	−2.62144e11	−0.111803
$81$	2.53863e12	0.998728
$82$	−4.50798e11	−0.163754
$83$	−4.55684e12	−1.52988	−0.764939	−	0.644103i	$-0.777231\pi$
$83$	−4.55684e12	−1.52988	−0.764939	+	0.644103i	$0.777231\pi$
$84$	−5.73521e10	−0.0178129
$85$	3.00427e12	0.864004
$86$	−5.26592e11	−0.140357
$87$	−2.57362e10	−0.00636312
$88$	1.04723e12	0.240382
$89$	3.74839e12	0.799485	0.399742	−	0.916628i	$-0.369100\pi$
$89$	3.74839e12	0.799485	0.399742	+	0.916628i	$0.369100\pi$
$90$	−1.59365e12	−0.316094
$91$	−1.28358e13	−2.36948
$92$	−1.50269e12	−0.258373
$93$	8.95713e10	0.0143559
$94$	−2.92748e12	−0.437686
$95$	−2.60134e12	−0.363073
$96$	2.79173e10	0.00364007
$97$	−2.74398e12	−0.334476	−0.167238	−	0.985917i	$-0.553485\pi$
$97$	−2.74398e12	−0.334476	−0.167238	+	0.985917i	$0.553485\pi$
$98$	−1.23606e13	−1.40951
$99$	6.36638e12	0.679616
$100$	1.00000e12	0.100000
$101$	1.27162e13	1.19198	0.595990	−	0.802992i	$-0.296760\pi$
$101$	1.27162e13	1.19198	0.595990	+	0.802992i	$0.296760\pi$
$102$	−3.19943e11	−0.0281301
$103$	1.92667e13	1.58988	0.794941	−	0.606687i	$-0.207502\pi$
$103$	1.92667e13	1.58988	0.794941	+	0.606687i	$0.207502\pi$
$104$	6.24806e12	0.484204
$105$	2.18781e11	0.0159323
$106$	5.79789e12	0.396992
$107$	−8.98383e12	−0.578718	−0.289359	−	0.957221i	$-0.593442\pi$
$107$	−8.98383e12	−0.578718	−0.289359	+	0.957221i	$0.593442\pi$
$108$	3.39506e11	0.0205870
$109$	−4.67505e11	−0.0267002	−0.0133501	−	0.999911i	$-0.504250\pi$
$109$	−4.67505e11	−0.0267002	−0.0133501	+	0.999911i	$0.504250\pi$
$110$	−3.99485e12	−0.215005
$111$	7.65176e11	0.0388295
$112$	9.03517e12	0.432533
$113$	1.67877e13	0.758543	0.379272	−	0.925285i	$-0.376175\pi$
$113$	1.67877e13	0.758543	0.379272	+	0.925285i	$0.376175\pi$
$114$	2.77032e11	0.0118209
$115$	5.73230e12	0.231096
$116$	4.05445e12	0.154509
$117$	3.79837e13	1.36895
$118$	−8.06612e12	−0.275063
$119$	−1.03546e14	−3.34257
$120$	−1.06496e11	−0.00325578
$121$	−1.85639e13	−0.537730
$122$	1.86959e13	0.513343
$123$	−1.83137e11	−0.00476861
$124$	−1.41109e13	−0.348590
$125$	−3.81470e12	−0.0894427
$126$	5.49273e13	1.22287
$127$	−4.14046e13	−0.875638	−0.437819	−	0.899063i	$-0.644249\pi$
$127$	−4.14046e13	−0.875638	−0.437819	+	0.899063i	$0.644249\pi$
$128$	−4.39805e12	−0.0883883
$129$	−2.13928e11	−0.00408728
$130$	−2.38344e13	−0.433085
$131$	−5.76041e13	−0.995841	−0.497921	−	0.867223i	$-0.665903\pi$
$131$	−5.76041e13	−0.995841	−0.497921	+	0.867223i	$0.665903\pi$
$132$	4.25435e11	0.00700008
$133$	8.96589e13	1.40462
$134$	−3.66337e13	−0.546638
$135$	−1.29511e12	−0.0184136
$136$	5.04033e13	0.683055
$137$	−1.13720e13	−0.146945	−0.0734723	−	0.997297i	$-0.523408\pi$
$137$	−1.13720e13	−0.146945	−0.0734723	+	0.997297i	$0.523408\pi$
$138$	−6.10467e11	−0.00752398
$139$	1.13307e13	0.133247	0.0666237	−	0.997778i	$-0.478777\pi$
$139$	1.13307e13	0.133247	0.0666237	+	0.997778i	$0.478777\pi$
$140$	−3.44664e13	−0.386869
$141$	−1.18929e12	−0.0127457
$142$	8.21971e13	0.841361
$143$	9.52150e13	0.931153
$144$	−2.67370e13	−0.249894
$145$	−1.54665e13	−0.138197
$146$	−1.25757e13	−0.107458
$147$	−5.02149e12	−0.0410459
$148$	−1.20545e14	−0.942859
$149$	−5.56816e13	−0.416870	−0.208435	−	0.978036i	$-0.566837\pi$
$149$	−5.56816e13	−0.416870	−0.208435	+	0.978036i	$0.566837\pi$
$150$	4.06250e11	0.00291206
$151$	1.28907e14	0.884962	0.442481	−	0.896778i	$-0.354098\pi$
$151$	1.28907e14	0.884962	0.442481	+	0.896778i	$0.354098\pi$
$152$	−4.36432e13	−0.287034
$153$	3.06416e14	1.93115
$154$	1.37688e14	0.831787
$155$	5.38289e13	0.311788
$156$	2.53827e12	0.0141003
$157$	2.75939e13	0.147050	0.0735251	−	0.997293i	$-0.476575\pi$
$157$	2.75939e13	0.147050	0.0735251	+	0.997293i	$0.476575\pi$
$158$	−2.41715e14	−1.23604
$159$	2.35539e12	0.0115606
$160$	1.67772e13	0.0790569
$161$	−1.97572e14	−0.894040
$162$	−1.62473e14	−0.706207
$163$	−1.25480e14	−0.524030	−0.262015	−	0.965064i	$-0.584387\pi$
$163$	−1.25480e14	−0.524030	−0.262015	+	0.965064i	$0.584387\pi$
$164$	2.88510e13	0.115791
$165$	−1.62291e12	−0.00626106
$166$	2.91638e14	1.08179
$167$	−4.65642e14	−1.66110	−0.830549	−	0.556945i	$-0.811973\pi$
$167$	−4.65642e14	−1.66110	−0.830549	+	0.556945i	$0.811973\pi$
$168$	3.67054e12	0.0125956
$169$	2.65206e14	0.875627
$170$	−1.92273e14	−0.610943
$171$	−2.65320e14	−0.811511
$172$	3.37019e13	0.0992475
$173$	−2.37044e14	−0.672249	−0.336125	−	0.941818i	$-0.609116\pi$
$173$	−2.37044e14	−0.672249	−0.336125	+	0.941818i	$0.609116\pi$
$174$	1.64712e12	0.00449940
$175$	1.31479e14	0.346026
$176$	−6.70224e13	−0.169976
$177$	−3.27686e12	−0.00800999
$178$	−2.39897e14	−0.565321
$179$	3.84186e14	0.872966	0.436483	−	0.899713i	$-0.356224\pi$
$179$	3.84186e14	0.872966	0.436483	+	0.899713i	$0.356224\pi$
$180$	1.01993e14	0.223512
$181$	−7.30498e14	−1.54422	−0.772109	−	0.635491i	$-0.780798\pi$
$181$	−7.30498e14	−1.54422	−0.772109	+	0.635491i	$0.780798\pi$
$182$	8.21488e14	1.67547
$183$	7.59522e12	0.0149489
$184$	9.61720e13	0.182698
$185$	4.59841e14	0.843319
$186$	−5.73256e12	−0.0101511
$187$	7.68102e14	1.31356
$188$	1.87359e14	0.309491
$189$	4.46379e13	0.0712364
$190$	1.66486e14	0.256731
$191$	4.54589e14	0.677488	0.338744	−	0.940879i	$-0.389998\pi$
$191$	4.54589e14	0.677488	0.338744	+	0.940879i	$0.389998\pi$
$192$	−1.78671e12	−0.00257392
$193$	−1.02844e15	−1.43238	−0.716188	−	0.697907i	$-0.754115\pi$
$193$	−1.02844e15	−1.43238	−0.716188	+	0.697907i	$0.754115\pi$
$194$	1.75615e14	0.236510
$195$	−9.68274e12	−0.0126117
$196$	7.91078e14	0.996677
$197$	−5.41868e14	−0.660486	−0.330243	−	0.943896i	$-0.607131\pi$
$197$	−5.41868e14	−0.660486	−0.330243	+	0.943896i	$0.607131\pi$
$198$	−4.07448e14	−0.480561
$199$	3.86534e14	0.441207	0.220604	−	0.975364i	$-0.429197\pi$
$199$	3.86534e14	0.441207	0.220604	+	0.975364i	$0.429197\pi$
$200$	−6.40000e13	−0.0707107
$201$	−1.48825e13	−0.0159184
$202$	−8.13838e14	−0.842857
$203$	5.33075e14	0.534643
$204$	2.04763e13	0.0198910
$205$	−1.10058e14	−0.103567
$206$	−1.23307e15	−1.12422
$207$	5.84656e14	0.516528
$208$	−3.99876e14	−0.342384
$209$	−6.65085e14	−0.551984
$210$	−1.40020e13	−0.0112659
$211$	−1.69158e15	−1.31964	−0.659820	−	0.751424i	$-0.729367\pi$
$211$	−1.69158e15	−1.31964	−0.659820	+	0.751424i	$0.729367\pi$
$212$	−3.71065e14	−0.280716
$213$	3.33926e13	0.0245009
$214$	5.74965e14	0.409215
$215$	−1.28563e14	−0.0887697
$216$	−2.17284e13	−0.0145572
$217$	−1.85529e15	−1.20621
$218$	2.99203e13	0.0188799
$219$	−5.10887e12	−0.00312923
$220$	2.55670e14	0.152031
$221$	4.58273e15	2.64590
$222$	−4.89713e13	−0.0274566
$223$	1.17782e15	0.641356	0.320678	−	0.947188i	$-0.396089\pi$
$223$	1.17782e15	0.641356	0.320678	+	0.947188i	$0.396089\pi$
$224$	−5.78251e14	−0.305847
$225$	−3.89074e14	−0.199915
$226$	−1.07441e15	−0.536371
$227$	2.84874e15	1.38193	0.690964	−	0.722889i	$-0.257186\pi$
$227$	2.84874e15	1.38193	0.690964	+	0.722889i	$0.257186\pi$
$228$	−1.77301e13	−0.00835861
$229$	−1.50065e15	−0.687622	−0.343811	−	0.939039i	$-0.611718\pi$
$229$	−1.50065e15	−0.687622	−0.343811	+	0.939039i	$0.611718\pi$
$230$	−3.66867e14	−0.163410
$231$	5.59358e13	0.0242221
$232$	−2.59485e14	−0.109255
$233$	−3.28693e14	−0.134579	−0.0672895	−	0.997733i	$-0.521435\pi$
$233$	−3.28693e14	−0.134579	−0.0672895	+	0.997733i	$0.521435\pi$
$234$	−2.43096e15	−0.967997
$235$	−7.14717e14	−0.276817
$236$	5.16232e14	0.194499
$237$	−9.81967e13	−0.0359942
$238$	6.62697e15	2.36355
$239$	3.86741e15	1.34225	0.671126	−	0.741343i	$-0.265811\pi$
$239$	3.86741e15	1.34225	0.671126	+	0.741343i	$0.265811\pi$
$240$	6.81574e12	0.00230218
$241$	−2.19290e15	−0.720955	−0.360478	−	0.932768i	$-0.617386\pi$
$241$	−2.19290e15	−0.720955	−0.360478	+	0.932768i	$0.617386\pi$
$242$	1.18809e15	0.380233
$243$	−1.98153e14	−0.0617392
$244$	−1.19654e15	−0.362988
$245$	−3.01772e15	−0.891455
$246$	1.17207e13	0.00337192
$247$	−3.96810e15	−1.11186
$248$	9.03099e14	0.246490
$249$	1.18478e14	0.0315023
$250$	2.44141e14	0.0632456
$251$	5.77342e15	1.45732	0.728658	−	0.684877i	$-0.240144\pi$
$251$	5.77342e15	1.45732	0.728658	+	0.684877i	$0.240144\pi$
$252$	−3.51535e15	−0.864699
$253$	1.46558e15	0.351338
$254$	2.64989e15	0.619169
$255$	−7.81110e13	−0.0177910
$256$	2.81475e14	0.0625000
$257$	4.70192e15	1.01791	0.508956	−	0.860792i	$-0.330032\pi$
$257$	4.70192e15	1.01791	0.508956	+	0.860792i	$0.330032\pi$
$258$	1.36914e13	0.00289015
$259$	−1.58491e16	−3.26254
$260$	1.52540e15	0.306237
$261$	−1.57748e15	−0.308888
$262$	3.68666e15	0.704166
$263$	−6.04427e15	−1.12624	−0.563121	−	0.826374i	$-0.690400\pi$
$263$	−6.04427e15	−1.12624	−0.563121	+	0.826374i	$0.690400\pi$
$264$	−2.72279e13	−0.00494980
$265$	1.41550e15	0.251080
$266$	−5.73817e15	−0.993214
$267$	−9.74582e13	−0.0164625
$268$	2.34456e15	0.386532
$269$	−6.09440e15	−0.980711	−0.490355	−	0.871523i	$-0.663133\pi$
$269$	−6.09440e15	−0.980711	−0.490355	+	0.871523i	$0.663133\pi$
$270$	8.28872e13	0.0130204
$271$	6.69938e15	1.02739	0.513694	−	0.857974i	$-0.328277\pi$
$271$	6.69938e15	1.02739	0.513694	+	0.857974i	$0.328277\pi$
$272$	−3.22581e15	−0.482993
$273$	3.33730e14	0.0487908
$274$	7.27808e14	0.103905
$275$	−9.75305e14	−0.135981
$276$	3.90699e13	0.00532026
$277$	7.37760e15	0.981288	0.490644	−	0.871360i	$-0.336762\pi$
$277$	7.37760e15	0.981288	0.490644	+	0.871360i	$0.336762\pi$
$278$	−7.25162e14	−0.0942202
$279$	5.49019e15	0.696883
$280$	2.20585e15	0.273558
$281$	−9.52412e14	−0.115407	−0.0577037	−	0.998334i	$-0.518378\pi$
$281$	−9.52412e14	−0.115407	−0.0577037	+	0.998334i	$0.518378\pi$
$282$	7.61145e13	0.00901256
$283$	−5.72764e15	−0.662771	−0.331386	−	0.943495i	$-0.607516\pi$
$283$	−5.72764e15	−0.662771	−0.331386	+	0.943495i	$0.607516\pi$
$284$	−5.26061e15	−0.594932
$285$	6.76348e13	0.00747616
$286$	−6.09376e15	−0.658425
$287$	3.79331e15	0.400669
$288$	1.71117e15	0.176702
$289$	2.70644e16	2.73252
$290$	9.89856e14	0.0977203
$291$	7.13435e13	0.00688732
$292$	8.04843e14	0.0759841
$293$	1.28919e15	0.119036	0.0595181	−	0.998227i	$-0.481044\pi$
$293$	1.28919e15	0.119036	0.0595181	+	0.998227i	$0.481044\pi$
$294$	3.21375e14	0.0290238
$295$	−1.96927e15	−0.173965
$296$	7.71486e15	0.666702
$297$	−3.31122e14	−0.0279944
$298$	3.56362e15	0.294772
$299$	8.74407e15	0.707703
$300$	−2.60000e13	−0.00205914
$301$	4.43109e15	0.343422
$302$	−8.25002e15	−0.625763
$303$	−3.30622e14	−0.0245445
$304$	2.79317e15	0.202964
$305$	4.56443e15	0.324667
$306$	−1.96106e16	−1.36553
$307$	−1.51285e16	−1.03133	−0.515665	−	0.856790i	$-0.672455\pi$
$307$	−1.51285e16	−1.03133	−0.515665	+	0.856790i	$0.672455\pi$
$308$	−8.81204e15	−0.588162
$309$	−5.00933e14	−0.0327378
$310$	−3.44505e15	−0.220467
$311$	−2.05656e16	−1.28884	−0.644420	−	0.764672i	$-0.722901\pi$
$311$	−2.05656e16	−1.28884	−0.644420	+	0.764672i	$0.722901\pi$
$312$	−1.62449e14	−0.00997042
$313$	−2.32153e16	−1.39552	−0.697759	−	0.716332i	$-0.745819\pi$
$313$	−2.32153e16	−1.39552	−0.697759	+	0.716332i	$0.745819\pi$
$314$	−1.76601e15	−0.103980
$315$	1.34100e16	0.773410
$316$	1.54698e16	0.874012
$317$	−4.63884e15	−0.256758	−0.128379	−	0.991725i	$-0.540977\pi$
$317$	−4.63884e15	−0.256758	−0.128379	+	0.991725i	$0.540977\pi$
$318$	−1.50745e14	−0.00817460
$319$	−3.95432e15	−0.210103
$320$	−1.07374e15	−0.0559017
$321$	2.33579e14	0.0119166
$322$	1.26446e16	0.632181
$323$	−3.20107e16	−1.56848
$324$	1.03982e16	0.499364
$325$	−5.81896e15	−0.273907
$326$	8.03073e15	0.370545
$327$	1.21551e13	0.000549794 0
$328$	−1.84647e15	−0.0818769
$329$	2.46337e16	1.07092
$330$	1.03866e14	0.00442724
$331$	−1.44506e16	−0.603955	−0.301978	−	0.953315i	$-0.597647\pi$
$331$	−1.44506e16	−0.603955	−0.301978	+	0.953315i	$0.597647\pi$
$332$	−1.86648e16	−0.764939
$333$	4.69008e16	1.88492
$334$	2.98011e16	1.17457
$335$	−8.94378e15	−0.345724
$336$	−2.34914e14	−0.00890644
$337$	−3.32442e16	−1.23629	−0.618147	−	0.786062i	$-0.712116\pi$
$337$	−3.32442e16	−1.23629	−0.618147	+	0.786062i	$0.712116\pi$
$338$	−1.69732e16	−0.619162
$339$	−4.36479e14	−0.0156194
$340$	1.23055e16	0.432002
$341$	1.37624e16	0.474015
$342$	1.69804e16	0.573825
$343$	5.18317e16	1.71863
$344$	−2.15692e15	−0.0701786
$345$	−1.49040e14	−0.00475859
$346$	1.51708e16	0.475352
$347$	2.13639e16	0.656959	0.328480	−	0.944511i	$-0.393464\pi$
$347$	2.13639e16	0.656959	0.328480	+	0.944511i	$0.393464\pi$
$348$	−1.05416e14	−0.00318156
$349$	−4.44451e16	−1.31661	−0.658307	−	0.752749i	$-0.728727\pi$
$349$	−4.44451e16	−1.31661	−0.658307	+	0.752749i	$0.728727\pi$
$350$	−8.41466e15	−0.244678
$351$	−1.97557e15	−0.0563893
$352$	4.28944e15	0.120191
$353$	−3.00225e16	−0.825870	−0.412935	−	0.910761i	$-0.635496\pi$
$353$	−3.00225e16	−0.825870	−0.412935	+	0.910761i	$0.635496\pi$
$354$	2.09719e14	0.00566392
$355$	2.00676e16	0.532123
$356$	1.53534e16	0.399742
$357$	2.69221e15	0.0688280
$358$	−2.45879e16	−0.617280
$359$	−4.61828e15	−0.113859	−0.0569293	−	0.998378i	$-0.518131\pi$
$359$	−4.61828e15	−0.113859	−0.0569293	+	0.998378i	$0.518131\pi$
$360$	−6.52758e15	−0.158047
$361$	−1.43355e16	−0.340891
$362$	4.67519e16	1.09193
$363$	4.82661e14	0.0110726
$364$	−5.25753e16	−1.18474
$365$	−3.07023e15	−0.0679623
$366$	−4.86094e14	−0.0105704
$367$	6.78431e16	1.44936	0.724680	−	0.689085i	$-0.241987\pi$
$367$	6.78431e16	1.44936	0.724680	+	0.689085i	$0.241987\pi$
$368$	−6.15501e15	−0.129187
$369$	−1.12252e16	−0.231485
$370$	−2.94299e16	−0.596317
$371$	−4.87872e16	−0.971350
$372$	3.66884e14	0.00717794
$373$	5.36183e16	1.03087	0.515437	−	0.856927i	$-0.327629\pi$
$373$	5.36183e16	1.03087	0.515437	+	0.856927i	$0.327629\pi$
$374$	−4.91585e16	−0.928824
$375$	9.91821e13	0.00184175
$376$	−1.19910e16	−0.218843
$377$	−2.35927e16	−0.423212
$378$	−2.85683e15	−0.0503718
$379$	−5.48074e16	−0.949914	−0.474957	−	0.880009i	$-0.657536\pi$
$379$	−5.48074e16	−0.949914	−0.474957	+	0.880009i	$0.657536\pi$
$380$	−1.06551e16	−0.181536
$381$	1.07652e15	0.0180306
$382$	−2.90937e16	−0.479056
$383$	8.01304e16	1.29720	0.648598	−	0.761131i	$-0.275356\pi$
$383$	8.01304e16	1.29720	0.648598	+	0.761131i	$0.275356\pi$
$384$	1.14349e14	0.00182004
$385$	3.36153e16	0.526068
$386$	6.58202e16	1.01284
$387$	−1.31125e16	−0.198411
$388$	−1.12393e16	−0.167238
$389$	−5.93509e16	−0.868470	−0.434235	−	0.900800i	$-0.642981\pi$
$389$	−5.93509e16	−0.868470	−0.434235	+	0.900800i	$0.642981\pi$
$390$	6.19696e14	0.00891782
$391$	7.05387e16	0.998340
$392$	−5.06290e16	−0.704757
$393$	1.49771e15	0.0205057
$394$	3.46796e16	0.467034
$395$	−5.90125e16	−0.781740
$396$	2.60767e16	0.339808
$397$	−1.13437e17	−1.45417	−0.727087	−	0.686545i	$-0.759126\pi$
$397$	−1.13437e17	−1.45417	−0.727087	+	0.686545i	$0.759126\pi$
$398$	−2.47382e16	−0.311981
$399$	−2.33113e15	−0.0289230
$400$	4.09600e15	0.0500000
$401$	1.76418e16	0.211887	0.105944	−	0.994372i	$-0.466214\pi$
$401$	1.76418e16	0.211887	0.105944	+	0.994372i	$0.466214\pi$
$402$	9.52477e14	0.0112560
$403$	8.21108e16	0.954811
$404$	5.20856e16	0.595990
$405$	−3.96661e16	−0.446645
$406$	−3.41168e16	−0.378050
$407$	1.17568e17	1.28211
$408$	−1.31049e15	−0.0140650
$409$	7.49234e16	0.791437	0.395718	−	0.918372i	$-0.370496\pi$
$409$	7.49234e16	0.791437	0.395718	+	0.918372i	$0.370496\pi$
$410$	7.04371e15	0.0732330
$411$	2.95672e14	0.00302579
$412$	7.89163e16	0.794941
$413$	6.78736e16	0.673016
$414$	−3.74180e16	−0.365240
$415$	7.12007e16	0.684182
$416$	2.55920e16	0.242102
$417$	−2.94597e14	−0.00274375
$418$	4.25655e16	0.390312
$419$	−6.35209e16	−0.573490	−0.286745	−	0.958007i	$-0.592573\pi$
$419$	−6.35209e16	−0.573490	−0.286745	+	0.958007i	$0.592573\pi$
$420$	8.96127e14	0.00796616
$421$	−1.09306e17	−0.956773	−0.478387	−	0.878149i	$-0.658778\pi$
$421$	−1.09306e17	−0.956773	−0.478387	+	0.878149i	$0.658778\pi$
$422$	1.08261e17	0.933126
$423$	−7.28964e16	−0.618719
$424$	2.37481e16	0.198496
$425$	−4.69417e16	−0.386394
$426$	−2.13712e15	−0.0173248
$427$	−1.57320e17	−1.25604
$428$	−3.67978e16	−0.289359
$429$	−2.47559e15	−0.0191737
$430$	8.22801e15	0.0627696
$431$	1.62040e17	1.21765	0.608823	−	0.793306i	$-0.291642\pi$
$431$	1.62040e17	1.21765	0.608823	+	0.793306i	$0.291642\pi$
$432$	1.39062e15	0.0102935
$433$	−4.81928e16	−0.351407	−0.175704	−	0.984443i	$-0.556220\pi$
$433$	−4.81928e16	−0.351407	−0.175704	+	0.984443i	$0.556220\pi$
$434$	1.18739e17	0.852920
$435$	4.02129e14	0.00284567
$436$	−1.91490e15	−0.0133501
$437$	−6.10781e16	−0.419523
$438$	3.26968e14	0.00221270
$439$	8.23200e16	0.548891	0.274445	−	0.961603i	$-0.411506\pi$
$439$	8.23200e16	0.548891	0.274445	+	0.961603i	$0.411506\pi$
$440$	−1.63629e16	−0.107502
$441$	−3.07788e17	−1.99251
$442$	−2.93294e17	−1.87094
$443$	−2.71619e17	−1.70740	−0.853702	−	0.520763i	$-0.825648\pi$
$443$	−2.71619e17	−1.70740	−0.853702	+	0.520763i	$0.825648\pi$
$444$	3.13416e15	0.0194148
$445$	−5.85687e16	−0.357540
$446$	−7.53808e16	−0.453507
$447$	1.44772e15	0.00858392
$448$	3.70080e16	0.216266
$449$	2.62585e17	1.51241	0.756204	−	0.654336i	$-0.227052\pi$
$449$	2.62585e17	1.51241	0.756204	+	0.654336i	$0.227052\pi$
$450$	2.49007e16	0.141361
$451$	−2.81386e16	−0.157454
$452$	6.87623e16	0.379272
$453$	−3.35157e15	−0.0182226
$454$	−1.82320e17	−0.977170
$455$	2.00559e17	1.05966
$456$	1.13472e15	0.00591043
$457$	1.49994e17	0.770227	0.385114	−	0.922869i	$-0.374162\pi$
$457$	1.49994e17	0.770227	0.385114	+	0.922869i	$0.374162\pi$
$458$	9.60418e16	0.486222
$459$	−1.59370e16	−0.0795470
$460$	2.34795e16	0.115548
$461$	1.97033e17	0.956053	0.478026	−	0.878345i	$-0.341352\pi$
$461$	1.97033e17	0.956053	0.478026	+	0.878345i	$0.341352\pi$
$462$	−3.57989e15	−0.0171276
$463$	−3.43379e17	−1.61994	−0.809968	−	0.586474i	$-0.800516\pi$
$463$	−3.43379e17	−1.61994	−0.809968	+	0.586474i	$0.800516\pi$
$464$	1.66070e16	0.0772547
$465$	−1.39955e15	−0.00642014
$466$	2.10364e16	0.0951617
$467$	2.44273e17	1.08972	0.544862	−	0.838526i	$-0.316582\pi$
$467$	2.44273e17	1.08972	0.544862	+	0.838526i	$0.316582\pi$
$468$	1.55581e17	0.684477
$469$	3.08260e17	1.33750
$470$	4.57419e16	0.195739
$471$	−7.17442e14	−0.00302797
$472$	−3.30388e16	−0.137531
$473$	−3.28696e16	−0.134958
$474$	6.28459e15	0.0254518
$475$	4.06459e16	0.162371
$476$	−4.24126e17	−1.67128
$477$	1.44372e17	0.561193
$478$	−2.47514e17	−0.949116
$479$	−1.62575e17	−0.614999	−0.307499	−	0.951548i	$-0.599492\pi$
$479$	−1.62575e17	−0.614999	−0.307499	+	0.951548i	$0.599492\pi$
$480$	−4.36208e14	−0.00162789
$481$	7.01444e17	2.58256
$482$	1.40346e17	0.509792
$483$	5.13687e15	0.0184095
$484$	−7.60377e16	−0.268865
$485$	4.28747e16	0.149582
$486$	1.26818e16	0.0436562
$487$	2.98785e17	1.01489	0.507447	−	0.861683i	$-0.330589\pi$
$487$	2.98785e17	1.01489	0.507447	+	0.861683i	$0.330589\pi$
$488$	7.65785e16	0.256672
$489$	3.26249e15	0.0107905
$490$	1.93134e17	0.630354
$491$	−5.02804e17	−1.61946	−0.809729	−	0.586805i	$-0.800386\pi$
$491$	−5.02804e17	−1.61946	−0.809729	+	0.586805i	$0.800386\pi$
$492$	−7.50127e14	−0.00238430
$493$	−1.90323e17	−0.597016
$494$	2.53958e17	0.786207
$495$	−9.94746e16	−0.303934
$496$	−5.77983e16	−0.174295
$497$	−6.91660e17	−2.05862
$498$	−7.58259e15	−0.0222755
$499$	−3.95020e17	−1.14542	−0.572711	−	0.819757i	$-0.694108\pi$
$499$	−3.95020e17	−1.14542	−0.572711	+	0.819757i	$0.694108\pi$
$500$	−1.56250e16	−0.0447214
$501$	1.21067e16	0.0342043
$502$	−3.69499e17	−1.03048
$503$	3.24644e17	0.893750	0.446875	−	0.894596i	$-0.352537\pi$
$503$	3.24644e17	0.893750	0.446875	+	0.894596i	$0.352537\pi$
$504$	2.24982e17	0.611434
$505$	−1.98691e17	−0.533070
$506$	−9.37970e16	−0.248434
$507$	−6.89535e15	−0.0180304
$508$	−1.69593e17	−0.437819
$509$	3.87835e17	0.988511	0.494255	−	0.869317i	$-0.335441\pi$
$509$	3.87835e17	0.988511	0.494255	+	0.869317i	$0.335441\pi$
$510$	4.99910e15	0.0125802
$511$	1.05820e17	0.262925
$512$	−1.80144e16	−0.0441942
$513$	1.37995e16	0.0334273
$514$	−3.00923e17	−0.719773
$515$	−3.01042e17	−0.711017
$516$	−8.76250e14	−0.00204364
$517$	−1.82732e17	−0.420848
$518$	1.01434e18	2.30696
$519$	6.16316e15	0.0138425
$520$	−9.76259e16	−0.216543
$521$	−1.43084e17	−0.313433	−0.156716	−	0.987644i	$-0.550091\pi$
$521$	−1.43084e17	−0.313433	−0.156716	+	0.987644i	$0.550091\pi$
$522$	1.00959e17	0.218417
$523$	−4.99639e17	−1.06757	−0.533784	−	0.845621i	$-0.679230\pi$
$523$	−4.99639e17	−1.06757	−0.533784	+	0.845621i	$0.679230\pi$
$524$	−2.35946e17	−0.497921
$525$	−3.41845e15	−0.00712515
$526$	3.86833e17	0.796373
$527$	6.62391e17	1.34693
$528$	1.74258e15	0.00350004
$529$	−3.69445e17	−0.732973
$530$	−9.05920e16	−0.177540
$531$	−2.00852e17	−0.388832
$532$	3.67243e17	0.702308
$533$	−1.67883e17	−0.317161
$534$	6.23733e15	0.0116407
$535$	1.40372e17	0.258810
$536$	−1.50052e17	−0.273319
$537$	−9.98885e15	−0.0179756
$538$	3.90041e17	0.693467
$539$	−7.71542e17	−1.35529
$540$	−5.30478e15	−0.00920679
$541$	1.07584e18	1.84488	0.922438	−	0.386145i	$-0.126193\pi$
$541$	1.07584e18	1.84488	0.922438	+	0.386145i	$0.126193\pi$
$542$	−4.28760e17	−0.726473
$543$	1.89929e16	0.0317975
$544$	2.06452e17	0.341528
$545$	7.30477e15	0.0119407
$546$	−2.13587e16	−0.0345003
$547$	−5.60885e17	−0.895274	−0.447637	−	0.894215i	$-0.647734\pi$
$547$	−5.60885e17	−0.895274	−0.447637	+	0.894215i	$0.647734\pi$
$548$	−4.65797e16	−0.0734723
$549$	4.65542e17	0.725669
$550$	6.24195e16	0.0961530
$551$	1.64797e17	0.250879
$552$	−2.50047e15	−0.00376199
$553$	2.03395e18	3.02431
$554$	−4.72166e17	−0.693875
$555$	−1.19559e16	−0.0173651
$556$	4.64104e16	0.0666237
$557$	−6.48157e17	−0.919648	−0.459824	−	0.888010i	$-0.652087\pi$
$557$	−6.48157e17	−0.919648	−0.459824	+	0.888010i	$0.652087\pi$
$558$	−3.51372e17	−0.492771
$559$	−1.96110e17	−0.271846
$560$	−1.41175e17	−0.193435
$561$	−1.99707e16	−0.0270479
$562$	6.09544e16	0.0816054
$563$	−1.21997e17	−0.161453	−0.0807264	−	0.996736i	$-0.525724\pi$
$563$	−1.21997e17	−0.161453	−0.0807264	+	0.996736i	$0.525724\pi$
$564$	−4.87133e15	−0.00637284
$565$	−2.62307e17	−0.339231
$566$	3.66569e17	0.468650
$567$	1.36715e18	1.72793
$568$	3.36679e17	0.420680
$569$	−1.25979e17	−0.155621	−0.0778105	−	0.996968i	$-0.524793\pi$
$569$	−1.25979e17	−0.155621	−0.0778105	+	0.996968i	$0.524793\pi$
$570$	−4.32863e15	−0.00528645
$571$	7.87361e17	0.950690	0.475345	−	0.879799i	$-0.342323\pi$
$571$	7.87361e17	0.950690	0.475345	+	0.879799i	$0.342323\pi$
$572$	3.90001e17	0.465577
$573$	−1.18193e16	−0.0139504
$574$	−2.42772e17	−0.283316
$575$	−8.95671e16	−0.103349
$576$	−1.09515e17	−0.124947
$577$	−9.73545e17	−1.09828	−0.549140	−	0.835730i	$-0.685045\pi$
$577$	−9.73545e17	−1.09828	−0.549140	+	0.835730i	$0.685045\pi$
$578$	−1.73212e18	−1.93218
$579$	2.67395e16	0.0294946
$580$	−6.33508e16	−0.0690987
$581$	−2.45403e18	−2.64689
$582$	−4.56599e15	−0.00487007
$583$	3.61901e17	0.381719
$584$	−5.15100e16	−0.0537289
$585$	−5.93495e17	−0.612215
$586$	−8.25084e16	−0.0841712
$587$	1.37587e18	1.38813	0.694063	−	0.719914i	$-0.255819\pi$
$587$	1.37587e18	1.38813	0.694063	+	0.719914i	$0.255819\pi$
$588$	−2.05680e16	−0.0205230
$589$	−5.73551e17	−0.566009
$590$	1.26033e17	0.123012
$591$	1.40886e16	0.0136003
$592$	−4.93751e17	−0.471430
$593$	2.60674e17	0.246174	0.123087	−	0.992396i	$-0.460721\pi$
$593$	2.60674e17	0.246174	0.123087	+	0.992396i	$0.460721\pi$
$594$	2.11918e16	0.0197950
$595$	1.61791e18	1.49484
$596$	−2.28072e17	−0.208435
$597$	−1.00499e16	−0.00908506
$598$	−5.59621e17	−0.500421
$599$	−1.12469e18	−0.994854	−0.497427	−	0.867506i	$-0.665722\pi$
$599$	−1.12469e18	−0.994854	−0.497427	+	0.867506i	$0.665722\pi$
$600$	1.66400e15	0.00145603
$601$	8.31214e17	0.719497	0.359748	−	0.933049i	$-0.382863\pi$
$601$	8.31214e17	0.719497	0.359748	+	0.933049i	$0.382863\pi$
$602$	−2.83590e17	−0.242836
$603$	−9.12207e17	−0.772735
$604$	5.28001e17	0.442481
$605$	2.90061e17	0.240480
$606$	2.11598e16	0.0173556
$607$	1.34369e17	0.109037	0.0545184	−	0.998513i	$-0.482638\pi$
$607$	1.34369e17	0.109037	0.0545184	+	0.998513i	$0.482638\pi$
$608$	−1.78763e17	−0.143517
$609$	−1.38599e16	−0.0110090
$610$	−2.92124e17	−0.229574
$611$	−1.09023e18	−0.847717
$612$	1.25508e18	0.965576
$613$	−1.38254e18	−1.05241	−0.526204	−	0.850358i	$-0.676385\pi$
$613$	−1.38254e18	−1.05241	−0.526204	+	0.850358i	$0.676385\pi$
$614$	9.68227e17	0.729261
$615$	2.86151e15	0.00213259
$616$	5.63971e17	0.415893
$617$	1.68618e16	0.0123041	0.00615206	−	0.999981i	$-0.498042\pi$
$617$	1.68618e16	0.0123041	0.00615206	+	0.999981i	$0.498042\pi$
$618$	3.20597e16	0.0231491
$619$	3.30206e16	0.0235937	0.0117969	−	0.999930i	$-0.496245\pi$
$619$	3.30206e16	0.0235937	0.0117969	+	0.999930i	$0.496245\pi$
$620$	2.20483e17	0.155894
$621$	−3.04086e16	−0.0212765
$622$	1.31620e18	0.911347
$623$	2.01865e18	1.38321
$624$	1.03968e16	0.00705015
$625$	5.96046e16	0.0400000
$626$	1.48578e18	0.986780
$627$	1.72922e16	0.0113661
$628$	1.13025e17	0.0735251
$629$	5.65857e18	3.64316
$630$	−8.58239e17	−0.546884
$631$	−4.58206e17	−0.288981	−0.144491	−	0.989506i	$-0.546154\pi$
$631$	−4.58206e17	−0.288981	−0.144491	+	0.989506i	$0.546154\pi$
$632$	−9.90065e17	−0.618020
$633$	4.39810e16	0.0271732
$634$	2.96886e17	0.181555
$635$	6.46947e17	0.391597
$636$	9.64768e15	0.00578032
$637$	−4.60325e18	−2.72997
$638$	2.53077e17	0.148565
$639$	2.04677e18	1.18936
$640$	6.87195e16	0.0395285
$641$	−2.67525e18	−1.52330	−0.761652	−	0.647986i	$-0.775611\pi$
$641$	−2.67525e18	−1.52330	−0.761652	+	0.647986i	$0.775611\pi$
$642$	−1.49491e16	−0.00842630
$643$	−2.19580e18	−1.22524	−0.612621	−	0.790377i	$-0.709885\pi$
$643$	−2.19580e18	−1.22524	−0.612621	+	0.790377i	$0.709885\pi$
$644$	−8.09254e17	−0.447020
$645$	3.34263e15	0.00182789
$646$	2.04869e18	1.10908
$647$	5.29588e16	0.0283831	0.0141916	−	0.999899i	$-0.495483\pi$
$647$	5.29588e16	0.0283831	0.0141916	+	0.999899i	$0.495483\pi$
$648$	−6.65487e17	−0.353104
$649$	−5.03483e17	−0.264481
$650$	3.72413e17	0.193682
$651$	4.82375e16	0.0248375
$652$	−5.13967e17	−0.262015
$653$	2.58483e17	0.130466	0.0652328	−	0.997870i	$-0.479221\pi$
$653$	2.58483e17	0.130466	0.0652328	+	0.997870i	$0.479221\pi$
$654$	−7.77929e14	−0.000388763 0
$655$	9.00064e17	0.445354
$656$	1.18174e17	0.0578957
$657$	−3.13144e17	−0.151904
$658$	−1.57656e18	−0.757254
$659$	−3.03104e18	−1.44157	−0.720785	−	0.693159i	$-0.756219\pi$
$659$	−3.03104e18	−1.44157	−0.720785	+	0.693159i	$0.756219\pi$
$660$	−6.64743e15	−0.00313053
$661$	−5.49397e17	−0.256198	−0.128099	−	0.991761i	$-0.540888\pi$
$661$	−5.49397e17	−0.256198	−0.128099	+	0.991761i	$0.540888\pi$
$662$	9.24840e17	0.427061
$663$	−1.19151e17	−0.0544828
$664$	1.19455e18	0.540893
$665$	−1.40092e18	−0.628164
$666$	−3.00165e18	−1.33284
$667$	−3.63145e17	−0.159684
$668$	−1.90727e18	−0.830549
$669$	−3.06234e16	−0.0132064
$670$	5.72402e17	0.244464
$671$	1.16699e18	0.493595
$672$	1.50345e16	0.00629781
$673$	−8.33991e17	−0.345990	−0.172995	−	0.984923i	$-0.555344\pi$
$673$	−8.33991e17	−0.345990	−0.172995	+	0.984923i	$0.555344\pi$
$674$	2.12763e18	0.874192
$675$	2.02361e16	0.00823480
$676$	1.08628e18	0.437814
$677$	2.68034e18	1.06995	0.534975	−	0.844868i	$-0.320321\pi$
$677$	2.68034e18	1.06995	0.534975	+	0.844868i	$0.320321\pi$
$678$	2.79347e16	0.0110446
$679$	−1.47774e18	−0.578687
$680$	−7.87551e17	−0.305472
$681$	−7.40673e16	−0.0284558
$682$	−8.80796e17	−0.335179
$683$	4.37733e18	1.64997	0.824983	−	0.565157i	$-0.191185\pi$
$683$	4.37733e18	1.64997	0.824983	+	0.565157i	$0.191185\pi$
$684$	−1.08675e18	−0.405756
$685$	1.77688e17	0.0657156
$686$	−3.31723e18	−1.21526
$687$	3.90170e16	0.0141591
$688$	1.38043e17	0.0496238
$689$	2.15921e18	0.768900
$690$	9.53854e15	0.00336483
$691$	1.85207e18	0.647216	0.323608	−	0.946191i	$-0.395104\pi$
$691$	1.85207e18	0.647216	0.323608	+	0.946191i	$0.395104\pi$
$692$	−9.70934e17	−0.336125
$693$	3.42854e18	1.17583
$694$	−1.36729e18	−0.464540
$695$	−1.77041e17	−0.0595901
$696$	6.74660e15	0.00224970
$697$	−1.35432e18	−0.447412
$698$	2.84449e18	0.930987
$699$	8.54602e15	0.00277116
$700$	5.38538e17	0.173013
$701$	2.17943e18	0.693708	0.346854	−	0.937919i	$-0.387250\pi$
$701$	2.17943e18	0.693708	0.346854	+	0.937919i	$0.387250\pi$
$702$	1.26437e17	0.0398732
$703$	−4.89965e18	−1.53093
$704$	−2.74524e17	−0.0849880
$705$	1.85826e16	0.00570004
$706$	1.92144e18	0.583978
$707$	6.84817e18	2.06228
$708$	−1.34220e16	−0.00400499
$709$	−8.99593e17	−0.265978	−0.132989	−	0.991118i	$-0.542457\pi$
$709$	−8.99593e17	−0.265978	−0.132989	+	0.991118i	$0.542457\pi$
$710$	−1.28433e18	−0.376268
$711$	−6.01888e18	−1.74728
$712$	−9.82619e17	−0.282661
$713$	1.26387e18	0.360265
$714$	−1.72301e17	−0.0486687
$715$	−1.48773e18	−0.416424
$716$	1.57363e18	0.436483
$717$	−1.00553e17	−0.0276388
$718$	2.95570e17	0.0805102
$719$	−9.53229e17	−0.257312	−0.128656	−	0.991689i	$-0.541066\pi$
$719$	−9.53229e17	−0.257312	−0.128656	+	0.991689i	$0.541066\pi$
$720$	4.17765e17	0.111756
$721$	1.03758e19	2.75070
$722$	9.17471e17	0.241046
$723$	5.70154e16	0.0148455
$724$	−2.99212e18	−0.772109
$725$	2.41664e17	0.0618038
$726$	−3.08903e16	−0.00782951
$727$	−1.32662e18	−0.333253	−0.166627	−	0.986020i	$-0.553287\pi$
$727$	−1.32662e18	−0.333253	−0.166627	+	0.986020i	$0.553287\pi$
$728$	3.36482e18	0.837736
$729$	−4.04225e18	−0.997457
$730$	1.96495e17	0.0480566
$731$	−1.58203e18	−0.383487
$732$	3.11100e16	0.00747443
$733$	2.87320e18	0.684210	0.342105	−	0.939662i	$-0.388860\pi$
$733$	2.87320e18	0.684210	0.342105	+	0.939662i	$0.388860\pi$
$734$	−4.34196e18	−1.02485
$735$	7.84608e16	0.0183563
$736$	3.93920e17	0.0913488
$737$	−2.28666e18	−0.525609
$738$	7.18412e17	0.163684
$739$	−6.25648e18	−1.41300	−0.706498	−	0.707715i	$-0.749726\pi$
$739$	−6.25648e18	−1.41300	−0.706498	+	0.707715i	$0.749726\pi$
$740$	1.88351e18	0.421659
$741$	1.03170e17	0.0228948
$742$	3.12238e18	0.686848
$743$	−6.93379e18	−1.51197	−0.755985	−	0.654589i	$-0.772842\pi$
$743$	−6.93379e18	−1.51197	−0.755985	+	0.654589i	$0.772842\pi$
$744$	−2.34806e16	−0.00507557
$745$	8.70024e17	0.186430
$746$	−3.43157e18	−0.728939
$747$	7.26200e18	1.52923
$748$	3.14615e18	0.656778
$749$	−4.83813e18	−1.00126
$750$	−6.34766e15	−0.00130231
$751$	1.99137e17	0.0405035	0.0202518	−	0.999795i	$-0.493553\pi$
$751$	1.99137e17	0.0405035	0.0202518	+	0.999795i	$0.493553\pi$
$752$	7.67421e17	0.154745
$753$	−1.50109e17	−0.0300081
$754$	1.50993e18	0.299256
$755$	−2.01416e18	−0.395767
$756$	1.82837e17	0.0356182
$757$	−6.83318e18	−1.31977	−0.659887	−	0.751365i	$-0.729396\pi$
$757$	−6.83318e18	−1.31977	−0.659887	+	0.751365i	$0.729396\pi$
$758$	3.50767e18	0.671691
$759$	−3.81050e16	−0.00723454
$760$	6.81926e17	0.128366
$761$	−1.23923e18	−0.231286	−0.115643	−	0.993291i	$-0.536893\pi$
$761$	−1.23923e18	−0.231286	−0.115643	+	0.993291i	$0.536893\pi$
$762$	−6.88973e16	−0.0127495
$763$	−2.51769e17	−0.0461948
$764$	1.86199e18	0.338744
$765$	−4.78774e18	−0.863638
$766$	−5.12835e18	−0.917256
$767$	−3.00393e18	−0.532746
$768$	−7.31835e15	−0.00128696
$769$	1.00332e19	1.74951	0.874757	−	0.484562i	$-0.161021\pi$
$769$	1.00332e19	1.74951	0.874757	+	0.484562i	$0.161021\pi$
$770$	−2.15138e18	−0.371986
$771$	−1.22250e17	−0.0209602
$772$	−4.21250e18	−0.716188
$773$	−3.19326e18	−0.538353	−0.269177	−	0.963091i	$-0.586752\pi$
$773$	−3.19326e18	−0.538353	−0.269177	+	0.963091i	$0.586752\pi$
$774$	8.39202e17	0.140298
$775$	−8.41076e17	−0.139436
$776$	7.19318e17	0.118255
$777$	4.12076e17	0.0671802
$778$	3.79846e18	0.614101
$779$	1.17268e18	0.188012
$780$	−3.96605e16	−0.00630585
$781$	5.13070e18	0.808993
$782$	−4.51448e18	−0.705933
$783$	8.20464e16	0.0127235
$784$	3.24025e18	0.498339
$785$	−4.31155e17	−0.0657629
$786$	−9.58533e16	−0.0144997
$787$	−5.21985e17	−0.0783109	−0.0391554	−	0.999233i	$-0.512467\pi$
$787$	−5.21985e17	−0.0783109	−0.0391554	+	0.999233i	$0.512467\pi$
$788$	−2.21949e18	−0.330243
$789$	1.57151e17	0.0231909
$790$	3.77680e18	0.552774
$791$	9.04079e18	1.31238
$792$	−1.66891e18	−0.240281
$793$	6.96261e18	0.994251
$794$	7.25997e18	1.02826
$795$	−3.68030e16	−0.00517007
$796$	1.58324e18	0.220604
$797$	9.98335e18	1.37974	0.689870	−	0.723934i	$-0.257668\pi$
$797$	9.98335e18	1.37974	0.689870	+	0.723934i	$0.257668\pi$
$798$	1.49192e17	0.0204516
$799$	−8.79493e18	−1.19586
$800$	−2.62144e17	−0.0353553
$801$	−5.97362e18	−0.799146
$802$	−1.12908e18	−0.149827
$803$	−7.84968e17	−0.103324
$804$	−6.09585e16	−0.00795921
$805$	3.08706e18	0.399827
$806$	−5.25509e18	−0.675154
$807$	1.58454e17	0.0201942
$808$	−3.33348e18	−0.421429
$809$	1.32158e19	1.65740	0.828702	−	0.559690i	$-0.189080\pi$
$809$	1.32158e19	1.65740	0.828702	+	0.559690i	$0.189080\pi$
$810$	2.53863e18	0.315826
$811$	2.60256e18	0.321192	0.160596	−	0.987020i	$-0.448658\pi$
$811$	2.60256e18	0.321192	0.160596	+	0.987020i	$0.448658\pi$
$812$	2.18347e18	0.267322
$813$	−1.74184e17	−0.0211553
$814$	−7.52434e18	−0.906587
$815$	1.96063e18	0.234353
$816$	8.38710e16	0.00994549
$817$	1.36985e18	0.161149
$818$	−4.79510e18	−0.559630
$819$	2.04557e19	2.36847
$820$	−4.50798e17	−0.0517835
$821$	−6.89915e18	−0.786258	−0.393129	−	0.919483i	$-0.628607\pi$
$821$	−6.89915e18	−0.786258	−0.393129	+	0.919483i	$0.628607\pi$
$822$	−1.89230e16	−0.00213956
$823$	4.94809e17	0.0555059	0.0277529	−	0.999615i	$-0.491165\pi$
$823$	4.94809e17	0.0555059	0.0277529	+	0.999615i	$0.491165\pi$
$824$	−5.05064e18	−0.562108
$825$	2.53579e16	0.00280003
$826$	−4.34391e18	−0.475894
$827$	−8.43301e18	−0.916636	−0.458318	−	0.888788i	$-0.651548\pi$
$827$	−8.43301e18	−0.916636	−0.458318	+	0.888788i	$0.651548\pi$
$828$	2.39475e18	0.258264
$829$	2.23464e18	0.239113	0.119556	−	0.992827i	$-0.461853\pi$
$829$	2.23464e18	0.239113	0.119556	+	0.992827i	$0.461853\pi$
$830$	−4.55684e18	−0.483790
$831$	−1.91818e17	−0.0202061
$832$	−1.63789e18	−0.171192
$833$	−3.71345e19	−3.85111
$834$	1.88542e16	0.00194012
$835$	7.27566e18	0.742866
$836$	−2.72419e18	−0.275992
$837$	−2.85550e17	−0.0287057
$838$	4.06534e18	0.405518
$839$	−1.17716e19	−1.16516	−0.582578	−	0.812775i	$-0.697956\pi$
$839$	−1.17716e19	−1.16516	−0.582578	+	0.812775i	$0.697956\pi$
$840$	−5.73521e16	−0.00563293
$841$	−9.28081e18	−0.904507
$842$	6.99556e18	0.676541
$843$	2.47627e16	0.00237640
$844$	−6.92869e18	−0.659820
$845$	−4.14384e18	−0.391592
$846$	4.66537e18	0.437501
$847$	−9.99737e18	−0.930344
$848$	−1.51988e18	−0.140358
$849$	1.48919e17	0.0136474
$850$	3.00427e18	0.273222
$851$	1.07968e19	0.974439
$852$	1.36776e17	0.0122505
$853$	6.76183e18	0.601030	0.300515	−	0.953777i	$-0.402842\pi$
$853$	6.76183e18	0.601030	0.300515	+	0.953777i	$0.402842\pi$
$854$	1.00685e19	0.888151
$855$	4.14562e18	0.362919
$856$	2.35506e18	0.204608
$857$	−1.42227e18	−0.122633	−0.0613165	−	0.998118i	$-0.519530\pi$
$857$	−1.42227e18	−0.122633	−0.0613165	+	0.998118i	$0.519530\pi$
$858$	1.58438e17	0.0135579
$859$	2.14250e19	1.81956	0.909778	−	0.415096i	$-0.136252\pi$
$859$	2.14250e19	1.81956	0.909778	+	0.415096i	$0.136252\pi$
$860$	−5.26592e17	−0.0443848
$861$	−9.86260e16	−0.00825032
$862$	−1.03706e19	−0.861006
$863$	5.34773e18	0.440656	0.220328	−	0.975426i	$-0.429287\pi$
$863$	5.34773e18	0.440656	0.220328	+	0.975426i	$0.429287\pi$
$864$	−8.89995e16	−0.00727860
$865$	3.70382e18	0.300639
$866$	3.08434e18	0.248482
$867$	−7.03675e17	−0.0562662
$868$	−7.59927e18	−0.603106
$869$	−1.50877e19	−1.18849
$870$	−2.57362e16	−0.00201220
$871$	−1.36429e19	−1.05874
$872$	1.22554e17	0.00943994
$873$	4.37294e18	0.334334
$874$	3.90900e18	0.296648
$875$	−2.05436e18	−0.154748
$876$	−2.09259e16	−0.00156462
$877$	1.73071e19	1.28448	0.642240	−	0.766504i	$-0.278005\pi$
$877$	1.73071e19	1.28448	0.642240	+	0.766504i	$0.278005\pi$
$878$	−5.26848e18	−0.388124
$879$	−3.35190e16	−0.00245112
$880$	1.04723e18	0.0760156
$881$	−1.11075e19	−0.800338	−0.400169	−	0.916441i	$-0.631048\pi$
$881$	−1.11075e19	−0.800338	−0.400169	+	0.916441i	$0.631048\pi$
$882$	1.96984e19	1.40892
$883$	3.47824e18	0.246954	0.123477	−	0.992347i	$-0.460596\pi$
$883$	3.47824e18	0.246954	0.123477	+	0.992347i	$0.460596\pi$
$884$	1.87708e19	1.32295
$885$	5.12009e16	0.00358217
$886$	1.73836e19	1.20732
$887$	2.70934e19	1.86793	0.933963	−	0.357369i	$-0.116326\pi$
$887$	2.70934e19	1.86793	0.933963	+	0.357369i	$0.116326\pi$
$888$	−2.00586e17	−0.0137283
$889$	−2.22980e19	−1.51497
$890$	3.74839e18	0.252819
$891$	−1.01415e19	−0.679040
$892$	4.82437e18	0.320678
$893$	7.61537e18	0.502524
$894$	−9.26541e16	−0.00606975
$895$	−6.00291e18	−0.390402
$896$	−2.36852e18	−0.152923
$897$	−2.27346e17	−0.0145726
$898$	−1.68055e19	−1.06943
$899$	−3.41010e18	−0.215441
$900$	−1.59365e18	−0.0999576
$901$	1.74184e19	1.08467
$902$	1.80087e18	0.111337
$903$	−1.15208e17	−0.00707154
$904$	−4.40078e18	−0.268186
$905$	1.14140e19	0.690595
$906$	2.14501e17	0.0128853
$907$	−1.34136e19	−0.800015	−0.400007	−	0.916512i	$-0.630992\pi$
$907$	−1.34136e19	−0.800015	−0.400007	+	0.916512i	$0.630992\pi$
$908$	1.16685e19	0.690964
$909$	−2.02652e19	−1.19147
$910$	−1.28358e19	−0.749294
$911$	−1.28662e19	−0.745728	−0.372864	−	0.927886i	$-0.621624\pi$
$911$	−1.28662e19	−0.745728	−0.372864	+	0.927886i	$0.621624\pi$
$912$	−7.26223e16	−0.00417930
$913$	1.82039e19	1.04017
$914$	−9.59963e18	−0.544633
$915$	−1.18675e17	−0.00668533
$916$	−6.14667e18	−0.343811
$917$	−3.10220e19	−1.72294
$918$	1.01997e18	0.0562482
$919$	1.28399e19	0.703089	0.351544	−	0.936171i	$-0.385657\pi$
$919$	1.28399e19	0.703089	0.351544	+	0.936171i	$0.385657\pi$
$920$	−1.50269e18	−0.0817048
$921$	3.93342e17	0.0212365
$922$	−1.26101e19	−0.676031
$923$	3.06113e19	1.62956
$924$	2.29113e17	0.0121111
$925$	−7.18502e18	−0.377144
$926$	2.19763e19	1.14547
$927$	−3.07043e19	−1.58921
$928$	−1.06285e18	−0.0546273
$929$	8.41438e18	0.429457	0.214729	−	0.976674i	$-0.431113\pi$
$929$	8.41438e18	0.429457	0.214729	+	0.976674i	$0.431113\pi$
$930$	8.95713e16	0.00453972
$931$	3.21541e19	1.61832
$932$	−1.34633e18	−0.0672895
$933$	5.34706e17	0.0265390
$934$	−1.56335e19	−0.770551
$935$	−1.20016e19	−0.587440
$936$	−9.95720e18	−0.483999
$937$	−2.21089e17	−0.0106723	−0.00533617	−	0.999986i	$-0.501699\pi$
$937$	−2.21089e17	−0.0106723	−0.00533617	+	0.999986i	$0.501699\pi$
$938$	−1.97287e19	−0.945756
$939$	6.03597e17	0.0287356
$940$	−2.92748e18	−0.138408
$941$	−1.00979e19	−0.474131	−0.237066	−	0.971494i	$-0.576186\pi$
$941$	−1.00979e19	−0.474131	−0.237066	+	0.971494i	$0.576186\pi$
$942$	4.59163e16	0.00214110
$943$	−2.58411e18	−0.119670
$944$	2.11448e18	0.0972493
$945$	−6.97467e17	−0.0318579
$946$	2.10366e18	0.0954294
$947$	1.18021e19	0.531723	0.265861	−	0.964011i	$-0.414344\pi$
$947$	1.18021e19	0.531723	0.265861	+	0.964011i	$0.414344\pi$
$948$	−4.02214e17	−0.0179971
$949$	−4.68335e18	−0.208126
$950$	−2.60134e18	−0.114814
$951$	1.20610e17	0.00528700
$952$	2.71441e19	1.18178
$953$	1.35613e19	0.586407	0.293203	−	0.956050i	$-0.405279\pi$
$953$	1.35613e19	0.586407	0.293203	+	0.956050i	$0.405279\pi$
$954$	−9.23978e18	−0.396823
$955$	−7.10295e18	−0.302982
$956$	1.58409e19	0.671126
$957$	1.02812e17	0.00432631
$958$	1.04048e19	0.434870
$959$	−6.12426e18	−0.254233
$960$	2.79173e16	0.00115109
$961$	−1.25492e19	−0.513941
$962$	−4.48924e19	−1.82614
$963$	1.43170e19	0.578472
$964$	−8.98212e18	−0.360478
$965$	1.60694e19	0.640578
$966$	−3.28759e17	−0.0130175
$967$	−3.76100e17	−0.0147922	−0.00739608	−	0.999973i	$-0.502354\pi$
$967$	−3.76100e17	−0.0147922	−0.00739608	+	0.999973i	$0.502354\pi$
$968$	4.86642e18	0.190116
$969$	8.32279e17	0.0322972
$970$	−2.74398e18	−0.105771
$971$	−9.20189e17	−0.0352332	−0.0176166	−	0.999845i	$-0.505608\pi$
$971$	−9.20189e17	−0.0352332	−0.0176166	+	0.999845i	$0.505608\pi$
$972$	−8.11637e17	−0.0308696
$973$	6.10199e18	0.230536
$974$	−1.91222e19	−0.717638
$975$	1.51293e17	0.00564012
$976$	−4.90102e18	−0.181494
$977$	3.90955e19	1.43817	0.719087	−	0.694920i	$-0.244560\pi$
$977$	3.90955e19	1.43817	0.719087	+	0.694920i	$0.244560\pi$
$978$	−2.08799e17	−0.00763003
$979$	−1.49743e19	−0.543573
$980$	−1.23606e19	−0.445728
$981$	7.45039e17	0.0266889
$982$	3.21795e19	1.14513
$983$	2.09634e19	0.741078	0.370539	−	0.928817i	$-0.379173\pi$
$983$	2.09634e19	0.741078	0.370539	+	0.928817i	$0.379173\pi$
$984$	4.80081e16	0.00168596
$985$	8.46669e18	0.295378
$986$	1.21807e19	0.422154
$987$	−6.40477e17	−0.0220517
$988$	−1.62533e19	−0.555932
$989$	−3.01858e18	−0.102572
$990$	6.36638e18	0.214913
$991$	−2.87942e19	−0.965666	−0.482833	−	0.875713i	$-0.660392\pi$
$991$	−2.87942e19	−0.965666	−0.482833	+	0.875713i	$0.660392\pi$
$992$	3.69909e18	0.123245
$993$	3.75716e17	0.0124363
$994$	4.42663e19	1.45566
$995$	−6.03960e18	−0.197314
$996$	4.85286e17	0.0157511
$997$	4.15503e19	1.33985	0.669924	−	0.742430i	$-0.266327\pi$
$997$	4.15503e19	1.33985	0.669924	+	0.742430i	$0.266327\pi$
$998$	2.52813e19	0.809936
$999$	−2.43936e18	−0.0776426

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.14.a.a.1.1	✓	1
3.2	odd	2		90.14.a.i.1.1		1
4.3	odd	2		80.14.a.b.1.1		1
5.2	odd	4		50.14.b.c.49.1		2
5.3	odd	4		50.14.b.c.49.2		2
5.4	even	2		50.14.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.14.a.a.1.1	✓	1	1.1	even	1	trivial
50.14.a.d.1.1		1	5.4	even	2
50.14.b.c.49.1		2	5.2	odd	4
50.14.b.c.49.2		2	5.3	odd	4
80.14.a.b.1.1		1	4.3	odd	2
90.14.a.i.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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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