LMFDB - Embedded newform 10.26.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,26,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, 26, names="a")

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

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 26 $
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:	$39.5996779952$
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)

$f(q)$

$=$

$q+4096.00 q^{2} +162864. q^{3} +1.67772e7 q^{4} +2.44141e8 q^{5} +6.67091e8 q^{6} -1.76009e10 q^{7} +6.87195e10 q^{8} -8.20764e11 q^{9} +O(q^{10})$

\(q+4096.00 q^{2} +162864. q^{3} +1.67772e7 q^{4} +2.44141e8 q^{5} +6.67091e8 q^{6} -1.76009e10 q^{7} +6.87195e10 q^{8} -8.20764e11 q^{9} +1.00000e12 q^{10} -1.12404e13 q^{11} +2.73240e12 q^{12} +4.24221e12 q^{13} -7.20933e13 q^{14} +3.97617e13 q^{15} +2.81475e14 q^{16} -1.13786e15 q^{17} -3.36185e15 q^{18} +2.98985e15 q^{19} +4.09600e15 q^{20} -2.86655e15 q^{21} -4.60406e16 q^{22} -1.22305e17 q^{23} +1.11919e16 q^{24} +5.96046e16 q^{25} +1.73761e16 q^{26} -2.71666e17 q^{27} -2.95294e17 q^{28} -2.12048e18 q^{29} +1.62864e17 q^{30} +4.22586e18 q^{31} +1.15292e18 q^{32} -1.83065e18 q^{33} -4.66066e18 q^{34} -4.29709e18 q^{35} -1.37701e19 q^{36} +2.41679e19 q^{37} +1.22464e19 q^{38} +6.90903e17 q^{39} +1.67772e19 q^{40} -1.61564e20 q^{41} -1.17414e19 q^{42} -3.11612e20 q^{43} -1.88582e20 q^{44} -2.00382e20 q^{45} -5.00963e20 q^{46} -1.22586e21 q^{47} +4.58421e19 q^{48} -1.03128e21 q^{49} +2.44141e20 q^{50} -1.85316e20 q^{51} +7.11725e19 q^{52} -4.78915e20 q^{53} -1.11274e21 q^{54} -2.74423e21 q^{55} -1.20952e21 q^{56} +4.86938e20 q^{57} -8.68547e21 q^{58} +1.21434e22 q^{59} +6.67091e20 q^{60} -2.03328e22 q^{61} +1.73091e22 q^{62} +1.44462e22 q^{63} +4.72237e21 q^{64} +1.03570e21 q^{65} -7.49835e21 q^{66} +6.15653e22 q^{67} -1.90901e22 q^{68} -1.99192e22 q^{69} -1.76009e22 q^{70} +1.34077e23 q^{71} -5.64025e22 q^{72} +2.23779e23 q^{73} +9.89916e22 q^{74} +9.70745e21 q^{75} +5.01613e22 q^{76} +1.97841e23 q^{77} +2.82994e21 q^{78} +3.82350e23 q^{79} +6.87195e22 q^{80} +6.51179e23 q^{81} -6.61767e23 q^{82} -7.71818e23 q^{83} -4.80928e22 q^{84} -2.77797e23 q^{85} -1.27636e24 q^{86} -3.45349e23 q^{87} -7.72433e23 q^{88} -8.40581e23 q^{89} -8.20764e23 q^{90} -7.46667e22 q^{91} -2.05195e24 q^{92} +6.88241e23 q^{93} -5.02111e24 q^{94} +7.29943e23 q^{95} +1.87769e23 q^{96} -6.19164e24 q^{97} -4.22411e24 q^{98} +9.22569e24 q^{99} +O(q^{100})\)

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 $

$2$	4096.00	0.707107
$2$	4096.00	0.707107
$3$	162864.	0.176933	0.0884666	−	0.996079i	$-0.471803\pi$
$3$	162864.	0.176933	0.0884666	+	0.996079i	$0.471803\pi$
$4$	1.67772e7	0.500000
$5$	2.44141e8	0.447214
$5$	2.44141e8	0.447214
$6$	6.67091e8	0.125111
$7$	−1.76009e10	−0.480628	−0.240314	−	0.970695i	$-0.577250\pi$
$7$	−1.76009e10	−0.480628	−0.240314	+	0.970695i	$0.577250\pi$
$8$	6.87195e10	0.353553
$9$	−8.20764e11	−0.968695
$10$	1.00000e12	0.316228
$11$	−1.12404e13	−1.07987	−0.539936	−	0.841706i	$-0.681552\pi$
$11$	−1.12404e13	−1.07987	−0.539936	+	0.841706i	$0.681552\pi$
$12$	2.73240e12	0.0884666
$13$	4.24221e12	0.0505010	0.0252505	−	0.999681i	$-0.491962\pi$
$13$	4.24221e12	0.0505010	0.0252505	+	0.999681i	$0.491962\pi$
$14$	−7.20933e13	−0.339855
$15$	3.97617e13	0.0791269
$16$	2.81475e14	0.250000
$17$	−1.13786e15	−0.473670	−0.236835	−	0.971550i	$-0.576110\pi$
$17$	−1.13786e15	−0.473670	−0.236835	+	0.971550i	$0.576110\pi$
$18$	−3.36185e15	−0.684971
$19$	2.98985e15	0.309905	0.154953	−	0.987922i	$-0.450478\pi$
$19$	2.98985e15	0.309905	0.154953	+	0.987922i	$0.450478\pi$
$20$	4.09600e15	0.223607
$21$	−2.86655e15	−0.0850391
$22$	−4.60406e16	−0.763585
$23$	−1.22305e17	−1.16372	−0.581859	−	0.813290i	$-0.697675\pi$
$23$	−1.22305e17	−1.16372	−0.581859	+	0.813290i	$0.697675\pi$
$24$	1.11919e16	0.0625553
$25$	5.96046e16	0.200000
$26$	1.73761e16	0.0357096
$27$	−2.71666e17	−0.348328
$28$	−2.95294e17	−0.240314
$29$	−2.12048e18	−1.11291	−0.556453	−	0.830879i	$-0.687838\pi$
$29$	−2.12048e18	−1.11291	−0.556453	+	0.830879i	$0.687838\pi$
$30$	1.62864e17	0.0559512
$31$	4.22586e18	0.963594	0.481797	−	0.876283i	$-0.339984\pi$
$31$	4.22586e18	0.963594	0.481797	+	0.876283i	$0.339984\pi$
$32$	1.15292e18	0.176777
$33$	−1.83065e18	−0.191065
$34$	−4.66066e18	−0.334935
$35$	−4.29709e18	−0.214943
$36$	−1.37701e19	−0.484347
$37$	2.41679e19	0.603555	0.301778	−	0.953378i	$-0.402420\pi$
$37$	2.41679e19	0.603555	0.301778	+	0.953378i	$0.402420\pi$
$38$	1.22464e19	0.219136
$39$	6.90903e17	0.00893531
$40$	1.67772e19	0.158114
$41$	−1.61564e20	−1.11827	−0.559136	−	0.829076i	$-0.688867\pi$
$41$	−1.61564e20	−1.11827	−0.559136	+	0.829076i	$0.688867\pi$
$42$	−1.17414e19	−0.0601317
$43$	−3.11612e20	−1.18921	−0.594605	−	0.804018i	$-0.702692\pi$
$43$	−3.11612e20	−1.18921	−0.594605	+	0.804018i	$0.702692\pi$
$44$	−1.88582e20	−0.539936
$45$	−2.00382e20	−0.433213
$46$	−5.00963e20	−0.822873
$47$	−1.22586e21	−1.53892	−0.769461	−	0.638694i	$-0.779475\pi$
$47$	−1.22586e21	−1.53892	−0.769461	+	0.638694i	$0.779475\pi$
$48$	4.58421e19	0.0442333
$49$	−1.03128e21	−0.768997
$50$	2.44141e20	0.141421
$51$	−1.85316e20	−0.0838079
$52$	7.11725e19	0.0252505
$53$	−4.78915e20	−0.133909	−0.0669546	−	0.997756i	$-0.521328\pi$
$53$	−4.78915e20	−0.133909	−0.0669546	+	0.997756i	$0.521328\pi$
$54$	−1.11274e21	−0.246305
$55$	−2.74423e21	−0.482933
$56$	−1.20952e21	−0.169928
$57$	4.86938e20	0.0548325
$58$	−8.68547e21	−0.786943
$59$	1.21434e22	0.888566	0.444283	−	0.895887i	$-0.353459\pi$
$59$	1.21434e22	0.888566	0.444283	+	0.895887i	$0.353459\pi$
$60$	6.67091e20	0.0395635
$61$	−2.03328e22	−0.980786	−0.490393	−	0.871501i	$-0.663147\pi$
$61$	−2.03328e22	−0.980786	−0.490393	+	0.871501i	$0.663147\pi$
$62$	1.73091e22	0.681364
$63$	1.44462e22	0.465582
$64$	4.72237e21	0.125000
$65$	1.03570e21	0.0225847
$66$	−7.49835e21	−0.135104
$67$	6.15653e22	0.919180	0.459590	−	0.888131i	$-0.347996\pi$
$67$	6.15653e22	0.919180	0.459590	+	0.888131i	$0.347996\pi$
$68$	−1.90901e22	−0.236835
$69$	−1.99192e22	−0.205900
$70$	−1.76009e22	−0.151988
$71$	1.34077e23	0.969669	0.484835	−	0.874606i	$-0.338880\pi$
$71$	1.34077e23	0.969669	0.484835	+	0.874606i	$0.338880\pi$
$72$	−5.64025e22	−0.342485
$73$	2.23779e23	1.14362	0.571811	−	0.820385i	$-0.306241\pi$
$73$	2.23779e23	1.14362	0.571811	+	0.820385i	$0.306241\pi$
$74$	9.89916e22	0.426778
$75$	9.70745e21	0.0353866
$76$	5.01613e22	0.154953
$77$	1.97841e23	0.519017
$78$	2.82994e21	0.00631822
$79$	3.82350e23	0.727985	0.363992	−	0.931402i	$-0.381413\pi$
$79$	3.82350e23	0.727985	0.363992	+	0.931402i	$0.381413\pi$
$80$	6.87195e22	0.111803
$81$	6.51179e23	0.907064
$82$	−6.61767e23	−0.790737
$83$	−7.71818e23	−0.792572	−0.396286	−	0.918127i	$-0.629701\pi$
$83$	−7.71818e23	−0.792572	−0.396286	+	0.918127i	$0.629701\pi$
$84$	−4.80928e22	−0.0425195
$85$	−2.77797e23	−0.211832
$86$	−1.27636e24	−0.840899
$87$	−3.45349e23	−0.196910
$88$	−7.72433e23	−0.381792
$89$	−8.40581e23	−0.360748	−0.180374	−	0.983598i	$-0.557731\pi$
$89$	−8.40581e23	−0.360748	−0.180374	+	0.983598i	$0.557731\pi$
$90$	−8.20764e23	−0.306328
$91$	−7.46667e22	−0.0242722
$92$	−2.05195e24	−0.581859
$93$	6.88241e23	0.170492
$94$	−5.02111e24	−1.08818
$95$	7.29943e23	0.138594
$96$	1.87769e23	0.0312777
$97$	−6.19164e24	−0.906064	−0.453032	−	0.891494i	$-0.649658\pi$
$97$	−6.19164e24	−0.906064	−0.453032	+	0.891494i	$0.649658\pi$
$98$	−4.22411e24	−0.543763
$99$	9.22569e24	1.04607
$100$	1.00000e24	0.100000
$101$	6.64342e24	0.586644	0.293322	−	0.956014i	$-0.405239\pi$
$101$	6.64342e24	0.586644	0.293322	+	0.956014i	$0.405239\pi$
$102$	−7.59053e23	−0.0592612
$103$	1.36741e25	0.945004	0.472502	−	0.881330i	$-0.343351\pi$
$103$	1.36741e25	0.945004	0.472502	+	0.881330i	$0.343351\pi$
$104$	2.91522e23	0.0178548
$105$	−6.99842e23	−0.0380306
$106$	−1.96164e24	−0.0946881
$107$	1.97392e24	0.0847290	0.0423645	−	0.999102i	$-0.486511\pi$
$107$	1.97392e24	0.0847290	0.0423645	+	0.999102i	$0.486511\pi$
$108$	−4.55779e24	−0.174164
$109$	4.86252e25	1.65588	0.827942	−	0.560813i	$-0.189511\pi$
$109$	4.86252e25	1.65588	0.827942	+	0.560813i	$0.189511\pi$
$110$	−1.12404e25	−0.341485
$111$	3.93608e24	0.106789
$112$	−4.95421e24	−0.120157
$113$	4.58410e25	0.994886	0.497443	−	0.867497i	$-0.334272\pi$
$113$	4.58410e25	0.994886	0.497443	+	0.867497i	$0.334272\pi$
$114$	1.99450e24	0.0387724
$115$	−2.98597e25	−0.520431
$116$	−3.55757e25	−0.556453
$117$	−3.48185e24	−0.0489201
$118$	4.97393e25	0.628311
$119$	2.00273e25	0.227659
$120$	2.73240e24	0.0279756
$121$	1.79989e25	0.166123
$122$	−8.32832e25	−0.693521
$123$	−2.63130e25	−0.197859
$124$	7.08982e25	0.481797
$125$	1.45519e25	0.0894427
$126$	5.91715e25	0.329216
$127$	−1.31721e26	−0.663911	−0.331955	−	0.943295i	$-0.607708\pi$
$127$	−1.31721e26	−0.663911	−0.331955	+	0.943295i	$0.607708\pi$
$128$	1.93428e25	0.0883883
$129$	−5.07504e25	−0.210411
$130$	4.24221e24	0.0159698
$131$	−7.36281e25	−0.251856	−0.125928	−	0.992039i	$-0.540191\pi$
$131$	−7.36281e25	−0.251856	−0.125928	+	0.992039i	$0.540191\pi$
$132$	−3.07132e25	−0.0955326
$133$	−5.26240e25	−0.148949
$134$	2.52171e26	0.649959
$135$	−6.63246e25	−0.155777
$136$	−7.81929e25	−0.167468
$137$	−9.58320e26	−1.87285	−0.936426	−	0.350866i	$-0.885887\pi$
$137$	−9.58320e26	−1.87285	−0.936426	+	0.350866i	$0.885887\pi$
$138$	−8.15889e25	−0.145594
$139$	−4.90566e26	−0.799858	−0.399929	−	0.916546i	$-0.630965\pi$
$139$	−4.90566e26	−0.799858	−0.399929	+	0.916546i	$0.630965\pi$
$140$	−7.20933e25	−0.107472
$141$	−1.99648e26	−0.272286
$142$	5.49178e26	0.685660
$143$	−4.76840e25	−0.0545346
$144$	−2.31025e26	−0.242174
$145$	−5.17694e26	−0.497706
$146$	9.16597e26	0.808664
$147$	−1.67958e26	−0.136061
$148$	4.05470e26	0.301778
$149$	9.09615e26	0.622342	0.311171	−	0.950354i	$-0.399279\pi$
$149$	9.09615e26	0.622342	0.311171	+	0.950354i	$0.399279\pi$
$150$	3.97617e25	0.0250221
$151$	8.24560e26	0.477541	0.238770	−	0.971076i	$-0.423256\pi$
$151$	8.24560e26	0.477541	0.238770	+	0.971076i	$0.423256\pi$
$152$	2.05461e26	0.109568
$153$	9.33911e26	0.458841
$154$	8.10355e26	0.367000
$155$	1.03170e27	0.430932
$156$	1.15914e25	0.00446765
$157$	9.72907e26	0.346199	0.173099	−	0.984904i	$-0.444622\pi$
$157$	9.72907e26	0.346199	0.173099	+	0.984904i	$0.444622\pi$
$158$	1.56610e27	0.514763
$159$	−7.79981e25	−0.0236930
$160$	2.81475e26	0.0790569
$161$	2.15269e27	0.559316
$162$	2.66723e27	0.641391
$163$	−2.54973e27	−0.567740	−0.283870	−	0.958863i	$-0.591618\pi$
$163$	−2.54973e27	−0.567740	−0.283870	+	0.958863i	$0.591618\pi$
$164$	−2.71060e27	−0.559136
$165$	−4.46937e26	−0.0854470
$166$	−3.16137e27	−0.560433
$167$	8.09067e27	1.33054	0.665271	−	0.746602i	$-0.268316\pi$
$167$	8.09067e27	1.33054	0.665271	+	0.746602i	$0.268316\pi$
$168$	−1.96988e26	−0.0300659
$169$	−7.03841e27	−0.997450
$170$	−1.13786e27	−0.149788
$171$	−2.45396e27	−0.300203
$172$	−5.22799e27	−0.594605
$173$	4.51555e27	0.477677	0.238838	−	0.971059i	$-0.423233\pi$
$173$	4.51555e27	0.477677	0.238838	+	0.971059i	$0.423233\pi$
$174$	−1.41455e27	−0.139236
$175$	−1.04910e27	−0.0961256
$176$	−3.16388e27	−0.269968
$177$	1.97772e27	0.157217
$178$	−3.44302e27	−0.255088
$179$	−1.94694e28	−1.34490	−0.672450	−	0.740143i	$-0.734758\pi$
$179$	−1.94694e28	−1.34490	−0.672450	+	0.740143i	$0.734758\pi$
$180$	−3.36185e27	−0.216607
$181$	−1.21952e28	−0.733176	−0.366588	−	0.930383i	$-0.619474\pi$
$181$	−1.21952e28	−0.733176	−0.366588	+	0.930383i	$0.619474\pi$
$182$	−3.05835e26	−0.0171630
$183$	−3.31148e27	−0.173534
$184$	−8.40477e27	−0.411437
$185$	5.90036e27	0.269918
$186$	2.81903e27	0.120556
$187$	1.27899e28	0.511503
$188$	−2.05665e28	−0.769461
$189$	4.78156e27	0.167416
$190$	2.98985e27	0.0980006
$191$	6.11119e28	1.87590	0.937948	−	0.346775i	$-0.112723\pi$
$191$	6.11119e28	1.87590	0.937948	+	0.346775i	$0.112723\pi$
$192$	7.69103e26	0.0221167
$193$	6.48935e28	1.74878	0.874389	−	0.485226i	$-0.161263\pi$
$193$	6.48935e28	1.74878	0.874389	+	0.485226i	$0.161263\pi$
$194$	−2.53610e28	−0.640684
$195$	1.68678e26	0.00399599
$196$	−1.73020e28	−0.384498
$197$	−3.17525e28	−0.662140	−0.331070	−	0.943606i	$-0.607410\pi$
$197$	−3.17525e28	−0.662140	−0.331070	+	0.943606i	$0.607410\pi$
$198$	3.77884e28	0.739680
$199$	−7.39236e28	−1.35869	−0.679344	−	0.733820i	$-0.737735\pi$
$199$	−7.39236e28	−1.35869	−0.679344	+	0.733820i	$0.737735\pi$
$200$	4.09600e27	0.0707107
$201$	1.00268e28	0.162634
$202$	2.72115e28	0.414820
$203$	3.73223e28	0.534894
$204$	−3.10908e27	−0.0419040
$205$	−3.94444e28	−0.500106
$206$	5.60091e28	0.668218
$207$	1.00384e29	1.12729
$208$	1.19408e27	0.0126253
$209$	−3.36070e28	−0.334658
$210$	−2.86655e27	−0.0268917
$211$	1.18016e28	0.104330	0.0521652	−	0.998638i	$-0.483388\pi$
$211$	1.18016e28	0.104330	0.0521652	+	0.998638i	$0.483388\pi$
$212$	−8.03487e27	−0.0669546
$213$	2.18363e28	0.171567
$214$	8.08517e27	0.0599124
$215$	−7.60772e28	−0.531831
$216$	−1.86687e28	−0.123152
$217$	−7.43790e28	−0.463131
$218$	1.99169e29	1.17089
$219$	3.64455e28	0.202345
$220$	−4.60406e28	−0.241467
$221$	−4.82702e27	−0.0239208
$222$	1.61222e28	0.0755112
$223$	1.55992e28	0.0690704	0.0345352	−	0.999403i	$-0.489005\pi$
$223$	1.55992e28	0.0690704	0.0345352	+	0.999403i	$0.489005\pi$
$224$	−2.02924e28	−0.0849639
$225$	−4.89213e28	−0.193739
$226$	1.87765e29	0.703491
$227$	−3.57748e29	−1.26839	−0.634197	−	0.773171i	$-0.718669\pi$
$227$	−3.57748e29	−1.26839	−0.634197	+	0.773171i	$0.718669\pi$
$228$	8.16947e27	0.0274163
$229$	−6.16468e29	−1.95870	−0.979348	−	0.202179i	$-0.935198\pi$
$229$	−6.16468e29	−1.95870	−0.979348	+	0.202179i	$0.935198\pi$
$230$	−1.22305e29	−0.368000
$231$	3.22211e28	0.0918313
$232$	−1.45718e29	−0.393472
$233$	5.68344e29	1.45433	0.727163	−	0.686464i	$-0.240838\pi$
$233$	5.68344e29	1.45433	0.727163	+	0.686464i	$0.240838\pi$
$234$	−1.42617e28	−0.0345917
$235$	−2.99282e29	−0.688227
$236$	2.03732e29	0.444283
$237$	6.22710e28	0.128805
$238$	8.20317e28	0.160979
$239$	−5.96388e29	−1.11059	−0.555296	−	0.831653i	$-0.687395\pi$
$239$	−5.96388e29	−1.11059	−0.555296	+	0.831653i	$0.687395\pi$
$240$	1.11919e28	0.0197817
$241$	−4.97938e29	−0.835530	−0.417765	−	0.908555i	$-0.637187\pi$
$241$	−4.97938e29	−0.835530	−0.417765	+	0.908555i	$0.637187\pi$
$242$	7.37237e28	0.117467
$243$	3.36233e29	0.508817
$244$	−3.41128e29	−0.490393
$245$	−2.51777e29	−0.343906
$246$	−1.07778e29	−0.139908
$247$	1.26835e28	0.0156505
$248$	2.90399e29	0.340682
$249$	−1.25701e29	−0.140232
$250$	5.96046e28	0.0632456
$251$	1.75610e30	1.77267	0.886335	−	0.463044i	$-0.153243\pi$
$251$	1.75610e30	1.77267	0.886335	+	0.463044i	$0.153243\pi$
$252$	2.42367e29	0.232791
$253$	1.37476e30	1.25667
$254$	−5.39531e29	−0.469456
$255$	−4.52431e28	−0.0374801
$256$	7.92282e28	0.0625000
$257$	1.22065e30	0.917123	0.458562	−	0.888663i	$-0.348365\pi$
$257$	1.22065e30	0.917123	0.458562	+	0.888663i	$0.348365\pi$
$258$	−2.07874e29	−0.148783
$259$	−4.25376e29	−0.290086
$260$	1.73761e28	0.0112924
$261$	1.74041e30	1.07807
$262$	−3.01581e29	−0.178089
$263$	2.27827e30	1.28280	0.641399	−	0.767207i	$-0.278354\pi$
$263$	2.27827e30	1.28280	0.641399	+	0.767207i	$0.278354\pi$
$264$	−1.25801e29	−0.0675518
$265$	−1.16923e29	−0.0598860
$266$	−2.15548e29	−0.105323
$267$	−1.36900e29	−0.0638284
$268$	1.03289e30	0.459590
$269$	−3.12815e30	−1.32857	−0.664284	−	0.747480i	$-0.731264\pi$
$269$	−3.12815e30	−1.32857	−0.664284	+	0.747480i	$0.731264\pi$
$270$	−2.71666e29	−0.110151
$271$	1.31818e30	0.510339	0.255170	−	0.966896i	$-0.417869\pi$
$271$	1.31818e30	0.510339	0.255170	+	0.966896i	$0.417869\pi$
$272$	−3.20278e29	−0.118417
$273$	−1.21605e28	−0.00429456
$274$	−3.92528e30	−1.32431
$275$	−6.69978e29	−0.215974
$276$	−3.34188e29	−0.102950
$277$	2.11862e30	0.623815	0.311908	−	0.950112i	$-0.399032\pi$
$277$	2.11862e30	0.623815	0.311908	+	0.950112i	$0.399032\pi$
$278$	−2.00936e30	−0.565585
$279$	−3.46844e30	−0.933429
$280$	−2.95294e29	−0.0759940
$281$	−6.37141e30	−1.56822	−0.784109	−	0.620623i	$-0.786880\pi$
$281$	−6.37141e30	−1.56822	−0.784109	+	0.620623i	$0.786880\pi$
$282$	−8.17758e29	−0.192536
$283$	3.00725e30	0.677391	0.338695	−	0.940896i	$-0.390014\pi$
$283$	3.00725e30	0.677391	0.338695	+	0.940896i	$0.390014\pi$
$284$	2.24943e30	0.484835
$285$	1.18881e29	0.0245218
$286$	−1.95314e29	−0.0385618
$287$	2.84368e30	0.537473
$288$	−9.46276e29	−0.171243
$289$	−4.47591e30	−0.775637
$290$	−2.12048e30	−0.351932
$291$	−1.00840e30	−0.160313
$292$	3.75438e30	0.571811
$293$	−7.19334e30	−1.04975	−0.524875	−	0.851180i	$-0.675888\pi$
$293$	−7.19334e30	−1.04975	−0.524875	+	0.851180i	$0.675888\pi$
$294$	−6.87956e29	−0.0962097
$295$	2.96469e30	0.397379
$296$	1.66080e30	0.213389
$297$	3.05362e30	0.376149
$298$	3.72578e30	0.440063
$299$	−5.18845e29	−0.0587690
$300$	1.62864e29	0.0176933
$301$	5.48465e30	0.571568
$302$	3.37740e30	0.337672
$303$	1.08197e30	0.103797
$304$	8.41567e29	0.0774763
$305$	−4.96406e30	−0.438621
$306$	3.82530e30	0.324450
$307$	−6.08638e30	−0.495597	−0.247799	−	0.968812i	$-0.579707\pi$
$307$	−6.08638e30	−0.495597	−0.247799	+	0.968812i	$0.579707\pi$
$308$	3.31921e30	0.259508
$309$	2.22702e30	0.167203
$310$	4.22586e30	0.304715
$311$	3.60168e30	0.249460	0.124730	−	0.992191i	$-0.460194\pi$
$311$	3.60168e30	0.249460	0.124730	+	0.992191i	$0.460194\pi$
$312$	4.74785e28	0.00315911
$313$	3.07166e30	0.196367	0.0981835	−	0.995168i	$-0.468697\pi$
$313$	3.07166e30	0.196367	0.0981835	+	0.995168i	$0.468697\pi$
$314$	3.98503e30	0.244800
$315$	3.52690e30	0.208215
$316$	6.41476e30	0.363992
$317$	−2.80660e31	−1.53088	−0.765438	−	0.643510i	$-0.777478\pi$
$317$	−2.80660e31	−1.53088	−0.765438	+	0.643510i	$0.777478\pi$
$318$	−3.19480e29	−0.0167535
$319$	2.38349e31	1.20180
$320$	1.15292e30	0.0559017
$321$	3.21480e29	0.0149914
$322$	8.81740e30	0.395496
$323$	−3.40201e30	−0.146793
$324$	1.09250e31	0.453532
$325$	2.52855e29	0.0101002
$326$	−1.04437e31	−0.401453
$327$	7.91929e30	0.292981
$328$	−1.11026e31	−0.395369
$329$	2.15762e31	0.739649
$330$	−1.83065e30	−0.0604201
$331$	−1.79893e31	−0.571694	−0.285847	−	0.958275i	$-0.592275\pi$
$331$	−1.79893e31	−0.571694	−0.285847	+	0.958275i	$0.592275\pi$
$332$	−1.29490e31	−0.396286
$333$	−1.98361e31	−0.584661
$334$	3.31394e31	0.940835
$335$	1.50306e31	0.411070
$336$	−8.06863e29	−0.0212598
$337$	−3.37680e31	−0.857296	−0.428648	−	0.903472i	$-0.641010\pi$
$337$	−3.37680e31	−0.857296	−0.428648	+	0.903472i	$0.641010\pi$
$338$	−2.88293e31	−0.705303
$339$	7.46585e30	0.176028
$340$	−4.66066e30	−0.105916
$341$	−4.75003e31	−1.04056
$342$	−1.00514e31	−0.212276
$343$	4.17554e31	0.850230
$344$	−2.14138e31	−0.420450
$345$	−4.86308e30	−0.0920815
$346$	1.84957e31	0.337769
$347$	−3.07070e30	−0.0540902	−0.0270451	−	0.999634i	$-0.508610\pi$
$347$	−3.07070e30	−0.0540902	−0.0270451	+	0.999634i	$0.508610\pi$
$348$	−5.79400e30	−0.0984550
$349$	4.73553e31	0.776338	0.388169	−	0.921588i	$-0.373108\pi$
$349$	4.73553e31	0.776338	0.388169	+	0.921588i	$0.373108\pi$
$350$	−4.29709e30	−0.0679711
$351$	−1.15246e30	−0.0175909
$352$	−1.29593e31	−0.190896
$353$	−1.13735e32	−1.61700	−0.808500	−	0.588496i	$-0.799720\pi$
$353$	−1.13735e32	−1.61700	−0.808500	+	0.588496i	$0.799720\pi$
$354$	8.10074e30	0.111169
$355$	3.27336e31	0.433649
$356$	−1.41026e31	−0.180374
$357$	3.26172e30	0.0402805
$358$	−7.97467e31	−0.950988
$359$	7.58317e31	0.873313	0.436656	−	0.899628i	$-0.356163\pi$
$359$	7.58317e31	0.873313	0.436656	+	0.899628i	$0.356163\pi$
$360$	−1.37701e31	−0.153164
$361$	−8.41373e31	−0.903959
$362$	−4.99517e31	−0.518434
$363$	2.93138e30	0.0293927
$364$	−1.25270e30	−0.0121361
$365$	5.46335e31	0.511444
$366$	−1.35638e31	−0.122707
$367$	6.65888e31	0.582205	0.291102	−	0.956692i	$-0.405978\pi$
$367$	6.65888e31	0.582205	0.291102	+	0.956692i	$0.405978\pi$
$368$	−3.44259e31	−0.290930
$369$	1.32606e32	1.08326
$370$	2.41679e31	0.190861
$371$	8.42934e30	0.0643605
$372$	1.15468e31	0.0852459
$373$	4.03892e31	0.288340	0.144170	−	0.989553i	$-0.453949\pi$
$373$	4.03892e31	0.288340	0.144170	+	0.989553i	$0.453949\pi$
$374$	5.23875e31	0.361687
$375$	2.36998e30	0.0158254
$376$	−8.42403e31	−0.544091
$377$	−8.99550e30	−0.0562029
$378$	1.95853e31	0.118381
$379$	3.00036e32	1.75462	0.877309	−	0.479926i	$-0.159336\pi$
$379$	3.00036e32	1.75462	0.877309	+	0.479926i	$0.159336\pi$
$380$	1.22464e31	0.0692969
$381$	−2.14527e31	−0.117468
$382$	2.50314e32	1.32646
$383$	−5.83515e31	−0.299273	−0.149636	−	0.988741i	$-0.547810\pi$
$383$	−5.83515e31	−0.299273	−0.149636	+	0.988741i	$0.547810\pi$
$384$	3.15025e30	0.0156388
$385$	4.83009e31	0.232111
$386$	2.65804e32	1.23657
$387$	2.55760e32	1.15198
$388$	−1.03879e32	−0.453032
$389$	−4.65526e32	−1.96595	−0.982977	−	0.183726i	$-0.941184\pi$
$389$	−4.65526e32	−1.96595	−0.982977	+	0.183726i	$0.941184\pi$
$390$	6.90903e29	0.00282559
$391$	1.39166e32	0.551218
$392$	−7.08688e31	−0.271881
$393$	−1.19914e31	−0.0445617
$394$	−1.30058e32	−0.468204
$395$	9.33471e31	0.325565
$396$	1.54781e32	0.523033
$397$	−3.57088e32	−1.16922	−0.584608	−	0.811316i	$-0.698752\pi$
$397$	−3.57088e32	−1.16922	−0.584608	+	0.811316i	$0.698752\pi$
$398$	−3.02791e32	−0.960737
$399$	−8.57055e30	−0.0263540
$400$	1.67772e31	0.0500000
$401$	−5.85410e32	−1.69105	−0.845523	−	0.533940i	$-0.820711\pi$
$401$	−5.85410e32	−1.69105	−0.845523	+	0.533940i	$0.820711\pi$
$402$	4.10696e31	0.114999
$403$	1.79270e31	0.0486625
$404$	1.11458e32	0.293322
$405$	1.58979e32	0.405651
$406$	1.52872e32	0.378227
$407$	−2.71656e32	−0.651762
$408$	−1.27348e31	−0.0296306
$409$	−5.85778e32	−1.32188	−0.660939	−	0.750439i	$-0.729842\pi$
$409$	−5.85778e32	−1.32188	−0.660939	+	0.750439i	$0.729842\pi$
$410$	−1.61564e32	−0.353628
$411$	−1.56076e32	−0.331370
$412$	2.29413e32	0.472502
$413$	−2.13734e32	−0.427070
$414$	4.11172e32	0.797113
$415$	−1.88432e32	−0.354449
$416$	4.89093e30	0.00892740
$417$	−7.98956e31	−0.141521
$418$	−1.37654e32	−0.236639
$419$	−2.15945e32	−0.360303	−0.180152	−	0.983639i	$-0.557659\pi$
$419$	−2.15945e32	−0.360303	−0.180152	+	0.983639i	$0.557659\pi$
$420$	−1.17414e31	−0.0190153
$421$	−2.57301e32	−0.404497	−0.202249	−	0.979334i	$-0.564825\pi$
$421$	−2.57301e32	−0.404497	−0.202249	+	0.979334i	$0.564825\pi$
$422$	4.83394e31	0.0737727
$423$	1.00614e33	1.49075
$424$	−3.29108e31	−0.0473441
$425$	−6.78215e31	−0.0947340
$426$	8.94413e31	0.121316
$427$	3.57876e32	0.471394
$428$	3.31169e31	0.0423645
$429$	−7.76601e30	−0.00964899
$430$	−3.11612e32	−0.376061
$431$	−4.87420e32	−0.571396	−0.285698	−	0.958320i	$-0.592225\pi$
$431$	−4.87420e32	−0.571396	−0.285698	+	0.958320i	$0.592225\pi$
$432$	−7.64671e31	−0.0870819
$433$	1.34127e33	1.48394	0.741970	−	0.670433i	$-0.233892\pi$
$433$	1.34127e33	1.48394	0.741970	+	0.670433i	$0.233892\pi$
$434$	−3.04656e32	−0.327483
$435$	−8.43138e31	−0.0880608
$436$	8.15795e32	0.827942
$437$	−3.65674e32	−0.360642
$438$	1.49281e32	0.143079
$439$	3.20033e32	0.298118	0.149059	−	0.988828i	$-0.452376\pi$
$439$	3.20033e32	0.298118	0.149059	+	0.988828i	$0.452376\pi$
$440$	−1.88582e32	−0.170743
$441$	8.46435e32	0.744923
$442$	−1.97715e31	−0.0169146
$443$	1.50899e33	1.25499	0.627494	−	0.778622i	$-0.284081\pi$
$443$	1.50899e33	1.25499	0.627494	+	0.778622i	$0.284081\pi$
$444$	6.60364e31	0.0533945
$445$	−2.05220e32	−0.161332
$446$	6.38944e31	0.0488402
$447$	1.48144e32	0.110113
$448$	−8.31179e31	−0.0600785
$449$	−7.32432e32	−0.514859	−0.257429	−	0.966297i	$-0.582875\pi$
$449$	−7.32432e32	−0.514859	−0.257429	+	0.966297i	$0.582875\pi$
$450$	−2.00382e32	−0.136994
$451$	1.81604e33	1.20759
$452$	7.69084e32	0.497443
$453$	1.34291e32	0.0844928
$454$	−1.46534e33	−0.896890
$455$	−1.82292e31	−0.0108549
$456$	3.34621e31	0.0193862
$457$	−1.80848e33	−1.01944	−0.509718	−	0.860341i	$-0.670250\pi$
$457$	−1.80848e33	−1.01944	−0.509718	+	0.860341i	$0.670250\pi$
$458$	−2.52505e33	−1.38501
$459$	3.09116e32	0.164992
$460$	−5.00963e32	−0.260215
$461$	−2.02348e33	−1.02291	−0.511454	−	0.859311i	$-0.670893\pi$
$461$	−2.02348e33	−1.02291	−0.511454	+	0.859311i	$0.670893\pi$
$462$	1.31978e32	0.0649345
$463$	4.00896e33	1.91986	0.959930	−	0.280239i	$-0.0904137\pi$
$463$	4.00896e33	1.91986	0.959930	+	0.280239i	$0.0904137\pi$
$464$	−5.96861e32	−0.278226
$465$	1.68028e32	0.0762463
$466$	2.32794e33	1.02836
$467$	−1.11951e33	−0.481466	−0.240733	−	0.970591i	$-0.577388\pi$
$467$	−1.11951e33	−0.481466	−0.240733	+	0.970591i	$0.577388\pi$
$468$	−5.84158e31	−0.0244600
$469$	−1.08360e33	−0.441784
$470$	−1.22586e33	−0.486650
$471$	1.58452e32	0.0612541
$472$	8.34487e32	0.314155
$473$	3.50264e33	1.28420
$474$	2.55062e32	0.0910786
$475$	1.78209e32	0.0619810
$476$	3.36002e32	0.113830
$477$	3.93077e32	0.129717
$478$	−2.44280e33	−0.785308
$479$	−5.66968e33	−1.77568	−0.887841	−	0.460151i	$-0.847795\pi$
$479$	−5.66968e33	−1.77568	−0.887841	+	0.460151i	$0.847795\pi$
$480$	4.58421e31	0.0139878
$481$	1.02525e32	0.0304802
$482$	−2.03955e33	−0.590809
$483$	3.50595e32	0.0989616
$484$	3.01972e32	0.0830615
$485$	−1.51163e33	−0.405204
$486$	1.37721e33	0.359788
$487$	1.76093e33	0.448363	0.224182	−	0.974547i	$-0.428029\pi$
$487$	1.76093e33	0.448363	0.224182	+	0.974547i	$0.428029\pi$
$488$	−1.39726e33	−0.346760
$489$	−4.15260e32	−0.100452
$490$	−1.03128e33	−0.243178
$491$	−5.58354e33	−1.28348	−0.641742	−	0.766920i	$-0.721788\pi$
$491$	−5.58354e33	−1.28348	−0.641742	+	0.766920i	$0.721788\pi$
$492$	−4.41459e32	−0.0989297
$493$	2.41280e33	0.527150
$494$	5.19518e31	0.0110666
$495$	2.25237e33	0.467815
$496$	1.18947e33	0.240899
$497$	−2.35987e33	−0.466050
$498$	−5.14873e32	−0.0991593
$499$	−4.37368e33	−0.821468	−0.410734	−	0.911755i	$-0.634727\pi$
$499$	−4.37368e33	−0.821468	−0.410734	+	0.911755i	$0.634727\pi$
$500$	2.44141e32	0.0447214
$501$	1.31768e33	0.235417
$502$	7.19299e33	1.25347
$503$	−4.32379e33	−0.734962	−0.367481	−	0.930031i	$-0.619780\pi$
$503$	−4.32379e33	−0.734962	−0.367481	+	0.930031i	$0.619780\pi$
$504$	9.92734e32	0.164608
$505$	1.62193e33	0.262355
$506$	5.63101e33	0.888597
$507$	−1.14630e33	−0.176482
$508$	−2.20992e33	−0.331955
$509$	1.81736e33	0.266360	0.133180	−	0.991092i	$-0.457481\pi$
$509$	1.81736e33	0.266360	0.133180	+	0.991092i	$0.457481\pi$
$510$	−1.85316e32	−0.0265024
$511$	−3.93870e33	−0.549657
$512$	3.24519e32	0.0441942
$513$	−8.12238e32	−0.107948
$514$	4.99979e33	0.648504
$515$	3.33840e33	0.422618
$516$	−8.51451e32	−0.105205
$517$	1.37791e34	1.66184
$518$	−1.74234e33	−0.205121
$519$	7.35420e32	0.0845169
$520$	7.11725e31	0.00798491
$521$	−7.48131e33	−0.819419	−0.409710	−	0.912216i	$-0.634370\pi$
$521$	−7.48131e33	−0.819419	−0.409710	+	0.912216i	$0.634370\pi$
$522$	7.12872e33	0.762308
$523$	1.34405e34	1.40328	0.701641	−	0.712531i	$-0.252451\pi$
$523$	1.34405e34	1.40328	0.701641	+	0.712531i	$0.252451\pi$
$524$	−1.23527e33	−0.125928
$525$	−1.70860e32	−0.0170078
$526$	9.33180e33	0.907076
$527$	−4.80842e33	−0.456426
$528$	−5.15283e32	−0.0477663
$529$	3.91286e33	0.354240
$530$	−4.78915e32	−0.0423458
$531$	−9.96685e33	−0.860749
$532$	−8.82883e32	−0.0744746
$533$	−6.85390e32	−0.0564739
$534$	−5.60744e32	−0.0451335
$535$	4.81914e32	0.0378920
$536$	4.23073e33	0.324979
$537$	−3.17087e33	−0.237958
$538$	−1.28129e34	−0.939440
$539$	1.15919e34	0.830418
$540$	−1.11274e33	−0.0778884
$541$	−9.16620e33	−0.626937	−0.313468	−	0.949599i	$-0.601491\pi$
$541$	−9.16620e33	−0.626937	−0.313468	+	0.949599i	$0.601491\pi$
$542$	5.39927e33	0.360864
$543$	−1.98617e33	−0.129723
$544$	−1.31186e33	−0.0837338
$545$	1.18714e34	0.740534
$546$	−4.98095e31	−0.00303671
$547$	−2.47403e34	−1.47423	−0.737113	−	0.675770i	$-0.763811\pi$
$547$	−2.47403e34	−1.47423	−0.737113	+	0.675770i	$0.763811\pi$
$548$	−1.60779e34	−0.936426
$549$	1.66884e34	0.950082
$550$	−2.74423e33	−0.152717
$551$	−6.33989e33	−0.344895
$552$	−1.36883e33	−0.0727968
$553$	−6.72970e33	−0.349890
$554$	8.67787e33	0.441104
$555$	9.60956e32	0.0477575
$556$	−8.23034e33	−0.399929
$557$	−2.03083e34	−0.964905	−0.482452	−	0.875922i	$-0.660254\pi$
$557$	−2.03083e34	−0.964905	−0.482452	+	0.875922i	$0.660254\pi$
$558$	−1.42067e34	−0.660034
$559$	−1.32192e33	−0.0600564
$560$	−1.20952e33	−0.0537359
$561$	2.08302e33	0.0905018
$562$	−2.60973e34	−1.10890
$563$	−3.26297e34	−1.35599	−0.677997	−	0.735064i	$-0.737152\pi$
$563$	−3.26297e34	−1.35599	−0.677997	+	0.735064i	$0.737152\pi$
$564$	−3.34954e33	−0.136143
$565$	1.11916e34	0.444927
$566$	1.23177e34	0.478988
$567$	−1.14613e34	−0.435960
$568$	9.21368e33	0.342830
$569$	3.41443e34	1.24284	0.621419	−	0.783478i	$-0.286556\pi$
$569$	3.41443e34	1.24284	0.621419	+	0.783478i	$0.286556\pi$
$570$	4.86938e32	0.0173396
$571$	1.36450e33	0.0475359	0.0237679	−	0.999718i	$-0.492434\pi$
$571$	1.36450e33	0.0475359	0.0237679	+	0.999718i	$0.492434\pi$
$572$	−8.00005e32	−0.0272673
$573$	9.95293e33	0.331908
$574$	1.16477e34	0.380051
$575$	−7.28997e33	−0.232744
$576$	−3.87595e33	−0.121087
$577$	3.92987e34	1.20138	0.600691	−	0.799481i	$-0.294892\pi$
$577$	3.92987e34	1.20138	0.600691	+	0.799481i	$0.294892\pi$
$578$	−1.83333e34	−0.548458
$579$	1.05688e34	0.309417
$580$	−8.68547e33	−0.248853
$581$	1.35847e34	0.380933
$582$	−4.13039e33	−0.113358
$583$	5.38319e33	0.144605
$584$	1.53780e34	0.404332
$585$	−8.50062e32	−0.0218777
$586$	−2.94639e34	−0.742285
$587$	3.72718e34	0.919187	0.459594	−	0.888129i	$-0.347995\pi$
$587$	3.72718e34	0.919187	0.459594	+	0.888129i	$0.347995\pi$
$588$	−2.81787e33	−0.0680305
$589$	1.26347e34	0.298623
$590$	1.21434e34	0.280989
$591$	−5.17134e33	−0.117155
$592$	6.80265e33	0.150889
$593$	7.75169e34	1.68350	0.841749	−	0.539870i	$-0.181526\pi$
$593$	7.75169e34	1.68350	0.841749	+	0.539870i	$0.181526\pi$
$594$	1.25076e34	0.265978
$595$	4.88947e33	0.101812
$596$	1.52608e34	0.311171
$597$	−1.20395e34	−0.240397
$598$	−2.12519e33	−0.0415559
$599$	6.18820e34	1.18503	0.592515	−	0.805559i	$-0.298135\pi$
$599$	6.18820e34	1.18503	0.592515	+	0.805559i	$0.298135\pi$
$600$	6.67091e32	0.0125111
$601$	−2.95852e34	−0.543430	−0.271715	−	0.962378i	$-0.587591\pi$
$601$	−2.95852e34	−0.543430	−0.271715	+	0.962378i	$0.587591\pi$
$602$	2.24651e34	0.404160
$603$	−5.05305e34	−0.890405
$604$	1.38338e34	0.238770
$605$	4.39427e33	0.0742925
$606$	4.43177e33	0.0733954
$607$	−1.00617e35	−1.63234	−0.816171	−	0.577810i	$-0.803907\pi$
$607$	−1.00617e35	−1.63234	−0.816171	+	0.577810i	$0.803907\pi$
$608$	3.44706e33	0.0547840
$609$	6.07845e33	0.0946405
$610$	−2.03328e34	−0.310152
$611$	−5.20034e33	−0.0777171
$612$	1.56684e34	0.229421
$613$	−4.47446e34	−0.641926	−0.320963	−	0.947092i	$-0.604007\pi$
$613$	−4.47446e34	−0.641926	−0.320963	+	0.947092i	$0.604007\pi$
$614$	−2.49298e34	−0.350440
$615$	−6.42408e33	−0.0884854
$616$	1.35955e34	0.183500
$617$	2.58799e34	0.342293	0.171147	−	0.985246i	$-0.445253\pi$
$617$	2.58799e34	0.342293	0.171147	+	0.985246i	$0.445253\pi$
$618$	9.12187e33	0.118230
$619$	−1.37687e35	−1.74889	−0.874443	−	0.485129i	$-0.838773\pi$
$619$	−1.37687e35	−1.74889	−0.874443	+	0.485129i	$0.838773\pi$
$620$	1.73091e34	0.215466
$621$	3.32262e34	0.405355
$622$	1.47525e34	0.176395
$623$	1.47950e34	0.173386
$624$	1.94472e32	0.00223383
$625$	3.55271e33	0.0400000
$626$	1.25815e34	0.138852
$627$	−5.47337e33	−0.0592121
$628$	1.63227e34	0.173099
$629$	−2.74996e34	−0.285886
$630$	1.44462e34	0.147230
$631$	−2.83484e34	−0.283244	−0.141622	−	0.989921i	$-0.545232\pi$
$631$	−2.83484e34	−0.283244	−0.141622	+	0.989921i	$0.545232\pi$
$632$	2.62749e34	0.257381
$633$	1.92206e33	0.0184595
$634$	−1.14958e35	−1.08249
$635$	−3.21585e34	−0.296910
$636$	−1.30859e33	−0.0118465
$637$	−4.37489e33	−0.0388351
$638$	9.76279e34	0.849798
$639$	−1.10045e35	−0.939314
$640$	4.72237e33	0.0395285
$641$	−1.36368e34	−0.111940	−0.0559701	−	0.998432i	$-0.517825\pi$
$641$	−1.36368e34	−0.111940	−0.0559701	+	0.998432i	$0.517825\pi$
$642$	1.31678e33	0.0106005
$643$	8.47939e32	0.00669464	0.00334732	−	0.999994i	$-0.498935\pi$
$643$	8.47939e32	0.00669464	0.00334732	+	0.999994i	$0.498935\pi$
$644$	3.61161e34	0.279658
$645$	−1.23902e34	−0.0940986
$646$	−1.39346e34	−0.103798
$647$	2.50478e35	1.83007	0.915033	−	0.403379i	$-0.132164\pi$
$647$	2.50478e35	1.83007	0.915033	+	0.403379i	$0.132164\pi$
$648$	4.47487e34	0.320696
$649$	−1.36496e35	−0.959537
$650$	1.03570e33	0.00714192
$651$	−1.21137e34	−0.0819432
$652$	−4.27774e34	−0.283870
$653$	−1.55775e35	−1.01410	−0.507051	−	0.861916i	$-0.669265\pi$
$653$	−1.55775e35	−1.01410	−0.507051	+	0.861916i	$0.669265\pi$
$654$	3.24374e34	0.207169
$655$	−1.79756e34	−0.112633
$656$	−4.54763e34	−0.279568
$657$	−1.83669e35	−1.10782
$658$	8.83760e34	0.523011
$659$	−1.85485e35	−1.07706	−0.538531	−	0.842605i	$-0.681021\pi$
$659$	−1.85485e35	−1.07706	−0.538531	+	0.842605i	$0.681021\pi$
$660$	−7.49835e33	−0.0427235
$661$	2.92623e35	1.63602	0.818012	−	0.575202i	$-0.195076\pi$
$661$	2.92623e35	1.63602	0.818012	+	0.575202i	$0.195076\pi$
$662$	−7.36840e34	−0.404248
$663$	−7.86148e32	−0.00423239
$664$	−5.30389e34	−0.280217
$665$	−1.28476e34	−0.0666121
$666$	−8.12488e34	−0.413417
$667$	2.59346e35	1.29511
$668$	1.35739e35	0.665271
$669$	2.54055e33	0.0122209
$670$	6.15653e34	0.290670
$671$	2.28548e35	1.05912
$672$	−3.30491e33	−0.0150329
$673$	2.13829e35	0.954724	0.477362	−	0.878707i	$-0.341593\pi$
$673$	2.13829e35	0.954724	0.477362	+	0.878707i	$0.341593\pi$
$674$	−1.38314e35	−0.606200
$675$	−1.61925e34	−0.0696655
$676$	−1.18085e35	−0.498725
$677$	1.59208e35	0.660096	0.330048	−	0.943964i	$-0.392935\pi$
$677$	1.59208e35	0.660096	0.330048	+	0.943964i	$0.392935\pi$
$678$	3.05801e34	0.124471
$679$	1.08978e35	0.435480
$680$	−1.90901e34	−0.0748938
$681$	−5.82643e34	−0.224421
$682$	−1.94561e35	−0.735786
$683$	4.23003e35	1.57067	0.785335	−	0.619071i	$-0.212491\pi$
$683$	4.23003e35	1.57067	0.785335	+	0.619071i	$0.212491\pi$
$684$	−4.11706e34	−0.150102
$685$	−2.33965e35	−0.837565
$686$	1.71030e35	0.601203
$687$	−1.00401e35	−0.346559
$688$	−8.77111e34	−0.297303
$689$	−2.03166e33	−0.00676255
$690$	−1.99192e34	−0.0651114
$691$	3.02759e35	0.971899	0.485950	−	0.873987i	$-0.338474\pi$
$691$	3.02759e35	0.971899	0.485950	+	0.873987i	$0.338474\pi$
$692$	7.57584e34	0.238838
$693$	−1.62380e35	−0.502769
$694$	−1.25776e34	−0.0382476
$695$	−1.19767e35	−0.357707
$696$	−2.37322e34	−0.0696182
$697$	1.83837e35	0.529692
$698$	1.93967e35	0.548954
$699$	9.25627e34	0.257319
$700$	−1.76009e34	−0.0480628
$701$	2.66145e35	0.713909	0.356954	−	0.934122i	$-0.383815\pi$
$701$	2.66145e35	0.713909	0.356954	+	0.934122i	$0.383815\pi$
$702$	−4.72049e33	−0.0124386
$703$	7.22582e34	0.187045
$704$	−5.30812e34	−0.134984
$705$	−4.87422e34	−0.121770
$706$	−4.65859e35	−1.14339
$707$	−1.16930e35	−0.281958
$708$	3.31806e34	0.0786084
$709$	2.81745e34	0.0655810	0.0327905	−	0.999462i	$-0.489561\pi$
$709$	2.81745e34	0.0655810	0.0327905	+	0.999462i	$0.489561\pi$
$710$	1.34077e35	0.306636
$711$	−3.13819e35	−0.705195
$712$	−5.77643e34	−0.127544
$713$	−5.16846e35	−1.12135
$714$	1.33600e34	0.0284826
$715$	−1.16416e34	−0.0243886
$716$	−3.26643e35	−0.672450
$717$	−9.71301e34	−0.196501
$718$	3.10606e35	0.617526
$719$	2.87441e35	0.561613	0.280806	−	0.959764i	$-0.409398\pi$
$719$	2.87441e35	0.561613	0.280806	+	0.959764i	$0.409398\pi$
$720$	−5.64025e34	−0.108303
$721$	−2.40676e35	−0.454195
$722$	−3.44626e35	−0.639195
$723$	−8.10962e34	−0.147833
$724$	−2.04602e35	−0.366588
$725$	−1.26390e35	−0.222581
$726$	1.20069e34	0.0207838
$727$	−4.98046e35	−0.847402	−0.423701	−	0.905802i	$-0.639269\pi$
$727$	−4.98046e35	−0.847402	−0.423701	+	0.905802i	$0.639269\pi$
$728$	−5.13105e33	−0.00858152
$729$	−4.96977e35	−0.817037
$730$	2.23779e35	0.361645
$731$	3.54570e35	0.563293
$732$	−5.55575e34	−0.0867668
$733$	−8.47339e35	−1.30094	−0.650471	−	0.759531i	$-0.725428\pi$
$733$	−8.47339e35	−1.30094	−0.650471	+	0.759531i	$0.725428\pi$
$734$	2.72748e35	0.411681
$735$	−4.10054e34	−0.0608484
$736$	−1.41009e35	−0.205718
$737$	−6.92016e35	−0.992597
$738$	5.43155e35	0.765983
$739$	7.12136e35	0.987433	0.493716	−	0.869623i	$-0.335638\pi$
$739$	7.12136e35	0.987433	0.493716	+	0.869623i	$0.335638\pi$
$740$	9.89916e34	0.134959
$741$	2.06569e33	0.00276910
$742$	3.45266e34	0.0455098
$743$	−6.18867e35	−0.802116	−0.401058	−	0.916053i	$-0.631357\pi$
$743$	−6.18867e35	−0.802116	−0.401058	+	0.916053i	$0.631357\pi$
$744$	4.72956e34	0.0602780
$745$	2.22074e35	0.278320
$746$	1.65434e35	0.203887
$747$	6.33481e35	0.767761
$748$	2.14579e35	0.255751
$749$	−3.47427e34	−0.0407231
$750$	9.70745e33	0.0111902
$751$	1.34082e36	1.52009	0.760046	−	0.649869i	$-0.225176\pi$
$751$	1.34082e36	1.52009	0.760046	+	0.649869i	$0.225176\pi$
$752$	−3.45048e35	−0.384731
$753$	2.86006e35	0.313644
$754$	−3.68456e34	−0.0397414
$755$	2.01308e35	0.213563
$756$	8.02213e34	0.0837080
$757$	8.81045e35	0.904274	0.452137	−	0.891949i	$-0.350662\pi$
$757$	8.81045e35	0.904274	0.452137	+	0.891949i	$0.350662\pi$
$758$	1.22895e36	1.24070
$759$	2.23899e35	0.222346
$760$	5.01613e34	0.0490003
$761$	−9.08045e35	−0.872568	−0.436284	−	0.899809i	$-0.643706\pi$
$761$	−9.08045e35	−0.872568	−0.436284	+	0.899809i	$0.643706\pi$
$762$	−8.78701e34	−0.0830623
$763$	−8.55847e35	−0.795865
$764$	1.02529e36	0.937948
$765$	2.28006e35	0.205200
$766$	−2.39008e35	−0.211618
$767$	5.15148e34	0.0448735
$768$	1.29034e34	0.0110583
$769$	1.57427e36	1.32739	0.663696	−	0.748003i	$-0.268987\pi$
$769$	1.57427e36	1.32739	0.663696	+	0.748003i	$0.268987\pi$
$770$	1.97841e35	0.164128
$771$	1.98800e35	0.162270
$772$	1.08873e36	0.874389
$773$	−1.97307e36	−1.55919	−0.779595	−	0.626284i	$-0.784575\pi$
$773$	−1.97307e36	−1.55919	−0.779595	+	0.626284i	$0.784575\pi$
$774$	1.04759e36	0.814574
$775$	2.51881e35	0.192719
$776$	−4.25486e35	−0.320342
$777$	−6.92785e34	−0.0513258
$778$	−1.90679e36	−1.39014
$779$	−4.83052e35	−0.346558
$780$	2.82994e33	0.00199800
$781$	−1.50707e36	−1.04712
$782$	5.70024e35	0.389770
$783$	5.76061e35	0.387656
$784$	−2.90279e35	−0.192249
$785$	2.37526e35	0.154825
$786$	−4.91166e34	−0.0315099
$787$	9.52553e35	0.601458	0.300729	−	0.953710i	$-0.402770\pi$
$787$	9.52553e35	0.601458	0.300729	+	0.953710i	$0.402770\pi$
$788$	−5.32719e35	−0.331070
$789$	3.71048e35	0.226970
$790$	3.82350e35	0.230209
$791$	−8.06842e35	−0.478170
$792$	6.33985e35	0.369840
$793$	−8.62560e34	−0.0495307
$794$	−1.46263e36	−0.826760
$795$	−1.90425e34	−0.0105958
$796$	−1.24023e36	−0.679344
$797$	3.70863e35	0.199979	0.0999894	−	0.994989i	$-0.468119\pi$
$797$	3.70863e35	0.199979	0.0999894	+	0.994989i	$0.468119\pi$
$798$	−3.51050e34	−0.0186351
$799$	1.39485e36	0.728941
$800$	6.87195e34	0.0353553
$801$	6.89918e35	0.349455
$802$	−2.39784e36	−1.19575
$803$	−2.51536e36	−1.23497
$804$	1.68221e35	0.0813168
$805$	5.25558e35	0.250134
$806$	7.34290e34	0.0344096
$807$	−5.09463e35	−0.235068
$808$	4.56532e35	0.207410
$809$	−2.08152e36	−0.931159	−0.465580	−	0.885006i	$-0.654154\pi$
$809$	−2.08152e36	−0.931159	−0.465580	+	0.885006i	$0.654154\pi$
$810$	6.51179e35	0.286839
$811$	−9.20046e34	−0.0399070	−0.0199535	−	0.999801i	$-0.506352\pi$
$811$	−9.20046e34	−0.0399070	−0.0199535	+	0.999801i	$0.506352\pi$
$812$	6.26164e35	0.267447
$813$	2.14684e35	0.0902960
$814$	−1.11270e36	−0.460865
$815$	−6.22493e35	−0.253901
$816$	−5.21618e34	−0.0209520
$817$	−9.31673e35	−0.368543
$818$	−2.39935e36	−0.934709
$819$	6.12837e34	0.0235124
$820$	−6.61767e35	−0.250053
$821$	9.64905e35	0.359083	0.179542	−	0.983750i	$-0.442539\pi$
$821$	9.64905e35	0.359083	0.179542	+	0.983750i	$0.442539\pi$
$822$	−6.39286e35	−0.234314
$823$	4.33977e35	0.156664	0.0783319	−	0.996927i	$-0.475041\pi$
$823$	4.33977e35	0.156664	0.0783319	+	0.996927i	$0.475041\pi$
$824$	9.39677e35	0.334109
$825$	−1.09115e35	−0.0382130
$826$	−8.75456e35	−0.301984
$827$	1.42223e36	0.483227	0.241614	−	0.970373i	$-0.422323\pi$
$827$	1.42223e36	0.483227	0.241614	+	0.970373i	$0.422323\pi$
$828$	1.68416e36	0.563644
$829$	4.07234e36	1.34249	0.671247	−	0.741234i	$-0.265759\pi$
$829$	4.07234e36	1.34249	0.671247	+	0.741234i	$0.265759\pi$
$830$	−7.71818e35	−0.250633
$831$	3.45047e35	0.110374
$832$	2.00333e34	0.00631263
$833$	1.17344e36	0.364251
$834$	−3.27252e35	−0.100071
$835$	1.97526e36	0.595036
$836$	−5.63832e35	−0.167329
$837$	−1.14802e36	−0.335646
$838$	−8.84511e35	−0.254773
$839$	1.54259e36	0.437750	0.218875	−	0.975753i	$-0.429761\pi$
$839$	1.54259e36	0.437750	0.218875	+	0.975753i	$0.429761\pi$
$840$	−4.80928e34	−0.0134459
$841$	8.66055e35	0.238559
$842$	−1.05391e36	−0.286023
$843$	−1.03767e36	−0.277470
$844$	1.97998e35	0.0521652
$845$	−1.71836e36	−0.446073
$846$	4.12115e36	1.05412
$847$	−3.16798e35	−0.0798434
$848$	−1.34803e35	−0.0334773
$849$	4.89773e35	0.119853
$850$	−2.77797e35	−0.0669870
$851$	−2.95586e36	−0.702368
$852$	3.66352e35	0.0857834
$853$	7.94652e36	1.83364	0.916820	−	0.399300i	$-0.130747\pi$
$853$	7.94652e36	1.83364	0.916820	+	0.399300i	$0.130747\pi$
$854$	1.46586e36	0.333326
$855$	−5.99111e35	−0.134255
$856$	1.35647e35	0.0299562
$857$	−7.37212e35	−0.160447	−0.0802236	−	0.996777i	$-0.525563\pi$
$857$	−7.37212e35	−0.160447	−0.0802236	+	0.996777i	$0.525563\pi$
$858$	−3.18096e34	−0.00682286
$859$	−6.08537e36	−1.28639	−0.643195	−	0.765703i	$-0.722391\pi$
$859$	−6.08537e36	−1.28639	−0.643195	+	0.765703i	$0.722391\pi$
$860$	−1.27636e36	−0.265916
$861$	4.63133e35	0.0950968
$862$	−1.99647e36	−0.404038
$863$	3.30325e36	0.658880	0.329440	−	0.944177i	$-0.393140\pi$
$863$	3.30325e36	0.658880	0.329440	+	0.944177i	$0.393140\pi$
$864$	−3.13209e35	−0.0615762
$865$	1.10243e36	0.213624
$866$	5.49382e36	1.04930
$867$	−7.28965e35	−0.137236
$868$	−1.24787e36	−0.231565
$869$	−4.29775e36	−0.786130
$870$	−3.45349e35	−0.0622684
$871$	2.61173e35	0.0464195
$872$	3.34150e36	0.585444
$873$	5.08188e36	0.877700
$874$	−1.49780e36	−0.255013
$875$	−2.56127e35	−0.0429887
$876$	6.11454e35	0.101172
$877$	−2.53964e35	−0.0414264	−0.0207132	−	0.999785i	$-0.506594\pi$
$877$	−2.53964e35	−0.0414264	−0.0207132	+	0.999785i	$0.506594\pi$
$878$	1.31085e36	0.210801
$879$	−1.17154e36	−0.185736
$880$	−7.72433e35	−0.120733
$881$	7.01270e35	0.108065	0.0540327	−	0.998539i	$-0.482792\pi$
$881$	7.01270e35	0.108065	0.0540327	+	0.998539i	$0.482792\pi$
$882$	3.46700e36	0.526740
$883$	7.67538e36	1.14972	0.574858	−	0.818253i	$-0.305057\pi$
$883$	7.67538e36	1.14972	0.574858	+	0.818253i	$0.305057\pi$
$884$	−8.09840e34	−0.0119604
$885$	4.82842e35	0.0703095
$886$	6.18082e36	0.887410
$887$	−1.19088e37	−1.68586	−0.842929	−	0.538024i	$-0.819171\pi$
$887$	−1.19088e37	−1.68586	−0.842929	+	0.538024i	$0.819171\pi$
$888$	2.70485e35	0.0377556
$889$	2.31841e36	0.319094
$890$	−8.40581e35	−0.114079
$891$	−7.31950e36	−0.979513
$892$	2.61712e35	0.0345352
$893$	−3.66512e36	−0.476920
$894$	6.06796e35	0.0778617
$895$	−4.75327e36	−0.601458
$896$	−3.40451e35	−0.0424819
$897$	−8.45012e34	−0.0103982
$898$	−3.00004e36	−0.364060
$899$	−8.96084e36	−1.07239
$900$	−8.20764e35	−0.0968695
$901$	5.44937e35	0.0634288
$902$	7.43851e36	0.853895
$903$	8.93253e35	0.101129
$904$	3.15017e36	0.351745
$905$	−2.97736e36	−0.327886
$906$	5.50056e35	0.0597454
$907$	6.98769e36	0.748587	0.374294	−	0.927310i	$-0.377885\pi$
$907$	6.98769e36	0.748587	0.374294	+	0.927310i	$0.377885\pi$
$908$	−6.00202e36	−0.634197
$909$	−5.45268e36	−0.568279
$910$	−7.46667e34	−0.00767555
$911$	−8.23719e36	−0.835217	−0.417608	−	0.908627i	$-0.637132\pi$
$911$	−8.23719e36	−0.835217	−0.417608	+	0.908627i	$0.637132\pi$
$912$	1.37061e35	0.0137081
$913$	8.67553e36	0.855877
$914$	−7.40751e36	−0.720850
$915$	−8.08467e35	−0.0776066
$916$	−1.03426e37	−0.979348
$917$	1.29592e36	0.121049
$918$	1.26614e36	0.116667
$919$	−8.31177e36	−0.755526	−0.377763	−	0.925902i	$-0.623307\pi$
$919$	−8.31177e36	−0.755526	−0.377763	+	0.925902i	$0.623307\pi$
$920$	−2.05195e36	−0.184000
$921$	−9.91251e35	−0.0876877
$922$	−8.28816e36	−0.723305
$923$	5.68781e35	0.0489693
$924$	5.40581e35	0.0459157
$925$	1.44052e36	0.120711
$926$	1.64207e37	1.35755
$927$	−1.12232e37	−0.915420
$928$	−2.44474e36	−0.196736
$929$	−1.48672e37	−1.18041	−0.590205	−	0.807253i	$-0.700953\pi$
$929$	−1.48672e37	−1.18041	−0.590205	+	0.807253i	$0.700953\pi$
$930$	6.88241e35	0.0539143
$931$	−3.08336e36	−0.238316
$932$	9.53522e36	0.727163
$933$	5.86585e35	0.0441378
$934$	−4.58550e36	−0.340448
$935$	3.12254e36	0.228751
$936$	−2.39271e35	−0.0172959
$937$	2.25559e37	1.60885	0.804424	−	0.594055i	$-0.202474\pi$
$937$	2.25559e37	1.60885	0.804424	+	0.594055i	$0.202474\pi$
$938$	−4.43844e36	−0.312388
$939$	5.00263e35	0.0347439
$940$	−5.02111e36	−0.344113
$941$	2.40580e37	1.62701	0.813504	−	0.581559i	$-0.197557\pi$
$941$	2.40580e37	1.62701	0.813504	+	0.581559i	$0.197557\pi$
$942$	6.49017e35	0.0433132
$943$	1.97602e37	1.30135
$944$	3.41806e36	0.222141
$945$	1.16737e36	0.0748707
$946$	1.43468e37	0.908063
$947$	−2.05868e35	−0.0128592	−0.00642962	−	0.999979i	$-0.502047\pi$
$947$	−2.05868e35	−0.0128592	−0.00642962	+	0.999979i	$0.502047\pi$
$948$	1.04473e36	0.0644023
$949$	9.49316e35	0.0577541
$950$	7.29943e35	0.0438272
$951$	−4.57094e36	−0.270863
$952$	1.37626e36	0.0804896
$953$	7.96109e36	0.459528	0.229764	−	0.973246i	$-0.426205\pi$
$953$	7.96109e36	0.459528	0.229764	+	0.973246i	$0.426205\pi$
$954$	1.61004e36	0.0917239
$955$	1.49199e37	0.838927
$956$	−1.00057e37	−0.555296
$957$	3.88185e36	0.212638
$958$	−2.32230e37	−1.25560
$959$	1.68673e37	0.900145
$960$	1.87769e35	0.00989087
$961$	−1.37487e36	−0.0714859
$962$	4.19943e35	0.0215527
$963$	−1.62012e36	−0.0820765
$964$	−8.35401e36	−0.417765
$965$	1.58431e37	0.782077
$966$	1.43604e36	0.0699764
$967$	4.83856e36	0.232748	0.116374	−	0.993205i	$-0.462873\pi$
$967$	4.83856e36	0.232748	0.116374	+	0.993205i	$0.462873\pi$
$968$	1.23688e36	0.0587334
$969$	−5.54066e35	−0.0259725
$970$	−6.19164e36	−0.286523
$971$	1.24060e37	0.566749	0.283375	−	0.959009i	$-0.408546\pi$
$971$	1.24060e37	0.566749	0.283375	+	0.959009i	$0.408546\pi$
$972$	5.64105e36	0.254409
$973$	8.63441e36	0.384434
$974$	7.21277e36	0.317041
$975$	4.11810e34	0.00178706
$976$	−5.72318e36	−0.245197
$977$	5.52484e36	0.233688	0.116844	−	0.993150i	$-0.462722\pi$
$977$	5.52484e36	0.233688	0.116844	+	0.993150i	$0.462722\pi$
$978$	−1.70090e36	−0.0710303
$979$	9.44844e36	0.389562
$980$	−4.22411e36	−0.171953
$981$	−3.99098e37	−1.60405
$982$	−2.28702e37	−0.907561
$983$	−3.62327e37	−1.41965	−0.709826	−	0.704377i	$-0.751226\pi$
$983$	−3.62327e37	−1.41965	−0.709826	+	0.704377i	$0.751226\pi$
$984$	−1.80822e36	−0.0699539
$985$	−7.75207e36	−0.296118
$986$	9.88281e36	0.372751
$987$	3.51398e36	0.130869
$988$	2.12795e35	0.00782526
$989$	3.81119e37	1.38391
$990$	9.22569e36	0.330795
$991$	−1.55999e37	−0.552334	−0.276167	−	0.961110i	$-0.589064\pi$
$991$	−1.55999e37	−0.552334	−0.276167	+	0.961110i	$0.589064\pi$
$992$	4.87209e36	0.170341
$993$	−2.92980e36	−0.101152
$994$	−9.66602e36	−0.329547
$995$	−1.80477e37	−0.607623
$996$	−2.10892e36	−0.0701162
$997$	−5.89404e37	−1.93519	−0.967596	−	0.252505i	$-0.918746\pi$
$997$	−5.89404e37	−1.93519	−0.967596	+	0.252505i	$0.918746\pi$
$998$	−1.79146e37	−0.580865
$999$	−6.56558e36	−0.210235

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.26.a.a.1.1	✓	1
5.2	odd	4		50.26.b.b.49.2		2
5.3	odd	4		50.26.b.b.49.1		2
5.4	even	2		50.26.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.26.a.a.1.1	✓	1	1.1	even	1	trivial
50.26.a.a.1.1		1	5.4	even	2
50.26.b.b.49.1		2	5.3	odd	4
50.26.b.b.49.2		2	5.2	odd	4

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:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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