LMFDB - Embedded newform 150.10.a.k.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,10,Mod(1,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("150.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	150.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:	$77.2553754246$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 30)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	150.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+16.0000 q^{2} +81.0000 q^{3} +256.000 q^{4} +1296.00 q^{6} +7168.00 q^{7} +4096.00 q^{8} +6561.00 q^{9} +O(q^{10})$

\(q+16.0000 q^{2} +81.0000 q^{3} +256.000 q^{4} +1296.00 q^{6} +7168.00 q^{7} +4096.00 q^{8} +6561.00 q^{9} -83748.0 q^{11} +20736.0 q^{12} -128126. q^{13} +114688. q^{14} +65536.0 q^{16} -560802. q^{17} +104976. q^{18} -577660. q^{19} +580608. q^{21} -1.33997e6 q^{22} -2.43130e6 q^{23} +331776. q^{24} -2.05002e6 q^{26} +531441. q^{27} +1.83501e6 q^{28} +5.79171e6 q^{29} +4.14531e6 q^{31} +1.04858e6 q^{32} -6.78359e6 q^{33} -8.97283e6 q^{34} +1.67962e6 q^{36} +7.01166e6 q^{37} -9.24256e6 q^{38} -1.03782e7 q^{39} -8.88140e6 q^{41} +9.28973e6 q^{42} +1.57307e7 q^{43} -2.14395e7 q^{44} -3.89007e7 q^{46} -6.05521e7 q^{47} +5.30842e6 q^{48} +1.10266e7 q^{49} -4.54250e7 q^{51} -3.28003e7 q^{52} -3.02734e7 q^{53} +8.50306e6 q^{54} +2.93601e7 q^{56} -4.67905e7 q^{57} +9.26674e7 q^{58} +4.59577e7 q^{59} +3.75951e7 q^{61} +6.63250e7 q^{62} +4.70292e7 q^{63} +1.67772e7 q^{64} -1.08537e8 q^{66} -1.96784e8 q^{67} -1.43565e8 q^{68} -1.96935e8 q^{69} +5.60480e7 q^{71} +2.68739e7 q^{72} +1.59688e8 q^{73} +1.12187e8 q^{74} -1.47881e8 q^{76} -6.00306e8 q^{77} -1.66051e8 q^{78} +2.01923e8 q^{79} +4.30467e7 q^{81} -1.42102e8 q^{82} +3.62955e8 q^{83} +1.48636e8 q^{84} +2.51691e8 q^{86} +4.69129e8 q^{87} -3.43032e8 q^{88} -2.72479e8 q^{89} -9.18407e8 q^{91} -6.22412e8 q^{92} +3.35770e8 q^{93} -9.68833e8 q^{94} +8.49347e7 q^{96} +6.00852e8 q^{97} +1.76426e8 q^{98} -5.49471e8 q^{99} +O(q^{100})\)

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 $

$2$	16.0000	0.707107
$2$	16.0000	0.707107
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	256.000	0.500000
$5$	0	0
$5$	0	0
$6$	1296.00	0.408248
$7$	7168.00	1.12838	0.564192	−	0.825644i	$-0.309188\pi$
$7$	7168.00	1.12838	0.564192	+	0.825644i	$0.309188\pi$
$8$	4096.00	0.353553
$9$	6561.00	0.333333
$10$	0	0
$11$	−83748.0	−1.72468	−0.862338	−	0.506334i	$-0.831000\pi$
$11$	−83748.0	−1.72468	−0.862338	+	0.506334i	$0.831000\pi$
$12$	20736.0	0.288675
$13$	−128126.	−1.24421	−0.622103	−	0.782936i	$-0.713721\pi$
$13$	−128126.	−1.24421	−0.622103	+	0.782936i	$0.713721\pi$
$14$	114688.	0.797888
$15$	0	0
$16$	65536.0	0.250000
$17$	−560802.	−1.62851	−0.814253	−	0.580510i	$-0.802853\pi$
$17$	−560802.	−1.62851	−0.814253	+	0.580510i	$0.802853\pi$
$18$	104976.	0.235702
$19$	−577660.	−1.01691	−0.508453	−	0.861090i	$-0.669783\pi$
$19$	−577660.	−1.01691	−0.508453	+	0.861090i	$0.669783\pi$
$20$	0	0
$21$	580608.	0.651473
$22$	−1.33997e6	−1.21953
$23$	−2.43130e6	−1.81160	−0.905801	−	0.423704i	$-0.860730\pi$
$23$	−2.43130e6	−1.81160	−0.905801	+	0.423704i	$0.860730\pi$
$24$	331776.	0.204124
$25$	0	0
$26$	−2.05002e6	−0.879786
$27$	531441.	0.192450
$28$	1.83501e6	0.564192
$29$	5.79171e6	1.52060	0.760301	−	0.649570i	$-0.225051\pi$
$29$	5.79171e6	1.52060	0.760301	+	0.649570i	$0.225051\pi$
$30$	0	0
$31$	4.14531e6	0.806176	0.403088	−	0.915161i	$-0.367937\pi$
$31$	4.14531e6	0.806176	0.403088	+	0.915161i	$0.367937\pi$
$32$	1.04858e6	0.176777
$33$	−6.78359e6	−0.995742
$34$	−8.97283e6	−1.15153
$35$	0	0
$36$	1.67962e6	0.166667
$37$	7.01166e6	0.615054	0.307527	−	0.951539i	$-0.400499\pi$
$37$	7.01166e6	0.615054	0.307527	+	0.951539i	$0.400499\pi$
$38$	−9.24256e6	−0.719062
$39$	−1.03782e7	−0.718342
$40$	0	0
$41$	−8.88140e6	−0.490856	−0.245428	−	0.969415i	$-0.578928\pi$
$41$	−8.88140e6	−0.490856	−0.245428	+	0.969415i	$0.578928\pi$
$42$	9.28973e6	0.460661
$43$	1.57307e7	0.701681	0.350840	−	0.936435i	$-0.385896\pi$
$43$	1.57307e7	0.701681	0.350840	+	0.936435i	$0.385896\pi$
$44$	−2.14395e7	−0.862338
$45$	0	0
$46$	−3.89007e7	−1.28100
$47$	−6.05521e7	−1.81004	−0.905021	−	0.425367i	$-0.860145\pi$
$47$	−6.05521e7	−1.81004	−0.905021	+	0.425367i	$0.860145\pi$
$48$	5.30842e6	0.144338
$49$	1.10266e7	0.273250
$50$	0	0
$51$	−4.54250e7	−0.940218
$52$	−3.28003e7	−0.622103
$53$	−3.02734e7	−0.527011	−0.263505	−	0.964658i	$-0.584879\pi$
$53$	−3.02734e7	−0.527011	−0.263505	+	0.964658i	$0.584879\pi$
$54$	8.50306e6	0.136083
$55$	0	0
$56$	2.93601e7	0.398944
$57$	−4.67905e7	−0.587111
$58$	9.26674e7	1.07523
$59$	4.59577e7	0.493769	0.246885	−	0.969045i	$-0.420593\pi$
$59$	4.59577e7	0.493769	0.246885	+	0.969045i	$0.420593\pi$
$60$	0	0
$61$	3.75951e7	0.347654	0.173827	−	0.984776i	$-0.444387\pi$
$61$	3.75951e7	0.347654	0.173827	+	0.984776i	$0.444387\pi$
$62$	6.63250e7	0.570052
$63$	4.70292e7	0.376128
$64$	1.67772e7	0.125000
$65$	0	0
$66$	−1.08537e8	−0.704096
$67$	−1.96784e8	−1.19304	−0.596518	−	0.802600i	$-0.703449\pi$
$67$	−1.96784e8	−1.19304	−0.596518	+	0.802600i	$0.703449\pi$
$68$	−1.43565e8	−0.814253
$69$	−1.96935e8	−1.04593
$70$	0	0
$71$	5.60480e7	0.261757	0.130878	−	0.991398i	$-0.458220\pi$
$71$	5.60480e7	0.261757	0.130878	+	0.991398i	$0.458220\pi$
$72$	2.68739e7	0.117851
$73$	1.59688e8	0.658142	0.329071	−	0.944305i	$-0.393264\pi$
$73$	1.59688e8	0.658142	0.329071	+	0.944305i	$0.393264\pi$
$74$	1.12187e8	0.434909
$75$	0	0
$76$	−1.47881e8	−0.508453
$77$	−6.00306e8	−1.94610
$78$	−1.66051e8	−0.507945
$79$	2.01923e8	0.583263	0.291632	−	0.956531i	$-0.405802\pi$
$79$	2.01923e8	0.583263	0.291632	+	0.956531i	$0.405802\pi$
$80$	0	0
$81$	4.30467e7	0.111111
$82$	−1.42102e8	−0.347088
$83$	3.62955e8	0.839464	0.419732	−	0.907648i	$-0.362124\pi$
$83$	3.62955e8	0.839464	0.419732	+	0.907648i	$0.362124\pi$
$84$	1.48636e8	0.325736
$85$	0	0
$86$	2.51691e8	0.496163
$87$	4.69129e8	0.877920
$88$	−3.43032e8	−0.609765
$89$	−2.72479e8	−0.460339	−0.230170	−	0.973151i	$-0.573928\pi$
$89$	−2.72479e8	−0.460339	−0.230170	+	0.973151i	$0.573928\pi$
$90$	0	0
$91$	−9.18407e8	−1.40394
$92$	−6.22412e8	−0.905801
$93$	3.35770e8	0.465446
$94$	−9.68833e8	−1.27989
$95$	0	0
$96$	8.49347e7	0.102062
$97$	6.00852e8	0.689120	0.344560	−	0.938764i	$-0.388028\pi$
$97$	6.00852e8	0.689120	0.344560	+	0.938764i	$0.388028\pi$
$98$	1.76426e8	0.193217
$99$	−5.49471e8	−0.574892
$100$	0	0
$101$	−4.32498e8	−0.413560	−0.206780	−	0.978388i	$-0.566298\pi$
$101$	−4.32498e8	−0.413560	−0.206780	+	0.978388i	$0.566298\pi$
$102$	−7.26799e8	−0.664835
$103$	8.76503e8	0.767336	0.383668	−	0.923471i	$-0.374661\pi$
$103$	8.76503e8	0.767336	0.383668	+	0.923471i	$0.374661\pi$
$104$	−5.24804e8	−0.439893
$105$	0	0
$106$	−4.84374e8	−0.372653
$107$	−1.48170e9	−1.09278	−0.546392	−	0.837530i	$-0.683999\pi$
$107$	−1.48170e9	−1.09278	−0.546392	+	0.837530i	$0.683999\pi$
$108$	1.36049e8	0.0962250
$109$	−1.78904e9	−1.21395	−0.606976	−	0.794721i	$-0.707617\pi$
$109$	−1.78904e9	−1.21395	−0.606976	+	0.794721i	$0.707617\pi$
$110$	0	0
$111$	5.67944e8	0.355101
$112$	4.69762e8	0.282096
$113$	9.80881e8	0.565931	0.282966	−	0.959130i	$-0.408682\pi$
$113$	9.80881e8	0.565931	0.282966	+	0.959130i	$0.408682\pi$
$114$	−7.48647e8	−0.415150
$115$	0	0
$116$	1.48268e9	0.760301
$117$	−8.40635e8	−0.414735
$118$	7.35323e8	0.349147
$119$	−4.01983e9	−1.83758
$120$	0	0
$121$	4.65578e9	1.97451
$122$	6.01522e8	0.245828
$123$	−7.19393e8	−0.283396
$124$	1.06120e9	0.403088
$125$	0	0
$126$	7.52468e8	0.265963
$127$	−5.47630e9	−1.86797	−0.933986	−	0.357309i	$-0.883694\pi$
$127$	−5.47630e9	−1.86797	−0.933986	+	0.357309i	$0.883694\pi$
$128$	2.68435e8	0.0883883
$129$	1.27419e9	0.405116
$130$	0	0
$131$	2.38950e9	0.708902	0.354451	−	0.935075i	$-0.384668\pi$
$131$	2.38950e9	0.708902	0.354451	+	0.935075i	$0.384668\pi$
$132$	−1.73660e9	−0.497871
$133$	−4.14067e9	−1.14746
$134$	−3.14854e9	−0.843603
$135$	0	0
$136$	−2.29704e9	−0.575764
$137$	1.76190e8	0.0427307	0.0213653	−	0.999772i	$-0.493199\pi$
$137$	1.76190e8	0.0427307	0.0213653	+	0.999772i	$0.493199\pi$
$138$	−3.15096e9	−0.739583
$139$	1.44281e8	0.0327825	0.0163912	−	0.999866i	$-0.494782\pi$
$139$	1.44281e8	0.0327825	0.0163912	+	0.999866i	$0.494782\pi$
$140$	0	0
$141$	−4.90472e9	−1.04503
$142$	8.96768e8	0.185090
$143$	1.07303e10	2.14585
$144$	4.29982e8	0.0833333
$145$	0	0
$146$	2.55501e9	0.465377
$147$	8.93156e8	0.157761
$148$	1.79498e9	0.307527
$149$	5.51263e9	0.916264	0.458132	−	0.888884i	$-0.348519\pi$
$149$	5.51263e9	0.916264	0.458132	+	0.888884i	$0.348519\pi$
$150$	0	0
$151$	−2.30532e9	−0.360857	−0.180429	−	0.983588i	$-0.557749\pi$
$151$	−2.30532e9	−0.360857	−0.180429	+	0.983588i	$0.557749\pi$
$152$	−2.36610e9	−0.359531
$153$	−3.67942e9	−0.542835
$154$	−9.60489e9	−1.37610
$155$	0	0
$156$	−2.65682e9	−0.359171
$157$	−1.35158e10	−1.77539	−0.887693	−	0.460437i	$-0.847693\pi$
$157$	−1.35158e10	−1.77539	−0.887693	+	0.460437i	$0.847693\pi$
$158$	3.23077e9	0.412429
$159$	−2.45214e9	−0.304270
$160$	0	0
$161$	−1.74275e10	−2.04418
$162$	6.88748e8	0.0785674
$163$	3.82037e9	0.423898	0.211949	−	0.977281i	$-0.432019\pi$
$163$	3.82037e9	0.423898	0.211949	+	0.977281i	$0.432019\pi$
$164$	−2.27364e9	−0.245428
$165$	0	0
$166$	5.80729e9	0.593590
$167$	1.81102e9	0.180176	0.0900882	−	0.995934i	$-0.471285\pi$
$167$	1.81102e9	0.180176	0.0900882	+	0.995934i	$0.471285\pi$
$168$	2.37817e9	0.230330
$169$	5.81177e9	0.548048
$170$	0	0
$171$	−3.79003e9	−0.338969
$172$	4.02706e9	0.350840
$173$	7.19389e8	0.0610599	0.0305299	−	0.999534i	$-0.490281\pi$
$173$	7.19389e8	0.0610599	0.0305299	+	0.999534i	$0.490281\pi$
$174$	7.50606e9	0.620784
$175$	0	0
$176$	−5.48851e9	−0.431169
$177$	3.72257e9	0.285078
$178$	−4.35967e9	−0.325509
$179$	1.78725e8	0.0130121	0.00650605	−	0.999979i	$-0.497929\pi$
$179$	1.78725e8	0.0130121	0.00650605	+	0.999979i	$0.497929\pi$
$180$	0	0
$181$	3.20937e8	0.0222263	0.0111131	−	0.999938i	$-0.496463\pi$
$181$	3.20937e8	0.0222263	0.0111131	+	0.999938i	$0.496463\pi$
$182$	−1.46945e10	−0.992737
$183$	3.04520e9	0.200718
$184$	−9.95859e9	−0.640498
$185$	0	0
$186$	5.37232e9	0.329120
$187$	4.69660e10	2.80864
$188$	−1.55013e10	−0.905021
$189$	3.80937e9	0.217158
$190$	0	0
$191$	1.56921e10	0.853160	0.426580	−	0.904450i	$-0.359718\pi$
$191$	1.56921e10	0.853160	0.426580	+	0.904450i	$0.359718\pi$
$192$	1.35895e9	0.0721688
$193$	−1.28959e10	−0.669027	−0.334514	−	0.942391i	$-0.608572\pi$
$193$	−1.28959e10	−0.669027	−0.334514	+	0.942391i	$0.608572\pi$
$194$	9.61364e9	0.487282
$195$	0	0
$196$	2.82281e9	0.136625
$197$	−3.15931e10	−1.49450	−0.747248	−	0.664545i	$-0.768625\pi$
$197$	−3.15931e10	−1.49450	−0.747248	+	0.664545i	$0.768625\pi$
$198$	−8.79153e9	−0.406510
$199$	2.79853e10	1.26500	0.632500	−	0.774560i	$-0.282029\pi$
$199$	2.79853e10	1.26500	0.632500	+	0.774560i	$0.282029\pi$
$200$	0	0
$201$	−1.59395e10	−0.688799
$202$	−6.91997e9	−0.292431
$203$	4.15150e10	1.71582
$204$	−1.16288e10	−0.470109
$205$	0	0
$206$	1.40240e10	0.542589
$207$	−1.59517e10	−0.603867
$208$	−8.39687e9	−0.311051
$209$	4.83779e10	1.75383
$210$	0	0
$211$	−3.80423e10	−1.32128	−0.660642	−	0.750701i	$-0.729716\pi$
$211$	−3.80423e10	−1.32128	−0.660642	+	0.750701i	$0.729716\pi$
$212$	−7.74998e9	−0.263505
$213$	4.53989e9	0.151125
$214$	−2.37072e10	−0.772715
$215$	0	0
$216$	2.17678e9	0.0680414
$217$	2.97136e10	0.909675
$218$	−2.86247e10	−0.858393
$219$	1.29347e10	0.379978
$220$	0	0
$221$	7.18533e10	2.02620
$222$	9.08711e9	0.251095
$223$	−3.15782e10	−0.855098	−0.427549	−	0.903992i	$-0.640623\pi$
$223$	−3.15782e10	−0.855098	−0.427549	+	0.903992i	$0.640623\pi$
$224$	7.51619e9	0.199472
$225$	0	0
$226$	1.56941e10	0.400174
$227$	6.25898e10	1.56454	0.782271	−	0.622938i	$-0.214061\pi$
$227$	6.25898e10	1.56454	0.782271	+	0.622938i	$0.214061\pi$
$228$	−1.19784e10	−0.293556
$229$	−2.48849e10	−0.597964	−0.298982	−	0.954259i	$-0.596647\pi$
$229$	−2.48849e10	−0.597964	−0.298982	+	0.954259i	$0.596647\pi$
$230$	0	0
$231$	−4.86248e10	−1.12358
$232$	2.37228e10	0.537614
$233$	−1.59432e10	−0.354385	−0.177192	−	0.984176i	$-0.556701\pi$
$233$	−1.59432e10	−0.354385	−0.177192	+	0.984176i	$0.556701\pi$
$234$	−1.34502e10	−0.293262
$235$	0	0
$236$	1.17652e10	0.246885
$237$	1.63558e10	0.336747
$238$	−6.43173e10	−1.29937
$239$	4.96336e10	0.983977	0.491989	−	0.870602i	$-0.336270\pi$
$239$	4.96336e10	0.983977	0.491989	+	0.870602i	$0.336270\pi$
$240$	0	0
$241$	9.62461e10	1.83783	0.918917	−	0.394450i	$-0.129065\pi$
$241$	9.62461e10	1.83783	0.918917	+	0.394450i	$0.129065\pi$
$242$	7.44925e10	1.39619
$243$	3.48678e9	0.0641500
$244$	9.62435e9	0.173827
$245$	0	0
$246$	−1.15103e10	−0.200391
$247$	7.40133e10	1.26524
$248$	1.69792e10	0.285026
$249$	2.93994e10	0.484665
$250$	0	0
$251$	−4.88371e10	−0.776637	−0.388318	−	0.921525i	$-0.626944\pi$
$251$	−4.88371e10	−0.776637	−0.388318	+	0.921525i	$0.626944\pi$
$252$	1.20395e10	0.188064
$253$	2.03616e11	3.12442
$254$	−8.76208e10	−1.32086
$255$	0	0
$256$	4.29497e9	0.0625000
$257$	−1.79144e8	−0.00256155	−0.00128077	−	0.999999i	$-0.500408\pi$
$257$	−1.79144e8	−0.00256155	−0.00128077	+	0.999999i	$0.500408\pi$
$258$	2.03870e10	0.286460
$259$	5.02596e10	0.694016
$260$	0	0
$261$	3.79994e10	0.506868
$262$	3.82320e10	0.501269
$263$	−5.73776e10	−0.739506	−0.369753	−	0.929130i	$-0.620558\pi$
$263$	−5.73776e10	−0.739506	−0.369753	+	0.929130i	$0.620558\pi$
$264$	−2.77856e10	−0.352048
$265$	0	0
$266$	−6.62507e10	−0.811377
$267$	−2.20708e10	−0.265777
$268$	−5.03767e10	−0.596518
$269$	−2.00413e10	−0.233367	−0.116684	−	0.993169i	$-0.537226\pi$
$269$	−2.00413e10	−0.233367	−0.116684	+	0.993169i	$0.537226\pi$
$270$	0	0
$271$	6.15187e10	0.692860	0.346430	−	0.938076i	$-0.387394\pi$
$271$	6.15187e10	0.692860	0.346430	+	0.938076i	$0.387394\pi$
$272$	−3.67527e10	−0.407127
$273$	−7.43910e10	−0.810566
$274$	2.81905e9	0.0302152
$275$	0	0
$276$	−5.04154e10	−0.522964
$277$	8.29005e10	0.846054	0.423027	−	0.906117i	$-0.360968\pi$
$277$	8.29005e10	0.846054	0.423027	+	0.906117i	$0.360968\pi$
$278$	2.30849e9	0.0231807
$279$	2.71974e10	0.268725
$280$	0	0
$281$	−1.99491e11	−1.90873	−0.954367	−	0.298635i	$-0.903469\pi$
$281$	−1.99491e11	−1.90873	−0.954367	+	0.298635i	$0.903469\pi$
$282$	−7.84755e10	−0.738947
$283$	−6.47436e10	−0.600009	−0.300004	−	0.953938i	$-0.596988\pi$
$283$	−6.47436e10	−0.600009	−0.300004	+	0.953938i	$0.596988\pi$
$284$	1.43483e10	0.130878
$285$	0	0
$286$	1.71685e11	1.51735
$287$	−6.36619e10	−0.553874
$288$	6.87971e9	0.0589256
$289$	1.95911e11	1.65203
$290$	0	0
$291$	4.86691e10	0.397864
$292$	4.08801e10	0.329071
$293$	2.21983e9	0.0175961	0.00879805	−	0.999961i	$-0.497199\pi$
$293$	2.21983e9	0.0175961	0.00879805	+	0.999961i	$0.497199\pi$
$294$	1.42905e10	0.111554
$295$	0	0
$296$	2.87198e10	0.217454
$297$	−4.45071e10	−0.331914
$298$	8.82020e10	0.647896
$299$	3.11512e11	2.25400
$300$	0	0
$301$	1.12758e11	0.791765
$302$	−3.68852e10	−0.255165
$303$	−3.50323e10	−0.238769
$304$	−3.78575e10	−0.254227
$305$	0	0
$306$	−5.88708e10	−0.383843
$307$	2.36701e10	0.152082	0.0760409	−	0.997105i	$-0.475772\pi$
$307$	2.36701e10	0.152082	0.0760409	+	0.997105i	$0.475772\pi$
$308$	−1.53678e11	−0.973048
$309$	7.09967e10	0.443022
$310$	0	0
$311$	−1.60673e11	−0.973916	−0.486958	−	0.873426i	$-0.661893\pi$
$311$	−1.60673e11	−0.973916	−0.486958	+	0.873426i	$0.661893\pi$
$312$	−4.25091e10	−0.253972
$313$	2.03532e11	1.19863	0.599313	−	0.800515i	$-0.295440\pi$
$313$	2.03532e11	1.19863	0.599313	+	0.800515i	$0.295440\pi$
$314$	−2.16252e11	−1.25539
$315$	0	0
$316$	5.16924e10	0.291632
$317$	−1.98619e11	−1.10472	−0.552362	−	0.833605i	$-0.686273\pi$
$317$	−1.98619e11	−1.10472	−0.552362	+	0.833605i	$0.686273\pi$
$318$	−3.92343e10	−0.215151
$319$	−4.85044e11	−2.62255
$320$	0	0
$321$	−1.20018e11	−0.630919
$322$	−2.78840e11	−1.44545
$323$	3.23953e11	1.65604
$324$	1.10200e10	0.0555556
$325$	0	0
$326$	6.11259e10	0.299741
$327$	−1.44912e11	−0.700875
$328$	−3.63782e10	−0.173544
$329$	−4.34037e11	−2.04242
$330$	0	0
$331$	7.88482e10	0.361049	0.180524	−	0.983571i	$-0.442221\pi$
$331$	7.88482e10	0.361049	0.180524	+	0.983571i	$0.442221\pi$
$332$	9.29166e10	0.419732
$333$	4.60035e10	0.205018
$334$	2.89763e10	0.127404
$335$	0	0
$336$	3.80507e10	0.162868
$337$	1.55474e11	0.656634	0.328317	−	0.944568i	$-0.393519\pi$
$337$	1.55474e11	0.656634	0.328317	+	0.944568i	$0.393519\pi$
$338$	9.29884e10	0.387528
$339$	7.94514e10	0.326740
$340$	0	0
$341$	−3.47162e11	−1.39039
$342$	−6.06404e10	−0.239687
$343$	−2.10216e11	−0.820053
$344$	6.44329e10	0.248082
$345$	0	0
$346$	1.15102e10	0.0431759
$347$	−1.05926e11	−0.392212	−0.196106	−	0.980583i	$-0.562830\pi$
$347$	−1.05926e11	−0.392212	−0.196106	+	0.980583i	$0.562830\pi$
$348$	1.20097e11	0.438960
$349$	−3.73230e11	−1.34667	−0.673337	−	0.739336i	$-0.735140\pi$
$349$	−3.73230e11	−1.34667	−0.673337	+	0.739336i	$0.735140\pi$
$350$	0	0
$351$	−6.80914e10	−0.239447
$352$	−8.78161e10	−0.304882
$353$	−4.41395e11	−1.51301	−0.756504	−	0.653989i	$-0.773094\pi$
$353$	−4.41395e11	−1.51301	−0.756504	+	0.653989i	$0.773094\pi$
$354$	5.95611e10	0.201580
$355$	0	0
$356$	−6.97547e10	−0.230170
$357$	−3.25606e11	−1.06093
$358$	2.85960e9	0.00920094
$359$	−2.44731e11	−0.777613	−0.388806	−	0.921320i	$-0.627112\pi$
$359$	−2.44731e11	−0.777613	−0.388806	+	0.921320i	$0.627112\pi$
$360$	0	0
$361$	1.10034e10	0.0340992
$362$	5.13500e9	0.0157163
$363$	3.77118e11	1.13998
$364$	−2.35112e11	−0.701971
$365$	0	0
$366$	4.87233e10	0.141929
$367$	−1.49188e9	−0.00429275	−0.00214638	−	0.999998i	$-0.500683\pi$
$367$	−1.49188e9	−0.00429275	−0.00214638	+	0.999998i	$0.500683\pi$
$368$	−1.59337e11	−0.452900
$369$	−5.82709e10	−0.163619
$370$	0	0
$371$	−2.16999e11	−0.594670
$372$	8.59572e10	0.232723
$373$	2.61041e11	0.698263	0.349131	−	0.937074i	$-0.386477\pi$
$373$	2.61041e11	0.698263	0.349131	+	0.937074i	$0.386477\pi$
$374$	7.51457e11	1.98601
$375$	0	0
$376$	−2.48021e11	−0.639946
$377$	−7.42069e11	−1.89194
$378$	6.09499e10	0.153554
$379$	4.33535e11	1.07931	0.539656	−	0.841885i	$-0.318554\pi$
$379$	4.33535e11	1.07931	0.539656	+	0.841885i	$0.318554\pi$
$380$	0	0
$381$	−4.43580e11	−1.07847
$382$	2.51073e11	0.603275
$383$	−5.15845e11	−1.22497	−0.612484	−	0.790483i	$-0.709830\pi$
$383$	−5.15845e11	−1.22497	−0.612484	+	0.790483i	$0.709830\pi$
$384$	2.17433e10	0.0510310
$385$	0	0
$386$	−2.06334e11	−0.473074
$387$	1.03209e11	0.233894
$388$	1.53818e11	0.344560
$389$	−1.65642e11	−0.366773	−0.183386	−	0.983041i	$-0.558706\pi$
$389$	−1.65642e11	−0.366773	−0.183386	+	0.983041i	$0.558706\pi$
$390$	0	0
$391$	1.36348e12	2.95020
$392$	4.51650e10	0.0966084
$393$	1.93550e11	0.409285
$394$	−5.05490e11	−1.05677
$395$	0	0
$396$	−1.40664e11	−0.287446
$397$	4.58102e11	0.925560	0.462780	−	0.886473i	$-0.346852\pi$
$397$	4.58102e11	0.925560	0.462780	+	0.886473i	$0.346852\pi$
$398$	4.47764e11	0.894490
$399$	−3.35394e11	−0.662487
$400$	0	0
$401$	3.59781e11	0.694846	0.347423	−	0.937709i	$-0.387057\pi$
$401$	3.59781e11	0.694846	0.347423	+	0.937709i	$0.387057\pi$
$402$	−2.55032e11	−0.487055
$403$	−5.31122e11	−1.00305
$404$	−1.10720e11	−0.206780
$405$	0	0
$406$	6.64240e11	1.21327
$407$	−5.87212e11	−1.06077
$408$	−1.86061e11	−0.332417
$409$	−7.08479e11	−1.25191	−0.625954	−	0.779860i	$-0.715290\pi$
$409$	−7.08479e11	−1.25191	−0.625954	+	0.779860i	$0.715290\pi$
$410$	0	0
$411$	1.42714e10	0.0246706
$412$	2.24385e11	0.383668
$413$	3.29425e11	0.557161
$414$	−2.55228e11	−0.426998
$415$	0	0
$416$	−1.34350e11	−0.219947
$417$	1.16867e10	0.0189270
$418$	7.74046e11	1.24015
$419$	7.83198e11	1.24139	0.620695	−	0.784052i	$-0.286850\pi$
$419$	7.83198e11	1.24139	0.620695	+	0.784052i	$0.286850\pi$
$420$	0	0
$421$	3.87009e11	0.600415	0.300207	−	0.953874i	$-0.402944\pi$
$421$	3.87009e11	0.600415	0.300207	+	0.953874i	$0.402944\pi$
$422$	−6.08677e11	−0.934289
$423$	−3.97282e11	−0.603347
$424$	−1.24000e11	−0.186326
$425$	0	0
$426$	7.26382e10	0.106862
$427$	2.69482e11	0.392287
$428$	−3.79316e11	−0.546392
$429$	8.69154e11	1.23891
$430$	0	0
$431$	−6.45135e10	−0.0900540	−0.0450270	−	0.998986i	$-0.514337\pi$
$431$	−6.45135e10	−0.0900540	−0.0450270	+	0.998986i	$0.514337\pi$
$432$	3.48285e10	0.0481125
$433$	3.00405e11	0.410687	0.205344	−	0.978690i	$-0.434169\pi$
$433$	3.00405e11	0.410687	0.205344	+	0.978690i	$0.434169\pi$
$434$	4.75418e11	0.643238
$435$	0	0
$436$	−4.57995e11	−0.606976
$437$	1.40446e12	1.84223
$438$	2.06956e11	0.268685
$439$	5.23613e11	0.672852	0.336426	−	0.941710i	$-0.390782\pi$
$439$	5.23613e11	0.672852	0.336426	+	0.941710i	$0.390782\pi$
$440$	0	0
$441$	7.23456e10	0.0910833
$442$	1.14965e12	1.43274
$443$	4.31162e11	0.531893	0.265946	−	0.963988i	$-0.414316\pi$
$443$	4.31162e11	0.531893	0.265946	+	0.963988i	$0.414316\pi$
$444$	1.45394e11	0.177551
$445$	0	0
$446$	−5.05252e11	−0.604646
$447$	4.46523e11	0.529005
$448$	1.20259e11	0.141048
$449$	−9.29627e11	−1.07944	−0.539722	−	0.841843i	$-0.681471\pi$
$449$	−9.29627e11	−1.07944	−0.539722	+	0.841843i	$0.681471\pi$
$450$	0	0
$451$	7.43799e11	0.846567
$452$	2.51106e11	0.282966
$453$	−1.86731e11	−0.208341
$454$	1.00144e12	1.10630
$455$	0	0
$456$	−1.91654e11	−0.207575
$457$	−1.87400e11	−0.200977	−0.100489	−	0.994938i	$-0.532041\pi$
$457$	−1.87400e11	−0.200977	−0.100489	+	0.994938i	$0.532041\pi$
$458$	−3.98158e11	−0.422825
$459$	−2.98033e11	−0.313406
$460$	0	0
$461$	1.25156e12	1.29062	0.645310	−	0.763920i	$-0.276728\pi$
$461$	1.25156e12	1.29062	0.645310	+	0.763920i	$0.276728\pi$
$462$	−7.77996e11	−0.794490
$463$	1.03208e12	1.04375	0.521877	−	0.853021i	$-0.325232\pi$
$463$	1.03208e12	1.04375	0.521877	+	0.853021i	$0.325232\pi$
$464$	3.79566e11	0.380151
$465$	0	0
$466$	−2.55092e11	−0.250588
$467$	4.13576e10	0.0402374	0.0201187	−	0.999798i	$-0.493596\pi$
$467$	4.13576e10	0.0402374	0.0201187	+	0.999798i	$0.493596\pi$
$468$	−2.15202e11	−0.207368
$469$	−1.41055e12	−1.34620
$470$	0	0
$471$	−1.09478e12	−1.02502
$472$	1.88243e11	0.174574
$473$	−1.31741e12	−1.21017
$474$	2.61693e11	0.238116
$475$	0	0
$476$	−1.02908e12	−0.918790
$477$	−1.98624e11	−0.175670
$478$	7.94137e11	0.695777
$479$	−1.44832e12	−1.25706	−0.628530	−	0.777785i	$-0.716343\pi$
$479$	−1.44832e12	−1.25706	−0.628530	+	0.777785i	$0.716343\pi$
$480$	0	0
$481$	−8.98376e11	−0.765253
$482$	1.53994e12	1.29955
$483$	−1.41163e12	−1.18021
$484$	1.19188e12	0.987253
$485$	0	0
$486$	5.57886e10	0.0453609
$487$	−8.70547e11	−0.701313	−0.350657	−	0.936504i	$-0.614042\pi$
$487$	−8.70547e11	−0.701313	−0.350657	+	0.936504i	$0.614042\pi$
$488$	1.53990e11	0.122914
$489$	3.09450e11	0.244738
$490$	0	0
$491$	−2.41556e12	−1.87565	−0.937824	−	0.347110i	$-0.887163\pi$
$491$	−2.41556e12	−1.87565	−0.937824	+	0.347110i	$0.887163\pi$
$492$	−1.84165e11	−0.141698
$493$	−3.24800e12	−2.47631
$494$	1.18421e12	0.894661
$495$	0	0
$496$	2.71667e11	0.201544
$497$	4.01752e11	0.295362
$498$	4.70390e11	0.342710
$499$	1.13970e12	0.822880	0.411440	−	0.911437i	$-0.365026\pi$
$499$	1.13970e12	0.822880	0.411440	+	0.911437i	$0.365026\pi$
$500$	0	0
$501$	1.46692e11	0.104025
$502$	−7.81393e11	−0.549165
$503$	1.92139e12	1.33832	0.669161	−	0.743117i	$-0.266654\pi$
$503$	1.92139e12	1.33832	0.669161	+	0.743117i	$0.266654\pi$
$504$	1.92632e11	0.132981
$505$	0	0
$506$	3.25786e12	2.20930
$507$	4.70754e11	0.316416
$508$	−1.40193e12	−0.933986
$509$	2.64605e11	0.174730	0.0873650	−	0.996176i	$-0.472155\pi$
$509$	2.64605e11	0.174730	0.0873650	+	0.996176i	$0.472155\pi$
$510$	0	0
$511$	1.14464e12	0.742637
$512$	6.87195e10	0.0441942
$513$	−3.06992e11	−0.195704
$514$	−2.86630e9	−0.00181129
$515$	0	0
$516$	3.26191e11	0.202558
$517$	5.07111e12	3.12173
$518$	8.04153e11	0.490744
$519$	5.82705e10	0.0352529
$520$	0	0
$521$	1.98227e12	1.17868	0.589338	−	0.807887i	$-0.299389\pi$
$521$	1.98227e12	1.17868	0.589338	+	0.807887i	$0.299389\pi$
$522$	6.07991e11	0.358410
$523$	−2.95588e12	−1.72754	−0.863771	−	0.503885i	$-0.831904\pi$
$523$	−2.95588e12	−1.72754	−0.863771	+	0.503885i	$0.831904\pi$
$524$	6.11712e11	0.354451
$525$	0	0
$526$	−9.18042e11	−0.522910
$527$	−2.32470e12	−1.31286
$528$	−4.44569e11	−0.248935
$529$	4.11005e12	2.28190
$530$	0	0
$531$	3.01528e11	0.164590
$532$	−1.06001e12	−0.573730
$533$	1.13794e12	0.610726
$534$	−3.53133e11	−0.187933
$535$	0	0
$536$	−8.06027e11	−0.421802
$537$	1.44767e10	0.00751254
$538$	−3.20661e11	−0.165016
$539$	−9.23457e11	−0.471267
$540$	0	0
$541$	−1.11433e12	−0.559277	−0.279638	−	0.960105i	$-0.590215\pi$
$541$	−1.11433e12	−0.559277	−0.279638	+	0.960105i	$0.590215\pi$
$542$	9.84299e11	0.489926
$543$	2.59959e10	0.0128323
$544$	−5.88044e11	−0.287882
$545$	0	0
$546$	−1.19026e12	−0.573157
$547$	5.57205e11	0.266117	0.133058	−	0.991108i	$-0.457520\pi$
$547$	5.57205e11	0.266117	0.133058	+	0.991108i	$0.457520\pi$
$548$	4.51048e10	0.0213653
$549$	2.46661e11	0.115885
$550$	0	0
$551$	−3.34564e12	−1.54631
$552$	−8.06646e11	−0.369792
$553$	1.44739e12	0.658145
$554$	1.32641e12	0.598250
$555$	0	0
$556$	3.69359e10	0.0163912
$557$	−4.04322e12	−1.77983	−0.889915	−	0.456126i	$-0.849237\pi$
$557$	−4.04322e12	−1.77983	−0.889915	+	0.456126i	$0.849237\pi$
$558$	4.35158e11	0.190017
$559$	−2.01551e12	−0.873035
$560$	0	0
$561$	3.80425e12	1.62157
$562$	−3.19186e12	−1.34968
$563$	−1.13141e12	−0.474603	−0.237302	−	0.971436i	$-0.576263\pi$
$563$	−1.13141e12	−0.474603	−0.237302	+	0.971436i	$0.576263\pi$
$564$	−1.25561e12	−0.522514
$565$	0	0
$566$	−1.03590e12	−0.424270
$567$	3.08559e11	0.125376
$568$	2.29573e11	0.0925449
$569$	1.84799e12	0.739086	0.369543	−	0.929214i	$-0.379514\pi$
$569$	1.84799e12	0.739086	0.369543	+	0.929214i	$0.379514\pi$
$570$	0	0
$571$	−4.05547e12	−1.59654	−0.798268	−	0.602302i	$-0.794250\pi$
$571$	−4.05547e12	−1.59654	−0.798268	+	0.602302i	$0.794250\pi$
$572$	2.74696e12	1.07293
$573$	1.27106e12	0.492572
$574$	−1.01859e12	−0.391648
$575$	0	0
$576$	1.10075e11	0.0416667
$577$	−1.04147e12	−0.391162	−0.195581	−	0.980688i	$-0.562659\pi$
$577$	−1.04147e12	−0.391162	−0.195581	+	0.980688i	$0.562659\pi$
$578$	3.13458e12	1.16816
$579$	−1.04457e12	−0.386263
$580$	0	0
$581$	2.60166e12	0.947237
$582$	7.78705e11	0.281332
$583$	2.53533e12	0.908922
$584$	6.54082e11	0.232688
$585$	0	0
$586$	3.55174e10	0.0124423
$587$	4.34862e12	1.51175	0.755875	−	0.654716i	$-0.227212\pi$
$587$	4.34862e12	1.51175	0.755875	+	0.654716i	$0.227212\pi$
$588$	2.28648e11	0.0788804
$589$	−2.39458e12	−0.819805
$590$	0	0
$591$	−2.55904e12	−0.862848
$592$	4.59516e11	0.153763
$593$	1.43368e11	0.0476109	0.0238055	−	0.999717i	$-0.492422\pi$
$593$	1.43368e11	0.0476109	0.0238055	+	0.999717i	$0.492422\pi$
$594$	−7.12114e11	−0.234699
$595$	0	0
$596$	1.41123e12	0.458132
$597$	2.26681e12	0.730348
$598$	4.98420e12	1.59382
$599$	−3.34258e11	−0.106087	−0.0530434	−	0.998592i	$-0.516892\pi$
$599$	−3.34258e11	−0.106087	−0.0530434	+	0.998592i	$0.516892\pi$
$600$	0	0
$601$	1.27776e12	0.399497	0.199749	−	0.979847i	$-0.435987\pi$
$601$	1.27776e12	0.399497	0.199749	+	0.979847i	$0.435987\pi$
$602$	1.80412e12	0.559862
$603$	−1.29110e12	−0.397678
$604$	−5.90163e11	−0.180429
$605$	0	0
$606$	−5.60518e11	−0.168835
$607$	−1.72745e11	−0.0516483	−0.0258242	−	0.999667i	$-0.508221\pi$
$607$	−1.72745e11	−0.0516483	−0.0258242	+	0.999667i	$0.508221\pi$
$608$	−6.05720e11	−0.179765
$609$	3.36271e12	0.990631
$610$	0	0
$611$	7.75829e12	2.25206
$612$	−9.41932e11	−0.271418
$613$	−3.84405e11	−0.109956	−0.0549778	−	0.998488i	$-0.517509\pi$
$613$	−3.84405e11	−0.109956	−0.0549778	+	0.998488i	$0.517509\pi$
$614$	3.78722e11	0.107538
$615$	0	0
$616$	−2.45885e12	−0.688049
$617$	−5.88618e12	−1.63512	−0.817562	−	0.575841i	$-0.804675\pi$
$617$	−5.88618e12	−1.63512	−0.817562	+	0.575841i	$0.804675\pi$
$618$	1.13595e12	0.313264
$619$	1.61207e12	0.441343	0.220671	−	0.975348i	$-0.429175\pi$
$619$	1.61207e12	0.441343	0.220671	+	0.975348i	$0.429175\pi$
$620$	0	0
$621$	−1.29209e12	−0.348643
$622$	−2.57077e12	−0.688662
$623$	−1.95313e12	−0.519440
$624$	−6.80146e11	−0.179586
$625$	0	0
$626$	3.25652e12	0.847557
$627$	3.91861e12	1.01258
$628$	−3.46004e12	−0.887693
$629$	−3.93215e12	−1.00162
$630$	0	0
$631$	−2.77824e12	−0.697651	−0.348825	−	0.937188i	$-0.613419\pi$
$631$	−2.77824e12	−0.697651	−0.348825	+	0.937188i	$0.613419\pi$
$632$	8.27078e11	0.206215
$633$	−3.08143e12	−0.762844
$634$	−3.17790e12	−0.781157
$635$	0	0
$636$	−6.27749e11	−0.152135
$637$	−1.41280e12	−0.339979
$638$	−7.76071e12	−1.85442
$639$	3.67731e11	0.0872522
$640$	0	0
$641$	2.39223e12	0.559682	0.279841	−	0.960046i	$-0.409718\pi$
$641$	2.39223e12	0.559682	0.279841	+	0.960046i	$0.409718\pi$
$642$	−1.92029e12	−0.446127
$643$	4.16259e11	0.0960317	0.0480159	−	0.998847i	$-0.484710\pi$
$643$	4.16259e11	0.0960317	0.0480159	+	0.998847i	$0.484710\pi$
$644$	−4.46145e12	−1.02209
$645$	0	0
$646$	5.18325e12	1.17100
$647$	−5.92410e12	−1.32909	−0.664543	−	0.747250i	$-0.731374\pi$
$647$	−5.92410e12	−1.32909	−0.664543	+	0.747250i	$0.731374\pi$
$648$	1.76319e11	0.0392837
$649$	−3.84886e12	−0.851591
$650$	0	0
$651$	2.40680e12	0.525201
$652$	9.78015e11	0.211949
$653$	7.00012e12	1.50659	0.753297	−	0.657681i	$-0.228462\pi$
$653$	7.00012e12	1.50659	0.753297	+	0.657681i	$0.228462\pi$
$654$	−2.31860e12	−0.495593
$655$	0	0
$656$	−5.82051e11	−0.122714
$657$	1.04771e12	0.219381
$658$	−6.94460e12	−1.44421
$659$	−6.28327e12	−1.29778	−0.648891	−	0.760881i	$-0.724767\pi$
$659$	−6.28327e12	−1.29778	−0.648891	+	0.760881i	$0.724767\pi$
$660$	0	0
$661$	−5.85530e12	−1.19301	−0.596503	−	0.802611i	$-0.703444\pi$
$661$	−5.85530e12	−1.19301	−0.596503	+	0.802611i	$0.703444\pi$
$662$	1.26157e12	0.255300
$663$	5.82012e12	1.16983
$664$	1.48667e12	0.296795
$665$	0	0
$666$	7.36056e11	0.144970
$667$	−1.40814e13	−2.75473
$668$	4.63620e11	0.0900882
$669$	−2.55784e12	−0.493691
$670$	0	0
$671$	−3.14851e12	−0.599590
$672$	6.08812e11	0.115165
$673$	6.75419e12	1.26913	0.634564	−	0.772870i	$-0.281180\pi$
$673$	6.75419e12	1.26913	0.634564	+	0.772870i	$0.281180\pi$
$674$	2.48758e12	0.464310
$675$	0	0
$676$	1.48781e12	0.274024
$677$	2.09879e12	0.383991	0.191995	−	0.981396i	$-0.438504\pi$
$677$	2.09879e12	0.383991	0.191995	+	0.981396i	$0.438504\pi$
$678$	1.27122e12	0.231040
$679$	4.30691e12	0.777592
$680$	0	0
$681$	5.06978e12	0.903289
$682$	−5.55459e12	−0.983155
$683$	8.15979e12	1.43478	0.717391	−	0.696671i	$-0.245336\pi$
$683$	8.15979e12	1.43478	0.717391	+	0.696671i	$0.245336\pi$
$684$	−9.70247e11	−0.169484
$685$	0	0
$686$	−3.36345e12	−0.579865
$687$	−2.01567e12	−0.345235
$688$	1.03093e12	0.175420
$689$	3.87881e12	0.655710
$690$	0	0
$691$	−4.11014e12	−0.685813	−0.342906	−	0.939370i	$-0.611411\pi$
$691$	−4.11014e12	−0.685813	−0.342906	+	0.939370i	$0.611411\pi$
$692$	1.84163e11	0.0305299
$693$	−3.93861e12	−0.648699
$694$	−1.69482e12	−0.277335
$695$	0	0
$696$	1.92155e12	0.310392
$697$	4.98071e12	0.799362
$698$	−5.97169e12	−0.952242
$699$	−1.29140e12	−0.204604
$700$	0	0
$701$	−8.59786e12	−1.34480	−0.672402	−	0.740186i	$-0.734738\pi$
$701$	−8.59786e12	−1.34480	−0.672402	+	0.740186i	$0.734738\pi$
$702$	−1.08946e12	−0.169315
$703$	−4.05035e12	−0.625452
$704$	−1.40506e12	−0.215584
$705$	0	0
$706$	−7.06232e12	−1.06986
$707$	−3.10015e12	−0.466654
$708$	9.52978e11	0.142539
$709$	4.30182e12	0.639358	0.319679	−	0.947526i	$-0.396425\pi$
$709$	4.30182e12	0.639358	0.319679	+	0.947526i	$0.396425\pi$
$710$	0	0
$711$	1.32482e12	0.194421
$712$	−1.11607e12	−0.162755
$713$	−1.00785e13	−1.46047
$714$	−5.20970e12	−0.750189
$715$	0	0
$716$	4.57537e10	0.00650605
$717$	4.02032e12	0.568099
$718$	−3.91569e12	−0.549855
$719$	−3.62771e12	−0.506236	−0.253118	−	0.967435i	$-0.581456\pi$
$719$	−3.62771e12	−0.506236	−0.253118	+	0.967435i	$0.581456\pi$
$720$	0	0
$721$	6.28277e12	0.865850
$722$	1.76054e11	0.0241117
$723$	7.79593e12	1.06107
$724$	8.21599e10	0.0111131
$725$	0	0
$726$	6.03389e12	0.806088
$727$	−1.23938e13	−1.64551	−0.822755	−	0.568395i	$-0.807564\pi$
$727$	−1.23938e13	−1.64551	−0.822755	+	0.568395i	$0.807564\pi$
$728$	−3.76180e12	−0.496368
$729$	2.82430e11	0.0370370
$730$	0	0
$731$	−8.82180e12	−1.14269
$732$	7.79572e11	0.100359
$733$	9.62758e12	1.23183	0.615913	−	0.787814i	$-0.288787\pi$
$733$	9.62758e12	1.23183	0.615913	+	0.787814i	$0.288787\pi$
$734$	−2.38700e10	−0.00303543
$735$	0	0
$736$	−2.54940e12	−0.320249
$737$	1.64803e13	2.05760
$738$	−9.32334e11	−0.115696
$739$	1.11915e13	1.38035	0.690175	−	0.723642i	$-0.257533\pi$
$739$	1.11915e13	1.38035	0.690175	+	0.723642i	$0.257533\pi$
$740$	0	0
$741$	5.99507e12	0.730487
$742$	−3.47199e12	−0.420495
$743$	1.24600e13	1.49992	0.749958	−	0.661486i	$-0.230074\pi$
$743$	1.24600e13	1.49992	0.749958	+	0.661486i	$0.230074\pi$
$744$	1.37532e12	0.164560
$745$	0	0
$746$	4.17665e12	0.493746
$747$	2.38135e12	0.279821
$748$	1.20233e13	1.40432
$749$	−1.06208e13	−1.23308
$750$	0	0
$751$	−1.35860e13	−1.55852	−0.779258	−	0.626703i	$-0.784404\pi$
$751$	−1.35860e13	−1.55852	−0.779258	+	0.626703i	$0.784404\pi$
$752$	−3.96834e12	−0.452510
$753$	−3.95580e12	−0.448392
$754$	−1.18731e13	−1.33781
$755$	0	0
$756$	9.75198e11	0.108579
$757$	1.08763e13	1.20379	0.601894	−	0.798576i	$-0.294413\pi$
$757$	1.08763e13	1.20379	0.601894	+	0.798576i	$0.294413\pi$
$758$	6.93655e12	0.763189
$759$	1.64929e13	1.80389
$760$	0	0
$761$	6.27003e12	0.677702	0.338851	−	0.940840i	$-0.389962\pi$
$761$	6.27003e12	0.677702	0.338851	+	0.940840i	$0.389962\pi$
$762$	−7.09729e12	−0.762597
$763$	−1.28238e13	−1.36980
$764$	4.01717e12	0.426580
$765$	0	0
$766$	−8.25352e12	−0.866183
$767$	−5.88837e12	−0.614350
$768$	3.47892e11	0.0360844
$769$	3.67914e12	0.379383	0.189692	−	0.981844i	$-0.439251\pi$
$769$	3.67914e12	0.379383	0.189692	+	0.981844i	$0.439251\pi$
$770$	0	0
$771$	−1.45106e10	−0.00147891
$772$	−3.30135e12	−0.334514
$773$	4.91202e12	0.494826	0.247413	−	0.968910i	$-0.420420\pi$
$773$	4.91202e12	0.494826	0.247413	+	0.968910i	$0.420420\pi$
$774$	1.65134e12	0.165388
$775$	0	0
$776$	2.46109e12	0.243641
$777$	4.07102e12	0.400691
$778$	−2.65027e12	−0.259347
$779$	5.13043e12	0.499155
$780$	0	0
$781$	−4.69391e12	−0.451445
$782$	2.18156e13	2.08611
$783$	3.07795e12	0.292640
$784$	7.22640e11	0.0683125
$785$	0	0
$786$	3.09679e12	0.289408
$787$	−7.13212e12	−0.662723	−0.331362	−	0.943504i	$-0.607508\pi$
$787$	−7.13212e12	−0.662723	−0.331362	+	0.943504i	$0.607508\pi$
$788$	−8.08784e12	−0.747248
$789$	−4.64759e12	−0.426954
$790$	0	0
$791$	7.03096e12	0.638587
$792$	−2.25063e12	−0.203255
$793$	−4.81691e12	−0.432553
$794$	7.32963e12	0.654470
$795$	0	0
$796$	7.16423e12	0.632500
$797$	3.63173e12	0.318824	0.159412	−	0.987212i	$-0.449040\pi$
$797$	3.63173e12	0.318824	0.159412	+	0.987212i	$0.449040\pi$
$798$	−5.36630e12	−0.468449
$799$	3.39577e13	2.94766
$800$	0	0
$801$	−1.78774e12	−0.153446
$802$	5.75649e12	0.491330
$803$	−1.33736e13	−1.13508
$804$	−4.08051e12	−0.344400
$805$	0	0
$806$	−8.49796e12	−0.709262
$807$	−1.62334e12	−0.134735
$808$	−1.77151e12	−0.146215
$809$	6.06966e12	0.498191	0.249095	−	0.968479i	$-0.419867\pi$
$809$	6.06966e12	0.498191	0.249095	+	0.968479i	$0.419867\pi$
$810$	0	0
$811$	−1.28377e13	−1.04206	−0.521030	−	0.853538i	$-0.674452\pi$
$811$	−1.28377e13	−1.04206	−0.521030	+	0.853538i	$0.674452\pi$
$812$	1.06278e13	0.857912
$813$	4.98302e12	0.400023
$814$	−9.39540e12	−0.750076
$815$	0	0
$816$	−2.97697e12	−0.235055
$817$	−9.08699e12	−0.713544
$818$	−1.13357e13	−0.885232
$819$	−6.02567e12	−0.467980
$820$	0	0
$821$	1.37951e13	1.05969	0.529846	−	0.848094i	$-0.322250\pi$
$821$	1.37951e13	1.05969	0.529846	+	0.848094i	$0.322250\pi$
$822$	2.28343e11	0.0174447
$823$	−4.09424e12	−0.311082	−0.155541	−	0.987829i	$-0.549712\pi$
$823$	−4.09424e12	−0.311082	−0.155541	+	0.987829i	$0.549712\pi$
$824$	3.59016e12	0.271294
$825$	0	0
$826$	5.27079e12	0.393972
$827$	−4.18459e12	−0.311084	−0.155542	−	0.987829i	$-0.549712\pi$
$827$	−4.18459e12	−0.311084	−0.155542	+	0.987829i	$0.549712\pi$
$828$	−4.08364e12	−0.301934
$829$	2.05638e13	1.51219	0.756097	−	0.654460i	$-0.227104\pi$
$829$	2.05638e13	1.51219	0.756097	+	0.654460i	$0.227104\pi$
$830$	0	0
$831$	6.71494e12	0.488469
$832$	−2.14960e12	−0.155526
$833$	−6.18375e12	−0.444989
$834$	1.86988e11	0.0133834
$835$	0	0
$836$	1.23847e13	0.876917
$837$	2.20299e12	0.155149
$838$	1.25312e13	0.877796
$839$	−1.47348e13	−1.02664	−0.513318	−	0.858199i	$-0.671584\pi$
$839$	−1.47348e13	−1.02664	−0.513318	+	0.858199i	$0.671584\pi$
$840$	0	0
$841$	1.90368e13	1.31223
$842$	6.19214e12	0.424558
$843$	−1.61588e13	−1.10201
$844$	−9.73884e12	−0.660642
$845$	0	0
$846$	−6.35651e12	−0.426631
$847$	3.33726e13	2.22800
$848$	−1.98400e12	−0.131753
$849$	−5.24423e12	−0.346415
$850$	0	0
$851$	−1.70474e13	−1.11423
$852$	1.16221e12	0.0755626
$853$	4.74917e12	0.307147	0.153574	−	0.988137i	$-0.450922\pi$
$853$	4.74917e12	0.307147	0.153574	+	0.988137i	$0.450922\pi$
$854$	4.31171e12	0.277389
$855$	0	0
$856$	−6.06905e12	−0.386357
$857$	5.47177e12	0.346508	0.173254	−	0.984877i	$-0.444572\pi$
$857$	5.47177e12	0.346508	0.173254	+	0.984877i	$0.444572\pi$
$858$	1.39065e13	0.876040
$859$	−1.50282e13	−0.941752	−0.470876	−	0.882199i	$-0.656062\pi$
$859$	−1.50282e13	−0.941752	−0.470876	+	0.882199i	$0.656062\pi$
$860$	0	0
$861$	−5.15661e12	−0.319779
$862$	−1.03222e12	−0.0636778
$863$	−2.63870e13	−1.61935	−0.809676	−	0.586877i	$-0.800357\pi$
$863$	−2.63870e13	−1.61935	−0.809676	+	0.586877i	$0.800357\pi$
$864$	5.57256e11	0.0340207
$865$	0	0
$866$	4.80648e12	0.290400
$867$	1.58688e13	0.953801
$868$	7.60668e12	0.454838
$869$	−1.69107e13	−1.00594
$870$	0	0
$871$	2.52131e13	1.48438
$872$	−7.32791e12	−0.429197
$873$	3.94219e12	0.229707
$874$	2.24714e13	1.30265
$875$	0	0
$876$	3.31129e12	0.189989
$877$	2.90063e13	1.65575	0.827873	−	0.560915i	$-0.189551\pi$
$877$	2.90063e13	1.65575	0.827873	+	0.560915i	$0.189551\pi$
$878$	8.37780e12	0.475778
$879$	1.79807e11	0.0101591
$880$	0	0
$881$	−1.99979e13	−1.11839	−0.559196	−	0.829036i	$-0.688890\pi$
$881$	−1.99979e13	−1.11839	−0.559196	+	0.829036i	$0.688890\pi$
$882$	1.15753e12	0.0644056
$883$	6.77203e12	0.374883	0.187442	−	0.982276i	$-0.439980\pi$
$883$	6.77203e12	0.374883	0.187442	+	0.982276i	$0.439980\pi$
$884$	1.83944e13	1.01310
$885$	0	0
$886$	6.89860e12	0.376105
$887$	−2.49633e13	−1.35408	−0.677042	−	0.735945i	$-0.736738\pi$
$887$	−2.49633e13	−1.35408	−0.677042	+	0.735945i	$0.736738\pi$
$888$	2.32630e12	0.125547
$889$	−3.92541e13	−2.10779
$890$	0	0
$891$	−3.60508e12	−0.191631
$892$	−8.08403e12	−0.427549
$893$	3.49785e13	1.84064
$894$	7.14436e12	0.374063
$895$	0	0
$896$	1.92415e12	0.0997360
$897$	2.52325e13	1.30135
$898$	−1.48740e13	−0.763282
$899$	2.40084e13	1.22587
$900$	0	0
$901$	1.69774e13	0.858240
$902$	1.19008e13	0.598613
$903$	9.13336e12	0.457126
$904$	4.01769e12	0.200087
$905$	0	0
$906$	−2.98770e12	−0.147319
$907$	1.69162e13	0.829984	0.414992	−	0.909825i	$-0.363784\pi$
$907$	1.69162e13	0.829984	0.414992	+	0.909825i	$0.363784\pi$
$908$	1.60230e13	0.782271
$909$	−2.83762e12	−0.137853
$910$	0	0
$911$	1.10887e13	0.533394	0.266697	−	0.963780i	$-0.414068\pi$
$911$	1.10887e13	0.533394	0.266697	+	0.963780i	$0.414068\pi$
$912$	−3.06646e12	−0.146778
$913$	−3.03968e13	−1.44780
$914$	−2.99840e12	−0.142112
$915$	0	0
$916$	−6.37052e12	−0.298982
$917$	1.71279e13	0.799914
$918$	−4.76853e12	−0.221612
$919$	−2.51165e13	−1.16155	−0.580777	−	0.814063i	$-0.697251\pi$
$919$	−2.51165e13	−1.16155	−0.580777	+	0.814063i	$0.697251\pi$
$920$	0	0
$921$	1.91728e12	0.0878045
$922$	2.00250e13	0.912607
$923$	−7.18121e12	−0.325679
$924$	−1.24479e13	−0.561789
$925$	0	0
$926$	1.65132e13	0.738045
$927$	5.75074e12	0.255779
$928$	6.07305e12	0.268807
$929$	2.76475e13	1.21782	0.608912	−	0.793238i	$-0.291606\pi$
$929$	2.76475e13	1.21782	0.608912	+	0.793238i	$0.291606\pi$
$930$	0	0
$931$	−6.36964e12	−0.277870
$932$	−4.08147e12	−0.177192
$933$	−1.30145e13	−0.562290
$934$	6.61722e11	0.0284521
$935$	0	0
$936$	−3.44324e12	−0.146631
$937$	−4.35096e13	−1.84398	−0.921991	−	0.387211i	$-0.873438\pi$
$937$	−4.35096e13	−1.84398	−0.921991	+	0.387211i	$0.873438\pi$
$938$	−2.25688e13	−0.951908
$939$	1.64861e13	0.692027
$940$	0	0
$941$	2.82087e13	1.17282	0.586409	−	0.810015i	$-0.300541\pi$
$941$	2.82087e13	1.17282	0.586409	+	0.810015i	$0.300541\pi$
$942$	−1.75164e13	−0.724798
$943$	2.15933e13	0.889235
$944$	3.01188e12	0.123442
$945$	0	0
$946$	−2.10786e13	−0.855720
$947$	−3.18522e13	−1.28696	−0.643480	−	0.765463i	$-0.722510\pi$
$947$	−3.18522e13	−1.28696	−0.643480	+	0.765463i	$0.722510\pi$
$948$	4.18708e12	0.168374
$949$	−2.04602e13	−0.818864
$950$	0	0
$951$	−1.60881e13	−0.637812
$952$	−1.64652e13	−0.649683
$953$	2.69813e13	1.05961	0.529804	−	0.848120i	$-0.322266\pi$
$953$	2.69813e13	1.05961	0.529804	+	0.848120i	$0.322266\pi$
$954$	−3.17798e12	−0.124218
$955$	0	0
$956$	1.27062e13	0.491989
$957$	−3.92886e13	−1.51413
$958$	−2.31732e13	−0.888875
$959$	1.26293e12	0.0482166
$960$	0	0
$961$	−9.25601e12	−0.350081
$962$	−1.43740e13	−0.541116
$963$	−9.72145e12	−0.364261
$964$	2.46390e13	0.918917
$965$	0	0
$966$	−2.25861e13	−0.834533
$967$	−4.22694e12	−0.155456	−0.0777279	−	0.996975i	$-0.524767\pi$
$967$	−4.22694e12	−0.155456	−0.0777279	+	0.996975i	$0.524767\pi$
$968$	1.90701e13	0.698093
$969$	2.62402e13	0.956114
$970$	0	0
$971$	−3.92945e13	−1.41855	−0.709275	−	0.704932i	$-0.750978\pi$
$971$	−3.92945e13	−1.41855	−0.709275	+	0.704932i	$0.750978\pi$
$972$	8.92617e11	0.0320750
$973$	1.03420e12	0.0369912
$974$	−1.39288e13	−0.495903
$975$	0	0
$976$	2.46383e12	0.0869135
$977$	−5.46792e13	−1.91998	−0.959990	−	0.280036i	$-0.909654\pi$
$977$	−5.46792e13	−1.91998	−0.959990	+	0.280036i	$0.909654\pi$
$978$	4.95120e12	0.173056
$979$	2.28196e13	0.793936
$980$	0	0
$981$	−1.17379e13	−0.404650
$982$	−3.86490e13	−1.32628
$983$	−1.73573e12	−0.0592914	−0.0296457	−	0.999560i	$-0.509438\pi$
$983$	−1.73573e12	−0.0592914	−0.0296457	+	0.999560i	$0.509438\pi$
$984$	−2.94663e12	−0.100196
$985$	0	0
$986$	−5.19680e13	−1.75102
$987$	−3.51570e13	−1.17919
$988$	1.89474e13	0.632621
$989$	−3.82459e13	−1.27117
$990$	0	0
$991$	−3.81948e13	−1.25798	−0.628989	−	0.777414i	$-0.716531\pi$
$991$	−3.81948e13	−1.25798	−0.628989	+	0.777414i	$0.716531\pi$
$992$	4.34667e12	0.142513
$993$	6.38670e12	0.208452
$994$	6.42803e12	0.208852
$995$	0	0
$996$	7.52624e12	0.242332
$997$	4.66870e13	1.49647	0.748234	−	0.663435i	$-0.230902\pi$
$997$	4.66870e13	1.49647	0.748234	+	0.663435i	$0.230902\pi$
$998$	1.82351e13	0.581864
$999$	3.72628e12	0.118367

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.10.a.k.1.1		1
5.2	odd	4		150.10.c.f.49.2		2
5.3	odd	4		150.10.c.f.49.1		2
5.4	even	2		30.10.a.b.1.1	✓	1
15.14	odd	2		90.10.a.f.1.1		1
20.19	odd	2		240.10.a.i.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.10.a.b.1.1	✓	1	5.4	even	2
90.10.a.f.1.1		1	15.14	odd	2
150.10.a.k.1.1		1	1.1	even	1	trivial
150.10.c.f.49.1		2	5.3	odd	4
150.10.c.f.49.2		2	5.2	odd	4
240.10.a.i.1.1		1	20.19	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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	150.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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