LMFDB - Embedded newform 150.10.a.e.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:	$0$
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)

$f(q)$

$=$

$q-16.0000 q^{2} +81.0000 q^{3} +256.000 q^{4} -1296.00 q^{6} +10336.0 q^{7} -4096.00 q^{8} +6561.00 q^{9} +O(q^{10})$

\(q-16.0000 q^{2} +81.0000 q^{3} +256.000 q^{4} -1296.00 q^{6} +10336.0 q^{7} -4096.00 q^{8} +6561.00 q^{9} +27420.0 q^{11} +20736.0 q^{12} +169762. q^{13} -165376. q^{14} +65536.0 q^{16} +385086. q^{17} -104976. q^{18} -637084. q^{19} +837216. q^{21} -438720. q^{22} +1.29840e6 q^{23} -331776. q^{24} -2.71619e6 q^{26} +531441. q^{27} +2.64602e6 q^{28} +7.16297e6 q^{29} -7.03187e6 q^{31} -1.04858e6 q^{32} +2.22102e6 q^{33} -6.16138e6 q^{34} +1.67962e6 q^{36} -1.92604e6 q^{37} +1.01933e7 q^{38} +1.37507e7 q^{39} +8.89607e6 q^{41} -1.33955e7 q^{42} -3.24294e7 q^{43} +7.01952e6 q^{44} -2.07744e7 q^{46} -1.72064e7 q^{47} +5.30842e6 q^{48} +6.64793e7 q^{49} +3.11920e7 q^{51} +4.34591e7 q^{52} +2.06422e7 q^{53} -8.50306e6 q^{54} -4.23363e7 q^{56} -5.16038e7 q^{57} -1.14608e8 q^{58} -6.31934e7 q^{59} -6.37580e7 q^{61} +1.12510e8 q^{62} +6.78145e7 q^{63} +1.67772e7 q^{64} -3.55363e7 q^{66} -1.45262e8 q^{67} +9.85820e7 q^{68} +1.05170e8 q^{69} -3.67657e8 q^{71} -2.68739e7 q^{72} -2.52486e8 q^{73} +3.08166e7 q^{74} -1.63094e8 q^{76} +2.83413e8 q^{77} -2.20012e8 q^{78} -1.85524e8 q^{79} +4.30467e7 q^{81} -1.42337e8 q^{82} +4.67898e8 q^{83} +2.14327e8 q^{84} +5.18871e8 q^{86} +5.80201e8 q^{87} -1.12312e8 q^{88} +5.79096e8 q^{89} +1.75466e9 q^{91} +3.32390e8 q^{92} -5.69582e8 q^{93} +2.75303e8 q^{94} -8.49347e7 q^{96} +1.31452e9 q^{97} -1.06367e9 q^{98} +1.79903e8 q^{99} +O(q^{100})\)

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
$7$	10336.0	1.62709	0.813545	−	0.581503i	$-0.197535\pi$
$7$	10336.0	1.62709	0.813545	+	0.581503i	$0.197535\pi$
$8$	−4096.00	−0.353553
$9$	6561.00	0.333333
$10$	0	0
$11$	27420.0	0.564677	0.282339	−	0.959315i	$-0.408890\pi$
$11$	27420.0	0.564677	0.282339	+	0.959315i	$0.408890\pi$
$12$	20736.0	0.288675
$13$	169762.	1.64852	0.824262	−	0.566208i	$-0.191590\pi$
$13$	169762.	1.64852	0.824262	+	0.566208i	$0.191590\pi$
$14$	−165376.	−1.15053
$15$	0	0
$16$	65536.0	0.250000
$17$	385086.	1.11825	0.559123	−	0.829085i	$-0.311138\pi$
$17$	385086.	1.11825	0.559123	+	0.829085i	$0.311138\pi$
$18$	−104976.	−0.235702
$19$	−637084.	−1.12152	−0.560758	−	0.827980i	$-0.689490\pi$
$19$	−637084.	−1.12152	−0.560758	+	0.827980i	$0.689490\pi$
$20$	0	0
$21$	837216.	0.939400
$22$	−438720.	−0.399287
$23$	1.29840e6	0.967461	0.483730	−	0.875217i	$-0.339282\pi$
$23$	1.29840e6	0.967461	0.483730	+	0.875217i	$0.339282\pi$
$24$	−331776.	−0.204124
$25$	0	0
$26$	−2.71619e6	−1.16568
$27$	531441.	0.192450
$28$	2.64602e6	0.813545
$29$	7.16297e6	1.88063	0.940313	−	0.340311i	$-0.110532\pi$
$29$	7.16297e6	1.88063	0.940313	+	0.340311i	$0.110532\pi$
$30$	0	0
$31$	−7.03187e6	−1.36755	−0.683775	−	0.729693i	$-0.739663\pi$
$31$	−7.03187e6	−1.36755	−0.683775	+	0.729693i	$0.739663\pi$
$32$	−1.04858e6	−0.176777
$33$	2.22102e6	0.326017
$34$	−6.16138e6	−0.790720
$35$	0	0
$36$	1.67962e6	0.166667
$37$	−1.92604e6	−0.168950	−0.0844748	−	0.996426i	$-0.526921\pi$
$37$	−1.92604e6	−0.168950	−0.0844748	+	0.996426i	$0.526921\pi$
$38$	1.01933e7	0.793032
$39$	1.37507e7	0.951776
$40$	0	0
$41$	8.89607e6	0.491667	0.245833	−	0.969312i	$-0.420938\pi$
$41$	8.89607e6	0.491667	0.245833	+	0.969312i	$0.420938\pi$
$42$	−1.33955e7	−0.664256
$43$	−3.24294e7	−1.44654	−0.723272	−	0.690564i	$-0.757363\pi$
$43$	−3.24294e7	−1.44654	−0.723272	+	0.690564i	$0.757363\pi$
$44$	7.01952e6	0.282339
$45$	0	0
$46$	−2.07744e7	−0.684098
$47$	−1.72064e7	−0.514340	−0.257170	−	0.966366i	$-0.582790\pi$
$47$	−1.72064e7	−0.514340	−0.257170	+	0.966366i	$0.582790\pi$
$48$	5.30842e6	0.144338
$49$	6.64793e7	1.64742
$50$	0	0
$51$	3.11920e7	0.645620
$52$	4.34591e7	0.824262
$53$	2.06422e7	0.359347	0.179673	−	0.983726i	$-0.442496\pi$
$53$	2.06422e7	0.359347	0.179673	+	0.983726i	$0.442496\pi$
$54$	−8.50306e6	−0.136083
$55$	0	0
$56$	−4.23363e7	−0.575263
$57$	−5.16038e7	−0.647508
$58$	−1.14608e8	−1.32980
$59$	−6.31934e7	−0.678950	−0.339475	−	0.940615i	$-0.610249\pi$
$59$	−6.31934e7	−0.678950	−0.339475	+	0.940615i	$0.610249\pi$
$60$	0	0
$61$	−6.37580e7	−0.589591	−0.294795	−	0.955560i	$-0.595252\pi$
$61$	−6.37580e7	−0.589591	−0.294795	+	0.955560i	$0.595252\pi$
$62$	1.12510e8	0.967004
$63$	6.78145e7	0.542363
$64$	1.67772e7	0.125000
$65$	0	0
$66$	−3.55363e7	−0.230529
$67$	−1.45262e8	−0.880674	−0.440337	−	0.897833i	$-0.645141\pi$
$67$	−1.45262e8	−0.880674	−0.440337	+	0.897833i	$0.645141\pi$
$68$	9.85820e7	0.559123
$69$	1.05170e8	0.558564
$70$	0	0
$71$	−3.67657e8	−1.71704	−0.858519	−	0.512781i	$-0.828615\pi$
$71$	−3.67657e8	−1.71704	−0.858519	+	0.512781i	$0.828615\pi$
$72$	−2.68739e7	−0.117851
$73$	−2.52486e8	−1.04060	−0.520301	−	0.853983i	$-0.674180\pi$
$73$	−2.52486e8	−1.04060	−0.520301	+	0.853983i	$0.674180\pi$
$74$	3.08166e7	0.119465
$75$	0	0
$76$	−1.63094e8	−0.560758
$77$	2.83413e8	0.918780
$78$	−2.20012e8	−0.673007
$79$	−1.85524e8	−0.535892	−0.267946	−	0.963434i	$-0.586345\pi$
$79$	−1.85524e8	−0.535892	−0.267946	+	0.963434i	$0.586345\pi$
$80$	0	0
$81$	4.30467e7	0.111111
$82$	−1.42337e8	−0.347661
$83$	4.67898e8	1.08218	0.541090	−	0.840965i	$-0.318012\pi$
$83$	4.67898e8	1.08218	0.541090	+	0.840965i	$0.318012\pi$
$84$	2.14327e8	0.469700
$85$	0	0
$86$	5.18871e8	1.02286
$87$	5.80201e8	1.08578
$88$	−1.12312e8	−0.199644
$89$	5.79096e8	0.978354	0.489177	−	0.872185i	$-0.337297\pi$
$89$	5.79096e8	0.978354	0.489177	+	0.872185i	$0.337297\pi$
$90$	0	0
$91$	1.75466e9	2.68230
$92$	3.32390e8	0.483730
$93$	−5.69582e8	−0.789556
$94$	2.75303e8	0.363694
$95$	0	0
$96$	−8.49347e7	−0.102062
$97$	1.31452e9	1.50763	0.753813	−	0.657090i	$-0.228213\pi$
$97$	1.31452e9	1.50763	0.753813	+	0.657090i	$0.228213\pi$
$98$	−1.06367e9	−1.16490
$99$	1.79903e8	0.188226
$100$	0	0
$101$	−4.40286e8	−0.421006	−0.210503	−	0.977593i	$-0.567510\pi$
$101$	−4.40286e8	−0.421006	−0.210503	+	0.977593i	$0.567510\pi$
$102$	−4.99071e8	−0.456522
$103$	5.91306e8	0.517660	0.258830	−	0.965923i	$-0.416663\pi$
$103$	5.91306e8	0.517660	0.258830	+	0.965923i	$0.416663\pi$
$104$	−6.95345e8	−0.582841
$105$	0	0
$106$	−3.30274e8	−0.254096
$107$	9.15121e8	0.674918	0.337459	−	0.941340i	$-0.390432\pi$
$107$	9.15121e8	0.674918	0.337459	+	0.941340i	$0.390432\pi$
$108$	1.36049e8	0.0962250
$109$	2.37000e9	1.60816	0.804079	−	0.594523i	$-0.202659\pi$
$109$	2.37000e9	1.60816	0.804079	+	0.594523i	$0.202659\pi$
$110$	0	0
$111$	−1.56009e8	−0.0975431
$112$	6.77380e8	0.406772
$113$	−2.26842e8	−0.130879	−0.0654394	−	0.997857i	$-0.520845\pi$
$113$	−2.26842e8	−0.130879	−0.0654394	+	0.997857i	$0.520845\pi$
$114$	8.25661e8	0.457857
$115$	0	0
$116$	1.83372e9	0.940313
$117$	1.11381e9	0.549508
$118$	1.01109e9	0.480090
$119$	3.98025e9	1.81949
$120$	0	0
$121$	−1.60609e9	−0.681139
$122$	1.02013e9	0.416904
$123$	7.20582e8	0.283864
$124$	−1.80016e9	−0.683775
$125$	0	0
$126$	−1.08503e9	−0.383509
$127$	4.44062e9	1.51470	0.757350	−	0.653009i	$-0.226494\pi$
$127$	4.44062e9	1.51470	0.757350	+	0.653009i	$0.226494\pi$
$128$	−2.68435e8	−0.0883883
$129$	−2.62678e9	−0.835162
$130$	0	0
$131$	2.56985e9	0.762407	0.381204	−	0.924491i	$-0.375510\pi$
$131$	2.56985e9	0.762407	0.381204	+	0.924491i	$0.375510\pi$
$132$	5.68581e8	0.163008
$133$	−6.58490e9	−1.82481
$134$	2.32419e9	0.622731
$135$	0	0
$136$	−1.57731e9	−0.395360
$137$	3.05072e9	0.739878	0.369939	−	0.929056i	$-0.379379\pi$
$137$	3.05072e9	0.739878	0.369939	+	0.929056i	$0.379379\pi$
$138$	−1.68273e9	−0.394964
$139$	2.21959e9	0.504321	0.252160	−	0.967685i	$-0.418859\pi$
$139$	2.21959e9	0.504321	0.252160	+	0.967685i	$0.418859\pi$
$140$	0	0
$141$	−1.39372e9	−0.296955
$142$	5.88251e9	1.21413
$143$	4.65487e9	0.930884
$144$	4.29982e8	0.0833333
$145$	0	0
$146$	4.03978e9	0.735817
$147$	5.38482e9	0.951138
$148$	−4.93066e8	−0.0844748
$149$	2.77268e9	0.460853	0.230426	−	0.973090i	$-0.425988\pi$
$149$	2.77268e9	0.460853	0.230426	+	0.973090i	$0.425988\pi$
$150$	0	0
$151$	−2.53999e9	−0.397591	−0.198795	−	0.980041i	$-0.563703\pi$
$151$	−2.53999e9	−0.397591	−0.198795	+	0.980041i	$0.563703\pi$
$152$	2.60950e9	0.396516
$153$	2.52655e9	0.372749
$154$	−4.53461e9	−0.649676
$155$	0	0
$156$	3.52018e9	0.475888
$157$	−9.52972e9	−1.25179	−0.625895	−	0.779907i	$-0.715266\pi$
$157$	−9.52972e9	−1.25179	−0.625895	+	0.779907i	$0.715266\pi$
$158$	2.96838e9	0.378933
$159$	1.67201e9	0.207469
$160$	0	0
$161$	1.34203e10	1.57414
$162$	−6.88748e8	−0.0785674
$163$	−3.29763e9	−0.365896	−0.182948	−	0.983123i	$-0.558564\pi$
$163$	−3.29763e9	−0.365896	−0.182948	+	0.983123i	$0.558564\pi$
$164$	2.27739e9	0.245833
$165$	0	0
$166$	−7.48636e9	−0.765217
$167$	−1.07574e10	−1.07025	−0.535123	−	0.844774i	$-0.679735\pi$
$167$	−1.07574e10	−1.07025	−0.535123	+	0.844774i	$0.679735\pi$
$168$	−3.42924e9	−0.332128
$169$	1.82146e10	1.71763
$170$	0	0
$171$	−4.17991e9	−0.373839
$172$	−8.30194e9	−0.723272
$173$	−8.56587e9	−0.727049	−0.363525	−	0.931585i	$-0.618427\pi$
$173$	−8.56587e9	−0.727049	−0.363525	+	0.931585i	$0.618427\pi$
$174$	−9.28321e9	−0.767762
$175$	0	0
$176$	1.79700e9	0.141169
$177$	−5.11866e9	−0.391992
$178$	−9.26554e9	−0.691800
$179$	−6.25110e9	−0.455112	−0.227556	−	0.973765i	$-0.573073\pi$
$179$	−6.25110e9	−0.455112	−0.227556	+	0.973765i	$0.573073\pi$
$180$	0	0
$181$	−2.24946e10	−1.55785	−0.778925	−	0.627117i	$-0.784235\pi$
$181$	−2.24946e10	−1.55785	−0.778925	+	0.627117i	$0.784235\pi$
$182$	−2.80746e10	−1.89667
$183$	−5.16440e9	−0.340400
$184$	−5.31825e9	−0.342049
$185$	0	0
$186$	9.11331e9	0.558300
$187$	1.05591e10	0.631449
$188$	−4.40485e9	−0.257170
$189$	5.49297e9	0.313133
$190$	0	0
$191$	−2.69014e10	−1.46260	−0.731300	−	0.682056i	$-0.761086\pi$
$191$	−2.69014e10	−1.46260	−0.731300	+	0.682056i	$0.761086\pi$
$192$	1.35895e9	0.0721688
$193$	1.35021e10	0.700476	0.350238	−	0.936661i	$-0.386101\pi$
$193$	1.35021e10	0.700476	0.350238	+	0.936661i	$0.386101\pi$
$194$	−2.10323e10	−1.06605
$195$	0	0
$196$	1.70187e10	0.823709
$197$	2.11455e10	1.00028	0.500138	−	0.865945i	$-0.333282\pi$
$197$	2.11455e10	1.00028	0.500138	+	0.865945i	$0.333282\pi$
$198$	−2.87844e9	−0.133096
$199$	5.66505e9	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$199$	5.66505e9	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$200$	0	0
$201$	−1.17662e10	−0.508458
$202$	7.04458e9	0.297697
$203$	7.40365e10	3.05995
$204$	7.98514e9	0.322810
$205$	0	0
$206$	−9.46089e9	−0.366041
$207$	8.51880e9	0.322487
$208$	1.11255e10	0.412131
$209$	−1.74688e10	−0.633295
$210$	0	0
$211$	−2.18540e10	−0.759031	−0.379516	−	0.925185i	$-0.623909\pi$
$211$	−2.18540e10	−0.759031	−0.379516	+	0.925185i	$0.623909\pi$
$212$	5.28439e9	0.179673
$213$	−2.97802e10	−0.991333
$214$	−1.46419e10	−0.477239
$215$	0	0
$216$	−2.17678e9	−0.0680414
$217$	−7.26814e10	−2.22513
$218$	−3.79200e10	−1.13714
$219$	−2.04514e10	−0.600792
$220$	0	0
$221$	6.53730e10	1.84346
$222$	2.49615e9	0.0689734
$223$	3.41926e10	0.925891	0.462945	−	0.886387i	$-0.346793\pi$
$223$	3.41926e10	0.925891	0.462945	+	0.886387i	$0.346793\pi$
$224$	−1.08381e10	−0.287631
$225$	0	0
$226$	3.62946e9	0.0925453
$227$	2.23784e10	0.559388	0.279694	−	0.960089i	$-0.409767\pi$
$227$	2.23784e10	0.559388	0.279694	+	0.960089i	$0.409767\pi$
$228$	−1.32106e10	−0.323754
$229$	−2.76787e9	−0.0665099	−0.0332550	−	0.999447i	$-0.510587\pi$
$229$	−2.76787e9	−0.0665099	−0.0332550	+	0.999447i	$0.510587\pi$
$230$	0	0
$231$	2.29565e10	0.530458
$232$	−2.93395e10	−0.664902
$233$	6.55570e10	1.45719	0.728597	−	0.684942i	$-0.240173\pi$
$233$	6.55570e10	1.45719	0.728597	+	0.684942i	$0.240173\pi$
$234$	−1.78209e10	−0.388561
$235$	0	0
$236$	−1.61775e10	−0.339475
$237$	−1.50274e10	−0.309398
$238$	−6.36840e10	−1.28657
$239$	2.70069e10	0.535406	0.267703	−	0.963501i	$-0.413735\pi$
$239$	2.70069e10	0.535406	0.267703	+	0.963501i	$0.413735\pi$
$240$	0	0
$241$	−1.73578e10	−0.331450	−0.165725	−	0.986172i	$-0.552996\pi$
$241$	−1.73578e10	−0.331450	−0.165725	+	0.986172i	$0.552996\pi$
$242$	2.56975e10	0.481638
$243$	3.48678e9	0.0641500
$244$	−1.63221e10	−0.294795
$245$	0	0
$246$	−1.15293e10	−0.200722
$247$	−1.08153e11	−1.84885
$248$	2.88025e10	0.483502
$249$	3.78997e10	0.624797
$250$	0	0
$251$	−2.23811e10	−0.355918	−0.177959	−	0.984038i	$-0.556949\pi$
$251$	−2.23811e10	−0.355918	−0.177959	+	0.984038i	$0.556949\pi$
$252$	1.73605e10	0.271182
$253$	3.56021e10	0.546303
$254$	−7.10499e10	−1.07105
$255$	0	0
$256$	4.29497e9	0.0625000
$257$	−1.29994e11	−1.85876	−0.929380	−	0.369125i	$-0.879657\pi$
$257$	−1.29994e11	−1.85876	−0.929380	+	0.369125i	$0.879657\pi$
$258$	4.20286e10	0.590549
$259$	−1.99075e10	−0.274896
$260$	0	0
$261$	4.69963e10	0.626875
$262$	−4.11176e10	−0.539103
$263$	−7.50129e10	−0.966796	−0.483398	−	0.875401i	$-0.660598\pi$
$263$	−7.50129e10	−0.966796	−0.483398	+	0.875401i	$0.660598\pi$
$264$	−9.09730e9	−0.115264
$265$	0	0
$266$	1.05358e11	1.29033
$267$	4.69068e10	0.564853
$268$	−3.71871e10	−0.440337
$269$	−3.22655e10	−0.375710	−0.187855	−	0.982197i	$-0.560154\pi$
$269$	−3.22655e10	−0.375710	−0.187855	+	0.982197i	$0.560154\pi$
$270$	0	0
$271$	−3.88817e10	−0.437909	−0.218954	−	0.975735i	$-0.570265\pi$
$271$	−3.88817e10	−0.437909	−0.218954	+	0.975735i	$0.570265\pi$
$272$	2.52370e10	0.279562
$273$	1.42127e11	1.54862
$274$	−4.88115e10	−0.523172
$275$	0	0
$276$	2.69236e10	0.279282
$277$	1.39247e11	1.42110	0.710552	−	0.703645i	$-0.248445\pi$
$277$	1.39247e11	1.42110	0.710552	+	0.703645i	$0.248445\pi$
$278$	−3.55135e10	−0.356608
$279$	−4.61361e10	−0.455850
$280$	0	0
$281$	1.21771e11	1.16511	0.582553	−	0.812793i	$-0.302054\pi$
$281$	1.21771e11	1.16511	0.582553	+	0.812793i	$0.302054\pi$
$282$	2.22995e10	0.209979
$283$	−1.12442e11	−1.04205	−0.521025	−	0.853541i	$-0.674450\pi$
$283$	−1.12442e11	−1.04205	−0.521025	+	0.853541i	$0.674450\pi$
$284$	−9.41202e10	−0.858519
$285$	0	0
$286$	−7.44780e10	−0.658235
$287$	9.19498e10	0.799986
$288$	−6.87971e9	−0.0589256
$289$	2.97034e10	0.250475
$290$	0	0
$291$	1.06476e11	0.870428
$292$	−6.46365e10	−0.520301
$293$	5.73383e10	0.454507	0.227253	−	0.973836i	$-0.427025\pi$
$293$	5.73383e10	0.454507	0.227253	+	0.973836i	$0.427025\pi$
$294$	−8.61572e10	−0.672556
$295$	0	0
$296$	7.88905e9	0.0597327
$297$	1.45721e10	0.108672
$298$	−4.43629e10	−0.325872
$299$	2.20419e11	1.59488
$300$	0	0
$301$	−3.35191e11	−2.35365
$302$	4.06399e10	0.281139
$303$	−3.56632e10	−0.243068
$304$	−4.17519e10	−0.280379
$305$	0	0
$306$	−4.04248e10	−0.263573
$307$	1.59602e11	1.02545	0.512727	−	0.858552i	$-0.328635\pi$
$307$	1.59602e11	1.02545	0.512727	+	0.858552i	$0.328635\pi$
$308$	7.25538e10	0.459390
$309$	4.78958e10	0.298871
$310$	0	0
$311$	−1.22091e11	−0.740051	−0.370025	−	0.929022i	$-0.620651\pi$
$311$	−1.22091e11	−0.740051	−0.370025	+	0.929022i	$0.620651\pi$
$312$	−5.63230e10	−0.336504
$313$	1.28323e11	0.755707	0.377854	−	0.925865i	$-0.376662\pi$
$313$	1.28323e11	0.755707	0.377854	+	0.925865i	$0.376662\pi$
$314$	1.52476e11	0.885150
$315$	0	0
$316$	−4.74941e10	−0.267946
$317$	−1.25978e11	−0.700694	−0.350347	−	0.936620i	$-0.613936\pi$
$317$	−1.25978e11	−0.700694	−0.350347	+	0.936620i	$0.613936\pi$
$318$	−2.67522e10	−0.146703
$319$	1.96409e11	1.06195
$320$	0	0
$321$	7.41248e10	0.389664
$322$	−2.14724e11	−1.11309
$323$	−2.45332e11	−1.25413
$324$	1.10200e10	0.0555556
$325$	0	0
$326$	5.27621e10	0.258728
$327$	1.91970e11	0.928470
$328$	−3.64383e10	−0.173831
$329$	−1.77846e11	−0.836878
$330$	0	0
$331$	−2.67273e11	−1.22385	−0.611926	−	0.790915i	$-0.709605\pi$
$331$	−2.67273e11	−1.22385	−0.611926	+	0.790915i	$0.709605\pi$
$332$	1.19782e11	0.541090
$333$	−1.26367e10	−0.0563165
$334$	1.72119e11	0.756779
$335$	0	0
$336$	5.48678e10	0.234850
$337$	−3.93835e11	−1.66333	−0.831667	−	0.555275i	$-0.812613\pi$
$337$	−3.93835e11	−1.66333	−0.831667	+	0.555275i	$0.812613\pi$
$338$	−2.91434e11	−1.21455
$339$	−1.83742e10	−0.0755630
$340$	0	0
$341$	−1.92814e11	−0.772225
$342$	6.68785e10	0.264344
$343$	2.70035e11	1.05341
$344$	1.32831e11	0.511430
$345$	0	0
$346$	1.37054e11	0.514101
$347$	2.50368e11	0.927035	0.463518	−	0.886088i	$-0.346587\pi$
$347$	2.50368e11	0.927035	0.463518	+	0.886088i	$0.346587\pi$
$348$	1.48531e11	0.542890
$349$	1.69543e11	0.611739	0.305869	−	0.952073i	$-0.401053\pi$
$349$	1.69543e11	0.611739	0.305869	+	0.952073i	$0.401053\pi$
$350$	0	0
$351$	9.02185e10	0.317259
$352$	−2.87520e10	−0.0998218
$353$	−4.12724e11	−1.41473	−0.707365	−	0.706848i	$-0.750116\pi$
$353$	−4.12724e11	−1.41473	−0.707365	+	0.706848i	$0.750116\pi$
$354$	8.18986e10	0.277180
$355$	0	0
$356$	1.48249e11	0.489177
$357$	3.22400e11	1.05048
$358$	1.00018e11	0.321813
$359$	3.52888e11	1.12127	0.560637	−	0.828062i	$-0.310556\pi$
$359$	3.52888e11	1.12127	0.560637	+	0.828062i	$0.310556\pi$
$360$	0	0
$361$	8.31883e10	0.257798
$362$	3.59914e11	1.10157
$363$	−1.30093e11	−0.393256
$364$	4.49193e11	1.34115
$365$	0	0
$366$	8.26304e10	0.240699
$367$	−5.62062e11	−1.61729	−0.808644	−	0.588299i	$-0.799798\pi$
$367$	−5.62062e11	−1.61729	−0.808644	+	0.588299i	$0.799798\pi$
$368$	8.50919e10	0.241865
$369$	5.83671e10	0.163889
$370$	0	0
$371$	2.13357e11	0.584689
$372$	−1.45813e11	−0.394778
$373$	1.89328e10	0.0506436	0.0253218	−	0.999679i	$-0.491939\pi$
$373$	1.89328e10	0.0506436	0.0253218	+	0.999679i	$0.491939\pi$
$374$	−1.68945e11	−0.446502
$375$	0	0
$376$	7.04776e10	0.181847
$377$	1.21600e12	3.10026
$378$	−8.78876e10	−0.221419
$379$	7.10525e11	1.76890	0.884449	−	0.466637i	$-0.154535\pi$
$379$	7.10525e11	1.76890	0.884449	+	0.466637i	$0.154535\pi$
$380$	0	0
$381$	3.59690e11	0.874512
$382$	4.30423e11	1.03421
$383$	6.37883e11	1.51477	0.757385	−	0.652969i	$-0.226477\pi$
$383$	6.37883e11	1.51477	0.757385	+	0.652969i	$0.226477\pi$
$384$	−2.17433e10	−0.0510310
$385$	0	0
$386$	−2.16034e11	−0.495311
$387$	−2.12770e11	−0.482181
$388$	3.36516e11	0.753813
$389$	−8.56047e11	−1.89550	−0.947751	−	0.319010i	$-0.896650\pi$
$389$	−8.56047e11	−1.89550	−0.947751	+	0.319010i	$0.896650\pi$
$390$	0	0
$391$	4.99996e11	1.08186
$392$	−2.72299e11	−0.582450
$393$	2.08158e11	0.440176
$394$	−3.38328e11	−0.707303
$395$	0	0
$396$	4.60551e10	0.0941129
$397$	4.22739e11	0.854113	0.427057	−	0.904225i	$-0.359550\pi$
$397$	4.22739e11	0.854113	0.427057	+	0.904225i	$0.359550\pi$
$398$	−9.06408e10	−0.181071
$399$	−5.33377e11	−1.05355
$400$	0	0
$401$	−8.96364e10	−0.173115	−0.0865575	−	0.996247i	$-0.527587\pi$
$401$	−8.96364e10	−0.173115	−0.0865575	+	0.996247i	$0.527587\pi$
$402$	1.88260e11	0.359534
$403$	−1.19374e12	−2.25444
$404$	−1.12713e11	−0.210503
$405$	0	0
$406$	−1.18458e12	−2.16371
$407$	−5.28120e10	−0.0954020
$408$	−1.27762e11	−0.228261
$409$	5.75119e10	0.101626	0.0508128	−	0.998708i	$-0.483819\pi$
$409$	5.75119e10	0.101626	0.0508128	+	0.998708i	$0.483819\pi$
$410$	0	0
$411$	2.47108e11	0.427169
$412$	1.51374e11	0.258830
$413$	−6.53167e11	−1.10471
$414$	−1.36301e11	−0.228033
$415$	0	0
$416$	−1.78008e11	−0.291421
$417$	1.79787e11	0.291170
$418$	2.79501e11	0.447807
$419$	−6.82070e11	−1.08110	−0.540550	−	0.841312i	$-0.681784\pi$
$419$	−6.82070e11	−1.08110	−0.540550	+	0.841312i	$0.681784\pi$
$420$	0	0
$421$	−1.18903e12	−1.84469	−0.922343	−	0.386373i	$-0.873728\pi$
$421$	−1.18903e12	−1.84469	−0.922343	+	0.386373i	$0.873728\pi$
$422$	3.49664e11	0.536716
$423$	−1.12891e11	−0.171447
$424$	−8.45503e10	−0.127048
$425$	0	0
$426$	4.76483e11	0.700978
$427$	−6.59003e11	−0.959317
$428$	2.34271e11	0.337459
$429$	3.77045e11	0.537446
$430$	0	0
$431$	1.08626e12	1.51631	0.758155	−	0.652074i	$-0.226101\pi$
$431$	1.08626e12	1.51631	0.758155	+	0.652074i	$0.226101\pi$
$432$	3.48285e10	0.0481125
$433$	−2.75569e11	−0.376734	−0.188367	−	0.982099i	$-0.560319\pi$
$433$	−2.75569e11	−0.376734	−0.188367	+	0.982099i	$0.560319\pi$
$434$	1.16290e12	1.57340
$435$	0	0
$436$	6.06719e11	0.804079
$437$	−8.27190e11	−1.08502
$438$	3.27222e11	0.424824
$439$	−1.31894e11	−0.169487	−0.0847434	−	0.996403i	$-0.527007\pi$
$439$	−1.31894e11	−0.169487	−0.0847434	+	0.996403i	$0.527007\pi$
$440$	0	0
$441$	4.36171e11	0.549140
$442$	−1.04597e12	−1.30352
$443$	1.17850e12	1.45382	0.726912	−	0.686730i	$-0.240955\pi$
$443$	1.17850e12	1.45382	0.726912	+	0.686730i	$0.240955\pi$
$444$	−3.99383e10	−0.0487715
$445$	0	0
$446$	−5.47081e11	−0.654704
$447$	2.24587e11	0.266073
$448$	1.73409e11	0.203386
$449$	−1.32158e11	−0.153457	−0.0767283	−	0.997052i	$-0.524447\pi$
$449$	−1.32158e11	−0.153457	−0.0767283	+	0.997052i	$0.524447\pi$
$450$	0	0
$451$	2.43930e11	0.277633
$452$	−5.80714e10	−0.0654394
$453$	−2.05740e11	−0.229549
$454$	−3.58055e11	−0.395547
$455$	0	0
$456$	2.11369e11	0.228929
$457$	7.17700e10	0.0769697	0.0384849	−	0.999259i	$-0.487747\pi$
$457$	7.17700e10	0.0769697	0.0384849	+	0.999259i	$0.487747\pi$
$458$	4.42860e10	0.0470296
$459$	2.04650e11	0.215207
$460$	0	0
$461$	1.64460e12	1.69592	0.847961	−	0.530059i	$-0.177830\pi$
$461$	1.64460e12	1.69592	0.847961	+	0.530059i	$0.177830\pi$
$462$	−3.67303e11	−0.375090
$463$	−1.22023e12	−1.23404	−0.617018	−	0.786949i	$-0.711659\pi$
$463$	−1.22023e12	−1.23404	−0.617018	+	0.786949i	$0.711659\pi$
$464$	4.69433e11	0.470156
$465$	0	0
$466$	−1.04891e12	−1.03039
$467$	5.18912e11	0.504856	0.252428	−	0.967616i	$-0.418771\pi$
$467$	5.18912e11	0.504856	0.252428	+	0.967616i	$0.418771\pi$
$468$	2.85135e11	0.274754
$469$	−1.50143e12	−1.43294
$470$	0	0
$471$	−7.71907e11	−0.722722
$472$	2.58840e11	0.240045
$473$	−8.89215e11	−0.816830
$474$	2.40439e11	0.218777
$475$	0	0
$476$	1.01894e12	0.909743
$477$	1.35433e11	0.119782
$478$	−4.32110e11	−0.378589
$479$	−1.51788e12	−1.31743	−0.658717	−	0.752391i	$-0.728900\pi$
$479$	−1.51788e12	−1.31743	−0.658717	+	0.752391i	$0.728900\pi$
$480$	0	0
$481$	−3.26968e11	−0.278518
$482$	2.77725e11	0.234371
$483$	1.08704e12	0.908833
$484$	−4.11159e11	−0.340570
$485$	0	0
$486$	−5.57886e10	−0.0453609
$487$	−2.11955e12	−1.70751	−0.853754	−	0.520677i	$-0.825680\pi$
$487$	−2.11955e12	−1.70751	−0.853754	+	0.520677i	$0.825680\pi$
$488$	2.61153e11	0.208452
$489$	−2.67108e11	−0.211250
$490$	0	0
$491$	−6.34518e11	−0.492694	−0.246347	−	0.969182i	$-0.579230\pi$
$491$	−6.34518e11	−0.492694	−0.246347	+	0.969182i	$0.579230\pi$
$492$	1.84469e11	0.141932
$493$	2.75836e12	2.10300
$494$	1.73044e12	1.30733
$495$	0	0
$496$	−4.60841e11	−0.341888
$497$	−3.80010e12	−2.79377
$498$	−6.06395e11	−0.441798
$499$	3.71937e11	0.268545	0.134273	−	0.990944i	$-0.457130\pi$
$499$	3.71937e11	0.268545	0.134273	+	0.990944i	$0.457130\pi$
$500$	0	0
$501$	−8.71351e11	−0.617907
$502$	3.58098e11	0.251672
$503$	1.30603e12	0.909696	0.454848	−	0.890569i	$-0.349694\pi$
$503$	1.30603e12	0.909696	0.454848	+	0.890569i	$0.349694\pi$
$504$	−2.77768e11	−0.191754
$505$	0	0
$506$	−5.69634e11	−0.386295
$507$	1.47539e12	0.991676
$508$	1.13680e12	0.757350
$509$	−2.46188e12	−1.62569	−0.812844	−	0.582481i	$-0.802082\pi$
$509$	−2.46188e12	−1.62569	−0.812844	+	0.582481i	$0.802082\pi$
$510$	0	0
$511$	−2.60970e12	−1.69315
$512$	−6.87195e10	−0.0441942
$513$	−3.38573e11	−0.215836
$514$	2.07990e12	1.31434
$515$	0	0
$516$	−6.72457e11	−0.417581
$517$	−4.71801e11	−0.290436
$518$	3.18520e11	0.194381
$519$	−6.93835e11	−0.419762
$520$	0	0
$521$	−3.38151e11	−0.201067	−0.100533	−	0.994934i	$-0.532055\pi$
$521$	−3.38151e11	−0.201067	−0.100533	+	0.994934i	$0.532055\pi$
$522$	−7.51940e11	−0.443268
$523$	−1.35866e12	−0.794061	−0.397030	−	0.917805i	$-0.629959\pi$
$523$	−1.35866e12	−0.794061	−0.397030	+	0.917805i	$0.629959\pi$
$524$	6.57882e11	0.381204
$525$	0	0
$526$	1.20021e12	0.683628
$527$	−2.70788e12	−1.52926
$528$	1.45557e11	0.0815042
$529$	−1.15310e11	−0.0640202
$530$	0	0
$531$	−4.14612e11	−0.226317
$532$	−1.68573e12	−0.912403
$533$	1.51022e12	0.810525
$534$	−7.50509e11	−0.399411
$535$	0	0
$536$	5.94993e11	0.311365
$537$	−5.06339e11	−0.262759
$538$	5.16248e11	0.265667
$539$	1.82286e12	0.930260
$540$	0	0
$541$	2.72399e12	1.36716	0.683578	−	0.729877i	$-0.260423\pi$
$541$	2.72399e12	1.36716	0.683578	+	0.729877i	$0.260423\pi$
$542$	6.22107e11	0.309648
$543$	−1.82207e12	−0.899425
$544$	−4.03792e11	−0.197680
$545$	0	0
$546$	−2.27404e12	−1.09504
$547$	2.29514e12	1.09614	0.548070	−	0.836433i	$-0.315363\pi$
$547$	2.29514e12	1.09614	0.548070	+	0.836433i	$0.315363\pi$
$548$	7.80984e11	0.369939
$549$	−4.18317e11	−0.196530
$550$	0	0
$551$	−4.56342e12	−2.10915
$552$	−4.30778e11	−0.197482
$553$	−1.91757e12	−0.871944
$554$	−2.22795e12	−1.00487
$555$	0	0
$556$	5.68216e11	0.252160
$557$	3.66541e11	0.161352	0.0806760	−	0.996740i	$-0.474292\pi$
$557$	3.66541e11	0.161352	0.0806760	+	0.996740i	$0.474292\pi$
$558$	7.38178e11	0.322335
$559$	−5.50529e12	−2.38466
$560$	0	0
$561$	8.55284e11	0.364567
$562$	−1.94834e12	−0.823855
$563$	−2.20274e12	−0.924006	−0.462003	−	0.886878i	$-0.652869\pi$
$563$	−2.20274e12	−0.924006	−0.462003	+	0.886878i	$0.652869\pi$
$564$	−3.56793e11	−0.148477
$565$	0	0
$566$	1.79907e12	0.736841
$567$	4.44931e11	0.180788
$568$	1.50592e12	0.607065
$569$	2.30440e12	0.921620	0.460810	−	0.887499i	$-0.347559\pi$
$569$	2.30440e12	0.921620	0.460810	+	0.887499i	$0.347559\pi$
$570$	0	0
$571$	1.91693e12	0.754647	0.377323	−	0.926082i	$-0.376845\pi$
$571$	1.91693e12	0.754647	0.377323	+	0.926082i	$0.376845\pi$
$572$	1.19165e12	0.465442
$573$	−2.17902e12	−0.844432
$574$	−1.47120e12	−0.565675
$575$	0	0
$576$	1.10075e11	0.0416667
$577$	4.61602e12	1.73371	0.866856	−	0.498559i	$-0.166137\pi$
$577$	4.61602e12	1.73371	0.866856	+	0.498559i	$0.166137\pi$
$578$	−4.75254e11	−0.177113
$579$	1.09367e12	0.404420
$580$	0	0
$581$	4.83619e12	1.76080
$582$	−1.70361e12	−0.615485
$583$	5.66008e11	0.202915
$584$	1.03418e12	0.367908
$585$	0	0
$586$	−9.17412e11	−0.321385
$587$	−3.31976e11	−0.115408	−0.0577039	−	0.998334i	$-0.518378\pi$
$587$	−3.31976e11	−0.115408	−0.0577039	+	0.998334i	$0.518378\pi$
$588$	1.37851e12	0.475569
$589$	4.47989e12	1.53373
$590$	0	0
$591$	1.71279e12	0.577510
$592$	−1.26225e11	−0.0422374
$593$	−2.45977e12	−0.816861	−0.408431	−	0.912789i	$-0.633924\pi$
$593$	−2.45977e12	−0.816861	−0.408431	+	0.912789i	$0.633924\pi$
$594$	−2.33154e11	−0.0768429
$595$	0	0
$596$	7.09807e11	0.230426
$597$	4.58869e11	0.147844
$598$	−3.52670e12	−1.12775
$599$	−1.26724e12	−0.402198	−0.201099	−	0.979571i	$-0.564451\pi$
$599$	−1.26724e12	−0.402198	−0.201099	+	0.979571i	$0.564451\pi$
$600$	0	0
$601$	2.25368e12	0.704624	0.352312	−	0.935883i	$-0.385396\pi$
$601$	2.25368e12	0.704624	0.352312	+	0.935883i	$0.385396\pi$
$602$	5.36305e12	1.66429
$603$	−9.53064e11	−0.293558
$604$	−6.50239e11	−0.198795
$605$	0	0
$606$	5.70611e11	0.171875
$607$	−1.54071e12	−0.460652	−0.230326	−	0.973114i	$-0.573979\pi$
$607$	−1.54071e12	−0.460652	−0.230326	+	0.973114i	$0.573979\pi$
$608$	6.68031e11	0.198258
$609$	5.99696e12	1.76666
$610$	0	0
$611$	−2.92100e12	−0.847903
$612$	6.46797e11	0.186374
$613$	6.24615e11	0.178665	0.0893327	−	0.996002i	$-0.471527\pi$
$613$	6.24615e11	0.178665	0.0893327	+	0.996002i	$0.471527\pi$
$614$	−2.55363e12	−0.725105
$615$	0	0
$616$	−1.16086e12	−0.324838
$617$	−1.83847e11	−0.0510709	−0.0255355	−	0.999674i	$-0.508129\pi$
$617$	−1.83847e11	−0.0510709	−0.0255355	+	0.999674i	$0.508129\pi$
$618$	−7.66332e11	−0.211334
$619$	3.53823e12	0.968675	0.484337	−	0.874881i	$-0.339061\pi$
$619$	3.53823e12	0.968675	0.484337	+	0.874881i	$0.339061\pi$
$620$	0	0
$621$	6.90023e11	0.186188
$622$	1.95345e12	0.523295
$623$	5.98554e12	1.59187
$624$	9.01167e11	0.237944
$625$	0	0
$626$	−2.05316e12	−0.534366
$627$	−1.41498e12	−0.365633
$628$	−2.43961e12	−0.625895
$629$	−7.41690e11	−0.188927
$630$	0	0
$631$	−8.92700e11	−0.224168	−0.112084	−	0.993699i	$-0.535753\pi$
$631$	−8.92700e11	−0.224168	−0.112084	+	0.993699i	$0.535753\pi$
$632$	7.59905e11	0.189467
$633$	−1.77017e12	−0.438227
$634$	2.01565e12	0.495465
$635$	0	0
$636$	4.28036e11	0.103734
$637$	1.12857e13	2.71581
$638$	−3.14254e12	−0.750910
$639$	−2.41220e12	−0.572346
$640$	0	0
$641$	2.07063e12	0.484442	0.242221	−	0.970221i	$-0.422124\pi$
$641$	2.07063e12	0.484442	0.242221	+	0.970221i	$0.422124\pi$
$642$	−1.18600e12	−0.275534
$643$	−1.78129e12	−0.410946	−0.205473	−	0.978663i	$-0.565873\pi$
$643$	−1.78129e12	−0.410946	−0.205473	+	0.978663i	$0.565873\pi$
$644$	3.43559e12	0.787072
$645$	0	0
$646$	3.92531e12	0.886805
$647$	−5.92399e12	−1.32906	−0.664531	−	0.747261i	$-0.731369\pi$
$647$	−5.92399e12	−1.32906	−0.664531	+	0.747261i	$0.731369\pi$
$648$	−1.76319e11	−0.0392837
$649$	−1.73276e12	−0.383387
$650$	0	0
$651$	−5.88720e12	−1.28468
$652$	−8.44194e11	−0.182948
$653$	8.11273e12	1.74605	0.873027	−	0.487671i	$-0.162153\pi$
$653$	8.11273e12	1.74605	0.873027	+	0.487671i	$0.162153\pi$
$654$	−3.07152e12	−0.656528
$655$	0	0
$656$	5.83013e11	0.122917
$657$	−1.65656e12	−0.346867
$658$	2.84553e12	0.591762
$659$	−3.93328e12	−0.812401	−0.406200	−	0.913784i	$-0.633147\pi$
$659$	−3.93328e12	−0.812401	−0.406200	+	0.913784i	$0.633147\pi$
$660$	0	0
$661$	−2.15528e11	−0.0439134	−0.0219567	−	0.999759i	$-0.506990\pi$
$661$	−2.15528e11	−0.0439134	−0.0219567	+	0.999759i	$0.506990\pi$
$662$	4.27636e12	0.865394
$663$	5.29521e12	1.06432
$664$	−1.91651e12	−0.382608
$665$	0	0
$666$	2.02188e11	0.0398218
$667$	9.30041e12	1.81943
$668$	−2.75390e12	−0.535123
$669$	2.76960e12	0.534563
$670$	0	0
$671$	−1.74825e12	−0.332929
$672$	−8.77885e11	−0.166064
$673$	5.04401e12	0.947782	0.473891	−	0.880584i	$-0.342849\pi$
$673$	5.04401e12	0.947782	0.473891	+	0.880584i	$0.342849\pi$
$674$	6.30135e12	1.17615
$675$	0	0
$676$	4.66295e12	0.858816
$677$	7.45393e12	1.36376	0.681878	−	0.731466i	$-0.261164\pi$
$677$	7.45393e12	1.36376	0.681878	+	0.731466i	$0.261164\pi$
$678$	2.93987e11	0.0534311
$679$	1.35868e13	2.45304
$680$	0	0
$681$	1.81265e12	0.322963
$682$	3.08502e12	0.546045
$683$	−2.99014e12	−0.525773	−0.262886	−	0.964827i	$-0.584674\pi$
$683$	−2.99014e12	−0.525773	−0.262886	+	0.964827i	$0.584674\pi$
$684$	−1.07006e12	−0.186919
$685$	0	0
$686$	−4.32056e12	−0.744872
$687$	−2.24198e11	−0.0383995
$688$	−2.12530e12	−0.361636
$689$	3.50425e12	0.592392
$690$	0	0
$691$	6.56691e12	1.09575	0.547873	−	0.836562i	$-0.315438\pi$
$691$	6.56691e12	1.09575	0.547873	+	0.836562i	$0.315438\pi$
$692$	−2.19286e12	−0.363525
$693$	1.85947e12	0.306260
$694$	−4.00589e12	−0.655513
$695$	0	0
$696$	−2.37650e12	−0.383881
$697$	3.42575e12	0.549805
$698$	−2.71269e12	−0.432565
$699$	5.31012e12	0.841312
$700$	0	0
$701$	−6.97167e12	−1.09045	−0.545225	−	0.838290i	$-0.683556\pi$
$701$	−6.97167e12	−1.09045	−0.545225	+	0.838290i	$0.683556\pi$
$702$	−1.44350e12	−0.224336
$703$	1.22705e12	0.189480
$704$	4.60031e11	0.0705847
$705$	0	0
$706$	6.60359e12	1.00037
$707$	−4.55080e12	−0.685015
$708$	−1.31038e12	−0.195996
$709$	−7.35853e12	−1.09366	−0.546831	−	0.837243i	$-0.684166\pi$
$709$	−7.35853e12	−1.09366	−0.546831	+	0.837243i	$0.684166\pi$
$710$	0	0
$711$	−1.21722e12	−0.178631
$712$	−2.37198e12	−0.345900
$713$	−9.13018e12	−1.32305
$714$	−5.15840e12	−0.742802
$715$	0	0
$716$	−1.60028e12	−0.227556
$717$	2.18756e12	0.309117
$718$	−5.64620e12	−0.792860
$719$	2.14069e12	0.298727	0.149364	−	0.988782i	$-0.452278\pi$
$719$	2.14069e12	0.298727	0.149364	+	0.988782i	$0.452278\pi$
$720$	0	0
$721$	6.11174e12	0.842279
$722$	−1.33101e12	−0.182291
$723$	−1.40598e12	−0.191363
$724$	−5.75863e12	−0.778925
$725$	0	0
$726$	2.08149e12	0.278074
$727$	−6.36038e12	−0.844458	−0.422229	−	0.906489i	$-0.638752\pi$
$727$	−6.36038e12	−0.844458	−0.422229	+	0.906489i	$0.638752\pi$
$728$	−7.18709e12	−0.948335
$729$	2.82430e11	0.0370370
$730$	0	0
$731$	−1.24881e13	−1.61759
$732$	−1.32209e12	−0.170200
$733$	−1.99432e12	−0.255169	−0.127584	−	0.991828i	$-0.540722\pi$
$733$	−1.99432e12	−0.255169	−0.127584	+	0.991828i	$0.540722\pi$
$734$	8.99300e12	1.14359
$735$	0	0
$736$	−1.36147e12	−0.171024
$737$	−3.98308e12	−0.497297
$738$	−9.33874e11	−0.115887
$739$	1.14331e13	1.41015	0.705074	−	0.709134i	$-0.250914\pi$
$739$	1.14331e13	1.41015	0.705074	+	0.709134i	$0.250914\pi$
$740$	0	0
$741$	−8.76036e12	−1.06743
$742$	−3.41372e12	−0.413438
$743$	−7.54874e12	−0.908709	−0.454354	−	0.890821i	$-0.650130\pi$
$743$	−7.54874e12	−0.908709	−0.454354	+	0.890821i	$0.650130\pi$
$744$	2.33301e12	0.279150
$745$	0	0
$746$	−3.02924e11	−0.0358104
$747$	3.06988e12	0.360727
$748$	2.70312e12	0.315724
$749$	9.45869e12	1.09815
$750$	0	0
$751$	1.26303e13	1.44889	0.724445	−	0.689333i	$-0.242096\pi$
$751$	1.26303e13	1.44889	0.724445	+	0.689333i	$0.242096\pi$
$752$	−1.12764e12	−0.128585
$753$	−1.81287e12	−0.205489
$754$	−1.94560e13	−2.19221
$755$	0	0
$756$	1.40620e12	0.156567
$757$	−2.57624e12	−0.285138	−0.142569	−	0.989785i	$-0.545536\pi$
$757$	−2.57624e12	−0.285138	−0.142569	+	0.989785i	$0.545536\pi$
$758$	−1.13684e13	−1.25080
$759$	2.88377e12	0.315408
$760$	0	0
$761$	6.30666e12	0.681660	0.340830	−	0.940125i	$-0.389292\pi$
$761$	6.30666e12	0.681660	0.340830	+	0.940125i	$0.389292\pi$
$762$	−5.75504e12	−0.618374
$763$	2.44963e13	2.61662
$764$	−6.88677e12	−0.731300
$765$	0	0
$766$	−1.02061e13	−1.07110
$767$	−1.07278e13	−1.11927
$768$	3.47892e11	0.0360844
$769$	−7.10661e12	−0.732814	−0.366407	−	0.930455i	$-0.619412\pi$
$769$	−7.10661e12	−0.732814	−0.366407	+	0.930455i	$0.619412\pi$
$770$	0	0
$771$	−1.05295e13	−1.07316
$772$	3.45654e12	0.350238
$773$	7.86838e12	0.792643	0.396322	−	0.918112i	$-0.370287\pi$
$773$	7.86838e12	0.792643	0.396322	+	0.918112i	$0.370287\pi$
$774$	3.40431e12	0.340954
$775$	0	0
$776$	−5.38426e12	−0.533026
$777$	−1.61251e12	−0.158711
$778$	1.36968e13	1.34032
$779$	−5.66755e12	−0.551412
$780$	0	0
$781$	−1.00812e13	−0.969573
$782$	−7.99993e12	−0.764990
$783$	3.80670e12	0.361927
$784$	4.35679e12	0.411855
$785$	0	0
$786$	−3.33053e12	−0.311251
$787$	−6.06449e12	−0.563518	−0.281759	−	0.959485i	$-0.590918\pi$
$787$	−6.06449e12	−0.563518	−0.281759	+	0.959485i	$0.590918\pi$
$788$	5.41325e12	0.500138
$789$	−6.07604e12	−0.558180
$790$	0	0
$791$	−2.34463e12	−0.212952
$792$	−7.36881e11	−0.0665479
$793$	−1.08237e13	−0.971955
$794$	−6.76383e12	−0.603949
$795$	0	0
$796$	1.45025e12	0.128037
$797$	4.14199e12	0.363619	0.181809	−	0.983334i	$-0.441805\pi$
$797$	4.14199e12	0.363619	0.181809	+	0.983334i	$0.441805\pi$
$798$	8.53403e12	0.744974
$799$	−6.62596e12	−0.575159
$800$	0	0
$801$	3.79945e12	0.326118
$802$	1.43418e12	0.122411
$803$	−6.92317e12	−0.587605
$804$	−3.01215e12	−0.254229
$805$	0	0
$806$	1.90999e13	1.59413
$807$	−2.61350e12	−0.216916
$808$	1.80341e12	0.148848
$809$	−1.73515e13	−1.42419	−0.712097	−	0.702081i	$-0.752255\pi$
$809$	−1.73515e13	−1.42419	−0.712097	+	0.702081i	$0.752255\pi$
$810$	0	0
$811$	−7.02987e11	−0.0570628	−0.0285314	−	0.999593i	$-0.509083\pi$
$811$	−7.02987e11	−0.0570628	−0.0285314	+	0.999593i	$0.509083\pi$
$812$	1.89533e13	1.52997
$813$	−3.14942e12	−0.252827
$814$	8.44991e11	0.0674594
$815$	0	0
$816$	2.04420e12	0.161405
$817$	2.06603e13	1.62232
$818$	−9.20190e11	−0.0718601
$819$	1.15123e13	0.894099
$820$	0	0
$821$	−1.14184e13	−0.877122	−0.438561	−	0.898701i	$-0.644512\pi$
$821$	−1.14184e13	−0.877122	−0.438561	+	0.898701i	$0.644512\pi$
$822$	−3.95373e12	−0.302054
$823$	−2.20408e13	−1.67467	−0.837335	−	0.546691i	$-0.815887\pi$
$823$	−2.20408e13	−1.67467	−0.837335	+	0.546691i	$0.815887\pi$
$824$	−2.42199e12	−0.183020
$825$	0	0
$826$	1.04507e13	0.781149
$827$	−2.61998e13	−1.94771	−0.973853	−	0.227180i	$-0.927049\pi$
$827$	−2.61998e13	−1.94771	−0.973853	+	0.227180i	$0.927049\pi$
$828$	2.18081e12	0.161243
$829$	−2.45093e13	−1.80234	−0.901169	−	0.433468i	$-0.857290\pi$
$829$	−2.45093e13	−1.80234	−0.901169	+	0.433468i	$0.857290\pi$
$830$	0	0
$831$	1.12790e13	0.820475
$832$	2.84813e12	0.206066
$833$	2.56002e13	1.84222
$834$	−2.87659e12	−0.205888
$835$	0	0
$836$	−4.47202e12	−0.316647
$837$	−3.73703e12	−0.263185
$838$	1.09131e13	0.764454
$839$	1.14689e12	0.0799087	0.0399543	−	0.999202i	$-0.487279\pi$
$839$	1.14689e12	0.0799087	0.0399543	+	0.999202i	$0.487279\pi$
$840$	0	0
$841$	3.68011e13	2.53675
$842$	1.90244e13	1.30439
$843$	9.86345e12	0.672674
$844$	−5.59462e12	−0.379516
$845$	0	0
$846$	1.80626e12	0.121231
$847$	−1.66006e13	−1.10827
$848$	1.35280e12	0.0898367
$849$	−9.10778e12	−0.601628
$850$	0	0
$851$	−2.50077e12	−0.163452
$852$	−7.62373e12	−0.495666
$853$	−2.17660e12	−0.140769	−0.0703847	−	0.997520i	$-0.522423\pi$
$853$	−2.17660e12	−0.140769	−0.0703847	+	0.997520i	$0.522423\pi$
$854$	1.05441e13	0.678339
$855$	0	0
$856$	−3.74833e12	−0.238620
$857$	−2.79690e13	−1.77119	−0.885593	−	0.464463i	$-0.846247\pi$
$857$	−2.79690e13	−1.77119	−0.885593	+	0.464463i	$0.846247\pi$
$858$	−6.03272e12	−0.380032
$859$	8.22473e12	0.515409	0.257705	−	0.966224i	$-0.417034\pi$
$859$	8.22473e12	0.515409	0.257705	+	0.966224i	$0.417034\pi$
$860$	0	0
$861$	7.44794e12	0.461872
$862$	−1.73802e13	−1.07219
$863$	2.67759e13	1.64322	0.821610	−	0.570050i	$-0.193076\pi$
$863$	2.67759e13	1.64322	0.821610	+	0.570050i	$0.193076\pi$
$864$	−5.57256e11	−0.0340207
$865$	0	0
$866$	4.40911e12	0.266391
$867$	2.40597e12	0.144612
$868$	−1.86064e13	−1.11256
$869$	−5.08706e12	−0.302606
$870$	0	0
$871$	−2.46600e13	−1.45181
$872$	−9.70751e12	−0.568570
$873$	8.62455e12	0.502542
$874$	1.32350e13	0.767227
$875$	0	0
$876$	−5.23555e12	−0.300396
$877$	1.39444e13	0.795982	0.397991	−	0.917389i	$-0.369708\pi$
$877$	1.39444e13	0.795982	0.397991	+	0.917389i	$0.369708\pi$
$878$	2.11031e12	0.119845
$879$	4.64440e12	0.262409
$880$	0	0
$881$	−1.26780e13	−0.709020	−0.354510	−	0.935052i	$-0.615352\pi$
$881$	−1.26780e13	−0.709020	−0.354510	+	0.935052i	$0.615352\pi$
$882$	−6.97873e12	−0.388300
$883$	−1.29515e13	−0.716964	−0.358482	−	0.933537i	$-0.616706\pi$
$883$	−1.29515e13	−0.716964	−0.358482	+	0.933537i	$0.616706\pi$
$884$	1.67355e13	0.921728
$885$	0	0
$886$	−1.88560e13	−1.02801
$887$	1.51647e13	0.822578	0.411289	−	0.911505i	$-0.365079\pi$
$887$	1.51647e13	0.822578	0.411289	+	0.911505i	$0.365079\pi$
$888$	6.39013e11	0.0344867
$889$	4.58982e13	2.46455
$890$	0	0
$891$	1.18034e12	0.0627419
$892$	8.75330e12	0.462945
$893$	1.09619e13	0.576841
$894$	−3.59340e12	−0.188142
$895$	0	0
$896$	−2.77455e12	−0.143816
$897$	1.78539e13	0.920806
$898$	2.11453e12	0.108510
$899$	−5.03691e13	−2.57185
$900$	0	0
$901$	7.94900e12	0.401838
$902$	−3.90289e12	−0.196316
$903$	−2.71504e13	−1.35888
$904$	9.29143e11	0.0462727
$905$	0	0
$906$	3.29183e12	0.162316
$907$	−1.69425e13	−0.831275	−0.415637	−	0.909530i	$-0.636441\pi$
$907$	−1.69425e13	−0.831275	−0.415637	+	0.909530i	$0.636441\pi$
$908$	5.72887e12	0.279694
$909$	−2.88872e12	−0.140335
$910$	0	0
$911$	−5.05250e11	−0.0243038	−0.0121519	−	0.999926i	$-0.503868\pi$
$911$	−5.05250e11	−0.0243038	−0.0121519	+	0.999926i	$0.503868\pi$
$912$	−3.38191e12	−0.161877
$913$	1.28298e13	0.611082
$914$	−1.14832e12	−0.0544258
$915$	0	0
$916$	−7.08576e11	−0.0332550
$917$	2.65620e13	1.24050
$918$	−3.27441e12	−0.152174
$919$	−8.02347e12	−0.371059	−0.185529	−	0.982639i	$-0.559400\pi$
$919$	−8.02347e12	−0.371059	−0.185529	+	0.982639i	$0.559400\pi$
$920$	0	0
$921$	1.29278e13	0.592046
$922$	−2.63136e13	−1.19920
$923$	−6.24142e13	−2.83058
$924$	5.87685e12	0.265229
$925$	0	0
$926$	1.95237e13	0.872595
$927$	3.87956e12	0.172553
$928$	−7.51092e12	−0.332451
$929$	−9.53417e11	−0.0419964	−0.0209982	−	0.999780i	$-0.506684\pi$
$929$	−9.53417e11	−0.0419964	−0.0209982	+	0.999780i	$0.506684\pi$
$930$	0	0
$931$	−4.23529e13	−1.84761
$932$	1.67826e13	0.728597
$933$	−9.88936e12	−0.427268
$934$	−8.30258e12	−0.356987
$935$	0	0
$936$	−4.56216e12	−0.194280
$937$	−1.30100e13	−0.551377	−0.275688	−	0.961247i	$-0.588906\pi$
$937$	−1.30100e13	−0.551377	−0.275688	+	0.961247i	$0.588906\pi$
$938$	2.40228e13	1.01324
$939$	1.03941e13	0.436308
$940$	0	0
$941$	3.64039e13	1.51354	0.756771	−	0.653680i	$-0.226776\pi$
$941$	3.64039e13	1.51354	0.756771	+	0.653680i	$0.226776\pi$
$942$	1.23505e13	0.511041
$943$	1.15507e13	0.475668
$944$	−4.14144e12	−0.169737
$945$	0	0
$946$	1.42274e13	0.577586
$947$	−9.30409e12	−0.375923	−0.187962	−	0.982176i	$-0.560188\pi$
$947$	−9.30409e12	−0.375923	−0.187962	+	0.982176i	$0.560188\pi$
$948$	−3.84702e12	−0.154699
$949$	−4.28626e13	−1.71546
$950$	0	0
$951$	−1.02042e13	−0.404546
$952$	−1.63031e13	−0.643286
$953$	9.85076e11	0.0386858	0.0193429	−	0.999813i	$-0.493843\pi$
$953$	9.85076e11	0.0386858	0.0193429	+	0.999813i	$0.493843\pi$
$954$	−2.16693e12	−0.0846988
$955$	0	0
$956$	6.91376e12	0.267703
$957$	1.59091e13	0.613115
$958$	2.42861e13	0.931566
$959$	3.15322e13	1.20385
$960$	0	0
$961$	2.30076e13	0.870194
$962$	5.23149e12	0.196942
$963$	6.00411e12	0.224973
$964$	−4.44360e12	−0.165725
$965$	0	0
$966$	−1.73927e13	−0.642642
$967$	4.74300e13	1.74435	0.872175	−	0.489194i	$-0.162709\pi$
$967$	4.74300e13	1.74435	0.872175	+	0.489194i	$0.162709\pi$
$968$	6.57855e12	0.240819
$969$	−1.98719e13	−0.724073
$970$	0	0
$971$	7.49831e12	0.270693	0.135346	−	0.990798i	$-0.456785\pi$
$971$	7.49831e12	0.270693	0.135346	+	0.990798i	$0.456785\pi$
$972$	8.92617e11	0.0320750
$973$	2.29417e13	0.820574
$974$	3.39127e13	1.20739
$975$	0	0
$976$	−4.17845e12	−0.147398
$977$	2.38786e12	0.0838462	0.0419231	−	0.999121i	$-0.486652\pi$
$977$	2.38786e12	0.0838462	0.0419231	+	0.999121i	$0.486652\pi$
$978$	4.27373e12	0.149377
$979$	1.58788e13	0.552454
$980$	0	0
$981$	1.55496e13	0.536053
$982$	1.01523e13	0.348387
$983$	1.59099e13	0.543472	0.271736	−	0.962372i	$-0.412402\pi$
$983$	1.59099e13	0.543472	0.271736	+	0.962372i	$0.412402\pi$
$984$	−2.95150e12	−0.100361
$985$	0	0
$986$	−4.41338e13	−1.48705
$987$	−1.44055e13	−0.483172
$988$	−2.76871e13	−0.924423
$989$	−4.21064e13	−1.39947
$990$	0	0
$991$	−5.42340e13	−1.78624	−0.893121	−	0.449816i	$-0.851489\pi$
$991$	−5.42340e13	−1.78624	−0.893121	+	0.449816i	$0.851489\pi$
$992$	7.37345e12	0.241751
$993$	−2.16491e13	−0.706591
$994$	6.08016e13	1.97550
$995$	0	0
$996$	9.70233e12	0.312398
$997$	−3.98284e12	−0.127663	−0.0638314	−	0.997961i	$-0.520332\pi$
$997$	−3.98284e12	−0.127663	−0.0638314	+	0.997961i	$0.520332\pi$
$998$	−5.95100e12	−0.189890
$999$	−1.02358e12	−0.0325144

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.10.a.e.1.1	✓	1	5.4	even	2
90.10.a.a.1.1		1	15.14	odd	2
150.10.a.e.1.1		1	1.1	even	1	trivial
150.10.c.c.49.1		2	5.2	odd	4
150.10.c.c.49.2		2	5.3	odd	4
240.10.a.j.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

Related objects

Downloads

Learn more