LMFDB - Embedded newform 150.10.a.c.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:	yes
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)

$f(q)$

$=$

$q-16.0000 q^{2} +81.0000 q^{3} +256.000 q^{4} -1296.00 q^{6} -3269.00 q^{7} -4096.00 q^{8} +6561.00 q^{9} +O(q^{10})$

\(q-16.0000 q^{2} +81.0000 q^{3} +256.000 q^{4} -1296.00 q^{6} -3269.00 q^{7} -4096.00 q^{8} +6561.00 q^{9} -70470.0 q^{11} +20736.0 q^{12} -61793.0 q^{13} +52304.0 q^{14} +65536.0 q^{16} -9834.00 q^{17} -104976. q^{18} -309709. q^{19} -264789. q^{21} +1.12752e6 q^{22} +401250. q^{23} -331776. q^{24} +988688. q^{26} +531441. q^{27} -836864. q^{28} +4.44275e6 q^{29} -899467. q^{31} -1.04858e6 q^{32} -5.70807e6 q^{33} +157344. q^{34} +1.67962e6 q^{36} +1.51000e7 q^{37} +4.95534e6 q^{38} -5.00523e6 q^{39} +1.51429e7 q^{41} +4.23662e6 q^{42} +357511. q^{43} -1.80403e7 q^{44} -6.42000e6 q^{46} +3.17482e7 q^{47} +5.30842e6 q^{48} -2.96672e7 q^{49} -796554. q^{51} -1.58190e7 q^{52} -4.28703e7 q^{53} -8.50306e6 q^{54} +1.33898e7 q^{56} -2.50864e7 q^{57} -7.10841e7 q^{58} -1.24821e8 q^{59} -3.89479e7 q^{61} +1.43915e7 q^{62} -2.14479e7 q^{63} +1.67772e7 q^{64} +9.13291e7 q^{66} +1.05968e8 q^{67} -2.51750e6 q^{68} +3.25012e7 q^{69} -6.28414e7 q^{71} -2.68739e7 q^{72} +4.66544e8 q^{73} -2.41600e8 q^{74} -7.92855e7 q^{76} +2.30366e8 q^{77} +8.00837e7 q^{78} -5.51942e8 q^{79} +4.30467e7 q^{81} -2.42287e8 q^{82} +4.44962e8 q^{83} -6.77860e7 q^{84} -5.72018e6 q^{86} +3.59863e8 q^{87} +2.88645e8 q^{88} +6.42049e8 q^{89} +2.02001e8 q^{91} +1.02720e8 q^{92} -7.28568e7 q^{93} -5.07971e8 q^{94} -8.49347e7 q^{96} +2.04187e8 q^{97} +4.74676e8 q^{98} -4.62354e8 q^{99} +O(q^{100})\)

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
$7$	−3269.00	−0.514605	−0.257302	−	0.966331i	$-0.582834\pi$
$7$	−3269.00	−0.514605	−0.257302	+	0.966331i	$0.582834\pi$
$8$	−4096.00	−0.353553
$9$	6561.00	0.333333
$10$	0	0
$11$	−70470.0	−1.45123	−0.725617	−	0.688099i	$-0.758445\pi$
$11$	−70470.0	−1.45123	−0.725617	+	0.688099i	$0.758445\pi$
$12$	20736.0	0.288675
$13$	−61793.0	−0.600059	−0.300030	−	0.953930i	$-0.596997\pi$
$13$	−61793.0	−0.600059	−0.300030	+	0.953930i	$0.596997\pi$
$14$	52304.0	0.363880
$15$	0	0
$16$	65536.0	0.250000
$17$	−9834.00	−0.0285568	−0.0142784	−	0.999898i	$-0.504545\pi$
$17$	−9834.00	−0.0285568	−0.0142784	+	0.999898i	$0.504545\pi$
$18$	−104976.	−0.235702
$19$	−309709.	−0.545209	−0.272604	−	0.962126i	$-0.587885\pi$
$19$	−309709.	−0.545209	−0.272604	+	0.962126i	$0.587885\pi$
$20$	0	0
$21$	−264789.	−0.297107
$22$	1.12752e6	1.02618
$23$	401250.	0.298978	0.149489	−	0.988763i	$-0.452237\pi$
$23$	401250.	0.298978	0.149489	+	0.988763i	$0.452237\pi$
$24$	−331776.	−0.204124
$25$	0	0
$26$	988688.	0.424306
$27$	531441.	0.192450
$28$	−836864.	−0.257302
$29$	4.44275e6	1.16644	0.583218	−	0.812315i	$-0.301793\pi$
$29$	4.44275e6	1.16644	0.583218	+	0.812315i	$0.301793\pi$
$30$	0	0
$31$	−899467.	−0.174927	−0.0874637	−	0.996168i	$-0.527876\pi$
$31$	−899467.	−0.174927	−0.0874637	+	0.996168i	$0.527876\pi$
$32$	−1.04858e6	−0.176777
$33$	−5.70807e6	−0.837870
$34$	157344.	0.0201927
$35$	0	0
$36$	1.67962e6	0.166667
$37$	1.51000e7	1.32455	0.662275	−	0.749260i	$-0.269591\pi$
$37$	1.51000e7	1.32455	0.662275	+	0.749260i	$0.269591\pi$
$38$	4.95534e6	0.385521
$39$	−5.00523e6	−0.346444
$40$	0	0
$41$	1.51429e7	0.836918	0.418459	−	0.908236i	$-0.362570\pi$
$41$	1.51429e7	0.836918	0.418459	+	0.908236i	$0.362570\pi$
$42$	4.23662e6	0.210086
$43$	357511.	0.0159471	0.00797354	−	0.999968i	$-0.497462\pi$
$43$	357511.	0.0159471	0.00797354	+	0.999968i	$0.497462\pi$
$44$	−1.80403e7	−0.725617
$45$	0	0
$46$	−6.42000e6	−0.211410
$47$	3.17482e7	0.949027	0.474514	−	0.880248i	$-0.342624\pi$
$47$	3.17482e7	0.949027	0.474514	+	0.880248i	$0.342624\pi$
$48$	5.30842e6	0.144338
$49$	−2.96672e7	−0.735182
$50$	0	0
$51$	−796554.	−0.0164873
$52$	−1.58190e7	−0.300030
$53$	−4.28703e7	−0.746302	−0.373151	−	0.927771i	$-0.621723\pi$
$53$	−4.28703e7	−0.746302	−0.373151	+	0.927771i	$0.621723\pi$
$54$	−8.50306e6	−0.136083
$55$	0	0
$56$	1.33898e7	0.181940
$57$	−2.50864e7	−0.314776
$58$	−7.10841e7	−0.824795
$59$	−1.24821e8	−1.34108	−0.670538	−	0.741875i	$-0.733937\pi$
$59$	−1.24821e8	−1.34108	−0.670538	+	0.741875i	$0.733937\pi$
$60$	0	0
$61$	−3.89479e7	−0.360164	−0.180082	−	0.983652i	$-0.557636\pi$
$61$	−3.89479e7	−0.360164	−0.180082	+	0.983652i	$0.557636\pi$
$62$	1.43915e7	0.123692
$63$	−2.14479e7	−0.171535
$64$	1.67772e7	0.125000
$65$	0	0
$66$	9.13291e7	0.592463
$67$	1.05968e8	0.642447	0.321223	−	0.947003i	$-0.395906\pi$
$67$	1.05968e8	0.642447	0.321223	+	0.947003i	$0.395906\pi$
$68$	−2.51750e6	−0.0142784
$69$	3.25012e7	0.172615
$70$	0	0
$71$	−6.28414e7	−0.293483	−0.146742	−	0.989175i	$-0.546879\pi$
$71$	−6.28414e7	−0.293483	−0.146742	+	0.989175i	$0.546879\pi$
$72$	−2.68739e7	−0.117851
$73$	4.66544e8	1.92282	0.961412	−	0.275114i	$-0.0887156\pi$
$73$	4.66544e8	1.92282	0.961412	+	0.275114i	$0.0887156\pi$
$74$	−2.41600e8	−0.936599
$75$	0	0
$76$	−7.92855e7	−0.272604
$77$	2.30366e8	0.746811
$78$	8.00837e7	0.244973
$79$	−5.51942e8	−1.59430	−0.797152	−	0.603778i	$-0.793661\pi$
$79$	−5.51942e8	−1.59430	−0.797152	+	0.603778i	$0.793661\pi$
$80$	0	0
$81$	4.30467e7	0.111111
$82$	−2.42287e8	−0.591790
$83$	4.44962e8	1.02913	0.514567	−	0.857450i	$-0.327953\pi$
$83$	4.44962e8	1.02913	0.514567	+	0.857450i	$0.327953\pi$
$84$	−6.77860e7	−0.148554
$85$	0	0
$86$	−5.72018e6	−0.0112763
$87$	3.59863e8	0.673443
$88$	2.88645e8	0.513088
$89$	6.42049e8	1.08471	0.542355	−	0.840150i	$-0.317533\pi$
$89$	6.42049e8	1.08471	0.542355	+	0.840150i	$0.317533\pi$
$90$	0	0
$91$	2.02001e8	0.308793
$92$	1.02720e8	0.149489
$93$	−7.28568e7	−0.100994
$94$	−5.07971e8	−0.671063
$95$	0	0
$96$	−8.49347e7	−0.102062
$97$	2.04187e8	0.234183	0.117092	−	0.993121i	$-0.462643\pi$
$97$	2.04187e8	0.234183	0.117092	+	0.993121i	$0.462643\pi$
$98$	4.74676e8	0.519852
$99$	−4.62354e8	−0.483744
$100$	0	0
$101$	1.06575e9	1.01908	0.509539	−	0.860448i	$-0.329816\pi$
$101$	1.06575e9	1.01908	0.509539	+	0.860448i	$0.329816\pi$
$102$	1.27449e7	0.0116583
$103$	5.86663e8	0.513595	0.256798	−	0.966465i	$-0.417333\pi$
$103$	5.86663e8	0.513595	0.256798	+	0.966465i	$0.417333\pi$
$104$	2.53104e8	0.212153
$105$	0	0
$106$	6.85924e8	0.527716
$107$	8.95969e8	0.660794	0.330397	−	0.943842i	$-0.392817\pi$
$107$	8.95969e8	0.660794	0.330397	+	0.943842i	$0.392817\pi$
$108$	1.36049e8	0.0962250
$109$	−1.67910e8	−0.113935	−0.0569677	−	0.998376i	$-0.518143\pi$
$109$	−1.67910e8	−0.113935	−0.0569677	+	0.998376i	$0.518143\pi$
$110$	0	0
$111$	1.22310e9	0.764730
$112$	−2.14237e8	−0.128651
$113$	3.29738e9	1.90246	0.951230	−	0.308483i	$-0.0998214\pi$
$113$	3.29738e9	1.90246	0.951230	+	0.308483i	$0.0998214\pi$
$114$	4.01383e8	0.222580
$115$	0	0
$116$	1.13735e9	0.583218
$117$	−4.05424e8	−0.200020
$118$	1.99714e9	0.948284
$119$	3.21473e7	0.0146955
$120$	0	0
$121$	2.60807e9	1.10608
$122$	6.23167e8	0.254674
$123$	1.22658e9	0.483195
$124$	−2.30264e8	−0.0874637
$125$	0	0
$126$	3.43167e8	0.121293
$127$	−1.83308e9	−0.625266	−0.312633	−	0.949874i	$-0.601211\pi$
$127$	−1.83308e9	−0.625266	−0.312633	+	0.949874i	$0.601211\pi$
$128$	−2.68435e8	−0.0883883
$129$	2.89584e7	0.00920705
$130$	0	0
$131$	3.55920e9	1.05592	0.527961	−	0.849269i	$-0.322957\pi$
$131$	3.55920e9	1.05592	0.527961	+	0.849269i	$0.322957\pi$
$132$	−1.46127e9	−0.418935
$133$	1.01244e9	0.280567
$134$	−1.69548e9	−0.454279
$135$	0	0
$136$	4.02801e7	0.0100964
$137$	4.84686e9	1.17549	0.587744	−	0.809047i	$-0.300016\pi$
$137$	4.84686e9	1.17549	0.587744	+	0.809047i	$0.300016\pi$
$138$	−5.20020e8	−0.122057
$139$	−2.41039e9	−0.547672	−0.273836	−	0.961776i	$-0.588293\pi$
$139$	−2.41039e9	−0.547672	−0.273836	+	0.961776i	$0.588293\pi$
$140$	0	0
$141$	2.57160e9	0.547921
$142$	1.00546e9	0.207524
$143$	4.35455e9	0.870826
$144$	4.29982e8	0.0833333
$145$	0	0
$146$	−7.46470e9	−1.35964
$147$	−2.40305e9	−0.424458
$148$	3.86560e9	0.662275
$149$	−4.36786e9	−0.725990	−0.362995	−	0.931791i	$-0.618246\pi$
$149$	−4.36786e9	−0.725990	−0.362995	+	0.931791i	$0.618246\pi$
$150$	0	0
$151$	7.49402e9	1.17306	0.586528	−	0.809929i	$-0.300494\pi$
$151$	7.49402e9	1.17306	0.586528	+	0.809929i	$0.300494\pi$
$152$	1.26857e9	0.192760
$153$	−6.45209e7	−0.00951894
$154$	−3.68586e9	−0.528075
$155$	0	0
$156$	−1.28134e9	−0.173222
$157$	9.10542e9	1.19606	0.598028	−	0.801475i	$-0.295951\pi$
$157$	9.10542e9	1.19606	0.598028	+	0.801475i	$0.295951\pi$
$158$	8.83107e9	1.12734
$159$	−3.47249e9	−0.430878
$160$	0	0
$161$	−1.31169e9	−0.153856
$162$	−6.88748e8	−0.0785674
$163$	−2.11771e9	−0.234975	−0.117488	−	0.993074i	$-0.537484\pi$
$163$	−2.11771e9	−0.234975	−0.117488	+	0.993074i	$0.537484\pi$
$164$	3.87659e9	0.418459
$165$	0	0
$166$	−7.11940e9	−0.727707
$167$	4.21448e9	0.419295	0.209648	−	0.977777i	$-0.432768\pi$
$167$	4.21448e9	0.419295	0.209648	+	0.977777i	$0.432768\pi$
$168$	1.08458e9	0.105043
$169$	−6.78612e9	−0.639929
$170$	0	0
$171$	−2.03200e9	−0.181736
$172$	9.15228e7	0.00797354
$173$	−7.40027e9	−0.628116	−0.314058	−	0.949404i	$-0.601689\pi$
$173$	−7.40027e9	−0.628116	−0.314058	+	0.949404i	$0.601689\pi$
$174$	−5.75781e9	−0.476196
$175$	0	0
$176$	−4.61832e9	−0.362808
$177$	−1.01105e10	−0.774271
$178$	−1.02728e10	−0.767005
$179$	1.98504e10	1.44521	0.722603	−	0.691263i	$-0.242945\pi$
$179$	1.98504e10	1.44521	0.722603	+	0.691263i	$0.242945\pi$
$180$	0	0
$181$	−6.40621e9	−0.443657	−0.221829	−	0.975086i	$-0.571203\pi$
$181$	−6.40621e9	−0.443657	−0.221829	+	0.975086i	$0.571203\pi$
$182$	−3.23202e9	−0.218350
$183$	−3.15478e9	−0.207941
$184$	−1.64352e9	−0.105705
$185$	0	0
$186$	1.16571e9	0.0714138
$187$	6.93002e8	0.0414426
$188$	8.12754e9	0.474514
$189$	−1.73728e9	−0.0990357
$190$	0	0
$191$	−1.23644e10	−0.672237	−0.336119	−	0.941820i	$-0.609114\pi$
$191$	−1.23644e10	−0.672237	−0.336119	+	0.941820i	$0.609114\pi$
$192$	1.35895e9	0.0721688
$193$	−3.08813e10	−1.60209	−0.801047	−	0.598601i	$-0.795723\pi$
$193$	−3.08813e10	−1.60209	−0.801047	+	0.598601i	$0.795723\pi$
$194$	−3.26699e9	−0.165592
$195$	0	0
$196$	−7.59481e9	−0.367591
$197$	1.43188e10	0.677342	0.338671	−	0.940905i	$-0.390023\pi$
$197$	1.43188e10	0.677342	0.338671	+	0.940905i	$0.390023\pi$
$198$	7.39766e9	0.342059
$199$	−2.85060e10	−1.28854	−0.644269	−	0.764799i	$-0.722838\pi$
$199$	−2.85060e10	−1.28854	−0.644269	+	0.764799i	$0.722838\pi$
$200$	0	0
$201$	8.58339e9	0.370917
$202$	−1.70519e10	−0.720597
$203$	−1.45234e10	−0.600254
$204$	−2.03918e8	−0.00824365
$205$	0	0
$206$	−9.38660e9	−0.363167
$207$	2.63260e9	0.0996595
$208$	−4.04967e9	−0.150015
$209$	2.18252e10	0.791225
$210$	0	0
$211$	5.39094e10	1.87238	0.936189	−	0.351497i	$-0.114327\pi$
$211$	5.39094e10	1.87238	0.936189	+	0.351497i	$0.114327\pi$
$212$	−1.09748e10	−0.373151
$213$	−5.09015e9	−0.169443
$214$	−1.43355e10	−0.467252
$215$	0	0
$216$	−2.17678e9	−0.0680414
$217$	2.94036e9	0.0900184
$218$	2.68657e9	0.0805645
$219$	3.77900e10	1.11014
$220$	0	0
$221$	6.07672e8	0.0171358
$222$	−1.95696e10	−0.540746
$223$	−5.45073e10	−1.47599	−0.737993	−	0.674808i	$-0.764226\pi$
$223$	−5.45073e10	−1.47599	−0.737993	+	0.674808i	$0.764226\pi$
$224$	3.42779e9	0.0909701
$225$	0	0
$226$	−5.27580e10	−1.34524
$227$	4.01768e10	1.00429	0.502144	−	0.864784i	$-0.332545\pi$
$227$	4.01768e10	1.00429	0.502144	+	0.864784i	$0.332545\pi$
$228$	−6.42213e9	−0.157388
$229$	7.25814e10	1.74408	0.872038	−	0.489438i	$-0.162798\pi$
$229$	7.25814e10	1.74408	0.872038	+	0.489438i	$0.162798\pi$
$230$	0	0
$231$	1.86597e10	0.431172
$232$	−1.81975e10	−0.412398
$233$	−6.31880e10	−1.40454	−0.702269	−	0.711912i	$-0.747829\pi$
$233$	−6.31880e10	−1.40454	−0.702269	+	0.711912i	$0.747829\pi$
$234$	6.48678e9	0.141435
$235$	0	0
$236$	−3.19542e10	−0.670538
$237$	−4.47073e10	−0.920472
$238$	−5.14358e8	−0.0103913
$239$	6.88210e10	1.36436	0.682182	−	0.731182i	$-0.261031\pi$
$239$	6.88210e10	1.36436	0.682182	+	0.731182i	$0.261031\pi$
$240$	0	0
$241$	−4.12730e10	−0.788115	−0.394057	−	0.919086i	$-0.628929\pi$
$241$	−4.12730e10	−0.788115	−0.394057	+	0.919086i	$0.628929\pi$
$242$	−4.17292e10	−0.782115
$243$	3.48678e9	0.0641500
$244$	−9.97067e9	−0.180082
$245$	0	0
$246$	−1.96253e10	−0.341670
$247$	1.91378e10	0.327157
$248$	3.68422e9	0.0618461
$249$	3.60419e10	0.594170
$250$	0	0
$251$	1.51053e10	0.240214	0.120107	−	0.992761i	$-0.461676\pi$
$251$	1.51053e10	0.240214	0.120107	+	0.992761i	$0.461676\pi$
$252$	−5.49066e9	−0.0857674
$253$	−2.82761e10	−0.433887
$254$	2.93293e10	0.442130
$255$	0	0
$256$	4.29497e9	0.0625000
$257$	−6.81230e10	−0.974080	−0.487040	−	0.873380i	$-0.661923\pi$
$257$	−6.81230e10	−0.974080	−0.487040	+	0.873380i	$0.661923\pi$
$258$	−4.63334e8	−0.00651037
$259$	−4.93618e10	−0.681620
$260$	0	0
$261$	2.91489e10	0.388812
$262$	−5.69472e10	−0.746650
$263$	8.39213e10	1.08161	0.540806	−	0.841148i	$-0.318119\pi$
$263$	8.39213e10	1.08161	0.540806	+	0.841148i	$0.318119\pi$
$264$	2.33803e10	0.296232
$265$	0	0
$266$	−1.61990e10	−0.198391
$267$	5.20060e10	0.626257
$268$	2.71277e10	0.321223
$269$	1.31646e11	1.53293	0.766466	−	0.642285i	$-0.222013\pi$
$269$	1.31646e11	1.53293	0.766466	+	0.642285i	$0.222013\pi$
$270$	0	0
$271$	−1.54817e11	−1.74364	−0.871820	−	0.489826i	$-0.837060\pi$
$271$	−1.54817e11	−1.74364	−0.871820	+	0.489826i	$0.837060\pi$
$272$	−6.44481e8	−0.00713921
$273$	1.63621e10	0.178282
$274$	−7.75498e10	−0.831195
$275$	0	0
$276$	8.32032e9	0.0863076
$277$	9.59194e10	0.978920	0.489460	−	0.872026i	$-0.337194\pi$
$277$	9.59194e10	0.978920	0.489460	+	0.872026i	$0.337194\pi$
$278$	3.85662e10	0.387263
$279$	−5.90140e9	−0.0583091
$280$	0	0
$281$	1.33695e11	1.27919	0.639597	−	0.768710i	$-0.279101\pi$
$281$	1.33695e11	1.27919	0.639597	+	0.768710i	$0.279101\pi$
$282$	−4.11457e10	−0.387439
$283$	−1.58943e11	−1.47300	−0.736499	−	0.676439i	$-0.763522\pi$
$283$	−1.58943e11	−1.47300	−0.736499	+	0.676439i	$0.763522\pi$
$284$	−1.60874e10	−0.146742
$285$	0	0
$286$	−6.96728e10	−0.615767
$287$	−4.95023e10	−0.430682
$288$	−6.87971e9	−0.0589256
$289$	−1.18491e11	−0.999185
$290$	0	0
$291$	1.65392e10	0.135206
$292$	1.19435e11	0.961412
$293$	−7.62836e10	−0.604682	−0.302341	−	0.953200i	$-0.597768\pi$
$293$	−7.62836e10	−0.604682	−0.302341	+	0.953200i	$0.597768\pi$
$294$	3.84488e10	0.300137
$295$	0	0
$296$	−6.18495e10	−0.468299
$297$	−3.74506e10	−0.279290
$298$	6.98857e10	0.513352
$299$	−2.47944e10	−0.179405
$300$	0	0
$301$	−1.16870e9	−0.00820645
$302$	−1.19904e11	−0.829476
$303$	8.63254e10	0.588365
$304$	−2.02971e10	−0.136302
$305$	0	0
$306$	1.03233e9	0.00673091
$307$	1.08632e11	0.697964	0.348982	−	0.937129i	$-0.386527\pi$
$307$	1.08632e11	0.697964	0.348982	+	0.937129i	$0.386527\pi$
$308$	5.89738e10	0.373406
$309$	4.75197e10	0.296524
$310$	0	0
$311$	1.49493e11	0.906150	0.453075	−	0.891472i	$-0.350327\pi$
$311$	1.49493e11	0.906150	0.453075	+	0.891472i	$0.350327\pi$
$312$	2.05014e10	0.122487
$313$	−6.52788e10	−0.384435	−0.192217	−	0.981352i	$-0.561568\pi$
$313$	−6.52788e10	−0.384435	−0.192217	+	0.981352i	$0.561568\pi$
$314$	−1.45687e11	−0.845740
$315$	0	0
$316$	−1.41297e11	−0.797152
$317$	−1.25629e11	−0.698754	−0.349377	−	0.936982i	$-0.613607\pi$
$317$	−1.25629e11	−0.698754	−0.349377	+	0.936982i	$0.613607\pi$
$318$	5.55599e10	0.304677
$319$	−3.13081e11	−1.69277
$320$	0	0
$321$	7.25735e10	0.381509
$322$	2.09870e10	0.108792
$323$	3.04568e9	0.0155694
$324$	1.10200e10	0.0555556
$325$	0	0
$326$	3.38834e10	0.166153
$327$	−1.36007e10	−0.0657806
$328$	−6.20255e10	−0.295895
$329$	−1.03785e11	−0.488374
$330$	0	0
$331$	3.72928e11	1.70765	0.853826	−	0.520559i	$-0.174276\pi$
$331$	3.72928e11	1.70765	0.853826	+	0.520559i	$0.174276\pi$
$332$	1.13910e11	0.514567
$333$	9.90710e10	0.441517
$334$	−6.74317e10	−0.296487
$335$	0	0
$336$	−1.73532e10	−0.0742768
$337$	4.19902e11	1.77343	0.886713	−	0.462321i	$-0.152983\pi$
$337$	4.19902e11	1.77343	0.886713	+	0.462321i	$0.152983\pi$
$338$	1.08578e11	0.452498
$339$	2.67087e11	1.09839
$340$	0	0
$341$	6.33854e10	0.253860
$342$	3.25120e10	0.128507
$343$	2.28898e11	0.892933
$344$	−1.46437e9	−0.00563815
$345$	0	0
$346$	1.18404e11	0.444145
$347$	3.51651e9	0.0130205	0.00651027	−	0.999979i	$-0.497928\pi$
$347$	3.51651e9	0.0130205	0.00651027	+	0.999979i	$0.497928\pi$
$348$	9.21249e10	0.336721
$349$	−4.56719e11	−1.64792	−0.823958	−	0.566651i	$-0.808239\pi$
$349$	−4.56719e11	−1.64792	−0.823958	+	0.566651i	$0.808239\pi$
$350$	0	0
$351$	−3.28393e10	−0.115481
$352$	7.38932e10	0.256544
$353$	−2.68705e9	−0.00921062	−0.00460531	−	0.999989i	$-0.501466\pi$
$353$	−2.68705e9	−0.00921062	−0.00460531	+	0.999989i	$0.501466\pi$
$354$	1.61768e11	0.547492
$355$	0	0
$356$	1.64365e11	0.542355
$357$	2.60394e9	0.00848444
$358$	−3.17606e11	−1.02192
$359$	−1.33878e11	−0.425388	−0.212694	−	0.977119i	$-0.568224\pi$
$359$	−1.33878e11	−0.425388	−0.212694	+	0.977119i	$0.568224\pi$
$360$	0	0
$361$	−2.26768e11	−0.702748
$362$	1.02499e11	0.313713
$363$	2.11254e11	0.638594
$364$	5.17123e10	0.154397
$365$	0	0
$366$	5.04765e10	0.147036
$367$	3.77304e11	1.08566	0.542830	−	0.839843i	$-0.317353\pi$
$367$	3.77304e11	1.08566	0.542830	+	0.839843i	$0.317353\pi$
$368$	2.62963e10	0.0747446
$369$	9.93529e10	0.278973
$370$	0	0
$371$	1.40143e11	0.384051
$372$	−1.86513e10	−0.0504972
$373$	−2.49347e10	−0.0666984	−0.0333492	−	0.999444i	$-0.510617\pi$
$373$	−2.49347e10	−0.0666984	−0.0333492	+	0.999444i	$0.510617\pi$
$374$	−1.10880e10	−0.0293044
$375$	0	0
$376$	−1.30041e11	−0.335532
$377$	−2.74531e11	−0.699931
$378$	2.77965e10	0.0700288
$379$	−5.44786e11	−1.35628	−0.678140	−	0.734933i	$-0.737214\pi$
$379$	−5.44786e11	−1.35628	−0.678140	+	0.734933i	$0.737214\pi$
$380$	0	0
$381$	−1.48480e11	−0.360998
$382$	1.97830e11	0.475344
$383$	7.81595e11	1.85604	0.928020	−	0.372530i	$-0.121510\pi$
$383$	7.81595e11	1.85604	0.928020	+	0.372530i	$0.121510\pi$
$384$	−2.17433e10	−0.0510310
$385$	0	0
$386$	4.94101e11	1.13285
$387$	2.34563e9	0.00531570
$388$	5.22719e10	0.117092
$389$	3.10798e11	0.688185	0.344092	−	0.938936i	$-0.388187\pi$
$389$	3.10798e11	0.688185	0.344092	+	0.938936i	$0.388187\pi$
$390$	0	0
$391$	−3.94589e9	−0.00853788
$392$	1.21517e11	0.259926
$393$	2.88295e11	0.609637
$394$	−2.29100e11	−0.478953
$395$	0	0
$396$	−1.18363e11	−0.241872
$397$	2.15337e11	0.435072	0.217536	−	0.976052i	$-0.430198\pi$
$397$	2.15337e11	0.435072	0.217536	+	0.976052i	$0.430198\pi$
$398$	4.56096e11	0.911134
$399$	8.20075e10	0.161985
$400$	0	0
$401$	1.96190e11	0.378902	0.189451	−	0.981890i	$-0.439329\pi$
$401$	1.96190e11	0.378902	0.189451	+	0.981890i	$0.439329\pi$
$402$	−1.37334e11	−0.262278
$403$	5.55808e10	0.104967
$404$	2.72831e11	0.509539
$405$	0	0
$406$	2.32374e11	0.424444
$407$	−1.06410e12	−1.92223
$408$	3.26269e9	0.00582914
$409$	−3.75622e9	−0.00663736	−0.00331868	−	0.999994i	$-0.501056\pi$
$409$	−3.75622e9	−0.00663736	−0.00331868	+	0.999994i	$0.501056\pi$
$410$	0	0
$411$	3.92596e11	0.678668
$412$	1.50186e11	0.256798
$413$	4.08040e11	0.690124
$414$	−4.21216e10	−0.0704699
$415$	0	0
$416$	6.47947e10	0.106077
$417$	−1.95242e11	−0.316199
$418$	−3.49203e11	−0.559480
$419$	1.87024e11	0.296438	0.148219	−	0.988955i	$-0.452646\pi$
$419$	1.87024e11	0.296438	0.148219	+	0.988955i	$0.452646\pi$
$420$	0	0
$421$	−5.38101e11	−0.834823	−0.417412	−	0.908718i	$-0.637063\pi$
$421$	−5.38101e11	−0.834823	−0.417412	+	0.908718i	$0.637063\pi$
$422$	−8.62551e11	−1.32397
$423$	2.08300e11	0.316342
$424$	1.75597e11	0.263858
$425$	0	0
$426$	8.14424e10	0.119814
$427$	1.27321e11	0.185342
$428$	2.29368e11	0.330397
$429$	3.52719e11	0.502772
$430$	0	0
$431$	−1.08097e12	−1.50892	−0.754458	−	0.656349i	$-0.772100\pi$
$431$	−1.08097e12	−1.50892	−0.754458	+	0.656349i	$0.772100\pi$
$432$	3.48285e10	0.0481125
$433$	−3.47771e11	−0.475442	−0.237721	−	0.971333i	$-0.576400\pi$
$433$	−3.47771e11	−0.475442	−0.237721	+	0.971333i	$0.576400\pi$
$434$	−4.70457e10	−0.0636526
$435$	0	0
$436$	−4.29851e10	−0.0569677
$437$	−1.24271e11	−0.163006
$438$	−6.04640e11	−0.784989
$439$	−9.56321e10	−0.122889	−0.0614445	−	0.998111i	$-0.519571\pi$
$439$	−9.56321e10	−0.122889	−0.0614445	+	0.998111i	$0.519571\pi$
$440$	0	0
$441$	−1.94647e11	−0.245061
$442$	−9.72276e9	−0.0121168
$443$	−1.18277e12	−1.45910	−0.729549	−	0.683928i	$-0.760270\pi$
$443$	−1.18277e12	−1.45910	−0.729549	+	0.683928i	$0.760270\pi$
$444$	3.13113e11	0.382365
$445$	0	0
$446$	8.72116e11	1.04368
$447$	−3.53797e11	−0.419150
$448$	−5.48447e10	−0.0643256
$449$	1.22170e12	1.41858	0.709292	−	0.704915i	$-0.249015\pi$
$449$	1.22170e12	1.41858	0.709292	+	0.704915i	$0.249015\pi$
$450$	0	0
$451$	−1.06712e12	−1.21456
$452$	8.44128e11	0.951230
$453$	6.07016e11	0.677264
$454$	−6.42828e11	−0.710139
$455$	0	0
$456$	1.02754e11	0.111290
$457$	−1.24710e12	−1.33745	−0.668725	−	0.743510i	$-0.733160\pi$
$457$	−1.24710e12	−1.33745	−0.668725	+	0.743510i	$0.733160\pi$
$458$	−1.16130e12	−1.23325
$459$	−5.22619e9	−0.00549577
$460$	0	0
$461$	−4.98955e11	−0.514526	−0.257263	−	0.966341i	$-0.582821\pi$
$461$	−4.98955e11	−0.514526	−0.257263	+	0.966341i	$0.582821\pi$
$462$	−2.98555e11	−0.304884
$463$	3.05620e10	0.0309078	0.0154539	−	0.999881i	$-0.495081\pi$
$463$	3.05620e10	0.0309078	0.0154539	+	0.999881i	$0.495081\pi$
$464$	2.91160e11	0.291609
$465$	0	0
$466$	1.01101e12	0.993158
$467$	5.89962e11	0.573982	0.286991	−	0.957933i	$-0.407345\pi$
$467$	5.89962e11	0.573982	0.286991	+	0.957933i	$0.407345\pi$
$468$	−1.03789e11	−0.100010
$469$	−3.46409e11	−0.330606
$470$	0	0
$471$	7.37539e11	0.690544
$472$	5.11267e11	0.474142
$473$	−2.51938e10	−0.0231429
$474$	7.15317e11	0.650872
$475$	0	0
$476$	8.22972e9	0.00734774
$477$	−2.81272e11	−0.248767
$478$	−1.10114e12	−0.964751
$479$	−9.92075e11	−0.861063	−0.430531	−	0.902576i	$-0.641674\pi$
$479$	−9.92075e11	−0.861063	−0.430531	+	0.902576i	$0.641674\pi$
$480$	0	0
$481$	−9.33073e11	−0.794809
$482$	6.60368e11	0.557281
$483$	−1.06247e11	−0.0888286
$484$	6.67667e11	0.553039
$485$	0	0
$486$	−5.57886e10	−0.0453609
$487$	1.44827e12	1.16673	0.583363	−	0.812212i	$-0.301737\pi$
$487$	1.44827e12	1.16673	0.583363	+	0.812212i	$0.301737\pi$
$488$	1.59531e11	0.127337
$489$	−1.71535e11	−0.135663
$490$	0	0
$491$	−1.11554e12	−0.866197	−0.433098	−	0.901347i	$-0.642580\pi$
$491$	−1.11554e12	−0.866197	−0.433098	+	0.901347i	$0.642580\pi$
$492$	3.14004e11	0.241597
$493$	−4.36900e10	−0.0333097
$494$	−3.06206e11	−0.231335
$495$	0	0
$496$	−5.89475e10	−0.0437318
$497$	2.05428e11	0.151028
$498$	−5.76671e11	−0.420142
$499$	−5.96482e11	−0.430670	−0.215335	−	0.976540i	$-0.569084\pi$
$499$	−5.96482e11	−0.430670	−0.215335	+	0.976540i	$0.569084\pi$
$500$	0	0
$501$	3.41373e11	0.242080
$502$	−2.41685e11	−0.169857
$503$	−1.96444e12	−1.36830	−0.684152	−	0.729340i	$-0.739827\pi$
$503$	−1.96444e12	−1.36830	−0.684152	+	0.729340i	$0.739827\pi$
$504$	8.78506e10	0.0606467
$505$	0	0
$506$	4.52417e11	0.306805
$507$	−5.49676e11	−0.369463
$508$	−4.69269e11	−0.312633
$509$	2.27926e12	1.50510	0.752549	−	0.658537i	$-0.228824\pi$
$509$	2.27926e12	1.50510	0.752549	+	0.658537i	$0.228824\pi$
$510$	0	0
$511$	−1.52513e12	−0.989494
$512$	−6.87195e10	−0.0441942
$513$	−1.64592e11	−0.104925
$514$	1.08997e12	0.688779
$515$	0	0
$516$	7.41335e9	0.00460353
$517$	−2.23729e12	−1.37726
$518$	7.89789e11	0.481978
$519$	−5.99422e11	−0.362643
$520$	0	0
$521$	−1.71480e12	−1.01963	−0.509817	−	0.860283i	$-0.670287\pi$
$521$	−1.71480e12	−1.01963	−0.509817	+	0.860283i	$0.670287\pi$
$522$	−4.66383e11	−0.274932
$523$	−2.62599e12	−1.53474	−0.767372	−	0.641202i	$-0.778436\pi$
$523$	−2.62599e12	−1.53474	−0.767372	+	0.641202i	$0.778436\pi$
$524$	9.11156e11	0.527961
$525$	0	0
$526$	−1.34274e12	−0.764815
$527$	8.84536e9	0.00499537
$528$	−3.74084e11	−0.209467
$529$	−1.64015e12	−0.910612
$530$	0	0
$531$	−8.18950e11	−0.447025
$532$	2.59184e11	0.140283
$533$	−9.35728e11	−0.502201
$534$	−8.32096e11	−0.442831
$535$	0	0
$536$	−4.34044e11	−0.227139
$537$	1.60788e12	0.834390
$538$	−2.10634e12	−1.08395
$539$	2.09065e12	1.06692
$540$	0	0
$541$	3.23250e12	1.62237	0.811187	−	0.584787i	$-0.198822\pi$
$541$	3.23250e12	1.62237	0.811187	+	0.584787i	$0.198822\pi$
$542$	2.47707e12	1.23294
$543$	−5.18903e11	−0.256146
$544$	1.03117e10	0.00504818
$545$	0	0
$546$	−2.61794e11	−0.126064
$547$	−1.29275e12	−0.617409	−0.308705	−	0.951158i	$-0.599895\pi$
$547$	−1.29275e12	−0.617409	−0.308705	+	0.951158i	$0.599895\pi$
$548$	1.24080e12	0.587744
$549$	−2.55537e11	−0.120055
$550$	0	0
$551$	−1.37596e12	−0.635951
$552$	−1.33125e11	−0.0610287
$553$	1.80430e12	0.820437
$554$	−1.53471e12	−0.692201
$555$	0	0
$556$	−6.17060e11	−0.273836
$557$	−4.64666e11	−0.204547	−0.102273	−	0.994756i	$-0.532612\pi$
$557$	−4.64666e11	−0.204547	−0.102273	+	0.994756i	$0.532612\pi$
$558$	9.44224e10	0.0412308
$559$	−2.20917e10	−0.00956920
$560$	0	0
$561$	5.61332e10	0.0239269
$562$	−2.13912e12	−0.904527
$563$	6.55678e11	0.275044	0.137522	−	0.990499i	$-0.456086\pi$
$563$	6.55678e11	0.275044	0.137522	+	0.990499i	$0.456086\pi$
$564$	6.58330e11	0.273961
$565$	0	0
$566$	2.54309e12	1.04157
$567$	−1.40720e11	−0.0571783
$568$	2.57398e11	0.103762
$569$	−1.34208e12	−0.536750	−0.268375	−	0.963314i	$-0.586487\pi$
$569$	−1.34208e12	−0.536750	−0.268375	+	0.963314i	$0.586487\pi$
$570$	0	0
$571$	−8.39060e11	−0.330317	−0.165158	−	0.986267i	$-0.552813\pi$
$571$	−8.39060e11	−0.330317	−0.165158	+	0.986267i	$0.552813\pi$
$572$	1.11477e12	0.435413
$573$	−1.00152e12	−0.388116
$574$	7.92037e11	0.304538
$575$	0	0
$576$	1.10075e11	0.0416667
$577$	−5.73884e11	−0.215542	−0.107771	−	0.994176i	$-0.534371\pi$
$577$	−5.73884e11	−0.215542	−0.107771	+	0.994176i	$0.534371\pi$
$578$	1.89586e12	0.706530
$579$	−2.50139e12	−0.924969
$580$	0	0
$581$	−1.45458e12	−0.529597
$582$	−2.64626e11	−0.0956048
$583$	3.02107e12	1.08306
$584$	−1.91096e12	−0.679821
$585$	0	0
$586$	1.22054e12	0.427575
$587$	−2.66776e12	−0.927417	−0.463709	−	0.885988i	$-0.653482\pi$
$587$	−2.66776e12	−0.927417	−0.463709	+	0.885988i	$0.653482\pi$
$588$	−6.15180e11	−0.212229
$589$	2.78573e11	0.0953719
$590$	0	0
$591$	1.15982e12	0.391063
$592$	9.89592e11	0.331138
$593$	−3.30195e11	−0.109654	−0.0548271	−	0.998496i	$-0.517461\pi$
$593$	−3.30195e11	−0.109654	−0.0548271	+	0.998496i	$0.517461\pi$
$594$	5.99210e11	0.197488
$595$	0	0
$596$	−1.11817e12	−0.362995
$597$	−2.30898e12	−0.743938
$598$	3.96711e11	0.126858
$599$	5.46904e11	0.173576	0.0867882	−	0.996227i	$-0.472340\pi$
$599$	5.46904e11	0.173576	0.0867882	+	0.996227i	$0.472340\pi$
$600$	0	0
$601$	3.25074e12	1.01636	0.508179	−	0.861251i	$-0.330319\pi$
$601$	3.25074e12	1.01636	0.508179	+	0.861251i	$0.330319\pi$
$602$	1.86993e10	0.00580283
$603$	6.95255e11	0.214149
$604$	1.91847e12	0.586528
$605$	0	0
$606$	−1.38121e12	−0.416037
$607$	5.86019e11	0.175211	0.0876057	−	0.996155i	$-0.472078\pi$
$607$	5.86019e11	0.175211	0.0876057	+	0.996155i	$0.472078\pi$
$608$	3.24753e11	0.0963802
$609$	−1.17639e12	−0.346557
$610$	0	0
$611$	−1.96182e12	−0.569473
$612$	−1.65173e10	−0.00475947
$613$	5.02414e12	1.43711	0.718555	−	0.695470i	$-0.244804\pi$
$613$	5.02414e12	1.43711	0.718555	+	0.695470i	$0.244804\pi$
$614$	−1.73810e12	−0.493535
$615$	0	0
$616$	−9.43581e11	−0.264038
$617$	6.87781e11	0.191059	0.0955294	−	0.995427i	$-0.469546\pi$
$617$	6.87781e11	0.191059	0.0955294	+	0.995427i	$0.469546\pi$
$618$	−7.60315e11	−0.209674
$619$	3.19704e12	0.875266	0.437633	−	0.899154i	$-0.355817\pi$
$619$	3.19704e12	0.875266	0.437633	+	0.899154i	$0.355817\pi$
$620$	0	0
$621$	2.13241e11	0.0575384
$622$	−2.39189e12	−0.640745
$623$	−2.09886e12	−0.558196
$624$	−3.28023e11	−0.0866111
$625$	0	0
$626$	1.04446e12	0.271836
$627$	1.76784e12	0.456814
$628$	2.33099e12	0.598028
$629$	−1.48493e11	−0.0378250
$630$	0	0
$631$	7.30991e12	1.83561	0.917804	−	0.397034i	$-0.129961\pi$
$631$	7.30991e12	1.83561	0.917804	+	0.397034i	$0.129961\pi$
$632$	2.26075e12	0.563672
$633$	4.36666e12	1.08102
$634$	2.01007e12	0.494094
$635$	0	0
$636$	−8.88958e11	−0.215439
$637$	1.83323e12	0.441153
$638$	5.00929e12	1.19697
$639$	−4.12302e11	−0.0978277
$640$	0	0
$641$	4.72287e12	1.10495	0.552477	−	0.833528i	$-0.313683\pi$
$641$	4.72287e12	1.10495	0.552477	+	0.833528i	$0.313683\pi$
$642$	−1.16118e12	−0.269768
$643$	4.94330e12	1.14043	0.570214	−	0.821496i	$-0.306860\pi$
$643$	4.94330e12	1.14043	0.570214	+	0.821496i	$0.306860\pi$
$644$	−3.35792e11	−0.0769278
$645$	0	0
$646$	−4.87309e10	−0.0110092
$647$	8.37420e12	1.87877	0.939386	−	0.342860i	$-0.111396\pi$
$647$	8.37420e12	1.87877	0.939386	+	0.342860i	$0.111396\pi$
$648$	−1.76319e11	−0.0392837
$649$	8.79613e12	1.94621
$650$	0	0
$651$	2.38169e11	0.0519722
$652$	−5.42134e11	−0.117488
$653$	−9.65636e11	−0.207828	−0.103914	−	0.994586i	$-0.533137\pi$
$653$	−9.65636e11	−0.207828	−0.103914	+	0.994586i	$0.533137\pi$
$654$	2.17612e11	0.0465139
$655$	0	0
$656$	9.92408e11	0.209230
$657$	3.06099e12	0.640941
$658$	1.66056e12	0.345332
$659$	−4.75815e12	−0.982775	−0.491387	−	0.870941i	$-0.663510\pi$
$659$	−4.75815e12	−0.982775	−0.491387	+	0.870941i	$0.663510\pi$
$660$	0	0
$661$	6.35592e12	1.29501	0.647504	−	0.762062i	$-0.275813\pi$
$661$	6.35592e12	1.29501	0.647504	+	0.762062i	$0.275813\pi$
$662$	−5.96685e12	−1.20749
$663$	4.92215e10	0.00989336
$664$	−1.82257e12	−0.363854
$665$	0	0
$666$	−1.58514e12	−0.312200
$667$	1.78266e12	0.348739
$668$	1.07891e12	0.209648
$669$	−4.41509e12	−0.852161
$670$	0	0
$671$	2.74466e12	0.522682
$672$	2.77651e11	0.0525216
$673$	2.69115e12	0.505674	0.252837	−	0.967509i	$-0.418636\pi$
$673$	2.69115e12	0.505674	0.252837	+	0.967509i	$0.418636\pi$
$674$	−6.71842e12	−1.25400
$675$	0	0
$676$	−1.73725e12	−0.319964
$677$	1.86883e12	0.341917	0.170958	−	0.985278i	$-0.445314\pi$
$677$	1.86883e12	0.341917	0.170958	+	0.985278i	$0.445314\pi$
$678$	−4.27340e12	−0.776676
$679$	−6.67488e11	−0.120512
$680$	0	0
$681$	3.25432e12	0.579826
$682$	−1.01417e12	−0.179506
$683$	−5.91404e12	−1.03990	−0.519950	−	0.854197i	$-0.674049\pi$
$683$	−5.91404e12	−1.03990	−0.519950	+	0.854197i	$0.674049\pi$
$684$	−5.20192e11	−0.0908681
$685$	0	0
$686$	−3.66237e12	−0.631399
$687$	5.87909e12	1.00694
$688$	2.34298e10	0.00398677
$689$	2.64908e12	0.447826
$690$	0	0
$691$	−4.37919e11	−0.0730706	−0.0365353	−	0.999332i	$-0.511632\pi$
$691$	−4.37919e11	−0.0730706	−0.0365353	+	0.999332i	$0.511632\pi$
$692$	−1.89447e12	−0.314058
$693$	1.51143e12	0.248937
$694$	−5.62641e10	−0.00920691
$695$	0	0
$696$	−1.47400e12	−0.238098
$697$	−1.48916e11	−0.0238997
$698$	7.30751e12	1.16525
$699$	−5.11823e12	−0.810910
$700$	0	0
$701$	9.99765e11	0.156375	0.0781875	−	0.996939i	$-0.475087\pi$
$701$	9.99765e11	0.156375	0.0781875	+	0.996939i	$0.475087\pi$
$702$	5.25429e11	0.0816577
$703$	−4.67660e12	−0.722156
$704$	−1.18229e12	−0.181404
$705$	0	0
$706$	4.29927e10	0.00651289
$707$	−3.48392e12	−0.524422
$708$	−2.58829e12	−0.387135
$709$	5.09447e12	0.757166	0.378583	−	0.925567i	$-0.376411\pi$
$709$	5.09447e12	0.757166	0.378583	+	0.925567i	$0.376411\pi$
$710$	0	0
$711$	−3.62129e12	−0.531435
$712$	−2.62983e12	−0.383503
$713$	−3.60911e11	−0.0522995
$714$	−4.16630e10	−0.00599940
$715$	0	0
$716$	5.08169e12	0.722603
$717$	5.57450e12	0.787716
$718$	2.14206e12	0.300795
$719$	−4.87984e12	−0.680966	−0.340483	−	0.940251i	$-0.610591\pi$
$719$	−4.87984e12	−0.680966	−0.340483	+	0.940251i	$0.610591\pi$
$720$	0	0
$721$	−1.91780e12	−0.264298
$722$	3.62829e12	0.496918
$723$	−3.34311e12	−0.455018
$724$	−1.63999e12	−0.221829
$725$	0	0
$726$	−3.38006e12	−0.451554
$727$	8.66752e11	0.115077	0.0575387	−	0.998343i	$-0.481675\pi$
$727$	8.66752e11	0.115077	0.0575387	+	0.998343i	$0.481675\pi$
$728$	−8.27397e11	−0.109175
$729$	2.82430e11	0.0370370
$730$	0	0
$731$	−3.51576e9	−0.000455398 0
$732$	−8.07625e11	−0.103970
$733$	1.42013e13	1.81702	0.908511	−	0.417861i	$-0.137220\pi$
$733$	1.42013e13	1.81702	0.908511	+	0.417861i	$0.137220\pi$
$734$	−6.03686e12	−0.767677
$735$	0	0
$736$	−4.20741e11	−0.0528524
$737$	−7.46755e12	−0.932340
$738$	−1.58965e12	−0.197263
$739$	−8.23229e12	−1.01536	−0.507681	−	0.861545i	$-0.669497\pi$
$739$	−8.23229e12	−1.01536	−0.507681	+	0.861545i	$0.669497\pi$
$740$	0	0
$741$	1.55017e12	0.188884
$742$	−2.24229e12	−0.271565
$743$	−1.44319e13	−1.73730	−0.868649	−	0.495427i	$-0.835011\pi$
$743$	−1.44319e13	−1.73730	−0.868649	+	0.495427i	$0.835011\pi$
$744$	2.98422e11	0.0357069
$745$	0	0
$746$	3.98956e11	0.0471629
$747$	2.91940e12	0.343044
$748$	1.77409e11	0.0207213
$749$	−2.92892e12	−0.340047
$750$	0	0
$751$	6.03033e12	0.691770	0.345885	−	0.938277i	$-0.387579\pi$
$751$	6.03033e12	0.691770	0.345885	+	0.938277i	$0.387579\pi$
$752$	2.08065e12	0.237257
$753$	1.22353e12	0.138688
$754$	4.39250e12	0.494926
$755$	0	0
$756$	−4.44744e11	−0.0495179
$757$	−3.96859e12	−0.439243	−0.219621	−	0.975585i	$-0.570482\pi$
$757$	−3.96859e12	−0.439243	−0.219621	+	0.975585i	$0.570482\pi$
$758$	8.71657e12	0.959034
$759$	−2.29036e12	−0.250505
$760$	0	0
$761$	−1.15147e12	−0.124458	−0.0622288	−	0.998062i	$-0.519821\pi$
$761$	−1.15147e12	−0.124458	−0.0622288	+	0.998062i	$0.519821\pi$
$762$	2.37567e12	0.255264
$763$	5.48899e11	0.0586317
$764$	−3.16528e12	−0.336119
$765$	0	0
$766$	−1.25055e13	−1.31242
$767$	7.71306e12	0.804725
$768$	3.47892e11	0.0360844
$769$	1.70040e13	1.75341	0.876703	−	0.481032i	$-0.159738\pi$
$769$	1.70040e13	1.75341	0.876703	+	0.481032i	$0.159738\pi$
$770$	0	0
$771$	−5.51796e12	−0.562386
$772$	−7.90562e12	−0.801047
$773$	−9.72900e12	−0.980078	−0.490039	−	0.871701i	$-0.663017\pi$
$773$	−9.72900e12	−0.980078	−0.490039	+	0.871701i	$0.663017\pi$
$774$	−3.75301e10	−0.00375876
$775$	0	0
$776$	−8.36350e11	−0.0827962
$777$	−3.99831e12	−0.393534
$778$	−4.97277e12	−0.486620
$779$	−4.68991e12	−0.456295
$780$	0	0
$781$	4.42843e12	0.425912
$782$	6.31343e10	0.00603719
$783$	2.36106e12	0.224481
$784$	−1.94427e12	−0.183796
$785$	0	0
$786$	−4.61273e12	−0.431078
$787$	−3.11202e12	−0.289172	−0.144586	−	0.989492i	$-0.546185\pi$
$787$	−3.11202e12	−0.289172	−0.144586	+	0.989492i	$0.546185\pi$
$788$	3.66561e12	0.338671
$789$	6.79762e12	0.624469
$790$	0	0
$791$	−1.07791e13	−0.979015
$792$	1.89380e12	0.171029
$793$	2.40671e12	0.216120
$794$	−3.44539e12	−0.307642
$795$	0	0
$796$	−7.29753e12	−0.644269
$797$	−8.71912e12	−0.765438	−0.382719	−	0.923865i	$-0.625012\pi$
$797$	−8.71912e12	−0.765438	−0.382719	+	0.923865i	$0.625012\pi$
$798$	−1.31212e12	−0.114541
$799$	−3.12212e11	−0.0271012
$800$	0	0
$801$	4.21249e12	0.361570
$802$	−3.13904e12	−0.267924
$803$	−3.28773e13	−2.79046
$804$	2.19735e12	0.185458
$805$	0	0
$806$	−8.89292e11	−0.0742227
$807$	1.06633e13	0.885039
$808$	−4.36529e12	−0.360298
$809$	8.09556e12	0.664474	0.332237	−	0.943196i	$-0.392197\pi$
$809$	8.09556e12	0.664474	0.332237	+	0.943196i	$0.392197\pi$
$810$	0	0
$811$	−6.98205e12	−0.566747	−0.283373	−	0.959010i	$-0.591454\pi$
$811$	−6.98205e12	−0.566747	−0.283373	+	0.959010i	$0.591454\pi$
$812$	−3.71798e12	−0.300127
$813$	−1.25402e13	−1.00669
$814$	1.70255e13	1.35922
$815$	0	0
$816$	−5.22030e10	−0.00412182
$817$	−1.10724e11	−0.00869449
$818$	6.00995e10	0.00469333
$819$	1.32533e12	0.102931
$820$	0	0
$821$	−1.05711e13	−0.812036	−0.406018	−	0.913865i	$-0.633083\pi$
$821$	−1.05711e13	−0.812036	−0.406018	+	0.913865i	$0.633083\pi$
$822$	−6.28153e12	−0.479891
$823$	−9.20281e12	−0.699231	−0.349616	−	0.936893i	$-0.613688\pi$
$823$	−9.20281e12	−0.699231	−0.349616	+	0.936893i	$0.613688\pi$
$824$	−2.40297e12	−0.181583
$825$	0	0
$826$	−6.52864e12	−0.487991
$827$	6.15946e12	0.457897	0.228948	−	0.973439i	$-0.426471\pi$
$827$	6.15946e12	0.457897	0.228948	+	0.973439i	$0.426471\pi$
$828$	6.73946e11	0.0498297
$829$	1.57834e13	1.16066	0.580329	−	0.814382i	$-0.302924\pi$
$829$	1.57834e13	1.16066	0.580329	+	0.814382i	$0.302924\pi$
$830$	0	0
$831$	7.76947e12	0.565180
$832$	−1.03671e12	−0.0750074
$833$	2.91748e11	0.0209945
$834$	3.12387e12	0.223586
$835$	0	0
$836$	5.58725e12	0.395612
$837$	−4.78014e11	−0.0336648
$838$	−2.99238e12	−0.209613
$839$	7.77432e12	0.541669	0.270834	−	0.962626i	$-0.412700\pi$
$839$	7.77432e12	0.541669	0.270834	+	0.962626i	$0.412700\pi$
$840$	0	0
$841$	5.23092e12	0.360575
$842$	8.60962e12	0.590309
$843$	1.08293e13	0.738543
$844$	1.38008e13	0.936189
$845$	0	0
$846$	−3.33280e12	−0.223688
$847$	−8.52579e12	−0.569193
$848$	−2.80955e12	−0.186576
$849$	−1.28744e13	−0.850436
$850$	0	0
$851$	6.05887e12	0.396012
$852$	−1.30308e12	−0.0847213
$853$	9.55011e12	0.617643	0.308822	−	0.951120i	$-0.400065\pi$
$853$	9.55011e12	0.617643	0.308822	+	0.951120i	$0.400065\pi$
$854$	−2.03713e12	−0.131057
$855$	0	0
$856$	−3.66989e12	−0.233626
$857$	−2.52411e13	−1.59844	−0.799218	−	0.601042i	$-0.794753\pi$
$857$	−2.52411e13	−1.59844	−0.799218	+	0.601042i	$0.794753\pi$
$858$	−5.64350e12	−0.355513
$859$	−1.06421e13	−0.666894	−0.333447	−	0.942769i	$-0.608212\pi$
$859$	−1.06421e13	−0.666894	−0.333447	+	0.942769i	$0.608212\pi$
$860$	0	0
$861$	−4.00968e12	−0.248654
$862$	1.72955e13	1.06696
$863$	1.17082e13	0.718524	0.359262	−	0.933237i	$-0.383028\pi$
$863$	1.17082e13	0.718524	0.359262	+	0.933237i	$0.383028\pi$
$864$	−5.57256e11	−0.0340207
$865$	0	0
$866$	5.56433e12	0.336188
$867$	−9.59778e12	−0.576879
$868$	7.52732e11	0.0450092
$869$	3.88953e13	2.31371
$870$	0	0
$871$	−6.54807e12	−0.385506
$872$	6.87761e11	0.0402822
$873$	1.33967e12	0.0780610
$874$	1.98833e12	0.115262
$875$	0	0
$876$	9.67425e12	0.555071
$877$	1.12684e13	0.643224	0.321612	−	0.946871i	$-0.395775\pi$
$877$	1.12684e13	0.643224	0.321612	+	0.946871i	$0.395775\pi$
$878$	1.53011e12	0.0868957
$879$	−6.17897e12	−0.349113
$880$	0	0
$881$	6.89165e12	0.385418	0.192709	−	0.981256i	$-0.438273\pi$
$881$	6.89165e12	0.385418	0.192709	+	0.981256i	$0.438273\pi$
$882$	3.11435e12	0.173284
$883$	1.16654e12	0.0645767	0.0322884	−	0.999479i	$-0.489721\pi$
$883$	1.16654e12	0.0645767	0.0322884	+	0.999479i	$0.489721\pi$
$884$	1.55564e11	0.00856790
$885$	0	0
$886$	1.89244e13	1.03174
$887$	−1.90546e13	−1.03358	−0.516789	−	0.856113i	$-0.672873\pi$
$887$	−1.90546e13	−1.03358	−0.516789	+	0.856113i	$0.672873\pi$
$888$	−5.00981e12	−0.270373
$889$	5.99234e12	0.321765
$890$	0	0
$891$	−3.03350e12	−0.161248
$892$	−1.39539e13	−0.737993
$893$	−9.83270e12	−0.517418
$894$	5.66075e12	0.296384
$895$	0	0
$896$	8.77516e11	0.0454851
$897$	−2.00835e12	−0.103579
$898$	−1.95471e13	−1.00309
$899$	−3.99611e12	−0.204042
$900$	0	0
$901$	4.21586e11	0.0213120
$902$	1.70740e13	0.858826
$903$	−9.46650e10	−0.00473799
$904$	−1.35061e13	−0.672621
$905$	0	0
$906$	−9.71225e12	−0.478898
$907$	1.77580e12	0.0871285	0.0435643	−	0.999051i	$-0.486129\pi$
$907$	1.77580e12	0.0871285	0.0435643	+	0.999051i	$0.486129\pi$
$908$	1.02853e13	0.502144
$909$	6.99236e12	0.339693
$910$	0	0
$911$	−2.41098e13	−1.15974	−0.579870	−	0.814709i	$-0.696897\pi$
$911$	−2.41098e13	−1.15974	−0.579870	+	0.814709i	$0.696897\pi$
$912$	−1.64406e12	−0.0786941
$913$	−3.13565e13	−1.49351
$914$	1.99536e13	0.945720
$915$	0	0
$916$	1.85808e13	0.872038
$917$	−1.16350e13	−0.543382
$918$	8.36191e10	0.00388609
$919$	−1.08237e13	−0.500560	−0.250280	−	0.968174i	$-0.580523\pi$
$919$	−1.08237e13	−0.500560	−0.250280	+	0.968174i	$0.580523\pi$
$920$	0	0
$921$	8.79916e12	0.402970
$922$	7.98328e12	0.363825
$923$	3.88316e12	0.176107
$924$	4.77688e12	0.215586
$925$	0	0
$926$	−4.88993e11	−0.0218551
$927$	3.84909e12	0.171198
$928$	−4.65857e12	−0.206199
$929$	9.34014e12	0.411417	0.205709	−	0.978613i	$-0.434050\pi$
$929$	9.34014e12	0.411417	0.205709	+	0.978613i	$0.434050\pi$
$930$	0	0
$931$	9.18821e12	0.400827
$932$	−1.61761e13	−0.702269
$933$	1.21090e13	0.523166
$934$	−9.43939e12	−0.405866
$935$	0	0
$936$	1.66062e12	0.0707177
$937$	−3.04868e13	−1.29206	−0.646032	−	0.763310i	$-0.723573\pi$
$937$	−3.04868e13	−1.29206	−0.646032	+	0.763310i	$0.723573\pi$
$938$	5.54254e12	0.233774
$939$	−5.28758e12	−0.221953
$940$	0	0
$941$	−1.55212e13	−0.645313	−0.322657	−	0.946516i	$-0.604576\pi$
$941$	−1.55212e13	−0.645313	−0.322657	+	0.946516i	$0.604576\pi$
$942$	−1.18006e13	−0.488288
$943$	6.07611e12	0.250220
$944$	−8.18027e12	−0.335269
$945$	0	0
$946$	4.03101e11	0.0163645
$947$	4.06050e13	1.64061	0.820304	−	0.571928i	$-0.193804\pi$
$947$	4.06050e13	1.64061	0.820304	+	0.571928i	$0.193804\pi$
$948$	−1.14451e13	−0.460236
$949$	−2.88291e13	−1.15381
$950$	0	0
$951$	−1.01760e13	−0.403426
$952$	−1.31676e11	−0.00519564
$953$	2.71162e13	1.06490	0.532452	−	0.846460i	$-0.321271\pi$
$953$	2.71162e13	1.06490	0.532452	+	0.846460i	$0.321271\pi$
$954$	4.50035e12	0.175905
$955$	0	0
$956$	1.76182e13	0.682182
$957$	−2.53596e13	−0.977322
$958$	1.58732e13	0.608863
$959$	−1.58444e13	−0.604912
$960$	0	0
$961$	−2.56306e13	−0.969400
$962$	1.49292e13	0.562015
$963$	5.87845e12	0.220265
$964$	−1.05659e13	−0.394057
$965$	0	0
$966$	1.69995e12	0.0628113
$967$	4.97380e13	1.82924	0.914618	−	0.404320i	$-0.132492\pi$
$967$	4.97380e13	1.82924	0.914618	+	0.404320i	$0.132492\pi$
$968$	−1.06827e13	−0.391057
$969$	2.46700e11	0.00898901
$970$	0	0
$971$	−3.12908e12	−0.112961	−0.0564806	−	0.998404i	$-0.517988\pi$
$971$	−3.12908e12	−0.112961	−0.0564806	+	0.998404i	$0.517988\pi$
$972$	8.92617e11	0.0320750
$973$	7.87957e12	0.281835
$974$	−2.31723e13	−0.824999
$975$	0	0
$976$	−2.55249e12	−0.0900410
$977$	2.46969e13	0.867196	0.433598	−	0.901106i	$-0.357244\pi$
$977$	2.46969e13	0.867196	0.433598	+	0.901106i	$0.357244\pi$
$978$	2.74455e12	0.0959283
$979$	−4.52452e13	−1.57417
$980$	0	0
$981$	−1.10166e12	−0.0379785
$982$	1.78486e13	0.612494
$983$	2.40564e13	0.821752	0.410876	−	0.911691i	$-0.365223\pi$
$983$	2.40564e13	0.821752	0.410876	+	0.911691i	$0.365223\pi$
$984$	−5.02407e12	−0.170835
$985$	0	0
$986$	6.99041e11	0.0235535
$987$	−8.40657e12	−0.281963
$988$	4.89929e12	0.163579
$989$	1.43451e11	0.00476783
$990$	0	0
$991$	−3.80903e13	−1.25454	−0.627268	−	0.778804i	$-0.715827\pi$
$991$	−3.80903e13	−1.25454	−0.627268	+	0.778804i	$0.715827\pi$
$992$	9.43160e11	0.0309231
$993$	3.02072e13	0.985913
$994$	−3.28685e12	−0.106793
$995$	0	0
$996$	9.22674e12	0.297085
$997$	−2.29817e13	−0.736637	−0.368319	−	0.929700i	$-0.620066\pi$
$997$	−2.29817e13	−0.736637	−0.368319	+	0.929700i	$0.620066\pi$
$998$	9.54371e12	0.304530
$999$	8.02475e12	0.254910

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.10.a.c.1.1	✓	1
5.2	odd	4		150.10.c.a.49.1		2
5.3	odd	4		150.10.c.a.49.2		2
5.4	even	2		150.10.a.g.1.1	yes	1

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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