LMFDB - Embedded newform 361.10.a.e.1.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [361,10,Mod(1,361)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(361, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 10, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("361.1"); S:= CuspForms(chi, 10); N := Newforms(S);

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	361.a (trivial)

Newform invariants

comment:select newform

sage:traces = [14,-15] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$185.927936855$
Analytic rank:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 5069 x^{12} + 6049 x^{11} + 9806858 x^{10} - 13799702 x^{9} - 9054174058 x^{8} + \cdots - 17\!\cdots\!44 $ x^14 - x^13 - 5069x^12 + 6049x^11 + 9806858x^10 - 13799702x^9 - 9054174058x^8 + 14987065714x^7 + 4091858205557x^6 - 7191639085837x^5 - 853231603258457x^4 + 901465319435261x^3 + 73615201302121104x^2 + 11736003542411028x - 1795361907615663744
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{4}\cdot 19 $
Twist minimal:	no (minimal twist has level 19)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$-40.9292$ of defining polynomial
Character	$\chi$	$=$	361.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+39.9292 q^{2} -107.016 q^{3} +1082.34 q^{4} +181.893 q^{5} -4273.07 q^{6} +6421.38 q^{7} +22773.3 q^{8} -8230.53 q^{9} +7262.85 q^{10} -18234.9 q^{11} -115828. q^{12} -64367.6 q^{13} +256401. q^{14} -19465.5 q^{15} +355162. q^{16} +330639. q^{17} -328639. q^{18} +196871. q^{20} -687192. q^{21} -728105. q^{22} -1.73454e6 q^{23} -2.43712e6 q^{24} -1.92004e6 q^{25} -2.57015e6 q^{26} +2.98720e6 q^{27} +6.95013e6 q^{28} -3.22275e6 q^{29} -777242. q^{30} -6.34620e6 q^{31} +2.52139e6 q^{32} +1.95143e6 q^{33} +1.32022e7 q^{34} +1.16800e6 q^{35} -8.90826e6 q^{36} +1.71570e7 q^{37} +6.88838e6 q^{39} +4.14231e6 q^{40} +8.37540e6 q^{41} -2.74390e7 q^{42} -3.17434e7 q^{43} -1.97364e7 q^{44} -1.49708e6 q^{45} -6.92589e7 q^{46} +3.65671e7 q^{47} -3.80081e7 q^{48} +880523. q^{49} -7.66657e7 q^{50} -3.53837e7 q^{51} -6.96678e7 q^{52} -5.01405e7 q^{53} +1.19277e8 q^{54} -3.31680e6 q^{55} +1.46236e8 q^{56} -1.28682e8 q^{58} -2.30069e7 q^{59} -2.10683e7 q^{60} +1.33499e8 q^{61} -2.53399e8 q^{62} -5.28514e7 q^{63} -8.11656e7 q^{64} -1.17080e7 q^{65} +7.79191e7 q^{66} -3.98117e7 q^{67} +3.57865e8 q^{68} +1.85624e8 q^{69} +4.66375e7 q^{70} -4.02544e8 q^{71} -1.87437e8 q^{72} +3.15273e8 q^{73} +6.85067e8 q^{74} +2.05475e8 q^{75} -1.17093e8 q^{77} +2.75048e8 q^{78} +2.13887e7 q^{79} +6.46015e7 q^{80} -1.57677e8 q^{81} +3.34423e8 q^{82} -4.17337e8 q^{83} -7.43777e8 q^{84} +6.01410e7 q^{85} -1.26749e9 q^{86} +3.44886e8 q^{87} -4.15269e8 q^{88} -8.58032e8 q^{89} -5.97771e7 q^{90} -4.13329e8 q^{91} -1.87737e9 q^{92} +6.79146e8 q^{93} +1.46010e9 q^{94} -2.69830e8 q^{96} -8.94373e8 q^{97} +3.51586e7 q^{98} +1.50083e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 15 q^{2} + 74 q^{3} + 2987 q^{4} + 285 q^{5} + 535 q^{6} - 1338 q^{7} - 12135 q^{8} + 57928 q^{9} - 41180 q^{10} - 57405 q^{11} + 117729 q^{12} - 98671 q^{13} + 148290 q^{14} - 428251 q^{15} + 279203 q^{16}+ \cdots + 736622698 q^{99}+O(q^{100}) $ 14 * q - 15 * q^2 + 74 * q^3 + 2987 * q^4 + 285 * q^5 + 535 * q^6 - 1338 * q^7 - 12135 * q^8 + 57928 * q^9 - 41180 * q^10 - 57405 * q^11 + 117729 * q^12 - 98671 * q^13 + 148290 * q^14 - 428251 * q^15 + 279203 * q^16 - 466251 * q^17 + 367482 * q^18 - 1671810 * q^20 - 689090 * q^21 + 1689395 * q^22 + 3087747 * q^23 + 234183 * q^24 + 3260823 * q^25 + 4516572 * q^26 + 2108270 * q^27 + 703814 * q^28 - 7831383 * q^29 - 5929612 * q^30 - 4632816 * q^31 - 11470815 * q^32 - 22791973 * q^33 - 13457096 * q^34 + 13222428 * q^35 - 7355018 * q^36 + 13602510 * q^37 - 10387851 * q^39 + 16500258 * q^40 - 20419440 * q^41 + 10220798 * q^42 - 27415427 * q^43 - 41775405 * q^44 - 42991294 * q^45 - 68617354 * q^46 + 90906681 * q^47 - 33057375 * q^48 + 114912446 * q^49 + 22203357 * q^50 - 134429123 * q^51 - 66195006 * q^52 - 47827863 * q^53 + 130507669 * q^54 + 157712310 * q^55 + 191229558 * q^56 - 172013024 * q^58 - 255540 * q^59 - 287916794 * q^60 - 304035459 * q^61 - 693626280 * q^62 + 122148024 * q^63 - 454245757 * q^64 - 712480095 * q^65 + 611099417 * q^66 - 165758480 * q^67 + 178759254 * q^68 + 135618639 * q^69 - 1167527028 * q^70 - 685508589 * q^71 - 142349670 * q^72 + 602867050 * q^73 + 82104492 * q^74 + 950137387 * q^75 - 245997378 * q^77 + 911449840 * q^78 - 78162339 * q^79 - 227607150 * q^80 - 1230916118 * q^81 - 360208019 * q^82 + 206919963 * q^83 - 233652462 * q^84 + 1440537237 * q^85 - 936824310 * q^86 - 339438159 * q^87 - 823388847 * q^88 - 1256827551 * q^89 - 1879090924 * q^90 - 537759588 * q^91 + 677003592 * q^92 + 492493440 * q^93 - 424187592 * q^94 - 3020794465 * q^96 - 2109813492 * q^97 - 2689941591 * q^98 + 736622698 * q^99

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 $

$2$	39.9292	1.76464	0.882319	−	0.470651i	$-0.155981\pi$
$2$	39.9292	1.76464	0.882319	+	0.470651i	$0.155981\pi$
$3$	−107.016	−0.762788	−0.381394	−	0.924413i	$-0.624556\pi$
$3$	−107.016	−0.762788	−0.381394	+	0.924413i	$0.624556\pi$
$4$	1082.34	2.11395
$5$	181.893	0.130152	0.0650760	−	0.997880i	$-0.479271\pi$
$5$	181.893	0.130152	0.0650760	+	0.997880i	$0.479271\pi$
$6$	−4273.07	−1.34605
$7$	6421.38	1.01085	0.505426	−	0.862870i	$-0.331336\pi$
$7$	6421.38	1.01085	0.505426	+	0.862870i	$0.331336\pi$
$8$	22773.3	1.96572
$9$	−8230.53	−0.418154
$10$	7262.85	0.229671
$11$	−18234.9	−0.375523	−0.187761	−	0.982215i	$-0.560123\pi$
$11$	−18234.9	−0.375523	−0.187761	+	0.982215i	$0.560123\pi$
$12$	−115828.	−1.61250
$13$	−64367.6	−0.625061	−0.312530	−	0.949908i	$-0.601177\pi$
$13$	−64367.6	−0.625061	−0.312530	+	0.949908i	$0.601177\pi$
$14$	256401.	1.78379
$15$	−19465.5	−0.0992784
$16$	355162.	1.35484
$17$	330639.	0.960139	0.480069	−	0.877230i	$-0.340611\pi$
$17$	330639.	0.960139	0.480069	+	0.877230i	$0.340611\pi$
$18$	−328639.	−0.737891
$19$	0	0
$19$	0	0
$20$	196871.	0.275135
$21$	−687192.	−0.771065
$22$	−728105.	−0.662662
$23$	−1.73454e6	−1.29244	−0.646218	−	0.763153i	$-0.723650\pi$
$23$	−1.73454e6	−1.29244	−0.646218	+	0.763153i	$0.723650\pi$
$24$	−2.43712e6	−1.49943
$25$	−1.92004e6	−0.983060
$26$	−2.57015e6	−1.10301
$27$	2.98720e6	1.08175
$28$	6.95013e6	2.13689
$29$	−3.22275e6	−0.846126	−0.423063	−	0.906100i	$-0.639045\pi$
$29$	−3.22275e6	−0.846126	−0.423063	+	0.906100i	$0.639045\pi$
$30$	−777242.	−0.175191
$31$	−6.34620e6	−1.23420	−0.617101	−	0.786884i	$-0.711693\pi$
$31$	−6.34620e6	−1.23420	−0.617101	+	0.786884i	$0.711693\pi$
$32$	2.52139e6	0.425075
$33$	1.95143e6	0.286444
$34$	1.32022e7	1.69430
$35$	1.16800e6	0.131564
$36$	−8.90826e6	−0.883958
$37$	1.71570e7	1.50499	0.752497	−	0.658596i	$-0.228849\pi$
$37$	1.71570e7	1.50499	0.752497	+	0.658596i	$0.228849\pi$
$38$	0	0
$39$	6.88838e6	0.476789
$40$	4.14231e6	0.255843
$41$	8.37540e6	0.462890	0.231445	−	0.972848i	$-0.425655\pi$
$41$	8.37540e6	0.462890	0.231445	+	0.972848i	$0.425655\pi$
$42$	−2.74390e7	−1.36065
$43$	−3.17434e7	−1.41594	−0.707970	−	0.706243i	$-0.750389\pi$
$43$	−3.17434e7	−1.41594	−0.707970	+	0.706243i	$0.750389\pi$
$44$	−1.97364e7	−0.793837
$45$	−1.49708e6	−0.0544237
$46$	−6.92589e7	−2.28068
$47$	3.65671e7	1.09308	0.546538	−	0.837434i	$-0.315945\pi$
$47$	3.65671e7	1.09308	0.546538	+	0.837434i	$0.315945\pi$
$48$	−3.80081e7	−1.03345
$49$	880523.	0.0218202
$50$	−7.66657e7	−1.73475
$51$	−3.53837e7	−0.732382
$52$	−6.96678e7	−1.32135
$53$	−5.01405e7	−0.872865	−0.436432	−	0.899737i	$-0.643758\pi$
$53$	−5.01405e7	−0.872865	−0.436432	+	0.899737i	$0.643758\pi$
$54$	1.19277e8	1.90890
$55$	−3.31680e6	−0.0488751
$56$	1.46236e8	1.98705
$57$	0	0
$58$	−1.28682e8	−1.49311
$59$	−2.30069e7	−0.247186	−0.123593	−	0.992333i	$-0.539442\pi$
$59$	−2.30069e7	−0.247186	−0.123593	+	0.992333i	$0.539442\pi$
$60$	−2.10683e7	−0.209870
$61$	1.33499e8	1.23451	0.617254	−	0.786764i	$-0.288245\pi$
$61$	1.33499e8	1.23451	0.617254	+	0.786764i	$0.288245\pi$
$62$	−2.53399e8	−2.17792
$63$	−5.28514e7	−0.422692
$64$	−8.11656e7	−0.604731
$65$	−1.17080e7	−0.0813530
$66$	7.79191e7	0.505471
$67$	−3.98117e7	−0.241365	−0.120682	−	0.992691i	$-0.538508\pi$
$67$	−3.98117e7	−0.241365	−0.120682	+	0.992691i	$0.538508\pi$
$68$	3.57865e8	2.02969
$69$	1.85624e8	0.985855
$70$	4.66375e7	0.232164
$71$	−4.02544e8	−1.87997	−0.939985	−	0.341216i	$-0.889161\pi$
$71$	−4.02544e8	−1.87997	−0.939985	+	0.341216i	$0.889161\pi$
$72$	−1.87437e8	−0.821974
$73$	3.15273e8	1.29937	0.649686	−	0.760203i	$-0.274900\pi$
$73$	3.15273e8	1.29937	0.649686	+	0.760203i	$0.274900\pi$
$74$	6.85067e8	2.65577
$75$	2.05475e8	0.749867
$76$	0	0
$77$	−1.17093e8	−0.379598
$78$	2.75048e8	0.841360
$79$	2.13887e7	0.0617820	0.0308910	−	0.999523i	$-0.490166\pi$
$79$	2.13887e7	0.0617820	0.0308910	+	0.999523i	$0.490166\pi$
$80$	6.46015e7	0.176335
$81$	−1.57677e8	−0.406993
$82$	3.34423e8	0.816834
$83$	−4.17337e8	−0.965241	−0.482620	−	0.875830i	$-0.660315\pi$
$83$	−4.17337e8	−0.965241	−0.482620	+	0.875830i	$0.660315\pi$
$84$	−7.43777e8	−1.62999
$85$	6.01410e7	0.124964
$86$	−1.26749e9	−2.49862
$87$	3.44886e8	0.645415
$88$	−4.15269e8	−0.738173
$89$	−8.58032e8	−1.44960	−0.724801	−	0.688959i	$-0.758068\pi$
$89$	−8.58032e8	−1.44960	−0.724801	+	0.688959i	$0.758068\pi$
$90$	−5.97771e7	−0.0960381
$91$	−4.13329e8	−0.631844
$92$	−1.87737e9	−2.73215
$93$	6.79146e8	0.941434
$94$	1.46010e9	1.92888
$95$	0	0
$96$	−2.69830e8	−0.324242
$97$	−8.94373e8	−1.02576	−0.512880	−	0.858460i	$-0.671421\pi$
$97$	−8.94373e8	−1.02576	−0.512880	+	0.858460i	$0.671421\pi$
$98$	3.51586e7	0.0385047
$99$	1.50083e8	0.157027
$100$	−2.07814e9	−2.07814
$101$	2.68012e8	0.256276	0.128138	−	0.991756i	$-0.459100\pi$
$101$	2.68012e8	0.256276	0.128138	+	0.991756i	$0.459100\pi$
$102$	−1.41285e9	−1.29239
$103$	−2.12213e8	−0.185782	−0.0928912	−	0.995676i	$-0.529611\pi$
$103$	−2.12213e8	−0.185782	−0.0928912	+	0.995676i	$0.529611\pi$
$104$	−1.46587e9	−1.22869
$105$	−1.24995e8	−0.100356
$106$	−2.00207e9	−1.54029
$107$	−9.27967e8	−0.684393	−0.342196	−	0.939628i	$-0.611171\pi$
$107$	−9.27967e8	−0.684393	−0.342196	+	0.939628i	$0.611171\pi$
$108$	3.23317e9	2.28677
$109$	1.21742e9	0.826076	0.413038	−	0.910714i	$-0.364468\pi$
$109$	1.21742e9	0.826076	0.413038	+	0.910714i	$0.364468\pi$
$110$	−1.32437e8	−0.0862468
$111$	−1.83608e9	−1.14799
$112$	2.28063e9	1.36954
$113$	−2.75119e8	−0.158733	−0.0793667	−	0.996845i	$-0.525290\pi$
$113$	−2.75119e8	−0.158733	−0.0793667	+	0.996845i	$0.525290\pi$
$114$	0	0
$115$	−3.15501e8	−0.168213
$116$	−3.48812e9	−1.78867
$117$	5.29780e8	0.261372
$118$	−9.18646e8	−0.436194
$119$	2.12316e9	0.970558
$120$	−4.43294e8	−0.195154
$121$	−2.02544e9	−0.858983
$122$	5.33052e9	2.17846
$123$	−8.96303e8	−0.353087
$124$	−6.86876e9	−2.60904
$125$	−7.04502e8	−0.258099
$126$	−2.11031e9	−0.745898
$127$	4.72670e9	1.61228	0.806141	−	0.591723i	$-0.201552\pi$
$127$	4.72670e9	1.61228	0.806141	+	0.591723i	$0.201552\pi$
$128$	−4.53183e9	−1.49221
$129$	3.39705e9	1.08006
$130$	−4.67492e8	−0.143559
$131$	3.03299e9	0.899808	0.449904	−	0.893077i	$-0.351458\pi$
$131$	3.03299e9	0.899808	0.449904	+	0.893077i	$0.351458\pi$
$132$	2.11212e9	0.605529
$133$	0	0
$134$	−1.58965e9	−0.425922
$135$	5.43351e8	0.140792
$136$	7.52975e9	1.88736
$137$	5.03854e9	1.22197	0.610987	−	0.791640i	$-0.290773\pi$
$137$	5.03854e9	1.22197	0.610987	+	0.791640i	$0.290773\pi$
$138$	7.41182e9	1.73968
$139$	−8.23751e9	−1.87167	−0.935835	−	0.352439i	$-0.885352\pi$
$139$	−8.23751e9	−1.87167	−0.935835	+	0.352439i	$0.885352\pi$
$140$	1.26418e9	0.278121
$141$	−3.91327e9	−0.833785
$142$	−1.60733e10	−3.31747
$143$	1.17374e9	0.234725
$144$	−2.92317e9	−0.566530
$145$	−5.86195e8	−0.110125
$146$	1.25886e10	2.29292
$147$	−9.42302e7	−0.0166442
$148$	1.85698e10	3.18148
$149$	−7.50611e9	−1.24760	−0.623802	−	0.781583i	$-0.714413\pi$
$149$	−7.50611e9	−1.24760	−0.623802	+	0.781583i	$0.714413\pi$
$150$	8.20447e9	1.32324
$151$	1.91537e9	0.299817	0.149909	−	0.988700i	$-0.452102\pi$
$151$	1.91537e9	0.299817	0.149909	+	0.988700i	$0.452102\pi$
$152$	0	0
$153$	−2.72134e9	−0.401486
$154$	−4.67544e9	−0.669853
$155$	−1.15433e9	−0.160634
$156$	7.45558e9	1.00791
$157$	3.88860e9	0.510793	0.255396	−	0.966836i	$-0.417794\pi$
$157$	3.88860e9	0.510793	0.255396	+	0.966836i	$0.417794\pi$
$158$	8.54033e8	0.109023
$159$	5.36584e9	0.665811
$160$	4.58624e8	0.0553244
$161$	−1.11381e10	−1.30646
$162$	−6.29593e9	−0.718195
$163$	1.50186e9	0.166643	0.0833214	−	0.996523i	$-0.473447\pi$
$163$	1.50186e9	0.166643	0.0833214	+	0.996523i	$0.473447\pi$
$164$	9.06505e9	0.978527
$165$	3.54952e8	0.0372813
$166$	−1.66640e10	−1.70330
$167$	−1.86656e10	−1.85703	−0.928515	−	0.371295i	$-0.878914\pi$
$167$	−1.86656e10	−1.85703	−0.928515	+	0.371295i	$0.878914\pi$
$168$	−1.56496e10	−1.51570
$169$	−6.46131e9	−0.609299
$170$	2.40138e9	0.220516
$171$	0	0
$172$	−3.43572e10	−2.99323
$173$	−5.03149e9	−0.427060	−0.213530	−	0.976937i	$-0.568496\pi$
$173$	−5.03149e9	−0.427060	−0.213530	+	0.976937i	$0.568496\pi$
$174$	1.37710e10	1.13892
$175$	−1.23293e10	−0.993728
$176$	−6.47634e9	−0.508772
$177$	2.46211e9	0.188550
$178$	−3.42606e10	−2.55802
$179$	4.65070e9	0.338595	0.169297	−	0.985565i	$-0.445850\pi$
$179$	4.65070e9	0.338595	0.169297	+	0.985565i	$0.445850\pi$
$180$	−1.62035e9	−0.115049
$181$	3.11760e9	0.215907	0.107953	−	0.994156i	$-0.465570\pi$
$181$	3.11760e9	0.215907	0.107953	+	0.994156i	$0.465570\pi$
$182$	−1.65039e10	−1.11498
$183$	−1.42866e10	−0.941668
$184$	−3.95013e10	−2.54057
$185$	3.12075e9	0.195878
$186$	2.71178e10	1.66129
$187$	−6.02917e9	−0.360554
$188$	3.95781e10	2.31071
$189$	1.91819e10	1.09349
$190$	0	0
$191$	6.59491e9	0.358558	0.179279	−	0.983798i	$-0.442624\pi$
$191$	6.59491e9	0.358558	0.179279	+	0.983798i	$0.442624\pi$
$192$	8.68604e9	0.461282
$193$	−3.51626e10	−1.82420	−0.912100	−	0.409967i	$-0.865540\pi$
$193$	−3.51626e10	−1.82420	−0.912100	+	0.409967i	$0.865540\pi$
$194$	−3.57116e10	−1.81010
$195$	1.25295e9	0.0620551
$196$	9.53027e8	0.0461268
$197$	−3.06100e10	−1.44799	−0.723994	−	0.689806i	$-0.757696\pi$
$197$	−3.06100e10	−1.44799	−0.723994	+	0.689806i	$0.757696\pi$
$198$	5.99270e9	0.277095
$199$	2.50639e10	1.13295	0.566474	−	0.824080i	$-0.308307\pi$
$199$	2.50639e10	1.13295	0.566474	+	0.824080i	$0.308307\pi$
$200$	−4.37257e10	−1.93242
$201$	4.26050e9	0.184110
$202$	1.07015e10	0.452234
$203$	−2.06945e10	−0.855308
$204$	−3.82973e10	−1.54822
$205$	1.52343e9	0.0602461
$206$	−8.47350e9	−0.327839
$207$	1.42762e10	0.540438
$208$	−2.28609e10	−0.846855
$209$	0	0
$210$	−4.99097e9	−0.177092
$211$	−2.75875e10	−0.958166	−0.479083	−	0.877770i	$-0.659031\pi$
$211$	−2.75875e10	−0.958166	−0.479083	+	0.877770i	$0.659031\pi$
$212$	−5.42692e10	−1.84519
$213$	4.30787e10	1.43402
$214$	−3.70530e10	−1.20771
$215$	−5.77389e9	−0.184287
$216$	6.80285e10	2.12642
$217$	−4.07514e10	−1.24759
$218$	4.86105e10	1.45773
$219$	−3.37393e10	−0.991145
$220$	−3.58992e9	−0.103319
$221$	−2.12824e10	−0.600145
$222$	−7.33133e10	−2.02579
$223$	−2.54059e10	−0.687958	−0.343979	−	0.938977i	$-0.611775\pi$
$223$	−2.54059e10	−0.687958	−0.343979	+	0.938977i	$0.611775\pi$
$224$	1.61908e10	0.429688
$225$	1.58030e10	0.411071
$226$	−1.09853e10	−0.280107
$227$	−2.45390e10	−0.613394	−0.306697	−	0.951807i	$-0.599224\pi$
$227$	−2.45390e10	−0.613394	−0.306697	+	0.951807i	$0.599224\pi$
$228$	0	0
$229$	−2.99198e10	−0.718950	−0.359475	−	0.933155i	$-0.617044\pi$
$229$	−2.99198e10	−0.718950	−0.359475	+	0.933155i	$0.617044\pi$
$230$	−1.25977e10	−0.296836
$231$	1.25309e10	0.289553
$232$	−7.33927e10	−1.66325
$233$	−2.01019e10	−0.446823	−0.223411	−	0.974724i	$-0.571719\pi$
$233$	−2.01019e10	−0.446823	−0.223411	+	0.974724i	$0.571719\pi$
$234$	2.11537e10	0.461227
$235$	6.65130e9	0.142266
$236$	−2.49013e10	−0.522538
$237$	−2.28893e9	−0.0471266
$238$	8.47761e10	1.71268
$239$	3.34671e10	0.663480	0.331740	−	0.943371i	$-0.392364\pi$
$239$	3.34671e10	0.663480	0.331740	+	0.943371i	$0.392364\pi$
$240$	−6.91341e9	−0.134506
$241$	−2.19604e10	−0.419337	−0.209669	−	0.977772i	$-0.567239\pi$
$241$	−2.19604e10	−0.419337	−0.209669	+	0.977772i	$0.567239\pi$
$242$	−8.08741e10	−1.51579
$243$	−4.19230e10	−0.771302
$244$	1.44492e11	2.60969
$245$	1.60161e8	0.00283994
$246$	−3.57887e10	−0.623071
$247$	0	0
$248$	−1.44524e11	−2.42609
$249$	4.46618e10	0.736274
$250$	−2.81302e10	−0.455452
$251$	6.17049e9	0.0981269	0.0490635	−	0.998796i	$-0.484376\pi$
$251$	6.17049e9	0.0981269	0.0490635	+	0.998796i	$0.484376\pi$
$252$	−5.72033e10	−0.893550
$253$	3.16292e10	0.485339
$254$	1.88733e11	2.84510
$255$	−6.43606e9	−0.0953211
$256$	−1.39396e11	−2.02848
$257$	1.03169e11	1.47520	0.737601	−	0.675237i	$-0.235959\pi$
$257$	1.03169e11	1.47520	0.737601	+	0.675237i	$0.235959\pi$
$258$	1.35642e11	1.90592
$259$	1.10172e11	1.52132
$260$	−1.26721e10	−0.171976
$261$	2.65249e10	0.353811
$262$	1.21105e11	1.58784
$263$	1.39732e11	1.80093	0.900464	−	0.434930i	$-0.143227\pi$
$263$	1.39732e11	1.80093	0.900464	+	0.434930i	$0.143227\pi$
$264$	4.44406e10	0.563069
$265$	−9.12020e9	−0.113605
$266$	0	0
$267$	9.18233e10	1.10574
$268$	−4.30899e10	−0.510233
$269$	5.18387e10	0.603627	0.301814	−	0.953367i	$-0.402408\pi$
$269$	5.18387e10	0.603627	0.301814	+	0.953367i	$0.402408\pi$
$270$	2.16956e10	0.248447
$271$	1.43226e11	1.61309	0.806546	−	0.591171i	$-0.201334\pi$
$271$	1.43226e11	1.61309	0.806546	+	0.591171i	$0.201334\pi$
$272$	1.17430e11	1.30083
$273$	4.42329e10	0.481963
$274$	2.01185e11	2.15634
$275$	3.50117e10	0.369162
$276$	2.00909e11	2.08405
$277$	−6.54070e10	−0.667522	−0.333761	−	0.942658i	$-0.608318\pi$
$277$	−6.54070e10	−0.667522	−0.333761	+	0.942658i	$0.608318\pi$
$278$	−3.28917e11	−3.30282
$279$	5.22326e10	0.516087
$280$	2.65994e10	0.258619
$281$	6.76622e9	0.0647392	0.0323696	−	0.999476i	$-0.489695\pi$
$281$	6.76622e9	0.0647392	0.0323696	+	0.999476i	$0.489695\pi$
$282$	−1.56254e11	−1.47133
$283$	−9.51839e10	−0.882114	−0.441057	−	0.897479i	$-0.645396\pi$
$283$	−9.51839e10	−0.882114	−0.441057	+	0.897479i	$0.645396\pi$
$284$	−4.35691e11	−3.97416
$285$	0	0
$286$	4.68664e10	0.414204
$287$	5.37816e10	0.467913
$288$	−2.07524e10	−0.177747
$289$	−9.26566e9	−0.0781333
$290$	−2.34063e10	−0.194331
$291$	9.57124e10	0.782438
$292$	3.41233e11	2.74681
$293$	8.03280e10	0.636741	0.318370	−	0.947966i	$-0.396864\pi$
$293$	8.03280e10	0.636741	0.318370	+	0.947966i	$0.396864\pi$
$294$	−3.76254e9	−0.0293710
$295$	−4.18479e9	−0.0321717
$296$	3.90723e11	2.95840
$297$	−5.44713e10	−0.406222
$298$	−2.99713e11	−2.20157
$299$	1.11648e11	0.807852
$300$	2.22395e11	1.58518
$301$	−2.03836e11	−1.43130
$302$	7.64793e10	0.529069
$303$	−2.86816e10	−0.195484
$304$	0	0
$305$	2.42826e10	0.160674
$306$	−1.08661e11	−0.708478
$307$	−1.85563e11	−1.19225	−0.596127	−	0.802890i	$-0.703294\pi$
$307$	−1.85563e11	−1.19225	−0.596127	+	0.802890i	$0.703294\pi$
$308$	−1.26735e11	−0.802451
$309$	2.27102e10	0.141713
$310$	−4.60915e10	−0.283461
$311$	9.88281e10	0.599044	0.299522	−	0.954089i	$-0.403173\pi$
$311$	9.88281e10	0.599044	0.299522	+	0.954089i	$0.403173\pi$
$312$	1.56871e11	0.937234
$313$	2.06245e11	1.21460	0.607302	−	0.794471i	$-0.292252\pi$
$313$	2.06245e11	1.21460	0.607302	+	0.794471i	$0.292252\pi$
$314$	1.55269e11	0.901365
$315$	−9.61330e9	−0.0550142
$316$	2.31499e10	0.130604
$317$	1.88922e11	1.05079	0.525395	−	0.850859i	$-0.323918\pi$
$317$	1.88922e11	1.05079	0.525395	+	0.850859i	$0.323918\pi$
$318$	2.14254e11	1.17492
$319$	5.87665e10	0.317740
$320$	−1.47635e10	−0.0787070
$321$	9.93075e10	0.522047
$322$	−4.44738e11	−2.30543
$323$	0	0
$324$	−1.70661e11	−0.860362
$325$	1.23588e11	0.614473
$326$	5.99683e10	0.294064
$327$	−1.30283e11	−0.630121
$328$	1.90736e11	0.909913
$329$	2.34811e11	1.10494
$330$	1.41729e10	0.0657881
$331$	2.71848e11	1.24480	0.622402	−	0.782698i	$-0.286157\pi$
$331$	2.71848e11	1.24480	0.622402	+	0.782698i	$0.286157\pi$
$332$	−4.51702e11	−2.04047
$333$	−1.41212e11	−0.629320
$334$	−7.45305e11	−3.27699
$335$	−7.24147e9	−0.0314141
$336$	−2.44064e11	−1.04467
$337$	−1.23731e11	−0.522568	−0.261284	−	0.965262i	$-0.584146\pi$
$337$	−1.23731e11	−0.522568	−0.261284	+	0.965262i	$0.584146\pi$
$338$	−2.57995e11	−1.07519
$339$	2.94422e10	0.121080
$340$	6.50931e10	0.264168
$341$	1.15722e11	0.463471
$342$	0	0
$343$	−2.53472e11	−0.988794
$344$	−7.22902e11	−2.78334
$345$	3.37637e10	0.128311
$346$	−2.00903e11	−0.753606
$347$	−1.41674e9	−0.00524576	−0.00262288	−	0.999997i	$-0.500835\pi$
$347$	−1.41674e9	−0.00524576	−0.00262288	+	0.999997i	$0.500835\pi$
$348$	3.73285e11	1.36438
$349$	2.08793e11	0.753359	0.376680	−	0.926344i	$-0.377066\pi$
$349$	2.08793e11	0.753359	0.376680	+	0.926344i	$0.377066\pi$
$350$	−4.92300e11	−1.75357
$351$	−1.92279e11	−0.676160
$352$	−4.59774e10	−0.159625
$353$	1.94968e11	0.668309	0.334154	−	0.942518i	$-0.391549\pi$
$353$	1.94968e11	0.668309	0.334154	+	0.942518i	$0.391549\pi$
$354$	9.83100e10	0.332723
$355$	−7.32200e10	−0.244682
$356$	−9.28685e11	−3.06438
$357$	−2.27212e11	−0.740330
$358$	1.85699e11	0.597497
$359$	−1.83608e11	−0.583401	−0.291700	−	0.956510i	$-0.594221\pi$
$359$	−1.83608e11	−0.583401	−0.291700	+	0.956510i	$0.594221\pi$
$360$	−3.40934e10	−0.106982
$361$	0	0
$362$	1.24483e11	0.380997
$363$	2.16754e11	0.655222
$364$	−4.47364e11	−1.33569
$365$	5.73459e10	0.169116
$366$	−5.70452e11	−1.66170
$367$	3.69522e10	0.106327	0.0531635	−	0.998586i	$-0.483070\pi$
$367$	3.69522e10	0.106327	0.0531635	+	0.998586i	$0.483070\pi$
$368$	−6.16043e11	−1.75104
$369$	−6.89340e10	−0.193560
$370$	1.24609e11	0.345654
$371$	−3.21971e11	−0.882337
$372$	7.35069e11	1.99015
$373$	4.19970e11	1.12338	0.561692	−	0.827346i	$-0.310150\pi$
$373$	4.19970e11	1.12338	0.561692	+	0.827346i	$0.310150\pi$
$374$	−2.40740e11	−0.636248
$375$	7.53931e10	0.196875
$376$	8.32755e11	2.14868
$377$	2.07441e11	0.528880
$378$	7.65920e11	1.92961
$379$	2.17132e11	0.540565	0.270282	−	0.962781i	$-0.412883\pi$
$379$	2.17132e11	0.540565	0.270282	+	0.962781i	$0.412883\pi$
$380$	0	0
$381$	−5.05833e11	−1.22983
$382$	2.63330e11	0.632725
$383$	−1.28220e11	−0.304481	−0.152241	−	0.988343i	$-0.548649\pi$
$383$	−1.28220e11	−0.304481	−0.152241	+	0.988343i	$0.548649\pi$
$384$	4.84980e11	1.13824
$385$	−2.12984e10	−0.0494054
$386$	−1.40401e12	−3.21906
$387$	2.61265e11	0.592081
$388$	−9.68018e11	−2.16841
$389$	6.65133e11	1.47277	0.736386	−	0.676562i	$-0.236531\pi$
$389$	6.65133e11	1.47277	0.736386	+	0.676562i	$0.236531\pi$
$390$	5.00292e10	0.109505
$391$	−5.73507e11	−1.24092
$392$	2.00524e10	0.0428924
$393$	−3.24579e11	−0.686362
$394$	−1.22223e12	−2.55518
$395$	3.89045e9	0.00804105
$396$	1.62441e11	0.331946
$397$	7.36476e11	1.48799	0.743997	−	0.668183i	$-0.232928\pi$
$397$	7.36476e11	1.48799	0.743997	+	0.668183i	$0.232928\pi$
$398$	1.00078e12	1.99924
$399$	0	0
$400$	−6.81925e11	−1.33189
$401$	1.75865e11	0.339649	0.169824	−	0.985474i	$-0.445680\pi$
$401$	1.75865e11	0.339649	0.169824	+	0.985474i	$0.445680\pi$
$402$	1.70118e11	0.324888
$403$	4.08490e11	0.771451
$404$	2.90080e11	0.541754
$405$	−2.86804e10	−0.0529709
$406$	−8.26315e11	−1.50931
$407$	−3.12857e11	−0.565160
$408$	−8.05806e11	−1.43966
$409$	−9.19184e11	−1.62423	−0.812115	−	0.583497i	$-0.801684\pi$
$409$	−9.19184e11	−1.62423	−0.812115	+	0.583497i	$0.801684\pi$
$410$	6.08292e10	0.106313
$411$	−5.39206e11	−0.932108
$412$	−2.29687e11	−0.392735
$413$	−1.47736e11	−0.249868
$414$	5.70037e11	0.953678
$415$	−7.59107e10	−0.125628
$416$	−1.62296e11	−0.265698
$417$	8.81547e11	1.42769
$418$	0	0
$419$	7.74552e10	0.122769	0.0613843	−	0.998114i	$-0.480448\pi$
$419$	7.74552e10	0.122769	0.0613843	+	0.998114i	$0.480448\pi$
$420$	−1.35288e11	−0.212147
$421$	4.12516e11	0.639988	0.319994	−	0.947420i	$-0.396319\pi$
$421$	4.12516e11	0.639988	0.319994	+	0.947420i	$0.396319\pi$
$422$	−1.10155e12	−1.69082
$423$	−3.00967e11	−0.457074
$424$	−1.14187e12	−1.71581
$425$	−6.34840e11	−0.943875
$426$	1.72010e12	2.53052
$427$	8.57249e11	1.24790
$428$	−1.00438e12	−1.44677
$429$	−1.25609e11	−0.179045
$430$	−2.30547e11	−0.325201
$431$	5.92960e11	0.827709	0.413854	−	0.910343i	$-0.364182\pi$
$431$	5.92960e11	0.827709	0.413854	+	0.910343i	$0.364182\pi$
$432$	1.06094e12	1.46559
$433$	1.60832e10	0.0219875	0.0109938	−	0.999940i	$-0.496501\pi$
$433$	1.60832e10	0.0219875	0.0109938	+	0.999940i	$0.496501\pi$
$434$	−1.62717e12	−2.20155
$435$	6.27324e10	0.0840021
$436$	1.31766e12	1.74628
$437$	0	0
$438$	−1.34718e12	−1.74901
$439$	6.10409e11	0.784387	0.392194	−	0.919883i	$-0.371716\pi$
$439$	6.10409e11	0.784387	0.392194	+	0.919883i	$0.371716\pi$
$440$	−7.55346e10	−0.0960747
$441$	−7.24717e9	−0.00912420
$442$	−8.49792e11	−1.05904
$443$	1.38930e12	1.71388	0.856939	−	0.515418i	$-0.172363\pi$
$443$	1.38930e12	1.71388	0.856939	+	0.515418i	$0.172363\pi$
$444$	−1.98727e12	−2.42680
$445$	−1.56070e11	−0.188669
$446$	−1.01444e12	−1.21400
$447$	8.03275e11	0.951657
$448$	−5.21195e11	−0.611293
$449$	−8.03312e11	−0.932773	−0.466386	−	0.884581i	$-0.654444\pi$
$449$	−8.03312e11	−0.932773	−0.466386	+	0.884581i	$0.654444\pi$
$450$	6.31000e11	0.725392
$451$	−1.52725e11	−0.173826
$452$	−2.97773e11	−0.335554
$453$	−2.04976e11	−0.228697
$454$	−9.79821e11	−1.08242
$455$	−7.51817e10	−0.0822357
$456$	0	0
$457$	4.96584e11	0.532562	0.266281	−	0.963895i	$-0.414205\pi$
$457$	4.96584e11	0.532562	0.266281	+	0.963895i	$0.414205\pi$
$458$	−1.19467e12	−1.26869
$459$	9.87685e11	1.03863
$460$	−3.41480e11	−0.355595
$461$	5.85369e11	0.603636	0.301818	−	0.953366i	$-0.402406\pi$
$461$	5.85369e11	0.603636	0.301818	+	0.953366i	$0.402406\pi$
$462$	5.00348e11	0.510956
$463$	8.41165e11	0.850681	0.425340	−	0.905033i	$-0.360154\pi$
$463$	8.41165e11	0.850681	0.425340	+	0.905033i	$0.360154\pi$
$464$	−1.14460e12	−1.14636
$465$	1.23532e11	0.122530
$466$	−8.02653e11	−0.788481
$467$	−6.37598e11	−0.620328	−0.310164	−	0.950683i	$-0.600384\pi$
$467$	−6.37598e11	−0.620328	−0.310164	+	0.950683i	$0.600384\pi$
$468$	5.73403e11	0.552527
$469$	−2.55646e11	−0.243984
$470$	2.65581e11	0.251048
$471$	−4.16143e11	−0.389627
$472$	−5.23943e11	−0.485898
$473$	5.78837e11	0.531718
$474$	−9.13954e10	−0.0831614
$475$	0	0
$476$	2.29799e12	2.05171
$477$	4.12683e11	0.364992
$478$	1.33632e12	1.17080
$479$	1.94352e12	1.68686	0.843429	−	0.537241i	$-0.180533\pi$
$479$	1.94352e12	1.68686	0.843429	+	0.537241i	$0.180533\pi$
$480$	−4.90802e10	−0.0422008
$481$	−1.10436e12	−0.940713
$482$	−8.76861e11	−0.739979
$483$	1.19196e12	0.996553
$484$	−2.19222e12	−1.81585
$485$	−1.62680e11	−0.133505
$486$	−1.67395e12	−1.36107
$487$	7.63579e11	0.615139	0.307570	−	0.951526i	$-0.400484\pi$
$487$	7.63579e11	0.615139	0.307570	+	0.951526i	$0.400484\pi$
$488$	3.04022e12	2.42670
$489$	−1.60724e11	−0.127113
$490$	6.39510e9	0.00501147
$491$	−1.54877e12	−1.20260	−0.601298	−	0.799025i	$-0.705350\pi$
$491$	−1.54877e12	−1.20260	−0.601298	+	0.799025i	$0.705350\pi$
$492$	−9.70107e11	−0.746409
$493$	−1.06557e12	−0.812399
$494$	0	0
$495$	2.72990e10	0.0204373
$496$	−2.25393e12	−1.67214
$497$	−2.58489e12	−1.90037
$498$	1.78331e12	1.29926
$499$	2.24210e12	1.61883	0.809417	−	0.587234i	$-0.199783\pi$
$499$	2.24210e12	1.61883	0.809417	+	0.587234i	$0.199783\pi$
$500$	−7.62512e11	−0.545609
$501$	1.99753e12	1.41652
$502$	2.46383e11	0.173159
$503$	−2.20646e11	−0.153688	−0.0768439	−	0.997043i	$-0.524484\pi$
$503$	−2.20646e11	−0.153688	−0.0768439	+	0.997043i	$0.524484\pi$
$504$	−1.20360e12	−0.830894
$505$	4.87495e10	0.0333548
$506$	1.26293e12	0.856449
$507$	6.91465e11	0.464766
$508$	5.11591e12	3.40828
$509$	−2.80660e12	−1.85332	−0.926662	−	0.375896i	$-0.877335\pi$
$509$	−2.80660e12	−1.85332	−0.926662	+	0.375896i	$0.877335\pi$
$510$	−2.56987e11	−0.168207
$511$	2.02449e12	1.31347
$512$	−3.24567e12	−2.08732
$513$	0	0
$514$	4.11947e12	2.60320
$515$	−3.86001e10	−0.0241800
$516$	3.67677e12	2.28320
$517$	−6.66798e11	−0.410475
$518$	4.39908e12	2.68459
$519$	5.38450e11	0.325756
$520$	−2.66631e11	−0.159917
$521$	−1.44996e12	−0.862155	−0.431077	−	0.902315i	$-0.641866\pi$
$521$	−1.44996e12	−0.862155	−0.431077	+	0.902315i	$0.641866\pi$
$522$	1.05912e12	0.624349
$523$	2.88902e11	0.168847	0.0844233	−	0.996430i	$-0.473095\pi$
$523$	2.88902e11	0.168847	0.0844233	+	0.996430i	$0.473095\pi$
$524$	3.28273e12	1.90215
$525$	1.31944e12	0.758004
$526$	5.57941e12	3.17799
$527$	−2.09830e12	−1.18500
$528$	6.93074e11	0.388085
$529$	1.20748e12	0.670393
$530$	−3.64163e11	−0.200472
$531$	1.89359e11	0.103362
$532$	0	0
$533$	−5.39104e11	−0.289335
$534$	3.66643e12	1.95123
$535$	−1.68791e11	−0.0890752
$536$	−9.06645e11	−0.474456
$537$	−4.97701e11	−0.258276
$538$	2.06988e12	1.06518
$539$	−1.60562e10	−0.00819398
$540$	5.88092e11	0.297628
$541$	7.39497e11	0.371149	0.185575	−	0.982630i	$-0.440585\pi$
$541$	7.39497e11	0.371149	0.185575	+	0.982630i	$0.440585\pi$
$542$	5.71889e12	2.84652
$543$	−3.33633e11	−0.164691
$544$	8.33672e11	0.408131
$545$	2.21440e11	0.107515
$546$	1.76618e12	0.850490
$547$	−1.60956e12	−0.768712	−0.384356	−	0.923185i	$-0.625577\pi$
$547$	−1.60956e12	−0.768712	−0.384356	+	0.923185i	$0.625577\pi$
$548$	5.45343e12	2.58319
$549$	−1.09877e12	−0.516215
$550$	1.39799e12	0.651437
$551$	0	0
$552$	4.22728e12	1.93792
$553$	1.37345e11	0.0624524
$554$	−2.61165e12	−1.17793
$555$	−3.33971e11	−0.149413
$556$	−8.91580e12	−3.95662
$557$	−4.85306e10	−0.0213632	−0.0106816	−	0.999943i	$-0.503400\pi$
$557$	−4.85306e10	−0.0213632	−0.0106816	+	0.999943i	$0.503400\pi$
$558$	2.08561e12	0.910707
$559$	2.04324e12	0.885048
$560$	4.14831e11	0.178248
$561$	6.45219e11	0.275026
$562$	2.70170e11	0.114241
$563$	−4.23336e12	−1.77581	−0.887906	−	0.460025i	$-0.847840\pi$
$563$	−4.23336e12	−1.77581	−0.887906	+	0.460025i	$0.847840\pi$
$564$	−4.23550e12	−1.76258
$565$	−5.00423e10	−0.0206595
$566$	−3.80062e12	−1.55661
$567$	−1.01251e12	−0.411409
$568$	−9.16727e12	−3.69549
$569$	3.38804e12	1.35501	0.677505	−	0.735518i	$-0.263061\pi$
$569$	3.38804e12	1.35501	0.677505	+	0.735518i	$0.263061\pi$
$570$	0	0
$571$	−1.94511e12	−0.765740	−0.382870	−	0.923802i	$-0.625064\pi$
$571$	−1.94511e12	−0.765740	−0.382870	+	0.923802i	$0.625064\pi$
$572$	1.27039e12	0.496196
$573$	−7.05762e11	−0.273503
$574$	2.14746e12	0.825698
$575$	3.33039e12	1.27054
$576$	6.68036e11	0.252871
$577$	3.75269e12	1.40945	0.704727	−	0.709478i	$-0.251069\pi$
$577$	3.75269e12	1.40945	0.704727	+	0.709478i	$0.251069\pi$
$578$	−3.69971e11	−0.137877
$579$	3.76296e12	1.39148
$580$	−6.34464e11	−0.232799
$581$	−2.67988e12	−0.975715
$582$	3.82172e12	1.38072
$583$	9.14307e11	0.327781
$584$	7.17981e12	2.55420
$585$	9.63632e10	0.0340181
$586$	3.20743e12	1.12362
$587$	−3.23541e12	−1.12476	−0.562378	−	0.826880i	$-0.690113\pi$
$587$	−3.23541e12	−1.12476	−0.562378	+	0.826880i	$0.690113\pi$
$588$	−1.01989e11	−0.0351850
$589$	0	0
$590$	−1.67095e11	−0.0567715
$591$	3.27576e12	1.10451
$592$	6.09353e12	2.03902
$593$	7.00335e11	0.232573	0.116287	−	0.993216i	$-0.462901\pi$
$593$	7.00335e11	0.232573	0.116287	+	0.993216i	$0.462901\pi$
$594$	−2.17500e12	−0.716836
$595$	3.86188e11	0.126320
$596$	−8.12418e12	−2.63737
$597$	−2.68224e12	−0.864199
$598$	4.45803e12	1.42557
$599$	3.39955e12	1.07895	0.539475	−	0.842002i	$-0.318623\pi$
$599$	3.39955e12	1.07895	0.539475	+	0.842002i	$0.318623\pi$
$600$	4.67936e12	1.47403
$601$	−5.37340e12	−1.68002	−0.840010	−	0.542571i	$-0.817451\pi$
$601$	−5.37340e12	−1.68002	−0.840010	+	0.542571i	$0.817451\pi$
$602$	−8.13902e12	−2.52574
$603$	3.27671e11	0.100928
$604$	2.07309e12	0.633799
$605$	−3.68413e11	−0.111798
$606$	−1.14523e12	−0.344959
$607$	−2.42544e12	−0.725171	−0.362586	−	0.931950i	$-0.618106\pi$
$607$	−2.42544e12	−0.725171	−0.362586	+	0.931950i	$0.618106\pi$
$608$	0	0
$609$	2.21464e12	0.652419
$610$	9.69584e11	0.283531
$611$	−2.35374e12	−0.683239
$612$	−2.94542e12	−0.848722
$613$	−4.05784e12	−1.16071	−0.580354	−	0.814364i	$-0.697086\pi$
$613$	−4.05784e12	−1.16071	−0.580354	+	0.814364i	$0.697086\pi$
$614$	−7.40938e12	−2.10390
$615$	−1.63031e11	−0.0459550
$616$	−2.66660e12	−0.746183
$617$	7.01475e12	1.94863	0.974314	−	0.225193i	$-0.0723012\pi$
$617$	7.01475e12	1.94863	0.974314	+	0.225193i	$0.0723012\pi$
$618$	9.06802e11	0.250072
$619$	2.70616e12	0.740876	0.370438	−	0.928857i	$-0.379208\pi$
$619$	2.70616e12	0.740876	0.370438	+	0.928857i	$0.379208\pi$
$620$	−1.24938e12	−0.339572
$621$	−5.18142e12	−1.39809
$622$	3.94613e12	1.05710
$623$	−5.50975e12	−1.46533
$624$	2.44649e12	0.645971
$625$	3.62193e12	0.949468
$626$	8.23522e12	2.14334
$627$	0	0
$628$	4.20880e12	1.07979
$629$	5.67279e12	1.44500
$630$	−3.83852e11	−0.0970802
$631$	−3.52498e12	−0.885166	−0.442583	−	0.896728i	$-0.645938\pi$
$631$	−3.52498e12	−0.885166	−0.442583	+	0.896728i	$0.645938\pi$
$632$	4.87091e11	0.121446
$633$	2.95231e12	0.730878
$634$	7.54351e12	1.85426
$635$	8.59753e11	0.209842
$636$	5.80768e12	1.40749
$637$	−5.66772e10	−0.0136389
$638$	2.34650e12	0.560696
$639$	3.31315e12	0.786118
$640$	−8.24309e11	−0.194214
$641$	−7.85515e12	−1.83778	−0.918890	−	0.394514i	$-0.870913\pi$
$641$	−7.85515e12	−1.83778	−0.918890	+	0.394514i	$0.870913\pi$
$642$	3.96527e12	0.921224
$643$	1.50093e12	0.346266	0.173133	−	0.984898i	$-0.444611\pi$
$643$	1.50093e12	0.346266	0.173133	+	0.984898i	$0.444611\pi$
$644$	−1.20553e13	−2.76179
$645$	6.17900e11	0.140572
$646$	0	0
$647$	2.99482e12	0.671896	0.335948	−	0.941881i	$-0.390943\pi$
$647$	2.99482e12	0.671896	0.335948	+	0.941881i	$0.390943\pi$
$648$	−3.59084e12	−0.800033
$649$	4.19528e11	0.0928239
$650$	4.93479e12	1.08432
$651$	4.36106e12	0.951650
$652$	1.62553e12	0.352274
$653$	−6.21285e12	−1.33715	−0.668577	−	0.743643i	$-0.733096\pi$
$653$	−6.21285e12	−1.33715	−0.668577	+	0.743643i	$0.733096\pi$
$654$	−5.20211e12	−1.11194
$655$	5.51679e11	0.117112
$656$	2.97462e12	0.627140
$657$	−2.59486e12	−0.543338
$658$	9.37583e12	1.94981
$659$	3.55299e12	0.733853	0.366927	−	0.930250i	$-0.380410\pi$
$659$	3.55299e12	0.733853	0.366927	+	0.930250i	$0.380410\pi$
$660$	3.84179e11	0.0788109
$661$	−6.55156e12	−1.33487	−0.667433	−	0.744670i	$-0.732607\pi$
$661$	−6.55156e12	−1.33487	−0.667433	+	0.744670i	$0.732607\pi$
$662$	1.08547e13	2.19663
$663$	2.27757e12	0.457784
$664$	−9.50416e12	−1.89739
$665$	0	0
$666$	−5.63847e12	−1.11052
$667$	5.58999e12	1.09356
$668$	−2.02026e13	−3.92567
$669$	2.71884e12	0.524766
$670$	−2.89146e11	−0.0554346
$671$	−2.43434e12	−0.463586
$672$	−1.73268e12	−0.327761
$673$	7.46519e12	1.40273	0.701364	−	0.712803i	$-0.252575\pi$
$673$	7.46519e12	1.40273	0.701364	+	0.712803i	$0.252575\pi$
$674$	−4.94046e12	−0.922143
$675$	−5.73554e12	−1.06343
$676$	−6.99335e12	−1.28803
$677$	8.56904e10	0.0156777	0.00783887	−	0.999969i	$-0.497505\pi$
$677$	8.56904e10	0.0156777	0.00783887	+	0.999969i	$0.497505\pi$
$678$	1.17561e12	0.213662
$679$	−5.74311e12	−1.03689
$680$	1.36961e12	0.245644
$681$	2.62607e12	0.467890
$682$	4.62070e12	0.817859
$683$	−4.60458e11	−0.0809648	−0.0404824	−	0.999180i	$-0.512889\pi$
$683$	−4.60458e11	−0.0809648	−0.0404824	+	0.999180i	$0.512889\pi$
$684$	0	0
$685$	9.16476e11	0.159043
$686$	−1.01209e13	−1.74486
$687$	3.20190e12	0.548406
$688$	−1.12740e13	−1.91837
$689$	3.22742e12	0.545594
$690$	1.34816e12	0.226423
$691$	4.05489e12	0.676594	0.338297	−	0.941039i	$-0.390149\pi$
$691$	4.05489e12	0.676594	0.338297	+	0.941039i	$0.390149\pi$
$692$	−5.44579e12	−0.902783
$693$	9.63740e11	0.158730
$694$	−5.65694e10	−0.00925687
$695$	−1.49835e12	−0.243602
$696$	7.85421e12	1.26871
$697$	2.76923e12	0.444439
$698$	8.33695e12	1.32941
$699$	2.15123e12	0.340831
$700$	−1.33445e13	−2.10069
$701$	5.47520e12	0.856385	0.428193	−	0.903688i	$-0.359150\pi$
$701$	5.47520e12	0.856385	0.428193	+	0.903688i	$0.359150\pi$
$702$	−7.67755e12	−1.19318
$703$	0	0
$704$	1.48005e12	0.227090
$705$	−7.11797e11	−0.108519
$706$	7.78492e12	1.17932
$707$	1.72101e12	0.259057
$708$	2.66484e12	0.398586
$709$	8.06770e12	1.19906	0.599531	−	0.800352i	$-0.295354\pi$
$709$	8.06770e12	1.19906	0.599531	+	0.800352i	$0.295354\pi$
$710$	−2.92362e12	−0.431775
$711$	−1.76040e11	−0.0258344
$712$	−1.95402e13	−2.84951
$713$	1.10077e13	1.59513
$714$	−9.07242e12	−1.30641
$715$	2.13495e11	0.0305499
$716$	5.03366e12	0.715772
$717$	−3.58153e12	−0.506095
$718$	−7.33133e12	−1.02949
$719$	−1.14018e13	−1.59109	−0.795545	−	0.605895i	$-0.792815\pi$
$719$	−1.14018e13	−1.59109	−0.795545	+	0.605895i	$0.792815\pi$
$720$	−5.31705e11	−0.0737351
$721$	−1.36270e12	−0.187798
$722$	0	0
$723$	2.35012e12	0.319865
$724$	3.37431e12	0.456416
$725$	6.18780e12	0.831793
$726$	8.65484e12	1.15623
$727$	−1.31502e12	−0.174594	−0.0872969	−	0.996182i	$-0.527823\pi$
$727$	−1.31502e12	−0.174594	−0.0872969	+	0.996182i	$0.527823\pi$
$728$	−9.41288e12	−1.24203
$729$	7.59001e12	0.995333
$730$	2.28978e12	0.298428
$731$	−1.04956e13	−1.35950
$732$	−1.54630e13	−1.99064
$733$	−3.41047e12	−0.436361	−0.218180	−	0.975908i	$-0.570012\pi$
$733$	−3.41047e12	−0.436361	−0.218180	+	0.975908i	$0.570012\pi$
$734$	1.47547e12	0.187629
$735$	−1.71398e10	−0.00216627
$736$	−4.37346e12	−0.549383
$737$	7.25962e11	0.0906380
$738$	−2.75248e12	−0.341563
$739$	4.55484e12	0.561789	0.280895	−	0.959739i	$-0.409369\pi$
$739$	4.55484e12	0.561789	0.280895	+	0.959739i	$0.409369\pi$
$740$	3.37772e12	0.414076
$741$	0	0
$742$	−1.28561e13	−1.55701
$743$	−3.75058e12	−0.451491	−0.225746	−	0.974186i	$-0.572482\pi$
$743$	−3.75058e12	−0.451491	−0.225746	+	0.974186i	$0.572482\pi$
$744$	1.54664e13	1.85060
$745$	−1.36531e12	−0.162378
$746$	1.67691e13	1.98237
$747$	3.43491e12	0.403620
$748$	−6.52563e12	−0.762193
$749$	−5.95883e12	−0.691819
$750$	3.01039e12	0.347414
$751$	−2.90529e12	−0.333281	−0.166640	−	0.986018i	$-0.553292\pi$
$751$	−2.90529e12	−0.333281	−0.166640	+	0.986018i	$0.553292\pi$
$752$	1.29872e13	1.48094
$753$	−6.60343e11	−0.0748501
$754$	8.28294e12	0.933283
$755$	3.48393e11	0.0390218
$756$	2.07614e13	2.31158
$757$	−6.68973e12	−0.740418	−0.370209	−	0.928948i	$-0.620714\pi$
$757$	−6.68973e12	−0.740418	−0.370209	+	0.928948i	$0.620714\pi$
$758$	8.66992e12	0.953901
$759$	−3.38483e12	−0.370211
$760$	0	0
$761$	−5.25844e12	−0.568363	−0.284182	−	0.958770i	$-0.591722\pi$
$761$	−5.25844e12	−0.568363	−0.284182	+	0.958770i	$0.591722\pi$
$762$	−2.01975e13	−2.17020
$763$	7.81750e12	0.835040
$764$	7.13795e12	0.757973
$765$	−4.94992e11	−0.0522543
$766$	−5.11971e12	−0.537299
$767$	1.48090e12	0.154506
$768$	1.49176e13	1.54730
$769$	1.45825e13	1.50371	0.751856	−	0.659327i	$-0.229159\pi$
$769$	1.45825e13	1.50371	0.751856	+	0.659327i	$0.229159\pi$
$770$	−8.50430e11	−0.0871827
$771$	−1.10408e13	−1.12527
$772$	−3.80579e13	−3.85627
$773$	−2.26984e12	−0.228659	−0.114329	−	0.993443i	$-0.536472\pi$
$773$	−2.26984e12	−0.228659	−0.114329	+	0.993443i	$0.536472\pi$
$774$	1.04321e13	1.04481
$775$	1.21850e13	1.21329
$776$	−2.03679e13	−2.01636
$777$	−1.17902e13	−1.16045
$778$	2.65582e13	2.59891
$779$	0	0
$780$	1.35612e12	0.131181
$781$	7.34035e12	0.705972
$782$	−2.28997e13	−2.18977
$783$	−9.62699e12	−0.915298
$784$	3.12728e11	0.0295628
$785$	7.07309e11	0.0664807
$786$	−1.29602e13	−1.21118
$787$	1.90845e13	1.77335	0.886673	−	0.462396i	$-0.153010\pi$
$787$	1.90845e13	1.77335	0.886673	+	0.462396i	$0.153010\pi$
$788$	−3.31305e13	−3.06098
$789$	−1.49536e13	−1.37373
$790$	1.55343e11	0.0141896
$791$	−1.76665e12	−0.160456
$792$	3.41789e12	0.308670
$793$	−8.59302e12	−0.771643
$794$	2.94069e13	2.62577
$795$	9.76010e11	0.0866567
$796$	2.71277e13	2.39499
$797$	−1.20818e12	−0.106065	−0.0530323	−	0.998593i	$-0.516889\pi$
$797$	−1.20818e12	−0.106065	−0.0530323	+	0.998593i	$0.516889\pi$
$798$	0	0
$799$	1.20905e13	1.04950
$800$	−4.84118e12	−0.417875
$801$	7.06206e12	0.606157
$802$	7.02216e12	0.599358
$803$	−5.74896e12	−0.487944
$804$	4.61132e12	0.389200
$805$	−2.02595e12	−0.170039
$806$	1.63107e13	1.36133
$807$	−5.54758e12	−0.460439
$808$	6.10352e12	0.503766
$809$	1.70303e13	1.39783	0.698914	−	0.715206i	$-0.253667\pi$
$809$	1.70303e13	1.39783	0.698914	+	0.715206i	$0.253667\pi$
$810$	−1.14519e12	−0.0934745
$811$	1.48908e13	1.20871	0.604356	−	0.796714i	$-0.293430\pi$
$811$	1.48908e13	1.20871	0.604356	+	0.796714i	$0.293430\pi$
$812$	−2.23985e13	−1.80808
$813$	−1.53275e13	−1.23045
$814$	−1.24921e13	−0.997303
$815$	2.73179e11	0.0216889
$816$	−1.25670e13	−0.992258
$817$	0	0
$818$	−3.67023e13	−2.86618
$819$	3.40192e12	0.264208
$820$	1.64887e12	0.127357
$821$	−1.02969e13	−0.790971	−0.395486	−	0.918472i	$-0.629424\pi$
$821$	−1.02969e13	−0.790971	−0.395486	+	0.918472i	$0.629424\pi$
$822$	−2.15301e13	−1.64483
$823$	−2.00908e13	−1.52651	−0.763254	−	0.646099i	$-0.776399\pi$
$823$	−2.00908e13	−1.52651	−0.763254	+	0.646099i	$0.776399\pi$
$824$	−4.83280e12	−0.365196
$825$	−3.74682e12	−0.281592
$826$	−5.89898e12	−0.440927
$827$	−9.60395e12	−0.713962	−0.356981	−	0.934112i	$-0.616194\pi$
$827$	−9.60395e12	−0.713962	−0.356981	+	0.934112i	$0.616194\pi$
$828$	1.54517e13	1.14246
$829$	−6.82720e12	−0.502051	−0.251025	−	0.967981i	$-0.580768\pi$
$829$	−6.82720e12	−0.502051	−0.251025	+	0.967981i	$0.580768\pi$
$830$	−3.03106e12	−0.221688
$831$	6.99961e12	0.509178
$832$	5.22444e12	0.377994
$833$	2.91135e11	0.0209504
$834$	3.51995e13	2.51935
$835$	−3.39515e12	−0.241696
$836$	0	0
$837$	−1.89574e13	−1.33510
$838$	3.09273e12	0.216642
$839$	5.53094e12	0.385363	0.192682	−	0.981261i	$-0.438282\pi$
$839$	5.53094e12	0.385363	0.192682	+	0.981261i	$0.438282\pi$
$840$	−2.84656e12	−0.197271
$841$	−4.12105e12	−0.284070
$842$	1.64715e13	1.12935
$843$	−7.24095e11	−0.0493823
$844$	−2.98591e13	−2.02552
$845$	−1.17527e12	−0.0793015
$846$	−1.20174e13	−0.806571
$847$	−1.30061e13	−0.868304
$848$	−1.78080e13	−1.18259
$849$	1.01862e13	0.672866
$850$	−2.53487e13	−1.66560
$851$	−2.97596e13	−1.94511
$852$	4.66259e13	3.03144
$853$	6.69016e10	0.00432679	0.00216339	−	0.999998i	$-0.499311\pi$
$853$	6.69016e10	0.00432679	0.00216339	+	0.999998i	$0.499311\pi$
$854$	3.42293e13	2.20210
$855$	0	0
$856$	−2.11329e13	−1.34532
$857$	−5.34699e12	−0.338607	−0.169304	−	0.985564i	$-0.554152\pi$
$857$	−5.34699e12	−0.338607	−0.169304	+	0.985564i	$0.554152\pi$
$858$	−5.01546e12	−0.315950
$859$	4.05640e12	0.254198	0.127099	−	0.991890i	$-0.459433\pi$
$859$	4.05640e12	0.254198	0.127099	+	0.991890i	$0.459433\pi$
$860$	−6.24933e12	−0.389575
$861$	−5.75550e12	−0.356919
$862$	2.36764e13	1.46061
$863$	−2.76880e13	−1.69920	−0.849598	−	0.527431i	$-0.823155\pi$
$863$	−2.76880e13	−1.69920	−0.849598	+	0.527431i	$0.823155\pi$
$864$	7.53191e12	0.459826
$865$	−9.15192e11	−0.0555827
$866$	6.42189e11	0.0388001
$867$	9.91576e11	0.0595992
$868$	−4.41069e13	−2.63735
$869$	−3.90020e11	−0.0232005
$870$	2.50485e12	0.148233
$871$	2.56258e12	0.150868
$872$	2.77246e13	1.62383
$873$	7.36117e12	0.428926
$874$	0	0
$875$	−4.52387e12	−0.260900
$876$	−3.65175e13	−2.09523
$877$	1.42514e12	0.0813503	0.0406752	−	0.999172i	$-0.487049\pi$
$877$	1.42514e12	0.0813503	0.0406752	+	0.999172i	$0.487049\pi$
$878$	2.43731e13	1.38416
$879$	−8.59640e12	−0.485698
$880$	−1.17800e12	−0.0662177
$881$	3.73378e12	0.208813	0.104406	−	0.994535i	$-0.466706\pi$
$881$	3.73378e12	0.208813	0.104406	+	0.994535i	$0.466706\pi$
$882$	−2.89374e11	−0.0161009
$883$	6.19997e12	0.343215	0.171608	−	0.985165i	$-0.445104\pi$
$883$	6.19997e12	0.343215	0.171608	+	0.985165i	$0.445104\pi$
$884$	−2.30349e13	−1.26868
$885$	4.47840e11	0.0245402
$886$	5.54737e13	3.02437
$887$	−1.18291e13	−0.641645	−0.320822	−	0.947139i	$-0.603959\pi$
$887$	−1.18291e13	−0.641645	−0.320822	+	0.947139i	$0.603959\pi$
$888$	−4.18137e13	−2.25663
$889$	3.03519e13	1.62978
$890$	−6.23176e12	−0.332932
$891$	2.87523e12	0.152835
$892$	−2.74978e13	−1.45431
$893$	0	0
$894$	3.20741e13	1.67933
$895$	8.45931e11	0.0440688
$896$	−2.91006e13	−1.50840
$897$	−1.19482e13	−0.616220
$898$	−3.20756e13	−1.64601
$899$	2.04522e13	1.04429
$900$	1.71042e13	0.868984
$901$	−1.65784e13	−0.838072
$902$	−6.09817e12	−0.306740
$903$	2.18138e13	1.09178
$904$	−6.26538e12	−0.312025
$905$	5.67069e11	0.0281007
$906$	−8.18452e12	−0.403568
$907$	−3.41302e13	−1.67458	−0.837290	−	0.546760i	$-0.815861\pi$
$907$	−3.41302e13	−1.67458	−0.837290	+	0.546760i	$0.815861\pi$
$908$	−2.65596e13	−1.29669
$909$	−2.20588e12	−0.107163
$910$	−3.00194e12	−0.145116
$911$	−1.93918e13	−0.932795	−0.466398	−	0.884575i	$-0.654448\pi$
$911$	−1.93918e13	−0.932795	−0.466398	+	0.884575i	$0.654448\pi$
$912$	0	0
$913$	7.61010e12	0.362470
$914$	1.98282e13	0.939780
$915$	−2.59863e12	−0.122560
$916$	−3.23834e13	−1.51982
$917$	1.94760e13	0.909572
$918$	3.94375e13	1.83281
$919$	−8.70535e12	−0.402593	−0.201296	−	0.979530i	$-0.564515\pi$
$919$	−8.70535e12	−0.402593	−0.201296	+	0.979530i	$0.564515\pi$
$920$	−7.18501e12	−0.330660
$921$	1.98582e13	0.909437
$922$	2.33733e13	1.06520
$923$	2.59108e13	1.17510
$924$	1.35627e13	0.612100
$925$	−3.29422e13	−1.47950
$926$	3.35871e13	1.50114
$927$	1.74663e12	0.0776858
$928$	−8.12582e12	−0.359667
$929$	−3.68510e12	−0.162322	−0.0811612	−	0.996701i	$-0.525863\pi$
$929$	−3.68510e12	−0.162322	−0.0811612	+	0.996701i	$0.525863\pi$
$930$	4.93253e12	0.216221
$931$	0	0
$932$	−2.17571e13	−0.944561
$933$	−1.05762e13	−0.456944
$934$	−2.54588e13	−1.09465
$935$	−1.09666e12	−0.0469269
$936$	1.20649e13	0.513784
$937$	−1.93364e13	−0.819496	−0.409748	−	0.912199i	$-0.634383\pi$
$937$	−1.93364e13	−0.819496	−0.409748	+	0.912199i	$0.634383\pi$
$938$	−1.02077e13	−0.430544
$939$	−2.20716e13	−0.926486
$940$	7.19899e12	0.300743
$941$	−2.68822e13	−1.11766	−0.558831	−	0.829281i	$-0.688750\pi$
$941$	−2.68822e13	−1.11766	−0.558831	+	0.829281i	$0.688750\pi$
$942$	−1.66163e13	−0.687550
$943$	−1.45275e13	−0.598256
$944$	−8.17116e12	−0.334896
$945$	3.48906e12	0.142320
$946$	2.31125e13	0.938290
$947$	−7.58766e12	−0.306572	−0.153286	−	0.988182i	$-0.548986\pi$
$947$	−7.58766e12	−0.306572	−0.153286	+	0.988182i	$0.548986\pi$
$948$	−2.47741e12	−0.0996232
$949$	−2.02933e13	−0.812186
$950$	0	0
$951$	−2.02177e13	−0.801530
$952$	4.83514e13	1.90784
$953$	8.62064e12	0.338549	0.169274	−	0.985569i	$-0.445858\pi$
$953$	8.62064e12	0.338549	0.169274	+	0.985569i	$0.445858\pi$
$954$	1.64781e13	0.644080
$955$	1.19957e12	0.0466670
$956$	3.62229e13	1.40256
$957$	−6.28896e12	−0.242368
$958$	7.76031e13	2.97669
$959$	3.23544e13	1.23523
$960$	1.57993e12	0.0600367
$961$	1.38346e13	0.523253
$962$	−4.40962e13	−1.66002
$963$	7.63766e12	0.286182
$964$	−2.37687e13	−0.886458
$965$	−6.39583e12	−0.237424
$966$	4.75941e13	1.75856
$967$	−3.25923e13	−1.19866	−0.599330	−	0.800502i	$-0.704566\pi$
$967$	−3.25923e13	−1.19866	−0.599330	+	0.800502i	$0.704566\pi$
$968$	−4.61259e13	−1.68852
$969$	0	0
$970$	−6.49569e12	−0.235588
$971$	−2.82778e13	−1.02084	−0.510422	−	0.859924i	$-0.670511\pi$
$971$	−2.82778e13	−1.02084	−0.510422	+	0.859924i	$0.670511\pi$
$972$	−4.53751e13	−1.63049
$973$	−5.28962e13	−1.89198
$974$	3.04891e13	1.08550
$975$	−1.32260e13	−0.468712
$976$	4.74138e13	1.67256
$977$	2.35542e13	0.827071	0.413536	−	0.910488i	$-0.364294\pi$
$977$	2.35542e13	0.827071	0.413536	+	0.910488i	$0.364294\pi$
$978$	−6.41757e12	−0.224309
$979$	1.56461e13	0.544358
$980$	1.73349e11	0.00600350
$981$	−1.00200e13	−0.345427
$982$	−6.18411e13	−2.12215
$983$	5.24215e13	1.79068	0.895342	−	0.445380i	$-0.146931\pi$
$983$	5.24215e13	1.79068	0.895342	+	0.445380i	$0.146931\pi$
$984$	−2.04118e13	−0.694070
$985$	−5.56774e12	−0.188459
$986$	−4.25472e13	−1.43359
$987$	−2.51286e13	−0.842833
$988$	0	0
$989$	5.50601e13	1.83001
$990$	1.09003e12	0.0360645
$991$	6.06921e12	0.199894	0.0999472	−	0.994993i	$-0.468133\pi$
$991$	6.06921e12	0.199894	0.0999472	+	0.994993i	$0.468133\pi$
$992$	−1.60013e13	−0.524629
$993$	−2.90922e13	−0.949521
$994$	−1.03213e14	−3.35347
$995$	4.55895e12	0.147455
$996$	4.83394e13	1.55645
$997$	−5.37864e13	−1.72403	−0.862014	−	0.506884i	$-0.830797\pi$
$997$	−5.37864e13	−1.72403	−0.862014	+	0.506884i	$0.830797\pi$
$998$	8.95253e13	2.85666
$999$	5.12515e13	1.62803

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.10.a.e.1.14		14
19.7	even	3		19.10.c.a.11.1	yes	28
19.11	even	3		19.10.c.a.7.1	✓	28
19.18	odd	2		361.10.a.f.1.1		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.10.c.a.7.1	✓	28	19.11	even	3
19.10.c.a.11.1	yes	28	19.7	even	3
361.10.a.e.1.14		14	1.1	even	1	trivial
361.10.a.f.1.1		14	19.18	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	361.a (trivial)

\(f(q)\)	\(=\)	\(q+39.9292 q^{2} -107.016 q^{3} +1082.34 q^{4} +181.893 q^{5} -4273.07 q^{6} +6421.38 q^{7} +22773.3 q^{8} -8230.53 q^{9} +7262.85 q^{10} -18234.9 q^{11} -115828. q^{12} -64367.6 q^{13} +256401. q^{14} -19465.5 q^{15} +355162. q^{16} +330639. q^{17} -328639. q^{18} +196871. q^{20} -687192. q^{21} -728105. q^{22} -1.73454e6 q^{23} -2.43712e6 q^{24} -1.92004e6 q^{25} -2.57015e6 q^{26} +2.98720e6 q^{27} +6.95013e6 q^{28} -3.22275e6 q^{29} -777242. q^{30} -6.34620e6 q^{31} +2.52139e6 q^{32} +1.95143e6 q^{33} +1.32022e7 q^{34} +1.16800e6 q^{35} -8.90826e6 q^{36} +1.71570e7 q^{37} +6.88838e6 q^{39} +4.14231e6 q^{40} +8.37540e6 q^{41} -2.74390e7 q^{42} -3.17434e7 q^{43} -1.97364e7 q^{44} -1.49708e6 q^{45} -6.92589e7 q^{46} +3.65671e7 q^{47} -3.80081e7 q^{48} +880523. q^{49} -7.66657e7 q^{50} -3.53837e7 q^{51} -6.96678e7 q^{52} -5.01405e7 q^{53} +1.19277e8 q^{54} -3.31680e6 q^{55} +1.46236e8 q^{56} -1.28682e8 q^{58} -2.30069e7 q^{59} -2.10683e7 q^{60} +1.33499e8 q^{61} -2.53399e8 q^{62} -5.28514e7 q^{63} -8.11656e7 q^{64} -1.17080e7 q^{65} +7.79191e7 q^{66} -3.98117e7 q^{67} +3.57865e8 q^{68} +1.85624e8 q^{69} +4.66375e7 q^{70} -4.02544e8 q^{71} -1.87437e8 q^{72} +3.15273e8 q^{73} +6.85067e8 q^{74} +2.05475e8 q^{75} -1.17093e8 q^{77} +2.75048e8 q^{78} +2.13887e7 q^{79} +6.46015e7 q^{80} -1.57677e8 q^{81} +3.34423e8 q^{82} -4.17337e8 q^{83} -7.43777e8 q^{84} +6.01410e7 q^{85} -1.26749e9 q^{86} +3.44886e8 q^{87} -4.15269e8 q^{88} -8.58032e8 q^{89} -5.97771e7 q^{90} -4.13329e8 q^{91} -1.87737e9 q^{92} +6.79146e8 q^{93} +1.46010e9 q^{94} -2.69830e8 q^{96} -8.94373e8 q^{97} +3.51586e7 q^{98} +1.50083e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 15 q^{2} + 74 q^{3} + 2987 q^{4} + 285 q^{5} + 535 q^{6} - 1338 q^{7} - 12135 q^{8} + 57928 q^{9} - 41180 q^{10} - 57405 q^{11} + 117729 q^{12} - 98671 q^{13} + 148290 q^{14} - 428251 q^{15} + 279203 q^{16}+ \cdots + 736622698 q^{99}+O(q^{100}) \) 14 * q - 15 * q^2 + 74 * q^3 + 2987 * q^4 + 285 * q^5 + 535 * q^6 - 1338 * q^7 - 12135 * q^8 + 57928 * q^9 - 41180 * q^10 - 57405 * q^11 + 117729 * q^12 - 98671 * q^13 + 148290 * q^14 - 428251 * q^15 + 279203 * q^16 - 466251 * q^17 + 367482 * q^18 - 1671810 * q^20 - 689090 * q^21 + 1689395 * q^22 + 3087747 * q^23 + 234183 * q^24 + 3260823 * q^25 + 4516572 * q^26 + 2108270 * q^27 + 703814 * q^28 - 7831383 * q^29 - 5929612 * q^30 - 4632816 * q^31 - 11470815 * q^32 - 22791973 * q^33 - 13457096 * q^34 + 13222428 * q^35 - 7355018 * q^36 + 13602510 * q^37 - 10387851 * q^39 + 16500258 * q^40 - 20419440 * q^41 + 10220798 * q^42 - 27415427 * q^43 - 41775405 * q^44 - 42991294 * q^45 - 68617354 * q^46 + 90906681 * q^47 - 33057375 * q^48 + 114912446 * q^49 + 22203357 * q^50 - 134429123 * q^51 - 66195006 * q^52 - 47827863 * q^53 + 130507669 * q^54 + 157712310 * q^55 + 191229558 * q^56 - 172013024 * q^58 - 255540 * q^59 - 287916794 * q^60 - 304035459 * q^61 - 693626280 * q^62 + 122148024 * q^63 - 454245757 * q^64 - 712480095 * q^65 + 611099417 * q^66 - 165758480 * q^67 + 178759254 * q^68 + 135618639 * q^69 - 1167527028 * q^70 - 685508589 * q^71 - 142349670 * q^72 + 602867050 * q^73 + 82104492 * q^74 + 950137387 * q^75 - 245997378 * q^77 + 911449840 * q^78 - 78162339 * q^79 - 227607150 * q^80 - 1230916118 * q^81 - 360208019 * q^82 + 206919963 * q^83 - 233652462 * q^84 + 1440537237 * q^85 - 936824310 * q^86 - 339438159 * q^87 - 823388847 * q^88 - 1256827551 * q^89 - 1879090924 * q^90 - 537759588 * q^91 + 677003592 * q^92 + 492493440 * q^93 - 424187592 * q^94 - 3020794465 * q^96 - 2109813492 * q^97 - 2689941591 * q^98 + 736622698 * q^99

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