LMFDB - Embedded newform 361.10.a.f.1.2

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:	$0$
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			1.2
Root			$-35.1331$ 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)

$f(q)$	$=$	\(q-34.1331 q^{2} -208.441 q^{3} +653.070 q^{4} -2506.72 q^{5} +7114.73 q^{6} +4067.64 q^{7} -4815.16 q^{8} +23764.5 q^{9} +85562.3 q^{10} -30956.0 q^{11} -136126. q^{12} -141149. q^{13} -138841. q^{14} +522504. q^{15} -170015. q^{16} -402249. q^{17} -811158. q^{18} -1.63707e6 q^{20} -847862. q^{21} +1.05663e6 q^{22} +706002. q^{23} +1.00368e6 q^{24} +4.33054e6 q^{25} +4.81787e6 q^{26} -850757. q^{27} +2.65645e6 q^{28} +3.73855e6 q^{29} -1.78347e7 q^{30} +2.57084e6 q^{31} +8.26852e6 q^{32} +6.45250e6 q^{33} +1.37300e7 q^{34} -1.01965e7 q^{35} +1.55199e7 q^{36} +1.01623e6 q^{37} +2.94213e7 q^{39} +1.20703e7 q^{40} +3.55106e7 q^{41} +2.89402e7 q^{42} -7.55220e6 q^{43} -2.02165e7 q^{44} -5.95711e7 q^{45} -2.40981e7 q^{46} -1.71794e6 q^{47} +3.54381e7 q^{48} -2.38079e7 q^{49} -1.47815e8 q^{50} +8.38450e7 q^{51} -9.21805e7 q^{52} -6.33193e7 q^{53} +2.90390e7 q^{54} +7.75982e7 q^{55} -1.95863e7 q^{56} -1.27608e8 q^{58} +1.29382e8 q^{59} +3.41231e8 q^{60} -8.17249e7 q^{61} -8.77509e7 q^{62} +9.66656e7 q^{63} -1.95182e8 q^{64} +3.53823e8 q^{65} -2.20244e8 q^{66} -1.18446e8 q^{67} -2.62697e8 q^{68} -1.47160e8 q^{69} +3.48037e8 q^{70} +1.62123e8 q^{71} -1.14430e8 q^{72} -3.04412e7 q^{73} -3.46871e7 q^{74} -9.02662e8 q^{75} -1.25918e8 q^{77} -1.00424e9 q^{78} -6.30999e8 q^{79} +4.26182e8 q^{80} -2.90425e8 q^{81} -1.21209e9 q^{82} +2.53183e8 q^{83} -5.53713e8 q^{84} +1.00833e9 q^{85} +2.57780e8 q^{86} -7.79266e8 q^{87} +1.49058e8 q^{88} +6.19200e8 q^{89} +2.03335e9 q^{90} -5.74145e8 q^{91} +4.61069e8 q^{92} -5.35868e8 q^{93} +5.86386e7 q^{94} -1.72350e9 q^{96} +5.61676e8 q^{97} +8.12638e8 q^{98} -7.35655e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−34.1331	−1.50849	−0.754243	−	0.656596i	$-0.771996\pi$
$2$	−34.1331	−1.50849	−0.754243	+	0.656596i	$0.771996\pi$
$3$	−208.441	−1.48572	−0.742860	−	0.669447i	$-0.766531\pi$
$3$	−208.441	−1.48572	−0.742860	+	0.669447i	$0.766531\pi$
$4$	653.070	1.27553
$5$	−2506.72	−1.79367	−0.896833	−	0.442369i	$-0.854138\pi$
$5$	−2506.72	−1.79367	−0.896833	+	0.442369i	$0.854138\pi$
$6$	7114.73	2.24119
$7$	4067.64	0.640326	0.320163	−	0.947362i	$-0.396262\pi$
$7$	4067.64	0.640326	0.320163	+	0.947362i	$0.396262\pi$
$8$	−4815.16	−0.415629
$9$	23764.5	1.20736
$10$	85562.3	2.70572
$11$	−30956.0	−0.637497	−0.318748	−	0.947839i	$-0.603263\pi$
$11$	−30956.0	−0.637497	−0.318748	+	0.947839i	$0.603263\pi$
$12$	−136126.	−1.89508
$13$	−141149.	−1.37067	−0.685337	−	0.728226i	$-0.740345\pi$
$13$	−141149.	−1.37067	−0.685337	+	0.728226i	$0.740345\pi$
$14$	−138841.	−0.965923
$15$	522504.	2.66489
$16$	−170015.	−0.648557
$17$	−402249.	−1.16809	−0.584043	−	0.811723i	$-0.698530\pi$
$17$	−402249.	−1.16809	−0.584043	+	0.811723i	$0.698530\pi$
$18$	−811158.	−1.82129
$19$	0	0
$19$	0	0
$20$	−1.63707e6	−2.28787
$21$	−847862.	−0.951345
$22$	1.05663e6	0.961655
$23$	706002.	0.526054	0.263027	−	0.964788i	$-0.415279\pi$
$23$	706002.	0.526054	0.263027	+	0.964788i	$0.415279\pi$
$24$	1.00368e6	0.617508
$25$	4.33054e6	2.21724
$26$	4.81787e6	2.06764
$27$	−850757.	−0.308084
$28$	2.65645e6	0.816754
$29$	3.73855e6	0.981550	0.490775	−	0.871286i	$-0.336714\pi$
$29$	3.73855e6	0.981550	0.490775	+	0.871286i	$0.336714\pi$
$30$	−1.78347e7	−4.01994
$31$	2.57084e6	0.499974	0.249987	−	0.968249i	$-0.419574\pi$
$31$	2.57084e6	0.499974	0.249987	+	0.968249i	$0.419574\pi$
$32$	8.26852e6	1.39397
$33$	6.45250e6	0.947142
$34$	1.37300e7	1.76204
$35$	−1.01965e7	−1.14853
$36$	1.55199e7	1.54002
$37$	1.01623e6	0.0891424	0.0445712	−	0.999006i	$-0.485808\pi$
$37$	1.01623e6	0.0891424	0.0445712	+	0.999006i	$0.485808\pi$
$38$	0	0
$39$	2.94213e7	2.03644
$40$	1.20703e7	0.745500
$41$	3.55106e7	1.96260	0.981298	−	0.192495i	$-0.0616580\pi$
$41$	3.55106e7	1.96260	0.981298	+	0.192495i	$0.0616580\pi$
$42$	2.89402e7	1.43509
$43$	−7.55220e6	−0.336872	−0.168436	−	0.985713i	$-0.553872\pi$
$43$	−7.55220e6	−0.336872	−0.168436	+	0.985713i	$0.553872\pi$
$44$	−2.02165e7	−0.813145
$45$	−5.95711e7	−2.16561
$46$	−2.40981e7	−0.793545
$47$	−1.71794e6	−0.0513532	−0.0256766	−	0.999670i	$-0.508174\pi$
$47$	−1.71794e6	−0.0513532	−0.0256766	+	0.999670i	$0.508174\pi$
$48$	3.54381e7	0.963574
$49$	−2.38079e7	−0.589982
$50$	−1.47815e8	−3.34467
$51$	8.38450e7	1.73545
$52$	−9.21805e7	−1.74833
$53$	−6.33193e7	−1.10229	−0.551144	−	0.834410i	$-0.685808\pi$
$53$	−6.33193e7	−1.10229	−0.551144	+	0.834410i	$0.685808\pi$
$54$	2.90390e7	0.464740
$55$	7.75982e7	1.14346
$56$	−1.95863e7	−0.266138
$57$	0	0
$58$	−1.27608e8	−1.48065
$59$	1.29382e8	1.39008	0.695042	−	0.718969i	$-0.255386\pi$
$59$	1.29382e8	1.39008	0.695042	+	0.718969i	$0.255386\pi$
$60$	3.41231e8	3.39913
$61$	−8.17249e7	−0.755736	−0.377868	−	0.925859i	$-0.623343\pi$
$61$	−8.17249e7	−0.755736	−0.377868	+	0.925859i	$0.623343\pi$
$62$	−8.77509e7	−0.754204
$63$	9.66656e7	0.773106
$64$	−1.95182e8	−1.45422
$65$	3.53823e8	2.45853
$66$	−2.20244e8	−1.42875
$67$	−1.18446e8	−0.718099	−0.359050	−	0.933318i	$-0.616899\pi$
$67$	−1.18446e8	−0.718099	−0.359050	+	0.933318i	$0.616899\pi$
$68$	−2.62697e8	−1.48992
$69$	−1.47160e8	−0.781569
$70$	3.48037e8	1.73254
$71$	1.62123e8	0.757151	0.378575	−	0.925570i	$-0.376414\pi$
$71$	1.62123e8	0.757151	0.378575	+	0.925570i	$0.376414\pi$
$72$	−1.14430e8	−0.501815
$73$	−3.04412e7	−0.125461	−0.0627305	−	0.998031i	$-0.519981\pi$
$73$	−3.04412e7	−0.125461	−0.0627305	+	0.998031i	$0.519981\pi$
$74$	−3.46871e7	−0.134470
$75$	−9.02662e8	−3.29420
$76$	0	0
$77$	−1.25918e8	−0.408206
$78$	−1.00424e9	−3.07194
$79$	−6.30999e8	−1.82266	−0.911332	−	0.411672i	$-0.864945\pi$
$79$	−6.30999e8	−1.82266	−0.911332	+	0.411672i	$0.864945\pi$
$80$	4.26182e8	1.16330
$81$	−2.90425e8	−0.749637
$82$	−1.21209e9	−2.96055
$83$	2.53183e8	0.585576	0.292788	−	0.956177i	$-0.405417\pi$
$83$	2.53183e8	0.585576	0.292788	+	0.956177i	$0.405417\pi$
$84$	−5.53713e8	−1.21347
$85$	1.00833e9	2.09515
$86$	2.57780e8	0.508167
$87$	−7.79266e8	−1.45831
$88$	1.49058e8	0.264962
$89$	6.19200e8	1.04611	0.523053	−	0.852300i	$-0.324793\pi$
$89$	6.19200e8	1.04611	0.523053	+	0.852300i	$0.324793\pi$
$90$	2.03335e9	3.26679
$91$	−5.74145e8	−0.877679
$92$	4.61069e8	0.670997
$93$	−5.35868e8	−0.742822
$94$	5.86386e7	0.0774655
$95$	0	0
$96$	−1.72350e9	−2.07105
$97$	5.61676e8	0.644188	0.322094	−	0.946708i	$-0.395613\pi$
$97$	5.61676e8	0.644188	0.322094	+	0.946708i	$0.395613\pi$
$98$	8.12638e8	0.889979
$99$	−7.35655e8	−0.769690
$100$	2.82815e9	2.82815
$101$	−4.32424e8	−0.413488	−0.206744	−	0.978395i	$-0.566287\pi$
$101$	−4.32424e8	−0.413488	−0.206744	+	0.978395i	$0.566287\pi$
$102$	−2.86189e9	−2.61790
$103$	6.31374e8	0.552738	0.276369	−	0.961052i	$-0.410869\pi$
$103$	6.31374e8	0.552738	0.276369	+	0.961052i	$0.410869\pi$
$104$	6.79657e8	0.569692
$105$	2.12536e9	1.70640
$106$	2.16129e9	1.66278
$107$	1.19398e9	0.880581	0.440290	−	0.897855i	$-0.354875\pi$
$107$	1.19398e9	0.880581	0.440290	+	0.897855i	$0.354875\pi$
$108$	−5.55604e8	−0.392969
$109$	−2.69404e8	−0.182804	−0.0914018	−	0.995814i	$-0.529135\pi$
$109$	−2.69404e8	−0.182804	−0.0914018	+	0.995814i	$0.529135\pi$
$110$	−2.64867e9	−1.72489
$111$	−2.11824e8	−0.132441
$112$	−6.91562e8	−0.415288
$113$	−4.67502e8	−0.269731	−0.134866	−	0.990864i	$-0.543060\pi$
$113$	−4.67502e8	−0.269731	−0.134866	+	0.990864i	$0.543060\pi$
$114$	0	0
$115$	−1.76975e9	−0.943566
$116$	2.44154e9	1.25199
$117$	−3.35435e9	−1.65490
$118$	−4.41623e9	−2.09692
$119$	−1.63620e9	−0.747956
$120$	−2.51594e9	−1.10760
$121$	−1.39967e9	−0.593598
$122$	2.78953e9	1.14002
$123$	−7.40186e9	−2.91587
$124$	1.67894e9	0.637731
$125$	−5.95954e9	−2.18332
$126$	−3.29950e9	−1.16622
$127$	−3.86526e9	−1.31844	−0.659222	−	0.751948i	$-0.729114\pi$
$127$	−3.86526e9	−1.31844	−0.659222	+	0.751948i	$0.729114\pi$
$128$	2.42870e9	0.799705
$129$	1.57419e9	0.500498
$130$	−1.20771e10	−3.70866
$131$	−8.09124e8	−0.240046	−0.120023	−	0.992771i	$-0.538297\pi$
$131$	−8.09124e8	−0.240046	−0.120023	+	0.992771i	$0.538297\pi$
$132$	4.21393e9	1.20811
$133$	0	0
$134$	4.04294e9	1.08324
$135$	2.13261e9	0.552599
$136$	1.93689e9	0.485490
$137$	−6.13933e8	−0.148895	−0.0744473	−	0.997225i	$-0.523719\pi$
$137$	−6.13933e8	−0.148895	−0.0744473	+	0.997225i	$0.523719\pi$
$138$	5.02302e9	1.17899
$139$	2.98974e8	0.0679308	0.0339654	−	0.999423i	$-0.489186\pi$
$139$	2.98974e8	0.0679308	0.0339654	+	0.999423i	$0.489186\pi$
$140$	−6.65900e9	−1.46498
$141$	3.58088e8	0.0762964
$142$	−5.53377e9	−1.14215
$143$	4.36943e9	0.873801
$144$	−4.04034e9	−0.783044
$145$	−9.37152e9	−1.76057
$146$	1.03905e9	0.189256
$147$	4.96254e9	0.876548
$148$	6.63669e8	0.113704
$149$	−8.51918e9	−1.41599	−0.707994	−	0.706218i	$-0.750400\pi$
$149$	−8.51918e9	−1.41599	−0.707994	+	0.706218i	$0.750400\pi$
$150$	3.08107e10	4.96925
$151$	2.60207e8	0.0407308	0.0203654	−	0.999793i	$-0.493517\pi$
$151$	2.60207e8	0.0407308	0.0203654	+	0.999793i	$0.493517\pi$
$152$	0	0
$153$	−9.55925e9	−1.41030
$154$	4.29797e9	0.615773
$155$	−6.44439e9	−0.896787
$156$	1.92142e10	2.59753
$157$	−4.14012e8	−0.0543831	−0.0271916	−	0.999630i	$-0.508656\pi$
$157$	−4.14012e8	−0.0543831	−0.0271916	+	0.999630i	$0.508656\pi$
$158$	2.15380e10	2.74946
$159$	1.31983e10	1.63769
$160$	−2.07269e10	−2.50031
$161$	2.87176e9	0.336846
$162$	9.91311e9	1.13082
$163$	−6.26572e9	−0.695227	−0.347614	−	0.937638i	$-0.613008\pi$
$163$	−6.26572e9	−0.695227	−0.347614	+	0.937638i	$0.613008\pi$
$164$	2.31909e10	2.50334
$165$	−1.61746e10	−1.69886
$166$	−8.64192e9	−0.883332
$167$	−1.24324e10	−1.23689	−0.618444	−	0.785829i	$-0.712236\pi$
$167$	−1.24324e10	−1.23689	−0.618444	+	0.785829i	$0.712236\pi$
$168$	4.08259e9	0.395407
$169$	9.31868e9	0.878748
$170$	−3.44173e10	−3.16051
$171$	0	0
$172$	−4.93212e9	−0.429690
$173$	−2.36048e9	−0.200351	−0.100176	−	0.994970i	$-0.531941\pi$
$173$	−2.36048e9	−0.200351	−0.100176	+	0.994970i	$0.531941\pi$
$174$	2.65988e10	2.19984
$175$	1.76151e10	1.41976
$176$	5.26300e9	0.413453
$177$	−2.69686e10	−2.06528
$178$	−2.11352e10	−1.57804
$179$	−1.13959e9	−0.0829680	−0.0414840	−	0.999139i	$-0.513209\pi$
$179$	−1.13959e9	−0.0829680	−0.0414840	+	0.999139i	$0.513209\pi$
$180$	−3.89041e10	−2.76229
$181$	1.34460e10	0.931194	0.465597	−	0.884997i	$-0.345840\pi$
$181$	1.34460e10	0.931194	0.465597	+	0.884997i	$0.345840\pi$
$182$	1.95974e10	1.32397
$183$	1.70348e10	1.12281
$184$	−3.39951e9	−0.218643
$185$	−2.54741e9	−0.159892
$186$	1.82909e10	1.12054
$187$	1.24520e10	0.744651
$188$	−1.12193e9	−0.0655024
$189$	−3.46057e9	−0.197274
$190$	0	0
$191$	−2.51377e9	−0.136671	−0.0683354	−	0.997662i	$-0.521769\pi$
$191$	−2.51377e9	−0.136671	−0.0683354	+	0.997662i	$0.521769\pi$
$192$	4.06840e10	2.16057
$193$	−3.17663e10	−1.64801	−0.824003	−	0.566586i	$-0.808264\pi$
$193$	−3.17663e10	−1.64801	−0.824003	+	0.566586i	$0.808264\pi$
$194$	−1.91717e10	−0.971748
$195$	−7.37511e10	−3.65269
$196$	−1.55482e10	−0.752538
$197$	3.13458e10	1.48280	0.741399	−	0.671065i	$-0.234163\pi$
$197$	3.13458e10	1.48280	0.741399	+	0.671065i	$0.234163\pi$
$198$	2.51102e10	1.16107
$199$	−1.60392e9	−0.0725009	−0.0362505	−	0.999343i	$-0.511541\pi$
$199$	−1.60392e9	−0.0725009	−0.0362505	+	0.999343i	$0.511541\pi$
$200$	−2.08523e10	−0.921548
$201$	2.46890e10	1.06689
$202$	1.47600e10	0.623741
$203$	1.52071e10	0.628512
$204$	5.47567e10	2.21361
$205$	−8.90153e10	−3.52024
$206$	−2.15508e10	−0.833797
$207$	1.67778e10	0.635139
$208$	2.39976e10	0.888961
$209$	0	0
$210$	−7.25450e10	−2.57407
$211$	−4.19652e10	−1.45753	−0.728767	−	0.684762i	$-0.759906\pi$
$211$	−4.19652e10	−1.45753	−0.728767	+	0.684762i	$0.759906\pi$
$212$	−4.13519e10	−1.40600
$213$	−3.37931e10	−1.12491
$214$	−4.07542e10	−1.32834
$215$	1.89313e10	0.604237
$216$	4.09653e9	0.128048
$217$	1.04573e10	0.320147
$218$	9.19560e9	0.275756
$219$	6.34518e9	0.186400
$220$	5.06771e10	1.45851
$221$	5.67772e10	1.60106
$222$	7.23020e9	0.199785
$223$	1.24367e10	0.336770	0.168385	−	0.985721i	$-0.446145\pi$
$223$	1.24367e10	0.336770	0.168385	+	0.985721i	$0.446145\pi$
$224$	3.36334e10	0.892594
$225$	1.02913e11	2.67701
$226$	1.59573e10	0.406885
$227$	−5.60406e10	−1.40083	−0.700416	−	0.713735i	$-0.747002\pi$
$227$	−5.60406e10	−1.40083	−0.700416	+	0.713735i	$0.747002\pi$
$228$	0	0
$229$	5.10125e10	1.22579	0.612896	−	0.790164i	$-0.290004\pi$
$229$	5.10125e10	1.22579	0.612896	+	0.790164i	$0.290004\pi$
$230$	6.04072e10	1.42336
$231$	2.62464e10	0.606480
$232$	−1.80017e10	−0.407960
$233$	8.02937e10	1.78476	0.892381	−	0.451284i	$-0.149034\pi$
$233$	8.02937e10	1.78476	0.892381	+	0.451284i	$0.149034\pi$
$234$	1.14494e11	2.49639
$235$	4.30640e9	0.0921105
$236$	8.44958e10	1.77309
$237$	1.31526e11	2.70797
$238$	5.58487e10	1.12828
$239$	1.25824e10	0.249444	0.124722	−	0.992192i	$-0.460196\pi$
$239$	1.25824e10	0.249444	0.124722	+	0.992192i	$0.460196\pi$
$240$	−8.88337e10	−1.72833
$241$	4.47908e10	0.855288	0.427644	−	0.903947i	$-0.359344\pi$
$241$	4.47908e10	0.855288	0.427644	+	0.903947i	$0.359344\pi$
$242$	4.77752e10	0.895433
$243$	7.72818e10	1.42183
$244$	−5.33721e10	−0.963962
$245$	5.96799e10	1.05823
$246$	2.52649e11	4.39854
$247$	0	0
$248$	−1.23790e10	−0.207804
$249$	−5.27736e10	−0.870001
$250$	2.03418e11	3.29351
$251$	−7.41227e10	−1.17874	−0.589372	−	0.807862i	$-0.700625\pi$
$251$	−7.41227e10	−1.17874	−0.589372	+	0.807862i	$0.700625\pi$
$252$	6.31294e10	0.986118
$253$	−2.18550e10	−0.335358
$254$	1.31933e11	1.98885
$255$	−2.10176e11	−3.11281
$256$	1.70341e10	0.247879
$257$	−9.36541e10	−1.33915	−0.669573	−	0.742747i	$-0.733523\pi$
$257$	−9.36541e10	−1.33915	−0.669573	+	0.742747i	$0.733523\pi$
$258$	−5.37319e10	−0.754994
$259$	4.13366e9	0.0570802
$260$	2.31071e11	3.13592
$261$	8.88449e10	1.18509
$262$	2.76179e10	0.362106
$263$	−7.80524e10	−1.00597	−0.502986	−	0.864295i	$-0.667765\pi$
$263$	−7.80524e10	−1.00597	−0.502986	+	0.864295i	$0.667765\pi$
$264$	−3.10698e10	−0.393660
$265$	1.58724e11	1.97714
$266$	0	0
$267$	−1.29066e11	−1.55422
$268$	−7.73536e10	−0.915955
$269$	−7.06085e10	−0.822190	−0.411095	−	0.911593i	$-0.634853\pi$
$269$	−7.06085e10	−0.822190	−0.411095	+	0.911593i	$0.634853\pi$
$270$	−7.27928e10	−0.833588
$271$	−3.48345e10	−0.392327	−0.196163	−	0.980571i	$-0.562848\pi$
$271$	−3.48345e10	−0.392327	−0.196163	+	0.980571i	$0.562848\pi$
$272$	6.83885e10	0.757570
$273$	1.19675e11	1.30398
$274$	2.09555e10	0.224605
$275$	−1.34056e11	−1.41348
$276$	−9.61055e10	−0.996913
$277$	−1.79253e10	−0.182940	−0.0914699	−	0.995808i	$-0.529157\pi$
$277$	−1.79253e10	−0.182940	−0.0914699	+	0.995808i	$0.529157\pi$
$278$	−1.02049e10	−0.102473
$279$	6.10949e10	0.603651
$280$	4.90976e10	0.477363
$281$	−6.11878e10	−0.585445	−0.292723	−	0.956197i	$-0.594561\pi$
$281$	−6.11878e10	−0.585445	−0.292723	+	0.956197i	$0.594561\pi$
$282$	−1.22227e10	−0.115092
$283$	−1.80604e11	−1.67374	−0.836871	−	0.547400i	$-0.815617\pi$
$283$	−1.80604e11	−1.67374	−0.836871	+	0.547400i	$0.815617\pi$
$284$	1.05878e11	0.965766
$285$	0	0
$286$	−1.49142e11	−1.31812
$287$	1.44444e11	1.25670
$288$	1.96497e11	1.68303
$289$	4.32161e10	0.364423
$290$	3.19879e11	2.65580
$291$	−1.17076e11	−0.957083
$292$	−1.98802e10	−0.160029
$293$	1.52036e10	0.120515	0.0602577	−	0.998183i	$-0.480808\pi$
$293$	1.52036e10	0.120515	0.0602577	+	0.998183i	$0.480808\pi$
$294$	−1.69387e11	−1.32226
$295$	−3.24326e11	−2.49335
$296$	−4.89331e9	−0.0370501
$297$	2.63361e10	0.196402
$298$	2.90786e11	2.13600
$299$	−9.96518e10	−0.721049
$300$	−5.89501e11	−4.20184
$301$	−3.07196e10	−0.215708
$302$	−8.88168e9	−0.0614418
$303$	9.01347e10	0.614328
$304$	0	0
$305$	2.04862e11	1.35554
$306$	3.26287e11	2.12742
$307$	−1.53582e11	−0.986774	−0.493387	−	0.869810i	$-0.664241\pi$
$307$	−1.53582e11	−0.986774	−0.493387	+	0.869810i	$0.664241\pi$
$308$	−8.22333e10	−0.520678
$309$	−1.31604e11	−0.821214
$310$	2.19967e11	1.35279
$311$	7.14306e9	0.0432974	0.0216487	−	0.999766i	$-0.493108\pi$
$311$	7.14306e9	0.0432974	0.0216487	+	0.999766i	$0.493108\pi$
$312$	−1.41668e11	−0.846402
$313$	−1.02636e11	−0.604434	−0.302217	−	0.953239i	$-0.597727\pi$
$313$	−1.02636e11	−0.604434	−0.302217	+	0.953239i	$0.597727\pi$
$314$	1.41315e10	0.0820362
$315$	−2.42314e11	−1.38669
$316$	−4.12086e11	−2.32486
$317$	2.72143e10	0.151367	0.0756835	−	0.997132i	$-0.475886\pi$
$317$	2.72143e10	0.151367	0.0756835	+	0.997132i	$0.475886\pi$
$318$	−4.50500e11	−2.47043
$319$	−1.15731e11	−0.625735
$320$	4.89269e11	2.60839
$321$	−2.48874e11	−1.30830
$322$	−9.80222e10	−0.508128
$323$	0	0
$324$	−1.89668e11	−0.956183
$325$	−6.11254e11	−3.03911
$326$	2.13869e11	1.04874
$327$	5.61547e10	0.271595
$328$	−1.70989e11	−0.815711
$329$	−6.98796e9	−0.0328828
$330$	5.52091e11	2.56270
$331$	−3.18775e10	−0.145968	−0.0729841	−	0.997333i	$-0.523252\pi$
$331$	−3.18775e10	−0.145968	−0.0729841	+	0.997333i	$0.523252\pi$
$332$	1.65346e11	0.746918
$333$	2.41502e10	0.107627
$334$	4.24356e11	1.86583
$335$	2.96912e11	1.28803
$336$	1.44150e11	0.617002
$337$	4.36969e11	1.84551	0.922755	−	0.385387i	$-0.125932\pi$
$337$	4.36969e11	1.84551	0.922755	+	0.385387i	$0.125932\pi$
$338$	−3.18076e11	−1.32558
$339$	9.74465e10	0.400745
$340$	6.58508e11	2.67243
$341$	−7.95831e10	−0.318732
$342$	0	0
$343$	−2.60986e11	−1.01811
$344$	3.63650e10	0.140014
$345$	3.68889e11	1.40187
$346$	8.05705e10	0.302227
$347$	8.37067e10	0.309940	0.154970	−	0.987919i	$-0.450472\pi$
$347$	8.37067e10	0.309940	0.154970	+	0.987919i	$0.450472\pi$
$348$	−5.08915e11	−1.86011
$349$	1.29123e11	0.465896	0.232948	−	0.972489i	$-0.425163\pi$
$349$	1.29123e11	0.465896	0.232948	+	0.972489i	$0.425163\pi$
$350$	−6.01258e11	−2.14168
$351$	1.20084e11	0.422282
$352$	−2.55960e11	−0.888650
$353$	6.74363e10	0.231157	0.115579	−	0.993298i	$-0.463128\pi$
$353$	6.74363e10	0.231157	0.115579	+	0.993298i	$0.463128\pi$
$354$	9.20521e11	3.11544
$355$	−4.06398e11	−1.35808
$356$	4.04381e11	1.33434
$357$	3.41051e11	1.11125
$358$	3.88978e10	0.125156
$359$	4.52320e11	1.43721	0.718606	−	0.695417i	$-0.244780\pi$
$359$	4.52320e11	1.43721	0.718606	+	0.695417i	$0.244780\pi$
$360$	2.86845e11	0.900089
$361$	0	0
$362$	−4.58955e11	−1.40469
$363$	2.91749e11	0.881920
$364$	−3.74957e11	−1.11950
$365$	7.63077e10	0.225035
$366$	−5.81451e11	−1.69375
$367$	−1.69351e11	−0.487294	−0.243647	−	0.969864i	$-0.578344\pi$
$367$	−1.69351e11	−0.487294	−0.243647	+	0.969864i	$0.578344\pi$
$368$	−1.20031e11	−0.341176
$369$	8.43893e11	2.36957
$370$	8.69510e10	0.241194
$371$	−2.57560e11	−0.705824
$372$	−3.49959e11	−0.947490
$373$	−2.28609e11	−0.611510	−0.305755	−	0.952110i	$-0.598909\pi$
$373$	−2.28609e11	−0.611510	−0.305755	+	0.952110i	$0.598909\pi$
$374$	−4.25026e11	−1.12329
$375$	1.24221e12	3.24380
$376$	8.27215e9	0.0213439
$377$	−5.27695e11	−1.34538
$378$	1.18120e11	0.297585
$379$	−5.28445e11	−1.31560	−0.657799	−	0.753193i	$-0.728513\pi$
$379$	−5.28445e11	−1.31560	−0.657799	+	0.753193i	$0.728513\pi$
$380$	0	0
$381$	8.05677e11	1.95884
$382$	8.58029e10	0.206166
$383$	−1.24398e11	−0.295406	−0.147703	−	0.989032i	$-0.547188\pi$
$383$	−1.24398e11	−0.295406	−0.147703	+	0.989032i	$0.547188\pi$
$384$	−5.06241e11	−1.18814
$385$	3.15642e11	0.732186
$386$	1.08428e12	2.48599
$387$	−1.79474e11	−0.406727
$388$	3.66814e11	0.821680
$389$	−3.46547e11	−0.767342	−0.383671	−	0.923470i	$-0.625340\pi$
$389$	−3.46547e11	−0.767342	−0.383671	+	0.923470i	$0.625340\pi$
$390$	2.51736e12	5.51003
$391$	−2.83988e11	−0.614476
$392$	1.14639e11	0.245214
$393$	1.68654e11	0.356641
$394$	−1.06993e12	−2.23678
$395$	1.58174e12	3.26925
$396$	−4.80435e11	−0.981761
$397$	5.41660e11	1.09438	0.547192	−	0.837007i	$-0.315697\pi$
$397$	5.41660e11	1.09438	0.547192	+	0.837007i	$0.315697\pi$
$398$	5.47468e10	0.109367
$399$	0	0
$400$	−7.36259e11	−1.43801
$401$	4.34240e11	0.838649	0.419325	−	0.907836i	$-0.362267\pi$
$401$	4.34240e11	0.838649	0.419325	+	0.907836i	$0.362267\pi$
$402$	−8.42713e11	−1.60939
$403$	−3.62873e11	−0.685302
$404$	−2.82403e11	−0.527416
$405$	7.28015e11	1.34460
$406$	−5.19065e11	−0.948101
$407$	−3.14584e10	−0.0568280
$408$	−4.03727e11	−0.721302
$409$	−3.57810e11	−0.632263	−0.316131	−	0.948715i	$-0.602384\pi$
$409$	−3.57810e11	−0.632263	−0.316131	+	0.948715i	$0.602384\pi$
$410$	3.03837e12	5.31023
$411$	1.27969e11	0.221216
$412$	4.12331e11	0.705032
$413$	5.26281e11	0.890108
$414$	−5.72679e11	−0.958097
$415$	−6.34660e11	−1.05033
$416$	−1.16710e12	−1.91068
$417$	−6.23184e10	−0.100926
$418$	0	0
$419$	−3.09461e11	−0.490504	−0.245252	−	0.969459i	$-0.578871\pi$
$419$	−3.09461e11	−0.490504	−0.245252	+	0.969459i	$0.578871\pi$
$420$	1.38801e12	2.17656
$421$	2.05249e11	0.318428	0.159214	−	0.987244i	$-0.449104\pi$
$421$	2.05249e11	0.318428	0.159214	+	0.987244i	$0.449104\pi$
$422$	1.43240e12	2.19867
$423$	−4.08260e10	−0.0620019
$424$	3.04893e11	0.458142
$425$	−1.74196e12	−2.58992
$426$	1.15346e12	1.69692
$427$	−3.32428e11	−0.483918
$428$	7.79751e11	1.12321
$429$	−9.10767e11	−1.29822
$430$	−6.46184e11	−0.911482
$431$	8.36945e11	1.16829	0.584143	−	0.811650i	$-0.301431\pi$
$431$	8.36945e11	1.16829	0.584143	+	0.811650i	$0.301431\pi$
$432$	1.44642e11	0.199810
$433$	1.54146e11	0.210735	0.105367	−	0.994433i	$-0.466398\pi$
$433$	1.54146e11	0.210735	0.105367	+	0.994433i	$0.466398\pi$
$434$	−3.56939e11	−0.482937
$435$	1.95341e12	2.61572
$436$	−1.75940e11	−0.233171
$437$	0	0
$438$	−2.16581e11	−0.281181
$439$	2.94967e11	0.379038	0.189519	−	0.981877i	$-0.439307\pi$
$439$	2.94967e11	0.379038	0.189519	+	0.981877i	$0.439307\pi$
$440$	−3.73648e11	−0.475254
$441$	−5.65784e11	−0.712323
$442$	−1.93798e12	−2.41518
$443$	−1.22510e12	−1.51131	−0.755655	−	0.654970i	$-0.772681\pi$
$443$	−1.22510e12	−1.51131	−0.755655	+	0.654970i	$0.772681\pi$
$444$	−1.38336e11	−0.168932
$445$	−1.55216e12	−1.87636
$446$	−4.24503e11	−0.508012
$447$	1.77574e12	2.10376
$448$	−7.93932e11	−0.931177
$449$	1.38448e12	1.60760	0.803802	−	0.594897i	$-0.202807\pi$
$449$	1.38448e12	1.60760	0.803802	+	0.594897i	$0.202807\pi$
$450$	−3.51275e12	−4.03823
$451$	−1.09927e12	−1.25115
$452$	−3.05312e11	−0.344049
$453$	−5.42377e10	−0.0605145
$454$	1.91284e12	2.11314
$455$	1.43922e12	1.57426
$456$	0	0
$457$	1.41558e12	1.51814	0.759070	−	0.651009i	$-0.225654\pi$
$457$	1.41558e12	1.51814	0.759070	+	0.651009i	$0.225654\pi$
$458$	−1.74122e12	−1.84909
$459$	3.42216e11	0.359868
$460$	−1.15577e12	−1.20354
$461$	9.94561e10	0.102560	0.0512799	−	0.998684i	$-0.483670\pi$
$461$	9.94561e10	0.102560	0.0512799	+	0.998684i	$0.483670\pi$
$462$	−8.95873e11	−0.914866
$463$	9.82855e11	0.993974	0.496987	−	0.867758i	$-0.334440\pi$
$463$	9.82855e11	0.993974	0.496987	+	0.867758i	$0.334440\pi$
$464$	−6.35611e11	−0.636591
$465$	1.34327e12	1.33237
$466$	−2.74068e12	−2.69229
$467$	−1.82782e12	−1.77831	−0.889157	−	0.457603i	$-0.848708\pi$
$467$	−1.82782e12	−1.77831	−0.889157	+	0.457603i	$0.848708\pi$
$468$	−2.19063e12	−2.11087
$469$	−4.81796e11	−0.459818
$470$	−1.46991e11	−0.138947
$471$	8.62969e10	0.0807981
$472$	−6.22997e11	−0.577759
$473$	2.33786e11	0.214755
$474$	−4.48939e12	−4.08493
$475$	0	0
$476$	−1.06856e12	−0.954038
$477$	−1.50475e12	−1.33086
$478$	−4.29476e11	−0.376282
$479$	1.99914e12	1.73513	0.867567	−	0.497321i	$-0.165683\pi$
$479$	1.99914e12	1.73513	0.867567	+	0.497321i	$0.165683\pi$
$480$	4.32033e12	3.71477
$481$	−1.43440e11	−0.122185
$482$	−1.52885e12	−1.29019
$483$	−5.98592e11	−0.500459
$484$	−9.14084e11	−0.757150
$485$	−1.40797e12	−1.15546
$486$	−2.63787e12	−2.14482
$487$	1.44418e12	1.16343	0.581716	−	0.813392i	$-0.302382\pi$
$487$	1.44418e12	1.16343	0.581716	+	0.813392i	$0.302382\pi$
$488$	3.93519e11	0.314106
$489$	1.30603e12	1.03291
$490$	−2.03706e12	−1.59633
$491$	−1.53011e12	−1.18811	−0.594056	−	0.804424i	$-0.702474\pi$
$491$	−1.53011e12	−1.18811	−0.594056	+	0.804424i	$0.702474\pi$
$492$	−4.83393e12	−3.71927
$493$	−1.50383e12	−1.14653
$494$	0	0
$495$	1.84409e12	1.38057
$496$	−4.37083e11	−0.324262
$497$	6.59458e11	0.484824
$498$	1.80133e12	1.31238
$499$	−3.25360e8	−0.000234915 0	−0.000117458	−	1.00000i	$-0.500037\pi$
$499$	−3.25360e8	−0.000234915 0	−0.000117458		1.00000i	$0.500037\pi$
$500$	−3.89199e12	−2.78488
$501$	2.59141e12	1.83767
$502$	2.53004e12	1.77812
$503$	5.20981e11	0.362882	0.181441	−	0.983402i	$-0.441924\pi$
$503$	5.20981e11	0.362882	0.181441	+	0.983402i	$0.441924\pi$
$504$	−4.65460e11	−0.321325
$505$	1.08397e12	0.741660
$506$	7.45980e11	0.505883
$507$	−1.94239e12	−1.30557
$508$	−2.52428e12	−1.68171
$509$	6.70739e11	0.442918	0.221459	−	0.975170i	$-0.428918\pi$
$509$	6.70739e11	0.442918	0.221459	+	0.975170i	$0.428918\pi$
$510$	7.17398e12	4.69563
$511$	−1.23824e11	−0.0803360
$512$	−1.82493e12	−1.17363
$513$	0	0
$514$	3.19671e12	2.02008
$515$	−1.58268e12	−0.991427
$516$	1.02805e12	0.638399
$517$	5.31806e10	0.0327375
$518$	−1.41095e11	−0.0861046
$519$	4.92020e11	0.297666
$520$	−1.70371e12	−1.02184
$521$	−2.52718e12	−1.50268	−0.751339	−	0.659917i	$-0.770592\pi$
$521$	−2.52718e12	−1.50268	−0.751339	+	0.659917i	$0.770592\pi$
$522$	−3.03255e12	−1.78769
$523$	1.06654e12	0.623333	0.311666	−	0.950192i	$-0.399113\pi$
$523$	1.06654e12	0.623333	0.311666	+	0.950192i	$0.399113\pi$
$524$	−5.28414e11	−0.306185
$525$	−3.67170e12	−2.10936
$526$	2.66417e12	1.51749
$527$	−1.03412e12	−0.584013
$528$	−1.09702e12	−0.614276
$529$	−1.30271e12	−0.723267
$530$	−5.41775e12	−2.98248
$531$	3.07471e12	1.67834
$532$	0	0
$533$	−5.01231e12	−2.69008
$534$	4.40544e12	2.34452
$535$	−2.99297e12	−1.57947
$536$	5.70337e11	0.298463
$537$	2.37537e11	0.123267
$538$	2.41009e12	1.24026
$539$	7.36998e11	0.376112
$540$	1.39275e12	0.704855
$541$	1.68314e12	0.844758	0.422379	−	0.906419i	$-0.361195\pi$
$541$	1.68314e12	0.844758	0.422379	+	0.906419i	$0.361195\pi$
$542$	1.18901e12	0.591819
$543$	−2.80270e12	−1.38349
$544$	−3.32600e12	−1.62827
$545$	6.75322e11	0.327889
$546$	−4.08489e12	−1.96704
$547$	−2.61181e12	−1.24738	−0.623690	−	0.781672i	$-0.714367\pi$
$547$	−2.61181e12	−1.24738	−0.623690	+	0.781672i	$0.714367\pi$
$548$	−4.00942e11	−0.189919
$549$	−1.94215e12	−0.912448
$550$	4.57577e12	2.13222
$551$	0	0
$552$	7.08597e11	0.324843
$553$	−2.56668e12	−1.16710
$554$	6.11847e11	0.275962
$555$	5.30984e11	0.237554
$556$	1.95251e11	0.0866476
$557$	−5.23423e11	−0.230412	−0.115206	−	0.993342i	$-0.536753\pi$
$557$	−5.23423e11	−0.230412	−0.115206	+	0.993342i	$0.536753\pi$
$558$	−2.08536e12	−0.910598
$559$	1.06599e12	0.461742
$560$	1.73355e12	0.744889
$561$	−2.59551e12	−1.10634
$562$	2.08853e12	0.883135
$563$	−2.15892e12	−0.905625	−0.452813	−	0.891606i	$-0.649579\pi$
$563$	−2.15892e12	−0.905625	−0.452813	+	0.891606i	$0.649579\pi$
$564$	2.33857e11	0.0973182
$565$	1.17190e12	0.483807
$566$	6.16458e12	2.52481
$567$	−1.18134e12	−0.480012
$568$	−7.80649e11	−0.314694
$569$	−3.81657e11	−0.152640	−0.0763199	−	0.997083i	$-0.524317\pi$
$569$	−3.81657e11	−0.152640	−0.0763199	+	0.997083i	$0.524317\pi$
$570$	0	0
$571$	4.13241e12	1.62683	0.813413	−	0.581687i	$-0.197607\pi$
$571$	4.13241e12	1.62683	0.813413	+	0.581687i	$0.197607\pi$
$572$	2.85354e12	1.11456
$573$	5.23972e11	0.203055
$574$	−4.93034e12	−1.89572
$575$	3.05737e12	1.16639
$576$	−4.63842e12	−1.75577
$577$	−3.52348e12	−1.32337	−0.661684	−	0.749783i	$-0.730158\pi$
$577$	−3.52348e12	−1.32337	−0.661684	+	0.749783i	$0.730158\pi$
$578$	−1.47510e12	−0.549727
$579$	6.62139e12	2.44847
$580$	−6.12026e12	−2.24566
$581$	1.02986e12	0.374959
$582$	3.99617e12	1.44375
$583$	1.96011e12	0.702705
$584$	1.46579e11	0.0521452
$585$	8.40844e12	2.96834
$586$	−5.18947e11	−0.181796
$587$	−1.02613e12	−0.356721	−0.178361	−	0.983965i	$-0.557079\pi$
$587$	−1.02613e12	−0.356721	−0.178361	+	0.983965i	$0.557079\pi$
$588$	3.24088e12	1.11806
$589$	0	0
$590$	1.10703e13	3.76118
$591$	−6.53375e12	−2.20302
$592$	−1.72775e11	−0.0578139
$593$	−2.00737e12	−0.666626	−0.333313	−	0.942816i	$-0.608167\pi$
$593$	−2.00737e12	−0.666626	−0.333313	+	0.942816i	$0.608167\pi$
$594$	−8.98932e11	−0.296270
$595$	4.10151e12	1.34158
$596$	−5.56362e12	−1.80613
$597$	3.34322e11	0.107716
$598$	3.40143e12	1.08769
$599$	5.91194e11	0.187633	0.0938165	−	0.995590i	$-0.470093\pi$
$599$	5.91194e11	0.187633	0.0938165	+	0.995590i	$0.470093\pi$
$600$	4.34646e12	1.36916
$601$	−2.13322e11	−0.0666961	−0.0333481	−	0.999444i	$-0.510617\pi$
$601$	−2.13322e11	−0.0666961	−0.0333481	+	0.999444i	$0.510617\pi$
$602$	1.04856e12	0.325393
$603$	−2.81482e12	−0.867007
$604$	1.69933e11	0.0519532
$605$	3.50859e12	1.06472
$606$	−3.07658e12	−0.926704
$607$	−2.87264e12	−0.858880	−0.429440	−	0.903095i	$-0.641289\pi$
$607$	−2.87264e12	−0.858880	−0.429440	+	0.903095i	$0.641289\pi$
$608$	0	0
$609$	−3.16977e12	−0.933793
$610$	−6.99258e12	−2.04481
$611$	2.42486e11	0.0703885
$612$	−6.24286e12	−1.79888
$613$	−6.05905e12	−1.73313	−0.866567	−	0.499060i	$-0.833679\pi$
$613$	−6.05905e12	−1.73313	−0.866567	+	0.499060i	$0.833679\pi$
$614$	5.24224e12	1.48853
$615$	1.85544e13	5.23009
$616$	6.06315e11	0.169662
$617$	1.30247e12	0.361812	0.180906	−	0.983500i	$-0.442097\pi$
$617$	1.30247e12	0.361812	0.180906	+	0.983500i	$0.442097\pi$
$618$	4.49206e12	1.23879
$619$	−1.00261e11	−0.0274489	−0.0137245	−	0.999906i	$-0.504369\pi$
$619$	−1.00261e11	−0.0274489	−0.0137245	+	0.999906i	$0.504369\pi$
$620$	−4.20864e12	−1.14388
$621$	−6.00636e11	−0.162069
$622$	−2.43815e11	−0.0653136
$623$	2.51868e12	0.669849
$624$	−5.00207e12	−1.32075
$625$	6.48082e12	1.69891
$626$	3.50328e12	0.911780
$627$	0	0
$628$	−2.70379e11	−0.0693672
$629$	−4.08777e11	−0.104126
$630$	8.27093e12	2.09181
$631$	−6.06750e11	−0.152362	−0.0761812	−	0.997094i	$-0.524273\pi$
$631$	−6.06750e11	−0.152362	−0.0761812	+	0.997094i	$0.524273\pi$
$632$	3.03836e12	0.757552
$633$	8.74726e12	2.16549
$634$	−9.28910e11	−0.228335
$635$	9.68914e12	2.36485
$636$	8.61943e12	2.08892
$637$	3.36047e12	0.808673
$638$	3.95025e12	0.943912
$639$	3.85278e12	0.914156
$640$	−6.08810e12	−1.43440
$641$	5.03899e12	1.17891	0.589457	−	0.807800i	$-0.299342\pi$
$641$	5.03899e12	1.17891	0.589457	+	0.807800i	$0.299342\pi$
$642$	8.49483e12	1.97355
$643$	3.67766e12	0.848442	0.424221	−	0.905559i	$-0.360548\pi$
$643$	3.67766e12	0.848442	0.424221	+	0.905559i	$0.360548\pi$
$644$	1.87546e12	0.429657
$645$	−3.94605e12	−0.897726
$646$	0	0
$647$	1.29323e11	0.0290139	0.0145070	−	0.999895i	$-0.495382\pi$
$647$	1.29323e11	0.0290139	0.0145070	+	0.999895i	$0.495382\pi$
$648$	1.39844e12	0.311571
$649$	−4.00517e12	−0.886175
$650$	2.08640e13	4.58446
$651$	−2.17972e12	−0.475648
$652$	−4.09195e12	−0.886781
$653$	−5.47148e12	−1.17759	−0.588796	−	0.808281i	$-0.700398\pi$
$653$	−5.47148e12	−1.17759	−0.588796	+	0.808281i	$0.700398\pi$
$654$	−1.91674e12	−0.409697
$655$	2.02825e12	0.430562
$656$	−6.03735e12	−1.27286
$657$	−7.23420e11	−0.151477
$658$	2.38521e11	0.0496032
$659$	5.72024e12	1.18149	0.590744	−	0.806859i	$-0.298834\pi$
$659$	5.72024e12	1.18149	0.590744	+	0.806859i	$0.298834\pi$
$660$	−1.05632e13	−2.16694
$661$	3.56131e12	0.725610	0.362805	−	0.931865i	$-0.381819\pi$
$661$	3.56131e12	0.725610	0.362805	+	0.931865i	$0.381819\pi$
$662$	1.08808e12	0.220191
$663$	−1.18347e13	−2.37873
$664$	−1.21912e12	−0.243382
$665$	0	0
$666$	−8.24322e11	−0.162354
$667$	2.63942e12	0.516349
$668$	−8.11921e12	−1.57768
$669$	−2.59231e12	−0.500345
$670$	−1.01345e13	−1.94297
$671$	2.52988e12	0.481780
$672$	−7.01056e12	−1.32615
$673$	−1.33660e12	−0.251151	−0.125575	−	0.992084i	$-0.540078\pi$
$673$	−1.33660e12	−0.251151	−0.125575	+	0.992084i	$0.540078\pi$
$674$	−1.49151e13	−2.78392
$675$	−3.68424e12	−0.683095
$676$	6.08575e12	1.12087
$677$	1.01411e13	1.85539	0.927694	−	0.373343i	$-0.121788\pi$
$677$	1.01411e13	1.85539	0.927694	+	0.373343i	$0.121788\pi$
$678$	−3.32615e12	−0.604517
$679$	2.28469e12	0.412491
$680$	−4.85525e12	−0.870807
$681$	1.16811e13	2.08124
$682$	2.71642e12	0.480803
$683$	−8.19823e12	−1.44154	−0.720770	−	0.693174i	$-0.756212\pi$
$683$	−8.19823e12	−1.44154	−0.720770	+	0.693174i	$0.756212\pi$
$684$	0	0
$685$	1.53896e12	0.267067
$686$	8.90827e12	1.53580
$687$	−1.06331e13	−1.82118
$688$	1.28399e12	0.218481
$689$	8.93749e12	1.51088
$690$	−1.25913e13	−2.11471
$691$	7.58904e12	1.26630	0.633148	−	0.774031i	$-0.281762\pi$
$691$	7.58904e12	1.26630	0.633148	+	0.774031i	$0.281762\pi$
$692$	−1.54156e12	−0.255554
$693$	−2.99238e12	−0.492853
$694$	−2.85717e12	−0.467540
$695$	−7.49446e11	−0.121845
$696$	3.75229e12	0.606115
$697$	−1.42841e13	−2.29248
$698$	−4.40737e12	−0.702798
$699$	−1.67365e13	−2.65165
$700$	1.15039e13	1.81094
$701$	−5.16852e12	−0.808417	−0.404208	−	0.914667i	$-0.632453\pi$
$701$	−5.16852e12	−0.808417	−0.404208	+	0.914667i	$0.632453\pi$
$702$	−4.09884e12	−0.637007
$703$	0	0
$704$	6.04207e12	0.927063
$705$	−8.97629e11	−0.136850
$706$	−2.30181e12	−0.348697
$707$	−1.75894e12	−0.264767
$708$	−1.76124e13	−2.63432
$709$	−1.21897e13	−1.81170	−0.905848	−	0.423604i	$-0.860765\pi$
$709$	−1.21897e13	−1.81170	−0.905848	+	0.423604i	$0.860765\pi$
$710$	1.38716e13	2.04864
$711$	−1.49954e13	−2.20062
$712$	−2.98154e12	−0.434792
$713$	1.81502e12	0.263014
$714$	−1.16411e13	−1.67631
$715$	−1.09530e13	−1.56731
$716$	−7.44233e11	−0.105828
$717$	−2.62268e12	−0.370604
$718$	−1.54391e13	−2.16801
$719$	7.19508e12	1.00405	0.502025	−	0.864853i	$-0.332588\pi$
$719$	7.19508e12	1.00405	0.502025	+	0.864853i	$0.332588\pi$
$720$	1.01280e13	1.40452
$721$	2.56820e12	0.353933
$722$	0	0
$723$	−9.33623e12	−1.27072
$724$	8.78120e12	1.18776
$725$	1.61900e13	2.17633
$726$	−9.95829e12	−1.33036
$727$	2.69280e12	0.357520	0.178760	−	0.983893i	$-0.442791\pi$
$727$	2.69280e12	0.357520	0.178760	+	0.983893i	$0.442791\pi$
$728$	2.76460e12	0.364789
$729$	−1.03922e13	−1.36281
$730$	−2.60462e12	−0.339462
$731$	3.03786e12	0.393496
$732$	1.11249e13	1.43218
$733$	1.42163e12	0.181894	0.0909470	−	0.995856i	$-0.471011\pi$
$733$	1.42163e12	0.181894	0.0909470	+	0.995856i	$0.471011\pi$
$734$	5.78048e12	0.735075
$735$	−1.24397e13	−1.57224
$736$	5.83759e12	0.733303
$737$	3.66662e12	0.457786
$738$	−2.88047e13	−3.57445
$739$	1.01945e13	1.25737	0.628687	−	0.777659i	$-0.283593\pi$
$739$	1.01945e13	1.25737	0.628687	+	0.777659i	$0.283593\pi$
$740$	−1.66364e12	−0.203946
$741$	0	0
$742$	8.79133e12	1.06472
$743$	6.41623e12	0.772378	0.386189	−	0.922420i	$-0.373791\pi$
$743$	6.41623e12	0.772378	0.386189	+	0.922420i	$0.373791\pi$
$744$	2.58029e12	0.308738
$745$	2.13552e13	2.53981
$746$	7.80313e12	0.922453
$747$	6.01677e12	0.707002
$748$	8.13204e12	0.949822
$749$	4.85667e12	0.563859
$750$	−4.24005e13	−4.89323
$751$	7.84873e12	0.900367	0.450183	−	0.892936i	$-0.351359\pi$
$751$	7.84873e12	0.900367	0.450183	+	0.892936i	$0.351359\pi$
$752$	2.92076e11	0.0333055
$753$	1.54502e13	1.75128
$754$	1.80119e13	2.02949
$755$	−6.52268e11	−0.0730574
$756$	−2.26000e12	−0.251628
$757$	−1.77164e13	−1.96085	−0.980425	−	0.196892i	$-0.936915\pi$
$757$	−1.77164e13	−1.96085	−0.980425	+	0.196892i	$0.936915\pi$
$758$	1.80375e13	1.98456
$759$	4.55548e12	0.498248
$760$	0	0
$761$	−1.63568e11	−0.0176794	−0.00883972	−	0.999961i	$-0.502814\pi$
$761$	−1.63568e11	−0.0176794	−0.00883972	+	0.999961i	$0.502814\pi$
$762$	−2.75003e13	−2.95488
$763$	−1.09584e12	−0.117054
$764$	−1.64167e12	−0.174327
$765$	2.39624e13	2.52961
$766$	4.24610e12	0.445616
$767$	−1.82623e13	−1.90535
$768$	−3.55061e12	−0.368279
$769$	1.12646e13	1.16157	0.580786	−	0.814056i	$-0.302745\pi$
$769$	1.12646e13	1.16157	0.580786	+	0.814056i	$0.302745\pi$
$770$	−1.07738e13	−1.10449
$771$	1.95213e13	1.98959
$772$	−2.07456e13	−2.10208
$773$	−1.83700e12	−0.185056	−0.0925278	−	0.995710i	$-0.529495\pi$
$773$	−1.83700e12	−0.185056	−0.0925278	+	0.995710i	$0.529495\pi$
$774$	6.12602e12	0.613542
$775$	1.11331e13	1.10856
$776$	−2.70456e12	−0.267743
$777$	−8.61622e11	−0.0848052
$778$	1.18287e13	1.15752
$779$	0	0
$780$	−4.81646e13	−4.65911
$781$	−5.01869e12	−0.482681
$782$	9.69341e12	0.926928
$783$	−3.18060e12	−0.302399
$784$	4.04771e12	0.382637
$785$	1.03781e12	0.0975452
$786$	−5.75670e12	−0.537987
$787$	−5.98053e11	−0.0555716	−0.0277858	−	0.999614i	$-0.508846\pi$
$787$	−5.98053e11	−0.0555716	−0.0277858	+	0.999614i	$0.508846\pi$
$788$	2.04710e13	1.89135
$789$	1.62693e13	1.49459
$790$	−5.39897e13	−4.93162
$791$	−1.90163e12	−0.172716
$792$	3.54230e12	0.319906
$793$	1.15354e13	1.03587
$794$	−1.84885e13	−1.65086
$795$	−3.30846e13	−2.93747
$796$	−1.04747e12	−0.0924769
$797$	−9.81580e12	−0.861715	−0.430857	−	0.902420i	$-0.641789\pi$
$797$	−9.81580e12	−0.861715	−0.430857	+	0.902420i	$0.641789\pi$
$798$	0	0
$799$	6.91039e11	0.0599849
$800$	3.58072e13	3.09076
$801$	1.47150e13	1.26303
$802$	−1.48220e13	−1.26509
$803$	9.42338e11	0.0799810
$804$	1.61236e13	1.36085
$805$	−7.19872e12	−0.604190
$806$	1.23860e13	1.03377
$807$	1.47177e13	1.22154
$808$	2.08219e12	0.171858
$809$	1.46061e12	0.119886	0.0599429	−	0.998202i	$-0.480908\pi$
$809$	1.46061e12	0.119886	0.0599429	+	0.998202i	$0.480908\pi$
$810$	−2.48494e13	−2.02831
$811$	7.20885e11	0.0585157	0.0292579	−	0.999572i	$-0.490686\pi$
$811$	7.20885e11	0.0585157	0.0292579	+	0.999572i	$0.490686\pi$
$812$	9.93129e12	0.801684
$813$	7.26093e12	0.582888
$814$	1.07377e12	0.0857242
$815$	1.57064e13	1.24701
$816$	−1.42549e13	−1.12554
$817$	0	0
$818$	1.22132e13	0.953759
$819$	−1.36443e13	−1.05968
$820$	−5.81333e13	−4.49016
$821$	−9.58084e12	−0.735969	−0.367984	−	0.929832i	$-0.619952\pi$
$821$	−9.58084e12	−0.735969	−0.367984	+	0.929832i	$0.619952\pi$
$822$	−4.36797e12	−0.333700
$823$	5.01674e12	0.381173	0.190586	−	0.981670i	$-0.438961\pi$
$823$	5.01674e12	0.381173	0.190586	+	0.981670i	$0.438961\pi$
$824$	−3.04017e12	−0.229734
$825$	2.79428e13	2.10004
$826$	−1.79636e13	−1.34271
$827$	−9.34995e11	−0.0695080	−0.0347540	−	0.999396i	$-0.511065\pi$
$827$	−9.34995e11	−0.0695080	−0.0347540	+	0.999396i	$0.511065\pi$
$828$	1.09571e13	0.810137
$829$	1.49880e13	1.10217	0.551085	−	0.834449i	$-0.314214\pi$
$829$	1.49880e13	1.10217	0.551085	+	0.834449i	$0.314214\pi$
$830$	2.16629e13	1.58440
$831$	3.73637e12	0.271797
$832$	2.75499e13	1.99327
$833$	9.57670e12	0.689149
$834$	2.12712e12	0.152246
$835$	3.11646e13	2.21856
$836$	0	0
$837$	−2.18716e12	−0.154034
$838$	1.05629e13	0.739918
$839$	1.58708e13	1.10578	0.552892	−	0.833253i	$-0.313524\pi$
$839$	1.58708e13	1.10578	0.552892	+	0.833253i	$0.313524\pi$
$840$	−1.02339e13	−0.709228
$841$	−5.30382e11	−0.0365601
$842$	−7.00579e12	−0.480344
$843$	1.27540e13	0.869808
$844$	−2.74062e13	−1.85912
$845$	−2.33594e13	−1.57618
$846$	1.39352e12	0.0935290
$847$	−5.69336e12	−0.380096
$848$	1.07653e13	0.714897
$849$	3.76452e13	2.48671
$850$	5.94584e13	3.90686
$851$	7.17460e11	0.0468937
$852$	−2.20692e13	−1.43486
$853$	−3.63511e12	−0.235097	−0.117549	−	0.993067i	$-0.537504\pi$
$853$	−3.63511e12	−0.235097	−0.117549	+	0.993067i	$0.537504\pi$
$854$	1.13468e13	0.729983
$855$	0	0
$856$	−5.74919e12	−0.365995
$857$	2.33818e13	1.48069	0.740345	−	0.672227i	$-0.234662\pi$
$857$	2.33818e13	1.48069	0.740345	+	0.672227i	$0.234662\pi$
$858$	3.10873e13	1.95835
$859$	−2.68917e13	−1.68519	−0.842595	−	0.538547i	$-0.818973\pi$
$859$	−2.68917e13	−1.68519	−0.842595	+	0.538547i	$0.818973\pi$
$860$	1.23635e13	0.770720
$861$	−3.01081e13	−1.86711
$862$	−2.85676e13	−1.76234
$863$	−2.63772e13	−1.61875	−0.809375	−	0.587293i	$-0.800194\pi$
$863$	−2.63772e13	−1.61875	−0.809375	+	0.587293i	$0.800194\pi$
$864$	−7.03450e12	−0.429459
$865$	5.91707e12	0.359364
$866$	−5.26147e12	−0.317890
$867$	−9.00800e12	−0.541430
$868$	6.82932e12	0.408356
$869$	1.95332e13	1.16194
$870$	−6.66758e13	−3.94577
$871$	1.67186e13	0.984280
$872$	1.29722e12	0.0759784
$873$	1.33480e13	0.777769
$874$	0	0
$875$	−2.42413e13	−1.39804
$876$	4.14385e12	0.237758
$877$	6.08610e12	0.347409	0.173704	−	0.984798i	$-0.444426\pi$
$877$	6.08610e12	0.347409	0.173704	+	0.984798i	$0.444426\pi$
$878$	−1.00681e13	−0.571773
$879$	−3.16905e12	−0.179052
$880$	−1.31929e13	−0.741597
$881$	−2.57026e13	−1.43743	−0.718713	−	0.695307i	$-0.755269\pi$
$881$	−2.57026e13	−1.43743	−0.718713	+	0.695307i	$0.755269\pi$
$882$	1.93120e13	1.07453
$883$	−1.20949e13	−0.669543	−0.334771	−	0.942299i	$-0.608659\pi$
$883$	−1.20949e13	−0.669543	−0.334771	+	0.942299i	$0.608659\pi$
$884$	3.70795e13	2.04220
$885$	6.76028e13	3.70442
$886$	4.18164e13	2.27979
$887$	−2.23314e13	−1.21132	−0.605661	−	0.795723i	$-0.707091\pi$
$887$	−2.23314e13	−1.21132	−0.605661	+	0.795723i	$0.707091\pi$
$888$	1.01996e12	0.0550461
$889$	−1.57225e13	−0.844234
$890$	5.29802e13	2.83047
$891$	8.99040e12	0.477892
$892$	8.12203e12	0.429559
$893$	0	0
$894$	−6.06117e13	−3.17349
$895$	2.85664e12	0.148817
$896$	9.87910e12	0.512072
$897$	2.07715e13	1.07128
$898$	−4.72567e13	−2.42505
$899$	9.61122e12	0.490750
$900$	6.72096e13	3.41460
$901$	2.54701e13	1.28757
$902$	3.75214e13	1.88734
$903$	6.40322e12	0.320482
$904$	2.25110e12	0.112108
$905$	−3.37055e13	−1.67025
$906$	1.85130e12	0.0912853
$907$	−3.16396e13	−1.55238	−0.776190	−	0.630500i	$-0.782850\pi$
$907$	−3.16396e13	−1.55238	−0.776190	+	0.630500i	$0.782850\pi$
$908$	−3.65984e13	−1.78680
$909$	−1.02763e13	−0.499231
$910$	−4.91252e13	−2.37475
$911$	−2.77199e13	−1.33340	−0.666698	−	0.745328i	$-0.732293\pi$
$911$	−2.77199e13	−1.33340	−0.666698	+	0.745328i	$0.732293\pi$
$912$	0	0
$913$	−7.83754e12	−0.373303
$914$	−4.83182e13	−2.29009
$915$	−4.27016e13	−2.01395
$916$	3.33147e13	1.56353
$917$	−3.29122e12	−0.153708
$918$	−1.16809e13	−0.542855
$919$	1.66068e13	0.768008	0.384004	−	0.923331i	$-0.374545\pi$
$919$	1.66068e13	0.768008	0.384004	+	0.923331i	$0.374545\pi$
$920$	8.52164e12	0.392173
$921$	3.20128e13	1.46607
$922$	−3.39475e12	−0.154710
$923$	−2.28836e13	−1.03781
$924$	1.71408e13	0.773582
$925$	4.40083e12	0.197650
$926$	−3.35479e13	−1.49939
$927$	1.50043e13	0.667355
$928$	3.09123e13	1.36825
$929$	−6.20497e12	−0.273319	−0.136659	−	0.990618i	$-0.543637\pi$
$929$	−6.20497e12	−0.273319	−0.136659	+	0.990618i	$0.543637\pi$
$930$	−4.58501e13	−2.00987
$931$	0	0
$932$	5.24374e13	2.27651
$933$	−1.48890e12	−0.0643279
$934$	6.23893e13	2.68256
$935$	−3.12138e13	−1.33566
$936$	1.61517e13	0.687825
$937$	−8.96609e12	−0.379992	−0.189996	−	0.981785i	$-0.560848\pi$
$937$	−8.96609e12	−0.379992	−0.189996	+	0.981785i	$0.560848\pi$
$938$	1.64452e13	0.693628
$939$	2.13935e13	0.898020
$940$	2.81238e12	0.117489
$941$	−3.53782e13	−1.47090	−0.735450	−	0.677580i	$-0.763029\pi$
$941$	−3.53782e13	−1.47090	−0.735450	+	0.677580i	$0.763029\pi$
$942$	−2.94558e12	−0.121883
$943$	2.50706e13	1.03243
$944$	−2.19970e13	−0.901549
$945$	8.67471e12	0.353844
$946$	−7.97985e12	−0.323955
$947$	4.19688e13	1.69571	0.847854	−	0.530230i	$-0.177894\pi$
$947$	4.19688e13	1.69571	0.847854	+	0.530230i	$0.177894\pi$
$948$	8.58956e13	3.45409
$949$	4.29676e12	0.171966
$950$	0	0
$951$	−5.67258e12	−0.224889
$952$	7.87858e12	0.310872
$953$	−2.65644e13	−1.04323	−0.521617	−	0.853180i	$-0.674671\pi$
$953$	−2.65644e13	−1.04323	−0.521617	+	0.853180i	$0.674671\pi$
$954$	5.13619e13	2.00758
$955$	6.30134e12	0.245142
$956$	8.21718e12	0.318172
$957$	2.41230e13	0.929667
$958$	−6.82368e13	−2.61742
$959$	−2.49726e12	−0.0953411
$960$	−1.01984e14	−3.87534
$961$	−1.98304e13	−0.750026
$962$	4.89607e12	0.184314
$963$	2.83743e13	1.06318
$964$	2.92516e13	1.09094
$965$	7.96294e13	2.95597
$966$	2.04318e13	0.754936
$967$	−1.49735e13	−0.550685	−0.275343	−	0.961346i	$-0.588791\pi$
$967$	−1.49735e13	−0.550685	−0.275343	+	0.961346i	$0.588791\pi$
$968$	6.73964e12	0.246716
$969$	0	0
$970$	4.80583e13	1.74299
$971$	4.02523e13	1.45313	0.726565	−	0.687097i	$-0.241115\pi$
$971$	4.02523e13	1.45313	0.726565	+	0.687097i	$0.241115\pi$
$972$	5.04704e13	1.81359
$973$	1.21612e12	0.0434979
$974$	−4.92944e13	−1.75502
$975$	1.27410e14	4.51527
$976$	1.38945e13	0.490138
$977$	2.48678e12	0.0873198	0.0436599	−	0.999046i	$-0.486098\pi$
$977$	2.48678e12	0.0873198	0.0436599	+	0.999046i	$0.486098\pi$
$978$	−4.45789e13	−1.55813
$979$	−1.91680e13	−0.666889
$980$	3.89751e13	1.34980
$981$	−6.40226e12	−0.220710
$982$	5.22276e13	1.79225
$983$	−1.73760e12	−0.0593552	−0.0296776	−	0.999560i	$-0.509448\pi$
$983$	−1.73760e12	−0.0593552	−0.0296776	+	0.999560i	$0.509448\pi$
$984$	3.56411e13	1.21192
$985$	−7.85754e13	−2.65964
$986$	5.13303e13	1.72953
$987$	1.45657e12	0.0488546
$988$	0	0
$989$	−5.33187e12	−0.177213
$990$	−6.29444e13	−2.08257
$991$	−4.68023e13	−1.54147	−0.770735	−	0.637155i	$-0.780111\pi$
$991$	−4.68023e13	−1.54147	−0.770735	+	0.637155i	$0.780111\pi$
$992$	2.12571e13	0.696948
$993$	6.64457e12	0.216868
$994$	−2.25094e13	−0.731349
$995$	4.02058e12	0.130042
$996$	−3.44649e13	−1.10971
$997$	−1.43322e13	−0.459394	−0.229697	−	0.973262i	$-0.573774\pi$
$997$	−1.43322e13	−0.459394	−0.229697	+	0.973262i	$0.573774\pi$
$998$	1.11055e10	0.000354366 0
$999$	−8.64565e11	−0.0274633

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.10.a.f.1.2		14
19.8	odd	6		19.10.c.a.7.2	✓	28
19.12	odd	6		19.10.c.a.11.2	yes	28
19.18	odd	2		361.10.a.e.1.13		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.10.c.a.7.2	✓	28	19.8	odd	6
19.10.c.a.11.2	yes	28	19.12	odd	6
361.10.a.e.1.13		14	19.18	odd	2
361.10.a.f.1.2		14	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q-34.1331 q^{2} -208.441 q^{3} +653.070 q^{4} -2506.72 q^{5} +7114.73 q^{6} +4067.64 q^{7} -4815.16 q^{8} +23764.5 q^{9} +85562.3 q^{10} -30956.0 q^{11} -136126. q^{12} -141149. q^{13} -138841. q^{14} +522504. q^{15} -170015. q^{16} -402249. q^{17} -811158. q^{18} -1.63707e6 q^{20} -847862. q^{21} +1.05663e6 q^{22} +706002. q^{23} +1.00368e6 q^{24} +4.33054e6 q^{25} +4.81787e6 q^{26} -850757. q^{27} +2.65645e6 q^{28} +3.73855e6 q^{29} -1.78347e7 q^{30} +2.57084e6 q^{31} +8.26852e6 q^{32} +6.45250e6 q^{33} +1.37300e7 q^{34} -1.01965e7 q^{35} +1.55199e7 q^{36} +1.01623e6 q^{37} +2.94213e7 q^{39} +1.20703e7 q^{40} +3.55106e7 q^{41} +2.89402e7 q^{42} -7.55220e6 q^{43} -2.02165e7 q^{44} -5.95711e7 q^{45} -2.40981e7 q^{46} -1.71794e6 q^{47} +3.54381e7 q^{48} -2.38079e7 q^{49} -1.47815e8 q^{50} +8.38450e7 q^{51} -9.21805e7 q^{52} -6.33193e7 q^{53} +2.90390e7 q^{54} +7.75982e7 q^{55} -1.95863e7 q^{56} -1.27608e8 q^{58} +1.29382e8 q^{59} +3.41231e8 q^{60} -8.17249e7 q^{61} -8.77509e7 q^{62} +9.66656e7 q^{63} -1.95182e8 q^{64} +3.53823e8 q^{65} -2.20244e8 q^{66} -1.18446e8 q^{67} -2.62697e8 q^{68} -1.47160e8 q^{69} +3.48037e8 q^{70} +1.62123e8 q^{71} -1.14430e8 q^{72} -3.04412e7 q^{73} -3.46871e7 q^{74} -9.02662e8 q^{75} -1.25918e8 q^{77} -1.00424e9 q^{78} -6.30999e8 q^{79} +4.26182e8 q^{80} -2.90425e8 q^{81} -1.21209e9 q^{82} +2.53183e8 q^{83} -5.53713e8 q^{84} +1.00833e9 q^{85} +2.57780e8 q^{86} -7.79266e8 q^{87} +1.49058e8 q^{88} +6.19200e8 q^{89} +2.03335e9 q^{90} -5.74145e8 q^{91} +4.61069e8 q^{92} -5.35868e8 q^{93} +5.86386e7 q^{94} -1.72350e9 q^{96} +5.61676e8 q^{97} +8.12638e8 q^{98} -7.35655e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 15 q^{2} - 74 q^{3} + 2987 q^{4} + 285 q^{5} + 535 q^{6} - 1338 q^{7} + 12135 q^{8} + 57928 q^{9} + 41180 q^{10} - 57405 q^{11} - 117729 q^{12} + 98671 q^{13} - 148290 q^{14} + 428251 q^{15} + 279203 q^{16}+ \cdots + 736622698 q^{99}+O(q^{100}) \) 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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