LMFDB - Embedded newform 361.10.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [361,10,Mod(1,361)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$185.927936855$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 2124x^{4} - 384x^{3} + 1071312x^{2} + 1260144x - 135644992 $ x^6 - 3x^5 - 2124x^4 - 384x^3 + 1071312x^2 + 1260144*x - 135644992
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 19)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$12.6748$ 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)

$f(q)$	$=$	\(q-6.67485 q^{2} -204.622 q^{3} -467.446 q^{4} -2305.86 q^{5} +1365.82 q^{6} -8934.31 q^{7} +6537.66 q^{8} +22187.1 q^{9} +15391.2 q^{10} +76011.2 q^{11} +95649.8 q^{12} +105878. q^{13} +59635.2 q^{14} +471829. q^{15} +195695. q^{16} -118507. q^{17} -148096. q^{18} +1.07786e6 q^{20} +1.82816e6 q^{21} -507363. q^{22} +464530. q^{23} -1.33775e6 q^{24} +3.36385e6 q^{25} -706722. q^{26} -512401. q^{27} +4.17631e6 q^{28} +4.26351e6 q^{29} -3.14939e6 q^{30} +3.30855e6 q^{31} -4.65351e6 q^{32} -1.55536e7 q^{33} +791015. q^{34} +2.06012e7 q^{35} -1.03713e7 q^{36} +5.43488e6 q^{37} -2.16650e7 q^{39} -1.50749e7 q^{40} +3.60719e6 q^{41} -1.22027e7 q^{42} -2.52643e7 q^{43} -3.55312e7 q^{44} -5.11604e7 q^{45} -3.10067e6 q^{46} +2.04296e7 q^{47} -4.00434e7 q^{48} +3.94683e7 q^{49} -2.24532e7 q^{50} +2.42491e7 q^{51} -4.94925e7 q^{52} -3.66196e7 q^{53} +3.42020e6 q^{54} -1.75271e8 q^{55} -5.84095e7 q^{56} -2.84583e7 q^{58} +6.15867e7 q^{59} -2.20555e8 q^{60} +1.82995e8 q^{61} -2.20840e7 q^{62} -1.98227e8 q^{63} -6.91342e7 q^{64} -2.44140e8 q^{65} +1.03818e8 q^{66} +2.11382e8 q^{67} +5.53956e7 q^{68} -9.50531e7 q^{69} -1.37510e8 q^{70} +3.66751e8 q^{71} +1.45052e8 q^{72} +3.38405e8 q^{73} -3.62770e7 q^{74} -6.88318e8 q^{75} -6.79108e8 q^{77} +1.44611e8 q^{78} +2.31930e8 q^{79} -4.51244e8 q^{80} -3.31861e8 q^{81} -2.40774e7 q^{82} +4.29926e8 q^{83} -8.54565e8 q^{84} +2.73260e8 q^{85} +1.68636e8 q^{86} -8.72407e8 q^{87} +4.96935e8 q^{88} +9.51115e8 q^{89} +3.41488e8 q^{90} -9.45951e8 q^{91} -2.17143e8 q^{92} -6.77001e8 q^{93} -1.36364e8 q^{94} +9.52211e8 q^{96} -2.29994e8 q^{97} -2.63445e8 q^{98} +1.68647e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 33 q^{2} + 155 q^{3} + 1365 q^{4} - 3612 q^{5} + 5581 q^{6} + 4085 q^{7} + 23511 q^{8} + 17625 q^{9} + 93884 q^{10} - 69312 q^{11} + 460165 q^{12} + 191747 q^{13} + 644691 q^{14} + 326428 q^{15} + 13905 q^{16}+ \cdots + 1045331674 q^{99}+O(q^{100}) $ 6 * q + 33 * q^2 + 155 * q^3 + 1365 * q^4 - 3612 * q^5 + 5581 * q^6 + 4085 * q^7 + 23511 * q^8 + 17625 * q^9 + 93884 * q^10 - 69312 * q^11 + 460165 * q^12 + 191747 * q^13 + 644691 * q^14 + 326428 * q^15 + 13905 * q^16 - 288195 * q^17 + 1159386 * q^18 - 1551444 * q^20 + 3260767 * q^21 - 2409710 * q^22 - 50697 * q^23 + 5457255 * q^24 + 7126888 * q^25 + 4394073 * q^26 - 3854359 * q^27 + 19295623 * q^28 + 7178667 * q^29 + 7527236 * q^30 + 4310716 * q^31 + 5388975 * q^32 - 17592194 * q^33 - 18049 * q^34 - 4166490 * q^35 + 21311958 * q^36 + 15687040 * q^37 - 42886175 * q^39 - 33173148 * q^40 + 25134306 * q^41 + 64728563 * q^42 - 75118674 * q^43 - 94242102 * q^44 - 90343732 * q^45 + 85549087 * q^46 - 83731938 * q^47 + 63665473 * q^48 + 21010019 * q^49 - 141211941 * q^50 + 134793629 * q^51 - 147001043 * q^52 + 138019203 * q^53 + 160916047 * q^54 - 1518258 * q^55 + 182020629 * q^56 + 14051197 * q^58 + 7809915 * q^59 - 651478180 * q^60 + 191946566 * q^61 + 564818736 * q^62 + 152217316 * q^63 + 167338593 * q^64 + 146177172 * q^65 + 14789186 * q^66 + 16109787 * q^67 + 561722511 * q^68 + 20855199 * q^69 - 692634996 * q^70 + 264469698 * q^71 + 768475026 * q^72 - 287572857 * q^73 + 376807098 * q^74 + 186644613 * q^75 - 1619915436 * q^77 + 80663153 * q^78 + 86534002 * q^79 - 1300596708 * q^80 - 1155245802 * q^81 + 1582686496 * q^82 - 359214570 * q^83 + 2245098407 * q^84 - 648092718 * q^85 + 1061832924 * q^86 + 347964645 * q^87 - 779241042 * q^88 + 2263866306 * q^89 - 1188734960 * q^90 - 1172864023 * q^91 - 373904061 * q^92 + 1467983860 * q^93 + 864022488 * q^94 + 3402264767 * q^96 - 2705893460 * q^97 + 4245664590 * q^98 + 1045331674 * 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 $

$2$	−6.67485	−0.294989	−0.147495	−	0.989063i	$-0.547121\pi$
$2$	−6.67485	−0.294989	−0.147495	+	0.989063i	$0.547121\pi$
$3$	−204.622	−1.45850	−0.729250	−	0.684247i	$-0.760131\pi$
$3$	−204.622	−1.45850	−0.729250	+	0.684247i	$0.760131\pi$
$4$	−467.446	−0.912981
$5$	−2305.86	−1.64994	−0.824969	−	0.565179i	$-0.808807\pi$
$5$	−2305.86	−1.64994	−0.824969	+	0.565179i	$0.808807\pi$
$6$	1365.82	0.430242
$7$	−8934.31	−1.40644	−0.703218	−	0.710974i	$-0.748254\pi$
$7$	−8934.31	−1.40644	−0.703218	+	0.710974i	$0.748254\pi$
$8$	6537.66	0.564309
$9$	22187.1	1.12722
$10$	15391.2	0.486714
$11$	76011.2	1.56535	0.782673	−	0.622433i	$-0.213856\pi$
$11$	76011.2	1.56535	0.782673	+	0.622433i	$0.213856\pi$
$12$	95649.8	1.33158
$13$	105878.	1.02816	0.514082	−	0.857741i	$-0.328133\pi$
$13$	105878.	1.02816	0.514082	+	0.857741i	$0.328133\pi$
$14$	59635.2	0.414884
$15$	471829.	2.40643
$16$	195695.	0.746516
$17$	−118507.	−0.344130	−0.172065	−	0.985086i	$-0.555044\pi$
$17$	−118507.	−0.344130	−0.172065	+	0.985086i	$0.555044\pi$
$18$	−148096.	−0.332519
$19$	0	0
$19$	0	0
$20$	1.07786e6	1.50636
$21$	1.82816e6	2.05129
$22$	−507363.	−0.461761
$23$	464530.	0.346130	0.173065	−	0.984910i	$-0.444633\pi$
$23$	464530.	0.346130	0.173065	+	0.984910i	$0.444633\pi$
$24$	−1.33775e6	−0.823045
$25$	3.36385e6	1.72229
$26$	−706722.	−0.303297
$27$	−512401.	−0.185555
$28$	4.17631e6	1.28405
$29$	4.26351e6	1.11938	0.559688	−	0.828704i	$-0.310921\pi$
$29$	4.26351e6	1.11938	0.559688	+	0.828704i	$0.310921\pi$
$30$	−3.14939e6	−0.709873
$31$	3.30855e6	0.643442	0.321721	−	0.946834i	$-0.395739\pi$
$31$	3.30855e6	0.643442	0.321721	+	0.946834i	$0.395739\pi$
$32$	−4.65351e6	−0.784524
$33$	−1.55536e7	−2.28306
$34$	791015.	0.101515
$35$	2.06012e7	2.32053
$36$	−1.03713e7	−1.02913
$37$	5.43488e6	0.476740	0.238370	−	0.971174i	$-0.423387\pi$
$37$	5.43488e6	0.476740	0.238370	+	0.971174i	$0.423387\pi$
$38$	0	0
$39$	−2.16650e7	−1.49958
$40$	−1.50749e7	−0.931075
$41$	3.60719e6	0.199361	0.0996807	−	0.995019i	$-0.468218\pi$
$41$	3.60719e6	0.199361	0.0996807	+	0.995019i	$0.468218\pi$
$42$	−1.22027e7	−0.605108
$43$	−2.52643e7	−1.12694	−0.563469	−	0.826137i	$-0.690534\pi$
$43$	−2.52643e7	−1.12694	−0.563469	+	0.826137i	$0.690534\pi$
$44$	−3.55312e7	−1.42913
$45$	−5.11604e7	−1.85985
$46$	−3.10067e6	−0.102105
$47$	2.04296e7	0.610687	0.305343	−	0.952242i	$-0.401229\pi$
$47$	2.04296e7	0.610687	0.305343	+	0.952242i	$0.401229\pi$
$48$	−4.00434e7	−1.08879
$49$	3.94683e7	0.978062
$50$	−2.24532e7	−0.508058
$51$	2.42491e7	0.501914
$52$	−4.94925e7	−0.938694
$53$	−3.66196e7	−0.637489	−0.318744	−	0.947841i	$-0.603261\pi$
$53$	−3.66196e7	−0.637489	−0.318744	+	0.947841i	$0.603261\pi$
$54$	3.42020e6	0.0547368
$55$	−1.75271e8	−2.58272
$56$	−5.84095e7	−0.793665
$57$	0	0
$58$	−2.84583e7	−0.330204
$59$	6.15867e7	0.661687	0.330843	−	0.943686i	$-0.392667\pi$
$59$	6.15867e7	0.661687	0.330843	+	0.943686i	$0.392667\pi$
$60$	−2.20555e8	−2.19703
$61$	1.82995e8	1.69221	0.846107	−	0.533013i	$-0.178940\pi$
$61$	1.82995e8	1.69221	0.846107	+	0.533013i	$0.178940\pi$
$62$	−2.20840e7	−0.189809
$63$	−1.98227e8	−1.58537
$64$	−6.91342e7	−0.515090
$65$	−2.44140e8	−1.69641
$66$	1.03818e8	0.673478
$67$	2.11382e8	1.28154	0.640768	−	0.767735i	$-0.278616\pi$
$67$	2.11382e8	1.28154	0.640768	+	0.767735i	$0.278616\pi$
$68$	5.53956e7	0.314185
$69$	−9.50531e7	−0.504830
$70$	−1.37510e8	−0.684532
$71$	3.66751e8	1.71281	0.856404	−	0.516306i	$-0.172693\pi$
$71$	3.66751e8	1.71281	0.856404	+	0.516306i	$0.172693\pi$
$72$	1.45052e8	0.636103
$73$	3.38405e8	1.39471	0.697354	−	0.716727i	$-0.254360\pi$
$73$	3.38405e8	1.39471	0.697354	+	0.716727i	$0.254360\pi$
$74$	−3.62770e7	−0.140633
$75$	−6.88318e8	−2.51196
$76$	0	0
$77$	−6.79108e8	−2.20156
$78$	1.44611e8	0.442359
$79$	2.31930e8	0.669939	0.334969	−	0.942229i	$-0.391274\pi$
$79$	2.31930e8	0.669939	0.334969	+	0.942229i	$0.391274\pi$
$80$	−4.51244e8	−1.23170
$81$	−3.31861e8	−0.856591
$82$	−2.40774e7	−0.0588095
$83$	4.29926e8	0.994357	0.497179	−	0.867648i	$-0.334369\pi$
$83$	4.29926e8	0.994357	0.497179	+	0.867648i	$0.334369\pi$
$84$	−8.54565e8	−1.87279
$85$	2.73260e8	0.567794
$86$	1.68636e8	0.332435
$87$	−8.72407e8	−1.63261
$88$	4.96935e8	0.883340
$89$	9.51115e8	1.60686	0.803430	−	0.595399i	$-0.203006\pi$
$89$	9.51115e8	1.60686	0.803430	+	0.595399i	$0.203006\pi$
$90$	3.41488e8	0.548635
$91$	−9.45951e8	−1.44605
$92$	−2.17143e8	−0.316010
$93$	−6.77001e8	−0.938461
$94$	−1.36364e8	−0.180146
$95$	0	0
$96$	9.52211e8	1.14423
$97$	−2.29994e8	−0.263781	−0.131890	−	0.991264i	$-0.542105\pi$
$97$	−2.29994e8	−0.263781	−0.131890	+	0.991264i	$0.542105\pi$
$98$	−2.63445e8	−0.288518
$99$	1.68647e9	1.76450
$100$	−1.57242e9	−1.57242
$101$	5.35844e8	0.512380	0.256190	−	0.966626i	$-0.417533\pi$
$101$	5.35844e8	0.512380	0.256190	+	0.966626i	$0.417533\pi$
$102$	−1.61859e8	−0.148059
$103$	−4.79490e8	−0.419771	−0.209885	−	0.977726i	$-0.567309\pi$
$103$	−4.79490e8	−0.419771	−0.209885	+	0.977726i	$0.567309\pi$
$104$	6.92197e8	0.580202
$105$	−4.21547e9	−3.38449
$106$	2.44430e8	0.188052
$107$	1.29774e9	0.957108	0.478554	−	0.878058i	$-0.341161\pi$
$107$	1.29774e9	0.957108	0.478554	+	0.878058i	$0.341161\pi$
$108$	2.39520e8	0.169408
$109$	1.27800e9	0.867185	0.433593	−	0.901109i	$-0.357246\pi$
$109$	1.27800e9	0.867185	0.433593	+	0.901109i	$0.357246\pi$
$110$	1.16991e9	0.761876
$111$	−1.11210e9	−0.695326
$112$	−1.74840e9	−1.04993
$113$	−3.72652e8	−0.215006	−0.107503	−	0.994205i	$-0.534285\pi$
$113$	−3.72652e8	−0.215006	−0.107503	+	0.994205i	$0.534285\pi$
$114$	0	0
$115$	−1.07114e9	−0.571092
$116$	−1.99296e9	−1.02197
$117$	2.34914e9	1.15897
$118$	−4.11082e8	−0.195191
$119$	1.05878e9	0.483997
$120$	3.08466e9	1.35797
$121$	3.41976e9	1.45031
$122$	−1.22147e9	−0.499185
$123$	−7.38109e8	−0.290769
$124$	−1.54657e9	−0.587451
$125$	−3.25294e9	−1.19174
$126$	1.32313e9	0.467667
$127$	−4.35656e9	−1.48603	−0.743013	−	0.669277i	$-0.766604\pi$
$127$	−4.35656e9	−1.48603	−0.743013	+	0.669277i	$0.766604\pi$
$128$	2.84406e9	0.936470
$129$	5.16964e9	1.64364
$130$	1.62960e9	0.500422
$131$	−1.83771e9	−0.545200	−0.272600	−	0.962128i	$-0.587883\pi$
$131$	−1.83771e9	−0.545200	−0.272600	+	0.962128i	$0.587883\pi$
$132$	7.27046e9	2.08439
$133$	0	0
$134$	−1.41094e9	−0.378039
$135$	1.18152e9	0.306154
$136$	−7.74757e8	−0.194196
$137$	−1.41943e9	−0.344247	−0.172124	−	0.985075i	$-0.555063\pi$
$137$	−1.41943e9	−0.344247	−0.172124	+	0.985075i	$0.555063\pi$
$138$	6.34465e8	0.148920
$139$	3.62124e9	0.822793	0.411397	−	0.911456i	$-0.365041\pi$
$139$	3.62124e9	0.822793	0.411397	+	0.911456i	$0.365041\pi$
$140$	−9.62998e9	−2.11860
$141$	−4.18034e9	−0.890687
$142$	−2.44801e9	−0.505260
$143$	8.04794e9	1.60943
$144$	4.34190e9	0.841490
$145$	−9.83104e9	−1.84690
$146$	−2.25880e9	−0.411424
$147$	−8.07608e9	−1.42650
$148$	−2.54051e9	−0.435255
$149$	−4.51486e9	−0.750423	−0.375211	−	0.926939i	$-0.622430\pi$
$149$	−4.51486e9	−0.750423	−0.375211	+	0.926939i	$0.622430\pi$
$150$	4.59442e9	0.741003
$151$	−3.40803e9	−0.533467	−0.266733	−	0.963770i	$-0.585944\pi$
$151$	−3.40803e9	−0.533467	−0.266733	+	0.963770i	$0.585944\pi$
$152$	0	0
$153$	−2.62933e9	−0.387912
$154$	4.53294e9	0.649437
$155$	−7.62903e9	−1.06164
$156$	1.01272e10	1.36909
$157$	5.43812e9	0.714332	0.357166	−	0.934041i	$-0.383743\pi$
$157$	5.43812e9	0.714332	0.357166	+	0.934041i	$0.383743\pi$
$158$	−1.54810e9	−0.197625
$159$	7.49318e9	0.929778
$160$	1.07303e10	1.29441
$161$	−4.15026e9	−0.486809
$162$	2.21512e9	0.252685
$163$	1.25182e10	1.38898	0.694492	−	0.719500i	$-0.255629\pi$
$163$	1.25182e10	1.38898	0.694492	+	0.719500i	$0.255629\pi$
$164$	−1.68617e9	−0.182013
$165$	3.58643e10	3.76690
$166$	−2.86969e9	−0.293325
$167$	1.43828e9	0.143093	0.0715465	−	0.997437i	$-0.477207\pi$
$167$	1.43828e9	0.143093	0.0715465	+	0.997437i	$0.477207\pi$
$168$	1.19519e10	1.15756
$169$	6.05733e8	0.0571204
$170$	−1.82397e9	−0.167493
$171$	0	0
$172$	1.18097e10	1.02887
$173$	−5.79291e9	−0.491688	−0.245844	−	0.969309i	$-0.579065\pi$
$173$	−5.79291e9	−0.491688	−0.245844	+	0.969309i	$0.579065\pi$
$174$	5.82318e9	0.481603
$175$	−3.00537e10	−2.42229
$176$	1.48750e10	1.16856
$177$	−1.26020e10	−0.965071
$178$	−6.34855e9	−0.474007
$179$	2.28942e10	1.66681	0.833406	−	0.552661i	$-0.186387\pi$
$179$	2.28942e10	1.66681	0.833406	+	0.552661i	$0.186387\pi$
$180$	2.39147e10	1.69801
$181$	8.50176e9	0.588783	0.294391	−	0.955685i	$-0.404883\pi$
$181$	8.50176e9	0.588783	0.294391	+	0.955685i	$0.404883\pi$
$182$	6.31408e9	0.426568
$183$	−3.74448e10	−2.46810
$184$	3.03694e9	0.195324
$185$	−1.25320e10	−0.786592
$186$	4.51888e9	0.276836
$187$	−9.00784e9	−0.538683
$188$	−9.54972e9	−0.557546
$189$	4.57795e9	0.260971
$190$	0	0
$191$	−1.83546e10	−0.997920	−0.498960	−	0.866625i	$-0.666285\pi$
$191$	−1.83546e10	−0.997920	−0.498960	+	0.866625i	$0.666285\pi$
$192$	1.41464e10	0.751259
$193$	1.79372e10	0.930566	0.465283	−	0.885162i	$-0.345953\pi$
$193$	1.79372e10	0.930566	0.465283	+	0.885162i	$0.345953\pi$
$194$	1.53517e9	0.0778126
$195$	4.99565e10	2.47421
$196$	−1.84493e10	−0.892952
$197$	−1.55392e10	−0.735074	−0.367537	−	0.930009i	$-0.619799\pi$
$197$	−1.55392e10	−0.735074	−0.367537	+	0.930009i	$0.619799\pi$
$198$	−1.12569e10	−0.520507
$199$	3.81671e9	0.172524	0.0862621	−	0.996272i	$-0.472508\pi$
$199$	3.81671e9	0.172524	0.0862621	+	0.996272i	$0.472508\pi$
$200$	2.19917e10	0.971906
$201$	−4.32533e10	−1.86912
$202$	−3.57668e9	−0.151147
$203$	−3.80915e10	−1.57433
$204$	−1.13351e10	−0.458238
$205$	−8.31766e9	−0.328934
$206$	3.20052e9	0.123828
$207$	1.03066e10	0.390166
$208$	2.07198e10	0.767541
$209$	0	0
$210$	2.81376e10	0.998390
$211$	5.81601e9	0.202001	0.101001	−	0.994886i	$-0.467796\pi$
$211$	5.81601e9	0.202001	0.101001	+	0.994886i	$0.467796\pi$
$212$	1.71177e10	0.582015
$213$	−7.50453e10	−2.49813
$214$	−8.66222e9	−0.282337
$215$	5.82560e10	1.85938
$216$	−3.34990e9	−0.104711
$217$	−2.95596e10	−0.904960
$218$	−8.53046e9	−0.255810
$219$	−6.92450e10	−2.03418
$220$	8.19298e10	2.35798
$221$	−1.25473e10	−0.353822
$222$	7.42307e9	0.205114
$223$	5.10133e10	1.38137	0.690687	−	0.723154i	$-0.257308\pi$
$223$	5.10133e10	1.38137	0.690687	+	0.723154i	$0.257308\pi$
$224$	4.15759e10	1.10338
$225$	7.46342e10	1.94141
$226$	2.48739e9	0.0634244
$227$	−5.88744e10	−1.47167	−0.735834	−	0.677162i	$-0.763210\pi$
$227$	−5.88744e10	−1.47167	−0.735834	+	0.677162i	$0.763210\pi$
$228$	0	0
$229$	7.84154e10	1.88426	0.942132	−	0.335243i	$-0.108819\pi$
$229$	7.84154e10	1.88426	0.942132	+	0.335243i	$0.108819\pi$
$230$	7.14970e9	0.168466
$231$	1.38960e11	3.21098
$232$	2.78733e10	0.631674
$233$	1.69774e10	0.377372	0.188686	−	0.982037i	$-0.439577\pi$
$233$	1.69774e10	0.377372	0.188686	+	0.982037i	$0.439577\pi$
$234$	−1.56801e10	−0.341884
$235$	−4.71076e10	−1.00759
$236$	−2.87885e10	−0.604108
$237$	−4.74580e10	−0.977106
$238$	−7.06717e9	−0.142774
$239$	3.66064e10	0.725716	0.362858	−	0.931844i	$-0.381801\pi$
$239$	3.66064e10	0.725716	0.362858	+	0.931844i	$0.381801\pi$
$240$	9.23344e10	1.79644
$241$	2.36351e10	0.451316	0.225658	−	0.974207i	$-0.427547\pi$
$241$	2.36351e10	0.451316	0.225658	+	0.974207i	$0.427547\pi$
$242$	−2.28264e10	−0.427826
$243$	7.79916e10	1.43489
$244$	−8.55404e10	−1.54496
$245$	−9.10083e10	−1.61374
$246$	4.92677e9	0.0857737
$247$	0	0
$248$	2.16301e10	0.363100
$249$	−8.79723e10	−1.45027
$250$	2.17129e10	0.351550
$251$	−3.94031e10	−0.626612	−0.313306	−	0.949652i	$-0.601437\pi$
$251$	−3.94031e10	−0.626612	−0.313306	+	0.949652i	$0.601437\pi$
$252$	9.26604e10	1.44741
$253$	3.53095e10	0.541813
$254$	2.90793e10	0.438362
$255$	−5.59149e10	−0.828127
$256$	1.64130e10	0.238841
$257$	−5.99175e10	−0.856751	−0.428375	−	0.903601i	$-0.640914\pi$
$257$	−5.99175e10	−0.856751	−0.428375	+	0.903601i	$0.640914\pi$
$258$	−3.45066e10	−0.484856
$259$	−4.85569e10	−0.670505
$260$	1.14123e11	1.54879
$261$	9.45950e10	1.26179
$262$	1.22664e10	0.160828
$263$	9.34155e10	1.20398	0.601989	−	0.798505i	$-0.294375\pi$
$263$	9.34155e10	1.20398	0.601989	+	0.798505i	$0.294375\pi$
$264$	−1.01684e11	−1.28835
$265$	8.44396e10	1.05182
$266$	0	0
$267$	−1.94619e11	−2.34361
$268$	−9.88096e10	−1.17002
$269$	−2.63361e10	−0.306667	−0.153333	−	0.988175i	$-0.549001\pi$
$269$	−2.63361e10	−0.306667	−0.153333	+	0.988175i	$0.549001\pi$
$270$	−7.88649e9	−0.0903123
$271$	−6.96232e10	−0.784137	−0.392069	−	0.919936i	$-0.628240\pi$
$271$	−6.96232e10	−0.784137	−0.392069	+	0.919936i	$0.628240\pi$
$272$	−2.31911e10	−0.256899
$273$	1.93562e11	2.10906
$274$	9.47446e9	0.101549
$275$	2.55690e11	2.69598
$276$	4.44322e10	0.460901
$277$	1.58893e10	0.162160	0.0810802	−	0.996708i	$-0.474163\pi$
$277$	1.58893e10	0.162160	0.0810802	+	0.996708i	$0.474163\pi$
$278$	−2.41712e10	−0.242715
$279$	7.34072e10	0.725303
$280$	1.34684e11	1.30950
$281$	6.63158e10	0.634510	0.317255	−	0.948340i	$-0.397239\pi$
$281$	6.63158e10	0.634510	0.317255	+	0.948340i	$0.397239\pi$
$282$	2.79031e10	0.262743
$283$	1.14819e11	1.06408	0.532040	−	0.846719i	$-0.321425\pi$
$283$	1.14819e11	1.06408	0.532040	+	0.846719i	$0.321425\pi$
$284$	−1.71436e11	−1.56376
$285$	0	0
$286$	−5.37188e10	−0.474766
$287$	−3.22277e10	−0.280389
$288$	−1.03248e11	−0.884333
$289$	−1.04544e11	−0.881574
$290$	6.56207e10	0.544816
$291$	4.70618e10	0.384725
$292$	−1.58186e11	−1.27334
$293$	7.78874e9	0.0617395	0.0308697	−	0.999523i	$-0.490172\pi$
$293$	7.78874e9	0.0617395	0.0308697	+	0.999523i	$0.490172\pi$
$294$	5.39066e10	0.420804
$295$	−1.42010e11	−1.09174
$296$	3.55314e10	0.269029
$297$	−3.89482e10	−0.290458
$298$	3.01360e10	0.221367
$299$	4.91837e10	0.355878
$300$	3.21752e11	2.29338
$301$	2.25720e11	1.58497
$302$	2.27481e10	0.157367
$303$	−1.09645e11	−0.747306
$304$	0	0
$305$	−4.21961e11	−2.79205
$306$	1.75504e10	0.114430
$307$	1.28574e11	0.826097	0.413048	−	0.910709i	$-0.364464\pi$
$307$	1.28574e11	0.826097	0.413048	+	0.910709i	$0.364464\pi$
$308$	3.17447e11	2.00998
$309$	9.81142e10	0.612236
$310$	5.09227e10	0.313172
$311$	−1.18442e11	−0.717933	−0.358966	−	0.933350i	$-0.616871\pi$
$311$	−1.18442e11	−0.717933	−0.358966	+	0.933350i	$0.616871\pi$
$312$	−1.41639e11	−0.846225
$313$	−6.29440e10	−0.370685	−0.185342	−	0.982674i	$-0.559339\pi$
$313$	−6.29440e10	−0.370685	−0.185342	+	0.982674i	$0.559339\pi$
$314$	−3.62986e10	−0.210720
$315$	4.57083e11	2.61576
$316$	−1.08415e11	−0.611642
$317$	2.91415e11	1.62086	0.810430	−	0.585836i	$-0.199234\pi$
$317$	2.91415e11	1.62086	0.810430	+	0.585836i	$0.199234\pi$
$318$	−5.00158e10	−0.274275
$319$	3.24074e11	1.75221
$320$	1.59414e11	0.849866
$321$	−2.65546e11	−1.39594
$322$	2.77024e10	0.143604
$323$	0	0
$324$	1.55127e11	0.782051
$325$	3.56159e11	1.77080
$326$	−8.35571e10	−0.409736
$327$	−2.61507e11	−1.26479
$328$	2.35825e10	0.112502
$329$	−1.82524e11	−0.858892
$330$	−2.39389e11	−1.11120
$331$	−1.96067e11	−0.897798	−0.448899	−	0.893582i	$-0.648184\pi$
$331$	−1.96067e11	−0.897798	−0.448899	+	0.893582i	$0.648184\pi$
$332$	−2.00967e11	−0.907829
$333$	1.20584e11	0.537393
$334$	−9.60028e9	−0.0422109
$335$	−4.87416e11	−2.11445
$336$	3.57760e11	1.53132
$337$	−1.46927e11	−0.620538	−0.310269	−	0.950649i	$-0.600419\pi$
$337$	−1.46927e11	−0.620538	−0.310269	+	0.950649i	$0.600419\pi$
$338$	−4.04318e9	−0.0168499
$339$	7.62527e10	0.313586
$340$	−1.27734e11	−0.518385
$341$	2.51487e11	1.00721
$342$	0	0
$343$	7.90939e9	0.0308546
$344$	−1.65170e11	−0.635942
$345$	2.19179e11	0.832938
$346$	3.86668e10	0.145043
$347$	−2.39730e11	−0.887645	−0.443822	−	0.896115i	$-0.646378\pi$
$347$	−2.39730e11	−0.887645	−0.443822	+	0.896115i	$0.646378\pi$
$348$	4.07803e11	1.49054
$349$	2.99376e11	1.08020	0.540098	−	0.841602i	$-0.318387\pi$
$349$	2.99376e11	1.08020	0.540098	+	0.841602i	$0.318387\pi$
$350$	2.00604e11	0.714551
$351$	−5.42522e10	−0.190781
$352$	−3.53719e11	−1.22805
$353$	−2.24547e11	−0.769701	−0.384850	−	0.922979i	$-0.625747\pi$
$353$	−2.24547e11	−0.769701	−0.384850	+	0.922979i	$0.625747\pi$
$354$	8.41163e10	0.284686
$355$	−8.45675e11	−2.82603
$356$	−4.44595e11	−1.46703
$357$	−2.16649e11	−0.705910
$358$	−1.52815e11	−0.491692
$359$	−1.04257e11	−0.331267	−0.165633	−	0.986187i	$-0.552967\pi$
$359$	−1.04257e11	−0.331267	−0.165633	+	0.986187i	$0.552967\pi$
$360$	−3.34469e11	−1.04953
$361$	0	0
$362$	−5.67479e10	−0.173685
$363$	−6.99757e11	−2.11528
$364$	4.42181e11	1.32021
$365$	−7.80313e11	−2.30118
$366$	2.49939e11	0.728062
$367$	−2.80297e11	−0.806530	−0.403265	−	0.915083i	$-0.632125\pi$
$367$	−2.80297e11	−0.806530	−0.403265	+	0.915083i	$0.632125\pi$
$368$	9.09061e10	0.258391
$369$	8.00331e10	0.224725
$370$	8.36495e10	0.232036
$371$	3.27171e11	0.896587
$372$	3.16462e11	0.856797
$373$	2.80055e10	0.0749124	0.0374562	−	0.999298i	$-0.488075\pi$
$373$	2.80055e10	0.0749124	0.0374562	+	0.999298i	$0.488075\pi$
$374$	6.01260e10	0.158906
$375$	6.65622e11	1.73815
$376$	1.33561e11	0.344616
$377$	4.51413e11	1.15090
$378$	−3.05571e10	−0.0769838
$379$	6.77032e11	1.68552	0.842758	−	0.538292i	$-0.180930\pi$
$379$	6.77032e11	1.68552	0.842758	+	0.538292i	$0.180930\pi$
$380$	0	0
$381$	8.91447e11	2.16737
$382$	1.22514e11	0.294376
$383$	1.90210e11	0.451689	0.225844	−	0.974163i	$-0.427486\pi$
$383$	1.90210e11	0.451689	0.225844	+	0.974163i	$0.427486\pi$
$384$	−5.81957e11	−1.36584
$385$	1.56593e12	3.63244
$386$	−1.19728e11	−0.274507
$387$	−5.60544e11	−1.27031
$388$	1.07510e11	0.240827
$389$	8.42755e11	1.86607	0.933036	−	0.359784i	$-0.117150\pi$
$389$	8.42755e11	1.86607	0.933036	+	0.359784i	$0.117150\pi$
$390$	−3.33452e11	−0.729865
$391$	−5.50500e10	−0.119114
$392$	2.58030e11	0.551929
$393$	3.76035e11	0.795174
$394$	1.03722e11	0.216839
$395$	−5.34798e11	−1.10536
$396$	−7.88335e11	−1.61095
$397$	3.69683e11	0.746917	0.373459	−	0.927647i	$-0.378172\pi$
$397$	3.69683e11	0.746917	0.373459	+	0.927647i	$0.378172\pi$
$398$	−2.54759e10	−0.0508928
$399$	0	0
$400$	6.58288e11	1.28572
$401$	1.48924e11	0.287617	0.143809	−	0.989606i	$-0.454065\pi$
$401$	1.48924e11	0.287617	0.143809	+	0.989606i	$0.454065\pi$
$402$	2.88709e11	0.551371
$403$	3.50304e11	0.661564
$404$	−2.50478e11	−0.467793
$405$	7.65224e11	1.41332
$406$	2.54255e11	0.464411
$407$	4.13112e11	0.746264
$408$	1.58532e11	0.283235
$409$	1.01326e12	1.79046	0.895232	−	0.445600i	$-0.147010\pi$
$409$	1.01326e12	1.79046	0.895232	+	0.445600i	$0.147010\pi$
$410$	5.55191e10	0.0970320
$411$	2.90446e11	0.502084
$412$	2.24136e11	0.383243
$413$	−5.50234e11	−0.930620
$414$	−6.87950e10	−0.115095
$415$	−9.91348e11	−1.64063
$416$	−4.92706e11	−0.806619
$417$	−7.40985e11	−1.20004
$418$	0	0
$419$	4.76920e11	0.755931	0.377966	−	0.925820i	$-0.376624\pi$
$419$	4.76920e11	0.755931	0.377966	+	0.925820i	$0.376624\pi$
$420$	1.97050e12	3.08998
$421$	8.54935e11	1.32637	0.663183	−	0.748457i	$-0.269205\pi$
$421$	8.54935e11	1.32637	0.663183	+	0.748457i	$0.269205\pi$
$422$	−3.88210e10	−0.0595883
$423$	4.53273e11	0.688381
$424$	−2.39407e11	−0.359741
$425$	−3.98639e11	−0.592693
$426$	5.00916e11	0.736922
$427$	−1.63494e12	−2.37999
$428$	−6.06624e11	−0.873821
$429$	−1.64679e12	−2.34736
$430$	−3.88850e11	−0.548497
$431$	4.31075e11	0.601735	0.300867	−	0.953666i	$-0.402724\pi$
$431$	4.31075e11	0.601735	0.300867	+	0.953666i	$0.402724\pi$
$432$	−1.00274e11	−0.138520
$433$	−1.83795e11	−0.251269	−0.125634	−	0.992077i	$-0.540097\pi$
$433$	−1.83795e11	−0.251269	−0.125634	+	0.992077i	$0.540097\pi$
$434$	1.97306e11	0.266954
$435$	2.01165e12	2.69370
$436$	−5.97397e11	−0.791724
$437$	0	0
$438$	4.62200e11	0.600062
$439$	−9.40513e11	−1.20858	−0.604289	−	0.796765i	$-0.706543\pi$
$439$	−9.40513e11	−1.20858	−0.604289	+	0.796765i	$0.706543\pi$
$440$	−1.14586e12	−1.45745
$441$	8.75689e11	1.10249
$442$	8.37514e10	0.104374
$443$	−8.33396e11	−1.02810	−0.514049	−	0.857761i	$-0.671855\pi$
$443$	−8.33396e11	−1.02810	−0.514049	+	0.857761i	$0.671855\pi$
$444$	5.19845e11	0.634820
$445$	−2.19314e12	−2.65122
$446$	−3.40506e11	−0.407491
$447$	9.23839e11	1.09449
$448$	6.17666e11	0.724441
$449$	2.09414e11	0.243163	0.121581	−	0.992581i	$-0.461203\pi$
$449$	2.09414e11	0.243163	0.121581	+	0.992581i	$0.461203\pi$
$450$	−4.98172e11	−0.572695
$451$	2.74187e11	0.312070
$452$	1.74195e11	0.196296
$453$	6.97358e11	0.778061
$454$	3.92978e11	0.434127
$455$	2.18123e12	2.38589
$456$	0	0
$457$	−1.13033e12	−1.21222	−0.606112	−	0.795379i	$-0.707272\pi$
$457$	−1.13033e12	−1.21222	−0.606112	+	0.795379i	$0.707272\pi$
$458$	−5.23411e11	−0.555838
$459$	6.07230e10	0.0638552
$460$	5.00701e11	0.521397
$461$	−6.77650e11	−0.698797	−0.349399	−	0.936974i	$-0.613614\pi$
$461$	−6.77650e11	−0.698797	−0.349399	+	0.936974i	$0.613614\pi$
$462$	−9.27539e11	−0.947204
$463$	6.18893e11	0.625894	0.312947	−	0.949771i	$-0.398684\pi$
$463$	6.18893e11	0.625894	0.312947	+	0.949771i	$0.398684\pi$
$464$	8.34345e11	0.835632
$465$	1.56107e12	1.54840
$466$	−1.13322e11	−0.111321
$467$	1.10573e12	1.07578	0.537890	−	0.843015i	$-0.319222\pi$
$467$	1.10573e12	1.07578	0.537890	+	0.843015i	$0.319222\pi$
$468$	−1.09810e12	−1.05812
$469$	−1.88855e12	−1.80240
$470$	3.14436e11	0.297230
$471$	−1.11276e12	−1.04185
$472$	4.02632e11	0.373396
$473$	−1.92037e12	−1.76405
$474$	3.16775e11	0.288236
$475$	0	0
$476$	−4.94921e11	−0.441881
$477$	−8.12485e11	−0.718592
$478$	−2.44342e11	−0.214079
$479$	−1.45718e11	−0.126475	−0.0632374	−	0.997999i	$-0.520143\pi$
$479$	−1.45718e11	−0.126475	−0.0632374	+	0.997999i	$0.520143\pi$
$480$	−2.19566e12	−1.88790
$481$	5.75436e11	0.490167
$482$	−1.57761e11	−0.133133
$483$	8.49234e11	0.710012
$484$	−1.59855e12	−1.32411
$485$	5.30333e11	0.435222
$486$	−5.20582e11	−0.423278
$487$	−1.18303e12	−0.953051	−0.476526	−	0.879161i	$-0.658104\pi$
$487$	−1.18303e12	−0.953051	−0.476526	+	0.879161i	$0.658104\pi$
$488$	1.19636e12	0.954932
$489$	−2.56150e12	−2.02583
$490$	6.07467e11	0.476036
$491$	−9.48949e11	−0.736845	−0.368422	−	0.929658i	$-0.620102\pi$
$491$	−9.48949e11	−0.736845	−0.368422	+	0.929658i	$0.620102\pi$
$492$	3.45027e11	0.265466
$493$	−5.05254e11	−0.385211
$494$	0	0
$495$	−3.88876e12	−2.91131
$496$	6.47465e11	0.480340
$497$	−3.27667e12	−2.40896
$498$	5.87202e11	0.427814
$499$	−2.14745e12	−1.55050	−0.775249	−	0.631656i	$-0.782376\pi$
$499$	−2.14745e12	−1.55050	−0.775249	+	0.631656i	$0.782376\pi$
$500$	1.52057e12	1.08803
$501$	−2.94303e11	−0.208701
$502$	2.63010e11	0.184844
$503$	1.70992e12	1.19102	0.595512	−	0.803347i	$-0.296949\pi$
$503$	1.70992e12	1.19102	0.595512	+	0.803347i	$0.296949\pi$
$504$	−1.29594e12	−0.894637
$505$	−1.23558e12	−0.845395
$506$	−2.35686e11	−0.159829
$507$	−1.23946e11	−0.0833101
$508$	2.03646e12	1.35671
$509$	6.70208e11	0.442568	0.221284	−	0.975209i	$-0.428975\pi$
$509$	6.70208e11	0.442568	0.221284	+	0.975209i	$0.428975\pi$
$510$	3.73224e11	0.244289
$511$	−3.02341e12	−1.96157
$512$	−1.56571e12	−1.00693
$513$	0	0
$514$	3.99940e11	0.252732
$515$	1.10564e12	0.692595
$516$	−2.41653e12	−1.50061
$517$	1.55288e12	0.955937
$518$	3.24110e11	0.197792
$519$	1.18536e12	0.717127
$520$	−1.59611e12	−0.957297
$521$	1.19280e12	0.709245	0.354623	−	0.935010i	$-0.384609\pi$
$521$	1.19280e12	0.709245	0.354623	+	0.935010i	$0.384609\pi$
$522$	−6.31407e11	−0.372214
$523$	−2.45031e12	−1.43207	−0.716035	−	0.698065i	$-0.754045\pi$
$523$	−2.45031e12	−1.43207	−0.716035	+	0.698065i	$0.754045\pi$
$524$	8.59030e11	0.497757
$525$	6.14965e12	3.53292
$526$	−6.23535e11	−0.355161
$527$	−3.92085e11	−0.221428
$528$	−3.04375e12	−1.70434
$529$	−1.58536e12	−0.880194
$530$	−5.63622e11	−0.310275
$531$	1.36643e12	0.745869
$532$	0	0
$533$	3.81923e11	0.204976
$534$	1.29905e12	0.691339
$535$	−2.99240e12	−1.57917
$536$	1.38194e12	0.723182
$537$	−4.68466e12	−2.43105
$538$	1.75790e11	0.0904635
$539$	3.00003e12	1.53101
$540$	−5.52299e11	−0.279513
$541$	−3.32515e12	−1.66888	−0.834438	−	0.551102i	$-0.814207\pi$
$541$	−3.32515e12	−1.66888	−0.834438	+	0.551102i	$0.814207\pi$
$542$	4.64724e11	0.231312
$543$	−1.73965e12	−0.858740
$544$	5.51473e11	0.269978
$545$	−2.94689e12	−1.43080
$546$	−1.29200e12	−0.622150
$547$	1.97053e12	0.941112	0.470556	−	0.882370i	$-0.344053\pi$
$547$	1.97053e12	0.941112	0.470556	+	0.882370i	$0.344053\pi$
$548$	6.63506e11	0.314291
$549$	4.06014e12	1.90750
$550$	−1.70670e12	−0.795287
$551$	0	0
$552$	−6.21425e11	−0.284880
$553$	−2.07214e12	−0.942226
$554$	−1.06058e11	−0.0478356
$555$	2.56433e12	1.14724
$556$	−1.69274e12	−0.751195
$557$	−2.11594e12	−0.931439	−0.465720	−	0.884932i	$-0.654204\pi$
$557$	−2.11594e12	−0.931439	−0.465720	+	0.884932i	$0.654204\pi$
$558$	−4.89982e11	−0.213957
$559$	−2.67495e12	−1.15868
$560$	4.03155e12	1.73231
$561$	1.84320e12	0.785670
$562$	−4.42648e11	−0.187174
$563$	3.09779e12	1.29946	0.649732	−	0.760163i	$-0.274881\pi$
$563$	3.09779e12	1.29946	0.649732	+	0.760163i	$0.274881\pi$
$564$	1.95408e12	0.813181
$565$	8.59281e11	0.354746
$566$	−7.66399e11	−0.313893
$567$	2.96495e12	1.20474
$568$	2.39769e12	0.966554
$569$	−4.16039e12	−1.66391	−0.831953	−	0.554846i	$-0.812777\pi$
$569$	−4.16039e12	−1.66391	−0.831953	+	0.554846i	$0.812777\pi$
$570$	0	0
$571$	9.42885e11	0.371190	0.185595	−	0.982626i	$-0.440579\pi$
$571$	9.42885e11	0.371190	0.185595	+	0.982626i	$0.440579\pi$
$572$	−3.76198e12	−1.46938
$573$	3.75576e12	1.45547
$574$	2.15115e11	0.0827118
$575$	1.56261e12	0.596137
$576$	−1.53389e12	−0.580621
$577$	1.91777e12	0.720285	0.360142	−	0.932897i	$-0.382728\pi$
$577$	1.91777e12	0.720285	0.360142	+	0.932897i	$0.382728\pi$
$578$	6.97816e11	0.260055
$579$	−3.67035e12	−1.35723
$580$	4.59548e12	1.68618
$581$	−3.84109e12	−1.39850
$582$	−3.14130e11	−0.113490
$583$	−2.78350e12	−0.997891
$584$	2.21237e12	0.787047
$585$	−5.41678e12	−1.91223
$586$	−5.19887e10	−0.0182125
$587$	1.72476e12	0.599592	0.299796	−	0.954003i	$-0.403081\pi$
$587$	1.72476e12	0.599592	0.299796	+	0.954003i	$0.403081\pi$
$588$	3.77514e12	1.30237
$589$	0	0
$590$	9.47896e11	0.322052
$591$	3.17967e12	1.07211
$592$	1.06358e12	0.355894
$593$	−1.87438e12	−0.622459	−0.311229	−	0.950335i	$-0.600741\pi$
$593$	−1.87438e12	−0.622459	−0.311229	+	0.950335i	$0.600741\pi$
$594$	2.59973e11	0.0856821
$595$	−2.44139e12	−0.798565
$596$	2.11045e12	0.685122
$597$	−7.80982e11	−0.251627
$598$	−3.28294e11	−0.104980
$599$	−4.13876e12	−1.31356	−0.656780	−	0.754082i	$-0.728082\pi$
$599$	−4.13876e12	−1.31356	−0.656780	+	0.754082i	$0.728082\pi$
$600$	−4.49999e12	−1.41752
$601$	−3.75120e12	−1.17283	−0.586415	−	0.810011i	$-0.699461\pi$
$601$	−3.75120e12	−1.17283	−0.586415	+	0.810011i	$0.699461\pi$
$602$	−1.50664e12	−0.467548
$603$	4.68995e12	1.44458
$604$	1.59307e12	0.487045
$605$	−7.88547e12	−2.39292
$606$	7.31867e11	0.220448
$607$	5.07062e12	1.51605	0.758023	−	0.652228i	$-0.226166\pi$
$607$	5.07062e12	1.51605	0.758023	+	0.652228i	$0.226166\pi$
$608$	0	0
$609$	7.79435e12	2.29616
$610$	2.81652e12	0.823624
$611$	2.16305e12	0.627886
$612$	1.22907e12	0.354156
$613$	−3.48244e12	−0.996119	−0.498059	−	0.867143i	$-0.665954\pi$
$613$	−3.48244e12	−0.996119	−0.498059	+	0.867143i	$0.665954\pi$
$614$	−8.58213e11	−0.243690
$615$	1.70198e12	0.479750
$616$	−4.43977e12	−1.24236
$617$	2.13066e12	0.591876	0.295938	−	0.955207i	$-0.404368\pi$
$617$	2.13066e12	0.591876	0.295938	+	0.955207i	$0.404368\pi$
$618$	−6.54897e11	−0.180603
$619$	6.28642e12	1.72106	0.860529	−	0.509401i	$-0.170133\pi$
$619$	6.28642e12	1.72106	0.860529	+	0.509401i	$0.170133\pi$
$620$	3.56616e12	0.969257
$621$	−2.38026e11	−0.0642262
$622$	7.90582e11	0.211783
$623$	−8.49756e12	−2.25995
$624$	−4.23973e12	−1.11946
$625$	9.30780e11	0.243998
$626$	4.20142e11	0.109348
$627$	0	0
$628$	−2.54203e12	−0.652171
$629$	−6.44070e11	−0.164061
$630$	−3.05096e12	−0.771620
$631$	5.62080e12	1.41145	0.705726	−	0.708485i	$-0.250621\pi$
$631$	5.62080e12	1.41145	0.705726	+	0.708485i	$0.250621\pi$
$632$	1.51628e12	0.378053
$633$	−1.19008e12	−0.294619
$634$	−1.94515e12	−0.478136
$635$	1.00456e13	2.45185
$636$	−3.50266e12	−0.848869
$637$	4.17884e12	1.00561
$638$	−2.16315e12	−0.516884
$639$	8.13715e12	1.93072
$640$	−6.55799e12	−1.54512
$641$	−6.97041e11	−0.163079	−0.0815393	−	0.996670i	$-0.525984\pi$
$641$	−6.97041e11	−0.163079	−0.0815393	+	0.996670i	$0.525984\pi$
$642$	1.77248e12	0.411788
$643$	−4.68540e12	−1.08093	−0.540465	−	0.841366i	$-0.681752\pi$
$643$	−4.68540e12	−1.08093	−0.540465	+	0.841366i	$0.681752\pi$
$644$	1.94002e12	0.444448
$645$	−1.19205e13	−2.71190
$646$	0	0
$647$	4.07646e12	0.914563	0.457281	−	0.889322i	$-0.348823\pi$
$647$	4.07646e12	0.914563	0.457281	+	0.889322i	$0.348823\pi$
$648$	−2.16959e12	−0.483382
$649$	4.68128e12	1.03577
$650$	−2.37731e12	−0.522367
$651$	6.04854e12	1.31988
$652$	−5.85159e12	−1.26812
$653$	−4.46719e11	−0.0961447	−0.0480724	−	0.998844i	$-0.515308\pi$
$653$	−4.46719e11	−0.0961447	−0.0480724	+	0.998844i	$0.515308\pi$
$654$	1.74552e12	0.373100
$655$	4.23749e12	0.899545
$656$	7.05907e11	0.148827
$657$	7.50823e12	1.57215
$658$	1.21832e12	0.253364
$659$	5.24715e12	1.08377	0.541887	−	0.840451i	$-0.317710\pi$
$659$	5.24715e12	1.08377	0.541887	+	0.840451i	$0.317710\pi$
$660$	−1.67646e13	−3.43911
$661$	−4.75587e11	−0.0968999	−0.0484500	−	0.998826i	$-0.515428\pi$
$661$	−4.75587e11	−0.0968999	−0.0484500	+	0.998826i	$0.515428\pi$
$662$	1.30872e12	0.264841
$663$	2.56745e12	0.516050
$664$	2.81071e12	0.561125
$665$	0	0
$666$	−8.04882e11	−0.158525
$667$	1.98053e12	0.387449
$668$	−6.72317e11	−0.130641
$669$	−1.04384e13	−2.01473
$670$	3.25343e12	0.623741
$671$	1.39097e13	2.64890
$672$	−8.50735e12	−1.60928
$673$	2.75268e12	0.517235	0.258618	−	0.965980i	$-0.416733\pi$
$673$	2.75268e12	0.517235	0.258618	+	0.965980i	$0.416733\pi$
$674$	9.80719e11	0.183052
$675$	−1.72364e12	−0.319580
$676$	−2.83148e11	−0.0521498
$677$	−6.68978e12	−1.22395	−0.611974	−	0.790878i	$-0.709624\pi$
$677$	−6.68978e12	−1.22395	−0.611974	+	0.790878i	$0.709624\pi$
$678$	−5.08975e11	−0.0925045
$679$	2.05484e12	0.370991
$680$	1.78648e12	0.320411
$681$	1.20470e13	2.14643
$682$	−1.67864e12	−0.297116
$683$	8.30964e12	1.46113	0.730565	−	0.682843i	$-0.239257\pi$
$683$	8.30964e12	1.46113	0.730565	+	0.682843i	$0.239257\pi$
$684$	0	0
$685$	3.27299e12	0.567986
$686$	−5.27940e10	−0.00910177
$687$	−1.60455e13	−2.74820
$688$	−4.94410e12	−0.841277
$689$	−3.87723e12	−0.655443
$690$	−1.46299e12	−0.245708
$691$	−5.91591e10	−0.00987120	−0.00493560	−	0.999988i	$-0.501571\pi$
$691$	−5.91591e10	−0.00987120	−0.00493560	+	0.999988i	$0.501571\pi$
$692$	2.70788e12	0.448902
$693$	−1.50675e13	−2.48165
$694$	1.60016e12	0.261846
$695$	−8.35006e12	−1.35756
$696$	−5.70350e12	−0.921297
$697$	−4.27476e11	−0.0686064
$698$	−1.99829e12	−0.318647
$699$	−3.47395e12	−0.550397
$700$	1.40485e13	2.21151
$701$	1.76503e11	0.0276071	0.0138035	−	0.999905i	$-0.495606\pi$
$701$	1.76503e11	0.0276071	0.0138035	+	0.999905i	$0.495606\pi$
$702$	3.62125e11	0.0562784
$703$	0	0
$704$	−5.25497e12	−0.806294
$705$	9.63926e12	1.46958
$706$	1.49882e12	0.227054
$707$	−4.78740e12	−0.720630
$708$	5.89075e12	0.881091
$709$	−2.23398e12	−0.332025	−0.166013	−	0.986124i	$-0.553089\pi$
$709$	−2.23398e12	−0.332025	−0.166013	+	0.986124i	$0.553089\pi$
$710$	5.64476e12	0.833648
$711$	5.14586e12	0.755171
$712$	6.21806e12	0.906766
$713$	1.53692e12	0.222715
$714$	1.44610e12	0.208236
$715$	−1.85574e13	−2.65546
$716$	−1.07018e13	−1.52177
$717$	−7.49048e12	−1.05846
$718$	6.95896e11	0.0977203
$719$	−1.02723e13	−1.43347	−0.716734	−	0.697347i	$-0.754364\pi$
$719$	−1.02723e13	−1.43347	−0.716734	+	0.697347i	$0.754364\pi$
$720$	−1.00118e13	−1.38841
$721$	4.28391e12	0.590381
$722$	0	0
$723$	−4.83626e12	−0.658245
$724$	−3.97412e12	−0.537548
$725$	1.43418e13	1.92789
$726$	4.67077e12	0.623985
$727$	−1.33972e13	−1.77873	−0.889363	−	0.457202i	$-0.848852\pi$
$727$	−1.33972e13	−1.77873	−0.889363	+	0.457202i	$0.848852\pi$
$728$	−6.18430e12	−0.816017
$729$	−9.42678e12	−1.23620
$730$	5.20847e12	0.678824
$731$	2.99400e12	0.387814
$732$	1.75034e13	2.25332
$733$	2.35708e12	0.301583	0.150792	−	0.988566i	$-0.451818\pi$
$733$	2.35708e12	0.301583	0.150792	+	0.988566i	$0.451818\pi$
$734$	1.87094e12	0.237918
$735$	1.86223e13	2.35364
$736$	−2.16170e12	−0.271547
$737$	1.60674e13	2.00605
$738$	−5.34209e11	−0.0662915
$739$	6.64587e12	0.819695	0.409847	−	0.912154i	$-0.365582\pi$
$739$	6.64587e12	0.819695	0.409847	+	0.912154i	$0.365582\pi$
$740$	5.85806e12	0.718143
$741$	0	0
$742$	−2.18382e12	−0.264484
$743$	−9.38217e12	−1.12942	−0.564708	−	0.825291i	$-0.691011\pi$
$743$	−9.38217e12	−1.12942	−0.564708	+	0.825291i	$0.691011\pi$
$744$	−4.42600e12	−0.529582
$745$	1.04106e13	1.23815
$746$	−1.86933e11	−0.0220984
$747$	9.53883e12	1.12086
$748$	4.21068e12	0.491808
$749$	−1.15944e13	−1.34611
$750$	−4.44293e12	−0.512735
$751$	−7.58462e12	−0.870070	−0.435035	−	0.900413i	$-0.643264\pi$
$751$	−7.58462e12	−0.870070	−0.435035	+	0.900413i	$0.643264\pi$
$752$	3.99796e12	0.455888
$753$	8.06274e12	0.913914
$754$	−3.01311e12	−0.339504
$755$	7.85843e12	0.880186
$756$	−2.13995e12	−0.238262
$757$	2.07498e12	0.229659	0.114829	−	0.993385i	$-0.463368\pi$
$757$	2.07498e12	0.229659	0.114829	+	0.993385i	$0.463368\pi$
$758$	−4.51909e12	−0.497210
$759$	−7.22510e12	−0.790235
$760$	0	0
$761$	1.17842e13	1.27371	0.636853	−	0.770986i	$-0.280236\pi$
$761$	1.17842e13	1.27371	0.636853	+	0.770986i	$0.280236\pi$
$762$	−5.95027e12	−0.639351
$763$	−1.14181e13	−1.21964
$764$	8.57981e12	0.911082
$765$	6.06285e12	0.640030
$766$	−1.26962e12	−0.133243
$767$	6.52070e12	0.680322
$768$	−3.35847e12	−0.348350
$769$	7.58999e12	0.782660	0.391330	−	0.920251i	$-0.372015\pi$
$769$	7.58999e12	0.782660	0.391330	+	0.920251i	$0.372015\pi$
$770$	−1.04523e13	−1.07153
$771$	1.22604e13	1.24957
$772$	−8.38469e12	−0.849589
$773$	1.20443e13	1.21332	0.606658	−	0.794963i	$-0.292510\pi$
$773$	1.20443e13	1.21332	0.606658	+	0.794963i	$0.292510\pi$
$774$	3.74154e12	0.374728
$775$	1.11295e13	1.10820
$776$	−1.50362e12	−0.148854
$777$	9.93580e12	0.977931
$778$	−5.62526e12	−0.550471
$779$	0	0
$780$	−2.33520e13	−2.25891
$781$	2.78772e13	2.68114
$782$	3.67451e11	0.0351373
$783$	−2.18462e12	−0.207706
$784$	7.72374e12	0.730139
$785$	−1.25395e13	−1.17860
$786$	−2.50998e12	−0.234568
$787$	−2.47137e12	−0.229642	−0.114821	−	0.993386i	$-0.536629\pi$
$787$	−2.47137e12	−0.229642	−0.114821	+	0.993386i	$0.536629\pi$
$788$	7.26375e12	0.671109
$789$	−1.91149e13	−1.75600
$790$	3.56969e12	0.326069
$791$	3.32939e12	0.302392
$792$	1.10256e13	0.995721
$793$	1.93752e13	1.73987
$794$	−2.46758e12	−0.220333
$795$	−1.72782e13	−1.53407
$796$	−1.78411e12	−0.157511
$797$	−4.88208e12	−0.428591	−0.214295	−	0.976769i	$-0.568746\pi$
$797$	−4.88208e12	−0.428591	−0.214295	+	0.976769i	$0.568746\pi$
$798$	0	0
$799$	−2.42104e12	−0.210156
$800$	−1.56537e13	−1.35118
$801$	2.11025e13	1.81129
$802$	−9.94045e11	−0.0848441
$803$	2.57225e13	2.18320
$804$	2.02186e13	1.70647
$805$	9.56991e12	0.803205
$806$	−2.33822e12	−0.195154
$807$	5.38895e12	0.447274
$808$	3.50316e12	0.289141
$809$	−3.93058e12	−0.322618	−0.161309	−	0.986904i	$-0.551572\pi$
$809$	−3.93058e12	−0.322618	−0.161309	+	0.986904i	$0.551572\pi$
$810$	−5.10775e12	−0.416915
$811$	3.88693e12	0.315510	0.157755	−	0.987478i	$-0.449574\pi$
$811$	3.88693e12	0.315510	0.157755	+	0.987478i	$0.449574\pi$
$812$	1.78057e13	1.43733
$813$	1.42464e13	1.14366
$814$	−2.75746e12	−0.220140
$815$	−2.88652e13	−2.29174
$816$	4.74542e12	0.374687
$817$	0	0
$818$	−6.76335e12	−0.528168
$819$	−2.09879e13	−1.63002
$820$	3.88806e12	0.300310
$821$	8.47867e12	0.651304	0.325652	−	0.945490i	$-0.394416\pi$
$821$	8.47867e12	0.651304	0.325652	+	0.945490i	$0.394416\pi$
$822$	−1.93868e12	−0.148110
$823$	2.05411e13	1.56072	0.780358	−	0.625333i	$-0.215037\pi$
$823$	2.05411e13	1.56072	0.780358	+	0.625333i	$0.215037\pi$
$824$	−3.13474e12	−0.236881
$825$	−5.23199e13	−3.93209
$826$	3.67273e12	0.274523
$827$	−1.45545e13	−1.08199	−0.540993	−	0.841027i	$-0.681951\pi$
$827$	−1.45545e13	−1.08199	−0.540993	+	0.841027i	$0.681951\pi$
$828$	−4.81778e12	−0.356214
$829$	1.84020e13	1.35322	0.676611	−	0.736341i	$-0.263448\pi$
$829$	1.84020e13	1.35322	0.676611	+	0.736341i	$0.263448\pi$
$830$	6.61710e12	0.483968
$831$	−3.25129e12	−0.236511
$832$	−7.31982e12	−0.529597
$833$	−4.67726e12	−0.336581
$834$	4.94596e12	0.354000
$835$	−3.31646e12	−0.236094
$836$	0	0
$837$	−1.69530e12	−0.119394
$838$	−3.18337e12	−0.222992
$839$	2.53355e13	1.76523	0.882614	−	0.470098i	$-0.155781\pi$
$839$	2.53355e13	1.76523	0.882614	+	0.470098i	$0.155781\pi$
$840$	−2.75593e13	−1.90990
$841$	3.67034e12	0.253002
$842$	−5.70656e12	−0.391264
$843$	−1.35697e13	−0.925433
$844$	−2.71867e12	−0.184423
$845$	−1.39673e12	−0.0942450
$846$	−3.02553e12	−0.203065
$847$	−3.05532e13	−2.03977
$848$	−7.16627e12	−0.475895
$849$	−2.34945e13	−1.55196
$850$	2.66086e12	0.174838
$851$	2.52467e12	0.165014
$852$	3.50797e13	2.28075
$853$	−2.28826e13	−1.47991	−0.739954	−	0.672658i	$-0.765153\pi$
$853$	−2.28826e13	−1.47991	−0.739954	+	0.672658i	$0.765153\pi$
$854$	1.09130e13	0.702072
$855$	0	0
$856$	8.48418e12	0.540105
$857$	4.94627e12	0.313231	0.156615	−	0.987660i	$-0.449942\pi$
$857$	4.94627e12	0.313231	0.156615	+	0.987660i	$0.449942\pi$
$858$	1.09920e13	0.692446
$859$	−1.13612e13	−0.711959	−0.355980	−	0.934494i	$-0.615853\pi$
$859$	−1.13612e13	−0.711959	−0.355980	+	0.934494i	$0.615853\pi$
$860$	−2.72315e13	−1.69758
$861$	6.59450e12	0.408948
$862$	−2.87736e12	−0.177505
$863$	2.24359e13	1.37688	0.688439	−	0.725294i	$-0.258296\pi$
$863$	2.24359e13	1.37688	0.688439	+	0.725294i	$0.258296\pi$
$864$	2.38446e12	0.145572
$865$	1.33576e13	0.811254
$866$	1.22681e12	0.0741217
$867$	2.13920e13	1.28578
$868$	1.38175e13	0.826212
$869$	1.76293e13	1.04869
$870$	−1.34274e13	−0.794614
$871$	2.23807e13	1.31763
$872$	8.35513e12	0.489361
$873$	−5.10290e12	−0.297340
$874$	0	0
$875$	2.90627e13	1.67610
$876$	3.23683e13	1.85717
$877$	−1.66824e13	−0.952271	−0.476136	−	0.879372i	$-0.657963\pi$
$877$	−1.66824e13	−0.952271	−0.476136	+	0.879372i	$0.657963\pi$
$878$	6.27779e12	0.356518
$879$	−1.59375e12	−0.0900471
$880$	−3.42996e13	−1.92804
$881$	3.25032e13	1.81775	0.908874	−	0.417070i	$-0.136943\pi$
$881$	3.25032e13	1.81775	0.908874	+	0.417070i	$0.136943\pi$
$882$	−5.84509e12	−0.325224
$883$	1.40457e13	0.777534	0.388767	−	0.921336i	$-0.372901\pi$
$883$	1.40457e13	0.777534	0.388767	+	0.921336i	$0.372901\pi$
$884$	5.86519e12	0.323033
$885$	2.90584e13	1.59231
$886$	5.56279e12	0.303278
$887$	−7.68674e11	−0.0416952	−0.0208476	−	0.999783i	$-0.506636\pi$
$887$	−7.68674e11	−0.0416952	−0.0208476	+	0.999783i	$0.506636\pi$
$888$	−7.27050e12	−0.392379
$889$	3.89228e13	2.09000
$890$	1.46388e13	0.782081
$891$	−2.52251e13	−1.34086
$892$	−2.38460e13	−1.26117
$893$	0	0
$894$	−6.16649e12	−0.322863
$895$	−5.27908e13	−2.75014
$896$	−2.54097e13	−1.31708
$897$	−1.00641e13	−0.519048
$898$	−1.39781e12	−0.0717305
$899$	1.41060e13	0.720254
$900$	−3.48875e13	−1.77247
$901$	4.33967e12	0.219379
$902$	−1.83015e12	−0.0920573
$903$	−4.61872e13	−2.31167
$904$	−2.43627e12	−0.121330
$905$	−1.96038e13	−0.971455
$906$	−4.65476e12	−0.229520
$907$	−3.11104e13	−1.52642	−0.763208	−	0.646153i	$-0.776377\pi$
$907$	−3.11104e13	−1.52642	−0.763208	+	0.646153i	$0.776377\pi$
$908$	2.75206e13	1.34361
$909$	1.18888e13	0.577567
$910$	−1.45594e13	−0.703811
$911$	−3.18191e13	−1.53058	−0.765289	−	0.643687i	$-0.777404\pi$
$911$	−3.18191e13	−1.53058	−0.765289	+	0.643687i	$0.777404\pi$
$912$	0	0
$913$	3.26792e13	1.55651
$914$	7.54479e12	0.357593
$915$	8.63424e13	4.07220
$916$	−3.66550e13	−1.72030
$917$	1.64187e13	0.766788
$918$	−4.05317e11	−0.0188366
$919$	−5.77595e12	−0.267118	−0.133559	−	0.991041i	$-0.542641\pi$
$919$	−5.77595e12	−0.267118	−0.133559	+	0.991041i	$0.542641\pi$
$920$	−7.00275e12	−0.322273
$921$	−2.63091e13	−1.20486
$922$	4.52321e12	0.206138
$923$	3.88310e13	1.76105
$924$	−6.49565e13	−2.93156
$925$	1.82821e13	0.821086
$926$	−4.13102e12	−0.184632
$927$	−1.06385e13	−0.473175
$928$	−1.98403e13	−0.878177
$929$	−1.60303e13	−0.706106	−0.353053	−	0.935603i	$-0.614857\pi$
$929$	−1.60303e13	−0.706106	−0.353053	+	0.935603i	$0.614857\pi$
$930$	−1.04199e13	−0.456762
$931$	0	0
$932$	−7.93603e12	−0.344534
$933$	2.42358e13	1.04711
$934$	−7.38059e12	−0.317344
$935$	2.07708e13	0.888794
$936$	1.53579e13	0.654017
$937$	3.75207e13	1.59017	0.795084	−	0.606500i	$-0.207427\pi$
$937$	3.75207e13	1.59017	0.795084	+	0.606500i	$0.207427\pi$
$938$	1.26058e13	0.531688
$939$	1.28797e13	0.540644
$940$	2.20203e13	0.919915
$941$	3.45204e13	1.43523	0.717617	−	0.696438i	$-0.245233\pi$
$941$	3.45204e13	1.43523	0.717617	+	0.696438i	$0.245233\pi$
$942$	7.42749e12	0.307336
$943$	1.67565e12	0.0690049
$944$	1.20522e13	0.493960
$945$	−1.05561e13	−0.430586
$946$	1.28182e13	0.520376
$947$	−2.01077e13	−0.812435	−0.406217	−	0.913777i	$-0.633152\pi$
$947$	−2.01077e13	−0.812435	−0.406217	+	0.913777i	$0.633152\pi$
$948$	2.21841e13	0.892080
$949$	3.58297e13	1.43399
$950$	0	0
$951$	−5.96299e13	−2.36402
$952$	6.92192e12	0.273124
$953$	−3.88414e13	−1.52538	−0.762689	−	0.646766i	$-0.776121\pi$
$953$	−3.88414e13	−1.52538	−0.762689	+	0.646766i	$0.776121\pi$
$954$	5.42321e12	0.211977
$955$	4.23232e13	1.64650
$956$	−1.71115e13	−0.662565
$957$	−6.63127e13	−2.55560
$958$	9.72647e11	0.0373087
$959$	1.26816e13	0.484161
$960$	−3.26195e13	−1.23953
$961$	−1.54931e13	−0.585982
$962$	−3.84095e12	−0.144594
$963$	2.87931e13	1.07887
$964$	−1.10481e13	−0.412043
$965$	−4.13607e13	−1.53537
$966$	−5.66851e12	−0.209446
$967$	1.77102e13	0.651337	0.325668	−	0.945484i	$-0.394411\pi$
$967$	1.77102e13	0.651337	0.325668	+	0.945484i	$0.394411\pi$
$968$	2.23572e13	0.818424
$969$	0	0
$970$	−3.53989e12	−0.128386
$971$	−4.88393e12	−0.176312	−0.0881562	−	0.996107i	$-0.528097\pi$
$971$	−4.88393e12	−0.176312	−0.0881562	+	0.996107i	$0.528097\pi$
$972$	−3.64569e13	−1.31003
$973$	−3.23533e13	−1.15721
$974$	7.89656e12	0.281140
$975$	−7.28780e13	−2.58271
$976$	3.58112e13	1.26327
$977$	−1.99517e13	−0.700574	−0.350287	−	0.936642i	$-0.613916\pi$
$977$	−1.99517e13	−0.700574	−0.350287	+	0.936642i	$0.613916\pi$
$978$	1.70976e13	0.597600
$979$	7.22954e13	2.51529
$980$	4.25415e13	1.47331
$981$	2.83552e13	0.977511
$982$	6.33409e12	0.217361
$983$	2.96029e13	1.01121	0.505607	−	0.862764i	$-0.331269\pi$
$983$	2.96029e13	1.01121	0.505607	+	0.862764i	$0.331269\pi$
$984$	−4.82551e12	−0.164084
$985$	3.58312e13	1.21283
$986$	3.37250e12	0.113633
$987$	3.73484e13	1.25269
$988$	0	0
$989$	−1.17361e13	−0.390067
$990$	2.59569e13	0.858805
$991$	3.44145e13	1.13347	0.566735	−	0.823900i	$-0.308206\pi$
$991$	3.44145e13	1.13347	0.566735	+	0.823900i	$0.308206\pi$
$992$	−1.53964e13	−0.504796
$993$	4.01196e13	1.30944
$994$	2.18713e13	0.710616
$995$	−8.80078e12	−0.284654
$996$	4.11223e13	1.32407
$997$	−1.37634e13	−0.441162	−0.220581	−	0.975369i	$-0.570795\pi$
$997$	−1.37634e13	−0.441162	−0.220581	+	0.975369i	$0.570795\pi$
$998$	1.43339e13	0.457381
$999$	−2.78484e12	−0.0884616

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.10.a.b.1.3		6
19.18	odd	2		19.10.a.a.1.4	✓	6
57.56	even	2		171.10.a.c.1.3		6
76.75	even	2		304.10.a.f.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.10.a.a.1.4	✓	6	19.18	odd	2
171.10.a.c.1.3		6	57.56	even	2
304.10.a.f.1.1		6	76.75	even	2
361.10.a.b.1.3		6	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-6.67485 q^{2} -204.622 q^{3} -467.446 q^{4} -2305.86 q^{5} +1365.82 q^{6} -8934.31 q^{7} +6537.66 q^{8} +22187.1 q^{9} +15391.2 q^{10} +76011.2 q^{11} +95649.8 q^{12} +105878. q^{13} +59635.2 q^{14} +471829. q^{15} +195695. q^{16} -118507. q^{17} -148096. q^{18} +1.07786e6 q^{20} +1.82816e6 q^{21} -507363. q^{22} +464530. q^{23} -1.33775e6 q^{24} +3.36385e6 q^{25} -706722. q^{26} -512401. q^{27} +4.17631e6 q^{28} +4.26351e6 q^{29} -3.14939e6 q^{30} +3.30855e6 q^{31} -4.65351e6 q^{32} -1.55536e7 q^{33} +791015. q^{34} +2.06012e7 q^{35} -1.03713e7 q^{36} +5.43488e6 q^{37} -2.16650e7 q^{39} -1.50749e7 q^{40} +3.60719e6 q^{41} -1.22027e7 q^{42} -2.52643e7 q^{43} -3.55312e7 q^{44} -5.11604e7 q^{45} -3.10067e6 q^{46} +2.04296e7 q^{47} -4.00434e7 q^{48} +3.94683e7 q^{49} -2.24532e7 q^{50} +2.42491e7 q^{51} -4.94925e7 q^{52} -3.66196e7 q^{53} +3.42020e6 q^{54} -1.75271e8 q^{55} -5.84095e7 q^{56} -2.84583e7 q^{58} +6.15867e7 q^{59} -2.20555e8 q^{60} +1.82995e8 q^{61} -2.20840e7 q^{62} -1.98227e8 q^{63} -6.91342e7 q^{64} -2.44140e8 q^{65} +1.03818e8 q^{66} +2.11382e8 q^{67} +5.53956e7 q^{68} -9.50531e7 q^{69} -1.37510e8 q^{70} +3.66751e8 q^{71} +1.45052e8 q^{72} +3.38405e8 q^{73} -3.62770e7 q^{74} -6.88318e8 q^{75} -6.79108e8 q^{77} +1.44611e8 q^{78} +2.31930e8 q^{79} -4.51244e8 q^{80} -3.31861e8 q^{81} -2.40774e7 q^{82} +4.29926e8 q^{83} -8.54565e8 q^{84} +2.73260e8 q^{85} +1.68636e8 q^{86} -8.72407e8 q^{87} +4.96935e8 q^{88} +9.51115e8 q^{89} +3.41488e8 q^{90} -9.45951e8 q^{91} -2.17143e8 q^{92} -6.77001e8 q^{93} -1.36364e8 q^{94} +9.52211e8 q^{96} -2.29994e8 q^{97} -2.63445e8 q^{98} +1.68647e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 33 q^{2} + 155 q^{3} + 1365 q^{4} - 3612 q^{5} + 5581 q^{6} + 4085 q^{7} + 23511 q^{8} + 17625 q^{9} + 93884 q^{10} - 69312 q^{11} + 460165 q^{12} + 191747 q^{13} + 644691 q^{14} + 326428 q^{15} + 13905 q^{16}+ \cdots + 1045331674 q^{99}+O(q^{100}) \) 6 * q + 33 * q^2 + 155 * q^3 + 1365 * q^4 - 3612 * q^5 + 5581 * q^6 + 4085 * q^7 + 23511 * q^8 + 17625 * q^9 + 93884 * q^10 - 69312 * q^11 + 460165 * q^12 + 191747 * q^13 + 644691 * q^14 + 326428 * q^15 + 13905 * q^16 - 288195 * q^17 + 1159386 * q^18 - 1551444 * q^20 + 3260767 * q^21 - 2409710 * q^22 - 50697 * q^23 + 5457255 * q^24 + 7126888 * q^25 + 4394073 * q^26 - 3854359 * q^27 + 19295623 * q^28 + 7178667 * q^29 + 7527236 * q^30 + 4310716 * q^31 + 5388975 * q^32 - 17592194 * q^33 - 18049 * q^34 - 4166490 * q^35 + 21311958 * q^36 + 15687040 * q^37 - 42886175 * q^39 - 33173148 * q^40 + 25134306 * q^41 + 64728563 * q^42 - 75118674 * q^43 - 94242102 * q^44 - 90343732 * q^45 + 85549087 * q^46 - 83731938 * q^47 + 63665473 * q^48 + 21010019 * q^49 - 141211941 * q^50 + 134793629 * q^51 - 147001043 * q^52 + 138019203 * q^53 + 160916047 * q^54 - 1518258 * q^55 + 182020629 * q^56 + 14051197 * q^58 + 7809915 * q^59 - 651478180 * q^60 + 191946566 * q^61 + 564818736 * q^62 + 152217316 * q^63 + 167338593 * q^64 + 146177172 * q^65 + 14789186 * q^66 + 16109787 * q^67 + 561722511 * q^68 + 20855199 * q^69 - 692634996 * q^70 + 264469698 * q^71 + 768475026 * q^72 - 287572857 * q^73 + 376807098 * q^74 + 186644613 * q^75 - 1619915436 * q^77 + 80663153 * q^78 + 86534002 * q^79 - 1300596708 * q^80 - 1155245802 * q^81 + 1582686496 * q^82 - 359214570 * q^83 + 2245098407 * q^84 - 648092718 * q^85 + 1061832924 * q^86 + 347964645 * q^87 - 779241042 * q^88 + 2263866306 * q^89 - 1188734960 * q^90 - 1172864023 * q^91 - 373904061 * q^92 + 1467983860 * q^93 + 864022488 * q^94 + 3402264767 * q^96 - 2705893460 * q^97 + 4245664590 * q^98 + 1045331674 * q^99

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