LMFDB - Embedded newform 197.8.a.b.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [197,8,Mod(1,197)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(197, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("197.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	197.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:	$61.5398500204$
Analytic rank:	$0$
Dimension:	$60$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	197.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-8.25431 q^{2} -14.1669 q^{3} -59.8663 q^{4} +11.5658 q^{5} +116.938 q^{6} -664.362 q^{7} +1550.71 q^{8} -1986.30 q^{9} -95.4680 q^{10} -3556.40 q^{11} +848.118 q^{12} -6714.69 q^{13} +5483.85 q^{14} -163.852 q^{15} -5137.13 q^{16} +13719.6 q^{17} +16395.5 q^{18} -34381.8 q^{19} -692.405 q^{20} +9411.91 q^{21} +29355.7 q^{22} -36355.9 q^{23} -21968.6 q^{24} -77991.2 q^{25} +55425.2 q^{26} +59122.5 q^{27} +39772.9 q^{28} -46569.7 q^{29} +1352.48 q^{30} -287094. q^{31} -156087. q^{32} +50383.0 q^{33} -113246. q^{34} -7683.90 q^{35} +118913. q^{36} -374998. q^{37} +283798. q^{38} +95126.1 q^{39} +17935.2 q^{40} +8647.96 q^{41} -77688.9 q^{42} -326648. q^{43} +212909. q^{44} -22973.2 q^{45} +300093. q^{46} +322881. q^{47} +72776.9 q^{48} -382167. q^{49} +643764. q^{50} -194363. q^{51} +401984. q^{52} -1.15879e6 q^{53} -488016. q^{54} -41132.8 q^{55} -1.03023e6 q^{56} +487082. q^{57} +384401. q^{58} -381147. q^{59} +9809.20 q^{60} +681676. q^{61} +2.36976e6 q^{62} +1.31962e6 q^{63} +1.94594e6 q^{64} -77661.1 q^{65} -415877. q^{66} -3.84661e6 q^{67} -821342. q^{68} +515049. q^{69} +63425.3 q^{70} +3.36103e6 q^{71} -3.08017e6 q^{72} -3.33642e6 q^{73} +3.09535e6 q^{74} +1.10489e6 q^{75} +2.05831e6 q^{76} +2.36274e6 q^{77} -785201. q^{78} +2.91848e6 q^{79} -59415.2 q^{80} +3.50646e6 q^{81} -71383.0 q^{82} +6.89244e6 q^{83} -563457. q^{84} +158679. q^{85} +2.69626e6 q^{86} +659746. q^{87} -5.51494e6 q^{88} +432784. q^{89} +189628. q^{90} +4.46098e6 q^{91} +2.17650e6 q^{92} +4.06722e6 q^{93} -2.66516e6 q^{94} -397654. q^{95} +2.21126e6 q^{96} -6.90655e6 q^{97} +3.15452e6 q^{98} +7.06408e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 16 q^{2} + 296 q^{3} + 4224 q^{4} + 554 q^{5} + 1200 q^{6} + 4959 q^{7} + 2571 q^{8} + 47384 q^{9} + 16237 q^{10} + 12452 q^{11} + 38656 q^{12} + 36460 q^{13} - 567 q^{14} + 55139 q^{15} + 319488 q^{16}+ \cdots + 64628303 q^{99}+O(q^{100}) $ 60 * q + 16 * q^2 + 296 * q^3 + 4224 * q^4 + 554 * q^5 + 1200 * q^6 + 4959 * q^7 + 2571 * q^8 + 47384 * q^9 + 16237 * q^10 + 12452 * q^11 + 38656 * q^12 + 36460 * q^13 - 567 * q^14 + 55139 * q^15 + 319488 * q^16 + 13657 * q^17 + 75985 * q^18 + 179089 * q^19 + 78379 * q^20 + 71390 * q^21 + 220057 * q^22 + 159428 * q^23 + 288645 * q^24 + 1250470 * q^25 + 245262 * q^26 + 789647 * q^27 + 775366 * q^28 + 111693 * q^29 + 200635 * q^30 + 1035260 * q^31 + 688764 * q^32 + 535514 * q^33 + 1430866 * q^34 + 698672 * q^35 + 4315642 * q^36 + 1226630 * q^37 + 133058 * q^38 + 1107523 * q^39 + 2427846 * q^40 + 1766062 * q^41 + 693163 * q^42 + 3240035 * q^43 + 2056578 * q^44 + 1462797 * q^45 + 1088877 * q^46 + 3015185 * q^47 + 4531442 * q^48 + 8513327 * q^49 - 8803339 * q^50 - 1200965 * q^51 + 2403172 * q^52 - 2021580 * q^53 - 9268097 * q^54 + 2538479 * q^55 - 13776768 * q^56 - 638299 * q^57 + 3745679 * q^58 + 6845183 * q^59 + 5842749 * q^60 + 6328462 * q^61 + 7784379 * q^62 + 11502133 * q^63 + 28157685 * q^64 + 14369523 * q^65 + 25244790 * q^66 + 20888346 * q^67 + 18152427 * q^68 + 7874901 * q^69 + 23377047 * q^70 + 7085107 * q^71 + 50177539 * q^72 + 21946913 * q^73 + 32718747 * q^74 + 44992638 * q^75 + 52601230 * q^76 + 22159370 * q^77 + 86884893 * q^78 + 9667191 * q^79 + 50245998 * q^80 + 56936064 * q^81 + 55357649 * q^82 + 57432744 * q^83 + 65898868 * q^84 + 32071274 * q^85 + 91529136 * q^86 + 38121559 * q^87 + 95846511 * q^88 + 46839682 * q^89 + 136287359 * q^90 + 81150673 * q^91 + 99073310 * q^92 + 81689463 * q^93 + 55616387 * q^94 + 30995799 * q^95 + 156893033 * q^96 + 72697122 * q^97 + 69757306 * q^98 + 64628303 * 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 $

$2$	−8.25431	−0.729585	−0.364792	−	0.931089i	$-0.618860\pi$
$2$	−8.25431	−0.729585	−0.364792	+	0.931089i	$0.618860\pi$
$3$	−14.1669	−0.302935	−0.151467	−	0.988462i	$-0.548400\pi$
$3$	−14.1669	−0.302935	−0.151467	+	0.988462i	$0.548400\pi$
$4$	−59.8663	−0.467706
$5$	11.5658	0.0413792	0.0206896	−	0.999786i	$-0.493414\pi$
$5$	11.5658	0.0413792	0.0206896	+	0.999786i	$0.493414\pi$
$6$	116.938	0.221017
$7$	−664.362	−0.732085	−0.366042	−	0.930598i	$-0.619287\pi$
$7$	−664.362	−0.732085	−0.366042	+	0.930598i	$0.619287\pi$
$8$	1550.71	1.07082
$9$	−1986.30	−0.908231
$10$	−95.4680	−0.0301896
$11$	−3556.40	−0.805632	−0.402816	−	0.915281i	$-0.631969\pi$
$11$	−3556.40	−0.805632	−0.402816	+	0.915281i	$0.631969\pi$
$12$	848.118	0.141684
$13$	−6714.69	−0.847666	−0.423833	−	0.905740i	$-0.639316\pi$
$13$	−6714.69	−0.847666	−0.423833	+	0.905740i	$0.639316\pi$
$14$	5483.85	0.534118
$15$	−163.852	−0.0125352
$16$	−5137.13	−0.313545
$17$	13719.6	0.677282	0.338641	−	0.940916i	$-0.390033\pi$
$17$	13719.6	0.677282	0.338641	+	0.940916i	$0.390033\pi$
$18$	16395.5	0.662631
$19$	−34381.8	−1.14998	−0.574991	−	0.818160i	$-0.694994\pi$
$19$	−34381.8	−1.14998	−0.574991	+	0.818160i	$0.694994\pi$
$20$	−692.405	−0.0193533
$21$	9411.91	0.221774
$22$	29355.7	0.587777
$23$	−36355.9	−0.623057	−0.311529	−	0.950237i	$-0.600841\pi$
$23$	−36355.9	−0.623057	−0.311529	+	0.950237i	$0.600841\pi$
$24$	−21968.6	−0.324387
$25$	−77991.2	−0.998288
$26$	55425.2	0.618444
$27$	59122.5	0.578069
$28$	39772.9	0.342400
$29$	−46569.7	−0.354577	−0.177288	−	0.984159i	$-0.556733\pi$
$29$	−46569.7	−0.354577	−0.177288	+	0.984159i	$0.556733\pi$
$30$	1352.48	0.00914549
$31$	−287094.	−1.73084	−0.865422	−	0.501044i	$-0.832950\pi$
$31$	−287094.	−1.73084	−0.865422	+	0.501044i	$0.832950\pi$
$32$	−156087.	−0.842058
$33$	50383.0	0.244054
$34$	−113246.	−0.494135
$35$	−7683.90	−0.0302931
$36$	118913.	0.424785
$37$	−374998.	−1.21709	−0.608545	−	0.793519i	$-0.708247\pi$
$37$	−374998.	−1.21709	−0.608545	+	0.793519i	$0.708247\pi$
$38$	283798.	0.839009
$39$	95126.1	0.256787
$40$	17935.2	0.0443095
$41$	8647.96	0.0195961	0.00979807	−	0.999952i	$-0.496881\pi$
$41$	8647.96	0.0195961	0.00979807	+	0.999952i	$0.496881\pi$
$42$	−77688.9	−0.161803
$43$	−326648.	−0.626528	−0.313264	−	0.949666i	$-0.601423\pi$
$43$	−326648.	−0.626528	−0.313264	+	0.949666i	$0.601423\pi$
$44$	212909.	0.376799
$45$	−22973.2	−0.0375819
$46$	300093.	0.454573
$47$	322881.	0.453629	0.226814	−	0.973938i	$-0.427169\pi$
$47$	322881.	0.453629	0.226814	+	0.973938i	$0.427169\pi$
$48$	72776.9	0.0949838
$49$	−382167.	−0.464052
$50$	643764.	0.728336
$51$	−194363.	−0.205172
$52$	401984.	0.396458
$53$	−1.15879e6	−1.06915	−0.534577	−	0.845120i	$-0.679529\pi$
$53$	−1.15879e6	−1.06915	−0.534577	+	0.845120i	$0.679529\pi$
$54$	−488016.	−0.421751
$55$	−41132.8	−0.0333364
$56$	−1.03023e6	−0.783928
$57$	487082.	0.348369
$58$	384401.	0.258694
$59$	−381147.	−0.241607	−0.120804	−	0.992676i	$-0.538547\pi$
$59$	−381147.	−0.241607	−0.120804	+	0.992676i	$0.538547\pi$
$60$	9809.20	0.00586279
$61$	681676.	0.384524	0.192262	−	0.981344i	$-0.438418\pi$
$61$	681676.	0.384524	0.192262	+	0.981344i	$0.438418\pi$
$62$	2.36976e6	1.26280
$63$	1.31962e6	0.664902
$64$	1.94594e6	0.927898
$65$	−77661.1	−0.0350757
$66$	−415877.	−0.178058
$67$	−3.84661e6	−1.56249	−0.781244	−	0.624226i	$-0.785414\pi$
$67$	−3.84661e6	−1.56249	−0.781244	+	0.624226i	$0.785414\pi$
$68$	−821342.	−0.316769
$69$	515049.	0.188746
$70$	63425.3	0.0221014
$71$	3.36103e6	1.11447	0.557234	−	0.830355i	$-0.311863\pi$
$71$	3.36103e6	1.11447	0.557234	+	0.830355i	$0.311863\pi$
$72$	−3.08017e6	−0.972548
$73$	−3.33642e6	−1.00381	−0.501904	−	0.864923i	$-0.667367\pi$
$73$	−3.33642e6	−1.00381	−0.501904	+	0.864923i	$0.667367\pi$
$74$	3.09535e6	0.887971
$75$	1.10489e6	0.302416
$76$	2.05831e6	0.537853
$77$	2.36274e6	0.589791
$78$	−785201.	−0.187348
$79$	2.91848e6	0.665981	0.332991	−	0.942930i	$-0.391942\pi$
$79$	2.91848e6	0.665981	0.332991	+	0.942930i	$0.391942\pi$
$80$	−59415.2	−0.0129743
$81$	3.50646e6	0.733113
$82$	−71383.0	−0.0142970
$83$	6.89244e6	1.32312	0.661560	−	0.749892i	$-0.269895\pi$
$83$	6.89244e6	1.32312	0.661560	+	0.749892i	$0.269895\pi$
$84$	−563457.	−0.103725
$85$	158679.	0.0280254
$86$	2.69626e6	0.457106
$87$	659746.	0.107414
$88$	−5.51494e6	−0.862683
$89$	432784.	0.0650738	0.0325369	−	0.999471i	$-0.489641\pi$
$89$	432784.	0.0650738	0.0325369	+	0.999471i	$0.489641\pi$
$90$	189628.	0.0274192
$91$	4.46098e6	0.620563
$92$	2.17650e6	0.291408
$93$	4.06722e6	0.524333
$94$	−2.66516e6	−0.330961
$95$	−397654.	−0.0475853
$96$	2.21126e6	0.255089
$97$	−6.90655e6	−0.768352	−0.384176	−	0.923260i	$-0.625514\pi$
$97$	−6.90655e6	−0.768352	−0.384176	+	0.923260i	$0.625514\pi$
$98$	3.15452e6	0.338565
$99$	7.06408e6	0.731699
$100$	4.66905e6	0.466905
$101$	1.36825e6	0.132142	0.0660711	−	0.997815i	$-0.478954\pi$
$101$	1.36825e6	0.132142	0.0660711	+	0.997815i	$0.478954\pi$
$102$	1.60434e6	0.149691
$103$	1.35466e6	0.122152	0.0610760	−	0.998133i	$-0.480547\pi$
$103$	1.35466e6	0.122152	0.0610760	+	0.998133i	$0.480547\pi$
$104$	−1.04125e7	−0.907694
$105$	108857.	0.00917683
$106$	9.56504e6	0.780039
$107$	1.27997e7	1.01008	0.505039	−	0.863096i	$-0.331478\pi$
$107$	1.27997e7	1.01008	0.505039	+	0.863096i	$0.331478\pi$
$108$	−3.53945e6	−0.270366
$109$	1.20453e7	0.890891	0.445446	−	0.895309i	$-0.353045\pi$
$109$	1.20453e7	0.890891	0.445446	+	0.895309i	$0.353045\pi$
$110$	339523.	0.0243217
$111$	5.31254e6	0.368699
$112$	3.41291e6	0.229542
$113$	8.88122e6	0.579026	0.289513	−	0.957174i	$-0.406507\pi$
$113$	8.88122e6	0.579026	0.289513	+	0.957174i	$0.406507\pi$
$114$	−4.02053e6	−0.254165
$115$	−420487.	−0.0257816
$116$	2.78796e6	0.165838
$117$	1.33374e7	0.769876
$118$	3.14611e6	0.176273
$119$	−9.11477e6	−0.495828
$120$	−254086.	−0.0134229
$121$	−6.83917e6	−0.350957
$122$	−5.62676e6	−0.280543
$123$	−122514.	−0.00593635
$124$	1.71873e7	0.809526
$125$	−1.80562e6	−0.0826876
$126$	−1.08926e7	−0.485102
$127$	−3.50062e6	−0.151646	−0.0758232	−	0.997121i	$-0.524158\pi$
$127$	−3.50062e6	−0.151646	−0.0758232	+	0.997121i	$0.524158\pi$
$128$	3.91672e6	0.165078
$129$	4.62758e6	0.189797
$130$	641039.	0.0255907
$131$	1.48152e7	0.575783	0.287892	−	0.957663i	$-0.407046\pi$
$131$	1.48152e7	0.575783	0.287892	+	0.957663i	$0.407046\pi$
$132$	−3.01625e6	−0.114145
$133$	2.28419e7	0.841884
$134$	3.17511e7	1.13997
$135$	683802.	0.0239200
$136$	2.12751e7	0.725245
$137$	1.09864e7	0.365034	0.182517	−	0.983203i	$-0.441576\pi$
$137$	1.09864e7	0.365034	0.182517	+	0.983203i	$0.441576\pi$
$138$	−4.25138e6	−0.137706
$139$	1.25769e7	0.397211	0.198606	−	0.980079i	$-0.436359\pi$
$139$	1.25769e7	0.397211	0.198606	+	0.980079i	$0.436359\pi$
$140$	460007.	0.0141683
$141$	−4.57421e6	−0.137420
$142$	−2.77430e7	−0.813099
$143$	2.38802e7	0.682906
$144$	1.02039e7	0.284771
$145$	−538618.	−0.0146721
$146$	2.75398e7	0.732363
$147$	5.41410e6	0.140577
$148$	2.24498e7	0.569240
$149$	4.33466e7	1.07350	0.536751	−	0.843741i	$-0.319651\pi$
$149$	4.33466e7	1.07350	0.536751	+	0.843741i	$0.319651\pi$
$150$	−9.12011e6	−0.220638
$151$	−1.97642e7	−0.467153	−0.233577	−	0.972338i	$-0.575043\pi$
$151$	−1.97642e7	−0.467153	−0.233577	+	0.972338i	$0.575043\pi$
$152$	−5.33161e7	−1.23142
$153$	−2.72512e7	−0.615129
$154$	−1.95028e7	−0.430302
$155$	−3.32048e6	−0.0716209
$156$	−5.69485e6	−0.120101
$157$	−4.88463e7	−1.00736	−0.503678	−	0.863891i	$-0.668020\pi$
$157$	−4.88463e7	−1.00736	−0.503678	+	0.863891i	$0.668020\pi$
$158$	−2.40900e7	−0.485890
$159$	1.64165e7	0.323884
$160$	−1.80528e6	−0.0348437
$161$	2.41535e7	0.456131
$162$	−2.89434e7	−0.534868
$163$	−4.25840e7	−0.770176	−0.385088	−	0.922880i	$-0.625829\pi$
$163$	−4.25840e7	−0.770176	−0.385088	+	0.922880i	$0.625829\pi$
$164$	−517722.	−0.00916523
$165$	582722.	0.0100988
$166$	−5.68923e7	−0.965329
$167$	−8.93370e7	−1.48431	−0.742154	−	0.670230i	$-0.766196\pi$
$167$	−8.93370e7	−1.48431	−0.742154	+	0.670230i	$0.766196\pi$
$168$	1.45951e7	0.237479
$169$	−1.76614e7	−0.281463
$170$	−1.30978e6	−0.0204469
$171$	6.82926e7	1.04445
$172$	1.95552e7	0.293031
$173$	2.27349e7	0.333835	0.166918	−	0.985971i	$-0.446619\pi$
$173$	2.27349e7	0.333835	0.166918	+	0.985971i	$0.446619\pi$
$174$	−5.44575e6	−0.0783674
$175$	5.18144e7	0.730831
$176$	1.82697e7	0.252602
$177$	5.39965e6	0.0731913
$178$	−3.57234e6	−0.0474769
$179$	−3.65563e6	−0.0476406	−0.0238203	−	0.999716i	$-0.507583\pi$
$179$	−3.65563e6	−0.0476406	−0.0238203	+	0.999716i	$0.507583\pi$
$180$	1.37532e6	0.0175773
$181$	−7.40252e7	−0.927908	−0.463954	−	0.885859i	$-0.653570\pi$
$181$	−7.40252e7	−0.927908	−0.463954	+	0.885859i	$0.653570\pi$
$182$	−3.68224e7	−0.452753
$183$	−9.65720e6	−0.116486
$184$	−5.63774e7	−0.667180
$185$	−4.33717e6	−0.0503622
$186$	−3.35721e7	−0.382545
$187$	−4.87924e7	−0.545640
$188$	−1.93297e7	−0.212165
$189$	−3.92787e7	−0.423196
$190$	3.28236e6	0.0347175
$191$	−7.21721e7	−0.749467	−0.374734	−	0.927132i	$-0.622266\pi$
$191$	−7.21721e7	−0.749467	−0.374734	+	0.927132i	$0.622266\pi$
$192$	−2.75679e7	−0.281093
$193$	−1.98181e7	−0.198432	−0.0992160	−	0.995066i	$-0.531633\pi$
$193$	−1.98181e7	−0.198432	−0.0992160	+	0.995066i	$0.531633\pi$
$194$	5.70088e7	0.560578
$195$	1.10021e6	0.0106257
$196$	2.28789e7	0.217040
$197$	−7.64537e6	−0.0712470
$197$	−7.64537e6	−0.0712470
$198$	−5.83091e7	−0.533837
$199$	−9.86165e7	−0.887082	−0.443541	−	0.896254i	$-0.646278\pi$
$199$	−9.86165e7	−0.887082	−0.443541	+	0.896254i	$0.646278\pi$
$200$	−1.20942e8	−1.06898
$201$	5.44944e7	0.473332
$202$	−1.12940e7	−0.0964089
$203$	3.09391e7	0.259580
$204$	1.16358e7	0.0959603
$205$	100021.	0.000810872 0
$206$	−1.11818e7	−0.0891202
$207$	7.22138e7	0.565880
$208$	3.44942e7	0.265782
$209$	1.22276e8	0.926462
$210$	−898537.	−0.00669527
$211$	−5.66199e7	−0.414936	−0.207468	−	0.978242i	$-0.566522\pi$
$211$	−5.66199e7	−0.414936	−0.207468	+	0.978242i	$0.566522\pi$
$212$	6.93727e7	0.500050
$213$	−4.76152e7	−0.337611
$214$	−1.05652e8	−0.736938
$215$	−3.77796e6	−0.0259252
$216$	9.16818e7	0.619006
$217$	1.90734e8	1.26712
$218$	−9.94256e7	−0.649981
$219$	4.72666e7	0.304088
$220$	2.46247e6	0.0155916
$221$	−9.21228e7	−0.574109
$222$	−4.38514e7	−0.268997
$223$	−1.29085e7	−0.0779490	−0.0389745	−	0.999240i	$-0.512409\pi$
$223$	−1.29085e7	−0.0779490	−0.0389745	+	0.999240i	$0.512409\pi$
$224$	1.03698e8	0.616458
$225$	1.54914e8	0.906675
$226$	−7.33083e7	−0.422448
$227$	9.61523e7	0.545593	0.272797	−	0.962072i	$-0.412051\pi$
$227$	9.61523e7	0.545593	0.272797	+	0.962072i	$0.412051\pi$
$228$	−2.91598e7	−0.162934
$229$	−2.53548e8	−1.39520	−0.697598	−	0.716489i	$-0.745748\pi$
$229$	−2.53548e8	−1.39520	−0.697598	+	0.716489i	$0.745748\pi$
$230$	3.47083e6	0.0188099
$231$	−3.34726e7	−0.178668
$232$	−7.22160e7	−0.379687
$233$	−1.26742e8	−0.656410	−0.328205	−	0.944607i	$-0.606444\pi$
$233$	−1.26742e8	−0.656410	−0.328205	+	0.944607i	$0.606444\pi$
$234$	−1.10091e8	−0.561690
$235$	3.73439e6	0.0187708
$236$	2.28179e7	0.113001
$237$	−4.13457e7	−0.201749
$238$	7.52361e7	0.361749
$239$	−1.57899e8	−0.748146	−0.374073	−	0.927399i	$-0.622039\pi$
$239$	−1.57899e8	−0.748146	−0.374073	+	0.927399i	$0.622039\pi$
$240$	841726.	0.00393035
$241$	−1.51861e7	−0.0698854	−0.0349427	−	0.999389i	$-0.511125\pi$
$241$	−1.51861e7	−0.0698854	−0.0349427	+	0.999389i	$0.511125\pi$
$242$	5.64526e7	0.256053
$243$	−1.78976e8	−0.800155
$244$	−4.08094e7	−0.179844
$245$	−4.42008e6	−0.0192021
$246$	1.01127e6	0.00433107
$247$	2.30863e8	0.974800
$248$	−4.45198e8	−1.85342
$249$	−9.76441e7	−0.400819
$250$	1.49041e7	0.0603276
$251$	−1.35485e8	−0.540797	−0.270399	−	0.962748i	$-0.587155\pi$
$251$	−1.35485e8	−0.540797	−0.270399	+	0.962748i	$0.587155\pi$
$252$	−7.90009e7	−0.310978
$253$	1.29296e8	0.501955
$254$	2.88952e7	0.110639
$255$	−2.24798e6	−0.00848987
$256$	−2.81411e8	−1.04834
$257$	2.50898e8	0.922000	0.461000	−	0.887400i	$-0.347491\pi$
$257$	2.50898e8	0.922000	0.461000	+	0.887400i	$0.347491\pi$
$258$	−3.81975e7	−0.138473
$259$	2.49134e8	0.891013
$260$	4.64929e6	0.0164051
$261$	9.25014e7	0.322038
$262$	−1.22290e8	−0.420083
$263$	−2.64736e8	−0.897362	−0.448681	−	0.893692i	$-0.648106\pi$
$263$	−2.64736e8	−0.897362	−0.448681	+	0.893692i	$0.648106\pi$
$264$	7.81294e7	0.261337
$265$	−1.34024e7	−0.0442408
$266$	−1.88544e8	−0.614226
$267$	−6.13119e6	−0.0197131
$268$	2.30283e8	0.730785
$269$	−2.75003e8	−0.861398	−0.430699	−	0.902496i	$-0.641733\pi$
$269$	−2.75003e8	−0.861398	−0.430699	+	0.902496i	$0.641733\pi$
$270$	−5.64431e6	−0.0174517
$271$	5.61337e8	1.71329	0.856646	−	0.515905i	$-0.172544\pi$
$271$	5.61337e8	1.71329	0.856646	+	0.515905i	$0.172544\pi$
$272$	−7.04793e7	−0.212359
$273$	−6.31981e7	−0.187990
$274$	−9.06851e7	−0.266323
$275$	2.77368e8	0.804252
$276$	−3.08341e7	−0.0882775
$277$	5.96151e8	1.68530	0.842650	−	0.538462i	$-0.180994\pi$
$277$	5.96151e8	1.68530	0.842650	+	0.538462i	$0.180994\pi$
$278$	−1.03814e8	−0.289799
$279$	5.70255e8	1.57201
$280$	−1.19155e7	−0.0324383
$281$	6.92463e8	1.86176	0.930881	−	0.365322i	$-0.119041\pi$
$281$	6.92463e8	1.86176	0.930881	+	0.365322i	$0.119041\pi$
$282$	3.77570e7	0.100259
$283$	6.08991e7	0.159720	0.0798598	−	0.996806i	$-0.474553\pi$
$283$	6.08991e7	0.159720	0.0798598	+	0.996806i	$0.474553\pi$
$284$	−2.01212e8	−0.521243
$285$	5.63351e6	0.0144152
$286$	−1.97114e8	−0.498238
$287$	−5.74537e6	−0.0143460
$288$	3.10036e8	0.764783
$289$	−2.22112e8	−0.541289
$290$	4.44592e6	0.0107046
$291$	9.78441e7	0.232760
$292$	1.99739e8	0.469487
$293$	−6.64918e8	−1.54430	−0.772150	−	0.635440i	$-0.780819\pi$
$293$	−6.64918e8	−1.54430	−0.772150	+	0.635440i	$0.780819\pi$
$294$	−4.46897e7	−0.102563
$295$	−4.40828e6	−0.00999752
$296$	−5.81512e8	−1.30328
$297$	−2.10264e8	−0.465711
$298$	−3.57796e8	−0.783211
$299$	2.44119e8	0.528144
$300$	−6.61458e7	−0.141442
$301$	2.17013e8	0.458672
$302$	1.63140e8	0.340828
$303$	−1.93838e7	−0.0400304
$304$	1.76624e8	0.360571
$305$	7.88415e6	0.0159113
$306$	2.24940e8	0.448789
$307$	4.87322e8	0.961241	0.480620	−	0.876929i	$-0.340412\pi$
$307$	4.87322e8	0.961241	0.480620	+	0.876929i	$0.340412\pi$
$308$	−1.41448e8	−0.275849
$309$	−1.91913e7	−0.0370041
$310$	2.74083e7	0.0522536
$311$	7.96951e8	1.50235	0.751173	−	0.660105i	$-0.229488\pi$
$311$	7.96951e8	1.50235	0.751173	+	0.660105i	$0.229488\pi$
$312$	1.47513e8	0.274972
$313$	−8.04789e7	−0.148346	−0.0741732	−	0.997245i	$-0.523632\pi$
$313$	−8.04789e7	−0.148346	−0.0741732	+	0.997245i	$0.523632\pi$
$314$	4.03193e8	0.734952
$315$	1.52625e7	0.0275131
$316$	−1.74719e8	−0.311483
$317$	−8.24931e8	−1.45449	−0.727244	−	0.686379i	$-0.759199\pi$
$317$	−8.24931e8	−1.45449	−0.727244	+	0.686379i	$0.759199\pi$
$318$	−1.35507e8	−0.236301
$319$	1.65621e8	0.285658
$320$	2.25065e7	0.0383957
$321$	−1.81331e8	−0.305988
$322$	−1.99370e8	−0.332786
$323$	−4.71704e8	−0.778862
$324$	−2.09919e8	−0.342881
$325$	5.23687e8	0.846214
$326$	3.51502e8	0.561909
$327$	−1.70644e8	−0.269882
$328$	1.34105e7	0.0209839
$329$	−2.14510e8	−0.332094
$330$	−4.80997e6	−0.00736790
$331$	2.72216e8	0.412588	0.206294	−	0.978490i	$-0.433860\pi$
$331$	2.72216e8	0.412588	0.206294	+	0.978490i	$0.433860\pi$
$332$	−4.12625e8	−0.618831
$333$	7.44859e8	1.10540
$334$	7.37416e8	1.08293
$335$	−4.44893e7	−0.0646545
$336$	−4.83502e7	−0.0695362
$337$	−8.19304e8	−1.16611	−0.583056	−	0.812432i	$-0.698143\pi$
$337$	−8.19304e8	−1.16611	−0.583056	+	0.812432i	$0.698143\pi$
$338$	1.45783e8	0.205351
$339$	−1.25819e8	−0.175407
$340$	−9.49950e6	−0.0131076
$341$	1.02102e9	1.39442
$342$	−5.63708e8	−0.762014
$343$	8.01027e8	1.07181
$344$	−5.06536e8	−0.670897
$345$	5.95698e6	0.00781015
$346$	−1.87661e8	−0.243561
$347$	1.08036e8	0.138809	0.0694043	−	0.997589i	$-0.477890\pi$
$347$	1.08036e8	0.138809	0.0694043	+	0.997589i	$0.477890\pi$
$348$	−3.94966e7	−0.0502380
$349$	−2.32572e8	−0.292866	−0.146433	−	0.989221i	$-0.546779\pi$
$349$	−2.32572e8	−0.292866	−0.146433	+	0.989221i	$0.546779\pi$
$350$	−4.27692e8	−0.533203
$351$	−3.96990e8	−0.490009
$352$	5.55109e8	0.678389
$353$	−6.96581e8	−0.842869	−0.421435	−	0.906859i	$-0.638473\pi$
$353$	−6.96581e8	−0.842869	−0.421435	+	0.906859i	$0.638473\pi$
$354$	−4.45704e7	−0.0533993
$355$	3.88731e7	0.0461158
$356$	−2.59092e7	−0.0304354
$357$	1.29128e8	0.150204
$358$	3.01747e7	0.0347579
$359$	−5.53880e8	−0.631808	−0.315904	−	0.948791i	$-0.602308\pi$
$359$	−5.53880e8	−0.631808	−0.315904	+	0.948791i	$0.602308\pi$
$360$	−3.56248e7	−0.0402433
$361$	2.88236e8	0.322458
$362$	6.11027e8	0.676987
$363$	9.68895e7	0.106317
$364$	−2.67063e8	−0.290241
$365$	−3.85885e7	−0.0415368
$366$	7.97136e7	0.0849862
$367$	−9.17961e7	−0.0969378	−0.0484689	−	0.998825i	$-0.515434\pi$
$367$	−9.17961e7	−0.0969378	−0.0484689	+	0.998825i	$0.515434\pi$
$368$	1.86765e8	0.195357
$369$	−1.71775e7	−0.0177978
$370$	3.58003e7	0.0367435
$371$	7.69858e8	0.782712
$372$	−2.43489e8	−0.245233
$373$	1.60597e8	0.160235	0.0801175	−	0.996785i	$-0.474470\pi$
$373$	1.60597e8	0.160235	0.0801175	+	0.996785i	$0.474470\pi$
$374$	4.02747e8	0.398091
$375$	2.55799e7	0.0250489
$376$	5.00694e8	0.485753
$377$	3.12701e8	0.300563
$378$	3.24219e8	0.308757
$379$	−5.89008e8	−0.555756	−0.277878	−	0.960616i	$-0.589631\pi$
$379$	−5.89008e8	−0.555756	−0.277878	+	0.960616i	$0.589631\pi$
$380$	2.38061e7	0.0222559
$381$	4.95928e7	0.0459390
$382$	5.95731e8	0.546800
$383$	1.20792e9	1.09861	0.549305	−	0.835622i	$-0.314893\pi$
$383$	1.20792e9	1.09861	0.549305	+	0.835622i	$0.314893\pi$
$384$	−5.54876e7	−0.0500077
$385$	2.73270e7	0.0244051
$386$	1.63585e8	0.144773
$387$	6.48822e8	0.569032
$388$	4.13470e8	0.359363
$389$	3.81729e8	0.328800	0.164400	−	0.986394i	$-0.447431\pi$
$389$	3.81729e8	0.328800	0.164400	+	0.986394i	$0.447431\pi$
$390$	−9.08150e6	−0.00775232
$391$	−4.98788e8	−0.421986
$392$	−5.92629e8	−0.496914
$393$	−2.09885e8	−0.174425
$394$	6.31073e7	0.0519808
$395$	3.37547e7	0.0275578
$396$	−4.22901e8	−0.342220
$397$	3.24022e8	0.259901	0.129951	−	0.991520i	$-0.458518\pi$
$397$	3.24022e8	0.259901	0.129951	+	0.991520i	$0.458518\pi$
$398$	8.14011e8	0.647201
$399$	−3.23598e8	−0.255036
$400$	4.00651e8	0.313009
$401$	1.18362e9	0.916658	0.458329	−	0.888783i	$-0.348448\pi$
$401$	1.18362e9	0.916658	0.458329	+	0.888783i	$0.348448\pi$
$402$	−4.49814e8	−0.345336
$403$	1.92775e9	1.46718
$404$	−8.19123e7	−0.0618037
$405$	4.05551e7	0.0303356
$406$	−2.55381e8	−0.189386
$407$	1.33364e9	0.980527
$408$	−3.01401e8	−0.219702
$409$	−2.85737e8	−0.206507	−0.103254	−	0.994655i	$-0.532925\pi$
$409$	−2.85737e8	−0.206507	−0.103254	+	0.994655i	$0.532925\pi$
$410$	−825604.	−0.000591600 0
$411$	−1.55643e8	−0.110581
$412$	−8.10986e7	−0.0571312
$413$	2.53219e8	0.176877
$414$	−5.96075e8	−0.412857
$415$	7.97168e7	0.0547497
$416$	1.04808e9	0.713784
$417$	−1.78175e8	−0.120329
$418$	−1.00930e9	−0.675933
$419$	−2.31695e9	−1.53875	−0.769376	−	0.638797i	$-0.779433\pi$
$419$	−2.31695e9	−1.53875	−0.769376	+	0.638797i	$0.779433\pi$
$420$	−6.51685e6	−0.00429206
$421$	1.99117e9	1.30054	0.650268	−	0.759705i	$-0.274657\pi$
$421$	1.99117e9	1.30054	0.650268	+	0.759705i	$0.274657\pi$
$422$	4.67358e8	0.302731
$423$	−6.41339e8	−0.411999
$424$	−1.79695e9	−1.14487
$425$	−1.07001e9	−0.676123
$426$	3.93030e8	0.246316
$427$	−4.52879e8	−0.281504
$428$	−7.66268e8	−0.472419
$429$	−3.38307e8	−0.206876
$430$	3.11845e7	0.0189147
$431$	−2.00750e8	−0.120777	−0.0603886	−	0.998175i	$-0.519234\pi$
$431$	−2.00750e8	−0.120777	−0.0603886	+	0.998175i	$0.519234\pi$
$432$	−3.03720e8	−0.181251
$433$	−2.15542e9	−1.27592	−0.637962	−	0.770068i	$-0.720222\pi$
$433$	−2.15542e9	−1.27592	−0.637962	+	0.770068i	$0.720222\pi$
$434$	−1.57438e9	−0.924475
$435$	7.63052e6	0.00444469
$436$	−7.21108e8	−0.416675
$437$	1.24998e9	0.716504
$438$	−3.90153e8	−0.221858
$439$	1.03334e9	0.582929	0.291465	−	0.956582i	$-0.405857\pi$
$439$	1.03334e9	0.582929	0.291465	+	0.956582i	$0.405857\pi$
$440$	−6.37849e7	−0.0356972
$441$	7.59098e8	0.421466
$442$	7.60411e8	0.418861
$443$	−1.59156e9	−0.869780	−0.434890	−	0.900483i	$-0.643213\pi$
$443$	−1.59156e9	−0.869780	−0.434890	+	0.900483i	$0.643213\pi$
$444$	−3.18043e8	−0.172443
$445$	5.00551e6	0.00269270
$446$	1.06551e8	0.0568704
$447$	−6.14085e8	−0.325201
$448$	−1.29281e9	−0.679300
$449$	−1.37310e9	−0.715877	−0.357939	−	0.933745i	$-0.616520\pi$
$449$	−1.37310e9	−0.715877	−0.357939	+	0.933745i	$0.616520\pi$
$450$	−1.27871e9	−0.661497
$451$	−3.07556e7	−0.0157873
$452$	−5.31686e8	−0.270814
$453$	2.79996e8	0.141517
$454$	−7.93671e8	−0.398057
$455$	5.15950e7	0.0256784
$456$	7.55321e8	0.373040
$457$	2.25601e9	1.10569	0.552847	−	0.833283i	$-0.313541\pi$
$457$	2.25601e9	1.10569	0.552847	+	0.833283i	$0.313541\pi$
$458$	2.09286e9	1.01791
$459$	8.11137e8	0.391516
$460$	2.51730e7	0.0120582
$461$	−1.88925e9	−0.898125	−0.449062	−	0.893500i	$-0.648242\pi$
$461$	−1.88925e9	−0.898125	−0.449062	+	0.893500i	$0.648242\pi$
$462$	2.76293e8	0.130354
$463$	−2.88415e8	−0.135047	−0.0675233	−	0.997718i	$-0.521510\pi$
$463$	−2.88415e8	−0.135047	−0.0675233	+	0.997718i	$0.521510\pi$
$464$	2.39235e8	0.111176
$465$	4.70408e7	0.0216965
$466$	1.04617e9	0.478907
$467$	7.47402e8	0.339582	0.169791	−	0.985480i	$-0.445691\pi$
$467$	7.47402e8	0.339582	0.169791	+	0.985480i	$0.445691\pi$
$468$	−7.98461e8	−0.360075
$469$	2.55554e9	1.14387
$470$	−3.08248e7	−0.0136949
$471$	6.91999e8	0.305163
$472$	−5.91047e8	−0.258717
$473$	1.16169e9	0.504751
$474$	3.41280e8	0.147193
$475$	2.68148e9	1.14801
$476$	5.45668e8	0.231902
$477$	2.30171e9	0.971039
$478$	1.30335e9	0.545836
$479$	−9.92413e8	−0.412590	−0.206295	−	0.978490i	$-0.566141\pi$
$479$	−9.92413e8	−0.412590	−0.206295	+	0.978490i	$0.566141\pi$
$480$	2.55751e7	0.0105554
$481$	2.51800e9	1.03169
$482$	1.25351e8	0.0509873
$483$	−3.42179e8	−0.138178
$484$	4.09436e8	0.164145
$485$	−7.98800e7	−0.0317938
$486$	1.47733e9	0.583781
$487$	−3.61900e9	−1.41983	−0.709917	−	0.704286i	$-0.751267\pi$
$487$	−3.61900e9	−1.41983	−0.709917	+	0.704286i	$0.751267\pi$
$488$	1.05708e9	0.411754
$489$	6.03282e8	0.233313
$490$	3.64847e7	0.0140096
$491$	4.95756e7	0.0189009	0.00945045	−	0.999955i	$-0.496992\pi$
$491$	4.95756e7	0.0189009	0.00945045	+	0.999955i	$0.496992\pi$
$492$	7.33449e6	0.00277647
$493$	−6.38917e8	−0.240149
$494$	−1.90562e9	−0.711199
$495$	8.17021e7	0.0302771
$496$	1.47484e9	0.542698
$497$	−2.23294e9	−0.815885
$498$	8.05985e8	0.292432
$499$	2.11782e8	0.0763022	0.0381511	−	0.999272i	$-0.487853\pi$
$499$	2.11782e8	0.0763022	0.0381511	+	0.999272i	$0.487853\pi$
$500$	1.08096e8	0.0386735
$501$	1.26562e9	0.449648
$502$	1.11834e9	0.394557
$503$	−5.16907e9	−1.81102	−0.905512	−	0.424321i	$-0.860513\pi$
$503$	−5.16907e9	−1.81102	−0.905512	+	0.424321i	$0.860513\pi$
$504$	2.04635e9	0.711987
$505$	1.58250e7	0.00546794
$506$	−1.06725e9	−0.366219
$507$	2.50206e8	0.0852649
$508$	2.09569e8	0.0709259
$509$	−1.88195e8	−0.0632550	−0.0316275	−	0.999500i	$-0.510069\pi$
$509$	−1.88195e8	−0.0632550	−0.0316275	+	0.999500i	$0.510069\pi$
$510$	1.85555e7	0.00619408
$511$	2.21659e9	0.734873
$512$	1.82151e9	0.599773
$513$	−2.03274e9	−0.664769
$514$	−2.07099e9	−0.672677
$515$	1.56678e7	0.00505455
$516$	−2.77036e8	−0.0887693
$517$	−1.14830e9	−0.365458
$518$	−2.05643e9	−0.650070
$519$	−3.22082e8	−0.101130
$520$	−1.20430e8	−0.0375596
$521$	−3.82610e9	−1.18529	−0.592645	−	0.805464i	$-0.701916\pi$
$521$	−3.82610e9	−1.18529	−0.592645	+	0.805464i	$0.701916\pi$
$522$	−7.63536e8	−0.234954
$523$	−3.91879e9	−1.19783	−0.598916	−	0.800812i	$-0.704402\pi$
$523$	−3.91879e9	−1.19783	−0.598916	+	0.800812i	$0.704402\pi$
$524$	−8.86934e8	−0.269297
$525$	−7.34047e8	−0.221394
$526$	2.18521e9	0.654702
$527$	−3.93881e9	−1.17227
$528$	−2.58824e8	−0.0765220
$529$	−2.08307e9	−0.611800
$530$	1.10628e8	0.0322774
$531$	7.57072e8	0.219435
$532$	−1.36746e9	−0.393754
$533$	−5.80684e7	−0.0166110
$534$	5.06088e7	0.0143824
$535$	1.48039e8	0.0417962
$536$	−5.96497e9	−1.67314
$537$	5.17889e7	0.0144320
$538$	2.26996e9	0.628463
$539$	1.35914e9	0.373855
$540$	−4.09367e7	−0.0111875
$541$	−5.44753e9	−1.47914	−0.739570	−	0.673080i	$-0.764971\pi$
$541$	−5.44753e9	−1.47914	−0.739570	+	0.673080i	$0.764971\pi$
$542$	−4.63345e9	−1.24999
$543$	1.04870e9	0.281095
$544$	−2.14145e9	−0.570311
$545$	1.39314e8	0.0368644
$546$	5.21657e8	0.137155
$547$	3.56310e9	0.930834	0.465417	−	0.885092i	$-0.345904\pi$
$547$	3.56310e9	0.930834	0.465417	+	0.885092i	$0.345904\pi$
$548$	−6.57715e8	−0.170728
$549$	−1.35401e9	−0.349236
$550$	−2.28948e9	−0.586770
$551$	1.60115e9	0.407757
$552$	7.98691e8	0.202112
$553$	−1.93893e9	−0.487555
$554$	−4.92082e9	−1.22957
$555$	6.14440e7	0.0152565
$556$	−7.52933e8	−0.185778
$557$	5.36288e8	0.131494	0.0657468	−	0.997836i	$-0.479057\pi$
$557$	5.36288e8	0.131494	0.0657468	+	0.997836i	$0.479057\pi$
$558$	−4.70706e9	−1.14691
$559$	2.19334e9	0.531087
$560$	3.94732e7	0.00949826
$561$	6.91235e8	0.165293
$562$	−5.71580e9	−1.35831
$563$	1.04961e9	0.247884	0.123942	−	0.992289i	$-0.460446\pi$
$563$	1.04961e9	0.247884	0.123942	+	0.992289i	$0.460446\pi$
$564$	2.73841e8	0.0642721
$565$	1.02719e8	0.0239596
$566$	−5.02680e8	−0.116529
$567$	−2.32956e9	−0.536701
$568$	5.21197e9	1.19339
$569$	−3.50902e9	−0.798532	−0.399266	−	0.916835i	$-0.630735\pi$
$569$	−3.50902e9	−0.798532	−0.399266	+	0.916835i	$0.630735\pi$
$570$	−4.65008e7	−0.0105171
$571$	−5.00548e9	−1.12517	−0.562587	−	0.826738i	$-0.690194\pi$
$571$	−5.00548e9	−1.12517	−0.562587	+	0.826738i	$0.690194\pi$
$572$	−1.42962e9	−0.319399
$573$	1.02245e9	0.227040
$574$	4.74241e7	0.0104666
$575$	2.83544e9	0.621990
$576$	−3.86523e9	−0.842746
$577$	1.34452e9	0.291375	0.145688	−	0.989331i	$-0.453461\pi$
$577$	1.34452e9	0.291375	0.145688	+	0.989331i	$0.453461\pi$
$578$	1.83338e9	0.394916
$579$	2.80760e8	0.0601119
$580$	3.22451e7	0.00686223
$581$	−4.57907e9	−0.968636
$582$	−8.07635e8	−0.169818
$583$	4.12114e9	0.861345
$584$	−5.17381e9	−1.07489
$585$	1.54258e8	0.0318568
$586$	5.48844e9	1.12670
$587$	7.52304e9	1.53518	0.767591	−	0.640940i	$-0.221455\pi$
$587$	7.52304e9	1.53518	0.767591	+	0.640940i	$0.221455\pi$
$588$	−3.24123e8	−0.0657489
$589$	9.87080e9	1.99044
$590$	3.63873e7	0.00729404
$591$	1.08311e8	0.0215832
$592$	1.92641e9	0.381613
$593$	−7.56574e9	−1.48991	−0.744955	−	0.667114i	$-0.767529\pi$
$593$	−7.56574e9	−1.48991	−0.744955	+	0.667114i	$0.767529\pi$
$594$	1.73558e9	0.339776
$595$	−1.05420e8	−0.0205170
$596$	−2.59500e9	−0.502083
$597$	1.39709e9	0.268728
$598$	−2.01503e9	−0.385326
$599$	5.39804e9	1.02622	0.513112	−	0.858322i	$-0.328493\pi$
$599$	5.39804e9	1.02622	0.513112	+	0.858322i	$0.328493\pi$
$600$	1.71336e9	0.323832
$601$	−5.41597e9	−1.01769	−0.508845	−	0.860858i	$-0.669927\pi$
$601$	−5.41597e9	−1.01769	−0.508845	+	0.860858i	$0.669927\pi$
$602$	−1.79129e9	−0.334640
$603$	7.64053e9	1.41910
$604$	1.18321e9	0.218490
$605$	−7.91007e7	−0.0145223
$606$	1.60000e8	0.0292056
$607$	5.29850e9	0.961595	0.480798	−	0.876832i	$-0.340347\pi$
$607$	5.29850e9	0.961595	0.480798	+	0.876832i	$0.340347\pi$
$608$	5.36655e9	0.968351
$609$	−4.38310e8	−0.0786359
$610$	−6.50782e7	−0.0116086
$611$	−2.16805e9	−0.384525
$612$	1.63143e9	0.287699
$613$	−7.31057e8	−0.128186	−0.0640928	−	0.997944i	$-0.520415\pi$
$613$	−7.31057e8	−0.128186	−0.0640928	+	0.997944i	$0.520415\pi$
$614$	−4.02251e9	−0.701307
$615$	−1.41698e6	−0.000245641 0
$616$	3.66391e9	0.631557
$617$	3.25921e9	0.558617	0.279308	−	0.960201i	$-0.409895\pi$
$617$	3.25921e9	0.558617	0.279308	+	0.960201i	$0.409895\pi$
$618$	1.58411e8	0.0269976
$619$	−7.52009e9	−1.27440	−0.637200	−	0.770698i	$-0.719907\pi$
$619$	−7.52009e9	−1.27440	−0.637200	+	0.770698i	$0.719907\pi$
$620$	1.98785e8	0.0334975
$621$	−2.14946e9	−0.360170
$622$	−6.57828e9	−1.09609
$623$	−2.87525e8	−0.0476396
$624$	−4.88675e8	−0.0805145
$625$	6.07218e9	0.994866
$626$	6.64298e8	0.108231
$627$	−1.73226e9	−0.280657
$628$	2.92425e9	0.471146
$629$	−5.14482e9	−0.824314
$630$	−1.25982e8	−0.0200731
$631$	9.37784e8	0.148594	0.0742968	−	0.997236i	$-0.476329\pi$
$631$	9.37784e8	0.148594	0.0742968	+	0.997236i	$0.476329\pi$
$632$	4.52571e9	0.713143
$633$	8.02126e8	0.125698
$634$	6.80924e9	1.06117
$635$	−4.04876e7	−0.00627501
$636$	−9.82793e8	−0.151482
$637$	2.56613e9	0.393361
$638$	−1.36708e9	−0.208412
$639$	−6.67601e9	−1.01219
$640$	4.53002e7	0.00683078
$641$	−8.70085e9	−1.30484	−0.652422	−	0.757856i	$-0.726247\pi$
$641$	−8.70085e9	−1.30484	−0.652422	+	0.757856i	$0.726247\pi$
$642$	1.49676e9	0.223244
$643$	7.11195e9	1.05499	0.527497	−	0.849557i	$-0.323131\pi$
$643$	7.11195e9	1.05499	0.527497	+	0.849557i	$0.323131\pi$
$644$	−1.44598e9	−0.213335
$645$	5.35218e7	0.00785366
$646$	3.89359e9	0.568246
$647$	−8.41505e9	−1.22150	−0.610748	−	0.791825i	$-0.709131\pi$
$647$	−8.41505e9	−1.22150	−0.610748	+	0.791825i	$0.709131\pi$
$648$	5.43749e9	0.785029
$649$	1.35551e9	0.194647
$650$	−4.32268e9	−0.617385
$651$	−2.70210e9	−0.383856
$652$	2.54935e9	0.360216
$653$	−6.82007e9	−0.958502	−0.479251	−	0.877678i	$-0.659092\pi$
$653$	−6.82007e9	−0.958502	−0.479251	+	0.877678i	$0.659092\pi$
$654$	1.40855e9	0.196902
$655$	1.71351e8	0.0238255
$656$	−4.44257e7	−0.00614428
$657$	6.62713e9	0.911689
$658$	1.77063e9	0.242291
$659$	1.07296e10	1.46045	0.730224	−	0.683208i	$-0.239416\pi$
$659$	1.07296e10	1.46045	0.730224	+	0.683208i	$0.239416\pi$
$660$	−3.48855e7	−0.00472325
$661$	8.40206e9	1.13157	0.565784	−	0.824553i	$-0.308574\pi$
$661$	8.40206e9	1.13157	0.565784	+	0.824553i	$0.308574\pi$
$662$	−2.24696e9	−0.301018
$663$	1.30509e9	0.173918
$664$	1.06881e10	1.41682
$665$	2.64186e8	0.0348365
$666$	−6.14829e9	−0.806482
$667$	1.69309e9	0.220922
$668$	5.34828e9	0.694219
$669$	1.82874e8	0.0236135
$670$	3.67229e8	0.0471709
$671$	−2.42431e9	−0.309785
$672$	−1.46908e9	−0.186746
$673$	9.11306e9	1.15242	0.576211	−	0.817301i	$-0.304531\pi$
$673$	9.11306e9	1.15242	0.576211	+	0.817301i	$0.304531\pi$
$674$	6.76279e9	0.850778
$675$	−4.61104e9	−0.577080
$676$	1.05732e9	0.131642
$677$	2.44302e9	0.302598	0.151299	−	0.988488i	$-0.451654\pi$
$677$	2.44302e9	0.302598	0.151299	+	0.988488i	$0.451654\pi$
$678$	1.03855e9	0.127974
$679$	4.58844e9	0.562498
$680$	2.46064e8	0.0300101
$681$	−1.36218e9	−0.165279
$682$	−8.42783e9	−1.01735
$683$	8.03044e9	0.964422	0.482211	−	0.876055i	$-0.339834\pi$
$683$	8.03044e9	0.964422	0.482211	+	0.876055i	$0.339834\pi$
$684$	−4.08843e9	−0.488495
$685$	1.27067e8	0.0151048
$686$	−6.61193e9	−0.781976
$687$	3.59197e9	0.422653
$688$	1.67803e9	0.196445
$689$	7.78094e9	0.906285
$690$	−4.91707e7	−0.00569816
$691$	−2.28558e8	−0.0263526	−0.0131763	−	0.999913i	$-0.504194\pi$
$691$	−2.28558e8	−0.0263526	−0.0131763	+	0.999913i	$0.504194\pi$
$692$	−1.36106e9	−0.156137
$693$	−4.69311e9	−0.535666
$694$	−8.91765e8	−0.101273
$695$	1.45462e8	0.0164363
$696$	1.02307e9	0.115020
$697$	1.18647e8	0.0132721
$698$	1.91972e9	0.213671
$699$	1.79554e9	0.198849
$700$	−3.10194e9	−0.341814
$701$	1.42983e10	1.56773	0.783864	−	0.620932i	$-0.213246\pi$
$701$	1.42983e10	1.56773	0.783864	+	0.620932i	$0.213246\pi$
$702$	3.27688e9	0.357504
$703$	1.28931e10	1.39963
$704$	−6.92056e9	−0.747544
$705$	−5.29046e7	−0.00568632
$706$	5.74980e9	0.614945
$707$	−9.09014e8	−0.0967392
$708$	−3.23258e8	−0.0342320
$709$	1.32839e10	1.39979	0.699894	−	0.714246i	$-0.253230\pi$
$709$	1.32839e10	1.39979	0.699894	+	0.714246i	$0.253230\pi$
$710$	−3.20871e8	−0.0336454
$711$	−5.79698e9	−0.604864
$712$	6.71122e8	0.0696821
$713$	1.04376e10	1.07841
$714$	−1.06586e9	−0.109586
$715$	2.76194e8	0.0282581
$716$	2.18850e8	0.0222818
$717$	2.23693e9	0.226639
$718$	4.57190e9	0.460957
$719$	−7.10546e9	−0.712920	−0.356460	−	0.934311i	$-0.616016\pi$
$719$	−7.10546e9	−0.712920	−0.356460	+	0.934311i	$0.616016\pi$
$720$	1.18016e8	0.0117836
$721$	−8.99985e8	−0.0894256
$722$	−2.37919e9	−0.235260
$723$	2.15139e8	0.0211707
$724$	4.43162e9	0.433988
$725$	3.63203e9	0.353970
$726$	−7.99756e8	−0.0775674
$727$	9.98976e9	0.964239	0.482119	−	0.876106i	$-0.339867\pi$
$727$	9.98976e9	0.964239	0.482119	+	0.876106i	$0.339867\pi$
$728$	6.91768e9	0.664509
$729$	−5.13309e9	−0.490719
$730$	3.18521e8	0.0303046
$731$	−4.48148e9	−0.424337
$732$	5.78141e8	0.0544810
$733$	−3.14329e9	−0.294795	−0.147398	−	0.989077i	$-0.547090\pi$
$733$	−3.14329e9	−0.294795	−0.147398	+	0.989077i	$0.547090\pi$
$734$	7.57714e8	0.0707243
$735$	6.26186e7	0.00581698
$736$	5.67469e9	0.524650
$737$	1.36801e10	1.25879
$738$	1.41788e8	0.0129850
$739$	−1.52632e10	−1.39120	−0.695599	−	0.718430i	$-0.744861\pi$
$739$	−1.52632e10	−1.39120	−0.695599	+	0.718430i	$0.744861\pi$
$740$	2.59650e8	0.0235547
$741$	−3.27061e9	−0.295301
$742$	−6.35465e9	−0.571055
$743$	1.35283e10	1.20999	0.604994	−	0.796230i	$-0.293175\pi$
$743$	1.35283e10	1.20999	0.604994	+	0.796230i	$0.293175\pi$
$744$	6.30706e9	0.561464
$745$	5.01340e8	0.0444207
$746$	−1.32562e9	−0.116905
$747$	−1.36904e10	−1.20170
$748$	2.92102e9	0.255199
$749$	−8.50360e9	−0.739463
$750$	−2.11144e8	−0.0182753
$751$	−1.78250e10	−1.53565	−0.767823	−	0.640662i	$-0.778660\pi$
$751$	−1.78250e10	−1.53565	−0.767823	+	0.640662i	$0.778660\pi$
$752$	−1.65868e9	−0.142233
$753$	1.91940e9	0.163826
$754$	−2.58113e9	−0.219286
$755$	−2.28589e8	−0.0193304
$756$	2.35147e9	0.197931
$757$	−8.14422e9	−0.682361	−0.341180	−	0.939998i	$-0.610827\pi$
$757$	−8.14422e9	−0.682361	−0.341180	+	0.939998i	$0.610827\pi$
$758$	4.86186e9	0.405471
$759$	−1.83172e9	−0.152060
$760$	−6.16645e8	−0.0509551
$761$	1.58821e10	1.30636	0.653180	−	0.757203i	$-0.273435\pi$
$761$	1.58821e10	1.30636	0.653180	+	0.757203i	$0.273435\pi$
$762$	−4.09355e8	−0.0335164
$763$	−8.00243e9	−0.652208
$764$	4.32068e9	0.350530
$765$	−3.15183e8	−0.0254535
$766$	−9.97056e9	−0.801529
$767$	2.55929e9	0.204802
$768$	3.98670e9	0.317577
$769$	−2.05162e9	−0.162687	−0.0813437	−	0.996686i	$-0.525921\pi$
$769$	−2.05162e9	−0.162687	−0.0813437	+	0.996686i	$0.525921\pi$
$770$	−2.25566e8	−0.0178056
$771$	−3.55443e9	−0.279306
$772$	1.18644e9	0.0928078
$773$	−6.64726e9	−0.517624	−0.258812	−	0.965928i	$-0.583331\pi$
$773$	−6.64726e9	−0.517624	−0.258812	+	0.965928i	$0.583331\pi$
$774$	−5.35558e9	−0.415157
$775$	2.23908e10	1.72788
$776$	−1.07100e10	−0.822763
$777$	−3.52945e9	−0.269919
$778$	−3.15091e9	−0.239888
$779$	−2.97333e8	−0.0225352
$780$	−6.58658e7	−0.00496968
$781$	−1.19532e10	−0.897851
$782$	4.11716e9	0.307874
$783$	−2.75332e9	−0.204970
$784$	1.96324e9	0.145501
$785$	−5.64949e8	−0.0416836
$786$	1.73246e9	0.127258
$787$	8.88179e9	0.649515	0.324757	−	0.945797i	$-0.394717\pi$
$787$	8.88179e9	0.649515	0.324757	+	0.945797i	$0.394717\pi$
$788$	4.57701e8	0.0333227
$789$	3.75048e9	0.271842
$790$	−2.78622e8	−0.0201057
$791$	−5.90034e9	−0.423896
$792$	1.09543e10	0.783515
$793$	−4.57725e9	−0.325948
$794$	−2.67458e9	−0.189620
$795$	1.89870e8	0.0134021
$796$	5.90381e9	0.414893
$797$	−1.89614e10	−1.32668	−0.663341	−	0.748317i	$-0.730862\pi$
$797$	−1.89614e10	−1.32668	−0.663341	+	0.748317i	$0.730862\pi$
$798$	2.67108e9	0.186070
$799$	4.42980e9	0.307235
$800$	1.21734e10	0.840616
$801$	−8.59639e8	−0.0591020
$802$	−9.76997e9	−0.668780
$803$	1.18657e10	0.808700
$804$	−3.26238e9	−0.221380
$805$	2.79355e8	0.0188743
$806$	−1.59122e10	−1.07043
$807$	3.89592e9	0.260947
$808$	2.12176e9	0.141500
$809$	8.92048e9	0.592336	0.296168	−	0.955136i	$-0.404291\pi$
$809$	8.92048e9	0.592336	0.296168	+	0.955136i	$0.404291\pi$
$810$	−3.34755e8	−0.0221324
$811$	2.13219e10	1.40363	0.701815	−	0.712359i	$-0.252373\pi$
$811$	2.13219e10	1.40363	0.701815	+	0.712359i	$0.252373\pi$
$812$	−1.85221e9	−0.121407
$813$	−7.95238e9	−0.519016
$814$	−1.10083e10	−0.715378
$815$	−4.92520e8	−0.0318693
$816$	9.98470e8	0.0643308
$817$	1.12308e10	0.720496
$818$	2.35856e9	0.150665
$819$	−8.86085e9	−0.563614
$820$	−5.98789e6	−0.000379250 0
$821$	−2.80733e9	−0.177049	−0.0885244	−	0.996074i	$-0.528215\pi$
$821$	−2.80733e9	−0.177049	−0.0885244	+	0.996074i	$0.528215\pi$
$822$	1.28472e9	0.0806785
$823$	−2.51291e10	−1.57137	−0.785684	−	0.618628i	$-0.787689\pi$
$823$	−2.51291e10	−1.57137	−0.785684	+	0.618628i	$0.787689\pi$
$824$	2.10068e9	0.130802
$825$	−3.92944e9	−0.243636
$826$	−2.09015e9	−0.129047
$827$	−5.59383e9	−0.343906	−0.171953	−	0.985105i	$-0.555008\pi$
$827$	−5.59383e9	−0.343906	−0.171953	+	0.985105i	$0.555008\pi$
$828$	−4.32318e9	−0.264665
$829$	−2.79239e10	−1.70230	−0.851148	−	0.524925i	$-0.824093\pi$
$829$	−2.79239e10	−1.70230	−0.851148	+	0.524925i	$0.824093\pi$
$830$	−6.58007e8	−0.0399445
$831$	−8.44559e9	−0.510536
$832$	−1.30664e10	−0.786547
$833$	−5.24317e9	−0.314294
$834$	1.47071e9	0.0877903
$835$	−1.03326e9	−0.0614195
$836$	−7.32019e9	−0.433312
$837$	−1.69737e10	−1.00055
$838$	1.91249e10	1.12265
$839$	1.27967e9	0.0748050	0.0374025	−	0.999300i	$-0.488092\pi$
$839$	1.27967e9	0.0748050	0.0374025	+	0.999300i	$0.488092\pi$
$840$	1.68805e8	0.00982669
$841$	−1.50811e10	−0.874275
$842$	−1.64358e10	−0.948851
$843$	−9.81002e9	−0.563992
$844$	3.38963e9	0.194068
$845$	−2.04269e8	−0.0116467
$846$	5.29381e9	0.300588
$847$	4.54368e9	0.256931
$848$	5.95287e9	0.335228
$849$	−8.62749e8	−0.0483846
$850$	8.83217e9	0.493289
$851$	1.36334e10	0.758317
$852$	2.85055e9	0.157903
$853$	−2.24153e10	−1.23658	−0.618290	−	0.785950i	$-0.712174\pi$
$853$	−2.24153e10	−1.23658	−0.618290	+	0.785950i	$0.712174\pi$
$854$	3.73821e9	0.205381
$855$	7.89861e8	0.0432184
$856$	1.98485e10	1.08161
$857$	−7.10390e9	−0.385535	−0.192768	−	0.981244i	$-0.561746\pi$
$857$	−7.10390e9	−0.385535	−0.192768	+	0.981244i	$0.561746\pi$
$858$	2.79249e9	0.150934
$859$	−2.60820e10	−1.40399	−0.701995	−	0.712182i	$-0.747707\pi$
$859$	−2.60820e10	−1.40399	−0.701995	+	0.712182i	$0.747707\pi$
$860$	2.26173e8	0.0121254
$861$	8.13939e7	0.00434591
$862$	1.65705e9	0.0881173
$863$	2.10561e10	1.11517	0.557585	−	0.830120i	$-0.311728\pi$
$863$	2.10561e10	1.11517	0.557585	+	0.830120i	$0.311728\pi$
$864$	−9.22826e9	−0.486768
$865$	2.62948e8	0.0138138
$866$	1.77915e10	0.930895
$867$	3.14662e9	0.163975
$868$	−1.14186e10	−0.592641
$869$	−1.03793e10	−0.536535
$870$	−6.29847e7	−0.00324278
$871$	2.58288e10	1.32447
$872$	1.86787e10	0.953981
$873$	1.37185e10	0.697840
$874$	−1.03177e10	−0.522751
$875$	1.19958e9	0.0605343
$876$	−2.82968e9	−0.142224
$877$	−1.35854e10	−0.680101	−0.340051	−	0.940407i	$-0.610444\pi$
$877$	−1.35854e10	−0.680101	−0.340051	+	0.940407i	$0.610444\pi$
$878$	−8.52948e9	−0.425296
$879$	9.41980e9	0.467822
$880$	2.11304e8	0.0104525
$881$	−6.40798e9	−0.315723	−0.157861	−	0.987461i	$-0.550460\pi$
$881$	−6.40798e9	−0.315723	−0.157861	+	0.987461i	$0.550460\pi$
$882$	−6.26583e9	−0.307495
$883$	−2.46152e10	−1.20321	−0.601603	−	0.798795i	$-0.705471\pi$
$883$	−2.46152e10	−1.20321	−0.601603	+	0.798795i	$0.705471\pi$
$884$	5.51506e9	0.268514
$885$	6.24515e7	0.00302860
$886$	1.31372e10	0.634579
$887$	−1.55262e10	−0.747020	−0.373510	−	0.927626i	$-0.621846\pi$
$887$	−1.55262e10	−0.747020	−0.373510	+	0.927626i	$0.621846\pi$
$888$	8.23820e9	0.394809
$889$	2.32568e9	0.111018
$890$	−4.13171e7	−0.00196456
$891$	−1.24704e10	−0.590619
$892$	7.72788e8	0.0364572
$893$	−1.11012e10	−0.521665
$894$	5.06885e9	0.237262
$895$	−4.22805e7	−0.00197133
$896$	−2.60212e9	−0.120851
$897$	−3.45840e9	−0.159993
$898$	1.13340e10	0.522293
$899$	1.33699e10	0.613717
$900$	−9.27414e9	−0.424057
$901$	−1.58982e10	−0.724120
$902$	2.53867e8	0.0115182
$903$	−3.07439e9	−0.138948
$904$	1.37722e10	0.620030
$905$	−8.56164e8	−0.0383961
$906$	−2.31117e9	−0.103249
$907$	5.42068e9	0.241228	0.120614	−	0.992699i	$-0.461514\pi$
$907$	5.42068e9	0.241228	0.120614	+	0.992699i	$0.461514\pi$
$908$	−5.75629e9	−0.255177
$909$	−2.71776e9	−0.120016
$910$	−4.25881e8	−0.0187346
$911$	6.21006e9	0.272133	0.136067	−	0.990700i	$-0.456554\pi$
$911$	6.21006e9	0.272133	0.136067	+	0.990700i	$0.456554\pi$
$912$	−2.50220e9	−0.109230
$913$	−2.45123e10	−1.06595
$914$	−1.86218e10	−0.806698
$915$	−1.11694e8	−0.00482008
$916$	1.51790e10	0.652541
$917$	−9.84267e9	−0.421522
$918$	−6.69538e9	−0.285644
$919$	2.46977e10	1.04967	0.524835	−	0.851204i	$-0.324127\pi$
$919$	2.46977e10	1.04967	0.524835	+	0.851204i	$0.324127\pi$
$920$	−6.52052e8	−0.0276074
$921$	−6.90383e9	−0.291193
$922$	1.55945e10	0.655258
$923$	−2.25683e10	−0.944696
$924$	2.00388e9	0.0835641
$925$	2.92466e10	1.21501
$926$	2.38066e9	0.0985280
$927$	−2.69076e9	−0.110942
$928$	7.26893e9	0.298574
$929$	−1.03175e10	−0.422201	−0.211100	−	0.977464i	$-0.567705\pi$
$929$	−1.03175e10	−0.422201	−0.211100	+	0.977464i	$0.567705\pi$
$930$	−3.88289e8	−0.0158294
$931$	1.31396e10	0.533651
$932$	7.58758e9	0.307007
$933$	−1.12903e10	−0.455113
$934$	−6.16929e9	−0.247754
$935$	−5.64325e8	−0.0225782
$936$	2.06824e10	0.824395
$937$	−3.69314e9	−0.146659	−0.0733293	−	0.997308i	$-0.523362\pi$
$937$	−3.69314e9	−0.146659	−0.0733293	+	0.997308i	$0.523362\pi$
$938$	−2.10942e10	−0.834553
$939$	1.14013e9	0.0449393
$940$	−2.23564e8	−0.00877921
$941$	−4.47084e10	−1.74914	−0.874572	−	0.484896i	$-0.838858\pi$
$941$	−4.47084e10	−1.74914	−0.874572	+	0.484896i	$0.838858\pi$
$942$	−5.71197e9	−0.222642
$943$	−3.14405e8	−0.0122095
$944$	1.95800e9	0.0757549
$945$	−4.54292e8	−0.0175115
$946$	−9.58898e9	−0.368259
$947$	−3.44488e9	−0.131810	−0.0659050	−	0.997826i	$-0.520993\pi$
$947$	−3.44488e9	−0.131810	−0.0659050	+	0.997826i	$0.520993\pi$
$948$	2.47521e9	0.0943591
$949$	2.24030e10	0.850894
$950$	−2.21338e10	−0.837573
$951$	1.16867e10	0.440615
$952$	−1.41343e10	−0.530941
$953$	−1.90963e10	−0.714702	−0.357351	−	0.933970i	$-0.616320\pi$
$953$	−1.90963e10	−0.714702	−0.357351	+	0.933970i	$0.616320\pi$
$954$	−1.89990e10	−0.708455
$955$	−8.34731e8	−0.0310124
$956$	9.45282e9	0.349912
$957$	−2.34632e9	−0.0865359
$958$	8.19169e9	0.301019
$959$	−7.29894e9	−0.267236
$960$	−3.18846e8	−0.0116314
$961$	5.49102e10	1.99582
$962$	−2.07843e10	−0.752702
$963$	−2.54240e10	−0.917384
$964$	9.09136e8	0.0326858
$965$	−2.29213e8	−0.00821096
$966$	2.82445e9	0.100812
$967$	−2.14635e10	−0.763322	−0.381661	−	0.924302i	$-0.624648\pi$
$967$	−2.14635e10	−0.763322	−0.381661	+	0.924302i	$0.624648\pi$
$968$	−1.06055e10	−0.375811
$969$	6.68256e9	0.235944
$970$	6.59355e8	0.0231963
$971$	−2.34216e10	−0.821012	−0.410506	−	0.911858i	$-0.634648\pi$
$971$	−2.34216e10	−0.821012	−0.410506	+	0.911858i	$0.634648\pi$
$972$	1.07147e10	0.374237
$973$	−8.35560e9	−0.290792
$974$	2.98724e10	1.03589
$975$	−7.41900e9	−0.256348
$976$	−3.50186e9	−0.120566
$977$	−4.40383e10	−1.51077	−0.755387	−	0.655279i	$-0.772551\pi$
$977$	−4.40383e10	−1.51077	−0.755387	+	0.655279i	$0.772551\pi$
$978$	−4.97967e9	−0.170222
$979$	−1.53915e9	−0.0524255
$980$	2.64614e8	0.00898094
$981$	−2.39256e10	−0.809135
$982$	−4.09212e8	−0.0137898
$983$	3.83832e10	1.28885	0.644427	−	0.764666i	$-0.277096\pi$
$983$	3.83832e10	1.28885	0.644427	+	0.764666i	$0.277096\pi$
$984$	−1.89984e8	−0.00635674
$985$	−8.84252e7	−0.00294815
$986$	5.27382e9	0.175209
$987$	3.03893e9	0.100603
$988$	−1.38209e10	−0.455920
$989$	1.18756e10	0.390363
$990$	−6.74394e8	−0.0220897
$991$	3.50069e10	1.14260	0.571302	−	0.820740i	$-0.306438\pi$
$991$	3.50069e10	1.14260	0.571302	+	0.820740i	$0.306438\pi$
$992$	4.48116e10	1.45747
$993$	−3.85645e9	−0.124987
$994$	1.84314e10	0.595257
$995$	−1.14058e9	−0.0367067
$996$	5.84560e9	0.187465
$997$	4.69124e10	1.49918	0.749592	−	0.661900i	$-0.230250\pi$
$997$	4.69124e10	1.49918	0.749592	+	0.661900i	$0.230250\pi$
$998$	−1.74811e9	−0.0556690
$999$	−2.21708e10	−0.703563

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.8.a.b.1.20	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.8.a.b.1.20	✓	60	1.1	even	1	trivial

Overview	Random
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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:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	197.a (trivial)

\(f(q)\)	\(=\)	\(q-8.25431 q^{2} -14.1669 q^{3} -59.8663 q^{4} +11.5658 q^{5} +116.938 q^{6} -664.362 q^{7} +1550.71 q^{8} -1986.30 q^{9} -95.4680 q^{10} -3556.40 q^{11} +848.118 q^{12} -6714.69 q^{13} +5483.85 q^{14} -163.852 q^{15} -5137.13 q^{16} +13719.6 q^{17} +16395.5 q^{18} -34381.8 q^{19} -692.405 q^{20} +9411.91 q^{21} +29355.7 q^{22} -36355.9 q^{23} -21968.6 q^{24} -77991.2 q^{25} +55425.2 q^{26} +59122.5 q^{27} +39772.9 q^{28} -46569.7 q^{29} +1352.48 q^{30} -287094. q^{31} -156087. q^{32} +50383.0 q^{33} -113246. q^{34} -7683.90 q^{35} +118913. q^{36} -374998. q^{37} +283798. q^{38} +95126.1 q^{39} +17935.2 q^{40} +8647.96 q^{41} -77688.9 q^{42} -326648. q^{43} +212909. q^{44} -22973.2 q^{45} +300093. q^{46} +322881. q^{47} +72776.9 q^{48} -382167. q^{49} +643764. q^{50} -194363. q^{51} +401984. q^{52} -1.15879e6 q^{53} -488016. q^{54} -41132.8 q^{55} -1.03023e6 q^{56} +487082. q^{57} +384401. q^{58} -381147. q^{59} +9809.20 q^{60} +681676. q^{61} +2.36976e6 q^{62} +1.31962e6 q^{63} +1.94594e6 q^{64} -77661.1 q^{65} -415877. q^{66} -3.84661e6 q^{67} -821342. q^{68} +515049. q^{69} +63425.3 q^{70} +3.36103e6 q^{71} -3.08017e6 q^{72} -3.33642e6 q^{73} +3.09535e6 q^{74} +1.10489e6 q^{75} +2.05831e6 q^{76} +2.36274e6 q^{77} -785201. q^{78} +2.91848e6 q^{79} -59415.2 q^{80} +3.50646e6 q^{81} -71383.0 q^{82} +6.89244e6 q^{83} -563457. q^{84} +158679. q^{85} +2.69626e6 q^{86} +659746. q^{87} -5.51494e6 q^{88} +432784. q^{89} +189628. q^{90} +4.46098e6 q^{91} +2.17650e6 q^{92} +4.06722e6 q^{93} -2.66516e6 q^{94} -397654. q^{95} +2.21126e6 q^{96} -6.90655e6 q^{97} +3.15452e6 q^{98} +7.06408e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 16 q^{2} + 296 q^{3} + 4224 q^{4} + 554 q^{5} + 1200 q^{6} + 4959 q^{7} + 2571 q^{8} + 47384 q^{9} + 16237 q^{10} + 12452 q^{11} + 38656 q^{12} + 36460 q^{13} - 567 q^{14} + 55139 q^{15} + 319488 q^{16}+ \cdots + 64628303 q^{99}+O(q^{100}) \) 60 * q + 16 * q^2 + 296 * q^3 + 4224 * q^4 + 554 * q^5 + 1200 * q^6 + 4959 * q^7 + 2571 * q^8 + 47384 * q^9 + 16237 * q^10 + 12452 * q^11 + 38656 * q^12 + 36460 * q^13 - 567 * q^14 + 55139 * q^15 + 319488 * q^16 + 13657 * q^17 + 75985 * q^18 + 179089 * q^19 + 78379 * q^20 + 71390 * q^21 + 220057 * q^22 + 159428 * q^23 + 288645 * q^24 + 1250470 * q^25 + 245262 * q^26 + 789647 * q^27 + 775366 * q^28 + 111693 * q^29 + 200635 * q^30 + 1035260 * q^31 + 688764 * q^32 + 535514 * q^33 + 1430866 * q^34 + 698672 * q^35 + 4315642 * q^36 + 1226630 * q^37 + 133058 * q^38 + 1107523 * q^39 + 2427846 * q^40 + 1766062 * q^41 + 693163 * q^42 + 3240035 * q^43 + 2056578 * q^44 + 1462797 * q^45 + 1088877 * q^46 + 3015185 * q^47 + 4531442 * q^48 + 8513327 * q^49 - 8803339 * q^50 - 1200965 * q^51 + 2403172 * q^52 - 2021580 * q^53 - 9268097 * q^54 + 2538479 * q^55 - 13776768 * q^56 - 638299 * q^57 + 3745679 * q^58 + 6845183 * q^59 + 5842749 * q^60 + 6328462 * q^61 + 7784379 * q^62 + 11502133 * q^63 + 28157685 * q^64 + 14369523 * q^65 + 25244790 * q^66 + 20888346 * q^67 + 18152427 * q^68 + 7874901 * q^69 + 23377047 * q^70 + 7085107 * q^71 + 50177539 * q^72 + 21946913 * q^73 + 32718747 * q^74 + 44992638 * q^75 + 52601230 * q^76 + 22159370 * q^77 + 86884893 * q^78 + 9667191 * q^79 + 50245998 * q^80 + 56936064 * q^81 + 55357649 * q^82 + 57432744 * q^83 + 65898868 * q^84 + 32071274 * q^85 + 91529136 * q^86 + 38121559 * q^87 + 95846511 * q^88 + 46839682 * q^89 + 136287359 * q^90 + 81150673 * q^91 + 99073310 * q^92 + 81689463 * q^93 + 55616387 * q^94 + 30995799 * q^95 + 156893033 * q^96 + 72697122 * q^97 + 69757306 * q^98 + 64628303 * q^99

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