LMFDB - Embedded newform 197.10.a.b.1.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [197,10,Mod(1,197)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("197.1"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(197, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 10, names="a")

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	197.a (trivial)

Newform invariants

comment:select newform

sage:traces = [76] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	yes
Analytic conductor:	$101.462059724$
Analytic rank:	$0$
Dimension:	$76$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
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)

$f(q)$	$=$	\(q-31.2026 q^{2} +46.5765 q^{3} +461.602 q^{4} +1445.56 q^{5} -1453.31 q^{6} +12293.0 q^{7} +1572.55 q^{8} -17513.6 q^{9} -45105.3 q^{10} -86595.8 q^{11} +21499.8 q^{12} -40662.2 q^{13} -383573. q^{14} +67329.2 q^{15} -285408. q^{16} +408685. q^{17} +546471. q^{18} -936171. q^{19} +667274. q^{20} +572565. q^{21} +2.70201e6 q^{22} +1.81909e6 q^{23} +73243.7 q^{24} +136525. q^{25} +1.26877e6 q^{26} -1.73249e6 q^{27} +5.67447e6 q^{28} +5.50146e6 q^{29} -2.10085e6 q^{30} -4.56489e6 q^{31} +8.10032e6 q^{32} -4.03333e6 q^{33} -1.27520e7 q^{34} +1.77703e7 q^{35} -8.08433e6 q^{36} -2.08848e6 q^{37} +2.92110e7 q^{38} -1.89390e6 q^{39} +2.27321e6 q^{40} -1.00893e7 q^{41} -1.78655e7 q^{42} +2.32855e7 q^{43} -3.99728e7 q^{44} -2.53170e7 q^{45} -5.67604e7 q^{46} +6.38197e6 q^{47} -1.32933e7 q^{48} +1.10764e8 q^{49} -4.25994e6 q^{50} +1.90351e7 q^{51} -1.87698e7 q^{52} -3.41704e7 q^{53} +5.40581e7 q^{54} -1.25180e8 q^{55} +1.93313e7 q^{56} -4.36036e7 q^{57} -1.71660e8 q^{58} +8.11553e7 q^{59} +3.10793e7 q^{60} +7.77621e7 q^{61} +1.42436e8 q^{62} -2.15295e8 q^{63} -1.06622e8 q^{64} -5.87798e7 q^{65} +1.25850e8 q^{66} +2.44553e8 q^{67} +1.88650e8 q^{68} +8.47269e7 q^{69} -5.54479e8 q^{70} +1.21218e8 q^{71} -2.75410e7 q^{72} +2.68295e8 q^{73} +6.51659e7 q^{74} +6.35886e6 q^{75} -4.32139e8 q^{76} -1.06452e9 q^{77} +5.90947e7 q^{78} -1.87233e8 q^{79} -4.12575e8 q^{80} +2.64028e8 q^{81} +3.14811e8 q^{82} -3.74220e8 q^{83} +2.64297e8 q^{84} +5.90780e8 q^{85} -7.26569e8 q^{86} +2.56239e8 q^{87} -1.36176e8 q^{88} -8.05730e8 q^{89} +7.89957e8 q^{90} -4.99861e8 q^{91} +8.39697e8 q^{92} -2.12617e8 q^{93} -1.99134e8 q^{94} -1.35329e9 q^{95} +3.77284e8 q^{96} -9.14702e8 q^{97} -3.45613e9 q^{98} +1.51661e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 48 q^{2} + 890 q^{3} + 20736 q^{4} + 5171 q^{5} + 2688 q^{6} + 38986 q^{7} + 36507 q^{8} + 518318 q^{9} + 121093 q^{10} + 120464 q^{11} + 415744 q^{12} + 480131 q^{13} + 330849 q^{14} + 544874 q^{15}+ \cdots + 8731109606 q^{99}+O(q^{100}) $ 76 * q + 48 * q^2 + 890 * q^3 + 20736 * q^4 + 5171 * q^5 + 2688 * q^6 + 38986 * q^7 + 36507 * q^8 + 518318 * q^9 + 121093 * q^10 + 120464 * q^11 + 415744 * q^12 + 480131 * q^13 + 330849 * q^14 + 544874 * q^15 + 5963776 * q^16 + 942582 * q^17 + 1483945 * q^18 + 3097319 * q^19 + 3237739 * q^20 + 889076 * q^21 + 3791921 * q^22 + 5139200 * q^23 + 1999533 * q^24 + 34080519 * q^25 + 2791454 * q^26 + 24386486 * q^27 + 20891166 * q^28 + 6886818 * q^29 + 14171083 * q^30 + 28002851 * q^31 + 16857332 * q^32 + 30921422 * q^33 + 33506194 * q^34 + 16271736 * q^35 + 151430458 * q^36 + 55950976 * q^37 + 62370882 * q^38 - 11569592 * q^39 + 129854766 * q^40 + 14990859 * q^41 + 82216531 * q^42 + 169867467 * q^43 + 41872434 * q^44 + 205007649 * q^45 + 144032301 * q^46 + 78743342 * q^47 + 156250562 * q^48 + 533861890 * q^49 + 626841163 * q^50 + 477099244 * q^51 + 560784114 * q^52 + 188670216 * q^53 + 525901687 * q^54 + 298497914 * q^55 + 56575048 * q^56 + 213972590 * q^57 + 338315251 * q^58 + 208222151 * q^59 - 615921507 * q^60 - 233556134 * q^61 - 399368105 * q^62 + 329825056 * q^63 + 876517017 * q^64 - 840557006 * q^65 - 2482481592 * q^66 + 1210808414 * q^67 - 1266757099 * q^68 + 327801786 * q^69 - 546384313 * q^70 + 345300221 * q^71 - 1549481681 * q^72 + 1192286460 * q^73 - 1471133595 * q^74 + 761630676 * q^75 - 398699826 * q^76 - 101106252 * q^77 - 2609825943 * q^78 + 955627631 * q^79 + 1059617770 * q^80 + 3387041436 * q^81 + 1062705523 * q^82 + 1538917201 * q^83 + 1394513218 * q^84 + 225481100 * q^85 + 701644810 * q^86 + 1758812842 * q^87 + 3151474875 * q^88 + 855413630 * q^89 + 6070671455 * q^90 + 4652436248 * q^91 + 8082863606 * q^92 + 3462095982 * q^93 + 2660342117 * q^94 + 1036805508 * q^95 + 12370989029 * q^96 + 6393874545 * q^97 + 7510976010 * q^98 + 8731109606 * 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 $

$2$	−31.2026	−1.37897	−0.689486	−	0.724299i	$-0.742164\pi$
$2$	−31.2026	−1.37897	−0.689486	+	0.724299i	$0.742164\pi$
$3$	46.5765	0.331987	0.165994	−	0.986127i	$-0.446917\pi$
$3$	46.5765	0.331987	0.165994	+	0.986127i	$0.446917\pi$
$4$	461.602	0.901567
$5$	1445.56	1.03436	0.517180	−	0.855877i	$-0.326982\pi$
$5$	1445.56	1.03436	0.517180	+	0.855877i	$0.326982\pi$
$6$	−1453.31	−0.457801
$7$	12293.0	1.93516	0.967579	−	0.252567i	$-0.0812747\pi$
$7$	12293.0	1.93516	0.967579	+	0.252567i	$0.0812747\pi$
$8$	1572.55	0.135737
$9$	−17513.6	−0.889785
$10$	−45105.3	−1.42635
$11$	−86595.8	−1.78332	−0.891661	−	0.452704i	$-0.850459\pi$
$11$	−86595.8	−1.78332	−0.891661	+	0.452704i	$0.850459\pi$
$12$	21499.8	0.299308
$13$	−40662.2	−0.394863	−0.197431	−	0.980317i	$-0.563260\pi$
$13$	−40662.2	−0.394863	−0.197431	+	0.980317i	$0.563260\pi$
$14$	−383573.	−2.66853
$15$	67329.2	0.343394
$16$	−285408.	−1.08874
$17$	408685.	1.18678	0.593388	−	0.804916i	$-0.297790\pi$
$17$	408685.	1.18678	0.593388	+	0.804916i	$0.297790\pi$
$18$	546471.	1.22699
$19$	−936171.	−1.64803	−0.824013	−	0.566570i	$-0.808270\pi$
$19$	−936171.	−1.64803	−0.824013	+	0.566570i	$0.808270\pi$
$20$	667274.	0.932544
$21$	572565.	0.642448
$22$	2.70201e6	2.45915
$23$	1.81909e6	1.35544	0.677719	−	0.735321i	$-0.262969\pi$
$23$	1.81909e6	1.35544	0.677719	+	0.735321i	$0.262969\pi$
$24$	73243.7	0.0450630
$25$	136525.	0.0699008
$26$	1.26877e6	0.544505
$27$	−1.73249e6	−0.627384
$28$	5.67447e6	1.74467
$29$	5.50146e6	1.44440	0.722199	−	0.691685i	$-0.243131\pi$
$29$	5.50146e6	1.44440	0.722199	+	0.691685i	$0.243131\pi$
$30$	−2.10085e6	−0.473531
$31$	−4.56489e6	−0.887775	−0.443887	−	0.896083i	$-0.646401\pi$
$31$	−4.56489e6	−0.887775	−0.443887	+	0.896083i	$0.646401\pi$
$32$	8.10032e6	1.36561
$33$	−4.03333e6	−0.592040
$34$	−1.27520e7	−1.63653
$35$	1.77703e7	2.00165
$36$	−8.08433e6	−0.802200
$37$	−2.08848e6	−0.183199	−0.0915993	−	0.995796i	$-0.529198\pi$
$37$	−2.08848e6	−0.183199	−0.0915993	+	0.995796i	$0.529198\pi$
$38$	2.92110e7	2.27258
$39$	−1.89390e6	−0.131089
$40$	2.27321e6	0.140401
$41$	−1.00893e7	−0.557612	−0.278806	−	0.960347i	$-0.589939\pi$
$41$	−1.00893e7	−0.557612	−0.278806	+	0.960347i	$0.589939\pi$
$42$	−1.78655e7	−0.885918
$43$	2.32855e7	1.03867	0.519336	−	0.854570i	$-0.326179\pi$
$43$	2.32855e7	1.03867	0.519336	+	0.854570i	$0.326179\pi$
$44$	−3.99728e7	−1.60778
$45$	−2.53170e7	−0.920358
$46$	−5.67604e7	−1.86911
$47$	6.38197e6	0.190772	0.0953860	−	0.995440i	$-0.469591\pi$
$47$	6.38197e6	0.190772	0.0953860	+	0.995440i	$0.469591\pi$
$48$	−1.32933e7	−0.361449
$49$	1.10764e8	2.74484
$50$	−4.25994e6	−0.0963913
$51$	1.90351e7	0.393995
$52$	−1.87698e7	−0.355995
$53$	−3.41704e7	−0.594851	−0.297426	−	0.954745i	$-0.596128\pi$
$53$	−3.41704e7	−0.594851	−0.297426	+	0.954745i	$0.596128\pi$
$54$	5.40581e7	0.865146
$55$	−1.25180e8	−1.84460
$56$	1.93313e7	0.262673
$57$	−4.36036e7	−0.547123
$58$	−1.71660e8	−1.99179
$59$	8.11553e7	0.871932	0.435966	−	0.899963i	$-0.356407\pi$
$59$	8.11553e7	0.871932	0.435966	+	0.899963i	$0.356407\pi$
$60$	3.10793e7	0.309593
$61$	7.77621e7	0.719091	0.359545	−	0.933128i	$-0.382932\pi$
$61$	7.77621e7	0.719091	0.359545	+	0.933128i	$0.382932\pi$
$62$	1.42436e8	1.22422
$63$	−2.15295e8	−1.72187
$64$	−1.06622e8	−0.794398
$65$	−5.87798e7	−0.408430
$66$	1.25850e8	0.816407
$67$	2.44553e8	1.48264	0.741322	−	0.671149i	$-0.234199\pi$
$67$	2.44553e8	1.48264	0.741322	+	0.671149i	$0.234199\pi$
$68$	1.88650e8	1.06996
$69$	8.47269e7	0.449988
$70$	−5.54479e8	−2.76022
$71$	1.21218e8	0.566117	0.283058	−	0.959103i	$-0.408651\pi$
$71$	1.21218e8	0.566117	0.283058	+	0.959103i	$0.408651\pi$
$72$	−2.75410e7	−0.120777
$73$	2.68295e8	1.10576	0.552879	−	0.833261i	$-0.313529\pi$
$73$	2.68295e8	1.10576	0.552879	+	0.833261i	$0.313529\pi$
$74$	6.51659e7	0.252626
$75$	6.35886e6	0.0232062
$76$	−4.32139e8	−1.48581
$77$	−1.06452e9	−3.45101
$78$	5.90947e7	0.180769
$79$	−1.87233e8	−0.540830	−0.270415	−	0.962744i	$-0.587161\pi$
$79$	−1.87233e8	−0.540830	−0.270415	+	0.962744i	$0.587161\pi$
$80$	−4.12575e8	−1.12615
$81$	2.64028e8	0.681501
$82$	3.14811e8	0.768932
$83$	−3.74220e8	−0.865517	−0.432759	−	0.901510i	$-0.642460\pi$
$83$	−3.74220e8	−0.865517	−0.432759	+	0.901510i	$0.642460\pi$
$84$	2.64297e8	0.579209
$85$	5.90780e8	1.22755
$86$	−7.26569e8	−1.43230
$87$	2.56239e8	0.479521
$88$	−1.36176e8	−0.242063
$89$	−8.05730e8	−1.36124	−0.680620	−	0.732637i	$-0.738289\pi$
$89$	−8.05730e8	−1.36124	−0.680620	+	0.732637i	$0.738289\pi$
$90$	7.89957e8	1.26915
$91$	−4.99861e8	−0.764122
$92$	8.39697e8	1.22202
$93$	−2.12617e8	−0.294730
$94$	−1.99134e8	−0.263069
$95$	−1.35329e9	−1.70465
$96$	3.77284e8	0.453365
$97$	−9.14702e8	−1.04908	−0.524538	−	0.851387i	$-0.675762\pi$
$97$	−9.14702e8	−1.04908	−0.524538	+	0.851387i	$0.675762\pi$
$98$	−3.45613e9	−3.78506
$99$	1.51661e9	1.58677
$100$	6.30202e7	0.0630202
$101$	−1.44299e8	−0.137980	−0.0689902	−	0.997617i	$-0.521978\pi$
$101$	−1.44299e8	−0.137980	−0.0689902	+	0.997617i	$0.521978\pi$
$102$	−5.93946e8	−0.543308
$103$	1.12278e9	0.982940	0.491470	−	0.870894i	$-0.336460\pi$
$103$	1.12278e9	0.982940	0.491470	+	0.870894i	$0.336460\pi$
$104$	−6.39432e7	−0.0535975
$105$	8.27678e8	0.664522
$106$	1.06620e9	0.820284
$107$	2.00542e9	1.47904	0.739518	−	0.673137i	$-0.235054\pi$
$107$	2.00542e9	1.47904	0.739518	+	0.673137i	$0.235054\pi$
$108$	−7.99720e8	−0.565628
$109$	1.07055e9	0.726417	0.363209	−	0.931708i	$-0.381681\pi$
$109$	1.07055e9	0.726417	0.363209	+	0.931708i	$0.381681\pi$
$110$	3.90593e9	2.54365
$111$	−9.72739e7	−0.0608195
$112$	−3.50852e9	−2.10689
$113$	2.18735e9	1.26202	0.631009	−	0.775775i	$-0.282641\pi$
$113$	2.18735e9	1.26202	0.631009	+	0.775775i	$0.282641\pi$
$114$	1.36054e9	0.754468
$115$	2.62961e9	1.40201
$116$	2.53948e9	1.30222
$117$	7.12143e8	0.351343
$118$	−2.53225e9	−1.20237
$119$	5.02397e9	2.29660
$120$	1.05878e8	0.0466113
$121$	5.14088e9	2.18024
$122$	−2.42638e9	−0.991607
$123$	−4.69922e8	−0.185120
$124$	−2.10716e9	−0.800388
$125$	−2.62601e9	−0.962057
$126$	6.71776e9	2.37442
$127$	4.25498e9	1.45138	0.725689	−	0.688022i	$-0.241521\pi$
$127$	4.25498e9	1.45138	0.725689	+	0.688022i	$0.241521\pi$
$128$	−8.20473e8	−0.270159
$129$	1.08456e9	0.344825
$130$	1.83408e9	0.563214
$131$	3.02024e9	0.896025	0.448012	−	0.894027i	$-0.352132\pi$
$131$	3.02024e9	0.896025	0.448012	+	0.894027i	$0.352132\pi$
$132$	−1.86179e9	−0.533763
$133$	−1.15084e10	−3.18919
$134$	−7.63070e9	−2.04453
$135$	−2.50442e9	−0.648941
$136$	6.42677e8	0.161090
$137$	−4.05566e9	−0.983602	−0.491801	−	0.870708i	$-0.663661\pi$
$137$	−4.05566e9	−0.983602	−0.491801	+	0.870708i	$0.663661\pi$
$138$	−2.64370e9	−0.620521
$139$	2.76294e9	0.627777	0.313888	−	0.949460i	$-0.398368\pi$
$139$	2.76294e9	0.627777	0.313888	+	0.949460i	$0.398368\pi$
$140$	8.20280e9	1.80462
$141$	2.97250e8	0.0633338
$142$	−3.78233e9	−0.780660
$143$	3.52118e9	0.704167
$144$	4.99853e9	0.968748
$145$	7.95270e9	1.49403
$146$	−8.37151e9	−1.52481
$147$	5.15901e9	0.911251
$148$	−9.64045e8	−0.165166
$149$	5.84332e9	0.971228	0.485614	−	0.874173i	$-0.338596\pi$
$149$	5.84332e9	0.971228	0.485614	+	0.874173i	$0.338596\pi$
$150$	−1.98413e8	−0.0320007
$151$	6.99174e9	1.09443	0.547216	−	0.836991i	$-0.315688\pi$
$151$	6.99174e9	1.09443	0.547216	+	0.836991i	$0.315688\pi$
$152$	−1.47217e9	−0.223698
$153$	−7.15757e9	−1.05598
$154$	3.32158e10	4.75885
$155$	−6.59883e9	−0.918279
$156$	−8.74230e8	−0.118186
$157$	−9.43558e8	−0.123942	−0.0619712	−	0.998078i	$-0.519739\pi$
$157$	−9.43558e8	−0.123942	−0.0619712	+	0.998078i	$0.519739\pi$
$158$	5.84216e9	0.745790
$159$	−1.59154e9	−0.197483
$160$	1.17095e10	1.41253
$161$	2.23621e10	2.62299
$162$	−8.23835e9	−0.939772
$163$	7.97804e9	0.885222	0.442611	−	0.896714i	$-0.354052\pi$
$163$	7.97804e9	0.885222	0.442611	+	0.896714i	$0.354052\pi$
$164$	−4.65723e9	−0.502724
$165$	−5.83042e9	−0.612382
$166$	1.16766e10	1.19352
$167$	−1.77239e10	−1.76334	−0.881668	−	0.471871i	$-0.843579\pi$
$167$	−1.77239e10	−1.76334	−0.881668	+	0.471871i	$0.843579\pi$
$168$	9.00385e8	0.0872040
$169$	−8.95108e9	−0.844084
$170$	−1.84339e10	−1.69276
$171$	1.63958e10	1.46639
$172$	1.07486e10	0.936431
$173$	−1.88412e9	−0.159920	−0.0799599	−	0.996798i	$-0.525479\pi$
$173$	−1.88412e9	−0.159920	−0.0799599	+	0.996798i	$0.525479\pi$
$174$	−7.99531e9	−0.661247
$175$	1.67830e9	0.135269
$176$	2.47151e10	1.94158
$177$	3.77993e9	0.289470
$178$	2.51409e10	1.87711
$179$	−9.19717e9	−0.669600	−0.334800	−	0.942289i	$-0.608669\pi$
$179$	−9.19717e9	−0.669600	−0.334800	+	0.942289i	$0.608669\pi$
$180$	−1.16864e10	−0.829764
$181$	−4.28577e9	−0.296808	−0.148404	−	0.988927i	$-0.547414\pi$
$181$	−4.28577e9	−0.296808	−0.148404	+	0.988927i	$0.547414\pi$
$182$	1.55969e10	1.05370
$183$	3.62189e9	0.238729
$184$	2.86061e9	0.183983
$185$	−3.01902e9	−0.189493
$186$	6.63419e9	0.406424
$187$	−3.53904e10	−2.11640
$188$	2.94593e9	0.171994
$189$	−2.12975e10	−1.21409
$190$	4.22263e10	2.35067
$191$	−9.98683e9	−0.542972	−0.271486	−	0.962442i	$-0.587515\pi$
$191$	−9.98683e9	−0.542972	−0.271486	+	0.962442i	$0.587515\pi$
$192$	−4.96609e9	−0.263730
$193$	3.49142e10	1.81131	0.905657	−	0.424011i	$-0.139378\pi$
$193$	3.49142e10	1.81131	0.905657	+	0.424011i	$0.139378\pi$
$194$	2.85411e10	1.44665
$195$	−2.73775e9	−0.135593
$196$	5.11290e10	2.47466
$197$	1.50614e9	0.0712470
$197$	1.50614e9	0.0712470
$198$	−4.73221e10	−2.18812
$199$	−2.40299e10	−1.08621	−0.543105	−	0.839665i	$-0.682751\pi$
$199$	−2.40299e10	−1.08621	−0.543105	+	0.839665i	$0.682751\pi$
$200$	2.14692e8	0.00948813
$201$	1.13904e10	0.492219
$202$	4.50251e9	0.190271
$203$	6.76294e10	2.79514
$204$	8.78666e9	0.355212
$205$	−1.45847e10	−0.576772
$206$	−3.50337e10	−1.35545
$207$	−3.18589e10	−1.20605
$208$	1.16053e10	0.429904
$209$	8.10685e10	2.93896
$210$	−2.58257e10	−0.916358
$211$	−3.86383e10	−1.34198	−0.670992	−	0.741465i	$-0.734131\pi$
$211$	−3.86383e10	−1.34198	−0.670992	+	0.741465i	$0.734131\pi$
$212$	−1.57731e10	−0.536298
$213$	5.64593e9	0.187943
$214$	−6.25744e10	−2.03955
$215$	3.36607e10	1.07436
$216$	−2.72442e9	−0.0851593
$217$	−5.61162e10	−1.71799
$218$	−3.34038e10	−1.00171
$219$	1.24963e10	0.367098
$220$	−5.77831e10	−1.66303
$221$	−1.66181e10	−0.468614
$222$	3.03520e9	0.0838685
$223$	4.08743e10	1.10682	0.553412	−	0.832907i	$-0.313325\pi$
$223$	4.08743e10	1.10682	0.553412	+	0.832907i	$0.313325\pi$
$224$	9.95772e10	2.64268
$225$	−2.39105e9	−0.0621967
$226$	−6.82511e10	−1.74029
$227$	−4.27943e9	−0.106972	−0.0534859	−	0.998569i	$-0.517033\pi$
$227$	−4.27943e9	−0.106972	−0.0534859	+	0.998569i	$0.517033\pi$
$228$	−2.01275e10	−0.493268
$229$	5.85902e10	1.40788	0.703939	−	0.710260i	$-0.251423\pi$
$229$	5.85902e10	1.40788	0.703939	+	0.710260i	$0.251423\pi$
$230$	−8.20507e10	−1.93333
$231$	−4.95817e10	−1.14569
$232$	8.65130e9	0.196058
$233$	−9.96716e9	−0.221549	−0.110775	−	0.993846i	$-0.535333\pi$
$233$	−9.96716e9	−0.221549	−0.110775	+	0.993846i	$0.535333\pi$
$234$	−2.22207e10	−0.484492
$235$	9.22554e9	0.197327
$236$	3.74614e10	0.786105
$237$	−8.72067e9	−0.179549
$238$	−1.56761e11	−3.16695
$239$	−3.47175e10	−0.688268	−0.344134	−	0.938921i	$-0.611827\pi$
$239$	−3.47175e10	−0.688268	−0.344134	+	0.938921i	$0.611827\pi$
$240$	−1.92163e10	−0.373868
$241$	2.89062e10	0.551968	0.275984	−	0.961162i	$-0.410996\pi$
$241$	2.89062e10	0.551968	0.275984	+	0.961162i	$0.410996\pi$
$242$	−1.60409e11	−3.00649
$243$	4.63980e10	0.853634
$244$	3.58951e10	0.648308
$245$	1.60117e11	2.83915
$246$	1.46628e10	0.255275
$247$	3.80668e10	0.650744
$248$	−7.17850e9	−0.120504
$249$	−1.74299e10	−0.287340
$250$	8.19383e10	1.32665
$251$	−1.90919e10	−0.303611	−0.151805	−	0.988410i	$-0.548509\pi$
$251$	−1.90919e10	−0.303611	−0.151805	+	0.988410i	$0.548509\pi$
$252$	−9.93806e10	−1.55238
$253$	−1.57526e11	−2.41718
$254$	−1.32766e11	−2.00141
$255$	2.75165e10	0.407532
$256$	8.01915e10	1.16694
$257$	1.58632e10	0.226826	0.113413	−	0.993548i	$-0.463822\pi$
$257$	1.58632e10	0.226826	0.113413	+	0.993548i	$0.463822\pi$
$258$	−3.38410e10	−0.475505
$259$	−2.56736e10	−0.354518
$260$	−2.71329e10	−0.368227
$261$	−9.63505e10	−1.28520
$262$	−9.42392e10	−1.23559
$263$	−4.73637e10	−0.610442	−0.305221	−	0.952282i	$-0.598730\pi$
$263$	−4.73637e10	−0.610442	−0.305221	+	0.952282i	$0.598730\pi$
$264$	−6.34260e9	−0.0803617
$265$	−4.93954e10	−0.615291
$266$	3.59091e11	4.39781
$267$	−3.75281e10	−0.451914
$268$	1.12886e11	1.33670
$269$	3.21049e9	0.0373840	0.0186920	−	0.999825i	$-0.494050\pi$
$269$	3.21049e9	0.0373840	0.0186920	+	0.999825i	$0.494050\pi$
$270$	7.81444e10	0.894872
$271$	1.27577e11	1.43684	0.718421	−	0.695608i	$-0.244865\pi$
$271$	1.27577e11	1.43684	0.718421	+	0.695608i	$0.244865\pi$
$272$	−1.16642e11	−1.29210
$273$	−2.32817e10	−0.253679
$274$	1.26547e11	1.35636
$275$	−1.18225e10	−0.124656
$276$	3.91101e10	0.405694
$277$	−2.95217e10	−0.301289	−0.150644	−	0.988588i	$-0.548135\pi$
$277$	−2.95217e10	−0.301289	−0.150644	+	0.988588i	$0.548135\pi$
$278$	−8.62110e10	−0.865688
$279$	7.99478e10	0.789928
$280$	2.79446e10	0.271698
$281$	1.29567e11	1.23970	0.619848	−	0.784722i	$-0.287194\pi$
$281$	1.29567e11	1.23970	0.619848	+	0.784722i	$0.287194\pi$
$282$	−9.27497e9	−0.0873356
$283$	8.56254e10	0.793531	0.396765	−	0.917920i	$-0.370133\pi$
$283$	8.56254e10	0.793531	0.396765	+	0.917920i	$0.370133\pi$
$284$	5.59547e10	0.510392
$285$	−6.30317e10	−0.565923
$286$	−1.09870e11	−0.971027
$287$	−1.24027e11	−1.07907
$288$	−1.41866e11	−1.21510
$289$	4.84360e10	0.408439
$290$	−2.48145e11	−2.06022
$291$	−4.26036e10	−0.348279
$292$	1.23846e11	0.996915
$293$	7.52574e10	0.596547	0.298274	−	0.954480i	$-0.403589\pi$
$293$	7.52574e10	0.596547	0.298274	+	0.954480i	$0.403589\pi$
$294$	−1.60974e11	−1.25659
$295$	1.17315e11	0.901892
$296$	−3.28423e9	−0.0248668
$297$	1.50026e11	1.11883
$298$	−1.82327e11	−1.33930
$299$	−7.39683e10	−0.535212
$300$	2.93526e9	0.0209219
$301$	2.86249e11	2.00999
$302$	−2.18160e11	−1.50919
$303$	−6.72094e9	−0.0458077
$304$	2.67191e11	1.79428
$305$	1.12410e11	0.743799
$306$	2.23335e11	1.45616
$307$	3.06863e11	1.97161	0.985806	−	0.167890i	$-0.0536954\pi$
$307$	3.06863e11	1.97161	0.985806	+	0.167890i	$0.0536954\pi$
$308$	−4.91385e11	−3.11132
$309$	5.22952e10	0.326323
$310$	2.05901e11	1.26628
$311$	−1.07149e11	−0.649484	−0.324742	−	0.945803i	$-0.605277\pi$
$311$	−1.07149e11	−0.649484	−0.324742	+	0.945803i	$0.605277\pi$
$312$	−2.97825e9	−0.0177937
$313$	−2.42161e11	−1.42612	−0.713059	−	0.701104i	$-0.752691\pi$
$313$	−2.42161e11	−1.42612	−0.713059	+	0.701104i	$0.752691\pi$
$314$	2.94415e10	0.170913
$315$	−3.11222e11	−1.78104
$316$	−8.64272e10	−0.487594
$317$	3.20101e11	1.78041	0.890205	−	0.455560i	$-0.150561\pi$
$317$	3.20101e11	1.78041	0.890205	+	0.455560i	$0.150561\pi$
$318$	4.96601e10	0.272324
$319$	−4.76403e11	−2.57583
$320$	−1.54129e11	−0.821693
$321$	9.34055e10	0.491021
$322$	−6.97756e11	−3.61703
$323$	−3.82600e11	−1.95584
$324$	1.21876e11	0.614419
$325$	−5.55141e9	−0.0276012
$326$	−2.48936e11	−1.22070
$327$	4.98623e10	0.241161
$328$	−1.58658e10	−0.0756887
$329$	7.84536e10	0.369174
$330$	1.81924e11	0.844458
$331$	−3.05648e11	−1.39957	−0.699786	−	0.714353i	$-0.746721\pi$
$331$	−3.05648e11	−1.39957	−0.699786	+	0.714353i	$0.746721\pi$
$332$	−1.72741e11	−0.780321
$333$	3.65768e10	0.163007
$334$	5.53031e11	2.43159
$335$	3.53517e11	1.53359
$336$	−1.63414e11	−0.699461
$337$	−3.59989e11	−1.52039	−0.760195	−	0.649695i	$-0.774897\pi$
$337$	−3.59989e11	−1.52039	−0.760195	+	0.649695i	$0.774897\pi$
$338$	2.79297e11	1.16397
$339$	1.01879e11	0.418974
$340$	2.72705e11	1.10672
$341$	3.95300e11	1.58319
$342$	−5.11590e11	−2.02211
$343$	8.65557e11	3.37654
$344$	3.66176e10	0.140986
$345$	1.22478e11	0.465449
$346$	5.87896e10	0.220525
$347$	−7.14683e10	−0.264625	−0.132313	−	0.991208i	$-0.542240\pi$
$347$	−7.14683e10	−0.264625	−0.132313	+	0.991208i	$0.542240\pi$
$348$	1.18280e11	0.432320
$349$	−1.44317e11	−0.520720	−0.260360	−	0.965512i	$-0.583841\pi$
$349$	−1.44317e11	−0.520720	−0.260360	+	0.965512i	$0.583841\pi$
$350$	−5.23674e10	−0.186533
$351$	7.04468e10	0.247730
$352$	−7.01454e11	−2.43532
$353$	1.61006e11	0.551893	0.275946	−	0.961173i	$-0.411009\pi$
$353$	1.61006e11	0.551893	0.275946	+	0.961173i	$0.411009\pi$
$354$	−1.17944e11	−0.399171
$355$	1.75229e11	0.585569
$356$	−3.71927e11	−1.22725
$357$	2.33999e11	0.762442
$358$	2.86975e11	0.923360
$359$	4.26328e11	1.35462	0.677311	−	0.735696i	$-0.263145\pi$
$359$	4.26328e11	1.35462	0.677311	+	0.735696i	$0.263145\pi$
$360$	−3.98122e10	−0.124927
$361$	5.53729e11	1.71599
$362$	1.33727e11	0.409290
$363$	2.39444e11	0.723810
$364$	−2.30737e11	−0.688907
$365$	3.87838e11	1.14375
$366$	−1.13012e11	−0.329201
$367$	−1.84405e11	−0.530611	−0.265305	−	0.964164i	$-0.585473\pi$
$367$	−1.84405e11	−0.530611	−0.265305	+	0.964164i	$0.585473\pi$
$368$	−5.19183e11	−1.47573
$369$	1.76700e11	0.496155
$370$	9.42014e10	0.261306
$371$	−4.20057e11	−1.15113
$372$	−9.81442e10	−0.265718
$373$	5.10016e11	1.36425	0.682125	−	0.731235i	$-0.261056\pi$
$373$	5.10016e11	1.36425	0.682125	+	0.731235i	$0.261056\pi$
$374$	1.10427e12	2.91846
$375$	−1.22310e11	−0.319391
$376$	1.00360e10	0.0258948
$377$	−2.23702e11	−0.570339
$378$	6.64537e11	1.67419
$379$	1.65397e11	0.411766	0.205883	−	0.978577i	$-0.433993\pi$
$379$	1.65397e11	0.411766	0.205883	+	0.978577i	$0.433993\pi$
$380$	−6.24683e11	−1.53686
$381$	1.98182e11	0.481839
$382$	3.11615e11	0.748744
$383$	−4.95447e11	−1.17653	−0.588265	−	0.808668i	$-0.700189\pi$
$383$	−4.95447e11	−1.17653	−0.588265	+	0.808668i	$0.700189\pi$
$384$	−3.82148e10	−0.0896893
$385$	−1.53883e12	−3.56959
$386$	−1.08941e12	−2.49775
$387$	−4.07814e11	−0.924194
$388$	−4.22228e11	−0.945811
$389$	−7.07474e11	−1.56653	−0.783263	−	0.621691i	$-0.786446\pi$
$389$	−7.07474e11	−1.56653	−0.783263	+	0.621691i	$0.786446\pi$
$390$	8.54251e10	0.186980
$391$	7.43437e11	1.60860
$392$	1.74182e11	0.372577
$393$	1.40672e11	0.297469
$394$	−4.69954e10	−0.0982478
$395$	−2.70657e11	−0.559413
$396$	7.00069e11	1.43058
$397$	8.24687e11	1.66622	0.833109	−	0.553109i	$-0.186559\pi$
$397$	8.24687e11	1.66622	0.833109	+	0.553109i	$0.186559\pi$
$398$	7.49796e11	1.49785
$399$	−5.36019e11	−1.05877
$400$	−3.89653e10	−0.0761041
$401$	3.12876e10	0.0604258	0.0302129	−	0.999543i	$-0.490381\pi$
$401$	3.12876e10	0.0604258	0.0302129	+	0.999543i	$0.490381\pi$
$402$	−3.55411e11	−0.678756
$403$	1.85619e11	0.350549
$404$	−6.66088e10	−0.124399
$405$	3.81668e11	0.704918
$406$	−2.11021e12	−3.85442
$407$	1.80853e11	0.326702
$408$	2.99336e10	0.0534797
$409$	−1.02785e11	−0.181624	−0.0908122	−	0.995868i	$-0.528946\pi$
$409$	−1.02785e11	−0.181624	−0.0908122	+	0.995868i	$0.528946\pi$
$410$	4.55079e11	0.795353
$411$	−1.88899e11	−0.326543
$412$	5.18278e11	0.886186
$413$	9.97641e11	1.68733
$414$	9.94081e11	1.66311
$415$	−5.40958e11	−0.895256
$416$	−3.29377e11	−0.539229
$417$	1.28688e11	0.208414
$418$	−2.52955e12	−4.05275
$419$	−7.57669e11	−1.20093	−0.600463	−	0.799653i	$-0.705017\pi$
$419$	−7.57669e11	−1.20093	−0.600463	+	0.799653i	$0.705017\pi$
$420$	3.82058e11	0.599111
$421$	4.37253e10	0.0678365	0.0339183	−	0.999425i	$-0.489201\pi$
$421$	4.37253e10	0.0678365	0.0339183	+	0.999425i	$0.489201\pi$
$422$	1.20562e12	1.85056
$423$	−1.11772e11	−0.169746
$424$	−5.37345e10	−0.0807434
$425$	5.57958e10	0.0829567
$426$	−1.76168e11	−0.259169
$427$	9.55929e11	1.39156
$428$	9.25707e11	1.33345
$429$	1.64004e11	0.233774
$430$	−1.05030e12	−1.48151
$431$	−5.11576e11	−0.714105	−0.357053	−	0.934084i	$-0.616218\pi$
$431$	−5.11576e11	−0.714105	−0.357053	+	0.934084i	$0.616218\pi$
$432$	4.94466e11	0.683061
$433$	−2.85601e11	−0.390449	−0.195225	−	0.980759i	$-0.562544\pi$
$433$	−2.85601e11	−0.390449	−0.195225	+	0.980759i	$0.562544\pi$
$434$	1.75097e12	2.36906
$435$	3.70409e11	0.495998
$436$	4.94166e11	0.654913
$437$	−1.70298e12	−2.23380
$438$	−3.89916e11	−0.506218
$439$	5.70005e11	0.732468	0.366234	−	0.930523i	$-0.380647\pi$
$439$	5.70005e11	0.732468	0.366234	+	0.930523i	$0.380647\pi$
$440$	−1.96851e11	−0.250380
$441$	−1.93988e12	−2.44232
$442$	5.18527e11	0.646206
$443$	4.94387e11	0.609889	0.304944	−	0.952370i	$-0.401362\pi$
$443$	4.94387e11	0.609889	0.304944	+	0.952370i	$0.401362\pi$
$444$	−4.49018e10	−0.0548329
$445$	−1.16473e12	−1.40801
$446$	−1.27539e12	−1.52628
$447$	2.72161e11	0.322435
$448$	−1.31071e12	−1.53729
$449$	2.95682e11	0.343334	0.171667	−	0.985155i	$-0.445085\pi$
$449$	2.95682e11	0.343334	0.171667	+	0.985155i	$0.445085\pi$
$450$	7.46069e10	0.0857675
$451$	8.73688e11	0.994401
$452$	1.00969e12	1.13779
$453$	3.25651e11	0.363337
$454$	1.33529e11	0.147511
$455$	−7.22580e11	−0.790377
$456$	−6.85687e10	−0.0742650
$457$	−4.62739e11	−0.496265	−0.248132	−	0.968726i	$-0.579817\pi$
$457$	−4.62739e11	−0.496265	−0.248132	+	0.968726i	$0.579817\pi$
$458$	−1.82817e12	−1.94143
$459$	−7.08043e11	−0.744565
$460$	1.21383e12	1.26401
$461$	4.07104e11	0.419808	0.209904	−	0.977722i	$-0.432685\pi$
$461$	4.07104e11	0.419808	0.209904	+	0.977722i	$0.432685\pi$
$462$	1.54708e12	1.57988
$463$	−9.94253e11	−1.00550	−0.502751	−	0.864431i	$-0.667679\pi$
$463$	−9.94253e11	−1.00550	−0.502751	+	0.864431i	$0.667679\pi$
$464$	−1.57016e12	−1.57258
$465$	−3.07350e11	−0.304857
$466$	3.11001e11	0.305510
$467$	6.74387e11	0.656120	0.328060	−	0.944657i	$-0.393605\pi$
$467$	6.74387e11	0.656120	0.328060	+	0.944657i	$0.393605\pi$
$468$	3.28727e11	0.316759
$469$	3.00629e12	2.86915
$470$	−2.87861e11	−0.272109
$471$	−4.39476e10	−0.0411473
$472$	1.27620e11	0.118354
$473$	−2.01643e12	−1.85228
$474$	2.72107e11	0.247593
$475$	−1.27811e11	−0.115198
$476$	2.31907e12	2.07054
$477$	5.98448e11	0.529290
$478$	1.08327e12	0.949103
$479$	8.65710e11	0.751385	0.375693	−	0.926744i	$-0.377405\pi$
$479$	8.65710e11	0.751385	0.375693	+	0.926744i	$0.377405\pi$
$480$	5.45388e11	0.468943
$481$	8.49221e10	0.0723382
$482$	−9.01948e11	−0.761149
$483$	1.04155e12	0.870798
$484$	2.37304e12	1.96563
$485$	−1.32226e12	−1.08512
$486$	−1.44774e12	−1.17714
$487$	−8.06845e11	−0.649995	−0.324998	−	0.945715i	$-0.605363\pi$
$487$	−8.06845e11	−0.649995	−0.324998	+	0.945715i	$0.605363\pi$
$488$	1.22285e11	0.0976073
$489$	3.71589e11	0.293882
$490$	−4.99605e12	−3.91512
$491$	2.01242e12	1.56262	0.781308	−	0.624146i	$-0.214553\pi$
$491$	2.01242e12	1.56262	0.781308	+	0.624146i	$0.214553\pi$
$492$	−2.16917e11	−0.166898
$493$	2.24837e12	1.71418
$494$	−1.18778e12	−0.897358
$495$	2.19235e12	1.64129
$496$	1.30286e12	0.966560
$497$	1.49014e12	1.09553
$498$	5.43857e11	0.396235
$499$	1.11143e11	0.0802468	0.0401234	−	0.999195i	$-0.487225\pi$
$499$	1.11143e11	0.0802468	0.0401234	+	0.999195i	$0.487225\pi$
$500$	−1.21217e12	−0.867359
$501$	−8.25516e11	−0.585404
$502$	5.95716e11	0.418671
$503$	1.85745e12	1.29379	0.646893	−	0.762581i	$-0.276068\pi$
$503$	1.85745e12	1.29379	0.646893	+	0.762581i	$0.276068\pi$
$504$	−3.38562e11	−0.233722
$505$	−2.08593e11	−0.142721
$506$	4.91521e12	3.33323
$507$	−4.16910e11	−0.280225
$508$	1.96411e12	1.30851
$509$	2.38168e12	1.57273	0.786364	−	0.617763i	$-0.211961\pi$
$509$	2.38168e12	1.57273	0.786364	+	0.617763i	$0.211961\pi$
$510$	−8.58585e11	−0.561976
$511$	3.29815e12	2.13982
$512$	−2.08210e12	−1.33902
$513$	1.62191e12	1.03395
$514$	−4.94974e11	−0.312786
$515$	1.62305e12	1.01671
$516$	5.00634e11	0.310883
$517$	−5.52652e11	−0.340208
$518$	8.01085e11	0.488871
$519$	−8.77559e10	−0.0530913
$520$	−9.24339e10	−0.0554391
$521$	−1.86431e12	−1.10853	−0.554267	−	0.832339i	$-0.687001\pi$
$521$	−1.86431e12	−1.10853	−0.554267	+	0.832339i	$0.687001\pi$
$522$	3.00639e12	1.77226
$523$	4.15395e11	0.242775	0.121387	−	0.992605i	$-0.461266\pi$
$523$	4.15395e11	0.242775	0.121387	+	0.992605i	$0.461266\pi$
$524$	1.39415e12	0.807826
$525$	7.81694e10	0.0449076
$526$	1.47787e12	0.841783
$527$	−1.86560e12	−1.05359
$528$	1.15114e12	0.644580
$529$	1.50795e12	0.837211
$530$	1.54127e12	0.848469
$531$	−1.42132e12	−0.775832
$532$	−5.31228e12	−2.87527
$533$	4.10252e11	0.220180
$534$	1.17097e12	0.623177
$535$	2.89896e12	1.52986
$536$	3.84572e11	0.201250
$537$	−4.28372e11	−0.222298
$538$	−1.00176e11	−0.0515515
$539$	−9.59171e12	−4.89493
$540$	−1.15605e12	−0.585063
$541$	1.19662e12	0.600579	0.300290	−	0.953848i	$-0.402917\pi$
$541$	1.19662e12	0.600579	0.300290	+	0.953848i	$0.402917\pi$
$542$	−3.98072e12	−1.98137
$543$	−1.99616e11	−0.0985364
$544$	3.31048e12	1.62068
$545$	1.54754e12	0.751377
$546$	7.26451e11	0.349816
$547$	−2.98315e11	−0.142473	−0.0712365	−	0.997459i	$-0.522695\pi$
$547$	−2.98315e11	−0.142473	−0.0712365	+	0.997459i	$0.522695\pi$
$548$	−1.87210e12	−0.886782
$549$	−1.36190e12	−0.639836
$550$	3.68892e11	0.171897
$551$	−5.15031e12	−2.38041
$552$	1.33237e11	0.0610800
$553$	−2.30166e12	−1.04659
$554$	9.21155e11	0.415469
$555$	−1.40616e11	−0.0629093
$556$	1.27538e12	0.565983
$557$	3.34481e11	0.147239	0.0736195	−	0.997286i	$-0.476545\pi$
$557$	3.34481e11	0.147239	0.0736195	+	0.997286i	$0.476545\pi$
$558$	−2.49458e12	−1.08929
$559$	−9.46841e11	−0.410132
$560$	−5.07178e12	−2.17929
$561$	−1.64836e12	−0.702619
$562$	−4.04282e12	−1.70951
$563$	−6.04936e11	−0.253759	−0.126880	−	0.991918i	$-0.540496\pi$
$563$	−6.04936e11	−0.253759	−0.126880	+	0.991918i	$0.540496\pi$
$564$	1.37211e11	0.0570997
$565$	3.16195e12	1.30538
$566$	−2.67173e12	−1.09426
$567$	3.24569e12	1.31881
$568$	1.90622e11	0.0768431
$569$	1.84663e12	0.738539	0.369270	−	0.929322i	$-0.379608\pi$
$569$	1.84663e12	0.738539	0.369270	+	0.929322i	$0.379608\pi$
$570$	1.96675e12	0.780392
$571$	2.83836e12	1.11739	0.558695	−	0.829373i	$-0.311302\pi$
$571$	2.83836e12	1.11739	0.558695	+	0.829373i	$0.311302\pi$
$572$	1.62538e12	0.634853
$573$	−4.65151e11	−0.180260
$574$	3.86997e12	1.48801
$575$	2.48352e11	0.0947462
$576$	1.86734e12	0.706843
$577$	−1.43760e12	−0.539940	−0.269970	−	0.962869i	$-0.587014\pi$
$577$	−1.43760e12	−0.539940	−0.269970	+	0.962869i	$0.587014\pi$
$578$	−1.51133e12	−0.563227
$579$	1.62618e12	0.601333
$580$	3.67098e12	1.34697
$581$	−4.60029e12	−1.67491
$582$	1.32934e12	0.480268
$583$	2.95901e12	1.06081
$584$	4.21907e11	0.150093
$585$	1.02945e12	0.363415
$586$	−2.34823e12	−0.822623
$587$	1.19986e12	0.417119	0.208560	−	0.978010i	$-0.433123\pi$
$587$	1.19986e12	0.417119	0.208560	+	0.978010i	$0.433123\pi$
$588$	2.38141e12	0.821554
$589$	4.27352e12	1.46308
$590$	−3.66053e12	−1.24368
$591$	7.01506e10	0.0236531
$592$	5.96068e11	0.199456
$593$	−3.39418e11	−0.112717	−0.0563584	−	0.998411i	$-0.517949\pi$
$593$	−3.39418e11	−0.112717	−0.0563584	+	0.998411i	$0.517949\pi$
$594$	−4.68121e12	−1.54283
$595$	7.26246e12	2.37551
$596$	2.69729e12	0.875627
$597$	−1.11923e12	−0.360607
$598$	2.30800e12	0.738042
$599$	−1.03503e12	−0.328499	−0.164249	−	0.986419i	$-0.552520\pi$
$599$	−1.03503e12	−0.328499	−0.164249	+	0.986419i	$0.552520\pi$
$600$	9.99960e9	0.00314994
$601$	−2.63834e12	−0.824890	−0.412445	−	0.910983i	$-0.635325\pi$
$601$	−2.63834e12	−0.824890	−0.412445	+	0.910983i	$0.635325\pi$
$602$	−8.93171e12	−2.77173
$603$	−4.28302e12	−1.31923
$604$	3.22740e12	0.986704
$605$	7.43146e12	2.25515
$606$	2.09711e11	0.0631676
$607$	−6.37908e11	−0.190726	−0.0953628	−	0.995443i	$-0.530401\pi$
$607$	−6.37908e11	−0.190726	−0.0953628	+	0.995443i	$0.530401\pi$
$608$	−7.58329e12	−2.25056
$609$	3.14994e12	0.927950
$610$	−3.50748e12	−1.02568
$611$	−2.59505e11	−0.0753287
$612$	−3.30395e12	−0.952032
$613$	5.75692e12	1.64671	0.823356	−	0.567525i	$-0.192099\pi$
$613$	5.75692e12	1.64671	0.823356	+	0.567525i	$0.192099\pi$
$614$	−9.57491e12	−2.71880
$615$	−6.79302e11	−0.191481
$616$	−1.67401e12	−0.468430
$617$	−5.92878e12	−1.64696	−0.823478	−	0.567348i	$-0.807969\pi$
$617$	−5.92878e12	−1.64696	−0.823478	+	0.567348i	$0.807969\pi$
$618$	−1.63174e12	−0.449991
$619$	1.33347e12	0.365069	0.182535	−	0.983199i	$-0.441570\pi$
$619$	1.33347e12	0.365069	0.182535	+	0.983199i	$0.441570\pi$
$620$	−3.04603e12	−0.827889
$621$	−3.15156e12	−0.850380
$622$	3.34334e12	0.895620
$623$	−9.90484e12	−2.63422
$624$	5.40535e11	0.142723
$625$	−4.06271e12	−1.06501
$626$	7.55606e12	1.96658
$627$	3.77589e12	0.975697
$628$	−4.35548e11	−0.111742
$629$	−8.53530e11	−0.217416
$630$	9.71095e12	2.45600
$631$	−3.17468e12	−0.797201	−0.398601	−	0.917125i	$-0.630504\pi$
$631$	−3.17468e12	−0.797201	−0.398601	+	0.917125i	$0.630504\pi$
$632$	−2.94433e11	−0.0734107
$633$	−1.79964e12	−0.445521
$634$	−9.98798e12	−2.45514
$635$	6.15084e12	1.50125
$636$	−7.34657e11	−0.178044
$637$	−4.50392e12	−1.08383
$638$	1.48650e13	3.55199
$639$	−2.12297e12	−0.503722
$640$	−1.18605e12	−0.279442
$641$	−7.86922e12	−1.84107	−0.920536	−	0.390659i	$-0.872247\pi$
$641$	−7.86922e12	−1.84107	−0.920536	+	0.390659i	$0.872247\pi$
$642$	−2.91449e12	−0.677104
$643$	3.04218e12	0.701836	0.350918	−	0.936406i	$-0.385870\pi$
$643$	3.04218e12	0.701836	0.350918	+	0.936406i	$0.385870\pi$
$644$	1.03224e13	2.36480
$645$	1.56780e12	0.356674
$646$	1.19381e13	2.69705
$647$	−2.52321e12	−0.566089	−0.283044	−	0.959107i	$-0.591344\pi$
$647$	−2.52321e12	−0.566089	−0.283044	+	0.959107i	$0.591344\pi$
$648$	4.15196e11	0.0925050
$649$	−7.02770e12	−1.55493
$650$	1.73218e11	0.0380613
$651$	−2.61370e12	−0.570349
$652$	3.68268e12	0.798087
$653$	3.01932e11	0.0649830	0.0324915	−	0.999472i	$-0.489656\pi$
$653$	3.01932e11	0.0649830	0.0324915	+	0.999472i	$0.489656\pi$
$654$	−1.55583e12	−0.332555
$655$	4.36594e12	0.926812
$656$	2.87955e12	0.607097
$657$	−4.69883e12	−0.983887
$658$	−2.44796e12	−0.509081
$659$	2.70646e11	0.0559008	0.0279504	−	0.999609i	$-0.491102\pi$
$659$	2.70646e11	0.0559008	0.0279504	+	0.999609i	$0.491102\pi$
$660$	−2.69134e12	−0.552103
$661$	7.51895e12	1.53197	0.765986	−	0.642857i	$-0.222251\pi$
$661$	7.51895e12	1.53197	0.765986	+	0.642857i	$0.222251\pi$
$662$	9.53700e12	1.92997
$663$	−7.74011e11	−0.155574
$664$	−5.88479e11	−0.117483
$665$	−1.66360e13	−3.29877
$666$	−1.14129e12	−0.224783
$667$	1.00077e13	1.95779
$668$	−8.18138e12	−1.58976
$669$	1.90378e12	0.367452
$670$	−1.10306e13	−2.11478
$671$	−6.73387e12	−1.28237
$672$	4.63796e12	0.877334
$673$	1.33126e12	0.250146	0.125073	−	0.992148i	$-0.460083\pi$
$673$	1.33126e12	0.250146	0.125073	+	0.992148i	$0.460083\pi$
$674$	1.12326e13	2.09658
$675$	−2.36528e11	−0.0438546
$676$	−4.13184e12	−0.760997
$677$	7.88756e11	0.144309	0.0721545	−	0.997393i	$-0.477013\pi$
$677$	7.88756e11	0.144309	0.0721545	+	0.997393i	$0.477013\pi$
$678$	−3.17890e12	−0.577754
$679$	−1.12444e13	−2.03013
$680$	9.29030e11	0.166625
$681$	−1.99321e11	−0.0355133
$682$	−1.23344e13	−2.18317
$683$	7.89860e12	1.38885	0.694427	−	0.719563i	$-0.255658\pi$
$683$	7.89860e12	1.38885	0.694427	+	0.719563i	$0.255658\pi$
$684$	7.56832e12	1.32205
$685$	−5.86271e12	−1.01740
$686$	−2.70076e13	−4.65616
$687$	2.72892e12	0.467397
$688$	−6.64587e12	−1.13085
$689$	1.38944e12	0.234885
$690$	−3.82163e12	−0.641842
$691$	−3.17401e10	−0.00529611	−0.00264805	−	0.999996i	$-0.500843\pi$
$691$	−3.17401e10	−0.00529611	−0.00264805	+	0.999996i	$0.500843\pi$
$692$	−8.69716e11	−0.144178
$693$	1.86436e13	3.07066
$694$	2.23000e12	0.364911
$695$	3.99401e12	0.649347
$696$	4.02947e11	0.0650889
$697$	−4.12334e12	−0.661761
$698$	4.50307e12	0.718058
$699$	−4.64235e11	−0.0735514
$700$	7.74708e11	0.121954
$701$	−9.29151e12	−1.45330	−0.726650	−	0.687008i	$-0.758924\pi$
$701$	−9.29151e12	−1.45330	−0.726650	+	0.687008i	$0.758924\pi$
$702$	−2.19812e12	−0.341614
$703$	1.95517e12	0.301916
$704$	9.23304e12	1.41667
$705$	4.29693e11	0.0655100
$706$	−5.02379e12	−0.761045
$707$	−1.77387e12	−0.267014
$708$	1.74482e12	0.260977
$709$	−8.29711e12	−1.23316	−0.616579	−	0.787293i	$-0.711482\pi$
$709$	−8.29711e12	−1.23316	−0.616579	+	0.787293i	$0.711482\pi$
$710$	−5.46759e12	−0.807483
$711$	3.27913e12	0.481222
$712$	−1.26705e12	−0.184771
$713$	−8.30396e12	−1.20332
$714$	−7.30137e12	−1.05139
$715$	5.09008e12	0.728362
$716$	−4.24543e12	−0.603689
$717$	−1.61702e12	−0.228496
$718$	−1.33025e13	−1.86799
$719$	1.16398e13	1.62430	0.812151	−	0.583447i	$-0.198297\pi$
$719$	1.16398e13	1.62430	0.812151	+	0.583447i	$0.198297\pi$
$720$	7.22568e12	1.00203
$721$	1.38023e13	1.90215
$722$	−1.72778e13	−2.36631
$723$	1.34635e12	0.183246
$724$	−1.97832e12	−0.267592
$725$	7.51087e11	0.100965
$726$	−7.47128e12	−0.998114
$727$	2.00029e12	0.265575	0.132788	−	0.991145i	$-0.457607\pi$
$727$	2.00029e12	0.265575	0.132788	+	0.991145i	$0.457607\pi$
$728$	−7.86054e11	−0.103720
$729$	−3.03580e12	−0.398106
$730$	−1.21015e13	−1.57720
$731$	9.51646e12	1.23267
$732$	1.67187e12	0.215230
$733$	−1.40013e13	−1.79143	−0.895716	−	0.444627i	$-0.853336\pi$
$733$	−1.40013e13	−1.79143	−0.895716	+	0.444627i	$0.853336\pi$
$734$	5.75392e12	0.731698
$735$	7.45767e12	0.942562
$736$	1.47352e13	1.85100
$737$	−2.11773e13	−2.64403
$738$	−5.51349e12	−0.684184
$739$	−4.43378e12	−0.546858	−0.273429	−	0.961892i	$-0.588158\pi$
$739$	−4.43378e12	−0.546858	−0.273429	+	0.961892i	$0.588158\pi$
$740$	−1.39359e12	−0.170841
$741$	1.77302e12	0.216039
$742$	1.31069e13	1.58738
$743$	3.91662e11	0.0471478	0.0235739	−	0.999722i	$-0.492495\pi$
$743$	3.91662e11	0.0471478	0.0235739	+	0.999722i	$0.492495\pi$
$744$	−3.34350e11	−0.0400058
$745$	8.44688e12	1.00460
$746$	−1.59138e13	−1.88127
$747$	6.55395e12	0.770124
$748$	−1.63363e13	−1.90808
$749$	2.46526e13	2.86217
$750$	3.81640e12	0.440431
$751$	−4.37652e12	−0.502053	−0.251027	−	0.967980i	$-0.580768\pi$
$751$	−4.37652e12	−0.502053	−0.251027	+	0.967980i	$0.580768\pi$
$752$	−1.82147e12	−0.207702
$753$	−8.89233e11	−0.100795
$754$	6.98007e12	0.786482
$755$	1.01070e13	1.13204
$756$	−9.83096e12	−1.09458
$757$	1.09648e13	1.21358	0.606788	−	0.794863i	$-0.292458\pi$
$757$	1.09648e13	1.21358	0.606788	+	0.794863i	$0.292458\pi$
$758$	−5.16081e12	−0.567815
$759$	−7.33700e12	−0.802473
$760$	−2.12812e12	−0.231385
$761$	1.69314e12	0.183005	0.0915025	−	0.995805i	$-0.470833\pi$
$761$	1.69314e12	0.183005	0.0915025	+	0.995805i	$0.470833\pi$
$762$	−6.18379e12	−0.664443
$763$	1.31602e13	1.40573
$764$	−4.60994e12	−0.489525
$765$	−1.03467e13	−1.09226
$766$	1.54592e13	1.62240
$767$	−3.29995e12	−0.344293
$768$	3.73504e12	0.387409
$769$	2.24899e12	0.231910	0.115955	−	0.993254i	$-0.463007\pi$
$769$	2.24899e12	0.231910	0.115955	+	0.993254i	$0.463007\pi$
$770$	4.80156e13	4.92236
$771$	7.38853e11	0.0753032
$772$	1.61165e13	1.63302
$773$	−1.21268e13	−1.22162	−0.610812	−	0.791776i	$-0.709157\pi$
$773$	−1.21268e13	−1.22162	−0.610812	+	0.791776i	$0.709157\pi$
$774$	1.27249e13	1.27444
$775$	−6.23222e11	−0.0620562
$776$	−1.43841e12	−0.142398
$777$	−1.19579e12	−0.117695
$778$	2.20750e13	2.16020
$779$	9.44528e12	0.918959
$780$	−1.26375e12	−0.122247
$781$	−1.04970e13	−1.00957
$782$	−2.31972e13	−2.21822
$783$	−9.53121e12	−0.906192
$784$	−3.16130e13	−2.98843
$785$	−1.36397e12	−0.128201
$786$	−4.38933e12	−0.410201
$787$	1.72151e13	1.59965	0.799823	−	0.600236i	$-0.204927\pi$
$787$	1.72151e13	1.59965	0.799823	+	0.600236i	$0.204927\pi$
$788$	6.95237e11	0.0642340
$789$	−2.20603e12	−0.202659
$790$	8.44521e12	0.771416
$791$	2.68891e13	2.44221
$792$	2.38493e12	0.215384
$793$	−3.16198e12	−0.283942
$794$	−2.57324e13	−2.29767
$795$	−2.30067e12	−0.204268
$796$	−1.10923e13	−0.979290
$797$	−5.44893e12	−0.478354	−0.239177	−	0.970976i	$-0.576878\pi$
$797$	−5.44893e12	−0.478354	−0.239177	+	0.970976i	$0.576878\pi$
$798$	1.67252e13	1.46002
$799$	2.60822e12	0.226404
$800$	1.10590e12	0.0954574
$801$	1.41113e13	1.21121
$802$	−9.76254e11	−0.0833256
$803$	−2.32332e13	−1.97192
$804$	5.25785e12	0.443768
$805$	3.23258e13	2.71311
$806$	−5.79178e12	−0.483398
$807$	1.49533e11	0.0124110
$808$	−2.26917e11	−0.0187291
$809$	−1.22067e13	−1.00192	−0.500958	−	0.865471i	$-0.667019\pi$
$809$	−1.22067e13	−1.00192	−0.500958	+	0.865471i	$0.667019\pi$
$810$	−1.19090e13	−0.972063
$811$	8.50738e12	0.690561	0.345280	−	0.938500i	$-0.387784\pi$
$811$	8.50738e12	0.690561	0.345280	+	0.938500i	$0.387784\pi$
$812$	3.12179e13	2.52000
$813$	5.94207e12	0.477013
$814$	−5.64309e12	−0.450513
$815$	1.15328e13	0.915638
$816$	−5.43278e12	−0.428959
$817$	−2.17992e13	−1.71176
$818$	3.20715e12	0.250455
$819$	8.75437e12	0.679904
$820$	−6.73231e12	−0.519998
$821$	−1.39764e13	−1.07362	−0.536809	−	0.843704i	$-0.680370\pi$
$821$	−1.39764e13	−1.07362	−0.536809	+	0.843704i	$0.680370\pi$
$822$	5.89412e12	0.450294
$823$	−8.04585e12	−0.611326	−0.305663	−	0.952140i	$-0.598878\pi$
$823$	−8.04585e12	−0.611326	−0.305663	+	0.952140i	$0.598878\pi$
$824$	1.76562e12	0.133422
$825$	−5.50650e11	−0.0413840
$826$	−3.11290e13	−2.32678
$827$	2.11210e11	0.0157014	0.00785071	−	0.999969i	$-0.497501\pi$
$827$	2.11210e11	0.0157014	0.00785071	+	0.999969i	$0.497501\pi$
$828$	−1.47061e13	−1.08733
$829$	6.46363e12	0.475315	0.237657	−	0.971349i	$-0.423620\pi$
$829$	6.46363e12	0.475315	0.237657	+	0.971349i	$0.423620\pi$
$830$	1.68793e13	1.23453
$831$	−1.37502e12	−0.100024
$832$	4.33550e12	0.313678
$833$	4.52677e13	3.25751
$834$	−4.01541e12	−0.287397
$835$	−2.56210e13	−1.82392
$836$	3.74214e13	2.64967
$837$	7.90862e12	0.556976
$838$	2.36412e13	1.65604
$839$	−4.34313e12	−0.302604	−0.151302	−	0.988488i	$-0.548347\pi$
$839$	−4.34313e12	−0.302604	−0.151302	+	0.988488i	$0.548347\pi$
$840$	1.30156e12	0.0902003
$841$	1.57589e13	1.08629
$842$	−1.36434e12	−0.0935448
$843$	6.03476e12	0.411563
$844$	−1.78355e13	−1.20989
$845$	−1.29393e13	−0.873086
$846$	3.48756e12	0.234075
$847$	6.31968e13	4.21910
$848$	9.75250e12	0.647641
$849$	3.98813e12	0.263442
$850$	−1.74097e12	−0.114395
$851$	−3.79913e12	−0.248314
$852$	2.60617e12	0.169444
$853$	1.29660e13	0.838562	0.419281	−	0.907856i	$-0.362282\pi$
$853$	1.29660e13	0.838562	0.419281	+	0.907856i	$0.362282\pi$
$854$	−2.98275e13	−1.91892
$855$	2.37011e13	1.51677
$856$	3.15362e12	0.200760
$857$	2.80902e13	1.77886	0.889430	−	0.457071i	$-0.151102\pi$
$857$	2.80902e13	1.77886	0.889430	+	0.457071i	$0.151102\pi$
$858$	−5.11735e12	−0.322368
$859$	−1.16878e13	−0.732424	−0.366212	−	0.930532i	$-0.619345\pi$
$859$	−1.16878e13	−0.732424	−0.366212	+	0.930532i	$0.619345\pi$
$860$	1.55378e13	0.968607
$861$	−5.77676e12	−0.358237
$862$	1.59625e13	0.984732
$863$	−2.84641e13	−1.74682	−0.873412	−	0.486982i	$-0.838098\pi$
$863$	−2.84641e13	−1.74682	−0.873412	+	0.486982i	$0.838098\pi$
$864$	−1.40337e13	−0.856763
$865$	−2.72362e12	−0.165415
$866$	8.91150e12	0.538419
$867$	2.25598e12	0.135597
$868$	−2.59033e13	−1.54888
$869$	1.62136e13	0.964474
$870$	−1.15577e13	−0.683968
$871$	−9.94408e12	−0.585441
$872$	1.68348e12	0.0986018
$873$	1.60197e13	0.933451
$874$	5.31375e13	3.08035
$875$	−3.22815e13	−1.86173
$876$	5.76830e12	0.330963
$877$	−2.02826e13	−1.15778	−0.578889	−	0.815407i	$-0.696513\pi$
$877$	−2.02826e13	−1.15778	−0.578889	+	0.815407i	$0.696513\pi$
$878$	−1.77856e13	−1.01005
$879$	3.50522e12	0.198046
$880$	3.57272e13	2.00829
$881$	−1.63790e13	−0.915999	−0.457999	−	0.888952i	$-0.651434\pi$
$881$	−1.63790e13	−0.915999	−0.457999	+	0.888952i	$0.651434\pi$
$882$	6.05294e13	3.36789
$883$	−1.92775e13	−1.06715	−0.533576	−	0.845752i	$-0.679152\pi$
$883$	−1.92775e13	−1.06715	−0.533576	+	0.845752i	$0.679152\pi$
$884$	−7.67093e12	−0.422486
$885$	5.46412e12	0.299416
$886$	−1.54262e13	−0.841020
$887$	2.23762e13	1.21375	0.606876	−	0.794796i	$-0.292422\pi$
$887$	2.23762e13	1.21375	0.606876	+	0.794796i	$0.292422\pi$
$888$	−1.52968e11	−0.00825547
$889$	5.23065e13	2.80865
$890$	3.63427e13	1.94161
$891$	−2.28637e13	−1.21534
$892$	1.88677e13	0.997876
$893$	−5.97462e12	−0.314397
$894$	−8.49214e12	−0.444629
$895$	−1.32951e13	−0.692607
$896$	−1.00861e13	−0.522801
$897$	−3.44519e12	−0.177683
$898$	−9.22605e12	−0.473448
$899$	−2.51136e13	−1.28230
$900$	−1.10371e12	−0.0560744
$901$	−1.39649e13	−0.705956
$902$	−2.72613e13	−1.37125
$903$	1.33325e13	0.667292
$904$	3.43971e12	0.171303
$905$	−6.19535e12	−0.307006
$906$	−1.01611e13	−0.501032
$907$	−2.81130e13	−1.37935	−0.689675	−	0.724119i	$-0.742247\pi$
$907$	−2.81130e13	−1.37935	−0.689675	+	0.724119i	$0.742247\pi$
$908$	−1.97539e12	−0.0964423
$909$	2.52720e12	0.122773
$910$	2.25464e13	1.08991
$911$	2.91401e13	1.40171	0.700855	−	0.713304i	$-0.252802\pi$
$911$	2.91401e13	1.40171	0.700855	+	0.713304i	$0.252802\pi$
$912$	1.24448e13	0.595678
$913$	3.24059e13	1.54350
$914$	1.44387e13	0.684336
$915$	5.23566e12	0.246932
$916$	2.70453e13	1.26930
$917$	3.71278e13	1.73395
$918$	2.20928e13	1.02673
$919$	−1.08797e13	−0.503149	−0.251574	−	0.967838i	$-0.580948\pi$
$919$	−1.08797e13	−0.503149	−0.251574	+	0.967838i	$0.580948\pi$
$920$	4.13519e12	0.190305
$921$	1.42926e13	0.654549
$922$	−1.27027e13	−0.578904
$923$	−4.92901e12	−0.223538
$924$	−2.28870e13	−1.03292
$925$	−2.85129e11	−0.0128057
$926$	3.10233e13	1.38656
$927$	−1.96640e13	−0.874605
$928$	4.45636e13	1.97249
$929$	−9.63079e11	−0.0424220	−0.0212110	−	0.999775i	$-0.506752\pi$
$929$	−9.63079e11	−0.0424220	−0.0212110	+	0.999775i	$0.506752\pi$
$930$	9.59013e12	0.420389
$931$	−1.03694e14	−4.52357
$932$	−4.60086e12	−0.199741
$933$	−4.99065e12	−0.215620
$934$	−2.10426e13	−0.904771
$935$	−5.11591e13	−2.18912
$936$	1.11988e12	0.0476902
$937$	−3.60399e12	−0.152741	−0.0763704	−	0.997080i	$-0.524333\pi$
$937$	−3.60399e12	−0.152741	−0.0763704	+	0.997080i	$0.524333\pi$
$938$	−9.38042e13	−3.95648
$939$	−1.12790e13	−0.473452
$940$	4.25853e12	0.177903
$941$	2.69458e13	1.12031	0.560155	−	0.828388i	$-0.310742\pi$
$941$	2.69458e13	1.12031	0.560155	+	0.828388i	$0.310742\pi$
$942$	1.37128e12	0.0567410
$943$	−1.83533e13	−0.755808
$944$	−2.31623e13	−0.949311
$945$	−3.07868e13	−1.25580
$946$	6.29178e13	2.55425
$947$	−1.52014e13	−0.614199	−0.307100	−	0.951677i	$-0.599359\pi$
$947$	−1.52014e13	−0.614199	−0.307100	+	0.951677i	$0.599359\pi$
$948$	−4.02548e12	−0.161875
$949$	−1.09095e13	−0.436623
$950$	3.98803e12	0.158855
$951$	1.49092e13	0.591073
$952$	7.90043e12	0.311734
$953$	3.27833e12	0.128746	0.0643731	−	0.997926i	$-0.479495\pi$
$953$	3.27833e12	0.128746	0.0643731	+	0.997926i	$0.479495\pi$
$954$	−1.86731e13	−0.729876
$955$	−1.44366e13	−0.561628
$956$	−1.60257e13	−0.620519
$957$	−2.21892e13	−0.855141
$958$	−2.70124e13	−1.03614
$959$	−4.98563e13	−1.90343
$960$	−7.17879e12	−0.272791
$961$	−5.60140e12	−0.211856
$962$	−2.64979e12	−0.0997525
$963$	−3.51222e13	−1.31602
$964$	1.33432e13	0.497636
$965$	5.04706e13	1.87355
$966$	−3.24990e13	−1.20081
$967$	−4.57794e13	−1.68365	−0.841824	−	0.539752i	$-0.818518\pi$
$967$	−4.57794e13	−1.68365	−0.841824	+	0.539752i	$0.818518\pi$
$968$	8.08427e12	0.295939
$969$	−1.78202e13	−0.649313
$970$	4.12579e13	1.49635
$971$	−3.40025e13	−1.22751	−0.613753	−	0.789498i	$-0.710341\pi$
$971$	−3.40025e13	−1.22751	−0.613753	+	0.789498i	$0.710341\pi$
$972$	2.14174e13	0.769607
$973$	3.39649e13	1.21485
$974$	2.51757e13	0.896326
$975$	−2.58565e11	−0.00916324
$976$	−2.21939e13	−0.782906
$977$	4.35906e13	1.53062	0.765310	−	0.643662i	$-0.222586\pi$
$977$	4.35906e13	1.53062	0.765310	+	0.643662i	$0.222586\pi$
$978$	−1.15946e13	−0.405256
$979$	6.97728e13	2.42753
$980$	7.39101e13	2.55969
$981$	−1.87491e13	−0.646355
$982$	−6.27928e13	−2.15481
$983$	−2.19441e13	−0.749594	−0.374797	−	0.927107i	$-0.622288\pi$
$983$	−2.19441e13	−0.749594	−0.374797	+	0.927107i	$0.622288\pi$
$984$	−7.38975e11	−0.0251276
$985$	2.17722e12	0.0736951
$986$	−7.01549e13	−2.36381
$987$	3.65409e12	0.122561
$988$	1.75717e13	0.586689
$989$	4.23585e13	1.40785
$990$	−6.84070e13	−2.26330
$991$	4.48590e13	1.47747	0.738733	−	0.673998i	$-0.235424\pi$
$991$	4.48590e13	1.47747	0.738733	+	0.673998i	$0.235424\pi$
$992$	−3.69771e13	−1.21236
$993$	−1.42360e13	−0.464640
$994$	−4.64962e13	−1.51070
$995$	−3.47367e13	−1.12353
$996$	−8.04566e12	−0.259057
$997$	−3.80257e13	−1.21885	−0.609423	−	0.792845i	$-0.708599\pi$
$997$	−3.80257e13	−1.21885	−0.609423	+	0.792845i	$0.708599\pi$
$998$	−3.46794e12	−0.110658
$999$	3.61826e12	0.114936

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.10.a.b.1.16	✓	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.10.a.b.1.16	✓	76	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	197.a (trivial)

\(f(q)\)	\(=\)	\(q-31.2026 q^{2} +46.5765 q^{3} +461.602 q^{4} +1445.56 q^{5} -1453.31 q^{6} +12293.0 q^{7} +1572.55 q^{8} -17513.6 q^{9} -45105.3 q^{10} -86595.8 q^{11} +21499.8 q^{12} -40662.2 q^{13} -383573. q^{14} +67329.2 q^{15} -285408. q^{16} +408685. q^{17} +546471. q^{18} -936171. q^{19} +667274. q^{20} +572565. q^{21} +2.70201e6 q^{22} +1.81909e6 q^{23} +73243.7 q^{24} +136525. q^{25} +1.26877e6 q^{26} -1.73249e6 q^{27} +5.67447e6 q^{28} +5.50146e6 q^{29} -2.10085e6 q^{30} -4.56489e6 q^{31} +8.10032e6 q^{32} -4.03333e6 q^{33} -1.27520e7 q^{34} +1.77703e7 q^{35} -8.08433e6 q^{36} -2.08848e6 q^{37} +2.92110e7 q^{38} -1.89390e6 q^{39} +2.27321e6 q^{40} -1.00893e7 q^{41} -1.78655e7 q^{42} +2.32855e7 q^{43} -3.99728e7 q^{44} -2.53170e7 q^{45} -5.67604e7 q^{46} +6.38197e6 q^{47} -1.32933e7 q^{48} +1.10764e8 q^{49} -4.25994e6 q^{50} +1.90351e7 q^{51} -1.87698e7 q^{52} -3.41704e7 q^{53} +5.40581e7 q^{54} -1.25180e8 q^{55} +1.93313e7 q^{56} -4.36036e7 q^{57} -1.71660e8 q^{58} +8.11553e7 q^{59} +3.10793e7 q^{60} +7.77621e7 q^{61} +1.42436e8 q^{62} -2.15295e8 q^{63} -1.06622e8 q^{64} -5.87798e7 q^{65} +1.25850e8 q^{66} +2.44553e8 q^{67} +1.88650e8 q^{68} +8.47269e7 q^{69} -5.54479e8 q^{70} +1.21218e8 q^{71} -2.75410e7 q^{72} +2.68295e8 q^{73} +6.51659e7 q^{74} +6.35886e6 q^{75} -4.32139e8 q^{76} -1.06452e9 q^{77} +5.90947e7 q^{78} -1.87233e8 q^{79} -4.12575e8 q^{80} +2.64028e8 q^{81} +3.14811e8 q^{82} -3.74220e8 q^{83} +2.64297e8 q^{84} +5.90780e8 q^{85} -7.26569e8 q^{86} +2.56239e8 q^{87} -1.36176e8 q^{88} -8.05730e8 q^{89} +7.89957e8 q^{90} -4.99861e8 q^{91} +8.39697e8 q^{92} -2.12617e8 q^{93} -1.99134e8 q^{94} -1.35329e9 q^{95} +3.77284e8 q^{96} -9.14702e8 q^{97} -3.45613e9 q^{98} +1.51661e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 48 q^{2} + 890 q^{3} + 20736 q^{4} + 5171 q^{5} + 2688 q^{6} + 38986 q^{7} + 36507 q^{8} + 518318 q^{9} + 121093 q^{10} + 120464 q^{11} + 415744 q^{12} + 480131 q^{13} + 330849 q^{14} + 544874 q^{15}+ \cdots + 8731109606 q^{99}+O(q^{100}) \) 76 * q + 48 * q^2 + 890 * q^3 + 20736 * q^4 + 5171 * q^5 + 2688 * q^6 + 38986 * q^7 + 36507 * q^8 + 518318 * q^9 + 121093 * q^10 + 120464 * q^11 + 415744 * q^12 + 480131 * q^13 + 330849 * q^14 + 544874 * q^15 + 5963776 * q^16 + 942582 * q^17 + 1483945 * q^18 + 3097319 * q^19 + 3237739 * q^20 + 889076 * q^21 + 3791921 * q^22 + 5139200 * q^23 + 1999533 * q^24 + 34080519 * q^25 + 2791454 * q^26 + 24386486 * q^27 + 20891166 * q^28 + 6886818 * q^29 + 14171083 * q^30 + 28002851 * q^31 + 16857332 * q^32 + 30921422 * q^33 + 33506194 * q^34 + 16271736 * q^35 + 151430458 * q^36 + 55950976 * q^37 + 62370882 * q^38 - 11569592 * q^39 + 129854766 * q^40 + 14990859 * q^41 + 82216531 * q^42 + 169867467 * q^43 + 41872434 * q^44 + 205007649 * q^45 + 144032301 * q^46 + 78743342 * q^47 + 156250562 * q^48 + 533861890 * q^49 + 626841163 * q^50 + 477099244 * q^51 + 560784114 * q^52 + 188670216 * q^53 + 525901687 * q^54 + 298497914 * q^55 + 56575048 * q^56 + 213972590 * q^57 + 338315251 * q^58 + 208222151 * q^59 - 615921507 * q^60 - 233556134 * q^61 - 399368105 * q^62 + 329825056 * q^63 + 876517017 * q^64 - 840557006 * q^65 - 2482481592 * q^66 + 1210808414 * q^67 - 1266757099 * q^68 + 327801786 * q^69 - 546384313 * q^70 + 345300221 * q^71 - 1549481681 * q^72 + 1192286460 * q^73 - 1471133595 * q^74 + 761630676 * q^75 - 398699826 * q^76 - 101106252 * q^77 - 2609825943 * q^78 + 955627631 * q^79 + 1059617770 * q^80 + 3387041436 * q^81 + 1062705523 * q^82 + 1538917201 * q^83 + 1394513218 * q^84 + 225481100 * q^85 + 701644810 * q^86 + 1758812842 * q^87 + 3151474875 * q^88 + 855413630 * q^89 + 6070671455 * q^90 + 4652436248 * q^91 + 8082863606 * q^92 + 3462095982 * q^93 + 2660342117 * q^94 + 1036805508 * q^95 + 12370989029 * q^96 + 6393874545 * q^97 + 7510976010 * q^98 + 8731109606 * q^99

Introduction

L-functions

Modular forms

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Database

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