LMFDB - Embedded newform 197.10.a.b.1.57

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [197,10,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, 10, names="a")

//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);

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 10 $
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:	$101.462059724$
Analytic rank:	$0$
Dimension:	$76$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.57
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)

$f(q)$	$=$	\(q+23.7806 q^{2} +158.559 q^{3} +53.5170 q^{4} +2244.00 q^{5} +3770.63 q^{6} +8565.95 q^{7} -10903.0 q^{8} +5458.04 q^{9} +53363.8 q^{10} -4170.46 q^{11} +8485.61 q^{12} +100163. q^{13} +203703. q^{14} +355808. q^{15} -286681. q^{16} +137572. q^{17} +129796. q^{18} -554.482 q^{19} +120092. q^{20} +1.35821e6 q^{21} -99176.1 q^{22} -298742. q^{23} -1.72877e6 q^{24} +3.08243e6 q^{25} +2.38193e6 q^{26} -2.25550e6 q^{27} +458424. q^{28} +7.04446e6 q^{29} +8.46132e6 q^{30} -1.69791e6 q^{31} -1.23510e6 q^{32} -661266. q^{33} +3.27155e6 q^{34} +1.92220e7 q^{35} +292098. q^{36} -733666. q^{37} -13185.9 q^{38} +1.58817e7 q^{39} -2.44664e7 q^{40} +2.29376e7 q^{41} +3.22991e7 q^{42} -2.16998e7 q^{43} -223191. q^{44} +1.22479e7 q^{45} -7.10426e6 q^{46} -2.29201e7 q^{47} -4.54559e7 q^{48} +3.30219e7 q^{49} +7.33021e7 q^{50} +2.18133e7 q^{51} +5.36041e6 q^{52} -6.52649e7 q^{53} -5.36371e7 q^{54} -9.35854e6 q^{55} -9.33946e7 q^{56} -87918.3 q^{57} +1.67522e8 q^{58} +1.63111e8 q^{59} +1.90418e7 q^{60} -2.09496e8 q^{61} -4.03773e7 q^{62} +4.67533e7 q^{63} +1.17409e8 q^{64} +2.24766e8 q^{65} -1.57253e7 q^{66} +5.38355e6 q^{67} +7.36244e6 q^{68} -4.73683e7 q^{69} +4.57111e8 q^{70} +2.16257e7 q^{71} -5.95091e7 q^{72} -2.05407e8 q^{73} -1.74470e7 q^{74} +4.88748e8 q^{75} -29674.2 q^{76} -3.57240e7 q^{77} +3.77677e8 q^{78} -1.95725e8 q^{79} -6.43313e8 q^{80} -4.65061e8 q^{81} +5.45469e8 q^{82} +7.62342e8 q^{83} +7.26873e7 q^{84} +3.08712e8 q^{85} -5.16033e8 q^{86} +1.11696e9 q^{87} +4.54706e7 q^{88} +5.30222e8 q^{89} +2.91262e8 q^{90} +8.57989e8 q^{91} -1.59878e7 q^{92} -2.69219e8 q^{93} -5.45054e8 q^{94} -1.24426e6 q^{95} -1.95837e8 q^{96} +7.83842e8 q^{97} +7.85280e8 q^{98} -2.27626e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	23.7806	1.05096	0.525482	−	0.850805i	$-0.323885\pi$
$2$	23.7806	1.05096	0.525482	+	0.850805i	$0.323885\pi$
$3$	158.559	1.13018	0.565088	−	0.825031i	$-0.308842\pi$
$3$	158.559	1.13018	0.565088	+	0.825031i	$0.308842\pi$
$4$	53.5170	0.104525
$5$	2244.00	1.60568	0.802839	−	0.596195i	$-0.203322\pi$
$5$	2244.00	1.60568	0.802839	+	0.596195i	$0.203322\pi$
$6$	3770.63	1.18777
$7$	8565.95	1.34845	0.674224	−	0.738527i	$-0.264478\pi$
$7$	8565.95	1.34845	0.674224	+	0.738527i	$0.264478\pi$
$8$	−10903.0	−0.941112
$9$	5458.04	0.277297
$10$	53363.8	1.68751
$11$	−4170.46	−0.0858850	−0.0429425	−	0.999078i	$-0.513673\pi$
$11$	−4170.46	−0.0858850	−0.0429425	+	0.999078i	$0.513673\pi$
$12$	8485.61	0.118132
$13$	100163.	0.972660	0.486330	−	0.873775i	$-0.338335\pi$
$13$	100163.	0.972660	0.486330	+	0.873775i	$0.338335\pi$
$14$	203703.	1.41717
$15$	355808.	1.81470
$16$	−286681.	−1.09360
$17$	137572.	0.399494	0.199747	−	0.979848i	$-0.435988\pi$
$17$	137572.	0.399494	0.199747	+	0.979848i	$0.435988\pi$
$18$	129796.	0.291430
$19$	−554.482	−0.000976104 0	−0.000488052	−	1.00000i	$-0.500155\pi$
$19$	−554.482	−0.000976104 0	−0.000488052		1.00000i	$0.500155\pi$
$20$	120092.	0.167834
$21$	1.35821e6	1.52398
$22$	−99176.1	−0.0902620
$23$	−298742.	−0.222598	−0.111299	−	0.993787i	$-0.535501\pi$
$23$	−298742.	−0.222598	−0.111299	+	0.993787i	$0.535501\pi$
$24$	−1.72877e6	−1.06362
$25$	3.08243e6	1.57820
$26$	2.38193e6	1.02223
$27$	−2.25550e6	−0.816781
$28$	458424.	0.140947
$29$	7.04446e6	1.84951	0.924755	−	0.380562i	$-0.124269\pi$
$29$	7.04446e6	1.84951	0.924755	+	0.380562i	$0.124269\pi$
$30$	8.46132e6	1.90718
$31$	−1.69791e6	−0.330207	−0.165104	−	0.986276i	$-0.552796\pi$
$31$	−1.69791e6	−0.330207	−0.165104	+	0.986276i	$0.552796\pi$
$32$	−1.23510e6	−0.208222
$33$	−661266.	−0.0970651
$34$	3.27155e6	0.419854
$35$	1.92220e7	2.16518
$36$	292098.	0.0289846
$37$	−733666.	−0.0643563	−0.0321781	−	0.999482i	$-0.510244\pi$
$37$	−733666.	−0.0643563	−0.0321781	+	0.999482i	$0.510244\pi$
$38$	−13185.9	−0.00102585
$39$	1.58817e7	1.09928
$40$	−2.44664e7	−1.51112
$41$	2.29376e7	1.26771	0.633855	−	0.773452i	$-0.281472\pi$
$41$	2.29376e7	1.26771	0.633855	+	0.773452i	$0.281472\pi$
$42$	3.22991e7	1.60165
$43$	−2.16998e7	−0.967937	−0.483968	−	0.875085i	$-0.660805\pi$
$43$	−2.16998e7	−0.967937	−0.483968	+	0.875085i	$0.660805\pi$
$44$	−223191.	−0.00897716
$45$	1.22479e7	0.445251
$46$	−7.10426e6	−0.233942
$47$	−2.29201e7	−0.685135	−0.342568	−	0.939493i	$-0.611297\pi$
$47$	−2.29201e7	−0.685135	−0.342568	+	0.939493i	$0.611297\pi$
$48$	−4.54559e7	−1.23596
$49$	3.30219e7	0.818313
$50$	7.33021e7	1.65864
$51$	2.18133e7	0.451498
$52$	5.36041e6	0.101668
$53$	−6.52649e7	−1.13616	−0.568078	−	0.822975i	$-0.692313\pi$
$53$	−6.52649e7	−1.13616	−0.568078	+	0.822975i	$0.692313\pi$
$54$	−5.36371e7	−0.858407
$55$	−9.35854e6	−0.137904
$56$	−9.33946e7	−1.26904
$57$	−87918.3	−0.00110317
$58$	1.67522e8	1.94377
$59$	1.63111e8	1.75246	0.876232	−	0.481889i	$-0.160049\pi$
$59$	1.63111e8	1.75246	0.876232	+	0.481889i	$0.160049\pi$
$60$	1.90418e7	0.189682
$61$	−2.09496e8	−1.93727	−0.968636	−	0.248485i	$-0.920067\pi$
$61$	−2.09496e8	−1.93727	−0.968636	+	0.248485i	$0.920067\pi$
$62$	−4.03773e7	−0.347036
$63$	4.67533e7	0.373921
$64$	1.17409e8	0.874766
$65$	2.24766e8	1.56178
$66$	−1.57253e7	−0.102012
$67$	5.38355e6	0.0326387	0.0163193	−	0.999867i	$-0.494805\pi$
$67$	5.38355e6	0.0326387	0.0163193	+	0.999867i	$0.494805\pi$
$68$	7.36244e6	0.0417572
$69$	−4.73683e7	−0.251574
$70$	4.57111e8	2.27552
$71$	2.16257e7	0.100997	0.0504983	−	0.998724i	$-0.483919\pi$
$71$	2.16257e7	0.100997	0.0504983	+	0.998724i	$0.483919\pi$
$72$	−5.95091e7	−0.260968
$73$	−2.05407e8	−0.846567	−0.423284	−	0.905997i	$-0.639123\pi$
$73$	−2.05407e8	−0.846567	−0.423284	+	0.905997i	$0.639123\pi$
$74$	−1.74470e7	−0.0676361
$75$	4.88748e8	1.78365
$76$	−29674.2	−0.000102028 0
$77$	−3.57240e7	−0.115811
$78$	3.77677e8	1.15530
$79$	−1.95725e8	−0.565358	−0.282679	−	0.959215i	$-0.591223\pi$
$79$	−1.95725e8	−0.565358	−0.282679	+	0.959215i	$0.591223\pi$
$80$	−6.43313e8	−1.75597
$81$	−4.65061e8	−1.20040
$82$	5.45469e8	1.33232
$83$	7.62342e8	1.76319	0.881594	−	0.472008i	$-0.156471\pi$
$83$	7.62342e8	1.76319	0.881594	+	0.472008i	$0.156471\pi$
$84$	7.26873e7	0.159295
$85$	3.08712e8	0.641459
$86$	−5.16033e8	−1.01727
$87$	1.11696e9	2.09027
$88$	4.54706e7	0.0808274
$89$	5.30222e8	0.895782	0.447891	−	0.894088i	$-0.352175\pi$
$89$	5.30222e8	0.895782	0.447891	+	0.894088i	$0.352175\pi$
$90$	2.91262e8	0.467942
$91$	8.57989e8	1.31158
$92$	−1.59878e7	−0.0232671
$93$	−2.69219e8	−0.373192
$94$	−5.45054e8	−0.720053
$95$	−1.24426e6	−0.00156731
$96$	−1.95837e8	−0.235328
$97$	7.83842e8	0.898992	0.449496	−	0.893282i	$-0.351604\pi$
$97$	7.83842e8	0.898992	0.449496	+	0.893282i	$0.351604\pi$
$98$	7.85280e8	0.860017
$99$	−2.27626e7	−0.0238157
$100$	1.64962e8	0.164962
$101$	−2.89399e7	−0.0276726	−0.0138363	−	0.999904i	$-0.504404\pi$
$101$	−2.89399e7	−0.0276726	−0.0138363	+	0.999904i	$0.504404\pi$
$102$	5.18734e8	0.474508
$103$	−1.14914e9	−1.00602	−0.503010	−	0.864281i	$-0.667774\pi$
$103$	−1.14914e9	−1.00602	−0.503010	+	0.864281i	$0.667774\pi$
$104$	−1.09207e9	−0.915381
$105$	3.04783e9	2.44703
$106$	−1.55204e9	−1.19406
$107$	−1.07154e9	−0.790281	−0.395140	−	0.918621i	$-0.629304\pi$
$107$	−1.07154e9	−0.790281	−0.395140	+	0.918621i	$0.629304\pi$
$108$	−1.20707e8	−0.0853743
$109$	−2.09621e9	−1.42238	−0.711191	−	0.702999i	$-0.751844\pi$
$109$	−2.09621e9	−1.42238	−0.711191	+	0.702999i	$0.751844\pi$
$110$	−2.22552e8	−0.144932
$111$	−1.16330e8	−0.0727339
$112$	−2.45569e9	−1.47466
$113$	−1.30068e9	−0.750440	−0.375220	−	0.926936i	$-0.622433\pi$
$113$	−1.30068e9	−0.750440	−0.375220	+	0.926936i	$0.622433\pi$
$114$	−2.09075e6	−0.00115939
$115$	−6.70378e8	−0.357420
$116$	3.76998e8	0.193321
$117$	5.46692e8	0.269716
$118$	3.87888e9	1.84178
$119$	1.17843e9	0.538697
$120$	−3.87937e9	−1.70783
$121$	−2.34055e9	−0.992624
$122$	−4.98193e9	−2.03600
$123$	3.63696e9	1.43273
$124$	−9.08669e7	−0.0345150
$125$	2.53417e9	0.928412
$126$	1.11182e9	0.392978
$127$	4.96308e9	1.69291	0.846457	−	0.532458i	$-0.178731\pi$
$127$	4.96308e9	1.69291	0.846457	+	0.532458i	$0.178731\pi$
$128$	3.42443e9	1.12757
$129$	−3.44070e9	−1.09394
$130$	5.34506e9	1.64137
$131$	4.96424e9	1.47276	0.736380	−	0.676568i	$-0.236534\pi$
$131$	4.96424e9	1.47276	0.736380	+	0.676568i	$0.236534\pi$
$132$	−3.53889e7	−0.0101458
$133$	−4.74967e6	−0.00131623
$134$	1.28024e8	0.0343021
$135$	−5.06135e9	−1.31149
$136$	−1.49995e9	−0.375968
$137$	8.16975e8	0.198137	0.0990687	−	0.995081i	$-0.468414\pi$
$137$	8.16975e8	0.198137	0.0990687	+	0.995081i	$0.468414\pi$
$138$	−1.12645e9	−0.264396
$139$	8.12069e9	1.84513	0.922563	−	0.385846i	$-0.126090\pi$
$139$	8.12069e9	1.84513	0.922563	+	0.385846i	$0.126090\pi$
$140$	1.02871e9	0.226316
$141$	−3.63420e9	−0.774323
$142$	5.14271e8	0.106144
$143$	−4.17725e8	−0.0835369
$144$	−1.56472e9	−0.303252
$145$	1.58078e10	2.96972
$146$	−4.88469e9	−0.889712
$147$	5.23592e9	0.924837
$148$	−3.92636e7	−0.00672686
$149$	−7.89285e9	−1.31189	−0.655943	−	0.754811i	$-0.727729\pi$
$149$	−7.89285e9	−1.31189	−0.655943	+	0.754811i	$0.727729\pi$
$150$	1.16227e10	1.87455
$151$	6.23547e9	0.976053	0.488026	−	0.872829i	$-0.337717\pi$
$151$	6.23547e9	0.976053	0.488026	+	0.872829i	$0.337717\pi$
$152$	6.04552e6	0.000918623 0
$153$	7.50874e8	0.110779
$154$	−8.49538e8	−0.121714
$155$	−3.81011e9	−0.530207
$156$	8.49942e8	0.114902
$157$	6.29986e9	0.827527	0.413764	−	0.910384i	$-0.364214\pi$
$157$	6.29986e9	0.827527	0.413764	+	0.910384i	$0.364214\pi$
$158$	−4.65445e9	−0.594171
$159$	−1.03483e10	−1.28406
$160$	−2.77157e9	−0.334338
$161$	−2.55901e9	−0.300161
$162$	−1.10594e10	−1.26158
$163$	−1.43520e10	−1.59246	−0.796229	−	0.604996i	$-0.793175\pi$
$163$	−1.43520e10	−1.59246	−0.796229	+	0.604996i	$0.793175\pi$
$164$	1.22755e9	0.132508
$165$	−1.48388e9	−0.155855
$166$	1.81290e10	1.85305
$167$	−1.01542e10	−1.01023	−0.505115	−	0.863052i	$-0.668550\pi$
$167$	−1.01542e10	−1.01023	−0.505115	+	0.863052i	$0.668550\pi$
$168$	−1.48086e10	−1.43424
$169$	−5.71933e8	−0.0539330
$170$	7.34136e9	0.674150
$171$	−3.02639e6	−0.000270671 0
$172$	−1.16131e9	−0.101174
$173$	1.78773e9	0.151738	0.0758691	−	0.997118i	$-0.475827\pi$
$173$	1.78773e9	0.151738	0.0758691	+	0.997118i	$0.475827\pi$
$174$	2.65621e10	2.19680
$175$	2.64040e10	2.12813
$176$	1.19559e9	0.0939238
$177$	2.58628e10	1.98059
$178$	1.26090e10	0.941435
$179$	−1.01569e10	−0.739476	−0.369738	−	0.929136i	$-0.620553\pi$
$179$	−1.01569e10	−0.739476	−0.369738	+	0.929136i	$0.620553\pi$
$180$	6.55469e8	0.0465400
$181$	2.32029e8	0.0160690	0.00803450	−	0.999968i	$-0.497443\pi$
$181$	2.32029e8	0.0160690	0.00803450	+	0.999968i	$0.497443\pi$
$182$	2.04035e10	1.37842
$183$	−3.32175e10	−2.18946
$184$	3.25718e9	0.209489
$185$	−1.64635e9	−0.103336
$186$	−6.40219e9	−0.392212
$187$	−5.73739e8	−0.0343105
$188$	−1.22662e9	−0.0716140
$189$	−1.93205e10	−1.10139
$190$	−2.95893e7	−0.00164719
$191$	−7.95227e9	−0.432356	−0.216178	−	0.976354i	$-0.569359\pi$
$191$	−7.95227e9	−0.432356	−0.216178	+	0.976354i	$0.569359\pi$
$192$	1.86163e10	0.988639
$193$	5.32743e9	0.276382	0.138191	−	0.990406i	$-0.455871\pi$
$193$	5.32743e9	0.276382	0.138191	+	0.990406i	$0.455871\pi$
$194$	1.86402e10	0.944809
$195$	3.56387e10	1.76509
$196$	1.76723e9	0.0855344
$197$	1.50614e9	0.0712470
$197$	1.50614e9	0.0712470
$198$	−5.41308e8	−0.0250294
$199$	−1.42328e10	−0.643355	−0.321677	−	0.946849i	$-0.604247\pi$
$199$	−1.42328e10	−0.643355	−0.321677	+	0.946849i	$0.604247\pi$
$200$	−3.36078e10	−1.48527
$201$	8.53612e8	0.0368874
$202$	−6.88207e8	−0.0290829
$203$	6.03425e10	2.49397
$204$	1.16738e9	0.0471930
$205$	5.14720e10	2.03553
$206$	−2.73273e10	−1.05729
$207$	−1.63055e9	−0.0617257
$208$	−2.87147e10	−1.06370
$209$	2.31245e6	8.38327e−5 0
$210$	7.24793e10	2.57174
$211$	−3.55505e9	−0.123474	−0.0617369	−	0.998092i	$-0.519664\pi$
$211$	−3.55505e9	−0.123474	−0.0617369	+	0.998092i	$0.519664\pi$
$212$	−3.49278e9	−0.118757
$213$	3.42895e9	0.114144
$214$	−2.54819e10	−0.830557
$215$	−4.86944e10	−1.55420
$216$	2.45917e10	0.768682
$217$	−1.45442e10	−0.445267
$218$	−4.98492e10	−1.49487
$219$	−3.25691e10	−0.956770
$220$	−5.00841e8	−0.0144144
$221$	1.37796e10	0.388571
$222$	−2.76639e9	−0.0764407
$223$	5.54414e9	0.150128	0.0750641	−	0.997179i	$-0.476084\pi$
$223$	5.54414e9	0.150128	0.0750641	+	0.997179i	$0.476084\pi$
$224$	−1.05798e10	−0.280777
$225$	1.68240e10	0.437632
$226$	−3.09309e10	−0.788686
$227$	−2.25076e10	−0.562617	−0.281309	−	0.959617i	$-0.590768\pi$
$227$	−2.25076e10	−0.562617	−0.281309	+	0.959617i	$0.590768\pi$
$228$	−4.70512e6	−0.000115309 0
$229$	2.75097e10	0.661038	0.330519	−	0.943799i	$-0.392776\pi$
$229$	2.75097e10	0.661038	0.330519	+	0.943799i	$0.392776\pi$
$230$	−1.59420e10	−0.375636
$231$	−5.66437e9	−0.130887
$232$	−7.68058e10	−1.74060
$233$	3.97314e10	0.883146	0.441573	−	0.897225i	$-0.354421\pi$
$233$	3.97314e10	0.883146	0.441573	+	0.897225i	$0.354421\pi$
$234$	1.30007e10	0.283462
$235$	−5.14328e10	−1.10011
$236$	8.72921e9	0.183177
$237$	−3.10340e10	−0.638954
$238$	2.80239e10	0.566151
$239$	5.57823e10	1.10587	0.552937	−	0.833223i	$-0.313507\pi$
$239$	5.57823e10	1.10587	0.552937	+	0.833223i	$0.313507\pi$
$240$	−1.02003e11	−1.98456
$241$	−4.89201e10	−0.934137	−0.467068	−	0.884221i	$-0.654690\pi$
$241$	−4.89201e10	−0.934137	−0.467068	+	0.884221i	$0.654690\pi$
$242$	−5.56598e10	−1.04321
$243$	−2.93447e10	−0.539886
$244$	−1.12116e10	−0.202494
$245$	7.41012e10	1.31395
$246$	8.64892e10	1.50575
$247$	−5.55384e7	−0.000949418 0
$248$	1.85123e10	0.310762
$249$	1.20876e11	1.99271
$250$	6.02641e10	0.975727
$251$	−1.94889e9	−0.0309925	−0.0154962	−	0.999880i	$-0.504933\pi$
$251$	−1.94889e9	−0.0309925	−0.0154962	+	0.999880i	$0.504933\pi$
$252$	2.50210e9	0.0390842
$253$	1.24589e9	0.0191178
$254$	1.18025e11	1.77919
$255$	4.89492e10	0.724961
$256$	2.13216e10	0.310269
$257$	−1.79219e10	−0.256262	−0.128131	−	0.991757i	$-0.540898\pi$
$257$	−1.79219e10	−0.256262	−0.128131	+	0.991757i	$0.540898\pi$
$258$	−8.18219e10	−1.14969
$259$	−6.28455e9	−0.0867811
$260$	1.20288e10	0.163246
$261$	3.84490e10	0.512865
$262$	1.18053e11	1.54782
$263$	2.63408e10	0.339490	0.169745	−	0.985488i	$-0.445706\pi$
$263$	2.63408e10	0.339490	0.169745	+	0.985488i	$0.445706\pi$
$264$	7.20978e9	0.0913491
$265$	−1.46455e11	−1.82430
$266$	−1.12950e8	−0.00138331
$267$	8.40716e10	1.01239
$268$	2.88112e8	0.00341157
$269$	−9.24297e10	−1.07628	−0.538141	−	0.842855i	$-0.680873\pi$
$269$	−9.24297e10	−1.07628	−0.538141	+	0.842855i	$0.680873\pi$
$270$	−1.20362e11	−1.37833
$271$	−1.51011e11	−1.70077	−0.850387	−	0.526158i	$-0.823632\pi$
$271$	−1.51011e11	−1.70077	−0.850387	+	0.526158i	$0.823632\pi$
$272$	−3.94392e10	−0.436886
$273$	1.36042e11	1.48232
$274$	1.94282e10	0.208235
$275$	−1.28552e10	−0.135544
$276$	−2.53501e9	−0.0262959
$277$	−1.30060e11	−1.32735	−0.663675	−	0.748021i	$-0.731004\pi$
$277$	−1.30060e11	−1.32735	−0.663675	+	0.748021i	$0.731004\pi$
$278$	1.93115e11	1.93916
$279$	−9.26726e9	−0.0915656
$280$	−2.09578e11	−2.03767
$281$	1.11447e10	0.106633	0.0533163	−	0.998578i	$-0.483021\pi$
$281$	1.11447e10	0.106633	0.0533163	+	0.998578i	$0.483021\pi$
$282$	−8.64234e10	−0.813786
$283$	−5.98959e10	−0.555084	−0.277542	−	0.960714i	$-0.589520\pi$
$283$	−5.98959e10	−0.555084	−0.277542	+	0.960714i	$0.589520\pi$
$284$	1.15734e9	0.0105567
$285$	−1.97289e8	−0.00177134
$286$	−9.93375e9	−0.0877942
$287$	1.96482e11	1.70944
$288$	−6.74123e9	−0.0577395
$289$	−9.96618e10	−0.840405
$290$	3.75919e11	3.12107
$291$	1.24285e11	1.01602
$292$	−1.09927e10	−0.0884878
$293$	5.85554e9	0.0464154	0.0232077	−	0.999731i	$-0.492612\pi$
$293$	5.85554e9	0.0464154	0.0232077	+	0.999731i	$0.492612\pi$
$294$	1.24513e11	0.971971
$295$	3.66022e11	2.81389
$296$	7.99917e9	0.0605664
$297$	9.40648e9	0.0701492
$298$	−1.87697e11	−1.37874
$299$	−2.99228e10	−0.216512
$300$	2.61563e10	0.186437
$301$	−1.85879e11	−1.30521
$302$	1.48283e11	1.02580
$303$	−4.58868e9	−0.0312749
$304$	1.58959e8	0.00106747
$305$	−4.70109e11	−3.11064
$306$	1.78562e10	0.116424
$307$	−4.59056e10	−0.294946	−0.147473	−	0.989066i	$-0.547114\pi$
$307$	−4.59056e10	−0.294946	−0.147473	+	0.989066i	$0.547114\pi$
$308$	−1.91184e9	−0.0121052
$309$	−1.82207e11	−1.13698
$310$	−9.06068e10	−0.557228
$311$	−2.23914e11	−1.35725	−0.678626	−	0.734484i	$-0.737424\pi$
$311$	−2.23914e11	−1.35725	−0.678626	+	0.734484i	$0.737424\pi$
$312$	−1.73158e11	−1.03454
$313$	−3.12792e11	−1.84207	−0.921036	−	0.389477i	$-0.872656\pi$
$313$	−3.12792e11	−1.84207	−0.921036	+	0.389477i	$0.872656\pi$
$314$	1.49814e11	0.869701
$315$	1.04915e11	0.600397
$316$	−1.04746e10	−0.0590943
$317$	−2.66335e11	−1.48136	−0.740682	−	0.671856i	$-0.765497\pi$
$317$	−2.66335e11	−1.48136	−0.740682	+	0.671856i	$0.765497\pi$
$318$	−2.46090e11	−1.34950
$319$	−2.93787e10	−0.158845
$320$	2.63466e11	1.40459
$321$	−1.69903e11	−0.893156
$322$	−6.08547e10	−0.315459
$323$	−7.62812e7	−0.000389948 0
$324$	−2.48887e10	−0.125473
$325$	3.08745e11	1.53506
$326$	−3.41299e11	−1.67362
$327$	−3.32374e11	−1.60754
$328$	−2.50088e11	−1.19306
$329$	−1.96333e11	−0.923870
$330$	−3.52876e10	−0.163798
$331$	4.11103e10	0.188246	0.0941228	−	0.995561i	$-0.469995\pi$
$331$	4.11103e10	0.188246	0.0941228	+	0.995561i	$0.469995\pi$
$332$	4.07983e10	0.184298
$333$	−4.00438e9	−0.0178458
$334$	−2.41472e11	−1.06171
$335$	1.20807e10	0.0524072
$336$	−3.89373e11	−1.66663
$337$	1.24733e11	0.526802	0.263401	−	0.964686i	$-0.415156\pi$
$337$	1.24733e11	0.526802	0.263401	+	0.964686i	$0.415156\pi$
$338$	−1.36009e10	−0.0566817
$339$	−2.06234e11	−0.848130
$340$	1.65213e10	0.0670487
$341$	7.08106e9	0.0283598
$342$	−7.19693e7	−0.000284466 0
$343$	−6.28032e10	−0.244996
$344$	2.36593e11	0.910937
$345$	−1.06295e11	−0.403948
$346$	4.25134e10	0.159471
$347$	−2.80347e11	−1.03804	−0.519019	−	0.854763i	$-0.673703\pi$
$347$	−2.80347e11	−1.03804	−0.519019	+	0.854763i	$0.673703\pi$
$348$	5.97766e10	0.218486
$349$	4.37696e11	1.57927	0.789637	−	0.613574i	$-0.210269\pi$
$349$	4.37696e11	1.57927	0.789637	+	0.613574i	$0.210269\pi$
$350$	6.27902e11	2.23659
$351$	−2.25917e11	−0.794450
$352$	5.15094e9	0.0178832
$353$	2.17796e11	0.746560	0.373280	−	0.927719i	$-0.378233\pi$
$353$	2.17796e11	0.746560	0.373280	+	0.927719i	$0.378233\pi$
$354$	6.15032e11	2.08153
$355$	4.85281e10	0.162168
$356$	2.83759e10	0.0936320
$357$	1.86852e11	0.608822
$358$	−2.41538e11	−0.777163
$359$	2.17952e11	0.692526	0.346263	−	0.938137i	$-0.387450\pi$
$359$	2.17952e11	0.692526	0.346263	+	0.938137i	$0.387450\pi$
$360$	−1.33539e11	−0.419030
$361$	−3.22687e11	−0.999999
$362$	5.51779e9	0.0168879
$363$	−3.71117e11	−1.12184
$364$	4.59170e10	0.137094
$365$	−4.60933e11	−1.35932
$366$	−7.89931e11	−2.30104
$367$	1.91047e11	0.549722	0.274861	−	0.961484i	$-0.411368\pi$
$367$	1.91047e11	0.549722	0.274861	+	0.961484i	$0.411368\pi$
$368$	8.56435e10	0.243433
$369$	1.25194e11	0.351533
$370$	−3.91512e10	−0.108602
$371$	−5.59055e11	−1.53205
$372$	−1.44078e10	−0.0390081
$373$	−2.81096e11	−0.751908	−0.375954	−	0.926638i	$-0.622685\pi$
$373$	−2.81096e11	−0.751908	−0.375954	+	0.926638i	$0.622685\pi$
$374$	−1.36439e10	−0.0360591
$375$	4.01816e11	1.04927
$376$	2.49898e11	0.644789
$377$	7.05592e11	1.79894
$378$	−4.59453e11	−1.15752
$379$	−5.38419e11	−1.34043	−0.670215	−	0.742167i	$-0.733798\pi$
$379$	−5.38419e11	−1.34043	−0.670215	+	0.742167i	$0.733798\pi$
$380$	−6.65891e7	−0.000163824 0
$381$	7.86943e11	1.91329
$382$	−1.89110e11	−0.454390
$383$	−1.72797e11	−0.410338	−0.205169	−	0.978727i	$-0.565774\pi$
$383$	−1.72797e11	−0.410338	−0.205169	+	0.978727i	$0.565774\pi$
$384$	5.42975e11	1.27435
$385$	−8.01648e10	−0.185956
$386$	1.26690e11	0.290468
$387$	−1.18438e11	−0.268406
$388$	4.19489e10	0.0939675
$389$	−2.34366e11	−0.518945	−0.259472	−	0.965751i	$-0.583549\pi$
$389$	−2.34366e11	−0.518945	−0.259472	+	0.965751i	$0.583549\pi$
$390$	8.47509e11	1.85504
$391$	−4.10985e10	−0.0889264
$392$	−3.60038e11	−0.770124
$393$	7.87126e11	1.66448
$394$	3.58169e10	0.0748781
$395$	−4.39207e11	−0.907784
$396$	−1.21818e9	−0.00248934
$397$	4.12727e11	0.833883	0.416941	−	0.908933i	$-0.363102\pi$
$397$	4.12727e11	0.833883	0.416941	+	0.908933i	$0.363102\pi$
$398$	−3.38464e11	−0.676143
$399$	−7.53103e8	−0.00148757
$400$	−8.83673e11	−1.72592
$401$	1.09972e11	0.212389	0.106194	−	0.994345i	$-0.466133\pi$
$401$	1.09972e11	0.212389	0.106194	+	0.994345i	$0.466133\pi$
$402$	2.02994e10	0.0387674
$403$	−1.70067e11	−0.321179
$404$	−1.54877e9	−0.00289249
$405$	−1.04360e12	−1.92746
$406$	1.43498e12	2.62107
$407$	3.05973e9	0.00552724
$408$	−2.37831e11	−0.424910
$409$	−7.11319e11	−1.25693	−0.628463	−	0.777840i	$-0.716316\pi$
$409$	−7.11319e11	−1.25693	−0.628463	+	0.777840i	$0.716316\pi$
$410$	1.22403e12	2.13927
$411$	1.29539e11	0.223930
$412$	−6.14987e10	−0.105155
$413$	1.39720e12	2.36311
$414$	−3.87753e10	−0.0648715
$415$	1.71070e12	2.83111
$416$	−1.23711e11	−0.202530
$417$	1.28761e12	2.08532
$418$	5.49914e7	8.81052e−5 0
$419$	−2.09162e9	−0.00331527	−0.00165764	−	0.999999i	$-0.500528\pi$
$419$	−2.09162e9	−0.00331527	−0.00165764	+	0.999999i	$0.500528\pi$
$420$	1.63111e11	0.255777
$421$	−1.05011e12	−1.62917	−0.814584	−	0.580046i	$-0.803034\pi$
$421$	−1.05011e12	−1.62917	−0.814584	+	0.580046i	$0.803034\pi$
$422$	−8.45412e10	−0.129766
$423$	−1.25099e11	−0.189986
$424$	7.11583e11	1.06925
$425$	4.24056e11	0.630483
$426$	8.15425e10	0.119961
$427$	−1.79453e12	−2.61231
$428$	−5.73456e10	−0.0826044
$429$	−6.62342e10	−0.0944114
$430$	−1.15798e12	−1.63340
$431$	−5.40212e11	−0.754079	−0.377039	−	0.926197i	$-0.623058\pi$
$431$	−5.40212e11	−0.754079	−0.377039	+	0.926197i	$0.623058\pi$
$432$	6.46608e11	0.893232
$433$	4.53104e11	0.619445	0.309722	−	0.950827i	$-0.399764\pi$
$433$	4.53104e11	0.619445	0.309722	+	0.950827i	$0.399764\pi$
$434$	−3.45870e11	−0.467960
$435$	2.50647e12	3.35631
$436$	−1.12183e11	−0.148675
$437$	1.65647e8	0.000217279 0
$438$	−7.74513e11	−1.00553
$439$	7.34930e11	0.944399	0.472200	−	0.881492i	$-0.343460\pi$
$439$	7.34930e11	0.944399	0.472200	+	0.881492i	$0.343460\pi$
$440$	1.02036e11	0.129783
$441$	1.80235e11	0.226916
$442$	3.27687e11	0.408375
$443$	7.37000e11	0.909181	0.454591	−	0.890700i	$-0.349786\pi$
$443$	7.37000e11	0.909181	0.454591	+	0.890700i	$0.349786\pi$
$444$	−6.22561e9	−0.00760254
$445$	1.18982e12	1.43834
$446$	1.31843e11	0.157779
$447$	−1.25149e12	−1.48266
$448$	1.00572e12	1.17958
$449$	−3.83736e11	−0.445578	−0.222789	−	0.974867i	$-0.571516\pi$
$449$	−3.83736e11	−0.445578	−0.222789	+	0.974867i	$0.571516\pi$
$450$	4.00086e11	0.459936
$451$	−9.56603e10	−0.108877
$452$	−6.96083e10	−0.0784401
$453$	9.88692e11	1.10311
$454$	−5.35244e11	−0.591290
$455$	1.92533e12	2.10598
$456$	9.58573e8	0.00103821
$457$	5.41880e11	0.581140	0.290570	−	0.956854i	$-0.406155\pi$
$457$	5.41880e11	0.581140	0.290570	+	0.956854i	$0.406155\pi$
$458$	6.54198e11	0.694727
$459$	−3.10294e11	−0.326299
$460$	−3.58766e10	−0.0373595
$461$	−1.84902e11	−0.190672	−0.0953359	−	0.995445i	$-0.530393\pi$
$461$	−1.84902e11	−0.190672	−0.0953359	+	0.995445i	$0.530393\pi$
$462$	−1.34702e11	−0.137558
$463$	8.43885e11	0.853432	0.426716	−	0.904386i	$-0.359670\pi$
$463$	8.43885e11	0.853432	0.426716	+	0.904386i	$0.359670\pi$
$464$	−2.01951e12	−2.02262
$465$	−6.04129e11	−0.599227
$466$	9.44838e11	0.928155
$467$	2.67178e11	0.259941	0.129971	−	0.991518i	$-0.458512\pi$
$467$	2.67178e11	0.259941	0.129971	+	0.991518i	$0.458512\pi$
$468$	2.92573e10	0.0281922
$469$	4.61152e10	0.0440116
$470$	−1.22310e12	−1.15617
$471$	9.98901e11	0.935251
$472$	−1.77840e12	−1.64926
$473$	9.04981e10	0.0831312
$474$	−7.38006e11	−0.671518
$475$	−1.70915e9	−0.00154049
$476$	6.30663e10	0.0563075
$477$	−3.56218e11	−0.315053
$478$	1.32654e12	1.16223
$479$	2.90355e11	0.252011	0.126006	−	0.992030i	$-0.459784\pi$
$479$	2.90355e11	0.252011	0.126006	+	0.992030i	$0.459784\pi$
$480$	−4.39458e11	−0.377861
$481$	−7.34860e10	−0.0625968
$482$	−1.16335e12	−0.981744
$483$	−4.05754e11	−0.339235
$484$	−1.25259e11	−0.103754
$485$	1.75895e12	1.44349
$486$	−6.97836e11	−0.567401
$487$	−8.26528e11	−0.665851	−0.332926	−	0.942953i	$-0.608036\pi$
$487$	−8.26528e11	−0.665851	−0.332926	+	0.942953i	$0.608036\pi$
$488$	2.28413e12	1.82319
$489$	−2.27564e12	−1.79976
$490$	1.76217e12	1.38091
$491$	2.30239e12	1.78777	0.893887	−	0.448292i	$-0.147967\pi$
$491$	2.30239e12	1.78777	0.893887	+	0.448292i	$0.147967\pi$
$492$	1.94639e11	0.149757
$493$	9.69121e11	0.738868
$494$	−1.32074e9	−0.000997804 0
$495$	−5.10793e10	−0.0382403
$496$	4.86757e11	0.361115
$497$	1.85244e11	0.136189
$498$	2.87451e12	2.09427
$499$	1.71934e12	1.24139	0.620696	−	0.784051i	$-0.286850\pi$
$499$	1.71934e12	1.24139	0.620696	+	0.784051i	$0.286850\pi$
$500$	1.35621e11	0.0970426
$501$	−1.61004e12	−1.14174
$502$	−4.63458e10	−0.0325720
$503$	1.78429e12	1.24282	0.621411	−	0.783485i	$-0.286560\pi$
$503$	1.78429e12	1.24282	0.621411	+	0.783485i	$0.286560\pi$
$504$	−5.09752e11	−0.351902
$505$	−6.49412e10	−0.0444333
$506$	2.96280e10	0.0200921
$507$	−9.06852e10	−0.0609538
$508$	2.65609e11	0.176952
$509$	−2.01708e12	−1.33196	−0.665982	−	0.745968i	$-0.731987\pi$
$509$	−2.01708e12	−1.33196	−0.665982	+	0.745968i	$0.731987\pi$
$510$	1.16404e12	0.761908
$511$	−1.75950e12	−1.14155
$512$	−1.24627e12	−0.801487
$513$	1.25063e9	0.000797264 0
$514$	−4.26193e11	−0.269322
$515$	−2.57868e12	−1.61535
$516$	−1.84136e11	−0.114344
$517$	9.55875e10	0.0588428
$518$	−1.49450e11	−0.0912038
$519$	2.83462e11	0.171491
$520$	−2.45062e12	−1.46981
$521$	4.31991e11	0.256865	0.128432	−	0.991718i	$-0.459005\pi$
$521$	4.31991e11	0.256865	0.128432	+	0.991718i	$0.459005\pi$
$522$	9.14340e11	0.539002
$523$	1.53890e12	0.899398	0.449699	−	0.893180i	$-0.351531\pi$
$523$	1.53890e12	0.899398	0.449699	+	0.893180i	$0.351531\pi$
$524$	2.65671e11	0.153941
$525$	4.18659e12	2.40516
$526$	6.26399e11	0.356792
$527$	−2.33585e11	−0.131916
$528$	1.89572e11	0.106150
$529$	−1.71191e12	−0.950450
$530$	−3.48278e12	−1.91728
$531$	8.90267e11	0.485954
$532$	−2.54188e8	−0.000137579 0
$533$	2.29749e12	1.23305
$534$	1.99927e12	1.06399
$535$	−2.40454e12	−1.26894
$536$	−5.86969e10	−0.0307166
$537$	−1.61048e12	−0.835738
$538$	−2.19803e12	−1.13113
$539$	−1.37717e11	−0.0702808
$540$	−2.70868e11	−0.137084
$541$	1.72086e12	0.863691	0.431846	−	0.901948i	$-0.357863\pi$
$541$	1.72086e12	0.863691	0.431846	+	0.901948i	$0.357863\pi$
$542$	−3.59113e12	−1.78745
$543$	3.67904e10	0.0181608
$544$	−1.69915e11	−0.0831836
$545$	−4.70391e12	−2.28389
$546$	3.23516e12	1.55786
$547$	2.82751e12	1.35040	0.675199	−	0.737636i	$-0.264058\pi$
$547$	2.82751e12	1.35040	0.675199	+	0.737636i	$0.264058\pi$
$548$	4.37221e10	0.0207104
$549$	−1.14344e12	−0.537200
$550$	−3.05704e11	−0.142452
$551$	−3.90603e9	−0.00180532
$552$	5.16456e11	0.236760
$553$	−1.67657e12	−0.762356
$554$	−3.09291e12	−1.39500
$555$	−2.61044e11	−0.116787
$556$	4.34595e11	0.192863
$557$	6.12723e11	0.269722	0.134861	−	0.990865i	$-0.456941\pi$
$557$	6.12723e11	0.269722	0.134861	+	0.990865i	$0.456941\pi$
$558$	−2.20381e11	−0.0962321
$559$	−2.17351e12	−0.941473
$560$	−5.51058e12	−2.36784
$561$	−9.09717e10	−0.0387769
$562$	2.65027e11	0.112067
$563$	−1.16674e12	−0.489427	−0.244714	−	0.969595i	$-0.578694\pi$
$563$	−1.16674e12	−0.489427	−0.244714	+	0.969595i	$0.578694\pi$
$564$	−1.94491e11	−0.0809364
$565$	−2.91872e12	−1.20497
$566$	−1.42436e12	−0.583373
$567$	−3.98369e12	−1.61868
$568$	−2.35785e11	−0.0950491
$569$	3.24089e12	1.29616	0.648080	−	0.761573i	$-0.275572\pi$
$569$	3.24089e12	1.29616	0.648080	+	0.761573i	$0.275572\pi$
$570$	−4.69165e9	−0.00186161
$571$	−1.24221e12	−0.489025	−0.244512	−	0.969646i	$-0.578628\pi$
$571$	−1.24221e12	−0.489025	−0.244512	+	0.969646i	$0.578628\pi$
$572$	−2.23554e10	−0.00873172
$573$	−1.26091e12	−0.488638
$574$	4.67246e12	1.79656
$575$	−9.20851e11	−0.351305
$576$	6.40824e11	0.242570
$577$	−4.32191e12	−1.62325	−0.811624	−	0.584181i	$-0.801416\pi$
$577$	−4.32191e12	−1.62325	−0.811624	+	0.584181i	$0.801416\pi$
$578$	−2.37002e12	−0.883235
$579$	8.44714e11	0.312361
$580$	8.45986e11	0.310411
$581$	6.53019e12	2.37757
$582$	2.95558e12	1.06780
$583$	2.72185e11	0.0975788
$584$	2.23955e12	0.796714
$585$	1.22678e12	0.433077
$586$	1.39248e11	0.0487810
$587$	−1.30220e12	−0.452696	−0.226348	−	0.974047i	$-0.572679\pi$
$587$	−1.30220e12	−0.452696	−0.226348	+	0.974047i	$0.572679\pi$
$588$	2.80211e11	0.0966690
$589$	9.41460e8	0.000322317 0
$590$	8.70422e12	2.95730
$591$	2.38812e11	0.0805217
$592$	2.10328e11	0.0703800
$593$	1.44029e12	0.478304	0.239152	−	0.970982i	$-0.423131\pi$
$593$	1.44029e12	0.478304	0.239152	+	0.970982i	$0.423131\pi$
$594$	2.23692e11	0.0737243
$595$	2.64441e12	0.864974
$596$	−4.22402e11	−0.137125
$597$	−2.25674e12	−0.727104
$598$	−7.11582e11	−0.227546
$599$	−3.03567e12	−0.963460	−0.481730	−	0.876320i	$-0.659991\pi$
$599$	−3.03567e12	−0.963460	−0.481730	+	0.876320i	$0.659991\pi$
$600$	−5.32882e12	−1.67861
$601$	−4.54193e12	−1.42005	−0.710027	−	0.704174i	$-0.751317\pi$
$601$	−4.54193e12	−1.42005	−0.710027	+	0.704174i	$0.751317\pi$
$602$	−4.42032e12	−1.37173
$603$	2.93837e10	0.00905062
$604$	3.33704e11	0.102022
$605$	−5.25222e12	−1.59384
$606$	−1.09122e11	−0.0328688
$607$	−2.62894e11	−0.0786017	−0.0393008	−	0.999227i	$-0.512513\pi$
$607$	−2.62894e11	−0.0786017	−0.0393008	+	0.999227i	$0.512513\pi$
$608$	6.84841e8	0.000203247 0
$609$	9.56786e12	2.81862
$610$	−1.11795e13	−3.26917
$611$	−2.29574e12	−0.666404
$612$	4.01845e10	0.0115792
$613$	6.55616e12	1.87533	0.937664	−	0.347542i	$-0.112984\pi$
$613$	6.55616e12	1.87533	0.937664	+	0.347542i	$0.112984\pi$
$614$	−1.09166e12	−0.309978
$615$	8.16136e12	2.30051
$616$	3.89499e11	0.108992
$617$	2.72693e11	0.0757515	0.0378757	−	0.999282i	$-0.487941\pi$
$617$	2.72693e11	0.0757515	0.0378757	+	0.999282i	$0.487941\pi$
$618$	−4.33300e12	−1.19492
$619$	−2.38402e11	−0.0652682	−0.0326341	−	0.999467i	$-0.510390\pi$
$619$	−2.38402e11	−0.0652682	−0.0326341	+	0.999467i	$0.510390\pi$
$620$	−2.03906e11	−0.0554201
$621$	6.73811e11	0.181814
$622$	−5.32482e12	−1.42642
$623$	4.54185e12	1.20792
$624$	−4.55298e12	−1.20217
$625$	−3.33687e11	−0.0874741
$626$	−7.43839e12	−1.93595
$627$	3.66660e8	9.47457e−5 0
$628$	3.37149e11	0.0864976
$629$	−1.00932e11	−0.0257099
$630$	2.49493e12	0.630996
$631$	−4.61151e11	−0.115801	−0.0579003	−	0.998322i	$-0.518441\pi$
$631$	−4.61151e11	−0.115801	−0.0579003	+	0.998322i	$0.518441\pi$
$632$	2.13399e12	0.532065
$633$	−5.63686e11	−0.139547
$634$	−6.33361e12	−1.55686
$635$	1.11372e13	2.71828
$636$	−5.53812e11	−0.134216
$637$	3.30756e12	0.795940
$638$	−6.98643e11	−0.166941
$639$	1.18034e11	0.0280061
$640$	7.68443e12	1.81051
$641$	7.93360e12	1.85613	0.928067	−	0.372413i	$-0.121470\pi$
$641$	7.93360e12	1.85613	0.928067	+	0.372413i	$0.121470\pi$
$642$	−4.04039e12	−0.938675
$643$	4.97067e12	1.14674	0.573371	−	0.819296i	$-0.305635\pi$
$643$	4.97067e12	1.14674	0.573371	+	0.819296i	$0.305635\pi$
$644$	−1.36950e11	−0.0313745
$645$	−7.72094e12	−1.75651
$646$	−1.81401e9	−0.000409821 0
$647$	−1.99656e11	−0.0447933	−0.0223966	−	0.999749i	$-0.507130\pi$
$647$	−1.99656e11	−0.0447933	−0.0223966	+	0.999749i	$0.507130\pi$
$648$	5.07056e12	1.12971
$649$	−6.80248e11	−0.150510
$650$	7.34213e12	1.61329
$651$	−2.30612e12	−0.503230
$652$	−7.68075e11	−0.166452
$653$	−7.28925e12	−1.56882	−0.784410	−	0.620242i	$-0.787034\pi$
$653$	−7.28925e12	−1.56882	−0.784410	+	0.620242i	$0.787034\pi$
$654$	−7.90405e12	−1.68947
$655$	1.11398e13	2.36478
$656$	−6.57575e12	−1.38637
$657$	−1.12112e12	−0.234751
$658$	−4.66890e12	−0.970954
$659$	8.57265e11	0.177064	0.0885321	−	0.996073i	$-0.471782\pi$
$659$	8.57265e11	0.177064	0.0885321	+	0.996073i	$0.471782\pi$
$660$	−7.94130e10	−0.0162908
$661$	9.07957e12	1.84994	0.924972	−	0.380034i	$-0.124088\pi$
$661$	9.07957e12	1.84994	0.924972	+	0.380034i	$0.124088\pi$
$662$	9.77628e11	0.197839
$663$	2.18488e12	0.439154
$664$	−8.31182e12	−1.65936
$665$	−1.06583e10	−0.00211344
$666$	−9.52267e10	−0.0187553
$667$	−2.10447e12	−0.411697
$668$	−5.43420e11	−0.105595
$669$	8.79075e11	0.169671
$670$	2.87287e11	0.0550781
$671$	8.73693e11	0.166383
$672$	−1.67753e12	−0.317328
$673$	4.62204e12	0.868492	0.434246	−	0.900794i	$-0.357015\pi$
$673$	4.62204e12	0.868492	0.434246	+	0.900794i	$0.357015\pi$
$674$	2.96623e12	0.553650
$675$	−6.95242e12	−1.28905
$676$	−3.06081e10	−0.00563737
$677$	1.25321e12	0.229285	0.114642	−	0.993407i	$-0.463428\pi$
$677$	1.25321e12	0.229285	0.114642	+	0.993407i	$0.463428\pi$
$678$	−4.90438e12	−0.891354
$679$	6.71435e12	1.21224
$680$	−3.36589e12	−0.603684
$681$	−3.56879e12	−0.635856
$682$	1.68392e11	0.0298052
$683$	−7.78380e12	−1.36867	−0.684335	−	0.729168i	$-0.739907\pi$
$683$	−7.78380e12	−1.36867	−0.684335	+	0.729168i	$0.739907\pi$
$684$	−1.61963e8	−2.82920e−5 0
$685$	1.83330e12	0.318145
$686$	−1.49350e12	−0.257482
$687$	4.36192e12	0.747089
$688$	6.22090e12	1.05854
$689$	−6.53710e12	−1.10509
$690$	−2.52775e12	−0.424535
$691$	9.19423e12	1.53414	0.767069	−	0.641565i	$-0.221715\pi$
$691$	9.19423e12	1.53414	0.767069	+	0.641565i	$0.221715\pi$
$692$	9.56741e10	0.0158605
$693$	−1.94983e11	−0.0321142
$694$	−6.66682e12	−1.09094
$695$	1.82229e13	2.96268
$696$	−1.21783e13	−1.96718
$697$	3.15557e12	0.506442
$698$	1.04087e13	1.65976
$699$	6.29979e12	0.998111
$700$	1.41306e12	0.222443
$701$	4.61654e12	0.722081	0.361040	−	0.932550i	$-0.382422\pi$
$701$	4.61654e12	0.722081	0.361040	+	0.932550i	$0.382422\pi$
$702$	−5.37244e12	−0.834938
$703$	4.06805e8	6.28184e−5 0
$704$	−4.89650e11	−0.0751292
$705$	−8.15515e12	−1.24331
$706$	5.17933e12	0.784607
$707$	−2.47897e11	−0.0373151
$708$	1.38410e12	0.207022
$709$	9.21112e12	1.36900	0.684501	−	0.729012i	$-0.260020\pi$
$709$	9.21112e12	1.36900	0.684501	+	0.729012i	$0.260020\pi$
$710$	1.15403e12	0.170433
$711$	−1.06827e12	−0.156772
$712$	−5.78101e12	−0.843031
$713$	5.07236e11	0.0735034
$714$	4.44345e12	0.639850
$715$	−9.37377e11	−0.134133
$716$	−5.43569e11	−0.0772940
$717$	8.84480e12	1.24983
$718$	5.18303e12	0.727820
$719$	−7.33461e12	−1.02352	−0.511761	−	0.859128i	$-0.671007\pi$
$719$	−7.33461e12	−1.02352	−0.511761	+	0.859128i	$0.671007\pi$
$720$	−3.51123e12	−0.486926
$721$	−9.84350e12	−1.35657
$722$	−7.67370e12	−1.05096
$723$	−7.75673e12	−1.05574
$724$	1.24175e10	0.00167962
$725$	2.17141e13	2.91891
$726$	−8.82538e12	−1.17901
$727$	1.75751e11	0.0233342	0.0116671	−	0.999932i	$-0.496286\pi$
$727$	1.75751e11	0.0233342	0.0116671	+	0.999932i	$0.496286\pi$
$728$	−9.35465e12	−1.23434
$729$	4.50091e12	0.590237
$730$	−1.09613e13	−1.42859
$731$	−2.98528e12	−0.386685
$732$	−1.77770e12	−0.228854
$733$	4.96599e12	0.635386	0.317693	−	0.948194i	$-0.397092\pi$
$733$	4.96599e12	0.635386	0.317693	+	0.948194i	$0.397092\pi$
$734$	4.54321e12	0.577738
$735$	1.17494e13	1.48499
$736$	3.68976e11	0.0463498
$737$	−2.24519e10	−0.00280317
$738$	2.97719e12	0.369448
$739$	−4.37258e12	−0.539309	−0.269654	−	0.962957i	$-0.586909\pi$
$739$	−4.37258e12	−0.539309	−0.269654	+	0.962957i	$0.586909\pi$
$740$	−8.81077e10	−0.0108012
$741$	−8.80613e9	−0.00107301
$742$	−1.32947e13	−1.61013
$743$	6.72449e12	0.809486	0.404743	−	0.914430i	$-0.367361\pi$
$743$	6.72449e12	0.809486	0.404743	+	0.914430i	$0.367361\pi$
$744$	2.93530e12	0.351216
$745$	−1.77116e13	−2.10647
$746$	−6.68463e12	−0.790228
$747$	4.16090e12	0.488927
$748$	−3.07048e10	−0.00358632
$749$	−9.17876e12	−1.06565
$750$	9.55543e12	1.10274
$751$	−5.15186e11	−0.0590996	−0.0295498	−	0.999563i	$-0.509407\pi$
$751$	−5.15186e11	−0.0590996	−0.0295498	+	0.999563i	$0.509407\pi$
$752$	6.57075e12	0.749264
$753$	−3.09015e11	−0.0350269
$754$	1.67794e13	1.89063
$755$	1.39924e13	1.56723
$756$	−1.03397e12	−0.115123
$757$	−1.58558e13	−1.75491	−0.877457	−	0.479655i	$-0.840762\pi$
$757$	−1.58558e13	−1.75491	−0.877457	+	0.479655i	$0.840762\pi$
$758$	−1.28039e13	−1.40874
$759$	1.97548e11	0.0216065
$760$	1.35662e10	0.00147501
$761$	−1.53136e13	−1.65518	−0.827591	−	0.561332i	$-0.810289\pi$
$761$	−1.53136e13	−1.65518	−0.827591	+	0.561332i	$0.810289\pi$
$762$	1.87140e13	2.01080
$763$	−1.79561e13	−1.91801
$764$	−4.25582e11	−0.0451921
$765$	1.68497e12	0.177875
$766$	−4.10921e12	−0.431250
$767$	1.63376e13	1.70455
$768$	3.38073e12	0.350659
$769$	−2.52343e12	−0.260210	−0.130105	−	0.991500i	$-0.541531\pi$
$769$	−2.52343e12	−0.260210	−0.130105	+	0.991500i	$0.541531\pi$
$770$	−1.90637e12	−0.195433
$771$	−2.84168e12	−0.289621
$772$	2.85108e11	0.0288890
$773$	1.19609e13	1.20492	0.602459	−	0.798150i	$-0.294188\pi$
$773$	1.19609e13	1.20492	0.602459	+	0.798150i	$0.294188\pi$
$774$	−2.81653e12	−0.282085
$775$	−5.23369e12	−0.521135
$776$	−8.54624e12	−0.846052
$777$	−9.96474e11	−0.0980779
$778$	−5.57336e12	−0.545392
$779$	−1.27185e10	−0.00123742
$780$	1.90727e12	0.184496
$781$	−9.01890e10	−0.00867409
$782$	−9.77347e11	−0.0934584
$783$	−1.58888e13	−1.51065
$784$	−9.46673e12	−0.894907
$785$	1.41369e13	1.32874
$786$	1.87183e13	1.74931
$787$	−2.09638e11	−0.0194798	−0.00973989	−	0.999953i	$-0.503100\pi$
$787$	−2.09638e11	−0.0194798	−0.00973989	+	0.999953i	$0.503100\pi$
$788$	8.06040e10	0.00744712
$789$	4.17657e12	0.383684
$790$	−1.04446e13	−0.954048
$791$	−1.11415e13	−1.01193
$792$	2.48180e11	0.0224132
$793$	−2.09836e13	−1.88431
$794$	9.81489e12	0.876381
$795$	−2.32217e13	−2.06178
$796$	−7.61695e11	−0.0672469
$797$	7.68479e12	0.674636	0.337318	−	0.941391i	$-0.390480\pi$
$797$	7.68479e12	0.674636	0.337318	+	0.941391i	$0.390480\pi$
$798$	−1.79093e10	−0.00156338
$799$	−3.15317e12	−0.273707
$800$	−3.80711e12	−0.328618
$801$	2.89397e12	0.248398
$802$	2.61519e12	0.223213
$803$	8.56641e11	0.0727074
$804$	4.56828e10	0.00385567
$805$	−5.74242e12	−0.481963
$806$	−4.04430e12	−0.337548
$807$	−1.46556e13	−1.21639
$808$	3.15531e11	0.0260430
$809$	1.00029e13	0.821026	0.410513	−	0.911855i	$-0.365350\pi$
$809$	1.00029e13	0.821026	0.410513	+	0.911855i	$0.365350\pi$
$810$	−2.48174e13	−2.02569
$811$	8.31787e12	0.675178	0.337589	−	0.941294i	$-0.390389\pi$
$811$	8.31787e12	0.675178	0.337589	+	0.941294i	$0.390389\pi$
$812$	3.22935e12	0.260683
$813$	−2.39442e13	−1.92217
$814$	7.27622e10	0.00580893
$815$	−3.22059e13	−2.55698
$816$	−6.25346e12	−0.493758
$817$	1.20321e10	0.000944807 0
$818$	−1.69156e13	−1.32098
$819$	4.68294e12	0.363698
$820$	2.75463e12	0.212765
$821$	1.78699e13	1.37271	0.686353	−	0.727269i	$-0.259211\pi$
$821$	1.78699e13	1.37271	0.686353	+	0.727269i	$0.259211\pi$
$822$	3.08052e12	0.235342
$823$	1.36245e13	1.03519	0.517596	−	0.855625i	$-0.326827\pi$
$823$	1.36245e13	1.03519	0.517596	+	0.855625i	$0.326827\pi$
$824$	1.25291e13	0.946777
$825$	−2.03831e12	−0.153189
$826$	3.32263e13	2.48354
$827$	1.90995e13	1.41987	0.709933	−	0.704269i	$-0.248725\pi$
$827$	1.90995e13	1.41987	0.709933	+	0.704269i	$0.248725\pi$
$828$	−8.72619e10	−0.00645191
$829$	−2.52205e13	−1.85464	−0.927319	−	0.374273i	$-0.877892\pi$
$829$	−2.52205e13	−1.85464	−0.927319	+	0.374273i	$0.877892\pi$
$830$	4.06815e13	2.97540
$831$	−2.06223e13	−1.50014
$832$	1.17600e13	0.850849
$833$	4.54289e12	0.326911
$834$	3.06201e13	2.19159
$835$	−2.27860e13	−1.62210
$836$	1.23755e8	8.76265e−6 0
$837$	3.82963e12	0.269707
$838$	−4.97400e10	−0.00348423
$839$	1.69055e13	1.17787	0.588937	−	0.808179i	$-0.299546\pi$
$839$	1.69055e13	1.17787	0.588937	+	0.808179i	$0.299546\pi$
$840$	−3.32305e13	−2.30293
$841$	3.51173e13	2.42069
$842$	−2.49723e13	−1.71220
$843$	1.76709e12	0.120513
$844$	−1.90255e11	−0.0129061
$845$	−1.28342e12	−0.0865991
$846$	−2.97493e12	−0.199669
$847$	−2.00491e13	−1.33850
$848$	1.87102e13	1.24250
$849$	−9.49706e12	−0.627342
$850$	1.00843e13	0.662615
$851$	2.19177e11	0.0143256
$852$	1.83507e11	0.0119309
$853$	−6.13701e12	−0.396905	−0.198452	−	0.980111i	$-0.563592\pi$
$853$	−6.13701e12	−0.396905	−0.198452	+	0.980111i	$0.563592\pi$
$854$	−4.26749e13	−2.74544
$855$	−6.79123e9	−0.000434611 0
$856$	1.16830e13	0.743742
$857$	2.13966e13	1.35498	0.677488	−	0.735534i	$-0.263069\pi$
$857$	2.13966e13	1.35498	0.677488	+	0.735534i	$0.263069\pi$
$858$	−1.57509e12	−0.0992229
$859$	1.84548e13	1.15649	0.578243	−	0.815865i	$-0.303739\pi$
$859$	1.84548e13	1.15649	0.578243	+	0.815865i	$0.303739\pi$
$860$	−2.60598e12	−0.162453
$861$	3.11540e13	1.93197
$862$	−1.28466e13	−0.792510
$863$	9.62324e12	0.590572	0.295286	−	0.955409i	$-0.404585\pi$
$863$	9.62324e12	0.590572	0.295286	+	0.955409i	$0.404585\pi$
$864$	2.78577e12	0.170072
$865$	4.01168e12	0.243643
$866$	1.07751e13	0.651014
$867$	−1.58023e13	−0.949805
$868$	−7.78361e11	−0.0465417
$869$	8.16263e11	0.0485558
$870$	5.96055e13	3.52736
$871$	5.39231e11	0.0317463
$872$	2.28550e13	1.33862
$873$	4.27825e12	0.249288
$874$	3.93918e9	0.000228352 0
$875$	2.17076e13	1.25191
$876$	−1.74300e12	−0.100007
$877$	1.42853e11	0.00815439	0.00407719	−	0.999992i	$-0.498702\pi$
$877$	1.42853e11	0.00815439	0.00407719	+	0.999992i	$0.498702\pi$
$878$	1.74771e13	0.992529
$879$	9.28450e11	0.0524576
$880$	2.68291e12	0.150811
$881$	9.76224e12	0.545956	0.272978	−	0.962020i	$-0.411991\pi$
$881$	9.76224e12	0.545956	0.272978	+	0.962020i	$0.411991\pi$
$882$	4.28609e12	0.238481
$883$	2.76372e13	1.52992	0.764962	−	0.644075i	$-0.222757\pi$
$883$	2.76372e13	1.52992	0.764962	+	0.644075i	$0.222757\pi$
$884$	7.37442e11	0.0406156
$885$	5.80361e13	3.18020
$886$	1.75263e13	0.955517
$887$	2.27482e13	1.23393	0.616966	−	0.786990i	$-0.288362\pi$
$887$	2.27482e13	1.23393	0.616966	+	0.786990i	$0.288362\pi$
$888$	1.26834e12	0.0684507
$889$	4.25135e13	2.28281
$890$	2.82946e13	1.51164
$891$	1.93952e12	0.103097
$892$	2.96706e11	0.0156922
$893$	1.27088e10	0.000668764 0
$894$	−2.97611e13	−1.55822
$895$	−2.27922e13	−1.18736
$896$	2.93335e13	1.52047
$897$	−4.74453e12	−0.244696
$898$	−9.12547e12	−0.468287
$899$	−1.19609e13	−0.610722
$900$	9.00372e11	0.0457437
$901$	−8.97862e12	−0.453887
$902$	−2.27486e12	−0.114426
$903$	−2.94729e13	−1.47512
$904$	1.41813e13	0.706248
$905$	5.20674e11	0.0258017
$906$	2.35117e13	1.15933
$907$	5.97360e12	0.293092	0.146546	−	0.989204i	$-0.453184\pi$
$907$	5.97360e12	0.293092	0.146546	+	0.989204i	$0.453184\pi$
$908$	−1.20454e12	−0.0588078
$909$	−1.57955e11	−0.00767354
$910$	4.57855e13	2.21331
$911$	−3.67352e13	−1.76706	−0.883528	−	0.468379i	$-0.844838\pi$
$911$	−3.67352e13	−1.76706	−0.883528	+	0.468379i	$0.844838\pi$
$912$	2.52045e10	0.00120643
$913$	−3.17932e12	−0.151431
$914$	1.28862e13	0.610757
$915$	−7.45401e13	−3.51557
$916$	1.47224e12	0.0690952
$917$	4.25234e13	1.98594
$918$	−7.37897e12	−0.342928
$919$	−3.98052e13	−1.84086	−0.920429	−	0.390910i	$-0.872160\pi$
$919$	−3.98052e13	−1.84086	−0.920429	+	0.390910i	$0.872160\pi$
$920$	7.30913e12	0.336372
$921$	−7.27876e12	−0.333341
$922$	−4.39707e12	−0.200389
$923$	2.16608e12	0.0982353
$924$	−3.03140e11	−0.0136810
$925$	−2.26148e12	−0.101567
$926$	2.00681e13	0.896927
$927$	−6.27208e12	−0.278967
$928$	−8.70062e12	−0.385110
$929$	−4.51327e12	−0.198802	−0.0994010	−	0.995047i	$-0.531693\pi$
$929$	−4.51327e12	−0.198802	−0.0994010	+	0.995047i	$0.531693\pi$
$930$	−1.43665e13	−0.629766
$931$	−1.83100e10	−0.000798759 0
$932$	2.12631e12	0.0923112
$933$	−3.55037e13	−1.53393
$934$	6.35366e12	0.273189
$935$	−1.28747e12	−0.0550917
$936$	−5.96059e12	−0.253833
$937$	3.40701e13	1.44393	0.721964	−	0.691930i	$-0.243239\pi$
$937$	3.40701e13	1.44393	0.721964	+	0.691930i	$0.243239\pi$
$938$	1.09665e12	0.0462546
$939$	−4.95961e13	−2.08187
$940$	−2.75253e12	−0.114989
$941$	3.85951e12	0.160464	0.0802322	−	0.996776i	$-0.474434\pi$
$941$	3.85951e12	0.160464	0.0802322	+	0.996776i	$0.474434\pi$
$942$	2.37545e13	0.982915
$943$	−6.85241e12	−0.282189
$944$	−4.67608e13	−1.91649
$945$	−4.33553e13	−1.76847
$946$	2.15210e12	0.0873679
$947$	−5.45263e12	−0.220308	−0.110154	−	0.993915i	$-0.535134\pi$
$947$	−5.45263e12	−0.220308	−0.110154	+	0.993915i	$0.535134\pi$
$948$	−1.66084e12	−0.0667869
$949$	−2.05741e13	−0.823422
$950$	−4.06447e10	−0.00161900
$951$	−4.22299e13	−1.67420
$952$	−1.28485e13	−0.506974
$953$	−1.58521e13	−0.622542	−0.311271	−	0.950321i	$-0.600755\pi$
$953$	−1.58521e13	−0.622542	−0.311271	+	0.950321i	$0.600755\pi$
$954$	−8.47109e12	−0.331109
$955$	−1.78449e13	−0.694224
$956$	2.98530e12	0.115592
$957$	−4.65826e12	−0.179523
$958$	6.90482e12	0.264855
$959$	6.99817e12	0.267178
$960$	4.17750e13	1.58744
$961$	−2.35567e13	−0.890963
$962$	−1.74754e12	−0.0657869
$963$	−5.84851e12	−0.219143
$964$	−2.61805e12	−0.0976410
$965$	1.19548e13	0.443781
$966$	−9.64908e12	−0.356524
$967$	−2.12205e13	−0.780435	−0.390218	−	0.920723i	$-0.627600\pi$
$967$	−2.12205e13	−0.780435	−0.390218	+	0.920723i	$0.627600\pi$
$968$	2.55191e13	0.934170
$969$	−1.20951e10	−0.000440709 0
$970$	4.18288e13	1.51706
$971$	−1.93515e13	−0.698601	−0.349300	−	0.937011i	$-0.613581\pi$
$971$	−1.93515e13	−0.698601	−0.349300	+	0.937011i	$0.613581\pi$
$972$	−1.57044e12	−0.0564318
$973$	6.95614e13	2.48806
$974$	−1.96553e13	−0.699786
$975$	4.89543e13	1.73488
$976$	6.00583e13	2.11860
$977$	−4.73169e13	−1.66146	−0.830732	−	0.556672i	$-0.812078\pi$
$977$	−4.73169e13	−1.66146	−0.830732	+	0.556672i	$0.812078\pi$
$978$	−5.41161e13	−1.89148
$979$	−2.21127e12	−0.0769343
$980$	3.96567e12	0.137341
$981$	−1.14412e13	−0.394423
$982$	5.47523e13	1.87889
$983$	−3.20581e12	−0.109508	−0.0547542	−	0.998500i	$-0.517438\pi$
$983$	−3.20581e12	−0.109508	−0.0547542	+	0.998500i	$0.517438\pi$
$984$	−3.96538e13	−1.34836
$985$	3.37978e12	0.114400
$986$	2.30463e13	0.776524
$987$	−3.11303e13	−1.04414
$988$	−2.97225e9	−9.92382e−5 0
$989$	6.48262e12	0.215460
$990$	−1.21470e12	−0.0401892
$991$	−3.75990e13	−1.23835	−0.619177	−	0.785252i	$-0.712534\pi$
$991$	−3.75990e13	−1.23835	−0.619177	+	0.785252i	$0.712534\pi$
$992$	2.09709e12	0.0687565
$993$	6.51842e12	0.212751
$994$	4.40522e12	0.143129
$995$	−3.19384e13	−1.03302
$996$	6.46894e12	0.208289
$997$	−3.65301e13	−1.17091	−0.585453	−	0.810706i	$-0.699083\pi$
$997$	−3.65301e13	−1.17091	−0.585453	+	0.810706i	$0.699083\pi$
$998$	4.08869e13	1.30466
$999$	1.65478e12	0.0525650

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.10.a.b.1.57	✓	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.10.a.b.1.57	✓	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+23.7806 q^{2} +158.559 q^{3} +53.5170 q^{4} +2244.00 q^{5} +3770.63 q^{6} +8565.95 q^{7} -10903.0 q^{8} +5458.04 q^{9} +53363.8 q^{10} -4170.46 q^{11} +8485.61 q^{12} +100163. q^{13} +203703. q^{14} +355808. q^{15} -286681. q^{16} +137572. q^{17} +129796. q^{18} -554.482 q^{19} +120092. q^{20} +1.35821e6 q^{21} -99176.1 q^{22} -298742. q^{23} -1.72877e6 q^{24} +3.08243e6 q^{25} +2.38193e6 q^{26} -2.25550e6 q^{27} +458424. q^{28} +7.04446e6 q^{29} +8.46132e6 q^{30} -1.69791e6 q^{31} -1.23510e6 q^{32} -661266. q^{33} +3.27155e6 q^{34} +1.92220e7 q^{35} +292098. q^{36} -733666. q^{37} -13185.9 q^{38} +1.58817e7 q^{39} -2.44664e7 q^{40} +2.29376e7 q^{41} +3.22991e7 q^{42} -2.16998e7 q^{43} -223191. q^{44} +1.22479e7 q^{45} -7.10426e6 q^{46} -2.29201e7 q^{47} -4.54559e7 q^{48} +3.30219e7 q^{49} +7.33021e7 q^{50} +2.18133e7 q^{51} +5.36041e6 q^{52} -6.52649e7 q^{53} -5.36371e7 q^{54} -9.35854e6 q^{55} -9.33946e7 q^{56} -87918.3 q^{57} +1.67522e8 q^{58} +1.63111e8 q^{59} +1.90418e7 q^{60} -2.09496e8 q^{61} -4.03773e7 q^{62} +4.67533e7 q^{63} +1.17409e8 q^{64} +2.24766e8 q^{65} -1.57253e7 q^{66} +5.38355e6 q^{67} +7.36244e6 q^{68} -4.73683e7 q^{69} +4.57111e8 q^{70} +2.16257e7 q^{71} -5.95091e7 q^{72} -2.05407e8 q^{73} -1.74470e7 q^{74} +4.88748e8 q^{75} -29674.2 q^{76} -3.57240e7 q^{77} +3.77677e8 q^{78} -1.95725e8 q^{79} -6.43313e8 q^{80} -4.65061e8 q^{81} +5.45469e8 q^{82} +7.62342e8 q^{83} +7.26873e7 q^{84} +3.08712e8 q^{85} -5.16033e8 q^{86} +1.11696e9 q^{87} +4.54706e7 q^{88} +5.30222e8 q^{89} +2.91262e8 q^{90} +8.57989e8 q^{91} -1.59878e7 q^{92} -2.69219e8 q^{93} -5.45054e8 q^{94} -1.24426e6 q^{95} -1.95837e8 q^{96} +7.83842e8 q^{97} +7.85280e8 q^{98} -2.27626e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 48 q^{2} + 890 q^{3} + 20736 q^{4} + 5171 q^{5} + 2688 q^{6} + 38986 q^{7} + 36507 q^{8} + 518318 q^{9} + 121093 q^{10} + 120464 q^{11} + 415744 q^{12} + 480131 q^{13} + 330849 q^{14} + 544874 q^{15}+ \cdots + 8731109606 q^{99}+O(q^{100}) \) 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

Varieties

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Database

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