LMFDB - Embedded newform 197.14.a.b.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [197,14,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, 14, names="a")

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

chi := DirichletCharacter("197.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 14 $
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:	$211.244930035$
Analytic rank:	$0$
Dimension:	$109$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
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)

$f(q)$	$=$	\(q-136.248 q^{2} -2369.27 q^{3} +10371.7 q^{4} +626.226 q^{5} +322809. q^{6} -79078.9 q^{7} -296974. q^{8} +4.01912e6 q^{9} -85322.4 q^{10} -9.86296e6 q^{11} -2.45732e7 q^{12} -703969. q^{13} +1.07744e7 q^{14} -1.48370e6 q^{15} -4.45023e7 q^{16} -4.75057e7 q^{17} -5.47598e8 q^{18} +8.73708e7 q^{19} +6.49500e6 q^{20} +1.87359e8 q^{21} +1.34381e9 q^{22} -6.38177e8 q^{23} +7.03612e8 q^{24} -1.22031e9 q^{25} +9.59148e7 q^{26} -5.74499e9 q^{27} -8.20179e8 q^{28} -5.24014e9 q^{29} +2.02152e8 q^{30} +8.56915e9 q^{31} +8.49618e9 q^{32} +2.33680e10 q^{33} +6.47257e9 q^{34} -4.95213e7 q^{35} +4.16849e10 q^{36} +6.61988e9 q^{37} -1.19041e10 q^{38} +1.66789e9 q^{39} -1.85973e8 q^{40} +1.28318e9 q^{41} -2.55274e10 q^{42} +7.65409e10 q^{43} -1.02295e11 q^{44} +2.51688e9 q^{45} +8.69506e10 q^{46} -6.38396e10 q^{47} +1.05438e11 q^{48} -9.06355e10 q^{49} +1.66266e11 q^{50} +1.12554e11 q^{51} -7.30132e9 q^{52} -5.66925e10 q^{53} +7.82746e11 q^{54} -6.17644e9 q^{55} +2.34844e10 q^{56} -2.07005e11 q^{57} +7.13961e11 q^{58} +1.77115e11 q^{59} -1.53884e10 q^{60} +1.00419e11 q^{61} -1.16753e12 q^{62} -3.17827e11 q^{63} -7.93029e11 q^{64} -4.40844e8 q^{65} -3.18386e12 q^{66} -1.82171e11 q^{67} -4.92712e11 q^{68} +1.51201e12 q^{69} +6.74720e9 q^{70} -2.29472e11 q^{71} -1.19357e12 q^{72} +8.52469e11 q^{73} -9.01948e11 q^{74} +2.89125e12 q^{75} +9.06179e11 q^{76} +7.79952e11 q^{77} -2.27248e11 q^{78} -1.12377e12 q^{79} -2.78685e10 q^{80} +7.20366e12 q^{81} -1.74832e11 q^{82} -2.74958e12 q^{83} +1.94323e12 q^{84} -2.97493e10 q^{85} -1.04286e13 q^{86} +1.24153e13 q^{87} +2.92904e12 q^{88} -7.83448e12 q^{89} -3.42921e11 q^{90} +5.56691e10 q^{91} -6.61895e12 q^{92} -2.03026e13 q^{93} +8.69805e12 q^{94} +5.47139e10 q^{95} -2.01297e13 q^{96} -2.16953e12 q^{97} +1.23490e13 q^{98} -3.96404e13 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 109 q + 192 q^{2} + 8018 q^{3} + 471040 q^{4} + 88496 q^{5} + 383232 q^{6} + 1680731 q^{7} + 1820859 q^{8} + 59521391 q^{9} + 16373653 q^{10} + 21199298 q^{11} + 63225856 q^{12} + 59695238 q^{13} + 37888529 q^{14}+ \cdots + 12084396239183 q^{99}+O(q^{100}) $ 109 * q + 192 * q^2 + 8018 * q^3 + 471040 * q^4 + 88496 * q^5 + 383232 * q^6 + 1680731 * q^7 + 1820859 * q^8 + 59521391 * q^9 + 16373653 * q^10 + 21199298 * q^11 + 63225856 * q^12 + 59695238 * q^13 + 37888529 * q^14 + 87246239 * q^15 + 2130706432 * q^16 + 228353715 * q^17 + 400647337 * q^18 + 1139301305 * q^19 + 1109969259 * q^20 + 539982398 * q^21 + 1613315649 * q^22 + 920306804 * q^23 + 5542439613 * q^24 + 31241700999 * q^25 + 1864366110 * q^26 + 17825460755 * q^27 + 20413389070 * q^28 + 7185436621 * q^29 + 2050251883 * q^30 + 28475592572 * q^31 + 8334714660 * q^32 + 19623425846 * q^33 + 37845014194 * q^34 + 25255003636 * q^35 + 287968706746 * q^36 + 71523920490 * q^37 + 67778214914 * q^38 + 44951568463 * q^39 + 169184871486 * q^40 + 69139231052 * q^41 + 58715177635 * q^42 + 247544146139 * q^43 + 63861560722 * q^44 + 257443045479 * q^45 + 160530477869 * q^46 + 308496573061 * q^47 + 412228130018 * q^48 + 1736616239908 * q^49 + 1680360028531 * q^50 + 756579032995 * q^51 + 928015404666 * q^52 + 342783723680 * q^53 - 597894730601 * q^54 + 59276330527 * q^55 - 3822929869144 * q^56 - 562905761941 * q^57 + 62740419347 * q^58 + 827401964151 * q^59 - 2247133283907 * q^60 + 988213134514 * q^61 + 1937380192071 * q^62 + 1788190111357 * q^63 + 11682175668457 * q^64 + 2494670804291 * q^65 + 11819807890512 * q^66 + 8038740399790 * q^67 + 10126245189885 * q^68 + 5225665164579 * q^69 + 11464042631319 * q^70 + 4867145119603 * q^71 + 18133468947055 * q^72 + 9684156738615 * q^73 + 16996786880941 * q^74 + 16718732018262 * q^75 + 21454522032798 * q^76 + 6593100920650 * q^77 + 33749579076633 * q^78 + 7591753073823 * q^79 + 24349241260570 * q^80 + 38778649605417 * q^81 + 25555033184251 * q^82 + 16945724819556 * q^83 + 21855489402730 * q^84 + 15544906794766 * q^85 + 18664144286914 * q^86 + 19049540636401 * q^87 + 17318749473003 * q^88 + 11289674998576 * q^89 + 20983303956671 * q^90 + 47242561944227 * q^91 - 25046698097386 * q^92 - 5411884145985 * q^93 + 18338784709341 * q^94 + 6784117894603 * q^95 - 36827486682955 * q^96 + 45969533477736 * q^97 - 42983409526150 * q^98 + 12084396239183 * 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 $

$2$	−136.248	−1.50535	−0.752674	−	0.658394i	$-0.771236\pi$
$2$	−136.248	−1.50535	−0.752674	+	0.658394i	$0.771236\pi$
$3$	−2369.27	−1.87640	−0.938202	−	0.346088i	$-0.887510\pi$
$3$	−2369.27	−1.87640	−0.938202	+	0.346088i	$0.887510\pi$
$4$	10371.7	1.26607
$5$	626.226	0.0179236	0.00896182	−	0.999960i	$-0.497147\pi$
$5$	626.226	0.0179236	0.00896182	+	0.999960i	$0.497147\pi$
$6$	322809.	2.82464
$7$	−79078.9	−0.254053	−0.127026	−	0.991899i	$-0.540543\pi$
$7$	−79078.9	−0.254053	−0.127026	+	0.991899i	$0.540543\pi$
$8$	−296974.	−0.400529
$9$	4.01912e6	2.52089
$10$	−85322.4	−0.0269813
$11$	−9.86296e6	−1.67863	−0.839314	−	0.543646i	$-0.817043\pi$
$11$	−9.86296e6	−1.67863	−0.839314	+	0.543646i	$0.817043\pi$
$12$	−2.45732e7	−2.37566
$13$	−703969.	−0.0404503	−0.0202252	−	0.999795i	$-0.506438\pi$
$13$	−703969.	−0.0404503	−0.0202252	+	0.999795i	$0.506438\pi$
$14$	1.07744e7	0.382437
$15$	−1.48370e6	−0.0336320
$16$	−4.45023e7	−0.663136
$17$	−4.75057e7	−0.477339	−0.238670	−	0.971101i	$-0.576711\pi$
$17$	−4.75057e7	−0.477339	−0.238670	+	0.971101i	$0.576711\pi$
$18$	−5.47598e8	−3.79482
$19$	8.73708e7	0.426057	0.213029	−	0.977046i	$-0.431667\pi$
$19$	8.73708e7	0.426057	0.213029	+	0.977046i	$0.431667\pi$
$20$	6.49500e6	0.0226926
$21$	1.87359e8	0.476705
$22$	1.34381e9	2.52692
$23$	−6.38177e8	−0.898897	−0.449449	−	0.893306i	$-0.648380\pi$
$23$	−6.38177e8	−0.898897	−0.449449	+	0.893306i	$0.648380\pi$
$24$	7.03612e8	0.751554
$25$	−1.22031e9	−0.999679
$26$	9.59148e7	0.0608918
$27$	−5.74499e9	−2.85381
$28$	−8.20179e8	−0.321648
$29$	−5.24014e9	−1.63590	−0.817948	−	0.575292i	$-0.804889\pi$
$29$	−5.24014e9	−1.63590	−0.817948	+	0.575292i	$0.804889\pi$
$30$	2.02152e8	0.0506278
$31$	8.56915e9	1.73415	0.867075	−	0.498178i	$-0.165997\pi$
$31$	8.56915e9	1.73415	0.867075	+	0.498178i	$0.165997\pi$
$32$	8.49618e9	1.39878
$33$	2.33680e10	3.14979
$34$	6.47257e9	0.718562
$35$	−4.95213e7	−0.00455355
$36$	4.16849e10	3.19163
$37$	6.61988e9	0.424169	0.212084	−	0.977251i	$-0.431975\pi$
$37$	6.61988e9	0.424169	0.212084	+	0.977251i	$0.431975\pi$
$38$	−1.19041e10	−0.641364
$39$	1.66789e9	0.0759011
$40$	−1.85973e8	−0.00717893
$41$	1.28318e9	0.0421884	0.0210942	−	0.999777i	$-0.493285\pi$
$41$	1.28318e9	0.0421884	0.0210942	+	0.999777i	$0.493285\pi$
$42$	−2.55274e10	−0.717607
$43$	7.65409e10	1.84650	0.923248	−	0.384204i	$-0.125524\pi$
$43$	7.65409e10	1.84650	0.923248	+	0.384204i	$0.125524\pi$
$44$	−1.02295e11	−2.12526
$45$	2.51688e9	0.0451836
$46$	8.69506e10	1.35315
$47$	−6.38396e10	−0.863881	−0.431941	−	0.901902i	$-0.642171\pi$
$47$	−6.38396e10	−0.863881	−0.431941	+	0.901902i	$0.642171\pi$
$48$	1.05438e11	1.24431
$49$	−9.06355e10	−0.935457
$50$	1.66266e11	1.50486
$51$	1.12554e11	0.895682
$52$	−7.30132e9	−0.0512130
$53$	−5.66925e10	−0.351344	−0.175672	−	0.984449i	$-0.556210\pi$
$53$	−5.66925e10	−0.351344	−0.175672	+	0.984449i	$0.556210\pi$
$54$	7.82746e11	4.29597
$55$	−6.17644e9	−0.0300871
$56$	2.34844e10	0.101755
$57$	−2.07005e11	−0.799455
$58$	7.13961e11	2.46259
$59$	1.77115e11	0.546661	0.273331	−	0.961920i	$-0.411875\pi$
$59$	1.77115e11	0.546661	0.273331	+	0.961920i	$0.411875\pi$
$60$	−1.53884e10	−0.0425805
$61$	1.00419e11	0.249557	0.124779	−	0.992185i	$-0.460178\pi$
$61$	1.00419e11	0.249557	0.124779	+	0.992185i	$0.460178\pi$
$62$	−1.16753e12	−2.61050
$63$	−3.17827e11	−0.640439
$64$	−7.93029e11	−1.44251
$65$	−4.40844e8	−0.000725017 0
$66$	−3.18386e12	−4.74152
$67$	−1.82171e11	−0.246033	−0.123016	−	0.992405i	$-0.539257\pi$
$67$	−1.82171e11	−0.246033	−0.123016	+	0.992405i	$0.539257\pi$
$68$	−4.92712e11	−0.604345
$69$	1.51201e12	1.68669
$70$	6.74720e9	0.00685467
$71$	−2.29472e11	−0.212594	−0.106297	−	0.994334i	$-0.533899\pi$
$71$	−2.29472e11	−0.212594	−0.106297	+	0.994334i	$0.533899\pi$
$72$	−1.19357e12	−1.00969
$73$	8.52469e11	0.659295	0.329648	−	0.944104i	$-0.393070\pi$
$73$	8.52469e11	0.659295	0.329648	+	0.944104i	$0.393070\pi$
$74$	−9.01948e11	−0.638521
$75$	2.89125e12	1.87580
$76$	9.06179e11	0.539418
$77$	7.79952e11	0.426460
$78$	−2.27248e11	−0.114258
$79$	−1.12377e12	−0.520119	−0.260060	−	0.965593i	$-0.583742\pi$
$79$	−1.12377e12	−0.520119	−0.260060	+	0.965593i	$0.583742\pi$
$80$	−2.78685e10	−0.0118858
$81$	7.20366e12	2.83400
$82$	−1.74832e11	−0.0635082
$83$	−2.74958e12	−0.923120	−0.461560	−	0.887109i	$-0.652710\pi$
$83$	−2.74958e12	−0.923120	−0.461560	+	0.887109i	$0.652710\pi$
$84$	1.94323e12	0.603542
$85$	−2.97493e10	−0.00855566
$86$	−1.04286e13	−2.77962
$87$	1.24153e13	3.06960
$88$	2.92904e12	0.672339
$89$	−7.83448e12	−1.67099	−0.835497	−	0.549495i	$-0.814820\pi$
$89$	−7.83448e12	−1.67099	−0.835497	+	0.549495i	$0.814820\pi$
$90$	−3.42921e11	−0.0680170
$91$	5.56691e10	0.0102765
$92$	−6.61895e12	−1.13807
$93$	−2.03026e13	−3.25397
$94$	8.69805e12	1.30044
$95$	5.47139e10	0.00763650
$96$	−2.01297e13	−2.62467
$97$	−2.16953e12	−0.264454	−0.132227	−	0.991219i	$-0.542213\pi$
$97$	−2.16953e12	−0.264454	−0.132227	+	0.991219i	$0.542213\pi$
$98$	1.23490e13	1.40819
$99$	−3.96404e13	−4.23164
$100$	−1.26566e13	−1.26566
$101$	1.27709e13	1.19711	0.598555	−	0.801082i	$-0.295742\pi$
$101$	1.27709e13	1.19711	0.598555	+	0.801082i	$0.295742\pi$
$102$	−1.53353e13	−1.34831
$103$	−2.12732e13	−1.75546	−0.877729	−	0.479158i	$-0.840942\pi$
$103$	−2.12732e13	−1.75546	−0.877729	+	0.479158i	$0.840942\pi$
$104$	2.09061e11	0.0162015
$105$	1.17329e11	0.00854429
$106$	7.72427e12	0.528895
$107$	8.67980e12	0.559133	0.279567	−	0.960126i	$-0.409809\pi$
$107$	8.67980e12	0.559133	0.279567	+	0.960126i	$0.409809\pi$
$108$	−5.95850e13	−3.61312
$109$	−2.40084e13	−1.37117	−0.685583	−	0.727994i	$-0.740453\pi$
$109$	−2.40084e13	−1.37117	−0.685583	+	0.727994i	$0.740453\pi$
$110$	8.41531e11	0.0452916
$111$	−1.56843e13	−0.795912
$112$	3.51919e12	0.168471
$113$	8.09782e11	0.0365896	0.0182948	−	0.999833i	$-0.494176\pi$
$113$	8.09782e11	0.0365896	0.0182948	+	0.999833i	$0.494176\pi$
$114$	2.82041e13	1.20346
$115$	−3.99643e11	−0.0161115
$116$	−5.43489e13	−2.07116
$117$	−2.82933e12	−0.101971
$118$	−2.41317e13	−0.822915
$119$	3.75670e12	0.121269
$120$	4.40620e11	0.0134706
$121$	6.27552e13	1.81780
$122$	−1.36819e13	−0.375670
$123$	−3.04021e12	−0.0791625
$124$	8.88762e13	2.19556
$125$	−1.52863e12	−0.0358415
$126$	4.33035e13	0.964083
$127$	5.37622e13	1.13698	0.568490	−	0.822690i	$-0.307528\pi$
$127$	5.37622e13	1.13698	0.568490	+	0.822690i	$0.307528\pi$
$128$	3.84483e13	0.772702
$129$	−1.81346e14	−3.46477
$130$	6.00643e10	0.00109140
$131$	−7.04996e13	−1.21877	−0.609387	−	0.792873i	$-0.708584\pi$
$131$	−7.04996e13	−1.21877	−0.609387	+	0.792873i	$0.708584\pi$
$132$	2.42365e14	3.98785
$133$	−6.90919e12	−0.108241
$134$	2.48205e13	0.370365
$135$	−3.59766e12	−0.0511506
$136$	1.41079e13	0.191188
$137$	−6.77775e13	−0.875794	−0.437897	−	0.899025i	$-0.644277\pi$
$137$	−6.77775e13	−0.875794	−0.437897	+	0.899025i	$0.644277\pi$
$138$	−2.06009e14	−2.53906
$139$	−9.87016e13	−1.16072	−0.580361	−	0.814360i	$-0.697088\pi$
$139$	−9.87016e13	−1.16072	−0.580361	+	0.814360i	$0.697088\pi$
$140$	−5.13618e11	−0.00576511
$141$	1.51253e14	1.62099
$142$	3.12652e13	0.320027
$143$	6.94322e12	0.0679011
$144$	−1.78860e14	−1.67169
$145$	−3.28151e12	−0.0293212
$146$	−1.16148e14	−0.992468
$147$	2.14740e14	1.75530
$148$	6.86591e13	0.537028
$149$	9.85241e12	0.0737619	0.0368809	−	0.999320i	$-0.488258\pi$
$149$	9.85241e12	0.0737619	0.0368809	+	0.999320i	$0.488258\pi$
$150$	−3.93928e14	−2.82373
$151$	−1.83204e14	−1.25772	−0.628860	−	0.777518i	$-0.716478\pi$
$151$	−1.83204e14	−1.25772	−0.628860	+	0.777518i	$0.716478\pi$
$152$	−2.59469e13	−0.170648
$153$	−1.90931e14	−1.20332
$154$	−1.06267e14	−0.641970
$155$	5.36623e12	0.0310823
$156$	1.72988e13	0.0960962
$157$	−1.53477e13	−0.0817890	−0.0408945	−	0.999163i	$-0.513021\pi$
$157$	−1.53477e13	−0.0817890	−0.0408945	+	0.999163i	$0.513021\pi$
$158$	1.53113e14	0.782960
$159$	1.34320e14	0.659264
$160$	5.32053e12	0.0250712
$161$	5.04663e13	0.228367
$162$	−9.81487e14	−4.26616
$163$	7.53023e12	0.0314477	0.0157238	−	0.999876i	$-0.494995\pi$
$163$	7.53023e12	0.0314477	0.0157238	+	0.999876i	$0.494995\pi$
$164$	1.33087e13	0.0534135
$165$	1.46337e13	0.0564556
$166$	3.74626e14	1.38962
$167$	4.88678e14	1.74327	0.871637	−	0.490152i	$-0.163059\pi$
$167$	4.88678e14	1.74327	0.871637	+	0.490152i	$0.163059\pi$
$168$	−5.56409e13	−0.190934
$169$	−3.02380e14	−0.998364
$170$	4.05330e12	0.0128792
$171$	3.51153e14	1.07404
$172$	7.93855e14	2.33779
$173$	−3.98296e14	−1.12955	−0.564777	−	0.825244i	$-0.691038\pi$
$173$	−3.98296e14	−1.12955	−0.564777	+	0.825244i	$0.691038\pi$
$174$	−1.69157e15	−4.62082
$175$	9.65009e13	0.253971
$176$	4.38924e14	1.11316
$177$	−4.19634e14	−1.02576
$178$	1.06744e15	2.51543
$179$	−1.65770e14	−0.376670	−0.188335	−	0.982105i	$-0.560309\pi$
$179$	−1.65770e14	−0.376670	−0.188335	+	0.982105i	$0.560309\pi$
$180$	2.61042e13	0.0572056
$181$	−5.03538e14	−1.06444	−0.532221	−	0.846606i	$-0.678642\pi$
$181$	−5.03538e14	−1.06444	−0.532221	+	0.846606i	$0.678642\pi$
$182$	−7.58484e12	−0.0154697
$183$	−2.37919e14	−0.468270
$184$	1.89522e14	0.360034
$185$	4.14554e12	0.00760265
$186$	2.76620e15	4.89835
$187$	4.68546e14	0.801276
$188$	−6.62122e14	−1.09373
$189$	4.54308e14	0.725017
$190$	−7.45468e12	−0.0114956
$191$	−6.71364e14	−1.00056	−0.500278	−	0.865865i	$-0.666769\pi$
$191$	−6.71364e14	−1.00056	−0.500278	+	0.865865i	$0.666769\pi$
$192$	1.87890e15	2.70673
$193$	−1.88722e14	−0.262845	−0.131422	−	0.991326i	$-0.541954\pi$
$193$	−1.88722e14	−0.262845	−0.131422	+	0.991326i	$0.541954\pi$
$194$	2.95595e14	0.398095
$195$	1.04448e12	0.00136042
$196$	−9.40040e14	−1.18435
$197$	5.84517e13	0.0712470
$197$	5.84517e13	0.0712470
$198$	5.40094e15	6.37009
$199$	2.61523e14	0.298514	0.149257	−	0.988798i	$-0.452312\pi$
$199$	2.61523e14	0.298514	0.149257	+	0.988798i	$0.452312\pi$
$200$	3.62401e14	0.400400
$201$	4.31612e14	0.461657
$202$	−1.74002e15	−1.80207
$203$	4.14385e14	0.415604
$204$	1.16737e15	1.13400
$205$	8.03563e11	0.000756170 0
$206$	2.89844e15	2.64257
$207$	−2.56491e15	−2.26602
$208$	3.13282e13	0.0268241
$209$	−8.61734e14	−0.715192
$210$	−1.59859e13	−0.0128621
$211$	2.50873e15	1.95712	0.978561	−	0.205958i	$-0.0660312\pi$
$211$	2.50873e15	1.95712	0.978561	+	0.205958i	$0.0660312\pi$
$212$	−5.87995e14	−0.444826
$213$	5.43681e14	0.398912
$214$	−1.18261e15	−0.841690
$215$	4.79319e13	0.0330959
$216$	1.70611e15	1.14303
$217$	−6.77639e14	−0.440565
$218$	3.27110e15	2.06408
$219$	−2.01973e15	−1.23710
$220$	−6.40599e13	−0.0380925
$221$	3.34425e13	0.0193085
$222$	2.13696e15	1.19812
$223$	−3.56146e15	−1.93931	−0.969654	−	0.244481i	$-0.921382\pi$
$223$	−3.56146e15	−1.93931	−0.969654	+	0.244481i	$0.921382\pi$
$224$	−6.71869e14	−0.355363
$225$	−4.90457e15	−2.52008
$226$	−1.10332e14	−0.0550801
$227$	−2.83498e15	−1.37525	−0.687625	−	0.726066i	$-0.741347\pi$
$227$	−2.83498e15	−1.37525	−0.687625	+	0.726066i	$0.741347\pi$
$228$	−2.14698e15	−1.01217
$229$	−2.34206e15	−1.07317	−0.536583	−	0.843847i	$-0.680285\pi$
$229$	−2.34206e15	−1.07317	−0.536583	+	0.843847i	$0.680285\pi$
$230$	5.44508e13	0.0242534
$231$	−1.84792e15	−0.800211
$232$	1.55619e15	0.655224
$233$	3.02838e15	1.23993	0.619965	−	0.784630i	$-0.287147\pi$
$233$	3.02838e15	1.23993	0.619965	+	0.784630i	$0.287147\pi$
$234$	3.85492e14	0.153502
$235$	−3.99780e13	−0.0154839
$236$	1.83698e15	0.692112
$237$	2.66252e15	0.975954
$238$	−5.11844e14	−0.182552
$239$	3.12486e15	1.08454	0.542268	−	0.840206i	$-0.317566\pi$
$239$	3.12486e15	1.08454	0.542268	+	0.840206i	$0.317566\pi$
$240$	6.60280e13	0.0223026
$241$	3.53540e15	1.16233	0.581163	−	0.813787i	$-0.302598\pi$
$241$	3.53540e15	1.16233	0.581163	+	0.813787i	$0.302598\pi$
$242$	−8.55030e15	−2.73641
$243$	−7.90804e15	−2.46393
$244$	1.04151e15	0.315957
$245$	−5.67584e13	−0.0167668
$246$	4.14223e14	0.119167
$247$	−6.15063e13	−0.0172341
$248$	−2.54481e15	−0.694577
$249$	6.51449e15	1.73215
$250$	2.08273e14	0.0539540
$251$	−3.28125e15	−0.828248	−0.414124	−	0.910220i	$-0.635912\pi$
$251$	−3.28125e15	−0.828248	−0.414124	+	0.910220i	$0.635912\pi$
$252$	−3.29639e15	−0.810841
$253$	6.29431e15	1.50891
$254$	−7.32502e15	−1.71155
$255$	7.04841e13	0.0160539
$256$	1.25797e15	0.279326
$257$	−4.88124e15	−1.05673	−0.528366	−	0.849017i	$-0.677195\pi$
$257$	−4.88124e15	−1.05673	−0.528366	+	0.849017i	$0.677195\pi$
$258$	2.47081e16	5.21569
$259$	−5.23493e14	−0.107761
$260$	−4.57228e12	−0.000917923 0
$261$	−2.10607e16	−4.12392
$262$	9.60546e15	1.83468
$263$	−6.94251e15	−1.29361	−0.646806	−	0.762655i	$-0.723896\pi$
$263$	−6.94251e15	−1.29361	−0.646806	+	0.762655i	$0.723896\pi$
$264$	−6.93969e15	−1.26158
$265$	−3.55024e13	−0.00629737
$266$	9.41366e14	0.162940
$267$	1.85620e16	3.13546
$268$	−1.88941e15	−0.311495
$269$	−6.84319e15	−1.10121	−0.550603	−	0.834767i	$-0.685602\pi$
$269$	−6.84319e15	−1.10121	−0.550603	+	0.834767i	$0.685602\pi$
$270$	4.90176e14	0.0769995
$271$	−1.06166e15	−0.162811	−0.0814054	−	0.996681i	$-0.525941\pi$
$271$	−1.06166e15	−0.162811	−0.0814054	+	0.996681i	$0.525941\pi$
$272$	2.11411e15	0.316541
$273$	−1.31895e14	−0.0192829
$274$	9.23459e15	1.31837
$275$	1.20359e16	1.67809
$276$	1.56821e16	2.13547
$277$	−2.08301e15	−0.277060	−0.138530	−	0.990358i	$-0.544238\pi$
$277$	−2.08301e15	−0.277060	−0.138530	+	0.990358i	$0.544238\pi$
$278$	1.34479e16	1.74729
$279$	3.44404e16	4.37160
$280$	1.47065e13	0.00182383
$281$	−9.15500e15	−1.10935	−0.554673	−	0.832068i	$-0.687157\pi$
$281$	−9.15500e15	−1.10935	−0.554673	+	0.832068i	$0.687157\pi$
$282$	−2.06080e16	−2.44015
$283$	−6.75751e15	−0.781943	−0.390971	−	0.920403i	$-0.627861\pi$
$283$	−6.75751e15	−0.781943	−0.390971	+	0.920403i	$0.627861\pi$
$284$	−2.38000e15	−0.269159
$285$	−1.29632e14	−0.0143292
$286$	−9.46003e14	−0.102215
$287$	−1.01473e14	−0.0107181
$288$	3.41471e16	3.52617
$289$	−7.64779e15	−0.772147
$290$	4.47101e14	0.0441386
$291$	5.14020e15	0.496222
$292$	8.84151e15	0.834714
$293$	−6.83001e14	−0.0630641	−0.0315320	−	0.999503i	$-0.510039\pi$
$293$	−6.83001e14	−0.0630641	−0.0315320	+	0.999503i	$0.510039\pi$
$294$	−2.92580e16	−2.64233
$295$	1.10914e14	0.00979816
$296$	−1.96593e15	−0.169892
$297$	5.66626e16	4.79048
$298$	−1.34238e15	−0.111037
$299$	4.49257e14	0.0363607
$300$	2.99870e16	2.37490
$301$	−6.05277e15	−0.469107
$302$	2.49612e16	1.89331
$303$	−3.02578e16	−2.24626
$304$	−3.88820e15	−0.282534
$305$	6.28848e13	0.00447297
$306$	2.60140e16	1.81142
$307$	1.98495e16	1.35316	0.676582	−	0.736368i	$-0.263461\pi$
$307$	1.98495e16	1.35316	0.676582	+	0.736368i	$0.263461\pi$
$308$	8.08939e15	0.539928
$309$	5.04019e16	3.29395
$310$	−7.31140e14	−0.0467896
$311$	−2.14229e16	−1.34256	−0.671282	−	0.741202i	$-0.734256\pi$
$311$	−2.14229e16	−1.34256	−0.671282	+	0.741202i	$0.734256\pi$
$312$	−4.95321e14	−0.0304006
$313$	2.45494e16	1.47572	0.737859	−	0.674955i	$-0.235837\pi$
$313$	2.45494e16	1.47572	0.737859	+	0.674955i	$0.235837\pi$
$314$	2.09110e15	0.123121
$315$	−1.99032e14	−0.0114790
$316$	−1.16554e16	−0.658508
$317$	−1.24886e16	−0.691242	−0.345621	−	0.938374i	$-0.612332\pi$
$317$	−1.24886e16	−0.691242	−0.345621	+	0.938374i	$0.612332\pi$
$318$	−1.83009e16	−0.992421
$319$	5.16833e16	2.74606
$320$	−4.96616e14	−0.0258551
$321$	−2.05648e16	−1.04916
$322$	−6.87596e15	−0.343772
$323$	−4.15061e15	−0.203374
$324$	7.47138e16	3.58805
$325$	8.59061e14	0.0404373
$326$	−1.02598e15	−0.0473397
$327$	5.68823e16	2.57286
$328$	−3.81072e14	−0.0168977
$329$	5.04837e15	0.219471
$330$	−1.99381e15	−0.0849854
$331$	−2.01808e16	−0.843444	−0.421722	−	0.906725i	$-0.638574\pi$
$331$	−2.01808e16	−0.843444	−0.421722	+	0.906725i	$0.638574\pi$
$332$	−2.85177e16	−1.16874
$333$	2.66061e16	1.06928
$334$	−6.65816e16	−2.62423
$335$	−1.14080e14	−0.00440981
$336$	−8.33792e15	−0.316120
$337$	−4.21449e16	−1.56729	−0.783647	−	0.621206i	$-0.786643\pi$
$337$	−4.21449e16	−1.56729	−0.783647	+	0.621206i	$0.786643\pi$
$338$	4.11988e16	1.50288
$339$	−1.91859e15	−0.0686569
$340$	−3.08549e14	−0.0108321
$341$	−8.45171e16	−2.91099
$342$	−4.78441e16	−1.61681
$343$	1.48292e16	0.491708
$344$	−2.27307e16	−0.739575
$345$	9.46862e14	0.0302317
$346$	5.42673e16	1.70037
$347$	−4.66388e16	−1.43419	−0.717094	−	0.696977i	$-0.754528\pi$
$347$	−4.66388e16	−1.43419	−0.717094	+	0.696977i	$0.754528\pi$
$348$	1.28767e17	3.88633
$349$	−2.41535e16	−0.715508	−0.357754	−	0.933816i	$-0.616457\pi$
$349$	−2.41535e16	−0.715508	−0.357754	+	0.933816i	$0.616457\pi$
$350$	−1.31481e16	−0.382314
$351$	4.04429e15	0.115437
$352$	−8.37975e16	−2.34803
$353$	2.55915e16	0.703980	0.351990	−	0.936004i	$-0.385505\pi$
$353$	2.55915e16	0.703980	0.351990	+	0.936004i	$0.385505\pi$
$354$	5.71745e16	1.54412
$355$	−1.43701e14	−0.00381045
$356$	−8.12564e16	−2.11560
$357$	−8.90063e15	−0.227550
$358$	2.25859e16	0.567019
$359$	−6.99003e15	−0.172332	−0.0861659	−	0.996281i	$-0.527462\pi$
$359$	−6.99003e15	−0.172332	−0.0861659	+	0.996281i	$0.527462\pi$
$360$	−7.47447e14	−0.0180973
$361$	−3.44193e16	−0.818475
$362$	6.86064e16	1.60235
$363$	−1.48684e17	−3.41092
$364$	5.77381e14	0.0130108
$365$	5.33839e14	0.0118170
$366$	3.24161e16	0.704909
$367$	4.72910e16	1.01030	0.505149	−	0.863032i	$-0.331438\pi$
$367$	4.72910e16	1.01030	0.505149	+	0.863032i	$0.331438\pi$
$368$	2.84003e16	0.596091
$369$	5.15726e15	0.106352
$370$	−5.64824e14	−0.0114446
$371$	4.48319e15	0.0892599
$372$	−2.10572e17	−4.11975
$373$	−4.10822e15	−0.0789854	−0.0394927	−	0.999220i	$-0.512574\pi$
$373$	−4.10822e15	−0.0789854	−0.0394927	+	0.999220i	$0.512574\pi$
$374$	−6.38387e16	−1.20620
$375$	3.62173e15	0.0672532
$376$	1.89587e16	0.346009
$377$	3.68890e15	0.0661725
$378$	−6.18987e16	−1.09140
$379$	−1.00785e16	−0.174678	−0.0873392	−	0.996179i	$-0.527836\pi$
$379$	−1.00785e16	−0.174678	−0.0873392	+	0.996179i	$0.527836\pi$
$380$	5.67473e14	0.00966834
$381$	−1.27377e17	−2.13343
$382$	9.14723e16	1.50618
$383$	7.10771e16	1.15064	0.575318	−	0.817930i	$-0.304878\pi$
$383$	7.10771e16	1.15064	0.575318	+	0.817930i	$0.304878\pi$
$384$	−9.10944e16	−1.44990
$385$	4.88427e14	0.00764372
$386$	2.57131e16	0.395673
$387$	3.07627e17	4.65482
$388$	−2.25016e16	−0.334817
$389$	−1.03822e17	−1.51920	−0.759602	−	0.650388i	$-0.774606\pi$
$389$	−1.03822e17	−1.51920	−0.759602	+	0.650388i	$0.774606\pi$
$390$	−1.42309e14	−0.00204791
$391$	3.03170e16	0.429079
$392$	2.69164e16	0.374677
$393$	1.67032e17	2.28691
$394$	−7.96396e15	−0.107252
$395$	−7.03737e14	−0.00932243
$396$	−4.11136e17	−5.35756
$397$	−1.30696e17	−1.67543	−0.837713	−	0.546111i	$-0.816108\pi$
$397$	−1.30696e17	−1.67543	−0.837713	+	0.546111i	$0.816108\pi$
$398$	−3.56321e16	−0.449367
$399$	1.63697e16	0.203104
$400$	5.43066e16	0.662923
$401$	−3.71176e16	−0.445802	−0.222901	−	0.974841i	$-0.571553\pi$
$401$	−3.71176e16	−0.445802	−0.222901	+	0.974841i	$0.571553\pi$
$402$	−5.88065e16	−0.694954
$403$	−6.03242e15	−0.0701469
$404$	1.32456e17	1.51563
$405$	4.51112e15	0.0507957
$406$	−5.64593e16	−0.625628
$407$	−6.52916e16	−0.712022
$408$	−3.34255e16	−0.358746
$409$	−1.28149e17	−1.35367	−0.676834	−	0.736136i	$-0.736648\pi$
$409$	−1.28149e17	−1.35367	−0.676834	+	0.736136i	$0.736648\pi$
$410$	−1.09484e14	−0.00113830
$411$	1.60583e17	1.64334
$412$	−2.20638e17	−2.22253
$413$	−1.40061e16	−0.138881
$414$	3.49465e17	3.41115
$415$	−1.72186e15	−0.0165457
$416$	−5.98105e15	−0.0565810
$417$	2.33851e17	2.17798
$418$	1.17410e17	1.07661
$419$	−1.09499e17	−0.988593	−0.494297	−	0.869293i	$-0.664574\pi$
$419$	−1.09499e17	−0.988593	−0.494297	+	0.869293i	$0.664574\pi$
$420$	1.21690e15	0.0108177
$421$	−1.48757e17	−1.30210	−0.651049	−	0.759035i	$-0.725671\pi$
$421$	−1.48757e17	−1.30210	−0.651049	+	0.759035i	$0.725671\pi$
$422$	−3.41811e17	−2.94615
$423$	−2.56579e17	−2.17775
$424$	1.68362e16	0.140723
$425$	5.79717e16	0.477186
$426$	−7.40757e16	−0.600501
$427$	−7.94099e15	−0.0634006
$428$	9.00239e16	0.707902
$429$	−1.64504e16	−0.127410
$430$	−6.53065e15	−0.0498209
$431$	5.40844e16	0.406415	0.203207	−	0.979136i	$-0.434863\pi$
$431$	5.40844e16	0.406415	0.203207	+	0.979136i	$0.434863\pi$
$432$	2.55665e17	1.89246
$433$	−1.87138e17	−1.36455	−0.682276	−	0.731095i	$-0.739010\pi$
$433$	−1.87138e17	−1.36455	−0.682276	+	0.731095i	$0.739010\pi$
$434$	9.23273e16	0.663204
$435$	7.77479e15	0.0550185
$436$	−2.49006e17	−1.73599
$437$	−5.57580e16	−0.382982
$438$	2.75185e17	1.86227
$439$	−2.28784e17	−1.52548	−0.762740	−	0.646705i	$-0.776147\pi$
$439$	−2.28784e17	−1.52548	−0.762740	+	0.646705i	$0.776147\pi$
$440$	1.83424e15	0.0120508
$441$	−3.64275e17	−2.35819
$442$	−4.55649e15	−0.0290660
$443$	1.62704e17	1.02276	0.511379	−	0.859355i	$-0.329135\pi$
$443$	1.62704e17	1.02276	0.511379	+	0.859355i	$0.329135\pi$
$444$	−1.62672e17	−1.00768
$445$	−4.90616e15	−0.0299503
$446$	4.85244e17	2.91933
$447$	−2.33430e16	−0.138407
$448$	6.27119e16	0.366474
$449$	−1.11714e17	−0.643440	−0.321720	−	0.946835i	$-0.604261\pi$
$449$	−1.11714e17	−0.643440	−0.321720	+	0.946835i	$0.604261\pi$
$450$	6.68240e17	3.79360
$451$	−1.26560e16	−0.0708187
$452$	8.39877e15	0.0463251
$453$	4.34059e17	2.35999
$454$	3.86261e17	2.07023
$455$	3.48615e13	0.000184192 0
$456$	6.14751e16	0.320205
$457$	−2.37317e17	−1.21863	−0.609317	−	0.792927i	$-0.708556\pi$
$457$	−2.37317e17	−1.21863	−0.609317	+	0.792927i	$0.708556\pi$
$458$	3.19102e17	1.61549
$459$	2.72919e17	1.36223
$460$	−4.14496e15	−0.0203983
$461$	1.04990e17	0.509437	0.254718	−	0.967015i	$-0.418017\pi$
$461$	1.04990e17	0.509437	0.254718	+	0.967015i	$0.418017\pi$
$462$	2.51776e17	1.20460
$463$	1.64857e17	0.777733	0.388867	−	0.921294i	$-0.372867\pi$
$463$	1.64857e17	0.777733	0.388867	+	0.921294i	$0.372867\pi$
$464$	2.33198e17	1.08482
$465$	−1.27140e16	−0.0583229
$466$	−4.12612e17	−1.86652
$467$	2.68820e16	0.119923	0.0599615	−	0.998201i	$-0.480902\pi$
$467$	2.68820e16	0.119923	0.0599615	+	0.998201i	$0.480902\pi$
$468$	−2.93449e16	−0.129102
$469$	1.44059e16	0.0625053
$470$	5.44695e15	0.0233087
$471$	3.63628e16	0.153469
$472$	−5.25987e16	−0.218953
$473$	−7.54919e17	−3.09958
$474$	−3.62765e17	−1.46915
$475$	−1.06620e17	−0.425920
$476$	3.89631e16	0.153536
$477$	−2.27854e17	−0.885701
$478$	−4.25757e17	−1.63260
$479$	−4.10601e17	−1.55324	−0.776622	−	0.629967i	$-0.783068\pi$
$479$	−4.10601e17	−1.55324	−0.776622	+	0.629967i	$0.783068\pi$
$480$	−1.26058e16	−0.0470437
$481$	−4.66019e15	−0.0171578
$482$	−4.81693e17	−1.74970
$483$	−1.19568e17	−0.428509
$484$	6.50875e17	2.30146
$485$	−1.35862e15	−0.00473997
$486$	1.07746e18	3.70907
$487$	1.18143e17	0.401300	0.200650	−	0.979663i	$-0.435695\pi$
$487$	1.18143e17	0.401300	0.200650	+	0.979663i	$0.435695\pi$
$488$	−2.98217e16	−0.0999548
$489$	−1.78411e16	−0.0590085
$490$	7.73324e15	0.0252399
$491$	5.16001e17	1.66196	0.830981	−	0.556301i	$-0.187780\pi$
$491$	5.16001e17	1.66196	0.830981	+	0.556301i	$0.187780\pi$
$492$	−3.15319e16	−0.100225
$493$	2.48936e17	0.780878
$494$	8.38015e15	0.0259434
$495$	−2.48238e16	−0.0758464
$496$	−3.81347e17	−1.14998
$497$	1.81464e16	0.0540100
$498$	−8.87589e17	−2.60748
$499$	4.36609e16	0.126601	0.0633007	−	0.997994i	$-0.479837\pi$
$499$	4.36609e16	0.126601	0.0633007	+	0.997994i	$0.479837\pi$
$500$	−1.58544e16	−0.0453779
$501$	−1.15781e18	−3.27109
$502$	4.47066e17	1.24680
$503$	3.25378e17	0.895769	0.447884	−	0.894092i	$-0.352178\pi$
$503$	3.25378e17	0.895769	0.447884	+	0.894092i	$0.352178\pi$
$504$	9.43865e16	0.256514
$505$	7.99750e15	0.0214566
$506$	−8.57590e17	−2.27144
$507$	7.16419e17	1.87333
$508$	5.57603e17	1.43950
$509$	1.57153e17	0.400551	0.200276	−	0.979740i	$-0.435816\pi$
$509$	1.57153e17	0.400551	0.200276	+	0.979740i	$0.435816\pi$
$510$	−9.60335e15	−0.0241667
$511$	−6.74123e16	−0.167496
$512$	−4.86365e17	−1.19319
$513$	−5.01944e17	−1.21588
$514$	6.65061e17	1.59075
$515$	−1.33218e16	−0.0314642
$516$	−1.88086e18	−4.38665
$517$	6.29647e17	1.45014
$518$	7.13251e16	0.162218
$519$	9.43672e17	2.11950
$520$	1.30919e14	0.000290390 0
$521$	−6.48115e17	−1.41973	−0.709866	−	0.704336i	$-0.751245\pi$
$521$	−6.48115e17	−1.41973	−0.709866	+	0.704336i	$0.751245\pi$
$522$	2.86949e18	6.20793
$523$	3.56821e17	0.762412	0.381206	−	0.924490i	$-0.375509\pi$
$523$	3.56821e17	0.762412	0.381206	+	0.924490i	$0.375509\pi$
$524$	−7.31197e17	−1.54305
$525$	−2.28637e17	−0.476552
$526$	9.45906e17	1.94733
$527$	−4.07083e17	−0.827778
$528$	−1.03993e18	−2.08874
$529$	−9.67668e16	−0.191984
$530$	4.83714e15	0.00947973
$531$	7.11847e17	1.37807
$532$	−7.16597e16	−0.137041
$533$	−9.03321e14	−0.00170654
$534$	−2.52904e18	−4.71996
$535$	5.43552e15	0.0100217
$536$	5.41001e16	0.0985432
$537$	3.92754e17	0.706785
$538$	9.32374e17	1.65770
$539$	8.93934e17	1.57029
$540$	−3.73137e16	−0.0647603
$541$	3.67709e17	0.630554	0.315277	−	0.949000i	$-0.397903\pi$
$541$	3.67709e17	0.630554	0.315277	+	0.949000i	$0.397903\pi$
$542$	1.44649e17	0.245087
$543$	1.19302e18	1.99732
$544$	−4.03617e17	−0.667692
$545$	−1.50347e16	−0.0245763
$546$	1.79705e16	0.0290274
$547$	1.05798e18	1.68873	0.844366	−	0.535766i	$-0.179977\pi$
$547$	1.05798e18	1.68873	0.844366	+	0.535766i	$0.179977\pi$
$548$	−7.02965e17	−1.10882
$549$	4.03594e17	0.629107
$550$	−1.63987e18	−2.52611
$551$	−4.57835e17	−0.696985
$552$	−4.49029e17	−0.675569
$553$	8.88669e16	0.132138
$554$	2.83808e17	0.417072
$555$	−9.82191e15	−0.0142656
$556$	−1.02370e18	−1.46956
$557$	−2.26477e17	−0.321340	−0.160670	−	0.987008i	$-0.551365\pi$
$557$	−2.26477e17	−0.321340	−0.160670	+	0.987008i	$0.551365\pi$
$558$	−4.69245e18	−6.58078
$559$	−5.38824e16	−0.0746914
$560$	2.20381e15	0.00301962
$561$	−1.11011e18	−1.50352
$562$	1.24735e18	1.66995
$563$	5.10889e17	0.676117	0.338058	−	0.941125i	$-0.390230\pi$
$563$	5.10889e17	0.676117	0.338058	+	0.941125i	$0.390230\pi$
$564$	1.56875e18	2.05229
$565$	5.07107e14	0.000655820 0
$566$	9.20701e17	1.17710
$567$	−5.69658e17	−0.719986
$568$	6.81472e16	0.0851499
$569$	2.78542e17	0.344081	0.172040	−	0.985090i	$-0.444964\pi$
$569$	2.78542e17	0.344081	0.172040	+	0.985090i	$0.444964\pi$
$570$	1.76622e16	0.0215704
$571$	1.03530e17	0.125006	0.0625029	−	0.998045i	$-0.480092\pi$
$571$	1.03530e17	0.125006	0.0625029	+	0.998045i	$0.480092\pi$
$572$	7.20126e16	0.0859675
$573$	1.59064e18	1.87745
$574$	1.38255e16	0.0161344
$575$	7.78774e17	0.898608
$576$	−3.18728e18	−3.63642
$577$	−7.51933e16	−0.0848274	−0.0424137	−	0.999100i	$-0.513505\pi$
$577$	−7.51933e16	−0.0848274	−0.0424137	+	0.999100i	$0.513505\pi$
$578$	1.04200e18	1.16235
$579$	4.47133e17	0.493203
$580$	−3.40347e16	−0.0371227
$581$	2.17434e17	0.234521
$582$	−7.00345e17	−0.746986
$583$	5.59156e17	0.589776
$584$	−2.53161e17	−0.264067
$585$	−1.77180e15	−0.00182769
$586$	9.30579e16	0.0949334
$587$	−3.03752e17	−0.306459	−0.153229	−	0.988191i	$-0.548967\pi$
$587$	−3.03752e17	−0.306459	−0.153229	+	0.988191i	$0.548967\pi$
$588$	2.22721e18	2.22233
$589$	7.48693e17	0.738847
$590$	−1.51119e16	−0.0147496
$591$	−1.38488e17	−0.133688
$592$	−2.94600e17	−0.281282
$593$	9.79565e17	0.925077	0.462538	−	0.886599i	$-0.346939\pi$
$593$	9.79565e17	0.925077	0.462538	+	0.886599i	$0.346939\pi$
$594$	−7.72019e18	−7.21134
$595$	2.35254e15	0.00217359
$596$	1.02186e17	0.0933877
$597$	−6.19618e17	−0.560132
$598$	−6.12106e16	−0.0547355
$599$	−6.42197e17	−0.568059	−0.284030	−	0.958815i	$-0.591671\pi$
$599$	−6.42197e17	−0.568059	−0.284030	+	0.958815i	$0.591671\pi$
$600$	−8.58625e17	−0.751312
$601$	1.01195e17	0.0875940	0.0437970	−	0.999040i	$-0.486055\pi$
$601$	1.01195e17	0.0875940	0.0437970	+	0.999040i	$0.486055\pi$
$602$	8.24681e17	0.706169
$603$	−7.32167e17	−0.620222
$604$	−1.90012e18	−1.59236
$605$	3.92990e16	0.0325815
$606$	4.12258e18	3.38140
$607$	4.63457e17	0.376082	0.188041	−	0.982161i	$-0.439786\pi$
$607$	4.63457e17	0.376082	0.188041	+	0.982161i	$0.439786\pi$
$608$	7.42318e17	0.595959
$609$	−9.81789e17	−0.779840
$610$	−8.56795e15	−0.00673338
$611$	4.49411e16	0.0349443
$612$	−1.98027e18	−1.52349
$613$	−1.47621e18	−1.12371	−0.561854	−	0.827236i	$-0.689912\pi$
$613$	−1.47621e18	−1.12371	−0.561854	+	0.827236i	$0.689912\pi$
$614$	−2.70446e18	−2.03698
$615$	−1.90386e15	−0.00141888
$616$	−2.31626e17	−0.170809
$617$	−7.11214e17	−0.518975	−0.259488	−	0.965746i	$-0.583554\pi$
$617$	−7.11214e17	−0.518975	−0.259488	+	0.965746i	$0.583554\pi$
$618$	−6.86718e18	−4.95853
$619$	−7.83011e16	−0.0559472	−0.0279736	−	0.999609i	$-0.508905\pi$
$619$	−7.83011e16	−0.0559472	−0.0279736	+	0.999609i	$0.508905\pi$
$620$	5.56566e16	0.0393524
$621$	3.66632e18	2.56528
$622$	2.91883e18	2.02102
$623$	6.19542e17	0.424520
$624$	−7.42251e16	−0.0503328
$625$	1.48868e18	0.999036
$626$	−3.34482e18	−2.22147
$627$	2.04168e18	1.34199
$628$	−1.59181e17	−0.103551
$629$	−3.14482e17	−0.202473
$630$	2.71178e16	0.0172799
$631$	−1.43794e18	−0.906878	−0.453439	−	0.891287i	$-0.649803\pi$
$631$	−1.43794e18	−0.906878	−0.453439	+	0.891287i	$0.649803\pi$
$632$	3.33732e17	0.208323
$633$	−5.94386e18	−3.67235
$634$	1.70156e18	1.04056
$635$	3.36673e16	0.0203788
$636$	1.39312e18	0.834674
$637$	6.38046e16	0.0378395
$638$	−7.04177e18	−4.13378
$639$	−9.22274e17	−0.535926
$640$	2.40773e16	0.0138496
$641$	−2.14598e18	−1.22194	−0.610969	−	0.791655i	$-0.709220\pi$
$641$	−2.14598e18	−1.22194	−0.610969	+	0.791655i	$0.709220\pi$
$642$	2.80192e18	1.57935
$643$	−4.58616e17	−0.255904	−0.127952	−	0.991780i	$-0.540840\pi$
$643$	−4.58616e17	−0.255904	−0.127952	+	0.991780i	$0.540840\pi$
$644$	5.23419e17	0.289129
$645$	−1.13564e17	−0.0621014
$646$	5.65514e17	0.306148
$647$	−2.06850e18	−1.10861	−0.554303	−	0.832315i	$-0.687015\pi$
$647$	−2.06850e18	−1.10861	−0.554303	+	0.832315i	$0.687015\pi$
$648$	−2.13930e18	−1.13510
$649$	−1.74688e18	−0.917641
$650$	−1.17046e17	−0.0608722
$651$	1.60551e18	0.826678
$652$	7.81009e16	0.0398150
$653$	−8.97096e17	−0.452797	−0.226398	−	0.974035i	$-0.572695\pi$
$653$	−8.97096e17	−0.452797	−0.226398	+	0.974035i	$0.572695\pi$
$654$	−7.75012e18	−3.87305
$655$	−4.41487e16	−0.0218449
$656$	−5.71046e16	−0.0279767
$657$	3.42617e18	1.66201
$658$	−6.87833e17	−0.330381
$659$	3.01280e18	1.43290	0.716448	−	0.697641i	$-0.245767\pi$
$659$	3.01280e18	1.43290	0.716448	+	0.697641i	$0.245767\pi$
$660$	1.51775e17	0.0714768
$661$	−1.28367e18	−0.598609	−0.299305	−	0.954158i	$-0.596755\pi$
$661$	−1.28367e18	−0.598609	−0.299305	+	0.954158i	$0.596755\pi$
$662$	2.74960e18	1.26968
$663$	−7.92344e16	−0.0362306
$664$	8.16553e17	0.369736
$665$	−4.32672e15	−0.00194007
$666$	−3.62504e18	−1.60964
$667$	3.34414e18	1.47050
$668$	5.06840e18	2.20711
$669$	8.43807e18	3.63893
$670$	1.55433e16	0.00663829
$671$	−9.90424e17	−0.418914
$672$	1.59184e18	0.666805
$673$	1.45837e18	0.605020	0.302510	−	0.953146i	$-0.402175\pi$
$673$	1.45837e18	0.605020	0.302510	+	0.953146i	$0.402175\pi$
$674$	5.74218e18	2.35932
$675$	7.01067e18	2.85289
$676$	−3.13617e18	−1.26400
$677$	1.37831e17	0.0550199	0.0275099	−	0.999622i	$-0.491242\pi$
$677$	1.37831e17	0.0550199	0.0275099	+	0.999622i	$0.491242\pi$
$678$	2.61405e17	0.103353
$679$	1.71564e17	0.0671851
$680$	8.83477e15	0.00342679
$681$	6.71682e18	2.58052
$682$	1.15153e19	4.38206
$683$	−5.96219e17	−0.224735	−0.112368	−	0.993667i	$-0.535843\pi$
$683$	−5.96219e17	−0.224735	−0.112368	+	0.993667i	$0.535843\pi$
$684$	3.64204e18	1.35982
$685$	−4.24441e16	−0.0156974
$686$	−2.02046e18	−0.740191
$687$	5.54897e18	2.01369
$688$	−3.40624e18	−1.22448
$689$	3.99098e16	0.0142120
$690$	−1.29009e17	−0.0455092
$691$	4.94046e18	1.72647	0.863237	−	0.504799i	$-0.168433\pi$
$691$	4.94046e18	1.72647	0.863237	+	0.504799i	$0.168433\pi$
$692$	−4.13099e18	−1.43009
$693$	3.13472e18	1.07506
$694$	6.35447e18	2.15895
$695$	−6.18095e16	−0.0208044
$696$	−3.68702e18	−1.22946
$697$	−6.09584e16	−0.0201382
$698$	3.29088e18	1.07709
$699$	−7.17505e18	−2.32661
$700$	1.00087e18	0.321545
$701$	5.50789e18	1.75315	0.876573	−	0.481269i	$-0.159824\pi$
$701$	5.50789e18	1.75315	0.876573	+	0.481269i	$0.159824\pi$
$702$	−5.51029e17	−0.173773
$703$	5.78384e17	0.180720
$704$	7.82161e18	2.42144
$705$	9.47188e16	0.0290541
$706$	−3.48680e18	−1.05973
$707$	−1.00991e18	−0.304129
$708$	−4.35230e18	−1.29868
$709$	4.79429e18	1.41750	0.708752	−	0.705458i	$-0.249259\pi$
$709$	4.79429e18	1.41750	0.708752	+	0.705458i	$0.249259\pi$
$710$	1.95791e16	0.00573606
$711$	−4.51658e18	−1.31116
$712$	2.32664e18	0.669281
$713$	−5.46863e18	−1.55882
$714$	1.21270e18	0.342542
$715$	4.34803e15	0.00121703
$716$	−1.71931e18	−0.476891
$717$	−7.40363e18	−2.03503
$718$	9.52381e17	0.259419
$719$	9.28230e16	0.0250564	0.0125282	−	0.999922i	$-0.496012\pi$
$719$	9.28230e16	0.0250564	0.0125282	+	0.999922i	$0.496012\pi$
$720$	−1.12007e17	−0.0299628
$721$	1.68226e18	0.445978
$722$	4.68958e18	1.23209
$723$	−8.37632e18	−2.18099
$724$	−5.22252e18	−1.34766
$725$	6.39460e18	1.63537
$726$	2.02580e19	5.13462
$727$	5.23730e18	1.31563	0.657815	−	0.753179i	$-0.271481\pi$
$727$	5.23730e18	1.31563	0.657815	+	0.753179i	$0.271481\pi$
$728$	−1.65323e16	−0.00411604
$729$	7.25132e18	1.78932
$730$	−7.27347e16	−0.0177887
$731$	−3.63612e18	−0.881406
$732$	−2.46761e18	−0.592863
$733$	−1.33014e18	−0.316753	−0.158377	−	0.987379i	$-0.550626\pi$
$733$	−1.33014e18	−0.316753	−0.158377	+	0.987379i	$0.550626\pi$
$734$	−6.44333e18	−1.52085
$735$	1.34476e17	0.0314613
$736$	−5.42207e18	−1.25736
$737$	1.79675e18	0.412998
$738$	−7.02669e17	−0.160097
$739$	6.19070e18	1.39814	0.699071	−	0.715053i	$-0.253597\pi$
$739$	6.19070e18	1.39814	0.699071	+	0.715053i	$0.253597\pi$
$740$	4.29961e16	0.00962549
$741$	1.45725e17	0.0323382
$742$	−6.10827e17	−0.134367
$743$	1.12440e18	0.245185	0.122593	−	0.992457i	$-0.460879\pi$
$743$	1.12440e18	0.245185	0.122593	+	0.992457i	$0.460879\pi$
$744$	6.02935e18	1.30331
$745$	6.16984e15	0.00132208
$746$	5.59739e17	0.118900
$747$	−1.10509e19	−2.32709
$748$	4.85960e18	1.01447
$749$	−6.86390e17	−0.142049
$750$	−4.93455e17	−0.101239
$751$	−3.01610e17	−0.0613460	−0.0306730	−	0.999529i	$-0.509765\pi$
$751$	−3.01610e17	−0.0613460	−0.0306730	+	0.999529i	$0.509765\pi$
$752$	2.84101e18	0.572871
$753$	7.77417e18	1.55413
$754$	−5.02607e17	−0.0996127
$755$	−1.14727e17	−0.0225429
$756$	4.71192e18	0.917923
$757$	6.78214e18	1.30992	0.654958	−	0.755666i	$-0.272686\pi$
$757$	6.78214e18	1.30992	0.654958	+	0.755666i	$0.272686\pi$
$758$	1.37317e18	0.262952
$759$	−1.49129e19	−2.83133
$760$	−1.62486e16	−0.00305864
$761$	−1.50584e18	−0.281047	−0.140523	−	0.990077i	$-0.544878\pi$
$761$	−1.50584e18	−0.281047	−0.140523	+	0.990077i	$0.544878\pi$
$762$	1.73549e19	3.21156
$763$	1.89856e18	0.348348
$764$	−6.96315e18	−1.26677
$765$	−1.19566e17	−0.0215679
$766$	−9.68415e18	−1.73211
$767$	−1.24684e17	−0.0221126
$768$	−2.98048e18	−0.524128
$769$	8.57909e18	1.49596	0.747980	−	0.663721i	$-0.231024\pi$
$769$	8.57909e18	1.49596	0.747980	+	0.663721i	$0.231024\pi$
$770$	−6.65474e16	−0.0115064
$771$	1.15650e19	1.98285
$772$	−1.95736e18	−0.332780
$773$	−7.00576e18	−1.18110	−0.590552	−	0.806999i	$-0.701090\pi$
$773$	−7.00576e18	−1.18110	−0.590552	+	0.806999i	$0.701090\pi$
$774$	−4.19137e19	−7.00712
$775$	−1.04570e19	−1.73359
$776$	6.44294e17	0.105921
$777$	1.24030e18	0.202204
$778$	1.41456e19	2.28693
$779$	1.12113e17	0.0179747
$780$	1.08330e16	0.00172239
$781$	2.26327e18	0.356866
$782$	−4.13065e18	−0.645913
$783$	3.01045e19	4.66853
$784$	4.03349e18	0.620335
$785$	−9.61111e15	−0.00146596
$786$	−2.27579e19	−3.44260
$787$	3.27393e18	0.491172	0.245586	−	0.969375i	$-0.421020\pi$
$787$	3.27393e18	0.491172	0.245586	+	0.969375i	$0.421020\pi$
$788$	6.06241e17	0.0902038
$789$	1.64487e19	2.42734
$790$	9.58831e16	0.0140335
$791$	−6.40367e16	−0.00929569
$792$	1.17722e19	1.69489
$793$	−7.06916e16	−0.0100947
$794$	1.78072e19	2.52210
$795$	8.41147e16	0.0118164
$796$	2.71242e18	0.377939
$797$	5.28257e18	0.730072	0.365036	−	0.930993i	$-0.381057\pi$
$797$	5.28257e18	0.730072	0.365036	+	0.930993i	$0.381057\pi$
$798$	−2.23035e18	−0.305742
$799$	3.03274e18	0.412365
$800$	−1.03680e19	−1.39833
$801$	−3.14877e19	−4.21239
$802$	5.05722e18	0.671087
$803$	−8.40787e18	−1.10671
$804$	4.47653e18	0.584490
$805$	3.16034e16	0.00409317
$806$	8.21908e17	0.105595
$807$	1.62134e19	2.06631
$808$	−3.79264e18	−0.479477
$809$	−3.64046e18	−0.456553	−0.228276	−	0.973596i	$-0.573309\pi$
$809$	−3.64046e18	−0.456553	−0.228276	+	0.973596i	$0.573309\pi$
$810$	−6.14633e17	−0.0764651
$811$	−1.09182e19	−1.34746	−0.673732	−	0.738976i	$-0.735310\pi$
$811$	−1.09182e19	−1.34746	−0.673732	+	0.738976i	$0.735310\pi$
$812$	4.29785e18	0.526184
$813$	2.51535e18	0.305499
$814$	8.89588e18	1.07184
$815$	4.71563e15	0.000563657 0
$816$	−5.00890e18	−0.593959
$817$	6.68744e18	0.786713
$818$	1.74600e19	2.03774
$819$	2.23741e17	0.0259060
$820$	8.33427e15	0.000957365 0
$821$	−4.74287e18	−0.540519	−0.270259	−	0.962788i	$-0.587109\pi$
$821$	−4.74287e18	−0.540519	−0.270259	+	0.962788i	$0.587109\pi$
$822$	−2.18792e19	−2.47380
$823$	2.23773e18	0.251020	0.125510	−	0.992092i	$-0.459943\pi$
$823$	2.23773e18	0.251020	0.125510	+	0.992092i	$0.459943\pi$
$824$	6.31758e18	0.703111
$825$	−2.85162e19	−3.14877
$826$	1.90831e18	0.209064
$827$	1.35164e19	1.46918	0.734590	−	0.678511i	$-0.237375\pi$
$827$	1.35164e19	1.46918	0.734590	+	0.678511i	$0.237375\pi$
$828$	−2.66023e19	−2.86894
$829$	1.00669e19	1.07719	0.538596	−	0.842564i	$-0.318955\pi$
$829$	1.00669e19	1.07719	0.538596	+	0.842564i	$0.318955\pi$
$830$	2.34600e17	0.0249070
$831$	4.93522e18	0.519877
$832$	5.58268e17	0.0583500
$833$	4.30570e18	0.446531
$834$	−3.18618e19	−3.27862
$835$	3.06023e17	0.0312458
$836$	−8.93761e18	−0.905483
$837$	−4.92297e19	−4.94893
$838$	1.49190e19	1.48818
$839$	4.63747e18	0.459017	0.229508	−	0.973307i	$-0.426288\pi$
$839$	4.63747e18	0.459017	0.229508	+	0.973307i	$0.426288\pi$
$840$	−3.48438e16	−0.00342223
$841$	1.71984e19	1.67616
$842$	2.02679e19	1.96011
$843$	2.16907e19	2.08158
$844$	2.60197e19	2.47785
$845$	−1.89358e17	−0.0178943
$846$	3.49585e19	3.27827
$847$	−4.96262e18	−0.461815
$848$	2.52295e18	0.232989
$849$	1.60104e19	1.46724
$850$	−7.89855e18	−0.718331
$851$	−4.22465e18	−0.381284
$852$	5.63887e18	0.505050
$853$	7.05953e18	0.627490	0.313745	−	0.949507i	$-0.398416\pi$
$853$	7.05953e18	0.627490	0.313745	+	0.949507i	$0.398416\pi$
$854$	1.08195e18	0.0954400
$855$	2.19901e17	0.0192508
$856$	−2.57768e18	−0.223949
$857$	−1.81868e19	−1.56813	−0.784064	−	0.620680i	$-0.786857\pi$
$857$	−1.81868e19	−1.56813	−0.784064	+	0.620680i	$0.786857\pi$
$858$	2.24134e18	0.191796
$859$	−1.28581e19	−1.09199	−0.545997	−	0.837787i	$-0.683849\pi$
$859$	−1.28581e19	−1.09199	−0.545997	+	0.837787i	$0.683849\pi$
$860$	4.97133e17	0.0419018
$861$	2.40416e17	0.0201114
$862$	−7.36891e18	−0.611795
$863$	−9.45460e17	−0.0779064	−0.0389532	−	0.999241i	$-0.512402\pi$
$863$	−9.45460e17	−0.0779064	−0.0389532	+	0.999241i	$0.512402\pi$
$864$	−4.88105e19	−3.99184
$865$	−2.49424e17	−0.0202457
$866$	2.54972e19	2.05412
$867$	1.81197e19	1.44886
$868$	−7.02824e18	−0.557787
$869$	1.10837e19	0.873087
$870$	−1.05930e18	−0.0828219
$871$	1.28243e17	0.00995211
$872$	7.12986e18	0.549191
$873$	−8.71960e18	−0.666659
$874$	7.59694e18	0.576520
$875$	1.20882e17	0.00910563
$876$	−2.09479e19	−1.56626
$877$	2.00346e19	1.48691	0.743453	−	0.668788i	$-0.233187\pi$
$877$	2.00346e19	1.48691	0.743453	+	0.668788i	$0.233187\pi$
$878$	3.11715e19	2.29638
$879$	1.61821e18	0.118334
$880$	2.74866e17	0.0199519
$881$	−2.43626e19	−1.75541	−0.877707	−	0.479198i	$-0.840928\pi$
$881$	−2.43626e19	−1.75541	−0.877707	+	0.479198i	$0.840928\pi$
$882$	4.96319e19	3.54989
$883$	7.74618e18	0.549975	0.274988	−	0.961448i	$-0.411326\pi$
$883$	7.74618e18	0.549975	0.274988	+	0.961448i	$0.411326\pi$
$884$	3.46854e17	0.0244460
$885$	−2.62786e17	−0.0183853
$886$	−2.21681e19	−1.53961
$887$	−4.26835e18	−0.294277	−0.147139	−	0.989116i	$-0.547006\pi$
$887$	−4.26835e18	−0.294277	−0.147139	+	0.989116i	$0.547006\pi$
$888$	4.65782e18	0.318786
$889$	−4.25146e18	−0.288853
$890$	6.68456e17	0.0450856
$891$	−7.10494e19	−4.75724
$892$	−3.69382e19	−2.45530
$893$	−5.57772e18	−0.368063
$894$	3.18045e18	0.208351
$895$	−1.03810e17	−0.00675130
$896$	−3.04045e18	−0.196307
$897$	−1.06441e18	−0.0682273
$898$	1.52209e19	0.968601
$899$	−4.49035e19	−2.83689
$900$	−5.08685e19	−3.19060
$901$	2.69322e18	0.167710
$902$	1.72436e18	0.106607
$903$	1.43406e19	0.880234
$904$	−2.40484e17	−0.0146552
$905$	−3.15329e17	−0.0190787
$906$	−5.91399e19	−3.55261
$907$	−2.47002e19	−1.47317	−0.736584	−	0.676346i	$-0.763562\pi$
$907$	−2.47002e19	−1.47317	−0.736584	+	0.676346i	$0.763562\pi$
$908$	−2.94034e19	−1.74116
$909$	5.13279e19	3.01778
$910$	−4.74982e15	−0.000277274 0
$911$	−1.76009e19	−1.02015	−0.510077	−	0.860129i	$-0.670383\pi$
$911$	−1.76009e19	−1.02015	−0.510077	+	0.860129i	$0.670383\pi$
$912$	9.21219e18	0.530147
$913$	2.71190e19	1.54958
$914$	3.23340e19	1.83447
$915$	−1.48991e17	−0.00839311
$916$	−2.42910e19	−1.35870
$917$	5.57503e18	0.309633
$918$	−3.71849e19	−2.05064
$919$	9.58308e17	0.0524752	0.0262376	−	0.999656i	$-0.491647\pi$
$919$	9.58308e17	0.0524752	0.0262376	+	0.999656i	$0.491647\pi$
$920$	1.18684e17	0.00645312
$921$	−4.70288e19	−2.53908
$922$	−1.43047e19	−0.766879
$923$	1.61541e17	0.00859948
$924$	−1.91659e19	−1.01312
$925$	−8.07831e18	−0.424033
$926$	−2.24615e19	−1.17076
$927$	−8.54993e19	−4.42532
$928$	−4.45212e19	−2.28826
$929$	1.38796e19	0.708395	0.354198	−	0.935171i	$-0.384754\pi$
$929$	1.38796e19	0.708395	0.354198	+	0.935171i	$0.384754\pi$
$930$	1.73227e18	0.0877963
$931$	−7.91890e18	−0.398558
$932$	3.14093e19	1.56984
$933$	5.07565e19	2.51919
$934$	−3.66263e18	−0.180526
$935$	2.93416e17	0.0143618
$936$	8.40239e17	0.0408423
$937$	9.25448e16	0.00446729	0.00223365	−	0.999998i	$-0.499289\pi$
$937$	9.25448e16	0.00446729	0.00223365	+	0.999998i	$0.499289\pi$
$938$	−1.96278e18	−0.0940922
$939$	−5.81643e19	−2.76904
$940$	−4.14638e17	−0.0196037
$941$	2.50315e19	1.17531	0.587657	−	0.809110i	$-0.300051\pi$
$941$	2.50315e19	1.17531	0.587657	+	0.809110i	$0.300051\pi$
$942$	−4.95437e18	−0.231024
$943$	−8.18897e17	−0.0379231
$944$	−7.88204e18	−0.362511
$945$	2.84499e17	0.0129949
$946$	1.02857e20	4.66595
$947$	1.42433e19	0.641706	0.320853	−	0.947129i	$-0.396030\pi$
$947$	1.42433e19	0.641706	0.320853	+	0.947129i	$0.396030\pi$
$948$	2.76148e19	1.23563
$949$	−6.00112e17	−0.0266687
$950$	1.45267e19	0.641158
$951$	2.95890e19	1.29705
$952$	−1.11564e18	−0.0485718
$953$	−3.92069e19	−1.69535	−0.847674	−	0.530518i	$-0.821997\pi$
$953$	−3.92069e19	−1.69535	−0.847674	+	0.530518i	$0.821997\pi$
$954$	3.10447e19	1.33329
$955$	−4.20426e17	−0.0179336
$956$	3.24099e19	1.37310
$957$	−1.22452e20	−5.15272
$958$	5.59438e19	2.33817
$959$	5.35977e18	0.222498
$960$	1.17662e18	0.0485145
$961$	4.90128e19	2.00728
$962$	6.34944e17	0.0258284
$963$	3.48851e19	1.40951
$964$	3.66679e19	1.47159
$965$	−1.18183e17	−0.00471114
$966$	1.62910e19	0.645055
$967$	−3.61528e19	−1.42190	−0.710952	−	0.703241i	$-0.751736\pi$
$967$	−3.61528e19	−1.42190	−0.710952	+	0.703241i	$0.751736\pi$
$968$	−1.86367e19	−0.728079
$969$	9.83391e18	0.381612
$970$	1.85110e17	0.00713531
$971$	−3.37605e19	−1.29266	−0.646330	−	0.763058i	$-0.723697\pi$
$971$	−3.37605e19	−1.29266	−0.646330	+	0.763058i	$0.723697\pi$
$972$	−8.20194e19	−3.11951
$973$	7.80522e18	0.294884
$974$	−1.60968e19	−0.604096
$975$	−2.03535e18	−0.0758767
$976$	−4.46886e18	−0.165490
$977$	−6.92540e17	−0.0254759	−0.0127380	−	0.999919i	$-0.504055\pi$
$977$	−6.92540e17	−0.0254759	−0.0127380	+	0.999919i	$0.504055\pi$
$978$	2.43083e18	0.0888283
$979$	7.72711e19	2.80498
$980$	−5.88678e17	−0.0212280
$981$	−9.64923e19	−3.45656
$982$	−7.03044e19	−2.50183
$983$	2.09144e19	0.739347	0.369674	−	0.929162i	$-0.379470\pi$
$983$	2.09144e19	0.739347	0.369674	+	0.929162i	$0.379470\pi$
$984$	9.02862e17	0.0317069
$985$	3.66040e16	0.00127701
$986$	−3.39172e19	−1.17549
$987$	−1.19609e19	−0.411817
$988$	−6.37922e17	−0.0218196
$989$	−4.88466e19	−1.65981
$990$	3.38221e18	0.114175
$991$	2.52710e19	0.847507	0.423753	−	0.905778i	$-0.360712\pi$
$991$	2.52710e19	0.847507	0.423753	+	0.905778i	$0.360712\pi$
$992$	7.28050e19	2.42569
$993$	4.78138e19	1.58264
$994$	−2.47242e18	−0.0813038
$995$	1.63772e17	0.00535045
$996$	6.75660e19	2.19302
$997$	−2.32003e19	−0.748127	−0.374063	−	0.927403i	$-0.622036\pi$
$997$	−2.32003e19	−0.748127	−0.374063	+	0.927403i	$0.622036\pi$
$998$	−5.94873e18	−0.190579
$999$	−3.80311e19	−1.21050

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.14.a.b.1.14	✓	109

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.14.a.b.1.14	✓	109	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:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	197.a (trivial)

\(f(q)\)	\(=\)	\(q-136.248 q^{2} -2369.27 q^{3} +10371.7 q^{4} +626.226 q^{5} +322809. q^{6} -79078.9 q^{7} -296974. q^{8} +4.01912e6 q^{9} -85322.4 q^{10} -9.86296e6 q^{11} -2.45732e7 q^{12} -703969. q^{13} +1.07744e7 q^{14} -1.48370e6 q^{15} -4.45023e7 q^{16} -4.75057e7 q^{17} -5.47598e8 q^{18} +8.73708e7 q^{19} +6.49500e6 q^{20} +1.87359e8 q^{21} +1.34381e9 q^{22} -6.38177e8 q^{23} +7.03612e8 q^{24} -1.22031e9 q^{25} +9.59148e7 q^{26} -5.74499e9 q^{27} -8.20179e8 q^{28} -5.24014e9 q^{29} +2.02152e8 q^{30} +8.56915e9 q^{31} +8.49618e9 q^{32} +2.33680e10 q^{33} +6.47257e9 q^{34} -4.95213e7 q^{35} +4.16849e10 q^{36} +6.61988e9 q^{37} -1.19041e10 q^{38} +1.66789e9 q^{39} -1.85973e8 q^{40} +1.28318e9 q^{41} -2.55274e10 q^{42} +7.65409e10 q^{43} -1.02295e11 q^{44} +2.51688e9 q^{45} +8.69506e10 q^{46} -6.38396e10 q^{47} +1.05438e11 q^{48} -9.06355e10 q^{49} +1.66266e11 q^{50} +1.12554e11 q^{51} -7.30132e9 q^{52} -5.66925e10 q^{53} +7.82746e11 q^{54} -6.17644e9 q^{55} +2.34844e10 q^{56} -2.07005e11 q^{57} +7.13961e11 q^{58} +1.77115e11 q^{59} -1.53884e10 q^{60} +1.00419e11 q^{61} -1.16753e12 q^{62} -3.17827e11 q^{63} -7.93029e11 q^{64} -4.40844e8 q^{65} -3.18386e12 q^{66} -1.82171e11 q^{67} -4.92712e11 q^{68} +1.51201e12 q^{69} +6.74720e9 q^{70} -2.29472e11 q^{71} -1.19357e12 q^{72} +8.52469e11 q^{73} -9.01948e11 q^{74} +2.89125e12 q^{75} +9.06179e11 q^{76} +7.79952e11 q^{77} -2.27248e11 q^{78} -1.12377e12 q^{79} -2.78685e10 q^{80} +7.20366e12 q^{81} -1.74832e11 q^{82} -2.74958e12 q^{83} +1.94323e12 q^{84} -2.97493e10 q^{85} -1.04286e13 q^{86} +1.24153e13 q^{87} +2.92904e12 q^{88} -7.83448e12 q^{89} -3.42921e11 q^{90} +5.56691e10 q^{91} -6.61895e12 q^{92} -2.03026e13 q^{93} +8.69805e12 q^{94} +5.47139e10 q^{95} -2.01297e13 q^{96} -2.16953e12 q^{97} +1.23490e13 q^{98} -3.96404e13 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 109 q + 192 q^{2} + 8018 q^{3} + 471040 q^{4} + 88496 q^{5} + 383232 q^{6} + 1680731 q^{7} + 1820859 q^{8} + 59521391 q^{9} + 16373653 q^{10} + 21199298 q^{11} + 63225856 q^{12} + 59695238 q^{13} + 37888529 q^{14}+ \cdots + 12084396239183 q^{99}+O(q^{100}) \) 109 * q + 192 * q^2 + 8018 * q^3 + 471040 * q^4 + 88496 * q^5 + 383232 * q^6 + 1680731 * q^7 + 1820859 * q^8 + 59521391 * q^9 + 16373653 * q^10 + 21199298 * q^11 + 63225856 * q^12 + 59695238 * q^13 + 37888529 * q^14 + 87246239 * q^15 + 2130706432 * q^16 + 228353715 * q^17 + 400647337 * q^18 + 1139301305 * q^19 + 1109969259 * q^20 + 539982398 * q^21 + 1613315649 * q^22 + 920306804 * q^23 + 5542439613 * q^24 + 31241700999 * q^25 + 1864366110 * q^26 + 17825460755 * q^27 + 20413389070 * q^28 + 7185436621 * q^29 + 2050251883 * q^30 + 28475592572 * q^31 + 8334714660 * q^32 + 19623425846 * q^33 + 37845014194 * q^34 + 25255003636 * q^35 + 287968706746 * q^36 + 71523920490 * q^37 + 67778214914 * q^38 + 44951568463 * q^39 + 169184871486 * q^40 + 69139231052 * q^41 + 58715177635 * q^42 + 247544146139 * q^43 + 63861560722 * q^44 + 257443045479 * q^45 + 160530477869 * q^46 + 308496573061 * q^47 + 412228130018 * q^48 + 1736616239908 * q^49 + 1680360028531 * q^50 + 756579032995 * q^51 + 928015404666 * q^52 + 342783723680 * q^53 - 597894730601 * q^54 + 59276330527 * q^55 - 3822929869144 * q^56 - 562905761941 * q^57 + 62740419347 * q^58 + 827401964151 * q^59 - 2247133283907 * q^60 + 988213134514 * q^61 + 1937380192071 * q^62 + 1788190111357 * q^63 + 11682175668457 * q^64 + 2494670804291 * q^65 + 11819807890512 * q^66 + 8038740399790 * q^67 + 10126245189885 * q^68 + 5225665164579 * q^69 + 11464042631319 * q^70 + 4867145119603 * q^71 + 18133468947055 * q^72 + 9684156738615 * q^73 + 16996786880941 * q^74 + 16718732018262 * q^75 + 21454522032798 * q^76 + 6593100920650 * q^77 + 33749579076633 * q^78 + 7591753073823 * q^79 + 24349241260570 * q^80 + 38778649605417 * q^81 + 25555033184251 * q^82 + 16945724819556 * q^83 + 21855489402730 * q^84 + 15544906794766 * q^85 + 18664144286914 * q^86 + 19049540636401 * q^87 + 17318749473003 * q^88 + 11289674998576 * q^89 + 20983303956671 * q^90 + 47242561944227 * q^91 - 25046698097386 * q^92 - 5411884145985 * q^93 + 18338784709341 * q^94 + 6784117894603 * q^95 - 36827486682955 * q^96 + 45969533477736 * q^97 - 42983409526150 * q^98 + 12084396239183 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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