LMFDB - Embedded newform 197.14.a.b.1.1

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			1.1
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)

$f(q)$	$=$	\(q-179.919 q^{2} +949.600 q^{3} +24179.0 q^{4} -44809.9 q^{5} -170851. q^{6} +555727. q^{7} -2.87636e6 q^{8} -692583. q^{9} +8.06216e6 q^{10} -2.55797e6 q^{11} +2.29603e7 q^{12} -2.39165e7 q^{13} -9.99861e7 q^{14} -4.25515e7 q^{15} +3.19439e8 q^{16} -3.92961e7 q^{17} +1.24609e8 q^{18} -2.10089e8 q^{19} -1.08346e9 q^{20} +5.27719e8 q^{21} +4.60229e8 q^{22} -5.41937e8 q^{23} -2.73139e9 q^{24} +7.87221e8 q^{25} +4.30304e9 q^{26} -2.17165e9 q^{27} +1.34369e10 q^{28} -3.63889e9 q^{29} +7.65583e9 q^{30} -5.70814e9 q^{31} -3.39101e10 q^{32} -2.42905e9 q^{33} +7.07012e9 q^{34} -2.49021e10 q^{35} -1.67459e10 q^{36} -5.77354e9 q^{37} +3.77991e10 q^{38} -2.27111e10 q^{39} +1.28889e11 q^{40} -5.15758e10 q^{41} -9.49468e10 q^{42} -2.92164e10 q^{43} -6.18491e10 q^{44} +3.10345e10 q^{45} +9.75050e10 q^{46} -7.37675e10 q^{47} +3.03339e11 q^{48} +2.11944e11 q^{49} -1.41636e11 q^{50} -3.73155e10 q^{51} -5.78277e11 q^{52} -2.11878e11 q^{53} +3.90721e11 q^{54} +1.14622e11 q^{55} -1.59847e12 q^{56} -1.99501e11 q^{57} +6.54706e11 q^{58} +3.58741e11 q^{59} -1.02885e12 q^{60} +5.12315e10 q^{61} +1.02700e12 q^{62} -3.84887e11 q^{63} +3.48424e12 q^{64} +1.07170e12 q^{65} +4.37033e11 q^{66} +1.03738e12 q^{67} -9.50138e11 q^{68} -5.14624e11 q^{69} +4.48036e12 q^{70} +1.71362e12 q^{71} +1.99212e12 q^{72} +8.16173e11 q^{73} +1.03877e12 q^{74} +7.47545e11 q^{75} -5.07974e12 q^{76} -1.42154e12 q^{77} +4.08617e12 q^{78} -2.72383e12 q^{79} -1.43140e13 q^{80} -9.57995e11 q^{81} +9.27947e12 q^{82} +1.23717e12 q^{83} +1.27597e13 q^{84} +1.76085e12 q^{85} +5.25659e12 q^{86} -3.45549e12 q^{87} +7.35765e12 q^{88} -2.00795e12 q^{89} -5.58371e12 q^{90} -1.32911e13 q^{91} -1.31035e13 q^{92} -5.42045e12 q^{93} +1.32722e13 q^{94} +9.41407e12 q^{95} -3.22010e13 q^{96} +2.76413e12 q^{97} -3.81328e13 q^{98} +1.77161e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−179.919	−1.98785	−0.993923	−	0.110076i	$-0.964890\pi$
$2$	−179.919	−1.98785	−0.993923	+	0.110076i	$0.964890\pi$
$3$	949.600	0.752060	0.376030	−	0.926607i	$-0.377289\pi$
$3$	949.600	0.752060	0.376030	+	0.926607i	$0.377289\pi$
$4$	24179.0	2.95153
$5$	−44809.9	−1.28253	−0.641267	−	0.767318i	$-0.721591\pi$
$5$	−44809.9	−1.28253	−0.641267	+	0.767318i	$0.721591\pi$
$6$	−170851.	−1.49498
$7$	555727.	1.78535	0.892677	−	0.450696i	$-0.148824\pi$
$7$	555727.	1.78535	0.892677	+	0.450696i	$0.148824\pi$
$8$	−2.87636e6	−3.87935
$9$	−692583.	−0.434405
$10$	8.06216e6	2.54948
$11$	−2.55797e6	−0.435355	−0.217677	−	0.976021i	$-0.569848\pi$
$11$	−2.55797e6	−0.435355	−0.217677	+	0.976021i	$0.569848\pi$
$12$	2.29603e7	2.21973
$13$	−2.39165e7	−1.37425	−0.687126	−	0.726538i	$-0.741128\pi$
$13$	−2.39165e7	−1.37425	−0.687126	+	0.726538i	$0.741128\pi$
$14$	−9.99861e7	−3.54901
$15$	−4.25515e7	−0.964542
$16$	3.19439e8	4.76001
$17$	−3.92961e7	−0.394849	−0.197425	−	0.980318i	$-0.563258\pi$
$17$	−3.92961e7	−0.394849	−0.197425	+	0.980318i	$0.563258\pi$
$18$	1.24609e8	0.863531
$19$	−2.10089e8	−1.02448	−0.512242	−	0.858841i	$-0.671185\pi$
$19$	−2.10089e8	−1.02448	−0.512242	+	0.858841i	$0.671185\pi$
$20$	−1.08346e9	−3.78544
$21$	5.27719e8	1.34269
$22$	4.60229e8	0.865418
$23$	−5.41937e8	−0.763340	−0.381670	−	0.924299i	$-0.624651\pi$
$23$	−5.41937e8	−0.763340	−0.381670	+	0.924299i	$0.624651\pi$
$24$	−2.73139e9	−2.91750
$25$	7.87221e8	0.644892
$26$	4.30304e9	2.73180
$27$	−2.17165e9	−1.07876
$28$	1.34369e10	5.26953
$29$	−3.63889e9	−1.13601	−0.568004	−	0.823026i	$-0.692284\pi$
$29$	−3.63889e9	−1.13601	−0.568004	+	0.823026i	$0.692284\pi$
$30$	7.65583e9	1.91736
$31$	−5.70814e9	−1.15516	−0.577582	−	0.816333i	$-0.696004\pi$
$31$	−5.70814e9	−1.15516	−0.577582	+	0.816333i	$0.696004\pi$
$32$	−3.39101e10	−5.58283
$33$	−2.42905e9	−0.327413
$34$	7.07012e9	0.784899
$35$	−2.49021e10	−2.28978
$36$	−1.67459e10	−1.28216
$37$	−5.77354e9	−0.369940	−0.184970	−	0.982744i	$-0.559219\pi$
$37$	−5.77354e9	−0.369940	−0.184970	+	0.982744i	$0.559219\pi$
$38$	3.77991e10	2.03652
$39$	−2.27111e10	−1.03352
$40$	1.28889e11	4.97539
$41$	−5.15758e10	−1.69571	−0.847853	−	0.530231i	$-0.822105\pi$
$41$	−5.15758e10	−1.69571	−0.847853	+	0.530231i	$0.822105\pi$
$42$	−9.49468e10	−2.66907
$43$	−2.92164e10	−0.704825	−0.352412	−	0.935845i	$-0.614639\pi$
$43$	−2.92164e10	−0.704825	−0.352412	+	0.935845i	$0.614639\pi$
$44$	−6.18491e10	−1.28496
$45$	3.10345e10	0.557139
$46$	9.75050e10	1.51740
$47$	−7.37675e10	−0.998226	−0.499113	−	0.866537i	$-0.666341\pi$
$47$	−7.37675e10	−0.998226	−0.499113	+	0.866537i	$0.666341\pi$
$48$	3.03339e11	3.57982
$49$	2.11944e11	2.18749
$50$	−1.41636e11	−1.28195
$51$	−3.73155e10	−0.296950
$52$	−5.78277e11	−4.05615
$53$	−2.11878e11	−1.31309	−0.656544	−	0.754288i	$-0.727982\pi$
$53$	−2.11878e11	−1.31309	−0.656544	+	0.754288i	$0.727982\pi$
$54$	3.90721e11	2.14441
$55$	1.14622e11	0.558357
$56$	−1.59847e12	−6.92601
$57$	−1.99501e11	−0.770474
$58$	6.54706e11	2.25821
$59$	3.58741e11	1.10724	0.553621	−	0.832768i	$-0.313245\pi$
$59$	3.58741e11	1.10724	0.553621	+	0.832768i	$0.313245\pi$
$60$	−1.02885e12	−2.84688
$61$	5.12315e10	0.127319	0.0636595	−	0.997972i	$-0.479723\pi$
$61$	5.12315e10	0.127319	0.0636595	+	0.997972i	$0.479723\pi$
$62$	1.02700e12	2.29629
$63$	−3.84887e11	−0.775568
$64$	3.48424e12	6.33779
$65$	1.07170e12	1.76252
$66$	4.37033e11	0.650847
$67$	1.03738e12	1.40105	0.700525	−	0.713628i	$-0.252949\pi$
$67$	1.03738e12	1.40105	0.700525	+	0.713628i	$0.252949\pi$
$68$	−9.50138e11	−1.16541
$69$	−5.14624e11	−0.574078
$70$	4.48036e12	4.55172
$71$	1.71362e12	1.58758	0.793791	−	0.608191i	$-0.208105\pi$
$71$	1.71362e12	1.58758	0.793791	+	0.608191i	$0.208105\pi$
$72$	1.99212e12	1.68521
$73$	8.16173e11	0.631224	0.315612	−	0.948888i	$-0.397790\pi$
$73$	8.16173e11	0.631224	0.315612	+	0.948888i	$0.397790\pi$
$74$	1.03877e12	0.735384
$75$	7.47545e11	0.484997
$76$	−5.07974e12	−3.02380
$77$	−1.42154e12	−0.777263
$78$	4.08617e12	2.05448
$79$	−2.72383e12	−1.26068	−0.630339	−	0.776320i	$-0.717084\pi$
$79$	−2.72383e12	−1.26068	−0.630339	+	0.776320i	$0.717084\pi$
$80$	−1.43140e13	−6.10487
$81$	−9.57995e11	−0.376886
$82$	9.27947e12	3.37080
$83$	1.23717e12	0.415358	0.207679	−	0.978197i	$-0.433409\pi$
$83$	1.23717e12	0.415358	0.207679	+	0.978197i	$0.433409\pi$
$84$	1.27597e13	3.96301
$85$	1.76085e12	0.506407
$86$	5.25659e12	1.40108
$87$	−3.45549e12	−0.854346
$88$	7.35765e12	1.68889
$89$	−2.00795e12	−0.428271	−0.214135	−	0.976804i	$-0.568693\pi$
$89$	−2.00795e12	−0.428271	−0.214135	+	0.976804i	$0.568693\pi$
$90$	−5.58371e12	−1.10751
$91$	−1.32911e13	−2.45353
$92$	−1.31035e13	−2.25302
$93$	−5.42045e12	−0.868753
$94$	1.32722e13	1.98432
$95$	9.41407e12	1.31393
$96$	−3.22010e13	−4.19862
$97$	2.76413e12	0.336932	0.168466	−	0.985708i	$-0.446119\pi$
$97$	2.76413e12	0.336932	0.168466	+	0.985708i	$0.446119\pi$
$98$	−3.81328e13	−4.34840
$99$	1.77161e12	0.189121
$100$	1.90342e13	1.90342
$101$	−1.05063e13	−0.984831	−0.492416	−	0.870360i	$-0.663886\pi$
$101$	−1.05063e13	−0.984831	−0.492416	+	0.870360i	$0.663886\pi$
$102$	6.71379e12	0.590291
$103$	6.36512e12	0.525248	0.262624	−	0.964898i	$-0.415412\pi$
$103$	6.36512e12	0.525248	0.262624	+	0.964898i	$0.415412\pi$
$104$	6.87926e13	5.33120
$105$	−2.36470e13	−1.72205
$106$	3.81210e13	2.61022
$107$	2.64173e13	1.70174	0.850871	−	0.525375i	$-0.176075\pi$
$107$	2.64173e13	1.70174	0.850871	+	0.525375i	$0.176075\pi$
$108$	−5.25081e13	−3.18399
$109$	−2.48408e13	−1.41871	−0.709354	−	0.704852i	$-0.751013\pi$
$109$	−2.48408e13	−1.41871	−0.709354	+	0.704852i	$0.751013\pi$
$110$	−2.06228e13	−1.10993
$111$	−5.48256e12	−0.278217
$112$	1.77521e14	8.49831
$113$	1.75783e13	0.794266	0.397133	−	0.917761i	$-0.370005\pi$
$113$	1.75783e13	0.794266	0.397133	+	0.917761i	$0.370005\pi$
$114$	3.58940e13	1.53158
$115$	2.42841e13	0.979009
$116$	−8.79845e13	−3.35296
$117$	1.65642e13	0.596982
$118$	−6.45444e13	−2.20103
$119$	−2.18379e13	−0.704946
$120$	1.22393e14	3.74179
$121$	−2.79795e13	−0.810466
$122$	−9.21753e12	−0.253091
$123$	−4.89763e13	−1.27527
$124$	−1.38017e14	−3.40950
$125$	1.94243e13	0.455438
$126$	6.92486e13	1.54171
$127$	−4.33881e13	−0.917584	−0.458792	−	0.888544i	$-0.651718\pi$
$127$	−4.33881e13	−0.917584	−0.458792	+	0.888544i	$0.651718\pi$
$128$	−3.49090e14	−7.01572
$129$	−2.77439e13	−0.530071
$130$	−1.92819e14	−3.50363
$131$	5.74817e13	0.993724	0.496862	−	0.867829i	$-0.334485\pi$
$131$	5.74817e13	0.993724	0.496862	+	0.867829i	$0.334485\pi$
$132$	−5.87319e13	−0.966370
$133$	−1.16752e14	−1.82907
$134$	−1.86646e14	−2.78507
$135$	9.73112e13	1.38354
$136$	1.13030e14	1.53176
$137$	−6.87709e13	−0.888631	−0.444315	−	0.895870i	$-0.646553\pi$
$137$	−6.87709e13	−0.888631	−0.444315	+	0.895870i	$0.646553\pi$
$138$	9.25907e13	1.14118
$139$	3.98393e13	0.468507	0.234253	−	0.972176i	$-0.424735\pi$
$139$	3.98393e13	0.468507	0.234253	+	0.972176i	$0.424735\pi$
$140$	−6.02106e14	−6.75835
$141$	−7.00496e13	−0.750726
$142$	−3.08314e14	−3.15587
$143$	6.11778e13	0.598287
$144$	−2.21238e14	−2.06778
$145$	1.63058e14	1.45697
$146$	−1.46845e14	−1.25478
$147$	2.01262e14	1.64513
$148$	−1.39598e14	−1.09189
$149$	−9.47011e13	−0.708997	−0.354498	−	0.935057i	$-0.615348\pi$
$149$	−9.47011e13	−0.708997	−0.354498	+	0.935057i	$0.615348\pi$
$150$	−1.34498e14	−0.964100
$151$	−3.29571e13	−0.226255	−0.113127	−	0.993580i	$-0.536087\pi$
$151$	−3.29571e13	−0.226255	−0.113127	+	0.993580i	$0.536087\pi$
$152$	6.04292e14	3.97433
$153$	2.72158e13	0.171525
$154$	2.55762e14	1.54508
$155$	2.55781e14	1.48154
$156$	−5.49132e14	−3.05047
$157$	−7.31077e13	−0.389597	−0.194798	−	0.980843i	$-0.562405\pi$
$157$	−7.31077e13	−0.389597	−0.194798	+	0.980843i	$0.562405\pi$
$158$	4.90070e14	2.50604
$159$	−2.01200e14	−0.987521
$160$	1.51951e15	7.16016
$161$	−3.01169e14	−1.36283
$162$	1.72362e14	0.749192
$163$	−1.07246e14	−0.447882	−0.223941	−	0.974603i	$-0.571892\pi$
$163$	−1.07246e14	−0.447882	−0.223941	+	0.974603i	$0.571892\pi$
$164$	−1.24705e15	−5.00493
$165$	1.08845e14	0.419918
$166$	−2.22591e14	−0.825668
$167$	−1.01900e14	−0.363512	−0.181756	−	0.983344i	$-0.558178\pi$
$167$	−1.01900e14	−0.363512	−0.181756	+	0.983344i	$0.558178\pi$
$168$	−1.51791e15	−5.20878
$169$	2.69125e14	0.888568
$170$	−3.16811e14	−1.00666
$171$	1.45504e14	0.445041
$172$	−7.06421e14	−2.08031
$173$	−3.58284e14	−1.01608	−0.508040	−	0.861334i	$-0.669630\pi$
$173$	−3.58284e14	−1.01608	−0.508040	+	0.861334i	$0.669630\pi$
$174$	6.21709e14	1.69831
$175$	4.37480e14	1.15136
$176$	−8.17116e14	−2.07229
$177$	3.40660e14	0.832713
$178$	3.61270e14	0.851337
$179$	−7.27116e13	−0.165219	−0.0826093	−	0.996582i	$-0.526325\pi$
$179$	−7.27116e13	−0.165219	−0.0826093	+	0.996582i	$0.526325\pi$
$180$	7.50383e14	1.64442
$181$	6.54752e14	1.38410	0.692048	−	0.721852i	$-0.256709\pi$
$181$	6.54752e14	1.38410	0.692048	+	0.721852i	$0.256709\pi$
$182$	2.39132e15	4.87724
$183$	4.86494e13	0.0957515
$184$	1.55881e15	2.96126
$185$	2.58712e14	0.474460
$186$	9.75244e14	1.72695
$187$	1.00518e14	0.171899
$188$	−1.78362e15	−2.94630
$189$	−1.20684e15	−1.92597
$190$	−1.69377e15	−2.61190
$191$	−8.62822e13	−0.128589	−0.0642946	−	0.997931i	$-0.520480\pi$
$191$	−8.62822e13	−0.128589	−0.0642946	+	0.997931i	$0.520480\pi$
$192$	3.30863e15	4.76640
$193$	−1.89475e14	−0.263893	−0.131947	−	0.991257i	$-0.542123\pi$
$193$	−1.89475e14	−0.263893	−0.131947	+	0.991257i	$0.542123\pi$
$194$	−4.97320e14	−0.669768
$195$	1.01768e15	1.32552
$196$	5.12458e15	6.45646
$197$	5.84517e13	0.0712470
$197$	5.84517e13	0.0712470
$198$	−3.18746e14	−0.375942
$199$	1.07497e15	1.22702	0.613511	−	0.789686i	$-0.289757\pi$
$199$	1.07497e15	1.22702	0.613511	+	0.789686i	$0.289757\pi$
$200$	−2.26433e15	−2.50176
$201$	9.85101e14	1.05367
$202$	1.89029e15	1.95769
$203$	−2.02223e15	−2.02818
$204$	−9.02251e14	−0.876458
$205$	2.31110e15	2.17480
$206$	−1.14521e15	−1.04411
$207$	3.75336e14	0.331599
$208$	−7.63987e15	−6.54146
$209$	5.37402e14	0.446014
$210$	4.25455e15	3.42317
$211$	2.40819e15	1.87868	0.939342	−	0.342981i	$-0.111437\pi$
$211$	2.40819e15	1.87868	0.939342	+	0.342981i	$0.111437\pi$
$212$	−5.12300e15	−3.87562
$213$	1.62726e15	1.19396
$214$	−4.75298e15	−3.38280
$215$	1.30918e15	0.903961
$216$	6.24644e15	4.18488
$217$	−3.17217e15	−2.06238
$218$	4.46934e15	2.82017
$219$	7.75038e14	0.474719
$220$	2.77145e15	1.64801
$221$	9.39825e14	0.542622
$222$	9.86418e14	0.553053
$223$	−1.46402e15	−0.797197	−0.398599	−	0.917126i	$-0.630503\pi$
$223$	−1.46402e15	−0.797197	−0.398599	+	0.917126i	$0.630503\pi$
$224$	−1.88448e16	−9.96733
$225$	−5.45216e14	−0.280144
$226$	−3.16267e15	−1.57888
$227$	1.73723e15	0.842731	0.421365	−	0.906891i	$-0.361551\pi$
$227$	1.73723e15	0.842731	0.421365	+	0.906891i	$0.361551\pi$
$228$	−4.82372e15	−2.27408
$229$	−1.38840e15	−0.636187	−0.318093	−	0.948059i	$-0.603043\pi$
$229$	−1.38840e15	−0.636187	−0.318093	+	0.948059i	$0.603043\pi$
$230$	−4.36918e15	−1.94612
$231$	−1.34989e15	−0.584548
$232$	1.04668e16	4.40697
$233$	2.04504e14	0.0837313	0.0418657	−	0.999123i	$-0.486670\pi$
$233$	2.04504e14	0.0837313	0.0418657	+	0.999123i	$0.486670\pi$
$234$	−2.98021e15	−1.18671
$235$	3.30551e15	1.28026
$236$	8.67398e15	3.26806
$237$	−2.58655e15	−0.948106
$238$	3.92906e15	1.40132
$239$	−2.39140e14	−0.0829976	−0.0414988	−	0.999139i	$-0.513213\pi$
$239$	−2.39140e14	−0.0829976	−0.0414988	+	0.999139i	$0.513213\pi$
$240$	−1.35926e16	−4.59123
$241$	−4.55803e15	−1.49853	−0.749267	−	0.662268i	$-0.769594\pi$
$241$	−4.55803e15	−1.49853	−0.749267	+	0.662268i	$0.769594\pi$
$242$	5.03405e15	1.61108
$243$	2.55259e15	0.795318
$244$	1.23872e15	0.375786
$245$	−9.49718e15	−2.80553
$246$	8.81179e15	2.53505
$247$	5.02460e15	1.40790
$248$	1.64187e16	4.48128
$249$	1.17482e15	0.312374
$250$	−3.49480e15	−0.905341
$251$	−3.34116e15	−0.843370	−0.421685	−	0.906742i	$-0.638561\pi$
$251$	−3.34116e15	−0.843370	−0.421685	+	0.906742i	$0.638561\pi$
$252$	−9.30617e15	−2.28911
$253$	1.38626e15	0.332324
$254$	7.80635e15	1.82402
$255$	1.67210e15	0.380849
$256$	3.42651e16	7.60839
$257$	−3.94292e15	−0.853597	−0.426798	−	0.904347i	$-0.640359\pi$
$257$	−3.94292e15	−0.853597	−0.426798	+	0.904347i	$0.640359\pi$
$258$	4.99165e15	1.05370
$259$	−3.20852e15	−0.660474
$260$	2.59125e16	5.20215
$261$	2.52023e15	0.493488
$262$	−1.03421e16	−1.97537
$263$	−8.18969e15	−1.52600	−0.763001	−	0.646398i	$-0.776275\pi$
$263$	−8.18969e15	−1.52600	−0.763001	+	0.646398i	$0.776275\pi$
$264$	6.98683e15	1.27015
$265$	9.49425e15	1.68408
$266$	2.10060e16	3.63591
$267$	−1.90675e15	−0.322086
$268$	2.50829e16	4.13524
$269$	−2.24633e15	−0.361480	−0.180740	−	0.983531i	$-0.557849\pi$
$269$	−2.24633e15	−0.361480	−0.180740	+	0.983531i	$0.557849\pi$
$270$	−1.75082e16	−2.75027
$271$	−6.38241e15	−0.978779	−0.489389	−	0.872065i	$-0.662780\pi$
$271$	−6.38241e15	−0.978779	−0.489389	+	0.872065i	$0.662780\pi$
$272$	−1.25527e16	−1.87949
$273$	−1.26212e16	−1.84520
$274$	1.23732e16	1.76646
$275$	−2.01369e15	−0.280757
$276$	−1.24431e16	−1.69441
$277$	−1.21980e16	−1.62244	−0.811221	−	0.584739i	$-0.801197\pi$
$277$	−1.21980e16	−1.62244	−0.811221	+	0.584739i	$0.801197\pi$
$278$	−7.16786e15	−0.931319
$279$	3.95336e15	0.501810
$280$	7.16274e16	8.88284
$281$	1.40647e16	1.70428	0.852138	−	0.523317i	$-0.175305\pi$
$281$	1.40647e16	1.70428	0.852138	+	0.523317i	$0.175305\pi$
$282$	1.26033e16	1.49233
$283$	−8.61075e15	−0.996390	−0.498195	−	0.867065i	$-0.666004\pi$
$283$	−8.61075e15	−0.996390	−0.498195	+	0.867065i	$0.666004\pi$
$284$	4.14336e16	4.68580
$285$	8.93960e15	0.988158
$286$	−1.10071e16	−1.18930
$287$	−2.86621e16	−3.02744
$288$	2.34855e16	2.42521
$289$	−8.36040e15	−0.844094
$290$	−2.93373e16	−2.89623
$291$	2.62482e15	0.253393
$292$	1.97342e16	1.86308
$293$	−4.30153e15	−0.397176	−0.198588	−	0.980083i	$-0.563636\pi$
$293$	−4.30153e15	−0.397176	−0.198588	+	0.980083i	$0.563636\pi$
$294$	−3.62109e16	−3.27026
$295$	−1.60751e16	−1.42008
$296$	1.66068e16	1.43513
$297$	5.55501e15	0.469643
$298$	1.70386e16	1.40938
$299$	1.29613e16	1.04902
$300$	1.80749e16	1.43149
$301$	−1.62363e16	−1.25836
$302$	5.92961e15	0.449760
$303$	−9.97681e15	−0.740652
$304$	−6.71107e16	−4.87656
$305$	−2.29568e15	−0.163291
$306$	−4.89664e15	−0.340964
$307$	−2.23744e14	−0.0152529	−0.00762646	−	0.999971i	$-0.502428\pi$
$307$	−2.23744e14	−0.0152529	−0.00762646	+	0.999971i	$0.502428\pi$
$308$	−3.43712e16	−2.29412
$309$	6.04432e15	0.395018
$310$	−4.60200e16	−2.94507
$311$	5.67402e15	0.355589	0.177795	−	0.984068i	$-0.443104\pi$
$311$	5.67402e15	0.355589	0.177795	+	0.984068i	$0.443104\pi$
$312$	6.53255e16	4.00938
$313$	−3.48732e15	−0.209630	−0.104815	−	0.994492i	$-0.533425\pi$
$313$	−3.48732e15	−0.209630	−0.104815	+	0.994492i	$0.533425\pi$
$314$	1.31535e16	0.774458
$315$	1.72467e16	0.994692
$316$	−6.58594e16	−3.72093
$317$	2.55013e15	0.141149	0.0705743	−	0.997507i	$-0.477517\pi$
$317$	2.55013e15	0.141149	0.0705743	+	0.997507i	$0.477517\pi$
$318$	3.61997e16	1.96304
$319$	9.30817e15	0.494567
$320$	−1.56128e17	−8.12842
$321$	2.50859e16	1.27981
$322$	5.41862e16	2.70910
$323$	8.25568e15	0.404516
$324$	−2.31633e16	−1.11239
$325$	−1.88276e16	−0.886243
$326$	1.92957e16	0.890321
$327$	−2.35888e16	−1.06695
$328$	1.48351e17	6.57823
$329$	−4.09946e16	−1.78219
$330$	−1.95834e16	−0.834733
$331$	3.94321e16	1.64804	0.824019	−	0.566562i	$-0.191727\pi$
$331$	3.94321e16	1.64804	0.824019	+	0.566562i	$0.191727\pi$
$332$	2.99135e16	1.22594
$333$	3.99866e15	0.160704
$334$	1.83338e16	0.722605
$335$	−4.64851e16	−1.79689
$336$	1.68574e17	6.39124
$337$	1.07163e16	0.398520	0.199260	−	0.979947i	$-0.436146\pi$
$337$	1.07163e16	0.398520	0.199260	+	0.979947i	$0.436146\pi$
$338$	−4.84208e16	−1.76634
$339$	1.66923e16	0.597336
$340$	4.25755e16	1.49468
$341$	1.46013e16	0.502906
$342$	−2.61790e16	−0.884674
$343$	6.39392e16	2.12010
$344$	8.40368e16	2.73426
$345$	2.30602e16	0.736274
$346$	6.44622e16	2.01981
$347$	−2.18057e16	−0.670547	−0.335273	−	0.942121i	$-0.608829\pi$
$347$	−2.18057e16	−0.670547	−0.335273	+	0.942121i	$0.608829\pi$
$348$	−8.35500e16	−2.52163
$349$	5.38017e16	1.59379	0.796895	−	0.604118i	$-0.206475\pi$
$349$	5.38017e16	1.59379	0.796895	+	0.604118i	$0.206475\pi$
$350$	−7.87112e16	−2.28873
$351$	5.19382e16	1.48249
$352$	8.67411e16	2.43051
$353$	5.29552e16	1.45671	0.728355	−	0.685200i	$-0.240285\pi$
$353$	5.29552e16	1.45671	0.728355	+	0.685200i	$0.240285\pi$
$354$	−6.12914e16	−1.65531
$355$	−7.67872e16	−2.03613
$356$	−4.85502e16	−1.26406
$357$	−2.07373e16	−0.530162
$358$	1.30822e16	0.328429
$359$	−2.11409e16	−0.521206	−0.260603	−	0.965446i	$-0.583921\pi$
$359$	−2.11409e16	−0.521206	−0.260603	+	0.965446i	$0.583921\pi$
$360$	−8.92666e16	−2.16134
$361$	2.08446e15	0.0495674
$362$	−1.17803e17	−2.75137
$363$	−2.65693e16	−0.609519
$364$	−3.21364e17	−7.24167
$365$	−3.65726e16	−0.809566
$366$	−8.75297e15	−0.190339
$367$	1.72307e15	0.0368106	0.0184053	−	0.999831i	$-0.494141\pi$
$367$	1.72307e15	0.0368106	0.0184053	+	0.999831i	$0.494141\pi$
$368$	−1.73116e17	−3.63351
$369$	3.57205e16	0.736624
$370$	−4.65472e16	−0.943154
$371$	−1.17747e17	−2.34433
$372$	−1.31061e17	−2.56415
$373$	3.67155e16	0.705899	0.352949	−	0.935642i	$-0.385179\pi$
$373$	3.67155e16	0.705899	0.352949	+	0.935642i	$0.385179\pi$
$374$	−1.80852e16	−0.341710
$375$	1.84453e16	0.342517
$376$	2.12182e17	3.87247
$377$	8.70295e16	1.56116
$378$	2.17134e17	3.82853
$379$	2.67731e16	0.464028	0.232014	−	0.972712i	$-0.425468\pi$
$379$	2.67731e16	0.464028	0.232014	+	0.972712i	$0.425468\pi$
$380$	2.27622e17	3.87812
$381$	−4.12013e16	−0.690079
$382$	1.55238e16	0.255615
$383$	−1.85352e16	−0.300058	−0.150029	−	0.988682i	$-0.547937\pi$
$383$	−1.85352e16	−0.300058	−0.150029	+	0.988682i	$0.547937\pi$
$384$	−3.31496e17	−5.27624
$385$	6.36988e16	0.996866
$386$	3.40901e16	0.524579
$387$	2.02347e16	0.306180
$388$	6.68337e16	0.994465
$389$	1.15175e17	1.68533	0.842666	−	0.538437i	$-0.180985\pi$
$389$	1.15175e17	1.68533	0.842666	+	0.538437i	$0.180985\pi$
$390$	−1.83101e17	−2.63494
$391$	2.12960e16	0.301404
$392$	−6.09628e17	−8.48604
$393$	5.45846e16	0.747341
$394$	−1.05166e16	−0.141628
$395$	1.22055e17	1.61686
$396$	4.28356e16	0.558195
$397$	−9.98843e15	−0.128044	−0.0640219	−	0.997948i	$-0.520393\pi$
$397$	−9.98843e15	−0.128044	−0.0640219	+	0.997948i	$0.520393\pi$
$398$	−1.93408e17	−2.43913
$399$	−1.10868e17	−1.37557
$400$	2.51469e17	3.06969
$401$	1.08698e16	0.130552	0.0652761	−	0.997867i	$-0.479207\pi$
$401$	1.08698e16	0.130552	0.0652761	+	0.997867i	$0.479207\pi$
$402$	−1.77239e17	−2.09454
$403$	1.36519e17	1.58749
$404$	−2.54032e17	−2.90676
$405$	4.29276e16	0.483369
$406$	3.63838e17	4.03171
$407$	1.47686e16	0.161055
$408$	1.07333e17	1.15197
$409$	2.72337e16	0.287677	0.143838	−	0.989601i	$-0.454055\pi$
$409$	2.72337e16	0.287677	0.143838	+	0.989601i	$0.454055\pi$
$410$	−4.15812e17	−4.32317
$411$	−6.53049e16	−0.668304
$412$	1.53902e17	1.55029
$413$	1.99362e17	1.97682
$414$	−6.75302e16	−0.659168
$415$	−5.54375e16	−0.532710
$416$	8.11012e17	7.67221
$417$	3.78314e16	0.352345
$418$	−9.66890e16	−0.886607
$419$	−7.15857e16	−0.646302	−0.323151	−	0.946347i	$-0.604742\pi$
$419$	−7.15857e16	−0.646302	−0.323151	+	0.946347i	$0.604742\pi$
$420$	−5.71760e17	−5.08269
$421$	−1.30140e17	−1.13914	−0.569568	−	0.821944i	$-0.692890\pi$
$421$	−1.30140e17	−1.13914	−0.569568	+	0.821944i	$0.692890\pi$
$422$	−4.33279e17	−3.73454
$423$	5.10901e16	0.433635
$424$	6.09439e17	5.09392
$425$	−3.09347e16	−0.254635
$426$	−2.92775e17	−2.37340
$427$	2.84707e16	0.227310
$428$	6.38742e17	5.02275
$429$	5.80945e16	0.449948
$430$	−2.35547e17	−1.79694
$431$	1.06072e17	0.797077	0.398539	−	0.917152i	$-0.369518\pi$
$431$	1.06072e17	0.797077	0.398539	+	0.917152i	$0.369518\pi$
$432$	−6.93708e17	−5.13491
$433$	−1.27008e17	−0.926105	−0.463053	−	0.886331i	$-0.653246\pi$
$433$	−1.27008e17	−0.926105	−0.463053	+	0.886331i	$0.653246\pi$
$434$	5.70735e17	4.09969
$435$	1.54840e17	1.09573
$436$	−6.00624e17	−4.18736
$437$	1.13855e17	0.782030
$438$	−1.39444e17	−0.943668
$439$	−1.15719e17	−0.771585	−0.385793	−	0.922585i	$-0.626072\pi$
$439$	−1.15719e17	−0.771585	−0.385793	+	0.922585i	$0.626072\pi$
$440$	−3.29695e17	−2.16606
$441$	−1.46789e17	−0.950259
$442$	−1.69093e17	−1.07865
$443$	−1.20090e17	−0.754887	−0.377444	−	0.926033i	$-0.623197\pi$
$443$	−1.20090e17	−0.754887	−0.377444	+	0.926033i	$0.623197\pi$
$444$	−1.32563e17	−0.821167
$445$	8.99761e16	0.549272
$446$	2.63406e17	1.58471
$447$	−8.99282e16	−0.533208
$448$	1.93629e18	11.3152
$449$	−1.75762e17	−1.01233	−0.506167	−	0.862436i	$-0.668938\pi$
$449$	−1.75762e17	−1.01233	−0.506167	+	0.862436i	$0.668938\pi$
$450$	9.80948e16	0.556884
$451$	1.31929e17	0.738234
$452$	4.25024e17	2.34430
$453$	−3.12960e16	−0.170157
$454$	−3.12561e17	−1.67522
$455$	5.95571e17	3.14673
$456$	5.73836e17	2.98893
$457$	−1.32882e17	−0.682354	−0.341177	−	0.939999i	$-0.610826\pi$
$457$	−1.32882e17	−0.682354	−0.341177	+	0.939999i	$0.610826\pi$
$458$	2.49800e17	1.26464
$459$	8.53371e16	0.425947
$460$	5.87165e17	2.88958
$461$	3.09208e17	1.50036	0.750178	−	0.661236i	$-0.229968\pi$
$461$	3.09208e17	1.50036	0.750178	+	0.661236i	$0.229968\pi$
$462$	2.42871e17	1.16199
$463$	2.90252e16	0.136930	0.0684649	−	0.997654i	$-0.478190\pi$
$463$	2.90252e16	0.136930	0.0684649	+	0.997654i	$0.478190\pi$
$464$	−1.16240e18	−5.40741
$465$	2.42890e17	1.11420
$466$	−3.67942e16	−0.166445
$467$	2.30131e17	1.02664	0.513318	−	0.858199i	$-0.328416\pi$
$467$	2.30131e17	1.02664	0.513318	+	0.858199i	$0.328416\pi$
$468$	4.00504e17	1.76201
$469$	5.76503e17	2.50137
$470$	−5.94725e17	−2.54496
$471$	−6.94231e16	−0.293000
$472$	−1.03187e18	−4.29538
$473$	7.47346e16	0.306849
$474$	4.65371e17	1.88469
$475$	−1.65387e17	−0.660681
$476$	−5.28018e17	−2.08067
$477$	1.46743e17	0.570412
$478$	4.30259e16	0.164987
$479$	−3.81414e17	−1.44283	−0.721415	−	0.692503i	$-0.756508\pi$
$479$	−3.81414e17	−1.44283	−0.721415	+	0.692503i	$0.756508\pi$
$480$	1.44292e18	5.38487
$481$	1.38083e17	0.508391
$482$	8.20078e17	2.97886
$483$	−2.85990e17	−1.02493
$484$	−6.76515e17	−2.39212
$485$	−1.23860e17	−0.432126
$486$	−4.59261e17	−1.58097
$487$	4.68618e17	1.59177	0.795886	−	0.605446i	$-0.207005\pi$
$487$	4.68618e17	1.59177	0.795886	+	0.605446i	$0.207005\pi$
$488$	−1.47360e17	−0.493914
$489$	−1.01841e17	−0.336834
$490$	1.70873e18	5.57697
$491$	2.44995e17	0.789092	0.394546	−	0.918876i	$-0.370902\pi$
$491$	2.44995e17	0.789092	0.394546	+	0.918876i	$0.370902\pi$
$492$	−1.18420e18	−3.76401
$493$	1.42994e17	0.448552
$494$	−9.04023e17	−2.79869
$495$	−7.93855e16	−0.242553
$496$	−1.82340e18	−5.49860
$497$	9.52307e17	2.83440
$498$	−2.11373e17	−0.620952
$499$	−5.79975e17	−1.68173	−0.840864	−	0.541247i	$-0.817952\pi$
$499$	−5.79975e17	−1.68173	−0.840864	+	0.541247i	$0.817952\pi$
$500$	4.69659e17	1.34424
$501$	−9.67645e16	−0.273383
$502$	6.01139e17	1.67649
$503$	−1.22373e17	−0.336894	−0.168447	−	0.985711i	$-0.553875\pi$
$503$	−1.22373e17	−0.336894	−0.168447	+	0.985711i	$0.553875\pi$
$504$	1.10707e18	3.00870
$505$	4.70787e17	1.26308
$506$	−2.49415e17	−0.660608
$507$	2.55561e17	0.668257
$508$	−1.04908e18	−2.70828
$509$	−1.55692e17	−0.396827	−0.198413	−	0.980118i	$-0.563579\pi$
$509$	−1.55692e17	−0.396827	−0.198413	+	0.980118i	$0.563579\pi$
$510$	−3.00844e17	−0.757068
$511$	4.53570e17	1.12696
$512$	−3.30522e18	−8.10858
$513$	4.56239e17	1.10517
$514$	7.09408e17	1.69682
$515$	−2.85220e17	−0.673649
$516$	−6.70817e17	−1.56452
$517$	1.88695e17	0.434583
$518$	5.77274e17	1.31292
$519$	−3.40226e17	−0.764153
$520$	−3.08259e18	−6.83744
$521$	−3.93047e17	−0.860992	−0.430496	−	0.902592i	$-0.641661\pi$
$521$	−3.93047e17	−0.860992	−0.430496	+	0.902592i	$0.641661\pi$
$522$	−4.53438e17	−0.980978
$523$	9.83337e16	0.210107	0.105054	−	0.994467i	$-0.466499\pi$
$523$	9.83337e16	0.210107	0.105054	+	0.994467i	$0.466499\pi$
$524$	1.38985e18	2.93301
$525$	4.15431e17	0.865892
$526$	1.47348e18	3.03346
$527$	2.24307e17	0.456115
$528$	−7.75934e17	−1.55849
$529$	−2.10340e17	−0.417312
$530$	−1.70820e18	−3.34769
$531$	−2.48458e17	−0.480992
$532$	−2.82295e18	−5.39855
$533$	1.23351e18	2.33033
$534$	3.43062e17	0.640257
$535$	−1.18375e18	−2.18254
$536$	−2.98389e18	−5.43516
$537$	−6.90469e16	−0.124254
$538$	4.04159e17	0.718567
$539$	−5.42147e17	−0.952335
$540$	2.35288e18	4.08358
$541$	−6.47497e17	−1.11034	−0.555169	−	0.831737i	$-0.687347\pi$
$541$	−6.47497e17	−1.11034	−0.555169	+	0.831737i	$0.687347\pi$
$542$	1.14832e18	1.94566
$543$	6.21753e17	1.04092
$544$	1.33253e18	2.20437
$545$	1.11311e18	1.81954
$546$	2.27080e18	3.66797
$547$	1.09348e18	1.74540	0.872699	−	0.488258i	$-0.162367\pi$
$547$	1.09348e18	1.74540	0.872699	+	0.488258i	$0.162367\pi$
$548$	−1.66281e18	−2.62282
$549$	−3.54820e16	−0.0553080
$550$	3.62302e17	0.558101
$551$	7.64490e17	1.16382
$552$	1.48024e18	2.22705
$553$	−1.51371e18	−2.25076
$554$	2.19465e18	3.22517
$555$	2.45673e17	0.356823
$556$	9.63273e17	1.38281
$557$	−3.99173e17	−0.566373	−0.283187	−	0.959065i	$-0.591392\pi$
$557$	−3.99173e17	−0.566373	−0.283187	+	0.959065i	$0.591392\pi$
$558$	−7.11286e17	−0.997520
$559$	6.98754e17	0.968606
$560$	−7.95469e18	−10.8994
$561$	9.54521e16	0.129279
$562$	−2.53052e18	−3.38784
$563$	−1.22152e18	−1.61658	−0.808289	−	0.588786i	$-0.799606\pi$
$563$	−1.22152e18	−1.61658	−0.808289	+	0.588786i	$0.799606\pi$
$564$	−1.69373e18	−2.21579
$565$	−7.87680e17	−1.01867
$566$	1.54924e18	1.98067
$567$	−5.32384e17	−0.672876
$568$	−4.92900e18	−6.15878
$569$	−1.25761e18	−1.55352	−0.776758	−	0.629799i	$-0.783137\pi$
$569$	−1.25761e18	−1.55352	−0.776758	+	0.629799i	$0.783137\pi$
$570$	−1.60841e18	−1.96431
$571$	−5.65025e16	−0.0682234	−0.0341117	−	0.999418i	$-0.510860\pi$
$571$	−5.65025e16	−0.0682234	−0.0341117	+	0.999418i	$0.510860\pi$
$572$	1.47922e18	1.76586
$573$	−8.19336e16	−0.0967068
$574$	5.15686e18	6.01808
$575$	−4.26624e17	−0.492272
$576$	−2.41312e18	−2.75317
$577$	3.40172e17	0.383757	0.191878	−	0.981419i	$-0.438542\pi$
$577$	3.40172e17	0.383757	0.191878	+	0.981419i	$0.438542\pi$
$578$	1.50420e18	1.67793
$579$	−1.79925e17	−0.198464
$580$	3.94257e18	4.30029
$581$	6.87531e17	0.741561
$582$	−4.72255e17	−0.503706
$583$	5.41979e17	0.571659
$584$	−2.34761e18	−2.44874
$585$	−7.42238e17	−0.765650
$586$	7.73928e17	0.789525
$587$	2.21946e17	0.223923	0.111962	−	0.993713i	$-0.464287\pi$
$587$	2.21946e17	0.223923	0.111962	+	0.993713i	$0.464287\pi$
$588$	4.86631e18	4.85564
$589$	1.19922e18	1.18345
$590$	2.89223e18	2.82289
$591$	5.55058e16	0.0535821
$592$	−1.84430e18	−1.76092
$593$	6.07196e17	0.573421	0.286710	−	0.958017i	$-0.407438\pi$
$593$	6.07196e17	0.573421	0.286710	+	0.958017i	$0.407438\pi$
$594$	−9.99453e17	−0.933578
$595$	9.78553e17	0.904116
$596$	−2.28977e18	−2.09263
$597$	1.02079e18	0.922794
$598$	−2.33198e18	−2.08529
$599$	−5.09986e17	−0.451111	−0.225556	−	0.974230i	$-0.572420\pi$
$599$	−5.09986e17	−0.451111	−0.225556	+	0.974230i	$0.572420\pi$
$600$	−2.15021e18	−1.88147
$601$	−1.49306e18	−1.29239	−0.646196	−	0.763171i	$-0.723641\pi$
$601$	−1.49306e18	−1.29239	−0.646196	+	0.763171i	$0.723641\pi$
$602$	2.92123e18	2.50143
$603$	−7.18475e17	−0.608624
$604$	−7.96867e17	−0.667799
$605$	1.25376e18	1.03945
$606$	1.79502e18	1.47230
$607$	1.36674e18	1.10907	0.554534	−	0.832161i	$-0.312897\pi$
$607$	1.36674e18	1.10907	0.554534	+	0.832161i	$0.312897\pi$
$608$	7.12414e18	5.71952
$609$	−1.92031e18	−1.52531
$610$	4.13036e17	0.324597
$611$	1.76426e18	1.37181
$612$	6.58049e17	0.506260
$613$	9.93340e17	0.756144	0.378072	−	0.925776i	$-0.376587\pi$
$613$	9.93340e17	0.756144	0.378072	+	0.925776i	$0.376587\pi$
$614$	4.02559e16	0.0303204
$615$	2.19462e18	1.63558
$616$	4.08885e18	3.01527
$617$	1.42569e18	1.04033	0.520165	−	0.854066i	$-0.325870\pi$
$617$	1.42569e18	1.04033	0.520165	+	0.854066i	$0.325870\pi$
$618$	−1.08749e18	−0.785236
$619$	−2.09244e18	−1.49508	−0.747540	−	0.664217i	$-0.768765\pi$
$619$	−2.09244e18	−1.49508	−0.747540	+	0.664217i	$0.768765\pi$
$620$	6.18452e18	4.37280
$621$	1.17690e18	0.823460
$622$	−1.02087e18	−0.706857
$623$	−1.11587e18	−0.764616
$624$	−7.25482e18	−4.91957
$625$	−1.83136e18	−1.22901
$626$	6.27437e17	0.416713
$627$	5.10317e17	0.335429
$628$	−1.76767e18	−1.14991
$629$	2.26878e17	0.146070
$630$	−3.10302e18	−1.97729
$631$	−7.86264e17	−0.495881	−0.247941	−	0.968775i	$-0.579754\pi$
$631$	−7.86264e17	−0.495881	−0.247941	+	0.968775i	$0.579754\pi$
$632$	7.83473e18	4.89061
$633$	2.28681e18	1.41288
$634$	−4.58817e17	−0.280582
$635$	1.94421e18	1.17683
$636$	−4.86480e18	−2.91470
$637$	−5.06896e18	−3.00617
$638$	−1.67472e18	−0.983122
$639$	−1.18683e18	−0.689654
$640$	1.56427e19	8.99790
$641$	3.27038e18	1.86217	0.931087	−	0.364796i	$-0.118861\pi$
$641$	3.27038e18	1.86217	0.931087	+	0.364796i	$0.118861\pi$
$642$	−4.51343e18	−2.54407
$643$	−3.06098e18	−1.70800	−0.854002	−	0.520270i	$-0.825831\pi$
$643$	−3.06098e18	−1.70800	−0.854002	+	0.520270i	$0.825831\pi$
$644$	−7.28196e18	−4.02245
$645$	1.24320e18	0.679833
$646$	−1.48536e18	−0.804117
$647$	−1.53058e18	−0.820309	−0.410155	−	0.912016i	$-0.634525\pi$
$647$	−1.53058e18	−0.820309	−0.410155	+	0.912016i	$0.634525\pi$
$648$	2.75554e18	1.46207
$649$	−9.17649e17	−0.482044
$650$	3.38745e18	1.76172
$651$	−3.01229e18	−1.55103
$652$	−2.59311e18	−1.32194
$653$	−1.57615e18	−0.795537	−0.397769	−	0.917486i	$-0.630215\pi$
$653$	−1.57615e18	−0.795537	−0.397769	+	0.917486i	$0.630215\pi$
$654$	4.24408e18	2.12094
$655$	−2.57575e18	−1.27448
$656$	−1.64753e19	−8.07158
$657$	−5.65267e17	−0.274207
$658$	7.37572e18	3.54272
$659$	2.49587e18	1.18705	0.593523	−	0.804817i	$-0.297737\pi$
$659$	2.49587e18	1.18705	0.593523	+	0.804817i	$0.297737\pi$
$660$	2.63177e18	1.23940
$661$	3.73226e18	1.74045	0.870227	−	0.492651i	$-0.163972\pi$
$661$	3.73226e18	1.74045	0.870227	+	0.492651i	$0.163972\pi$
$662$	−7.09459e18	−3.27605
$663$	8.92458e17	0.408084
$664$	−3.55856e18	−1.61132
$665$	5.23165e18	2.34584
$666$	−7.19436e17	−0.319455
$667$	1.97205e18	0.867160
$668$	−2.46384e18	−1.07292
$669$	−1.39023e18	−0.599540
$670$	8.36356e18	3.57195
$671$	−1.31049e17	−0.0554289
$672$	−1.78950e19	−7.49603
$673$	−1.97434e18	−0.819075	−0.409538	−	0.912293i	$-0.634310\pi$
$673$	−1.97434e18	−0.819075	−0.409538	+	0.912293i	$0.634310\pi$
$674$	−1.92807e18	−0.792196
$675$	−1.70957e18	−0.695683
$676$	6.50717e18	2.62264
$677$	−9.89801e17	−0.395113	−0.197557	−	0.980291i	$-0.563301\pi$
$677$	−9.89801e17	−0.395113	−0.197557	+	0.980291i	$0.563301\pi$
$678$	−3.00327e18	−1.18741
$679$	1.53610e18	0.601542
$680$	−5.06485e18	−1.96453
$681$	1.64967e18	0.633784
$682$	−2.62705e18	−0.999700
$683$	2.17179e18	0.818621	0.409310	−	0.912395i	$-0.365769\pi$
$683$	2.17179e18	0.818621	0.409310	+	0.912395i	$0.365769\pi$
$684$	3.51814e18	1.31355
$685$	3.08162e18	1.13970
$686$	−1.15039e19	−4.21442
$687$	−1.31843e18	−0.478451
$688$	−9.33284e18	−3.35497
$689$	5.06740e18	1.80451
$690$	−4.14898e18	−1.46360
$691$	3.72762e18	1.30264	0.651321	−	0.758803i	$-0.274215\pi$
$691$	3.72762e18	1.30264	0.651321	+	0.758803i	$0.274215\pi$
$692$	−8.66293e18	−2.99899
$693$	9.84531e17	0.337647
$694$	3.92327e18	1.33294
$695$	−1.78520e18	−0.600875
$696$	9.93923e18	3.31431
$697$	2.02672e18	0.669548
$698$	−9.67997e18	−3.16821
$699$	1.94197e17	0.0629710
$700$	1.05778e19	3.39828
$701$	2.23745e18	0.712175	0.356087	−	0.934453i	$-0.384111\pi$
$701$	2.23745e18	0.712175	0.356087	+	0.934453i	$0.384111\pi$
$702$	−9.34469e18	−2.94696
$703$	1.21296e18	0.378998
$704$	−8.91258e18	−2.75919
$705$	3.13891e18	0.962831
$706$	−9.52767e18	−2.89572
$707$	−5.83865e18	−1.75827
$708$	8.23681e18	2.45778
$709$	−3.34421e17	−0.0988765	−0.0494383	−	0.998777i	$-0.515743\pi$
$709$	−3.34421e17	−0.0988765	−0.0494383	+	0.998777i	$0.515743\pi$
$710$	1.38155e19	4.04751
$711$	1.88648e18	0.547646
$712$	5.77560e18	1.66141
$713$	3.09345e18	0.881783
$714$	3.73104e18	1.05388
$715$	−2.74137e18	−0.767323
$716$	−1.75809e18	−0.487648
$717$	−2.27087e17	−0.0624192
$718$	3.80365e18	1.03608
$719$	−4.70240e18	−1.26935	−0.634675	−	0.772779i	$-0.718866\pi$
$719$	−4.70240e18	−1.26935	−0.634675	+	0.772779i	$0.718866\pi$
$720$	9.91364e18	2.65199
$721$	3.53727e18	0.937755
$722$	−3.75034e17	−0.0985324
$723$	−4.32831e18	−1.12699
$724$	1.58312e19	4.08520
$725$	−2.86461e18	−0.732602
$726$	4.78034e18	1.21163
$727$	4.48755e18	1.12729	0.563645	−	0.826017i	$-0.309399\pi$
$727$	4.48755e18	1.12729	0.563645	+	0.826017i	$0.309399\pi$
$728$	3.82299e19	9.51808
$729$	3.95130e18	0.975013
$730$	6.58012e18	1.60929
$731$	1.14809e18	0.278299
$732$	1.17629e18	0.282614
$733$	−5.17738e17	−0.123292	−0.0616459	−	0.998098i	$-0.519635\pi$
$733$	−5.17738e17	−0.123292	−0.0616459	+	0.998098i	$0.519635\pi$
$734$	−3.10013e17	−0.0731738
$735$	−9.01852e18	−2.10993
$736$	1.83771e19	4.26159
$737$	−2.65360e18	−0.609954
$738$	−6.42680e18	−1.46429
$739$	−2.71391e18	−0.612924	−0.306462	−	0.951883i	$-0.599145\pi$
$739$	−2.71391e18	−0.612924	−0.306462	+	0.951883i	$0.599145\pi$
$740$	6.25538e18	1.40039
$741$	4.77136e18	1.05882
$742$	2.11849e19	4.66016
$743$	−4.43179e18	−0.966389	−0.483195	−	0.875513i	$-0.660524\pi$
$743$	−4.43179e18	−0.966389	−0.483195	+	0.875513i	$0.660524\pi$
$744$	1.55912e19	3.37019
$745$	4.24354e18	0.909312
$746$	−6.60583e18	−1.40322
$747$	−8.56844e17	−0.180434
$748$	2.43043e18	0.507367
$749$	1.46808e19	3.03821
$750$	−3.31866e18	−0.680871
$751$	−4.61250e18	−0.938160	−0.469080	−	0.883156i	$-0.655414\pi$
$751$	−4.61250e18	−0.938160	−0.469080	+	0.883156i	$0.655414\pi$
$752$	−2.35642e19	−4.75157
$753$	−3.17276e18	−0.634265
$754$	−1.56583e19	−3.10335
$755$	1.47680e18	0.290180
$756$	−2.91802e19	−5.68456
$757$	−4.52388e18	−0.873751	−0.436876	−	0.899522i	$-0.643915\pi$
$757$	−4.52388e18	−0.873751	−0.436876	+	0.899522i	$0.643915\pi$
$758$	−4.81700e18	−0.922417
$759$	1.31639e18	0.249927
$760$	−2.70783e19	−5.09721
$761$	−1.47709e18	−0.275680	−0.137840	−	0.990454i	$-0.544016\pi$
$761$	−1.47709e18	−0.275680	−0.137840	+	0.990454i	$0.544016\pi$
$762$	7.41291e18	1.37177
$763$	−1.38047e19	−2.53290
$764$	−2.08621e18	−0.379535
$765$	−1.21954e18	−0.219986
$766$	3.33484e18	0.596469
$767$	−8.57984e18	−1.52163
$768$	3.25382e19	5.72197
$769$	4.28730e18	0.747588	0.373794	−	0.927512i	$-0.378057\pi$
$769$	4.28730e18	0.747588	0.373794	+	0.927512i	$0.378057\pi$
$770$	−1.14606e19	−1.98162
$771$	−3.74420e18	−0.641956
$772$	−4.58130e18	−0.778890
$773$	8.06317e18	1.35937	0.679687	−	0.733502i	$-0.262115\pi$
$773$	8.06317e18	1.35937	0.679687	+	0.733502i	$0.262115\pi$
$774$	−3.64062e18	−0.608638
$775$	−4.49357e18	−0.744956
$776$	−7.95063e18	−1.30707
$777$	−3.04681e18	−0.496716
$778$	−2.07222e19	−3.35018
$779$	1.08355e19	1.73722
$780$	2.46065e19	3.91233
$781$	−4.38340e18	−0.691161
$782$	−3.83156e18	−0.599145
$783$	7.90237e18	1.22548
$784$	6.77032e19	10.4125
$785$	3.27595e18	0.499671
$786$	−9.82082e18	−1.48560
$787$	1.04577e17	0.0156892	0.00784459	−	0.999969i	$-0.497503\pi$
$787$	1.04577e17	0.0156892	0.00784459	+	0.999969i	$0.497503\pi$
$788$	1.41330e18	0.210288
$789$	−7.77693e18	−1.14764
$790$	−2.19600e19	−3.21407
$791$	9.76873e18	1.41805
$792$	−5.09578e18	−0.733664
$793$	−1.22528e18	−0.174968
$794$	1.79711e18	0.254532
$795$	9.01574e18	1.26653
$796$	2.59917e19	3.62159
$797$	2.01353e18	0.278278	0.139139	−	0.990273i	$-0.455567\pi$
$797$	2.01353e18	0.278278	0.139139	+	0.990273i	$0.455567\pi$
$798$	1.99473e19	2.73442
$799$	2.89877e18	0.394149
$800$	−2.66947e19	−3.60032
$801$	1.39067e18	0.186043
$802$	−1.95569e18	−0.259518
$803$	−2.08775e18	−0.274807
$804$	2.38187e19	3.10995
$805$	1.34954e19	1.74788
$806$	−2.45624e19	−3.15568
$807$	−2.13312e18	−0.271855
$808$	3.02200e19	3.82050
$809$	−1.22832e19	−1.54045	−0.770223	−	0.637775i	$-0.779855\pi$
$809$	−1.22832e19	−1.54045	−0.770223	+	0.637775i	$0.779855\pi$
$810$	−7.72351e18	−0.960864
$811$	1.18857e19	1.46687	0.733433	−	0.679762i	$-0.237917\pi$
$811$	1.18857e19	1.46687	0.733433	+	0.679762i	$0.237917\pi$
$812$	−4.88954e19	−5.98623
$813$	−6.06074e18	−0.736100
$814$	−2.65715e18	−0.320153
$815$	4.80570e18	0.574424
$816$	−1.19200e19	−1.41349
$817$	6.13804e18	0.722081
$818$	−4.89986e18	−0.571857
$819$	9.20516e18	1.06583
$820$	5.58801e19	6.41899
$821$	9.46016e18	1.07812	0.539061	−	0.842267i	$-0.318779\pi$
$821$	9.46016e18	1.07812	0.539061	+	0.842267i	$0.318779\pi$
$822$	1.17496e19	1.32849
$823$	1.10832e19	1.24327	0.621635	−	0.783307i	$-0.286469\pi$
$823$	1.10832e19	1.24327	0.621635	+	0.783307i	$0.286469\pi$
$824$	−1.83084e19	−2.03762
$825$	−1.91220e18	−0.211146
$826$	−3.58691e19	−3.92962
$827$	2.09887e18	0.228139	0.114070	−	0.993473i	$-0.463611\pi$
$827$	2.09887e18	0.228139	0.114070	+	0.993473i	$0.463611\pi$
$828$	9.07524e18	0.978725
$829$	−2.98771e18	−0.319694	−0.159847	−	0.987142i	$-0.551100\pi$
$829$	−2.98771e18	−0.319694	−0.159847	+	0.987142i	$0.551100\pi$
$830$	9.97428e18	1.05895
$831$	−1.15832e19	−1.22017
$832$	−8.33308e19	−8.70972
$833$	−8.32856e18	−0.863729
$834$	−6.80661e18	−0.700408
$835$	4.56614e18	0.466216
$836$	1.29938e19	1.31642
$837$	1.23961e19	1.24614
$838$	1.28797e19	1.28475
$839$	2.28066e18	0.225739	0.112870	−	0.993610i	$-0.463996\pi$
$839$	2.28066e18	0.225739	0.112870	+	0.993610i	$0.463996\pi$
$840$	6.80174e19	6.68043
$841$	2.98086e18	0.290514
$842$	2.34146e19	2.26443
$843$	1.33559e19	1.28172
$844$	5.82274e19	5.54500
$845$	−1.20595e19	−1.13962
$846$	−9.19209e18	−0.861999
$847$	−1.55490e19	−1.44697
$848$	−6.76823e19	−6.25031
$849$	−8.17677e18	−0.749345
$850$	5.56575e18	0.506175
$851$	3.12890e18	0.282390
$852$	3.93454e19	3.52400
$853$	7.21495e18	0.641305	0.320653	−	0.947197i	$-0.396098\pi$
$853$	7.21495e18	0.641305	0.320653	+	0.947197i	$0.396098\pi$
$854$	−5.12244e18	−0.451856
$855$	−6.52002e18	−0.570780
$856$	−7.59857e19	−6.60165
$857$	1.06390e18	0.0917328	0.0458664	−	0.998948i	$-0.485395\pi$
$857$	1.06390e18	0.0917328	0.0458664	+	0.998948i	$0.485395\pi$
$858$	−1.04523e19	−0.894427
$859$	−2.05252e19	−1.74314	−0.871571	−	0.490269i	$-0.836899\pi$
$859$	−2.05252e19	−1.74314	−0.871571	+	0.490269i	$0.836899\pi$
$860$	3.16546e19	2.66807
$861$	−2.72175e19	−2.27681
$862$	−1.90845e19	−1.58447
$863$	2.82686e18	0.232935	0.116467	−	0.993195i	$-0.462843\pi$
$863$	2.82686e18	0.232935	0.116467	+	0.993195i	$0.462843\pi$
$864$	7.36407e19	6.02253
$865$	1.60547e19	1.30316
$866$	2.28512e19	1.84096
$867$	−7.93903e18	−0.634810
$868$	−7.66998e19	−6.08718
$869$	6.96749e18	0.548843
$870$	−2.78587e19	−2.17814
$871$	−2.48106e19	−1.92540
$872$	7.14511e19	5.50366
$873$	−1.91439e18	−0.146365
$874$	−2.04847e19	−1.55455
$875$	1.07946e19	0.813119
$876$	1.87396e19	1.40115
$877$	2.36214e19	1.75311	0.876554	−	0.481304i	$-0.159837\pi$
$877$	2.36214e19	1.75311	0.876554	+	0.481304i	$0.159837\pi$
$878$	2.08200e19	1.53379
$879$	−4.08473e18	−0.298700
$880$	3.66149e19	2.65779
$881$	1.44046e19	1.03791	0.518953	−	0.854803i	$-0.326322\pi$
$881$	1.44046e19	1.03791	0.518953	+	0.854803i	$0.326322\pi$
$882$	2.64101e19	1.88897
$883$	−5.10220e17	−0.0362254	−0.0181127	−	0.999836i	$-0.505766\pi$
$883$	−5.10220e17	−0.0362254	−0.0181127	+	0.999836i	$0.505766\pi$
$884$	2.27240e19	1.60157
$885$	−1.52650e19	−1.06798
$886$	2.16065e19	1.50060
$887$	2.00565e19	1.38278	0.691388	−	0.722483i	$-0.256999\pi$
$887$	2.00565e19	1.38278	0.691388	+	0.722483i	$0.256999\pi$
$888$	1.57698e19	1.07930
$889$	−2.41119e19	−1.63821
$890$	−1.61884e19	−1.09187
$891$	2.45052e18	0.164079
$892$	−3.53985e19	−2.35295
$893$	1.54977e19	1.02267
$894$	1.61798e19	1.05994
$895$	3.25820e18	0.211898
$896$	−1.93999e20	−12.5256
$897$	1.23080e19	0.788927
$898$	3.16230e19	2.01236
$899$	2.07713e19	1.31228
$900$	−1.31827e19	−0.826855
$901$	8.32599e18	0.518471
$902$	−2.37366e19	−1.46750
$903$	−1.54180e19	−0.946364
$904$	−5.05615e19	−3.08123
$905$	−2.93393e19	−1.77515
$906$	5.63076e18	0.338247
$907$	−6.20694e18	−0.370195	−0.185097	−	0.982720i	$-0.559260\pi$
$907$	−6.20694e18	−0.370195	−0.185097	+	0.982720i	$0.559260\pi$
$908$	4.20044e19	2.48735
$909$	7.27650e18	0.427816
$910$	−1.07155e20	−6.25522
$911$	1.78419e19	1.03412	0.517062	−	0.855948i	$-0.327026\pi$
$911$	1.78419e19	1.03412	0.517062	+	0.855948i	$0.327026\pi$
$912$	−6.37283e19	−3.66746
$913$	−3.16465e18	−0.180828
$914$	2.39080e19	1.35642
$915$	−2.17997e18	−0.122805
$916$	−3.35701e19	−1.87773
$917$	3.19441e19	1.77415
$918$	−1.53538e19	−0.846717
$919$	1.78621e18	0.0978099	0.0489049	−	0.998803i	$-0.484427\pi$
$919$	1.78621e18	0.0978099	0.0489049	+	0.998803i	$0.484427\pi$
$920$	−6.98500e19	−3.79792
$921$	−2.12468e17	−0.0114711
$922$	−5.56324e19	−2.98248
$923$	−4.09839e19	−2.18174
$924$	−3.26389e19	−1.72531
$925$	−4.54506e18	−0.238571
$926$	−5.22219e18	−0.272196
$927$	−4.40837e18	−0.228171
$928$	1.23395e20	6.34214
$929$	7.35740e18	0.375511	0.187755	−	0.982216i	$-0.439879\pi$
$929$	7.35740e18	0.375511	0.187755	+	0.982216i	$0.439879\pi$
$930$	−4.37006e19	−2.21487
$931$	−4.45271e19	−2.24105
$932$	4.94469e18	0.247136
$933$	5.38805e18	0.267424
$934$	−4.14051e19	−2.04079
$935$	−4.50421e18	−0.220467
$936$	−4.76446e19	−2.31590
$937$	4.43507e18	0.214089	0.107044	−	0.994254i	$-0.465861\pi$
$937$	4.43507e18	0.214089	0.107044	+	0.994254i	$0.465861\pi$
$938$	−1.03724e20	−4.97234
$939$	−3.31156e18	−0.157655
$940$	7.99238e19	3.77872
$941$	−1.47756e19	−0.693766	−0.346883	−	0.937908i	$-0.612760\pi$
$941$	−1.47756e19	−0.693766	−0.346883	+	0.937908i	$0.612760\pi$
$942$	1.24905e19	0.582439
$943$	2.79508e19	1.29440
$944$	1.14596e20	5.27049
$945$	5.40785e19	2.47012
$946$	−1.34462e19	−0.609968
$947$	−1.40884e18	−0.0634726	−0.0317363	−	0.999496i	$-0.510104\pi$
$947$	−1.40884e18	−0.0634726	−0.0317363	+	0.999496i	$0.510104\pi$
$948$	−6.25401e19	−2.79837
$949$	−1.95200e19	−0.867461
$950$	2.97562e19	1.31333
$951$	2.42160e18	0.106152
$952$	6.28137e19	2.73473
$953$	2.82781e18	0.122277	0.0611386	−	0.998129i	$-0.480527\pi$
$953$	2.82781e18	0.122277	0.0611386	+	0.998129i	$0.480527\pi$
$954$	−2.64020e19	−1.13389
$955$	3.86629e18	0.164920
$956$	−5.78215e18	−0.244970
$957$	8.83904e18	0.371944
$958$	6.86237e19	2.86813
$959$	−3.82179e19	−1.58652
$960$	−1.48259e20	−6.11306
$961$	8.16533e18	0.334404
$962$	−2.48438e19	−1.01060
$963$	−1.82961e19	−0.739246
$964$	−1.10208e20	−4.42297
$965$	8.49033e18	0.338452
$966$	5.14552e19	2.03741
$967$	−4.46149e19	−1.75472	−0.877360	−	0.479832i	$-0.840697\pi$
$967$	−4.46149e19	−1.75472	−0.877360	+	0.479832i	$0.840697\pi$
$968$	8.04791e19	3.14408
$969$	7.83959e18	0.304221
$970$	2.22848e19	0.859000
$971$	−1.36662e19	−0.523267	−0.261634	−	0.965167i	$-0.584261\pi$
$971$	−1.36662e19	−0.523267	−0.261634	+	0.965167i	$0.584261\pi$
$972$	6.17190e19	2.34741
$973$	2.21398e19	0.836451
$974$	−8.43135e19	−3.16420
$975$	−1.78787e19	−0.666508
$976$	1.63653e19	0.606040
$977$	3.04745e19	1.12104	0.560520	−	0.828141i	$-0.310601\pi$
$977$	3.04745e19	1.12104	0.560520	+	0.828141i	$0.310601\pi$
$978$	1.83232e19	0.669575
$979$	5.13629e18	0.186450
$980$	−2.29632e20	−8.28062
$981$	1.72043e19	0.616295
$982$	−4.40793e19	−1.56859
$983$	4.75117e19	1.67959	0.839794	−	0.542905i	$-0.182676\pi$
$983$	4.75117e19	1.67959	0.839794	+	0.542905i	$0.182676\pi$
$984$	1.40874e20	4.94723
$985$	−2.61921e18	−0.0913767
$986$	−2.57274e19	−0.891652
$987$	−3.89285e19	−1.34031
$988$	1.21490e20	4.15546
$989$	1.58334e19	0.538021
$990$	1.42830e19	0.482159
$991$	−3.03259e19	−1.01703	−0.508517	−	0.861052i	$-0.669806\pi$
$991$	−3.03259e19	−1.01703	−0.508517	+	0.861052i	$0.669806\pi$
$992$	1.93564e20	6.44908
$993$	3.74447e19	1.23942
$994$	−1.71338e20	−5.63434
$995$	−4.81694e19	−1.57370
$996$	2.84059e19	0.921983
$997$	−3.94393e19	−1.27178	−0.635889	−	0.771781i	$-0.719366\pi$
$997$	−3.94393e19	−1.27178	−0.635889	+	0.771781i	$0.719366\pi$
$998$	1.04349e20	3.34302
$999$	1.25381e19	0.399076

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.14.a.b.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-179.919 q^{2} +949.600 q^{3} +24179.0 q^{4} -44809.9 q^{5} -170851. q^{6} +555727. q^{7} -2.87636e6 q^{8} -692583. q^{9} +8.06216e6 q^{10} -2.55797e6 q^{11} +2.29603e7 q^{12} -2.39165e7 q^{13} -9.99861e7 q^{14} -4.25515e7 q^{15} +3.19439e8 q^{16} -3.92961e7 q^{17} +1.24609e8 q^{18} -2.10089e8 q^{19} -1.08346e9 q^{20} +5.27719e8 q^{21} +4.60229e8 q^{22} -5.41937e8 q^{23} -2.73139e9 q^{24} +7.87221e8 q^{25} +4.30304e9 q^{26} -2.17165e9 q^{27} +1.34369e10 q^{28} -3.63889e9 q^{29} +7.65583e9 q^{30} -5.70814e9 q^{31} -3.39101e10 q^{32} -2.42905e9 q^{33} +7.07012e9 q^{34} -2.49021e10 q^{35} -1.67459e10 q^{36} -5.77354e9 q^{37} +3.77991e10 q^{38} -2.27111e10 q^{39} +1.28889e11 q^{40} -5.15758e10 q^{41} -9.49468e10 q^{42} -2.92164e10 q^{43} -6.18491e10 q^{44} +3.10345e10 q^{45} +9.75050e10 q^{46} -7.37675e10 q^{47} +3.03339e11 q^{48} +2.11944e11 q^{49} -1.41636e11 q^{50} -3.73155e10 q^{51} -5.78277e11 q^{52} -2.11878e11 q^{53} +3.90721e11 q^{54} +1.14622e11 q^{55} -1.59847e12 q^{56} -1.99501e11 q^{57} +6.54706e11 q^{58} +3.58741e11 q^{59} -1.02885e12 q^{60} +5.12315e10 q^{61} +1.02700e12 q^{62} -3.84887e11 q^{63} +3.48424e12 q^{64} +1.07170e12 q^{65} +4.37033e11 q^{66} +1.03738e12 q^{67} -9.50138e11 q^{68} -5.14624e11 q^{69} +4.48036e12 q^{70} +1.71362e12 q^{71} +1.99212e12 q^{72} +8.16173e11 q^{73} +1.03877e12 q^{74} +7.47545e11 q^{75} -5.07974e12 q^{76} -1.42154e12 q^{77} +4.08617e12 q^{78} -2.72383e12 q^{79} -1.43140e13 q^{80} -9.57995e11 q^{81} +9.27947e12 q^{82} +1.23717e12 q^{83} +1.27597e13 q^{84} +1.76085e12 q^{85} +5.25659e12 q^{86} -3.45549e12 q^{87} +7.35765e12 q^{88} -2.00795e12 q^{89} -5.58371e12 q^{90} -1.32911e13 q^{91} -1.31035e13 q^{92} -5.42045e12 q^{93} +1.32722e13 q^{94} +9.41407e12 q^{95} -3.22010e13 q^{96} +2.76413e12 q^{97} -3.81328e13 q^{98} +1.77161e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 109 q + 192 q^{2} + 8018 q^{3} + 471040 q^{4} + 88496 q^{5} + 383232 q^{6} + 1680731 q^{7} + 1820859 q^{8} + 59521391 q^{9} + 16373653 q^{10} + 21199298 q^{11} + 63225856 q^{12} + 59695238 q^{13} + 37888529 q^{14}+ \cdots + 12084396239183 q^{99}+O(q^{100}) \) 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

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Database

Properties

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