LMFDB - Embedded newform 197.14.a.b.1.18

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			1.18
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)

$f(q)$	$=$	$q-133.322 q^{2} +64.3497 q^{3} +9582.75 q^{4} +19563.1 q^{5} -8579.24 q^{6} +177321. q^{7} -185418. q^{8} -1.59018e6 q^{9} +O(q^{10})$	\(q-133.322 q^{2} +64.3497 q^{3} +9582.75 q^{4} +19563.1 q^{5} -8579.24 q^{6} +177321. q^{7} -185418. q^{8} -1.59018e6 q^{9} -2.60819e6 q^{10} -336016. q^{11} +616648. q^{12} +1.41878e7 q^{13} -2.36408e7 q^{14} +1.25888e6 q^{15} -5.37816e7 q^{16} +1.10884e8 q^{17} +2.12006e8 q^{18} -1.18009e8 q^{19} +1.87469e8 q^{20} +1.14106e7 q^{21} +4.47983e7 q^{22} -7.03272e8 q^{23} -1.19316e7 q^{24} -8.37987e8 q^{25} -1.89154e9 q^{26} -2.04922e8 q^{27} +1.69922e9 q^{28} -3.44657e9 q^{29} -1.67837e8 q^{30} -5.07264e9 q^{31} +8.68922e9 q^{32} -2.16225e7 q^{33} -1.47832e10 q^{34} +3.46895e9 q^{35} -1.52383e10 q^{36} +2.95097e10 q^{37} +1.57332e10 q^{38} +9.12980e8 q^{39} -3.62736e9 q^{40} +3.95254e10 q^{41} -1.52128e9 q^{42} -5.83732e10 q^{43} -3.21996e9 q^{44} -3.11089e10 q^{45} +9.37617e10 q^{46} +8.53901e10 q^{47} -3.46083e9 q^{48} -6.54462e10 q^{49} +1.11722e11 q^{50} +7.13534e9 q^{51} +1.35958e11 q^{52} -2.30840e11 q^{53} +2.73206e10 q^{54} -6.57352e9 q^{55} -3.28785e10 q^{56} -7.59387e9 q^{57} +4.59503e11 q^{58} +2.95758e11 q^{59} +1.20636e10 q^{60} +3.76657e11 q^{61} +6.76294e11 q^{62} -2.81973e11 q^{63} -7.17885e11 q^{64} +2.77557e11 q^{65} +2.88276e9 q^{66} +5.34143e11 q^{67} +1.06257e12 q^{68} -4.52554e10 q^{69} -4.62488e11 q^{70} +1.73500e12 q^{71} +2.94848e11 q^{72} +6.32699e11 q^{73} -3.93429e12 q^{74} -5.39243e10 q^{75} -1.13085e12 q^{76} -5.95827e10 q^{77} -1.21720e11 q^{78} -1.64725e12 q^{79} -1.05214e12 q^{80} +2.52208e12 q^{81} -5.26960e12 q^{82} -7.58482e11 q^{83} +1.09345e11 q^{84} +2.16923e12 q^{85} +7.78243e12 q^{86} -2.21786e11 q^{87} +6.23034e10 q^{88} +1.01548e11 q^{89} +4.14750e12 q^{90} +2.51579e12 q^{91} -6.73929e12 q^{92} -3.26423e11 q^{93} -1.13844e13 q^{94} -2.30863e12 q^{95} +5.59149e11 q^{96} -1.06120e12 q^{97} +8.72542e12 q^{98} +5.34326e11 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+O(q^{10}) $ 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	\( 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}+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

Display 100 coefficients 10 coefficients

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 $

$2$	−133.322	−1.47301	−0.736507	−	0.676430i	$-0.763526\pi$
$2$	−133.322	−1.47301	−0.736507	+	0.676430i	$0.763526\pi$
$3$	64.3497	0.0509634	0.0254817	−	0.999675i	$-0.491888\pi$
$3$	64.3497	0.0509634	0.0254817	+	0.999675i	$0.491888\pi$
$4$	9582.75	1.16977
$5$	19563.1	0.559929	0.279965	−	0.960010i	$-0.409677\pi$
$5$	19563.1	0.559929	0.279965	+	0.960010i	$0.409677\pi$
$6$	−8579.24	−0.0750698
$7$	177321.	0.569670	0.284835	−	0.958577i	$-0.408061\pi$
$7$	177321.	0.569670	0.284835	+	0.958577i	$0.408061\pi$
$8$	−185418.	−0.250073
$9$	−1.59018e6	−0.997403
$10$	−2.60819e6	−0.824784
$11$	−336016.	−0.0571883	−0.0285941	−	0.999591i	$-0.509103\pi$
$11$	−336016.	−0.0571883	−0.0285941	+	0.999591i	$0.509103\pi$
$12$	616648.	0.0596155
$13$	1.41878e7	0.815235	0.407617	−	0.913153i	$-0.366360\pi$
$13$	1.41878e7	0.815235	0.407617	+	0.913153i	$0.366360\pi$
$14$	−2.36408e7	−0.839131
$15$	1.25888e6	0.0285359
$16$	−5.37816e7	−0.801409
$17$	1.10884e8	1.11417	0.557083	−	0.830457i	$-0.311920\pi$
$17$	1.10884e8	1.11417	0.557083	+	0.830457i	$0.311920\pi$
$18$	2.12006e8	1.46919
$19$	−1.18009e8	−0.575464	−0.287732	−	0.957711i	$-0.592901\pi$
$19$	−1.18009e8	−0.575464	−0.287732	+	0.957711i	$0.592901\pi$
$20$	1.87469e8	0.654988
$21$	1.14106e7	0.0290323
$22$	4.47983e7	0.0842392
$23$	−7.03272e8	−0.990587	−0.495293	−	0.868726i	$-0.664939\pi$
$23$	−7.03272e8	−0.990587	−0.495293	+	0.868726i	$0.664939\pi$
$24$	−1.19316e7	−0.0127446
$25$	−8.37987e8	−0.686479
$26$	−1.89154e9	−1.20085
$27$	−2.04922e8	−0.101795
$28$	1.69922e9	0.666382
$29$	−3.44657e9	−1.07597	−0.537984	−	0.842955i	$-0.680814\pi$
$29$	−3.44657e9	−1.07597	−0.537984	+	0.842955i	$0.680814\pi$
$30$	−1.67837e8	−0.0420338
$31$	−5.07264e9	−1.02656	−0.513278	−	0.858222i	$-0.671569\pi$
$31$	−5.07264e9	−1.02656	−0.513278	+	0.858222i	$0.671569\pi$
$32$	8.68922e9	1.43056
$33$	−2.16225e7	−0.00291451
$34$	−1.47832e10	−1.64118
$35$	3.46895e9	0.318975
$36$	−1.52383e10	−1.16673
$37$	2.95097e10	1.89084	0.945418	−	0.325860i	$-0.105654\pi$
$37$	2.95097e10	1.89084	0.945418	+	0.325860i	$0.105654\pi$
$38$	1.57332e10	0.847666
$39$	9.12980e8	0.0415472
$40$	−3.62736e9	−0.140023
$41$	3.95254e10	1.29951	0.649757	−	0.760142i	$-0.274871\pi$
$41$	3.95254e10	1.29951	0.649757	+	0.760142i	$0.274871\pi$
$42$	−1.52128e9	−0.0427650
$43$	−5.83732e10	−1.40821	−0.704107	−	0.710094i	$-0.748652\pi$
$43$	−5.83732e10	−1.40821	−0.704107	+	0.710094i	$0.748652\pi$
$44$	−3.21996e9	−0.0668971
$45$	−3.11089e10	−0.558475
$46$	9.37617e10	1.45915
$47$	8.53901e10	1.15550	0.577752	−	0.816212i	$-0.303930\pi$
$47$	8.53901e10	1.15550	0.577752	+	0.816212i	$0.303930\pi$
$48$	−3.46083e9	−0.0408425
$49$	−6.54462e10	−0.675476
$50$	1.11722e11	1.01119
$51$	7.13534e9	0.0567818
$52$	1.35958e11	0.953637
$53$	−2.30840e11	−1.43060	−0.715301	−	0.698817i	$-0.753710\pi$
$53$	−2.30840e11	−1.43060	−0.715301	+	0.698817i	$0.753710\pi$
$54$	2.73206e10	0.149945
$55$	−6.57352e9	−0.0320214
$56$	−3.28785e10	−0.142459
$57$	−7.59387e9	−0.0293276
$58$	4.59503e11	1.58492
$59$	2.95758e11	0.912848	0.456424	−	0.889762i	$-0.349130\pi$
$59$	2.95758e11	0.912848	0.456424	+	0.889762i	$0.349130\pi$
$60$	1.20636e10	0.0333805
$61$	3.76657e11	0.936057	0.468029	−	0.883713i	$-0.344964\pi$
$61$	3.76657e11	0.936057	0.468029	+	0.883713i	$0.344964\pi$
$62$	6.76294e11	1.51213
$63$	−2.81973e11	−0.568190
$64$	−7.17885e11	−1.30582
$65$	2.77557e11	0.456474
$66$	2.88276e9	0.00429312
$67$	5.34143e11	0.721393	0.360696	−	0.932683i	$-0.382539\pi$
$67$	5.34143e11	0.721393	0.360696	+	0.932683i	$0.382539\pi$
$68$	1.06257e12	1.30332
$69$	−4.52554e10	−0.0504837
$70$	−4.62488e11	−0.469854
$71$	1.73500e12	1.60739	0.803695	−	0.595042i	$-0.202865\pi$
$71$	1.73500e12	1.60739	0.803695	+	0.595042i	$0.202865\pi$
$72$	2.94848e11	0.249424
$73$	6.32699e11	0.489326	0.244663	−	0.969608i	$-0.421323\pi$
$73$	6.32699e11	0.489326	0.244663	+	0.969608i	$0.421323\pi$
$74$	−3.93429e12	−2.78523
$75$	−5.39243e10	−0.0349853
$76$	−1.13085e12	−0.673160
$77$	−5.95827e10	−0.0325784
$78$	−1.21720e11	−0.0611995
$79$	−1.64725e12	−0.762402	−0.381201	−	0.924492i	$-0.624489\pi$
$79$	−1.64725e12	−0.762402	−0.381201	+	0.924492i	$0.624489\pi$
$80$	−1.05214e12	−0.448732
$81$	2.52208e12	0.992215
$82$	−5.26960e12	−1.91420
$83$	−7.58482e11	−0.254646	−0.127323	−	0.991861i	$-0.540639\pi$
$83$	−7.58482e11	−0.254646	−0.127323	+	0.991861i	$0.540639\pi$
$84$	1.09345e11	0.0339611
$85$	2.16923e12	0.623854
$86$	7.78243e12	2.07432
$87$	−2.21786e11	−0.0548351
$88$	6.23034e10	0.0143013
$89$	1.01548e11	0.0216589	0.0108294	−	0.999941i	$-0.496553\pi$
$89$	1.01548e11	0.0216589	0.0108294	+	0.999941i	$0.496553\pi$
$90$	4.14750e12	0.822641
$91$	2.51579e12	0.464414
$92$	−6.73929e12	−1.15876
$93$	−3.26423e11	−0.0523168
$94$	−1.13844e13	−1.70207
$95$	−2.30863e12	−0.322219
$96$	5.59149e11	0.0729062
$97$	−1.06120e12	−0.129355	−0.0646773	−	0.997906i	$-0.520602\pi$
$97$	−1.06120e12	−0.129355	−0.0646773	+	0.997906i	$0.520602\pi$
$98$	8.72542e12	0.994986
$99$	5.34326e11	0.0570398
$100$	−8.03023e12	−0.803023
$101$	2.50396e12	0.234714	0.117357	−	0.993090i	$-0.462558\pi$
$101$	2.50396e12	0.234714	0.117357	+	0.993090i	$0.462558\pi$
$102$	−9.51298e11	−0.0836403
$103$	1.64465e13	1.35716	0.678582	−	0.734524i	$-0.262595\pi$
$103$	1.64465e13	1.35716	0.678582	+	0.734524i	$0.262595\pi$
$104$	−2.63067e12	−0.203868
$105$	2.23226e11	0.0162560
$106$	3.07761e13	2.10730
$107$	−2.35354e13	−1.51610	−0.758048	−	0.652199i	$-0.773847\pi$
$107$	−2.35354e13	−1.51610	−0.758048	+	0.652199i	$0.773847\pi$
$108$	−1.96372e12	−0.119076
$109$	1.08183e13	0.617855	0.308927	−	0.951086i	$-0.400030\pi$
$109$	1.08183e13	0.617855	0.308927	+	0.951086i	$0.400030\pi$
$110$	8.76394e11	0.0471680
$111$	1.89894e12	0.0963635
$112$	−9.53662e12	−0.456538
$113$	−2.02866e13	−0.916642	−0.458321	−	0.888787i	$-0.651549\pi$
$113$	−2.02866e13	−0.916642	−0.458321	+	0.888787i	$0.651549\pi$
$114$	1.01243e12	0.0432000
$115$	−1.37582e13	−0.554659
$116$	−3.30276e13	−1.25864
$117$	−2.25611e13	−0.813117
$118$	−3.94311e13	−1.34464
$119$	1.96620e13	0.634707
$120$	−2.33419e11	−0.00713607
$121$	−3.44098e13	−0.996729
$122$	−5.02167e13	−1.37883
$123$	2.54345e12	0.0662277
$124$	−4.86098e13	−1.20083
$125$	−4.02744e13	−0.944309
$126$	3.75932e13	0.836952
$127$	−1.11600e12	−0.0236015	−0.0118007	−	0.999930i	$-0.503756\pi$
$127$	−1.11600e12	−0.0236015	−0.0118007	+	0.999930i	$0.503756\pi$
$128$	2.45278e13	0.492939
$129$	−3.75630e12	−0.0717674
$130$	−3.70045e13	−0.672392
$131$	−7.66177e11	−0.0132454	−0.00662271	−	0.999978i	$-0.502108\pi$
$131$	−7.66177e11	−0.0132454	−0.00662271	+	0.999978i	$0.502108\pi$
$132$	−2.07203e11	−0.00340931
$133$	−2.09256e13	−0.327824
$134$	−7.12131e13	−1.06262
$135$	−4.00892e12	−0.0569977
$136$	−2.05599e13	−0.278623
$137$	−1.13516e14	−1.46681	−0.733406	−	0.679790i	$-0.762071\pi$
$137$	−1.13516e14	−1.46681	−0.733406	+	0.679790i	$0.762071\pi$
$138$	6.03354e12	0.0743632
$139$	9.84064e13	1.15725	0.578625	−	0.815594i	$-0.303590\pi$
$139$	9.84064e13	1.15725	0.578625	+	0.815594i	$0.303590\pi$
$140$	3.32421e13	0.373127
$141$	5.49483e12	0.0588885
$142$	−2.31314e14	−2.36771
$143$	−4.76732e12	−0.0466219
$144$	8.55226e13	0.799327
$145$	−6.74256e13	−0.602466
$146$	−8.43527e13	−0.720785
$147$	−4.21145e12	−0.0344246
$148$	2.82784e14	2.21184
$149$	8.88962e13	0.665537	0.332769	−	0.943008i	$-0.392017\pi$
$149$	8.88962e13	0.665537	0.332769	+	0.943008i	$0.392017\pi$
$150$	7.18929e12	0.0515339
$151$	−1.35348e14	−0.929184	−0.464592	−	0.885525i	$-0.653799\pi$
$151$	−1.35348e14	−0.929184	−0.464592	+	0.885525i	$0.653799\pi$
$152$	2.18811e13	0.143908
$153$	−1.76325e14	−1.11127
$154$	7.94368e12	0.0479885
$155$	−9.92366e13	−0.574799
$156$	8.74886e12	0.0486006
$157$	−1.27304e14	−0.678415	−0.339208	−	0.940711i	$-0.610159\pi$
$157$	−1.27304e14	−0.678415	−0.339208	+	0.940711i	$0.610159\pi$
$158$	2.19615e14	1.12303
$159$	−1.48545e13	−0.0729084
$160$	1.69988e14	0.801012
$161$	−1.24705e14	−0.564307
$162$	−3.36248e14	−1.46155
$163$	−2.35957e14	−0.985402	−0.492701	−	0.870199i	$-0.663990\pi$
$163$	−2.35957e14	−0.985402	−0.492701	+	0.870199i	$0.663990\pi$
$164$	3.78762e14	1.52013
$165$	−4.23004e11	−0.00163192
$166$	1.01122e14	0.375098
$167$	5.14608e14	1.83577	0.917887	−	0.396841i	$-0.129894\pi$
$167$	5.14608e14	1.83577	0.917887	+	0.396841i	$0.129894\pi$
$168$	−2.11573e12	−0.00726021
$169$	−1.01582e14	−0.335393
$170$	−2.89207e14	−0.918946
$171$	1.87656e14	0.573969
$172$	−5.59376e14	−1.64729
$173$	−2.64003e13	−0.0748703	−0.0374352	−	0.999299i	$-0.511919\pi$
$173$	−2.64003e13	−0.0748703	−0.0374352	+	0.999299i	$0.511919\pi$
$174$	2.95689e13	0.0807728
$175$	−1.48593e14	−0.391066
$176$	1.80715e13	0.0458312
$177$	1.90320e13	0.0465219
$178$	−1.35386e13	−0.0319038
$179$	−7.41778e13	−0.168550	−0.0842751	−	0.996443i	$-0.526857\pi$
$179$	−7.41778e13	−0.168550	−0.0842751	+	0.996443i	$0.526857\pi$
$180$	−2.98109e14	−0.653287
$181$	4.92340e13	0.104077	0.0520384	−	0.998645i	$-0.483428\pi$
$181$	4.92340e13	0.104077	0.0520384	+	0.998645i	$0.483428\pi$
$182$	−3.35410e14	−0.684089
$183$	2.42378e13	0.0477047
$184$	1.30399e14	0.247719
$185$	5.77302e14	1.05873
$186$	4.35193e13	0.0770634
$187$	−3.72587e13	−0.0637173
$188$	8.18273e14	1.35167
$189$	−3.63370e13	−0.0579892
$190$	3.07791e14	0.474633
$191$	1.11945e15	1.66835	0.834177	−	0.551497i	$-0.185943\pi$
$191$	1.11945e15	1.66835	0.834177	+	0.551497i	$0.185943\pi$
$192$	−4.61957e13	−0.0665493
$193$	8.33791e14	1.16127	0.580637	−	0.814163i	$-0.302804\pi$
$193$	8.33791e14	1.16127	0.580637	+	0.814163i	$0.302804\pi$
$194$	1.41482e14	0.190541
$195$	1.78607e13	0.0232635
$196$	−6.27155e14	−0.790152
$197$	5.84517e13	0.0712470
$197$	5.84517e13	0.0712470
$198$	−7.12374e13	−0.0840204
$199$	−7.17125e14	−0.818559	−0.409279	−	0.912409i	$-0.634220\pi$
$199$	−7.17125e14	−0.818559	−0.409279	+	0.912409i	$0.634220\pi$
$200$	1.55378e14	0.171670
$201$	3.43720e13	0.0367646
$202$	−3.33833e14	−0.345737
$203$	−6.11149e14	−0.612947
$204$	6.83762e13	0.0664216
$205$	7.73240e14	0.727636
$206$	−2.19268e15	−1.99912
$207$	1.11833e15	0.988014
$208$	−7.63042e14	−0.653336
$209$	3.96530e13	0.0329098
$210$	−2.97610e13	−0.0239454
$211$	2.41815e15	1.88646	0.943228	−	0.332145i	$-0.107772\pi$
$211$	2.41815e15	1.88646	0.943228	+	0.332145i	$0.107772\pi$
$212$	−2.21209e15	−1.67347
$213$	1.11647e14	0.0819181
$214$	3.13778e15	2.23323
$215$	−1.14196e15	−0.788500
$216$	3.79963e13	0.0254561
$217$	−8.99485e14	−0.584798
$218$	−1.44232e15	−0.910108
$219$	4.07140e13	0.0249378
$220$	−6.29924e13	−0.0374577
$221$	1.57319e15	0.908307
$222$	−2.53171e14	−0.141945
$223$	−8.73928e14	−0.475876	−0.237938	−	0.971280i	$-0.576472\pi$
$223$	−8.73928e14	−0.475876	−0.237938	+	0.971280i	$0.576472\pi$
$224$	1.54078e15	0.814946
$225$	1.33255e15	0.684696
$226$	2.70465e15	1.35023
$227$	−6.91282e14	−0.335341	−0.167671	−	0.985843i	$-0.553624\pi$
$227$	−6.91282e14	−0.335341	−0.167671	+	0.985843i	$0.553624\pi$
$228$	−7.27702e13	−0.0343066
$229$	−1.47272e15	−0.674821	−0.337410	−	0.941358i	$-0.609551\pi$
$229$	−1.47272e15	−0.674821	−0.337410	+	0.941358i	$0.609551\pi$
$230$	1.83427e15	0.817020
$231$	−3.83413e12	−0.00166031
$232$	6.39056e14	0.269071
$233$	1.15513e15	0.472951	0.236476	−	0.971637i	$-0.424008\pi$
$233$	1.15513e15	0.472951	0.236476	+	0.971637i	$0.424008\pi$
$234$	3.00790e15	1.19773
$235$	1.67050e15	0.647001
$236$	2.83418e15	1.06782
$237$	−1.06000e14	−0.0388546
$238$	−2.62138e15	−0.934932
$239$	−2.45789e15	−0.853054	−0.426527	−	0.904475i	$-0.640263\pi$
$239$	−2.45789e15	−0.853054	−0.426527	+	0.904475i	$0.640263\pi$
$240$	−6.77047e13	−0.0228689
$241$	1.42030e15	0.466949	0.233474	−	0.972363i	$-0.424990\pi$
$241$	1.42030e15	0.466949	0.233474	+	0.972363i	$0.424990\pi$
$242$	4.58758e15	1.46820
$243$	4.89007e14	0.152361
$244$	3.60941e15	1.09497
$245$	−1.28033e15	−0.378219
$246$	−3.39098e14	−0.0975543
$247$	−1.67429e15	−0.469138
$248$	9.40558e14	0.256714
$249$	−4.88081e13	−0.0129777
$250$	5.36947e15	1.39098
$251$	6.31094e15	1.59300	0.796498	−	0.604641i	$-0.206684\pi$
$251$	6.31094e15	1.59300	0.796498	+	0.604641i	$0.206684\pi$
$252$	−2.70208e15	−0.664652
$253$	2.36311e14	0.0566500
$254$	1.48787e14	0.0347653
$255$	1.39590e14	0.0317938
$256$	2.61082e15	0.579719
$257$	−6.01618e15	−1.30243	−0.651217	−	0.758891i	$-0.725741\pi$
$257$	−6.01618e15	−1.30243	−0.651217	+	0.758891i	$0.725741\pi$
$258$	5.00798e14	0.105714
$259$	5.23270e15	1.07715
$260$	2.65976e15	0.533969
$261$	5.48067e15	1.07317
$262$	1.02148e14	0.0195107
$263$	2.35468e14	0.0438753	0.0219376	−	0.999759i	$-0.493016\pi$
$263$	2.35468e14	0.0438753	0.0219376	+	0.999759i	$0.493016\pi$
$264$	4.00921e12	0.000728841 0
$265$	−4.51596e15	−0.801036
$266$	2.78984e15	0.482890
$267$	6.53458e12	0.00110381
$268$	5.11856e15	0.843863
$269$	4.65931e15	0.749777	0.374888	−	0.927070i	$-0.377681\pi$
$269$	4.65931e15	0.749777	0.374888	+	0.927070i	$0.377681\pi$
$270$	5.34477e14	0.0839584
$271$	5.40905e15	0.829509	0.414754	−	0.909933i	$-0.363868\pi$
$271$	5.40905e15	0.829509	0.414754	+	0.909933i	$0.363868\pi$
$272$	−5.96351e15	−0.892903
$273$	1.61891e14	0.0236682
$274$	1.51342e16	2.16064
$275$	2.81577e14	0.0392586
$276$	−4.33671e14	−0.0590543
$277$	2.80004e14	0.0372431	0.0186216	−	0.999827i	$-0.494072\pi$
$277$	2.80004e14	0.0372431	0.0186216	+	0.999827i	$0.494072\pi$
$278$	−1.31197e16	−1.70464
$279$	8.06641e15	1.02389
$280$	−6.43207e14	−0.0797670
$281$	−4.84246e15	−0.586779	−0.293390	−	0.955993i	$-0.594783\pi$
$281$	−4.84246e15	−0.586779	−0.293390	+	0.955993i	$0.594783\pi$
$282$	−7.32582e14	−0.0867435
$283$	1.37940e16	1.59617	0.798087	−	0.602543i	$-0.205846\pi$
$283$	1.37940e16	1.59617	0.798087	+	0.602543i	$0.205846\pi$
$284$	1.66261e16	1.88028
$285$	−1.48560e14	−0.0164214
$286$	6.35588e14	0.0686747
$287$	7.00869e15	0.740294
$288$	−1.38174e16	−1.42684
$289$	2.39064e15	0.241367
$290$	8.98932e15	0.887441
$291$	−6.82881e13	−0.00659236
$292$	6.06300e15	0.572399
$293$	−7.51639e15	−0.694017	−0.347008	−	0.937862i	$-0.612802\pi$
$293$	−7.51639e15	−0.694017	−0.347008	+	0.937862i	$0.612802\pi$
$294$	5.61479e14	0.0507079
$295$	5.78595e15	0.511130
$296$	−5.47163e15	−0.472847
$297$	6.88571e13	0.00582145
$298$	−1.18518e16	−0.980346
$299$	−9.97787e15	−0.807561
$300$	−5.16743e14	−0.0409248
$301$	−1.03508e16	−0.802217
$302$	1.80449e16	1.36870
$303$	1.61129e14	0.0119618
$304$	6.34673e15	0.461182
$305$	7.36859e15	0.524126
$306$	2.35081e16	1.63692
$307$	1.13907e16	0.776515	0.388258	−	0.921551i	$-0.373077\pi$
$307$	1.13907e16	0.776515	0.388258	+	0.921551i	$0.373077\pi$
$308$	−5.70966e14	−0.0381093
$309$	1.05833e15	0.0691658
$310$	1.32304e16	0.846687
$311$	1.58816e16	0.995293	0.497646	−	0.867380i	$-0.334198\pi$
$311$	1.58816e16	0.995293	0.497646	+	0.867380i	$0.334198\pi$
$312$	−1.69283e14	−0.0103898
$313$	1.69022e16	1.01602	0.508012	−	0.861350i	$-0.330381\pi$
$313$	1.69022e16	1.01602	0.508012	+	0.861350i	$0.330381\pi$
$314$	1.69725e16	0.999315
$315$	−5.51627e15	−0.318146
$316$	−1.57852e16	−0.891835
$317$	−1.99751e16	−1.10561	−0.552807	−	0.833309i	$-0.686443\pi$
$317$	−1.99751e16	−1.10561	−0.552807	+	0.833309i	$0.686443\pi$
$318$	1.98043e15	0.107395
$319$	1.15810e15	0.0615328
$320$	−1.40441e16	−0.731169
$321$	−1.51450e15	−0.0772655
$322$	1.66259e16	0.831233
$323$	−1.30853e16	−0.641163
$324$	2.41684e16	1.16066
$325$	−1.18892e16	−0.559642
$326$	3.14583e16	1.45151
$327$	6.96154e14	0.0314880
$328$	−7.32872e15	−0.324974
$329$	1.51415e16	0.658256
$330$	5.63958e13	0.00240384
$331$	−1.37750e15	−0.0575717	−0.0287859	−	0.999586i	$-0.509164\pi$
$331$	−1.37750e15	−0.0575717	−0.0287859	+	0.999586i	$0.509164\pi$
$332$	−7.26834e15	−0.297878
$333$	−4.69258e16	−1.88592
$334$	−6.86085e16	−2.70412
$335$	1.04495e16	0.403929
$336$	−6.13679e14	−0.0232668
$337$	−2.54029e16	−0.944689	−0.472344	−	0.881414i	$-0.656592\pi$
$337$	−2.54029e16	−0.944689	−0.472344	+	0.881414i	$0.656592\pi$
$338$	1.35431e16	0.494038
$339$	−1.30544e15	−0.0467152
$340$	2.07872e16	0.729766
$341$	1.70449e15	0.0587070
$342$	−2.50187e16	−0.845465
$343$	−2.87855e16	−0.954468
$344$	1.08234e16	0.352156
$345$	−8.85337e14	−0.0282673
$346$	3.51974e15	0.110285
$347$	6.09352e16	1.87381	0.936907	−	0.349577i	$-0.113675\pi$
$347$	6.09352e16	1.87381	0.936907	+	0.349577i	$0.113675\pi$
$348$	−2.12532e15	−0.0641444
$349$	1.41610e15	0.0419496	0.0209748	−	0.999780i	$-0.493323\pi$
$349$	1.41610e15	0.0419496	0.0209748	+	0.999780i	$0.493323\pi$
$350$	1.98107e16	0.576046
$351$	−2.90739e15	−0.0829864
$352$	−2.91971e15	−0.0818112
$353$	5.95627e16	1.63847	0.819235	−	0.573458i	$-0.194398\pi$
$353$	5.95627e16	1.63847	0.819235	+	0.573458i	$0.194398\pi$
$354$	−2.53738e15	−0.0685274
$355$	3.39421e16	0.900024
$356$	9.73109e14	0.0253359
$357$	1.26525e15	0.0323468
$358$	9.88953e15	0.248277
$359$	−1.22769e16	−0.302674	−0.151337	−	0.988482i	$-0.548358\pi$
$359$	−1.22769e16	−0.302674	−0.151337	+	0.988482i	$0.548358\pi$
$360$	5.76816e15	0.139660
$361$	−2.81268e16	−0.668841
$362$	−6.56397e15	−0.153307
$363$	−2.21426e15	−0.0507968
$364$	2.41082e16	0.543258
$365$	1.23776e16	0.273988
$366$	−3.23143e15	−0.0702697
$367$	1.96459e16	0.419703	0.209852	−	0.977733i	$-0.432702\pi$
$367$	1.96459e16	0.419703	0.209852	+	0.977733i	$0.432702\pi$
$368$	3.78231e16	0.793865
$369$	−6.28526e16	−1.29614
$370$	−7.69671e16	−1.55953
$371$	−4.09329e16	−0.814970
$372$	−3.12803e15	−0.0611986
$373$	9.84179e16	1.89220	0.946099	−	0.323878i	$-0.104987\pi$
$373$	9.84179e16	1.89220	0.946099	+	0.323878i	$0.104987\pi$
$374$	4.96740e15	0.0938564
$375$	−2.59165e15	−0.0481252
$376$	−1.58329e16	−0.288961
$377$	−4.88991e16	−0.877167
$378$	4.84452e15	0.0854190
$379$	−9.72245e16	−1.68508	−0.842541	−	0.538633i	$-0.818941\pi$
$379$	−9.72245e16	−1.68508	−0.842541	+	0.538633i	$0.818941\pi$
$380$	−2.21231e16	−0.376922
$381$	−7.18142e13	−0.00120281
$382$	−1.49247e17	−2.45751
$383$	−1.02352e17	−1.65694	−0.828468	−	0.560036i	$-0.810787\pi$
$383$	−1.02352e17	−1.65694	−0.828468	+	0.560036i	$0.810787\pi$
$384$	1.57835e15	0.0251219
$385$	−1.16562e15	−0.0182416
$386$	−1.11163e17	−1.71057
$387$	9.28240e16	1.40456
$388$	−1.01692e16	−0.151315
$389$	1.27759e16	0.186947	0.0934735	−	0.995622i	$-0.470203\pi$
$389$	1.27759e16	0.186947	0.0934735	+	0.995622i	$0.470203\pi$
$390$	−2.38123e15	−0.0342674
$391$	−7.79815e16	−1.10368
$392$	1.21349e16	0.168918
$393$	−4.93033e13	−0.000675032 0
$394$	−7.79290e15	−0.104948
$395$	−3.22254e16	−0.426891
$396$	5.12032e15	0.0667234
$397$	6.63410e16	0.850440	0.425220	−	0.905090i	$-0.360197\pi$
$397$	6.63410e16	0.850440	0.425220	+	0.905090i	$0.360197\pi$
$398$	9.56085e16	1.20575
$399$	−1.34655e15	−0.0167071
$400$	4.50683e16	0.550150
$401$	4.58285e16	0.550424	0.275212	−	0.961384i	$-0.411252\pi$
$401$	4.58285e16	0.550424	0.275212	+	0.961384i	$0.411252\pi$
$402$	−4.58254e15	−0.0541548
$403$	−7.19694e16	−0.836884
$404$	2.39948e16	0.274561
$405$	4.93397e16	0.555570
$406$	8.14796e16	0.902879
$407$	−9.91573e15	−0.108134
$408$	−1.32302e15	−0.0141996
$409$	1.15184e17	1.21672	0.608358	−	0.793663i	$-0.291829\pi$
$409$	1.15184e17	1.21672	0.608358	+	0.793663i	$0.291829\pi$
$410$	−1.03090e17	−1.07182
$411$	−7.30475e15	−0.0747538
$412$	1.57603e17	1.58757
$413$	5.24441e16	0.520022
$414$	−1.49098e17	−1.45536
$415$	−1.48383e16	−0.142584
$416$	1.23281e17	1.16624
$417$	6.33243e15	0.0589774
$418$	−5.28662e15	−0.0484766
$419$	−1.68424e17	−1.52060	−0.760298	−	0.649575i	$-0.774947\pi$
$419$	−1.68424e17	−1.52060	−0.760298	+	0.649575i	$0.774947\pi$
$420$	2.13912e15	0.0190158
$421$	7.75103e16	0.678462	0.339231	−	0.940703i	$-0.389833\pi$
$421$	7.75103e16	0.678462	0.339231	+	0.940703i	$0.389833\pi$
$422$	−3.22392e17	−2.77878
$423$	−1.35786e17	−1.15250
$424$	4.28020e16	0.357755
$425$	−9.29192e16	−0.764852
$426$	−1.48850e16	−0.120666
$427$	6.67893e16	0.533244
$428$	−2.25534e17	−1.77348
$429$	−3.06776e14	−0.00237601
$430$	1.52249e17	1.16147
$431$	8.81664e16	0.662523	0.331261	−	0.943539i	$-0.392526\pi$
$431$	8.81664e16	0.662523	0.331261	+	0.943539i	$0.392526\pi$
$432$	1.10210e16	0.0815790
$433$	1.11461e17	0.812738	0.406369	−	0.913709i	$-0.366795\pi$
$433$	1.11461e17	0.812738	0.406369	+	0.913709i	$0.366795\pi$
$434$	1.19921e17	0.861415
$435$	−4.33882e15	−0.0307038
$436$	1.03669e17	0.722748
$437$	8.29927e16	0.570047
$438$	−5.42808e15	−0.0367337
$439$	1.70987e17	1.14010	0.570051	−	0.821609i	$-0.306923\pi$
$439$	1.70987e17	1.14010	0.570051	+	0.821609i	$0.306923\pi$
$440$	1.21885e15	0.00800769
$441$	1.04071e17	0.673722
$442$	−2.09741e17	−1.33795
$443$	1.30826e16	0.0822375	0.0411187	−	0.999154i	$-0.486908\pi$
$443$	1.30826e16	0.0822375	0.0411187	+	0.999154i	$0.486908\pi$
$444$	1.81971e16	0.112723
$445$	1.98659e15	0.0121274
$446$	1.16514e17	0.700973
$447$	5.72045e15	0.0339181
$448$	−1.27296e17	−0.743889
$449$	−2.91690e17	−1.68004	−0.840021	−	0.542554i	$-0.817457\pi$
$449$	−2.91690e17	−1.68004	−0.840021	+	0.542554i	$0.817457\pi$
$450$	−1.77659e17	−1.00857
$451$	−1.32812e16	−0.0743170
$452$	−1.94402e17	−1.07226
$453$	−8.70961e15	−0.0473544
$454$	9.21630e16	0.493962
$455$	4.92168e16	0.260039
$456$	1.40804e15	0.00733405
$457$	−1.33514e17	−0.685602	−0.342801	−	0.939408i	$-0.611376\pi$
$457$	−1.33514e17	−0.685602	−0.342801	+	0.939408i	$0.611376\pi$
$458$	1.96345e17	0.994020
$459$	−2.27225e16	−0.113416
$460$	−1.31841e17	−0.648823
$461$	3.76065e17	1.82476	0.912382	−	0.409339i	$-0.134241\pi$
$461$	3.76065e17	1.82476	0.912382	+	0.409339i	$0.134241\pi$
$462$	5.11174e14	0.00244566
$463$	1.15716e17	0.545906	0.272953	−	0.962027i	$-0.412000\pi$
$463$	1.15716e17	0.545906	0.272953	+	0.962027i	$0.412000\pi$
$464$	1.85362e17	0.862291
$465$	−6.38585e15	−0.0292937
$466$	−1.54004e17	−0.696663
$467$	1.76242e17	0.786232	0.393116	−	0.919489i	$-0.371397\pi$
$467$	1.76242e17	0.786232	0.393116	+	0.919489i	$0.371397\pi$
$468$	−2.16198e17	−0.951160
$469$	9.47149e16	0.410956
$470$	−2.22714e17	−0.953041
$471$	−8.19201e15	−0.0345744
$472$	−5.48389e16	−0.228279
$473$	1.96143e16	0.0805333
$474$	1.41322e16	0.0572334
$475$	9.88904e16	0.395044
$476$	1.88416e17	0.742461
$477$	3.67078e17	1.42689
$478$	3.27691e17	1.25656
$479$	6.87114e16	0.259925	0.129962	−	0.991519i	$-0.458514\pi$
$479$	6.87114e16	0.259925	0.129962	+	0.991519i	$0.458514\pi$
$480$	1.09387e16	0.0408223
$481$	4.18677e17	1.54147
$482$	−1.89357e17	−0.687822
$483$	−8.02474e15	−0.0287590
$484$	−3.29741e17	−1.16594
$485$	−2.07604e16	−0.0724295
$486$	−6.51954e16	−0.224430
$487$	4.38161e17	1.48832	0.744158	−	0.668004i	$-0.232851\pi$
$487$	4.38161e17	1.48832	0.744158	+	0.668004i	$0.232851\pi$
$488$	−6.98390e16	−0.234083
$489$	−1.51838e16	−0.0502195
$490$	1.70697e17	0.557122
$491$	7.76075e16	0.249962	0.124981	−	0.992159i	$-0.460113\pi$
$491$	7.76075e16	0.249962	0.124981	+	0.992159i	$0.460113\pi$
$492$	2.43732e16	0.0774712
$493$	−3.82168e17	−1.19881
$494$	2.23220e17	0.691047
$495$	1.04531e16	0.0319382
$496$	2.72815e17	0.822691
$497$	3.07653e17	0.915681
$498$	6.50719e15	0.0191163
$499$	6.07391e17	1.76123	0.880613	−	0.473837i	$-0.157131\pi$
$499$	6.07391e17	1.76123	0.880613	+	0.473837i	$0.157131\pi$
$500$	−3.85940e17	−1.10462
$501$	3.31149e16	0.0935574
$502$	−8.41387e17	−2.34650
$503$	−1.67159e17	−0.460192	−0.230096	−	0.973168i	$-0.573904\pi$
$503$	−1.67159e17	−0.460192	−0.230096	+	0.973168i	$0.573904\pi$
$504$	5.22828e16	0.142089
$505$	4.89853e16	0.131423
$506$	−3.15054e16	−0.0834462
$507$	−6.53678e15	−0.0170928
$508$	−1.06943e16	−0.0276083
$509$	−5.48168e17	−1.39717	−0.698583	−	0.715529i	$-0.746186\pi$
$509$	−5.48168e17	−1.39717	−0.698583	+	0.715529i	$0.746186\pi$
$510$	−1.86104e16	−0.0468327
$511$	1.12191e17	0.278754
$512$	−5.49011e17	−1.34687
$513$	2.41827e16	0.0585791
$514$	8.02090e17	1.91850
$515$	3.21746e17	0.759916
$516$	−3.59957e16	−0.0839513
$517$	−2.86924e16	−0.0660813
$518$	−6.97633e17	−1.58666
$519$	−1.69885e15	−0.00381565
$520$	−5.14641e16	−0.114152
$521$	−2.56918e17	−0.562793	−0.281397	−	0.959592i	$-0.590798\pi$
$521$	−2.56918e17	−0.562793	−0.281397	+	0.959592i	$0.590798\pi$
$522$	−7.30694e17	−1.58080
$523$	−2.45376e17	−0.524290	−0.262145	−	0.965028i	$-0.584430\pi$
$523$	−2.45376e17	−0.524290	−0.262145	+	0.965028i	$0.584430\pi$
$524$	−7.34208e15	−0.0154941
$525$	−9.56191e15	−0.0199301
$526$	−3.13931e16	−0.0646289
$527$	−5.62473e17	−1.14375
$528$	1.16289e15	0.00233571
$529$	−9.44437e15	−0.0187375
$530$	6.02077e17	1.17994
$531$	−4.70309e17	−0.910477
$532$	−2.00524e17	−0.383479
$533$	5.60777e17	1.05941
$534$	−8.71204e14	−0.00162593
$535$	−4.60426e17	−0.848907
$536$	−9.90398e16	−0.180401
$537$	−4.77332e15	−0.00858990
$538$	−6.21189e17	−1.10443
$539$	2.19910e16	0.0386293
$540$	−3.84165e16	−0.0666742
$541$	−2.75528e17	−0.472481	−0.236240	−	0.971695i	$-0.575915\pi$
$541$	−2.75528e17	−0.472481	−0.236240	+	0.971695i	$0.575915\pi$
$542$	−7.21146e17	−1.22188
$543$	3.16819e15	0.00530411
$544$	9.63493e17	1.59388
$545$	2.11640e17	0.345955
$546$	−2.15836e16	−0.0348635
$547$	−6.71677e17	−1.07212	−0.536059	−	0.844180i	$-0.680088\pi$
$547$	−6.71677e17	−1.07212	−0.536059	+	0.844180i	$0.680088\pi$
$548$	−1.08780e18	−1.71583
$549$	−5.98954e17	−0.933626
$550$	−3.75404e16	−0.0578284
$551$	4.06727e17	0.619181
$552$	8.39117e15	0.0126246
$553$	−2.92093e17	−0.434317
$554$	−3.73307e16	−0.0548596
$555$	3.71493e16	0.0539567
$556$	9.43004e17	1.35372
$557$	1.29772e18	1.84129	0.920644	−	0.390403i	$-0.127664\pi$
$557$	1.29772e18	1.84129	0.920644	+	0.390403i	$0.127664\pi$
$558$	−1.07543e18	−1.50820
$559$	−8.28186e17	−1.14802
$560$	−1.86566e17	−0.255629
$561$	−2.39759e15	−0.00324725
$562$	6.45606e17	0.864334
$563$	−3.23275e17	−0.427827	−0.213913	−	0.976853i	$-0.568621\pi$
$563$	−3.23275e17	−0.427827	−0.213913	+	0.976853i	$0.568621\pi$
$564$	5.26556e16	0.0688859
$565$	−3.96869e17	−0.513254
$566$	−1.83905e18	−2.35118
$567$	4.47218e17	0.565235
$568$	−3.21701e17	−0.401965
$569$	1.41375e18	1.74639	0.873196	−	0.487370i	$-0.162044\pi$
$569$	1.41375e18	1.74639	0.873196	+	0.487370i	$0.162044\pi$
$570$	1.98063e16	0.0241889
$571$	−1.29622e18	−1.56510	−0.782551	−	0.622586i	$-0.786082\pi$
$571$	−1.29622e18	−1.56510	−0.782551	+	0.622586i	$0.786082\pi$
$572$	−4.56840e16	−0.0545369
$573$	7.20364e16	0.0850251
$574$	−9.34412e17	−1.09046
$575$	5.89333e17	0.680017
$576$	1.14157e18	1.30243
$577$	6.57893e17	0.742185	0.371093	−	0.928596i	$-0.378983\pi$
$577$	6.57893e17	0.742185	0.371093	+	0.928596i	$0.378983\pi$
$578$	−3.18725e17	−0.355537
$579$	5.36542e16	0.0591825
$580$	−6.46123e17	−0.704747
$581$	−1.34495e17	−0.145064
$582$	9.10431e15	0.00971063
$583$	7.75660e16	0.0818137
$584$	−1.17314e17	−0.122367
$585$	−4.41367e17	−0.455288
$586$	1.00210e18	1.02230
$587$	−8.27563e17	−0.834936	−0.417468	−	0.908692i	$-0.637082\pi$
$587$	−8.27563e17	−0.834936	−0.417468	+	0.908692i	$0.637082\pi$
$588$	−4.03573e16	−0.0402689
$589$	5.98619e17	0.590746
$590$	−7.71395e17	−0.752902
$591$	3.76135e15	0.00363099
$592$	−1.58708e18	−1.51533
$593$	1.47638e18	1.39425	0.697126	−	0.716948i	$-0.254462\pi$
$593$	1.47638e18	1.39425	0.697126	+	0.716948i	$0.254462\pi$
$594$	−9.18016e15	−0.00857508
$595$	3.84651e17	0.355391
$596$	8.51870e17	0.778526
$597$	−4.61468e16	−0.0417166
$598$	1.33027e18	1.18955
$599$	−1.32348e18	−1.17069	−0.585345	−	0.810784i	$-0.699041\pi$
$599$	−1.32348e18	−1.17069	−0.585345	+	0.810784i	$0.699041\pi$
$600$	9.99853e15	0.00874889
$601$	1.74144e18	1.50738	0.753691	−	0.657229i	$-0.228272\pi$
$601$	1.74144e18	1.50738	0.753691	+	0.657229i	$0.228272\pi$
$602$	1.37999e18	1.18168
$603$	−8.49385e17	−0.719519
$604$	−1.29701e18	−1.08693
$605$	−6.73163e17	−0.558098
$606$	−2.14821e16	−0.0176199
$607$	1.16961e18	0.949105	0.474553	−	0.880227i	$-0.342610\pi$
$607$	1.16961e18	0.949105	0.474553	+	0.880227i	$0.342610\pi$
$608$	−1.02541e18	−0.823235
$609$	−3.93273e16	−0.0312379
$610$	−9.82395e17	−0.772045
$611$	1.21150e18	0.942007
$612$	−1.68968e18	−1.29993
$613$	−1.86809e18	−1.42202	−0.711009	−	0.703183i	$-0.751761\pi$
$613$	−1.86809e18	−1.42202	−0.711009	+	0.703183i	$0.751761\pi$
$614$	−1.51863e18	−1.14382
$615$	4.97578e16	0.0370828
$616$	1.10477e16	0.00814699
$617$	−1.49993e18	−1.09450	−0.547251	−	0.836969i	$-0.684326\pi$
$617$	−1.49993e18	−1.09450	−0.547251	+	0.836969i	$0.684326\pi$
$618$	−1.41099e17	−0.101882
$619$	1.28869e18	0.920785	0.460393	−	0.887715i	$-0.347709\pi$
$619$	1.28869e18	0.920785	0.460393	+	0.887715i	$0.347709\pi$
$620$	−9.50960e17	−0.672382
$621$	1.44116e17	0.100836
$622$	−2.11736e18	−1.46608
$623$	1.80066e16	0.0123384
$624$	−4.91015e16	−0.0332962
$625$	2.35040e17	0.157733
$626$	−2.25343e18	−1.49662
$627$	2.55166e15	0.00167720
$628$	−1.21993e18	−0.793590
$629$	3.27215e18	2.10671
$630$	7.35440e17	0.468634
$631$	2.76876e18	1.74620	0.873101	−	0.487540i	$-0.162106\pi$
$631$	2.76876e18	1.74620	0.873101	+	0.487540i	$0.162106\pi$
$632$	3.05430e17	0.190656
$633$	1.55607e17	0.0961403
$634$	2.66312e18	1.62858
$635$	−2.18324e16	−0.0132152
$636$	−1.42347e17	−0.0852860
$637$	−9.28537e17	−0.550672
$638$	−1.54400e17	−0.0906387
$639$	−2.75897e18	−1.60321
$640$	4.79839e17	0.276011
$641$	2.68534e18	1.52905	0.764524	−	0.644595i	$-0.222974\pi$
$641$	2.68534e18	1.52905	0.764524	+	0.644595i	$0.222974\pi$
$642$	2.01916e17	0.113813
$643$	2.92849e18	1.63408	0.817038	−	0.576584i	$-0.195614\pi$
$643$	2.92849e18	1.63408	0.817038	+	0.576584i	$0.195614\pi$
$644$	−1.19502e18	−0.660110
$645$	−7.34850e16	−0.0401847
$646$	1.74456e18	0.944441
$647$	−1.53528e18	−0.822830	−0.411415	−	0.911448i	$-0.634965\pi$
$647$	−1.53528e18	−0.822830	−0.411415	+	0.911448i	$0.634965\pi$
$648$	−4.67639e17	−0.248126
$649$	−9.93794e16	−0.0522042
$650$	1.58509e18	0.824360
$651$	−5.78817e16	−0.0298033
$652$	−2.26112e18	−1.15269
$653$	1.78601e18	0.901464	0.450732	−	0.892659i	$-0.351163\pi$
$653$	1.78601e18	0.901464	0.450732	+	0.892659i	$0.351163\pi$
$654$	−9.28127e16	−0.0463823
$655$	−1.49888e16	−0.00741649
$656$	−2.12574e18	−1.04144
$657$	−1.00611e18	−0.488055
$658$	−2.01869e18	−0.969620
$659$	2.00624e18	0.954174	0.477087	−	0.878856i	$-0.341693\pi$
$659$	2.00624e18	0.954174	0.477087	+	0.878856i	$0.341693\pi$
$660$	−4.05354e15	−0.00190897
$661$	−3.79500e18	−1.76971	−0.884856	−	0.465865i	$-0.845743\pi$
$661$	−3.79500e18	−1.76971	−0.884856	+	0.465865i	$0.845743\pi$
$662$	1.83651e17	0.0848040
$663$	1.01235e17	0.0462904
$664$	1.40636e17	0.0636802
$665$	−4.09369e17	−0.183558
$666$	6.25624e18	2.77799
$667$	2.42387e18	1.06584
$668$	4.93136e18	2.14743
$669$	−5.62371e16	−0.0242523
$670$	−1.39315e18	−0.594993
$671$	−1.26563e17	−0.0535315
$672$	9.91489e16	0.0415325
$673$	6.85819e17	0.284519	0.142260	−	0.989829i	$-0.454563\pi$
$673$	6.85819e17	0.284519	0.142260	+	0.989829i	$0.454563\pi$
$674$	3.38676e18	1.39154
$675$	1.71722e17	0.0698798
$676$	−9.73436e17	−0.392332
$677$	3.08893e18	1.23305	0.616527	−	0.787334i	$-0.288539\pi$
$677$	3.08893e18	1.23305	0.616527	+	0.787334i	$0.288539\pi$
$678$	1.74044e17	0.0688121
$679$	−1.88174e17	−0.0736894
$680$	−4.02215e17	−0.156009
$681$	−4.44838e16	−0.0170901
$682$	−2.27245e17	−0.0864762
$683$	−3.58816e18	−1.35250	−0.676250	−	0.736672i	$-0.736396\pi$
$683$	−3.58816e18	−1.35250	−0.676250	+	0.736672i	$0.736396\pi$
$684$	1.79827e18	0.671412
$685$	−2.22073e18	−0.821311
$686$	3.83774e18	1.40594
$687$	−9.47689e16	−0.0343912
$688$	3.13941e18	1.12855
$689$	−3.27511e18	−1.16628
$690$	1.18035e17	0.0416381
$691$	1.65030e18	0.576708	0.288354	−	0.957524i	$-0.406892\pi$
$691$	1.65030e18	0.576708	0.288354	+	0.957524i	$0.406892\pi$
$692$	−2.52988e17	−0.0875810
$693$	9.47473e16	0.0324938
$694$	−8.12400e18	−2.76016
$695$	1.92514e18	0.647978
$696$	4.11231e16	0.0137128
$697$	4.38273e18	1.44788
$698$	−1.88797e17	−0.0617923
$699$	7.43321e16	0.0241032
$700$	−1.42393e18	−0.457458
$701$	−8.59076e17	−0.273441	−0.136721	−	0.990610i	$-0.543656\pi$
$701$	−8.59076e17	−0.273441	−0.136721	+	0.990610i	$0.543656\pi$
$702$	3.87619e17	0.122240
$703$	−3.48242e18	−1.08811
$704$	2.41221e17	0.0746779
$705$	1.07496e17	0.0329734
$706$	−7.94101e18	−2.41349
$707$	4.44005e17	0.133709
$708$	1.82379e17	0.0544199
$709$	2.40726e18	0.711743	0.355872	−	0.934535i	$-0.384184\pi$
$709$	2.40726e18	0.711743	0.355872	+	0.934535i	$0.384184\pi$
$710$	−4.52523e18	−1.32575
$711$	2.61943e18	0.760422
$712$	−1.88288e16	−0.00541631
$713$	3.56744e18	1.01689
$714$	−1.68685e17	−0.0476474
$715$	−9.32636e16	−0.0261050
$716$	−7.10828e17	−0.197165
$717$	−1.58165e17	−0.0434746
$718$	1.63678e18	0.445843
$719$	−3.57856e17	−0.0965985	−0.0482992	−	0.998833i	$-0.515380\pi$
$719$	−3.57856e17	−0.0965985	−0.0482992	+	0.998833i	$0.515380\pi$
$720$	1.67309e18	0.447567
$721$	2.91632e18	0.773136
$722$	3.74992e18	0.985212
$723$	9.13960e16	0.0237973
$724$	4.71797e17	0.121746
$725$	2.88818e18	0.738630
$726$	2.95210e17	0.0748243
$727$	7.11920e18	1.78837	0.894185	−	0.447698i	$-0.147756\pi$
$727$	7.11920e18	1.78837	0.894185	+	0.447698i	$0.147756\pi$
$728$	−4.66473e17	−0.116138
$729$	−3.98954e18	−0.984450
$730$	−1.65020e18	−0.403588
$731$	−6.47264e18	−1.56898
$732$	2.32265e17	0.0558035
$733$	7.20770e18	1.71641	0.858205	−	0.513307i	$-0.171580\pi$
$733$	7.20770e18	1.71641	0.858205	+	0.513307i	$0.171580\pi$
$734$	−2.61923e18	−0.618229
$735$	−8.23891e16	−0.0192753
$736$	−6.11089e18	−1.41709
$737$	−1.79481e17	−0.0412552
$738$	8.37963e18	1.90923
$739$	−8.70530e17	−0.196605	−0.0983026	−	0.995157i	$-0.531341\pi$
$739$	−8.70530e17	−0.196605	−0.0983026	+	0.995157i	$0.531341\pi$
$740$	5.53214e18	1.23848
$741$	−1.07740e17	−0.0239089
$742$	5.45725e18	1.20046
$743$	2.00355e18	0.436892	0.218446	−	0.975849i	$-0.429901\pi$
$743$	2.00355e18	0.436892	0.218446	+	0.975849i	$0.429901\pi$
$744$	6.05247e16	0.0130830
$745$	1.73909e18	0.372654
$746$	−1.31213e19	−2.78723
$747$	1.20612e18	0.253985
$748$	−3.57041e17	−0.0745346
$749$	−4.17332e18	−0.863674
$750$	3.45524e17	0.0708891
$751$	3.55821e18	0.723723	0.361861	−	0.932232i	$-0.382141\pi$
$751$	3.55821e18	0.723723	0.361861	+	0.932232i	$0.382141\pi$
$752$	−4.59242e18	−0.926031
$753$	4.06107e17	0.0811845
$754$	6.51933e18	1.29208
$755$	−2.64783e18	−0.520278
$756$	−3.48209e17	−0.0678341
$757$	3.93179e17	0.0759394	0.0379697	−	0.999279i	$-0.487911\pi$
$757$	3.93179e17	0.0759394	0.0379697	+	0.999279i	$0.487911\pi$
$758$	1.29622e19	2.48215
$759$	1.52065e16	0.00288708
$760$	4.28062e17	0.0805783
$761$	4.45561e18	0.831585	0.415793	−	0.909459i	$-0.363504\pi$
$761$	4.45561e18	0.831585	0.415793	+	0.909459i	$0.363504\pi$
$762$	9.57441e15	0.00177176
$763$	1.91831e18	0.351973
$764$	1.07274e19	1.95159
$765$	−3.44948e18	−0.622234
$766$	1.36458e19	2.44069
$767$	4.19615e18	0.744185
$768$	1.68006e17	0.0295445
$769$	5.83473e18	1.01742	0.508710	−	0.860938i	$-0.330123\pi$
$769$	5.83473e18	1.01742	0.508710	+	0.860938i	$0.330123\pi$
$770$	1.55403e17	0.0268702
$771$	−3.87140e17	−0.0663765
$772$	7.99001e18	1.35842
$773$	−2.92948e18	−0.493882	−0.246941	−	0.969031i	$-0.579425\pi$
$773$	−2.92948e18	−0.493882	−0.246941	+	0.969031i	$0.579425\pi$
$774$	−1.23755e19	−2.06893
$775$	4.25080e18	0.704709
$776$	1.96766e17	0.0323481
$777$	3.36723e17	0.0548954
$778$	−1.70331e18	−0.275376
$779$	−4.66437e18	−0.747824
$780$	1.71155e17	0.0272129
$781$	−5.82989e17	−0.0919239
$782$	1.03967e19	1.62573
$783$	7.06278e17	0.109528
$784$	3.51980e18	0.541333
$785$	−2.49047e18	−0.379865
$786$	6.57321e15	0.000994331 0
$787$	7.19182e18	1.07895	0.539477	−	0.842000i	$-0.318622\pi$
$787$	7.19182e18	1.07895	0.539477	+	0.842000i	$0.318622\pi$
$788$	5.60129e17	0.0833426
$789$	1.51523e16	0.00223604
$790$	4.29635e18	0.628817
$791$	−3.59724e18	−0.522183
$792$	−9.90737e16	−0.0142641
$793$	5.34393e18	0.763106
$794$	−8.84471e18	−1.25271
$795$	−2.90601e17	−0.0408235
$796$	−6.87203e18	−0.957525
$797$	−1.25524e19	−1.73479	−0.867395	−	0.497620i	$-0.834207\pi$
$797$	−1.25524e19	−1.73479	−0.867395	+	0.497620i	$0.834207\pi$
$798$	1.79525e17	0.0246097
$799$	9.46838e18	1.28742
$800$	−7.28145e18	−0.982049
$801$	−1.61480e17	−0.0216026
$802$	−6.10995e18	−0.810782
$803$	−2.12597e17	−0.0279837
$804$	3.29378e17	0.0430062
$805$	−2.43962e18	−0.315972
$806$	9.59511e18	1.23274
$807$	2.99826e17	0.0382112
$808$	−4.64279e17	−0.0586956
$809$	1.12068e19	1.40545	0.702726	−	0.711461i	$-0.251966\pi$
$809$	1.12068e19	1.40545	0.702726	+	0.711461i	$0.251966\pi$
$810$	−6.57807e18	−0.818363
$811$	1.29000e19	1.59204	0.796021	−	0.605268i	$-0.206934\pi$
$811$	1.29000e19	1.59204	0.796021	+	0.605268i	$0.206934\pi$
$812$	−5.85649e18	−0.717007
$813$	3.48071e17	0.0422746
$814$	1.32198e18	0.159282
$815$	−4.61606e18	−0.551756
$816$	−3.83750e17	−0.0455054
$817$	6.88859e18	0.810376
$818$	−1.53565e19	−1.79224
$819$	−4.00057e18	−0.463208
$820$	7.40977e18	0.851167
$821$	1.08760e19	1.23948	0.619738	−	0.784809i	$-0.287239\pi$
$821$	1.08760e19	1.23948	0.619738	+	0.784809i	$0.287239\pi$
$822$	9.73884e17	0.110113
$823$	−5.10795e18	−0.572991	−0.286495	−	0.958082i	$-0.592490\pi$
$823$	−5.10795e18	−0.572991	−0.286495	+	0.958082i	$0.592490\pi$
$824$	−3.04948e18	−0.339390
$825$	1.81194e16	0.00200075
$826$	−6.99196e18	−0.765999
$827$	8.30477e18	0.902697	0.451349	−	0.892348i	$-0.350943\pi$
$827$	8.30477e18	0.902697	0.451349	+	0.892348i	$0.350943\pi$
$828$	1.07167e19	1.15575
$829$	4.61268e17	0.0493571	0.0246785	−	0.999695i	$-0.492144\pi$
$829$	4.61268e17	0.0493571	0.0246785	+	0.999695i	$0.492144\pi$
$830$	1.97827e18	0.210028
$831$	1.80182e16	0.00189804
$832$	−1.01852e19	−1.06455
$833$	−7.25693e18	−0.752593
$834$	−8.44252e17	−0.0868746
$835$	1.00673e19	1.02790
$836$	3.79985e17	0.0384969
$837$	1.03950e18	0.104498
$838$	2.24547e19	2.23986
$839$	−8.49861e18	−0.841192	−0.420596	−	0.907248i	$-0.638179\pi$
$839$	−8.49861e18	−0.841192	−0.420596	+	0.907248i	$0.638179\pi$
$840$	−4.13902e16	−0.00406520
$841$	1.61819e18	0.157709
$842$	−1.03338e19	−0.999384
$843$	−3.11611e17	−0.0299043
$844$	2.31725e19	2.20672
$845$	−1.98726e18	−0.187796
$846$	1.81032e19	1.69765
$847$	−6.10158e18	−0.567807
$848$	1.24150e19	1.14650
$849$	8.87644e17	0.0813465
$850$	1.23882e19	1.12664
$851$	−2.07534e19	−1.87304
$852$	1.06989e18	0.0958253
$853$	−2.14697e19	−1.90835	−0.954174	−	0.299252i	$-0.903263\pi$
$853$	−2.14697e19	−1.90835	−0.954174	+	0.299252i	$0.903263\pi$
$854$	−8.90448e18	−0.785475
$855$	3.67115e18	0.321382
$856$	4.36388e18	0.379135
$857$	−1.24634e19	−1.07463	−0.537317	−	0.843380i	$-0.680562\pi$
$857$	−1.24634e19	−1.07463	−0.537317	+	0.843380i	$0.680562\pi$
$858$	4.08999e16	0.00349990
$859$	3.16481e18	0.268777	0.134389	−	0.990929i	$-0.457093\pi$
$859$	3.16481e18	0.268777	0.134389	+	0.990929i	$0.457093\pi$
$860$	−1.09431e19	−0.922364
$861$	4.51007e17	0.0377279
$862$	−1.17545e19	−0.975905
$863$	−8.02569e18	−0.661321	−0.330660	−	0.943750i	$-0.607271\pi$
$863$	−8.02569e18	−0.661321	−0.330660	+	0.943750i	$0.607271\pi$
$864$	−1.78061e18	−0.145623
$865$	−5.16473e17	−0.0419221
$866$	−1.48602e19	−1.19717
$867$	1.53837e17	0.0123009
$868$	−8.61955e18	−0.684079
$869$	5.53503e17	0.0436005
$870$	5.78460e17	0.0452271
$871$	7.57831e18	0.588104
$872$	−2.00591e18	−0.154509
$873$	1.68751e18	0.129019
$874$	−1.10648e19	−0.839687
$875$	−7.14150e18	−0.537944
$876$	3.90152e17	0.0291714
$877$	−3.68350e18	−0.273378	−0.136689	−	0.990614i	$-0.543646\pi$
$877$	−3.68350e18	−0.273378	−0.136689	+	0.990614i	$0.543646\pi$
$878$	−2.27963e19	−1.67939
$879$	−4.83678e17	−0.0353695
$880$	3.53534e17	0.0256622
$881$	−4.70489e17	−0.0339005	−0.0169502	−	0.999856i	$-0.505396\pi$
$881$	−4.70489e17	−0.0339005	−0.0169502	+	0.999856i	$0.505396\pi$
$882$	−1.38750e19	−0.992402
$883$	2.53314e18	0.179851	0.0899257	−	0.995948i	$-0.471337\pi$
$883$	2.53314e18	0.179851	0.0899257	+	0.995948i	$0.471337\pi$
$884$	1.50755e19	1.06251
$885$	3.72324e17	0.0260490
$886$	−1.74420e18	−0.121137
$887$	1.68924e19	1.16463	0.582315	−	0.812964i	$-0.302147\pi$
$887$	1.68924e19	1.16463	0.582315	+	0.812964i	$0.302147\pi$
$888$	−3.52098e17	−0.0240979
$889$	−1.97890e17	−0.0134450
$890$	−2.64857e17	−0.0178639
$891$	−8.47458e17	−0.0567431
$892$	−8.37464e18	−0.556666
$893$	−1.00768e19	−0.664951
$894$	−7.62662e17	−0.0499618
$895$	−1.45115e18	−0.0943762
$896$	4.34929e18	0.280812
$897$	−6.42073e17	−0.0411561
$898$	3.88887e19	2.47472
$899$	1.74832e19	1.10454
$900$	1.27695e19	0.800937
$901$	−2.55965e19	−1.59393
$902$	1.77067e18	0.109470
$903$	−6.66071e17	−0.0408837
$904$	3.76150e18	0.229227
$905$	9.63170e17	0.0582757
$906$	1.16118e18	0.0697537
$907$	−1.44478e19	−0.861694	−0.430847	−	0.902425i	$-0.641785\pi$
$907$	−1.44478e19	−0.861694	−0.430847	+	0.902425i	$0.641785\pi$
$908$	−6.62438e18	−0.392272
$909$	−3.98175e18	−0.234104
$910$	−6.56168e18	−0.383041
$911$	−2.55988e19	−1.48371	−0.741857	−	0.670558i	$-0.766055\pi$
$911$	−2.55988e19	−1.48371	−0.741857	+	0.670558i	$0.766055\pi$
$912$	4.08411e17	0.0235034
$913$	2.54862e17	0.0145628
$914$	1.78004e19	1.00990
$915$	4.74167e17	0.0267113
$916$	−1.41127e19	−0.789385
$917$	−1.35859e17	−0.00754551
$918$	3.02941e18	0.167063
$919$	2.18967e18	0.119902	0.0599511	−	0.998201i	$-0.480906\pi$
$919$	2.18967e18	0.119902	0.0599511	+	0.998201i	$0.480906\pi$
$920$	2.55102e18	0.138705
$921$	7.32987e17	0.0395739
$922$	−5.01377e19	−2.68790
$923$	2.46158e19	1.31040
$924$	−3.67415e16	−0.00194218
$925$	−2.47288e19	−1.29802
$926$	−1.54275e19	−0.804128
$927$	−2.61530e19	−1.35364
$928$	−2.99480e19	−1.53924
$929$	−3.72441e19	−1.90088	−0.950441	−	0.310906i	$-0.899368\pi$
$929$	−3.72441e19	−1.90088	−0.950441	+	0.310906i	$0.899368\pi$
$930$	8.51374e17	0.0431501
$931$	7.72327e18	0.388712
$932$	1.10693e19	0.553244
$933$	1.02198e18	0.0507235
$934$	−2.34970e19	−1.15813
$935$	−7.28897e17	−0.0356772
$936$	4.18324e18	0.203339
$937$	−3.34630e19	−1.61532	−0.807659	−	0.589650i	$-0.799266\pi$
$937$	−3.34630e19	−1.61532	−0.807659	+	0.589650i	$0.799266\pi$
$938$	−1.26276e19	−0.605343
$939$	1.08765e18	0.0517801
$940$	1.60080e19	0.756842
$941$	1.96087e19	0.920696	0.460348	−	0.887739i	$-0.347725\pi$
$941$	1.96087e19	0.920696	0.460348	+	0.887739i	$0.347725\pi$
$942$	1.09217e18	0.0509285
$943$	−2.77971e19	−1.28728
$944$	−1.59063e19	−0.731564
$945$	−7.10865e17	−0.0324699
$946$	−2.61502e18	−0.118627
$947$	−1.87378e18	−0.0844196	−0.0422098	−	0.999109i	$-0.513440\pi$
$947$	−1.87378e18	−0.0844196	−0.0422098	+	0.999109i	$0.513440\pi$
$948$	−1.01577e18	−0.0454510
$949$	8.97659e18	0.398916
$950$	−1.31843e19	−0.581905
$951$	−1.28539e18	−0.0563459
$952$	−3.64570e18	−0.158723
$953$	−8.42229e18	−0.364189	−0.182094	−	0.983281i	$-0.558288\pi$
$953$	−8.42229e18	−0.364189	−0.182094	+	0.983281i	$0.558288\pi$
$954$	−4.89396e19	−2.10182
$955$	2.19000e19	0.934160
$956$	−2.35534e19	−0.997877
$957$	7.45235e16	0.00313592
$958$	−9.16074e18	−0.382873
$959$	−2.01288e19	−0.835599
$960$	−9.03732e17	−0.0372629
$961$	1.31409e18	0.0538173
$962$	−5.58189e19	−2.27061
$963$	3.74255e19	1.51216
$964$	1.36104e19	0.546223
$965$	1.63115e19	0.650231
$966$	1.06987e18	0.0423625
$967$	6.28151e17	0.0247054	0.0123527	−	0.999924i	$-0.496068\pi$
$967$	6.28151e17	0.0247054	0.0123527	+	0.999924i	$0.496068\pi$
$968$	6.38020e18	0.249255
$969$	−8.42038e17	−0.0326759
$970$	2.76782e18	0.106690
$971$	−1.77608e19	−0.680045	−0.340023	−	0.940417i	$-0.610435\pi$
$971$	−1.77608e19	−0.680045	−0.340023	+	0.940417i	$0.610435\pi$
$972$	4.68603e18	0.178228
$973$	1.74495e19	0.659250
$974$	−5.84165e19	−2.19231
$975$	−7.65066e17	−0.0285213
$976$	−2.02572e19	−0.750164
$977$	1.51925e19	0.558875	0.279438	−	0.960164i	$-0.409852\pi$
$977$	1.51925e19	0.558875	0.279438	+	0.960164i	$0.409852\pi$
$978$	2.02433e18	0.0739740
$979$	−3.41217e16	−0.00123863
$980$	−1.22691e19	−0.442429
$981$	−1.72030e19	−0.616250
$982$	−1.03468e19	−0.368197
$983$	5.32971e19	1.88411	0.942054	−	0.335461i	$-0.108892\pi$
$983$	5.32971e19	1.88411	0.942054	+	0.335461i	$0.108892\pi$
$984$	−4.71601e17	−0.0165618
$985$	1.14350e18	0.0398933
$986$	5.09514e19	1.76586
$987$	9.74350e17	0.0335470
$988$	−1.60443e19	−0.548784
$989$	4.10523e19	1.39496
$990$	−1.39363e18	−0.0470455
$991$	5.83926e19	1.95830	0.979150	−	0.203138i	$-0.0651140\pi$
$991$	5.83926e19	1.95830	0.979150	+	0.203138i	$0.0651140\pi$
$992$	−4.40772e19	−1.46855
$993$	−8.86417e16	−0.00293405
$994$	−4.10169e19	−1.34881
$995$	−1.40292e19	−0.458335
$996$	−4.67716e17	−0.0151809
$997$	4.71791e19	1.52136	0.760678	−	0.649129i	$-0.224867\pi$
$997$	4.71791e19	1.52136	0.760678	+	0.649129i	$0.224867\pi$
$998$	−8.09786e19	−2.59431
$999$	−6.04719e18	−0.192477

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.14.a.b.1.18	✓	109

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.14.a.b.1.18	✓	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)

\(f(q)\)	\(=\)	\(q-133.322 q^{2} +64.3497 q^{3} +9582.75 q^{4} +19563.1 q^{5} -8579.24 q^{6} +177321. q^{7} -185418. q^{8} -1.59018e6 q^{9} +O(q^{10})\)	\(q-133.322 q^{2} +64.3497 q^{3} +9582.75 q^{4} +19563.1 q^{5} -8579.24 q^{6} +177321. q^{7} -185418. q^{8} -1.59018e6 q^{9} -2.60819e6 q^{10} -336016. q^{11} +616648. q^{12} +1.41878e7 q^{13} -2.36408e7 q^{14} +1.25888e6 q^{15} -5.37816e7 q^{16} +1.10884e8 q^{17} +2.12006e8 q^{18} -1.18009e8 q^{19} +1.87469e8 q^{20} +1.14106e7 q^{21} +4.47983e7 q^{22} -7.03272e8 q^{23} -1.19316e7 q^{24} -8.37987e8 q^{25} -1.89154e9 q^{26} -2.04922e8 q^{27} +1.69922e9 q^{28} -3.44657e9 q^{29} -1.67837e8 q^{30} -5.07264e9 q^{31} +8.68922e9 q^{32} -2.16225e7 q^{33} -1.47832e10 q^{34} +3.46895e9 q^{35} -1.52383e10 q^{36} +2.95097e10 q^{37} +1.57332e10 q^{38} +9.12980e8 q^{39} -3.62736e9 q^{40} +3.95254e10 q^{41} -1.52128e9 q^{42} -5.83732e10 q^{43} -3.21996e9 q^{44} -3.11089e10 q^{45} +9.37617e10 q^{46} +8.53901e10 q^{47} -3.46083e9 q^{48} -6.54462e10 q^{49} +1.11722e11 q^{50} +7.13534e9 q^{51} +1.35958e11 q^{52} -2.30840e11 q^{53} +2.73206e10 q^{54} -6.57352e9 q^{55} -3.28785e10 q^{56} -7.59387e9 q^{57} +4.59503e11 q^{58} +2.95758e11 q^{59} +1.20636e10 q^{60} +3.76657e11 q^{61} +6.76294e11 q^{62} -2.81973e11 q^{63} -7.17885e11 q^{64} +2.77557e11 q^{65} +2.88276e9 q^{66} +5.34143e11 q^{67} +1.06257e12 q^{68} -4.52554e10 q^{69} -4.62488e11 q^{70} +1.73500e12 q^{71} +2.94848e11 q^{72} +6.32699e11 q^{73} -3.93429e12 q^{74} -5.39243e10 q^{75} -1.13085e12 q^{76} -5.95827e10 q^{77} -1.21720e11 q^{78} -1.64725e12 q^{79} -1.05214e12 q^{80} +2.52208e12 q^{81} -5.26960e12 q^{82} -7.58482e11 q^{83} +1.09345e11 q^{84} +2.16923e12 q^{85} +7.78243e12 q^{86} -2.21786e11 q^{87} +6.23034e10 q^{88} +1.01548e11 q^{89} +4.14750e12 q^{90} +2.51579e12 q^{91} -6.73929e12 q^{92} -3.26423e11 q^{93} -1.13844e13 q^{94} -2.30863e12 q^{95} +5.59149e11 q^{96} -1.06120e12 q^{97} +8.72542e12 q^{98} +5.34326e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 109 q + 192 q^{2} + 8018 q^{3} + 471040 q^{4} + 88496 q^{5} + 383232 q^{6} + 1680731 q^{7} + 1820859 q^{8} + 59521391 q^{9}+O(q^{10}) \) 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	\( 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}+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

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