LMFDB - Embedded newform 177.12.a.a.1.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,12,Mod(1,177)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	177.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:	$135.996742959$
Analytic rank:	$1$
Dimension:	$26$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.25
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+77.8742 q^{2} -243.000 q^{3} +4016.40 q^{4} +5396.11 q^{5} -18923.4 q^{6} -42803.5 q^{7} +153287. q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+77.8742 q^{2} -243.000 q^{3} +4016.40 q^{4} +5396.11 q^{5} -18923.4 q^{6} -42803.5 q^{7} +153287. q^{8} +59049.0 q^{9} +420218. q^{10} -104647. q^{11} -975984. q^{12} -1.47062e6 q^{13} -3.33329e6 q^{14} -1.31126e6 q^{15} +3.71156e6 q^{16} +8.81579e6 q^{17} +4.59840e6 q^{18} +6.43944e6 q^{19} +2.16729e7 q^{20} +1.04013e7 q^{21} -8.14929e6 q^{22} -4.37186e7 q^{23} -3.72488e7 q^{24} -1.97101e7 q^{25} -1.14524e8 q^{26} -1.43489e7 q^{27} -1.71916e8 q^{28} +5.52631e7 q^{29} -1.02113e8 q^{30} -1.63519e8 q^{31} -2.48979e7 q^{32} +2.54292e7 q^{33} +6.86523e8 q^{34} -2.30973e8 q^{35} +2.37164e8 q^{36} -3.81734e8 q^{37} +5.01466e8 q^{38} +3.57362e8 q^{39} +8.27156e8 q^{40} +1.35956e8 q^{41} +8.09989e8 q^{42} -3.37684e8 q^{43} -4.20303e8 q^{44} +3.18635e8 q^{45} -3.40456e9 q^{46} -5.89592e8 q^{47} -9.01908e8 q^{48} -1.45187e8 q^{49} -1.53491e9 q^{50} -2.14224e9 q^{51} -5.90661e9 q^{52} -2.20250e9 q^{53} -1.11741e9 q^{54} -5.64686e8 q^{55} -6.56124e9 q^{56} -1.56478e9 q^{57} +4.30357e9 q^{58} +7.14924e8 q^{59} -5.26652e9 q^{60} +6.83368e8 q^{61} -1.27339e10 q^{62} -2.52750e9 q^{63} -9.54017e9 q^{64} -7.93566e9 q^{65} +1.98028e9 q^{66} +1.58327e10 q^{67} +3.54077e10 q^{68} +1.06236e10 q^{69} -1.79868e10 q^{70} -8.59408e9 q^{71} +9.05147e9 q^{72} +2.85810e9 q^{73} -2.97272e10 q^{74} +4.78955e9 q^{75} +2.58633e10 q^{76} +4.47925e9 q^{77} +2.78293e10 q^{78} -2.26178e10 q^{79} +2.00280e10 q^{80} +3.48678e9 q^{81} +1.05875e10 q^{82} -4.45327e10 q^{83} +4.17755e10 q^{84} +4.75710e10 q^{85} -2.62969e10 q^{86} -1.34289e10 q^{87} -1.60410e10 q^{88} -2.58664e10 q^{89} +2.48135e10 q^{90} +6.29479e10 q^{91} -1.75591e11 q^{92} +3.97351e10 q^{93} -4.59141e10 q^{94} +3.47479e10 q^{95} +6.05020e9 q^{96} +6.65290e10 q^{97} -1.13063e10 q^{98} -6.17929e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9}+O(q^{10}) $ 26 * q - 78 * q^2 - 6318 * q^3 + 23070 * q^4 + 3808 * q^5 + 18954 * q^6 - 98819 * q^7 - 117645 * q^8 + 1535274 * q^9	\( 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9} - 859751 q^{10} + 579094 q^{11} - 5606010 q^{12} - 2018538 q^{13} + 4157413 q^{14} - 925344 q^{15} + 20190274 q^{16} - 13084493 q^{17} - 4605822 q^{18} + 9917231 q^{19} + 10165633 q^{20} + 24013017 q^{21} - 89820518 q^{22} - 63513223 q^{23} + 28587735 q^{24} + 218986852 q^{25} - 77999532 q^{26} - 373071582 q^{27} - 444601862 q^{28} + 81530981 q^{29} + 208919493 q^{30} - 408861231 q^{31} - 26253128 q^{32} - 140719842 q^{33} - 508910076 q^{34} - 75731421 q^{35} + 1362260430 q^{36} - 802381301 q^{37} + 732704675 q^{38} + 490504734 q^{39} - 646130800 q^{40} - 1354472849 q^{41} - 1010251359 q^{42} + 282952194 q^{43} + 1846047996 q^{44} + 224858592 q^{45} + 9629305849 q^{46} - 1196794197 q^{47} - 4906236582 q^{48} + 10889725683 q^{49} - 6236232091 q^{50} + 3179531799 q^{51} - 1968200812 q^{52} - 8276044236 q^{53} + 1119214746 q^{54} - 6672895076 q^{55} + 2579741342 q^{56} - 2409887133 q^{57} - 9401656060 q^{58} + 18588031774 q^{59} - 2470248819 q^{60} - 21181559029 q^{61} - 6117706514 q^{62} - 5835163131 q^{63} + 42975855037 q^{64} + 25680681860 q^{65} + 21826385874 q^{66} + 26234163394 q^{67} + 19707344091 q^{68} + 15433713189 q^{69} + 129203099090 q^{70} + 52088830406 q^{71} - 6946819605 q^{72} + 20943384867 q^{73} + 41969200146 q^{74} - 53213805036 q^{75} + 223987219368 q^{76} + 94604773153 q^{77} + 18953886276 q^{78} + 68965662774 q^{79} + 218947784293 q^{80} + 90656394426 q^{81} + 11938614923 q^{82} + 17947446393 q^{83} + 108038252466 q^{84} - 52849386709 q^{85} + 384986147852 q^{86} - 19812028383 q^{87} - 49061112607 q^{88} + 38570593981 q^{89} - 50767436799 q^{90} - 226268806999 q^{91} - 79559686310 q^{92} + 99353279133 q^{93} - 16709400108 q^{94} - 252795831501 q^{95} + 6379510104 q^{96} - 186894587836 q^{97} - 252443311612 q^{98} + 34194921606 q^{99}+O(q^{100}) \) 26 * q - 78 * q^2 - 6318 * q^3 + 23070 * q^4 + 3808 * q^5 + 18954 * q^6 - 98819 * q^7 - 117645 * q^8 + 1535274 * q^9 - 859751 * q^10 + 579094 * q^11 - 5606010 * q^12 - 2018538 * q^13 + 4157413 * q^14 - 925344 * q^15 + 20190274 * q^16 - 13084493 * q^17 - 4605822 * q^18 + 9917231 * q^19 + 10165633 * q^20 + 24013017 * q^21 - 89820518 * q^22 - 63513223 * q^23 + 28587735 * q^24 + 218986852 * q^25 - 77999532 * q^26 - 373071582 * q^27 - 444601862 * q^28 + 81530981 * q^29 + 208919493 * q^30 - 408861231 * q^31 - 26253128 * q^32 - 140719842 * q^33 - 508910076 * q^34 - 75731421 * q^35 + 1362260430 * q^36 - 802381301 * q^37 + 732704675 * q^38 + 490504734 * q^39 - 646130800 * q^40 - 1354472849 * q^41 - 1010251359 * q^42 + 282952194 * q^43 + 1846047996 * q^44 + 224858592 * q^45 + 9629305849 * q^46 - 1196794197 * q^47 - 4906236582 * q^48 + 10889725683 * q^49 - 6236232091 * q^50 + 3179531799 * q^51 - 1968200812 * q^52 - 8276044236 * q^53 + 1119214746 * q^54 - 6672895076 * q^55 + 2579741342 * q^56 - 2409887133 * q^57 - 9401656060 * q^58 + 18588031774 * q^59 - 2470248819 * q^60 - 21181559029 * q^61 - 6117706514 * q^62 - 5835163131 * q^63 + 42975855037 * q^64 + 25680681860 * q^65 + 21826385874 * q^66 + 26234163394 * q^67 + 19707344091 * q^68 + 15433713189 * q^69 + 129203099090 * q^70 + 52088830406 * q^71 - 6946819605 * q^72 + 20943384867 * q^73 + 41969200146 * q^74 - 53213805036 * q^75 + 223987219368 * q^76 + 94604773153 * q^77 + 18953886276 * q^78 + 68965662774 * q^79 + 218947784293 * q^80 + 90656394426 * q^81 + 11938614923 * q^82 + 17947446393 * q^83 + 108038252466 * q^84 - 52849386709 * q^85 + 384986147852 * q^86 - 19812028383 * q^87 - 49061112607 * q^88 + 38570593981 * q^89 - 50767436799 * q^90 - 226268806999 * q^91 - 79559686310 * q^92 + 99353279133 * q^93 - 16709400108 * q^94 - 252795831501 * q^95 + 6379510104 * q^96 - 186894587836 * q^97 - 252443311612 * q^98 + 34194921606 * 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 $

$2$	77.8742	1.72079	0.860397	−	0.509625i	$-0.170216\pi$
$2$	77.8742	1.72079	0.860397	+	0.509625i	$0.170216\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	4016.40	1.96113
$5$	5396.11	0.772229	0.386114	−	0.922451i	$-0.373817\pi$
$5$	5396.11	0.772229	0.386114	+	0.922451i	$0.373817\pi$
$6$	−18923.4	−0.993501
$7$	−42803.5	−0.962587	−0.481294	−	0.876559i	$-0.659833\pi$
$7$	−42803.5	−0.962587	−0.481294	+	0.876559i	$0.659833\pi$
$8$	153287.	1.65391
$9$	59049.0	0.333333
$10$	420218.	1.32885
$11$	−104647.	−0.195914	−0.0979572	−	0.995191i	$-0.531231\pi$
$11$	−104647.	−0.195914	−0.0979572	+	0.995191i	$0.531231\pi$
$12$	−975984.	−1.13226
$13$	−1.47062e6	−1.09853	−0.549267	−	0.835647i	$-0.685093\pi$
$13$	−1.47062e6	−1.09853	−0.549267	+	0.835647i	$0.685093\pi$
$14$	−3.33329e6	−1.65641
$15$	−1.31126e6	−0.445846
$16$	3.71156e6	0.884904
$17$	8.81579e6	1.50589	0.752943	−	0.658086i	$-0.228634\pi$
$17$	8.81579e6	1.50589	0.752943	+	0.658086i	$0.228634\pi$
$18$	4.59840e6	0.573598
$19$	6.43944e6	0.596627	0.298314	−	0.954468i	$-0.403576\pi$
$19$	6.43944e6	0.596627	0.298314	+	0.954468i	$0.403576\pi$
$20$	2.16729e7	1.51444
$21$	1.04013e7	0.555750
$22$	−8.14929e6	−0.337128
$23$	−4.37186e7	−1.41633	−0.708163	−	0.706049i	$-0.750476\pi$
$23$	−4.37186e7	−1.41633	−0.708163	+	0.706049i	$0.750476\pi$
$24$	−3.72488e7	−0.954884
$25$	−1.97101e7	−0.403663
$26$	−1.14524e8	−1.89035
$27$	−1.43489e7	−0.192450
$28$	−1.71916e8	−1.88776
$29$	5.52631e7	0.500318	0.250159	−	0.968205i	$-0.419517\pi$
$29$	5.52631e7	0.500318	0.250159	+	0.968205i	$0.419517\pi$
$30$	−1.02113e8	−0.767210
$31$	−1.63519e8	−1.02584	−0.512918	−	0.858437i	$-0.671436\pi$
$31$	−1.63519e8	−1.02584	−0.512918	+	0.858437i	$0.671436\pi$
$32$	−2.48979e7	−0.131171
$33$	2.54292e7	0.113111
$34$	6.86523e8	2.59132
$35$	−2.30973e8	−0.743338
$36$	2.37164e8	0.653710
$37$	−3.81734e8	−0.905005	−0.452502	−	0.891763i	$-0.649469\pi$
$37$	−3.81734e8	−0.905005	−0.452502	+	0.891763i	$0.649469\pi$
$38$	5.01466e8	1.02667
$39$	3.57362e8	0.634239
$40$	8.27156e8	1.27720
$41$	1.35956e8	0.183269	0.0916344	−	0.995793i	$-0.470791\pi$
$41$	1.35956e8	0.183269	0.0916344	+	0.995793i	$0.470791\pi$
$42$	8.09989e8	0.956331
$43$	−3.37684e8	−0.350295	−0.175148	−	0.984542i	$-0.556040\pi$
$43$	−3.37684e8	−0.350295	−0.175148	+	0.984542i	$0.556040\pi$
$44$	−4.20303e8	−0.384214
$45$	3.18635e8	0.257410
$46$	−3.40456e9	−2.43721
$47$	−5.89592e8	−0.374985	−0.187492	−	0.982266i	$-0.560036\pi$
$47$	−5.89592e8	−0.374985	−0.187492	+	0.982266i	$0.560036\pi$
$48$	−9.01908e8	−0.510900
$49$	−1.45187e8	−0.0734258
$50$	−1.53491e9	−0.694620
$51$	−2.14224e9	−0.869424
$52$	−5.90661e9	−2.15437
$53$	−2.20250e9	−0.723432	−0.361716	−	0.932288i	$-0.617809\pi$
$53$	−2.20250e9	−0.723432	−0.361716	+	0.932288i	$0.617809\pi$
$54$	−1.11741e9	−0.331167
$55$	−5.64686e8	−0.151291
$56$	−6.56124e9	−1.59203
$57$	−1.56478e9	−0.344463
$58$	4.30357e9	0.860944
$59$	7.14924e8	0.130189
$59$	7.14924e8	0.130189
$60$	−5.26652e9	−0.874363
$61$	6.83368e8	0.103595	0.0517977	−	0.998658i	$-0.483505\pi$
$61$	6.83368e8	0.103595	0.0517977	+	0.998658i	$0.483505\pi$
$62$	−1.27339e10	−1.76525
$63$	−2.52750e9	−0.320862
$64$	−9.54017e9	−1.11062
$65$	−7.93566e9	−0.848319
$66$	1.98028e9	0.194641
$67$	1.58327e10	1.43266	0.716331	−	0.697761i	$-0.245820\pi$
$67$	1.58327e10	1.43266	0.716331	+	0.697761i	$0.245820\pi$
$68$	3.54077e10	2.95324
$69$	1.06236e10	0.817717
$70$	−1.79868e10	−1.27913
$71$	−8.59408e9	−0.565300	−0.282650	−	0.959223i	$-0.591213\pi$
$71$	−8.59408e9	−0.565300	−0.282650	+	0.959223i	$0.591213\pi$
$72$	9.05147e9	0.551303
$73$	2.85810e9	0.161362	0.0806812	−	0.996740i	$-0.474290\pi$
$73$	2.85810e9	0.161362	0.0806812	+	0.996740i	$0.474290\pi$
$74$	−2.97272e10	−1.55733
$75$	4.78955e9	0.233055
$76$	2.58633e10	1.17006
$77$	4.47925e9	0.188585
$78$	2.78293e10	1.09139
$79$	−2.26178e10	−0.826993	−0.413497	−	0.910506i	$-0.635693\pi$
$79$	−2.26178e10	−0.826993	−0.413497	+	0.910506i	$0.635693\pi$
$80$	2.00280e10	0.683348
$81$	3.48678e9	0.111111
$82$	1.05875e10	0.315368
$83$	−4.45327e10	−1.24094	−0.620468	−	0.784232i	$-0.713057\pi$
$83$	−4.45327e10	−1.24094	−0.620468	+	0.784232i	$0.713057\pi$
$84$	4.17755e10	1.08990
$85$	4.75710e10	1.16289
$86$	−2.62969e10	−0.602786
$87$	−1.34289e10	−0.288859
$88$	−1.60410e10	−0.324024
$89$	−2.58664e10	−0.491011	−0.245505	−	0.969395i	$-0.578954\pi$
$89$	−2.58664e10	−0.491011	−0.245505	+	0.969395i	$0.578954\pi$
$90$	2.48135e10	0.442949
$91$	6.29479e10	1.05743
$92$	−1.75591e11	−2.77760
$93$	3.97351e10	0.592267
$94$	−4.59141e10	−0.645271
$95$	3.47479e10	0.460733
$96$	6.05020e9	0.0757317
$97$	6.65290e10	0.786623	0.393311	−	0.919405i	$-0.371329\pi$
$97$	6.65290e10	0.786623	0.393311	+	0.919405i	$0.371329\pi$
$98$	−1.13063e10	−0.126351
$99$	−6.17929e9	−0.0653048
$100$	−7.91635e10	−0.791635
$101$	4.20758e10	0.398350	0.199175	−	0.979964i	$-0.436174\pi$
$101$	4.20758e10	0.398350	0.199175	+	0.979964i	$0.436174\pi$
$102$	−1.66825e11	−1.49610
$103$	−6.10736e10	−0.519097	−0.259549	−	0.965730i	$-0.583574\pi$
$103$	−6.10736e10	−0.519097	−0.259549	+	0.965730i	$0.583574\pi$
$104$	−2.25428e11	−1.81687
$105$	5.61263e10	0.429166
$106$	−1.71518e11	−1.24488
$107$	−8.40382e10	−0.579250	−0.289625	−	0.957140i	$-0.593531\pi$
$107$	−8.40382e10	−0.579250	−0.289625	+	0.957140i	$0.593531\pi$
$108$	−5.76309e10	−0.377420
$109$	−5.86064e10	−0.364837	−0.182419	−	0.983221i	$-0.558393\pi$
$109$	−5.86064e10	−0.364837	−0.182419	+	0.983221i	$0.558393\pi$
$110$	−4.39745e10	−0.260340
$111$	9.27613e10	0.522505
$112$	−1.58868e11	−0.851797
$113$	1.56405e11	0.798580	0.399290	−	0.916825i	$-0.369257\pi$
$113$	1.56405e11	0.798580	0.399290	+	0.916825i	$0.369257\pi$
$114$	−1.21856e11	−0.592750
$115$	−2.35911e11	−1.09373
$116$	2.21959e11	0.981189
$117$	−8.68389e10	−0.366178
$118$	5.56742e10	0.224028
$119$	−3.77347e11	−1.44955
$120$	−2.00999e11	−0.737389
$121$	−2.74361e11	−0.961618
$122$	5.32168e10	0.178266
$123$	−3.30374e10	−0.105810
$124$	−6.56756e11	−2.01180
$125$	−3.69840e11	−1.08395
$126$	−1.96827e11	−0.552138
$127$	−6.21564e11	−1.66942	−0.834709	−	0.550691i	$-0.814364\pi$
$127$	−6.21564e11	−1.66942	−0.834709	+	0.550691i	$0.814364\pi$
$128$	−6.91943e11	−1.77998
$129$	8.20573e10	0.202243
$130$	−6.17983e11	−1.45978
$131$	5.16819e10	0.117043	0.0585216	−	0.998286i	$-0.481361\pi$
$131$	5.16819e10	0.117043	0.0585216	+	0.998286i	$0.481361\pi$
$132$	1.02134e11	0.221826
$133$	−2.75630e11	−0.574306
$134$	1.23296e12	2.46532
$135$	−7.74283e10	−0.148615
$136$	1.35135e12	2.49060
$137$	7.23574e10	0.128091	0.0640457	−	0.997947i	$-0.479600\pi$
$137$	7.23574e10	0.128091	0.0640457	+	0.997947i	$0.479600\pi$
$138$	8.27307e11	1.40712
$139$	−7.61381e11	−1.24457	−0.622287	−	0.782789i	$-0.713796\pi$
$139$	−7.61381e11	−1.24457	−0.622287	+	0.782789i	$0.713796\pi$
$140$	−9.27677e11	−1.45778
$141$	1.43271e11	0.216498
$142$	−6.69258e11	−0.972764
$143$	1.53896e11	0.215219
$144$	2.19164e11	0.294968
$145$	2.98206e11	0.386360
$146$	2.22573e11	0.277671
$147$	3.52804e10	0.0423924
$148$	−1.53319e12	−1.77483
$149$	−6.86106e11	−0.765362	−0.382681	−	0.923881i	$-0.624999\pi$
$149$	−6.86106e11	−0.765362	−0.382681	+	0.923881i	$0.624999\pi$
$150$	3.72983e11	0.401039
$151$	1.64324e12	1.70344	0.851721	−	0.523996i	$-0.175559\pi$
$151$	1.64324e12	1.70344	0.851721	+	0.523996i	$0.175559\pi$
$152$	9.87084e11	0.986767
$153$	5.20563e11	0.501962
$154$	3.48818e11	0.324515
$155$	−8.82366e11	−0.792181
$156$	1.43531e12	1.24383
$157$	−1.22304e11	−0.102328	−0.0511639	−	0.998690i	$-0.516293\pi$
$157$	−1.22304e11	−0.102328	−0.0511639	+	0.998690i	$0.516293\pi$
$158$	−1.76135e12	−1.42309
$159$	5.35207e11	0.417674
$160$	−1.34352e11	−0.101294
$161$	1.87131e12	1.36334
$162$	2.71531e11	0.191199
$163$	−1.93170e12	−1.31495	−0.657473	−	0.753478i	$-0.728374\pi$
$163$	−1.93170e12	−1.31495	−0.657473	+	0.753478i	$0.728374\pi$
$164$	5.46055e11	0.359414
$165$	1.37219e11	0.0873477
$166$	−3.46795e12	−2.13540
$167$	8.38255e11	0.499385	0.249693	−	0.968325i	$-0.419670\pi$
$167$	8.38255e11	0.499385	0.249693	+	0.968325i	$0.419670\pi$
$168$	1.59438e12	0.919160
$169$	3.70577e11	0.206777
$170$	3.70455e12	2.00109
$171$	3.80242e11	0.198876
$172$	−1.35627e12	−0.686975
$173$	9.76928e11	0.479302	0.239651	−	0.970859i	$-0.422967\pi$
$173$	9.76928e11	0.479302	0.239651	+	0.970859i	$0.422967\pi$
$174$	−1.04577e12	−0.497066
$175$	8.43661e11	0.388561
$176$	−3.88402e11	−0.173365
$177$	−1.73727e11	−0.0751646
$178$	−2.01433e12	−0.844929
$179$	4.30929e11	0.175272	0.0876362	−	0.996153i	$-0.472069\pi$
$179$	4.30929e11	0.175272	0.0876362	+	0.996153i	$0.472069\pi$
$180$	1.27976e12	0.504814
$181$	2.90266e12	1.11062	0.555308	−	0.831645i	$-0.312600\pi$
$181$	2.90266e12	1.11062	0.555308	+	0.831645i	$0.312600\pi$
$182$	4.90202e12	1.81963
$183$	−1.66059e11	−0.0598109
$184$	−6.70151e12	−2.34247
$185$	−2.05988e12	−0.698871
$186$	3.09434e12	1.01917
$187$	−9.22544e11	−0.295025
$188$	−2.36804e12	−0.735394
$189$	6.14183e11	0.185250
$190$	2.70597e12	0.792826
$191$	−5.53063e12	−1.57431	−0.787156	−	0.616754i	$-0.788447\pi$
$191$	−5.53063e12	−1.57431	−0.787156	+	0.616754i	$0.788447\pi$
$192$	2.31826e12	0.641218
$193$	6.63889e12	1.78456	0.892278	−	0.451486i	$-0.149106\pi$
$193$	6.63889e12	1.78456	0.892278	+	0.451486i	$0.149106\pi$
$194$	5.18090e12	1.35362
$195$	1.92836e12	0.489777
$196$	−5.83128e11	−0.143998
$197$	−1.77773e12	−0.426877	−0.213438	−	0.976957i	$-0.568466\pi$
$197$	−1.77773e12	−0.426877	−0.213438	+	0.976957i	$0.568466\pi$
$198$	−4.81207e11	−0.112376
$199$	6.02465e12	1.36848	0.684242	−	0.729255i	$-0.260133\pi$
$199$	6.02465e12	1.36848	0.684242	+	0.729255i	$0.260133\pi$
$200$	−3.02131e12	−0.667621
$201$	−3.84735e12	−0.827148
$202$	3.27662e12	0.685478
$203$	−2.36545e12	−0.481600
$204$	−8.60407e12	−1.70505
$205$	7.33636e11	0.141525
$206$	−4.75606e12	−0.893259
$207$	−2.58154e12	−0.472109
$208$	−5.45831e12	−0.972097
$209$	−6.73866e11	−0.116888
$210$	4.37079e12	0.738506
$211$	6.08817e12	1.00215	0.501076	−	0.865404i	$-0.332938\pi$
$211$	6.08817e12	1.00215	0.501076	+	0.865404i	$0.332938\pi$
$212$	−8.84610e12	−1.41875
$213$	2.08836e12	0.326376
$214$	−6.54441e12	−0.996769
$215$	−1.82218e12	−0.270508
$216$	−2.19951e12	−0.318295
$217$	6.99918e12	0.987458
$218$	−4.56393e12	−0.627810
$219$	−6.94519e11	−0.0931626
$220$	−2.26800e12	−0.296701
$221$	−1.29647e13	−1.65427
$222$	7.22371e12	0.899123
$223$	1.08511e13	1.31764	0.658819	−	0.752302i	$-0.271056\pi$
$223$	1.08511e13	1.31764	0.658819	+	0.752302i	$0.271056\pi$
$224$	1.06572e12	0.126264
$225$	−1.16386e12	−0.134554
$226$	1.21799e13	1.37419
$227$	−1.54657e12	−0.170305	−0.0851527	−	0.996368i	$-0.527138\pi$
$227$	−1.54657e12	−0.170305	−0.0851527	+	0.996368i	$0.527138\pi$
$228$	−6.28479e12	−0.675537
$229$	3.68566e12	0.386741	0.193370	−	0.981126i	$-0.438058\pi$
$229$	3.68566e12	0.386741	0.193370	+	0.981126i	$0.438058\pi$
$230$	−1.83714e13	−1.88208
$231$	−1.08846e12	−0.108879
$232$	8.47114e12	0.827480
$233$	−3.13366e12	−0.298947	−0.149474	−	0.988766i	$-0.547758\pi$
$233$	−3.13366e12	−0.298947	−0.149474	+	0.988766i	$0.547758\pi$
$234$	−6.76251e12	−0.630117
$235$	−3.18151e12	−0.289574
$236$	2.87142e12	0.255318
$237$	5.49613e12	0.477465
$238$	−2.93856e13	−2.49437
$239$	1.90888e13	1.58339	0.791697	−	0.610913i	$-0.209198\pi$
$239$	1.90888e13	1.58339	0.791697	+	0.610913i	$0.209198\pi$
$240$	−4.86680e12	−0.394531
$241$	−6.58157e12	−0.521478	−0.260739	−	0.965409i	$-0.583966\pi$
$241$	−6.58157e12	−0.521478	−0.260739	+	0.965409i	$0.583966\pi$
$242$	−2.13656e13	−1.65475
$243$	−8.47289e11	−0.0641500
$244$	2.74468e12	0.203164
$245$	−7.83444e11	−0.0567015
$246$	−2.57276e12	−0.182078
$247$	−9.46999e12	−0.655415
$248$	−2.50654e13	−1.69664
$249$	1.08214e13	0.716455
$250$	−2.88010e13	−1.86525
$251$	7.40258e12	0.469005	0.234503	−	0.972115i	$-0.424654\pi$
$251$	7.40258e12	0.469005	0.234503	+	0.972115i	$0.424654\pi$
$252$	−1.01515e13	−0.629253
$253$	4.57502e12	0.277479
$254$	−4.84038e13	−2.87272
$255$	−1.15597e13	−0.671394
$256$	−3.43462e13	−1.95236
$257$	−2.22788e13	−1.23954	−0.619770	−	0.784784i	$-0.712774\pi$
$257$	−2.22788e13	−1.23954	−0.619770	+	0.784784i	$0.712774\pi$
$258$	6.39015e12	0.348019
$259$	1.63395e13	0.871146
$260$	−3.18727e13	−1.66367
$261$	3.26323e12	0.166773
$262$	4.02469e12	0.201407
$263$	−2.64820e12	−0.129776	−0.0648879	−	0.997893i	$-0.520669\pi$
$263$	−2.64820e12	−0.129776	−0.0648879	+	0.997893i	$0.520669\pi$
$264$	3.89797e12	0.187076
$265$	−1.18849e13	−0.558655
$266$	−2.14645e13	−0.988262
$267$	6.28554e12	0.283485
$268$	6.35904e13	2.80964
$269$	7.40265e12	0.320442	0.160221	−	0.987081i	$-0.448779\pi$
$269$	7.40265e12	0.320442	0.160221	+	0.987081i	$0.448779\pi$
$270$	−6.02967e12	−0.255737
$271$	−1.06902e13	−0.444277	−0.222139	−	0.975015i	$-0.571304\pi$
$271$	−1.06902e13	−0.444277	−0.222139	+	0.975015i	$0.571304\pi$
$272$	3.27203e13	1.33256
$273$	−1.52963e13	−0.610510
$274$	5.63478e12	0.220419
$275$	2.06260e12	0.0790833
$276$	4.26687e13	1.60365
$277$	3.53316e13	1.30174	0.650871	−	0.759189i	$-0.274404\pi$
$277$	3.53316e13	1.30174	0.650871	+	0.759189i	$0.274404\pi$
$278$	−5.92920e13	−2.14166
$279$	−9.65562e12	−0.341946
$280$	−3.54052e13	−1.22941
$281$	4.04775e13	1.37825	0.689126	−	0.724642i	$-0.257995\pi$
$281$	4.04775e13	1.37825	0.689126	+	0.724642i	$0.257995\pi$
$282$	1.11571e13	0.372548
$283$	1.78525e12	0.0584621	0.0292310	−	0.999573i	$-0.490694\pi$
$283$	1.78525e12	0.0584621	0.0292310	+	0.999573i	$0.490694\pi$
$284$	−3.45172e13	−1.10863
$285$	−8.44374e12	−0.266004
$286$	1.19845e13	0.370347
$287$	−5.81941e12	−0.176412
$288$	−1.47020e12	−0.0437237
$289$	4.34462e13	1.26769
$290$	2.32226e13	0.664846
$291$	−1.61666e13	−0.454157
$292$	1.14793e13	0.316453
$293$	1.25701e13	0.340069	0.170035	−	0.985438i	$-0.445612\pi$
$293$	1.25701e13	0.340069	0.170035	+	0.985438i	$0.445612\pi$
$294$	2.74743e12	0.0729486
$295$	3.85781e12	0.100536
$296$	−5.85149e13	−1.49679
$297$	1.50157e12	0.0377037
$298$	−5.34300e13	−1.31703
$299$	6.42937e13	1.55588
$300$	1.92367e13	0.457051
$301$	1.44541e13	0.337190
$302$	1.27966e14	2.93127
$303$	−1.02244e13	−0.229988
$304$	2.39003e13	0.527958
$305$	3.68753e12	0.0799994
$306$	4.05385e13	0.863773
$307$	6.19612e13	1.29676	0.648379	−	0.761318i	$-0.275447\pi$
$307$	6.19612e13	1.29676	0.648379	+	0.761318i	$0.275447\pi$
$308$	1.79904e13	0.369839
$309$	1.48409e13	0.299701
$310$	−6.87136e13	−1.36318
$311$	−4.78671e13	−0.932943	−0.466471	−	0.884536i	$-0.654475\pi$
$311$	−4.78671e13	−0.932943	−0.466471	+	0.884536i	$0.654475\pi$
$312$	5.47791e13	1.04897
$313$	9.75359e13	1.83515	0.917573	−	0.397568i	$-0.130146\pi$
$313$	9.75359e13	1.83515	0.917573	+	0.397568i	$0.130146\pi$
$314$	−9.52436e12	−0.176085
$315$	−1.36387e13	−0.247779
$316$	−9.08422e13	−1.62184
$317$	−6.70236e13	−1.17598	−0.587992	−	0.808866i	$-0.700082\pi$
$317$	−6.70236e13	−1.17598	−0.587992	+	0.808866i	$0.700082\pi$
$318$	4.16788e13	0.718731
$319$	−5.78311e12	−0.0980195
$320$	−5.14799e13	−0.857655
$321$	2.04213e13	0.334430
$322$	1.45727e14	2.34602
$323$	5.67687e13	0.898452
$324$	1.40043e13	0.217903
$325$	2.89862e13	0.443437
$326$	−1.50430e14	−2.26275
$327$	1.42414e13	0.210639
$328$	2.08404e13	0.303110
$329$	2.52366e13	0.360956
$330$	1.06858e13	0.150307
$331$	−4.41551e13	−0.610840	−0.305420	−	0.952218i	$-0.598797\pi$
$331$	−4.41551e13	−0.610840	−0.305420	+	0.952218i	$0.598797\pi$
$332$	−1.78861e14	−2.43364
$333$	−2.25410e13	−0.301668
$334$	6.52785e13	0.859339
$335$	8.54350e13	1.10634
$336$	3.86048e13	0.491785
$337$	−7.03111e13	−0.881169	−0.440585	−	0.897711i	$-0.645229\pi$
$337$	−7.03111e13	−0.881169	−0.440585	+	0.897711i	$0.645229\pi$
$338$	2.88584e13	0.355820
$339$	−3.80064e13	−0.461061
$340$	1.91064e14	2.28058
$341$	1.71117e13	0.200976
$342$	2.96111e13	0.342224
$343$	9.08510e13	1.03327
$344$	−5.17627e13	−0.579356
$345$	5.73263e13	0.631464
$346$	7.60775e13	0.824779
$347$	−1.09335e14	−1.16667	−0.583334	−	0.812232i	$-0.698252\pi$
$347$	−1.09335e14	−1.16667	−0.583334	+	0.812232i	$0.698252\pi$
$348$	−5.39359e13	−0.566490
$349$	1.23936e14	1.28132	0.640662	−	0.767823i	$-0.278660\pi$
$349$	1.23936e14	1.28132	0.640662	+	0.767823i	$0.278660\pi$
$350$	6.56995e13	0.668633
$351$	2.11019e13	0.211413
$352$	2.60549e12	0.0256983
$353$	−1.68876e14	−1.63986	−0.819931	−	0.572463i	$-0.805988\pi$
$353$	−1.68876e14	−1.63986	−0.819931	+	0.572463i	$0.805988\pi$
$354$	−1.35288e13	−0.129343
$355$	−4.63746e13	−0.436541
$356$	−1.03890e14	−0.962937
$357$	9.16952e13	0.836896
$358$	3.35582e13	0.301608
$359$	8.02239e13	0.710042	0.355021	−	0.934858i	$-0.384474\pi$
$359$	8.02239e13	0.710042	0.355021	+	0.934858i	$0.384474\pi$
$360$	4.88427e13	0.425732
$361$	−7.50239e13	−0.644036
$362$	2.26042e14	1.91114
$363$	6.66697e13	0.555190
$364$	2.52824e14	2.07377
$365$	1.54226e13	0.124609
$366$	−1.29317e13	−0.102922
$367$	−7.45564e13	−0.584550	−0.292275	−	0.956334i	$-0.594412\pi$
$367$	−7.45564e13	−0.584550	−0.292275	+	0.956334i	$0.594412\pi$
$368$	−1.62264e14	−1.25331
$369$	8.02809e12	0.0610896
$370$	−1.60411e14	−1.20261
$371$	9.42746e13	0.696367
$372$	1.59592e14	1.16151
$373$	1.61453e14	1.15784	0.578920	−	0.815384i	$-0.303474\pi$
$373$	1.61453e14	1.15784	0.578920	+	0.815384i	$0.303474\pi$
$374$	−7.18424e13	−0.507676
$375$	8.98711e13	0.625818
$376$	−9.03771e13	−0.620190
$377$	−8.12713e13	−0.549616
$378$	4.78291e13	0.318777
$379$	1.11432e14	0.731974	0.365987	−	0.930620i	$-0.380732\pi$
$379$	1.11432e14	0.731974	0.365987	+	0.930620i	$0.380732\pi$
$380$	1.39561e14	0.903557
$381$	1.51040e14	0.963839
$382$	−4.30693e14	−2.70907
$383$	−5.16610e13	−0.320309	−0.160155	−	0.987092i	$-0.551199\pi$
$383$	−5.16610e13	−0.320309	−0.160155	+	0.987092i	$0.551199\pi$
$384$	1.68142e14	1.02767
$385$	2.41705e13	0.145630
$386$	5.16998e14	3.07085
$387$	−1.99399e13	−0.116765
$388$	2.67207e14	1.54267
$389$	−1.20196e13	−0.0684177	−0.0342088	−	0.999415i	$-0.510891\pi$
$389$	−1.20196e13	−0.0684177	−0.0342088	+	0.999415i	$0.510891\pi$
$390$	1.50170e14	0.842806
$391$	−3.85414e14	−2.13283
$392$	−2.22553e13	−0.121440
$393$	−1.25587e13	−0.0675749
$394$	−1.38440e14	−0.734566
$395$	−1.22048e14	−0.638628
$396$	−2.48185e13	−0.128071
$397$	−2.35587e14	−1.19896	−0.599479	−	0.800390i	$-0.704626\pi$
$397$	−2.35587e14	−1.19896	−0.599479	+	0.800390i	$0.704626\pi$
$398$	4.69165e14	2.35488
$399$	6.69782e13	0.331576
$400$	−7.31551e13	−0.357203
$401$	1.06399e14	0.512440	0.256220	−	0.966618i	$-0.417523\pi$
$401$	1.06399e14	0.512440	0.256220	+	0.966618i	$0.417523\pi$
$402$	−2.99609e14	−1.42335
$403$	2.40475e14	1.12692
$404$	1.68993e14	0.781217
$405$	1.88151e13	0.0858032
$406$	−1.84208e14	−0.828734
$407$	3.99472e13	0.177303
$408$	−3.28378e14	−1.43795
$409$	3.80134e14	1.64232	0.821161	−	0.570697i	$-0.193327\pi$
$409$	3.80134e14	1.64232	0.821161	+	0.570697i	$0.193327\pi$
$410$	5.71314e13	0.243536
$411$	−1.75829e13	−0.0739536
$412$	−2.45296e14	−1.01802
$413$	−3.06013e13	−0.125318
$414$	−2.01036e14	−0.812402
$415$	−2.40304e14	−0.958287
$416$	3.66155e13	0.144096
$417$	1.85016e14	0.718555
$418$	−5.24768e13	−0.201140
$419$	−3.57217e14	−1.35131	−0.675655	−	0.737218i	$-0.736139\pi$
$419$	−3.57217e14	−1.35131	−0.675655	+	0.737218i	$0.736139\pi$
$420$	2.25426e14	0.841651
$421$	3.94684e14	1.45445	0.727224	−	0.686400i	$-0.240810\pi$
$421$	3.94684e14	1.45445	0.727224	+	0.686400i	$0.240810\pi$
$422$	4.74111e14	1.72450
$423$	−3.48148e13	−0.124995
$424$	−3.37615e14	−1.19649
$425$	−1.73760e14	−0.607870
$426$	1.62630e14	0.561626
$427$	−2.92506e13	−0.0997197
$428$	−3.37531e14	−1.13598
$429$	−3.73968e13	−0.124256
$430$	−1.41901e14	−0.465489
$431$	3.08872e14	1.00035	0.500177	−	0.865923i	$-0.333268\pi$
$431$	3.08872e14	1.00035	0.500177	+	0.865923i	$0.333268\pi$
$432$	−5.32568e13	−0.170300
$433$	2.32369e13	0.0733660	0.0366830	−	0.999327i	$-0.488321\pi$
$433$	2.32369e13	0.0733660	0.0366830	+	0.999327i	$0.488321\pi$
$434$	5.45056e14	1.69921
$435$	−7.24640e13	−0.223065
$436$	−2.35387e14	−0.715494
$437$	−2.81523e14	−0.845019
$438$	−5.40852e13	−0.160314
$439$	−6.82067e14	−1.99651	−0.998257	−	0.0590219i	$-0.981202\pi$
$439$	−6.82067e14	−1.99651	−0.998257	+	0.0590219i	$0.981202\pi$
$440$	−8.65592e13	−0.250221
$441$	−8.57314e12	−0.0244753
$442$	−1.00962e15	−2.84665
$443$	2.35809e14	0.656660	0.328330	−	0.944563i	$-0.393514\pi$
$443$	2.35809e14	0.656660	0.328330	+	0.944563i	$0.393514\pi$
$444$	3.72566e14	1.02470
$445$	−1.39578e14	−0.379173
$446$	8.45019e14	2.26738
$447$	1.66724e14	0.441882
$448$	4.08353e14	1.06907
$449$	6.07499e14	1.57105	0.785527	−	0.618828i	$-0.212392\pi$
$449$	6.07499e14	1.57105	0.785527	+	0.618828i	$0.212392\pi$
$450$	−9.06348e13	−0.231540
$451$	−1.42274e13	−0.0359050
$452$	6.28184e14	1.56612
$453$	−3.99307e14	−0.983482
$454$	−1.20438e14	−0.293061
$455$	3.39674e14	0.816582
$456$	−2.39861e14	−0.569710
$457$	6.85321e14	1.60825	0.804127	−	0.594457i	$-0.202633\pi$
$457$	6.85321e14	1.60825	0.804127	+	0.594457i	$0.202633\pi$
$458$	2.87018e14	0.665501
$459$	−1.26497e14	−0.289808
$460$	−9.47511e14	−2.14494
$461$	3.17516e13	0.0710249	0.0355125	−	0.999369i	$-0.488694\pi$
$461$	3.17516e13	0.0710249	0.0355125	+	0.999369i	$0.488694\pi$
$462$	−8.47628e13	−0.187359
$463$	−1.56337e14	−0.341480	−0.170740	−	0.985316i	$-0.554616\pi$
$463$	−1.56337e14	−0.341480	−0.170740	+	0.985316i	$0.554616\pi$
$464$	2.05112e14	0.442734
$465$	2.14415e14	0.457366
$466$	−2.44032e14	−0.514427
$467$	−6.16025e14	−1.28338	−0.641691	−	0.766963i	$-0.721767\pi$
$467$	−6.16025e14	−1.28338	−0.641691	+	0.766963i	$0.721767\pi$
$468$	−3.48780e14	−0.718123
$469$	−6.77695e14	−1.37906
$470$	−2.47757e14	−0.498297
$471$	2.97200e13	0.0590790
$472$	1.09589e14	0.215321
$473$	3.53376e13	0.0686279
$474$	4.28007e14	0.821619
$475$	−1.26922e14	−0.240836
$476$	−1.51557e15	−2.84275
$477$	−1.30055e14	−0.241144
$478$	1.48652e15	2.72470
$479$	3.66005e13	0.0663195	0.0331598	−	0.999450i	$-0.489443\pi$
$479$	3.66005e13	0.0663195	0.0331598	+	0.999450i	$0.489443\pi$
$480$	3.26475e13	0.0584822
$481$	5.61387e14	0.994178
$482$	−5.12535e14	−0.897356
$483$	−4.54729e14	−0.787124
$484$	−1.10194e15	−1.88586
$485$	3.58998e14	0.607453
$486$	−6.59820e13	−0.110389
$487$	1.63155e14	0.269893	0.134947	−	0.990853i	$-0.456914\pi$
$487$	1.63155e14	0.269893	0.134947	+	0.990853i	$0.456914\pi$
$488$	1.04752e14	0.171337
$489$	4.69403e14	0.759184
$490$	−6.10101e13	−0.0975716
$491$	−3.05048e14	−0.482414	−0.241207	−	0.970474i	$-0.577543\pi$
$491$	−3.05048e14	−0.482414	−0.241207	+	0.970474i	$0.577543\pi$
$492$	−1.32691e14	−0.207508
$493$	4.87188e14	0.753422
$494$	−7.37469e14	−1.12783
$495$	−3.33441e13	−0.0504302
$496$	−6.06909e14	−0.907767
$497$	3.67857e14	0.544150
$498$	8.42712e14	1.23287
$499$	−9.64542e14	−1.39562	−0.697812	−	0.716281i	$-0.745843\pi$
$499$	−9.64542e14	−1.39562	−0.697812	+	0.716281i	$0.745843\pi$
$500$	−1.48542e15	−2.12577
$501$	−2.03696e14	−0.288320
$502$	5.76470e14	0.807061
$503$	1.12900e14	0.156339	0.0781697	−	0.996940i	$-0.475092\pi$
$503$	1.12900e14	0.156339	0.0781697	+	0.996940i	$0.475092\pi$
$504$	−3.87434e14	−0.530677
$505$	2.27046e14	0.307617
$506$	3.56276e14	0.477484
$507$	−9.00502e13	−0.119383
$508$	−2.49645e15	−3.27395
$509$	−3.93540e14	−0.510553	−0.255277	−	0.966868i	$-0.582167\pi$
$509$	−3.93540e14	−0.510553	−0.255277	+	0.966868i	$0.582167\pi$
$510$	−9.00207e14	−1.15533
$511$	−1.22337e14	−0.155325
$512$	−1.25759e15	−1.57962
$513$	−9.23989e13	−0.114821
$514$	−1.73495e15	−2.13299
$515$	−3.29560e14	−0.400862
$516$	3.29575e14	0.396625
$517$	6.16989e13	0.0734649
$518$	1.27243e15	1.49906
$519$	−2.37393e14	−0.276725
$520$	−1.21644e15	−1.40304
$521$	5.65783e14	0.645717	0.322858	−	0.946447i	$-0.395356\pi$
$521$	5.65783e14	0.645717	0.322858	+	0.946447i	$0.395356\pi$
$522$	2.54122e14	0.286981
$523$	4.32732e14	0.483571	0.241785	−	0.970330i	$-0.422267\pi$
$523$	4.32732e14	0.483571	0.241785	+	0.970330i	$0.422267\pi$
$524$	2.07575e14	0.229537
$525$	−2.05010e14	−0.224336
$526$	−2.06226e14	−0.223317
$527$	−1.44155e15	−1.54479
$528$	9.43818e13	0.100093
$529$	9.58509e14	1.00598
$530$	−9.25529e14	−0.961330
$531$	4.22156e13	0.0433963
$532$	−1.10704e15	−1.12629
$533$	−1.99941e14	−0.201327
$534$	4.89482e14	0.487820
$535$	−4.53479e14	−0.447313
$536$	2.42695e15	2.36949
$537$	−1.04716e14	−0.101194
$538$	5.76476e14	0.551415
$539$	1.51933e13	0.0143852
$540$	−3.10983e14	−0.291454
$541$	−6.72162e14	−0.623576	−0.311788	−	0.950152i	$-0.600928\pi$
$541$	−6.72162e14	−0.623576	−0.311788	+	0.950152i	$0.600928\pi$
$542$	−8.32490e14	−0.764510
$543$	−7.05346e14	−0.641215
$544$	−2.19495e14	−0.197529
$545$	−3.16247e14	−0.281738
$546$	−1.19119e15	−1.05056
$547$	−5.78452e14	−0.505053	−0.252527	−	0.967590i	$-0.581262\pi$
$547$	−5.78452e14	−0.505053	−0.252527	+	0.967590i	$0.581262\pi$
$548$	2.90616e14	0.251204
$549$	4.03522e13	0.0345318
$550$	1.60623e14	0.136086
$551$	3.55863e14	0.298503
$552$	1.62847e15	1.35243
$553$	9.68123e14	0.796053
$554$	2.75142e15	2.24003
$555$	5.00550e14	0.403493
$556$	−3.05801e15	−2.44077
$557$	−5.09124e14	−0.402365	−0.201182	−	0.979554i	$-0.564478\pi$
$557$	−5.09124e14	−0.402365	−0.201182	+	0.979554i	$0.564478\pi$
$558$	−7.51924e14	−0.588418
$559$	4.96607e14	0.384811
$560$	−8.57267e14	−0.657782
$561$	2.24178e14	0.170333
$562$	3.15215e15	2.37169
$563$	1.68196e15	1.25320	0.626598	−	0.779343i	$-0.284447\pi$
$563$	1.68196e15	1.25320	0.626598	+	0.779343i	$0.284447\pi$
$564$	5.75433e14	0.424580
$565$	8.43978e14	0.616687
$566$	1.39025e14	0.100601
$567$	−1.49247e14	−0.106954
$568$	−1.31736e15	−0.934954
$569$	−2.81997e14	−0.198211	−0.0991054	−	0.995077i	$-0.531598\pi$
$569$	−2.81997e14	−0.198211	−0.0991054	+	0.995077i	$0.531598\pi$
$570$	−6.57550e14	−0.457738
$571$	2.26252e15	1.55989	0.779944	−	0.625849i	$-0.215247\pi$
$571$	2.26252e15	1.55989	0.779944	+	0.625849i	$0.215247\pi$
$572$	6.18108e14	0.422072
$573$	1.34394e15	0.908930
$574$	−4.53182e14	−0.303569
$575$	8.61698e14	0.571718
$576$	−5.63338e14	−0.370207
$577$	2.78163e14	0.181064	0.0905319	−	0.995894i	$-0.471143\pi$
$577$	2.78163e14	0.181064	0.0905319	+	0.995894i	$0.471143\pi$
$578$	3.38334e15	2.18144
$579$	−1.61325e15	−1.03031
$580$	1.19771e15	0.757703
$581$	1.90616e15	1.19451
$582$	−1.25896e15	−0.781510
$583$	2.30484e14	0.141731
$584$	4.38111e14	0.266879
$585$	−4.68593e14	−0.282773
$586$	9.78887e14	0.585189
$587$	3.23144e15	1.91375	0.956877	−	0.290494i	$-0.0938197\pi$
$587$	3.23144e15	1.91375	0.956877	+	0.290494i	$0.0938197\pi$
$588$	1.41700e14	0.0831371
$589$	−1.05297e15	−0.612042
$590$	3.00424e14	0.173001
$591$	4.31989e14	0.246457
$592$	−1.41683e15	−0.800842
$593$	9.11583e14	0.510500	0.255250	−	0.966875i	$-0.417842\pi$
$593$	9.11583e14	0.510500	0.255250	+	0.966875i	$0.417842\pi$
$594$	1.16933e14	0.0648803
$595$	−2.03620e15	−1.11938
$596$	−2.75567e15	−1.50097
$597$	−1.46399e15	−0.790095
$598$	5.00682e15	2.67735
$599$	2.57603e15	1.36491	0.682454	−	0.730928i	$-0.260913\pi$
$599$	2.57603e15	1.36491	0.682454	+	0.730928i	$0.260913\pi$
$600$	7.34178e14	0.385451
$601$	1.06560e15	0.554350	0.277175	−	0.960819i	$-0.410602\pi$
$601$	1.06560e15	0.554350	0.277175	+	0.960819i	$0.410602\pi$
$602$	1.12560e15	0.580234
$603$	9.34905e14	0.477554
$604$	6.59989e15	3.34067
$605$	−1.48048e15	−0.742589
$606$	−7.96219e14	−0.395761
$607$	−3.74358e15	−1.84395	−0.921975	−	0.387250i	$-0.873425\pi$
$607$	−3.74358e15	−1.84395	−0.921975	+	0.387250i	$0.873425\pi$
$608$	−1.60329e14	−0.0782603
$609$	5.74805e14	0.278052
$610$	2.87164e14	0.137662
$611$	8.67069e14	0.411933
$612$	2.09079e15	0.984413
$613$	1.08273e15	0.505227	0.252614	−	0.967567i	$-0.418710\pi$
$613$	1.08273e15	0.505227	0.252614	+	0.967567i	$0.418710\pi$
$614$	4.82518e15	2.23145
$615$	−1.78274e14	−0.0817097
$616$	6.86612e14	0.311902
$617$	−2.72413e15	−1.22648	−0.613238	−	0.789898i	$-0.710133\pi$
$617$	−2.72413e15	−1.22648	−0.613238	+	0.789898i	$0.710133\pi$
$618$	1.15572e15	0.515723
$619$	−3.16544e15	−1.40002	−0.700012	−	0.714131i	$-0.746822\pi$
$619$	−3.16544e15	−1.40002	−0.700012	+	0.714131i	$0.746822\pi$
$620$	−3.54393e15	−1.55357
$621$	6.27315e14	0.272572
$622$	−3.72761e15	−1.60540
$623$	1.10717e15	0.472641
$624$	1.32637e15	0.561240
$625$	−1.03329e15	−0.433394
$626$	7.59553e15	3.15791
$627$	1.63750e14	0.0674852
$628$	−4.91223e14	−0.200678
$629$	−3.36528e15	−1.36283
$630$	−1.06210e15	−0.426377
$631$	−4.10184e15	−1.63237	−0.816183	−	0.577794i	$-0.803914\pi$
$631$	−4.10184e15	−1.63237	−0.816183	+	0.577794i	$0.803914\pi$
$632$	−3.46703e15	−1.36777
$633$	−1.47943e15	−0.578592
$634$	−5.21941e15	−2.02363
$635$	−3.35403e15	−1.28917
$636$	2.14960e15	0.819113
$637$	2.13515e14	0.0806607
$638$	−4.50355e14	−0.168671
$639$	−5.07472e14	−0.188433
$640$	−3.73380e15	−1.37455
$641$	−5.33760e14	−0.194817	−0.0974085	−	0.995244i	$-0.531055\pi$
$641$	−5.33760e14	−0.194817	−0.0974085	+	0.995244i	$0.531055\pi$
$642$	1.59029e15	0.575485
$643$	−6.54185e11	−0.000234715 0	−0.000117357	−	1.00000i	$-0.500037\pi$
$643$	−6.54185e11	−0.000234715 0	−0.000117357		1.00000i	$0.500037\pi$
$644$	7.51593e15	2.67368
$645$	4.42790e14	0.156178
$646$	4.42082e15	1.54605
$647$	−4.26725e15	−1.47970	−0.739852	−	0.672770i	$-0.765104\pi$
$647$	−4.26725e15	−1.47970	−0.739852	+	0.672770i	$0.765104\pi$
$648$	5.34480e14	0.183768
$649$	−7.48145e13	−0.0255059
$650$	2.25727e15	0.763064
$651$	−1.70080e15	−0.570109
$652$	−7.75847e15	−2.57878
$653$	−2.87486e15	−0.947532	−0.473766	−	0.880651i	$-0.657106\pi$
$653$	−2.87486e15	−0.947532	−0.473766	+	0.880651i	$0.657106\pi$
$654$	1.10903e15	0.362466
$655$	2.78881e14	0.0903842
$656$	5.04610e14	0.162175
$657$	1.68768e14	0.0537875
$658$	1.96528e15	0.621130
$659$	−9.79323e14	−0.306942	−0.153471	−	0.988153i	$-0.549045\pi$
$659$	−9.79323e14	−0.306942	−0.153471	+	0.988153i	$0.549045\pi$
$660$	5.51125e14	0.171300
$661$	−5.98174e15	−1.84382	−0.921912	−	0.387400i	$-0.873373\pi$
$661$	−5.98174e15	−1.84382	−0.921912	+	0.387400i	$0.873373\pi$
$662$	−3.43855e15	−1.05113
$663$	3.15043e15	0.955091
$664$	−6.82630e15	−2.05240
$665$	−1.48733e15	−0.443495
$666$	−1.75536e15	−0.519109
$667$	−2.41603e15	−0.708614
$668$	3.36677e15	0.979360
$669$	−2.63681e15	−0.760738
$670$	6.65319e15	1.90379
$671$	−7.15123e13	−0.0202958
$672$	−2.58970e14	−0.0728984
$673$	−2.22879e15	−0.622281	−0.311140	−	0.950364i	$-0.600711\pi$
$673$	−2.22879e15	−0.622281	−0.311140	+	0.950364i	$0.600711\pi$
$674$	−5.47542e15	−1.51631
$675$	2.82818e14	0.0776849
$676$	1.48838e15	0.405516
$677$	1.98615e15	0.536753	0.268376	−	0.963314i	$-0.413513\pi$
$677$	1.98615e15	0.536753	0.268376	+	0.963314i	$0.413513\pi$
$678$	−2.95972e15	−0.793390
$679$	−2.84768e15	−0.757193
$680$	7.29203e15	1.92331
$681$	3.75818e14	0.0983259
$682$	1.33256e15	0.345838
$683$	2.00524e14	0.0516242	0.0258121	−	0.999667i	$-0.491783\pi$
$683$	2.00524e14	0.0516242	0.0258121	+	0.999667i	$0.491783\pi$
$684$	1.52720e15	0.390021
$685$	3.90449e14	0.0989159
$686$	7.07495e15	1.77804
$687$	−8.95615e14	−0.223285
$688$	−1.25333e15	−0.309978
$689$	3.23905e15	0.794715
$690$	4.46424e15	1.08662
$691$	1.18641e15	0.286487	0.143244	−	0.989687i	$-0.454247\pi$
$691$	1.18641e15	0.286487	0.143244	+	0.989687i	$0.454247\pi$
$692$	3.92373e15	0.939973
$693$	2.64495e14	0.0628615
$694$	−8.51438e15	−2.00760
$695$	−4.10850e15	−0.961096
$696$	−2.05849e15	−0.477746
$697$	1.19856e15	0.275982
$698$	9.65146e15	2.20490
$699$	7.61480e14	0.172597
$700$	3.38848e15	0.762018
$701$	−3.45091e15	−0.769989	−0.384995	−	0.922919i	$-0.625797\pi$
$701$	−3.45091e15	−0.769989	−0.384995	+	0.922919i	$0.625797\pi$
$702$	1.64329e15	0.363798
$703$	−2.45815e15	−0.539950
$704$	9.98349e14	0.217587
$705$	7.73106e14	0.167186
$706$	−1.31511e16	−2.82186
$707$	−1.80099e15	−0.383447
$708$	−6.97755e14	−0.147408
$709$	4.42409e14	0.0927406	0.0463703	−	0.998924i	$-0.485235\pi$
$709$	4.42409e14	0.0927406	0.0463703	+	0.998924i	$0.485235\pi$
$710$	−3.61139e15	−0.751196
$711$	−1.33556e15	−0.275664
$712$	−3.96499e15	−0.812087
$713$	7.14882e15	1.45292
$714$	7.14069e15	1.44013
$715$	8.30441e14	0.166198
$716$	1.73078e15	0.343732
$717$	−4.63857e15	−0.914173
$718$	6.24737e15	1.22184
$719$	−9.07096e14	−0.176053	−0.0880266	−	0.996118i	$-0.528056\pi$
$719$	−9.07096e14	−0.176053	−0.0880266	+	0.996118i	$0.528056\pi$
$720$	1.18263e15	0.227783
$721$	2.61416e15	0.499676
$722$	−5.84243e15	−1.10825
$723$	1.59932e15	0.301075
$724$	1.16582e16	2.17806
$725$	−1.08924e15	−0.201960
$726$	5.19185e15	0.955368
$727$	−5.84790e15	−1.06797	−0.533987	−	0.845493i	$-0.679307\pi$
$727$	−5.84790e15	−1.06797	−0.533987	+	0.845493i	$0.679307\pi$
$728$	9.64912e15	1.74890
$729$	2.05891e14	0.0370370
$730$	1.20103e15	0.214426
$731$	−2.97695e15	−0.527505
$732$	−6.66957e14	−0.117297
$733$	−5.01036e14	−0.0874576	−0.0437288	−	0.999043i	$-0.513924\pi$
$733$	−5.01036e14	−0.0874576	−0.0437288	+	0.999043i	$0.513924\pi$
$734$	−5.80602e15	−1.00589
$735$	1.90377e14	0.0327366
$736$	1.08850e15	0.185781
$737$	−1.65684e15	−0.280679
$738$	6.25181e14	0.105123
$739$	−4.31786e15	−0.720649	−0.360325	−	0.932827i	$-0.617334\pi$
$739$	−4.31786e15	−0.720649	−0.360325	+	0.932827i	$0.617334\pi$
$740$	−8.27328e15	−1.37058
$741$	2.30121e15	0.378404
$742$	7.34156e15	1.19830
$743$	−1.04432e15	−0.169198	−0.0845989	−	0.996415i	$-0.526961\pi$
$743$	−1.04432e15	−0.169198	−0.0845989	+	0.996415i	$0.526961\pi$
$744$	6.09088e15	0.979556
$745$	−3.70230e15	−0.591034
$746$	1.25731e16	1.99240
$747$	−2.62961e15	−0.413646
$748$	−3.70530e15	−0.578582
$749$	3.59713e15	0.557578
$750$	6.99864e15	1.07690
$751$	3.22407e15	0.492476	0.246238	−	0.969209i	$-0.420806\pi$
$751$	3.22407e15	0.492476	0.246238	+	0.969209i	$0.420806\pi$
$752$	−2.18830e15	−0.331825
$753$	−1.79883e15	−0.270780
$754$	−6.32894e15	−0.945777
$755$	8.86710e15	1.31545
$756$	2.46680e15	0.363300
$757$	−5.76768e15	−0.843283	−0.421642	−	0.906763i	$-0.638546\pi$
$757$	−5.76768e15	−0.843283	−0.421642	+	0.906763i	$0.638546\pi$
$758$	8.67771e15	1.25958
$759$	−1.11173e15	−0.160202
$760$	5.32642e15	0.762010
$761$	−8.21110e15	−1.16623	−0.583117	−	0.812388i	$-0.698167\pi$
$761$	−8.21110e15	−1.16623	−0.583117	+	0.812388i	$0.698167\pi$
$762$	1.17621e16	1.65857
$763$	2.50856e15	0.351188
$764$	−2.22132e16	−3.08743
$765$	2.80902e15	0.387629
$766$	−4.02306e15	−0.551186
$767$	−1.05139e15	−0.143017
$768$	8.34614e15	1.12719
$769$	−8.40435e15	−1.12696	−0.563481	−	0.826129i	$-0.690538\pi$
$769$	−8.40435e15	−1.12696	−0.563481	+	0.826129i	$0.690538\pi$
$770$	1.88226e15	0.250600
$771$	5.41376e15	0.715648
$772$	2.66644e16	3.49975
$773$	−7.93186e15	−1.03368	−0.516842	−	0.856081i	$-0.672893\pi$
$773$	−7.93186e15	−1.03368	−0.516842	+	0.856081i	$0.672893\pi$
$774$	−1.55281e15	−0.200929
$775$	3.22297e15	0.414092
$776$	1.01981e16	1.30100
$777$	−3.97051e15	−0.502956
$778$	−9.36019e14	−0.117733
$779$	8.75483e14	0.109343
$780$	7.74508e15	0.960518
$781$	8.99343e14	0.110750
$782$	−3.00138e16	−3.67015
$783$	−7.92965e14	−0.0962863
$784$	−5.38869e14	−0.0649748
$785$	−6.59968e14	−0.0790205
$786$	−9.77999e14	−0.116283
$787$	−7.76946e13	−0.00917339	−0.00458670	−	0.999989i	$-0.501460\pi$
$787$	−7.76946e13	−0.00917339	−0.00458670	+	0.999989i	$0.501460\pi$
$788$	−7.14008e15	−0.837161
$789$	6.43512e14	0.0749261
$790$	−9.50443e15	−1.09895
$791$	−6.69467e15	−0.768703
$792$	−9.47207e14	−0.108008
$793$	−1.00498e15	−0.113803
$794$	−1.83462e16	−2.06316
$795$	2.88804e15	0.322540
$796$	2.41974e16	2.68378
$797$	4.83657e15	0.532741	0.266371	−	0.963871i	$-0.414175\pi$
$797$	4.83657e15	0.532741	0.266371	+	0.963871i	$0.414175\pi$
$798$	5.21588e15	0.570573
$799$	−5.19772e15	−0.564684
$800$	4.90740e14	0.0529489
$801$	−1.52739e15	−0.163670
$802$	8.28574e15	0.881804
$803$	−2.99091e14	−0.0316132
$804$	−1.54525e16	−1.62214
$805$	1.00978e16	1.05281
$806$	1.87268e16	1.93919
$807$	−1.79884e15	−0.185007
$808$	6.44969e15	0.658835
$809$	7.69640e15	0.780856	0.390428	−	0.920634i	$-0.372327\pi$
$809$	7.69640e15	0.780856	0.390428	+	0.920634i	$0.372327\pi$
$810$	1.46521e15	0.147650
$811$	2.16669e15	0.216862	0.108431	−	0.994104i	$-0.465417\pi$
$811$	2.16669e15	0.216862	0.108431	+	0.994104i	$0.465417\pi$
$812$	−9.50060e15	−0.944480
$813$	2.59772e15	0.256504
$814$	3.11086e15	0.305103
$815$	−1.04237e16	−1.01544
$816$	−7.95103e15	−0.769356
$817$	−2.17450e15	−0.208996
$818$	2.96026e16	2.82610
$819$	3.71701e15	0.352478
$820$	2.94657e15	0.277550
$821$	−4.69662e15	−0.439439	−0.219719	−	0.975563i	$-0.570514\pi$
$821$	−4.69662e15	−0.439439	−0.219719	+	0.975563i	$0.570514\pi$
$822$	−1.36925e15	−0.127259
$823$	−8.61708e15	−0.795538	−0.397769	−	0.917486i	$-0.630215\pi$
$823$	−8.61708e15	−0.795538	−0.397769	+	0.917486i	$0.630215\pi$
$824$	−9.36181e15	−0.858539
$825$	−5.01211e14	−0.0456588
$826$	−2.38305e15	−0.215647
$827$	7.88563e15	0.708852	0.354426	−	0.935084i	$-0.384676\pi$
$827$	7.88563e15	0.708852	0.354426	+	0.935084i	$0.384676\pi$
$828$	−1.03685e16	−0.925868
$829$	3.94131e15	0.349615	0.174808	−	0.984603i	$-0.444070\pi$
$829$	3.94131e15	0.349615	0.174808	+	0.984603i	$0.444070\pi$
$830$	−1.87135e16	−1.64901
$831$	−8.58558e15	−0.751561
$832$	1.40300e16	1.22006
$833$	−1.27994e15	−0.110571
$834$	1.44080e16	1.23649
$835$	4.52332e15	0.385640
$836$	−2.70651e15	−0.229232
$837$	2.34632e15	0.197422
$838$	−2.78180e16	−2.32533
$839$	−1.34558e16	−1.11743	−0.558713	−	0.829361i	$-0.688705\pi$
$839$	−1.34558e16	−1.11743	−0.558713	+	0.829361i	$0.688705\pi$
$840$	8.60346e15	0.709801
$841$	−9.14650e15	−0.749682
$842$	3.07357e16	2.50281
$843$	−9.83602e15	−0.795734
$844$	2.44525e16	1.96535
$845$	1.99968e15	0.159679
$846$	−2.71118e15	−0.215090
$847$	1.17436e16	0.925641
$848$	−8.17469e15	−0.640168
$849$	−4.33816e14	−0.0337531
$850$	−1.35314e16	−1.04602
$851$	1.66889e16	1.28178
$852$	8.38769e15	0.640066
$853$	−1.04802e16	−0.794603	−0.397302	−	0.917688i	$-0.630053\pi$
$853$	−1.04802e16	−0.794603	−0.397302	+	0.917688i	$0.630053\pi$
$854$	−2.27786e15	−0.171597
$855$	2.05183e15	0.153578
$856$	−1.28820e16	−0.958026
$857$	3.31991e15	0.245320	0.122660	−	0.992449i	$-0.460858\pi$
$857$	3.31991e15	0.245320	0.122660	+	0.992449i	$0.460858\pi$
$858$	−2.91225e15	−0.213820
$859$	−2.98270e14	−0.0217594	−0.0108797	−	0.999941i	$-0.503463\pi$
$859$	−2.98270e14	−0.0217594	−0.0108797	+	0.999941i	$0.503463\pi$
$860$	−7.31861e15	−0.530502
$861$	1.41412e15	0.101852
$862$	2.40532e16	1.72140
$863$	7.21171e15	0.512837	0.256418	−	0.966566i	$-0.417458\pi$
$863$	7.21171e15	0.512837	0.256418	+	0.966566i	$0.417458\pi$
$864$	3.57258e14	0.0252439
$865$	5.27161e15	0.370131
$866$	1.80956e15	0.126248
$867$	−1.05574e16	−0.731902
$868$	2.81115e16	1.93653
$869$	2.36688e15	0.162020
$870$	−5.64308e15	−0.383849
$871$	−2.32840e16	−1.57383
$872$	−8.98362e15	−0.603408
$873$	3.92847e15	0.262208
$874$	−2.19234e16	−1.45410
$875$	1.58304e16	1.04340
$876$	−2.78946e15	−0.182704
$877$	−1.44250e16	−0.938899	−0.469450	−	0.882959i	$-0.655548\pi$
$877$	−1.44250e16	−0.938899	−0.469450	+	0.882959i	$0.655548\pi$
$878$	−5.31155e16	−3.43559
$879$	−3.05454e15	−0.196339
$880$	−2.09586e15	−0.133878
$881$	4.68326e15	0.297290	0.148645	−	0.988891i	$-0.452509\pi$
$881$	4.68326e15	0.297290	0.148645	+	0.988891i	$0.452509\pi$
$882$	−6.67626e14	−0.0421169
$883$	2.44441e16	1.53247	0.766233	−	0.642563i	$-0.222129\pi$
$883$	2.44441e16	1.53247	0.766233	+	0.642563i	$0.222129\pi$
$884$	−5.20714e16	−3.24423
$885$	−9.37448e14	−0.0580443
$886$	1.83635e16	1.12998
$887$	−1.19337e16	−0.729788	−0.364894	−	0.931049i	$-0.618895\pi$
$887$	−1.19337e16	−0.729788	−0.364894	+	0.931049i	$0.618895\pi$
$888$	1.42191e16	0.864175
$889$	2.66051e16	1.60696
$890$	−1.08695e16	−0.652478
$891$	−3.64881e14	−0.0217683
$892$	4.35822e16	2.58406
$893$	−3.79664e15	−0.223726
$894$	1.29835e16	0.760387
$895$	2.32534e15	0.135350
$896$	2.96176e16	1.71339
$897$	−1.56234e16	−0.898290
$898$	4.73085e16	2.70346
$899$	−9.03656e15	−0.513245
$900$	−4.67453e15	−0.263878
$901$	−1.94167e16	−1.08941
$902$	−1.10795e15	−0.0617851
$903$	−3.51234e15	−0.194677
$904$	2.39749e16	1.32078
$905$	1.56631e16	0.857650
$906$	−3.10957e16	−1.69237
$907$	−2.90802e15	−0.157310	−0.0786552	−	0.996902i	$-0.525063\pi$
$907$	−2.90802e15	−0.157310	−0.0786552	+	0.996902i	$0.525063\pi$
$908$	−6.21166e15	−0.333991
$909$	2.48453e15	0.132783
$910$	2.64518e16	1.40517
$911$	−1.93461e16	−1.02151	−0.510754	−	0.859727i	$-0.670634\pi$
$911$	−1.93461e16	−1.02151	−0.510754	+	0.859727i	$0.670634\pi$
$912$	−5.80778e15	−0.304817
$913$	4.66021e15	0.243117
$914$	5.33688e16	2.76747
$915$	−8.96070e14	−0.0461877
$916$	1.48031e16	0.758449
$917$	−2.21217e15	−0.112664
$918$	−9.85085e15	−0.498700
$919$	1.96369e16	0.988185	0.494092	−	0.869409i	$-0.335500\pi$
$919$	1.96369e16	0.988185	0.494092	+	0.869409i	$0.335500\pi$
$920$	−3.61621e16	−1.80893
$921$	−1.50566e16	−0.748683
$922$	2.47263e15	0.122219
$923$	1.26387e16	0.621001
$924$	−4.37168e15	−0.213527
$925$	7.52400e15	0.365317
$926$	−1.21746e16	−0.587616
$927$	−3.60633e15	−0.173032
$928$	−1.37594e15	−0.0656273
$929$	−1.86386e16	−0.883746	−0.441873	−	0.897078i	$-0.645686\pi$
$929$	−1.86386e16	−0.883746	−0.441873	+	0.897078i	$0.645686\pi$
$930$	1.66974e16	0.787032
$931$	−9.34921e14	−0.0438078
$932$	−1.25860e16	−0.586275
$933$	1.16317e16	0.538635
$934$	−4.79725e16	−2.20844
$935$	−4.97815e15	−0.227826
$936$	−1.33113e16	−0.605625
$937$	−2.24835e16	−1.01694	−0.508471	−	0.861079i	$-0.669789\pi$
$937$	−2.24835e16	−1.01694	−0.508471	+	0.861079i	$0.669789\pi$
$938$	−5.27750e16	−2.37308
$939$	−2.37012e16	−1.05952
$940$	−1.27782e16	−0.567893
$941$	1.97946e16	0.874590	0.437295	−	0.899318i	$-0.355937\pi$
$941$	1.97946e16	0.874590	0.437295	+	0.899318i	$0.355937\pi$
$942$	2.31442e15	0.101663
$943$	−5.94383e15	−0.259569
$944$	2.65348e15	0.115205
$945$	3.31420e15	0.143055
$946$	2.75189e15	0.118094
$947$	−4.39330e16	−1.87442	−0.937209	−	0.348769i	$-0.886600\pi$
$947$	−4.39330e16	−1.87442	−0.937209	+	0.348769i	$0.886600\pi$
$948$	2.20747e16	0.936371
$949$	−4.20320e15	−0.177262
$950$	−9.88394e15	−0.414429
$951$	1.62867e16	0.678955
$952$	−5.78425e16	−2.39742
$953$	4.01548e14	0.0165473	0.00827363	−	0.999966i	$-0.497366\pi$
$953$	4.01548e14	0.0165473	0.00827363	+	0.999966i	$0.497366\pi$
$954$	−1.01279e16	−0.414959
$955$	−2.98439e16	−1.21573
$956$	7.66680e16	3.10524
$957$	1.40529e15	0.0565916
$958$	2.85023e15	0.114122
$959$	−3.09715e15	−0.123299
$960$	1.25096e16	0.495167
$961$	1.32992e15	0.0523414
$962$	4.37176e16	1.71078
$963$	−4.96237e15	−0.193083
$964$	−2.64342e16	−1.02269
$965$	3.58242e16	1.37809
$966$	−3.54116e16	−1.35448
$967$	−4.33307e16	−1.64797	−0.823986	−	0.566610i	$-0.808255\pi$
$967$	−4.33307e16	−1.64797	−0.823986	+	0.566610i	$0.808255\pi$
$968$	−4.20560e16	−1.59043
$969$	−1.37948e16	−0.518722
$970$	2.79567e16	1.04530
$971$	−2.19939e15	−0.0817703	−0.0408851	−	0.999164i	$-0.513018\pi$
$971$	−2.19939e15	−0.0817703	−0.0408851	+	0.999164i	$0.513018\pi$
$972$	−3.40305e15	−0.125807
$973$	3.25898e16	1.19801
$974$	1.27056e16	0.464430
$975$	−7.04364e15	−0.256019
$976$	2.53636e15	0.0916720
$977$	4.37872e16	1.57372	0.786859	−	0.617133i	$-0.211706\pi$
$977$	4.37872e16	1.57372	0.786859	+	0.617133i	$0.211706\pi$
$978$	3.65544e16	1.30640
$979$	2.70684e15	0.0961961
$980$	−3.14662e15	−0.111199
$981$	−3.46065e15	−0.121612
$982$	−2.37554e16	−0.830134
$983$	−5.63062e16	−1.95664	−0.978321	−	0.207092i	$-0.933600\pi$
$983$	−5.63062e16	−1.95664	−0.978321	+	0.207092i	$0.933600\pi$
$984$	−5.06422e15	−0.175001
$985$	−9.59285e15	−0.329646
$986$	3.79394e16	1.29648
$987$	−6.13250e15	−0.208398
$988$	−3.80353e16	−1.28536
$989$	1.47631e16	0.496133
$990$	−2.59665e15	−0.0867800
$991$	−2.53375e16	−0.842090	−0.421045	−	0.907040i	$-0.638337\pi$
$991$	−2.53375e16	−0.842090	−0.421045	+	0.907040i	$0.638337\pi$
$992$	4.07128e15	0.134560
$993$	1.07297e16	0.352668
$994$	2.86466e16	0.936370
$995$	3.25097e16	1.05678
$996$	4.34632e16	1.40506
$997$	−5.94499e16	−1.91130	−0.955648	−	0.294513i	$-0.904843\pi$
$997$	−5.94499e16	−1.91130	−0.955648	+	0.294513i	$0.904843\pi$
$998$	−7.51130e16	−2.40158
$999$	5.47746e15	0.174168

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.a.1.25	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.a.1.25	✓	26	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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q+77.8742 q^{2} -243.000 q^{3} +4016.40 q^{4} +5396.11 q^{5} -18923.4 q^{6} -42803.5 q^{7} +153287. q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+77.8742 q^{2} -243.000 q^{3} +4016.40 q^{4} +5396.11 q^{5} -18923.4 q^{6} -42803.5 q^{7} +153287. q^{8} +59049.0 q^{9} +420218. q^{10} -104647. q^{11} -975984. q^{12} -1.47062e6 q^{13} -3.33329e6 q^{14} -1.31126e6 q^{15} +3.71156e6 q^{16} +8.81579e6 q^{17} +4.59840e6 q^{18} +6.43944e6 q^{19} +2.16729e7 q^{20} +1.04013e7 q^{21} -8.14929e6 q^{22} -4.37186e7 q^{23} -3.72488e7 q^{24} -1.97101e7 q^{25} -1.14524e8 q^{26} -1.43489e7 q^{27} -1.71916e8 q^{28} +5.52631e7 q^{29} -1.02113e8 q^{30} -1.63519e8 q^{31} -2.48979e7 q^{32} +2.54292e7 q^{33} +6.86523e8 q^{34} -2.30973e8 q^{35} +2.37164e8 q^{36} -3.81734e8 q^{37} +5.01466e8 q^{38} +3.57362e8 q^{39} +8.27156e8 q^{40} +1.35956e8 q^{41} +8.09989e8 q^{42} -3.37684e8 q^{43} -4.20303e8 q^{44} +3.18635e8 q^{45} -3.40456e9 q^{46} -5.89592e8 q^{47} -9.01908e8 q^{48} -1.45187e8 q^{49} -1.53491e9 q^{50} -2.14224e9 q^{51} -5.90661e9 q^{52} -2.20250e9 q^{53} -1.11741e9 q^{54} -5.64686e8 q^{55} -6.56124e9 q^{56} -1.56478e9 q^{57} +4.30357e9 q^{58} +7.14924e8 q^{59} -5.26652e9 q^{60} +6.83368e8 q^{61} -1.27339e10 q^{62} -2.52750e9 q^{63} -9.54017e9 q^{64} -7.93566e9 q^{65} +1.98028e9 q^{66} +1.58327e10 q^{67} +3.54077e10 q^{68} +1.06236e10 q^{69} -1.79868e10 q^{70} -8.59408e9 q^{71} +9.05147e9 q^{72} +2.85810e9 q^{73} -2.97272e10 q^{74} +4.78955e9 q^{75} +2.58633e10 q^{76} +4.47925e9 q^{77} +2.78293e10 q^{78} -2.26178e10 q^{79} +2.00280e10 q^{80} +3.48678e9 q^{81} +1.05875e10 q^{82} -4.45327e10 q^{83} +4.17755e10 q^{84} +4.75710e10 q^{85} -2.62969e10 q^{86} -1.34289e10 q^{87} -1.60410e10 q^{88} -2.58664e10 q^{89} +2.48135e10 q^{90} +6.29479e10 q^{91} -1.75591e11 q^{92} +3.97351e10 q^{93} -4.59141e10 q^{94} +3.47479e10 q^{95} +6.05020e9 q^{96} +6.65290e10 q^{97} -1.13063e10 q^{98} -6.17929e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9}+O(q^{10}) \) 26 * q - 78 * q^2 - 6318 * q^3 + 23070 * q^4 + 3808 * q^5 + 18954 * q^6 - 98819 * q^7 - 117645 * q^8 + 1535274 * q^9	\( 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9} - 859751 q^{10} + 579094 q^{11} - 5606010 q^{12} - 2018538 q^{13} + 4157413 q^{14} - 925344 q^{15} + 20190274 q^{16} - 13084493 q^{17} - 4605822 q^{18} + 9917231 q^{19} + 10165633 q^{20} + 24013017 q^{21} - 89820518 q^{22} - 63513223 q^{23} + 28587735 q^{24} + 218986852 q^{25} - 77999532 q^{26} - 373071582 q^{27} - 444601862 q^{28} + 81530981 q^{29} + 208919493 q^{30} - 408861231 q^{31} - 26253128 q^{32} - 140719842 q^{33} - 508910076 q^{34} - 75731421 q^{35} + 1362260430 q^{36} - 802381301 q^{37} + 732704675 q^{38} + 490504734 q^{39} - 646130800 q^{40} - 1354472849 q^{41} - 1010251359 q^{42} + 282952194 q^{43} + 1846047996 q^{44} + 224858592 q^{45} + 9629305849 q^{46} - 1196794197 q^{47} - 4906236582 q^{48} + 10889725683 q^{49} - 6236232091 q^{50} + 3179531799 q^{51} - 1968200812 q^{52} - 8276044236 q^{53} + 1119214746 q^{54} - 6672895076 q^{55} + 2579741342 q^{56} - 2409887133 q^{57} - 9401656060 q^{58} + 18588031774 q^{59} - 2470248819 q^{60} - 21181559029 q^{61} - 6117706514 q^{62} - 5835163131 q^{63} + 42975855037 q^{64} + 25680681860 q^{65} + 21826385874 q^{66} + 26234163394 q^{67} + 19707344091 q^{68} + 15433713189 q^{69} + 129203099090 q^{70} + 52088830406 q^{71} - 6946819605 q^{72} + 20943384867 q^{73} + 41969200146 q^{74} - 53213805036 q^{75} + 223987219368 q^{76} + 94604773153 q^{77} + 18953886276 q^{78} + 68965662774 q^{79} + 218947784293 q^{80} + 90656394426 q^{81} + 11938614923 q^{82} + 17947446393 q^{83} + 108038252466 q^{84} - 52849386709 q^{85} + 384986147852 q^{86} - 19812028383 q^{87} - 49061112607 q^{88} + 38570593981 q^{89} - 50767436799 q^{90} - 226268806999 q^{91} - 79559686310 q^{92} + 99353279133 q^{93} - 16709400108 q^{94} - 252795831501 q^{95} + 6379510104 q^{96} - 186894587836 q^{97} - 252443311612 q^{98} + 34194921606 q^{99}+O(q^{100}) \) 26 * q - 78 * q^2 - 6318 * q^3 + 23070 * q^4 + 3808 * q^5 + 18954 * q^6 - 98819 * q^7 - 117645 * q^8 + 1535274 * q^9 - 859751 * q^10 + 579094 * q^11 - 5606010 * q^12 - 2018538 * q^13 + 4157413 * q^14 - 925344 * q^15 + 20190274 * q^16 - 13084493 * q^17 - 4605822 * q^18 + 9917231 * q^19 + 10165633 * q^20 + 24013017 * q^21 - 89820518 * q^22 - 63513223 * q^23 + 28587735 * q^24 + 218986852 * q^25 - 77999532 * q^26 - 373071582 * q^27 - 444601862 * q^28 + 81530981 * q^29 + 208919493 * q^30 - 408861231 * q^31 - 26253128 * q^32 - 140719842 * q^33 - 508910076 * q^34 - 75731421 * q^35 + 1362260430 * q^36 - 802381301 * q^37 + 732704675 * q^38 + 490504734 * q^39 - 646130800 * q^40 - 1354472849 * q^41 - 1010251359 * q^42 + 282952194 * q^43 + 1846047996 * q^44 + 224858592 * q^45 + 9629305849 * q^46 - 1196794197 * q^47 - 4906236582 * q^48 + 10889725683 * q^49 - 6236232091 * q^50 + 3179531799 * q^51 - 1968200812 * q^52 - 8276044236 * q^53 + 1119214746 * q^54 - 6672895076 * q^55 + 2579741342 * q^56 - 2409887133 * q^57 - 9401656060 * q^58 + 18588031774 * q^59 - 2470248819 * q^60 - 21181559029 * q^61 - 6117706514 * q^62 - 5835163131 * q^63 + 42975855037 * q^64 + 25680681860 * q^65 + 21826385874 * q^66 + 26234163394 * q^67 + 19707344091 * q^68 + 15433713189 * q^69 + 129203099090 * q^70 + 52088830406 * q^71 - 6946819605 * q^72 + 20943384867 * q^73 + 41969200146 * q^74 - 53213805036 * q^75 + 223987219368 * q^76 + 94604773153 * q^77 + 18953886276 * q^78 + 68965662774 * q^79 + 218947784293 * q^80 + 90656394426 * q^81 + 11938614923 * q^82 + 17947446393 * q^83 + 108038252466 * q^84 - 52849386709 * q^85 + 384986147852 * q^86 - 19812028383 * q^87 - 49061112607 * q^88 + 38570593981 * q^89 - 50767436799 * q^90 - 226268806999 * q^91 - 79559686310 * q^92 + 99353279133 * q^93 - 16709400108 * q^94 - 252795831501 * q^95 + 6379510104 * q^96 - 186894587836 * q^97 - 252443311612 * q^98 + 34194921606 * q^99

Introduction

L-functions

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