LMFDB - Embedded newform 177.12.a.a.1.17

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			1.17
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)

$f(q)$	$=$	$q+20.9819 q^{2} -243.000 q^{3} -1607.76 q^{4} +5799.05 q^{5} -5098.61 q^{6} +22173.1 q^{7} -76704.8 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+20.9819 q^{2} -243.000 q^{3} -1607.76 q^{4} +5799.05 q^{5} -5098.61 q^{6} +22173.1 q^{7} -76704.8 q^{8} +59049.0 q^{9} +121675. q^{10} +936055. q^{11} +390685. q^{12} -1.11415e6 q^{13} +465235. q^{14} -1.40917e6 q^{15} +1.68328e6 q^{16} -9.92639e6 q^{17} +1.23896e6 q^{18} -1.60881e7 q^{19} -9.32347e6 q^{20} -5.38807e6 q^{21} +1.96402e7 q^{22} -9.19924e6 q^{23} +1.86393e7 q^{24} -1.51992e7 q^{25} -2.33769e7 q^{26} -1.43489e7 q^{27} -3.56490e7 q^{28} +1.93966e8 q^{29} -2.95671e7 q^{30} +2.28248e8 q^{31} +1.92410e8 q^{32} -2.27461e8 q^{33} -2.08275e8 q^{34} +1.28583e8 q^{35} -9.49366e7 q^{36} +6.39964e8 q^{37} -3.37559e8 q^{38} +2.70737e8 q^{39} -4.44815e8 q^{40} +2.59523e8 q^{41} -1.13052e8 q^{42} -5.30335e6 q^{43} -1.50495e9 q^{44} +3.42428e8 q^{45} -1.93018e8 q^{46} +9.16945e8 q^{47} -4.09036e8 q^{48} -1.48568e9 q^{49} -3.18908e8 q^{50} +2.41211e9 q^{51} +1.79128e9 q^{52} -4.20629e9 q^{53} -3.01068e8 q^{54} +5.42823e9 q^{55} -1.70079e9 q^{56} +3.90940e9 q^{57} +4.06977e9 q^{58} +7.14924e8 q^{59} +2.26560e9 q^{60} -8.56840e9 q^{61} +4.78907e9 q^{62} +1.30930e9 q^{63} +5.89780e8 q^{64} -6.46098e9 q^{65} -4.77258e9 q^{66} +1.23134e10 q^{67} +1.59592e10 q^{68} +2.23541e9 q^{69} +2.69792e9 q^{70} -4.22731e9 q^{71} -4.52934e9 q^{72} -6.29909e9 q^{73} +1.34277e10 q^{74} +3.69340e9 q^{75} +2.58658e10 q^{76} +2.07553e10 q^{77} +5.68059e9 q^{78} -5.22111e10 q^{79} +9.76140e9 q^{80} +3.48678e9 q^{81} +5.44529e9 q^{82} -7.62439e9 q^{83} +8.66272e9 q^{84} -5.75636e10 q^{85} -1.11274e8 q^{86} -4.71337e10 q^{87} -7.18000e10 q^{88} -9.11126e10 q^{89} +7.18480e9 q^{90} -2.47041e10 q^{91} +1.47902e10 q^{92} -5.54642e10 q^{93} +1.92393e10 q^{94} -9.32956e10 q^{95} -4.67556e10 q^{96} +1.48369e11 q^{97} -3.11724e10 q^{98} +5.52731e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	20.9819	0.463639	0.231820	−	0.972759i	$-0.425532\pi$
$2$	20.9819	0.463639	0.231820	+	0.972759i	$0.425532\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	−1607.76	−0.785039
$5$	5799.05	0.829892	0.414946	−	0.909846i	$-0.363800\pi$
$5$	5799.05	0.829892	0.414946	+	0.909846i	$0.363800\pi$
$6$	−5098.61	−0.267682
$7$	22173.1	0.498641	0.249320	−	0.968421i	$-0.419793\pi$
$7$	22173.1	0.498641	0.249320	+	0.968421i	$0.419793\pi$
$8$	−76704.8	−0.827614
$9$	59049.0	0.333333
$10$	121675.	0.384771
$11$	936055.	1.75243	0.876217	−	0.481916i	$-0.160059\pi$
$11$	936055.	1.75243	0.876217	+	0.481916i	$0.160059\pi$
$12$	390685.	0.453242
$13$	−1.11415e6	−0.832249	−0.416125	−	0.909308i	$-0.636612\pi$
$13$	−1.11415e6	−0.832249	−0.416125	+	0.909308i	$0.636612\pi$
$14$	465235.	0.231189
$15$	−1.40917e6	−0.479138
$16$	1.68328e6	0.401324
$17$	−9.92639e6	−1.69559	−0.847797	−	0.530320i	$-0.822072\pi$
$17$	−9.92639e6	−1.69559	−0.847797	+	0.530320i	$0.822072\pi$
$18$	1.23896e6	0.154546
$19$	−1.60881e7	−1.49059	−0.745297	−	0.666732i	$-0.767692\pi$
$19$	−1.60881e7	−1.49059	−0.745297	+	0.666732i	$0.767692\pi$
$20$	−9.32347e6	−0.651497
$21$	−5.38807e6	−0.287890
$22$	1.96402e7	0.812497
$23$	−9.19924e6	−0.298022	−0.149011	−	0.988836i	$-0.547609\pi$
$23$	−9.19924e6	−0.298022	−0.149011	+	0.988836i	$0.547609\pi$
$24$	1.86393e7	0.477823
$25$	−1.51992e7	−0.311279
$26$	−2.33769e7	−0.385863
$27$	−1.43489e7	−0.192450
$28$	−3.56490e7	−0.391452
$29$	1.93966e8	1.75605	0.878024	−	0.478617i	$-0.158862\pi$
$29$	1.93966e8	1.75605	0.878024	+	0.478617i	$0.158862\pi$
$30$	−2.95671e7	−0.222147
$31$	2.28248e8	1.43191	0.715957	−	0.698144i	$-0.245991\pi$
$31$	2.28248e8	1.43191	0.715957	+	0.698144i	$0.245991\pi$
$32$	1.92410e8	1.01368
$33$	−2.27461e8	−1.01177
$34$	−2.08275e8	−0.786144
$35$	1.28583e8	0.413818
$36$	−9.49366e7	−0.261680
$37$	6.39964e8	1.51721	0.758605	−	0.651550i	$-0.225881\pi$
$37$	6.39964e8	1.51721	0.758605	+	0.651550i	$0.225881\pi$
$38$	−3.37559e8	−0.691098
$39$	2.70737e8	0.480499
$40$	−4.44815e8	−0.686830
$41$	2.59523e8	0.349836	0.174918	−	0.984583i	$-0.444034\pi$
$41$	2.59523e8	0.349836	0.174918	+	0.984583i	$0.444034\pi$
$42$	−1.13052e8	−0.133477
$43$	−5.30335e6	−0.00550141	−0.00275070	−	0.999996i	$-0.500876\pi$
$43$	−5.30335e6	−0.00550141	−0.00275070	+	0.999996i	$0.500876\pi$
$44$	−1.50495e9	−1.37573
$45$	3.42428e8	0.276631
$46$	−1.93018e8	−0.138175
$47$	9.16945e8	0.583183	0.291592	−	0.956543i	$-0.405815\pi$
$47$	9.16945e8	0.583183	0.291592	+	0.956543i	$0.405815\pi$
$48$	−4.09036e8	−0.231705
$49$	−1.48568e9	−0.751358
$50$	−3.18908e8	−0.144321
$51$	2.41211e9	0.978952
$52$	1.79128e9	0.653348
$53$	−4.20629e9	−1.38160	−0.690800	−	0.723046i	$-0.742741\pi$
$53$	−4.20629e9	−1.38160	−0.690800	+	0.723046i	$0.742741\pi$
$54$	−3.01068e8	−0.0892274
$55$	5.42823e9	1.45433
$56$	−1.70079e9	−0.412682
$57$	3.90940e9	0.860595
$58$	4.06977e9	0.814172
$59$	7.14924e8	0.130189
$59$	7.14924e8	0.130189
$60$	2.26560e9	0.376142
$61$	−8.56840e9	−1.29893	−0.649465	−	0.760392i	$-0.725007\pi$
$61$	−8.56840e9	−1.29893	−0.649465	+	0.760392i	$0.725007\pi$
$62$	4.78907e9	0.663892
$63$	1.30930e9	0.166214
$64$	5.89780e8	0.0686594
$65$	−6.46098e9	−0.690677
$66$	−4.77258e9	−0.469096
$67$	1.23134e10	1.11421	0.557106	−	0.830442i	$-0.311912\pi$
$67$	1.23134e10	1.11421	0.557106	+	0.830442i	$0.311912\pi$
$68$	1.59592e10	1.33111
$69$	2.23541e9	0.172063
$70$	2.69792e9	0.191862
$71$	−4.22731e9	−0.278063	−0.139031	−	0.990288i	$-0.544399\pi$
$71$	−4.22731e9	−0.278063	−0.139031	+	0.990288i	$0.544399\pi$
$72$	−4.52934e9	−0.275871
$73$	−6.29909e9	−0.355633	−0.177817	−	0.984064i	$-0.556903\pi$
$73$	−6.29909e9	−0.355633	−0.177817	+	0.984064i	$0.556903\pi$
$74$	1.34277e10	0.703439
$75$	3.69340e9	0.179717
$76$	2.58658e10	1.17017
$77$	2.07553e10	0.873835
$78$	5.68059e9	0.222778
$79$	−5.22111e10	−1.90903	−0.954517	−	0.298155i	$-0.903629\pi$
$79$	−5.22111e10	−1.90903	−0.954517	+	0.298155i	$0.903629\pi$
$80$	9.76140e9	0.333056
$81$	3.48678e9	0.111111
$82$	5.44529e9	0.162198
$83$	−7.62439e9	−0.212459	−0.106230	−	0.994342i	$-0.533878\pi$
$83$	−7.62439e9	−0.212459	−0.106230	+	0.994342i	$0.533878\pi$
$84$	8.66272e9	0.226005
$85$	−5.75636e10	−1.40716
$86$	−1.11274e8	−0.00255067
$87$	−4.71337e10	−1.01385
$88$	−7.18000e10	−1.45034
$89$	−9.11126e10	−1.72955	−0.864775	−	0.502159i	$-0.832539\pi$
$89$	−9.11126e10	−1.72955	−0.864775	+	0.502159i	$0.832539\pi$
$90$	7.18480e9	0.128257
$91$	−2.47041e10	−0.414993
$92$	1.47902e10	0.233959
$93$	−5.54642e10	−0.826716
$94$	1.92393e10	0.270387
$95$	−9.32956e10	−1.23703
$96$	−4.67556e10	−0.585251
$97$	1.48369e11	1.75428	0.877139	−	0.480237i	$-0.159449\pi$
$97$	1.48369e11	1.75428	0.877139	+	0.480237i	$0.159449\pi$
$98$	−3.11724e10	−0.348359
$99$	5.52731e10	0.584145
$100$	2.44366e10	0.244366
$101$	6.76905e10	0.640855	0.320428	−	0.947273i	$-0.396173\pi$
$101$	6.76905e10	0.640855	0.320428	+	0.947273i	$0.396173\pi$
$102$	5.06107e10	0.453881
$103$	−9.24360e10	−0.785664	−0.392832	−	0.919610i	$-0.628505\pi$
$103$	−9.24360e10	−0.785664	−0.392832	+	0.919610i	$0.628505\pi$
$104$	8.54603e10	0.688781
$105$	−3.12457e10	−0.238918
$106$	−8.82561e10	−0.640564
$107$	−7.51409e9	−0.0517924	−0.0258962	−	0.999665i	$-0.508244\pi$
$107$	−7.51409e9	−0.0517924	−0.0258962	+	0.999665i	$0.508244\pi$
$108$	2.30696e10	0.151081
$109$	−1.87393e11	−1.16656	−0.583281	−	0.812270i	$-0.698232\pi$
$109$	−1.87393e11	−1.16656	−0.583281	+	0.812270i	$0.698232\pi$
$110$	1.13895e11	0.674285
$111$	−1.55511e11	−0.875962
$112$	3.73235e10	0.200117
$113$	−6.22501e10	−0.317840	−0.158920	−	0.987291i	$-0.550801\pi$
$113$	−6.22501e10	−0.317840	−0.158920	+	0.987291i	$0.550801\pi$
$114$	8.20268e10	0.399006
$115$	−5.33468e10	−0.247326
$116$	−3.11850e11	−1.37856
$117$	−6.57892e10	−0.277416
$118$	1.50005e10	0.0603607
$119$	−2.20099e11	−0.845492
$120$	1.08090e11	0.396542
$121$	5.90888e11	2.07103
$122$	−1.79781e11	−0.602235
$123$	−6.30641e10	−0.201978
$124$	−3.66967e11	−1.12411
$125$	−3.71297e11	−1.08822
$126$	2.74716e10	0.0770631
$127$	4.50859e11	1.21093	0.605467	−	0.795870i	$-0.292986\pi$
$127$	4.50859e11	1.21093	0.605467	+	0.795870i	$0.292986\pi$
$128$	−3.81681e11	−0.981851
$129$	1.28871e9	0.00317624
$130$	−1.35564e11	−0.320225
$131$	−4.06406e11	−0.920382	−0.460191	−	0.887820i	$-0.652219\pi$
$131$	−4.06406e11	−0.920382	−0.460191	+	0.887820i	$0.652219\pi$
$132$	3.65703e11	0.794277
$133$	−3.56723e11	−0.743271
$134$	2.58359e11	0.516592
$135$	−8.32100e10	−0.159713
$136$	7.61402e11	1.40330
$137$	−9.22476e11	−1.63302	−0.816511	−	0.577330i	$-0.804095\pi$
$137$	−9.22476e11	−1.63302	−0.816511	+	0.577330i	$0.804095\pi$
$138$	4.69033e10	0.0797753
$139$	1.60565e11	0.262463	0.131232	−	0.991352i	$-0.458107\pi$
$139$	1.60565e11	0.262463	0.131232	+	0.991352i	$0.458107\pi$
$140$	−2.06730e11	−0.324863
$141$	−2.22818e11	−0.336701
$142$	−8.86970e10	−0.128921
$143$	−1.04290e12	−1.45846
$144$	9.93957e10	0.133775
$145$	1.12482e12	1.45733
$146$	−1.32167e11	−0.164886
$147$	3.61020e11	0.433796
$148$	−1.02891e12	−1.19107
$149$	−4.86839e11	−0.543076	−0.271538	−	0.962428i	$-0.587532\pi$
$149$	−4.86839e11	−0.543076	−0.271538	+	0.962428i	$0.587532\pi$
$150$	7.74946e10	0.0833239
$151$	1.17088e12	1.21378	0.606891	−	0.794785i	$-0.292416\pi$
$151$	1.17088e12	1.21378	0.606891	+	0.794785i	$0.292416\pi$
$152$	1.23403e12	1.23364
$153$	−5.86143e11	−0.565198
$154$	4.35485e11	0.405144
$155$	1.32362e12	1.18833
$156$	−4.35280e11	−0.377210
$157$	−1.01892e11	−0.0852499	−0.0426250	−	0.999091i	$-0.513572\pi$
$157$	−1.01892e11	−0.0852499	−0.0426250	+	0.999091i	$0.513572\pi$
$158$	−1.09549e12	−0.885104
$159$	1.02213e12	0.797667
$160$	1.11579e12	0.841248
$161$	−2.03976e11	−0.148606
$162$	7.31594e10	0.0515155
$163$	−3.58023e11	−0.243713	−0.121857	−	0.992548i	$-0.538885\pi$
$163$	−3.58023e11	−0.243713	−0.121857	+	0.992548i	$0.538885\pi$
$164$	−4.17251e11	−0.274635
$165$	−1.31906e12	−0.839659
$166$	−1.59974e11	−0.0985044
$167$	−3.69568e11	−0.220168	−0.110084	−	0.993922i	$-0.535112\pi$
$167$	−3.69568e11	−0.220168	−0.110084	+	0.993922i	$0.535112\pi$
$168$	4.13291e11	0.238262
$169$	−5.50841e11	−0.307362
$170$	−1.20779e12	−0.652415
$171$	−9.49985e11	−0.496865
$172$	8.52651e9	0.00431882
$173$	−6.32932e11	−0.310530	−0.155265	−	0.987873i	$-0.549623\pi$
$173$	−6.32932e11	−0.310530	−0.155265	+	0.987873i	$0.549623\pi$
$174$	−9.88955e11	−0.470063
$175$	−3.37013e11	−0.155216
$176$	1.57564e12	0.703294
$177$	−1.73727e11	−0.0751646
$178$	−1.91172e12	−0.801888
$179$	6.95997e11	0.283084	0.141542	−	0.989932i	$-0.454794\pi$
$179$	6.95997e11	0.283084	0.141542	+	0.989932i	$0.454794\pi$
$180$	−5.50542e11	−0.217166
$181$	−1.21927e12	−0.466517	−0.233258	−	0.972415i	$-0.574939\pi$
$181$	−1.21927e12	−0.466517	−0.233258	+	0.972415i	$0.574939\pi$
$182$	−5.18339e11	−0.192407
$183$	2.08212e12	0.749937
$184$	7.05626e11	0.246647
$185$	3.71118e12	1.25912
$186$	−1.16374e12	−0.383298
$187$	−9.29165e12	−2.97142
$188$	−1.47423e12	−0.457821
$189$	−3.18160e11	−0.0959634
$190$	−1.95752e12	−0.573537
$191$	−2.61439e12	−0.744195	−0.372097	−	0.928194i	$-0.621361\pi$
$191$	−2.61439e12	−0.744195	−0.372097	+	0.928194i	$0.621361\pi$
$192$	−1.43317e11	−0.0396405
$193$	−8.15687e11	−0.219259	−0.109630	−	0.993972i	$-0.534966\pi$
$193$	−8.15687e11	−0.219259	−0.109630	+	0.993972i	$0.534966\pi$
$194$	3.11306e12	0.813352
$195$	1.57002e12	0.398763
$196$	2.38861e12	0.589845
$197$	−5.44207e12	−1.30677	−0.653386	−	0.757025i	$-0.726652\pi$
$197$	−5.44207e12	−1.30677	−0.653386	+	0.757025i	$0.726652\pi$
$198$	1.15974e12	0.270832
$199$	−2.55159e12	−0.579588	−0.289794	−	0.957089i	$-0.593587\pi$
$199$	−2.55159e12	−0.579588	−0.289794	+	0.957089i	$0.593587\pi$
$200$	1.16585e12	0.257619
$201$	−2.99216e12	−0.643290
$202$	1.42028e12	0.297126
$203$	4.30083e12	0.875636
$204$	−3.87809e12	−0.768515
$205$	1.50499e12	0.290326
$206$	−1.93949e12	−0.364264
$207$	−5.43206e11	−0.0993408
$208$	−1.87541e12	−0.334002
$209$	−1.50593e13	−2.61217
$210$	−6.55594e11	−0.110772
$211$	4.77860e12	0.786587	0.393294	−	0.919413i	$-0.371336\pi$
$211$	4.77860e12	0.786587	0.393294	+	0.919413i	$0.371336\pi$
$212$	6.76270e12	1.08461
$213$	1.02724e12	0.160540
$214$	−1.57660e11	−0.0240130
$215$	−3.07544e10	−0.00456558
$216$	1.10063e12	0.159274
$217$	5.06096e12	0.714011
$218$	−3.93187e12	−0.540864
$219$	1.53068e12	0.205325
$220$	−8.72729e12	−1.14171
$221$	1.10594e13	1.41116
$222$	−3.26292e12	−0.406130
$223$	9.75032e12	1.18397	0.591987	−	0.805948i	$-0.298344\pi$
$223$	9.75032e12	1.18397	0.591987	+	0.805948i	$0.298344\pi$
$224$	4.26633e12	0.505464
$225$	−8.97496e11	−0.103760
$226$	−1.30613e12	−0.147363
$227$	−1.40190e13	−1.54375	−0.771874	−	0.635776i	$-0.780680\pi$
$227$	−1.40190e13	−1.54375	−0.771874	+	0.635776i	$0.780680\pi$
$228$	−6.28538e12	−0.675600
$229$	−9.22670e12	−0.968169	−0.484085	−	0.875021i	$-0.660847\pi$
$229$	−9.22670e12	−0.968169	−0.484085	+	0.875021i	$0.660847\pi$
$230$	−1.11932e12	−0.114670
$231$	−5.04353e12	−0.504509
$232$	−1.48781e13	−1.45333
$233$	4.25657e12	0.406071	0.203036	−	0.979171i	$-0.434919\pi$
$233$	4.25657e12	0.406071	0.203036	+	0.979171i	$0.434919\pi$
$234$	−1.38038e12	−0.128621
$235$	5.31741e12	0.483979
$236$	−1.14943e12	−0.102203
$237$	1.26873e13	1.10218
$238$	−4.61810e12	−0.392004
$239$	−3.90272e12	−0.323727	−0.161864	−	0.986813i	$-0.551750\pi$
$239$	−3.90272e12	−0.323727	−0.161864	+	0.986813i	$0.551750\pi$
$240$	−2.37202e12	−0.192290
$241$	−1.17046e13	−0.927393	−0.463697	−	0.885994i	$-0.653477\pi$
$241$	−1.17046e13	−0.927393	−0.463697	+	0.885994i	$0.653477\pi$
$242$	1.23980e13	0.960209
$243$	−8.47289e11	−0.0641500
$244$	1.37759e13	1.01971
$245$	−8.61553e12	−0.623546
$246$	−1.32321e12	−0.0936450
$247$	1.79245e13	1.24055
$248$	−1.75077e13	−1.18507
$249$	1.85273e12	0.122663
$250$	−7.79053e12	−0.504542
$251$	1.43145e13	0.906925	0.453462	−	0.891275i	$-0.350189\pi$
$251$	1.43145e13	0.906925	0.453462	+	0.891275i	$0.350189\pi$
$252$	−2.10504e12	−0.130484
$253$	−8.61100e12	−0.522265
$254$	9.45989e12	0.561437
$255$	1.39880e13	0.812425
$256$	−9.21626e12	−0.523884
$257$	−3.42210e13	−1.90397	−0.951986	−	0.306143i	$-0.900961\pi$
$257$	−3.42210e13	−1.90397	−0.951986	+	0.306143i	$0.900961\pi$
$258$	2.70397e10	0.00147263
$259$	1.41900e13	0.756543
$260$	1.03877e13	0.542208
$261$	1.14535e13	0.585349
$262$	−8.52718e12	−0.426725
$263$	1.24549e13	0.610358	0.305179	−	0.952295i	$-0.401284\pi$
$263$	1.24549e13	0.610358	0.305179	+	0.952295i	$0.401284\pi$
$264$	1.74474e13	0.837354
$265$	−2.43925e13	−1.14658
$266$	−7.48473e12	−0.344610
$267$	2.21404e13	0.998556
$268$	−1.97970e13	−0.874699
$269$	−4.26154e12	−0.184472	−0.0922358	−	0.995737i	$-0.529401\pi$
$269$	−4.26154e12	−0.184472	−0.0922358	+	0.995737i	$0.529401\pi$
$270$	−1.74591e12	−0.0740491
$271$	−1.52799e11	−0.00635022	−0.00317511	−	0.999995i	$-0.501011\pi$
$271$	−1.52799e11	−0.00635022	−0.00317511	+	0.999995i	$0.501011\pi$
$272$	−1.67088e13	−0.680483
$273$	6.00309e12	0.239596
$274$	−1.93553e13	−0.757133
$275$	−1.42273e13	−0.545496
$276$	−3.59401e12	−0.135076
$277$	−3.10248e13	−1.14306	−0.571532	−	0.820579i	$-0.693651\pi$
$277$	−3.10248e13	−1.14306	−0.571532	+	0.820579i	$0.693651\pi$
$278$	3.36896e12	0.121688
$279$	1.34778e13	0.477305
$280$	−9.86294e12	−0.342482
$281$	−5.05962e13	−1.72279	−0.861397	−	0.507932i	$-0.830410\pi$
$281$	−5.05962e13	−1.72279	−0.861397	+	0.507932i	$0.830410\pi$
$282$	−4.67514e12	−0.156108
$283$	−3.42911e13	−1.12294	−0.561469	−	0.827498i	$-0.689764\pi$
$283$	−3.42911e13	−1.12294	−0.561469	+	0.827498i	$0.689764\pi$
$284$	6.79649e12	0.218290
$285$	2.26708e13	0.714201
$286$	−2.18821e13	−0.676200
$287$	5.75444e12	0.174443
$288$	1.13616e13	0.337895
$289$	6.42612e13	1.87504
$290$	2.36008e13	0.675675
$291$	−3.60536e13	−1.01283
$292$	1.01274e13	0.279186
$293$	−9.74901e12	−0.263748	−0.131874	−	0.991267i	$-0.542099\pi$
$293$	−9.74901e12	−0.263748	−0.131874	+	0.991267i	$0.542099\pi$
$294$	7.57489e12	0.201125
$295$	4.14588e12	0.108043
$296$	−4.90883e13	−1.25567
$297$	−1.34314e13	−0.337256
$298$	−1.02148e13	−0.251791
$299$	1.02493e13	0.248029
$300$	−5.93810e12	−0.141085
$301$	−1.17592e11	−0.00274323
$302$	2.45674e13	0.562757
$303$	−1.64488e13	−0.369998
$304$	−2.70807e13	−0.598212
$305$	−4.96885e13	−1.07797
$306$	−1.22984e13	−0.262048
$307$	3.11117e13	0.651122	0.325561	−	0.945521i	$-0.394447\pi$
$307$	3.11117e13	0.651122	0.325561	+	0.945521i	$0.394447\pi$
$308$	−3.33695e13	−0.685994
$309$	2.24620e13	0.453603
$310$	2.77721e13	0.550958
$311$	−6.72271e13	−1.31027	−0.655137	−	0.755510i	$-0.727389\pi$
$311$	−6.72271e13	−1.31027	−0.655137	+	0.755510i	$0.727389\pi$
$312$	−2.07669e13	−0.397668
$313$	1.61471e13	0.303809	0.151905	−	0.988395i	$-0.451459\pi$
$313$	1.61471e13	0.303809	0.151905	+	0.988395i	$0.451459\pi$
$314$	−2.13790e12	−0.0395252
$315$	7.59270e12	0.137939
$316$	8.39429e13	1.49867
$317$	6.58020e13	1.15455	0.577276	−	0.816549i	$-0.304116\pi$
$317$	6.58020e13	1.15455	0.577276	+	0.816549i	$0.304116\pi$
$318$	2.14462e13	0.369830
$319$	1.81563e14	3.07736
$320$	3.42016e12	0.0569799
$321$	1.82592e12	0.0299023
$322$	−4.27980e12	−0.0688996
$323$	1.59697e14	2.52744
$324$	−5.60591e12	−0.0872265
$325$	1.69341e13	0.259062
$326$	−7.51201e12	−0.112995
$327$	4.55366e13	0.673515
$328$	−1.99067e13	−0.289529
$329$	2.03315e13	0.290799
$330$	−2.76764e13	−0.389299
$331$	−2.91682e13	−0.403511	−0.201755	−	0.979436i	$-0.564665\pi$
$331$	−2.91682e13	−0.403511	−0.201755	+	0.979436i	$0.564665\pi$
$332$	1.22582e13	0.166789
$333$	3.77892e13	0.505737
$334$	−7.75425e12	−0.102078
$335$	7.14062e13	0.924675
$336$	−9.06960e12	−0.115537
$337$	−1.82154e13	−0.228283	−0.114142	−	0.993464i	$-0.536412\pi$
$337$	−1.82154e13	−0.228283	−0.114142	+	0.993464i	$0.536412\pi$
$338$	−1.15577e13	−0.142505
$339$	1.51268e13	0.183505
$340$	9.25484e13	1.10468
$341$	2.13652e14	2.50934
$342$	−1.99325e13	−0.230366
$343$	−7.67857e13	−0.873298
$344$	4.06793e11	0.00455304
$345$	1.29633e13	0.142794
$346$	−1.32801e13	−0.143974
$347$	−6.67404e13	−0.712159	−0.356079	−	0.934456i	$-0.615887\pi$
$347$	−6.67404e13	−0.712159	−0.356079	+	0.934456i	$0.615887\pi$
$348$	7.57796e13	0.795915
$349$	−1.11830e14	−1.15616	−0.578081	−	0.815979i	$-0.696198\pi$
$349$	−1.11830e14	−1.15616	−0.578081	+	0.815979i	$0.696198\pi$
$350$	−7.07118e12	−0.0719644
$351$	1.59868e13	0.160166
$352$	1.80106e14	1.77641
$353$	1.25238e13	0.121612	0.0608058	−	0.998150i	$-0.480633\pi$
$353$	1.25238e13	0.121612	0.0608058	+	0.998150i	$0.480633\pi$
$354$	−3.64512e12	−0.0348493
$355$	−2.45143e13	−0.230762
$356$	1.46487e14	1.35776
$357$	5.34840e13	0.488145
$358$	1.46034e13	0.131249
$359$	2.07626e14	1.83765	0.918825	−	0.394665i	$-0.129139\pi$
$359$	2.07626e14	1.83765	0.918825	+	0.394665i	$0.129139\pi$
$360$	−2.62659e13	−0.228943
$361$	1.42336e14	1.22187
$362$	−2.55826e13	−0.216295
$363$	−1.43586e14	−1.19571
$364$	3.97182e13	0.325786
$365$	−3.65288e13	−0.295137
$366$	4.36869e13	0.347700
$367$	−3.41773e13	−0.267963	−0.133981	−	0.990984i	$-0.542776\pi$
$367$	−3.41773e13	−0.267963	−0.133981	+	0.990984i	$0.542776\pi$
$368$	−1.54849e13	−0.119604
$369$	1.53246e13	0.116612
$370$	7.78677e13	0.583778
$371$	−9.32666e13	−0.688921
$372$	8.91730e13	0.649004
$373$	3.25095e13	0.233137	0.116568	−	0.993183i	$-0.462811\pi$
$373$	3.25095e13	0.233137	0.116568	+	0.993183i	$0.462811\pi$
$374$	−1.94957e14	−1.37767
$375$	9.02253e13	0.628284
$376$	−7.03341e13	−0.482651
$377$	−2.16106e14	−1.46147
$378$	−6.67561e12	−0.0444924
$379$	−1.12920e14	−0.741749	−0.370874	−	0.928683i	$-0.620942\pi$
$379$	−1.12920e14	−0.741749	−0.370874	+	0.928683i	$0.620942\pi$
$380$	1.49997e14	0.971118
$381$	−1.09559e14	−0.699133
$382$	−5.48549e13	−0.345038
$383$	−1.21687e14	−0.754488	−0.377244	−	0.926114i	$-0.623128\pi$
$383$	−1.21687e14	−0.754488	−0.377244	+	0.926114i	$0.623128\pi$
$384$	9.27484e13	0.566872
$385$	1.20361e14	0.725189
$386$	−1.71147e13	−0.101657
$387$	−3.13158e11	−0.00183380
$388$	−2.38541e14	−1.37718
$389$	1.67697e14	0.954559	0.477280	−	0.878751i	$-0.341623\pi$
$389$	1.67697e14	0.954559	0.477280	+	0.878751i	$0.341623\pi$
$390$	3.29420e13	0.184882
$391$	9.13152e13	0.505325
$392$	1.13959e14	0.621834
$393$	9.87566e13	0.531383
$394$	−1.14185e14	−0.605871
$395$	−3.02775e14	−1.58429
$396$	−8.88659e13	−0.458576
$397$	−1.86310e14	−0.948174	−0.474087	−	0.880478i	$-0.657222\pi$
$397$	−1.86310e14	−0.948174	−0.474087	+	0.880478i	$0.657222\pi$
$398$	−5.35374e13	−0.268720
$399$	8.66837e13	0.429128
$400$	−2.55844e13	−0.124924
$401$	−1.10456e14	−0.531981	−0.265990	−	0.963976i	$-0.585699\pi$
$401$	−1.10456e14	−0.531981	−0.265990	+	0.963976i	$0.585699\pi$
$402$	−6.27813e13	−0.298255
$403$	−2.54301e14	−1.19171
$404$	−1.08830e14	−0.503096
$405$	2.02200e13	0.0922102
$406$	9.02396e13	0.405979
$407$	5.99042e14	2.65881
$408$	−1.85021e14	−0.810195
$409$	3.44348e14	1.48771	0.743856	−	0.668340i	$-0.232995\pi$
$409$	3.44348e14	1.48771	0.743856	+	0.668340i	$0.232995\pi$
$410$	3.15775e13	0.134607
$411$	2.24162e14	0.942825
$412$	1.48615e14	0.616776
$413$	1.58521e13	0.0649175
$414$	−1.13975e13	−0.0460583
$415$	−4.42142e13	−0.176318
$416$	−2.14373e14	−0.843637
$417$	−3.90172e13	−0.151533
$418$	−3.15974e14	−1.21110
$419$	−9.24903e13	−0.349880	−0.174940	−	0.984579i	$-0.555973\pi$
$419$	−9.24903e13	−0.349880	−0.174940	+	0.984579i	$0.555973\pi$
$420$	5.02355e13	0.187560
$421$	1.47656e14	0.544127	0.272064	−	0.962279i	$-0.412294\pi$
$421$	1.47656e14	0.544127	0.272064	+	0.962279i	$0.412294\pi$
$422$	1.00264e14	0.364693
$423$	5.41447e13	0.194394
$424$	3.22643e14	1.14343
$425$	1.50873e14	0.527803
$426$	2.15534e13	0.0744325
$427$	−1.89988e14	−0.647699
$428$	1.20808e13	0.0406590
$429$	2.53425e14	0.842043
$430$	−6.45286e11	−0.00211678
$431$	3.73758e14	1.21050	0.605252	−	0.796034i	$-0.293072\pi$
$431$	3.73758e14	1.21050	0.605252	+	0.796034i	$0.293072\pi$
$432$	−2.41532e13	−0.0772349
$433$	3.24128e13	0.102337	0.0511685	−	0.998690i	$-0.483705\pi$
$433$	3.24128e13	0.102337	0.0511685	+	0.998690i	$0.483705\pi$
$434$	1.06189e14	0.331043
$435$	−2.73331e14	−0.841390
$436$	3.01283e14	0.915797
$437$	1.47998e14	0.444230
$438$	3.21166e13	0.0951967
$439$	−1.98839e14	−0.582031	−0.291015	−	0.956718i	$-0.593993\pi$
$439$	−1.98839e14	−0.582031	−0.291015	+	0.956718i	$0.593993\pi$
$440$	−4.16371e14	−1.20363
$441$	−8.77279e13	−0.250453
$442$	2.32048e14	0.654268
$443$	−4.47598e14	−1.24643	−0.623214	−	0.782051i	$-0.714174\pi$
$443$	−4.47598e14	−1.24643	−0.623214	+	0.782051i	$0.714174\pi$
$444$	2.50025e14	0.687664
$445$	−5.28366e14	−1.43534
$446$	2.04580e14	0.548937
$447$	1.18302e14	0.313545
$448$	1.30773e13	0.0342364
$449$	1.09020e14	0.281937	0.140969	−	0.990014i	$-0.454978\pi$
$449$	1.09020e14	0.281937	0.140969	+	0.990014i	$0.454978\pi$
$450$	−1.88312e13	−0.0481071
$451$	2.42928e14	0.613065
$452$	1.00083e14	0.249517
$453$	−2.84525e14	−0.700778
$454$	−2.94147e14	−0.715742
$455$	−1.43260e14	−0.344400
$456$	−2.99870e14	−0.712241
$457$	−5.84990e14	−1.37281	−0.686403	−	0.727222i	$-0.740811\pi$
$457$	−5.84990e14	−1.37281	−0.686403	+	0.727222i	$0.740811\pi$
$458$	−1.93594e14	−0.448881
$459$	1.42433e14	0.326317
$460$	8.57688e13	0.194161
$461$	5.81689e14	1.30117	0.650587	−	0.759432i	$-0.274523\pi$
$461$	5.81689e14	1.30117	0.650587	+	0.759432i	$0.274523\pi$
$462$	−1.05823e14	−0.233910
$463$	−4.75087e14	−1.03771	−0.518857	−	0.854861i	$-0.673642\pi$
$463$	−4.75087e14	−1.03771	−0.518857	+	0.854861i	$0.673642\pi$
$464$	3.26498e14	0.704744
$465$	−3.21639e14	−0.686085
$466$	8.93111e13	0.188271
$467$	−7.16934e14	−1.49361	−0.746803	−	0.665045i	$-0.768412\pi$
$467$	−7.16934e14	−1.49361	−0.746803	+	0.665045i	$0.768412\pi$
$468$	1.05773e14	0.217783
$469$	2.73027e14	0.555591
$470$	1.11569e14	0.224392
$471$	2.47599e13	0.0492191
$472$	−5.48382e13	−0.107746
$473$	−4.96423e12	−0.00964086
$474$	2.66204e14	0.511015
$475$	2.44526e14	0.463991
$476$	3.53866e14	0.663744
$477$	−2.48377e14	−0.460533
$478$	−8.18866e13	−0.150093
$479$	7.87256e14	1.42650	0.713248	−	0.700912i	$-0.247223\pi$
$479$	7.87256e14	1.42650	0.713248	+	0.700912i	$0.247223\pi$
$480$	−2.71138e14	−0.485695
$481$	−7.13013e14	−1.26270
$482$	−2.45586e14	−0.429976
$483$	4.95661e13	0.0857977
$484$	−9.50005e14	−1.62584
$485$	8.60398e14	1.45586
$486$	−1.77777e13	−0.0297425
$487$	3.00862e14	0.497689	0.248844	−	0.968543i	$-0.419949\pi$
$487$	3.00862e14	0.497689	0.248844	+	0.968543i	$0.419949\pi$
$488$	6.57238e14	1.07501
$489$	8.69995e13	0.140708
$490$	−1.80770e14	−0.289100
$491$	1.05712e14	0.167177	0.0835887	−	0.996500i	$-0.473362\pi$
$491$	1.05712e14	0.167177	0.0835887	+	0.996500i	$0.473362\pi$
$492$	1.01392e14	0.158561
$493$	−1.92538e15	−2.97754
$494$	3.76090e14	0.575166
$495$	3.20532e14	0.484777
$496$	3.84204e14	0.574662
$497$	−9.37326e13	−0.138653
$498$	3.88737e13	0.0568715
$499$	−1.27645e15	−1.84694	−0.923469	−	0.383673i	$-0.874659\pi$
$499$	−1.27645e15	−1.84694	−0.923469	+	0.383673i	$0.874659\pi$
$500$	5.96957e14	0.854295
$501$	8.98051e13	0.127114
$502$	3.00346e14	0.420486
$503$	−6.89981e14	−0.955462	−0.477731	−	0.878506i	$-0.658541\pi$
$503$	−6.89981e14	−0.955462	−0.477731	+	0.878506i	$0.658541\pi$
$504$	−1.00430e14	−0.137561
$505$	3.92540e14	0.531841
$506$	−1.80675e14	−0.242142
$507$	1.33854e14	0.177455
$508$	−7.24873e14	−0.950630
$509$	−1.24066e14	−0.160955	−0.0804776	−	0.996756i	$-0.525645\pi$
$509$	−1.24066e14	−0.160955	−0.0804776	+	0.996756i	$0.525645\pi$
$510$	2.93494e14	0.376672
$511$	−1.39671e14	−0.177333
$512$	5.88307e14	0.738957
$513$	2.30846e14	0.286865
$514$	−7.18022e14	−0.882756
$515$	−5.36041e14	−0.652016
$516$	−2.07194e12	−0.00249347
$517$	8.58311e14	1.02199
$518$	2.97733e14	0.350763
$519$	1.53803e14	0.179285
$520$	4.95588e14	0.571614
$521$	1.85354e14	0.211541	0.105771	−	0.994391i	$-0.466269\pi$
$521$	1.85354e14	0.211541	0.105771	+	0.994391i	$0.466269\pi$
$522$	2.40316e14	0.271391
$523$	−4.44489e14	−0.496708	−0.248354	−	0.968669i	$-0.579890\pi$
$523$	−4.44489e14	−0.496708	−0.248354	+	0.968669i	$0.579890\pi$
$524$	6.53403e14	0.722535
$525$	8.18942e13	0.0896142
$526$	2.61328e14	0.282986
$527$	−2.26567e15	−2.42795
$528$	−3.82880e14	−0.406047
$529$	−8.68184e14	−0.911183
$530$	−5.11801e14	−0.531599
$531$	4.22156e13	0.0433963
$532$	5.73525e14	0.583496
$533$	−2.89146e14	−0.291151
$534$	4.64547e14	0.462970
$535$	−4.35746e13	−0.0429821
$536$	−9.44500e14	−0.922137
$537$	−1.69127e14	−0.163439
$538$	−8.94153e13	−0.0855282
$539$	−1.39068e15	−1.31670
$540$	1.33782e14	0.125381
$541$	2.10768e15	1.95533	0.977665	−	0.210169i	$-0.0674014\pi$
$541$	2.10768e15	1.95533	0.977665	+	0.210169i	$0.0674014\pi$
$542$	−3.20601e12	−0.00294421
$543$	2.96282e14	0.269343
$544$	−1.90993e15	−1.71880
$545$	−1.08670e15	−0.968121
$546$	1.25956e14	0.111086
$547$	−1.26350e14	−0.110317	−0.0551587	−	0.998478i	$-0.517566\pi$
$547$	−1.26350e14	−0.110317	−0.0551587	+	0.998478i	$0.517566\pi$
$548$	1.48312e15	1.28198
$549$	−5.05955e14	−0.432976
$550$	−2.98515e14	−0.252913
$551$	−3.12054e15	−2.61755
$552$	−1.71467e14	−0.142402
$553$	−1.15768e15	−0.951922
$554$	−6.50961e14	−0.529970
$555$	−9.01817e14	−0.726954
$556$	−2.58149e14	−0.206044
$557$	1.08838e15	0.860152	0.430076	−	0.902793i	$-0.358487\pi$
$557$	1.08838e15	0.860152	0.430076	+	0.902793i	$0.358487\pi$
$558$	2.82790e14	0.221297
$559$	5.90870e12	0.00457854
$560$	2.16441e14	0.166075
$561$	2.25787e15	1.71555
$562$	−1.06161e15	−0.798755
$563$	1.44529e15	1.07686	0.538429	−	0.842671i	$-0.319018\pi$
$563$	1.44529e15	1.07686	0.538429	+	0.842671i	$0.319018\pi$
$564$	3.58237e14	0.264323
$565$	−3.60991e14	−0.263773
$566$	−7.19493e14	−0.520638
$567$	7.73129e13	0.0554045
$568$	3.24255e14	0.230129
$569$	1.80278e15	1.26714	0.633571	−	0.773685i	$-0.281588\pi$
$569$	1.80278e15	1.26714	0.633571	+	0.773685i	$0.281588\pi$
$570$	4.75677e14	0.331132
$571$	−2.82982e13	−0.0195101	−0.00975506	−	0.999952i	$-0.503105\pi$
$571$	−2.82982e13	−0.0195101	−0.00975506	+	0.999952i	$0.503105\pi$
$572$	1.67673e15	1.14495
$573$	6.35296e14	0.429661
$574$	1.20739e14	0.0808784
$575$	1.39821e14	0.0927681
$576$	3.48259e13	0.0228865
$577$	−9.32447e14	−0.606956	−0.303478	−	0.952838i	$-0.598148\pi$
$577$	−9.32447e14	−0.606956	−0.303478	+	0.952838i	$0.598148\pi$
$578$	1.34832e15	0.869343
$579$	1.98212e14	0.126589
$580$	−1.80843e15	−1.14406
$581$	−1.69056e14	−0.105941
$582$	−7.56475e14	−0.469589
$583$	−3.93732e15	−2.42116
$584$	4.83171e14	0.294327
$585$	−3.81514e14	−0.230226
$586$	−2.04553e14	−0.122284
$587$	−2.28177e15	−1.35134	−0.675668	−	0.737206i	$-0.736145\pi$
$587$	−2.28177e15	−1.35134	−0.675668	+	0.737206i	$0.736145\pi$
$588$	−5.80433e14	−0.340547
$589$	−3.67207e15	−2.13440
$590$	8.69885e13	0.0500929
$591$	1.32242e15	0.754465
$592$	1.07724e15	0.608893
$593$	3.18237e15	1.78217	0.891085	−	0.453835i	$-0.149945\pi$
$593$	3.18237e15	1.78217	0.891085	+	0.453835i	$0.149945\pi$
$594$	−2.81816e14	−0.156365
$595$	−1.27636e15	−0.701668
$596$	7.82719e14	0.426336
$597$	6.20037e14	0.334626
$598$	2.15050e14	0.114996
$599$	1.65920e15	0.879127	0.439564	−	0.898211i	$-0.355133\pi$
$599$	1.65920e15	0.879127	0.439564	+	0.898211i	$0.355133\pi$
$600$	−2.83302e14	−0.148736
$601$	−1.92039e15	−0.999034	−0.499517	−	0.866304i	$-0.666489\pi$
$601$	−1.92039e15	−0.999034	−0.499517	+	0.866304i	$0.666489\pi$
$602$	−2.46730e12	−0.00127187
$603$	7.27096e14	0.371404
$604$	−1.88250e15	−0.952866
$605$	3.42659e15	1.71873
$606$	−3.45127e14	−0.171546
$607$	3.30391e15	1.62738	0.813692	−	0.581296i	$-0.197454\pi$
$607$	3.30391e15	1.62738	0.813692	+	0.581296i	$0.197454\pi$
$608$	−3.09551e15	−1.51099
$609$	−1.04510e15	−0.505549
$610$	−1.04256e15	−0.499790
$611$	−1.02161e15	−0.485354
$612$	9.42377e14	0.443702
$613$	−1.00720e15	−0.469984	−0.234992	−	0.971997i	$-0.575506\pi$
$613$	−1.00720e15	−0.469984	−0.234992	+	0.971997i	$0.575506\pi$
$614$	6.52782e14	0.301886
$615$	−3.65712e14	−0.167620
$616$	−1.59203e15	−0.723198
$617$	1.41632e15	0.637666	0.318833	−	0.947811i	$-0.396709\pi$
$617$	1.41632e15	0.637666	0.318833	+	0.947811i	$0.396709\pi$
$618$	4.71295e14	0.210308
$619$	2.38868e15	1.05648	0.528238	−	0.849096i	$-0.322853\pi$
$619$	2.38868e15	1.05648	0.528238	+	0.849096i	$0.322853\pi$
$620$	−2.12806e15	−0.932888
$621$	1.31999e14	0.0573544
$622$	−1.41055e15	−0.607494
$623$	−2.02025e15	−0.862424
$624$	4.55725e14	0.192836
$625$	−1.41102e15	−0.591826
$626$	3.38798e14	0.140858
$627$	3.65942e15	1.50814
$628$	1.63819e14	0.0669245
$629$	−6.35253e15	−2.57258
$630$	1.59309e14	0.0639541
$631$	3.09629e15	1.23220	0.616099	−	0.787669i	$-0.288712\pi$
$631$	3.09629e15	1.23220	0.616099	+	0.787669i	$0.288712\pi$
$632$	4.00484e15	1.57994
$633$	−1.16120e15	−0.454136
$634$	1.38065e15	0.535296
$635$	2.61455e15	1.00494
$636$	−1.64334e15	−0.626199
$637$	1.65526e15	0.625317
$638$	3.80953e15	1.42678
$639$	−2.49618e14	−0.0926876
$640$	−2.21338e15	−0.814830
$641$	2.23695e15	0.816463	0.408232	−	0.912878i	$-0.366146\pi$
$641$	2.23695e15	0.816463	0.408232	+	0.912878i	$0.366146\pi$
$642$	3.83114e13	0.0138639
$643$	3.70986e15	1.33106	0.665529	−	0.746372i	$-0.268206\pi$
$643$	3.70986e15	1.33106	0.665529	+	0.746372i	$0.268206\pi$
$644$	3.27944e14	0.116661
$645$	7.47332e12	0.00263594
$646$	3.35074e15	1.17182
$647$	3.78140e15	1.31123	0.655615	−	0.755096i	$-0.272410\pi$
$647$	3.78140e15	1.31123	0.655615	+	0.755096i	$0.272410\pi$
$648$	−2.67453e14	−0.0919571
$649$	6.69209e14	0.228148
$650$	3.55310e14	0.120111
$651$	−1.22981e15	−0.412234
$652$	5.75614e14	0.191324
$653$	4.33846e15	1.42992	0.714962	−	0.699163i	$-0.246444\pi$
$653$	4.33846e15	1.42992	0.714962	+	0.699163i	$0.246444\pi$
$654$	9.55444e14	0.312268
$655$	−2.35677e15	−0.763817
$656$	4.36849e14	0.140398
$657$	−3.71955e14	−0.118544
$658$	4.26595e14	0.134826
$659$	1.70685e15	0.534965	0.267482	−	0.963563i	$-0.413808\pi$
$659$	1.70685e15	0.534965	0.267482	+	0.963563i	$0.413808\pi$
$660$	2.12073e15	0.659164
$661$	2.39059e15	0.736880	0.368440	−	0.929651i	$-0.379892\pi$
$661$	2.39059e15	0.736880	0.368440	+	0.929651i	$0.379892\pi$
$662$	−6.12004e14	−0.187084
$663$	−2.68744e15	−0.814732
$664$	5.84827e14	0.175834
$665$	−2.06865e15	−0.616835
$666$	7.92891e14	0.234480
$667$	−1.78434e15	−0.523341
$668$	5.94177e14	0.172840
$669$	−2.36933e15	−0.683567
$670$	1.49824e15	0.428716
$671$	−8.02049e15	−2.27629
$672$	−1.03672e15	−0.291830
$673$	−4.28194e15	−1.19552	−0.597761	−	0.801674i	$-0.703943\pi$
$673$	−4.28194e15	−1.19552	−0.597761	+	0.801674i	$0.703943\pi$
$674$	−3.82194e14	−0.105841
$675$	2.18092e14	0.0599057
$676$	8.85620e14	0.241291
$677$	2.18531e14	0.0590576	0.0295288	−	0.999564i	$-0.490599\pi$
$677$	2.18531e14	0.0590576	0.0295288	+	0.999564i	$0.490599\pi$
$678$	3.17389e14	0.0850802
$679$	3.28980e15	0.874754
$680$	4.41541e15	1.16459
$681$	3.40663e15	0.891283
$682$	4.48284e15	1.16343
$683$	−4.04892e15	−1.04238	−0.521189	−	0.853441i	$-0.674511\pi$
$683$	−4.04892e15	−1.04238	−0.521189	+	0.853441i	$0.674511\pi$
$684$	1.52735e15	0.390058
$685$	−5.34948e15	−1.35523
$686$	−1.61111e15	−0.404895
$687$	2.24209e15	0.558973
$688$	−8.92700e12	−0.00220785
$689$	4.68642e15	1.14983
$690$	2.71994e14	0.0662049
$691$	−1.81826e15	−0.439062	−0.219531	−	0.975606i	$-0.570453\pi$
$691$	−1.81826e15	−0.439062	−0.219531	+	0.975606i	$0.570453\pi$
$692$	1.01760e15	0.243778
$693$	1.22558e15	0.291278
$694$	−1.40034e15	−0.330185
$695$	9.31122e14	0.217816
$696$	3.61538e15	0.839080
$697$	−2.57613e15	−0.593181
$698$	−2.34641e15	−0.536042
$699$	−1.03435e15	−0.234445
$700$	5.41836e14	0.121851
$701$	2.38322e15	0.531759	0.265879	−	0.964006i	$-0.414338\pi$
$701$	2.38322e15	0.531759	0.265879	+	0.964006i	$0.414338\pi$
$702$	3.35433e14	0.0742594
$703$	−1.02958e16	−2.26155
$704$	5.52067e14	0.120321
$705$	−1.29213e15	−0.279426
$706$	2.62773e14	0.0563839
$707$	1.50091e15	0.319556
$708$	2.79311e14	0.0590071
$709$	2.96484e15	0.621509	0.310754	−	0.950490i	$-0.399418\pi$
$709$	2.96484e15	0.621509	0.310754	+	0.950490i	$0.399418\pi$
$710$	−5.14358e14	−0.106990
$711$	−3.08301e15	−0.636345
$712$	6.98878e15	1.43140
$713$	−2.09970e15	−0.426742
$714$	1.12220e15	0.226323
$715$	−6.04784e15	−1.21037
$716$	−1.11900e15	−0.222232
$717$	9.48362e14	0.186904
$718$	4.35640e15	0.852007
$719$	−4.68185e15	−0.908675	−0.454338	−	0.890830i	$-0.650124\pi$
$719$	−4.68185e15	−0.908675	−0.454338	+	0.890830i	$0.650124\pi$
$720$	5.76401e14	0.111019
$721$	−2.04960e15	−0.391764
$722$	2.98649e15	0.566508
$723$	2.84423e15	0.535431
$724$	1.96029e15	0.366233
$725$	−2.94812e15	−0.546621
$726$	−3.01271e15	−0.554377
$727$	−6.06976e15	−1.10849	−0.554246	−	0.832353i	$-0.686993\pi$
$727$	−6.06976e15	−1.10849	−0.554246	+	0.832353i	$0.686993\pi$
$728$	1.89492e15	0.343454
$729$	2.05891e14	0.0370370
$730$	−7.66443e14	−0.136837
$731$	5.26431e13	0.00932816
$732$	−3.34755e15	−0.588730
$733$	6.27486e15	1.09530	0.547649	−	0.836708i	$-0.315523\pi$
$733$	6.27486e15	1.09530	0.547649	+	0.836708i	$0.315523\pi$
$734$	−7.17105e14	−0.124238
$735$	2.09357e15	0.360004
$736$	−1.77002e15	−0.302100
$737$	1.15261e16	1.95258
$738$	3.21539e14	0.0540659
$739$	5.07444e15	0.846923	0.423461	−	0.905914i	$-0.360815\pi$
$739$	5.07444e15	0.846923	0.423461	+	0.905914i	$0.360815\pi$
$740$	−5.96668e15	−0.988459
$741$	−4.35564e15	−0.716229
$742$	−1.95691e15	−0.319411
$743$	5.18914e15	0.840731	0.420365	−	0.907355i	$-0.361902\pi$
$743$	5.18914e15	0.840731	0.420365	+	0.907355i	$0.361902\pi$
$744$	4.25437e15	0.684202
$745$	−2.82320e15	−0.450694
$746$	6.82111e14	0.108091
$747$	−4.50212e14	−0.0708197
$748$	1.49387e16	2.33268
$749$	−1.66611e14	−0.0258258
$750$	1.89310e15	0.291297
$751$	1.07342e16	1.63964	0.819822	−	0.572619i	$-0.194072\pi$
$751$	1.07342e16	1.63964	0.819822	+	0.572619i	$0.194072\pi$
$752$	1.54347e15	0.234046
$753$	−3.47843e15	−0.523613
$754$	−4.53432e15	−0.677594
$755$	6.79002e15	1.00731
$756$	5.11525e14	0.0753350
$757$	−3.18630e15	−0.465865	−0.232932	−	0.972493i	$-0.574832\pi$
$757$	−3.18630e15	−0.465865	−0.232932	+	0.972493i	$0.574832\pi$
$758$	−2.36929e15	−0.343904
$759$	2.09247e15	0.301530
$760$	7.15622e15	1.02379
$761$	−5.24754e15	−0.745315	−0.372657	−	0.927969i	$-0.621553\pi$
$761$	−5.24754e15	−0.745315	−0.372657	+	0.927969i	$0.621553\pi$
$762$	−2.29875e15	−0.324146
$763$	−4.15509e15	−0.581696
$764$	4.20331e15	0.584221
$765$	−3.39907e15	−0.469054
$766$	−2.55323e15	−0.349810
$767$	−7.96529e14	−0.108350
$768$	2.23955e15	0.302465
$769$	−2.97443e15	−0.398850	−0.199425	−	0.979913i	$-0.563907\pi$
$769$	−2.97443e15	−0.398850	−0.199425	+	0.979913i	$0.563907\pi$
$770$	2.52540e15	0.336226
$771$	8.31570e15	1.09926
$772$	1.31143e15	0.172127
$773$	4.08767e15	0.532707	0.266353	−	0.963875i	$-0.414181\pi$
$773$	4.08767e15	0.532707	0.266353	+	0.963875i	$0.414181\pi$
$774$	−6.57065e12	−0.000850223 0
$775$	−3.46918e15	−0.445725
$776$	−1.13806e16	−1.45187
$777$	−3.44817e15	−0.436790
$778$	3.51861e15	0.442571
$779$	−4.17523e15	−0.521464
$780$	−2.52421e15	−0.313044
$781$	−3.95699e15	−0.487287
$782$	1.91597e15	0.234289
$783$	−2.78320e15	−0.337951
$784$	−2.50081e15	−0.301538
$785$	−5.90879e14	−0.0707482
$786$	2.07210e15	0.246370
$787$	−1.59650e16	−1.88498	−0.942491	−	0.334233i	$-0.891523\pi$
$787$	−1.59650e16	−1.88498	−0.942491	+	0.334233i	$0.891523\pi$
$788$	8.74954e15	1.02587
$789$	−3.02655e15	−0.352390
$790$	−6.35279e15	−0.734540
$791$	−1.38028e15	−0.158488
$792$	−4.23972e15	−0.483446
$793$	9.54644e15	1.08103
$794$	−3.90914e15	−0.439611
$795$	5.92737e15	0.661977
$796$	4.10235e15	0.454999
$797$	−1.32433e15	−0.145873	−0.0729365	−	0.997337i	$-0.523237\pi$
$797$	−1.32433e15	−0.145873	−0.0729365	+	0.997337i	$0.523237\pi$
$798$	1.81879e15	0.198960
$799$	−9.10195e15	−0.988843
$800$	−2.92447e15	−0.315538
$801$	−5.38011e15	−0.576517
$802$	−2.31758e15	−0.246647
$803$	−5.89630e15	−0.623224
$804$	4.81068e15	0.505008
$805$	−1.18287e15	−0.123327
$806$	−5.33572e15	−0.552523
$807$	1.03555e15	0.106505
$808$	−5.19219e15	−0.530381
$809$	1.26213e16	1.28052	0.640262	−	0.768157i	$-0.278826\pi$
$809$	1.26213e16	1.28052	0.640262	+	0.768157i	$0.278826\pi$
$810$	4.24255e14	0.0427523
$811$	−5.72424e15	−0.572932	−0.286466	−	0.958090i	$-0.592481\pi$
$811$	−5.72424e15	−0.572932	−0.286466	+	0.958090i	$0.592481\pi$
$812$	−6.91469e15	−0.687408
$813$	3.71301e13	0.00366630
$814$	1.25690e16	1.23273
$815$	−2.07619e15	−0.202256
$816$	4.06025e15	0.392877
$817$	8.53208e13	0.00820037
$818$	7.22508e15	0.689762
$819$	−1.45875e15	−0.138331
$820$	−2.41966e15	−0.227917
$821$	4.67650e15	0.437556	0.218778	−	0.975775i	$-0.429793\pi$
$821$	4.67650e15	0.437556	0.218778	+	0.975775i	$0.429793\pi$
$822$	4.70334e15	0.437131
$823$	1.27239e16	1.17468	0.587340	−	0.809340i	$-0.300175\pi$
$823$	1.27239e16	1.17468	0.587340	+	0.809340i	$0.300175\pi$
$824$	7.09029e15	0.650226
$825$	3.45723e15	0.314942
$826$	3.32608e14	0.0300983
$827$	−1.69863e16	−1.52693	−0.763463	−	0.645851i	$-0.776503\pi$
$827$	−1.69863e16	−1.52693	−0.763463	+	0.645851i	$0.776503\pi$
$828$	8.73344e14	0.0779863
$829$	1.04792e16	0.929564	0.464782	−	0.885425i	$-0.346133\pi$
$829$	1.04792e16	0.929564	0.464782	+	0.885425i	$0.346133\pi$
$830$	−9.27698e14	−0.0817480
$831$	7.53904e15	0.659949
$832$	−6.57100e14	−0.0571417
$833$	1.47474e16	1.27400
$834$	−8.18656e14	−0.0702568
$835$	−2.14314e15	−0.182716
$836$	2.42118e16	2.05065
$837$	−3.27510e15	−0.275572
$838$	−1.94062e15	−0.162218
$839$	−1.14027e15	−0.0946927	−0.0473464	−	0.998879i	$-0.515076\pi$
$839$	−1.14027e15	−0.0946927	−0.0473464	+	0.998879i	$0.515076\pi$
$840$	2.39669e15	0.197732
$841$	2.54222e16	2.08370
$842$	3.09811e15	0.252279
$843$	1.22949e16	0.994656
$844$	−7.68283e15	−0.617501
$845$	−3.19435e15	−0.255077
$846$	1.13606e15	0.0901289
$847$	1.31018e16	1.03270
$848$	−7.08035e15	−0.554469
$849$	8.33274e15	0.648329
$850$	3.16560e15	0.244710
$851$	−5.88718e15	−0.452163
$852$	−1.65155e15	−0.126030
$853$	−1.95747e16	−1.48414	−0.742072	−	0.670320i	$-0.766157\pi$
$853$	−1.95747e16	−1.48414	−0.742072	+	0.670320i	$0.766157\pi$
$854$	−3.98632e15	−0.300299
$855$	−5.50901e15	−0.412344
$856$	5.76367e14	0.0428641
$857$	1.25651e16	0.928478	0.464239	−	0.885710i	$-0.346328\pi$
$857$	1.25651e16	0.928478	0.464239	+	0.885710i	$0.346328\pi$
$858$	5.31734e15	0.390404
$859$	−1.22364e16	−0.892674	−0.446337	−	0.894865i	$-0.647272\pi$
$859$	−1.22364e16	−0.892674	−0.446337	+	0.894865i	$0.647272\pi$
$860$	4.94456e13	0.00358415
$861$	−1.39833e15	−0.100714
$862$	7.84217e15	0.561237
$863$	−1.15780e16	−0.823330	−0.411665	−	0.911335i	$-0.635053\pi$
$863$	−1.15780e16	−0.823330	−0.411665	+	0.911335i	$0.635053\pi$
$864$	−2.76087e15	−0.195084
$865$	−3.67040e15	−0.257706
$866$	6.80083e14	0.0474475
$867$	−1.56155e16	−1.08256
$868$	−8.13681e15	−0.560526
$869$	−4.88725e16	−3.34546
$870$	−5.73500e15	−0.390101
$871$	−1.37189e16	−0.927301
$872$	1.43740e16	0.965464
$873$	8.76104e15	0.584759
$874$	3.10528e15	0.205963
$875$	−8.23282e15	−0.542631
$876$	−2.46096e15	−0.161188
$877$	9.00687e14	0.0586241	0.0293121	−	0.999570i	$-0.490668\pi$
$877$	9.00687e14	0.0586241	0.0293121	+	0.999570i	$0.490668\pi$
$878$	−4.17202e15	−0.269852
$879$	2.36901e15	0.152275
$880$	9.13721e15	0.583658
$881$	−2.87968e16	−1.82800	−0.914001	−	0.405712i	$-0.867024\pi$
$881$	−2.87968e16	−1.82800	−0.914001	+	0.405712i	$0.867024\pi$
$882$	−1.84070e15	−0.116120
$883$	−1.92900e16	−1.20934	−0.604671	−	0.796475i	$-0.706695\pi$
$883$	−1.92900e16	−1.20934	−0.604671	+	0.796475i	$0.706695\pi$
$884$	−1.77809e16	−1.10781
$885$	−1.00745e15	−0.0623785
$886$	−9.39146e15	−0.577893
$887$	1.91234e16	1.16946	0.584730	−	0.811228i	$-0.301201\pi$
$887$	1.91234e16	1.16946	0.584730	+	0.811228i	$0.301201\pi$
$888$	1.19285e16	0.724959
$889$	9.99696e15	0.603821
$890$	−1.10861e16	−0.665480
$891$	3.26382e15	0.194715
$892$	−1.56762e16	−0.929465
$893$	−1.47519e16	−0.869290
$894$	2.48220e15	0.145372
$895$	4.03612e15	0.234929
$896$	−8.46305e15	−0.489591
$897$	−2.49058e15	−0.143199
$898$	2.28746e15	0.130717
$899$	4.42722e16	2.51451
$900$	1.44296e15	0.0814554
$901$	4.17533e16	2.34263
$902$	5.09710e15	0.284241
$903$	2.85748e13	0.00158380
$904$	4.77489e15	0.263049
$905$	−7.07059e15	−0.387158
$906$	−5.96988e15	−0.324908
$907$	−2.57494e16	−1.39292	−0.696461	−	0.717595i	$-0.745243\pi$
$907$	−2.57494e16	−1.39292	−0.696461	+	0.717595i	$0.745243\pi$
$908$	2.25393e16	1.21190
$909$	3.99705e15	0.213618
$910$	−3.00587e15	−0.159677
$911$	1.39563e16	0.736917	0.368459	−	0.929644i	$-0.379886\pi$
$911$	1.39563e16	0.736917	0.368459	+	0.929644i	$0.379886\pi$
$912$	6.58061e15	0.345378
$913$	−7.13685e15	−0.372321
$914$	−1.22742e16	−0.636487
$915$	1.20743e16	0.622367
$916$	1.48343e16	0.760050
$917$	−9.01129e15	−0.458940
$918$	2.98851e15	0.151294
$919$	−3.54732e16	−1.78511	−0.892556	−	0.450936i	$-0.851090\pi$
$919$	−3.54732e16	−1.78511	−0.892556	+	0.450936i	$0.851090\pi$
$920$	4.09196e15	0.204691
$921$	−7.56013e15	−0.375925
$922$	1.22049e16	0.603276
$923$	4.70983e15	0.231417
$924$	8.10878e15	0.396059
$925$	−9.72692e15	−0.472276
$926$	−9.96823e15	−0.481125
$927$	−5.45826e15	−0.261888
$928$	3.73209e16	1.78008
$929$	1.56899e16	0.743934	0.371967	−	0.928246i	$-0.378683\pi$
$929$	1.56899e16	0.743934	0.371967	+	0.928246i	$0.378683\pi$
$930$	−6.74861e15	−0.318096
$931$	2.39017e16	1.11997
$932$	−6.84354e15	−0.318782
$933$	1.63362e16	0.756487
$934$	−1.50426e16	−0.692495
$935$	−5.38827e16	−2.46596
$936$	5.04635e15	0.229594
$937$	−2.75211e16	−1.24480	−0.622399	−	0.782700i	$-0.713842\pi$
$937$	−2.75211e16	−1.24480	−0.622399	+	0.782700i	$0.713842\pi$
$938$	5.72863e15	0.257594
$939$	−3.92375e15	−0.175404
$940$	−8.54911e15	−0.379942
$941$	1.84209e16	0.813893	0.406946	−	0.913452i	$-0.366594\pi$
$941$	1.84209e16	0.813893	0.406946	+	0.913452i	$0.366594\pi$
$942$	5.19510e14	0.0228199
$943$	−2.38741e15	−0.104259
$944$	1.20341e15	0.0522480
$945$	−1.84503e15	−0.0796393
$946$	−1.04159e14	−0.00446988
$947$	−1.07792e16	−0.459899	−0.229950	−	0.973203i	$-0.573856\pi$
$947$	−1.07792e16	−0.459899	−0.229950	+	0.973203i	$0.573856\pi$
$948$	−2.03981e16	−0.865255
$949$	7.01811e15	0.295975
$950$	5.13062e15	0.215124
$951$	−1.59899e16	−0.666581
$952$	1.68827e16	0.699741
$953$	−1.89737e16	−0.781881	−0.390940	−	0.920416i	$-0.627850\pi$
$953$	−1.89737e16	−0.781881	−0.390940	+	0.920416i	$0.627850\pi$
$954$	−5.21143e15	−0.213521
$955$	−1.51610e16	−0.617601
$956$	6.27464e15	0.254138
$957$	−4.41197e16	−1.77671
$958$	1.65181e16	0.661380
$959$	−2.04542e16	−0.814291
$960$	−8.31099e14	−0.0328974
$961$	2.66885e16	1.05038
$962$	−1.49604e16	−0.585436
$963$	−4.43700e14	−0.0172641
$964$	1.88182e16	0.728040
$965$	−4.73021e15	−0.181962
$966$	1.03999e15	0.0397792
$967$	3.78791e16	1.44064	0.720318	−	0.693644i	$-0.243996\pi$
$967$	3.78791e16	1.44064	0.720318	+	0.693644i	$0.243996\pi$
$968$	−4.53240e16	−1.71401
$969$	−3.88063e16	−1.45922
$970$	1.80528e16	0.674995
$971$	4.82137e16	1.79252	0.896262	−	0.443525i	$-0.146272\pi$
$971$	4.82137e16	1.79252	0.896262	+	0.443525i	$0.146272\pi$
$972$	1.36224e15	0.0503602
$973$	3.56022e15	0.130875
$974$	6.31266e15	0.230748
$975$	−4.11498e15	−0.149569
$976$	−1.44230e16	−0.521292
$977$	1.43458e16	0.515590	0.257795	−	0.966200i	$-0.417004\pi$
$977$	1.43458e16	0.515590	0.257795	+	0.966200i	$0.417004\pi$
$978$	1.82542e15	0.0652377
$979$	−8.52864e16	−3.03092
$980$	1.38517e16	0.489507
$981$	−1.10654e16	−0.388854
$982$	2.21805e15	0.0775100
$983$	−1.40114e16	−0.486898	−0.243449	−	0.969914i	$-0.578279\pi$
$983$	−1.40114e16	−0.486898	−0.243449	+	0.969914i	$0.578279\pi$
$984$	4.83732e15	0.167160
$985$	−3.15588e16	−1.08448
$986$	−4.03982e16	−1.38051
$987$	−4.94056e15	−0.167893
$988$	−2.88182e16	−0.973876
$989$	4.87868e13	0.00163954
$990$	6.72537e15	0.224762
$991$	−2.49514e16	−0.829259	−0.414630	−	0.909990i	$-0.636089\pi$
$991$	−2.49514e16	−0.829259	−0.414630	+	0.909990i	$0.636089\pi$
$992$	4.39171e16	1.45151
$993$	7.08787e15	0.232967
$994$	−1.96669e15	−0.0642851
$995$	−1.47968e16	−0.480996
$996$	−2.97874e15	−0.0962954
$997$	−1.67167e16	−0.537438	−0.268719	−	0.963219i	$-0.586600\pi$
$997$	−1.67167e16	−0.537438	−0.268719	+	0.963219i	$0.586600\pi$
$998$	−2.67825e16	−0.856313
$999$	−9.18278e15	−0.291987

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.a.1.17	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.a.1.17	✓	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)

\(f(q)\)	\(=\)	\(q+20.9819 q^{2} -243.000 q^{3} -1607.76 q^{4} +5799.05 q^{5} -5098.61 q^{6} +22173.1 q^{7} -76704.8 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+20.9819 q^{2} -243.000 q^{3} -1607.76 q^{4} +5799.05 q^{5} -5098.61 q^{6} +22173.1 q^{7} -76704.8 q^{8} +59049.0 q^{9} +121675. q^{10} +936055. q^{11} +390685. q^{12} -1.11415e6 q^{13} +465235. q^{14} -1.40917e6 q^{15} +1.68328e6 q^{16} -9.92639e6 q^{17} +1.23896e6 q^{18} -1.60881e7 q^{19} -9.32347e6 q^{20} -5.38807e6 q^{21} +1.96402e7 q^{22} -9.19924e6 q^{23} +1.86393e7 q^{24} -1.51992e7 q^{25} -2.33769e7 q^{26} -1.43489e7 q^{27} -3.56490e7 q^{28} +1.93966e8 q^{29} -2.95671e7 q^{30} +2.28248e8 q^{31} +1.92410e8 q^{32} -2.27461e8 q^{33} -2.08275e8 q^{34} +1.28583e8 q^{35} -9.49366e7 q^{36} +6.39964e8 q^{37} -3.37559e8 q^{38} +2.70737e8 q^{39} -4.44815e8 q^{40} +2.59523e8 q^{41} -1.13052e8 q^{42} -5.30335e6 q^{43} -1.50495e9 q^{44} +3.42428e8 q^{45} -1.93018e8 q^{46} +9.16945e8 q^{47} -4.09036e8 q^{48} -1.48568e9 q^{49} -3.18908e8 q^{50} +2.41211e9 q^{51} +1.79128e9 q^{52} -4.20629e9 q^{53} -3.01068e8 q^{54} +5.42823e9 q^{55} -1.70079e9 q^{56} +3.90940e9 q^{57} +4.06977e9 q^{58} +7.14924e8 q^{59} +2.26560e9 q^{60} -8.56840e9 q^{61} +4.78907e9 q^{62} +1.30930e9 q^{63} +5.89780e8 q^{64} -6.46098e9 q^{65} -4.77258e9 q^{66} +1.23134e10 q^{67} +1.59592e10 q^{68} +2.23541e9 q^{69} +2.69792e9 q^{70} -4.22731e9 q^{71} -4.52934e9 q^{72} -6.29909e9 q^{73} +1.34277e10 q^{74} +3.69340e9 q^{75} +2.58658e10 q^{76} +2.07553e10 q^{77} +5.68059e9 q^{78} -5.22111e10 q^{79} +9.76140e9 q^{80} +3.48678e9 q^{81} +5.44529e9 q^{82} -7.62439e9 q^{83} +8.66272e9 q^{84} -5.75636e10 q^{85} -1.11274e8 q^{86} -4.71337e10 q^{87} -7.18000e10 q^{88} -9.11126e10 q^{89} +7.18480e9 q^{90} -2.47041e10 q^{91} +1.47902e10 q^{92} -5.54642e10 q^{93} +1.92393e10 q^{94} -9.32956e10 q^{95} -4.67556e10 q^{96} +1.48369e11 q^{97} -3.11724e10 q^{98} +5.52731e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9}+O(q^{10}) \) 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

Modular forms

Varieties

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Database

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