LMFDB - Embedded newform 177.12.a.a.1.20

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			1.20
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)

$f(q)$	$=$	$q+40.1266 q^{2} -243.000 q^{3} -437.857 q^{4} +10858.4 q^{5} -9750.76 q^{6} -2158.10 q^{7} -99749.0 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+40.1266 q^{2} -243.000 q^{3} -437.857 q^{4} +10858.4 q^{5} -9750.76 q^{6} -2158.10 q^{7} -99749.0 q^{8} +59049.0 q^{9} +435712. q^{10} -558147. q^{11} +106399. q^{12} +1.91592e6 q^{13} -86597.0 q^{14} -2.63860e6 q^{15} -3.10585e6 q^{16} +3.75206e6 q^{17} +2.36943e6 q^{18} -1.12096e7 q^{19} -4.75444e6 q^{20} +524417. q^{21} -2.23966e7 q^{22} -2.13872e7 q^{23} +2.42390e7 q^{24} +6.90776e7 q^{25} +7.68793e7 q^{26} -1.43489e7 q^{27} +944937. q^{28} -6.39291e7 q^{29} -1.05878e8 q^{30} -1.05258e7 q^{31} +7.96585e7 q^{32} +1.35630e8 q^{33} +1.50557e8 q^{34} -2.34336e7 q^{35} -2.58550e7 q^{36} +1.08708e8 q^{37} -4.49804e8 q^{38} -4.65568e8 q^{39} -1.08312e9 q^{40} +4.74439e8 q^{41} +2.10431e7 q^{42} -2.55553e8 q^{43} +2.44389e8 q^{44} +6.41180e8 q^{45} -8.58193e8 q^{46} -1.53163e8 q^{47} +7.54723e8 q^{48} -1.97267e9 q^{49} +2.77185e9 q^{50} -9.11750e8 q^{51} -8.38898e8 q^{52} +1.48167e8 q^{53} -5.75773e8 q^{54} -6.06061e9 q^{55} +2.15268e8 q^{56} +2.72394e9 q^{57} -2.56526e9 q^{58} +7.14924e8 q^{59} +1.15533e9 q^{60} -5.86726e9 q^{61} -4.22364e8 q^{62} -1.27433e8 q^{63} +9.55721e9 q^{64} +2.08039e10 q^{65} +5.44236e9 q^{66} +2.74066e9 q^{67} -1.64286e9 q^{68} +5.19708e9 q^{69} -9.40309e8 q^{70} +1.81330e10 q^{71} -5.89008e9 q^{72} -1.43546e9 q^{73} +4.36210e9 q^{74} -1.67859e10 q^{75} +4.90821e9 q^{76} +1.20454e9 q^{77} -1.86817e10 q^{78} -1.94641e10 q^{79} -3.37247e10 q^{80} +3.48678e9 q^{81} +1.90376e10 q^{82} -2.81052e10 q^{83} -2.29620e8 q^{84} +4.07415e10 q^{85} -1.02545e10 q^{86} +1.55348e10 q^{87} +5.56746e10 q^{88} -1.07723e10 q^{89} +2.57284e10 q^{90} -4.13474e9 q^{91} +9.36451e9 q^{92} +2.55776e9 q^{93} -6.14589e9 q^{94} -1.21719e11 q^{95} -1.93570e10 q^{96} -2.86797e10 q^{97} -7.91565e10 q^{98} -3.29581e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	40.1266	0.886681	0.443340	−	0.896353i	$-0.353793\pi$
$2$	40.1266	0.886681	0.443340	+	0.896353i	$0.353793\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	−437.857	−0.213797
$5$	10858.4	1.55393	0.776967	−	0.629542i	$-0.216757\pi$
$5$	10858.4	1.55393	0.776967	+	0.629542i	$0.216757\pi$
$6$	−9750.76	−0.511925
$7$	−2158.10	−0.0485324	−0.0242662	−	0.999706i	$-0.507725\pi$
$7$	−2158.10	−0.0485324	−0.0242662	+	0.999706i	$0.507725\pi$
$8$	−99749.0	−1.07625
$9$	59049.0	0.333333
$10$	435712.	1.37784
$11$	−558147.	−1.04493	−0.522467	−	0.852659i	$-0.674988\pi$
$11$	−558147.	−1.04493	−0.522467	+	0.852659i	$0.674988\pi$
$12$	106399.	0.123436
$13$	1.91592e6	1.43116	0.715581	−	0.698530i	$-0.246162\pi$
$13$	1.91592e6	1.43116	0.715581	+	0.698530i	$0.246162\pi$
$14$	−86597.0	−0.0430327
$15$	−2.63860e6	−0.897164
$16$	−3.10585e6	−0.740493
$17$	3.75206e6	0.640915	0.320457	−	0.947263i	$-0.396163\pi$
$17$	3.75206e6	0.640915	0.320457	+	0.947263i	$0.396163\pi$
$18$	2.36943e6	0.295560
$19$	−1.12096e7	−1.03859	−0.519297	−	0.854594i	$-0.673806\pi$
$19$	−1.12096e7	−1.03859	−0.519297	+	0.854594i	$0.673806\pi$
$20$	−4.75444e6	−0.332227
$21$	524417.	0.0280202
$22$	−2.23966e7	−0.926524
$23$	−2.13872e7	−0.692867	−0.346433	−	0.938075i	$-0.612607\pi$
$23$	−2.13872e7	−0.692867	−0.346433	+	0.938075i	$0.612607\pi$
$24$	2.42390e7	0.621374
$25$	6.90776e7	1.41471
$26$	7.68793e7	1.26898
$27$	−1.43489e7	−0.192450
$28$	944937.	0.0103761
$29$	−6.39291e7	−0.578775	−0.289388	−	0.957212i	$-0.593452\pi$
$29$	−6.39291e7	−0.578775	−0.289388	+	0.957212i	$0.593452\pi$
$30$	−1.05878e8	−0.795498
$31$	−1.05258e7	−0.0660336	−0.0330168	−	0.999455i	$-0.510511\pi$
$31$	−1.05258e7	−0.0660336	−0.0330168	+	0.999455i	$0.510511\pi$
$32$	7.96585e7	0.419669
$33$	1.35630e8	0.603293
$34$	1.50557e8	0.568287
$35$	−2.34336e7	−0.0754161
$36$	−2.58550e7	−0.0712658
$37$	1.08708e8	0.257723	0.128862	−	0.991663i	$-0.458868\pi$
$37$	1.08708e8	0.257723	0.128862	+	0.991663i	$0.458868\pi$
$38$	−4.49804e8	−0.920902
$39$	−4.65568e8	−0.826281
$40$	−1.08312e9	−1.67242
$41$	4.74439e8	0.639542	0.319771	−	0.947495i	$-0.396394\pi$
$41$	4.74439e8	0.639542	0.319771	+	0.947495i	$0.396394\pi$
$42$	2.10431e7	0.0248450
$43$	−2.55553e8	−0.265097	−0.132548	−	0.991177i	$-0.542316\pi$
$43$	−2.55553e8	−0.265097	−0.132548	+	0.991177i	$0.542316\pi$
$44$	2.44389e8	0.223404
$45$	6.41180e8	0.517978
$46$	−8.58193e8	−0.614352
$47$	−1.53163e8	−0.0974125	−0.0487062	−	0.998813i	$-0.515510\pi$
$47$	−1.53163e8	−0.0974125	−0.0487062	+	0.998813i	$0.515510\pi$
$48$	7.54723e8	0.427524
$49$	−1.97267e9	−0.997645
$50$	2.77185e9	1.25440
$51$	−9.11750e8	−0.370032
$52$	−8.38898e8	−0.305978
$53$	1.48167e8	0.0486669	0.0243334	−	0.999704i	$-0.492254\pi$
$53$	1.48167e8	0.0486669	0.0243334	+	0.999704i	$0.492254\pi$
$54$	−5.75773e8	−0.170642
$55$	−6.06061e9	−1.62376
$56$	2.15268e8	0.0522330
$57$	2.72394e9	0.599633
$58$	−2.56526e9	−0.513189
$59$	7.14924e8	0.130189
$59$	7.14924e8	0.130189
$60$	1.15533e9	0.191811
$61$	−5.86726e9	−0.889449	−0.444724	−	0.895667i	$-0.646698\pi$
$61$	−5.86726e9	−0.889449	−0.444724	+	0.895667i	$0.646698\pi$
$62$	−4.22364e8	−0.0585507
$63$	−1.27433e8	−0.0161775
$64$	9.55721e9	1.11261
$65$	2.08039e10	2.22393
$66$	5.44236e9	0.534929
$67$	2.74066e9	0.247996	0.123998	−	0.992282i	$-0.460428\pi$
$67$	2.74066e9	0.247996	0.123998	+	0.992282i	$0.460428\pi$
$68$	−1.64286e9	−0.137026
$69$	5.19708e9	0.400027
$70$	−9.40309e8	−0.0668700
$71$	1.81330e10	1.19275	0.596374	−	0.802707i	$-0.296608\pi$
$71$	1.81330e10	1.19275	0.596374	+	0.802707i	$0.296608\pi$
$72$	−5.89008e9	−0.358750
$73$	−1.43546e9	−0.0810432	−0.0405216	−	0.999179i	$-0.512902\pi$
$73$	−1.43546e9	−0.0810432	−0.0405216	+	0.999179i	$0.512902\pi$
$74$	4.36210e9	0.228518
$75$	−1.67859e10	−0.816783
$76$	4.90821e9	0.222049
$77$	1.20454e9	0.0507132
$78$	−1.86817e10	−0.732648
$79$	−1.94641e10	−0.711682	−0.355841	−	0.934547i	$-0.615805\pi$
$79$	−1.94641e10	−0.711682	−0.355841	+	0.934547i	$0.615805\pi$
$80$	−3.37247e10	−1.15068
$81$	3.48678e9	0.111111
$82$	1.90376e10	0.567070
$83$	−2.81052e10	−0.783172	−0.391586	−	0.920141i	$-0.628074\pi$
$83$	−2.81052e10	−0.783172	−0.391586	+	0.920141i	$0.628074\pi$
$84$	−2.29620e8	−0.00599064
$85$	4.07415e10	0.995939
$86$	−1.02545e10	−0.235056
$87$	1.55348e10	0.334156
$88$	5.56746e10	1.12461
$89$	−1.07723e10	−0.204486	−0.102243	−	0.994759i	$-0.532602\pi$
$89$	−1.07723e10	−0.204486	−0.102243	+	0.994759i	$0.532602\pi$
$90$	2.57284e10	0.459281
$91$	−4.13474e9	−0.0694576
$92$	9.36451e9	0.148133
$93$	2.55776e9	0.0381245
$94$	−6.14589e9	−0.0863738
$95$	−1.21719e11	−1.61391
$96$	−1.93570e10	−0.242296
$97$	−2.86797e10	−0.339101	−0.169551	−	0.985521i	$-0.554232\pi$
$97$	−2.86797e10	−0.339101	−0.169551	+	0.985521i	$0.554232\pi$
$98$	−7.91565e10	−0.884592
$99$	−3.29581e10	−0.348312
$100$	−3.02461e10	−0.302461
$101$	−1.71283e11	−1.62161	−0.810806	−	0.585315i	$-0.800971\pi$
$101$	−1.71283e11	−1.62161	−0.810806	+	0.585315i	$0.800971\pi$
$102$	−3.65854e10	−0.328101
$103$	−7.69354e10	−0.653915	−0.326957	−	0.945039i	$-0.606023\pi$
$103$	−7.69354e10	−0.653915	−0.326957	+	0.945039i	$0.606023\pi$
$104$	−1.91111e11	−1.54029
$105$	5.69435e9	0.0435415
$106$	5.94543e9	0.0431520
$107$	−1.36485e11	−0.940750	−0.470375	−	0.882467i	$-0.655881\pi$
$107$	−1.36485e11	−0.940750	−0.470375	+	0.882467i	$0.655881\pi$
$108$	6.28277e9	0.0411453
$109$	−2.74257e10	−0.170731	−0.0853654	−	0.996350i	$-0.527206\pi$
$109$	−2.74257e10	−0.170731	−0.0853654	+	0.996350i	$0.527206\pi$
$110$	−2.43192e11	−1.43976
$111$	−2.64162e10	−0.148797
$112$	6.70273e9	0.0359379
$113$	−7.83794e10	−0.400194	−0.200097	−	0.979776i	$-0.564126\pi$
$113$	−7.83794e10	−0.400194	−0.200097	+	0.979776i	$0.564126\pi$
$114$	1.09302e11	0.531683
$115$	−2.32231e11	−1.07667
$116$	2.79918e10	0.123741
$117$	1.13133e11	0.477054
$118$	2.86875e10	0.115436
$119$	−8.09730e9	−0.0311051
$120$	2.63198e11	0.965573
$121$	2.62169e10	0.0918887
$122$	−2.35433e11	−0.788657
$123$	−1.15289e11	−0.369240
$124$	4.60878e9	0.0141178
$125$	2.19878e11	0.644430
$126$	−5.11347e9	−0.0143442
$127$	−5.37437e11	−1.44347	−0.721734	−	0.692170i	$-0.756655\pi$
$127$	−5.37437e11	−1.44347	−0.721734	+	0.692170i	$0.756655\pi$
$128$	2.20358e11	0.566857
$129$	6.20994e10	0.153054
$130$	8.34789e11	1.97191
$131$	−5.78286e11	−1.30964	−0.654818	−	0.755786i	$-0.727255\pi$
$131$	−5.78286e11	−1.30964	−0.654818	+	0.755786i	$0.727255\pi$
$132$	−5.93865e10	−0.128983
$133$	2.41914e10	0.0504055
$134$	1.09973e11	0.219893
$135$	−1.55807e11	−0.299055
$136$	−3.74264e11	−0.689785
$137$	2.75240e10	0.0487246	0.0243623	−	0.999703i	$-0.492244\pi$
$137$	2.75240e10	0.0487246	0.0243623	+	0.999703i	$0.492244\pi$
$138$	2.08541e11	0.354696
$139$	3.79830e11	0.620880	0.310440	−	0.950593i	$-0.399524\pi$
$139$	3.79830e11	0.620880	0.310440	+	0.950593i	$0.399524\pi$
$140$	1.02605e10	0.0161238
$141$	3.72185e10	0.0562411
$142$	7.27615e11	1.05759
$143$	−1.06936e12	−1.49547
$144$	−1.83398e11	−0.246831
$145$	−6.94171e11	−0.899378
$146$	−5.76003e10	−0.0718594
$147$	4.79359e11	0.575990
$148$	−4.75988e10	−0.0551006
$149$	−1.48988e12	−1.66198	−0.830991	−	0.556286i	$-0.812226\pi$
$149$	−1.48988e12	−1.66198	−0.830991	+	0.556286i	$0.812226\pi$
$150$	−6.73559e11	−0.724225
$151$	−7.02101e11	−0.727824	−0.363912	−	0.931433i	$-0.618559\pi$
$151$	−7.02101e11	−0.727824	−0.363912	+	0.931433i	$0.618559\pi$
$152$	1.11815e12	1.11779
$153$	2.21555e11	0.213638
$154$	4.83339e10	0.0449664
$155$	−1.14294e11	−0.102612
$156$	2.03852e11	0.176657
$157$	5.96631e11	0.499181	0.249590	−	0.968351i	$-0.419704\pi$
$157$	5.96631e11	0.499181	0.249590	+	0.968351i	$0.419704\pi$
$158$	−7.81029e11	−0.631034
$159$	−3.60045e10	−0.0280978
$160$	8.64967e11	0.652138
$161$	4.61555e10	0.0336265
$162$	1.39913e11	0.0985201
$163$	−1.53294e12	−1.04350	−0.521752	−	0.853097i	$-0.674721\pi$
$163$	−1.53294e12	−1.04350	−0.521752	+	0.853097i	$0.674721\pi$
$164$	−2.07736e11	−0.136732
$165$	1.47273e12	0.937478
$166$	−1.12777e12	−0.694424
$167$	−2.13729e12	−1.27328	−0.636638	−	0.771163i	$-0.719675\pi$
$167$	−2.13729e12	−1.27328	−0.636638	+	0.771163i	$0.719675\pi$
$168$	−5.23101e10	−0.0301567
$169$	1.87858e12	1.04822
$170$	1.63482e12	0.883080
$171$	−6.61917e11	−0.346198
$172$	1.11896e11	0.0566770
$173$	9.85994e11	0.483750	0.241875	−	0.970307i	$-0.422238\pi$
$173$	9.85994e11	0.483750	0.241875	+	0.970307i	$0.422238\pi$
$174$	6.23358e11	0.296290
$175$	−1.49076e11	−0.0686592
$176$	1.73352e12	0.773767
$177$	−1.73727e11	−0.0751646
$178$	−4.32255e11	−0.181313
$179$	1.30693e12	0.531572	0.265786	−	0.964032i	$-0.414369\pi$
$179$	1.30693e12	0.531572	0.265786	+	0.964032i	$0.414369\pi$
$180$	−2.80745e11	−0.110742
$181$	3.58189e12	1.37050	0.685251	−	0.728307i	$-0.259692\pi$
$181$	3.58189e12	1.37050	0.685251	+	0.728307i	$0.259692\pi$
$182$	−1.65913e11	−0.0615868
$183$	1.42574e12	0.513524
$184$	2.13335e12	0.745699
$185$	1.18040e12	0.400485
$186$	1.02634e11	0.0338043
$187$	−2.09420e12	−0.669714
$188$	6.70633e10	0.0208265
$189$	3.09663e10	0.00934006
$190$	−4.88417e12	−1.43102
$191$	−3.87812e12	−1.10392	−0.551960	−	0.833870i	$-0.686120\pi$
$191$	−3.87812e12	−1.10392	−0.551960	+	0.833870i	$0.686120\pi$
$192$	−2.32240e12	−0.642363
$193$	−2.07161e12	−0.556856	−0.278428	−	0.960457i	$-0.589813\pi$
$193$	−2.07161e12	−0.556856	−0.278428	+	0.960457i	$0.589813\pi$
$194$	−1.15082e12	−0.300675
$195$	−5.05534e12	−1.28399
$196$	8.63747e11	0.213294
$197$	−2.68438e12	−0.644585	−0.322292	−	0.946640i	$-0.604453\pi$
$197$	−2.68438e12	−0.644585	−0.322292	+	0.946640i	$0.604453\pi$
$198$	−1.32249e12	−0.308841
$199$	−2.89870e12	−0.658433	−0.329216	−	0.944254i	$-0.606785\pi$
$199$	−2.89870e12	−0.658433	−0.329216	+	0.944254i	$0.606785\pi$
$200$	−6.89042e12	−1.52258
$201$	−6.65981e11	−0.143180
$202$	−6.87301e12	−1.43785
$203$	1.37965e11	0.0280893
$204$	3.99216e11	0.0791119
$205$	5.15167e12	0.993806
$206$	−3.08715e12	−0.579814
$207$	−1.26289e12	−0.230956
$208$	−5.95056e12	−1.05977
$209$	6.25662e12	1.08526
$210$	2.28495e11	0.0386074
$211$	−3.14739e12	−0.518081	−0.259041	−	0.965866i	$-0.583406\pi$
$211$	−3.14739e12	−0.518081	−0.259041	+	0.965866i	$0.583406\pi$
$212$	−6.48758e10	−0.0104048
$213$	−4.40632e12	−0.688633
$214$	−5.47668e12	−0.834145
$215$	−2.77491e12	−0.411943
$216$	1.43129e12	0.207125
$217$	2.27156e10	0.00320477
$218$	−1.10050e12	−0.151384
$219$	3.48818e11	0.0467903
$220$	2.65368e12	0.347155
$221$	7.18863e12	0.917252
$222$	−1.05999e12	−0.131935
$223$	9.66744e12	1.17391	0.586955	−	0.809620i	$-0.300327\pi$
$223$	9.66744e12	1.17391	0.586955	+	0.809620i	$0.300327\pi$
$224$	−1.71911e11	−0.0203676
$225$	4.07896e12	0.471570
$226$	−3.14510e12	−0.354844
$227$	1.62019e13	1.78412	0.892058	−	0.451920i	$-0.149261\pi$
$227$	1.62019e13	1.78412	0.892058	+	0.451920i	$0.149261\pi$
$228$	−1.19270e12	−0.128200
$229$	−4.47309e12	−0.469367	−0.234683	−	0.972072i	$-0.575405\pi$
$229$	−4.47309e12	−0.469367	−0.234683	+	0.972072i	$0.575405\pi$
$230$	−9.31864e12	−0.954662
$231$	−2.92702e11	−0.0292793
$232$	6.37687e12	0.622907
$233$	1.56446e13	1.49247	0.746236	−	0.665682i	$-0.231859\pi$
$233$	1.56446e13	1.49247	0.746236	+	0.665682i	$0.231859\pi$
$234$	4.53964e12	0.422994
$235$	−1.66311e12	−0.151372
$236$	−3.13035e11	−0.0278340
$237$	4.72978e12	0.410890
$238$	−3.24917e11	−0.0275803
$239$	−1.58472e13	−1.31451	−0.657253	−	0.753670i	$-0.728282\pi$
$239$	−1.58472e13	−1.31451	−0.657253	+	0.753670i	$0.728282\pi$
$240$	8.19511e12	0.664344
$241$	−2.76301e11	−0.0218921	−0.0109461	−	0.999940i	$-0.503484\pi$
$241$	−2.76301e11	−0.0218921	−0.0109461	+	0.999940i	$0.503484\pi$
$242$	1.05200e12	0.0814760
$243$	−8.47289e11	−0.0641500
$244$	2.56902e12	0.190162
$245$	−2.14201e13	−1.55027
$246$	−4.62614e12	−0.327398
$247$	−2.14767e13	−1.48640
$248$	1.04994e12	0.0710687
$249$	6.82957e12	0.452165
$250$	8.82294e12	0.571404
$251$	−1.15243e13	−0.730143	−0.365071	−	0.930980i	$-0.618955\pi$
$251$	−1.15243e13	−0.730143	−0.365071	+	0.930980i	$0.618955\pi$
$252$	5.57976e10	0.00345870
$253$	1.19372e13	0.724001
$254$	−2.15655e13	−1.27990
$255$	−9.90018e12	−0.575006
$256$	−1.07310e13	−0.609985
$257$	2.04756e13	1.13921	0.569606	−	0.821918i	$-0.307096\pi$
$257$	2.04756e13	1.13921	0.569606	+	0.821918i	$0.307096\pi$
$258$	2.49184e12	0.135710
$259$	−2.34603e11	−0.0125079
$260$	−9.10912e12	−0.475470
$261$	−3.77495e12	−0.192925
$262$	−2.32047e13	−1.16123
$263$	−1.74761e13	−0.856422	−0.428211	−	0.903679i	$-0.640856\pi$
$263$	−1.74761e13	−0.856422	−0.428211	+	0.903679i	$0.640856\pi$
$264$	−1.35289e13	−0.649295
$265$	1.60886e12	0.0756251
$266$	9.70720e11	0.0446936
$267$	2.61766e12	0.118060
$268$	−1.20002e12	−0.0530208
$269$	−4.83367e12	−0.209237	−0.104619	−	0.994512i	$-0.533362\pi$
$269$	−4.83367e12	−0.209237	−0.104619	+	0.994512i	$0.533362\pi$
$270$	−6.25199e12	−0.265166
$271$	−5.58792e12	−0.232231	−0.116115	−	0.993236i	$-0.537044\pi$
$271$	−5.58792e12	−0.232231	−0.116115	+	0.993236i	$0.537044\pi$
$272$	−1.16533e13	−0.474593
$273$	1.00474e12	0.0401014
$274$	1.10444e12	0.0432032
$275$	−3.85555e13	−1.47828
$276$	−2.27558e12	−0.0855247
$277$	−2.08713e13	−0.768971	−0.384486	−	0.923131i	$-0.625621\pi$
$277$	−2.08713e13	−0.768971	−0.384486	+	0.923131i	$0.625621\pi$
$278$	1.52413e13	0.550522
$279$	−6.21537e11	−0.0220112
$280$	2.33747e12	0.0811666
$281$	−1.47528e13	−0.502330	−0.251165	−	0.967944i	$-0.580814\pi$
$281$	−1.47528e13	−0.502330	−0.251165	+	0.967944i	$0.580814\pi$
$282$	1.49345e12	0.0498679
$283$	4.39824e13	1.44030	0.720150	−	0.693818i	$-0.244073\pi$
$283$	4.39824e13	1.44030	0.720150	+	0.693818i	$0.244073\pi$
$284$	−7.93965e12	−0.255006
$285$	2.95777e13	0.931790
$286$	−4.29100e13	−1.32600
$287$	−1.02389e12	−0.0310385
$288$	4.70376e12	0.139890
$289$	−2.01940e13	−0.589228
$290$	−2.78547e13	−0.797461
$291$	6.96916e12	0.195780
$292$	6.28528e11	0.0173268
$293$	−5.15348e12	−0.139421	−0.0697106	−	0.997567i	$-0.522208\pi$
$293$	−5.15348e12	−0.139421	−0.0697106	+	0.997567i	$0.522208\pi$
$294$	1.92350e13	0.510720
$295$	7.76296e12	0.202305
$296$	−1.08436e13	−0.277375
$297$	8.00881e12	0.201098
$298$	−5.97837e13	−1.47365
$299$	−4.09760e13	−0.991604
$300$	7.34980e12	0.174626
$301$	5.51508e11	0.0128658
$302$	−2.81729e13	−0.645347
$303$	4.16218e13	0.936238
$304$	3.48154e13	0.769072
$305$	−6.37093e13	−1.38214
$306$	8.89025e12	0.189429
$307$	4.55568e13	0.953438	0.476719	−	0.879056i	$-0.341826\pi$
$307$	4.55568e13	0.953438	0.476719	+	0.879056i	$0.341826\pi$
$308$	−5.27414e11	−0.0108423
$309$	1.86953e13	0.377538
$310$	−4.58621e12	−0.0909839
$311$	5.09748e13	0.993512	0.496756	−	0.867890i	$-0.334524\pi$
$311$	5.09748e13	0.993512	0.496756	+	0.867890i	$0.334524\pi$
$312$	4.64399e13	0.889286
$313$	9.18436e13	1.72805	0.864023	−	0.503453i	$-0.167937\pi$
$313$	9.18436e13	1.72805	0.864023	+	0.503453i	$0.167937\pi$
$314$	2.39408e13	0.442614
$315$	−1.38373e12	−0.0251387
$316$	8.52250e12	0.152156
$317$	4.83350e13	0.848077	0.424039	−	0.905644i	$-0.360612\pi$
$317$	4.83350e13	0.848077	0.424039	+	0.905644i	$0.360612\pi$
$318$	−1.44474e12	−0.0249138
$319$	3.56819e13	0.604782
$320$	1.03776e14	1.72892
$321$	3.31659e13	0.543142
$322$	1.85206e12	0.0298159
$323$	−4.20591e13	−0.665651
$324$	−1.52671e12	−0.0237553
$325$	1.32347e14	2.02468
$326$	−6.15117e13	−0.925254
$327$	6.66444e12	0.0985715
$328$	−4.73248e13	−0.688308
$329$	3.30540e11	0.00472766
$330$	5.90956e13	0.831243
$331$	5.34555e13	0.739500	0.369750	−	0.929131i	$-0.379443\pi$
$331$	5.34555e13	0.739500	0.369750	+	0.929131i	$0.379443\pi$
$332$	1.23061e13	0.167440
$333$	6.41913e12	0.0859078
$334$	−8.57621e13	−1.12899
$335$	2.97593e13	0.385369
$336$	−1.62876e12	−0.0207488
$337$	1.11660e14	1.39937	0.699683	−	0.714453i	$-0.253324\pi$
$337$	1.11660e14	1.39937	0.699683	+	0.714453i	$0.253324\pi$
$338$	7.53811e13	0.929438
$339$	1.90462e13	0.231052
$340$	−1.78389e13	−0.212929
$341$	5.87494e12	0.0690008
$342$	−2.65605e13	−0.306967
$343$	8.52447e12	0.0969504
$344$	2.54912e13	0.285311
$345$	5.64322e13	0.621615
$346$	3.95646e13	0.428931
$347$	−6.57924e12	−0.0702043	−0.0351021	−	0.999384i	$-0.511176\pi$
$347$	−6.57924e12	−0.0702043	−0.0351021	+	0.999384i	$0.511176\pi$
$348$	−6.80201e12	−0.0714417
$349$	−1.00714e14	−1.04124	−0.520621	−	0.853788i	$-0.674299\pi$
$349$	−1.00714e14	−1.04124	−0.520621	+	0.853788i	$0.674299\pi$
$350$	−5.98191e12	−0.0608788
$351$	−2.74913e13	−0.275427
$352$	−4.44612e13	−0.438527
$353$	1.51736e14	1.47343	0.736713	−	0.676206i	$-0.236377\pi$
$353$	1.51736e14	1.47343	0.736713	+	0.676206i	$0.236377\pi$
$354$	−6.97106e12	−0.0666470
$355$	1.96896e14	1.85345
$356$	4.71672e12	0.0437185
$357$	1.96764e12	0.0179586
$358$	5.24428e13	0.471335
$359$	−1.24269e14	−1.09988	−0.549940	−	0.835204i	$-0.685349\pi$
$359$	−1.24269e14	−1.09988	−0.549940	+	0.835204i	$0.685349\pi$
$360$	−6.39570e13	−0.557474
$361$	9.16534e12	0.0786790
$362$	1.43729e14	1.21520
$363$	−6.37071e12	−0.0530520
$364$	1.81042e12	0.0148499
$365$	−1.55869e13	−0.125936
$366$	5.72102e13	0.455331
$367$	7.27399e13	0.570308	0.285154	−	0.958482i	$-0.407955\pi$
$367$	7.27399e13	0.570308	0.285154	+	0.958482i	$0.407955\pi$
$368$	6.64254e13	0.513063
$369$	2.80152e13	0.213181
$370$	4.73656e13	0.355102
$371$	−3.19758e11	−0.00236192
$372$	−1.11993e12	−0.00815092
$373$	1.81085e14	1.29862	0.649311	−	0.760523i	$-0.275057\pi$
$373$	1.81085e14	1.29862	0.649311	+	0.760523i	$0.275057\pi$
$374$	−8.40331e13	−0.593823
$375$	−5.34303e13	−0.372062
$376$	1.52778e13	0.104840
$377$	−1.22483e14	−0.828321
$378$	1.24257e12	0.00828165
$379$	9.85582e13	0.647407	0.323703	−	0.946159i	$-0.395072\pi$
$379$	9.85582e13	0.647407	0.323703	+	0.946159i	$0.395072\pi$
$380$	5.32955e13	0.345049
$381$	1.30597e14	0.833387
$382$	−1.55616e14	−0.978825
$383$	1.40097e14	0.868632	0.434316	−	0.900761i	$-0.356990\pi$
$383$	1.40097e14	0.868632	0.434316	+	0.900761i	$0.356990\pi$
$384$	−5.35469e13	−0.327275
$385$	1.30794e13	0.0788049
$386$	−8.31266e13	−0.493753
$387$	−1.50902e13	−0.0883657
$388$	1.25576e13	0.0724990
$389$	−1.72756e14	−0.983353	−0.491677	−	0.870778i	$-0.663616\pi$
$389$	−1.72756e14	−0.983353	−0.491677	+	0.870778i	$0.663616\pi$
$390$	−2.02854e14	−1.13849
$391$	−8.02458e13	−0.444069
$392$	1.96772e14	1.07372
$393$	1.40524e14	0.756119
$394$	−1.07715e14	−0.571541
$395$	−2.11350e14	−1.10591
$396$	1.44309e13	0.0744681
$397$	8.48196e13	0.431667	0.215833	−	0.976430i	$-0.430753\pi$
$397$	8.48196e13	0.431667	0.215833	+	0.976430i	$0.430753\pi$
$398$	−1.16315e14	−0.583820
$399$	−5.87852e12	−0.0291016
$400$	−2.14545e14	−1.04758
$401$	3.89323e14	1.87506	0.937531	−	0.347902i	$-0.113106\pi$
$401$	3.89323e14	1.87506	0.937531	+	0.347902i	$0.113106\pi$
$402$	−2.67235e13	−0.126955
$403$	−2.01665e13	−0.0945047
$404$	7.49975e13	0.346696
$405$	3.78610e13	0.172659
$406$	5.53607e12	0.0249063
$407$	−6.06754e13	−0.269304
$408$	9.09461e13	0.398248
$409$	−3.33404e14	−1.44043	−0.720216	−	0.693750i	$-0.755957\pi$
$409$	−3.33404e14	−1.44043	−0.720216	+	0.693750i	$0.755957\pi$
$410$	2.06719e14	0.881189
$411$	−6.68833e12	−0.0281312
$412$	3.36867e13	0.139805
$413$	−1.54288e12	−0.00631838
$414$	−5.06755e13	−0.204784
$415$	−3.05179e14	−1.21700
$416$	1.52619e14	0.600615
$417$	−9.22986e13	−0.358465
$418$	2.51057e14	0.962282
$419$	−1.70717e14	−0.645803	−0.322902	−	0.946433i	$-0.604658\pi$
$419$	−1.70717e14	−0.645803	−0.322902	+	0.946433i	$0.604658\pi$
$420$	−2.49331e12	−0.00930906
$421$	−4.50291e14	−1.65937	−0.829683	−	0.558235i	$-0.811479\pi$
$421$	−4.50291e14	−1.65937	−0.829683	+	0.558235i	$0.811479\pi$
$422$	−1.26294e14	−0.459372
$423$	−9.04410e12	−0.0324708
$424$	−1.47795e13	−0.0523778
$425$	2.59183e14	0.906708
$426$	−1.76810e14	−0.610598
$427$	1.26621e13	0.0431671
$428$	5.97609e13	0.201130
$429$	2.59856e14	0.863410
$430$	−1.11348e14	−0.365262
$431$	2.26249e12	0.00732761	0.00366380	−	0.999993i	$-0.498834\pi$
$431$	2.26249e12	0.00732761	0.00366380	+	0.999993i	$0.498834\pi$
$432$	4.45656e13	0.142508
$433$	−3.42076e14	−1.08004	−0.540020	−	0.841652i	$-0.681583\pi$
$433$	−3.42076e14	−1.08004	−0.540020	+	0.841652i	$0.681583\pi$
$434$	9.11501e11	0.00284160
$435$	1.68683e14	0.519256
$436$	1.20085e13	0.0365018
$437$	2.39742e14	0.719608
$438$	1.39969e13	0.0414881
$439$	−3.48639e14	−1.02052	−0.510260	−	0.860020i	$-0.670451\pi$
$439$	−3.48639e14	−1.02052	−0.510260	+	0.860020i	$0.670451\pi$
$440$	6.04540e14	1.74757
$441$	−1.16484e14	−0.332548
$442$	2.88455e14	0.813310
$443$	3.29245e14	0.916851	0.458425	−	0.888733i	$-0.348414\pi$
$443$	3.29245e14	0.916851	0.458425	+	0.888733i	$0.348414\pi$
$444$	1.15665e13	0.0318123
$445$	−1.16970e14	−0.317757
$446$	3.87921e14	1.04088
$447$	3.62040e14	0.959545
$448$	−2.06254e13	−0.0539974
$449$	−6.86507e14	−1.77537	−0.887687	−	0.460448i	$-0.847689\pi$
$449$	−6.86507e14	−1.77537	−0.887687	+	0.460448i	$0.847689\pi$
$450$	1.63675e14	0.418132
$451$	−2.64807e14	−0.668280
$452$	3.43190e13	0.0855604
$453$	1.70610e14	0.420209
$454$	6.50126e14	1.58194
$455$	−4.48968e13	−0.107933
$456$	−2.71710e14	−0.645355
$457$	−5.36365e14	−1.25870	−0.629348	−	0.777123i	$-0.716678\pi$
$457$	−5.36365e14	−1.25870	−0.629348	+	0.777123i	$0.716678\pi$
$458$	−1.79490e14	−0.416179
$459$	−5.38379e13	−0.123344
$460$	1.01684e14	0.230189
$461$	−4.90388e14	−1.09694	−0.548472	−	0.836169i	$-0.684790\pi$
$461$	−4.90388e14	−1.09694	−0.548472	+	0.836169i	$0.684790\pi$
$462$	−1.17451e13	−0.0259614
$463$	2.19955e14	0.480438	0.240219	−	0.970719i	$-0.422781\pi$
$463$	2.19955e14	0.480438	0.240219	+	0.970719i	$0.422781\pi$
$464$	1.98555e14	0.428579
$465$	2.77733e13	0.0592429
$466$	6.27763e14	1.32335
$467$	4.97412e14	1.03627	0.518135	−	0.855299i	$-0.326626\pi$
$467$	4.97412e14	1.03627	0.518135	+	0.855299i	$0.326626\pi$
$468$	−4.95361e13	−0.101993
$469$	−5.91461e12	−0.0120358
$470$	−6.67348e13	−0.134219
$471$	−1.44981e14	−0.288202
$472$	−7.13130e13	−0.140116
$473$	1.42636e14	0.277009
$474$	1.89790e14	0.364328
$475$	−7.74334e14	−1.46931
$476$	3.54546e12	0.00665019
$477$	8.74910e12	0.0162223
$478$	−6.35892e14	−1.16555
$479$	−2.32774e14	−0.421783	−0.210892	−	0.977509i	$-0.567637\pi$
$479$	−2.32774e14	−0.421783	−0.210892	+	0.977509i	$0.567637\pi$
$480$	−2.10187e14	−0.376512
$481$	2.08277e14	0.368844
$482$	−1.10870e13	−0.0194113
$483$	−1.12158e13	−0.0194143
$484$	−1.14793e13	−0.0196456
$485$	−3.11416e14	−0.526941
$486$	−3.39988e13	−0.0568806
$487$	−7.87944e14	−1.30342	−0.651712	−	0.758466i	$-0.725949\pi$
$487$	−7.87944e14	−1.30342	−0.651712	+	0.758466i	$0.725949\pi$
$488$	5.85253e14	0.957270
$489$	3.72505e14	0.602467
$490$	−8.59516e14	−1.37460
$491$	6.20707e14	0.981609	0.490805	−	0.871270i	$-0.336703\pi$
$491$	6.20707e14	0.981609	0.490805	+	0.871270i	$0.336703\pi$
$492$	5.04800e13	0.0789425
$493$	−2.39866e14	−0.370946
$494$	−8.61787e14	−1.31796
$495$	−3.57873e14	−0.541253
$496$	3.26915e13	0.0488974
$497$	−3.91327e13	−0.0578869
$498$	2.74047e14	0.400926
$499$	1.10067e15	1.59259	0.796295	−	0.604909i	$-0.206791\pi$
$499$	1.10067e15	1.59259	0.796295	+	0.604909i	$0.206791\pi$
$500$	−9.62749e13	−0.137777
$501$	5.19361e14	0.735126
$502$	−4.62430e14	−0.647404
$503$	−5.36081e14	−0.742346	−0.371173	−	0.928564i	$-0.621044\pi$
$503$	−5.36081e14	−0.742346	−0.371173	+	0.928564i	$0.621044\pi$
$504$	1.27114e13	0.0174110
$505$	−1.85987e15	−2.51988
$506$	4.78998e14	0.641958
$507$	−4.56495e14	−0.605191
$508$	2.35321e14	0.308610
$509$	−4.38157e13	−0.0568436	−0.0284218	−	0.999596i	$-0.509048\pi$
$509$	−4.38157e13	−0.0568436	−0.0284218	+	0.999596i	$0.509048\pi$
$510$	−3.97260e14	−0.509846
$511$	3.09787e12	0.00393322
$512$	−8.81890e14	−1.10772
$513$	1.60846e14	0.199878
$514$	8.21616e14	1.01012
$515$	−8.35398e14	−1.01614
$516$	−2.71907e13	−0.0327225
$517$	8.54873e13	0.101790
$518$	−9.41383e12	−0.0110905
$519$	−2.39596e14	−0.279293
$520$	−2.07517e15	−2.39351
$521$	1.26388e15	1.44245	0.721223	−	0.692703i	$-0.243580\pi$
$521$	1.26388e15	1.44245	0.721223	+	0.692703i	$0.243580\pi$
$522$	−1.51476e14	−0.171063
$523$	1.39636e14	0.156041	0.0780203	−	0.996952i	$-0.475140\pi$
$523$	1.39636e14	0.156041	0.0780203	+	0.996952i	$0.475140\pi$
$524$	2.53207e14	0.279997
$525$	3.62255e13	0.0396404
$526$	−7.01256e14	−0.759373
$527$	−3.94933e13	−0.0423219
$528$	−4.21247e14	−0.446735
$529$	−4.95400e14	−0.519935
$530$	6.45581e13	0.0670553
$531$	4.22156e13	0.0433963
$532$	−1.05924e13	−0.0107766
$533$	9.08987e14	0.915288
$534$	1.05038e14	0.104681
$535$	−1.48201e15	−1.46186
$536$	−2.73378e14	−0.266905
$537$	−3.17585e14	−0.306903
$538$	−1.93959e14	−0.185527
$539$	1.10104e15	1.04247
$540$	6.82211e13	0.0639371
$541$	1.31181e15	1.21698	0.608492	−	0.793560i	$-0.291775\pi$
$541$	1.31181e15	1.21698	0.608492	+	0.793560i	$0.291775\pi$
$542$	−2.24224e14	−0.205914
$543$	−8.70399e14	−0.791260
$544$	2.98883e14	0.268972
$545$	−2.97800e14	−0.265304
$546$	4.03168e13	0.0355571
$547$	1.39679e15	1.21955	0.609775	−	0.792575i	$-0.291260\pi$
$547$	1.39679e15	1.21955	0.609775	+	0.792575i	$0.291260\pi$
$548$	−1.20516e13	−0.0104172
$549$	−3.46456e14	−0.296483
$550$	−1.54710e15	−1.31076
$551$	7.16621e14	0.601113
$552$	−5.18403e14	−0.430529
$553$	4.20054e13	0.0345396
$554$	−8.37493e14	−0.681832
$555$	−2.86838e14	−0.231220
$556$	−1.66311e14	−0.132742
$557$	−4.83859e13	−0.0382398	−0.0191199	−	0.999817i	$-0.506086\pi$
$557$	−4.83859e13	−0.0382398	−0.0191199	+	0.999817i	$0.506086\pi$
$558$	−2.49401e13	−0.0195169
$559$	−4.89619e14	−0.379396
$560$	7.27812e13	0.0558451
$561$	5.08891e14	0.386660
$562$	−5.91979e14	−0.445406
$563$	−6.29975e14	−0.469383	−0.234691	−	0.972070i	$-0.575408\pi$
$563$	−6.29975e14	−0.469383	−0.234691	+	0.972070i	$0.575408\pi$
$564$	−1.62964e13	−0.0120242
$565$	−8.51078e14	−0.621875
$566$	1.76486e15	1.27709
$567$	−7.52482e12	−0.00539249
$568$	−1.80875e15	−1.28370
$569$	1.74779e15	1.22849	0.614244	−	0.789116i	$-0.289461\pi$
$569$	1.74779e15	1.22849	0.614244	+	0.789116i	$0.289461\pi$
$570$	1.18685e15	0.826200
$571$	−1.39780e15	−0.963709	−0.481855	−	0.876251i	$-0.660037\pi$
$571$	−1.39780e15	−0.963709	−0.481855	+	0.876251i	$0.660037\pi$
$572$	4.68229e14	0.319727
$573$	9.42383e14	0.637349
$574$	−4.10850e13	−0.0275212
$575$	−1.47737e15	−0.980205
$576$	5.64344e14	0.370869
$577$	8.30902e14	0.540858	0.270429	−	0.962740i	$-0.412835\pi$
$577$	8.30902e14	0.540858	0.270429	+	0.962740i	$0.412835\pi$
$578$	−8.10315e14	−0.522457
$579$	5.03401e14	0.321501
$580$	3.03947e14	0.192285
$581$	6.06538e13	0.0380092
$582$	2.79649e14	0.173595
$583$	−8.26989e13	−0.0508537
$584$	1.43186e14	0.0872228
$585$	1.22845e15	0.741310
$586$	−2.06792e14	−0.123622
$587$	2.27138e15	1.34518	0.672590	−	0.740015i	$-0.265182\pi$
$587$	2.27138e15	1.34518	0.672590	+	0.740015i	$0.265182\pi$
$588$	−2.09891e14	−0.123145
$589$	1.17990e14	0.0685821
$590$	3.11501e14	0.179380
$591$	6.52305e14	0.372151
$592$	−3.37633e14	−0.190843
$593$	−1.99332e15	−1.11629	−0.558143	−	0.829745i	$-0.688486\pi$
$593$	−1.99332e15	−1.11629	−0.558143	+	0.829745i	$0.688486\pi$
$594$	3.21366e14	0.178310
$595$	−8.79240e13	−0.0483353
$596$	6.52353e14	0.355327
$597$	7.04384e14	0.380146
$598$	−1.64423e15	−0.879236
$599$	−2.10272e15	−1.11412	−0.557061	−	0.830471i	$-0.688071\pi$
$599$	−2.10272e15	−1.11412	−0.557061	+	0.830471i	$0.688071\pi$
$600$	1.67437e15	0.879063
$601$	2.78719e15	1.44996	0.724982	−	0.688768i	$-0.241848\pi$
$601$	2.78719e15	1.44996	0.724982	+	0.688768i	$0.241848\pi$
$602$	2.21301e13	0.0114078
$603$	1.61833e14	0.0826652
$604$	3.07420e14	0.155607
$605$	2.84675e14	0.142789
$606$	1.67014e15	0.830144
$607$	−1.91153e15	−0.941549	−0.470774	−	0.882254i	$-0.656025\pi$
$607$	−1.91153e15	−0.941549	−0.470774	+	0.882254i	$0.656025\pi$
$608$	−8.92942e14	−0.435867
$609$	−3.35256e13	−0.0162174
$610$	−2.55644e15	−1.22552
$611$	−2.93447e14	−0.139413
$612$	−9.70095e13	−0.0456753
$613$	−1.74172e15	−0.812728	−0.406364	−	0.913711i	$-0.633203\pi$
$613$	−1.74172e15	−0.812728	−0.406364	+	0.913711i	$0.633203\pi$
$614$	1.82804e15	0.845395
$615$	−1.25186e15	−0.573774
$616$	−1.20151e14	−0.0545801
$617$	1.16947e15	0.526529	0.263264	−	0.964724i	$-0.415201\pi$
$617$	1.16947e15	0.526529	0.263264	+	0.964724i	$0.415201\pi$
$618$	7.50178e14	0.334756
$619$	−2.65006e15	−1.17208	−0.586039	−	0.810283i	$-0.699313\pi$
$619$	−2.65006e15	−1.17208	−0.586039	+	0.810283i	$0.699313\pi$
$620$	5.00442e13	0.0219381
$621$	3.06882e14	0.133342
$622$	2.04544e15	0.880928
$623$	2.32476e13	0.00992417
$624$	1.44599e15	0.611856
$625$	−9.85402e14	−0.413307
$626$	3.68537e15	1.53222
$627$	−1.52036e15	−0.626577
$628$	−2.61239e14	−0.106724
$629$	4.07880e14	0.165179
$630$	−5.55243e13	−0.0222900
$631$	−5.42479e14	−0.215885	−0.107942	−	0.994157i	$-0.534426\pi$
$631$	−5.42479e14	−0.215885	−0.107942	+	0.994157i	$0.534426\pi$
$632$	1.94153e15	0.765948
$633$	7.64817e14	0.299114
$634$	1.93952e15	0.751974
$635$	−5.83573e15	−2.24305
$636$	1.57648e13	0.00600724
$637$	−3.77947e15	−1.42779
$638$	1.43179e15	0.536249
$639$	1.07073e15	0.397582
$640$	2.39274e15	0.880858
$641$	3.75984e15	1.37231	0.686153	−	0.727458i	$-0.259298\pi$
$641$	3.75984e15	1.37231	0.686153	+	0.727458i	$0.259298\pi$
$642$	1.33083e15	0.481594
$643$	3.89589e15	1.39780	0.698901	−	0.715218i	$-0.253673\pi$
$643$	3.89589e15	1.39780	0.698901	+	0.715218i	$0.253673\pi$
$644$	−2.02095e13	−0.00718925
$645$	6.74303e14	0.237835
$646$	−1.68769e15	−0.590220
$647$	9.79556e14	0.339669	0.169834	−	0.985473i	$-0.445677\pi$
$647$	9.79556e14	0.339669	0.169834	+	0.985473i	$0.445677\pi$
$648$	−3.47803e14	−0.119583
$649$	−3.99033e14	−0.136039
$650$	5.31063e15	1.79524
$651$	−5.51990e12	−0.00185027
$652$	6.71209e14	0.223098
$653$	−3.23399e15	−1.06590	−0.532950	−	0.846147i	$-0.678917\pi$
$653$	−3.23399e15	−1.06590	−0.532950	+	0.846147i	$0.678917\pi$
$654$	2.67421e14	0.0874014
$655$	−6.27929e15	−2.03509
$656$	−1.47354e15	−0.473577
$657$	−8.47627e13	−0.0270144
$658$	1.32634e13	0.00419192
$659$	−3.35560e15	−1.05172	−0.525861	−	0.850571i	$-0.676257\pi$
$659$	−3.35560e15	−1.05172	−0.525861	+	0.850571i	$0.676257\pi$
$660$	−6.44844e14	−0.200430
$661$	4.39193e15	1.35378	0.676890	−	0.736085i	$-0.263327\pi$
$661$	4.39193e15	1.35378	0.676890	+	0.736085i	$0.263327\pi$
$662$	2.14499e15	0.655701
$663$	−1.74684e15	−0.529576
$664$	2.80347e15	0.842890
$665$	2.62681e14	0.0783267
$666$	2.57578e14	0.0761728
$667$	1.36726e15	0.401014
$668$	9.35827e14	0.272223
$669$	−2.34919e15	−0.677757
$670$	1.19414e15	0.341699
$671$	3.27479e15	0.929416
$672$	4.17743e13	0.0117592
$673$	−2.16401e14	−0.0604195	−0.0302097	−	0.999544i	$-0.509618\pi$
$673$	−2.16401e14	−0.0604195	−0.0302097	+	0.999544i	$0.509618\pi$
$674$	4.48052e15	1.24079
$675$	−9.91188e14	−0.272261
$676$	−8.22550e14	−0.224107
$677$	−4.65762e14	−0.125871	−0.0629356	−	0.998018i	$-0.520046\pi$
$677$	−4.65762e14	−0.125871	−0.0629356	+	0.998018i	$0.520046\pi$
$678$	7.64259e14	0.204869
$679$	6.18935e13	0.0164574
$680$	−4.06392e15	−1.07188
$681$	−3.93706e15	−1.03006
$682$	2.35741e14	0.0611817
$683$	1.65412e15	0.425845	0.212923	−	0.977069i	$-0.431702\pi$
$683$	1.65412e15	0.425845	0.212923	+	0.977069i	$0.431702\pi$
$684$	2.89825e14	0.0740163
$685$	2.98868e14	0.0757148
$686$	3.42058e14	0.0859641
$687$	1.08696e15	0.270989
$688$	7.93711e14	0.196303
$689$	2.83875e14	0.0696501
$690$	2.26443e15	0.551174
$691$	−6.25409e15	−1.51020	−0.755101	−	0.655609i	$-0.772412\pi$
$691$	−6.25409e15	−1.51020	−0.755101	+	0.655609i	$0.772412\pi$
$692$	−4.31724e14	−0.103424
$693$	7.11266e13	0.0169044
$694$	−2.64002e14	−0.0622488
$695$	4.12436e15	0.964806
$696$	−1.54958e15	−0.359636
$697$	1.78012e15	0.409892
$698$	−4.04132e15	−0.923248
$699$	−3.80163e15	−0.861679
$700$	6.52740e13	0.0146792
$701$	−1.83887e15	−0.410300	−0.205150	−	0.978731i	$-0.565768\pi$
$701$	−1.83887e15	−0.410300	−0.205150	+	0.978731i	$0.565768\pi$
$702$	−1.10313e15	−0.244216
$703$	−1.21858e15	−0.267670
$704$	−5.33434e15	−1.16260
$705$	4.04135e14	0.0873949
$706$	6.08866e15	1.30646
$707$	3.69645e14	0.0787007
$708$	7.60674e13	0.0160700
$709$	9.16067e15	1.92032	0.960158	−	0.279456i	$-0.0901541\pi$
$709$	9.16067e15	1.92032	0.960158	+	0.279456i	$0.0901541\pi$
$710$	7.90076e15	1.64342
$711$	−1.14934e15	−0.237227
$712$	1.07452e15	0.220078
$713$	2.25116e14	0.0457525
$714$	7.89548e13	0.0159235
$715$	−1.16116e16	−2.32386
$716$	−5.72251e14	−0.113649
$717$	3.85086e15	0.758931
$718$	−4.98651e15	−0.975241
$719$	−5.97641e14	−0.115993	−0.0579965	−	0.998317i	$-0.518471\pi$
$719$	−5.97641e14	−0.115993	−0.0579965	+	0.998317i	$0.518471\pi$
$720$	−1.99141e15	−0.383559
$721$	1.66034e14	0.0317360
$722$	3.67774e14	0.0697631
$723$	6.71410e13	0.0126394
$724$	−1.56835e15	−0.293010
$725$	−4.41607e15	−0.818798
$726$	−2.55635e14	−0.0470402
$727$	3.53545e15	0.645662	0.322831	−	0.946457i	$-0.395365\pi$
$727$	3.53545e15	0.645662	0.322831	+	0.946457i	$0.395365\pi$
$728$	4.12436e14	0.0747538
$729$	2.05891e14	0.0370370
$730$	−6.25449e14	−0.111665
$731$	−9.58850e14	−0.169905
$732$	−6.24272e14	−0.109790
$733$	−2.96392e15	−0.517362	−0.258681	−	0.965963i	$-0.583288\pi$
$733$	−2.96392e15	−0.517362	−0.258681	+	0.965963i	$0.583288\pi$
$734$	2.91880e15	0.505681
$735$	5.20509e15	0.895051
$736$	−1.70367e15	−0.290775
$737$	−1.52969e15	−0.259139
$738$	1.12415e15	0.189023
$739$	−3.78463e15	−0.631654	−0.315827	−	0.948817i	$-0.602282\pi$
$739$	−3.78463e15	−0.631654	−0.315827	+	0.948817i	$0.602282\pi$
$740$	−5.16848e14	−0.0856226
$741$	5.21884e15	0.858171
$742$	−1.28308e13	−0.00209427
$743$	1.09269e16	1.77036	0.885178	−	0.465253i	$-0.154037\pi$
$743$	1.09269e16	1.77036	0.885178	+	0.465253i	$0.154037\pi$
$744$	−2.55134e14	−0.0410315
$745$	−1.61777e16	−2.58261
$746$	7.26631e15	1.15146
$747$	−1.65958e15	−0.261057
$748$	9.16961e14	0.143183
$749$	2.94548e14	0.0456568
$750$	−2.14397e15	−0.329900
$751$	−2.74996e14	−0.0420055	−0.0210028	−	0.999779i	$-0.506686\pi$
$751$	−2.74996e14	−0.0420055	−0.0210028	+	0.999779i	$0.506686\pi$
$752$	4.75701e14	0.0721333
$753$	2.80040e15	0.421548
$754$	−4.91483e15	−0.734456
$755$	−7.62372e15	−1.13099
$756$	−1.35588e13	−0.00199688
$757$	2.81151e15	0.411067	0.205534	−	0.978650i	$-0.434107\pi$
$757$	2.81151e15	0.411067	0.205534	+	0.978650i	$0.434107\pi$
$758$	3.95480e15	0.574043
$759$	−2.90074e15	−0.418002
$760$	1.21413e16	1.73697
$761$	6.70712e15	0.952622	0.476311	−	0.879277i	$-0.341974\pi$
$761$	6.70712e15	0.952622	0.476311	+	0.879277i	$0.341974\pi$
$762$	5.24042e15	0.738948
$763$	5.91873e13	0.00828597
$764$	1.69806e15	0.236015
$765$	2.40574e15	0.331980
$766$	5.62162e15	0.770199
$767$	1.36974e15	0.186321
$768$	2.60763e15	0.352175
$769$	7.23241e15	0.969814	0.484907	−	0.874566i	$-0.338854\pi$
$769$	7.23241e15	0.969814	0.484907	+	0.874566i	$0.338854\pi$
$770$	5.24831e14	0.0698748
$771$	−4.97557e15	−0.657724
$772$	9.07069e14	0.119054
$773$	1.30804e16	1.70464	0.852322	−	0.523018i	$-0.175194\pi$
$773$	1.30804e16	1.70464	0.852322	+	0.523018i	$0.175194\pi$
$774$	−6.05517e14	−0.0783521
$775$	−7.27095e14	−0.0934183
$776$	2.86077e15	0.364958
$777$	5.70086e13	0.00722146
$778$	−6.93210e15	−0.871920
$779$	−5.31828e15	−0.664225
$780$	2.21352e15	0.274513
$781$	−1.01209e16	−1.24634
$782$	−3.21999e15	−0.393747
$783$	9.17313e14	0.111385
$784$	6.12682e15	0.738749
$785$	6.47848e15	0.775694
$786$	5.63873e15	0.670436
$787$	4.25105e15	0.501921	0.250960	−	0.967997i	$-0.419254\pi$
$787$	4.25105e15	0.501921	0.250960	+	0.967997i	$0.419254\pi$
$788$	1.17538e15	0.137810
$789$	4.24669e15	0.494455
$790$	−8.48075e15	−0.980586
$791$	1.69150e14	0.0194224
$792$	3.28753e15	0.374871
$793$	−1.12412e16	−1.27294
$794$	3.40352e15	0.382750
$795$	−3.90953e14	−0.0436622
$796$	1.26922e15	0.140771
$797$	1.64370e15	0.181052	0.0905259	−	0.995894i	$-0.471145\pi$
$797$	1.64370e15	0.181052	0.0905259	+	0.995894i	$0.471145\pi$
$798$	−2.35885e14	−0.0258038
$799$	−5.74675e14	−0.0624331
$800$	5.50262e15	0.593710
$801$	−6.36092e14	−0.0681619
$802$	1.56222e16	1.66258
$803$	8.01201e14	0.0846848
$804$	2.91604e14	0.0306116
$805$	5.01177e14	0.0522533
$806$	−8.09214e14	−0.0837955
$807$	1.17458e15	0.120803
$808$	1.70853e16	1.74526
$809$	−1.93364e16	−1.96182	−0.980908	−	0.194471i	$-0.937701\pi$
$809$	−1.93364e16	−1.96182	−0.980908	+	0.194471i	$0.937701\pi$
$810$	1.51923e15	0.153094
$811$	5.64125e15	0.564626	0.282313	−	0.959322i	$-0.408898\pi$
$811$	5.64125e15	0.564626	0.282313	+	0.959322i	$0.408898\pi$
$812$	−6.04090e13	−0.00600542
$813$	1.35787e15	0.134078
$814$	−2.43470e15	−0.238787
$815$	−1.66454e16	−1.62154
$816$	2.83176e15	0.274007
$817$	2.86465e15	0.275328
$818$	−1.33784e16	−1.27720
$819$	−2.44152e14	−0.0231525
$820$	−2.25569e15	−0.212473
$821$	−1.49473e16	−1.39854	−0.699271	−	0.714856i	$-0.746492\pi$
$821$	−1.49473e16	−1.39854	−0.699271	+	0.714856i	$0.746492\pi$
$822$	−2.68380e14	−0.0249434
$823$	−3.25771e15	−0.300756	−0.150378	−	0.988629i	$-0.548049\pi$
$823$	−3.25771e15	−0.300756	−0.150378	+	0.988629i	$0.548049\pi$
$824$	7.67422e15	0.703776
$825$	9.36898e15	0.853485
$826$	−6.19103e13	−0.00560238
$827$	−1.34022e16	−1.20475	−0.602373	−	0.798214i	$-0.705778\pi$
$827$	−1.34022e16	−1.20475	−0.602373	+	0.798214i	$0.705778\pi$
$828$	5.52965e14	0.0493777
$829$	1.18044e16	1.04712	0.523559	−	0.851989i	$-0.324604\pi$
$829$	1.18044e16	1.04712	0.523559	+	0.851989i	$0.324604\pi$
$830$	−1.22458e16	−1.07909
$831$	5.07172e15	0.443966
$832$	1.83108e16	1.59232
$833$	−7.40157e15	−0.639405
$834$	−3.70363e15	−0.317844
$835$	−2.32076e16	−1.97859
$836$	−2.73951e15	−0.232027
$837$	1.51033e14	0.0127082
$838$	−6.85030e15	−0.572621
$839$	−1.85159e16	−1.53764	−0.768819	−	0.639466i	$-0.779155\pi$
$839$	−1.85159e16	−1.53764	−0.768819	+	0.639466i	$0.779155\pi$
$840$	−5.68006e14	−0.0468616
$841$	−8.11357e15	−0.665019
$842$	−1.80687e16	−1.47133
$843$	3.58493e15	0.290020
$844$	1.37811e15	0.110764
$845$	2.03985e16	1.62887
$846$	−3.62909e14	−0.0287913
$847$	−5.65787e13	−0.00445958
$848$	−4.60184e14	−0.0360375
$849$	−1.06877e16	−0.831558
$850$	1.04001e16	0.803961
$851$	−2.32496e15	−0.178568
$852$	1.92934e15	0.147228
$853$	−1.44922e16	−1.09879	−0.549395	−	0.835563i	$-0.685142\pi$
$853$	−1.44922e16	−1.09879	−0.549395	+	0.835563i	$0.685142\pi$
$854$	5.08087e14	0.0382754
$855$	−7.18738e15	−0.537969
$856$	1.36142e16	1.01248
$857$	1.32162e15	0.0976589	0.0488294	−	0.998807i	$-0.484451\pi$
$857$	1.32162e15	0.0976589	0.0488294	+	0.998807i	$0.484451\pi$
$858$	1.04271e16	0.765569
$859$	1.00009e16	0.729586	0.364793	−	0.931089i	$-0.381140\pi$
$859$	1.00009e16	0.729586	0.364793	+	0.931089i	$0.381140\pi$
$860$	1.21501e15	0.0880723
$861$	2.48804e14	0.0179201
$862$	9.07861e13	0.00649725
$863$	−5.30862e15	−0.377505	−0.188752	−	0.982025i	$-0.560444\pi$
$863$	−5.30862e15	−0.377505	−0.188752	+	0.982025i	$0.560444\pi$
$864$	−1.14301e15	−0.0807654
$865$	1.07064e16	0.751715
$866$	−1.37264e16	−0.957650
$867$	4.90713e15	0.340191
$868$	−9.94620e12	−0.000685171 0
$869$	1.08639e16	0.743661
$870$	6.76869e15	0.460414
$871$	5.25088e15	0.354922
$872$	2.73568e15	0.183749
$873$	−1.69351e15	−0.113034
$874$	9.62002e15	0.638062
$875$	−4.74517e14	−0.0312757
$876$	−1.52732e14	−0.0100036
$877$	−8.01495e15	−0.521679	−0.260839	−	0.965382i	$-0.583999\pi$
$877$	−8.01495e15	−0.521679	−0.260839	+	0.965382i	$0.583999\pi$
$878$	−1.39897e16	−0.904875
$879$	1.25230e15	0.0804948
$880$	1.88234e16	1.20238
$881$	−2.14390e16	−1.36093	−0.680466	−	0.732779i	$-0.738223\pi$
$881$	−2.14390e16	−1.36093	−0.680466	+	0.732779i	$0.738223\pi$
$882$	−4.67411e15	−0.294864
$883$	−1.67860e16	−1.05235	−0.526177	−	0.850375i	$-0.676375\pi$
$883$	−1.67860e16	−1.05235	−0.526177	+	0.850375i	$0.676375\pi$
$884$	−3.14759e15	−0.196106
$885$	−1.88640e15	−0.116801
$886$	1.32115e16	0.812954
$887$	2.63626e16	1.61216	0.806079	−	0.591808i	$-0.201585\pi$
$887$	2.63626e16	1.61216	0.806079	+	0.591808i	$0.201585\pi$
$888$	2.63498e15	0.160143
$889$	1.15984e15	0.0700550
$890$	−4.69361e15	−0.281749
$891$	−1.94614e15	−0.116104
$892$	−4.23296e15	−0.250979
$893$	1.71689e15	0.101172
$894$	1.45274e16	0.850810
$895$	1.41913e16	0.826028
$896$	−4.75553e14	−0.0275109
$897$	9.95718e15	0.572503
$898$	−2.75472e16	−1.57419
$899$	6.72904e14	0.0382186
$900$	−1.78600e15	−0.100820
$901$	5.55930e14	0.0311913
$902$	−1.06258e16	−0.592551
$903$	−1.34017e14	−0.00742806
$904$	7.81826e15	0.430709
$905$	3.88937e16	2.12967
$906$	6.84602e15	0.372591
$907$	5.82362e15	0.315031	0.157515	−	0.987517i	$-0.449652\pi$
$907$	5.82362e15	0.315031	0.157515	+	0.987517i	$0.449652\pi$
$908$	−7.09411e15	−0.381439
$909$	−1.01141e16	−0.540537
$910$	−1.80155e15	−0.0957017
$911$	−8.45962e14	−0.0446684	−0.0223342	−	0.999751i	$-0.507110\pi$
$911$	−8.45962e14	−0.0446684	−0.0223342	+	0.999751i	$0.507110\pi$
$912$	−8.46015e15	−0.444024
$913$	1.56869e16	0.818364
$914$	−2.15225e16	−1.11606
$915$	1.54813e16	0.797981
$916$	1.95857e15	0.100349
$917$	1.24800e15	0.0635598
$918$	−2.16033e15	−0.109367
$919$	5.10553e15	0.256925	0.128462	−	0.991714i	$-0.458996\pi$
$919$	5.10553e15	0.256925	0.128462	+	0.991714i	$0.458996\pi$
$920$	2.31648e16	1.15877
$921$	−1.10703e16	−0.550468
$922$	−1.96776e16	−0.972639
$923$	3.47413e16	1.70701
$924$	1.28162e14	0.00625983
$925$	7.50932e15	0.364604
$926$	8.82603e15	0.425996
$927$	−4.54296e15	−0.217972
$928$	−5.09250e15	−0.242894
$929$	7.11854e15	0.337524	0.168762	−	0.985657i	$-0.446023\pi$
$929$	7.11854e15	0.337524	0.168762	+	0.985657i	$0.446023\pi$
$930$	1.11445e15	0.0525296
$931$	2.21129e16	1.03615
$932$	−6.85008e15	−0.319086
$933$	−1.23869e16	−0.573605
$934$	1.99594e16	0.918841
$935$	−2.27398e16	−1.04069
$936$	−1.12849e16	−0.513429
$937$	1.39346e16	0.630271	0.315135	−	0.949047i	$-0.397950\pi$
$937$	1.39346e16	0.630271	0.315135	+	0.949047i	$0.397950\pi$
$938$	−2.37333e14	−0.0106719
$939$	−2.23180e16	−0.997687
$940$	7.28203e14	0.0323630
$941$	−2.95060e16	−1.30367	−0.651834	−	0.758362i	$-0.726000\pi$
$941$	−2.95060e16	−1.30367	−0.651834	+	0.758362i	$0.726000\pi$
$942$	−5.81761e15	−0.255543
$943$	−1.01469e16	−0.443118
$944$	−2.22045e15	−0.0964040
$945$	3.36246e14	0.0145138
$946$	5.72351e15	0.245619
$947$	−2.92627e16	−1.24850	−0.624251	−	0.781224i	$-0.714596\pi$
$947$	−2.92627e16	−1.24850	−0.624251	+	0.781224i	$0.714596\pi$
$948$	−2.07097e15	−0.0878471
$949$	−2.75023e15	−0.115986
$950$	−3.10714e16	−1.30281
$951$	−1.17454e16	−0.489638
$952$	8.07697e14	0.0334769
$953$	−1.08778e16	−0.448259	−0.224130	−	0.974559i	$-0.571954\pi$
$953$	−1.08778e16	−0.448259	−0.224130	+	0.974559i	$0.571954\pi$
$954$	3.51072e14	0.0143840
$955$	−4.21103e16	−1.71542
$956$	6.93879e15	0.281038
$957$	−8.67070e15	−0.349171
$958$	−9.34043e15	−0.373987
$959$	−5.93994e13	−0.00236472
$960$	−2.52177e16	−0.998190
$961$	−2.52977e16	−0.995640
$962$	8.35743e15	0.327047
$963$	−8.05930e15	−0.313583
$964$	1.20980e14	0.00468048
$965$	−2.24944e16	−0.865317
$966$	−4.50052e14	−0.0172142
$967$	−3.45076e16	−1.31241	−0.656204	−	0.754584i	$-0.727839\pi$
$967$	−3.45076e16	−1.31241	−0.656204	+	0.754584i	$0.727839\pi$
$968$	−2.61511e15	−0.0988953
$969$	1.02204e16	0.384314
$970$	−1.24961e16	−0.467228
$971$	1.99218e16	0.740666	0.370333	−	0.928899i	$-0.379244\pi$
$971$	1.99218e16	0.740666	0.370333	+	0.928899i	$0.379244\pi$
$972$	3.70991e14	0.0137151
$973$	−8.19709e14	−0.0301328
$974$	−3.16175e16	−1.15572
$975$	−3.21603e16	−1.16895
$976$	1.82228e16	0.658631
$977$	−8.01737e15	−0.288145	−0.144073	−	0.989567i	$-0.546020\pi$
$977$	−8.01737e15	−0.288145	−0.144073	+	0.989567i	$0.546020\pi$
$978$	1.49474e16	0.534196
$979$	6.01252e15	0.213674
$980$	9.37894e15	0.331444
$981$	−1.61946e15	−0.0569103
$982$	2.49069e16	0.870374
$983$	4.41167e16	1.53306	0.766530	−	0.642209i	$-0.221982\pi$
$983$	4.41167e16	1.53306	0.766530	+	0.642209i	$0.221982\pi$
$984$	1.14999e16	0.397395
$985$	−2.91482e16	−1.00164
$986$	−9.62500e15	−0.328910
$987$	−8.03211e13	−0.00272951
$988$	9.40373e15	0.317788
$989$	5.46555e15	0.183677
$990$	−1.43602e16	−0.479919
$991$	−4.98490e16	−1.65673	−0.828364	−	0.560190i	$-0.810728\pi$
$991$	−4.98490e16	−1.65673	−0.828364	+	0.560190i	$0.810728\pi$
$992$	−8.38468e14	−0.0277123
$993$	−1.29897e16	−0.426951
$994$	−1.57026e15	−0.0513272
$995$	−3.14754e16	−1.02316
$996$	−2.99037e15	−0.0966716
$997$	−3.71813e16	−1.19537	−0.597684	−	0.801732i	$-0.703912\pi$
$997$	−3.71813e16	−1.19537	−0.597684	+	0.801732i	$0.703912\pi$
$998$	4.41661e16	1.41212
$999$	−1.55985e15	−0.0495989

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.a.1.20	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.a.1.20	✓	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)

\(f(q)\)	\(=\)	\(q+40.1266 q^{2} -243.000 q^{3} -437.857 q^{4} +10858.4 q^{5} -9750.76 q^{6} -2158.10 q^{7} -99749.0 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+40.1266 q^{2} -243.000 q^{3} -437.857 q^{4} +10858.4 q^{5} -9750.76 q^{6} -2158.10 q^{7} -99749.0 q^{8} +59049.0 q^{9} +435712. q^{10} -558147. q^{11} +106399. q^{12} +1.91592e6 q^{13} -86597.0 q^{14} -2.63860e6 q^{15} -3.10585e6 q^{16} +3.75206e6 q^{17} +2.36943e6 q^{18} -1.12096e7 q^{19} -4.75444e6 q^{20} +524417. q^{21} -2.23966e7 q^{22} -2.13872e7 q^{23} +2.42390e7 q^{24} +6.90776e7 q^{25} +7.68793e7 q^{26} -1.43489e7 q^{27} +944937. q^{28} -6.39291e7 q^{29} -1.05878e8 q^{30} -1.05258e7 q^{31} +7.96585e7 q^{32} +1.35630e8 q^{33} +1.50557e8 q^{34} -2.34336e7 q^{35} -2.58550e7 q^{36} +1.08708e8 q^{37} -4.49804e8 q^{38} -4.65568e8 q^{39} -1.08312e9 q^{40} +4.74439e8 q^{41} +2.10431e7 q^{42} -2.55553e8 q^{43} +2.44389e8 q^{44} +6.41180e8 q^{45} -8.58193e8 q^{46} -1.53163e8 q^{47} +7.54723e8 q^{48} -1.97267e9 q^{49} +2.77185e9 q^{50} -9.11750e8 q^{51} -8.38898e8 q^{52} +1.48167e8 q^{53} -5.75773e8 q^{54} -6.06061e9 q^{55} +2.15268e8 q^{56} +2.72394e9 q^{57} -2.56526e9 q^{58} +7.14924e8 q^{59} +1.15533e9 q^{60} -5.86726e9 q^{61} -4.22364e8 q^{62} -1.27433e8 q^{63} +9.55721e9 q^{64} +2.08039e10 q^{65} +5.44236e9 q^{66} +2.74066e9 q^{67} -1.64286e9 q^{68} +5.19708e9 q^{69} -9.40309e8 q^{70} +1.81330e10 q^{71} -5.89008e9 q^{72} -1.43546e9 q^{73} +4.36210e9 q^{74} -1.67859e10 q^{75} +4.90821e9 q^{76} +1.20454e9 q^{77} -1.86817e10 q^{78} -1.94641e10 q^{79} -3.37247e10 q^{80} +3.48678e9 q^{81} +1.90376e10 q^{82} -2.81052e10 q^{83} -2.29620e8 q^{84} +4.07415e10 q^{85} -1.02545e10 q^{86} +1.55348e10 q^{87} +5.56746e10 q^{88} -1.07723e10 q^{89} +2.57284e10 q^{90} -4.13474e9 q^{91} +9.36451e9 q^{92} +2.55776e9 q^{93} -6.14589e9 q^{94} -1.21719e11 q^{95} -1.93570e10 q^{96} -2.86797e10 q^{97} -7.91565e10 q^{98} -3.29581e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9}+O(q^{10}) \) 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

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