LMFDB - Embedded newform 177.12.a.a.1.10

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			1.10
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)

$f(q)$	$=$	$q-35.6107 q^{2} -243.000 q^{3} -779.875 q^{4} -1849.70 q^{5} +8653.41 q^{6} +64152.0 q^{7} +100703. q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-35.6107 q^{2} -243.000 q^{3} -779.875 q^{4} -1849.70 q^{5} +8653.41 q^{6} +64152.0 q^{7} +100703. q^{8} +59049.0 q^{9} +65869.2 q^{10} -256626. q^{11} +189510. q^{12} +1.02774e6 q^{13} -2.28450e6 q^{14} +449477. q^{15} -1.98891e6 q^{16} -1.90460e6 q^{17} -2.10278e6 q^{18} -1.21243e7 q^{19} +1.44254e6 q^{20} -1.55889e7 q^{21} +9.13866e6 q^{22} -3.64620e6 q^{23} -2.44708e7 q^{24} -4.54067e7 q^{25} -3.65987e7 q^{26} -1.43489e7 q^{27} -5.00306e7 q^{28} +2.53853e7 q^{29} -1.60062e7 q^{30} +5.61268e7 q^{31} -1.35412e8 q^{32} +6.23602e7 q^{33} +6.78242e7 q^{34} -1.18662e8 q^{35} -4.60509e7 q^{36} -5.07666e7 q^{37} +4.31756e8 q^{38} -2.49742e8 q^{39} -1.86270e8 q^{40} +1.16411e9 q^{41} +5.55134e8 q^{42} -1.61126e8 q^{43} +2.00137e8 q^{44} -1.09223e8 q^{45} +1.29844e8 q^{46} -7.75113e6 q^{47} +4.83306e8 q^{48} +2.13815e9 q^{49} +1.61697e9 q^{50} +4.62818e8 q^{51} -8.01511e8 q^{52} +3.09350e9 q^{53} +5.10975e8 q^{54} +4.74682e8 q^{55} +6.46028e9 q^{56} +2.94621e9 q^{57} -9.03990e8 q^{58} +7.14924e8 q^{59} -3.50536e8 q^{60} -6.22795e9 q^{61} -1.99872e9 q^{62} +3.78811e9 q^{63} +8.89543e9 q^{64} -1.90102e9 q^{65} -2.22069e9 q^{66} -1.55950e10 q^{67} +1.48535e9 q^{68} +8.86026e8 q^{69} +4.22564e9 q^{70} -2.68594e10 q^{71} +5.94640e9 q^{72} +2.50826e10 q^{73} +1.80783e9 q^{74} +1.10338e10 q^{75} +9.45547e9 q^{76} -1.64631e10 q^{77} +8.89348e9 q^{78} -1.58824e10 q^{79} +3.67889e9 q^{80} +3.48678e9 q^{81} -4.14548e10 q^{82} +3.36086e10 q^{83} +1.21574e10 q^{84} +3.52294e9 q^{85} +5.73782e9 q^{86} -6.16863e9 q^{87} -2.58430e10 q^{88} +1.40070e10 q^{89} +3.88951e9 q^{90} +6.59318e10 q^{91} +2.84358e9 q^{92} -1.36388e10 q^{93} +2.76023e8 q^{94} +2.24264e10 q^{95} +3.29052e10 q^{96} +7.46648e10 q^{97} -7.61412e10 q^{98} -1.51535e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−35.6107	−0.786894	−0.393447	−	0.919347i	$-0.628717\pi$
$2$	−35.6107	−0.786894	−0.393447	+	0.919347i	$0.628717\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	−779.875	−0.380799
$5$	−1849.70	−0.264708	−0.132354	−	0.991203i	$-0.542253\pi$
$5$	−1849.70	−0.264708	−0.132354	+	0.991203i	$0.542253\pi$
$6$	8653.41	0.454313
$7$	64152.0	1.44268	0.721342	−	0.692579i	$-0.243526\pi$
$7$	64152.0	1.44268	0.721342	+	0.692579i	$0.243526\pi$
$8$	100703.	1.08654
$9$	59049.0	0.333333
$10$	65869.2	0.208297
$11$	−256626.	−0.480443	−0.240221	−	0.970718i	$-0.577220\pi$
$11$	−256626.	−0.480443	−0.240221	+	0.970718i	$0.577220\pi$
$12$	189510.	0.219854
$13$	1.02774e6	0.767708	0.383854	−	0.923394i	$-0.374597\pi$
$13$	1.02774e6	0.767708	0.383854	+	0.923394i	$0.374597\pi$
$14$	−2.28450e6	−1.13524
$15$	449477.	0.152829
$16$	−1.98891e6	−0.474194
$17$	−1.90460e6	−0.325338	−0.162669	−	0.986681i	$-0.552010\pi$
$17$	−1.90460e6	−0.325338	−0.162669	+	0.986681i	$0.552010\pi$
$18$	−2.10278e6	−0.262298
$19$	−1.21243e7	−1.12334	−0.561672	−	0.827360i	$-0.689842\pi$
$19$	−1.21243e7	−1.12334	−0.561672	+	0.827360i	$0.689842\pi$
$20$	1.44254e6	0.100800
$21$	−1.55889e7	−0.832934
$22$	9.13866e6	0.378057
$23$	−3.64620e6	−0.118124	−0.0590619	−	0.998254i	$-0.518811\pi$
$23$	−3.64620e6	−0.118124	−0.0590619	+	0.998254i	$0.518811\pi$
$24$	−2.44708e7	−0.627315
$25$	−4.54067e7	−0.929930
$26$	−3.65987e7	−0.604104
$27$	−1.43489e7	−0.192450
$28$	−5.00306e7	−0.549372
$29$	2.53853e7	0.229823	0.114911	−	0.993376i	$-0.463342\pi$
$29$	2.53853e7	0.229823	0.114911	+	0.993376i	$0.463342\pi$
$30$	−1.60062e7	−0.120260
$31$	5.61268e7	0.352112	0.176056	−	0.984380i	$-0.443666\pi$
$31$	5.61268e7	0.352112	0.176056	+	0.984380i	$0.443666\pi$
$32$	−1.35412e8	−0.713401
$33$	6.23602e7	0.277384
$34$	6.78242e7	0.256006
$35$	−1.18662e8	−0.381889
$36$	−4.60509e7	−0.126933
$37$	−5.07666e7	−0.120356	−0.0601781	−	0.998188i	$-0.519167\pi$
$37$	−5.07666e7	−0.120356	−0.0601781	+	0.998188i	$0.519167\pi$
$38$	4.31756e8	0.883953
$39$	−2.49742e8	−0.443236
$40$	−1.86270e8	−0.287616
$41$	1.16411e9	1.56922	0.784608	−	0.619992i	$-0.212864\pi$
$41$	1.16411e9	1.56922	0.784608	+	0.619992i	$0.212864\pi$
$42$	5.55134e8	0.655430
$43$	−1.61126e8	−0.167144	−0.0835718	−	0.996502i	$-0.526633\pi$
$43$	−1.61126e8	−0.167144	−0.0835718	+	0.996502i	$0.526633\pi$
$44$	2.00137e8	0.182952
$45$	−1.09223e8	−0.0882359
$46$	1.29844e8	0.0929508
$47$	−7.75113e6	−0.00492977	−0.00246488	−	0.999997i	$-0.500785\pi$
$47$	−7.75113e6	−0.00492977	−0.00246488	+	0.999997i	$0.500785\pi$
$48$	4.83306e8	0.273776
$49$	2.13815e9	1.08134
$50$	1.61697e9	0.731756
$51$	4.62818e8	0.187834
$52$	−8.01511e8	−0.292342
$53$	3.09350e9	1.01609	0.508046	−	0.861330i	$-0.330368\pi$
$53$	3.09350e9	1.01609	0.508046	+	0.861330i	$0.330368\pi$
$54$	5.10975e8	0.151438
$55$	4.74682e8	0.127177
$56$	6.46028e9	1.56754
$57$	2.94621e9	0.648563
$58$	−9.03990e8	−0.180846
$59$	7.14924e8	0.130189
$59$	7.14924e8	0.130189
$60$	−3.50536e8	−0.0581970
$61$	−6.22795e9	−0.944128	−0.472064	−	0.881564i	$-0.656491\pi$
$61$	−6.22795e9	−0.944128	−0.472064	+	0.881564i	$0.656491\pi$
$62$	−1.99872e9	−0.277075
$63$	3.78811e9	0.480894
$64$	8.89543e9	1.03556
$65$	−1.90102e9	−0.203218
$66$	−2.22069e9	−0.218271
$67$	−1.55950e10	−1.41115	−0.705576	−	0.708634i	$-0.749312\pi$
$67$	−1.55950e10	−1.41115	−0.705576	+	0.708634i	$0.749312\pi$
$68$	1.48535e9	0.123888
$69$	8.86026e8	0.0681988
$70$	4.22564e9	0.300506
$71$	−2.68594e10	−1.76675	−0.883376	−	0.468664i	$-0.844735\pi$
$71$	−2.68594e10	−1.76675	−0.883376	+	0.468664i	$0.844735\pi$
$72$	5.94640e9	0.362180
$73$	2.50826e10	1.41611	0.708056	−	0.706157i	$-0.249573\pi$
$73$	2.50826e10	1.41611	0.708056	+	0.706157i	$0.249573\pi$
$74$	1.80783e9	0.0947075
$75$	1.10338e10	0.536895
$76$	9.45547e9	0.427768
$77$	−1.64631e10	−0.693127
$78$	8.89348e9	0.348780
$79$	−1.58824e10	−0.580721	−0.290361	−	0.956917i	$-0.593775\pi$
$79$	−1.58824e10	−0.580721	−0.290361	+	0.956917i	$0.593775\pi$
$80$	3.67889e9	0.125523
$81$	3.48678e9	0.111111
$82$	−4.14548e10	−1.23481
$83$	3.36086e10	0.936528	0.468264	−	0.883589i	$-0.344880\pi$
$83$	3.36086e10	0.936528	0.468264	+	0.883589i	$0.344880\pi$
$84$	1.21574e10	0.317180
$85$	3.52294e9	0.0861194
$86$	5.73782e9	0.131524
$87$	−6.16863e9	−0.132688
$88$	−2.58430e10	−0.522021
$89$	1.40070e10	0.265889	0.132944	−	0.991123i	$-0.457557\pi$
$89$	1.40070e10	0.265889	0.132944	+	0.991123i	$0.457557\pi$
$90$	3.88951e9	0.0694322
$91$	6.59318e10	1.10756
$92$	2.84358e9	0.0449814
$93$	−1.36388e10	−0.203292
$94$	2.76023e8	0.00387920
$95$	2.24264e10	0.297358
$96$	3.29052e10	0.411882
$97$	7.46648e10	0.882818	0.441409	−	0.897306i	$-0.354479\pi$
$97$	7.46648e10	0.882818	0.441409	+	0.897306i	$0.354479\pi$
$98$	−7.61412e10	−0.850896
$99$	−1.51535e10	−0.160148
$100$	3.54116e10	0.354116
$101$	2.53766e10	0.240251	0.120126	−	0.992759i	$-0.461670\pi$
$101$	2.53766e10	0.240251	0.120126	+	0.992759i	$0.461670\pi$
$102$	−1.64813e10	−0.147805
$103$	8.90840e10	0.757173	0.378586	−	0.925566i	$-0.376410\pi$
$103$	8.90840e10	0.757173	0.378586	+	0.925566i	$0.376410\pi$
$104$	1.03497e11	0.834147
$105$	2.88349e10	0.220484
$106$	−1.10162e11	−0.799557
$107$	5.21521e10	0.359469	0.179734	−	0.983715i	$-0.442476\pi$
$107$	5.21521e10	0.359469	0.179734	+	0.983715i	$0.442476\pi$
$108$	1.11904e10	0.0732847
$109$	−3.18182e10	−0.198075	−0.0990377	−	0.995084i	$-0.531576\pi$
$109$	−3.18182e10	−0.198075	−0.0990377	+	0.995084i	$0.531576\pi$
$110$	−1.69038e10	−0.100075
$111$	1.23363e10	0.0694876
$112$	−1.27593e11	−0.684112
$113$	4.14883e9	0.0211833	0.0105917	−	0.999944i	$-0.496629\pi$
$113$	4.14883e9	0.0211833	0.0105917	+	0.999944i	$0.496629\pi$
$114$	−1.04917e11	−0.510350
$115$	6.74438e9	0.0312683
$116$	−1.97974e10	−0.0875163
$117$	6.06872e10	0.255903
$118$	−2.54590e10	−0.102445
$119$	−1.22184e11	−0.469360
$120$	4.52636e10	0.166055
$121$	−2.19455e11	−0.769175
$122$	2.21782e11	0.742928
$123$	−2.82879e11	−0.905987
$124$	−4.37719e10	−0.134084
$125$	1.74306e11	0.510867
$126$	−1.34897e11	−0.378413
$127$	−2.47912e11	−0.665850	−0.332925	−	0.942953i	$-0.608036\pi$
$127$	−2.47912e11	−0.665850	−0.332925	+	0.942953i	$0.608036\pi$
$128$	−3.94482e10	−0.101478
$129$	3.91537e10	0.0965004
$130$	6.76966e10	0.159911
$131$	1.83558e11	0.415700	0.207850	−	0.978161i	$-0.433353\pi$
$131$	1.83558e11	0.415700	0.207850	+	0.978161i	$0.433353\pi$
$132$	−4.86332e10	−0.105627
$133$	−7.77800e11	−1.62063
$134$	5.55349e11	1.11043
$135$	2.65412e10	0.0509430
$136$	−1.91798e11	−0.353493
$137$	−1.86742e11	−0.330582	−0.165291	−	0.986245i	$-0.552856\pi$
$137$	−1.86742e11	−0.330582	−0.165291	+	0.986245i	$0.552856\pi$
$138$	−3.15521e10	−0.0536652
$139$	6.72902e11	1.09994	0.549972	−	0.835183i	$-0.314638\pi$
$139$	6.72902e11	1.09994	0.549972	+	0.835183i	$0.314638\pi$
$140$	9.25416e10	0.145423
$141$	1.88352e9	0.00284620
$142$	9.56484e11	1.39025
$143$	−2.63746e11	−0.368840
$144$	−1.17443e11	−0.158065
$145$	−4.69552e10	−0.0608359
$146$	−8.93211e11	−1.11433
$147$	−5.19571e11	−0.624309
$148$	3.95916e10	0.0458314
$149$	−1.23789e12	−1.38089	−0.690445	−	0.723385i	$-0.742585\pi$
$149$	−1.23789e12	−1.38089	−0.690445	+	0.723385i	$0.742585\pi$
$150$	−3.92923e11	−0.422479
$151$	−8.09856e11	−0.839527	−0.419763	−	0.907634i	$-0.637887\pi$
$151$	−8.09856e11	−0.839527	−0.419763	+	0.907634i	$0.637887\pi$
$152$	−1.22095e12	−1.22056
$153$	−1.12465e11	−0.108446
$154$	5.86263e11	0.545417
$155$	−1.03818e11	−0.0932068
$156$	1.94767e11	0.168784
$157$	−2.64498e10	−0.0221297	−0.0110648	−	0.999939i	$-0.503522\pi$
$157$	−2.64498e10	−0.0221297	−0.0110648	+	0.999939i	$0.503522\pi$
$158$	5.65585e11	0.456966
$159$	−7.51721e11	−0.586641
$160$	2.50473e11	0.188843
$161$	−2.33911e11	−0.170415
$162$	−1.24167e11	−0.0874326
$163$	1.81641e12	1.23647	0.618234	−	0.785994i	$-0.287849\pi$
$163$	1.81641e12	1.23647	0.618234	+	0.785994i	$0.287849\pi$
$164$	−9.07860e11	−0.597555
$165$	−1.15348e11	−0.0734256
$166$	−1.19683e12	−0.736948
$167$	5.52860e11	0.329363	0.164681	−	0.986347i	$-0.447340\pi$
$167$	5.52860e11	0.329363	0.164681	+	0.986347i	$0.447340\pi$
$168$	−1.56985e12	−0.905017
$169$	−7.35905e11	−0.410625
$170$	−1.25454e11	−0.0677668
$171$	−7.15930e11	−0.374448
$172$	1.25658e11	0.0636480
$173$	−6.45797e11	−0.316842	−0.158421	−	0.987372i	$-0.550640\pi$
$173$	−6.45797e11	−0.316842	−0.158421	+	0.987372i	$0.550640\pi$
$174$	2.19669e11	0.104412
$175$	−2.91293e12	−1.34159
$176$	5.10408e11	0.227823
$177$	−1.73727e11	−0.0751646
$178$	−4.98800e11	−0.209226
$179$	6.07973e11	0.247282	0.123641	−	0.992327i	$-0.460543\pi$
$179$	6.07973e11	0.247282	0.123641	+	0.992327i	$0.460543\pi$
$180$	8.51803e10	0.0336001
$181$	1.62761e12	0.622757	0.311378	−	0.950286i	$-0.399209\pi$
$181$	1.62761e12	0.622757	0.311378	+	0.950286i	$0.399209\pi$
$182$	−2.34788e12	−0.871531
$183$	1.51339e12	0.545093
$184$	−3.67182e11	−0.128346
$185$	9.39029e10	0.0318592
$186$	4.85688e11	0.159969
$187$	4.88771e11	0.156306
$188$	6.04491e9	0.00187725
$189$	−9.20511e11	−0.277645
$190$	−7.98620e11	−0.233989
$191$	−3.35256e12	−0.954318	−0.477159	−	0.878817i	$-0.658333\pi$
$191$	−3.35256e12	−0.954318	−0.477159	+	0.878817i	$0.658333\pi$
$192$	−2.16159e12	−0.597884
$193$	6.68094e11	0.179586	0.0897930	−	0.995960i	$-0.471379\pi$
$193$	6.68094e11	0.179586	0.0897930	+	0.995960i	$0.471379\pi$
$194$	−2.65887e12	−0.694684
$195$	4.61947e11	0.117328
$196$	−1.66749e12	−0.411771
$197$	1.14574e11	0.0275120	0.0137560	−	0.999905i	$-0.495621\pi$
$197$	1.14574e11	0.0275120	0.0137560	+	0.999905i	$0.495621\pi$
$198$	5.39628e11	0.126019
$199$	−7.33403e12	−1.66591	−0.832954	−	0.553343i	$-0.813352\pi$
$199$	−7.33403e12	−1.66591	−0.832954	+	0.553343i	$0.813352\pi$
$200$	−4.57258e12	−1.01041
$201$	3.78958e12	0.814729
$202$	−9.03678e11	−0.189052
$203$	1.62852e12	0.331562
$204$	−3.60940e11	−0.0715269
$205$	−2.15325e12	−0.415383
$206$	−3.17235e12	−0.595814
$207$	−2.15304e11	−0.0393746
$208$	−2.04409e12	−0.364042
$209$	3.11142e12	0.539703
$210$	−1.02683e12	−0.173497
$211$	−9.42510e12	−1.55143	−0.775716	−	0.631082i	$-0.782611\pi$
$211$	−9.42510e12	−1.55143	−0.775716	+	0.631082i	$0.782611\pi$
$212$	−2.41255e12	−0.386927
$213$	6.52684e12	1.02004
$214$	−1.85718e12	−0.282864
$215$	2.98035e11	0.0442442
$216$	−1.44497e12	−0.209105
$217$	3.60065e12	0.507986
$218$	1.13307e12	0.155864
$219$	−6.09508e12	−0.817592
$220$	−3.70193e11	−0.0484287
$221$	−1.95744e12	−0.249765
$222$	−4.39304e11	−0.0546794
$223$	−5.99688e12	−0.728197	−0.364098	−	0.931361i	$-0.618623\pi$
$223$	−5.99688e12	−0.728197	−0.364098	+	0.931361i	$0.618623\pi$
$224$	−8.68698e12	−1.02921
$225$	−2.68122e12	−0.309977
$226$	−1.47743e11	−0.0166690
$227$	1.12448e13	1.23825	0.619124	−	0.785293i	$-0.287488\pi$
$227$	1.12448e13	1.23825	0.619124	+	0.785293i	$0.287488\pi$
$228$	−2.29768e12	−0.246972
$229$	−6.49006e12	−0.681010	−0.340505	−	0.940243i	$-0.610598\pi$
$229$	−6.49006e12	−0.681010	−0.340505	+	0.940243i	$0.610598\pi$
$230$	−2.40172e11	−0.0246048
$231$	4.00053e12	0.400177
$232$	2.55637e12	0.249712
$233$	−2.50458e12	−0.238934	−0.119467	−	0.992838i	$-0.538119\pi$
$233$	−2.50458e12	−0.238934	−0.119467	+	0.992838i	$0.538119\pi$
$234$	−2.16112e12	−0.201368
$235$	1.43373e10	0.00130495
$236$	−5.57552e11	−0.0495757
$237$	3.85943e12	0.335279
$238$	4.35106e12	0.369336
$239$	6.55750e12	0.543938	0.271969	−	0.962306i	$-0.412325\pi$
$239$	6.55750e12	0.543938	0.271969	+	0.962306i	$0.412325\pi$
$240$	−8.93971e11	−0.0724706
$241$	−6.37839e12	−0.505379	−0.252690	−	0.967547i	$-0.581315\pi$
$241$	−6.37839e12	−0.505379	−0.252690	+	0.967547i	$0.581315\pi$
$242$	7.81494e12	0.605259
$243$	−8.47289e11	−0.0641500
$244$	4.85702e12	0.359523
$245$	−3.95494e12	−0.286238
$246$	1.00735e13	0.712916
$247$	−1.24607e13	−0.862401
$248$	5.65212e12	0.382584
$249$	−8.16688e12	−0.540705
$250$	−6.20717e12	−0.401998
$251$	8.28791e12	0.525097	0.262548	−	0.964919i	$-0.415437\pi$
$251$	8.28791e12	0.525097	0.262548	+	0.964919i	$0.415437\pi$
$252$	−2.95426e12	−0.183124
$253$	9.35711e11	0.0567517
$254$	8.82832e12	0.523953
$255$	−8.56074e11	−0.0497211
$256$	−1.68131e13	−0.955712
$257$	1.57395e13	0.875707	0.437853	−	0.899046i	$-0.355739\pi$
$257$	1.57395e13	0.875707	0.437853	+	0.899046i	$0.355739\pi$
$258$	−1.39429e12	−0.0759356
$259$	−3.25678e12	−0.173636
$260$	1.48256e12	0.0773851
$261$	1.49898e12	0.0766077
$262$	−6.53662e12	−0.327112
$263$	−2.95972e13	−1.45042	−0.725211	−	0.688527i	$-0.758258\pi$
$263$	−2.95972e13	−1.45042	−0.725211	+	0.688527i	$0.758258\pi$
$264$	6.27984e12	0.301389
$265$	−5.72205e12	−0.268967
$266$	2.76980e13	1.27526
$267$	−3.40370e12	−0.153511
$268$	1.21622e13	0.537365
$269$	3.30233e12	0.142949	0.0714747	−	0.997442i	$-0.477229\pi$
$269$	3.30233e12	0.142949	0.0714747	+	0.997442i	$0.477229\pi$
$270$	−9.45151e11	−0.0400867
$271$	−2.81967e13	−1.17184	−0.585919	−	0.810370i	$-0.699266\pi$
$271$	−2.81967e13	−1.17184	−0.585919	+	0.810370i	$0.699266\pi$
$272$	3.78809e12	0.154273
$273$	−1.60214e13	−0.639450
$274$	6.65003e12	0.260133
$275$	1.16526e13	0.446778
$276$	−6.90990e11	−0.0259700
$277$	1.63593e13	0.602736	0.301368	−	0.953508i	$-0.402557\pi$
$277$	1.63593e13	0.602736	0.301368	+	0.953508i	$0.402557\pi$
$278$	−2.39626e13	−0.865539
$279$	3.31423e12	0.117371
$280$	−1.19496e13	−0.414938
$281$	−3.16455e13	−1.07752	−0.538762	−	0.842458i	$-0.681108\pi$
$281$	−3.16455e13	−1.07752	−0.538762	+	0.842458i	$0.681108\pi$
$282$	−6.70737e10	−0.00223966
$283$	2.01915e13	0.661215	0.330607	−	0.943768i	$-0.392746\pi$
$283$	2.01915e13	0.661215	0.330607	+	0.943768i	$0.392746\pi$
$284$	2.09470e13	0.672777
$285$	−5.44961e12	−0.171680
$286$	9.39219e12	0.290238
$287$	7.46800e13	2.26388
$288$	−7.99597e12	−0.237800
$289$	−3.06444e13	−0.894155
$290$	1.67211e12	0.0478714
$291$	−1.81435e13	−0.509695
$292$	−1.95613e13	−0.539253
$293$	6.35243e13	1.71857	0.859287	−	0.511494i	$-0.170908\pi$
$293$	6.35243e13	1.71857	0.859287	+	0.511494i	$0.170908\pi$
$294$	1.85023e13	0.491265
$295$	−1.32240e12	−0.0344620
$296$	−5.11233e12	−0.130772
$297$	3.68231e12	0.0924612
$298$	4.40823e13	1.08661
$299$	−3.74736e12	−0.0906846
$300$	−8.60502e12	−0.204449
$301$	−1.03366e13	−0.241135
$302$	2.88396e13	0.660618
$303$	−6.16651e12	−0.138709
$304$	2.41143e13	0.532683
$305$	1.15198e13	0.249918
$306$	4.00495e12	0.0853355
$307$	9.58100e12	0.200516	0.100258	−	0.994961i	$-0.468033\pi$
$307$	9.58100e12	0.200516	0.100258	+	0.994961i	$0.468033\pi$
$308$	1.28392e13	0.263942
$309$	−2.16474e13	−0.437154
$310$	3.69703e12	0.0733438
$311$	−1.56977e13	−0.305953	−0.152976	−	0.988230i	$-0.548886\pi$
$311$	−1.56977e13	−0.305953	−0.152976	+	0.988230i	$0.548886\pi$
$312$	−2.51497e13	−0.481595
$313$	6.24401e13	1.17482	0.587408	−	0.809291i	$-0.300149\pi$
$313$	6.24401e13	1.17482	0.587408	+	0.809291i	$0.300149\pi$
$314$	9.41898e11	0.0174137
$315$	−7.00687e12	−0.127296
$316$	1.23863e13	0.221138
$317$	8.62202e13	1.51281	0.756403	−	0.654106i	$-0.226955\pi$
$317$	8.62202e13	1.51281	0.756403	+	0.654106i	$0.226955\pi$
$318$	2.67693e13	0.461624
$319$	−6.51454e12	−0.110417
$320$	−1.64539e13	−0.274122
$321$	−1.26730e13	−0.207539
$322$	8.32974e12	0.134099
$323$	2.30920e13	0.365467
$324$	−2.71926e12	−0.0423109
$325$	−4.66664e13	−0.713915
$326$	−6.46838e13	−0.972968
$327$	7.73183e12	0.114359
$328$	1.17229e14	1.70502
$329$	−4.97250e11	−0.00711210
$330$	4.10762e12	0.0577781
$331$	−1.00373e14	−1.38855	−0.694275	−	0.719710i	$-0.744275\pi$
$331$	−1.00373e14	−1.38855	−0.694275	+	0.719710i	$0.744275\pi$
$332$	−2.62105e13	−0.356628
$333$	−2.99771e12	−0.0401187
$334$	−1.96878e13	−0.259174
$335$	2.88461e13	0.373543
$336$	3.10051e13	0.394972
$337$	−8.43673e13	−1.05733	−0.528664	−	0.848831i	$-0.677307\pi$
$337$	−8.43673e13	−1.05733	−0.528664	+	0.848831i	$0.677307\pi$
$338$	2.62061e13	0.323118
$339$	−1.00817e12	−0.0122302
$340$	−2.74745e12	−0.0327941
$341$	−1.44036e13	−0.169170
$342$	2.54948e13	0.294651
$343$	1.03174e13	0.117341
$344$	−1.62259e13	−0.181608
$345$	−1.63888e12	−0.0180527
$346$	2.29973e13	0.249321
$347$	1.98663e13	0.211985	0.105992	−	0.994367i	$-0.466198\pi$
$347$	1.98663e13	0.211985	0.105992	+	0.994367i	$0.466198\pi$
$348$	4.81076e12	0.0505275
$349$	−1.08915e13	−0.112602	−0.0563012	−	0.998414i	$-0.517931\pi$
$349$	−1.08915e13	−0.112602	−0.0563012	+	0.998414i	$0.517931\pi$
$350$	1.03732e14	1.05569
$351$	−1.47470e13	−0.147745
$352$	3.47504e13	0.342748
$353$	−2.77510e13	−0.269474	−0.134737	−	0.990881i	$-0.543019\pi$
$353$	−2.77510e13	−0.269474	−0.134737	+	0.990881i	$0.543019\pi$
$354$	6.18653e12	0.0591465
$355$	4.96819e13	0.467673
$356$	−1.09237e13	−0.101250
$357$	2.96907e13	0.270985
$358$	−2.16504e13	−0.194585
$359$	3.68376e13	0.326041	0.163020	−	0.986623i	$-0.447876\pi$
$359$	3.68376e13	0.326041	0.163020	+	0.986623i	$0.447876\pi$
$360$	−1.09990e13	−0.0958719
$361$	3.05092e13	0.261903
$362$	−5.79604e13	−0.490043
$363$	5.33275e13	0.444083
$364$	−5.14186e13	−0.421757
$365$	−4.63954e13	−0.374855
$366$	−5.38930e13	−0.428930
$367$	3.19123e13	0.250204	0.125102	−	0.992144i	$-0.460074\pi$
$367$	3.19123e13	0.250204	0.125102	+	0.992144i	$0.460074\pi$
$368$	7.25198e12	0.0560136
$369$	6.87395e13	0.523072
$370$	−3.34395e12	−0.0250698
$371$	1.98454e14	1.46590
$372$	1.06366e13	0.0774133
$373$	−1.72704e14	−1.23852	−0.619262	−	0.785185i	$-0.712568\pi$
$373$	−1.72704e14	−1.23852	−0.619262	+	0.785185i	$0.712568\pi$
$374$	−1.74055e13	−0.122996
$375$	−4.23564e13	−0.294949
$376$	−7.80560e11	−0.00535640
$377$	2.60896e13	0.176437
$378$	3.27801e13	0.218477
$379$	−2.30989e13	−0.151731	−0.0758657	−	0.997118i	$-0.524172\pi$
$379$	−2.30989e13	−0.151731	−0.0758657	+	0.997118i	$0.524172\pi$
$380$	−1.74898e13	−0.113233
$381$	6.02426e13	0.384429
$382$	1.19387e14	0.750947
$383$	−6.49064e13	−0.402434	−0.201217	−	0.979547i	$-0.564490\pi$
$383$	−6.49064e13	−0.402434	−0.201217	+	0.979547i	$0.564490\pi$
$384$	9.58591e12	0.0585884
$385$	3.04518e13	0.183476
$386$	−2.37913e13	−0.141315
$387$	−9.51434e12	−0.0557145
$388$	−5.82292e13	−0.336176
$389$	2.01526e13	0.114712	0.0573560	−	0.998354i	$-0.481733\pi$
$389$	2.01526e13	0.114712	0.0573560	+	0.998354i	$0.481733\pi$
$390$	−1.64503e13	−0.0923247
$391$	6.94455e12	0.0384302
$392$	2.15318e14	1.17492
$393$	−4.46045e13	−0.240005
$394$	−4.08007e12	−0.0216490
$395$	2.93777e13	0.153721
$396$	1.18179e13	0.0609839
$397$	−2.26240e14	−1.15139	−0.575694	−	0.817666i	$-0.695268\pi$
$397$	−2.26240e14	−1.15139	−0.575694	+	0.817666i	$0.695268\pi$
$398$	2.61170e14	1.31089
$399$	1.89005e14	0.935672
$400$	9.03101e13	0.440967
$401$	−2.19454e14	−1.05694	−0.528468	−	0.848953i	$-0.677233\pi$
$401$	−2.19454e14	−1.05694	−0.528468	+	0.848953i	$0.677233\pi$
$402$	−1.34950e14	−0.641105
$403$	5.76839e13	0.270319
$404$	−1.97906e13	−0.0914872
$405$	−6.44951e12	−0.0294120
$406$	−5.79927e13	−0.260904
$407$	1.30280e13	0.0578242
$408$	4.66070e13	0.204089
$409$	−2.37577e14	−1.02642	−0.513212	−	0.858262i	$-0.671545\pi$
$409$	−2.37577e14	−1.02642	−0.513212	+	0.858262i	$0.671545\pi$
$410$	7.66790e13	0.326862
$411$	4.53784e13	0.190862
$412$	−6.94744e13	−0.288330
$413$	4.58638e13	0.187821
$414$	7.66715e12	0.0309836
$415$	−6.21658e13	−0.247906
$416$	−1.39169e14	−0.547684
$417$	−1.63515e14	−0.635053
$418$	−1.10800e14	−0.424689
$419$	8.85726e13	0.335060	0.167530	−	0.985867i	$-0.446421\pi$
$419$	8.85726e13	0.335060	0.167530	+	0.985867i	$0.446421\pi$
$420$	−2.24876e13	−0.0839599
$421$	6.42170e13	0.236646	0.118323	−	0.992975i	$-0.462248\pi$
$421$	6.42170e13	0.236646	0.118323	+	0.992975i	$0.462248\pi$
$422$	3.35635e14	1.22081
$423$	−4.57696e11	−0.00164326
$424$	3.11524e14	1.10403
$425$	8.64817e13	0.302542
$426$	−2.32426e14	−0.802659
$427$	−3.99535e14	−1.36208
$428$	−4.06722e13	−0.136885
$429$	6.40903e13	0.212950
$430$	−1.06133e13	−0.0348155
$431$	−2.80219e14	−0.907555	−0.453778	−	0.891115i	$-0.649924\pi$
$431$	−2.80219e14	−0.907555	−0.453778	+	0.891115i	$0.649924\pi$
$432$	2.85387e13	0.0912587
$433$	−2.24303e13	−0.0708192	−0.0354096	−	0.999373i	$-0.511274\pi$
$433$	−2.24303e13	−0.0708192	−0.0354096	+	0.999373i	$0.511274\pi$
$434$	−1.28222e14	−0.399731
$435$	1.14101e13	0.0351236
$436$	2.48143e13	0.0754268
$437$	4.42077e13	0.132694
$438$	2.17050e14	0.643358
$439$	9.75244e13	0.285469	0.142734	−	0.989761i	$-0.454411\pi$
$439$	9.75244e13	0.285469	0.142734	+	0.989761i	$0.454411\pi$
$440$	4.78018e13	0.138183
$441$	1.26256e14	0.360445
$442$	6.97059e13	0.196538
$443$	4.85637e14	1.35236	0.676179	−	0.736737i	$-0.263635\pi$
$443$	4.85637e14	1.35236	0.676179	+	0.736737i	$0.263635\pi$
$444$	−9.62076e12	−0.0264608
$445$	−2.59088e13	−0.0703828
$446$	2.13553e14	0.573013
$447$	3.00808e14	0.797257
$448$	5.70660e14	1.49399
$449$	5.64094e14	1.45880	0.729401	−	0.684086i	$-0.239799\pi$
$449$	5.64094e14	1.45880	0.729401	+	0.684086i	$0.239799\pi$
$450$	9.54803e13	0.243919
$451$	−2.98741e14	−0.753918
$452$	−3.23557e12	−0.00806658
$453$	1.96795e14	0.484701
$454$	−4.00434e14	−0.974370
$455$	−1.21954e14	−0.293179
$456$	2.96692e14	0.704691
$457$	−6.46165e13	−0.151637	−0.0758184	−	0.997122i	$-0.524157\pi$
$457$	−6.46165e13	−0.151637	−0.0758184	+	0.997122i	$0.524157\pi$
$458$	2.31116e14	0.535882
$459$	2.73289e13	0.0626113
$460$	−5.25977e12	−0.0119069
$461$	−1.14661e14	−0.256483	−0.128242	−	0.991743i	$-0.540933\pi$
$461$	−1.14661e14	−0.256483	−0.128242	+	0.991743i	$0.540933\pi$
$462$	−1.42462e14	−0.314897
$463$	−3.67887e14	−0.803562	−0.401781	−	0.915736i	$-0.631609\pi$
$463$	−3.67887e14	−0.803562	−0.401781	+	0.915736i	$0.631609\pi$
$464$	−5.04892e13	−0.108981
$465$	2.52277e13	0.0538129
$466$	8.91900e13	0.188015
$467$	−6.88247e14	−1.43384	−0.716921	−	0.697154i	$-0.754449\pi$
$467$	−6.88247e14	−1.43384	−0.716921	+	0.697154i	$0.754449\pi$
$468$	−4.73284e13	−0.0974473
$469$	−1.00045e15	−2.03585
$470$	−5.10560e11	−0.00102685
$471$	6.42731e12	0.0127766
$472$	7.19948e13	0.141456
$473$	4.13493e13	0.0803029
$474$	−1.37437e14	−0.263829
$475$	5.50526e14	1.04463
$476$	9.52882e13	0.178731
$477$	1.82668e14	0.338698
$478$	−2.33517e14	−0.428022
$479$	4.85519e13	0.0879753	0.0439876	−	0.999032i	$-0.485994\pi$
$479$	4.85519e13	0.0879753	0.0439876	+	0.999032i	$0.485994\pi$
$480$	−6.08648e13	−0.109028
$481$	−5.21750e13	−0.0923984
$482$	2.27139e14	0.397680
$483$	5.68404e13	0.0983893
$484$	1.71147e14	0.292901
$485$	−1.38107e14	−0.233689
$486$	3.01726e13	0.0504792
$487$	9.11754e14	1.50823	0.754116	−	0.656741i	$-0.228066\pi$
$487$	9.11754e14	1.50823	0.754116	+	0.656741i	$0.228066\pi$
$488$	−6.27172e14	−1.02583
$489$	−4.41388e14	−0.713875
$490$	1.40838e14	0.225239
$491$	6.96377e14	1.10128	0.550638	−	0.834744i	$-0.314384\pi$
$491$	6.96377e14	1.10128	0.550638	+	0.834744i	$0.314384\pi$
$492$	2.20610e14	0.344999
$493$	−4.83489e13	−0.0747702
$494$	4.43735e14	0.678618
$495$	2.80295e13	0.0423923
$496$	−1.11631e14	−0.166969
$497$	−1.72309e15	−2.54886
$498$	2.90829e14	0.425477
$499$	−9.18652e14	−1.32922	−0.664612	−	0.747189i	$-0.731403\pi$
$499$	−9.18652e14	−1.32922	−0.664612	+	0.747189i	$0.731403\pi$
$500$	−1.35937e14	−0.194537
$501$	−1.34345e14	−0.190158
$502$	−2.95138e14	−0.413195
$503$	−4.53959e14	−0.628627	−0.314314	−	0.949319i	$-0.601774\pi$
$503$	−4.53959e14	−0.628627	−0.314314	+	0.949319i	$0.601774\pi$
$504$	3.81473e14	0.522512
$505$	−4.69390e13	−0.0635963
$506$	−3.33214e13	−0.0446575
$507$	1.78825e14	0.237074
$508$	1.93340e14	0.253555
$509$	−6.03821e14	−0.783358	−0.391679	−	0.920102i	$-0.628106\pi$
$509$	−6.03821e14	−0.783358	−0.391679	+	0.920102i	$0.628106\pi$
$510$	3.04854e13	0.0391252
$511$	1.60910e15	2.04300
$512$	6.79516e14	0.853522
$513$	1.73971e14	0.216188
$514$	−5.60495e14	−0.689088
$515$	−1.64779e14	−0.200429
$516$	−3.05350e13	−0.0367472
$517$	1.98914e12	0.00236847
$518$	1.15976e14	0.136633
$519$	1.56929e14	0.182929
$520$	−1.91438e14	−0.220805
$521$	−1.34344e15	−1.53325	−0.766624	−	0.642097i	$-0.778065\pi$
$521$	−1.34344e15	−1.53325	−0.766624	+	0.642097i	$0.778065\pi$
$522$	−5.33797e13	−0.0602821
$523$	−5.11309e14	−0.571379	−0.285690	−	0.958322i	$-0.592223\pi$
$523$	−5.11309e14	−0.571379	−0.285690	+	0.958322i	$0.592223\pi$
$524$	−1.43152e14	−0.158298
$525$	7.07843e14	0.774570
$526$	1.05398e15	1.14133
$527$	−1.06899e14	−0.114555
$528$	−1.24029e14	−0.131534
$529$	−9.39515e14	−0.986047
$530$	2.03767e14	0.211649
$531$	4.22156e13	0.0433963
$532$	6.06587e14	0.617134
$533$	1.19641e15	1.20470
$534$	1.21208e14	0.120797
$535$	−9.64658e13	−0.0951541
$536$	−1.57046e15	−1.53328
$537$	−1.47737e14	−0.142768
$538$	−1.17598e14	−0.112486
$539$	−5.48707e14	−0.519520
$540$	−2.06988e13	−0.0193990
$541$	−1.49339e15	−1.38544	−0.692720	−	0.721206i	$-0.743588\pi$
$541$	−1.49339e15	−1.38544	−0.692720	+	0.721206i	$0.743588\pi$
$542$	1.00411e15	0.922112
$543$	−3.95509e14	−0.359549
$544$	2.57907e14	0.232097
$545$	5.88542e13	0.0524320
$546$	5.70535e14	0.503179
$547$	−5.32530e14	−0.464958	−0.232479	−	0.972601i	$-0.574684\pi$
$547$	−5.32530e14	−0.464958	−0.232479	+	0.972601i	$0.574684\pi$
$548$	1.45636e14	0.125885
$549$	−3.67754e14	−0.314709
$550$	−4.14956e14	−0.351567
$551$	−3.07780e14	−0.258170
$552$	8.92253e13	0.0741008
$553$	−1.01889e15	−0.837797
$554$	−5.82568e14	−0.474289
$555$	−2.28184e13	−0.0183939
$556$	−5.24780e14	−0.418857
$557$	−1.29608e15	−1.02430	−0.512151	−	0.858896i	$-0.671151\pi$
$557$	−1.29608e15	−1.02430	−0.512151	+	0.858896i	$0.671151\pi$
$558$	−1.18022e14	−0.0923583
$559$	−1.65596e14	−0.128317
$560$	2.36008e14	0.181090
$561$	−1.18771e14	−0.0902435
$562$	1.12692e15	0.847897
$563$	−2.22397e15	−1.65704	−0.828518	−	0.559962i	$-0.810816\pi$
$563$	−2.22397e15	−1.65704	−0.828518	+	0.559962i	$0.810816\pi$
$564$	−1.46891e12	−0.00108383
$565$	−7.67409e12	−0.00560739
$566$	−7.19033e14	−0.520306
$567$	2.23684e14	0.160298
$568$	−2.70482e15	−1.91965
$569$	−1.05219e15	−0.739569	−0.369784	−	0.929118i	$-0.620568\pi$
$569$	−1.05219e15	−0.739569	−0.369784	+	0.929118i	$0.620568\pi$
$570$	1.94065e14	0.135094
$571$	−1.22798e15	−0.846631	−0.423316	−	0.905982i	$-0.639134\pi$
$571$	−1.22798e15	−0.846631	−0.423316	+	0.905982i	$0.639134\pi$
$572$	2.05689e14	0.140454
$573$	8.14672e14	0.550976
$574$	−2.65941e15	−1.78143
$575$	1.65562e14	0.109847
$576$	5.25267e14	0.345188
$577$	−2.13168e15	−1.38757	−0.693786	−	0.720182i	$-0.744058\pi$
$577$	−2.13168e15	−1.38757	−0.693786	+	0.720182i	$0.744058\pi$
$578$	1.09127e15	0.703605
$579$	−1.62347e14	−0.103684
$580$	3.66192e13	0.0231662
$581$	2.15606e15	1.35111
$582$	6.46105e14	0.401076
$583$	−7.93875e14	−0.488174
$584$	2.52589e15	1.53866
$585$	−1.12253e14	−0.0677394
$586$	−2.26215e15	−1.35233
$587$	6.85096e14	0.405735	0.202867	−	0.979206i	$-0.434974\pi$
$587$	6.85096e14	0.405735	0.202867	+	0.979206i	$0.434974\pi$
$588$	4.05201e14	0.237736
$589$	−6.80500e14	−0.395543
$590$	4.70915e13	0.0271179
$591$	−2.78415e13	−0.0158841
$592$	1.00970e14	0.0570722
$593$	6.09078e14	0.341092	0.170546	−	0.985350i	$-0.445447\pi$
$593$	6.09078e14	0.341092	0.170546	+	0.985350i	$0.445447\pi$
$594$	−1.31130e14	−0.0727571
$595$	2.26004e14	0.124243
$596$	9.65403e14	0.525840
$597$	1.78217e15	0.961812
$598$	1.33446e14	0.0713591
$599$	−2.10851e15	−1.11719	−0.558596	−	0.829440i	$-0.688660\pi$
$599$	−2.10851e15	−1.11719	−0.558596	+	0.829440i	$0.688660\pi$
$600$	1.11114e15	0.583359
$601$	−3.51373e15	−1.82793	−0.913963	−	0.405799i	$-0.866993\pi$
$601$	−3.51373e15	−1.82793	−0.913963	+	0.405799i	$0.866993\pi$
$602$	3.68093e14	0.189748
$603$	−9.20869e14	−0.470384
$604$	6.31587e14	0.319691
$605$	4.05925e14	0.203606
$606$	2.19594e14	0.109149
$607$	−1.15275e15	−0.567801	−0.283901	−	0.958854i	$-0.591629\pi$
$607$	−1.15275e15	−0.567801	−0.283901	+	0.958854i	$0.591629\pi$
$608$	1.64179e15	0.801396
$609$	−3.95730e14	−0.191427
$610$	−4.10230e14	−0.196659
$611$	−7.96617e12	−0.00378462
$612$	8.77085e13	0.0412961
$613$	−3.88504e15	−1.81286	−0.906428	−	0.422361i	$-0.861202\pi$
$613$	−3.88504e15	−1.81286	−0.906428	+	0.422361i	$0.861202\pi$
$614$	−3.41186e14	−0.157785
$615$	5.23241e14	0.239822
$616$	−1.65788e15	−0.753111
$617$	−3.26822e15	−1.47144	−0.735720	−	0.677286i	$-0.763156\pi$
$617$	−3.26822e15	−1.47144	−0.735720	+	0.677286i	$0.763156\pi$
$618$	7.70880e14	0.343994
$619$	1.74251e15	0.770683	0.385341	−	0.922774i	$-0.374084\pi$
$619$	1.74251e15	0.770683	0.385341	+	0.922774i	$0.374084\pi$
$620$	8.09649e13	0.0354930
$621$	5.23190e13	0.0227329
$622$	5.59007e14	0.240752
$623$	8.98577e14	0.383594
$624$	4.96714e14	0.210180
$625$	1.89471e15	0.794700
$626$	−2.22354e15	−0.924454
$627$	−7.56076e14	−0.311598
$628$	2.06276e13	0.00842694
$629$	9.66900e13	0.0391564
$630$	2.49520e14	0.100169
$631$	1.38785e15	0.552307	0.276153	−	0.961114i	$-0.410940\pi$
$631$	1.38785e15	0.552307	0.276153	+	0.961114i	$0.410940\pi$
$632$	−1.59940e15	−0.630978
$633$	2.29030e15	0.895720
$634$	−3.07037e15	−1.19042
$635$	4.58562e14	0.176256
$636$	5.86249e14	0.223392
$637$	2.19747e15	0.830150
$638$	2.31988e14	0.0868862
$639$	−1.58602e15	−0.588918
$640$	7.29673e13	0.0268620
$641$	2.45583e15	0.896352	0.448176	−	0.893945i	$-0.352074\pi$
$641$	2.45583e15	0.896352	0.448176	+	0.893945i	$0.352074\pi$
$642$	4.51294e14	0.163311
$643$	1.80437e15	0.647388	0.323694	−	0.946162i	$-0.395075\pi$
$643$	1.80437e15	0.647388	0.323694	+	0.946162i	$0.395075\pi$
$644$	1.82421e14	0.0648939
$645$	−7.24226e13	−0.0255444
$646$	−8.22324e14	−0.287583
$647$	4.67983e15	1.62277	0.811384	−	0.584514i	$-0.198715\pi$
$647$	4.67983e15	1.62277	0.811384	+	0.584514i	$0.198715\pi$
$648$	3.51129e14	0.120727
$649$	−1.83468e14	−0.0625483
$650$	1.66183e15	0.561775
$651$	−8.74957e14	−0.293286
$652$	−1.41658e15	−0.470845
$653$	−3.01278e15	−0.992989	−0.496494	−	0.868040i	$-0.665380\pi$
$653$	−3.01278e15	−0.992989	−0.496494	+	0.868040i	$0.665380\pi$
$654$	−2.75336e14	−0.0899883
$655$	−3.39527e14	−0.110039
$656$	−2.31531e15	−0.744113
$657$	1.48110e15	0.472037
$658$	1.77075e13	0.00559646
$659$	−2.52199e15	−0.790450	−0.395225	−	0.918584i	$-0.629333\pi$
$659$	−2.52199e15	−0.790450	−0.395225	+	0.918584i	$0.629333\pi$
$660$	8.99568e13	0.0279603
$661$	3.09070e15	0.952684	0.476342	−	0.879260i	$-0.341962\pi$
$661$	3.09070e15	0.952684	0.476342	+	0.879260i	$0.341962\pi$
$662$	3.57434e15	1.09264
$663$	4.75658e14	0.144202
$664$	3.38448e15	1.01758
$665$	1.43870e15	0.428993
$666$	1.06751e14	0.0315692
$667$	−9.25599e13	−0.0271476
$668$	−4.31162e14	−0.125421
$669$	1.45724e15	0.420425
$670$	−1.02723e15	−0.293938
$671$	1.59826e15	0.453599
$672$	2.11094e15	0.594216
$673$	3.83543e15	1.07085	0.535427	−	0.844581i	$-0.320151\pi$
$673$	3.83543e15	1.07085	0.535427	+	0.844581i	$0.320151\pi$
$674$	3.00438e15	0.832005
$675$	6.51537e14	0.178965
$676$	5.73914e14	0.156365
$677$	4.12234e15	1.11405	0.557027	−	0.830494i	$-0.311942\pi$
$677$	4.12234e15	1.11405	0.557027	+	0.830494i	$0.311942\pi$
$678$	3.59015e13	0.00962387
$679$	4.78989e15	1.27363
$680$	3.54770e14	0.0935723
$681$	−2.73247e15	−0.714903
$682$	5.12924e14	0.133119
$683$	6.95455e15	1.79042	0.895211	−	0.445643i	$-0.147025\pi$
$683$	6.95455e15	1.79042	0.895211	+	0.445643i	$0.147025\pi$
$684$	5.58336e14	0.142589
$685$	3.45417e14	0.0875076
$686$	−3.67409e14	−0.0923351
$687$	1.57708e15	0.393181
$688$	3.20466e14	0.0792585
$689$	3.17933e15	0.780062
$690$	5.83618e13	0.0142056
$691$	2.64766e15	0.639343	0.319671	−	0.947528i	$-0.396427\pi$
$691$	2.64766e15	0.639343	0.319671	+	0.947528i	$0.396427\pi$
$692$	5.03641e14	0.120653
$693$	−9.72130e14	−0.231042
$694$	−7.07453e14	−0.166809
$695$	−1.24467e15	−0.291164
$696$	−6.21198e14	−0.144171
$697$	−2.21716e15	−0.510526
$698$	3.87854e14	0.0886061
$699$	6.08613e14	0.137948
$700$	2.27172e15	0.510877
$701$	3.22140e15	0.718779	0.359389	−	0.933188i	$-0.382985\pi$
$701$	3.22140e15	0.718779	0.359389	+	0.933188i	$0.382985\pi$
$702$	5.25151e14	0.116260
$703$	6.15511e14	0.135201
$704$	−2.28280e15	−0.497530
$705$	−3.48395e12	−0.000753412 0
$706$	9.88233e14	0.212048
$707$	1.62796e15	0.346606
$708$	1.35485e14	0.0286226
$709$	−7.37651e14	−0.154631	−0.0773155	−	0.997007i	$-0.524635\pi$
$709$	−7.37651e14	−0.154631	−0.0773155	+	0.997007i	$0.524635\pi$
$710$	−1.76921e15	−0.368009
$711$	−9.37841e14	−0.193574
$712$	1.41054e15	0.288899
$713$	−2.04650e14	−0.0415928
$714$	−1.05731e15	−0.213236
$715$	4.87851e14	0.0976346
$716$	−4.74143e14	−0.0941646
$717$	−1.59347e15	−0.314043
$718$	−1.31181e15	−0.256559
$719$	1.65357e15	0.320933	0.160467	−	0.987041i	$-0.448700\pi$
$719$	1.65357e15	0.320933	0.160467	+	0.987041i	$0.448700\pi$
$720$	2.17235e14	0.0418409
$721$	5.71492e15	1.09236
$722$	−1.08645e15	−0.206090
$723$	1.54995e15	0.291781
$724$	−1.26933e15	−0.237145
$725$	−1.15266e15	−0.213719
$726$	−1.89903e15	−0.349446
$727$	−1.93205e15	−0.352841	−0.176420	−	0.984315i	$-0.556452\pi$
$727$	−1.93205e15	−0.352841	−0.176420	+	0.984315i	$0.556452\pi$
$728$	6.63951e15	1.20341
$729$	2.05891e14	0.0370370
$730$	1.65217e15	0.294971
$731$	3.06881e14	0.0543782
$732$	−1.18026e15	−0.207570
$733$	−1.52030e15	−0.265373	−0.132686	−	0.991158i	$-0.542360\pi$
$733$	−1.52030e15	−0.265373	−0.132686	+	0.991158i	$0.542360\pi$
$734$	−1.13642e15	−0.196884
$735$	9.61051e14	0.165259
$736$	4.93741e14	0.0842696
$737$	4.00209e15	0.677978
$738$	−2.44786e15	−0.411602
$739$	−1.10640e16	−1.84658	−0.923291	−	0.384100i	$-0.874512\pi$
$739$	−1.10640e16	−1.84658	−0.923291	+	0.384100i	$0.874512\pi$
$740$	−7.32326e13	−0.0121319
$741$	3.02795e15	0.497907
$742$	−7.06711e15	−1.15351
$743$	−8.63150e15	−1.39845	−0.699226	−	0.714900i	$-0.746472\pi$
$743$	−8.63150e15	−1.39845	−0.699226	+	0.714900i	$0.746472\pi$
$744$	−1.37347e15	−0.220885
$745$	2.28973e15	0.365532
$746$	6.15012e15	0.974586
$747$	1.98455e15	0.312176
$748$	−3.81180e14	−0.0595212
$749$	3.34566e15	0.518600
$750$	1.50834e15	0.232094
$751$	−1.80297e15	−0.275403	−0.137701	−	0.990474i	$-0.543971\pi$
$751$	−1.80297e15	−0.275403	−0.137701	+	0.990474i	$0.543971\pi$
$752$	1.54163e13	0.00233767
$753$	−2.01396e15	−0.303165
$754$	−9.29069e14	−0.138837
$755$	1.49799e15	0.222229
$756$	7.17884e14	0.105727
$757$	2.21410e15	0.323721	0.161860	−	0.986814i	$-0.448251\pi$
$757$	2.21410e15	0.323721	0.161860	+	0.986814i	$0.448251\pi$
$758$	8.22568e14	0.119396
$759$	−2.27378e14	−0.0327656
$760$	2.25840e15	0.323092
$761$	−8.34704e15	−1.18554	−0.592771	−	0.805371i	$-0.701966\pi$
$761$	−8.34704e15	−1.18554	−0.592771	+	0.805371i	$0.701966\pi$
$762$	−2.14528e15	−0.302505
$763$	−2.04120e15	−0.285760
$764$	2.61458e15	0.363403
$765$	2.08026e14	0.0287065
$766$	2.31136e15	0.316672
$767$	7.34758e14	0.0999471
$768$	4.08558e15	0.551781
$769$	1.19175e16	1.59805	0.799027	−	0.601296i	$-0.205349\pi$
$769$	1.19175e16	1.59805	0.799027	+	0.601296i	$0.205349\pi$
$770$	−1.08441e15	−0.144376
$771$	−3.82470e15	−0.505589
$772$	−5.21030e14	−0.0683861
$773$	−2.58218e15	−0.336511	−0.168256	−	0.985743i	$-0.553813\pi$
$773$	−2.58218e15	−0.336511	−0.168256	+	0.985743i	$0.553813\pi$
$774$	3.38813e14	0.0438414
$775$	−2.54854e15	−0.327440
$776$	7.51894e15	0.959218
$777$	7.91397e14	0.100249
$778$	−7.17649e14	−0.0902661
$779$	−1.41141e16	−1.76277
$780$	−3.60261e14	−0.0446783
$781$	6.89284e15	0.848823
$782$	−2.47301e14	−0.0302404
$783$	−3.64251e14	−0.0442295
$784$	−4.25260e15	−0.512763
$785$	4.89243e13	0.00585789
$786$	1.58840e15	0.188858
$787$	−1.06275e16	−1.25478	−0.627392	−	0.778703i	$-0.715878\pi$
$787$	−1.06275e16	−1.25478	−0.627392	+	0.778703i	$0.715878\pi$
$788$	−8.93535e13	−0.0104765
$789$	7.19212e15	0.837401
$790$	−1.04616e15	−0.120962
$791$	2.66156e14	0.0305608
$792$	−1.52600e15	−0.174007
$793$	−6.40073e15	−0.724815
$794$	8.05657e15	0.906019
$795$	1.39046e15	0.155288
$796$	5.71963e15	0.634375
$797$	5.37985e15	0.592583	0.296292	−	0.955098i	$-0.404250\pi$
$797$	5.37985e15	0.592583	0.296292	+	0.955098i	$0.404250\pi$
$798$	−6.73062e15	−0.736274
$799$	1.47628e13	0.00160384
$800$	6.14864e15	0.663413
$801$	8.27100e14	0.0886296
$802$	7.81491e15	0.831696
$803$	−6.43687e15	−0.680360
$804$	−2.95540e15	−0.310248
$805$	4.32665e14	0.0451102
$806$	−2.05417e15	−0.212713
$807$	−8.02465e14	−0.0825319
$808$	2.55549e15	0.261043
$809$	1.16160e16	1.17853	0.589265	−	0.807940i	$-0.299418\pi$
$809$	1.16160e16	1.17853	0.589265	+	0.807940i	$0.299418\pi$
$810$	2.29672e14	0.0231441
$811$	−1.16748e16	−1.16851	−0.584256	−	0.811569i	$-0.698614\pi$
$811$	−1.16748e16	−1.16851	−0.584256	+	0.811569i	$0.698614\pi$
$812$	−1.27004e15	−0.126258
$813$	6.85181e15	0.676561
$814$	−4.63938e14	−0.0455015
$815$	−3.35982e15	−0.327302
$816$	−9.20505e14	−0.0890698
$817$	1.95355e15	0.187760
$818$	8.46030e15	0.807686
$819$	3.89321e15	0.369187
$820$	1.67927e15	0.158177
$821$	2.93787e15	0.274881	0.137441	−	0.990510i	$-0.456112\pi$
$821$	2.93787e15	0.274881	0.137441	+	0.990510i	$0.456112\pi$
$822$	−1.61596e15	−0.150188
$823$	−1.24942e16	−1.15348	−0.576740	−	0.816928i	$-0.695675\pi$
$823$	−1.24942e16	−1.15348	−0.576740	+	0.816928i	$0.695675\pi$
$824$	8.97100e15	0.822700
$825$	−2.83157e15	−0.257947
$826$	−1.63324e15	−0.147795
$827$	1.35197e16	1.21531	0.607654	−	0.794202i	$-0.292111\pi$
$827$	1.35197e16	1.21531	0.607654	+	0.794202i	$0.292111\pi$
$828$	1.67911e14	0.0149938
$829$	−1.02560e16	−0.909761	−0.454881	−	0.890552i	$-0.650318\pi$
$829$	−1.02560e16	−0.909761	−0.454881	+	0.890552i	$0.650318\pi$
$830$	2.21377e15	0.195076
$831$	−3.97532e15	−0.347990
$832$	9.14222e15	0.795011
$833$	−4.07233e15	−0.351800
$834$	5.82290e15	0.499719
$835$	−1.02263e15	−0.0871848
$836$	−2.42652e15	−0.205518
$837$	−8.05358e14	−0.0677640
$838$	−3.15414e15	−0.263656
$839$	−1.43075e16	−1.18816	−0.594079	−	0.804407i	$-0.702483\pi$
$839$	−1.43075e16	−1.18816	−0.594079	+	0.804407i	$0.702483\pi$
$840$	2.90375e15	0.239565
$841$	−1.15561e16	−0.947181
$842$	−2.28681e15	−0.186215
$843$	7.68985e15	0.622109
$844$	7.35041e15	0.590783
$845$	1.36120e15	0.108695
$846$	1.62989e13	0.00129307
$847$	−1.40785e16	−1.10968
$848$	−6.15271e15	−0.481825
$849$	−4.90653e15	−0.381753
$850$	−3.07968e15	−0.238068
$851$	1.85105e14	0.0142169
$852$	−5.09012e15	−0.388428
$853$	−1.00565e16	−0.762477	−0.381239	−	0.924477i	$-0.624502\pi$
$853$	−1.00565e16	−0.762477	−0.381239	+	0.924477i	$0.624502\pi$
$854$	1.42278e16	1.07181
$855$	1.32426e15	0.0991193
$856$	5.25186e15	0.390578
$857$	−5.67045e15	−0.419008	−0.209504	−	0.977808i	$-0.567185\pi$
$857$	−5.67045e15	−0.419008	−0.209504	+	0.977808i	$0.567185\pi$
$858$	−2.28230e15	−0.167569
$859$	−3.48425e15	−0.254183	−0.127092	−	0.991891i	$-0.540564\pi$
$859$	−3.48425e15	−0.254183	−0.127092	+	0.991891i	$0.540564\pi$
$860$	−2.32430e14	−0.0168481
$861$	−1.81472e16	−1.30705
$862$	9.97882e15	0.714150
$863$	−1.46753e16	−1.04358	−0.521791	−	0.853074i	$-0.674736\pi$
$863$	−1.46753e16	−1.04358	−0.521791	+	0.853074i	$0.674736\pi$
$864$	1.94302e15	0.137294
$865$	1.19453e15	0.0838704
$866$	7.98758e14	0.0557272
$867$	7.44659e15	0.516241
$868$	−2.80806e15	−0.193440
$869$	4.07585e15	0.279003
$870$	−4.06323e14	−0.0276385
$871$	−1.60276e16	−1.08335
$872$	−3.20418e15	−0.215217
$873$	4.40888e15	0.294273
$874$	−1.57427e15	−0.104416
$875$	1.11821e16	0.737019
$876$	4.75340e15	0.311338
$877$	4.80789e15	0.312937	0.156469	−	0.987683i	$-0.449989\pi$
$877$	4.80789e15	0.312937	0.156469	+	0.987683i	$0.449989\pi$
$878$	−3.47292e15	−0.224634
$879$	−1.54364e16	−0.992219
$880$	−9.44101e14	−0.0603065
$881$	−7.85415e15	−0.498576	−0.249288	−	0.968429i	$-0.580197\pi$
$881$	−7.85415e15	−0.498576	−0.249288	+	0.968429i	$0.580197\pi$
$882$	−4.49606e15	−0.283632
$883$	−9.07255e15	−0.568781	−0.284391	−	0.958708i	$-0.591791\pi$
$883$	−9.07255e15	−0.568781	−0.284391	+	0.958708i	$0.591791\pi$
$884$	1.52656e15	0.0951100
$885$	3.21342e14	0.0198966
$886$	−1.72939e16	−1.06416
$887$	2.32586e16	1.42234	0.711170	−	0.703020i	$-0.248165\pi$
$887$	2.32586e16	1.42234	0.711170	+	0.703020i	$0.248165\pi$
$888$	1.24230e15	0.0755012
$889$	−1.59040e16	−0.960611
$890$	9.22630e14	0.0553838
$891$	−8.94801e14	−0.0533825
$892$	4.67682e15	0.277296
$893$	9.39772e13	0.00553783
$894$	−1.07120e16	−0.627356
$895$	−1.12457e15	−0.0654574
$896$	−2.53068e15	−0.146401
$897$	9.10607e14	0.0523568
$898$	−2.00878e16	−1.14792
$899$	1.42480e15	0.0809235
$900$	2.09102e15	0.118039
$901$	−5.89189e15	−0.330574
$902$	1.06384e16	0.593253
$903$	2.51179e15	0.139220
$904$	4.17799e14	0.0230166
$905$	−3.01059e15	−0.164848
$906$	−7.00802e15	−0.381408
$907$	2.26790e16	1.22683	0.613413	−	0.789762i	$-0.289796\pi$
$907$	2.26790e16	1.22683	0.613413	+	0.789762i	$0.289796\pi$
$908$	−8.76951e15	−0.471523
$909$	1.49846e15	0.0800837
$910$	4.34287e15	0.230701
$911$	−9.60184e15	−0.506994	−0.253497	−	0.967336i	$-0.581581\pi$
$911$	−9.60184e15	−0.506994	−0.253497	+	0.967336i	$0.581581\pi$
$912$	−5.85976e15	−0.307545
$913$	−8.62485e15	−0.449948
$914$	2.30104e15	0.119322
$915$	−2.79932e15	−0.144290
$916$	5.06143e15	0.259327
$917$	1.17756e16	0.599724
$918$	−9.73204e14	−0.0492685
$919$	2.29750e16	1.15617	0.578084	−	0.815978i	$-0.303801\pi$
$919$	2.29750e16	1.15617	0.578084	+	0.815978i	$0.303801\pi$
$920$	6.79177e14	0.0339743
$921$	−2.32818e15	−0.115768
$922$	4.08315e15	0.201825
$923$	−2.76046e16	−1.35635
$924$	−3.11992e15	−0.152387
$925$	2.30514e15	0.111923
$926$	1.31007e16	0.632318
$927$	5.26032e15	0.252391
$928$	−3.43749e15	−0.163956
$929$	−1.95032e16	−0.924740	−0.462370	−	0.886687i	$-0.653001\pi$
$929$	−1.95032e16	−0.924740	−0.462370	+	0.886687i	$0.653001\pi$
$930$	−8.98378e14	−0.0423451
$931$	−2.59237e16	−1.21471
$932$	1.95326e15	0.0909856
$933$	3.81454e15	0.176642
$934$	2.45090e16	1.12828
$935$	−9.04079e14	−0.0413754
$936$	6.11137e15	0.278049
$937$	1.01829e16	0.460580	0.230290	−	0.973122i	$-0.426033\pi$
$937$	1.01829e16	0.460580	0.230290	+	0.973122i	$0.426033\pi$
$938$	3.56268e16	1.60199
$939$	−1.51729e16	−0.678280
$940$	−1.11813e13	−0.000496922 0
$941$	−1.58357e16	−0.699672	−0.349836	−	0.936811i	$-0.613763\pi$
$941$	−1.58357e16	−0.699672	−0.349836	+	0.936811i	$0.613763\pi$
$942$	−2.28881e14	−0.0100538
$943$	−4.24458e15	−0.185362
$944$	−1.42192e15	−0.0617348
$945$	1.70267e15	0.0734946
$946$	−1.47248e15	−0.0631899
$947$	−2.42419e16	−1.03429	−0.517145	−	0.855898i	$-0.673005\pi$
$947$	−2.42419e16	−1.03429	−0.517145	+	0.855898i	$0.673005\pi$
$948$	−3.00987e15	−0.127674
$949$	2.57785e16	1.08716
$950$	−1.96046e16	−0.822014
$951$	−2.09515e16	−0.873419
$952$	−1.23043e16	−0.509979
$953$	−2.71994e16	−1.12085	−0.560427	−	0.828204i	$-0.689363\pi$
$953$	−2.71994e16	−1.12085	−0.560427	+	0.828204i	$0.689363\pi$
$954$	−6.50495e15	−0.266519
$955$	6.20123e15	0.252615
$956$	−5.11403e15	−0.207131
$957$	1.58303e15	0.0637491
$958$	−1.72897e15	−0.0692272
$959$	−1.19799e16	−0.476925
$960$	3.99829e15	0.158264
$961$	−2.22583e16	−0.876017
$962$	1.85799e15	0.0727077
$963$	3.07953e15	0.119823
$964$	4.97435e15	0.192448
$965$	−1.23577e15	−0.0475378
$966$	−2.02413e15	−0.0774219
$967$	−3.21332e16	−1.22211	−0.611053	−	0.791590i	$-0.709254\pi$
$967$	−3.21332e16	−1.22211	−0.611053	+	0.791590i	$0.709254\pi$
$968$	−2.20997e16	−0.835740
$969$	−5.61136e15	−0.211002
$970$	4.91811e15	0.183888
$971$	−4.64451e15	−0.172677	−0.0863385	−	0.996266i	$-0.527517\pi$
$971$	−4.64451e15	−0.172677	−0.0863385	+	0.996266i	$0.527517\pi$
$972$	6.60779e14	0.0244282
$973$	4.31680e16	1.58687
$974$	−3.24682e16	−1.18682
$975$	1.13399e16	0.412179
$976$	1.23869e16	0.447700
$977$	5.01867e14	0.0180372	0.00901858	−	0.999959i	$-0.497129\pi$
$977$	5.01867e14	0.0180372	0.00901858	+	0.999959i	$0.497129\pi$
$978$	1.57182e16	0.561743
$979$	−3.59457e15	−0.127744
$980$	3.08436e15	0.108999
$981$	−1.87884e15	−0.0660251
$982$	−2.47985e16	−0.866587
$983$	5.28237e16	1.83563	0.917813	−	0.397013i	$-0.129953\pi$
$983$	5.28237e16	1.83563	0.917813	+	0.397013i	$0.129953\pi$
$984$	−2.84867e16	−0.984393
$985$	−2.11928e14	−0.00728263
$986$	1.72174e15	0.0588362
$987$	1.20832e14	0.00410617
$988$	9.71779e15	0.328401
$989$	5.87498e14	0.0197436
$990$	−9.98151e14	−0.0333582
$991$	4.61147e16	1.53262	0.766310	−	0.642471i	$-0.222091\pi$
$991$	4.61147e16	1.53262	0.766310	+	0.642471i	$0.222091\pi$
$992$	−7.60027e15	−0.251197
$993$	2.43905e16	0.801679
$994$	6.13604e16	2.00569
$995$	1.35658e16	0.440978
$996$	6.36915e15	0.205899
$997$	3.25603e16	1.04680	0.523402	−	0.852086i	$-0.324663\pi$
$997$	3.25603e16	1.04680	0.523402	+	0.852086i	$0.324663\pi$
$998$	3.27139e16	1.04596
$999$	7.28445e14	0.0231625

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.a.1.10	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.a.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-35.6107 q^{2} -243.000 q^{3} -779.875 q^{4} -1849.70 q^{5} +8653.41 q^{6} +64152.0 q^{7} +100703. q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-35.6107 q^{2} -243.000 q^{3} -779.875 q^{4} -1849.70 q^{5} +8653.41 q^{6} +64152.0 q^{7} +100703. q^{8} +59049.0 q^{9} +65869.2 q^{10} -256626. q^{11} +189510. q^{12} +1.02774e6 q^{13} -2.28450e6 q^{14} +449477. q^{15} -1.98891e6 q^{16} -1.90460e6 q^{17} -2.10278e6 q^{18} -1.21243e7 q^{19} +1.44254e6 q^{20} -1.55889e7 q^{21} +9.13866e6 q^{22} -3.64620e6 q^{23} -2.44708e7 q^{24} -4.54067e7 q^{25} -3.65987e7 q^{26} -1.43489e7 q^{27} -5.00306e7 q^{28} +2.53853e7 q^{29} -1.60062e7 q^{30} +5.61268e7 q^{31} -1.35412e8 q^{32} +6.23602e7 q^{33} +6.78242e7 q^{34} -1.18662e8 q^{35} -4.60509e7 q^{36} -5.07666e7 q^{37} +4.31756e8 q^{38} -2.49742e8 q^{39} -1.86270e8 q^{40} +1.16411e9 q^{41} +5.55134e8 q^{42} -1.61126e8 q^{43} +2.00137e8 q^{44} -1.09223e8 q^{45} +1.29844e8 q^{46} -7.75113e6 q^{47} +4.83306e8 q^{48} +2.13815e9 q^{49} +1.61697e9 q^{50} +4.62818e8 q^{51} -8.01511e8 q^{52} +3.09350e9 q^{53} +5.10975e8 q^{54} +4.74682e8 q^{55} +6.46028e9 q^{56} +2.94621e9 q^{57} -9.03990e8 q^{58} +7.14924e8 q^{59} -3.50536e8 q^{60} -6.22795e9 q^{61} -1.99872e9 q^{62} +3.78811e9 q^{63} +8.89543e9 q^{64} -1.90102e9 q^{65} -2.22069e9 q^{66} -1.55950e10 q^{67} +1.48535e9 q^{68} +8.86026e8 q^{69} +4.22564e9 q^{70} -2.68594e10 q^{71} +5.94640e9 q^{72} +2.50826e10 q^{73} +1.80783e9 q^{74} +1.10338e10 q^{75} +9.45547e9 q^{76} -1.64631e10 q^{77} +8.89348e9 q^{78} -1.58824e10 q^{79} +3.67889e9 q^{80} +3.48678e9 q^{81} -4.14548e10 q^{82} +3.36086e10 q^{83} +1.21574e10 q^{84} +3.52294e9 q^{85} +5.73782e9 q^{86} -6.16863e9 q^{87} -2.58430e10 q^{88} +1.40070e10 q^{89} +3.88951e9 q^{90} +6.59318e10 q^{91} +2.84358e9 q^{92} -1.36388e10 q^{93} +2.76023e8 q^{94} +2.24264e10 q^{95} +3.29052e10 q^{96} +7.46648e10 q^{97} -7.61412e10 q^{98} -1.51535e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9}+O(q^{10}) \) 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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