LMFDB - Embedded newform 177.12.a.b.1.6

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:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
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)

$f(q)$	$=$	$q-63.4822 q^{2} +243.000 q^{3} +1982.00 q^{4} -1374.17 q^{5} -15426.2 q^{6} -16112.8 q^{7} +4190.11 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-63.4822 q^{2} +243.000 q^{3} +1982.00 q^{4} -1374.17 q^{5} -15426.2 q^{6} -16112.8 q^{7} +4190.11 q^{8} +59049.0 q^{9} +87235.4 q^{10} +391891. q^{11} +481625. q^{12} -1.24240e6 q^{13} +1.02288e6 q^{14} -333923. q^{15} -4.32512e6 q^{16} +824345. q^{17} -3.74856e6 q^{18} +4.80225e6 q^{19} -2.72360e6 q^{20} -3.91541e6 q^{21} -2.48781e7 q^{22} +2.79540e7 q^{23} +1.01820e6 q^{24} -4.69398e7 q^{25} +7.88702e7 q^{26} +1.43489e7 q^{27} -3.19355e7 q^{28} +4.28560e7 q^{29} +2.11982e7 q^{30} -1.46002e8 q^{31} +2.65987e8 q^{32} +9.52295e7 q^{33} -5.23313e7 q^{34} +2.21418e7 q^{35} +1.17035e8 q^{36} +6.91833e8 q^{37} -3.04857e8 q^{38} -3.01903e8 q^{39} -5.75793e6 q^{40} -1.20424e9 q^{41} +2.48559e8 q^{42} +3.82608e8 q^{43} +7.76726e8 q^{44} -8.11434e7 q^{45} -1.77458e9 q^{46} -1.39550e7 q^{47} -1.05101e9 q^{48} -1.71770e9 q^{49} +2.97984e9 q^{50} +2.00316e8 q^{51} -2.46243e9 q^{52} -4.64080e9 q^{53} -9.10901e8 q^{54} -5.38525e8 q^{55} -6.75145e7 q^{56} +1.16695e9 q^{57} -2.72059e9 q^{58} -7.14924e8 q^{59} -6.61835e8 q^{60} -4.97725e9 q^{61} +9.26851e9 q^{62} -9.51446e8 q^{63} -8.02761e9 q^{64} +1.70727e9 q^{65} -6.04538e9 q^{66} +1.85064e10 q^{67} +1.63385e9 q^{68} +6.79282e9 q^{69} -1.40561e9 q^{70} +4.49987e9 q^{71} +2.47422e8 q^{72} +2.44140e10 q^{73} -4.39191e10 q^{74} -1.14064e10 q^{75} +9.51803e9 q^{76} -6.31447e9 q^{77} +1.91655e10 q^{78} -1.48608e10 q^{79} +5.94346e9 q^{80} +3.48678e9 q^{81} +7.64476e10 q^{82} +5.49701e10 q^{83} -7.76033e9 q^{84} -1.13279e9 q^{85} -2.42888e10 q^{86} +1.04140e10 q^{87} +1.64207e9 q^{88} +4.35958e10 q^{89} +5.15116e9 q^{90} +2.00185e10 q^{91} +5.54047e10 q^{92} -3.54784e10 q^{93} +8.85893e8 q^{94} -6.59911e9 q^{95} +6.46349e10 q^{96} +1.25330e11 q^{97} +1.09044e11 q^{98} +2.31408e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9}+O(q^{10}) $ 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9	\( 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9} - 383719 q^{10} - 1816556 q^{11} + 6352506 q^{12} - 3951804 q^{13} - 6207867 q^{14} - 4176684 q^{15} + 28295194 q^{16} - 17723275 q^{17} - 7558272 q^{18} - 19573013 q^{19} - 48468099 q^{20} - 30758697 q^{21} - 1729910 q^{22} - 88593797 q^{23} - 86458671 q^{24} + 345714963 q^{25} - 6676346 q^{26} + 387420489 q^{27} + 126954286 q^{28} - 276632427 q^{29} - 93243717 q^{30} - 357680917 q^{31} - 859842334 q^{32} - 441423108 q^{33} + 232730000 q^{34} - 510315139 q^{35} + 1543658958 q^{36} - 660238257 q^{37} - 2067286961 q^{38} - 960288372 q^{39} - 3388951110 q^{40} - 1671147569 q^{41} - 1508511681 q^{42} - 1883107790 q^{43} - 3895687630 q^{44} - 1014934212 q^{45} - 1720344243 q^{46} - 5818572501 q^{47} + 6875732142 q^{48} - 18858180 q^{49} - 21474519647 q^{50} - 4306755825 q^{51} - 42214560062 q^{52} - 11444513368 q^{53} - 1836660096 q^{54} - 24401486484 q^{55} - 50583585764 q^{56} - 4756242159 q^{57} - 45017395090 q^{58} - 19302956073 q^{59} - 11777748057 q^{60} + 408637955 q^{61} - 28543084070 q^{62} - 7474363371 q^{63} + 33067284293 q^{64} - 21656714730 q^{65} - 420368130 q^{66} - 49803132690 q^{67} - 16500749319 q^{68} - 21528292671 q^{69} - 45808890782 q^{70} - 34127492216 q^{71} - 21009457053 q^{72} - 55734362153 q^{73} - 40367816298 q^{74} + 84008736009 q^{75} - 14840406404 q^{76} - 99723443615 q^{77} - 1622352078 q^{78} - 76484916442 q^{79} + 93882788915 q^{80} + 94143178827 q^{81} + 52951239205 q^{82} - 140433865655 q^{83} + 30849891498 q^{84} + 34329063335 q^{85} + 175223869508 q^{86} - 67221679761 q^{87} + 268823645069 q^{88} - 1191878597 q^{89} - 22658223231 q^{90} + 201632581559 q^{91} - 206501888812 q^{92} - 86916462831 q^{93} + 319770144384 q^{94} - 81387074885 q^{95} - 208941687162 q^{96} - 144896178730 q^{97} + 135739195260 q^{98} - 107265815244 q^{99}+O(q^{100}) \) 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9 - 383719 * q^10 - 1816556 * q^11 + 6352506 * q^12 - 3951804 * q^13 - 6207867 * q^14 - 4176684 * q^15 + 28295194 * q^16 - 17723275 * q^17 - 7558272 * q^18 - 19573013 * q^19 - 48468099 * q^20 - 30758697 * q^21 - 1729910 * q^22 - 88593797 * q^23 - 86458671 * q^24 + 345714963 * q^25 - 6676346 * q^26 + 387420489 * q^27 + 126954286 * q^28 - 276632427 * q^29 - 93243717 * q^30 - 357680917 * q^31 - 859842334 * q^32 - 441423108 * q^33 + 232730000 * q^34 - 510315139 * q^35 + 1543658958 * q^36 - 660238257 * q^37 - 2067286961 * q^38 - 960288372 * q^39 - 3388951110 * q^40 - 1671147569 * q^41 - 1508511681 * q^42 - 1883107790 * q^43 - 3895687630 * q^44 - 1014934212 * q^45 - 1720344243 * q^46 - 5818572501 * q^47 + 6875732142 * q^48 - 18858180 * q^49 - 21474519647 * q^50 - 4306755825 * q^51 - 42214560062 * q^52 - 11444513368 * q^53 - 1836660096 * q^54 - 24401486484 * q^55 - 50583585764 * q^56 - 4756242159 * q^57 - 45017395090 * q^58 - 19302956073 * q^59 - 11777748057 * q^60 + 408637955 * q^61 - 28543084070 * q^62 - 7474363371 * q^63 + 33067284293 * q^64 - 21656714730 * q^65 - 420368130 * q^66 - 49803132690 * q^67 - 16500749319 * q^68 - 21528292671 * q^69 - 45808890782 * q^70 - 34127492216 * q^71 - 21009457053 * q^72 - 55734362153 * q^73 - 40367816298 * q^74 + 84008736009 * q^75 - 14840406404 * q^76 - 99723443615 * q^77 - 1622352078 * q^78 - 76484916442 * q^79 + 93882788915 * q^80 + 94143178827 * q^81 + 52951239205 * q^82 - 140433865655 * q^83 + 30849891498 * q^84 + 34329063335 * q^85 + 175223869508 * q^86 - 67221679761 * q^87 + 268823645069 * q^88 - 1191878597 * q^89 - 22658223231 * q^90 + 201632581559 * q^91 - 206501888812 * q^92 - 86916462831 * q^93 + 319770144384 * q^94 - 81387074885 * q^95 - 208941687162 * q^96 - 144896178730 * q^97 + 135739195260 * q^98 - 107265815244 * 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 $

$2$	−63.4822	−1.40277	−0.701386	−	0.712781i	$-0.747435\pi$
$2$	−63.4822	−1.40277	−0.701386	+	0.712781i	$0.747435\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	1982.00	0.967771
$5$	−1374.17	−0.196655	−0.0983276	−	0.995154i	$-0.531349\pi$
$5$	−1374.17	−0.196655	−0.0983276	+	0.995154i	$0.531349\pi$
$6$	−15426.2	−0.809891
$7$	−16112.8	−0.362353	−0.181177	−	0.983451i	$-0.557991\pi$
$7$	−16112.8	−0.362353	−0.181177	+	0.983451i	$0.557991\pi$
$8$	4190.11	0.0452096
$9$	59049.0	0.333333
$10$	87235.4	0.275863
$11$	391891.	0.733678	0.366839	−	0.930284i	$-0.380440\pi$
$11$	391891.	0.733678	0.366839	+	0.930284i	$0.380440\pi$
$12$	481625.	0.558743
$13$	−1.24240e6	−0.928052	−0.464026	−	0.885822i	$-0.653595\pi$
$13$	−1.24240e6	−0.928052	−0.464026	+	0.885822i	$0.653595\pi$
$14$	1.02288e6	0.508299
$15$	−333923.	−0.113539
$16$	−4.32512e6	−1.03119
$17$	824345.	0.140812	0.0704061	−	0.997518i	$-0.477570\pi$
$17$	824345.	0.140812	0.0704061	+	0.997518i	$0.477570\pi$
$18$	−3.74856e6	−0.467591
$19$	4.80225e6	0.444938	0.222469	−	0.974940i	$-0.428588\pi$
$19$	4.80225e6	0.444938	0.222469	+	0.974940i	$0.428588\pi$
$20$	−2.72360e6	−0.190317
$21$	−3.91541e6	−0.209205
$22$	−2.48781e7	−1.02918
$23$	2.79540e7	0.905609	0.452804	−	0.891610i	$-0.350424\pi$
$23$	2.79540e7	0.905609	0.452804	+	0.891610i	$0.350424\pi$
$24$	1.01820e6	0.0261018
$25$	−4.69398e7	−0.961327
$26$	7.88702e7	1.30185
$27$	1.43489e7	0.192450
$28$	−3.19355e7	−0.350675
$29$	4.28560e7	0.387992	0.193996	−	0.981002i	$-0.437855\pi$
$29$	4.28560e7	0.387992	0.193996	+	0.981002i	$0.437855\pi$
$30$	2.11982e7	0.159269
$31$	−1.46002e8	−0.915943	−0.457972	−	0.888967i	$-0.651424\pi$
$31$	−1.46002e8	−0.915943	−0.457972	+	0.888967i	$0.651424\pi$
$32$	2.65987e8	1.40132
$33$	9.52295e7	0.423589
$34$	−5.23313e7	−0.197527
$35$	2.21418e7	0.0712587
$36$	1.17035e8	0.322590
$37$	6.91833e8	1.64018	0.820090	−	0.572235i	$-0.193923\pi$
$37$	6.91833e8	1.64018	0.820090	+	0.572235i	$0.193923\pi$
$38$	−3.04857e8	−0.624147
$39$	−3.01903e8	−0.535811
$40$	−5.75793e6	−0.00889070
$41$	−1.20424e9	−1.62331	−0.811653	−	0.584139i	$-0.801432\pi$
$41$	−1.20424e9	−1.62331	−0.811653	+	0.584139i	$0.801432\pi$
$42$	2.48559e8	0.293467
$43$	3.82608e8	0.396897	0.198448	−	0.980111i	$-0.436410\pi$
$43$	3.82608e8	0.396897	0.198448	+	0.980111i	$0.436410\pi$
$44$	7.76726e8	0.710033
$45$	−8.11434e7	−0.0655517
$46$	−1.77458e9	−1.27036
$47$	−1.39550e7	−0.00887545	−0.00443773	−	0.999990i	$-0.501413\pi$
$47$	−1.39550e7	−0.00887545	−0.00443773	+	0.999990i	$0.501413\pi$
$48$	−1.05101e9	−0.595358
$49$	−1.71770e9	−0.868700
$50$	2.97984e9	1.34852
$51$	2.00316e8	0.0812979
$52$	−2.46243e9	−0.898142
$53$	−4.64080e9	−1.52432	−0.762158	−	0.647391i	$-0.775860\pi$
$53$	−4.64080e9	−1.52432	−0.762158	+	0.647391i	$0.775860\pi$
$54$	−9.10901e8	−0.269964
$55$	−5.38525e8	−0.144282
$56$	−6.75145e7	−0.0163818
$57$	1.16695e9	0.256885
$58$	−2.72059e9	−0.544264
$59$	−7.14924e8	−0.130189
$59$	−7.14924e8	−0.130189
$60$	−6.61835e8	−0.109880
$61$	−4.97725e9	−0.754528	−0.377264	−	0.926106i	$-0.623135\pi$
$61$	−4.97725e9	−0.754528	−0.377264	+	0.926106i	$0.623135\pi$
$62$	9.26851e9	1.28486
$63$	−9.51446e8	−0.120784
$64$	−8.02761e9	−0.934537
$65$	1.70727e9	0.182506
$66$	−6.04538e9	−0.594199
$67$	1.85064e10	1.67460	0.837299	−	0.546745i	$-0.184133\pi$
$67$	1.85064e10	1.67460	0.837299	+	0.546745i	$0.184133\pi$
$68$	1.63385e9	0.136274
$69$	6.79282e9	0.522853
$70$	−1.40561e9	−0.0999597
$71$	4.49987e9	0.295991	0.147996	−	0.988988i	$-0.452718\pi$
$71$	4.49987e9	0.295991	0.147996	+	0.988988i	$0.452718\pi$
$72$	2.47422e8	0.0150699
$73$	2.44140e10	1.37836	0.689182	−	0.724588i	$-0.257970\pi$
$73$	2.44140e10	1.37836	0.689182	+	0.724588i	$0.257970\pi$
$74$	−4.39191e10	−2.30080
$75$	−1.14064e10	−0.555022
$76$	9.51803e9	0.430598
$77$	−6.31447e9	−0.265851
$78$	1.91655e10	0.751621
$79$	−1.48608e10	−0.543368	−0.271684	−	0.962387i	$-0.587581\pi$
$79$	−1.48608e10	−0.543368	−0.271684	+	0.962387i	$0.587581\pi$
$80$	5.94346e9	0.202789
$81$	3.48678e9	0.111111
$82$	7.64476e10	2.27713
$83$	5.49701e10	1.53178	0.765891	−	0.642971i	$-0.222298\pi$
$83$	5.49701e10	1.53178	0.765891	+	0.642971i	$0.222298\pi$
$84$	−7.76033e9	−0.202462
$85$	−1.13279e9	−0.0276914
$86$	−2.42888e10	−0.556756
$87$	1.04140e10	0.224007
$88$	1.64207e9	0.0331693
$89$	4.35958e10	0.827560	0.413780	−	0.910377i	$-0.364208\pi$
$89$	4.35958e10	0.827560	0.413780	+	0.910377i	$0.364208\pi$
$90$	5.15116e9	0.0919542
$91$	2.00185e10	0.336282
$92$	5.54047e10	0.876422
$93$	−3.54784e10	−0.528820
$94$	8.85893e8	0.0124502
$95$	−6.59911e9	−0.0874994
$96$	6.46349e10	0.809050
$97$	1.25330e11	1.48187	0.740937	−	0.671574i	$-0.234382\pi$
$97$	1.25330e11	1.48187	0.740937	+	0.671574i	$0.234382\pi$
$98$	1.09044e11	1.21859
$99$	2.31408e10	0.244559
$100$	−9.30344e10	−0.930344
$101$	−4.85151e10	−0.459313	−0.229657	−	0.973272i	$-0.573760\pi$
$101$	−4.85151e10	−0.459313	−0.229657	+	0.973272i	$0.573760\pi$
$102$	−1.27165e10	−0.114043
$103$	−1.20559e11	−1.02469	−0.512346	−	0.858779i	$-0.671223\pi$
$103$	−1.20559e11	−1.02469	−0.512346	+	0.858779i	$0.671223\pi$
$104$	−5.20578e9	−0.0419568
$105$	5.38045e9	0.0411412
$106$	2.94608e11	2.13827
$107$	−9.35045e10	−0.644498	−0.322249	−	0.946655i	$-0.604439\pi$
$107$	−9.35045e10	−0.644498	−0.322249	+	0.946655i	$0.604439\pi$
$108$	2.84395e10	0.186248
$109$	1.39138e11	0.866162	0.433081	−	0.901355i	$-0.357426\pi$
$109$	1.39138e11	0.866162	0.433081	+	0.901355i	$0.357426\pi$
$110$	3.41868e10	0.202394
$111$	1.68115e11	0.946958
$112$	6.96899e10	0.373655
$113$	−1.28480e11	−0.656001	−0.328000	−	0.944678i	$-0.606375\pi$
$113$	−1.28480e11	−0.656001	−0.328000	+	0.944678i	$0.606375\pi$
$114$	−7.40804e10	−0.360352
$115$	−3.84135e10	−0.178093
$116$	8.49403e10	0.375487
$117$	−7.33623e10	−0.309351
$118$	4.53850e10	0.182625
$119$	−1.32825e10	−0.0510237
$120$	−1.39918e9	−0.00513305
$121$	−1.31733e11	−0.461717
$122$	3.15967e11	1.05843
$123$	−2.92629e11	−0.937217
$124$	−2.89375e11	−0.886423
$125$	1.31601e11	0.385705
$126$	6.03999e10	0.169433
$127$	−1.20433e10	−0.0323464	−0.0161732	−	0.999869i	$-0.505148\pi$
$127$	−1.20433e10	−0.0323464	−0.0161732	+	0.999869i	$0.505148\pi$
$128$	−3.51309e10	−0.0903722
$129$	9.29737e10	0.229148
$130$	−1.08381e11	−0.256015
$131$	5.85420e11	1.32579	0.662896	−	0.748711i	$-0.269327\pi$
$131$	5.85420e11	1.32579	0.662896	+	0.748711i	$0.269327\pi$
$132$	1.88744e11	0.409937
$133$	−7.73777e10	−0.161225
$134$	−1.17483e12	−2.34908
$135$	−1.97178e10	−0.0378463
$136$	3.45410e9	0.00636606
$137$	−4.31517e11	−0.763897	−0.381948	−	0.924184i	$-0.624747\pi$
$137$	−4.31517e11	−0.763897	−0.381948	+	0.924184i	$0.624747\pi$
$138$	−4.31223e11	−0.733445
$139$	5.71359e11	0.933960	0.466980	−	0.884268i	$-0.345342\pi$
$139$	5.71359e11	0.933960	0.466980	+	0.884268i	$0.345342\pi$
$140$	4.38849e10	0.0689621
$141$	−3.39106e9	−0.00512425
$142$	−2.85662e11	−0.415208
$143$	−4.86884e11	−0.680891
$144$	−2.55394e11	−0.343730
$145$	−5.88914e10	−0.0763006
$146$	−1.54986e12	−1.93353
$147$	−4.17402e11	−0.501544
$148$	1.37121e12	1.58732
$149$	−1.13013e12	−1.26068	−0.630338	−	0.776321i	$-0.717084\pi$
$149$	−1.13013e12	−1.26068	−0.630338	+	0.776321i	$0.717084\pi$
$150$	7.24102e11	0.778570
$151$	7.30726e11	0.757497	0.378749	−	0.925500i	$-0.376354\pi$
$151$	7.30726e11	0.757497	0.378749	+	0.925500i	$0.376354\pi$
$152$	2.01219e10	0.0201155
$153$	4.86768e10	0.0469374
$154$	4.00857e11	0.372928
$155$	2.00631e11	0.180125
$156$	−5.98370e11	−0.518542
$157$	−4.75618e11	−0.397933	−0.198967	−	0.980006i	$-0.563759\pi$
$157$	−4.75618e11	−0.397933	−0.198967	+	0.980006i	$0.563759\pi$
$158$	9.43398e11	0.762221
$159$	−1.12771e12	−0.880064
$160$	−3.65512e11	−0.275576
$161$	−4.50417e11	−0.328150
$162$	−2.21349e11	−0.155864
$163$	1.66878e12	1.13597	0.567985	−	0.823039i	$-0.307723\pi$
$163$	1.66878e12	1.13597	0.567985	+	0.823039i	$0.307723\pi$
$164$	−2.38679e12	−1.57099
$165$	−1.30862e11	−0.0833010
$166$	−3.48962e12	−2.14874
$167$	−4.86847e10	−0.0290036	−0.0145018	−	0.999895i	$-0.504616\pi$
$167$	−4.86847e10	−0.0290036	−0.0145018	+	0.999895i	$0.504616\pi$
$168$	−1.64060e10	−0.00945806
$169$	−2.48609e11	−0.138720
$170$	7.19121e10	0.0388448
$171$	2.83568e11	0.148313
$172$	7.58327e11	0.384105
$173$	−3.95225e12	−1.93906	−0.969528	−	0.244981i	$-0.921218\pi$
$173$	−3.95225e12	−1.93906	−0.969528	+	0.244981i	$0.921218\pi$
$174$	−6.61104e11	−0.314231
$175$	7.56332e11	0.348340
$176$	−1.69498e12	−0.756561
$177$	−1.73727e11	−0.0751646
$178$	−2.76756e12	−1.16088
$179$	2.86039e12	1.16341	0.581706	−	0.813399i	$-0.302386\pi$
$179$	2.86039e12	1.16341	0.581706	+	0.813399i	$0.302386\pi$
$180$	−1.60826e11	−0.0634391
$181$	−4.07848e12	−1.56051	−0.780254	−	0.625462i	$-0.784910\pi$
$181$	−4.07848e12	−1.56051	−0.780254	+	0.625462i	$0.784910\pi$
$182$	−1.27082e12	−0.471728
$183$	−1.20947e12	−0.435627
$184$	1.17130e11	0.0409422
$185$	−9.50696e11	−0.322550
$186$	2.25225e12	0.741814
$187$	3.23054e11	0.103311
$188$	−2.76587e10	−0.00858941
$189$	−2.31201e11	−0.0697349
$190$	4.18926e11	0.122742
$191$	−3.61284e12	−1.02841	−0.514204	−	0.857668i	$-0.671912\pi$
$191$	−3.61284e12	−1.02841	−0.514204	+	0.857668i	$0.671912\pi$
$192$	−1.95071e12	−0.539555
$193$	−3.43973e12	−0.924612	−0.462306	−	0.886720i	$-0.652978\pi$
$193$	−3.43973e12	−0.924612	−0.462306	+	0.886720i	$0.652978\pi$
$194$	−7.95624e12	−2.07873
$195$	4.14866e11	0.105370
$196$	−3.40448e12	−0.840703
$197$	−4.20044e12	−1.00863	−0.504313	−	0.863521i	$-0.668254\pi$
$197$	−4.20044e12	−1.00863	−0.504313	+	0.863521i	$0.668254\pi$
$198$	−1.46903e12	−0.343061
$199$	−1.56899e12	−0.356393	−0.178197	−	0.983995i	$-0.557026\pi$
$199$	−1.56899e12	−0.356393	−0.178197	+	0.983995i	$0.557026\pi$
$200$	−1.96683e11	−0.0434612
$201$	4.49706e12	0.966830
$202$	3.07985e12	0.644312
$203$	−6.90530e11	−0.140590
$204$	3.97025e11	0.0786778
$205$	1.65483e12	0.319232
$206$	7.65333e12	1.43741
$207$	1.65065e12	0.301870
$208$	5.37352e12	0.956997
$209$	1.88196e12	0.326441
$210$	−3.41563e11	−0.0577118
$211$	−1.07129e13	−1.76341	−0.881707	−	0.471796i	$-0.843606\pi$
$211$	−1.07129e13	−1.76341	−0.881707	+	0.471796i	$0.843606\pi$
$212$	−9.19804e12	−1.47519
$213$	1.09347e12	0.170891
$214$	5.93588e12	0.904085
$215$	−5.25768e11	−0.0780518
$216$	6.01235e10	0.00870059
$217$	2.35250e12	0.331895
$218$	−8.83277e12	−1.21503
$219$	5.93261e12	0.795799
$220$	−1.06735e12	−0.139632
$221$	−1.02416e12	−0.130681
$222$	−1.06723e13	−1.32837
$223$	−9.90267e12	−1.20247	−0.601237	−	0.799071i	$-0.705325\pi$
$223$	−9.90267e12	−1.20247	−0.601237	+	0.799071i	$0.705325\pi$
$224$	−4.28580e12	−0.507771
$225$	−2.77175e12	−0.320442
$226$	8.15620e12	0.920220
$227$	−1.03526e13	−1.14001	−0.570005	−	0.821641i	$-0.693059\pi$
$227$	−1.03526e13	−1.14001	−0.570005	+	0.821641i	$0.693059\pi$
$228$	2.31288e12	0.248606
$229$	−1.12813e13	−1.18376	−0.591882	−	0.806024i	$-0.701615\pi$
$229$	−1.12813e13	−1.18376	−0.591882	+	0.806024i	$0.701615\pi$
$230$	2.43858e12	0.249824
$231$	−1.53442e12	−0.153489
$232$	1.79571e11	0.0175409
$233$	−1.19919e13	−1.14401	−0.572007	−	0.820249i	$-0.693835\pi$
$233$	−1.19919e13	−1.14401	−0.572007	+	0.820249i	$0.693835\pi$
$234$	4.65720e12	0.433948
$235$	1.91765e10	0.00174540
$236$	−1.41698e12	−0.125993
$237$	−3.61118e12	−0.313714
$238$	8.43204e11	0.0715747
$239$	1.78812e13	1.48323	0.741615	−	0.670826i	$-0.234060\pi$
$239$	1.78812e13	1.48323	0.741615	+	0.670826i	$0.234060\pi$
$240$	1.44426e12	0.117080
$241$	1.29149e13	1.02329	0.511645	−	0.859197i	$-0.329036\pi$
$241$	1.29149e13	1.02329	0.511645	+	0.859197i	$0.329036\pi$
$242$	8.36271e12	0.647683
$243$	8.47289e11	0.0641500
$244$	−9.86489e12	−0.730210
$245$	2.36042e12	0.170834
$246$	1.85768e13	1.31470
$247$	−5.96630e12	−0.412926
$248$	−6.11763e11	−0.0414094
$249$	1.33577e13	0.884375
$250$	−8.35435e12	−0.541057
$251$	−1.76652e13	−1.11921	−0.559606	−	0.828759i	$-0.689048\pi$
$251$	−1.76652e13	−1.11921	−0.559606	+	0.828759i	$0.689048\pi$
$252$	−1.88576e12	−0.116892
$253$	1.09549e13	0.664425
$254$	7.64537e11	0.0453746
$255$	−2.75268e11	−0.0159877
$256$	1.86707e13	1.06131
$257$	−4.11262e12	−0.228816	−0.114408	−	0.993434i	$-0.536497\pi$
$257$	−4.11262e12	−0.228816	−0.114408	+	0.993434i	$0.536497\pi$
$258$	−5.90218e12	−0.321443
$259$	−1.11474e13	−0.594325
$260$	3.38379e12	0.176624
$261$	2.53060e12	0.129331
$262$	−3.71638e13	−1.85979
$263$	2.38482e13	1.16869	0.584344	−	0.811506i	$-0.301352\pi$
$263$	2.38482e13	1.16869	0.584344	+	0.811506i	$0.301352\pi$
$264$	3.99022e11	0.0191503
$265$	6.37724e12	0.299765
$266$	4.91211e12	0.226162
$267$	1.05938e13	0.477792
$268$	3.66796e13	1.62063
$269$	2.08896e13	0.904256	0.452128	−	0.891953i	$-0.350665\pi$
$269$	2.08896e13	0.904256	0.452128	+	0.891953i	$0.350665\pi$
$270$	1.25173e12	0.0530898
$271$	2.73735e13	1.13762	0.568812	−	0.822467i	$-0.307403\pi$
$271$	2.73735e13	1.13762	0.568812	+	0.822467i	$0.307403\pi$
$272$	−3.56540e12	−0.145204
$273$	4.86450e12	0.194153
$274$	2.73937e13	1.07157
$275$	−1.83953e13	−0.705304
$276$	1.34633e13	0.506003
$277$	2.07159e13	0.763246	0.381623	−	0.924318i	$-0.375365\pi$
$277$	2.07159e13	0.763246	0.381623	+	0.924318i	$0.375365\pi$
$278$	−3.62712e13	−1.31013
$279$	−8.62125e12	−0.305314
$280$	9.27764e10	0.00322158
$281$	−2.37571e13	−0.808924	−0.404462	−	0.914555i	$-0.632541\pi$
$281$	−2.37571e13	−0.808924	−0.404462	+	0.914555i	$0.632541\pi$
$282$	2.15272e11	0.00718815
$283$	−3.77963e13	−1.23772	−0.618862	−	0.785500i	$-0.712406\pi$
$283$	−3.77963e13	−1.23772	−0.618862	+	0.785500i	$0.712406\pi$
$284$	8.91871e12	0.286452
$285$	−1.60358e12	−0.0505178
$286$	3.09085e13	0.955135
$287$	1.94036e13	0.588210
$288$	1.57063e13	0.467105
$289$	−3.35924e13	−0.980172
$290$	3.73856e12	0.107032
$291$	3.04552e13	0.855560
$292$	4.83885e13	1.33394
$293$	−2.72248e13	−0.736535	−0.368268	−	0.929720i	$-0.620049\pi$
$293$	−2.72248e13	−0.736535	−0.368268	+	0.929720i	$0.620049\pi$
$294$	2.64976e13	0.703553
$295$	9.82428e11	0.0256023
$296$	2.89885e12	0.0741519
$297$	5.62321e12	0.141196
$298$	7.17431e13	1.76844
$299$	−3.47300e13	−0.840452
$300$	−2.26074e13	−0.537135
$301$	−6.16489e12	−0.143817
$302$	−4.63881e13	−1.06260
$303$	−1.17892e13	−0.265185
$304$	−2.07703e13	−0.458816
$305$	6.83959e12	0.148382
$306$	−3.09011e12	−0.0658425
$307$	−1.75539e13	−0.367378	−0.183689	−	0.982984i	$-0.558804\pi$
$307$	−1.75539e13	−0.367378	−0.183689	+	0.982984i	$0.558804\pi$
$308$	−1.25152e13	−0.257283
$309$	−2.92957e13	−0.591606
$310$	−1.27365e13	−0.252674
$311$	4.35889e13	0.849560	0.424780	−	0.905297i	$-0.360351\pi$
$311$	4.35889e13	0.849560	0.424780	+	0.905297i	$0.360351\pi$
$312$	−1.26501e12	−0.0242238
$313$	6.40792e13	1.20566	0.602828	−	0.797871i	$-0.294041\pi$
$313$	6.40792e13	1.20566	0.602828	+	0.797871i	$0.294041\pi$
$314$	3.01933e13	0.558210
$315$	1.30745e12	0.0237529
$316$	−2.94541e13	−0.525856
$317$	−8.58063e13	−1.50554	−0.752771	−	0.658282i	$-0.771283\pi$
$317$	−8.58063e13	−1.50554	−0.752771	+	0.658282i	$0.771283\pi$
$318$	7.15898e13	1.23453
$319$	1.67949e13	0.284661
$320$	1.10313e13	0.183782
$321$	−2.27216e13	−0.372101
$322$	2.85935e13	0.460320
$323$	3.95871e12	0.0626527
$324$	6.91079e12	0.107530
$325$	5.83179e13	0.892161
$326$	−1.05938e14	−1.59351
$327$	3.38105e13	0.500079
$328$	−5.04588e12	−0.0733890
$329$	2.24854e11	0.00321605
$330$	8.30739e12	0.116852
$331$	−1.07052e12	−0.0148095	−0.00740474	−	0.999973i	$-0.502357\pi$
$331$	−1.07052e12	−0.0148095	−0.00740474	+	0.999973i	$0.502357\pi$
$332$	1.08950e14	1.48241
$333$	4.08520e13	0.546727
$334$	3.09062e12	0.0406855
$335$	−2.54309e13	−0.329318
$336$	1.69347e13	0.215730
$337$	−4.69489e13	−0.588384	−0.294192	−	0.955746i	$-0.595051\pi$
$337$	−4.69489e13	−0.588384	−0.294192	+	0.955746i	$0.595051\pi$
$338$	1.57823e13	0.194593
$339$	−3.12207e13	−0.378742
$340$	−2.24519e12	−0.0267990
$341$	−5.72167e13	−0.672007
$342$	−1.80015e13	−0.208049
$343$	5.95373e13	0.677130
$344$	1.60317e12	0.0179435
$345$	−9.33449e12	−0.102822
$346$	2.50897e14	2.72005
$347$	−1.53442e14	−1.63731	−0.818656	−	0.574284i	$-0.805281\pi$
$347$	−1.53442e14	−1.63731	−0.818656	+	0.574284i	$0.805281\pi$
$348$	2.06405e13	0.216788
$349$	−1.46212e14	−1.51162	−0.755811	−	0.654789i	$-0.772757\pi$
$349$	−1.46212e14	−1.51162	−0.755811	+	0.654789i	$0.772757\pi$
$350$	−4.80136e13	−0.488642
$351$	−1.78270e13	−0.178604
$352$	1.04238e14	1.02811
$353$	−1.86216e14	−1.80824	−0.904121	−	0.427277i	$-0.859473\pi$
$353$	−1.86216e14	−1.80824	−0.904121	+	0.427277i	$0.859473\pi$
$354$	1.10286e13	0.105439
$355$	−6.18358e12	−0.0582082
$356$	8.64067e13	0.800889
$357$	−3.22765e12	−0.0294586
$358$	−1.81584e14	−1.63200
$359$	−1.52519e14	−1.34991	−0.674956	−	0.737858i	$-0.735838\pi$
$359$	−1.52519e14	−1.34991	−0.674956	+	0.737858i	$0.735838\pi$
$360$	−3.40000e11	−0.00296357
$361$	−9.34287e13	−0.802030
$362$	2.58911e14	2.18904
$363$	−3.20111e13	−0.266572
$364$	3.96766e13	0.325445
$365$	−3.35491e13	−0.271063
$366$	7.67800e13	0.611086
$367$	1.95702e14	1.53437	0.767187	−	0.641424i	$-0.221656\pi$
$367$	1.95702e14	1.53437	0.767187	+	0.641424i	$0.221656\pi$
$368$	−1.20904e14	−0.933855
$369$	−7.11090e13	−0.541102
$370$	6.03523e13	0.452464
$371$	7.47763e13	0.552341
$372$	−7.03180e13	−0.511777
$373$	−2.51032e14	−1.80024	−0.900119	−	0.435644i	$-0.856521\pi$
$373$	−2.51032e14	−1.80024	−0.900119	+	0.435644i	$0.856521\pi$
$374$	−2.05082e13	−0.144922
$375$	3.19791e13	0.222687
$376$	−5.84729e10	−0.000401256 0
$377$	−5.32441e13	−0.360076
$378$	1.46772e13	0.0978222
$379$	−2.50484e14	−1.64537	−0.822686	−	0.568496i	$-0.807526\pi$
$379$	−2.50484e14	−1.64537	−0.822686	+	0.568496i	$0.807526\pi$
$380$	−1.30794e13	−0.0846794
$381$	−2.92653e12	−0.0186752
$382$	2.29351e14	1.44262
$383$	−2.39133e14	−1.48268	−0.741338	−	0.671131i	$-0.765809\pi$
$383$	−2.39133e14	−1.48268	−0.741338	+	0.671131i	$0.765809\pi$
$384$	−8.53682e12	−0.0521764
$385$	8.67715e12	0.0522809
$386$	2.18362e14	1.29702
$387$	2.25926e13	0.132299
$388$	2.48404e14	1.43412
$389$	−1.82634e14	−1.03958	−0.519791	−	0.854294i	$-0.673990\pi$
$389$	−1.82634e14	−1.03958	−0.519791	+	0.854294i	$0.673990\pi$
$390$	−2.63366e13	−0.147810
$391$	2.30437e13	0.127521
$392$	−7.19737e12	−0.0392736
$393$	1.42257e14	0.765447
$394$	2.66653e14	1.41487
$395$	2.04213e13	0.106856
$396$	4.58649e13	0.236678
$397$	2.44665e14	1.24516	0.622578	−	0.782558i	$-0.286085\pi$
$397$	2.44665e14	1.24516	0.622578	+	0.782558i	$0.286085\pi$
$398$	9.96033e13	0.499939
$399$	−1.88028e13	−0.0930832
$400$	2.03020e14	0.991311
$401$	3.83666e14	1.84782	0.923910	−	0.382609i	$-0.124974\pi$
$401$	3.83666e14	1.84782	0.923910	+	0.382609i	$0.124974\pi$
$402$	−2.85483e14	−1.35624
$403$	1.81392e14	0.850042
$404$	−9.61566e13	−0.444510
$405$	−4.79144e12	−0.0218506
$406$	4.38364e13	0.197216
$407$	2.71123e14	1.20336
$408$	8.39346e11	0.00367545
$409$	1.75721e14	0.759180	0.379590	−	0.925155i	$-0.376065\pi$
$409$	1.75721e14	0.759180	0.379590	+	0.925155i	$0.376065\pi$
$410$	−1.05052e14	−0.447810
$411$	−1.04859e14	−0.441036
$412$	−2.38947e14	−0.991668
$413$	1.15194e13	0.0471744
$414$	−1.04787e14	−0.423454
$415$	−7.55383e13	−0.301233
$416$	−3.30462e14	−1.30049
$417$	1.38840e14	0.539222
$418$	−1.19471e14	−0.457923
$419$	4.20566e13	0.159095	0.0795475	−	0.996831i	$-0.474652\pi$
$419$	4.20566e13	0.159095	0.0795475	+	0.996831i	$0.474652\pi$
$420$	1.06640e13	0.0398153
$421$	2.80170e14	1.03245	0.516226	−	0.856453i	$-0.327337\pi$
$421$	2.80170e14	1.03245	0.516226	+	0.856453i	$0.327337\pi$
$422$	6.80080e14	2.47367
$423$	−8.24027e11	−0.00295848
$424$	−1.94454e13	−0.0689137
$425$	−3.86946e13	−0.135366
$426$	−6.94158e13	−0.239721
$427$	8.01975e13	0.273406
$428$	−1.85326e14	−0.623727
$429$	−1.18313e14	−0.393113
$430$	3.33770e13	0.109489
$431$	−5.24917e14	−1.70007	−0.850033	−	0.526729i	$-0.823418\pi$
$431$	−5.24917e14	−1.70007	−0.850033	+	0.526729i	$0.823418\pi$
$432$	−6.20608e13	−0.198453
$433$	1.62531e14	0.513161	0.256580	−	0.966523i	$-0.417404\pi$
$433$	1.62531e14	0.513161	0.256580	+	0.966523i	$0.417404\pi$
$434$	−1.49342e14	−0.465573
$435$	−1.43106e13	−0.0440522
$436$	2.75770e14	0.838246
$437$	1.34242e14	0.402940
$438$	−3.76616e14	−1.11633
$439$	6.65170e14	1.94705	0.973526	−	0.228574i	$-0.0734064\pi$
$439$	6.65170e14	1.94705	0.973526	+	0.228574i	$0.0734064\pi$
$440$	−2.25648e12	−0.00652291
$441$	−1.01429e14	−0.289567
$442$	6.50163e13	0.183316
$443$	−6.13790e14	−1.70923	−0.854613	−	0.519266i	$-0.826206\pi$
$443$	−6.13790e14	−1.70923	−0.854613	+	0.519266i	$0.826206\pi$
$444$	3.33204e14	0.916439
$445$	−5.99080e13	−0.162744
$446$	6.28644e14	1.68680
$447$	−2.74621e14	−0.727851
$448$	1.29347e14	0.338633
$449$	4.50418e14	1.16482	0.582412	−	0.812894i	$-0.302109\pi$
$449$	4.50418e14	1.16482	0.582412	+	0.812894i	$0.302109\pi$
$450$	1.75957e14	0.449508
$451$	−4.71929e14	−1.19098
$452$	−2.54647e14	−0.634859
$453$	1.77566e14	0.437341
$454$	6.57209e14	1.59918
$455$	−2.75089e13	−0.0661317
$456$	4.88963e12	0.0116137
$457$	−2.60319e14	−0.610896	−0.305448	−	0.952209i	$-0.598806\pi$
$457$	−2.60319e14	−0.610896	−0.305448	+	0.952209i	$0.598806\pi$
$458$	7.16165e14	1.66055
$459$	1.18285e13	0.0270993
$460$	−7.61355e13	−0.172353
$461$	3.15031e14	0.704691	0.352345	−	0.935870i	$-0.385384\pi$
$461$	3.15031e14	0.704691	0.352345	+	0.935870i	$0.385384\pi$
$462$	9.74081e13	0.215310
$463$	1.15008e14	0.251208	0.125604	−	0.992080i	$-0.459913\pi$
$463$	1.15008e14	0.251208	0.125604	+	0.992080i	$0.459913\pi$
$464$	−1.85357e14	−0.400093
$465$	4.87534e13	0.103995
$466$	7.61274e14	1.60479
$467$	−1.62777e14	−0.339117	−0.169559	−	0.985520i	$-0.554234\pi$
$467$	−1.62777e14	−0.339117	−0.169559	+	0.985520i	$0.554234\pi$
$468$	−1.45404e14	−0.299381
$469$	−2.98190e14	−0.606796
$470$	−1.21737e12	−0.00244841
$471$	−1.15575e14	−0.229747
$472$	−2.99561e12	−0.00588579
$473$	1.49941e14	0.291194
$474$	2.29246e14	0.440069
$475$	−2.25416e14	−0.427731
$476$	−2.63259e13	−0.0493793
$477$	−2.74034e14	−0.508105
$478$	−1.13514e15	−2.08063
$479$	2.72531e14	0.493823	0.246911	−	0.969038i	$-0.420584\pi$
$479$	2.72531e14	0.493823	0.246911	+	0.969038i	$0.420584\pi$
$480$	−8.88194e13	−0.159104
$481$	−8.59531e14	−1.52217
$482$	−8.19869e14	−1.43544
$483$	−1.09451e14	−0.189458
$484$	−2.61094e14	−0.446836
$485$	−1.72225e14	−0.291418
$486$	−5.37878e13	−0.0899879
$487$	−4.45484e13	−0.0736924	−0.0368462	−	0.999321i	$-0.511731\pi$
$487$	−4.45484e13	−0.0736924	−0.0368462	+	0.999321i	$0.511731\pi$
$488$	−2.08552e13	−0.0341119
$489$	4.05513e14	0.655853
$490$	−1.49845e14	−0.239642
$491$	2.32630e14	0.367890	0.183945	−	0.982937i	$-0.441113\pi$
$491$	2.32630e14	0.367890	0.183945	+	0.982937i	$0.441113\pi$
$492$	−5.79990e14	−0.907011
$493$	3.53281e13	0.0546339
$494$	3.78754e14	0.579241
$495$	−3.17994e13	−0.0480939
$496$	6.31475e14	0.944511
$497$	−7.25055e13	−0.107253
$498$	−8.47979e14	−1.24058
$499$	−4.19440e14	−0.606900	−0.303450	−	0.952847i	$-0.598139\pi$
$499$	−4.19440e14	−0.606900	−0.303450	+	0.952847i	$0.598139\pi$
$500$	2.60833e14	0.373274
$501$	−1.18304e13	−0.0167452
$502$	1.12143e15	1.57000
$503$	1.42016e14	0.196659	0.0983294	−	0.995154i	$-0.468650\pi$
$503$	1.42016e14	0.196659	0.0983294	+	0.995154i	$0.468650\pi$
$504$	−3.98666e12	−0.00546061
$505$	6.66680e13	0.0903264
$506$	−6.95443e14	−0.932038
$507$	−6.04120e13	−0.0800902
$508$	−2.38698e13	−0.0313039
$509$	−2.48643e14	−0.322574	−0.161287	−	0.986908i	$-0.551564\pi$
$509$	−2.48643e14	−0.322574	−0.161287	+	0.986908i	$0.551564\pi$
$510$	1.74746e13	0.0224271
$511$	−3.93379e14	−0.499455
$512$	−1.11331e15	−1.39840
$513$	6.89070e13	0.0856284
$514$	2.61078e14	0.320977
$515$	1.65668e14	0.201511
$516$	1.84274e14	0.221763
$517$	−5.46883e12	−0.00651173
$518$	7.07660e14	0.833702
$519$	−9.60396e14	−1.11951
$520$	7.15363e12	0.00825103
$521$	−1.12001e15	−1.27825	−0.639125	−	0.769103i	$-0.720703\pi$
$521$	−1.12001e15	−1.27825	−0.639125	+	0.769103i	$0.720703\pi$
$522$	−1.60648e14	−0.181421
$523$	3.76657e14	0.420908	0.210454	−	0.977604i	$-0.432506\pi$
$523$	3.76657e14	0.420908	0.210454	+	0.977604i	$0.432506\pi$
$524$	1.16030e15	1.28306
$525$	1.83789e14	0.201114
$526$	−1.51394e15	−1.63940
$527$	−1.20356e14	−0.128976
$528$	−4.11879e14	−0.436801
$529$	−1.71384e14	−0.179873
$530$	−4.04842e14	−0.420502
$531$	−4.22156e13	−0.0433963
$532$	−1.53362e14	−0.156029
$533$	1.49614e15	1.50651
$534$	−6.72517e14	−0.670234
$535$	1.28491e14	0.126744
$536$	7.75439e13	0.0757079
$537$	6.95074e14	0.671696
$538$	−1.32612e15	−1.26847
$539$	−6.73153e14	−0.637346
$540$	−3.90807e13	−0.0366266
$541$	−6.25461e14	−0.580250	−0.290125	−	0.956989i	$-0.593697\pi$
$541$	−6.25461e14	−0.580250	−0.290125	+	0.956989i	$0.593697\pi$
$542$	−1.73773e15	−1.59583
$543$	−9.91071e14	−0.900960
$544$	2.19265e14	0.197322
$545$	−1.91199e14	−0.170335
$546$	−3.08809e14	−0.272352
$547$	1.69694e14	0.148162	0.0740809	−	0.997252i	$-0.476398\pi$
$547$	1.69694e14	0.148162	0.0740809	+	0.997252i	$0.476398\pi$
$548$	−8.55265e14	−0.739277
$549$	−2.93902e14	−0.251509
$550$	1.16777e15	0.989382
$551$	2.05805e14	0.172632
$552$	2.84627e13	0.0236380
$553$	2.39450e14	0.196891
$554$	−1.31509e15	−1.07066
$555$	−2.31019e14	−0.186224
$556$	1.13243e15	0.903859
$557$	9.00925e14	0.712009	0.356004	−	0.934484i	$-0.384139\pi$
$557$	9.00925e14	0.712009	0.356004	+	0.934484i	$0.384139\pi$
$558$	5.47297e14	0.428287
$559$	−4.75351e14	−0.368341
$560$	−9.57658e13	−0.0734812
$561$	7.85020e13	0.0596465
$562$	1.50815e15	1.13474
$563$	2.55254e15	1.90185	0.950923	−	0.309426i	$-0.100137\pi$
$563$	2.55254e15	1.90185	0.950923	+	0.309426i	$0.100137\pi$
$564$	−6.72106e12	−0.00495910
$565$	1.76554e14	0.129006
$566$	2.39939e15	1.73624
$567$	−5.61819e13	−0.0402615
$568$	1.88549e13	0.0133816
$569$	1.45933e15	1.02574	0.512869	−	0.858467i	$-0.328583\pi$
$569$	1.45933e15	1.02574	0.512869	+	0.858467i	$0.328583\pi$
$570$	1.01799e14	0.0708650
$571$	6.41354e14	0.442180	0.221090	−	0.975253i	$-0.429039\pi$
$571$	6.41354e14	0.442180	0.221090	+	0.975253i	$0.429039\pi$
$572$	−9.65003e14	−0.658947
$573$	−8.77920e14	−0.593751
$574$	−1.23179e15	−0.825126
$575$	−1.31215e15	−0.870586
$576$	−4.74023e14	−0.311512
$577$	−1.66562e15	−1.08420	−0.542098	−	0.840315i	$-0.682370\pi$
$577$	−1.66562e15	−1.08420	−0.542098	+	0.840315i	$0.682370\pi$
$578$	2.13252e15	1.37496
$579$	−8.35855e14	−0.533825
$580$	−1.16722e14	−0.0738415
$581$	−8.85723e14	−0.555046
$582$	−1.93337e15	−1.20016
$583$	−1.81869e15	−1.11836
$584$	1.02298e14	0.0623153
$585$	1.00812e14	0.0608354
$586$	1.72829e15	1.03319
$587$	8.16234e14	0.483398	0.241699	−	0.970351i	$-0.422295\pi$
$587$	8.16234e14	0.483398	0.241699	+	0.970351i	$0.422295\pi$
$588$	−8.27289e14	−0.485380
$589$	−7.01136e14	−0.407538
$590$	−6.23667e13	−0.0359143
$591$	−1.02071e15	−0.582330
$592$	−2.99226e15	−1.69134
$593$	−2.77779e15	−1.55561	−0.777803	−	0.628509i	$-0.783666\pi$
$593$	−2.77779e15	−1.55561	−0.777803	+	0.628509i	$0.783666\pi$
$594$	−3.56974e14	−0.198066
$595$	1.82524e13	0.0100341
$596$	−2.23991e15	−1.22005
$597$	−3.81266e14	−0.205764
$598$	2.20474e15	1.17896
$599$	8.71268e14	0.461641	0.230820	−	0.972996i	$-0.425859\pi$
$599$	8.71268e14	0.461641	0.230820	+	0.972996i	$0.425859\pi$
$600$	−4.77939e13	−0.0250923
$601$	−6.04340e14	−0.314392	−0.157196	−	0.987567i	$-0.550246\pi$
$601$	−6.04340e14	−0.314392	−0.157196	+	0.987567i	$0.550246\pi$
$602$	3.91361e14	0.201742
$603$	1.09278e15	0.558199
$604$	1.44829e15	0.733084
$605$	1.81024e14	0.0907990
$606$	7.48402e14	0.371994
$607$	1.64594e14	0.0810732	0.0405366	−	0.999178i	$-0.487093\pi$
$607$	1.64594e14	0.0810732	0.0405366	+	0.999178i	$0.487093\pi$
$608$	1.27734e15	0.623499
$609$	−1.67799e14	−0.0811697
$610$	−4.34192e14	−0.208146
$611$	1.73376e13	0.00823688
$612$	9.64771e13	0.0454246
$613$	−1.47340e15	−0.687525	−0.343763	−	0.939057i	$-0.611702\pi$
$613$	−1.47340e15	−0.687525	−0.343763	+	0.939057i	$0.611702\pi$
$614$	1.11436e15	0.515348
$615$	4.02123e14	0.184309
$616$	−2.64583e13	−0.0120190
$617$	−2.66219e15	−1.19859	−0.599295	−	0.800529i	$-0.704552\pi$
$617$	−2.66219e15	−1.19859	−0.599295	+	0.800529i	$0.704552\pi$
$618$	1.85976e15	0.829889
$619$	−2.51176e15	−1.11091	−0.555456	−	0.831546i	$-0.687456\pi$
$619$	−2.51176e15	−1.11091	−0.555456	+	0.831546i	$0.687456\pi$
$620$	3.97650e14	0.174320
$621$	4.01109e14	0.174284
$622$	−2.76712e15	−1.19174
$623$	−7.02451e14	−0.299869
$624$	1.30577e15	0.552523
$625$	2.11114e15	0.885476
$626$	−4.06789e15	−1.69126
$627$	4.57316e14	0.188471
$628$	−9.42673e14	−0.385109
$629$	5.70309e14	0.230957
$630$	−8.29997e13	−0.0333199
$631$	2.30101e15	0.915707	0.457853	−	0.889028i	$-0.348618\pi$
$631$	2.30101e15	0.915707	0.457853	+	0.889028i	$0.348618\pi$
$632$	−6.22685e13	−0.0245654
$633$	−2.60324e15	−1.01811
$634$	5.44717e15	2.11193
$635$	1.65496e13	0.00636109
$636$	−2.23512e15	−0.851701
$637$	2.13407e15	0.806198
$638$	−1.06618e15	−0.399314
$639$	2.65713e14	0.0986637
$640$	4.82759e13	0.0177722
$641$	−1.77314e15	−0.647180	−0.323590	−	0.946197i	$-0.604890\pi$
$641$	−1.77314e15	−0.647180	−0.323590	+	0.946197i	$0.604890\pi$
$642$	1.44242e15	0.521973
$643$	2.86869e15	1.02926	0.514628	−	0.857413i	$-0.327930\pi$
$643$	2.86869e15	1.02926	0.514628	+	0.857413i	$0.327930\pi$
$644$	−8.92725e14	−0.317574
$645$	−1.27762e14	−0.0450632
$646$	−2.51308e14	−0.0878875
$647$	−4.03348e14	−0.139864	−0.0699321	−	0.997552i	$-0.522278\pi$
$647$	−4.03348e14	−0.139864	−0.0699321	+	0.997552i	$0.522278\pi$
$648$	1.46100e13	0.00502329
$649$	−2.80172e14	−0.0955167
$650$	−3.70215e15	−1.25150
$651$	5.71657e14	0.191620
$652$	3.30751e15	1.09936
$653$	−9.72103e14	−0.320398	−0.160199	−	0.987085i	$-0.551214\pi$
$653$	−9.72103e14	−0.320398	−0.160199	+	0.987085i	$0.551214\pi$
$654$	−2.14636e15	−0.701497
$655$	−8.04467e14	−0.260724
$656$	5.20847e15	1.67394
$657$	1.44162e15	0.459455
$658$	−1.42742e13	−0.00451139
$659$	6.57482e14	0.206070	0.103035	−	0.994678i	$-0.467145\pi$
$659$	6.57482e14	0.206070	0.103035	+	0.994678i	$0.467145\pi$
$660$	−2.59367e14	−0.0806164
$661$	−5.07978e15	−1.56580	−0.782901	−	0.622147i	$-0.786261\pi$
$661$	−5.07978e15	−1.56580	−0.782901	+	0.622147i	$0.786261\pi$
$662$	6.79589e13	0.0207743
$663$	−2.48872e14	−0.0754487
$664$	2.30331e14	0.0692512
$665$	1.06330e14	0.0317057
$666$	−2.59338e15	−0.766933
$667$	1.19799e15	0.351369
$668$	−9.64929e13	−0.0280689
$669$	−2.40635e15	−0.694249
$670$	1.61441e15	0.461959
$671$	−1.95054e15	−0.553581
$672$	−1.04145e15	−0.293162
$673$	2.44434e15	0.682462	0.341231	−	0.939979i	$-0.389156\pi$
$673$	2.44434e15	0.682462	0.341231	+	0.939979i	$0.389156\pi$
$674$	2.98042e15	0.825369
$675$	−6.73535e14	−0.185007
$676$	−4.92742e14	−0.134250
$677$	−2.97668e15	−0.804442	−0.402221	−	0.915543i	$-0.631762\pi$
$677$	−2.97668e15	−0.804442	−0.402221	+	0.915543i	$0.631762\pi$
$678$	1.98196e15	0.531289
$679$	−2.01942e15	−0.536962
$680$	−4.74652e12	−0.00125192
$681$	−2.51569e15	−0.658186
$682$	3.63225e15	0.942674
$683$	6.09320e15	1.56867	0.784335	−	0.620338i	$-0.213004\pi$
$683$	6.09320e15	1.56867	0.784335	+	0.620338i	$0.213004\pi$
$684$	5.62030e14	0.143533
$685$	5.92978e14	0.150224
$686$	−3.77956e15	−0.949859
$687$	−2.74136e15	−0.683447
$688$	−1.65483e15	−0.409276
$689$	5.76571e15	1.41464
$690$	5.92574e14	0.144236
$691$	7.54517e15	1.82196	0.910982	−	0.412447i	$-0.135326\pi$
$691$	7.54517e15	1.82196	0.910982	+	0.412447i	$0.135326\pi$
$692$	−7.83333e15	−1.87656
$693$	−3.72863e14	−0.0886169
$694$	9.74083e15	2.29678
$695$	−7.85145e14	−0.183668
$696$	4.36358e13	0.0101273
$697$	−9.92707e14	−0.228581
$698$	9.28187e15	2.12046
$699$	−2.91404e15	−0.660496
$700$	1.49905e15	0.337113
$701$	9.37328e13	0.0209143	0.0104571	−	0.999945i	$-0.496671\pi$
$701$	9.37328e13	0.0209143	0.0104571	+	0.999945i	$0.496671\pi$
$702$	1.13170e15	0.250540
$703$	3.32235e15	0.729779
$704$	−3.14595e15	−0.685649
$705$	4.65989e12	0.00100771
$706$	1.18214e16	2.53655
$707$	7.81714e14	0.166434
$708$	−3.44325e14	−0.0727421
$709$	7.32883e15	1.53632	0.768158	−	0.640261i	$-0.221174\pi$
$709$	7.32883e15	1.53632	0.768158	+	0.640261i	$0.221174\pi$
$710$	3.92548e14	0.0816529
$711$	−8.77517e14	−0.181123
$712$	1.82671e14	0.0374137
$713$	−4.08133e15	−0.829486
$714$	2.04899e14	0.0413237
$715$	6.69062e14	0.133901
$716$	5.66928e15	1.12592
$717$	4.34513e15	0.856343
$718$	9.68228e15	1.89362
$719$	−2.09644e15	−0.406887	−0.203444	−	0.979087i	$-0.565213\pi$
$719$	−2.09644e15	−0.406887	−0.203444	+	0.979087i	$0.565213\pi$
$720$	3.50955e14	0.0675963
$721$	1.94254e15	0.371301
$722$	5.93106e15	1.12507
$723$	3.13833e15	0.590796
$724$	−8.08353e15	−1.51022
$725$	−2.01165e15	−0.372987
$726$	2.03214e15	0.373940
$727$	2.30351e15	0.420678	0.210339	−	0.977628i	$-0.432543\pi$
$727$	2.30351e15	0.420678	0.210339	+	0.977628i	$0.432543\pi$
$728$	8.38798e13	0.0152032
$729$	2.05891e14	0.0370370
$730$	2.12977e15	0.380239
$731$	3.15401e14	0.0558879
$732$	−2.39717e15	−0.421587
$733$	−6.47539e15	−1.13030	−0.565150	−	0.824988i	$-0.691182\pi$
$733$	−6.47539e15	−1.13030	−0.565150	+	0.824988i	$0.691182\pi$
$734$	−1.24236e16	−2.15238
$735$	5.73582e14	0.0986313
$736$	7.43540e15	1.26904
$737$	7.25249e15	1.22862
$738$	4.51416e15	0.759043
$739$	−6.76817e15	−1.12961	−0.564803	−	0.825226i	$-0.691048\pi$
$739$	−6.76817e15	−1.12961	−0.564803	+	0.825226i	$0.691048\pi$
$740$	−1.88427e15	−0.312155
$741$	−1.44981e15	−0.238403
$742$	−4.74697e15	−0.774809
$743$	2.76218e15	0.447521	0.223760	−	0.974644i	$-0.428167\pi$
$743$	2.76218e15	0.447521	0.223760	+	0.974644i	$0.428167\pi$
$744$	−1.48658e14	−0.0239077
$745$	1.55299e15	0.247919
$746$	1.59361e16	2.52532
$747$	3.24593e15	0.510594
$748$	6.40291e14	0.0999812
$749$	1.50662e15	0.233536
$750$	−2.03011e15	−0.312379
$751$	8.20164e15	1.25280	0.626399	−	0.779502i	$-0.284528\pi$
$751$	8.20164e15	1.25280	0.626399	+	0.779502i	$0.284528\pi$
$752$	6.03570e13	0.00915228
$753$	−4.29264e15	−0.646178
$754$	3.38006e15	0.505105
$755$	−1.00414e15	−0.148966
$756$	−4.58240e14	−0.0674874
$757$	5.71284e15	0.835266	0.417633	−	0.908616i	$-0.362860\pi$
$757$	5.71284e15	0.835266	0.417633	+	0.908616i	$0.362860\pi$
$758$	1.59013e16	2.30808
$759$	2.66204e15	0.383606
$760$	−2.76510e13	−0.00395581
$761$	−8.05028e15	−1.14339	−0.571696	−	0.820465i	$-0.693715\pi$
$761$	−8.05028e15	−1.14339	−0.571696	+	0.820465i	$0.693715\pi$
$762$	1.85783e14	0.0261971
$763$	−2.24190e15	−0.313856
$764$	−7.16063e15	−0.995263
$765$	−6.68902e13	−0.00923048
$766$	1.51807e16	2.07986
$767$	8.88220e14	0.120822
$768$	4.53699e15	0.612747
$769$	−3.93277e15	−0.527356	−0.263678	−	0.964611i	$-0.584936\pi$
$769$	−3.93277e15	−0.527356	−0.263678	+	0.964611i	$0.584936\pi$
$770$	−5.50845e14	−0.0733382
$771$	−9.99366e14	−0.132107
$772$	−6.81754e15	−0.894813
$773$	−7.74208e15	−1.00895	−0.504476	−	0.863426i	$-0.668314\pi$
$773$	−7.74208e15	−1.00895	−0.504476	+	0.863426i	$0.668314\pi$
$774$	−1.43423e15	−0.185585
$775$	6.85329e15	0.880521
$776$	5.25148e14	0.0669949
$777$	−2.70881e15	−0.343133
$778$	1.15940e16	1.45830
$779$	−5.78304e15	−0.722271
$780$	8.22262e14	0.101974
$781$	1.76346e15	0.217162
$782$	−1.46287e15	−0.178883
$783$	6.14936e14	0.0746690
$784$	7.42928e15	0.895795
$785$	6.53581e14	0.0782557
$786$	−9.03080e15	−1.07375
$787$	8.87344e15	1.04769	0.523843	−	0.851815i	$-0.324498\pi$
$787$	8.87344e15	1.04769	0.523843	+	0.851815i	$0.324498\pi$
$788$	−8.32524e15	−0.976119
$789$	5.79510e15	0.674742
$790$	−1.29639e15	−0.149895
$791$	2.07018e15	0.237704
$792$	9.69624e13	0.0110564
$793$	6.18372e15	0.700241
$794$	−1.55319e16	−1.74667
$795$	1.54967e15	0.173069
$796$	−3.10974e15	−0.344907
$797$	−5.75633e15	−0.634052	−0.317026	−	0.948417i	$-0.602684\pi$
$797$	−5.75633e15	−0.634052	−0.317026	+	0.948417i	$0.602684\pi$
$798$	1.19364e15	0.130575
$799$	−1.15037e13	−0.00124977
$800$	−1.24854e16	−1.34712
$801$	2.57429e15	0.275853
$802$	−2.43560e16	−2.59207
$803$	9.56764e15	1.01128
$804$	8.91314e15	0.935670
$805$	6.18950e14	0.0645325
$806$	−1.15152e16	−1.19242
$807$	5.07616e15	0.522073
$808$	−2.03284e14	−0.0207654
$809$	4.45104e15	0.451590	0.225795	−	0.974175i	$-0.427502\pi$
$809$	4.45104e15	0.451590	0.225795	+	0.974175i	$0.427502\pi$
$810$	3.04171e14	0.0306514
$811$	−1.29435e16	−1.29550	−0.647751	−	0.761852i	$-0.724290\pi$
$811$	−1.29435e16	−1.29550	−0.647751	+	0.761852i	$0.724290\pi$
$812$	−1.36863e15	−0.136059
$813$	6.65176e15	0.656808
$814$	−1.72115e16	−1.68805
$815$	−2.29319e15	−0.223394
$816$	−8.66391e14	−0.0838336
$817$	1.83738e15	0.176595
$818$	−1.11552e16	−1.06496
$819$	1.18207e15	0.112094
$820$	3.27986e15	0.308943
$821$	4.69898e15	0.439659	0.219830	−	0.975538i	$-0.429450\pi$
$821$	4.69898e15	0.439659	0.219830	+	0.975538i	$0.429450\pi$
$822$	6.65666e15	0.618673
$823$	−4.08560e15	−0.377187	−0.188593	−	0.982055i	$-0.560393\pi$
$823$	−4.08560e15	−0.377187	−0.188593	+	0.982055i	$0.560393\pi$
$824$	−5.05154e14	−0.0463259
$825$	−4.47005e15	−0.407208
$826$	−7.31280e14	−0.0661749
$827$	−1.25404e16	−1.12728	−0.563640	−	0.826021i	$-0.690599\pi$
$827$	−1.25404e16	−1.12728	−0.563640	+	0.826021i	$0.690599\pi$
$828$	3.27159e15	0.292141
$829$	−1.41486e16	−1.25506	−0.627529	−	0.778593i	$-0.715934\pi$
$829$	−1.41486e16	−1.25506	−0.627529	+	0.778593i	$0.715934\pi$
$830$	4.79534e15	0.422561
$831$	5.03396e15	0.440660
$832$	9.97349e15	0.867299
$833$	−1.41598e15	−0.122324
$834$	−8.81390e15	−0.756406
$835$	6.69011e13	0.00570371
$836$	3.73003e15	0.315921
$837$	−2.09496e15	−0.176273
$838$	−2.66985e15	−0.223174
$839$	−4.25727e15	−0.353542	−0.176771	−	0.984252i	$-0.556565\pi$
$839$	−4.25727e15	−0.353542	−0.176771	+	0.984252i	$0.556565\pi$
$840$	2.25447e13	0.00185998
$841$	−1.03639e16	−0.849463
$842$	−1.77858e16	−1.44829
$843$	−5.77296e15	−0.467033
$844$	−2.12330e16	−1.70658
$845$	3.41631e14	0.0272801
$846$	5.23111e13	0.00415008
$847$	2.12259e15	0.167304
$848$	2.00720e16	1.57186
$849$	−9.18450e15	−0.714600
$850$	2.45642e15	0.189888
$851$	1.93395e16	1.48536
$852$	2.16725e15	0.165383
$853$	−1.06217e16	−0.805329	−0.402665	−	0.915348i	$-0.631916\pi$
$853$	−1.06217e16	−0.805329	−0.402665	+	0.915348i	$0.631916\pi$
$854$	−5.09112e15	−0.383526
$855$	−3.89671e14	−0.0291665
$856$	−3.91794e14	−0.0291375
$857$	−2.07068e16	−1.53010	−0.765049	−	0.643972i	$-0.777285\pi$
$857$	−2.07068e16	−1.53010	−0.765049	+	0.643972i	$0.777285\pi$
$858$	7.51077e15	0.551448
$859$	1.44569e15	0.105466	0.0527331	−	0.998609i	$-0.483207\pi$
$859$	1.44569e15	0.105466	0.0527331	+	0.998609i	$0.483207\pi$
$860$	−1.04207e15	−0.0755363
$861$	4.71508e15	0.339603
$862$	3.33229e16	2.38481
$863$	3.39961e15	0.241752	0.120876	−	0.992668i	$-0.461430\pi$
$863$	3.39961e15	0.241752	0.120876	+	0.992668i	$0.461430\pi$
$864$	3.81663e15	0.269683
$865$	5.43106e15	0.381326
$866$	−1.03178e16	−0.719848
$867$	−8.16294e15	−0.565903
$868$	4.66264e15	0.321198
$869$	−5.82382e15	−0.398657
$870$	9.08469e14	0.0617952
$871$	−2.29923e16	−1.55411
$872$	5.83002e14	0.0391588
$873$	7.40062e15	0.493958
$874$	−8.52198e15	−0.565233
$875$	−2.12047e15	−0.139762
$876$	1.17584e16	0.770151
$877$	−1.87390e16	−1.21968	−0.609842	−	0.792523i	$-0.708767\pi$
$877$	−1.87390e16	−1.21968	−0.609842	+	0.792523i	$0.708767\pi$
$878$	−4.22265e16	−2.73127
$879$	−6.61564e15	−0.425239
$880$	2.32919e15	0.148782
$881$	1.90703e15	0.121057	0.0605285	−	0.998166i	$-0.480721\pi$
$881$	1.90703e15	0.121057	0.0605285	+	0.998166i	$0.480721\pi$
$882$	6.43892e15	0.406196
$883$	4.45112e15	0.279052	0.139526	−	0.990218i	$-0.455442\pi$
$883$	4.45112e15	0.279052	0.139526	+	0.990218i	$0.455442\pi$
$884$	−2.02989e15	−0.126469
$885$	2.38730e14	0.0147815
$886$	3.89648e16	2.39766
$887$	−6.97407e15	−0.426488	−0.213244	−	0.976999i	$-0.568403\pi$
$887$	−6.97407e15	−0.426488	−0.213244	+	0.976999i	$0.568403\pi$
$888$	7.04422e14	0.0428116
$889$	1.94052e14	0.0117208
$890$	3.80310e15	0.228293
$891$	1.36644e15	0.0815198
$892$	−1.96271e16	−1.16372
$893$	−6.70152e13	−0.00394903
$894$	1.74336e16	1.02101
$895$	−3.93066e15	−0.228791
$896$	5.66058e14	0.0327467
$897$	−8.43938e15	−0.485235
$898$	−2.85935e16	−1.63398
$899$	−6.25704e15	−0.355378
$900$	−5.49359e15	−0.310115
$901$	−3.82562e15	−0.214642
$902$	2.99591e16	1.67068
$903$	−1.49807e15	−0.0830327
$904$	−5.38346e14	−0.0296575
$905$	5.60453e15	0.306882
$906$	−1.12723e16	−0.613490
$907$	−3.26700e16	−1.76729	−0.883647	−	0.468153i	$-0.844920\pi$
$907$	−3.26700e16	−1.76729	−0.883647	+	0.468153i	$0.844920\pi$
$908$	−2.05189e16	−1.10327
$909$	−2.86477e15	−0.153104
$910$	1.74632e15	0.0927678
$911$	−1.41035e16	−0.744690	−0.372345	−	0.928094i	$-0.621446\pi$
$911$	−1.41035e16	−0.744690	−0.372345	+	0.928094i	$0.621446\pi$
$912$	−5.04719e15	−0.264897
$913$	2.15423e16	1.12383
$914$	1.65257e16	0.856948
$915$	1.66202e15	0.0856683
$916$	−2.23596e16	−1.14561
$917$	−9.43277e15	−0.480405
$918$	−7.50897e14	−0.0380142
$919$	2.92523e14	0.0147206	0.00736030	−	0.999973i	$-0.497657\pi$
$919$	2.92523e14	0.0147206	0.00736030	+	0.999973i	$0.497657\pi$
$920$	−1.60957e14	−0.00805150
$921$	−4.26560e15	−0.212106
$922$	−1.99989e16	−0.988521
$923$	−5.59062e15	−0.274695
$924$	−3.04120e15	−0.148542
$925$	−3.24745e16	−1.57675
$926$	−7.30099e15	−0.352388
$927$	−7.11886e15	−0.341564
$928$	1.13991e16	0.543699
$929$	4.93609e15	0.234044	0.117022	−	0.993129i	$-0.462665\pi$
$929$	4.93609e15	0.234044	0.117022	+	0.993129i	$0.462665\pi$
$930$	−3.09497e15	−0.145882
$931$	−8.24884e15	−0.386518
$932$	−2.37679e16	−1.10714
$933$	1.05921e16	0.490494
$934$	1.03334e16	0.475704
$935$	−4.43931e14	−0.0203166
$936$	−3.07396e14	−0.0139856
$937$	3.91617e16	1.77131	0.885654	−	0.464345i	$-0.153710\pi$
$937$	3.91617e16	1.77131	0.885654	+	0.464345i	$0.153710\pi$
$938$	1.89298e16	0.851197
$939$	1.55712e16	0.696085
$940$	3.80077e13	0.00168915
$941$	−7.71148e15	−0.340718	−0.170359	−	0.985382i	$-0.554493\pi$
$941$	−7.71148e15	−0.340718	−0.170359	+	0.985382i	$0.554493\pi$
$942$	7.33698e15	0.322283
$943$	−3.36632e16	−1.47008
$944$	3.09214e15	0.134250
$945$	3.17710e14	0.0137137
$946$	−9.51857e15	−0.408480
$947$	4.41750e15	0.188474	0.0942371	−	0.995550i	$-0.469959\pi$
$947$	4.41750e15	0.188474	0.0942371	+	0.995550i	$0.469959\pi$
$948$	−7.15734e15	−0.303603
$949$	−3.03319e16	−1.27919
$950$	1.43099e16	0.600009
$951$	−2.08509e16	−0.869225
$952$	−5.56552e13	−0.00230676
$953$	2.33786e16	0.963403	0.481702	−	0.876335i	$-0.340019\pi$
$953$	2.33786e16	0.963403	0.481702	+	0.876335i	$0.340019\pi$
$954$	1.73963e16	0.712756
$955$	4.96466e15	0.202242
$956$	3.54405e16	1.43543
$957$	4.08115e15	0.164349
$958$	−1.73009e16	−0.692721
$959$	6.95295e15	0.276800
$960$	2.68061e15	0.106106
$961$	−4.09199e15	−0.161048
$962$	5.45650e16	2.13526
$963$	−5.52135e15	−0.214833
$964$	2.55973e16	0.990310
$965$	4.72678e15	0.181830
$966$	6.94822e15	0.265766
$967$	−1.00913e16	−0.383797	−0.191898	−	0.981415i	$-0.561464\pi$
$967$	−1.00913e16	−0.383797	−0.191898	+	0.981415i	$0.561464\pi$
$968$	−5.51976e14	−0.0208740
$969$	9.61967e14	0.0361726
$970$	1.09332e16	0.408794
$971$	4.57498e16	1.70092	0.850460	−	0.526041i	$-0.176324\pi$
$971$	4.57498e16	1.70092	0.850460	+	0.526041i	$0.176324\pi$
$972$	1.67932e15	0.0620826
$973$	−9.20621e15	−0.338423
$974$	2.82803e15	0.103374
$975$	1.41712e16	0.515089
$976$	2.15272e16	0.778062
$977$	−1.62337e16	−0.583442	−0.291721	−	0.956503i	$-0.594228\pi$
$977$	−1.62337e16	−0.583442	−0.291721	+	0.956503i	$0.594228\pi$
$978$	−2.57429e16	−0.920012
$979$	1.70848e16	0.607163
$980$	4.67834e15	0.165329
$981$	8.21594e15	0.288721
$982$	−1.47679e16	−0.516065
$983$	2.21897e16	0.771094	0.385547	−	0.922688i	$-0.374013\pi$
$983$	2.21897e16	0.771094	0.385547	+	0.922688i	$0.374013\pi$
$984$	−1.22615e15	−0.0423712
$985$	5.77211e15	0.198352
$986$	−2.24271e15	−0.0766390
$987$	5.46395e13	0.00185679
$988$	−1.18252e16	−0.399618
$989$	1.06954e16	0.359433
$990$	2.01869e15	0.0674648
$991$	2.43549e16	0.809435	0.404717	−	0.914442i	$-0.367370\pi$
$991$	2.43549e16	0.809435	0.404717	+	0.914442i	$0.367370\pi$
$992$	−3.88346e16	−1.28353
$993$	−2.60136e14	−0.00855026
$994$	4.60281e15	0.150452
$995$	2.15607e15	0.0700866
$996$	2.64750e16	0.855872
$997$	−2.23125e16	−0.717339	−0.358669	−	0.933465i	$-0.616769\pi$
$997$	−2.23125e16	−0.717339	−0.358669	+	0.933465i	$0.616769\pi$
$998$	2.66270e16	0.851343
$999$	9.92704e15	0.315653

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.b.1.6	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.b.1.6	✓	27	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)

\(f(q)\)	\(=\)	\(q-63.4822 q^{2} +243.000 q^{3} +1982.00 q^{4} -1374.17 q^{5} -15426.2 q^{6} -16112.8 q^{7} +4190.11 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-63.4822 q^{2} +243.000 q^{3} +1982.00 q^{4} -1374.17 q^{5} -15426.2 q^{6} -16112.8 q^{7} +4190.11 q^{8} +59049.0 q^{9} +87235.4 q^{10} +391891. q^{11} +481625. q^{12} -1.24240e6 q^{13} +1.02288e6 q^{14} -333923. q^{15} -4.32512e6 q^{16} +824345. q^{17} -3.74856e6 q^{18} +4.80225e6 q^{19} -2.72360e6 q^{20} -3.91541e6 q^{21} -2.48781e7 q^{22} +2.79540e7 q^{23} +1.01820e6 q^{24} -4.69398e7 q^{25} +7.88702e7 q^{26} +1.43489e7 q^{27} -3.19355e7 q^{28} +4.28560e7 q^{29} +2.11982e7 q^{30} -1.46002e8 q^{31} +2.65987e8 q^{32} +9.52295e7 q^{33} -5.23313e7 q^{34} +2.21418e7 q^{35} +1.17035e8 q^{36} +6.91833e8 q^{37} -3.04857e8 q^{38} -3.01903e8 q^{39} -5.75793e6 q^{40} -1.20424e9 q^{41} +2.48559e8 q^{42} +3.82608e8 q^{43} +7.76726e8 q^{44} -8.11434e7 q^{45} -1.77458e9 q^{46} -1.39550e7 q^{47} -1.05101e9 q^{48} -1.71770e9 q^{49} +2.97984e9 q^{50} +2.00316e8 q^{51} -2.46243e9 q^{52} -4.64080e9 q^{53} -9.10901e8 q^{54} -5.38525e8 q^{55} -6.75145e7 q^{56} +1.16695e9 q^{57} -2.72059e9 q^{58} -7.14924e8 q^{59} -6.61835e8 q^{60} -4.97725e9 q^{61} +9.26851e9 q^{62} -9.51446e8 q^{63} -8.02761e9 q^{64} +1.70727e9 q^{65} -6.04538e9 q^{66} +1.85064e10 q^{67} +1.63385e9 q^{68} +6.79282e9 q^{69} -1.40561e9 q^{70} +4.49987e9 q^{71} +2.47422e8 q^{72} +2.44140e10 q^{73} -4.39191e10 q^{74} -1.14064e10 q^{75} +9.51803e9 q^{76} -6.31447e9 q^{77} +1.91655e10 q^{78} -1.48608e10 q^{79} +5.94346e9 q^{80} +3.48678e9 q^{81} +7.64476e10 q^{82} +5.49701e10 q^{83} -7.76033e9 q^{84} -1.13279e9 q^{85} -2.42888e10 q^{86} +1.04140e10 q^{87} +1.64207e9 q^{88} +4.35958e10 q^{89} +5.15116e9 q^{90} +2.00185e10 q^{91} +5.54047e10 q^{92} -3.54784e10 q^{93} +8.85893e8 q^{94} -6.59911e9 q^{95} +6.46349e10 q^{96} +1.25330e11 q^{97} +1.09044e11 q^{98} +2.31408e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9}+O(q^{10}) \) 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9	\( 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9} - 383719 q^{10} - 1816556 q^{11} + 6352506 q^{12} - 3951804 q^{13} - 6207867 q^{14} - 4176684 q^{15} + 28295194 q^{16} - 17723275 q^{17} - 7558272 q^{18} - 19573013 q^{19} - 48468099 q^{20} - 30758697 q^{21} - 1729910 q^{22} - 88593797 q^{23} - 86458671 q^{24} + 345714963 q^{25} - 6676346 q^{26} + 387420489 q^{27} + 126954286 q^{28} - 276632427 q^{29} - 93243717 q^{30} - 357680917 q^{31} - 859842334 q^{32} - 441423108 q^{33} + 232730000 q^{34} - 510315139 q^{35} + 1543658958 q^{36} - 660238257 q^{37} - 2067286961 q^{38} - 960288372 q^{39} - 3388951110 q^{40} - 1671147569 q^{41} - 1508511681 q^{42} - 1883107790 q^{43} - 3895687630 q^{44} - 1014934212 q^{45} - 1720344243 q^{46} - 5818572501 q^{47} + 6875732142 q^{48} - 18858180 q^{49} - 21474519647 q^{50} - 4306755825 q^{51} - 42214560062 q^{52} - 11444513368 q^{53} - 1836660096 q^{54} - 24401486484 q^{55} - 50583585764 q^{56} - 4756242159 q^{57} - 45017395090 q^{58} - 19302956073 q^{59} - 11777748057 q^{60} + 408637955 q^{61} - 28543084070 q^{62} - 7474363371 q^{63} + 33067284293 q^{64} - 21656714730 q^{65} - 420368130 q^{66} - 49803132690 q^{67} - 16500749319 q^{68} - 21528292671 q^{69} - 45808890782 q^{70} - 34127492216 q^{71} - 21009457053 q^{72} - 55734362153 q^{73} - 40367816298 q^{74} + 84008736009 q^{75} - 14840406404 q^{76} - 99723443615 q^{77} - 1622352078 q^{78} - 76484916442 q^{79} + 93882788915 q^{80} + 94143178827 q^{81} + 52951239205 q^{82} - 140433865655 q^{83} + 30849891498 q^{84} + 34329063335 q^{85} + 175223869508 q^{86} - 67221679761 q^{87} + 268823645069 q^{88} - 1191878597 q^{89} - 22658223231 q^{90} + 201632581559 q^{91} - 206501888812 q^{92} - 86916462831 q^{93} + 319770144384 q^{94} - 81387074885 q^{95} - 208941687162 q^{96} - 144896178730 q^{97} + 135739195260 q^{98} - 107265815244 q^{99}+O(q^{100}) \) 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9 - 383719 * q^10 - 1816556 * q^11 + 6352506 * q^12 - 3951804 * q^13 - 6207867 * q^14 - 4176684 * q^15 + 28295194 * q^16 - 17723275 * q^17 - 7558272 * q^18 - 19573013 * q^19 - 48468099 * q^20 - 30758697 * q^21 - 1729910 * q^22 - 88593797 * q^23 - 86458671 * q^24 + 345714963 * q^25 - 6676346 * q^26 + 387420489 * q^27 + 126954286 * q^28 - 276632427 * q^29 - 93243717 * q^30 - 357680917 * q^31 - 859842334 * q^32 - 441423108 * q^33 + 232730000 * q^34 - 510315139 * q^35 + 1543658958 * q^36 - 660238257 * q^37 - 2067286961 * q^38 - 960288372 * q^39 - 3388951110 * q^40 - 1671147569 * q^41 - 1508511681 * q^42 - 1883107790 * q^43 - 3895687630 * q^44 - 1014934212 * q^45 - 1720344243 * q^46 - 5818572501 * q^47 + 6875732142 * q^48 - 18858180 * q^49 - 21474519647 * q^50 - 4306755825 * q^51 - 42214560062 * q^52 - 11444513368 * q^53 - 1836660096 * q^54 - 24401486484 * q^55 - 50583585764 * q^56 - 4756242159 * q^57 - 45017395090 * q^58 - 19302956073 * q^59 - 11777748057 * q^60 + 408637955 * q^61 - 28543084070 * q^62 - 7474363371 * q^63 + 33067284293 * q^64 - 21656714730 * q^65 - 420368130 * q^66 - 49803132690 * q^67 - 16500749319 * q^68 - 21528292671 * q^69 - 45808890782 * q^70 - 34127492216 * q^71 - 21009457053 * q^72 - 55734362153 * q^73 - 40367816298 * q^74 + 84008736009 * q^75 - 14840406404 * q^76 - 99723443615 * q^77 - 1622352078 * q^78 - 76484916442 * q^79 + 93882788915 * q^80 + 94143178827 * q^81 + 52951239205 * q^82 - 140433865655 * q^83 + 30849891498 * q^84 + 34329063335 * q^85 + 175223869508 * q^86 - 67221679761 * q^87 + 268823645069 * q^88 - 1191878597 * q^89 - 22658223231 * q^90 + 201632581559 * q^91 - 206501888812 * q^92 - 86916462831 * q^93 + 319770144384 * q^94 - 81387074885 * q^95 - 208941687162 * q^96 - 144896178730 * q^97 + 135739195260 * q^98 - 107265815244 * q^99

Introduction

L-functions

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