LMFDB - Embedded newform 177.14.a.a.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,14,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, 14, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 14 $
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:	$189.798744245$
Analytic rank:	$1$
Dimension:	$30$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
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)

$f(q)$	$=$	$q-28.5091 q^{2} +729.000 q^{3} -7379.23 q^{4} -13887.1 q^{5} -20783.1 q^{6} +351614. q^{7} +443921. q^{8} +531441. q^{9} +O(q^{10})$	\(q-28.5091 q^{2} +729.000 q^{3} -7379.23 q^{4} -13887.1 q^{5} -20783.1 q^{6} +351614. q^{7} +443921. q^{8} +531441. q^{9} +395908. q^{10} +8.63075e6 q^{11} -5.37946e6 q^{12} -2.28844e7 q^{13} -1.00242e7 q^{14} -1.01237e7 q^{15} +4.77949e7 q^{16} -1.05266e6 q^{17} -1.51509e7 q^{18} -3.21912e7 q^{19} +1.02476e8 q^{20} +2.56327e8 q^{21} -2.46055e8 q^{22} -5.53544e8 q^{23} +3.23619e8 q^{24} -1.02785e9 q^{25} +6.52412e8 q^{26} +3.87420e8 q^{27} -2.59464e9 q^{28} +2.88836e8 q^{29} +2.88617e8 q^{30} -8.59752e9 q^{31} -4.99919e9 q^{32} +6.29182e9 q^{33} +3.00105e7 q^{34} -4.88289e9 q^{35} -3.92163e9 q^{36} -1.31624e10 q^{37} +9.17741e8 q^{38} -1.66827e10 q^{39} -6.16477e9 q^{40} +3.93009e10 q^{41} -7.30763e9 q^{42} +7.30345e10 q^{43} -6.36883e10 q^{44} -7.38016e9 q^{45} +1.57810e10 q^{46} +7.35107e10 q^{47} +3.48425e10 q^{48} +2.67435e10 q^{49} +2.93031e10 q^{50} -7.67392e8 q^{51} +1.68869e11 q^{52} +1.27010e11 q^{53} -1.10450e10 q^{54} -1.19856e11 q^{55} +1.56089e11 q^{56} -2.34674e10 q^{57} -8.23445e9 q^{58} +4.21805e10 q^{59} +7.47050e10 q^{60} -2.72300e11 q^{61} +2.45107e11 q^{62} +1.86862e11 q^{63} -2.49014e11 q^{64} +3.17797e11 q^{65} -1.79374e11 q^{66} +1.83024e11 q^{67} +7.76785e9 q^{68} -4.03533e11 q^{69} +1.39207e11 q^{70} -3.93666e11 q^{71} +2.35918e11 q^{72} +1.61325e10 q^{73} +3.75249e11 q^{74} -7.49304e11 q^{75} +2.37546e11 q^{76} +3.03469e12 q^{77} +4.75609e11 q^{78} -1.21179e12 q^{79} -6.63732e11 q^{80} +2.82430e11 q^{81} -1.12043e12 q^{82} +2.98190e12 q^{83} -1.89149e12 q^{84} +1.46184e10 q^{85} -2.08215e12 q^{86} +2.10561e11 q^{87} +3.83137e12 q^{88} -4.57582e12 q^{89} +2.10402e11 q^{90} -8.04647e12 q^{91} +4.08473e12 q^{92} -6.26759e12 q^{93} -2.09572e12 q^{94} +4.47042e11 q^{95} -3.64441e12 q^{96} +7.94437e12 q^{97} -7.62432e11 q^{98} +4.58674e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 138 q^{2} + 21870 q^{3} + 114598 q^{4} - 137742 q^{5} - 100602 q^{6} - 879443 q^{7} - 872301 q^{8} + 15943230 q^{9}+O(q^{10}) $ 30 * q - 138 * q^2 + 21870 * q^3 + 114598 * q^4 - 137742 * q^5 - 100602 * q^6 - 879443 * q^7 - 872301 * q^8 + 15943230 * q^9	\( 30 q - 138 q^{2} + 21870 q^{3} + 114598 q^{4} - 137742 q^{5} - 100602 q^{6} - 879443 q^{7} - 872301 q^{8} + 15943230 q^{9} - 5352519 q^{10} - 13950782 q^{11} + 83541942 q^{12} - 17256988 q^{13} + 33780109 q^{14} - 100413918 q^{15} + 499996762 q^{16} - 317583695 q^{17} - 73338858 q^{18} - 863401469 q^{19} - 1841280623 q^{20} - 641113947 q^{21} - 2723764842 q^{22} - 3142075981 q^{23} - 635907429 q^{24} + 5435751692 q^{25} - 6441414040 q^{26} + 11622614670 q^{27} - 7538400046 q^{28} - 4604589283 q^{29} - 3901986351 q^{30} + 4308675373 q^{31} + 6094556360 q^{32} - 10170120078 q^{33} + 38097713432 q^{34} - 15447827315 q^{35} + 60902075718 q^{36} - 19633376949 q^{37} - 18152222923 q^{38} - 12580344252 q^{39} + 14680384170 q^{40} - 103644439493 q^{41} + 24625699461 q^{42} - 64494894924 q^{43} - 199714496208 q^{44} - 73201746222 q^{45} - 265425792847 q^{46} - 293365585139 q^{47} + 364497639498 q^{48} + 414396765797 q^{49} - 126058522207 q^{50} - 231518513655 q^{51} + 156029960316 q^{52} - 76747013118 q^{53} - 53464027482 q^{54} - 433465885754 q^{55} - 502955241518 q^{56} - 629419670901 q^{57} - 1755031845830 q^{58} + 1265416009230 q^{59} - 1342293574167 q^{60} - 2022612531219 q^{61} - 3816005187046 q^{62} - 467372067363 q^{63} - 3570205594131 q^{64} - 3889749040576 q^{65} - 1985624569818 q^{66} - 502618987776 q^{67} - 8953998390517 q^{68} - 2290573390149 q^{69} - 6805178272420 q^{70} - 1599540605456 q^{71} - 463576515741 q^{72} - 3826795087235 q^{73} - 7573387813210 q^{74} + 3962662983468 q^{75} - 19498723328388 q^{76} - 9088623115219 q^{77} - 4695790835160 q^{78} - 8595482172338 q^{79} - 17452527463963 q^{80} + 8472886094430 q^{81} - 11181116792901 q^{82} - 13548556984389 q^{83} - 5495493633534 q^{84} - 12851795888367 q^{85} + 8539949468848 q^{86} - 3356745587307 q^{87} - 25134826741387 q^{88} - 21826401667403 q^{89} - 2844548049879 q^{90} - 26577050621355 q^{91} - 34908210763168 q^{92} + 3141024346917 q^{93} - 26426808959500 q^{94} - 29105233533993 q^{95} + 4442931586440 q^{96} + 417815797414 q^{97} + 29159956938360 q^{98} - 7414017536862 q^{99}+O(q^{100}) \) 30 * q - 138 * q^2 + 21870 * q^3 + 114598 * q^4 - 137742 * q^5 - 100602 * q^6 - 879443 * q^7 - 872301 * q^8 + 15943230 * q^9 - 5352519 * q^10 - 13950782 * q^11 + 83541942 * q^12 - 17256988 * q^13 + 33780109 * q^14 - 100413918 * q^15 + 499996762 * q^16 - 317583695 * q^17 - 73338858 * q^18 - 863401469 * q^19 - 1841280623 * q^20 - 641113947 * q^21 - 2723764842 * q^22 - 3142075981 * q^23 - 635907429 * q^24 + 5435751692 * q^25 - 6441414040 * q^26 + 11622614670 * q^27 - 7538400046 * q^28 - 4604589283 * q^29 - 3901986351 * q^30 + 4308675373 * q^31 + 6094556360 * q^32 - 10170120078 * q^33 + 38097713432 * q^34 - 15447827315 * q^35 + 60902075718 * q^36 - 19633376949 * q^37 - 18152222923 * q^38 - 12580344252 * q^39 + 14680384170 * q^40 - 103644439493 * q^41 + 24625699461 * q^42 - 64494894924 * q^43 - 199714496208 * q^44 - 73201746222 * q^45 - 265425792847 * q^46 - 293365585139 * q^47 + 364497639498 * q^48 + 414396765797 * q^49 - 126058522207 * q^50 - 231518513655 * q^51 + 156029960316 * q^52 - 76747013118 * q^53 - 53464027482 * q^54 - 433465885754 * q^55 - 502955241518 * q^56 - 629419670901 * q^57 - 1755031845830 * q^58 + 1265416009230 * q^59 - 1342293574167 * q^60 - 2022612531219 * q^61 - 3816005187046 * q^62 - 467372067363 * q^63 - 3570205594131 * q^64 - 3889749040576 * q^65 - 1985624569818 * q^66 - 502618987776 * q^67 - 8953998390517 * q^68 - 2290573390149 * q^69 - 6805178272420 * q^70 - 1599540605456 * q^71 - 463576515741 * q^72 - 3826795087235 * q^73 - 7573387813210 * q^74 + 3962662983468 * q^75 - 19498723328388 * q^76 - 9088623115219 * q^77 - 4695790835160 * q^78 - 8595482172338 * q^79 - 17452527463963 * q^80 + 8472886094430 * q^81 - 11181116792901 * q^82 - 13548556984389 * q^83 - 5495493633534 * q^84 - 12851795888367 * q^85 + 8539949468848 * q^86 - 3356745587307 * q^87 - 25134826741387 * q^88 - 21826401667403 * q^89 - 2844548049879 * q^90 - 26577050621355 * q^91 - 34908210763168 * q^92 + 3141024346917 * q^93 - 26426808959500 * q^94 - 29105233533993 * q^95 + 4442931586440 * q^96 + 417815797414 * q^97 + 29159956938360 * q^98 - 7414017536862 * 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 $

$2$	−28.5091	−0.314984	−0.157492	−	0.987520i	$-0.550341\pi$
$2$	−28.5091	−0.314984	−0.157492	+	0.987520i	$0.550341\pi$
$3$	729.000	0.577350
$3$	729.000	0.577350
$4$	−7379.23	−0.900785
$5$	−13887.1	−0.397471	−0.198736	−	0.980053i	$-0.563684\pi$
$5$	−13887.1	−0.397471	−0.198736	+	0.980053i	$0.563684\pi$
$6$	−20783.1	−0.181856
$7$	351614.	1.12961	0.564806	−	0.825224i	$-0.308951\pi$
$7$	351614.	1.12961	0.564806	+	0.825224i	$0.308951\pi$
$8$	443921.	0.598716
$9$	531441.	0.333333
$10$	395908.	0.125197
$11$	8.63075e6	1.46891	0.734457	−	0.678656i	$-0.237437\pi$
$11$	8.63075e6	1.46891	0.734457	+	0.678656i	$0.237437\pi$
$12$	−5.37946e6	−0.520069
$13$	−2.28844e7	−1.31494	−0.657472	−	0.753479i	$-0.728374\pi$
$13$	−2.28844e7	−1.31494	−0.657472	+	0.753479i	$0.728374\pi$
$14$	−1.00242e7	−0.355809
$15$	−1.01237e7	−0.229480
$16$	4.77949e7	0.712199
$17$	−1.05266e6	−0.0105772	−0.00528861	−	0.999986i	$-0.501683\pi$
$17$	−1.05266e6	−0.0105772	−0.00528861	+	0.999986i	$0.501683\pi$
$18$	−1.51509e7	−0.104995
$19$	−3.21912e7	−0.156978	−0.0784890	−	0.996915i	$-0.525010\pi$
$19$	−3.21912e7	−0.156978	−0.0784890	+	0.996915i	$0.525010\pi$
$20$	1.02476e8	0.358036
$21$	2.56327e8	0.652181
$22$	−2.46055e8	−0.462684
$23$	−5.53544e8	−0.779688	−0.389844	−	0.920881i	$-0.627471\pi$
$23$	−5.53544e8	−0.779688	−0.389844	+	0.920881i	$0.627471\pi$
$24$	3.23619e8	0.345669
$25$	−1.02785e9	−0.842016
$26$	6.52412e8	0.414186
$27$	3.87420e8	0.192450
$28$	−2.59464e9	−1.01754
$29$	2.88836e8	0.0901705	0.0450852	−	0.998983i	$-0.485644\pi$
$29$	2.88836e8	0.0901705	0.0450852	+	0.998983i	$0.485644\pi$
$30$	2.88617e8	0.0722825
$31$	−8.59752e9	−1.73989	−0.869946	−	0.493148i	$-0.835846\pi$
$31$	−8.59752e9	−1.73989	−0.869946	+	0.493148i	$0.835846\pi$
$32$	−4.99919e9	−0.823047
$33$	6.29182e9	0.848077
$34$	3.00105e7	0.00333165
$35$	−4.88289e9	−0.448988
$36$	−3.92163e9	−0.300262
$37$	−1.31624e10	−0.843384	−0.421692	−	0.906739i	$-0.638564\pi$
$37$	−1.31624e10	−0.843384	−0.421692	+	0.906739i	$0.638564\pi$
$38$	9.17741e8	0.0494455
$39$	−1.66827e10	−0.759184
$40$	−6.16477e9	−0.237973
$41$	3.93009e10	1.29213	0.646066	−	0.763281i	$-0.276413\pi$
$41$	3.93009e10	1.29213	0.646066	+	0.763281i	$0.276413\pi$
$42$	−7.30763e9	−0.205426
$43$	7.30345e10	1.76191	0.880954	−	0.473202i	$-0.156902\pi$
$43$	7.30345e10	1.76191	0.880954	+	0.473202i	$0.156902\pi$
$44$	−6.36883e10	−1.32318
$45$	−7.38016e9	−0.132490
$46$	1.57810e10	0.245589
$47$	7.35107e10	0.994751	0.497375	−	0.867535i	$-0.334297\pi$
$47$	7.35107e10	0.994751	0.497375	+	0.867535i	$0.334297\pi$
$48$	3.48425e10	0.411189
$49$	2.67435e10	0.276022
$50$	2.93031e10	0.265221
$51$	−7.67392e8	−0.00610676
$52$	1.68869e11	1.18448
$53$	1.27010e11	0.787127	0.393564	−	0.919297i	$-0.371242\pi$
$53$	1.27010e11	0.787127	0.393564	+	0.919297i	$0.371242\pi$
$54$	−1.10450e10	−0.0606186
$55$	−1.19856e11	−0.583851
$56$	1.56089e11	0.676317
$57$	−2.34674e10	−0.0906313
$58$	−8.23445e9	−0.0284022
$59$	4.21805e10	0.130189
$59$	4.21805e10	0.130189
$60$	7.47050e10	0.206712
$61$	−2.72300e11	−0.676711	−0.338356	−	0.941018i	$-0.609871\pi$
$61$	−2.72300e11	−0.676711	−0.338356	+	0.941018i	$0.609871\pi$
$62$	2.45107e11	0.548037
$63$	1.86862e11	0.376537
$64$	−2.49014e11	−0.452953
$65$	3.17797e11	0.522653
$66$	−1.79374e11	−0.267131
$67$	1.83024e11	0.247185	0.123593	−	0.992333i	$-0.460558\pi$
$67$	1.83024e11	0.247185	0.123593	+	0.992333i	$0.460558\pi$
$68$	7.76785e9	0.00952781
$69$	−4.03533e11	−0.450153
$70$	1.39207e11	0.141424
$71$	−3.93666e11	−0.364711	−0.182355	−	0.983233i	$-0.558372\pi$
$71$	−3.93666e11	−0.364711	−0.182355	+	0.983233i	$0.558372\pi$
$72$	2.35918e11	0.199572
$73$	1.61325e10	0.0124768	0.00623839	−	0.999981i	$-0.498014\pi$
$73$	1.61325e10	0.0124768	0.00623839	+	0.999981i	$0.498014\pi$
$74$	3.75249e11	0.265652
$75$	−7.49304e11	−0.486138
$76$	2.37546e11	0.141404
$77$	3.03469e12	1.65930
$78$	4.75609e11	0.239130
$79$	−1.21179e12	−0.560855	−0.280428	−	0.959875i	$-0.590476\pi$
$79$	−1.21179e12	−0.560855	−0.280428	+	0.959875i	$0.590476\pi$
$80$	−6.63732e11	−0.283079
$81$	2.82430e11	0.111111
$82$	−1.12043e12	−0.407001
$83$	2.98190e12	1.00112	0.500560	−	0.865702i	$-0.333128\pi$
$83$	2.98190e12	1.00112	0.500560	+	0.865702i	$0.333128\pi$
$84$	−1.89149e12	−0.587475
$85$	1.46184e10	0.00420414
$86$	−2.08215e12	−0.554972
$87$	2.10561e11	0.0520600
$88$	3.83137e12	0.879462
$89$	−4.57582e12	−0.975965	−0.487982	−	0.872853i	$-0.662267\pi$
$89$	−4.57582e12	−0.975965	−0.487982	+	0.872853i	$0.662267\pi$
$90$	2.10402e11	0.0417323
$91$	−8.04647e12	−1.48538
$92$	4.08473e12	0.702332
$93$	−6.26759e12	−1.00453
$94$	−2.09572e12	−0.313330
$95$	4.47042e11	0.0623943
$96$	−3.64441e12	−0.475187
$97$	7.94437e12	0.968374	0.484187	−	0.874965i	$-0.339115\pi$
$97$	7.94437e12	0.968374	0.484187	+	0.874965i	$0.339115\pi$
$98$	−7.62432e11	−0.0869424
$99$	4.58674e12	0.489638
$100$	7.58476e12	0.758476
$101$	−1.54993e13	−1.45285	−0.726427	−	0.687243i	$-0.758821\pi$
$101$	−1.54993e13	−1.45285	−0.726427	+	0.687243i	$0.758821\pi$
$102$	2.18776e10	0.00192353
$103$	−8.48603e12	−0.700265	−0.350133	−	0.936700i	$-0.613864\pi$
$103$	−8.48603e12	−0.700265	−0.350133	+	0.936700i	$0.613864\pi$
$104$	−1.01589e13	−0.787279
$105$	−3.55963e12	−0.259223
$106$	−3.62094e12	−0.247932
$107$	−1.86668e13	−1.20248	−0.601238	−	0.799070i	$-0.705326\pi$
$107$	−1.86668e13	−1.20248	−0.601238	+	0.799070i	$0.705326\pi$
$108$	−2.85887e12	−0.173356
$109$	−1.05822e13	−0.604371	−0.302186	−	0.953249i	$-0.597716\pi$
$109$	−1.05822e13	−0.604371	−0.302186	+	0.953249i	$0.597716\pi$
$110$	3.41698e12	0.183904
$111$	−9.59542e12	−0.486928
$112$	1.68054e13	0.804509
$113$	1.22087e13	0.551645	0.275823	−	0.961209i	$-0.411050\pi$
$113$	1.22087e13	0.551645	0.275823	+	0.961209i	$0.411050\pi$
$114$	6.69033e11	0.0285474
$115$	7.68711e12	0.309904
$116$	−2.13139e12	−0.0812242
$117$	−1.21617e13	−0.438315
$118$	−1.20253e12	−0.0410074
$119$	−3.70132e11	−0.0119482
$120$	−4.49412e12	−0.137394
$121$	3.99672e13	1.15771
$122$	7.76301e12	0.213153
$123$	2.86503e13	0.746013
$124$	6.34431e13	1.56727
$125$	3.12259e13	0.732149
$126$	−5.32727e12	−0.118603
$127$	1.91808e13	0.405641	0.202821	−	0.979216i	$-0.434989\pi$
$127$	1.91808e13	0.405641	0.202821	+	0.979216i	$0.434989\pi$
$128$	4.80525e13	0.965720
$129$	5.32422e13	1.01724
$130$	−9.06010e12	−0.164627
$131$	−6.83174e13	−1.18105	−0.590525	−	0.807020i	$-0.701079\pi$
$131$	−6.83174e13	−1.18105	−0.590525	+	0.807020i	$0.701079\pi$
$132$	−4.64288e13	−0.763936
$133$	−1.13189e13	−0.177324
$134$	−5.21785e12	−0.0778592
$135$	−5.38014e12	−0.0764934
$136$	−4.67300e11	−0.00633276
$137$	−6.79224e13	−0.877666	−0.438833	−	0.898569i	$-0.644608\pi$
$137$	−6.79224e13	−0.877666	−0.438833	+	0.898569i	$0.644608\pi$
$138$	1.15044e13	0.141791
$139$	−4.06817e13	−0.478413	−0.239207	−	0.970969i	$-0.576887\pi$
$139$	−4.06817e13	−0.478413	−0.239207	+	0.970969i	$0.576887\pi$
$140$	3.60320e13	0.404442
$141$	5.35893e13	0.574320
$142$	1.12230e13	0.114878
$143$	−1.97509e14	−1.93154
$144$	2.54002e13	0.237400
$145$	−4.01109e12	−0.0358402
$146$	−4.59922e11	−0.00392998
$147$	1.94960e13	0.159361
$148$	9.71287e13	0.759708
$149$	7.21391e13	0.540082	0.270041	−	0.962849i	$-0.412963\pi$
$149$	7.21391e13	0.540082	0.270041	+	0.962849i	$0.412963\pi$
$150$	2.13620e13	0.153126
$151$	−2.69194e14	−1.84806	−0.924029	−	0.382322i	$-0.875125\pi$
$151$	−2.69194e14	−1.84806	−0.924029	+	0.382322i	$0.875125\pi$
$152$	−1.42904e13	−0.0939853
$153$	−5.59429e11	−0.00352574
$154$	−8.65163e13	−0.522653
$155$	1.19394e14	0.691557
$156$	1.23106e14	0.683861
$157$	1.62695e13	0.0867015	0.0433508	−	0.999060i	$-0.486197\pi$
$157$	1.62695e13	0.0867015	0.0433508	+	0.999060i	$0.486197\pi$
$158$	3.45470e13	0.176660
$159$	9.25903e13	0.454448
$160$	6.94242e13	0.327138
$161$	−1.94634e14	−0.880745
$162$	−8.05180e12	−0.0349982
$163$	1.38855e14	0.579886	0.289943	−	0.957044i	$-0.406364\pi$
$163$	1.38855e14	0.579886	0.289943	+	0.957044i	$0.406364\pi$
$164$	−2.90010e14	−1.16393
$165$	−8.73750e13	−0.337087
$166$	−8.50112e13	−0.315336
$167$	5.31168e14	1.89485	0.947425	−	0.319977i	$-0.103675\pi$
$167$	5.31168e14	1.89485	0.947425	+	0.319977i	$0.103675\pi$
$168$	1.13789e14	0.390472
$169$	2.20820e14	0.729079
$170$	−4.16758e11	−0.00132424
$171$	−1.71077e13	−0.0523260
$172$	−5.38939e14	−1.58710
$173$	6.72325e14	1.90669	0.953344	−	0.301886i	$-0.0976163\pi$
$173$	6.72325e14	1.90669	0.953344	+	0.301886i	$0.0976163\pi$
$174$	−6.00291e12	−0.0163980
$175$	−3.61407e14	−0.951151
$176$	4.12506e14	1.04616
$177$	3.07496e13	0.0751646
$178$	1.30452e14	0.307413
$179$	2.07313e14	0.471065	0.235533	−	0.971866i	$-0.424317\pi$
$179$	2.07313e14	0.471065	0.235533	+	0.971866i	$0.424317\pi$
$180$	5.44599e13	0.119345
$181$	−4.27304e14	−0.903287	−0.451644	−	0.892198i	$-0.649162\pi$
$181$	−4.27304e14	−0.903287	−0.451644	+	0.892198i	$0.649162\pi$
$182$	2.29397e14	0.467869
$183$	−1.98506e14	−0.390699
$184$	−2.45730e14	−0.466812
$185$	1.82788e14	0.335221
$186$	1.78683e14	0.316409
$187$	−9.08528e12	−0.0155370
$188$	−5.42452e14	−0.896057
$189$	1.36223e14	0.217394
$190$	−1.27447e13	−0.0196532
$191$	−9.23322e14	−1.37606	−0.688028	−	0.725684i	$-0.741523\pi$
$191$	−9.23322e14	−1.37606	−0.688028	+	0.725684i	$0.741523\pi$
$192$	−1.81531e14	−0.261513
$193$	−3.94874e14	−0.549966	−0.274983	−	0.961449i	$-0.588672\pi$
$193$	−3.94874e14	−0.549966	−0.274983	+	0.961449i	$0.588672\pi$
$194$	−2.26486e14	−0.305022
$195$	2.31674e14	0.301754
$196$	−1.97346e14	−0.248636
$197$	−1.08265e15	−1.31964	−0.659821	−	0.751423i	$-0.729368\pi$
$197$	−1.08265e15	−1.31964	−0.659821	+	0.751423i	$0.729368\pi$
$198$	−1.30764e14	−0.154228
$199$	3.77522e14	0.430920	0.215460	−	0.976513i	$-0.430875\pi$
$199$	3.77522e14	0.430920	0.215460	+	0.976513i	$0.430875\pi$
$200$	−4.56285e14	−0.504129
$201$	1.33425e14	0.142712
$202$	4.41870e14	0.457625
$203$	1.01559e14	0.101858
$204$	5.66276e12	0.00550088
$205$	−5.45774e14	−0.513586
$206$	2.41929e14	0.220572
$207$	−2.94176e14	−0.259896
$208$	−1.09376e15	−0.936503
$209$	−2.77834e14	−0.230587
$210$	1.01482e14	0.0816512
$211$	−3.40644e14	−0.265745	−0.132872	−	0.991133i	$-0.542420\pi$
$211$	−3.40644e14	−0.265745	−0.132872	+	0.991133i	$0.542420\pi$
$212$	−9.37237e14	−0.709033
$213$	−2.86982e14	−0.210566
$214$	5.32174e14	0.378760
$215$	−1.01424e15	−0.700308
$216$	1.71984e14	0.115223
$217$	−3.02301e15	−1.96540
$218$	3.01689e14	0.190367
$219$	1.17606e13	0.00720347
$220$	8.84445e14	0.525924
$221$	2.40896e13	0.0139085
$222$	2.73556e14	0.153374
$223$	−2.17805e15	−1.18601	−0.593003	−	0.805200i	$-0.702058\pi$
$223$	−2.17805e15	−1.18601	−0.593003	+	0.805200i	$0.702058\pi$
$224$	−1.75779e15	−0.929724
$225$	−5.46243e14	−0.280672
$226$	−3.48059e14	−0.173759
$227$	−2.22259e15	−1.07818	−0.539089	−	0.842249i	$-0.681232\pi$
$227$	−2.22259e15	−1.07818	−0.539089	+	0.842249i	$0.681232\pi$
$228$	1.73171e14	0.0816394
$229$	−3.60209e15	−1.65053	−0.825267	−	0.564743i	$-0.808975\pi$
$229$	−3.60209e15	−1.65053	−0.825267	+	0.564743i	$0.808975\pi$
$230$	−2.19152e14	−0.0976147
$231$	2.21229e15	0.957998
$232$	1.28220e14	0.0539865
$233$	1.70998e15	0.700130	0.350065	−	0.936725i	$-0.386159\pi$
$233$	1.70998e15	0.700130	0.350065	+	0.936725i	$0.386159\pi$
$234$	3.46719e14	0.138062
$235$	−1.02085e15	−0.395385
$236$	−3.11260e14	−0.117272
$237$	−8.83394e14	−0.323810
$238$	1.05521e13	0.00376347
$239$	8.90085e14	0.308919	0.154460	−	0.987999i	$-0.450636\pi$
$239$	8.90085e14	0.308919	0.154460	+	0.987999i	$0.450636\pi$
$240$	−4.83860e14	−0.163436
$241$	−3.26021e15	−1.07185	−0.535926	−	0.844265i	$-0.680037\pi$
$241$	−3.26021e15	−1.07185	−0.535926	+	0.844265i	$0.680037\pi$
$242$	−1.13943e15	−0.364659
$243$	2.05891e14	0.0641500
$244$	2.00936e15	0.609571
$245$	−3.71389e14	−0.109711
$246$	−8.16794e14	−0.234982
$247$	7.36676e14	0.206417
$248$	−3.81662e15	−1.04170
$249$	2.17381e15	0.577996
$250$	−8.90220e14	−0.230615
$251$	2.75607e15	0.695683	0.347842	−	0.937553i	$-0.386915\pi$
$251$	2.75607e15	0.695683	0.347842	+	0.937553i	$0.386915\pi$
$252$	−1.37890e15	−0.339179
$253$	−4.77750e15	−1.14529
$254$	−5.46826e14	−0.127770
$255$	1.06568e13	0.00242726
$256$	6.69987e14	0.148767
$257$	3.87564e15	0.839031	0.419516	−	0.907748i	$-0.362200\pi$
$257$	3.87564e15	0.839031	0.419516	+	0.907748i	$0.362200\pi$
$258$	−1.51788e15	−0.320413
$259$	−4.62810e15	−0.952696
$260$	−2.34510e15	−0.470798
$261$	1.53499e14	0.0300568
$262$	1.94767e15	0.372011
$263$	−3.36264e15	−0.626568	−0.313284	−	0.949659i	$-0.601429\pi$
$263$	−3.36264e15	−0.626568	−0.313284	+	0.949659i	$0.601429\pi$
$264$	2.79307e15	0.507758
$265$	−1.76380e15	−0.312861
$266$	3.22691e14	0.0558542
$267$	−3.33577e15	−0.563474
$268$	−1.35058e15	−0.222661
$269$	−3.02785e15	−0.487241	−0.243621	−	0.969871i	$-0.578335\pi$
$269$	−3.02785e15	−0.487241	−0.243621	+	0.969871i	$0.578335\pi$
$270$	1.53383e14	0.0240942
$271$	1.12641e16	1.72741	0.863707	−	0.503994i	$-0.168137\pi$
$271$	1.12641e16	1.72741	0.863707	+	0.503994i	$0.168137\pi$
$272$	−5.03120e13	−0.00753309
$273$	−5.86588e15	−0.857582
$274$	1.93640e15	0.276450
$275$	−8.87114e15	−1.23685
$276$	2.97777e15	0.405492
$277$	−9.99312e15	−1.32918	−0.664588	−	0.747210i	$-0.731393\pi$
$277$	−9.99312e15	−1.32918	−0.664588	+	0.747210i	$0.731393\pi$
$278$	1.15980e15	0.150692
$279$	−4.56907e15	−0.579964
$280$	−2.16762e15	−0.268817
$281$	2.44336e15	0.296071	0.148036	−	0.988982i	$-0.452705\pi$
$281$	2.44336e15	0.296071	0.148036	+	0.988982i	$0.452705\pi$
$282$	−1.52778e15	−0.180901
$283$	5.35686e15	0.619866	0.309933	−	0.950758i	$-0.399693\pi$
$283$	5.35686e15	0.619866	0.309933	+	0.950758i	$0.399693\pi$
$284$	2.90495e15	0.328526
$285$	3.25894e14	0.0360234
$286$	5.63081e15	0.608403
$287$	1.38187e16	1.45961
$288$	−2.65678e15	−0.274349
$289$	−9.90347e15	−0.999888
$290$	1.14352e14	0.0112891
$291$	5.79144e15	0.559091
$292$	−1.19045e14	−0.0112389
$293$	−4.38241e15	−0.404644	−0.202322	−	0.979319i	$-0.564849\pi$
$293$	−4.38241e15	−0.404644	−0.202322	+	0.979319i	$0.564849\pi$
$294$	−5.55813e14	−0.0501962
$295$	−5.85764e14	−0.0517464
$296$	−5.84309e15	−0.504948
$297$	3.34373e15	0.282692
$298$	−2.05662e15	−0.170117
$299$	1.26675e16	1.02525
$300$	5.52929e15	0.437906
$301$	2.56800e16	1.99027
$302$	7.67448e15	0.582108
$303$	−1.12990e16	−0.838806
$304$	−1.53858e15	−0.111800
$305$	3.78145e15	0.268973
$306$	1.59488e13	0.00111055
$307$	1.56810e16	1.06899	0.534496	−	0.845171i	$-0.320501\pi$
$307$	1.56810e16	1.06899	0.534496	+	0.845171i	$0.320501\pi$
$308$	−2.23937e16	−1.49467
$309$	−6.18632e15	−0.404298
$310$	−3.40382e15	−0.217829
$311$	−2.23004e16	−1.39756	−0.698780	−	0.715336i	$-0.746273\pi$
$311$	−2.23004e16	−1.39756	−0.698780	+	0.715336i	$0.746273\pi$
$312$	−7.40581e15	−0.454536
$313$	−1.44804e16	−0.870446	−0.435223	−	0.900323i	$-0.643331\pi$
$313$	−1.44804e16	−0.870446	−0.435223	+	0.900323i	$0.643331\pi$
$314$	−4.63829e14	−0.0273096
$315$	−2.59497e15	−0.149663
$316$	8.94207e15	0.505210
$317$	−3.38376e16	−1.87290	−0.936450	−	0.350802i	$-0.885909\pi$
$317$	−3.38376e16	−1.87290	−0.936450	+	0.350802i	$0.885909\pi$
$318$	−2.63966e15	−0.143144
$319$	2.49287e15	0.132453
$320$	3.45807e15	0.180036
$321$	−1.36081e16	−0.694249
$322$	5.54883e15	0.277420
$323$	3.38865e13	0.00166039
$324$	−2.08411e15	−0.100087
$325$	2.35218e16	1.10720
$326$	−3.95863e15	−0.182655
$327$	−7.71442e15	−0.348934
$328$	1.74465e16	0.773621
$329$	2.58474e16	1.12368
$330$	2.49098e15	0.106177
$331$	−3.60933e16	−1.50850	−0.754249	−	0.656589i	$-0.771999\pi$
$331$	−3.60933e16	−1.50850	−0.754249	+	0.656589i	$0.771999\pi$
$332$	−2.20041e16	−0.901793
$333$	−6.99506e15	−0.281128
$334$	−1.51431e16	−0.596847
$335$	−2.54167e15	−0.0982490
$336$	1.22511e16	0.464483
$337$	3.87035e16	1.43931	0.719657	−	0.694330i	$-0.244299\pi$
$337$	3.87035e16	1.43931	0.719657	+	0.694330i	$0.244299\pi$
$338$	−6.29537e15	−0.229648
$339$	8.90015e15	0.318492
$340$	−1.07873e14	−0.00378703
$341$	−7.42030e16	−2.55575
$342$	4.87725e14	0.0164818
$343$	−2.46642e16	−0.817814
$344$	3.24216e16	1.05488
$345$	5.60390e15	0.178923
$346$	−1.91674e16	−0.600575
$347$	−1.73062e16	−0.532181	−0.266091	−	0.963948i	$-0.585732\pi$
$347$	−1.73062e16	−0.532181	−0.266091	+	0.963948i	$0.585732\pi$
$348$	−1.55378e15	−0.0468948
$349$	−1.01041e16	−0.299319	−0.149659	−	0.988738i	$-0.547818\pi$
$349$	−1.01041e16	−0.299319	−0.149659	+	0.988738i	$0.547818\pi$
$350$	1.03034e16	0.299597
$351$	−8.86588e15	−0.253061
$352$	−4.31468e16	−1.20899
$353$	−2.85177e16	−0.784475	−0.392237	−	0.919864i	$-0.628299\pi$
$353$	−2.85177e16	−0.784475	−0.392237	+	0.919864i	$0.628299\pi$
$354$	−8.76643e14	−0.0236756
$355$	5.46687e15	0.144962
$356$	3.37661e16	0.879135
$357$	−2.69826e14	−0.00689827
$358$	−5.91029e15	−0.148378
$359$	−7.41117e15	−0.182714	−0.0913572	−	0.995818i	$-0.529121\pi$
$359$	−7.41117e15	−0.182714	−0.0913572	+	0.995818i	$0.529121\pi$
$360$	−3.27621e15	−0.0793242
$361$	−4.10167e16	−0.975358
$362$	1.21820e16	0.284521
$363$	2.91361e16	0.668402
$364$	5.93768e16	1.33801
$365$	−2.24033e14	−0.00495916
$366$	5.65923e15	0.123064
$367$	6.15779e16	1.31551	0.657757	−	0.753230i	$-0.271505\pi$
$367$	6.15779e16	1.31551	0.657757	+	0.753230i	$0.271505\pi$
$368$	−2.64566e16	−0.555294
$369$	2.08861e16	0.430711
$370$	−5.21111e15	−0.105589
$371$	4.46585e16	0.889148
$372$	4.62500e16	0.904863
$373$	−7.92109e16	−1.52292	−0.761461	−	0.648211i	$-0.775517\pi$
$373$	−7.92109e16	−1.52292	−0.761461	+	0.648211i	$0.775517\pi$
$374$	2.59013e14	0.00489391
$375$	2.27637e16	0.422706
$376$	3.26330e16	0.595573
$377$	−6.60983e15	−0.118569
$378$	−3.88358e15	−0.0684755
$379$	1.00585e17	1.74332	0.871662	−	0.490108i	$-0.163043\pi$
$379$	1.00585e17	1.74332	0.871662	+	0.490108i	$0.163043\pi$
$380$	−3.29883e15	−0.0562039
$381$	1.39828e16	0.234197
$382$	2.63230e16	0.433435
$383$	−5.05935e16	−0.819035	−0.409518	−	0.912302i	$-0.634303\pi$
$383$	−5.05935e16	−0.819035	−0.409518	+	0.912302i	$0.634303\pi$
$384$	3.50303e16	0.557559
$385$	−4.21430e16	−0.659525
$386$	1.12575e16	0.173230
$387$	3.88135e16	0.587303
$388$	−5.86233e16	−0.872297
$389$	−7.82463e16	−1.14496	−0.572482	−	0.819918i	$-0.694019\pi$
$389$	−7.82463e16	−1.14496	−0.572482	+	0.819918i	$0.694019\pi$
$390$	−6.60481e15	−0.0950475
$391$	5.82696e14	0.00824694
$392$	1.18720e16	0.165259
$393$	−4.98034e16	−0.681879
$394$	3.08652e16	0.415666
$395$	1.68282e16	0.222924
$396$	−3.38466e16	−0.441059
$397$	1.93045e16	0.247468	0.123734	−	0.992315i	$-0.460513\pi$
$397$	1.93045e16	0.247468	0.123734	+	0.992315i	$0.460513\pi$
$398$	−1.07628e16	−0.135733
$399$	−8.25147e15	−0.102378
$400$	−4.91261e16	−0.599684
$401$	−7.95006e16	−0.954843	−0.477421	−	0.878675i	$-0.658428\pi$
$401$	−7.95006e16	−0.954843	−0.477421	+	0.878675i	$0.658428\pi$
$402$	−3.80381e15	−0.0449520
$403$	1.96749e17	2.28786
$404$	1.14373e17	1.30871
$405$	−3.92212e15	−0.0441635
$406$	−2.89535e15	−0.0320835
$407$	−1.13602e17	−1.23886
$408$	−3.40662e14	−0.00365622
$409$	2.84293e16	0.300307	0.150153	−	0.988663i	$-0.452023\pi$
$409$	2.84293e16	0.300307	0.150153	+	0.988663i	$0.452023\pi$
$410$	1.55595e16	0.161771
$411$	−4.95154e16	−0.506721
$412$	6.26204e16	0.630789
$413$	1.48313e16	0.147063
$414$	8.38668e15	0.0818630
$415$	−4.14099e16	−0.397916
$416$	1.14403e17	1.08226
$417$	−2.96570e16	−0.276212
$418$	7.92080e15	0.0726312
$419$	1.64125e17	1.48178	0.740890	−	0.671626i	$-0.234404\pi$
$419$	1.64125e17	1.48178	0.740890	+	0.671626i	$0.234404\pi$
$420$	2.62673e16	0.233505
$421$	−9.53757e16	−0.834842	−0.417421	−	0.908713i	$-0.637066\pi$
$421$	−9.53757e16	−0.834842	−0.417421	+	0.908713i	$0.637066\pi$
$422$	9.71144e15	0.0837053
$423$	3.90666e16	0.331584
$424$	5.63825e16	0.471266
$425$	1.08198e15	0.00890620
$426$	8.18160e15	0.0663248
$427$	−9.57444e16	−0.764420
$428$	1.37747e17	1.08317
$429$	−1.43984e17	−1.11517
$430$	2.89149e16	0.220586
$431$	−1.02116e17	−0.767343	−0.383672	−	0.923470i	$-0.625341\pi$
$431$	−1.02116e17	−0.767343	−0.383672	+	0.923470i	$0.625341\pi$
$432$	1.85167e16	0.137063
$433$	−1.80916e17	−1.31919	−0.659594	−	0.751622i	$-0.729272\pi$
$433$	−1.80916e17	−1.31919	−0.659594	+	0.751622i	$0.729272\pi$
$434$	8.61831e16	0.619069
$435$	−2.92408e15	−0.0206923
$436$	7.80885e16	0.544409
$437$	1.78192e16	0.122394
$438$	−3.35283e14	−0.00226898
$439$	1.37200e17	0.914817	0.457409	−	0.889257i	$-0.348778\pi$
$439$	1.37200e17	0.914817	0.457409	+	0.889257i	$0.348778\pi$
$440$	−5.32066e16	−0.349561
$441$	1.42126e16	0.0920073
$442$	−6.86771e14	−0.00438094
$443$	−1.81802e16	−0.114281	−0.0571404	−	0.998366i	$-0.518198\pi$
$443$	−1.81802e16	−0.114281	−0.0571404	+	0.998366i	$0.518198\pi$
$444$	7.08068e16	0.438617
$445$	6.35448e16	0.387918
$446$	6.20943e16	0.373573
$447$	5.25894e16	0.311817
$448$	−8.75567e16	−0.511661
$449$	−3.30969e16	−0.190628	−0.0953139	−	0.995447i	$-0.530385\pi$
$449$	−3.30969e16	−0.190628	−0.0953139	+	0.995447i	$0.530385\pi$
$450$	1.55729e16	0.0884071
$451$	3.39196e17	1.89803
$452$	−9.00909e16	−0.496914
$453$	−1.96243e17	−1.06698
$454$	6.33639e16	0.339609
$455$	1.11742e17	0.590395
$456$	−1.04177e16	−0.0542624
$457$	3.29643e17	1.69273	0.846366	−	0.532602i	$-0.178786\pi$
$457$	3.29643e17	1.69273	0.846366	+	0.532602i	$0.178786\pi$
$458$	1.02692e17	0.519891
$459$	−4.07824e14	−0.00203559
$460$	−5.67250e16	−0.279157
$461$	−1.54107e17	−0.747765	−0.373882	−	0.927476i	$-0.621974\pi$
$461$	−1.54107e17	−0.747765	−0.373882	+	0.927476i	$0.621974\pi$
$462$	−6.30704e16	−0.301754
$463$	2.39877e17	1.13165	0.565826	−	0.824525i	$-0.308557\pi$
$463$	2.39877e17	1.13165	0.565826	+	0.824525i	$0.308557\pi$
$464$	1.38049e16	0.0642194
$465$	8.70385e16	0.399271
$466$	−4.87501e16	−0.220530
$467$	−2.00169e17	−0.892971	−0.446485	−	0.894791i	$-0.647324\pi$
$467$	−2.00169e17	−0.892971	−0.446485	+	0.894791i	$0.647324\pi$
$468$	8.97440e16	0.394828
$469$	6.43539e16	0.279223
$470$	2.91034e16	0.124540
$471$	1.18605e16	0.0500572
$472$	1.87248e16	0.0779462
$473$	6.30343e17	2.58809
$474$	2.51847e16	0.101995
$475$	3.30878e16	0.132178
$476$	2.73129e15	0.0107627
$477$	6.74984e16	0.262376
$478$	−2.53755e16	−0.0973045
$479$	2.23924e17	0.847071	0.423536	−	0.905879i	$-0.360789\pi$
$479$	2.23924e17	0.847071	0.423536	+	0.905879i	$0.360789\pi$
$480$	5.06102e16	0.188873
$481$	3.01214e17	1.10900
$482$	9.29456e16	0.337616
$483$	−1.41888e17	−0.508498
$484$	−2.94927e17	−1.04284
$485$	−1.10324e17	−0.384901
$486$	−5.86976e15	−0.0202062
$487$	6.07459e16	0.206338	0.103169	−	0.994664i	$-0.467102\pi$
$487$	6.07459e16	0.206338	0.103169	+	0.994664i	$0.467102\pi$
$488$	−1.20880e17	−0.405158
$489$	1.01225e17	0.334797
$490$	1.05879e16	0.0345571
$491$	−2.21938e17	−0.714829	−0.357414	−	0.933946i	$-0.616342\pi$
$491$	−2.21938e17	−0.714829	−0.357414	+	0.933946i	$0.616342\pi$
$492$	−2.11418e17	−0.671998
$493$	−3.04047e14	−0.000953754 0
$494$	−2.10019e16	−0.0650181
$495$	−6.36964e16	−0.194617
$496$	−4.10917e17	−1.23915
$497$	−1.38418e17	−0.411981
$498$	−6.19732e16	−0.182059
$499$	−6.83126e16	−0.198083	−0.0990415	−	0.995083i	$-0.531578\pi$
$499$	−6.83126e16	−0.198083	−0.0990415	+	0.995083i	$0.531578\pi$
$500$	−2.30423e17	−0.659509
$501$	3.87222e17	1.09399
$502$	−7.85731e16	−0.219129
$503$	−3.67361e17	−1.01135	−0.505675	−	0.862724i	$-0.668756\pi$
$503$	−3.67361e17	−1.01135	−0.505675	+	0.862724i	$0.668756\pi$
$504$	8.29521e16	0.225439
$505$	2.15240e17	0.577468
$506$	1.36202e17	0.360749
$507$	1.60978e17	0.420934
$508$	−1.41539e17	−0.365396
$509$	−8.54196e16	−0.217717	−0.108858	−	0.994057i	$-0.534720\pi$
$509$	−8.54196e16	−0.217717	−0.108858	+	0.994057i	$0.534720\pi$
$510$	−3.03816e14	−0.000764548 0
$511$	5.67241e15	0.0140939
$512$	−4.12747e17	−1.01258
$513$	−1.24715e16	−0.0302104
$514$	−1.10491e17	−0.264281
$515$	1.17846e17	0.278335
$516$	−3.92886e17	−0.916313
$517$	6.34452e17	1.46120
$518$	1.31943e17	0.300084
$519$	4.90125e17	1.10083
$520$	1.41077e17	0.312921
$521$	2.39318e17	0.524239	0.262120	−	0.965035i	$-0.415578\pi$
$521$	2.39318e17	0.524239	0.262120	+	0.965035i	$0.415578\pi$
$522$	−4.37612e15	−0.00946741
$523$	−2.06052e17	−0.440267	−0.220134	−	0.975470i	$-0.570649\pi$
$523$	−2.06052e17	−0.440267	−0.220134	+	0.975470i	$0.570649\pi$
$524$	5.04130e17	1.06387
$525$	−2.63466e17	−0.549147
$526$	9.58658e16	0.197359
$527$	9.05030e15	0.0184032
$528$	3.00717e17	0.604000
$529$	−1.97626e17	−0.392086
$530$	5.02843e16	0.0985460
$531$	2.24165e16	0.0433963
$532$	8.35247e16	0.159731
$533$	−8.99376e17	−1.69908
$534$	9.50998e16	0.177485
$535$	2.59228e17	0.477950
$536$	8.12483e16	0.147994
$537$	1.51131e17	0.271970
$538$	8.63211e16	0.153473
$539$	2.30816e17	0.405452
$540$	3.97013e16	0.0689041
$541$	2.86330e17	0.491004	0.245502	−	0.969396i	$-0.421047\pi$
$541$	2.86330e17	0.491004	0.245502	+	0.969396i	$0.421047\pi$
$542$	−3.21129e17	−0.544107
$543$	−3.11504e17	−0.521513
$544$	5.26247e15	0.00870556
$545$	1.46956e17	0.240220
$546$	1.67231e17	0.270124
$547$	−1.15937e17	−0.185057	−0.0925284	−	0.995710i	$-0.529495\pi$
$547$	−1.15937e17	−0.185057	−0.0925284	+	0.995710i	$0.529495\pi$
$548$	5.01215e17	0.790588
$549$	−1.44711e17	−0.225570
$550$	2.52908e17	0.389587
$551$	−9.29798e15	−0.0141548
$552$	−1.79137e17	−0.269514
$553$	−4.26082e17	−0.633549
$554$	2.84894e17	0.418669
$555$	1.33252e17	0.193540
$556$	3.00200e17	0.430948
$557$	−5.43030e17	−0.770487	−0.385244	−	0.922815i	$-0.625883\pi$
$557$	−5.43030e17	−0.770487	−0.385244	+	0.922815i	$0.625883\pi$
$558$	1.30260e17	0.182679
$559$	−1.67135e18	−2.31681
$560$	−2.33377e17	−0.319769
$561$	−6.62317e15	−0.00897031
$562$	−6.96579e16	−0.0932576
$563$	−3.96722e17	−0.525027	−0.262513	−	0.964928i	$-0.584551\pi$
$563$	−3.96722e17	−0.525027	−0.262513	+	0.964928i	$0.584551\pi$
$564$	−3.95448e17	−0.517339
$565$	−1.69543e17	−0.219263
$566$	−1.52719e17	−0.195248
$567$	9.93062e16	0.125512
$568$	−1.74757e17	−0.218358
$569$	−5.32908e17	−0.658298	−0.329149	−	0.944278i	$-0.606762\pi$
$569$	−5.32908e17	−0.658298	−0.329149	+	0.944278i	$0.606762\pi$
$570$	−9.29092e15	−0.0113468
$571$	9.76614e17	1.17920	0.589601	−	0.807695i	$-0.299285\pi$
$571$	9.76614e17	1.17920	0.589601	+	0.807695i	$0.299285\pi$
$572$	1.45747e18	1.73990
$573$	−6.73102e17	−0.794466
$574$	−3.93959e17	−0.459753
$575$	5.68961e17	0.656511
$576$	−1.32336e17	−0.150984
$577$	1.00111e18	1.12938	0.564691	−	0.825303i	$-0.308995\pi$
$577$	1.00111e18	1.12938	0.564691	+	0.825303i	$0.308995\pi$
$578$	2.82339e17	0.314948
$579$	−2.87863e17	−0.317523
$580$	2.95988e16	0.0322843
$581$	1.04848e18	1.13088
$582$	−1.65109e17	−0.176104
$583$	1.09619e18	1.15622
$584$	7.16155e15	0.00747005
$585$	1.68890e17	0.174218
$586$	1.24938e17	0.127456
$587$	6.07115e17	0.612524	0.306262	−	0.951947i	$-0.400922\pi$
$587$	6.07115e17	0.612524	0.306262	+	0.951947i	$0.400922\pi$
$588$	−1.43866e17	−0.143550
$589$	2.76764e17	0.273125
$590$	1.66996e16	0.0162993
$591$	−7.89249e17	−0.761896
$592$	−6.29098e17	−0.600658
$593$	−1.05140e17	−0.0992918	−0.0496459	−	0.998767i	$-0.515809\pi$
$593$	−1.05140e17	−0.0992918	−0.0496459	+	0.998767i	$0.515809\pi$
$594$	−9.53266e16	−0.0890435
$595$	5.14005e15	0.00474905
$596$	−5.32331e17	−0.486498
$597$	2.75213e17	0.248792
$598$	−3.61139e17	−0.322936
$599$	5.11951e17	0.452850	0.226425	−	0.974029i	$-0.427296\pi$
$599$	5.11951e17	0.452850	0.226425	+	0.974029i	$0.427296\pi$
$600$	−3.32632e17	−0.291059
$601$	4.35137e17	0.376653	0.188327	−	0.982106i	$-0.439694\pi$
$601$	4.35137e17	0.376653	0.188327	+	0.982106i	$0.439694\pi$
$602$	−7.32112e17	−0.626903
$603$	9.72665e16	0.0823950
$604$	1.98645e18	1.66470
$605$	−5.55027e17	−0.460155
$606$	3.22123e17	0.264210
$607$	6.37842e17	0.517591	0.258795	−	0.965932i	$-0.416674\pi$
$607$	6.37842e17	0.517591	0.258795	+	0.965932i	$0.416674\pi$
$608$	1.60930e17	0.129200
$609$	7.40364e16	0.0588075
$610$	−1.07806e17	−0.0847222
$611$	−1.68225e18	−1.30804
$612$	4.12816e15	0.00317594
$613$	−1.89096e18	−1.43943	−0.719713	−	0.694272i	$-0.755726\pi$
$613$	−1.89096e18	−1.43943	−0.719713	+	0.694272i	$0.755726\pi$
$614$	−4.47051e17	−0.336715
$615$	−3.97870e17	−0.296519
$616$	1.34717e18	0.993451
$617$	−3.63664e17	−0.265367	−0.132684	−	0.991158i	$-0.542359\pi$
$617$	−3.63664e17	−0.265367	−0.132684	+	0.991158i	$0.542359\pi$
$618$	1.76366e17	0.127347
$619$	−1.56151e18	−1.11572	−0.557860	−	0.829935i	$-0.688377\pi$
$619$	−1.56151e18	−1.11572	−0.557860	+	0.829935i	$0.688377\pi$
$620$	−8.81039e17	−0.622944
$621$	−2.14454e17	−0.150051
$622$	6.35764e17	0.440209
$623$	−1.60892e18	−1.10246
$624$	−7.97349e17	−0.540690
$625$	8.21066e17	0.551008
$626$	4.12822e17	0.274176
$627$	−2.02541e17	−0.133130
$628$	−1.20057e17	−0.0780995
$629$	1.38556e16	0.00892066
$630$	7.39802e16	0.0471413
$631$	−1.19333e18	−0.752607	−0.376304	−	0.926496i	$-0.622805\pi$
$631$	−1.19333e18	−0.752607	−0.376304	+	0.926496i	$0.622805\pi$
$632$	−5.37939e17	−0.335793
$633$	−2.48330e17	−0.153428
$634$	9.64678e17	0.589933
$635$	−2.66365e17	−0.161231
$636$	−6.83246e17	−0.409360
$637$	−6.12008e17	−0.362953
$638$	−7.10694e16	−0.0417204
$639$	−2.09210e17	−0.121570
$640$	−6.67309e17	−0.383846
$641$	−1.40011e18	−0.797230	−0.398615	−	0.917118i	$-0.630509\pi$
$641$	−1.40011e18	−0.797230	−0.398615	+	0.917118i	$0.630509\pi$
$642$	3.87955e17	0.218677
$643$	1.60800e17	0.0897251	0.0448626	−	0.998993i	$-0.485715\pi$
$643$	1.60800e17	0.0897251	0.0448626	+	0.998993i	$0.485715\pi$
$644$	1.43625e18	0.793362
$645$	−7.39378e17	−0.404323
$646$	−9.66073e14	−0.000522996 0
$647$	5.35884e17	0.287206	0.143603	−	0.989635i	$-0.454131\pi$
$647$	5.35884e17	0.287206	0.143603	+	0.989635i	$0.454131\pi$
$648$	1.25376e17	0.0665240
$649$	3.64050e17	0.191236
$650$	−6.70583e17	−0.348751
$651$	−2.20377e18	−1.13472
$652$	−1.02464e18	−0.522353
$653$	−1.01990e18	−0.514780	−0.257390	−	0.966308i	$-0.582862\pi$
$653$	−1.01990e18	−0.514780	−0.257390	+	0.966308i	$0.582862\pi$
$654$	2.19931e17	0.109908
$655$	9.48730e17	0.469433
$656$	1.87838e18	0.920256
$657$	8.57346e15	0.00415893
$658$	−7.36885e17	−0.353941
$659$	2.60808e18	1.24041	0.620207	−	0.784438i	$-0.287049\pi$
$659$	2.60808e18	1.24041	0.620207	+	0.784438i	$0.287049\pi$
$660$	6.44760e17	0.303643
$661$	−1.54930e18	−0.722481	−0.361240	−	0.932473i	$-0.617647\pi$
$661$	−1.54930e18	−0.722481	−0.361240	+	0.932473i	$0.617647\pi$
$662$	1.02899e18	0.475152
$663$	1.75613e16	0.00803006
$664$	1.32373e18	0.599386
$665$	1.57186e17	0.0704813
$666$	1.99423e17	0.0885507
$667$	−1.59883e17	−0.0703049
$668$	−3.91961e18	−1.70685
$669$	−1.58780e18	−0.684741
$670$	7.24607e16	0.0309468
$671$	−2.35015e18	−0.994030
$672$	−1.28143e18	−0.536776
$673$	−2.84284e18	−1.17938	−0.589691	−	0.807629i	$-0.700750\pi$
$673$	−2.84284e18	−1.17938	−0.589691	+	0.807629i	$0.700750\pi$
$674$	−1.10340e18	−0.453360
$675$	−3.98211e17	−0.162046
$676$	−1.62948e18	−0.656744
$677$	−7.89265e17	−0.315062	−0.157531	−	0.987514i	$-0.550353\pi$
$677$	−7.89265e17	−0.315062	−0.157531	+	0.987514i	$0.550353\pi$
$678$	−2.53735e17	−0.100320
$679$	2.79335e18	1.09389
$680$	6.48943e15	0.00251709
$681$	−1.62027e18	−0.622487
$682$	2.11546e18	0.805019
$683$	−3.01912e18	−1.13801	−0.569004	−	0.822335i	$-0.692671\pi$
$683$	−3.01912e18	−1.13801	−0.569004	+	0.822335i	$0.692671\pi$
$684$	1.26242e17	0.0471345
$685$	9.43243e17	0.348847
$686$	7.03152e17	0.257598
$687$	−2.62593e18	−0.952936
$688$	3.49068e18	1.25483
$689$	−2.90655e18	−1.03503
$690$	−1.59762e17	−0.0563578
$691$	1.38525e18	0.484084	0.242042	−	0.970266i	$-0.422183\pi$
$691$	1.38525e18	0.484084	0.242042	+	0.970266i	$0.422183\pi$
$692$	−4.96124e18	−1.71752
$693$	1.61276e18	0.553100
$694$	4.93383e17	0.167628
$695$	5.64951e17	0.190156
$696$	9.34727e16	0.0311691
$697$	−4.13706e16	−0.0136672
$698$	2.88060e17	0.0942805
$699$	1.24658e18	0.404220
$700$	2.66691e18	0.856783
$701$	−3.52896e18	−1.12326	−0.561628	−	0.827390i	$-0.689825\pi$
$701$	−3.52896e18	−1.12326	−0.561628	+	0.827390i	$0.689825\pi$
$702$	2.52758e17	0.0797101
$703$	4.23715e17	0.132393
$704$	−2.14917e18	−0.665349
$705$	−7.44199e17	−0.228276
$706$	8.13013e17	0.247097
$707$	−5.44976e18	−1.64116
$708$	−2.26909e17	−0.0677072
$709$	1.25029e18	0.369666	0.184833	−	0.982770i	$-0.440826\pi$
$709$	1.25029e18	0.369666	0.184833	+	0.982770i	$0.440826\pi$
$710$	−1.55855e17	−0.0456607
$711$	−6.43994e17	−0.186952
$712$	−2.03131e18	−0.584326
$713$	4.75910e18	1.35657
$714$	7.69248e15	0.00217284
$715$	2.74283e18	0.767732
$716$	−1.52981e18	−0.424329
$717$	6.48872e17	0.178355
$718$	2.11285e17	0.0575520
$719$	2.28080e18	0.615673	0.307837	−	0.951439i	$-0.400395\pi$
$719$	2.28080e18	0.615673	0.307837	+	0.951439i	$0.400395\pi$
$720$	−3.52734e17	−0.0943596
$721$	−2.98381e18	−0.791028
$722$	1.16935e18	0.307222
$723$	−2.37669e18	−0.618834
$724$	3.15317e18	0.813668
$725$	−2.96881e17	−0.0759250
$726$	−8.30642e17	−0.210536
$727$	3.07421e18	0.772253	0.386127	−	0.922446i	$-0.373813\pi$
$727$	3.07421e18	0.772253	0.386127	+	0.922446i	$0.373813\pi$
$728$	−3.57200e18	−0.889319
$729$	1.50095e17	0.0370370
$730$	6.38697e15	0.00156206
$731$	−7.68808e16	−0.0186361
$732$	1.46483e18	0.351936
$733$	−2.26677e18	−0.539799	−0.269899	−	0.962889i	$-0.586990\pi$
$733$	−2.26677e18	−0.539799	−0.269899	+	0.962889i	$0.586990\pi$
$734$	−1.75553e18	−0.414366
$735$	−2.70742e17	−0.0633416
$736$	2.76727e18	0.641721
$737$	1.57964e18	0.363093
$738$	−5.95443e17	−0.135667
$739$	6.19047e18	1.39809	0.699044	−	0.715078i	$-0.253609\pi$
$739$	6.19047e18	1.39809	0.699044	+	0.715078i	$0.253609\pi$
$740$	−1.34883e18	−0.301962
$741$	5.37037e17	0.119175
$742$	−1.27317e18	−0.280067
$743$	−1.26049e18	−0.274860	−0.137430	−	0.990511i	$-0.543884\pi$
$743$	−1.26049e18	−0.274860	−0.137430	+	0.990511i	$0.543884\pi$
$744$	−2.78232e18	−0.601426
$745$	−1.00180e18	−0.214667
$746$	2.25823e18	0.479695
$747$	1.58470e18	0.333706
$748$	6.70424e16	0.0139955
$749$	−6.56352e18	−1.35833
$750$	−6.48971e17	−0.133146
$751$	7.96765e18	1.62058	0.810290	−	0.586029i	$-0.199310\pi$
$751$	7.96765e18	1.62058	0.810290	+	0.586029i	$0.199310\pi$
$752$	3.51344e18	0.708461
$753$	2.00918e18	0.401653
$754$	1.88440e17	0.0373474
$755$	3.73832e18	0.734550
$756$	−1.00522e18	−0.195825
$757$	2.89061e17	0.0558298	0.0279149	−	0.999610i	$-0.491113\pi$
$757$	2.89061e17	0.0558298	0.0279149	+	0.999610i	$0.491113\pi$
$758$	−2.86758e18	−0.549118
$759$	−3.48280e18	−0.661236
$760$	1.98451e17	0.0373565
$761$	4.62524e18	0.863245	0.431623	−	0.902054i	$-0.357941\pi$
$761$	4.62524e18	0.863245	0.431623	+	0.902054i	$0.357941\pi$
$762$	−3.98636e17	−0.0737682
$763$	−3.72085e18	−0.682704
$764$	6.81341e18	1.23953
$765$	7.76883e15	0.00140138
$766$	1.44237e18	0.257983
$767$	−9.65276e17	−0.171191
$768$	4.88420e17	0.0858907
$769$	−7.42290e18	−1.29435	−0.647176	−	0.762341i	$-0.724050\pi$
$769$	−7.42290e18	−1.29435	−0.647176	+	0.762341i	$0.724050\pi$
$770$	1.20146e18	0.207740
$771$	2.82534e18	0.484415
$772$	2.91387e18	0.495401
$773$	6.76017e17	0.113970	0.0569850	−	0.998375i	$-0.481851\pi$
$773$	6.76017e17	0.113970	0.0569850	+	0.998375i	$0.481851\pi$
$774$	−1.10654e18	−0.184991
$775$	8.83698e18	1.46502
$776$	3.52667e18	0.579781
$777$	−3.37389e18	−0.550039
$778$	2.23073e18	0.360645
$779$	−1.26514e18	−0.202836
$780$	−1.70958e18	−0.271815
$781$	−3.39763e18	−0.535728
$782$	−1.66121e16	−0.00259765
$783$	1.11901e17	0.0173533
$784$	1.27820e18	0.196583
$785$	−2.25936e17	−0.0344614
$786$	1.41985e18	0.214781
$787$	−1.48624e18	−0.222973	−0.111486	−	0.993766i	$-0.535561\pi$
$787$	−1.48624e18	−0.222973	−0.111486	+	0.993766i	$0.535561\pi$
$788$	7.98910e18	1.18871
$789$	−2.45137e18	−0.361749
$790$	−4.79757e17	−0.0702174
$791$	4.29275e18	0.623144
$792$	2.03615e18	0.293154
$793$	6.23141e18	0.889837
$794$	−5.50352e17	−0.0779484
$795$	−1.28581e18	−0.180630
$796$	−2.78582e18	−0.388166
$797$	1.89092e17	0.0261332	0.0130666	−	0.999915i	$-0.495841\pi$
$797$	1.89092e17	0.0261332	0.0130666	+	0.999915i	$0.495841\pi$
$798$	2.35242e17	0.0322474
$799$	−7.73820e16	−0.0105217
$800$	5.13843e18	0.693019
$801$	−2.43178e18	−0.325322
$802$	2.26649e18	0.300760
$803$	1.39235e17	0.0183273
$804$	−9.84571e17	−0.128553
$805$	2.70290e18	0.350071
$806$	−5.60913e18	−0.720639
$807$	−2.20730e18	−0.281309
$808$	−6.88045e18	−0.869848
$809$	−3.14457e18	−0.394363	−0.197182	−	0.980367i	$-0.563179\pi$
$809$	−3.14457e18	−0.394363	−0.197182	+	0.980367i	$0.563179\pi$
$810$	1.11816e17	0.0139108
$811$	−1.07894e19	−1.33156	−0.665782	−	0.746147i	$-0.731902\pi$
$811$	−1.07894e19	−1.33156	−0.665782	+	0.746147i	$0.731902\pi$
$812$	−7.49426e17	−0.0917518
$813$	8.21153e18	0.997323
$814$	3.23868e18	0.390220
$815$	−1.92829e18	−0.230488
$816$	−3.66774e16	−0.00434923
$817$	−2.35107e18	−0.276581
$818$	−8.10493e17	−0.0945917
$819$	−4.27623e18	−0.495125
$820$	4.02740e18	0.462631
$821$	6.50342e18	0.741159	0.370579	−	0.928801i	$-0.379159\pi$
$821$	6.50342e18	0.741159	0.370579	+	0.928801i	$0.379159\pi$
$822$	1.41164e18	0.159609
$823$	8.81513e18	0.988848	0.494424	−	0.869221i	$-0.335379\pi$
$823$	8.81513e18	0.988848	0.494424	+	0.869221i	$0.335379\pi$
$824$	−3.76713e18	−0.419260
$825$	−6.46706e18	−0.714095
$826$	−4.22826e17	−0.0463224
$827$	−1.30734e19	−1.42103	−0.710516	−	0.703681i	$-0.751538\pi$
$827$	−1.30734e19	−1.42103	−0.710516	+	0.703681i	$0.751538\pi$
$828$	2.17079e18	0.234111
$829$	−9.25838e18	−0.990673	−0.495337	−	0.868701i	$-0.664955\pi$
$829$	−9.25838e18	−0.990673	−0.495337	+	0.868701i	$0.664955\pi$
$830$	1.18056e18	0.125337
$831$	−7.28498e18	−0.767400
$832$	5.69852e18	0.595608
$833$	−2.81519e16	−0.00291954
$834$	8.45493e17	0.0870023
$835$	−7.37637e18	−0.753149
$836$	2.05020e18	0.207709
$837$	−3.33085e18	−0.334842
$838$	−4.67905e18	−0.466736
$839$	5.55006e18	0.549345	0.274672	−	0.961538i	$-0.411431\pi$
$839$	5.55006e18	0.549345	0.274672	+	0.961538i	$0.411431\pi$
$840$	−1.58020e18	−0.155201
$841$	−1.01772e19	−0.991869
$842$	2.71907e18	0.262962
$843$	1.78121e18	0.170937
$844$	2.51369e18	0.239379
$845$	−3.06654e18	−0.289788
$846$	−1.11375e18	−0.104443
$847$	1.40530e19	1.30776
$848$	6.07043e18	0.560592
$849$	3.90515e18	0.357880
$850$	−3.08463e16	−0.00280531
$851$	7.28599e18	0.657577
$852$	2.11771e18	0.189675
$853$	1.09917e19	0.977001	0.488501	−	0.872563i	$-0.337544\pi$
$853$	1.09917e19	0.977001	0.488501	+	0.872563i	$0.337544\pi$
$854$	2.72958e18	0.240780
$855$	2.37576e17	0.0207981
$856$	−8.28661e18	−0.719942
$857$	1.31498e19	1.13382	0.566911	−	0.823779i	$-0.308138\pi$
$857$	1.31498e19	1.13382	0.566911	+	0.823779i	$0.308138\pi$
$858$	4.10486e18	0.351262
$859$	−1.16888e19	−0.992690	−0.496345	−	0.868125i	$-0.665325\pi$
$859$	−1.16888e19	−0.992690	−0.496345	+	0.868125i	$0.665325\pi$
$860$	7.48428e18	0.630827
$861$	1.00739e19	0.842705
$862$	2.91122e18	0.241701
$863$	1.12732e19	0.928919	0.464459	−	0.885594i	$-0.346249\pi$
$863$	1.12732e19	0.928919	0.464459	+	0.885594i	$0.346249\pi$
$864$	−1.93679e18	−0.158396
$865$	−9.33663e18	−0.757854
$866$	5.15776e18	0.415523
$867$	−7.21963e18	−0.577286
$868$	2.23075e19	1.77040
$869$	−1.04587e19	−0.823848
$870$	8.33629e16	0.00651775
$871$	−4.18839e18	−0.325035
$872$	−4.69766e18	−0.361847
$873$	4.22196e18	0.322791
$874$	−5.08010e17	−0.0385521
$875$	1.09795e19	0.827044
$876$	−8.67841e16	−0.00648878
$877$	2.49089e19	1.84866	0.924330	−	0.381594i	$-0.124625\pi$
$877$	2.49089e19	1.84866	0.924330	+	0.381594i	$0.124625\pi$
$878$	−3.91144e18	−0.288152
$879$	−3.19478e18	−0.233621
$880$	−5.72850e18	−0.415818
$881$	−1.57792e19	−1.13695	−0.568474	−	0.822701i	$-0.692466\pi$
$881$	−1.57792e19	−1.13695	−0.568474	+	0.822701i	$0.692466\pi$
$882$	−4.05187e17	−0.0289808
$883$	2.74760e19	1.95078	0.975390	−	0.220485i	$-0.0707639\pi$
$883$	2.74760e19	1.95078	0.975390	+	0.220485i	$0.0707639\pi$
$884$	−1.77763e17	−0.0125285
$885$	−4.27022e17	−0.0298758
$886$	5.18299e17	0.0359966
$887$	2.05266e19	1.41518	0.707592	−	0.706622i	$-0.249782\pi$
$887$	2.05266e19	1.41518	0.707592	+	0.706622i	$0.249782\pi$
$888$	−4.25961e18	−0.291532
$889$	6.74423e18	0.458217
$890$	−1.81160e18	−0.122188
$891$	2.43758e18	0.163213
$892$	1.60724e19	1.06834
$893$	−2.36640e18	−0.156154
$894$	−1.49927e18	−0.0982171
$895$	−2.87897e18	−0.187235
$896$	1.68959e19	1.09089
$897$	9.23462e18	0.591927
$898$	9.43562e17	0.0600446
$899$	−2.48327e18	−0.156887
$900$	4.03085e18	0.252825
$901$	−1.33699e17	−0.00832562
$902$	−9.67016e18	−0.597849
$903$	1.87207e19	1.14908
$904$	5.41970e18	0.330279
$905$	5.93400e18	0.359031
$906$	5.59469e18	0.336080
$907$	1.15329e18	0.0687848	0.0343924	−	0.999408i	$-0.489050\pi$
$907$	1.15329e18	0.0687848	0.0343924	+	0.999408i	$0.489050\pi$
$908$	1.64010e19	0.971208
$909$	−8.23694e18	−0.484285
$910$	−3.18566e18	−0.185965
$911$	−1.98215e19	−1.14886	−0.574429	−	0.818554i	$-0.694776\pi$
$911$	−1.98215e19	−1.14886	−0.574429	+	0.818554i	$0.694776\pi$
$912$	−1.12162e18	−0.0645476
$913$	2.57361e19	1.47056
$914$	−9.39780e18	−0.533183
$915$	2.75668e18	0.155292
$916$	2.65807e19	1.48678
$917$	−2.40214e19	−1.33413
$918$	1.16267e16	0.000641177 0
$919$	2.36827e19	1.29682	0.648411	−	0.761291i	$-0.275434\pi$
$919$	2.36827e19	1.29682	0.648411	+	0.761291i	$0.275434\pi$
$920$	3.41247e18	0.185544
$921$	1.14315e19	0.617183
$922$	4.39343e18	0.235534
$923$	9.00880e18	0.479574
$924$	−1.63250e19	−0.862950
$925$	1.35290e19	0.710143
$926$	−6.83868e18	−0.356452
$927$	−4.50982e18	−0.233422
$928$	−1.44395e18	−0.0742146
$929$	−3.24255e19	−1.65495	−0.827474	−	0.561504i	$-0.810223\pi$
$929$	−3.24255e19	−1.65495	−0.827474	+	0.561504i	$0.810223\pi$
$930$	−2.48139e18	−0.125764
$931$	−8.60905e17	−0.0433294
$932$	−1.26184e19	−0.630667
$933$	−1.62570e19	−0.806882
$934$	5.70663e18	0.281271
$935$	1.26168e17	0.00617552
$936$	−5.39884e18	−0.262426
$937$	−2.25450e19	−1.08829	−0.544144	−	0.838992i	$-0.683145\pi$
$937$	−2.25450e19	−1.08829	−0.544144	+	0.838992i	$0.683145\pi$
$938$	−1.83467e18	−0.0879507
$939$	−1.05562e19	−0.502552
$940$	7.53308e18	0.356157
$941$	−2.02666e19	−0.951585	−0.475793	−	0.879558i	$-0.657839\pi$
$941$	−2.02666e19	−0.951585	−0.475793	+	0.879558i	$0.657839\pi$
$942$	−3.38131e17	−0.0157672
$943$	−2.17548e19	−1.00746
$944$	2.01601e18	0.0927205
$945$	−1.89173e18	−0.0864078
$946$	−1.79705e19	−0.815206
$947$	2.79538e19	1.25941	0.629704	−	0.776835i	$-0.283176\pi$
$947$	2.79538e19	1.25941	0.629704	+	0.776835i	$0.283176\pi$
$948$	6.51877e18	0.291683
$949$	−3.69182e17	−0.0164063
$950$	−9.43302e17	−0.0416339
$951$	−2.46676e19	−1.08132
$952$	−1.64309e17	−0.00715355
$953$	−1.55403e18	−0.0671978	−0.0335989	−	0.999435i	$-0.510697\pi$
$953$	−1.55403e18	−0.0671978	−0.0335989	+	0.999435i	$0.510697\pi$
$954$	−1.92431e18	−0.0826441
$955$	1.28222e19	0.546943
$956$	−6.56814e18	−0.278270
$957$	1.81730e18	0.0764716
$958$	−6.38387e18	−0.266814
$959$	−2.38825e19	−0.991421
$960$	2.52093e18	0.103944
$961$	4.94998e19	2.02722
$962$	−8.58734e18	−0.349318
$963$	−9.92032e18	−0.400825
$964$	2.40579e19	0.965509
$965$	5.48364e18	0.218596
$966$	4.04510e18	0.160169
$967$	4.03274e19	1.58609	0.793045	−	0.609163i	$-0.208494\pi$
$967$	4.03274e19	1.58609	0.793045	+	0.609163i	$0.208494\pi$
$968$	1.77423e19	0.693138
$969$	2.47033e16	0.000958628 0
$970$	3.14524e18	0.121237
$971$	−4.44653e19	−1.70254	−0.851269	−	0.524730i	$-0.824166\pi$
$971$	−4.44653e19	−1.70254	−0.851269	+	0.524730i	$0.824166\pi$
$972$	−1.51932e18	−0.0577854
$973$	−1.43043e19	−0.540421
$974$	−1.73181e18	−0.0649930
$975$	1.71474e19	0.639245
$976$	−1.30145e19	−0.481953
$977$	2.19233e19	0.806477	0.403238	−	0.915095i	$-0.367885\pi$
$977$	2.19233e19	0.806477	0.403238	+	0.915095i	$0.367885\pi$
$978$	−2.88584e18	−0.105456
$979$	−3.94928e19	−1.43361
$980$	2.74057e18	0.0988259
$981$	−5.62381e18	−0.201457
$982$	6.32724e18	0.225159
$983$	−4.97073e19	−1.75720	−0.878601	−	0.477556i	$-0.841523\pi$
$983$	−4.97073e19	−1.75720	−0.878601	+	0.477556i	$0.841523\pi$
$984$	1.27185e19	0.446650
$985$	1.50348e19	0.524520
$986$	8.66810e15	0.000300417 0
$987$	1.88427e19	0.648758
$988$	−5.43610e18	−0.185938
$989$	−4.04278e19	−1.37374
$990$	1.81592e18	0.0613012
$991$	4.02493e19	1.34983	0.674915	−	0.737895i	$-0.264180\pi$
$991$	4.02493e19	1.34983	0.674915	+	0.737895i	$0.264180\pi$
$992$	4.29806e19	1.43201
$993$	−2.63120e19	−0.870932
$994$	3.94618e18	0.129767
$995$	−5.24267e18	−0.171278
$996$	−1.60410e19	−0.520651
$997$	−5.73143e19	−1.84818	−0.924091	−	0.382173i	$-0.875176\pi$
$997$	−5.73143e19	−1.84818	−0.924091	+	0.382173i	$0.875176\pi$
$998$	1.94753e18	0.0623929
$999$	−5.09940e18	−0.162309

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.a.1.14	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.a.1.14	✓	30	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:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-28.5091 q^{2} +729.000 q^{3} -7379.23 q^{4} -13887.1 q^{5} -20783.1 q^{6} +351614. q^{7} +443921. q^{8} +531441. q^{9} +O(q^{10})\)	\(q-28.5091 q^{2} +729.000 q^{3} -7379.23 q^{4} -13887.1 q^{5} -20783.1 q^{6} +351614. q^{7} +443921. q^{8} +531441. q^{9} +395908. q^{10} +8.63075e6 q^{11} -5.37946e6 q^{12} -2.28844e7 q^{13} -1.00242e7 q^{14} -1.01237e7 q^{15} +4.77949e7 q^{16} -1.05266e6 q^{17} -1.51509e7 q^{18} -3.21912e7 q^{19} +1.02476e8 q^{20} +2.56327e8 q^{21} -2.46055e8 q^{22} -5.53544e8 q^{23} +3.23619e8 q^{24} -1.02785e9 q^{25} +6.52412e8 q^{26} +3.87420e8 q^{27} -2.59464e9 q^{28} +2.88836e8 q^{29} +2.88617e8 q^{30} -8.59752e9 q^{31} -4.99919e9 q^{32} +6.29182e9 q^{33} +3.00105e7 q^{34} -4.88289e9 q^{35} -3.92163e9 q^{36} -1.31624e10 q^{37} +9.17741e8 q^{38} -1.66827e10 q^{39} -6.16477e9 q^{40} +3.93009e10 q^{41} -7.30763e9 q^{42} +7.30345e10 q^{43} -6.36883e10 q^{44} -7.38016e9 q^{45} +1.57810e10 q^{46} +7.35107e10 q^{47} +3.48425e10 q^{48} +2.67435e10 q^{49} +2.93031e10 q^{50} -7.67392e8 q^{51} +1.68869e11 q^{52} +1.27010e11 q^{53} -1.10450e10 q^{54} -1.19856e11 q^{55} +1.56089e11 q^{56} -2.34674e10 q^{57} -8.23445e9 q^{58} +4.21805e10 q^{59} +7.47050e10 q^{60} -2.72300e11 q^{61} +2.45107e11 q^{62} +1.86862e11 q^{63} -2.49014e11 q^{64} +3.17797e11 q^{65} -1.79374e11 q^{66} +1.83024e11 q^{67} +7.76785e9 q^{68} -4.03533e11 q^{69} +1.39207e11 q^{70} -3.93666e11 q^{71} +2.35918e11 q^{72} +1.61325e10 q^{73} +3.75249e11 q^{74} -7.49304e11 q^{75} +2.37546e11 q^{76} +3.03469e12 q^{77} +4.75609e11 q^{78} -1.21179e12 q^{79} -6.63732e11 q^{80} +2.82430e11 q^{81} -1.12043e12 q^{82} +2.98190e12 q^{83} -1.89149e12 q^{84} +1.46184e10 q^{85} -2.08215e12 q^{86} +2.10561e11 q^{87} +3.83137e12 q^{88} -4.57582e12 q^{89} +2.10402e11 q^{90} -8.04647e12 q^{91} +4.08473e12 q^{92} -6.26759e12 q^{93} -2.09572e12 q^{94} +4.47042e11 q^{95} -3.64441e12 q^{96} +7.94437e12 q^{97} -7.62432e11 q^{98} +4.58674e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 138 q^{2} + 21870 q^{3} + 114598 q^{4} - 137742 q^{5} - 100602 q^{6} - 879443 q^{7} - 872301 q^{8} + 15943230 q^{9}+O(q^{10}) \) 30 * q - 138 * q^2 + 21870 * q^3 + 114598 * q^4 - 137742 * q^5 - 100602 * q^6 - 879443 * q^7 - 872301 * q^8 + 15943230 * q^9	\( 30 q - 138 q^{2} + 21870 q^{3} + 114598 q^{4} - 137742 q^{5} - 100602 q^{6} - 879443 q^{7} - 872301 q^{8} + 15943230 q^{9} - 5352519 q^{10} - 13950782 q^{11} + 83541942 q^{12} - 17256988 q^{13} + 33780109 q^{14} - 100413918 q^{15} + 499996762 q^{16} - 317583695 q^{17} - 73338858 q^{18} - 863401469 q^{19} - 1841280623 q^{20} - 641113947 q^{21} - 2723764842 q^{22} - 3142075981 q^{23} - 635907429 q^{24} + 5435751692 q^{25} - 6441414040 q^{26} + 11622614670 q^{27} - 7538400046 q^{28} - 4604589283 q^{29} - 3901986351 q^{30} + 4308675373 q^{31} + 6094556360 q^{32} - 10170120078 q^{33} + 38097713432 q^{34} - 15447827315 q^{35} + 60902075718 q^{36} - 19633376949 q^{37} - 18152222923 q^{38} - 12580344252 q^{39} + 14680384170 q^{40} - 103644439493 q^{41} + 24625699461 q^{42} - 64494894924 q^{43} - 199714496208 q^{44} - 73201746222 q^{45} - 265425792847 q^{46} - 293365585139 q^{47} + 364497639498 q^{48} + 414396765797 q^{49} - 126058522207 q^{50} - 231518513655 q^{51} + 156029960316 q^{52} - 76747013118 q^{53} - 53464027482 q^{54} - 433465885754 q^{55} - 502955241518 q^{56} - 629419670901 q^{57} - 1755031845830 q^{58} + 1265416009230 q^{59} - 1342293574167 q^{60} - 2022612531219 q^{61} - 3816005187046 q^{62} - 467372067363 q^{63} - 3570205594131 q^{64} - 3889749040576 q^{65} - 1985624569818 q^{66} - 502618987776 q^{67} - 8953998390517 q^{68} - 2290573390149 q^{69} - 6805178272420 q^{70} - 1599540605456 q^{71} - 463576515741 q^{72} - 3826795087235 q^{73} - 7573387813210 q^{74} + 3962662983468 q^{75} - 19498723328388 q^{76} - 9088623115219 q^{77} - 4695790835160 q^{78} - 8595482172338 q^{79} - 17452527463963 q^{80} + 8472886094430 q^{81} - 11181116792901 q^{82} - 13548556984389 q^{83} - 5495493633534 q^{84} - 12851795888367 q^{85} + 8539949468848 q^{86} - 3356745587307 q^{87} - 25134826741387 q^{88} - 21826401667403 q^{89} - 2844548049879 q^{90} - 26577050621355 q^{91} - 34908210763168 q^{92} + 3141024346917 q^{93} - 26426808959500 q^{94} - 29105233533993 q^{95} + 4442931586440 q^{96} + 417815797414 q^{97} + 29159956938360 q^{98} - 7414017536862 q^{99}+O(q^{100}) \) 30 * q - 138 * q^2 + 21870 * q^3 + 114598 * q^4 - 137742 * q^5 - 100602 * q^6 - 879443 * q^7 - 872301 * q^8 + 15943230 * q^9 - 5352519 * q^10 - 13950782 * q^11 + 83541942 * q^12 - 17256988 * q^13 + 33780109 * q^14 - 100413918 * q^15 + 499996762 * q^16 - 317583695 * q^17 - 73338858 * q^18 - 863401469 * q^19 - 1841280623 * q^20 - 641113947 * q^21 - 2723764842 * q^22 - 3142075981 * q^23 - 635907429 * q^24 + 5435751692 * q^25 - 6441414040 * q^26 + 11622614670 * q^27 - 7538400046 * q^28 - 4604589283 * q^29 - 3901986351 * q^30 + 4308675373 * q^31 + 6094556360 * q^32 - 10170120078 * q^33 + 38097713432 * q^34 - 15447827315 * q^35 + 60902075718 * q^36 - 19633376949 * q^37 - 18152222923 * q^38 - 12580344252 * q^39 + 14680384170 * q^40 - 103644439493 * q^41 + 24625699461 * q^42 - 64494894924 * q^43 - 199714496208 * q^44 - 73201746222 * q^45 - 265425792847 * q^46 - 293365585139 * q^47 + 364497639498 * q^48 + 414396765797 * q^49 - 126058522207 * q^50 - 231518513655 * q^51 + 156029960316 * q^52 - 76747013118 * q^53 - 53464027482 * q^54 - 433465885754 * q^55 - 502955241518 * q^56 - 629419670901 * q^57 - 1755031845830 * q^58 + 1265416009230 * q^59 - 1342293574167 * q^60 - 2022612531219 * q^61 - 3816005187046 * q^62 - 467372067363 * q^63 - 3570205594131 * q^64 - 3889749040576 * q^65 - 1985624569818 * q^66 - 502618987776 * q^67 - 8953998390517 * q^68 - 2290573390149 * q^69 - 6805178272420 * q^70 - 1599540605456 * q^71 - 463576515741 * q^72 - 3826795087235 * q^73 - 7573387813210 * q^74 + 3962662983468 * q^75 - 19498723328388 * q^76 - 9088623115219 * q^77 - 4695790835160 * q^78 - 8595482172338 * q^79 - 17452527463963 * q^80 + 8472886094430 * q^81 - 11181116792901 * q^82 - 13548556984389 * q^83 - 5495493633534 * q^84 - 12851795888367 * q^85 + 8539949468848 * q^86 - 3356745587307 * q^87 - 25134826741387 * q^88 - 21826401667403 * q^89 - 2844548049879 * q^90 - 26577050621355 * q^91 - 34908210763168 * q^92 + 3141024346917 * q^93 - 26426808959500 * q^94 - 29105233533993 * q^95 + 4442931586440 * q^96 + 417815797414 * q^97 + 29159956938360 * q^98 - 7414017536862 * q^99

Introduction

L-functions

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