LMFDB - Embedded newform 177.8.a.b.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,8,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, 8, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 8 $
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:	$55.2921495107$
Analytic rank:	$1$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 2 x^{16} - 1639 x^{15} + 1625 x^{14} + 1070274 x^{13} - 274939 x^{12} - 357079564 x^{11} + \cdots - 58\!\cdots\!76 $ x^17 - 2x^16 - 1639x^15 + 1625x^14 + 1070274x^13 - 274939x^12 - 357079564x^11 - 89298188x^10 + 64650816672x^9 + 33122051904x^8 - 6210397064704x^7 - 2735256748800x^6 + 288860762071040x^5 - 34502173230080x^4 - 5633463408885760x^3 + 4719471961341952x^2 + 37636623107620864x - 58321181718347776
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{10}\cdot 3^{5} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$12.7630$ of defining polynomial
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)

$f(q)$	$=$	$q+10.7630 q^{2} +27.0000 q^{3} -12.1577 q^{4} +451.863 q^{5} +290.601 q^{6} -504.672 q^{7} -1508.52 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+10.7630 q^{2} +27.0000 q^{3} -12.1577 q^{4} +451.863 q^{5} +290.601 q^{6} -504.672 q^{7} -1508.52 q^{8} +729.000 q^{9} +4863.40 q^{10} -8070.72 q^{11} -328.258 q^{12} -4674.69 q^{13} -5431.79 q^{14} +12200.3 q^{15} -14680.0 q^{16} -13499.0 q^{17} +7846.23 q^{18} -11364.6 q^{19} -5493.61 q^{20} -13626.1 q^{21} -86865.2 q^{22} -66475.4 q^{23} -40730.0 q^{24} +126055. q^{25} -50313.7 q^{26} +19683.0 q^{27} +6135.65 q^{28} -174542. q^{29} +131312. q^{30} +62482.4 q^{31} +35089.3 q^{32} -217909. q^{33} -145289. q^{34} -228043. q^{35} -8862.96 q^{36} +277403. q^{37} -122318. q^{38} -126217. q^{39} -681643. q^{40} +529842. q^{41} -146658. q^{42} +675111. q^{43} +98121.3 q^{44} +329408. q^{45} -715475. q^{46} +175110. q^{47} -396360. q^{48} -568849. q^{49} +1.35673e6 q^{50} -364472. q^{51} +56833.4 q^{52} -313480. q^{53} +211848. q^{54} -3.64686e6 q^{55} +761307. q^{56} -306845. q^{57} -1.87860e6 q^{58} -205379. q^{59} -148328. q^{60} -3.01895e6 q^{61} +672499. q^{62} -367906. q^{63} +2.25671e6 q^{64} -2.11232e6 q^{65} -2.34536e6 q^{66} -885587. q^{67} +164116. q^{68} -1.79484e6 q^{69} -2.45442e6 q^{70} -1.15026e6 q^{71} -1.09971e6 q^{72} +33498.4 q^{73} +2.98569e6 q^{74} +3.40349e6 q^{75} +138168. q^{76} +4.07307e6 q^{77} -1.35847e6 q^{78} -694337. q^{79} -6.63335e6 q^{80} +531441. q^{81} +5.70270e6 q^{82} -672731. q^{83} +165663. q^{84} -6.09968e6 q^{85} +7.26622e6 q^{86} -4.71263e6 q^{87} +1.21748e7 q^{88} +7.67580e6 q^{89} +3.54542e6 q^{90} +2.35918e6 q^{91} +808188. q^{92} +1.68703e6 q^{93} +1.88471e6 q^{94} -5.13525e6 q^{95} +947412. q^{96} +4.89911e6 q^{97} -6.12253e6 q^{98} -5.88355e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 32 q^{2} + 459 q^{3} + 1166 q^{4} - 1072 q^{5} - 864 q^{6} - 2407 q^{7} - 6645 q^{8} + 12393 q^{9}+O(q^{10}) $ 17 * q - 32 * q^2 + 459 * q^3 + 1166 * q^4 - 1072 * q^5 - 864 * q^6 - 2407 * q^7 - 6645 * q^8 + 12393 * q^9	\( 17 q - 32 q^{2} + 459 q^{3} + 1166 q^{4} - 1072 q^{5} - 864 q^{6} - 2407 q^{7} - 6645 q^{8} + 12393 q^{9} - 6391 q^{10} - 8888 q^{11} + 31482 q^{12} - 12702 q^{13} - 17555 q^{14} - 28944 q^{15} + 139226 q^{16} - 36167 q^{17} - 23328 q^{18} - 71037 q^{19} - 274883 q^{20} - 64989 q^{21} - 325182 q^{22} - 269995 q^{23} - 179415 q^{24} + 97329 q^{25} - 336906 q^{26} + 334611 q^{27} - 901362 q^{28} - 543825 q^{29} - 172557 q^{30} - 633109 q^{31} - 837062 q^{32} - 239976 q^{33} - 529288 q^{34} - 287621 q^{35} + 850014 q^{36} - 867607 q^{37} - 1727169 q^{38} - 342954 q^{39} - 815662 q^{40} - 1428939 q^{41} - 473985 q^{42} - 477060 q^{43} - 1667926 q^{44} - 781488 q^{45} + 5305549 q^{46} - 1217849 q^{47} + 3759102 q^{48} + 4350738 q^{49} + 4561369 q^{50} - 976509 q^{51} + 4175994 q^{52} - 3487068 q^{53} - 629856 q^{54} - 960484 q^{55} - 5363196 q^{56} - 1917999 q^{57} - 3082906 q^{58} - 3491443 q^{59} - 7421841 q^{60} + 998917 q^{61} - 5742614 q^{62} - 1754703 q^{63} + 17531621 q^{64} - 6075816 q^{65} - 8779914 q^{66} - 356026 q^{67} - 16149231 q^{68} - 7289865 q^{69} - 548798 q^{70} - 12879428 q^{71} - 4844205 q^{72} - 6176157 q^{73} - 5971906 q^{74} + 2627883 q^{75} - 17624580 q^{76} + 239687 q^{77} - 9096462 q^{78} - 18886490 q^{79} - 70463349 q^{80} + 9034497 q^{81} - 19351611 q^{82} - 22824893 q^{83} - 24336774 q^{84} - 7973079 q^{85} - 27502196 q^{86} - 14683275 q^{87} - 62527651 q^{88} - 30609647 q^{89} - 4659039 q^{90} - 36301521 q^{91} - 41388548 q^{92} - 17093943 q^{93} + 1010176 q^{94} - 29303629 q^{95} - 22600674 q^{96} - 26249806 q^{97} - 93110852 q^{98} - 6479352 q^{99}+O(q^{100}) \) 17 * q - 32 * q^2 + 459 * q^3 + 1166 * q^4 - 1072 * q^5 - 864 * q^6 - 2407 * q^7 - 6645 * q^8 + 12393 * q^9 - 6391 * q^10 - 8888 * q^11 + 31482 * q^12 - 12702 * q^13 - 17555 * q^14 - 28944 * q^15 + 139226 * q^16 - 36167 * q^17 - 23328 * q^18 - 71037 * q^19 - 274883 * q^20 - 64989 * q^21 - 325182 * q^22 - 269995 * q^23 - 179415 * q^24 + 97329 * q^25 - 336906 * q^26 + 334611 * q^27 - 901362 * q^28 - 543825 * q^29 - 172557 * q^30 - 633109 * q^31 - 837062 * q^32 - 239976 * q^33 - 529288 * q^34 - 287621 * q^35 + 850014 * q^36 - 867607 * q^37 - 1727169 * q^38 - 342954 * q^39 - 815662 * q^40 - 1428939 * q^41 - 473985 * q^42 - 477060 * q^43 - 1667926 * q^44 - 781488 * q^45 + 5305549 * q^46 - 1217849 * q^47 + 3759102 * q^48 + 4350738 * q^49 + 4561369 * q^50 - 976509 * q^51 + 4175994 * q^52 - 3487068 * q^53 - 629856 * q^54 - 960484 * q^55 - 5363196 * q^56 - 1917999 * q^57 - 3082906 * q^58 - 3491443 * q^59 - 7421841 * q^60 + 998917 * q^61 - 5742614 * q^62 - 1754703 * q^63 + 17531621 * q^64 - 6075816 * q^65 - 8779914 * q^66 - 356026 * q^67 - 16149231 * q^68 - 7289865 * q^69 - 548798 * q^70 - 12879428 * q^71 - 4844205 * q^72 - 6176157 * q^73 - 5971906 * q^74 + 2627883 * q^75 - 17624580 * q^76 + 239687 * q^77 - 9096462 * q^78 - 18886490 * q^79 - 70463349 * q^80 + 9034497 * q^81 - 19351611 * q^82 - 22824893 * q^83 - 24336774 * q^84 - 7973079 * q^85 - 27502196 * q^86 - 14683275 * q^87 - 62527651 * q^88 - 30609647 * q^89 - 4659039 * q^90 - 36301521 * q^91 - 41388548 * q^92 - 17093943 * q^93 + 1010176 * q^94 - 29303629 * q^95 - 22600674 * q^96 - 26249806 * q^97 - 93110852 * q^98 - 6479352 * 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 $

$2$	10.7630	0.951324	0.475662	−	0.879628i	$-0.342208\pi$
$2$	10.7630	0.951324	0.475662	+	0.879628i	$0.342208\pi$
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	−12.1577	−0.0949820
$5$	451.863	1.61663	0.808317	−	0.588748i	$-0.200379\pi$
$5$	451.863	1.61663	0.808317	+	0.588748i	$0.200379\pi$
$6$	290.601	0.549247
$7$	−504.672	−0.556117	−0.278058	−	0.960564i	$-0.589691\pi$
$7$	−504.672	−0.556117	−0.278058	+	0.960564i	$0.589691\pi$
$8$	−1508.52	−1.04168
$9$	729.000	0.333333
$10$	4863.40	1.53794
$11$	−8070.72	−1.82826	−0.914129	−	0.405422i	$-0.867124\pi$
$11$	−8070.72	−1.82826	−0.914129	+	0.405422i	$0.867124\pi$
$12$	−328.258	−0.0548379
$13$	−4674.69	−0.590134	−0.295067	−	0.955477i	$-0.595342\pi$
$13$	−4674.69	−0.590134	−0.295067	+	0.955477i	$0.595342\pi$
$14$	−5431.79	−0.529048
$15$	12200.3	0.933364
$16$	−14680.0	−0.895996
$17$	−13499.0	−0.666391	−0.333196	−	0.942858i	$-0.608127\pi$
$17$	−13499.0	−0.666391	−0.333196	+	0.942858i	$0.608127\pi$
$18$	7846.23	0.317108
$19$	−11364.6	−0.380117	−0.190059	−	0.981773i	$-0.560868\pi$
$19$	−11364.6	−0.380117	−0.190059	+	0.981773i	$0.560868\pi$
$20$	−5493.61	−0.153551
$21$	−13626.1	−0.321074
$22$	−86865.2	−1.73927
$23$	−66475.4	−1.13924	−0.569618	−	0.821910i	$-0.692909\pi$
$23$	−66475.4	−1.13924	−0.569618	+	0.821910i	$0.692909\pi$
$24$	−40730.0	−0.601416
$25$	126055.	1.61350
$26$	−50313.7	−0.561409
$27$	19683.0	0.192450
$28$	6135.65	0.0528211
$29$	−174542.	−1.32894	−0.664472	−	0.747313i	$-0.731343\pi$
$29$	−174542.	−1.32894	−0.664472	+	0.747313i	$0.731343\pi$
$30$	131312.	0.887932
$31$	62482.4	0.376697	0.188348	−	0.982102i	$-0.439687\pi$
$31$	62482.4	0.376697	0.188348	+	0.982102i	$0.439687\pi$
$32$	35089.3	0.189300
$33$	−217909.	−1.05555
$34$	−145289.	−0.633954
$35$	−228043.	−0.899038
$36$	−8862.96	−0.0316607
$37$	277403.	0.900336	0.450168	−	0.892944i	$-0.351364\pi$
$37$	277403.	0.900336	0.450168	+	0.892944i	$0.351364\pi$
$38$	−122318.	−0.361615
$39$	−126217.	−0.340714
$40$	−681643.	−1.68402
$41$	529842.	1.20061	0.600307	−	0.799770i	$-0.295045\pi$
$41$	529842.	1.20061	0.600307	+	0.799770i	$0.295045\pi$
$42$	−146658.	−0.305446
$43$	675111.	1.29490	0.647449	−	0.762109i	$-0.275836\pi$
$43$	675111.	1.29490	0.647449	+	0.762109i	$0.275836\pi$
$44$	98121.3	0.173652
$45$	329408.	0.538878
$46$	−715475.	−1.08378
$47$	175110.	0.246019	0.123010	−	0.992405i	$-0.460745\pi$
$47$	175110.	0.246019	0.123010	+	0.992405i	$0.460745\pi$
$48$	−396360.	−0.517304
$49$	−568849.	−0.690734
$50$	1.35673e6	1.53497
$51$	−364472.	−0.384741
$52$	56833.4	0.0560521
$53$	−313480.	−0.289231	−0.144615	−	0.989488i	$-0.546195\pi$
$53$	−313480.	−0.289231	−0.144615	+	0.989488i	$0.546195\pi$
$54$	211848.	0.183082
$55$	−3.64686e6	−2.95563
$56$	761307.	0.579298
$57$	−306845.	−0.219461
$58$	−1.87860e6	−1.26426
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	−148328.	−0.0886528
$61$	−3.01895e6	−1.70295	−0.851474	−	0.524396i	$-0.824291\pi$
$61$	−3.01895e6	−1.70295	−0.851474	+	0.524396i	$0.824291\pi$
$62$	672499.	0.358361
$63$	−367906.	−0.185372
$64$	2.25671e6	1.07608
$65$	−2.11232e6	−0.954031
$66$	−2.34536e6	−1.00417
$67$	−885587.	−0.359724	−0.179862	−	0.983692i	$-0.557565\pi$
$67$	−885587.	−0.359724	−0.179862	+	0.983692i	$0.557565\pi$
$68$	164116.	0.0632952
$69$	−1.79484e6	−0.657738
$70$	−2.45442e6	−0.855276
$71$	−1.15026e6	−0.381411	−0.190706	−	0.981647i	$-0.561078\pi$
$71$	−1.15026e6	−0.381411	−0.190706	+	0.981647i	$0.561078\pi$
$72$	−1.09971e6	−0.347228
$73$	33498.4	0.0100785	0.00503923	−	0.999987i	$-0.498396\pi$
$73$	33498.4	0.0100785	0.00503923	+	0.999987i	$0.498396\pi$
$74$	2.98569e6	0.856511
$75$	3.40349e6	0.931558
$76$	138168.	0.0361043
$77$	4.07307e6	1.01673
$78$	−1.35847e6	−0.324130
$79$	−694337.	−0.158444	−0.0792219	−	0.996857i	$-0.525244\pi$
$79$	−694337.	−0.158444	−0.0792219	+	0.996857i	$0.525244\pi$
$80$	−6.63335e6	−1.44850
$81$	531441.	0.111111
$82$	5.70270e6	1.14217
$83$	−672731.	−0.129142	−0.0645711	−	0.997913i	$-0.520568\pi$
$83$	−672731.	−0.129142	−0.0645711	+	0.997913i	$0.520568\pi$
$84$	165663.	0.0304963
$85$	−6.09968e6	−1.07731
$86$	7.26622e6	1.23187
$87$	−4.71263e6	−0.767266
$88$	1.21748e7	1.90447
$89$	7.67580e6	1.15414	0.577070	−	0.816695i	$-0.304196\pi$
$89$	7.67580e6	1.15414	0.577070	+	0.816695i	$0.304196\pi$
$90$	3.54542e6	0.512648
$91$	2.35918e6	0.328184
$92$	808188.	0.108207
$93$	1.68703e6	0.217486
$94$	1.88471e6	0.234044
$95$	−5.13525e6	−0.614510
$96$	947412.	0.109292
$97$	4.89911e6	0.545025	0.272512	−	0.962152i	$-0.412145\pi$
$97$	4.89911e6	0.545025	0.272512	+	0.962152i	$0.412145\pi$
$98$	−6.12253e6	−0.657112
$99$	−5.88355e6	−0.609420
$100$	−1.53254e6	−0.153254
$101$	−1.84644e7	−1.78324	−0.891621	−	0.452782i	$-0.850432\pi$
$101$	−1.84644e7	−1.78324	−0.891621	+	0.452782i	$0.850432\pi$
$102$	−3.92281e6	−0.366014
$103$	−5.21469e6	−0.470217	−0.235109	−	0.971969i	$-0.575545\pi$
$103$	−5.21469e6	−0.470217	−0.235109	+	0.971969i	$0.575545\pi$
$104$	7.05185e6	0.614733
$105$	−6.15715e6	−0.519060
$106$	−3.37399e6	−0.275152
$107$	−2.16312e6	−0.170701	−0.0853506	−	0.996351i	$-0.527201\pi$
$107$	−2.16312e6	−0.170701	−0.0853506	+	0.996351i	$0.527201\pi$
$108$	−239300.	−0.0182793
$109$	−1.59770e7	−1.18169	−0.590845	−	0.806785i	$-0.701206\pi$
$109$	−1.59770e7	−1.18169	−0.590845	+	0.806785i	$0.701206\pi$
$110$	−3.92511e7	−2.81176
$111$	7.48987e6	0.519809
$112$	7.40859e6	0.498279
$113$	9.29263e6	0.605849	0.302924	−	0.953015i	$-0.402037\pi$
$113$	9.29263e6	0.605849	0.302924	+	0.953015i	$0.402037\pi$
$114$	−3.30257e6	−0.208778
$115$	−3.00378e7	−1.84173
$116$	2.12203e6	0.126226
$117$	−3.40785e6	−0.196711
$118$	−2.21050e6	−0.123852
$119$	6.81255e6	0.370591
$120$	−1.84044e7	−0.972269
$121$	4.56493e7	2.34253
$122$	−3.24930e7	−1.62006
$123$	1.43057e7	0.693175
$124$	−759642.	−0.0357794
$125$	2.16578e7	0.991813
$126$	−3.95977e6	−0.176349
$127$	8.17874e6	0.354302	0.177151	−	0.984184i	$-0.443312\pi$
$127$	8.17874e6	0.354302	0.177151	+	0.984184i	$0.443312\pi$
$128$	1.97975e7	0.834403
$129$	1.82280e7	0.747610
$130$	−2.27349e7	−0.907593
$131$	4.40912e6	0.171357	0.0856787	−	0.996323i	$-0.472694\pi$
$131$	4.40912e6	0.171357	0.0856787	+	0.996323i	$0.472694\pi$
$132$	2.64928e6	0.100258
$133$	5.73541e6	0.211390
$134$	−9.53158e6	−0.342214
$135$	8.89402e6	0.311121
$136$	2.03634e7	0.694168
$137$	−8.21867e6	−0.273073	−0.136537	−	0.990635i	$-0.543597\pi$
$137$	−8.21867e6	−0.273073	−0.136537	+	0.990635i	$0.543597\pi$
$138$	−1.93178e7	−0.625722
$139$	−5.56805e7	−1.75854	−0.879268	−	0.476328i	$-0.841968\pi$
$139$	−5.56805e7	−1.75854	−0.879268	+	0.476328i	$0.841968\pi$
$140$	2.77247e6	0.0853924
$141$	4.72798e6	0.142039
$142$	−1.23803e7	−0.362846
$143$	3.77281e7	1.07892
$144$	−1.07017e7	−0.298665
$145$	−7.88690e7	−2.14842
$146$	360544.	0.00958789
$147$	−1.53589e7	−0.398795
$148$	−3.37258e6	−0.0855157
$149$	2.85493e7	0.707039	0.353520	−	0.935427i	$-0.384985\pi$
$149$	2.85493e7	0.707039	0.353520	+	0.935427i	$0.384985\pi$
$150$	3.66318e7	0.886213
$151$	−1.41537e7	−0.334541	−0.167271	−	0.985911i	$-0.553495\pi$
$151$	−1.41537e7	−0.334541	−0.167271	+	0.985911i	$0.553495\pi$
$152$	1.71437e7	0.395962
$153$	−9.84074e6	−0.222130
$154$	4.38384e7	0.967236
$155$	2.82335e7	0.608981
$156$	1.53450e6	0.0323617
$157$	6.04002e7	1.24563	0.622816	−	0.782368i	$-0.285989\pi$
$157$	6.04002e7	1.24563	0.622816	+	0.782368i	$0.285989\pi$
$158$	−7.47315e6	−0.150732
$159$	−8.46397e6	−0.166988
$160$	1.58556e7	0.306029
$161$	3.35483e7	0.633548
$162$	5.71990e6	0.105703
$163$	7.29006e7	1.31848	0.659241	−	0.751931i	$-0.270878\pi$
$163$	7.29006e7	1.31848	0.659241	+	0.751931i	$0.270878\pi$
$164$	−6.44166e6	−0.114037
$165$	−9.84652e7	−1.70643
$166$	−7.24061e6	−0.122856
$167$	−9.50243e7	−1.57880	−0.789400	−	0.613879i	$-0.789608\pi$
$167$	−9.50243e7	−1.57880	−0.789400	+	0.613879i	$0.789608\pi$
$168$	2.05553e7	0.334458
$169$	−4.08958e7	−0.651742
$170$	−6.56509e7	−1.02487
$171$	−8.28481e6	−0.126706
$172$	−8.20779e6	−0.122992
$173$	5.86358e7	0.860996	0.430498	−	0.902592i	$-0.358338\pi$
$173$	5.86358e7	0.860996	0.430498	+	0.902592i	$0.358338\pi$
$174$	−5.07221e7	−0.729919
$175$	−6.36165e7	−0.897298
$176$	1.18478e8	1.63811
$177$	−5.54523e6	−0.0751646
$178$	8.26147e7	1.09796
$179$	−3.55324e7	−0.463061	−0.231531	−	0.972828i	$-0.574373\pi$
$179$	−3.55324e7	−0.463061	−0.231531	+	0.972828i	$0.574373\pi$
$180$	−4.00484e6	−0.0511837
$181$	1.28354e8	1.60892	0.804459	−	0.594008i	$-0.202455\pi$
$181$	1.28354e8	1.60892	0.804459	+	0.594008i	$0.202455\pi$
$182$	2.53919e7	0.312209
$183$	−8.15117e7	−0.983198
$184$	1.00279e8	1.18672
$185$	1.25348e8	1.45551
$186$	1.81575e7	0.206900
$187$	1.08946e8	1.21834
$188$	−2.12894e6	−0.0233674
$189$	−9.93346e6	−0.107025
$190$	−5.52708e7	−0.584599
$191$	−8.71206e7	−0.904699	−0.452350	−	0.891841i	$-0.649414\pi$
$191$	−8.71206e7	−0.904699	−0.452350	+	0.891841i	$0.649414\pi$
$192$	6.09311e7	0.621276
$193$	3.34478e7	0.334902	0.167451	−	0.985880i	$-0.446446\pi$
$193$	3.34478e7	0.334902	0.167451	+	0.985880i	$0.446446\pi$
$194$	5.27292e7	0.518495
$195$	−5.70326e7	−0.550810
$196$	6.91589e6	0.0656073
$197$	1.43873e8	1.34074	0.670372	−	0.742025i	$-0.266134\pi$
$197$	1.43873e8	1.34074	0.670372	+	0.742025i	$0.266134\pi$
$198$	−6.33247e7	−0.579756
$199$	−3.39107e7	−0.305036	−0.152518	−	0.988301i	$-0.548738\pi$
$199$	−3.39107e7	−0.305036	−0.152518	+	0.988301i	$0.548738\pi$
$200$	−1.90156e8	−1.68076
$201$	−2.39109e7	−0.207687
$202$	−1.98732e8	−1.69644
$203$	8.80864e7	0.739048
$204$	4.43114e6	0.0365435
$205$	2.39416e8	1.94095
$206$	−5.61258e7	−0.447329
$207$	−4.84606e7	−0.379745
$208$	6.86244e7	0.528758
$209$	9.17207e7	0.694953
$210$	−6.62694e7	−0.493794
$211$	−1.13428e8	−0.831249	−0.415624	−	0.909536i	$-0.636437\pi$
$211$	−1.13428e8	−0.831249	−0.415624	+	0.909536i	$0.636437\pi$
$212$	3.81120e6	0.0274717
$213$	−3.10572e7	−0.220208
$214$	−2.32816e7	−0.162392
$215$	3.05058e8	2.09338
$216$	−2.96922e7	−0.200472
$217$	−3.15331e7	−0.209487
$218$	−1.71961e8	−1.12417
$219$	904458.	0.00581881
$220$	4.43374e7	0.280731
$221$	6.31034e7	0.393260
$222$	8.06135e7	0.494507
$223$	−1.58906e8	−0.959565	−0.479782	−	0.877387i	$-0.659284\pi$
$223$	−1.58906e8	−0.959565	−0.479782	+	0.877387i	$0.659284\pi$
$224$	−1.77086e7	−0.105273
$225$	9.18942e7	0.537835
$226$	1.00017e8	0.576358
$227$	−2.46698e7	−0.139983	−0.0699915	−	0.997548i	$-0.522297\pi$
$227$	−2.46698e7	−0.139983	−0.0699915	+	0.997548i	$0.522297\pi$
$228$	3.73053e6	0.0208448
$229$	2.79166e6	0.0153617	0.00768084	−	0.999971i	$-0.497555\pi$
$229$	2.79166e6	0.0153617	0.00768084	+	0.999971i	$0.497555\pi$
$230$	−3.23297e8	−1.75208
$231$	1.09973e8	0.587007
$232$	2.63300e8	1.38434
$233$	1.72078e8	0.891207	0.445604	−	0.895230i	$-0.352989\pi$
$233$	1.72078e8	0.891207	0.445604	+	0.895230i	$0.352989\pi$
$234$	−3.66787e7	−0.187136
$235$	7.91259e7	0.397723
$236$	2.49694e6	0.0123656
$237$	−1.87471e7	−0.0914776
$238$	7.33235e7	0.352553
$239$	−3.26143e8	−1.54531	−0.772656	−	0.634825i	$-0.781072\pi$
$239$	−3.26143e8	−1.54531	−0.772656	+	0.634825i	$0.781072\pi$
$240$	−1.79100e8	−0.836291
$241$	4.12780e8	1.89958	0.949792	−	0.312882i	$-0.101294\pi$
$241$	4.12780e8	1.89958	0.949792	+	0.312882i	$0.101294\pi$
$242$	4.91324e8	2.22851
$243$	1.43489e7	0.0641500
$244$	3.67035e7	0.161750
$245$	−2.57042e8	−1.11666
$246$	1.53973e8	0.659434
$247$	5.31261e7	0.224320
$248$	−9.42559e7	−0.392399
$249$	−1.81637e7	−0.0745603
$250$	2.33103e8	0.943536
$251$	4.66684e8	1.86279	0.931397	−	0.364005i	$-0.118591\pi$
$251$	4.66684e8	1.86279	0.931397	+	0.364005i	$0.118591\pi$
$252$	4.47289e6	0.0176070
$253$	5.36504e8	2.08282
$254$	8.80278e7	0.337056
$255$	−1.64691e8	−0.621985
$256$	−7.57777e7	−0.282294
$257$	−9.36406e7	−0.344111	−0.172055	−	0.985087i	$-0.555041\pi$
$257$	−9.36406e7	−0.344111	−0.172055	+	0.985087i	$0.555041\pi$
$258$	1.96188e8	0.711219
$259$	−1.39997e8	−0.500692
$260$	2.56809e7	0.0906158
$261$	−1.27241e8	−0.442981
$262$	4.74554e7	0.163016
$263$	−5.00867e8	−1.69776	−0.848882	−	0.528582i	$-0.822724\pi$
$263$	−5.00867e8	−1.69776	−0.848882	+	0.528582i	$0.822724\pi$
$264$	3.28720e8	1.09954
$265$	−1.41650e8	−0.467581
$266$	6.17303e7	0.201100
$267$	2.07247e8	0.666343
$268$	1.07667e7	0.0341673
$269$	7.84305e7	0.245670	0.122835	−	0.992427i	$-0.460801\pi$
$269$	7.84305e7	0.245670	0.122835	+	0.992427i	$0.460801\pi$
$270$	9.57264e7	0.295977
$271$	3.97558e8	1.21341	0.606705	−	0.794927i	$-0.292491\pi$
$271$	3.97558e8	1.21341	0.606705	+	0.794927i	$0.292491\pi$
$272$	1.98165e8	0.597084
$273$	6.36980e7	0.189477
$274$	−8.84576e7	−0.259781
$275$	−1.01735e9	−2.94990
$276$	2.18211e7	0.0624733
$277$	−9.64793e7	−0.272744	−0.136372	−	0.990658i	$-0.543544\pi$
$277$	−9.64793e7	−0.272744	−0.136372	+	0.990658i	$0.543544\pi$
$278$	−5.99289e8	−1.67294
$279$	4.55497e7	0.125566
$280$	3.44006e8	0.936512
$281$	−5.37086e8	−1.44402	−0.722008	−	0.691885i	$-0.756781\pi$
$281$	−5.37086e8	−1.44402	−0.722008	+	0.691885i	$0.756781\pi$
$282$	5.08873e7	0.135125
$283$	−6.18129e8	−1.62116	−0.810582	−	0.585626i	$-0.800849\pi$
$283$	−6.18129e8	−1.62116	−0.810582	+	0.585626i	$0.800849\pi$
$284$	1.39846e7	0.0362272
$285$	−1.38652e8	−0.354788
$286$	4.06067e8	1.02640
$287$	−2.67397e8	−0.667682
$288$	2.55801e7	0.0630999
$289$	−2.28117e8	−0.555923
$290$	−8.48867e8	−2.04384
$291$	1.32276e8	0.314670
$292$	−407264.	−0.000957273 0
$293$	3.39223e8	0.787858	0.393929	−	0.919141i	$-0.371116\pi$
$293$	3.39223e8	0.787858	0.393929	+	0.919141i	$0.371116\pi$
$294$	−1.65308e8	−0.379384
$295$	−9.28031e7	−0.210468
$296$	−4.18467e8	−0.937864
$297$	−1.58856e8	−0.351849
$298$	3.07276e8	0.672623
$299$	3.10752e8	0.672302
$300$	−4.13786e7	−0.0884812
$301$	−3.40710e8	−0.720115
$302$	−1.52336e8	−0.318257
$303$	−4.98539e8	−1.02956
$304$	1.66833e8	0.340584
$305$	−1.36415e9	−2.75304
$306$	−1.05916e8	−0.211318
$307$	−9.62816e7	−0.189915	−0.0949575	−	0.995481i	$-0.530272\pi$
$307$	−9.62816e7	−0.189915	−0.0949575	+	0.995481i	$0.530272\pi$
$308$	−4.95191e7	−0.0965707
$309$	−1.40797e8	−0.271480
$310$	3.03877e8	0.579338
$311$	−7.91196e8	−1.49150	−0.745749	−	0.666227i	$-0.767908\pi$
$311$	−7.91196e8	−1.49150	−0.745749	+	0.666227i	$0.767908\pi$
$312$	1.90400e8	0.354916
$313$	−8.83580e7	−0.162870	−0.0814349	−	0.996679i	$-0.525950\pi$
$313$	−8.83580e7	−0.162870	−0.0814349	+	0.996679i	$0.525950\pi$
$314$	6.50088e8	1.18500
$315$	−1.66243e8	−0.299679
$316$	8.44154e6	0.0150493
$317$	−3.65056e8	−0.643654	−0.321827	−	0.946799i	$-0.604297\pi$
$317$	−3.65056e8	−0.643654	−0.321827	+	0.946799i	$0.604297\pi$
$318$	−9.10978e7	−0.158859
$319$	1.40868e9	2.42965
$320$	1.01972e9	1.73963
$321$	−5.84041e7	−0.0985544
$322$	3.61080e8	0.602710
$323$	1.53411e8	0.253307
$324$	−6.46110e6	−0.0105536
$325$	−5.89268e8	−0.952184
$326$	7.84630e8	1.25430
$327$	−4.31380e8	−0.682249
$328$	−7.99277e8	−1.25066
$329$	−8.83733e7	−0.136816
$330$	−1.05978e9	−1.62337
$331$	8.84610e8	1.34077	0.670384	−	0.742014i	$-0.266129\pi$
$331$	8.84610e8	1.34077	0.670384	+	0.742014i	$0.266129\pi$
$332$	8.17886e6	0.0122662
$333$	2.02226e8	0.300112
$334$	−1.02275e9	−1.50195
$335$	−4.00164e8	−0.581542
$336$	2.00032e8	0.287681
$337$	−1.01312e9	−1.44197	−0.720983	−	0.692953i	$-0.756309\pi$
$337$	−1.01312e9	−1.44197	−0.720983	+	0.692953i	$0.756309\pi$
$338$	−4.40162e8	−0.620018
$339$	2.50901e8	0.349787
$340$	7.41581e7	0.102325
$341$	−5.04278e8	−0.688699
$342$	−8.91695e7	−0.120538
$343$	7.02701e8	0.940246
$344$	−1.01842e9	−1.34887
$345$	−8.11019e8	−1.06332
$346$	6.31097e8	0.819086
$347$	−4.59045e8	−0.589796	−0.294898	−	0.955529i	$-0.595286\pi$
$347$	−4.59045e8	−0.589796	−0.294898	+	0.955529i	$0.595286\pi$
$348$	5.72947e7	0.0728765
$349$	6.65833e8	0.838448	0.419224	−	0.907883i	$-0.362302\pi$
$349$	6.65833e8	0.838448	0.419224	+	0.907883i	$0.362302\pi$
$350$	−6.84705e8	−0.853621
$351$	−9.20118e7	−0.113571
$352$	−2.83196e8	−0.346089
$353$	−7.46486e7	−0.0903255	−0.0451627	−	0.998980i	$-0.514381\pi$
$353$	−7.46486e7	−0.0903255	−0.0451627	+	0.998980i	$0.514381\pi$
$354$	−5.96834e7	−0.0715059
$355$	−5.19762e8	−0.616603
$356$	−9.33201e7	−0.109623
$357$	1.83939e8	0.213961
$358$	−3.82435e8	−0.440521
$359$	−1.55696e9	−1.77601	−0.888005	−	0.459833i	$-0.847909\pi$
$359$	−1.55696e9	−1.77601	−0.888005	+	0.459833i	$0.847909\pi$
$360$	−4.96918e8	−0.561340
$361$	−7.64717e8	−0.855511
$362$	1.38147e9	1.53060
$363$	1.23253e9	1.35246
$364$	−2.86822e7	−0.0311715
$365$	1.51367e7	0.0162932
$366$	−8.77311e8	−0.935340
$367$	−4.78302e7	−0.0505092	−0.0252546	−	0.999681i	$-0.508040\pi$
$367$	−4.78302e7	−0.0505092	−0.0252546	+	0.999681i	$0.508040\pi$
$368$	9.75859e8	1.02075
$369$	3.86255e8	0.400205
$370$	1.34912e9	1.38467
$371$	1.58205e8	0.160846
$372$	−2.05103e7	−0.0206573
$373$	−1.46088e9	−1.45759	−0.728793	−	0.684735i	$-0.759918\pi$
$373$	−1.46088e9	−1.45759	−0.728793	+	0.684735i	$0.759918\pi$
$374$	1.17259e9	1.15903
$375$	5.84761e8	0.572623
$376$	−2.64157e8	−0.256274
$377$	8.15928e8	0.784255
$378$	−1.06914e8	−0.101815
$379$	8.99699e8	0.848907	0.424453	−	0.905450i	$-0.360466\pi$
$379$	8.99699e8	0.848907	0.424453	+	0.905450i	$0.360466\pi$
$380$	6.24329e7	0.0583674
$381$	2.20826e8	0.204556
$382$	−9.37680e8	−0.860662
$383$	7.51806e8	0.683770	0.341885	−	0.939742i	$-0.388935\pi$
$383$	7.51806e8	0.683770	0.341885	+	0.939742i	$0.388935\pi$
$384$	5.34533e8	0.481743
$385$	1.84047e9	1.64367
$386$	3.59999e8	0.318600
$387$	4.92156e8	0.431633
$388$	−5.95619e7	−0.0517675
$389$	1.98944e9	1.71359	0.856794	−	0.515660i	$-0.172453\pi$
$389$	1.98944e9	1.71359	0.856794	+	0.515660i	$0.172453\pi$
$390$	−6.13842e8	−0.523999
$391$	8.97349e8	0.759176
$392$	8.58119e8	0.719526
$393$	1.19046e8	0.0989332
$394$	1.54850e9	1.27548
$395$	−3.13745e8	−0.256146
$396$	7.15305e7	0.0578839
$397$	−2.39171e9	−1.91841	−0.959207	−	0.282704i	$-0.908769\pi$
$397$	−2.39171e9	−1.91841	−0.959207	+	0.282704i	$0.908769\pi$
$398$	−3.64981e8	−0.290188
$399$	1.54856e8	0.122046
$400$	−1.85049e9	−1.44569
$401$	1.23670e9	0.957767	0.478883	−	0.877879i	$-0.341042\pi$
$401$	1.23670e9	0.957767	0.478883	+	0.877879i	$0.341042\pi$
$402$	−2.57353e8	−0.197577
$403$	−2.92086e8	−0.222302
$404$	2.24485e8	0.169376
$405$	2.40138e8	0.179626
$406$	9.48075e8	0.703075
$407$	−2.23884e9	−1.64605
$408$	5.49813e8	0.400778
$409$	1.08001e9	0.780545	0.390272	−	0.920699i	$-0.372381\pi$
$409$	1.08001e9	0.780545	0.390272	+	0.920699i	$0.372381\pi$
$410$	2.57684e9	1.84648
$411$	−2.21904e8	−0.157659
$412$	6.33986e7	0.0446622
$413$	1.03649e8	0.0724003
$414$	−5.21581e8	−0.361261
$415$	−3.03982e8	−0.208776
$416$	−1.64032e8	−0.111712
$417$	−1.50337e9	−1.01529
$418$	9.87190e8	0.661125
$419$	−1.95040e9	−1.29531	−0.647656	−	0.761933i	$-0.724251\pi$
$419$	−1.95040e9	−1.29531	−0.647656	+	0.761933i	$0.724251\pi$
$420$	7.48568e7	0.0493013
$421$	4.11047e8	0.268475	0.134238	−	0.990949i	$-0.457141\pi$
$421$	4.11047e8	0.268475	0.134238	+	0.990949i	$0.457141\pi$
$422$	−1.22082e9	−0.790787
$423$	1.27655e8	0.0820065
$424$	4.72891e8	0.301287
$425$	−1.70161e9	−1.07523
$426$	−3.34268e8	−0.209489
$427$	1.52358e9	0.947039
$428$	2.62985e7	0.0162135
$429$	1.01866e9	0.622914
$430$	3.28334e9	1.99148
$431$	−2.36621e9	−1.42358	−0.711792	−	0.702390i	$-0.752116\pi$
$431$	−2.36621e9	−1.42358	−0.711792	+	0.702390i	$0.752116\pi$
$432$	−2.88947e8	−0.172435
$433$	−2.22967e8	−0.131987	−0.0659937	−	0.997820i	$-0.521022\pi$
$433$	−2.22967e8	−0.131987	−0.0659937	+	0.997820i	$0.521022\pi$
$434$	−3.39391e8	−0.199291
$435$	−2.12946e9	−1.24039
$436$	1.94244e8	0.112239
$437$	7.55468e8	0.433043
$438$	9.73469e6	0.00553557
$439$	−6.34602e8	−0.357994	−0.178997	−	0.983850i	$-0.557285\pi$
$439$	−6.34602e8	−0.357994	−0.178997	+	0.983850i	$0.557285\pi$
$440$	5.50135e9	3.07882
$441$	−4.14691e8	−0.230245
$442$	6.79182e8	0.374118
$443$	−1.44884e9	−0.791788	−0.395894	−	0.918296i	$-0.629565\pi$
$443$	−1.44884e9	−0.791788	−0.395894	+	0.918296i	$0.629565\pi$
$444$	−9.10596e7	−0.0493725
$445$	3.46841e9	1.86582
$446$	−1.71031e9	−0.912857
$447$	7.70831e8	0.408209
$448$	−1.13890e9	−0.598427
$449$	3.21927e9	1.67840	0.839199	−	0.543825i	$-0.183024\pi$
$449$	3.21927e9	1.67840	0.839199	+	0.543825i	$0.183024\pi$
$450$	9.89057e8	0.511656
$451$	−4.27621e9	−2.19503
$452$	−1.12977e8	−0.0575447
$453$	−3.82149e8	−0.193147
$454$	−2.65521e8	−0.133169
$455$	1.06603e9	0.530553
$456$	4.62881e8	0.228609
$457$	−1.03131e9	−0.505454	−0.252727	−	0.967538i	$-0.581328\pi$
$457$	−1.03131e9	−0.505454	−0.252727	+	0.967538i	$0.581328\pi$
$458$	3.00467e7	0.0146139
$459$	−2.65700e8	−0.128247
$460$	3.65190e8	0.174931
$461$	3.21305e9	1.52744	0.763720	−	0.645547i	$-0.223371\pi$
$461$	3.21305e9	1.52744	0.763720	+	0.645547i	$0.223371\pi$
$462$	1.18364e9	0.558434
$463$	−1.66945e9	−0.781698	−0.390849	−	0.920455i	$-0.627819\pi$
$463$	−1.66945e9	−0.781698	−0.390849	+	0.920455i	$0.627819\pi$
$464$	2.56228e9	1.19073
$465$	7.62304e8	0.351595
$466$	1.85207e9	0.847827
$467$	3.79498e8	0.172425	0.0862125	−	0.996277i	$-0.472524\pi$
$467$	3.79498e8	0.172425	0.0862125	+	0.996277i	$0.472524\pi$
$468$	4.14316e7	0.0186840
$469$	4.46931e8	0.200049
$470$	8.51632e8	0.378364
$471$	1.63081e9	0.719166
$472$	3.09818e8	0.135616
$473$	−5.44863e9	−2.36741
$474$	−2.01775e8	−0.0870249
$475$	−1.43257e9	−0.613321
$476$	−8.28249e7	−0.0351995
$477$	−2.28527e8	−0.0964103
$478$	−3.51028e9	−1.47009
$479$	1.60692e9	0.668068	0.334034	−	0.942561i	$-0.391590\pi$
$479$	1.60692e9	0.668068	0.334034	+	0.942561i	$0.391590\pi$
$480$	4.28100e8	0.176686
$481$	−1.29677e9	−0.531319
$482$	4.44275e9	1.80712
$483$	9.05803e8	0.365779
$484$	−5.54990e8	−0.222498
$485$	2.21373e9	0.881105
$486$	1.54437e8	0.0610275
$487$	4.45492e9	1.74779	0.873893	−	0.486118i	$-0.161587\pi$
$487$	4.45492e9	1.74779	0.873893	+	0.486118i	$0.161587\pi$
$488$	4.55414e9	1.77393
$489$	1.96832e9	0.761226
$490$	−2.76654e9	−1.06231
$491$	−3.60524e9	−1.37451	−0.687256	−	0.726415i	$-0.741185\pi$
$491$	−3.60524e9	−1.37451	−0.687256	+	0.726415i	$0.741185\pi$
$492$	−1.73925e8	−0.0658391
$493$	2.35613e9	0.885596
$494$	5.71796e8	0.213401
$495$	−2.65856e9	−0.985208
$496$	−9.17242e8	−0.337519
$497$	5.80507e8	0.212109
$498$	−1.95496e8	−0.0709310
$499$	−2.51714e9	−0.906893	−0.453446	−	0.891284i	$-0.649806\pi$
$499$	−2.51714e9	−0.906893	−0.453446	+	0.891284i	$0.649806\pi$
$500$	−2.63309e8	−0.0942044
$501$	−2.56566e9	−0.911520
$502$	5.02292e9	1.77212
$503$	3.07735e9	1.07817	0.539087	−	0.842250i	$-0.318770\pi$
$503$	3.07735e9	1.07817	0.539087	+	0.842250i	$0.318770\pi$
$504$	5.54993e8	0.193099
$505$	−8.34338e9	−2.88285
$506$	5.77440e9	1.98143
$507$	−1.10419e9	−0.376283
$508$	−9.94346e7	−0.0336523
$509$	−5.06424e9	−1.70217	−0.851083	−	0.525031i	$-0.824054\pi$
$509$	−5.06424e9	−1.70217	−0.851083	+	0.525031i	$0.824054\pi$
$510$	−1.77257e9	−0.591710
$511$	−1.69057e7	−0.00560481
$512$	−3.34968e9	−1.10296
$513$	−2.23690e8	−0.0731536
$514$	−1.00785e9	−0.327361
$515$	−2.35633e9	−0.760169
$516$	−2.21610e8	−0.0710095
$517$	−1.41327e9	−0.449787
$518$	−1.50679e9	−0.476320
$519$	1.58317e9	0.497096
$520$	3.18647e9	0.993798
$521$	−3.99436e9	−1.23741	−0.618707	−	0.785622i	$-0.712343\pi$
$521$	−3.99436e9	−1.23741	−0.618707	+	0.785622i	$0.712343\pi$
$522$	−1.36950e9	−0.421419
$523$	6.31987e9	1.93175	0.965877	−	0.259001i	$-0.0833931\pi$
$523$	6.31987e9	1.93175	0.965877	+	0.259001i	$0.0833931\pi$
$524$	−5.36048e7	−0.0162759
$525$	−1.71764e9	−0.518055
$526$	−5.39084e9	−1.61513
$527$	−8.43448e8	−0.251027
$528$	3.19891e9	0.945765
$529$	1.01415e9	0.297857
$530$	−1.52458e9	−0.444821
$531$	−1.49721e8	−0.0433963
$532$	−6.97294e7	−0.0200782
$533$	−2.47685e9	−0.708523
$534$	2.23060e9	0.633909
$535$	−9.77432e8	−0.275961
$536$	1.33592e9	0.374718
$537$	−9.59374e8	−0.267349
$538$	8.44148e8	0.233712
$539$	4.59102e9	1.26284
$540$	−1.08131e8	−0.0295509
$541$	−4.36436e9	−1.18503	−0.592516	−	0.805559i	$-0.701865\pi$
$541$	−4.36436e9	−1.18503	−0.592516	+	0.805559i	$0.701865\pi$
$542$	4.27892e9	1.15435
$543$	3.46556e9	0.928910
$544$	−4.73670e8	−0.126148
$545$	−7.21943e9	−1.91036
$546$	6.85581e8	0.180254
$547$	−2.77236e9	−0.724258	−0.362129	−	0.932128i	$-0.617950\pi$
$547$	−2.77236e9	−0.724258	−0.362129	+	0.932128i	$0.617950\pi$
$548$	9.99201e7	0.0259371
$549$	−2.20082e9	−0.567650
$550$	−1.09498e10	−2.80632
$551$	1.98360e9	0.505154
$552$	2.70754e9	0.685154
$553$	3.50412e8	0.0881133
$554$	−1.03841e9	−0.259468
$555$	3.38439e9	0.840341
$556$	6.76946e8	0.167029
$557$	6.99835e9	1.71594	0.857970	−	0.513699i	$-0.171725\pi$
$557$	6.99835e9	1.71594	0.857970	+	0.513699i	$0.171725\pi$
$558$	4.90252e8	0.119454
$559$	−3.15593e9	−0.764163
$560$	3.34767e9	0.805534
$561$	2.94155e9	0.703406
$562$	−5.78066e9	−1.37373
$563$	1.13060e9	0.267012	0.133506	−	0.991048i	$-0.457376\pi$
$563$	1.13060e9	0.267012	0.133506	+	0.991048i	$0.457376\pi$
$564$	−5.74813e7	−0.0134912
$565$	4.19899e9	0.979435
$566$	−6.65293e9	−1.54225
$567$	−2.68203e8	−0.0617908
$568$	1.73520e9	0.397310
$569$	−4.34076e9	−0.987810	−0.493905	−	0.869516i	$-0.664431\pi$
$569$	−4.34076e9	−0.987810	−0.493905	+	0.869516i	$0.664431\pi$
$570$	−1.49231e9	−0.337518
$571$	1.60830e9	0.361526	0.180763	−	0.983527i	$-0.442143\pi$
$571$	1.60830e9	0.361526	0.180763	+	0.983527i	$0.442143\pi$
$572$	−4.58686e8	−0.102478
$573$	−2.35226e9	−0.522328
$574$	−2.87799e9	−0.635182
$575$	−8.37956e9	−1.83816
$576$	1.64514e9	0.358694
$577$	4.44207e9	0.962654	0.481327	−	0.876541i	$-0.340155\pi$
$577$	4.44207e9	0.962654	0.481327	+	0.876541i	$0.340155\pi$
$578$	−2.45522e9	−0.528863
$579$	9.03091e8	0.193355
$580$	9.58865e8	0.204061
$581$	3.39509e8	0.0718181
$582$	1.42369e9	0.299353
$583$	2.53001e9	0.528789
$584$	−5.05330e7	−0.0104986
$585$	−1.53988e9	−0.318010
$586$	3.65106e9	0.749509
$587$	5.12698e8	0.104623	0.0523116	−	0.998631i	$-0.483341\pi$
$587$	5.12698e8	0.104623	0.0523116	+	0.998631i	$0.483341\pi$
$588$	1.86729e8	0.0378784
$589$	−7.10089e8	−0.143189
$590$	−9.98841e8	−0.200223
$591$	3.88456e9	0.774079
$592$	−4.07227e9	−0.806698
$593$	4.79247e9	0.943774	0.471887	−	0.881659i	$-0.343573\pi$
$593$	4.79247e9	0.943774	0.471887	+	0.881659i	$0.343573\pi$
$594$	−1.70977e9	−0.334722
$595$	3.07834e9	0.599111
$596$	−3.47094e8	−0.0671560
$597$	−9.15589e8	−0.176113
$598$	3.34462e9	0.639577
$599$	6.08958e9	1.15769	0.578846	−	0.815437i	$-0.303503\pi$
$599$	6.08958e9	1.15769	0.578846	+	0.815437i	$0.303503\pi$
$600$	−5.13422e9	−0.970388
$601$	−5.35978e9	−1.00713	−0.503566	−	0.863957i	$-0.667979\pi$
$601$	−5.35978e9	−1.00713	−0.503566	+	0.863957i	$0.667979\pi$
$602$	−3.66706e9	−0.685063
$603$	−6.45593e8	−0.119908
$604$	1.72076e8	0.0317754
$605$	2.06272e10	3.78701
$606$	−5.36578e9	−0.979441
$607$	9.02137e9	1.63724	0.818619	−	0.574337i	$-0.194740\pi$
$607$	9.02137e9	1.63724	0.818619	+	0.574337i	$0.194740\pi$
$608$	−3.98777e8	−0.0719561
$609$	2.37833e9	0.426690
$610$	−1.46824e10	−2.61904
$611$	−8.18586e8	−0.145184
$612$	1.19641e8	0.0210984
$613$	7.72450e9	1.35444	0.677219	−	0.735782i	$-0.263185\pi$
$613$	7.72450e9	1.35444	0.677219	+	0.735782i	$0.263185\pi$
$614$	−1.03628e9	−0.180671
$615$	6.46424e9	1.12061
$616$	−6.14429e9	−1.05911
$617$	−4.39185e9	−0.752748	−0.376374	−	0.926468i	$-0.622829\pi$
$617$	−4.39185e9	−0.752748	−0.376374	+	0.926468i	$0.622829\pi$
$618$	−1.51540e9	−0.258265
$619$	3.33323e9	0.564870	0.282435	−	0.959286i	$-0.408858\pi$
$619$	3.33323e9	0.564870	0.282435	+	0.959286i	$0.408858\pi$
$620$	−3.43254e8	−0.0578422
$621$	−1.30843e9	−0.219246
$622$	−8.51565e9	−1.41890
$623$	−3.87376e9	−0.641837
$624$	1.85286e9	0.305279
$625$	−6.16859e7	−0.0101066
$626$	−9.50998e8	−0.154942
$627$	2.47646e9	0.401231
$628$	−7.34327e8	−0.118313
$629$	−3.74465e9	−0.599976
$630$	−1.78928e9	−0.285092
$631$	−7.87439e9	−1.24771	−0.623856	−	0.781540i	$-0.714435\pi$
$631$	−7.87439e9	−1.24771	−0.623856	+	0.781540i	$0.714435\pi$
$632$	1.04742e9	0.165048
$633$	−3.06255e9	−0.479922
$634$	−3.92910e9	−0.612323
$635$	3.69567e9	0.572776
$636$	1.02902e8	0.0158608
$637$	2.65919e9	0.407626
$638$	1.51616e10	2.31139
$639$	−8.38543e8	−0.127137
$640$	8.94577e9	1.34892
$641$	2.66936e8	0.0400316	0.0200158	−	0.999800i	$-0.493628\pi$
$641$	2.66936e8	0.0400316	0.0200158	+	0.999800i	$0.493628\pi$
$642$	−6.28604e8	−0.0937572
$643$	−9.18242e9	−1.36213	−0.681065	−	0.732223i	$-0.738483\pi$
$643$	−9.18242e9	−1.36213	−0.681065	+	0.732223i	$0.738483\pi$
$644$	−4.07870e8	−0.0601757
$645$	8.23655e9	1.20861
$646$	1.65116e9	0.240977
$647$	7.79548e9	1.13156	0.565781	−	0.824556i	$-0.308575\pi$
$647$	7.79548e9	1.13156	0.565781	+	0.824556i	$0.308575\pi$
$648$	−8.01688e8	−0.115743
$649$	1.65756e9	0.238019
$650$	−6.34229e9	−0.905836
$651$	−8.51395e8	−0.120948
$652$	−8.86303e8	−0.125232
$653$	−7.64228e8	−0.107406	−0.0537028	−	0.998557i	$-0.517102\pi$
$653$	−7.64228e8	−0.107406	−0.0537028	+	0.998557i	$0.517102\pi$
$654$	−4.64295e9	−0.649040
$655$	1.99232e9	0.277022
$656$	−7.77809e9	−1.07575
$657$	2.44204e7	0.00335949
$658$	−9.51162e8	−0.130156
$659$	−4.42497e9	−0.602299	−0.301149	−	0.953577i	$-0.597370\pi$
$659$	−4.42497e9	−0.602299	−0.301149	+	0.953577i	$0.597370\pi$
$660$	1.19711e9	0.162080
$661$	−1.21787e9	−0.164019	−0.0820097	−	0.996632i	$-0.526134\pi$
$661$	−1.21787e9	−0.164019	−0.0820097	+	0.996632i	$0.526134\pi$
$662$	9.52106e9	1.27551
$663$	1.70379e9	0.227049
$664$	1.01483e9	0.134525
$665$	2.59162e9	0.341740
$666$	2.17657e9	0.285504
$667$	1.16027e10	1.51398
$668$	1.15528e9	0.149958
$669$	−4.29047e9	−0.554005
$670$	−4.30697e9	−0.553235
$671$	2.43651e10	3.11343
$672$	−4.78132e8	−0.0607793
$673$	−6.63758e9	−0.839377	−0.419689	−	0.907668i	$-0.637861\pi$
$673$	−6.63758e9	−0.839377	−0.419689	+	0.907668i	$0.637861\pi$
$674$	−1.09042e10	−1.37178
$675$	2.48114e9	0.310519
$676$	4.97199e8	0.0619037
$677$	1.51749e9	0.187961	0.0939803	−	0.995574i	$-0.470041\pi$
$677$	1.51749e9	0.187961	0.0939803	+	0.995574i	$0.470041\pi$
$678$	2.70045e9	0.332761
$679$	−2.47244e9	−0.303098
$680$	9.20148e9	1.12222
$681$	−6.66085e8	−0.0808193
$682$	−5.42755e9	−0.655176
$683$	−1.25832e10	−1.51119	−0.755595	−	0.655039i	$-0.772652\pi$
$683$	−1.25832e10	−1.51119	−0.755595	+	0.655039i	$0.772652\pi$
$684$	1.00724e8	0.0120348
$685$	−3.71371e9	−0.441460
$686$	7.56318e9	0.894479
$687$	7.53749e7	0.00886907
$688$	−9.91063e9	−1.16022
$689$	1.46542e9	0.170685
$690$	−8.72901e9	−1.01156
$691$	−5.99235e9	−0.690914	−0.345457	−	0.938435i	$-0.612276\pi$
$691$	−5.99235e9	−0.690914	−0.345457	+	0.938435i	$0.612276\pi$
$692$	−7.12876e8	−0.0817791
$693$	2.96926e9	0.338909
$694$	−4.94070e9	−0.561088
$695$	−2.51599e10	−2.84291
$696$	7.10909e9	0.799248
$697$	−7.15232e9	−0.800078
$698$	7.16636e9	0.797636
$699$	4.64610e9	0.514539
$700$	7.73430e8	0.0852271
$701$	−1.16633e10	−1.27881	−0.639406	−	0.768869i	$-0.720820\pi$
$701$	−1.16633e10	−1.27881	−0.639406	+	0.768869i	$0.720820\pi$
$702$	−9.90324e8	−0.108043
$703$	−3.15258e9	−0.342233
$704$	−1.82132e10	−1.96736
$705$	2.13640e9	0.229626
$706$	−8.03443e8	−0.0859288
$707$	9.31847e9	0.991691
$708$	6.74173e7	0.00713928
$709$	−5.32106e9	−0.560707	−0.280353	−	0.959897i	$-0.590452\pi$
$709$	−5.32106e9	−0.560707	−0.280353	+	0.959897i	$0.590452\pi$
$710$	−5.59420e9	−0.586589
$711$	−5.06172e8	−0.0528146
$712$	−1.15791e10	−1.20225
$713$	−4.15354e9	−0.429146
$714$	1.97974e9	0.203546
$715$	1.70479e10	1.74422
$716$	4.31992e8	0.0439825
$717$	−8.80587e9	−0.892186
$718$	−1.67575e10	−1.68956
$719$	−1.68037e9	−0.168599	−0.0842993	−	0.996440i	$-0.526865\pi$
$719$	−1.68037e9	−0.168599	−0.0842993	+	0.996440i	$0.526865\pi$
$720$	−4.83571e9	−0.482833
$721$	2.63171e9	0.261496
$722$	−8.23065e9	−0.813868
$723$	1.11450e10	1.09673
$724$	−1.56049e9	−0.152818
$725$	−2.20019e10	−2.14426
$726$	1.32657e10	1.28663
$727$	6.43210e9	0.620844	0.310422	−	0.950599i	$-0.399530\pi$
$727$	6.43210e9	0.620844	0.310422	+	0.950599i	$0.399530\pi$
$728$	−3.55887e9	−0.341863
$729$	3.87420e8	0.0370370
$730$	1.62916e8	0.0155001
$731$	−9.11330e9	−0.862908
$732$	9.90994e8	0.0933861
$733$	9.99078e9	0.936991	0.468495	−	0.883466i	$-0.344796\pi$
$733$	9.99078e9	0.936991	0.468495	+	0.883466i	$0.344796\pi$
$734$	−5.14796e8	−0.0480507
$735$	−6.94013e9	−0.644706
$736$	−2.33258e9	−0.215657
$737$	7.14732e9	0.657669
$738$	4.15727e9	0.380724
$739$	5.40356e9	0.492521	0.246260	−	0.969204i	$-0.420798\pi$
$739$	5.40356e9	0.492521	0.246260	+	0.969204i	$0.420798\pi$
$740$	−1.52394e9	−0.138248
$741$	1.43440e9	0.129511
$742$	1.70276e9	0.153017
$743$	−1.37163e10	−1.22680	−0.613402	−	0.789771i	$-0.710199\pi$
$743$	−1.37163e10	−1.22680	−0.613402	+	0.789771i	$0.710199\pi$
$744$	−2.54491e9	−0.226551
$745$	1.29004e10	1.14302
$746$	−1.57235e10	−1.38664
$747$	−4.90421e8	−0.0430474
$748$	−1.32454e9	−0.115720
$749$	1.09166e9	0.0949299
$750$	6.29379e9	0.544751
$751$	1.22637e9	0.105653	0.0528264	−	0.998604i	$-0.483177\pi$
$751$	1.22637e9	0.105653	0.0528264	+	0.998604i	$0.483177\pi$
$752$	−2.57062e9	−0.220432
$753$	1.26005e10	1.07548
$754$	8.78184e9	0.746081
$755$	−6.39552e9	−0.540831
$756$	1.20768e8	0.0101654
$757$	−1.17911e10	−0.987912	−0.493956	−	0.869487i	$-0.664450\pi$
$757$	−1.17911e10	−0.987912	−0.493956	+	0.869487i	$0.664450\pi$
$758$	9.68347e9	0.807586
$759$	1.44856e10	1.20251
$760$	7.74662e9	0.640125
$761$	−1.03626e10	−0.852359	−0.426179	−	0.904639i	$-0.640141\pi$
$761$	−1.03626e10	−0.852359	−0.426179	+	0.904639i	$0.640141\pi$
$762$	2.37675e9	0.194599
$763$	8.06317e9	0.657158
$764$	1.05919e9	0.0859301
$765$	−4.44667e9	−0.359103
$766$	8.09169e9	0.650487
$767$	9.60082e8	0.0768289
$768$	−2.04600e9	−0.162983
$769$	7.77986e9	0.616921	0.308460	−	0.951237i	$-0.400186\pi$
$769$	7.77986e9	0.616921	0.308460	+	0.951237i	$0.400186\pi$
$770$	1.98090e10	1.56367
$771$	−2.52830e9	−0.198672
$772$	−4.06648e8	−0.0318096
$773$	8.05208e9	0.627018	0.313509	−	0.949585i	$-0.398495\pi$
$773$	8.05208e9	0.627018	0.313509	+	0.949585i	$0.398495\pi$
$774$	5.29708e9	0.410623
$775$	7.87623e9	0.607802
$776$	−7.39040e9	−0.567743
$777$	−3.77993e9	−0.289075
$778$	2.14123e10	1.63018
$779$	−6.02146e9	−0.456374
$780$	6.93385e8	0.0523170
$781$	9.28346e9	0.697319
$782$	9.65817e9	0.722223
$783$	−3.43551e9	−0.255755
$784$	8.35071e9	0.618895
$785$	2.72926e10	2.01373
$786$	1.28130e9	0.0941176
$787$	2.48655e10	1.81838	0.909192	−	0.416377i	$-0.136700\pi$
$787$	2.48655e10	1.81838	0.909192	+	0.416377i	$0.136700\pi$
$788$	−1.74916e9	−0.127347
$789$	−1.35234e10	−0.980205
$790$	−3.37684e9	−0.243678
$791$	−4.68973e9	−0.336923
$792$	8.87545e9	0.634822
$793$	1.41126e10	1.00497
$794$	−2.57420e10	−1.82503
$795$	−3.82455e9	−0.269958
$796$	4.12276e8	0.0289729
$797$	−1.33668e9	−0.0935241	−0.0467621	−	0.998906i	$-0.514890\pi$
$797$	−1.33668e9	−0.0935241	−0.0467621	+	0.998906i	$0.514890\pi$
$798$	1.66672e9	0.116105
$799$	−2.36381e9	−0.163945
$800$	4.42319e9	0.305436
$801$	5.59566e9	0.384713
$802$	1.33106e10	0.911147
$803$	−2.70356e8	−0.0184261
$804$	2.90701e8	0.0197265
$805$	1.51592e10	1.02422
$806$	−3.14372e9	−0.211481
$807$	2.11762e9	0.141838
$808$	2.78539e10	1.85757
$809$	−5.48115e9	−0.363959	−0.181979	−	0.983302i	$-0.558250\pi$
$809$	−5.48115e9	−0.363959	−0.181979	+	0.983302i	$0.558250\pi$
$810$	2.58461e9	0.170883
$811$	1.52888e10	1.00647	0.503233	−	0.864151i	$-0.332144\pi$
$811$	1.52888e10	1.00647	0.503233	+	0.864151i	$0.332144\pi$
$812$	−1.07093e9	−0.0701963
$813$	1.07341e10	0.700563
$814$	−2.40966e10	−1.56592
$815$	3.29411e10	2.13150
$816$	5.35045e9	0.344727
$817$	−7.67238e9	−0.492213
$818$	1.16242e10	0.742551
$819$	1.71984e9	0.109395
$820$	−2.91075e9	−0.184356
$821$	5.00980e9	0.315951	0.157975	−	0.987443i	$-0.449503\pi$
$821$	5.00980e9	0.315951	0.157975	+	0.987443i	$0.449503\pi$
$822$	−2.38835e9	−0.149985
$823$	−1.43300e10	−0.896077	−0.448038	−	0.894014i	$-0.647877\pi$
$823$	−1.43300e10	−0.896077	−0.448038	+	0.894014i	$0.647877\pi$
$824$	7.86646e9	0.489817
$825$	−2.74686e10	−1.70313
$826$	1.11558e9	0.0688761
$827$	2.07445e10	1.27536	0.637682	−	0.770300i	$-0.279893\pi$
$827$	2.07445e10	1.27536	0.637682	+	0.770300i	$0.279893\pi$
$828$	5.89169e8	0.0360689
$829$	−3.94434e9	−0.240455	−0.120227	−	0.992746i	$-0.538362\pi$
$829$	−3.94434e9	−0.240455	−0.120227	+	0.992746i	$0.538362\pi$
$830$	−3.27176e9	−0.198613
$831$	−2.60494e9	−0.157469
$832$	−1.05494e10	−0.635033
$833$	7.67887e9	0.460299
$834$	−1.61808e10	−0.965871
$835$	−4.29380e10	−2.55234
$836$	−1.11511e9	−0.0660080
$837$	1.22984e9	0.0724953
$838$	−2.09922e10	−1.23226
$839$	−1.52467e10	−0.891268	−0.445634	−	0.895215i	$-0.647022\pi$
$839$	−1.52467e10	−0.891268	−0.445634	+	0.895215i	$0.647022\pi$
$840$	9.28817e9	0.540696
$841$	1.32150e10	0.766091
$842$	4.42410e9	0.255407
$843$	−1.45013e10	−0.833703
$844$	1.37902e9	0.0789537
$845$	−1.84793e10	−1.05363
$846$	1.37396e9	0.0780147
$847$	−2.30379e10	−1.30272
$848$	4.60189e9	0.259150
$849$	−1.66895e10	−0.935979
$850$	−1.83145e10	−1.02289
$851$	−1.84404e10	−1.02569
$852$	3.77583e8	0.0209158
$853$	−2.14258e10	−1.18200	−0.590998	−	0.806673i	$-0.701266\pi$
$853$	−2.14258e10	−1.18200	−0.590998	+	0.806673i	$0.701266\pi$
$854$	1.63983e10	0.900941
$855$	−3.74360e9	−0.204837
$856$	3.26310e9	0.177817
$857$	2.49225e10	1.35257	0.676283	−	0.736642i	$-0.263590\pi$
$857$	2.49225e10	1.35257	0.676283	+	0.736642i	$0.263590\pi$
$858$	1.09638e10	0.592593
$859$	−8.80692e9	−0.474076	−0.237038	−	0.971500i	$-0.576177\pi$
$859$	−8.80692e9	−0.474076	−0.237038	+	0.971500i	$0.576177\pi$
$860$	−3.70880e9	−0.198833
$861$	−7.21971e9	−0.385486
$862$	−2.54675e10	−1.35429
$863$	5.86301e9	0.310515	0.155257	−	0.987874i	$-0.450379\pi$
$863$	5.86301e9	0.310515	0.155257	+	0.987874i	$0.450379\pi$
$864$	6.90663e8	0.0364308
$865$	2.64953e10	1.39192
$866$	−2.39979e9	−0.125563
$867$	−6.15915e9	−0.320962
$868$	3.83370e8	0.0198975
$869$	5.60380e9	0.289676
$870$	−2.29194e10	−1.18001
$871$	4.13984e9	0.212285
$872$	2.41017e10	1.23095
$873$	3.57145e9	0.181675
$874$	8.13111e9	0.411964
$875$	−1.09301e10	−0.551564
$876$	−1.09961e7	−0.000552682 0
$877$	3.56534e10	1.78485	0.892427	−	0.451193i	$-0.149001\pi$
$877$	3.56534e10	1.78485	0.892427	+	0.451193i	$0.149001\pi$
$878$	−6.83022e9	−0.340568
$879$	9.15901e9	0.454870
$880$	5.35359e10	2.64823
$881$	3.92292e10	1.93283	0.966414	−	0.256989i	$-0.0827306\pi$
$881$	3.92292e10	1.93283	0.966414	+	0.256989i	$0.0827306\pi$
$882$	−4.46332e9	−0.219037
$883$	2.18077e10	1.06598	0.532988	−	0.846123i	$-0.321069\pi$
$883$	2.18077e10	1.06598	0.532988	+	0.846123i	$0.321069\pi$
$884$	−7.67192e8	−0.0373526
$885$	−2.50569e9	−0.121514
$886$	−1.55939e10	−0.753247
$887$	4.76501e9	0.229262	0.114631	−	0.993408i	$-0.463431\pi$
$887$	4.76501e9	0.229262	0.114631	+	0.993408i	$0.463431\pi$
$888$	−1.12986e10	−0.541476
$889$	−4.12758e9	−0.197033
$890$	3.73305e10	1.77500
$891$	−4.28911e9	−0.203140
$892$	1.93194e9	0.0911414
$893$	−1.99006e9	−0.0935162
$894$	8.29646e9	0.388339
$895$	−1.60558e10	−0.748601
$896$	−9.99126e9	−0.464026
$897$	8.39029e9	0.388153
$898$	3.46490e10	1.59670
$899$	−1.09058e10	−0.500609
$900$	−1.11722e9	−0.0510846
$901$	4.23166e9	0.192741
$902$	−4.60249e10	−2.08819
$903$	−9.19916e9	−0.415758
$904$	−1.40181e10	−0.631102
$905$	5.79984e10	2.60103
$906$	−4.11307e9	−0.183746
$907$	−8.85912e9	−0.394244	−0.197122	−	0.980379i	$-0.563159\pi$
$907$	−8.85912e9	−0.394244	−0.197122	+	0.980379i	$0.563159\pi$
$908$	2.99928e8	0.0132959
$909$	−1.34605e10	−0.594414
$910$	1.14737e10	0.504728
$911$	−5.66060e9	−0.248055	−0.124028	−	0.992279i	$-0.539581\pi$
$911$	−5.66060e9	−0.248055	−0.124028	+	0.992279i	$0.539581\pi$
$912$	4.50449e9	0.196636
$913$	5.42942e9	0.236105
$914$	−1.11000e10	−0.480851
$915$	−3.68321e10	−1.58947
$916$	−3.39402e7	−0.00145908
$917$	−2.22516e9	−0.0952947
$918$	−2.85973e9	−0.122005
$919$	3.15687e10	1.34169	0.670846	−	0.741597i	$-0.265931\pi$
$919$	3.15687e10	1.34169	0.670846	+	0.741597i	$0.265931\pi$
$920$	4.53125e10	1.91849
$921$	−2.59960e9	−0.109647
$922$	3.45821e10	1.45309
$923$	5.37713e9	0.225084
$924$	−1.33702e9	−0.0557551
$925$	3.49680e10	1.45270
$926$	−1.79683e10	−0.743649
$927$	−3.80151e9	−0.156739
$928$	−6.12456e9	−0.251569
$929$	2.88328e10	1.17986	0.589932	−	0.807453i	$-0.299155\pi$
$929$	2.88328e10	1.17986	0.589932	+	0.807453i	$0.299155\pi$
$930$	8.20468e9	0.334481
$931$	6.46476e9	0.262560
$932$	−2.09207e9	−0.0846487
$933$	−2.13623e10	−0.861117
$934$	4.08454e9	0.164032
$935$	4.92288e10	1.96960
$936$	5.14080e9	0.204911
$937$	−4.19782e10	−1.66700	−0.833500	−	0.552520i	$-0.813666\pi$
$937$	−4.19782e10	−1.66700	−0.833500	+	0.552520i	$0.813666\pi$
$938$	4.81032e9	0.190311
$939$	−2.38567e9	−0.0940330
$940$	−9.61988e8	−0.0377766
$941$	−4.83827e10	−1.89289	−0.946447	−	0.322860i	$-0.895356\pi$
$941$	−4.83827e10	−1.89289	−0.946447	+	0.322860i	$0.895356\pi$
$942$	1.75524e10	0.684160
$943$	−3.52215e10	−1.36778
$944$	3.01496e9	0.116649
$945$	−4.48856e9	−0.173020
$946$	−5.86436e10	−2.25217
$947$	−7.76682e9	−0.297179	−0.148590	−	0.988899i	$-0.547473\pi$
$947$	−7.76682e9	−0.297179	−0.148590	+	0.988899i	$0.547473\pi$
$948$	2.27922e8	0.00868873
$949$	−1.56595e8	−0.00594765
$950$	−1.54187e10	−0.583467
$951$	−9.85651e9	−0.371614
$952$	−1.02769e10	−0.386039
$953$	−4.85606e9	−0.181743	−0.0908717	−	0.995863i	$-0.528965\pi$
$953$	−4.85606e9	−0.181743	−0.0908717	+	0.995863i	$0.528965\pi$
$954$	−2.45964e9	−0.0917175
$955$	−3.93666e10	−1.46257
$956$	3.96515e9	0.146777
$957$	3.80343e10	1.40276
$958$	1.72953e10	0.635549
$959$	4.14773e9	0.151861
$960$	2.75325e10	1.00438
$961$	−2.36086e10	−0.858100
$962$	−1.39571e10	−0.505457
$963$	−1.57691e9	−0.0569004
$964$	−5.01845e9	−0.180426
$965$	1.51138e10	0.541413
$966$	9.74917e9	0.347975
$967$	−2.84618e10	−1.01221	−0.506103	−	0.862473i	$-0.668915\pi$
$967$	−2.84618e10	−1.01221	−0.506103	+	0.862473i	$0.668915\pi$
$968$	−6.88628e10	−2.44017
$969$	4.14209e9	0.146247
$970$	2.38264e10	0.838217
$971$	−3.54110e10	−1.24128	−0.620642	−	0.784094i	$-0.713128\pi$
$971$	−3.54110e10	−1.24128	−0.620642	+	0.784094i	$0.713128\pi$
$972$	−1.74450e8	−0.00609310
$973$	2.81004e10	0.977952
$974$	4.79483e10	1.66271
$975$	−1.59102e10	−0.549744
$976$	4.43182e10	1.52584
$977$	4.07835e10	1.39911	0.699557	−	0.714577i	$-0.253381\pi$
$977$	4.07835e10	1.39911	0.699557	+	0.714577i	$0.253381\pi$
$978$	2.11850e10	0.724173
$979$	−6.19492e10	−2.11007
$980$	3.12504e9	0.106063
$981$	−1.16473e10	−0.393897
$982$	−3.88032e10	−1.30761
$983$	−4.57225e10	−1.53530	−0.767649	−	0.640871i	$-0.778573\pi$
$983$	−4.57225e10	−1.53530	−0.767649	+	0.640871i	$0.778573\pi$
$984$	−2.15805e10	−0.722068
$985$	6.50107e10	2.16749
$986$	2.53591e10	0.842489
$987$	−2.38608e9	−0.0789905
$988$	−6.45891e8	−0.0213064
$989$	−4.48782e10	−1.47519
$990$	−2.86141e10	−0.937253
$991$	7.18635e9	0.234558	0.117279	−	0.993099i	$-0.462583\pi$
$991$	7.18635e9	0.234558	0.117279	+	0.993099i	$0.462583\pi$
$992$	2.19247e9	0.0713086
$993$	2.38845e10	0.774093
$994$	6.24800e9	0.201785
$995$	−1.53230e10	−0.493131
$996$	2.20829e8	0.00708188
$997$	5.76916e10	1.84365	0.921827	−	0.387602i	$-0.126696\pi$
$997$	5.76916e10	1.84365	0.921827	+	0.387602i	$0.126696\pi$
$998$	−2.70920e10	−0.862749
$999$	5.46012e9	0.173270

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.8.a.b.1.13	✓	17
3.2	odd	2		531.8.a.d.1.5		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.b.1.13	✓	17	1.1	even	1	trivial
531.8.a.d.1.5		17	3.2	odd	2

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:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q+10.7630 q^{2} +27.0000 q^{3} -12.1577 q^{4} +451.863 q^{5} +290.601 q^{6} -504.672 q^{7} -1508.52 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+10.7630 q^{2} +27.0000 q^{3} -12.1577 q^{4} +451.863 q^{5} +290.601 q^{6} -504.672 q^{7} -1508.52 q^{8} +729.000 q^{9} +4863.40 q^{10} -8070.72 q^{11} -328.258 q^{12} -4674.69 q^{13} -5431.79 q^{14} +12200.3 q^{15} -14680.0 q^{16} -13499.0 q^{17} +7846.23 q^{18} -11364.6 q^{19} -5493.61 q^{20} -13626.1 q^{21} -86865.2 q^{22} -66475.4 q^{23} -40730.0 q^{24} +126055. q^{25} -50313.7 q^{26} +19683.0 q^{27} +6135.65 q^{28} -174542. q^{29} +131312. q^{30} +62482.4 q^{31} +35089.3 q^{32} -217909. q^{33} -145289. q^{34} -228043. q^{35} -8862.96 q^{36} +277403. q^{37} -122318. q^{38} -126217. q^{39} -681643. q^{40} +529842. q^{41} -146658. q^{42} +675111. q^{43} +98121.3 q^{44} +329408. q^{45} -715475. q^{46} +175110. q^{47} -396360. q^{48} -568849. q^{49} +1.35673e6 q^{50} -364472. q^{51} +56833.4 q^{52} -313480. q^{53} +211848. q^{54} -3.64686e6 q^{55} +761307. q^{56} -306845. q^{57} -1.87860e6 q^{58} -205379. q^{59} -148328. q^{60} -3.01895e6 q^{61} +672499. q^{62} -367906. q^{63} +2.25671e6 q^{64} -2.11232e6 q^{65} -2.34536e6 q^{66} -885587. q^{67} +164116. q^{68} -1.79484e6 q^{69} -2.45442e6 q^{70} -1.15026e6 q^{71} -1.09971e6 q^{72} +33498.4 q^{73} +2.98569e6 q^{74} +3.40349e6 q^{75} +138168. q^{76} +4.07307e6 q^{77} -1.35847e6 q^{78} -694337. q^{79} -6.63335e6 q^{80} +531441. q^{81} +5.70270e6 q^{82} -672731. q^{83} +165663. q^{84} -6.09968e6 q^{85} +7.26622e6 q^{86} -4.71263e6 q^{87} +1.21748e7 q^{88} +7.67580e6 q^{89} +3.54542e6 q^{90} +2.35918e6 q^{91} +808188. q^{92} +1.68703e6 q^{93} +1.88471e6 q^{94} -5.13525e6 q^{95} +947412. q^{96} +4.89911e6 q^{97} -6.12253e6 q^{98} -5.88355e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 32 q^{2} + 459 q^{3} + 1166 q^{4} - 1072 q^{5} - 864 q^{6} - 2407 q^{7} - 6645 q^{8} + 12393 q^{9}+O(q^{10}) \) 17 * q - 32 * q^2 + 459 * q^3 + 1166 * q^4 - 1072 * q^5 - 864 * q^6 - 2407 * q^7 - 6645 * q^8 + 12393 * q^9	\( 17 q - 32 q^{2} + 459 q^{3} + 1166 q^{4} - 1072 q^{5} - 864 q^{6} - 2407 q^{7} - 6645 q^{8} + 12393 q^{9} - 6391 q^{10} - 8888 q^{11} + 31482 q^{12} - 12702 q^{13} - 17555 q^{14} - 28944 q^{15} + 139226 q^{16} - 36167 q^{17} - 23328 q^{18} - 71037 q^{19} - 274883 q^{20} - 64989 q^{21} - 325182 q^{22} - 269995 q^{23} - 179415 q^{24} + 97329 q^{25} - 336906 q^{26} + 334611 q^{27} - 901362 q^{28} - 543825 q^{29} - 172557 q^{30} - 633109 q^{31} - 837062 q^{32} - 239976 q^{33} - 529288 q^{34} - 287621 q^{35} + 850014 q^{36} - 867607 q^{37} - 1727169 q^{38} - 342954 q^{39} - 815662 q^{40} - 1428939 q^{41} - 473985 q^{42} - 477060 q^{43} - 1667926 q^{44} - 781488 q^{45} + 5305549 q^{46} - 1217849 q^{47} + 3759102 q^{48} + 4350738 q^{49} + 4561369 q^{50} - 976509 q^{51} + 4175994 q^{52} - 3487068 q^{53} - 629856 q^{54} - 960484 q^{55} - 5363196 q^{56} - 1917999 q^{57} - 3082906 q^{58} - 3491443 q^{59} - 7421841 q^{60} + 998917 q^{61} - 5742614 q^{62} - 1754703 q^{63} + 17531621 q^{64} - 6075816 q^{65} - 8779914 q^{66} - 356026 q^{67} - 16149231 q^{68} - 7289865 q^{69} - 548798 q^{70} - 12879428 q^{71} - 4844205 q^{72} - 6176157 q^{73} - 5971906 q^{74} + 2627883 q^{75} - 17624580 q^{76} + 239687 q^{77} - 9096462 q^{78} - 18886490 q^{79} - 70463349 q^{80} + 9034497 q^{81} - 19351611 q^{82} - 22824893 q^{83} - 24336774 q^{84} - 7973079 q^{85} - 27502196 q^{86} - 14683275 q^{87} - 62527651 q^{88} - 30609647 q^{89} - 4659039 q^{90} - 36301521 q^{91} - 41388548 q^{92} - 17093943 q^{93} + 1010176 q^{94} - 29303629 q^{95} - 22600674 q^{96} - 26249806 q^{97} - 93110852 q^{98} - 6479352 q^{99}+O(q^{100}) \) 17 * q - 32 * q^2 + 459 * q^3 + 1166 * q^4 - 1072 * q^5 - 864 * q^6 - 2407 * q^7 - 6645 * q^8 + 12393 * q^9 - 6391 * q^10 - 8888 * q^11 + 31482 * q^12 - 12702 * q^13 - 17555 * q^14 - 28944 * q^15 + 139226 * q^16 - 36167 * q^17 - 23328 * q^18 - 71037 * q^19 - 274883 * q^20 - 64989 * q^21 - 325182 * q^22 - 269995 * q^23 - 179415 * q^24 + 97329 * q^25 - 336906 * q^26 + 334611 * q^27 - 901362 * q^28 - 543825 * q^29 - 172557 * q^30 - 633109 * q^31 - 837062 * q^32 - 239976 * q^33 - 529288 * q^34 - 287621 * q^35 + 850014 * q^36 - 867607 * q^37 - 1727169 * q^38 - 342954 * q^39 - 815662 * q^40 - 1428939 * q^41 - 473985 * q^42 - 477060 * q^43 - 1667926 * q^44 - 781488 * q^45 + 5305549 * q^46 - 1217849 * q^47 + 3759102 * q^48 + 4350738 * q^49 + 4561369 * q^50 - 976509 * q^51 + 4175994 * q^52 - 3487068 * q^53 - 629856 * q^54 - 960484 * q^55 - 5363196 * q^56 - 1917999 * q^57 - 3082906 * q^58 - 3491443 * q^59 - 7421841 * q^60 + 998917 * q^61 - 5742614 * q^62 - 1754703 * q^63 + 17531621 * q^64 - 6075816 * q^65 - 8779914 * q^66 - 356026 * q^67 - 16149231 * q^68 - 7289865 * q^69 - 548798 * q^70 - 12879428 * q^71 - 4844205 * q^72 - 6176157 * q^73 - 5971906 * q^74 + 2627883 * q^75 - 17624580 * q^76 + 239687 * q^77 - 9096462 * q^78 - 18886490 * q^79 - 70463349 * q^80 + 9034497 * q^81 - 19351611 * q^82 - 22824893 * q^83 - 24336774 * q^84 - 7973079 * q^85 - 27502196 * q^86 - 14683275 * q^87 - 62527651 * q^88 - 30609647 * q^89 - 4659039 * q^90 - 36301521 * q^91 - 41388548 * q^92 - 17093943 * q^93 + 1010176 * q^94 - 29303629 * q^95 - 22600674 * q^96 - 26249806 * q^97 - 93110852 * q^98 - 6479352 * q^99

Introduction

L-functions

Modular forms

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