LMFDB - Embedded newform 177.6.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,6,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, 6, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 6 $
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:	$28.3879361069$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 331 x^{11} - 41 x^{10} + 41990 x^{9} + 7229 x^{8} - 2592364 x^{7} - 312100 x^{6} + \cdots - 6400833792 $ x^13 - 331x^11 - 41x^10 + 41990x^9 + 7229x^8 - 2592364x^7 - 312100x^6 + 81977088x^5 - 3773728x^4 - 1245415104x^3 + 453320896x^2 + 6872784896*x - 6400833792
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-10.3652$ 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)

$f(q)$	$=$	$q-10.3652 q^{2} -9.00000 q^{3} +75.4381 q^{4} -24.0297 q^{5} +93.2871 q^{6} -107.618 q^{7} -450.246 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-10.3652 q^{2} -9.00000 q^{3} +75.4381 q^{4} -24.0297 q^{5} +93.2871 q^{6} -107.618 q^{7} -450.246 q^{8} +81.0000 q^{9} +249.073 q^{10} -183.516 q^{11} -678.943 q^{12} +1154.66 q^{13} +1115.49 q^{14} +216.267 q^{15} +2252.88 q^{16} -886.414 q^{17} -839.584 q^{18} -2104.48 q^{19} -1812.75 q^{20} +968.563 q^{21} +1902.18 q^{22} -1569.47 q^{23} +4052.21 q^{24} -2547.57 q^{25} -11968.4 q^{26} -729.000 q^{27} -8118.50 q^{28} -5236.85 q^{29} -2241.66 q^{30} +1509.60 q^{31} -8943.81 q^{32} +1651.64 q^{33} +9187.89 q^{34} +2586.03 q^{35} +6110.48 q^{36} -2164.04 q^{37} +21813.4 q^{38} -10392.0 q^{39} +10819.3 q^{40} -15941.6 q^{41} -10039.4 q^{42} +12379.6 q^{43} -13844.1 q^{44} -1946.40 q^{45} +16267.9 q^{46} +16357.6 q^{47} -20276.0 q^{48} -5225.35 q^{49} +26406.2 q^{50} +7977.73 q^{51} +87105.6 q^{52} -22194.9 q^{53} +7556.26 q^{54} +4409.82 q^{55} +48454.6 q^{56} +18940.3 q^{57} +54281.2 q^{58} +3481.00 q^{59} +16314.8 q^{60} -7397.09 q^{61} -15647.3 q^{62} -8717.06 q^{63} +20612.4 q^{64} -27746.2 q^{65} -17119.6 q^{66} +49029.2 q^{67} -66869.4 q^{68} +14125.2 q^{69} -26804.8 q^{70} +32909.7 q^{71} -36469.9 q^{72} +48535.7 q^{73} +22430.8 q^{74} +22928.2 q^{75} -158758. q^{76} +19749.6 q^{77} +107715. q^{78} +77853.3 q^{79} -54136.1 q^{80} +6561.00 q^{81} +165239. q^{82} +12149.1 q^{83} +73066.5 q^{84} +21300.3 q^{85} -128318. q^{86} +47131.7 q^{87} +82627.1 q^{88} -53040.7 q^{89} +20174.9 q^{90} -124263. q^{91} -118397. q^{92} -13586.4 q^{93} -169550. q^{94} +50570.0 q^{95} +80494.3 q^{96} -42061.8 q^{97} +54162.0 q^{98} -14864.8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q - 117 q^{3} + 246 q^{4} - 14 q^{5} + 373 q^{7} + 123 q^{8} + 1053 q^{9}+O(q^{10}) $ 13 * q - 117 * q^3 + 246 * q^4 - 14 * q^5 + 373 * q^7 + 123 * q^8 + 1053 * q^9	\( 13 q - 117 q^{3} + 246 q^{4} - 14 q^{5} + 373 q^{7} + 123 q^{8} + 1053 q^{9} + 137 q^{10} + 250 q^{11} - 2214 q^{12} + 1054 q^{13} - 575 q^{14} + 126 q^{15} + 922 q^{16} + 271 q^{17} + 671 q^{19} - 5491 q^{20} - 3357 q^{21} + 1094 q^{22} + 3975 q^{23} - 1107 q^{24} + 15569 q^{25} + 4622 q^{26} - 9477 q^{27} + 21214 q^{28} - 10613 q^{29} - 1233 q^{30} + 25597 q^{31} + 15966 q^{32} - 2250 q^{33} + 31796 q^{34} + 6729 q^{35} + 19926 q^{36} + 17585 q^{37} + 34903 q^{38} - 9486 q^{39} + 31382 q^{40} + 12537 q^{41} + 5175 q^{42} + 26644 q^{43} + 6654 q^{44} - 1134 q^{45} + 149005 q^{46} + 52087 q^{47} - 8298 q^{48} + 95384 q^{49} + 121821 q^{50} - 2439 q^{51} + 263630 q^{52} + 20014 q^{53} + 120932 q^{55} + 126688 q^{56} - 6039 q^{57} + 86066 q^{58} + 45253 q^{59} + 49419 q^{60} - 11667 q^{61} + 164794 q^{62} + 30213 q^{63} + 151893 q^{64} - 28674 q^{65} - 9846 q^{66} + 1106 q^{67} - 4043 q^{68} - 35775 q^{69} + 56066 q^{70} + 21230 q^{71} + 9963 q^{72} + 81131 q^{73} + 102042 q^{74} - 140121 q^{75} + 73900 q^{76} - 104655 q^{77} - 41598 q^{78} - 13470 q^{79} - 191969 q^{80} + 85293 q^{81} + 79909 q^{82} - 76149 q^{83} - 190926 q^{84} + 10035 q^{85} - 321496 q^{86} + 95517 q^{87} - 276779 q^{88} - 190205 q^{89} + 11097 q^{90} + 80601 q^{91} + 45672 q^{92} - 230373 q^{93} + 36768 q^{94} + 9875 q^{95} - 143694 q^{96} + 160850 q^{97} - 116644 q^{98} + 20250 q^{99}+O(q^{100}) \) 13 * q - 117 * q^3 + 246 * q^4 - 14 * q^5 + 373 * q^7 + 123 * q^8 + 1053 * q^9 + 137 * q^10 + 250 * q^11 - 2214 * q^12 + 1054 * q^13 - 575 * q^14 + 126 * q^15 + 922 * q^16 + 271 * q^17 + 671 * q^19 - 5491 * q^20 - 3357 * q^21 + 1094 * q^22 + 3975 * q^23 - 1107 * q^24 + 15569 * q^25 + 4622 * q^26 - 9477 * q^27 + 21214 * q^28 - 10613 * q^29 - 1233 * q^30 + 25597 * q^31 + 15966 * q^32 - 2250 * q^33 + 31796 * q^34 + 6729 * q^35 + 19926 * q^36 + 17585 * q^37 + 34903 * q^38 - 9486 * q^39 + 31382 * q^40 + 12537 * q^41 + 5175 * q^42 + 26644 * q^43 + 6654 * q^44 - 1134 * q^45 + 149005 * q^46 + 52087 * q^47 - 8298 * q^48 + 95384 * q^49 + 121821 * q^50 - 2439 * q^51 + 263630 * q^52 + 20014 * q^53 + 120932 * q^55 + 126688 * q^56 - 6039 * q^57 + 86066 * q^58 + 45253 * q^59 + 49419 * q^60 - 11667 * q^61 + 164794 * q^62 + 30213 * q^63 + 151893 * q^64 - 28674 * q^65 - 9846 * q^66 + 1106 * q^67 - 4043 * q^68 - 35775 * q^69 + 56066 * q^70 + 21230 * q^71 + 9963 * q^72 + 81131 * q^73 + 102042 * q^74 - 140121 * q^75 + 73900 * q^76 - 104655 * q^77 - 41598 * q^78 - 13470 * q^79 - 191969 * q^80 + 85293 * q^81 + 79909 * q^82 - 76149 * q^83 - 190926 * q^84 + 10035 * q^85 - 321496 * q^86 + 95517 * q^87 - 276779 * q^88 - 190205 * q^89 + 11097 * q^90 + 80601 * q^91 + 45672 * q^92 - 230373 * q^93 + 36768 * q^94 + 9875 * q^95 - 143694 * q^96 + 160850 * q^97 - 116644 * q^98 + 20250 * 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 $

$2$	−10.3652	−1.83233	−0.916166	−	0.400799i	$-0.868732\pi$
$2$	−10.3652	−1.83233	−0.916166	+	0.400799i	$0.868732\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	75.4381	2.35744
$5$	−24.0297	−0.429856	−0.214928	−	0.976630i	$-0.568952\pi$
$5$	−24.0297	−0.429856	−0.214928	+	0.976630i	$0.568952\pi$
$6$	93.2871	1.05790
$7$	−107.618	−0.830119	−0.415059	−	0.909794i	$-0.636239\pi$
$7$	−107.618	−0.830119	−0.415059	+	0.909794i	$0.636239\pi$
$8$	−450.246	−2.48728
$9$	81.0000	0.333333
$10$	249.073	0.787639
$11$	−183.516	−0.457289	−0.228645	−	0.973510i	$-0.573429\pi$
$11$	−183.516	−0.457289	−0.228645	+	0.973510i	$0.573429\pi$
$12$	−678.943	−1.36107
$13$	1154.66	1.89495	0.947474	−	0.319834i	$-0.103627\pi$
$13$	1154.66	1.89495	0.947474	+	0.319834i	$0.103627\pi$
$14$	1115.49	1.52105
$15$	216.267	0.248178
$16$	2252.88	2.20008
$17$	−886.414	−0.743900	−0.371950	−	0.928253i	$-0.621311\pi$
$17$	−886.414	−0.743900	−0.371950	+	0.928253i	$0.621311\pi$
$18$	−839.584	−0.610777
$19$	−2104.48	−1.33740	−0.668699	−	0.743533i	$-0.733149\pi$
$19$	−2104.48	−1.33740	−0.668699	+	0.743533i	$0.733149\pi$
$20$	−1812.75	−1.01336
$21$	968.563	0.479269
$22$	1902.18	0.837906
$23$	−1569.47	−0.618632	−0.309316	−	0.950959i	$-0.600100\pi$
$23$	−1569.47	−0.618632	−0.309316	+	0.950959i	$0.600100\pi$
$24$	4052.21	1.43603
$25$	−2547.57	−0.815224
$26$	−11968.4	−3.47217
$27$	−729.000	−0.192450
$28$	−8118.50	−1.95695
$29$	−5236.85	−1.15631	−0.578157	−	0.815926i	$-0.696228\pi$
$29$	−5236.85	−1.15631	−0.578157	+	0.815926i	$0.696228\pi$
$30$	−2241.66	−0.454744
$31$	1509.60	0.282135	0.141068	−	0.990000i	$-0.454947\pi$
$31$	1509.60	0.282135	0.141068	+	0.990000i	$0.454947\pi$
$32$	−8943.81	−1.54400
$33$	1651.64	0.264016
$34$	9187.89	1.36307
$35$	2586.03	0.356832
$36$	6110.48	0.785813
$37$	−2164.04	−0.259873	−0.129937	−	0.991522i	$-0.541477\pi$
$37$	−2164.04	−0.259873	−0.129937	+	0.991522i	$0.541477\pi$
$38$	21813.4	2.45056
$39$	−10392.0	−1.09405
$40$	10819.3	1.06917
$41$	−15941.6	−1.48106	−0.740530	−	0.672023i	$-0.765426\pi$
$41$	−15941.6	−1.48106	−0.740530	+	0.672023i	$0.765426\pi$
$42$	−10039.4	−0.878180
$43$	12379.6	1.02102	0.510512	−	0.859871i	$-0.329456\pi$
$43$	12379.6	1.02102	0.510512	+	0.859871i	$0.329456\pi$
$44$	−13844.1	−1.07803
$45$	−1946.40	−0.143285
$46$	16267.9	1.13354
$47$	16357.6	1.08013	0.540064	−	0.841624i	$-0.318400\pi$
$47$	16357.6	1.08013	0.540064	+	0.841624i	$0.318400\pi$
$48$	−20276.0	−1.27022
$49$	−5225.35	−0.310903
$50$	26406.2	1.49376
$51$	7977.73	0.429491
$52$	87105.6	4.46722
$53$	−22194.9	−1.08534	−0.542668	−	0.839948i	$-0.682586\pi$
$53$	−22194.9	−1.08534	−0.542668	+	0.839948i	$0.682586\pi$
$54$	7556.26	0.352632
$55$	4409.82	0.196569
$56$	48454.6	2.06474
$57$	18940.3	0.772147
$58$	54281.2	2.11875
$59$	3481.00	0.130189
$59$	3481.00	0.130189
$60$	16314.8	0.585064
$61$	−7397.09	−0.254528	−0.127264	−	0.991869i	$-0.540620\pi$
$61$	−7397.09	−0.254528	−0.127264	+	0.991869i	$0.540620\pi$
$62$	−15647.3	−0.516965
$63$	−8717.06	−0.276706
$64$	20612.4	0.629039
$65$	−27746.2	−0.814555
$66$	−17119.6	−0.483765
$67$	49029.2	1.33434	0.667172	−	0.744903i	$-0.267504\pi$
$67$	49029.2	1.33434	0.667172	+	0.744903i	$0.267504\pi$
$68$	−66869.4	−1.75370
$69$	14125.2	0.357167
$70$	−26804.8	−0.653834
$71$	32909.7	0.774779	0.387389	−	0.921916i	$-0.373377\pi$
$71$	32909.7	0.774779	0.387389	+	0.921916i	$0.373377\pi$
$72$	−36469.9	−0.829093
$73$	48535.7	1.06599	0.532996	−	0.846118i	$-0.321066\pi$
$73$	48535.7	1.06599	0.532996	+	0.846118i	$0.321066\pi$
$74$	22430.8	0.476174
$75$	22928.2	0.470670
$76$	−158758.	−3.15284
$77$	19749.6	0.379604
$78$	107715.	2.00466
$79$	77853.3	1.40349	0.701745	−	0.712429i	$-0.252405\pi$
$79$	77853.3	1.40349	0.701745	+	0.712429i	$0.252405\pi$
$80$	−54136.1	−0.945719
$81$	6561.00	0.111111
$82$	165239.	2.71380
$83$	12149.1	0.193576	0.0967878	−	0.995305i	$-0.469143\pi$
$83$	12149.1	0.193576	0.0967878	+	0.995305i	$0.469143\pi$
$84$	73066.5	1.12985
$85$	21300.3	0.319770
$86$	−128318.	−1.87085
$87$	47131.7	0.667598
$88$	82627.1	1.13741
$89$	−53040.7	−0.709797	−0.354899	−	0.934905i	$-0.615485\pi$
$89$	−53040.7	−0.709797	−0.354899	+	0.934905i	$0.615485\pi$
$90$	20174.9	0.262546
$91$	−124263.	−1.57303
$92$	−118397.	−1.45839
$93$	−13586.4	−0.162891
$94$	−169550.	−1.97915
$95$	50570.0	0.574889
$96$	80494.3	0.891429
$97$	−42061.8	−0.453898	−0.226949	−	0.973907i	$-0.572875\pi$
$97$	−42061.8	−0.453898	−0.226949	+	0.973907i	$0.572875\pi$
$98$	54162.0	0.569678
$99$	−14864.8	−0.152430
$100$	−192184.	−1.92184
$101$	49228.8	0.480193	0.240097	−	0.970749i	$-0.422821\pi$
$101$	49228.8	0.480193	0.240097	+	0.970749i	$0.422821\pi$
$102$	−82691.0	−0.786969
$103$	−73290.9	−0.680702	−0.340351	−	0.940299i	$-0.610546\pi$
$103$	−73290.9	−0.680702	−0.340351	+	0.940299i	$0.610546\pi$
$104$	−519882.	−4.71326
$105$	−23274.3	−0.206017
$106$	230056.	1.98869
$107$	180528.	1.52435	0.762176	−	0.647370i	$-0.224131\pi$
$107$	180528.	1.52435	0.762176	+	0.647370i	$0.224131\pi$
$108$	−54994.4	−0.453689
$109$	8801.25	0.0709542	0.0354771	−	0.999370i	$-0.488705\pi$
$109$	8801.25	0.0709542	0.0354771	+	0.999370i	$0.488705\pi$
$110$	−45708.8	−0.360179
$111$	19476.4	0.150038
$112$	−242451.	−1.82633
$113$	123514.	0.909954	0.454977	−	0.890503i	$-0.349648\pi$
$113$	123514.	0.909954	0.454977	+	0.890503i	$0.349648\pi$
$114$	−196321.	−1.41483
$115$	37713.8	0.265923
$116$	−395058.	−2.72594
$117$	93527.8	0.631649
$118$	−36081.4	−0.238549
$119$	95394.2	0.617525
$120$	−97373.4	−0.617287
$121$	−127373.	−0.790886
$122$	76672.5	0.466380
$123$	143475.	0.855091
$124$	113881.	0.665116
$125$	136310.	0.780285
$126$	90354.4	0.507018
$127$	−286860.	−1.57820	−0.789098	−	0.614268i	$-0.789452\pi$
$127$	−286860.	−1.57820	−0.789098	+	0.614268i	$0.789452\pi$
$128$	72549.9	0.391392
$129$	−111416.	−0.589488
$130$	287596.	1.49253
$131$	310694.	1.58181	0.790906	−	0.611937i	$-0.209609\pi$
$131$	310694.	1.58181	0.790906	+	0.611937i	$0.209609\pi$
$132$	124597.	0.622402
$133$	226480.	1.11020
$134$	−508200.	−2.44496
$135$	17517.6	0.0827258
$136$	399104.	1.85029
$137$	275512.	1.25412	0.627059	−	0.778972i	$-0.284258\pi$
$137$	275512.	1.25412	0.627059	+	0.778972i	$0.284258\pi$
$138$	−146411.	−0.654449
$139$	340395.	1.49433	0.747165	−	0.664639i	$-0.231415\pi$
$139$	340395.	1.49433	0.747165	+	0.664639i	$0.231415\pi$
$140$	195085.	0.841209
$141$	−147219.	−0.623612
$142$	−341116.	−1.41965
$143$	−211899.	−0.866539
$144$	182484.	0.733361
$145$	125840.	0.497048
$146$	−503084.	−1.95325
$147$	47028.1	0.179500
$148$	−163251.	−0.612636
$149$	−390850.	−1.44226	−0.721132	−	0.692798i	$-0.756378\pi$
$149$	−390850.	−1.44226	−0.721132	+	0.692798i	$0.756378\pi$
$150$	−237656.	−0.862423
$151$	−148168.	−0.528824	−0.264412	−	0.964410i	$-0.585178\pi$
$151$	−148168.	−0.528824	−0.264412	+	0.964410i	$0.585178\pi$
$152$	947533.	3.32648
$153$	−71799.5	−0.247967
$154$	−204709.	−0.695561
$155$	−36275.2	−0.121277
$156$	−783950.	−2.57915
$157$	192325.	0.622710	0.311355	−	0.950294i	$-0.399217\pi$
$157$	192325.	0.622710	0.311355	+	0.950294i	$0.399217\pi$
$158$	−806967.	−2.57166
$159$	199754.	0.626619
$160$	214917.	0.663698
$161$	168903.	0.513538
$162$	−68006.3	−0.203592
$163$	−318167.	−0.937965	−0.468982	−	0.883208i	$-0.655379\pi$
$163$	−318167.	−0.937965	−0.468982	+	0.883208i	$0.655379\pi$
$164$	−1.20261e6	−3.49151
$165$	−39688.4	−0.113489
$166$	−125929.	−0.354695
$167$	−19329.3	−0.0536322	−0.0268161	−	0.999640i	$-0.508537\pi$
$167$	−19329.3	−0.0536322	−0.0268161	+	0.999640i	$0.508537\pi$
$168$	−436091.	−1.19208
$169$	961955.	2.59083
$170$	−220782.	−0.585924
$171$	−170463.	−0.445799
$172$	933894.	2.40700
$173$	−261648.	−0.664664	−0.332332	−	0.943163i	$-0.607835\pi$
$173$	−261648.	−0.664664	−0.332332	+	0.943163i	$0.607835\pi$
$174$	−488531.	−1.22326
$175$	274165.	0.676732
$176$	−413439.	−1.00607
$177$	−31329.0	−0.0751646
$178$	549780.	1.30058
$179$	301837.	0.704109	0.352055	−	0.935979i	$-0.385483\pi$
$179$	301837.	0.704109	0.352055	+	0.935979i	$0.385483\pi$
$180$	−146833.	−0.337787
$181$	−833246.	−1.89050	−0.945250	−	0.326347i	$-0.894182\pi$
$181$	−833246.	−1.89050	−0.945250	+	0.326347i	$0.894182\pi$
$182$	1.28801e6	2.88231
$183$	66573.8	0.146952
$184$	706645.	1.53871
$185$	52001.3	0.111708
$186$	140826.	0.298470
$187$	162671.	0.340177
$188$	1.23399e6	2.54634
$189$	78453.6	0.159756
$190$	−524170.	−1.05339
$191$	−205250.	−0.407098	−0.203549	−	0.979065i	$-0.565248\pi$
$191$	−205250.	−0.407098	−0.203549	+	0.979065i	$0.565248\pi$
$192$	−185511.	−0.363176
$193$	688563.	1.33061	0.665305	−	0.746572i	$-0.268302\pi$
$193$	688563.	1.33061	0.665305	+	0.746572i	$0.268302\pi$
$194$	435980.	0.831692
$195$	249716.	0.470283
$196$	−394190.	−0.732935
$197$	395692.	0.726427	0.363213	−	0.931706i	$-0.381680\pi$
$197$	395692.	0.726427	0.363213	+	0.931706i	$0.381680\pi$
$198$	154077.	0.279302
$199$	−196403.	−0.351573	−0.175787	−	0.984428i	$-0.556247\pi$
$199$	−196403.	−0.351573	−0.175787	+	0.984428i	$0.556247\pi$
$200$	1.14703e6	2.02769
$201$	−441263.	−0.770384
$202$	−510268.	−0.879873
$203$	563580.	0.959877
$204$	601824.	1.01250
$205$	383072.	0.636643
$206$	759677.	1.24727
$207$	−127127.	−0.206211
$208$	2.60132e6	4.16904
$209$	386205.	0.611578
$210$	241243.	0.377491
$211$	165586.	0.256046	0.128023	−	0.991771i	$-0.459137\pi$
$211$	165586.	0.256046	0.128023	+	0.991771i	$0.459137\pi$
$212$	−1.67434e6	−2.55861
$213$	−296187.	−0.447319
$214$	−1.87122e6	−2.79312
$215$	−297478.	−0.438893
$216$	328229.	0.478677
$217$	−162460.	−0.234206
$218$	−91227.0	−0.130012
$219$	−436821.	−0.615451
$220$	332668.	0.463399
$221$	−1.02351e6	−1.40965
$222$	−201877.	−0.274919
$223$	583505.	0.785746	0.392873	−	0.919593i	$-0.371481\pi$
$223$	583505.	0.785746	0.392873	+	0.919593i	$0.371481\pi$
$224$	962515.	1.28170
$225$	−206354.	−0.271741
$226$	−1.28025e6	−1.66734
$227$	724730.	0.933495	0.466747	−	0.884391i	$-0.345426\pi$
$227$	724730.	0.933495	0.466747	+	0.884391i	$0.345426\pi$
$228$	1.42882e6	1.82029
$229$	1.26049e6	1.58836	0.794181	−	0.607682i	$-0.207900\pi$
$229$	1.26049e6	1.58836	0.794181	+	0.607682i	$0.207900\pi$
$230$	−390912.	−0.487258
$231$	−177746.	−0.219165
$232$	2.35787e6	2.87607
$233$	203051.	0.245028	0.122514	−	0.992467i	$-0.460904\pi$
$233$	203051.	0.245028	0.122514	+	0.992467i	$0.460904\pi$
$234$	−969437.	−1.15739
$235$	−393068.	−0.464300
$236$	262600.	0.306913
$237$	−700679.	−0.810305
$238$	−988783.	−1.13151
$239$	1.30710e6	1.48018	0.740090	−	0.672507i	$-0.234783\pi$
$239$	1.30710e6	1.48018	0.740090	+	0.672507i	$0.234783\pi$
$240$	487225.	0.546011
$241$	−1.25071e6	−1.38712	−0.693560	−	0.720399i	$-0.743959\pi$
$241$	−1.25071e6	−1.38712	−0.693560	+	0.720399i	$0.743959\pi$
$242$	1.32025e6	1.44917
$243$	−59049.0	−0.0641500
$244$	−558022.	−0.600035
$245$	125564.	0.133644
$246$	−1.48715e6	−1.56681
$247$	−2.42997e6	−2.53430
$248$	−679690.	−0.701749
$249$	−109342.	−0.111761
$250$	−1.41289e6	−1.42974
$251$	609504.	0.610650	0.305325	−	0.952248i	$-0.401235\pi$
$251$	609504.	0.610650	0.305325	+	0.952248i	$0.401235\pi$
$252$	−657599.	−0.652318
$253$	288021.	0.282894
$254$	2.97337e6	2.89178
$255$	−191702.	−0.184619
$256$	−1.41159e6	−1.34620
$257$	−1.12559e6	−1.06304	−0.531519	−	0.847046i	$-0.678379\pi$
$257$	−1.12559e6	−1.06304	−0.531519	+	0.847046i	$0.678379\pi$
$258$	1.15486e6	1.08014
$259$	232890.	0.215726
$260$	−2.09312e6	−1.92026
$261$	−424185.	−0.385438
$262$	−3.22042e6	−2.89841
$263$	−456092.	−0.406596	−0.203298	−	0.979117i	$-0.565166\pi$
$263$	−456092.	−0.406596	−0.203298	+	0.979117i	$0.565166\pi$
$264$	−743644.	−0.656682
$265$	533337.	0.466538
$266$	−2.34752e6	−2.03425
$267$	477367.	0.409802
$268$	3.69867e6	3.14564
$269$	1.90215e6	1.60275	0.801374	−	0.598164i	$-0.204103\pi$
$269$	1.90215e6	1.60275	0.801374	+	0.598164i	$0.204103\pi$
$270$	−181574.	−0.151581
$271$	−1.66399e6	−1.37634	−0.688172	−	0.725547i	$-0.741587\pi$
$271$	−1.66399e6	−1.37634	−0.688172	+	0.725547i	$0.741587\pi$
$272$	−1.99699e6	−1.63664
$273$	1.11836e6	0.908190
$274$	−2.85574e6	−2.29796
$275$	467520.	0.372793
$276$	1.06558e6	0.842000
$277$	−168344.	−0.131825	−0.0659127	−	0.997825i	$-0.520996\pi$
$277$	−168344.	−0.131825	−0.0659127	+	0.997825i	$0.520996\pi$
$278$	−3.52827e6	−2.73811
$279$	122277.	0.0940450
$280$	−1.16435e6	−0.887540
$281$	130677.	0.0987262	0.0493631	−	0.998781i	$-0.484281\pi$
$281$	130677.	0.0987262	0.0493631	+	0.998781i	$0.484281\pi$
$282$	1.52595e6	1.14266
$283$	−646735.	−0.480021	−0.240011	−	0.970770i	$-0.577151\pi$
$283$	−646735.	−0.480021	−0.240011	+	0.970770i	$0.577151\pi$
$284$	2.48264e6	1.82649
$285$	−455130.	−0.331912
$286$	2.19638e6	1.58779
$287$	1.71561e6	1.22946
$288$	−724448.	−0.514667
$289$	−634127.	−0.446613
$290$	−1.30436e6	−0.910757
$291$	378556.	0.262058
$292$	3.66144e6	2.51301
$293$	−250933.	−0.170761	−0.0853804	−	0.996348i	$-0.527211\pi$
$293$	−250933.	−0.170761	−0.0853804	+	0.996348i	$0.527211\pi$
$294$	−487458.	−0.328904
$295$	−83647.3	−0.0559625
$296$	974352.	0.646378
$297$	133783.	0.0880054
$298$	4.05126e6	2.64271
$299$	−1.81220e6	−1.17227
$300$	1.72966e6	1.10958
$301$	−1.33227e6	−0.847571
$302$	1.53579e6	0.968981
$303$	−443059.	−0.277240
$304$	−4.74115e6	−2.94239
$305$	177750.	0.109411
$306$	744219.	0.454357
$307$	1.37902e6	0.835074	0.417537	−	0.908660i	$-0.362893\pi$
$307$	1.37902e6	0.835074	0.417537	+	0.908660i	$0.362893\pi$
$308$	1.48987e6	0.894895
$309$	659618.	0.393003
$310$	376001.	0.222221
$311$	−1.53975e6	−0.902714	−0.451357	−	0.892343i	$-0.649060\pi$
$311$	−1.53975e6	−0.902714	−0.451357	+	0.892343i	$0.649060\pi$
$312$	4.67894e6	2.72120
$313$	−630915.	−0.364007	−0.182004	−	0.983298i	$-0.558258\pi$
$313$	−630915.	−0.364007	−0.182004	+	0.983298i	$0.558258\pi$
$314$	−1.99349e6	−1.14101
$315$	209468.	0.118944
$316$	5.87310e6	3.30864
$317$	−200120.	−0.111852	−0.0559258	−	0.998435i	$-0.517811\pi$
$317$	−200120.	−0.111852	−0.0559258	+	0.998435i	$0.517811\pi$
$318$	−2.07050e6	−1.14817
$319$	961044.	0.528770
$320$	−495309.	−0.270396
$321$	−1.62475e6	−0.880085
$322$	−1.75072e6	−0.940971
$323$	1.86544e6	0.994890
$324$	494949.	0.261938
$325$	−2.94159e6	−1.54481
$326$	3.29788e6	1.71866
$327$	−79211.2	−0.0409654
$328$	7.17765e6	3.68381
$329$	−1.76037e6	−0.896634
$330$	411380.	0.207949
$331$	−1.76239e6	−0.884160	−0.442080	−	0.896976i	$-0.645759\pi$
$331$	−1.76239e6	−0.884160	−0.442080	+	0.896976i	$0.645759\pi$
$332$	916508.	0.456343
$333$	−175288.	−0.0866245
$334$	200353.	0.0982719
$335$	−1.17816e6	−0.573576
$336$	2.18206e6	1.05443
$337$	2.91218e6	1.39683	0.698414	−	0.715694i	$-0.253889\pi$
$337$	2.91218e6	1.39683	0.698414	+	0.715694i	$0.253889\pi$
$338$	−9.97089e6	−4.74725
$339$	−1.11162e6	−0.525362
$340$	1.60685e6	0.753838
$341$	−277035.	−0.129017
$342$	1.76689e6	0.816853
$343$	2.37108e6	1.08821
$344$	−5.57387e6	−2.53957
$345$	−339424.	−0.153530
$346$	2.71204e6	1.21788
$347$	2.14394e6	0.955850	0.477925	−	0.878401i	$-0.341389\pi$
$347$	2.14394e6	0.955850	0.477925	+	0.878401i	$0.341389\pi$
$348$	3.55552e6	1.57382
$349$	−1.47165e6	−0.646756	−0.323378	−	0.946270i	$-0.604819\pi$
$349$	−1.47165e6	−0.646756	−0.323378	+	0.946270i	$0.604819\pi$
$350$	−2.84178e6	−1.24000
$351$	−841750.	−0.364683
$352$	1.64133e6	0.706055
$353$	2.59817e6	1.10976	0.554881	−	0.831929i	$-0.312764\pi$
$353$	2.59817e6	1.10976	0.554881	+	0.831929i	$0.312764\pi$
$354$	324732.	0.137726
$355$	−790809.	−0.333043
$356$	−4.00129e6	−1.67330
$357$	−858548.	−0.356528
$358$	−3.12861e6	−1.29016
$359$	3.88077e6	1.58921	0.794606	−	0.607126i	$-0.207678\pi$
$359$	3.88077e6	1.58921	0.794606	+	0.607126i	$0.207678\pi$
$360$	876360.	0.356391
$361$	1.95274e6	0.788634
$362$	8.63679e6	3.46402
$363$	1.14636e6	0.456618
$364$	−9.37414e6	−3.70833
$365$	−1.16630e6	−0.458223
$366$	−690053.	−0.269265
$367$	2.40348e6	0.931484	0.465742	−	0.884921i	$-0.345787\pi$
$367$	2.40348e6	0.931484	0.465742	+	0.884921i	$0.345787\pi$
$368$	−3.53582e6	−1.36104
$369$	−1.29127e6	−0.493687
$370$	−539006.	−0.204686
$371$	2.38857e6	0.900957
$372$	−1.02493e6	−0.384005
$373$	−3.79925e6	−1.41392	−0.706961	−	0.707253i	$-0.749934\pi$
$373$	−3.79925e6	−1.41392	−0.706961	+	0.707253i	$0.749934\pi$
$374$	−1.68612e6	−0.623318
$375$	−1.22679e6	−0.450498
$376$	−7.36495e6	−2.68658
$377$	−6.04681e6	−2.19115
$378$	−813190.	−0.292727
$379$	4.30088e6	1.53801	0.769005	−	0.639243i	$-0.220752\pi$
$379$	4.30088e6	1.53801	0.769005	+	0.639243i	$0.220752\pi$
$380$	3.81490e6	1.35527
$381$	2.58174e6	0.911172
$382$	2.12746e6	0.745939
$383$	−1.40933e6	−0.490926	−0.245463	−	0.969406i	$-0.578940\pi$
$383$	−1.40933e6	−0.490926	−0.245463	+	0.969406i	$0.578940\pi$
$384$	−652949.	−0.225970
$385$	−474577.	−0.163175
$386$	−7.13712e6	−2.43812
$387$	1.00275e6	0.340341
$388$	−3.17306e6	−1.07004
$389$	4.36630e6	1.46298	0.731492	−	0.681851i	$-0.238825\pi$
$389$	4.36630e6	1.46298	0.731492	+	0.681851i	$0.238825\pi$
$390$	−2.58836e6	−0.861715
$391$	1.39120e6	0.460200
$392$	2.35269e6	0.773303
$393$	−2.79625e6	−0.913260
$394$	−4.10144e6	−1.33105
$395$	−1.87079e6	−0.603298
$396$	−1.12137e6	−0.359344
$397$	−1.04034e6	−0.331282	−0.165641	−	0.986186i	$-0.552969\pi$
$397$	−1.04034e6	−0.331282	−0.165641	+	0.986186i	$0.552969\pi$
$398$	2.03577e6	0.644199
$399$	−2.03832e6	−0.640974
$400$	−5.73939e6	−1.79356
$401$	−662871.	−0.205858	−0.102929	−	0.994689i	$-0.532821\pi$
$401$	−662871.	−0.205858	−0.102929	+	0.994689i	$0.532821\pi$
$402$	4.57380e6	1.41160
$403$	1.74308e6	0.534631
$404$	3.71373e6	1.13203
$405$	−157659.	−0.0477618
$406$	−5.84164e6	−1.75881
$407$	397136.	0.118837
$408$	−3.59194e6	−1.06826
$409$	−2.15772e6	−0.637803	−0.318902	−	0.947788i	$-0.603314\pi$
$409$	−2.15772e6	−0.637803	−0.318902	+	0.947788i	$0.603314\pi$
$410$	−3.97063e6	−1.16654
$411$	−2.47960e6	−0.724066
$412$	−5.52892e6	−1.60471
$413$	−374619.	−0.108072
$414$	1.31770e6	0.377846
$415$	−291940.	−0.0832097
$416$	−1.03271e7	−2.92580
$417$	−3.06356e6	−0.862751
$418$	−4.00310e6	−1.12061
$419$	1.81635e6	0.505433	0.252717	−	0.967540i	$-0.418676\pi$
$419$	1.81635e6	0.505433	0.252717	+	0.967540i	$0.418676\pi$
$420$	−1.75577e6	−0.485672
$421$	5.94058e6	1.63352	0.816759	−	0.576979i	$-0.195769\pi$
$421$	5.94058e6	1.63352	0.816759	+	0.576979i	$0.195769\pi$
$422$	−1.71634e6	−0.469161
$423$	1.32497e6	0.360043
$424$	9.99317e6	2.69953
$425$	2.25821e6	0.606445
$426$	3.07005e6	0.819636
$427$	796060.	0.211289
$428$	1.36187e7	3.59357
$429$	1.90709e6	0.500297
$430$	3.08343e6	0.804198
$431$	6.77311e6	1.75629	0.878143	−	0.478399i	$-0.158783\pi$
$431$	6.77311e6	1.75629	0.878143	+	0.478399i	$0.158783\pi$
$432$	−1.64235e6	−0.423406
$433$	4.36419e6	1.11862	0.559312	−	0.828957i	$-0.311065\pi$
$433$	4.36419e6	1.11862	0.559312	+	0.828957i	$0.311065\pi$
$434$	1.68394e6	0.429142
$435$	−1.13256e6	−0.286971
$436$	663949.	0.167270
$437$	3.30291e6	0.827357
$438$	4.52775e6	1.12771
$439$	−3.94713e6	−0.977507	−0.488754	−	0.872422i	$-0.662548\pi$
$439$	−3.94713e6	−0.977507	−0.488754	+	0.872422i	$0.662548\pi$
$440$	−1.98550e6	−0.488921
$441$	−423253.	−0.103634
$442$	1.06089e7	2.58295
$443$	−7.17357e6	−1.73670	−0.868352	−	0.495948i	$-0.834821\pi$
$443$	−7.17357e6	−1.73670	−0.868352	+	0.495948i	$0.834821\pi$
$444$	1.46926e6	0.353705
$445$	1.27455e6	0.305111
$446$	−6.04816e6	−1.43975
$447$	3.51765e6	0.832692
$448$	−2.21826e6	−0.522177
$449$	−3.43967e6	−0.805194	−0.402597	−	0.915377i	$-0.631892\pi$
$449$	−3.43967e6	−0.805194	−0.402597	+	0.915377i	$0.631892\pi$
$450$	2.13890e6	0.497920
$451$	2.92554e6	0.677274
$452$	9.31764e6	2.14516
$453$	1.33351e6	0.305317
$454$	−7.51200e6	−1.71047
$455$	2.98599e6	0.676177
$456$	−8.52780e6	−1.92055
$457$	241102.	0.0540021	0.0270010	−	0.999635i	$-0.491404\pi$
$457$	241102.	0.0540021	0.0270010	+	0.999635i	$0.491404\pi$
$458$	−1.30652e7	−2.91040
$459$	646196.	0.143164
$460$	2.84505e6	0.626896
$461$	4.47148e6	0.979938	0.489969	−	0.871740i	$-0.337008\pi$
$461$	4.47148e6	0.979938	0.489969	+	0.871740i	$0.337008\pi$
$462$	1.84238e6	0.401583
$463$	−3.15606e6	−0.684215	−0.342107	−	0.939661i	$-0.611141\pi$
$463$	−3.15606e6	−0.684215	−0.342107	+	0.939661i	$0.611141\pi$
$464$	−1.17980e7	−2.54398
$465$	326476.	0.0700196
$466$	−2.10468e6	−0.448973
$467$	−4.67572e6	−0.992102	−0.496051	−	0.868293i	$-0.665217\pi$
$467$	−4.67572e6	−0.992102	−0.496051	+	0.868293i	$0.665217\pi$
$468$	7.05555e6	1.48907
$469$	−5.27643e6	−1.10766
$470$	4.07424e6	0.850751
$471$	−1.73092e6	−0.359522
$472$	−1.56731e6	−0.323816
$473$	−2.27185e6	−0.466903
$474$	7.26270e6	1.48475
$475$	5.36132e6	1.09028
$476$	7.19635e6	1.45578
$477$	−1.79779e6	−0.361778
$478$	−1.35484e7	−2.71218
$479$	3.99257e6	0.795086	0.397543	−	0.917584i	$-0.369863\pi$
$479$	3.99257e6	0.795086	0.397543	+	0.917584i	$0.369863\pi$
$480$	−1.93425e6	−0.383186
$481$	−2.49874e6	−0.492446
$482$	1.29639e7	2.54166
$483$	−1.52013e6	−0.296491
$484$	−9.60878e6	−1.86447
$485$	1.01073e6	0.195111
$486$	612057.	0.117544
$487$	6.94127e6	1.32622	0.663111	−	0.748521i	$-0.269236\pi$
$487$	6.94127e6	1.32622	0.663111	+	0.748521i	$0.269236\pi$
$488$	3.33051e6	0.633083
$489$	2.86351e6	0.541534
$490$	−1.30150e6	−0.244879
$491$	−7.13013e6	−1.33473	−0.667365	−	0.744730i	$-0.732578\pi$
$491$	−7.13013e6	−1.33473	−0.667365	+	0.744730i	$0.732578\pi$
$492$	1.08234e7	2.01583
$493$	4.64202e6	0.860181
$494$	2.51872e7	4.64368
$495$	357196.	0.0655229
$496$	3.40095e6	0.620720
$497$	−3.54168e6	−0.643158
$498$	1.13336e6	0.204783
$499$	646998.	0.116319	0.0581596	−	0.998307i	$-0.481477\pi$
$499$	646998.	0.116319	0.0581596	+	0.998307i	$0.481477\pi$
$500$	1.02830e7	1.83947
$501$	173964.	0.0309645
$502$	−6.31765e6	−1.11891
$503$	3.65695e6	0.644465	0.322232	−	0.946661i	$-0.395567\pi$
$503$	3.65695e6	0.644465	0.322232	+	0.946661i	$0.395567\pi$
$504$	3.92482e6	0.688246
$505$	−1.18295e6	−0.206414
$506$	−2.98541e6	−0.518355
$507$	−8.65760e6	−1.49581
$508$	−2.16402e7	−3.72050
$509$	−526059.	−0.0899995	−0.0449998	−	0.998987i	$-0.514329\pi$
$509$	−526059.	−0.0899995	−0.0449998	+	0.998987i	$0.514329\pi$
$510$	1.98704e6	0.338284
$511$	−5.22332e6	−0.884900
$512$	1.23099e7	2.07529
$513$	1.53417e6	0.257382
$514$	1.16670e7	1.94784
$515$	1.76116e6	0.292604
$516$	−8.40504e6	−1.38968
$517$	−3.00188e6	−0.493931
$518$	−2.41396e6	−0.395281
$519$	2.35483e6	0.383744
$520$	1.24926e7	2.02603
$521$	7.14463e6	1.15315	0.576574	−	0.817045i	$-0.304389\pi$
$521$	7.14463e6	1.15315	0.576574	+	0.817045i	$0.304389\pi$
$522$	4.39678e6	0.706250
$523$	−8.33059e6	−1.33175	−0.665873	−	0.746065i	$-0.731941\pi$
$523$	−8.33059e6	−1.33175	−0.665873	+	0.746065i	$0.731941\pi$
$524$	2.34382e7	3.72903
$525$	−2.46749e6	−0.390712
$526$	4.72750e6	0.745018
$527$	−1.33813e6	−0.209880
$528$	3.72095e6	0.580857
$529$	−3.97312e6	−0.617295
$530$	−5.52816e6	−0.854852
$531$	281961.	0.0433963
$532$	1.70852e7	2.61723
$533$	−1.84072e7	−2.80653
$534$	−4.94802e6	−0.750893
$535$	−4.33803e6	−0.655252
$536$	−2.20752e7	−3.31889
$537$	−2.71653e6	−0.406518
$538$	−1.97163e7	−2.93676
$539$	958933.	0.142173
$540$	1.32150e6	0.195021
$541$	1.15571e7	1.69768	0.848842	−	0.528647i	$-0.177301\pi$
$541$	1.15571e7	1.69768	0.848842	+	0.528647i	$0.177301\pi$
$542$	1.72476e7	2.52192
$543$	7.49921e6	1.09148
$544$	7.92792e6	1.14858
$545$	−211491.	−0.0305001
$546$	−1.15921e7	−1.66411
$547$	7.15348e6	1.02223	0.511115	−	0.859512i	$-0.329232\pi$
$547$	7.15348e6	1.02223	0.511115	+	0.859512i	$0.329232\pi$
$548$	2.07841e7	2.95651
$549$	−599164.	−0.0848428
$550$	−4.84595e6	−0.683081
$551$	1.10209e7	1.54645
$552$	−6.35981e6	−0.888375
$553$	−8.37842e6	−1.16506
$554$	1.74493e6	0.241548
$555$	−468012.	−0.0644947
$556$	2.56787e7	3.52279
$557$	2.14733e6	0.293266	0.146633	−	0.989191i	$-0.453156\pi$
$557$	2.14733e6	0.293266	0.146633	+	0.989191i	$0.453156\pi$
$558$	−1.26743e6	−0.172322
$559$	1.42943e7	1.93479
$560$	5.82602e6	0.785059
$561$	−1.46404e6	−0.196402
$562$	−1.35449e6	−0.180899
$563$	−2.84832e6	−0.378719	−0.189360	−	0.981908i	$-0.560641\pi$
$563$	−2.84832e6	−0.378719	−0.189360	+	0.981908i	$0.560641\pi$
$564$	−1.11059e7	−1.47013
$565$	−2.96800e6	−0.391149
$566$	6.70356e6	0.879558
$567$	−706082.	−0.0922354
$568$	−1.48174e7	−1.92709
$569$	−4.02345e6	−0.520976	−0.260488	−	0.965477i	$-0.583883\pi$
$569$	−4.02345e6	−0.520976	−0.260488	+	0.965477i	$0.583883\pi$
$570$	4.71753e6	0.608173
$571$	−1.04667e6	−0.134345	−0.0671724	−	0.997741i	$-0.521398\pi$
$571$	−1.04667e6	−0.134345	−0.0671724	+	0.997741i	$0.521398\pi$
$572$	−1.59852e7	−2.04281
$573$	1.84725e6	0.235038
$574$	−1.77827e7	−2.25277
$575$	3.99833e6	0.504323
$576$	1.66960e6	0.209680
$577$	4.52735e6	0.566115	0.283057	−	0.959103i	$-0.408651\pi$
$577$	4.52735e6	0.566115	0.283057	+	0.959103i	$0.408651\pi$
$578$	6.57287e6	0.818344
$579$	−6.19707e6	−0.768228
$580$	9.49313e6	1.17176
$581$	−1.30747e6	−0.160691
$582$	−3.92382e6	−0.480178
$583$	4.07311e6	0.496312
$584$	−2.18530e7	−2.65142
$585$	−2.24744e6	−0.271518
$586$	2.60098e6	0.312891
$587$	−1.14528e7	−1.37188	−0.685938	−	0.727660i	$-0.740608\pi$
$587$	−1.14528e7	−1.37188	−0.685938	+	0.727660i	$0.740608\pi$
$588$	3.54771e6	0.423160
$589$	−3.17692e6	−0.377327
$590$	867024.	0.102542
$591$	−3.56123e6	−0.419403
$592$	−4.87534e6	−0.571743
$593$	6.39698e6	0.747031	0.373515	−	0.927624i	$-0.378152\pi$
$593$	6.39698e6	0.747031	0.373515	+	0.927624i	$0.378152\pi$
$594$	−1.38669e6	−0.161255
$595$	−2.29229e6	−0.265447
$596$	−2.94850e7	−3.40005
$597$	1.76763e6	0.202981
$598$	1.87839e7	2.14800
$599$	−2.97718e6	−0.339030	−0.169515	−	0.985528i	$-0.554220\pi$
$599$	−2.97718e6	−0.339030	−0.169515	+	0.985528i	$0.554220\pi$
$600$	−1.03233e7	−1.17069
$601$	795349.	0.0898197	0.0449098	−	0.998991i	$-0.485700\pi$
$601$	795349.	0.0898197	0.0449098	+	0.998991i	$0.485700\pi$
$602$	1.38093e7	1.55303
$603$	3.97137e6	0.444782
$604$	−1.11775e7	−1.24667
$605$	3.06073e6	0.339967
$606$	4.59242e6	0.507995
$607$	1.48437e6	0.163520	0.0817601	−	0.996652i	$-0.473946\pi$
$607$	1.48437e6	0.163520	0.0817601	+	0.996652i	$0.473946\pi$
$608$	1.88221e7	2.06494
$609$	−5.07222e6	−0.554185
$610$	−1.84242e6	−0.200476
$611$	1.88875e7	2.04679
$612$	−5.41642e6	−0.584566
$613$	−5.32825e6	−0.572708	−0.286354	−	0.958124i	$-0.592443\pi$
$613$	−5.32825e6	−0.572708	−0.286354	+	0.958124i	$0.592443\pi$
$614$	−1.42939e7	−1.53013
$615$	−3.44765e6	−0.367566
$616$	−8.89217e6	−0.944183
$617$	−1.34206e7	−1.41925	−0.709625	−	0.704580i	$-0.751136\pi$
$617$	−1.34206e7	−1.41925	−0.709625	+	0.704580i	$0.751136\pi$
$618$	−6.83709e6	−0.720112
$619$	−179809.	−0.0188619	−0.00943094	−	0.999956i	$-0.503002\pi$
$619$	−179809.	−0.0188619	−0.00943094	+	0.999956i	$0.503002\pi$
$620$	−2.73653e6	−0.285904
$621$	1.14414e6	0.119056
$622$	1.59599e7	1.65407
$623$	5.70814e6	0.589216
$624$	−2.34119e7	−2.40700
$625$	4.68568e6	0.479813
$626$	6.53958e6	0.666982
$627$	−3.47584e6	−0.353095
$628$	1.45086e7	1.46800
$629$	1.91824e6	0.193320
$630$	−2.17119e6	−0.217945
$631$	61593.7	0.00615832	0.00307916	−	0.999995i	$-0.499020\pi$
$631$	61593.7	0.00615832	0.00307916	+	0.999995i	$0.499020\pi$
$632$	−3.50531e7	−3.49087
$633$	−1.49028e6	−0.147828
$634$	2.07429e6	0.204949
$635$	6.89316e6	0.678397
$636$	1.50691e7	1.47722
$637$	−6.03352e6	−0.589145
$638$	−9.96145e6	−0.968882
$639$	2.66568e6	0.258260
$640$	−1.74335e6	−0.168242
$641$	−1.56476e7	−1.50419	−0.752094	−	0.659056i	$-0.770956\pi$
$641$	−1.56476e7	−1.50419	−0.752094	+	0.659056i	$0.770956\pi$
$642$	1.68409e7	1.61261
$643$	−8.28513e6	−0.790264	−0.395132	−	0.918624i	$-0.629301\pi$
$643$	−8.28513e6	−0.790264	−0.395132	+	0.918624i	$0.629301\pi$
$644$	1.27417e7	1.21063
$645$	2.67730e6	0.253395
$646$	−1.93357e7	−1.82297
$647$	−3.23124e6	−0.303465	−0.151732	−	0.988422i	$-0.548485\pi$
$647$	−3.23124e6	−0.303465	−0.151732	+	0.988422i	$0.548485\pi$
$648$	−2.95406e6	−0.276364
$649$	−638818.	−0.0595340
$650$	3.04903e7	2.83060
$651$	1.46214e6	0.135219
$652$	−2.40019e7	−2.21120
$653$	−9.71737e6	−0.891796	−0.445898	−	0.895084i	$-0.647116\pi$
$653$	−9.71737e6	−0.891796	−0.445898	+	0.895084i	$0.647116\pi$
$654$	821043.	0.0750622
$655$	−7.46589e6	−0.679952
$656$	−3.59146e7	−3.25846
$657$	3.93139e6	0.355331
$658$	1.82467e7	1.64293
$659$	−4.36014e6	−0.391100	−0.195550	−	0.980694i	$-0.562649\pi$
$659$	−4.36014e6	−0.391100	−0.195550	+	0.980694i	$0.562649\pi$
$660$	−2.99402e6	−0.267543
$661$	−1.71786e7	−1.52927	−0.764636	−	0.644463i	$-0.777081\pi$
$661$	−1.71786e7	−1.52927	−0.764636	+	0.644463i	$0.777081\pi$
$662$	1.82675e7	1.62008
$663$	9.21159e6	0.813862
$664$	−5.47010e6	−0.481477
$665$	−5.44225e6	−0.477226
$666$	1.81690e6	0.158725
$667$	8.21906e6	0.715332
$668$	−1.45817e6	−0.126435
$669$	−5.25154e6	−0.453651
$670$	1.22119e7	1.05098
$671$	1.35748e6	0.116393
$672$	−8.66264e6	−0.739992
$673$	1.84521e7	1.57040	0.785198	−	0.619245i	$-0.212561\pi$
$673$	1.84521e7	1.57040	0.785198	+	0.619245i	$0.212561\pi$
$674$	−3.01854e7	−2.55945
$675$	1.85718e6	0.156890
$676$	7.25680e7	6.10771
$677$	−2.03553e7	−1.70689	−0.853446	−	0.521181i	$-0.825492\pi$
$677$	−2.03553e7	−1.70689	−0.853446	+	0.521181i	$0.825492\pi$
$678$	1.15222e7	0.962637
$679$	4.52661e6	0.376789
$680$	−9.59035e6	−0.795357
$681$	−6.52257e6	−0.538953
$682$	2.87153e6	0.236403
$683$	−1.95888e7	−1.60678	−0.803388	−	0.595455i	$-0.796972\pi$
$683$	−1.95888e7	−1.60678	−0.803388	+	0.595455i	$0.796972\pi$
$684$	−1.28594e7	−1.05095
$685$	−6.62046e6	−0.539090
$686$	−2.45768e7	−1.99395
$687$	−1.13444e7	−0.917041
$688$	2.78898e7	2.24634
$689$	−2.56277e7	−2.05665
$690$	3.51821e6	0.281319
$691$	−9.42374e6	−0.750807	−0.375403	−	0.926862i	$-0.622496\pi$
$691$	−9.42374e6	−0.750807	−0.375403	+	0.926862i	$0.622496\pi$
$692$	−1.97382e7	−1.56690
$693$	1.59972e6	0.126535
$694$	−2.22225e7	−1.75143
$695$	−8.17959e6	−0.642346
$696$	−2.12208e7	−1.66050
$697$	1.41309e7	1.10176
$698$	1.52540e7	1.18507
$699$	−1.82746e6	−0.141467
$700$	2.06825e7	1.59536
$701$	−1.84234e7	−1.41604	−0.708018	−	0.706194i	$-0.750411\pi$
$701$	−1.84234e7	−1.41604	−0.708018	+	0.706194i	$0.750411\pi$
$702$	8.72493e6	0.668220
$703$	4.55419e6	0.347554
$704$	−3.78269e6	−0.287653
$705$	3.53761e6	0.268064
$706$	−2.69306e7	−2.03345
$707$	−5.29791e6	−0.398617
$708$	−2.36340e6	−0.177196
$709$	1.93635e6	0.144667	0.0723334	−	0.997381i	$-0.476955\pi$
$709$	1.93635e6	0.144667	0.0723334	+	0.997381i	$0.476955\pi$
$710$	8.19692e6	0.610246
$711$	6.30611e6	0.467830
$712$	2.38814e7	1.76546
$713$	−2.36926e6	−0.174538
$714$	8.89905e6	0.653278
$715$	5.09186e6	0.372487
$716$	2.27700e7	1.65989
$717$	−1.17639e7	−0.854583
$718$	−4.02251e7	−2.91196
$719$	−1.27399e7	−0.919063	−0.459531	−	0.888162i	$-0.651983\pi$
$719$	−1.27399e7	−0.919063	−0.459531	+	0.888162i	$0.651983\pi$
$720$	−4.38502e6	−0.315240
$721$	7.88742e6	0.565063
$722$	−2.02406e7	−1.44504
$723$	1.12564e7	0.800854
$724$	−6.28585e7	−4.45674
$725$	1.33413e7	0.942654
$726$	−1.18823e7	−0.836676
$727$	−4.14616e6	−0.290944	−0.145472	−	0.989362i	$-0.546470\pi$
$727$	−4.14616e6	−0.290944	−0.145472	+	0.989362i	$0.546470\pi$
$728$	5.59487e7	3.91257
$729$	531441.	0.0370370
$730$	1.20889e7	0.839617
$731$	−1.09735e7	−0.759539
$732$	5.02220e6	0.346430
$733$	1.99625e7	1.37232	0.686160	−	0.727450i	$-0.259295\pi$
$733$	1.99625e7	1.37232	0.686160	+	0.727450i	$0.259295\pi$
$734$	−2.49126e7	−1.70679
$735$	−1.13007e6	−0.0771592
$736$	1.40370e7	0.955168
$737$	−8.99763e6	−0.610182
$738$	1.33843e7	0.904598
$739$	−1.09285e7	−0.736120	−0.368060	−	0.929802i	$-0.619978\pi$
$739$	−1.09285e7	−0.736120	−0.368060	+	0.929802i	$0.619978\pi$
$740$	3.92288e6	0.263345
$741$	2.18697e7	1.46318
$742$	−2.47581e7	−1.65085
$743$	−9.59066e6	−0.637348	−0.318674	−	0.947864i	$-0.603238\pi$
$743$	−9.59066e6	−0.637348	−0.318674	+	0.947864i	$0.603238\pi$
$744$	6.11721e6	0.405155
$745$	9.39201e6	0.619966
$746$	3.93801e7	2.59077
$747$	984081.	0.0645252
$748$	1.22716e7	0.801948
$749$	−1.94281e7	−1.26539
$750$	1.27160e7	0.825461
$751$	2.88768e7	1.86831	0.934155	−	0.356868i	$-0.116156\pi$
$751$	2.88768e7	1.86831	0.934155	+	0.356868i	$0.116156\pi$
$752$	3.68518e7	2.37637
$753$	−5.48553e6	−0.352559
$754$	6.26766e7	4.01492
$755$	3.56042e6	0.227318
$756$	5.91839e6	0.376616
$757$	1.63783e7	1.03879	0.519396	−	0.854534i	$-0.326157\pi$
$757$	1.63783e7	1.03879	0.519396	+	0.854534i	$0.326157\pi$
$758$	−4.45796e7	−2.81814
$759$	−2.59219e6	−0.163329
$760$	−2.27689e7	−1.42991
$761$	1.04568e7	0.654544	0.327272	−	0.944930i	$-0.393871\pi$
$761$	1.04568e7	0.654544	0.327272	+	0.944930i	$0.393871\pi$
$762$	−2.67603e7	−1.66957
$763$	−947173.	−0.0589004
$764$	−1.54836e7	−0.959710
$765$	1.72532e6	0.106590
$766$	1.46080e7	0.899539
$767$	4.01938e6	0.246701
$768$	1.27043e7	0.777228
$769$	1.72862e7	1.05410	0.527052	−	0.849833i	$-0.323297\pi$
$769$	1.72862e7	1.05410	0.527052	+	0.849833i	$0.323297\pi$
$770$	4.91910e6	0.298991
$771$	1.01303e7	0.613745
$772$	5.19439e7	3.13683
$773$	2.00179e7	1.20495	0.602476	−	0.798137i	$-0.294181\pi$
$773$	2.00179e7	1.20495	0.602476	+	0.798137i	$0.294181\pi$
$774$	−1.03937e7	−0.623618
$775$	−3.84581e6	−0.230003
$776$	1.89381e7	1.12897
$777$	−2.09601e6	−0.124549
$778$	−4.52577e7	−2.68067
$779$	3.35488e7	1.98077
$780$	1.88381e7	1.10866
$781$	−6.03944e6	−0.354298
$782$	−1.44201e7	−0.843239
$783$	3.81767e6	0.222533
$784$	−1.17721e7	−0.684013
$785$	−4.62151e6	−0.267676
$786$	2.89838e7	1.67340
$787$	2.56779e7	1.47783	0.738913	−	0.673801i	$-0.235339\pi$
$787$	2.56779e7	1.47783	0.738913	+	0.673801i	$0.235339\pi$
$788$	2.98502e7	1.71251
$789$	4.10482e6	0.234748
$790$	1.93912e7	1.10544
$791$	−1.32923e7	−0.755369
$792$	6.69280e6	0.379136
$793$	−8.54115e6	−0.482318
$794$	1.07834e7	0.607019
$795$	−4.80003e6	−0.269356
$796$	−1.48163e7	−0.828813
$797$	3.44432e7	1.92069	0.960346	−	0.278812i	$-0.0899406\pi$
$797$	3.44432e7	1.92069	0.960346	+	0.278812i	$0.0899406\pi$
$798$	2.11277e7	1.17448
$799$	−1.44996e7	−0.803507
$800$	2.27850e7	1.25871
$801$	−4.29630e6	−0.236599
$802$	6.87082e6	0.377201
$803$	−8.90705e6	−0.487467
$804$	−3.32880e7	−1.81613
$805$	−4.05868e6	−0.220747
$806$	−1.80674e7	−0.979621
$807$	−1.71194e7	−0.925346
$808$	−2.21651e7	−1.19438
$809$	−2.29612e7	−1.23345	−0.616726	−	0.787178i	$-0.711541\pi$
$809$	−2.29612e7	−1.23345	−0.616726	+	0.787178i	$0.711541\pi$
$810$	1.63417e6	0.0875154
$811$	−2.87822e7	−1.53664	−0.768319	−	0.640067i	$-0.778907\pi$
$811$	−2.87822e7	−1.53664	−0.768319	+	0.640067i	$0.778907\pi$
$812$	4.25154e7	2.26285
$813$	1.49759e7	0.794633
$814$	−4.11641e6	−0.217749
$815$	7.64546e6	0.403190
$816$	1.79729e7	0.944915
$817$	−2.60526e7	−1.36552
$818$	2.23653e7	1.16867
$819$	−1.00653e7	−0.524344
$820$	2.88982e7	1.50085
$821$	3.20155e7	1.65769	0.828843	−	0.559481i	$-0.189000\pi$
$821$	3.20155e7	1.65769	0.828843	+	0.559481i	$0.189000\pi$
$822$	2.57017e7	1.32673
$823$	−2.11330e7	−1.08758	−0.543790	−	0.839221i	$-0.683011\pi$
$823$	−2.11330e7	−1.08758	−0.543790	+	0.839221i	$0.683011\pi$
$824$	3.29989e7	1.69310
$825$	−4.20768e6	−0.215232
$826$	3.88301e6	0.198024
$827$	1.90142e7	0.966750	0.483375	−	0.875413i	$-0.339411\pi$
$827$	1.90142e7	0.966750	0.483375	+	0.875413i	$0.339411\pi$
$828$	−9.59019e6	−0.486129
$829$	−2.25270e7	−1.13846	−0.569229	−	0.822179i	$-0.692758\pi$
$829$	−2.25270e7	−1.13846	−0.569229	+	0.822179i	$0.692758\pi$
$830$	3.02603e6	0.152468
$831$	1.51510e6	0.0761094
$832$	2.38003e7	1.19200
$833$	4.63182e6	0.231281
$834$	3.17545e7	1.58085
$835$	464477.	0.0230541
$836$	2.91345e7	1.44176
$837$	−1.10050e6	−0.0542969
$838$	−1.88269e7	−0.926121
$839$	1.03990e6	0.0510018	0.0255009	−	0.999675i	$-0.491882\pi$
$839$	1.03990e6	0.0510018	0.0255009	+	0.999675i	$0.491882\pi$
$840$	1.04791e7	0.512421
$841$	6.91350e6	0.337060
$842$	−6.15755e7	−2.99315
$843$	−1.17609e6	−0.0569996
$844$	1.24915e7	0.603613
$845$	−2.31155e7	−1.11368
$846$	−1.37336e7	−0.659718
$847$	1.37076e7	0.656529
$848$	−5.00026e7	−2.38783
$849$	5.82062e6	0.277140
$850$	−2.34068e7	−1.11121
$851$	3.39639e6	0.160766
$852$	−2.23438e7	−1.05453
$853$	3.24783e7	1.52834	0.764172	−	0.645012i	$-0.223148\pi$
$853$	3.24783e7	1.52834	0.764172	+	0.645012i	$0.223148\pi$
$854$	−8.25135e6	−0.387151
$855$	4.09617e6	0.191630
$856$	−8.12820e7	−3.79149
$857$	4.10677e7	1.91007	0.955034	−	0.296498i	$-0.0958188\pi$
$857$	4.10677e7	1.91007	0.955034	+	0.296498i	$0.0958188\pi$
$858$	−1.97674e7	−0.916710
$859$	−6.92358e6	−0.320146	−0.160073	−	0.987105i	$-0.551173\pi$
$859$	−6.92358e6	−0.320146	−0.160073	+	0.987105i	$0.551173\pi$
$860$	−2.24412e7	−1.03466
$861$	−1.54405e7	−0.709827
$862$	−7.02049e7	−3.21810
$863$	−1.97360e7	−0.902051	−0.451026	−	0.892511i	$-0.648942\pi$
$863$	−1.97360e7	−0.902051	−0.451026	+	0.892511i	$0.648942\pi$
$864$	6.52004e6	0.297143
$865$	6.28732e6	0.285710
$866$	−4.52359e7	−2.04969
$867$	5.70714e6	0.257852
$868$	−1.22557e7	−0.552125
$869$	−1.42873e7	−0.641801
$870$	1.17392e7	0.525826
$871$	5.66123e7	2.52851
$872$	−3.96272e6	−0.176483
$873$	−3.40701e6	−0.151299
$874$	−3.42354e7	−1.51599
$875$	−1.46694e7	−0.647729
$876$	−3.29529e7	−1.45089
$877$	−4.10707e7	−1.80316	−0.901578	−	0.432617i	$-0.857590\pi$
$877$	−4.10707e7	−1.80316	−0.901578	+	0.432617i	$0.857590\pi$
$878$	4.09129e7	1.79112
$879$	2.25839e6	0.0985888
$880$	9.93482e6	0.432467
$881$	−2.66676e7	−1.15756	−0.578782	−	0.815482i	$-0.696472\pi$
$881$	−2.66676e7	−1.15756	−0.578782	+	0.815482i	$0.696472\pi$
$882$	4.38712e6	0.189893
$883$	−1.21010e7	−0.522299	−0.261149	−	0.965298i	$-0.584102\pi$
$883$	−1.21010e7	−0.522299	−0.261149	+	0.965298i	$0.584102\pi$
$884$	−7.72116e7	−3.32317
$885$	752826.	0.0323100
$886$	7.43557e7	3.18222
$887$	3.94963e7	1.68557	0.842787	−	0.538248i	$-0.180913\pi$
$887$	3.94963e7	1.68557	0.842787	+	0.538248i	$0.180913\pi$
$888$	−8.76917e6	−0.373186
$889$	3.08713e7	1.31009
$890$	−1.32110e7	−0.559064
$891$	−1.20405e6	−0.0508099
$892$	4.40185e7	1.85235
$893$	−3.44243e7	−1.44456
$894$	−3.64613e7	−1.52577
$895$	−7.25305e6	−0.302666
$896$	−7.80768e6	−0.324902
$897$	1.63098e7	0.676813
$898$	3.56529e7	1.47538
$899$	−7.90554e6	−0.326236
$900$	−1.55669e7	−0.640614
$901$	1.96739e7	0.807381
$902$	−3.03239e7	−1.24099
$903$	1.19904e7	0.489345
$904$	−5.56116e7	−2.26331
$905$	2.00226e7	0.812643
$906$	−1.38221e7	−0.559441
$907$	2.07260e7	0.836558	0.418279	−	0.908319i	$-0.362633\pi$
$907$	2.07260e7	0.836558	0.418279	+	0.908319i	$0.362633\pi$
$908$	5.46723e7	2.20066
$909$	3.98754e6	0.160064
$910$	−3.09505e7	−1.23898
$911$	−4.61836e7	−1.84371	−0.921854	−	0.387538i	$-0.873325\pi$
$911$	−4.61836e7	−1.84371	−0.921854	+	0.387538i	$0.873325\pi$
$912$	4.26703e7	1.69879
$913$	−2.22956e6	−0.0885201
$914$	−2.49908e6	−0.0989497
$915$	−1.59975e6	−0.0631682
$916$	9.50886e7	3.74447
$917$	−3.34363e7	−1.31309
$918$	−6.69797e6	−0.262323
$919$	−3.09603e6	−0.120925	−0.0604626	−	0.998170i	$-0.519258\pi$
$919$	−3.09603e6	−0.120925	−0.0604626	+	0.998170i	$0.519258\pi$
$920$	−1.69805e7	−0.661424
$921$	−1.24112e7	−0.482130
$922$	−4.63479e7	−1.79557
$923$	3.79996e7	1.46816
$924$	−1.34088e7	−0.516668
$925$	5.51306e6	0.211855
$926$	3.27133e7	1.25371
$927$	−5.93656e6	−0.226901
$928$	4.68374e7	1.78535
$929$	3.67908e7	1.39862	0.699311	−	0.714817i	$-0.253490\pi$
$929$	3.67908e7	1.39862	0.699311	+	0.714817i	$0.253490\pi$
$930$	−3.38400e6	−0.128299
$931$	1.09966e7	0.415801
$932$	1.53178e7	0.577640
$933$	1.38578e7	0.521182
$934$	4.84649e7	1.81786
$935$	−3.90893e6	−0.146227
$936$	−4.21105e7	−1.57109
$937$	4.64702e7	1.72912	0.864561	−	0.502527i	$-0.167596\pi$
$937$	4.64702e7	1.72912	0.864561	+	0.502527i	$0.167596\pi$
$938$	5.46915e7	2.02961
$939$	5.67823e6	0.210160
$940$	−2.96523e7	−1.09456
$941$	1.24284e7	0.457554	0.228777	−	0.973479i	$-0.426527\pi$
$941$	1.24284e7	0.457554	0.228777	+	0.973479i	$0.426527\pi$
$942$	1.79414e7	0.658764
$943$	2.50198e7	0.916231
$944$	7.84229e6	0.286426
$945$	−1.88522e6	−0.0686723
$946$	2.35483e7	0.855522
$947$	−1.45531e7	−0.527327	−0.263664	−	0.964615i	$-0.584931\pi$
$947$	−1.45531e7	−0.527327	−0.263664	+	0.964615i	$0.584931\pi$
$948$	−5.28579e7	−1.91024
$949$	5.60424e7	2.02000
$950$	−5.55713e7	−1.99775
$951$	1.80108e6	0.0645776
$952$	−4.29508e7	−1.53596
$953$	−3.32745e7	−1.18681	−0.593403	−	0.804906i	$-0.702216\pi$
$953$	−3.32745e7	−1.18681	−0.593403	+	0.804906i	$0.702216\pi$
$954$	1.86345e7	0.662898
$955$	4.93209e6	0.174994
$956$	9.86053e7	3.48944
$957$	−8.64940e6	−0.305285
$958$	−4.13839e7	−1.45686
$959$	−2.96500e7	−1.04107
$960$	4.45778e6	0.156113
$961$	−2.63503e7	−0.920400
$962$	2.59001e7	0.902325
$963$	1.46228e7	0.508117
$964$	−9.43511e7	−3.27005
$965$	−1.65460e7	−0.571970
$966$	1.57565e7	0.543270
$967$	7.31485e6	0.251559	0.125779	−	0.992058i	$-0.459857\pi$
$967$	7.31485e6	0.251559	0.125779	+	0.992058i	$0.459857\pi$
$968$	5.73492e7	1.96716
$969$	−1.67890e7	−0.574400
$970$	−1.04765e7	−0.357508
$971$	2.70477e7	0.920625	0.460312	−	0.887757i	$-0.347737\pi$
$971$	2.70477e7	0.920625	0.460312	+	0.887757i	$0.347737\pi$
$972$	−4.45454e6	−0.151230
$973$	−3.66327e7	−1.24047
$974$	−7.19478e7	−2.43008
$975$	2.64743e7	0.891894
$976$	−1.66648e7	−0.559983
$977$	3.60762e7	1.20916	0.604580	−	0.796544i	$-0.293341\pi$
$977$	3.60762e7	1.20916	0.604580	+	0.796544i	$0.293341\pi$
$978$	−2.96809e7	−0.992270
$979$	9.73380e6	0.324583
$980$	9.47227e6	0.315057
$981$	712901.	0.0236514
$982$	7.39055e7	2.44567
$983$	3.96833e7	1.30986	0.654929	−	0.755690i	$-0.272699\pi$
$983$	3.96833e7	1.30986	0.654929	+	0.755690i	$0.272699\pi$
$984$	−6.45988e7	−2.12685
$985$	−9.50836e6	−0.312259
$986$	−4.81156e7	−1.57614
$987$	1.58434e7	0.517672
$988$	−1.83312e8	−5.97446
$989$	−1.94294e7	−0.631637
$990$	−3.70242e6	−0.120060
$991$	5.23939e7	1.69471	0.847357	−	0.531023i	$-0.178192\pi$
$991$	5.23939e7	1.69471	0.847357	+	0.531023i	$0.178192\pi$
$992$	−1.35016e7	−0.435617
$993$	1.58615e7	0.510470
$994$	3.67103e7	1.17848
$995$	4.71951e6	0.151126
$996$	−8.24858e6	−0.263470
$997$	−4.22636e7	−1.34657	−0.673284	−	0.739384i	$-0.735117\pi$
$997$	−4.22636e7	−1.34657	−0.673284	+	0.739384i	$0.735117\pi$
$998$	−6.70629e6	−0.213135
$999$	1.57759e6	0.0500127

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.6.a.d.1.1	✓	13
3.2	odd	2		531.6.a.e.1.13		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.6.a.d.1.1	✓	13	1.1	even	1	trivial
531.6.a.e.1.13		13	3.2	odd	2

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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:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-10.3652 q^{2} -9.00000 q^{3} +75.4381 q^{4} -24.0297 q^{5} +93.2871 q^{6} -107.618 q^{7} -450.246 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-10.3652 q^{2} -9.00000 q^{3} +75.4381 q^{4} -24.0297 q^{5} +93.2871 q^{6} -107.618 q^{7} -450.246 q^{8} +81.0000 q^{9} +249.073 q^{10} -183.516 q^{11} -678.943 q^{12} +1154.66 q^{13} +1115.49 q^{14} +216.267 q^{15} +2252.88 q^{16} -886.414 q^{17} -839.584 q^{18} -2104.48 q^{19} -1812.75 q^{20} +968.563 q^{21} +1902.18 q^{22} -1569.47 q^{23} +4052.21 q^{24} -2547.57 q^{25} -11968.4 q^{26} -729.000 q^{27} -8118.50 q^{28} -5236.85 q^{29} -2241.66 q^{30} +1509.60 q^{31} -8943.81 q^{32} +1651.64 q^{33} +9187.89 q^{34} +2586.03 q^{35} +6110.48 q^{36} -2164.04 q^{37} +21813.4 q^{38} -10392.0 q^{39} +10819.3 q^{40} -15941.6 q^{41} -10039.4 q^{42} +12379.6 q^{43} -13844.1 q^{44} -1946.40 q^{45} +16267.9 q^{46} +16357.6 q^{47} -20276.0 q^{48} -5225.35 q^{49} +26406.2 q^{50} +7977.73 q^{51} +87105.6 q^{52} -22194.9 q^{53} +7556.26 q^{54} +4409.82 q^{55} +48454.6 q^{56} +18940.3 q^{57} +54281.2 q^{58} +3481.00 q^{59} +16314.8 q^{60} -7397.09 q^{61} -15647.3 q^{62} -8717.06 q^{63} +20612.4 q^{64} -27746.2 q^{65} -17119.6 q^{66} +49029.2 q^{67} -66869.4 q^{68} +14125.2 q^{69} -26804.8 q^{70} +32909.7 q^{71} -36469.9 q^{72} +48535.7 q^{73} +22430.8 q^{74} +22928.2 q^{75} -158758. q^{76} +19749.6 q^{77} +107715. q^{78} +77853.3 q^{79} -54136.1 q^{80} +6561.00 q^{81} +165239. q^{82} +12149.1 q^{83} +73066.5 q^{84} +21300.3 q^{85} -128318. q^{86} +47131.7 q^{87} +82627.1 q^{88} -53040.7 q^{89} +20174.9 q^{90} -124263. q^{91} -118397. q^{92} -13586.4 q^{93} -169550. q^{94} +50570.0 q^{95} +80494.3 q^{96} -42061.8 q^{97} +54162.0 q^{98} -14864.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 117 q^{3} + 246 q^{4} - 14 q^{5} + 373 q^{7} + 123 q^{8} + 1053 q^{9}+O(q^{10}) \) 13 * q - 117 * q^3 + 246 * q^4 - 14 * q^5 + 373 * q^7 + 123 * q^8 + 1053 * q^9	\( 13 q - 117 q^{3} + 246 q^{4} - 14 q^{5} + 373 q^{7} + 123 q^{8} + 1053 q^{9} + 137 q^{10} + 250 q^{11} - 2214 q^{12} + 1054 q^{13} - 575 q^{14} + 126 q^{15} + 922 q^{16} + 271 q^{17} + 671 q^{19} - 5491 q^{20} - 3357 q^{21} + 1094 q^{22} + 3975 q^{23} - 1107 q^{24} + 15569 q^{25} + 4622 q^{26} - 9477 q^{27} + 21214 q^{28} - 10613 q^{29} - 1233 q^{30} + 25597 q^{31} + 15966 q^{32} - 2250 q^{33} + 31796 q^{34} + 6729 q^{35} + 19926 q^{36} + 17585 q^{37} + 34903 q^{38} - 9486 q^{39} + 31382 q^{40} + 12537 q^{41} + 5175 q^{42} + 26644 q^{43} + 6654 q^{44} - 1134 q^{45} + 149005 q^{46} + 52087 q^{47} - 8298 q^{48} + 95384 q^{49} + 121821 q^{50} - 2439 q^{51} + 263630 q^{52} + 20014 q^{53} + 120932 q^{55} + 126688 q^{56} - 6039 q^{57} + 86066 q^{58} + 45253 q^{59} + 49419 q^{60} - 11667 q^{61} + 164794 q^{62} + 30213 q^{63} + 151893 q^{64} - 28674 q^{65} - 9846 q^{66} + 1106 q^{67} - 4043 q^{68} - 35775 q^{69} + 56066 q^{70} + 21230 q^{71} + 9963 q^{72} + 81131 q^{73} + 102042 q^{74} - 140121 q^{75} + 73900 q^{76} - 104655 q^{77} - 41598 q^{78} - 13470 q^{79} - 191969 q^{80} + 85293 q^{81} + 79909 q^{82} - 76149 q^{83} - 190926 q^{84} + 10035 q^{85} - 321496 q^{86} + 95517 q^{87} - 276779 q^{88} - 190205 q^{89} + 11097 q^{90} + 80601 q^{91} + 45672 q^{92} - 230373 q^{93} + 36768 q^{94} + 9875 q^{95} - 143694 q^{96} + 160850 q^{97} - 116644 q^{98} + 20250 q^{99}+O(q^{100}) \) 13 * q - 117 * q^3 + 246 * q^4 - 14 * q^5 + 373 * q^7 + 123 * q^8 + 1053 * q^9 + 137 * q^10 + 250 * q^11 - 2214 * q^12 + 1054 * q^13 - 575 * q^14 + 126 * q^15 + 922 * q^16 + 271 * q^17 + 671 * q^19 - 5491 * q^20 - 3357 * q^21 + 1094 * q^22 + 3975 * q^23 - 1107 * q^24 + 15569 * q^25 + 4622 * q^26 - 9477 * q^27 + 21214 * q^28 - 10613 * q^29 - 1233 * q^30 + 25597 * q^31 + 15966 * q^32 - 2250 * q^33 + 31796 * q^34 + 6729 * q^35 + 19926 * q^36 + 17585 * q^37 + 34903 * q^38 - 9486 * q^39 + 31382 * q^40 + 12537 * q^41 + 5175 * q^42 + 26644 * q^43 + 6654 * q^44 - 1134 * q^45 + 149005 * q^46 + 52087 * q^47 - 8298 * q^48 + 95384 * q^49 + 121821 * q^50 - 2439 * q^51 + 263630 * q^52 + 20014 * q^53 + 120932 * q^55 + 126688 * q^56 - 6039 * q^57 + 86066 * q^58 + 45253 * q^59 + 49419 * q^60 - 11667 * q^61 + 164794 * q^62 + 30213 * q^63 + 151893 * q^64 - 28674 * q^65 - 9846 * q^66 + 1106 * q^67 - 4043 * q^68 - 35775 * q^69 + 56066 * q^70 + 21230 * q^71 + 9963 * q^72 + 81131 * q^73 + 102042 * q^74 - 140121 * q^75 + 73900 * q^76 - 104655 * q^77 - 41598 * q^78 - 13470 * q^79 - 191969 * q^80 + 85293 * q^81 + 79909 * q^82 - 76149 * q^83 - 190926 * q^84 + 10035 * q^85 - 321496 * q^86 + 95517 * q^87 - 276779 * q^88 - 190205 * q^89 + 11097 * q^90 + 80601 * q^91 + 45672 * q^92 - 230373 * q^93 + 36768 * q^94 + 9875 * q^95 - 143694 * q^96 + 160850 * q^97 - 116644 * q^98 + 20250 * q^99

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