LMFDB - Embedded newform 177.5.b.a.119.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,5,Mod(119,177)]

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([1, 0]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("177.119");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	177.b (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$18.2964834658$
Analytic rank:	$0$
Dimension:	$78$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			119.7
Character	$\chi$	$=$	177.119
Dual form			177.5.b.a.119.72

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-6.87418i q^{2} +(8.98827 + 0.459381i) q^{3} -31.2543 q^{4} +23.0718i q^{5} +(3.15787 - 61.7870i) q^{6} +23.0938 q^{7} +104.861i q^{8} +(80.5779 + 8.25808i) q^{9} +O(q^{10})$	\(q-6.87418i q^{2} +(8.98827 + 0.459381i) q^{3} -31.2543 q^{4} +23.0718i q^{5} +(3.15787 - 61.7870i) q^{6} +23.0938 q^{7} +104.861i q^{8} +(80.5779 + 8.25808i) q^{9} +158.600 q^{10} +26.5708i q^{11} +(-280.922 - 14.3576i) q^{12} +309.103 q^{13} -158.751i q^{14} +(-10.5987 + 207.375i) q^{15} +220.764 q^{16} +148.246i q^{17} +(56.7675 - 553.907i) q^{18} +30.3588 q^{19} -721.093i q^{20} +(207.573 + 10.6089i) q^{21} +182.653 q^{22} -899.995i q^{23} +(-48.1712 + 942.519i) q^{24} +92.6930 q^{25} -2124.83i q^{26} +(720.463 + 111.242i) q^{27} -721.782 q^{28} -161.427i q^{29} +(1425.54 + 72.8576i) q^{30} -275.870 q^{31} +160.205i q^{32} +(-12.2061 + 238.826i) q^{33} +1019.07 q^{34} +532.816i q^{35} +(-2518.41 - 258.101i) q^{36} +1786.76 q^{37} -208.692i q^{38} +(2778.30 + 141.996i) q^{39} -2419.33 q^{40} +1895.31i q^{41} +(72.9272 - 1426.90i) q^{42} -1301.72 q^{43} -830.454i q^{44} +(-190.529 + 1859.08i) q^{45} -6186.73 q^{46} -2728.57i q^{47} +(1984.29 + 101.415i) q^{48} -1867.68 q^{49} -637.188i q^{50} +(-68.1013 + 1332.47i) q^{51} -9660.81 q^{52} +1992.52i q^{53} +(764.696 - 4952.59i) q^{54} -613.037 q^{55} +2421.64i q^{56} +(272.873 + 13.9462i) q^{57} -1109.68 q^{58} +453.188i q^{59} +(331.257 - 6481.38i) q^{60} +4427.43 q^{61} +1896.38i q^{62} +(1860.85 + 190.711i) q^{63} +4633.50 q^{64} +7131.56i q^{65} +(1641.73 + 83.9072i) q^{66} -3928.08 q^{67} -4633.32i q^{68} +(413.441 - 8089.40i) q^{69} +3662.67 q^{70} -526.218i q^{71} +(-865.951 + 8449.48i) q^{72} -3454.42 q^{73} -12282.5i q^{74} +(833.149 + 42.5814i) q^{75} -948.843 q^{76} +613.622i q^{77} +(976.106 - 19098.5i) q^{78} +738.873 q^{79} +5093.42i q^{80} +(6424.61 + 1330.84i) q^{81} +13028.7 q^{82} +3710.55i q^{83} +(-6487.57 - 331.573i) q^{84} -3420.29 q^{85} +8948.25i q^{86} +(74.1566 - 1450.95i) q^{87} -2786.25 q^{88} -7525.97i q^{89} +(12779.6 + 1309.73i) q^{90} +7138.37 q^{91} +28128.7i q^{92} +(-2479.59 - 126.729i) q^{93} -18756.7 q^{94} +700.431i q^{95} +(-73.5952 + 1439.97i) q^{96} +607.333 q^{97} +12838.7i q^{98} +(-219.424 + 2141.02i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9}+O(q^{10}) $ 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9	$ 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9} - 156 q^{10} - 4 q^{13} + 13 q^{15} + 4948 q^{16} + 22 q^{18} + 812 q^{19} - 173 q^{21} - 1644 q^{22} - 678 q^{24} - 8238 q^{25} + 777 q^{27} - 3764 q^{28} + 1374 q^{30} + 4664 q^{31} - 1042 q^{33} + 3244 q^{34} + 3648 q^{36} - 3960 q^{37} - 7078 q^{39} - 1576 q^{40} + 4934 q^{42} - 1492 q^{43} - 2063 q^{45} - 2036 q^{46} - 2620 q^{48} + 24274 q^{49} + 7300 q^{51} + 8408 q^{52} - 14766 q^{54} + 9780 q^{55} + 6939 q^{57} - 3856 q^{58} + 4712 q^{60} - 212 q^{61} - 7438 q^{63} - 45760 q^{64} + 3048 q^{66} - 12972 q^{67} + 21672 q^{69} + 5828 q^{70} - 866 q^{72} - 5240 q^{73} - 20922 q^{75} + 12368 q^{76} - 16508 q^{78} - 14976 q^{79} + 25524 q^{81} - 14484 q^{82} + 9540 q^{84} + 11572 q^{85} + 5695 q^{87} + 62160 q^{88} - 31672 q^{90} + 8284 q^{91} - 9590 q^{93} - 10992 q^{94} + 34102 q^{96} - 55000 q^{97} - 14254 q^{99}+O(q^{100}) $ 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9 - 156 * q^10 - 4 * q^13 + 13 * q^15 + 4948 * q^16 + 22 * q^18 + 812 * q^19 - 173 * q^21 - 1644 * q^22 - 678 * q^24 - 8238 * q^25 + 777 * q^27 - 3764 * q^28 + 1374 * q^30 + 4664 * q^31 - 1042 * q^33 + 3244 * q^34 + 3648 * q^36 - 3960 * q^37 - 7078 * q^39 - 1576 * q^40 + 4934 * q^42 - 1492 * q^43 - 2063 * q^45 - 2036 * q^46 - 2620 * q^48 + 24274 * q^49 + 7300 * q^51 + 8408 * q^52 - 14766 * q^54 + 9780 * q^55 + 6939 * q^57 - 3856 * q^58 + 4712 * q^60 - 212 * q^61 - 7438 * q^63 - 45760 * q^64 + 3048 * q^66 - 12972 * q^67 + 21672 * q^69 + 5828 * q^70 - 866 * q^72 - 5240 * q^73 - 20922 * q^75 + 12368 * q^76 - 16508 * q^78 - 14976 * q^79 + 25524 * q^81 - 14484 * q^82 + 9540 * q^84 + 11572 * q^85 + 5695 * q^87 + 62160 * q^88 - 31672 * q^90 + 8284 * q^91 - 9590 * q^93 - 10992 * q^94 + 34102 * q^96 - 55000 * q^97 - 14254 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	6.87418i		−	1.71854i	−0.511518	−	0.859272i	$-0.670917\pi$
$2$		−	6.87418i		−	1.71854i	0.511518	−	0.859272i	$-0.329083\pi$
$3$	8.98827	+	0.459381i	0.998696	+	0.0510423i
$3$	8.98827	+	0.459381i	0.998696	+	0.0510423i
$4$	−31.2543			−1.95340
$5$			23.0718i			0.922871i	0.887174	+	0.461436i	$0.152665\pi$
$5$			23.0718i			0.922871i	−0.887174	+	0.461436i	$0.847335\pi$
$6$	3.15787	−	61.7870i	0.0877185	−	1.71630i
$7$	23.0938			0.471303			0.235651	−	0.971838i	$-0.424278\pi$
$7$	23.0938			0.471303			0.235651	+	0.971838i	$0.424278\pi$
$8$			104.861i			1.63845i
$9$	80.5779	+	8.25808i	0.994789	+	0.101952i
$10$	158.600			1.58600
$11$			26.5708i			0.219594i	0.993954	+	0.109797i	$0.0350200\pi$
$11$			26.5708i			0.219594i	−0.993954	+	0.109797i	$0.964980\pi$
$12$	−280.922	−	14.3576i	−1.95085	−	0.0997059i
$13$	309.103			1.82901			0.914506	−	0.404572i	$-0.132580\pi$
$13$	309.103			1.82901			0.914506	+	0.404572i	$0.132580\pi$
$14$		−	158.751i		−	0.809954i
$15$	−10.5987	+	207.375i	−0.0471055	+	0.921668i
$16$	220.764			0.862359
$17$			148.246i			0.512961i	0.966549	+	0.256480i	$0.0825629\pi$
$17$			148.246i			0.512961i	−0.966549	+	0.256480i	$0.917437\pi$
$18$	56.7675	−	553.907i	0.175208	−	1.70959i
$19$	30.3588			0.0840963			0.0420482	−	0.999116i	$-0.486612\pi$
$19$	30.3588			0.0840963			0.0420482	+	0.999116i	$0.486612\pi$
$20$		−	721.093i		−	1.80273i
$21$	207.573	+	10.6089i	0.470688	+	0.0240564i
$22$	182.653			0.377382
$23$		−	899.995i		−	1.70131i	−0.525721	−	0.850657i	$-0.676204\pi$
$23$		−	899.995i		−	1.70131i	0.525721	−	0.850657i	$-0.323796\pi$
$24$	−48.1712	+	942.519i	−0.0836305	+	1.63632i
$25$	92.6930			0.148309
$26$		−	2124.83i		−	3.14324i
$27$	720.463	+	111.242i	0.988289	+	0.152595i
$28$	−721.782			−0.920640
$29$		−	161.427i		−	0.191947i	−0.995384	−	0.0959734i	$-0.969404\pi$
$29$		−	161.427i		−	0.191947i	0.995384	−	0.0959734i	$-0.0305964\pi$
$30$	1425.54	+	72.8576i	1.58393	+	0.0809529i
$31$	−275.870			−0.287065			−0.143533	−	0.989646i	$-0.545846\pi$
$31$	−275.870			−0.287065			−0.143533	+	0.989646i	$0.545846\pi$
$32$			160.205i			0.156450i
$33$	−12.2061	+	238.826i	−0.0112086	+	0.219308i
$34$	1019.07			0.881546
$35$			532.816i			0.434952i
$36$	−2518.41	−	258.101i	−1.94322	−	0.199152i
$37$	1786.76			1.30516			0.652579	−	0.757721i	$-0.273687\pi$
$37$	1786.76			1.30516			0.652579	+	0.757721i	$0.273687\pi$
$38$		−	208.692i		−	0.144523i
$39$	2778.30	+	141.996i	1.82663	+	0.0933570i
$40$	−2419.33			−1.51208
$41$			1895.31i			1.12749i	0.825950	+	0.563744i	$0.190639\pi$
$41$			1895.31i			1.12749i	−0.825950	+	0.563744i	$0.809361\pi$
$42$	72.9272	−	1426.90i	0.0413420	−	0.808899i
$43$	−1301.72			−0.704012			−0.352006	−	0.935998i	$-0.614500\pi$
$43$	−1301.72			−0.704012			−0.352006	+	0.935998i	$0.614500\pi$
$44$		−	830.454i		−	0.428954i
$45$	−190.529	+	1859.08i	−0.0940882	+	0.918062i
$46$	−6186.73			−2.92378
$47$		−	2728.57i		−	1.23520i	−0.786490	−	0.617602i	$-0.788104\pi$
$47$		−	2728.57i		−	1.23520i	0.786490	−	0.617602i	$-0.211896\pi$
$48$	1984.29	+	101.415i	0.861235	+	0.0440168i
$49$	−1867.68			−0.777874
$50$		−	637.188i		−	0.254875i
$51$	−68.1013	+	1332.47i	−0.0261827	+	0.512292i
$52$	−9660.81			−3.57278
$53$			1992.52i			0.709333i	0.934993	+	0.354667i	$0.115406\pi$
$53$			1992.52i			0.709333i	−0.934993	+	0.354667i	$0.884594\pi$
$54$	764.696	−	4952.59i	0.262241	−	1.69842i
$55$	−613.037			−0.202657
$56$			2421.64i			0.772207i
$57$	272.873	+	13.9462i	0.0839867	+	0.00429247i
$58$	−1109.68			−0.329869
$59$			453.188i			0.130189i
$59$			453.188i			0.130189i
$60$	331.257	−	6481.38i	0.0920157	−	1.80038i
$61$	4427.43			1.18985			0.594924	−	0.803782i	$-0.297182\pi$
$61$	4427.43			1.18985			0.594924	+	0.803782i	$0.297182\pi$
$62$			1896.38i			0.493334i
$63$	1860.85	+	190.711i	0.468847	+	0.0480501i
$64$	4633.50			1.13123
$65$			7131.56i			1.68794i
$66$	1641.73	+	83.9072i	0.376890	+	0.0192624i
$67$	−3928.08			−0.875046			−0.437523	−	0.899207i	$-0.644144\pi$
$67$	−3928.08			−0.875046			−0.437523	+	0.899207i	$0.644144\pi$
$68$		−	4633.32i		−	1.00202i
$69$	413.441	−	8089.40i	0.0868391	−	1.69910i
$70$	3662.67			0.747484
$71$		−	526.218i		−	0.104388i	−0.998637	−	0.0521938i	$-0.983379\pi$
$71$		−	526.218i		−	0.104388i	0.998637	−	0.0521938i	$-0.0166213\pi$
$72$	−865.951	+	8449.48i	−0.167043	+	1.62992i
$73$	−3454.42			−0.648231			−0.324115	−	0.946018i	$-0.605067\pi$
$73$	−3454.42			−0.648231			−0.324115	+	0.946018i	$0.605067\pi$
$74$		−	12282.5i		−	2.24297i
$75$	833.149	+	42.5814i	0.148115	+	0.00757003i
$76$	−948.843			−0.164273
$77$			613.622i			0.103495i
$78$	976.106	−	19098.5i	0.160438	−	3.13914i
$79$	738.873			0.118390			0.0591951	−	0.998246i	$-0.481147\pi$
$79$	738.873			0.118390			0.0591951	+	0.998246i	$0.481147\pi$
$80$			5093.42i			0.795846i
$81$	6424.61	+	1330.84i	0.979212	+	0.202841i
$82$	13028.7			1.93764
$83$			3710.55i			0.538619i	0.963054	+	0.269310i	$0.0867955\pi$
$83$			3710.55i			0.538619i	−0.963054	+	0.269310i	$0.913204\pi$
$84$	−6487.57	−	331.573i	−0.919440	−	0.0469916i
$85$	−3420.29			−0.473397
$86$			8948.25i			1.20988i
$87$	74.1566	−	1450.95i	0.00979741	−	0.191697i
$88$	−2786.25			−0.359794
$89$		−	7525.97i		−	0.950129i	−0.879951	−	0.475064i	$-0.842425\pi$
$89$		−	7525.97i		−	0.950129i	0.879951	−	0.475064i	$-0.157575\pi$
$90$	12779.6	+	1309.73i	1.57773	+	0.161695i
$91$	7138.37			0.862018
$92$			28128.7i			3.32334i
$93$	−2479.59	−	126.729i	−0.286691	−	0.0146525i
$94$	−18756.7			−2.12275
$95$			700.431i			0.0776101i
$96$	−73.5952	+	1439.97i	−0.00798559	+	0.156246i
$97$	607.333			0.0645481			0.0322740	−	0.999479i	$-0.489725\pi$
$97$	607.333			0.0645481			0.0322740	+	0.999479i	$0.489725\pi$
$98$			12838.7i			1.33681i
$99$	−219.424	+	2141.02i	−0.0223879	+	0.218450i
$100$	−2897.06			−0.289706
$101$			11870.0i			1.16361i	0.813327	+	0.581807i	$0.197654\pi$
$101$			11870.0i			1.16361i	−0.813327	+	0.581807i	$0.802346\pi$
$102$	9159.65	+	468.140i	0.880397	+	0.0449962i
$103$	−11295.9			−1.06475			−0.532375	−	0.846509i	$-0.678700\pi$
$103$	−11295.9			−1.06475			−0.532375	+	0.846509i	$0.678700\pi$
$104$			32412.9i			2.99675i
$105$	−244.765	+	4789.09i	−0.0222009	+	0.434385i
$106$	13696.9			1.21902
$107$			14375.5i			1.25561i	0.778369	+	0.627807i	$0.216047\pi$
$107$			14375.5i			1.25561i	−0.778369	+	0.627807i	$0.783953\pi$
$108$	−22517.6	−	3476.79i	−1.93052	−	0.298079i
$109$	14936.2			1.25715			0.628573	−	0.777750i	$-0.283639\pi$
$109$	14936.2			1.25715			0.628573	+	0.777750i	$0.283639\pi$
$110$			4214.12i			0.348275i
$111$	16059.9	+	820.804i	1.30346	+	0.0666183i
$112$	5098.28			0.406432
$113$		−	20530.9i		−	1.60787i	−0.594718	−	0.803935i	$-0.702736\pi$
$113$		−	20530.9i		−	1.60787i	0.594718	−	0.803935i	$-0.297264\pi$
$114$	95.8690	−	1875.78i	0.00737681	−	0.144335i
$115$	20764.5			1.57009
$116$			5045.30i			0.374948i
$117$	24906.9	+	2552.60i	1.81948	+	0.186471i
$118$	3115.29			0.223735
$119$			3423.56i			0.241760i
$120$	−21745.6	−	1111.39i	−1.51011	−	0.0771802i
$121$	13935.0			0.951779
$122$		−	30434.9i		−	2.04481i
$123$	−870.668	+	17035.5i	−0.0575496	+	1.12602i
$124$	8622.12			0.560752
$125$			16558.5i			1.05974i
$126$	1310.98	−	12791.8i	0.0825762	−	0.805734i
$127$	−23339.4			−1.44705			−0.723523	−	0.690300i	$-0.757478\pi$
$127$	−23339.4			−1.44705			−0.723523	+	0.690300i	$0.757478\pi$
$128$		−	29288.2i		−	1.78761i
$129$	−11700.2	−	597.985i	−0.703095	−	0.0359344i
$130$	49023.6			2.90080
$131$		−	1138.83i		−	0.0663614i	−0.999449	−	0.0331807i	$-0.989436\pi$
$131$		−	1138.83i		−	0.0663614i	0.999449	−	0.0331807i	$-0.0105637\pi$
$132$	381.495	−	7464.34i	0.0218948	−	0.428394i
$133$	701.100			0.0396348
$134$			27002.3i			1.50381i
$135$	−2566.55	+	16622.4i	−0.140826	+	0.912063i
$136$	−15545.2			−0.840462
$137$		−	27914.4i		−	1.48726i	−0.668591	−	0.743630i	$-0.733102\pi$
$137$		−	27914.4i		−	1.48726i	0.668591	−	0.743630i	$-0.266898\pi$
$138$	−55608.0	−	2842.07i	−2.91997	−	0.149237i
$139$	−27635.8			−1.43035			−0.715175	−	0.698946i	$-0.753653\pi$
$139$	−27635.8			−1.43035			−0.715175	+	0.698946i	$0.753653\pi$
$140$		−	16652.8i		−	0.849632i
$141$	1253.45	−	24525.1i	0.0630477	−	1.23359i
$142$	−3617.31			−0.179395
$143$			8213.13i			0.401640i
$144$	17788.7	+	1823.09i	0.857866	+	0.0879189i
$145$	3724.41			0.177142
$146$			23746.3i			1.11401i
$147$	−16787.2	−	857.975i	−0.776860	−	0.0397045i
$148$	−55844.0			−2.54949
$149$		−	9243.56i		−	0.416358i	−0.978091	−	0.208179i	$-0.933246\pi$
$149$		−	9243.56i		−	0.416358i	0.978091	−	0.208179i	$-0.0667536\pi$
$150$	292.712	−	5727.22i	0.0130094	−	0.254543i
$151$	5292.22			0.232105			0.116052	−	0.993243i	$-0.462976\pi$
$151$	5292.22			0.232105			0.116052	+	0.993243i	$0.462976\pi$
$152$			3183.45i			0.137788i
$153$	−1224.22	+	11945.3i	−0.0522972	+	0.510288i
$154$	4218.15			0.177861
$155$		−	6364.80i		−	0.264924i
$156$	−86833.9	−	4437.99i	−3.56813	−	0.182363i
$157$	−26208.0			−1.06325			−0.531624	−	0.846981i	$-0.678418\pi$
$157$	−26208.0			−1.06325			−0.531624	+	0.846981i	$0.678418\pi$
$158$		−	5079.15i		−	0.203459i
$159$	−915.325	+	17909.3i	−0.0362060	+	0.708409i
$160$	−3696.22			−0.144384
$161$		−	20784.3i		−	0.801834i
$162$	9148.42	−	44163.9i	0.348591	−	1.68282i
$163$	−30024.1			−1.13004			−0.565021	−	0.825077i	$-0.691132\pi$
$163$	−30024.1			−1.13004			−0.565021	+	0.825077i	$0.691132\pi$
$164$		−	59236.5i		−	2.20243i
$165$	−5510.14	−	281.617i	−0.202393	−	0.0103441i
$166$	25507.0			0.925641
$167$		−	17501.5i		−	0.627541i	−0.949499	−	0.313771i	$-0.898408\pi$
$167$		−	17501.5i		−	0.627541i	0.949499	−	0.313771i	$-0.101592\pi$
$168$	−1112.46	+	21766.4i	−0.0394153	+	0.771201i
$169$	66983.7			2.34528
$170$			23511.7i			0.813554i
$171$	2446.25	+	250.705i	0.0836582	+	0.00857376i
$172$	40684.4			1.37521
$173$		−	18255.7i		−	0.609966i	−0.952358	−	0.304983i	$-0.901349\pi$
$173$		−	18255.7i		−	0.609966i	0.952358	−	0.304983i	$-0.0986509\pi$
$174$	−9974.10	−	509.766i	−0.329439	−	0.0168373i
$175$	2140.63			0.0698983
$176$			5865.89i			0.189369i
$177$	−208.186	+	4073.37i	−0.00664515	+	0.130019i
$178$	−51734.9			−1.63284
$179$		−	10728.6i		−	0.334840i	−0.985886	−	0.167420i	$-0.946456\pi$
$179$		−	10728.6i		−	0.334840i	0.985886	−	0.167420i	$-0.0535437\pi$
$180$	5954.84	−	58104.2i	0.183792	−	1.79334i
$181$	−24990.8			−0.762821			−0.381410	−	0.924406i	$-0.624561\pi$
$181$	−24990.8			−0.762821			−0.381410	+	0.924406i	$0.624561\pi$
$182$		−	49070.4i		−	1.48142i
$183$	39794.9	+	2033.88i	1.18830	+	0.0607326i
$184$	94374.4			2.78752
$185$			41223.8i			1.20449i
$186$	−871.160	+	17045.1i	−0.0251809	+	0.492691i
$187$	−3939.01			−0.112643
$188$			85279.6i			2.41284i
$189$	16638.2	+	2569.00i	0.465783	+	0.0719185i
$190$	4814.89			0.133376
$191$			55736.7i			1.52783i	0.645317	+	0.763915i	$0.276725\pi$
$191$			55736.7i			1.52783i	−0.645317	+	0.763915i	$0.723275\pi$
$192$	41647.2	+	2128.54i	1.12975	+	0.0577404i
$193$	−60148.8			−1.61478			−0.807389	−	0.590020i	$-0.799120\pi$
$193$	−60148.8			−1.61478			−0.807389	+	0.590020i	$0.799120\pi$
$194$		−	4174.91i		−	0.110929i
$195$	−3276.10	+	64100.3i	−0.0861565	+	1.68574i
$196$	58372.9			1.51950
$197$			37142.7i			0.957064i	0.878070	+	0.478532i	$0.158831\pi$
$197$			37142.7i			0.957064i	−0.878070	+	0.478532i	$0.841169\pi$
$198$	14717.8	+	1508.36i	0.375415	+	0.0384747i
$199$	−23649.3			−0.597189			−0.298594	−	0.954380i	$-0.596518\pi$
$199$	−23649.3			−0.597189			−0.298594	+	0.954380i	$0.596518\pi$
$200$			9719.88i			0.242997i
$201$	−35306.6	−	1804.49i	−0.873905	−	0.0446644i
$202$	81596.7			1.99972
$203$		−	3727.97i		−	0.0904650i
$204$	2128.46	−	41645.5i	0.0511452	−	1.00071i
$205$	−43728.1			−1.04053
$206$			77650.3i			1.82982i
$207$	7432.23	−	72519.8i	0.173452	−	1.69245i
$208$	68238.8			1.57727
$209$			806.659i			0.0184670i
$210$	32921.1	+	1682.56i	0.746509	+	0.0381533i
$211$	20215.3			0.454062			0.227031	−	0.973888i	$-0.427098\pi$
$211$	20215.3			0.454062			0.227031	+	0.973888i	$0.427098\pi$
$212$		−	62274.8i		−	1.38561i
$213$	241.734	−	4729.79i	0.00532818	−	0.104251i
$214$	98820.0			2.15783
$215$		−	30033.0i		−	0.649713i
$216$	−11664.9	+	75548.4i	−0.250020	+	1.61926i
$217$	−6370.89			−0.135295
$218$		−	102674.i		−	2.16046i
$219$	−31049.3	−	1586.90i	−0.647386	−	0.0330872i
$220$	19160.1			0.395869
$221$			45823.2i			0.938211i
$222$	5642.36	−	110399.i	0.114487	−	2.24005i
$223$	−59089.4			−1.18823			−0.594114	−	0.804381i	$-0.702497\pi$
$223$	−59089.4			−1.18823			−0.594114	+	0.804381i	$0.702497\pi$
$224$			3699.75i			0.0737355i
$225$	7469.01	+	765.466i	0.147536	+	0.0151203i
$226$	−141133.			−2.76320
$227$			18810.9i			0.365055i	0.983201	+	0.182528i	$0.0584279\pi$
$227$			18810.9i			0.365055i	−0.983201	+	0.182528i	$0.941572\pi$
$228$	−8528.46	−	435.881i	−0.164059	−	0.00838490i
$229$	−88005.3			−1.67818			−0.839089	−	0.543994i	$-0.816911\pi$
$229$	−88005.3			−1.67818			−0.839089	+	0.543994i	$0.816911\pi$
$230$		−	142739.i		−	2.69828i
$231$	−281.887	+	5515.40i	−0.00528263	+	0.103360i
$232$	16927.4			0.314496
$233$			6710.57i			0.123608i	0.998088	+	0.0618041i	$0.0196854\pi$
$233$			6710.57i			0.123608i	−0.998088	+	0.0618041i	$0.980315\pi$
$234$	17547.0	−	171214.i	0.320458	−	3.12686i
$235$	62952.9			1.13993
$236$		−	14164.1i		−	0.254310i
$237$	6641.19	+	339.424i	0.118236	+	0.00604291i
$238$	23534.2			0.415475
$239$			69891.0i			1.22356i	0.791028	+	0.611780i	$0.209546\pi$
$239$			69891.0i			1.22356i	−0.791028	+	0.611780i	$0.790454\pi$
$240$	−2339.82	+	45781.0i	−0.0406219	+	0.794809i
$241$	−16723.6			−0.287935			−0.143968	−	0.989582i	$-0.545986\pi$
$241$	−16723.6			−0.287935			−0.143968	+	0.989582i	$0.545986\pi$
$242$		−	95791.6i		−	1.63567i
$243$	57134.7	+	14913.3i	0.967582	+	0.252558i
$244$	−138376.			−2.32424
$245$		−	43090.6i		−	0.717877i
$246$	117105.	+	5985.13i	1.93511	+	0.0989016i
$247$	9383.99			0.153813
$248$		−	28928.0i		−	0.470343i
$249$	−1704.56	+	33351.4i	−0.0274924	+	0.537917i
$250$	113826.			1.82121
$251$			106808.i			1.69534i	0.530525	+	0.847669i	$0.321995\pi$
$251$			106808.i			1.69534i	−0.530525	+	0.847669i	$0.678005\pi$
$252$	−58159.7	−	5960.53i	−0.915843	−	0.0938608i
$253$	23913.6			0.373598
$254$			160439.i			2.48681i
$255$	−30742.5	−	1571.22i	−0.472780	−	0.0241633i
$256$	−127197.			−1.94087
$257$			99904.2i			1.51258i	0.654238	+	0.756289i	$0.272989\pi$
$257$			99904.2i			1.51258i	−0.654238	+	0.756289i	$0.727011\pi$
$258$	−4110.66	+	80429.3i	−0.0617549	+	1.20830i
$259$	41263.1			0.615124
$260$		−	222892.i		−	3.29722i
$261$	1333.08	−	13007.5i	0.0195693	−	0.190947i
$262$	−7828.51			−0.114045
$263$		−	134698.i		−	1.94737i	−0.227888	−	0.973687i	$-0.573182\pi$
$263$		−	134698.i		−	1.94737i	0.227888	−	0.973687i	$-0.426818\pi$
$264$	−25043.5	−	1279.95i	−0.359325	−	0.0183647i
$265$	−45970.9			−0.654623
$266$		−	4819.49i		−	0.0681142i
$267$	3457.29	−	67645.4i	0.0484968	−	0.948890i
$268$	122770.			1.70931
$269$			40912.3i			0.565391i	0.959210	+	0.282696i	$0.0912286\pi$
$269$			40912.3i			0.565391i	−0.959210	+	0.282696i	$0.908771\pi$
$270$	114265.	+	17642.9i	1.56742	+	0.242015i
$271$	−84953.4			−1.15676			−0.578378	−	0.815769i	$-0.696314\pi$
$271$	−84953.4			−1.15676			−0.578378	+	0.815769i	$0.696314\pi$
$272$			32727.3i			0.442356i
$273$	64161.6	+	3279.23i	0.860894	+	0.0439994i
$274$	−191889.			−2.55592
$275$			2462.93i			0.0325677i
$276$	−12921.8	+	252829.i	−0.169631	+	3.31901i
$277$	73776.7			0.961523			0.480761	−	0.876851i	$-0.340360\pi$
$277$	73776.7			0.961523			0.480761	+	0.876851i	$0.340360\pi$
$278$			189973.i			2.45812i
$279$	−22229.0	−	2278.15i	−0.285569	−	0.0292668i
$280$	−55871.6			−0.712648
$281$		−	121705.i		−	1.54133i	−0.637241	−	0.770665i	$-0.719924\pi$
$281$		−	121705.i		−	1.54133i	0.637241	−	0.770665i	$-0.280076\pi$
$282$	−168590.	−	8616.45i	−2.11999	−	0.108350i
$283$	−16658.8			−0.208004			−0.104002	−	0.994577i	$-0.533165\pi$
$283$	−16658.8			−0.208004			−0.104002	+	0.994577i	$0.533165\pi$
$284$			16446.6i			0.203910i
$285$	−321.765	+	6295.66i	−0.00396140	+	0.0775089i
$286$	56458.5			0.690236
$287$			43769.9i			0.531388i
$288$	−1322.99	+	12909.0i	−0.0159504	+	0.155635i
$289$	61544.2			0.736871
$290$		−	25602.3i		−	0.304427i
$291$	5458.87	+	278.997i	0.0644639	+	0.00329469i
$292$	107966.			1.26625
$293$		−	56581.4i		−	0.659081i	−0.944142	−	0.329540i	$-0.893106\pi$
$293$		−	56581.4i		−	0.659081i	0.944142	−	0.329540i	$-0.106894\pi$
$294$	−5897.87	+	115398.i	−0.0682340	+	1.33507i
$295$	−10455.8			−0.120148
$296$			187362.i			2.13844i
$297$	−2955.79	+	19143.3i	−0.0335089	+	0.217022i
$298$	−63541.9			−0.715529
$299$		−	278191.i		−	3.11172i
$300$	−26039.5	−	1330.85i	−0.289328	−	0.0147873i
$301$	−30061.7			−0.331803
$302$		−	36379.7i		−	0.398882i
$303$	−5452.86	+	106691.i	−0.0593936	+	1.16210i
$304$	6702.12			0.0725213
$305$			102149.i			1.09808i
$306$	82114.3	+	8415.54i	0.876953	+	0.0898750i
$307$	−55789.7			−0.591939			−0.295970	−	0.955197i	$-0.595643\pi$
$307$	−55789.7			−0.591939			−0.295970	+	0.955197i	$0.595643\pi$
$308$		−	19178.4i		−	0.202167i
$309$	−101531.	−	5189.14i	−1.06336	−	0.0543473i
$310$	−43752.8			−0.455284
$311$			82190.7i			0.849771i	0.905247	+	0.424885i	$0.139686\pi$
$311$			82190.7i			0.849771i	−0.905247	+	0.424885i	$0.860314\pi$
$312$	−14889.9	+	291335.i	−0.152961	+	2.99284i
$313$	−99391.8			−1.01452			−0.507261	−	0.861792i	$-0.669342\pi$
$313$	−99391.8			−1.01452			−0.507261	+	0.861792i	$0.669342\pi$
$314$			180158.i			1.82724i
$315$	−4400.03	+	42933.2i	−0.0443440	+	0.432685i
$316$	−23093.0			−0.231263
$317$		−	23818.1i		−	0.237022i	−0.992953	−	0.118511i	$-0.962188\pi$
$317$		−	23818.1i		−	0.237022i	0.992953	−	0.118511i	$-0.0378122\pi$
$318$	123112.	+	6292.11i	1.21743	+	0.0622217i
$319$	4289.26			0.0421503
$320$			106903.i			1.04398i
$321$	−6603.85	+	129211.i	−0.0640895	+	1.25398i
$322$	−142875.			−1.37799
$323$			4500.56i			0.0431381i
$324$	−200797.	−	41594.5i	−1.91279	−	0.396228i
$325$	28651.7			0.271258
$326$			206391.i			1.94203i
$327$	134250.	+	6861.39i	1.25551	+	0.0641677i
$328$	−198744.			−1.84734
$329$		−	63013.1i		−	0.582155i
$330$	−1935.89	+	37877.7i	−0.0177768	+	0.347821i
$331$	153951.			1.40516			0.702579	−	0.711606i	$-0.252032\pi$
$331$	153951.			1.40516			0.702579	+	0.711606i	$0.252032\pi$
$332$		−	115971.i		−	1.05214i
$333$	143974.	+	14755.2i	1.29836	+	0.133063i
$334$	−120308.			−1.07846
$335$		−	90627.8i		−	0.807555i
$336$	45824.7	+	2342.06i	0.405902	+	0.0207452i
$337$	162616.			1.43187			0.715935	−	0.698167i	$-0.246001\pi$
$337$	162616.			1.43187			0.715935	+	0.698167i	$0.246001\pi$
$338$		−	460458.i		−	4.03048i
$339$	9431.50	−	184537.i	0.0820694	−	1.60577i
$340$	106899.			0.924731
$341$		−	7330.09i		−	0.0630377i
$342$	1723.39	−	16815.9i	0.0147344	−	0.143770i
$343$	−98580.0			−0.837916
$344$		−	136500.i		−	1.15349i
$345$	186637.	+	9538.81i	1.56805	+	0.0801413i
$346$	−125493.			−1.04825
$347$		−	38712.6i		−	0.321509i	−0.986994	−	0.160754i	$-0.948607\pi$
$347$		−	38712.6i		−	0.321509i	0.986994	−	0.160754i	$-0.0513927\pi$
$348$	−2317.71	+	45348.5i	−0.0191382	+	0.374459i
$349$	−132581.			−1.08851			−0.544254	−	0.838920i	$-0.683187\pi$
$349$	−132581.			−1.08851			−0.544254	+	0.838920i	$0.683187\pi$
$350$		−	14715.1i		−	0.120123i
$351$	222697.	+	34385.2i	1.80759	+	0.279098i
$352$	−4256.79			−0.0343555
$353$		−	93039.8i		−	0.746654i	−0.927700	−	0.373327i	$-0.878217\pi$
$353$		−	93039.8i		−	0.746654i	0.927700	−	0.373327i	$-0.121783\pi$
$354$	28001.1	+	1431.11i	0.223444	+	0.0114200i
$355$	12140.8			0.0963363
$356$			235219.i			1.85598i
$357$	−1572.72	+	30771.9i	−0.0123400	+	0.241445i
$358$	−73750.5			−0.575438
$359$		−	222462.i		−	1.72611i	−0.505114	−	0.863053i	$-0.668550\pi$
$359$		−	222462.i		−	1.72611i	0.505114	−	0.863053i	$-0.331450\pi$
$360$	−194945.	−	19979.0i	−1.50420	−	0.154159i
$361$	−129399.			−0.992928
$362$			171791.i			1.31094i
$363$	125251.	+	6401.47i	0.950538	+	0.0485810i
$364$	−223105.			−1.68386
$365$		−	79699.6i		−	0.598233i
$366$	13981.2	−	273557.i	0.104372	−	2.04214i
$367$	−103258.			−0.766637			−0.383319	−	0.923616i	$-0.625219\pi$
$367$	−103258.			−0.766637			−0.383319	+	0.923616i	$0.625219\pi$
$368$		−	198686.i		−	1.46714i
$369$	−15651.6	+	152720.i	−0.114949	+	1.12161i
$370$	283379.			2.06997
$371$			46014.8i			0.334311i
$372$	77498.0	+	3960.84i	0.560021	+	0.0286221i
$373$	139399.			1.00194			0.500972	−	0.865464i	$-0.332976\pi$
$373$	139399.			1.00194			0.500972	+	0.865464i	$0.332976\pi$
$374$			27077.5i			0.193582i
$375$	−7606.64	+	148832.i	−0.0540917	+	1.05836i
$376$	286120.			2.02383
$377$		−	49897.6i		−	0.351073i
$378$	17659.8	−	114374.i	0.123595	−	0.800469i
$379$	54321.9			0.378178			0.189089	−	0.981960i	$-0.439447\pi$
$379$	54321.9			0.378178			0.189089	+	0.981960i	$0.439447\pi$
$380$		−	21891.5i		−	0.151603i
$381$	−209781.	−	10721.7i	−1.44516	−	0.0738606i
$382$	383144.			2.62564
$383$		−	35259.1i		−	0.240366i	−0.992752	−	0.120183i	$-0.961652\pi$
$383$		−	35259.1i		−	0.240366i	0.992752	−	0.120183i	$-0.0383482\pi$
$384$	13454.5	−	263251.i	0.0912439	−	1.78528i
$385$	−14157.4			−0.0955126
$386$			413474.i			2.77507i
$387$	−104890.	−	10749.7i	−0.700344	−	0.0717752i
$388$	−18981.8			−0.126088
$389$		−	6941.86i		−	0.0458751i	−0.999737	−	0.0229375i	$-0.992698\pi$
$389$		−	6941.86i		−	0.0458751i	0.999737	−	0.0229375i	$-0.00730189\pi$
$390$	440637.	+	22520.5i	2.89702	+	0.148064i
$391$	133420.			0.872708
$392$		−	195846.i		−	1.27451i
$393$	523.156	−	10236.1i	0.00338724	−	0.0662749i
$394$	255325.			1.64476
$395$			17047.1i			0.109259i
$396$	6857.96	−	66916.3i	0.0437325	−	0.426718i
$397$	187412.			1.18909			0.594546	−	0.804061i	$-0.297332\pi$
$397$	187412.			1.18909			0.594546	+	0.804061i	$0.297332\pi$
$398$			162569.i			1.02630i
$399$	6301.68	+	322.072i	0.0395832	+	0.00202305i
$400$	20463.3			0.127895
$401$		−	235928.i		−	1.46721i	−0.679578	−	0.733604i	$-0.737837\pi$
$401$		−	235928.i		−	1.46721i	0.679578	−	0.733604i	$-0.262163\pi$
$402$	−12404.4	+	242704.i	−0.0767578	+	1.50185i
$403$	−85272.1			−0.525046
$404$		−	370990.i		−	2.27300i
$405$	−30704.8	+	148227.i	−0.187196	+	0.903686i
$406$	−25626.7			−0.155468
$407$			47475.8i			0.286605i
$408$	−139724.	−	7141.17i	−0.839367	−	0.0428992i
$409$	106205.			0.634890			0.317445	−	0.948277i	$-0.397175\pi$
$409$	106205.			0.634890			0.317445	+	0.948277i	$0.397175\pi$
$410$			300595.i			1.78819i
$411$	12823.3	−	250902.i	0.0759133	−	1.48532i
$412$	353047.			2.07988
$413$			10465.8i			0.0613584i
$414$	−498514.	−	51090.5i	−2.90855	−	0.298085i
$415$	−85609.0			−0.497076
$416$			49519.9i			0.286150i
$417$	−248398.	−	12695.4i	−1.42849	−	0.0730084i
$418$	5545.11			0.0317364
$419$			180870.i			1.03024i	0.857118	+	0.515120i	$0.172253\pi$
$419$			180870.i			1.03024i	−0.857118	+	0.515120i	$0.827747\pi$
$420$	7649.98	−	149680.i	0.0433672	−	0.848525i
$421$	14021.8			0.0791117			0.0395558	−	0.999217i	$-0.487406\pi$
$421$	14021.8			0.0791117			0.0395558	+	0.999217i	$0.487406\pi$
$422$		−	138964.i		−	0.780326i
$423$	22532.7	−	219862.i	0.125931	−	1.22877i
$424$	−208937.			−1.16221
$425$			13741.3i			0.0760766i
$426$	−32513.4	−	1661.73i	−0.179161	−	0.00915672i
$427$	102246.			0.560779
$428$		−	449298.i		−	2.45271i
$429$	−3772.96	+	73821.8i	−0.0205006	+	0.401116i
$430$	−206452.			−1.11656
$431$		−	74917.2i		−	0.403299i	−0.979458	−	0.201649i	$-0.935370\pi$
$431$		−	74917.2i		−	0.403299i	0.979458	−	0.201649i	$-0.0646301\pi$
$432$	159052.	+	24558.2i	0.852260	+	0.131592i
$433$	−76413.8			−0.407564			−0.203782	−	0.979016i	$-0.565323\pi$
$433$	−76413.8			−0.407564			−0.203782	+	0.979016i	$0.565323\pi$
$434$			43794.6i			0.232510i
$435$	33476.0	+	1710.92i	0.176911	+	0.00904175i
$436$	−466820.			−2.45570
$437$		−	27322.8i		−	0.143074i
$438$	−10908.6	+	213438.i	−0.0568618	+	1.11256i
$439$	207056.			1.07438			0.537191	−	0.843460i	$-0.319485\pi$
$439$	207056.			1.07438			0.537191	+	0.843460i	$0.319485\pi$
$440$		−	64283.6i		−	0.332044i
$441$	−150493.	−	15423.4i	−0.773821	−	0.0793055i
$442$	314997.			1.61236
$443$		−	383130.i		−	1.95226i	−0.217179	−	0.976132i	$-0.569686\pi$
$443$		−	383130.i		−	1.95226i	0.217179	−	0.976132i	$-0.430314\pi$
$444$	−501941.	−	25653.7i	−2.54617	−	0.130132i
$445$	173638.			0.876846
$446$			406191.i			2.04202i
$447$	4246.31	−	83083.6i	0.0212519	−	0.415815i
$448$	107005.			0.533150
$449$		−	125237.i		−	0.621214i	−0.950538	−	0.310607i	$-0.899468\pi$
$449$		−	125237.i		−	0.621214i	0.950538	−	0.310607i	$-0.100532\pi$
$450$	5261.95	−	51343.3i	0.0259849	−	0.253547i
$451$	−50359.9			−0.247589
$452$			641679.i			3.14081i
$453$	47567.9	+	2431.14i	0.231802	+	0.0118472i
$454$	129310.			0.627364
$455$			164695.i			0.795531i
$456$	−1462.42	+	28613.7i	−0.00703302	+	0.137608i
$457$	18503.6			0.0885982			0.0442991	−	0.999018i	$-0.485895\pi$
$457$	18503.6			0.0885982			0.0442991	+	0.999018i	$0.485895\pi$
$458$			604964.i			2.88402i
$459$	−16491.1	+	106805.i	−0.0782753	+	0.506953i
$460$	−648980.			−3.06701
$461$			134584.i			0.633272i	0.948547	+	0.316636i	$0.102553\pi$
$461$			134584.i			0.633272i	−0.948547	+	0.316636i	$0.897447\pi$
$462$	37913.9	+	1937.74i	0.177629	+	0.00907844i
$463$	−207903.			−0.969838			−0.484919	−	0.874559i	$-0.661151\pi$
$463$	−207903.			−0.969838			−0.484919	+	0.874559i	$0.661151\pi$
$464$		−	35637.3i		−	0.165527i
$465$	2923.87	−	57208.6i	0.0135224	−	0.264579i
$466$	46129.7			0.212426
$467$		−	297233.i		−	1.36290i	−0.731865	−	0.681449i	$-0.761350\pi$
$467$		−	297233.i		−	1.36290i	0.731865	−	0.681449i	$-0.238650\pi$
$468$	−778448.	−	79779.7i	−3.55417	−	0.364251i
$469$	−90714.4			−0.412411
$470$		−	432750.i		−	1.95903i
$471$	−235564.	−	12039.5i	−1.06186	−	0.0542707i
$472$	−47521.7			−0.213308
$473$		−	34587.8i		−	0.154597i
$474$	2333.26	−	45652.7i	0.0103850	−	0.203194i
$475$	2814.05			0.0124722
$476$		−	107001.i		−	0.472252i
$477$	−16454.4	+	160553.i	−0.0723177	+	0.705637i
$478$	480443.			2.10274
$479$			74164.6i			0.323240i	0.986853	+	0.161620i	$0.0516719\pi$
$479$			74164.6i			0.323240i	−0.986853	+	0.161620i	$0.948328\pi$
$480$	−33222.6	−	1697.97i	−0.144195	−	0.00736967i
$481$	552293.			2.38715
$482$			114961.i			0.494830i
$483$	9547.93	−	186815.i	0.0409275	−	0.800788i
$484$	−435529.			−1.85920
$485$			14012.3i			0.0595696i
$486$	102517.	−	392754.i	0.434032	−	1.66283i
$487$	−5375.18			−0.0226639			−0.0113320	−	0.999936i	$-0.503607\pi$
$487$	−5375.18			−0.0226639			−0.0113320	+	0.999936i	$0.503607\pi$
$488$			464264.i			1.94951i
$489$	−269864.	−	13792.5i	−1.12857	−	0.0576800i
$490$	−296212.			−1.23370
$491$		−	321129.i		−	1.33204i	−0.745934	−	0.666020i	$-0.767997\pi$
$491$		−	321129.i		−	1.33204i	0.745934	−	0.666020i	$-0.232003\pi$
$492$	27212.1	−	532434.i	0.112417	−	2.19956i
$493$	23930.9			0.0984611
$494$		−	64507.2i		−	0.264335i
$495$	−49397.2	−	5062.51i	−0.201601	−	0.0206612i
$496$	−60902.1			−0.247553
$497$		−	12152.4i		−	0.0491981i
$498$	229264.	+	11717.4i	0.924435	+	0.0472469i
$499$	−166114.			−0.667122			−0.333561	−	0.942729i	$-0.608250\pi$
$499$	−166114.			−0.667122			−0.333561	+	0.942729i	$0.608250\pi$
$500$		−	517523.i		−	2.07009i
$501$	8039.86	−	157308.i	0.0320312	−	0.626723i
$502$	734217.			2.91351
$503$			208387.i			0.823635i	0.911266	+	0.411817i	$0.135106\pi$
$503$			208387.i			0.823635i	−0.911266	+	0.411817i	$0.864894\pi$
$504$	−19998.1	+	195131.i	−0.0787278	+	0.768183i
$505$	−273863.			−1.07387
$506$		−	164387.i		−	0.642045i
$507$	602067.	+	30771.0i	2.34223	+	0.119709i
$508$	729457.			2.82665
$509$			258742.i			0.998690i	0.866403	+	0.499345i	$0.166426\pi$
$509$			258742.i			0.998690i	−0.866403	+	0.499345i	$0.833574\pi$
$510$	−10800.8	+	211329.i	−0.0415257	+	0.812493i
$511$	−79775.8			−0.305513
$512$			405760.i			1.54785i
$513$	21872.4	+	3377.17i	0.0831115	+	0.0128327i
$514$	686759.			2.59943
$515$		−	260617.i		−	0.982627i
$516$	365682.	+	18689.6i	1.37342	+	0.0701942i
$517$	72500.3			0.271243
$518$		−	283650.i		−	1.05712i
$519$	8386.32	−	164087.i	0.0311341	−	0.609171i
$520$	−747822.			−2.76561
$521$		−	3325.78i		−	0.0122523i	−0.999981	−	0.00612615i	$-0.998050\pi$
$521$		−	3325.78i		−	0.0122523i	0.999981	−	0.00612615i	$-0.00195003\pi$
$522$	−89415.7	−	9163.82i	−0.328150	−	0.0336307i
$523$	152454.			0.557359			0.278680	−	0.960384i	$-0.410103\pi$
$523$	152454.			0.557359			0.278680	+	0.960384i	$0.410103\pi$
$524$			35593.3i			0.129630i
$525$	19240.6	+	983.367i	0.0698072	+	0.00356777i
$526$	−925938.			−3.34665
$527$		−	40896.5i		−	0.147253i
$528$	−2694.68	+	52724.1i	−0.00966582	+	0.189122i
$529$	−530150.			−1.89447
$530$			316012.i			1.12500i
$531$	−3742.46	+	36516.9i	−0.0132730	+	0.129511i
$532$	−21912.4			−0.0774225
$533$			585845.i			2.06219i
$534$	−465007.	−	23766.0i	−1.63071	−	0.0833439i
$535$	−331669.			−1.15877
$536$		−	411903.i		−	1.43372i
$537$	4928.53	−	96431.7i	0.0170910	−	0.334404i
$538$	281238.			0.971650
$539$		−	49625.7i		−	0.170816i
$540$	80215.7	−	519521.i	0.275088	−	1.78162i
$541$	12862.5			0.0439473			0.0219736	−	0.999759i	$-0.493005\pi$
$541$	12862.5			0.0439473			0.0219736	+	0.999759i	$0.493005\pi$
$542$			583985.i			1.98794i
$543$	−224624.	−	11480.3i	−0.761826	−	0.0389362i
$544$	−23749.7			−0.0802529
$545$			344604.i			1.16018i
$546$	22542.0	−	441058.i	0.0756150	−	1.47949i
$547$	194890.			0.651352			0.325676	−	0.945481i	$-0.394408\pi$
$547$	194890.			0.651352			0.325676	+	0.945481i	$0.394408\pi$
$548$			872446.i			2.90521i
$549$	356753.	+	36562.0i	1.18365	+	0.121307i
$550$	16930.6			0.0559690
$551$		−	4900.73i		−	0.0161420i
$552$	848262.	+	43353.8i	2.78389	+	0.142282i
$553$	17063.4			0.0557976
$554$		−	507154.i		−	1.65242i
$555$	−18937.4	+	370530.i	−0.0614801	+	1.20292i
$556$	863738.			2.79404
$557$			417151.i			1.34457i	0.740293	+	0.672284i	$0.234687\pi$
$557$			417151.i			1.34457i	−0.740293	+	0.672284i	$0.765313\pi$
$558$	−15660.4	+	152806.i	−0.0502962	+	0.490764i
$559$	−402365.			−1.28765
$560$			117626.i			0.375084i
$561$	−35404.9	−	1809.51i	−0.112496	−	0.00574956i
$562$	−836622.			−2.64884
$563$		−	595171.i		−	1.87770i	−0.344333	−	0.938848i	$-0.611895\pi$
$563$		−	595171.i		−	1.87770i	0.344333	−	0.938848i	$-0.388105\pi$
$564$	−39175.8	+	766516.i	−0.123157	+	2.40970i
$565$	473684.			1.48386
$566$			114516.i			0.357463i
$567$	148369.	+	30734.1i	0.461505	+	0.0955994i
$568$	55179.7			0.171034
$569$			272434.i			0.841465i	0.907185	+	0.420733i	$0.138227\pi$
$569$			272434.i			0.841465i	−0.907185	+	0.420733i	$0.861773\pi$
$570$	43277.5	+	2211.87i	0.133203	+	0.00680784i
$571$	136619.			0.419025			0.209512	−	0.977806i	$-0.432812\pi$
$571$	136619.			0.419025			0.209512	+	0.977806i	$0.432812\pi$
$572$		−	256696.i		−	0.784561i
$573$	−25604.4	+	500977.i	−0.0779840	+	1.52584i
$574$	300882.			0.913214
$575$		−	83423.2i		−	0.252320i
$576$	373358.	+	38263.8i	1.12533	+	0.115330i
$577$	183983.			0.552619			0.276310	−	0.961069i	$-0.410888\pi$
$577$	183983.			0.552619			0.276310	+	0.961069i	$0.410888\pi$
$578$		−	423066.i		−	1.26635i
$579$	−540634.	−	27631.2i	−1.61267	−	0.0824220i
$580$	−116404.			−0.346029
$581$			85690.8i			0.253853i
$582$	1917.88	−	37525.3i	0.00566206	−	0.110784i
$583$	−52942.9			−0.155765
$584$		−	362234.i		−	1.06210i
$585$	−58893.0	+	574646.i	−0.172088	+	1.67915i
$586$	−388951.			−1.13266
$587$			128452.i			0.372791i	0.982475	+	0.186396i	$0.0596807\pi$
$587$			128452.i			0.372791i	−0.982475	+	0.186396i	$0.940319\pi$
$588$	524672.	+	26815.4i	1.51751	+	0.0775586i
$589$	−8375.07			−0.0241411
$590$			71875.3i			0.206479i
$591$	−17062.6	+	333848.i	−0.0488508	+	0.955816i
$592$	394452.			1.12551
$593$		−	467110.i		−	1.32834i	−0.747581	−	0.664171i	$-0.768785\pi$
$593$		−	467110.i		−	1.32834i	0.747581	−	0.664171i	$-0.231215\pi$
$594$	131594.	+	20318.6i	0.372962	+	0.0575866i
$595$	−78987.6			−0.223113
$596$			288901.i			0.813311i
$597$	−212566.	−	10864.0i	−0.596410	−	0.0304819i
$598$	−1.91234e6			−5.34764
$599$		−	491820.i		−	1.37073i	−0.728199	−	0.685366i	$-0.759642\pi$
$599$		−	491820.i		−	1.37073i	0.728199	−	0.685366i	$-0.240358\pi$
$600$	−4465.13	+	87364.9i	−0.0124031	+	0.242680i
$601$	546800.			1.51384			0.756920	−	0.653508i	$-0.226703\pi$
$601$	546800.			1.51384			0.756920	+	0.653508i	$0.226703\pi$
$602$			206649.i			0.570218i
$603$	−316517.	−	32438.4i	−0.870486	−	0.0892124i
$604$	−165405.			−0.453392
$605$			321505.i			0.878369i
$606$	733413.	+	37484.0i	1.99712	+	0.102070i
$607$	−603563.			−1.63812			−0.819059	−	0.573709i	$-0.805504\pi$
$607$	−603563.			−1.63812			−0.819059	+	0.573709i	$0.805504\pi$
$608$			4863.63i			0.0131569i
$609$	1712.56	−	33508.0i	0.00461754	−	0.0903470i
$610$	702188.			1.88709
$611$		−	843408.i		−	2.25920i
$612$	38262.3	−	373343.i	0.102157	−	0.996794i
$613$	372913.			0.992399			0.496200	−	0.868208i	$-0.334728\pi$
$613$	372913.			0.992399			0.496200	+	0.868208i	$0.334728\pi$
$614$			383508.i			1.01727i
$615$	−393040.	−	20087.9i	−1.03917	−	0.0531109i
$616$	−64345.1			−0.169572
$617$			559864.i			1.47066i	0.677709	+	0.735330i	$0.262973\pi$
$617$			559864.i			1.47066i	−0.677709	+	0.735330i	$0.737027\pi$
$618$	−35671.1	+	697941.i	−0.0933983	+	1.82744i
$619$	385336.			1.00568			0.502838	−	0.864381i	$-0.332289\pi$
$619$	385336.			1.00568			0.502838	+	0.864381i	$0.332289\pi$
$620$			198928.i			0.517502i
$621$	100117.	−	648413.i	0.259612	−	1.68139i
$622$	564993.			1.46037
$623$		−	173803.i		−	0.447798i
$624$	613349.	+	31347.6i	1.57521	+	0.0805073i
$625$	−324100.			−0.829696
$626$			683237.i			1.74350i
$627$	−370.564	+	7250.46i	−0.000942601	+	0.0184430i
$628$	819113.			2.07694
$629$			264880.i			0.669495i
$630$	295130.	+	30246.6i	0.743589	+	0.0762072i
$631$	791453.			1.98777			0.993886	−	0.110415i	$-0.0352179\pi$
$631$	791453.			1.98777			0.993886	+	0.110415i	$0.0352179\pi$
$632$			77479.0i			0.193977i
$633$	181701.	+	9286.53i	0.453470	+	0.0231764i
$634$	−163730.			−0.407334
$635$		−	538482.i		−	1.33544i
$636$	28607.9	−	559743.i	0.0707247	−	1.38380i
$637$	−577304.			−1.42274
$638$		−	29485.1i		−	0.0724372i
$639$	4345.55	−	42401.5i	0.0106425	−	0.103844i
$640$	675732.			1.64974
$641$		−	571714.i		−	1.39144i	−0.718315	−	0.695718i	$-0.755087\pi$
$641$		−	571714.i		−	1.39144i	0.718315	−	0.695718i	$-0.244913\pi$
$642$	888220.	+	45396.0i	2.15502	+	0.110141i
$643$	100352.			0.242718			0.121359	−	0.992609i	$-0.461275\pi$
$643$	100352.			0.242718			0.121359	+	0.992609i	$0.461275\pi$
$644$			649600.i			1.56630i
$645$	13796.6	−	269944.i	0.0331629	−	0.648866i
$646$	30937.6			0.0741348
$647$			7039.72i			0.0168169i	0.999965	+	0.00840847i	$0.00267653\pi$
$647$			7039.72i			0.0168169i	−0.999965	+	0.00840847i	$0.997323\pi$
$648$	−139553.	+	673691.i	−0.332345	+	1.60439i
$649$	−12041.6			−0.0285887
$650$		−	196957.i		−	0.466170i
$651$	−57263.2	−	2926.66i	−0.135118	−	0.00690575i
$652$	938383.			2.20742
$653$			699199.i			1.63974i	0.572551	+	0.819869i	$0.305954\pi$
$653$			699199.i			1.63974i	−0.572551	+	0.819869i	$0.694046\pi$
$654$	47166.4	−	922860.i	0.110275	−	2.15765i
$655$	26274.8			0.0612431
$656$			418415.i			0.972299i
$657$	−278350.	−	28526.9i	−0.644853	−	0.0660882i
$658$	−433163.			−1.00046
$659$			440423.i			1.01414i	0.861904	+	0.507072i	$0.169272\pi$
$659$			440423.i			1.01414i	−0.861904	+	0.507072i	$0.830728\pi$
$660$	172216.	+	8801.77i	0.395353	+	0.0202061i
$661$	−410057.			−0.938515			−0.469257	−	0.883061i	$-0.655478\pi$
$661$	−410057.			−0.938515			−0.469257	+	0.883061i	$0.655478\pi$
$662$		−	1.05828e6i		−	2.41483i
$663$	−21050.3	+	411871.i	−0.0478885	+	0.936988i
$664$	−389092.			−0.882503
$665$			16175.6i			0.0365778i
$666$	101430.	−	989700.i	0.228675	−	2.23128i
$667$	−145284.			−0.326562
$668$			546998.i			1.22584i
$669$	−531111.	−	27144.6i	−1.18668	−	0.0606499i
$670$	−622992.			−1.38782
$671$			117640.i			0.261283i
$672$	−1699.60	+	33254.3i	−0.00376363	+	0.0736393i
$673$	−488999.			−1.07964			−0.539819	−	0.841781i	$-0.681507\pi$
$673$	−488999.			−1.07964			−0.539819	+	0.841781i	$0.681507\pi$
$674$		−	1.11785e6i		−	2.46073i
$675$	66781.8	+	10311.3i	0.146572	+	0.0226312i
$676$	−2.09353e6			−4.58127
$677$		−	781793.i		−	1.70575i	−0.522119	−	0.852873i	$-0.674858\pi$
$677$		−	781793.i		−	1.70575i	0.522119	−	0.852873i	$-0.325142\pi$
$678$	−1.26854e6	−	64833.8i	−2.75959	−	0.141040i
$679$	14025.6			0.0304217
$680$		−	358655.i		−	0.775638i
$681$	−8641.38	+	169078.i	−0.0186333	+	0.364579i
$682$	−50388.4			−0.108333
$683$			839447.i			1.79950i	0.436406	+	0.899750i	$0.356251\pi$
$683$			839447.i			1.79950i	−0.436406	+	0.899750i	$0.643749\pi$
$684$	−76455.8	−	7835.63i	−0.163417	−	0.0167479i
$685$	644035.			1.37255
$686$			677657.i			1.44000i
$687$	−791016.	−	40428.0i	−1.67599	−	0.0856582i
$688$	−287373.			−0.607112
$689$			615893.i			1.29738i
$690$	65571.5	−	1.28297e6i	0.137726	−	2.69476i
$691$	−347890.			−0.728595			−0.364297	−	0.931283i	$-0.618691\pi$
$691$	−347890.			−0.728595			−0.364297	+	0.931283i	$0.618691\pi$
$692$			570569.i			1.19151i
$693$	−5067.34	+	49444.4i	−0.0105515	+	0.102956i
$694$	−266117.			−0.552527
$695$		−	637607.i		−	1.32003i
$696$	152148.	+	7776.13i	0.314086	+	0.0160526i
$697$	−280971.			−0.578357
$698$			911388.i			1.87065i
$699$	−3082.71	+	60316.4i	−0.00630926	+	0.123447i
$700$	−66904.1			−0.136539
$701$			87614.4i			0.178295i	0.996018	+	0.0891476i	$0.0284143\pi$
$701$			87614.4i			0.178295i	−0.996018	+	0.0891476i	$0.971586\pi$
$702$	236370.	−	1.53086e6i	0.479643	−	3.10643i
$703$	54243.9			0.109759
$704$			123116.i			0.248410i
$705$	565838.	+	28919.4i	1.13845	+	0.0581850i
$706$	−639573.			−1.28316
$707$			274124.i			0.548414i
$708$	6506.71	−	127311.i	0.0129806	−	0.253979i
$709$	342766.			0.681876			0.340938	−	0.940086i	$-0.389255\pi$
$709$	342766.			0.681876			0.340938	+	0.940086i	$0.389255\pi$
$710$		−	83457.9i		−	0.165558i
$711$	59536.9	+	6101.67i	0.117773	+	0.0120701i
$712$	789181.			1.55674
$713$			248281.i			0.488388i
$714$	211531.	+	10811.1i	0.414933	+	0.0212068i
$715$	−189491.			−0.370662
$716$			335316.i			0.654076i
$717$	−32106.6	+	628199.i	−0.0624534	+	1.22197i
$718$	−1.52924e6			−2.96639
$719$		−	124920.i		−	0.241643i	−0.992674	−	0.120821i	$-0.961447\pi$
$719$		−	124920.i		−	0.241643i	0.992674	−	0.120821i	$-0.0385529\pi$
$720$	−42061.9	+	410417.i	−0.0811378	+	0.791700i
$721$	−260866.			−0.501819
$722$			889514.i			1.70639i
$723$	−150316.	−	7682.50i	−0.287560	−	0.0146969i
$724$	781070.			1.49009
$725$		−	14963.2i		−	0.0284674i
$726$	44004.9	−	861001.i	0.0834886	−	1.63354i
$727$	795417.			1.50496			0.752482	−	0.658612i	$-0.228856\pi$
$727$	795417.			1.50496			0.752482	+	0.658612i	$0.228856\pi$
$728$			748537.i			1.41238i
$729$	506692.	+	160291.i	0.953429	+	0.301616i
$730$	−547870.			−1.02809
$731$		−	192974.i		−	0.361131i
$732$	−1.24376e6	−	63567.4i	−2.32122	−	0.118635i
$733$	−456048.			−0.848795			−0.424398	−	0.905476i	$-0.639514\pi$
$733$	−456048.			−0.848795			−0.424398	+	0.905476i	$0.639514\pi$
$734$			709811.i			1.31750i
$735$	19795.0	−	387310.i	0.0366421	−	0.716942i
$736$	144184.			0.266171
$737$		−	104372.i		−	0.192155i
$738$	1.04982e6	+	107592.i	1.92754	+	0.197545i
$739$	−623496.			−1.14168			−0.570840	−	0.821061i	$-0.693383\pi$
$739$	−623496.			−1.14168			−0.570840	+	0.821061i	$0.693383\pi$
$740$		−	1.28842e6i		−	2.35285i
$741$	84345.8	+	4310.83i	0.153613	+	0.00785099i
$742$	316314.			0.574528
$743$		−	814960.i		−	1.47625i	−0.674666	−	0.738123i	$-0.735712\pi$
$743$		−	814960.i		−	1.47625i	0.674666	−	0.738123i	$-0.264288\pi$
$744$	13289.0	−	260012.i	0.0240074	−	0.469730i
$745$	213265.			0.384244
$746$		−	958257.i		−	1.72189i
$747$	−30642.0	+	298988.i	−0.0549131	+	0.535813i
$748$	123111.			0.220036
$749$			331986.i			0.591774i
$750$	1.02310e6	+	52289.4i	1.81884	+	0.0929589i
$751$	502089.			0.890226			0.445113	−	0.895474i	$-0.353163\pi$
$751$	502089.			0.890226			0.445113	+	0.895474i	$0.353163\pi$
$752$		−	602369.i		−	1.06519i
$753$	−49065.6	+	960019.i	−0.0865340	+	1.69313i
$754$	−343005.			−0.603334
$755$			122101.i			0.214203i
$756$	−520017.	−	80292.3i	−0.909859	−	0.140485i
$757$	−815505.			−1.42310			−0.711549	−	0.702636i	$-0.752006\pi$
$757$	−815505.			−1.42310			−0.711549	+	0.702636i	$0.752006\pi$
$758$		−	373418.i		−	0.649916i
$759$	214942.	+	10985.5i	0.373111	+	0.0190693i
$760$	−73447.9			−0.127161
$761$			246488.i			0.425625i	0.977093	+	0.212812i	$0.0682623\pi$
$761$			246488.i			0.425625i	−0.977093	+	0.212812i	$0.931738\pi$
$762$	−73702.7	+	1.44207e6i	−0.126933	+	2.48357i
$763$	344933.			0.592496
$764$		−	1.74201e6i		−	2.98446i
$765$	−275600.	−	28245.0i	−0.470930	−	0.0482636i
$766$	−242377.			−0.413080
$767$			140082.i			0.238117i
$768$	−1.14328e6	−	58431.7i	−1.93834	−	0.0990663i
$769$	620106.			1.04861			0.524304	−	0.851531i	$-0.324326\pi$
$769$	620106.			1.04861			0.524304	+	0.851531i	$0.324326\pi$
$770$			97320.2i			0.164143i
$771$	−45894.1	+	897966.i	−0.0772055	+	1.51061i
$772$	1.87991e6			3.15430
$773$			401136.i			0.671324i	0.941982	+	0.335662i	$0.108960\pi$
$773$			401136.i			0.671324i	−0.941982	+	0.335662i	$0.891040\pi$
$774$	−73895.4	+	721031.i	−0.123349	+	1.20357i
$775$	−25571.2			−0.0425743
$776$			63685.5i			0.105759i
$777$	370884.	+	18955.5i	0.614322	+	0.0313974i
$778$	−47719.6			−0.0788384
$779$			57539.2i			0.0948176i
$780$	102392.	−	2.00341e6i	0.168298	−	3.29292i
$781$	13982.0			0.0229229
$782$		−	917156.i		−	1.49979i
$783$	17957.5	−	116302.i	0.0292901	−	0.189699i
$784$	−412315.			−0.670807
$785$		−	604665.i		−	0.981241i
$786$	−70364.8	−	3596.27i	−0.113896	−	0.00582113i
$787$	−933440.			−1.50708			−0.753541	−	0.657400i	$-0.771656\pi$
$787$	−933440.			−1.50708			−0.753541	+	0.657400i	$0.771656\pi$
$788$		−	1.16087e6i		−	1.86952i
$789$	61877.7	−	1.21070e6i	0.0993986	−	1.94484i
$790$	117185.			0.187766
$791$		−	474137.i		−	0.757793i
$792$	−224510.	−	23009.0i	−0.357919	−	0.0366816i
$793$	1.36853e6			2.17625
$794$		−	1.28830e6i		−	2.04351i
$795$	−413199.	−	21118.2i	−0.653770	−	0.0334135i
$796$	739142.			1.16655
$797$			677669.i			1.06684i	0.845849	+	0.533422i	$0.179094\pi$
$797$			677669.i			1.06684i	−0.845849	+	0.533422i	$0.820906\pi$
$798$	2213.98	−	43318.9i	0.00347671	−	0.0680254i
$799$	404498.			0.633612
$800$			14849.9i			0.0232030i
$801$	62150.1	−	606427.i	0.0968672	−	0.945178i
$802$	−1.62181e6			−2.52146
$803$		−	91786.9i		−	0.142347i
$804$	1.10349e6	+	56398.0i	1.70708	+	0.0872472i
$805$	479531.			0.739989
$806$			586176.i			0.902314i
$807$	−18794.3	+	367731.i	−0.0288589	+	0.564654i
$808$	−1.24470e6			−1.90653
$809$		−	717377.i		−	1.09610i	−0.836445	−	0.548050i	$-0.815370\pi$
$809$		−	717377.i		−	1.09610i	0.836445	−	0.548050i	$-0.184630\pi$
$810$	1.01894e6	+	211070.i	1.55303	+	0.321705i
$811$	1.08303e6			1.64664			0.823322	−	0.567574i	$-0.192118\pi$
$811$	1.08303e6			1.64664			0.823322	+	0.567574i	$0.192118\pi$
$812$			116515.i			0.176714i
$813$	−763584.	−	39026.0i	−1.15525	−	0.0590436i
$814$	326357.			0.492543
$815$		−	692709.i		−	1.04288i
$816$	−15034.3	+	294162.i	−0.0225789	+	0.441780i
$817$	−39518.6			−0.0592049
$818$		−	730072.i		−	1.09109i
$819$	575195.	+	58949.2i	0.857526	+	0.0878841i
$820$	1.36669e6			2.03256
$821$			1.27112e6i			1.88583i	0.333040	+	0.942913i	$0.391926\pi$
$821$			1.27112e6i			1.88583i	−0.333040	+	0.942913i	$0.608074\pi$
$822$	−1.72475e6	−	88150.0i	−2.55259	−	0.130460i
$823$	−524369.			−0.774172			−0.387086	−	0.922044i	$-0.626518\pi$
$823$	−524369.			−0.774172			−0.387086	+	0.922044i	$0.626518\pi$
$824$		−	1.18450e6i		−	1.74454i
$825$	−1131.42	+	22137.5i	−0.00166233	+	0.0325252i
$826$	71944.0			0.105447
$827$		−	546041.i		−	0.798389i	−0.916866	−	0.399195i	$-0.869290\pi$
$827$		−	546041.i		−	0.798389i	0.916866	−	0.399195i	$-0.130710\pi$
$828$	−232289.	+	2.26656e6i	−0.338820	+	3.30602i
$829$	−109348.			−0.159112			−0.0795560	−	0.996830i	$-0.525350\pi$
$829$	−109348.			−0.159112			−0.0795560	+	0.996830i	$0.525350\pi$
$830$			588491.i			0.854248i
$831$	663125.	+	33891.6i	0.960270	+	0.0490784i
$832$	1.43223e6			2.06903
$833$		−	276875.i		−	0.399019i
$834$	−87270.2	+	1.70753e6i	−0.125468	+	2.45492i
$835$	403791.			0.579140
$836$		−	25211.6i		−	0.0360734i
$837$	−198754.	−	30688.2i	−0.283703	−	0.0438047i
$838$	1.24333e6			1.77051
$839$			376167.i			0.534387i	0.963643	+	0.267194i	$0.0860964\pi$
$839$			376167.i			0.534387i	−0.963643	+	0.267194i	$0.913904\pi$
$840$	−502189.	−	25666.3i	−0.711719	−	0.0363752i
$841$	681222.			0.963156
$842$		−	96388.6i		−	0.135957i
$843$	55909.0	−	1.09392e6i	0.0786731	−	1.53932i
$844$	−631816.			−0.886963
$845$			1.54543e6i			2.16440i
$846$	−1.51137e6	−	154894.i	−2.11169	−	0.216418i
$847$	321812.			0.448576
$848$			439876.i			0.611700i
$849$	−149734.	−	7652.74i	−0.207732	−	0.0106170i
$850$	94460.4			0.130741
$851$		−	1.60808e6i		−	2.22048i
$852$	−7555.25	+	147826.i	−0.0104081	+	0.203644i
$853$	546852.			0.751574			0.375787	−	0.926706i	$-0.377372\pi$
$853$	546852.			0.751574			0.375787	+	0.926706i	$0.377372\pi$
$854$		−	702859.i		−	0.963723i
$855$	−5784.22	+	56439.3i	−0.00791247	+	0.0772057i
$856$	−1.50743e6			−2.05727
$857$			321657.i			0.437957i	0.975730	+	0.218979i	$0.0702725\pi$
$857$			321657.i			0.437957i	−0.975730	+	0.218979i	$0.929728\pi$
$858$	507464.	+	25936.0i	0.689336	+	0.0352312i
$859$	363405.			0.492497			0.246249	−	0.969207i	$-0.420802\pi$
$859$	363405.			0.492497			0.246249	+	0.969207i	$0.420802\pi$
$860$			938661.i			1.26915i
$861$	−20107.1	+	393415.i	−0.0271233	+	0.530695i
$862$	−514994.			−0.693087
$863$		−	921517.i		−	1.23732i	−0.785659	−	0.618660i	$-0.787676\pi$
$863$		−	921517.i		−	1.23732i	0.785659	−	0.618660i	$-0.212324\pi$
$864$	−17821.5	+	115422.i	−0.0238736	+	0.154618i
$865$	421191.			0.562920
$866$			525282.i			0.700417i
$867$	553176.	+	28272.2i	0.735911	+	0.0376116i
$868$	199118.			0.264284
$869$			19632.5i			0.0259977i
$870$	11761.2	−	230120.i	0.0155386	−	0.304030i
$871$	−1.21418e6			−1.60047
$872$			1.56622e6i			2.05978i
$873$	48937.6	+	5015.40i	0.0642117	+	0.00658078i
$874$	−187822.			−0.245880
$875$			382398.i			0.499459i
$876$	970424.	+	49597.4i	1.26460	+	0.0646324i
$877$	1.23974e6			1.61188			0.805941	−	0.591996i	$-0.201660\pi$
$877$	1.23974e6			1.61188			0.805941	+	0.591996i	$0.201660\pi$
$878$		−	1.42334e6i		−	1.84637i
$879$	25992.4	−	508569.i	0.0336410	−	0.658221i
$880$	−135336.			−0.174763
$881$			662653.i			0.853757i	0.904309	+	0.426878i	$0.140387\pi$
$881$			662653.i			0.853757i	−0.904309	+	0.426878i	$0.859613\pi$
$882$	−106023.	+	1.03452e6i	−0.136290	+	1.32985i
$883$	1.39969e6			1.79519			0.897594	−	0.440822i	$-0.145313\pi$
$883$	1.39969e6			1.79519			0.897594	+	0.440822i	$0.145313\pi$
$884$		−	1.43217e6i		−	1.83270i
$885$	−93979.9	−	4803.22i	−0.119991	−	0.00613261i
$886$	−2.63370e6			−3.35505
$887$			1.39586e6i			1.77417i	0.461608	+	0.887084i	$0.347273\pi$
$887$			1.39586e6i			1.77417i	−0.461608	+	0.887084i	$0.652727\pi$
$888$	−86070.4	+	1.68406e6i	−0.109151	+	2.13565i
$889$	−538996.			−0.681996
$890$		−	1.19362e6i		−	1.50690i
$891$	−35361.5	+	170707.i	−0.0445426	+	0.215029i
$892$	1.84680e6			2.32108
$893$		−	82836.0i		−	0.103876i
$894$	−571131.	−	29189.9i	−0.714597	−	0.0365223i
$895$	247528.			0.309015
$896$		−	676377.i		−	0.842506i
$897$	127796.	−	2.50046e6i	0.158830	−	3.10767i
$898$	−860904.			−1.06758
$899$			44532.9i			0.0551012i
$900$	−233439.	−	23924.1i	−0.288196	−	0.0295360i
$901$	−295382.			−0.363860
$902$			346183.i			0.425493i
$903$	−270202.	−	13809.8i	−0.331370	−	0.0169360i
$904$	2.15289e6			2.63442
$905$		−	576581.i		−	0.703985i
$906$	16712.1	−	326990.i	0.0203599	−	0.398362i
$907$	1.03798e6			1.26175			0.630876	−	0.775884i	$-0.282696\pi$
$907$	1.03798e6			1.26175			0.630876	+	0.775884i	$0.282696\pi$
$908$		−	587923.i		−	0.713097i
$909$	−98023.6	+	956462.i	−0.118632	+	1.15755i
$910$	1.13214e6			1.36716
$911$			498603.i			0.600784i	0.953816	+	0.300392i	$0.0971175\pi$
$911$			498603.i			0.600784i	−0.953816	+	0.300392i	$0.902883\pi$
$912$	60240.5	+	3078.83i	0.0724267	+	0.00370165i
$913$	−98592.4			−0.118277
$914$		−	127197.i		−	0.152260i
$915$	−46925.1	+	918139.i	−0.0560484	+	1.09665i
$916$	2.75055e6			3.27815
$917$		−	26299.9i		−	0.0312763i
$918$	734200.	+	113363.i	0.871222	+	0.134520i
$919$	−466122.			−0.551910			−0.275955	−	0.961170i	$-0.588994\pi$
$919$	−466122.			−0.551910			−0.275955	+	0.961170i	$0.588994\pi$
$920$			2.17739e6i			2.57253i
$921$	−501453.	−	25628.7i	−0.591168	−	0.0302140i
$922$	925151.			1.08831
$923$		−	162655.i		−	0.190926i
$924$	8810.18	−	172380.i	0.0103191	−	0.201903i
$925$	165620.			0.193566
$926$			1.42916e6i			1.66671i
$927$	−910203.	−	93282.7i	−1.05920	−	0.108553i
$928$	25861.5			0.0300301
$929$			11409.3i			0.0132199i	0.999978	+	0.00660993i	$0.00210402\pi$
$929$			11409.3i			0.0132199i	−0.999978	+	0.00660993i	$0.997896\pi$
$930$	−393262.	−	20099.2i	−0.454691	−	0.0232388i
$931$	−56700.3			−0.0654164
$932$		−	209734.i		−	0.241456i
$933$	−37756.8	+	738752.i	−0.0433743	+	0.848663i
$934$	−2.04323e6			−2.34220
$935$		−	90880.0i		−	0.103955i
$936$	−267668.	+	2.61176e6i	−0.305524	+	2.98114i
$937$	−1.54705e6			−1.76208			−0.881038	−	0.473045i	$-0.843155\pi$
$937$	−1.54705e6			−1.76208			−0.881038	+	0.473045i	$0.843155\pi$
$938$			623587.i			0.708747i
$939$	−893360.	−	45658.7i	−1.01320	−	0.0517836i
$940$	−1.96755e6			−2.22674
$941$			1.64573e6i			1.85857i	0.369362	+	0.929286i	$0.379576\pi$
$941$			1.64573e6i			1.85857i	−0.369362	+	0.929286i	$0.620424\pi$
$942$	−82761.4	+	1.61931e6i	−0.0932665	+	1.82486i
$943$	1.70577e6			1.91821
$944$			100047.i			0.112270i
$945$	−59271.4	+	383874.i	−0.0663715	+	0.429858i
$946$	−237763.			−0.265681
$947$			1.72019e6i			1.91812i	0.283199	+	0.959061i	$0.408604\pi$
$947$			1.72019e6i			1.91812i	−0.283199	+	0.959061i	$0.591396\pi$
$948$	−207566.	−	10608.5i	−0.230961	−	0.0118042i
$949$	−1.06777e6			−1.18562
$950$		−	19344.3i		−	0.0214341i
$951$	10941.6	−	214084.i	0.0120982	−	0.236713i
$952$	−358998.			−0.396112
$953$		−	746998.i		−	0.822495i	−0.911524	−	0.411248i	$-0.865093\pi$
$953$		−	746998.i		−	0.822495i	0.911524	−	0.411248i	$-0.134907\pi$
$954$	1.10367e6	+	113110.i	1.21267	+	0.124281i
$955$	−1.28595e6			−1.40999
$956$		−	2.18440e6i		−	2.39010i
$957$	38553.0	+	1970.40i	0.0420954	+	0.00215145i
$958$	509821.			0.555503
$959$		−	644650.i		−	0.700950i
$960$	−49109.3	+	960874.i	−0.0532870	+	1.04262i
$961$	−847417.			−0.917594
$962$		−	3.79656e6i		−	4.10242i
$963$	−118714.	+	1.15835e6i	−0.128012	+	1.24907i
$964$	522684.			0.562452
$965$		−	1.38774e6i		−	1.49023i
$966$	−1.28420e6	−	65634.2i	−1.37619	−	0.0703357i
$967$	−84955.9			−0.0908533			−0.0454267	−	0.998968i	$-0.514465\pi$
$967$	−84955.9			−0.0908533			−0.0454267	+	0.998968i	$0.514465\pi$
$968$			1.46124e6i			1.55944i
$969$	−2067.47	+	40452.2i	−0.00220187	+	0.0430819i
$970$	96322.7			0.102373
$971$			822202.i			0.872047i	0.899935	+	0.436024i	$0.143614\pi$
$971$			822202.i			0.872047i	−0.899935	+	0.436024i	$0.856386\pi$
$972$	−1.78571e6	−	466104.i	−1.89007	−	0.493345i
$973$	−638216.			−0.674127
$974$			36950.0i			0.0389490i
$975$	257529.	+	13162.0i	0.270905	+	0.0138457i
$976$	977416.			1.02608
$977$		−	325993.i		−	0.341523i	−0.985312	−	0.170761i	$-0.945377\pi$
$977$		−	325993.i		−	0.341523i	0.985312	−	0.170761i	$-0.0546227\pi$
$978$	−94812.1	+	1.85510e6i	−0.0991256	+	1.93950i
$979$	199971.			0.208642
$980$			1.34677e6i			1.40230i
$981$	1.20352e6	+	123344.i	1.25060	+	0.128168i
$982$	−2.20750e6			−2.28917
$983$			1.32018e6i			1.36623i	0.730309	+	0.683117i	$0.239376\pi$
$983$			1.32018e6i			1.36623i	−0.730309	+	0.683117i	$0.760624\pi$
$984$	−1.78636e6	−	91299.1i	−1.84493	−	0.0942923i
$985$	−856948.			−0.883246
$986$		−	164505.i		−	0.169210i
$987$	28947.0	−	566378.i	0.0297146	−	0.581396i
$988$	−293290.			−0.300458
$989$			1.17154e6i			1.19775i
$990$	−34800.6	+	339565.i	−0.0355072	+	0.346460i
$991$	−600284.			−0.611237			−0.305618	−	0.952154i	$-0.598863\pi$
$991$	−600284.			−0.611237			−0.305618	+	0.952154i	$0.598863\pi$
$992$		−	44195.8i		−	0.0449115i
$993$	1.38375e6	+	70722.0i	1.40333	+	0.0717226i
$994$	−83537.6			−0.0845492
$995$		−	545631.i		−	0.551128i
$996$	53274.8	−	1.04238e6i	0.0537035	−	1.05077i
$997$	−925753.			−0.931332			−0.465666	−	0.884960i	$-0.654185\pi$
$997$	−925753.			−0.931332			−0.465666	+	0.884960i	$0.654185\pi$
$998$			1.14190e6i			1.14648i
$999$	1.28729e6	+	198763.i	1.28987	+	0.199161i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.5.b.a.119.7	✓	78
3.2	odd	2	inner	177.5.b.a.119.72	yes	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.5.b.a.119.7	✓	78	1.1	even	1	trivial
177.5.b.a.119.72	yes	78	3.2	odd	2	inner

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:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	177.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-6.87418i q^{2} +(8.98827 + 0.459381i) q^{3} -31.2543 q^{4} +23.0718i q^{5} +(3.15787 - 61.7870i) q^{6} +23.0938 q^{7} +104.861i q^{8} +(80.5779 + 8.25808i) q^{9} +O(q^{10})\)	\(q-6.87418i q^{2} +(8.98827 + 0.459381i) q^{3} -31.2543 q^{4} +23.0718i q^{5} +(3.15787 - 61.7870i) q^{6} +23.0938 q^{7} +104.861i q^{8} +(80.5779 + 8.25808i) q^{9} +158.600 q^{10} +26.5708i q^{11} +(-280.922 - 14.3576i) q^{12} +309.103 q^{13} -158.751i q^{14} +(-10.5987 + 207.375i) q^{15} +220.764 q^{16} +148.246i q^{17} +(56.7675 - 553.907i) q^{18} +30.3588 q^{19} -721.093i q^{20} +(207.573 + 10.6089i) q^{21} +182.653 q^{22} -899.995i q^{23} +(-48.1712 + 942.519i) q^{24} +92.6930 q^{25} -2124.83i q^{26} +(720.463 + 111.242i) q^{27} -721.782 q^{28} -161.427i q^{29} +(1425.54 + 72.8576i) q^{30} -275.870 q^{31} +160.205i q^{32} +(-12.2061 + 238.826i) q^{33} +1019.07 q^{34} +532.816i q^{35} +(-2518.41 - 258.101i) q^{36} +1786.76 q^{37} -208.692i q^{38} +(2778.30 + 141.996i) q^{39} -2419.33 q^{40} +1895.31i q^{41} +(72.9272 - 1426.90i) q^{42} -1301.72 q^{43} -830.454i q^{44} +(-190.529 + 1859.08i) q^{45} -6186.73 q^{46} -2728.57i q^{47} +(1984.29 + 101.415i) q^{48} -1867.68 q^{49} -637.188i q^{50} +(-68.1013 + 1332.47i) q^{51} -9660.81 q^{52} +1992.52i q^{53} +(764.696 - 4952.59i) q^{54} -613.037 q^{55} +2421.64i q^{56} +(272.873 + 13.9462i) q^{57} -1109.68 q^{58} +453.188i q^{59} +(331.257 - 6481.38i) q^{60} +4427.43 q^{61} +1896.38i q^{62} +(1860.85 + 190.711i) q^{63} +4633.50 q^{64} +7131.56i q^{65} +(1641.73 + 83.9072i) q^{66} -3928.08 q^{67} -4633.32i q^{68} +(413.441 - 8089.40i) q^{69} +3662.67 q^{70} -526.218i q^{71} +(-865.951 + 8449.48i) q^{72} -3454.42 q^{73} -12282.5i q^{74} +(833.149 + 42.5814i) q^{75} -948.843 q^{76} +613.622i q^{77} +(976.106 - 19098.5i) q^{78} +738.873 q^{79} +5093.42i q^{80} +(6424.61 + 1330.84i) q^{81} +13028.7 q^{82} +3710.55i q^{83} +(-6487.57 - 331.573i) q^{84} -3420.29 q^{85} +8948.25i q^{86} +(74.1566 - 1450.95i) q^{87} -2786.25 q^{88} -7525.97i q^{89} +(12779.6 + 1309.73i) q^{90} +7138.37 q^{91} +28128.7i q^{92} +(-2479.59 - 126.729i) q^{93} -18756.7 q^{94} +700.431i q^{95} +(-73.5952 + 1439.97i) q^{96} +607.333 q^{97} +12838.7i q^{98} +(-219.424 + 2141.02i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9}+O(q^{10}) \) 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9	\( 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9} - 156 q^{10} - 4 q^{13} + 13 q^{15} + 4948 q^{16} + 22 q^{18} + 812 q^{19} - 173 q^{21} - 1644 q^{22} - 678 q^{24} - 8238 q^{25} + 777 q^{27} - 3764 q^{28} + 1374 q^{30} + 4664 q^{31} - 1042 q^{33} + 3244 q^{34} + 3648 q^{36} - 3960 q^{37} - 7078 q^{39} - 1576 q^{40} + 4934 q^{42} - 1492 q^{43} - 2063 q^{45} - 2036 q^{46} - 2620 q^{48} + 24274 q^{49} + 7300 q^{51} + 8408 q^{52} - 14766 q^{54} + 9780 q^{55} + 6939 q^{57} - 3856 q^{58} + 4712 q^{60} - 212 q^{61} - 7438 q^{63} - 45760 q^{64} + 3048 q^{66} - 12972 q^{67} + 21672 q^{69} + 5828 q^{70} - 866 q^{72} - 5240 q^{73} - 20922 q^{75} + 12368 q^{76} - 16508 q^{78} - 14976 q^{79} + 25524 q^{81} - 14484 q^{82} + 9540 q^{84} + 11572 q^{85} + 5695 q^{87} + 62160 q^{88} - 31672 q^{90} + 8284 q^{91} - 9590 q^{93} - 10992 q^{94} + 34102 q^{96} - 55000 q^{97} - 14254 q^{99}+O(q^{100}) \) 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9 - 156 * q^10 - 4 * q^13 + 13 * q^15 + 4948 * q^16 + 22 * q^18 + 812 * q^19 - 173 * q^21 - 1644 * q^22 - 678 * q^24 - 8238 * q^25 + 777 * q^27 - 3764 * q^28 + 1374 * q^30 + 4664 * q^31 - 1042 * q^33 + 3244 * q^34 + 3648 * q^36 - 3960 * q^37 - 7078 * q^39 - 1576 * q^40 + 4934 * q^42 - 1492 * q^43 - 2063 * q^45 - 2036 * q^46 - 2620 * q^48 + 24274 * q^49 + 7300 * q^51 + 8408 * q^52 - 14766 * q^54 + 9780 * q^55 + 6939 * q^57 - 3856 * q^58 + 4712 * q^60 - 212 * q^61 - 7438 * q^63 - 45760 * q^64 + 3048 * q^66 - 12972 * q^67 + 21672 * q^69 + 5828 * q^70 - 866 * q^72 - 5240 * q^73 - 20922 * q^75 + 12368 * q^76 - 16508 * q^78 - 14976 * q^79 + 25524 * q^81 - 14484 * q^82 + 9540 * q^84 + 11572 * q^85 + 5695 * q^87 + 62160 * q^88 - 31672 * q^90 + 8284 * q^91 - 9590 * q^93 - 10992 * q^94 + 34102 * q^96 - 55000 * q^97 - 14254 * q^99

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