LMFDB - Embedded newform 177.5.c.a.58.36

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,5,Mod(58,177)]

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, 1]))

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

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

chi := DirichletCharacter("177.58");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	177.c (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:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			58.36
Character	$\chi$	$=$	177.58
Dual form			177.5.c.a.58.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+6.70986i q^{2} +5.19615 q^{3} -29.0222 q^{4} -41.0870 q^{5} +34.8655i q^{6} -6.70931 q^{7} -87.3773i q^{8} +27.0000 q^{9} +O(q^{10})$	\(q+6.70986i q^{2} +5.19615 q^{3} -29.0222 q^{4} -41.0870 q^{5} +34.8655i q^{6} -6.70931 q^{7} -87.3773i q^{8} +27.0000 q^{9} -275.688i q^{10} -21.2822i q^{11} -150.804 q^{12} -73.2439i q^{13} -45.0185i q^{14} -213.494 q^{15} +121.934 q^{16} +76.4439 q^{17} +181.166i q^{18} +439.767 q^{19} +1192.43 q^{20} -34.8626 q^{21} +142.801 q^{22} -164.608i q^{23} -454.026i q^{24} +1063.14 q^{25} +491.456 q^{26} +140.296 q^{27} +194.719 q^{28} -788.819 q^{29} -1432.52i q^{30} -754.698i q^{31} -579.878i q^{32} -110.586i q^{33} +512.928i q^{34} +275.665 q^{35} -783.600 q^{36} -1700.99i q^{37} +2950.77i q^{38} -380.586i q^{39} +3590.07i q^{40} +72.3910 q^{41} -233.923i q^{42} -2692.60i q^{43} +617.657i q^{44} -1109.35 q^{45} +1104.50 q^{46} +2903.21i q^{47} +633.587 q^{48} -2355.99 q^{49} +7133.51i q^{50} +397.214 q^{51} +2125.70i q^{52} +1176.18 q^{53} +941.367i q^{54} +874.422i q^{55} +586.241i q^{56} +2285.10 q^{57} -5292.86i q^{58} +(-3479.47 + 103.350i) q^{59} +6196.07 q^{60} -2041.78i q^{61} +5063.92 q^{62} -181.151 q^{63} +5841.84 q^{64} +3009.37i q^{65} +742.014 q^{66} -796.587i q^{67} -2218.57 q^{68} -855.330i q^{69} +1849.67i q^{70} -4861.25 q^{71} -2359.19i q^{72} -1824.82i q^{73} +11413.4 q^{74} +5524.23 q^{75} -12763.0 q^{76} +142.789i q^{77} +2553.68 q^{78} -7086.59 q^{79} -5009.89 q^{80} +729.000 q^{81} +485.734i q^{82} -4425.07i q^{83} +1011.79 q^{84} -3140.85 q^{85} +18067.0 q^{86} -4098.82 q^{87} -1859.58 q^{88} -8041.54i q^{89} -7443.57i q^{90} +491.415i q^{91} +4777.30i q^{92} -3921.52i q^{93} -19480.1 q^{94} -18068.7 q^{95} -3013.13i q^{96} +2354.04i q^{97} -15808.3i q^{98} -574.620i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 320 q^{4} + 80 q^{7} + 1080 q^{9}+O(q^{10}) $ 40 * q - 320 * q^4 + 80 * q^7 + 1080 * q^9	$ 40 q - 320 q^{4} + 80 q^{7} + 1080 q^{9} + 360 q^{12} + 144 q^{15} + 3944 q^{16} - 528 q^{17} + 444 q^{19} + 444 q^{20} + 1304 q^{22} + 4880 q^{25} - 1452 q^{26} - 1160 q^{28} - 996 q^{29} + 10320 q^{35} - 8640 q^{36} - 5196 q^{41} - 10476 q^{46} + 576 q^{48} + 5104 q^{49} + 936 q^{51} - 2184 q^{53} - 2520 q^{57} - 11736 q^{59} - 11448 q^{60} + 15240 q^{62} + 2160 q^{63} - 81012 q^{64} + 17352 q^{66} + 29568 q^{68} - 5964 q^{71} + 14376 q^{74} - 2736 q^{75} + 3480 q^{76} + 37692 q^{78} + 19020 q^{79} + 33096 q^{80} + 29160 q^{81} + 25128 q^{84} + 20220 q^{85} - 65880 q^{86} + 1512 q^{87} - 14932 q^{88} - 17864 q^{94} + 11004 q^{95}+O(q^{100}) $ 40 * q - 320 * q^4 + 80 * q^7 + 1080 * q^9 + 360 * q^12 + 144 * q^15 + 3944 * q^16 - 528 * q^17 + 444 * q^19 + 444 * q^20 + 1304 * q^22 + 4880 * q^25 - 1452 * q^26 - 1160 * q^28 - 996 * q^29 + 10320 * q^35 - 8640 * q^36 - 5196 * q^41 - 10476 * q^46 + 576 * q^48 + 5104 * q^49 + 936 * q^51 - 2184 * q^53 - 2520 * q^57 - 11736 * q^59 - 11448 * q^60 + 15240 * q^62 + 2160 * q^63 - 81012 * q^64 + 17352 * q^66 + 29568 * q^68 - 5964 * q^71 + 14376 * q^74 - 2736 * q^75 + 3480 * q^76 + 37692 * q^78 + 19020 * q^79 + 33096 * q^80 + 29160 * q^81 + 25128 * q^84 + 20220 * q^85 - 65880 * q^86 + 1512 * q^87 - 14932 * q^88 - 17864 * q^94 + 11004 * q^95

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 $

$2$			6.70986i			1.67747i	0.544544	+	0.838733i	$0.316703\pi$
$2$			6.70986i			1.67747i	−0.544544	+	0.838733i	$0.683297\pi$
$3$	5.19615			0.577350
$3$	5.19615			0.577350
$4$	−29.0222			−1.81389
$5$	−41.0870			−1.64348			−0.821739	−	0.569864i	$-0.806996\pi$
$5$	−41.0870			−1.64348			−0.821739	+	0.569864i	$0.806996\pi$
$6$			34.8655i			0.968485i
$7$	−6.70931			−0.136925			−0.0684623	−	0.997654i	$-0.521809\pi$
$7$	−6.70931			−0.136925			−0.0684623	+	0.997654i	$0.521809\pi$
$8$		−	87.3773i		−	1.36527i
$9$	27.0000			0.333333
$10$		−	275.688i		−	2.75688i
$11$		−	21.2822i		−	0.175886i	−0.996126	−	0.0879430i	$-0.971971\pi$
$11$		−	21.2822i		−	0.175886i	0.996126	−	0.0879430i	$-0.0280293\pi$
$12$	−150.804			−1.04725
$13$		−	73.2439i		−	0.433396i	−0.976239	−	0.216698i	$-0.930471\pi$
$13$		−	73.2439i		−	0.433396i	0.976239	−	0.216698i	$-0.0695286\pi$
$14$		−	45.0185i		−	0.229686i
$15$	−213.494			−0.948863
$16$	121.934			0.476304
$17$	76.4439			0.264512			0.132256	−	0.991216i	$-0.457778\pi$
$17$	76.4439			0.264512			0.132256	+	0.991216i	$0.457778\pi$
$18$			181.166i			0.559155i
$19$	439.767			1.21819			0.609095	−	0.793097i	$-0.291533\pi$
$19$	439.767			1.21819			0.609095	+	0.793097i	$0.291533\pi$
$20$	1192.43			2.98109
$21$	−34.8626			−0.0790535
$22$	142.801			0.295043
$23$		−	164.608i		−	0.311169i	−0.987823	−	0.155584i	$-0.950274\pi$
$23$		−	164.608i		−	0.311169i	0.987823	−	0.155584i	$-0.0497260\pi$
$24$		−	454.026i		−	0.788239i
$25$	1063.14			1.70102
$26$	491.456			0.727006
$27$	140.296			0.192450
$28$	194.719			0.248366
$29$	−788.819			−0.937954			−0.468977	−	0.883211i	$-0.655377\pi$
$29$	−788.819			−0.937954			−0.468977	+	0.883211i	$0.655377\pi$
$30$		−	1432.52i		−	1.59168i
$31$		−	754.698i		−	0.785325i	−0.919683	−	0.392663i	$-0.871554\pi$
$31$		−	754.698i		−	0.785325i	0.919683	−	0.392663i	$-0.128446\pi$
$32$		−	579.878i		−	0.566287i
$33$		−	110.586i		−	0.101548i
$34$			512.928i			0.443709i
$35$	275.665			0.225033
$36$	−783.600			−0.604630
$37$		−	1700.99i		−	1.24251i	−0.783610	−	0.621253i	$-0.786624\pi$
$37$		−	1700.99i		−	1.24251i	0.783610	−	0.621253i	$-0.213376\pi$
$38$			2950.77i			2.04347i
$39$		−	380.586i		−	0.250221i
$40$			3590.07i			2.24379i
$41$	72.3910			0.0430643			0.0215321	−	0.999768i	$-0.493146\pi$
$41$	72.3910			0.0430643			0.0215321	+	0.999768i	$0.493146\pi$
$42$		−	233.923i		−	0.132609i
$43$		−	2692.60i		−	1.45625i	−0.685447	−	0.728123i	$-0.740393\pi$
$43$		−	2692.60i		−	1.45625i	0.685447	−	0.728123i	$-0.259607\pi$
$44$			617.657i			0.319038i
$45$	−1109.35			−0.547826
$46$	1104.50			0.521975
$47$			2903.21i			1.31426i	0.753775	+	0.657132i	$0.228231\pi$
$47$			2903.21i			1.31426i	−0.753775	+	0.657132i	$0.771769\pi$
$48$	633.587			0.274994
$49$	−2355.99			−0.981252
$50$			7133.51i			2.85340i
$51$	397.214			0.152716
$52$			2125.70i			0.786131i
$53$	1176.18			0.418719			0.209360	−	0.977839i	$-0.432862\pi$
$53$	1176.18			0.418719			0.209360	+	0.977839i	$0.432862\pi$
$54$			941.367i			0.322828i
$55$			874.422i			0.289065i
$56$			586.241i			0.186939i
$57$	2285.10			0.703323
$58$		−	5292.86i		−	1.57338i
$59$	−3479.47	+	103.350i	−0.999559	+	0.0296897i
$59$	−3479.47	+	103.350i	−0.999559	+	0.0296897i
$60$	6196.07			1.72113
$61$		−	2041.78i		−	0.548718i	−0.961627	−	0.274359i	$-0.911534\pi$
$61$		−	2041.78i		−	0.548718i	0.961627	−	0.274359i	$-0.0884657\pi$
$62$	5063.92			1.31736
$63$	−181.151			−0.0456415
$64$	5841.84			1.42623
$65$			3009.37i			0.712276i
$66$	742.014			0.170343
$67$		−	796.587i		−	0.177453i	−0.996056	−	0.0887266i	$-0.971720\pi$
$67$		−	796.587i		−	0.177453i	0.996056	−	0.0887266i	$-0.0282797\pi$
$68$	−2218.57			−0.479795
$69$		−	855.330i		−	0.179653i
$70$			1849.67i			0.377484i
$71$	−4861.25			−0.964343			−0.482171	−	0.876077i	$-0.660152\pi$
$71$	−4861.25			−0.964343			−0.482171	+	0.876077i	$0.660152\pi$
$72$		−	2359.19i		−	0.455090i
$73$		−	1824.82i		−	0.342433i	−0.985233	−	0.171216i	$-0.945230\pi$
$73$		−	1824.82i		−	0.342433i	0.985233	−	0.171216i	$-0.0547697\pi$
$74$	11413.4			2.08426
$75$	5524.23			0.982085
$76$	−12763.0			−2.20966
$77$			142.789i			0.0240831i
$78$	2553.68			0.419737
$79$	−7086.59			−1.13549			−0.567745	−	0.823204i	$-0.692184\pi$
$79$	−7086.59			−1.13549			−0.567745	+	0.823204i	$0.692184\pi$
$80$	−5009.89			−0.782795
$81$	729.000			0.111111
$82$			485.734i			0.0722388i
$83$		−	4425.07i		−	0.642338i	−0.947022	−	0.321169i	$-0.895924\pi$
$83$		−	4425.07i		−	0.642338i	0.947022	−	0.321169i	$-0.104076\pi$
$84$	1011.79			0.143394
$85$	−3140.85			−0.434719
$86$	18067.0			2.44280
$87$	−4098.82			−0.541528
$88$	−1859.58			−0.240132
$89$		−	8041.54i		−	1.01522i	−0.861588	−	0.507609i	$-0.830529\pi$
$89$		−	8041.54i		−	1.01522i	0.861588	−	0.507609i	$-0.169471\pi$
$90$		−	7443.57i		−	0.918959i
$91$			491.415i			0.0593425i
$92$			4777.30i			0.564425i
$93$		−	3921.52i		−	0.453408i
$94$	−19480.1			−2.20463
$95$	−18068.7			−2.00207
$96$		−	3013.13i		−	0.326946i
$97$			2354.04i			0.250190i	0.992145	+	0.125095i	$0.0399235\pi$
$97$			2354.04i			0.250190i	−0.992145	+	0.125095i	$0.960076\pi$
$98$		−	15808.3i		−	1.64602i
$99$		−	574.620i		−	0.0586287i
$100$	−30854.6			−3.08546
$101$			15071.0i			1.47741i	0.674032	+	0.738703i	$0.264561\pi$
$101$			15071.0i			1.47741i	−0.674032	+	0.738703i	$0.735439\pi$
$102$			2665.25i			0.256176i
$103$		−	13089.2i		−	1.23378i	−0.787048	−	0.616892i	$-0.788392\pi$
$103$		−	13089.2i		−	1.23378i	0.787048	−	0.616892i	$-0.211608\pi$
$104$	−6399.85			−0.591702
$105$	1432.40			0.129923
$106$			7892.02i			0.702387i
$107$	−264.977			−0.0231441			−0.0115721	−	0.999933i	$-0.503684\pi$
$107$	−264.977			−0.0231441			−0.0115721	+	0.999933i	$0.503684\pi$
$108$	−4071.70			−0.349083
$109$		−	13760.9i		−	1.15823i	−0.815247	−	0.579113i	$-0.803399\pi$
$109$		−	13760.9i		−	1.15823i	0.815247	−	0.579113i	$-0.196601\pi$
$110$	−5867.25			−0.484896
$111$		−	8838.61i		−	0.717361i
$112$	−818.091			−0.0652177
$113$		−	8838.66i		−	0.692197i	−0.938198	−	0.346098i	$-0.887506\pi$
$113$		−	8838.66i		−	0.692197i	0.938198	−	0.346098i	$-0.112494\pi$
$114$			15332.7i			1.17980i
$115$			6763.25i			0.511399i
$116$	22893.3			1.70134
$117$		−	1977.58i		−	0.144465i
$118$	−693.464	−	23346.7i	−0.0498035	−	1.67673i
$119$	−512.886			−0.0362182
$120$			18654.5i			1.29545i
$121$	14188.1			0.969064
$122$	13700.1			0.920456
$123$	376.155			0.0248632
$124$			21903.0i			1.42449i
$125$	−18001.8			−1.15211
$126$		−	1215.50i		−	0.0765621i
$127$	−12508.4			−0.775524			−0.387762	−	0.921759i	$-0.626752\pi$
$127$	−12508.4			−0.775524			−0.387762	+	0.921759i	$0.626752\pi$
$128$			29919.9i			1.82616i
$129$		−	13991.2i		−	0.840764i
$130$	−20192.4			−1.19482
$131$		−	30033.4i		−	1.75010i	−0.484036	−	0.875048i	$-0.660830\pi$
$131$		−	30033.4i		−	1.75010i	0.484036	−	0.875048i	$-0.339170\pi$
$132$			3209.44i			0.184197i
$133$	−2950.53			−0.166800
$134$	5344.99			0.297672
$135$	−5764.34			−0.316288
$136$		−	6679.46i		−	0.361130i
$137$	30546.6			1.62750			0.813751	−	0.581213i	$-0.197422\pi$
$137$	30546.6			1.62750			0.813751	+	0.581213i	$0.197422\pi$
$138$	5739.14			0.301362
$139$	13641.7			0.706056			0.353028	−	0.935613i	$-0.385152\pi$
$139$	13641.7			0.706056			0.353028	+	0.935613i	$0.385152\pi$
$140$	−8000.41			−0.408184
$141$			15085.5i			0.758791i
$142$		−	32618.3i		−	1.61765i
$143$	−1558.79			−0.0762283
$144$	3292.21			0.158768
$145$	32410.2			1.54151
$146$	12244.3			0.574419
$147$	−12242.1			−0.566526
$148$			49366.5i			2.25377i
$149$			18026.1i			0.811949i	0.913884	+	0.405975i	$0.133068\pi$
$149$			18026.1i			0.811949i	−0.913884	+	0.405975i	$0.866932\pi$
$150$			37066.8i			1.64741i
$151$			39094.7i			1.71460i	0.514814	+	0.857302i	$0.327861\pi$
$151$			39094.7i			1.71460i	−0.514814	+	0.857302i	$0.672139\pi$
$152$		−	38425.6i		−	1.66316i
$153$	2063.99			0.0881706
$154$	−958.094			−0.0403986
$155$			31008.2i			1.29067i
$156$			11045.5i			0.453873i
$157$			27675.1i			1.12277i	0.827556	+	0.561383i	$0.189731\pi$
$157$			27675.1i			1.12277i	−0.827556	+	0.561383i	$0.810269\pi$
$158$		−	47550.1i		−	1.90475i
$159$	6111.62			0.241748
$160$			23825.4i			0.930680i
$161$			1104.41i			0.0426067i
$162$			4891.49i			0.186385i
$163$	−28910.4			−1.08813			−0.544063	−	0.839044i	$-0.683115\pi$
$163$	−28910.4			−1.08813			−0.544063	+	0.839044i	$0.683115\pi$
$164$	−2100.95			−0.0781138
$165$			4543.63i			0.166892i
$166$	29691.6			1.07750
$167$	−44721.0			−1.60354			−0.801768	−	0.597635i	$-0.796107\pi$
$167$	−44721.0			−1.60354			−0.801768	+	0.597635i	$0.796107\pi$
$168$			3046.20i			0.107929i
$169$	23196.3			0.812168
$170$		−	21074.6i		−	0.729227i
$171$	11873.7			0.406064
$172$			78145.2i			2.64147i
$173$		−	37239.4i		−	1.24426i	−0.782914	−	0.622129i	$-0.786268\pi$
$173$		−	37239.4i		−	1.24426i	0.782914	−	0.622129i	$-0.213732\pi$
$174$		−	27502.5i		−	0.908394i
$175$	−7132.92			−0.232912
$176$		−	2595.02i		−	0.0837752i
$177$	−18079.8	+	537.022i	−0.577096	+	0.0171414i
$178$	53957.6			1.70299
$179$			23586.9i			0.736147i	0.929797	+	0.368073i	$0.119983\pi$
$179$			23586.9i			0.736147i	−0.929797	+	0.368073i	$0.880017\pi$
$180$	32195.7			0.993696
$181$	−1350.22			−0.0412144			−0.0206072	−	0.999788i	$-0.506560\pi$
$181$	−1350.22			−0.0412144			−0.0206072	+	0.999788i	$0.506560\pi$
$182$	−3297.33			−0.0995450
$183$		−	10609.4i		−	0.316803i
$184$	−14383.0			−0.424829
$185$			69888.5i			2.04203i
$186$	26312.9			0.760576
$187$		−	1626.90i		−	0.0465239i
$188$		−	84257.6i		−	2.38393i
$189$	−941.290			−0.0263512
$190$		−	121238.i		−	3.35840i
$191$		−	34964.8i		−	0.958438i	−0.877695	−	0.479219i	$-0.840920\pi$
$191$		−	34964.8i		−	0.958438i	0.877695	−	0.479219i	$-0.159080\pi$
$192$	30355.1			0.823435
$193$	−28062.0			−0.753362			−0.376681	−	0.926343i	$-0.622935\pi$
$193$	−28062.0			−0.753362			−0.376681	+	0.926343i	$0.622935\pi$
$194$	−15795.3			−0.419685
$195$			15637.1i			0.411233i
$196$	68375.9			1.77988
$197$	−8658.99			−0.223118			−0.111559	−	0.993758i	$-0.535584\pi$
$197$	−8658.99			−0.223118			−0.111559	+	0.993758i	$0.535584\pi$
$198$	3855.62			0.0983476
$199$	−31291.6			−0.790173			−0.395087	−	0.918644i	$-0.629285\pi$
$199$	−31291.6			−0.790173			−0.395087	+	0.918644i	$0.629285\pi$
$200$		−	92894.1i		−	2.32235i
$201$		−	4139.19i		−	0.102453i
$202$	−101124.			−2.47830
$203$	5292.43			0.128429
$204$	−11528.0			−0.277010
$205$	−2974.33			−0.0707752
$206$	87826.8			2.06963
$207$		−	4444.42i		−	0.103723i
$208$		−	8930.90i		−	0.206428i
$209$		−	9359.21i		−	0.214263i
$210$			9611.19i			0.217941i
$211$		−	1277.25i		−	0.0286888i	−0.999897	−	0.0143444i	$-0.995434\pi$
$211$		−	1277.25i		−	0.0286888i	0.999897	−	0.0143444i	$-0.00456612\pi$
$212$	−34135.4			−0.759510
$213$	−25259.8			−0.556764
$214$		−	1777.96i		−	0.0388235i
$215$			110631.i			2.39331i
$216$		−	12258.7i		−	0.262746i
$217$			5063.50i			0.107530i
$218$	92333.7			1.94288
$219$		−	9482.07i		−	0.197704i
$220$		−	25377.7i		−	0.524332i
$221$		−	5599.05i		−	0.114638i
$222$	59305.8			1.20335
$223$	18556.2			0.373146			0.186573	−	0.982441i	$-0.440262\pi$
$223$	18556.2			0.373146			0.186573	+	0.982441i	$0.440262\pi$
$224$			3890.58i			0.0775386i
$225$	28704.7			0.567007
$226$	59306.2			1.16114
$227$			61320.0i			1.19001i	0.803722	+	0.595005i	$0.202850\pi$
$227$			61320.0i			1.19001i	−0.803722	+	0.595005i	$0.797150\pi$
$228$	−66318.6			−1.27575
$229$		−	86222.5i		−	1.64418i	−0.569356	−	0.822091i	$-0.692807\pi$
$229$		−	86222.5i		−	1.64418i	0.569356	−	0.822091i	$-0.307193\pi$
$230$	−45380.5			−0.857854
$231$			741.953i			0.0139044i
$232$			68924.9i			1.28056i
$233$			40899.5i			0.753367i	0.926342	+	0.376683i	$0.122936\pi$
$233$			40899.5i			0.753367i	−0.926342	+	0.376683i	$0.877064\pi$
$234$	13269.3			0.242335
$235$		−	119284.i		−	2.15997i
$236$	100982.	−	2999.45i	1.81309	−	0.0538539i
$237$	−36823.0			−0.655576
$238$		−	3441.39i		−	0.0607547i
$239$	4438.81			0.0777089			0.0388544	−	0.999245i	$-0.487629\pi$
$239$	4438.81			0.0777089			0.0388544	+	0.999245i	$0.487629\pi$
$240$	−26032.1			−0.451947
$241$	−65511.7			−1.12794			−0.563968	−	0.825797i	$-0.690726\pi$
$241$	−65511.7			−1.12794			−0.563968	+	0.825797i	$0.690726\pi$
$242$			95199.9i			1.62557i
$243$	3788.00			0.0641500
$244$			59257.0i			0.995314i
$245$	96800.3			1.61267
$246$			2523.95i			0.0417071i
$247$		−	32210.2i		−	0.527959i
$248$	−65943.4			−1.07218
$249$		−	22993.3i		−	0.370854i
$250$		−	120789.i		−	1.93263i
$251$	−26481.1			−0.420328			−0.210164	−	0.977666i	$-0.567400\pi$
$251$	−26481.1			−0.420328			−0.210164	+	0.977666i	$0.567400\pi$
$252$	5257.41			0.0827887
$253$	−3503.23			−0.0547302
$254$		−	83929.8i		−	1.30091i
$255$	−16320.3			−0.250985
$256$	−107289.			−1.63710
$257$	−73530.4			−1.11327			−0.556635	−	0.830757i	$-0.687908\pi$
$257$	−73530.4			−1.11327			−0.556635	+	0.830757i	$0.687908\pi$
$258$	93878.7			1.41035
$259$			11412.5i			0.170130i
$260$		−	87338.5i		−	1.29199i
$261$	−21298.1			−0.312651
$262$	201520.			2.93573
$263$	−58037.1			−0.839062			−0.419531	−	0.907741i	$-0.637806\pi$
$263$	−58037.1			−0.839062			−0.419531	+	0.907741i	$0.637806\pi$
$264$	−9662.67			−0.138640
$265$	−48325.8			−0.688156
$266$		−	19797.6i		−	0.279802i
$267$		−	41785.1i		−	0.586136i
$268$			23118.7i			0.321880i
$269$			119064.i			1.64542i	0.568464	+	0.822708i	$0.307538\pi$
$269$			119064.i			1.64542i	−0.568464	+	0.822708i	$0.692462\pi$
$270$		−	38677.9i		−	0.530561i
$271$	95279.2			1.29736			0.648679	−	0.761062i	$-0.275322\pi$
$271$	95279.2			1.29736			0.648679	+	0.761062i	$0.275322\pi$
$272$	9321.10			0.125988
$273$			2553.47i			0.0342614i
$274$			204963.i			2.73008i
$275$		−	22625.9i		−	0.299186i
$276$			24823.6i			0.325871i
$277$	−70994.3			−0.925260			−0.462630	−	0.886551i	$-0.653094\pi$
$277$	−70994.3			−0.925260			−0.462630	+	0.886551i	$0.653094\pi$
$278$			91534.0i			1.18438i
$279$		−	20376.8i		−	0.261775i
$280$		−	24086.9i		−	0.307230i
$281$	89157.2			1.12913			0.564565	−	0.825389i	$-0.309044\pi$
$281$	89157.2			1.12913			0.564565	+	0.825389i	$0.309044\pi$
$282$	−101222.			−1.27285
$283$			121771.i			1.52044i	0.649664	+	0.760222i	$0.274910\pi$
$283$			121771.i			1.52044i	−0.649664	+	0.760222i	$0.725090\pi$
$284$	141084.			1.74921
$285$	−93887.6			−1.15590
$286$		−	10459.3i		−	0.127870i
$287$	−485.693			−0.00589656
$288$		−	15656.7i		−	0.188762i
$289$	−77677.3			−0.930034
$290$			217468.i			2.58582i
$291$			12231.9i			0.144447i
$292$			52960.5i			0.621135i
$293$	−14072.9			−0.163927			−0.0819633	−	0.996635i	$-0.526119\pi$
$293$	−14072.9			−0.163927			−0.0819633	+	0.996635i	$0.526119\pi$
$294$		−	82142.5i		−	0.950327i
$295$	142961.	−	4246.34i	1.64275	−	0.0487944i
$296$	−148628.			−1.69636
$297$		−	2985.81i		−	0.0338493i
$298$	−120953.			−1.36202
$299$	−12056.5			−0.134859
$300$	−160325.			−1.78139
$301$			18065.5i			0.199396i
$302$	−262320.			−2.87619
$303$			78311.3i			0.852980i
$304$	53622.4			0.580229
$305$			83890.6i			0.901807i
$306$			13849.1i			0.147903i
$307$	84061.4			0.891908			0.445954	−	0.895056i	$-0.352865\pi$
$307$	84061.4			0.891908			0.445954	+	0.895056i	$0.352865\pi$
$308$		−	4144.05i		−	0.0436841i
$309$		−	68013.5i		−	0.712325i
$310$	−208061.			−2.16505
$311$	−27808.7			−0.287514			−0.143757	−	0.989613i	$-0.545918\pi$
$311$	−27808.7			−0.287514			−0.143757	+	0.989613i	$0.545918\pi$
$312$	−33254.6			−0.341619
$313$			3675.80i			0.0375200i	0.999824	+	0.0187600i	$0.00597184\pi$
$313$			3675.80i			0.0375200i	−0.999824	+	0.0187600i	$0.994028\pi$
$314$	−185696.			−1.88340
$315$	7442.96			0.0750109
$316$	205669.			2.05965
$317$	30461.2			0.303129			0.151565	−	0.988447i	$-0.451569\pi$
$317$	30461.2			0.303129			0.151565	+	0.988447i	$0.451569\pi$
$318$			41008.1i			0.405523i
$319$			16787.8i			0.164973i
$320$	−240023.			−2.34398
$321$	−1376.86			−0.0133623
$322$	−7410.42			−0.0714712
$323$	33617.5			0.322226
$324$	−21157.2			−0.201543
$325$		−	77868.4i		−	0.737215i
$326$		−	193985.i		−	1.82529i
$327$		−	71503.7i		−	0.668703i
$328$		−	6325.33i		−	0.0587943i
$329$		−	19478.5i		−	0.179955i
$330$	−30487.1			−0.279955
$331$	206607.			1.88577			0.942884	−	0.333120i	$-0.108102\pi$
$331$	206607.			1.88577			0.942884	+	0.333120i	$0.108102\pi$
$332$			128425.i			1.16513i
$333$		−	45926.7i		−	0.414169i
$334$		−	300072.i		−	2.68988i
$335$			32729.4i			0.291641i
$336$	−4250.93			−0.0376535
$337$			145823.i			1.28401i	0.766702	+	0.642004i	$0.221897\pi$
$337$			145823.i			1.28401i	−0.766702	+	0.642004i	$0.778103\pi$
$338$			155644.i			1.36238i
$339$		−	45927.0i		−	0.399640i
$340$	91154.4			0.788533
$341$	−16061.6			−0.138128
$342$			79670.9i			0.681158i
$343$	31916.1			0.271282
$344$	−235272.			−1.98817
$345$			35142.9i			0.295256i
$346$	249871.			2.08720
$347$		−	32401.9i		−	0.269098i	−0.990907	−	0.134549i	$-0.957041\pi$
$347$		−	32401.9i		−	0.269098i	0.990907	−	0.134549i	$-0.0429586\pi$
$348$	118957.			0.982271
$349$		−	165183.i		−	1.35617i	−0.734982	−	0.678086i	$-0.762809\pi$
$349$		−	165183.i		−	1.35617i	0.734982	−	0.678086i	$-0.237191\pi$
$350$		−	47860.9i		−	0.390701i
$351$		−	10275.8i		−	0.0834070i
$352$	−12341.1			−0.0996020
$353$		−	193446.i		−	1.55242i	−0.630472	−	0.776212i	$-0.717139\pi$
$353$		−	193446.i		−	1.55242i	0.630472	−	0.776212i	$-0.282861\pi$
$354$	−3603.34	−	121313.i	−0.0287541	−	0.968058i
$355$	199734.			1.58488
$356$			233383.i			1.84149i
$357$	−2665.03			−0.0209106
$358$	−158265.			−1.23486
$359$	−94638.7			−0.734311			−0.367155	−	0.930160i	$-0.619668\pi$
$359$	−94638.7			−0.734311			−0.367155	+	0.930160i	$0.619668\pi$
$360$			96931.8i			0.747931i
$361$	63073.9			0.483989
$362$		−	9059.82i		−	0.0691357i
$363$	73723.4			0.559489
$364$		−	14262.0i		−	0.107641i
$365$			74976.5i			0.562781i
$366$	71187.6			0.531425
$367$		−	250626.i		−	1.86078i	−0.366576	−	0.930388i	$-0.619470\pi$
$367$		−	250626.i		−	1.86078i	0.366576	−	0.930388i	$-0.380530\pi$
$368$		−	20071.3i		−	0.148211i
$369$	1954.56			0.0143548
$370$	−468942.			−3.42544
$371$	−7891.37			−0.0573330
$372$			113811.i			0.822431i
$373$	65456.3			0.470472			0.235236	−	0.971938i	$-0.424414\pi$
$373$	65456.3			0.470472			0.235236	+	0.971938i	$0.424414\pi$
$374$	10916.2			0.0780423
$375$	−93540.0			−0.665173
$376$	253675.			1.79433
$377$			57776.1i			0.406505i
$378$		−	6315.92i		−	0.0442031i
$379$	60322.5			0.419953			0.209977	−	0.977706i	$-0.432661\pi$
$379$	60322.5			0.419953			0.209977	+	0.977706i	$0.432661\pi$
$380$	524393.			3.63153
$381$	−64995.7			−0.447749
$382$	234609.			1.60775
$383$	−53450.5			−0.364380			−0.182190	−	0.983263i	$-0.558319\pi$
$383$	−53450.5			−0.364380			−0.182190	+	0.983263i	$0.558319\pi$
$384$			155468.i			1.05434i
$385$		−	5866.76i		−	0.0395801i
$386$		−	188292.i		−	1.26374i
$387$		−	72700.2i		−	0.485415i
$388$		−	68319.4i		−	0.453817i
$389$	49209.3			0.325198			0.162599	−	0.986692i	$-0.448012\pi$
$389$	49209.3			0.325198			0.162599	+	0.986692i	$0.448012\pi$
$390$	−104923.			−0.689829
$391$		−	12583.3i		−	0.0823078i
$392$			205860.i			1.33967i
$393$		−	156058.i		−	1.01042i
$394$		−	58100.6i		−	0.374273i
$395$	291167.			1.86615
$396$			16676.7i			0.106346i
$397$			75598.4i			0.479658i	0.970815	+	0.239829i	$0.0770914\pi$
$397$			75598.4i			0.479658i	−0.970815	+	0.239829i	$0.922909\pi$
$398$		−	209963.i		−	1.32549i
$399$	−15331.4			−0.0963022
$400$	129633.			0.810203
$401$		−	289441.i		−	1.80000i	−0.435893	−	0.899999i	$-0.643567\pi$
$401$		−	289441.i		−	1.80000i	0.435893	−	0.899999i	$-0.356433\pi$
$402$	27773.4			0.171861
$403$	−55277.0			−0.340357
$404$		−	437394.i		−	2.67985i
$405$	−29952.4			−0.182609
$406$			35511.4i			0.215435i
$407$	−36200.9			−0.218540
$408$		−	34707.5i		−	0.208498i
$409$		−	157956.i		−	0.944256i	−0.881530	−	0.472128i	$-0.843486\pi$
$409$		−	157956.i		−	0.944256i	0.881530	−	0.472128i	$-0.156514\pi$
$410$		−	19957.3i		−	0.118723i
$411$	158725.			0.939639
$412$			379878.i			2.23795i
$413$	23344.8	−	693.407i	0.136864	−	0.00406526i
$414$	29821.5			0.173992
$415$			181813.i			1.05567i
$416$	−42472.5			−0.245426
$417$	70884.4			0.407642
$418$	62799.0			0.359418
$419$		−	280260.i		−	1.59637i	−0.602412	−	0.798185i	$-0.705794\pi$
$419$		−	280260.i		−	1.59637i	0.602412	−	0.798185i	$-0.294206\pi$
$420$	−41571.4			−0.235665
$421$			123028.i			0.694126i	0.937842	+	0.347063i	$0.112821\pi$
$421$			123028.i			0.694126i	−0.937842	+	0.347063i	$0.887179\pi$
$422$	8570.20			0.0481245
$423$			78386.7i			0.438088i
$424$		−	102772.i		−	0.571665i
$425$	81270.4			0.449940
$426$		−	169490.i		−	0.933951i
$427$			13698.9i			0.0751331i
$428$	7690.23			0.0419809
$429$	−8099.72			−0.0440104
$430$	−742317.			−4.01469
$431$		−	118678.i		−	0.638877i	−0.947607	−	0.319438i	$-0.896506\pi$
$431$		−	118678.i		−	0.638877i	0.947607	−	0.319438i	$-0.103494\pi$
$432$	17106.8			0.0916647
$433$	−336890.			−1.79685			−0.898425	−	0.439127i	$-0.855288\pi$
$433$	−336890.			−1.79685			−0.898425	+	0.439127i	$0.855288\pi$
$434$	−33975.4			−0.180378
$435$	168408.			0.889989
$436$			399372.i			2.10089i
$437$		−	72389.3i		−	0.379063i
$438$	63623.3			0.331641
$439$	333202.			1.72893			0.864466	−	0.502691i	$-0.167657\pi$
$439$	333202.			1.72893			0.864466	+	0.502691i	$0.167657\pi$
$440$	76404.6			0.394652
$441$	−63611.6			−0.327084
$442$	37568.8			0.192302
$443$		−	79729.2i		−	0.406265i	−0.979151	−	0.203133i	$-0.934888\pi$
$443$		−	79729.2i		−	0.406265i	0.979151	−	0.203133i	$-0.0651123\pi$
$444$			256516.i			1.30121i
$445$			330403.i			1.66849i
$446$			124509.i			0.625940i
$447$			93666.3i			0.468779i
$448$	−39194.7			−0.195286
$449$	−278079.			−1.37935			−0.689676	−	0.724118i	$-0.742247\pi$
$449$	−278079.			−1.37935			−0.689676	+	0.724118i	$0.742247\pi$
$450$			192605.i			0.951135i
$451$		−	1540.64i		−	0.00757440i
$452$			256518.i			1.25557i
$453$			203142.i			0.989927i
$454$	−411449.			−1.99620
$455$		−	20190.8i		−	0.0975282i
$456$		−	199665.i		−	0.960226i
$457$			175865.i			0.842067i	0.907045	+	0.421033i	$0.138332\pi$
$457$			175865.i			0.842067i	−0.907045	+	0.421033i	$0.861668\pi$
$458$	578541.			2.75806
$459$	10724.8			0.0509053
$460$		−	196285.i		−	0.927621i
$461$	−158569.			−0.746134			−0.373067	−	0.927804i	$-0.621694\pi$
$461$	−158569.			−0.746134			−0.373067	+	0.927804i	$0.621694\pi$
$462$	−4978.40			−0.0233242
$463$		−	77926.4i		−	0.363515i	−0.983343	−	0.181758i	$-0.941821\pi$
$463$		−	77926.4i		−	0.363515i	0.983343	−	0.181758i	$-0.0581786\pi$
$464$	−96183.7			−0.446751
$465$			161124.i			0.745166i
$466$	−274430.			−1.26375
$467$			408542.i			1.87328i	0.350291	+	0.936641i	$0.386083\pi$
$467$			408542.i			1.87328i	−0.350291	+	0.936641i	$0.613917\pi$
$468$			57393.9i			0.262044i
$469$			5344.55i			0.0242977i
$470$	800380.			3.62327
$471$			143804.i			0.648230i
$472$	9030.44	+	304026.i	0.0405345	+	1.36467i
$473$	−57304.5			−0.256133
$474$		−	247077.i		−	1.09971i
$475$	467533.			2.07217
$476$	14885.1			0.0656957
$477$	31756.9			0.139573
$478$			29783.8i			0.130354i
$479$	−161846.			−0.705393			−0.352697	−	0.935738i	$-0.614735\pi$
$479$	−161846.			−0.705393			−0.352697	+	0.935738i	$0.614735\pi$
$480$			123801.i			0.537329i
$481$	−124587.			−0.538497
$482$		−	439574.i		−	1.89207i
$483$			5738.67i			0.0245990i
$484$	−411769.			−1.75777
$485$		−	96720.2i		−	0.411182i
$486$			25416.9i			0.107609i
$487$	−156630.			−0.660414			−0.330207	−	0.943909i	$-0.607119\pi$
$487$	−156630.			−0.660414			−0.330207	+	0.943909i	$0.607119\pi$
$488$	−178405.			−0.749149
$489$	−150223.			−0.628230
$490$			649516.i			2.70519i
$491$	289340.			1.20018			0.600089	−	0.799933i	$-0.295132\pi$
$491$	289340.			1.20018			0.600089	+	0.799933i	$0.295132\pi$
$492$	−10916.8			−0.0450990
$493$	−60300.4			−0.248100
$494$	216126.			0.885632
$495$			23609.4i			0.0963550i
$496$		−	92023.2i		−	0.374054i
$497$	32615.6			0.132042
$498$	154282.			0.622095
$499$	366469.			1.47176			0.735878	−	0.677114i	$-0.236769\pi$
$499$	366469.			1.47176			0.735878	+	0.677114i	$0.236769\pi$
$500$	522452.			2.08981
$501$	−232377.			−0.925802
$502$		−	177684.i		−	0.705085i
$503$		−	160477.i		−	0.634274i	−0.948380	−	0.317137i	$-0.897278\pi$
$503$		−	160477.i		−	0.634274i	0.948380	−	0.317137i	$-0.102722\pi$
$504$			15828.5i			0.0623130i
$505$		−	619222.i		−	2.42808i
$506$		−	23506.2i		−	0.0918081i
$507$	120532.			0.468906
$508$	363022.			1.40671
$509$		−	244953.i		−	0.945468i	−0.881205	−	0.472734i	$-0.843267\pi$
$509$		−	244953.i		−	0.945468i	0.881205	−	0.472734i	$-0.156733\pi$
$510$		−	109507.i		−	0.421019i
$511$			12243.3i			0.0468875i
$512$		−	241175.i		−	0.920008i
$513$	61697.6			0.234441
$514$		−	493379.i		−	1.86747i
$515$			537796.i			2.02770i
$516$			406054.i			1.52505i
$517$	61786.8			0.231161
$518$	−76576.1			−0.285387
$519$		−	193502.i		−	0.718373i
$520$	262950.			0.972450
$521$	−366691.			−1.35090			−0.675452	−	0.737404i	$-0.736052\pi$
$521$	−366691.			−1.35090			−0.675452	+	0.737404i	$0.736052\pi$
$522$		−	142907.i		−	0.524461i
$523$	97476.4			0.356366			0.178183	−	0.983997i	$-0.442978\pi$
$523$	97476.4			0.356366			0.178183	+	0.983997i	$0.442978\pi$
$524$			871636.i			3.17448i
$525$	−37063.7			−0.134472
$526$		−	389421.i		−	1.40750i
$527$		−	57692.0i		−	0.207728i
$528$		−	13484.1i		−	0.0483677i
$529$	252745.			0.903174
$530$		−	324259.i		−	1.15436i
$531$	−93945.6	+	2790.45i	−0.333186	+	0.00989658i
$532$	85631.0			0.302557
$533$		−	5302.20i		−	0.0186639i
$534$	280372.			0.983223
$535$	10887.1			0.0380369
$536$	−69603.6			−0.242272
$537$			122561.i			0.425015i
$538$	−798903.			−2.76013
$539$			50140.6i			0.172589i
$540$	167294.			0.573711
$541$		−	321027.i		−	1.09685i	−0.836199	−	0.548425i	$-0.815227\pi$
$541$		−	321027.i		−	1.09685i	0.836199	−	0.548425i	$-0.184773\pi$
$542$			639310.i			2.17627i
$543$	−7015.97			−0.0237951
$544$		−	44328.1i		−	0.149790i
$545$			565393.i			1.90352i
$546$	−17133.4			−0.0574723
$547$	−82148.9			−0.274554			−0.137277	−	0.990533i	$-0.543835\pi$
$547$	−82148.9			−0.274554			−0.137277	+	0.990533i	$0.543835\pi$
$548$	−886530.			−2.95211
$549$		−	55128.1i		−	0.182906i
$550$	151817.			0.501874
$551$	−346896.			−1.14261
$552$	−74736.4			−0.245275
$553$	47546.1			0.155477
$554$		−	476362.i		−	1.55209i
$555$			363151.i			1.17897i
$556$	−395913.			−1.28071
$557$	−92439.5			−0.297953			−0.148976	−	0.988841i	$-0.547598\pi$
$557$	−92439.5			−0.297953			−0.148976	+	0.988841i	$0.547598\pi$
$558$	136726.			0.439119
$559$	−197216.			−0.631131
$560$	33612.9			0.107184
$561$		−	8453.60i		−	0.0268606i
$562$			598232.i			1.89408i
$563$		−	332807.i		−	1.04997i	−0.851112	−	0.524984i	$-0.824071\pi$
$563$		−	332807.i		−	1.04997i	0.851112	−	0.524984i	$-0.175929\pi$
$564$		−	437815.i		−	1.37636i
$565$			363154.i			1.13761i
$566$	−817065.			−2.55049
$567$	−4891.08			−0.0152138
$568$			424763.i			1.31659i
$569$		−	71655.2i		−	0.221321i	−0.993858	−	0.110661i	$-0.964703\pi$
$569$		−	71655.2i		−	0.221321i	0.993858	−	0.110661i	$-0.0352966\pi$
$570$		−	629973.i		−	1.93897i
$571$			235330.i			0.721780i	0.932608	+	0.360890i	$0.117527\pi$
$571$			235330.i			0.721780i	−0.932608	+	0.360890i	$0.882473\pi$
$572$	45239.6			0.138270
$573$		−	181682.i		−	0.553354i
$574$		−	3258.94i		−	0.00989127i
$575$		−	175001.i		−	0.529305i
$576$	157730.			0.475410
$577$	582269.			1.74893			0.874465	−	0.485089i	$-0.161213\pi$
$577$	582269.			1.74893			0.874465	+	0.485089i	$0.161213\pi$
$578$		−	521204.i		−	1.56010i
$579$	−145814.			−0.434954
$580$	−940615.			−2.79612
$581$			29689.1i			0.0879519i
$582$	−82074.6			−0.242305
$583$		−	25031.8i		−	0.0736469i
$584$	−159448.			−0.467513
$585$			81252.9i			0.237425i
$586$		−	94427.4i		−	0.274981i
$587$		−	535088.i		−	1.55292i	−0.630166	−	0.776460i	$-0.717013\pi$
$587$		−	535088.i		−	1.55292i	0.630166	−	0.776460i	$-0.282987\pi$
$588$	355292.			1.02762
$589$		−	331891.i		−	0.956676i
$590$	28492.3	+	959246.i	0.0818510	+	2.75566i
$591$	−44993.4			−0.128817
$592$		−	207408.i		−	0.591810i
$593$	439880.			1.25091			0.625453	−	0.780262i	$-0.284914\pi$
$593$	439880.			1.25091			0.625453	+	0.780262i	$0.284914\pi$
$594$	20034.4			0.0567810
$595$	21072.9			0.0595238
$596$		−	523157.i		−	1.47279i
$597$	−162596.			−0.456207
$598$		−	80897.7i		−	0.226222i
$599$	−177415.			−0.494465			−0.247233	−	0.968956i	$-0.579521\pi$
$599$	−177415.			−0.494465			−0.247233	+	0.968956i	$0.579521\pi$
$600$		−	482692.i		−	1.34081i
$601$			602513.i			1.66808i	0.551703	+	0.834041i	$0.313978\pi$
$601$			602513.i			1.66808i	−0.551703	+	0.834041i	$0.686022\pi$
$602$	−121217.			−0.334480
$603$		−	21507.9i		−	0.0591511i
$604$		−	1.13461e6i		−	3.11010i
$605$	−582945.			−1.59264
$606$	−525458.			−1.43084
$607$	−235674.			−0.639639			−0.319820	−	0.947478i	$-0.603622\pi$
$607$	−235674.			−0.639639			−0.319820	+	0.947478i	$0.603622\pi$
$608$		−	255011.i		−	0.689846i
$609$	27500.3			0.0741485
$610$	−562894.			−1.51275
$611$	212642.			0.569597
$612$	−59901.4			−0.159932
$613$			3306.79i			0.00880006i	0.999990	+	0.00440003i	$0.00140058\pi$
$613$			3306.79i			0.00880006i	−0.999990	+	0.00440003i	$0.998599\pi$
$614$			564040.i			1.49614i
$615$	−15455.1			−0.0408621
$616$	12476.5			0.0328800
$617$	194814.			0.511740			0.255870	−	0.966711i	$-0.417638\pi$
$617$	194814.			0.511740			0.255870	+	0.966711i	$0.417638\pi$
$618$	456361.			1.19490
$619$	−346456.			−0.904206			−0.452103	−	0.891966i	$-0.649326\pi$
$619$	−346456.			−0.904206			−0.452103	+	0.891966i	$0.649326\pi$
$620$		−	899928.i		−	2.34112i
$621$		−	23093.9i		−	0.0598844i
$622$		−	186592.i		−	0.482295i
$623$			53953.2i			0.139008i
$624$		−	46406.3i		−	0.119181i
$625$	75176.8			0.192453
$626$	−24664.1			−0.0629385
$627$		−	48631.9i		−	0.123705i
$628$		−	803192.i		−	2.03657i
$629$		−	130030.i		−	0.328657i
$630$			49941.2i			0.125828i
$631$	694008.			1.74303			0.871517	−	0.490365i	$-0.163136\pi$
$631$	694008.			1.74303			0.871517	+	0.490365i	$0.163136\pi$
$632$			619207.i			1.55025i
$633$		−	6636.81i		−	0.0165635i
$634$			204390.i			0.508489i
$635$	513933.			1.27456
$636$	−177373.			−0.438503
$637$			172561.i			0.425270i
$638$	−112644.			−0.276736
$639$	−131254.			−0.321448
$640$		−	1.22932e6i		−	3.00126i
$641$	−97669.8			−0.237708			−0.118854	−	0.992912i	$-0.537922\pi$
$641$	−97669.8			−0.237708			−0.118854	+	0.992912i	$0.537922\pi$
$642$		−	9238.55i		−	0.0224147i
$643$	−128561.			−0.310947			−0.155474	−	0.987840i	$-0.549690\pi$
$643$	−128561.			−0.310947			−0.155474	+	0.987840i	$0.549690\pi$
$644$		−	32052.3i		−	0.0772837i
$645$			574854.i			1.38178i
$646$			225569.i			0.540523i
$647$	−280631.			−0.670390			−0.335195	−	0.942149i	$-0.608802\pi$
$647$	−280631.			−0.670390			−0.335195	+	0.942149i	$0.608802\pi$
$648$		−	63698.0i		−	0.151697i
$649$	2199.52	+	74050.7i	0.00522201	+	0.175809i
$650$	522486.			1.23665
$651$			26310.7i			0.0620827i
$652$	839044.			1.97374
$653$	380413.			0.892132			0.446066	−	0.895000i	$-0.352825\pi$
$653$	380413.			0.892132			0.446066	+	0.895000i	$0.352825\pi$
$654$	479780.			1.12173
$655$			1.23398e6i			2.87625i
$656$	8826.91			0.0205117
$657$		−	49270.3i		−	0.114144i
$658$	130698.			0.301869
$659$			59943.3i			0.138029i	0.997616	+	0.0690145i	$0.0219855\pi$
$659$			59943.3i			0.138029i	−0.997616	+	0.0690145i	$0.978015\pi$
$660$		−	131866.i		−	0.302723i
$661$	−87318.8			−0.199850			−0.0999252	−	0.994995i	$-0.531860\pi$
$661$	−87318.8			−0.199850			−0.0999252	+	0.994995i	$0.531860\pi$
$662$			1.38630e6i			3.16331i
$663$		−	29093.5i		−	0.0661864i
$664$	−386650.			−0.876965
$665$	121228.			0.274133
$666$	308162.			0.694753
$667$			129846.i			0.291862i
$668$	1.29790e6			2.90864
$669$	96420.8			0.215436
$670$	−219609.			−0.489217
$671$	−43453.6			−0.0965119
$672$			20216.0i			0.0447669i
$673$			598287.i			1.32093i	0.750857	+	0.660465i	$0.229641\pi$
$673$			598287.i			1.32093i	−0.750857	+	0.660465i	$0.770359\pi$
$674$	−978455.			−2.15388
$675$	149154.			0.327362
$676$	−673209.			−1.47318
$677$	874864.			1.90881			0.954406	−	0.298512i	$-0.0964902\pi$
$677$	874864.			1.90881			0.954406	+	0.298512i	$0.0964902\pi$
$678$	308164.			0.670382
$679$		−	15794.0i		−	0.0342572i
$680$			274439.i			0.593509i
$681$			318628.i			0.687053i
$682$		−	107771.i		−	0.231705i
$683$			742238.i			1.59112i	0.605878	+	0.795558i	$0.292822\pi$
$683$			742238.i			1.59112i	−0.605878	+	0.795558i	$0.707178\pi$
$684$	−344601.			−0.736554
$685$	−1.25507e6			−2.67477
$686$			214152.i			0.455066i
$687$		−	448025.i		−	0.949269i
$688$		−	328319.i		−	0.693616i
$689$		−	86148.1i		−	0.181471i
$690$	−235804.			−0.495282
$691$		−	339025.i		−	0.710028i	−0.934861	−	0.355014i	$-0.884476\pi$
$691$		−	339025.i		−	0.710028i	0.934861	−	0.355014i	$-0.115524\pi$
$692$			1.08077e6i			2.25695i
$693$			3855.30i			0.00802771i
$694$	217412.			0.451403
$695$	−560496.			−1.16039
$696$			358144.i			0.739332i
$697$	5533.85			0.0113910
$698$	1.10836e6			2.27493
$699$			212520.i			0.434957i
$700$	207013.			0.422476
$701$			288735.i			0.587576i	0.955871	+	0.293788i	$0.0949159\pi$
$701$			288735.i			0.587576i	−0.955871	+	0.293788i	$0.905084\pi$
$702$	68949.4			0.139912
$703$		−	748039.i		−	1.51361i
$704$		−	124327.i		−	0.250854i
$705$		−	619818.i		−	1.24706i
$706$	1.29800e6			2.60414
$707$		−	101116.i		−	0.202293i
$708$	524717.	−	15585.6i	1.04679	−	0.0310925i
$709$	−65496.9			−0.130295			−0.0651476	−	0.997876i	$-0.520752\pi$
$709$	−65496.9			−0.130295			−0.0651476	+	0.997876i	$0.520752\pi$
$710$			1.34019e6i			2.65858i
$711$	−191338.			−0.378497
$712$	−702648.			−1.38605
$713$	−124229.			−0.244369
$714$		−	17882.0i		−	0.0350768i
$715$	64046.0			0.125279
$716$		−	684544.i		−	1.33529i
$717$	23064.7			0.0448652
$718$		−	635013.i		−	1.23178i
$719$			616651.i			1.19284i	0.802673	+	0.596420i	$0.203411\pi$
$719$			616651.i			1.19284i	−0.802673	+	0.596420i	$0.796589\pi$
$720$	−135267.			−0.260932
$721$			87819.5i			0.168935i
$722$			423217.i			0.811875i
$723$	−340409.			−0.651214
$724$	39186.5			0.0747583
$725$	−838624.			−1.59548
$726$			494673.i			0.938524i
$727$	79727.7			0.150848			0.0754241	−	0.997152i	$-0.475969\pi$
$727$	79727.7			0.150848			0.0754241	+	0.997152i	$0.475969\pi$
$728$	42938.5			0.0810186
$729$	19683.0			0.0370370
$730$	−503082.			−0.944045
$731$		−	205833.i		−	0.385194i
$732$			307909.i			0.574645i
$733$	−797529.			−1.48436			−0.742179	−	0.670202i	$-0.766207\pi$
$733$	−797529.			−1.48436			−0.742179	+	0.670202i	$0.766207\pi$
$734$	1.68167e6			3.12139
$735$	502989.			0.931073
$736$	−95452.7			−0.176211
$737$	−16953.1			−0.0312115
$738$			13114.8i			0.0240796i
$739$			924588.i			1.69301i	0.532381	+	0.846505i	$0.321297\pi$
$739$			924588.i			1.69301i	−0.532381	+	0.846505i	$0.678703\pi$
$740$		−	2.02832e6i		−	3.70402i
$741$		−	167369.i		−	0.304817i
$742$		−	52950.0i		−	0.0961741i
$743$	671065.			1.21559			0.607795	−	0.794094i	$-0.292054\pi$
$743$	671065.			1.21559			0.607795	+	0.794094i	$0.292054\pi$
$744$	−342652.			−0.619024
$745$		−	740637.i		−	1.33442i
$746$			439202.i			0.789200i
$747$		−	119477.i		−	0.214113i
$748$			47216.1i			0.0843893i
$749$	1777.81			0.00316900
$750$		−	627640.i		−	1.11580i
$751$			405680.i			0.719289i	0.933089	+	0.359645i	$0.117102\pi$
$751$			405680.i			0.719289i	−0.933089	+	0.359645i	$0.882898\pi$
$752$			354000.i			0.625989i
$753$	−137600.			−0.242676
$754$	−387670.			−0.681898
$755$		−	1.60628e6i		−	2.81791i
$756$	27318.3			0.0477981
$757$	−843491.			−1.47193			−0.735967	−	0.677017i	$-0.763272\pi$
$757$	−843491.			−1.47193			−0.735967	+	0.677017i	$0.763272\pi$
$758$			404755.i			0.704457i
$759$	−18203.3			−0.0315985
$760$			1.57879e6i			2.73337i
$761$	−953711.			−1.64682			−0.823412	−	0.567444i	$-0.807932\pi$
$761$	−953711.			−1.64682			−0.823412	+	0.567444i	$0.807932\pi$
$762$		−	436112.i		−	0.751084i
$763$			92326.0i			0.158590i
$764$			1.01476e6i			1.73850i
$765$	−84802.9			−0.144906
$766$		−	358645.i		−	0.611234i
$767$	7569.75	+	254849.i	0.0128674	+	0.433205i
$768$	−557489.			−0.945178
$769$			551211.i			0.932106i	0.884757	+	0.466053i	$0.154324\pi$
$769$			551211.i			0.932106i	−0.884757	+	0.466053i	$0.845676\pi$
$770$	39365.2			0.0663943
$771$	−382075.			−0.642747
$772$	814421.			1.36651
$773$			98128.0i			0.164223i	0.996623	+	0.0821115i	$0.0261664\pi$
$773$			98128.0i			0.164223i	−0.996623	+	0.0821115i	$0.973834\pi$
$774$	487808.			0.814267
$775$		−	802348.i		−	1.33586i
$776$	205689.			0.341577
$777$			59300.9i			0.0982244i
$778$			330187.i			0.545508i
$779$	31835.2			0.0524605
$780$		−	453824.i		−	0.745931i
$781$			103458.i			0.169614i
$782$	84432.2			0.138068
$783$	−110668.			−0.180509
$784$	−287274.			−0.467374
$785$		−	1.13708e6i		−	1.84524i
$786$	1.04713e6			1.69494
$787$	975267.			1.57461			0.787307	−	0.616561i	$-0.211475\pi$
$787$	975267.			1.57461			0.787307	+	0.616561i	$0.211475\pi$
$788$	251303.			0.404712
$789$	−301570.			−0.484433
$790$			1.95369e6i			3.13041i
$791$			59301.3i			0.0947788i
$792$	−50208.7			−0.0800440
$793$	−149548.			−0.237812
$794$	−507255.			−0.804610
$795$	−251108.			−0.397307
$796$	908153.			1.43329
$797$		−	838974.i		−	1.32078i	−0.750921	−	0.660392i	$-0.770390\pi$
$797$		−	838974.i		−	1.32078i	0.750921	−	0.660392i	$-0.229610\pi$
$798$		−	102872.i		−	0.161544i
$799$			221933.i			0.347638i
$800$		−	616490.i		−	0.963266i
$801$		−	217122.i		−	0.338406i
$802$	1.94211e6			3.01943
$803$	−38836.3			−0.0602292
$804$			120128.i			0.185838i
$805$		−	45376.7i		−	0.0700231i
$806$		−	370901.i		−	0.570936i
$807$			618675.i			0.949982i
$808$	1.31686e6			2.01706
$809$		−	620319.i		−	0.947804i	−0.880578	−	0.473902i	$-0.842845\pi$
$809$		−	620319.i		−	0.947804i	0.880578	−	0.473902i	$-0.157155\pi$
$810$		−	200976.i		−	0.306320i
$811$		−	1.20442e6i		−	1.83120i	−0.402093	−	0.915599i	$-0.631717\pi$
$811$		−	1.20442e6i		−	1.83120i	0.402093	−	0.915599i	$-0.368283\pi$
$812$	−153598.			−0.232956
$813$	495085.			0.749030
$814$		−	242903.i		−	0.366592i
$815$	1.18784e6			1.78831
$816$	48433.8			0.0727392
$817$		−	1.18412e6i		−	1.77399i
$818$	1.05986e6			1.58396
$819$			13268.2i			0.0197808i
$820$	86321.6			0.128378
$821$		−	254507.i		−	0.377584i	−0.982017	−	0.188792i	$-0.939543\pi$
$821$		−	254507.i		−	0.377584i	0.982017	−	0.188792i	$-0.0604571\pi$
$822$			1.06502e6i			1.57621i
$823$			272405.i			0.402175i	0.979573	+	0.201088i	$0.0644476\pi$
$823$			272405.i			0.402175i	−0.979573	+	0.201088i	$0.935552\pi$
$824$	−1.14370e6			−1.68445
$825$		−	117568.i		−	0.172735i
$826$	4652.66	+	156640.i	0.00681932	+	0.229585i
$827$	460578.			0.673430			0.336715	−	0.941607i	$-0.390684\pi$
$827$	460578.			0.673430			0.336715	+	0.941607i	$0.390684\pi$
$828$			128987.i			0.188142i
$829$	−106117.			−0.154411			−0.0772053	−	0.997015i	$-0.524600\pi$
$829$	−106117.			−0.154411			−0.0772053	+	0.997015i	$0.524600\pi$
$830$	−1.21994e6			−1.77085
$831$	−368897.			−0.534199
$832$		−	427879.i		−	0.618122i
$833$	−180101.			−0.259553
$834$			475624.i			0.683805i
$835$	1.83745e6			2.63538
$836$			271625.i			0.388649i
$837$		−	105881.i		−	0.151136i
$838$	1.88051e6			2.67786
$839$		−	1.07945e6i		−	1.53348i	−0.641957	−	0.766741i	$-0.721877\pi$
$839$		−	1.07945e6i		−	1.53348i	0.641957	−	0.766741i	$-0.278123\pi$
$840$		−	125159.i		−	0.177380i
$841$	−85045.7			−0.120243
$842$	−825498.			−1.16437
$843$	463274.			0.651903
$844$			37068.8i			0.0520383i
$845$	−953067.			−1.33478
$846$	−525964.			−0.734878
$847$	−95192.1			−0.132689
$848$	143416.			0.199438
$849$			632740.i			0.877829i
$850$			545313.i			0.754759i
$851$	−279997.			−0.386629
$852$	733096.			1.00991
$853$	−694278.			−0.954191			−0.477096	−	0.878851i	$-0.658311\pi$
$853$	−694278.			−0.954191			−0.477096	+	0.878851i	$0.658311\pi$
$854$	−91917.9			−0.126033
$855$	−487855.			−0.667357
$856$			23153.0i			0.0315980i
$857$			565662.i			0.770186i	0.922878	+	0.385093i	$0.125831\pi$
$857$			565662.i			0.770186i	−0.922878	+	0.385093i	$0.874169\pi$
$858$		−	54348.0i		−	0.0738259i
$859$		−	918130.i		−	1.24428i	−0.782906	−	0.622139i	$-0.786264\pi$
$859$		−	918130.i		−	1.24428i	0.782906	−	0.622139i	$-0.213736\pi$
$860$		−	3.21075e6i		−	4.34120i
$861$	−2523.74			−0.00340438
$862$	796316.			1.07169
$863$		−	930295.i		−	1.24911i	−0.780982	−	0.624553i	$-0.785281\pi$
$863$		−	930295.i		−	1.24911i	0.780982	−	0.624553i	$-0.214719\pi$
$864$		−	81354.6i		−	0.108982i
$865$			1.53005e6i			2.04491i
$866$		−	2.26048e6i		−	3.01415i
$867$	−403623.			−0.536955
$868$		−	146954.i		−	0.195048i
$869$			150818.i			0.199717i
$870$			1.13000e6i			1.49293i
$871$	−58345.1			−0.0769074
$872$	−1.20239e6			−1.58129
$873$			63559.0i			0.0833966i
$874$	485722.			0.635865
$875$	120779.			0.157753
$876$			275191.i			0.358613i
$877$	−313247.			−0.407275			−0.203638	−	0.979046i	$-0.565276\pi$
$877$	−313247.			−0.407275			−0.203638	+	0.979046i	$0.565276\pi$
$878$			2.23574e6i			2.90022i
$879$	−73125.1			−0.0946431
$880$			106622.i			0.137683i
$881$			185355.i			0.238810i	0.992846	+	0.119405i	$0.0380988\pi$
$881$			185355.i			0.238810i	−0.992846	+	0.119405i	$0.961901\pi$
$882$		−	426825.i		−	0.548672i
$883$	−613135.			−0.786384			−0.393192	−	0.919456i	$-0.628629\pi$
$883$	−613135.			−0.786384			−0.393192	+	0.919456i	$0.628629\pi$
$884$			162497.i			0.207941i
$885$	742845.	−	22064.6i	0.948444	−	0.0281715i
$886$	534972.			0.681496
$887$			673956.i			0.856612i	0.903634	+	0.428306i	$0.140889\pi$
$887$			673956.i			0.856612i	−0.903634	+	0.428306i	$0.859111\pi$
$888$	−772293.			−0.979392
$889$	83922.9			0.106188
$890$	−2.21695e6			−2.79883
$891$		−	15514.7i		−	0.0195429i
$892$	−538542.			−0.676846
$893$			1.27674e6i			1.60103i
$894$	−628488.			−0.786361
$895$		−	969113.i		−	1.20984i
$896$		−	200742.i		−	0.250047i
$897$	−62647.6			−0.0778610
$898$		−	1.86587e6i		−	2.31382i
$899$			595320.i			0.736599i
$900$	−833075.			−1.02849
$901$	89912.0			0.110756
$902$	10337.5			0.0127058
$903$			93870.9i			0.115121i
$904$	−772298.			−0.945036
$905$	55476.6			0.0677349
$906$	−1.36305e6			−1.66057
$907$	1.07679e6			1.30894			0.654468	−	0.756090i	$-0.272893\pi$
$907$	1.07679e6			1.30894			0.654468	+	0.756090i	$0.272893\pi$
$908$		−	1.77964e6i		−	2.15855i
$909$			406917.i			0.492468i
$910$	135477.			0.163600
$911$	288010.			0.347033			0.173516	−	0.984831i	$-0.444487\pi$
$911$	288010.			0.347033			0.173516	+	0.984831i	$0.444487\pi$
$912$	278630.			0.334995
$913$	−94175.3			−0.112978
$914$	−1.18003e6			−1.41254
$915$			435908.i			0.520658i
$916$			2.50237e6i			2.98236i
$917$			201503.i			0.239631i
$918$			71961.8i			0.0853919i
$919$			90535.9i			0.107199i	0.998563	+	0.0535994i	$0.0170694\pi$
$919$			90535.9i			0.107199i	−0.998563	+	0.0535994i	$0.982931\pi$
$920$	590955.			0.698198
$921$	436796.			0.514943
$922$		−	1.06398e6i		−	1.25161i
$923$			356057.i			0.417942i
$924$		−	21533.1i		−	0.0252210i
$925$		−	1.80839e6i		−	2.11353i
$926$	522875.			0.609784
$927$		−	353409.i		−	0.411261i
$928$			457419.i			0.531151i
$929$		−	922758.i		−	1.06919i	−0.845107	−	0.534597i	$-0.820463\pi$
$929$		−	922758.i		−	1.06919i	0.845107	−	0.534597i	$-0.179537\pi$
$930$	−1.08112e6			−1.24999
$931$	−1.03608e6			−1.19535
$932$		−	1.18700e6i		−	1.36652i
$933$	−144498.			−0.165997
$934$	−2.74126e6			−3.14237
$935$			66844.2i			0.0764611i
$936$	−172796.			−0.197234
$937$		−	1.63873e6i		−	1.86650i	−0.359226	−	0.933251i	$-0.616959\pi$
$937$		−	1.63873e6i		−	1.86650i	0.359226	−	0.933251i	$-0.383041\pi$
$938$	−35861.2			−0.0407586
$939$			19100.0i			0.0216622i
$940$			3.46189e6i			3.91794i
$941$			432139.i			0.488028i	0.969772	+	0.244014i	$0.0784642\pi$
$941$			432139.i			0.488028i	−0.969772	+	0.244014i	$0.921536\pi$
$942$	−964904.			−1.08738
$943$		−	11916.2i		−	0.0134002i
$944$	−424264.	+	12601.9i	−0.476094	+	0.0141413i
$945$	38674.7			0.0433076
$946$		−	384505.i		−	0.429655i
$947$	−1.68549e6			−1.87943			−0.939716	−	0.341956i	$-0.888911\pi$
$947$	−1.68549e6			−1.87943			−0.939716	+	0.341956i	$0.888911\pi$
$948$	1.06869e6			1.18914
$949$	−133657.			−0.148409
$950$			3.13708e6i			3.47599i
$951$	158281.			0.175012
$952$			44814.5i			0.0494476i
$953$	−1.30178e6			−1.43335			−0.716677	−	0.697405i	$-0.754338\pi$
$953$	−1.30178e6			−1.43335			−0.716677	+	0.697405i	$0.754338\pi$
$954$			213085.i			0.234129i
$955$			1.43660e6i			1.57517i
$956$	−128824.			−0.140955
$957$			87232.0i			0.0952472i
$958$		−	1.08596e6i		−	1.18327i
$959$	−204946.			−0.222845
$960$	−1.24720e6			−1.35330
$961$	353952.			0.383264
$962$		−	835962.i		−	0.903309i
$963$	−7154.38			−0.00771471
$964$	1.90129e6			2.04595
$965$	1.15298e6			1.23813
$966$	−38505.7			−0.0412639
$967$			1.16546e6i			1.24636i	0.782077	+	0.623182i	$0.214160\pi$
$967$			1.16546e6i			1.24636i	−0.782077	+	0.623182i	$0.785840\pi$
$968$		−	1.23971e6i		−	1.32303i
$969$	174682.			0.186037
$970$	648979.			0.689743
$971$	158501.			0.168110			0.0840550	−	0.996461i	$-0.473213\pi$
$971$	158501.			0.168110			0.0840550	+	0.996461i	$0.473213\pi$
$972$	−109936.			−0.116361
$973$	−91526.4			−0.0966764
$974$		−	1.05096e6i		−	1.10782i
$975$		−	404616.i		−	0.425631i
$976$		−	248962.i		−	0.261357i
$977$			510200.i			0.534504i	0.963627	+	0.267252i	$0.0861157\pi$
$977$			510200.i			0.534504i	−0.963627	+	0.267252i	$0.913884\pi$
$978$		−	1.00797e6i		−	1.05383i
$979$	−171142.			−0.178563
$980$	−2.80936e6			−2.92520
$981$		−	371544.i		−	0.386076i
$982$			1.94143e6i			2.01326i
$983$			853370.i			0.883141i	0.897226	+	0.441571i	$0.145579\pi$
$983$			853370.i			0.883141i	−0.897226	+	0.441571i	$0.854421\pi$
$984$		−	32867.4i		−	0.0339449i
$985$	355772.			0.366690
$986$		−	404607.i		−	0.416179i
$987$		−	101213.i		−	0.103897i
$988$			934812.i			0.957658i
$989$	−443224.			−0.453138
$990$	−158416.			−0.161632
$991$			609956.i			0.621086i	0.950559	+	0.310543i	$0.100511\pi$
$991$			609956.i			0.621086i	−0.950559	+	0.310543i	$0.899489\pi$
$992$	−437632.			−0.444719
$993$	1.07356e6			1.08875
$994$			218846.i			0.221496i
$995$	1.28568e6			1.29863
$996$			667318.i			0.672688i
$997$	712553.			0.716847			0.358424	−	0.933559i	$-0.383314\pi$
$997$	712553.			0.716847			0.358424	+	0.933559i	$0.383314\pi$
$998$			2.45896e6i			2.46882i
$999$		−	238642.i		−	0.239120i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.5.c.a.58.36	yes	40
3.2	odd	2		531.5.c.d.235.5		40
59.58	odd	2	inner	177.5.c.a.58.5	✓	40
177.176	even	2		531.5.c.d.235.36		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.5.c.a.58.5	✓	40	59.58	odd	2	inner
177.5.c.a.58.36	yes	40	1.1	even	1	trivial
531.5.c.d.235.5		40	3.2	odd	2
531.5.c.d.235.36		40	177.176	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+6.70986i q^{2} +5.19615 q^{3} -29.0222 q^{4} -41.0870 q^{5} +34.8655i q^{6} -6.70931 q^{7} -87.3773i q^{8} +27.0000 q^{9} +O(q^{10})\)	\(q+6.70986i q^{2} +5.19615 q^{3} -29.0222 q^{4} -41.0870 q^{5} +34.8655i q^{6} -6.70931 q^{7} -87.3773i q^{8} +27.0000 q^{9} -275.688i q^{10} -21.2822i q^{11} -150.804 q^{12} -73.2439i q^{13} -45.0185i q^{14} -213.494 q^{15} +121.934 q^{16} +76.4439 q^{17} +181.166i q^{18} +439.767 q^{19} +1192.43 q^{20} -34.8626 q^{21} +142.801 q^{22} -164.608i q^{23} -454.026i q^{24} +1063.14 q^{25} +491.456 q^{26} +140.296 q^{27} +194.719 q^{28} -788.819 q^{29} -1432.52i q^{30} -754.698i q^{31} -579.878i q^{32} -110.586i q^{33} +512.928i q^{34} +275.665 q^{35} -783.600 q^{36} -1700.99i q^{37} +2950.77i q^{38} -380.586i q^{39} +3590.07i q^{40} +72.3910 q^{41} -233.923i q^{42} -2692.60i q^{43} +617.657i q^{44} -1109.35 q^{45} +1104.50 q^{46} +2903.21i q^{47} +633.587 q^{48} -2355.99 q^{49} +7133.51i q^{50} +397.214 q^{51} +2125.70i q^{52} +1176.18 q^{53} +941.367i q^{54} +874.422i q^{55} +586.241i q^{56} +2285.10 q^{57} -5292.86i q^{58} +(-3479.47 + 103.350i) q^{59} +6196.07 q^{60} -2041.78i q^{61} +5063.92 q^{62} -181.151 q^{63} +5841.84 q^{64} +3009.37i q^{65} +742.014 q^{66} -796.587i q^{67} -2218.57 q^{68} -855.330i q^{69} +1849.67i q^{70} -4861.25 q^{71} -2359.19i q^{72} -1824.82i q^{73} +11413.4 q^{74} +5524.23 q^{75} -12763.0 q^{76} +142.789i q^{77} +2553.68 q^{78} -7086.59 q^{79} -5009.89 q^{80} +729.000 q^{81} +485.734i q^{82} -4425.07i q^{83} +1011.79 q^{84} -3140.85 q^{85} +18067.0 q^{86} -4098.82 q^{87} -1859.58 q^{88} -8041.54i q^{89} -7443.57i q^{90} +491.415i q^{91} +4777.30i q^{92} -3921.52i q^{93} -19480.1 q^{94} -18068.7 q^{95} -3013.13i q^{96} +2354.04i q^{97} -15808.3i q^{98} -574.620i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 320 q^{4} + 80 q^{7} + 1080 q^{9}+O(q^{10}) \) 40 * q - 320 * q^4 + 80 * q^7 + 1080 * q^9	\( 40 q - 320 q^{4} + 80 q^{7} + 1080 q^{9} + 360 q^{12} + 144 q^{15} + 3944 q^{16} - 528 q^{17} + 444 q^{19} + 444 q^{20} + 1304 q^{22} + 4880 q^{25} - 1452 q^{26} - 1160 q^{28} - 996 q^{29} + 10320 q^{35} - 8640 q^{36} - 5196 q^{41} - 10476 q^{46} + 576 q^{48} + 5104 q^{49} + 936 q^{51} - 2184 q^{53} - 2520 q^{57} - 11736 q^{59} - 11448 q^{60} + 15240 q^{62} + 2160 q^{63} - 81012 q^{64} + 17352 q^{66} + 29568 q^{68} - 5964 q^{71} + 14376 q^{74} - 2736 q^{75} + 3480 q^{76} + 37692 q^{78} + 19020 q^{79} + 33096 q^{80} + 29160 q^{81} + 25128 q^{84} + 20220 q^{85} - 65880 q^{86} + 1512 q^{87} - 14932 q^{88} - 17864 q^{94} + 11004 q^{95}+O(q^{100}) \) 40 * q - 320 * q^4 + 80 * q^7 + 1080 * q^9 + 360 * q^12 + 144 * q^15 + 3944 * q^16 - 528 * q^17 + 444 * q^19 + 444 * q^20 + 1304 * q^22 + 4880 * q^25 - 1452 * q^26 - 1160 * q^28 - 996 * q^29 + 10320 * q^35 - 8640 * q^36 - 5196 * q^41 - 10476 * q^46 + 576 * q^48 + 5104 * q^49 + 936 * q^51 - 2184 * q^53 - 2520 * q^57 - 11736 * q^59 - 11448 * q^60 + 15240 * q^62 + 2160 * q^63 - 81012 * q^64 + 17352 * q^66 + 29568 * q^68 - 5964 * q^71 + 14376 * q^74 - 2736 * q^75 + 3480 * q^76 + 37692 * q^78 + 19020 * q^79 + 33096 * q^80 + 29160 * q^81 + 25128 * q^84 + 20220 * q^85 - 65880 * q^86 + 1512 * q^87 - 14932 * q^88 - 17864 * q^94 + 11004 * q^95

Introduction

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