LMFDB - Embedded newform 177.5.c.a.58.37

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			58.37
Character	$\chi$	$=$	177.58
Dual form			177.5.c.a.58.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+6.76718i q^{2} +5.19615 q^{3} -29.7948 q^{4} +6.77685 q^{5} +35.1633i q^{6} +45.8846 q^{7} -93.3518i q^{8} +27.0000 q^{9} +O(q^{10})$	\(q+6.76718i q^{2} +5.19615 q^{3} -29.7948 q^{4} +6.77685 q^{5} +35.1633i q^{6} +45.8846 q^{7} -93.3518i q^{8} +27.0000 q^{9} +45.8602i q^{10} +152.372i q^{11} -154.818 q^{12} +138.574i q^{13} +310.510i q^{14} +35.2135 q^{15} +155.012 q^{16} +61.1978 q^{17} +182.714i q^{18} -184.090 q^{19} -201.915 q^{20} +238.423 q^{21} -1031.13 q^{22} +55.4703i q^{23} -485.070i q^{24} -579.074 q^{25} -937.758 q^{26} +140.296 q^{27} -1367.12 q^{28} +290.483 q^{29} +238.296i q^{30} +681.108i q^{31} -444.632i q^{32} +791.748i q^{33} +414.137i q^{34} +310.953 q^{35} -804.459 q^{36} +1422.17i q^{37} -1245.77i q^{38} +720.053i q^{39} -632.631i q^{40} +1532.90 q^{41} +1613.46i q^{42} -404.708i q^{43} -4539.89i q^{44} +182.975 q^{45} -375.377 q^{46} -1601.56i q^{47} +805.467 q^{48} -295.602 q^{49} -3918.70i q^{50} +317.993 q^{51} -4128.79i q^{52} -1325.56 q^{53} +949.410i q^{54} +1032.60i q^{55} -4283.41i q^{56} -956.562 q^{57} +1965.75i q^{58} +(3430.65 - 589.891i) q^{59} -1049.18 q^{60} -2732.09i q^{61} -4609.19 q^{62} +1238.88 q^{63} +5489.10 q^{64} +939.097i q^{65} -5357.90 q^{66} +2225.52i q^{67} -1823.37 q^{68} +288.232i q^{69} +2104.28i q^{70} -6157.04 q^{71} -2520.50i q^{72} +2816.89i q^{73} -9624.09 q^{74} -3008.96 q^{75} +5484.93 q^{76} +6991.53i q^{77} -4872.73 q^{78} +7747.95 q^{79} +1050.49 q^{80} +729.000 q^{81} +10373.4i q^{82} -648.806i q^{83} -7103.77 q^{84} +414.728 q^{85} +2738.73 q^{86} +1509.40 q^{87} +14224.2 q^{88} -5751.21i q^{89} +1238.22i q^{90} +6358.43i q^{91} -1652.72i q^{92} +3539.14i q^{93} +10838.1 q^{94} -1247.55 q^{95} -2310.38i q^{96} -1510.67i q^{97} -2000.39i q^{98} +4114.04i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			6.76718i			1.69180i	0.533345	+	0.845898i	$0.320935\pi$
$2$			6.76718i			1.69180i	−0.533345	+	0.845898i	$0.679065\pi$
$3$	5.19615			0.577350
$3$	5.19615			0.577350
$4$	−29.7948			−1.86217
$5$	6.77685			0.271074			0.135537	−	0.990772i	$-0.456724\pi$
$5$	6.77685			0.271074			0.135537	+	0.990772i	$0.456724\pi$
$6$			35.1633i			0.976759i
$7$	45.8846			0.936421			0.468210	−	0.883617i	$-0.344899\pi$
$7$	45.8846			0.936421			0.468210	+	0.883617i	$0.344899\pi$
$8$		−	93.3518i		−	1.45862i
$9$	27.0000			0.333333
$10$			45.8602i			0.458602i
$11$			152.372i			1.25927i	0.776890	+	0.629636i	$0.216796\pi$
$11$			152.372i			1.25927i	−0.776890	+	0.629636i	$0.783204\pi$
$12$	−154.818			−1.07513
$13$			138.574i			0.819966i	0.912093	+	0.409983i	$0.134465\pi$
$13$			138.574i			0.819966i	−0.912093	+	0.409983i	$0.865535\pi$
$14$			310.510i			1.58423i
$15$	35.2135			0.156505
$16$	155.012			0.605517
$17$	61.1978			0.211757			0.105878	−	0.994379i	$-0.466235\pi$
$17$	61.1978			0.211757			0.105878	+	0.994379i	$0.466235\pi$
$18$			182.714i			0.563932i
$19$	−184.090			−0.509946			−0.254973	−	0.966948i	$-0.582067\pi$
$19$	−184.090			−0.509946			−0.254973	+	0.966948i	$0.582067\pi$
$20$	−201.915			−0.504787
$21$	238.423			0.540643
$22$	−1031.13			−2.13043
$23$			55.4703i			0.104859i	0.998625	+	0.0524294i	$0.0166964\pi$
$23$			55.4703i			0.104859i	−0.998625	+	0.0524294i	$0.983304\pi$
$24$		−	485.070i		−	0.842136i
$25$	−579.074			−0.926519
$26$	−937.758			−1.38722
$27$	140.296			0.192450
$28$	−1367.12			−1.74378
$29$	290.483			0.345402			0.172701	−	0.984974i	$-0.444750\pi$
$29$	290.483			0.345402			0.172701	+	0.984974i	$0.444750\pi$
$30$			238.296i			0.264774i
$31$			681.108i			0.708750i	0.935103	+	0.354375i	$0.115306\pi$
$31$			681.108i			0.708750i	−0.935103	+	0.354375i	$0.884694\pi$
$32$		−	444.632i		−	0.434211i
$33$			791.748i			0.727041i
$34$			414.137i			0.358250i
$35$	310.953			0.253839
$36$	−804.459			−0.620724
$37$			1422.17i			1.03884i	0.854519	+	0.519420i	$0.173852\pi$
$37$			1422.17i			1.03884i	−0.854519	+	0.519420i	$0.826148\pi$
$38$		−	1245.77i		−	0.862725i
$39$			720.053i			0.473408i
$40$		−	632.631i		−	0.395394i
$41$	1532.90			0.911895			0.455948	−	0.890007i	$-0.349300\pi$
$41$	1532.90			0.911895			0.455948	+	0.890007i	$0.349300\pi$
$42$			1613.46i			0.914657i
$43$		−	404.708i		−	0.218879i	−0.993993	−	0.109440i	$-0.965094\pi$
$43$		−	404.708i		−	0.218879i	0.993993	−	0.109440i	$-0.0349056\pi$
$44$		−	4539.89i		−	2.34498i
$45$	182.975			0.0903580
$46$	−375.377			−0.177400
$47$		−	1601.56i		−	0.725016i	−0.931981	−	0.362508i	$-0.881921\pi$
$47$		−	1601.56i		−	0.725016i	0.931981	−	0.362508i	$-0.118079\pi$
$48$	805.467			0.349595
$49$	−295.602			−0.123116
$50$		−	3918.70i		−	1.56748i
$51$	317.993			0.122258
$52$		−	4128.79i		−	1.52692i
$53$	−1325.56			−0.471897			−0.235949	−	0.971766i	$-0.575820\pi$
$53$	−1325.56			−0.471897			−0.235949	+	0.971766i	$0.575820\pi$
$54$			949.410i			0.325586i
$55$			1032.60i			0.341356i
$56$		−	4283.41i		−	1.36588i
$57$	−956.562			−0.294417
$58$			1965.75i			0.584350i
$59$	3430.65	−	589.891i	0.985537	−	0.169460i
$59$	3430.65	−	589.891i	0.985537	−	0.169460i
$60$	−1049.18			−0.291439
$61$		−	2732.09i		−	0.734236i	−0.930174	−	0.367118i	$-0.880344\pi$
$61$		−	2732.09i		−	0.734236i	0.930174	−	0.367118i	$-0.119656\pi$
$62$	−4609.19			−1.19906
$63$	1238.88			0.312140
$64$	5489.10			1.34011
$65$			939.097i			0.222271i
$66$	−5357.90			−1.23001
$67$			2225.52i			0.495771i	0.968789	+	0.247885i	$0.0797357\pi$
$67$			2225.52i			0.495771i	−0.968789	+	0.247885i	$0.920264\pi$
$68$	−1823.37			−0.394328
$69$			288.232i			0.0605402i
$70$			2104.28i			0.429444i
$71$	−6157.04			−1.22139			−0.610696	−	0.791865i	$-0.709110\pi$
$71$	−6157.04			−1.22139			−0.610696	+	0.791865i	$0.709110\pi$
$72$		−	2520.50i		−	0.486207i
$73$			2816.89i			0.528597i	0.964441	+	0.264298i	$0.0851404\pi$
$73$			2816.89i			0.528597i	−0.964441	+	0.264298i	$0.914860\pi$
$74$	−9624.09			−1.75750
$75$	−3008.96			−0.534926
$76$	5484.93			0.949608
$77$			6991.53i			1.17921i
$78$	−4872.73			−0.800909
$79$	7747.95			1.24146			0.620730	−	0.784025i	$-0.286836\pi$
$79$	7747.95			1.24146			0.620730	+	0.784025i	$0.286836\pi$
$80$	1050.49			0.164140
$81$	729.000			0.111111
$82$			10373.4i			1.54274i
$83$		−	648.806i		−	0.0941800i	−0.998891	−	0.0470900i	$-0.985005\pi$
$83$		−	648.806i		−	0.0941800i	0.998891	−	0.0470900i	$-0.0149948\pi$
$84$	−7103.77			−1.00677
$85$	414.728			0.0574018
$86$	2738.73			0.370299
$87$	1509.40			0.199418
$88$	14224.2			1.83680
$89$		−	5751.21i		−	0.726071i	−0.931775	−	0.363036i	$-0.881740\pi$
$89$		−	5751.21i		−	0.726071i	0.931775	−	0.363036i	$-0.118260\pi$
$90$			1238.22i			0.152867i
$91$			6358.43i			0.767833i
$92$		−	1652.72i		−	0.195265i
$93$			3539.14i			0.409197i
$94$	10838.1			1.22658
$95$	−1247.55			−0.138233
$96$		−	2310.38i		−	0.250692i
$97$		−	1510.67i		−	0.160556i	−0.996773	−	0.0802779i	$-0.974419\pi$
$97$		−	1510.67i		−	0.160556i	0.996773	−	0.0802779i	$-0.0255808\pi$
$98$		−	2000.39i		−	0.208287i
$99$			4114.04i			0.419758i
$100$	17253.4			1.72534
$101$		−	2457.45i		−	0.240903i	−0.992719	−	0.120451i	$-0.961566\pi$
$101$		−	2457.45i		−	0.240903i	0.992719	−	0.120451i	$-0.0384342\pi$
$102$			2151.92i			0.206835i
$103$			8751.92i			0.824952i	0.910968	+	0.412476i	$0.135336\pi$
$103$			8751.92i			0.824952i	−0.910968	+	0.412476i	$0.864664\pi$
$104$	12936.2			1.19602
$105$	1615.76			0.146554
$106$		−	8970.31i		−	0.798354i
$107$	21034.2			1.83721			0.918603	−	0.395182i	$-0.129319\pi$
$107$	21034.2			1.83721			0.918603	+	0.395182i	$0.129319\pi$
$108$	−4180.09			−0.358375
$109$			9627.62i			0.810338i	0.914242	+	0.405169i	$0.132787\pi$
$109$			9627.62i			0.810338i	−0.914242	+	0.405169i	$0.867213\pi$
$110$	−6987.81			−0.577505
$111$			7389.82i			0.599774i
$112$	7112.68			0.567018
$113$			23222.8i			1.81869i	0.416044	+	0.909344i	$0.363416\pi$
$113$			23222.8i			1.81869i	−0.416044	+	0.909344i	$0.636584\pi$
$114$		−	6473.23i		−	0.498094i
$115$			375.914i			0.0284245i
$116$	−8654.89			−0.643199
$117$			3741.51i			0.273322i
$118$	3991.90	+	23215.9i	0.286692	+	1.66733i
$119$	2808.04			0.198294
$120$		−	3287.25i		−	0.228281i
$121$	−8576.22			−0.585768
$122$	18488.6			1.24218
$123$	7965.16			0.526483
$124$		−	20293.5i		−	1.31981i
$125$	−8159.83			−0.522229
$126$			8383.76i			0.528078i
$127$	3258.32			0.202016			0.101008	−	0.994886i	$-0.467793\pi$
$127$	3258.32			0.202016			0.101008	+	0.994886i	$0.467793\pi$
$128$			30031.7i			1.83299i
$129$		−	2102.92i		−	0.126370i
$130$	−6355.04			−0.376038
$131$		−	23879.6i		−	1.39151i	−0.718281	−	0.695753i	$-0.755071\pi$
$131$		−	23879.6i		−	1.39151i	0.718281	−	0.695753i	$-0.244929\pi$
$132$		−	23590.0i		−	1.35388i
$133$	−8446.92			−0.477524
$134$	−15060.5			−0.838743
$135$	950.766			0.0521682
$136$		−	5712.92i		−	0.308873i
$137$	25992.0			1.38483			0.692417	−	0.721497i	$-0.256546\pi$
$137$	25992.0			1.38483			0.692417	+	0.721497i	$0.256546\pi$
$138$	−1950.52			−0.102422
$139$	10296.8			0.532931			0.266466	−	0.963844i	$-0.414144\pi$
$139$	10296.8			0.532931			0.266466	+	0.963844i	$0.414144\pi$
$140$	−9264.78			−0.472693
$141$		−	8321.95i		−	0.418588i
$142$		−	41665.8i		−	2.06635i
$143$	−21114.8			−1.03256
$144$	4185.33			0.201839
$145$	1968.56			0.0936296
$146$	−19062.4			−0.894278
$147$	−1535.99			−0.0710811
$148$		−	42373.3i		−	1.93450i
$149$		−	34672.4i		−	1.56175i	−0.624687	−	0.780875i	$-0.714773\pi$
$149$		−	34672.4i		−	1.56175i	0.624687	−	0.780875i	$-0.285227\pi$
$150$		−	20362.2i		−	0.904986i
$151$			8100.65i			0.355276i	0.984096	+	0.177638i	$0.0568456\pi$
$151$			8100.65i			0.355276i	−0.984096	+	0.177638i	$0.943154\pi$
$152$			17185.2i			0.743818i
$153$	1652.34			0.0705857
$154$	−47313.0			−1.99498
$155$			4615.77i			0.192124i
$156$		−	21453.8i		−	0.881567i
$157$		−	35250.4i		−	1.43009i	−0.699077	−	0.715046i	$-0.746406\pi$
$157$		−	35250.4i		−	1.43009i	0.699077	−	0.715046i	$-0.253594\pi$
$158$			52431.8i			2.10030i
$159$	−6887.81			−0.272450
$160$		−	3013.21i		−	0.117703i
$161$			2545.23i			0.0981919i
$162$			4933.28i			0.187977i
$163$	−12118.8			−0.456126			−0.228063	−	0.973646i	$-0.573239\pi$
$163$	−12118.8			−0.456126			−0.228063	+	0.973646i	$0.573239\pi$
$164$	−45672.3			−1.69811
$165$			5365.56i			0.197082i
$166$	4390.59			0.159333
$167$	24887.2			0.892365			0.446182	−	0.894942i	$-0.352783\pi$
$167$	24887.2			0.892365			0.446182	+	0.894942i	$0.352783\pi$
$168$		−	22257.3i		−	0.788593i
$169$	9358.17			0.327656
$170$			2806.54i			0.0971121i
$171$	−4970.44			−0.169982
$172$			12058.2i			0.407591i
$173$		−	6149.40i		−	0.205466i	−0.994709	−	0.102733i	$-0.967241\pi$
$173$		−	6149.40i		−	0.205466i	0.994709	−	0.102733i	$-0.0327588\pi$
$174$			10214.4i			0.337375i
$175$	−26570.6			−0.867612
$176$			23619.5i			0.762510i
$177$	17826.2	−	3065.16i	0.569000	−	0.0978379i
$178$	38919.5			1.22836
$179$		−	17529.1i		−	0.547082i	−0.961860	−	0.273541i	$-0.911805\pi$
$179$		−	17529.1i		−	0.547082i	0.961860	−	0.273541i	$-0.0881949\pi$
$180$	−5451.70			−0.168262
$181$	20780.3			0.634299			0.317150	−	0.948376i	$-0.397274\pi$
$181$	20780.3			0.634299			0.317150	+	0.948376i	$0.397274\pi$
$182$	−43028.6			−1.29902
$183$		−	14196.4i		−	0.423912i
$184$	5178.25			0.152949
$185$			9637.84i			0.281602i
$186$	−23950.0			−0.692277
$187$			9324.83i			0.266660i
$188$			47718.1i			1.35011i
$189$	6437.43			0.180214
$190$		−	8442.42i		−	0.233862i
$191$		−	13668.6i		−	0.374676i	−0.982296	−	0.187338i	$-0.940014\pi$
$191$		−	13668.6i		−	0.374676i	0.982296	−	0.187338i	$-0.0599860\pi$
$192$	28522.2			0.773715
$193$	24606.0			0.660582			0.330291	−	0.943879i	$-0.392853\pi$
$193$	24606.0			0.660582			0.330291	+	0.943879i	$0.392853\pi$
$194$	10223.0			0.271628
$195$			4879.69i			0.128328i
$196$	8807.38			0.229263
$197$	7657.45			0.197311			0.0986556	−	0.995122i	$-0.468546\pi$
$197$	7657.45			0.197311			0.0986556	+	0.995122i	$0.468546\pi$
$198$	−27840.5			−0.710144
$199$	50335.0			1.27105			0.635527	−	0.772079i	$-0.280783\pi$
$199$	50335.0			1.27105			0.635527	+	0.772079i	$0.280783\pi$
$200$			54057.6i			1.35144i
$201$			11564.1i			0.286233i
$202$	16630.0			0.407558
$203$	13328.7			0.323442
$204$	−9474.53			−0.227665
$205$	10388.2			0.247191
$206$	−59225.8			−1.39565
$207$			1497.70i			0.0349529i
$208$			21480.7i			0.496503i
$209$		−	28050.2i		−	0.642161i
$210$			10934.1i			0.247940i
$211$			34304.2i			0.770518i	0.922809	+	0.385259i	$0.125888\pi$
$211$			34304.2i			0.770518i	−0.922809	+	0.385259i	$0.874112\pi$
$212$	39494.7			0.878755
$213$	−31992.9			−0.705171
$214$			142342.i			3.10818i
$215$		−	2742.64i		−	0.0593324i
$216$		−	13096.9i		−	0.280712i
$217$			31252.4i			0.663688i
$218$	−65151.9			−1.37093
$219$			14637.0i			0.305185i
$220$		−	30766.1i		−	0.635664i
$221$			8480.44i			0.173634i
$222$	−50008.2			−1.01470
$223$	12252.7			0.246390			0.123195	−	0.992383i	$-0.460686\pi$
$223$	12252.7			0.246390			0.123195	+	0.992383i	$0.460686\pi$
$224$		−	20401.8i		−	0.406604i
$225$	−15635.0			−0.308840
$226$	−157153.			−3.07685
$227$		−	83145.6i		−	1.61357i	−0.590846	−	0.806784i	$-0.701206\pi$
$227$		−	83145.6i		−	1.61357i	0.590846	−	0.806784i	$-0.298794\pi$
$228$	28500.6			0.548256
$229$		−	84147.1i		−	1.60460i	−0.596918	−	0.802302i	$-0.703608\pi$
$229$		−	84147.1i		−	1.60460i	0.596918	−	0.802302i	$-0.296392\pi$
$230$	−2543.88			−0.0480884
$231$			36329.1i			0.680817i
$232$		−	27117.1i		−	0.503811i
$233$			10889.2i			0.200578i	0.994958	+	0.100289i	$0.0319767\pi$
$233$			10889.2i			0.200578i	−0.994958	+	0.100289i	$0.968023\pi$
$234$	−25319.5			−0.462405
$235$		−	10853.5i		−	0.196533i
$236$	−102216.	+	17575.7i	−1.83524	+	0.315564i
$237$	40259.5			0.716757
$238$			19002.5i			0.335472i
$239$	62954.4			1.10212			0.551061	−	0.834465i	$-0.314223\pi$
$239$	62954.4			1.10212			0.551061	+	0.834465i	$0.314223\pi$
$240$	5458.53			0.0947661
$241$	−63118.5			−1.08673			−0.543366	−	0.839496i	$-0.682851\pi$
$241$	−63118.5			−1.08673			−0.543366	+	0.839496i	$0.682851\pi$
$242$		−	58036.9i		−	0.990999i
$243$	3788.00			0.0641500
$244$			81402.1i			1.36728i
$245$	−2003.25			−0.0333736
$246$			53901.7i			0.890702i
$247$		−	25510.2i		−	0.418138i
$248$	63582.7			1.03380
$249$		−	3371.29i		−	0.0543748i
$250$		−	55219.1i		−	0.883505i
$251$	−66048.7			−1.04838			−0.524188	−	0.851603i	$-0.675631\pi$
$251$	−66048.7			−1.04838			−0.524188	+	0.851603i	$0.675631\pi$
$252$	−36912.3			−0.581259
$253$	−8452.12			−0.132046
$254$			22049.6i			0.341770i
$255$	2154.99			0.0331409
$256$	−115404.			−1.76093
$257$	91076.3			1.37892			0.689460	−	0.724323i	$-0.257848\pi$
$257$	91076.3			1.37892			0.689460	+	0.724323i	$0.257848\pi$
$258$	14230.9			0.213792
$259$			65255.8i			0.972791i
$260$		−	27980.2i		−	0.413908i
$261$	7843.05			0.115134
$262$	161598.			2.35414
$263$	−83369.8			−1.20531			−0.602653	−	0.798003i	$-0.705890\pi$
$263$	−83369.8			−1.20531			−0.602653	+	0.798003i	$0.705890\pi$
$264$	73911.1			1.06048
$265$	−8983.12			−0.127919
$266$		−	57161.9i		−	0.807873i
$267$		−	29884.2i		−	0.419198i
$268$		−	66308.7i		−	0.923211i
$269$		−	13600.6i		−	0.187955i	−0.995574	−	0.0939775i	$-0.970042\pi$
$269$		−	13600.6i		−	0.187955i	0.995574	−	0.0939775i	$-0.0299582\pi$
$270$			6434.00i			0.0882580i
$271$	−374.789			−0.00510327			−0.00255164	−	0.999997i	$-0.500812\pi$
$271$	−374.789			−0.00510327			−0.00255164	+	0.999997i	$0.500812\pi$
$272$	9486.40			0.128222
$273$			33039.4i			0.443309i
$274$			175892.i			2.34286i
$275$		−	88234.7i		−	1.16674i
$276$		−	8587.81i		−	0.112736i
$277$	−34517.8			−0.449866			−0.224933	−	0.974374i	$-0.572216\pi$
$277$	−34517.8			−0.449866			−0.224933	+	0.974374i	$0.572216\pi$
$278$			69680.1i			0.901611i
$279$			18389.9i			0.236250i
$280$		−	29028.0i		−	0.370255i
$281$	100630.			1.27442			0.637210	−	0.770690i	$-0.280088\pi$
$281$	100630.			1.27442			0.637210	+	0.770690i	$0.280088\pi$
$282$	56316.2			0.708166
$283$		−	85403.6i		−	1.06636i	−0.846002	−	0.533179i	$-0.820997\pi$
$283$		−	85403.6i		−	1.06636i	0.846002	−	0.533179i	$-0.179003\pi$
$284$	183448.			2.27444
$285$	−6482.48			−0.0798089
$286$		−	142888.i		−	1.74688i
$287$	70336.4			0.853918
$288$		−	12005.1i		−	0.144737i
$289$	−79775.8			−0.955159
$290$			13321.6i			0.158402i
$291$		−	7849.67i		−	0.0926969i
$292$		−	83928.7i		−	0.984339i
$293$	133357.			1.55339			0.776696	−	0.629876i	$-0.216894\pi$
$293$	133357.			1.55339			0.776696	+	0.629876i	$0.216894\pi$
$294$		−	10394.3i		−	0.120255i
$295$	23249.0	−	3997.60i	0.267153	−	0.0459362i
$296$	132762.			1.51527
$297$			21377.2i			0.242347i
$298$	234635.			2.64216
$299$	−7686.75			−0.0859806
$300$	89651.2			0.996125
$301$		−	18569.9i		−	0.204963i
$302$	−54818.6			−0.601055
$303$		−	12769.3i		−	0.139085i
$304$	−28536.3			−0.308781
$305$		−	18515.0i		−	0.199032i
$306$			11181.7i			0.119417i
$307$	20011.7			0.212328			0.106164	−	0.994349i	$-0.466143\pi$
$307$	20011.7			0.212328			0.106164	+	0.994349i	$0.466143\pi$
$308$		−	208311.i		−	2.19589i
$309$			45476.3i			0.476286i
$310$	−31235.8			−0.325034
$311$	32402.1			0.335006			0.167503	−	0.985872i	$-0.446430\pi$
$311$	32402.1			0.335006			0.167503	+	0.985872i	$0.446430\pi$
$312$	67218.2			0.690523
$313$			191288.i			1.95254i	0.216568	+	0.976268i	$0.430514\pi$
$313$			191288.i			1.95254i	−0.216568	+	0.976268i	$0.569486\pi$
$314$	238546.			2.41943
$315$	8395.73			0.0846131
$316$	−230848.			−2.31181
$317$	−127089.			−1.26470			−0.632351	−	0.774682i	$-0.717910\pi$
$317$	−127089.			−1.26470			−0.632351	+	0.774682i	$0.717910\pi$
$318$		−	46611.1i		−	0.460930i
$319$			44261.5i			0.434956i
$320$	37198.8			0.363270
$321$	109297.			1.06071
$322$	−17224.1			−0.166121
$323$	−11265.9			−0.107985
$324$	−21720.4			−0.206908
$325$		−	80244.8i		−	0.759714i
$326$		−	82010.3i		−	0.771673i
$327$			50026.6i			0.467849i
$328$		−	143099.i		−	1.33011i
$329$		−	73487.0i		−	0.678920i
$330$	−36309.7			−0.333422
$331$	−190707.			−1.74064			−0.870321	−	0.492484i	$-0.836089\pi$
$331$	−190707.			−1.74064			−0.870321	+	0.492484i	$0.836089\pi$
$332$			19331.0i			0.175379i
$333$			38398.6i			0.346280i
$334$			168416.i			1.50970i
$335$			15082.0i			0.134391i
$336$	36958.6			0.327368
$337$			121592.i			1.07065i	0.844648	+	0.535323i	$0.179810\pi$
$337$			121592.i			1.07065i	−0.844648	+	0.535323i	$0.820190\pi$
$338$			63328.5i			0.554326i
$339$			120669.i			1.05002i
$340$	−12356.7			−0.106892
$341$	−103782.			−0.892509
$342$		−	33635.9i		−	0.287575i
$343$	−123733.			−1.05171
$344$	−37780.2			−0.319262
$345$			1953.30i			0.0164109i
$346$	41614.1			0.347607
$347$		−	11383.8i		−	0.0945426i	−0.998882	−	0.0472713i	$-0.984947\pi$
$347$		−	11383.8i		−	0.0945426i	0.998882	−	0.0472713i	$-0.0150525\pi$
$348$	−44972.1			−0.371351
$349$			133595.i			1.09683i	0.836207	+	0.548414i	$0.184768\pi$
$349$			133595.i			1.09683i	−0.836207	+	0.548414i	$0.815232\pi$
$350$		−	179808.i		−	1.46782i
$351$			19441.4i			0.157803i
$352$	67749.5			0.546790
$353$		−	152806.i		−	1.22628i	−0.789973	−	0.613141i	$-0.789906\pi$
$353$		−	152806.i		−	1.22628i	0.789973	−	0.613141i	$-0.210094\pi$
$354$	20742.5	+	120633.i	0.165522	+	0.962632i
$355$	−41725.3			−0.331088
$356$			171356.i			1.35207i
$357$	14591.0			0.114485
$358$	118622.			0.925551
$359$	−84352.3			−0.654497			−0.327249	−	0.944938i	$-0.606121\pi$
$359$	−84352.3			−0.654497			−0.327249	+	0.944938i	$0.606121\pi$
$360$		−	17081.0i		−	0.131798i
$361$	−96431.7			−0.739955
$362$			140624.i			1.07310i
$363$	−44563.4			−0.338193
$364$		−	189448.i		−	1.42984i
$365$			19089.6i			0.143289i
$366$	96069.5			0.717172
$367$		−	22612.6i		−	0.167888i	−0.996470	−	0.0839439i	$-0.973248\pi$
$367$		−	22612.6i		−	0.167888i	0.996470	−	0.0839439i	$-0.0267517\pi$
$368$			8598.57i			0.0634937i
$369$	41388.2			0.303965
$370$	−65221.0			−0.476414
$371$	−60822.8			−0.441894
$372$		−	105448.i		−	0.761995i
$373$	−142008.			−1.02069			−0.510347	−	0.859968i	$-0.670483\pi$
$373$	−142008.			−1.02069			−0.510347	+	0.859968i	$0.670483\pi$
$374$	−63102.8			−0.451134
$375$	−42399.7			−0.301509
$376$	−149509.			−1.05752
$377$			40253.5i			0.283218i
$378$			43563.3i			0.304886i
$379$	−71134.7			−0.495226			−0.247613	−	0.968859i	$-0.579646\pi$
$379$	−71134.7			−0.495226			−0.247613	+	0.968859i	$0.579646\pi$
$380$	37170.6			0.257414
$381$	16930.7			0.116634
$382$	92497.6			0.633875
$383$	5389.15			0.0367386			0.0183693	−	0.999831i	$-0.494153\pi$
$383$	5389.15			0.0367386			0.0183693	+	0.999831i	$0.494153\pi$
$384$			156049.i			1.05828i
$385$			47380.5i			0.319653i
$386$			166514.i			1.11757i
$387$		−	10927.1i		−	0.0729597i
$388$			45010.1i			0.298983i
$389$	227686.			1.50466			0.752329	−	0.658787i	$-0.228930\pi$
$389$	227686.			1.50466			0.752329	+	0.658787i	$0.228930\pi$
$390$	−33021.8			−0.217106
$391$			3394.66i			0.0222046i
$392$			27594.9i			0.179580i
$393$		−	124082.i		−	0.803387i
$394$			51819.4i			0.333810i
$395$	52506.7			0.336527
$396$		−	122577.i		−	0.781661i
$397$			66414.0i			0.421385i	0.977552	+	0.210692i	$0.0675718\pi$
$397$			66414.0i			0.421385i	−0.977552	+	0.210692i	$0.932428\pi$
$398$			340626.i			2.15036i
$399$	−43891.5			−0.275699
$400$	−89763.6			−0.561022
$401$			185618.i			1.15434i	0.816625	+	0.577168i	$0.195842\pi$
$401$			185618.i			1.15434i	−0.816625	+	0.577168i	$0.804158\pi$
$402$	−78256.5			−0.484249
$403$	−94384.1			−0.581151
$404$			73219.1i			0.448602i
$405$	4940.32			0.0301193
$406$			90197.9i			0.547198i
$407$	−216699.			−1.30818
$408$		−	29685.2i		−	0.178328i
$409$		−	69799.6i		−	0.417260i	−0.977995	−	0.208630i	$-0.933100\pi$
$409$		−	69799.6i		−	0.417260i	0.977995	−	0.208630i	$-0.0669004\pi$
$410$			70298.9i			0.418197i
$411$	135058.			0.799535
$412$		−	260761.i		−	1.53620i
$413$	157414.	−	27066.9i	0.922877	−	0.158686i
$414$	−10135.2			−0.0591332
$415$		−	4396.86i		−	0.0255297i
$416$	61614.6			0.356038
$417$	53503.5			0.307688
$418$	189821.			1.08641
$419$			68851.9i			0.392182i	0.980586	+	0.196091i	$0.0628248\pi$
$419$			68851.9i			0.392182i	−0.980586	+	0.196091i	$0.937175\pi$
$420$	−48141.2			−0.272909
$421$			52611.8i			0.296837i	0.988925	+	0.148419i	$0.0474183\pi$
$421$			52611.8i			0.296837i	−0.988925	+	0.148419i	$0.952582\pi$
$422$	−232143.			−1.30356
$423$		−	43242.1i		−	0.241672i
$424$			123743.i			0.688320i
$425$	−35438.1			−0.196197
$426$		−	216502.i		−	1.19301i
$427$		−	125361.i		−	0.687554i
$428$	−626708.			−3.42120
$429$	−109716.			−0.596149
$430$	18560.0			0.100378
$431$			127282.i			0.685193i	0.939483	+	0.342596i	$0.111306\pi$
$431$			127282.i			0.685193i	−0.939483	+	0.342596i	$0.888694\pi$
$432$	21747.6			0.116532
$433$	67016.8			0.357444			0.178722	−	0.983900i	$-0.442804\pi$
$433$	67016.8			0.357444			0.178722	+	0.983900i	$0.442804\pi$
$434$	−211491.			−1.12282
$435$	10229.0			0.0540571
$436$		−	286853.i		−	1.50899i
$437$		−	10211.5i		−	0.0534723i
$438$	−99051.3			−0.516311
$439$	131134.			0.680434			0.340217	−	0.940347i	$-0.389499\pi$
$439$	131134.			0.680434			0.340217	+	0.940347i	$0.389499\pi$
$440$	96395.2			0.497909
$441$	−7981.24			−0.0410387
$442$	−57388.7			−0.293753
$443$			238014.i			1.21282i	0.795154	+	0.606408i	$0.207390\pi$
$443$			238014.i			1.21282i	−0.795154	+	0.606408i	$0.792610\pi$
$444$		−	220178.i		−	1.11688i
$445$		−	38975.1i		−	0.196819i
$446$			82916.3i			0.416841i
$447$		−	180163.i		−	0.901677i
$448$	251865.			1.25491
$449$	−140599.			−0.697411			−0.348706	−	0.937232i	$-0.613379\pi$
$449$	−140599.			−0.697411			−0.348706	+	0.937232i	$0.613379\pi$
$450$		−	105805.i		−	0.522494i
$451$			233570.i			1.14832i
$452$		−	691919.i		−	3.38671i
$453$			42092.2i			0.205119i
$454$	562661.			2.72983
$455$			43090.1i			0.208140i
$456$			89296.8i			0.429444i
$457$		−	381250.i		−	1.82548i	−0.408539	−	0.912741i	$-0.633962\pi$
$457$		−	381250.i		−	1.82548i	0.408539	−	0.912741i	$-0.366038\pi$
$458$	569439.			2.71466
$459$	8585.81			0.0407526
$460$		−	11200.3i		−	0.0529313i
$461$	−66518.7			−0.312998			−0.156499	−	0.987678i	$-0.550021\pi$
$461$	−66518.7			−0.312998			−0.156499	+	0.987678i	$0.550021\pi$
$462$	−245845.			−1.15180
$463$		−	362433.i		−	1.69070i	−0.534216	−	0.845348i	$-0.679393\pi$
$463$		−	362433.i		−	1.69070i	0.534216	−	0.845348i	$-0.320607\pi$
$464$	45028.5			0.209147
$465$			23984.2i			0.110923i
$466$	−73689.1			−0.339337
$467$			184210.i			0.844656i	0.906443	+	0.422328i	$0.138787\pi$
$467$			184210.i			0.844656i	−0.906443	+	0.422328i	$0.861213\pi$
$468$		−	111477.i		−	0.508973i
$469$			102117.i			0.464250i
$470$	73447.9			0.332494
$471$		−	183166.i		−	0.825664i
$472$	−55067.4	−	320258.i	−0.247178	−	1.43753i
$473$	61666.1			0.275629
$474$			272444.i			1.21261i
$475$	106602.			0.472475
$476$	−83664.8			−0.369257
$477$	−35790.1			−0.157299
$478$			426024.i			1.86457i
$479$	−348835.			−1.52037			−0.760185	−	0.649707i	$-0.774892\pi$
$479$	−348835.			−1.52037			−0.760185	+	0.649707i	$0.774892\pi$
$480$		−	15657.1i		−	0.0679561i
$481$	−197076.			−0.851813
$482$		−	427135.i		−	1.83853i
$483$			13225.4i			0.0566911i
$484$	255527.			1.09080
$485$		−	10237.6i		−	0.0435225i
$486$			25634.1i			0.108529i
$487$	−451419.			−1.90336			−0.951681	−	0.307087i	$-0.900646\pi$
$487$	−451419.			−1.90336			−0.951681	+	0.307087i	$0.900646\pi$
$488$	−255046.			−1.07097
$489$	−62971.3			−0.263345
$490$		−	13556.3i		−	0.0564612i
$491$	−64824.7			−0.268892			−0.134446	−	0.990921i	$-0.542925\pi$
$491$	−64824.7			−0.268892			−0.134446	+	0.990921i	$0.542925\pi$
$492$	−237320.			−0.980403
$493$	17776.9			0.0731414
$494$	172632.			0.707405
$495$			27880.3i			0.113785i
$496$			105580.i			0.429160i
$497$	−282513.			−1.14374
$498$	22814.2			0.0919911
$499$	−151617.			−0.608900			−0.304450	−	0.952528i	$-0.598473\pi$
$499$	−151617.			−0.608900			−0.304450	+	0.952528i	$0.598473\pi$
$500$	243120.			0.972481
$501$	129317.			0.515207
$502$		−	446964.i		−	1.77364i
$503$			154559.i			0.610883i	0.952211	+	0.305442i	$0.0988040\pi$
$503$			154559.i			0.610883i	−0.952211	+	0.305442i	$0.901196\pi$
$504$		−	115652.i		−	0.455295i
$505$		−	16653.8i		−	0.0653024i
$506$		−	57197.0i		−	0.223394i
$507$	48626.5			0.189172
$508$	−97080.8			−0.376189
$509$		−	6251.16i		−	0.0241282i	−0.999927	−	0.0120641i	$-0.996160\pi$
$509$		−	6251.16i		−	0.0241282i	0.999927	−	0.0120641i	$-0.00384022\pi$
$510$			14583.2i			0.0560677i
$511$			129252.i			0.494989i
$512$		−	300454.i		−	1.14614i
$513$	−25827.2			−0.0981391
$514$			616330.i			2.33285i
$515$			59310.4i			0.223623i
$516$			62656.1i			0.235323i
$517$	244033.			0.912993
$518$	−441598.			−1.64576
$519$		−	31953.2i		−	0.118626i
$520$	87666.4			0.324210
$521$	351023.			1.29318			0.646591	−	0.762836i	$-0.276194\pi$
$521$	351023.			1.29318			0.646591	+	0.762836i	$0.276194\pi$
$522$			53075.4i			0.194783i
$523$	−58841.2			−0.215119			−0.107559	−	0.994199i	$-0.534304\pi$
$523$	−58841.2			−0.215119			−0.107559	+	0.994199i	$0.534304\pi$
$524$			711489.i			2.59123i
$525$	−138065.			−0.500916
$526$		−	564179.i		−	2.03913i
$527$			41682.3i			0.150083i
$528$			122731.i			0.440236i
$529$	276764.			0.989005
$530$		−	60790.4i		−	0.216413i
$531$	92627.7	−	15927.1i	0.328512	−	0.0564867i
$532$	251674.			0.889233
$533$			212420.i			0.747723i
$534$	202232.			0.709197
$535$	142545.			0.498019
$536$	207756.			0.723142
$537$		−	91083.6i		−	0.315858i
$538$	92037.8			0.317981
$539$		−	45041.4i		−	0.155037i
$540$	−28327.8			−0.0971462
$541$		−	451192.i		−	1.54158i	−0.637088	−	0.770791i	$-0.719861\pi$
$541$		−	451192.i		−	1.54158i	0.637088	−	0.770791i	$-0.280139\pi$
$542$		−	2536.27i		−	0.00863369i
$543$	107977.			0.366213
$544$		−	27210.5i		−	0.0919472i
$545$			65244.9i			0.219661i
$546$	−223583.			−0.749988
$547$	−341064.			−1.13988			−0.569942	−	0.821685i	$-0.693034\pi$
$547$	−341064.			−1.13988			−0.569942	+	0.821685i	$0.693034\pi$
$548$	−774425.			−2.57880
$549$		−	73766.5i		−	0.244745i
$550$	597100.			1.97389
$551$	−53475.2			−0.176137
$552$	26907.0			0.0883053
$553$	355512.			1.16253
$554$		−	233588.i		−	0.761082i
$555$			50079.7i			0.162583i
$556$	−306790.			−0.992410
$557$	333403.			1.07463			0.537315	−	0.843382i	$-0.319439\pi$
$557$	333403.			1.07463			0.537315	+	0.843382i	$0.319439\pi$
$558$	−124448.			−0.399687
$559$	56082.1			0.179474
$560$	48201.5			0.153704
$561$			48453.2i			0.153956i
$562$			680978.i			2.15606i
$563$		−	48980.2i		−	0.154527i	−0.997011	−	0.0772634i	$-0.975382\pi$
$563$		−	48980.2i		−	0.154527i	0.997011	−	0.0772634i	$-0.0246182\pi$
$564$			247951.i			0.779484i
$565$			157378.i			0.492999i
$566$	577942.			1.80406
$567$	33449.9			0.104047
$568$			574771.i			1.78155i
$569$		−	47923.5i		−	0.148021i	−0.997257	−	0.0740106i	$-0.976420\pi$
$569$		−	47923.5i		−	0.148021i	0.997257	−	0.0740106i	$-0.0235799\pi$
$570$		−	43868.1i		−	0.135020i
$571$		−	518303.i		−	1.58969i	−0.606815	−	0.794843i	$-0.707553\pi$
$571$		−	518303.i		−	1.58969i	0.606815	−	0.794843i	$-0.292447\pi$
$572$	629112.			1.92281
$573$		−	71023.9i		−	0.216319i
$574$			475979.i			1.44465i
$575$		−	32121.4i		−	0.0971536i
$576$	148206.			0.446704
$577$	92997.1			0.279330			0.139665	−	0.990199i	$-0.455397\pi$
$577$	92997.1			0.279330			0.139665	+	0.990199i	$0.455397\pi$
$578$		−	539858.i		−	1.61593i
$579$	127857.			0.381387
$580$	−58652.9			−0.174355
$581$		−	29770.2i		−	0.0881921i
$582$	53120.2			0.156824
$583$		−	201978.i		−	0.594247i
$584$	262962.			0.771022
$585$			25355.6i			0.0740905i
$586$			902452.i			2.62802i
$587$		−	333846.i		−	0.968881i	−0.874824	−	0.484440i	$-0.839023\pi$
$587$		−	333846.i		−	0.968881i	0.874824	−	0.484440i	$-0.160977\pi$
$588$	45764.5			0.132365
$589$		−	125386.i		−	0.361424i
$590$	27052.5	+	157330.i	0.0777147	+	0.451969i
$591$	39789.3			0.113918
$592$			220454.i			0.629034i
$593$	122051.			0.347081			0.173541	−	0.984827i	$-0.444479\pi$
$593$	122051.			0.347081			0.173541	+	0.984827i	$0.444479\pi$
$594$	−144663.			−0.410002
$595$	19029.6			0.0537522
$596$			1.03306e6i			2.90825i
$597$	261548.			0.733843
$598$		−	52017.7i		−	0.145462i
$599$	−118410.			−0.330015			−0.165008	−	0.986292i	$-0.552765\pi$
$599$	−118410.			−0.330015			−0.165008	+	0.986292i	$0.552765\pi$
$600$			280892.i			0.780255i
$601$		−	316761.i		−	0.876966i	−0.898740	−	0.438483i	$-0.855516\pi$
$601$		−	316761.i		−	0.876966i	0.898740	−	0.438483i	$-0.144484\pi$
$602$	125666.			0.346756
$603$			60088.9i			0.165257i
$604$		−	241357.i		−	0.661586i
$605$	−58119.8			−0.158786
$606$	86412.0			0.235304
$607$	−635965.			−1.72606			−0.863030	−	0.505153i	$-0.831436\pi$
$607$	−635965.			−1.72606			−0.863030	+	0.505153i	$0.831436\pi$
$608$			81852.6i			0.221424i
$609$	69258.1			0.186739
$610$	125294.			0.336722
$611$	221935.			0.594489
$612$	−49231.1			−0.131443
$613$			664506.i			1.76839i	0.467119	+	0.884195i	$0.345292\pi$
$613$			664506.i			1.76839i	−0.467119	+	0.884195i	$0.654708\pi$
$614$			135423.i			0.359215i
$615$	53978.7			0.142716
$616$	652672.			1.72002
$617$	214690.			0.563952			0.281976	−	0.959422i	$-0.409010\pi$
$617$	214690.			0.563952			0.281976	+	0.959422i	$0.409010\pi$
$618$	−307746.			−0.805779
$619$	−638321.			−1.66594			−0.832968	−	0.553322i	$-0.813360\pi$
$619$	−638321.			−1.66594			−0.832968	+	0.553322i	$0.813360\pi$
$620$		−	137526.i		−	0.357767i
$621$			7782.26i			0.0201801i
$622$			219271.i			0.566761i
$623$		−	263892.i		−	0.679908i
$624$			111617.i			0.286656i
$625$	306624.			0.784956
$626$	−1.29448e6			−3.30329
$627$		−	145753.i		−	0.370752i
$628$			1.05028e6i			2.66308i
$629$			87033.7i			0.219981i
$630$			56815.5i			0.143148i
$631$	−375421.			−0.942888			−0.471444	−	0.881896i	$-0.656267\pi$
$631$	−375421.			−0.942888			−0.471444	+	0.881896i	$0.656267\pi$
$632$		−	723285.i		−	1.81082i
$633$			178250.i			0.444859i
$634$		−	860032.i		−	2.13962i
$635$	22081.1			0.0547613
$636$	205221.			0.507349
$637$		−	40962.8i		−	0.100951i
$638$	−299526.			−0.735857
$639$	−166240.			−0.407131
$640$			203520.i			0.496875i
$641$	704608.			1.71487			0.857435	−	0.514592i	$-0.172057\pi$
$641$	704608.			1.71487			0.857435	+	0.514592i	$0.172057\pi$
$642$			739631.i			1.79451i
$643$	−448900.			−1.08574			−0.542872	−	0.839816i	$-0.682663\pi$
$643$	−448900.			−1.08574			−0.542872	+	0.839816i	$0.682663\pi$
$644$		−	75834.6i		−	0.182850i
$645$		−	14251.2i		−	0.0342556i
$646$		−	76238.6i		−	0.182688i
$647$	−211597.			−0.505477			−0.252738	−	0.967535i	$-0.581331\pi$
$647$	−211597.			−0.505477			−0.252738	+	0.967535i	$0.581331\pi$
$648$		−	68053.4i		−	0.162069i
$649$	89882.8	+	522736.i	0.213397	+	1.24106i
$650$	543031.			1.28528
$651$			162392.i			0.383180i
$652$	361078.			0.849387
$653$	−171313.			−0.401757			−0.200878	−	0.979616i	$-0.564380\pi$
$653$	−171313.			−0.401757			−0.200878	+	0.979616i	$0.564380\pi$
$654$	−338539.			−0.791504
$655$		−	161829.i		−	0.377201i
$656$	237618.			0.552168
$657$			76056.1i			0.176199i
$658$	497300.			1.14859
$659$			123614.i			0.284641i	0.989821	+	0.142321i	$0.0454564\pi$
$659$			123614.i			0.284641i	−0.989821	+	0.142321i	$0.954544\pi$
$660$		−	159866.i		−	0.367001i
$661$	759419.			1.73811			0.869057	−	0.494712i	$-0.164726\pi$
$661$	759419.			1.73811			0.869057	+	0.494712i	$0.164726\pi$
$662$		−	1.29055e6i		−	2.94481i
$663$			44065.6i			0.100247i
$664$	−60567.2			−0.137373
$665$	−57243.5			−0.129444
$666$	−259850.			−0.585835
$667$			16113.2i			0.0362185i
$668$	−741507.			−1.66174
$669$	63667.0			0.142253
$670$	−102063.			−0.227361
$671$	416295.			0.924604
$672$		−	106011.i		−	0.234753i
$673$		−	366990.i		−	0.810260i	−0.914259	−	0.405130i	$-0.867226\pi$
$673$		−	366990.i		−	0.810260i	0.914259	−	0.405130i	$-0.132774\pi$
$674$	−822836.			−1.81131
$675$	−81241.9			−0.178309
$676$	−278825.			−0.610152
$677$	411628.			0.898105			0.449053	−	0.893505i	$-0.351762\pi$
$677$	411628.			0.898105			0.449053	+	0.893505i	$0.351762\pi$
$678$	−816592.			−1.77642
$679$		−	69316.5i		−	0.150348i
$680$		−	38715.6i		−	0.0837275i
$681$		−	432037.i		−	0.931594i
$682$		−	702311.i		−	1.50994i
$683$		−	654877.i		−	1.40384i	−0.712254	−	0.701921i	$-0.752326\pi$
$683$		−	654877.i		−	1.40384i	0.712254	−	0.701921i	$-0.247674\pi$
$684$	148093.			0.316536
$685$	176144.			0.375393
$686$		−	837321.i		−	1.77928i
$687$		−	437241.i		−	0.926419i
$688$		−	62734.6i		−	0.132535i
$689$		−	183688.i		−	0.386940i
$690$	−13218.4			−0.0277639
$691$		−	628200.i		−	1.31565i	−0.753169	−	0.657827i	$-0.771476\pi$
$691$		−	628200.i		−	1.31565i	0.753169	−	0.657827i	$-0.228524\pi$
$692$			183220.i			0.382614i
$693$			188771.i			0.393070i
$694$	77036.1			0.159947
$695$	69779.6			0.144464
$696$		−	140905.i		−	0.290876i
$697$	93809.8			0.193100
$698$	−904060.			−1.85561
$699$			56581.9i			0.115804i
$700$	791665.			1.61564
$701$			517988.i			1.05410i	0.849833	+	0.527052i	$0.176703\pi$
$701$			517988.i			1.05410i	−0.849833	+	0.527052i	$0.823297\pi$
$702$	−131564.			−0.266970
$703$		−	261808.i		−	0.529752i
$704$			836386.i			1.68757i
$705$		−	56396.6i		−	0.113468i
$706$	1.03407e6			2.07462
$707$		−	112759.i		−	0.225586i
$708$	−531128.	+	91325.8i	−1.05958	+	0.182191i
$709$	417989.			0.831519			0.415759	−	0.909475i	$-0.363516\pi$
$709$	417989.			0.831519			0.415759	+	0.909475i	$0.363516\pi$
$710$		−	282363.i		−	0.560133i
$711$	209195.			0.413820
$712$	−536886.			−1.05906
$713$	−37781.3			−0.0743186
$714$			98739.9i			0.193685i
$715$	−143092.			−0.279900
$716$			522274.i			1.01876i
$717$	327120.			0.636311
$718$		−	570827.i		−	1.10728i
$719$		−	88171.5i		−	0.170557i	−0.996357	−	0.0852787i	$-0.972822\pi$
$719$		−	88171.5i		−	0.170557i	0.996357	−	0.0852787i	$-0.0271781\pi$
$720$	28363.3			0.0547132
$721$			401578.i			0.772502i
$722$		−	652571.i		−	1.25185i
$723$	−327973.			−0.627425
$724$	−619144.			−1.18117
$725$	−168212.			−0.320022
$726$		−	301568.i		−	0.572154i
$727$	765157.			1.44771			0.723855	−	0.689952i	$-0.242368\pi$
$727$	765157.			1.44771			0.723855	+	0.689952i	$0.242368\pi$
$728$	593571.			1.11998
$729$	19683.0			0.0370370
$730$	−129183.			−0.242415
$731$		−	24767.2i		−	0.0463492i
$732$			422978.i			0.789397i
$733$	45126.1			0.0839885			0.0419943	−	0.999118i	$-0.486629\pi$
$733$	45126.1			0.0839885			0.0419943	+	0.999118i	$0.486629\pi$
$734$	153024.			0.284032
$735$	−10409.2			−0.0192682
$736$	24663.9			0.0455308
$737$	−339106.			−0.624311
$738$			280082.i			0.514247i
$739$			1.03826e6i			1.90116i	0.310476	+	0.950581i	$0.399512\pi$
$739$			1.03826e6i			1.90116i	−0.310476	+	0.950581i	$0.600488\pi$
$740$		−	287157.i		−	0.524392i
$741$		−	132555.i		−	0.241412i
$742$		−	411599.i		−	0.747595i
$743$	−432123.			−0.782763			−0.391381	−	0.920229i	$-0.628003\pi$
$743$	−432123.			−0.782763			−0.391381	+	0.920229i	$0.628003\pi$
$744$	330385.			0.596863
$745$		−	234970.i		−	0.423350i
$746$		−	960995.i		−	1.72681i
$747$		−	17517.8i		−	0.0313933i
$748$		−	277831.i		−	0.496567i
$749$	965145.			1.72040
$750$		−	286927.i		−	0.510092i
$751$			586786.i			1.04040i	0.854045	+	0.520200i	$0.174142\pi$
$751$			586786.i			1.04040i	−0.854045	+	0.520200i	$0.825858\pi$
$752$		−	248262.i		−	0.439009i
$753$	−343199.			−0.605280
$754$	−272403.			−0.479148
$755$			54896.9i			0.0963061i
$756$	−191802.			−0.335590
$757$	−69647.3			−0.121538			−0.0607690	−	0.998152i	$-0.519355\pi$
$757$	−69647.3			−0.121538			−0.0607690	+	0.998152i	$0.519355\pi$
$758$		−	481382.i		−	0.837821i
$759$	−43918.5			−0.0762366
$760$			116461.i			0.201630i
$761$	−533970.			−0.922035			−0.461017	−	0.887391i	$-0.652515\pi$
$761$	−533970.			−0.922035			−0.461017	+	0.887391i	$0.652515\pi$
$762$			114573.i			0.197321i
$763$			441760.i			0.758817i
$764$			407252.i			0.697712i
$765$	11197.7			0.0191339
$766$			36469.4i			0.0621542i
$767$	81743.7	+	475400.i	0.138952	+	0.808107i
$768$	−599657.			−1.01667
$769$			316009.i			0.534376i	0.963644	+	0.267188i	$0.0860945\pi$
$769$			316009.i			0.534376i	−0.963644	+	0.267188i	$0.913905\pi$
$770$	−320633.			−0.540787
$771$	473246.			0.796120
$772$	−733131.			−1.23012
$773$			42404.6i			0.0709666i	0.999370	+	0.0354833i	$0.0112971\pi$
$773$			42404.6i			0.0709666i	−0.999370	+	0.0354833i	$0.988703\pi$
$774$	73945.7			0.123433
$775$		−	394412.i		−	0.656670i
$776$	−141024.			−0.234190
$777$			339079.i			0.561641i
$778$			1.54080e6i			2.54558i
$779$	−282192.			−0.465017
$780$		−	145389.i		−	0.238970i
$781$		−	938160.i		−	1.53807i
$782$	−22972.3			−0.0375656
$783$	40753.7			0.0664727
$784$	−45821.9			−0.0745488
$785$		−	238886.i		−	0.387661i
$786$	839687.			1.35917
$787$	−952711.			−1.53820			−0.769098	−	0.639131i	$-0.779294\pi$
$787$	−952711.			−1.53820			−0.769098	+	0.639131i	$0.779294\pi$
$788$	−228152.			−0.367428
$789$	−433202.			−0.695884
$790$			355322.i			0.569335i
$791$			1.06557e6i			1.70306i
$792$	384053.			0.612267
$793$	378598.			0.602049
$794$	−449436.			−0.712897
$795$	−46677.6			−0.0738541
$796$	−1.49972e6			−2.36692
$797$			821853.i			1.29383i	0.762562	+	0.646915i	$0.223941\pi$
$797$			821853.i			1.29383i	−0.762562	+	0.646915i	$0.776059\pi$
$798$		−	297022.i		−	0.466426i
$799$		−	98012.0i		−	0.153527i
$800$			257475.i			0.402305i
$801$		−	155283.i		−	0.242024i
$802$	−1.25611e6			−1.95290
$803$	−429215.			−0.665647
$804$		−	344550.i		−	0.533016i
$805$			17248.7i			0.0266173i
$806$		−	638715.i		−	0.983188i
$807$		−	70670.8i		−	0.108516i
$808$	−229407.			−0.351386
$809$		−	460917.i		−	0.704249i	−0.935953	−	0.352124i	$-0.885459\pi$
$809$		−	460917.i		−	0.704249i	0.935953	−	0.352124i	$-0.114541\pi$
$810$			33432.1i			0.0509558i
$811$		−	690476.i		−	1.04980i	−0.851164	−	0.524901i	$-0.824102\pi$
$811$		−	690476.i		−	1.04980i	0.851164	−	0.524901i	$-0.175898\pi$
$812$	−397126.			−0.602305
$813$	−1947.46			−0.00294637
$814$		−	1.46644e6i		−	2.21318i
$815$	−82127.4			−0.123644
$816$	49292.8			0.0740292
$817$			74502.8i			0.111617i
$818$	472347.			0.705918
$819$			171678.i			0.255944i
$820$	−309514.			−0.460313
$821$			936452.i			1.38931i	0.719343	+	0.694655i	$0.244443\pi$
$821$			936452.i			1.38931i	−0.719343	+	0.694655i	$0.755557\pi$
$822$			913964.i			1.35265i
$823$			348374.i			0.514336i	0.966367	+	0.257168i	$0.0827893\pi$
$823$			348374.i			0.514336i	−0.966367	+	0.257168i	$0.917211\pi$
$824$	817007.			1.20329
$825$		−	458481.i		−	0.673618i
$826$	183167.	+	1.06525e6i	0.268464	+	1.56132i
$827$	441747.			0.645896			0.322948	−	0.946417i	$-0.395326\pi$
$827$	441747.			0.645896			0.322948	+	0.946417i	$0.395326\pi$
$828$		−	44623.6i		−	0.0650884i
$829$	104727.			0.152387			0.0761936	−	0.997093i	$-0.475723\pi$
$829$	104727.			0.152387			0.0761936	+	0.997093i	$0.475723\pi$
$830$	29754.4			0.0431911
$831$	−179360.			−0.259730
$832$			760649.i			1.09885i
$833$	−18090.2			−0.0260707
$834$			362068.i			0.520545i
$835$	168657.			0.241897
$836$			835750.i			1.19582i
$837$			95556.9i			0.136399i
$838$	−465933.			−0.663492
$839$			750204.i			1.06575i	0.846194	+	0.532875i	$0.178888\pi$
$839$			750204.i			1.06575i	−0.846194	+	0.532875i	$0.821112\pi$
$840$		−	150834.i		−	0.213767i
$841$	−622900.			−0.880697
$842$	−356033.			−0.502188
$843$	522886.			0.735787
$844$		−	1.02209e6i		−	1.43484i
$845$	63418.9			0.0888189
$846$	292628.			0.408860
$847$	−393517.			−0.548525
$848$	−205478.			−0.285742
$849$		−	443770.i		−	0.615663i
$850$		−	239816.i		−	0.331925i
$851$	−78888.2			−0.108931
$852$	953222.			1.31315
$853$	389367.			0.535132			0.267566	−	0.963540i	$-0.413781\pi$
$853$	389367.			0.535132			0.267566	+	0.963540i	$0.413781\pi$
$854$	848341.			1.16320
$855$	−33683.9			−0.0460777
$856$		−	1.96358e6i		−	2.67979i
$857$			608191.i			0.828091i	0.910256	+	0.414046i	$0.135885\pi$
$857$			608191.i			0.828091i	−0.910256	+	0.414046i	$0.864115\pi$
$858$		−	742468.i		−	1.00856i
$859$			667593.i			0.904743i	0.891830	+	0.452371i	$0.149422\pi$
$859$			667593.i			0.904743i	−0.891830	+	0.452371i	$0.850578\pi$
$860$			81716.4i			0.110487i
$861$	365478.			0.493010
$862$	−861341.			−1.15921
$863$		−	507853.i		−	0.681894i	−0.940083	−	0.340947i	$-0.889252\pi$
$863$		−	507853.i		−	0.681894i	0.940083	−	0.340947i	$-0.110748\pi$
$864$		−	62380.2i		−	0.0835640i
$865$		−	41673.6i		−	0.0556966i
$866$			453515.i			0.604722i
$867$	−414527.			−0.551461
$868$		−	931158.i		−	1.23590i
$869$			1.18057e6i			1.56334i
$870$			69221.2i			0.0914535i
$871$	−308399.			−0.406515
$872$	898756.			1.18198
$873$		−	40788.1i		−	0.0535186i
$874$	69103.4			0.0904642
$875$	−374411.			−0.489026
$876$		−	436106.i		−	0.568308i
$877$	501363.			0.651858			0.325929	−	0.945394i	$-0.394323\pi$
$877$	501363.			0.651858			0.325929	+	0.945394i	$0.394323\pi$
$878$			887408.i			1.15116i
$879$	692944.			0.896851
$880$			160066.i			0.206697i
$881$			1.42120e6i			1.83106i	0.402248	+	0.915531i	$0.368229\pi$
$881$			1.42120e6i			1.83106i	−0.402248	+	0.915531i	$0.631771\pi$
$882$		−	54010.5i		−	0.0694291i
$883$	352600.			0.452231			0.226116	−	0.974100i	$-0.427397\pi$
$883$	352600.			0.452231			0.226116	+	0.974100i	$0.427397\pi$
$884$		−	252673.i		−	0.323336i
$885$	120805.	−	20772.1i	0.154241	−	0.0265213i
$886$	−1.61068e6			−2.05184
$887$			1.03662e6i			1.31756i	0.752336	+	0.658780i	$0.228927\pi$
$887$			1.03662e6i			1.31756i	−0.752336	+	0.658780i	$0.771073\pi$
$888$	689853.			0.874843
$889$	149507.			0.189172
$890$	263752.			0.332978
$891$			111079.i			0.139919i
$892$	−365067.			−0.458820
$893$			294832.i			0.369719i
$894$	1.21920e6			1.52545
$895$		−	118792.i		−	0.148300i
$896$			1.37799e6i			1.71645i
$897$	−39941.5			−0.0496409
$898$		−	951458.i		−	1.17988i
$899$			197851.i			0.244804i
$900$	465842.			0.575113
$901$	−81121.3			−0.0999275
$902$	−1.58061e6			−1.94273
$903$		−	96491.8i		−	0.118335i
$904$	2.16789e6			2.65278
$905$	140825.			0.171942
$906$	−284846.			−0.347019
$907$	−1.36132e6			−1.65480			−0.827402	−	0.561610i	$-0.810182\pi$
$907$	−1.36132e6			−1.65480			−0.827402	+	0.561610i	$0.810182\pi$
$908$			2.47730e6i			3.00474i
$909$		−	66351.1i		−	0.0803009i
$910$	−291599.			−0.352130
$911$	863937.			1.04099			0.520493	−	0.853866i	$-0.325748\pi$
$911$	863937.			1.04099			0.520493	+	0.853866i	$0.325748\pi$
$912$	−148279.			−0.178275
$913$	98859.8			0.118598
$914$	2.57999e6			3.08834
$915$		−	96206.7i		−	0.114911i
$916$			2.50714e6i			2.98805i
$917$		−	1.09571e6i		−	1.30304i
$918$			58101.7i			0.0689452i
$919$		−	354665.i		−	0.419940i	−0.977708	−	0.209970i	$-0.932663\pi$
$919$		−	354665.i		−	0.419940i	0.977708	−	0.209970i	$-0.0673367\pi$
$920$	35092.2			0.0414605
$921$	103984.			0.122587
$922$		−	450144.i		−	0.529529i
$923$		−	853207.i		−	1.00150i
$924$		−	1.08242e6i		−	1.26780i
$925$		−	823543.i		−	0.962504i
$926$	2.45265e6			2.86031
$927$			236302.i			0.274984i
$928$		−	129158.i		−	0.149978i
$929$		−	163853.i		−	0.189855i	−0.995484	−	0.0949275i	$-0.969738\pi$
$929$		−	163853.i		−	0.189855i	0.995484	−	0.0949275i	$-0.0302619\pi$
$930$	−162306.			−0.187658
$931$	54417.5			0.0627825
$932$		−	324441.i		−	0.373511i
$933$	168366.			0.193416
$934$	−1.24658e6			−1.42899
$935$			63192.9i			0.0722845i
$936$	349276.			0.398673
$937$			89081.6i			0.101463i	0.998712	+	0.0507316i	$0.0161553\pi$
$937$			89081.6i			0.101463i	−0.998712	+	0.0507316i	$0.983845\pi$
$938$	−691044.			−0.785417
$939$			993961.i			1.12730i
$940$			323379.i			0.365979i
$941$		−	1.32463e6i		−	1.49594i	−0.663730	−	0.747972i	$-0.731028\pi$
$941$		−	1.32463e6i		−	1.49594i	0.663730	−	0.747972i	$-0.268972\pi$
$942$	1.23952e6			1.39686
$943$			85030.2i			0.0956202i
$944$	531793.	−	91440.3i	0.596759	−	0.102611i
$945$	43625.5			0.0488514
$946$			417306.i			0.466307i
$947$	406812.			0.453622			0.226811	−	0.973939i	$-0.427170\pi$
$947$	406812.			0.453622			0.226811	+	0.973939i	$0.427170\pi$
$948$	−1.19952e6			−1.33473
$949$	−390349.			−0.433431
$950$			721396.i			0.799331i
$951$	−660372.			−0.730176
$952$		−	262135.i		−	0.289235i
$953$	−618044.			−0.680508			−0.340254	−	0.940334i	$-0.610513\pi$
$953$	−618044.			−0.680508			−0.340254	+	0.940334i	$0.610513\pi$
$954$		−	242198.i		−	0.266118i
$955$		−	92629.7i		−	0.101565i
$956$	−1.87571e6			−2.05234
$957$			229990.i			0.251122i
$958$		−	2.36063e6i		−	2.57216i
$959$	1.19263e6			1.29679
$960$	193291.			0.209734
$961$	459612.			0.497674
$962$		−	1.33365e6i		−	1.44109i
$963$	567922.			0.612402
$964$	1.88060e6			2.02368
$965$	166751.			0.179067
$966$	−89498.8			−0.0959098
$967$			1.04471e6i			1.11723i	0.829426	+	0.558617i	$0.188668\pi$
$967$			1.04471e6i			1.11723i	−0.829426	+	0.558617i	$0.811332\pi$
$968$			800606.i			0.854413i
$969$	−58539.5			−0.0623449
$970$	69279.6			0.0736312
$971$	1.24646e6			1.32203			0.661013	−	0.750375i	$-0.270127\pi$
$971$	1.24646e6			1.32203			0.661013	+	0.750375i	$0.270127\pi$
$972$	−112862.			−0.119458
$973$	472463.			0.499048
$974$		−	3.05483e6i		−	3.22010i
$975$		−	416964.i		−	0.438621i
$976$		−	423508.i		−	0.444592i
$977$		−	1.30541e6i		−	1.36759i	−0.729673	−	0.683796i	$-0.760328\pi$
$977$		−	1.30541e6i		−	1.36759i	0.729673	−	0.683796i	$-0.239672\pi$
$978$		−	426138.i		−	0.445526i
$979$	876324.			0.914322
$980$	59686.3			0.0621473
$981$			259946.i			0.270113i
$982$		−	438681.i		−	0.454910i
$983$		−	1.73019e6i		−	1.79055i	−0.445510	−	0.895277i	$-0.646978\pi$
$983$		−	1.73019e6i		−	1.79055i	0.445510	−	0.895277i	$-0.353022\pi$
$984$		−	743562.i		−	0.767940i
$985$	51893.4			0.0534859
$986$			120300.i			0.123740i
$987$		−	381850.i		−	0.391975i
$988$			760071.i			0.778646i
$989$	22449.2			0.0229514
$990$	−188671.			−0.192502
$991$			88862.9i			0.0904843i	0.998976	+	0.0452421i	$0.0144059\pi$
$991$			88862.9i			0.0904843i	−0.998976	+	0.0452421i	$0.985594\pi$
$992$	302843.			0.307747
$993$	−990940.			−1.00496
$994$		−	1.91182e6i		−	1.93497i
$995$	341113.			0.344549
$996$			100447.i			0.101255i
$997$	1.35339e6			1.36155			0.680773	−	0.732494i	$-0.261644\pi$
$997$	1.35339e6			1.36155			0.680773	+	0.732494i	$0.261644\pi$
$998$		−	1.02602e6i		−	1.03013i
$999$			199525.i			0.199925i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.5.c.a.58.37	yes	40
3.2	odd	2		531.5.c.d.235.4		40
59.58	odd	2	inner	177.5.c.a.58.4	✓	40
177.176	even	2		531.5.c.d.235.37		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.5.c.a.58.4	✓	40	59.58	odd	2	inner
177.5.c.a.58.37	yes	40	1.1	even	1	trivial
531.5.c.d.235.4		40	3.2	odd	2
531.5.c.d.235.37		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)

\(f(q)\)	\(=\)	\(q+6.76718i q^{2} +5.19615 q^{3} -29.7948 q^{4} +6.77685 q^{5} +35.1633i q^{6} +45.8846 q^{7} -93.3518i q^{8} +27.0000 q^{9} +O(q^{10})\)	\(q+6.76718i q^{2} +5.19615 q^{3} -29.7948 q^{4} +6.77685 q^{5} +35.1633i q^{6} +45.8846 q^{7} -93.3518i q^{8} +27.0000 q^{9} +45.8602i q^{10} +152.372i q^{11} -154.818 q^{12} +138.574i q^{13} +310.510i q^{14} +35.2135 q^{15} +155.012 q^{16} +61.1978 q^{17} +182.714i q^{18} -184.090 q^{19} -201.915 q^{20} +238.423 q^{21} -1031.13 q^{22} +55.4703i q^{23} -485.070i q^{24} -579.074 q^{25} -937.758 q^{26} +140.296 q^{27} -1367.12 q^{28} +290.483 q^{29} +238.296i q^{30} +681.108i q^{31} -444.632i q^{32} +791.748i q^{33} +414.137i q^{34} +310.953 q^{35} -804.459 q^{36} +1422.17i q^{37} -1245.77i q^{38} +720.053i q^{39} -632.631i q^{40} +1532.90 q^{41} +1613.46i q^{42} -404.708i q^{43} -4539.89i q^{44} +182.975 q^{45} -375.377 q^{46} -1601.56i q^{47} +805.467 q^{48} -295.602 q^{49} -3918.70i q^{50} +317.993 q^{51} -4128.79i q^{52} -1325.56 q^{53} +949.410i q^{54} +1032.60i q^{55} -4283.41i q^{56} -956.562 q^{57} +1965.75i q^{58} +(3430.65 - 589.891i) q^{59} -1049.18 q^{60} -2732.09i q^{61} -4609.19 q^{62} +1238.88 q^{63} +5489.10 q^{64} +939.097i q^{65} -5357.90 q^{66} +2225.52i q^{67} -1823.37 q^{68} +288.232i q^{69} +2104.28i q^{70} -6157.04 q^{71} -2520.50i q^{72} +2816.89i q^{73} -9624.09 q^{74} -3008.96 q^{75} +5484.93 q^{76} +6991.53i q^{77} -4872.73 q^{78} +7747.95 q^{79} +1050.49 q^{80} +729.000 q^{81} +10373.4i q^{82} -648.806i q^{83} -7103.77 q^{84} +414.728 q^{85} +2738.73 q^{86} +1509.40 q^{87} +14224.2 q^{88} -5751.21i q^{89} +1238.22i q^{90} +6358.43i q^{91} -1652.72i q^{92} +3539.14i q^{93} +10838.1 q^{94} -1247.55 q^{95} -2310.38i q^{96} -1510.67i q^{97} -2000.39i q^{98} +4114.04i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 320 q^{4} + 80 q^{7} + 1080 q^{9}+O(q^{10}) \) 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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