LMFDB - Embedded newform 147.4.g.e.80.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,4,Mod(68,147)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("147.68");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	147.g (of order $6$, degree $2$, not 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:	$8.67328077084$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			80.17
Character	$\chi$	$=$	147.80
Dual form			147.4.g.e.68.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.48522 - 1.43484i) q^{2} +(-5.19260 + 0.192239i) q^{3} +(0.117558 - 0.203616i) q^{4} +(-2.78530 - 4.82427i) q^{5} +(-12.6289 + 7.92832i) q^{6} +22.2828i q^{8} +(26.9261 - 1.99644i) q^{9} +O(q^{10})$	\(q+(2.48522 - 1.43484i) q^{2} +(-5.19260 + 0.192239i) q^{3} +(0.117558 - 0.203616i) q^{4} +(-2.78530 - 4.82427i) q^{5} +(-12.6289 + 7.92832i) q^{6} +22.2828i q^{8} +(26.9261 - 1.99644i) q^{9} +(-13.8442 - 7.99293i) q^{10} +(36.9964 + 21.3599i) q^{11} +(-0.571286 + 1.07989i) q^{12} +69.8357i q^{13} +(15.3903 + 24.5151i) q^{15} +(32.9128 + 57.0067i) q^{16} +(-33.7517 + 58.4597i) q^{17} +(64.0528 - 43.5963i) q^{18} +(68.7116 - 39.6707i) q^{19} -1.30973 q^{20} +122.593 q^{22} +(-180.853 + 104.416i) q^{23} +(-4.28362 - 115.706i) q^{24} +(46.9843 - 81.3791i) q^{25} +(100.203 + 173.557i) q^{26} +(-139.432 + 15.5429i) q^{27} +5.72587i q^{29} +(73.4237 + 38.8427i) q^{30} +(167.397 + 96.6466i) q^{31} +(9.21163 + 5.31834i) q^{32} +(-196.214 - 103.801i) q^{33} +193.714i q^{34} +(2.75886 - 5.71727i) q^{36} +(-81.8043 - 141.689i) q^{37} +(113.842 - 197.181i) q^{38} +(-13.4251 - 362.629i) q^{39} +(107.498 - 62.0642i) q^{40} +58.1164 q^{41} +58.9508 q^{43} +(8.69842 - 5.02203i) q^{44} +(-84.6285 - 124.338i) q^{45} +(-299.640 + 518.992i) q^{46} +(-74.2859 - 128.667i) q^{47} +(-181.862 - 289.685i) q^{48} -269.660i q^{50} +(164.021 - 310.046i) q^{51} +(14.2196 + 8.20971i) q^{52} +(87.1582 + 50.3208i) q^{53} +(-324.219 + 238.692i) q^{54} -237.975i q^{55} +(-349.165 + 219.203i) q^{57} +(8.21573 + 14.2301i) q^{58} +(-369.345 + 639.725i) q^{59} +(6.80090 - 0.251781i) q^{60} +(309.124 - 178.473i) q^{61} +554.692 q^{62} -496.081 q^{64} +(336.907 - 194.513i) q^{65} +(-636.573 + 23.5670i) q^{66} +(-360.579 + 624.542i) q^{67} +(7.93554 + 13.7448i) q^{68} +(919.024 - 576.955i) q^{69} +308.915i q^{71} +(44.4862 + 599.989i) q^{72} +(716.319 + 413.567i) q^{73} +(-406.604 - 234.753i) q^{74} +(-228.326 + 431.601i) q^{75} -18.6543i q^{76} +(-553.680 - 881.950i) q^{78} +(-233.602 - 404.610i) q^{79} +(183.344 - 317.561i) q^{80} +(721.028 - 107.512i) q^{81} +(144.432 - 83.3880i) q^{82} -274.704 q^{83} +376.034 q^{85} +(146.506 - 84.5852i) q^{86} +(-1.10073 - 29.7321i) q^{87} +(-475.958 + 824.384i) q^{88} +(-270.537 - 468.584i) q^{89} +(-388.727 - 187.579i) q^{90} +49.0993i q^{92} +(-887.804 - 469.667i) q^{93} +(-369.234 - 213.178i) q^{94} +(-382.764 - 220.989i) q^{95} +(-48.8547 - 25.8451i) q^{96} +41.4658i q^{97} +(1038.81 + 501.277i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 96 q^{4} + 64 q^{9}+O(q^{10}) $ 48 * q + 96 * q^4 + 64 * q^9	$ 48 q + 96 q^{4} + 64 q^{9} + 512 q^{15} - 864 q^{16} + 32 q^{18} - 768 q^{22} - 744 q^{25} + 1704 q^{30} + 1168 q^{36} - 432 q^{37} + 2368 q^{39} - 1248 q^{43} - 3744 q^{46} + 2160 q^{51} + 4064 q^{57} - 6384 q^{58} + 5832 q^{60} - 7008 q^{64} - 3792 q^{67} + 7472 q^{72} + 4496 q^{78} - 2784 q^{79} + 1968 q^{81} - 7488 q^{85} + 624 q^{88} + 3232 q^{93} + 2640 q^{99}+O(q^{100}) $ 48 * q + 96 * q^4 + 64 * q^9 + 512 * q^15 - 864 * q^16 + 32 * q^18 - 768 * q^22 - 744 * q^25 + 1704 * q^30 + 1168 * q^36 - 432 * q^37 + 2368 * q^39 - 1248 * q^43 - 3744 * q^46 + 2160 * q^51 + 4064 * q^57 - 6384 * q^58 + 5832 * q^60 - 7008 * q^64 - 3792 * q^67 + 7472 * q^72 + 4496 * q^78 - 2784 * q^79 + 1968 * q^81 - 7488 * q^85 + 624 * q^88 + 3232 * q^93 + 2640 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	2.48522	−	1.43484i	0.878659	−	0.507294i	0.00844313	−	0.999964i	$-0.497312\pi$
$2$	2.48522	−	1.43484i	0.878659	−	0.507294i	0.870216	+	0.492670i	$0.163979\pi$
$3$	−5.19260	+	0.192239i	−0.999315	+	0.0369964i
$3$	−5.19260	+	0.192239i	−0.999315	+	0.0369964i
$4$	0.117558	−	0.203616i	0.0146947	−	0.0254519i
$5$	−2.78530	−	4.82427i	−0.249124	−	0.431496i	0.714159	−	0.699984i	$-0.246809\pi$
$5$	−2.78530	−	4.82427i	−0.249124	−	0.431496i	−0.963283	+	0.268488i	$0.913476\pi$
$6$	−12.6289	+	7.92832i	−0.859290	+	0.539454i
$7$		0			0
$7$		0			0
$8$			22.2828i			0.984770i
$9$	26.9261	−	1.99644i	0.997263	−	0.0739421i
$10$	−13.8442	−	7.99293i	−0.437791	−	0.252759i
$11$	36.9964	+	21.3599i	1.01408	+	0.585477i	0.912383	−	0.409338i	$-0.134240\pi$
$11$	36.9964	+	21.3599i	1.01408	+	0.585477i	0.101694	+	0.994816i	$0.467574\pi$
$12$	−0.571286	+	1.07989i	−0.0137430	+	0.0259782i
$13$			69.8357i			1.48992i	0.667110	+	0.744959i	$0.267531\pi$
$13$			69.8357i			1.48992i	−0.667110	+	0.744959i	$0.732469\pi$
$14$		0			0
$15$	15.3903	+	24.5151i	0.264918	+	0.421984i
$16$	32.9128	+	57.0067i	0.514263	+	0.890729i
$17$	−33.7517	+	58.4597i	−0.481529	+	0.834033i	−0.999775	−	0.0211986i	$-0.993252\pi$
$17$	−33.7517	+	58.4597i	−0.481529	+	0.834033i	0.518246	+	0.855232i	$0.326585\pi$
$18$	64.0528	−	43.5963i	0.838744	−	0.570875i
$19$	68.7116	−	39.6707i	0.829659	−	0.479004i	−0.0240769	−	0.999710i	$-0.507665\pi$
$19$	68.7116	−	39.6707i	0.829659	−	0.479004i	0.853736	+	0.520706i	$0.174331\pi$
$20$	−1.30973			−0.0146432
$21$		0			0
$22$	122.593			1.18804
$23$	−180.853	+	104.416i	−1.63959	+	0.946615i	−0.658610	+	0.752484i	$0.728855\pi$
$23$	−180.853	+	104.416i	−1.63959	+	0.946615i	−0.980976	+	0.194131i	$0.937811\pi$
$24$	−4.28362	−	115.706i	−0.0364329	−	0.984096i
$25$	46.9843	−	81.3791i	0.375874	−	0.651033i
$26$	100.203	+	173.557i	0.755827	+	1.30913i
$27$	−139.432	+	15.5429i	−0.993844	+	0.110787i
$28$		0			0
$29$			5.72587i			0.0366644i	0.999832	+	0.0183322i	$0.00583564\pi$
$29$			5.72587i			0.0366644i	−0.999832	+	0.0183322i	$0.994164\pi$
$30$	73.4237	+	38.8427i	0.446842	+	0.236389i
$31$	167.397	+	96.6466i	0.969851	+	0.559944i	0.899191	−	0.437557i	$-0.144156\pi$
$31$	167.397	+	96.6466i	0.969851	+	0.559944i	0.0706600	+	0.997500i	$0.477489\pi$
$32$	9.21163	+	5.31834i	0.0508876	+	0.0293800i
$33$	−196.214	−	103.801i	−1.03504	−	0.547559i
$34$			193.714i			0.977108i
$35$		0			0
$36$	2.75886	−	5.71727i	0.0127725	−	0.0264688i
$37$	−81.8043	−	141.689i	−0.363474	−	0.629556i	0.625056	−	0.780580i	$-0.285076\pi$
$37$	−81.8043	−	141.689i	−0.363474	−	0.629556i	−0.988530	+	0.151024i	$0.951743\pi$
$38$	113.842	−	197.181i	0.485992	−	0.841762i
$39$	−13.4251	−	362.629i	−0.0551216	−	1.48890i
$40$	107.498	−	62.0642i	0.424925	−	0.245330i
$41$	58.1164			0.221372			0.110686	−	0.993855i	$-0.464695\pi$
$41$	58.1164			0.221372			0.110686	+	0.993855i	$0.464695\pi$
$42$		0			0
$43$	58.9508			0.209068			0.104534	−	0.994521i	$-0.466665\pi$
$43$	58.9508			0.209068			0.104534	+	0.994521i	$0.466665\pi$
$44$	8.69842	−	5.02203i	0.0298031	−	0.0172068i
$45$	−84.6285	−	124.338i	−0.280348	−	0.411894i
$46$	−299.640	+	518.992i	−0.960425	+	1.66350i
$47$	−74.2859	−	128.667i	−0.230547	−	0.399319i	0.727422	−	0.686190i	$-0.240718\pi$
$47$	−74.2859	−	128.667i	−0.230547	−	0.399319i	−0.957969	+	0.286871i	$0.907385\pi$
$48$	−181.862	−	289.685i	−0.546865	−	0.871094i
$49$		0			0
$50$		−	269.660i		−	0.762715i
$51$	164.021	−	310.046i	0.450343	−	0.851277i
$52$	14.2196	+	8.20971i	0.0379213	+	0.0218939i
$53$	87.1582	+	50.3208i	0.225889	+	0.130417i	0.608674	−	0.793420i	$-0.291702\pi$
$53$	87.1582	+	50.3208i	0.225889	+	0.130417i	−0.382785	+	0.923837i	$0.625035\pi$
$54$	−324.219	+	238.692i	−0.817049	+	0.601515i
$55$		−	237.975i		−	0.583427i
$56$		0			0
$57$	−349.165	+	219.203i	−0.811370	+	0.509370i
$58$	8.21573	+	14.2301i	0.0185996	+	0.0322155i
$59$	−369.345	+	639.725i	−0.814994	+	1.41161i	0.0943381	+	0.995540i	$0.469927\pi$
$59$	−369.345	+	639.725i	−0.814994	+	1.41161i	−0.909332	+	0.416071i	$0.863407\pi$
$60$	6.80090	−	0.251781i	0.0146332	−	0.000541746i
$61$	309.124	−	178.473i	0.648841	−	0.374609i	−0.139171	−	0.990268i	$-0.544444\pi$
$61$	309.124	−	178.473i	0.648841	−	0.374609i	0.788012	+	0.615660i	$0.211110\pi$
$62$	554.692			1.13622
$63$		0			0
$64$	−496.081			−0.968909
$65$	336.907	−	194.513i	0.642894	−	0.371175i
$66$	−636.573	+	23.5670i	−1.18722	+	0.0439531i
$67$	−360.579	+	624.542i	−0.657489	+	1.13880i	0.323774	+	0.946134i	$0.395048\pi$
$67$	−360.579	+	624.542i	−0.657489	+	1.13880i	−0.981264	+	0.192670i	$0.938285\pi$
$68$	7.93554	+	13.7448i	0.0141518	+	0.0245117i
$69$	919.024	−	576.955i	1.60344	−	1.00663i
$70$		0			0
$71$			308.915i			0.516359i	0.966097	+	0.258180i	$0.0831226\pi$
$71$			308.915i			0.516359i	−0.966097	+	0.258180i	$0.916877\pi$
$72$	44.4862	+	599.989i	0.0728160	+	0.982074i
$73$	716.319	+	413.567i	1.14848	+	0.663073i	0.948516	−	0.316731i	$-0.102585\pi$
$73$	716.319	+	413.567i	1.14848	+	0.663073i	0.199961	+	0.979804i	$0.435918\pi$
$74$	−406.604	−	234.753i	−0.638740	−	0.368777i
$75$	−228.326	+	431.601i	−0.351531	+	0.664493i
$76$		−	18.6543i		−	0.0281552i
$77$		0			0
$78$	−553.680	−	881.950i	−0.803743	−	1.28027i
$79$	−233.602	−	404.610i	−0.332686	−	0.576230i	0.650351	−	0.759634i	$-0.274622\pi$
$79$	−233.602	−	404.610i	−0.332686	−	0.576230i	−0.983038	+	0.183404i	$0.941288\pi$
$80$	183.344	−	317.561i	0.256231	−	0.443805i
$81$	721.028	−	107.512i	0.989065	−	0.147479i
$82$	144.432	−	83.3880i	0.194511	−	0.112301i
$83$	−274.704			−0.363285			−0.181643	−	0.983365i	$-0.558141\pi$
$83$	−274.704			−0.363285			−0.181643	+	0.983365i	$0.558141\pi$
$84$		0			0
$85$	376.034			0.479843
$86$	146.506	−	84.5852i	0.183699	−	0.106059i
$87$	−1.10073	−	29.7321i	−0.00135645	−	0.0366393i
$88$	−475.958	+	824.384i	−0.576561	+	0.998632i
$89$	−270.537	−	468.584i	−0.322212	−	0.558087i	0.658732	−	0.752377i	$-0.271093\pi$
$89$	−270.537	−	468.584i	−0.322212	−	0.558087i	−0.980944	+	0.194290i	$0.937760\pi$
$90$	−388.727	−	187.579i	−0.455282	−	0.219696i
$91$		0			0
$92$			49.0993i			0.0556409i
$93$	−887.804	−	469.667i	−0.989903	−	0.523679i
$94$	−369.234	−	213.178i	−0.405145	−	0.233910i
$95$	−382.764	−	220.989i	−0.413377	−	0.238663i
$96$	−48.8547	−	25.8451i	−0.0519397	−	0.0274772i
$97$			41.4658i			0.0434042i	0.999764	+	0.0217021i	$0.00690854\pi$
$97$			41.4658i			0.0434042i	−0.999764	+	0.0217021i	$0.993091\pi$
$98$		0			0
$99$	1038.81	+	501.277i	1.05459	+	0.508892i
$100$	−11.0467	−	19.1335i	−0.0110467	−	0.0191335i
$101$	631.839	−	1094.38i	0.622479	−	1.07816i	−0.366544	−	0.930401i	$-0.619459\pi$
$101$	631.839	−	1094.38i	0.622479	−	1.07816i	0.989023	−	0.147764i	$-0.0472076\pi$
$102$	−37.2393	−	1005.88i	−0.0361494	−	0.976439i
$103$	267.968	−	154.711i	0.256346	−	0.148001i	−0.366321	−	0.930489i	$-0.619383\pi$
$103$	267.968	−	154.711i	0.256346	−	0.148001i	0.622667	+	0.782487i	$0.286049\pi$
$104$	−1556.14			−1.46723
$105$		0			0
$106$	288.810			0.264639
$107$	775.712	−	447.858i	0.700850	−	0.404636i	−0.106814	−	0.994279i	$-0.534065\pi$
$107$	775.712	−	447.858i	0.700850	−	0.404636i	0.807664	+	0.589643i	$0.200732\pi$
$108$	−13.2266	+	30.2178i	−0.0117845	+	0.0269232i
$109$	795.304	−	1377.51i	0.698865	−	1.21047i	−0.269995	−	0.962862i	$-0.587022\pi$
$109$	795.304	−	1377.51i	0.698865	−	1.21047i	0.968860	−	0.247608i	$-0.0796445\pi$
$110$	−341.456	−	591.420i	−0.295969	−	0.512633i
$111$	452.015	+	720.009i	0.386517	+	0.615678i
$112$		0			0
$113$		−	859.839i		−	0.715812i	−0.933758	−	0.357906i	$-0.883491\pi$
$113$		−	859.839i		−	0.715812i	0.933758	−	0.357906i	$-0.116509\pi$
$114$	−553.232	+	1045.77i	−0.454517	+	0.859166i
$115$	1007.46	+	581.657i	0.816922	+	0.471650i
$116$	1.16588	+	0.673119i	0.000933180	+	0.000538772i
$117$	139.423	+	1880.40i	0.110168	+	1.48584i
$118$			2119.81i			1.65377i
$119$		0			0
$120$	−546.264	+	342.940i	−0.415557	+	0.260883i
$121$	246.990	+	427.800i	0.185567	+	0.321412i
$122$	512.162	−	887.091i	0.380074	−	0.658307i
$123$	−301.775	+	11.1722i	−0.221221	+	0.00818997i
$124$	39.3575	−	22.7231i	0.0285033	−	0.0164564i
$125$	−1219.78			−0.872807
$126$		0			0
$127$	1382.66			0.966075			0.483038	−	0.875600i	$-0.339533\pi$
$127$	1382.66			0.966075			0.483038	+	0.875600i	$0.339533\pi$
$128$	−1306.57	+	754.346i	−0.902228	+	0.520902i
$129$	−306.107	+	11.3326i	−0.208924	+	0.00773474i
$130$	558.192	−	966.817i	0.376590	−	0.652273i
$131$	439.948	+	762.012i	0.293423	+	0.508223i	0.974617	−	0.223880i	$-0.0718723\pi$
$131$	439.948	+	762.012i	0.293423	+	0.508223i	−0.681194	+	0.732103i	$0.738539\pi$
$132$	−44.2019	+	27.7496i	−0.0291461	+	0.0182976i
$133$		0			0
$134$			2069.50i			1.33416i
$135$	463.344	+	629.369i	0.295395	+	0.401240i
$136$	−1302.65	−	752.083i	−0.821331	−	0.474196i
$137$	2630.48	+	1518.71i	1.64041	+	0.947093i	0.980686	+	0.195589i	$0.0626619\pi$
$137$	2630.48	+	1518.71i	1.64041	+	0.947093i	0.659728	+	0.751504i	$0.270671\pi$
$138$	1456.14	−	2752.52i	0.898224	−	1.69790i
$139$		−	652.162i		−	0.397954i	−0.980004	−	0.198977i	$-0.936238\pi$
$139$		−	652.162i		−	0.397954i	0.980004	−	0.198977i	$-0.0637620\pi$
$140$		0			0
$141$	410.472	+	653.835i	0.245163	+	0.390517i
$142$	443.245	+	767.724i	0.261946	+	0.453704i
$143$	−1491.68	+	2583.67i	−0.872314	+	1.51089i
$144$	1000.02	+	1469.26i	0.578717	+	0.850265i
$145$	27.6232	−	15.9482i	0.0158205	−	0.00913399i
$146$	2373.62			1.34549
$147$		0			0
$148$	−38.4669			−0.0213646
$149$	342.491	−	197.737i	0.188308	−	0.108720i	−0.402882	−	0.915252i	$-0.631992\pi$
$149$	342.491	−	197.737i	0.188308	−	0.108720i	0.591190	+	0.806532i	$0.298658\pi$
$150$	51.8392	+	1400.24i	0.0282177	+	0.762193i
$151$	352.564	−	610.659i	0.190008	−	0.329104i	−0.755244	−	0.655443i	$-0.772482\pi$
$151$	352.564	−	610.659i	0.190008	−	0.329104i	0.945253	+	0.326339i	$0.105815\pi$
$152$	883.973	+	1531.09i	0.471709	+	0.817023i
$153$	−792.091	+	1641.47i	−0.418541	+	0.867355i
$154$		0			0
$155$		−	1076.76i		−	0.557983i
$156$	−75.4151	−	39.8961i	−0.0387054	−	0.0204759i
$157$	−1383.73	−	798.896i	−0.703398	−	0.406107i	0.105214	−	0.994450i	$-0.466447\pi$
$157$	−1383.73	−	798.896i	−0.703398	−	0.406107i	−0.808612	+	0.588342i	$0.799781\pi$
$158$	−1161.10	−	670.364i	−0.584636	−	0.337540i
$159$	−462.251	−	244.540i	−0.230559	−	0.121970i
$160$		−	59.2526i		−	0.0292771i
$161$		0			0
$162$	1637.65	−	1301.76i	0.794236	−	0.631331i
$163$	1368.21	+	2369.81i	0.657463	+	1.13876i	0.981270	+	0.192636i	$0.0617038\pi$
$163$	1368.21	+	2369.81i	0.657463	+	1.13876i	−0.323807	+	0.946123i	$0.604963\pi$
$164$	6.83202	−	11.8334i	0.00325300	−	0.00563435i
$165$	45.7479	+	1235.71i	0.0215847	+	0.583027i
$166$	−682.701	+	394.158i	−0.319204	+	0.184293i
$167$	−24.6732			−0.0114328			−0.00571638	−	0.999984i	$-0.501820\pi$
$167$	−24.6732			−0.0114328			−0.00571638	+	0.999984i	$0.501820\pi$
$168$		0			0
$169$	−2680.03			−1.21986
$170$	934.529	−	539.551i	0.421618	−	0.243421i
$171$	1770.93	−	1205.35i	0.791969	−	0.539039i
$172$	6.93011	−	12.0033i	0.00307218	−	0.00532118i
$173$	−701.805	−	1215.56i	−0.308424	−	0.534205i	0.669594	−	0.742727i	$-0.266468\pi$
$173$	−701.805	−	1215.56i	−0.308424	−	0.534205i	−0.978018	+	0.208522i	$0.933135\pi$
$174$	−45.3965	−	72.3116i	−0.0197787	−	0.0315053i
$175$		0			0
$176$			2812.06i			1.20436i
$177$	1794.88	−	3392.83i	0.762212	−	1.44080i
$178$	−1344.69	−	776.357i	−0.566229	−	0.326912i
$179$	−1484.82	−	857.262i	−0.620004	−	0.357959i	0.156867	−	0.987620i	$-0.449861\pi$
$179$	−1484.82	−	857.262i	−0.620004	−	0.357959i	−0.776871	+	0.629660i	$0.783194\pi$
$180$	−35.2659	+	2.61479i	−0.0146031	+	0.00108275i
$181$		−	2046.41i		−	0.840377i	−0.907437	−	0.420189i	$-0.861964\pi$
$181$		−	2046.41i		−	0.840377i	0.907437	−	0.420189i	$-0.138036\pi$
$182$		0			0
$183$	−1570.85	+	986.164i	−0.634538	+	0.398357i
$184$	−2326.67	−	4029.91i	−0.932199	−	1.61462i
$185$	−455.699	+	789.293i	−0.181101	+	0.313676i
$186$	−2880.29	+	106.633i	−1.13545	+	0.0420362i
$187$	−2497.39	+	1441.87i	−0.976615	+	0.563849i
$188$	−34.9315			−0.0135513
$189$		0			0
$190$	−1268.34			−0.484290
$191$	−2921.20	+	1686.56i	−1.10665	+	0.638926i	−0.937960	−	0.346743i	$-0.887288\pi$
$191$	−2921.20	+	1686.56i	−1.10665	+	0.638926i	−0.168692	+	0.985669i	$0.553954\pi$
$192$	2575.95	−	95.3661i	0.968245	−	0.0358461i
$193$	212.464	−	367.999i	0.0792409	−	0.137249i	−0.823682	−	0.567052i	$-0.808084\pi$
$193$	212.464	−	367.999i	0.0792409	−	0.137249i	0.902923	+	0.429803i	$0.141417\pi$
$194$	59.4969	+	103.052i	0.0220187	+	0.0381375i
$195$	−1712.03	+	1074.79i	−0.628722	+	0.394706i
$196$		0			0
$197$		−	4420.59i		−	1.59875i	−0.600832	−	0.799375i	$-0.705164\pi$
$197$		−	4420.59i		−	1.59875i	0.600832	−	0.799375i	$-0.294836\pi$
$198$	3300.94	−	244.748i	1.18478	−	0.0878459i
$199$	1366.41	+	788.899i	0.486746	+	0.281023i	0.723224	−	0.690614i	$-0.242660\pi$
$199$	1366.41	+	788.899i	0.486746	+	0.281023i	−0.236478	+	0.971637i	$0.575993\pi$
$200$	1813.35	+	1046.94i	0.641118	+	0.370150i
$201$	1752.28	−	3312.31i	0.614907	−	1.16235i
$202$		−	3626.36i		−	1.26312i
$203$		0			0
$204$	−43.8483	−	69.8454i	−0.0150490	−	0.0239714i
$205$	−161.871	−	280.370i	−0.0551492	−	0.0955213i
$206$	443.973	−	768.984i	0.150161	−	0.260086i
$207$	−4661.21	+	3172.56i	−1.56510	+	1.06526i
$208$	−3981.10	+	2298.49i	−1.32711	+	0.766210i
$209$	3389.44			1.12178
$210$		0			0
$211$	911.064			0.297252			0.148626	−	0.988893i	$-0.452515\pi$
$211$	911.064			0.297252			0.148626	+	0.988893i	$0.452515\pi$
$212$	20.4922	−	11.8312i	0.00663872	−	0.00383287i
$213$	−59.3855	−	1604.07i	−0.0191034	−	0.516006i
$214$	1285.21	−	2226.05i	0.410539	−	0.711074i
$215$	−164.195	−	284.395i	−0.0520839	−	0.0902119i
$216$	−346.340	−	3106.95i	−0.109099	−	0.978708i
$217$		0			0
$218$		−	4564.55i		−	1.41812i
$219$	−3799.06	−	2009.78i	−1.17222	−	0.620130i
$220$	−48.4553	−	27.9757i	−0.0148494	−	0.00857328i
$221$	−4082.57	−	2357.08i	−1.24264	−	0.717439i
$222$	2156.46	+	1140.81i	0.651946	+	0.344893i
$223$		−	3070.23i		−	0.921964i	−0.887410	−	0.460982i	$-0.847497\pi$
$223$		−	3070.23i		−	0.921964i	0.887410	−	0.460982i	$-0.152503\pi$
$224$		0			0
$225$	1102.63	−	2285.02i	0.326706	−	0.677044i
$226$	−1233.73	−	2136.89i	−0.363127	−	0.628955i
$227$	1676.33	−	2903.50i	0.490142	−	0.848951i	−0.509794	−	0.860297i	$-0.670278\pi$
$227$	1676.33	−	2903.50i	0.490142	−	0.848951i	0.999936	+	0.0113460i	$0.00361161\pi$
$228$	3.58609	+	96.8644i	0.00104164	+	0.0281360i
$229$	3770.24	−	2176.75i	1.08797	−	0.628138i	0.154933	−	0.987925i	$-0.450484\pi$
$229$	3770.24	−	2176.75i	1.08797	−	0.628138i	0.933035	+	0.359787i	$0.117151\pi$
$230$	3338.35			0.957061
$231$		0			0
$232$	−127.588			−0.0361060
$233$	−3190.02	+	1841.76i	−0.896932	+	0.517844i	−0.876204	−	0.481941i	$-0.839932\pi$
$233$	−3190.02	+	1841.76i	−0.896932	+	0.517844i	−0.0207285	+	0.999785i	$0.506599\pi$
$234$	3044.58	+	4473.17i	0.850558	+	1.24966i
$235$	−413.817	+	716.751i	−0.114870	+	0.198960i
$236$	86.8386	+	150.409i	0.0239522	+	0.0414864i
$237$	1290.78	+	2056.07i	0.353777	+	0.563527i
$238$		0			0
$239$			4537.46i			1.22805i	0.789287	+	0.614025i	$0.210451\pi$
$239$			4537.46i			1.22805i	−0.789287	+	0.614025i	$0.789549\pi$
$240$	−890.983	+	1684.21i	−0.239636	+	0.452981i
$241$	−1923.53	−	1110.55i	−0.514130	−	0.296833i	0.220400	−	0.975410i	$-0.429264\pi$
$241$	−1923.53	−	1110.55i	−0.514130	−	0.296833i	−0.734530	+	0.678576i	$0.762597\pi$
$242$	1227.65	+	708.785i	0.326101	+	0.188275i
$243$	−3723.34	+	696.878i	−0.982932	+	0.183970i
$244$		−	83.9234i		−	0.0220190i
$245$		0			0
$246$	−733.948	+	460.766i	−0.190223	+	0.119420i
$247$	2770.43	+	4798.52i	0.713677	+	1.23612i
$248$	−2153.56	+	3730.07i	−0.551416	+	0.955080i
$249$	1426.43	−	52.8088i	0.363037	−	0.0134402i
$250$	−3031.44	+	1750.20i	−0.766900	+	0.442770i
$251$	−652.142			−0.163995			−0.0819976	−	0.996633i	$-0.526130\pi$
$251$	−652.142			−0.163995			−0.0819976	+	0.996633i	$0.526130\pi$
$252$		0			0
$253$	−8921.22			−2.21689
$254$	3436.23	−	1983.91i	0.848851	−	0.490084i
$255$	−1952.59	+	72.2884i	−0.479514	+	0.0177524i
$256$	−180.414	+	312.486i	−0.0440464	+	0.0762905i
$257$	3436.92	+	5952.92i	0.834199	+	1.44487i	0.894681	+	0.446705i	$0.147403\pi$
$257$	3436.92	+	5952.92i	0.834199	+	1.44487i	−0.0604827	+	0.998169i	$0.519264\pi$
$258$	−744.485	+	467.381i	−0.179650	+	0.112782i
$259$		0			0
$260$		−	91.4659i		−	0.0218172i
$261$	11.4313	+	154.175i	0.00271104	+	0.0365640i
$262$	2186.74	+	1262.51i	0.515638	+	0.297703i
$263$	2845.41	+	1642.80i	0.667132	+	0.385169i	0.794989	−	0.606624i	$-0.207477\pi$
$263$	2845.41	+	1642.80i	0.667132	+	0.385169i	−0.127857	+	0.991793i	$0.540810\pi$
$264$	2312.98	−	4372.19i	0.539220	−	1.01928i
$265$		−	560.633i		−	0.129960i
$266$		0			0
$267$	1494.87	+	2381.16i	0.342638	+	0.545785i
$268$	84.7776	+	146.839i	0.0193232	+	0.0334688i
$269$	−628.789	+	1089.09i	−0.142520	+	0.246852i	−0.928445	−	0.371470i	$-0.878854\pi$
$269$	−628.789	+	1089.09i	−0.142520	+	0.246852i	0.785925	+	0.618322i	$0.212187\pi$
$270$	2054.56	+	899.296i	0.463098	+	0.202701i
$271$	321.083	−	185.377i	0.0719720	−	0.0415530i	−0.463582	−	0.886054i	$-0.653436\pi$
$271$	321.083	−	185.377i	0.0719720	−	0.0415530i	0.535554	+	0.844501i	$0.320103\pi$
$272$	−4443.46			−0.990530
$273$		0			0
$274$	8716.43			1.92182
$275$	3476.50	−	2007.16i	0.762330	−	0.440131i
$276$	−9.43880	−	254.953i	−0.00205851	−	0.0556028i
$277$	770.082	−	1333.82i	0.167039	−	0.289320i	−0.770339	−	0.637635i	$-0.779913\pi$
$277$	770.082	−	1333.82i	0.167039	−	0.289320i	0.937377	+	0.348315i	$0.113246\pi$
$278$	−935.751	−	1620.77i	−0.201880	−	0.349666i
$279$	4700.29	+	2268.12i	1.00860	+	0.486698i
$280$		0			0
$281$			3782.78i			0.803066i	0.915845	+	0.401533i	$0.131522\pi$
$281$			3782.78i			0.803066i	−0.915845	+	0.401533i	$0.868478\pi$
$282$	1958.27	+	1035.96i	0.413521	+	0.218761i
$283$	−8022.06	−	4631.54i	−1.68502	−	0.972849i	−0.958232	−	0.285990i	$-0.907677\pi$
$283$	−8022.06	−	4631.54i	−1.68502	−	0.972849i	−0.726791	−	0.686858i	$-0.758989\pi$
$284$	62.9000	+	36.3153i	0.0131423	+	0.00758774i
$285$	2030.02	+	1073.92i	0.421923	+	0.223206i
$286$			8561.34i			1.77008i
$287$		0			0
$288$	258.651	+	124.812i	0.0529207	+	0.0255368i
$289$	178.142	+	308.551i	0.0362594	+	0.0628031i
$290$	45.7665	−	79.2699i	0.00926724	−	0.0160513i
$291$	−7.97133	−	215.315i	−0.00160580	−	0.0433745i
$292$	168.417	−	97.2358i	0.0337530	−	0.0194873i
$293$	−7316.39			−1.45880			−0.729399	−	0.684089i	$-0.760200\pi$
$293$	−7316.39			−1.45880			−0.729399	+	0.684089i	$0.760200\pi$
$294$		0			0
$295$	4114.94			0.812140
$296$	3157.23	−	1822.83i	0.619968	−	0.357939i
$297$	−5490.50	−	2403.23i	−1.07270	−	0.469527i
$298$	567.444	−	982.842i	0.110306	−	0.191055i
$299$	−7291.94	−	12630.0i	−1.41038	−	2.44285i
$300$	61.0393	+	97.2287i	0.0117470	+	0.0187117i
$301$		0			0
$302$		−	2023.50i		−	0.385561i
$303$	−3070.50	+	5804.12i	−0.582164	+	1.10046i
$304$	4522.98	+	2611.35i	0.853325	+	0.492668i
$305$	−1722.01	−	994.201i	−0.323285	−	0.186648i
$306$	386.738	+	5215.96i	0.0722494	+	0.974433i
$307$			4347.69i			0.808260i	0.914701	+	0.404130i	$0.132426\pi$
$307$			4347.69i			0.808260i	−0.914701	+	0.404130i	$0.867574\pi$
$308$		0			0
$309$	−1361.71	+	854.867i	−0.250695	+	0.157384i
$310$	−1544.98	−	2675.98i	−0.283061	−	0.490277i
$311$	2275.17	−	3940.71i	0.414833	−	0.718513i	−0.580577	−	0.814205i	$-0.697173\pi$
$311$	2275.17	−	3940.71i	0.414833	−	0.718513i	0.995411	+	0.0956923i	$0.0305065\pi$
$312$	8080.38	−	299.150i	1.46622	−	0.0542821i
$313$	7315.95	−	4223.87i	1.32116	−	0.762770i	0.337243	−	0.941418i	$-0.390506\pi$
$313$	7315.95	−	4223.87i	1.32116	−	0.762770i	0.983913	+	0.178647i	$0.0571722\pi$
$314$	−4585.17			−0.824063
$315$		0			0
$316$	−109.846			−0.0195549
$317$	2886.93	−	1666.77i	0.511502	−	0.295316i	−0.221949	−	0.975058i	$-0.571242\pi$
$317$	2886.93	−	1666.77i	0.511502	−	0.295316i	0.733451	+	0.679742i	$0.237908\pi$
$318$	−1499.67	+	55.5205i	−0.264458	+	0.00979068i
$319$	−122.304	+	211.837i	−0.0214662	+	0.0371805i
$320$	1381.73	+	2393.23i	0.241379	+	0.418080i
$321$	−3941.86	+	2474.67i	−0.685400	+	0.430288i
$322$		0			0
$323$			5355.81i			0.922617i
$324$	62.8711	−	159.452i	0.0107804	−	0.0273408i
$325$	5683.17	+	3281.18i	0.969986	+	0.560022i
$326$	6800.62	+	3926.34i	1.15537	+	0.667054i
$327$	−3864.88	+	7305.72i	−0.653603	+	1.23550i
$328$			1295.00i			0.218001i
$329$		0			0
$330$	1886.74	+	3005.36i	0.314732	+	0.501333i
$331$	3748.44	+	6492.50i	0.622457	+	1.07813i	0.989027	+	0.147736i	$0.0471986\pi$
$331$	3748.44	+	6492.50i	0.622457	+	1.07813i	−0.366570	+	0.930390i	$0.619468\pi$
$332$	−32.2935	+	55.9340i	−0.00533836	+	0.00924632i
$333$	−2485.54	−	3651.82i	−0.409030	−	0.600957i
$334$	−61.3185	+	35.4023i	−0.0100455	+	0.00579978i
$335$	4017.28			0.655186
$336$		0			0
$337$	5107.78			0.825633			0.412817	−	0.910814i	$-0.364545\pi$
$337$	5107.78			0.825633			0.412817	+	0.910814i	$0.364545\pi$
$338$	−6660.46	+	3845.42i	−1.07184	+	0.618826i
$339$	165.294	+	4464.79i	0.0264825	+	0.715322i
$340$	44.2056	−	76.5664i	0.00705114	−	0.0122129i
$341$	4128.72	+	7151.16i	0.655669	+	1.13565i
$342$	2671.67	−	5536.59i	0.422420	−	0.875393i
$343$		0			0
$344$			1313.59i			0.205884i
$345$	−5343.14	−	2826.63i	−0.833812	−	0.441104i
$346$	−3488.29	−	2013.96i	−0.541998	−	0.312923i
$347$	−2568.93	−	1483.17i	−0.397428	−	0.229455i	0.287946	−	0.957647i	$-0.407028\pi$
$347$	−2568.93	−	1483.17i	−0.397428	−	0.229455i	−0.685374	+	0.728192i	$0.740361\pi$
$348$	−6.18332	−	3.27111i	−0.000952474	−	0.000503879i
$349$			2869.90i			0.440178i	0.975480	+	0.220089i	$0.0706348\pi$
$349$			2869.90i			0.440178i	−0.975480	+	0.220089i	$0.929365\pi$
$350$		0			0
$351$	−1085.45	−	9737.37i	−0.165063	−	1.48075i
$352$	227.198	+	393.519i	0.0344026	+	0.0595870i
$353$	6326.61	−	10958.0i	0.953913	−	1.65223i	0.217077	−	0.976154i	$-0.430348\pi$
$353$	6326.61	−	10958.0i	0.953913	−	1.65223i	0.736836	−	0.676072i	$-0.236319\pi$
$354$	−407.510	−	11007.3i	−0.0611834	−	1.65263i
$355$	1490.29	−	860.421i	0.222807	−	0.128638i
$356$	−127.215			−0.0189392
$357$		0			0
$358$	−4920.15			−0.726363
$359$	−5708.19	+	3295.63i	−0.839184	+	0.484503i	−0.856987	−	0.515339i	$-0.827666\pi$
$359$	−5708.19	+	3295.63i	−0.839184	+	0.484503i	0.0178029	+	0.999842i	$0.494333\pi$
$360$	2770.60	−	1885.76i	0.405621	−	0.276079i
$361$	−281.978	+	488.401i	−0.0411107	+	0.0712058i
$362$	−2936.28	−	5085.78i	−0.426318	−	0.738405i
$363$	−1364.76	−	2173.91i	−0.197331	−	0.314327i
$364$		0			0
$365$		−	4607.62i		−	0.660751i
$366$	−2488.92	+	4704.76i	−0.355459	+	0.671918i
$367$	8907.93	+	5143.00i	1.26700	+	0.731505i	0.974420	−	0.224735i	$-0.0721517\pi$
$367$	8907.93	+	5143.00i	1.26700	+	0.731505i	0.292584	+	0.956240i	$0.405485\pi$
$368$	−11904.8	−	6873.22i	−1.68636	−	0.973618i
$369$	1564.85	−	116.026i	0.220766	−	0.0163687i
$370$			2615.43i			0.367485i
$371$		0			0
$372$	−199.999	+	125.558i	−0.0278750	+	0.0174996i
$373$	−2205.50	−	3820.04i	−0.306157	−	0.530280i	0.671361	−	0.741130i	$-0.265710\pi$
$373$	−2205.50	−	3820.04i	−0.306157	−	0.530280i	−0.977518	+	0.210851i	$0.932377\pi$
$374$	−4137.71	+	7166.72i	−0.572074	+	0.990862i
$375$	6333.85	−	234.490i	0.872209	−	0.0322907i
$376$	2867.06	−	1655.30i	0.393238	−	0.227036i
$377$	−399.870			−0.0546269
$378$		0			0
$379$	3838.27			0.520207			0.260103	−	0.965581i	$-0.416243\pi$
$379$	3838.27			0.520207			0.260103	+	0.965581i	$0.416243\pi$
$380$	−89.9936	+	51.9578i	−0.0121489	+	0.00701416i
$381$	−7179.61	+	265.802i	−0.965414	+	0.0357413i
$382$	−4839.89	+	8382.94i	−0.648247	+	1.12280i
$383$	1063.38	+	1841.82i	0.141869	+	0.245725i	0.928201	−	0.372080i	$-0.121355\pi$
$383$	1063.38	+	1841.82i	0.141869	+	0.245725i	−0.786331	+	0.617805i	$0.788022\pi$
$384$	6639.45	−	4168.19i	0.882339	−	0.553924i
$385$		0			0
$386$		−	1219.41i		−	0.160794i
$387$	1587.31	−	117.691i	0.208495	−	0.0154589i
$388$	8.44307	+	4.87461i	0.00110472	+	0.000637812i
$389$	6251.47	+	3609.29i	0.814812	+	0.470432i	0.848624	−	0.528996i	$-0.177431\pi$
$389$	6251.47	+	3609.29i	0.814812	+	0.470432i	−0.0338119	+	0.999428i	$0.510765\pi$
$390$	−2712.61	+	5127.60i	−0.352200	+	0.665759i
$391$		−	14096.8i		−	1.82329i
$392$		0			0
$393$	−2430.96	−	3872.24i	−0.312025	−	0.497020i
$394$	−6342.86	−	10986.1i	−0.811037	−	1.40476i
$395$	−1301.30	+	2253.92i	−0.165761	+	0.287106i
$396$	224.188	−	152.590i	0.0284492	−	0.0193634i
$397$	−99.9816	+	57.7244i	−0.0126396	+	0.00729750i	−0.506307	−	0.862354i	$-0.668990\pi$
$397$	−99.9816	+	57.7244i	−0.0126396	+	0.00729750i	0.493667	+	0.869651i	$0.335656\pi$
$398$	4527.79			0.570245
$399$		0			0
$400$	6185.54			0.773192
$401$	7712.55	−	4452.84i	0.960464	−	0.554524i	0.0641483	−	0.997940i	$-0.479567\pi$
$401$	7712.55	−	4452.84i	0.960464	−	0.554524i	0.896316	+	0.443416i	$0.146234\pi$
$402$	−397.838	−	10746.1i	−0.0493591	−	1.33325i
$403$	−6749.39	+	11690.3i	−0.834270	+	1.44500i
$404$	−148.555	−	257.305i	−0.0182943	−	0.0316866i
$405$	−2526.95	−	3178.99i	−0.310037	−	0.390037i
$406$		0			0
$407$		−	6989.33i		−	0.851224i
$408$	6908.69	+	3654.84i	0.838312	+	0.443485i
$409$	5847.94	+	3376.31i	0.706997	+	0.408185i	0.809948	−	0.586502i	$-0.199495\pi$
$409$	5847.94	+	3376.31i	0.706997	+	0.408185i	−0.102951	+	0.994686i	$0.532829\pi$
$410$	−804.573	−	464.521i	−0.0969148	−	0.0559538i
$411$	−13951.0	−	7380.35i	−1.67433	−	0.885756i
$412$		−	72.7499i		−	0.00869934i
$413$		0			0
$414$	−7032.00	+	14572.6i	−0.834793	+	1.72997i
$415$	765.132	+	1325.25i	0.0905033	+	0.156756i
$416$	−371.410	+	643.301i	−0.0437737	+	0.0758183i
$417$	125.371	+	3386.41i	0.0147229	+	0.397682i
$418$	8423.53	−	4863.33i	0.985665	−	0.569074i
$419$	888.062			0.103543			0.0517717	−	0.998659i	$-0.483513\pi$
$419$	888.062			0.103543			0.0517717	+	0.998659i	$0.483513\pi$
$420$		0			0
$421$	−14976.0			−1.73369			−0.866847	−	0.498574i	$-0.833857\pi$
$421$	−14976.0			−1.73369			−0.866847	+	0.498574i	$0.833857\pi$
$422$	2264.20	−	1307.23i	0.261183	−	0.150794i
$423$	−2257.11	−	3316.19i	−0.259443	−	0.381179i
$424$	−1121.29	+	1942.13i	−0.128431	+	0.222448i
$425$	3171.60	+	5493.37i	0.361989	+	0.626983i
$426$	−2449.18	−	3901.27i	−0.278552	−	0.443702i
$427$		0			0
$428$		−	210.596i		−	0.0237840i
$429$	7249.03	−	13702.7i	0.815819	−	1.54213i
$430$	−816.124	−	471.190i	−0.0915279	−	0.0528437i
$431$	−948.626	−	547.690i	−0.106018	−	0.0612095i	0.446054	−	0.895006i	$-0.352829\pi$
$431$	−948.626	−	547.690i	−0.106018	−	0.0612095i	−0.552071	+	0.833797i	$0.686162\pi$
$432$	−5475.17	−	7437.02i	−0.609778	−	0.828273i
$433$			12688.2i			1.40822i	0.710093	+	0.704108i	$0.248653\pi$
$433$			12688.2i			1.40822i	−0.710093	+	0.704108i	$0.751347\pi$
$434$		0			0
$435$	−140.370	+	88.1230i	−0.0154718	+	0.00971304i
$436$	−186.988	−	323.872i	−0.0205392	−	0.0355749i
$437$	−8284.47	+	14349.1i	−0.906865	+	1.57074i
$438$	−12325.2	+	456.301i	−1.34457	+	0.0497784i
$439$	−11643.9	+	6722.62i	−1.26591	+	0.730873i	−0.974211	−	0.225637i	$-0.927554\pi$
$439$	−11643.9	+	6722.62i	−1.26591	+	0.730873i	−0.291698	+	0.956510i	$0.594220\pi$
$440$	5302.74			0.574541
$441$		0			0
$442$	−13528.1			−1.45581
$443$	1971.92	−	1138.49i	0.211487	−	0.122102i	−0.390516	−	0.920596i	$-0.627703\pi$
$443$	1971.92	−	1138.49i	0.211487	−	0.122102i	0.602002	+	0.798495i	$0.294370\pi$
$444$	199.743	−	7.39482i	0.0213499	−	0.000790412i
$445$	−1507.05	+	2610.29i	−0.160542	+	0.278066i
$446$	−4405.30	−	7630.21i	−0.467707	−	0.810092i
$447$	−1740.40	+	1092.61i	−0.184157	+	0.115612i
$448$		0			0
$449$			1685.89i			0.177198i	0.996067	+	0.0885991i	$0.0282390\pi$
$449$			1685.89i			0.177198i	−0.996067	+	0.0885991i	$0.971761\pi$
$450$	−538.360	−	7260.90i	−0.0563967	−	0.760627i
$451$	2150.10	+	1241.36i	0.224488	+	0.129608i
$452$	−175.077	−	101.080i	−0.0182188	−	0.0105186i
$453$	−1713.33	+	3238.68i	−0.177703	+	0.335908i
$454$		−	9621.12i		−	0.994585i
$455$		0			0
$456$	−4884.45	−	7780.38i	−0.501613	−	0.799013i
$457$	1041.80	+	1804.45i	0.106637	+	0.184701i	0.914406	−	0.404798i	$-0.132658\pi$
$457$	1041.80	+	1804.45i	0.106637	+	0.184701i	−0.807769	+	0.589500i	$0.799325\pi$
$458$	6246.59	−	10819.4i	0.637302	−	1.10384i
$459$	3797.45	−	8675.78i	0.386165	−	0.882246i
$460$	236.869	−	136.756i	0.0240088	−	0.0138615i
$461$	14128.1			1.42736			0.713679	−	0.700473i	$-0.247028\pi$
$461$	14128.1			1.42736			0.713679	+	0.700473i	$0.247028\pi$
$462$		0			0
$463$	16141.5			1.62021			0.810106	−	0.586283i	$-0.199409\pi$
$463$	16141.5			1.62021			0.810106	+	0.586283i	$0.199409\pi$
$464$	−326.413	+	188.454i	−0.0326580	+	0.0188551i
$465$	206.995	+	5591.17i	0.0206433	+	0.557601i
$466$	−5285.28	+	9154.37i	−0.525398	+	0.910017i
$467$	3124.69	+	5412.12i	0.309622	+	0.536281i	0.978280	−	0.207289i	$-0.0664642\pi$
$467$	3124.69	+	5412.12i	0.309622	+	0.536281i	−0.668658	+	0.743570i	$0.733131\pi$
$468$	399.269	+	192.667i	0.0394364	+	0.0190300i
$469$		0			0
$470$			2375.05i			0.233091i
$471$	7338.72	+	3882.34i	0.717941	+	0.379806i
$472$	−14254.9	−	8230.05i	−1.39011	−	0.802582i
$473$	2180.97	+	1259.18i	0.212011	+	0.122404i
$474$	6158.01	+	3257.72i	0.596723	+	0.315679i
$475$		−	7455.58i		−	0.720180i
$476$		0			0
$477$	2447.29	+	1180.94i	0.234914	+	0.113357i
$478$	6510.55	+	11276.6i	0.622983	+	1.07904i
$479$	−5312.09	+	9200.81i	−0.506713	+	0.877653i	0.493256	+	0.869884i	$0.335806\pi$
$479$	−5312.09	+	9200.81i	−0.506713	+	0.877653i	−0.999970	+	0.00776940i	$0.997527\pi$
$480$	11.3906	+	307.675i	0.00108315	+	0.0292570i
$481$	9894.97	−	5712.86i	0.937987	−	0.541547i
$482$	−6373.86			−0.602327
$483$		0			0
$484$	116.142			0.0109074
$485$	200.042	−	115.494i	0.0187288	−	0.0108131i
$486$	−8253.42	+	7074.31i	−0.770335	+	0.660283i
$487$	1985.08	−	3438.25i	0.184707	−	0.319922i	−0.758771	−	0.651358i	$-0.774200\pi$
$487$	1985.08	−	3438.25i	0.184707	−	0.319922i	0.943478	+	0.331436i	$0.107533\pi$
$488$	3976.88	+	6888.16i	0.368904	+	0.638960i
$489$	−7560.13	−	12042.4i	−0.699143	−	1.11366i
$490$		0			0
$491$			4184.69i			0.384628i	0.981333	+	0.192314i	$0.0615993\pi$
$491$			4184.69i			0.384628i	−0.981333	+	0.192314i	$0.938401\pi$
$492$	−33.2011	+	62.7595i	−0.00304232	+	0.00575085i
$493$	−334.733	−	193.258i	−0.0305793	−	0.0176550i
$494$	13770.3	+	7950.27i	1.25416	+	0.724088i
$495$	−475.101	−	6407.72i	−0.0431398	−	0.581830i
$496$			12723.7i			1.15183i
$497$		0			0
$498$	3469.22	−	2177.94i	0.312167	−	0.195976i
$499$	−9231.14	−	15988.8i	−0.828141	−	1.43438i	−0.899495	−	0.436931i	$-0.856065\pi$
$499$	−9231.14	−	15988.8i	−0.828141	−	1.43438i	0.0713539	−	0.997451i	$-0.477268\pi$
$500$	−143.395	+	248.367i	−0.0128256	+	0.0222146i
$501$	128.118	−	4.74315i	0.0114249	−	0.000422971i
$502$	−1620.72	+	935.722i	−0.144096	+	0.0831938i
$503$	11828.5			1.04853			0.524263	−	0.851557i	$-0.324341\pi$
$503$	11828.5			1.04853			0.524263	+	0.851557i	$0.324341\pi$
$504$		0			0
$505$	−7039.44			−0.620299
$506$	−22171.2	+	12800.6i	−1.94789	+	1.12461i
$507$	13916.3	−	515.205i	1.21902	−	0.0451303i
$508$	162.543	−	281.532i	0.0141962	−	0.0245885i
$509$	398.570	+	690.343i	0.0347078	+	0.0601157i	0.882858	−	0.469641i	$-0.155617\pi$
$509$	398.570	+	690.343i	0.0347078	+	0.0601157i	−0.848150	+	0.529757i	$0.822283\pi$
$510$	−4748.91	+	2981.32i	−0.412324	+	0.258853i
$511$		0			0
$512$		−	11034.1i		−	0.952425i
$513$	−8964.03	+	6599.36i	−0.771485	+	0.567970i
$514$	17083.0	+	9862.89i	1.46595	+	0.846368i
$515$	−1492.74	−	861.833i	−0.127724	−	0.0737416i
$516$	−33.6777	+	63.6605i	−0.00287322	+	0.00543119i
$517$		−	6346.96i		−	0.539921i
$518$		0			0
$519$	3877.87	+	6177.01i	0.327976	+	0.522429i
$520$	4334.30	+	7507.22i	0.365522	+	0.633103i
$521$	4182.88	−	7244.95i	0.351737	−	0.609227i	−0.634817	−	0.772663i	$-0.718924\pi$
$521$	4182.88	−	7244.95i	0.351737	−	0.609227i	0.986554	+	0.163436i	$0.0522577\pi$
$522$	249.627	+	366.758i	0.0209308	+	0.0307520i
$523$	−3137.64	+	1811.52i	−0.262332	+	0.151457i	−0.625398	−	0.780306i	$-0.715063\pi$
$523$	−3137.64	+	1811.52i	−0.262332	+	0.151457i	0.363066	+	0.931763i	$0.381730\pi$
$524$	206.877			0.0172470
$525$		0			0
$526$	9428.65			0.781575
$527$	−11299.9	+	6523.98i	−0.934023	+	0.539258i
$528$	−540.587	−	14601.9i	−0.0445568	−	1.20353i
$529$	15721.7	−	27230.8i	1.29216	−	2.23809i
$530$	−804.421	−	1393.30i	−0.0659280	−	0.114191i
$531$	−8667.85	+	17962.7i	−0.708386	+	1.46801i
$532$		0			0
$533$			4058.60i			0.329827i
$534$	7131.67	+	3772.81i	0.577936	+	0.305740i
$535$	−4321.18	−	2494.83i	−0.349198	−	0.201609i
$536$	−13916.5	−	8034.72i	−1.12146	−	0.647476i
$537$	7874.87	+	4165.97i	0.632823	+	0.334776i
$538$			3608.86i			0.289199i
$539$		0			0
$540$	182.619	−	20.3570i	0.0145531	−	0.00162227i
$541$	−1110.48	−	1923.41i	−0.0882501	−	0.152854i	0.818521	−	0.574476i	$-0.194794\pi$
$541$	−1110.48	−	1923.41i	−0.0882501	−	0.152854i	−0.906772	+	0.421622i	$0.861461\pi$
$542$	531.975	−	921.409i	0.0421592	−	0.0730219i
$543$	393.399	+	10626.2i	0.0310909	+	0.839802i
$544$	−621.817	+	359.006i	−0.0490077	+	0.0282946i
$545$	−8860.62			−0.696417
$546$		0			0
$547$	10592.4			0.827969			0.413985	−	0.910284i	$-0.364137\pi$
$547$	10592.4			0.827969			0.413985	+	0.910284i	$0.364137\pi$
$548$	618.464	−	357.071i	0.0482107	−	0.0278345i
$549$	7967.20	−	5422.73i	0.619366	−	0.421560i
$550$	5759.92	−	9976.47i	0.446552	−	0.773451i
$551$	227.149	+	393.434i	0.0175624	+	0.0304189i
$552$	12856.2	+	20478.4i	0.991295	+	1.57902i
$553$		0			0
$554$		−	4419.79i		−	0.338951i
$555$	2214.53	−	4186.08i	0.169372	−	0.320161i
$556$	−132.790	−	76.6666i	−0.0101287	−	0.00584782i
$557$	−857.005	−	494.792i	−0.0651929	−	0.0376392i	0.467049	−	0.884231i	$-0.345317\pi$
$557$	−857.005	−	494.792i	−0.0651929	−	0.0376392i	−0.532242	+	0.846592i	$0.678650\pi$
$558$	14935.7	−	1107.41i	1.13311	−	0.0840148i
$559$			4116.87i			0.311494i
$560$		0			0
$561$	12690.7	−	7967.12i	0.955086	−	0.599594i
$562$	5427.70	+	9401.05i	0.407391	+	0.705621i
$563$	8394.87	−	14540.3i	0.628422	−	1.08846i	−0.359446	−	0.933166i	$-0.617034\pi$
$563$	8394.87	−	14540.3i	0.628422	−	1.08846i	0.987868	−	0.155293i	$-0.0496323\pi$
$564$	181.385	−	6.71519i	0.0135420	−	0.000501348i
$565$	−4148.10	+	2394.90i	−0.308870	+	0.178326i
$566$	−26582.1			−1.97408
$567$		0			0
$568$	−6883.50			−0.508495
$569$	9593.60	−	5538.87i	0.706827	−	0.408087i	−0.103058	−	0.994675i	$-0.532863\pi$
$569$	9593.60	−	5538.87i	0.706827	−	0.408087i	0.809885	+	0.586588i	$0.199529\pi$
$570$	6585.97	−	243.824i	0.483958	−	0.0179170i
$571$	2106.59	−	3648.73i	0.154393	−	0.267416i	−0.778445	−	0.627713i	$-0.783991\pi$
$571$	2106.59	−	3648.73i	0.154393	−	0.267416i	0.932838	+	0.360297i	$0.117325\pi$
$572$	350.717	+	607.460i	0.0256368	+	0.0444042i
$573$	14844.4	−	9319.17i	1.08226	−	0.679431i
$574$		0			0
$575$			19623.6i			1.42323i
$576$	−13357.5	+	990.395i	−0.966256	+	0.0716431i
$577$	1451.75	+	838.168i	0.104744	+	0.0604738i	0.551457	−	0.834203i	$-0.314072\pi$
$577$	1451.75	+	838.168i	0.104744	+	0.0604738i	−0.446713	+	0.894677i	$0.647406\pi$
$578$	885.447	+	511.213i	0.0637193	+	0.0367883i
$579$	−1032.50	+	1951.71i	−0.0741089	+	0.140087i
$580$		−	7.49934i		−	0.000536885i
$581$		0			0
$582$	−328.754	−	523.668i	−0.0234146	−	0.0372968i
$583$	2149.69	+	3723.38i	0.152712	+	0.264505i
$584$	−9215.43	+	15961.6i	−0.652975	+	1.13099i
$585$	8683.24	−	5910.09i	0.613689	−	0.417696i
$586$	−18182.9	+	10497.9i	−1.28179	+	0.740040i
$587$	−22687.3			−1.59524			−0.797620	−	0.603161i	$-0.793908\pi$
$587$	−22687.3			−1.59524			−0.797620	+	0.603161i	$0.793908\pi$
$588$		0			0
$589$	15336.1			1.07286
$590$	10226.6	−	5904.30i	0.713594	−	0.411994i
$591$	849.808	+	22954.3i	0.0591480	+	1.59766i
$592$	5384.82	−	9326.79i	0.373843	−	0.647515i
$593$	−8980.77	−	15555.2i	−0.621916	−	1.07719i	−0.989129	−	0.147053i	$-0.953021\pi$
$593$	−8980.77	−	15555.2i	−0.621916	−	1.07719i	0.367213	−	0.930137i	$-0.380312\pi$
$594$	−17093.4	+	1905.45i	−1.18072	+	0.131619i
$595$		0			0
$596$		−	92.9820i		−	0.00639042i
$597$	−7246.89	−	3833.76i	−0.496810	−	0.262823i
$598$	−36244.2	−	20925.6i	−2.47849	−	1.43095i
$599$	5975.10	+	3449.73i	0.407573	+	0.235312i	0.689746	−	0.724051i	$-0.257722\pi$
$599$	5975.10	+	3449.73i	0.407573	+	0.235312i	−0.282174	+	0.959363i	$0.591055\pi$
$600$	−9617.28	−	5087.74i	−0.654373	−	0.346177i
$601$			19792.8i			1.34337i	0.740838	+	0.671684i	$0.234429\pi$
$601$			19792.8i			1.34337i	−0.740838	+	0.671684i	$0.765571\pi$
$602$		0			0
$603$	−8462.13	+	17536.3i	−0.571484	+	1.18430i
$604$	−82.8931	−	143.575i	−0.00558423	−	0.00967217i
$605$	1375.88	−	2383.10i	0.0924588	−	0.160143i
$606$	697.128	+	18830.2i	0.0467308	+	1.26225i
$607$	15448.3	−	8919.08i	1.03299	−	0.596399i	0.115153	−	0.993348i	$-0.463264\pi$
$607$	15448.3	−	8919.08i	1.03299	−	0.596399i	0.917841	+	0.396949i	$0.129931\pi$
$608$	843.928			0.0562924
$609$		0			0
$610$	−5706.09			−0.378743
$611$	8985.55	−	5187.81i	0.594953	−	0.343496i
$612$	241.114	+	354.250i	0.0159255	+	0.0233982i
$613$	−3392.55	+	5876.06i	−0.223530	+	0.387165i	−0.955877	−	0.293766i	$-0.905091\pi$
$613$	−3392.55	+	5876.06i	−0.223530	+	0.387165i	0.732348	+	0.680931i	$0.238425\pi$
$614$	6238.26	+	10805.0i	0.410026	+	0.710186i
$615$	894.431	+	1424.73i	0.0586454	+	0.0934155i
$616$		0			0
$617$			3472.07i			0.226549i	0.993564	+	0.113274i	$0.0361339\pi$
$617$			3472.07i			0.226549i	−0.993564	+	0.113274i	$0.963866\pi$
$618$	−2157.54	+	4078.37i	−0.140436	+	0.265463i
$619$	−6373.89	−	3679.97i	−0.413875	−	0.238951i	0.278579	−	0.960413i	$-0.410137\pi$
$619$	−6373.89	−	3679.97i	−0.413875	−	0.238951i	−0.692453	+	0.721463i	$0.743470\pi$
$620$	−219.245	−	126.581i	−0.0142017	−	0.00819938i
$621$	23593.9	−	17369.9i	1.52462	−	1.12243i
$622$		−	13058.1i		−	0.841770i
$623$		0			0
$624$	20230.4	−	12700.5i	1.29786	−	0.814784i
$625$	−2475.57	−	4287.82i	−0.158437	−	0.274420i
$626$	12121.2	−	20994.5i	0.773898	−	1.34043i
$627$	−17600.0	+	651.583i	−1.12102	+	0.0415019i
$628$	−325.335	+	187.832i	−0.0206724	+	0.0119352i
$629$	11044.2			0.700094
$630$		0			0
$631$	−14566.0			−0.918957			−0.459479	−	0.888189i	$-0.651964\pi$
$631$	−14566.0			−0.918957			−0.459479	+	0.888189i	$0.651964\pi$
$632$	9015.84	−	5205.30i	0.567454	−	0.327620i
$633$	−4730.79	+	175.142i	−0.297049	+	0.0109973i
$634$	4783.11	−	8284.60i	0.299624	−	0.518964i
$635$	−3851.13	−	6670.35i	−0.240673	−	0.416858i
$636$	−104.133	+	65.3739i	−0.00649238	+	0.00407585i
$637$		0			0
$638$			701.949i			0.0435586i
$639$	616.730	+	8317.88i	0.0381807	+	0.514946i
$640$	7278.34	+	4202.15i	0.449534	+	0.259539i
$641$	−1809.13	−	1044.50i	−0.111476	−	0.0643609i	0.443225	−	0.896410i	$-0.353834\pi$
$641$	−1809.13	−	1044.50i	−0.111476	−	0.0643609i	−0.554701	+	0.832049i	$0.687168\pi$
$642$	−6245.65	+	11806.1i	−0.383951	+	0.725776i
$643$		−	9732.76i		−	0.596925i	−0.954421	−	0.298462i	$-0.903526\pi$
$643$		−	9732.76i		−	0.596925i	0.954421	−	0.298462i	$-0.0964737\pi$
$644$		0			0
$645$	907.272	+	1445.18i	0.0553857	+	0.0882232i
$646$	7684.76	+	13310.4i	0.468038	+	0.810666i
$647$	−9245.50	+	16013.7i	−0.561790	+	0.973049i	0.435550	+	0.900164i	$0.356554\pi$
$647$	−9245.50	+	16013.7i	−0.561790	+	0.973049i	−0.997340	+	0.0728845i	$0.976780\pi$
$648$	2395.68	+	16066.5i	0.145233	+	0.974002i
$649$	−27328.9	+	15778.4i	−1.65293	+	0.954321i
$650$	18831.9			1.13638
$651$		0			0
$652$	643.373			0.0386449
$653$	4843.40	−	2796.34i	0.290256	−	0.167579i	−0.347801	−	0.937568i	$-0.613072\pi$
$653$	4843.40	−	2796.34i	0.290256	−	0.167579i	0.638057	+	0.769989i	$0.279738\pi$
$654$	877.483	+	23701.8i	0.0524653	+	1.41715i
$655$	2450.77	−	4244.86i	0.146198	−	0.253222i
$656$	1912.78	+	3313.02i	0.113843	+	0.197183i
$657$	20113.3	+	9705.65i	1.19436	+	0.576337i
$658$		0			0
$659$		−	9543.49i		−	0.564130i	−0.959395	−	0.282065i	$-0.908981\pi$
$659$		−	9543.49i		−	0.564130i	0.959395	−	0.282065i	$-0.0910193\pi$
$660$	256.987	+	135.951i	0.0151564	+	0.00801804i
$661$	−5870.71	−	3389.46i	−0.345453	−	0.199447i	0.317228	−	0.948349i	$-0.397248\pi$
$661$	−5870.71	−	3389.46i	−0.345453	−	0.199447i	−0.662681	+	0.748902i	$0.730581\pi$
$662$	18631.4	+	10756.9i	1.09385	+	0.631537i
$663$	21652.3	+	11454.5i	1.26833	+	0.670975i
$664$		−	6121.18i		−	0.357753i
$665$		0			0
$666$	−11416.9	−	5509.22i	−0.664260	−	0.320538i
$667$	−597.870	−	1035.54i	−0.0347071	−	0.0601144i
$668$	−2.90052	+	5.02386i	−0.000168001	+	0.000290986i
$669$	590.218	+	15942.5i	0.0341093	+	0.921332i
$670$	9983.84	−	5764.17i	0.575686	−	0.332372i
$671$	15248.7			0.877300
$672$		0			0
$673$	−25094.5			−1.43733			−0.718663	−	0.695359i	$-0.755246\pi$
$673$	−25094.5			−1.43733			−0.718663	+	0.695359i	$0.755246\pi$
$674$	12694.0	−	7328.87i	0.725450	−	0.418839i
$675$	−5286.26	+	12077.2i	−0.301435	+	0.688667i
$676$	−315.057	+	545.695i	−0.0179254	+	0.0310477i
$677$	−13166.1	−	22804.3i	−0.747435	−	1.29460i	−0.949048	−	0.315130i	$-0.897952\pi$
$677$	−13166.1	−	22804.3i	−0.747435	−	1.29460i	0.201614	−	0.979465i	$-0.435381\pi$
$678$	6817.08	+	10858.8i	0.386148	+	0.615090i
$679$		0			0
$680$			8379.10i			0.472535i
$681$	−8146.36	+	15398.9i	−0.458398	+	0.866503i
$682$	20521.6	+	11848.2i	1.15222	+	0.665234i
$683$	−2032.33	−	1173.37i	−0.113858	−	0.0657359i	0.441990	−	0.897020i	$-0.354273\pi$
$683$	−2032.33	−	1173.37i	−0.113858	−	0.0657359i	−0.555848	+	0.831284i	$0.687606\pi$
$684$	−37.2422	−	502.288i	−0.00208186	−	0.0280782i
$685$		−	16920.2i		−	0.943777i
$686$		0			0
$687$	−19158.9	+	12027.8i	−1.06398	+	0.667959i
$688$	1940.24	+	3360.59i	0.107516	+	0.186223i
$689$	−3514.19	+	6086.75i	−0.194310	+	0.336556i
$690$	−17334.7	+	641.760i	−0.956406	+	0.0354078i
$691$	−9728.19	+	5616.58i	−0.535569	+	0.309211i	−0.743281	−	0.668979i	$-0.766732\pi$
$691$	−9728.19	+	5616.58i	−0.535569	+	0.309211i	0.207712	+	0.978190i	$0.433398\pi$
$692$	−330.010			−0.0181288
$693$		0			0
$694$	−8512.50			−0.465605
$695$	−3146.21	+	1816.46i	−0.171716	+	0.0991402i
$696$	662.515	−	24.5274i	0.0360813	−	0.00133579i
$697$	−1961.53	+	3397.47i	−0.106597	+	0.184632i
$698$	4117.86	+	7132.34i	0.223300	+	0.386767i
$699$	16210.4	−	10176.8i	0.877160	−	0.550673i
$700$		0			0
$701$		−	17277.2i		−	0.930887i	−0.885078	−	0.465443i	$-0.845895\pi$
$701$		−	17277.2i		−	0.930887i	0.885078	−	0.465443i	$-0.154105\pi$
$702$	−16669.2	−	22642.1i	−0.896208	−	1.21734i
$703$	−11241.8	−	6490.46i	−0.603119	−	0.348211i
$704$	−18353.2	−	10596.2i	−0.982547	−	0.567274i
$705$	2010.99	−	3801.35i	0.107430	−	0.203074i
$706$		−	36310.8i		−	1.93566i
$707$		0			0
$708$	−479.832	−	764.319i	−0.0254706	−	0.0405718i
$709$	−9419.56	−	16315.2i	−0.498955	−	0.864215i	0.501044	−	0.865422i	$-0.332949\pi$
$709$	−9419.56	−	16315.2i	−0.498955	−	0.864215i	−0.999999	+	0.00120627i	$0.999616\pi$
$710$	2469.14	−	4276.68i	0.130514	−	0.226057i
$711$	−7097.75	−	10428.2i	−0.374383	−	0.550053i
$712$	10441.4	−	6028.32i	0.549588	−	0.317305i
$713$	−40365.7			−2.12020
$714$		0			0
$715$	16619.1			0.869259
$716$	−349.104	+	201.555i	−0.0182215	+	0.0105202i
$717$	−872.276	−	23561.2i	−0.0454334	−	1.22721i
$718$	−9457.43	+	16380.7i	−0.491571	+	0.851426i
$719$	5259.71	+	9110.08i	0.272815	+	0.472530i	0.969582	−	0.244768i	$-0.0787120\pi$
$719$	5259.71	+	9110.08i	0.272815	+	0.472530i	−0.696767	+	0.717298i	$0.745379\pi$
$720$	4302.74	−	8916.71i	0.222714	−	0.461536i
$721$		0			0
$722$			1618.38i			0.0834209i
$723$	10201.6	+	5396.86i	0.524760	+	0.277609i
$724$	−416.680	−	240.571i	−0.0213892	−	0.0123491i
$725$	465.966	+	269.026i	0.0238697	+	0.0137812i
$726$	−6510.96	−	3444.43i	−0.332843	−	0.176081i
$727$			1692.44i			0.0863401i	0.999068	+	0.0431700i	$0.0137457\pi$
$727$			1692.44i			0.0863401i	−0.999068	+	0.0431700i	$0.986254\pi$
$728$		0			0
$729$	19199.8	−	4334.38i	0.975453	−	0.220209i
$730$	−6611.23	−	11451.0i	−0.335195	−	0.580575i
$731$	−1989.69	+	3446.24i	−0.100672	+	0.174369i
$732$	16.1333	+	435.780i	0.000814625	+	0.0220040i
$733$	−26354.1	+	15215.6i	−1.32798	+	0.766712i	−0.984988	−	0.172625i	$-0.944775\pi$
$733$	−26354.1	+	15215.6i	−1.32798	+	0.766712i	−0.342996	+	0.939337i	$0.611442\pi$
$734$	29517.6			1.48435
$735$		0			0
$736$	−2221.27			−0.111246
$737$	−26680.3	+	15403.9i	−1.33349	+	0.769890i
$738$	3722.52	−	2533.66i	0.185674	−	0.126376i
$739$	−2456.69	+	4255.12i	−0.122288	+	0.211809i	−0.920670	−	0.390343i	$-0.872357\pi$
$739$	−2456.69	+	4255.12i	−0.122288	+	0.211809i	0.798382	+	0.602152i	$0.205690\pi$
$740$	107.142	+	185.575i	0.00532244	+	0.00921873i
$741$	−15308.2	−	24384.2i	−0.758920	−	1.20887i
$742$		0			0
$743$		−	27101.5i		−	1.33816i	−0.743188	−	0.669082i	$-0.766687\pi$
$743$		−	27101.5i		−	1.33816i	0.743188	−	0.669082i	$-0.233313\pi$
$744$	10465.5	−	19782.8i	0.515704	−	0.974827i
$745$	−1907.88	−	1101.51i	−0.0938244	−	0.0541696i
$746$	−10962.3	−	6329.11i	−0.538015	−	0.310623i
$747$	−7396.70	+	548.429i	−0.362291	+	0.0268621i
$748$			678.009i			0.0331423i
$749$		0			0
$750$	15404.6	−	9670.84i	0.749994	−	0.470839i
$751$	−8308.45	−	14390.7i	−0.403701	−	0.699231i	0.590468	−	0.807061i	$-0.298943\pi$
$751$	−8308.45	−	14390.7i	−0.403701	−	0.699231i	−0.994169	+	0.107830i	$0.965610\pi$
$752$	4889.92	−	8469.59i	0.237124	−	0.410710i
$753$	3386.31	−	125.367i	0.163883	−	0.00606723i
$754$	−993.767	+	573.751i	−0.0479985	+	0.0277119i
$755$	−3927.98			−0.189343
$756$		0			0
$757$	−29748.9			−1.42833			−0.714163	−	0.699980i	$-0.753192\pi$
$757$	−29748.9			−1.42833			−0.714163	+	0.699980i	$0.753192\pi$
$758$	9538.95	−	5507.31i	0.457085	−	0.263898i
$759$	46324.3	−	1715.01i	2.21537	−	0.0820168i
$760$	4924.26	−	8529.06i	0.235028	−	0.407081i
$761$	2378.08	+	4118.96i	0.113279	+	0.196205i	0.917091	−	0.398679i	$-0.130531\pi$
$761$	2378.08	+	4118.96i	0.113279	+	0.196205i	−0.803811	+	0.594884i	$0.797198\pi$
$762$	−17461.6	+	10962.2i	−0.830139	+	0.521153i
$763$		0			0
$764$			793.069i			0.0375553i
$765$	10125.1	−	750.728i	0.478529	−	0.0354806i
$766$	5285.46	+	3051.56i	0.249310	+	0.143939i
$767$	−44675.6	−	25793.5i	−2.10319	−	1.21427i
$768$	876.744	−	1657.30i	0.0411937	−	0.0778679i
$769$			9226.71i			0.432671i	0.976319	+	0.216335i	$0.0694104\pi$
$769$			9226.71i			0.432671i	−0.976319	+	0.216335i	$0.930590\pi$
$770$		0			0
$771$	−18990.9	−	30250.4i	−0.887083	−	1.41302i
$772$	−49.9535	−	86.5220i	−0.00232884	−	0.00403367i
$773$	2372.51	−	4109.31i	0.110392	−	0.191205i	−0.805536	−	0.592547i	$-0.798123\pi$
$773$	2372.51	−	4109.31i	0.110392	−	0.191205i	0.915928	+	0.401342i	$0.131456\pi$
$774$	3775.96	−	2570.04i	0.175354	−	0.119352i
$775$	15730.0	−	9081.74i	0.729083	−	0.420936i
$776$	−923.973			−0.0427432
$777$		0			0
$778$	20715.1			0.954590
$779$	3993.27	−	2305.52i	0.183663	−	0.106038i
$780$	17.5833	+	474.945i	0.000807158	+	0.0218023i
$781$	−6598.40	+	11428.8i	−0.302317	+	0.523628i
$782$	−20226.7	−	35033.8i	−0.924945	−	1.60205i
$783$	−88.9968	−	798.372i	−0.00406192	−	0.0364387i
$784$		0			0
$785$			8900.65i			0.404685i
$786$	−11597.5	−	6135.34i	−0.526299	−	0.278423i
$787$	−15230.6	−	8793.41i	−0.689852	−	0.398286i	0.113705	−	0.993515i	$-0.463728\pi$
$787$	−15230.6	−	8793.41i	−0.689852	−	0.398286i	−0.803557	+	0.595228i	$0.797062\pi$
$788$	−900.101	−	519.673i	−0.0406913	−	0.0234931i
$789$	−15090.9	−	7983.39i	−0.680925	−	0.360224i
$790$			7468.65i			0.336358i
$791$		0			0
$792$	−11169.9	+	23147.7i	−0.501141	+	1.03853i
$793$	12463.8	+	21587.9i	0.558137	+	0.966721i
$794$	−165.651	+	286.916i	−0.00740395	+	0.0128240i
$795$	107.775	+	2911.14i	0.00480805	+	0.129871i
$796$	321.264	−	185.482i	0.0143052	−	0.00825909i
$797$	14578.6			0.647930			0.323965	−	0.946069i	$-0.394984\pi$
$797$	14578.6			0.647930			0.323965	+	0.946069i	$0.394984\pi$
$798$		0			0
$799$	10029.1			0.444061
$800$	865.603	−	499.756i	0.0382546	−	0.0220863i
$801$	−8220.00	−	12077.0i	−0.362596	−	0.532735i
$802$	12778.3	−	22132.6i	0.562614	−	0.974476i
$803$	17667.5	+	30601.0i	0.776429	+	1.34481i
$804$	−468.444	−	746.179i	−0.0205482	−	0.0327310i
$805$		0			0
$806$			38737.3i			1.69288i
$807$	3055.68	−	5776.10i	0.133290	−	0.251956i
$808$	24385.8	+	14079.2i	1.06174	+	0.612999i
$809$	39237.2	+	22653.6i	1.70520	+	0.984497i	0.940300	+	0.340347i	$0.110545\pi$
$809$	39237.2	+	22653.6i	1.70520	+	0.984497i	0.764899	+	0.644150i	$0.222789\pi$
$810$	−10841.4	−	4274.71i	−0.470281	−	0.185430i
$811$			36799.2i			1.59334i	0.604417	+	0.796668i	$0.293406\pi$
$811$			36799.2i			1.59334i	−0.604417	+	0.796668i	$0.706594\pi$
$812$		0			0
$813$	−1631.62	+	1024.31i	−0.0703854	+	0.0441873i
$814$	−10028.6	−	17370.0i	−0.431821	−	0.747936i
$815$	7621.74	−	13201.2i	0.327580	−	0.567386i
$816$	23073.1	−	854.205i	0.989852	−	0.0366460i
$817$	4050.60	−	2338.62i	0.173455	−	0.100144i
$818$	19377.9			0.828279
$819$		0			0
$820$	−76.1168			−0.00324160
$821$	−3337.88	+	1927.12i	−0.141891	+	0.0819210i	−0.569265	−	0.822154i	$-0.692772\pi$
$821$	−3337.88	+	1927.12i	−0.141891	+	0.0819210i	0.427374	+	0.904075i	$0.359439\pi$
$822$	−45260.9	+	1675.64i	−1.92050	+	0.0711004i
$823$	−13143.5	+	22765.2i	−0.556688	+	0.964212i	0.441082	+	0.897467i	$0.354595\pi$
$823$	−13143.5	+	22765.2i	−0.556688	+	0.964212i	−0.997770	+	0.0667452i	$0.978739\pi$
$824$	3447.40	+	5971.07i	0.145747	+	0.252442i
$825$	−17666.2	+	11090.7i	−0.745525	+	0.468034i
$826$		0			0
$827$		−	17592.8i		−	0.739735i	−0.929085	−	0.369868i	$-0.879403\pi$
$827$		−	17592.8i		−	0.739735i	0.929085	−	0.369868i	$-0.120597\pi$
$828$	98.0237	+	1322.05i	0.00411420	+	0.0554886i
$829$	25637.3	+	14801.7i	1.07409	+	0.620127i	0.929296	−	0.369335i	$-0.120414\pi$
$829$	25637.3	+	14801.7i	1.07409	+	0.620127i	0.144795	+	0.989462i	$0.453748\pi$
$830$	3803.05	+	2195.69i	0.159043	+	0.0918235i
$831$	−3742.31	+	7074.04i	−0.156221	+	0.295302i
$832$		−	34644.2i		−	1.44359i
$833$		0			0
$834$	5170.55	+	8236.11i	0.214678	+	0.341958i
$835$	68.7223	+	119.030i	0.00284818	+	0.00493320i
$836$	398.455	−	690.144i	0.0164843	−	0.0285516i
$837$	−24842.7	−	10873.8i	−1.02591	−	0.449050i
$838$	2207.03	−	1274.23i	0.0909793	−	0.0525269i
$839$	−29706.3			−1.22238			−0.611189	−	0.791485i	$-0.709308\pi$
$839$	−29706.3			−1.22238			−0.611189	+	0.791485i	$0.709308\pi$
$840$		0			0
$841$	24356.2			0.998656
$842$	−37218.7	+	21488.2i	−1.52333	+	0.879493i
$843$	−727.197	−	19642.4i	−0.0297105	−	0.802516i
$844$	107.102	−	185.507i	0.00436803	−	0.00756565i
$845$	7464.67	+	12929.2i	0.303896	+	0.526364i
$846$	−10367.6	−	5002.88i	−0.421332	−	0.203313i
$847$		0			0
$848$			6624.80i			0.268274i
$849$	42545.6	+	22507.5i	1.71986	+	0.909843i
$850$	15764.3	+	9101.50i	0.636129	+	0.367269i
$851$	29589.1	+	17083.3i	1.19189	+	0.688141i
$852$	−333.595	−	176.479i	−0.0134141	−	0.00709632i
$853$			12651.1i			0.507813i	0.967229	+	0.253906i	$0.0817155\pi$
$853$			12651.1i			0.507813i	−0.967229	+	0.253906i	$0.918284\pi$
$854$		0			0
$855$	−10747.5	−	5186.21i	−0.429892	−	0.207444i
$856$	9979.53	+	17285.0i	0.398473	+	0.690176i
$857$	−20438.9	+	35401.2i	−0.814678	+	1.41106i	0.0948815	+	0.995489i	$0.469753\pi$
$857$	−20438.9	+	35401.2i	−0.814678	+	1.41106i	−0.909559	+	0.415575i	$0.863581\pi$
$858$	−1645.82	−	44455.5i	−0.0654865	−	1.76887i
$859$	33811.5	−	19521.1i	1.34299	−	0.775378i	0.355749	−	0.934582i	$-0.384226\pi$
$859$	33811.5	−	19521.1i	1.34299	−	0.775378i	0.987246	+	0.159204i	$0.0508926\pi$
$860$	−77.2096			−0.00306142
$861$		0			0
$862$	−3143.40			−0.124205
$863$	−18096.8	+	10448.2i	−0.713815	+	0.412121i	−0.812472	−	0.583000i	$-0.801879\pi$
$863$	−18096.8	+	10448.2i	−0.713815	+	0.412121i	0.0986569	+	0.995122i	$0.468545\pi$
$864$	−1367.06	−	598.373i	−0.0538292	−	0.0235614i
$865$	−3909.47	+	6771.40i	−0.153672	+	0.266167i
$866$	18205.6	+	31533.1i	0.714379	+	1.23734i
$867$	−984.336	−	1567.94i	−0.0385580	−	0.0614186i
$868$		0			0
$869$		−	19958.8i		−	0.779121i
$870$	−222.408	+	420.414i	−0.00866706	+	0.0163832i
$871$	−43615.3	−	25181.3i	−1.69673	−	0.979605i
$872$	30694.7	+	17721.6i	1.19203	+	0.688221i
$873$	82.7838	+	1116.51i	0.00320940	+	0.0432854i
$874$			47547.7i			1.84019i
$875$		0			0
$876$	−855.831	+	537.282i	−0.0330089	+	0.0207227i
$877$	15775.9	+	27324.6i	0.607427	+	1.05209i	0.991663	+	0.128859i	$0.0411316\pi$
$877$	15775.9	+	27324.6i	0.607427	+	1.05209i	−0.384236	+	0.923235i	$0.625535\pi$
$878$	−19291.8	+	33414.4i	−0.741535	+	1.28438i
$879$	37991.0	−	1406.49i	1.45780	−	0.0539702i
$880$	13566.1	−	7832.41i	0.519675	−	0.300035i
$881$	43754.6			1.67325			0.836623	−	0.547779i	$-0.184527\pi$
$881$	43754.6			1.67325			0.836623	+	0.547779i	$0.184527\pi$
$882$		0			0
$883$	11781.7			0.449020			0.224510	−	0.974472i	$-0.427922\pi$
$883$	11781.7			0.449020			0.224510	+	0.974472i	$0.427922\pi$
$884$	−959.875	+	554.184i	−0.0365205	+	0.0210851i
$885$	−21367.2	+	791.052i	−0.811584	+	0.0300462i
$886$	3267.10	−	5658.78i	0.123883	−	0.214572i
$887$	−17357.8	−	30064.7i	−0.657068	−	1.13808i	−0.981371	−	0.192122i	$-0.938463\pi$
$887$	−17357.8	−	30064.7i	−0.657068	−	1.13808i	0.324303	−	0.945953i	$-0.394870\pi$
$888$	−16043.8	+	10072.2i	−0.606301	+	0.380630i
$889$		0			0
$890$			8649.53i			0.325767i
$891$	28971.9	+	11423.5i	1.08933	+	0.429520i
$892$	−625.147	−	360.929i	−0.0234658	−	0.0135480i
$893$	−10208.6	−	5893.94i	−0.382551	−	0.220866i
$894$	−2757.57	+	5212.59i	−0.103162	+	0.195006i
$895$			9550.91i			0.356706i
$896$		0			0
$897$	40292.0	+	64180.7i	1.49979	+	2.38900i
$898$	2418.99	+	4189.81i	0.0898917	+	0.155697i
$899$	−553.386	+	958.493i	−0.0205300	+	0.0355590i
$900$	−335.643	−	493.135i	−0.0124312	−	0.0182643i
$901$	−5883.48	+	3396.83i	−0.217544	+	0.125599i
$902$	7124.64			0.262998
$903$		0			0
$904$	19159.6			0.704911
$905$	−9872.43	+	5699.85i	−0.362619	+	0.209358i
$906$	388.995	+	10507.2i	0.0142643	+	0.385297i
$907$	1491.75	−	2583.79i	0.0546117	−	0.0945902i	−0.837427	−	0.546549i	$-0.815941\pi$
$907$	1491.75	−	2583.79i	0.0546117	−	0.0945902i	0.892039	+	0.451959i	$0.149275\pi$
$908$	−394.131	−	682.656i	−0.0144050	−	0.0249501i
$909$	14828.1	−	30728.7i	0.541053	−	1.12124i
$910$		0			0
$911$			16802.5i			0.611076i	0.952180	+	0.305538i	$0.0988363\pi$
$911$			16802.5i			0.611076i	−0.952180	+	0.305538i	$0.901164\pi$
$912$	−23988.0	−	12690.2i	−0.870968	−	0.460760i
$913$	−10163.1	−	5867.65i	−0.368399	−	0.212695i
$914$	5178.20	+	2989.63i	0.187396	+	0.108193i
$915$	9132.80	+	4831.45i	0.329969	+	0.174560i
$916$		−	1023.57i		−	0.0369212i
$917$		0			0
$918$	−3010.88	−	27010.0i	−0.108250	−	0.971093i
$919$	−6452.36	−	11175.8i	−0.231604	−	0.401149i	0.726676	−	0.686980i	$-0.241064\pi$
$919$	−6452.36	−	11175.8i	−0.231604	−	0.401149i	−0.958280	+	0.285830i	$0.907731\pi$
$920$	−12960.9	+	22449.0i	−0.464467	+	0.804480i
$921$	−835.795	−	22575.8i	−0.0299027	−	0.807707i
$922$	35111.5	−	20271.7i	1.25416	−	0.724090i
$923$	−21573.3			−0.769333
$924$		0			0
$925$	−15374.1			−0.546482
$926$	40115.2	−	23160.5i	1.42361	−	0.821924i
$927$	6906.45	−	4700.75i	0.244701	−	0.166551i
$928$	−30.4521	+	52.7446i	−0.00107720	+	0.00186576i
$929$	12362.8	+	21413.0i	0.436610	+	0.756231i	0.997426	−	0.0717096i	$-0.0228455\pi$
$929$	12362.8	+	21413.0i	0.436610	+	0.756231i	−0.560815	+	0.827941i	$0.689512\pi$
$930$	8536.89	+	13598.3i	0.301006	+	0.479469i
$931$		0			0
$932$			866.050i			0.0304382i
$933$	−11056.5	+	20899.9i	−0.387967	+	0.733368i
$934$	15531.1	+	8966.89i	0.544104	+	0.314139i
$935$	13911.9	+	8032.05i	0.486597	+	0.280937i
$936$	−41900.6	+	3106.73i	−1.46321	+	0.108490i
$937$			42100.7i			1.46785i	0.679233	+	0.733923i	$0.262313\pi$
$937$			42100.7i			1.46785i	−0.679233	+	0.733923i	$0.737687\pi$
$938$		0			0
$939$	−37176.8	+	23339.2i	−1.29203	+	0.811126i
$940$	97.2945	+	168.519i	0.00337595	+	0.00584732i
$941$	26092.7	−	45193.8i	0.903928	−	1.56565i	0.0815788	−	0.996667i	$-0.474004\pi$
$941$	26092.7	−	45193.8i	0.903928	−	1.56565i	0.822349	−	0.568983i	$-0.192663\pi$
$942$	23808.9	−	881.447i	0.823499	−	0.0304874i
$943$	−10510.5	+	6068.26i	−0.362959	+	0.209554i
$944$	−48624.8			−1.67648
$945$		0			0
$946$	7226.92			0.248380
$947$	18079.0	−	10437.9i	0.620369	−	0.358170i	−0.156644	−	0.987655i	$-0.550067\pi$
$947$	18079.0	−	10437.9i	0.620369	−	0.358170i	0.777013	+	0.629485i	$0.216734\pi$
$948$	570.388	−	21.1168i	0.0195415	−	0.000723460i
$949$	−28881.7	+	50024.6i	−0.987925	+	1.71114i
$950$	−10697.6	−	18528.8i	−0.365343	−	0.632793i
$951$	−14670.2	+	9209.85i	−0.500226	+	0.314038i
$952$		0			0
$953$			3810.33i			0.129516i	0.997901	+	0.0647579i	$0.0206275\pi$
$953$			3810.33i			0.129516i	−0.997901	+	0.0647579i	$0.979372\pi$
$954$	7776.52	−	576.591i	0.263914	−	0.0195679i
$955$	16272.8	+	9395.11i	0.551388	+	0.318344i
$956$	923.898	+	533.413i	0.0312563	+	0.0180458i
$957$	594.352	−	1123.49i	0.0200759	−	0.0379492i
$958$			30488.1i			1.02821i
$959$		0			0
$960$	−7634.85	−	12161.5i	−0.256681	−	0.408864i
$961$	3785.65	+	6556.94i	0.127074	+	0.220098i
$962$	16394.1	−	28395.5i	0.549447	−	0.951671i
$963$	19992.8	−	13607.7i	0.669012	−	0.455350i
$964$	−452.250	+	261.107i	−0.0151100	+	0.00872374i
$965$	−2367.10			−0.0789634
$966$		0			0
$967$	−141.303			−0.00469905			−0.00234953	−	0.999997i	$-0.500748\pi$
$967$	−141.303			−0.00469905			−0.00234953	+	0.999997i	$0.500748\pi$
$968$	−9532.58	+	5503.64i	−0.316517	+	0.182741i
$969$	−1029.59	−	27810.6i	−0.0341335	−	0.921986i
$970$	331.433	−	574.059i	0.0109708	−	0.0190020i
$971$	12141.6	+	21029.9i	0.401280	+	0.695037i	0.993881	−	0.110459i	$-0.0352321\pi$
$971$	12141.6	+	21029.9i	0.401280	+	0.695037i	−0.592601	+	0.805496i	$0.701899\pi$
$972$	−295.811	+	840.054i	−0.00976148	+	0.0277209i
$973$		0			0
$974$		−	11393.1i		−	0.374803i
$975$	−30141.2	−	15945.3i	−0.990041	−	0.523752i
$976$	20348.3	+	11748.1i	0.667350	+	0.385295i
$977$	−27311.1	−	15768.1i	−0.894331	−	0.516342i	−0.0189740	−	0.999820i	$-0.506040\pi$
$977$	−27311.1	−	15768.1i	−0.894331	−	0.516342i	−0.875357	+	0.483478i	$0.839373\pi$
$978$	−36067.6	−	19080.5i	−1.17926	−	0.623853i
$979$		−	23114.6i		−	0.754591i
$980$		0			0
$981$	18664.3	−	38678.6i	0.607447	−	1.25883i
$982$	6004.38	+	10399.9i	0.195120	+	0.337957i
$983$	8325.82	−	14420.8i	0.270145	−	0.467905i	−0.698754	−	0.715362i	$-0.746262\pi$
$983$	8325.82	−	14420.8i	0.270145	−	0.467905i	0.968899	+	0.247457i	$0.0795950\pi$
$984$	−248.949	−	6724.39i	−0.00806524	−	0.217851i
$985$	−21326.1	+	12312.6i	−0.689855	+	0.398288i
$986$	−1109.18			−0.0358250
$987$		0			0
$988$	1302.74			0.0419490
$989$	−10661.4	+	6155.38i	−0.342784	+	0.197907i
$990$	−10374.8	−	15242.9i	−0.333064	−	0.489346i
$991$	6310.29	−	10929.7i	0.202274	−	0.350348i	−0.746987	−	0.664839i	$-0.768500\pi$
$991$	6310.29	−	10929.7i	0.202274	−	0.350348i	0.949261	+	0.314491i	$0.101834\pi$
$992$	1028.00	+	1780.55i	0.0329022	+	0.0569883i
$993$	−20712.3	−	32992.3i	−0.661917	−	1.05436i
$994$		0			0
$995$		−	8789.27i		−	0.280039i
$996$	156.934	−	296.651i	0.00499263	−	0.00943749i
$997$	36131.9	+	20860.8i	1.14775	+	0.662655i	0.948338	−	0.317261i	$-0.102763\pi$
$997$	36131.9	+	20860.8i	1.14775	+	0.662655i	0.199413	+	0.979916i	$0.436096\pi$
$998$	−45882.9	−	26490.5i	−1.45531	−	0.840222i
$999$	13608.4	+	18484.6i	0.430983	+	0.585413i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.4.g.e.80.17		48
3.2	odd	2	inner	147.4.g.e.80.7		48
7.2	even	3	inner	147.4.g.e.68.8		48
7.3	odd	6		147.4.c.b.146.17	yes	24
7.4	even	3		147.4.c.b.146.18	yes	24
7.5	odd	6	inner	147.4.g.e.68.7		48
7.6	odd	2	inner	147.4.g.e.80.18		48
21.2	odd	6	inner	147.4.g.e.68.18		48
21.5	even	6	inner	147.4.g.e.68.17		48
21.11	odd	6		147.4.c.b.146.7	✓	24
21.17	even	6		147.4.c.b.146.8	yes	24
21.20	even	2	inner	147.4.g.e.80.8		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.4.c.b.146.7	✓	24	21.11	odd	6
147.4.c.b.146.8	yes	24	21.17	even	6
147.4.c.b.146.17	yes	24	7.3	odd	6
147.4.c.b.146.18	yes	24	7.4	even	3
147.4.g.e.68.7		48	7.5	odd	6	inner
147.4.g.e.68.8		48	7.2	even	3	inner
147.4.g.e.68.17		48	21.5	even	6	inner
147.4.g.e.68.18		48	21.2	odd	6	inner
147.4.g.e.80.7		48	3.2	odd	2	inner
147.4.g.e.80.8		48	21.20	even	2	inner
147.4.g.e.80.17		48	1.1	even	1	trivial
147.4.g.e.80.18		48	7.6	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	147.g (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.48522 - 1.43484i) q^{2} +(-5.19260 + 0.192239i) q^{3} +(0.117558 - 0.203616i) q^{4} +(-2.78530 - 4.82427i) q^{5} +(-12.6289 + 7.92832i) q^{6} +22.2828i q^{8} +(26.9261 - 1.99644i) q^{9} +O(q^{10})\)	\(q+(2.48522 - 1.43484i) q^{2} +(-5.19260 + 0.192239i) q^{3} +(0.117558 - 0.203616i) q^{4} +(-2.78530 - 4.82427i) q^{5} +(-12.6289 + 7.92832i) q^{6} +22.2828i q^{8} +(26.9261 - 1.99644i) q^{9} +(-13.8442 - 7.99293i) q^{10} +(36.9964 + 21.3599i) q^{11} +(-0.571286 + 1.07989i) q^{12} +69.8357i q^{13} +(15.3903 + 24.5151i) q^{15} +(32.9128 + 57.0067i) q^{16} +(-33.7517 + 58.4597i) q^{17} +(64.0528 - 43.5963i) q^{18} +(68.7116 - 39.6707i) q^{19} -1.30973 q^{20} +122.593 q^{22} +(-180.853 + 104.416i) q^{23} +(-4.28362 - 115.706i) q^{24} +(46.9843 - 81.3791i) q^{25} +(100.203 + 173.557i) q^{26} +(-139.432 + 15.5429i) q^{27} +5.72587i q^{29} +(73.4237 + 38.8427i) q^{30} +(167.397 + 96.6466i) q^{31} +(9.21163 + 5.31834i) q^{32} +(-196.214 - 103.801i) q^{33} +193.714i q^{34} +(2.75886 - 5.71727i) q^{36} +(-81.8043 - 141.689i) q^{37} +(113.842 - 197.181i) q^{38} +(-13.4251 - 362.629i) q^{39} +(107.498 - 62.0642i) q^{40} +58.1164 q^{41} +58.9508 q^{43} +(8.69842 - 5.02203i) q^{44} +(-84.6285 - 124.338i) q^{45} +(-299.640 + 518.992i) q^{46} +(-74.2859 - 128.667i) q^{47} +(-181.862 - 289.685i) q^{48} -269.660i q^{50} +(164.021 - 310.046i) q^{51} +(14.2196 + 8.20971i) q^{52} +(87.1582 + 50.3208i) q^{53} +(-324.219 + 238.692i) q^{54} -237.975i q^{55} +(-349.165 + 219.203i) q^{57} +(8.21573 + 14.2301i) q^{58} +(-369.345 + 639.725i) q^{59} +(6.80090 - 0.251781i) q^{60} +(309.124 - 178.473i) q^{61} +554.692 q^{62} -496.081 q^{64} +(336.907 - 194.513i) q^{65} +(-636.573 + 23.5670i) q^{66} +(-360.579 + 624.542i) q^{67} +(7.93554 + 13.7448i) q^{68} +(919.024 - 576.955i) q^{69} +308.915i q^{71} +(44.4862 + 599.989i) q^{72} +(716.319 + 413.567i) q^{73} +(-406.604 - 234.753i) q^{74} +(-228.326 + 431.601i) q^{75} -18.6543i q^{76} +(-553.680 - 881.950i) q^{78} +(-233.602 - 404.610i) q^{79} +(183.344 - 317.561i) q^{80} +(721.028 - 107.512i) q^{81} +(144.432 - 83.3880i) q^{82} -274.704 q^{83} +376.034 q^{85} +(146.506 - 84.5852i) q^{86} +(-1.10073 - 29.7321i) q^{87} +(-475.958 + 824.384i) q^{88} +(-270.537 - 468.584i) q^{89} +(-388.727 - 187.579i) q^{90} +49.0993i q^{92} +(-887.804 - 469.667i) q^{93} +(-369.234 - 213.178i) q^{94} +(-382.764 - 220.989i) q^{95} +(-48.8547 - 25.8451i) q^{96} +41.4658i q^{97} +(1038.81 + 501.277i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 96 q^{4} + 64 q^{9}+O(q^{10}) \) 48 * q + 96 * q^4 + 64 * q^9	\( 48 q + 96 q^{4} + 64 q^{9} + 512 q^{15} - 864 q^{16} + 32 q^{18} - 768 q^{22} - 744 q^{25} + 1704 q^{30} + 1168 q^{36} - 432 q^{37} + 2368 q^{39} - 1248 q^{43} - 3744 q^{46} + 2160 q^{51} + 4064 q^{57} - 6384 q^{58} + 5832 q^{60} - 7008 q^{64} - 3792 q^{67} + 7472 q^{72} + 4496 q^{78} - 2784 q^{79} + 1968 q^{81} - 7488 q^{85} + 624 q^{88} + 3232 q^{93} + 2640 q^{99}+O(q^{100}) \) 48 * q + 96 * q^4 + 64 * q^9 + 512 * q^15 - 864 * q^16 + 32 * q^18 - 768 * q^22 - 744 * q^25 + 1704 * q^30 + 1168 * q^36 - 432 * q^37 + 2368 * q^39 - 1248 * q^43 - 3744 * q^46 + 2160 * q^51 + 4064 * q^57 - 6384 * q^58 + 5832 * q^60 - 7008 * q^64 - 3792 * q^67 + 7472 * q^72 + 4496 * q^78 - 2784 * q^79 + 1968 * q^81 - 7488 * q^85 + 624 * q^88 + 3232 * q^93 + 2640 * q^99

Introduction

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