LMFDB - Embedded newform 207.2.i.e.154.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,2,Mod(55,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("207.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	207.i (of order $11$, degree $10$, 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:	$1.65290332184$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			154.3
Character	$\chi$	$=$	207.154
Dual form			207.2.i.e.82.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.858969 - 0.991303i) q^{2} +(0.0397758 + 0.276647i) q^{4} +(-1.24955 - 2.73614i) q^{5} +(3.30268 - 0.969753i) q^{7} +(2.51532 + 1.61650i) q^{8} +O(q^{10})$	\(q+(0.858969 - 0.991303i) q^{2} +(0.0397758 + 0.276647i) q^{4} +(-1.24955 - 2.73614i) q^{5} +(3.30268 - 0.969753i) q^{7} +(2.51532 + 1.61650i) q^{8} +(-3.78567 - 1.11157i) q^{10} +(-0.569092 - 0.656767i) q^{11} +(-3.98313 - 1.16955i) q^{13} +(1.87558 - 4.10694i) q^{14} +(3.22668 - 0.947439i) q^{16} +(0.634803 - 4.41515i) q^{17} +(1.01094 + 7.03126i) q^{19} +(0.707242 - 0.454517i) q^{20} -1.13989 q^{22} +(-0.157683 + 4.79324i) q^{23} +(-2.65076 + 3.05915i) q^{25} +(-4.58077 + 2.94388i) q^{26} +(0.399646 + 0.875102i) q^{28} +(-1.24846 + 8.68321i) q^{29} +(-1.28761 - 0.827495i) q^{31} +(-0.651736 + 1.42710i) q^{32} +(-3.83148 - 4.42176i) q^{34} +(-6.78024 - 7.82482i) q^{35} +(0.503213 - 1.10188i) q^{37} +(7.83847 + 5.03748i) q^{38} +(1.27994 - 8.90216i) q^{40} +(1.29601 + 2.83786i) q^{41} +(-0.478538 + 0.307537i) q^{43} +(0.159056 - 0.183561i) q^{44} +(4.61611 + 4.27355i) q^{46} -1.54648 q^{47} +(4.07847 - 2.62107i) q^{49} +(0.755615 + 5.25542i) q^{50} +(0.165121 - 1.14844i) q^{52} +(-10.2463 + 3.00858i) q^{53} +(-1.08590 + 2.37778i) q^{55} +(9.87489 + 2.89953i) q^{56} +(7.53531 + 8.69621i) q^{58} +(-9.17058 - 2.69273i) q^{59} +(4.38624 + 2.81886i) q^{61} +(-1.92631 + 0.565617i) q^{62} +(3.64887 + 7.98991i) q^{64} +(1.77707 + 12.3598i) q^{65} +(8.41554 - 9.71205i) q^{67} +1.24669 q^{68} -13.5808 q^{70} +(5.17277 - 5.96970i) q^{71} +(-1.68880 - 11.7459i) q^{73} +(-0.660056 - 1.44532i) q^{74} +(-1.90496 + 0.559348i) q^{76} +(-2.51643 - 1.61721i) q^{77} +(0.640855 + 0.188172i) q^{79} +(-6.62423 - 7.64477i) q^{80} +(3.92641 + 1.15290i) q^{82} +(4.42633 - 9.69231i) q^{83} +(-12.8737 + 3.78005i) q^{85} +(-0.106186 + 0.738541i) q^{86} +(-0.369786 - 2.57192i) q^{88} +(8.58265 - 5.51573i) q^{89} -14.2892 q^{91} +(-1.33231 + 0.147032i) q^{92} +(-1.32838 + 1.53303i) q^{94} +(17.9753 - 11.5520i) q^{95} +(-2.74809 - 6.01749i) q^{97} +(0.905001 - 6.29442i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{4} + 8 q^{7}+O(q^{10}) $ 40 * q - 4 * q^4 + 8 * q^7	$ 40 q - 4 q^{4} + 8 q^{7} - 56 q^{16} - 14 q^{19} - 28 q^{22} - 48 q^{25} - 64 q^{28} - 22 q^{31} - 10 q^{34} + 52 q^{37} + 6 q^{40} + 68 q^{43} + 84 q^{46} + 4 q^{49} + 110 q^{52} + 50 q^{55} + 18 q^{58} + 36 q^{61} + 116 q^{64} - 18 q^{67} + 96 q^{70} + 14 q^{73} + 34 q^{76} - 36 q^{79} - 72 q^{82} - 238 q^{85} - 160 q^{88} - 176 q^{91} - 206 q^{94} - 92 q^{97}+O(q^{100}) $ 40 * q - 4 * q^4 + 8 * q^7 - 56 * q^16 - 14 * q^19 - 28 * q^22 - 48 * q^25 - 64 * q^28 - 22 * q^31 - 10 * q^34 + 52 * q^37 + 6 * q^40 + 68 * q^43 + 84 * q^46 + 4 * q^49 + 110 * q^52 + 50 * q^55 + 18 * q^58 + 36 * q^61 + 116 * q^64 - 18 * q^67 + 96 * q^70 + 14 * q^73 + 34 * q^76 - 36 * q^79 - 72 * q^82 - 238 * q^85 - 160 * q^88 - 176 * q^91 - 206 * q^94 - 92 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{4}{11}\right)$	$1$

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 $

$2$	0.858969	−	0.991303i	0.607383	−	0.700957i	−0.365877	−	0.930663i	$-0.619231\pi$
$2$	0.858969	−	0.991303i	0.607383	−	0.700957i	0.973260	+	0.229706i	$0.0737765\pi$
$3$		0			0
$3$		0			0
$4$	0.0397758	+	0.276647i	0.0198879	+	0.138323i
$5$	−1.24955	−	2.73614i	−0.558817	−	1.22364i	−0.952541	−	0.304409i	$-0.901541\pi$
$5$	−1.24955	−	2.73614i	−0.558817	−	1.22364i	0.393725	−	0.919228i	$-0.371186\pi$
$6$		0			0
$7$	3.30268	−	0.969753i	1.24829	−	0.366532i	0.410169	−	0.912010i	$-0.365470\pi$
$7$	3.30268	−	0.969753i	1.24829	−	0.366532i	0.838125	+	0.545478i	$0.183652\pi$
$8$	2.51532	+	1.61650i	0.889300	+	0.571518i
$9$		0			0
$10$	−3.78567	−	1.11157i	−1.19713	−	0.351510i
$11$	−0.569092	−	0.656767i	−0.171588	−	0.198023i	0.663442	−	0.748228i	$-0.269095\pi$
$11$	−0.569092	−	0.656767i	−0.171588	−	0.198023i	−0.835030	+	0.550205i	$0.814550\pi$
$12$		0			0
$13$	−3.98313	−	1.16955i	−1.10472	−	0.324376i	−0.321996	−	0.946741i	$-0.604354\pi$
$13$	−3.98313	−	1.16955i	−1.10472	−	0.324376i	−0.782727	+	0.622365i	$0.786172\pi$
$14$	1.87558	−	4.10694i	0.501269	−	1.09763i
$15$		0			0
$16$	3.22668	−	0.947439i	0.806670	−	0.236860i
$17$	0.634803	−	4.41515i	0.153962	−	1.07083i	−0.755531	−	0.655113i	$-0.772621\pi$
$17$	0.634803	−	4.41515i	0.153962	−	1.07083i	0.909493	−	0.415719i	$-0.136470\pi$
$18$		0			0
$19$	1.01094	+	7.03126i	0.231926	+	1.61308i	0.689756	+	0.724041i	$0.257718\pi$
$19$	1.01094	+	7.03126i	0.231926	+	1.61308i	−0.457830	+	0.889040i	$0.651373\pi$
$20$	0.707242	−	0.454517i	0.158144	−	0.101633i
$21$		0			0
$22$	−1.13989			−0.243025
$23$	−0.157683	+	4.79324i	−0.0328792	+	0.999459i
$23$	−0.157683	+	4.79324i	−0.0328792	+	0.999459i
$24$		0			0
$25$	−2.65076	+	3.05915i	−0.530153	+	0.611829i
$26$	−4.58077	+	2.94388i	−0.898363	+	0.577343i
$27$		0			0
$28$	0.399646	+	0.875102i	0.0755259	+	0.165379i
$29$	−1.24846	+	8.68321i	−0.231833	+	1.61243i	0.458333	+	0.888781i	$0.348447\pi$
$29$	−1.24846	+	8.68321i	−0.231833	+	1.61243i	−0.690165	+	0.723652i	$0.742462\pi$
$30$		0			0
$31$	−1.28761	−	0.827495i	−0.231261	−	0.148623i	0.419879	−	0.907580i	$-0.362073\pi$
$31$	−1.28761	−	0.827495i	−0.231261	−	0.148623i	−0.651140	+	0.758958i	$0.725709\pi$
$32$	−0.651736	+	1.42710i	−0.115212	+	0.252278i
$33$		0			0
$34$	−3.83148	−	4.42176i	−0.657093	−	0.758325i
$35$	−6.78024	−	7.82482i	−1.14607	−	1.32264i
$36$		0			0
$37$	0.503213	−	1.10188i	0.0827278	−	0.181149i	−0.863748	−	0.503925i	$-0.831889\pi$
$37$	0.503213	−	1.10188i	0.0827278	−	0.181149i	0.946475	+	0.322776i	$0.104616\pi$
$38$	7.83847	+	5.03748i	1.27157	+	0.817187i
$39$		0			0
$40$	1.27994	−	8.90216i	0.202376	−	1.40756i
$41$	1.29601	+	2.83786i	0.202403	+	0.443200i	0.983428	−	0.181299i	$-0.0580303\pi$
$41$	1.29601	+	2.83786i	0.202403	+	0.443200i	−0.781025	+	0.624499i	$0.785303\pi$
$42$		0			0
$43$	−0.478538	+	0.307537i	−0.0729763	+	0.0468990i	−0.576620	−	0.817012i	$-0.695629\pi$
$43$	−0.478538	+	0.307537i	−0.0729763	+	0.0468990i	0.503644	+	0.863911i	$0.331992\pi$
$44$	0.159056	−	0.183561i	0.0239787	−	0.0276728i
$45$		0			0
$46$	4.61611	+	4.27355i	0.680608	+	0.630101i
$47$	−1.54648			−0.225578			−0.112789	−	0.993619i	$-0.535978\pi$
$47$	−1.54648			−0.225578			−0.112789	+	0.993619i	$0.535978\pi$
$48$		0			0
$49$	4.07847	−	2.62107i	0.582639	−	0.374439i
$50$	0.755615	+	5.25542i	0.106860	+	0.743229i
$51$		0			0
$52$	0.165121	−	1.14844i	0.0228981	−	0.159260i
$53$	−10.2463	+	3.00858i	−1.40743	+	0.413260i	−0.895230	−	0.445604i	$-0.852989\pi$
$53$	−10.2463	+	3.00858i	−1.40743	+	0.413260i	−0.512204	+	0.858864i	$0.671171\pi$
$54$		0			0
$55$	−1.08590	+	2.37778i	−0.146422	+	0.320620i
$56$	9.87489	+	2.89953i	1.31959	+	0.387466i
$57$		0			0
$58$	7.53531	+	8.69621i	0.989434	+	1.14187i
$59$	−9.17058	−	2.69273i	−1.19391	−	0.350563i	−0.376387	−	0.926462i	$-0.622834\pi$
$59$	−9.17058	−	2.69273i	−1.19391	−	0.350563i	−0.817521	+	0.575899i	$0.804652\pi$
$60$		0			0
$61$	4.38624	+	2.81886i	0.561600	+	0.360918i	0.790434	−	0.612547i	$-0.209855\pi$
$61$	4.38624	+	2.81886i	0.561600	+	0.360918i	−0.228834	+	0.973465i	$0.573491\pi$
$62$	−1.92631	+	0.565617i	−0.244642	+	0.0718334i
$63$		0			0
$64$	3.64887	+	7.98991i	0.456109	+	0.998739i
$65$	1.77707	+	12.3598i	0.220419	+	1.53305i
$66$		0			0
$67$	8.41554	−	9.71205i	1.02812	−	1.18652i	0.0458696	−	0.998947i	$-0.485394\pi$
$67$	8.41554	−	9.71205i	1.02812	−	1.18652i	0.982252	−	0.187568i	$-0.0600604\pi$
$68$	1.24669			0.151183
$69$		0			0
$70$	−13.5808			−1.62321
$71$	5.17277	−	5.96970i	0.613895	−	0.708473i	−0.360641	−	0.932705i	$-0.617442\pi$
$71$	5.17277	−	5.96970i	0.613895	−	0.708473i	0.974536	+	0.224232i	$0.0719874\pi$
$72$		0			0
$73$	−1.68880	−	11.7459i	−0.197660	−	1.37475i	−0.811052	−	0.584974i	$-0.801105\pi$
$73$	−1.68880	−	11.7459i	−0.197660	−	1.37475i	0.613392	−	0.789779i	$-0.289805\pi$
$74$	−0.660056	−	1.44532i	−0.0767299	−	0.168015i
$75$		0			0
$76$	−1.90496	+	0.559348i	−0.218514	+	0.0641616i
$77$	−2.51643	−	1.61721i	−0.286774	−	0.184298i
$78$		0			0
$79$	0.640855	+	0.188172i	0.0721018	+	0.0211710i	0.317585	−	0.948230i	$-0.397128\pi$
$79$	0.640855	+	0.188172i	0.0721018	+	0.0211710i	−0.245483	+	0.969401i	$0.578946\pi$
$80$	−6.62423	−	7.64477i	−0.740611	−	0.854711i
$81$		0			0
$82$	3.92641	+	1.15290i	0.433600	+	0.127316i
$83$	4.42633	−	9.69231i	0.485853	−	1.06387i	−0.494960	−	0.868916i	$-0.664817\pi$
$83$	4.42633	−	9.69231i	0.485853	−	1.06387i	0.980813	−	0.194953i	$-0.0624555\pi$
$84$		0			0
$85$	−12.8737	+	3.78005i	−1.39635	+	0.410004i
$86$	−0.106186	+	0.738541i	−0.0114503	+	0.0796389i
$87$		0			0
$88$	−0.369786	−	2.57192i	−0.0394193	−	0.274167i
$89$	8.58265	−	5.51573i	0.909759	−	0.584667i	8.97572e−5	−	1.00000i	$-0.499971\pi$
$89$	8.58265	−	5.51573i	0.909759	−	0.584667i	0.909669	+	0.415333i	$0.136335\pi$
$90$		0			0
$91$	−14.2892			−1.49791
$92$	−1.33231	+	0.147032i	−0.138902	+	0.0153292i
$93$		0			0
$94$	−1.32838	+	1.53303i	−0.137012	+	0.158120i
$95$	17.9753	−	11.5520i	1.84422	−	1.18521i
$96$		0			0
$97$	−2.74809	−	6.01749i	−0.279027	−	0.610983i	0.717286	−	0.696779i	$-0.245384\pi$
$97$	−2.74809	−	6.01749i	−0.279027	−	0.610983i	−0.996313	+	0.0857956i	$0.972657\pi$
$98$	0.905001	−	6.29442i	0.0914189	−	0.635832i
$99$		0			0
$100$	−0.951739	−	0.611645i	−0.0951739	−	0.0611645i
$101$	−4.04725	+	8.86224i	−0.402716	+	0.881826i	0.594271	+	0.804265i	$0.297441\pi$
$101$	−4.04725	+	8.86224i	−0.402716	+	0.881826i	−0.996988	+	0.0775612i	$0.975287\pi$
$102$		0			0
$103$	4.12426	+	4.75965i	0.406376	+	0.468983i	0.921638	−	0.388050i	$-0.126851\pi$
$103$	4.12426	+	4.75965i	0.406376	+	0.468983i	−0.515263	+	0.857032i	$0.672306\pi$
$104$	−8.12828	−	9.38053i	−0.797043	−	0.919837i
$105$		0			0
$106$	−5.81882	+	12.7414i	−0.565174	+	1.23756i
$107$	5.25855	+	3.37946i	0.508363	+	0.326705i	0.769554	−	0.638582i	$-0.220479\pi$
$107$	5.25855	+	3.37946i	0.508363	+	0.326705i	−0.261191	+	0.965287i	$0.584115\pi$
$108$		0			0
$109$	−1.48430	+	10.3236i	−0.142170	+	0.988817i	0.786415	+	0.617698i	$0.211935\pi$
$109$	−1.48430	+	10.3236i	−0.142170	+	0.988817i	−0.928586	+	0.371118i	$0.878974\pi$
$110$	1.42435	+	3.11889i	0.135806	+	0.297374i
$111$		0			0
$112$	9.73790	−	6.25817i	0.920145	−	0.591341i
$113$	−9.42405	+	10.8759i	−0.886540	+	1.02312i	0.113024	+	0.993592i	$0.463946\pi$
$113$	−9.42405	+	10.8759i	−0.886540	+	1.02312i	−0.999564	+	0.0295296i	$0.990599\pi$
$114$		0			0
$115$	13.3120	−	5.55796i	1.24135	−	0.518282i
$116$	−2.45184			−0.227648
$117$		0			0
$118$	−10.5465	+	6.77786i	−0.970889	+	0.623952i
$119$	−2.18506	−	15.1974i	−0.200304	−	1.39314i
$120$		0			0
$121$	1.45799	−	10.1405i	0.132544	−	0.921865i
$122$	6.56199	−	1.92677i	0.594094	−	0.174442i
$123$		0			0
$124$	0.177708	−	0.389127i	0.0159587	−	0.0349446i
$125$	−2.74808	−	0.806908i	−0.245795	−	0.0721720i
$126$		0			0
$127$	−10.0146	−	11.5575i	−0.888655	−	1.02556i	−0.999497	−	0.0317246i	$-0.989900\pi$
$127$	−10.0146	−	11.5575i	−0.888655	−	1.02556i	0.110842	−	0.993838i	$-0.464645\pi$
$128$	8.04403	+	2.36194i	0.710998	+	0.208768i
$129$		0			0
$130$	13.7788	+	8.85508i	1.20848	+	0.776642i
$131$	0.330256	−	0.0969720i	0.0288546	−	0.00847249i	−0.267273	−	0.963621i	$-0.586123\pi$
$131$	0.330256	−	0.0969720i	0.0288546	−	0.00847249i	0.296128	+	0.955148i	$0.404304\pi$
$132$		0			0
$133$	10.1574	+	22.2416i	0.880758	+	1.92859i
$134$	−2.39890	−	16.6847i	−0.207233	−	1.44134i
$135$		0			0
$136$	8.73382	−	10.0794i	0.748919	−	0.864298i
$137$	19.3166			1.65033			0.825163	−	0.564894i	$-0.191083\pi$
$137$	19.3166			1.65033			0.825163	+	0.564894i	$0.191083\pi$
$138$		0			0
$139$	−22.0403			−1.86943			−0.934717	−	0.355393i	$-0.884347\pi$
$139$	−22.0403			−1.86943			−0.934717	+	0.355393i	$0.884347\pi$
$140$	1.89502	−	2.18697i	0.160158	−	0.184833i
$141$		0			0
$142$	−1.47453	−	10.2556i	−0.123740	−	0.860628i
$143$	1.49865	+	3.28158i	0.125323	+	0.274419i
$144$		0			0
$145$	25.3185	−	7.43418i	2.10259	−	0.617375i
$146$	−13.0944	−	8.41524i	−1.08370	−	0.696450i
$147$		0			0
$148$	0.324848	+	0.0953840i	0.0267024	+	0.00784052i
$149$	−5.87531	−	6.78047i	−0.481324	−	0.555478i	0.462203	−	0.886774i	$-0.347059\pi$
$149$	−5.87531	−	6.78047i	−0.481324	−	0.555478i	−0.943527	+	0.331297i	$0.892514\pi$
$150$		0			0
$151$	−4.33911	−	1.27408i	−0.353112	−	0.103683i	0.100366	−	0.994951i	$-0.467999\pi$
$151$	−4.33911	−	1.27408i	−0.353112	−	0.103683i	−0.453478	+	0.891268i	$0.649817\pi$
$152$	−8.82317	+	19.3200i	−0.715654	+	1.56706i
$153$		0			0
$154$	−3.76468	+	1.10541i	−0.303366	+	0.0890764i
$155$	−0.655208	+	4.55707i	−0.0526276	+	0.366033i
$156$		0			0
$157$	0.848389	+	5.90067i	0.0677088	+	0.470925i	0.995262	+	0.0972330i	$0.0309992\pi$
$157$	0.848389	+	5.90067i	0.0677088	+	0.470925i	−0.927553	+	0.373692i	$0.878092\pi$
$158$	0.737010	−	0.473648i	0.0586334	−	0.0376814i
$159$		0			0
$160$	4.71912			0.373080
$161$	4.12748	+	15.9834i	0.325291	+	1.25967i
$162$		0			0
$163$	4.70906	−	5.43454i	0.368842	−	0.425666i	−0.540741	−	0.841189i	$-0.681856\pi$
$163$	4.70906	−	5.43454i	0.368842	−	0.425666i	0.909583	+	0.415523i	$0.136401\pi$
$164$	−0.733536	+	0.471415i	−0.0572795	+	0.0368113i
$165$		0			0
$166$	−5.80593	−	12.7132i	−0.450628	−	0.986738i
$167$	0.0289597	−	0.201419i	0.00224097	−	0.0155863i	−0.988670	−	0.150104i	$-0.952039\pi$
$167$	0.0289597	−	0.201419i	0.00224097	−	0.0155863i	0.990911	+	0.134517i	$0.0429484\pi$
$168$		0			0
$169$	3.56121	+	2.28865i	0.273939	+	0.176050i
$170$	−7.31091	+	16.0087i	−0.560721	+	1.22781i
$171$		0			0
$172$	−0.104113	−	0.120153i	−0.00793858	−	0.00916160i
$173$	15.6118	+	18.0169i	1.18694	+	1.36980i	0.912950	+	0.408071i	$0.133798\pi$
$173$	15.6118	+	18.0169i	1.18694	+	1.36980i	0.273991	+	0.961732i	$0.411656\pi$
$174$		0			0
$175$	−5.78800	+	12.6740i	−0.437532	+	0.958061i
$176$	−2.45852	−	1.58000i	−0.185318	−	0.119097i
$177$		0			0
$178$	1.90447	−	13.2458i	0.142746	−	0.992818i
$179$	−9.88420	−	21.6434i	−0.738780	−	1.61770i	−0.785551	−	0.618797i	$-0.787620\pi$
$179$	−9.88420	−	21.6434i	−0.738780	−	1.61770i	0.0467714	−	0.998906i	$-0.485107\pi$
$180$		0			0
$181$	4.89252	−	3.14423i	0.363658	−	0.233709i	−0.346032	−	0.938223i	$-0.612471\pi$
$181$	4.89252	−	3.14423i	0.363658	−	0.233709i	0.709690	+	0.704514i	$0.248835\pi$
$182$	−12.2740	+	14.1649i	−0.909806	+	1.04997i
$183$		0			0
$184$	−8.14489	+	11.8016i	−0.600449	+	0.870028i
$185$	−3.64370			−0.267890
$186$		0			0
$187$	−3.26099	+	2.09571i	−0.238467	+	0.153253i
$188$	−0.0615126	−	0.427830i	−0.00448627	−	0.0312027i
$189$		0			0
$190$	3.98866	−	27.7417i	0.289368	−	2.01260i
$191$	2.71257	−	0.796481i	0.196274	−	0.0576314i	−0.182118	−	0.983277i	$-0.558295\pi$
$191$	2.71257	−	0.796481i	0.196274	−	0.0576314i	0.378392	+	0.925645i	$0.376477\pi$
$192$		0			0
$193$	−8.48624	+	18.5823i	−0.610853	+	1.33758i	0.311136	+	0.950365i	$0.399290\pi$
$193$	−8.48624	+	18.5823i	−0.610853	+	1.33758i	−0.921989	+	0.387216i	$0.873437\pi$
$194$	−8.32568	−	2.44464i	−0.597749	−	0.175515i
$195$		0			0
$196$	0.887336	+	1.02404i	0.0633811	+	0.0731457i
$197$	1.75495	+	0.515301i	0.125035	+	0.0367137i	0.343652	−	0.939097i	$-0.388336\pi$
$197$	1.75495	+	0.515301i	0.125035	+	0.0367137i	−0.218616	+	0.975811i	$0.570154\pi$
$198$		0			0
$199$	5.47482	+	3.51845i	0.388100	+	0.249417i	0.720111	−	0.693859i	$-0.244091\pi$
$199$	5.47482	+	3.51845i	0.388100	+	0.249417i	−0.332011	+	0.943275i	$0.607727\pi$
$200$	−11.6126	+	3.40977i	−0.821137	+	0.241107i
$201$		0			0
$202$	5.30870	+	11.6244i	0.373519	+	0.817893i
$203$	4.29732	+	29.8885i	0.301613	+	2.09776i
$204$		0			0
$205$	6.14536	−	7.09212i	0.429210	−	0.495335i
$206$	8.26087			0.575562
$207$		0			0
$208$	−13.9604			−0.967978
$209$	4.04258	−	4.66539i	0.279631	−	0.322711i
$210$		0			0
$211$	2.54735	+	17.7172i	0.175367	+	1.21970i	0.867317	+	0.497756i	$0.165843\pi$
$211$	2.54735	+	17.7172i	0.175367	+	1.21970i	−0.691950	+	0.721945i	$0.743248\pi$
$212$	−1.23987	−	2.71493i	−0.0851544	−	0.186462i
$213$		0			0
$214$	7.86700	−	2.30996i	0.537777	−	0.157906i
$215$	1.43942	+	0.925061i	0.0981678	+	0.0630886i
$216$		0			0
$217$	−5.05502	−	1.48429i	−0.343157	−	0.100760i
$218$	8.95879	+	10.3390i	0.606766	+	0.700245i
$219$		0			0
$220$	−0.700997	−	0.205831i	−0.0472612	−	0.0138771i
$221$	−7.69226	+	16.8437i	−0.517438	+	1.13303i
$222$		0			0
$223$	7.45932	−	2.19025i	0.499513	−	0.146670i	−0.0222641	−	0.999752i	$-0.507087\pi$
$223$	7.45932	−	2.19025i	0.499513	−	0.146670i	0.521777	+	0.853082i	$0.325269\pi$
$224$	−0.768535	+	5.34528i	−0.0513499	+	0.357146i
$225$		0			0
$226$	2.68638	+	18.6842i	0.178695	+	1.24285i
$227$	−2.01522	+	1.29510i	−0.133755	+	0.0859588i	−0.605807	−	0.795612i	$-0.707150\pi$
$227$	−2.01522	+	1.29510i	−0.133755	+	0.0859588i	0.472052	+	0.881570i	$0.343513\pi$
$228$		0			0
$229$	−14.7075			−0.971897			−0.485949	−	0.873987i	$-0.661526\pi$
$229$	−14.7075			−0.971897			−0.485949	+	0.873987i	$0.661526\pi$
$230$	5.92497	−	17.9703i	0.390681	−	1.18493i
$231$		0			0
$232$	−17.1767	+	19.8229i	−1.12770	+	1.30144i
$233$	9.15669	−	5.88465i	0.599875	−	0.385516i	−0.205173	−	0.978726i	$-0.565776\pi$
$233$	9.15669	−	5.88465i	0.599875	−	0.385516i	0.805048	+	0.593210i	$0.202139\pi$
$234$		0			0
$235$	1.93241	+	4.23139i	0.126057	+	0.276026i
$236$	0.380167	−	2.64412i	0.0247467	−	0.172117i
$237$		0			0
$238$	−16.9421	−	10.8881i	−1.09820	−	0.705767i
$239$	0.232935	−	0.510057i	0.0150673	−	0.0329928i	−0.901949	−	0.431843i	$-0.857863\pi$
$239$	0.232935	−	0.510057i	0.0150673	−	0.0329928i	0.917016	+	0.398850i	$0.130591\pi$
$240$		0			0
$241$	−18.5886	−	21.4524i	−1.19740	−	1.38187i	−0.904912	−	0.425598i	$-0.860064\pi$
$241$	−18.5886	−	21.4524i	−1.19740	−	1.38187i	−0.292484	−	0.956270i	$-0.594482\pi$
$242$	−8.79996	−	10.1557i	−0.565683	−	0.652832i
$243$		0			0
$244$	−0.605363	+	1.32556i	−0.0387544	+	0.0848603i
$245$	−12.2679	−	7.88409i	−0.783766	−	0.503696i
$246$		0			0
$247$	4.19671	−	29.1888i	0.267031	−	1.85724i
$248$	−1.90110	−	4.16283i	−0.120720	−	0.264340i
$249$		0			0
$250$	−3.16040	+	2.03107i	−0.199881	+	0.128456i
$251$	12.1736	−	14.0491i	0.768391	−	0.886770i	−0.227823	−	0.973702i	$-0.573161\pi$
$251$	12.1736	−	14.0491i	0.768391	−	0.886770i	0.996214	+	0.0869321i	$0.0277063\pi$
$252$		0			0
$253$	3.23778	−	2.62423i	0.203557	−	0.164984i
$254$	−20.0592			−1.25863
$255$		0			0
$256$	−5.52762	+	3.55239i	−0.345476	+	0.222024i
$257$	1.99671	+	13.8875i	0.124552	+	0.866276i	0.952297	+	0.305172i	$0.0987140\pi$
$257$	1.99671	+	13.8875i	0.124552	+	0.866276i	−0.827746	+	0.561104i	$0.810377\pi$
$258$		0			0
$259$	0.593395	−	4.12716i	0.0368718	−	0.256449i
$260$	−3.34862	+	0.983244i	−0.207673	+	0.0609782i
$261$		0			0
$262$	0.187551	−	0.410680i	0.0115870	−	0.0253719i
$263$	−8.32875	−	2.44554i	−0.513573	−	0.150799i	0.0146693	−	0.999892i	$-0.495330\pi$
$263$	−8.32875	−	2.44554i	−0.513573	−	0.150799i	−0.528242	+	0.849094i	$0.677149\pi$
$264$		0			0
$265$	21.0351	+	24.2758i	1.29218	+	1.49125i
$266$	30.7730	+	9.03578i	1.88682	+	0.554019i
$267$		0			0
$268$	3.02154	+	1.94183i	0.184570	+	0.118616i
$269$	4.37978	−	1.28602i	0.267040	−	0.0784100i	−0.145471	−	0.989362i	$-0.546470\pi$
$269$	4.37978	−	1.28602i	0.267040	−	0.0784100i	0.412511	+	0.910952i	$0.364652\pi$
$270$		0			0
$271$	1.02969	+	2.25471i	0.0625493	+	0.136964i	0.938325	−	0.345754i	$-0.112377\pi$
$271$	1.02969	+	2.25471i	0.0625493	+	0.136964i	−0.875776	+	0.482718i	$0.839650\pi$
$272$	−2.13478	−	14.8477i	−0.129440	−	0.900275i
$273$		0			0
$274$	16.5923	−	19.1486i	1.00238	−	1.15681i
$275$	3.51767			0.212124
$276$		0			0
$277$	−11.7486			−0.705905			−0.352953	−	0.935641i	$-0.614822\pi$
$277$	−11.7486			−0.705905			−0.352953	+	0.935641i	$0.614822\pi$
$278$	−18.9319	+	21.8486i	−1.13546	+	1.31039i
$279$		0			0
$280$	−4.40568	−	30.6422i	−0.263290	−	1.83122i
$281$	0.354164	+	0.775510i	0.0211276	+	0.0462631i	0.919902	−	0.392149i	$-0.128268\pi$
$281$	0.354164	+	0.775510i	0.0211276	+	0.0462631i	−0.898774	+	0.438412i	$0.855541\pi$
$282$		0			0
$283$	14.3774	−	4.22157i	0.854645	−	0.250946i	0.175073	−	0.984555i	$-0.443984\pi$
$283$	14.3774	−	4.22157i	0.854645	−	0.250946i	0.679572	+	0.733609i	$0.262166\pi$
$284$	1.85725	+	1.19358i	0.110207	+	0.0708260i
$285$		0			0
$286$	4.54032	+	1.33316i	0.268475	+	0.0788314i
$287$	7.03232	+	8.11574i	0.415105	+	0.479057i
$288$		0			0
$289$	−2.77921	−	0.816049i	−0.163483	−	0.0480029i
$290$	14.3783	−	31.4840i	0.844321	−	1.84880i
$291$		0			0
$292$	3.18229	−	0.934405i	0.186229	−	0.0546819i
$293$	2.26984	−	15.7871i	0.132605	−	0.922290i	−0.809535	−	0.587071i	$-0.800281\pi$
$293$	2.26984	−	15.7871i	0.132605	−	0.922290i	0.942140	−	0.335218i	$-0.108810\pi$
$294$		0			0
$295$	4.09145	+	28.4567i	0.238214	+	1.65681i
$296$	3.04694	−	1.95815i	0.177100	−	0.113815i
$297$		0			0
$298$	−11.7682			−0.681714
$299$	6.23402	−	18.9077i	0.360523	−	1.09346i
$300$		0			0
$301$	−1.28222	+	1.47976i	−0.0739059	+	0.0852919i
$302$	−4.99016	+	3.20698i	−0.287152	+	0.184541i
$303$		0			0
$304$	9.92367	+	21.7298i	0.569162	+	1.24629i
$305$	2.23197	−	15.5237i	0.127802	−	0.888882i
$306$		0			0
$307$	16.8344	+	10.8188i	0.960790	+	0.617463i	0.924217	−	0.381868i	$-0.124719\pi$
$307$	16.8344	+	10.8188i	0.960790	+	0.617463i	0.0365738	+	0.999331i	$0.488356\pi$
$308$	0.347303	−	0.760487i	0.0197894	−	0.0433328i
$309$		0			0
$310$	3.95463	+	4.56389i	0.224608	+	0.259212i
$311$	−4.32422	−	4.99042i	−0.245204	−	0.282981i	0.619784	−	0.784772i	$-0.287220\pi$
$311$	−4.32422	−	4.99042i	−0.245204	−	0.282981i	−0.864989	+	0.501791i	$0.832675\pi$
$312$		0			0
$313$	5.41251	−	11.8517i	0.305933	−	0.669900i	−0.692752	−	0.721176i	$-0.743602\pi$
$313$	5.41251	−	11.8517i	0.305933	−	0.669900i	0.998684	+	0.0512766i	$0.0163290\pi$
$314$	6.57809	+	4.22748i	0.371223	+	0.238571i
$315$		0			0
$316$	−0.0265667	+	0.184775i	−0.00149449	+	0.0103944i
$317$	−4.07735	−	8.92815i	−0.229007	−	0.501455i	0.759891	−	0.650050i	$-0.225252\pi$
$317$	−4.07735	−	8.92815i	−0.229007	−	0.501455i	−0.988898	+	0.148595i	$0.952525\pi$
$318$		0			0
$319$	6.41334	−	4.12160i	0.359078	−	0.230765i
$320$	17.3020	−	19.9676i	0.967213	−	1.11622i
$321$		0			0
$322$	19.3898	+	9.63768i	1.08055	+	0.537087i
$323$	31.6858			1.76305
$324$		0			0
$325$	14.1362	−	9.08478i	0.784135	−	0.503933i
$326$	−1.34234	−	9.33620i	−0.0743455	−	0.517085i
$327$		0			0
$328$	−1.32752	+	9.23313i	−0.0733003	+	0.509814i
$329$	−5.10753	+	1.49971i	−0.281587	+	0.0826815i
$330$		0			0
$331$	2.65014	−	5.80299i	0.145665	−	0.318961i	−0.822710	−	0.568461i	$-0.807539\pi$
$331$	2.65014	−	5.80299i	0.145665	−	0.318961i	0.968375	+	0.249500i	$0.0802662\pi$
$332$	2.85741	+	0.839010i	0.156821	+	0.0460467i
$333$		0			0
$334$	−0.174792	−	0.201721i	−0.00956419	−	0.0110377i
$335$	−37.0891	−	10.8904i	−2.02640	−	0.595004i
$336$		0			0
$337$	−10.9533	−	7.03927i	−0.596665	−	0.383454i	0.207170	−	0.978305i	$-0.433575\pi$
$337$	−10.9533	−	7.03927i	−0.596665	−	0.383454i	−0.803836	+	0.594851i	$0.797211\pi$
$338$	5.32771	−	1.56436i	0.289789	−	0.0850898i
$339$		0			0
$340$	−1.55780	−	3.41111i	−0.0844836	−	0.184993i
$341$	0.189296	+	1.31658i	0.0102509	+	0.0712968i
$342$		0			0
$343$	−4.85062	+	5.59792i	−0.261909	+	0.302259i
$344$	−1.70081			−0.0917015
$345$		0			0
$346$	31.2703			1.68110
$347$	5.08019	−	5.86285i	0.272719	−	0.314734i	−0.602824	−	0.797874i	$-0.705958\pi$
$347$	5.08019	−	5.86285i	0.272719	−	0.314734i	0.875543	+	0.483139i	$0.160504\pi$
$348$		0			0
$349$	−2.88325	−	20.0534i	−0.154337	−	1.07343i	−0.908842	−	0.417141i	$-0.863032\pi$
$349$	−2.88325	−	20.0534i	−0.154337	−	1.07343i	0.754505	−	0.656294i	$-0.227877\pi$
$350$	7.59201	+	16.6242i	0.405810	+	0.888600i
$351$		0			0
$352$	1.30817	−	0.384114i	0.0697257	−	0.0204733i
$353$	6.97419	+	4.48204i	0.371199	+	0.238555i	0.712918	−	0.701247i	$-0.247373\pi$
$353$	6.97419	+	4.48204i	0.371199	+	0.238555i	−0.341720	+	0.939802i	$0.611009\pi$
$354$		0			0
$355$	−22.7976	−	6.69397i	−1.20997	−	0.355279i
$356$	1.86729	+	2.15497i	0.0989662	+	0.114213i
$357$		0			0
$358$	−29.9454	−	8.79275i	−1.58266	−	0.464711i
$359$	−7.08275	+	15.5091i	−0.373813	+	0.818537i	0.625454	+	0.780261i	$0.284914\pi$
$359$	−7.08275	+	15.5091i	−0.373813	+	0.818537i	−0.999267	+	0.0382760i	$0.987813\pi$
$360$		0			0
$361$	−30.1862	+	8.86347i	−1.58875	+	0.466498i
$362$	1.08564	−	7.55076i	0.0570597	−	0.396859i
$363$		0			0
$364$	−0.568363	−	3.95305i	−0.0297903	−	0.207196i
$365$	−30.0281	+	19.2979i	−1.57174	+	1.01010i
$366$		0			0
$367$	−17.2878			−0.902418			−0.451209	−	0.892418i	$-0.649007\pi$
$367$	−17.2878			−0.902418			−0.451209	+	0.892418i	$0.649007\pi$
$368$	4.03251	+	15.6156i	0.210209	+	0.814022i
$369$		0			0
$370$	−3.12982	+	3.61201i	−0.162712	+	0.187779i
$371$	−30.9225	+	19.8727i	−1.60542	+	1.03174i
$372$		0			0
$373$	−12.6292	−	27.6540i	−0.653913	−	1.43187i	−0.888087	−	0.459676i	$-0.847966\pi$
$373$	−12.6292	−	27.6540i	−0.653913	−	1.43187i	0.234174	−	0.972195i	$-0.424762\pi$
$374$	−0.723604	+	5.03277i	−0.0374167	+	0.260239i
$375$		0			0
$376$	−3.88990	−	2.49989i	−0.200606	−	0.128922i
$377$	15.1283	−	33.1263i	0.779145	−	1.70609i
$378$		0			0
$379$	−2.50334	−	2.88901i	−0.128588	−	0.148398i	0.687804	−	0.725896i	$-0.258575\pi$
$379$	−2.50334	−	2.88901i	−0.128588	−	0.148398i	−0.816392	+	0.577498i	$0.804029\pi$
$380$	3.91080	+	4.51331i	0.200620	+	0.231528i
$381$		0			0
$382$	1.54046	−	3.37313i	0.0788166	−	0.172584i
$383$	−14.1030	−	9.06347i	−0.720631	−	0.463122i	0.128225	−	0.991745i	$-0.459072\pi$
$383$	−14.1030	−	9.06347i	−0.720631	−	0.463122i	−0.848856	+	0.528623i	$0.822708\pi$
$384$		0			0
$385$	−1.28050	+	8.90608i	−0.0652604	+	0.453896i
$386$	11.1312	+	24.3740i	0.566565	+	1.24061i
$387$		0			0
$388$	1.55541	−	0.999602i	0.0789640	−	0.0507471i
$389$	9.09722	−	10.4988i	0.461247	−	0.532308i	−0.476709	−	0.879061i	$-0.658170\pi$
$389$	9.09722	−	10.4988i	0.461247	−	0.532308i	0.937956	+	0.346753i	$0.112716\pi$
$390$		0			0
$391$	21.0628	+	3.73896i	1.06519	+	0.189087i
$392$	14.4956			0.732139
$393$		0			0
$394$	2.01827	−	1.29706i	0.101679	−	0.0653451i
$395$	−0.285917	−	1.98860i	−0.0143861	−	0.100057i
$396$		0			0
$397$	−3.52808	+	24.5384i	−0.177069	+	1.23154i	0.686430	+	0.727195i	$0.259177\pi$
$397$	−3.52808	+	24.5384i	−0.177069	+	1.23154i	−0.863500	+	0.504349i	$0.831732\pi$
$398$	8.19055	−	2.40496i	0.410555	−	0.120550i
$399$		0			0
$400$	−5.65482	+	12.3823i	−0.282741	+	0.619116i
$401$	7.13156	+	2.09401i	0.356133	+	0.104570i	0.454905	−	0.890540i	$-0.349673\pi$
$401$	7.13156	+	2.09401i	0.356133	+	0.104570i	−0.0987719	+	0.995110i	$0.531491\pi$
$402$		0			0
$403$	4.16091	+	4.80195i	0.207270	+	0.239202i
$404$	−2.61269	−	0.767156i	−0.129986	−	0.0381674i
$405$		0			0
$406$	33.3199	+	21.4134i	1.65364	+	1.06273i
$407$	−1.01006	+	0.296579i	−0.0500666	+	0.0147009i
$408$		0			0
$409$	6.52917	+	14.2969i	0.322847	+	0.706935i	0.999571	−	0.0293014i	$-0.00932825\pi$
$409$	6.52917	+	14.2969i	0.322847	+	0.706935i	−0.676724	+	0.736237i	$0.736601\pi$
$410$	−1.75177	−	12.1838i	−0.0865137	−	0.601716i
$411$		0			0
$412$	−1.15270	+	1.33028i	−0.0567893	+	0.0655383i
$413$	−32.8987			−1.61884
$414$		0			0
$415$	−32.0504			−1.57329
$416$	4.26502	−	4.92210i	0.209110	−	0.241326i
$417$		0			0
$418$	−1.15236	−	8.01484i	−0.0563638	−	0.392019i
$419$	−10.8963	−	23.8596i	−0.532319	−	1.16562i	−0.964561	−	0.263859i	$-0.915005\pi$
$419$	−10.8963	−	23.8596i	−0.532319	−	1.16562i	0.432242	−	0.901758i	$-0.357723\pi$
$420$		0			0
$421$	−7.34806	+	2.15759i	−0.358123	+	0.105154i	−0.455844	−	0.890059i	$-0.650663\pi$
$421$	−7.34806	+	2.15759i	−0.358123	+	0.105154i	0.0977217	+	0.995214i	$0.468844\pi$
$422$	19.7512	+	12.6933i	0.961473	+	0.617901i
$423$		0			0
$424$	−30.6360	−	8.99555i	−1.48782	−	0.436862i
$425$	11.8239	+	13.6455i	0.573542	+	0.661903i
$426$		0			0
$427$	17.2199	+	5.05622i	0.833330	+	0.244688i
$428$	−0.725754	+	1.58918i	−0.0350807	+	0.0768159i
$429$		0			0
$430$	2.15343	−	0.632305i	0.103848	−	0.0304925i
$431$	−3.23355	+	22.4898i	−0.155754	+	1.08330i	0.750594	+	0.660764i	$0.229768\pi$
$431$	−3.23355	+	22.4898i	−0.155754	+	1.08330i	−0.906348	+	0.422532i	$0.861141\pi$
$432$		0			0
$433$	1.60809	+	11.1845i	0.0772798	+	0.537493i	0.991279	+	0.131778i	$0.0420685\pi$
$433$	1.60809	+	11.1845i	0.0772798	+	0.537493i	−0.913999	+	0.405715i	$0.867022\pi$
$434$	−5.81348	+	3.73610i	−0.279056	+	0.179338i
$435$		0			0
$436$	−2.91502			−0.139604
$437$	−33.8619	+	3.73698i	−1.61983	+	0.178764i
$438$		0			0
$439$	7.44940	−	8.59707i	0.355540	−	0.410316i	−0.549600	−	0.835428i	$-0.685220\pi$
$439$	7.44940	−	8.59707i	0.355540	−	0.410316i	0.905141	+	0.425112i	$0.139765\pi$
$440$	−6.57505	+	4.22553i	−0.313453	+	0.201444i
$441$		0			0
$442$	10.0898	+	22.0936i	0.479923	+	1.05088i
$443$	−3.02791	+	21.0596i	−0.143860	+	1.00057i	0.782155	+	0.623084i	$0.214120\pi$
$443$	−3.02791	+	21.0596i	−0.143860	+	1.00057i	−0.926015	+	0.377486i	$0.876789\pi$
$444$		0			0
$445$	−25.8163	−	16.5911i	−1.22381	−	0.786494i
$446$	4.23612	−	9.27580i	0.200586	−	0.439222i
$447$		0			0
$448$	19.7993	+	22.8496i	0.935428	+	1.07954i
$449$	26.1691	+	30.2007i	1.23499	+	1.42526i	0.869124	+	0.494593i	$0.164683\pi$
$449$	26.1691	+	30.2007i	1.23499	+	1.42526i	0.365870	+	0.930666i	$0.380772\pi$
$450$		0			0
$451$	1.12627	−	2.46618i	0.0530339	−	0.116128i
$452$	−3.38364	−	2.17453i	−0.159153	−	0.102281i
$453$		0			0
$454$	−0.447170	+	3.11014i	−0.0209867	+	0.145966i
$455$	17.8551	+	39.0972i	0.837059	+	1.83290i
$456$		0			0
$457$	6.23920	−	4.00969i	0.291858	−	0.187566i	−0.386516	−	0.922283i	$-0.626322\pi$
$457$	6.23920	−	4.00969i	0.291858	−	0.187566i	0.678373	+	0.734717i	$0.262685\pi$
$458$	−12.6333	+	14.5796i	−0.590313	+	0.681258i
$459$		0			0
$460$	2.06709	+	3.46165i	0.0963784	+	0.161400i
$461$	−33.8156			−1.57495			−0.787474	−	0.616348i	$-0.788611\pi$
$461$	−33.8156			−1.57495			−0.787474	+	0.616348i	$0.788611\pi$
$462$		0			0
$463$	17.8600	−	11.4779i	0.830024	−	0.533424i	−0.0552615	−	0.998472i	$-0.517599\pi$
$463$	17.8600	−	11.4779i	0.830024	−	0.533424i	0.885286	+	0.465048i	$0.153963\pi$
$464$	4.19844	+	29.2008i	0.194908	+	1.35561i
$465$		0			0
$466$	2.03184	−	14.1318i	0.0941233	−	0.654642i
$467$	2.99399	−	0.879115i	0.138545	−	0.0406806i	−0.211725	−	0.977329i	$-0.567908\pi$
$467$	2.99399	−	0.879115i	0.138545	−	0.0406806i	0.350270	+	0.936649i	$0.386090\pi$
$468$		0			0
$469$	18.3755	−	40.2367i	0.848502	−	1.85796i
$470$	5.85447	+	1.71903i	0.270047	+	0.0792928i
$471$		0			0
$472$	−18.7142	−	21.5973i	−0.861389	−	0.994096i
$473$	0.474312	+	0.139271i	0.0218089	+	0.00640367i
$474$		0			0
$475$	−24.1894	−	15.5456i	−1.10989	−	0.713281i
$476$	4.11740	−	1.20898i	0.188721	−	0.0554134i
$477$		0			0
$478$	−0.305537	−	0.669032i	−0.0139749	−	0.0306008i
$479$	−4.15697	−	28.9124i	−0.189937	−	1.32104i	−0.832166	−	0.554527i	$-0.812899\pi$
$479$	−4.15697	−	28.9124i	−0.189937	−	1.32104i	0.642229	−	0.766513i	$-0.278010\pi$
$480$		0			0
$481$	−3.29308	+	3.80041i	−0.150151	+	0.173284i
$482$	−37.2328			−1.69591
$483$		0			0
$484$	2.86333			0.130151
$485$	−13.0308	+	15.0383i	−0.591697	+	0.682855i
$486$		0			0
$487$	5.35024	+	37.2117i	0.242442	+	1.68622i	0.639785	+	0.768554i	$0.279023\pi$
$487$	5.35024	+	37.2117i	0.242442	+	1.68622i	−0.397343	+	0.917670i	$0.630068\pi$
$488$	6.47610	+	14.1807i	0.293159	+	0.641930i
$489$		0			0
$490$	−18.3532	+	5.38900i	−0.829115	+	0.243450i
$491$	21.3184	+	13.7005i	0.962087	+	0.618296i	0.924575	−	0.381000i	$-0.124420\pi$
$491$	21.3184	+	13.7005i	0.962087	+	0.618296i	0.0375123	+	0.999296i	$0.488057\pi$
$492$		0			0
$493$	37.5452	+	11.0243i	1.69095	+	0.496508i
$494$	−25.3301	−	29.2325i	−1.13965	−	1.31523i
$495$		0			0
$496$	−4.93870	−	1.45013i	−0.221754	−	0.0651129i
$497$	11.2949	−	24.7323i	0.506643	−	1.10939i
$498$		0			0
$499$	15.7316	−	4.61920i	0.704242	−	0.206784i	0.0900458	−	0.995938i	$-0.471299\pi$
$499$	15.7316	−	4.61920i	0.704242	−	0.206784i	0.614196	+	0.789154i	$0.289480\pi$
$500$	0.113921	−	0.792341i	0.00509472	−	0.0354346i
$501$		0			0
$502$	−3.47015	−	24.1354i	−0.154881	−	1.07722i
$503$	24.2380	−	15.5768i	1.08072	−	0.694535i	0.125994	−	0.992031i	$-0.459788\pi$
$503$	24.2380	−	15.5768i	1.08072	−	0.694535i	0.954723	+	0.297496i	$0.0961516\pi$
$504$		0			0
$505$	29.3056			1.30408
$506$	0.179741	−	5.46375i	0.00799046	−	0.242893i
$507$		0			0
$508$	2.79901	−	3.23022i	0.124186	−	0.143318i
$509$	−5.83624	+	3.75072i	−0.258687	+	0.166248i	−0.663556	−	0.748127i	$-0.730953\pi$
$509$	−5.83624	+	3.75072i	−0.258687	+	0.166248i	0.404869	+	0.914375i	$0.367317\pi$
$510$		0			0
$511$	−16.9682	−	37.1552i	−0.750629	−	1.64365i
$512$	−3.61279	+	25.1275i	−0.159664	+	1.11049i
$513$		0			0
$514$	15.4818	+	9.94954i	0.682872	+	0.438855i
$515$	7.86958	−	17.2320i	0.346775	−	0.759332i
$516$		0			0
$517$	0.880091	+	1.01568i	0.0387064	+	0.0446695i
$518$	−3.58155	−	4.13333i	−0.157364	−	0.181608i
$519$		0			0
$520$	−15.5097	+	33.9616i	−0.680146	+	1.48931i
$521$	−8.05562	−	5.17704i	−0.352923	−	0.226810i	0.352151	−	0.935943i	$-0.385450\pi$
$521$	−8.05562	−	5.17704i	−0.352923	−	0.226810i	−0.705075	+	0.709133i	$0.749087\pi$
$522$		0			0
$523$	0.967665	−	6.73026i	0.0423130	−	0.294294i	−0.957666	−	0.287880i	$-0.907049\pi$
$523$	0.967665	−	6.73026i	0.0423130	−	0.294294i	0.999979	−	0.00641336i	$-0.00204145\pi$
$524$	0.0399632	+	0.0875072i	0.00174580	+	0.00382277i
$525$		0			0
$526$	−9.57841	+	6.15567i	−0.417638	+	0.268400i
$527$	−4.47089	+	5.15969i	−0.194755	+	0.224759i
$528$		0			0
$529$	−22.9503	−	1.51163i	−0.997838	−	0.0657229i
$530$	42.1332			1.83015
$531$		0			0
$532$	−5.74905	+	3.69469i	−0.249253	+	0.160185i
$533$	−1.84314	−	12.8193i	−0.0798354	−	0.555268i
$534$		0			0
$535$	2.67585	−	18.6109i	0.115687	−	0.804620i
$536$	36.8673	−	10.8252i	1.59242	−	0.467578i
$537$		0			0
$538$	2.48726	−	5.44634i	0.107233	−	0.234808i
$539$	−4.04246	−	1.18697i	−0.174121	−	0.0511266i
$540$		0			0
$541$	13.1694	+	15.1983i	0.566196	+	0.653425i	0.964579	−	0.263794i	$-0.0849739\pi$
$541$	13.1694	+	15.1983i	0.566196	+	0.653425i	−0.398383	+	0.917219i	$0.630428\pi$
$542$	3.11957	+	0.915989i	0.133997	+	0.0393451i
$543$		0			0
$544$	5.88715	+	3.78344i	0.252409	+	0.162214i
$545$	30.1014	−	8.83856i	1.28940	−	0.378602i
$546$		0			0
$547$	8.96854	+	19.6384i	0.383467	+	0.839676i	0.998682	+	0.0513167i	$0.0163418\pi$
$547$	8.96854	+	19.6384i	0.383467	+	0.839676i	−0.615215	+	0.788359i	$0.710931\pi$
$548$	0.768332	+	5.34387i	0.0328215	+	0.228279i
$549$		0			0
$550$	3.02157	−	3.48708i	0.128840	−	0.148690i
$551$	−62.3160			−2.65475
$552$		0			0
$553$	2.29902			0.0977642
$554$	−10.0917	+	11.6464i	−0.428755	+	0.494809i
$555$		0			0
$556$	−0.876671	−	6.09738i	−0.0371791	−	0.258586i
$557$	−4.10982	−	8.99924i	−0.174138	−	0.381310i	0.802358	−	0.596843i	$-0.203578\pi$
$557$	−4.10982	−	8.99924i	−0.174138	−	0.381310i	−0.976497	+	0.215533i	$0.930851\pi$
$558$		0			0
$559$	2.26576	−	0.665288i	0.0958315	−	0.0281387i
$560$	−29.2912	−	18.8243i	−1.23778	−	0.795473i
$561$		0			0
$562$	1.07298	+	0.315056i	0.0452610	+	0.0132898i
$563$	14.1827	+	16.3677i	0.597729	+	0.689816i	0.971320	−	0.237778i	$-0.0764191\pi$
$563$	14.1827	+	16.3677i	0.597729	+	0.689816i	−0.373591	+	0.927594i	$0.621874\pi$
$564$		0			0
$565$	41.5339	+	12.1955i	1.74734	+	0.513067i
$566$	8.16484	−	17.8785i	0.343194	−	0.751490i
$567$		0			0
$568$	22.6612	−	6.65392i	0.950842	−	0.279192i
$569$	−1.56897	+	10.9124i	−0.0657746	+	0.457472i	0.930142	+	0.367199i	$0.119683\pi$
$569$	−1.56897	+	10.9124i	−0.0657746	+	0.457472i	−0.995917	+	0.0902734i	$0.971226\pi$
$570$		0			0
$571$	−2.97761	−	20.7097i	−0.124609	−	0.866674i	−0.952229	−	0.305385i	$-0.901215\pi$
$571$	−2.97761	−	20.7097i	−0.124609	−	0.866674i	0.827620	−	0.561289i	$-0.189694\pi$
$572$	−0.848227	+	0.545123i	−0.0354662	+	0.0227927i
$573$		0			0
$574$	14.0857			0.587926
$575$	−14.2452	−	13.1881i	−0.594067	−	0.549983i
$576$		0			0
$577$	−15.9718	+	18.4325i	−0.664917	+	0.767355i	−0.983572	−	0.180516i	$-0.942223\pi$
$577$	−15.9718	+	18.4325i	−0.664917	+	0.767355i	0.318655	+	0.947871i	$0.396769\pi$
$578$	−3.19620	+	2.05408i	−0.132945	+	0.0854383i
$579$		0			0
$580$	3.06370	+	6.70857i	0.127213	+	0.278558i
$581$	5.21958	−	36.3030i	0.216545	−	1.50610i
$582$		0			0
$583$	7.80701	+	5.01726i	0.323333	+	0.207794i
$584$	14.7393	−	32.2746i	0.609918	−	1.33553i
$585$		0			0
$586$	−13.7000	−	15.8107i	−0.565943	−	0.653133i
$587$	18.3542	+	21.1819i	0.757559	+	0.874270i	0.995278	−	0.0970640i	$-0.0309451\pi$
$587$	18.3542	+	21.1819i	0.757559	+	0.874270i	−0.237719	+	0.971334i	$0.576400\pi$
$588$		0			0
$589$	4.51663	−	9.89005i	0.186105	−	0.407512i
$590$	31.7236	+	20.3875i	1.30604	+	0.839341i
$591$		0			0
$592$	0.579741	−	4.03219i	0.0238272	−	0.165722i
$593$	−0.327016	−	0.716064i	−0.0134289	−	0.0294052i	0.902799	−	0.430063i	$-0.141509\pi$
$593$	−0.327016	−	0.716064i	−0.0134289	−	0.0294052i	−0.916228	+	0.400658i	$0.868782\pi$
$594$		0			0
$595$	−38.8519	+	24.9686i	−1.59277	+	1.02361i
$596$	1.64210	−	1.89508i	0.0672630	−	0.0776256i
$597$		0			0
$598$	−13.3884	−	22.4209i	−0.547493	−	0.916860i
$599$	3.65036			0.149150			0.0745748	−	0.997215i	$-0.476240\pi$
$599$	3.65036			0.149150			0.0745748	+	0.997215i	$0.476240\pi$
$600$		0			0
$601$	−15.5028	+	9.96307i	−0.632374	+	0.406402i	−0.817188	−	0.576371i	$-0.804468\pi$
$601$	−15.5028	+	9.96307i	−0.632374	+	0.406402i	0.184814	+	0.982774i	$0.440832\pi$
$602$	0.365504	+	2.54214i	0.0148968	+	0.103610i
$603$		0			0
$604$	0.179878	−	1.25108i	0.00731913	−	0.0509057i
$605$	−29.5677	+	8.68185i	−1.20210	+	0.352967i
$606$		0			0
$607$	−18.9019	+	41.3895i	−0.767206	+	1.67995i	−0.0344971	+	0.999405i	$0.510983\pi$
$607$	−18.9019	+	41.3895i	−0.767206	+	1.67995i	−0.732709	+	0.680542i	$0.761744\pi$
$608$	−10.6932	−	3.13980i	−0.433666	−	0.127336i
$609$		0			0
$610$	−13.4715	−	15.5469i	−0.545444	−	0.629475i
$611$	6.15985	+	1.80870i	0.249201	+	0.0731720i
$612$		0			0
$613$	−7.45468	−	4.79083i	−0.301092	−	0.193500i	0.381368	−	0.924423i	$-0.375453\pi$
$613$	−7.45468	−	4.79083i	−0.301092	−	0.193500i	−0.682459	+	0.730924i	$0.739090\pi$
$614$	25.1850	−	7.39497i	1.01638	−	0.298437i
$615$		0			0
$616$	−3.71541	−	8.13560i	−0.149698	−	0.327793i
$617$	−4.13191	−	28.7380i	−0.166344	−	1.15695i	−0.886362	−	0.462994i	$-0.846775\pi$
$617$	−4.13191	−	28.7380i	−0.166344	−	1.15695i	0.720017	−	0.693956i	$-0.244134\pi$
$618$		0			0
$619$	−9.41353	+	10.8638i	−0.378362	+	0.436653i	−0.912708	−	0.408613i	$-0.866013\pi$
$619$	−9.41353	+	10.8638i	−0.378362	+	0.436653i	0.534346	+	0.845266i	$0.320558\pi$
$620$	−1.28676			−0.0516775
$621$		0			0
$622$	−8.66139			−0.347290
$623$	22.9968	−	26.5397i	0.921348	−	1.06329i
$624$		0			0
$625$	4.10638	+	28.5605i	0.164255	+	1.14242i
$626$	−7.09949	−	15.5457i	−0.283753	−	0.621331i
$627$		0			0
$628$	−1.59866	+	0.469408i	−0.0637933	+	0.0187314i
$629$	−4.54554	−	2.92124i	−0.181243	−	0.116478i
$630$		0			0
$631$	26.2710	+	7.71387i	1.04583	+	0.307084i	0.759133	−	0.650936i	$-0.225623\pi$
$631$	26.2710	+	7.71387i	1.04583	+	0.307084i	0.286701	+	0.958020i	$0.407441\pi$
$632$	1.30778	+	1.50925i	0.0520205	+	0.0600349i
$633$		0			0
$634$	−12.3528	−	3.62711i	−0.490593	−	0.144051i
$635$	−19.1091	+	41.8431i	−0.758322	+	1.66049i
$636$		0			0
$637$	−19.3106	+	5.67010i	−0.765113	+	0.224658i
$638$	1.42310	−	9.89788i	0.0563411	−	0.391861i
$639$		0			0
$640$	−3.58884	−	24.9609i	−0.141861	−	0.986668i
$641$	16.5142	−	10.6130i	0.652271	−	0.419189i	−0.172224	−	0.985058i	$-0.555095\pi$
$641$	16.5142	−	10.6130i	0.652271	−	0.419189i	0.824495	+	0.565869i	$0.191459\pi$
$642$		0			0
$643$	−9.24128			−0.364441			−0.182220	−	0.983258i	$-0.558328\pi$
$643$	−9.24128			−0.364441			−0.182220	+	0.983258i	$0.558328\pi$
$644$	−4.25759	+	1.77761i	−0.167772	+	0.0700476i
$645$		0			0
$646$	27.2171	−	31.4102i	1.07084	−	1.23582i
$647$	−3.52818	+	2.26742i	−0.138707	+	0.0891416i	−0.608154	−	0.793819i	$-0.708090\pi$
$647$	−3.52818	+	2.26742i	−0.138707	+	0.0891416i	0.469447	+	0.882961i	$0.344453\pi$
$648$		0			0
$649$	3.45041	+	7.55534i	0.135440	+	0.296573i
$650$	3.13678	−	21.8168i	0.123035	−	0.855725i
$651$		0			0
$652$	1.69075	+	1.08658i	0.0662151	+	0.0425538i
$653$	13.4137	−	29.3720i	0.524920	−	1.14941i	−0.442623	−	0.896708i	$-0.645952\pi$
$653$	13.4137	−	29.3720i	0.524920	−	1.14941i	0.967543	−	0.252707i	$-0.0813208\pi$
$654$		0			0
$655$	−0.678001	−	0.782455i	−0.0264917	−	0.0305731i
$656$	6.87051	+	7.92899i	0.268248	+	0.309575i
$657$		0			0
$658$	−2.90055	+	6.35131i	−0.113075	+	0.247600i
$659$	−8.22217	−	5.28407i	−0.320290	−	0.205838i	0.370609	−	0.928789i	$-0.379149\pi$
$659$	−8.22217	−	5.28407i	−0.320290	−	0.205838i	−0.690899	+	0.722951i	$0.742785\pi$
$660$		0			0
$661$	−3.28349	+	22.8371i	−0.127713	+	0.888262i	0.820731	+	0.571315i	$0.193567\pi$
$661$	−3.28349	+	22.8371i	−0.127713	+	0.888262i	−0.948443	+	0.316947i	$0.897342\pi$
$662$	−3.47614	−	7.61167i	−0.135104	−	0.295836i
$663$		0			0
$664$	26.8012	−	17.2241i	1.04009	−	0.668425i
$665$	48.1639	−	55.5841i	1.86771	−	2.15546i
$666$		0			0
$667$	−41.4239	−	7.35335i	−1.60394	−	0.284723i
$668$	0.0568738			0.00220052
$669$		0			0
$670$	−42.6541	+	27.4121i	−1.64787	+	1.05902i
$671$	−0.644835	−	4.48493i	−0.0248936	−	0.173139i
$672$		0			0
$673$	−1.15240	+	8.01513i	−0.0444218	+	0.308961i	0.955481	+	0.295051i	$0.0953367\pi$
$673$	−1.15240	+	8.01513i	−0.0444218	+	0.308961i	−0.999903	+	0.0139094i	$0.995572\pi$
$674$	−16.3866	+	4.81154i	−0.631189	+	0.185334i
$675$		0			0
$676$	−0.491498	+	1.07623i	−0.0189038	+	0.0413934i
$677$	35.5305	+	10.4327i	1.36555	+	0.400961i	0.880716	−	0.473645i	$-0.157062\pi$
$677$	35.5305	+	10.4327i	1.36555	+	0.400961i	0.484833	+	0.874607i	$0.338880\pi$
$678$		0			0
$679$	−14.9115	−	17.2088i	−0.572252	−	0.660414i
$680$	−38.4919	−	11.3022i	−1.47610	−	0.433421i
$681$		0			0
$682$	1.46773	+	0.943251i	0.0562022	+	0.0361190i
$683$	−30.6917	+	9.01190i	−1.17439	+	0.344831i	−0.810007	−	0.586420i	$-0.800537\pi$
$683$	−30.6917	+	9.01190i	−1.17439	+	0.344831i	−0.364379	+	0.931251i	$0.618719\pi$
$684$		0			0
$685$	−24.1371	−	52.8528i	−0.922230	−	2.01940i
$686$	1.38270	+	9.61688i	0.0527917	+	0.367174i
$687$		0			0
$688$	−1.25272	+	1.44571i	−0.0477593	+	0.0551172i
$689$	44.3310			1.68888
$690$		0			0
$691$	20.8081			0.791579			0.395789	−	0.918341i	$-0.370471\pi$
$691$	20.8081			0.791579			0.395789	+	0.918341i	$0.370471\pi$
$692$	−4.36336	+	5.03558i	−0.165870	+	0.191424i
$693$		0			0
$694$	−1.44814	−	10.0720i	−0.0549705	−	0.382329i
$695$	27.5405	+	60.3053i	1.04467	+	2.28751i
$696$		0			0
$697$	13.3523	−	3.92059i	0.505755	−	0.148503i
$698$	−22.3556	−	14.3671i	−0.846173	−	0.543802i
$699$		0			0
$700$	−3.73643	−	1.09711i	−0.141224	−	0.0414670i
$701$	4.80108	+	5.54074i	0.181334	+	0.209271i	0.839138	−	0.543918i	$-0.183060\pi$
$701$	4.80108	+	5.54074i	0.181334	+	0.209271i	−0.657804	+	0.753189i	$0.728514\pi$
$702$		0			0
$703$	8.25634	+	2.42428i	0.311394	+	0.0914335i
$704$	3.17097	−	6.94345i	0.119510	−	0.261691i
$705$		0			0
$706$	10.4337	−	3.06360i	0.392676	−	0.115300i
$707$	−4.77257	+	33.1939i	−0.179491	+	1.24839i
$708$		0			0
$709$	1.88132	+	13.0849i	0.0706544	+	0.491412i	0.994168	+	0.107846i	$0.0343952\pi$
$709$	1.88132	+	13.0849i	0.0706544	+	0.491412i	−0.923513	+	0.383567i	$0.874696\pi$
$710$	−26.2181	+	16.8494i	−0.983949	+	0.632346i
$711$		0			0
$712$	30.5043			1.14320
$713$	4.16942	−	6.04133i	0.156146	−	0.226250i
$714$		0			0
$715$	7.10621	−	8.20100i	0.265757	−	0.306700i
$716$	5.59442	−	3.59531i	0.209073	−	0.134363i
$717$		0			0
$718$	9.29032	+	20.3430i	0.346712	+	0.759192i
$719$	−3.05833	+	21.2712i	−0.114057	+	0.793281i	0.849847	+	0.527029i	$0.176694\pi$
$719$	−3.05833	+	21.2712i	−0.114057	+	0.793281i	−0.963904	+	0.266251i	$0.914215\pi$
$720$		0			0
$721$	18.2368	+	11.7201i	0.679174	+	0.436478i
$722$	−17.1426	+	37.5371i	−0.637982	+	1.39699i
$723$		0			0
$724$	1.06444	+	1.22843i	0.0395598	+	0.0456544i
$725$	−23.2538	−	26.8364i	−0.863626	−	0.996678i
$726$		0			0
$727$	11.6637	−	25.5400i	0.432584	−	0.947227i	−0.560316	−	0.828279i	$-0.689320\pi$
$727$	11.6637	−	25.5400i	0.432584	−	0.947227i	0.992900	−	0.118948i	$-0.0379523\pi$
$728$	−35.9419	−	23.0984i	−1.33209	−	0.856085i
$729$		0			0
$730$	−6.66316	+	46.3433i	−0.246615	+	1.71524i
$731$	1.05405	+	2.30804i	0.0389854	+	0.0853660i
$732$		0			0
$733$	26.1972	−	16.8359i	0.967614	−	0.621848i	0.0415191	−	0.999138i	$-0.486780\pi$
$733$	26.1972	−	16.8359i	0.967614	−	0.621848i	0.926095	+	0.377290i	$0.123144\pi$
$734$	−14.8497	+	17.1375i	−0.548113	+	0.632556i
$735$		0			0
$736$	−6.73767	−	3.34895i	−0.248354	−	0.123444i
$737$	−11.1678			−0.411370
$738$		0			0
$739$	30.3867	−	19.5284i	1.11779	−	0.718363i	0.154817	−	0.987943i	$-0.450521\pi$
$739$	30.3867	−	19.5284i	1.11779	−	0.718363i	0.962978	+	0.269580i	$0.0868850\pi$
$740$	−0.144931	−	1.00802i	−0.00532777	−	0.0370554i
$741$		0			0
$742$	−6.86162	+	47.7236i	−0.251898	+	1.75199i
$743$	40.0128	−	11.7488i	1.46793	−	0.431023i	0.552503	−	0.833511i	$-0.313673\pi$
$743$	40.0128	−	11.7488i	1.46793	−	0.431023i	0.915425	+	0.402488i	$0.131855\pi$
$744$		0			0
$745$	−11.2108	+	24.5482i	−0.410731	+	0.899376i
$746$	−38.2616	−	11.2346i	−1.40085	−	0.411328i
$747$		0			0
$748$	−0.709479	−	0.818783i	−0.0259411	−	0.0299377i
$749$	20.6445	+	6.06178i	0.754334	+	0.221493i
$750$		0			0
$751$	−18.1965	−	11.6942i	−0.664001	−	0.426728i	0.164757	−	0.986334i	$-0.447316\pi$
$751$	−18.1965	−	11.6942i	−0.664001	−	0.426728i	−0.828758	+	0.559606i	$0.810952\pi$
$752$	−4.99001	+	1.46520i	−0.181967	+	0.0534303i
$753$		0			0
$754$	−19.8435	−	43.4511i	−0.722656	−	1.58240i
$755$	1.93589	+	13.4644i	0.0704544	+	0.490021i
$756$		0			0
$757$	1.59111	−	1.83624i	0.0578300	−	0.0667394i	−0.726097	−	0.687592i	$-0.758668\pi$
$757$	1.59111	−	1.83624i	0.0578300	−	0.0667394i	0.783928	+	0.620852i	$0.213213\pi$
$758$	−5.01417			−0.182123
$759$		0			0
$760$	63.8873			2.31744
$761$	−13.3097	+	15.3602i	−0.482475	+	0.556806i	−0.943839	−	0.330405i	$-0.892815\pi$
$761$	−13.3097	+	15.3602i	−0.482475	+	0.556806i	0.461364	+	0.887211i	$0.347360\pi$
$762$		0			0
$763$	5.10913	+	35.5347i	0.184963	+	1.28644i
$764$	0.328238	+	0.718742i	0.0118753	+	0.0260032i
$765$		0			0
$766$	−21.0987	+	6.19514i	−0.762327	+	0.223839i
$767$	33.3784	+	21.4510i	1.20522	+	0.774550i
$768$		0			0
$769$	52.9226	+	15.5395i	1.90844	+	0.560368i	0.983717	+	0.179725i	$0.0575207\pi$
$769$	52.9226	+	15.5395i	1.90844	+	0.560368i	0.924722	+	0.380643i	$0.124297\pi$
$770$	7.72871	+	8.91941i	0.278523	+	0.321433i
$771$		0			0
$772$	−5.47827	−	1.60857i	−0.197167	−	0.0578935i
$773$	−2.17489	+	4.76235i	−0.0782254	+	0.171290i	−0.944704	−	0.327925i	$-0.893651\pi$
$773$	−2.17489	+	4.76235i	−0.0782254	+	0.171290i	0.866478	+	0.499215i	$0.166378\pi$
$774$		0			0
$775$	5.94457	−	1.74548i	0.213535	−	0.0626996i
$776$	2.81492	−	19.5782i	0.101050	−	0.702816i
$777$		0			0
$778$	−2.59321	−	18.0362i	−0.0929712	−	0.646629i
$779$	−18.6436	+	11.9815i	−0.667975	+	0.429281i
$780$		0			0
$781$	−6.86448			−0.245630
$782$	21.7987	−	17.6679i	0.779520	−	0.631804i
$783$		0			0
$784$	10.6766	−	12.3215i	0.381308	−	0.440052i
$785$	15.0849	−	9.69451i	0.538405	−	0.346012i
$786$		0			0
$787$	5.52309	+	12.0939i	0.196877	+	0.431100i	0.982163	−	0.188033i	$-0.0602113\pi$
$787$	5.52309	+	12.0939i	0.196877	+	0.431100i	−0.785286	+	0.619133i	$0.787484\pi$
$788$	−0.0727517	+	0.505999i	−0.00259167	+	0.0180255i
$789$		0			0
$790$	−2.21690	−	1.42471i	−0.0788737	−	0.0506890i
$791$	−20.5776	+	45.0587i	−0.731656	+	1.60210i
$792$		0			0
$793$	−14.1742	−	16.3579i	−0.503339	−	0.580884i
$794$	21.2944	+	24.5751i	0.755711	+	0.872137i
$795$		0			0
$796$	−0.755603	+	1.65454i	−0.0267816	+	0.0586436i
$797$	−21.1452	−	13.5892i	−0.749003	−	0.481355i	0.109613	−	0.993974i	$-0.465039\pi$
$797$	−21.1452	−	13.5892i	−0.749003	−	0.481355i	−0.858616	+	0.512619i	$0.828675\pi$
$798$		0			0
$799$	−0.981712	+	6.82796i	−0.0347305	+	0.241556i
$800$	−2.63811	−	5.77667i	−0.0932714	−	0.204236i
$801$		0			0
$802$	8.20159	−	5.27084i	0.289608	−	0.186120i
$803$	−6.75323	+	7.79365i	−0.238316	+	0.275032i
$804$		0			0
$805$	38.5753	−	31.2655i	1.35960	−	1.10196i
$806$	8.33428			0.293563
$807$		0			0
$808$	−24.5059	+	15.7490i	−0.862115	+	0.554048i
$809$	4.06307	+	28.2593i	0.142850	+	0.993543i	0.927558	+	0.373678i	$0.121903\pi$
$809$	4.06307	+	28.2593i	0.142850	+	0.993543i	−0.784709	+	0.619865i	$0.787187\pi$
$810$		0			0
$811$	3.02398	−	21.0323i	0.106186	−	0.738542i	−0.865267	−	0.501311i	$-0.832851\pi$
$811$	3.02398	−	21.0323i	0.106186	−	0.738542i	0.971453	−	0.237231i	$-0.0762398\pi$
$812$	−8.09764	+	2.37768i	−0.284171	+	0.0834402i
$813$		0			0
$814$	−0.573606	+	1.25602i	−0.0201049	+	0.0440236i
$815$	−20.7539	−	6.09389i	−0.726976	−	0.213460i
$816$		0			0
$817$	−2.64615	−	3.05382i	−0.0925770	−	0.106840i
$818$	19.7809	+	5.80819i	0.691623	+	0.203079i
$819$		0			0
$820$	2.20645	+	1.41800i	0.0770525	+	0.0495186i
$821$	−33.0199	+	9.69551i	−1.15240	+	0.338376i	−0.801475	−	0.598028i	$-0.795951\pi$
$821$	−33.0199	+	9.69551i	−1.15240	+	0.338376i	−0.350926	+	0.936403i	$0.614133\pi$
$822$		0			0
$823$	−2.86788	−	6.27977i	−0.0999678	−	0.218899i	0.853039	−	0.521846i	$-0.174757\pi$
$823$	−2.86788	−	6.27977i	−0.0999678	−	0.218899i	−0.953007	+	0.302947i	$0.902029\pi$
$824$	2.67987	+	18.6389i	0.0933577	+	0.649317i
$825$		0			0
$826$	−28.2590	+	32.6126i	−0.983256	+	1.13474i
$827$	39.7475			1.38216			0.691079	−	0.722779i	$-0.257136\pi$
$827$	39.7475			1.38216			0.691079	+	0.722779i	$0.257136\pi$
$828$		0			0
$829$	−32.5685			−1.13115			−0.565575	−	0.824697i	$-0.691346\pi$
$829$	−32.5685			−1.13115			−0.565575	+	0.824697i	$0.691346\pi$
$830$	−27.5303	+	31.7717i	−0.955591	+	1.10281i
$831$		0			0
$832$	−5.18931	−	36.0924i	−0.179907	−	1.25128i
$833$	−8.98341	−	19.6709i	−0.311257	−	0.681557i
$834$		0			0
$835$	−0.587297	+	0.172446i	−0.0203243	+	0.00596774i
$836$	1.45146	+	0.932797i	0.0501998	+	0.0322615i
$837$		0			0
$838$	−33.0117	−	9.69310i	−1.14037	−	0.334842i
$839$	12.3067	+	14.2027i	0.424873	+	0.490330i	0.927315	−	0.374281i	$-0.122110\pi$
$839$	12.3067	+	14.2027i	0.424873	+	0.490330i	−0.502442	+	0.864611i	$0.667565\pi$
$840$		0			0
$841$	−46.0143	−	13.5110i	−1.58670	−	0.465897i
$842$	−4.17294	+	9.13745i	−0.143809	+	0.314897i
$843$		0			0
$844$	−4.80008	+	1.40943i	−0.165225	+	0.0485146i
$845$	1.81215	−	12.6037i	0.0623397	−	0.433582i
$846$		0			0
$847$	−5.01854	−	34.9047i	−0.172439	−	1.19934i
$848$	−30.2110	+	19.4154i	−1.03745	+	0.666729i
$849$		0			0
$850$	23.6831			0.812325
$851$	5.20224	+	2.58577i	0.178331	+	0.0886390i
$852$		0			0
$853$	−3.68524	+	4.25300i	−0.126180	+	0.145620i	−0.815324	−	0.579005i	$-0.803441\pi$
$853$	−3.68524	+	4.25300i	−0.126180	+	0.145620i	0.689144	+	0.724624i	$0.257987\pi$
$854$	19.8036	−	12.7270i	0.677666	−	0.435509i
$855$		0			0
$856$	7.76403	+	17.0009i	0.265369	+	0.581078i
$857$	3.04834	−	21.2017i	0.104129	−	0.724236i	−0.869139	−	0.494567i	$-0.835327\pi$
$857$	3.04834	−	21.2017i	0.104129	−	0.724236i	0.973269	−	0.229669i	$-0.0737644\pi$
$858$		0			0
$859$	18.7303	+	12.0372i	0.639070	+	0.410705i	0.819658	−	0.572854i	$-0.194164\pi$
$859$	18.7303	+	12.0372i	0.639070	+	0.410705i	−0.180588	+	0.983559i	$0.557800\pi$
$860$	−0.198661	+	0.435007i	−0.00677428	+	0.0148336i
$861$		0			0
$862$	19.5167	+	22.5235i	0.664741	+	0.767152i
$863$	−18.9335	−	21.8504i	−0.644503	−	0.743796i	0.335661	−	0.941983i	$-0.391040\pi$
$863$	−18.9335	−	21.8504i	−0.644503	−	0.743796i	−0.980164	+	0.198186i	$0.936495\pi$
$864$		0			0
$865$	29.7891	−	65.2291i	1.01286	−	2.21786i
$866$	12.4685	+	8.01304i	0.423698	+	0.272294i
$867$		0			0
$868$	0.209556	−	1.45749i	0.00711279	−	0.0494705i
$869$	−0.241120	−	0.527980i	−0.00817945	−	0.0179105i
$870$		0			0
$871$	−44.8790	+	28.8420i	−1.52067	+	0.977273i
$872$	−20.4215	+	23.5677i	−0.691559	+	0.798102i
$873$		0			0
$874$	−25.3818	+	36.7773i	−0.858554	+	1.24401i
$875$	−9.85850			−0.333278
$876$		0			0
$877$	24.6253	−	15.8258i	0.831539	−	0.534398i	−0.0542277	−	0.998529i	$-0.517270\pi$
$877$	24.6253	−	15.8258i	0.831539	−	0.534398i	0.885767	+	0.464131i	$0.153633\pi$
$878$	−2.12349	−	14.7692i	−0.0716644	−	0.498437i
$879$		0			0
$880$	−1.25104	+	8.70115i	−0.0421724	+	0.293316i
$881$	7.96364	−	2.33833i	0.268302	−	0.0787805i	−0.144814	−	0.989459i	$-0.546259\pi$
$881$	7.96364	−	2.33833i	0.268302	−	0.0787805i	0.413116	+	0.910678i	$0.364440\pi$
$882$		0			0
$883$	21.9897	−	48.1508i	0.740013	−	1.62040i	−0.0435204	−	0.999053i	$-0.513857\pi$
$883$	21.9897	−	48.1508i	0.740013	−	1.62040i	0.783533	−	0.621350i	$-0.213415\pi$
$884$	−4.96572	−	1.45807i	−0.167015	−	0.0490401i
$885$		0			0
$886$	18.2755	+	21.0911i	0.613978	+	0.708568i
$887$	35.1430	+	10.3189i	1.17999	+	0.346476i	0.812169	−	0.583422i	$-0.198287\pi$
$887$	35.1430	+	10.3189i	1.17999	+	0.346476i	0.367818	+	0.929898i	$0.380105\pi$
$888$		0			0
$889$	−44.2830	−	28.4590i	−1.48520	−	0.954483i
$890$	−38.6222	+	11.3405i	−1.29462	+	0.380134i
$891$		0			0
$892$	0.902627	+	1.97648i	0.0302222	+	0.0661773i
$893$	−1.56341	−	10.8737i	−0.0523174	−	0.363875i
$894$		0			0
$895$	−46.8684	+	54.0891i	−1.56664	+	1.80800i
$896$	28.8573			0.964055
$897$		0			0
$898$	52.4165			1.74916
$899$	8.79284	−	10.1475i	0.293258	−	0.338437i
$900$		0			0
$901$	6.77896	+	47.1487i	0.225840	+	1.57075i
$902$	−1.47730	−	3.23484i	−0.0491888	−	0.107709i
$903$		0			0
$904$	−41.2854	+	12.1225i	−1.37313	+	0.403188i
$905$	−14.7165	−	9.45772i	−0.489193	−	0.314385i
$906$		0			0
$907$	−26.3530	−	7.73794i	−0.875037	−	0.256934i	−0.186781	−	0.982402i	$-0.559805\pi$
$907$	−26.3530	−	7.73794i	−0.875037	−	0.256934i	−0.688256	+	0.725468i	$0.741624\pi$
$908$	−0.438442	−	0.505989i	−0.0145502	−	0.0167918i
$909$		0			0
$910$	54.0941	+	15.8835i	1.79320	+	0.526531i
$911$	−9.61050	+	21.0441i	−0.318410	+	0.697221i	−0.999384	−	0.0350865i	$-0.988829\pi$
$911$	−9.61050	+	21.0441i	−0.318410	+	0.697221i	0.680974	+	0.732307i	$0.261557\pi$
$912$		0			0
$913$	−8.88458	+	2.60875i	−0.294037	+	0.0863369i
$914$	1.38446	−	9.62914i	0.0457939	−	0.318504i
$915$		0			0
$916$	−0.585001	−	4.06877i	−0.0193290	−	0.134436i
$917$	0.996691	−	0.640534i	0.0329136	−	0.0211523i
$918$		0			0
$919$	21.7546			0.717618			0.358809	−	0.933411i	$-0.383183\pi$
$919$	21.7546			0.717618			0.358809	+	0.933411i	$0.383183\pi$
$920$	42.4684	+	7.53877i	1.40014	+	0.248546i
$921$		0			0
$922$	−29.0465	+	33.5215i	−0.956596	+	1.10397i
$923$	−27.5857	+	17.7283i	−0.907995	+	0.583533i
$924$		0			0
$925$	2.03692	+	4.46024i	0.0669736	+	0.146652i
$926$	3.96308	−	27.5638i	0.130235	−	0.905804i
$927$		0			0
$928$	−11.5782	−	7.44084i	−0.380072	−	0.244257i
$929$	−18.4994	+	40.5081i	−0.606947	+	1.32903i	0.317696	+	0.948193i	$0.397091\pi$
$929$	−18.4994	+	40.5081i	−0.606947	+	1.32903i	−0.924643	+	0.380835i	$0.875636\pi$
$930$		0			0
$931$	22.5525	+	26.0270i	0.739130	+	0.853001i
$932$	1.99218	+	2.29910i	0.0652561	+	0.0753096i
$933$		0			0
$934$	1.70027	−	3.72308i	0.0556347	−	0.121823i
$935$	9.80892	+	6.30381i	0.320786	+	0.206157i
$936$		0			0
$937$	−1.87742	+	13.0577i	−0.0613325	+	0.426577i	0.935902	+	0.352260i	$0.114587\pi$
$937$	−1.87742	+	13.0577i	−0.0613325	+	0.426577i	−0.997235	+	0.0743168i	$0.976322\pi$
$938$	−24.1028	−	52.7778i	−0.786984	−	1.72326i
$939$		0			0
$940$	−1.09374	+	0.702902i	−0.0356738	+	0.0229261i
$941$	−13.3969	+	15.4608i	−0.436725	+	0.504008i	−0.930859	−	0.365378i	$-0.880940\pi$
$941$	−13.3969	+	15.4608i	−0.436725	+	0.504008i	0.494134	+	0.869386i	$0.335485\pi$
$942$		0			0
$943$	−13.8069	+	5.76460i	−0.449615	+	0.187721i
$944$	−32.1417			−1.04612
$945$		0			0
$946$	0.545479	−	0.350558i	0.0177351	−	0.0113976i
$947$	−4.51050	−	31.3712i	−0.146571	−	1.01943i	−0.921778	−	0.387719i	$-0.873263\pi$
$947$	−4.51050	−	31.3712i	−0.146571	−	1.01943i	0.775206	−	0.631708i	$-0.217646\pi$
$948$		0			0
$949$	−7.01072	+	48.7606i	−0.227578	+	1.58284i
$950$	−36.1883	+	10.6259i	−1.17410	+	0.344748i
$951$		0			0
$952$	19.0705	−	41.7585i	0.618078	−	1.35340i
$953$	25.3505	+	7.44358i	0.821183	+	0.241121i	0.665225	−	0.746643i	$-0.268335\pi$
$953$	25.3505	+	7.44358i	0.821183	+	0.241121i	0.155958	+	0.987764i	$0.450154\pi$
$954$		0			0
$955$	−5.56878	−	6.42671i	−0.180201	−	0.207963i
$956$	0.150371	+	0.0441528i	0.00486334	+	0.00142800i
$957$		0			0
$958$	−32.2316	−	20.7140i	−1.04136	−	0.669239i
$959$	63.7964	−	18.7323i	2.06009	−	0.604898i
$960$		0			0
$961$	−11.9047	−	26.0676i	−0.384022	−	0.840891i
$962$	0.938711	+	6.52888i	0.0302652	+	0.210499i
$963$		0			0
$964$	5.19535	−	5.99576i	0.167331	−	0.193110i
$965$	61.4477			1.97807
$966$		0			0
$967$	41.2669			1.32705			0.663527	−	0.748153i	$-0.269059\pi$
$967$	41.2669			1.32705			0.663527	+	0.748153i	$0.269059\pi$
$968$	20.0594	−	23.1498i	0.644734	−	0.744063i
$969$		0			0
$970$	3.71450	+	25.8349i	0.119265	+	0.829509i
$971$	−24.7805	−	54.2616i	−0.795243	−	1.74134i	−0.660994	−	0.750391i	$-0.729865\pi$
$971$	−24.7805	−	54.2616i	−0.795243	−	1.74134i	−0.134249	−	0.990948i	$-0.542862\pi$
$972$		0			0
$973$	−72.7920	+	21.3737i	−2.33360	+	0.685208i
$974$	41.4838	+	26.6600i	1.32923	+	0.854241i
$975$		0			0
$976$	16.8237	+	4.93988i	0.538513	+	0.158122i
$977$	−9.80911	−	11.3203i	−0.313821	−	0.362169i	0.576823	−	0.816869i	$-0.304292\pi$
$977$	−9.80911	−	11.3203i	−0.313821	−	0.362169i	−0.890645	+	0.454700i	$0.849747\pi$
$978$		0			0
$979$	−8.50687	−	2.49784i	−0.271881	−	0.0798314i
$980$	1.69314	−	3.70746i	0.0540855	−	0.118431i
$981$		0			0
$982$	31.8932	−	9.36470i	1.01775	−	0.298840i
$983$	−0.762680	+	5.30455i	−0.0243257	+	0.169189i	−0.998363	−	0.0571996i	$-0.981783\pi$
$983$	−0.762680	+	5.30455i	−0.0243257	+	0.169189i	0.974037	+	0.226389i	$0.0726919\pi$
$984$		0			0
$985$	−0.782972	−	5.44569i	−0.0249476	−	0.173514i
$986$	43.1785	−	27.7491i	1.37508	−	0.883713i
$987$		0			0
$988$	8.24191			0.262210
$989$	−1.39864	−	2.34224i	−0.0444743	−	0.0744789i
$990$		0			0
$991$	28.6136	−	33.0219i	0.908942	−	1.04898i	−0.0896520	−	0.995973i	$-0.528575\pi$
$991$	28.6136	−	33.0219i	0.908942	−	1.04898i	0.998594	−	0.0530023i	$-0.0168791\pi$
$992$	2.02010	−	1.29824i	0.0641382	−	0.0412191i
$993$		0			0
$994$	−14.8153	−	32.4409i	−0.469911	−	1.02896i
$995$	2.78590	−	19.3764i	0.0883189	−	0.614272i
$996$		0			0
$997$	−30.0823	−	19.3327i	−0.952717	−	0.612274i	−0.0307435	−	0.999527i	$-0.509787\pi$
$997$	−30.0823	−	19.3327i	−0.952717	−	0.612274i	−0.921973	+	0.387253i	$0.873424\pi$
$998$	8.93389	−	19.5625i	0.282797	−	0.619240i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.i.e.154.3	yes	40
3.2	odd	2	inner	207.2.i.e.154.2	yes	40
23.6	even	11		4761.2.a.bw.1.6		20
23.13	even	11	inner	207.2.i.e.82.3	yes	40
23.17	odd	22		4761.2.a.bx.1.6		20
69.17	even	22		4761.2.a.bx.1.15		20
69.29	odd	22		4761.2.a.bw.1.15		20
69.59	odd	22	inner	207.2.i.e.82.2	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.2.i.e.82.2	✓	40	69.59	odd	22	inner
207.2.i.e.82.3	yes	40	23.13	even	11	inner
207.2.i.e.154.2	yes	40	3.2	odd	2	inner
207.2.i.e.154.3	yes	40	1.1	even	1	trivial
4761.2.a.bw.1.6		20	23.6	even	11
4761.2.a.bw.1.15		20	69.29	odd	22
4761.2.a.bx.1.6		20	23.17	odd	22
4761.2.a.bx.1.15		20	69.17	even	22

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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	207.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.858969 - 0.991303i) q^{2} +(0.0397758 + 0.276647i) q^{4} +(-1.24955 - 2.73614i) q^{5} +(3.30268 - 0.969753i) q^{7} +(2.51532 + 1.61650i) q^{8} +O(q^{10})\)	\(q+(0.858969 - 0.991303i) q^{2} +(0.0397758 + 0.276647i) q^{4} +(-1.24955 - 2.73614i) q^{5} +(3.30268 - 0.969753i) q^{7} +(2.51532 + 1.61650i) q^{8} +(-3.78567 - 1.11157i) q^{10} +(-0.569092 - 0.656767i) q^{11} +(-3.98313 - 1.16955i) q^{13} +(1.87558 - 4.10694i) q^{14} +(3.22668 - 0.947439i) q^{16} +(0.634803 - 4.41515i) q^{17} +(1.01094 + 7.03126i) q^{19} +(0.707242 - 0.454517i) q^{20} -1.13989 q^{22} +(-0.157683 + 4.79324i) q^{23} +(-2.65076 + 3.05915i) q^{25} +(-4.58077 + 2.94388i) q^{26} +(0.399646 + 0.875102i) q^{28} +(-1.24846 + 8.68321i) q^{29} +(-1.28761 - 0.827495i) q^{31} +(-0.651736 + 1.42710i) q^{32} +(-3.83148 - 4.42176i) q^{34} +(-6.78024 - 7.82482i) q^{35} +(0.503213 - 1.10188i) q^{37} +(7.83847 + 5.03748i) q^{38} +(1.27994 - 8.90216i) q^{40} +(1.29601 + 2.83786i) q^{41} +(-0.478538 + 0.307537i) q^{43} +(0.159056 - 0.183561i) q^{44} +(4.61611 + 4.27355i) q^{46} -1.54648 q^{47} +(4.07847 - 2.62107i) q^{49} +(0.755615 + 5.25542i) q^{50} +(0.165121 - 1.14844i) q^{52} +(-10.2463 + 3.00858i) q^{53} +(-1.08590 + 2.37778i) q^{55} +(9.87489 + 2.89953i) q^{56} +(7.53531 + 8.69621i) q^{58} +(-9.17058 - 2.69273i) q^{59} +(4.38624 + 2.81886i) q^{61} +(-1.92631 + 0.565617i) q^{62} +(3.64887 + 7.98991i) q^{64} +(1.77707 + 12.3598i) q^{65} +(8.41554 - 9.71205i) q^{67} +1.24669 q^{68} -13.5808 q^{70} +(5.17277 - 5.96970i) q^{71} +(-1.68880 - 11.7459i) q^{73} +(-0.660056 - 1.44532i) q^{74} +(-1.90496 + 0.559348i) q^{76} +(-2.51643 - 1.61721i) q^{77} +(0.640855 + 0.188172i) q^{79} +(-6.62423 - 7.64477i) q^{80} +(3.92641 + 1.15290i) q^{82} +(4.42633 - 9.69231i) q^{83} +(-12.8737 + 3.78005i) q^{85} +(-0.106186 + 0.738541i) q^{86} +(-0.369786 - 2.57192i) q^{88} +(8.58265 - 5.51573i) q^{89} -14.2892 q^{91} +(-1.33231 + 0.147032i) q^{92} +(-1.32838 + 1.53303i) q^{94} +(17.9753 - 11.5520i) q^{95} +(-2.74809 - 6.01749i) q^{97} +(0.905001 - 6.29442i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{4} + 8 q^{7}+O(q^{10}) \) 40 * q - 4 * q^4 + 8 * q^7	\( 40 q - 4 q^{4} + 8 q^{7} - 56 q^{16} - 14 q^{19} - 28 q^{22} - 48 q^{25} - 64 q^{28} - 22 q^{31} - 10 q^{34} + 52 q^{37} + 6 q^{40} + 68 q^{43} + 84 q^{46} + 4 q^{49} + 110 q^{52} + 50 q^{55} + 18 q^{58} + 36 q^{61} + 116 q^{64} - 18 q^{67} + 96 q^{70} + 14 q^{73} + 34 q^{76} - 36 q^{79} - 72 q^{82} - 238 q^{85} - 160 q^{88} - 176 q^{91} - 206 q^{94} - 92 q^{97}+O(q^{100}) \) 40 * q - 4 * q^4 + 8 * q^7 - 56 * q^16 - 14 * q^19 - 28 * q^22 - 48 * q^25 - 64 * q^28 - 22 * q^31 - 10 * q^34 + 52 * q^37 + 6 * q^40 + 68 * q^43 + 84 * q^46 + 4 * q^49 + 110 * q^52 + 50 * q^55 + 18 * q^58 + 36 * q^61 + 116 * q^64 - 18 * q^67 + 96 * q^70 + 14 * q^73 + 34 * q^76 - 36 * q^79 - 72 * q^82 - 238 * q^85 - 160 * q^88 - 176 * q^91 - 206 * q^94 - 92 * q^97

Introduction

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