LMFDB - Embedded newform 975.2.bl.b.457.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(193,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 7]))

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

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

chi := DirichletCharacter("975.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.bl (of order $12$, degree $4$, 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:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			457.2
Root			$-0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	975.457
Dual form			975.2.bl.b.943.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.448288i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(0.866025 - 1.50000i) q^{4} +(-0.133975 - 0.500000i) q^{6} +1.93185 q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(0.258819 + 0.448288i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(0.866025 - 1.50000i) q^{4} +(-0.133975 - 0.500000i) q^{6} +1.93185 q^{8} +(0.866025 + 0.500000i) q^{9} +(-0.964102 + 3.59808i) q^{11} +(-1.22474 + 1.22474i) q^{12} +(-0.0693504 + 3.60488i) q^{13} +(-1.23205 - 2.13397i) q^{16} +(1.08604 + 4.05317i) q^{17} +0.517638i q^{18} +(7.09808 - 1.90192i) q^{19} +(-1.86250 + 0.499056i) q^{22} +(-0.965926 + 3.60488i) q^{23} +(-1.86603 - 0.500000i) q^{24} +(-1.63397 + 0.901924i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(7.56218 - 4.36603i) q^{29} +(3.00000 - 3.00000i) q^{31} +(2.56961 - 4.45069i) q^{32} +(1.86250 - 3.22595i) q^{33} +(-1.53590 + 1.53590i) q^{34} +(1.50000 - 0.866025i) q^{36} +(-4.69093 + 2.70831i) q^{37} +(2.68973 + 2.68973i) q^{38} +(1.00000 - 3.46410i) q^{39} +(-4.46410 - 1.19615i) q^{41} +(9.84873 - 2.63896i) q^{43} +(4.56218 + 4.56218i) q^{44} +(-1.86603 + 0.500000i) q^{46} -1.41421i q^{47} +(0.637756 + 2.38014i) q^{48} +(-3.50000 - 6.06218i) q^{49} -4.19615i q^{51} +(5.34727 + 3.22595i) q^{52} +(5.27792 - 5.27792i) q^{53} +(0.133975 - 0.500000i) q^{54} -7.34847 q^{57} +(3.91447 + 2.26002i) q^{58} +(2.36603 + 8.83013i) q^{59} +(0.598076 - 1.03590i) q^{61} +(2.12132 + 0.568406i) q^{62} -2.26795 q^{64} +1.92820 q^{66} +(-1.22474 - 2.12132i) q^{67} +(7.02030 + 1.88108i) q^{68} +(1.86603 - 3.23205i) q^{69} +(2.66987 + 9.96410i) q^{71} +(1.67303 + 0.965926i) q^{72} -0.896575 q^{73} +(-2.42820 - 1.40192i) q^{74} +(3.29423 - 12.2942i) q^{76} +(1.81173 - 0.448288i) q^{78} +8.73205i q^{79} +(0.500000 + 0.866025i) q^{81} +(-0.619174 - 2.31079i) q^{82} +9.76079i q^{83} +(3.73205 + 3.73205i) q^{86} +(-8.43451 + 2.26002i) q^{87} +(-1.86250 + 6.95095i) q^{88} +(10.8301 + 2.90192i) q^{89} +(4.57081 + 4.57081i) q^{92} +(-3.67423 + 2.12132i) q^{93} +(0.633975 - 0.366025i) q^{94} +(-3.63397 + 3.63397i) q^{96} +(-0.637756 + 1.10463i) q^{97} +(1.81173 - 3.13801i) q^{98} +(-2.63397 + 2.63397i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{6}+O(q^{10}) $ 8 * q - 8 * q^6	$ 8 q - 8 q^{6} + 20 q^{11} + 4 q^{16} + 36 q^{19} - 8 q^{24} - 20 q^{26} + 12 q^{29} + 24 q^{31} - 40 q^{34} + 12 q^{36} + 8 q^{39} - 8 q^{41} - 12 q^{44} - 8 q^{46} - 28 q^{49} + 8 q^{54} + 12 q^{59} - 16 q^{61} - 32 q^{64} - 40 q^{66} + 8 q^{69} + 56 q^{71} + 36 q^{74} - 36 q^{76} + 4 q^{81} + 16 q^{86} + 52 q^{89} + 12 q^{94} - 36 q^{96} - 28 q^{99}+O(q^{100}) $ 8 * q - 8 * q^6 + 20 * q^11 + 4 * q^16 + 36 * q^19 - 8 * q^24 - 20 * q^26 + 12 * q^29 + 24 * q^31 - 40 * q^34 + 12 * q^36 + 8 * q^39 - 8 * q^41 - 12 * q^44 - 8 * q^46 - 28 * q^49 + 8 * q^54 + 12 * q^59 - 16 * q^61 - 32 * q^64 - 40 * q^66 + 8 * q^69 + 56 * q^71 + 36 * q^74 - 36 * q^76 + 4 * q^81 + 16 * q^86 + 52 * q^89 + 12 * q^94 - 36 * q^96 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.258819	+	0.448288i	0.183013	+	0.316987i	0.942905	−	0.333062i	$-0.108082\pi$
$2$	0.258819	+	0.448288i	0.183013	+	0.316987i	−0.759892	+	0.650049i	$0.774748\pi$
$3$	−0.965926	−	0.258819i	−0.557678	−	0.149429i
$3$	−0.965926	−	0.258819i	−0.557678	−	0.149429i
$4$	0.866025	−	1.50000i	0.433013	−	0.750000i
$5$		0			0
$5$		0			0
$6$	−0.133975	−	0.500000i	−0.0546949	−	0.204124i
$7$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$7$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$8$	1.93185			0.683013
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$		0			0
$11$	−0.964102	+	3.59808i	−0.290688	+	1.08486i	0.653895	+	0.756586i	$0.273134\pi$
$11$	−0.964102	+	3.59808i	−0.290688	+	1.08486i	−0.944582	+	0.328275i	$0.893533\pi$
$12$	−1.22474	+	1.22474i	−0.353553	+	0.353553i
$13$	−0.0693504	+	3.60488i	−0.0192343	+	0.999815i
$13$	−0.0693504	+	3.60488i	−0.0192343	+	0.999815i
$14$		0			0
$15$		0			0
$16$	−1.23205	−	2.13397i	−0.308013	−	0.533494i
$17$	1.08604	+	4.05317i	0.263404	+	0.983039i	0.963220	+	0.268715i	$0.0865989\pi$
$17$	1.08604	+	4.05317i	0.263404	+	0.983039i	−0.699815	+	0.714324i	$0.746734\pi$
$18$			0.517638i			0.122008i
$19$	7.09808	−	1.90192i	1.62841	−	0.436331i	0.674953	−	0.737860i	$-0.264164\pi$
$19$	7.09808	−	1.90192i	1.62841	−	0.436331i	0.953457	+	0.301529i	$0.0974970\pi$
$20$		0			0
$21$		0			0
$22$	−1.86250	+	0.499056i	−0.397087	+	0.106399i
$23$	−0.965926	+	3.60488i	−0.201409	+	0.751670i	0.789105	+	0.614259i	$0.210545\pi$
$23$	−0.965926	+	3.60488i	−0.201409	+	0.751670i	−0.990514	+	0.137411i	$0.956122\pi$
$24$	−1.86603	−	0.500000i	−0.380901	−	0.102062i
$25$		0			0
$26$	−1.63397	+	0.901924i	−0.320449	+	0.176882i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$	7.56218	−	4.36603i	1.40426	−	0.810751i	0.409435	−	0.912339i	$-0.365726\pi$
$29$	7.56218	−	4.36603i	1.40426	−	0.810751i	0.994826	+	0.101589i	$0.0323926\pi$
$30$		0			0
$31$	3.00000	−	3.00000i	0.538816	−	0.538816i	−0.384365	−	0.923181i	$-0.625580\pi$
$31$	3.00000	−	3.00000i	0.538816	−	0.538816i	0.923181	+	0.384365i	$0.125580\pi$
$32$	2.56961	−	4.45069i	0.454247	−	0.786779i
$33$	1.86250	−	3.22595i	0.324220	−	0.561565i
$34$	−1.53590	+	1.53590i	−0.263404	+	0.263404i
$35$		0			0
$36$	1.50000	−	0.866025i	0.250000	−	0.144338i
$37$	−4.69093	+	2.70831i	−0.771184	+	0.445243i	−0.833297	−	0.552826i	$-0.813549\pi$
$37$	−4.69093	+	2.70831i	−0.771184	+	0.445243i	0.0621129	+	0.998069i	$0.480216\pi$
$38$	2.68973	+	2.68973i	0.436331	+	0.436331i
$39$	1.00000	−	3.46410i	0.160128	−	0.554700i
$40$		0			0
$41$	−4.46410	−	1.19615i	−0.697176	−	0.186808i	−0.107210	−	0.994236i	$-0.534192\pi$
$41$	−4.46410	−	1.19615i	−0.697176	−	0.186808i	−0.589965	+	0.807429i	$0.700859\pi$
$42$		0			0
$43$	9.84873	−	2.63896i	1.50192	−	0.402437i	0.588175	−	0.808733i	$-0.299847\pi$
$43$	9.84873	−	2.63896i	1.50192	−	0.402437i	0.913741	+	0.406296i	$0.133180\pi$
$44$	4.56218	+	4.56218i	0.687774	+	0.687774i
$45$		0			0
$46$	−1.86603	+	0.500000i	−0.275130	+	0.0737210i
$47$		−	1.41421i		−	0.206284i	−0.994667	−	0.103142i	$-0.967110\pi$
$47$		−	1.41421i		−	0.206284i	0.994667	−	0.103142i	$-0.0328896\pi$
$48$	0.637756	+	2.38014i	0.0920522	+	0.343544i
$49$	−3.50000	−	6.06218i	−0.500000	−	0.866025i
$50$		0			0
$51$		−	4.19615i		−	0.587579i
$52$	5.34727	+	3.22595i	0.741533	+	0.447358i
$53$	5.27792	−	5.27792i	0.724978	−	0.724978i	−0.244637	−	0.969615i	$-0.578669\pi$
$53$	5.27792	−	5.27792i	0.724978	−	0.724978i	0.969615	+	0.244637i	$0.0786688\pi$
$54$	0.133975	−	0.500000i	0.0182316	−	0.0680414i
$55$		0			0
$56$		0			0
$57$	−7.34847			−0.973329
$58$	3.91447	+	2.26002i	0.513995	+	0.296755i
$59$	2.36603	+	8.83013i	0.308030	+	1.14958i	0.930305	+	0.366786i	$0.119542\pi$
$59$	2.36603	+	8.83013i	0.308030	+	1.14958i	−0.622275	+	0.782799i	$0.713791\pi$
$60$		0			0
$61$	0.598076	−	1.03590i	0.0765758	−	0.132633i	−0.825195	−	0.564848i	$-0.808935\pi$
$61$	0.598076	−	1.03590i	0.0765758	−	0.132633i	0.901770	+	0.432215i	$0.142268\pi$
$62$	2.12132	+	0.568406i	0.269408	+	0.0721876i
$63$		0			0
$64$	−2.26795			−0.283494
$65$		0			0
$66$	1.92820			0.237345
$67$	−1.22474	−	2.12132i	−0.149626	−	0.259161i	0.781463	−	0.623952i	$-0.214474\pi$
$67$	−1.22474	−	2.12132i	−0.149626	−	0.259161i	−0.931089	+	0.364791i	$0.881140\pi$
$68$	7.02030	+	1.88108i	0.851336	+	0.228115i
$69$	1.86603	−	3.23205i	0.224643	−	0.389093i
$70$		0			0
$71$	2.66987	+	9.96410i	0.316856	+	1.18252i	0.922249	+	0.386595i	$0.126349\pi$
$71$	2.66987	+	9.96410i	0.316856	+	1.18252i	−0.605394	+	0.795926i	$0.706984\pi$
$72$	1.67303	+	0.965926i	0.197169	+	0.113835i
$73$	−0.896575			−0.104936			−0.0524681	−	0.998623i	$-0.516709\pi$
$73$	−0.896575			−0.104936			−0.0524681	+	0.998623i	$0.516709\pi$
$74$	−2.42820	−	1.40192i	−0.282273	−	0.162970i
$75$		0			0
$76$	3.29423	−	12.2942i	0.377874	−	1.41024i
$77$		0			0
$78$	1.81173	−	0.448288i	0.205138	−	0.0507586i
$79$			8.73205i			0.982432i	0.871038	+	0.491216i	$0.163448\pi$
$79$			8.73205i			0.982432i	−0.871038	+	0.491216i	$0.836552\pi$
$80$		0			0
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−0.619174	−	2.31079i	−0.0683763	−	0.255184i
$83$			9.76079i			1.07139i	0.844413	+	0.535693i	$0.179950\pi$
$83$			9.76079i			1.07139i	−0.844413	+	0.535693i	$0.820050\pi$
$84$		0			0
$85$		0			0
$86$	3.73205	+	3.73205i	0.402437	+	0.402437i
$87$	−8.43451	+	2.26002i	−0.904275	+	0.242300i
$88$	−1.86250	+	6.95095i	−0.198543	+	0.740974i
$89$	10.8301	+	2.90192i	1.14799	+	0.307603i	0.782160	−	0.623078i	$-0.214118\pi$
$89$	10.8301	+	2.90192i	1.14799	+	0.307603i	0.365831	+	0.930681i	$0.380785\pi$
$90$		0			0
$91$		0			0
$92$	4.57081	+	4.57081i	0.476540	+	0.476540i
$93$	−3.67423	+	2.12132i	−0.381000	+	0.219971i
$94$	0.633975	−	0.366025i	0.0653895	−	0.0377526i
$95$		0			0
$96$	−3.63397	+	3.63397i	−0.370891	+	0.370891i
$97$	−0.637756	+	1.10463i	−0.0647544	+	0.112158i	−0.896585	−	0.442872i	$-0.853960\pi$
$97$	−0.637756	+	1.10463i	−0.0647544	+	0.112158i	0.831831	+	0.555030i	$0.187293\pi$
$98$	1.81173	−	3.13801i	0.183013	−	0.316987i
$99$	−2.63397	+	2.63397i	−0.264724	+	0.264724i
$100$		0			0
$101$	−7.90192	+	4.56218i	−0.786271	+	0.453954i	−0.838648	−	0.544674i	$-0.816654\pi$
$101$	−7.90192	+	4.56218i	−0.786271	+	0.453954i	0.0523772	+	0.998627i	$0.483320\pi$
$102$	1.88108	−	1.08604i	0.186255	−	0.107534i
$103$	−6.55343	−	6.55343i	−0.645729	−	0.645729i	0.306229	−	0.951958i	$-0.400933\pi$
$103$	−6.55343	−	6.55343i	−0.645729	−	0.645729i	−0.951958	+	0.306229i	$0.900933\pi$
$104$	−0.133975	+	6.96410i	−0.0131373	+	0.682886i
$105$		0			0
$106$	3.73205	+	1.00000i	0.362489	+	0.0971286i
$107$	−1.79315	+	6.69213i	−0.173350	+	0.646953i	0.823476	+	0.567351i	$0.192032\pi$
$107$	−1.79315	+	6.69213i	−0.173350	+	0.646953i	−0.996827	+	0.0796020i	$0.974635\pi$
$108$	−1.67303	+	0.448288i	−0.160988	+	0.0431365i
$109$	−7.29423	−	7.29423i	−0.698660	−	0.698660i	0.265461	−	0.964122i	$-0.414476\pi$
$109$	−7.29423	−	7.29423i	−0.698660	−	0.698660i	−0.964122	+	0.265461i	$0.914476\pi$
$110$		0			0
$111$	5.23205	−	1.40192i	0.496604	−	0.133065i
$112$		0			0
$113$	−4.70951	−	17.5761i	−0.443034	−	1.65342i	−0.721077	−	0.692855i	$-0.756353\pi$
$113$	−4.70951	−	17.5761i	−0.443034	−	1.65342i	0.278043	−	0.960569i	$-0.410314\pi$
$114$	−1.90192	−	3.29423i	−0.178131	−	0.308533i
$115$		0			0
$116$		−	15.1244i		−	1.40426i
$117$	−1.86250	+	3.08725i	−0.172188	+	0.285416i
$118$	−3.34607	+	3.34607i	−0.308030	+	0.308030i
$119$		0			0
$120$		0			0
$121$	−2.49038	−	1.43782i	−0.226398	−	0.130711i
$122$	0.619174			0.0560574
$123$	4.00240	+	2.31079i	0.360885	+	0.208357i
$124$	−1.90192	−	7.09808i	−0.170798	−	0.637426i
$125$		0			0
$126$		0			0
$127$	−9.14162	−	2.44949i	−0.811188	−	0.217357i	−0.170698	−	0.985323i	$-0.554602\pi$
$127$	−9.14162	−	2.44949i	−0.811188	−	0.217357i	−0.640490	+	0.767966i	$0.721269\pi$
$128$	−5.72620	−	9.91808i	−0.506130	−	0.876642i
$129$	−10.1962			−0.897721
$130$		0			0
$131$	−12.0000			−1.04844			−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000			−1.04844			−0.524222	+	0.851581i	$0.675644\pi$
$132$	−3.22595	−	5.58750i	−0.280783	−	0.486330i
$133$		0			0
$134$	0.633975	−	1.09808i	0.0547671	−	0.0948593i
$135$		0			0
$136$	2.09808	+	7.83013i	0.179909	+	0.671428i
$137$	15.8338	+	9.14162i	1.35277	+	0.781021i	0.988636	−	0.150326i	$-0.0480323\pi$
$137$	15.8338	+	9.14162i	1.35277	+	0.781021i	0.364132	+	0.931347i	$0.381366\pi$
$138$	1.93185			0.164450
$139$	−5.36603	−	3.09808i	−0.455140	−	0.262775i	0.254858	−	0.966978i	$-0.417971\pi$
$139$	−5.36603	−	3.09808i	−0.455140	−	0.262775i	−0.709999	+	0.704203i	$0.751304\pi$
$140$		0			0
$141$	−0.366025	+	1.36603i	−0.0308249	+	0.115040i
$142$	−3.77577	+	3.77577i	−0.316856	+	0.316856i
$143$	−12.9038	−	3.72500i	−1.07907	−	0.311500i
$144$		−	2.46410i		−	0.205342i
$145$		0			0
$146$	−0.232051	−	0.401924i	−0.0192047	−	0.0332634i
$147$	1.81173	+	6.76148i	0.149429	+	0.557678i
$148$			9.38186i			0.771184i
$149$	9.09808	−	2.43782i	0.745343	−	0.199714i	0.133892	−	0.990996i	$-0.457253\pi$
$149$	9.09808	−	2.43782i	0.745343	−	0.199714i	0.611452	+	0.791282i	$0.290586\pi$
$150$		0			0
$151$	13.4641	+	13.4641i	1.09569	+	1.09569i	0.994908	+	0.100785i	$0.0321354\pi$
$151$	13.4641	+	13.4641i	1.09569	+	1.09569i	0.100785	+	0.994908i	$0.467865\pi$
$152$	13.7124	−	3.67423i	1.11222	−	0.298020i
$153$	−1.08604	+	4.05317i	−0.0878015	+	0.327680i
$154$		0			0
$155$		0			0
$156$	−4.33013	−	4.50000i	−0.346688	−	0.360288i
$157$	6.64136	+	6.64136i	0.530038	+	0.530038i	0.920584	−	0.390545i	$-0.127714\pi$
$157$	6.64136	+	6.64136i	0.530038	+	0.530038i	−0.390545	+	0.920584i	$0.627714\pi$
$158$	−3.91447	+	2.26002i	−0.311419	+	0.179798i
$159$	−6.46410	+	3.73205i	−0.512637	+	0.295971i
$160$		0			0
$161$		0			0
$162$	−0.258819	+	0.448288i	−0.0203347	+	0.0352208i
$163$	−0.896575	+	1.55291i	−0.0702252	+	0.121634i	−0.899000	−	0.437949i	$-0.855705\pi$
$163$	−0.896575	+	1.55291i	−0.0702252	+	0.121634i	0.828775	+	0.559582i	$0.189038\pi$
$164$	−5.66025	+	5.66025i	−0.441992	+	0.441992i
$165$		0			0
$166$	−4.37564	+	2.52628i	−0.339616	+	0.196077i
$167$	9.02150	−	5.20857i	0.698105	−	0.403051i	−0.108536	−	0.994092i	$-0.534616\pi$
$167$	9.02150	−	5.20857i	0.698105	−	0.403051i	0.806641	+	0.591042i	$0.201283\pi$
$168$		0			0
$169$	−12.9904	−	0.500000i	−0.999260	−	0.0384615i
$170$		0			0
$171$	7.09808	+	1.90192i	0.542803	+	0.145444i
$172$	4.57081	−	17.0585i	0.348521	−	1.30070i
$173$	−13.0053	+	3.48477i	−0.988776	+	0.264942i	−0.716736	−	0.697344i	$-0.754365\pi$
$173$	−13.0053	+	3.48477i	−0.988776	+	0.264942i	−0.272040	+	0.962286i	$0.587698\pi$
$174$	−3.19615	−	3.19615i	−0.242300	−	0.242300i
$175$		0			0
$176$	8.86603	−	2.37564i	0.668302	−	0.179071i
$177$		−	9.14162i		−	0.687126i
$178$	1.50215	+	5.60609i	0.112591	+	0.420194i
$179$	4.33013	+	7.50000i	0.323649	+	0.560576i	0.981238	−	0.192800i	$-0.0617570\pi$
$179$	4.33013	+	7.50000i	0.323649	+	0.560576i	−0.657589	+	0.753377i	$0.728424\pi$
$180$		0			0
$181$			2.60770i			0.193828i	0.995293	+	0.0969142i	$0.0308973\pi$
$181$			2.60770i			0.193828i	−0.995293	+	0.0969142i	$0.969103\pi$
$182$		0			0
$183$	−0.845807	+	0.845807i	−0.0625239	+	0.0625239i
$184$	−1.86603	+	6.96410i	−0.137565	+	0.513400i
$185$		0			0
$186$	−1.90192	−	1.09808i	−0.139456	−	0.0805149i
$187$	−15.6307			−1.14303
$188$	−2.12132	−	1.22474i	−0.154713	−	0.0893237i
$189$		0			0
$190$		0			0
$191$	−6.33013	+	10.9641i	−0.458032	+	0.793335i	−0.998857	−	0.0478006i	$-0.984779\pi$
$191$	−6.33013	+	10.9641i	−0.458032	+	0.793335i	0.540825	+	0.841135i	$0.318112\pi$
$192$	2.19067	+	0.586988i	0.158098	+	0.0423622i
$193$	−11.5725	−	20.0442i	−0.833009	−	1.44281i	−0.895641	−	0.444777i	$-0.853283\pi$
$193$	−11.5725	−	20.0442i	−0.833009	−	1.44281i	0.0626327	−	0.998037i	$-0.480050\pi$
$194$	−0.660254			−0.0474035
$195$		0			0
$196$	−12.1244			−0.866025
$197$	−12.2474	−	21.2132i	−0.872595	−	1.51138i	−0.859303	−	0.511466i	$-0.829102\pi$
$197$	−12.2474	−	21.2132i	−0.872595	−	1.51138i	−0.0132914	−	0.999912i	$-0.504231\pi$
$198$	−1.86250	−	0.499056i	−0.132362	−	0.0354663i
$199$	5.63397	−	9.75833i	0.399382	−	0.691750i	−0.594268	−	0.804267i	$-0.702558\pi$
$199$	5.63397	−	9.75833i	0.399382	−	0.691750i	0.993650	+	0.112517i	$0.0358914\pi$
$200$		0			0
$201$	0.633975	+	2.36603i	0.0447171	+	0.166887i
$202$	−4.09034	−	2.36156i	−0.287795	−	0.166159i
$203$		0			0
$204$	−6.29423	−	3.63397i	−0.440684	−	0.254429i
$205$		0			0
$206$	1.24167	−	4.63397i	0.0865112	−	0.322864i
$207$	−2.63896	+	2.63896i	−0.183420	+	0.183420i
$208$	7.77817	−	4.29341i	0.539319	−	0.297694i
$209$			27.3731i			1.89343i
$210$		0			0
$211$	−12.9282	−	22.3923i	−0.890014	−	1.54155i	−0.839856	−	0.542809i	$-0.817361\pi$
$211$	−12.9282	−	22.3923i	−0.890014	−	1.54155i	−0.0501577	−	0.998741i	$-0.515972\pi$
$212$	−3.34607	−	12.4877i	−0.229809	−	0.857658i
$213$		−	10.3156i		−	0.706813i
$214$	−3.46410	+	0.928203i	−0.236801	+	0.0634507i
$215$		0			0
$216$	−1.36603	−	1.36603i	−0.0929463	−	0.0929463i
$217$		0			0
$218$	1.38203	−	5.15780i	0.0936027	−	0.349330i
$219$	0.866025	+	0.232051i	0.0585206	+	0.0156805i
$220$		0			0
$221$	−14.6865	+	3.63397i	−0.987923	+	0.244448i
$222$	1.98262	+	1.98262i	0.133065	+	0.133065i
$223$	−4.57081	+	2.63896i	−0.306084	+	0.176718i	−0.645173	−	0.764037i	$-0.723215\pi$
$223$	−4.57081	+	2.63896i	−0.306084	+	0.176718i	0.339089	+	0.940754i	$0.389881\pi$
$224$		0			0
$225$		0			0
$226$	6.66025	−	6.66025i	0.443034	−	0.443034i
$227$	3.27671	−	5.67544i	0.217483	−	0.376692i	−0.736555	−	0.676378i	$-0.763549\pi$
$227$	3.27671	−	5.67544i	0.217483	−	0.376692i	0.954038	+	0.299686i	$0.0968819\pi$
$228$	−6.36396	+	11.0227i	−0.421464	+	0.729996i
$229$	−6.49038	+	6.49038i	−0.428896	+	0.428896i	−0.888252	−	0.459356i	$-0.848080\pi$
$229$	−6.49038	+	6.49038i	−0.428896	+	0.428896i	0.459356	+	0.888252i	$0.348080\pi$
$230$		0			0
$231$		0			0
$232$	14.6090	−	8.43451i	0.959128	−	0.553753i
$233$	1.55291	+	1.55291i	0.101735	+	0.101735i	0.756142	−	0.654407i	$-0.227082\pi$
$233$	1.55291	+	1.55291i	0.101735	+	0.101735i	−0.654407	+	0.756142i	$0.727082\pi$
$234$	−1.86603	−	0.0358984i	−0.121986	−	0.00234675i
$235$		0			0
$236$	15.2942	+	4.09808i	0.995569	+	0.266762i
$237$	2.26002	−	8.43451i	0.146804	−	0.547881i
$238$		0			0
$239$	−10.2942	−	10.2942i	−0.665878	−	0.665878i	0.290881	−	0.956759i	$-0.406052\pi$
$239$	−10.2942	−	10.2942i	−0.665878	−	0.665878i	−0.956759	+	0.290881i	$0.906052\pi$
$240$		0			0
$241$	5.83013	−	1.56218i	0.375551	−	0.100629i	−0.0661056	−	0.997813i	$-0.521057\pi$
$241$	5.83013	−	1.56218i	0.375551	−	0.100629i	0.441657	+	0.897184i	$0.354391\pi$
$242$		−	1.48854i		−	0.0956872i
$243$	−0.258819	−	0.965926i	−0.0166032	−	0.0619642i
$244$	−1.03590	−	1.79423i	−0.0663166	−	0.114864i
$245$		0			0
$246$			2.39230i			0.152528i
$247$	6.36396	+	25.7196i	0.404929	+	1.63650i
$248$	5.79555	−	5.79555i	0.368018	−	0.368018i
$249$	2.52628	−	9.42820i	0.160096	−	0.597488i
$250$		0			0
$251$	10.4545	+	6.03590i	0.659881	+	0.380983i	0.792232	−	0.610220i	$-0.208919\pi$
$251$	10.4545	+	6.03590i	0.659881	+	0.380983i	−0.132351	+	0.991203i	$0.542252\pi$
$252$		0			0
$253$	−12.0394	−	6.95095i	−0.756910	−	0.437002i
$254$	−1.26795	−	4.73205i	−0.0795582	−	0.296915i
$255$		0			0
$256$	0.696152	−	1.20577i	0.0435095	−	0.0753607i
$257$	14.6090	+	3.91447i	0.911285	+	0.244178i	0.683856	−	0.729617i	$-0.260302\pi$
$257$	14.6090	+	3.91447i	0.911285	+	0.244178i	0.227428	+	0.973795i	$0.426968\pi$
$258$	−2.63896	−	4.57081i	−0.164294	−	0.284566i
$259$		0			0
$260$		0			0
$261$	8.73205			0.540500
$262$	−3.10583	−	5.37945i	−0.191879	−	0.332344i
$263$	−13.6431	−	3.65565i	−0.841268	−	0.225417i	−0.187645	−	0.982237i	$-0.560085\pi$
$263$	−13.6431	−	3.65565i	−0.841268	−	0.225417i	−0.653624	+	0.756820i	$0.726752\pi$
$264$	3.59808	−	6.23205i	0.221446	−	0.383556i
$265$		0			0
$266$		0			0
$267$	−9.71003	−	5.60609i	−0.594244	−	0.343087i
$268$	−4.24264			−0.259161
$269$	−15.7583	−	9.09808i	−0.960802	−	0.554719i	−0.0643825	−	0.997925i	$-0.520508\pi$
$269$	−15.7583	−	9.09808i	−0.960802	−	0.554719i	−0.896420	+	0.443206i	$0.853841\pi$
$270$		0			0
$271$	−7.75833	+	28.9545i	−0.471285	+	1.75886i	0.163877	+	0.986481i	$0.447600\pi$
$271$	−7.75833	+	28.9545i	−0.471285	+	1.75886i	−0.635162	+	0.772379i	$0.719067\pi$
$272$	7.31130	−	7.31130i	0.443313	−	0.443313i
$273$		0			0
$274$			9.46410i			0.571747i
$275$		0			0
$276$	−3.23205	−	5.59808i	−0.194547	−	0.336965i
$277$	−6.67355	−	24.9060i	−0.400975	−	1.49646i	−0.811361	−	0.584546i	$-0.801273\pi$
$277$	−6.67355	−	24.9060i	−0.400975	−	1.49646i	0.410386	−	0.911912i	$-0.365394\pi$
$278$		−	3.20736i		−	0.192365i
$279$	4.09808	−	1.09808i	0.245345	−	0.0657401i
$280$		0			0
$281$	−5.00000	−	5.00000i	−0.298275	−	0.298275i	0.542063	−	0.840338i	$-0.317643\pi$
$281$	−5.00000	−	5.00000i	−0.298275	−	0.298275i	−0.840338	+	0.542063i	$0.817643\pi$
$282$	−0.707107	+	0.189469i	−0.0421076	+	0.0112827i
$283$	−1.93185	+	7.20977i	−0.114837	+	0.428576i	−0.999275	−	0.0380815i	$-0.987875\pi$
$283$	−1.93185	+	7.20977i	−0.114837	+	0.428576i	0.884438	+	0.466658i	$0.154542\pi$
$284$	17.2583	+	4.62436i	1.02409	+	0.274405i
$285$		0			0
$286$	−1.66987	−	6.74871i	−0.0987417	−	0.399060i
$287$		0			0
$288$	4.45069	−	2.56961i	0.262260	−	0.151416i
$289$	−0.526279	+	0.303848i	−0.0309576	+	0.0178734i
$290$		0			0
$291$	0.901924	−	0.901924i	0.0528717	−	0.0528717i
$292$	−0.776457	+	1.34486i	−0.0454387	+	0.0787022i
$293$	1.08604	−	1.88108i	0.0634474	−	0.109894i	−0.832557	−	0.553940i	$-0.813124\pi$
$293$	1.08604	−	1.88108i	0.0634474	−	0.109894i	0.896004	+	0.444046i	$0.146457\pi$
$294$	−2.56218	+	2.56218i	−0.149429	+	0.149429i
$295$		0			0
$296$	−9.06218	+	5.23205i	−0.526728	+	0.304107i
$297$	3.22595	−	1.86250i	0.187188	−	0.108073i
$298$	3.44760	+	3.44760i	0.199714	+	0.199714i
$299$	−12.9282	−	3.73205i	−0.747657	−	0.215830i
$300$		0			0
$301$		0			0
$302$	−2.55103	+	9.52056i	−0.146795	+	0.547847i
$303$	8.81345	−	2.36156i	0.506320	−	0.135668i
$304$	−12.8038	−	12.8038i	−0.734351	−	0.734351i
$305$		0			0
$306$	−2.09808	+	0.562178i	−0.119939	+	0.0321376i
$307$		−	16.3886i		−	0.935344i	−0.883902	−	0.467672i	$-0.845093\pi$
$307$		−	16.3886i		−	0.935344i	0.883902	−	0.467672i	$-0.154907\pi$
$308$		0			0
$309$	4.63397	+	8.02628i	0.263618	+	0.456599i
$310$		0			0
$311$		−	4.85641i		−	0.275382i	−0.990475	−	0.137691i	$-0.956032\pi$
$311$		−	4.85641i		−	0.275382i	0.990475	−	0.137691i	$-0.0439680\pi$
$312$	1.93185	−	6.69213i	0.109370	−	0.378867i
$313$	15.6443	−	15.6443i	0.884267	−	0.884267i	−0.109698	−	0.993965i	$-0.534988\pi$
$313$	15.6443	−	15.6443i	0.884267	−	0.884267i	0.993965	+	0.109698i	$0.0349883\pi$
$314$	−1.25833	+	4.69615i	−0.0710117	+	0.265019i
$315$		0			0
$316$	13.0981	+	7.56218i	0.736824	+	0.425406i
$317$	−4.62158			−0.259574			−0.129787	−	0.991542i	$-0.541429\pi$
$317$	−4.62158			−0.259574			−0.129787	+	0.991542i	$0.541429\pi$
$318$	−3.34607	−	1.93185i	−0.187638	−	0.108333i
$319$	8.41858	+	31.4186i	0.471350	+	1.75910i
$320$		0			0
$321$	3.46410	−	6.00000i	0.193347	−	0.334887i
$322$		0			0
$323$	15.4176	+	26.7042i	0.857861	+	1.48586i
$324$	1.73205			0.0962250
$325$		0			0
$326$	−0.928203			−0.0514084
$327$	5.15780	+	8.93357i	0.285227	+	0.494028i
$328$	−8.62398	−	2.31079i	−0.476180	−	0.127592i
$329$		0			0
$330$		0			0
$331$	5.92820	+	22.1244i	0.325844	+	1.21606i	0.913461	+	0.406926i	$0.133399\pi$
$331$	5.92820	+	22.1244i	0.325844	+	1.21606i	−0.587618	+	0.809139i	$0.699934\pi$
$332$	14.6412	+	8.45310i	0.803540	+	0.463924i
$333$	−5.41662			−0.296829
$334$	4.66987	+	2.69615i	0.255524	+	0.147527i
$335$		0			0
$336$		0			0
$337$	−16.7675	+	16.7675i	−0.913383	+	0.913383i	−0.996537	−	0.0831533i	$-0.973501\pi$
$337$	−16.7675	+	16.7675i	−0.913383	+	0.913383i	0.0831533	+	0.996537i	$0.473501\pi$
$338$	−3.13801	−	5.95284i	−0.170685	−	0.323792i
$339$			18.1962i			0.988279i
$340$		0			0
$341$	7.90192	+	13.6865i	0.427913	+	0.741167i
$342$	0.984508	+	3.67423i	0.0532361	+	0.198680i
$343$		0			0
$344$	19.0263	−	5.09808i	1.02583	−	0.274870i
$345$		0			0
$346$	−4.92820	−	4.92820i	−0.264942	−	0.264942i
$347$	−27.7344	+	7.43142i	−1.48886	+	0.398940i	−0.909353	−	0.416025i	$-0.863423\pi$
$347$	−27.7344	+	7.43142i	−1.48886	+	0.398940i	−0.579510	+	0.814965i	$0.696756\pi$
$348$	−3.91447	+	14.6090i	−0.209838	+	0.783125i
$349$	−7.33013	−	1.96410i	−0.392373	−	0.105136i	0.0572380	−	0.998361i	$-0.481771\pi$
$349$	−7.33013	−	1.96410i	−0.392373	−	0.105136i	−0.449611	+	0.893225i	$0.648437\pi$
$350$		0			0
$351$	2.59808	−	2.50000i	0.138675	−	0.133440i
$352$	13.5366	+	13.5366i	0.721501	+	0.721501i
$353$	−7.17260	+	4.14110i	−0.381759	+	0.220409i	−0.678583	−	0.734523i	$-0.737406\pi$
$353$	−7.17260	+	4.14110i	−0.381759	+	0.220409i	0.296824	+	0.954932i	$0.404072\pi$
$354$	4.09808	−	2.36603i	0.217810	−	0.125753i
$355$		0			0
$356$	13.7321	−	13.7321i	0.727797	−	0.727797i
$357$		0			0
$358$	−2.24144	+	3.88229i	−0.118464	+	0.205185i
$359$	13.5885	−	13.5885i	0.717171	−	0.717171i	−0.250854	−	0.968025i	$-0.580711\pi$
$359$	13.5885	−	13.5885i	0.717171	−	0.717171i	0.968025	+	0.250854i	$0.0807113\pi$
$360$		0			0
$361$	30.3109	−	17.5000i	1.59531	−	0.921053i
$362$	−1.16900	+	0.674921i	−0.0614412	+	0.0354731i
$363$	2.03339	+	2.03339i	0.106725	+	0.106725i
$364$		0			0
$365$		0			0
$366$	−0.598076	−	0.160254i	−0.0312619	−	0.00837661i
$367$	−1.74238	+	6.50266i	−0.0909517	+	0.339436i	−0.996375	−	0.0850745i	$-0.972887\pi$
$367$	−1.74238	+	6.50266i	−0.0909517	+	0.339436i	0.905423	+	0.424511i	$0.139554\pi$
$368$	8.88280	−	2.38014i	0.463048	−	0.124073i
$369$	−3.26795	−	3.26795i	−0.170123	−	0.170123i
$370$		0			0
$371$		0			0
$372$			7.34847i			0.381000i
$373$	−9.31251	−	34.7547i	−0.482183	−	1.79953i	−0.592422	−	0.805628i	$-0.701828\pi$
$373$	−9.31251	−	34.7547i	−0.482183	−	1.79953i	0.110239	−	0.993905i	$-0.464838\pi$
$374$	−4.04552	−	7.00704i	−0.209189	−	0.362325i
$375$		0			0
$376$		−	2.73205i		−	0.140895i
$377$	15.2146	+	27.5636i	0.783591	+	1.41960i
$378$		0			0
$379$	4.43782	−	16.5622i	0.227956	−	0.850742i	−0.753243	−	0.657742i	$-0.771512\pi$
$379$	4.43782	−	16.5622i	0.227956	−	0.850742i	0.981199	−	0.193000i	$-0.0618217\pi$
$380$		0			0
$381$	8.19615	+	4.73205i	0.419902	+	0.242430i
$382$	−6.55343			−0.335303
$383$	23.7828	+	13.7310i	1.21524	+	0.701622i	0.963897	−	0.266275i	$-0.0857929\pi$
$383$	23.7828	+	13.7310i	1.21524	+	0.701622i	0.251348	+	0.967897i	$0.419126\pi$
$384$	2.96410	+	11.0622i	0.151261	+	0.564514i
$385$		0			0
$386$	5.99038	−	10.3756i	0.304902	−	0.528106i
$387$	9.84873	+	2.63896i	0.500639	+	0.134146i
$388$	1.10463	+	1.91327i	0.0560789	+	0.0971315i
$389$	−34.9282			−1.77093			−0.885465	−	0.464706i	$-0.846160\pi$
$389$	−34.9282			−1.77093			−0.885465	+	0.464706i	$0.846160\pi$
$390$		0			0
$391$	−15.6603			−0.791973
$392$	−6.76148	−	11.7112i	−0.341506	−	0.591506i
$393$	11.5911	+	3.10583i	0.584694	+	0.156668i
$394$	6.33975	−	10.9808i	0.319392	−	0.553203i
$395$		0			0
$396$	1.66987	+	6.23205i	0.0839143	+	0.313172i
$397$	5.22715	+	3.01790i	0.262343	+	0.151464i	0.625403	−	0.780302i	$-0.284935\pi$
$397$	5.22715	+	3.01790i	0.262343	+	0.151464i	−0.363060	+	0.931766i	$0.618268\pi$
$398$	5.83272			0.292368
$399$		0			0
$400$		0			0
$401$	−4.97372	+	18.5622i	−0.248376	+	0.926951i	0.723281	+	0.690554i	$0.242633\pi$
$401$	−4.97372	+	18.5622i	−0.248376	+	0.926951i	−0.971657	+	0.236397i	$0.924033\pi$
$402$	−0.896575	+	0.896575i	−0.0447171	+	0.0447171i
$403$	10.6066	+	11.0227i	0.528352	+	0.549080i
$404$			15.8038i			0.786271i
$405$		0			0
$406$		0			0
$407$	−5.22217	−	19.4894i	−0.258853	−	0.966054i
$408$		−	8.10634i		−	0.401324i
$409$	31.4904	−	8.43782i	1.55710	−	0.417223i	0.625355	−	0.780340i	$-0.284954\pi$
$409$	31.4904	−	8.43782i	1.55710	−	0.417223i	0.931744	+	0.363117i	$0.118287\pi$
$410$		0			0
$411$	−12.9282	−	12.9282i	−0.637701	−	0.637701i
$412$	−15.5056	+	4.15471i	−0.763905	+	0.204688i
$413$		0			0
$414$	−1.86603	−	0.500000i	−0.0917101	−	0.0245737i
$415$		0			0
$416$	15.8660	+	9.57180i	0.777896	+	0.469296i
$417$	4.38134	+	4.38134i	0.214555	+	0.214555i
$418$	−12.2710	+	7.08467i	−0.600195	+	0.346523i
$419$	0.0621778	−	0.0358984i	0.00303759	−	0.00175375i	−0.498480	−	0.866901i	$-0.666108\pi$
$419$	0.0621778	−	0.0358984i	0.00303759	−	0.00175375i	0.501518	+	0.865147i	$0.332775\pi$
$420$		0			0
$421$	−17.1699	+	17.1699i	−0.836808	+	0.836808i	−0.988437	−	0.151629i	$-0.951548\pi$
$421$	−17.1699	+	17.1699i	−0.836808	+	0.836808i	0.151629	+	0.988437i	$0.451548\pi$
$422$	6.69213	−	11.5911i	0.325768	−	0.564246i
$423$	0.707107	−	1.22474i	0.0343807	−	0.0595491i
$424$	10.1962	−	10.1962i	0.495169	−	0.495169i
$425$		0			0
$426$	4.62436	−	2.66987i	0.224051	−	0.129356i
$427$		0			0
$428$	8.48528	+	8.48528i	0.410152	+	0.410152i
$429$	11.5000	+	6.93782i	0.555225	+	0.334961i
$430$		0			0
$431$	−27.7224	−	7.42820i	−1.33534	−	0.357804i	−0.480638	−	0.876919i	$-0.659595\pi$
$431$	−27.7224	−	7.42820i	−1.33534	−	0.357804i	−0.854704	+	0.519115i	$0.826262\pi$
$432$	−0.637756	+	2.38014i	−0.0306841	+	0.114515i
$433$	−8.74410	+	2.34297i	−0.420215	+	0.112596i	−0.462729	−	0.886500i	$-0.653130\pi$
$433$	−8.74410	+	2.34297i	−0.420215	+	0.112596i	0.0425146	+	0.999096i	$0.486463\pi$
$434$		0			0
$435$		0			0
$436$	−17.2583	+	4.62436i	−0.826524	+	0.221466i
$437$			27.4249i			1.31191i
$438$	0.120118	+	0.448288i	0.00573948	+	0.0214200i
$439$	11.1962	+	19.3923i	0.534363	+	0.925544i	0.999194	+	0.0401446i	$0.0127819\pi$
$439$	11.1962	+	19.3923i	0.534363	+	0.925544i	−0.464831	+	0.885400i	$0.653885\pi$
$440$		0			0
$441$		−	7.00000i		−	0.333333i
$442$	−5.43022	−	5.64325i	−0.258289	−	0.268422i
$443$	2.53742	−	2.53742i	0.120557	−	0.120557i	−0.644255	−	0.764811i	$-0.722832\pi$
$443$	2.53742	−	2.53742i	0.120557	−	0.120557i	0.764811	+	0.644255i	$0.222832\pi$
$444$	2.42820	−	9.06218i	0.115237	−	0.430072i
$445$		0			0
$446$	−2.36603	−	1.36603i	−0.112035	−	0.0646832i
$447$	−9.41902			−0.445504
$448$		0			0
$449$	−10.0000	−	37.3205i	−0.471929	−	1.76126i	−0.632828	−	0.774293i	$-0.718106\pi$
$449$	−10.0000	−	37.3205i	−0.471929	−	1.76126i	0.160898	−	0.986971i	$-0.448561\pi$
$450$		0			0
$451$	8.60770	−	14.9090i	0.405321	−	0.702036i
$452$	−30.4428	−	8.15711i	−1.43191	−	0.383678i
$453$	−9.52056	−	16.4901i	−0.447315	−	0.774772i
$454$	3.39230			0.159209
$455$		0			0
$456$	−14.1962			−0.664796
$457$	9.45121	+	16.3700i	0.442109	+	0.765755i	0.997846	−	0.0656032i	$-0.0208972\pi$
$457$	9.45121	+	16.3700i	0.442109	+	0.765755i	−0.555737	+	0.831358i	$0.687564\pi$
$458$	−4.58939	−	1.22972i	−0.214448	−	0.0574612i
$459$	2.09808	−	3.63397i	0.0979298	−	0.169619i
$460$		0			0
$461$	−2.16987	−	8.09808i	−0.101061	−	0.377165i	0.896807	−	0.442421i	$-0.145880\pi$
$461$	−2.16987	−	8.09808i	−0.101061	−	0.377165i	−0.997869	+	0.0652560i	$0.979214\pi$
$462$		0			0
$463$	19.5216			0.907245			0.453623	−	0.891194i	$-0.350131\pi$
$463$	19.5216			0.907245			0.453623	+	0.891194i	$0.350131\pi$
$464$	−18.6340	−	10.7583i	−0.865061	−	0.499443i
$465$		0			0
$466$	−0.294229	+	1.09808i	−0.0136299	+	0.0508674i
$467$	−17.0585	+	17.0585i	−0.789373	+	0.789373i	−0.981391	−	0.192018i	$-0.938497\pi$
$467$	−17.0585	+	17.0585i	−0.789373	+	0.789373i	0.192018	+	0.981391i	$0.438497\pi$
$468$	3.01790	+	5.46739i	0.139502	+	0.252730i
$469$		0			0
$470$		0			0
$471$	−4.69615	−	8.13397i	−0.216387	−	0.374794i
$472$	4.57081	+	17.0585i	0.210389	+	0.785181i
$473$			37.9807i			1.74635i
$474$	4.36603	−	1.16987i	0.200538	−	0.0537340i
$475$		0			0
$476$		0			0
$477$	7.20977	−	1.93185i	0.330113	−	0.0884534i
$478$	1.95043	−	7.27912i	0.0892108	−	0.332939i
$479$	29.2224	+	7.83013i	1.33521	+	0.357768i	0.854654	−	0.519198i	$-0.173769\pi$
$479$	29.2224	+	7.83013i	1.33521	+	0.357768i	0.480553	+	0.876966i	$0.340436\pi$
$480$		0			0
$481$	−9.43782	−	17.0981i	−0.430328	−	0.779605i
$482$	2.20925	+	2.20925i	0.100629	+	0.100629i
$483$		0			0
$484$	−4.31347	+	2.49038i	−0.196067	+	0.113199i
$485$		0			0
$486$	0.366025	−	0.366025i	0.0166032	−	0.0166032i
$487$	15.2653	−	26.4404i	0.691739	−	1.19813i	−0.279529	−	0.960137i	$-0.590178\pi$
$487$	15.2653	−	26.4404i	0.691739	−	1.19813i	0.971268	−	0.237989i	$-0.0764884\pi$
$488$	1.15539	−	2.00120i	0.0523023	−	0.0905902i
$489$	1.26795	−	1.26795i	0.0573386	−	0.0573386i
$490$		0			0
$491$	7.79423	−	4.50000i	0.351749	−	0.203082i	−0.313707	−	0.949520i	$-0.601571\pi$
$491$	7.79423	−	4.50000i	0.351749	−	0.203082i	0.665455	+	0.746438i	$0.268237\pi$
$492$	6.93237	−	4.00240i	0.312535	−	0.180442i
$493$	25.9091	+	25.9091i	1.16689	+	1.16689i
$494$	−9.88269	+	9.50962i	−0.444643	+	0.427858i
$495$		0			0
$496$	−10.0981	−	2.70577i	−0.453417	−	0.121493i
$497$		0			0
$498$	4.88040	−	1.30770i	0.218696	−	0.0585994i
$499$	−9.32051	−	9.32051i	−0.417243	−	0.417243i	0.467009	−	0.884252i	$-0.345331\pi$
$499$	−9.32051	−	9.32051i	−0.417243	−	0.417243i	−0.884252	+	0.467009i	$0.845331\pi$
$500$		0			0
$501$	−10.0622	+	2.69615i	−0.449545	+	0.120455i
$502$			6.24882i			0.278899i
$503$	8.03699	+	29.9945i	0.358352	+	1.33739i	0.876214	+	0.481923i	$0.160061\pi$
$503$	8.03699	+	29.9945i	0.358352	+	1.33739i	−0.517862	+	0.855464i	$0.673272\pi$
$504$		0			0
$505$		0			0
$506$		−	7.19615i		−	0.319908i
$507$	12.4183	+	3.84512i	0.551518	+	0.170768i
$508$	−11.5911	+	11.5911i	−0.514272	+	0.514272i
$509$	−0.633975	+	2.36603i	−0.0281004	+	0.104872i	−0.978552	−	0.206001i	$-0.933955\pi$
$509$	−0.633975	+	2.36603i	−0.0281004	+	0.104872i	0.950451	+	0.310874i	$0.100622\pi$
$510$		0			0
$511$		0			0
$512$	−22.1841			−0.980408
$513$	−6.36396	−	3.67423i	−0.280976	−	0.162221i
$514$	2.02628	+	7.56218i	0.0893754	+	0.333553i
$515$		0			0
$516$	−8.83013	+	15.2942i	−0.388725	+	0.673291i
$517$	5.08845	+	1.36345i	0.223790	+	0.0599643i
$518$		0			0
$519$	13.4641			0.591008
$520$		0			0
$521$	−24.3923			−1.06865			−0.534323	−	0.845280i	$-0.679433\pi$
$521$	−24.3923			−1.06865			−0.534323	+	0.845280i	$0.679433\pi$
$522$	2.26002	+	3.91447i	0.0989184	+	0.171332i
$523$	33.0309	+	8.85062i	1.44434	+	0.387010i	0.894052	−	0.447963i	$-0.147850\pi$
$523$	33.0309	+	8.85062i	1.44434	+	0.387010i	0.550290	+	0.834973i	$0.314517\pi$
$524$	−10.3923	+	18.0000i	−0.453990	+	0.786334i
$525$		0			0
$526$	−1.89230	−	7.06218i	−0.0825084	−	0.307926i
$527$	15.4176	+	8.90138i	0.671603	+	0.387750i
$528$	−9.17878			−0.399455
$529$	7.85641	+	4.53590i	0.341583	+	0.197213i
$530$		0			0
$531$	−2.36603	+	8.83013i	−0.102677	+	0.383195i
$532$		0			0
$533$	4.62158	−	16.0096i	0.200183	−	0.693453i
$534$		−	5.80385i		−	0.251157i
$535$		0			0
$536$	−2.36603	−	4.09808i	−0.102197	−	0.177010i
$537$	−2.24144	−	8.36516i	−0.0967252	−	0.360983i
$538$		−	9.41902i		−	0.406083i
$539$	25.1865	−	6.74871i	1.08486	−	0.290688i
$540$		0			0
$541$	−7.56218	−	7.56218i	−0.325123	−	0.325123i	0.525605	−	0.850729i	$-0.323839\pi$
$541$	−7.56218	−	7.56218i	−0.325123	−	0.325123i	−0.850729	+	0.525605i	$0.823839\pi$
$542$	−14.9879	+	4.01601i	−0.643787	+	0.172502i
$543$	0.674921	−	2.51884i	0.0289636	−	0.108094i
$544$	20.8301	+	5.58142i	0.893084	+	0.239301i
$545$		0			0
$546$		0			0
$547$	11.3137	+	11.3137i	0.483739	+	0.483739i	0.906324	−	0.422584i	$-0.138877\pi$
$547$	11.3137	+	11.3137i	0.483739	+	0.483739i	−0.422584	+	0.906324i	$0.638877\pi$
$548$	27.4249	−	15.8338i	1.17153	−	0.676384i
$549$	1.03590	−	0.598076i	0.0442111	−	0.0255253i
$550$		0			0
$551$	45.3731	−	45.3731i	1.93296	−	1.93296i
$552$	3.60488	−	6.24384i	0.153434	−	0.265756i
$553$		0			0
$554$	9.43782	−	9.43782i	0.400975	−	0.400975i
$555$		0			0
$556$	−9.29423	+	5.36603i	−0.394163	+	0.227570i
$557$	−13.0561	+	7.53794i	−0.553204	+	0.319393i	−0.750413	−	0.660969i	$-0.770146\pi$
$557$	−13.0561	+	7.53794i	−0.553204	+	0.319393i	0.197209	+	0.980361i	$0.436812\pi$
$558$	1.55291	+	1.55291i	0.0657401	+	0.0657401i
$559$	8.83013	+	35.6865i	0.373475	+	1.50938i
$560$		0			0
$561$	15.0981	+	4.04552i	0.637441	+	0.170802i
$562$	0.947343	−	3.53553i	0.0399613	−	0.149137i
$563$	−39.4643	+	10.5744i	−1.66322	+	0.445659i	−0.963270	−	0.268534i	$-0.913461\pi$
$563$	−39.4643	+	10.5744i	−1.66322	+	0.445659i	−0.699950	+	0.714192i	$0.746794\pi$
$564$	1.73205	+	1.73205i	0.0729325	+	0.0729325i
$565$		0			0
$566$	−3.73205	+	1.00000i	−0.156870	+	0.0420331i
$567$		0			0
$568$	5.15780	+	19.2492i	0.216416	+	0.807677i
$569$	−20.7583	−	35.9545i	−0.870234	−	1.50729i	−0.861754	−	0.507326i	$-0.830634\pi$
$569$	−20.7583	−	35.9545i	−0.870234	−	1.50729i	−0.00848042	−	0.999964i	$-0.502699\pi$
$570$		0			0
$571$		−	31.4641i		−	1.31673i	−0.752698	−	0.658366i	$-0.771248\pi$
$571$		−	31.4641i		−	1.31673i	0.752698	−	0.658366i	$-0.228752\pi$
$572$	−16.7625	+	16.1297i	−0.700876	+	0.674418i
$573$	8.95215	−	8.95215i	0.373981	−	0.373981i
$574$		0			0
$575$		0			0
$576$	−1.96410	−	1.13397i	−0.0818376	−	0.0472489i
$577$	−13.8004			−0.574517			−0.287258	−	0.957853i	$-0.592744\pi$
$577$	−13.8004			−0.574517			−0.287258	+	0.957853i	$0.592744\pi$
$578$	−0.272422	−	0.157283i	−0.0113313	−	0.00654211i
$579$	5.99038	+	22.3564i	0.248952	+	0.929101i
$580$		0			0
$581$		0			0
$582$	0.637756	+	0.170886i	0.0264359	+	0.00708347i
$583$	13.9019	+	24.0788i	0.575758	+	0.997242i
$584$	−1.73205			−0.0716728
$585$		0			0
$586$	1.12436			0.0464467
$587$	−23.6813	−	41.0172i	−0.977431	−	1.69296i	−0.671668	−	0.740852i	$-0.734422\pi$
$587$	−23.6813	−	41.0172i	−0.977431	−	1.69296i	−0.305763	−	0.952108i	$-0.598911\pi$
$588$	11.7112	+	3.13801i	0.482963	+	0.129410i
$589$	15.5885	−	27.0000i	0.642311	−	1.11252i
$590$		0			0
$591$	6.33975	+	23.6603i	0.260782	+	0.973253i
$592$	11.5589	+	6.67355i	0.475069	+	0.274281i
$593$	−7.24693			−0.297596			−0.148798	−	0.988868i	$-0.547540\pi$
$593$	−7.24693			−0.297596			−0.148798	+	0.988868i	$0.547540\pi$
$594$	1.66987	+	0.964102i	0.0685157	+	0.0395576i
$595$		0			0
$596$	4.22243	−	15.7583i	0.172958	−	0.645486i
$597$	−7.96764	+	7.96764i	−0.326094	+	0.326094i
$598$	−1.67303	−	6.76148i	−0.0684154	−	0.276498i
$599$		−	19.3923i		−	0.792348i	−0.918175	−	0.396174i	$-0.870338\pi$
$599$		−	19.3923i		−	0.792348i	0.918175	−	0.396174i	$-0.129662\pi$
$600$		0			0
$601$	18.7321	+	32.4449i	0.764096	+	1.32345i	0.940723	+	0.339176i	$0.110148\pi$
$601$	18.7321	+	32.4449i	0.764096	+	1.32345i	−0.176627	+	0.984278i	$0.556519\pi$
$602$		0			0
$603$		−	2.44949i		−	0.0997509i
$604$	31.8564	−	8.53590i	1.29622	−	0.347321i
$605$		0			0
$606$	3.33975	+	3.33975i	0.135668	+	0.135668i
$607$	−7.77817	+	2.08416i	−0.315706	+	0.0845933i	−0.413193	−	0.910644i	$-0.635586\pi$
$607$	−7.77817	+	2.08416i	−0.315706	+	0.0845933i	0.0974864	+	0.995237i	$0.468920\pi$
$608$	9.77440	−	36.4785i	0.396404	−	1.47940i
$609$		0			0
$610$		0			0
$611$	5.09808	+	0.0980762i	0.206246	+	0.00396774i
$612$	5.13922	+	5.13922i	0.207741	+	0.207741i
$613$	28.2335	−	16.3006i	1.14034	−	0.658376i	0.193826	−	0.981036i	$-0.437910\pi$
$613$	28.2335	−	16.3006i	1.14034	−	0.658376i	0.946515	+	0.322660i	$0.104577\pi$
$614$	7.34679	−	4.24167i	0.296492	−	0.171180i
$615$		0			0
$616$		0			0
$617$	17.1093	−	29.6341i	0.688793	−	1.19302i	−0.283436	−	0.958991i	$-0.591474\pi$
$617$	17.1093	−	29.6341i	0.688793	−	1.19302i	0.972229	−	0.234033i	$-0.0751925\pi$
$618$	−2.39872	+	4.15471i	−0.0964907	+	0.167127i
$619$	−14.5359	+	14.5359i	−0.584247	+	0.584247i	−0.936068	−	0.351820i	$-0.885563\pi$
$619$	−14.5359	+	14.5359i	−0.584247	+	0.584247i	0.351820	+	0.936068i	$0.385563\pi$
$620$		0			0
$621$	3.23205	−	1.86603i	0.129698	−	0.0748810i
$622$	2.17707	−	1.25693i	0.0872925	−	0.0503983i
$623$		0			0
$624$	−8.62436	+	2.13397i	−0.345251	+	0.0854274i
$625$		0			0
$626$	11.0622	+	2.96410i	0.442134	+	0.118469i
$627$	7.08467	−	26.4404i	0.282935	−	1.05593i
$628$	15.7136	−	4.21046i	0.627042	−	0.168015i
$629$	−16.0718	−	16.0718i	−0.640825	−	0.640825i
$630$		0			0
$631$	−9.29423	+	2.49038i	−0.369997	+	0.0991405i	−0.439026	−	0.898474i	$-0.644677\pi$
$631$	−9.29423	+	2.49038i	−0.369997	+	0.0991405i	0.0690290	+	0.997615i	$0.478010\pi$
$632$			16.8690i			0.671014i
$633$	6.69213	+	24.9754i	0.265988	+	0.992682i
$634$	−1.19615	−	2.07180i	−0.0475053	−	0.0822816i
$635$		0			0
$636$			12.9282i			0.512637i
$637$	22.0962	−	12.1967i	0.875482	−	0.483250i
$638$	−11.9057	+	11.9057i	−0.471350	+	0.471350i
$639$	−2.66987	+	9.96410i	−0.105619	+	0.394174i
$640$		0			0
$641$	−17.0718	−	9.85641i	−0.674295	−	0.389305i	0.123407	−	0.992356i	$-0.460618\pi$
$641$	−17.0718	−	9.85641i	−0.674295	−	0.389305i	−0.797702	+	0.603052i	$0.793951\pi$
$642$	3.58630			0.141540
$643$	−30.2905	−	17.4882i	−1.19454	−	0.689667i	−0.235206	−	0.971945i	$-0.575577\pi$
$643$	−30.2905	−	17.4882i	−1.19454	−	0.689667i	−0.959333	+	0.282278i	$0.908910\pi$
$644$		0			0
$645$		0			0
$646$	−7.98076	+	13.8231i	−0.313999	+	0.543862i
$647$	−40.3608	−	10.8147i	−1.58675	−	0.425168i	−0.645742	−	0.763556i	$-0.723452\pi$
$647$	−40.3608	−	10.8147i	−1.58675	−	0.425168i	−0.941007	+	0.338388i	$0.890118\pi$
$648$	0.965926	+	1.67303i	0.0379452	+	0.0657229i
$649$	−34.0526			−1.33668
$650$		0			0
$651$		0			0
$652$	1.55291	+	2.68973i	0.0608168	+	0.105338i
$653$	17.9043	+	4.79744i	0.700650	+	0.187738i	0.591521	−	0.806289i	$-0.298527\pi$
$653$	17.9043	+	4.79744i	0.700650	+	0.187738i	0.109128	+	0.994028i	$0.465194\pi$
$654$	−2.66987	+	4.62436i	−0.104400	+	0.180827i
$655$		0			0
$656$	2.94744	+	11.0000i	0.115078	+	0.429478i
$657$	−0.776457	−	0.448288i	−0.0302925	−	0.0174894i
$658$		0			0
$659$	−5.08846	−	2.93782i	−0.198218	−	0.114441i	0.397606	−	0.917556i	$-0.369841\pi$
$659$	−5.08846	−	2.93782i	−0.198218	−	0.114441i	−0.595824	+	0.803115i	$0.703174\pi$
$660$		0			0
$661$	−4.63397	+	17.2942i	−0.180241	+	0.672668i	0.815359	+	0.578956i	$0.196540\pi$
$661$	−4.63397	+	17.2942i	−0.180241	+	0.672668i	−0.995599	+	0.0937114i	$0.970127\pi$
$662$	−8.38375	+	8.38375i	−0.325844	+	0.325844i
$663$	15.1266	+	0.291005i	0.587470	+	0.0113017i
$664$			18.8564i			0.731770i
$665$		0			0
$666$	−1.40192	−	2.42820i	−0.0543234	−	0.0940910i
$667$	8.43451	+	31.4780i	0.326586	+	1.21883i
$668$		−	18.0430i		−	0.698105i
$669$	5.09808	−	1.36603i	0.197103	−	0.0528136i
$670$		0			0
$671$	3.15064	+	3.15064i	0.121629	+	0.121629i
$672$		0			0
$673$	2.51884	−	9.40044i	0.0970942	−	0.362360i	−0.900234	−	0.435405i	$-0.856605\pi$
$673$	2.51884	−	9.40044i	0.0970942	−	0.362360i	0.997329	+	0.0730451i	$0.0232717\pi$
$674$	−11.8564	−	3.17691i	−0.456692	−	0.122370i
$675$		0			0
$676$	−12.0000	+	19.0526i	−0.461538	+	0.732791i
$677$	19.5959	+	19.5959i	0.753132	+	0.753132i	0.975063	−	0.221930i	$-0.0712357\pi$
$677$	19.5959	+	19.5959i	0.753132	+	0.753132i	−0.221930	+	0.975063i	$0.571236\pi$
$678$	−8.15711	+	4.70951i	−0.313272	+	0.180868i
$679$		0			0
$680$		0			0
$681$	−4.63397	+	4.63397i	−0.177574	+	0.177574i
$682$	−4.09034	+	7.08467i	−0.156627	+	0.271286i
$683$	8.36516	−	14.4889i	0.320084	−	0.554402i	−0.660421	−	0.750896i	$-0.729622\pi$
$683$	8.36516	−	14.4889i	0.320084	−	0.554402i	0.980505	+	0.196494i	$0.0629555\pi$
$684$	9.00000	−	9.00000i	0.344124	−	0.344124i
$685$		0			0
$686$		0			0
$687$	7.94906	−	4.58939i	0.303276	−	0.175096i
$688$	−17.7656	−	17.7656i	−0.677307	−	0.677307i
$689$	18.6603	+	19.3923i	0.710899	+	0.738788i
$690$		0			0
$691$	43.3468	+	11.6147i	1.64899	+	0.441845i	0.959330	−	0.282288i	$-0.0910934\pi$
$691$	43.3468	+	11.6147i	1.64899	+	0.441845i	0.689660	+	0.724133i	$0.257760\pi$
$692$	−6.03579	+	22.5259i	−0.229446	+	0.856306i
$693$		0			0
$694$	−10.5096	−	10.5096i	−0.398940	−	0.398940i
$695$		0			0
$696$	−16.2942	+	4.36603i	−0.617631	+	0.165494i
$697$		−	19.3928i		−	0.734556i
$698$	−1.01669	−	3.79435i	−0.0384824	−	0.143618i
$699$	−1.09808	−	1.90192i	−0.0415331	−	0.0719374i
$700$		0			0
$701$		−	29.0718i		−	1.09803i	−0.835814	−	0.549013i	$-0.815004\pi$
$701$		−	29.0718i		−	1.09803i	0.835814	−	0.549013i	$-0.184996\pi$
$702$	1.79315	+	0.517638i	0.0676781	+	0.0195370i
$703$	−28.1456	+	28.1456i	−1.06153	+	1.06153i
$704$	2.18653	−	8.16025i	0.0824081	−	0.307551i
$705$		0			0
$706$	−3.71281	−	2.14359i	−0.139734	−	0.0806752i
$707$		0			0
$708$	−13.7124	−	7.91688i	−0.515345	−	0.297534i
$709$	3.74871	+	13.9904i	0.140786	+	0.525420i	0.999907	+	0.0136474i	$0.00434423\pi$
$709$	3.74871	+	13.9904i	0.140786	+	0.525420i	−0.859121	+	0.511772i	$0.828989\pi$
$710$		0			0
$711$	−4.36603	+	7.56218i	−0.163739	+	0.283604i
$712$	20.9222	+	5.60609i	0.784093	+	0.210097i
$713$	7.91688	+	13.7124i	0.296489	+	0.513535i
$714$		0			0
$715$		0			0
$716$	15.0000			0.560576
$717$	7.27912	+	12.6078i	0.271844	+	0.470847i
$718$	9.60849	+	2.57459i	0.358586	+	0.0960827i
$719$	13.4282	−	23.2583i	0.500787	−	0.867389i	−0.499212	−	0.866480i	$-0.666377\pi$
$719$	13.4282	−	23.2583i	0.500787	−	0.867389i	1.00000		0.000909539i	$-0.000289515\pi$
$720$		0			0
$721$		0			0
$722$	15.6901	+	9.05867i	0.583924	+	0.337129i
$723$	−6.03579			−0.224474
$724$	3.91154	+	2.25833i	0.145371	+	0.0839302i
$725$		0			0
$726$	−0.385263	+	1.43782i	−0.0142985	+	0.0533626i
$727$	14.5954	−	14.5954i	0.541314	−	0.541314i	−0.382600	−	0.923914i	$-0.624971\pi$
$727$	14.5954	−	14.5954i	0.541314	−	0.541314i	0.923914	+	0.382600i	$0.124971\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	21.3923	+	37.0526i	0.791223	+	1.37044i
$732$	0.536220	+	2.00120i	0.0198193	+	0.0739666i
$733$		−	8.17072i		−	0.301792i	−0.988550	−	0.150896i	$-0.951784\pi$
$733$		−	8.17072i		−	0.301792i	0.988550	−	0.150896i	$-0.0482159\pi$
$734$	−3.36603	+	0.901924i	−0.124242	+	0.0332906i
$735$		0			0
$736$	13.5622	+	13.5622i	0.499909	+	0.499909i
$737$	8.81345	−	2.36156i	0.324648	−	0.0869891i
$738$	0.619174	−	2.31079i	0.0227921	−	0.0850613i
$739$	12.1244	+	3.24871i	0.446002	+	0.119506i	0.474828	−	0.880079i	$-0.342510\pi$
$739$	12.1244	+	3.24871i	0.446002	+	0.119506i	−0.0288263	+	0.999584i	$0.509177\pi$
$740$		0			0
$741$	0.509619	−	26.4904i	0.0187213	−	0.973148i
$742$		0			0
$743$	−3.49837	+	2.01978i	−0.128343	+	0.0740987i	−0.562797	−	0.826595i	$-0.690275\pi$
$743$	−3.49837	+	2.01978i	−0.128343	+	0.0740987i	0.434454	+	0.900694i	$0.356941\pi$
$744$	−7.09808	+	4.09808i	−0.260228	+	0.150243i
$745$		0			0
$746$	13.1699	−	13.1699i	0.482183	−	0.482183i
$747$	−4.88040	+	8.45310i	−0.178564	+	0.309283i
$748$	−13.5366	+	23.4460i	−0.494946	+	0.857271i
$749$		0			0
$750$		0			0
$751$	46.0070	−	26.5622i	1.67882	−	0.969268i	0.716406	−	0.697684i	$-0.245786\pi$
$751$	46.0070	−	26.5622i	1.67882	−	0.969268i	0.962415	−	0.271584i	$-0.0875475\pi$
$752$	−3.01790	+	1.74238i	−0.110051	+	0.0635382i
$753$	−8.53605	−	8.53605i	−0.311071	−	0.311071i
$754$	−8.41858	+	13.9545i	−0.306587	+	0.508192i
$755$		0			0
$756$		0			0
$757$	9.41902	−	35.1523i	0.342340	−	1.27763i	−0.553349	−	0.832950i	$-0.686650\pi$
$757$	9.41902	−	35.1523i	0.342340	−	1.27763i	0.895689	−	0.444681i	$-0.146683\pi$
$758$	8.57321	−	2.29719i	0.311393	−	0.0834375i
$759$	9.83013	+	9.83013i	0.356811	+	0.356811i
$760$		0			0
$761$	23.5885	−	6.32051i	0.855081	−	0.229118i	0.195455	−	0.980713i	$-0.437382\pi$
$761$	23.5885	−	6.32051i	0.855081	−	0.229118i	0.659626	+	0.751594i	$0.270715\pi$
$762$			4.89898i			0.177471i
$763$		0			0
$764$	10.9641	+	18.9904i	0.396667	+	0.687048i
$765$		0			0
$766$			14.2154i			0.513623i
$767$	−31.9957	+	7.91688i	−1.15530	+	0.285862i
$768$	−0.984508	+	0.984508i	−0.0355254	+	0.0355254i
$769$	12.5096	−	46.6865i	0.451108	−	1.68356i	−0.248175	−	0.968715i	$-0.579831\pi$
$769$	12.5096	−	46.6865i	0.451108	−	1.68356i	0.699284	−	0.714844i	$-0.253502\pi$
$770$		0			0
$771$	−13.0981	−	7.56218i	−0.471716	−	0.272345i
$772$	−40.0884			−1.44281
$773$	−42.9304	−	24.7859i	−1.54410	−	0.891487i	−0.998574	−	0.0533938i	$-0.982996\pi$
$773$	−42.9304	−	24.7859i	−1.54410	−	0.891487i	−0.545527	−	0.838093i	$-0.683671\pi$
$774$	1.36603	+	5.09808i	0.0491008	+	0.183247i
$775$		0			0
$776$	−1.23205	+	2.13397i	−0.0442280	+	0.0766052i
$777$		0			0
$778$	−9.04008	−	15.6579i	−0.324103	−	0.561362i
$779$	−33.9615			−1.21680
$780$		0			0
$781$	−38.4256			−1.37498
$782$	−4.05317	−	7.02030i	−0.144941	−	0.251045i
$783$	−8.43451	−	2.26002i	−0.301425	−	0.0807666i
$784$	−8.62436	+	14.9378i	−0.308013	+	0.533494i
$785$		0			0
$786$	1.60770	+	6.00000i	0.0573446	+	0.214013i
$787$	−2.77766	−	1.60368i	−0.0990129	−	0.0571651i	0.449676	−	0.893192i	$-0.351539\pi$
$787$	−2.77766	−	1.60368i	−0.0990129	−	0.0571651i	−0.548689	+	0.836027i	$0.684873\pi$
$788$	−42.4264			−1.51138
$789$	12.2321	+	7.06218i	0.435473	+	0.251420i
$790$		0			0
$791$		0			0
$792$	−5.08845	+	5.08845i	−0.180810	+	0.180810i
$793$	3.69282	+	2.22784i	0.131136	+	0.0791128i
$794$			3.12436i			0.110879i
$795$		0			0
$796$	−9.75833	−	16.9019i	−0.345875	−	0.599073i
$797$	−11.7162	−	43.7255i	−0.415009	−	1.54884i	−0.784817	−	0.619728i	$-0.787243\pi$
$797$	−11.7162	−	43.7255i	−0.415009	−	1.54884i	0.369808	−	0.929108i	$-0.379424\pi$
$798$		0			0
$799$	5.73205	−	1.53590i	0.202785	−	0.0543362i
$800$		0			0
$801$	7.92820	+	7.92820i	0.280129	+	0.280129i
$802$	−9.60849	+	2.57459i	−0.339288	+	0.0909118i
$803$	0.864390	−	3.22595i	0.0305037	−	0.113841i
$804$	4.09808	+	1.09808i	0.144528	+	0.0387262i
$805$		0			0
$806$	−2.19615	+	7.60770i	−0.0773562	+	0.267970i
$807$	12.8666	+	12.8666i	0.452927	+	0.452927i
$808$	−15.2653	+	8.81345i	−0.537033	+	0.310056i
$809$	−23.3205	+	13.4641i	−0.819905	+	0.473373i	−0.850384	−	0.526163i	$-0.823630\pi$
$809$	−23.3205	+	13.4641i	−0.819905	+	0.473373i	0.0304784	+	0.999535i	$0.490297\pi$
$810$		0			0
$811$	−17.7846	+	17.7846i	−0.624502	+	0.624502i	−0.946679	−	0.322177i	$-0.895585\pi$
$811$	−17.7846	+	17.7846i	−0.624502	+	0.624502i	0.322177	+	0.946679i	$0.395585\pi$
$812$		0			0
$813$	14.9879	−	25.9599i	0.525650	−	0.910453i
$814$	7.38526	−	7.38526i	0.258853	−	0.258853i
$815$		0			0
$816$	−8.95448	+	5.16987i	−0.313470	+	0.180982i
$817$	64.8879	−	37.4631i	2.27014	−	1.31067i
$818$	11.9329	+	11.9329i	0.417223	+	0.417223i
$819$		0			0
$820$		0			0
$821$	−33.9545	−	9.09808i	−1.18502	−	0.317525i	−0.388104	−	0.921616i	$-0.626870\pi$
$821$	−33.9545	−	9.09808i	−1.18502	−	0.317525i	−0.796916	+	0.604091i	$0.793537\pi$
$822$	2.44949	−	9.14162i	0.0854358	−	0.318851i
$823$	−19.0411	+	5.10205i	−0.663732	+	0.177846i	−0.574929	−	0.818203i	$-0.694971\pi$
$823$	−19.0411	+	5.10205i	−0.663732	+	0.177846i	−0.0888021	+	0.996049i	$0.528304\pi$
$824$	−12.6603	−	12.6603i	−0.441041	−	0.441041i
$825$		0			0
$826$		0			0
$827$		−	9.83512i		−	0.342001i	−0.985271	−	0.171000i	$-0.945300\pi$
$827$		−	9.83512i		−	0.342001i	0.985271	−	0.171000i	$-0.0546999\pi$
$828$	1.67303	+	6.24384i	0.0581419	+	0.216989i
$829$	−1.00000	−	1.73205i	−0.0347314	−	0.0601566i	0.848137	−	0.529777i	$-0.177724\pi$
$829$	−1.00000	−	1.73205i	−0.0347314	−	0.0601566i	−0.882869	+	0.469620i	$0.844391\pi$
$830$		0			0
$831$			25.7846i			0.894458i
$832$	0.157283	−	8.17569i	0.00545281	−	0.283441i
$833$	20.7699	−	20.7699i	0.719634	−	0.719634i
$834$	−0.830127	+	3.09808i	−0.0287449	+	0.107278i
$835$		0			0
$836$	41.0596	+	23.7058i	1.42008	+	0.819881i
$837$	−4.24264			−0.146647
$838$	0.0321856	+	0.0185824i	0.00111183	+	0.000641917i
$839$	5.52628	+	20.6244i	0.190788	+	0.712032i	0.993317	+	0.115418i	$0.0368208\pi$
$839$	5.52628	+	20.6244i	0.190788	+	0.712032i	−0.802529	+	0.596614i	$0.796513\pi$
$840$		0			0
$841$	23.6244	−	40.9186i	0.814633	−	1.41099i
$842$	−12.1409	−	3.25315i	−0.418404	−	0.112111i
$843$	3.53553	+	6.12372i	0.121770	+	0.210912i
$844$	−44.7846			−1.54155
$845$		0			0
$846$	0.732051			0.0251684
$847$		0			0
$848$	−17.7656	−	4.76028i	−0.610073	−	0.163469i
$849$	3.73205	−	6.46410i	0.128084	−	0.221847i
$850$		0			0
$851$	−5.23205	−	19.5263i	−0.179352	−	0.669352i
$852$	−15.4734	−	8.93357i	−0.530110	−	0.306059i
$853$	9.97382			0.341497			0.170749	−	0.985315i	$-0.445381\pi$
$853$	9.97382			0.341497			0.170749	+	0.985315i	$0.445381\pi$
$854$		0			0
$855$		0			0
$856$	−3.46410	+	12.9282i	−0.118401	+	0.441877i
$857$	6.27603	−	6.27603i	0.214385	−	0.214385i	−0.591742	−	0.806127i	$-0.701560\pi$
$857$	6.27603	−	6.27603i	0.214385	−	0.214385i	0.806127	+	0.591742i	$0.201560\pi$
$858$	−0.133722	+	6.95095i	−0.00456518	+	0.237302i
$859$			30.5359i			1.04187i	0.853596	+	0.520936i	$0.174417\pi$
$859$			30.5359i			1.04187i	−0.853596	+	0.520936i	$0.825583\pi$
$860$		0			0
$861$		0			0
$862$	−3.84512	−	14.3502i	−0.130965	−	0.488769i
$863$			46.7805i			1.59243i	0.605015	+	0.796214i	$0.293167\pi$
$863$			46.7805i			1.59243i	−0.605015	+	0.796214i	$0.706833\pi$
$864$	−4.96410	+	1.33013i	−0.168882	+	0.0452518i
$865$		0			0
$866$	−3.31347	−	3.31347i	−0.112596	−	0.112596i
$867$	0.586988	−	0.157283i	0.0199352	−	0.00534161i
$868$		0			0
$869$	−31.4186	−	8.41858i	−1.06580	−	0.285581i
$870$		0			0
$871$	7.73205	−	4.26795i	0.261991	−	0.144614i
$872$	−14.0914	−	14.0914i	−0.477194	−	0.477194i
$873$	−1.10463	+	0.637756i	−0.0373859	+	0.0215848i
$874$	−12.2942	+	7.09808i	−0.415858	+	0.240096i
$875$		0			0
$876$	1.09808	−	1.09808i	0.0371006	−	0.0371006i
$877$	18.4034	−	31.8756i	0.621437	−	1.07636i	−0.367781	−	0.929912i	$-0.619882\pi$
$877$	18.4034	−	31.8756i	0.621437	−	1.07636i	0.989218	−	0.146448i	$-0.0467843\pi$
$878$	−5.79555	+	10.0382i	−0.195591	+	0.338773i
$879$	−1.53590	+	1.53590i	−0.0518046	+	0.0518046i
$880$		0			0
$881$	−20.1962	+	11.6603i	−0.680426	+	0.392844i	−0.800015	−	0.599979i	$-0.795175\pi$
$881$	−20.1962	+	11.6603i	−0.680426	+	0.392844i	0.119590	+	0.992823i	$0.461842\pi$
$882$	3.13801	−	1.81173i	0.105662	−	0.0610042i
$883$	−15.6950	−	15.6950i	−0.528180	−	0.528180i	0.391849	−	0.920030i	$-0.371836\pi$
$883$	−15.6950	−	15.6950i	−0.528180	−	0.528180i	−0.920030	+	0.391849i	$0.871836\pi$
$884$	−7.26795	+	25.1769i	−0.244448	+	0.846791i
$885$		0			0
$886$	1.79423	+	0.480762i	0.0602783	+	0.0161515i
$887$	−11.5267	+	43.0184i	−0.387030	+	1.44442i	0.447912	+	0.894078i	$0.352168\pi$
$887$	−11.5267	+	43.0184i	−0.387030	+	1.44442i	−0.834942	+	0.550338i	$0.814499\pi$
$888$	10.1075	−	2.70831i	0.339187	−	0.0908849i
$889$		0			0
$890$		0			0
$891$	−3.59808	+	0.964102i	−0.120540	+	0.0322986i
$892$			9.14162i			0.306084i
$893$	−2.68973	−	10.0382i	−0.0900083	−	0.335915i
$894$	−2.43782	−	4.22243i	−0.0815330	−	0.141219i
$895$		0			0
$896$		0			0
$897$	11.5218	+	6.95095i	0.384700	+	0.232085i
$898$	14.1421	−	14.1421i	0.471929	−	0.471929i
$899$	9.58846	−	35.7846i	0.319793	−	1.19348i
$900$		0			0
$901$	27.1244	+	15.6603i	0.903643	+	0.521719i
$902$	8.91134			0.296715
$903$		0			0
$904$	−9.09808	−	33.9545i	−0.302598	−	1.12931i
$905$		0			0
$906$	4.92820	−	8.53590i	0.163729	−	0.283586i
$907$	17.0077	+	4.55721i	0.564732	+	0.151320i	0.529880	−	0.848073i	$-0.322237\pi$
$907$	17.0077	+	4.55721i	0.564732	+	0.151320i	0.0348527	+	0.999392i	$0.488904\pi$
$908$	−5.67544	−	9.83014i	−0.188346	−	0.326225i
$909$	−9.12436			−0.302636
$910$		0			0
$911$	−42.9090			−1.42164			−0.710819	−	0.703375i	$-0.751675\pi$
$911$	−42.9090			−1.42164			−0.710819	+	0.703375i	$0.751675\pi$
$912$	9.05369	+	15.6814i	0.299798	+	0.519265i
$913$	−35.1201	−	9.41040i	−1.16231	−	0.311439i
$914$	−4.89230	+	8.47372i	−0.161823	+	0.280286i
$915$		0			0
$916$	4.11474	+	15.3564i	0.135955	+	0.507390i
$917$		0			0
$918$	2.17209			0.0716896
$919$	−1.48334	−	0.856406i	−0.0489309	−	0.0282502i	0.475335	−	0.879805i	$-0.342327\pi$
$919$	−1.48334	−	0.856406i	−0.0489309	−	0.0282502i	−0.524266	+	0.851555i	$0.675660\pi$
$920$		0			0
$921$	−4.24167	+	15.8301i	−0.139768	+	0.521620i
$922$	3.06866	−	3.06866i	0.101061	−	0.101061i
$923$	−36.1046	+	8.93357i	−1.18840	+	0.294052i
$924$		0			0
$925$		0			0
$926$	5.05256	+	8.75129i	0.166037	+	0.287585i
$927$	−2.39872	−	8.95215i	−0.0787844	−	0.294027i
$928$		−	44.8759i		−	1.47312i
$929$	−56.2750	+	15.0788i	−1.84632	+	0.494721i	−0.999320	−	0.0368684i	$-0.988262\pi$
$929$	−56.2750	+	15.0788i	−1.84632	+	0.494721i	−0.847002	+	0.531589i	$0.821595\pi$
$930$		0			0
$931$	−36.3731	−	36.3731i	−1.19208	−	1.19208i
$932$	3.67423	−	0.984508i	0.120354	−	0.0322486i
$933$	−1.25693	+	4.69093i	−0.0411501	+	0.153574i
$934$	−12.0622	−	3.23205i	−0.394687	−	0.105756i
$935$		0			0
$936$	−3.59808	+	5.96410i	−0.117607	+	0.194943i
$937$	29.9251	+	29.9251i	0.977611	+	0.977611i	0.999755	−	0.0221438i	$-0.00704917\pi$
$937$	29.9251	+	29.9251i	0.977611	+	0.977611i	−0.0221438	+	0.999755i	$0.507049\pi$
$938$		0			0
$939$	−19.1603	+	11.0622i	−0.625271	+	0.361001i
$940$		0			0
$941$	23.0000	−	23.0000i	0.749779	−	0.749779i	−0.224659	−	0.974437i	$-0.572127\pi$
$941$	23.0000	−	23.0000i	0.749779	−	0.749779i	0.974437	+	0.224659i	$0.0721268\pi$
$942$	2.43091	−	4.21046i	0.0792032	−	0.137184i
$943$	8.62398	−	14.9372i	0.280835	−	0.486421i
$944$	15.9282	−	15.9282i	0.518419	−	0.518419i
$945$		0			0
$946$	−17.0263	+	9.83013i	−0.553572	+	0.319605i
$947$	15.2975	−	8.83203i	0.497103	−	0.287003i	−0.230413	−	0.973093i	$-0.574008\pi$
$947$	15.2975	−	8.83203i	0.497103	−	0.287003i	0.727516	+	0.686090i	$0.240675\pi$
$948$	−10.6945	−	10.6945i	−0.347342	−	0.347342i
$949$	0.0621778	−	3.23205i	0.00201838	−	0.104917i
$950$		0			0
$951$	4.46410	+	1.19615i	0.144758	+	0.0387879i
$952$		0			0
$953$	19.5588	−	5.24075i	0.633570	−	0.169765i	0.0722809	−	0.997384i	$-0.476972\pi$
$953$	19.5588	−	5.24075i	0.633570	−	0.169765i	0.561289	+	0.827620i	$0.310306\pi$
$954$	2.73205	+	2.73205i	0.0884534	+	0.0884534i
$955$		0			0
$956$	−24.3564	+	6.52628i	−0.787742	+	0.211075i
$957$		−	32.5269i		−	1.05145i
$958$	4.05317	+	15.1266i	0.130952	+	0.488720i
$959$		0			0
$960$		0			0
$961$			13.0000i			0.419355i
$962$	5.22217	−	8.65617i	0.168370	−	0.279086i
$963$	−4.89898	+	4.89898i	−0.157867	+	0.157867i
$964$	2.70577	−	10.0981i	0.0871470	−	0.325237i
$965$		0			0
$966$		0			0
$967$	−5.75839			−0.185177			−0.0925887	−	0.995704i	$-0.529514\pi$
$967$	−5.75839			−0.185177			−0.0925887	+	0.995704i	$0.529514\pi$
$968$	−4.81105	−	2.77766i	−0.154633	−	0.0892773i
$969$	−7.98076	−	29.7846i	−0.256379	−	0.956820i
$970$		0			0
$971$	11.4641	−	19.8564i	0.367901	−	0.637222i	−0.621337	−	0.783544i	$-0.713410\pi$
$971$	11.4641	−	19.8564i	0.367901	−	0.637222i	0.989237	+	0.146321i	$0.0467434\pi$
$972$	−1.67303	−	0.448288i	−0.0536625	−	0.0143788i
$973$		0			0
$974$	15.8038			0.506388
$975$		0			0
$976$	−2.94744			−0.0943453
$977$	5.83272	+	10.1026i	0.186605	+	0.323210i	0.944116	−	0.329613i	$-0.106918\pi$
$977$	5.83272	+	10.1026i	0.186605	+	0.323210i	−0.757511	+	0.652822i	$0.773585\pi$
$978$	0.896575	+	0.240237i	0.0286693	+	0.00768192i
$979$	−20.8827	+	36.1699i	−0.667414	+	1.15599i
$980$		0			0
$981$	−2.66987	−	9.96410i	−0.0852425	−	0.318129i
$982$	4.03459	+	2.32937i	0.128749	+	0.0743332i
$983$	−12.7279			−0.405958			−0.202979	−	0.979183i	$-0.565062\pi$
$983$	−12.7279			−0.405958			−0.202979	+	0.979183i	$0.565062\pi$
$984$	7.73205	+	4.46410i	0.246489	+	0.142310i
$985$		0			0
$986$	−4.90897	+	18.3205i	−0.156333	+	0.583444i
$987$		0			0
$988$	44.0908	+	12.7279i	1.40272	+	0.404929i
$989$			38.0526i			1.21000i
$990$		0			0
$991$	−18.3923	−	31.8564i	−0.584251	−	1.01195i	−0.994968	−	0.100189i	$-0.968055\pi$
$991$	−18.3923	−	31.8564i	−0.584251	−	1.01195i	0.410718	−	0.911763i	$-0.365278\pi$
$992$	−5.64325	−	21.0609i	−0.179173	−	0.668684i
$993$		−	22.9048i		−	0.726862i
$994$		0			0
$995$		0			0
$996$	−11.9545	−	11.9545i	−0.378792	−	0.378792i
$997$	−27.5636	+	7.38563i	−0.872947	+	0.233905i	−0.667362	−	0.744734i	$-0.732576\pi$
$997$	−27.5636	+	7.38563i	−0.872947	+	0.233905i	−0.205585	+	0.978639i	$0.565910\pi$
$998$	1.76594	−	6.59059i	0.0559000	−	0.208622i
$999$	5.23205	+	1.40192i	0.165535	+	0.0443549i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bl.b.457.2	yes	8
5.2	odd	4		975.2.bu.a.418.1	yes	8
5.3	odd	4		975.2.bu.a.418.2	yes	8
5.4	even	2	inner	975.2.bl.b.457.1	✓	8
13.7	odd	12		975.2.bu.a.7.2	yes	8
65.7	even	12	inner	975.2.bl.b.943.1	yes	8
65.33	even	12	inner	975.2.bl.b.943.2	yes	8
65.59	odd	12		975.2.bu.a.7.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
975.2.bl.b.457.1	✓	8	5.4	even	2	inner
975.2.bl.b.457.2	yes	8	1.1	even	1	trivial
975.2.bl.b.943.1	yes	8	65.7	even	12	inner
975.2.bl.b.943.2	yes	8	65.33	even	12	inner
975.2.bu.a.7.1	yes	8	65.59	odd	12
975.2.bu.a.7.2	yes	8	13.7	odd	12
975.2.bu.a.418.1	yes	8	5.2	odd	4
975.2.bu.a.418.2	yes	8	5.3	odd	4

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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bl (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.448288i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(0.866025 - 1.50000i) q^{4} +(-0.133975 - 0.500000i) q^{6} +1.93185 q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.258819 + 0.448288i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(0.866025 - 1.50000i) q^{4} +(-0.133975 - 0.500000i) q^{6} +1.93185 q^{8} +(0.866025 + 0.500000i) q^{9} +(-0.964102 + 3.59808i) q^{11} +(-1.22474 + 1.22474i) q^{12} +(-0.0693504 + 3.60488i) q^{13} +(-1.23205 - 2.13397i) q^{16} +(1.08604 + 4.05317i) q^{17} +0.517638i q^{18} +(7.09808 - 1.90192i) q^{19} +(-1.86250 + 0.499056i) q^{22} +(-0.965926 + 3.60488i) q^{23} +(-1.86603 - 0.500000i) q^{24} +(-1.63397 + 0.901924i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(7.56218 - 4.36603i) q^{29} +(3.00000 - 3.00000i) q^{31} +(2.56961 - 4.45069i) q^{32} +(1.86250 - 3.22595i) q^{33} +(-1.53590 + 1.53590i) q^{34} +(1.50000 - 0.866025i) q^{36} +(-4.69093 + 2.70831i) q^{37} +(2.68973 + 2.68973i) q^{38} +(1.00000 - 3.46410i) q^{39} +(-4.46410 - 1.19615i) q^{41} +(9.84873 - 2.63896i) q^{43} +(4.56218 + 4.56218i) q^{44} +(-1.86603 + 0.500000i) q^{46} -1.41421i q^{47} +(0.637756 + 2.38014i) q^{48} +(-3.50000 - 6.06218i) q^{49} -4.19615i q^{51} +(5.34727 + 3.22595i) q^{52} +(5.27792 - 5.27792i) q^{53} +(0.133975 - 0.500000i) q^{54} -7.34847 q^{57} +(3.91447 + 2.26002i) q^{58} +(2.36603 + 8.83013i) q^{59} +(0.598076 - 1.03590i) q^{61} +(2.12132 + 0.568406i) q^{62} -2.26795 q^{64} +1.92820 q^{66} +(-1.22474 - 2.12132i) q^{67} +(7.02030 + 1.88108i) q^{68} +(1.86603 - 3.23205i) q^{69} +(2.66987 + 9.96410i) q^{71} +(1.67303 + 0.965926i) q^{72} -0.896575 q^{73} +(-2.42820 - 1.40192i) q^{74} +(3.29423 - 12.2942i) q^{76} +(1.81173 - 0.448288i) q^{78} +8.73205i q^{79} +(0.500000 + 0.866025i) q^{81} +(-0.619174 - 2.31079i) q^{82} +9.76079i q^{83} +(3.73205 + 3.73205i) q^{86} +(-8.43451 + 2.26002i) q^{87} +(-1.86250 + 6.95095i) q^{88} +(10.8301 + 2.90192i) q^{89} +(4.57081 + 4.57081i) q^{92} +(-3.67423 + 2.12132i) q^{93} +(0.633975 - 0.366025i) q^{94} +(-3.63397 + 3.63397i) q^{96} +(-0.637756 + 1.10463i) q^{97} +(1.81173 - 3.13801i) q^{98} +(-2.63397 + 2.63397i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{6}+O(q^{10}) \) 8 * q - 8 * q^6	\( 8 q - 8 q^{6} + 20 q^{11} + 4 q^{16} + 36 q^{19} - 8 q^{24} - 20 q^{26} + 12 q^{29} + 24 q^{31} - 40 q^{34} + 12 q^{36} + 8 q^{39} - 8 q^{41} - 12 q^{44} - 8 q^{46} - 28 q^{49} + 8 q^{54} + 12 q^{59} - 16 q^{61} - 32 q^{64} - 40 q^{66} + 8 q^{69} + 56 q^{71} + 36 q^{74} - 36 q^{76} + 4 q^{81} + 16 q^{86} + 52 q^{89} + 12 q^{94} - 36 q^{96} - 28 q^{99}+O(q^{100}) \) 8 * q - 8 * q^6 + 20 * q^11 + 4 * q^16 + 36 * q^19 - 8 * q^24 - 20 * q^26 + 12 * q^29 + 24 * q^31 - 40 * q^34 + 12 * q^36 + 8 * q^39 - 8 * q^41 - 12 * q^44 - 8 * q^46 - 28 * q^49 + 8 * q^54 + 12 * q^59 - 16 * q^61 - 32 * q^64 - 40 * q^66 + 8 * q^69 + 56 * q^71 + 36 * q^74 - 36 * q^76 + 4 * q^81 + 16 * q^86 + 52 * q^89 + 12 * q^94 - 36 * q^96 - 28 * q^99

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