LMFDB - Embedded newform 975.2.i.q.601.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [975,2,Mod(451,975)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("975.451"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(975, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [12,0,6,-4,0,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 8x^{10} + 48x^{8} - 2x^{7} + 116x^{6} - 32x^{5} + 208x^{4} - 32x^{3} + 100x^{2} + 12x + 36 $ x^12 + 8x^10 + 48x^8 - 2x^7 + 116x^6 - 32x^5 + 208x^4 - 32x^3 + 100x^2 + 12*x + 36
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			601.4
Root			$0.421315 - 0.729738i$ of defining polynomial
Character	$\chi$	$=$	975.601
Dual form			975.2.i.q.451.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.421315 + 0.729738i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.644988 - 1.11715i) q^{4} +(-0.421315 + 0.729738i) q^{6} +(0.200681 - 0.347589i) q^{7} +2.77223 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.45354 + 4.24965i) q^{11} +1.28998 q^{12} +(0.572960 - 3.55974i) q^{13} +0.338199 q^{14} +(-0.121995 - 0.211302i) q^{16} +(3.54033 - 6.13203i) q^{17} -0.842629 q^{18} +(-1.12724 + 1.95244i) q^{19} +0.401361 q^{21} +(-2.06742 + 3.58088i) q^{22} +(-0.497500 - 0.861695i) q^{23} +(1.38611 + 2.40082i) q^{24} +(2.83907 - 1.08166i) q^{26} -1.00000 q^{27} +(-0.258873 - 0.448381i) q^{28} +(3.94133 + 6.82658i) q^{29} -6.30120 q^{31} +(2.87503 - 4.97969i) q^{32} +(-2.45354 + 4.24965i) q^{33} +5.96637 q^{34} +(0.644988 + 1.11715i) q^{36} +(4.40338 + 7.62688i) q^{37} -1.89969 q^{38} +(3.36930 - 1.28367i) q^{39} +(-2.65994 - 4.60715i) q^{41} +(0.169099 + 0.292889i) q^{42} +(1.00699 - 1.74416i) q^{43} +6.33001 q^{44} +(0.419208 - 0.726090i) q^{46} -4.62317 q^{47} +(0.121995 - 0.211302i) q^{48} +(3.41945 + 5.92267i) q^{49} +7.08066 q^{51} +(-3.60721 - 2.93607i) q^{52} +10.8496 q^{53} +(-0.421315 - 0.729738i) q^{54} +(0.556333 - 0.963596i) q^{56} -2.25448 q^{57} +(-3.32108 + 5.75228i) q^{58} +(1.52224 - 2.63659i) q^{59} +(3.55088 - 6.15031i) q^{61} +(-2.65479 - 4.59822i) q^{62} +(0.200681 + 0.347589i) q^{63} +4.35718 q^{64} -4.13484 q^{66} +(3.07665 + 5.32891i) q^{67} +(-4.56694 - 7.91018i) q^{68} +(0.497500 - 0.861695i) q^{69} +(-3.16446 + 5.48101i) q^{71} +(-1.38611 + 2.40082i) q^{72} -1.01273 q^{73} +(-3.71042 + 6.42663i) q^{74} +(1.45411 + 2.51860i) q^{76} +1.96951 q^{77} +(2.35628 + 1.91788i) q^{78} -10.2755 q^{79} +(-0.500000 - 0.866025i) q^{81} +(2.24134 - 3.88212i) q^{82} -10.5337 q^{83} +(0.258873 - 0.448381i) q^{84} +1.69704 q^{86} +(-3.94133 + 6.82658i) q^{87} +(6.80177 + 11.7810i) q^{88} +(-0.262260 - 0.454247i) q^{89} +(-1.12234 - 0.913524i) q^{91} -1.28353 q^{92} +(-3.15060 - 5.45700i) q^{93} +(-1.94781 - 3.37371i) q^{94} +5.75005 q^{96} +(-4.71106 + 8.15979i) q^{97} +(-2.88133 + 4.99061i) q^{98} -4.90707 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} - 4 q^{4} - 2 q^{7} - 6 q^{9} + 2 q^{11} - 8 q^{12} - 8 q^{13} - 12 q^{14} + 8 q^{16} - 6 q^{17} + 8 q^{19} - 4 q^{21} - 14 q^{22} - 4 q^{23} - 24 q^{26} - 12 q^{27} - 8 q^{28} + 6 q^{29}+ \cdots - 4 q^{99}+O(q^{100}) $ 12 * q + 6 * q^3 - 4 * q^4 - 2 * q^7 - 6 * q^9 + 2 * q^11 - 8 * q^12 - 8 * q^13 - 12 * q^14 + 8 * q^16 - 6 * q^17 + 8 * q^19 - 4 * q^21 - 14 * q^22 - 4 * q^23 - 24 * q^26 - 12 * q^27 - 8 * q^28 + 6 * q^29 + 4 * q^31 + 10 * q^32 - 2 * q^33 + 16 * q^34 - 4 * q^36 + 14 * q^37 - 4 * q^39 - 20 * q^41 - 6 * q^42 - 20 * q^43 - 20 * q^44 - 12 * q^46 - 12 * q^47 - 8 * q^48 + 8 * q^49 - 12 * q^51 + 8 * q^52 + 40 * q^53 - 12 * q^56 + 16 * q^57 + 12 * q^58 - 6 * q^59 + 10 * q^61 + 2 * q^62 - 2 * q^63 - 24 * q^64 - 28 * q^66 + 6 * q^67 - 12 * q^68 + 4 * q^69 + 2 * q^71 + 6 * q^74 + 4 * q^76 + 8 * q^77 - 12 * q^78 - 68 * q^79 - 6 * q^81 + 4 * q^82 + 12 * q^83 + 8 * q^84 + 24 * q^86 - 6 * q^87 + 32 * q^89 + 30 * q^91 + 44 * q^92 + 2 * q^93 + 24 * q^94 + 20 * q^96 + 20 * q^97 + 4 * q^98 - 4 * q^99

Character values

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

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.421315	+	0.729738i	0.297914	+	0.516003i	0.975659	−	0.219295i	$-0.0703757\pi$
$2$	0.421315	+	0.729738i	0.297914	+	0.516003i	−0.677744	+	0.735298i	$0.737042\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.644988	−	1.11715i	0.322494	−	0.558576i
$5$		0			0
$5$		0			0
$6$	−0.421315	+	0.729738i	−0.172001	+	0.297914i
$7$	0.200681	−	0.347589i	0.0758501	−	0.131376i	−0.825606	−	0.564248i	$-0.809166\pi$
$7$	0.200681	−	0.347589i	0.0758501	−	0.131376i	0.901456	+	0.432871i	$0.142500\pi$
$8$	2.77223			0.980131
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	2.45354	+	4.24965i	0.739769	+	1.28132i	0.952599	+	0.304228i	$0.0983985\pi$
$11$	2.45354	+	4.24965i	0.739769	+	1.28132i	−0.212830	+	0.977089i	$0.568268\pi$
$12$	1.28998			0.372384
$13$	0.572960	−	3.55974i	0.158911	−	0.987293i
$13$	0.572960	−	3.55974i	0.158911	−	0.987293i
$14$	0.338199			0.0903874
$15$		0			0
$16$	−0.121995	−	0.211302i	−0.0304988	−	0.0528254i
$17$	3.54033	−	6.13203i	0.858656	−	1.48724i	−0.0145544	−	0.999894i	$-0.504633\pi$
$17$	3.54033	−	6.13203i	0.858656	−	1.48724i	0.873211	−	0.487343i	$-0.162034\pi$
$18$	−0.842629			−0.198610
$19$	−1.12724	+	1.95244i	−0.258607	+	0.447920i	−0.965869	−	0.259031i	$-0.916597\pi$
$19$	−1.12724	+	1.95244i	−0.258607	+	0.447920i	0.707262	+	0.706952i	$0.249930\pi$
$20$		0			0
$21$	0.401361			0.0875842
$22$	−2.06742	+	3.58088i	−0.440776	+	0.763446i
$23$	−0.497500	−	0.861695i	−0.103736	−	0.179676i	0.809485	−	0.587140i	$-0.199746\pi$
$23$	−0.497500	−	0.861695i	−0.103736	−	0.179676i	−0.913221	+	0.407465i	$0.866413\pi$
$24$	1.38611	+	2.40082i	0.282940	+	0.490066i
$25$		0			0
$26$	2.83907	−	1.08166i	0.556788	−	0.212130i
$27$	−1.00000			−0.192450
$28$	−0.258873	−	0.448381i	−0.0489224	−	0.0847361i
$29$	3.94133	+	6.82658i	0.731886	+	1.26766i	0.956076	+	0.293119i	$0.0946932\pi$
$29$	3.94133	+	6.82658i	0.731886	+	1.26766i	−0.224190	+	0.974546i	$0.571973\pi$
$30$		0			0
$31$	−6.30120			−1.13173			−0.565864	−	0.824499i	$-0.691457\pi$
$31$	−6.30120			−1.13173			−0.565864	+	0.824499i	$0.691457\pi$
$32$	2.87503	−	4.97969i	0.508238	−	0.880293i
$33$	−2.45354	+	4.24965i	−0.427106	+	0.739769i
$34$	5.96637			1.02322
$35$		0			0
$36$	0.644988	+	1.11715i	0.107498	+	0.186192i
$37$	4.40338	+	7.62688i	0.723912	+	1.25385i	0.959420	+	0.281980i	$0.0909910\pi$
$37$	4.40338	+	7.62688i	0.723912	+	1.25385i	−0.235509	+	0.971872i	$0.575676\pi$
$38$	−1.89969			−0.308171
$39$	3.36930	−	1.28367i	0.539520	−	0.205552i
$40$		0			0
$41$	−2.65994	−	4.60715i	−0.415413	−	0.719517i	0.580059	−	0.814575i	$-0.303030\pi$
$41$	−2.65994	−	4.60715i	−0.415413	−	0.719517i	−0.995472	+	0.0950582i	$0.969696\pi$
$42$	0.169099	+	0.292889i	0.0260926	+	0.0451937i
$43$	1.00699	−	1.74416i	0.153565	−	0.265982i	−0.778971	−	0.627060i	$-0.784258\pi$
$43$	1.00699	−	1.74416i	0.153565	−	0.265982i	0.932536	+	0.361078i	$0.117591\pi$
$44$	6.33001			0.954284
$45$		0			0
$46$	0.419208	−	0.726090i	0.0618088	−	0.107056i
$47$	−4.62317			−0.674359			−0.337180	−	0.941440i	$-0.609473\pi$
$47$	−4.62317			−0.674359			−0.337180	+	0.941440i	$0.609473\pi$
$48$	0.121995	−	0.211302i	0.0176085	−	0.0304988i
$49$	3.41945	+	5.92267i	0.488494	+	0.846096i
$50$		0			0
$51$	7.08066			0.991491
$52$	−3.60721	−	2.93607i	−0.500230	−	0.407160i
$53$	10.8496			1.49031			0.745156	−	0.666890i	$-0.232375\pi$
$53$	10.8496			1.49031			0.745156	+	0.666890i	$0.232375\pi$
$54$	−0.421315	−	0.729738i	−0.0573337	−	0.0993048i
$55$		0			0
$56$	0.556333	−	0.963596i	0.0743431	−	0.128766i
$57$	−2.25448			−0.298614
$58$	−3.32108	+	5.75228i	−0.436079	+	0.755311i
$59$	1.52224	−	2.63659i	0.198178	−	0.343255i	−0.749759	−	0.661711i	$-0.769831\pi$
$59$	1.52224	−	2.63659i	0.198178	−	0.343255i	0.947938	+	0.318455i	$0.103164\pi$
$60$		0			0
$61$	3.55088	−	6.15031i	0.454644	−	0.787466i	−0.544024	−	0.839070i	$-0.683100\pi$
$61$	3.55088	−	6.15031i	0.454644	−	0.787466i	0.998668	+	0.0516038i	$0.0164333\pi$
$62$	−2.65479	−	4.59822i	−0.337158	−	0.583975i
$63$	0.200681	+	0.347589i	0.0252834	+	0.0437921i
$64$	4.35718			0.544648
$65$		0			0
$66$	−4.13484			−0.508964
$67$	3.07665	+	5.32891i	0.375873	+	0.651030i	0.990457	−	0.137821i	$-0.0440097\pi$
$67$	3.07665	+	5.32891i	0.375873	+	0.651030i	−0.614585	+	0.788851i	$0.710676\pi$
$68$	−4.56694	−	7.91018i	−0.553823	−	0.959250i
$69$	0.497500	−	0.861695i	0.0598920	−	0.103736i
$70$		0			0
$71$	−3.16446	+	5.48101i	−0.375553	+	0.650476i	−0.990410	−	0.138162i	$-0.955880\pi$
$71$	−3.16446	+	5.48101i	−0.375553	+	0.650476i	0.614857	+	0.788639i	$0.289214\pi$
$72$	−1.38611	+	2.40082i	−0.163355	+	0.282940i
$73$	−1.01273			−0.118531			−0.0592655	−	0.998242i	$-0.518876\pi$
$73$	−1.01273			−0.118531			−0.0592655	+	0.998242i	$0.518876\pi$
$74$	−3.71042	+	6.42663i	−0.431327	+	0.747081i
$75$		0			0
$76$	1.45411	+	2.51860i	0.166798	+	0.288903i
$77$	1.96951			0.224446
$78$	2.35628	+	1.91788i	0.266796	+	0.217157i
$79$	−10.2755			−1.15608			−0.578042	−	0.816007i	$-0.696183\pi$
$79$	−10.2755			−1.15608			−0.578042	+	0.816007i	$0.696183\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	2.24134	−	3.88212i	0.247515	−	0.428709i
$83$	−10.5337			−1.15623			−0.578114	−	0.815956i	$-0.696211\pi$
$83$	−10.5337			−1.15623			−0.578114	+	0.815956i	$0.696211\pi$
$84$	0.258873	−	0.448381i	0.0282454	−	0.0489224i
$85$		0			0
$86$	1.69704			0.182997
$87$	−3.94133	+	6.82658i	−0.422555	+	0.731886i
$88$	6.80177	+	11.7810i	0.725071	+	1.25586i
$89$	−0.262260	−	0.454247i	−0.0277995	−	0.0481501i	0.851791	−	0.523882i	$-0.175517\pi$
$89$	−0.262260	−	0.454247i	−0.0277995	−	0.0481501i	−0.879590	+	0.475732i	$0.842183\pi$
$90$		0			0
$91$	−1.12234	−	0.913524i	−0.117653	−	0.0957634i
$92$	−1.28353			−0.133817
$93$	−3.15060	−	5.45700i	−0.326702	−	0.565864i
$94$	−1.94781	−	3.37371i	−0.200901	−	0.347971i
$95$		0			0
$96$	5.75005			0.586862
$97$	−4.71106	+	8.15979i	−0.478336	+	0.828502i	−0.999691	−	0.0248378i	$-0.992093\pi$
$97$	−4.71106	+	8.15979i	−0.478336	+	0.828502i	0.521356	+	0.853339i	$0.325426\pi$
$98$	−2.88133	+	4.99061i	−0.291059	+	0.504128i
$99$	−4.90707			−0.493179
$100$		0			0
$101$	2.87707	+	4.98324i	0.286280	+	0.495851i	0.972919	−	0.231148i	$-0.0742481\pi$
$101$	2.87707	+	4.98324i	0.286280	+	0.495851i	−0.686639	+	0.726998i	$0.740915\pi$
$102$	2.98319	+	5.16703i	0.295379	+	0.511612i
$103$	−15.3992			−1.51733			−0.758665	−	0.651481i	$-0.774148\pi$
$103$	−15.3992			−1.51733			−0.758665	+	0.651481i	$0.774148\pi$
$104$	1.58838	−	9.86840i	0.155753	−	0.967677i
$105$		0			0
$106$	4.57111	+	7.91739i	0.443985	+	0.769005i
$107$	−7.44919	−	12.9024i	−0.720141	−	1.24732i	−0.960943	−	0.276746i	$-0.910744\pi$
$107$	−7.44919	−	12.9024i	−0.720141	−	1.24732i	0.240802	−	0.970574i	$-0.422589\pi$
$108$	−0.644988	+	1.11715i	−0.0620640	+	0.107498i
$109$	−1.69762			−0.162602			−0.0813011	−	0.996690i	$-0.525908\pi$
$109$	−1.69762			−0.162602			−0.0813011	+	0.996690i	$0.525908\pi$
$110$		0			0
$111$	−4.40338	+	7.62688i	−0.417951	+	0.723912i
$112$	−0.0979282			−0.00925335
$113$	1.12402	−	1.94685i	0.105739	−	0.183145i	−0.808301	−	0.588769i	$-0.799613\pi$
$113$	1.12402	−	1.94685i	0.105739	−	0.183145i	0.914040	+	0.405625i	$0.132946\pi$
$114$	−0.949847	−	1.64518i	−0.0889613	−	0.154086i
$115$		0			0
$116$	10.1684			0.944116
$117$	2.79634	+	2.27607i	0.258522	+	0.210422i
$118$	2.56536			0.236161
$119$	−1.42095	−	2.46116i	−0.130258	−	0.225614i
$120$		0			0
$121$	−6.53968	+	11.3271i	−0.594516	+	1.02973i
$122$	5.98415			0.541780
$123$	2.65994	−	4.60715i	0.239839	−	0.415413i
$124$	−4.06420	+	7.03939i	−0.364976	+	0.632156i
$125$		0			0
$126$	−0.169099	+	0.292889i	−0.0150646	+	0.0260926i
$127$	−8.63173	−	14.9506i	−0.765942	−	1.32665i	−0.939747	−	0.341871i	$-0.888939\pi$
$127$	−8.63173	−	14.9506i	−0.765942	−	1.32665i	0.173804	−	0.984780i	$-0.444394\pi$
$128$	−3.91431	−	6.77978i	−0.345979	−	0.599254i
$129$	2.01398			0.177321
$130$		0			0
$131$	−4.59071			−0.401092			−0.200546	−	0.979684i	$-0.564272\pi$
$131$	−4.59071			−0.401092			−0.200546	+	0.979684i	$0.564272\pi$
$132$	3.16500	+	5.48195i	0.275478	+	0.477142i
$133$	0.452431	+	0.783633i	0.0392307	+	0.0679496i
$134$	−2.59247	+	4.49030i	−0.223956	+	0.387903i
$135$		0			0
$136$	9.81461	−	16.9994i	0.841596	−	1.45769i
$137$	2.47524	−	4.28724i	0.211474	−	0.366284i	−0.740702	−	0.671834i	$-0.765507\pi$
$137$	2.47524	−	4.28724i	0.211474	−	0.366284i	0.952176	+	0.305550i	$0.0988403\pi$
$138$	0.838416			0.0713707
$139$	6.63214	−	11.4872i	0.562530	−	0.974331i	−0.434744	−	0.900554i	$-0.643161\pi$
$139$	6.63214	−	11.4872i	0.562530	−	0.974331i	0.997275	−	0.0737774i	$-0.0235054\pi$
$140$		0			0
$141$	−2.31159	−	4.00379i	−0.194671	−	0.337180i
$142$	−5.33294			−0.447530
$143$	16.5334	−	6.29906i	1.38259	−	0.526754i
$144$	0.243990			0.0203325
$145$		0			0
$146$	−0.426678	−	0.739028i	−0.0353121	−	0.0611624i
$147$	−3.41945	+	5.92267i	−0.282032	+	0.488494i
$148$	11.3605			0.933829
$149$	1.57886	−	2.73467i	0.129345	−	0.224033i	−0.794078	−	0.607816i	$-0.792046\pi$
$149$	1.57886	−	2.73467i	0.129345	−	0.224033i	0.923423	+	0.383783i	$0.125379\pi$
$150$		0			0
$151$	−18.5878			−1.51266			−0.756328	−	0.654193i	$-0.773009\pi$
$151$	−18.5878			−1.51266			−0.756328	+	0.654193i	$0.773009\pi$
$152$	−3.12497	+	5.41261i	−0.253469	+	0.439021i
$153$	3.54033	+	6.13203i	0.286219	+	0.495746i
$154$	0.829782	+	1.43723i	0.0668658	+	0.115815i
$155$		0			0
$156$	0.739105	−	4.59197i	0.0591758	−	0.367652i
$157$	−10.7802			−0.860351			−0.430175	−	0.902745i	$-0.641548\pi$
$157$	−10.7802			−0.860351			−0.430175	+	0.902745i	$0.641548\pi$
$158$	−4.32922	−	7.49843i	−0.344414	−	0.596543i
$159$	5.42482	+	9.39606i	0.430216	+	0.745156i
$160$		0			0
$161$	−0.399354			−0.0314735
$162$	0.421315	−	0.729738i	0.0331016	−	0.0573337i
$163$	−0.786941	+	1.36302i	−0.0616380	+	0.106760i	−0.895198	−	0.445669i	$-0.852966\pi$
$163$	−0.786941	+	1.36302i	−0.0616380	+	0.106760i	0.833560	+	0.552429i	$0.186299\pi$
$164$	−6.86252			−0.535873
$165$		0			0
$166$	−4.43802	−	7.68687i	−0.344457	−	0.596617i
$167$	7.53397	+	13.0492i	0.582996	+	1.00978i	0.995122	+	0.0986516i	$0.0314529\pi$
$167$	7.53397	+	13.0492i	0.582996	+	1.00978i	−0.412126	+	0.911127i	$0.635214\pi$
$168$	1.11267			0.0858440
$169$	−12.3434	−	4.07917i	−0.949495	−	0.313783i
$170$		0			0
$171$	−1.12724	−	1.95244i	−0.0862023	−	0.149307i
$172$	−1.29900	−	2.24993i	−0.0990475	−	0.171555i
$173$	−1.70307	+	2.94981i	−0.129482	+	0.224270i	−0.923476	−	0.383656i	$-0.874665\pi$
$173$	−1.70307	+	2.94981i	−0.129482	+	0.224270i	0.793994	+	0.607926i	$0.207998\pi$
$174$	−6.64216			−0.503541
$175$		0			0
$176$	0.598639	−	1.03687i	0.0451241	−	0.0781572i
$177$	3.04448			0.228837
$178$	0.220988	−	0.382762i	0.0165637	−	0.0286892i
$179$	0.300516	+	0.520508i	0.0224616	+	0.0389046i	0.877038	−	0.480422i	$-0.159516\pi$
$179$	0.300516	+	0.520508i	0.0224616	+	0.0389046i	−0.854576	+	0.519326i	$0.826183\pi$
$180$		0			0
$181$	−17.0607			−1.26811			−0.634056	−	0.773287i	$-0.718611\pi$
$181$	−17.0607			−1.26811			−0.634056	+	0.773287i	$0.718611\pi$
$182$	0.193774	−	1.20390i	0.0143635	−	0.0892388i
$183$	7.10176			0.524977
$184$	−1.37918	−	2.38882i	−0.101675	−	0.176106i
$185$		0			0
$186$	2.65479	−	4.59822i	0.194658	−	0.337158i
$187$	34.7453			2.54083
$188$	−2.98189	+	5.16479i	−0.217477	+	0.376681i
$189$	−0.200681	+	0.347589i	−0.0145974	+	0.0252834i
$190$		0			0
$191$	−3.10083	+	5.37079i	−0.224368	+	0.388617i	−0.956130	−	0.292944i	$-0.905365\pi$
$191$	−3.10083	+	5.37079i	−0.224368	+	0.388617i	0.731762	+	0.681561i	$0.238698\pi$
$192$	2.17859	+	3.77343i	0.157226	+	0.272324i
$193$	4.56896	+	7.91367i	0.328881	+	0.569639i	0.982290	−	0.187366i	$-0.0599952\pi$
$193$	4.56896	+	7.91367i	0.328881	+	0.569639i	−0.653409	+	0.757005i	$0.726662\pi$
$194$	−7.93935			−0.570012
$195$		0			0
$196$	8.82203			0.630145
$197$	−10.8050	−	18.7148i	−0.769823	−	1.33337i	−0.937659	−	0.347557i	$-0.887011\pi$
$197$	−10.8050	−	18.7148i	−0.769823	−	1.33337i	0.167836	−	0.985815i	$-0.446322\pi$
$198$	−2.06742	−	3.58088i	−0.146925	−	0.254482i
$199$	−1.27223	+	2.20357i	−0.0901860	+	0.156207i	−0.907589	−	0.419859i	$-0.862079\pi$
$199$	−1.27223	+	2.20357i	−0.0901860	+	0.156207i	0.817403	+	0.576066i	$0.195413\pi$
$200$		0			0
$201$	−3.07665	+	5.32891i	−0.217010	+	0.375873i
$202$	−2.42431	+	4.19902i	−0.170574	+	0.295442i
$203$	3.16379			0.222055
$204$	4.56694	−	7.91018i	0.319750	−	0.553823i
$205$		0			0
$206$	−6.48792	−	11.2374i	−0.452034	−	0.782947i
$207$	0.995000			0.0691573
$208$	−0.822077	+	0.313203i	−0.0570008	+	0.0217167i
$209$	−11.0629			−0.765238
$210$		0			0
$211$	5.54061	+	9.59663i	0.381432	+	0.660659i	0.991267	−	0.131869i	$-0.0420978\pi$
$211$	5.54061	+	9.59663i	0.381432	+	0.660659i	−0.609836	+	0.792528i	$0.708765\pi$
$212$	6.99789	−	12.1207i	0.480617	−	0.832453i
$213$	−6.32893			−0.433651
$214$	6.27691	−	10.8719i	0.429081	−	0.743189i
$215$		0			0
$216$	−2.77223			−0.188626
$217$	−1.26453	+	2.19023i	−0.0858417	+	0.148682i
$218$	−0.715231	−	1.23882i	−0.0484416	−	0.0839032i
$219$	−0.506365	−	0.877050i	−0.0342170	−	0.0592655i
$220$		0			0
$221$	−19.7999	−	16.1161i	−1.33189	−	1.08408i
$222$	−7.42084			−0.498054
$223$	−0.265778	−	0.460340i	−0.0177978	−	0.0308267i	0.856989	−	0.515334i	$-0.172332\pi$
$223$	−0.265778	−	0.460340i	−0.0177978	−	0.0308267i	−0.874787	+	0.484507i	$0.838999\pi$
$224$	−1.15392	−	1.99865i	−0.0770998	−	0.133541i
$225$		0			0
$226$	1.89426			0.126004
$227$	10.6937	−	18.5220i	0.709764	−	1.22935i	−0.255180	−	0.966894i	$-0.582135\pi$
$227$	10.6937	−	18.5220i	0.709764	−	1.22935i	0.964944	−	0.262454i	$-0.0845319\pi$
$228$	−1.45411	+	2.51860i	−0.0963011	+	0.166798i
$229$	−0.406502			−0.0268624			−0.0134312	−	0.999910i	$-0.504275\pi$
$229$	−0.406502			−0.0268624			−0.0134312	+	0.999910i	$0.504275\pi$
$230$		0			0
$231$	0.984754	+	1.70564i	0.0647920	+	0.112223i
$232$	10.9263	+	18.9249i	0.717345	+	1.24248i
$233$	2.66379			0.174510			0.0872552	−	0.996186i	$-0.472190\pi$
$233$	2.66379			0.174510			0.0872552	+	0.996186i	$0.472190\pi$
$234$	−0.482793	+	2.99954i	−0.0315612	+	0.196086i
$235$		0			0
$236$	−1.96365	−	3.40114i	−0.127823	−	0.221395i
$237$	−5.13775	−	8.89885i	−0.333733	−	0.578042i
$238$	1.19734	−	2.07385i	0.0776117	−	0.134427i
$239$	−15.8317			−1.02407			−0.512034	−	0.858965i	$-0.671108\pi$
$239$	−15.8317			−1.02407			−0.512034	+	0.858965i	$0.671108\pi$
$240$		0			0
$241$	11.6570	−	20.1906i	0.750895	−	1.30059i	−0.196495	−	0.980505i	$-0.562956\pi$
$241$	11.6570	−	20.1906i	0.750895	−	1.30059i	0.947390	−	0.320083i	$-0.103711\pi$
$242$	−11.0210			−0.708460
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−4.58055	−	7.93375i	−0.293240	−	0.507906i
$245$		0			0
$246$	4.48269			0.285806
$247$	6.30431	+	5.13135i	0.401133	+	0.326500i
$248$	−17.4684			−1.10924
$249$	−5.26687	−	9.12248i	−0.333774	−	0.578114i
$250$		0			0
$251$	−0.650814	+	1.12724i	−0.0410790	+	0.0711509i	−0.885834	−	0.464002i	$-0.846413\pi$
$251$	−0.650814	+	1.12724i	−0.0410790	+	0.0711509i	0.844755	+	0.535153i	$0.179746\pi$
$252$	0.517746			0.0326149
$253$	2.44127	−	4.22840i	0.153481	−	0.265837i
$254$	7.27335	−	12.5978i	0.456371	−	0.790457i
$255$		0			0
$256$	7.65549	−	13.2597i	0.478468	−	0.828731i
$257$	4.93694	+	8.55103i	0.307958	+	0.533399i	0.977915	−	0.209001i	$-0.0670211\pi$
$257$	4.93694	+	8.55103i	0.307958	+	0.533399i	−0.669958	+	0.742399i	$0.733688\pi$
$258$	0.848521	+	1.46968i	0.0528266	+	0.0914983i
$259$	3.53469			0.219635
$260$		0			0
$261$	−7.88266			−0.487924
$262$	−1.93413	−	3.35001i	−0.119491	−	0.206965i
$263$	−0.266805	−	0.462121i	−0.0164519	−	0.0284956i	0.857682	−	0.514180i	$-0.171904\pi$
$263$	−0.266805	−	0.462121i	−0.0164519	−	0.0284956i	−0.874134	+	0.485685i	$0.838570\pi$
$264$	−6.80177	+	11.7810i	−0.418620	+	0.725071i
$265$		0			0
$266$	−0.381232	+	0.660312i	−0.0233748	+	0.0404864i
$267$	0.262260	−	0.454247i	0.0160500	−	0.0277995i
$268$	7.93761			0.484867
$269$	6.80199	−	11.7814i	0.414725	−	0.718324i	−0.580675	−	0.814136i	$-0.697211\pi$
$269$	6.80199	−	11.7814i	0.414725	−	0.718324i	0.995400	+	0.0958112i	$0.0305445\pi$
$270$		0			0
$271$	11.9163	+	20.6396i	0.723862	+	1.25377i	0.959441	+	0.281911i	$0.0909681\pi$
$271$	11.9163	+	20.6396i	0.723862	+	1.25377i	−0.235579	+	0.971855i	$0.575699\pi$
$272$	−1.72761			−0.104752
$273$	0.229964	−	1.42874i	0.0139181	−	0.0864712i
$274$	4.17142			0.252004
$275$		0			0
$276$	−0.641763	−	1.11157i	−0.0386296	−	0.0669084i
$277$	−9.60639	+	16.6388i	−0.577192	+	0.999726i	0.418608	+	0.908167i	$0.362518\pi$
$277$	−9.60639	+	16.6388i	−0.577192	+	0.999726i	−0.995800	+	0.0915586i	$0.970815\pi$
$278$	11.1769			0.670344
$279$	3.15060	−	5.45700i	0.188621	−	0.326702i
$280$		0			0
$281$	6.31792			0.376895			0.188448	−	0.982083i	$-0.439654\pi$
$281$	6.31792			0.376895			0.188448	+	0.982083i	$0.439654\pi$
$282$	1.94781	−	3.37371i	0.115990	−	0.200901i
$283$	−15.1027	−	26.1587i	−0.897765	−	1.55497i	−0.830345	−	0.557249i	$-0.811857\pi$
$283$	−15.1027	−	26.1587i	−0.897765	−	1.55497i	−0.0674193	−	0.997725i	$-0.521477\pi$
$284$	4.08208	+	7.07037i	0.242227	+	0.419549i
$285$		0			0
$286$	11.5624	+	9.41117i	0.683701	+	0.556494i
$287$	−2.13519			−0.126037
$288$	2.87503	+	4.97969i	0.169413	+	0.293431i
$289$	−16.5679	−	28.6964i	−0.974582	−	1.68803i
$290$		0			0
$291$	−9.42212			−0.552334
$292$	−0.653199	+	1.13137i	−0.0382256	+	0.0662086i
$293$	−3.56844	+	6.18072i	−0.208470	+	0.361081i	−0.951233	−	0.308474i	$-0.900182\pi$
$293$	−3.56844	+	6.18072i	−0.208470	+	0.361081i	0.742762	+	0.669555i	$0.233515\pi$
$294$	−5.76266			−0.336085
$295$		0			0
$296$	12.2072	+	21.1435i	0.709528	+	1.22894i
$297$	−2.45354	−	4.24965i	−0.142369	−	0.246590i
$298$	2.66079			0.154135
$299$	−3.35245	+	1.27725i	−0.193877	+	0.0738653i
$300$		0			0
$301$	−0.404167	−	0.700038i	−0.0232958	−	0.0403495i
$302$	−7.83132	−	13.5642i	−0.450642	−	0.780535i
$303$	−2.87707	+	4.98324i	−0.165284	+	0.286280i
$304$	0.550072			0.0315488
$305$		0			0
$306$	−2.98319	+	5.16703i	−0.170537	+	0.295379i
$307$	−9.91349			−0.565793			−0.282897	−	0.959150i	$-0.591295\pi$
$307$	−9.91349			−0.565793			−0.282897	+	0.959150i	$0.591295\pi$
$308$	1.27031	−	2.20024i	0.0723826	−	0.125370i
$309$	−7.69961	−	13.3361i	−0.438015	−	0.758665i
$310$		0			0
$311$	6.04584			0.342828			0.171414	−	0.985199i	$-0.445166\pi$
$311$	6.04584			0.342828			0.171414	+	0.985199i	$0.445166\pi$
$312$	9.34048	−	3.55863i	0.528800	−	0.201468i
$313$	−4.62017			−0.261148			−0.130574	−	0.991439i	$-0.541682\pi$
$313$	−4.62017			−0.261148			−0.130574	+	0.991439i	$0.541682\pi$
$314$	−4.54184	−	7.86670i	−0.256311	−	0.443944i
$315$		0			0
$316$	−6.62758	+	11.4793i	−0.372830	+	0.645761i
$317$	25.0793			1.40860			0.704298	−	0.709905i	$-0.251262\pi$
$317$	25.0793			1.40860			0.704298	+	0.709905i	$0.251262\pi$
$318$	−4.57111	+	7.91739i	−0.256335	+	0.443985i
$319$	−19.3404	+	33.4985i	−1.08285	+	1.87556i
$320$		0			0
$321$	7.44919	−	12.9024i	0.415773	−	0.720141i
$322$	−0.168254	−	0.291424i	−0.00937642	−	0.0162404i
$323$	7.98162	+	13.8246i	0.444109	+	0.769220i
$324$	−1.28998			−0.0716653
$325$		0			0
$326$	−1.32620			−0.0734514
$327$	−0.848809	−	1.47018i	−0.0469392	−	0.0813011i
$328$	−7.37397	−	12.7721i	−0.407159	−	0.705221i
$329$	−0.927781	+	1.60696i	−0.0511502	+	0.0885948i
$330$		0			0
$331$	−6.84346	+	11.8532i	−0.376150	+	0.651512i	−0.990499	−	0.137524i	$-0.956086\pi$
$331$	−6.84346	+	11.8532i	−0.376150	+	0.651512i	0.614348	+	0.789035i	$0.289419\pi$
$332$	−6.79413	+	11.7678i	−0.372877	+	0.645841i
$333$	−8.80677			−0.482608
$334$	−6.34834	+	10.9956i	−0.347366	+	0.601655i
$335$		0			0
$336$	−0.0489641	−	0.0848083i	−0.00267121	−	0.00462667i
$337$	−9.01512			−0.491085			−0.245543	−	0.969386i	$-0.578966\pi$
$337$	−9.01512			−0.491085			−0.245543	+	0.969386i	$0.578966\pi$
$338$	−2.22374	−	10.7261i	−0.120955	−	0.583422i
$339$	2.24803			0.122096
$340$		0			0
$341$	−15.4602	−	26.7779i	−0.837217	−	1.45010i
$342$	0.949847	−	1.64518i	0.0513618	−	0.0889613i
$343$	5.55440			0.299909
$344$	2.79161	−	4.83521i	0.150514	−	0.260697i
$345$		0			0
$346$	−2.87012			−0.154299
$347$	−5.43152	+	9.40767i	−0.291579	+	0.505030i	−0.974183	−	0.225758i	$-0.927514\pi$
$347$	−5.43152	+	9.40767i	−0.291579	+	0.505030i	0.682604	+	0.730788i	$0.260847\pi$
$348$	5.08422	+	8.80613i	0.272543	+	0.472058i
$349$	9.86492	+	17.0865i	0.528057	+	0.914622i	0.999465	+	0.0327066i	$0.0104127\pi$
$349$	9.86492	+	17.0865i	0.528057	+	0.914622i	−0.471408	+	0.881915i	$0.656254\pi$
$350$		0			0
$351$	−0.572960	+	3.55974i	−0.0305824	+	0.190005i
$352$	28.2159			1.50391
$353$	9.29831	+	16.1051i	0.494899	+	0.857190i	0.999983	−	0.00588009i	$-0.00187170\pi$
$353$	9.29831	+	16.1051i	0.494899	+	0.857190i	−0.505084	+	0.863070i	$0.668538\pi$
$354$	1.28268	+	2.22167i	0.0681738	+	0.118080i
$355$		0			0
$356$	−0.676618			−0.0358607
$357$	1.42095	−	2.46116i	0.0752047	−	0.130258i
$358$	−0.253223	+	0.438595i	−0.0133833	+	0.0231805i
$359$	12.1448			0.640976			0.320488	−	0.947253i	$-0.396153\pi$
$359$	12.1448			0.640976			0.320488	+	0.947253i	$0.396153\pi$
$360$		0			0
$361$	6.95865	+	12.0527i	0.366245	+	0.634355i
$362$	−7.18792	−	12.4498i	−0.377789	−	0.654350i
$363$	−13.0794			−0.686488
$364$	−1.74444	+	0.664615i	−0.0914337	+	0.0348353i
$365$		0			0
$366$	2.99208	+	5.18243i	0.156398	+	0.270890i
$367$	−15.5168	−	26.8759i	−0.809971	−	1.40291i	−0.912884	−	0.408220i	$-0.866150\pi$
$367$	−15.5168	−	26.8759i	−0.809971	−	1.40291i	0.102913	−	0.994690i	$-0.467184\pi$
$368$	−0.121385	+	0.210245i	−0.00632764	+	0.0109598i
$369$	5.31988			0.276942
$370$		0			0
$371$	2.17731	−	3.77121i	0.113040	−	0.195792i
$372$	−8.12839			−0.421437
$373$	−5.21567	+	9.03380i	−0.270057	+	0.467752i	−0.968876	−	0.247546i	$-0.920376\pi$
$373$	−5.21567	+	9.03380i	−0.270057	+	0.467752i	0.698819	+	0.715298i	$0.253709\pi$
$374$	14.6387	+	25.3550i	0.756950	+	1.31108i
$375$		0			0
$376$	−12.8165			−0.660961
$377$	26.5591	−	10.1187i	1.36786	−	0.521141i
$378$	−0.338199			−0.0173951
$379$	15.3621	+	26.6080i	0.789099	+	1.36676i	0.926519	+	0.376247i	$0.122786\pi$
$379$	15.3621	+	26.6080i	0.789099	+	1.36676i	−0.137420	+	0.990513i	$0.543881\pi$
$380$		0			0
$381$	8.63173	−	14.9506i	0.442217	−	0.765942i
$382$	−5.22569			−0.267370
$383$	4.25652	−	7.37251i	0.217498	−	0.376718i	−0.736544	−	0.676389i	$-0.763544\pi$
$383$	4.25652	−	7.37251i	0.217498	−	0.376718i	0.954042	+	0.299672i	$0.0968771\pi$
$384$	3.91431	−	6.77978i	0.199751	−	0.345979i
$385$		0			0
$386$	−3.84994	+	6.66829i	−0.195957	+	0.339407i
$387$	1.00699	+	1.74416i	0.0511883	+	0.0886607i
$388$	6.07715	+	10.5259i	0.308521	+	0.534374i
$389$	−21.6832			−1.09938			−0.549691	−	0.835368i	$-0.685255\pi$
$389$	−21.6832			−1.09938			−0.549691	+	0.835368i	$0.685255\pi$
$390$		0			0
$391$	−7.04526			−0.356294
$392$	9.47951	+	16.4190i	0.478788	+	0.829285i
$393$	−2.29535	−	3.97567i	−0.115785	−	0.200546i
$394$	9.10459	−	15.7696i	0.458683	−	0.794461i
$395$		0			0
$396$	−3.16500	+	5.48195i	−0.159047	+	0.275478i
$397$	−10.3915	+	17.9986i	−0.521535	+	0.903325i	0.478151	+	0.878278i	$0.341307\pi$
$397$	−10.3915	+	17.9986i	−0.521535	+	0.903325i	−0.999686	+	0.0250477i	$0.992026\pi$
$398$	−2.14404			−0.107471
$399$	−0.452431	+	0.783633i	−0.0226499	+	0.0392307i
$400$		0			0
$401$	18.3709	+	31.8194i	0.917400	+	1.58898i	0.803350	+	0.595508i	$0.203049\pi$
$401$	18.3709	+	31.8194i	0.917400	+	1.58898i	0.114050	+	0.993475i	$0.463618\pi$
$402$	−5.18495			−0.258602
$403$	−3.61034	+	22.4306i	−0.179844	+	1.11735i
$404$	7.42271			0.369294
$405$		0			0
$406$	1.33295	+	2.30874i	0.0661533	+	0.114581i
$407$	−21.6077	+	37.4257i	−1.07105	+	1.85512i
$408$	19.6292			0.971791
$409$	1.60553	−	2.78087i	0.0793885	−	0.137505i	−0.823598	−	0.567174i	$-0.808037\pi$
$409$	1.60553	−	2.78087i	0.0793885	−	0.137505i	0.902986	+	0.429669i	$0.141370\pi$
$410$		0			0
$411$	4.95048			0.244189
$412$	−9.93231	+	17.2033i	−0.489330	+	0.847544i
$413$	−0.610967	−	1.05823i	−0.0300637	−	0.0520719i
$414$	0.419208	+	0.726090i	0.0206029	+	0.0356854i
$415$		0			0
$416$	−16.0791	−	13.0875i	−0.788343	−	0.641667i
$417$	13.2643			0.649554
$418$	−4.66097	−	8.07303i	−0.227975	−	0.394865i
$419$	7.62605	+	13.2087i	0.372557	+	0.645288i	0.989958	−	0.141361i	$-0.0451477\pi$
$419$	7.62605	+	13.2087i	0.372557	+	0.645288i	−0.617401	+	0.786649i	$0.711814\pi$
$420$		0			0
$421$	0.122664			0.00597828			0.00298914	−	0.999996i	$-0.499049\pi$
$421$	0.122664			0.00597828			0.00298914	+	0.999996i	$0.499049\pi$
$422$	−4.66868	+	8.08640i	−0.227268	+	0.393640i
$423$	2.31159	−	4.00379i	0.112393	−	0.194671i
$424$	30.0777			1.46070
$425$		0			0
$426$	−2.66647	−	4.61846i	−0.129191	−	0.223765i
$427$	−1.42519	−	2.46849i	−0.0689695	−	0.119459i
$428$	−19.2186			−0.928964
$429$	13.7218	+	11.1688i	0.662497	+	0.539236i
$430$		0			0
$431$	−0.809141	−	1.40147i	−0.0389750	−	0.0675066i	0.845880	−	0.533373i	$-0.179076\pi$
$431$	−0.809141	−	1.40147i	−0.0389750	−	0.0675066i	−0.884855	+	0.465867i	$0.845743\pi$
$432$	0.121995	+	0.211302i	0.00586949	+	0.0101663i
$433$	7.78179	−	13.4785i	0.373969	−	0.647733i	−0.616203	−	0.787587i	$-0.711330\pi$
$433$	7.78179	−	13.4785i	0.373969	−	0.647733i	0.990172	+	0.139854i	$0.0446633\pi$
$434$	−2.13106			−0.102294
$435$		0			0
$436$	−1.09494	+	1.89650i	−0.0524383	+	0.0908257i
$437$	2.24321			0.107307
$438$	0.426678	−	0.739028i	0.0203875	−	0.0353121i
$439$	3.91196	+	6.77571i	0.186708	+	0.323387i	0.944151	−	0.329514i	$-0.106885\pi$
$439$	3.91196	+	6.77571i	0.186708	+	0.323387i	−0.757443	+	0.652901i	$0.773552\pi$
$440$		0			0
$441$	−6.83891			−0.325662
$442$	3.41850	−	21.2387i	0.162601	−	1.01022i
$443$	24.8136			1.17893			0.589465	−	0.807794i	$-0.299338\pi$
$443$	24.8136			1.17893			0.589465	+	0.807794i	$0.299338\pi$
$444$	5.68026	+	9.83850i	0.269573	+	0.466914i
$445$		0			0
$446$	0.223952	−	0.387896i	0.0106044	−	0.0183674i
$447$	3.15772			0.149355
$448$	0.874402	−	1.51451i	0.0413116	−	0.0715538i
$449$	16.7743	−	29.0539i	0.791626	−	1.37114i	−0.133333	−	0.991071i	$-0.542568\pi$
$449$	16.7743	−	29.0539i	0.791626	−	1.37114i	0.924959	−	0.380066i	$-0.124099\pi$
$450$		0			0
$451$	13.0525	−	22.6076i	0.614619	−	1.06455i
$452$	−1.44995	−	2.51140i	−0.0682001	−	0.118126i
$453$	−9.29391	−	16.0975i	−0.436666	−	0.756328i
$454$	18.0216			0.845796
$455$		0			0
$456$	−6.24995			−0.292681
$457$	−9.22831	−	15.9839i	−0.431682	−	0.747696i	0.565336	−	0.824861i	$-0.308746\pi$
$457$	−9.22831	−	15.9839i	−0.431682	−	0.747696i	−0.997018	+	0.0771651i	$0.975413\pi$
$458$	−0.171265	−	0.296640i	−0.00800271	−	0.0138611i
$459$	−3.54033	+	6.13203i	−0.165249	+	0.286219i
$460$		0			0
$461$	−3.47162	+	6.01302i	−0.161689	+	0.280054i	−0.935475	−	0.353394i	$-0.885028\pi$
$461$	−3.47162	+	6.01302i	−0.161689	+	0.280054i	0.773785	+	0.633448i	$0.218361\pi$
$462$	−0.829782	+	1.43723i	−0.0386050	+	0.0668658i
$463$	−41.2459			−1.91686			−0.958430	−	0.285329i	$-0.907897\pi$
$463$	−41.2459			−1.91686			−0.958430	+	0.285329i	$0.907897\pi$
$464$	0.961646	−	1.66562i	0.0446433	−	0.0773245i
$465$		0			0
$466$	1.12229	+	1.94387i	0.0519892	+	0.0900479i
$467$	−29.7045			−1.37456			−0.687280	−	0.726393i	$-0.741195\pi$
$467$	−29.7045			−1.37456			−0.687280	+	0.726393i	$0.741195\pi$
$468$	4.34632	−	1.65590i	0.200909	−	0.0765441i
$469$	2.46969			0.114040
$470$		0			0
$471$	−5.39008	−	9.33590i	−0.248362	−	0.430175i
$472$	4.21999	−	7.30924i	0.194241	−	0.336435i
$473$	9.88276			0.454410
$474$	4.32922	−	7.49843i	0.198848	−	0.344414i
$475$		0			0
$476$	−3.66599			−0.168030
$477$	−5.42482	+	9.39606i	−0.248385	+	0.430216i
$478$	−6.67013	−	11.5530i	−0.305084	−	0.528422i
$479$	9.86981	+	17.0950i	0.450963	+	0.781091i	0.998446	−	0.0557257i	$-0.0177472\pi$
$479$	9.86981	+	17.0950i	0.450963	+	0.781091i	−0.547483	+	0.836817i	$0.684414\pi$
$480$		0			0
$481$	29.6726	−	11.3050i	1.35296	−	0.515463i
$482$	19.6451			0.894809
$483$	−0.199677	−	0.345851i	−0.00908562	−	0.0157368i
$484$	8.43603	+	14.6116i	0.383456	+	0.664165i
$485$		0			0
$486$	0.842629			0.0382224
$487$	12.1517	−	21.0473i	0.550645	−	0.953745i	−0.447583	−	0.894242i	$-0.647715\pi$
$487$	12.1517	−	21.0473i	0.550645	−	0.953745i	0.998228	−	0.0595026i	$-0.0189515\pi$
$488$	9.84386	−	17.0501i	0.445610	−	0.771820i
$489$	−1.57388			−0.0711734
$490$		0			0
$491$	−3.45543	−	5.98497i	−0.155941	−	0.270098i	0.777460	−	0.628932i	$-0.216508\pi$
$491$	−3.45543	−	5.98497i	−0.155941	−	0.270098i	−0.933401	+	0.358834i	$0.883174\pi$
$492$	−3.43126	−	5.94312i	−0.154693	−	0.267936i
$493$	55.8144			2.51376
$494$	−1.08845	+	6.76241i	−0.0489716	+	0.304255i
$495$		0			0
$496$	0.768715	+	1.33145i	0.0345163	+	0.0597840i
$497$	1.27009	+	2.19986i	0.0569714	+	0.0986774i
$498$	4.43802	−	7.68687i	0.198872	−	0.344457i
$499$	2.21036			0.0989495			0.0494747	−	0.998775i	$-0.484245\pi$
$499$	2.21036			0.0989495			0.0494747	+	0.998775i	$0.484245\pi$
$500$		0			0
$501$	−7.53397	+	13.0492i	−0.336593	+	0.582996i
$502$	−1.09679			−0.0489521
$503$	−14.6140	+	25.3122i	−0.651607	+	1.12862i	0.331126	+	0.943587i	$0.392572\pi$
$503$	−14.6140	+	25.3122i	−0.651607	+	1.12862i	−0.982733	+	0.185030i	$0.940762\pi$
$504$	0.556333	+	0.963596i	0.0247810	+	0.0429220i
$505$		0			0
$506$	4.11417			0.182897
$507$	−2.63905	−	12.7293i	−0.117204	−	0.565329i
$508$	−22.2695			−0.988047
$509$	3.60746	+	6.24830i	0.159898	+	0.276951i	0.934832	−	0.355091i	$-0.115550\pi$
$509$	3.60746	+	6.24830i	0.159898	+	0.276951i	−0.774934	+	0.632042i	$0.782217\pi$
$510$		0			0
$511$	−0.203235	+	0.352014i	−0.00899060	+	0.0155722i
$512$	−2.75575			−0.121788
$513$	1.12724	−	1.95244i	0.0497689	−	0.0862023i
$514$	−4.16001	+	7.20535i	−0.183490	+	0.317814i
$515$		0			0
$516$	1.29900	−	2.24993i	0.0571851	−	0.0990475i
$517$	−11.3431	−	19.6469i	−0.498870	−	0.864068i
$518$	1.48922	+	2.57940i	0.0654325	+	0.113332i
$519$	−3.40615			−0.149513
$520$		0			0
$521$	38.0923			1.66886			0.834428	−	0.551118i	$-0.185798\pi$
$521$	38.0923			1.66886			0.834428	+	0.551118i	$0.185798\pi$
$522$	−3.32108	−	5.75228i	−0.145360	−	0.251770i
$523$	−0.0397056	−	0.0687721i	−0.00173620	−	0.00300719i	0.865156	−	0.501503i	$-0.167219\pi$
$523$	−0.0397056	−	0.0687721i	−0.00173620	−	0.00300719i	−0.866892	+	0.498496i	$0.833886\pi$
$524$	−2.96095	+	5.12852i	−0.129350	+	0.224040i
$525$		0			0
$526$	0.224818	−	0.389396i	0.00980253	−	0.0169785i
$527$	−22.3083	+	38.6391i	−0.971766	+	1.68315i
$528$	1.19728			0.0521048
$529$	11.0050	−	19.0612i	0.478478	−	0.828748i
$530$		0			0
$531$	1.52224	+	2.63659i	0.0660595	+	0.114418i
$532$	1.16725			0.0506067
$533$	−17.9243	+	6.82897i	−0.776387	+	0.295796i
$534$	0.441976			0.0191262
$535$		0			0
$536$	8.52918	+	14.7730i	0.368404	+	0.638095i
$537$	−0.300516	+	0.520508i	−0.0129682	+	0.0224616i
$538$	11.4631			0.494210
$539$	−16.7795	+	29.0630i	−0.722745	+	1.25183i
$540$		0			0
$541$	−29.1429			−1.25295			−0.626476	−	0.779441i	$-0.715503\pi$
$541$	−29.1429			−1.25295			−0.626476	+	0.779441i	$0.715503\pi$
$542$	−10.0410	+	17.3915i	−0.431298	+	0.747030i
$543$	−8.53035	−	14.7750i	−0.366072	−	0.634056i
$544$	−20.3571	−	35.2595i	−0.872803	−	1.51174i
$545$		0			0
$546$	1.13949	−	0.434135i	0.0487658	−	0.0185793i
$547$	12.9652			0.554354			0.277177	−	0.960819i	$-0.410601\pi$
$547$	12.9652			0.554354			0.277177	+	0.960819i	$0.410601\pi$
$548$	−3.19300	−	5.53043i	−0.136398	−	0.236248i
$549$	3.55088	+	6.15031i	0.151548	+	0.262489i
$550$		0			0
$551$	−17.7713			−0.757084
$552$	1.37918	−	2.38882i	0.0587020	−	0.101675i
$553$	−2.06209	+	3.57165i	−0.0876891	+	0.151882i
$554$	−16.1892			−0.687815
$555$		0			0
$556$	−8.55530	−	14.8182i	−0.362825	−	0.628432i
$557$	16.0443	+	27.7896i	0.679820	+	1.17748i	0.975035	+	0.222051i	$0.0712753\pi$
$557$	16.0443	+	27.7896i	0.679820	+	1.17748i	−0.295215	+	0.955431i	$0.595391\pi$
$558$	5.30957			0.224772
$559$	−5.63178	−	4.58396i	−0.238199	−	0.193881i
$560$		0			0
$561$	17.3727	+	30.0903i	0.733474	+	1.27041i
$562$	2.66183	+	4.61043i	0.112283	+	0.194479i
$563$	−0.759773	+	1.31596i	−0.0320206	+	0.0554613i	−0.881592	−	0.472013i	$-0.843528\pi$
$563$	−0.759773	+	1.31596i	−0.0320206	+	0.0554613i	0.849571	+	0.527474i	$0.176861\pi$
$564$	−5.96378			−0.251121
$565$		0			0
$566$	12.7260	−	22.0421i	0.534914	−	0.926498i
$567$	−0.401361			−0.0168556
$568$	−8.77262	+	15.1946i	−0.368091	+	0.637552i
$569$	−9.90956	−	17.1639i	−0.415430	−	0.719546i	0.580043	−	0.814586i	$-0.303036\pi$
$569$	−9.90956	−	17.1639i	−0.415430	−	0.719546i	−0.995474	+	0.0950394i	$0.969702\pi$
$570$		0			0
$571$	43.8106			1.83342			0.916708	−	0.399558i	$-0.130836\pi$
$571$	43.8106			1.83342			0.916708	+	0.399558i	$0.130836\pi$
$572$	3.62684	−	22.5331i	0.151646	−	0.942158i
$573$	−6.20165			−0.259078
$574$	−0.899588	−	1.55813i	−0.0375481	−	0.0650352i
$575$		0			0
$576$	−2.17859	+	3.77343i	−0.0907746	+	0.157226i
$577$	11.7411			0.488787			0.244393	−	0.969676i	$-0.421411\pi$
$577$	11.7411			0.488787			0.244393	+	0.969676i	$0.421411\pi$
$578$	13.9606	−	24.1805i	0.580684	−	1.00577i
$579$	−4.56896	+	7.91367i	−0.189880	+	0.328881i
$580$		0			0
$581$	−2.11392	+	3.66141i	−0.0877000	+	0.151901i
$582$	−3.96968	−	6.87568i	−0.164548	−	0.285006i
$583$	26.6200	+	46.1071i	1.10249	+	1.90956i
$584$	−2.80752			−0.116176
$585$		0			0
$586$	−6.01374			−0.248425
$587$	12.8957	+	22.3360i	0.532263	+	0.921907i	0.999290	+	0.0376643i	$0.0119918\pi$
$587$	12.8957	+	22.3360i	0.532263	+	0.921907i	−0.467027	+	0.884243i	$0.654675\pi$
$588$	4.41101	+	7.64010i	0.181907	+	0.315072i
$589$	7.10297	−	12.3027i	0.292673	−	0.506924i
$590$		0			0
$591$	10.8050	−	18.7148i	0.444457	−	0.769823i
$592$	1.07438	−	1.86089i	0.0441569	−	0.0764819i
$593$	−10.5017			−0.431252			−0.215626	−	0.976476i	$-0.569179\pi$
$593$	−10.5017			−0.431252			−0.215626	+	0.976476i	$0.569179\pi$
$594$	2.06742	−	3.58088i	0.0848273	−	0.146925i
$595$		0			0
$596$	−2.03669	−	3.52766i	−0.0834262	−	0.144498i
$597$	−2.54446			−0.104138
$598$	−2.34450	−	1.90829i	−0.0958736	−	0.0780358i
$599$	37.8214			1.54534			0.772669	−	0.634809i	$-0.218921\pi$
$599$	37.8214			1.54534			0.772669	+	0.634809i	$0.218921\pi$
$600$		0			0
$601$	14.8477	+	25.7170i	0.605652	+	1.04902i	0.991948	+	0.126645i	$0.0404208\pi$
$601$	14.8477	+	25.7170i	0.605652	+	1.04902i	−0.386297	+	0.922375i	$0.626246\pi$
$602$	0.340563	−	0.589873i	0.0138803	−	0.0240414i
$603$	−6.15330			−0.250582
$604$	−11.9889	+	20.7654i	−0.487823	+	0.844933i
$605$		0			0
$606$	−4.84861			−0.196961
$607$	8.09298	−	14.0175i	0.328484	−	0.568951i	−0.653727	−	0.756730i	$-0.726796\pi$
$607$	8.09298	−	14.0175i	0.328484	−	0.568951i	0.982211	+	0.187779i	$0.0601289\pi$
$608$	6.48170	+	11.2266i	0.262868	+	0.455300i
$609$	1.58190	+	2.73992i	0.0641017	+	0.111027i
$610$		0			0
$611$	−2.64890	+	16.4573i	−0.107163	+	0.665790i
$612$	9.13389			0.369215
$613$	12.7520	+	22.0871i	0.515048	+	0.892089i	0.999847	+	0.0174640i	$0.00555924\pi$
$613$	12.7520	+	22.0871i	0.515048	+	0.892089i	−0.484799	+	0.874625i	$0.661107\pi$
$614$	−4.17670	−	7.23426i	−0.168558	−	0.291951i
$615$		0			0
$616$	5.45993			0.219987
$617$	−5.87440	+	10.1748i	−0.236494	+	0.409620i	−0.959706	−	0.281006i	$-0.909332\pi$
$617$	−5.87440	+	10.1748i	−0.236494	+	0.409620i	0.723212	+	0.690626i	$0.242665\pi$
$618$	6.48792	−	11.2374i	0.260982	−	0.452034i
$619$	−9.49031			−0.381448			−0.190724	−	0.981644i	$-0.561083\pi$
$619$	−9.49031			−0.381448			−0.190724	+	0.981644i	$0.561083\pi$
$620$		0			0
$621$	0.497500	+	0.861695i	0.0199640	+	0.0345786i
$622$	2.54720	+	4.41188i	0.102133	+	0.176900i
$623$	−0.210522			−0.00843438
$624$	−0.682280	−	0.555338i	−0.0273131	−	0.0222313i
$625$		0			0
$626$	−1.94655	−	3.37152i	−0.0777997	−	0.134753i
$627$	−5.53146	−	9.58076i	−0.220905	−	0.382619i
$628$	−6.95308	+	12.0431i	−0.277458	+	0.480571i
$629$	62.3577			2.48637
$630$		0			0
$631$	−11.7563	+	20.3625i	−0.468010	+	0.810617i	−0.999332	−	0.0365534i	$-0.988362\pi$
$631$	−11.7563	+	20.3625i	−0.468010	+	0.810617i	0.531322	+	0.847170i	$0.321695\pi$
$632$	−28.4861			−1.13311
$633$	−5.54061	+	9.59663i	−0.220220	+	0.381432i
$634$	10.5663	+	18.3014i	0.419641	+	0.726839i
$635$		0			0
$636$	13.9958			0.554968
$637$	23.0423	−	8.77890i	0.912971	−	0.347833i
$638$	−32.5935			−1.29039
$639$	−3.16446	−	5.48101i	−0.125184	−	0.216825i
$640$		0			0
$641$	−9.54940	+	16.5400i	−0.377179	+	0.653292i	−0.990651	−	0.136424i	$-0.956439\pi$
$641$	−9.54940	+	16.5400i	−0.377179	+	0.653292i	0.613472	+	0.789717i	$0.289772\pi$
$642$	12.5538			0.495460
$643$	21.8202	−	37.7938i	0.860506	−	1.49044i	−0.0109350	−	0.999940i	$-0.503481\pi$
$643$	21.8202	−	37.7938i	0.860506	−	1.49044i	0.871441	−	0.490500i	$-0.163186\pi$
$644$	−0.257579	+	0.446139i	−0.0101500	+	0.0175804i
$645$		0			0
$646$	−6.72555	+	11.6490i	−0.264613	+	0.458323i
$647$	1.65503	+	2.86660i	0.0650661	+	0.112698i	0.896723	−	0.442592i	$-0.145941\pi$
$647$	1.65503	+	2.86660i	0.0650661	+	0.112698i	−0.831657	+	0.555289i	$0.812608\pi$
$648$	−1.38611	−	2.40082i	−0.0544517	−	0.0943132i
$649$	14.9395			0.586425
$650$		0			0
$651$	−2.52905			−0.0991215
$652$	1.01514	+	1.75827i	0.0397558	+	0.0688590i
$653$	1.80589	+	3.12790i	0.0706701	+	0.122404i	0.899195	−	0.437548i	$-0.144153\pi$
$653$	1.80589	+	3.12790i	0.0706701	+	0.122404i	−0.828525	+	0.559952i	$0.810820\pi$
$654$	0.715231	−	1.23882i	0.0279677	−	0.0484416i
$655$		0			0
$656$	−0.649000	+	1.12410i	−0.0253392	+	0.0438888i
$657$	0.506365	−	0.877050i	0.0197552	−	0.0342170i
$658$	−1.56355			−0.0609536
$659$	−21.5161	+	37.2670i	−0.838148	+	1.45172i	0.0532932	+	0.998579i	$0.483028\pi$
$659$	−21.5161	+	37.2670i	−0.838148	+	1.45172i	−0.891441	+	0.453136i	$0.850305\pi$
$660$		0			0
$661$	−18.8524	−	32.6533i	−0.733273	−	1.27007i	−0.955477	−	0.295066i	$-0.904658\pi$
$661$	−18.8524	−	32.6533i	−0.733273	−	1.27007i	0.222204	−	0.975000i	$-0.428675\pi$
$662$	−11.5330			−0.448242
$663$	4.05694	−	25.2053i	0.157558	−	0.978892i
$664$	−29.2019			−1.13325
$665$		0			0
$666$	−3.71042	−	6.42663i	−0.143776	−	0.249027i
$667$	3.92162	−	6.79245i	0.151846	−	0.263005i
$668$	19.4373			0.752051
$669$	0.265778	−	0.460340i	0.0102756	−	0.0177978i
$670$		0			0
$671$	34.8489			1.34532
$672$	1.15392	−	1.99865i	0.0445136	−	0.0770998i
$673$	−22.3893	−	38.7794i	−0.863045	−	1.49484i	−0.868975	−	0.494855i	$-0.835221\pi$
$673$	−22.3893	−	38.7794i	−0.863045	−	1.49484i	0.00593030	−	0.999982i	$-0.498112\pi$
$674$	−3.79820	−	6.57868i	−0.146301	−	0.253401i
$675$		0			0
$676$	−12.5184	+	11.1585i	−0.481478	+	0.429172i
$677$	41.0024			1.57585			0.787926	−	0.615770i	$-0.211155\pi$
$677$	41.0024			1.57585			0.787926	+	0.615770i	$0.211155\pi$
$678$	0.947129	+	1.64048i	0.0363743	+	0.0630021i
$679$	1.89084	+	3.27502i	0.0725636	+	0.125684i
$680$		0			0
$681$	21.3874			0.819565
$682$	13.0272	−	22.5638i	0.498838	−	0.864013i
$683$	−10.2395	+	17.7354i	−0.391805	+	0.678627i	−0.992688	−	0.120711i	$-0.961483\pi$
$683$	−10.2395	+	17.7354i	−0.391805	+	0.678627i	0.600882	+	0.799338i	$0.294816\pi$
$684$	−2.90823			−0.111199
$685$		0			0
$686$	2.34015	+	4.05326i	0.0893473	+	0.154754i
$687$	−0.203251	−	0.352041i	−0.00775452	−	0.0134312i
$688$	−0.491392			−0.0187342
$689$	6.21641	−	38.6218i	0.236826	−	1.47137i
$690$		0			0
$691$	−13.8702	−	24.0240i	−0.527649	−	0.913915i	−0.999481	−	0.0322263i	$-0.989740\pi$
$691$	−13.8702	−	24.0240i	−0.527649	−	0.913915i	0.471832	−	0.881689i	$-0.343593\pi$
$692$	2.19692	+	3.80518i	0.0835145	+	0.144651i
$693$	−0.984754	+	1.70564i	−0.0374077	+	0.0647920i
$694$	−9.15352			−0.347463
$695$		0			0
$696$	−10.9263	+	18.9249i	−0.414159	+	0.717345i
$697$	−37.6683			−1.42679
$698$	−8.31247	+	14.3976i	−0.314632	+	0.544958i
$699$	1.33189	+	2.30691i	0.0503768	+	0.0872552i
$700$		0			0
$701$	−6.02633			−0.227611			−0.113806	−	0.993503i	$-0.536304\pi$
$701$	−6.02633			−0.227611			−0.113806	+	0.993503i	$0.536304\pi$
$702$	−2.83907	+	1.08166i	−0.107154	+	0.0408245i
$703$	−19.8547			−0.748835
$704$	10.6905	+	18.5165i	0.402913	+	0.697867i
$705$		0			0
$706$	−7.83503	+	13.5707i	−0.294875	+	0.510739i
$707$	2.30949			0.0868573
$708$	1.96365	−	3.40114i	0.0737985	−	0.127823i
$709$	11.3864	−	19.7218i	0.427625	−	0.740668i	−0.569037	−	0.822312i	$-0.692684\pi$
$709$	11.3864	−	19.7218i	0.427625	−	0.740668i	0.996662	+	0.0816444i	$0.0260172\pi$
$710$		0			0
$711$	5.13775	−	8.89885i	0.192681	−	0.333733i
$712$	−0.727045	−	1.25928i	−0.0272471	−	0.0471934i
$713$	3.13484	+	5.42971i	0.117401	+	0.203344i
$714$	2.39467			0.0896183
$715$		0			0
$716$	0.775316			0.0289749
$717$	−7.91585	−	13.7107i	−0.295623	−	0.512034i
$718$	5.11677	+	8.86250i	0.190956	+	0.330746i
$719$	−13.1830	+	22.8336i	−0.491643	+	0.851551i	−0.999954	−	0.00962269i	$-0.996937\pi$
$719$	−13.1830	+	22.8336i	−0.491643	+	0.851551i	0.508310	+	0.861174i	$0.330270\pi$
$720$		0			0
$721$	−3.09032	+	5.35260i	−0.115090	+	0.199341i
$722$	−5.86356	+	10.1560i	−0.218219	+	0.377967i
$723$	23.3140			0.867058
$724$	−11.0039	+	19.0594i	−0.408959	+	0.708337i
$725$		0			0
$726$	−5.51052	−	9.54451i	−0.204515	−	0.354230i
$727$	1.91130			0.0708862			0.0354431	−	0.999372i	$-0.488716\pi$
$727$	1.91130			0.0708862			0.0354431	+	0.999372i	$0.488716\pi$
$728$	−3.11139	−	2.53250i	−0.115316	−	0.0938607i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−7.13017	−	12.3498i	−0.263719	−	0.456774i
$732$	4.58055	−	7.93375i	0.169302	−	0.293240i
$733$	−18.4077			−0.679904			−0.339952	−	0.940443i	$-0.610411\pi$
$733$	−18.4077			−0.679904			−0.339952	+	0.940443i	$0.610411\pi$
$734$	13.0749	−	22.6464i	0.482604	−	0.835894i
$735$		0			0
$736$	−5.72130			−0.210890
$737$	−15.0973	+	26.1494i	−0.556118	+	0.963224i
$738$	2.24134	+	3.88212i	0.0825050	+	0.142903i
$739$	0.909425	+	1.57517i	0.0334538	+	0.0579436i	0.882268	−	0.470748i	$-0.156016\pi$
$739$	0.909425	+	1.57517i	0.0334538	+	0.0579436i	−0.848814	+	0.528692i	$0.822683\pi$
$740$		0			0
$741$	−1.29173	+	8.02537i	−0.0474529	+	0.294819i
$742$	3.66933			0.134705
$743$	4.39871	+	7.61880i	0.161373	+	0.279507i	0.935361	−	0.353693i	$-0.115074\pi$
$743$	4.39871	+	7.61880i	0.161373	+	0.279507i	−0.773988	+	0.633200i	$0.781741\pi$
$744$	−8.73418	−	15.1280i	−0.320211	−	0.554621i
$745$		0			0
$746$	−8.78974			−0.321815
$747$	5.26687	−	9.12248i	0.192705	−	0.333774i
$748$	22.4103	−	38.8158i	0.819402	−	1.41925i
$749$	−5.97963			−0.218491
$750$		0			0
$751$	−18.0751	−	31.3070i	−0.659571	−	1.14241i	−0.980727	−	0.195384i	$-0.937405\pi$
$751$	−18.0751	−	31.3070i	−0.659571	−	1.14241i	0.321156	−	0.947026i	$-0.395929\pi$
$752$	0.564005	+	0.976885i	0.0205671	+	0.0356233i
$753$	−1.30163			−0.0474339
$754$	18.5737	+	15.1180i	0.676416	+	0.550565i
$755$		0			0
$756$	0.258873	+	0.448381i	0.00941512	+	0.0163075i
$757$	−14.5473	−	25.1967i	−0.528731	−	0.915789i	−0.999439	−	0.0334996i	$-0.989335\pi$
$757$	−14.5473	−	25.1967i	−0.528731	−	0.915789i	0.470708	−	0.882289i	$-0.343999\pi$
$758$	−12.9446	+	22.4207i	−0.470168	+	0.814355i
$759$	4.88254			0.177225
$760$		0			0
$761$	13.2927	−	23.0236i	0.481859	−	0.834603i	−0.517925	−	0.855426i	$-0.673295\pi$
$761$	13.2927	−	23.0236i	0.481859	−	0.834603i	0.999783	+	0.0208228i	$0.00662858\pi$
$762$	14.5467			0.526971
$763$	−0.340679	+	0.590073i	−0.0123334	+	0.0213621i
$764$	3.99999	+	6.92819i	0.144715	+	0.250653i
$765$		0			0
$766$	7.17334			0.259183
$767$	−8.51339	−	6.92943i	−0.307401	−	0.250207i
$768$	15.3110			0.552488
$769$	−12.4145	−	21.5026i	−0.447679	−	0.775403i	0.550556	−	0.834799i	$-0.314416\pi$
$769$	−12.4145	−	21.5026i	−0.447679	−	0.775403i	−0.998235	+	0.0593958i	$0.981083\pi$
$770$		0			0
$771$	−4.93694	+	8.55103i	−0.177800	+	0.307958i
$772$	11.7877			0.424249
$773$	−8.89469	+	15.4061i	−0.319920	+	0.554117i	−0.980471	−	0.196664i	$-0.936989\pi$
$773$	−8.89469	+	15.4061i	−0.319920	+	0.554117i	0.660551	+	0.750781i	$0.270323\pi$
$774$	−0.848521	+	1.46968i	−0.0304994	+	0.0528266i
$775$		0			0
$776$	−13.0601	+	22.6208i	−0.468832	+	0.812040i
$777$	1.76735	+	3.06113i	0.0634032	+	0.109818i
$778$	−9.13545	−	15.8231i	−0.327522	−	0.567285i
$779$	11.9936			0.429715
$780$		0			0
$781$	−31.0565			−1.11129
$782$	−2.96827	−	5.14120i	−0.106145	−	0.183849i
$783$	−3.94133	−	6.82658i	−0.140852	−	0.243962i
$784$	0.834314	−	1.44507i	0.0297969	−	0.0516098i
$785$		0			0
$786$	1.93413	−	3.35001i	0.0689882	−	0.119491i
$787$	−11.3791	+	19.7092i	−0.405622	+	0.702557i	−0.994394	−	0.105742i	$-0.966278\pi$
$787$	−11.3791	+	19.7092i	−0.405622	+	0.702557i	0.588772	+	0.808299i	$0.299612\pi$
$788$	−27.8763			−0.993053
$789$	0.266805	−	0.462121i	0.00949852	−	0.0164519i
$790$		0			0
$791$	−0.451137	−	0.781392i	−0.0160406	−	0.0277831i
$792$	−13.6035			−0.483380
$793$	−19.8589	−	16.1641i	−0.705212	−	0.574003i
$794$	−17.5124			−0.621491
$795$		0			0
$796$	1.64115	+	2.84255i	0.0581689	+	0.100751i
$797$	−11.9646	+	20.7232i	−0.423807	+	0.734055i	−0.996308	−	0.0858488i	$-0.972640\pi$
$797$	−11.9646	+	20.7232i	−0.423807	+	0.734055i	0.572501	+	0.819904i	$0.305973\pi$
$798$	−0.762463			−0.0269909
$799$	−16.3676	+	28.3495i	−0.579043	+	1.00293i
$800$		0			0
$801$	0.524520			0.0185330
$802$	−15.4799	+	26.8119i	−0.546613	+	0.946762i
$803$	−2.48477	−	4.30375i	−0.0876856	−	0.151876i
$804$	3.96880	+	6.87417i	0.139969	+	0.242433i
$805$		0			0
$806$	−17.8895	+	6.81574i	−0.630132	+	0.240074i
$807$	13.6040			0.478883
$808$	7.97591	+	13.8147i	0.280592	+	0.485999i
$809$	−8.39474	−	14.5401i	−0.295143	−	0.511203i	0.679875	−	0.733328i	$-0.262034\pi$
$809$	−8.39474	−	14.5401i	−0.295143	−	0.511203i	−0.975018	+	0.222125i	$0.928701\pi$
$810$		0			0
$811$	14.0218			0.492373			0.246186	−	0.969222i	$-0.420822\pi$
$811$	14.0218			0.492373			0.246186	+	0.969222i	$0.420822\pi$
$812$	2.04061	−	3.53444i	0.0716113	−	0.124034i
$813$	−11.9163	+	20.6396i	−0.417922	+	0.723862i
$814$	−36.4146			−1.27633
$815$		0			0
$816$	−0.863806	−	1.49616i	−0.0302393	−	0.0523760i
$817$	2.27025	+	3.93218i	0.0794259	+	0.137570i
$818$	2.70574			0.0946040
$819$	1.35231	−	0.515215i	0.0472534	−	0.0180031i
$820$		0			0
$821$	−19.4895	−	33.7568i	−0.680189	−	1.17812i	−0.974923	−	0.222542i	$-0.928564\pi$
$821$	−19.4895	−	33.7568i	−0.680189	−	1.17812i	0.294734	−	0.955579i	$-0.404769\pi$
$822$	2.08571	+	3.61255i	0.0727474	+	0.126002i
$823$	5.54278	−	9.60038i	0.193209	−	0.334648i	−0.753103	−	0.657903i	$-0.771444\pi$
$823$	5.54278	−	9.60038i	0.193209	−	0.334648i	0.946312	+	0.323255i	$0.104777\pi$
$824$	−42.6902			−1.48718
$825$		0			0
$826$	0.514819	−	0.891692i	0.0179128	−	0.0310259i
$827$	41.0529			1.42755			0.713775	−	0.700375i	$-0.246984\pi$
$827$	41.0529			1.42755			0.713775	+	0.700375i	$0.246984\pi$
$828$	0.641763	−	1.11157i	0.0223028	−	0.0386296i
$829$	−10.4901	−	18.1694i	−0.364337	−	0.631051i	0.624332	−	0.781159i	$-0.285371\pi$
$829$	−10.4901	−	18.1694i	−0.364337	−	0.631051i	−0.988670	+	0.150108i	$0.952038\pi$
$830$		0			0
$831$	−19.2128			−0.666484
$832$	2.49649	−	15.5104i	0.0865503	−	0.537727i
$833$	48.4240			1.67779
$834$	5.58843	+	9.67945i	0.193512	+	0.335172i
$835$		0			0
$836$	−7.13545	+	12.3590i	−0.246785	+	0.427443i
$837$	6.30120			0.217801
$838$	−6.42594	+	11.1300i	−0.221980	+	0.384481i
$839$	5.27731	−	9.14057i	0.182193	−	0.315568i	−0.760434	−	0.649415i	$-0.775014\pi$
$839$	5.27731	−	9.14057i	0.182193	−	0.315568i	0.942627	+	0.333848i	$0.108347\pi$
$840$		0			0
$841$	−16.5682	+	28.6969i	−0.571316	+	0.989548i
$842$	0.0516801	+	0.0895126i	0.00178101	+	0.00308481i
$843$	3.15896	+	5.47148i	0.108800	+	0.188448i
$844$	14.2945			0.492038
$845$		0			0
$846$	3.89562			0.133934
$847$	2.62477	+	4.54624i	0.0901882	+	0.156211i
$848$	−1.32360	−	2.29255i	−0.0454527	−	0.0787264i
$849$	15.1027	−	26.1587i	0.518325	−	0.897765i
$850$		0			0
$851$	4.38137	−	7.58875i	0.150191	−	0.260139i
$852$	−4.08208	+	7.07037i	−0.139850	+	0.242227i
$853$	32.3455			1.10749			0.553744	−	0.832687i	$-0.313199\pi$
$853$	32.3455			1.10749			0.553744	+	0.832687i	$0.313199\pi$
$854$	1.20090	−	2.08002i	0.0410940	−	0.0711770i
$855$		0			0
$856$	−20.6509	−	35.7684i	−0.705832	−	1.22254i
$857$	23.8618			0.815103			0.407551	−	0.913182i	$-0.366383\pi$
$857$	23.8618			0.815103			0.407551	+	0.913182i	$0.366383\pi$
$858$	−2.36910	+	14.7189i	−0.0808798	+	0.502496i
$859$	20.6605			0.704926			0.352463	−	0.935826i	$-0.385344\pi$
$859$	20.6605			0.704926			0.352463	+	0.935826i	$0.385344\pi$
$860$		0			0
$861$	−1.06760	−	1.84913i	−0.0363836	−	0.0630183i
$862$	0.681806	−	1.18092i	0.0232224	−	0.0402224i
$863$	−0.461666			−0.0157153			−0.00785765	−	0.999969i	$-0.502501\pi$
$863$	−0.461666			−0.0157153			−0.00785765	+	0.999969i	$0.502501\pi$
$864$	−2.87503	+	4.97969i	−0.0978104	+	0.169413i
$865$		0			0
$866$	13.1143			0.445643
$867$	16.5679	−	28.6964i	0.562675	−	0.974582i
$868$	1.63121	+	2.82534i	0.0553669	+	0.0958982i
$869$	−25.2113	−	43.6673i	−0.855235	−	1.48131i
$870$		0			0
$871$	20.7323	−	7.89880i	0.702488	−	0.267641i
$872$	−4.70619			−0.159372
$873$	−4.71106	−	8.15979i	−0.159445	−	0.276167i
$874$	0.945098	+	1.63696i	0.0319684	+	0.0553709i
$875$		0			0
$876$	−1.30640			−0.0441391
$877$	10.1974	−	17.6624i	0.344342	−	0.596417i	−0.640892	−	0.767631i	$-0.721435\pi$
$877$	10.1974	−	17.6624i	0.344342	−	0.596417i	0.985234	+	0.171214i	$0.0547688\pi$
$878$	−3.29633	+	5.70941i	−0.111246	+	0.192683i
$879$	−7.13688			−0.240721
$880$		0			0
$881$	12.6173	+	21.8538i	0.425087	+	0.736272i	0.996429	−	0.0844405i	$-0.0269103\pi$
$881$	12.6173	+	21.8538i	0.425087	+	0.736272i	−0.571342	+	0.820712i	$0.693577\pi$
$882$	−2.88133	−	4.99061i	−0.0970195	−	0.168043i
$883$	−8.44125			−0.284071			−0.142035	−	0.989862i	$-0.545365\pi$
$883$	−8.44125			−0.284071			−0.142035	+	0.989862i	$0.545365\pi$
$884$	−30.7748	+	11.7249i	−1.03507	+	0.394351i
$885$		0			0
$886$	10.4543	+	18.1075i	0.351221	+	0.608332i
$887$	−18.6894	−	32.3709i	−0.627527	−	1.08691i	−0.988046	−	0.154157i	$-0.950734\pi$
$887$	−18.6894	−	32.3709i	−0.627527	−	1.08691i	0.360519	−	0.932752i	$-0.382600\pi$
$888$	−12.2072	+	21.1435i	−0.409646	+	0.709528i
$889$	−6.92888			−0.232387
$890$		0			0
$891$	2.45354	−	4.24965i	0.0821965	−	0.142369i
$892$	−0.685693			−0.0229587
$893$	5.21144	−	9.02647i	0.174394	−	0.302059i
$894$	1.33039	+	2.30431i	0.0444951	+	0.0770677i
$895$		0			0
$896$	−3.14210			−0.104970
$897$	−2.78236	−	2.26469i	−0.0929003	−	0.0756156i
$898$	28.2690			0.943348
$899$	−24.8351	−	43.0156i	−0.828297	−	1.43465i
$900$		0			0
$901$	38.4113	−	66.5303i	1.27967	−	2.21645i
$902$	21.9969			0.732416
$903$	0.404167	−	0.700038i	0.0134498	−	0.0232958i
$904$	3.11603	−	5.39713i	0.103638	−	0.179506i
$905$		0			0
$906$	7.83132	−	13.5642i	0.260178	−	0.450642i
$907$	24.5616	+	42.5419i	0.815553	+	1.41258i	0.908930	+	0.416948i	$0.136900\pi$
$907$	24.5616	+	42.5419i	0.815553	+	1.41258i	−0.0933771	+	0.995631i	$0.529766\pi$
$908$	−13.7946	−	23.8929i	−0.457789	−	0.792915i
$909$	−5.75415			−0.190853
$910$		0			0
$911$	46.1927			1.53043			0.765217	−	0.643773i	$-0.222632\pi$
$911$	46.1927			1.53043			0.765217	+	0.643773i	$0.222632\pi$
$912$	0.275036	+	0.476376i	0.00910735	+	0.0157744i
$913$	−25.8449	−	44.7647i	−0.855341	−	1.48149i
$914$	7.77604	−	13.4685i	0.257209	−	0.445499i
$915$		0			0
$916$	−0.262189	+	0.454125i	−0.00866297	+	0.0150047i
$917$	−0.921265	+	1.59568i	−0.0304229	+	0.0526939i
$918$	−5.96637			−0.196920
$919$	14.7292	−	25.5118i	0.485872	−	0.841556i	−0.513996	−	0.857793i	$-0.671835\pi$
$919$	14.7292	−	25.5118i	0.485872	−	0.841556i	0.999868	+	0.0162371i	$0.00516867\pi$
$920$		0			0
$921$	−4.95675	−	8.58534i	−0.163330	−	0.282897i
$922$	−5.85057			−0.192678
$923$	17.6978	+	14.4051i	0.582531	+	0.474148i
$924$	2.54062			0.0835802
$925$		0			0
$926$	−17.3775	−	30.0987i	−0.571060	−	0.989105i
$927$	7.69961	−	13.3361i	0.252888	−	0.438015i
$928$	45.3257			1.48789
$929$	−11.3931	+	19.7334i	−0.373795	+	0.647432i	−0.990146	−	0.140040i	$-0.955277\pi$
$929$	−11.3931	+	19.7334i	−0.373795	+	0.647432i	0.616351	+	0.787472i	$0.288610\pi$
$930$		0			0
$931$	−15.4182			−0.505311
$932$	1.71811	−	2.97585i	0.0562786	−	0.0974773i
$933$	3.02292	+	5.23585i	0.0989659	+	0.171414i
$934$	−12.5149	−	21.6765i	−0.409501	−	0.709277i
$935$		0			0
$936$	7.75210	+	6.30978i	0.253385	+	0.206242i
$937$	−33.3968			−1.09103			−0.545513	−	0.838102i	$-0.683665\pi$
$937$	−33.3968			−1.09103			−0.545513	+	0.838102i	$0.683665\pi$
$938$	1.04052	+	1.80223i	0.0339741	+	0.0588449i
$939$	−2.31009	−	4.00119i	−0.0753869	−	0.130574i
$940$		0			0
$941$	−4.59203			−0.149696			−0.0748480	−	0.997195i	$-0.523847\pi$
$941$	−4.59203			−0.149696			−0.0748480	+	0.997195i	$0.523847\pi$
$942$	4.54184	−	7.86670i	0.147981	−	0.256311i
$943$	−2.64664	+	4.58412i	−0.0861865	+	0.149279i
$944$	−0.742822			−0.0241768
$945$		0			0
$946$	4.16375	+	7.21183i	0.135375	+	0.234477i
$947$	−4.82558	−	8.35815i	−0.156810	−	0.271603i	0.776906	−	0.629616i	$-0.216788\pi$
$947$	−4.82558	−	8.35815i	−0.156810	−	0.271603i	−0.933717	+	0.358013i	$0.883454\pi$
$948$	−13.2552			−0.430507
$949$	−0.580254	+	3.60505i	−0.0188359	+	0.117025i
$950$		0			0
$951$	12.5397	+	21.7193i	0.406627	+	0.704298i
$952$	−3.93920	−	6.82290i	−0.127670	−	0.221131i
$953$	16.9506	−	29.3593i	0.549083	−	0.951040i	−0.449254	−	0.893404i	$-0.648310\pi$
$953$	16.9506	−	29.3593i	0.549083	−	0.951040i	0.998338	−	0.0576363i	$-0.0183564\pi$
$954$	−9.14222			−0.295990
$955$		0			0
$956$	−10.2113	+	17.6864i	−0.330256	+	0.572020i
$957$	−38.6808			−1.25037
$958$	−8.31659	+	14.4048i	−0.268697	+	0.465397i
$959$	−0.993464	−	1.72073i	−0.0320806	−	0.0555653i
$960$		0			0
$961$	8.70507			0.280809
$962$	20.7512	+	16.8903i	0.669045	+	0.544566i
$963$	14.8984			0.480094
$964$	−15.0373	−	26.0453i	−0.484318	−	0.838863i
$965$		0			0
$966$	0.168254	−	0.291424i	0.00541348	−	0.00937642i
$967$	20.9057			0.672283			0.336141	−	0.941812i	$-0.390878\pi$
$967$	20.9057			0.672283			0.336141	+	0.941812i	$0.390878\pi$
$968$	−18.1295	+	31.4012i	−0.582704	+	1.00927i
$969$	−7.98162	+	13.8246i	−0.256407	+	0.444109i
$970$		0			0
$971$	−24.1043	+	41.7499i	−0.773545	+	1.33982i	0.162064	+	0.986780i	$0.448185\pi$
$971$	−24.1043	+	41.7499i	−0.773545	+	1.33982i	−0.935609	+	0.353038i	$0.885149\pi$
$972$	−0.644988	−	1.11715i	−0.0206880	−	0.0358327i
$973$	−2.66188	−	4.61051i	−0.0853360	−	0.147806i
$974$	20.4787			0.656180
$975$		0			0
$976$	−1.73276			−0.0554643
$977$	−16.4614	−	28.5119i	−0.526646	−	0.912177i	−0.999518	−	0.0310460i	$-0.990116\pi$
$977$	−16.4614	−	28.5119i	−0.526646	−	0.912177i	0.472872	−	0.881131i	$-0.343217\pi$
$978$	−0.663100	−	1.14852i	−0.0212036	−	0.0367257i
$979$	1.28693	−	2.22902i	0.0411304	−	0.0712399i
$980$		0			0
$981$	0.848809	−	1.47018i	0.0271004	−	0.0469392i
$982$	2.91164	−	5.04311i	0.0929143	−	0.160932i
$983$	−11.0460			−0.352312			−0.176156	−	0.984362i	$-0.556366\pi$
$983$	−11.0460			−0.352312			−0.176156	+	0.984362i	$0.556366\pi$
$984$	7.37397	−	12.7721i	0.235074	−	0.407159i
$985$		0			0
$986$	23.5154	+	40.7299i	0.748884	+	1.29711i
$987$	−1.85556			−0.0590632
$988$	9.79870	−	3.73321i	0.311738	−	0.118769i
$989$	−2.00391			−0.0637207
$990$		0			0
$991$	4.83587	+	8.37598i	0.153617	+	0.266072i	0.932554	−	0.361029i	$-0.117575\pi$
$991$	4.83587	+	8.37598i	0.153617	+	0.266072i	−0.778938	+	0.627101i	$0.784241\pi$
$992$	−18.1161	+	31.3780i	−0.575187	+	0.996253i
$993$	−13.6869			−0.434341
$994$	−1.07022	+	1.85367i	−0.0339452	+	0.0587948i
$995$		0			0
$996$	−13.5883			−0.430561
$997$	−25.2149	+	43.6735i	−0.798565	+	1.38315i	0.121986	+	0.992532i	$0.461074\pi$
$997$	−25.2149	+	43.6735i	−0.798565	+	1.38315i	−0.920551	+	0.390623i	$0.872260\pi$
$998$	0.931258	+	1.61299i	0.0294785	+	0.0510582i
$999$	−4.40338	−	7.62688i	−0.139317	−	0.241304i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.i.q.601.4		12
5.2	odd	4		195.2.ba.a.94.5	✓	24
5.3	odd	4		195.2.ba.a.94.8	yes	24
5.4	even	2		975.2.i.o.601.3		12
13.9	even	3	inner	975.2.i.q.451.4		12
15.2	even	4		585.2.bs.b.289.8		24
15.8	even	4		585.2.bs.b.289.5		24
65.9	even	6		975.2.i.o.451.3		12
65.22	odd	12		195.2.ba.a.139.8	yes	24
65.48	odd	12		195.2.ba.a.139.5	yes	24
195.113	even	12		585.2.bs.b.334.8		24
195.152	even	12		585.2.bs.b.334.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.ba.a.94.5	✓	24	5.2	odd	4
195.2.ba.a.94.8	yes	24	5.3	odd	4
195.2.ba.a.139.5	yes	24	65.48	odd	12
195.2.ba.a.139.8	yes	24	65.22	odd	12
585.2.bs.b.289.5		24	15.8	even	4
585.2.bs.b.289.8		24	15.2	even	4
585.2.bs.b.334.5		24	195.152	even	12
585.2.bs.b.334.8		24	195.113	even	12
975.2.i.o.451.3		12	65.9	even	6
975.2.i.o.601.3		12	5.4	even	2
975.2.i.q.451.4		12	13.9	even	3	inner
975.2.i.q.601.4		12	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(0.421315 + 0.729738i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.644988 - 1.11715i) q^{4} +(-0.421315 + 0.729738i) q^{6} +(0.200681 - 0.347589i) q^{7} +2.77223 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.45354 + 4.24965i) q^{11} +1.28998 q^{12} +(0.572960 - 3.55974i) q^{13} +0.338199 q^{14} +(-0.121995 - 0.211302i) q^{16} +(3.54033 - 6.13203i) q^{17} -0.842629 q^{18} +(-1.12724 + 1.95244i) q^{19} +0.401361 q^{21} +(-2.06742 + 3.58088i) q^{22} +(-0.497500 - 0.861695i) q^{23} +(1.38611 + 2.40082i) q^{24} +(2.83907 - 1.08166i) q^{26} -1.00000 q^{27} +(-0.258873 - 0.448381i) q^{28} +(3.94133 + 6.82658i) q^{29} -6.30120 q^{31} +(2.87503 - 4.97969i) q^{32} +(-2.45354 + 4.24965i) q^{33} +5.96637 q^{34} +(0.644988 + 1.11715i) q^{36} +(4.40338 + 7.62688i) q^{37} -1.89969 q^{38} +(3.36930 - 1.28367i) q^{39} +(-2.65994 - 4.60715i) q^{41} +(0.169099 + 0.292889i) q^{42} +(1.00699 - 1.74416i) q^{43} +6.33001 q^{44} +(0.419208 - 0.726090i) q^{46} -4.62317 q^{47} +(0.121995 - 0.211302i) q^{48} +(3.41945 + 5.92267i) q^{49} +7.08066 q^{51} +(-3.60721 - 2.93607i) q^{52} +10.8496 q^{53} +(-0.421315 - 0.729738i) q^{54} +(0.556333 - 0.963596i) q^{56} -2.25448 q^{57} +(-3.32108 + 5.75228i) q^{58} +(1.52224 - 2.63659i) q^{59} +(3.55088 - 6.15031i) q^{61} +(-2.65479 - 4.59822i) q^{62} +(0.200681 + 0.347589i) q^{63} +4.35718 q^{64} -4.13484 q^{66} +(3.07665 + 5.32891i) q^{67} +(-4.56694 - 7.91018i) q^{68} +(0.497500 - 0.861695i) q^{69} +(-3.16446 + 5.48101i) q^{71} +(-1.38611 + 2.40082i) q^{72} -1.01273 q^{73} +(-3.71042 + 6.42663i) q^{74} +(1.45411 + 2.51860i) q^{76} +1.96951 q^{77} +(2.35628 + 1.91788i) q^{78} -10.2755 q^{79} +(-0.500000 - 0.866025i) q^{81} +(2.24134 - 3.88212i) q^{82} -10.5337 q^{83} +(0.258873 - 0.448381i) q^{84} +1.69704 q^{86} +(-3.94133 + 6.82658i) q^{87} +(6.80177 + 11.7810i) q^{88} +(-0.262260 - 0.454247i) q^{89} +(-1.12234 - 0.913524i) q^{91} -1.28353 q^{92} +(-3.15060 - 5.45700i) q^{93} +(-1.94781 - 3.37371i) q^{94} +5.75005 q^{96} +(-4.71106 + 8.15979i) q^{97} +(-2.88133 + 4.99061i) q^{98} -4.90707 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} - 4 q^{4} - 2 q^{7} - 6 q^{9} + 2 q^{11} - 8 q^{12} - 8 q^{13} - 12 q^{14} + 8 q^{16} - 6 q^{17} + 8 q^{19} - 4 q^{21} - 14 q^{22} - 4 q^{23} - 24 q^{26} - 12 q^{27} - 8 q^{28} + 6 q^{29}+ \cdots - 4 q^{99}+O(q^{100}) \) 12 * q + 6 * q^3 - 4 * q^4 - 2 * q^7 - 6 * q^9 + 2 * q^11 - 8 * q^12 - 8 * q^13 - 12 * q^14 + 8 * q^16 - 6 * q^17 + 8 * q^19 - 4 * q^21 - 14 * q^22 - 4 * q^23 - 24 * q^26 - 12 * q^27 - 8 * q^28 + 6 * q^29 + 4 * q^31 + 10 * q^32 - 2 * q^33 + 16 * q^34 - 4 * q^36 + 14 * q^37 - 4 * q^39 - 20 * q^41 - 6 * q^42 - 20 * q^43 - 20 * q^44 - 12 * q^46 - 12 * q^47 - 8 * q^48 + 8 * q^49 - 12 * q^51 + 8 * q^52 + 40 * q^53 - 12 * q^56 + 16 * q^57 + 12 * q^58 - 6 * q^59 + 10 * q^61 + 2 * q^62 - 2 * q^63 - 24 * q^64 - 28 * q^66 + 6 * q^67 - 12 * q^68 + 4 * q^69 + 2 * q^71 + 6 * q^74 + 4 * q^76 + 8 * q^77 - 12 * q^78 - 68 * q^79 - 6 * q^81 + 4 * q^82 + 12 * q^83 + 8 * q^84 + 24 * q^86 - 6 * q^87 + 32 * q^89 + 30 * q^91 + 44 * q^92 + 2 * q^93 + 24 * q^94 + 20 * q^96 + 20 * q^97 + 4 * q^98 - 4 * q^99

Introduction

L-functions

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