LMFDB - Embedded newform 175.2.x.a.17.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,2,Mod(3,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([21, 10]))

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

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

chi := DirichletCharacter("175.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			17.4
Character	$\chi$	$=$	175.17
Dual form			175.2.x.a.103.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.80792 + 0.0947490i) q^{2} +(1.32895 - 1.64111i) q^{3} +(1.27055 - 0.133540i) q^{4} +(2.03223 + 0.932769i) q^{5} +(-2.24713 + 3.09291i) q^{6} +(0.405696 + 2.61446i) q^{7} +(1.29182 - 0.204604i) q^{8} +(-0.303414 - 1.42745i) q^{9} +O(q^{10})$	\(q+(-1.80792 + 0.0947490i) q^{2} +(1.32895 - 1.64111i) q^{3} +(1.27055 - 0.133540i) q^{4} +(2.03223 + 0.932769i) q^{5} +(-2.24713 + 3.09291i) q^{6} +(0.405696 + 2.61446i) q^{7} +(1.29182 - 0.204604i) q^{8} +(-0.303414 - 1.42745i) q^{9} +(-3.76248 - 1.49382i) q^{10} +(-2.23088 - 0.474189i) q^{11} +(1.46934 - 2.26258i) q^{12} +(4.21711 - 2.14873i) q^{13} +(-0.981183 - 4.68830i) q^{14} +(4.23149 - 2.09551i) q^{15} +(-4.81539 + 1.02354i) q^{16} +(1.33205 - 3.47011i) q^{17} +(0.683798 + 2.55197i) q^{18} +(-0.216377 + 2.05869i) q^{19} +(2.70661 + 0.913747i) q^{20} +(4.82977 + 2.80869i) q^{21} +(4.07818 + 0.645921i) q^{22} +(-0.0829354 - 1.58250i) q^{23} +(1.38098 - 2.39193i) q^{24} +(3.25988 + 3.79119i) q^{25} +(-7.42061 + 4.28429i) q^{26} +(2.89883 + 1.47703i) q^{27} +(0.864593 + 3.26763i) q^{28} +(-6.19928 - 8.53257i) q^{29} +(-7.45165 + 4.18944i) q^{30} +(1.38755 + 3.11648i) q^{31} +(6.08214 - 1.62970i) q^{32} +(-3.74292 + 3.03095i) q^{33} +(-2.07945 + 6.39988i) q^{34} +(-1.61422 + 5.69160i) q^{35} +(-0.576126 - 1.77313i) q^{36} +(-1.80623 - 1.17298i) q^{37} +(0.196133 - 3.74244i) q^{38} +(2.07801 - 9.77629i) q^{39} +(2.81612 + 0.789168i) q^{40} +(-4.99913 - 1.62432i) q^{41} +(-8.99795 - 4.62026i) q^{42} +(-6.27631 + 6.27631i) q^{43} +(-2.89777 - 0.304568i) q^{44} +(0.714876 - 3.18392i) q^{45} +(0.299881 + 2.85318i) q^{46} +(-6.00311 + 2.30438i) q^{47} +(-4.71964 + 9.26282i) q^{48} +(-6.67082 + 2.12135i) q^{49} +(-6.25282 - 6.54530i) q^{50} +(-3.92461 - 6.79762i) q^{51} +(5.07112 - 3.29322i) q^{52} +(-3.15205 - 2.55248i) q^{53} +(-5.38080 - 2.39569i) q^{54} +(-4.09135 - 3.04456i) q^{55} +(1.05902 + 3.29441i) q^{56} +(3.09098 + 3.09098i) q^{57} +(12.0162 + 14.8388i) q^{58} +(8.50113 + 9.44146i) q^{59} +(5.09650 - 3.22753i) q^{60} +(-0.722763 - 0.650779i) q^{61} +(-2.80386 - 5.50288i) q^{62} +(3.60892 - 1.37238i) q^{63} +(-1.47757 + 0.480090i) q^{64} +(10.5744 - 0.433105i) q^{65} +(6.47971 - 5.83436i) q^{66} +(9.57888 + 3.67699i) q^{67} +(1.22904 - 4.58683i) q^{68} +(-2.70728 - 1.96695i) q^{69} +(2.37911 - 10.4429i) q^{70} +(-1.86024 + 1.35154i) q^{71} +(-0.684019 - 1.78193i) q^{72} +(-4.27467 - 6.58242i) q^{73} +(3.37666 + 1.94951i) q^{74} +(10.5540 - 0.311540i) q^{75} +2.64456i q^{76} +(0.334689 - 6.02493i) q^{77} +(-2.83059 + 17.8716i) q^{78} +(-4.69941 + 10.5550i) q^{79} +(-10.7407 - 2.41158i) q^{80} +(10.2759 - 4.57511i) q^{81} +(9.19193 + 2.46297i) q^{82} +(-0.909079 - 5.73970i) q^{83} +(6.51154 + 2.92361i) q^{84} +(5.94383 - 5.80955i) q^{85} +(10.7524 - 11.9417i) q^{86} +(-22.2414 - 1.16562i) q^{87} +(-2.97892 - 0.156119i) q^{88} +(-4.47423 + 4.96914i) q^{89} +(-0.990766 + 5.82400i) q^{90} +(7.32863 + 10.1538i) q^{91} +(-0.316702 - 1.99958i) q^{92} +(6.95847 + 1.86452i) q^{93} +(10.6348 - 4.73492i) q^{94} +(-2.36000 + 3.98188i) q^{95} +(5.40831 - 12.1473i) q^{96} +(0.453302 - 2.86204i) q^{97} +(11.8593 - 4.46729i) q^{98} +3.32835i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22} - 40 q^{23} + 2 q^{25} - 48 q^{26} + 22 q^{28} - 58 q^{30} - 18 q^{31} + 8 q^{32} - 30 q^{33} - 2 q^{35} + 40 q^{36} - 10 q^{37} + 72 q^{38} + 30 q^{39} - 48 q^{40} + 6 q^{42} - 108 q^{43} - 10 q^{44} + 186 q^{45} - 6 q^{46} - 54 q^{47} - 248 q^{50} - 16 q^{51} + 216 q^{52} + 50 q^{53} - 30 q^{54} + 4 q^{56} - 216 q^{57} - 4 q^{58} + 90 q^{59} + 96 q^{60} - 18 q^{61} - 66 q^{63} - 100 q^{64} + 14 q^{65} - 90 q^{66} + 4 q^{67} + 342 q^{68} - 60 q^{70} - 24 q^{71} + 58 q^{72} - 6 q^{73} + 216 q^{75} - 80 q^{77} - 132 q^{78} - 10 q^{79} - 6 q^{80} - 10 q^{81} + 216 q^{82} + 20 q^{84} - 48 q^{85} - 6 q^{86} - 48 q^{87} - 122 q^{88} + 120 q^{89} - 12 q^{91} - 4 q^{92} + 106 q^{93} - 30 q^{94} - 98 q^{95} - 90 q^{96} + 222 q^{98}+O(q^{100}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{20}\right)$

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 $

$2$	−1.80792	+	0.0947490i	−1.27839	+	0.0669977i	−0.679407	−	0.733762i	$-0.737763\pi$
$2$	−1.80792	+	0.0947490i	−1.27839	+	0.0669977i	−0.598986	+	0.800760i	$0.704429\pi$
$3$	1.32895	−	1.64111i	0.767267	−	0.947496i	−0.232417	−	0.972616i	$-0.574664\pi$
$3$	1.32895	−	1.64111i	0.767267	−	0.947496i	0.999684	+	0.0251203i	$0.00799687\pi$
$4$	1.27055	−	0.133540i	0.635276	−	0.0667702i
$5$	2.03223	+	0.932769i	0.908839	+	0.417147i
$5$	2.03223	+	0.932769i	0.908839	+	0.417147i
$6$	−2.24713	+	3.09291i	−0.917388	+	1.26268i
$7$	0.405696	+	2.61446i	0.153339	+	0.988174i
$7$	0.405696	+	2.61446i	0.153339	+	0.988174i
$8$	1.29182	−	0.204604i	0.456728	−	0.0723385i
$9$	−0.303414	−	1.42745i	−0.101138	−	0.475817i
$10$	−3.76248	−	1.49382i	−1.18980	−	0.472387i
$11$	−2.23088	−	0.474189i	−0.672636	−	0.142973i	−0.141083	−	0.989998i	$-0.545058\pi$
$11$	−2.23088	−	0.474189i	−0.672636	−	0.142973i	−0.531554	+	0.847025i	$0.678392\pi$
$12$	1.46934	−	2.26258i	0.424162	−	0.653152i
$13$	4.21711	−	2.14873i	1.16962	−	0.595949i	0.242290	−	0.970204i	$-0.422101\pi$
$13$	4.21711	−	2.14873i	1.16962	−	0.595949i	0.927326	+	0.374254i	$0.122101\pi$
$14$	−0.981183	−	4.68830i	−0.262232	−	1.25300i
$15$	4.23149	−	2.09551i	1.09257	−	0.541058i
$16$	−4.81539	+	1.02354i	−1.20385	+	0.255886i
$17$	1.33205	−	3.47011i	0.323069	−	0.841625i	−0.671826	−	0.740709i	$-0.734490\pi$
$17$	1.33205	−	3.47011i	0.323069	−	0.841625i	0.994895	−	0.100915i	$-0.0321771\pi$
$18$	0.683798	+	2.55197i	0.161173	+	0.601505i
$19$	−0.216377	+	2.05869i	−0.0496402	+	0.472295i	0.941259	+	0.337686i	$0.109644\pi$
$19$	−0.216377	+	2.05869i	−0.0496402	+	0.472295i	−0.990899	+	0.134608i	$0.957022\pi$
$20$	2.70661	+	0.913747i	0.605216	+	0.204320i
$21$	4.82977	+	2.80869i	1.05394	+	0.612905i
$22$	4.07818	+	0.645921i	0.869472	+	0.137711i
$23$	−0.0829354	−	1.58250i	−0.0172932	−	0.329975i	−0.993553	−	0.113371i	$-0.963835\pi$
$23$	−0.0829354	−	1.58250i	−0.0172932	−	0.329975i	0.976260	−	0.216604i	$-0.0694981\pi$
$24$	1.38098	−	2.39193i	0.281892	−	0.488251i
$25$	3.25988	+	3.79119i	0.651977	+	0.758239i
$26$	−7.42061	+	4.28429i	−1.45530	+	0.840219i
$27$	2.89883	+	1.47703i	0.557880	+	0.284254i
$28$	0.864593	+	3.26763i	0.163393	+	0.617524i
$29$	−6.19928	−	8.53257i	−1.15118	−	1.58446i	−0.739543	−	0.673109i	$-0.764958\pi$
$29$	−6.19928	−	8.53257i	−1.15118	−	1.58446i	−0.411633	−	0.911350i	$-0.635042\pi$
$30$	−7.45165	+	4.18944i	−1.36048	+	0.764884i
$31$	1.38755	+	3.11648i	0.249211	+	0.559737i	0.994225	−	0.107312i	$-0.0342242\pi$
$31$	1.38755	+	3.11648i	0.249211	+	0.559737i	−0.745015	+	0.667048i	$0.767558\pi$
$32$	6.08214	−	1.62970i	1.07518	−	0.288094i
$33$	−3.74292	+	3.03095i	−0.651558	+	0.527621i
$34$	−2.07945	+	6.39988i	−0.356622	+	1.09757i
$35$	−1.61422	+	5.69160i	−0.272854	+	0.962056i
$36$	−0.576126	−	1.77313i	−0.0960209	−	0.295522i
$37$	−1.80623	−	1.17298i	−0.296942	−	0.192837i	0.387565	−	0.921842i	$-0.373316\pi$
$37$	−1.80623	−	1.17298i	−0.296942	−	0.192837i	−0.684508	+	0.729006i	$0.739983\pi$
$38$	0.196133	−	3.74244i	0.0318170	−	0.607104i
$39$	2.07801	−	9.77629i	0.332749	−	1.56546i
$40$	2.81612	+	0.789168i	0.445268	+	0.124778i
$41$	−4.99913	−	1.62432i	−0.780733	−	0.253676i	−0.108580	−	0.994088i	$-0.534630\pi$
$41$	−4.99913	−	1.62432i	−0.780733	−	0.253676i	−0.672153	+	0.740412i	$0.734630\pi$
$42$	−8.99795	−	4.62026i	−1.38841	−	0.712922i
$43$	−6.27631	+	6.27631i	−0.957128	+	0.957128i	−0.999118	−	0.0419898i	$-0.986630\pi$
$43$	−6.27631	+	6.27631i	−0.957128	+	0.957128i	0.0419898	+	0.999118i	$0.486630\pi$
$44$	−2.89777	−	0.304568i	−0.436856	−	0.0459154i
$45$	0.714876	−	3.18392i	0.106567	−	0.474631i
$46$	0.299881	+	2.85318i	0.0442151	+	0.420678i
$47$	−6.00311	+	2.30438i	−0.875644	+	0.336128i	−0.754337	−	0.656487i	$-0.772042\pi$
$47$	−6.00311	+	2.30438i	−0.875644	+	0.336128i	−0.121306	+	0.992615i	$0.538708\pi$
$48$	−4.71964	+	9.26282i	−0.681221	+	1.33697i
$49$	−6.67082	+	2.12135i	−0.952975	+	0.303050i
$50$	−6.25282	−	6.54530i	−0.884282	−	0.925646i
$51$	−3.92461	−	6.79762i	−0.549555	−	0.951858i
$52$	5.07112	−	3.29322i	0.703237	−	0.456688i
$53$	−3.15205	−	2.55248i	−0.432968	−	0.350610i	0.387927	−	0.921690i	$-0.373191\pi$
$53$	−3.15205	−	2.55248i	−0.432968	−	0.350610i	−0.820894	+	0.571080i	$0.806525\pi$
$54$	−5.38080	−	2.39569i	−0.732234	−	0.326011i
$55$	−4.09135	−	3.04456i	−0.551677	−	0.410528i
$56$	1.05902	+	3.29441i	0.141517	+	0.440234i
$57$	3.09098	+	3.09098i	0.409410	+	0.409410i
$58$	12.0162	+	14.8388i	1.57781	+	1.94843i
$59$	8.50113	+	9.44146i	1.10675	+	1.22917i	0.971165	+	0.238408i	$0.0766254\pi$
$59$	8.50113	+	9.44146i	1.10675	+	1.22917i	0.135587	+	0.990765i	$0.456708\pi$
$60$	5.09650	−	3.22753i	0.657955	−	0.416672i
$61$	−0.722763	−	0.650779i	−0.0925403	−	0.0833237i	0.621562	−	0.783365i	$-0.286498\pi$
$61$	−0.722763	−	0.650779i	−0.0925403	−	0.0833237i	−0.714103	+	0.700041i	$0.753165\pi$
$62$	−2.80386	−	5.50288i	−0.356090	−	0.698866i
$63$	3.60892	−	1.37238i	0.454682	−	0.172903i
$64$	−1.47757	+	0.480090i	−0.184696	+	0.0600113i
$65$	10.5744	−	0.433105i	1.31159	−	0.0537200i
$66$	6.47971	−	5.83436i	0.797597	−	0.718160i
$67$	9.57888	+	3.67699i	1.17025	+	0.449216i	0.864370	−	0.502856i	$-0.167717\pi$
$67$	9.57888	+	3.67699i	1.17025	+	0.449216i	0.305876	+	0.952071i	$0.401051\pi$
$68$	1.22904	−	4.58683i	0.149043	−	0.556235i
$69$	−2.70728	−	1.96695i	−0.325918	−	0.236793i
$70$	2.37911	−	10.4429i	0.284358	−	1.24816i
$71$	−1.86024	+	1.35154i	−0.220770	+	0.160399i	−0.692673	−	0.721252i	$-0.743567\pi$
$71$	−1.86024	+	1.35154i	−0.220770	+	0.160399i	0.471903	+	0.881650i	$0.343567\pi$
$72$	−0.684019	−	1.78193i	−0.0806125	−	0.210003i
$73$	−4.27467	−	6.58242i	−0.500312	−	0.770414i	0.494816	−	0.868998i	$-0.335235\pi$
$73$	−4.27467	−	6.58242i	−0.500312	−	0.770414i	−0.995129	+	0.0985840i	$0.968569\pi$
$74$	3.37666	+	1.94951i	0.392528	+	0.226626i
$75$	10.5540	−	0.311540i	1.21867	−	0.0359735i
$76$			2.64456i			0.303352i
$77$	0.334689	−	6.02493i	0.0381414	−	0.686605i
$78$	−2.83059	+	17.8716i	−0.320501	+	2.02356i
$79$	−4.69941	+	10.5550i	−0.528725	+	1.18754i	0.429904	+	0.902875i	$0.358547\pi$
$79$	−4.69941	+	10.5550i	−0.528725	+	1.18754i	−0.958628	+	0.284660i	$0.908119\pi$
$80$	−10.7407	−	2.41158i	−1.20084	−	0.269622i
$81$	10.2759	−	4.57511i	1.14176	−	0.508346i
$82$	9.19193	+	2.46297i	1.01508	+	0.271990i
$83$	−0.909079	−	5.73970i	−0.0997844	−	0.630014i	−0.986001	−	0.166742i	$-0.946675\pi$
$83$	−0.909079	−	5.73970i	−0.0997844	−	0.630014i	0.886216	−	0.463272i	$-0.153325\pi$
$84$	6.51154	+	2.92361i	0.710468	+	0.318992i
$85$	5.94383	−	5.80955i	0.644699	−	0.630134i
$86$	10.7524	−	11.9417i	1.15946	−	1.28771i
$87$	−22.2414	−	1.16562i	−2.38453	−	0.124968i
$88$	−2.97892	−	0.156119i	−0.317554	−	0.0166423i
$89$	−4.47423	+	4.96914i	−0.474268	+	0.526728i	−0.932047	−	0.362338i	$-0.881978\pi$
$89$	−4.47423	+	4.96914i	−0.474268	+	0.526728i	0.457779	+	0.889066i	$0.348645\pi$
$90$	−0.990766	+	5.82400i	−0.104436	+	0.613904i
$91$	7.32863	+	10.1538i	0.768249	+	1.06440i
$92$	−0.316702	−	1.99958i	−0.0330184	−	0.208470i
$93$	6.95847	+	1.86452i	0.721559	+	0.193341i
$94$	10.6348	−	4.73492i	1.09690	−	0.488370i
$95$	−2.36000	+	3.98188i	−0.242131	+	0.408533i
$96$	5.40831	−	12.1473i	0.551983	−	1.23977i
$97$	0.453302	−	2.86204i	0.0460259	−	0.290596i	−0.953930	−	0.300030i	$-0.903003\pi$
$97$	0.453302	−	2.86204i	0.0460259	−	0.290596i	0.999955	+	0.00943453i	$0.00300315\pi$
$98$	11.8593	−	4.46729i	1.19797	−	0.451264i
$99$			3.32835i			0.334512i
$100$	4.64813	+	4.38158i	0.464813	+	0.438158i
$101$	−3.29920	−	1.90480i	−0.328283	−	0.189534i	0.326796	−	0.945095i	$-0.394031\pi$
$101$	−3.29920	−	1.90480i	−0.328283	−	0.189534i	−0.655079	+	0.755561i	$0.727364\pi$
$102$	7.73945	+	11.9177i	0.766319	+	1.18003i
$103$	−6.13972	−	15.9945i	−0.604965	−	1.57599i	−0.803120	−	0.595817i	$-0.796828\pi$
$103$	−6.13972	−	15.9945i	−0.604965	−	1.57599i	0.198155	−	0.980171i	$-0.436505\pi$
$104$	5.00811	−	3.63861i	0.491086	−	0.356795i
$105$	7.19533	+	10.2129i	0.702192	+	0.996681i
$106$	5.94050	+	4.31603i	0.576992	+	0.419210i
$107$	−1.65467	+	6.17530i	−0.159963	+	0.596988i	0.838667	+	0.544645i	$0.183336\pi$
$107$	−1.65467	+	6.17530i	−0.159963	+	0.596988i	−0.998629	+	0.0523433i	$0.983331\pi$
$108$	3.88036	+	1.48953i	0.373387	+	0.143330i
$109$	−6.87193	+	6.18751i	−0.658211	+	0.592656i	−0.929044	−	0.369970i	$-0.879368\pi$
$109$	−6.87193	+	6.18751i	−0.658211	+	0.592656i	0.270832	+	0.962627i	$0.412701\pi$
$110$	7.68530	+	5.11666i	0.732764	+	0.487855i
$111$	−4.32537	+	1.40540i	−0.410546	+	0.133394i
$112$	−4.62959	−	12.1744i	−0.437455	−	1.15037i
$113$	0.716658	+	1.40652i	0.0674175	+	0.132314i	0.922256	−	0.386580i	$-0.126344\pi$
$113$	0.716658	+	1.40652i	0.0674175	+	0.132314i	−0.854838	+	0.518894i	$0.826344\pi$
$114$	−5.88111	−	5.29537i	−0.550816	−	0.495957i
$115$	1.30757	−	3.29336i	0.121931	−	0.307108i
$116$	−9.01594	−	10.0132i	−0.837109	−	0.929704i
$117$	−4.34673	−	5.36777i	−0.401856	−	0.496250i
$118$	−16.2639	−	16.2639i	−1.49722	−	1.49722i
$119$	9.61287	+	2.07478i	0.881210	+	0.190195i
$120$	5.03758	−	3.57280i	0.459866	−	0.326151i
$121$	−5.29702	−	2.35839i	−0.481547	−	0.214399i
$122$	1.36836	+	1.10807i	0.123885	+	0.100320i
$123$	−9.30926	+	6.04550i	−0.839387	+	0.545105i
$124$	2.17913	+	3.77436i	0.195691	+	0.338947i
$125$	3.08851	+	10.7453i	0.276245	+	0.961087i
$126$	−6.39461	+	2.82309i	−0.569677	+	0.251501i
$127$	5.78103	−	11.3459i	0.512984	−	1.00679i	−0.478687	−	0.877986i	$-0.658887\pi$
$127$	5.78103	−	11.3459i	0.512984	−	1.00679i	0.991670	−	0.128801i	$-0.0411129\pi$
$128$	−9.13111	+	3.50510i	−0.807083	+	0.309810i
$129$	1.95925	+	18.6410i	0.172502	+	1.64125i
$130$	−19.0766	+	1.78493i	−1.67313	+	0.156549i
$131$	−14.2509	−	1.49783i	−1.24511	−	0.130866i	−0.541040	−	0.840997i	$-0.681969\pi$
$131$	−14.2509	−	1.49783i	−1.24511	−	0.130866i	−0.704070	+	0.710131i	$0.748636\pi$
$132$	−4.35081	+	4.35081i	−0.378690	+	0.378690i
$133$	−5.47014	+	0.269491i	−0.474321	+	0.0233679i
$134$	−17.6662	−	5.74011i	−1.52613	−	0.495870i
$135$	4.51335	+	5.70559i	0.388447	+	0.491059i
$136$	1.01077	−	4.75530i	0.0866728	−	0.407764i
$137$	0.124811	−	2.38153i	0.0106633	−	0.203468i	−0.988102	−	0.153797i	$-0.950850\pi$
$137$	0.124811	−	2.38153i	0.0106633	−	0.203468i	0.998766	−	0.0496701i	$-0.0158170\pi$
$138$	5.08091	+	3.29958i	0.432516	+	0.280879i
$139$	−6.04915	−	18.6174i	−0.513082	−	1.57910i	−0.786745	−	0.617278i	$-0.788235\pi$
$139$	−6.04915	−	18.6174i	−0.513082	−	1.57910i	0.273663	−	0.961826i	$-0.411765\pi$
$140$	−1.29090	+	7.44703i	−0.109101	+	0.629389i
$141$	−4.19607	+	12.9142i	−0.353373	+	1.08757i
$142$	3.23511	−	2.61974i	0.271484	−	0.219843i
$143$	−10.4268	+	2.79385i	−0.871931	+	0.233633i
$144$	2.92211	+	6.56317i	0.243509	+	0.546931i
$145$	−4.63941	−	23.1226i	−0.385282	−	1.92023i
$146$	8.35194	+	11.4955i	0.691211	+	0.951371i
$147$	−5.38379	+	13.7667i	−0.444047	+	1.13546i
$148$	−2.45155	−	1.24913i	−0.201516	−	0.102678i
$149$	20.6257	−	11.9082i	1.68972	−	0.975561i	0.734995	−	0.678072i	$-0.237184\pi$
$149$	20.6257	−	11.9082i	1.68972	−	0.975561i	0.954725	−	0.297488i	$-0.0961490\pi$
$150$	−19.0512	+	1.56322i	−1.55553	+	0.127636i
$151$	4.22319	−	7.31478i	0.343678	−	0.595268i	−0.641434	−	0.767178i	$-0.721660\pi$
$151$	4.22319	−	7.31478i	0.343678	−	0.595268i	0.985113	+	0.171910i	$0.0549937\pi$
$152$	0.141696	+	2.70372i	0.0114931	+	0.219301i
$153$	−5.35757	−	0.848556i	−0.433134	−	0.0686017i
$154$	−0.0342342	+	10.9243i	−0.00275867	+	0.880306i
$155$	−0.0871488	+	7.62765i	−0.00699996	+	0.612668i
$156$	1.33470	−	12.6988i	0.106861	−	1.01672i
$157$	4.22483	+	15.7673i	0.337178	+	1.25837i	0.901489	+	0.432803i	$0.142475\pi$
$157$	4.22483	+	15.7673i	0.337178	+	1.25837i	−0.564311	+	0.825562i	$0.690858\pi$
$158$	7.49607	−	19.5279i	0.596355	−	1.55356i
$159$	−8.37781	+	1.78076i	−0.664403	+	0.141223i
$160$	13.8804	+	2.36130i	1.09734	+	0.186677i
$161$	4.10375	−	0.858846i	0.323421	−	0.0676865i
$162$	−18.1445	+	9.24507i	−1.42556	+	0.726361i
$163$	5.49953	−	8.46854i	0.430757	−	0.663307i	−0.554929	−	0.831897i	$-0.687255\pi$
$163$	5.49953	−	8.46854i	0.430757	−	0.663307i	0.985686	+	0.168590i	$0.0539214\pi$
$164$	−6.56857	−	1.39619i	−0.512919	−	0.109024i
$165$	−10.4336	+	2.66831i	−0.812257	+	0.207727i
$166$	2.18737	+	10.2908i	0.169773	+	0.798719i
$167$	−20.5308	+	3.25176i	−1.58872	+	0.251628i	−0.887325	−	0.461145i	$-0.847439\pi$
$167$	−20.5308	+	3.25176i	−1.58872	+	0.251628i	−0.701394	+	0.712773i	$0.747439\pi$
$168$	6.81387	+	2.64013i	0.525701	+	0.203690i
$169$	5.52581	−	7.60562i	0.425062	−	0.585048i
$170$	−10.1955	+	11.0664i	−0.781961	+	0.848751i
$171$	3.00432	−	0.315767i	0.229746	−	0.0241473i
$172$	−7.13623	+	8.81252i	−0.544133	+	0.671948i
$173$	15.7439	−	0.825101i	1.19698	−	0.0627313i	0.556596	−	0.830783i	$-0.312107\pi$
$173$	15.7439	−	0.825101i	1.19698	−	0.0627313i	0.640388	+	0.768052i	$0.278774\pi$
$174$	40.3211			3.05673
$175$	−8.58941	+	10.0609i	−0.649299	+	0.760534i
$176$	11.2279			0.846336
$177$	26.7920	−	1.40411i	2.01381	−	0.105539i
$178$	7.61823	−	9.40773i	0.571011	−	0.705139i
$179$	15.9352	−	1.67486i	1.19105	−	0.125185i	0.511810	−	0.859098i	$-0.328975\pi$
$179$	15.9352	−	1.67486i	1.19105	−	0.125185i	0.679243	+	0.733914i	$0.262308\pi$
$180$	0.483106	−	4.14080i	0.0360086	−	0.308637i
$181$	−5.00248	+	6.88532i	−0.371831	+	0.511782i	−0.953397	−	0.301717i	$-0.902440\pi$
$181$	−5.00248	+	6.88532i	−0.371831	+	0.511782i	0.581566	+	0.813499i	$0.302440\pi$
$182$	−14.2116	−	17.6628i	−1.05344	−	1.30925i
$183$	−2.02851	+	0.321285i	−0.149952	+	0.0237501i
$184$	−0.430925	−	2.02734i	−0.0317682	−	0.149458i
$185$	−2.57655	−	4.06855i	−0.189432	−	0.299126i
$186$	−12.7570	−	2.71159i	−0.935389	−	0.198823i
$187$	−4.61713	+	7.10976i	−0.337638	+	0.519917i
$188$	−7.31954	+	3.72949i	−0.533832	+	0.272001i
$189$	−2.68559	+	8.17810i	−0.195348	+	0.594869i
$190$	3.88942	−	7.42253i	0.282168	−	0.538487i
$191$	−11.8260	+	2.51369i	−0.855699	+	0.181884i	−0.614817	−	0.788670i	$-0.710770\pi$
$191$	−11.8260	+	2.51369i	−0.855699	+	0.181884i	−0.240882	+	0.970554i	$0.577437\pi$
$192$	−1.17572	+	3.06286i	−0.0848505	+	0.221043i
$193$	2.27295	+	8.48275i	0.163610	+	0.610602i	0.998213	+	0.0597499i	$0.0190303\pi$
$193$	2.27295	+	8.48275i	0.163610	+	0.610602i	−0.834603	+	0.550852i	$0.814303\pi$
$194$	−0.548359	+	5.21728i	−0.0393699	+	0.374579i
$195$	13.3420	−	17.9293i	0.955442	−	1.28395i
$196$	−8.19234	+	3.58611i	−0.585167	+	0.256151i
$197$	9.73798	+	1.54234i	0.693802	+	0.109887i	0.493369	−	0.869820i	$-0.335765\pi$
$197$	9.73798	+	1.54234i	0.693802	+	0.109887i	0.200433	+	0.979707i	$0.435765\pi$
$198$	−0.315358	−	6.01739i	−0.0224115	−	0.427637i
$199$	−2.51334	+	4.35324i	−0.178166	+	0.308593i	−0.941252	−	0.337704i	$-0.890350\pi$
$199$	−2.51334	+	4.35324i	−0.178166	+	0.308593i	0.763086	+	0.646297i	$0.223683\pi$
$200$	4.98688	+	4.23056i	0.352626	+	0.299146i
$201$	18.7642	−	10.8335i	1.32352	−	0.764136i
$202$	6.14517	+	3.13112i	0.432373	+	0.220305i
$203$	19.7931	−	19.6694i	1.38920	−	1.38052i
$204$	−5.89418	−	8.11264i	−0.412675	−	0.567998i
$205$	−8.64425	−	7.96401i	−0.603741	−	0.556231i
$206$	12.6156	+	28.3351i	0.878970	+	1.97420i
$207$	−2.23378	+	0.598540i	−0.155259	+	0.0416014i
$208$	−18.1077	+	14.6633i	−1.25554	+	1.01672i
$209$	1.45892	−	4.49008i	0.100915	−	0.310585i
$210$	−13.9762	−	17.7824i	−0.964452	−	1.22710i
$211$	5.17345	+	15.9222i	0.356155	+	1.09613i	0.955337	+	0.295519i	$0.0954927\pi$
$211$	5.17345	+	15.9222i	0.356155	+	1.09613i	−0.599182	+	0.800613i	$0.704507\pi$
$212$	−4.34570	−	2.82213i	−0.298464	−	0.193825i
$213$	−0.254125	+	4.84899i	−0.0174123	+	0.332247i
$214$	2.40640	−	11.3212i	0.164498	−	0.773902i
$215$	−18.6092	+	6.90053i	−1.26914	+	0.470612i
$216$	4.04697	+	1.31494i	0.275362	+	0.0894704i
$217$	−7.58500	+	4.89203i	−0.514903	+	0.332093i
$218$	11.8376	−	11.8376i	0.801746	−	0.801746i
$219$	−16.4833	−	1.73246i	−1.11384	−	0.117069i
$220$	−5.60484	−	3.32191i	−0.377878	−	0.223963i
$221$	−1.83891	−	17.4960i	−0.123698	−	1.17691i
$222$	7.68676	−	2.95067i	0.515902	−	0.198036i
$223$	4.83037	−	9.48013i	0.323465	−	0.634836i	−0.670817	−	0.741623i	$-0.734056\pi$
$223$	4.83037	−	9.48013i	0.323465	−	0.634836i	0.994282	+	0.106787i	$0.0340563\pi$
$224$	6.72830	+	15.2404i	0.449553	+	1.01829i
$225$	4.42265	−	5.80363i	0.294843	−	0.386908i
$226$	−1.42893	−	2.47497i	−0.0950507	−	0.164633i
$227$	−3.02015	+	1.96131i	−0.200455	+	0.130177i	−0.640963	−	0.767572i	$-0.721465\pi$
$227$	−3.02015	+	1.96131i	−0.200455	+	0.130177i	0.440509	+	0.897748i	$0.354798\pi$
$228$	4.34002	+	3.51448i	0.287425	+	0.232752i
$229$	−7.55461	−	3.36353i	−0.499222	−	0.222268i	0.141648	−	0.989917i	$-0.454760\pi$
$229$	−7.55461	−	3.36353i	−0.499222	−	0.222268i	−0.640871	+	0.767649i	$0.721426\pi$
$230$	−2.05193	+	6.07802i	−0.135300	+	0.400773i
$231$	−9.44280	−	8.55607i	−0.621291	−	0.562948i
$232$	−9.75415	−	9.75415i	−0.640392	−	0.640392i
$233$	2.47471	+	3.05602i	0.162124	+	0.200206i	0.851734	−	0.523975i	$-0.175551\pi$
$233$	2.47471	+	3.05602i	0.162124	+	0.200206i	−0.689610	+	0.724181i	$0.742218\pi$
$234$	8.36713	+	9.29264i	0.546977	+	0.607479i
$235$	−14.3491	−	0.916499i	−0.936034	−	0.0597858i
$236$	12.0619	+	10.8606i	0.785165	+	0.706966i
$237$	11.0767	+	21.7393i	0.719512	+	1.41212i
$238$	−17.5759	−	2.84023i	−1.13927	−	0.184105i
$239$	13.0724	−	4.24747i	0.845581	−	0.274746i	0.145987	−	0.989287i	$-0.453364\pi$
$239$	13.0724	−	4.24747i	0.845581	−	0.274746i	0.699594	+	0.714541i	$0.253364\pi$
$240$	−18.2314	+	14.4218i	−1.17683	+	0.930923i
$241$	7.90168	−	7.11470i	0.508992	−	0.458298i	−0.374174	−	0.927358i	$-0.622074\pi$
$241$	7.90168	−	7.11470i	0.508992	−	0.458298i	0.883166	+	0.469060i	$0.155407\pi$
$242$	9.80004	+	3.76188i	0.629970	+	0.241823i
$243$	3.62166	−	13.5162i	0.232329	−	0.867065i
$244$	−1.00521	−	0.730330i	−0.0643522	−	0.0467546i
$245$	−15.5353	−	1.91127i	−0.992517	−	0.122107i
$246$	16.2576	−	11.8118i	1.03655	−	0.753094i
$247$	3.51107	+	9.14664i	0.223404	+	0.581987i
$248$	2.43011	+	3.74204i	0.154312	+	0.237620i
$249$	−10.6276	−	6.13585i	−0.673497	−	0.388843i
$250$	−6.60188	−	19.1340i	−0.417540	−	1.21014i
$251$			7.76448i			0.490090i	0.969512	+	0.245045i	$0.0788027\pi$
$251$			7.76448i			0.490090i	−0.969512	+	0.245045i	$0.921197\pi$
$252$	4.40206	−	2.22561i	0.277303	−	0.140200i
$253$	−0.565386	+	3.56970i	−0.0355455	+	0.224425i
$254$	−9.37662	+	21.0602i	−0.588342	+	1.32144i
$255$	−1.63508	−	17.4751i	−0.102393	−	1.09433i
$256$	19.0148	−	8.46592i	1.18842	−	0.529120i
$257$	19.6899	+	5.27589i	1.22822	+	0.329101i	0.813887	−	0.581024i	$-0.197348\pi$
$257$	19.6899	+	5.27589i	1.22822	+	0.329101i	0.414335	+	0.910125i	$0.364014\pi$
$258$	−5.30838	−	33.5158i	−0.330485	−	2.08660i
$259$	2.33393	−	5.19819i	0.145023	−	0.323000i
$260$	13.3775	−	1.96239i	0.829636	−	0.121702i
$261$	−10.2989	+	11.4381i	−0.637485	+	0.707999i
$262$	25.9065	+	1.35770i	1.60051	+	0.0838790i
$263$	−19.5739	−	1.02582i	−1.20698	−	0.0632549i	−0.561789	−	0.827280i	$-0.689887\pi$
$263$	−19.5739	−	1.02582i	−1.20698	−	0.0632549i	−0.645186	+	0.764025i	$0.723220\pi$
$264$	−4.21503	+	4.68127i	−0.259417	+	0.288112i
$265$	−4.02481	−	8.12735i	−0.247242	−	0.499259i
$266$	9.86403	−	1.00551i	0.604803	−	0.0616517i
$267$	2.20890	+	13.9464i	0.135182	+	0.853508i
$268$	12.6615	+	3.39264i	0.773424	+	0.207238i
$269$	−18.9392	+	8.43229i	−1.15475	+	0.514126i	−0.892576	−	0.450896i	$-0.851104\pi$
$269$	−18.9392	+	8.43229i	−1.15475	+	0.514126i	−0.262169	+	0.965022i	$0.584438\pi$
$270$	−8.70037	−	9.88761i	−0.529488	−	0.601741i
$271$	−2.16651	+	4.86606i	−0.131606	+	0.295592i	−0.967314	−	0.253582i	$-0.918391\pi$
$271$	−2.16651	+	4.86606i	−0.131606	+	0.295592i	0.835708	+	0.549174i	$0.185058\pi$
$272$	−2.86253	+	18.0733i	−0.173567	+	1.09586i
$273$	26.4028	+	1.46669i	1.59797	+	0.0887682i
$274$			4.31743i			0.260826i
$275$	−5.47467	−	10.0035i	−0.330135	−	0.603234i
$276$	−3.70241	−	2.13758i	−0.222859	−	0.128667i
$277$	2.90567	+	4.47434i	0.174585	+	0.268837i	0.915121	−	0.403179i	$-0.132095\pi$
$277$	2.90567	+	4.47434i	0.174585	+	0.268837i	−0.740536	+	0.672017i	$0.765428\pi$
$278$	12.7004	+	33.0855i	0.761716	+	1.98434i
$279$	4.02762	−	2.92624i	0.241128	−	0.175189i
$280$	−0.920763	+	7.68280i	−0.0550261	+	0.459135i
$281$	−19.3712	−	14.0740i	−1.15559	−	0.839582i	−0.166372	−	0.986063i	$-0.553205\pi$
$281$	−19.3712	−	14.0740i	−1.15559	−	0.839582i	−0.989214	+	0.146481i	$0.953205\pi$
$282$	6.36255	−	23.7453i	0.378884	−	1.41401i
$283$	3.15108	+	1.20959i	0.187312	+	0.0719025i	0.450216	−	0.892920i	$-0.351347\pi$
$283$	3.15108	+	1.20959i	0.187312	+	0.0719025i	−0.262904	+	0.964822i	$0.584680\pi$
$284$	−2.18304	+	1.96562i	−0.129540	+	0.116638i
$285$	3.39840	+	9.16473i	0.201304	+	0.542872i
$286$	18.5861	−	6.03898i	1.09902	−	0.357092i
$287$	2.21859	−	13.7290i	0.130959	−	0.810398i
$288$	−4.17173	−	8.18748i	−0.245822	−	0.482452i
$289$	2.36618	+	2.13051i	0.139187	+	0.125324i
$290$	10.5785	+	41.3642i	0.621192	+	2.42899i
$291$	−4.09451	−	4.54741i	−0.240024	−	0.266574i
$292$	−6.31021	−	7.79246i	−0.369277	−	0.456019i
$293$	13.2445	+	13.2445i	0.773751	+	0.773751i	0.978760	−	0.205009i	$-0.0657223\pi$
$293$	13.2445	+	13.2445i	0.773751	+	0.773751i	−0.205009	+	0.978760i	$0.565722\pi$
$294$	8.42907	−	25.3992i	0.491593	−	1.48131i
$295$	8.46951	+	27.1168i	0.493114	+	1.57880i
$296$	−2.57332	−	1.14572i	−0.149571	−	0.0665934i
$297$	−5.76656	−	4.66967i	−0.334610	−	0.270962i
$298$	−36.1613	+	23.4834i	−2.09477	+	1.36036i
$299$	−3.75011	−	6.49539i	−0.216875	−	0.375638i
$300$	13.3678	−	1.80521i	0.771789	−	0.104224i
$301$	−18.9554	−	13.8629i	−1.09257	−	0.799044i
$302$	−6.94212	+	13.6247i	−0.399474	+	0.784012i
$303$	−7.51044	+	2.88299i	−0.431464	+	0.165623i
$304$	−1.06521	−	10.1348i	−0.0610942	−	0.581273i
$305$	−0.861792	−	1.99670i	−0.0493460	−	0.114331i
$306$	9.76646	+	1.02650i	0.558311	+	0.0586809i
$307$	−1.06555	+	1.06555i	−0.0608142	+	0.0608142i	−0.736860	−	0.676046i	$-0.763692\pi$
$307$	−1.06555	+	1.06555i	−0.0608142	+	0.0608142i	0.676046	+	0.736860i	$0.263692\pi$
$308$	−0.379332	−	7.69968i	−0.0216144	−	0.438730i
$309$	−34.4082	−	11.1799i	−1.95741	−	0.636002i
$310$	−0.565155	−	13.7984i	−0.0320986	−	0.783699i
$311$	1.04078	−	4.89649i	0.0590173	−	0.277655i	−0.938737	−	0.344634i	$-0.888003\pi$
$311$	1.04078	−	4.89649i	0.0590173	−	0.277655i	0.997754	+	0.0669796i	$0.0213363\pi$
$312$	0.684151	−	13.0544i	0.0387324	−	0.739059i
$313$	28.3794	+	18.4298i	1.60410	+	1.04171i	0.961234	+	0.275733i	$0.0889207\pi$
$313$	28.3794	+	18.4298i	1.60410	+	1.04171i	0.642864	+	0.765980i	$0.277746\pi$
$314$	−9.13208	−	28.1057i	−0.515353	−	1.58609i
$315$	8.61426	+	0.577315i	0.485358	+	0.0325280i
$316$	−4.56132	+	14.0383i	−0.256594	+	0.789715i
$317$	10.4624	−	8.47232i	0.587629	−	0.475853i	−0.288796	−	0.957391i	$-0.593255\pi$
$317$	10.4624	−	8.47232i	0.587629	−	0.475853i	0.876425	+	0.481538i	$0.159922\pi$
$318$	14.9777	−	4.01326i	0.839907	−	0.225052i
$319$	9.78380	+	21.9748i	0.547788	+	1.23035i
$320$	−3.45056	−	0.402576i	−0.192892	−	0.0225047i
$321$	7.93539	+	10.9221i	0.442910	+	0.609613i
$322$	−7.33787	+	1.94155i	−0.408923	+	0.108198i
$323$	6.85563	+	3.49312i	0.381458	+	0.194362i
$324$	12.4451	−	7.18516i	0.691393	−	0.399176i
$325$	21.8935	+	8.98330i	1.21443	+	0.498304i
$326$	−9.14033	+	15.8315i	−0.506236	+	0.876826i
$327$	1.02198	+	19.5005i	0.0565154	+	1.07838i
$328$	−6.79032	−	1.07548i	−0.374933	−	0.0593835i
$329$	−8.46015	−	14.7600i	−0.466423	−	0.813747i
$330$	18.6103	−	5.81266i	1.02447	−	0.319976i
$331$	1.28920	−	12.2659i	0.0708609	−	0.674196i	−0.900218	−	0.435439i	$-0.856593\pi$
$331$	1.28920	−	12.2659i	0.0708609	−	0.674196i	0.971079	−	0.238758i	$-0.0767401\pi$
$332$	−1.92151	−	7.17118i	−0.105457	−	0.393570i
$333$	−1.12634	+	2.93420i	−0.0617228	+	0.160793i
$334$	36.8099	−	7.82418i	2.01415	−	0.428120i
$335$	16.0367	+	16.4074i	0.876177	+	0.896430i
$336$	−26.1320	−	8.58144i	−1.42562	−	0.468156i
$337$	15.1805	−	7.73487i	0.826936	−	0.421345i	0.0113182	−	0.999936i	$-0.496397\pi$
$337$	15.1805	−	7.73487i	0.826936	−	0.421345i	0.815618	+	0.578591i	$0.196397\pi$
$338$	−9.26959	+	14.2739i	−0.504199	+	0.776398i
$339$	3.26065	+	0.693073i	0.177094	+	0.0376426i
$340$	6.77614	−	8.17507i	0.367488	−	0.443355i
$341$	−1.61765	−	7.61046i	−0.0876008	−	0.412130i
$342$	−5.40166	+	0.855539i	−0.292088	+	0.0462622i
$343$	−8.25252	−	16.5800i	−0.445594	−	0.895235i
$344$	−6.82371	+	9.39203i	−0.367910	+	0.506384i
$345$	−3.66709	−	6.52256i	−0.197429	−	0.351163i
$346$	−28.3855	+	2.98343i	−1.52601	+	0.160390i
$347$	−10.8488	+	13.3971i	−0.582392	+	0.719194i	−0.980141	−	0.198300i	$-0.936458\pi$
$347$	−10.8488	+	13.3971i	−0.582392	+	0.719194i	0.397749	+	0.917494i	$0.369791\pi$
$348$	−28.4145	+	1.48914i	−1.52318	+	0.0798263i
$349$	13.4664			0.720839			0.360419	−	0.932790i	$-0.382634\pi$
$349$	13.4664			0.720839			0.360419	+	0.932790i	$0.382634\pi$
$350$	14.5757	−	19.0032i	0.779104	−	1.01576i
$351$	15.3984			0.821907
$352$	−14.3413	+	0.751597i	−0.764395	+	0.0400602i
$353$	5.61091	−	6.92890i	0.298639	−	0.368788i	−0.605634	−	0.795743i	$-0.707080\pi$
$353$	5.61091	−	6.92890i	0.298639	−	0.368788i	0.904273	+	0.426955i	$0.140414\pi$
$354$	−48.3048	+	5.07704i	−2.56737	+	0.269841i
$355$	−5.04110	+	1.01147i	−0.267554	+	0.0536831i
$356$	−5.02116	+	6.91104i	−0.266121	+	0.366284i
$357$	16.1799	−	13.0185i	0.856333	−	0.689013i
$358$	−28.6509	+	4.53785i	−1.51425	+	0.239833i
$359$	4.52910	+	21.3077i	0.239037	+	1.12458i	0.919895	+	0.392164i	$0.128274\pi$
$359$	4.52910	+	21.3077i	0.239037	+	1.12458i	−0.680859	+	0.732415i	$0.738393\pi$
$360$	0.272049	−	4.25932i	0.0143382	−	0.224486i
$361$	14.3934	+	3.05942i	0.757549	+	0.161022i
$362$	8.39170	−	12.9221i	0.441058	−	0.679170i
$363$	−10.9098	+	5.55883i	−0.572617	+	0.291763i
$364$	10.6673	+	11.9222i	0.559120	+	0.624893i
$365$	−2.54722	−	17.3642i	−0.133328	−	0.908886i
$366$	3.63695	−	0.773057i	0.190106	−	0.0404083i
$367$	4.25793	−	11.0923i	0.222262	−	0.579012i	−0.776427	−	0.630207i	$-0.782970\pi$
$367$	4.25793	−	11.0923i	0.222262	−	0.579012i	0.998689	+	0.0511955i	$0.0163032\pi$
$368$	2.01912	+	7.53547i	0.105254	+	0.392814i
$369$	−0.801825	+	7.62886i	−0.0417414	+	0.397142i
$370$	5.04368	+	7.11149i	0.262209	+	0.369709i
$371$	5.39459	−	9.27645i	0.280073	−	0.481609i
$372$	9.09008	+	1.43973i	0.471299	+	0.0746464i
$373$	−1.04356	−	19.9123i	−0.0540334	−	1.03102i	−0.882301	−	0.470686i	$-0.844007\pi$
$373$	−1.04356	−	19.9123i	−0.0540334	−	1.03102i	0.828267	−	0.560333i	$-0.189327\pi$
$374$	7.67376	−	13.2913i	0.396801	−	0.687279i
$375$	21.7387	+	9.21131i	1.12258	+	0.475670i
$376$	−7.28346	+	4.20511i	−0.375616	+	0.216862i
$377$	−44.4772	−	22.6623i	−2.29069	−	1.16717i
$378$	4.08046	−	15.0398i	0.209876	−	0.773564i
$379$	11.9563	+	16.4564i	0.614154	+	0.845311i	0.996911	−	0.0785382i	$-0.0250252\pi$
$379$	11.9563	+	16.4564i	0.614154	+	0.845311i	−0.382757	+	0.923849i	$0.625025\pi$
$380$	−2.46676	+	5.37435i	−0.126542	+	0.275698i
$381$	−10.9372	−	24.5654i	−0.560331	−	1.25852i
$382$	21.1423	−	5.66505i	1.08173	−	0.289849i
$383$	8.55346	−	6.92646i	0.437062	−	0.353925i	−0.385397	−	0.922751i	$-0.625935\pi$
$383$	8.55346	−	6.92646i	0.437062	−	0.353925i	0.822458	+	0.568826i	$0.192602\pi$
$384$	−6.38248	+	19.6432i	−0.325704	+	1.00242i
$385$	6.30003	−	11.9318i	0.321079	−	0.608103i
$386$	−4.91303	−	15.1208i	−0.250067	−	0.769627i
$387$	10.8634	+	7.05480i	0.552220	+	0.358616i
$388$	0.193746	−	3.69690i	0.00983598	−	0.187682i
$389$	−1.22745	+	5.77469i	−0.0622341	+	0.292788i	−0.998248	−	0.0591758i	$-0.981153\pi$
$389$	−1.22745	+	5.77469i	−0.0622341	+	0.292788i	0.936013	+	0.351964i	$0.114486\pi$
$390$	−22.4225	+	33.6789i	−1.13541	+	1.70540i
$391$	−5.60193	−	1.82018i	−0.283302	−	0.0920503i
$392$	−8.18347	+	4.10528i	−0.413328	+	0.207348i
$393$	−21.3968	+	21.3968i	−1.07933	+	1.07933i
$394$	−17.7516	−	1.86577i	−0.894313	−	0.0939961i
$395$	−19.3957	+	17.0668i	−0.975902	+	0.858722i
$396$	0.444469	+	4.22884i	0.0223354	+	0.212507i
$397$	−15.9066	+	6.10596i	−0.798328	+	0.306450i	−0.723124	−	0.690719i	$-0.757294\pi$
$397$	−15.9066	+	6.10596i	−0.798328	+	0.306450i	−0.0752046	+	0.997168i	$0.523961\pi$
$398$	4.13146	−	8.10845i	0.207091	−	0.406440i
$399$	−6.82725	+	9.33524i	−0.341790	+	0.467347i
$400$	−19.5781	−	14.9194i	−0.978903	−	0.745972i
$401$	7.60244	+	13.1678i	0.379648	+	0.657569i	0.991011	−	0.133781i	$-0.0427119\pi$
$401$	7.60244	+	13.1678i	0.379648	+	0.657569i	−0.611363	+	0.791350i	$0.709379\pi$
$402$	−32.8976	+	21.3640i	−1.64078	+	1.06554i
$403$	12.5479	+	10.1611i	0.625056	+	0.506160i
$404$	−4.44618	−	1.97956i	−0.221205	−	0.0984870i
$405$	25.1504	+	0.287353i	1.24973	+	0.0142787i
$406$	−33.9206	+	37.4361i	−1.68345	+	1.85792i
$407$	3.47327	+	3.47327i	0.172164	+	0.172164i
$408$	−6.46072	−	7.97832i	−0.319853	−	0.394986i
$409$	7.61757	+	8.46017i	0.376665	+	0.418328i	0.901434	−	0.432916i	$-0.142515\pi$
$409$	7.61757	+	8.46017i	0.376665	+	0.418328i	−0.524770	+	0.851244i	$0.675849\pi$
$410$	16.3827	+	13.5793i	0.809084	+	0.670632i
$411$	−3.74248	−	3.36975i	−0.184603	−	0.166217i
$412$	−9.93675	−	19.5020i	−0.489549	−	0.960793i
$413$	−21.2355	+	26.0562i	−1.04493	+	1.28214i
$414$	3.98179	−	1.29376i	0.195694	−	0.0635849i
$415$	3.50636	−	12.5123i	0.172120	−	0.614206i
$416$	22.1473	−	19.9415i	1.08586	−	0.977712i
$417$	−38.5921	−	14.8141i	−1.88987	−	0.725451i
$418$	−2.21217	+	8.25594i	−0.108201	+	0.403811i
$419$	−11.5358	−	8.38127i	−0.563562	−	0.409452i	0.269199	−	0.963085i	$-0.413241\pi$
$419$	−11.5358	−	8.38127i	−0.563562	−	0.409452i	−0.832761	+	0.553633i	$0.813241\pi$
$420$	10.5059	+	12.0152i	0.512634	+	0.586282i
$421$	−7.49291	+	5.44392i	−0.365182	+	0.265320i	−0.755210	−	0.655483i	$-0.772465\pi$
$421$	−7.49291	+	5.44392i	−0.365182	+	0.265320i	0.390028	+	0.920803i	$0.372465\pi$
$422$	−10.8618	−	28.2960i	−0.528744	−	1.37743i
$423$	5.11082	+	7.86997i	0.248496	+	0.382651i
$424$	−4.59413	−	2.65242i	−0.223111	−	0.128813i
$425$	17.4982	−	6.26209i	0.848786	−	0.303756i
$426$		−	8.79066i		−	0.425909i
$427$	1.40821	−	2.15365i	0.0681483	−	0.104223i
$428$	−1.27769	+	8.06700i	−0.0617593	+	0.389933i
$429$	−9.27161	+	20.8244i	−0.447638	+	1.00541i
$430$	32.9902	−	14.2388i	1.59093	−	0.686656i
$431$	7.32382	−	3.26078i	0.352776	−	0.157066i	−0.222695	−	0.974888i	$-0.571485\pi$
$431$	7.32382	−	3.26078i	0.352776	−	0.157066i	0.575471	+	0.817822i	$0.304819\pi$
$432$	−15.4708	−	4.14538i	−0.744339	−	0.199445i
$433$	4.18286	+	26.4096i	0.201016	+	1.26916i	0.857366	+	0.514707i	$0.172099\pi$
$433$	4.18286	+	26.4096i	0.201016	+	1.26916i	−0.656351	+	0.754456i	$0.727901\pi$
$434$	13.2496	−	9.56307i	0.635999	−	0.459042i
$435$	−44.1123	−	23.1149i	−2.11502	−	1.10827i
$436$	−7.90486	+	8.77923i	−0.378574	+	0.420449i
$437$	3.27582	+	0.171678i	0.156704	+	0.00821249i
$438$	29.9646	+	1.57038i	1.43176	+	0.0750356i
$439$	11.7293	−	13.0267i	0.559809	−	0.621731i	−0.395097	−	0.918639i	$-0.629289\pi$
$439$	11.7293	−	13.0267i	0.559809	−	0.621731i	0.954906	+	0.296909i	$0.0959557\pi$
$440$	−5.90822	−	3.09591i	−0.281663	−	0.147592i
$441$	5.05215	+	8.87863i	0.240578	+	0.422792i
$442$	4.98233	+	31.4572i	0.236985	+	1.49627i
$443$	14.8689	+	3.98412i	0.706445	+	0.189291i	0.594116	−	0.804380i	$-0.297502\pi$
$443$	14.8689	+	3.98412i	0.706445	+	0.189291i	0.112329	+	0.993671i	$0.464169\pi$
$444$	−5.30793	+	2.36324i	−0.251903	+	0.112155i
$445$	−13.7277	+	5.92499i	−0.650756	+	0.280871i
$446$	−7.83468	+	17.5970i	−0.370983	+	0.833241i
$447$	7.86765	−	49.6744i	0.372127	−	2.34952i
$448$	−1.85462	−	3.66827i	−0.0876226	−	0.173310i
$449$			1.46011i			0.0689067i	0.999406	+	0.0344533i	$0.0109690\pi$
$449$			1.46011i			0.0689067i	−0.999406	+	0.0344533i	$0.989031\pi$
$450$	−7.44591	+	10.9115i	−0.351003	+	0.514375i
$451$	10.3822	+	5.99419i	0.488881	+	0.282255i
$452$	1.09838	+	1.69135i	0.0516633	+	0.0795546i
$453$	−6.39198	−	16.6517i	−0.300321	−	0.782364i
$454$	5.27436	−	3.83205i	0.247538	−	0.179847i
$455$	5.42232	+	27.4706i	0.254202	+	1.28784i
$456$	4.62542	+	3.36056i	0.216605	+	0.157373i
$457$	10.3382	−	38.5827i	0.483600	−	1.80482i	−0.102683	−	0.994714i	$-0.532743\pi$
$457$	10.3382	−	38.5827i	0.483600	−	1.80482i	0.586283	−	0.810106i	$-0.300591\pi$
$458$	13.9768	+	5.36519i	0.653093	+	0.250699i
$459$	8.98683	−	8.09178i	0.419469	−	0.377692i
$460$	1.22153	−	4.35900i	0.0569543	−	0.203239i
$461$	−16.1060	+	5.23314i	−0.750130	+	0.243732i	−0.659037	−	0.752111i	$-0.729036\pi$
$461$	−16.1060	+	5.23314i	−0.750130	+	0.243732i	−0.0910926	+	0.995842i	$0.529036\pi$
$462$	17.8825	+	14.5740i	0.831969	+	0.678043i
$463$	−5.84654	−	11.4745i	−0.271712	−	0.533265i	0.714320	−	0.699819i	$-0.246736\pi$
$463$	−5.84654	−	11.4745i	−0.271712	−	0.533265i	−0.986032	+	0.166554i	$0.946736\pi$
$464$	38.5854	+	34.7424i	1.79128	+	1.61288i
$465$	12.4020	+	10.2798i	0.575129	+	0.476712i
$466$	−4.76364	−	5.29055i	−0.220671	−	0.245080i
$467$	4.13448	+	5.10565i	0.191321	+	0.236261i	0.863776	−	0.503877i	$-0.168093\pi$
$467$	4.13448	+	5.10565i	0.191321	+	0.236261i	−0.672455	+	0.740138i	$0.734760\pi$
$468$	−6.23956	−	6.23956i	−0.288424	−	0.288424i
$469$	−5.72724	+	26.5354i	−0.264459	+	1.22529i
$470$	26.0289	+	0.297390i	1.20062	+	0.0137176i
$471$	31.4904	+	14.0204i	1.45100	+	0.646027i
$472$	12.9137	+	10.4573i	0.594401	+	0.481336i
$473$	16.9779	−	11.0256i	0.780643	−	0.506955i
$474$	−22.0856	−	38.2534i	−1.01443	−	1.75704i
$475$	−8.51024	+	5.89075i	−0.390477	+	0.270286i
$476$	12.4907	+	1.35242i	0.572511	+	0.0619879i
$477$	−2.68717	+	5.27386i	−0.123037	+	0.241473i
$478$	−23.2313	+	8.91767i	−1.06258	+	0.407885i
$479$	−1.06015	−	10.0866i	−0.0484393	−	0.460869i	−0.991677	−	0.128751i	$-0.958903\pi$
$479$	−1.06015	−	10.0866i	−0.0484393	−	0.460869i	0.943238	−	0.332118i	$-0.107763\pi$
$480$	22.3215	−	19.6413i	1.01883	−	0.896497i
$481$	−10.1375	−	1.06549i	−0.462230	−	0.0485823i
$482$	−13.6115	+	13.6115i	−0.619986	+	0.619986i
$483$	4.04419	−	7.87606i	0.184017	−	0.358373i
$484$	−7.04508	−	2.28908i	−0.320231	−	0.104049i
$485$	3.59083	−	5.39348i	0.163051	−	0.244905i
$486$	−5.26702	+	24.7794i	−0.238917	+	1.12401i
$487$	1.98949	−	37.9617i	0.0901523	−	1.72021i	−0.462350	−	0.886698i	$-0.652994\pi$
$487$	1.98949	−	37.9617i	0.0901523	−	1.72021i	0.552502	−	0.833511i	$-0.313673\pi$
$488$	−1.06683	−	0.692809i	−0.0482932	−	0.0313620i
$489$	−6.58923	−	20.2796i	−0.297975	−	0.917074i
$490$	28.2677	+	1.98347i	1.27701	+	0.0896038i
$491$	11.9197	−	36.6850i	0.537927	−	1.65557i	−0.199311	−	0.979936i	$-0.563870\pi$
$491$	11.9197	−	36.6850i	0.537927	−	1.65557i	0.737238	−	0.675633i	$-0.236130\pi$
$492$	−11.0206	+	8.92429i	−0.496846	+	0.402338i
$493$	−37.8667	+	10.1463i	−1.70543	+	0.456968i
$494$	−7.21436	−	16.2037i	−0.324589	−	0.729040i
$495$	−3.10458	+	6.76396i	−0.139541	+	0.304017i
$496$	−9.87143	−	13.5869i	−0.443240	−	0.610068i
$497$	−4.28825	−	4.31521i	−0.192354	−	0.193564i
$498$	19.7952	+	10.0862i	0.887044	+	0.451972i
$499$	2.65771	−	1.53443i	0.118976	−	0.0686906i	−0.439331	−	0.898325i	$-0.644785\pi$
$499$	2.65771	−	1.53443i	0.118976	−	0.0686906i	0.558307	+	0.829635i	$0.311451\pi$
$500$	5.35904	+	13.2400i	0.239664	+	0.592111i
$501$	−21.9478	+	38.0147i	−0.980555	+	1.69837i
$502$	−0.735677	−	14.0376i	−0.0328349	−	0.626527i
$503$	30.3701	+	4.81016i	1.35414	+	0.214474i	0.790963	−	0.611864i	$-0.209580\pi$
$503$	30.3701	+	4.81016i	1.35414	+	0.214474i	0.563174	+	0.826338i	$0.309580\pi$
$504$	4.38129	−	2.51126i	0.195158	−	0.111861i
$505$	−4.92799	−	6.94837i	−0.219293	−	0.309198i
$506$	0.683945	−	6.50731i	0.0304051	−	0.289285i
$507$	−5.13817	−	19.1759i	−0.228194	−	0.851632i
$508$	5.82996	−	15.1876i	0.258663	−	0.673839i
$509$	11.1394	−	2.36776i	0.493747	−	0.104949i	0.0456925	−	0.998956i	$-0.485451\pi$
$509$	11.1394	−	2.36776i	0.493747	−	0.104949i	0.448054	+	0.894006i	$0.352117\pi$
$510$	4.61184	+	31.4386i	0.204216	+	1.39212i
$511$	15.4753	−	13.8464i	0.684585	−	0.612530i
$512$	−16.1456	+	8.22662i	−0.713543	+	0.363569i
$513$	−3.66797	+	5.64818i	−0.161945	+	0.249373i
$514$	−36.0976	−	7.67278i	−1.59220	−	0.338432i
$515$	2.44190	−	38.2314i	0.107603	−	1.68468i
$516$	4.97865	+	23.4227i	0.219173	+	1.03113i
$517$	14.4849	−	2.29419i	0.637047	−	0.100898i
$518$	−3.72703	+	9.61905i	−0.163756	+	0.422637i
$519$	19.5687	−	26.9339i	0.858969	−	1.18227i
$520$	13.5716	−	2.72306i	0.595154	−	0.119414i
$521$	−34.8820	+	3.66624i	−1.52821	+	0.160621i	−0.831009	−	0.556259i	$-0.812236\pi$
$521$	−34.8820	+	3.66624i	−1.52821	+	0.160621i	−0.697197	+	0.716880i	$0.745570\pi$
$522$	17.5358	−	21.6549i	0.767521	−	0.947810i
$523$	−20.9061	+	1.09564i	−0.914160	+	0.0479091i	−0.503612	−	0.863930i	$-0.667996\pi$
$523$	−20.9061	+	1.09564i	−0.914160	+	0.0479091i	−0.410548	+	0.911839i	$0.634662\pi$
$524$	−18.3066			−0.799726
$525$	5.09621	+	27.4666i	0.222417	+	1.19874i
$526$	35.4852			1.54723
$527$	12.6628	−	0.663629i	0.551600	−	0.0289082i
$528$	14.9213	−	18.4263i	0.649366	−	0.801900i
$529$	20.3766	−	2.14166i	0.885938	−	0.0931158i
$530$	8.04658	+	14.3123i	0.349521	+	0.621685i
$531$	10.8979	−	14.9996i	0.472927	−	0.650928i
$532$	−6.91410	+	1.07289i	−0.299764	+	0.0465155i
$533$	−24.5721	+	3.89184i	−1.06434	+	0.168574i
$534$	−5.31492	−	25.0047i	−0.229999	−	1.08206i
$535$	−9.12278	+	11.0062i	−0.394412	+	0.475839i
$536$	13.1265	+	2.79013i	0.566980	+	0.120515i
$537$	18.4284	−	28.3772i	0.795244	−	1.22457i
$538$	33.4416	−	17.0394i	1.44177	−	0.734619i
$539$	15.8877	−	1.56926i	0.684333	−	0.0675927i
$540$	6.49637	+	6.64653i	0.279559	+	0.286021i
$541$	−14.0929	+	2.99554i	−0.605901	+	0.128788i	−0.500639	−	0.865656i	$-0.666901\pi$
$541$	−14.0929	+	2.99554i	−0.605901	+	0.128788i	−0.105262	+	0.994445i	$0.533568\pi$
$542$	3.45582	−	9.00272i	0.148440	−	0.386700i
$543$	4.65155	+	17.3598i	0.199617	+	0.744982i
$544$	2.44646	−	23.2765i	0.104891	−	0.997972i
$545$	−19.7368	+	6.16450i	−0.845433	+	0.264058i
$546$	−47.8731	−	0.150023i	−2.04878	−	0.00642038i
$547$	38.1667	+	6.04502i	1.63189	+	0.258466i	0.904096	−	0.427328i	$-0.140545\pi$
$547$	38.1667	+	6.04502i	1.63189	+	0.258466i	0.727795	+	0.685795i	$0.240545\pi$
$548$	−0.159452	−	3.04252i	−0.00681144	−	0.129970i
$549$	−0.709658	+	1.22916i	−0.0302875	+	0.0524595i
$550$	10.8456	+	17.5668i	0.462458	+	0.749052i
$551$	18.9073	−	10.9161i	0.805476	−	0.465042i
$552$	−3.89977	−	1.98703i	−0.165985	−	0.0845736i
$553$	−29.5023	−	8.00429i	−1.25456	−	0.340377i
$554$	−5.67716	−	7.81394i	−0.241199	−	0.331983i
$555$	−10.1010	−	1.17849i	−0.428765	−	0.0500239i
$556$	−10.1719	−	22.8465i	−0.431386	−	0.968908i
$557$	−25.1570	+	6.74079i	−1.06593	+	0.285616i	−0.748822	−	0.662772i	$-0.769380\pi$
$557$	−25.1570	+	6.74079i	−1.06593	+	0.285616i	−0.317113	+	0.948388i	$0.602713\pi$
$558$	−7.00436	+	5.67202i	−0.296518	+	0.240116i
$559$	−12.9818	+	39.9540i	−0.549073	+	1.68987i
$560$	1.94752	−	29.0595i	0.0822979	−	1.22799i
$561$	5.53199	+	17.0257i	0.233561	+	0.718826i
$562$	36.3550	+	23.6092i	1.53354	+	0.995894i
$563$	−0.268639	+	5.12594i	−0.0113218	+	0.216032i	0.987110	+	0.160045i	$0.0511640\pi$
$563$	−0.268639	+	5.12594i	−0.0113218	+	0.216032i	−0.998431	+	0.0559873i	$0.982169\pi$
$564$	−3.60676	+	16.9685i	−0.151872	+	0.714501i
$565$	0.144452	+	3.52684i	0.00607714	+	0.148375i
$566$	−5.81151	−	1.88827i	−0.244276	−	0.0793701i
$567$	16.1303	+	25.0098i	0.677411	+	1.05031i
$568$	−2.12656	+	2.12656i	−0.0892287	+	0.0892287i
$569$	8.90580	+	0.936038i	0.373351	+	0.0392407i	0.289346	−	0.957225i	$-0.406562\pi$
$569$	8.90580	+	0.936038i	0.373351	+	0.0392407i	0.0840048	+	0.996465i	$0.473229\pi$
$570$	−7.01238	−	16.2471i	−0.293716	−	0.680516i
$571$	2.13250	+	20.2894i	0.0892423	+	0.849084i	0.943975	+	0.330016i	$0.107054\pi$
$571$	2.13250	+	20.2894i	0.0892423	+	0.849084i	−0.854733	+	0.519068i	$0.826279\pi$
$572$	−12.8747	+	4.94212i	−0.538317	+	0.206641i
$573$	−11.5909	+	22.7483i	−0.484215	+	0.950325i
$574$	−2.71022	+	25.0312i	−0.113122	+	1.04478i
$575$	5.72922	−	5.47320i	0.238925	−	0.228248i
$576$	1.13362	+	1.96349i	0.0472342	+	0.0818120i
$577$	27.3014	−	17.7297i	1.13657	−	0.738097i	0.167742	−	0.985831i	$-0.446352\pi$
$577$	27.3014	−	17.7297i	1.13657	−	0.738097i	0.968828	+	0.247733i	$0.0796857\pi$
$578$	−4.47972	−	3.62760i	−0.186332	−	0.150888i
$579$	16.9418	+	7.54295i	0.704075	+	0.313474i
$580$	−8.98241	−	28.7589i	−0.372974	−	1.19415i
$581$	14.6374	−	4.70532i	0.607262	−	0.195210i
$582$	7.83340	+	7.83340i	0.324705	+	0.324705i
$583$	5.82150	+	7.18895i	0.241102	+	0.297736i
$584$	−6.86890	−	7.62869i	−0.284237	−	0.315677i
$585$	−3.82666	−	14.9630i	−0.158213	−	0.618645i
$586$	−25.1999	−	22.6901i	−1.04100	−	0.937318i
$587$	18.8559	+	37.0069i	0.778268	+	1.52744i	0.848074	+	0.529877i	$0.177762\pi$
$587$	18.8559	+	37.0069i	0.778268	+	1.52744i	−0.0698062	+	0.997561i	$0.522238\pi$
$588$	−5.00197	+	18.2103i	−0.206278	+	0.750979i
$589$	−6.71609	+	2.18219i	−0.276732	+	0.0899155i
$590$	−17.8815	−	48.2224i	−0.736169	−	1.98529i
$591$	15.4724	−	13.9314i	0.636449	−	0.573062i
$592$	9.89829	+	3.79960i	0.406817	+	0.156162i
$593$	4.38392	−	16.3610i	0.180026	−	0.671866i	−0.815615	−	0.578595i	$-0.803601\pi$
$593$	4.38392	−	16.3610i	0.180026	−	0.671866i	0.995641	−	0.0932706i	$-0.0297322\pi$
$594$	10.8679	+	7.89600i	0.445916	+	0.323977i
$595$	17.6002	+	13.1830i	0.721539	+	0.540451i
$596$	24.6157	−	17.8844i	1.00830	−	0.732573i
$597$	3.80405	+	9.90990i	0.155690	+	0.405585i
$598$	7.39533	+	11.3878i	0.302418	+	0.465682i
$599$	−2.39394	−	1.38214i	−0.0978138	−	0.0564728i	0.450295	−	0.892880i	$-0.351319\pi$
$599$	−2.39394	−	1.38214i	−0.0978138	−	0.0564728i	−0.548109	+	0.836407i	$0.684652\pi$
$600$	13.5701	−	2.56184i	0.553997	−	0.104587i
$601$			35.9435i			1.46616i	0.680140	+	0.733082i	$0.261919\pi$
$601$			35.9435i			1.46616i	−0.680140	+	0.733082i	$0.738081\pi$
$602$	35.5834	+	23.2670i	1.45027	+	0.948292i
$603$	2.34235	−	14.7890i	0.0953880	−	0.602256i
$604$	4.38896	−	9.85777i	0.178584	−	0.401107i
$605$	−8.56491	−	9.73367i	−0.348213	−	0.395730i
$606$	13.3051	−	5.92382i	0.540483	−	0.240639i
$607$	−14.4233	−	3.86472i	−0.585425	−	0.156864i	−0.0460635	−	0.998939i	$-0.514668\pi$
$607$	−14.4233	−	3.86472i	−0.585425	−	0.156864i	−0.539361	+	0.842074i	$0.681334\pi$
$608$	2.03902	+	12.8738i	0.0826930	+	0.522103i
$609$	−5.97576	−	58.6222i	−0.242150	−	2.37549i
$610$	1.74724	+	3.52822i	0.0707435	+	0.142853i
$611$	−20.3643	+	22.6169i	−0.823852	+	0.914980i
$612$	−6.92039	−	0.362682i	−0.279740	−	0.0146606i
$613$	48.1939	+	2.52574i	1.94654	+	0.102014i	0.984988	−	0.172625i	$-0.0552249\pi$
$613$	48.1939	+	2.52574i	1.94654	+	0.102014i	0.961548	+	0.274639i	$0.0885582\pi$
$614$	1.82547	−	2.02739i	0.0736700	−	0.0818189i
$615$	−24.5576	+	3.60244i	−0.990257	+	0.145264i
$616$	−0.800369	−	7.85161i	−0.0322478	−	0.316350i
$617$	4.01084	+	25.3234i	0.161470	+	1.01948i	0.926721	+	0.375750i	$0.122615\pi$
$617$	4.01084	+	25.3234i	0.161470	+	1.01948i	−0.765251	+	0.643732i	$0.777385\pi$
$618$	63.2665	+	16.9522i	2.54495	+	0.681917i
$619$	−1.31576	+	0.585813i	−0.0528847	+	0.0235458i	−0.433009	−	0.901390i	$-0.642548\pi$
$619$	−1.31576	+	0.585813i	−0.0528847	+	0.0235458i	0.380124	+	0.924936i	$0.375881\pi$
$620$	0.907873	+	9.70297i	0.0364610	+	0.389681i
$621$	2.09698	−	4.70990i	0.0841491	−	0.189002i
$622$	−1.41771	+	8.95108i	−0.0568451	+	0.358906i
$623$	−14.8068	−	9.68175i	−0.593222	−	0.387891i
$624$			49.2036i			1.96972i
$625$	−3.74632	+	24.7177i	−0.149853	+	0.988708i
$626$	−53.0539	−	30.6307i	−2.12046	−	1.22425i
$627$	−5.42990	−	8.36131i	−0.216849	−	0.333919i
$628$	7.47343	+	19.4689i	0.298222	+	0.776896i
$629$	−6.47635	+	4.70534i	−0.258229	+	0.187614i
$630$	−15.6286	−	0.227547i	−0.622658	−	0.00906568i
$631$	−9.94266	−	7.22377i	−0.395811	−	0.287574i	0.372021	−	0.928224i	$-0.378665\pi$
$631$	−9.94266	−	7.22377i	−0.395811	−	0.287574i	−0.767833	+	0.640650i	$0.778665\pi$
$632$	−3.91119	+	14.5967i	−0.155579	+	0.580627i
$633$	33.0054	+	12.6696i	1.31185	+	0.503571i
$634$	−18.1125	+	16.3086i	−0.719340	+	0.647696i
$635$	22.3315	−	17.6651i	0.886198	−	0.701018i
$636$	−10.4066	+	3.38132i	−0.412650	+	0.134078i
$637$	−23.5734	+	23.2797i	−0.934012	+	0.922377i
$638$	−19.7704	−	38.8016i	−0.782718	−	1.53617i
$639$	2.49368	+	2.24532i	0.0986487	+	0.0888236i
$640$	−21.8259	−	1.39405i	−0.862745	−	0.0551047i
$641$	−12.3273	−	13.6908i	−0.486899	−	0.540756i	0.448764	−	0.893650i	$-0.351864\pi$
$641$	−12.3273	−	13.6908i	−0.486899	−	0.540756i	−0.935663	+	0.352894i	$0.885198\pi$
$642$	−15.3814	−	18.9944i	−0.607055	−	0.749651i
$643$	−6.68684	−	6.68684i	−0.263703	−	0.263703i	0.562853	−	0.826557i	$-0.309704\pi$
$643$	−6.68684	−	6.68684i	−0.263703	−	0.263703i	−0.826557	+	0.562853i	$0.809704\pi$
$644$	5.09933	−	1.63922i	0.200942	−	0.0645945i
$645$	−13.4061	+	39.7102i	−0.527865	+	1.56359i
$646$	−12.7254	−	5.66571i	−0.500674	−	0.222915i
$647$	−14.9356	−	12.0946i	−0.587178	−	0.475488i	0.289096	−	0.957300i	$-0.406645\pi$
$647$	−14.9356	−	12.0946i	−0.587178	−	0.475488i	−0.876274	+	0.481812i	$0.839979\pi$
$648$	12.3385	−	8.01272i	0.484702	−	0.314769i
$649$	−14.4880	−	25.0939i	−0.568703	−	0.985022i
$650$	−40.4329	−	14.1667i	−1.58591	−	0.555663i
$651$	−2.05168	+	18.9491i	−0.0804119	+	0.742673i
$652$	5.85655	−	11.4941i	0.229360	−	0.450145i
$653$	−28.5075	+	10.9430i	−1.11558	+	0.428233i	−0.845162	−	0.534510i	$-0.820496\pi$
$653$	−28.5075	+	10.9430i	−1.11558	+	0.428233i	−0.270421	+	0.962742i	$0.587163\pi$
$654$	−3.69530	−	35.1584i	−0.144498	−	1.37480i
$655$	−27.5640	−	16.3368i	−1.07701	−	0.638330i
$656$	25.7353	+	2.70489i	1.00480	+	0.105608i
$657$	−8.09908	+	8.09908i	−0.315975	+	0.315975i
$658$	16.6938	+	25.8834i	0.650791	+	1.00904i
$659$	−38.5495	−	12.5255i	−1.50168	−	0.487924i	−0.561169	−	0.827701i	$-0.689648\pi$
$659$	−38.5495	−	12.5255i	−1.50168	−	0.487924i	−0.940506	+	0.339777i	$0.889648\pi$
$660$	−12.9001	+	4.78353i	−0.502137	+	0.186199i
$661$	−3.84813	+	18.1040i	−0.149675	+	0.704165i	0.837747	+	0.546059i	$0.183872\pi$
$661$	−3.84813	+	18.1040i	−0.149675	+	0.704165i	−0.987422	+	0.158107i	$0.949461\pi$
$662$	−1.16859	+	22.2980i	−0.0454184	+	0.866635i
$663$	−31.1568	−	20.2334i	−1.21003	−	0.785801i
$664$	−2.34873	−	7.22866i	−0.0911485	−	0.280526i
$665$	−11.3679	−	4.55471i	−0.440829	−	0.176624i
$666$	1.75831	−	5.41152i	0.0681331	−	0.209692i
$667$	−12.9887	+	10.5180i	−0.502924	+	0.407259i
$668$	−25.6512	+	6.87321i	−0.992474	+	0.265933i
$669$	−9.13865	−	20.5257i	−0.353321	−	0.793571i
$670$	−30.5476	−	28.1437i	−1.18016	−	1.08729i
$671$	1.30381	+	1.79454i	0.0503329	+	0.0692773i
$672$	33.9527	+	9.21172i	1.30975	+	0.355350i
$673$	−5.00671	−	2.55105i	−0.192994	−	0.0983356i	0.354823	−	0.934934i	$-0.384541\pi$
$673$	−5.00671	−	2.55105i	−0.192994	−	0.0983356i	−0.547817	+	0.836598i	$0.684541\pi$
$674$	−26.7123	+	15.4224i	−1.02892	+	0.594047i
$675$	3.85015	+	15.8050i	0.148192	+	0.608333i
$676$	6.00516	−	10.4012i	0.230968	−	0.400048i
$677$	1.29931	+	24.7924i	0.0499366	+	0.952847i	0.902625	+	0.430428i	$0.141637\pi$
$677$	1.29931	+	24.7924i	0.0499366	+	0.952847i	−0.852688	+	0.522420i	$0.825029\pi$
$678$	−5.96067	−	0.944077i	−0.228918	−	0.0362571i
$679$	7.66659	+	0.0240253i	0.294217	+	0.000922005i
$680$	6.48971	−	8.72103i	0.248869	−	0.334436i
$681$	−0.794891	+	7.56288i	−0.0304603	+	0.289810i
$682$	3.64567	+	13.6058i	0.139600	+	0.520994i
$683$	−13.6949	+	35.6764i	−0.524020	+	1.36512i	0.374925	+	0.927055i	$0.377669\pi$
$683$	−13.6949	+	35.6764i	−0.524020	+	1.36512i	−0.898944	+	0.438063i	$0.855665\pi$
$684$	3.77498	−	0.802397i	0.144340	−	0.0306804i
$685$	2.47506	−	4.72338i	0.0945671	−	0.180471i
$686$	16.4908	+	29.1934i	0.629623	+	1.11461i
$687$	−15.5596	+	7.92800i	−0.593635	+	0.302472i
$688$	23.7988	−	36.6469i	0.907320	−	1.39715i
$689$	−18.7771	−	3.99120i	−0.715352	−	0.152053i
$690$	7.24781	+	11.4448i	0.275919	+	0.435696i
$691$	−4.28899	−	20.1781i	−0.163161	−	0.767612i	−0.981284	−	0.192568i	$-0.938318\pi$
$691$	−4.28899	−	20.1781i	−0.163161	−	0.767612i	0.818123	−	0.575044i	$-0.195015\pi$
$692$	19.8932	−	3.15078i	0.756226	−	0.119775i
$693$	−8.70185	+	1.35030i	−0.330556	+	0.0512936i
$694$	18.3443	−	25.2488i	0.696341	−	0.958431i
$695$	5.07247	−	43.4771i	0.192410	−	1.64918i
$696$	−28.9704	+	3.04491i	−1.09812	+	0.115417i
$697$	−12.2956	+	15.1839i	−0.465731	+	0.575129i
$698$	−24.3461	+	1.27593i	−0.921515	+	0.0482945i
$699$	8.30402			0.314087
$700$	−9.56976	+	13.9299i	−0.361703	+	0.526502i
$701$	−16.8050			−0.634717			−0.317359	−	0.948306i	$-0.602796\pi$
$701$	−16.8050			−0.634717			−0.317359	+	0.948306i	$0.602796\pi$
$702$	−27.8391	+	1.45899i	−1.05072	+	0.0550659i
$703$	2.80562	−	3.46465i	0.105816	−	0.130672i
$704$	3.52393	−	0.370380i	0.132813	−	0.0139592i
$705$	−20.5733	+	22.3305i	−0.774835	+	0.841017i
$706$	−9.48757	+	13.0585i	−0.357069	+	0.491464i
$707$	3.64154	−	9.39841i	0.136954	−	0.353464i
$708$	33.8531	−	5.36181i	1.27228	−	0.201509i
$709$	3.71391	+	17.4726i	0.139479	+	0.656197i	0.991219	+	0.132232i	$0.0422144\pi$
$709$	3.71391	+	17.4726i	0.139479	+	0.656197i	−0.851740	+	0.523965i	$0.824452\pi$
$710$	9.01808	−	2.30629i	0.338442	−	0.0865535i
$711$	16.4927	+	3.50563i	0.618524	+	0.131471i
$712$	−4.76320	+	7.33469i	−0.178508	+	0.274879i
$713$	4.81676	−	2.45426i	0.180389	−	0.0919129i
$714$	−28.0185	+	25.0694i	−1.04857	+	0.938201i
$715$	−23.7956	−	4.04805i	−0.889905	−	0.151388i
$716$	20.0228	−	4.25599i	0.748289	−	0.159054i
$717$	10.4019	−	27.0978i	0.388466	−	1.01199i
$718$	−10.2071	−	38.0935i	−0.380927	−	1.42164i
$719$	−4.03131	+	38.3553i	−0.150342	+	1.43041i	0.615882	+	0.787839i	$0.288800\pi$
$719$	−4.03131	+	38.3553i	−0.150342	+	1.43041i	−0.766224	+	0.642574i	$0.777867\pi$
$720$	−0.183532	+	16.0635i	−0.00683982	+	0.598652i
$721$	39.3262	−	22.5410i	1.46459	−	0.839470i
$722$	−26.3121	−	4.16742i	−0.979233	−	0.155095i
$723$	−1.17512	−	22.4226i	−0.0437031	−	0.833905i
$724$	−5.43644	+	9.41619i	−0.202044	+	0.349950i
$725$	12.1397	−	51.3179i	0.450858	−	1.90590i
$726$	19.1974	−	11.0836i	0.712482	−	0.411352i
$727$	−24.0437	−	12.2509i	−0.891730	−	0.454359i	−0.0528040	−	0.998605i	$-0.516816\pi$
$727$	−24.0437	−	12.2509i	−0.891730	−	0.454359i	−0.838926	+	0.544246i	$0.816816\pi$
$728$	11.5448	+	11.6174i	0.427878	+	0.430568i
$729$	2.46622	+	3.39447i	0.0913416	+	0.125721i
$730$	6.25042	+	31.1518i	0.231338	+	1.15298i
$731$	13.4191	+	30.1398i	0.496324	+	1.11476i
$732$	−2.53443	+	0.679097i	−0.0936751	+	0.0251002i
$733$	17.4923	−	14.1650i	0.646094	−	0.523197i	−0.249326	−	0.968420i	$-0.580209\pi$
$733$	17.4923	−	14.1650i	0.646094	−	0.523197i	0.895420	+	0.445223i	$0.146876\pi$
$734$	−6.64700	+	20.4574i	−0.245345	+	0.755095i
$735$	−23.7822	+	22.9553i	−0.877221	+	0.846717i
$736$	−3.08344	−	9.48984i	−0.113657	−	0.349800i
$737$	−19.6258	−	12.7451i	−0.722925	−	0.469473i
$738$	0.726809	−	13.8683i	0.0267542	−	0.510500i
$739$	−2.85454	+	13.4296i	−0.105006	+	0.494015i	0.893943	+	0.448181i	$0.147928\pi$
$739$	−2.85454	+	13.4296i	−0.105006	+	0.494015i	−0.998949	+	0.0458340i	$0.985405\pi$
$740$	−3.81695	−	4.82524i	−0.140314	−	0.177379i
$741$	19.6767	+	6.39334i	0.722840	+	0.234865i
$742$	−8.87405	+	17.2822i	−0.325777	+	0.634450i
$743$	16.3770	−	16.3770i	0.600813	−	0.600813i	−0.339715	−	0.940528i	$-0.610331\pi$
$743$	16.3770	−	16.3770i	0.600813	−	0.600813i	0.940528	+	0.339715i	$0.110331\pi$
$744$	9.37058	+	0.984887i	0.343542	+	0.0361077i
$745$	53.0237	−	4.96124i	1.94264	−	0.181766i
$746$	3.77334	+	35.9009i	0.138152	+	1.31443i
$747$	−7.91731	+	3.03917i	−0.289679	+	0.111197i
$748$	−4.91686	+	9.64989i	−0.179778	+	0.352835i
$749$	−16.8164	−	1.82077i	−0.614457	−	0.0665295i
$750$	−40.1745	−	14.5936i	−1.46697	−	0.532882i
$751$	−6.00270	−	10.3970i	−0.219042	−	0.379391i	0.735474	−	0.677553i	$-0.236960\pi$
$751$	−6.00270	−	10.3970i	−0.219042	−	0.379391i	−0.954515	+	0.298162i	$0.903626\pi$
$752$	26.5487	−	17.2409i	0.968131	−	0.628711i
$753$	12.7424	+	10.3186i	0.464358	+	0.376030i
$754$	82.5584	+	36.7574i	3.00660	+	1.33862i
$755$	15.4055	−	10.9260i	0.560663	−	0.397639i
$756$	−2.32007	+	10.7493i	−0.0843803	+	0.390950i
$757$	−31.8390	−	31.8390i	−1.15721	−	1.15721i	−0.985073	−	0.172134i	$-0.944934\pi$
$757$	−31.8390	−	31.8390i	−1.15721	−	1.15721i	−0.172134	−	0.985073i	$-0.555066\pi$
$758$	−23.1753	−	28.6191i	−0.841764	−	1.03949i
$759$	5.10691	+	5.67180i	0.185369	+	0.205873i
$760$	−2.23399	+	5.62675i	−0.0810354	+	0.204104i
$761$	22.6106	+	20.3586i	0.819632	+	0.738000i	0.968005	−	0.250931i	$-0.0807368\pi$
$761$	22.6106	+	20.3586i	0.819632	+	0.738000i	−0.148373	+	0.988932i	$0.547404\pi$
$762$	22.1012	+	43.3760i	0.800641	+	1.57135i
$763$	−18.9649	−	15.4561i	−0.686576	−	0.559550i
$764$	−14.6899	+	4.77302i	−0.531460	+	0.172682i
$765$	−10.0963	−	6.72183i	−0.365032	−	0.243028i
$766$	−14.8077	+	13.3329i	−0.535024	+	0.481738i

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.80792 + 0.0947490i) q^{2} +(1.32895 - 1.64111i) q^{3} +(1.27055 - 0.133540i) q^{4} +(2.03223 + 0.932769i) q^{5} +(-2.24713 + 3.09291i) q^{6} +(0.405696 + 2.61446i) q^{7} +(1.29182 - 0.204604i) q^{8} +(-0.303414 - 1.42745i) q^{9} +O(q^{10})\)	\(q+(-1.80792 + 0.0947490i) q^{2} +(1.32895 - 1.64111i) q^{3} +(1.27055 - 0.133540i) q^{4} +(2.03223 + 0.932769i) q^{5} +(-2.24713 + 3.09291i) q^{6} +(0.405696 + 2.61446i) q^{7} +(1.29182 - 0.204604i) q^{8} +(-0.303414 - 1.42745i) q^{9} +(-3.76248 - 1.49382i) q^{10} +(-2.23088 - 0.474189i) q^{11} +(1.46934 - 2.26258i) q^{12} +(4.21711 - 2.14873i) q^{13} +(-0.981183 - 4.68830i) q^{14} +(4.23149 - 2.09551i) q^{15} +(-4.81539 + 1.02354i) q^{16} +(1.33205 - 3.47011i) q^{17} +(0.683798 + 2.55197i) q^{18} +(-0.216377 + 2.05869i) q^{19} +(2.70661 + 0.913747i) q^{20} +(4.82977 + 2.80869i) q^{21} +(4.07818 + 0.645921i) q^{22} +(-0.0829354 - 1.58250i) q^{23} +(1.38098 - 2.39193i) q^{24} +(3.25988 + 3.79119i) q^{25} +(-7.42061 + 4.28429i) q^{26} +(2.89883 + 1.47703i) q^{27} +(0.864593 + 3.26763i) q^{28} +(-6.19928 - 8.53257i) q^{29} +(-7.45165 + 4.18944i) q^{30} +(1.38755 + 3.11648i) q^{31} +(6.08214 - 1.62970i) q^{32} +(-3.74292 + 3.03095i) q^{33} +(-2.07945 + 6.39988i) q^{34} +(-1.61422 + 5.69160i) q^{35} +(-0.576126 - 1.77313i) q^{36} +(-1.80623 - 1.17298i) q^{37} +(0.196133 - 3.74244i) q^{38} +(2.07801 - 9.77629i) q^{39} +(2.81612 + 0.789168i) q^{40} +(-4.99913 - 1.62432i) q^{41} +(-8.99795 - 4.62026i) q^{42} +(-6.27631 + 6.27631i) q^{43} +(-2.89777 - 0.304568i) q^{44} +(0.714876 - 3.18392i) q^{45} +(0.299881 + 2.85318i) q^{46} +(-6.00311 + 2.30438i) q^{47} +(-4.71964 + 9.26282i) q^{48} +(-6.67082 + 2.12135i) q^{49} +(-6.25282 - 6.54530i) q^{50} +(-3.92461 - 6.79762i) q^{51} +(5.07112 - 3.29322i) q^{52} +(-3.15205 - 2.55248i) q^{53} +(-5.38080 - 2.39569i) q^{54} +(-4.09135 - 3.04456i) q^{55} +(1.05902 + 3.29441i) q^{56} +(3.09098 + 3.09098i) q^{57} +(12.0162 + 14.8388i) q^{58} +(8.50113 + 9.44146i) q^{59} +(5.09650 - 3.22753i) q^{60} +(-0.722763 - 0.650779i) q^{61} +(-2.80386 - 5.50288i) q^{62} +(3.60892 - 1.37238i) q^{63} +(-1.47757 + 0.480090i) q^{64} +(10.5744 - 0.433105i) q^{65} +(6.47971 - 5.83436i) q^{66} +(9.57888 + 3.67699i) q^{67} +(1.22904 - 4.58683i) q^{68} +(-2.70728 - 1.96695i) q^{69} +(2.37911 - 10.4429i) q^{70} +(-1.86024 + 1.35154i) q^{71} +(-0.684019 - 1.78193i) q^{72} +(-4.27467 - 6.58242i) q^{73} +(3.37666 + 1.94951i) q^{74} +(10.5540 - 0.311540i) q^{75} +2.64456i q^{76} +(0.334689 - 6.02493i) q^{77} +(-2.83059 + 17.8716i) q^{78} +(-4.69941 + 10.5550i) q^{79} +(-10.7407 - 2.41158i) q^{80} +(10.2759 - 4.57511i) q^{81} +(9.19193 + 2.46297i) q^{82} +(-0.909079 - 5.73970i) q^{83} +(6.51154 + 2.92361i) q^{84} +(5.94383 - 5.80955i) q^{85} +(10.7524 - 11.9417i) q^{86} +(-22.2414 - 1.16562i) q^{87} +(-2.97892 - 0.156119i) q^{88} +(-4.47423 + 4.96914i) q^{89} +(-0.990766 + 5.82400i) q^{90} +(7.32863 + 10.1538i) q^{91} +(-0.316702 - 1.99958i) q^{92} +(6.95847 + 1.86452i) q^{93} +(10.6348 - 4.73492i) q^{94} +(-2.36000 + 3.98188i) q^{95} +(5.40831 - 12.1473i) q^{96} +(0.453302 - 2.86204i) q^{97} +(11.8593 - 4.46729i) q^{98} +3.32835i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22} - 40 q^{23} + 2 q^{25} - 48 q^{26} + 22 q^{28} - 58 q^{30} - 18 q^{31} + 8 q^{32} - 30 q^{33} - 2 q^{35} + 40 q^{36} - 10 q^{37} + 72 q^{38} + 30 q^{39} - 48 q^{40} + 6 q^{42} - 108 q^{43} - 10 q^{44} + 186 q^{45} - 6 q^{46} - 54 q^{47} - 248 q^{50} - 16 q^{51} + 216 q^{52} + 50 q^{53} - 30 q^{54} + 4 q^{56} - 216 q^{57} - 4 q^{58} + 90 q^{59} + 96 q^{60} - 18 q^{61} - 66 q^{63} - 100 q^{64} + 14 q^{65} - 90 q^{66} + 4 q^{67} + 342 q^{68} - 60 q^{70} - 24 q^{71} + 58 q^{72} - 6 q^{73} + 216 q^{75} - 80 q^{77} - 132 q^{78} - 10 q^{79} - 6 q^{80} - 10 q^{81} + 216 q^{82} + 20 q^{84} - 48 q^{85} - 6 q^{86} - 48 q^{87} - 122 q^{88} + 120 q^{89} - 12 q^{91} - 4 q^{92} + 106 q^{93} - 30 q^{94} - 98 q^{95} - 90 q^{96} + 222 q^{98}+O(q^{100}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Introduction

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