LMFDB - Embedded newform 175.2.x.a.3.15

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			3.15
Character	$\chi$	$=$	175.3
Dual form			175.2.x.a.117.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.986015 - 1.51833i) q^{2} +(-0.756771 + 1.97146i) q^{3} +(-0.519626 - 1.16710i) q^{4} +(0.208311 - 2.22634i) q^{5} +(2.24713 + 3.09291i) q^{6} +(2.61446 - 0.405696i) q^{7} +(1.29182 + 0.204604i) q^{8} +(-1.08450 - 0.976490i) q^{9} +O(q^{10})$	\(q+(0.986015 - 1.51833i) q^{2} +(-0.756771 + 1.97146i) q^{3} +(-0.519626 - 1.16710i) q^{4} +(0.208311 - 2.22634i) q^{5} +(2.24713 + 3.09291i) q^{6} +(2.61446 - 0.405696i) q^{7} +(1.29182 + 0.204604i) q^{8} +(-1.08450 - 0.976490i) q^{9} +(-3.17493 - 2.51149i) q^{10} +(1.52610 + 1.69491i) q^{11} +(2.69413 - 0.141193i) q^{12} +(-4.21711 - 2.14873i) q^{13} +(1.96192 - 4.36964i) q^{14} +(4.23149 + 2.09551i) q^{15} +(3.29411 - 3.65848i) q^{16} +(-2.33918 + 2.88864i) q^{17} +(-2.55197 + 0.683798i) q^{18} +(-1.89106 - 0.841955i) q^{19} +(-2.70661 + 0.913747i) q^{20} +(-1.17874 + 5.46132i) q^{21} +(4.07818 - 0.645921i) q^{22} +(-1.32902 - 0.863075i) q^{23} +(-1.38098 + 2.39193i) q^{24} +(-4.91321 - 0.927545i) q^{25} +(-7.42061 + 4.28429i) q^{26} +(-2.89883 + 1.47703i) q^{27} +(-1.83203 - 2.84053i) q^{28} +(-6.19928 + 8.53257i) q^{29} +(7.35399 - 4.35860i) q^{30} +(3.39273 - 0.356590i) q^{31} +(-1.62970 - 6.08214i) q^{32} +(-4.49634 + 1.72598i) q^{33} +(2.07945 + 6.39988i) q^{34} +(-0.358596 - 5.90520i) q^{35} +(-0.576126 + 1.77313i) q^{36} +(-0.112715 - 2.15073i) q^{37} +(-3.14298 + 2.04108i) q^{38} +(7.42751 - 6.68776i) q^{39} +(0.724620 - 2.83342i) q^{40} +(4.99913 - 1.62432i) q^{41} +(7.12982 + 7.17465i) q^{42} +(-6.27631 - 6.27631i) q^{43} +(1.18512 - 2.66183i) q^{44} +(-2.39992 + 2.21106i) q^{45} +(-2.62087 + 1.16688i) q^{46} +(-4.99721 + 4.04666i) 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} +(-0.316455 + 6.03833i) q^{52} +(3.78654 + 1.45352i) q^{53} +(-0.615674 + 5.85775i) q^{54} +(4.09135 - 3.04456i) q^{55} +(3.46042 + 0.0108441i) q^{56} +(3.09098 - 3.09098i) q^{57} +(6.84268 + 17.8258i) q^{58} +(12.4271 + 2.64146i) q^{59} +(0.246872 - 6.02746i) q^{60} +(0.202209 + 0.951321i) q^{61} +(2.80386 - 5.50288i) q^{62} +(-3.23155 - 2.11302i) q^{63} +(-1.47757 - 0.480090i) q^{64} +(-5.66227 + 8.94114i) q^{65} +(-1.81285 + 8.52877i) q^{66} +(-7.97381 - 6.45706i) q^{67} +(4.58683 + 1.22904i) q^{68} +(2.70728 - 1.96695i) q^{69} +(-9.31962 - 5.27815i) q^{70} +(-1.86024 - 1.35154i) q^{71} +(-1.20119 - 1.48334i) q^{72} +(-7.83788 - 0.410766i) q^{73} +(-3.37666 - 1.94951i) q^{74} +(5.54679 - 8.98424i) q^{75} +2.64456i q^{76} +(4.67755 + 3.81214i) q^{77} +(-2.83059 - 17.8716i) q^{78} +(11.4906 + 1.20771i) q^{79} +(-7.45883 - 8.09592i) q^{80} +(-1.17577 - 11.1867i) q^{81} +(2.46297 - 9.19193i) q^{82} +(0.909079 - 5.73970i) q^{83} +(6.98641 - 1.46214i) q^{84} +(5.94383 + 5.80955i) q^{85} +(-15.7180 + 3.34097i) q^{86} +(-12.1302 - 18.6788i) q^{87} +(1.62466 + 2.50176i) q^{88} +(-6.54052 + 1.39023i) q^{89} +(0.990766 + 5.82400i) q^{90} +(-11.8972 - 3.90690i) q^{91} +(-0.316702 + 1.99958i) q^{92} +(-1.86452 + 6.95847i) q^{93} +(1.21684 + 11.5775i) q^{94} +(-2.26841 + 4.03477i) q^{95} +(13.2240 + 1.38990i) q^{96} +(-0.453302 - 2.86204i) q^{97} +(3.35662 - 12.2202i) 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 $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{20}\right)$

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 $

$2$	0.986015	−	1.51833i	0.697218	−	1.07362i	−0.295753	−	0.955264i	$-0.595571\pi$
$2$	0.986015	−	1.51833i	0.697218	−	1.07362i	0.992971	−	0.118357i	$-0.0377627\pi$
$3$	−0.756771	+	1.97146i	−0.436922	+	1.13822i	0.521597	+	0.853192i	$0.325336\pi$
$3$	−0.756771	+	1.97146i	−0.436922	+	1.13822i	−0.958519	+	0.285029i	$0.907997\pi$
$4$	−0.519626	−	1.16710i	−0.259813	−	0.583550i
$5$	0.208311	−	2.22634i	0.0931596	−	0.995651i
$5$	0.208311	−	2.22634i	0.0931596	−	0.995651i
$6$	2.24713	+	3.09291i	0.917388	+	1.26268i
$7$	2.61446	−	0.405696i	0.988174	−	0.153339i
$7$	2.61446	−	0.405696i	0.988174	−	0.153339i
$8$	1.29182	+	0.204604i	0.456728	+	0.0723385i
$9$	−1.08450	−	0.976490i	−0.361501	−	0.325497i
$10$	−3.17493	−	2.51149i	−1.00400	−	0.794204i
$11$	1.52610	+	1.69491i	0.460137	+	0.511033i	0.927905	−	0.372818i	$-0.121608\pi$
$11$	1.52610	+	1.69491i	0.460137	+	0.511033i	−0.467768	+	0.883851i	$0.654942\pi$
$12$	2.69413	−	0.141193i	0.777727	−	0.0407589i
$13$	−4.21711	−	2.14873i	−1.16962	−	0.595949i	−0.242290	−	0.970204i	$-0.577899\pi$
$13$	−4.21711	−	2.14873i	−1.16962	−	0.595949i	−0.927326	+	0.374254i	$0.877899\pi$
$14$	1.96192	−	4.36964i	0.524345	−	1.16783i
$15$	4.23149	+	2.09551i	1.09257	+	0.541058i
$16$	3.29411	−	3.65848i	0.823527	−	0.914619i
$17$	−2.33918	+	2.88864i	−0.567334	+	0.700599i	−0.977386	−	0.211463i	$-0.932177\pi$
$17$	−2.33918	+	2.88864i	−0.567334	+	0.700599i	0.410052	+	0.912062i	$0.365510\pi$
$18$	−2.55197	+	0.683798i	−0.601505	+	0.161173i
$19$	−1.89106	−	0.841955i	−0.433839	−	0.193158i	0.178184	−	0.983997i	$-0.442978\pi$
$19$	−1.89106	−	0.841955i	−0.433839	−	0.193158i	−0.612024	+	0.790839i	$0.709644\pi$
$20$	−2.70661	+	0.913747i	−0.605216	+	0.204320i
$21$	−1.17874	+	5.46132i	−0.257222	+	1.19176i
$22$	4.07818	−	0.645921i	0.869472	−	0.137711i
$23$	−1.32902	−	0.863075i	−0.277120	−	0.179964i	0.398595	−	0.917127i	$-0.369498\pi$
$23$	−1.32902	−	0.863075i	−0.277120	−	0.179964i	−0.675714	+	0.737164i	$0.736165\pi$
$24$	−1.38098	+	2.39193i	−0.281892	+	0.488251i
$25$	−4.91321	−	0.927545i	−0.982643	−	0.185509i
$26$	−7.42061	+	4.28429i	−1.45530	+	0.840219i
$27$	−2.89883	+	1.47703i	−0.557880	+	0.284254i
$28$	−1.83203	−	2.84053i	−0.346221	−	0.536809i
$29$	−6.19928	+	8.53257i	−1.15118	+	1.58446i	−0.411633	+	0.911350i	$0.635042\pi$
$29$	−6.19928	+	8.53257i	−1.15118	+	1.58446i	−0.739543	+	0.673109i	$0.764958\pi$
$30$	7.35399	−	4.35860i	1.34265	−	0.795768i
$31$	3.39273	−	0.356590i	0.609351	−	0.0640454i	0.205173	−	0.978726i	$-0.434224\pi$
$31$	3.39273	−	0.356590i	0.609351	−	0.0640454i	0.404178	+	0.914680i	$0.367558\pi$
$32$	−1.62970	−	6.08214i	−0.288094	−	1.07518i
$33$	−4.49634	+	1.72598i	−0.782713	+	0.300455i
$34$	2.07945	+	6.39988i	0.356622	+	1.09757i
$35$	−0.358596	−	5.90520i	−0.0606138	−	0.998161i
$36$	−0.576126	+	1.77313i	−0.0960209	+	0.295522i
$37$	−0.112715	−	2.15073i	−0.0185302	−	0.353578i	−0.992121	−	0.125280i	$-0.960017\pi$
$37$	−0.112715	−	2.15073i	−0.0185302	−	0.353578i	0.973591	−	0.228298i	$-0.0733161\pi$
$38$	−3.14298	+	2.04108i	−0.509859	+	0.331106i
$39$	7.42751	−	6.68776i	1.18935	−	1.07090i
$40$	0.724620	−	2.83342i	0.114573	−	0.448002i
$41$	4.99913	−	1.62432i	0.780733	−	0.253676i	0.108580	−	0.994088i	$-0.465370\pi$
$41$	4.99913	−	1.62432i	0.780733	−	0.253676i	0.672153	+	0.740412i	$0.265370\pi$
$42$	7.12982	+	7.17465i	1.10016	+	1.10707i
$43$	−6.27631	−	6.27631i	−0.957128	−	0.957128i	0.0419898	−	0.999118i	$-0.486630\pi$
$43$	−6.27631	−	6.27631i	−0.957128	−	0.957128i	−0.999118	+	0.0419898i	$0.986630\pi$
$44$	1.18512	−	2.66183i	0.178664	−	0.401286i
$45$	−2.39992	+	2.21106i	−0.357758	+	0.329605i
$46$	−2.62087	+	1.16688i	−0.386426	+	0.172048i
$47$	−4.99721	+	4.04666i	−0.728917	+	0.590266i	−0.920283	−	0.391253i	$-0.872042\pi$
$47$	−4.99721	+	4.04666i	−0.728917	+	0.590266i	0.191366	+	0.981519i	$0.438708\pi$
$48$	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
$52$	−0.316455	+	6.03833i	−0.0438845	+	0.837365i
$53$	3.78654	+	1.45352i	0.520121	+	0.199656i	0.604244	−	0.796800i	$-0.293475\pi$
$53$	3.78654	+	1.45352i	0.520121	+	0.199656i	−0.0841225	+	0.996455i	$0.526809\pi$
$54$	−0.615674	+	5.85775i	−0.0837827	+	0.797139i
$55$	4.09135	−	3.04456i	0.551677	−	0.410528i
$56$	3.46042	+	0.0108441i	0.462419	+	0.00144911i
$57$	3.09098	−	3.09098i	0.409410	−	0.409410i
$58$	6.84268	+	17.8258i	0.898488	+	2.34064i
$59$	12.4271	+	2.64146i	1.61787	+	0.343889i	0.925822	−	0.377961i	$-0.123375\pi$
$59$	12.4271	+	2.64146i	1.61787	+	0.343889i	0.692050	+	0.721850i	$0.256708\pi$
$60$	0.246872	−	6.02746i	0.0318710	−	0.778142i
$61$	0.202209	+	0.951321i	0.0258903	+	0.121804i	0.989195	−	0.146606i	$-0.0468350\pi$
$61$	0.202209	+	0.951321i	0.0258903	+	0.121804i	−0.963305	+	0.268410i	$0.913502\pi$
$62$	2.80386	−	5.50288i	0.356090	−	0.698866i
$63$	−3.23155	−	2.11302i	−0.407137	−	0.266215i
$64$	−1.47757	−	0.480090i	−0.184696	−	0.0600113i
$65$	−5.66227	+	8.94114i	−0.702319	+	1.10901i
$66$	−1.81285	+	8.52877i	−0.223146	+	1.04982i
$67$	−7.97381	−	6.45706i	−0.974156	−	0.788856i	0.00330051	−	0.999995i	$-0.498949\pi$
$67$	−7.97381	−	6.45706i	−0.974156	−	0.788856i	−0.977456	+	0.211139i	$0.932283\pi$
$68$	4.58683	+	1.22904i	0.556235	+	0.149043i
$69$	2.70728	−	1.96695i	0.325918	−	0.236793i
$70$	−9.31962	−	5.27815i	−1.11391	−	0.630860i
$71$	−1.86024	−	1.35154i	−0.220770	−	0.160399i	0.471903	−	0.881650i	$-0.343567\pi$
$71$	−1.86024	−	1.35154i	−0.220770	−	0.160399i	−0.692673	+	0.721252i	$0.743567\pi$
$72$	−1.20119	−	1.48334i	−0.141561	−	0.174814i
$73$	−7.83788	−	0.410766i	−0.917354	−	0.0480765i	−0.412188	−	0.911099i	$-0.635235\pi$
$73$	−7.83788	−	0.410766i	−0.917354	−	0.0480765i	−0.505166	+	0.863022i	$0.668569\pi$
$74$	−3.37666	−	1.94951i	−0.392528	−	0.226626i
$75$	5.54679	−	8.98424i	0.640488	−	1.03741i
$76$			2.64456i			0.303352i
$77$	4.67755	+	3.81214i	0.533056	+	0.434433i
$78$	−2.83059	−	17.8716i	−0.320501	−	2.02356i
$79$	11.4906	+	1.20771i	1.29280	+	0.135879i	0.725837	−	0.687866i	$-0.241453\pi$
$79$	11.4906	+	1.20771i	1.29280	+	0.135879i	0.566961	+	0.823745i	$0.308119\pi$
$80$	−7.45883	−	8.09592i	−0.833922	−	0.905151i
$81$	−1.17577	−	11.1867i	−0.130641	−	1.24297i
$82$	2.46297	−	9.19193i	0.271990	−	1.01508i
$83$	0.909079	−	5.73970i	0.0997844	−	0.630014i	−0.886216	−	0.463272i	$-0.846675\pi$
$83$	0.909079	−	5.73970i	0.0997844	−	0.630014i	0.986001	−	0.166742i	$-0.0533246\pi$
$84$	6.98641	−	1.46214i	0.762279	−	0.159532i
$85$	5.94383	+	5.80955i	0.644699	+	0.630134i
$86$	−15.7180	+	3.34097i	−1.69492	+	0.360266i
$87$	−12.1302	−	18.6788i	−1.30049	−	2.00258i
$88$	1.62466	+	2.50176i	0.173190	+	0.266689i
$89$	−6.54052	+	1.39023i	−0.693294	+	0.147364i	−0.541064	−	0.840981i	$-0.681978\pi$
$89$	−6.54052	+	1.39023i	−0.693294	+	0.147364i	−0.152229	+	0.988345i	$0.548645\pi$
$90$	0.990766	+	5.82400i	0.104436	+	0.613904i
$91$	−11.8972	−	3.90690i	−1.24717	−	0.409554i
$92$	−0.316702	+	1.99958i	−0.0330184	+	0.208470i
$93$	−1.86452	+	6.95847i	−0.193341	+	0.721559i
$94$	1.21684	+	11.5775i	0.125508	+	1.19412i
$95$	−2.26841	+	4.03477i	−0.232734	+	0.413958i
$96$	13.2240	+	1.38990i	1.34967	+	0.141856i
$97$	−0.453302	−	2.86204i	−0.0460259	−	0.290596i	0.953930	−	0.300030i	$-0.0969969\pi$
$97$	−0.453302	−	2.86204i	−0.0460259	−	0.290596i	−0.999955	+	0.00943453i	$0.996997\pi$
$98$	3.35662	−	12.2202i	0.339070	−	1.23443i
$99$		−	3.32835i		−	0.334512i
$100$	1.47050	+	6.21619i	0.147050	+	0.621619i
$101$	−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	$0.727364\pi$
$102$	−14.1908	−	0.743706i	−1.40509	−	0.0736379i
$103$	10.7818	+	13.3144i	1.06236	+	1.31191i	0.947930	+	0.318478i	$0.103172\pi$
$103$	10.7818	+	13.3144i	1.06236	+	1.31191i	0.114433	+	0.993431i	$0.463495\pi$
$104$	−5.00811	−	3.63861i	−0.491086	−	0.356795i
$105$	11.9132	+	3.76193i	1.16261	+	0.367127i
$106$	5.94050	−	4.31603i	0.576992	−	0.419210i
$107$	6.17530	+	1.65467i	0.596988	+	0.159963i	0.544645	−	0.838667i	$-0.316664\pi$
$107$	6.17530	+	1.65467i	0.596988	+	0.159963i	0.0523433	+	0.998629i	$0.483331\pi$
$108$	3.23015	+	2.61572i	0.310821	+	0.251698i
$109$	−1.92258	+	9.04502i	−0.184150	+	0.866356i	0.784926	+	0.619590i	$0.212701\pi$
$109$	−1.92258	+	9.04502i	−0.184150	+	0.866356i	−0.969075	+	0.246766i	$0.920632\pi$
$110$	−0.588511	−	9.21399i	−0.0561123	−	0.878520i
$111$	4.32537	+	1.40540i	0.410546	+	0.133394i
$112$	7.12809	−	10.9014i	0.673541	−	1.03008i
$113$	0.716658	−	1.40652i	0.0674175	−	0.132314i	−0.854838	−	0.518894i	$-0.826344\pi$
$113$	0.716658	−	1.40652i	0.0674175	−	0.132314i	0.922256	+	0.386580i	$0.126344\pi$
$114$	−1.64537	−	7.74087i	−0.154103	−	0.724999i
$115$	−2.19835	+	2.77907i	−0.204997	+	0.259149i
$116$	13.1797	+	2.80143i	1.22370	+	0.260106i
$117$	2.47526	+	6.44827i	0.228838	+	0.596142i
$118$	16.2639	−	16.2639i	1.49722	−	1.49722i
$119$	−4.94378	+	8.50124i	−0.453195	+	0.779307i
$120$	5.03758	+	3.57280i	0.459866	+	0.326151i
$121$	0.606088	−	5.76655i	0.0550990	−	0.524231i
$122$	1.64380	+	0.630996i	0.148823	+	0.0571277i
$123$	−0.580930	+	11.0848i	−0.0523807	+	0.999483i
$124$	−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	0.991670	+	0.128801i	$0.0411129\pi$
$127$	5.78103	+	11.3459i	0.512984	+	1.00679i	−0.478687	+	0.877986i	$0.658887\pi$
$128$	7.60106	−	6.15522i	0.671845	−	0.544050i
$129$	17.1232	−	7.62374i	1.50761	−	0.671233i
$130$	7.99251	+	17.4133i	0.700989	+	1.52725i
$131$	−5.82831	+	13.0906i	−0.509221	+	1.14373i	0.457805	+	0.889053i	$0.348636\pi$
$131$	−5.82831	+	13.0906i	−0.509221	+	1.14373i	−0.967026	+	0.254677i	$0.918031\pi$
$132$	4.35081	+	4.35081i	0.378690	+	0.378690i
$133$	−5.28569	−	1.43406i	−0.458327	−	0.124349i
$134$	−17.6662	+	5.74011i	−1.52613	+	0.495870i
$135$	2.68451	+	6.76147i	0.231046	+	0.581935i
$136$	−3.61282	+	3.25300i	−0.309797	+	0.278943i
$137$	2.00006	−	1.29885i	0.170876	−	0.110968i	−0.456367	−	0.889792i	$-0.650850\pi$
$137$	2.00006	−	1.29885i	0.170876	−	0.110968i	0.627244	+	0.778823i	$0.284183\pi$
$138$	−0.317066	−	6.04999i	−0.0269905	−	0.515009i
$139$	6.04915	−	18.6174i	0.513082	−	1.57910i	−0.273663	−	0.961826i	$-0.588235\pi$
$139$	6.04915	−	18.6174i	0.513082	−	1.57910i	0.786745	−	0.617278i	$-0.211765\pi$
$140$	−6.70563	+	3.48702i	−0.566729	+	0.294707i
$141$	−4.19607	−	12.9142i	−0.353373	−	1.08757i
$142$	−3.88631	+	1.49182i	−0.326132	+	0.125190i
$143$	−2.79385	−	10.4268i	−0.233633	−	0.871931i
$144$	−7.14493	+	0.750963i	−0.595411	+	0.0625802i
$145$	17.7051	+	15.5791i	1.47032	+	1.29378i
$146$	−8.35194	+	11.4955i	−0.691211	+	0.951371i
$147$	−0.866134	+	14.7566i	−0.0714375	+	1.21710i
$148$	−2.45155	+	1.24913i	−0.201516	+	0.102678i
$149$	−20.6257	+	11.9082i	−1.68972	+	0.975561i	−0.734995	+	0.678072i	$0.762816\pi$
$149$	−20.6257	+	11.9082i	−1.68972	+	0.975561i	−0.954725	+	0.297488i	$0.903851\pi$
$150$	−8.17183	−	17.2805i	−0.667227	−	1.41094i
$151$	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	$0.0549937\pi$
$152$	−2.27065	−	1.47457i	−0.184174	−	0.119604i
$153$	5.35757	−	0.848556i	0.433134	−	0.0686017i
$154$	10.4002	−	3.34324i	0.838073	−	0.269406i
$155$	−0.0871488	−	7.62765i	−0.00699996	−	0.612668i
$156$	−11.6648	−	5.19351i	−0.933933	−	0.415814i
$157$	15.7673	−	4.22483i	1.25837	−	0.337178i	0.432803	−	0.901489i	$-0.357525\pi$
$157$	15.7673	−	4.22483i	1.25837	−	0.337178i	0.825562	+	0.564311i	$0.190858\pi$
$158$	13.1637	−	16.2558i	1.04724	−	1.29324i
$159$	−5.73109	+	6.36502i	−0.454505	+	0.504779i
$160$	−13.8804	+	2.36130i	−1.09734	+	0.186677i
$161$	−3.82482	−	1.71730i	−0.301438	−	0.135342i
$162$	−18.1445	−	9.24507i	−1.42556	−	0.726361i
$163$	−10.0837	+	0.528466i	−0.789819	+	0.0413927i	−0.442980	−	0.896532i	$-0.646079\pi$
$163$	−10.0837	+	0.528466i	−0.789819	+	0.0413927i	−0.346840	+	0.937924i	$0.612745\pi$
$164$	−4.49342	−	4.99045i	−0.350877	−	0.389689i
$165$	2.90600	+	10.3699i	0.226231	+	0.807299i
$166$	−7.81839	−	7.03971i	−0.606825	−	0.546387i
$167$	20.5308	+	3.25176i	1.58872	+	0.251628i	0.887325	−	0.461145i	$-0.152561\pi$
$167$	20.5308	+	3.25176i	1.58872	+	0.251628i	0.701394	+	0.712773i	$0.252561\pi$
$168$	−2.64013	+	6.81387i	−0.203690	+	0.525701i
$169$	5.52581	+	7.60562i	0.425062	+	0.585048i
$170$	14.6815	−	3.29640i	1.12602	−	0.252822i
$171$	1.22870	+	2.75970i	0.0939610	+	0.211040i
$172$	−4.06375	+	10.5864i	−0.309858	+	0.807207i
$173$	8.58649	−	13.2220i	0.652819	−	1.00525i	−0.344958	−	0.938618i	$-0.612107\pi$
$173$	8.58649	−	13.2220i	0.652819	−	1.00525i	0.997777	−	0.0666350i	$-0.0212263\pi$
$174$	−40.3211			−3.05673
$175$	−13.2217	−	0.431761i	−0.999467	−	0.0326381i
$176$	11.2279			0.846336
$177$	−14.6120	+	22.5005i	−1.09831	+	1.69124i
$178$	−4.33822	+	11.3014i	−0.325163	+	0.847079i
$179$	−6.51713	−	14.6377i	−0.487113	−	1.09407i	−0.975209	−	0.221284i	$-0.928975\pi$
$179$	−6.51713	−	14.6377i	−0.487113	−	1.09407i	0.488096	−	0.872790i	$-0.337692\pi$
$180$	3.82759	+	1.65202i	0.285292	+	0.123134i
$181$	5.00248	+	6.88532i	0.371831	+	0.511782i	0.953397	−	0.301717i	$-0.0975599\pi$
$181$	5.00248	+	6.88532i	0.371831	+	0.511782i	−0.581566	+	0.813499i	$0.697560\pi$
$182$	−17.6628	+	14.2116i	−1.30925	+	1.05344i
$183$	−2.02851	−	0.321285i	−0.149952	−	0.0237501i
$184$	−1.54027	−	1.38686i	−0.113550	−	0.102241i
$185$	−4.81175	−	0.197079i	−0.353767	−	0.0144895i
$186$	8.72680	+	9.69210i	0.639880	+	0.710659i
$187$	−8.46579	+	0.443674i	−0.619080	+	0.0324446i
$188$	7.31954	+	3.72949i	0.533832	+	0.272001i
$189$	−6.97966	+	5.03767i	−0.507695	+	0.366437i
$190$	3.88942	+	7.42253i	0.282168	+	0.538487i
$191$	8.08992	−	8.98476i	0.585366	−	0.650115i	−0.375600	−	0.926782i	$-0.622563\pi$
$191$	8.08992	−	8.98476i	0.585366	−	0.650115i	0.960966	+	0.276667i	$0.0892300\pi$
$192$	2.06466	−	2.54964i	0.149004	−	0.184004i
$193$	−8.48275	+	2.27295i	−0.610602	+	0.163610i	−0.550852	−	0.834603i	$-0.685697\pi$
$193$	−8.48275	+	2.27295i	−0.610602	+	0.163610i	−0.0597499	+	0.998213i	$0.519030\pi$
$194$	−4.79248	−	2.13375i	−0.344080	−	0.153194i
$195$	−13.3420	−	17.9293i	−0.955442	−	1.28395i
$196$	−5.94217	−	6.68321i	−0.424440	−	0.477372i
$197$	9.73798	−	1.54234i	0.693802	−	0.109887i	0.200433	−	0.979707i	$-0.435765\pi$
$197$	9.73798	−	1.54234i	0.693802	−	0.109887i	0.493369	+	0.869820i	$0.335765\pi$
$198$	−5.05353	−	3.28180i	−0.359139	−	0.233228i
$199$	2.51334	−	4.35324i	0.178166	−	0.308593i	−0.763086	−	0.646297i	$-0.776317\pi$
$199$	2.51334	−	4.35324i	0.178166	−	0.308593i	0.941252	+	0.337704i	$0.109650\pi$
$200$	−6.15721	−	2.20349i	−0.435381	−	0.155810i
$201$	18.7642	−	10.8335i	1.32352	−	0.764136i
$202$	−6.14517	+	3.13112i	−0.432373	+	0.220305i
$203$	−12.7461	+	24.8231i	−0.894604	+	1.74224i
$204$	−5.89418	+	8.11264i	−0.412675	+	0.567998i
$205$	−2.57491	−	11.4681i	−0.179840	−	0.800970i
$206$	30.8467	−	3.24212i	2.14919	−	0.225889i
$207$	0.598540	+	2.23378i	0.0416014	+	0.155259i
$208$	−21.7527	+	8.35007i	−1.50828	+	0.578973i
$209$	−1.45892	−	4.49008i	−0.100915	−	0.310585i
$210$	17.4585	−	14.3789i	1.20475	−	0.992237i
$211$	5.17345	−	15.9222i	0.356155	−	1.09613i	−0.599182	−	0.800613i	$-0.704507\pi$
$211$	5.17345	−	15.9222i	0.356155	−	1.09613i	0.955337	−	0.295519i	$-0.0954927\pi$
$212$	−0.271187	−	5.17456i	−0.0186252	−	0.355390i
$213$	4.07228	−	2.64457i	0.279028	−	0.181203i
$214$	8.60126	−	7.74461i	0.587970	−	0.529411i
$215$	−15.2806	+	12.6658i	−1.04213	+	0.863800i
$216$	−4.04697	+	1.31494i	−0.275362	+	0.0894704i
$217$	8.72548	−	2.30870i	0.592324	−	0.156725i
$218$	11.8376	+	11.8376i	0.801746	+	0.801746i
$219$	6.74128	−	15.1412i	0.455534	−	1.02315i
$220$	−5.67927	−	3.19298i	−0.382897	−	0.215271i
$221$	16.0715	−	7.15548i	1.08108	−	0.481330i
$222$	6.39874	−	5.18159i	0.429455	−	0.347766i
$223$	−4.83037	−	9.48013i	−0.323465	−	0.634836i	0.670817	−	0.741623i	$-0.265944\pi$
$223$	−4.83037	−	9.48013i	−0.323465	−	0.634836i	−0.994282	+	0.106787i	$0.965944\pi$
$224$	−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
$227$	0.188468	−	3.59618i	0.0125091	−	0.238687i	−0.985218	−	0.171304i	$-0.945202\pi$
$227$	0.188468	−	3.59618i	0.0125091	−	0.238687i	0.997727	−	0.0673826i	$-0.0214648\pi$
$228$	−5.21364	−	2.00133i	−0.345281	−	0.132541i
$229$	−0.864403	+	8.22424i	−0.0571214	+	0.543473i	0.928117	+	0.372288i	$0.121426\pi$
$229$	−0.864403	+	8.22424i	−0.0571214	+	0.543473i	−0.985239	+	0.171186i	$0.945240\pi$
$230$	2.05193	+	6.07802i	0.135300	+	0.400773i
$231$	−11.0553	+	6.33667i	−0.727385	+	0.416922i
$232$	−9.75415	+	9.75415i	−0.640392	+	0.640392i
$233$	1.40923	+	3.67117i	0.0923218	+	0.240506i	0.971964	−	0.235129i	$-0.0755514\pi$
$233$	1.40923	+	3.67117i	0.0923218	+	0.240506i	−0.879642	+	0.475636i	$0.842218\pi$
$234$	12.2312	+	2.59983i	0.799581	+	0.169956i
$235$	7.96828	+	11.9685i	0.519793	+	0.780736i
$236$	−3.37460	−	15.8763i	−0.219668	−	1.03346i
$237$	−11.0767	+	21.7393i	−0.719512	+	1.41212i
$238$	8.03304	+	15.8886i	0.520705	+	1.02991i
$239$	13.0724	+	4.24747i	0.845581	+	0.274746i	0.699594	−	0.714541i	$-0.253364\pi$
$239$	13.0724	+	4.24747i	0.845581	+	0.274746i	0.145987	+	0.989287i	$0.453364\pi$
$240$	21.6054	−	8.57799i	1.39462	−	0.553707i
$241$	−2.21068	+	10.4004i	−0.142402	+	0.669949i	0.847801	+	0.530315i	$0.177926\pi$
$241$	−2.21068	+	10.4004i	−0.142402	+	0.669949i	−0.990203	+	0.139635i	$0.955407\pi$
$242$	−8.15791	−	6.60614i	−0.524410	−	0.424659i
$243$	13.5162	+	3.62166i	0.867065	+	0.232329i
$244$	1.00521	−	0.730330i	0.0643522	−	0.0467546i
$245$	−3.33325	−	15.2934i	−0.212954	−	0.977062i
$246$	16.2576	+	11.8118i	1.03655	+	0.753094i
$247$	6.16569	+	7.61399i	0.392313	+	0.484467i
$248$	4.45575	+	0.233516i	0.282941	+	0.0148283i
$249$	10.6276	+	6.13585i	0.673497	+	0.388843i
$250$	13.2696	+	15.2844i	0.839241	+	0.966669i
$251$			7.76448i			0.490090i	0.969512	+	0.245045i	$0.0788027\pi$
$251$			7.76448i			0.490090i	−0.969512	+	0.245045i	$0.921197\pi$
$252$	−0.786907	+	4.86952i	−0.0495705	+	0.306751i
$253$	−0.565386	−	3.56970i	−0.0355455	−	0.224425i
$254$	22.9270	+	2.40973i	1.43857	+	0.151200i
$255$	−15.9514	+	7.32151i	−0.998915	+	0.458491i
$256$	−2.17568	−	20.7002i	−0.135980	−	1.29377i
$257$	5.27589	−	19.6899i	0.329101	−	1.22822i	−0.581024	−	0.813887i	$-0.697348\pi$
$257$	5.27589	−	19.6899i	0.329101	−	1.22822i	0.910125	−	0.414335i	$-0.135986\pi$
$258$	5.30838	−	33.5158i	0.330485	−	2.08660i
$259$	−1.16723	−	5.57727i	−0.0725282	−	0.346555i
$260$	13.3775	+	1.96239i	0.829636	+	0.121702i
$261$	15.0551	−	3.20006i	0.931887	−	0.198079i
$262$	14.1290	+	21.7568i	0.872895	+	1.34414i
$263$	10.6753	+	16.4385i	0.658268	+	1.01364i	0.997340	+	0.0728838i	$0.0232202\pi$
$263$	10.6753	+	16.4385i	0.658268	+	1.01364i	−0.339072	+	0.940760i	$0.610113\pi$
$264$	−6.16161	+	1.30969i	−0.379221	+	0.0806059i
$265$	4.02481	−	8.12735i	0.247242	−	0.499259i
$266$	−7.38915	+	6.61141i	−0.453058	+	0.405371i
$267$	2.20890	−	13.9464i	0.135182	−	0.853508i
$268$	−3.39264	+	12.6615i	−0.207238	+	0.773424i
$269$	−2.16704	−	20.6180i	−0.132127	−	1.25710i	−0.836776	−	0.547546i	$-0.815562\pi$
$269$	−2.16704	−	20.6180i	−0.132127	−	1.25710i	0.704649	−	0.709556i	$-0.251104\pi$
$270$	12.9131	+	2.59094i	0.785867	+	0.157679i
$271$	−5.29739	−	0.556778i	−0.321793	−	0.0338218i	−0.0577452	−	0.998331i	$-0.518391\pi$
$271$	−5.29739	−	0.556778i	−0.321793	−	0.0338218i	−0.264048	+	0.964510i	$0.585058\pi$
$272$	2.86253	+	18.0733i	0.173567	+	1.09586i
$273$	16.7057	−	20.4982i	1.01108	−	1.24061i
$274$		−	4.31743i		−	0.260826i
$275$	−5.92596	−	9.74296i	−0.357349	−	0.587523i
$276$	−3.70241	−	2.13758i	−0.222859	−	0.128667i
$277$	−5.32773	−	0.279215i	−0.320112	−	0.0167764i	−0.108397	−	0.994108i	$-0.534572\pi$
$277$	−5.32773	−	0.279215i	−0.320112	−	0.0167764i	−0.211716	+	0.977331i	$0.567905\pi$
$278$	−22.3027	−	27.5416i	−1.33763	−	1.65184i
$279$	−4.02762	−	2.92624i	−0.241128	−	0.175189i
$280$	0.744988	−	7.70183i	0.0445215	−	0.460273i
$281$	−19.3712	+	14.0740i	−1.15559	+	0.839582i	−0.989214	−	0.146481i	$-0.953205\pi$
$281$	−19.3712	+	14.0740i	−1.15559	+	0.839582i	−0.166372	+	0.986063i	$0.553205\pi$
$282$	−23.7453	−	6.36255i	−1.41401	−	0.378884i
$283$	2.62307	+	2.12412i	0.155926	+	0.126266i	0.704108	−	0.710092i	$-0.251347\pi$
$283$	2.62307	+	2.12412i	0.155926	+	0.126266i	−0.548183	+	0.836358i	$0.684680\pi$
$284$	−0.610757	+	2.87338i	−0.0362417	+	0.170504i
$285$	−6.23769	−	7.52547i	−0.369489	−	0.445770i
$286$	−18.5861	−	6.03898i	−1.09902	−	0.357092i
$287$	12.4111	−	6.27484i	0.732602	−	0.370392i
$288$	−4.17173	+	8.18748i	−0.245822	+	0.482452i
$289$	0.661991	+	3.11442i	0.0389407	+	0.183201i
$290$	41.1117	−	11.5208i	2.41416	−	0.676527i
$291$	5.98543	+	1.27224i	0.350872	+	0.0745802i
$292$	3.59336	+	9.36103i	0.210286	+	0.547813i
$293$	−13.2445	+	13.2445i	−0.773751	+	0.773751i	−0.978760	−	0.205009i	$-0.934278\pi$
$293$	−13.2445	+	13.2445i	−0.773751	+	0.773751i	0.205009	+	0.978760i	$0.434278\pi$
$294$	21.5514	+	15.8653i	1.25690	+	0.925284i
$295$	8.46951	−	27.1168i	0.493114	−	1.57880i
$296$	0.294441	−	2.80142i	0.0171140	−	0.162829i
$297$	−6.92733	−	2.65915i	−0.401964	−	0.154300i
$298$	−2.25659	+	43.0583i	−0.130721	+	2.49430i
$299$	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
$303$	6.25196	−	5.06274i	0.359166	−	0.290847i
$304$	−9.30963	+	4.14492i	−0.533944	+	0.237727i
$305$	2.16009	−	0.252017i	0.123686	−	0.0144305i
$306$	3.99426	−	8.97125i	0.228336	−	0.512852i
$307$	1.06555	+	1.06555i	0.0608142	+	0.0608142i	0.736860	−	0.676046i	$-0.236308\pi$
$307$	1.06555	+	1.06555i	0.0608142	+	0.0608142i	−0.676046	+	0.736860i	$0.736308\pi$
$308$	2.01857	−	7.44005i	0.115019	−	0.423936i
$309$	−34.4082	+	11.1799i	−1.95741	+	0.636002i
$310$	−11.6672	−	7.38866i	−0.662654	−	0.419648i
$311$	−3.72010	+	3.34959i	−0.210947	+	0.189938i	−0.767831	−	0.640653i	$-0.778664\pi$
$311$	−3.72010	+	3.34959i	−0.210947	+	0.189938i	0.556883	+	0.830591i	$0.311997\pi$
$312$	10.9634	−	7.11968i	0.620678	−	0.403073i
$313$	−1.77097	−	33.7922i	−0.100101	−	1.91005i	−0.341926	−	0.939727i	$-0.611079\pi$
$313$	−1.77097	−	33.7922i	−0.100101	−	1.91005i	0.241825	−	0.970320i	$-0.422254\pi$
$314$	9.13208	−	28.1057i	0.515353	−	1.58609i
$315$	−5.37747	+	6.75437i	−0.302986	+	0.380566i
$316$	−4.56132	−	14.0383i	−0.256594	−	0.789715i
$317$	−12.5685	+	4.82458i	−0.705915	+	0.270976i	−0.684727	−	0.728800i	$-0.740078\pi$
$317$	−12.5685	+	4.82458i	−0.705915	+	0.270976i	−0.0211887	+	0.999775i	$0.506745\pi$
$318$	4.01326	+	14.9777i	0.225052	+	0.839907i
$319$	−23.9226	+	2.51437i	−1.33941	+	0.140778i
$320$	−1.37664	+	3.18956i	−0.0769565	+	0.178302i
$321$	−7.93539	+	10.9221i	−0.442910	+	0.609613i
$322$	−6.37875	+	4.11405i	−0.355474	+	0.229267i
$323$	6.85563	−	3.49312i	0.381458	−	0.194362i
$324$	−12.4451	+	7.18516i	−0.691393	+	0.399176i
$325$	18.7265	+	14.4687i	1.03876	+	0.802580i
$326$	−9.14033	+	15.8315i	−0.506236	+	0.876826i
$327$	−16.3769	−	10.6353i	−0.905645	−	0.588133i
$328$	6.79032	−	1.07548i	0.374933	−	0.0593835i
$329$	−11.4233	+	12.6072i	−0.629787	+	0.695056i
$330$	18.6103	+	5.81266i	1.02447	+	0.319976i
$331$	−11.2672	−	5.01648i	−0.619302	−	0.275731i	0.0730081	−	0.997331i	$-0.476740\pi$
$331$	−11.2672	−	5.01648i	−0.619302	−	0.275731i	−0.692310	+	0.721601i	$0.743407\pi$
$332$	−7.17118	+	1.92151i	−0.393570	+	0.105457i
$333$	−1.97793	+	2.44254i	−0.108390	+	0.133850i
$334$	25.1809	−	27.9662i	1.37784	−	1.53024i
$335$	−16.0367	+	16.4074i	−0.876177	+	0.896430i
$336$	16.0972	+	22.3025i	0.878175	+	1.21670i
$337$	15.1805	+	7.73487i	0.826936	+	0.421345i	0.815618	−	0.578591i	$-0.196397\pi$
$337$	15.1805	+	7.73487i	0.826936	+	0.421345i	0.0113182	+	0.999936i	$0.496397\pi$
$338$	16.9964	−	0.890742i	0.924480	−	0.0484500i
$339$	2.23055	+	2.47727i	0.121147	+	0.134547i
$340$	3.69175	−	9.95584i	0.200213	−	0.539931i
$341$	5.78203	+	5.20616i	0.313114	+	0.281929i
$342$	5.40166	+	0.855539i	0.292088	+	0.0462622i
$343$	16.5800	−	8.25252i	0.895235	−	0.445594i
$344$	−6.82371	−	9.39203i	−0.367910	−	0.506384i
$345$	−3.81516	−	6.43707i	−0.205401	−	0.346560i
$346$	−11.6090	−	26.0743i	−0.624104	−	1.40176i
$347$	−6.17785	+	16.0939i	−0.331645	+	0.863964i	0.661803	+	0.749677i	$0.269791\pi$
$347$	−6.17785	+	16.0939i	−0.331645	+	0.863964i	−0.993448	+	0.114286i	$0.963542\pi$
$348$	−15.4969	+	23.8631i	−0.830720	+	1.27920i
$349$	−13.4664			−0.720839			−0.360419	−	0.932790i	$-0.617366\pi$
$349$	−13.4664			−0.720839			−0.360419	+	0.932790i	$0.617366\pi$
$350$	−13.6924	+	19.6492i	−0.731887	+	1.05029i
$351$	15.3984			0.821907
$352$	7.82156	−	12.0442i	0.416891	−	0.641955i
$353$	−3.19515	+	8.32364i	−0.170061	+	0.443023i	−0.991951	−	0.126623i	$-0.959586\pi$
$353$	−3.19515	+	8.32364i	−0.170061	+	0.443023i	0.821890	+	0.569646i	$0.192920\pi$
$354$	19.7555	+	44.3717i	1.05000	+	2.35833i
$355$	−3.39651	+	3.85999i	−0.180268	+	0.204867i
$356$	5.02116	+	6.91104i	0.266121	+	0.366284i
$357$	−13.0185	−	16.1799i	−0.689013	−	0.856333i
$358$	−28.6509	−	4.53785i	−1.51425	−	0.239833i
$359$	16.1885	+	14.5762i	0.854396	+	0.769301i	0.974719	−	0.223433i	$-0.0717265\pi$
$359$	16.1885	+	14.5762i	0.854396	+	0.769301i	−0.120323	+	0.992735i	$0.538393\pi$
$360$	−3.55265	+	2.36526i	−0.187241	+	0.124660i
$361$	−9.84625	−	10.9354i	−0.518224	−	0.575546i
$362$	15.3867	−	0.806383i	0.808707	−	0.0423825i
$363$	10.9098	+	5.55883i	0.572617	+	0.291763i
$364$	1.62236	+	15.9154i	0.0850349	+	0.834192i
$365$	−2.54722	+	17.3642i	−0.133328	+	0.908886i
$366$	−2.48796	+	2.76316i	−0.130048	+	0.144433i
$367$	−7.47723	+	9.23361i	−0.390308	+	0.481990i	−0.933989	−	0.357302i	$-0.883697\pi$
$367$	−7.47723	+	9.23361i	−0.390308	+	0.481990i	0.543681	+	0.839292i	$0.317030\pi$
$368$	−7.53547	+	2.01912i	−0.392814	+	0.105254i
$369$	−7.00770	−	3.12003i	−0.364806	−	0.162422i
$370$	−5.04368	+	7.11149i	−0.262209	+	0.369709i
$371$	10.4894	+	2.26398i	0.544585	+	0.117540i
$372$	9.09008	−	1.43973i	0.471299	−	0.0746464i
$373$	−16.7228	−	10.8599i	−0.865872	−	0.562304i	0.0335246	−	0.999438i	$-0.489327\pi$
$373$	−16.7228	−	10.8599i	−0.865872	−	0.562304i	−0.899396	+	0.437134i	$0.855993\pi$
$374$	−7.67376	+	13.2913i	−0.396801	+	0.687279i
$375$	−18.8466	−	14.2206i	−0.973232	−	0.734348i
$376$	−7.28346	+	4.20511i	−0.375616	+	0.216862i
$377$	44.4772	−	22.6623i	2.29069	−	1.16717i
$378$	0.766806	+	15.5646i	0.0394403	+	0.800559i
$379$	11.9563	−	16.4564i	0.614154	−	0.845311i	−0.382757	−	0.923849i	$-0.625025\pi$
$379$	11.9563	−	16.4564i	0.614154	−	0.845311i	0.996911	+	0.0785382i	$0.0250252\pi$
$380$	5.88770	+	0.550892i	0.302033	+	0.0282601i
$381$	−26.7429	+	2.81079i	−1.37008	+	0.144001i
$382$	−5.66505	−	21.1423i	−0.289849	−	1.08173i
$383$	10.2752	−	3.94429i	0.525039	−	0.201544i	−0.0813883	−	0.996682i	$-0.525935\pi$
$383$	10.2752	−	3.94429i	0.525039	−	0.201544i	0.606427	+	0.795139i	$0.292602\pi$
$384$	6.38248	+	19.6432i	0.325704	+	1.00242i
$385$	9.46151	−	9.61972i	0.482203	−	0.490266i
$386$	−4.91303	+	15.1208i	−0.250067	+	0.769627i
$387$	0.677917	+	12.9354i	0.0344604	+	0.657544i
$388$	−3.10474	+	2.01624i	−0.157619	+	0.102359i
$389$	−4.38730	+	3.95035i	−0.222445	+	0.200290i	−0.772817	−	0.634629i	$-0.781153\pi$
$389$	−4.38730	+	3.95035i	−0.222445	+	0.200290i	0.550372	+	0.834920i	$0.314486\pi$
$390$	−40.3780	+	2.57900i	−2.04462	+	0.130593i
$391$	5.60193	−	1.82018i	0.283302	−	0.0920503i
$392$	9.05154	−	1.37553i	0.457172	−	0.0694746i
$393$	−21.3968	−	21.3968i	−1.07933	−	1.07933i
$394$	7.26000	−	16.3062i	0.365754	−	0.821496i
$395$	5.08242	−	25.3305i	0.255724	−	1.27452i
$396$	−3.88452	+	1.72950i	−0.195204	+	0.0869106i
$397$	−13.2412	+	10.7225i	−0.664557	+	0.538148i	−0.901175	−	0.433455i	$-0.857294\pi$
$397$	−13.2412	+	10.7225i	−0.664557	+	0.538148i	0.236618	+	0.971603i	$0.423961\pi$
$398$	−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	$0.709379\pi$
$402$	2.05293	−	39.1722i	0.102391	−	1.95373i
$403$	−15.0737	−	5.78626i	−0.750875	−	0.288234i
$404$	−0.508734	+	4.84028i	−0.0253105	+	0.240813i
$405$	−25.1504	+	0.287353i	−1.24973	+	0.0142787i
$406$	25.1218	+	43.8288i	1.24677	+	2.17519i
$407$	3.47327	−	3.47327i	0.172164	−	0.172164i
$408$	−3.67907	−	9.58430i	−0.182141	−	0.474494i
$409$	11.1355	+	2.36692i	0.550615	+	0.117037i	0.474814	−	0.880086i	$-0.342515\pi$
$409$	11.1355	+	2.36692i	0.550615	+	0.117037i	0.0758011	+	0.997123i	$0.475849\pi$
$410$	−19.9513	−	7.39820i	−0.985326	−	0.365371i
$411$	1.04705	+	4.92596i	0.0516469	+	0.242980i
$412$	9.93675	−	19.5020i	0.489549	−	0.960793i
$413$	33.5618	+	1.86438i	1.65147	+	0.0917402i
$414$	3.98179	+	1.29376i	0.195694	+	0.0635849i
$415$	−12.5892	−	3.21957i	−0.617978	−	0.158042i
$416$	−6.19620	+	29.1509i	−0.303794	+	1.42924i
$417$	32.1255	+	26.0147i	1.57319	+	1.27395i
$418$	−8.25594	−	2.21217i	−0.403811	−	0.108201i
$419$	11.5358	−	8.38127i	0.563562	−	0.409452i	−0.269199	−	0.963085i	$-0.586759\pi$
$419$	11.5358	−	8.38127i	0.563562	−	0.409452i	0.832761	+	0.553633i	$0.186759\pi$
$420$	−1.79988	−	15.8587i	−0.0878250	−	0.773826i
$421$	−7.49291	−	5.44392i	−0.365182	−	0.265320i	0.390028	−	0.920803i	$-0.372465\pi$
$421$	−7.49291	−	5.44392i	−0.365182	−	0.265320i	−0.755210	+	0.655483i	$0.772465\pi$
$422$	−19.0741	−	23.5546i	−0.928513	−	1.14662i
$423$	9.37100	+	0.491113i	0.455634	+	0.0238787i
$424$	4.59413	+	2.65242i	0.223111	+	0.128813i
$425$	14.1722	−	12.0228i	0.687453	−	0.583193i
$426$		−	8.79066i		−	0.425909i
$427$	0.914616	+	2.40516i	0.0442613	+	0.116394i
$428$	−1.27769	−	8.06700i	−0.0617593	−	0.389933i
$429$	22.6702	+	2.38274i	1.09453	+	0.115040i
$430$	4.16391	+	35.6897i	0.200802	+	1.72111i
$431$	−0.837996	−	7.97300i	−0.0403649	−	0.384046i	−0.995990	−	0.0894615i	$-0.971485\pi$
$431$	−0.837996	−	7.97300i	−0.0403649	−	0.384046i	0.955625	−	0.294585i	$-0.0951813\pi$
$432$	−4.14538	+	15.4708i	−0.199445	+	0.744339i
$433$	−4.18286	+	26.4096i	−0.201016	+	1.26916i	0.656351	+	0.754456i	$0.272099\pi$
$433$	−4.18286	+	26.4096i	−0.201016	+	1.26916i	−0.857366	+	0.514707i	$0.827901\pi$
$434$	5.09808	−	15.5246i	0.244716	−	0.745204i
$435$	−44.1123	+	23.1149i	−2.11502	+	1.10827i
$436$	11.5555	−	2.45619i	0.553407	−	0.117630i
$437$	1.78659	+	2.75110i	0.0854641	+	0.131603i
$438$	−16.3423	−	25.1649i	−0.780865	−	1.20243i
$439$	17.1461	−	3.64452i	0.818339	−	0.173943i	0.220322	−	0.975427i	$-0.429289\pi$
$439$	17.1461	−	3.64452i	0.818339	−	0.173943i	0.598016	+	0.801484i	$0.295956\pi$
$440$	5.90822	−	3.09591i	0.281663	−	0.147592i
$441$	−9.30600	−	4.21338i	−0.443143	−	0.200637i
$442$	4.98233	−	31.4572i	0.236985	−	1.49627i
$443$	−3.98412	+	14.8689i	−0.189291	+	0.706445i	0.804380	+	0.594116i	$0.202498\pi$
$443$	−3.98412	+	14.8689i	−0.189291	+	0.706445i	−0.993671	+	0.112329i	$0.964169\pi$
$444$	−0.607337	−	5.77842i	−0.0288229	−	0.274232i
$445$	1.73267	+	14.8510i	0.0821363	+	0.704007i
$446$	−19.1568	−	2.01346i	−0.907099	−	0.0953400i
$447$	−7.86765	−	49.6744i	−0.372127	−	2.34952i
$448$	−4.05781	−	0.655736i	−0.191714	−	0.0309806i
$449$		−	1.46011i		−	0.0689067i	−0.999406	−	0.0344533i	$-0.989031\pi$
$449$		−	1.46011i		−	0.0689067i	0.999406	−	0.0344533i	$-0.0109690\pi$
$450$	13.1726	−	0.992580i	0.620963	−	0.0467907i
$451$	10.3822	+	5.99419i	0.488881	+	0.282255i
$452$	−2.01394	−	0.105546i	−0.0947279	−	0.00496448i
$453$	11.2248	+	13.8614i	0.527386	+	0.651268i
$454$	−5.27436	−	3.83205i	−0.247538	−	0.179847i
$455$	−11.1764	+	25.6734i	−0.523959	+	1.20359i
$456$	4.62542	−	3.36056i	0.216605	−	0.157373i
$457$	−38.5827	−	10.3382i	−1.80482	−	0.483600i	−0.810106	−	0.586283i	$-0.800591\pi$
$457$	−38.5827	−	10.3382i	−1.80482	−	0.483600i	−0.994714	+	0.102683i	$0.967257\pi$
$458$	11.6348	+	9.42168i	0.543659	+	0.440246i
$459$	2.51427	−	11.8287i	0.117356	−	0.552117i
$460$	4.38577	+	1.12162i	0.204488	+	0.0522958i
$461$	16.1060	+	5.23314i	0.750130	+	0.243732i	0.659037	−	0.752111i	$-0.270964\pi$
$461$	16.1060	+	5.23314i	0.750130	+	0.243732i	0.0910926	+	0.995842i	$0.470964\pi$
$462$	−1.27953	+	23.0336i	−0.0595293	+	1.07162i
$463$	−5.84654	+	11.4745i	−0.271712	+	0.533265i	−0.986032	−	0.166554i	$-0.946736\pi$
$463$	−5.84654	+	11.4745i	−0.271712	+	0.533265i	0.714320	+	0.699819i	$0.246736\pi$
$464$	10.7951	+	50.7871i	0.501151	+	2.35773i
$465$	15.1035	+	5.60058i	0.700410	+	0.259721i
$466$	6.96357	+	1.48015i	0.322581	+	0.0685668i
$467$	−2.35439	−	6.13339i	−0.108948	−	0.283819i	0.868258	−	0.496113i	$-0.165240\pi$
$467$	−2.35439	−	6.13339i	−0.108948	−	0.283819i	−0.977206	+	0.212294i	$0.931907\pi$
$468$	6.23956	−	6.23956i	0.288424	−	0.288424i
$469$	−23.4668	−	13.6468i	−1.08360	−	0.630151i
$470$	26.0289	−	0.297390i	1.20062	−	0.0137176i
$471$	−3.60315	+	34.2817i	−0.166025	+	1.57962i
$472$	15.5131	+	5.95494i	0.714050	+	0.274098i
$473$	1.05948	−	20.2160i	0.0487148	−	0.929534i
$474$	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
$478$	19.3386	−	15.6601i	0.884527	−	0.716276i
$479$	−9.26533	+	4.12519i	−0.423344	+	0.188485i	−0.607340	−	0.794442i	$-0.707763\pi$
$479$	−9.26533	+	4.12519i	−0.423344	+	0.188485i	0.183996	+	0.982927i	$0.441097\pi$
$480$	5.84909	−	29.1516i	0.266973	−	1.33058i
$481$	−4.14600	+	9.31207i	−0.189041	+	0.424594i
$482$	13.6115	+	13.6115i	0.619986	+	0.619986i
$483$	6.28009	−	6.24086i	0.285754	−	0.283969i
$484$	−7.04508	+	2.28908i	−0.320231	+	0.104049i
$485$	−6.46631	+	0.413012i	−0.293620	+	0.0187539i
$486$	18.8261	−	16.9511i	0.853967	−	0.768915i
$487$	31.8811	−	20.7038i	1.44467	−	0.938179i	0.445591	−	0.895237i	$-0.352994\pi$
$487$	31.8811	−	20.7038i	1.44467	−	0.938179i	0.999078	−	0.0429419i	$-0.0136730\pi$
$488$	0.0665741	+	1.27031i	0.00301367	+	0.0575042i
$489$	6.58923	−	20.2796i	0.297975	−	0.917074i
$490$	−26.5071	−	10.0186i	−1.19747	−	0.452594i
$491$	11.9197	+	36.6850i	0.537927	+	1.65557i	0.737238	+	0.675633i	$0.236130\pi$
$491$	11.9197	+	36.6850i	0.537927	+	1.65557i	−0.199311	+	0.979936i	$0.563870\pi$
$492$	13.2389	−	5.08195i	0.596858	−	0.229112i
$493$	−10.1463	−	37.8667i	−0.456968	−	1.70543i
$494$	17.6400	−	1.85404i	0.793662	−	0.0834172i
$495$	−7.41005	−	0.693333i	−0.333057	−	0.0311630i
$496$	9.87143	−	13.5869i	0.443240	−	0.610068i
$497$	−5.41184	−	2.77887i	−0.242754	−	0.124649i
$498$	19.7952	−	10.0862i	0.887044	−	0.451972i
$499$	−2.65771	+	1.53443i	−0.118976	+	0.0686906i	−0.558307	−	0.829635i	$-0.688549\pi$
$499$	−2.65771	+	1.53443i	−0.118976	+	0.0686906i	0.439331	+	0.898325i	$0.355215\pi$
$500$	14.1457	−	1.97893i	0.632615	−	0.0885005i
$501$	−21.9478	+	38.0147i	−0.980555	+	1.69837i
$502$	11.7890	+	7.65589i	0.526171	+	0.341699i
$503$	−30.3701	+	4.81016i	−1.35414	+	0.214474i	−0.790963	−	0.611864i	$-0.790420\pi$
$503$	−30.3701	+	4.81016i	−1.35414	+	0.214474i	−0.563174	+	0.826338i	$0.690420\pi$
$504$	−3.74225	−	3.39083i	−0.166693	−	0.151040i
$505$	−4.92799	+	6.94837i	−0.219293	+	0.309198i
$506$	−5.97747	−	2.66134i	−0.265731	−	0.118311i
$507$	−19.1759	+	5.13817i	−0.851632	+	0.228194i
$508$	10.2378	−	12.6427i	0.454231	−	0.560928i
$509$	7.62025	−	8.46315i	0.337762	−	0.375123i	−0.550205	−	0.835029i	$-0.685451\pi$
$509$	7.62025	−	8.46315i	0.337762	−	0.375123i	0.887967	+	0.459907i	$0.152117\pi$
$510$	−4.61184	+	31.4386i	−0.204216	+	1.39212i
$511$	−20.6585	+	2.10586i	−0.913877	+	0.0931578i
$512$	−16.1456	−	8.22662i	−0.713543	−	0.363569i
$513$	6.72546	−	0.352466i	0.296936	−	0.0155618i
$514$	−24.6936	−	27.4251i	−1.08919	−	1.20967i
$515$	31.8884	−	21.2305i	1.40517	−	0.935526i
$516$	−17.7953	−	16.0230i	−0.783396	−	0.705373i
$517$	−14.4849	−	2.29419i	−0.637047	−	0.100898i
$518$	−9.61905	−	3.72703i	−0.422637	−	0.163756i
$519$	19.5687	+	26.9339i	0.858969	+	1.18227i
$520$	−9.14404	+	10.3918i	−0.400993	+	0.455712i
$521$	−14.2659	−	32.0418i	−0.625001	−	1.40378i	−0.897239	−	0.441546i	$-0.854430\pi$
$521$	−14.2659	−	32.0418i	−0.625001	−	1.40378i	0.272237	−	0.962230i	$-0.412236\pi$
$522$	9.98580	−	26.0139i	0.437067	−	1.13860i
$523$	−11.4019	+	17.5574i	−0.498570	+	0.767731i	−0.994950	−	0.100375i	$-0.967996\pi$
$523$	−11.4019	+	17.5574i	−0.498570	+	0.767731i	0.496379	+	0.868106i	$0.334662\pi$
$524$	18.3066			0.799726
$525$	10.8570	−	25.7393i	0.473839	−	1.12335i
$526$	35.4852			1.54723
$527$	−6.90612	+	10.6345i	−0.300835	+	0.463246i
$528$	−8.49696	+	22.1353i	−0.369783	+	0.963317i
$529$	−8.33355	−	18.7175i	−0.362328	−	0.813802i
$530$	−8.37148	−	14.1247i	−0.363634	−	0.613537i
$531$	−10.8979	−	14.9996i	−0.472927	−	0.650928i
$532$	1.07289	+	6.91410i	0.0465155	+	0.299764i
$533$	−24.5721	−	3.89184i	−1.06434	−	0.168574i
$534$	−18.9973	−	17.1052i	−0.822092	−	0.740215i
$535$	4.97024	−	13.4036i	0.214882	−	0.579490i
$536$	−8.97959	−	9.97284i	−0.387859	−	0.430761i
$537$	33.7896	−	1.77084i	1.45813	−	0.0764173i
$538$	−33.4416	−	17.0394i	−1.44177	−	0.734619i
$539$	13.7758	+	8.06902i	0.593367	+	0.347557i
$540$	6.49637	−	6.64653i	0.279559	−	0.286021i
$541$	9.64066	−	10.7070i	0.414484	−	0.460331i	−0.499361	−	0.866394i	$-0.666432\pi$
$541$	9.64066	−	10.7070i	0.414484	−	0.460331i	0.913845	+	0.406063i	$0.133099\pi$
$542$	−6.06867	+	7.49419i	−0.260672	+	0.321903i
$543$	−17.3598	+	4.65155i	−0.744982	+	0.199617i
$544$	21.3813	+	9.51956i	0.916715	+	0.408148i
$545$	19.7368	+	6.16450i	0.845433	+	0.264058i
$546$	−14.6509	−	45.5763i	−0.627001	−	1.95049i
$547$	38.1667	−	6.04502i	1.63189	−	0.258466i	0.727795	−	0.685795i	$-0.240545\pi$
$547$	38.1667	−	6.04502i	1.63189	−	0.258466i	0.904096	+	0.427328i	$0.140545\pi$
$548$	−2.55517	−	1.65935i	−0.109152	−	0.0708839i
$549$	0.709658	−	1.22916i	0.0302875	−	0.0524595i
$550$	−20.6361	−	0.609151i	−0.879927	−	0.0259743i
$551$	18.9073	−	10.9161i	0.805476	−	0.465042i
$552$	3.89977	−	1.98703i	0.165985	−	0.0845736i
$553$	30.5318	−	1.50418i	1.29834	−	0.0639641i
$554$	−5.67716	+	7.81394i	−0.241199	+	0.331983i
$555$	4.02992	−	9.33700i	0.171061	−	0.396334i
$556$	−24.8716	+	2.61411i	−1.05479	+	0.110863i
$557$	6.74079	+	25.1570i	0.285616	+	1.06593i	0.948388	+	0.317113i	$0.102713\pi$
$557$	6.74079	+	25.1570i	0.285616	+	1.06593i	−0.662772	+	0.748822i	$0.730620\pi$
$558$	−8.41429	+	3.22994i	−0.356205	+	0.136734i
$559$	12.9818	+	39.9540i	0.549073	+	1.68987i
$560$	−22.7853	−	18.1405i	−0.962855	−	0.766574i
$561$	5.53199	−	17.0257i	0.233561	−	0.718826i
$562$	2.26868	+	43.2889i	0.0956983	+	1.82603i
$563$	4.30487	−	2.79562i	0.181429	−	0.117821i	−0.450729	−	0.892661i	$-0.648836\pi$
$563$	4.30487	−	2.79562i	0.181429	−	0.117821i	0.632158	+	0.774840i	$0.282169\pi$
$564$	−12.8917	+	11.6078i	−0.542840	+	0.488775i
$565$	−2.98211	−	1.88852i	−0.125458	−	0.0794506i
$566$	5.81151	−	1.88827i	0.244276	−	0.0793701i
$567$	−7.61242	−	28.7703i	−0.319692	−	1.20824i
$568$	−2.12656	−	2.12656i	−0.0892287	−	0.0892287i
$569$	−3.64227	+	8.18067i	−0.152692	+	0.342952i	−0.973654	−	0.228031i	$-0.926771\pi$
$569$	−3.64227	+	8.18067i	−0.152692	+	0.342952i	0.820962	+	0.570983i	$0.193438\pi$
$570$	−17.5766	+	2.05066i	−0.736203	+	0.0858925i
$571$	−18.6374	+	8.29789i	−0.779949	+	0.347256i	−0.757790	−	0.652499i	$-0.773721\pi$
$571$	−18.6374	+	8.29789i	−0.779949	+	0.347256i	−0.0221593	+	0.999754i	$0.507054\pi$
$572$	−10.7173	+	8.67873i	−0.448115	+	0.362876i
$573$	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
$577$	−1.70370	+	32.5085i	−0.0709259	+	1.35335i	0.698958	+	0.715163i	$0.253648\pi$
$577$	−1.70370	+	32.5085i	−0.0709259	+	1.35335i	−0.769884	+	0.638184i	$0.779686\pi$
$578$	5.38146	+	2.06575i	0.223839	+	0.0859238i
$579$	1.93849	−	18.4435i	0.0805607	−	0.766484i
$580$	8.98241	−	28.7589i	0.372974	−	1.19415i
$581$	0.0481817	−	15.3750i	0.00199891	−	0.637864i
$582$	7.83340	−	7.83340i	0.324705	−	0.324705i
$583$	3.31507	+	8.63604i	0.137296	+	0.357668i
$584$	−10.0411	−	2.13430i	−0.415503	−	0.0883179i
$585$	14.8717	−	4.16753i	0.614868	−	0.172306i
$586$	7.05024	+	33.1688i	0.291243	+	1.37019i
$587$	−18.8559	+	37.0069i	−0.778268	+	1.52744i	0.0698062	+	0.997561i	$0.477762\pi$
$587$	−18.8559	+	37.0069i	−0.778268	+	1.52744i	−0.848074	+	0.529877i	$0.822238\pi$
$588$	17.6725	−	6.65706i	0.728802	−	0.274533i
$589$	−6.71609	−	2.18219i	−0.276732	−	0.0899155i
$590$	−32.8211	−	39.5970i	−1.35122	−	1.63018i
$591$	−4.32875	+	20.3652i	−0.178061	+	0.837712i
$592$	−8.23969	−	6.67237i	−0.338649	−	0.274233i
$593$	16.3610	+	4.38392i	0.671866	+	0.180026i	0.578595	−	0.815615i	$-0.303601\pi$
$593$	16.3610	+	4.38392i	0.671866	+	0.180026i	0.0932706	+	0.995641i	$0.470268\pi$
$594$	−10.8679	+	7.89600i	−0.445916	+	0.323977i
$595$	17.8968	+	12.7775i	0.733699	+	0.523824i
$596$	24.6157	+	17.8844i	1.00830	+	0.732573i
$597$	6.68020	+	8.24936i	0.273402	+	0.337624i
$598$	13.5598	+	0.710639i	0.554502	+	0.0290602i
$599$	2.39394	+	1.38214i	0.0978138	+	0.0564728i	0.548109	−	0.836407i	$-0.315348\pi$
$599$	2.39394	+	1.38214i	0.0978138	+	0.0564728i	−0.450295	+	0.892880i	$0.648681\pi$
$600$	9.00367	−	10.4711i	0.367573	−	0.427482i
$601$			35.9435i			1.46616i	0.680140	+	0.733082i	$0.261919\pi$
$601$			35.9435i			1.46616i	−0.680140	+	0.733082i	$0.738081\pi$
$602$	−39.7388	+	15.1116i	−1.61963	+	0.615902i
$603$	2.34235	+	14.7890i	0.0953880	+	0.602256i
$604$	−10.7316	−	1.12793i	−0.436661	−	0.0458949i
$605$	−12.7121	−	2.55060i	−0.516819	−	0.103697i
$606$	−1.52238	−	14.4845i	−0.0618425	−	0.588392i
$607$	−3.86472	+	14.4233i	−0.156864	+	0.585425i	0.842074	+	0.539361i	$0.181334\pi$
$607$	−3.86472	+	14.4233i	−0.156864	+	0.585425i	−0.998939	+	0.0460635i	$0.985332\pi$
$608$	−2.03902	+	12.8738i	−0.0826930	+	0.522103i
$609$	−39.2917	−	43.9139i	−1.59218	−	1.77948i
$610$	1.74724	−	3.52822i	0.0707435	−	0.142853i
$611$	29.7689	−	6.32758i	1.20432	−	0.255987i
$612$	−3.77429	−	5.81189i	−0.152566	−	0.234932i
$613$	−26.2843	−	40.4743i	−1.06161	−	1.63474i	−0.718618	−	0.695405i	$-0.755225\pi$
$613$	−26.2843	−	40.4743i	−1.06161	−	1.63474i	−0.342996	−	0.939337i	$-0.611442\pi$
$614$	2.66851	−	0.567209i	0.107692	−	0.0228907i
$615$	24.5576	+	3.60244i	0.990257	+	0.145264i
$616$	5.26257	+	5.88164i	0.212035	+	0.236978i
$617$	4.01084	−	25.3234i	0.161470	−	1.01948i	−0.765251	−	0.643732i	$-0.777385\pi$
$617$	4.01084	−	25.3234i	0.161470	−	1.01948i	0.926721	−	0.375750i	$-0.122615\pi$
$618$	−16.9522	+	63.2665i	−0.681917	+	2.54495i
$619$	−0.150550	−	1.43239i	−0.00605110	−	0.0575724i	0.991080	−	0.133271i	$-0.0425480\pi$
$619$	−0.150550	−	1.43239i	−0.00605110	−	0.0575724i	−0.997131	+	0.0756985i	$0.975881\pi$
$620$	−8.85695	+	4.06524i	−0.355704	+	0.163264i
$621$	5.12739	+	0.538910i	0.205755	+	0.0216257i
$622$	1.41771	+	8.95108i	0.0568451	+	0.358906i
$623$	−16.5359	+	6.28816i	−0.662498	+	0.251930i
$624$		−	49.2036i		−	1.96972i
$625$	23.2793	+	9.11445i	0.931173	+	0.364578i
$626$	−53.0539	−	30.6307i	−2.12046	−	1.22425i
$627$	9.95606	+	0.521775i	0.397607	+	0.0208377i
$628$	−13.1239	−	16.2067i	−0.523700	−	0.646716i
$629$	6.47635	+	4.70534i	0.258229	+	0.187614i
$630$	4.95309	+	14.8247i	0.197336	+	0.590629i
$631$	−9.94266	+	7.22377i	−0.395811	+	0.287574i	−0.767833	−	0.640650i	$-0.778665\pi$
$631$	−9.94266	+	7.22377i	−0.395811	+	0.287574i	0.372021	+	0.928224i	$0.378665\pi$
$632$	14.5967	+	3.91119i	0.580627	+	0.155579i
$633$	27.4749	+	22.2487i	1.09203	+	0.884307i
$634$	−5.06739	+	23.8402i	−0.201252	+	0.946815i
$635$	26.4642	−	10.5071i	1.05020	−	0.416961i
$636$	10.4066	+	3.38132i	0.412650	+	0.134078i
$637$	−32.6898	−	5.38779i	−1.29522	−	0.213472i
$638$	−19.7704	+	38.8016i	−0.782718	+	1.53617i
$639$	0.697665	+	3.28226i	0.0275992	+	0.129844i
$640$	−12.1202	−	18.2048i	−0.479095	−	0.719607i
$641$	18.0203	+	3.83033i	0.711758	+	0.151289i	0.549541	−	0.835466i	$-0.314802\pi$
$641$	18.0203	+	3.83033i	0.711758	+	0.151289i	0.162216	+	0.986755i	$0.448136\pi$
$642$	8.75897	+	22.8179i	0.345689	+	0.900551i
$643$	6.68684	−	6.68684i	0.263703	−	0.263703i	−0.562853	−	0.826557i	$-0.690296\pi$
$643$	6.68684	−	6.68684i	0.263703	−	0.263703i	0.826557	+	0.562853i	$0.190296\pi$
$644$	−0.0167854	+	5.35630i	−0.000661436	+	0.211068i
$645$	−13.4061	−	39.7102i	−0.527865	−	1.56359i
$646$	1.45605	−	13.8534i	0.0572875	−	0.545054i
$647$	−17.9420	−	6.88730i	−0.705374	−	0.270768i	−0.0208755	−	0.999782i	$-0.506645\pi$
$647$	−17.9420	−	6.88730i	−0.705374	−	0.270768i	−0.684498	+	0.729014i	$0.739979\pi$
$648$	0.769965	−	14.6918i	0.0302471	−	0.577149i
$649$	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
$653$	23.7307	−	19.2167i	0.928652	−	0.752008i	−0.0403176	−	0.999187i	$-0.512837\pi$
$653$	23.7307	−	19.2167i	0.928652	−	0.752008i	0.968970	+	0.247179i	$0.0795036\pi$
$654$	−32.2958	+	14.3790i	−1.26286	+	0.562263i
$655$	27.9300	+	15.7027i	1.09132	+	0.613556i
$656$	10.5252	−	23.6399i	0.410938	−	0.922982i
$657$	8.09908	+	8.09908i	0.315975	+	0.315975i
$658$	7.87831	+	29.7752i	0.307129	+	1.16076i
$659$	−38.5495	+	12.5255i	−1.50168	+	0.487924i	−0.940506	−	0.339777i	$-0.889648\pi$
$659$	−38.5495	+	12.5255i	−1.50168	+	0.487924i	−0.561169	+	0.827701i	$0.689648\pi$
$660$	10.5927	−	8.78009i	0.412322	−	0.341764i
$661$	13.7545	−	12.3846i	0.534988	−	0.481705i	−0.356786	−	0.934186i	$-0.616128\pi$
$661$	13.7545	−	12.3846i	0.534988	−	0.481705i	0.891774	+	0.452481i	$0.149461\pi$
$662$	−18.7263	+	12.1610i	−0.727819	+	0.472651i
$663$	1.94429	+	37.0993i	0.0755099	+	1.44082i
$664$	2.34873	−	7.22866i	0.0911485	−	0.280526i
$665$	−4.29379	+	11.4690i	−0.166506	+	0.444750i
$666$	1.75831	+	5.41152i	0.0681331	+	0.209692i
$667$	15.6032	−	5.98951i	0.604159	−	0.231915i
$668$	−6.87321	−	25.6512i	−0.265933	−	0.992474i
$669$	22.3451	−	2.34857i	0.863913	−	0.0908009i
$670$	9.09938	+	40.5269i	0.351540	+	1.56569i
$671$	−1.30381	+	1.79454i	−0.0503329	+	0.0692773i
$672$	35.1375	−	1.73108i	1.35546	−	0.0667779i
$673$	−5.00671	+	2.55105i	−0.192994	+	0.0983356i	−0.547817	−	0.836598i	$-0.684541\pi$
$673$	−5.00671	+	2.55105i	−0.192994	+	0.0983356i	0.354823	+	0.934934i	$0.384541\pi$
$674$	26.7123	−	15.4224i	1.02892	−	0.594047i
$675$	15.6126	−	4.56816i	0.600928	−	0.175828i
$676$	6.00516	−	10.4012i	0.230968	−	0.400048i
$677$	−20.8212	−	13.5214i	−0.800222	−	0.519670i	0.0785512	−	0.996910i	$-0.474971\pi$
$677$	−20.8212	−	13.5214i	−0.800222	−	0.519670i	−0.878773	+	0.477240i	$0.841637\pi$
$678$	5.96067	−	0.944077i	0.228918	−	0.0362571i
$679$	−2.34626	−	7.29879i	−0.0900411	−	0.280102i
$680$	6.48971	+	8.72103i	0.248869	+	0.334436i
$681$	6.94709	+	3.09304i	0.266213	+	0.118526i
$682$	13.6058	−	3.64567i	0.520994	−	0.139600i
$683$	−24.0492	+	29.6983i	−0.920217	+	1.13637i	0.0700989	+	0.997540i	$0.477669\pi$
$683$	−24.0492	+	29.6983i	−0.920217	+	1.13637i	−0.990316	+	0.138833i	$0.955665\pi$
$684$	2.58239	−	2.86803i	0.0987400	−	0.109662i
$685$	−2.47506	−	4.72338i	−0.0945671	−	0.180471i
$686$	3.81807	−	33.3110i	0.145775	−	1.27182i
$687$	−15.5596	−	7.92800i	−0.593635	−	0.302472i
$688$	−43.6366	+	2.28690i	−1.66363	+	0.0871871i
$689$	−12.8451	−	14.2659i	−0.489358	−	0.543487i
$690$	−13.5354	−	0.554381i	−0.515284	−	0.0211049i
$691$	15.3303	+	13.8034i	0.583191	+	0.525107i	0.907064	−	0.420993i	$-0.138318\pi$
$691$	15.3303	+	13.8034i	0.583191	+	0.525107i	−0.323873	+	0.946101i	$0.604985\pi$
$692$	−19.8932	−	3.15078i	−0.756226	−	0.119775i
$693$	−1.35030	−	8.70185i	−0.0512936	−	0.330556i
$694$	18.3443	+	25.2488i	0.696341	+	0.958431i
$695$	−40.1885	−	17.3457i	−1.52444	−	0.657959i
$696$	−11.8482	−	26.6115i	−0.449106	−	1.00871i
$697$	−7.00178	+	18.2403i	−0.265211	+	0.690899i
$698$	−13.2780	+	20.4464i	−0.502582	+	0.773908i
$699$	−8.30402			−0.314087
$700$	6.36644	+	15.6554i	0.240629	+	0.591719i
$701$	−16.8050			−0.634717			−0.317359	−	0.948306i	$-0.602796\pi$
$701$	−16.8050			−0.634717			−0.317359	+	0.948306i	$0.602796\pi$
$702$	15.1831	−	23.3799i	0.573048	−	0.882416i
$703$	−1.59767	+	4.16207i	−0.0602572	+	0.156975i
$704$	−1.44121	−	3.23700i	−0.0543175	−	0.121999i
$705$	−29.6255	+	6.65172i	−1.11576	+	0.250518i
$706$	9.48757	+	13.0585i	0.357069	+	0.491464i
$707$	−9.39841	−	3.64154i	−0.353464	−	0.136954i
$708$	33.8531	+	5.36181i	1.27228	+	0.201509i
$709$	13.2747	+	11.9526i	0.498544	+	0.448891i	0.879637	−	0.475646i	$-0.157786\pi$
$709$	13.2747	+	11.9526i	0.498544	+	0.448891i	−0.381093	+	0.924537i	$0.624452\pi$
$710$	2.51173	+	8.96303i	0.0942636	+	0.336376i
$711$	−11.2823	−	12.5303i	−0.423119	−	0.469922i
$712$	−8.73362	+	0.457710i	−0.327306	+	0.0171534i
$713$	−4.81676	−	2.45426i	−0.180389	−	0.0919129i
$714$	−37.4029	+	3.81274i	−1.39977	+	0.142688i
$715$	−23.7956	+	4.04805i	−0.889905	+	0.151388i
$716$	−13.6972	+	15.2123i	−0.511889	+	0.568510i
$717$	−18.2665	+	22.5572i	−0.682174	+	0.842415i
$718$	38.0935	−	10.2071i	1.42164	−	0.380927i
$719$	−35.2323	−	15.6864i	−1.31394	−	0.585006i	−0.374348	−	0.927288i	$-0.622133\pi$
$719$	−35.2323	−	15.6864i	−1.31394	−	0.585006i	−0.939597	+	0.342283i	$0.888800\pi$
$720$	0.183532	+	16.0635i	0.00683982	+	0.598652i
$721$	33.5902	+	30.4359i	1.25097	+	1.13349i
$722$	−26.3121	+	4.16742i	−0.979233	+	0.155095i
$723$	−18.8310	−	12.2290i	−0.700331	−	0.454801i
$724$	5.43644	−	9.41619i	0.202044	−	0.349950i
$725$	38.3727	−	36.1722i	1.42513	−	1.34340i
$726$	19.1974	−	11.0836i	0.712482	−	0.411352i
$727$	24.0437	−	12.2509i	0.891730	−	0.454359i	0.0528040	−	0.998605i	$-0.483184\pi$
$727$	24.0437	−	12.2509i	0.891730	−	0.454359i	0.838926	+	0.544246i	$0.183184\pi$
$728$	−14.5697	−	7.48123i	−0.539989	−	0.277273i
$729$	2.46622	−	3.39447i	0.0913416	−	0.125721i
$730$	23.8530	+	20.9889i	0.882841	+	0.776835i
$731$	32.8114	−	3.44862i	1.21357	−	0.127552i
$732$	0.679097	+	2.53443i	0.0251002	+	0.0936751i
$733$	21.0134	−	8.06630i	0.776149	−	0.297936i	0.0621355	−	0.998068i	$-0.480209\pi$
$733$	21.0134	−	8.06630i	0.776149	−	0.297936i	0.714013	+	0.700132i	$0.246876\pi$
$734$	6.64700	+	20.4574i	0.245345	+	0.755095i
$735$	32.6729	+	5.00228i	1.20516	+	0.184512i
$736$	−3.08344	+	9.48984i	−0.113657	+	0.349800i
$737$	−1.22472	−	23.3690i	−0.0451130	−	0.860807i
$738$	−11.6469	+	7.56360i	−0.428729	+	0.278420i
$739$	−10.2031	+	9.18689i	−0.375326	+	0.337945i	−0.835107	−	0.550087i	$-0.814595\pi$
$739$	−10.2031	+	9.18689i	−0.375326	+	0.337945i	0.459781	+	0.888032i	$0.347928\pi$
$740$	2.27030	+	5.71820i	0.0834579	+	0.210205i
$741$	−19.6767	+	6.39334i	−0.722840	+	0.234865i
$742$	13.7802	−	13.6941i	0.505888	−	0.502727i
$743$	16.3770	+	16.3770i	0.600813	+	0.600813i	0.940528	−	0.339715i	$-0.110331\pi$
$743$	16.3770	+	16.3770i	0.600813	+	0.600813i	−0.339715	+	0.940528i	$0.610331\pi$
$744$	−3.83235	+	8.60760i	−0.140501	+	0.315570i
$745$	22.2153	+	48.4004i	0.813904	+	1.77326i
$746$	−32.9778	+	14.6827i	−1.20740	+	0.537570i
$747$	−6.59065	+	5.33701i	−0.241139	+	0.195271i
$748$	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	$0.903626\pi$
$752$	−1.65673	+	31.6123i	−0.0604147	+	1.15278i
$753$	−15.3073	−	5.87593i	−0.557830	−	0.214131i
$754$	9.44639	−	89.8764i	0.344017	−	3.27310i
$755$	−15.4055	−	10.9260i	−0.560663	−	0.397639i
$756$	9.50628	+	5.52825i	0.345740	+	0.201060i
$757$	−31.8390	+	31.8390i	−1.15721	+	1.15721i	−0.172134	+	0.985073i	$0.555066\pi$
$757$	−31.8390	+	31.8390i	−1.15721	+	1.15721i	−0.985073	+	0.172134i	$0.944934\pi$
$758$	−13.1972	−	34.3799i	−0.479344	−	1.24874i
$759$	7.46538	+	1.58682i	0.270976	+	0.0575978i
$760$	−3.75591	+	4.74807i	−0.136241	+	0.172230i
$761$	−6.32582	−	29.7606i	−0.229311	−	1.07882i	−0.930626	−	0.365971i	$-0.880737\pi$
$761$	−6.32582	−	29.7606i	−0.229311	−	1.07882i	0.701315	−	0.712851i	$-0.252596\pi$
$762$	−22.1012	+	43.3760i	−0.800641	+	1.57135i
$763$	−1.35698	+	24.4278i	−0.0491261	+	0.884347i
$764$	−14.6899	−	4.77302i	−0.531460	−	0.172682i
$765$	−0.773135	−	12.1046i	−0.0279528	−	0.437641i
$766$	4.14279	−	19.4903i	0.149685	−	0.704213i
$767$

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)

\(f(q)\)	\(=\)	\(q+(0.986015 - 1.51833i) q^{2} +(-0.756771 + 1.97146i) q^{3} +(-0.519626 - 1.16710i) q^{4} +(0.208311 - 2.22634i) q^{5} +(2.24713 + 3.09291i) q^{6} +(2.61446 - 0.405696i) q^{7} +(1.29182 + 0.204604i) q^{8} +(-1.08450 - 0.976490i) q^{9} +O(q^{10})\)	\(q+(0.986015 - 1.51833i) q^{2} +(-0.756771 + 1.97146i) q^{3} +(-0.519626 - 1.16710i) q^{4} +(0.208311 - 2.22634i) q^{5} +(2.24713 + 3.09291i) q^{6} +(2.61446 - 0.405696i) q^{7} +(1.29182 + 0.204604i) q^{8} +(-1.08450 - 0.976490i) q^{9} +(-3.17493 - 2.51149i) q^{10} +(1.52610 + 1.69491i) q^{11} +(2.69413 - 0.141193i) q^{12} +(-4.21711 - 2.14873i) q^{13} +(1.96192 - 4.36964i) q^{14} +(4.23149 + 2.09551i) q^{15} +(3.29411 - 3.65848i) q^{16} +(-2.33918 + 2.88864i) q^{17} +(-2.55197 + 0.683798i) q^{18} +(-1.89106 - 0.841955i) q^{19} +(-2.70661 + 0.913747i) q^{20} +(-1.17874 + 5.46132i) q^{21} +(4.07818 - 0.645921i) q^{22} +(-1.32902 - 0.863075i) q^{23} +(-1.38098 + 2.39193i) q^{24} +(-4.91321 - 0.927545i) q^{25} +(-7.42061 + 4.28429i) q^{26} +(-2.89883 + 1.47703i) q^{27} +(-1.83203 - 2.84053i) q^{28} +(-6.19928 + 8.53257i) q^{29} +(7.35399 - 4.35860i) q^{30} +(3.39273 - 0.356590i) q^{31} +(-1.62970 - 6.08214i) q^{32} +(-4.49634 + 1.72598i) q^{33} +(2.07945 + 6.39988i) q^{34} +(-0.358596 - 5.90520i) q^{35} +(-0.576126 + 1.77313i) q^{36} +(-0.112715 - 2.15073i) q^{37} +(-3.14298 + 2.04108i) q^{38} +(7.42751 - 6.68776i) q^{39} +(0.724620 - 2.83342i) q^{40} +(4.99913 - 1.62432i) q^{41} +(7.12982 + 7.17465i) q^{42} +(-6.27631 - 6.27631i) q^{43} +(1.18512 - 2.66183i) q^{44} +(-2.39992 + 2.21106i) q^{45} +(-2.62087 + 1.16688i) q^{46} +(-4.99721 + 4.04666i) 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} +(-0.316455 + 6.03833i) q^{52} +(3.78654 + 1.45352i) q^{53} +(-0.615674 + 5.85775i) q^{54} +(4.09135 - 3.04456i) q^{55} +(3.46042 + 0.0108441i) q^{56} +(3.09098 - 3.09098i) q^{57} +(6.84268 + 17.8258i) q^{58} +(12.4271 + 2.64146i) q^{59} +(0.246872 - 6.02746i) q^{60} +(0.202209 + 0.951321i) q^{61} +(2.80386 - 5.50288i) q^{62} +(-3.23155 - 2.11302i) q^{63} +(-1.47757 - 0.480090i) q^{64} +(-5.66227 + 8.94114i) q^{65} +(-1.81285 + 8.52877i) q^{66} +(-7.97381 - 6.45706i) q^{67} +(4.58683 + 1.22904i) q^{68} +(2.70728 - 1.96695i) q^{69} +(-9.31962 - 5.27815i) q^{70} +(-1.86024 - 1.35154i) q^{71} +(-1.20119 - 1.48334i) q^{72} +(-7.83788 - 0.410766i) q^{73} +(-3.37666 - 1.94951i) q^{74} +(5.54679 - 8.98424i) q^{75} +2.64456i q^{76} +(4.67755 + 3.81214i) q^{77} +(-2.83059 - 17.8716i) q^{78} +(11.4906 + 1.20771i) q^{79} +(-7.45883 - 8.09592i) q^{80} +(-1.17577 - 11.1867i) q^{81} +(2.46297 - 9.19193i) q^{82} +(0.909079 - 5.73970i) q^{83} +(6.98641 - 1.46214i) q^{84} +(5.94383 + 5.80955i) q^{85} +(-15.7180 + 3.34097i) q^{86} +(-12.1302 - 18.6788i) q^{87} +(1.62466 + 2.50176i) q^{88} +(-6.54052 + 1.39023i) q^{89} +(0.990766 + 5.82400i) q^{90} +(-11.8972 - 3.90690i) q^{91} +(-0.316702 + 1.99958i) q^{92} +(-1.86452 + 6.95847i) q^{93} +(1.21684 + 11.5775i) q^{94} +(-2.26841 + 4.03477i) q^{95} +(13.2240 + 1.38990i) q^{96} +(-0.453302 - 2.86204i) q^{97} +(3.35662 - 12.2202i) 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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