LMFDB - Embedded newform 175.2.x.a.103.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [175,2,Mod(3,175)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("175.3"); S:= CuspForms(chi, 2); N := Newforms(S);

sage: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")

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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			103.2
Character	$\chi$	$=$	175.103
Dual form			175.2.x.a.17.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.42673 - 0.127179i) q^{2} +(-1.28700 - 1.58931i) q^{3} +(3.88379 + 0.408202i) q^{4} +(-2.16561 + 0.556914i) q^{5} +(2.92107 + 4.02051i) q^{6} +(-2.31224 - 1.28591i) q^{7} +(-4.57269 - 0.724243i) q^{8} +(-0.245810 + 1.15644i) q^{9} +(5.32616 - 1.07606i) q^{10} +(-2.02243 + 0.429882i) q^{11} +(-4.34967 - 6.69790i) q^{12} +(4.81187 + 2.45177i) q^{13} +(5.44763 + 3.41461i) q^{14} +(3.67224 + 2.72507i) q^{15} +(3.36489 + 0.715229i) q^{16} +(1.96169 + 5.11037i) q^{17} +(0.743588 - 2.77511i) q^{18} +(0.242645 + 2.30861i) q^{19} +(-8.63808 + 1.27893i) q^{20} +(0.932143 + 5.32983i) q^{21} +(4.96257 - 0.785994i) q^{22} +(-0.146917 + 2.80334i) q^{23} +(4.73400 + 8.19953i) q^{24} +(4.37969 - 2.41211i) q^{25} +(-11.3653 - 6.56174i) q^{26} +(-3.31219 + 1.68764i) q^{27} +(-8.45533 - 5.93804i) q^{28} +(3.75352 - 5.16628i) q^{29} +(-8.56496 - 7.08004i) q^{30} +(-2.88229 + 6.47373i) q^{31} +(0.869181 + 0.232896i) q^{32} +(3.28609 + 2.66102i) q^{33} +(-4.11055 - 12.6510i) q^{34} +(5.72353 + 1.49705i) q^{35} +(-1.42673 + 4.39104i) q^{36} +(0.340852 - 0.221352i) q^{37} +(-0.295225 - 5.63323i) q^{38} +(-2.29624 - 10.8030i) q^{39} +(10.3060 - 0.978172i) q^{40} +(-8.72248 + 2.83411i) q^{41} +(-1.58421 - 13.0526i) q^{42} +(-3.92695 - 3.92695i) q^{43} +(-8.03018 + 0.844006i) q^{44} +(-0.111713 - 2.64129i) q^{45} +(0.713054 - 6.78426i) q^{46} +(-2.50126 - 0.960145i) q^{47} +(-3.19388 - 6.26835i) q^{48} +(3.69289 + 5.94664i) q^{49} +(-10.9351 + 5.29653i) q^{50} +(5.59728 - 9.69478i) q^{51} +(17.6874 + 11.4864i) q^{52} +(-3.15369 + 2.55381i) q^{53} +(8.25240 - 3.67421i) q^{54} +(4.14039 - 2.05728i) q^{55} +(9.64184 + 7.55468i) q^{56} +(3.35682 - 3.35682i) q^{57} +(-9.76581 + 12.0598i) q^{58} +(0.0263546 - 0.0292698i) q^{59} +(13.1498 + 12.0826i) q^{60} +(-5.29174 + 4.76471i) q^{61} +(7.81785 - 15.3434i) q^{62} +(2.05545 - 2.35788i) q^{63} +(-8.62303 - 2.80179i) q^{64} +(-11.7860 - 2.62977i) q^{65} +(-7.63601 - 6.87550i) q^{66} +(-8.24200 + 3.16381i) q^{67} +(5.53271 + 20.6484i) q^{68} +(4.64447 - 3.37440i) q^{69} +(-13.6991 - 4.36084i) q^{70} +(9.94567 + 7.22595i) q^{71} +(1.96156 - 5.11003i) q^{72} +(-1.53012 + 2.35618i) q^{73} +(-0.855306 + 0.493811i) q^{74} +(-9.47026 - 3.85631i) q^{75} +9.06520i q^{76} +(5.22914 + 1.60667i) q^{77} +(4.19844 + 26.5079i) q^{78} +(3.25691 + 7.31514i) q^{79} +(-7.68534 + 0.325050i) q^{80} +(10.1852 + 4.53473i) q^{81} +(21.5275 - 5.76828i) q^{82} +(1.44682 - 9.13488i) q^{83} +(1.44459 + 21.0804i) q^{84} +(-7.09428 - 9.97456i) q^{85} +(9.03021 + 10.0291i) q^{86} +(-13.0416 + 0.683481i) q^{87} +(9.55931 - 0.500982i) q^{88} +(1.60882 + 1.78677i) q^{89} +(-0.0648213 + 6.42391i) q^{90} +(-7.97344 - 11.8567i) q^{91} +(-1.71492 + 10.8276i) q^{92} +(13.9983 - 3.75083i) q^{93} +(5.94777 + 2.64812i) q^{94} +(-1.81117 - 4.86441i) q^{95} +(-0.748490 - 1.68114i) q^{96} +(2.60779 + 16.4649i) q^{97} +(-8.20535 - 14.9005i) q^{98} -2.44450i 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} - 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}+ \cdots + 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

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{20}\right)$

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 $

$2$	−2.42673	−	0.127179i	−1.71596	−	0.0899294i	−0.831196	−	0.555979i	$-0.812344\pi$
$2$	−2.42673	−	0.127179i	−1.71596	−	0.0899294i	−0.884759	+	0.466050i	$0.845677\pi$
$3$	−1.28700	−	1.58931i	−0.743049	−	0.917590i	0.255742	−	0.966745i	$-0.417680\pi$
$3$	−1.28700	−	1.58931i	−0.743049	−	0.917590i	−0.998791	+	0.0491556i	$0.984347\pi$
$4$	3.88379	+	0.408202i	1.94189	+	0.204101i
$5$	−2.16561	+	0.556914i	−0.968488	+	0.249060i
$5$	−2.16561	+	0.556914i	−0.968488	+	0.249060i
$6$	2.92107	+	4.02051i	1.19252	+	1.64136i
$7$	−2.31224	−	1.28591i	−0.873944	−	0.486027i
$7$	−2.31224	−	1.28591i	−0.873944	−	0.486027i
$8$	−4.57269	−	0.724243i	−1.61669	−	0.256059i
$9$	−0.245810	+	1.15644i	−0.0819365	+	0.385481i
$10$	5.32616	−	1.07606i	1.68428	−	0.340279i
$11$	−2.02243	+	0.429882i	−0.609787	+	0.129614i	−0.502447	−	0.864608i	$-0.667567\pi$
$11$	−2.02243	+	0.429882i	−0.609787	+	0.129614i	−0.107340	+	0.994222i	$0.534233\pi$
$12$	−4.34967	−	6.69790i	−1.25564	−	1.93352i
$13$	4.81187	+	2.45177i	1.33457	+	0.679998i	0.968131	−	0.250443i	$-0.0805763\pi$
$13$	4.81187	+	2.45177i	1.33457	+	0.679998i	0.366441	+	0.930441i	$0.380576\pi$
$14$	5.44763	+	3.41461i	1.45594	+	0.912594i
$15$	3.67224	+	2.72507i	0.948169	+	0.703611i
$16$	3.36489	+	0.715229i	0.841221	+	0.178807i
$17$	1.96169	+	5.11037i	0.475779	+	1.23945i	0.936112	+	0.351701i	$0.114397\pi$
$17$	1.96169	+	5.11037i	0.475779	+	1.23945i	−0.460333	+	0.887746i	$0.652270\pi$
$18$	0.743588	−	2.77511i	0.175265	−	0.654100i
$19$	0.242645	+	2.30861i	0.0556666	+	0.529632i	0.986450	+	0.164061i	$0.0524595\pi$
$19$	0.242645	+	2.30861i	0.0556666	+	0.529632i	−0.930784	+	0.365571i	$0.880874\pi$
$20$	−8.63808	+	1.27893i	−1.93153	+	0.285977i
$21$	0.932143	+	5.32983i	0.203410	+	1.16306i
$22$	4.96257	−	0.785994i	1.05802	−	0.167574i
$23$	−0.146917	+	2.80334i	−0.0306343	+	0.584537i	0.939586	+	0.342313i	$0.111210\pi$
$23$	−0.146917	+	2.80334i	−0.0306343	+	0.584537i	−0.970220	+	0.242224i	$0.922123\pi$
$24$	4.73400	+	8.19953i	0.966324	+	1.67372i
$25$	4.37969	−	2.41211i	0.875939	−	0.482422i
$26$	−11.3653	−	6.56174i	−2.22891	−	1.28686i
$27$	−3.31219	+	1.68764i	−0.637430	+	0.324787i
$28$	−8.45533	−	5.93804i	−1.59791	−	1.12218i
$29$	3.75352	−	5.16628i	0.697011	−	0.959353i	−0.302969	−	0.953001i	$-0.597978\pi$
$29$	3.75352	−	5.16628i	0.697011	−	0.959353i	0.999980	−	0.00635297i	$-0.00202223\pi$
$30$	−8.56496	−	7.08004i	−1.56374	−	1.29263i
$31$	−2.88229	+	6.47373i	−0.517674	+	1.16272i	0.445853	+	0.895106i	$0.352900\pi$
$31$	−2.88229	+	6.47373i	−0.517674	+	1.16272i	−0.963527	+	0.267609i	$0.913766\pi$
$32$	0.869181	+	0.232896i	0.153651	+	0.0411706i
$33$	3.28609	+	2.66102i	0.572035	+	0.463224i
$34$	−4.11055	−	12.6510i	−0.704953	−	2.16962i
$35$	5.72353	+	1.49705i	0.967454	+	0.253047i
$36$	−1.42673	+	4.39104i	−0.237789	+	0.731839i
$37$	0.340852	−	0.221352i	0.0560357	−	0.0363900i	−0.516317	−	0.856397i	$-0.672697\pi$
$37$	0.340852	−	0.221352i	0.0560357	−	0.0363900i	0.572353	+	0.820007i	$0.306031\pi$
$38$	−0.295225	−	5.63323i	−0.0478919	−	0.913831i
$39$	−2.29624	−	10.8030i	−0.367693	−	1.72986i
$40$	10.3060	−	0.978172i	1.62952	−	0.154663i
$41$	−8.72248	+	2.83411i	−1.36222	+	0.442613i	−0.896784	−	0.442468i	$-0.854103\pi$
$41$	−8.72248	+	2.83411i	−1.36222	+	0.442613i	−0.465438	+	0.885081i	$0.654103\pi$
$42$	−1.58421	−	13.0526i	−0.244449	−	2.01406i
$43$	−3.92695	−	3.92695i	−0.598854	−	0.598854i	0.341153	−	0.940008i	$-0.389182\pi$
$43$	−3.92695	−	3.92695i	−0.598854	−	0.598854i	−0.940008	+	0.341153i	$0.889182\pi$
$44$	−8.03018	+	0.844006i	−1.21060	+	0.127239i
$45$	−0.111713	−	2.64129i	−0.0166532	−	0.393741i
$46$	0.713054	−	6.78426i	0.105134	−	1.00028i
$47$	−2.50126	−	0.960145i	−0.364847	−	0.140052i	0.169036	−	0.985610i	$-0.445934\pi$
$47$	−2.50126	−	0.960145i	−0.364847	−	0.140052i	−0.533883	+	0.845558i	$0.679268\pi$
$48$	−3.19388	−	6.26835i	−0.460997	−	0.904759i
$49$	3.69289	+	5.94664i	0.527556	+	0.849520i
$50$	−10.9351	+	5.29653i	−1.54646	+	0.749043i
$51$	5.59728	−	9.69478i	0.783777	−	1.35754i
$52$	17.6874	+	11.4864i	2.45281	+	1.59287i
$53$	−3.15369	+	2.55381i	−0.433193	+	0.350793i	−0.820981	−	0.570956i	$-0.806573\pi$
$53$	−3.15369	+	2.55381i	−0.433193	+	0.350793i	0.387788	+	0.921749i	$0.373239\pi$
$54$	8.25240	−	3.67421i	1.12301	−	0.499996i
$55$	4.14039	−	2.05728i	0.558290	−	0.277403i
$56$	9.64184	+	7.55468i	1.28845	+	1.00954i
$57$	3.35682	−	3.35682i	0.444622	−	0.444622i
$58$	−9.76581	+	12.0598i	−1.28231	+	1.58353i
$59$	0.0263546	−	0.0292698i	0.00343108	−	0.00381060i	−0.741427	−	0.671034i	$-0.765851\pi$
$59$	0.0263546	−	0.0292698i	0.00343108	−	0.00381060i	0.744858	+	0.667223i	$0.232517\pi$
$60$	13.1498	+	12.0826i	1.69763	+	1.55986i
$61$	−5.29174	+	4.76471i	−0.677538	+	0.610058i	−0.934330	−	0.356409i	$-0.884001\pi$
$61$	−5.29174	+	4.76471i	−0.677538	+	0.610058i	0.256792	+	0.966467i	$0.417334\pi$
$62$	7.81785	−	15.3434i	0.992868	−	1.94861i
$63$	2.05545	−	2.35788i	0.258962	−	0.297065i
$64$	−8.62303	−	2.80179i	−1.07788	−	0.350224i
$65$	−11.7860	−	2.62977i	−1.46188	−	0.326182i
$66$	−7.63601	−	6.87550i	−0.939928	−	0.846315i
$67$	−8.24200	+	3.16381i	−1.00692	+	0.386520i	−0.805251	−	0.592933i	$-0.797970\pi$
$67$	−8.24200	+	3.16381i	−1.00692	+	0.386520i	−0.201669	+	0.979454i	$0.564636\pi$
$68$	5.53271	+	20.6484i	0.670940	+	2.50398i
$69$	4.64447	−	3.37440i	0.559128	−	0.406230i
$70$	−13.6991	−	4.36084i	−1.63735	−	0.521220i
$71$	9.94567	+	7.22595i	1.18033	+	0.857562i	0.992209	−	0.124583i	$-0.0397592\pi$
$71$	9.94567	+	7.22595i	1.18033	+	0.857562i	0.188124	+	0.982145i	$0.439759\pi$
$72$	1.96156	−	5.11003i	0.231172	−	0.602223i
$73$	−1.53012	+	2.35618i	−0.179087	+	0.275769i	−0.916802	−	0.399343i	$-0.869238\pi$
$73$	−1.53012	+	2.35618i	−0.179087	+	0.275769i	0.737715	+	0.675112i	$0.235905\pi$
$74$	−0.855306	+	0.493811i	−0.0994273	+	0.0574044i
$75$	−9.47026	−	3.85631i	−1.09353	−	0.445288i
$76$			9.06520i			1.03985i
$77$	5.22914	+	1.60667i	0.595916	+	0.183097i
$78$	4.19844	+	26.5079i	0.475380	+	3.00143i
$79$	3.25691	+	7.31514i	0.366431	+	0.823017i	0.998829	+	0.0483740i	$0.0154039\pi$
$79$	3.25691	+	7.31514i	0.366431	+	0.823017i	−0.632398	+	0.774643i	$0.717929\pi$
$80$	−7.68534	+	0.325050i	−0.859247	+	0.0363416i
$81$	10.1852	+	4.53473i	1.13169	+	0.503859i
$82$	21.5275	−	5.76828i	2.37732	−	0.637000i
$83$	1.44682	−	9.13488i	0.158809	−	1.00268i	−0.771586	−	0.636125i	$-0.780536\pi$
$83$	1.44682	−	9.13488i	0.158809	−	1.00268i	0.930395	−	0.366558i	$-0.119464\pi$
$84$	1.44459	+	21.0804i	0.157618	+	2.30006i
$85$	−7.09428	−	9.97456i	−0.769483	−	1.08189i
$86$	9.03021	+	10.0291i	0.973752	+	1.08146i
$87$	−13.0416	+	0.683481i	−1.39821	+	0.0732769i
$88$	9.55931	−	0.500982i	1.01903	−	0.0534049i
$89$	1.60882	+	1.78677i	0.170534	+	0.189398i	0.822354	−	0.568977i	$-0.192661\pi$
$89$	1.60882	+	1.78677i	0.170534	+	0.189398i	−0.651819	+	0.758374i	$0.725994\pi$
$90$	−0.0648213	+	6.42391i	−0.00683276	+	0.677139i
$91$	−7.97344	−	11.8567i	−0.835843	−	1.24292i
$92$	−1.71492	+	10.8276i	−0.178793	+	1.12886i
$93$	13.9983	−	3.75083i	1.45155	−	0.388942i
$94$	5.94777	+	2.64812i	0.613466	+	0.273133i
$95$	−1.81117	−	4.86441i	−0.185822	−	0.499078i
$96$	−0.748490	−	1.68114i	−0.0763925	−	0.171580i
$97$	2.60779	+	16.4649i	0.264781	+	1.67176i	0.658539	+	0.752546i	$0.271175\pi$
$97$	2.60779	+	16.4649i	0.264781	+	1.67176i	−0.393758	+	0.919214i	$0.628825\pi$
$98$	−8.20535	−	14.9005i	−0.828865	−	1.50518i
$99$		−	2.44450i		−	0.245681i
$100$	17.9944	−	7.58033i	1.79944	−	0.758033i
$101$	2.70125	−	1.55957i	0.268784	−	0.155183i	−0.359551	−	0.933125i	$-0.617070\pi$
$101$	2.70125	−	1.55957i	0.268784	−	0.155183i	0.628335	+	0.777943i	$0.283737\pi$
$102$	−14.8161	+	22.8147i	−1.46701	+	2.25899i
$103$	3.97884	−	10.3652i	0.392046	−	1.02132i	−0.585514	−	0.810662i	$-0.699107\pi$
$103$	3.97884	−	10.3652i	0.392046	−	1.02132i	0.977561	−	0.210654i	$-0.0675593\pi$
$104$	−20.2275	−	14.6961i	−1.98347	−	1.44108i
$105$	−4.98691	−	11.0232i	−0.486673	−	1.07575i
$106$	7.97794	−	5.79632i	0.774886	−	0.562988i
$107$	1.42262	+	5.30928i	0.137530	+	0.513267i	0.999975	+	0.00711676i	$0.00226535\pi$
$107$	1.42262	+	5.30928i	0.137530	+	0.513267i	−0.862445	+	0.506151i	$0.831068\pi$
$108$	−13.5527	+	5.20240i	−1.30411	+	0.500601i
$109$	−7.84043	−	7.05955i	−0.750977	−	0.676183i	0.201946	−	0.979397i	$-0.435274\pi$
$109$	−7.84043	−	7.05955i	−0.750977	−	0.676183i	−0.952922	+	0.303214i	$0.901940\pi$
$110$	−10.3092	+	4.46588i	−0.982947	+	0.425805i
$111$	−0.790473	−	0.256840i	−0.0750284	−	0.0243782i
$112$	−6.86070	−	5.98071i	−0.648275	−	0.565124i
$113$	2.84806	−	5.58963i	0.267923	−	0.525828i	−0.717372	−	0.696690i	$-0.754655\pi$
$113$	2.84806	−	5.58963i	0.267923	−	0.525828i	0.985295	+	0.170862i	$0.0546552\pi$
$114$	−8.57301	+	7.71917i	−0.802936	+	0.722967i
$115$	−1.24306	−	6.15275i	−0.115916	−	0.573747i
$116$	16.6867	−	18.5325i	1.54933	−	1.72070i
$117$	−4.01813	+	4.96198i	−0.371477	+	0.458735i
$118$	−0.0676779	+	0.0676779i	−0.00623026	+	0.00623026i
$119$	2.03557	−	14.3389i	0.186600	−	1.31445i
$120$	−14.8184	−	15.1205i	−1.35273	−	1.38031i
$121$	−6.14356	+	2.73529i	−0.558505	+	0.248662i
$122$	13.4476	−	10.8896i	1.21749	−	0.985902i
$123$	15.7301	+	10.2152i	1.41834	+	0.921078i
$124$	−13.8368	+	23.9660i	−1.24258	+	2.15221i
$125$	−8.14135	+	7.66280i	−0.728184	+	0.685381i
$126$	−5.28788	+	5.46053i	−0.471082	+	0.486463i
$127$	0.0522005	+	0.102449i	0.00463204	+	0.00909090i	0.893311	−	0.449439i	$-0.148376\pi$
$127$	0.0522005	+	0.102449i	0.00463204	+	0.00909090i	−0.888679	+	0.458530i	$0.848376\pi$
$128$	18.8893	+	7.25090i	1.66959	+	0.640895i
$129$	−1.18717	+	11.2951i	−0.104524	+	0.994481i
$130$	28.2670	+	7.88067i	2.47918	+	0.691180i
$131$	4.48303	−	0.471186i	0.391685	−	0.0411677i	0.0933606	−	0.995632i	$-0.470239\pi$
$131$	4.48303	−	0.471186i	0.391685	−	0.0411677i	0.298324	+	0.954465i	$0.403572\pi$
$132$	11.6762	+	11.6762i	1.01628	+	1.01628i
$133$	2.40761	−	5.65008i	0.208766	−	0.489924i
$134$	20.4034	−	6.62948i	1.76259	−	0.572700i
$135$	6.23302	−	5.49937i	0.536453	−	0.473311i
$136$	−5.26904	−	24.7889i	−0.451817	−	2.12563i
$137$	0.773425	+	14.7578i	0.0660782	+	1.26085i	0.807524	+	0.589834i	$0.200807\pi$
$137$	0.773425	+	14.7578i	0.0660782	+	1.26085i	−0.741446	+	0.671012i	$0.765860\pi$
$138$	−11.7000	+	7.59807i	−0.995970	+	0.646791i
$139$	−6.53701	+	20.1189i	−0.554462	+	1.70646i	0.142897	+	0.989738i	$0.454358\pi$
$139$	−6.53701	+	20.1189i	−0.554462	+	1.70646i	−0.697359	+	0.716722i	$0.745642\pi$
$140$	21.6179	+	8.15057i	1.82704	+	0.688849i
$141$	1.69315	+	5.21099i	0.142589	+	0.438845i
$142$	−23.2164	−	18.8003i	−1.94828	−	1.57769i
$143$	−10.7857	−	2.89001i	−0.901942	−	0.241675i
$144$	−1.65424	+	3.71549i	−0.137854	+	0.309624i
$145$	−5.25147	+	13.2785i	−0.436111	+	1.10272i
$146$	4.01284	−	5.52319i	0.332105	−	0.457103i
$147$	4.69832	−	13.5225i	0.387511	−	1.11532i
$148$	1.41415	−	0.720546i	0.116243	−	0.0592286i
$149$	−6.08466	−	3.51298i	−0.498474	−	0.287794i	0.229609	−	0.973283i	$-0.426255\pi$
$149$	−6.08466	−	3.51298i	−0.498474	−	0.287794i	−0.728083	+	0.685489i	$0.759589\pi$
$150$	22.4913	+	10.5626i	1.83641	+	0.862436i
$151$	−9.79544	−	16.9662i	−0.797142	−	1.38069i	−0.921470	−	0.388449i	$-0.873011\pi$
$151$	−9.79544	−	16.9662i	−0.797142	−	1.38069i	0.124328	−	0.992241i	$-0.460322\pi$
$152$	0.562457	−	10.7323i	0.0456213	−	0.870505i
$153$	−6.39206	+	1.01240i	−0.516767	+	0.0818479i
$154$	−12.4854	−	4.56399i	−1.00610	−	0.367777i
$155$	2.63659	−	15.6247i	0.211776	−	1.25501i
$156$	−4.50832	−	42.8938i	−0.360954	−	3.43425i
$157$	−0.466587	+	1.74133i	−0.0372377	+	0.138973i	−0.982042	−	0.188662i	$-0.939585\pi$
$157$	−0.466587	+	1.74133i	−0.0372377	+	0.138973i	0.944804	+	0.327635i	$0.106252\pi$
$158$	−6.97330	−	18.1661i	−0.554766	−	1.44521i
$159$	8.11760	+	1.72545i	0.643768	+	0.136837i
$160$	−2.01201	−	0.0203024i	−0.159063	−	0.00160505i
$161$	3.94454	−	6.29307i	0.310873	−	0.495964i
$162$	−24.1399	−	12.2999i	−1.89661	−	0.966371i
$163$	0.714689	+	1.10052i	0.0559788	+	0.0861997i	0.865552	−	0.500819i	$-0.166968\pi$
$163$	0.714689	+	1.10052i	0.0559788	+	0.0861997i	−0.809573	+	0.587019i	$0.800301\pi$
$164$	−35.0331	+	7.44652i	−2.73563	+	0.581475i
$165$	−8.59833	−	3.93265i	−0.669379	−	0.306157i
$166$	−4.67281	+	21.9839i	−0.362681	+	1.70628i
$167$	0.192973	+	0.0305638i	0.0149327	+	0.00236510i	0.163896	−	0.986478i	$-0.447594\pi$
$167$	0.192973	+	0.0305638i	0.0149327	+	0.00236510i	−0.148964	+	0.988843i	$0.547594\pi$
$168$	−0.402310	−	25.0468i	−0.0310389	−	1.93240i
$169$	9.50169	+	13.0780i	0.730899	+	1.00600i
$170$	15.9473	+	25.1078i	1.22310	+	1.92568i
$171$	−2.72942	−	0.286874i	−0.208724	−	0.0219378i
$172$	−13.6484	−	16.8544i	−1.04068	−	1.28514i
$173$	−4.56378	−	0.239178i	−0.346978	−	0.0181843i	−0.121949	−	0.992536i	$-0.538914\pi$
$173$	−4.56378	−	0.239178i	−0.346978	−	0.0181843i	−0.225029	+	0.974352i	$0.572248\pi$
$174$	31.7353			2.40585
$175$	−13.2286	−	0.0544970i	−0.999992	−	0.00411959i
$176$	−7.11273			−0.536142
$177$	−0.0804371	−	0.00421553i	−0.00604602	−	0.000316859i
$178$	−3.67692	−	4.54062i	−0.275597	−	0.340334i
$179$	−16.2139	−	1.70415i	−1.21188	−	0.127374i	−0.523056	−	0.852298i	$-0.675208\pi$
$179$	−16.2139	−	1.70415i	−1.21188	−	0.127374i	−0.688829	+	0.724924i	$0.741875\pi$
$180$	0.644313	−	10.3038i	0.0480243	−	0.768001i
$181$	−6.42376	−	8.84155i	−0.477474	−	0.657187i	0.500543	−	0.865712i	$-0.333134\pi$
$181$	−6.42376	−	8.84155i	−0.477474	−	0.657187i	−0.978017	+	0.208525i	$0.933134\pi$
$182$	17.8414	+	29.7870i	1.32249	+	2.20796i
$183$	14.3831	+	2.27805i	1.06323	+	0.168399i
$184$	2.70211	−	12.7124i	0.199202	−	0.937172i
$185$	−0.614877	+	0.669186i	−0.0452066	+	0.0491995i
$186$	−34.4470	+	7.32194i	−2.52578	+	0.536871i
$187$	−6.16424	−	9.49210i	−0.450774	−	0.694131i
$188$	−9.32244	−	4.75002i	−0.679909	−	0.346431i
$189$	9.82871	+	0.356928i	0.714934	+	0.0259627i
$190$	3.77657	+	12.0349i	0.273981	+	0.873107i
$191$	25.8655	+	5.49788i	1.87156	+	0.397813i	0.996308	−	0.0858500i	$-0.0273606\pi$
$191$	25.8655	+	5.49788i	1.87156	+	0.397813i	0.875254	+	0.483663i	$0.160694\pi$
$192$	6.64491	+	17.3106i	0.479555	+	1.24928i
$193$	−3.32790	+	12.4199i	−0.239547	+	0.894002i	0.736499	+	0.676439i	$0.236478\pi$
$193$	−3.32790	+	12.4199i	−0.239547	+	0.894002i	−0.976046	+	0.217564i	$0.930189\pi$
$194$	−4.23439	−	40.2875i	−0.304012	−	2.89248i
$195$	10.9891	+	22.1162i	0.786945	+	1.58377i
$196$	11.9150	+	24.6029i	0.851068	+	1.75735i
$197$	−12.6628	+	2.00559i	−0.902189	+	0.142893i	−0.590260	−	0.807213i	$-0.700975\pi$
$197$	−12.6628	+	2.00559i	−0.902189	+	0.142893i	−0.311929	+	0.950106i	$0.600975\pi$
$198$	−0.310890	+	5.93213i	−0.0220940	+	0.421578i
$199$	0.816805	+	1.41475i	0.0579018	+	0.100289i	0.893523	−	0.449017i	$-0.148226\pi$
$199$	0.816805	+	1.41475i	0.0579018	+	0.100289i	−0.835622	+	0.549306i	$0.814892\pi$
$200$	−21.7739	+	7.85788i	−1.53965	+	0.555636i
$201$	15.6357	+	9.02728i	1.10286	+	0.636736i
$202$	−6.75353	+	3.44110i	−0.475177	+	0.242115i
$203$	−15.3224	+	7.11899i	−1.07542	+	0.499655i
$204$	25.6961	−	35.3676i	1.79909	−	2.47623i
$205$	17.3111	−	10.9952i	1.20906	−	0.767940i
$206$	−10.9738	+	24.6475i	−0.764580	+	1.71728i
$207$	−3.20579	−	0.858989i	−0.222818	−	0.0597039i
$208$	14.4378	+	11.6915i	1.00108	+	0.810660i
$209$	−1.48316	−	4.56471i	−0.102593	−	0.315748i
$210$	10.6999	+	27.3845i	0.738366	+	1.88971i
$211$	−1.38124	+	4.25101i	−0.0950883	+	0.292652i	−0.987277	−	0.159012i	$-0.949169\pi$
$211$	−1.38124	+	4.25101i	−0.0950883	+	0.292652i	0.892188	+	0.451664i	$0.149169\pi$
$212$	−13.2907	+	8.63111i	−0.912812	+	0.592787i
$213$	−1.31578	−	25.1066i	−0.0901557	−	1.72027i
$214$	−2.77707	−	13.0651i	−0.189837	−	0.893112i
$215$	10.6912	+	6.31725i	0.729134	+	0.430833i
$216$	16.3679	−	5.31824i	1.11369	−	0.361861i
$217$	14.9891	−	11.2624i	1.01753	−	0.764544i
$218$	18.1287	+	18.1287i	1.22783	+	1.22783i
$219$	5.71396	−	0.600561i	0.386113	−	0.0405822i
$220$	16.9202	−	6.29991i	1.14076	−	0.424740i
$221$	−3.09007	+	29.4000i	−0.207861	+	1.97766i
$222$	1.88560	+	0.723813i	0.126553	+	0.0485792i
$223$	8.27155	+	16.2338i	0.553904	+	1.08710i	0.982960	+	0.183820i	$0.0588463\pi$
$223$	8.27155	+	16.2338i	0.553904	+	1.08710i	−0.429056	+	0.903278i	$0.641154\pi$
$224$	−1.71027	−	1.65620i	−0.114272	−	0.110659i
$225$	1.71290	+	5.65779i	0.114193	+	0.377186i
$226$	−7.62235	+	13.2023i	−0.507031	+	0.878203i
$227$	−9.25783	−	6.01211i	−0.614464	−	0.399037i	0.199546	−	0.979888i	$-0.436053\pi$
$227$	−9.25783	−	6.01211i	−0.614464	−	0.399037i	−0.814010	+	0.580851i	$0.802720\pi$
$228$	14.4074	−	11.6669i	0.954156	−	0.772660i
$229$	18.2114	−	8.10823i	1.20344	−	0.535807i	0.295677	−	0.955288i	$-0.404455\pi$
$229$	18.2114	−	8.10823i	1.20344	−	0.535807i	0.907764	+	0.419481i	$0.137788\pi$
$230$	2.23406	+	15.0891i	0.147309	+	0.994948i
$231$	−4.17639	−	10.3785i	−0.274787	−	0.682856i
$232$	−20.9053	+	20.9053i	−1.37250	+	1.37250i
$233$	2.95068	−	3.64378i	0.193305	−	0.238712i	−0.671273	−	0.741210i	$-0.734252\pi$
$233$	2.95068	−	3.64378i	0.193305	−	0.238712i	0.864578	+	0.502498i	$0.167586\pi$
$234$	10.3820	−	11.5304i	0.678691	−	0.753763i
$235$	5.95147	+	0.686307i	0.388231	+	0.0447697i
$236$	0.114304	−	0.102919i	0.00744053	−	0.00669948i
$237$	7.43439	−	14.5908i	0.482916	−	0.947776i
$238$	−6.76339	+	34.5378i	−0.438406	+	2.23876i
$239$	15.3187	+	4.97734i	0.990884	+	0.321958i	0.759217	−	0.650838i	$-0.225582\pi$
$239$	15.3187	+	4.97734i	0.990884	+	0.321958i	0.231667	+	0.972795i	$0.425582\pi$
$240$	10.4076	+	11.7961i	0.671809	+	0.761432i
$241$	−10.1665	−	9.15393i	−0.654880	−	0.589657i	0.273236	−	0.961947i	$-0.411906\pi$
$241$	−10.1665	−	9.15393i	−0.654880	−	0.589657i	−0.928116	+	0.372290i	$0.878573\pi$
$242$	15.2566	−	5.85646i	0.980732	−	0.376468i
$243$	−3.01484	−	11.2515i	−0.193402	−	0.721786i
$244$	−22.4969	+	16.3450i	−1.44022	+	1.04638i
$245$	−11.3091	−	10.8215i	−0.722513	−	0.691358i
$246$	−36.8735	−	26.7902i	−2.35097	−	1.70808i
$247$	−4.49261	+	11.7036i	−0.285858	+	0.744685i
$248$	17.8684	−	27.5149i	1.13464	−	1.74720i
$249$	−16.3802	+	9.45713i	−1.03805	+	0.599321i
$250$	20.7314	−	17.5601i	1.31117	−	1.11060i
$251$			0.00533874i			0.000336978i	1.00000		0.000168489i	$5.36317e-5\pi$
$251$			0.00533874i			0.000336978i	−1.00000		0.000168489i	$0.999946\pi$
$252$	8.94541	−	8.31847i	0.563508	−	0.524015i
$253$	−0.907976	−	5.73273i	−0.0570839	−	0.360414i
$254$	−0.113647	−	0.255255i	−0.00713084	−	0.0160161i
$255$	−6.72235	+	24.1123i	−0.420970	+	1.50997i
$256$	−28.3510	−	12.6227i	−1.77194	−	0.788919i
$257$	−10.2934	+	2.75812i	−0.642087	+	0.172047i	−0.565148	−	0.824989i	$-0.691181\pi$
$257$	−10.2934	+	2.75812i	−0.642087	+	0.172047i	−0.0769383	+	0.997036i	$0.524514\pi$
$258$	4.31743	−	27.2592i	0.268792	−	1.69708i
$259$	−1.07277	+	0.0735145i	−0.0666586	+	0.00456797i
$260$	−44.7009	−	15.0245i	−2.77223	−	0.931782i
$261$	5.05185	+	5.61065i	0.312702	+	0.347291i
$262$	−10.9390	+	0.573290i	−0.675815	+	0.0354180i
$263$	2.06625	−	0.108288i	0.127410	−	0.00667729i	0.0114758	−	0.999934i	$-0.496347\pi$
$263$	2.06625	−	0.108288i	0.127410	−	0.00667729i	0.115935	+	0.993257i	$0.463014\pi$
$264$	−13.0990	−	14.5480i	−0.806190	−	0.895365i
$265$	5.40740	−	7.28688i	0.332174	−	0.447630i
$266$	−6.56118	+	13.4050i	−0.402292	+	0.821914i
$267$	0.769192	−	4.85649i	0.0470738	−	0.297212i
$268$	−33.3016	+	8.92314i	−2.03422	+	0.545068i
$269$	−3.16339	−	1.40843i	−0.192875	−	0.0858737i	0.308026	−	0.951378i	$-0.400332\pi$
$269$	−3.16339	−	1.40843i	−0.192875	−	0.0858737i	−0.500902	+	0.865504i	$0.666998\pi$
$270$	−15.8252	+	12.5528i	−0.963093	+	0.763937i
$271$	−1.32960	−	2.98633i	−0.0807674	−	0.181406i	0.868648	−	0.495430i	$-0.164990\pi$
$271$	−1.32960	−	2.98633i	−0.0807674	−	0.181406i	−0.949415	+	0.314024i	$0.898323\pi$
$272$	2.94577	+	18.5989i	0.178614	+	1.12772i
$273$	−8.58216	+	27.9318i	−0.519416	+	1.69051i
$274$		−	35.9116i		−	2.16950i
$275$	−7.82072	+	6.76109i	−0.471607	+	0.407709i
$276$	19.4155	−	11.2096i	1.16868	−	0.674737i
$277$	17.8069	−	27.4201i	1.06991	−	1.64752i	0.377506	−	0.926007i	$-0.376782\pi$
$277$	17.8069	−	27.4201i	1.06991	−	1.64752i	0.692404	−	0.721510i	$-0.256552\pi$
$278$	18.4223	−	47.9916i	1.10489	−	2.87835i
$279$	−6.77800	−	4.92451i	−0.405788	−	0.294822i
$280$	−25.0877	−	10.9908i	−1.49928	−	0.656824i
$281$	−15.0878	+	10.9619i	−0.900063	+	0.653934i	−0.938482	−	0.345328i	$-0.887768\pi$
$281$	−15.0878	+	10.9619i	−0.900063	+	0.653934i	0.0384191	+	0.999262i	$0.487768\pi$
$282$	−3.44609	−	12.8610i	−0.205212	−	0.765861i
$283$	21.4785	−	8.24482i	1.27676	−	0.490104i	0.376892	−	0.926257i	$-0.376993\pi$
$283$	21.4785	−	8.24482i	1.27676	−	0.490104i	0.899872	+	0.436153i	$0.143660\pi$
$284$	35.6772	+	32.1239i	2.11705	+	1.90620i
$285$	−5.40009	+	9.13901i	−0.319874	+	0.541348i
$286$	25.8063	+	8.38498i	1.52596	+	0.495814i
$287$	23.8128	+	4.66316i	1.40563	+	0.275258i
$288$	−0.482984	+	0.947910i	−0.0284601	+	0.0558561i
$289$	−9.63424	+	8.67470i	−0.566720	+	0.510277i
$290$	14.4326	−	31.5554i	0.847514	−	1.85300i
$291$	22.8117	−	25.3349i	1.33724	−	1.48516i
$292$	−6.90445	+	8.52628i	−0.404052	+	0.498963i
$293$	6.36211	−	6.36211i	0.371678	−	0.371678i	−0.496410	−	0.868088i	$-0.665349\pi$
$293$	6.36211	−	6.36211i	0.371678	−	0.371678i	0.868088	+	0.496410i	$0.165349\pi$
$294$	−13.1213	+	32.2178i	−0.765251	+	1.87898i
$295$	−0.0407729	+	0.0780640i	−0.00237389	+	0.00454506i
$296$	−1.71892	+	0.765314i	−0.0999104	+	0.0444830i
$297$	5.97319	−	4.83700i	0.346600	−	0.280671i
$298$	14.3190	+	9.29888i	0.829479	+	0.538670i
$299$	−7.58009	+	13.1291i	−0.438368	+	0.759276i
$300$	−35.2063	−	18.8429i	−2.03264	−	1.08789i
$301$	4.03035	+	14.1297i	0.232306	+	0.814424i
$302$	21.6131	+	42.4181i	1.24370	+	2.44089i
$303$	−5.95514	−	2.28596i	−0.342114	−	0.131325i
$304$	−0.834713	+	7.94177i	−0.0478741	+	0.455491i
$305$	8.80629	−	13.2655i	0.504247	−	0.759581i
$306$	15.6405	−	1.64389i	0.894110	−	0.0939747i
$307$	−18.7776	−	18.7776i	−1.07170	−	1.07170i	−0.997223	−	0.0744731i	$-0.976273\pi$
$307$	−18.7776	−	18.7776i	−1.07170	−	1.07170i	−0.0744731	−	0.997223i	$-0.523727\pi$
$308$	19.6530	+	8.37452i	1.11983	+	0.477182i
$309$	−21.5943	+	7.01642i	−1.22846	+	0.399150i
$310$	−8.38543	+	37.5816i	−0.476260	+	2.13449i
$311$	0.220027	+	1.03515i	0.0124766	+	0.0586977i	0.983945	−	0.178469i	$-0.0571145\pi$
$311$	0.220027	+	1.03515i	0.0124766	+	0.0586977i	−0.971469	+	0.237167i	$0.923781\pi$
$312$	2.67603	+	51.0618i	0.151501	+	2.89080i
$313$	−15.8425	+	10.2882i	−0.895470	+	0.581525i	−0.908266	−	0.418393i	$-0.862593\pi$
$313$	−15.8425	+	10.2882i	−0.895470	+	0.581525i	0.0127962	+	0.999918i	$0.495927\pi$
$314$	1.35374	−	4.16638i	0.0763960	−	0.235123i
$315$	−3.13815	+	6.25095i	−0.176815	+	0.352201i
$316$	9.66308	+	29.7399i	0.543591	+	1.67300i
$317$	−22.4500	−	18.1797i	−1.26092	−	1.02107i	−0.998423	−	0.0561385i	$-0.982121\pi$
$317$	−22.4500	−	18.1797i	−1.26092	−	1.02107i	−0.262496	−	0.964933i	$-0.584546\pi$
$318$	−19.4798	−	5.21959i	−1.09237	−	0.292700i
$319$	−5.37036	+	12.0620i	−0.300682	+	0.675344i
$320$	20.2344	+	1.26529i	1.13114	+	0.0707318i
$321$	6.60719	−	9.09402i	0.368778	−	0.507579i
$322$	−10.3727	+	14.7699i	−0.578047	+	0.823094i
$323$	−11.3219	+	5.76879i	−0.629966	+	0.320984i
$324$	37.7059	+	21.7695i	2.09477	+	1.20942i
$325$	26.9884	−	0.868769i	1.49705	−	0.0481906i
$326$	−1.59439	−	2.76157i	−0.0883052	−	0.152949i
$327$	−1.12921	+	21.5465i	−0.0624452	+	1.19153i
$328$	41.9378	−	6.64229i	2.31563	−	0.366759i
$329$	4.54886	+	5.43648i	0.250787	+	0.299723i
$330$	20.3656	+	10.6370i	1.12109	+	0.585548i
$331$	0.186826	+	1.77753i	0.0102689	+	0.0977018i	0.998456	−	0.0555514i	$-0.0176917\pi$
$331$	0.186826	+	1.77753i	0.0102689	+	0.0977018i	−0.988187	+	0.153253i	$0.951025\pi$
$332$	9.34803	−	34.8873i	0.513040	−	1.91469i
$333$	0.172196	+	0.448586i	0.00943629	+	0.0245824i
$334$	−0.464405	−	0.0987122i	−0.0254111	−	0.00540129i
$335$	16.0869	−	11.4416i	0.878923	−	0.625123i
$336$	−0.675491	+	18.6010i	−0.0368510	+	1.01477i
$337$	−12.9437	−	6.59514i	−0.705088	−	0.359260i	0.0643976	−	0.997924i	$-0.479487\pi$
$337$	−12.9437	−	6.59514i	−0.705088	−	0.359260i	−0.769486	+	0.638664i	$0.779487\pi$
$338$	−21.3948	−	32.9450i	−1.16372	−	1.79197i
$339$	−12.5491	+	2.66740i	−0.681574	+	0.144873i
$340$	−23.4810	−	41.6350i	−1.27344	−	2.25797i
$341$	3.04630	−	14.3317i	0.164967	−	0.776107i
$342$	6.58708	+	1.04329i	0.356189	+	0.0564147i
$343$	−0.892015	−	18.4988i	−0.0481643	−	0.998839i
$344$	15.1127	+	20.8008i	0.814820	+	1.12150i
$345$	−8.17883	+	9.89419i	−0.440333	+	0.532685i
$346$	11.0446	+	1.16084i	0.593763	+	0.0624070i
$347$	2.69478	+	3.32777i	0.144663	+	0.178644i	0.844327	−	0.535828i	$-0.180000\pi$
$347$	2.69478	+	3.32777i	0.144663	+	0.178644i	−0.699664	+	0.714472i	$0.746667\pi$
$348$	−50.9298	−	2.66912i	−2.73012	−	0.143080i
$349$	−9.54903			−0.511148			−0.255574	−	0.966789i	$-0.582264\pi$
$349$	−9.54903			−0.511148			−0.255574	+	0.966789i	$0.582264\pi$
$350$	32.0954	+	1.81466i	1.71557	+	0.0969977i
$351$	−20.0755			−1.07155
$352$	−1.85798	−	0.0973726i	−0.0990306	−	0.00518998i
$353$	3.61094	+	4.45914i	0.192191	+	0.237336i	0.864128	−	0.503272i	$-0.167871\pi$
$353$	3.61094	+	4.45914i	0.192191	+	0.237336i	−0.671937	+	0.740608i	$0.734537\pi$
$354$	0.194663	+	0.0204599i	0.0103462	+	0.00108743i
$355$	−25.5626	−	10.1097i	−1.35672	−	0.536566i
$356$	5.51894	+	7.59616i	0.292503	+	0.402596i
$357$	−25.4088	+	15.2191i	−1.34478	+	0.805478i
$358$	39.1300	+	6.19758i	2.06808	+	0.327552i
$359$	2.36718	−	11.1367i	0.124935	−	0.587772i	−0.870487	−	0.492192i	$-0.836196\pi$
$359$	2.36718	−	11.1367i	0.124935	−	0.587772i	0.995422	−	0.0955806i	$-0.0304708\pi$
$360$	−1.40211	+	12.1587i	−0.0738977	+	0.640821i
$361$	13.3140	−	2.82998i	0.700736	−	0.148946i
$362$	14.4643	+	22.2730i	0.760224	+	1.17064i
$363$	12.2540	+	6.24371i	0.643167	+	0.327710i
$364$	−26.1272	−	49.3036i	−1.36944	−	2.58421i
$365$	2.00144	−	5.95469i	0.104760	−	0.311683i
$366$	−34.6141	−	7.35745i	−1.80931	−	0.384580i
$367$	5.13732	+	13.3832i	0.268166	+	0.698596i	0.999856	+	0.0169586i	$0.00539834\pi$
$367$	5.13732	+	13.3832i	0.268166	+	0.698596i	−0.731690	+	0.681637i	$0.761268\pi$
$368$	−2.49939	+	9.32784i	−0.130290	+	0.486248i
$369$	−1.13341	−	10.7837i	−0.0590031	−	0.561377i
$370$	1.57724	−	1.54573i	0.0819971	−	0.0803588i
$371$	10.5761	−	1.84966i	0.549081	−	0.0960298i
$372$	55.8974	−	8.85327i	2.89814	−	0.459021i
$373$	1.32225	−	25.2300i	0.0684634	−	1.30636i	−0.721160	−	0.692768i	$-0.756391\pi$
$373$	1.32225	−	25.2300i	0.0684634	−	1.30636i	0.789624	−	0.613591i	$-0.210276\pi$
$374$	13.7517	+	23.8187i	0.711085	+	1.23164i
$375$	22.6565	+	3.07713i	1.16998	+	0.158902i
$376$	10.7421	+	6.20197i	0.553983	+	0.319842i
$377$	30.7280	−	15.6567i	1.58257	−	0.806360i
$378$	−23.8062	−	2.11618i	−1.22446	−	0.108844i
$379$	−16.0800	+	22.1322i	−0.825974	+	1.13686i	0.162685	+	0.986678i	$0.447985\pi$
$379$	−16.0800	+	22.1322i	−0.825974	+	1.13686i	−0.988659	+	0.150178i	$0.952015\pi$
$380$	−5.04854	−	19.6317i	−0.258985	−	1.00708i
$381$	0.0956418	−	0.214815i	0.00489988	−	0.0110053i
$382$	−62.0693	−	16.6314i	−3.17574	−	0.850937i
$383$	−4.06720	−	3.29355i	−0.207824	−	0.168293i	0.519757	−	0.854314i	$-0.326022\pi$
$383$	−4.06720	−	3.29355i	−0.207824	−	0.168293i	−0.727581	+	0.686021i	$0.759356\pi$
$384$	−12.7865	−	39.3528i	−0.652509	−	2.00821i
$385$	−12.2190	−	0.567238i	−0.622739	−	0.0289091i
$386$	9.65545	−	29.7164i	0.491449	−	1.51253i
$387$	5.50658	−	3.57601i	0.279915	−	0.181779i
$388$	3.40707	+	65.0108i	0.172968	+	3.30042i
$389$	3.49549	+	16.4450i	0.177228	+	0.833793i	0.973470	+	0.228815i	$0.0734849\pi$
$389$	3.49549	+	16.4450i	0.177228	+	0.833793i	−0.796242	+	0.604978i	$0.793182\pi$
$390$	−23.8548	−	55.0675i	−1.20793	−	2.78845i
$391$	−14.6143	+	4.74848i	−0.739078	+	0.240141i
$392$	−12.5796	−	29.8667i	−0.635367	−	1.50850i
$393$	−6.51852	−	6.51852i	−0.328816	−	0.328816i
$394$	30.9843	−	3.25658i	1.56097	−	0.164064i
$395$	−11.1271	−	14.0279i	−0.559864	−	0.705819i
$396$	0.997850	−	9.49391i	0.0501439	−	0.477087i
$397$	10.5952	+	4.06711i	0.531757	+	0.204122i	0.609406	−	0.792858i	$-0.291408\pi$
$397$	10.5952	+	4.06711i	0.531757	+	0.204122i	−0.0776488	+	0.996981i	$0.524741\pi$
$398$	−1.80224	−	3.53709i	−0.0903380	−	0.177298i
$399$	−12.0783	+	3.44521i	−0.604673	+	0.172476i
$400$	16.4624	−	4.98400i	0.823119	−	0.249200i
$401$	−4.66262	+	8.07589i	−0.232840	+	0.403291i	−0.958643	−	0.284612i	$-0.908135\pi$
$401$	−4.66262	+	8.07589i	−0.232840	+	0.403291i	0.725803	+	0.687903i	$0.241469\pi$
$402$	−36.7955	−	23.8953i	−1.83519	−	1.19179i
$403$	−29.7413	+	24.0840i	−1.48152	+	1.19971i
$404$	11.1277	−	4.95436i	0.553623	−	0.246489i
$405$	−24.5825	−	4.14817i	−1.22151	−	0.206124i
$406$	38.0886	−	15.3271i	1.89031	−	0.760674i
$407$	−0.594196	+	0.594196i	−0.0294532	+	0.0294532i
$408$	−32.6160	+	40.2775i	−1.61473	+	1.99403i
$409$	17.4737	−	19.4066i	0.864021	−	0.959592i	−0.135493	−	0.990778i	$-0.543262\pi$
$409$	17.4737	−	19.4066i	0.864021	−	0.959592i	0.999514	+	0.0311859i	$0.00992838\pi$
$410$	−43.4077	+	24.4808i	−2.14375	+	1.20902i
$411$	22.4594	−	20.2225i	1.10784	−	0.997504i
$412$	19.6841	−	38.6321i	0.969764	−	1.90327i
$413$	−0.0985763	+	0.0337891i	−0.00485062	+	0.00166265i
$414$	7.67033	+	2.49224i	0.376976	+	0.122487i
$415$	1.95410	+	20.5883i	0.0959228	+	1.01064i
$416$	3.61137	+	3.25170i	0.177062	+	0.159428i
$417$	40.3883	−	15.5036i	1.97782	−	0.759215i
$418$	3.01870	+	11.2659i	0.147649	+	0.551035i
$419$	−17.0065	+	12.3559i	−0.830820	+	0.603626i	−0.919791	−	0.392408i	$-0.871642\pi$
$419$	−17.0065	+	12.3559i	−0.830820	+	0.603626i	0.0889711	+	0.996034i	$0.471642\pi$
$420$	−14.8684	−	44.8473i	−0.725504	−	2.18833i
$421$	8.22355	+	5.97476i	0.400791	+	0.291192i	0.769863	−	0.638209i	$-0.220324\pi$
$421$	8.22355	+	5.97476i	0.400791	+	0.291192i	−0.369072	+	0.929401i	$0.620324\pi$
$422$	3.89253	−	10.1404i	0.189485	−	0.493626i
$423$	1.72519	−	2.65656i	0.0838815	−	0.129166i
$424$	16.2704	−	9.39375i	0.790163	−	0.456201i
$425$	20.9184	+	17.6501i	1.01469	+	0.856153i
$426$			61.0941i			2.96002i
$427$	18.3627	−	4.21245i	0.888635	−	0.203855i
$428$	3.35788	+	21.2008i	0.162309	+	1.02478i
$429$	9.28801	+	20.8612i	0.448429	+	1.00719i
$430$	−25.1412	−	16.6899i	−1.21242	−	0.804860i
$431$	−10.3970	−	4.62906i	−0.500807	−	0.222974i	0.140755	−	0.990044i	$-0.455047\pi$
$431$	−10.3970	−	4.62906i	−0.500807	−	0.222974i	−0.641563	+	0.767071i	$0.721714\pi$
$432$	−12.3522	+	3.30976i	−0.594294	+	0.159241i
$433$	−1.69255	+	10.6864i	−0.0813389	+	0.513553i	0.913057	+	0.407832i	$0.133715\pi$
$433$	−1.69255	+	10.6864i	−0.0813389	+	0.513553i	−0.994396	+	0.105721i	$0.966285\pi$
$434$	−37.8069	+	25.4246i	−1.81479	+	1.22042i
$435$	27.8623	−	8.74320i	1.33590	−	0.419204i
$436$	−27.5688	−	30.6183i	−1.32031	−	1.46635i
$437$	−6.50748	+	0.341043i	−0.311295	+	0.0163143i
$438$	−13.9426	+	0.730700i	−0.666203	+	0.0349142i
$439$	−3.84686	−	4.27237i	−0.183600	−	0.203909i	0.644318	−	0.764758i	$-0.277141\pi$
$439$	−3.84686	−	4.27237i	−0.183600	−	0.203909i	−0.827918	+	0.560849i	$0.810475\pi$
$440$	−20.4227	+	6.40865i	−0.973614	+	0.305520i
$441$	−7.78470	+	2.80888i	−0.370700	+	0.133756i
$442$	11.2378	−	70.9529i	0.534529	−	3.37488i
$443$	25.7790	−	6.90746i	1.22480	−	0.328183i	0.412246	−	0.911073i	$-0.364745\pi$
$443$	25.7790	−	6.90746i	1.22480	−	0.328183i	0.812552	+	0.582889i	$0.198078\pi$
$444$	−2.96519	−	1.32019i	−0.140721	−	0.0626532i
$445$	−4.47914	−	2.97347i	−0.212332	−	0.140956i
$446$	−18.0082	−	40.4470i	−0.852712	−	1.91522i
$447$	2.24773	+	14.1916i	0.106314	+	0.671240i
$448$	16.3356	+	17.5668i	0.771787	+	0.829954i
$449$		−	36.5758i		−	1.72612i	−0.505103	−	0.863059i	$-0.668546\pi$
$449$		−	36.5758i		−	1.72612i	0.505103	−	0.863059i	$-0.331454\pi$
$450$	−3.43719	−	13.9477i	−0.162031	−	0.657503i
$451$	16.4223	−	9.48143i	0.773297	−	0.446463i
$452$	13.3429	−	20.5463i	0.627600	−	0.966419i
$453$	−14.3579	+	37.4035i	−0.674591	+	1.75737i
$454$	21.7016	+	15.7671i	1.01851	+	0.739989i
$455$	23.8705	+	21.2364i	1.11907	+	0.995577i
$456$	−17.7809	+	12.9186i	−0.832665	+	0.604967i
$457$	4.98432	+	18.6017i	0.233157	+	0.870152i	0.978971	+	0.203999i	$0.0653938\pi$
$457$	4.98432	+	18.6017i	0.233157	+	0.870152i	−0.745815	+	0.666154i	$0.767940\pi$
$458$	−45.2252	+	17.3603i	−2.11324	+	0.811195i
$459$	−15.1220	−	13.6159i	−0.705833	−	0.635535i
$460$	−2.31620	−	24.4034i	−0.107993	−	1.13781i
$461$	−1.32261	−	0.429741i	−0.0615999	−	0.0200150i	0.278055	−	0.960565i	$-0.410310\pi$
$461$	−1.32261	−	0.429741i	−0.0615999	−	0.0200150i	−0.339655	+	0.940550i	$0.610310\pi$
$462$	8.81503	+	25.7170i	0.410112	+	1.19646i
$463$	0.899035	−	1.76446i	0.0417817	−	0.0820012i	−0.869172	−	0.494510i	$-0.835347\pi$
$463$	0.899035	−	1.76446i	0.0417817	−	0.0820012i	0.910954	+	0.412509i	$0.135347\pi$
$464$	16.3252	−	14.6993i	0.757880	−	0.682398i
$465$	−28.2258	+	15.9186i	−1.30894	+	0.738209i
$466$	−7.62390	+	8.46720i	−0.353170	+	0.392235i
$467$	−18.4577	+	22.7933i	−0.854120	+	1.05475i	0.143757	+	0.989613i	$0.454082\pi$
$467$	−18.4577	+	22.7933i	−0.854120	+	1.05475i	−0.997876	+	0.0651367i	$0.979252\pi$
$468$	−17.6311	+	17.6311i	−0.814996	+	0.814996i
$469$	23.1258	+	3.28296i	1.06785	+	0.151593i
$470$	−14.3553	−	2.42238i	−0.662161	−	0.111736i
$471$	3.36801	−	1.49953i	0.155190	−	0.0690949i
$472$	−0.141710	+	0.114754i	−0.00652273	+	0.00528200i
$473$	9.63012	+	6.25388i	0.442794	+	0.287554i
$474$	−19.8969	+	34.4624i	−0.913895	+	1.58291i
$475$	6.63134	+	9.52573i	0.304267	+	0.437070i
$476$	13.7589	−	54.8585i	0.630639	−	2.51443i
$477$	−2.17813	−	4.27482i	−0.0997296	−	0.195730i
$478$	−36.5413	−	14.0269i	−1.67136	−	0.641574i
$479$	−0.415418	+	3.95244i	−0.0189809	+	0.180592i	−0.999905	−	0.0138009i	$-0.995607\pi$
$479$	−0.415418	+	3.95244i	−0.0189809	+	0.180592i	0.980924	+	0.194393i	$0.0622736\pi$
$480$	2.55718	+	3.22383i	0.116719	+	0.147147i
$481$	2.18284	−	0.229426i	0.0995288	−	0.0104609i
$482$	23.5071	+	23.5071i	1.07072	+	1.07072i
$483$	−15.0783	+	1.83007i	−0.686085	+	0.0832712i
$484$	−24.9768	+	8.11545i	−1.13531	+	0.368884i
$485$	−14.8170	−	34.2042i	−0.672805	−	1.55313i
$486$	5.88523	+	27.6878i	0.266959	+	1.25595i
$487$	0.308672	+	5.88982i	0.0139873	+	0.266893i	0.996667	+	0.0815800i	$0.0259966\pi$
$487$	0.308672	+	5.88982i	0.0139873	+	0.266893i	−0.982680	+	0.185313i	$0.940670\pi$
$488$	27.6483	−	17.9550i	1.25158	−	0.812786i
$489$	0.829272	−	2.55224i	0.0375010	−	0.115416i
$490$	26.0679	+	27.6990i	1.17763	+	1.25131i
$491$	−0.371409	−	1.14308i	−0.0167615	−	0.0515864i	0.942326	−	0.334697i	$-0.108634\pi$
$491$	−0.371409	−	1.14308i	−0.0167615	−	0.0515864i	−0.959087	+	0.283110i	$0.908634\pi$
$492$	56.9224	+	46.0949i	2.56626	+	2.07812i
$493$	33.7648	+	9.04726i	1.52069	+	0.407468i
$494$	12.3908	−	27.8302i	0.557488	−	1.25214i
$495$	1.36138	+	5.29382i	0.0611893	+	0.237940i
$496$	−14.3288	+	19.7219i	−0.643381	+	0.885537i
$497$	−13.7049	−	29.4973i	−0.614747	−	1.32314i
$498$	40.9531	−	20.8666i	1.83515	−	0.935057i
$499$	13.6136	+	7.85984i	0.609430	+	0.351855i	0.772742	−	0.634720i	$-0.218884\pi$
$499$	13.6136	+	7.85984i	0.609430	+	0.351855i	−0.163312	+	0.986574i	$0.552218\pi$
$500$	−34.7472	+	26.4373i	−1.55394	+	1.18231i
$501$	−0.199780	−	0.346029i	−0.00892551	−	0.0154594i
$502$	0.000678977	−	0.0129557i	3.03042e−5	−	0.000578239i
$503$	−21.0385	+	3.33217i	−0.938061	+	0.148574i	−0.606701	−	0.794930i	$-0.707507\pi$
$503$	−21.0385	+	3.33217i	−0.938061	+	0.148574i	−0.331360	+	0.943504i	$0.607507\pi$
$504$	−11.1066	+	9.29323i	−0.494728	+	0.413953i
$505$	−4.98129	+	4.88177i	−0.221665	+	0.217236i
$506$	1.47432	+	14.0273i	0.0655417	+	0.623587i
$507$	8.55628	−	31.9325i	0.379998	−	1.41817i
$508$	0.160915	+	0.419199i	0.00713947	+	0.0185990i
$509$	35.8127	+	7.61222i	1.58737	+	0.337406i	0.915202	−	0.402994i	$-0.132031\pi$
$509$	35.8127	+	7.61222i	1.58737	+	0.337406i	0.672167	+	0.740400i	$0.265364\pi$
$510$	19.3799	−	57.6590i	0.858156	−	2.55318i
$511$	6.56782	−	3.48045i	0.290543	−	0.153966i
$512$	31.1392	+	15.8662i	1.37617	+	0.701194i
$513$	−4.69980	−	7.23706i	−0.207501	−	0.319524i
$514$	25.3301	−	5.38409i	1.11726	−	0.237482i
$515$	−2.84405	+	24.6629i	−0.125324	+	1.08678i
$516$	−9.22139	+	43.3832i	−0.405949	+	1.90984i
$517$	5.47139	+	0.866584i	0.240632	+	0.0381123i
$518$	2.61267	−	0.0419656i	0.114794	−	0.00184386i
$519$	5.49345	+	7.56109i	0.241136	+	0.331895i
$520$	51.9893	+	20.5611i	2.27988	+	0.901663i
$521$	−21.6306	−	2.27346i	−0.947653	−	0.0996023i	−0.381924	−	0.924194i	$-0.624738\pi$
$521$	−21.6306	−	2.27346i	−0.947653	−	0.0996023i	−0.565729	+	0.824591i	$0.691405\pi$
$522$	−11.5459	−	14.2580i	−0.505351	−	0.624056i
$523$	−8.55839	−	0.448526i	−0.374232	−	0.0196127i	−0.135707	−	0.990749i	$-0.543331\pi$
$523$	−8.55839	−	0.448526i	−0.374232	−	0.0196127i	−0.238525	+	0.971136i	$0.576664\pi$
$524$	17.6035			0.769012
$525$	16.9386	+	21.0946i	0.739263	+	0.920643i
$526$	−5.02799			−0.219231
$527$	−38.7373	−	2.03014i	−1.68742	−	0.0884341i
$528$	9.15407	+	11.3043i	0.398380	+	0.491958i
$529$	15.0369	+	1.58044i	0.653777	+	0.0687147i
$530$	−14.0490	+	16.9956i	−0.610251	+	0.738240i
$531$	0.0273706	+	0.0376724i	0.00118778	+	0.00163484i
$532$	11.6570	−	20.9609i	0.505395	−	0.908771i
$533$	−48.9200	−	7.74816i	−2.11896	−	0.335610i
$534$	−2.48426	+	11.6875i	−0.107505	+	0.505770i
$535$	−6.03764	−	10.7055i	−0.261030	−	0.462840i
$536$	39.9795	−	8.49790i	1.72685	−	0.367053i
$537$	18.1589	+	27.9622i	0.783613	+	1.20666i
$538$	7.49757	+	3.82020i	0.323243	+	0.164701i
$539$	−10.0250	−	10.4392i	−0.431807	−	0.449648i
$540$	26.4525	−	18.8140i	1.13834	−	0.809628i
$541$	29.8765	+	6.35044i	1.28449	+	0.273027i	0.799062	−	0.601249i	$-0.205330\pi$
$541$	29.8765	+	6.35044i	1.28449	+	0.273027i	0.485429	+	0.874276i	$0.338663\pi$
$542$	2.84677	+	7.41610i	0.122279	+	0.318549i
$543$	−5.78460	+	21.5884i	−0.248241	+	0.926448i
$544$	0.514875	+	4.89871i	0.0220751	+	0.210030i
$545$	20.9108	+	10.9218i	0.895722	+	0.467837i
$546$	24.3789	−	66.6914i	1.04332	−	2.85413i
$547$	24.3901	−	3.86301i	1.04285	−	0.165171i	0.388564	−	0.921422i	$-0.372971\pi$
$547$	24.3901	−	3.86301i	1.04285	−	0.165171i	0.654281	+	0.756251i	$0.272971\pi$
$548$	−3.02036	+	57.6320i	−0.129023	+	2.46192i
$549$	−4.20935	−	7.29081i	−0.179651	−	0.311164i
$550$	19.8386	−	15.4127i	0.845922	−	0.657199i
$551$	12.8377	+	7.41185i	0.546905	+	0.315756i
$552$	−23.6816	+	12.0664i	−1.00796	+	0.513579i
$553$	1.87583	−	21.1024i	0.0797685	−	0.897366i
$554$	−46.6996	+	64.2766i	−1.98408	+	2.73085i
$555$	1.85489	+	0.115989i	0.0787357	+	0.00492346i
$556$	−33.6009	+	75.4689i	−1.42500	+	3.20059i
$557$	10.8276	+	2.90126i	0.458782	+	0.122930i	0.480806	−	0.876827i	$-0.340344\pi$
$557$	10.8276	+	2.90126i	0.458782	+	0.122930i	−0.0220239	+	0.999757i	$0.507011\pi$
$558$	15.8221	+	12.8125i	0.669801	+	0.542394i
$559$	−9.26799	−	28.5239i	−0.391994	−	1.20643i
$560$	18.1883	+	9.13103i	0.768596	+	0.385856i
$561$	−7.15253	+	22.0132i	−0.301980	+	0.929400i
$562$	38.0081	−	24.6828i	1.60328	−	1.04118i
$563$	1.91065	+	36.4575i	0.0805245	+	1.53650i	0.678270	+	0.734813i	$0.262730\pi$
$563$	1.91065	+	36.4575i	0.0805245	+	1.53650i	−0.597746	+	0.801686i	$0.703937\pi$
$564$	4.44871	+	20.9295i	0.187324	+	0.881292i
$565$	−3.05483	+	13.6911i	−0.128518	+	0.575987i
$566$	−53.1710	+	17.2763i	−2.23494	+	0.726178i
$567$	−17.7193	−	23.5825i	−0.744140	−	0.990374i
$568$	−40.2451	−	40.2451i	−1.68865	−	1.68865i
$569$	−2.14347	+	0.225288i	−0.0898589	+	0.00944455i	−0.149351	−	0.988784i	$-0.547718\pi$
$569$	−2.14347	+	0.225288i	−0.0898589	+	0.00944455i	0.0594923	+	0.998229i	$0.481052\pi$
$570$	14.2668	−	21.4911i	0.597572	−	0.900163i
$571$	−1.57584	+	14.9931i	−0.0659469	+	0.627443i	0.910770	+	0.412913i	$0.135489\pi$
$571$	−1.57584	+	14.9931i	−0.0659469	+	0.627443i	−0.976717	+	0.214530i	$0.931178\pi$
$572$	−40.7095	−	15.6269i	−1.70215	−	0.653394i
$573$	−24.5510	−	48.1841i	−1.02563	−	2.01292i
$574$	−57.1942	−	14.3447i	−2.38724	−	0.598737i
$575$	6.11852	+	12.6322i	0.255160	+	0.526797i
$576$	5.35973	−	9.28333i	0.223322	−	0.386805i
$577$	−5.05336	−	3.28169i	−0.210374	−	0.136618i	0.435151	−	0.900357i	$-0.356695\pi$
$577$	−5.05336	−	3.28169i	−0.210374	−	0.136618i	−0.645525	+	0.763739i	$0.723362\pi$
$578$	24.4829	−	19.8259i	1.01835	−	0.824647i
$579$	24.0221	−	10.6953i	0.998322	−	0.444482i
$580$	−25.8159	+	49.4272i	−1.07195	+	2.05235i
$581$	−15.0920	+	19.2615i	−0.626122	+	0.799103i
$582$	−58.5798	+	58.5798i	−2.42821	+	2.42821i
$583$	5.28030	−	6.52063i	0.218688	−	0.270057i
$584$	8.70320	−	9.66589i	0.360141	−	0.399977i
$585$	5.93829	−	12.9835i	0.245518	−	0.536800i
$586$	−16.2482	+	14.6300i	−0.671208	+	0.604359i
$587$	−12.1632	+	23.8716i	−0.502028	+	0.985284i	0.491412	+	0.870927i	$0.336481\pi$
$587$	−12.1632	+	23.8716i	−0.502028	+	0.985284i	−0.993440	+	0.114357i	$0.963519\pi$
$588$	23.7672	−	50.6005i	0.980142	−	2.08673i
$589$	−15.6447	−	5.08327i	−0.644629	−	0.209453i
$590$	0.108873	−	0.184254i	0.00448223	−	0.00758564i
$591$	19.4846	+	17.5440i	0.801488	+	0.721663i
$592$	1.30524	−	0.501037i	0.0536452	−	0.0205925i
$593$	−7.52966	−	28.1011i	−0.309206	−	1.15397i	−0.929264	−	0.369416i	$-0.879558\pi$
$593$	−7.52966	−	28.1011i	−0.309206	−	1.15397i	0.620058	−	0.784556i	$-0.287109\pi$
$594$	−15.1105	+	10.9784i	−0.619990	+	0.450449i
$595$	3.57732	+	32.1861i	0.146656	+	1.31950i
$596$	−22.1975	−	16.1274i	−0.909245	−	0.660605i
$597$	1.19725	−	3.11894i	0.0490001	−	0.127650i
$598$	20.0646	−	30.8967i	0.820501	−	1.26346i
$599$	16.2419	−	9.37728i	0.663627	−	0.383145i	−0.130031	−	0.991510i	$-0.541508\pi$
$599$	16.2419	−	9.37728i	0.663627	−	0.383145i	0.793658	+	0.608365i	$0.208174\pi$
$600$	40.5117	+	24.4925i	1.65388	+	0.999902i
$601$			1.56485i			0.0638318i	0.999491	+	0.0319159i	$0.0101609\pi$
$601$			1.56485i			0.0638318i	−0.999491	+	0.0319159i	$0.989839\pi$
$602$	−7.98356	−	34.8016i	−0.325385	−	1.41841i
$603$	−1.63280	−	10.3091i	−0.0664927	−	0.419819i
$604$	−31.1178	−	69.8916i	−1.26616	−	2.84385i
$605$	11.7812	−	9.34499i	0.478974	−	0.379928i
$606$	14.1608	+	6.30478i	0.575242	+	0.256114i
$607$	−3.43453	+	0.920280i	−0.139403	+	0.0373530i	−0.327846	−	0.944731i	$-0.606323\pi$
$607$	−3.43453	+	0.920280i	−0.139403	+	0.0373530i	0.188443	+	0.982084i	$0.439656\pi$
$608$	−0.326765	+	2.06311i	−0.0132521	+	0.0836703i
$609$	31.0342	+	15.1899i	1.25757	+	0.615526i
$610$	−23.0576	+	31.0718i	−0.933574	+	1.25806i
$611$	−9.68170	−	10.7526i	−0.391680	−	0.435004i
$612$	−25.2386	+	1.32270i	−1.02021	+	0.0534670i
$613$	0.922284	−	0.0483349i	0.0372507	−	0.00195223i	−0.0337015	−	0.999432i	$-0.510730\pi$
$613$	0.922284	−	0.0483349i	0.0372507	−	0.00195223i	0.0709522	+	0.997480i	$0.477396\pi$
$614$	43.1801	+	47.9563i	1.74261	+	1.93536i
$615$	−39.7542	−	13.3619i	−1.60304	−	0.538803i
$616$	−22.7476	−	11.1340i	−0.916528	−	0.448601i
$617$	−6.94866	+	43.8721i	−0.279743	+	1.76622i	0.302442	+	0.953168i	$0.402198\pi$
$617$	−6.94866	+	43.8721i	−0.279743	+	1.76622i	−0.582184	+	0.813057i	$0.697802\pi$
$618$	53.2959	−	14.2806i	2.14388	−	0.574450i
$619$	−4.37292	−	1.94695i	−0.175763	−	0.0782546i	0.316969	−	0.948436i	$-0.397335\pi$
$619$	−4.37292	−	1.94695i	−0.175763	−	0.0782546i	−0.492732	+	0.870181i	$0.664002\pi$
$620$	16.6180	−	59.6068i	0.667395	−	2.39387i
$621$	−4.24442	−	9.53313i	−0.170323	−	0.382551i
$622$	−0.402296	−	2.54000i	−0.0161306	−	0.101845i
$623$	−1.42235	−	6.20023i	−0.0569851	−	0.248407i
$624$		−	37.9931i		−	1.52094i
$625$	13.3634	−	21.1286i	0.534537	−	0.845145i
$626$	39.7538	−	22.9519i	1.58888	−	0.917342i
$627$	−5.34592	+	8.23199i	−0.213495	+	0.328754i
$628$	−2.52294	+	6.57248i	−0.100676	+	0.262270i
$629$	1.79984	+	1.30766i	0.0717642	+	0.0521397i
$630$	8.41042	−	14.7702i	0.335079	−	0.588461i
$631$	6.66704	−	4.84388i	0.265410	−	0.192832i	−0.447118	−	0.894475i	$-0.647550\pi$
$631$	6.66704	−	4.84388i	0.265410	−	0.192832i	0.712529	+	0.701643i	$0.247550\pi$
$632$	−9.59490	−	35.8087i	−0.381665	−	1.42439i
$633$	8.53384	−	3.27583i	0.339190	−	0.130203i
$634$	52.1680	+	46.9723i	2.07186	+	1.86551i
$635$	−0.170101	−	0.192793i	−0.00675025	−	0.00765077i
$636$	30.8227	+	10.0149i	1.22220	+	0.397117i
$637$	3.18990	+	37.6686i	0.126389	+	1.49248i
$638$	14.5664	−	28.5882i	0.576691	−	1.13182i
$639$	−10.8011	+	9.72539i	−0.427286	+	0.384730i
$640$	−44.9448	−	5.18291i	−1.77660	−	0.204872i
$641$	−26.1981	+	29.0960i	−1.03476	+	1.14922i	−0.0461221	+	0.998936i	$0.514686\pi$
$641$	−26.1981	+	29.0960i	−1.03476	+	1.14922i	−0.988642	+	0.150287i	$0.951980\pi$
$642$	−17.1904	+	21.2284i	−0.678452	+	0.837818i
$643$	27.4043	−	27.4043i	1.08072	−	1.08072i	0.0842787	−	0.996442i	$-0.473141\pi$
$643$	27.4043	−	27.4043i	1.08072	−	1.08072i	0.996442	−	0.0842787i	$-0.0268586\pi$
$644$	17.8886	−	22.8308i	0.704909	−	0.899658i
$645$	−3.71948	−	25.1219i	−0.146455	−	0.989175i
$646$	28.2088	−	12.5594i	1.10986	−	0.494141i
$647$	−14.1821	+	11.4845i	−0.557557	+	0.451501i	−0.866214	−	0.499673i	$-0.833454\pi$
$647$	−14.1821	+	11.4845i	−0.557557	+	0.451501i	0.308657	+	0.951173i	$0.400120\pi$
$648$	−43.2894	−	28.1125i	−1.70057	−	1.10436i
$649$	−0.0407179	+	0.0705255i	−0.00159832	+	0.00276837i
$650$	−65.6041	−	1.32411i	−2.57320	−	0.0519358i
$651$	−37.1905	−	9.32766i	−1.45761	−	0.365580i
$652$	2.32646	+	4.56594i	0.0911113	+	0.178816i
$653$	−14.3960	−	5.52612i	−0.563361	−	0.216254i	0.0599863	−	0.998199i	$-0.480894\pi$
$653$	−14.3960	−	5.52612i	−0.563361	−	0.216254i	−0.623347	+	0.781945i	$0.714228\pi$
$654$	5.48055	−	52.1439i	0.214306	−	2.03899i
$655$	−9.44607	+	3.51707i	−0.369089	+	0.137423i
$656$	−31.3772	+	3.29787i	−1.22507	+	0.128760i
$657$	−2.34866	−	2.34866i	−0.0916301	−	0.0916301i
$658$	−10.3474	−	13.7714i	−0.403385	−	0.536864i
$659$	−18.2922	+	5.94351i	−0.712564	+	0.231526i	−0.642796	−	0.766037i	$-0.722226\pi$
$659$	−18.2922	+	5.94351i	−0.712564	+	0.231526i	−0.0697679	+	0.997563i	$0.522226\pi$
$660$	−31.7888	−	18.7834i	−1.23738	−	0.731144i
$661$	−6.95450	−	32.7184i	−0.270499	−	1.27260i	−0.878147	−	0.478391i	$-0.841220\pi$
$661$	−6.95450	−	32.7184i	−0.270499	−	1.27260i	0.607648	−	0.794206i	$-0.292113\pi$
$662$	−0.227310	−	4.33733i	−0.00883466	−	0.168575i
$663$	50.7028	−	32.9268i	1.96913	−	1.27877i
$664$	−13.2318	+	40.7231i	−0.513491	+	1.58036i
$665$	−2.06732	+	13.5767i	−0.0801671	+	0.526481i
$666$	−0.360822	−	1.11050i	−0.0139816	−	0.0430308i
$667$	13.9314	+	11.2814i	0.539425	+	0.436818i
$668$	0.736988	+	0.197475i	0.0285149	+	0.00764055i
$669$	15.1551	−	34.0390i	0.585932	−	1.31602i
$670$	−40.4938	+	25.7198i	−1.56441	+	0.993643i
$671$	8.65394	−	11.9111i	0.334082	−	0.459824i
$672$	−0.431096	+	4.84968i	−0.0166299	+	0.187080i
$673$	6.40269	−	3.26233i	0.246806	−	0.125754i	−0.326212	−	0.945296i	$-0.605772\pi$
$673$	6.40269	−	3.26233i	0.246806	−	0.125754i	0.573018	+	0.819543i	$0.305772\pi$
$674$	30.5721	+	17.6508i	1.17759	+	0.679883i
$675$	−10.4356	+	15.3807i	−0.401665	+	0.592004i
$676$	31.5641	+	54.6706i	1.21400	+	2.10271i
$677$	1.93963	−	37.0104i	0.0745462	−	1.42243i	−0.663752	−	0.747952i	$-0.731037\pi$
$677$	1.93963	−	37.0104i	0.0745462	−	1.42243i	0.738299	−	0.674474i	$-0.235630\pi$
$678$	30.7925	−	4.87706i	1.18258	−	0.187302i
$679$	15.1425	−	41.4242i	0.581117	−	1.58972i
$680$	25.2160	+	50.7486i	0.966988	+	1.94612i
$681$	2.35971	+	22.4512i	0.0904243	+	0.860330i
$682$	−9.21525	+	34.3918i	−0.352870	+	1.31693i
$683$	−3.23434	−	8.42575i	−0.123759	−	0.322402i	0.857678	−	0.514186i	$-0.171906\pi$
$683$	−3.23434	−	8.42575i	−0.123759	−	0.322402i	−0.981437	+	0.191784i	$0.938573\pi$
$684$	−10.4834	−	2.22831i	−0.400843	−	0.0852017i
$685$	−9.89378	−	31.5289i	−0.378022	−	1.20466i
$686$	−0.187983	+	45.0049i	−0.00717723	+	1.71829i
$687$	−36.3245	−	18.5083i	−1.38587	−	0.706134i
$688$	−10.4051	−	16.0224i	−0.396690	−	0.610848i
$689$	−21.4365	+	4.55647i	−0.816666	+	0.173588i
$690$	21.1061	−	22.9703i	0.803496	−	0.874465i
$691$	6.16559	−	29.0068i	0.234550	−	1.10347i	−0.690413	−	0.723416i	$-0.742571\pi$
$691$	6.16559	−	29.0068i	0.234550	−	1.10347i	0.924963	−	0.380057i	$-0.124096\pi$
$692$	−17.6271	−	2.79186i	−0.670082	−	0.106131i
$693$	−3.14340	+	5.65227i	−0.119408	+	0.214712i
$694$	−6.11626	−	8.41831i	−0.232170	−	0.319555i
$695$	2.95212	−	47.2101i	0.111980	−	1.79078i
$696$	60.1302	+	6.31994i	2.27923	+	0.239557i
$697$	−31.5941	−	39.0155i	−1.19671	−	1.47782i
$698$	23.1729	+	1.21444i	0.877107	+	0.0459672i
$699$	−9.58862			−0.362675
$700$	−51.3550	−	5.61162i	−1.94104	−	0.212099i
$701$	−14.4601			−0.546149			−0.273075	−	0.961993i	$-0.588041\pi$
$701$	−14.4601			−0.546149			−0.273075	+	0.961993i	$0.588041\pi$
$702$	48.7178	+	2.55319i	1.83873	+	0.0963640i
$703$	0.593722	+	0.733185i	0.0223926	+	0.0276526i
$704$	18.6439	+	1.95956i	0.702670	+	0.0738536i
$705$	−6.56878	−	10.3420i	−0.247395	−	0.389503i
$706$	−8.19565	−	11.2803i	−0.308448	−	0.424542i
$707$	−8.25138	+	0.132537i	−0.310325	+	0.00498456i
$708$	−0.310680	−	0.0492068i	−0.0116761	−	0.00184931i
$709$	−4.65117	+	21.8820i	−0.174678	+	0.821797i	0.800318	+	0.599576i	$0.204664\pi$
$709$	−4.65117	+	21.8820i	−0.174678	+	0.821797i	−0.974996	+	0.222221i	$0.928669\pi$
$710$	60.7478	+	27.7845i	2.27982	+	1.04273i
$711$	−9.26012	+	1.96830i	−0.347282	+	0.0738170i
$712$	−6.06257	−	9.33554i	−0.227204	−	0.349864i
$713$	−17.7246	−	9.03114i	−0.663792	−	0.338219i
$714$	63.5959	−	33.7010i	2.38002	−	1.26123i
$715$	24.9670	+	0.251933i	0.933712	+	0.00942174i
$716$	−62.2757	−	13.2371i	−2.32735	−	0.494694i
$717$	−11.8046	−	30.7520i	−0.440851	−	1.14846i
$718$	−7.16085	+	26.7247i	−0.267241	+	0.997356i
$719$	−1.98137	−	18.8514i	−0.0738925	−	0.703040i	−0.967273	−	0.253739i	$-0.918340\pi$
$719$	−1.98137	−	18.8514i	−0.0738925	−	0.703040i	0.893380	−	0.449301i	$-0.148327\pi$
$720$	1.51323	−	8.96755i	0.0563947	−	0.334201i
$721$	−22.5287	+	18.8505i	−0.839014	+	0.702028i
$722$	−32.6693	+	5.17431i	−1.21583	+	0.192568i
$723$	−1.46421	+	27.9388i	−0.0544546	+	1.03906i
$724$	−21.3394	−	36.9609i	−0.793071	−	1.37364i
$725$	3.97763	−	31.6806i	0.147725	−	1.17659i
$726$	−28.9430	−	16.7102i	−1.07417	−	0.620175i
$727$	−12.3162	+	6.27543i	−0.456783	+	0.232743i	−0.667214	−	0.744866i	$-0.732513\pi$
$727$	−12.3162	+	6.27543i	−0.456783	+	0.232743i	0.210431	+	0.977609i	$0.432513\pi$
$728$	27.8730	+	59.9917i	1.03304	+	2.22344i
$729$	5.65765	−	7.78708i	0.209543	−	0.288411i
$730$	−5.61427	+	14.1959i	−0.207794	+	0.525412i
$731$	12.3647	−	27.7716i	0.457326	−	1.02717i
$732$	54.9308	+	14.7187i	2.03030	+	0.544018i
$733$	8.73375	+	7.07245i	0.322588	+	0.261227i	0.776911	−	0.629610i	$-0.216785\pi$
$733$	8.73375	+	7.07245i	0.322588	+	0.261227i	−0.454323	+	0.890837i	$0.650119\pi$
$734$	−10.7648	−	33.1307i	−0.397336	−	1.22287i
$735$	−2.64385	+	31.9009i	−0.0975200	+	1.17668i
$736$	−0.780585	+	2.40239i	−0.0287728	+	0.0885534i
$737$	15.3088	−	9.94167i	0.563908	−	0.366206i
$738$	1.37902	+	26.3132i	0.0507624	+	0.968604i
$739$	2.04019	+	9.59835i	0.0750497	+	0.353081i	0.999609	−	0.0279568i	$-0.00890010\pi$
$739$	2.04019	+	9.59835i	0.0750497	+	0.353081i	−0.924559	+	0.381038i	$0.875567\pi$
$740$	−2.66121	+	2.34798i	−0.0978281	+	0.0863135i
$741$	24.3827	−	7.92243i	0.895722	−	0.291038i
$742$	−25.9004	+	3.14357i	−0.950835	+	0.115404i
$743$	−5.96596	−	5.96596i	−0.218870	−	0.218870i	0.589152	−	0.808022i	$-0.299462\pi$
$743$	−5.96596	−	5.96596i	−0.218870	−	0.218870i	−0.808022	+	0.589152i	$0.799462\pi$
$744$	−66.7263	+	7.01322i	−2.44630	+	0.257117i
$745$	15.1334	+	4.21909i	0.554445	+	0.154576i
$746$	−6.41747	+	61.0581i	−0.234960	+	2.23550i
$747$	10.2083	+	3.91861i	0.373503	+	0.143374i
$748$	−20.0659	−	39.3816i	−0.733682	−	1.43993i
$749$	3.53781	−	14.1057i	0.129269	−	0.515410i
$750$	−54.5897	−	10.3488i	−1.99334	−	0.377884i
$751$	−9.24200	+	16.0076i	−0.337245	+	0.584126i	−0.983914	−	0.178645i	$-0.942829\pi$
$751$	−9.24200	+	16.0076i	−0.337245	+	0.584126i	0.646668	+	0.762771i	$0.276162\pi$
$752$	−7.72975	−	5.01976i	−0.281875	−	0.183052i
$753$	0.00848492	−	0.00687095i	0.000309208	−	0.000250391i
$754$	−76.5596	+	34.0865i	−2.78813	+	1.24136i
$755$	30.6618	+	31.2869i	1.11590	+	1.13865i
$756$	38.0269	+	5.39834i	1.38303	+	0.196336i
$757$	16.1216	−	16.1216i	0.585951	−	0.585951i	−0.350581	−	0.936532i	$-0.614016\pi$
$757$	16.1216	−	16.1216i	0.585951	−	0.585951i	0.936532	+	0.350581i	$0.114016\pi$
$758$	41.8365	−	51.6638i	1.51957	−	1.87651i
$759$	−7.94254	+	8.82108i	−0.288296	+	0.320185i
$760$	4.75892	+	23.5552i	0.172624	+	0.854437i
$761$	12.2468	−	11.0270i	0.443945	−	0.399730i	−0.416612	−	0.909085i	$-0.636783\pi$
$761$	12.2468	−	11.0270i	0.443945	−	0.399730i	0.860557	+	0.509355i	$0.170116\pi$
$762$	−0.259416	+	0.509133i	−0.00939767	+	0.0184440i
$763$	9.05101	+	26.4054i	0.327669	+	0.955940i
$764$	98.2118	+	31.9110i	3.55318	+	1.15450i
$765$	13.2789	−	5.75229i	0.480098	−	0.207975i
$766$	9.45111	+	8.50981i	0.341482	+	0.307472i
$767$	0.198578	−	0.0762268i	0.00717022	−	0.00275239i
$768$	16.4264	+	61.3040i	0.592736	+	2.21212i
$769$	26.4586	−	19.2233i	0.954122	−	0.693210i	0.00234391	−	0.999997i	$-0.499254\pi$
$769$	26.4586	−	19.2233i	0.954122	−	0.693210i	0.951778	+	0.306787i	$0.0992539\pi$
$770$	29.5801	+	2.93054i	1.06599	+	0.105609i
$771$	17.6312	+	12.8098i	0.634970	+	0.461333i
$772$	−17.9947	+	46.8777i	−0.647642	+	1.68716i
$773$	−22.6802	+	34.9245i	−0.815751	+	1.25615i	0.147906	+	0.989001i	$0.452747\pi$
$773$	−22.6802	+	34.9245i	−0.815751	+	1.25615i	−0.963656	+	0.267145i	$0.913920\pi$
$774$	−13.8177	+	7.97768i	−0.496669	+	0.286752i
$775$	2.99181	+	35.3053i	0.107469	+	1.26821i
$776$		−	77.1777i		−	2.77052i
$777$	1.49749	+	1.61035i	0.0537221	+	0.0577710i
$778$	−6.39113	−	40.3520i	−0.229133	−	1.44669i
$779$	−8.65932	−	19.4491i	−0.310252	−	0.696838i
$780$	33.6514	+	90.3803i	1.20491	+	3.23613i
$781$	−23.2208	−	10.3386i	−0.830904	−	0.369942i
$782$	36.0689	−	9.66463i	1.28982	−	0.345606i
$783$	−3.71352	+	23.4463i	−0.132711	+	0.837901i
$784$	8.17294	+	22.6510i	0.291891	+	0.808966i
$785$	0.0406741	−	4.03088i	0.00145172	−	0.143868i
$786$	14.9897	+	16.6477i	0.534663	+	0.593804i
$787$	34.8845	−	1.82822i	1.24350	−	0.0651690i	0.580794	−	0.814050i	$-0.302742\pi$
$787$	34.8845	−	1.82822i	1.24350	−	0.0651690i	0.662704	+	0.748882i	$0.269409\pi$
$788$	−49.9984	+	2.62030i	−1.78112	+	0.0933445i
$789$	−2.83136	−	3.14455i	−0.100799	−	0.111949i
$790$	25.2183	+	35.4570i	0.897228	+	1.26150i
$791$	−13.7731	+	9.26222i	−0.489716	+	0.329327i
$792$	−1.77041	+	11.1779i	−0.0629089	+	0.397191i
$793$	−37.1451	+	9.95300i	−1.31906	+	0.353442i
$794$	−25.1944	−	11.2173i	−0.894115	−	0.398086i
$795$	−18.5404	+	0.784164i	−0.657562	+	0.0278114i
$796$	2.59479	+	5.82800i	0.0919700	+	0.206568i
$797$	4.32443	+	27.3034i	0.153179	+	0.967136i	0.937804	+	0.347165i	$0.112856\pi$
$797$	4.32443	+	27.3034i	0.153179	+	0.967136i	−0.784625	+	0.619971i	$0.787144\pi$
$798$	29.7490	−	6.82448i	1.05310	−	0.241584i
$799$		−	14.6659i		−	0.518842i
$800$	4.36852	−	1.07655i	0.154450	−	0.0380617i
$801$	−2.46176	+	1.42130i	−0.0869821	+	0.0502192i
$802$	12.3420	−	19.0050i	0.435811	−	0.671090i
$803$	2.08169	−	5.42298i	0.0734612	−	0.191373i
$804$	57.0408	+	41.4426i	2.01167	+	1.46157i
$805$	−5.03762	+	15.8251i	−0.177553	+	0.557761i
$806$	75.2369	−	54.6628i	2.65011	−	1.92542i
$807$	1.83284	+	6.84027i	0.0645192	+	0.240789i
$808$	−13.4815	+	5.17505i	−0.474277	+	0.182058i
$809$	−8.94230	−	8.05168i	−0.314394	−	0.283082i	0.496792	−	0.867870i	$-0.334511\pi$
$809$	−8.94230	−	8.05168i	−0.314394	−	0.283082i	−0.811186	+	0.584788i	$0.801178\pi$
$810$	59.1275	+	13.1929i	2.07753	+	0.463550i
$811$	−5.66612	−	1.84103i	−0.198964	−	0.0646475i	0.207840	−	0.978163i	$-0.433357\pi$
$811$	−5.66612	−	1.84103i	−0.198964	−	0.0646475i	−0.406804	+	0.913515i	$0.633357\pi$
$812$	−62.4148	+	21.3940i	−2.19033	+	0.750782i
$813$	−3.03501	+	5.95655i	−0.106443	+	0.208905i
$814$	1.51752	−	1.36638i	0.0531891	−	0.0478916i
$815$	−2.16063	−	1.98528i	−0.0756836	−	0.0695414i
$816$	25.7682	−	28.6185i	0.902068	−	1.00185i
$817$	8.11295	−	10.0187i	0.283836	−	0.350509i
$818$	−44.8721	+	44.8721i	−1.56892	+	1.56892i
$819$	15.6715	−	6.30634i	0.547607	−	0.220361i
$820$	71.7208	−	35.6367i	2.50460	−	1.24449i
$821$	46.5893	−	20.7429i	1.62598	−	0.723932i	0.627475	−	0.778637i	$-0.284089\pi$
$821$	46.5893	−	20.7429i	1.62598	−	0.723932i	0.998503	+	0.0547050i	$0.0174218\pi$
$822$	−57.0747	+	46.2182i	−1.99071	+	1.61204i
$823$	−7.24578	−	4.70546i	−0.252572	−	0.164022i	0.412143	−	0.911119i	$-0.364780\pi$
$823$	−7.24578	−	4.70546i	−0.252572	−	0.164022i	−0.664715	+	0.747097i	$0.731447\pi$
$824$	−25.7009	+	44.5153i	−0.895335	+	1.55077i
$825$	20.8107	+	3.72805i	0.724537	+	0.129794i
$826$	0.243515	−	0.0694600i	0.00847297	−	0.00241682i
$827$	24.4201	+	47.9272i	0.849171	+	1.66659i	0.740038	+	0.672565i	$0.234807\pi$
$827$	24.4201	+	47.9272i	0.849171	+	1.66659i	0.109133	+	0.994027i	$0.465193\pi$
$828$	−12.1000	−	4.64474i	−0.420503	−	0.161416i
$829$	−3.89407	+	37.0496i	−0.135247	+	1.28679i	0.690743	+	0.723100i	$0.257284\pi$
$829$	−3.89407	+	37.0496i	−0.135247	+	1.28679i	−0.825990	+	0.563685i	$0.809383\pi$
$830$	−2.12365	−	50.2107i	−0.0737130	−	1.74284i
$831$	−66.4966	+	6.98907i	−2.30674	+	0.242448i
$832$	−34.6235	−	34.6235i	−1.20035	−	1.20035i
$833$	−23.1453	+	30.5375i	−0.801936	+	1.05806i
$834$	−99.9830	+	32.4865i	−3.46213	+	1.12491i
$835$	−0.434924	+	0.0412799i	−0.0150512	+	0.00142855i
$836$	−3.89697	−	18.3338i	−0.134779	−	0.634087i
$837$	−1.37866	−	26.3065i	−0.0476536	−	0.909284i
$838$	42.8415	−	27.8216i	1.47993	−	0.961080i
$839$	10.5872	−	32.5840i	0.365510	−	1.12492i	−0.584151	−	0.811645i	$-0.698572\pi$
$839$	10.5872	−	32.5840i	0.365510	−	1.12492i	0.949661	−	0.313279i	$-0.101428\pi$
$840$	14.8201	+	54.0173i	0.511343	+	1.86378i
$841$	−3.64001	−	11.2028i	−0.125518	−	0.386304i
$842$	−19.1965	−	15.5450i	−0.661553	−	0.535715i
$843$	36.8399	+	9.87123i	1.26883	+	0.339983i
$844$	−7.09970	+	15.9462i	−0.244382	+	0.548891i
$845$	−27.8602	−	23.0301i	−0.958420	−	0.792258i
$846$	−4.52442	+	6.22733i	−0.155553	+	0.214100i
$847$	17.7227	+	1.57540i	0.608959	+	0.0541314i
$848$	−12.4384	+	6.33767i	−0.427136	+	0.217636i
$849$	−40.7464	−	23.5249i	−1.39841	−	0.807374i
$850$	−48.5185	−	45.4923i	−1.66417	−	1.56037i
$851$	0.570448	+	0.988045i	0.0195547	+	0.0338697i
$852$	5.13835	−	98.0456i	0.176037	−	3.35899i
$853$	−32.0290	+	5.07290i	−1.09665	+	0.173693i	−0.678440	−	0.734656i	$-0.737344\pi$
$853$	−32.0290	+	5.07290i	−1.09665	+	0.173693i	−0.418214	+	0.908349i	$0.637344\pi$
$854$	−45.0971	+	7.88710i	−1.54319	+	0.269891i
$855$	6.07062	−	0.898799i	0.207611	−	0.0307383i
$856$	−2.65998	−	25.3080i	−0.0909163	−	0.865010i
$857$	7.89972	−	29.4821i	0.269849	−	1.00709i	−0.689366	−	0.724413i	$-0.742111\pi$
$857$	7.89972	−	29.4821i	0.269849	−	1.00709i	0.959215	−	0.282677i	$-0.0912226\pi$
$858$	−19.8863	−	51.8057i	−0.678909	−	1.76862i
$859$	−21.6405	−	4.59984i	−0.738365	−	0.156944i	−0.176648	−	0.984274i	$-0.556526\pi$
$859$	−21.6405	−	4.59984i	−0.738365	−	0.156944i	−0.561717	+	0.827330i	$0.689859\pi$
$860$	38.9436	+	28.8990i	1.32797	+	0.985448i
$861$	−23.2359	−	43.8475i	−0.791877	−	1.49432i
$862$	24.6420	+	12.5557i	0.839311	+	0.427650i
$863$	14.9088	+	22.9575i	0.507500	+	0.781481i	0.995835	−	0.0911748i	$-0.0290622\pi$
$863$	14.9088	+	22.9575i	0.507500	+	0.781481i	−0.488335	+	0.872656i	$0.662396\pi$
$864$	−3.27193	+	0.695471i	−0.111313	+	0.0236604i
$865$	10.0166	−	2.02367i	0.340573	−	0.0688068i
$866$	5.46645	−	25.7176i	0.185757	−	0.873920i
$867$	26.1861	+	4.14746i	0.889325	+	0.140855i
$868$	62.8120	−	37.6223i	2.13198	−	1.27698i
$869$	−9.73153	−	13.3943i	−0.330120	−	0.454371i
$870$	−68.7262	+	17.6739i	−2.33004	+	0.599200i
$871$	−47.4163	−	4.98365i	−1.60664	−	0.168865i
$872$	30.7390	+	37.9595i	1.04095	+	1.28547i
$873$	−19.6818	−	1.03148i	−0.666127	−	0.0349102i
$874$	15.8352			0.535635
$875$	28.6784	−	7.24920i	0.969506	−	0.245068i
$876$	22.4369			0.758074
$877$	−12.9672	−	0.679582i	−0.437871	−	0.0229478i	−0.167873	−	0.985809i	$-0.553690\pi$
$877$	−12.9672	−	0.679582i	−0.437871	−	0.0229478i	−0.269998	+	0.962861i	$0.587023\pi$
$878$	8.79191	+	10.8571i	0.296713	+	0.366410i
$879$	−18.2994	−	1.92335i	−0.617224	−	0.0648728i
$880$	15.4034	−	3.96118i	0.519247	−	0.133531i
$881$	−34.7097	−	47.7739i	−1.16940	−	1.60954i	−0.667478	−	0.744629i	$-0.732626\pi$
$881$	−34.7097	−	47.7739i	−1.16940	−	1.60954i	−0.501923	−	0.864913i	$-0.667374\pi$
$882$	19.2486	−	5.82632i	0.648133	−	0.196182i
$883$	55.0566	+	8.72011i	1.85280	+	0.293455i	0.980649	−	0.195775i	$-0.0627223\pi$
$883$	55.0566	+	8.72011i	1.85280	+	0.293455i	0.872155	+	0.489231i	$0.162722\pi$
$884$	−24.0023	+	112.922i	−0.807286	+	3.79798i
$885$	0.176543	−	0.0356674i	0.00593442	−	0.00119895i
$886$	−63.4371	+	13.4840i	−2.13121	+	0.453003i
$887$	5.23868	+	8.06687i	0.175898	+	0.270859i	0.915613	−	0.402062i	$-0.131706\pi$
$887$	5.23868	+	8.06687i	0.175898	+	0.270859i	−0.739715	+	0.672921i	$0.765040\pi$
$888$	3.42858	+	1.74695i	0.115055	+	0.0586237i
$889$	0.0110401	−	0.304012i	0.000370275	−	0.0101962i
$890$	10.4915	+	7.78546i	0.351676	+	0.260969i
$891$	−22.5482	−	4.79278i	−0.755394	−	0.160564i
$892$	25.4982	+	66.4252i	0.853744	+	2.22408i
$893$	1.60968	−	6.00743i	0.0538660	−	0.201031i
$894$	−3.64975	−	34.7250i	−0.122066	−	1.16138i
$895$	36.0620	−	5.33924i	1.20542	−	0.178471i
$896$	−34.3525	−	41.0556i	−1.14764	−	1.37157i
$897$	30.6218	−	4.85002i	1.02243	−	0.161937i
$898$	−4.65168	+	88.7594i	−0.155229	+	2.96194i
$899$	22.6263	+	39.1900i	0.754630	+	1.30706i
$900$	4.34301	+	22.6728i	0.144767	+	0.755761i
$901$	−19.2375	−	11.1068i	−0.640894	−	0.370020i
$902$	−41.0583	+	20.9203i	−1.36709	+	0.696568i
$903$	17.2695	−	24.5904i	0.574693	−	0.818319i
$904$	−17.0716	+	23.4970i	−0.567791	+	0.781498i
$905$	18.8353	+	15.5698i	0.626107	+	0.517558i
$906$	39.5996	−	88.9421i	1.31561	−	2.95490i
$907$	46.3456	+	12.4183i	1.53888	+	0.412342i	0.925904	−	0.377759i	$-0.123305\pi$
$907$	46.3456	+	12.4183i	1.53888	+	0.412342i	0.612977	+	0.790101i	$0.289972\pi$
$908$	−33.5013	−	27.1288i	−1.11178	−	0.900301i
$909$	1.13956	+	3.50719i	0.0377967	+	0.116326i
$910$	−55.2263	−	54.5707i	−1.83073	−	1.80900i
$911$	−2.60677	+	8.02281i	−0.0863661	+	0.265808i	−0.984908	−	0.173081i	$-0.944628\pi$
$911$	−2.60677	+	8.02281i	−0.0863661	+	0.265808i	0.898541	+	0.438889i	$0.144628\pi$
$912$	13.6962	−	8.89443i	0.453527	−	0.294524i
$913$	1.00081	+	19.0967i	0.0331221	+	0.632007i
$914$	−9.72982	−	45.7752i	−0.321834	−	1.51411i
$915$	−32.4167	+	3.07677i	−1.07166	+	0.101715i
$916$	74.0389	−	24.0567i	2.44631	−	0.794855i
$917$	−10.9717	−	4.67527i	−0.362319	−	0.154391i
$918$	34.9652	+	34.9652i	1.15402	+	1.15402i
$919$	−49.0517	+	5.15554i	−1.61807	+	0.170066i	−0.869824	−	0.493362i	$-0.835768\pi$
$919$	−49.0517	+	5.15554i	−1.61807	+	0.170066i	−0.748241	+	0.663427i	$0.769101\pi$
$920$	1.22803	+	29.0349i	0.0404868	+	0.957253i
$921$	−5.67671	+	54.0103i	−0.187054	+	1.77970i
$922$	3.15495	+	1.21107i	0.103903	+	0.0398845i
$923$	30.1409	+	59.1548i	0.992099	+	1.94710i
$924$	−11.9837	−	42.0127i	−0.394234	−	1.38212i
$925$	0.958901	−	1.79163i	0.0315285	−	0.0589083i
$926$	−2.40612	+	4.16751i	−0.0790699	+	0.136953i
$927$	11.0088	+	7.14917i	0.361575	+	0.234810i
$928$	4.46569	−	3.61625i	0.146594	−	0.118709i
$929$	28.5524	−	12.7123i	0.936774	−	0.417079i	0.119179	−	0.992873i	$-0.461974\pi$
$929$	28.5524	−	12.7123i	0.936774	−	0.417079i	0.817595	+	0.575794i	$0.195307\pi$
$930$	70.5209	−	35.0405i	2.31247	−	1.14902i
$931$	−12.8324	+	9.96838i	−0.420566	+	0.326700i
$932$	12.9472	−	12.9472i	0.424099	−	0.424099i
$933$	1.36199	−	1.68192i	0.0445897	−	0.0550637i
$934$	47.6906	−	52.9658i	1.56048	−	1.73309i
$935$	18.6356	+	17.1232i	0.609450	+	0.559988i
$936$	21.9674	−	19.7795i	0.718026	−	0.646514i
$937$	−2.99169	+	5.87152i	−0.0977343	+	0.191814i	−0.934697	−	0.355446i	$-0.884329\pi$
$937$	−2.99169	+	5.87152i	−0.0977343	+	0.191814i	0.836963	+	0.547260i	$0.184329\pi$
$938$	−55.7025	−	10.9080i	−1.81875	−	0.356158i
$939$	36.7405	+	11.9377i	1.19898	+	0.389572i
$940$	22.8341	+	5.09487i	0.744766	+	0.166176i
$941$	12.4785	+	11.2357i	0.406788	+	0.366273i	0.846975	−	0.531633i	$-0.178421\pi$
$941$	12.4785	+	11.2357i	0.406788	+	0.366273i	−0.440187	+	0.897906i	$0.645088\pi$
$942$	−8.36394	+	3.21062i	−0.272512	+	0.104608i
$943$	−6.66348	−	24.8685i	−0.216993	−	0.809829i
$944$	0.109615	−	0.0796398i	0.00356766	−	0.00259206i
$945$	−21.4839	+	4.70078i	−0.698871	+	0.152916i
$946$	−22.5743	−	16.4012i	−0.733954	−	0.533249i
$947$	−14.9653	+	38.9858i	−0.486305	+	1.26687i	0.442656	+	0.896692i	$0.354036\pi$
$947$	−14.9653	+	38.9858i	−0.486305	+	1.26687i	−0.928961	+	0.370177i	$0.879297\pi$
$948$	34.8296	−	53.6329i	1.13121	−	1.74191i
$949$	−13.1395	+	7.58611i	−0.426527	+	0.246255i
$950$	−14.8810	−	23.9597i	−0.482803	−	0.777356i
$951$			59.0773i			1.91571i
$952$	−19.6929	+	64.0934i	−0.638251	+	2.07728i
$953$	8.84775	+	55.8625i	0.286607	+	1.80956i	0.539406	+	0.842046i	$0.318649\pi$
$953$	8.84775	+	55.8625i	0.286607	+	1.80956i	−0.252800	+	0.967519i	$0.581351\pi$
$954$	4.74205	+	10.6508i	0.153530	+	0.344833i
$955$	−59.0763	+	2.49862i	−1.91167	+	0.0808535i
$956$	57.4627	+	25.5841i	1.85848	+	0.827448i
$957$	26.0820	−	6.98864i	0.843110	−	0.225911i
$958$	1.51078	−	9.53866i	0.0488110	−	0.308180i
$959$	17.1888	−	35.1182i	0.555057	−	1.13402i
$960$	−24.0308	−	33.7872i	−0.775589	−	1.09048i
$961$	−12.8585	−	14.2808i	−0.414790	−	0.460671i
$962$	−5.32633	+	0.279141i	−0.171728	+	0.00899987i
$963$	−6.48957	+	0.340104i	−0.209124	+	0.0109597i
$964$	−35.7477	−	39.7019i	−1.15136	−	1.27871i
$965$	0.290105	−	28.7499i	0.00933880	−	0.925492i
$966$	36.8236	−	2.52344i	1.18478	−	0.0811904i
$967$	−1.99758	+	12.6122i	−0.0642378	+	0.405582i	0.934527	+	0.355892i	$0.115823\pi$
$967$	−1.99758	+	12.6122i	−0.0642378	+	0.405582i	−0.998765	+	0.0496891i	$0.984177\pi$
$968$	30.0736	−	8.05820i	0.966602	−	0.259000i
$969$	23.7397	+	10.5696i	0.762627	+	0.339544i
$970$	31.6067	+	84.8887i	1.01483	+	2.72561i
$971$	15.2849	+	34.3305i	0.490517	+	1.10172i	0.974038	+	0.226386i	$0.0726912\pi$
$971$	15.2849	+	34.3305i	0.490517	+	1.10172i	−0.483521	+	0.875333i	$0.660642\pi$
$972$	−7.11609	−	44.9292i	−0.228249	−	1.44110i
$973$	40.9861	−	38.1136i	1.31395	−	1.22187i
$974$		−	14.3322i		−	0.459235i
$975$	−36.1149	−	41.7749i	−1.15660	−	1.33787i
$976$	−21.2140	+	12.2479i	−0.679042	+	0.392045i
$977$	−15.7026	+	24.1799i	−0.502372	+	0.773584i	−0.995336	−	0.0964648i	$-0.969246\pi$
$977$	−15.7026	+	24.1799i	−0.502372	+	0.773584i	0.492965	+	0.870049i	$0.335913\pi$
$978$	−2.33701	+	6.08812i	−0.0747293	+	0.194677i
$979$	−4.02183	−	2.92203i	−0.128538	−	0.0933885i
$980$	−39.5048	−	46.6446i	−1.26194	−	1.49001i
$981$	10.0912	−	7.33170i	0.322188	−	0.234083i
$982$	0.755932	+	2.82118i	0.0241228	+	0.0900274i
$983$	26.1913	−	10.0539i	0.835372	−	0.320669i	0.0971855	−	0.995266i	$-0.469016\pi$
$983$	26.1913	−	10.0539i	0.835372	−	0.320669i	0.738186	+	0.674597i	$0.235683\pi$
$984$	−64.5306	−	58.1036i	−2.05716	−	1.85227i
$985$	26.3057	−	11.3954i	0.838171	−	0.363089i
$986$	−80.7874	−	26.2494i	−2.57280	−	0.835952i
$987$	2.78587	−	14.2263i	0.0886753	−	0.452828i
$988$	−22.2258	+	43.6206i	−0.707096	+	1.38775i
$989$	11.5855	−	10.4316i	0.368398	−	0.331707i
$990$	−2.63042	−	13.0198i	−0.0836004	−	0.413796i
$991$	25.3112	−	28.1110i	0.804038	−	0.892975i	−0.192046	−	0.981386i	$-0.561512\pi$
$991$	25.3112	−	28.1110i	0.804038	−	0.892975i	0.996084	+	0.0884113i	$0.0281790\pi$
$992$	−4.01294	+	4.95556i	−0.127411	+	0.157339i
$993$	2.58460	−	2.58460i	0.0820198	−	0.0820198i
$994$	29.5065	+	73.3249i	0.935889	+	2.32572i
$995$	−2.55677	−	2.60890i	−0.0810551	−	0.0827076i
$996$	−67.4777	+	30.0430i	−2.13811	+	0.951949i
$997$	41.9471	−	33.9681i	1.32848	−	1.07578i	0.337560	−	0.941304i	$-0.390399\pi$
$997$	41.9471	−	33.9681i	1.32848	−	1.07578i	0.990917	−	0.134475i	$-0.0429348\pi$
$998$	−32.0370	−	20.8050i	−1.01411	−	0.658572i
$999$	−0.755402	+	1.30839i	−0.0238999	+	0.0413958i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.x.a.103.2	yes	288
5.2	odd	4		875.2.bb.b.257.17		288
5.3	odd	4		875.2.bb.a.257.2		288
5.4	even	2		875.2.bb.c.243.17		288
7.3	odd	6	inner	175.2.x.a.3.17	✓	288
25.6	even	5		875.2.bb.b.768.17		288
25.8	odd	20		875.2.bb.c.607.2		288
25.17	odd	20	inner	175.2.x.a.117.17	yes	288
25.19	even	10		875.2.bb.a.768.2		288
35.3	even	12		875.2.bb.a.507.2		288
35.17	even	12		875.2.bb.b.507.17		288
35.24	odd	6		875.2.bb.c.493.2		288
175.17	even	60	inner	175.2.x.a.17.2	yes	288
175.31	odd	30		875.2.bb.b.143.17		288
175.94	odd	30		875.2.bb.a.143.2		288
175.108	even	60		875.2.bb.c.857.17		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.3.17	✓	288	7.3	odd	6	inner
175.2.x.a.17.2	yes	288	175.17	even	60	inner
175.2.x.a.103.2	yes	288	1.1	even	1	trivial
175.2.x.a.117.17	yes	288	25.17	odd	20	inner
875.2.bb.a.143.2		288	175.94	odd	30
875.2.bb.a.257.2		288	5.3	odd	4
875.2.bb.a.507.2		288	35.3	even	12
875.2.bb.a.768.2		288	25.19	even	10
875.2.bb.b.143.17		288	175.31	odd	30
875.2.bb.b.257.17		288	5.2	odd	4
875.2.bb.b.507.17		288	35.17	even	12
875.2.bb.b.768.17		288	25.6	even	5
875.2.bb.c.243.17		288	5.4	even	2
875.2.bb.c.493.2		288	35.24	odd	6
875.2.bb.c.607.2		288	25.8	odd	20
875.2.bb.c.857.17		288	175.108	even	60

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-2.42673 - 0.127179i) q^{2} +(-1.28700 - 1.58931i) q^{3} +(3.88379 + 0.408202i) q^{4} +(-2.16561 + 0.556914i) q^{5} +(2.92107 + 4.02051i) q^{6} +(-2.31224 - 1.28591i) q^{7} +(-4.57269 - 0.724243i) q^{8} +(-0.245810 + 1.15644i) q^{9} +(5.32616 - 1.07606i) q^{10} +(-2.02243 + 0.429882i) q^{11} +(-4.34967 - 6.69790i) q^{12} +(4.81187 + 2.45177i) q^{13} +(5.44763 + 3.41461i) q^{14} +(3.67224 + 2.72507i) q^{15} +(3.36489 + 0.715229i) q^{16} +(1.96169 + 5.11037i) q^{17} +(0.743588 - 2.77511i) q^{18} +(0.242645 + 2.30861i) q^{19} +(-8.63808 + 1.27893i) q^{20} +(0.932143 + 5.32983i) q^{21} +(4.96257 - 0.785994i) q^{22} +(-0.146917 + 2.80334i) q^{23} +(4.73400 + 8.19953i) q^{24} +(4.37969 - 2.41211i) q^{25} +(-11.3653 - 6.56174i) q^{26} +(-3.31219 + 1.68764i) q^{27} +(-8.45533 - 5.93804i) q^{28} +(3.75352 - 5.16628i) q^{29} +(-8.56496 - 7.08004i) q^{30} +(-2.88229 + 6.47373i) q^{31} +(0.869181 + 0.232896i) q^{32} +(3.28609 + 2.66102i) q^{33} +(-4.11055 - 12.6510i) q^{34} +(5.72353 + 1.49705i) q^{35} +(-1.42673 + 4.39104i) q^{36} +(0.340852 - 0.221352i) q^{37} +(-0.295225 - 5.63323i) q^{38} +(-2.29624 - 10.8030i) q^{39} +(10.3060 - 0.978172i) q^{40} +(-8.72248 + 2.83411i) q^{41} +(-1.58421 - 13.0526i) q^{42} +(-3.92695 - 3.92695i) q^{43} +(-8.03018 + 0.844006i) q^{44} +(-0.111713 - 2.64129i) q^{45} +(0.713054 - 6.78426i) q^{46} +(-2.50126 - 0.960145i) q^{47} +(-3.19388 - 6.26835i) q^{48} +(3.69289 + 5.94664i) q^{49} +(-10.9351 + 5.29653i) q^{50} +(5.59728 - 9.69478i) q^{51} +(17.6874 + 11.4864i) q^{52} +(-3.15369 + 2.55381i) q^{53} +(8.25240 - 3.67421i) q^{54} +(4.14039 - 2.05728i) q^{55} +(9.64184 + 7.55468i) q^{56} +(3.35682 - 3.35682i) q^{57} +(-9.76581 + 12.0598i) q^{58} +(0.0263546 - 0.0292698i) q^{59} +(13.1498 + 12.0826i) q^{60} +(-5.29174 + 4.76471i) q^{61} +(7.81785 - 15.3434i) q^{62} +(2.05545 - 2.35788i) q^{63} +(-8.62303 - 2.80179i) q^{64} +(-11.7860 - 2.62977i) q^{65} +(-7.63601 - 6.87550i) q^{66} +(-8.24200 + 3.16381i) q^{67} +(5.53271 + 20.6484i) q^{68} +(4.64447 - 3.37440i) q^{69} +(-13.6991 - 4.36084i) q^{70} +(9.94567 + 7.22595i) q^{71} +(1.96156 - 5.11003i) q^{72} +(-1.53012 + 2.35618i) q^{73} +(-0.855306 + 0.493811i) q^{74} +(-9.47026 - 3.85631i) q^{75} +9.06520i q^{76} +(5.22914 + 1.60667i) q^{77} +(4.19844 + 26.5079i) q^{78} +(3.25691 + 7.31514i) q^{79} +(-7.68534 + 0.325050i) q^{80} +(10.1852 + 4.53473i) q^{81} +(21.5275 - 5.76828i) q^{82} +(1.44682 - 9.13488i) q^{83} +(1.44459 + 21.0804i) q^{84} +(-7.09428 - 9.97456i) q^{85} +(9.03021 + 10.0291i) q^{86} +(-13.0416 + 0.683481i) q^{87} +(9.55931 - 0.500982i) q^{88} +(1.60882 + 1.78677i) q^{89} +(-0.0648213 + 6.42391i) q^{90} +(-7.97344 - 11.8567i) q^{91} +(-1.71492 + 10.8276i) q^{92} +(13.9983 - 3.75083i) q^{93} +(5.94777 + 2.64812i) q^{94} +(-1.81117 - 4.86441i) q^{95} +(-0.748490 - 1.68114i) q^{96} +(2.60779 + 16.4649i) q^{97} +(-8.20535 - 14.9005i) q^{98} -2.44450i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100}) \) 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

L-functions

Modular forms

Varieties

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