LMFDB - Embedded newform 175.2.x.a.117.11

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			117.11
Character	$\chi$	$=$	175.117
Dual form			175.2.x.a.3.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.437609 + 0.673859i) q^{2} +(1.12462 + 2.92974i) q^{3} +(0.550889 - 1.23732i) q^{4} +(-2.22451 - 0.227106i) q^{5} +(-1.48209 + 2.03992i) q^{6} +(-0.782993 + 2.52724i) q^{7} +(2.66204 - 0.421625i) q^{8} +(-5.08915 + 4.58229i) q^{9} +(-0.820427 - 1.59839i) q^{10} +(3.35615 - 3.72738i) q^{11} +(4.24455 + 0.222448i) q^{12} +(0.816789 - 0.416175i) q^{13} +(-2.04565 + 0.578315i) q^{14} +(-1.83636 - 6.77262i) q^{15} +(-0.363508 - 0.403716i) q^{16} +(-0.326203 - 0.402827i) q^{17} +(-5.31488 - 1.42412i) q^{18} +(-1.01710 + 0.452842i) q^{19} +(-1.50646 + 2.62731i) q^{20} +(-8.28471 + 0.548217i) q^{21} +(3.98041 + 0.630435i) q^{22} +(4.33381 - 2.81441i) q^{23} +(4.22903 + 7.32490i) q^{24} +(4.89685 + 1.01040i) q^{25} +(0.637878 + 0.368279i) q^{26} +(-10.7599 - 5.48243i) q^{27} +(2.69565 + 2.36104i) q^{28} +(-3.39698 - 4.67555i) q^{29} +(3.76018 - 4.20121i) q^{30} +(-0.340506 - 0.0357886i) q^{31} +(1.50812 - 5.62839i) q^{32} +(14.6946 + 5.64074i) q^{33} +(0.128699 - 0.396095i) q^{34} +(2.31572 - 5.44403i) q^{35} +(2.86619 + 8.82122i) q^{36} +(-0.334068 + 6.37440i) q^{37} +(-0.750244 - 0.487214i) q^{38} +(2.13786 + 1.92494i) q^{39} +(-6.01747 + 0.333344i) q^{40} +(6.75808 + 2.19583i) q^{41} +(-3.99489 - 5.34282i) q^{42} +(-3.02167 + 3.02167i) q^{43} +(-2.76308 - 6.20599i) q^{44} +(12.3615 - 9.03756i) q^{45} +(3.79303 + 1.68877i) q^{46} +(-9.91961 - 8.03274i) q^{47} +(0.773974 - 1.51901i) q^{48} +(-5.77384 - 3.95762i) q^{49} +(1.46204 + 3.74194i) q^{50} +(0.813322 - 1.40871i) q^{51} +(-0.0649800 - 1.23989i) q^{52} +(-5.47316 + 2.10095i) q^{53} +(-1.01424 - 9.64981i) q^{54} +(-8.31228 + 7.52937i) q^{55} +(-1.01881 + 7.05773i) q^{56} +(-2.47056 - 2.47056i) q^{57} +(1.66411 - 4.33515i) q^{58} +(8.60248 - 1.82851i) q^{59} +(-9.39151 - 1.45880i) q^{60} +(0.301099 - 1.41656i) q^{61} +(-0.124892 - 0.245114i) q^{62} +(-7.59576 - 16.4494i) q^{63} +(3.41938 - 1.11102i) q^{64} +(-1.91147 + 0.740286i) q^{65} +(2.62944 + 12.3706i) q^{66} +(-1.09328 + 0.885317i) q^{67} +(-0.678125 + 0.181703i) q^{68} +(13.1194 + 9.53177i) q^{69} +(4.68189 - 0.821886i) q^{70} +(-6.16371 + 4.47820i) q^{71} +(-11.6155 + 14.3439i) q^{72} +(-1.20435 + 0.0631171i) q^{73} +(-4.44164 + 2.56438i) q^{74} +(2.54690 + 15.4828i) q^{75} +1.50794i q^{76} +(6.79213 + 11.4003i) q^{77} +(-0.361590 + 2.28299i) q^{78} +(-4.83574 + 0.508257i) q^{79} +(0.716939 + 0.980624i) q^{80} +(1.81383 - 17.2574i) q^{81} +(1.47772 + 5.51491i) q^{82} +(-0.543025 - 3.42852i) q^{83} +(-3.88563 + 10.5528i) q^{84} +(0.634155 + 0.970172i) q^{85} +(-3.35849 - 0.713869i) q^{86} +(9.87780 - 15.2105i) q^{87} +(7.36263 - 11.3375i) q^{88} +(-3.07374 - 0.653343i) q^{89} +(11.4996 + 4.37500i) q^{90} +(0.412231 + 2.39008i) q^{91} +(-1.09487 - 6.91272i) q^{92} +(-0.278088 - 1.03784i) q^{93} +(1.07202 - 10.1996i) q^{94} +(2.36538 - 0.776360i) q^{95} +(18.1858 - 1.91140i) q^{96} +(-0.557021 + 3.51689i) q^{97} +(0.140190 - 5.62265i) q^{98} +34.3480i 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 $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{20}\right)$

Coefficient data

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

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

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

$2$	0.437609	+	0.673859i	0.309437	+	0.476491i	0.958837	−	0.283956i	$-0.0916469\pi$
$2$	0.437609	+	0.673859i	0.309437	+	0.476491i	−0.649401	+	0.760446i	$0.724980\pi$
$3$	1.12462	+	2.92974i	0.649300	+	1.69148i	0.719989	+	0.693986i	$0.244147\pi$
$3$	1.12462	+	2.92974i	0.649300	+	1.69148i	−0.0706887	+	0.997498i	$0.522520\pi$
$4$	0.550889	−	1.23732i	0.275444	−	0.618658i
$5$	−2.22451	−	0.227106i	−0.994829	−	0.101565i
$5$	−2.22451	−	0.227106i	−0.994829	−	0.101565i
$6$	−1.48209	+	2.03992i	−0.605059	+	0.832792i
$7$	−0.782993	+	2.52724i	−0.295944	+	0.955205i
$7$	−0.782993	+	2.52724i	−0.295944	+	0.955205i
$8$	2.66204	−	0.421625i	0.941172	−	0.149067i
$9$	−5.08915	+	4.58229i	−1.69638	+	1.52743i
$10$	−0.820427	−	1.59839i	−0.259442	−	0.505454i
$11$	3.35615	−	3.72738i	1.01192	−	1.12385i	0.0196392	−	0.999807i	$-0.493748\pi$
$11$	3.35615	−	3.72738i	1.01192	−	1.12385i	0.992277	−	0.124040i	$-0.0395851\pi$
$12$	4.24455	+	0.222448i	1.22530	+	0.0642151i
$13$	0.816789	−	0.416175i	0.226536	−	0.115426i	−0.337039	−	0.941491i	$-0.609425\pi$
$13$	0.816789	−	0.416175i	0.226536	−	0.115426i	0.563575	+	0.826065i	$0.309425\pi$
$14$	−2.04565	+	0.578315i	−0.546722	+	0.154561i
$15$	−1.83636	−	6.77262i	−0.474147	−	1.74868i
$16$	−0.363508	−	0.403716i	−0.0908770	−	0.100929i
$17$	−0.326203	−	0.402827i	−0.0791157	−	0.0976998i	0.736051	−	0.676926i	$-0.236688\pi$
$17$	−0.326203	−	0.402827i	−0.0791157	−	0.0976998i	−0.815167	+	0.579226i	$0.803355\pi$
$18$	−5.31488	−	1.42412i	−1.25273	−	0.335668i
$19$	−1.01710	+	0.452842i	−0.233339	+	0.103889i	−0.520075	−	0.854120i	$-0.674096\pi$
$19$	−1.01710	+	0.452842i	−0.233339	+	0.103889i	0.286737	+	0.958009i	$0.407429\pi$
$20$	−1.50646	+	2.62731i	−0.336854	+	0.587484i
$21$	−8.28471	+	0.548217i	−1.80787	+	0.119631i
$22$	3.98041	+	0.630435i	0.848626	+	0.134409i
$23$	4.33381	−	2.81441i	0.903661	−	0.586844i	−0.00701045	−	0.999975i	$-0.502232\pi$
$23$	4.33381	−	2.81441i	0.903661	−	0.586844i	0.910672	+	0.413131i	$0.135565\pi$
$24$	4.22903	+	7.32490i	0.863248	+	1.49519i
$25$	4.89685	+	1.01040i	0.979369	+	0.202079i
$26$	0.637878	+	0.368279i	0.125098	+	0.0722254i
$27$	−10.7599	−	5.48243i	−2.07074	−	1.05509i
$28$	2.69565	+	2.36104i	0.509430	+	0.446194i
$29$	−3.39698	−	4.67555i	−0.630804	−	0.868227i	0.367279	−	0.930111i	$-0.380289\pi$
$29$	−3.39698	−	4.67555i	−0.630804	−	0.868227i	−0.998083	+	0.0618834i	$0.980289\pi$
$30$	3.76018	−	4.20121i	0.686513	−	0.767033i
$31$	−0.340506	−	0.0357886i	−0.0611566	−	0.00642782i	0.0739007	−	0.997266i	$-0.476455\pi$
$31$	−0.340506	−	0.0357886i	−0.0611566	−	0.00642782i	−0.135057	+	0.990838i	$0.543122\pi$
$32$	1.50812	−	5.62839i	0.266601	−	0.994968i
$33$	14.6946	+	5.64074i	2.55801	+	0.981927i
$34$	0.128699	−	0.396095i	0.0220717	−	0.0679298i
$35$	2.31572	−	5.44403i	0.391428	−	0.920209i
$36$	2.86619	+	8.82122i	0.477698	+	1.47020i
$37$	−0.334068	+	6.37440i	−0.0549205	+	1.04794i	0.822666	+	0.568526i	$0.192486\pi$
$37$	−0.334068	+	6.37440i	−0.0549205	+	1.04794i	−0.877586	+	0.479419i	$0.840847\pi$
$38$	−0.750244	−	0.487214i	−0.121706	−	0.0790365i
$39$	2.13786	+	1.92494i	0.342332	+	0.308237i
$40$	−6.01747	+	0.333344i	−0.951445	+	0.0527063i
$41$	6.75808	+	2.19583i	1.05543	+	0.342931i	0.784799	−	0.619750i	$-0.212766\pi$
$41$	6.75808	+	2.19583i	1.05543	+	0.342931i	0.270635	+	0.962682i	$0.412766\pi$
$42$	−3.99489	−	5.34282i	−0.616424	−	0.824415i
$43$	−3.02167	+	3.02167i	−0.460800	+	0.460800i	−0.898918	−	0.438118i	$-0.855645\pi$
$43$	−3.02167	+	3.02167i	−0.460800	+	0.460800i	0.438118	+	0.898918i	$0.355645\pi$
$44$	−2.76308	−	6.20599i	−0.416551	−	0.935588i
$45$	12.3615	−	9.03756i	1.84274	−	1.34724i
$46$	3.79303	+	1.68877i	0.559252	+	0.248995i
$47$	−9.91961	−	8.03274i	−1.44692	−	1.17170i	−0.953302	−	0.302020i	$-0.902339\pi$
$47$	−9.91961	−	8.03274i	−1.44692	−	1.17170i	−0.493622	−	0.869676i	$-0.664327\pi$
$48$	0.773974	−	1.51901i	0.111714	−	0.219250i
$49$	−5.77384	−	3.95762i	−0.824835	−	0.565374i
$50$	1.46204	+	3.74194i	0.206764	+	0.529191i
$51$	0.813322	−	1.40871i	0.113888	−	0.197260i
$52$	−0.0649800	−	1.23989i	−0.00901111	−	0.171942i
$53$	−5.47316	+	2.10095i	−0.751796	+	0.288588i	−0.703933	−	0.710266i	$-0.748575\pi$
$53$	−5.47316	+	2.10095i	−0.751796	+	0.288588i	−0.0478633	+	0.998854i	$0.515241\pi$
$54$	−1.01424	−	9.64981i	−0.138020	−	1.31317i
$55$	−8.31228	+	7.52937i	−1.12083	+	1.01526i
$56$	−1.01881	+	7.05773i	−0.136144	+	0.943128i
$57$	−2.47056	−	2.47056i	−0.327233	−	0.327233i
$58$	1.66411	−	4.33515i	0.218508	−	0.569233i
$59$	8.60248	−	1.82851i	1.11995	−	0.238052i	0.389503	−	0.921025i	$-0.372647\pi$
$59$	8.60248	−	1.82851i	1.11995	−	0.238052i	0.730444	+	0.682973i	$0.239313\pi$
$60$	−9.39151	−	1.45880i	−1.21244	−	0.188330i
$61$	0.301099	−	1.41656i	0.0385518	−	0.181372i	−0.954659	−	0.297702i	$-0.903780\pi$
$61$	0.301099	−	1.41656i	0.0385518	−	0.181372i	0.993211	+	0.116330i	$0.0371131\pi$
$62$	−0.124892	−	0.245114i	−0.0158613	−	0.0311295i
$63$	−7.59576	−	16.4494i	−0.956976	−	2.07243i
$64$	3.41938	−	1.11102i	0.427422	−	0.138878i
$65$	−1.91147	+	0.740286i	−0.237088	+	0.0918211i
$66$	2.62944	+	12.3706i	0.323662	+	1.52271i
$67$	−1.09328	+	0.885317i	−0.133565	+	0.108159i	−0.693775	−	0.720192i	$-0.744054\pi$
$67$	−1.09328	+	0.885317i	−0.133565	+	0.108159i	0.560210	+	0.828351i	$0.310720\pi$
$68$	−0.678125	+	0.181703i	−0.0822348	+	0.0220347i
$69$	13.1194	+	9.53177i	1.57939	+	1.14749i
$70$	4.68189	−	0.821886i	0.559593	−	0.0982342i
$71$	−6.16371	+	4.47820i	−0.731498	+	0.531465i	−0.890037	−	0.455888i	$-0.849322\pi$
$71$	−6.16371	+	4.47820i	−0.731498	+	0.531465i	0.158539	+	0.987353i	$0.449322\pi$
$72$	−11.6155	+	14.3439i	−1.36890	+	1.69045i
$73$	−1.20435	+	0.0631171i	−0.140958	+	0.00738730i	−0.122684	−	0.992446i	$-0.539150\pi$
$73$	−1.20435	+	0.0631171i	−0.140958	+	0.00738730i	−0.0182736	+	0.999833i	$0.505817\pi$
$74$	−4.44164	+	2.56438i	−0.516330	+	0.298103i
$75$	2.54690	+	15.4828i	0.294091	+	1.78780i
$76$			1.50794i			0.172972i
$77$	6.79213	+	11.4003i	0.774035	+	1.29918i
$78$	−0.361590	+	2.28299i	−0.0409420	+	0.258497i
$79$	−4.83574	+	0.508257i	−0.544064	+	0.0571834i	−0.372574	−	0.928003i	$-0.621525\pi$
$79$	−4.83574	+	0.508257i	−0.544064	+	0.0571834i	−0.171490	+	0.985186i	$0.554858\pi$
$80$	0.716939	+	0.980624i	0.0801562	+	0.109637i
$81$	1.81383	−	17.2574i	0.201536	−	1.91749i
$82$	1.47772	+	5.51491i	0.163186	+	0.609020i
$83$	−0.543025	−	3.42852i	−0.0596047	−	0.376329i	−0.999401	−	0.0345952i	$-0.988986\pi$
$83$	−0.543025	−	3.42852i	−0.0596047	−	0.376329i	0.939797	−	0.341734i	$-0.111014\pi$
$84$	−3.88563	+	10.5528i	−0.423957	+	1.15141i
$85$	0.634155	+	0.970172i	0.0687838	+	0.105230i
$86$	−3.35849	−	0.713869i	−0.362155	−	0.0769784i
$87$	9.87780	−	15.2105i	1.05901	−	1.63074i
$88$	7.36263	−	11.3375i	0.784859	−	1.20858i
$89$	−3.07374	−	0.653343i	−0.325816	−	0.0692543i	0.0421001	−	0.999113i	$-0.486595\pi$
$89$	−3.07374	−	0.653343i	−0.325816	−	0.0692543i	−0.367916	+	0.929859i	$0.619929\pi$
$90$	11.4996	+	4.37500i	1.21216	+	0.461165i
$91$	0.412231	+	2.39008i	0.0432136	+	0.250549i
$92$	−1.09487	−	6.91272i	−0.114148	−	0.720700i
$93$	−0.278088	−	1.03784i	−0.0288364	−	0.107619i
$94$	1.07202	−	10.1996i	0.110571	−	1.05201i
$95$	2.36538	−	0.776360i	0.242683	−	0.0796528i
$96$	18.1858	−	1.91140i	1.85608	−	0.195081i
$97$	−0.557021	+	3.51689i	−0.0565569	+	0.357086i	0.943138	+	0.332400i	$0.107859\pi$
$97$	−0.557021	+	3.51689i	−0.0565569	+	0.357086i	−0.999695	+	0.0246858i	$0.992141\pi$
$98$	0.140190	−	5.62265i	0.0141613	−	0.567973i
$99$			34.3480i			3.45211i
$100$	3.94780	−	5.50233i	0.394780	−	0.550233i
$101$	−8.57568	+	4.95117i	−0.853312	+	0.492660i	−0.861767	−	0.507304i	$-0.830642\pi$
$101$	−8.57568	+	4.95117i	−0.853312	+	0.492660i	0.00845468	+	0.999964i	$0.497309\pi$
$102$	1.30519	−	0.0684023i	0.129233	−	0.00677283i
$103$	−4.67366	+	5.77149i	−0.460510	+	0.568682i	−0.953516	−	0.301344i	$-0.902565\pi$
$103$	−4.67366	+	5.77149i	−0.460510	+	0.568682i	0.493006	+	0.870026i	$0.335898\pi$
$104$	1.99885	−	1.45225i	0.196004	−	0.142405i
$105$	18.5539	+	0.661992i	1.81067	+	0.0646038i
$106$	−3.81085	−	2.76875i	−0.370143	−	0.268924i
$107$	−1.50667	+	0.403711i	−0.145655	+	0.0390282i	−0.330910	−	0.943662i	$-0.607356\pi$
$107$	−1.50667	+	0.403711i	−0.145655	+	0.0390282i	0.185255	+	0.982691i	$0.440689\pi$
$108$	−12.7110	+	10.2932i	−1.22312	+	0.990460i
$109$	−1.24225	−	5.84432i	−0.118986	−	0.559784i	−0.996741	−	0.0806741i	$-0.974293\pi$
$109$	−1.24225	−	5.84432i	−0.118986	−	0.559784i	0.877755	−	0.479110i	$-0.159041\pi$
$110$	−8.71127	−	2.30638i	−0.830587	−	0.219905i
$111$	−19.0510	+	6.19005i	−1.80824	+	0.587533i
$112$	1.30491	−	0.602563i	0.123302	−	0.0569368i
$113$	1.14628	+	2.24970i	0.107833	+	0.211634i	0.938617	−	0.344960i	$-0.112108\pi$
$113$	1.14628	+	2.24970i	0.107833	+	0.211634i	−0.830784	+	0.556595i	$0.812108\pi$
$114$	0.583669	−	2.74595i	0.0546656	−	0.257181i
$115$	−10.2797	+	5.27643i	−0.958591	+	0.492030i
$116$	−7.65649	+	1.62744i	−0.710888	+	0.151104i
$117$	−2.24973	+	5.86074i	−0.207987	+	0.541826i
$118$	4.99668	+	4.99668i	0.459982	+	0.459982i
$119$	1.27345	−	0.508980i	0.116737	−	0.0466581i
$120$	−7.74398	−	17.2547i	−0.706925	−	1.57513i
$121$	−1.47982	−	14.0795i	−0.134529	−	1.27996i
$122$	1.08633	−	0.417002i	0.0983514	−	0.0377536i
$123$	1.16706	+	22.2689i	0.105230	+	2.00792i
$124$	−0.231863	+	0.401598i	−0.0208219	+	0.0360645i
$125$	−10.6636	−	3.35973i	−0.953781	−	0.300503i
$126$	7.76060	−	12.3169i	0.691369	−	1.09728i
$127$	−4.18519	+	8.21389i	−0.371375	+	0.728865i	−0.998757	−	0.0498468i	$-0.984127\pi$
$127$	−4.18519	+	8.21389i	−0.371375	+	0.728865i	0.627381	+	0.778712i	$0.284127\pi$
$128$	−6.81173	−	5.51603i	−0.602078	−	0.487553i
$129$	−12.2509	−	5.45446i	−1.07863	−	0.480238i
$130$	−1.33532	−	0.964104i	−0.117116	−	0.0845575i
$131$	2.28451	+	5.13108i	0.199598	+	0.448305i	0.985418	−	0.170150i	$-0.0544254\pi$
$131$	2.28451	+	5.13108i	0.199598	+	0.448305i	−0.785820	+	0.618455i	$0.787759\pi$
$132$	15.0745	−	15.0745i	1.31207	−	1.31207i
$133$	−0.348056	−	2.92502i	−0.0301803	−	0.253631i
$134$	−1.07501	−	0.349291i	−0.0928664	−	0.0301741i
$135$	22.6903	+	14.6393i	1.95287	+	1.25995i
$136$	−1.03821	−	0.934804i	−0.0890254	−	0.0801588i
$137$	3.62566	+	2.35453i	0.309761	+	0.201161i	0.690152	−	0.723665i	$-0.257544\pi$
$137$	3.62566	+	2.35453i	0.309761	+	0.201161i	−0.380391	+	0.924826i	$0.624210\pi$
$138$	−0.681919	+	13.0118i	−0.0580488	+	1.10764i
$139$	−1.99140	−	6.12890i	−0.168908	−	0.519847i	0.830395	−	0.557176i	$-0.188115\pi$
$139$	−1.99140	−	6.12890i	−0.168908	−	0.519847i	−0.999303	+	0.0373290i	$0.988115\pi$
$140$	−5.46028	−	5.86434i	−0.461478	−	0.495627i
$141$	12.3780	−	38.0956i	1.04242	−	3.20823i
$142$	−5.71498	−	2.19377i	−0.479590	−	0.184097i
$143$	1.19002	−	4.44123i	0.0995147	−	0.371394i
$144$	3.69989	+	0.388874i	0.308324	+	0.0324062i
$145$	6.49477	+	11.1723i	0.539361	+	0.927805i
$146$	−0.569565	−	0.783939i	−0.0471376	−	0.0648793i
$147$	5.10140	−	21.3667i	0.420756	−	1.76229i
$148$	7.70311	+	3.92493i	0.633192	+	0.322627i
$149$	−1.92554	−	1.11171i	−0.157746	−	0.0910749i	0.419049	−	0.907964i	$-0.362364\pi$
$149$	−1.92554	−	1.11171i	−0.157746	−	0.0910749i	−0.576795	+	0.816889i	$0.695697\pi$
$150$	−9.31867	+	8.49166i	−0.760866	+	0.693341i
$151$	6.19286	+	10.7263i	0.503968	+	0.872897i	0.999989	+	0.00458736i	$0.00146021\pi$
$151$	6.19286	+	10.7263i	0.503968	+	0.872897i	−0.496022	+	0.868310i	$0.665206\pi$
$152$	−2.51663	+	1.63432i	−0.204125	+	0.132561i
$153$	3.50596	+	0.555290i	0.283440	+	0.0448925i
$154$	−4.70989	+	9.56581i	−0.379534	+	0.770835i
$155$	0.749329	+	0.156943i	0.0601875	+	0.0126059i
$156$	3.55948	−	1.58478i	0.284987	−	0.126884i
$157$	16.2535	+	4.35511i	1.29717	+	0.347576i	0.840380	−	0.541998i	$-0.182332\pi$
$157$	16.2535	+	4.35511i	1.29717	+	0.347576i	0.456791	+	0.889574i	$0.348999\pi$
$158$	−2.45866	−	3.03619i	−0.195601	−	0.241547i
$159$	−12.3105	−	13.6721i	−0.976283	−	1.08427i
$160$	−4.63306	+	12.1779i	−0.366276	+	0.962746i
$161$	3.71933	+	13.1562i	0.293124	+	1.03685i
$162$	12.4228	−	6.32974i	0.976029	−	0.497312i
$163$	18.1734	+	0.952430i	1.42345	+	0.0746001i	0.748439	−	0.663204i	$-0.230804\pi$
$163$	18.1734	+	0.952430i	1.42345	+	0.0746001i	0.675015	+	0.737804i	$0.264137\pi$
$164$	6.43989	−	7.15222i	0.502871	−	0.558495i
$165$	−31.4072	−	15.8851i	−2.44505	−	1.23665i
$166$	2.07271	−	1.86628i	0.160873	−	0.144851i
$167$	−0.334099	+	0.0529161i	−0.0258534	+	0.00409477i	−0.169348	−	0.985556i	$-0.554166\pi$
$167$	−0.334099	+	0.0529161i	−0.0258534	+	0.00409477i	0.143494	+	0.989651i	$0.454166\pi$
$168$	−21.8231	+	4.95242i	−1.68369	+	0.382087i
$169$	−7.14727	+	9.83737i	−0.549790	+	0.756721i
$170$	−0.376247	+	0.851888i	−0.0288569	+	0.0653368i
$171$	3.10112	−	6.96522i	0.237148	−	0.532644i
$172$	2.07416	+	5.40336i	0.158153	+	0.412002i
$173$	−9.69487	−	14.9288i	−0.737087	−	1.13501i	−0.986042	−	0.166499i	$-0.946754\pi$
$173$	−9.69487	−	14.9288i	−0.737087	−	1.13501i	0.248955	−	0.968515i	$-0.419913\pi$
$174$	14.5723			1.10473
$175$	−6.38771	+	11.5844i	−0.482865	+	0.875695i
$176$	−2.72479			−0.205389
$177$	15.0316	+	23.1466i	1.12984	+	1.73981i
$178$	−0.904835	−	2.35718i	−0.0678203	−	0.176678i
$179$	4.01032	−	9.00732i	0.299745	−	0.673239i	−0.699393	−	0.714737i	$-0.746546\pi$
$179$	4.01032	−	9.00732i	0.299745	−	0.673239i	0.999139	+	0.0414980i	$0.0132130\pi$
$180$	−4.37250	−	20.2738i	−0.325907	−	1.51112i
$181$	12.6158	−	17.3642i	0.937727	−	1.29067i	−0.0190405	−	0.999819i	$-0.506061\pi$
$181$	12.6158	−	17.3642i	0.937727	−	1.29067i	0.956768	−	0.290852i	$-0.0939388\pi$
$182$	−1.43018	+	1.32371i	−0.106012	+	0.0981197i
$183$	4.48877	−	0.710952i	0.331820	−	0.0525551i
$184$	10.3501	−	9.31930i	0.763022	−	0.687028i
$185$	2.19080	−	14.1040i	0.161071	−	1.03695i
$186$	0.577664	−	0.641561i	0.0423564	−	0.0470415i
$187$	−2.59627	−	0.136065i	−0.189858	−	0.00995004i
$188$	−15.4036	+	7.84855i	−1.12343	+	0.572414i
$189$	22.2803	−	22.9000i	1.62065	−	1.66573i
$190$	1.55827	+	1.25419i	0.113049	+	0.0909888i
$191$	0.485439	+	0.539134i	0.0351251	+	0.0390104i	0.760451	−	0.649395i	$-0.224978\pi$
$191$	0.485439	+	0.539134i	0.0351251	+	0.0390104i	−0.725326	+	0.688405i	$0.758311\pi$
$192$	7.10051	+	8.76840i	0.512435	+	0.632805i
$193$	14.2145	+	3.80877i	1.02318	+	0.274161i	0.731128	−	0.682240i	$-0.238994\pi$
$193$	14.2145	+	3.80877i	1.02318	+	0.274161i	0.292055	+	0.956401i	$0.405661\pi$
$194$	−2.61365	+	1.16367i	−0.187649	+	0.0835467i
$195$	−4.31852	−	4.76755i	−0.309255	−	0.341412i
$196$	−8.07757	+	4.96386i	−0.576969	+	0.354562i
$197$	24.1329	+	3.82227i	1.71940	+	0.272326i	0.936714	−	0.350095i	$-0.113851\pi$
$197$	24.1329	+	3.82227i	1.71940	+	0.272326i	0.782683	+	0.622420i	$0.213851\pi$
$198$	−23.1457	+	15.0310i	−1.64490	+	1.06821i
$199$	−0.487743	−	0.844796i	−0.0345752	−	0.0598860i	0.848220	−	0.529644i	$-0.177674\pi$
$199$	−0.487743	−	0.844796i	−0.0345752	−	0.0598860i	−0.882795	+	0.469758i	$0.844341\pi$
$200$	13.4616	+	0.625076i	0.951879	+	0.0441995i
$201$	−3.82326	−	2.20736i	−0.269672	−	0.155695i
$202$	−7.08919	−	3.61212i	−0.498794	−	0.254148i
$203$	14.4760	−	4.92406i	1.01602	−	0.345601i
$204$	−1.29498	−	1.78238i	−0.0906665	−	0.124792i
$205$	−14.5347	−	6.41944i	−1.01515	−	0.448353i
$206$	−5.93441	−	0.623732i	−0.413470	−	0.0434575i
$207$	−9.15896	+	34.1817i	−0.636592	+	2.37579i
$208$	−0.464926	−	0.178468i	−0.0322368	−	0.0123745i
$209$	−1.72562	+	5.31092i	−0.119364	+	0.367364i
$210$	7.67326	+	12.7924i	0.529505	+	0.882759i
$211$	−8.83060	−	27.1778i	−0.607923	−	1.87100i	−0.475287	−	0.879831i	$-0.657656\pi$
$211$	−8.83060	−	27.1778i	−0.607923	−	1.87100i	−0.132636	−	0.991165i	$-0.542344\pi$
$212$	−0.415563	+	7.92942i	−0.0285410	+	0.544595i
$213$	−20.0518	−	13.0218i	−1.37393	−	0.892238i
$214$	−0.931378	−	0.838617i	−0.0636677	−	0.0573266i
$215$	7.40795	−	6.03548i	0.505218	−	0.411616i
$216$	−30.9547	−	10.0578i	−2.10620	−	0.684347i
$217$	0.357060	−	0.832516i	0.0242388	−	0.0565148i
$218$	3.39463	−	3.39463i	0.229913	−	0.229913i
$219$	−1.53935	−	3.45743i	−0.104020	−	0.233632i
$220$	4.73708	+	14.4328i	0.319374	+	0.973057i
$221$	−0.434085	−	0.193267i	−0.0291997	−	0.0130005i
$222$	−12.5081	−	10.1289i	−0.839490	−	0.679806i
$223$	10.1540	−	19.9284i	0.679963	−	1.33450i	−0.250501	−	0.968116i	$-0.580595\pi$
$223$	10.1540	−	19.9284i	0.679963	−	1.33450i	0.930463	−	0.366385i	$-0.119405\pi$
$224$	13.0434	+	8.21837i	0.871500	+	0.549113i
$225$	−29.5507	+	17.2967i	−1.97005	+	1.15312i
$226$	−1.01436	+	1.75692i	−0.0674742	+	0.116869i
$227$	0.292004	+	5.57177i	0.0193810	+	0.369811i	0.991052	+	0.133475i	$0.0426134\pi$
$227$	0.292004	+	5.57177i	0.0193810	+	0.369811i	−0.971671	+	0.236337i	$0.924053\pi$
$228$	−4.41786	+	1.69586i	−0.292580	+	0.112311i
$229$	1.66622	+	15.8530i	0.110107	+	1.04760i	0.900458	+	0.434942i	$0.143231\pi$
$229$	1.66622	+	15.8530i	0.110107	+	1.04760i	−0.790352	+	0.612654i	$0.790102\pi$
$230$	−8.05408	−	4.61809i	−0.531071	−	0.304508i
$231$	−25.7613	+	32.7201i	−1.69497	+	2.15283i
$232$	−11.0142	−	11.0142i	−0.723119	−	0.723119i
$233$	−4.40142	+	11.4661i	−0.288346	+	0.751168i	0.710525	+	0.703672i	$0.248458\pi$
$233$	−4.40142	+	11.4661i	−0.288346	+	0.751168i	−0.998871	+	0.0474962i	$0.984876\pi$
$234$	−4.93382	+	1.04872i	−0.322534	+	0.0685567i
$235$	20.2419	+	20.1217i	1.32044	+	1.31259i
$236$	2.47656	−	11.6513i	0.161210	−	0.758435i
$237$	−6.92744	−	13.5959i	−0.449985	−	0.883146i
$238$	0.900256	+	0.635393i	0.0583549	+	0.0411864i
$239$	14.3549	−	4.66418i	0.928540	−	0.301701i	0.194574	−	0.980888i	$-0.437667\pi$
$239$	14.3549	−	4.66418i	0.928540	−	0.301701i	0.733965	+	0.679187i	$0.237667\pi$
$240$	−2.06669	+	3.20327i	−0.133404	+	0.206770i
$241$	4.82571	+	22.7032i	0.310851	+	1.46244i	0.805110	+	0.593125i	$0.202106\pi$
$241$	4.82571	+	22.7032i	0.310851	+	1.46244i	−0.494259	+	0.869315i	$0.664561\pi$
$242$	8.84004	−	7.15852i	0.568259	−	0.460167i
$243$	17.6057	−	4.71744i	1.12941	−	0.302624i
$244$	−1.58686	−	1.15292i	−0.101588	−	0.0738083i
$245$	11.9451	+	10.1150i	0.763147	+	0.646224i
$246$	−14.4954	+	10.5315i	−0.924191	+	0.671464i
$247$	−0.642294	+	0.793167i	−0.0408682	+	0.0504680i
$248$	−0.921528	+	0.0482952i	−0.0585171	+	0.00306675i
$249$	9.43397	−	5.44671i	0.597854	−	0.345171i
$250$	−2.40250	−	8.65601i	−0.151948	−	0.547454i
$251$			22.1623i			1.39887i	0.714697	+	0.699434i	$0.246565\pi$
$251$			22.1623i			1.39887i	−0.714697	+	0.699434i	$0.753435\pi$
$252$	−24.5375	+	0.336577i	−1.54572	+	0.0212024i
$253$	4.05453	−	25.5993i	0.254906	−	1.60941i
$254$	−7.36649	+	0.774249i	−0.462215	+	0.0485807i
$255$	−2.12917	+	2.94898i	−0.133334	+	0.184672i
$256$	1.48778	−	14.1553i	0.0929865	−	0.884708i
$257$	0.0610358	+	0.227789i	0.00380731	+	0.0142091i	0.967803	−	0.251708i	$-0.0809921\pi$
$257$	0.0610358	+	0.227789i	0.00380731	+	0.0142091i	−0.963996	+	0.265917i	$0.914325\pi$
$258$	−1.68558	−	10.6423i	−0.104939	−	0.662562i
$259$	−15.8480	−	5.83538i	−0.984749	−	0.362593i
$260$	−0.137038	+	2.77290i	−0.00849875	+	0.171968i
$261$	38.7125	+	8.22859i	2.39624	+	0.509337i
$262$	−2.45791	+	3.78485i	−0.151850	+	0.233829i
$263$	−12.4735	+	19.2075i	−0.769151	+	1.18439i	0.209289	+	0.977854i	$0.432885\pi$
$263$	−12.4735	+	19.2075i	−0.769151	+	1.18439i	−0.978439	+	0.206534i	$0.933782\pi$
$264$	41.4959	+	8.82023i	2.55390	+	0.542848i
$265$	12.6522	−	3.43059i	0.777219	−	0.210739i
$266$	1.81874	−	1.51456i	0.111514	−	0.0928635i
$267$	−1.54267	−	9.74001i	−0.0944096	−	0.596079i
$268$	0.493144	+	1.84044i	0.0301236	+	0.112423i
$269$	1.11584	−	10.6165i	0.0680340	−	0.647301i	−0.906368	−	0.422489i	$-0.861157\pi$
$269$	1.11584	−	10.6165i	0.0680340	−	0.647301i	0.974402	−	0.224812i	$-0.0721767\pi$
$270$	0.0646468	+	21.6964i	0.00393428	+	1.32040i
$271$	−18.3674	+	1.93050i	−1.11574	+	0.117269i	−0.644405	−	0.764684i	$-0.722895\pi$
$271$	−18.3674	+	1.93050i	−1.11574	+	0.117269i	−0.471337	+	0.881953i	$0.656228\pi$
$272$	−0.0440505	+	0.278124i	−0.00267095	+	0.0168637i
$273$	−6.53870	+	3.89566i	−0.395740	+	0.235776i
$274$			3.47355i			0.209845i
$275$	20.2007	−	14.8614i	1.21815	−	0.896174i
$276$	19.0211	−	10.9819i	1.14494	−	0.661030i
$277$	10.4242	−	0.546310i	0.626331	−	0.0328246i	0.263469	−	0.964668i	$-0.415133\pi$
$277$	10.4242	−	0.546310i	0.626331	−	0.0328246i	0.362861	+	0.931843i	$0.381800\pi$
$278$	3.25856	−	4.02399i	0.195436	−	0.241343i
$279$	1.89688	−	1.37816i	0.113563	−	0.0825084i
$280$	3.86920	−	15.4686i	0.231229	−	0.924424i
$281$	23.9465	+	17.3981i	1.42853	+	1.03789i	0.990288	+	0.139028i	$0.0443978\pi$
$281$	23.9465	+	17.3981i	1.42853	+	1.03789i	0.438239	+	0.898858i	$0.355602\pi$
$282$	31.0878	−	8.32996i	1.85125	−	0.496042i
$283$	−21.6568	+	17.5374i	−1.28737	+	1.04249i	−0.291051	+	0.956707i	$0.594005\pi$
$283$	−21.6568	+	17.5374i	−1.28737	+	1.04249i	−0.996314	+	0.0857806i	$0.972662\pi$
$284$	2.14543	+	10.0935i	0.127308	+	0.598936i
$285$	4.93469	+	6.05684i	0.292306	+	0.358776i
$286$	3.51353	−	1.14161i	0.207759	−	0.0675051i
$287$	−10.8409	+	15.3599i	−0.639919	+	0.906668i
$288$	18.1159	+	35.5544i	1.06749	+	2.09506i
$289$	3.47864	−	16.3657i	0.204626	−	0.962688i
$290$	−4.68636	+	9.26564i	−0.275192	+	0.544097i
$291$	−10.9300	+	2.32324i	−0.640728	+	0.136191i
$292$	−0.585365	+	1.52493i	−0.0342559	+	0.0892397i
$293$	4.85076	+	4.85076i	0.283385	+	0.283385i	0.834457	−	0.551073i	$-0.185781\pi$
$293$	4.85076	+	4.85076i	0.283385	+	0.283385i	−0.551073	+	0.834457i	$0.685781\pi$
$294$	16.6305	−	5.91263i	0.969913	−	0.344831i
$295$	−19.5515	+	2.11387i	−1.13833	+	0.123074i
$296$	1.79831	+	17.1097i	0.104524	+	0.994483i
$297$	−56.5468	+	21.7063i	−3.28118	+	1.25953i
$298$	−0.0934974	−	1.78404i	−0.00541616	−	0.103346i
$299$	2.36852	−	4.10240i	0.136975	−	0.237248i
$300$	20.5602	+	5.37797i	1.18704	+	0.310497i
$301$	−5.27052	−	10.0024i	−0.303788	−	0.576529i
$302$	−4.51799	+	8.86706i	−0.259981	+	0.510242i
$303$	−24.1500	−	19.5563i	−1.38738	−	1.12348i
$304$	0.552543	+	0.246008i	0.0316905	+	0.0141095i
$305$	−0.991506	+	3.08277i	−0.0567735	+	0.176519i
$306$	1.16006	+	2.60553i	0.0663159	+	0.148948i
$307$	4.10345	−	4.10345i	0.234196	−	0.234196i	−0.580245	−	0.814442i	$-0.697043\pi$
$307$	4.10345	−	4.10345i	0.234196	−	0.234196i	0.814442	+	0.580245i	$0.197043\pi$
$308$	17.8475	−	2.12372i	1.01695	−	0.121010i
$309$	−22.1650	−	7.20186i	−1.26093	−	0.409700i
$310$	0.222156	+	0.573622i	0.0126176	+	0.0325795i
$311$	−18.4026	−	16.5698i	−1.04352	−	0.939587i	−0.0452825	−	0.998974i	$-0.514419\pi$
$311$	−18.4026	−	16.5698i	−1.04352	−	0.939587i	−0.998235	+	0.0593868i	$0.981085\pi$
$312$	6.50267	+	4.22288i	0.368141	+	0.239074i
$313$	−0.374110	+	7.13845i	−0.0211460	+	0.403489i	0.967466	+	0.253001i	$0.0814177\pi$
$313$	−0.374110	+	7.13845i	−0.0211460	+	0.403489i	−0.988612	+	0.150488i	$0.951916\pi$
$314$	4.17795	+	12.8584i	0.235776	+	0.725642i
$315$	13.1611	+	38.3168i	0.741542	+	2.15891i
$316$	−2.03508	+	6.26334i	−0.114482	+	0.352340i
$317$	−6.42055	−	2.46462i	−0.360614	−	0.138427i	0.171314	−	0.985217i	$-0.445199\pi$
$317$	−6.42055	−	2.46462i	−0.360614	−	0.138427i	−0.531928	+	0.846790i	$0.678532\pi$
$318$	3.82593	−	14.2786i	0.214548	−	0.800703i
$319$	−28.8283	−	3.02998i	−1.61408	−	0.169646i
$320$	−7.85875	+	1.69492i	−0.439317	+	0.0947488i
$321$	−2.87720	−	3.96013i	−0.160590	−	0.221033i
$322$	−7.23782	+	8.26359i	−0.403348	+	0.460512i
$323$	0.514197	+	0.261996i	0.0286107	+	0.0145779i
$324$	−20.3537	−	11.7512i	−1.13076	−	0.652844i
$325$	4.42019	−	1.21266i	0.245188	−	0.0672665i
$326$	7.31107	+	12.6631i	0.404923	+	0.701347i
$327$	15.7253	−	10.2121i	0.869609	−	0.564731i
$328$	18.9161	+	2.99601i	1.04447	+	0.165427i
$329$	28.0676	−	18.7796i	1.54742	−	1.03535i
$330$	−3.03979	−	28.1155i	−0.167335	−	1.54771i
$331$	16.8201	−	7.48880i	0.924517	−	0.411622i	0.111436	−	0.993772i	$-0.464455\pi$
$331$	16.8201	−	7.48880i	0.924517	−	0.411622i	0.813081	+	0.582150i	$0.197788\pi$
$332$	−4.54131	−	1.21684i	−0.249237	−	0.0667828i
$333$	−27.5092	−	33.9711i	−1.50750	−	1.86160i
$334$	−0.181863	−	0.201979i	−0.00995110	−	0.0110518i
$335$	2.63306	−	1.72110i	0.143859	−	0.0940339i
$336$	3.23288	+	3.14539i	0.176368	+	0.171595i
$337$	11.2377	−	5.72591i	0.612158	−	0.311910i	−0.120284	−	0.992740i	$-0.538380\pi$
$337$	11.2377	−	5.72591i	0.612158	−	0.311910i	0.732442	+	0.680829i	$0.238380\pi$
$338$	−9.75671	−	0.511328i	−0.530695	−	0.0278126i
$339$	−5.30191	+	5.88837i	−0.287960	+	0.319812i
$340$	1.54976	−	0.250193i	0.0840475	−	0.0135686i
$341$	−1.27618	+	1.14908i	−0.0691093	+	0.0622263i
$342$	6.05066	−	0.958330i	0.327182	−	0.0518206i
$343$	14.5227	−	11.4931i	0.784153	−	0.620568i
$344$	−6.76978	+	9.31780i	−0.365002	+	0.502382i
$345$	−27.0194	−	24.1830i	−1.45467	−	1.30197i
$346$	5.81734	−	13.0660i	0.312742	−	0.702430i
$347$	−3.68869	−	9.60936i	−0.198019	−	0.515857i	0.798234	−	0.602348i	$-0.205768\pi$
$347$	−3.68869	−	9.60936i	−0.198019	−	0.515857i	−0.996253	+	0.0864907i	$0.972435\pi$
$348$	−13.3786	−	20.6013i	−0.717169	−	1.10434i
$349$	−11.2771			−0.603650			−0.301825	−	0.953363i	$-0.597596\pi$
$349$	−11.2771			−0.603650			−0.301825	+	0.953363i	$0.597596\pi$
$350$	−10.6015	+	0.765007i	−0.566676	+	0.0408913i
$351$	−11.0702			−0.590883
$352$	−15.9177	−	24.5110i	−0.848414	−	1.30644i
$353$	5.96258	+	15.5330i	0.317356	+	0.826740i	0.995755	+	0.0920465i	$0.0293408\pi$
$353$	5.96258	+	15.5330i	0.317356	+	0.826740i	−0.678399	+	0.734694i	$0.737326\pi$
$354$	−9.01960	+	20.2583i	−0.479386	+	1.07672i
$355$	14.7282	−	8.56196i	0.781694	−	0.454422i
$356$	−2.50168	+	3.44327i	−0.132589	+	0.182493i
$357$	2.92333	+	3.15847i	0.154719	+	0.167164i
$358$	7.82462	−	1.23930i	0.413544	−	0.0654990i
$359$	−12.9020	+	11.6170i	−0.680942	+	0.613123i	−0.935245	−	0.354001i	$-0.884821\pi$
$359$	−12.9020	+	11.6170i	−0.680942	+	0.613123i	0.254302	+	0.967125i	$0.418154\pi$
$360$	29.0963	−	29.2702i	1.53351	−	1.54268i
$361$	−11.8841	+	13.1986i	−0.625477	+	0.694662i
$362$	17.2218	+	0.902558i	0.905160	+	0.0474374i
$363$	39.5851	−	20.1696i	2.07768	−	1.05863i
$364$	3.18438	+	0.806608i	0.166907	+	0.0422777i
$365$	2.69341	+	0.133109i	0.140979	+	0.00696727i
$366$	2.44341	+	2.71368i	0.127719	+	0.141847i
$367$	−4.69672	−	5.79997i	−0.245167	−	0.302756i	0.639677	−	0.768644i	$-0.279068\pi$
$367$	−4.69672	−	5.79997i	−0.245167	−	0.302756i	−0.884844	+	0.465888i	$0.845735\pi$
$368$	−2.71160	−	0.726570i	−0.141352	−	0.0378751i
$369$	−44.4548	+	19.7926i	−2.31423	+	1.03036i
$370$	10.4628	−	4.69576i	0.543937	−	0.244121i
$371$	−1.02415	−	15.4770i	−0.0531710	−	0.803526i
$372$	−1.43733	−	0.227651i	−0.0745222	−	0.0118032i
$373$	−24.7530	+	16.0748i	−1.28166	+	0.832322i	−0.992174	−	0.124860i	$-0.960152\pi$
$373$	−24.7530	+	16.0748i	−1.28166	+	0.832322i	−0.289489	+	0.957181i	$0.593485\pi$
$374$	−1.04446	−	1.80906i	−0.0540080	−	0.0935445i
$375$	−2.14937	−	35.0199i	−0.110993	−	1.80842i
$376$	−29.7932	−	17.2011i	−1.53647	−	0.887079i
$377$	−4.72046	−	2.40520i	−0.243116	−	0.123874i
$378$	25.1815	+	4.99252i	1.29520	+	0.256788i
$379$	−0.558890	−	0.769246i	−0.0287082	−	0.0395135i	0.794422	−	0.607367i	$-0.207774\pi$
$379$	−0.558890	−	0.769246i	−0.0287082	−	0.0395135i	−0.823130	+	0.567853i	$0.807774\pi$
$380$	0.342461	−	3.35442i	0.0175679	−	0.172078i
$381$	−28.7713	−	3.02399i	−1.47400	−	0.154923i
$382$	−0.150868	+	0.563048i	−0.00771909	+	0.0288080i
$383$	−9.46458	−	3.63311i	−0.483618	−	0.185643i	0.104329	−	0.994543i	$-0.466730\pi$
$383$	−9.46458	−	3.63311i	−0.483618	−	0.185643i	−0.587947	+	0.808899i	$0.700064\pi$
$384$	8.49991	−	26.1600i	0.433759	−	1.33497i
$385$	−12.5200	−	26.9025i	−0.638081	−	1.37108i
$386$	3.65383	+	11.2453i	0.185975	+	0.572373i
$387$	1.53156	−	29.2239i	0.0778535	−	1.48553i
$388$	4.04465	+	2.62663i	0.205336	+	0.133347i
$389$	9.99997	+	9.00401i	0.507018	+	0.456521i	0.882503	−	0.470307i	$-0.155857\pi$
$389$	9.99997	+	9.00401i	0.507018	+	0.456521i	−0.375484	+	0.926829i	$0.622524\pi$
$390$	1.32284	−	4.99640i	0.0669845	−	0.253003i
$391$	−2.54742	−	0.827706i	−0.128828	−	0.0418589i
$392$	−17.0388	−	8.10093i	−0.860590	−	0.409159i
$393$	−12.4635	+	12.4635i	−0.628702	+	0.628702i
$394$	7.98510	+	17.9348i	0.402284	+	0.903544i
$395$	10.8726	−	0.0323960i	0.547058	−	0.00163002i
$396$	42.4994	+	18.9220i	2.13568	+	0.950864i
$397$	20.9639	+	16.9763i	1.05215	+	0.852014i	0.989283	−	0.146008i	$-0.0466426\pi$
$397$	20.9639	+	16.9763i	1.05215	+	0.852014i	0.0628659	+	0.998022i	$0.479976\pi$
$398$	0.355833	−	0.698361i	0.0178363	−	0.0350057i
$399$	8.17811	−	4.30925i	0.409418	−	0.215732i
$400$	−1.37213	−	2.34422i	−0.0686065	−	0.117211i
$401$	−7.65133	+	13.2525i	−0.382089	+	0.661798i	−0.991361	−	0.131164i	$-0.958129\pi$
$401$	−7.65133	+	13.2525i	−0.382089	+	0.661798i	0.609271	+	0.792962i	$0.291462\pi$
$402$	−0.185644	−	3.54231i	−0.00925910	−	0.176674i
$403$	−0.293015	+	0.112478i	−0.0145961	+	0.00560293i
$404$	1.40192	+	13.3384i	0.0697481	+	0.663609i
$405$	−7.95413	+	37.9773i	−0.395244	+	1.88711i
$406$	9.65297	+	7.59999i	0.479069	+	0.377181i
$407$	22.6386	+	22.6386i	1.12215	+	1.12215i
$408$	1.57114	−	4.09297i	0.0777832	−	0.202632i
$409$	−12.6937	+	2.69813i	−0.627664	+	0.133414i	−0.510752	−	0.859728i	$-0.670633\pi$
$409$	−12.6937	+	2.69813i	−0.627664	+	0.133414i	−0.116912	+	0.993142i	$0.537300\pi$
$410$	−2.03472	−	12.6035i	−0.100488	−	0.622445i
$411$	−2.82066	+	13.2702i	−0.139133	+	0.654570i
$412$	4.56649	+	8.96225i	0.224975	+	0.441538i
$413$	−2.11460	+	23.1722i	−0.104053	+	1.14023i
$414$	−27.0417	+	8.78639i	−1.32903	+	0.431827i
$415$	0.429324	+	7.75009i	0.0210747	+	0.380437i
$416$	−1.11058	−	5.22485i	−0.0544505	−	0.256169i
$417$	15.7165	−	12.7270i	0.769640	−	0.623243i
$418$	−4.33396	+	1.16128i	−0.211981	+	0.0568001i
$419$	14.8800	+	10.8109i	0.726935	+	0.528149i	0.888592	−	0.458698i	$-0.151684\pi$
$419$	14.8800	+	10.8109i	0.726935	+	0.528149i	−0.161658	+	0.986847i	$0.551684\pi$
$420$	11.0402	−	22.5923i	0.538707	−	1.10239i
$421$	19.9632	−	14.5041i	0.972947	−	0.706887i	0.0168253	−	0.999858i	$-0.494644\pi$
$421$	19.9632	−	14.5041i	0.972947	−	0.706887i	0.956121	+	0.292971i	$0.0946441\pi$
$422$	14.4496	−	17.8438i	0.703398	−	0.868624i
$423$	87.2908	−	4.57472i	4.24422	−	0.222430i
$424$	−13.6839	+	7.90043i	−0.664551	+	0.383679i
$425$	−1.19035	−	2.30217i	−0.0577404	−	0.111672i
$426$		−	19.2105i		−	0.930754i
$427$	3.34423	+	1.87011i	0.161838	+	0.0905008i
$428$	−0.330490	+	2.08663i	−0.0159748	+	0.100861i
$429$	14.3499	−	1.50824i	0.692822	−	0.0728185i
$430$	7.30885	+	2.35074i	0.352464	+	0.113363i
$431$	3.20202	−	30.4652i	0.154236	−	1.46746i	−0.594237	−	0.804290i	$-0.702546\pi$
$431$	3.20202	−	30.4652i	0.154236	−	1.46746i	0.748473	−	0.663165i	$-0.230787\pi$
$432$	1.69795	+	6.33685i	0.0816928	+	0.304882i
$433$	−4.05772	−	25.6195i	−0.195002	−	1.23119i	−0.869880	−	0.493263i	$-0.835804\pi$
$433$	−4.05772	−	25.6195i	−0.195002	−	1.23119i	0.674878	−	0.737929i	$-0.264196\pi$
$434$	0.717251	−	0.123709i	0.0344292	−	0.00593820i
$435$	−25.4276	+	31.5925i	−1.21916	+	1.51474i
$436$	−7.91562	−	1.68252i	−0.379089	−	0.0805779i
$437$	−3.13343	+	4.82506i	−0.149892	+	0.230814i
$438$	1.65619	−	2.55031i	0.0791359	−	0.121859i
$439$	−13.0257	−	2.76869i	−0.621681	−	0.132142i	−0.113706	−	0.993514i	$-0.536272\pi$
$439$	−13.0257	−	2.76869i	−0.621681	−	0.132142i	−0.507974	+	0.861372i	$0.669606\pi$
$440$	−18.9530	+	23.5481i	−0.903549	+	1.12261i
$441$	47.5189	−	6.31652i	2.26281	−	0.300787i
$442$	−0.0597248	−	0.377088i	−0.00284082	−	0.0179362i
$443$	−3.88763	−	14.5088i	−0.184707	−	0.689335i	−0.994693	−	0.102886i	$-0.967192\pi$
$443$	−3.88763	−	14.5088i	−0.184707	−	0.689335i	0.809986	−	0.586449i	$-0.199474\pi$
$444$	−2.83594	+	26.9822i	−0.134588	+	1.28052i
$445$	6.68917	+	2.15143i	0.317097	+	0.101988i
$446$	17.8724	−	1.87846i	0.846283	−	0.0889479i
$447$	1.09152	−	6.89157i	0.0516270	−	0.325960i
$448$	0.130468	+	9.51150i	0.00616402	+	0.449376i
$449$			3.87012i			0.182642i	0.995822	+	0.0913211i	$0.0291090\pi$
$449$			3.87012i			0.182642i	−0.995822	+	0.0913211i	$0.970891\pi$
$450$	−24.5872	−	12.3438i	−1.15905	−	0.581893i
$451$	30.8658	−	17.8204i	1.45341	−	0.839129i
$452$	3.41507	−	0.178976i	0.160631	−	0.00841833i
$453$	−24.4607	+	30.2065i	−1.14927	+	1.41923i
$454$	−3.62680	+	2.63503i	−0.170214	+	0.123668i
$455$	−0.374210	−	5.41037i	−0.0175433	−	0.253642i
$456$	−7.61836	−	5.53507i	−0.356763	−	0.259203i
$457$	−40.9235	+	10.9654i	−1.91432	+	0.512941i	−0.922371	+	0.386304i	$0.873751\pi$
$457$	−40.9235	+	10.9654i	−1.91432	+	0.512941i	−0.991949	+	0.126636i	$0.959582\pi$
$458$	−9.95354	+	8.06022i	−0.465098	+	0.376629i
$459$	1.30143	+	6.12275i	0.0607456	+	0.285785i
$460$	0.865620	+	15.6260i	0.0403597	+	0.728567i
$461$	21.8890	−	7.11217i	1.01947	−	0.331247i	0.248852	−	0.968541i	$-0.419947\pi$
$461$	21.8890	−	7.11217i	1.01947	−	0.331247i	0.770620	+	0.637295i	$0.219947\pi$
$462$	−33.3221	−	3.04084i	−1.55029	−	0.141473i
$463$	8.19728	+	16.0881i	0.380960	+	0.747676i	0.999268	−	0.0382600i	$-0.0121815\pi$
$463$	8.19728	+	16.0881i	0.380960	+	0.747676i	−0.618308	+	0.785936i	$0.712182\pi$
$464$	−0.652765	+	3.07102i	−0.0303038	+	0.142568i
$465$	0.382910	+	2.37184i	0.0177570	+	0.109991i
$466$	−9.65263	+	2.05173i	−0.447149	+	0.0950445i
$467$	9.82687	−	25.5999i	0.454733	−	1.18462i	−0.494257	−	0.869316i	$-0.664560\pi$
$467$	9.82687	−	25.5999i	0.454733	−	1.18462i	0.948990	−	0.315305i	$-0.102107\pi$
$468$	6.01224	+	6.01224i	0.277916	+	0.277916i
$469$	−1.38138	−	3.45616i	−0.0637861	−	0.159591i
$470$	−4.70112	+	22.4457i	−0.216846	+	1.03534i
$471$	5.51969	+	52.5163i	0.254334	+	2.41983i
$472$	22.1292	−	8.49459i	1.01858	−	0.390995i
$473$	1.12174	+	21.4041i	0.0515776	+	0.984160i
$474$	6.13019	−	10.6178i	0.281569	−	0.487691i
$475$	−5.43813	+	1.18982i	−0.249518	+	0.0545929i
$476$	0.0717609	−	1.85606i	0.00328916	−	0.0850721i
$477$	18.2266	−	35.7717i	0.834538	−	1.63787i
$478$	9.42483	+	7.63208i	0.431082	+	0.349083i
$479$	−33.3579	−	14.8519i	−1.52416	−	0.678600i	−0.537781	−	0.843084i	$-0.680737\pi$
$479$	−33.3579	−	14.8519i	−1.52416	−	0.678600i	−0.986380	+	0.164484i	$0.947404\pi$
$480$	−40.8884	+	0.121832i	−1.86629	+	0.00556083i
$481$	2.38000	+	5.34557i	0.108519	+	0.243737i
$482$	−13.1870	+	13.1870i	−0.600650	+	0.600650i
$483$	−34.3614	+	25.6924i	−1.56350	+	1.16904i
$484$	−18.2360	−	5.92525i	−0.828911	−	0.269330i
$485$	2.03780	−	7.69684i	0.0925318	−	0.349495i
$486$	10.8833	+	9.79939i	0.493678	+	0.444509i
$487$	−30.2483	−	19.6435i	−1.37068	−	0.890130i	−0.371415	−	0.928467i	$-0.621127\pi$
$487$	−30.2483	−	19.6435i	−1.37068	−	0.890130i	−0.999265	+	0.0383371i	$0.987794\pi$
$488$	0.204280	−	3.89789i	0.00924731	−	0.176449i
$489$	17.6479	+	54.3145i	0.798064	+	2.45619i
$490$	−1.58879	+	12.4758i	−0.0717741	+	0.563598i
$491$	2.89375	−	8.90606i	0.130593	−	0.401925i	−0.864285	−	0.503002i	$-0.832229\pi$
$491$	2.89375	−	8.90606i	0.130593	−	0.401925i	0.994879	+	0.101077i	$0.0322289\pi$
$492$	28.1966	+	10.8236i	1.27120	+	0.487968i
$493$	−0.775330	+	2.89357i	−0.0349191	+	0.130320i
$494$	−0.815557	−	0.0857185i	−0.0366936	−	0.00385666i
$495$	7.80063	−	76.4074i	0.350612	−	3.43426i
$496$	0.109328	+	0.150477i	0.00490897	+	0.00675662i
$497$	−6.49132	−	19.0836i	−0.291176	−	0.856015i
$498$	7.79871	+	3.97364i	0.349468	+	0.178063i
$499$	27.8046	+	16.0530i	1.24470	+	0.718630i	0.970048	−	0.242912i	$-0.0781027\pi$
$499$	27.8046	+	16.0530i	1.24470	+	0.718630i	0.274656	+	0.961543i	$0.411436\pi$
$500$	−10.0315	+	11.3434i	−0.448623	+	0.507292i
$501$	−0.530765	−	0.919313i	−0.0237128	−	0.0410719i
$502$	−14.9342	+	9.69841i	−0.666548	+	0.432861i
$503$	−31.9663	−	5.06296i	−1.42531	−	0.225746i	−0.604342	−	0.796725i	$-0.706564\pi$
$503$	−31.9663	−	5.06296i	−1.42531	−	0.225746i	−0.820965	+	0.570979i	$0.806564\pi$
$504$	−27.1557	−	40.5863i	−1.20961	−	1.80786i
$505$	20.2011	−	9.06632i	0.898937	−	0.403446i
$506$	19.0246	−	8.47031i	0.845748	−	0.376551i
$507$	−36.8589	−	9.87630i	−1.63696	−	0.438622i
$508$	7.85761	+	9.70335i	0.348625	+	0.430516i
$509$	17.6550	+	19.6079i	0.782546	+	0.869105i	0.994123	−	0.108256i	$-0.0345266\pi$
$509$	17.6550	+	19.6079i	0.782546	+	0.869105i	−0.211577	+	0.977361i	$0.567860\pi$
$510$	−2.91894	−	0.144255i	−0.129253	−	0.00638774i
$511$	0.783483	−	3.09309i	0.0346593	−	0.136830i
$512$	−5.42969	+	2.76657i	−0.239961	+	0.122266i
$513$	13.4265	+	0.703655i	0.592796	+	0.0310671i
$514$	−0.126788	+	0.140812i	−0.00559236	+	0.00621095i
$515$	11.7073	−	11.7773i	0.515886	−	0.518970i
$516$	−13.4978	+	12.1535i	−0.594207	+	0.535026i
$517$	−63.2328	+	10.0151i	−2.78097	+	0.440463i
$518$	−3.00302	−	13.2330i	−0.131945	−	0.581423i
$519$	32.8344	−	45.1926i	1.44127	−	1.98374i
$520$	−4.77627	+	2.77659i	−0.209453	+	0.121762i
$521$	3.65972	−	8.21986i	0.160335	−	0.360119i	−0.815457	−	0.578817i	$-0.803514\pi$
$521$	3.65972	−	8.21986i	0.160335	−	0.360119i	0.975792	+	0.218699i	$0.0701811\pi$
$522$	11.3960	+	29.6877i	0.498791	+	1.29939i
$523$	−3.70998	−	5.71287i	−0.162226	−	0.249806i	0.748204	−	0.663468i	$-0.230916\pi$
$523$	−3.70998	−	5.71287i	−0.162226	−	0.249806i	−0.910431	+	0.413662i	$0.864250\pi$
$524$	7.60728			0.332326
$525$	−41.1228	−	5.68629i	−1.79475	−	0.248170i
$526$	−18.4017			−0.802353
$527$	0.0966572	+	0.148839i	0.00421045	+	0.00648353i
$528$	−3.06435	−	7.98292i	−0.133359	−	0.347412i
$529$	1.50605	−	3.38265i	0.0654805	−	0.147072i
$530$	7.84846	+	7.02455i	0.340915	+	0.305127i
$531$	−35.4005	+	48.7246i	−1.53625	+	2.11447i
$532$	−3.81092	−	1.18071i	−0.165224	−	0.0511901i
$533$	6.43377	−	1.01901i	0.278678	−	0.0441382i
$534$	5.88831	−	5.30186i	0.254812	−	0.229434i
$535$	3.44328	−	0.555884i	0.148866	−	0.0240330i
$536$	−2.53707	+	2.81770i	−0.109585	+	0.121706i
$537$	30.8992	+	1.61936i	1.33340	+	0.0698804i
$538$	7.64234	−	3.89397i	0.329485	−	0.167881i
$539$	−34.1294	+	8.23895i	−1.47006	+	0.354877i
$540$	30.6133	−	20.0105i	1.31739	−	0.861113i
$541$	2.34511	+	2.60451i	0.100824	+	0.111977i	0.791445	−	0.611241i	$-0.209329\pi$
$541$	2.34511	+	2.60451i	0.100824	+	0.111977i	−0.690621	+	0.723217i	$0.742663\pi$
$542$	−9.33865	−	11.5323i	−0.401129	−	0.495353i
$543$	65.0606	+	17.4329i	2.79202	+	0.748118i
$544$	−2.75922	+	1.22848i	−0.118300	+	0.0526708i
$545$	1.43611	+	13.2828i	0.0615162	+	0.568975i
$546$	−5.48653	−	2.70139i	−0.234802	−	0.115609i
$547$	−29.8893	−	4.73400i	−1.27798	−	0.202411i	−0.519702	−	0.854348i	$-0.673957\pi$
$547$	−29.8893	−	4.73400i	−1.27798	−	0.202411i	−0.758274	+	0.651936i	$0.773957\pi$
$548$	4.91064	−	3.18900i	0.209772	−	0.136228i
$549$	4.95876	+	8.58882i	0.211635	+	0.366562i
$550$	18.8545	+	7.10893i	0.803957	+	0.303126i
$551$	5.57235	+	3.21720i	0.237390	+	0.137057i
$552$	38.9431	+	19.8425i	1.65753	+	0.844552i
$553$	2.50187	−	12.6190i	0.106390	−	0.536616i
$554$	4.92987	+	6.78539i	0.209450	+	0.288283i
$555$	43.7849	−	9.44320i	1.85856	−	0.400842i
$556$	−8.68043	−	0.912350i	−0.368132	−	0.0386923i
$557$	3.91007	−	14.5926i	0.165675	−	0.618307i	−0.832278	−	0.554358i	$-0.812964\pi$
$557$	3.91007	−	14.5926i	0.165675	−	0.618307i	0.997953	−	0.0639490i	$-0.0203695\pi$
$558$	1.75878	+	0.675132i	0.0744551	+	0.0285806i
$559$	−1.21052	+	3.72561i	−0.0511997	+	0.157576i
$560$	−3.03963	+	1.04405i	−0.128448	+	0.0441192i
$561$	−2.52119	−	7.75941i	−0.106445	−	0.327603i
$562$	−1.24469	+	23.7502i	−0.0525042	+	1.00184i
$563$	−29.4323	−	19.1136i	−1.24042	−	0.805540i	−0.253595	−	0.967310i	$-0.581613\pi$
$563$	−29.4323	−	19.1136i	−1.24042	−	0.805540i	−0.986828	+	0.161770i	$0.948280\pi$
$564$	−40.3174	−	36.3020i	−1.69767	−	1.52859i
$565$	−2.03899	−	5.26480i	−0.0857809	−	0.221492i
$566$	−21.2950	−	6.91915i	−0.895094	−	0.290834i
$567$	42.1934	+	18.0964i	1.77195	+	0.759978i
$568$	−14.5199	+	14.5199i	−0.609242	+	0.609242i
$569$	1.04675	+	2.35103i	0.0438819	+	0.0985603i	0.934156	−	0.356864i	$-0.116154\pi$
$569$	1.04675	+	2.35103i	0.0438819	+	0.0985603i	−0.890274	+	0.455425i	$0.849487\pi$
$570$	−1.92199	+	5.97582i	−0.0805035	+	0.250299i
$571$	−18.5051	−	8.23900i	−0.774414	−	0.344791i	−0.0188125	−	0.999823i	$-0.505989\pi$
$571$	−18.5051	−	8.23900i	−0.774414	−	0.344791i	−0.755601	+	0.655032i	$0.772655\pi$
$572$	−4.83963	−	3.91906i	−0.202355	−	0.163864i
$573$	−1.03359	+	2.02853i	−0.0431787	+	0.0847430i
$574$	−15.0945	−	0.583602i	−0.630033	−	0.0243591i
$575$	24.0656	−	9.40286i	1.00361	−	0.392126i
$576$	−12.3107	+	21.3228i	−0.512946	+	0.888449i
$577$	2.09736	+	40.0201i	0.0873144	+	1.66606i	0.594406	+	0.804165i	$0.297387\pi$
$577$	2.09736	+	40.0201i	0.0873144	+	1.66606i	−0.507091	+	0.861892i	$0.669279\pi$
$578$	12.5505	−	4.81767i	0.522031	−	0.200389i
$579$	4.82725	+	45.9282i	0.200614	+	1.90871i
$580$	17.4015	−	1.88141i	0.722558	−	0.0781213i
$581$	9.08987	+	1.31216i	0.377111	+	0.0544375i
$582$	−6.34861	−	6.34861i	−0.263158	−	0.263158i
$583$	−10.5377	+	27.4516i	−0.436427	+	1.13693i
$584$	−3.17940	+	0.675803i	−0.131565	+	0.0279649i
$585$	6.33554	−	12.5263i	0.261942	−	0.517900i
$586$	−1.14599	+	5.39147i	−0.0473405	+	0.222720i
$587$	−8.81418	−	17.2988i	−0.363800	−	0.713998i	0.634460	−	0.772955i	$-0.281222\pi$
$587$	−8.81418	−	17.2988i	−0.363800	−	0.713998i	−0.998261	+	0.0589574i	$0.981222\pi$
$588$	−23.6270	−	18.0827i	−0.974362	−	0.745718i
$589$	0.362534	−	0.117795i	0.0149380	−	0.00485364i
$590$	−9.98037	−	12.2499i	−0.410886	−	0.504321i
$591$	15.9421	+	75.0016i	0.655770	+	3.08515i
$592$	2.69489	−	2.18228i	0.110759	−	0.0896910i
$593$	−17.2078	+	4.61082i	−0.706640	+	0.189344i	−0.594203	−	0.804315i	$-0.702532\pi$
$593$	−17.2078	+	4.61082i	−0.706640	+	0.189344i	−0.112437	+	0.993659i	$0.535866\pi$
$594$	−39.3724	−	28.6057i	−1.61547	−	1.17371i
$595$	−2.94839	+	0.843021i	−0.120872	+	0.0345605i
$596$	−2.43630	+	1.77007i	−0.0997945	+	0.0725050i
$597$	1.92650	−	2.37904i	0.0788466	−	0.0973674i
$598$	3.80093	−	0.199198i	0.155431	−	0.00814581i
$599$	−12.9831	+	7.49578i	−0.530474	+	0.306269i	−0.741209	−	0.671274i	$-0.765747\pi$
$599$	−12.9831	+	7.49578i	−0.530474	+	0.306269i	0.210735	+	0.977543i	$0.432414\pi$
$600$	13.3079	+	40.1419i	0.543292	+	1.63879i
$601$		−	20.7383i		−	0.845932i	−0.906145	−	0.422966i	$-0.860989\pi$
$601$		−	20.7383i		−	0.845932i	0.906145	−	0.422966i	$-0.139011\pi$
$602$	4.43379	−	7.92874i	0.180708	−	0.323151i
$603$	1.50706	−	9.51522i	0.0613723	−	0.387490i
$604$	16.6835	−	1.75350i	0.678840	−	0.0713490i
$605$	0.0943228	+	31.6561i	0.00383477	+	1.28700i
$606$	2.60992	−	24.8317i	0.106021	−	1.00872i
$607$	5.62452	+	20.9910i	0.228292	+	0.851999i	0.981059	+	0.193711i	$0.0620524\pi$
$607$	5.62452	+	20.9910i	0.228292	+	0.851999i	−0.752766	+	0.658288i	$0.771281\pi$
$608$	1.01486	+	6.40757i	0.0411580	+	0.259861i
$609$	30.7062	+	36.8733i	1.24428	+	1.49418i
$610$	−2.51124	+	0.680912i	−0.101677	+	0.0275693i
$611$	−11.4453	−	2.43276i	−0.463025	−	0.0984191i
$612$	2.61847	−	4.03208i	0.105845	−	0.162987i
$613$	3.85709	−	5.93939i	0.155786	−	0.239890i	−0.752156	−	0.658985i	$-0.770986\pi$
$613$	3.85709	−	5.93939i	0.155786	−	0.239890i	0.907942	+	0.419095i	$0.137653\pi$
$614$	4.56086	+	0.969441i	0.184061	+	0.0391234i
$615$	2.46125	−	49.8023i	0.0992472	−	2.00822i
$616$	22.8875	+	27.4843i	0.922165	+	1.10737i
$617$	1.94396	+	12.2737i	0.0782608	+	0.494119i	0.995420	+	0.0955982i	$0.0304764\pi$
$617$	1.94396	+	12.2737i	0.0782608	+	0.494119i	−0.917159	+	0.398521i	$0.869524\pi$
$618$	−4.84659	−	18.0877i	−0.194959	−	0.727595i
$619$	2.86407	−	27.2498i	0.115117	−	1.09526i	−0.772607	−	0.634884i	$-0.781048\pi$
$619$	2.86407	−	27.2498i	0.115117	−	1.09526i	0.887724	−	0.460377i	$-0.152286\pi$
$620$	0.606984	−	0.840699i	0.0243771	−	0.0337633i
$621$	−62.0610	+	6.52288i	−2.49042	+	0.261754i
$622$	3.11255	−	19.6519i	0.124802	−	0.787969i
$623$	4.05787	−	7.25650i	0.162575	−	0.290726i
$624$		−	1.56282i		−	0.0625628i
$625$	22.9582	+	9.89550i	0.918328	+	0.395820i
$626$	−4.97403	+	2.87176i	−0.198802	+	0.114778i
$627$	−17.5003	+	0.917150i	−0.698893	+	0.0366274i
$628$	14.3425	−	17.7116i	0.572329	−	0.706768i
$629$	2.67675	−	1.94477i	0.106729	−	0.0775432i
$630$	−20.0607	+	25.6365i	−0.799238	+	1.02138i
$631$	29.5709	+	21.4845i	1.17720	+	0.855286i	0.991853	−	0.127387i	$-0.0406590\pi$
$631$	29.5709	+	21.4845i	1.17720	+	0.855286i	0.185347	+	0.982673i	$0.440659\pi$
$632$	−12.6586	+	3.39187i	−0.503534	+	0.134921i
$633$	69.6927	−	56.4360i	2.77003	−	2.24313i
$634$	−1.14889	−	5.40509i	−0.0456281	−	0.214663i
$635$	11.1754	−	17.3214i	0.443482	−	0.687378i
$636$	−23.6985	+	7.70010i	−0.939705	+	0.305329i
$637$	−6.36307	−	0.829611i	−0.252114	−	0.0328704i
$638$	−10.5738	−	20.7522i	−0.418619	−	0.821587i
$639$	10.8476	−	51.0342i	0.429126	−	2.01888i
$640$	13.9000	+	13.8174i	0.549446	+	0.546182i
$641$	−43.4516	+	9.23593i	−1.71624	+	0.364797i	−0.957908	−	0.287076i	$-0.907317\pi$
$641$	−43.4516	+	9.23593i	−1.71624	+	0.364797i	−0.758328	+	0.651873i	$0.773984\pi$
$642$	1.40948	−	3.67182i	0.0556277	−	0.144915i
$643$	−9.86123	−	9.86123i	−0.388889	−	0.388889i	0.485402	−	0.874291i	$-0.338673\pi$
$643$	−9.86123	−	9.86123i	−0.388889	−	0.388889i	−0.874291	+	0.485402i	$0.838673\pi$
$644$	18.3273	+	2.64562i	0.722198	+	0.104252i
$645$	26.0135	+	14.9157i	1.02428	+	0.587306i
$646$	0.0484687	+	0.461149i	0.00190697	+	0.0181436i
$647$	45.2888	−	17.3847i	1.78049	−	0.683464i	0.782322	−	0.622874i	$-0.214035\pi$
$647$	45.2888	−	17.3847i	1.78049	−	0.683464i	0.998163	−	0.0605906i	$-0.0192984\pi$
$648$	−2.44769	−	46.7046i	−0.0961542	−	1.83473i
$649$	22.0556	−	38.2014i	0.865759	−	1.49954i
$650$	2.75148	+	2.44791i	0.107922	+	0.0960151i
$651$	2.84061	+	0.109827i	0.111332	+	0.00430445i
$652$	11.1900	−	21.9616i	0.438235	−	0.860084i
$653$	35.2679	+	28.5594i	1.38014	+	1.11761i	0.979515	+	0.201372i	$0.0645400\pi$
$653$	35.2679	+	28.5594i	1.38014	+	1.11761i	0.400624	+	0.916243i	$0.368793\pi$
$654$	13.7630	+	6.12770i	0.538178	+	0.239612i
$655$	−3.91660	−	11.9329i	−0.153034	−	0.466259i
$656$	−1.57012	−	3.52655i	−0.0613029	−	0.137689i
$657$	5.83988	−	5.83988i	0.227835	−	0.227835i
$658$	24.9375	+	10.6955i	0.972164	+	0.416954i
$659$	22.0985	+	7.18025i	0.860837	+	0.279703i	0.705978	−	0.708234i	$-0.250508\pi$
$659$	22.0985	+	7.18025i	0.860837	+	0.279703i	0.154859	+	0.987937i	$0.450508\pi$
$660$	−36.9568	+	30.1098i	−1.43854	+	1.17202i
$661$	8.89784	+	8.01165i	0.346086	+	0.311617i	0.823781	−	0.566909i	$-0.191861\pi$
$661$	8.89784	+	8.01165i	0.346086	+	0.311617i	−0.477695	+	0.878526i	$0.658528\pi$
$662$	12.4070	+	8.05723i	0.482213	+	0.313153i
$663$	0.0780408	−	1.48911i	0.00303085	−	0.0578321i
$664$	−2.89110	−	8.89790i	−0.112197	−	0.345306i
$665$	0.109963	+	6.58577i	0.00426420	+	0.255385i
$666$	10.8534	−	33.4034i	0.420562	−	1.29436i
$667$	−27.8808	−	10.7024i	−1.07955	−	0.414399i
$668$	−0.118578	+	0.442538i	−0.00458790	+	0.0171223i
$669$	69.8042	+	7.33672i	2.69879	+	0.283654i
$670$	2.31203	+	1.02114i	0.0893216	+	0.0394500i
$671$	−4.26953	−	5.87650i	−0.164823	−	0.226860i
$672$	−9.40877	+	47.4563i	−0.362951	+	1.83067i
$673$	−20.5664	−	10.4791i	−0.792775	−	0.403939i	0.0102030	−	0.999948i	$-0.496752\pi$
$673$	−20.5664	−	10.4791i	−0.792775	−	0.403939i	−0.802978	+	0.596009i	$0.796752\pi$
$674$	8.77620	+	5.06694i	0.338046	+	0.195171i
$675$	−47.1500	−	37.7183i	−1.81481	−	1.45178i
$676$	8.23459	+	14.2627i	0.316715	+	0.548566i
$677$	−9.68378	+	6.28872i	−0.372178	+	0.241695i	−0.717152	−	0.696917i	$-0.754554\pi$
$677$	−9.68378	+	6.28872i	−0.372178	+	0.241695i	0.344974	+	0.938612i	$0.387888\pi$
$678$	−6.28809	−	0.995936i	−0.241493	−	0.0382487i
$679$	−8.45187	−	4.16142i	−0.324353	−	0.159701i
$680$	2.09719	+	2.31526i	0.0804237	+	0.0887861i
$681$	−15.9954	+	7.12162i	−0.612946	+	0.272901i
$682$	−1.33279	−	0.357120i	−0.0510352	−	0.0136748i
$683$	9.11124	+	11.2514i	0.348632	+	0.430524i	0.921054	−	0.389435i	$-0.127330\pi$
$683$	9.11124	+	11.2514i	0.348632	+	0.430524i	−0.572422	+	0.819959i	$0.693996\pi$
$684$	−6.90982	−	7.67413i	−0.264203	−	0.293428i
$685$	−7.53057	−	6.06107i	−0.287728	−	0.231582i
$686$	14.1000	+	4.75679i	0.538340	+	0.181615i
$687$	−44.5713	+	22.7102i	−1.70050	+	0.866448i
$688$	2.31830	+	0.121497i	0.0883842	+	0.00463202i
$689$	−3.59605	+	3.99382i	−0.136999	+	0.152153i
$690$	4.47199	−	28.7899i	0.170246	−	1.09601i
$691$	32.5795	−	29.3347i	1.23938	−	1.11594i	0.250362	−	0.968152i	$-0.419450\pi$
$691$	32.5795	−	29.3347i	1.23938	−	1.11594i	0.989019	−	0.147792i	$-0.0472165\pi$
$692$	−23.8124	+	3.77152i	−0.905213	+	0.143372i
$693$	−86.8056	−	26.8943i	−3.29747	−	1.02163i
$694$	4.86115	−	6.69080i	0.184527	−	0.253979i
$695$	3.03797	+	14.0860i	0.115237	+	0.534314i
$696$	19.8820	−	44.6556i	0.753624	−	1.69267i
$697$	−1.31996	−	3.43862i	−0.0499971	−	0.130247i
$698$	−4.93497	−	7.59919i	−0.186791	−	0.287633i
$699$	−38.5425			−1.45781
$700$	10.8146	+	14.2853i	0.408753	+	0.539934i
$701$	−30.4358			−1.14955			−0.574773	−	0.818313i	$-0.694910\pi$
$701$	−30.4358			−1.14955			−0.574773	+	0.818313i	$0.694910\pi$
$702$	−4.84442	−	7.45976i	−0.182841	−	0.281550i
$703$	−2.54681	−	6.63467i	−0.0960549	−	0.250231i
$704$	7.33474	−	16.4741i	0.276438	−	0.620890i
$705$	−36.1867	+	81.9328i	−1.36287	+	3.08577i
$706$	−7.85780	+	10.8153i	−0.295732	+	0.407041i
$707$	−5.79808	−	25.5495i	−0.218059	−	0.960888i
$708$	36.9204	−	5.84762i	1.38755	−	0.219767i
$709$	−3.18109	+	2.86427i	−0.119468	+	0.107570i	−0.726700	−	0.686955i	$-0.758947\pi$
$709$	−3.18109	+	2.86427i	−0.119468	+	0.107570i	0.607231	+	0.794525i	$0.292280\pi$
$710$	12.2148	+	6.17796i	0.458412	+	0.231855i
$711$	22.2808	−	24.7454i	0.835597	−	0.928025i
$712$	−8.45787	−	0.443258i	−0.316972	−	0.0166118i
$713$	−1.57641	+	0.803220i	−0.0590370	+	0.0300808i
$714$	−0.849089	+	3.35209i	−0.0317763	+	0.125449i
$715$	−3.65584	+	9.60927i	−0.136721	+	0.359366i
$716$	−8.93567	−	9.92407i	−0.333942	−	0.370880i
$717$	29.8086	+	36.8106i	1.11322	+	1.37472i
$718$	−13.4743	−	3.61042i	−0.502856	−	0.134740i
$719$	16.8483	−	7.50137i	0.628337	−	0.279754i	−0.0677597	−	0.997702i	$-0.521585\pi$
$719$	16.8483	−	7.50137i	0.628337	−	0.279754i	0.696097	+	0.717948i	$0.254918\pi$
$720$	−8.14212	−	1.70532i	−0.303439	−	0.0635535i
$721$	−10.9265	−	16.3305i	−0.406923	−	0.608179i
$722$	−14.0946	−	2.23236i	−0.524545	−	0.0830798i
$723$	−61.0872	+	39.6705i	−2.27186	+	1.47536i
$724$	−14.5351	−	25.1755i	−0.540193	−	0.935641i
$725$	−11.9104	−	26.3277i	−0.442340	−	0.977787i
$726$	30.9143	+	17.8484i	1.14734	+	0.662415i
$727$	30.7663	+	15.6762i	1.14106	+	0.581398i	0.919243	−	0.393690i	$-0.128802\pi$
$727$	30.7663	+	15.6762i	1.14106	+	0.581398i	0.221816	+	0.975089i	$0.428802\pi$
$728$	2.10509	+	6.18868i	0.0780200	+	0.229368i
$729$	3.02204	+	4.15948i	0.111927	+	0.154055i
$730$	1.08896	+	1.87323i	0.0403044	+	0.0693313i
$731$	2.20288	+	0.231532i	0.0814766	+	0.00856353i
$732$	1.59314	−	5.94569i	0.0588843	−	0.219759i
$733$	26.1246	+	10.0283i	0.964935	+	0.370404i	0.789270	−	0.614046i	$-0.210459\pi$
$733$	26.1246	+	10.0283i	0.964935	+	0.370404i	0.175665	+	0.984450i	$0.443792\pi$
$734$	1.85303	−	5.70305i	0.0683967	−	0.210504i
$735$	−16.2006	+	46.3717i	−0.597567	+	1.71045i
$736$	−9.30467	−	28.6368i	−0.342975	−	1.05557i
$737$	−0.369281	+	7.04630i	−0.0136026	+	0.259554i
$738$	−32.7913	−	21.2949i	−1.20706	−	0.783876i
$739$	6.19977	+	5.58230i	0.228062	+	0.205348i	0.775237	−	0.631670i	$-0.217630\pi$
$739$	6.19977	+	5.58230i	0.228062	+	0.205348i	−0.547175	+	0.837018i	$0.684297\pi$
$740$	−16.2442	−	10.4805i	−0.597150	−	0.385269i
$741$	−3.04611	−	0.989740i	−0.111902	−	0.0363590i
$742$	9.98114	−	7.46301i	0.366419	−	0.273976i
$743$	−31.5650	+	31.5650i	−1.15801	+	1.15801i	−0.173106	+	0.984903i	$0.555380\pi$
$743$	−31.5650	+	31.5650i	−1.15801	+	1.15801i	−0.984903	+	0.173106i	$0.944620\pi$
$744$	−1.17786	−	2.64552i	−0.0431825	−	0.0969895i
$745$	4.03089	+	2.91031i	0.147681	+	0.106625i
$746$	−21.6643	−	9.64557i	−0.793187	−	0.353150i
$747$	18.4740	+	14.9600i	0.675929	+	0.547357i
$748$	−1.59861	+	3.13745i	−0.0584510	+	0.114717i
$749$	0.159440	−	4.12382i	0.00582580	−	0.150681i
$750$	22.6579	−	16.7734i	0.827351	−	0.612479i
$751$	22.8072	−	39.5032i	0.832247	−	1.44149i	−0.0640055	−	0.997950i	$-0.520388\pi$
$751$	22.8072	−	39.5032i	0.832247	−	1.44149i	0.896252	−	0.443544i	$-0.146279\pi$
$752$	0.362907	+	6.92468i	0.0132339	+	0.252517i
$753$	−64.9296	+	24.9241i	−2.36616	+	0.908285i
$754$	−0.444955	−	4.23347i	−0.0162043	−	0.154174i
$755$	−11.3400	−	25.2672i	−0.412706	−	0.919569i
$756$	−16.0606	−	40.1832i	−0.584119	−	1.46145i
$757$	11.9819	+	11.9819i	0.435488	+	0.435488i	0.890490	−	0.455002i	$-0.150362\pi$
$757$	11.9819	+	11.9819i	0.435488	+	0.435488i	−0.455002	+	0.890490i	$0.650362\pi$
$758$	0.273788	−	0.713242i	0.00994443	−	0.0259061i
$759$	79.5590	−	16.9108i	2.88781	−	0.613823i
$760$	5.96941	−	3.06400i	0.216533	−	0.111143i
$761$	4.79969	−	22.5808i	0.173989	−	0.818552i	−0.801412	−	0.598112i	$-0.795918\pi$
$761$	4.79969	−	22.5808i	0.173989	−	0.818552i	0.975401	−	0.220439i	$-0.0707491\pi$
$762$	−10.5528	−	20.7111i	−0.382289	−	0.750285i
$763$	15.7427	+	1.43661i	0.569922	+	0.0520087i
$764$	0.934503	−	0.303638i	0.0338091	−	0.0109852i
$765$	−7.67292	−	2.03147i	−0.277415	−	0.0734479i
$766$	−1.69358	−	7.96768i	−0.0611917	−	0.287884i
$767$	6.26543	−	5.07364i	0.226231	−	0.183199i
$768$	43.1446	−	11.5606i	1.55685	−	0.417155i
$769$	33.2899	+	24.1865i	1.20046	+	0.872188i	0.994330	−	0.106336i	$-0.0339120\pi$
$769$	33.2899	+	24.1865i	1.20046	+	0.872188i	0.206133	+	0.978524i	$0.433912\pi$
$770$	12.6496	−	20.2096i	0.455861	−	0.728302i
$771$	−0.598719	+	0.434994i	−0.0215623	+	0.0156659i
$772$	12.5433	−	15.4897i	0.451442	−	0.557485i
$773$	18.0774	−	0.947395i	0.650198	−	0.0340754i	0.275614	−	0.961268i	$-0.411119\pi$
$773$	18.0774	−	0.947395i	0.650198	−	0.0340754i	0.374584	+	0.927193i	$0.377785\pi$
$774$	20.3630	−	11.7566i	0.731933	−	0.422582i
$775$	−1.63124	−	0.519296i	−0.0585960	−	0.0186537i
$776$			9.59695i			0.344510i
$777$	−0.726899	−	52.9932i	−0.0260773	−	1.90112i
$778$	−1.69136	+	10.6788i	−0.0606381	+	0.382854i
$779$	−7.86800	+	0.826960i	−0.281900	+	0.0296289i
$780$	−8.27800	+	2.71698i	−0.296400	+	0.0972835i
$781$	−3.99438	+	38.0040i	−0.142930	+	1.35989i
$782$	−0.557016	−	2.07881i	−0.0199189	−	0.0743382i
$783$	10.9178	+	68.9320i	0.390169	+	2.46343i
$784$	0.501082	+	3.76962i	0.0178958	+	0.134629i
$785$	−35.1669	−	13.3792i	−1.25516	−	0.477525i
$786$	−13.8528	−	2.94451i	−0.494114	−	0.105027i
$787$	−8.36192	+	12.8762i	−0.298070	+	0.458988i	−0.955695	−	0.294357i	$-0.904894\pi$
$787$	−8.36192	+	12.8762i	−0.298070	+	0.458988i	0.657625	+	0.753345i	$0.271561\pi$
$788$	18.0239	−	27.7544i	0.642075	−	0.988709i
$789$	−70.3010	−	14.9429i	−2.50278	−	0.531983i
$790$	4.77977	+	7.31240i	0.170056	+	0.260164i
$791$	−6.58306	+	1.13542i	−0.234067	+	0.0403709i
$792$	14.4820	+	91.4358i	0.514596	+	3.24903i
$793$	−0.343602	−	1.28234i	−0.0122017	−	0.0455373i
$794$	−2.26560	+	21.5557i	−0.0804030	+	0.764983i
$795$	24.2797	+	33.2095i	0.861111	+	1.17782i
$796$	−1.31397	+	0.138104i	−0.0465725	+	0.00489497i
$797$	−2.39964	+	15.1507i	−0.0849997	+	0.536667i	0.908040	+	0.418884i	$0.137579\pi$
$797$	−2.39964	+	15.1507i	−0.0849997	+	0.536667i	−0.993039	+	0.117783i	$0.962421\pi$
$798$	6.48265	+	3.62513i	0.229483	+	0.128328i
$799$			6.61618i			0.234064i
$800$	13.0719	−	26.0376i	0.462163	−	0.920566i
$801$	18.6365	−	10.7598i	0.658489	−	0.380179i
$802$	−12.2786	+	0.643495i	−0.433573	+	0.0227226i
$803$	−3.80670	+	4.70088i	−0.134336	+	0.165891i
$804$	−4.83740	+	3.51458i	−0.170602	+	0.123950i
$805$	−5.28582	−	30.1107i	−0.186301	−	1.06126i
$806$	−0.204021	−	0.148230i	−0.00718632	−	0.00522117i
$807$	32.3585	−	8.67043i	1.13907	−	0.305214i
$808$	−20.7413	+	16.7959i	−0.729675	+	0.590879i
$809$	−4.30722	−	20.2639i	−0.151434	−	0.712441i	−0.986694	−	0.162586i	$-0.948016\pi$
$809$	−4.30722	−	20.2639i	−0.151434	−	0.712441i	0.835260	−	0.549855i	$-0.185317\pi$
$810$	−29.0721	+	11.2593i	−1.02149	+	0.395610i
$811$	27.8184	−	9.03875i	0.976837	−	0.317394i	0.223264	−	0.974758i	$-0.428329\pi$
$811$	27.8184	−	9.03875i	0.976837	−	0.317394i	0.753573	+	0.657364i	$0.228329\pi$
$812$	1.88206	−	20.6240i	0.0660475	−	0.723762i
$813$	−26.3122	−	51.6407i	−0.922811	−	1.81112i
$814$	−5.34837	+	25.1621i	−0.187460	+	0.881932i
$815$	−40.2106	−	6.24598i	−1.40852	−	0.218787i
$816$	−0.864370	+	0.183728i	−0.0302590	+	0.00643175i
$817$	1.70500	−	4.44167i	0.0596503	−	0.155394i
$818$	−7.37305	−	7.37305i	−0.257793	−	0.257793i
$819$	−13.0500	−	10.2745i	−0.456002	−	0.359021i
$820$	−15.9499	+	14.4476i	−0.556994	+	0.504533i
$821$	−3.10205	−	29.5141i	−0.108262	−	1.03005i	−0.904910	−	0.425603i	$-0.860062\pi$
$821$	−3.10205	−	29.5141i	−0.108262	−	1.03005i	0.796647	−	0.604444i	$-0.206605\pi$
$822$	−10.1766	+	3.90643i	−0.354949	+	0.136252i
$823$	0.778726	+	14.8590i	0.0271447	+	0.517951i	0.978037	+	0.208430i	$0.0668354\pi$
$823$	0.778726	+	14.8590i	0.0271447	+	0.517951i	−0.950893	+	0.309521i	$0.899831\pi$
$824$	−10.0081	+	17.3345i	−0.348647	+	0.603875i
$825$	66.2580	+	42.4692i	2.30681	+	1.47859i
$826$	−16.5402	+	8.71543i	−0.575506	+	0.303249i
$827$	16.7900	−	32.9522i	0.583844	−	1.14586i	−0.390459	−	0.920620i	$-0.627684\pi$
$827$	16.7900	−	32.9522i	0.583844	−	1.14586i	0.974304	−	0.225239i	$-0.0723162\pi$
$828$	37.2480	+	30.1629i	1.29446	+	1.04823i
$829$	37.4078	+	16.6550i	1.29923	+	0.578453i	0.935590	−	0.353088i	$-0.114869\pi$
$829$	37.4078	+	16.6550i	1.29923	+	0.578453i	0.363636	+	0.931541i	$0.381535\pi$
$830$	−5.03459	+	3.68082i	−0.174753	+	0.127763i
$831$	13.3238	+	29.9258i	0.462199	+	1.03812i
$832$	2.33053	−	2.33053i	0.0807967	−	0.0807967i
$833$	0.289209	+	3.61684i	0.0100205	+	0.125316i
$834$	15.4539	+	5.02127i	0.535124	+	0.173872i
$835$	0.755223	−	0.0418364i	0.0261356	−	0.00144781i
$836$	5.62066	+	5.06086i	0.194395	+	0.175034i
$837$	3.46759	+	2.25188i	0.119857	+	0.0778363i
$838$	−0.773433	+	14.7580i	−0.0267178	+	0.509806i
$839$	6.83090	+	21.0234i	0.235829	+	0.725807i	0.997010	+	0.0772679i	$0.0246197\pi$
$839$	6.83090	+	21.0234i	0.235829	+	0.725807i	−0.761181	+	0.648539i	$0.775380\pi$
$840$	49.6702	−	6.06054i	1.71379	−	0.209108i
$841$	−1.35975	+	4.18488i	−0.0468879	+	0.144306i
$842$	18.5098	+	7.10525i	0.637890	+	0.244863i
$843$	−24.0413	+	89.7232i	−0.828025	+	3.09023i
$844$	−38.4922	−	4.04569i	−1.32496	−	0.139258i
$845$	18.1333	−	20.2601i	0.623803	−	0.696968i
$846$	41.2820	+	56.8198i	1.41930	+	1.95350i
$847$	36.7410	+	7.28433i	1.26243	+	0.250292i
$848$	2.83772	+	1.44589i	0.0974479	+	0.0496522i
$849$	−75.7356	−	43.7260i	−2.59924	−	1.50067i
$850$	1.03043	−	1.80958i	0.0353436	−	0.0620681i
$851$	16.4924	+	28.5656i	0.565351	+	0.979217i
$852$	−27.1584	+	17.6369i	−0.930430	+	0.604229i
$853$	−14.5805	−	2.30932i	−0.499226	−	0.0790697i	−0.0982567	−	0.995161i	$-0.531327\pi$
$853$	−14.5805	−	2.30932i	−0.499226	−	0.0790697i	−0.400969	+	0.916091i	$0.631327\pi$
$854$	0.203275	+	3.07191i	0.00695594	+	0.105119i
$855$	−8.48029	+	14.7899i	−0.290020	+	0.505804i
$856$	−3.84060	+	1.70995i	−0.131269	+	0.0584447i
$857$	18.6322	+	4.99249i	0.636465	+	0.170540i	0.562602	−	0.826728i	$-0.309800\pi$
$857$	18.6322	+	4.99249i	0.636465	+	0.170540i	0.0738633	+	0.997268i	$0.476467\pi$
$858$	7.29601	+	9.00983i	0.249082	+	0.307590i
$859$	20.0572	+	22.2758i	0.684344	+	0.760040i	0.980802	−	0.195005i	$-0.0624724\pi$
$859$	20.0572	+	22.2758i	0.684344	+	0.760040i	−0.296459	+	0.955046i	$0.595806\pi$
$860$	−3.38684	−	12.4909i	−0.115490	−	0.425935i
$861$	−57.1925	−	14.4869i	−1.94911	−	0.493713i
$862$	21.9305	−	11.1741i	0.746955	−	0.380592i
$863$	25.7384	+	1.34889i	0.876147	+	0.0459169i	0.485105	−	0.874456i	$-0.338781\pi$
$863$	25.7384	+	1.34889i	0.876147	+	0.0459169i	0.391042	+	0.920373i	$0.372115\pi$
$864$	−47.0845	+	52.2926i	−1.60185	+	1.77903i
$865$	18.1759	+	35.4109i	0.617998	+	1.20401i
$866$	15.4882	−	13.9456i	0.526311	−	0.473892i
$867$	51.8593	−	8.21371i	1.76124	−	0.278952i
$868$	−0.833385	−	0.900420i	−0.0282869	−	0.0305622i
$869$	−14.3350	+	19.7304i	−0.486282	+	0.669309i
$870$	−32.4163	−	3.30946i	−1.09901	−	0.112201i
$871$	−0.524529	+	1.17811i	−0.0177730	+	0.0399188i
$872$	−5.77103	−	15.0340i	−0.195432	−	0.509117i
$873$	−13.2807	−	20.4504i	−0.449482	−	0.692142i
$874$	−4.62263			−0.156363
$875$	16.8404	−	24.3188i	0.569308	−	0.822124i
$876$	−5.12595			−0.173190
$877$	11.7560	+	18.1027i	0.396973	+	0.611286i	0.979480	−	0.201540i	$-0.0645947\pi$
$877$	11.7560	+	18.1027i	0.396973	+	0.611286i	−0.582507	+	0.812826i	$0.697928\pi$
$878$	−3.83444	−	9.98906i	−0.129406	−	0.337115i
$879$	−8.75619	+	19.6667i	−0.295339	+	0.663342i
$880$	6.06131	+	0.618815i	0.204327	+	0.0208603i
$881$	18.9856	−	26.1314i	0.639640	−	0.880388i	−0.358957	−	0.933354i	$-0.616867\pi$
$881$	18.9856	−	26.1314i	0.639640	−	0.880388i	0.998596	+	0.0529657i	$0.0168674\pi$
$882$	25.0512	+	29.2569i	0.843517	+	0.985131i
$883$	−17.4297	+	2.76060i	−0.586557	+	0.0929015i	−0.442657	−	0.896691i	$-0.645964\pi$
$883$	−17.4297	+	2.76060i	−0.586557	+	0.0929015i	−0.143899	+	0.989592i	$0.545964\pi$
$884$	−0.478265	+	0.430632i	−0.0160858	+	0.0144837i
$885$	−28.1811	−	54.9035i	−0.947297	−	1.84556i
$886$	8.07564	−	8.96891i	0.271306	−	0.301316i
$887$	−23.0292	−	1.20691i	−0.773244	−	0.0405240i	−0.338368	−	0.941014i	$-0.609875\pi$
$887$	−23.0292	−	1.20691i	−0.773244	−	0.0405240i	−0.434877	+	0.900490i	$0.643208\pi$
$888$	−48.1046	+	24.5105i	−1.61429	+	0.822519i
$889$	−17.4815	−	17.0084i	−0.586310	−	0.570443i
$890$	1.47748	+	5.44904i	0.0495253	+	0.182652i
$891$	−58.2375	−	64.6793i	−1.95103	−	2.16684i
$892$	−19.0640	−	23.5420i	−0.638309	−	0.788245i
$893$	13.7268	+	3.67808i	0.459349	+	0.123082i
$894$	5.12161	−	2.28029i	0.171292	−	0.0762642i
$895$	−10.9666	+	19.1261i	−0.366573	+	0.639314i
$896$	19.2739	−	12.8958i	0.643894	−	0.430820i
$897$	14.6826	+	2.32550i	0.490239	+	0.0776462i
$898$	−2.60791	+	1.69360i	−0.0870273	+	0.0565162i
$899$	0.989361	+	1.71362i	0.0329970	+	0.0571525i
$900$	5.12237	+	46.0922i	0.170746	+	1.53641i
$901$	2.63168	+	1.51940i	0.0876739	+	0.0506185i
$902$	25.5156	+	13.0008i	0.849576	+	0.432881i
$903$	23.3771	−	26.6902i	0.777941	−	0.888193i
$904$	3.99998	+	5.50549i	0.133037	+	0.183110i
$905$	−32.0075	+	35.7616i	−1.06397	+	1.18876i
$906$	−31.0592	−	3.26445i	−1.03187	−	0.108454i
$907$	10.6692	−	39.8182i	0.354266	−	1.32214i	−0.527139	−	0.849779i	$-0.676735\pi$
$907$	10.6692	−	39.8182i	0.354266	−	1.32214i	0.881405	−	0.472361i	$-0.156598\pi$
$908$	7.05490	+	2.70812i	0.234125	+	0.0898722i
$909$	20.9552	−	64.4936i	0.695041	−	2.13912i
$910$	3.48207	−	2.61979i	0.115429	−	0.0868453i
$911$	0.709840	+	2.18466i	0.0235181	+	0.0723812i	0.962127	−	0.272603i	$-0.0878844\pi$
$911$	0.709840	+	2.18466i	0.0235181	+	0.0723812i	−0.938609	+	0.344984i	$0.887884\pi$
$912$	−0.0993374	+	1.89547i	−0.00328939	+	0.0627653i
$913$	−14.6019	−	9.48257i	−0.483251	−	0.313827i
$914$	−25.2977	−	22.7781i	−0.836772	−	0.753433i
$915$	−10.1468	+	0.562091i	−0.335442	+	0.0185821i
$916$	20.5331	+	6.67160i	0.678432	+	0.220436i
$917$	−14.7562	+	1.75588i	−0.487293	+	0.0579843i
$918$	−3.55635	+	3.55635i	−0.117377	+	0.117377i
$919$	10.3836	+	23.3219i	0.342523	+	0.769318i	0.999876	+	0.0157361i	$0.00500916\pi$
$919$	10.3836	+	23.3219i	0.342523	+	0.769318i	−0.657354	+	0.753582i	$0.728324\pi$
$920$	−25.1404	+	18.3803i	−0.828854	+	0.605979i
$921$	16.6369	+	7.40721i	0.548203	+	0.244076i
$922$	14.3714	+	11.6378i	0.473298	+	0.383269i
$923$	−3.17074	+	6.22293i	−0.104366	+	0.204830i
$924$	26.2936	+	49.9000i	0.864995	+	1.64159i
$925$	−8.07654	+	30.8769i	−0.265555	+	1.01523i
$926$	−7.25389	+	12.5641i	−0.238378	+	0.412882i
$927$	−2.66169	−	50.7881i	−0.0874214	−	1.66810i
$928$	−31.4389	+	12.0682i	−1.03203	+	0.396160i
$929$	−4.69716	−	44.6905i	−0.154109	−	1.46625i	−0.749069	−	0.662492i	$-0.769499\pi$
$929$	−4.69716	−	44.6905i	−0.154109	−	1.46625i	0.594960	−	0.803755i	$-0.297168\pi$
$930$	−1.43072	+	1.29597i	−0.0469151	+	0.0424964i
$931$	7.66474	+	1.41065i	0.251202	+	0.0462323i
$932$	11.7625	+	11.7625i	0.385293	+	0.385293i
$933$	27.8492	−	72.5496i	0.911741	−	2.37517i
$934$	21.5510	−	4.58082i	0.705172	−	0.149889i
$935$	5.74452	+	0.892305i	0.187866	+	0.0291815i
$936$	−3.51782	+	16.5501i	−0.114984	+	0.540956i
$937$	25.9319	+	50.8942i	0.847158	+	1.66264i	0.744202	+	0.667955i	$0.232830\pi$
$937$	25.9319	+	50.8942i	0.847158	+	1.66264i	0.102956	+	0.994686i	$0.467170\pi$
$938$	1.72446	−	2.44330i	0.0563057	−	0.0797767i
$939$	−21.3345	+	6.93200i	−0.696226	+	0.226217i
$940$	36.0479	−	13.9609i	1.17575	−	0.455354i
$941$	−6.78377	−	31.9151i	−0.221145	−	1.04040i	−0.938922	−	0.344131i	$-0.888174\pi$
$941$	−6.78377	−	31.9151i	−0.221145	−	1.04040i	0.717777	−	0.696273i	$-0.245160\pi$
$942$	−32.9732	+	26.7011i	−1.07432	+	0.869970i
$943$	35.4682	−	9.50367i	1.15500	−	0.309482i
$944$	−3.86527	−	2.80828i	−0.125804	−	0.0914018i
$945$	−54.7634	+	45.8813i	−1.78145	+	1.49252i
$946$	−13.9324	+	10.1225i	−0.452983	+	0.329111i
$947$	−23.0717	+	28.4911i	−0.749728	+	0.925837i	−0.999093	−	0.0425722i	$-0.986445\pi$
$947$	−23.0717	+	28.4911i	−0.749728	+	0.925837i	0.249365	+	0.968410i	$0.419778\pi$
$948$	−20.6386	+	1.08162i	−0.670312	+	0.0351295i
$949$	−0.957429	+	0.552772i	−0.0310795	+	0.0179437i
$950$	−3.18155	−	3.14385i	−0.103223	−	0.102000i
$951$		−	21.5823i		−	0.699854i
$952$	3.17538	−	1.89184i	0.102915	−	0.0613150i
$953$	−7.31025	+	46.1551i	−0.236802	+	1.49511i	0.527113	+	0.849795i	$0.323274\pi$
$953$	−7.31025	+	46.1551i	−0.236802	+	1.49511i	−0.763916	+	0.645316i	$0.776726\pi$
$954$	32.0812	−	3.37187i	1.03867	−	0.109168i
$955$	−0.957421	−	1.30955i	−0.0309814	−	0.0423761i
$956$	2.13687	−	20.3310i	0.0691114	−	0.657551i
$957$	−23.5439	−	87.8669i	−0.761065	−	2.84034i
$958$	−4.58964	−	28.9779i	−0.148285	−	0.936232i
$959$	−8.78932	+	7.31932i	−0.283822	+	0.236353i
$960$	−13.8038	−	21.1179i	−0.445515	−	0.681578i
$961$	−30.2079	−	6.42089i	−0.974449	−	0.207125i
$962$	−2.56065	+	3.94306i	−0.0825587	+	0.127129i
$963$	5.81775	−	8.95855i	0.187474	−	0.288685i
$964$	30.7494	+	6.53599i	0.990373	+	0.210510i
$965$	−30.7553	−	11.7008i	−0.990047	−	0.376663i
$966$	−32.3499	−	11.9115i	−1.04084	−	0.383247i
$967$	−1.12542	−	7.10565i	−0.0361912	−	0.228502i	0.962962	−	0.269635i	$-0.0869032\pi$
$967$	−1.12542	−	7.10565i	−0.0361912	−	0.228502i	−0.999154	+	0.0411332i	$0.986903\pi$
$968$	−9.87561	−	36.8563i	−0.317414	−	1.18461i
$969$	−0.189304	+	1.80111i	−0.00608132	+	0.0578599i
$970$	6.07835	−	1.99502i	0.195164	−	0.0640562i
$971$	22.1815	−	2.33137i	0.711839	−	0.0748173i	0.258314	−	0.966061i	$-0.416833\pi$
$971$	22.1815	−	2.33137i	0.711839	−	0.0748173i	0.453525	+	0.891244i	$0.350166\pi$
$972$	3.86183	−	24.3826i	0.123868	−	0.782074i
$973$	17.0484	−	0.233851i	0.546548	−	0.00749691i
$974$		−	28.9792i		−	0.928555i
$975$	8.52382	+	11.5862i	0.272981	+	0.371056i
$976$	−0.681341	+	0.393372i	−0.0218092	+	0.0125915i
$977$	−57.2875	+	3.00231i	−1.83279	+	0.0960525i	−0.937193	−	0.348812i	$-0.886585\pi$
$977$	−57.2875	+	3.00231i	−1.83279	+	0.0960525i	−0.895598	+	0.444865i	$0.853252\pi$
$978$	−28.8775	+	35.6607i	−0.923400	+	1.14030i
$979$	−12.7512	+	9.26427i	−0.407529	+	0.296087i
$980$	19.0959	−	9.20768i	0.609997	−	0.294129i
$981$	33.1024	+	24.0503i	1.05688	+	0.767867i
$982$	7.26776	−	1.94739i	0.231924	−	0.0621438i
$983$	−14.4736	+	11.7205i	−0.461635	+	0.373825i	−0.831740	−	0.555165i	$-0.812655\pi$
$983$	−14.4736	+	11.7205i	−0.461635	+	0.373825i	0.370105	+	0.928990i	$0.379322\pi$
$984$	12.4959	+	58.7885i	0.398354	+	1.87411i
$985$	−52.8157	−	13.9834i	−1.68285	−	0.445548i
$986$	−2.28915	+	0.743790i	−0.0729014	+	0.0236871i
$987$	86.5848	+	61.1108i	2.75602	+	1.94518i
$988$	0.627566	+	1.23167i	0.0199655	+	0.0391846i
$989$	−4.59112	+	21.5995i	−0.145989	+	0.686825i
$990$	54.9015	−	28.1801i	1.74488	−	0.895621i
$991$	41.3573	−	8.79076i	1.31376	−	0.279248i	0.502825	−	0.864388i	$-0.332294\pi$
$991$	41.3573	−	8.79076i	1.31376	−	0.279248i	0.810932	+	0.585140i	$0.198961\pi$
$992$	−0.714956	+	1.86252i	−0.0226999	+	0.0591352i
$993$	40.8565	+	40.8565i	1.29654	+	1.29654i
$994$	10.0190	−	12.7254i	0.317782	−	0.403625i
$995$	0.893130	+	1.99002i	0.0283141	+	0.0630880i
$996$	−1.54223	−	14.6733i	−0.0488674	−	0.464942i
$997$	15.9364	−	6.11742i	0.504712	−	0.193741i	−0.0926712	−	0.995697i	$-0.529541\pi$
$997$	15.9364	−	6.11742i	0.504712	−	0.193741i	0.597383	+	0.801956i	$0.296207\pi$
$998$	1.35009	+	25.7613i	0.0427365	+	0.815460i
$999$	38.5417	−	66.7562i	1.21941	−	2.11207i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.x.a.117.11	yes	288
5.2	odd	4		875.2.bb.a.768.8		288
5.3	odd	4		875.2.bb.b.768.11		288
5.4	even	2		875.2.bb.c.607.8		288
7.3	odd	6	inner	175.2.x.a.17.8	yes	288
25.3	odd	20	inner	175.2.x.a.103.8	yes	288
25.4	even	10		875.2.bb.a.257.8		288
25.21	even	5		875.2.bb.b.257.11		288
25.22	odd	20		875.2.bb.c.243.11		288
35.3	even	12		875.2.bb.b.143.11		288
35.17	even	12		875.2.bb.a.143.8		288
35.24	odd	6		875.2.bb.c.857.11		288
175.3	even	60	inner	175.2.x.a.3.11	✓	288
175.122	even	60		875.2.bb.c.493.8		288
175.129	odd	30		875.2.bb.a.507.8		288
175.171	odd	30		875.2.bb.b.507.11		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.3.11	✓	288	175.3	even	60	inner
175.2.x.a.17.8	yes	288	7.3	odd	6	inner
175.2.x.a.103.8	yes	288	25.3	odd	20	inner
175.2.x.a.117.11	yes	288	1.1	even	1	trivial
875.2.bb.a.143.8		288	35.17	even	12
875.2.bb.a.257.8		288	25.4	even	10
875.2.bb.a.507.8		288	175.129	odd	30
875.2.bb.a.768.8		288	5.2	odd	4
875.2.bb.b.143.11		288	35.3	even	12
875.2.bb.b.257.11		288	25.21	even	5
875.2.bb.b.507.11		288	175.171	odd	30
875.2.bb.b.768.11		288	5.3	odd	4
875.2.bb.c.243.11		288	25.22	odd	20
875.2.bb.c.493.8		288	175.122	even	60
875.2.bb.c.607.8		288	5.4	even	2
875.2.bb.c.857.11		288	35.24	odd	6

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+(0.437609 + 0.673859i) q^{2} +(1.12462 + 2.92974i) q^{3} +(0.550889 - 1.23732i) q^{4} +(-2.22451 - 0.227106i) q^{5} +(-1.48209 + 2.03992i) q^{6} +(-0.782993 + 2.52724i) q^{7} +(2.66204 - 0.421625i) q^{8} +(-5.08915 + 4.58229i) q^{9} +(-0.820427 - 1.59839i) q^{10} +(3.35615 - 3.72738i) q^{11} +(4.24455 + 0.222448i) q^{12} +(0.816789 - 0.416175i) q^{13} +(-2.04565 + 0.578315i) q^{14} +(-1.83636 - 6.77262i) q^{15} +(-0.363508 - 0.403716i) q^{16} +(-0.326203 - 0.402827i) q^{17} +(-5.31488 - 1.42412i) q^{18} +(-1.01710 + 0.452842i) q^{19} +(-1.50646 + 2.62731i) q^{20} +(-8.28471 + 0.548217i) q^{21} +(3.98041 + 0.630435i) q^{22} +(4.33381 - 2.81441i) q^{23} +(4.22903 + 7.32490i) q^{24} +(4.89685 + 1.01040i) q^{25} +(0.637878 + 0.368279i) q^{26} +(-10.7599 - 5.48243i) q^{27} +(2.69565 + 2.36104i) q^{28} +(-3.39698 - 4.67555i) q^{29} +(3.76018 - 4.20121i) q^{30} +(-0.340506 - 0.0357886i) q^{31} +(1.50812 - 5.62839i) q^{32} +(14.6946 + 5.64074i) q^{33} +(0.128699 - 0.396095i) q^{34} +(2.31572 - 5.44403i) q^{35} +(2.86619 + 8.82122i) q^{36} +(-0.334068 + 6.37440i) q^{37} +(-0.750244 - 0.487214i) q^{38} +(2.13786 + 1.92494i) q^{39} +(-6.01747 + 0.333344i) q^{40} +(6.75808 + 2.19583i) q^{41} +(-3.99489 - 5.34282i) q^{42} +(-3.02167 + 3.02167i) q^{43} +(-2.76308 - 6.20599i) q^{44} +(12.3615 - 9.03756i) q^{45} +(3.79303 + 1.68877i) q^{46} +(-9.91961 - 8.03274i) q^{47} +(0.773974 - 1.51901i) q^{48} +(-5.77384 - 3.95762i) q^{49} +(1.46204 + 3.74194i) q^{50} +(0.813322 - 1.40871i) q^{51} +(-0.0649800 - 1.23989i) q^{52} +(-5.47316 + 2.10095i) q^{53} +(-1.01424 - 9.64981i) q^{54} +(-8.31228 + 7.52937i) q^{55} +(-1.01881 + 7.05773i) q^{56} +(-2.47056 - 2.47056i) q^{57} +(1.66411 - 4.33515i) q^{58} +(8.60248 - 1.82851i) q^{59} +(-9.39151 - 1.45880i) q^{60} +(0.301099 - 1.41656i) q^{61} +(-0.124892 - 0.245114i) q^{62} +(-7.59576 - 16.4494i) q^{63} +(3.41938 - 1.11102i) q^{64} +(-1.91147 + 0.740286i) q^{65} +(2.62944 + 12.3706i) q^{66} +(-1.09328 + 0.885317i) q^{67} +(-0.678125 + 0.181703i) q^{68} +(13.1194 + 9.53177i) q^{69} +(4.68189 - 0.821886i) q^{70} +(-6.16371 + 4.47820i) q^{71} +(-11.6155 + 14.3439i) q^{72} +(-1.20435 + 0.0631171i) q^{73} +(-4.44164 + 2.56438i) q^{74} +(2.54690 + 15.4828i) q^{75} +1.50794i q^{76} +(6.79213 + 11.4003i) q^{77} +(-0.361590 + 2.28299i) q^{78} +(-4.83574 + 0.508257i) q^{79} +(0.716939 + 0.980624i) q^{80} +(1.81383 - 17.2574i) q^{81} +(1.47772 + 5.51491i) q^{82} +(-0.543025 - 3.42852i) q^{83} +(-3.88563 + 10.5528i) q^{84} +(0.634155 + 0.970172i) q^{85} +(-3.35849 - 0.713869i) q^{86} +(9.87780 - 15.2105i) q^{87} +(7.36263 - 11.3375i) q^{88} +(-3.07374 - 0.653343i) q^{89} +(11.4996 + 4.37500i) q^{90} +(0.412231 + 2.39008i) q^{91} +(-1.09487 - 6.91272i) q^{92} +(-0.278088 - 1.03784i) q^{93} +(1.07202 - 10.1996i) q^{94} +(2.36538 - 0.776360i) q^{95} +(18.1858 - 1.91140i) q^{96} +(-0.557021 + 3.51689i) q^{97} +(0.140190 - 5.62265i) q^{98} +34.3480i 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

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