LMFDB - Embedded newform 950.2.n.b.39.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(39,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([3, 0]))

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

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

chi := DirichletCharacter("950.39");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.n (of order $10$, degree $4$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			39.8
Character	$\chi$	$=$	950.39
Dual form			950.2.n.b.609.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 - 0.809017i) q^{2} +(0.702911 + 0.228390i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-0.520909 - 2.17455i) q^{5} +(-0.228390 - 0.702911i) q^{6} +2.52633i q^{7} +(0.951057 - 0.309017i) q^{8} +(-1.98513 - 1.44228i) q^{9} +O(q^{10})$	\(q+(-0.587785 - 0.809017i) q^{2} +(0.702911 + 0.228390i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-0.520909 - 2.17455i) q^{5} +(-0.228390 - 0.702911i) q^{6} +2.52633i q^{7} +(0.951057 - 0.309017i) q^{8} +(-1.98513 - 1.44228i) q^{9} +(-1.45306 + 1.69959i) q^{10} +(0.558172 - 0.405536i) q^{11} +(-0.434423 + 0.597932i) q^{12} +(0.161528 - 0.222324i) q^{13} +(2.04385 - 1.48494i) q^{14} +(0.130491 - 1.64748i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(6.08739 - 1.97791i) q^{17} +2.45375i q^{18} +(-0.309017 - 0.951057i) q^{19} +(2.22909 + 0.176558i) q^{20} +(-0.576989 + 1.77579i) q^{21} +(-0.656171 - 0.213203i) q^{22} +(-3.81162 - 5.24624i) q^{23} +0.739085 q^{24} +(-4.45731 + 2.26548i) q^{25} -0.274808 q^{26} +(-2.36924 - 3.26097i) q^{27} +(-2.40269 - 0.780680i) q^{28} +(1.12178 - 3.45248i) q^{29} +(-1.40954 + 0.862797i) q^{30} +(-2.16888 - 6.67511i) q^{31} +1.00000i q^{32} +(0.484966 - 0.157575i) q^{33} +(-5.17824 - 3.76221i) q^{34} +(5.49363 - 1.31599i) q^{35} +(1.98513 - 1.44228i) q^{36} +(-3.22472 + 4.43844i) q^{37} +(-0.587785 + 0.809017i) q^{38} +(0.164317 - 0.119383i) q^{39} +(-1.16739 - 1.90715i) q^{40} +(-0.275446 - 0.200123i) q^{41} +(1.77579 - 0.576989i) q^{42} -11.3234i q^{43} +(0.213203 + 0.656171i) q^{44} +(-2.10223 + 5.06805i) q^{45} +(-2.00389 + 6.16733i) q^{46} +(6.44050 + 2.09265i) q^{47} +(-0.434423 - 0.597932i) q^{48} +0.617643 q^{49} +(4.45275 + 2.27442i) q^{50} +4.73063 q^{51} +(0.161528 + 0.222324i) q^{52} +(-5.61381 - 1.82404i) q^{53} +(-1.24558 + 3.83351i) q^{54} +(-1.17261 - 1.00252i) q^{55} +(0.780680 + 2.40269i) q^{56} -0.739085i q^{57} +(-3.45248 + 1.12178i) q^{58} +(-1.56613 - 1.13786i) q^{59} +(1.52653 + 0.633205i) q^{60} +(-8.31697 + 6.04263i) q^{61} +(-4.12545 + 5.67819i) q^{62} +(3.64368 - 5.01509i) q^{63} +(0.809017 - 0.587785i) q^{64} +(-0.567596 - 0.235440i) q^{65} +(-0.412537 - 0.299725i) q^{66} +(9.92494 - 3.22481i) q^{67} +6.40066i q^{68} +(-1.48104 - 4.55818i) q^{69} +(-4.29373 - 3.67092i) q^{70} +(0.993288 - 3.05703i) q^{71} +(-2.33366 - 0.758252i) q^{72} +(-8.81748 - 12.1362i) q^{73} +5.48622 q^{74} +(-3.65051 + 0.574429i) q^{75} +1.00000 q^{76} +(1.02452 + 1.41013i) q^{77} +(-0.193166 - 0.0627633i) q^{78} +(-1.16332 + 3.58035i) q^{79} +(-0.856742 + 2.06543i) q^{80} +(1.35416 + 4.16769i) q^{81} +0.340470i q^{82} +(1.67358 - 0.543781i) q^{83} +(-1.51058 - 1.09750i) q^{84} +(-7.47204 - 12.2070i) q^{85} +(-9.16085 + 6.65575i) q^{86} +(1.57702 - 2.17058i) q^{87} +(0.405536 - 0.558172i) q^{88} +(-1.52476 + 1.10780i) q^{89} +(5.33580 - 1.27818i) q^{90} +(0.561665 + 0.408074i) q^{91} +(6.16733 - 2.00389i) q^{92} -5.18736i q^{93} +(-2.09265 - 6.44050i) q^{94} +(-1.90715 + 1.16739i) q^{95} +(-0.228390 + 0.702911i) q^{96} +(5.07870 + 1.65017i) q^{97} +(-0.363041 - 0.499683i) q^{98} -1.69294 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 24 q^{4} + 8 q^{5} - 6 q^{6} + 34 q^{9}+O(q^{10}) $ 96 * q + 24 * q^4 + 8 * q^5 - 6 * q^6 + 34 * q^9	$ 96 q + 24 q^{4} + 8 q^{5} - 6 q^{6} + 34 q^{9} - 24 q^{11} + 10 q^{12} + 10 q^{14} - 8 q^{15} - 24 q^{16} + 30 q^{17} + 24 q^{19} + 2 q^{20} - 24 q^{24} - 60 q^{25} + 84 q^{26} - 30 q^{27} - 10 q^{28} - 4 q^{29} + 16 q^{30} - 14 q^{31} + 100 q^{33} + 8 q^{34} + 42 q^{35} - 34 q^{36} - 30 q^{37} + 32 q^{39} + 12 q^{41} + 10 q^{42} + 4 q^{44} - 18 q^{45} - 10 q^{46} + 10 q^{48} - 132 q^{49} - 36 q^{50} + 36 q^{51} + 30 q^{53} + 24 q^{54} - 4 q^{55} - 10 q^{56} + 60 q^{58} + 16 q^{59} + 8 q^{60} + 42 q^{61} - 110 q^{63} + 24 q^{64} + 12 q^{65} - 20 q^{66} + 130 q^{67} - 8 q^{69} + 20 q^{70} - 8 q^{71} - 120 q^{73} - 124 q^{74} - 24 q^{75} + 96 q^{76} - 50 q^{78} + 4 q^{79} - 2 q^{80} - 10 q^{81} - 70 q^{83} + 52 q^{85} - 44 q^{86} - 70 q^{87} + 10 q^{88} - 26 q^{89} + 32 q^{90} - 4 q^{91} - 10 q^{92} + 10 q^{94} + 2 q^{95} - 6 q^{96} - 10 q^{97} - 60 q^{98} - 184 q^{99}+O(q^{100}) $ 96 * q + 24 * q^4 + 8 * q^5 - 6 * q^6 + 34 * q^9 - 24 * q^11 + 10 * q^12 + 10 * q^14 - 8 * q^15 - 24 * q^16 + 30 * q^17 + 24 * q^19 + 2 * q^20 - 24 * q^24 - 60 * q^25 + 84 * q^26 - 30 * q^27 - 10 * q^28 - 4 * q^29 + 16 * q^30 - 14 * q^31 + 100 * q^33 + 8 * q^34 + 42 * q^35 - 34 * q^36 - 30 * q^37 + 32 * q^39 + 12 * q^41 + 10 * q^42 + 4 * q^44 - 18 * q^45 - 10 * q^46 + 10 * q^48 - 132 * q^49 - 36 * q^50 + 36 * q^51 + 30 * q^53 + 24 * q^54 - 4 * q^55 - 10 * q^56 + 60 * q^58 + 16 * q^59 + 8 * q^60 + 42 * q^61 - 110 * q^63 + 24 * q^64 + 12 * q^65 - 20 * q^66 + 130 * q^67 - 8 * q^69 + 20 * q^70 - 8 * q^71 - 120 * q^73 - 124 * q^74 - 24 * q^75 + 96 * q^76 - 50 * q^78 + 4 * q^79 - 2 * q^80 - 10 * q^81 - 70 * q^83 + 52 * q^85 - 44 * q^86 - 70 * q^87 + 10 * q^88 - 26 * q^89 + 32 * q^90 - 4 * q^91 - 10 * q^92 + 10 * q^94 + 2 * q^95 - 6 * q^96 - 10 * q^97 - 60 * q^98 - 184 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$3$	0.702911	+	0.228390i	0.405826	+	0.131861i	0.504815	−	0.863228i	$-0.331561\pi$
$3$	0.702911	+	0.228390i	0.405826	+	0.131861i	−0.0989887	+	0.995089i	$0.531561\pi$
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	−0.520909	−	2.17455i	−0.232958	−	0.972487i
$5$	−0.520909	−	2.17455i	−0.232958	−	0.972487i
$6$	−0.228390	−	0.702911i	−0.0932397	−	0.286962i
$7$			2.52633i			0.954864i	0.878669	+	0.477432i	$0.158432\pi$
$7$			2.52633i			0.954864i	−0.878669	+	0.477432i	$0.841568\pi$
$8$	0.951057	−	0.309017i	0.336249	−	0.109254i
$9$	−1.98513	−	1.44228i	−0.661709	−	0.480760i
$10$	−1.45306	+	1.69959i	−0.459499	+	0.537458i
$11$	0.558172	−	0.405536i	0.168295	−	0.122274i	−0.500450	−	0.865766i	$-0.666832\pi$
$11$	0.558172	−	0.405536i	0.168295	−	0.122274i	0.668745	+	0.743492i	$0.266832\pi$
$12$	−0.434423	+	0.597932i	−0.125407	+	0.172608i
$13$	0.161528	−	0.222324i	0.0447998	−	0.0616617i	−0.786029	−	0.618189i	$-0.787867\pi$
$13$	0.161528	−	0.222324i	0.0447998	−	0.0616617i	0.830829	+	0.556527i	$0.187867\pi$
$14$	2.04385	−	1.48494i	0.546241	−	0.396867i
$15$	0.130491	−	1.64748i	0.0336928	−	0.425379i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	6.08739	−	1.97791i	1.47641	−	0.479714i	0.543371	−	0.839493i	$-0.317148\pi$
$17$	6.08739	−	1.97791i	1.47641	−	0.479714i	0.933038	+	0.359779i	$0.117148\pi$
$18$			2.45375i			0.578355i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$20$	2.22909	+	0.176558i	0.498439	+	0.0394796i
$21$	−0.576989	+	1.77579i	−0.125909	+	0.387509i
$22$	−0.656171	−	0.213203i	−0.139896	−	0.0454550i
$23$	−3.81162	−	5.24624i	−0.794778	−	1.09392i	−0.993497	−	0.113861i	$-0.963678\pi$
$23$	−3.81162	−	5.24624i	−0.794778	−	1.09392i	0.198719	−	0.980057i	$-0.436322\pi$
$24$	0.739085			0.150865
$25$	−4.45731	+	2.26548i	−0.891462	+	0.453096i
$26$	−0.274808			−0.0538943
$27$	−2.36924	−	3.26097i	−0.455960	−	0.627575i
$28$	−2.40269	−	0.780680i	−0.454065	−	0.147535i
$29$	1.12178	−	3.45248i	0.208309	−	0.641109i	−0.791252	−	0.611490i	$-0.790571\pi$
$29$	1.12178	−	3.45248i	0.208309	−	0.641109i	0.999561	−	0.0296192i	$-0.00942946\pi$
$30$	−1.40954	+	0.862797i	−0.257346	+	0.157524i
$31$	−2.16888	−	6.67511i	−0.389542	−	1.19889i	−0.933132	−	0.359535i	$-0.882935\pi$
$31$	−2.16888	−	6.67511i	−0.389542	−	1.19889i	0.543590	−	0.839351i	$-0.317065\pi$
$32$			1.00000i			0.176777i
$33$	0.484966	−	0.157575i	0.0844217	−	0.0274303i
$34$	−5.17824	−	3.76221i	−0.888061	−	0.645214i
$35$	5.49363	−	1.31599i	0.928593	−	0.222443i
$36$	1.98513	−	1.44228i	0.330855	−	0.240380i
$37$	−3.22472	+	4.43844i	−0.530140	+	0.729676i	−0.987152	−	0.159785i	$-0.948920\pi$
$37$	−3.22472	+	4.43844i	−0.530140	+	0.729676i	0.457011	+	0.889461i	$0.348920\pi$
$38$	−0.587785	+	0.809017i	−0.0953514	+	0.131240i
$39$	0.164317	−	0.119383i	0.0263117	−	0.0191166i
$40$	−1.16739	−	1.90715i	−0.184580	−	0.301546i
$41$	−0.275446	−	0.200123i	−0.0430175	−	0.0312540i	0.566069	−	0.824358i	$-0.308464\pi$
$41$	−0.275446	−	0.200123i	−0.0430175	−	0.0312540i	−0.609086	+	0.793104i	$0.708464\pi$
$42$	1.77579	−	0.576989i	0.274010	−	0.0890313i
$43$		−	11.3234i		−	1.72681i	−0.504514	−	0.863404i	$-0.668328\pi$
$43$		−	11.3234i		−	1.72681i	0.504514	−	0.863404i	$-0.331672\pi$
$44$	0.213203	+	0.656171i	0.0321415	+	0.0989214i
$45$	−2.10223	+	5.06805i	−0.313383	+	0.755500i
$46$	−2.00389	+	6.16733i	−0.295457	+	0.909323i
$47$	6.44050	+	2.09265i	0.939444	+	0.305244i	0.738419	−	0.674342i	$-0.235573\pi$
$47$	6.44050	+	2.09265i	0.939444	+	0.305244i	0.201025	+	0.979586i	$0.435573\pi$
$48$	−0.434423	−	0.597932i	−0.0627036	−	0.0863041i
$49$	0.617643			0.0882346
$50$	4.45275	+	2.27442i	0.629714	+	0.321652i
$51$	4.73063			0.662421
$52$	0.161528	+	0.222324i	0.0223999	+	0.0308308i
$53$	−5.61381	−	1.82404i	−0.771116	−	0.250551i	−0.103073	−	0.994674i	$-0.532868\pi$
$53$	−5.61381	−	1.82404i	−0.771116	−	0.250551i	−0.668043	+	0.744123i	$0.732868\pi$
$54$	−1.24558	+	3.83351i	−0.169502	+	0.521674i
$55$	−1.17261	−	1.00252i	−0.158115	−	0.135180i
$56$	0.780680	+	2.40269i	0.104323	+	0.321072i
$57$		−	0.739085i		−	0.0978942i
$58$	−3.45248	+	1.12178i	−0.453332	+	0.147297i
$59$	−1.56613	−	1.13786i	−0.203893	−	0.148137i	0.481153	−	0.876637i	$-0.340218\pi$
$59$	−1.56613	−	1.13786i	−0.203893	−	0.148137i	−0.685046	+	0.728499i	$0.740218\pi$
$60$	1.52653	+	0.633205i	0.197074	+	0.0817465i
$61$	−8.31697	+	6.04263i	−1.06488	+	0.773680i	−0.974985	−	0.222271i	$-0.928653\pi$
$61$	−8.31697	+	6.04263i	−1.06488	+	0.773680i	−0.0898942	+	0.995951i	$0.528653\pi$
$62$	−4.12545	+	5.67819i	−0.523932	+	0.721131i
$63$	3.64368	−	5.01509i	0.459061	−	0.631843i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	−0.567596	−	0.235440i	−0.0704016	−	0.0292027i
$66$	−0.412537	−	0.299725i	−0.0507797	−	0.0368936i
$67$	9.92494	−	3.22481i	1.21252	−	0.393973i	0.368170	−	0.929758i	$-0.379984\pi$
$67$	9.92494	−	3.22481i	1.21252	−	0.393973i	0.844354	+	0.535786i	$0.179984\pi$
$68$			6.40066i			0.776194i
$69$	−1.48104	−	4.55818i	−0.178297	−	0.548740i
$70$	−4.29373	−	3.67092i	−0.513199	−	0.438759i
$71$	0.993288	−	3.05703i	0.117882	−	0.362802i	−0.874656	−	0.484745i	$-0.838912\pi$
$71$	0.993288	−	3.05703i	0.117882	−	0.362802i	0.992537	+	0.121943i	$0.0389124\pi$
$72$	−2.33366	−	0.758252i	−0.275024	−	0.0893608i
$73$	−8.81748	−	12.1362i	−1.03201	−	1.42044i	−0.903429	−	0.428738i	$-0.858958\pi$
$73$	−8.81748	−	12.1362i	−1.03201	−	1.42044i	−0.128580	−	0.991699i	$-0.541042\pi$
$74$	5.48622			0.637760
$75$	−3.65051	+	0.574429i	−0.421524	+	0.0663294i
$76$	1.00000			0.114708
$77$	1.02452	+	1.41013i	0.116755	+	0.160699i
$78$	−0.193166	−	0.0627633i	−0.0218717	−	0.00710655i
$79$	−1.16332	+	3.58035i	−0.130884	+	0.402820i	−0.994927	−	0.100598i	$-0.967924\pi$
$79$	−1.16332	+	3.58035i	−0.130884	+	0.402820i	0.864043	+	0.503418i	$0.167924\pi$
$80$	−0.856742	+	2.06543i	−0.0957867	+	0.230922i
$81$	1.35416	+	4.16769i	0.150463	+	0.463077i
$82$			0.340470i			0.0375986i
$83$	1.67358	−	0.543781i	0.183700	−	0.0596877i	−0.215723	−	0.976455i	$-0.569211\pi$
$83$	1.67358	−	0.543781i	0.183700	−	0.0596877i	0.399422	+	0.916767i	$0.369211\pi$
$84$	−1.51058	−	1.09750i	−0.164817	−	0.119747i
$85$	−7.47204	−	12.2070i	−0.810456	−	1.32403i
$86$	−9.16085	+	6.65575i	−0.987840	+	0.717708i
$87$	1.57702	−	2.17058i	0.169074	−	0.232711i
$88$	0.405536	−	0.558172i	0.0432303	−	0.0595013i
$89$	−1.52476	+	1.10780i	−0.161624	+	0.117427i	−0.665658	−	0.746257i	$-0.731849\pi$
$89$	−1.52476	+	1.10780i	−0.161624	+	0.117427i	0.504033	+	0.863684i	$0.331849\pi$
$90$	5.33580	−	1.27818i	0.562443	−	0.134732i
$91$	0.561665	+	0.408074i	0.0588785	+	0.0427777i
$92$	6.16733	−	2.00389i	0.642989	−	0.208920i
$93$		−	5.18736i		−	0.537905i
$94$	−2.09265	−	6.44050i	−0.215840	−	0.664287i
$95$	−1.90715	+	1.16739i	−0.195669	+	0.119771i
$96$	−0.228390	+	0.702911i	−0.0233099	+	0.0717406i
$97$	5.07870	+	1.65017i	0.515664	+	0.167549i	0.555277	−	0.831666i	$-0.312612\pi$
$97$	5.07870	+	1.65017i	0.515664	+	0.167549i	−0.0396125	+	0.999215i	$0.512612\pi$
$98$	−0.363041	−	0.499683i	−0.0366727	−	0.0504756i
$99$	−1.69294			−0.170147
$100$	−0.777217	−	4.93922i	−0.0777217	−	0.493922i
$101$	8.16489			0.812437			0.406218	−	0.913776i	$-0.366847\pi$
$101$	8.16489			0.812437			0.406218	+	0.913776i	$0.366847\pi$
$102$	−2.78059	−	3.82716i	−0.275320	−	0.378945i
$103$	−2.15453	−	0.700050i	−0.212292	−	0.0689780i	0.200940	−	0.979604i	$-0.435600\pi$
$103$	−2.15453	−	0.700050i	−0.212292	−	0.0689780i	−0.413233	+	0.910626i	$0.635600\pi$
$104$	0.0849203	−	0.261358i	0.00832712	−	0.0256282i
$105$	4.16209	+	0.329665i	0.406179	+	0.0321720i
$106$	1.82404	+	5.61381i	0.177166	+	0.545261i
$107$		−	15.7544i		−	1.52304i	−0.648144	−	0.761518i	$-0.724455\pi$
$107$		−	15.7544i		−	1.52304i	0.648144	−	0.761518i	$-0.275545\pi$
$108$	3.83351	−	1.24558i	0.368879	−	0.119856i
$109$	8.58005	+	6.23377i	0.821820	+	0.597087i	0.917233	−	0.398351i	$-0.130417\pi$
$109$	8.58005	+	6.23377i	0.821820	+	0.597087i	−0.0954135	+	0.995438i	$0.530417\pi$
$110$	−0.121814	+	1.53793i	−0.0116145	+	0.146636i
$111$	−3.28039	+	2.38334i	−0.311361	+	0.226217i
$112$	1.48494	−	2.04385i	0.140314	−	0.193125i
$113$	−8.24838	+	11.3529i	−0.775943	+	1.06799i	0.219775	+	0.975550i	$0.429468\pi$
$113$	−8.24838	+	11.3529i	−0.775943	+	1.06799i	−0.995718	+	0.0924428i	$0.970532\pi$
$114$	−0.597932	+	0.434423i	−0.0560015	+	0.0406875i
$115$	−9.42270	+	11.0214i	−0.878671	+	1.02775i
$116$	2.93685	+	2.13375i	0.272680	+	0.198114i
$117$	−0.641308	+	0.208374i	−0.0592889	+	0.0192641i
$118$			1.93585i			0.178209i
$119$	4.99686	+	15.3788i	0.458062	+	1.40977i
$120$	−0.384996	−	1.60717i	−0.0351452	−	0.146714i
$121$	−3.25209	+	10.0089i	−0.295645	+	0.909900i
$122$	9.77719	+	3.17680i	0.885185	+	0.287614i
$123$	−0.147908	−	0.203578i	−0.0133364	−	0.0183560i
$124$	7.01863			0.630292
$125$	7.24825	+	8.51252i	0.648303	+	0.761383i
$126$	−6.19900			−0.552251
$127$	−12.7024	−	17.4834i	−1.12716	−	1.55140i	−0.793360	−	0.608753i	$-0.791670\pi$
$127$	−12.7024	−	17.4834i	−1.12716	−	1.55140i	−0.333797	−	0.942645i	$-0.608330\pi$
$128$	−0.951057	−	0.309017i	−0.0840623	−	0.0273135i
$129$	2.58616	−	7.95937i	0.227698	−	0.700783i
$130$	0.143150	+	0.597583i	0.0125551	+	0.0524115i
$131$	2.46960	+	7.60063i	0.215770	+	0.664070i	0.999098	+	0.0424625i	$0.0135203\pi$
$131$	2.46960	+	7.60063i	0.215770	+	0.664070i	−0.783329	+	0.621608i	$0.786480\pi$
$132$			0.509923i			0.0443831i
$133$	2.40269	−	0.780680i	0.208339	−	0.0676935i
$134$	−8.44266	−	6.13395i	−0.729334	−	0.529892i
$135$	−5.85699	+	6.85069i	−0.504089	+	0.589613i
$136$	5.17824	−	3.76221i	0.444031	−	0.322607i
$137$	7.15323	−	9.84558i	0.611142	−	0.841164i	−0.385529	−	0.922696i	$-0.625981\pi$
$137$	7.15323	−	9.84558i	0.611142	−	0.841164i	0.996671	+	0.0815312i	$0.0259810\pi$
$138$	−2.81711	+	3.87742i	−0.239808	+	0.330068i
$139$	−1.62143	+	1.17804i	−0.137528	+	0.0999200i	−0.654422	−	0.756129i	$-0.727088\pi$
$139$	−1.62143	+	1.17804i	−0.137528	+	0.0999200i	0.516894	+	0.856049i	$0.327088\pi$
$140$	−0.446045	+	5.63141i	−0.0376977	+	0.475941i
$141$	4.04916	+	2.94189i	0.341001	+	0.247752i
$142$	−3.05703	+	0.993288i	−0.256540	+	0.0833549i
$143$		−	0.189601i		−	0.0158552i
$144$	0.758252	+	2.33366i	0.0631876	+	0.194472i
$145$	−8.09192	−	0.640933i	−0.671997	−	0.0532266i
$146$	−4.63563	+	14.2670i	−0.383647	+	1.18074i
$147$	0.434148	+	0.141063i	0.0358079	+	0.0116347i
$148$	−3.22472	−	4.43844i	−0.265070	−	0.364838i
$149$	−9.00402			−0.737638			−0.368819	−	0.929501i	$-0.620238\pi$
$149$	−9.00402			−0.737638			−0.368819	+	0.929501i	$0.620238\pi$
$150$	2.61044	+	2.61568i	0.213141	+	0.213569i
$151$	16.9735			1.38129			0.690643	−	0.723195i	$-0.257327\pi$
$151$	16.9735			1.38129			0.690643	+	0.723195i	$0.257327\pi$
$152$	−0.587785	−	0.809017i	−0.0476757	−	0.0656199i
$153$	−14.9370	−	4.85331i	−1.20758	−	0.392367i
$154$	0.538621	−	1.65771i	0.0434033	−	0.133582i
$155$	−13.3856	+	8.19345i	−1.07515	+	0.658114i
$156$	0.0627633	+	0.193166i	0.00502509	+	0.0154656i
$157$			6.63957i			0.529895i	0.964263	+	0.264948i	$0.0853547\pi$
$157$			6.63957i			0.529895i	−0.964263	+	0.264948i	$0.914645\pi$
$158$	3.58035	−	1.16332i	0.284837	−	0.0925491i
$159$	−3.52942	−	2.56427i	−0.279901	−	0.203360i
$160$	2.17455	−	0.520909i	0.171913	−	0.0411815i
$161$	13.2538	−	9.62942i	1.04454	−	0.758905i
$162$	2.57577	−	3.54525i	0.202372	−	0.278541i
$163$	6.23289	−	8.57884i	0.488198	−	0.671947i	−0.491856	−	0.870676i	$-0.663681\pi$
$163$	6.23289	−	8.57884i	0.488198	−	0.671947i	0.980054	+	0.198729i	$0.0636815\pi$
$164$	0.275446	−	0.200123i	0.0215087	−	0.0156270i
$165$	−0.595277	−	0.972499i	−0.0463423	−	0.0757089i
$166$	−1.42364	−	1.03433i	−0.110496	−	0.0802798i
$167$	1.03200	−	0.335317i	0.0798584	−	0.0259476i	−0.268815	−	0.963192i	$-0.586632\pi$
$167$	1.03200	−	0.335317i	0.0798584	−	0.0259476i	0.348674	+	0.937244i	$0.386632\pi$
$168$			1.86717i			0.144056i
$169$	3.99388	+	12.2919i	0.307222	+	0.945532i
$170$	−5.48372	+	13.2201i	−0.420582	+	1.01394i
$171$	−0.758252	+	2.33366i	−0.0579849	+	0.178459i
$172$	10.7692	+	3.49913i	0.821146	+	0.266806i
$173$	10.5277	+	14.4901i	0.800406	+	1.10166i	0.992734	+	0.120333i	$0.0383963\pi$
$173$	10.5277	+	14.4901i	0.800406	+	1.10166i	−0.192328	+	0.981331i	$0.561604\pi$
$174$	−2.68299			−0.203397
$175$	−5.72336	−	11.2606i	−0.432645	−	0.851225i
$176$	−0.689939			−0.0520061
$177$	−0.840977	−	1.15751i	−0.0632117	−	0.0870034i
$178$	1.79246	+	0.582407i	0.134351	+	0.0436533i
$179$	−0.821855	+	2.52941i	−0.0614283	+	0.189057i	−0.977061	−	0.212958i	$-0.931690\pi$
$179$	−0.821855	+	2.52941i	−0.0614283	+	0.189057i	0.915633	+	0.402015i	$0.131690\pi$
$180$	−4.17038	−	3.56546i	−0.310842	−	0.265754i
$181$	2.30786	+	7.10287i	0.171542	+	0.527952i	0.999459	−	0.0328992i	$-0.0104740\pi$
$181$	2.30786	+	7.10287i	0.171542	+	0.527952i	−0.827917	+	0.560851i	$0.810474\pi$
$182$		−	0.694256i		−	0.0514617i
$183$	−7.22617	+	2.34793i	−0.534174	+	0.173564i
$184$	−5.24624	−	3.81162i	−0.386758	−	0.280996i
$185$	11.3314	+	4.70028i	0.833100	+	0.345571i
$186$	−4.19667	+	3.04906i	−0.307714	+	0.223568i
$187$	2.59570	−	3.57267i	0.189816	−	0.261259i
$188$	−3.98045	+	5.47862i	−0.290304	+	0.399569i
$189$	8.23831	−	5.98548i	0.599249	−	0.435380i
$190$	2.06543	+	0.856742i	0.149842	+	0.0621546i
$191$	−10.5556	−	7.66909i	−0.763776	−	0.554916i	0.136290	−	0.990669i	$-0.456482\pi$
$191$	−10.5556	−	7.66909i	−0.763776	−	0.554916i	−0.900066	+	0.435753i	$0.856482\pi$
$192$	0.702911	−	0.228390i	0.0507283	−	0.0164826i
$193$		−	15.0489i		−	1.08325i	−0.840621	−	0.541623i	$-0.817810\pi$
$193$		−	15.0489i		−	1.08325i	0.840621	−	0.541623i	$-0.182190\pi$
$194$	−1.65017	−	5.07870i	−0.118475	−	0.364630i
$195$	−0.345198	−	0.295126i	−0.0247201	−	0.0211344i
$196$	−0.190862	+	0.587413i	−0.0136330	+	0.0419581i
$197$	24.5440	+	7.97482i	1.74869	+	0.568182i	0.995931	−	0.0901194i	$-0.0287249\pi$
$197$	24.5440	+	7.97482i	1.74869	+	0.568182i	0.752754	+	0.658302i	$0.228725\pi$
$198$	0.995085	+	1.36962i	0.0707176	+	0.0973344i
$199$	3.12830			0.221759			0.110880	−	0.993834i	$-0.464633\pi$
$199$	3.12830			0.221759			0.110880	+	0.993834i	$0.464633\pi$
$200$	−3.53908	+	3.53198i	−0.250251	+	0.249749i
$201$	7.71287			0.544024
$202$	−4.79920	−	6.60553i	−0.337671	−	0.464764i
$203$	8.72211	+	2.83398i	0.612172	+	0.198907i
$204$	−1.46184	+	4.49910i	−0.102350	+	0.315000i
$205$	−0.291695	+	0.703216i	−0.0203729	+	0.0491148i
$206$	0.700050	+	2.15453i	0.0487748	+	0.150113i
$207$			15.9119i			1.10595i
$208$	−0.261358	+	0.0849203i	−0.0181219	+	0.00588817i
$209$	−0.558172	−	0.405536i	−0.0386096	−	0.0280515i
$210$	−2.17971	−	3.56098i	−0.150414	−	0.245731i
$211$	−17.5508	+	12.7514i	−1.20824	+	0.877841i	−0.995070	−	0.0991730i	$-0.968380\pi$
$211$	−17.5508	+	12.7514i	−1.20824	+	0.877841i	−0.213174	+	0.977014i	$0.568380\pi$
$212$	3.46952	−	4.77539i	0.238288	−	0.327975i
$213$	1.39639	−	1.92196i	0.0956789	−	0.131691i
$214$	−12.7456	+	9.26021i	−0.871270	+	0.633015i
$215$	−24.6233	+	5.89848i	−1.67930	+	0.402273i
$216$	−3.26097	−	2.36924i	−0.221881	−	0.161206i
$217$	16.8636	−	5.47930i	1.14477	−	0.371959i
$218$		−	10.6055i		−	0.718297i
$219$	−3.42612	−	10.5445i	−0.231516	−	0.712532i
$220$	1.31581	−	0.805425i	0.0887122	−	0.0543017i
$221$	0.543546	−	1.67286i	0.0365629	−	0.112529i
$222$	3.85633	+	1.25300i	0.258820	+	0.0840956i
$223$	6.02445	+	8.29195i	0.403427	+	0.555270i	0.961600	−	0.274455i	$-0.0884974\pi$
$223$	6.02445	+	8.29195i	0.403427	+	0.555270i	−0.558173	+	0.829725i	$0.688497\pi$
$224$	−2.52633			−0.168798
$225$	12.1158	+	1.93142i	0.807719	+	0.128761i
$226$	14.0330			0.933460
$227$	16.8629	+	23.2097i	1.11923	+	1.54048i	0.807071	+	0.590454i	$0.201051\pi$
$227$	16.8629	+	23.2097i	1.11923	+	1.54048i	0.312157	+	0.950031i	$0.398949\pi$
$228$	0.702911	+	0.228390i	0.0465514	+	0.0151255i
$229$	−1.79515	+	5.52492i	−0.118627	+	0.365097i	−0.992686	−	0.120723i	$-0.961479\pi$
$229$	−1.79515	+	5.52492i	−0.118627	+	0.365097i	0.874059	+	0.485820i	$0.161479\pi$
$230$	14.4550	+	1.14493i	0.953134	+	0.0754944i
$231$	0.398087	+	1.22518i	0.0261922	+	0.0806113i
$232$		−	3.63015i		−	0.238331i
$233$	2.08848	−	0.678588i	0.136821	−	0.0444558i	−0.239806	−	0.970821i	$-0.577084\pi$
$233$	2.08848	−	0.678588i	0.136821	−	0.0444558i	0.376627	+	0.926365i	$0.377084\pi$
$234$	0.545529	+	0.396350i	0.0356623	+	0.0259102i
$235$	1.19564	−	15.0953i	0.0779951	−	0.984706i
$236$	1.56613	−	1.13786i	0.101947	−	0.0740685i
$237$	−1.63543	+	2.25097i	−0.106232	+	0.146216i
$238$	9.50460	−	13.0820i	0.616092	−	0.847978i
$239$	1.24681	−	0.905859i	0.0806493	−	0.0585952i	−0.546730	−	0.837309i	$-0.684128\pi$
$239$	1.24681	−	0.905859i	0.0806493	−	0.0585952i	0.627379	+	0.778714i	$0.284128\pi$
$240$	−1.07394	+	1.25614i	−0.0693223	+	0.0810836i
$241$	13.7153	+	9.96472i	0.883478	+	0.641884i	0.934169	−	0.356830i	$-0.116143\pi$
$241$	13.7153	+	9.96472i	0.883478	+	0.641884i	−0.0506916	+	0.998714i	$0.516143\pi$
$242$	10.0089	−	3.25209i	0.643397	−	0.209052i
$243$			15.3312i			0.983494i
$244$	−3.17680	−	9.77719i	−0.203374	−	0.625920i
$245$	−0.321735	−	1.34309i	−0.0205549	−	0.0858070i
$246$	−0.0777599	+	0.239320i	−0.00495779	+	0.0152585i
$247$	−0.261358	−	0.0849203i	−0.0166298	−	0.00540335i
$248$	−4.12545	−	5.67819i	−0.261966	−	0.360566i
$249$	1.30058			0.0824207
$250$	2.62636	−	10.8675i	0.166105	−	0.687320i
$251$	11.9196			0.752358			0.376179	−	0.926547i	$-0.377238\pi$
$251$	11.9196			0.752358			0.376179	+	0.926547i	$0.377238\pi$
$252$	3.64368	+	5.01509i	0.229530	+	0.315921i
$253$	−4.25508	−	1.38256i	−0.267515	−	0.0869208i
$254$	−6.67805	+	20.5529i	−0.419018	+	1.28961i
$255$	−2.46423	−	10.2870i	−0.154316	−	0.644195i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$			5.73538i			0.357763i	0.983871	+	0.178881i	$0.0572479\pi$
$257$			5.73538i			0.357763i	−0.983871	+	0.178881i	$0.942752\pi$
$258$	−7.95937	+	2.58616i	−0.495529	+	0.161007i
$259$	−11.2130	−	8.14671i	−0.696741	−	0.506212i
$260$	0.399313	−	0.467061i	0.0247644	−	0.0289659i
$261$	−7.20631	+	5.23569i	−0.446060	+	0.324081i
$262$	4.69745	−	6.46548i	0.290209	−	0.399439i
$263$	8.88993	−	12.2359i	0.548176	−	0.754500i	−0.441587	−	0.897218i	$-0.645584\pi$
$263$	8.88993	−	12.2359i	0.548176	−	0.754500i	0.989763	+	0.142718i	$0.0455843\pi$
$264$	0.412537	−	0.299725i	0.0253899	−	0.0184468i
$265$	−1.04217	+	13.1576i	−0.0640201	+	0.808268i
$266$	−2.04385	−	1.48494i	−0.125316	−	0.0910476i
$267$	−1.32478	+	0.430448i	−0.0810754	+	0.0263430i
$268$			10.4357i			0.637462i
$269$	5.63449	+	17.3412i	0.343541	+	1.05731i	0.962360	+	0.271777i	$0.0876112\pi$
$269$	5.63449	+	17.3412i	0.343541	+	1.05731i	−0.618820	+	0.785533i	$0.712389\pi$
$270$	8.98497	+	0.711668i	0.546808	+	0.0433108i
$271$	3.65363	−	11.2447i	0.221942	−	0.683067i	−0.776646	−	0.629938i	$-0.783080\pi$
$271$	3.65363	−	11.2447i	0.221942	−	0.683067i	0.998588	−	0.0531296i	$-0.0169197\pi$
$272$	−6.08739	−	1.97791i	−0.369102	−	0.119929i
$273$	0.301601	+	0.415118i	0.0182537	+	0.0251241i
$274$	−12.1698			−0.735205
$275$	−1.56921	+	3.07213i	−0.0946270	+	0.185256i
$276$	4.79275			0.288490
$277$	5.53141	+	7.61333i	0.332350	+	0.457441i	0.942188	−	0.335086i	$-0.108765\pi$
$277$	5.53141	+	7.61333i	0.332350	+	0.457441i	−0.609838	+	0.792526i	$0.708765\pi$
$278$	1.90611	+	0.619332i	0.114321	+	0.0371450i
$279$	−5.32189	+	16.3791i	−0.318613	+	0.980590i
$280$	4.81809	−	2.94920i	0.287936	−	0.176249i
$281$	2.54946	+	7.84645i	0.152088	+	0.468080i	0.997854	−	0.0654744i	$-0.0208561\pi$
$281$	2.54946	+	7.84645i	0.152088	+	0.468080i	−0.845766	+	0.533554i	$0.820856\pi$
$282$		−	5.00504i		−	0.298046i
$283$	14.0081	−	4.55152i	0.832697	−	0.270560i	0.138516	−	0.990360i	$-0.455767\pi$
$283$	14.0081	−	4.55152i	0.832697	−	0.270560i	0.694181	+	0.719800i	$0.255767\pi$
$284$	2.60046	+	1.88935i	0.154309	+	0.112112i
$285$	−1.60717	+	0.384996i	−0.0952008	+	0.0228052i
$286$	−0.153390	+	0.111444i	−0.00907015	+	0.00658985i
$287$	0.505578	−	0.695869i	0.0298433	−	0.0410758i
$288$	1.44228	−	1.98513i	0.0849872	−	0.116975i
$289$	19.3909	−	14.0883i	1.14064	−	0.828723i
$290$	4.23778	+	6.92323i	0.248851	+	0.406546i
$291$	3.19300	+	2.31985i	0.187177	+	0.135992i
$292$	14.2670	−	4.63563i	0.834912	−	0.271279i
$293$		−	27.5289i		−	1.60826i	−0.594455	−	0.804129i	$-0.702632\pi$
$293$		−	27.5289i		−	1.60826i	0.594455	−	0.804129i	$-0.297368\pi$
$294$	−0.141063	−	0.434148i	−0.00822697	−	0.0253200i
$295$	−1.65852	+	3.99835i	−0.0965629	+	0.232793i
$296$	−1.69533	+	5.21770i	−0.0985393	+	0.303273i
$297$	−2.64488	−	0.859375i	−0.153472	−	0.0498660i
$298$	5.29243	+	7.28440i	0.306582	+	0.421974i
$299$	−1.78205			−0.103059
$300$	0.581754	−	3.64935i	0.0335876	−	0.210695i
$301$	28.6068			1.64887
$302$	−9.97680	−	13.7319i	−0.574100	−	0.790181i
$303$	5.73919	+	1.86478i	0.329708	+	0.107129i
$304$	−0.309017	+	0.951057i	−0.0177233	+	0.0545468i
$305$	17.4724	+	14.9380i	1.00047	+	0.855346i
$306$	4.85331	+	14.9370i	0.277445	+	0.853889i
$307$			12.6213i			0.720336i	0.932888	+	0.360168i	$0.117281\pi$
$307$			12.6213i			0.720336i	−0.932888	+	0.360168i	$0.882719\pi$
$308$	−1.65771	+	0.538621i	−0.0944565	+	0.0306908i
$309$	−1.35456	−	0.984147i	−0.0770583	−	0.0559861i
$310$	14.4965	+	6.01316i	0.823344	+	0.341524i
$311$	13.1075	−	9.52317i	0.743259	−	0.540009i	−0.150471	−	0.988614i	$-0.548079\pi$
$311$	13.1075	−	9.52317i	0.743259	−	0.540009i	0.893730	+	0.448605i	$0.148079\pi$
$312$	0.119383	−	0.164317i	0.00675873	−	0.00930259i
$313$	18.5700	−	25.5595i	1.04964	−	1.44471i	0.160521	−	0.987032i	$-0.448683\pi$
$313$	18.5700	−	25.5595i	1.04964	−	1.44471i	0.889120	−	0.457674i	$-0.151317\pi$
$314$	5.37152	−	3.90264i	0.303133	−	0.220239i
$315$	−12.8036	−	5.31094i	−0.721400	−	0.299238i
$316$	−3.04562	−	2.21277i	−0.171330	−	0.124478i
$317$	−10.1178	+	3.28749i	−0.568275	+	0.184644i	−0.579041	−	0.815298i	$-0.696573\pi$
$317$	−10.1178	+	3.28749i	−0.568275	+	0.184644i	0.0107663	+	0.999942i	$0.496573\pi$
$318$			4.36260i			0.244643i
$319$	−0.773958	−	2.38200i	−0.0433333	−	0.133366i
$320$	−1.69959	−	1.45306i	−0.0950100	−	0.0812287i
$321$	3.59814	−	11.0740i	0.200829	−	0.618088i
$322$	−15.5807	−	5.06249i	−0.868280	−	0.282121i
$323$	−3.76221	−	5.17824i	−0.209335	−	0.288125i
$324$	−4.38217			−0.243454
$325$	−0.216309	+	1.35691i	−0.0119986	+	0.0752676i
$326$	−10.6040			−0.587303
$327$	4.60729	+	6.34138i	0.254783	+	0.350679i
$328$	−0.323806	−	0.105211i	−0.0178792	−	0.00580931i
$329$	−5.28672	+	16.2709i	−0.291466	+	0.897041i
$330$	−0.436873	+	1.05321i	−0.0240491	+	0.0579773i
$331$	7.22180	+	22.2264i	0.396946	+	1.22167i	0.927435	+	0.373983i	$0.122008\pi$
$331$	7.22180	+	22.2264i	0.396946	+	1.22167i	−0.530489	+	0.847692i	$0.677992\pi$
$332$			1.75971i			0.0965767i
$333$	12.8030	−	4.15993i	0.701598	−	0.227963i
$334$	−0.877870	−	0.637810i	−0.0480349	−	0.0348994i
$335$	−12.1825	−	19.9024i	−0.665600	−	1.08738i
$336$	1.51058	−	1.09750i	0.0824087	−	0.0598734i
$337$	5.64551	−	7.77037i	0.307530	−	0.423279i	−0.627079	−	0.778956i	$-0.715750\pi$
$337$	5.64551	−	7.77037i	0.307530	−	0.423279i	0.934609	+	0.355677i	$0.115750\pi$
$338$	7.59682	−	10.4561i	0.413212	−	0.568738i
$339$	−8.39077	+	6.09625i	−0.455724	+	0.331103i
$340$	13.9185	−	3.33416i	0.754838	−	0.180820i
$341$	−3.91760	−	2.84631i	−0.212150	−	0.154136i
$342$	2.33366	−	0.758252i	0.126190	−	0.0410015i
$343$			19.2447i			1.03912i
$344$	−3.49913	−	10.7692i	−0.188661	−	0.580638i
$345$	−9.14049	+	5.59499i	−0.492107	+	0.301224i
$346$	5.53474	−	17.0342i	0.297549	−	0.915763i
$347$	−2.40209	−	0.780486i	−0.128951	−	0.0418987i	0.243831	−	0.969818i	$-0.421596\pi$
$347$	−2.40209	−	0.780486i	−0.128951	−	0.0418987i	−0.372782	+	0.927919i	$0.621596\pi$
$348$	1.57702	+	2.17058i	0.0845372	+	0.116355i
$349$	−25.1639			−1.34699			−0.673496	−	0.739191i	$-0.735208\pi$
$349$	−25.1639			−1.34699			−0.673496	+	0.739191i	$0.735208\pi$
$350$	−5.74595	+	11.2491i	−0.307134	+	0.601292i
$351$	−1.10769			−0.0591242
$352$	0.405536	+	0.558172i	0.0216151	+	0.0297507i
$353$	−25.8869	−	8.41117i	−1.37782	−	0.447682i	−0.475869	−	0.879516i	$-0.657866\pi$
$353$	−25.8869	−	8.41117i	−1.37782	−	0.447682i	−0.901953	+	0.431835i	$0.857866\pi$
$354$	−0.442128	+	1.36073i	−0.0234988	+	0.0723219i
$355$	−7.16506	−	0.567519i	−0.380282	−	0.0301208i
$356$	−0.582407	−	1.79246i	−0.0308675	−	0.0950004i
$357$			11.9511i			0.632522i
$358$	2.52941	−	0.821855i	0.133683	−	0.0434364i
$359$	−18.4021	−	13.3699i	−0.971227	−	0.705638i	−0.0154962	−	0.999880i	$-0.504933\pi$
$359$	−18.4021	−	13.3699i	−0.971227	−	0.705638i	−0.955731	+	0.294242i	$0.904933\pi$
$360$	−0.433230	+	5.46963i	−0.0228332	+	0.288275i
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	4.38981	−	6.04206i	0.230723	−	0.317564i
$363$	−4.57186	+	6.29263i	−0.239961	+	0.330277i
$364$	−0.561665	+	0.408074i	−0.0294393	+	0.0213889i
$365$	−21.7977	+	25.4959i	−1.14094	+	1.33452i
$366$	6.14695	+	4.46602i	0.321306	+	0.233443i
$367$	−23.2227	+	7.54553i	−1.21222	+	0.393873i	−0.844242	−	0.535962i	$-0.819949\pi$
$367$	−23.2227	+	7.54553i	−1.21222	+	0.393873i	−0.367976	+	0.929835i	$0.619949\pi$
$368$			6.48471i			0.338039i
$369$	0.258162	+	0.794541i	0.0134394	+	0.0413621i
$370$	−2.85782	−	11.9300i	−0.148571	−	0.620213i
$371$	4.60812	−	14.1823i	0.239242	−	0.736311i
$372$	4.93348	+	1.60298i	0.255789	+	0.0831108i
$373$	11.0735	+	15.2414i	0.573364	+	0.789168i	0.992948	−	0.118548i	$-0.0378241\pi$
$373$	11.0735	+	15.2414i	0.573364	+	0.789168i	−0.419584	+	0.907716i	$0.637824\pi$
$374$	−4.41606			−0.228349
$375$	3.15070	+	7.63897i	0.162702	+	0.394475i
$376$	6.77194			0.349236
$377$	−0.586371	−	0.807070i	−0.0301996	−	0.0415662i
$378$	−9.68471	−	3.14675i	−0.498128	−	0.161852i
$379$	3.89411	−	11.9848i	0.200027	−	0.615620i	−0.799854	−	0.600195i	$-0.795090\pi$
$379$	3.89411	−	11.9848i	0.200027	−	0.615620i	0.999881	−	0.0154251i	$-0.00491017\pi$
$380$	−0.520909	−	2.17455i	−0.0267221	−	0.111552i
$381$	−4.93565	−	15.1904i	−0.252861	−	0.778226i
$382$			13.0474i			0.667565i
$383$	−19.4543	+	6.32109i	−0.994070	+	0.322993i	−0.760493	−	0.649346i	$-0.775043\pi$
$383$	−19.4543	+	6.32109i	−0.994070	+	0.322993i	−0.233576	+	0.972338i	$0.575043\pi$
$384$	−0.597932	−	0.434423i	−0.0305131	−	0.0221691i
$385$	2.53271	−	2.96241i	0.129079	−	0.150978i
$386$	−12.1748	+	8.84554i	−0.619683	+	0.450226i
$387$	−16.3316	+	22.4785i	−0.830180	+	1.14264i
$388$	−3.13881	+	4.32020i	−0.159349	+	0.219325i
$389$	6.47996	−	4.70797i	0.328547	−	0.238703i	−0.411267	−	0.911515i	$-0.634914\pi$
$389$	6.47996	−	4.70797i	0.328547	−	0.238703i	0.739814	+	0.672812i	$0.234914\pi$
$390$	−0.0358601	+	0.452742i	−0.00181585	+	0.0229255i
$391$	−33.5794	−	24.3969i	−1.69818	−	1.23380i
$392$	0.587413	−	0.190862i	0.0296688	−	0.00963999i
$393$			5.90660i			0.297949i
$394$	−7.97482	−	24.5440i	−0.401766	−	1.23651i
$395$	8.39161	+	0.664670i	0.422228	+	0.0334432i
$396$	0.523147	−	1.61008i	0.0262891	−	0.0809096i
$397$	−25.4295	−	8.26254i	−1.27627	−	0.414685i	−0.409005	−	0.912532i	$-0.634124\pi$
$397$	−25.4295	−	8.26254i	−1.27627	−	0.414685i	−0.867265	+	0.497847i	$0.834124\pi$
$398$	−1.83877	−	2.53085i	−0.0921690	−	0.126860i
$399$	1.86717			0.0934756
$400$	4.93765	+	0.787127i	0.246883	+	0.0393563i
$401$	−22.0782			−1.10253			−0.551266	−	0.834329i	$-0.685855\pi$
$401$	−22.0782			−1.10253			−0.551266	+	0.834329i	$0.685855\pi$
$402$	−4.53351	−	6.23984i	−0.226111	−	0.311215i
$403$	−1.83437	−	0.596024i	−0.0913767	−	0.0296901i
$404$	−2.52309	+	7.76527i	−0.125528	+	0.386337i
$405$	8.35744	−	5.11568i	0.415284	−	0.254200i
$406$	−2.83398	−	8.72211i	−0.140648	−	0.432871i
$407$			3.78515i			0.187623i
$408$	4.49910	−	1.46184i	0.222738	−	0.0723721i
$409$	−31.0341	−	22.5476i	−1.53454	−	1.11491i	−0.953648	−	0.300923i	$-0.902705\pi$
$409$	−31.0341	−	22.5476i	−1.53454	−	1.11491i	−0.580889	−	0.813983i	$-0.697295\pi$
$410$	0.740368	−	0.177354i	0.0365642	−	0.00875888i
$411$	7.27672	−	5.28684i	0.358934	−	0.260781i
$412$	1.33157	−	1.83276i	0.0656020	−	0.0902934i
$413$	2.87462	−	3.95657i	0.141451	−	0.194690i
$414$	12.8730	−	9.35278i	0.632673	−	0.459664i
$415$	−2.05426	−	3.35603i	−0.100840	−	0.164741i
$416$	0.222324	+	0.161528i	0.0109003	+	0.00791956i
$417$	−1.40877	+	0.457739i	−0.0689880	+	0.0224156i
$418$			0.689939i			0.0337460i
$419$	3.53301	+	10.8735i	0.172599	+	0.531205i	0.999516	−	0.0311193i	$-0.00990718\pi$
$419$	3.53301	+	10.8735i	0.172599	+	0.531205i	−0.826917	+	0.562325i	$0.809907\pi$
$420$	−1.59969	+	3.85651i	−0.0780568	+	0.188179i
$421$	−6.62300	+	20.3835i	−0.322785	+	0.993431i	0.649645	+	0.760238i	$0.274918\pi$
$421$	−6.62300	+	20.3835i	−0.322785	+	0.993431i	−0.972430	+	0.233193i	$0.925082\pi$
$422$	20.6322	+	6.70380i	1.00436	+	0.326336i
$423$	−9.76704	−	13.4432i	−0.474890	−	0.653630i
$424$	−5.90271			−0.286661
$425$	−22.6524	+	22.6070i	−1.09880	+	1.09660i
$426$	−2.37568			−0.115102
$427$	−15.2657	−	21.0114i	−0.738759	−	1.01681i
$428$	14.9833	+	4.86838i	0.724246	+	0.235322i
$429$	0.0433028	−	0.133272i	0.00209068	−	0.00643445i
$430$	19.2452	+	16.4537i	0.928086	+	0.793466i
$431$	1.01991	+	3.13896i	0.0491274	+	0.151199i	0.972611	−	0.232440i	$-0.0746709\pi$
$431$	1.01991	+	3.13896i	0.0491274	+	0.151199i	−0.923483	+	0.383638i	$0.874671\pi$
$432$			4.03079i			0.193931i
$433$	12.6845	−	4.12146i	0.609580	−	0.198065i	0.0120717	−	0.999927i	$-0.496157\pi$
$433$	12.6845	−	4.12146i	0.609580	−	0.198065i	0.597509	+	0.801862i	$0.296157\pi$
$434$	−14.3450	−	10.4223i	−0.688582	−	0.500284i
$435$	−5.54152	−	2.29863i	−0.265696	−	0.110211i
$436$	−8.58005	+	6.23377i	−0.410910	+	0.298543i
$437$	−3.81162	+	5.24624i	−0.182335	+	0.250962i
$438$	−6.51687	+	8.96970i	−0.311388	+	0.428589i
$439$	−16.3776	+	11.8990i	−0.781661	+	0.567910i	−0.905477	−	0.424395i	$-0.860487\pi$
$439$	−16.3776	+	11.8990i	−0.781661	+	0.567910i	0.123816	+	0.992305i	$0.460487\pi$
$440$	−1.42502	−	0.591100i	−0.0679351	−	0.0281796i
$441$	−1.22610	−	0.890814i	−0.0583857	−	0.0424197i
$442$	−1.67286	+	0.543546i	−0.0795700	+	0.0258538i
$443$		−	2.38504i		−	0.113317i	−0.998394	−	0.0566583i	$-0.981955\pi$
$443$		−	2.38504i		−	0.113317i	0.998394	−	0.0566583i	$-0.0180446\pi$
$444$	−1.25300	−	3.85633i	−0.0594646	−	0.183013i
$445$	3.20323	+	2.73860i	0.151848	+	0.129822i
$446$	3.16724	−	9.74777i	0.149973	−	0.461570i
$447$	−6.32903	−	2.05643i	−0.299353	−	0.0972656i
$448$	1.48494	+	2.04385i	0.0701569	+	0.0965627i
$449$	12.0383			0.568123			0.284062	−	0.958806i	$-0.408318\pi$
$449$	12.0383			0.568123			0.284062	+	0.958806i	$0.408318\pi$
$450$	−5.55893	−	10.9371i	−0.262051	−	0.515582i
$451$	−0.234903			−0.0110612
$452$	−8.24838	−	11.3529i	−0.387971	−	0.533997i
$453$	11.9309	+	3.87658i	0.560562	+	0.182138i
$454$	8.86533	−	27.2847i	0.416071	−	1.28053i
$455$	0.594799	−	1.43394i	0.0278846	−	0.0672240i
$456$	−0.228390	−	0.702911i	−0.0106953	−	0.0329168i
$457$		−	26.8796i		−	1.25737i	−0.777658	−	0.628687i	$-0.783593\pi$
$457$		−	26.8796i		−	1.25737i	0.777658	−	0.628687i	$-0.216407\pi$
$458$	5.52492	−	1.79515i	0.258162	−	0.0838820i
$459$	−20.8724	−	15.1647i	−0.974240	−	0.707826i
$460$	−7.57016	−	12.3673i	−0.352961	−	0.576629i
$461$	−17.9527	+	13.0434i	−0.836142	+	0.607493i	−0.921290	−	0.388875i	$-0.872864\pi$
$461$	−17.9527	+	13.0434i	−0.836142	+	0.607493i	0.0851480	+	0.996368i	$0.472864\pi$
$462$	0.757206	−	1.04220i	0.0352284	−	0.0484877i
$463$	−8.83919	+	12.1661i	−0.410792	+	0.565407i	−0.963411	−	0.268027i	$-0.913628\pi$
$463$	−8.83919	+	12.1661i	−0.410792	+	0.565407i	0.552619	+	0.833434i	$0.313628\pi$
$464$	−2.93685	+	2.13375i	−0.136340	+	0.0990568i
$465$	−11.2802	+	2.70214i	−0.523105	+	0.125309i
$466$	−1.77657	−	1.29075i	−0.0822979	−	0.0597929i
$467$	−7.27652	+	2.36428i	−0.336717	+	0.109406i	−0.472495	−	0.881333i	$-0.656647\pi$
$467$	−7.27652	+	2.36428i	−0.336717	+	0.109406i	0.135778	+	0.990739i	$0.456647\pi$
$468$		−	0.674311i		−	0.0311700i
$469$	8.14694	+	25.0737i	0.376191	+	1.15780i
$470$	−12.9151	+	7.90547i	−0.595729	+	0.364652i
$471$	−1.51641	+	4.66703i	−0.0698725	+	0.215045i
$472$	−1.84110	−	0.598210i	−0.0847435	−	0.0275348i
$473$	−4.59206	−	6.32042i	−0.211143	−	0.290613i
$474$	2.78236			0.127798
$475$	3.53198	+	3.53908i	0.162059	+	0.162384i
$476$	−16.1702			−0.741160
$477$	8.51336	+	11.7176i	0.389800	+	0.536514i
$478$	−1.46571	−	0.476238i	−0.0670401	−	0.0217826i
$479$	7.51862	−	23.1399i	0.343534	−	1.05729i	−0.618829	−	0.785525i	$-0.712393\pi$
$479$	7.51862	−	23.1399i	0.343534	−	1.05729i	0.962364	−	0.271765i	$-0.0876072\pi$
$480$	1.64748	+	0.130491i	0.0751970	+	0.00595609i
$481$	0.465892	+	1.43387i	0.0212428	+	0.0653787i
$482$		−	16.9530i		−	0.772188i
$483$	11.5155	−	3.74161i	0.523973	−	0.170249i
$484$	−8.51408	−	6.18584i	−0.387004	−	0.281175i
$485$	0.942832	−	11.9035i	0.0428118	−	0.540509i
$486$	12.4032	−	9.01143i	0.562619	−	0.408767i
$487$	−2.48024	+	3.41376i	−0.112391	+	0.154692i	−0.861506	−	0.507747i	$-0.830479\pi$
$487$	−2.48024	+	3.41376i	−0.112391	+	0.154692i	0.749116	+	0.662439i	$0.230479\pi$
$488$	−6.04263	+	8.31697i	−0.273537	+	0.376492i
$489$	6.34049	−	4.60664i	0.286727	−	0.208319i
$490$	−0.897473	+	1.04974i	−0.0405437	+	0.0474224i
$491$	−2.29321	−	1.66612i	−0.103491	−	0.0751908i	0.534836	−	0.844956i	$-0.320373\pi$
$491$	−2.29321	−	1.66612i	−0.103491	−	0.0751908i	−0.638327	+	0.769765i	$0.720373\pi$
$492$	0.239320	−	0.0777599i	0.0107894	−	0.00350569i
$493$		−	23.2353i		−	1.04647i
$494$	0.0849203	+	0.261358i	0.00382075	+	0.0117590i
$495$	0.881867	+	3.68138i	0.0396370	+	0.165466i
$496$	−2.16888	+	6.67511i	−0.0973854	+	0.299721i
$497$	7.72306	+	2.50938i	0.346427	+	0.112561i
$498$	−0.764459	−	1.05219i	−0.0342562	−	0.0471497i
$499$	28.4616			1.27412			0.637058	−	0.770816i	$-0.280151\pi$
$499$	28.4616			1.27412			0.637058	+	0.770816i	$0.280151\pi$
$500$	−10.3357	+	4.26298i	−0.462227	+	0.190646i
$501$	0.801986			0.0358301
$502$	−7.00616	−	9.64315i	−0.312700	−	0.430395i
$503$	38.5309	+	12.5194i	1.71801	+	0.558214i	0.991633	−	0.129087i	$-0.0412047\pi$
$503$	38.5309	+	12.5194i	1.71801	+	0.558214i	0.726373	+	0.687301i	$0.241205\pi$
$504$	1.91560	−	5.89560i	0.0853274	−	0.262611i
$505$	−4.25316	−	17.7549i	−0.189263	−	0.790084i
$506$	1.38256	+	4.25508i	0.0614623	+	0.189161i
$507$			9.55229i			0.424232i
$508$	20.5529	−	6.67805i	0.911889	−	0.296291i
$509$	3.11712	+	2.26472i	0.138164	+	0.100382i	0.654720	−	0.755871i	$-0.272786\pi$
$509$	3.11712	+	2.26472i	0.138164	+	0.100382i	−0.516556	+	0.856253i	$0.672786\pi$
$510$	−6.87390	+	8.04013i	−0.304381	+	0.356023i
$511$	30.6601	−	22.2759i	1.35632	−	0.985428i
$512$	0.587785	−	0.809017i	0.0259767	−	0.0357538i
$513$	−2.36924	+	3.26097i	−0.104604	+	0.143976i
$514$	4.64002	−	3.37117i	0.204662	−	0.148696i
$515$	−0.399977	+	5.04980i	−0.0176251	+	0.222521i
$516$	6.77064	+	4.91916i	0.298061	+	0.216554i
$517$	4.44355	−	1.44380i	0.195427	−	0.0634981i
$518$			13.8600i			0.608974i
$519$	4.09064	+	12.5897i	0.179559	+	0.552626i
$520$	−0.612571	−	0.0485196i	−0.0268630	−	0.00212772i
$521$	5.78704	−	17.8107i	0.253535	−	0.780300i	−0.740580	−	0.671968i	$-0.765449\pi$
$521$	5.78704	−	17.8107i	0.253535	−	0.780300i	0.994115	−	0.108332i	$-0.0345509\pi$
$522$	8.47153	+	2.75257i	0.370789	+	0.120477i
$523$	−21.9691	−	30.2379i	−0.960643	−	1.32221i	−0.946634	−	0.322310i	$-0.895541\pi$
$523$	−21.9691	−	30.2379i	−0.960643	−	1.32221i	−0.0140093	−	0.999902i	$-0.504459\pi$
$524$	−7.99178			−0.349122
$525$	−1.45120	−	9.22239i	−0.0633355	−	0.402498i
$526$	−15.1244			−0.659457
$527$	−26.4056	−	36.3442i	−1.15025	−	1.58318i
$528$	−0.484966	−	0.157575i	−0.0211054	−	0.00685757i
$529$	−5.88725	+	18.1191i	−0.255967	+	0.787786i
$530$	11.2573	−	6.89074i	0.488987	−	0.299314i
$531$	1.46786	+	4.51761i	0.0636997	+	0.196047i
$532$			2.52633i			0.109530i
$533$	−0.0889845	+	0.0289128i	−0.00385435	+	0.00125235i
$534$	1.12693	+	0.818761i	0.0487669	+	0.0354313i
$535$	−34.2587	+	8.20661i	−1.48113	+	0.354803i
$536$	8.44266	−	6.13395i	0.364667	−	0.264946i
$537$	−1.15538	+	1.59025i	−0.0498584	+	0.0686243i
$538$	10.7174	−	14.7513i	0.462061	−	0.635973i
$539$	0.344751	−	0.250476i	0.0148495	−	0.0107888i
$540$	−4.70548	−	7.68730i	−0.202492	−	0.330809i
$541$	−15.7897	−	11.4719i	−0.678852	−	0.493215i	0.194125	−	0.980977i	$-0.437813\pi$
$541$	−15.7897	−	11.4719i	−0.678852	−	0.493215i	−0.872976	+	0.487762i	$0.837813\pi$
$542$	−11.2447	+	3.65363i	−0.483002	+	0.156937i
$543$			5.51978i			0.236876i
$544$	1.97791	+	6.08739i	0.0848023	+	0.260995i
$545$	9.08620	−	21.9049i	0.389210	−	0.938305i
$546$	0.158561	−	0.488001i	0.00678579	−	0.0208845i
$547$	−21.8606	−	7.10292i	−0.934690	−	0.303699i	−0.198211	−	0.980159i	$-0.563513\pi$
$547$	−21.8606	−	7.10292i	−0.934690	−	0.303699i	−0.736479	+	0.676460i	$0.763513\pi$
$548$	7.15323	+	9.84558i	0.305571	+	0.420582i
$549$	25.2254			1.07659
$550$	3.40776	−	0.536232i	0.145307	−	0.0228650i
$551$	−3.63015			−0.154650
$552$	−2.81711	−	3.87742i	−0.119904	−	0.165034i
$553$	−9.04514	−	2.93895i	−0.384639	−	0.124977i
$554$	2.90803	−	8.95001i	0.123551	−	0.380249i
$555$	6.89147	+	5.89185i	0.292527	+	0.250095i
$556$	−0.619332	−	1.90611i	−0.0262655	−	0.0808369i
$557$			23.1060i			0.979031i	0.871995	+	0.489516i	$0.162826\pi$
$557$			23.1060i			0.979031i	−0.871995	+	0.489516i	$0.837174\pi$
$558$	16.3791	−	5.32189i	0.693382	−	0.225293i
$559$	−2.51747	−	1.82905i	−0.106478	−	0.0773607i
$560$	−5.21796	−	2.16442i	−0.220499	−	0.0914633i
$561$	2.64051	−	1.91844i	0.111482	−	0.0809966i
$562$	4.84937	−	6.67459i	0.204558	−	0.281550i
$563$	5.31119	−	7.31022i	0.223840	−	0.308089i	−0.682296	−	0.731076i	$-0.739018\pi$
$563$	5.31119	−	7.31022i	0.223840	−	0.308089i	0.906136	+	0.422987i	$0.139018\pi$
$564$	−4.04916	+	2.94189i	−0.170501	+	0.123876i
$565$	28.9841	+	12.0227i	1.21937	+	0.505797i
$566$	−11.9160	−	8.65751i	−0.500868	−	0.363902i
$567$	−10.5290	+	3.42107i	−0.442175	+	0.143671i
$568$		−	3.21435i		−	0.134871i
$569$	13.3447	+	41.0709i	0.559441	+	1.72178i	0.683918	+	0.729559i	$0.260275\pi$
$569$	13.3447	+	41.0709i	0.559441	+	1.72178i	−0.124477	+	0.992222i	$0.539725\pi$
$570$	1.25614	+	1.07394i	0.0526140	+	0.0449823i
$571$	6.62420	−	20.3872i	0.277214	−	0.853177i	−0.711411	−	0.702776i	$-0.751944\pi$
$571$	6.62420	−	20.3872i	0.277214	−	0.853177i	0.988625	−	0.150401i	$-0.0480565\pi$
$572$	0.180321	+	0.0585898i	0.00753960	+	0.00244976i
$573$	−5.66811	−	7.80148i	−0.236789	−	0.325911i
$574$	−0.860141			−0.0359016
$575$	28.8748	+	14.7490i	1.20416	+	0.615075i
$576$	−2.45375			−0.102240
$577$	−11.5454	−	15.8908i	−0.480640	−	0.661544i	0.497988	−	0.867184i	$-0.334072\pi$
$577$	−11.5454	−	15.8908i	−0.480640	−	0.661544i	−0.978628	+	0.205640i	$0.934072\pi$
$578$	−22.7953	−	7.40665i	−0.948161	−	0.308076i
$579$	3.43702	−	10.5781i	0.142838	−	0.439610i
$580$	3.11010	−	7.49781i	0.129140	−	0.311330i
$581$	1.37377	+	4.22803i	0.0569936	+	0.175408i
$582$		−	3.94676i		−	0.163598i
$583$	−3.87318	+	1.25847i	−0.160411	+	0.0521207i
$584$	−12.1362	−	8.81748i	−0.502201	−	0.364870i
$585$	0.787181	+	1.28601i	0.0325459	+	0.0531700i
$586$	−22.2714	+	16.1811i	−0.920022	+	0.668435i
$587$	2.81651	−	3.87659i	0.116250	−	0.160004i	−0.746927	−	0.664906i	$-0.768472\pi$
$587$	2.81651	−	3.87659i	0.116250	−	0.160004i	0.863176	+	0.504902i	$0.168472\pi$
$588$	−0.268318	+	0.369308i	−0.0110653	+	0.0152300i
$589$	−5.67819	+	4.12545i	−0.233966	+	0.169986i
$590$	4.20959	−	1.00840i	0.173306	−	0.0415152i
$591$	15.4309	+	11.2112i	0.634741	+	0.461166i
$592$	5.21770	−	1.69533i	0.214446	−	0.0696778i
$593$		−	22.4976i		−	0.923868i	−0.886914	−	0.461934i	$-0.847156\pi$
$593$		−	22.4976i		−	0.923868i	0.886914	−	0.461934i	$-0.152844\pi$
$594$	0.859375	+	2.64488i	0.0352606	+	0.108521i
$595$	30.8389	−	18.8769i	1.26427	−	0.773876i
$596$	2.78239	−	8.56333i	0.113971	−	0.350768i
$597$	2.19892	+	0.714471i	0.0899956	+	0.0292413i
$598$	1.04746	+	1.44171i	0.0428340	+	0.0589559i
$599$	25.9173			1.05895			0.529476	−	0.848325i	$-0.322389\pi$
$599$	25.9173			1.05895			0.529476	+	0.848325i	$0.322389\pi$
$600$	−3.29433	+	1.67438i	−0.134490	+	0.0683564i
$601$	19.3842			0.790697			0.395349	−	0.918531i	$-0.370624\pi$
$601$	19.3842			0.790697			0.395349	+	0.918531i	$0.370624\pi$
$602$	−16.8146	−	23.1434i	−0.685313	−	0.943253i
$603$	−24.3534	−	7.91288i	−0.991745	−	0.322238i
$604$	−5.24511	+	16.1428i	−0.213421	+	0.656841i
$605$	23.4589	+	1.85810i	0.953739	+	0.0755423i
$606$	−1.86478	−	5.73919i	−0.0757514	−	0.233139i
$607$			41.9220i			1.70156i	0.525519	+	0.850782i	$0.323871\pi$
$607$			41.9220i			1.70156i	−0.525519	+	0.850782i	$0.676129\pi$
$608$	0.951057	−	0.309017i	0.0385704	−	0.0125323i
$609$	5.48362	+	3.98408i	0.222207	+	0.161443i
$610$	1.81508	−	22.9158i	0.0734904	−	0.927833i
$611$	1.50557	−	1.09386i	0.0609088	−	0.0442528i
$612$	9.23154	−	12.7061i	0.373163	−	0.513615i
$613$	−2.11643	+	2.91301i	−0.0854816	+	0.117655i	−0.849616	−	0.527402i	$-0.823166\pi$
$613$	−2.11643	+	2.91301i	−0.0854816	+	0.117655i	0.764135	+	0.645057i	$0.223166\pi$
$614$	10.2108	−	7.41861i	0.412076	−	0.299391i
$615$	−0.365643	+	0.427679i	−0.0147442	+	0.0172457i
$616$	1.41013	+	1.02452i	0.0568157	+	0.0412790i
$617$	29.2786	−	9.51321i	1.17871	−	0.382987i	0.346825	−	0.937930i	$-0.387260\pi$
$617$	29.2786	−	9.51321i	1.17871	−	0.382987i	0.831889	+	0.554942i	$0.187260\pi$
$618$			1.67433i			0.0673514i
$619$	−14.0646	−	43.2863i	−0.565302	−	1.73982i	−0.667052	−	0.745011i	$-0.732444\pi$
$619$	−14.0646	−	43.2863i	−0.565302	−	1.73982i	0.101749	−	0.994810i	$-0.467556\pi$
$620$	−3.65607	−	15.2623i	−0.146831	−	0.612950i
$621$	−8.07724	+	24.8592i	−0.324129	+	0.997565i
$622$	−15.4088	−	5.00663i	−0.617837	−	0.200747i
$623$	−2.79868	−	3.85205i	−0.112127	−	0.154329i
$624$	−0.203106			−0.00813076
$625$	14.7352	−	20.1959i	0.589408	−	0.807836i
$626$	−31.5932			−1.26272
$627$	−0.299725	−	0.412537i	−0.0119699	−	0.0164751i
$628$	−6.31461	−	2.05174i	−0.251980	−	0.0818733i
$629$	−10.8513	+	33.3967i	−0.432668	+	1.33162i
$630$	3.22911	+	13.4800i	0.128651	+	0.537057i
$631$	−1.62810	−	5.01078i	−0.0648137	−	0.199476i	0.913405	−	0.407051i	$-0.133443\pi$
$631$	−1.62810	−	5.01078i	−0.0648137	−	0.199476i	−0.978219	+	0.207575i	$0.933443\pi$
$632$			3.76460i			0.149748i
$633$	−15.2489	+	4.95467i	−0.606090	+	0.196931i
$634$	8.60675	+	6.25317i	0.341818	+	0.248345i
$635$	−31.4016	+	36.7292i	−1.24613	+	1.45756i
$636$	3.52942	−	2.56427i	0.139951	−	0.101680i
$637$	0.0997666	−	0.137317i	0.00395290	−	0.00544070i
$638$	−1.47216	+	2.02625i	−0.0582832	+	0.0802199i
$639$	−6.38089	+	4.63599i	−0.252424	+	0.183397i
$640$	−0.176558	+	2.22909i	−0.00697907	+	0.0881124i
$641$	13.6268	+	9.90043i	0.538225	+	0.391043i	0.823425	−	0.567425i	$-0.192060\pi$
$641$	13.6268	+	9.90043i	0.538225	+	0.391043i	−0.285200	+	0.958468i	$0.592060\pi$
$642$	−11.0740	+	3.59814i	−0.437054	+	0.142007i
$643$		−	25.9240i		−	1.02234i	−0.859479	−	0.511172i	$-0.829212\pi$
$643$		−	25.9240i		−	1.02234i	0.859479	−	0.511172i	$-0.170788\pi$
$644$	5.06249	+	15.5807i	0.199490	+	0.613967i
$645$	−18.6552	−	1.47761i	−0.734547	−	0.0581809i
$646$	−1.97791	+	6.08739i	−0.0778199	+	0.239505i
$647$	19.1033	+	6.20704i	0.751029	+	0.244024i	0.659424	−	0.751771i	$-0.270800\pi$
$647$	19.1033	+	6.20704i	0.751029	+	0.244024i	0.0916051	+	0.995795i	$0.470800\pi$
$648$	2.57577	+	3.54525i	0.101186	+	0.139270i
$649$	−1.33562			−0.0524275
$650$	1.22490	−	0.622572i	0.0480447	−	0.0244193i
$651$	13.1050			0.513626
$652$	6.23289	+	8.57884i	0.244099	+	0.335973i
$653$	−11.1186	−	3.61264i	−0.435103	−	0.141374i	0.0832721	−	0.996527i	$-0.473463\pi$
$653$	−11.1186	−	3.61264i	−0.435103	−	0.141374i	−0.518375	+	0.855153i	$0.673463\pi$
$654$	2.42219	−	7.45474i	0.0947152	−	0.291504i
$655$	15.2415	−	9.32949i	0.595535	−	0.364533i
$656$	0.105211	+	0.323806i	0.00410780	+	0.0126425i
$657$			36.8092i			1.43607i
$658$	16.2709	−	5.28672i	0.634304	−	0.206098i
$659$	−25.1255	−	18.2548i	−0.978752	−	0.711105i	−0.0213226	−	0.999773i	$-0.506788\pi$
$659$	−25.1255	−	18.2548i	−0.978752	−	0.711105i	−0.957429	+	0.288668i	$0.906788\pi$
$660$	1.10885	−	0.265624i	0.0431620	−	0.0103394i
$661$	−20.0933	+	14.5986i	−0.781538	+	0.567820i	−0.905440	−	0.424474i	$-0.860459\pi$
$661$	−20.0933	+	14.5986i	−0.781538	+	0.567820i	0.123902	+	0.992294i	$0.460459\pi$
$662$	13.7367	−	18.9069i	0.533892	−	0.734839i
$663$	0.764129	−	1.05173i	0.0296763	−	0.0408460i
$664$	1.42364	−	1.03433i	0.0552478	−	0.0401399i
$665$	−2.94920	−	4.81809i	−0.114365	−	0.186837i
$666$	−10.8908	−	7.91267i	−0.422012	−	0.306610i
$667$	−22.3883	+	7.27441i	−0.866880	+	0.281666i
$668$			1.08511i			0.0419841i
$669$	2.34086	+	7.20443i	0.0905029	+	0.278539i
$670$	−8.94070	+	21.5542i	−0.345410	+	0.832711i
$671$	−2.19180	+	6.74566i	−0.0846134	+	0.260413i
$672$	−1.77579	−	0.576989i	−0.0685025	−	0.0222578i
$673$	18.9777	+	26.1206i	0.731538	+	1.00688i	0.999061	+	0.0433244i	$0.0137949\pi$
$673$	18.9777	+	26.1206i	0.731538	+	1.00688i	−0.267523	+	0.963551i	$0.586205\pi$
$674$	−9.60471			−0.369960
$675$	17.9481	+	9.16771i	0.690823	+	0.352865i
$676$	−12.9245			−0.497095
$677$	18.3532	+	25.2610i	0.705371	+	0.970860i	0.999884	+	0.0152122i	$0.00484238\pi$
$677$	18.3532	+	25.2610i	0.705371	+	0.970860i	−0.294514	+	0.955647i	$0.595158\pi$
$678$	9.86395	+	3.20499i	0.378823	+	0.123087i
$679$	−4.16888	+	12.8305i	−0.159987	+	0.492389i
$680$	−10.8785	−	9.30056i	−0.417171	−	0.356660i
$681$	6.55223	+	20.1657i	0.251082	+	0.772751i
$682$			4.84242i			0.185426i
$683$	−8.99194	+	2.92166i	−0.344067	+	0.111794i	−0.475953	−	0.879471i	$-0.657897\pi$
$683$	−8.99194	+	2.92166i	−0.344067	+	0.111794i	0.131886	+	0.991265i	$0.457897\pi$
$684$	−1.98513	−	1.44228i	−0.0759033	−	0.0551470i
$685$	−25.1359	−	10.4264i	−0.960392	−	0.398372i
$686$	15.5693	−	11.3118i	0.594438	−	0.431885i
$687$	−2.52367	+	3.47353i	−0.0962840	+	0.132524i
$688$	−6.65575	+	9.16085i	−0.253748	+	0.349254i
$689$	−1.31232	+	0.953453i	−0.0499952	+	0.0363237i
$690$	9.89909	+	4.10616i	0.376852	+	0.156319i
$691$	35.3495	+	25.6829i	1.34476	+	0.977024i	0.999254	+	0.0386070i	$0.0122920\pi$
$691$	35.3495	+	25.6829i	1.34476	+	0.977024i	0.345504	+	0.938417i	$0.387708\pi$
$692$	−17.0342	+	5.53474i	−0.647542	+	0.210399i
$693$		−	4.27693i		−	0.162467i
$694$	0.780486	+	2.40209i	0.0296269	+	0.0911821i
$695$	3.40632	+	2.91223i	0.129209	+	0.110467i
$696$	0.829089	−	2.55167i	0.0314265	−	0.0967209i
$697$	−2.07257	−	0.673420i	−0.0785043	−	0.0255076i
$698$	14.7910	+	20.3580i	0.559846	+	0.770563i
$699$	1.62300			0.0613875
$700$	12.4781	−	1.96351i	0.471629	−	0.0742137i
$701$	−10.9684			−0.414270			−0.207135	−	0.978312i	$-0.566414\pi$
$701$	−10.9684			−0.414270			−0.207135	+	0.978312i	$0.566414\pi$
$702$	0.651085	+	0.896142i	0.0245736	+	0.0338227i
$703$	5.21770	+	1.69533i	0.196789	+	0.0639408i
$704$	0.213203	−	0.656171i	0.00803538	−	0.0247304i
$705$	4.28803	−	10.3376i	0.161497	−	0.389335i
$706$	8.41117	+	25.8869i	0.316559	+	0.974267i
$707$			20.6272i			0.775767i
$708$	1.36073	−	0.442128i	0.0511393	−	0.0166162i
$709$	−18.5722	−	13.4935i	−0.697494	−	0.506759i	0.181621	−	0.983369i	$-0.441866\pi$
$709$	−18.5722	−	13.4935i	−0.697494	−	0.506759i	−0.879115	+	0.476609i	$0.841866\pi$
$710$	3.75238	+	6.13023i	0.140824	+	0.230064i
$711$	7.47321	−	5.42960i	0.280267	−	0.203626i
$712$	−1.10780	+	1.52476i	−0.0415167	+	0.0571429i
$713$	−26.7524	+	36.8215i	−1.00188	+	1.37897i
$714$	9.66868	−	7.02471i	0.361841	−	0.262893i
$715$	−0.412295	+	0.0987646i	−0.0154190	+	0.00369359i
$716$	−2.15164	−	1.56326i	−0.0804107	−	0.0584218i
$717$	1.08328	−	0.351981i	0.0404560	−	0.0131450i
$718$			22.7463i			0.848884i
$719$	−8.63698	−	26.5819i	−0.322105	−	0.991337i	−0.972730	−	0.231938i	$-0.925493\pi$
$719$	−8.63698	−	26.5819i	−0.322105	−	0.991337i	0.650625	−	0.759399i	$-0.274507\pi$
$720$	4.67967	−	2.86448i	0.174401	−	0.106753i
$721$	1.76856	−	5.44307i	0.0658646	−	0.202710i
$722$	0.951057	+	0.309017i	0.0353947	+	0.0115004i
$723$	7.36477	+	10.1367i	0.273899	+	0.376989i
$724$	−7.46840			−0.277561
$725$	2.82141	+	17.9301i	0.104785	+	0.665908i
$726$	7.77812			0.288673
$727$	−3.40766	−	4.69025i	−0.126383	−	0.173952i	0.741136	−	0.671354i	$-0.234287\pi$
$727$	−3.40766	−	4.69025i	−0.126383	−	0.173952i	−0.867520	+	0.497403i	$0.834287\pi$
$728$	0.660277	+	0.214537i	0.0244715	+	0.00795127i
$729$	0.561014	−	1.72662i	0.0207783	−	0.0639490i
$730$	33.4390	+	2.64858i	1.23763	+	0.0980285i
$731$	−22.3968	−	68.9301i	−0.828374	−	2.54947i
$732$		−	7.59804i		−	0.280832i
$733$	−32.2426	+	10.4763i	−1.19091	+	0.386950i	−0.836409	−	0.548107i	$-0.815349\pi$
$733$	−32.2426	+	10.4763i	−1.19091	+	0.386950i	−0.354500	+	0.935056i	$0.615349\pi$
$734$	19.7544	+	14.3524i	0.729150	+	0.529759i
$735$	0.0805971	−	1.01756i	0.00297287	−	0.0375331i
$736$	5.24624	−	3.81162i	0.193379	−	0.140498i
$737$	4.23205	−	5.82491i	0.155890	−	0.214563i
$738$	0.491053	−	0.675877i	0.0180759	−	0.0248794i
$739$	34.6347	−	25.1636i	1.27406	−	0.925658i	0.274702	−	0.961529i	$-0.411421\pi$
$739$	34.6347	−	25.1636i	1.27406	−	0.925658i	0.999356	+	0.0358717i	$0.0114208\pi$
$740$	−7.97182	+	9.32433i	−0.293050	+	0.342769i
$741$	−0.164317	−	0.119383i	−0.00603632	−	0.00438564i
$742$	−14.1823	+	4.60812i	−0.520650	+	0.169170i
$743$			3.78397i			0.138821i	0.997588	+	0.0694103i	$0.0221118\pi$
$743$			3.78397i			0.138821i	−0.997588	+	0.0694103i	$0.977888\pi$
$744$	−1.60298	−	4.93348i	−0.0587682	−	0.180870i
$745$	4.69027	+	19.5797i	0.171838	+	0.717343i
$746$	5.82168	−	17.9173i	0.213147	−	0.655999i
$747$	−4.10657	−	1.33430i	−0.150251	−	0.0488196i
$748$	2.59570	+	3.57267i	0.0949080	+	0.130630i
$749$	39.8009			1.45429
$750$	4.32812	−	7.03905i	0.158041	−	0.257030i
$751$	−14.4651			−0.527838			−0.263919	−	0.964545i	$-0.585015\pi$
$751$	−14.4651			−0.527838			−0.263919	+	0.964545i	$0.585015\pi$
$752$	−3.98045	−	5.47862i	−0.145152	−	0.199785i
$753$	8.37842	+	2.72231i	0.305327	+	0.0992066i
$754$	−0.308273	+	0.948768i	−0.0112267	+	0.0345521i
$755$	−8.84167	−	36.9098i	−0.321781	−	1.34328i
$756$	3.14675	+	9.68471i	0.114446	+	0.352230i
$757$		−	15.6678i		−	0.569455i	−0.958609	−	0.284727i	$-0.908097\pi$
$757$		−	15.6678i		−	0.569455i	0.958609	−	0.284727i	$-0.0919031\pi$
$758$	−11.9848	+	3.89411i	−0.435309	+	0.141440i
$759$	−2.67518	−	1.94363i	−0.0971029	−	0.0705494i
$760$	−1.45306	+	1.69959i	−0.0527081	+	0.0616506i
$761$	36.1266	−	26.2475i	1.30959	−	0.951473i	0.309590	−	0.950870i	$-0.399808\pi$
$761$	36.1266	−	26.2475i	1.30959	−	0.951473i	1.00000		0.000602384i	$-0.000191745\pi$
$762$	−9.38816	+	12.9217i	−0.340097	+	0.468104i
$763$	−15.7486	+	21.6761i	−0.570137	+	0.784726i
$764$	10.5556	−	7.66909i	0.381888	−	0.277458i
$765$	−2.77296	+	35.0092i	−0.100257	+	1.26576i
$766$	16.5488	+	12.0234i	0.597934	+	0.434424i
$767$	−0.505949	+	0.164393i	−0.0182688	+	0.00593588i
$768$			0.739085i			0.0266694i
$769$	−6.95695	−	21.4113i	−0.250874	−	0.772111i	−0.994615	−	0.103643i	$-0.966950\pi$
$769$	−6.95695	−	21.4113i	−0.250874	−	0.772111i	0.743740	−	0.668469i	$-0.233050\pi$
$770$	−3.88533	−	0.307743i	−0.140018	−	0.0110903i
$771$	−1.30990	+	4.03146i	−0.0471749	+	0.145190i
$772$	14.3124	+	4.65038i	0.515114	+	0.167371i
$773$	13.9624	+	19.2176i	0.502193	+	0.691209i	0.982578	−	0.185848i	$-0.0595034\pi$
$773$	13.9624	+	19.2176i	0.502193	+	0.691209i	−0.480386	+	0.877057i	$0.659503\pi$
$774$	27.7849			0.998708
$775$	24.7897	+	24.8395i	0.890472	+	0.892261i
$776$	5.34006			0.191697
$777$	−6.02111	−	8.28735i	−0.216006	−	0.297307i
$778$	−7.61765	−	2.47512i	−0.273106	−	0.0887375i
$779$	−0.105211	+	0.323806i	−0.00376958	+	0.0116016i
$780$	0.387354	−	0.237103i	0.0138695	−	0.00848967i
$781$	−0.685308	−	2.10916i	−0.0245222	−	0.0754717i
$782$			41.5064i			1.48427i
$783$	−13.9162	+	4.52165i	−0.497324	+	0.161590i
$784$	−0.499683	−	0.363041i	−0.0178458	−	0.0129658i
$785$	14.4381	−	3.45861i	0.515316	−	0.123443i
$786$	4.77854	−	3.47181i	0.170445	−	0.123835i
$787$	11.9837	−	16.4941i	0.427171	−	0.587951i	−0.540130	−	0.841582i	$-0.681625\pi$
$787$	11.9837	−	16.4941i	0.427171	−	0.587951i	0.967301	+	0.253631i	$0.0816249\pi$
$788$	−15.1690	+	20.8783i	−0.540373	+	0.743760i
$789$	9.04339	−	6.57041i	0.321953	−	0.233913i
$790$	−4.39474	−	7.17964i	−0.156358	−	0.255440i
$791$	−28.6813	−	20.8382i	−1.01979	−	0.740920i
$792$	−1.61008	+	0.523147i	−0.0572117	+	0.0185892i
$793$			2.82512i			0.100323i
$794$	8.26254	+	25.4295i	0.293227	+	0.902459i
$795$	−3.73763	+	9.01064i	−0.132560	+	0.319574i
$796$	−0.966697	+	2.97519i	−0.0342637	+	0.105453i
$797$	34.4735	+	11.2011i	1.22111	+	0.396764i	0.847488	−	0.530815i	$-0.178114\pi$
$797$	34.4735	+	11.2011i	1.22111	+	0.396764i	0.373626	+	0.927579i	$0.378114\pi$
$798$	−1.09750	−	1.51058i	−0.0388510	−	0.0534738i
$799$	43.3449			1.53343
$800$	−2.26548	−	4.45731i	−0.0800969	−	0.157590i
$801$	4.62461			0.163403
$802$	12.9772	+	17.8616i	0.458242	+	0.630716i
$803$	−9.84335	−	3.19830i	−0.347364	−	0.112865i
$804$	−2.38341	+	7.33537i	−0.0840563	+	0.258699i
$805$	−27.8436	−	23.8049i	−0.981359	−	0.839011i
$806$	0.596024	+	1.83437i	0.0209941	+	0.0646131i
$807$			13.4762i			0.474383i
$808$	7.76527	−	2.52309i	0.273181	−	0.0887620i
$809$	9.02099	+	6.55413i	0.317161	+	0.230431i	0.734963	−	0.678107i	$-0.237199\pi$
$809$	9.02099	+	6.55413i	0.317161	+	0.230431i	−0.417802	+	0.908538i	$0.637199\pi$
$810$	−9.05105	−	3.75439i	−0.318022	−	0.131916i
$811$	−4.34480	+	3.15669i	−0.152567	+	0.110846i	−0.661450	−	0.749989i	$-0.730059\pi$
$811$	−4.34480	+	3.15669i	−0.152567	+	0.110846i	0.508883	+	0.860836i	$0.330059\pi$
$812$	−5.39056	+	7.41947i	−0.189172	+	0.260372i
$813$	5.13635	−	7.06958i	0.180140	−	0.247941i
$814$	3.06225	−	2.22486i	0.107332	−	0.0779812i
$815$	−21.9019	−	9.08493i	−0.767189	−	0.318231i
$816$	−3.82716	−	2.78059i	−0.133977	−	0.0973403i
$817$	−10.7692	+	3.49913i	−0.376767	+	0.122419i
$818$			38.3602i			1.34123i
$819$	−0.526421	−	1.62016i	−0.0183946	−	0.0566129i
$820$	−0.578660	−	0.494724i	−0.0202077	−	0.0172765i
$821$	9.77443	−	30.0826i	0.341130	−	1.04989i	−0.622493	−	0.782625i	$-0.713880\pi$
$821$	9.77443	−	30.0826i	0.341130	−	1.04989i	0.963623	−	0.267265i	$-0.0861199\pi$
$822$	−8.55429	−	2.77946i	−0.298365	−	0.0969448i
$823$	30.5797	+	42.0893i	1.06594	+	1.46714i	0.874120	+	0.485710i	$0.161439\pi$
$823$	30.5797	+	42.0893i	1.06594	+	1.46714i	0.191820	+	0.981430i	$0.438561\pi$
$824$	−2.26541			−0.0789193
$825$	−1.80466	+	1.80104i	−0.0628302	+	0.0627042i
$826$	−4.89059			−0.170166
$827$	−15.2052	−	20.9282i	−0.528738	−	0.727745i	0.458200	−	0.888849i	$-0.348494\pi$
$827$	−15.2052	−	20.9282i	−0.528738	−	0.727745i	−0.986937	+	0.161104i	$0.948494\pi$
$828$	−15.1331	−	4.91705i	−0.525912	−	0.170879i
$829$	−13.7163	+	42.2144i	−0.476386	+	1.46617i	0.367693	+	0.929947i	$0.380148\pi$
$829$	−13.7163	+	42.2144i	−0.476386	+	1.46617i	−0.844079	+	0.536219i	$0.819852\pi$
$830$	−1.50762	+	3.63456i	−0.0523302	+	0.126157i
$831$	2.14928	+	6.61481i	0.0745578	+	0.229465i
$832$		−	0.274808i		−	0.00952725i
$833$	3.75983	−	1.22164i	0.130270	−	0.0423274i
$834$	1.19838	+	0.870671i	0.0414963	+	0.0301489i
$835$	−1.26674	−	2.06946i	−0.0438373	−	0.0716166i
$836$	0.558172	−	0.405536i	0.0193048	−	0.0140257i
$837$	−16.6288	+	22.8876i	−0.574775	+	0.791110i
$838$	6.72019	−	9.24955i	0.232145	−	0.319520i
$839$	1.82013	−	1.32240i	0.0628378	−	0.0456543i	−0.555923	−	0.831234i	$-0.687635\pi$
$839$	1.82013	−	1.32240i	0.0628378	−	0.0456543i	0.618761	+	0.785580i	$0.287635\pi$
$840$	4.06026	−	0.972628i	0.140092	−	0.0335588i
$841$	12.8003	+	9.29995i	0.441389	+	0.320688i
$842$	20.3835	−	6.62300i	0.702462	−	0.228244i
$843$			6.09763i			0.210013i
$844$	−6.70380	−	20.6322i	−0.230754	−	0.710188i
$845$	24.6489	−	15.0879i	0.847948	−	0.519038i
$846$	−5.13484	+	15.8034i	−0.176539	+	0.543332i
$847$	−25.2858	−	8.21586i	−0.868831	−	0.282300i
$848$	3.46952	+	4.77539i	0.119144	+	0.163988i
$849$	10.8860			0.373607
$850$	31.6042	+	5.03813i	1.08402	+	0.172806i
$851$	35.5766			1.21955
$852$	1.39639	+	1.92196i	0.0478394	+	0.0658453i
$853$	−47.6436	−	15.4804i	−1.63129	−	0.530037i	−0.656721	−	0.754134i	$-0.728057\pi$
$853$	−47.6436	−	15.4804i	−1.63129	−	0.530037i	−0.974567	+	0.224097i	$0.928057\pi$
$854$	−8.02566	+	24.7004i	−0.274632	+	0.845231i
$855$	5.46963	+	0.433230i	0.187057	+	0.0148162i
$856$	−4.86838	−	14.9833i	−0.166398	−	0.512120i
$857$		−	26.1838i		−	0.894420i	−0.894429	−	0.447210i	$-0.852418\pi$
$857$		−	26.1838i		−	0.894420i	0.894429	−	0.447210i	$-0.147582\pi$
$858$	−0.133272	+	0.0433028i	−0.00454985	+	0.00147833i
$859$	24.3564	+	17.6959i	0.831028	+	0.603777i	0.919850	−	0.392270i	$-0.128310\pi$
$859$	24.3564	+	17.6959i	0.831028	+	0.603777i	−0.0888217	+	0.996048i	$0.528310\pi$
$860$	1.99924	−	25.2409i	0.0681737	−	0.860708i
$861$	0.514306	−	0.373665i	0.0175275	−	0.0127345i
$862$	1.93999	−	2.67016i	0.0660762	−	0.0909461i
$863$	32.8628	−	45.2317i	1.11866	−	1.53971i	0.310664	−	0.950520i	$-0.399449\pi$
$863$	32.8628	−	45.2317i	1.11866	−	1.53971i	0.807998	−	0.589185i	$-0.200551\pi$
$864$	3.26097	−	2.36924i	0.110941	−	0.0806031i
$865$	26.0255	−	30.4410i	0.884893	−	1.03503i
$866$	−10.7901	−	7.83948i	−0.366663	−	0.266396i
$867$	16.8477	−	5.47414i	0.572177	−	0.185912i
$868$			17.7314i			0.601843i
$869$	0.802623	+	2.47022i	0.0272271	+	0.0837964i
$870$	1.39759	+	5.83428i	0.0473828	+	0.197801i
$871$	0.886203	−	2.72745i	0.0300278	−	0.0924162i
$872$	10.0865	+	3.27729i	0.341570	+	0.110983i
$873$	−7.70187	−	10.6007i	−0.260669	−	0.358780i
$874$	6.48471			0.219349
$875$	−21.5054	+	18.3115i	−0.727017	+	0.619041i
$876$	11.0872			0.374600
$877$	−21.9561	−	30.2200i	−0.741405	−	1.02046i	−0.998537	−	0.0540805i	$-0.982777\pi$
$877$	−21.9561	−	30.2200i	−0.741405	−	1.02046i	0.257131	−	0.966377i	$-0.417223\pi$
$878$	19.2530	+	6.25569i	0.649758	+	0.211119i
$879$	6.28733	−	19.3504i	0.212066	−	0.652673i
$880$	0.359395	+	1.50030i	0.0121152	+	0.0505752i
$881$	−6.33713	−	19.5037i	−0.213503	−	0.657095i	−0.999256	−	0.0385552i	$-0.987724\pi$
$881$	−6.33713	−	19.5037i	−0.213503	−	0.657095i	0.785753	−	0.618540i	$-0.212276\pi$
$882$			1.51554i			0.0510310i
$883$	21.7649	−	7.07186i	0.732449	−	0.237987i	0.0810366	−	0.996711i	$-0.474177\pi$
$883$	21.7649	−	7.07186i	0.732449	−	0.237987i	0.651412	+	0.758724i	$0.274177\pi$
$884$	1.42302	+	1.03389i	0.0478614	+	0.0347733i
$885$	−2.07898	+	2.43170i	−0.0698841	+	0.0817406i
$886$	−1.92954	+	1.40189i	−0.0648240	+	0.0470974i
$887$	12.2037	−	16.7970i	0.409761	−	0.563988i	−0.553399	−	0.832916i	$-0.686669\pi$
$887$	12.2037	−	16.7970i	0.409761	−	0.563988i	0.963160	+	0.268928i	$0.0866694\pi$
$888$	−2.38334	+	3.28039i	−0.0799797	+	0.110083i
$889$	44.1688	−	32.0905i	1.48137	−	1.07628i
$890$	0.332761	−	4.20118i	0.0111542	−	0.140824i
$891$	2.44600	+	1.77713i	0.0819442	+	0.0595360i
$892$	−9.74777	+	3.16724i	−0.326379	+	0.106047i
$893$		−	6.77194i		−	0.226614i
$894$	2.05643	+	6.32903i	0.0687772	+	0.211674i
$895$	5.92843	+	0.469570i	0.198166	+	0.0156960i
$896$	0.780680	−	2.40269i	0.0260807	−	0.0802681i
$897$	−1.25262	−	0.407002i	−0.0418239	−	0.0135894i
$898$	−7.07595	−	9.73920i	−0.236127	−	0.325001i
$899$	−25.4787			−0.849761
$900$	−5.58087	+	10.9260i	−0.186029	+	0.364199i
$901$	−37.7812			−1.25867
$902$	0.138073	+	0.190041i	0.00459732	+	0.00632767i
$903$	20.1080	+	6.53349i	0.669153	+	0.217421i
$904$	−4.33643	+	13.3462i	−0.144228	+	0.443887i
$905$	14.2433	−	8.71850i	0.473464	−	0.289813i
$906$	−3.87658	−	11.9309i	−0.128791	−	0.396377i
$907$			51.1094i			1.69706i	0.529148	+	0.848530i	$0.322512\pi$
$907$			51.1094i			1.69706i	−0.529148	+	0.848530i	$0.677488\pi$
$908$	−27.2847	+	8.86533i	−0.905474	+	0.294206i
$909$	−16.2084	−	11.7761i	−0.537597	−	0.390587i
$910$	−1.50969	+	0.361644i	−0.0500458	+	0.0119884i
$911$	−22.5486	+	16.3826i	−0.747070	+	0.542778i	−0.894917	−	0.446232i	$-0.852766\pi$
$911$	−22.5486	+	16.3826i	−0.747070	+	0.542778i	0.147847	+	0.989010i	$0.452766\pi$
$912$	−0.434423	+	0.597932i	−0.0143852	+	0.0197995i
$913$	0.713626	−	0.982222i	0.0236176	−	0.0325068i
$914$	−21.7460	+	15.7994i	−0.719295	+	0.522599i
$915$	8.86985	+	14.4906i	0.293228	+	0.479044i
$916$	−4.69977	−	3.41459i	−0.155285	−	0.112821i
$917$	−19.2017	+	6.23902i	−0.634097	+	0.206031i
$918$			25.7997i			0.851517i
$919$	5.27211	+	16.2259i	0.173911	+	0.535242i	0.999582	−	0.0289092i	$-0.00920336\pi$
$919$	5.27211	+	16.2259i	0.173911	+	0.535242i	−0.825671	+	0.564152i	$0.809203\pi$
$920$	−5.55573	+	13.3937i	−0.183167	+	0.441578i
$921$	−2.88258	+	8.87166i	−0.0949841	+	0.292331i
$922$	21.1047	+	6.85734i	0.695047	+	0.225834i
$923$	−0.519207	−	0.714627i	−0.0170899	−	0.0235222i
$924$	−1.28824			−0.0423798
$925$	4.31835	−	27.0891i	0.141986	−	0.890683i
$926$	15.0381			0.494184
$927$	3.26736	+	4.49713i	0.107314	+	0.147705i
$928$	3.45248	+	1.12178i	0.113333	+	0.0368242i
$929$	6.19004	−	19.0510i	0.203089	−	0.625043i	−0.796698	−	0.604378i	$-0.793422\pi$
$929$	6.19004	−	19.0510i	0.203089	−	0.625043i	0.999786	−	0.0206648i	$-0.00657827\pi$
$930$	8.81639	+	7.53756i	0.289101	+	0.247166i
$931$	−0.190862	−	0.587413i	−0.00625525	−	0.0192517i
$932$			2.19596i			0.0719310i
$933$	11.3884	−	3.70032i	0.372840	−	0.121143i
$934$	6.18978	+	4.49713i	0.202536	+	0.147151i
$935$	−9.12106	−	3.78343i	−0.298290	−	0.123731i
$936$	−0.545529	+	0.396350i	−0.0178312	+	0.0129551i
$937$	17.7857	−	24.4800i	0.581035	−	0.799726i	−0.412773	−	0.910834i	$-0.635440\pi$
$937$	17.7857	−	24.4800i	0.581035	−	0.799726i	0.993808	+	0.111108i	$0.0354398\pi$
$938$	15.4964	−	21.3290i	0.505975	−	0.696415i
$939$	18.8906	−	13.7248i	0.616472	−	0.447893i
$940$	13.9870	+	5.80181i	0.456204	+	0.189234i
$941$	9.89210	+	7.18703i	0.322473	+	0.234290i	0.737230	−	0.675642i	$-0.236133\pi$
$941$	9.89210	+	7.18703i	0.322473	+	0.234290i	−0.414757	+	0.909932i	$0.636133\pi$
$942$	4.66703	−	1.51641i	0.152060	−	0.0494073i
$943$			2.20785i			0.0718975i
$944$	0.598210	+	1.84110i	0.0194701	+	0.0599227i
$945$	−17.3071	−	14.7967i	−0.563001	−	0.481337i
$946$	−2.41419	+	7.43010i	−0.0784920	+	0.241574i
$947$	−30.6416	−	9.95605i	−0.995717	−	0.323528i	−0.234564	−	0.972101i	$-0.575366\pi$
$947$	−30.6416	−	9.95605i	−0.995717	−	0.323528i	−0.761153	+	0.648572i	$0.775366\pi$
$948$	−1.63543	−	2.25097i	−0.0531162	−	0.0731082i
$949$	−4.12245			−0.133820
$950$	0.787127	−	4.93765i	0.0255378	−	0.160199i
$951$	−7.86278			−0.254968
$952$	9.50460	+	13.0820i	0.308046	+	0.423989i
$953$	52.4257	+	17.0341i	1.69823	+	0.551789i	0.988306	−	0.152485i	$-0.0487276\pi$
$953$	52.4257	+	17.0341i	1.69823	+	0.551789i	0.709928	+	0.704275i	$0.248728\pi$
$954$	4.47574	−	13.7749i	0.144907	−	0.445979i
$955$	−11.1783	+	26.9485i	−0.361721	+	0.872034i
$956$	0.476238	+	1.46571i	0.0154027	+	0.0474045i
$957$		−	1.85110i		−	0.0598375i
$958$	−23.1399	+	7.51862i	−0.747617	+	0.242915i
$959$	24.8732	+	18.0714i	0.803198	+	0.583557i
$960$	−0.862797	−	1.40954i	−0.0278467	−	0.0454928i
$961$	−14.7736	+	10.7336i	−0.476568	+	0.346247i
$962$	0.886178	−	1.21972i	0.0285715	−	0.0393253i
$963$	−22.7223	+	31.2745i	−0.732215	+	1.00781i
$964$	−13.7153	+	9.96472i	−0.441739	+	0.320942i
$965$	−32.7246	+	7.83912i	−1.05344	+	0.252350i
$966$	−9.79565	−	7.11696i	−0.315170	−	0.228984i
$967$	−19.1558	+	6.22408i	−0.616007	+	0.200153i	−0.600367	−	0.799725i	$-0.704979\pi$
$967$	−19.1558	+	6.22408i	−0.616007	+	0.200153i	−0.0156406	+	0.999878i	$0.504979\pi$
$968$			10.5240i			0.338254i
$969$	−1.46184	−	4.49910i	−0.0469612	−	0.144532i
$970$	−10.1843	+	6.23391i	−0.326998	+	0.200159i
$971$	8.66689	−	26.6740i	0.278134	−	0.856008i	−0.710239	−	0.703960i	$-0.751413\pi$
$971$	8.66689	−	26.6740i	0.278134	−	0.856008i	0.988373	−	0.152048i	$-0.0485867\pi$
$972$	−14.5808	−	4.73759i	−0.467679	−	0.151958i
$973$	−2.97612	−	4.09628i	−0.0954100	−	0.131321i
$974$	4.21964			0.135206
$975$	−0.461949	+	0.904383i	−0.0147942	+	0.0289634i
$976$	10.2803			0.329066
$977$	−1.33735	−	1.84071i	−0.0427857	−	0.0588895i	0.787088	−	0.616841i	$-0.211588\pi$
$977$	−1.33735	−	1.84071i	−0.0427857	−	0.0588895i	−0.829874	+	0.557951i	$0.811588\pi$
$978$	−7.45370	−	2.42185i	−0.238343	−	0.0774423i
$979$	−0.401825	+	1.23669i	−0.0128424	+	0.0395248i
$980$	1.37678	+	0.109050i	0.0439796	+	0.00348347i
$981$	−8.04165	−	24.7497i	−0.256750	−	0.790196i
$982$			2.83457i			0.0904547i
$983$	−0.508577	+	0.165247i	−0.0162211	+	0.00527055i	−0.317116	−	0.948387i	$-0.602715\pi$
$983$	−0.508577	+	0.165247i	−0.0162211	+	0.00527055i	0.300895	+	0.953657i	$0.402715\pi$
$984$	−0.203578	−	0.147908i	−0.00648983	−	0.00471514i
$985$	4.55645	−	57.5262i	0.145180	−	1.83294i
$986$	−18.7978	+	13.6574i	−0.598644	+	0.434940i
$987$	−7.43219	+	10.2295i	−0.236569	+	0.325610i
$988$	0.161528	−	0.222324i	0.00513889	−	0.00707308i
$989$	−59.4055	+	43.1606i	−1.88898	+	1.37243i
$990$	2.45995	−	2.87730i	0.0781823	−	0.0914467i
$991$	−3.86049	−	2.80481i	−0.122632	−	0.0890976i	0.524778	−	0.851239i	$-0.324148\pi$
$991$	−3.86049	−	2.80481i	−0.122632	−	0.0890976i	−0.647411	+	0.762141i	$0.724148\pi$
$992$	6.67511	−	2.16888i	0.211935	−	0.0688619i
$993$			17.2726i			0.548129i
$994$	−2.50938	−	7.72306i	−0.0795926	−	0.244961i
$995$	−1.62956	−	6.80263i	−0.0516604	−	0.215658i
$996$	−0.401900	+	1.23692i	−0.0127347	+	0.0391933i
$997$	45.9511	+	14.9304i	1.45529	+	0.472851i	0.926627	−	0.375983i	$-0.122695\pi$
$997$	45.9511	+	14.9304i	1.45529	+	0.472851i	0.528660	+	0.848834i	$0.322695\pi$
$998$	−16.7293	−	23.0259i	−0.529557	−	0.728872i
$999$	22.1138			0.699649

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.n.b.39.8	✓	96
25.9	even	10	inner	950.2.n.b.609.8	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.n.b.39.8	✓	96	1.1	even	1	trivial
950.2.n.b.609.8	yes	96	25.9	even	10	inner

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.n (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 - 0.809017i) q^{2} +(0.702911 + 0.228390i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-0.520909 - 2.17455i) q^{5} +(-0.228390 - 0.702911i) q^{6} +2.52633i q^{7} +(0.951057 - 0.309017i) q^{8} +(-1.98513 - 1.44228i) q^{9} +O(q^{10})\)	\(q+(-0.587785 - 0.809017i) q^{2} +(0.702911 + 0.228390i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-0.520909 - 2.17455i) q^{5} +(-0.228390 - 0.702911i) q^{6} +2.52633i q^{7} +(0.951057 - 0.309017i) q^{8} +(-1.98513 - 1.44228i) q^{9} +(-1.45306 + 1.69959i) q^{10} +(0.558172 - 0.405536i) q^{11} +(-0.434423 + 0.597932i) q^{12} +(0.161528 - 0.222324i) q^{13} +(2.04385 - 1.48494i) q^{14} +(0.130491 - 1.64748i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(6.08739 - 1.97791i) q^{17} +2.45375i q^{18} +(-0.309017 - 0.951057i) q^{19} +(2.22909 + 0.176558i) q^{20} +(-0.576989 + 1.77579i) q^{21} +(-0.656171 - 0.213203i) q^{22} +(-3.81162 - 5.24624i) q^{23} +0.739085 q^{24} +(-4.45731 + 2.26548i) q^{25} -0.274808 q^{26} +(-2.36924 - 3.26097i) q^{27} +(-2.40269 - 0.780680i) q^{28} +(1.12178 - 3.45248i) q^{29} +(-1.40954 + 0.862797i) q^{30} +(-2.16888 - 6.67511i) q^{31} +1.00000i q^{32} +(0.484966 - 0.157575i) q^{33} +(-5.17824 - 3.76221i) q^{34} +(5.49363 - 1.31599i) q^{35} +(1.98513 - 1.44228i) q^{36} +(-3.22472 + 4.43844i) q^{37} +(-0.587785 + 0.809017i) q^{38} +(0.164317 - 0.119383i) q^{39} +(-1.16739 - 1.90715i) q^{40} +(-0.275446 - 0.200123i) q^{41} +(1.77579 - 0.576989i) q^{42} -11.3234i q^{43} +(0.213203 + 0.656171i) q^{44} +(-2.10223 + 5.06805i) q^{45} +(-2.00389 + 6.16733i) q^{46} +(6.44050 + 2.09265i) q^{47} +(-0.434423 - 0.597932i) q^{48} +0.617643 q^{49} +(4.45275 + 2.27442i) q^{50} +4.73063 q^{51} +(0.161528 + 0.222324i) q^{52} +(-5.61381 - 1.82404i) q^{53} +(-1.24558 + 3.83351i) q^{54} +(-1.17261 - 1.00252i) q^{55} +(0.780680 + 2.40269i) q^{56} -0.739085i q^{57} +(-3.45248 + 1.12178i) q^{58} +(-1.56613 - 1.13786i) q^{59} +(1.52653 + 0.633205i) q^{60} +(-8.31697 + 6.04263i) q^{61} +(-4.12545 + 5.67819i) q^{62} +(3.64368 - 5.01509i) q^{63} +(0.809017 - 0.587785i) q^{64} +(-0.567596 - 0.235440i) q^{65} +(-0.412537 - 0.299725i) q^{66} +(9.92494 - 3.22481i) q^{67} +6.40066i q^{68} +(-1.48104 - 4.55818i) q^{69} +(-4.29373 - 3.67092i) q^{70} +(0.993288 - 3.05703i) q^{71} +(-2.33366 - 0.758252i) q^{72} +(-8.81748 - 12.1362i) q^{73} +5.48622 q^{74} +(-3.65051 + 0.574429i) q^{75} +1.00000 q^{76} +(1.02452 + 1.41013i) q^{77} +(-0.193166 - 0.0627633i) q^{78} +(-1.16332 + 3.58035i) q^{79} +(-0.856742 + 2.06543i) q^{80} +(1.35416 + 4.16769i) q^{81} +0.340470i q^{82} +(1.67358 - 0.543781i) q^{83} +(-1.51058 - 1.09750i) q^{84} +(-7.47204 - 12.2070i) q^{85} +(-9.16085 + 6.65575i) q^{86} +(1.57702 - 2.17058i) q^{87} +(0.405536 - 0.558172i) q^{88} +(-1.52476 + 1.10780i) q^{89} +(5.33580 - 1.27818i) q^{90} +(0.561665 + 0.408074i) q^{91} +(6.16733 - 2.00389i) q^{92} -5.18736i q^{93} +(-2.09265 - 6.44050i) q^{94} +(-1.90715 + 1.16739i) q^{95} +(-0.228390 + 0.702911i) q^{96} +(5.07870 + 1.65017i) q^{97} +(-0.363041 - 0.499683i) q^{98} -1.69294 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 24 q^{4} + 8 q^{5} - 6 q^{6} + 34 q^{9}+O(q^{10}) \) 96 * q + 24 * q^4 + 8 * q^5 - 6 * q^6 + 34 * q^9	\( 96 q + 24 q^{4} + 8 q^{5} - 6 q^{6} + 34 q^{9} - 24 q^{11} + 10 q^{12} + 10 q^{14} - 8 q^{15} - 24 q^{16} + 30 q^{17} + 24 q^{19} + 2 q^{20} - 24 q^{24} - 60 q^{25} + 84 q^{26} - 30 q^{27} - 10 q^{28} - 4 q^{29} + 16 q^{30} - 14 q^{31} + 100 q^{33} + 8 q^{34} + 42 q^{35} - 34 q^{36} - 30 q^{37} + 32 q^{39} + 12 q^{41} + 10 q^{42} + 4 q^{44} - 18 q^{45} - 10 q^{46} + 10 q^{48} - 132 q^{49} - 36 q^{50} + 36 q^{51} + 30 q^{53} + 24 q^{54} - 4 q^{55} - 10 q^{56} + 60 q^{58} + 16 q^{59} + 8 q^{60} + 42 q^{61} - 110 q^{63} + 24 q^{64} + 12 q^{65} - 20 q^{66} + 130 q^{67} - 8 q^{69} + 20 q^{70} - 8 q^{71} - 120 q^{73} - 124 q^{74} - 24 q^{75} + 96 q^{76} - 50 q^{78} + 4 q^{79} - 2 q^{80} - 10 q^{81} - 70 q^{83} + 52 q^{85} - 44 q^{86} - 70 q^{87} + 10 q^{88} - 26 q^{89} + 32 q^{90} - 4 q^{91} - 10 q^{92} + 10 q^{94} + 2 q^{95} - 6 q^{96} - 10 q^{97} - 60 q^{98} - 184 q^{99}+O(q^{100}) \) 96 * q + 24 * q^4 + 8 * q^5 - 6 * q^6 + 34 * q^9 - 24 * q^11 + 10 * q^12 + 10 * q^14 - 8 * q^15 - 24 * q^16 + 30 * q^17 + 24 * q^19 + 2 * q^20 - 24 * q^24 - 60 * q^25 + 84 * q^26 - 30 * q^27 - 10 * q^28 - 4 * q^29 + 16 * q^30 - 14 * q^31 + 100 * q^33 + 8 * q^34 + 42 * q^35 - 34 * q^36 - 30 * q^37 + 32 * q^39 + 12 * q^41 + 10 * q^42 + 4 * q^44 - 18 * q^45 - 10 * q^46 + 10 * q^48 - 132 * q^49 - 36 * q^50 + 36 * q^51 + 30 * q^53 + 24 * q^54 - 4 * q^55 - 10 * q^56 + 60 * q^58 + 16 * q^59 + 8 * q^60 + 42 * q^61 - 110 * q^63 + 24 * q^64 + 12 * q^65 - 20 * q^66 + 130 * q^67 - 8 * q^69 + 20 * q^70 - 8 * q^71 - 120 * q^73 - 124 * q^74 - 24 * q^75 + 96 * q^76 - 50 * q^78 + 4 * q^79 - 2 * q^80 - 10 * q^81 - 70 * q^83 + 52 * q^85 - 44 * q^86 - 70 * q^87 + 10 * q^88 - 26 * q^89 + 32 * q^90 - 4 * q^91 - 10 * q^92 + 10 * q^94 + 2 * q^95 - 6 * q^96 - 10 * q^97 - 60 * q^98 - 184 * q^99

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