LMFDB - Embedded newform 435.2.u.a.16.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [435,2,Mod(16,435)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("435.16"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(435, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 435 = 3 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	435.u (of order $7$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [30,1,-5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.47349248793$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			16.1
Character	$\chi$	$=$	435.16
Dual form			435.2.u.a.136.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.70259 - 0.819922i) q^{2} +(0.623490 - 0.781831i) q^{3} +(0.979547 + 1.22831i) q^{4} +(0.900969 + 0.433884i) q^{5} +(-1.70259 + 0.819922i) q^{6} +(-0.471718 + 0.591515i) q^{7} +(0.180366 + 0.790235i) q^{8} +(-0.222521 - 0.974928i) q^{9} +(-1.17823 - 1.47745i) q^{10} +(-1.24525 + 5.45580i) q^{11} +1.57107 q^{12} +(-0.791839 + 3.46927i) q^{13} +(1.28814 - 0.620334i) q^{14} +(0.900969 - 0.433884i) q^{15} +(1.04004 - 4.55669i) q^{16} -5.93679 q^{17} +(-0.420504 + 1.84235i) q^{18} +(2.66880 + 3.34657i) q^{19} +(0.349596 + 1.53168i) q^{20} +(0.168354 + 0.737608i) q^{21} +(6.59347 - 8.26795i) q^{22} +(-5.22802 + 2.51768i) q^{23} +(0.730287 + 0.351687i) q^{24} +(0.623490 + 0.781831i) q^{25} +(4.19271 - 5.25749i) q^{26} +(-0.900969 - 0.433884i) q^{27} -1.18864 q^{28} +(-3.92663 + 3.68532i) q^{29} -1.88973 q^{30} +(1.41925 + 0.683475i) q^{31} +(-4.49614 + 5.63798i) q^{32} +(3.48911 + 4.37521i) q^{33} +(10.1079 + 4.86771i) q^{34} +(-0.681652 + 0.328266i) q^{35} +(0.979547 - 1.22831i) q^{36} +(-1.87796 - 8.22786i) q^{37} +(-1.79993 - 7.88602i) q^{38} +(2.21868 + 2.78214i) q^{39} +(-0.180366 + 0.790235i) q^{40} +6.79874 q^{41} +(0.318144 - 1.39388i) q^{42} +(8.88301 - 4.27783i) q^{43} +(-7.92121 + 3.81465i) q^{44} +(0.222521 - 0.974928i) q^{45} +10.9655 q^{46} +(-0.234431 + 1.02711i) q^{47} +(-2.91411 - 3.65418i) q^{48} +(1.43027 + 6.26644i) q^{49} +(-0.420504 - 1.84235i) q^{50} +(-3.70153 + 4.64157i) q^{51} +(-5.03700 + 2.42569i) q^{52} +(6.60632 + 3.18144i) q^{53} +(1.17823 + 1.47745i) q^{54} +(-3.48911 + 4.37521i) q^{55} +(-0.552518 - 0.266079i) q^{56} +4.28042 q^{57} +(9.70710 - 3.05505i) q^{58} +10.0347 q^{59} +(1.41549 + 0.681663i) q^{60} +(-2.64308 + 3.31431i) q^{61} +(-1.85600 - 2.32735i) q^{62} +(0.681652 + 0.328266i) q^{63} +(3.85573 - 1.85682i) q^{64} +(-2.21868 + 2.78214i) q^{65} +(-2.35318 - 10.3100i) q^{66} +(-1.69053 - 7.40668i) q^{67} +(-5.81537 - 7.29224i) q^{68} +(-1.29121 + 5.65718i) q^{69} +1.42972 q^{70} +(2.66324 - 11.6684i) q^{71} +(0.730287 - 0.351687i) q^{72} +(-13.9331 + 6.70981i) q^{73} +(-3.54883 + 15.5484i) q^{74} +1.00000 q^{75} +(-1.49642 + 6.55624i) q^{76} +(-2.63978 - 3.31018i) q^{77} +(-1.49636 - 6.55598i) q^{78} +(1.58173 + 6.93002i) q^{79} +(2.91411 - 3.65418i) q^{80} +(-0.900969 + 0.433884i) q^{81} +(-11.5754 - 5.57444i) q^{82} +(0.0767989 + 0.0963027i) q^{83} +(-0.741103 + 0.929313i) q^{84} +(-5.34886 - 2.57588i) q^{85} -18.6316 q^{86} +(0.433087 + 5.36772i) q^{87} -4.53596 q^{88} +(-7.50065 - 3.61212i) q^{89} +(-1.17823 + 1.47745i) q^{90} +(-1.67860 - 2.10490i) q^{91} +(-8.21360 - 3.95546i) q^{92} +(1.41925 - 0.683475i) q^{93} +(1.24129 - 1.55653i) q^{94} +(0.952483 + 4.17310i) q^{95} +(1.60465 + 7.03044i) q^{96} +(5.07106 + 6.35891i) q^{97} +(2.70283 - 11.8419i) q^{98} +5.59610 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + q^{2} - 5 q^{3} - 3 q^{4} + 5 q^{5} + q^{6} - 5 q^{9} + 6 q^{10} - 18 q^{11} + 32 q^{12} - 5 q^{13} + 18 q^{14} + 5 q^{15} - 13 q^{16} + 44 q^{17} + q^{18} - 8 q^{19} + 10 q^{20} + 7 q^{21} - 19 q^{22}+ \cdots + 10 q^{99}+O(q^{100}) $ 30 * q + q^2 - 5 * q^3 - 3 * q^4 + 5 * q^5 + q^6 - 5 * q^9 + 6 * q^10 - 18 * q^11 + 32 * q^12 - 5 * q^13 + 18 * q^14 + 5 * q^15 - 13 * q^16 + 44 * q^17 + q^18 - 8 * q^19 + 10 * q^20 + 7 * q^21 - 19 * q^22 + 8 * q^23 + 14 * q^24 - 5 * q^25 - 34 * q^26 - 5 * q^27 - 102 * q^28 - 27 * q^29 - 8 * q^30 + 5 * q^31 - 2 * q^32 + 10 * q^33 - 5 * q^34 - 3 * q^36 + 9 * q^37 + 7 * q^38 + 2 * q^39 + 6 * q^41 - 17 * q^42 + 33 * q^43 + 5 * q^45 + 98 * q^46 - 30 * q^47 + q^48 - 9 * q^49 + q^50 - 26 * q^51 - 45 * q^52 + 38 * q^53 - 6 * q^54 - 10 * q^55 - 70 * q^56 - 8 * q^57 - 27 * q^58 + 102 * q^59 + 3 * q^60 + 8 * q^61 - 22 * q^62 + 30 * q^64 - 2 * q^65 - 40 * q^66 - 2 * q^67 + 23 * q^68 - 13 * q^69 + 24 * q^70 - 12 * q^71 + 14 * q^72 - 28 * q^73 - 65 * q^74 + 30 * q^75 - 41 * q^76 + 24 * q^77 + 71 * q^78 + 31 * q^79 - q^80 - 5 * q^81 - 39 * q^82 - 17 * q^83 - 11 * q^84 - 2 * q^85 + 38 * q^86 - 27 * q^87 + 22 * q^88 + 25 * q^89 + 6 * q^90 + 90 * q^91 + 39 * q^92 + 5 * q^93 + 11 * q^94 + 8 * q^95 - 16 * q^96 - 27 * q^97 - 47 * q^98 + 10 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/435\mathbb{Z}\right)^\times$.

$n$	$31$	$146$	$262$
$\chi(n)$	$e\left(\frac{1}{7}\right)$	$1$	$1$

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 $

$2$	−1.70259	−	0.819922i	−1.20391	−	0.579773i	−0.279122	−	0.960256i	$-0.590043\pi$
$2$	−1.70259	−	0.819922i	−1.20391	−	0.579773i	−0.924788	+	0.380483i	$0.875758\pi$
$3$	0.623490	−	0.781831i	0.359972	−	0.451391i
$3$	0.623490	−	0.781831i	0.359972	−	0.451391i
$4$	0.979547	+	1.22831i	0.489774	+	0.614157i
$5$	0.900969	+	0.433884i	0.402926	+	0.194039i
$5$	0.900969	+	0.433884i	0.402926	+	0.194039i
$6$	−1.70259	+	0.819922i	−0.695078	+	0.334732i
$7$	−0.471718	+	0.591515i	−0.178293	+	0.223572i	−0.862945	−	0.505298i	$-0.831383\pi$
$7$	−0.471718	+	0.591515i	−0.178293	+	0.223572i	0.684652	+	0.728870i	$0.259954\pi$
$8$	0.180366	+	0.790235i	0.0637690	+	0.279390i
$9$	−0.222521	−	0.974928i	−0.0741736	−	0.324976i
$10$	−1.17823	−	1.47745i	−0.372588	−	0.467210i
$11$	−1.24525	+	5.45580i	−0.375457	+	1.64498i	0.335713	+	0.941964i	$0.391023\pi$
$11$	−1.24525	+	5.45580i	−0.375457	+	1.64498i	−0.711170	+	0.703020i	$0.751834\pi$
$12$	1.57107			0.453529
$13$	−0.791839	+	3.46927i	−0.219617	+	0.962203i	0.738145	+	0.674642i	$0.235702\pi$
$13$	−0.791839	+	3.46927i	−0.219617	+	0.962203i	−0.957762	+	0.287562i	$0.907155\pi$
$14$	1.28814	−	0.620334i	0.344269	−	0.165791i
$15$	0.900969	−	0.433884i	0.232629	−	0.112028i
$16$	1.04004	−	4.55669i	0.260009	−	1.13917i
$17$	−5.93679			−1.43988			−0.719942	−	0.694035i	$-0.755831\pi$
$17$	−5.93679			−1.43988			−0.719942	+	0.694035i	$0.755831\pi$
$18$	−0.420504	+	1.84235i	−0.0991138	+	0.434246i
$19$	2.66880	+	3.34657i	0.612264	+	0.767755i	0.987233	−	0.159282i	$-0.0509181\pi$
$19$	2.66880	+	3.34657i	0.612264	+	0.767755i	−0.374969	+	0.927037i	$0.622347\pi$
$20$	0.349596	+	1.53168i	0.0781721	+	0.342495i
$21$	0.168354	+	0.737608i	0.0367379	+	0.160959i
$22$	6.59347	−	8.26795i	1.40573	−	1.76273i
$23$	−5.22802	+	2.51768i	−1.09012	+	0.524973i	−0.890538	−	0.454908i	$-0.849672\pi$
$23$	−5.22802	+	2.51768i	−1.09012	+	0.524973i	−0.199580	+	0.979882i	$0.563958\pi$
$24$	0.730287	+	0.351687i	0.149069	+	0.0717879i
$25$	0.623490	+	0.781831i	0.124698	+	0.156366i
$26$	4.19271	−	5.25749i	0.822258	−	1.03108i
$27$	−0.900969	−	0.433884i	−0.173392	−	0.0835010i
$28$	−1.18864			−0.224631
$29$	−3.92663	+	3.68532i	−0.729157	+	0.684347i
$29$	−3.92663	+	3.68532i	−0.729157	+	0.684347i
$30$	−1.88973			−0.345016
$31$	1.41925	+	0.683475i	0.254905	+	0.122756i	0.556973	−	0.830531i	$-0.311963\pi$
$31$	1.41925	+	0.683475i	0.254905	+	0.122756i	−0.302068	+	0.953286i	$0.597677\pi$
$32$	−4.49614	+	5.63798i	−0.794812	+	0.996663i
$33$	3.48911	+	4.37521i	0.607377	+	0.761626i
$34$	10.1079	+	4.86771i	1.73349	+	0.834805i
$35$	−0.681652	+	0.328266i	−0.115220	+	0.0554871i
$36$	0.979547	−	1.22831i	0.163258	−	0.204719i
$37$	−1.87796	−	8.22786i	−0.308734	−	1.35265i	−0.856555	−	0.516057i	$-0.827399\pi$
$37$	−1.87796	−	8.22786i	−0.308734	−	1.35265i	0.547820	−	0.836596i	$-0.315458\pi$
$38$	−1.79993	−	7.88602i	−0.291988	−	1.27928i
$39$	2.21868	+	2.78214i	0.355274	+	0.445499i
$40$	−0.180366	+	0.790235i	−0.0285184	+	0.124947i
$41$	6.79874			1.06178			0.530892	−	0.847439i	$-0.321857\pi$
$41$	6.79874			1.06178			0.530892	+	0.847439i	$0.321857\pi$
$42$	0.318144	−	1.39388i	0.0490906	−	0.215080i
$43$	8.88301	−	4.27783i	1.35465	−	0.652363i	0.391210	−	0.920302i	$-0.372057\pi$
$43$	8.88301	−	4.27783i	1.35465	−	0.652363i	0.963436	+	0.267939i	$0.0863424\pi$
$44$	−7.92121	+	3.81465i	−1.19417	+	0.575081i
$45$	0.222521	−	0.974928i	0.0331715	−	0.145334i
$46$	10.9655			1.61677
$47$	−0.234431	+	1.02711i	−0.0341953	+	0.149819i	−0.989143	−	0.146953i	$-0.953053\pi$
$47$	−0.234431	+	1.02711i	−0.0341953	+	0.149819i	0.954948	+	0.296773i	$0.0959104\pi$
$48$	−2.91411	−	3.65418i	−0.420616	−	0.527436i
$49$	1.43027	+	6.26644i	0.204325	+	0.895206i
$50$	−0.420504	−	1.84235i	−0.0594683	−	0.260547i
$51$	−3.70153	+	4.64157i	−0.518318	+	0.649950i
$52$	−5.03700	+	2.42569i	−0.698506	+	0.336383i
$53$	6.60632	+	3.18144i	0.907448	+	0.437004i	0.828573	−	0.559881i	$-0.189153\pi$
$53$	6.60632	+	3.18144i	0.907448	+	0.437004i	0.0788748	+	0.996885i	$0.474867\pi$
$54$	1.17823	+	1.47745i	0.160336	+	0.201055i
$55$	−3.48911	+	4.37521i	−0.470472	+	0.589953i
$56$	−0.552518	−	0.266079i	−0.0738333	−	0.0355562i
$57$	4.28042			0.566955
$58$	9.70710	−	3.05505i	1.27460	−	0.401147i
$59$	10.0347			1.30640			0.653201	−	0.757185i	$-0.273426\pi$
$59$	10.0347			1.30640			0.653201	+	0.757185i	$0.273426\pi$
$60$	1.41549	+	0.681663i	0.182739	+	0.0880023i
$61$	−2.64308	+	3.31431i	−0.338411	+	0.424355i	−0.921696	−	0.387914i	$-0.873196\pi$
$61$	−2.64308	+	3.31431i	−0.338411	+	0.424355i	0.583284	+	0.812268i	$0.301767\pi$
$62$	−1.85600	−	2.32735i	−0.235712	−	0.295574i
$63$	0.681652	+	0.328266i	0.0858801	+	0.0413577i
$64$	3.85573	−	1.85682i	0.481966	−	0.232102i
$65$	−2.21868	+	2.78214i	−0.275194	+	0.345082i
$66$	−2.35318	−	10.3100i	−0.289657	−	1.26907i
$67$	−1.69053	−	7.40668i	−0.206531	−	0.904870i	−0.966855	−	0.255326i	$-0.917817\pi$
$67$	−1.69053	−	7.40668i	−0.206531	−	0.904870i	0.760324	−	0.649544i	$-0.225040\pi$
$68$	−5.81537	−	7.29224i	−0.705217	−	0.884314i
$69$	−1.29121	+	5.65718i	−0.155444	+	0.681045i
$70$	1.42972			0.170885
$71$	2.66324	−	11.6684i	0.316068	−	1.38478i	−0.528317	−	0.849047i	$-0.677177\pi$
$71$	2.66324	−	11.6684i	0.316068	−	1.38478i	0.844385	−	0.535737i	$-0.179966\pi$
$72$	0.730287	−	0.351687i	0.0860651	−	0.0414468i
$73$	−13.9331	+	6.70981i	−1.63074	+	0.785323i	−0.630784	+	0.775958i	$0.717267\pi$
$73$	−13.9331	+	6.70981i	−1.63074	+	0.785323i	−0.999956	+	0.00936517i	$0.997019\pi$
$74$	−3.54883	+	15.5484i	−0.412543	+	1.80747i
$75$	1.00000			0.115470
$76$	−1.49642	+	6.55624i	−0.171651	+	0.752052i
$77$	−2.63978	−	3.31018i	−0.300831	−	0.377230i
$78$	−1.49636	−	6.55598i	−0.169429	−	0.742319i
$79$	1.58173	+	6.93002i	0.177959	+	0.779688i	0.982571	+	0.185888i	$0.0595161\pi$
$79$	1.58173	+	6.93002i	0.177959	+	0.779688i	−0.804612	+	0.593801i	$0.797627\pi$
$80$	2.91411	−	3.65418i	0.325808	−	0.408550i
$81$	−0.900969	+	0.433884i	−0.100108	+	0.0482093i
$82$	−11.5754	−	5.57444i	−1.27829	−	0.615594i
$83$	0.0767989	+	0.0963027i	0.00842977	+	0.0105706i	0.786029	−	0.618190i	$-0.212134\pi$
$83$	0.0767989	+	0.0963027i	0.00842977	+	0.0105706i	−0.777599	+	0.628761i	$0.783562\pi$
$84$	−0.741103	+	0.929313i	−0.0808609	+	0.101396i
$85$	−5.34886	−	2.57588i	−0.580166	−	0.279393i
$86$	−18.6316			−2.00909
$87$	0.433087	+	5.36772i	0.0464318	+	0.575480i
$88$	−4.53596			−0.483535
$89$	−7.50065	−	3.61212i	−0.795067	−	0.382884i	−0.00816853	−	0.999967i	$-0.502600\pi$
$89$	−7.50065	−	3.61212i	−0.795067	−	0.382884i	−0.786898	+	0.617083i	$0.788314\pi$
$90$	−1.17823	+	1.47745i	−0.124196	+	0.155737i
$91$	−1.67860	−	2.10490i	−0.175966	−	0.220654i
$92$	−8.21360	−	3.95546i	−0.856327	−	0.412385i
$93$	1.41925	−	0.683475i	0.147169	−	0.0708730i
$94$	1.24129	−	1.55653i	0.128029	−	0.160543i
$95$	0.952483	+	4.17310i	0.0977227	+	0.428151i
$96$	1.60465	+	7.03044i	0.163774	+	0.717541i
$97$	5.07106	+	6.35891i	0.514889	+	0.645650i	0.969515	−	0.245032i	$-0.0787986\pi$
$97$	5.07106	+	6.35891i	0.514889	+	0.645650i	−0.454626	+	0.890682i	$0.650227\pi$
$98$	2.70283	−	11.8419i	0.273027	−	1.19621i
$99$	5.59610			0.562429
$100$	−0.349596	+	1.53168i	−0.0349596	+	0.153168i
$101$	2.83317	−	1.36438i	0.281911	−	0.135761i	−0.287585	−	0.957755i	$-0.592853\pi$
$101$	2.83317	−	1.36438i	0.281911	−	0.135761i	0.569496	+	0.821994i	$0.307138\pi$
$102$	10.1079	−	4.86771i	1.00083	−	0.481975i
$103$	2.36115	−	10.3449i	0.232651	−	1.01931i	−0.714780	−	0.699349i	$-0.753473\pi$
$103$	2.36115	−	10.3449i	0.232651	−	1.01931i	0.947431	−	0.319960i	$-0.103670\pi$
$104$	−2.88436			−0.282835
$105$	−0.168354	+	0.737608i	−0.0164297	+	0.0719831i
$106$	−8.63930	−	10.8333i	−0.839123	−	1.05223i
$107$	−4.11243	−	18.0178i	−0.397564	−	1.74184i	−0.636939	−	0.770914i	$-0.719800\pi$
$107$	−4.11243	−	18.0178i	−0.397564	−	1.74184i	0.239375	−	0.970927i	$-0.423058\pi$
$108$	−0.349596	−	1.53168i	−0.0336399	−	0.147386i
$109$	5.62745	−	7.05660i	0.539012	−	0.675900i	−0.435512	−	0.900183i	$-0.643433\pi$
$109$	5.62745	−	7.05660i	0.539012	−	0.675900i	0.974524	+	0.224283i	$0.0720041\pi$
$110$	9.52785	−	4.58837i	0.908444	−	0.437484i
$111$	−7.60369	−	3.66174i	−0.721710	−	0.347557i
$112$	2.20475	+	2.76467i	0.208329	+	0.261237i
$113$	−10.6297	+	13.3293i	−0.999961	+	1.25391i	−0.0328753	+	0.999459i	$0.510466\pi$
$113$	−10.6297	+	13.3293i	−0.999961	+	1.25391i	−0.967085	+	0.254452i	$0.918105\pi$
$114$	−7.28778	−	3.50961i	−0.682563	−	0.328705i
$115$	−5.80267			−0.541102
$116$	−8.37305	−	1.21319i	−0.777418	−	0.112641i
$117$	3.55849			0.328983
$118$	−17.0849	−	8.22764i	−1.57279	−	0.757416i
$119$	2.80049	−	3.51170i	0.256720	−	0.321917i
$120$	0.505374	+	0.633719i	0.0461341	+	0.0578504i
$121$	−18.3044	−	8.81494i	−1.66404	−	0.801358i
$122$	7.21755	−	3.47579i	0.653446	−	0.314683i
$123$	4.23895	−	5.31547i	0.382213	−	0.479280i
$124$	0.550701	+	2.41278i	0.0494544	+	0.216674i
$125$	0.222521	+	0.974928i	0.0199029	+	0.0872002i
$126$	−0.891418	−	1.11780i	−0.0794139	−	0.0995818i
$127$	−2.47185	+	10.8299i	−0.219341	+	0.960996i	0.738625	+	0.674116i	$0.235475\pi$
$127$	−2.47185	+	10.8299i	−0.219341	+	0.960996i	−0.957967	+	0.286880i	$0.907382\pi$
$128$	6.33533			0.559969
$129$	2.19392	−	9.61220i	0.193164	−	0.846307i
$130$	6.05864	−	2.91769i	0.531378	−	0.255898i
$131$	−7.60398	+	3.66189i	−0.664363	+	0.319940i	−0.735499	−	0.677526i	$-0.763052\pi$
$131$	−7.60398	+	3.66189i	−0.664363	+	0.319940i	0.0711355	+	0.997467i	$0.477338\pi$
$132$	−1.95638	+	8.57145i	−0.170281	+	0.746049i
$133$	−3.23846			−0.280811
$134$	−3.19463	+	13.9966i	−0.275974	+	1.20912i
$135$	−0.623490	−	0.781831i	−0.0536615	−	0.0672893i
$136$	−1.07079	−	4.69146i	−0.0918199	−	0.402289i
$137$	2.79376	+	12.2402i	0.238687	+	1.04575i	0.942194	+	0.335067i	$0.108759\pi$
$137$	2.79376	+	12.2402i	0.238687	+	1.04575i	−0.703508	+	0.710688i	$0.748384\pi$
$138$	6.83685	−	8.57314i	0.581992	−	0.729795i
$139$	4.54160	−	2.18712i	0.385214	−	0.185509i	−0.231247	−	0.972895i	$-0.574280\pi$
$139$	4.54160	−	2.18712i	0.385214	−	0.185509i	0.616460	+	0.787386i	$0.288566\pi$
$140$	−1.07092	−	0.515730i	−0.0905096	−	0.0435871i
$141$	0.656861	+	0.823678i	0.0553177	+	0.0693662i
$142$	−14.1016	+	17.6828i	−1.18338	+	1.48391i
$143$	−17.9416	−	8.64022i	−1.50035	−	0.722532i
$144$	−4.67388			−0.389490
$145$	−5.13677	+	1.61666i	−0.426586	+	0.134256i
$146$	29.2237			2.41857
$147$	5.79106	+	2.78883i	0.477639	+	0.230019i
$148$	8.26685	−	10.3663i	0.679531	−	0.852105i
$149$	3.12917	+	3.92385i	0.256351	+	0.321454i	0.893308	−	0.449445i	$-0.148378\pi$
$149$	3.12917	+	3.92385i	0.256351	+	0.321454i	−0.636957	+	0.770900i	$0.719807\pi$
$150$	−1.70259	−	0.819922i	−0.139016	−	0.0669464i
$151$	−3.50341	+	1.68715i	−0.285103	+	0.137298i	−0.570970	−	0.820971i	$-0.693433\pi$
$151$	−3.50341	+	1.68715i	−0.285103	+	0.137298i	0.285867	+	0.958269i	$0.407718\pi$
$152$	−2.16321	+	2.71258i	−0.175460	+	0.220019i
$153$	1.32106	+	5.78794i	0.106801	+	0.467927i
$154$	1.78036	+	7.80028i	0.143466	+	0.628565i
$155$	0.982152	+	1.23158i	0.0788883	+	0.0989228i
$156$	−1.24404	+	5.45048i	−0.0996026	+	0.436388i
$157$	3.24588			0.259049			0.129525	−	0.991576i	$-0.458655\pi$
$157$	3.24588			0.259049			0.129525	+	0.991576i	$0.458655\pi$
$158$	2.98904	−	13.0959i	0.237796	−	1.04185i
$159$	6.60632	−	3.18144i	0.523915	−	0.252304i
$160$	−6.49710	+	3.12884i	−0.513641	+	0.247357i
$161$	0.976903	−	4.28009i	0.0769907	−	0.337318i
$162$	1.88973			0.148471
$163$	−1.96499	+	8.60919i	−0.153910	+	0.674324i	0.837816	+	0.545952i	$0.183832\pi$
$163$	−1.96499	+	8.60919i	−0.153910	+	0.674324i	−0.991726	+	0.128371i	$0.959025\pi$
$164$	6.65969	+	8.35099i	0.520034	+	0.652102i
$165$	1.24525	+	5.45580i	0.0969426	+	0.424733i
$166$	−0.0517959	−	0.226933i	−0.00402014	−	0.0176134i
$167$	5.39242	−	6.76188i	0.417278	−	0.523250i	−0.528119	−	0.849170i	$-0.677103\pi$
$167$	5.39242	−	6.76188i	0.417278	−	0.523250i	0.945397	+	0.325920i	$0.105674\pi$
$168$	−0.552518	+	0.266079i	−0.0426277	+	0.0205284i
$169$	0.303746	+	0.146277i	0.0233651	+	0.0112520i
$170$	6.99488	+	8.77130i	0.536483	+	0.672728i
$171$	2.66880	−	3.34657i	0.204088	−	0.255918i
$172$	13.9558	+	6.72078i	1.06412	+	0.512455i
$173$	19.7072			1.49831			0.749154	−	0.662396i	$-0.230460\pi$
$173$	19.7072			1.49831			0.749154	+	0.662396i	$0.230460\pi$
$174$	3.66375	−	9.49411i	0.277748	−	0.719746i
$175$	−0.756577			−0.0571918
$176$	23.5653	+	11.3484i	1.77630	+	0.855421i
$177$	6.25651	−	7.84541i	0.470268	−	0.589697i
$178$	9.80884	+	12.2999i	0.735204	+	0.921916i
$179$	−15.9154	−	7.66447i	−1.18958	−	0.572869i	−0.268888	−	0.963171i	$-0.586656\pi$
$179$	−15.9154	−	7.66447i	−1.18958	−	0.572869i	−0.920687	+	0.390302i	$0.872371\pi$
$180$	1.41549	−	0.681663i	0.105504	−	0.0508081i
$181$	−8.16784	+	10.2421i	−0.607111	+	0.761293i	−0.986467	−	0.163958i	$-0.947574\pi$
$181$	−8.16784	+	10.2421i	−0.607111	+	0.761293i	0.379357	+	0.925251i	$0.376145\pi$
$182$	1.13211	+	4.96010i	0.0839177	+	0.367667i
$183$	0.943304	+	4.13288i	0.0697310	+	0.305511i
$184$	−2.93252	−	3.67726i	−0.216188	−	0.271091i
$185$	1.87796	−	8.22786i	0.138070	−	0.604925i
$186$	−2.97679			−0.218269
$187$	7.39279	−	32.3899i	0.540614	−	2.36859i
$188$	−1.49125	+	0.718147i	−0.108760	+	0.0523763i
$189$	0.681652	−	0.328266i	0.0495829	−	0.0238779i
$190$	1.79993	−	7.88602i	0.130581	−	0.572112i
$191$	18.2246			1.31869			0.659343	−	0.751842i	$-0.270835\pi$
$191$	18.2246			1.31869			0.659343	+	0.751842i	$0.270835\pi$
$192$	0.952286	−	4.17224i	0.0687253	−	0.301105i
$193$	14.9177	+	18.7062i	1.07380	+	1.34650i	0.934383	+	0.356270i	$0.115952\pi$
$193$	14.9177	+	18.7062i	1.07380	+	1.34650i	0.139417	+	0.990234i	$0.455477\pi$
$194$	−3.42011	−	14.9845i	−0.245549	−	1.07582i
$195$	0.791839	+	3.46927i	0.0567048	+	0.248440i
$196$	−6.29613	+	7.89510i	−0.449724	+	0.563936i
$197$	−9.56271	+	4.60516i	−0.681315	+	0.328104i	−0.742332	−	0.670033i	$-0.766280\pi$
$197$	−9.56271	+	4.60516i	−0.681315	+	0.328104i	0.0610166	+	0.998137i	$0.480566\pi$
$198$	−9.52785	−	4.58837i	−0.677115	−	0.326081i
$199$	5.77595	+	7.24281i	0.409446	+	0.513429i	0.943207	−	0.332206i	$-0.107793\pi$
$199$	5.77595	+	7.24281i	0.409446	+	0.513429i	−0.533760	+	0.845636i	$0.679222\pi$
$200$	−0.505374	+	0.633719i	−0.0357353	+	0.0448107i
$201$	−6.84480	−	3.29628i	−0.482795	−	0.232502i
$202$	−5.94240			−0.418106
$203$	−0.327663	−	4.06109i	−0.0229975	−	0.285033i
$204$	−9.32713			−0.653029
$205$	6.12545	+	2.94986i	0.427820	+	0.206027i
$206$	−12.5020	+	15.6771i	−0.871058	+	1.09227i
$207$	3.61790	+	4.53671i	0.251462	+	0.315323i
$208$	14.9849	+	7.21633i	1.03901	+	0.500363i
$209$	−21.5815	+	10.3931i	−1.49282	+	0.718906i
$210$	0.891418	−	1.11780i	0.0615137	−	0.0771358i
$211$	2.57000	+	11.2599i	0.176926	+	0.775163i	0.983038	+	0.183400i	$0.0587105\pi$
$211$	2.57000	+	11.2599i	0.176926	+	0.775163i	−0.806112	+	0.591762i	$0.798432\pi$
$212$	2.56340	+	11.2310i	0.176055	+	0.771349i
$213$	−7.46223	−	9.35733i	−0.511303	−	0.641154i
$214$	−7.77138	+	34.0486i	−0.531241	+	2.32752i
$215$	9.85939			0.672405
$216$	0.180366	−	0.790235i	0.0122723	−	0.0537687i
$217$	−1.07377	+	0.517101i	−0.0728924	+	0.0351031i
$218$	−15.3671	+	7.40040i	−1.04079	+	0.501218i
$219$	−3.44118	+	15.0768i	−0.232533	+	1.01880i
$220$	−8.79188			−0.592748
$221$	4.70098	−	20.5963i	0.316222	−	1.38546i
$222$	9.94359	+	12.4689i	0.667370	+	0.836856i
$223$	−2.22155	−	9.73323i	−0.148766	−	0.651785i	−0.993229	−	0.116172i	$-0.962938\pi$
$223$	−2.22155	−	9.73323i	−0.148766	−	0.651785i	0.844463	−	0.535613i	$-0.179919\pi$
$224$	−1.21404	−	5.31907i	−0.0811166	−	0.355395i
$225$	0.623490	−	0.781831i	0.0415660	−	0.0521221i
$226$	29.0270	−	13.9787i	1.93085	−	0.929847i
$227$	19.2796	+	9.28459i	1.27963	+	0.616240i	0.945296	−	0.326213i	$-0.105773\pi$
$227$	19.2796	+	9.28459i	1.27963	+	0.616240i	0.334339	+	0.942453i	$0.391487\pi$
$228$	4.19287	+	5.25770i	0.277680	+	0.348199i
$229$	2.09677	−	2.62927i	0.138558	−	0.173747i	−0.707711	−	0.706502i	$-0.750272\pi$
$229$	2.09677	−	2.62927i	0.138558	−	0.173747i	0.846269	+	0.532755i	$0.178843\pi$
$230$	9.87954	+	4.75774i	0.651438	+	0.313716i
$231$	−4.23388			−0.278569
$232$	−3.62050	−	2.43825i	−0.237697	−	0.160079i
$233$	21.7208			1.42297			0.711487	−	0.702699i	$-0.248022\pi$
$233$	21.7208			1.42297			0.711487	+	0.702699i	$0.248022\pi$
$234$	−6.05864	−	2.91769i	−0.396066	−	0.190735i
$235$	−0.656861	+	0.823678i	−0.0428489	+	0.0537308i
$236$	9.82943	+	12.3257i	0.639841	+	0.802335i
$237$	6.40430	+	3.08415i	0.416004	+	0.200337i
$238$	−7.64740	+	3.68279i	−0.495707	+	0.238720i
$239$	7.24046	−	9.07925i	0.468347	−	0.587288i	−0.490419	−	0.871487i	$-0.663156\pi$
$239$	7.24046	−	9.07925i	0.468347	−	0.587288i	0.958765	+	0.284199i	$0.0917276\pi$
$240$	−1.04004	−	4.55669i	−0.0671340	−	0.294133i
$241$	0.504747	+	2.21144i	0.0325136	+	0.142451i	0.988579	−	0.150701i	$-0.0481529\pi$
$241$	0.504747	+	2.21144i	0.0325136	+	0.142451i	−0.956066	+	0.293152i	$0.905296\pi$
$242$	23.9373	+	30.0164i	1.53875	+	1.92953i
$243$	−0.222521	+	0.974928i	−0.0142747	+	0.0625417i
$244$	−6.66004			−0.426365
$245$	−1.43027	+	6.26644i	−0.0913768	+	0.400348i
$246$	−11.5754	+	5.57444i	−0.738023	+	0.355413i
$247$	−13.7234	+	6.60885i	−0.873200	+	0.420511i
$248$	−0.284121	+	1.24482i	−0.0180417	+	0.0790459i
$249$	0.123176			0.00780595
$250$	0.420504	−	1.84235i	0.0265950	−	0.116520i
$251$	1.19305	+	1.49604i	0.0753045	+	0.0944289i	0.818057	−	0.575137i	$-0.195051\pi$
$251$	1.19305	+	1.49604i	0.0753045	+	0.0944289i	−0.742752	+	0.669566i	$0.766480\pi$
$252$	0.264496	+	1.15883i	0.0166617	+	0.0729997i
$253$	−7.22577	−	31.6582i	−0.454280	−	1.99033i
$254$	13.0882	−	16.4121i	0.821226	−	1.02979i
$255$	−5.34886	+	2.57588i	−0.334959	+	0.161308i
$256$	−18.4979	−	8.90812i	−1.15612	−	0.556757i
$257$	−7.90623	−	9.91410i	−0.493177	−	0.618425i	0.471498	−	0.881867i	$-0.343713\pi$
$257$	−7.90623	−	9.91410i	−0.493177	−	0.618425i	−0.964675	+	0.263443i	$0.915142\pi$
$258$	−11.6166	+	14.5667i	−0.723218	+	0.906886i
$259$	5.75277	+	2.77039i	0.357460	+	0.172144i
$260$	−5.59065			−0.346717
$261$	4.46668	+	3.00812i	0.276480	+	0.186198i
$262$	15.9489			0.985326
$263$	4.57783	+	2.20457i	0.282281	+	0.135939i	0.569667	−	0.821875i	$-0.307072\pi$
$263$	4.57783	+	2.20457i	0.282281	+	0.135939i	−0.287386	+	0.957815i	$0.592786\pi$
$264$	−2.82812	+	3.54636i	−0.174059	+	0.218263i
$265$	4.57172	+	5.73275i	0.280838	+	0.352160i
$266$	5.51377	+	2.65529i	0.338071	+	0.162806i
$267$	−7.50065	+	3.61212i	−0.459032	+	0.221058i
$268$	7.44177	−	9.33169i	0.454579	−	0.570024i
$269$	−6.57828	−	28.8213i	−0.401085	−	1.75727i	−0.623021	−	0.782205i	$-0.714095\pi$
$269$	−6.57828	−	28.8213i	−0.401085	−	1.75727i	0.221936	−	0.975061i	$-0.428762\pi$
$270$	0.420504	+	1.84235i	0.0255911	+	0.112122i
$271$	−10.2404	−	12.8411i	−0.622060	−	0.780039i	0.366572	−	0.930390i	$-0.380531\pi$
$271$	−10.2404	−	12.8411i	−0.622060	−	0.780039i	−0.988633	+	0.150350i	$0.951960\pi$
$272$	−6.17447	+	27.0521i	−0.374382	+	1.64028i
$273$	−2.69227			−0.162944
$274$	5.27944	−	23.1307i	0.318943	−	1.39738i
$275$	−5.04191	+	2.42806i	−0.304039	+	0.146417i
$276$	−8.21360	+	3.95546i	−0.494401	+	0.238091i
$277$	−3.38363	+	14.8247i	−0.203303	+	0.890727i	0.765606	+	0.643309i	$0.222439\pi$
$277$	−3.38363	+	14.8247i	−0.203303	+	0.890727i	−0.968909	+	0.247418i	$0.920418\pi$
$278$	−9.52574			−0.571316
$279$	0.350526	−	1.53575i	0.0209854	−	0.0919432i
$280$	−0.382354	−	0.479457i	−0.0228500	−	0.0286530i
$281$	1.36695	+	5.98899i	0.0815453	+	0.357273i	0.999195	−	0.0401169i	$-0.0127730\pi$
$281$	1.36695	+	5.98899i	0.0815453	+	0.357273i	−0.917650	+	0.397390i	$0.869916\pi$
$282$	−0.443011	−	1.94096i	−0.0263809	−	0.115582i
$283$	−7.89748	+	9.90312i	−0.469456	+	0.588680i	−0.959038	−	0.283278i	$-0.908578\pi$
$283$	−7.89748	+	9.90312i	−0.469456	+	0.588680i	0.489582	+	0.871958i	$0.337150\pi$
$284$	16.9412	−	8.15847i	1.00528	−	0.484116i
$285$	3.85652	+	1.85720i	0.228441	+	0.110011i
$286$	23.4628	+	29.4215i	1.38739	+	1.73973i
$287$	−3.20709	+	4.02156i	−0.189308	+	0.237385i
$288$	6.49710	+	3.12884i	0.382846	+	0.184369i
$289$	18.2455			1.07326
$290$	10.0713	+	1.45925i	0.591409	+	0.0856902i
$291$	8.13335			0.476786
$292$	−21.8898	−	10.5416i	−1.28101	−	0.616900i
$293$	−19.8183	+	24.8514i	−1.15780	+	1.45183i	−0.288547	+	0.957466i	$0.593172\pi$
$293$	−19.8183	+	24.8514i	−1.15780	+	1.45183i	−0.869252	+	0.494369i	$0.835399\pi$
$294$	−7.57316	−	9.49644i	−0.441675	−	0.553844i
$295$	9.04092	+	4.35388i	0.526383	+	0.253492i
$296$	6.16322	−	2.96805i	0.358230	−	0.172515i
$297$	3.48911	−	4.37521i	0.202459	−	0.253875i
$298$	−2.11042	−	9.24636i	−0.122253	−	0.535627i
$299$	−4.59478	−	20.1310i	−0.265723	−	1.16421i
$300$	0.979547	+	1.22831i	0.0565542	+	0.0709167i
$301$	−1.65987	+	7.27236i	−0.0956733	+	0.419172i
$302$	7.34818			0.422840
$303$	0.699735	−	3.06574i	0.0401987	−	0.176122i
$304$	18.0249	−	8.68034i	1.03380	−	0.497852i
$305$	−3.81936	+	1.83931i	−0.218696	+	0.105318i
$306$	2.49644	−	10.9376i	0.142712	−	0.625263i
$307$	0.549073			0.0313372			0.0156686	−	0.999877i	$-0.495012\pi$
$307$	0.549073			0.0313372			0.0156686	+	0.999877i	$0.495012\pi$
$308$	1.48015	−	6.48496i	0.0843393	−	0.369515i
$309$	−6.61579	−	8.29594i	−0.376359	−	0.471939i
$310$	−0.662399	−	2.90216i	−0.0376217	−	0.164831i
$311$	0.0404546	+	0.177243i	0.00229397	+	0.0100505i	0.976062	−	0.217493i	$-0.0697878\pi$
$311$	0.0404546	+	0.177243i	0.00229397	+	0.0100505i	−0.973768	+	0.227543i	$0.926931\pi$
$312$	−1.79837	+	2.25508i	−0.101813	+	0.127669i
$313$	10.6573	−	5.13228i	0.602386	−	0.290094i	−0.107728	−	0.994180i	$-0.534358\pi$
$313$	10.6573	−	5.13228i	0.602386	−	0.290094i	0.710114	+	0.704087i	$0.248643\pi$
$314$	−5.52638	−	2.66137i	−0.311872	−	0.150190i
$315$	0.471718	+	0.591515i	0.0265783	+	0.0333281i
$316$	−6.96286	+	8.73115i	−0.391691	+	0.491165i
$317$	−14.7389	−	7.09790i	−0.827821	−	0.398658i	−0.0285237	−	0.999593i	$-0.509081\pi$
$317$	−14.7389	−	7.09790i	−0.827821	−	0.398658i	−0.799298	+	0.600935i	$0.794795\pi$
$318$	−13.8564			−0.777026
$319$	−15.2167	−	26.0120i	−0.851973	−	1.45639i
$320$	4.27953			0.239233
$321$	−16.6509	−	8.01865i	−0.929363	−	0.447558i
$322$	−5.17260	+	6.48624i	−0.288258	+	0.361464i
$323$	−15.8441	−	19.8679i	−0.881589	−	1.10548i
$324$	−1.41549	−	0.681663i	−0.0786382	−	0.0378701i
$325$	−3.20609	+	1.54397i	−0.177842	+	0.0856442i
$326$	10.4044	−	13.0467i	0.576248	−	0.722592i
$327$	−2.00841	−	8.79943i	−0.111066	−	0.486610i
$328$	1.22626	+	5.37260i	0.0677089	+	0.296652i
$329$	−0.496966	−	0.623175i	−0.0273986	−	0.0343568i
$330$	2.35318	−	10.3100i	0.129538	−	0.567545i
$331$	16.8826			0.927953			0.463977	−	0.885847i	$-0.346422\pi$
$331$	16.8826			0.927953			0.463977	+	0.885847i	$0.346422\pi$
$332$	−0.0430618	+	0.188666i	−0.00236333	+	0.0103544i
$333$	−7.60369	+	3.66174i	−0.416680	+	0.200662i
$334$	−14.7253	+	7.09132i	−0.805731	+	0.388020i
$335$	1.69053	−	7.40668i	0.0923633	−	0.404670i
$336$	3.53615			0.192913
$337$	3.57162	−	15.6483i	0.194558	−	0.852416i	−0.779551	−	0.626339i	$-0.784553\pi$
$337$	3.57162	−	15.6483i	0.194558	−	0.852416i	0.974109	−	0.226077i	$-0.0725902\pi$
$338$	−0.397219	−	0.498097i	−0.0216059	−	0.0270929i
$339$	3.79371	+	16.6213i	0.206046	+	0.902746i
$340$	−2.07548	−	9.09327i	−0.112559	−	0.493152i
$341$	−5.49622	+	6.89204i	−0.297637	+	0.373225i
$342$	−7.28778	+	3.50961i	−0.394078	+	0.189778i
$343$	−9.15294	−	4.40783i	−0.494213	−	0.238000i
$344$	4.98268	+	6.24808i	0.268648	+	0.336874i
$345$	−3.61790	+	4.53671i	−0.194781	+	0.244248i
$346$	−33.5531	−	16.1583i	−1.80383	−	0.868678i
$347$	21.8429			1.17259			0.586294	−	0.810098i	$-0.300586\pi$
$347$	21.8429			1.17259			0.586294	+	0.810098i	$0.300586\pi$
$348$	−6.16902	+	5.78990i	−0.330694	+	0.310371i
$349$	−21.5708			−1.15466			−0.577328	−	0.816512i	$-0.695905\pi$
$349$	−21.5708			−1.15466			−0.577328	+	0.816512i	$0.695905\pi$
$350$	1.28814	+	0.620334i	0.0688538	+	0.0331582i
$351$	2.21868	−	2.78214i	0.118425	−	0.148500i
$352$	−25.1608	−	31.5507i	−1.34108	−	1.68166i
$353$	7.03817	+	3.38940i	0.374604	+	0.180400i	0.611706	−	0.791085i	$-0.290483\pi$
$353$	7.03817	+	3.38940i	0.374604	+	0.180400i	−0.237102	+	0.971485i	$0.576198\pi$
$354$	−17.0849	+	8.22764i	−0.908051	+	0.437294i
$355$	7.46223	−	9.35733i	0.396054	−	0.496636i
$356$	−2.91042	−	12.7514i	−0.154252	−	0.675822i
$357$	−0.999483	−	4.37902i	−0.0528983	−	0.231762i
$358$	20.8131	+	26.0988i	1.10001	+	1.37937i
$359$	5.70295	−	24.9862i	0.300990	−	1.31872i	−0.567646	−	0.823273i	$-0.692146\pi$
$359$	5.70295	−	24.9862i	0.300990	−	1.31872i	0.868636	−	0.495451i	$-0.164997\pi$
$360$	0.810557			0.0427201
$361$	0.150873	−	0.661016i	0.00794066	−	0.0347903i
$362$	22.3042	−	10.7411i	1.17228	−	0.564542i
$363$	−18.3044	+	8.81494i	−0.960732	+	0.462664i
$364$	0.941209	−	4.12370i	0.0493327	−	0.216141i
$365$	−15.4645			−0.809450
$366$	1.78259	−	7.81002i	0.0931773	−	0.408237i
$367$	9.19221	+	11.5267i	0.479830	+	0.601687i	0.961547	−	0.274639i	$-0.0885584\pi$
$367$	9.19221	+	11.5267i	0.479830	+	0.601687i	−0.481718	+	0.876326i	$0.659987\pi$
$368$	6.03498	+	26.4410i	0.314595	+	1.37833i
$369$	−1.51286	−	6.62828i	−0.0787565	−	0.345055i
$370$	−9.94359	+	12.4689i	−0.516943	+	0.648226i
$371$	−4.99819	+	2.40700i	−0.259493	+	0.124965i
$372$	2.22974	+	1.07379i	0.115607	+	0.0556733i
$373$	−4.50549	−	5.64970i	−0.233285	−	0.292530i	0.651385	−	0.758747i	$-0.274188\pi$
$373$	−4.50549	−	5.64970i	−0.233285	−	0.292530i	−0.884671	+	0.466217i	$0.845617\pi$
$374$	−39.1441	+	49.0851i	−2.02409	+	2.53813i
$375$	0.900969	+	0.433884i	0.0465258	+	0.0224057i
$376$	−0.853940			−0.0440386
$377$	−9.67613	−	16.5407i	−0.498346	−	0.851891i
$378$	−1.42972			−0.0735371
$379$	25.3788	+	12.2218i	1.30362	+	0.627791i	0.951352	−	0.308107i	$-0.0996956\pi$
$379$	25.3788	+	12.2218i	1.30362	+	0.627791i	0.352270	+	0.935898i	$0.385410\pi$
$380$	−4.19287	+	5.25770i	−0.215090	+	0.269714i
$381$	6.92597	+	8.68489i	0.354828	+	0.444940i
$382$	−31.0290	−	14.9428i	−1.58758	−	0.764538i
$383$	3.23594	−	1.55835i	0.165349	−	0.0796277i	−0.349379	−	0.936982i	$-0.613607\pi$
$383$	3.23594	−	1.55835i	0.165349	−	0.0796277i	0.514728	+	0.857354i	$0.327893\pi$
$384$	3.95001	−	4.95316i	0.201573	−	0.252765i
$385$	−0.942127	−	4.12773i	−0.0480152	−	0.210368i
$386$	−10.0610	−	44.0803i	−0.512094	−	2.24363i
$387$	−6.14723	−	7.70838i	−0.312481	−	0.391839i
$388$	−2.84339	+	12.4577i	−0.144351	+	0.632445i
$389$	−28.4184			−1.44087			−0.720434	−	0.693523i	$-0.756057\pi$
$389$	−28.4184			−1.44087			−0.720434	+	0.693523i	$0.756057\pi$
$390$	1.49636	−	6.55598i	0.0757712	−	0.331975i
$391$	31.0377	−	14.9470i	1.56964	−	0.755900i
$392$	−4.69398	+	2.26050i	−0.237082	+	0.114173i
$393$	−1.87803	+	8.22818i	−0.0947340	+	0.415057i
$394$	20.0572			1.01047
$395$	−1.58173	+	6.93002i	−0.0795856	+	0.348687i
$396$	5.48165	+	6.87377i	0.275463	+	0.345420i
$397$	1.27169	+	5.57162i	0.0638241	+	0.279632i	0.996762	−	0.0804049i	$-0.0256213\pi$
$397$	1.27169	+	5.57162i	0.0638241	+	0.279632i	−0.932938	+	0.360037i	$0.882764\pi$
$398$	−3.89551	−	17.0673i	−0.195264	−	0.855509i
$399$	−2.01915	+	2.53193i	−0.101084	+	0.126755i
$400$	4.21102	−	2.02792i	0.210551	−	0.101396i
$401$	−1.92896	−	0.928940i	−0.0963278	−	0.0463890i	0.385099	−	0.922875i	$-0.374167\pi$
$401$	−1.92896	−	0.928940i	−0.0963278	−	0.0463890i	−0.481427	+	0.876486i	$0.659881\pi$
$402$	8.95117	+	11.2244i	0.446444	+	0.559822i
$403$	−3.49498	+	4.38256i	−0.174097	+	0.218311i
$404$	4.45111	+	2.14354i	0.221451	+	0.106645i
$405$	−1.00000			−0.0496904
$406$	−2.77191	+	7.18302i	−0.137567	+	0.356487i
$407$	47.2281			2.34101
$408$	−4.33556	−	2.08789i	−0.214642	−	0.103366i
$409$	−0.284578	+	0.356850i	−0.0140715	+	0.0176451i	−0.788817	−	0.614628i	$-0.789306\pi$
$409$	−0.284578	+	0.356850i	−0.0140715	+	0.0176451i	0.774746	+	0.632273i	$0.217878\pi$
$410$	−8.01045	−	10.0448i	−0.395608	−	0.496077i
$411$	11.3117	+	5.44742i	0.557964	+	0.268701i
$412$	15.0196	−	7.23305i	0.739962	−	0.356347i
$413$	−4.73353	+	5.93566i	−0.232922	+	0.292075i
$414$	−2.44005	−	10.6905i	−0.119922	−	0.525411i
$415$	0.0274092	+	0.120088i	0.00134546	+	0.00589487i
$416$	−15.9995	−	20.0627i	−0.784438	−	0.983654i
$417$	1.12168	−	4.91441i	0.0549290	−	0.240660i
$418$	45.2659			2.21403
$419$	−2.91190	+	12.7579i	−0.142256	+	0.623263i	0.852652	+	0.522479i	$0.174993\pi$
$419$	−2.91190	+	12.7579i	−0.142256	+	0.623263i	−0.994908	+	0.100785i	$0.967865\pi$
$420$	−1.07092	+	0.515730i	−0.0522558	+	0.0251650i
$421$	−6.89233	+	3.31917i	−0.335912	+	0.161767i	−0.594234	−	0.804292i	$-0.702545\pi$
$421$	−6.89233	+	3.31917i	−0.335912	+	0.161767i	0.258322	+	0.966059i	$0.416830\pi$
$422$	4.85659	−	21.2781i	0.236415	−	1.03580i
$423$	1.05352			0.0512240
$424$	−1.32253	+	5.79437i	−0.0642276	+	0.281399i
$425$	−3.70153	−	4.64157i	−0.179550	−	0.225149i
$426$	5.03279	+	22.0501i	0.243840	+	1.06833i
$427$	−0.713681	−	3.12684i	−0.0345375	−	0.151319i
$428$	18.1031	−	22.7006i	0.875048	−	1.09727i
$429$	−17.9416	+	8.64022i	−0.866229	+	0.417154i
$430$	−16.7865	−	8.08394i	−0.809515	−	0.389842i
$431$	9.24559	+	11.5936i	0.445344	+	0.558444i	0.952943	−	0.303150i	$-0.0980382\pi$
$431$	9.24559	+	11.5936i	0.445344	+	0.558444i	−0.507599	+	0.861594i	$0.669467\pi$
$432$	−2.91411	+	3.65418i	−0.140205	+	0.175812i
$433$	17.6564	+	8.50288i	0.848513	+	0.408622i	0.807025	−	0.590517i	$-0.201076\pi$
$433$	17.6564	+	8.50288i	0.848513	+	0.408622i	0.0414876	+	0.999139i	$0.486790\pi$
$434$	2.25217			0.108108
$435$	−1.93877	+	5.02406i	−0.0929569	+	0.240885i
$436$	14.1801			0.679102
$437$	−22.3781	−	10.7767i	−1.07049	−	0.515521i
$438$	18.2207	−	22.8480i	0.870619	−	1.09172i
$439$	−4.88259	−	6.12258i	−0.233033	−	0.292215i	0.651541	−	0.758613i	$-0.274123\pi$
$439$	−4.88259	−	6.12258i	−0.233033	−	0.292215i	−0.884575	+	0.466399i	$0.845551\pi$
$440$	−4.08676	−	1.96808i	−0.194829	−	0.0938245i
$441$	5.79106	−	2.78883i	0.275765	−	0.132801i
$442$	−24.8912	+	31.2126i	−1.18396	+	1.48463i
$443$	4.06382	+	17.8047i	0.193078	+	0.845929i	0.974938	+	0.222475i	$0.0714137\pi$
$443$	4.06382	+	17.8047i	0.193078	+	0.845929i	−0.781861	+	0.623453i	$0.785729\pi$
$444$	−2.95040	−	12.9266i	−0.140020	−	0.613468i
$445$	−5.19061	−	6.50882i	−0.246058	−	0.308548i
$446$	−4.19812	+	18.3932i	−0.198787	+	0.870941i
$447$	5.01879			0.237381
$448$	−0.720477	+	3.15662i	−0.0340393	+	0.149136i
$449$	8.77433	−	4.22549i	0.414086	−	0.199413i	−0.215229	−	0.976564i	$-0.569050\pi$
$449$	8.77433	−	4.22549i	0.414086	−	0.199413i	0.629315	+	0.777150i	$0.283336\pi$
$450$	−1.70259	+	0.819922i	−0.0802607	+	0.0386515i
$451$	−8.46613	+	37.0925i	−0.398655	+	1.74662i
$452$	−26.7848			−1.25985
$453$	−0.865270	+	3.79099i	−0.0406539	+	0.178116i
$454$	−25.2126	−	31.6156i	−1.18329	−	1.48379i
$455$	−0.599087	−	2.62477i	−0.0280856	−	0.123051i
$456$	0.772042	+	3.38253i	0.0361542	+	0.158402i
$457$	2.68901	−	3.37191i	0.125787	−	0.157731i	−0.714950	−	0.699175i	$-0.753551\pi$
$457$	2.68901	−	3.37191i	0.125787	−	0.157731i	0.840737	+	0.541444i	$0.182122\pi$
$458$	−5.72572	+	2.75736i	−0.267546	+	0.128843i
$459$	5.34886	+	2.57588i	0.249664	+	0.120232i
$460$	−5.68399	−	7.12750i	−0.265017	−	0.332321i
$461$	−16.9991	+	21.3162i	−0.791728	+	0.992795i	0.208164	+	0.978094i	$0.433251\pi$
$461$	−16.9991	+	21.3162i	−0.791728	+	0.992795i	−0.999892	+	0.0147014i	$0.995320\pi$
$462$	7.20855	+	3.47145i	0.335372	+	0.161507i
$463$	−2.41439			−0.112206			−0.0561031	−	0.998425i	$-0.517868\pi$
$463$	−2.41439			−0.112206			−0.0561031	+	0.998425i	$0.517868\pi$
$464$	12.7090	+	21.7253i	0.590002	+	1.00857i
$465$	1.57525			0.0730504
$466$	−36.9815	−	17.8093i	−1.71313	−	0.825002i
$467$	1.83780	−	2.30453i	0.0850434	−	0.106641i	−0.737489	−	0.675359i	$-0.763989\pi$
$467$	1.83780	−	2.30453i	0.0850434	−	0.106641i	0.822533	+	0.568718i	$0.192560\pi$
$468$	3.48571	+	4.37094i	0.161127	+	0.202047i
$469$	5.17861	+	2.49389i	0.239126	+	0.115157i
$470$	1.79371	−	0.863807i	0.0827379	−	0.0398444i
$471$	2.02377	−	2.53773i	0.0932504	−	0.116932i
$472$	1.80991	+	7.92974i	0.0833079	+	0.364996i
$473$	12.2774	+	53.7908i	0.564516	+	2.47331i
$474$	−8.37511	−	10.5021i	−0.384682	−	0.482376i
$475$	−0.952483	+	4.17310i	−0.0437029	+	0.191475i
$476$	7.05668			0.323443
$477$	1.63163	−	7.14862i	0.0747071	−	0.327313i
$478$	−19.7718	+	9.52159i	−0.904341	+	0.435508i
$479$	33.1791	−	15.9782i	1.51599	−	0.730063i	0.523460	−	0.852050i	$-0.324641\pi$
$479$	33.1791	−	15.9782i	1.51599	−	0.730063i	0.992532	+	0.121987i	$0.0389265\pi$
$480$	−1.60465	+	7.03044i	−0.0732420	+	0.320894i
$481$	30.0317			1.36933
$482$	0.953834	−	4.17902i	0.0434460	−	0.190349i
$483$	−2.73722	−	3.43237i	−0.124548	−	0.156178i
$484$	−7.10253	−	31.1182i	−0.322842	−	1.41446i
$485$	1.80984	+	7.92943i	0.0821807	+	0.360057i
$486$	1.17823	−	1.47745i	0.0534454	−	0.0670184i
$487$	−7.40152	+	3.56438i	−0.335395	+	0.161518i	−0.593999	−	0.804466i	$-0.702452\pi$
$487$	−7.40152	+	3.56438i	−0.335395	+	0.161518i	0.258604	+	0.965983i	$0.416737\pi$
$488$	−3.09581	−	1.49086i	−0.140141	−	0.0674882i
$489$	5.50578	+	6.90403i	0.248980	+	0.312211i
$490$	7.57316	−	9.49644i	0.342120	−	0.429005i
$491$	−10.3747	−	4.99619i	−0.468203	−	0.225475i	0.184880	−	0.982761i	$-0.440810\pi$
$491$	−10.3747	−	4.99619i	−0.468203	−	0.225475i	−0.653083	+	0.757286i	$0.726525\pi$
$492$	10.6813			0.481551
$493$	23.3116	−	21.8790i	1.04990	−	0.985379i
$494$	28.7840			1.29505
$495$	5.04191	+	2.42806i	0.226617	+	0.109133i
$496$	4.59046	−	5.75625i	0.206118	−	0.258463i
$497$	5.64574	+	7.07954i	0.253246	+	0.317561i
$498$	−0.209717	−	0.100995i	−0.00939766	−	0.00452568i
$499$	11.8733	−	5.71790i	0.531524	−	0.255968i	−0.148816	−	0.988865i	$-0.547546\pi$
$499$	11.8733	−	5.71790i	0.531524	−	0.255968i	0.680340	+	0.732896i	$0.261832\pi$
$500$	−0.979547	+	1.22831i	−0.0438067	+	0.0549319i
$501$	−1.92453	−	8.43193i	−0.0859818	−	0.376711i
$502$	−0.804635	−	3.52534i	−0.0359126	−	0.157343i
$503$	−1.62697	−	2.04016i	−0.0725431	−	0.0909662i	0.744236	−	0.667917i	$-0.232814\pi$
$503$	−1.62697	−	2.04016i	−0.0725431	−	0.0909662i	−0.816779	+	0.576951i	$0.804242\pi$
$504$	−0.136461	+	0.597873i	−0.00607844	+	0.0266314i
$505$	3.14458			0.139932
$506$	−13.6547	+	59.8253i	−0.607027	+	2.65956i
$507$	0.303746	−	0.146277i	0.0134898	−	0.00649637i
$508$	−15.7238	+	7.57217i	−0.697630	+	0.335961i
$509$	2.73042	−	11.9628i	0.121024	−	0.530240i	−0.877676	−	0.479255i	$-0.840907\pi$
$509$	2.73042	−	11.9628i	0.121024	−	0.530240i	0.998699	−	0.0509846i	$-0.0162360\pi$
$510$	11.2189			0.496782
$511$	2.60352	−	11.4068i	0.115173	−	0.504605i
$512$	16.2903	+	20.4274i	0.719935	+	0.902770i
$513$	−0.952483	−	4.17310i	−0.0420531	−	0.184247i
$514$	5.33225	+	23.3621i	0.235195	+	1.03046i
$515$	6.61579	−	8.29594i	0.291526	−	0.365563i
$516$	13.9558	−	6.72078i	0.614372	−	0.295866i
$517$	−5.31177	−	2.55801i	−0.233611	−	0.112501i
$518$	−7.52309	−	9.43365i	−0.330546	−	0.414491i
$519$	12.2872	−	15.4077i	0.539349	−	0.676322i
$520$	−2.59872	−	1.25148i	−0.113961	−	0.0548809i
$521$	−13.9092			−0.609374			−0.304687	−	0.952453i	$-0.598552\pi$
$521$	−13.9092			−0.609374			−0.304687	+	0.952453i	$0.598552\pi$
$522$	−5.13848	−	8.78391i	−0.224905	−	0.384461i
$523$	17.1609			0.750396			0.375198	−	0.926945i	$-0.377575\pi$
$523$	17.1609			0.750396			0.375198	+	0.926945i	$0.377575\pi$
$524$	−11.9464	−	5.75309i	−0.521881	−	0.251325i
$525$	−0.471718	+	0.591515i	−0.0205875	+	0.0258158i
$526$	−5.98658	−	7.50693i	−0.261027	−	0.327318i
$527$	−8.42579	−	4.05765i	−0.367033	−	0.176754i
$528$	23.5653	−	11.3484i	1.02555	−	0.493878i
$529$	6.65323	−	8.34288i	0.289271	−	0.362734i
$530$	−3.08333	−	13.5090i	−0.133931	−	0.586792i
$531$	−2.23292	−	9.78307i	−0.0969006	−	0.424549i
$532$	−3.17223	−	3.97785i	−0.137534	−	0.172462i
$533$	−5.38351	+	23.5867i	−0.233186	+	1.02165i
$534$	15.7322			0.680797
$535$	4.11243	−	18.0178i	0.177796	−	0.778975i
$536$	5.54810	−	2.67182i	0.239641	−	0.115405i
$537$	−15.9154	+	7.66447i	−0.686802	+	0.330746i
$538$	−12.4312	+	54.4644i	−0.535945	+	2.34813i
$539$	−35.9695			−1.54931
$540$	0.349596	−	1.53168i	0.0150442	−	0.0659131i
$541$	−10.9385	−	13.7165i	−0.470283	−	0.589717i	0.488957	−	0.872308i	$-0.337377\pi$
$541$	−10.9385	−	13.7165i	−0.470283	−	0.589717i	−0.959240	+	0.282591i	$0.908806\pi$
$542$	6.90650	+	30.2594i	0.296660	+	1.29975i
$543$	2.91507	+	12.7717i	0.125098	+	0.548088i
$544$	26.6926	−	33.4715i	1.14444	−	1.43508i
$545$	8.13190	−	3.91612i	0.348332	−	0.167748i
$546$	4.58383	+	2.20745i	0.196170	+	0.0944703i
$547$	9.37590	+	11.7570i	0.400885	+	0.502693i	0.940770	−	0.339045i	$-0.110104\pi$
$547$	9.37590	+	11.7570i	0.400885	+	0.502693i	−0.539886	+	0.841738i	$0.681532\pi$
$548$	−12.2982	+	15.4215i	−0.525355	+	0.658774i
$549$	3.81936	+	1.83931i	0.163006	+	0.0784997i
$550$	10.5751			0.450924
$551$	−22.8125	−	3.30535i	−0.971847	−	0.140813i
$552$	−4.70339			−0.200190
$553$	−4.84535	−	2.33340i	−0.206045	−	0.0992261i
$554$	17.9160	−	22.4659i	0.761177	−	0.954486i
$555$	−5.26192	−	6.59823i	−0.223356	−	0.280079i
$556$	7.13518	+	3.43612i	0.302599	+	0.145724i
$557$	8.06586	−	3.88431i	0.341761	−	0.164584i	−0.255128	−	0.966907i	$-0.582118\pi$
$557$	8.06586	−	3.88431i	0.341761	−	0.164584i	0.596889	+	0.802324i	$0.296403\pi$
$558$	−1.85600	+	2.32735i	−0.0785707	+	0.0985246i
$559$	7.80705	+	34.2049i	0.330203	+	1.44671i
$560$	0.786866	+	3.44749i	0.0332512	+	0.145683i
$561$	−20.7141	−	25.9747i	−0.874551	−	1.09665i
$562$	2.58316	−	11.3176i	0.108964	−	0.477403i
$563$	45.2721			1.90799			0.953995	−	0.299822i	$-0.0969273\pi$
$563$	45.2721			1.90799			0.953995	+	0.299822i	$0.0969273\pi$
$564$	−0.368308	+	1.61366i	−0.0155086	+	0.0679474i
$565$	−15.3604	+	7.39718i	−0.646217	+	0.311202i
$566$	21.5659	−	10.3856i	0.906484	−	0.436540i
$567$	0.168354	−	0.737608i	0.00707021	−	0.0309766i
$568$	9.70113			0.407051
$569$	−0.227013	+	0.994609i	−0.00951688	+	0.0416962i	−0.979463	−	0.201622i	$-0.935379\pi$
$569$	−0.227013	+	0.994609i	−0.00951688	+	0.0416962i	0.969947	+	0.243318i	$0.0782359\pi$
$570$	−5.04330	−	6.32410i	−0.211241	−	0.264887i
$571$	6.97152	+	30.5442i	0.291749	+	1.27824i	0.882089	+	0.471082i	$0.156136\pi$
$571$	6.97152	+	30.5442i	0.291749	+	1.27824i	−0.590340	+	0.807155i	$0.701006\pi$
$572$	−6.96175	−	30.5014i	−0.291086	−	1.27533i
$573$	11.3629	−	14.2486i	0.474690	−	0.595243i
$574$	8.75771	−	4.21749i	0.365540	−	0.176035i
$575$	−5.22802	−	2.51768i	−0.218024	−	0.104995i
$576$	−2.66825	−	3.34587i	−0.111177	−	0.139411i
$577$	18.6388	−	23.3723i	0.775943	−	0.973002i	−0.224056	−	0.974576i	$-0.571930\pi$
$577$	18.6388	−	23.3723i	0.775943	−	0.973002i	0.999999	+	0.00157441i	$0.000501152\pi$
$578$	−31.0645	−	14.9599i	−1.29211	−	0.622249i
$579$	23.9262			0.994337
$580$	−7.01747	−	4.72597i	−0.291385	−	0.196235i
$581$	−0.0931920			−0.00386625
$582$	−13.8477	−	6.66872i	−0.574007	−	0.276427i
$583$	−25.5838	+	32.0811i	−1.05957	+	1.32866i
$584$	−7.81537	−	9.80016i	−0.323402	−	0.405534i
$585$	3.20609	+	1.54397i	0.132556	+	0.0638354i
$586$	54.1186	−	26.0622i	2.23562	−	1.07662i
$587$	2.92122	−	3.66309i	0.120572	−	0.151192i	−0.717882	−	0.696164i	$-0.754888\pi$
$587$	2.92122	−	3.66309i	0.120572	−	0.151192i	0.838454	+	0.544972i	$0.183460\pi$
$588$	2.24706	+	9.84503i	0.0926673	+	0.406002i
$589$	1.50040	+	6.57367i	0.0618228	+	0.270863i
$590$	−11.8231	−	14.8257i	−0.486749	−	0.610364i
$591$	−2.36179	+	10.3477i	−0.0971513	+	0.425647i
$592$	−39.4450			−1.62118
$593$	9.50786	−	41.6567i	0.390441	−	1.71063i	−0.272666	−	0.962109i	$-0.587905\pi$
$593$	9.50786	−	41.6567i	0.390441	−	1.71063i	0.663107	−	0.748525i	$-0.269238\pi$
$594$	−9.52785	+	4.58837i	−0.390932	+	0.188263i
$595$	4.04682	−	1.94885i	0.165904	−	0.0798950i
$596$	−1.75455	+	7.68719i	−0.0718692	+	0.314880i
$597$	9.26391			0.379146
$598$	−8.68288	+	38.0422i	−0.355069	+	1.55566i
$599$	−7.19527	−	9.02258i	−0.293991	−	0.368653i	0.612797	−	0.790240i	$-0.290044\pi$
$599$	−7.19527	−	9.02258i	−0.293991	−	0.368653i	−0.906788	+	0.421588i	$0.861473\pi$
$600$	0.180366	+	0.790235i	0.00736341	+	0.0322612i
$601$	9.84390	+	43.1289i	0.401541	+	1.75927i	0.621163	+	0.783681i	$0.286660\pi$
$601$	9.84390	+	43.1289i	0.401541	+	1.75927i	−0.219622	+	0.975585i	$0.570482\pi$
$602$	8.78884	−	11.0209i	0.358207	−	0.449177i
$603$	−6.84480	+	3.29628i	−0.278742	+	0.134235i
$604$	−5.50410	−	2.65064i	−0.223959	−	0.107853i
$605$	−12.6670	−	15.8840i	−0.514988	−	0.645775i
$606$	−3.70503	+	4.64596i	−0.150506	+	0.188729i
$607$	−11.4863	−	5.53149i	−0.466213	−	0.224516i	0.186004	−	0.982549i	$-0.440446\pi$
$607$	−11.4863	−	5.53149i	−0.466213	−	0.224516i	−0.652216	+	0.758033i	$0.726161\pi$
$608$	−30.8671			−1.25183
$609$	−3.37938	−	2.27587i	−0.136940	−	0.0922230i
$610$	8.01087			0.324351
$611$	−3.37769	−	1.62661i	−0.136647	−	0.0658056i
$612$	−5.81537	+	7.29224i	−0.235072	+	0.294771i
$613$	−23.2249	−	29.1231i	−0.938046	−	1.17627i	−0.984150	−	0.177336i	$-0.943252\pi$
$613$	−23.2249	−	29.1231i	−0.938046	−	1.17627i	0.0461044	−	0.998937i	$-0.485319\pi$
$614$	−0.934843	−	0.450197i	−0.0377272	−	0.0181685i
$615$	6.12545	−	2.94986i	0.247002	−	0.118950i
$616$	2.13969	−	2.68309i	0.0862107	−	0.108105i
$617$	−6.41381	−	28.1007i	−0.258210	−	1.13129i	−0.923163	−	0.384408i	$-0.874406\pi$
$617$	−6.41381	−	28.1007i	−0.258210	−	1.13129i	0.664953	−	0.746885i	$-0.268452\pi$
$618$	4.46193	+	19.5490i	0.179485	+	0.786375i
$619$	6.77987	+	8.50169i	0.272506	+	0.341712i	0.899187	−	0.437564i	$-0.144159\pi$
$619$	6.77987	+	8.50169i	0.272506	+	0.341712i	−0.626681	+	0.779276i	$0.715587\pi$
$620$	−0.550701	+	2.41278i	−0.0221167	+	0.0968996i
$621$	5.80267			0.232853
$622$	0.0764482	−	0.334941i	0.00306529	−	0.0134299i
$623$	5.67481	−	2.73285i	0.227357	−	0.109489i
$624$	14.9849	−	7.21633i	0.599875	−	0.288885i
$625$	−0.222521	+	0.974928i	−0.00890084	+	0.0389971i
$626$	−22.3530			−0.893407
$627$	−5.33019	+	23.3531i	−0.212867	+	0.932633i
$628$	3.17949	+	3.98695i	0.126875	+	0.159097i
$629$	11.1490	+	48.8471i	0.444541	+	1.94766i
$630$	−0.318144	−	1.39388i	−0.0126751	−	0.0555334i
$631$	−18.3569	+	23.0188i	−0.730776	+	0.916364i	−0.998894	−	0.0470220i	$-0.985027\pi$
$631$	−18.3569	+	23.0188i	−0.730776	+	0.916364i	0.268118	+	0.963386i	$0.413598\pi$
$632$	−5.19105	+	2.49988i	−0.206489	+	0.0994398i
$633$	10.4057	+	5.01112i	0.413590	+	0.199174i
$634$	19.2746	+	24.1696i	0.765492	+	0.959896i
$635$	−6.92597	+	8.68489i	−0.274849	+	0.344649i
$636$	10.3790	+	4.99827i	0.411554	+	0.198194i
$637$	−22.8725			−0.906243
$638$	4.57994	+	56.7643i	0.181322	+	2.24732i
$639$	−11.9685			−0.473466
$640$	5.70794	+	2.74880i	0.225626	+	0.108656i
$641$	−21.2480	+	26.6441i	−0.839245	+	1.05238i	0.158638	+	0.987337i	$0.449290\pi$
$641$	−21.2480	+	26.6441i	−0.839245	+	1.05238i	−0.997882	+	0.0650427i	$0.979282\pi$
$642$	21.7749	+	27.3049i	0.859388	+	1.07764i
$643$	7.10801	+	3.42304i	0.280313	+	0.134991i	0.568758	−	0.822505i	$-0.307424\pi$
$643$	7.10801	+	3.42304i	0.280313	+	0.134991i	−0.288445	+	0.957496i	$0.593138\pi$
$644$	6.21422	−	2.99261i	0.244875	−	0.117925i
$645$	6.14723	−	7.70838i	0.242047	−	0.303517i
$646$	10.6858	+	46.8177i	0.420428	+	1.84202i
$647$	−9.42839	−	41.3085i	−0.370668	−	1.62400i	−0.724906	−	0.688848i	$-0.758117\pi$
$647$	−9.42839	−	41.3085i	−0.370668	−	1.62400i	0.354238	−	0.935155i	$-0.384740\pi$
$648$	−0.505374	−	0.633719i	−0.0198530	−	0.0248948i
$649$	−12.4957	+	54.7471i	−0.490498	+	2.14901i
$650$	6.72458			0.263760
$651$	−0.265200	+	1.16192i	−0.0103940	+	0.0455391i
$652$	−12.4996	+	6.01948i	−0.489522	+	0.235741i
$653$	31.6910	−	15.2616i	1.24016	−	0.597232i	0.305307	−	0.952254i	$-0.401241\pi$
$653$	31.6910	−	15.2616i	1.24016	−	0.597232i	0.934858	+	0.355022i	$0.115527\pi$
$654$	−3.79536	+	16.6285i	−0.148410	+	0.650227i
$655$	−8.43979			−0.329770
$656$	7.07093	−	30.9798i	0.276073	−	1.20956i
$657$	9.64197	+	12.0907i	0.376169	+	0.471701i
$658$	0.335172	+	1.46848i	0.0130663	+	0.0572474i
$659$	−9.87516	−	43.2659i	−0.384681	−	1.68540i	−0.682587	−	0.730804i	$-0.739145\pi$
$659$	−9.87516	−	43.2659i	−0.384681	−	1.68540i	0.297906	−	0.954595i	$-0.403712\pi$
$660$	−5.48165	+	6.87377i	−0.213373	+	0.267561i
$661$	−11.9124	+	5.73669i	−0.463337	+	0.223131i	−0.650963	−	0.759109i	$-0.725635\pi$
$661$	−11.9124	+	5.73669i	−0.463337	+	0.223131i	0.187627	+	0.982240i	$0.439921\pi$
$662$	−28.7441	−	13.8424i	−1.11717	−	0.538002i
$663$	−13.1719	−	16.5170i	−0.511553	−	0.641467i
$664$	−0.0622499	+	0.0780589i	−0.00241576	+	0.00302927i
$665$	−2.91776	−	1.40512i	−0.113146	−	0.0544881i
$666$	15.9483			0.617983
$667$	11.2500	−	29.1529i	0.435603	−	1.12881i
$668$	13.5878			0.525730
$669$	−8.99485	−	4.33169i	−0.347761	−	0.167473i
$670$	−8.95117	+	11.2244i	−0.345814	+	0.433637i
$671$	−14.7909	−	18.5472i	−0.570998	−	0.716008i
$672$	−4.91556	−	2.36721i	−0.189622	−	0.0913170i
$673$	7.89550	−	3.80227i	0.304349	−	0.146567i	−0.275476	−	0.961308i	$-0.588835\pi$
$673$	7.89550	−	3.80227i	0.304349	−	0.146567i	0.579825	+	0.814741i	$0.303121\pi$
$674$	−18.9114	+	23.7141i	−0.728439	+	0.913433i
$675$	−0.222521	−	0.974928i	−0.00856483	−	0.0375250i
$676$	0.117860	+	0.516381i	0.00453310	+	0.0198608i
$677$	26.9846	+	33.8376i	1.03710	+	1.30048i	0.952654	+	0.304057i	$0.0983413\pi$
$677$	26.9846	+	33.8376i	1.03710	+	1.30048i	0.0844482	+	0.996428i	$0.473087\pi$
$678$	7.16907	−	31.4098i	0.275327	−	1.20628i
$679$	−6.15351			−0.236150
$680$	1.07079	−	4.69146i	0.0410631	−	0.179909i
$681$	19.2796	−	9.28459i	0.738797	−	0.355786i
$682$	15.0087	−	7.22782i	0.574714	−	0.276768i
$683$	−6.89764	+	30.2205i	−0.263931	+	1.15636i	0.653015	+	0.757345i	$0.273504\pi$
$683$	−6.89764	+	30.2205i	−0.263931	+	1.15636i	−0.916946	+	0.399011i	$0.869353\pi$
$684$	6.72485			0.257131
$685$	−2.79376	+	12.2402i	−0.106744	+	0.467676i
$686$	11.9696	+	15.0094i	0.457002	+	0.573062i
$687$	−0.748328	−	3.27864i	−0.0285505	−	0.125088i
$688$	−10.2541	−	44.9262i	−0.390935	−	1.71280i
$689$	−16.2684	+	20.4000i	−0.619777	+	0.777176i
$690$	9.87954	−	4.75774i	0.376108	−	0.181124i
$691$	−37.2327	−	17.9303i	−1.41640	−	0.682102i	−0.439985	−	0.898005i	$-0.645016\pi$
$691$	−37.2327	−	17.9303i	−1.41640	−	0.682102i	−0.976415	+	0.215902i	$0.930731\pi$
$692$	19.3041	+	24.2066i	0.733832	+	0.920196i
$693$	−2.63978	+	3.31018i	−0.100277	+	0.125743i
$694$	−37.1894	−	17.9095i	−1.41169	−	0.679835i
$695$	5.04080			0.191208
$696$	−4.16365	+	1.31039i	−0.157823	+	0.0496704i
$697$	−40.3627			−1.52885
$698$	36.7261	+	17.6864i	1.39010	+	0.669438i
$699$	13.5427	−	16.9820i	0.512231	−	0.642317i
$700$	−0.741103	−	0.929313i	−0.0280110	−	0.0351247i
$701$	12.0372	+	5.79680i	0.454638	+	0.218942i	0.647166	−	0.762349i	$-0.275954\pi$
$701$	12.0372	+	5.79680i	0.454638	+	0.218942i	−0.192527	+	0.981292i	$0.561668\pi$
$702$	−6.05864	+	2.91769i	−0.228669	+	0.110121i
$703$	22.5232	−	28.2432i	0.849479	−	1.06521i
$704$	5.32909	+	23.3483i	0.200848	+	0.879971i
$705$	0.234431	+	1.02711i	0.00882918	+	0.0386832i
$706$	−9.20404	−	11.5415i	−0.346399	−	0.434370i
$707$	−0.529403	+	2.31947i	−0.0199103	+	0.0872325i
$708$	15.7652			0.592492
$709$	5.23218	−	22.9237i	0.196499	−	0.860917i	−0.776502	−	0.630115i	$-0.783008\pi$
$709$	5.23218	−	22.9237i	0.196499	−	0.860917i	0.973001	−	0.230802i	$-0.0741350\pi$
$710$	−20.3774	+	9.81322i	−0.764749	+	0.368284i
$711$	6.40430	−	3.08415i	0.240180	−	0.115665i
$712$	1.50156	−	6.57877i	0.0562734	−	0.246550i
$713$	−9.14064			−0.342320
$714$	−1.88875	+	8.27516i	−0.0706847	+	0.309690i
$715$	−12.4160	−	15.5691i	−0.464331	−	0.582253i
$716$	−6.17555	−	27.0569i	−0.230791	−	1.01116i
$717$	−2.58409	−	11.3216i	−0.0965046	−	0.422814i
$718$	−30.1965	+	37.8653i	−1.12692	+	1.41312i
$719$	34.7951	−	16.7564i	1.29764	−	0.624910i	0.347776	−	0.937577i	$-0.386937\pi$
$719$	34.7951	−	16.7564i	1.29764	−	0.624910i	0.949863	+	0.312667i	$0.101223\pi$
$720$	−4.21102	−	2.02792i	−0.156935	−	0.0755761i
$721$	5.00535	+	6.27651i	0.186409	+	0.233749i
$722$	−0.798855	+	1.00173i	−0.0297303	+	0.0372806i
$723$	2.04368	+	0.984184i	0.0760052	+	0.0366022i
$724$	−20.5814			−0.764900
$725$	−5.32951	−	0.772202i	−0.197933	−	0.0286789i
$726$	38.3924			1.42488
$727$	−8.87848	−	4.27565i	−0.329285	−	0.158575i	0.261935	−	0.965085i	$-0.415639\pi$
$727$	−8.87848	−	4.27565i	−0.329285	−	0.158575i	−0.591220	+	0.806510i	$0.701354\pi$
$728$	1.36060	−	1.70614i	0.0504273	−	0.0632339i
$729$	0.623490	+	0.781831i	0.0230922	+	0.0289567i
$730$	26.3297	+	12.6797i	0.974505	+	0.469297i
$731$	−52.7365	+	25.3966i	−1.95053	+	0.939326i
$732$	−4.15247	+	5.20703i	−0.153480	+	0.192457i
$733$	−8.64078	−	37.8577i	−0.319154	−	1.39831i	−0.839039	−	0.544071i	$-0.816882\pi$
$733$	−8.64078	−	37.8577i	−0.319154	−	1.39831i	0.519885	−	0.854236i	$-0.325975\pi$
$734$	−6.19956	−	27.1621i	−0.228830	−	1.00257i
$735$	4.00754	+	5.02529i	0.147820	+	0.185361i
$736$	9.31126	−	40.7953i	0.343218	−	1.50374i
$737$	42.5144			1.56604
$738$	−2.85890	+	12.5256i	−0.105237	+	0.461076i
$739$	−3.83634	+	1.84748i	−0.141122	+	0.0679608i	−0.503112	−	0.864221i	$-0.667812\pi$
$739$	−3.83634	+	1.84748i	−0.141122	+	0.0679608i	0.361990	+	0.932182i	$0.382097\pi$
$740$	11.9459	−	5.75286i	0.439142	−	0.211479i
$741$	−3.38940	+	14.8499i	−0.124513	+	0.545526i
$742$	10.4834			0.384858
$743$	0.317418	−	1.39070i	0.0116449	−	0.0510198i	−0.968772	−	0.247955i	$-0.920242\pi$
$743$	0.317418	−	1.39070i	0.0116449	−	0.0510198i	0.980417	+	0.196935i	$0.0630988\pi$
$744$	0.796090	+	0.998265i	0.0291861	+	0.0365982i
$745$	1.11679	+	4.89296i	0.0409159	+	0.179264i
$746$	3.03866	+	13.3133i	0.111253	+	0.487433i
$747$	0.0767989	−	0.0963027i	0.00280992	−	0.00352353i
$748$	47.0266	−	22.6468i	1.71946	−	0.828049i
$749$	12.5977	+	6.06673i	0.460309	+	0.221673i
$750$	−1.17823	−	1.47745i	−0.0430227	−	0.0539488i
$751$	5.83632	−	7.31851i	0.212970	−	0.267056i	−0.663859	−	0.747857i	$-0.731083\pi$
$751$	5.83632	−	7.31851i	0.212970	−	0.267056i	0.876830	+	0.480801i	$0.159654\pi$
$752$	4.43640	+	2.13646i	0.161779	+	0.0779087i
$753$	1.91350			0.0697319
$754$	2.91233	+	36.0957i	0.106061	+	1.31453i
$755$	−3.88849			−0.141517
$756$	1.07092	+	0.515730i	0.0389491	+	0.0187569i
$757$	−7.45362	+	9.34654i	−0.270906	+	0.339706i	−0.898611	−	0.438746i	$-0.855423\pi$
$757$	−7.45362	+	9.34654i	−0.270906	+	0.339706i	0.627705	+	0.778451i	$0.283994\pi$
$758$	−33.1887	−	41.6173i	−1.20547	−	1.51161i
$759$	−29.2565	−	14.0892i	−1.06195	−	0.511406i
$760$	−3.12593	+	1.50537i	−0.113389	+	0.0546055i
$761$	−17.5434	+	21.9987i	−0.635948	+	0.797453i	−0.990490	−	0.137587i	$-0.956065\pi$
$761$	−17.5434	+	21.9987i	−0.635948	+	0.797453i	0.354542	+	0.935040i	$0.384637\pi$
$762$	−4.67112	−	20.4655i	−0.169217	−	0.741388i
$763$	1.51952	+	6.65745i	0.0550103	+	0.241016i
$764$	17.8519	+	22.3855i	0.645858	+	0.809880i
$765$	−1.32106	+	5.78794i	−0.0477630	+	0.209263i
$766$	−6.78718			−0.245231
$767$	−7.94584	+	34.8130i	−0.286907	+	1.25702i
$768$	−18.4979	+	8.90812i	−0.667485	+	0.321444i
$769$	5.59544	−	2.69462i	0.201777	−	0.0971705i	−0.330267	−	0.943888i	$-0.607139\pi$
$769$	5.59544	−	2.69462i	0.201777	−	0.0971705i	0.532043	+	0.846717i	$0.321424\pi$
$770$	−1.78036	+	7.80028i	−0.0641599	+	0.281103i
$771$	−12.6806			−0.456681
$772$	−8.36450	+	36.6473i	−0.301045	+	1.31896i
$773$	19.0953	+	23.9448i	0.686811	+	0.861234i	0.995962	−	0.0897789i	$-0.0286160\pi$
$773$	19.0953	+	23.9448i	0.686811	+	0.861234i	−0.309150	+	0.951013i	$0.600045\pi$
$774$	4.14591	+	18.1644i	0.149022	+	0.652907i
$775$	0.350526	+	1.53575i	0.0125913	+	0.0551659i
$776$	−4.11039	+	5.15426i	−0.147554	+	0.185027i
$777$	5.75277	−	2.77039i	0.206380	−	0.0993872i
$778$	48.3847	+	23.3008i	1.73468	+	0.835376i
$779$	18.1445	+	22.7524i	0.650093	+	0.815191i
$780$	−3.48571	+	4.37094i	−0.124809	+	0.156505i
$781$	60.3440	+	29.0602i	2.15928	+	1.03985i
$782$	−65.0997			−2.32796
$783$	5.13677	−	1.61666i	0.183573	−	0.0577747i
$784$	30.0418			1.07292
$785$	2.92443	+	1.40833i	0.104377	+	0.0502655i
$786$	9.94398	−	12.4694i	0.354690	−	0.444767i
$787$	26.9359	+	33.7765i	0.960160	+	1.20400i	0.978934	+	0.204179i	$0.0654524\pi$
$787$	26.9359	+	33.7765i	0.960160	+	1.20400i	−0.0187736	+	0.999824i	$0.505976\pi$
$788$	−15.0237	−	7.23504i	−0.535198	−	0.257738i
$789$	4.57783	−	2.20457i	0.162975	−	0.0784847i
$790$	8.37511	−	10.5021i	0.297973	−	0.373647i
$791$	−2.87023	−	12.5753i	−0.102054	−	0.447126i
$792$	1.00935	+	4.42223i	0.0358655	+	0.157137i
$793$	−9.40537	−	11.7940i	−0.333995	−	0.418816i
$794$	2.40314	−	10.5288i	0.0852843	−	0.373655i
$795$	7.33246			0.260056
$796$	−3.23863	+	14.1894i	−0.114790	+	0.502928i
$797$	4.39577	−	2.11689i	0.155706	−	0.0749842i	−0.354408	−	0.935091i	$-0.615317\pi$
$797$	4.39577	−	2.11689i	0.155706	−	0.0749842i	0.510114	+	0.860107i	$0.329603\pi$
$798$	5.51377	−	2.65529i	0.195185	−	0.0939962i
$799$	1.39177	−	6.09773i	0.0492372	−	0.215722i
$800$	−7.21124			−0.254956
$801$	−1.85251	+	8.11636i	−0.0654551	+	0.286778i
$802$	2.52257	+	3.16320i	0.0890750	+	0.111696i
$803$	−19.2572	−	84.3713i	−0.679572	−	2.97740i
$804$	−2.65594	−	11.6364i	−0.0936677	−	0.410385i
$805$	2.73722	−	3.43237i	0.0964744	−	0.120975i
$806$	9.54386	−	4.59608i	0.336168	−	0.161890i
$807$	−26.6349	−	12.8267i	−0.937593	−	0.451521i
$808$	1.58919	+	1.99278i	0.0559075	+	0.0701058i
$809$	12.6596	−	15.8746i	0.445087	−	0.558121i	−0.507789	−	0.861481i	$-0.669537\pi$
$809$	12.6596	−	15.8746i	0.445087	−	0.558121i	0.952876	+	0.303360i	$0.0981086\pi$
$810$	1.70259	+	0.819922i	0.0598228	+	0.0288091i
$811$	34.3502			1.20620			0.603100	−	0.797666i	$-0.293932\pi$
$811$	34.3502			1.20620			0.603100	+	0.797666i	$0.293932\pi$
$812$	4.66733	−	4.38051i	0.163791	−	0.153726i
$813$	−16.4243			−0.576027
$814$	−80.4099	−	38.7233i	−2.81836	−	1.35725i
$815$	−5.50578	+	6.90403i	−0.192859	+	0.241838i
$816$	17.3005	+	21.6941i	0.605638	+	0.759446i
$817$	38.0230	+	18.3109i	1.33026	+	0.640617i
$818$	0.777108	−	0.374235i	0.0271709	−	0.0130848i
$819$	−1.67860	+	2.10490i	−0.0586552	+	0.0735513i
$820$	2.37682	+	10.4135i	0.0830020	+	0.363655i
$821$	−9.11465	−	39.9339i	−0.318103	−	1.39370i	−0.840875	−	0.541229i	$-0.817959\pi$
$821$	−9.11465	−	39.9339i	−0.318103	−	1.39370i	0.522772	−	0.852473i	$-0.324898\pi$
$822$	−14.7927	−	18.5494i	−0.515953	−	0.646985i
$823$	−3.35615	+	14.7043i	−0.116988	+	0.512558i	0.882147	+	0.470974i	$0.156097\pi$
$823$	−3.35615	+	14.7043i	−0.116988	+	0.512558i	−0.999135	+	0.0415838i	$0.986760\pi$
$824$	8.60074			0.299621
$825$	−1.24525	+	5.45580i	−0.0433540	+	0.189946i
$826$	12.9260	−	6.22484i	0.449754	−	0.216590i
$827$	20.8470	−	10.0394i	0.724922	−	0.349104i	−0.0347630	−	0.999396i	$-0.511068\pi$
$827$	20.8470	−	10.0394i	0.724922	−	0.349104i	0.759685	+	0.650292i	$0.225353\pi$
$828$	−2.02859	+	8.88784i	−0.0704984	+	0.308874i
$829$	−15.5168			−0.538921			−0.269461	−	0.963011i	$-0.586845\pi$
$829$	−15.5168			−0.538921			−0.269461	+	0.963011i	$0.586845\pi$
$830$	0.0517959	−	0.226933i	0.00179786	−	0.00787695i
$831$	9.48072	+	11.8884i	0.328883	+	0.412406i
$832$	3.38870	+	14.8469i	0.117482	+	0.514723i
$833$	−8.49123	−	37.2025i	−0.294204	−	1.28899i
$834$	−5.93920	+	7.44752i	−0.205658	+	0.257887i
$835$	7.79227	−	3.75256i	0.269663	−	0.129863i
$836$	−33.9061	−	16.3283i	−1.17267	−	0.564727i
$837$	−0.982152	−	1.23158i	−0.0339481	−	0.0425696i
$838$	15.4182	−	19.3339i	0.532614	−	0.667877i
$839$	−4.41853	−	2.12785i	−0.152545	−	0.0734617i	0.356054	−	0.934465i	$-0.384122\pi$
$839$	−4.41853	−	2.12785i	−0.152545	−	0.0734617i	−0.508599	+	0.861004i	$0.669836\pi$
$840$	−0.613248			−0.0211591
$841$	1.83683	−	28.9418i	0.0633388	−	0.997992i
$842$	14.4563			0.498195
$843$	5.53466	+	2.66535i	0.190624	+	0.0917996i
$844$	−11.3132	+	14.1864i	−0.389418	+	0.488315i
$845$	0.210199	+	0.263581i	0.00723106	+	0.00906747i
$846$	−1.79371	−	0.863807i	−0.0616692	−	0.0296983i
$847$	13.8487	−	6.66918i	0.475846	−	0.229156i
$848$	21.3676	−	26.7942i	0.733768	−	0.920116i
$849$	2.81858	+	12.3490i	0.0967333	+	0.423816i
$850$	2.49644	+	10.9376i	0.0856273	+	0.375158i
$851$	30.5332	+	38.2874i	1.04666	+	1.31247i
$852$	4.18414	−	18.3319i	0.143346	−	0.628041i
$853$	−17.2429			−0.590387			−0.295193	−	0.955438i	$-0.595384\pi$
$853$	−17.2429			−0.590387			−0.295193	+	0.955438i	$0.595384\pi$
$854$	−1.34866	+	5.90888i	−0.0461503	+	0.202198i
$855$	3.85652	−	1.85720i	0.131890	−	0.0635150i
$856$	13.4965	−	6.49958i	0.461301	−	0.222151i
$857$	−8.17153	+	35.8018i	−0.279134	+	1.22297i	0.619756	+	0.784794i	$0.287231\pi$
$857$	−8.17153	+	35.8018i	−0.279134	+	1.22297i	−0.898891	+	0.438173i	$0.855626\pi$
$858$	37.6315			1.28472
$859$	−0.689328	+	3.02014i	−0.0235196	+	0.103046i	−0.985325	−	0.170687i	$-0.945401\pi$
$859$	−0.689328	+	3.02014i	−0.0235196	+	0.103046i	0.961806	+	0.273733i	$0.0882585\pi$
$860$	9.65774	+	12.1104i	0.329326	+	0.412962i
$861$	1.14460	+	5.01480i	0.0390077	+	0.170904i
$862$	−6.23556	−	27.3198i	−0.212384	−	0.930515i
$863$	−19.4754	+	24.4214i	−0.662951	+	0.831314i	−0.993661	−	0.112418i	$-0.964140\pi$
$863$	−19.4754	+	24.4214i	−0.662951	+	0.831314i	0.330710	+	0.943732i	$0.392712\pi$
$864$	6.49710	−	3.12884i	0.221036	−	0.106445i
$865$	17.7555	+	8.55062i	0.603706	+	0.290730i
$866$	−23.0899	−	28.9538i	−0.784625	−	0.983889i
$867$	11.3759	−	14.2649i	0.386345	−	0.484461i
$868$	−1.68697	−	0.812403i	−0.0572596	−	0.0275748i
$869$	−39.7784			−1.34939
$870$	7.42026	−	6.96425i	0.251570	−	0.236110i
$871$	27.0344			0.916026
$872$	6.59137	+	3.17424i	0.223212	+	0.107493i
$873$	5.07106	−	6.35891i	0.171630	−	0.215217i
$874$	29.2646	+	36.6966i	0.989890	+	1.24128i
$875$	−0.681652	−	0.328266i	−0.0230440	−	0.0110974i
$876$	−21.8898	+	10.5416i	−0.739589	+	0.356167i
$877$	−11.1636	+	13.9987i	−0.376969	+	0.472704i	−0.933735	−	0.357965i	$-0.883471\pi$
$877$	−11.1636	+	13.9987i	−0.376969	+	0.472704i	0.556766	+	0.830669i	$0.312042\pi$
$878$	3.29300	+	14.4276i	0.111133	+	0.486907i
$879$	7.07308	+	30.9892i	0.238569	+	1.04524i
$880$	16.3077	+	20.4492i	0.549732	+	0.689342i
$881$	−3.75202	+	16.4387i	−0.126409	+	0.553833i	0.871569	+	0.490272i	$0.163103\pi$
$881$	−3.75202	+	16.4387i	−0.126409	+	0.553833i	−0.997978	+	0.0635605i	$0.979754\pi$
$882$	−12.1464			−0.408991
$883$	2.08657	−	9.14186i	0.0702187	−	0.307648i	−0.927607	−	0.373558i	$-0.878138\pi$
$883$	2.08657	−	9.14186i	0.0702187	−	0.307648i	0.997826	+	0.0659096i	$0.0209949\pi$
$884$	29.9036	−	14.4008i	1.00577	−	0.484352i
$885$	9.04092	−	4.35388i	0.303907	−	0.146354i
$886$	7.67951	−	33.6461i	0.257998	−	1.13036i
$887$	−26.1274			−0.877271			−0.438636	−	0.898665i	$-0.644538\pi$
$887$	−26.1274			−0.877271			−0.438636	+	0.898665i	$0.644538\pi$
$888$	1.52219	−	6.66915i	0.0510814	−	0.223802i
$889$	−5.24002	−	6.57078i	−0.175745	−	0.220377i
$890$	3.50073	+	15.3377i	0.117345	+	0.514121i
$891$	−1.24525	−	5.45580i	−0.0417174	−	0.182776i
$892$	9.77935	−	12.2629i	0.327437	−	0.410593i
$893$	−4.06294	+	1.95661i	−0.135961	+	0.0654754i
$894$	−8.54493	−	4.11502i	−0.285785	−	0.137627i
$895$	−11.0138	−	13.8109i	−0.368151	−	0.461647i
$896$	−2.98849	+	3.74745i	−0.0998384	+	0.125193i
$897$	−18.6039	−	8.95916i	−0.621165	−	0.299137i
$898$	−18.4036			−0.614137
$899$	−8.09169	+	2.54664i	−0.269873	+	0.0849352i
$900$	1.57107			0.0523691
$901$	−39.2203	−	18.8875i	−1.30662	−	0.629235i
$902$	44.8273	−	56.2117i	1.49259	−	1.87164i
$903$	4.65085	+	5.83198i	0.154771	+	0.194076i
$904$	−12.4505	−	5.99584i	−0.414097	−	0.199419i
$905$	−11.8029	+	5.68396i	−0.392341	+	0.188941i
$906$	4.58152	−	5.74504i	0.152211	−	0.190866i
$907$	−1.62586	−	7.12335i	−0.0539857	−	0.236527i	0.940736	−	0.339141i	$-0.110136\pi$
$907$	−1.62586	−	7.12335i	−0.0539857	−	0.236527i	−0.994721	+	0.102614i	$0.967279\pi$
$908$	7.48094	+	32.7761i	0.248264	+	1.08771i
$909$	−1.96061	−	2.45853i	−0.0650295	−	0.0815444i
$910$	−1.13211	+	4.96010i	−0.0375291	+	0.164426i
$911$	−7.86769			−0.260668			−0.130334	−	0.991470i	$-0.541605\pi$
$911$	−7.86769			−0.260668			−0.130334	+	0.991470i	$0.541605\pi$
$912$	4.45179	−	19.5046i	0.147413	−	0.645860i
$913$	−0.621042	+	0.299078i	−0.0205535	+	0.00989804i
$914$	−7.34297	+	3.53619i	−0.242884	+	0.116967i
$915$	−0.943304	+	4.13288i	−0.0311847	+	0.136629i
$916$	5.28345			0.174570
$917$	1.42087	−	6.22525i	0.0469214	−	0.205576i
$918$	−6.99488	−	8.77130i	−0.230865	−	0.289496i
$919$	11.7366	+	51.4214i	0.387155	+	1.69624i	0.674389	+	0.738376i	$0.264407\pi$
$919$	11.7366	+	51.4214i	0.387155	+	1.69624i	−0.287234	+	0.957860i	$0.592736\pi$
$920$	−1.04660	−	4.58547i	−0.0345055	−	0.151178i
$921$	0.342341	−	0.429282i	0.0112805	−	0.0141453i
$922$	46.4201	−	22.3547i	1.52876	−	0.736214i
$923$	38.3720	+	18.4790i	1.26303	+	0.608244i
$924$	−4.14729	−	5.20053i	−0.136436	−	0.171085i
$925$	5.26192	−	6.59823i	0.173011	−	0.216949i
$926$	4.11071	+	1.97961i	0.135086	+	0.0650541i
$927$	−10.6109			−0.348508
$928$	−3.12309	−	38.7079i	−0.102521	−	1.27065i
$929$	−4.38395			−0.143833			−0.0719164	−	0.997411i	$-0.522911\pi$
$929$	−4.38395			−0.143833			−0.0719164	+	0.997411i	$0.522911\pi$
$930$	−2.68200	−	1.29158i	−0.0879461	−	0.0423526i
$931$	−17.1539	+	21.5104i	−0.562198	+	0.704974i
$932$	21.2765	+	26.6799i	0.696936	+	0.873930i
$933$	0.163797	+	0.0788806i	0.00536248	+	0.00258244i
$934$	−5.01855	+	2.41681i	−0.164212	+	0.0790804i
$935$	20.7141	−	25.9747i	0.677424	−	0.849463i
$936$	0.641831	+	2.81204i	0.0209789	+	0.0919145i
$937$	1.52694	+	6.68998i	0.0498831	+	0.218552i	0.993726	−	0.111843i	$-0.0356753\pi$
$937$	1.52694	+	6.68998i	0.0498831	+	0.218552i	−0.943843	+	0.330395i	$0.892818\pi$
$938$	−6.77224	−	8.49212i	−0.221122	−	0.277278i
$939$	2.63213	−	11.5321i	0.0858965	−	0.376337i
$940$	−1.65516			−0.0539854
$941$	−8.44677	+	37.0077i	−0.275357	+	1.20642i	0.628236	+	0.778023i	$0.283777\pi$
$941$	−8.44677	+	37.0077i	−0.275357	+	1.20642i	−0.903592	+	0.428394i	$0.859080\pi$
$942$	−5.52638	+	2.66137i	−0.180059	+	0.0867120i
$943$	−35.5440	+	17.1171i	−1.15747	+	0.557409i
$944$	10.4364	−	45.7249i	0.339676	−	1.48822i
$945$	0.756577			0.0246114
$946$	23.2010	−	101.650i	0.754328	−	3.30493i
$947$	−1.59201	−	1.99632i	−0.0517333	−	0.0648715i	0.755292	−	0.655389i	$-0.227495\pi$
$947$	−1.59201	−	1.99632i	−0.0517333	−	0.0648715i	−0.807025	+	0.590517i	$0.798924\pi$
$948$	2.48502	+	10.8876i	0.0807095	+	0.353612i
$949$	−12.2454	−	53.6507i	−0.397503	−	1.74157i
$950$	5.04330	−	6.32410i	0.163626	−	0.205181i
$951$	−14.7389	+	7.09790i	−0.477943	+	0.230165i
$952$	3.28018	+	1.57965i	0.106311	+	0.0511968i
$953$	−21.2832	−	26.6883i	−0.689431	−	0.864519i	0.306754	−	0.951789i	$-0.400757\pi$
$953$	−21.2832	−	26.6883i	−0.689431	−	0.864519i	−0.996185	+	0.0872697i	$0.972186\pi$
$954$	−8.63930	+	10.8333i	−0.279708	+	0.350742i
$955$	16.4198	+	7.90736i	0.531332	+	0.255876i
$956$	18.2445			0.590071
$957$	−29.8245	−	4.32132i	−0.964089	−	0.139689i
$958$	−69.5912			−2.24839
$959$	−8.55816	−	4.12139i	−0.276357	−	0.133087i
$960$	2.66825	−	3.34587i	0.0861172	−	0.107988i
$961$	−17.7811	−	22.2967i	−0.573582	−	0.719249i
$962$	−51.1316	−	24.6237i	−1.64855	−	0.793900i
$963$	−16.6509	+	8.01865i	−0.536568	+	0.258397i
$964$	−2.22192	+	2.78620i	−0.0715632	+	0.0897374i
$965$	5.32407	+	23.3263i	0.171388	+	0.750899i
$966$	1.84608	+	8.08821i	0.0593967	+	0.260234i
$967$	17.1179	+	21.4652i	0.550475	+	0.690274i	0.976765	−	0.214312i	$-0.0687510\pi$
$967$	17.1179	+	21.4652i	0.550475	+	0.690274i	−0.426290	+	0.904587i	$0.640180\pi$
$968$	3.66438	−	16.0547i	0.117778	−	0.516017i
$969$	−25.4119			−0.816349
$970$	3.42011	−	14.9845i	0.109813	−	0.481122i
$971$	−23.9238	+	11.5211i	−0.767753	+	0.369730i	−0.776407	−	0.630232i	$-0.782960\pi$
$971$	−23.9238	+	11.5211i	−0.767753	+	0.369730i	0.00865393	+	0.999963i	$0.497245\pi$
$972$	−1.41549	+	0.681663i	−0.0454018	+	0.0218643i
$973$	−0.848639	+	3.71813i	−0.0272061	+	0.119198i
$974$	15.5242			0.497429
$975$	−0.791839	+	3.46927i	−0.0253591	+	0.111106i
$976$	12.3534	+	15.4907i	0.395423	+	0.495845i
$977$	11.1213	+	48.7256i	0.355802	+	1.55887i	0.763534	+	0.645767i	$0.223462\pi$
$977$	11.1213	+	48.7256i	0.355802	+	1.55887i	−0.407733	+	0.913101i	$0.633681\pi$
$978$	−3.71330	−	16.2690i	−0.118738	−	0.520226i
$979$	29.0472	−	36.4240i	0.928352	−	1.16412i
$980$	−9.09817	+	4.38145i	−0.290630	+	0.139960i
$981$	−8.13190	−	3.91612i	−0.259632	−	0.125032i
$982$	13.5673	+	17.0129i	0.432951	+	0.542903i
$983$	2.02810	−	2.54316i	0.0646864	−	0.0811141i	−0.748436	−	0.663207i	$-0.769195\pi$
$983$	2.02810	−	2.54316i	0.0646864	−	0.0811141i	0.813122	+	0.582093i	$0.197766\pi$
$984$	4.96503	+	2.39103i	0.158279	+	0.0762233i
$985$	−10.6138			−0.338184
$986$	−57.6290	+	18.1372i	−1.83528	+	0.577605i
$987$	−0.797071			−0.0253710
$988$	−21.5605	−	10.3830i	−0.685930	−	0.330326i
$989$	−35.6703	+	44.7292i	−1.13425	+	1.42231i
$990$	−6.59347	−	8.26795i	−0.209554	−	0.262773i
$991$	−2.22691	−	1.07242i	−0.0707401	−	0.0340666i	0.398179	−	0.917308i	$-0.369642\pi$
$991$	−2.22691	−	1.07242i	−0.0707401	−	0.0340666i	−0.468919	+	0.883241i	$0.655356\pi$
$992$	−10.2346	+	4.92870i	−0.324947	+	0.156486i
$993$	10.5261	−	13.1994i	0.334037	−	0.418869i
$994$	−3.80769	−	16.6826i	−0.120773	−	0.529140i
$995$	2.06141	+	9.03164i	0.0653512	+	0.286322i
$996$	0.120657	+	0.151299i	0.00382315	+	0.00479408i
$997$	−3.12200	+	13.6784i	−0.0988746	+	0.433198i	−1.00000		0.000360787i	$-0.999885\pi$
$997$	−3.12200	+	13.6784i	−0.0988746	+	0.433198i	0.901125	+	0.433559i	$0.142742\pi$
$998$	−24.9036			−0.788311
$999$	−1.87796	+	8.22786i	−0.0594159	+	0.260318i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	435.2.u.a.16.1	✓	30
29.20	even	7	inner	435.2.u.a.136.1	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.2.u.a.16.1	✓	30	1.1	even	1	trivial
435.2.u.a.136.1	yes	30	29.20	even	7	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	435.u (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.70259 - 0.819922i) q^{2} +(0.623490 - 0.781831i) q^{3} +(0.979547 + 1.22831i) q^{4} +(0.900969 + 0.433884i) q^{5} +(-1.70259 + 0.819922i) q^{6} +(-0.471718 + 0.591515i) q^{7} +(0.180366 + 0.790235i) q^{8} +(-0.222521 - 0.974928i) q^{9} +(-1.17823 - 1.47745i) q^{10} +(-1.24525 + 5.45580i) q^{11} +1.57107 q^{12} +(-0.791839 + 3.46927i) q^{13} +(1.28814 - 0.620334i) q^{14} +(0.900969 - 0.433884i) q^{15} +(1.04004 - 4.55669i) q^{16} -5.93679 q^{17} +(-0.420504 + 1.84235i) q^{18} +(2.66880 + 3.34657i) q^{19} +(0.349596 + 1.53168i) q^{20} +(0.168354 + 0.737608i) q^{21} +(6.59347 - 8.26795i) q^{22} +(-5.22802 + 2.51768i) q^{23} +(0.730287 + 0.351687i) q^{24} +(0.623490 + 0.781831i) q^{25} +(4.19271 - 5.25749i) q^{26} +(-0.900969 - 0.433884i) q^{27} -1.18864 q^{28} +(-3.92663 + 3.68532i) q^{29} -1.88973 q^{30} +(1.41925 + 0.683475i) q^{31} +(-4.49614 + 5.63798i) q^{32} +(3.48911 + 4.37521i) q^{33} +(10.1079 + 4.86771i) q^{34} +(-0.681652 + 0.328266i) q^{35} +(0.979547 - 1.22831i) q^{36} +(-1.87796 - 8.22786i) q^{37} +(-1.79993 - 7.88602i) q^{38} +(2.21868 + 2.78214i) q^{39} +(-0.180366 + 0.790235i) q^{40} +6.79874 q^{41} +(0.318144 - 1.39388i) q^{42} +(8.88301 - 4.27783i) q^{43} +(-7.92121 + 3.81465i) q^{44} +(0.222521 - 0.974928i) q^{45} +10.9655 q^{46} +(-0.234431 + 1.02711i) q^{47} +(-2.91411 - 3.65418i) q^{48} +(1.43027 + 6.26644i) q^{49} +(-0.420504 - 1.84235i) q^{50} +(-3.70153 + 4.64157i) q^{51} +(-5.03700 + 2.42569i) q^{52} +(6.60632 + 3.18144i) q^{53} +(1.17823 + 1.47745i) q^{54} +(-3.48911 + 4.37521i) q^{55} +(-0.552518 - 0.266079i) q^{56} +4.28042 q^{57} +(9.70710 - 3.05505i) q^{58} +10.0347 q^{59} +(1.41549 + 0.681663i) q^{60} +(-2.64308 + 3.31431i) q^{61} +(-1.85600 - 2.32735i) q^{62} +(0.681652 + 0.328266i) q^{63} +(3.85573 - 1.85682i) q^{64} +(-2.21868 + 2.78214i) q^{65} +(-2.35318 - 10.3100i) q^{66} +(-1.69053 - 7.40668i) q^{67} +(-5.81537 - 7.29224i) q^{68} +(-1.29121 + 5.65718i) q^{69} +1.42972 q^{70} +(2.66324 - 11.6684i) q^{71} +(0.730287 - 0.351687i) q^{72} +(-13.9331 + 6.70981i) q^{73} +(-3.54883 + 15.5484i) q^{74} +1.00000 q^{75} +(-1.49642 + 6.55624i) q^{76} +(-2.63978 - 3.31018i) q^{77} +(-1.49636 - 6.55598i) q^{78} +(1.58173 + 6.93002i) q^{79} +(2.91411 - 3.65418i) q^{80} +(-0.900969 + 0.433884i) q^{81} +(-11.5754 - 5.57444i) q^{82} +(0.0767989 + 0.0963027i) q^{83} +(-0.741103 + 0.929313i) q^{84} +(-5.34886 - 2.57588i) q^{85} -18.6316 q^{86} +(0.433087 + 5.36772i) q^{87} -4.53596 q^{88} +(-7.50065 - 3.61212i) q^{89} +(-1.17823 + 1.47745i) q^{90} +(-1.67860 - 2.10490i) q^{91} +(-8.21360 - 3.95546i) q^{92} +(1.41925 - 0.683475i) q^{93} +(1.24129 - 1.55653i) q^{94} +(0.952483 + 4.17310i) q^{95} +(1.60465 + 7.03044i) q^{96} +(5.07106 + 6.35891i) q^{97} +(2.70283 - 11.8419i) q^{98} +5.59610 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + q^{2} - 5 q^{3} - 3 q^{4} + 5 q^{5} + q^{6} - 5 q^{9} + 6 q^{10} - 18 q^{11} + 32 q^{12} - 5 q^{13} + 18 q^{14} + 5 q^{15} - 13 q^{16} + 44 q^{17} + q^{18} - 8 q^{19} + 10 q^{20} + 7 q^{21} - 19 q^{22}+ \cdots + 10 q^{99}+O(q^{100}) \) 30 * q + q^2 - 5 * q^3 - 3 * q^4 + 5 * q^5 + q^6 - 5 * q^9 + 6 * q^10 - 18 * q^11 + 32 * q^12 - 5 * q^13 + 18 * q^14 + 5 * q^15 - 13 * q^16 + 44 * q^17 + q^18 - 8 * q^19 + 10 * q^20 + 7 * q^21 - 19 * q^22 + 8 * q^23 + 14 * q^24 - 5 * q^25 - 34 * q^26 - 5 * q^27 - 102 * q^28 - 27 * q^29 - 8 * q^30 + 5 * q^31 - 2 * q^32 + 10 * q^33 - 5 * q^34 - 3 * q^36 + 9 * q^37 + 7 * q^38 + 2 * q^39 + 6 * q^41 - 17 * q^42 + 33 * q^43 + 5 * q^45 + 98 * q^46 - 30 * q^47 + q^48 - 9 * q^49 + q^50 - 26 * q^51 - 45 * q^52 + 38 * q^53 - 6 * q^54 - 10 * q^55 - 70 * q^56 - 8 * q^57 - 27 * q^58 + 102 * q^59 + 3 * q^60 + 8 * q^61 - 22 * q^62 + 30 * q^64 - 2 * q^65 - 40 * q^66 - 2 * q^67 + 23 * q^68 - 13 * q^69 + 24 * q^70 - 12 * q^71 + 14 * q^72 - 28 * q^73 - 65 * q^74 + 30 * q^75 - 41 * q^76 + 24 * q^77 + 71 * q^78 + 31 * q^79 - q^80 - 5 * q^81 - 39 * q^82 - 17 * q^83 - 11 * q^84 - 2 * q^85 + 38 * q^86 - 27 * q^87 + 22 * q^88 + 25 * q^89 + 6 * q^90 + 90 * q^91 + 39 * q^92 + 5 * q^93 + 11 * q^94 + 8 * q^95 - 16 * q^96 - 27 * q^97 - 47 * q^98 + 10 * q^99

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