LMFDB - Embedded newform 525.2.z.b.64.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(64,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 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("525.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.z (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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			64.4
Character	$\chi$	$=$	525.64
Dual form			525.2.z.b.484.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30460 - 1.79562i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.904259 + 2.78302i) q^{4} +(1.97142 - 1.05523i) q^{5} +(-0.685868 - 2.11088i) q^{6} -1.00000i q^{7} +(1.95519 - 0.635280i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-1.30460 - 1.79562i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.904259 + 2.78302i) q^{4} +(1.97142 - 1.05523i) q^{5} +(-0.685868 - 2.11088i) q^{6} -1.00000i q^{7} +(1.95519 - 0.635280i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-4.46670 - 2.16328i) q^{10} +(3.92672 - 2.85293i) q^{11} +(-1.72000 + 2.36738i) q^{12} +(-1.66575 + 2.29270i) q^{13} +(-1.79562 + 1.30460i) q^{14} +(2.20101 - 0.394380i) q^{15} +(1.04330 + 0.758002i) q^{16} +(0.0399357 - 0.0129759i) q^{17} -2.21951i q^{18} +(-1.29508 - 3.98583i) q^{19} +(1.15405 + 6.44070i) q^{20} +(0.309017 - 0.951057i) q^{21} +(-10.2456 - 3.32899i) q^{22} +(4.69792 + 6.46613i) q^{23} +2.05581 q^{24} +(2.77299 - 4.16059i) q^{25} +6.28997 q^{26} +(0.587785 + 0.809017i) q^{27} +(2.78302 + 0.904259i) q^{28} +(2.07118 - 6.37444i) q^{29} +(-3.57960 - 3.43769i) q^{30} +(-1.88158 - 5.79091i) q^{31} -6.97388i q^{32} +(4.61613 - 1.49987i) q^{33} +(-0.0753999 - 0.0547812i) q^{34} +(-1.05523 - 1.97142i) q^{35} +(-2.36738 + 1.72000i) q^{36} +(-3.42914 + 4.71981i) q^{37} +(-5.46751 + 7.52538i) q^{38} +(-2.29270 + 1.66575i) q^{39} +(3.18413 - 3.31557i) q^{40} +(-3.62085 - 2.63070i) q^{41} +(-2.11088 + 0.685868i) q^{42} -1.64437i q^{43} +(4.38899 + 13.5079i) q^{44} +(2.21516 + 0.305073i) q^{45} +(5.48185 - 16.8714i) q^{46} +(5.98410 + 1.94435i) q^{47} +(0.758002 + 1.04330i) q^{48} -1.00000 q^{49} +(-11.0885 + 0.448661i) q^{50} +0.0419909 q^{51} +(-4.87438 - 6.70901i) q^{52} +(-5.88600 - 1.91248i) q^{53} +(0.685868 - 2.11088i) q^{54} +(4.73071 - 9.76789i) q^{55} +(-0.635280 - 1.95519i) q^{56} -4.19095i q^{57} +(-14.1482 + 4.59701i) q^{58} +(5.71928 + 4.15530i) q^{59} +(-0.892718 + 6.48209i) q^{60} +(-0.153645 + 0.111630i) q^{61} +(-7.94359 + 10.9334i) q^{62} +(0.587785 - 0.809017i) q^{63} +(-10.4359 + 7.58210i) q^{64} +(-0.864559 + 6.27763i) q^{65} +(-8.71540 - 6.33211i) q^{66} +(-12.8703 + 4.18181i) q^{67} +0.122876i q^{68} +(2.46984 + 7.60139i) q^{69} +(-2.16328 + 4.46670i) q^{70} +(-1.53197 + 4.71493i) q^{71} +(1.95519 + 0.635280i) q^{72} +(-6.94882 - 9.56423i) q^{73} +12.9487 q^{74} +(3.92296 - 3.10006i) q^{75} +12.2637 q^{76} +(-2.85293 - 3.92672i) q^{77} +(5.98211 + 1.94371i) q^{78} +(-3.31780 + 10.2111i) q^{79} +(2.85665 + 0.393419i) q^{80} +(0.309017 + 0.951057i) q^{81} +9.93370i q^{82} +(-2.86165 + 0.929807i) q^{83} +(2.36738 + 1.72000i) q^{84} +(0.0650375 - 0.0677222i) q^{85} +(-2.95267 + 2.14524i) q^{86} +(3.93962 - 5.42242i) q^{87} +(5.86507 - 8.07257i) q^{88} +(0.516738 - 0.375432i) q^{89} +(-2.34209 - 4.37559i) q^{90} +(2.29270 + 1.66575i) q^{91} +(-22.2435 + 7.22735i) q^{92} -6.08892i q^{93} +(-4.31552 - 13.2818i) q^{94} +(-6.75910 - 6.49115i) q^{95} +(2.15505 - 6.63255i) q^{96} +(16.2901 + 5.29298i) q^{97} +(1.30460 + 1.79562i) q^{98} +4.85369 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 24 q^{4} - 2 q^{5} + 18 q^{9}+O(q^{10}) $ 72 * q + 24 * q^4 - 2 * q^5 + 18 * q^9	$ 72 q + 24 q^{4} - 2 q^{5} + 18 q^{9} - 28 q^{10} - 12 q^{11} - 20 q^{13} - 24 q^{16} + 10 q^{19} + 10 q^{20} - 18 q^{21} + 50 q^{22} - 10 q^{23} + 12 q^{25} + 36 q^{26} + 20 q^{28} - 2 q^{29} + 10 q^{30} - 16 q^{31} - 10 q^{33} + 24 q^{34} - 10 q^{35} - 24 q^{36} + 10 q^{37} - 100 q^{38} + 16 q^{39} - 14 q^{40} - 16 q^{41} - 18 q^{44} + 2 q^{45} - 44 q^{46} + 20 q^{47} - 72 q^{49} + 86 q^{50} + 32 q^{51} - 80 q^{52} + 70 q^{53} + 46 q^{55} - 40 q^{58} + 44 q^{59} - 62 q^{60} + 4 q^{61} - 50 q^{62} + 48 q^{64} + 38 q^{65} - 16 q^{66} - 20 q^{67} + 4 q^{69} + 10 q^{70} - 8 q^{71} - 20 q^{73} - 116 q^{74} - 8 q^{75} + 92 q^{76} + 20 q^{77} + 90 q^{78} + 28 q^{79} + 114 q^{80} - 18 q^{81} + 30 q^{83} + 24 q^{84} - 122 q^{85} + 40 q^{86} - 40 q^{87} - 270 q^{88} + 2 q^{89} - 12 q^{90} - 16 q^{91} - 100 q^{92} + 22 q^{94} + 116 q^{95} + 10 q^{96} + 190 q^{97} - 48 q^{99}+O(q^{100}) $ 72 * q + 24 * q^4 - 2 * q^5 + 18 * q^9 - 28 * q^10 - 12 * q^11 - 20 * q^13 - 24 * q^16 + 10 * q^19 + 10 * q^20 - 18 * q^21 + 50 * q^22 - 10 * q^23 + 12 * q^25 + 36 * q^26 + 20 * q^28 - 2 * q^29 + 10 * q^30 - 16 * q^31 - 10 * q^33 + 24 * q^34 - 10 * q^35 - 24 * q^36 + 10 * q^37 - 100 * q^38 + 16 * q^39 - 14 * q^40 - 16 * q^41 - 18 * q^44 + 2 * q^45 - 44 * q^46 + 20 * q^47 - 72 * q^49 + 86 * q^50 + 32 * q^51 - 80 * q^52 + 70 * q^53 + 46 * q^55 - 40 * q^58 + 44 * q^59 - 62 * q^60 + 4 * q^61 - 50 * q^62 + 48 * q^64 + 38 * q^65 - 16 * q^66 - 20 * q^67 + 4 * q^69 + 10 * q^70 - 8 * q^71 - 20 * q^73 - 116 * q^74 - 8 * q^75 + 92 * q^76 + 20 * q^77 + 90 * q^78 + 28 * q^79 + 114 * q^80 - 18 * q^81 + 30 * q^83 + 24 * q^84 - 122 * q^85 + 40 * q^86 - 40 * q^87 - 270 * q^88 + 2 * q^89 - 12 * q^90 - 16 * q^91 - 100 * q^92 + 22 * q^94 + 116 * q^95 + 10 * q^96 + 190 * q^97 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$	$1$

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 $

$2$	−1.30460	−	1.79562i	−0.922490	−	1.26970i	−0.962718	−	0.270508i	$-0.912808\pi$
$2$	−1.30460	−	1.79562i	−0.922490	−	1.26970i	0.0402280	−	0.999191i	$-0.487192\pi$
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$4$	−0.904259	+	2.78302i	−0.452129	+	1.39151i
$5$	1.97142	−	1.05523i	0.881645	−	0.471913i
$5$	1.97142	−	1.05523i	0.881645	−	0.471913i
$6$	−0.685868	−	2.11088i	−0.280004	−	0.861764i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	1.95519	−	0.635280i	0.691264	−	0.224605i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$	−4.46670	−	2.16328i	−1.41250	−	0.684089i
$11$	3.92672	−	2.85293i	1.18395	−	0.860189i	0.191338	−	0.981524i	$-0.438717\pi$
$11$	3.92672	−	2.85293i	1.18395	−	0.860189i	0.992612	+	0.121335i	$0.0387175\pi$
$12$	−1.72000	+	2.36738i	−0.496522	+	0.683404i
$13$	−1.66575	+	2.29270i	−0.461995	+	0.635882i	−0.974921	−	0.222551i	$-0.928562\pi$
$13$	−1.66575	+	2.29270i	−0.461995	+	0.635882i	0.512926	+	0.858433i	$0.328562\pi$
$14$	−1.79562	+	1.30460i	−0.479901	+	0.348668i
$15$	2.20101	−	0.394380i	0.568299	−	0.101828i
$16$	1.04330	+	0.758002i	0.260825	+	0.189500i
$17$	0.0399357	−	0.0129759i	0.00968583	−	0.00314712i	−0.304170	−	0.952618i	$-0.598379\pi$
$17$	0.0399357	−	0.0129759i	0.00968583	−	0.00314712i	0.313856	+	0.949471i	$0.398379\pi$
$18$		−	2.21951i		−	0.523144i
$19$	−1.29508	−	3.98583i	−0.297111	−	0.914413i	−0.982504	−	0.186240i	$-0.940370\pi$
$19$	−1.29508	−	3.98583i	−0.297111	−	0.914413i	0.685394	−	0.728173i	$-0.259630\pi$
$20$	1.15405	+	6.44070i	0.258054	+	1.44018i
$21$	0.309017	−	0.951057i	0.0674330	−	0.207538i
$22$	−10.2456	−	3.32899i	−2.18436	−	0.709742i
$23$	4.69792	+	6.46613i	0.979583	+	1.34828i	0.937054	+	0.349185i	$0.113542\pi$
$23$	4.69792	+	6.46613i	0.979583	+	1.34828i	0.0425295	+	0.999095i	$0.486458\pi$
$24$	2.05581			0.419640
$25$	2.77299	−	4.16059i	0.554597	−	0.832119i
$26$	6.28997			1.23356
$27$	0.587785	+	0.809017i	0.113119	+	0.155695i
$28$	2.78302	+	0.904259i	0.525942	+	0.170889i
$29$	2.07118	−	6.37444i	0.384608	−	1.18370i	−0.552155	−	0.833741i	$-0.686195\pi$
$29$	2.07118	−	6.37444i	0.384608	−	1.18370i	0.936764	−	0.349962i	$-0.113805\pi$
$30$	−3.57960	−	3.43769i	−0.653542	−	0.627633i
$31$	−1.88158	−	5.79091i	−0.337942	−	1.04008i	−0.965255	−	0.261310i	$-0.915845\pi$
$31$	−1.88158	−	5.79091i	−0.337942	−	1.04008i	0.627313	−	0.778767i	$-0.284155\pi$
$32$		−	6.97388i		−	1.23282i
$33$	4.61613	−	1.49987i	0.803565	−	0.261094i
$34$	−0.0753999	−	0.0547812i	−0.0129310	−	0.00939490i
$35$	−1.05523	−	1.97142i	−0.178366	−	0.333231i
$36$	−2.36738	+	1.72000i	−0.394563	+	0.286667i
$37$	−3.42914	+	4.71981i	−0.563748	+	0.775932i	−0.991797	−	0.127823i	$-0.959201\pi$
$37$	−3.42914	+	4.71981i	−0.563748	+	0.775932i	0.428049	+	0.903755i	$0.359201\pi$
$38$	−5.46751	+	7.52538i	−0.886947	+	1.22078i
$39$	−2.29270	+	1.66575i	−0.367127	+	0.266733i
$40$	3.18413	−	3.31557i	0.503456	−	0.524238i
$41$	−3.62085	−	2.63070i	−0.565482	−	0.410847i	0.267979	−	0.963425i	$-0.413644\pi$
$41$	−3.62085	−	2.63070i	−0.565482	−	0.410847i	−0.833461	+	0.552578i	$0.813644\pi$
$42$	−2.11088	+	0.685868i	−0.325716	+	0.105832i
$43$		−	1.64437i		−	0.250764i	−0.992109	−	0.125382i	$-0.959984\pi$
$43$		−	1.64437i		−	0.250764i	0.992109	−	0.125382i	$-0.0400156\pi$
$44$	4.38899	+	13.5079i	0.661665	+	2.03640i
$45$	2.21516	+	0.305073i	0.330216	+	0.0454776i
$46$	5.48185	−	16.8714i	0.808254	−	2.48755i
$47$	5.98410	+	1.94435i	0.872870	+	0.283613i	0.710994	−	0.703198i	$-0.248245\pi$
$47$	5.98410	+	1.94435i	0.872870	+	0.283613i	0.161877	+	0.986811i	$0.448245\pi$
$48$	0.758002	+	1.04330i	0.109408	+	0.150587i
$49$	−1.00000			−0.142857
$50$	−11.0885	+	0.448661i	−1.56815	+	0.0634503i
$51$	0.0419909			0.00587990
$52$	−4.87438	−	6.70901i	−0.675955	−	0.930372i
$53$	−5.88600	−	1.91248i	−0.808504	−	0.262699i	−0.124540	−	0.992215i	$-0.539745\pi$
$53$	−5.88600	−	1.91248i	−0.808504	−	0.262699i	−0.683964	+	0.729516i	$0.739745\pi$
$54$	0.685868	−	2.11088i	0.0933348	−	0.287255i
$55$	4.73071	−	9.76789i	0.637889	−	1.31710i
$56$	−0.635280	−	1.95519i	−0.0848928	−	0.261273i
$57$		−	4.19095i		−	0.555105i
$58$	−14.1482	+	4.59701i	−1.85774	+	0.603617i
$59$	5.71928	+	4.15530i	0.744586	+	0.540974i	0.894144	−	0.447779i	$-0.147785\pi$
$59$	5.71928	+	4.15530i	0.744586	+	0.540974i	−0.149558	+	0.988753i	$0.547785\pi$
$60$	−0.892718	+	6.48209i	−0.115249	+	0.836835i
$61$	−0.153645	+	0.111630i	−0.0196723	+	0.0142928i	−0.597578	−	0.801811i	$-0.703870\pi$
$61$	−0.153645	+	0.111630i	−0.0196723	+	0.0142928i	0.577906	+	0.816104i	$0.303870\pi$
$62$	−7.94359	+	10.9334i	−1.00884	+	1.38854i
$63$	0.587785	−	0.809017i	0.0740540	−	0.101927i
$64$	−10.4359	+	7.58210i	−1.30448	+	0.947763i
$65$	−0.864559	+	6.27763i	−0.107235	+	0.778644i
$66$	−8.71540	−	6.33211i	−1.07279	−	0.779429i
$67$	−12.8703	+	4.18181i	−1.57235	+	0.510889i	−0.960073	−	0.279751i	$-0.909748\pi$
$67$	−12.8703	+	4.18181i	−1.57235	+	0.510889i	−0.612282	+	0.790640i	$0.709748\pi$
$68$			0.122876i			0.0149009i
$69$	2.46984	+	7.60139i	0.297334	+	0.915100i
$70$	−2.16328	+	4.46670i	−0.258561	+	0.533873i
$71$	−1.53197	+	4.71493i	−0.181812	+	0.559559i	−0.999879	−	0.0155639i	$-0.995046\pi$
$71$	−1.53197	+	4.71493i	−0.181812	+	0.559559i	0.818067	+	0.575123i	$0.195046\pi$
$72$	1.95519	+	0.635280i	0.230421	+	0.0748684i
$73$	−6.94882	−	9.56423i	−0.813298	−	1.11941i	−0.990806	−	0.135289i	$-0.956804\pi$
$73$	−6.94882	−	9.56423i	−0.813298	−	1.11941i	0.177508	−	0.984119i	$-0.443196\pi$
$74$	12.9487			1.50525
$75$	3.92296	−	3.10006i	0.452984	−	0.357964i
$76$	12.2637			1.40675
$77$	−2.85293	−	3.92672i	−0.325121	−	0.447491i
$78$	5.98211	+	1.94371i	0.677341	+	0.220081i
$79$	−3.31780	+	10.2111i	−0.373282	+	1.14884i	0.571348	+	0.820708i	$0.306421\pi$
$79$	−3.31780	+	10.2111i	−0.373282	+	1.14884i	−0.944630	+	0.328136i	$0.893579\pi$
$80$	2.85665	+	0.393419i	0.319383	+	0.0439856i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$			9.93370i			1.09699i
$83$	−2.86165	+	0.929807i	−0.314107	+	0.102060i	−0.461828	−	0.886969i	$-0.652806\pi$
$83$	−2.86165	+	0.929807i	−0.314107	+	0.102060i	0.147721	+	0.989029i	$0.452806\pi$
$84$	2.36738	+	1.72000i	0.258302	+	0.187668i
$85$	0.0650375	−	0.0677222i	0.00705431	−	0.00734551i
$86$	−2.95267	+	2.14524i	−0.318395	+	0.231327i
$87$	3.93962	−	5.42242i	0.422371	−	0.581344i
$88$	5.86507	−	8.07257i	0.625218	−	0.860539i
$89$	0.516738	−	0.375432i	0.0547741	−	0.0397957i	−0.560061	−	0.828451i	$-0.689222\pi$
$89$	0.516738	−	0.375432i	0.0547741	−	0.0397957i	0.614835	+	0.788655i	$0.289222\pi$
$90$	−2.34209	−	4.37559i	−0.246878	−	0.461228i
$91$	2.29270	+	1.66575i	0.240341	+	0.174618i
$92$	−22.2435	+	7.22735i	−2.31905	+	0.753504i
$93$		−	6.08892i		−	0.631392i
$94$	−4.31552	−	13.2818i	−0.445111	−	1.36991i
$95$	−6.75910	−	6.49115i	−0.693469	−	0.665977i
$96$	2.15505	−	6.63255i	0.219949	−	0.676932i
$97$	16.2901	+	5.29298i	1.65401	+	0.537421i	0.979604	−	0.200939i	$-0.0643995\pi$
$97$	16.2901	+	5.29298i	1.65401	+	0.537421i	0.674407	+	0.738360i	$0.264399\pi$
$98$	1.30460	+	1.79562i	0.131784	+	0.181385i
$99$	4.85369			0.487814
$100$	9.07153	+	11.4795i	0.907153	+	1.14795i
$101$	5.52900			0.550156			0.275078	−	0.961422i	$-0.411296\pi$
$101$	5.52900			0.550156			0.275078	+	0.961422i	$0.411296\pi$
$102$	−0.0547812	−	0.0753999i	−0.00542415	−	0.00746570i
$103$	0.598574	+	0.194488i	0.0589792	+	0.0191635i	0.338358	−	0.941017i	$-0.390129\pi$
$103$	0.598574	+	0.194488i	0.0589792	+	0.0191635i	−0.279379	+	0.960181i	$0.590129\pi$
$104$	−1.80034	+	5.54089i	−0.176538	+	0.543329i
$105$	−0.394380	−	2.20101i	−0.0384875	−	0.214797i
$106$	4.24477	+	13.0641i	0.412288	+	1.26889i
$107$		−	4.44384i		−	0.429602i	−0.976658	−	0.214801i	$-0.931090\pi$
$107$		−	4.44384i		−	0.429602i	0.976658	−	0.214801i	$-0.0689103\pi$
$108$	−2.78302	+	0.904259i	−0.267796	+	0.0870123i
$109$	12.0063	+	8.72310i	1.15000	+	0.835522i	0.988481	−	0.151348i	$-0.0483614\pi$
$109$	12.0063	+	8.72310i	1.15000	+	0.835522i	0.161517	+	0.986870i	$0.448361\pi$
$110$	−23.7111	+	4.24859i	−2.26077	+	0.405087i
$111$	−4.71981	+	3.42914i	−0.447985	+	0.325480i
$112$	0.758002	−	1.04330i	0.0716244	−	0.0985826i
$113$	0.241262	−	0.332069i	0.0226960	−	0.0312384i	−0.797518	−	0.603295i	$-0.793854\pi$
$113$	0.241262	−	0.332069i	0.0226960	−	0.0312384i	0.820214	+	0.572056i	$0.193854\pi$
$114$	−7.52538	+	5.46751i	−0.704816	+	0.512079i
$115$	16.0848	+	7.79007i	1.49992	+	0.726428i
$116$	15.8673	+	11.5283i	1.47324	+	1.07037i
$117$	−2.69524	+	0.875735i	−0.249175	+	0.0809617i
$118$		−	15.6907i		−	1.44444i
$119$	−0.0129759	−	0.0399357i	−0.00118950	−	0.00366090i
$120$	4.05286	−	2.16935i	0.369974	−	0.198033i
$121$	3.88072	−	11.9436i	0.352793	−	1.08578i
$122$	0.400891	+	0.130257i	0.0362950	+	0.0117930i
$123$	−2.63070	−	3.62085i	−0.237203	−	0.326481i
$124$	17.8177			1.60007
$125$	1.07634	−	11.1284i	0.0962706	−	0.995355i
$126$	−2.21951			−0.197730
$127$	11.2139	+	15.4346i	0.995075	+	1.36960i	0.928299	+	0.371835i	$0.121271\pi$
$127$	11.2139	+	15.4346i	0.995075	+	1.36960i	0.0667762	+	0.997768i	$0.478729\pi$
$128$	13.9641	+	4.53722i	1.23426	+	0.401037i
$129$	0.508138	−	1.56389i	0.0447391	−	0.137693i
$130$	12.4002	−	6.63735i	1.08757	−	0.582134i
$131$	−0.698093	−	2.14851i	−0.0609926	−	0.187716i	0.915918	−	0.401367i	$-0.131465\pi$
$131$	−0.698093	−	2.14851i	−0.0609926	−	0.187716i	−0.976910	+	0.213650i	$0.931465\pi$
$132$			14.2031i			1.23622i
$133$	−3.98583	+	1.29508i	−0.345615	+	0.112297i
$134$	24.2995	+	17.6546i	2.09916	+	1.52513i
$135$	2.01247	+	0.974664i	0.173206	+	0.0838857i
$136$	0.0698386	−	0.0507407i	0.00598861	−	0.00435098i
$137$	10.7730	−	14.8278i	0.920401	−	1.26682i	−0.0430873	−	0.999071i	$-0.513719\pi$
$137$	10.7730	−	14.8278i	0.920401	−	1.26682i	0.963488	−	0.267752i	$-0.0862806\pi$
$138$	10.4271	−	14.3517i	0.887613	−	1.22169i
$139$	−17.2474	+	12.5310i	−1.46291	+	1.06286i	−0.480312	+	0.877098i	$0.659477\pi$
$139$	−17.2474	+	12.5310i	−1.46291	+	1.06286i	−0.982594	+	0.185766i	$0.940523\pi$
$140$	6.44070	−	1.15405i	0.544339	−	0.0975352i
$141$	5.09038	+	3.69838i	0.428687	+	0.311459i
$142$	10.4648	−	3.40023i	0.878190	−	0.285341i
$143$			13.7551i			1.15026i
$144$	0.398505	+	1.22647i	0.0332088	+	0.102206i
$145$	−2.64332	−	14.7523i	−0.219516	−	1.22511i
$146$	−8.10835	+	24.9549i	−0.671052	+	2.06529i
$147$	−0.951057	−	0.309017i	−0.0784418	−	0.0254873i
$148$	−10.0345	−	13.8113i	−0.824831	−	1.13528i
$149$	14.2663			1.16874			0.584370	−	0.811487i	$-0.301342\pi$
$149$	14.2663			1.16874			0.584370	+	0.811487i	$0.301342\pi$
$150$	−10.6844	−	2.99983i	−0.872380	−	0.244935i
$151$	16.4405			1.33791			0.668955	−	0.743303i	$-0.266742\pi$
$151$	16.4405			1.33791			0.668955	+	0.743303i	$0.266742\pi$
$152$	−5.06424	−	6.97032i	−0.410764	−	0.565368i
$153$	0.0399357	+	0.0129759i	0.00322861	+	0.00104904i
$154$	−3.32899	+	10.2456i	−0.268257	+	0.825611i
$155$	−9.82011	−	9.43081i	−0.788770	−	0.757501i
$156$	−2.56261	−	7.88691i	−0.205173	−	0.631458i
$157$			4.98858i			0.398132i	0.979986	+	0.199066i	$0.0637908\pi$
$157$			4.98858i			0.398132i	−0.979986	+	0.199066i	$0.936209\pi$
$158$	22.6638	−	7.36391i	1.80303	−	0.585841i
$159$	−5.00693	−	3.63775i	−0.397075	−	0.288492i
$160$	−7.35904	−	13.7484i	−0.581783	−	1.08691i
$161$	6.46613	−	4.69792i	0.509602	−	0.370248i
$162$	1.30460	−	1.79562i	0.102499	−	0.141078i
$163$	−10.6031	+	14.5939i	−0.830501	+	1.14309i	0.157329	+	0.987546i	$0.449712\pi$
$163$	−10.6031	+	14.5939i	−0.830501	+	1.14309i	−0.987830	+	0.155540i	$0.950288\pi$
$164$	10.5955	−	7.69808i	0.827369	−	0.601119i
$165$	7.51762	−	7.82795i	0.585246	−	0.609405i
$166$	5.40289	+	3.92543i	0.419346	+	0.304672i
$167$	−13.6056	+	4.42072i	−1.05283	+	0.342086i	−0.783779	−	0.621040i	$-0.786710\pi$
$167$	−13.6056	+	4.42072i	−1.05283	+	0.342086i	−0.269052	+	0.963126i	$0.586710\pi$
$168$		−	2.05581i		−	0.158609i
$169$	1.53544	+	4.72560i	0.118111	+	0.363508i
$170$	−0.206451	−	0.0284326i	−0.0158341	−	0.00218068i
$171$	1.29508	−	3.98583i	0.0990369	−	0.304804i
$172$	4.57632	+	1.48694i	0.348941	+	0.113378i
$173$	−0.740129	−	1.01870i	−0.0562710	−	0.0774503i	0.779954	−	0.625837i	$-0.215242\pi$
$173$	−0.740129	−	1.01870i	−0.0562710	−	0.0774503i	−0.836225	+	0.548386i	$0.815242\pi$
$174$	−14.8762			−1.12777
$175$	−4.16059	−	2.77299i	−0.314511	−	0.209618i
$176$	6.25926			0.471810
$177$	4.15530	+	5.71928i	0.312331	+	0.429887i
$178$	−1.34827	−	0.438080i	−0.101057	−	0.0328355i
$179$	−6.45691	+	19.8723i	−0.482612	+	1.48533i	0.352798	+	0.935700i	$0.385230\pi$
$179$	−6.45691	+	19.8723i	−0.482612	+	1.48533i	−0.835410	+	0.549627i	$0.814770\pi$
$180$	−2.85210	+	5.88897i	−0.212583	+	0.438938i
$181$	6.56685	+	20.2107i	0.488110	+	1.50225i	0.827425	+	0.561576i	$0.189805\pi$
$181$	6.56685	+	20.2107i	0.488110	+	1.50225i	−0.339315	+	0.940673i	$0.610195\pi$
$182$		−	6.28997i		−	0.466243i
$183$	−0.180621	+	0.0586874i	−0.0133519	+	0.00433829i
$184$	13.2931	+	9.65802i	0.979982	+	0.711998i
$185$	−1.77980	+	12.9233i	−0.130853	+	0.950137i
$186$	−10.9334	+	7.94359i	−0.801677	+	0.582452i
$187$	0.119797	−	0.164886i	0.00876042	−	0.0120577i
$188$	−10.8223	+	14.8957i	−0.789301	+	1.08638i
$189$	0.809017	−	0.587785i	0.0588473	−	0.0427551i
$190$	−2.83775	+	20.6051i	−0.205872	+	1.49485i
$191$	−14.1409	−	10.2740i	−1.02320	−	0.743399i	−0.0562645	−	0.998416i	$-0.517919\pi$
$191$	−14.1409	−	10.2740i	−1.02320	−	0.743399i	−0.966937	+	0.255017i	$0.917919\pi$
$192$	−12.2681	+	3.98615i	−0.885374	+	0.287675i
$193$			6.27280i			0.451526i	0.974182	+	0.225763i	$0.0724875\pi$
$193$			6.27280i			0.451526i	−0.974182	+	0.225763i	$0.927512\pi$
$194$	−11.7478	−	36.1561i	−0.843446	−	2.59586i
$195$	−2.76214	+	5.70321i	−0.197801	+	0.408416i
$196$	0.904259	−	2.78302i	0.0645899	−	0.198787i
$197$	7.66663	+	2.49104i	0.546224	+	0.177479i	0.569114	−	0.822259i	$-0.307286\pi$
$197$	7.66663	+	2.49104i	0.546224	+	0.177479i	−0.0228891	+	0.999738i	$0.507286\pi$
$198$	−6.33211	−	8.71540i	−0.450003	−	0.619376i
$199$	−16.3328			−1.15780			−0.578900	−	0.815398i	$-0.696518\pi$
$199$	−16.3328			−1.15780			−0.578900	+	0.815398i	$0.696518\pi$
$200$	2.77857	−	9.89638i	0.196475	−	0.699779i
$201$	−13.5326			−0.954517
$202$	−7.21312	−	9.92801i	−0.507513	−	0.698532i
$203$	−6.37444	−	2.07118i	−0.447398	−	0.145368i
$204$	−0.0379706	+	0.116862i	−0.00265848	+	0.00818195i
$205$	−9.91421	−	1.36539i	−0.692438	−	0.0953631i
$206$	−0.431670	−	1.32854i	−0.0300759	−	0.0925640i
$207$			7.99257i			0.555522i
$208$	−3.47575	+	1.12934i	−0.241000	+	0.0783056i
$209$	−16.4567	−	11.9565i	−1.13833	−	0.827047i
$210$	−3.43769	+	3.57960i	−0.237223	+	0.247016i
$211$	−13.4527	+	9.77399i	−0.926125	+	0.672869i	−0.945041	−	0.326952i	$-0.893978\pi$
$211$	−13.4527	+	9.77399i	−0.926125	+	0.672869i	0.0189163	+	0.999821i	$0.493978\pi$
$212$	10.6449	−	14.6515i	0.731097	−	1.00627i
$213$	−2.91398	+	4.01076i	−0.199663	+	0.274812i
$214$	−7.97946	+	5.79742i	−0.545465	+	0.396303i
$215$	−1.73519	−	3.24174i	−0.118339	−	0.221085i
$216$	1.66318	+	1.20837i	0.113165	+	0.0822194i
$217$	−5.79091	+	1.88158i	−0.393112	+	0.127730i
$218$		−	32.9390i		−	2.23091i
$219$	−3.65321	−	11.2434i	−0.246861	−	0.759760i
$220$	22.9065	+	21.9984i	1.54435	+	1.48313i
$221$	−0.0367729	+	0.113175i	−0.00247361	+	0.00761300i
$222$	12.3149	+	4.00136i	0.826522	+	0.268553i
$223$	−6.88425	−	9.47536i	−0.461003	−	0.634517i	0.513713	−	0.857962i	$-0.328270\pi$
$223$	−6.88425	−	9.47536i	−0.461003	−	0.634517i	−0.974716	+	0.223445i	$0.928270\pi$
$224$	−6.97388			−0.465962
$225$	4.68893	−	1.73607i	0.312595	−	0.115738i
$226$	−0.911021			−0.0606002
$227$	14.4143	+	19.8396i	0.956710	+	1.31680i	0.948481	+	0.316833i	$0.102619\pi$
$227$	14.4143	+	19.8396i	0.956710	+	1.31680i	0.00822908	+	0.999966i	$0.497381\pi$
$228$	11.6635	+	3.78970i	0.772435	+	0.250979i
$229$	3.47489	−	10.6946i	0.229627	−	0.706719i	−0.768162	−	0.640256i	$-0.778828\pi$
$229$	3.47489	−	10.6946i	0.229627	−	0.706719i	0.997789	−	0.0664635i	$-0.0211716\pi$
$230$	−6.99615	−	39.0452i	−0.461313	−	2.57456i
$231$	−1.49987	−	4.61613i	−0.0986843	−	0.303719i
$232$		−	13.7790i		−	0.904637i
$233$	−14.9818	+	4.86789i	−0.981491	+	0.318906i	−0.755446	−	0.655211i	$-0.772580\pi$
$233$	−14.9818	+	4.86789i	−0.981491	+	0.318906i	−0.226045	+	0.974117i	$0.572580\pi$
$234$	5.08869	+	3.69715i	0.332658	+	0.241690i
$235$	13.8489	−	2.48146i	0.903403	−	0.161873i
$236$	−16.7360	+	12.1594i	−1.08942	+	0.791510i
$237$	−6.31084	+	8.68612i	−0.409933	+	0.564224i
$238$	−0.0547812	+	0.0753999i	−0.00355094	+	0.00488745i
$239$	13.3728	−	9.71593i	0.865017	−	0.628471i	−0.0642284	−	0.997935i	$-0.520459\pi$
$239$	13.3728	−	9.71593i	0.865017	−	0.628471i	0.929245	+	0.369464i	$0.120459\pi$
$240$	2.59526	+	1.25692i	0.167523	+	0.0811336i
$241$	−14.6402	−	10.6367i	−0.943059	−	0.685172i	0.00609642	−	0.999981i	$-0.498059\pi$
$241$	−14.6402	−	10.6367i	−0.943059	−	0.685172i	−0.949155	+	0.314809i	$0.898059\pi$
$242$	−26.5091	+	8.61331i	−1.70407	+	0.553685i
$243$			1.00000i			0.0641500i
$244$	−0.171733	−	0.528541i	−0.0109941	−	0.0338364i
$245$	−1.97142	+	1.05523i	−0.125949	+	0.0674161i
$246$	−3.06968	+	9.44751i	−0.195716	+	0.602351i
$247$	11.2956	+	3.67016i	0.718722	+	0.233527i
$248$	−7.35769	−	10.1270i	−0.467214	−	0.643065i
$249$	−3.00892			−0.190683
$250$	−21.3866	+	12.5854i	−1.35261	+	0.795970i
$251$	11.7404			0.741046			0.370523	−	0.928823i	$-0.379178\pi$
$251$	11.7404			0.741046			0.370523	+	0.928823i	$0.379178\pi$
$252$	1.72000	+	2.36738i	0.108350	+	0.149131i
$253$	36.8948	+	11.9878i	2.31955	+	0.753669i
$254$	13.0852	−	40.2720i	0.821036	−	2.52689i
$255$	0.0827817	−	0.0443100i	0.00518399	−	0.00277480i
$256$	−2.09812	−	6.45735i	−0.131132	−	0.403584i
$257$			16.2263i			1.01217i	0.862483	+	0.506085i	$0.168908\pi$
$257$			16.2263i			1.01217i	−0.862483	+	0.506085i	$0.831092\pi$
$258$	−3.47107	+	1.12782i	−0.216099	+	0.0702150i
$259$	4.71981	+	3.42914i	0.293275	+	0.213077i
$260$	−16.6890	−	8.08268i	−1.03501	−	0.501267i
$261$	5.42242	−	3.93962i	0.335639	−	0.243856i
$262$	−2.94718	+	4.05645i	−0.182078	+	0.250608i
$263$	−3.15288	+	4.33956i	−0.194415	+	0.267589i	−0.895084	−	0.445897i	$-0.852885\pi$
$263$	−3.15288	+	4.33956i	−0.194415	+	0.267589i	0.700670	+	0.713486i	$0.252885\pi$
$264$	8.07257	−	5.86507i	0.496833	−	0.360970i
$265$	−13.6219	+	2.44078i	−0.836785	+	0.149936i
$266$	7.52538	+	5.46751i	0.461410	+	0.335234i
$267$	0.607462	−	0.197376i	0.0371761	−	0.0120792i
$268$		−	39.5997i		−	2.41894i
$269$	−5.72815	−	17.6294i	−0.349251	−	1.07488i	−0.959268	−	0.282497i	$-0.908837\pi$
$269$	−5.72815	−	17.6294i	−0.349251	−	1.07488i	0.610017	−	0.792388i	$-0.291163\pi$
$270$	−0.875332	−	4.88518i	−0.0532710	−	0.297303i
$271$	−4.48826	+	13.8134i	−0.272642	+	0.839107i	0.717191	+	0.696876i	$0.245427\pi$
$271$	−4.48826	+	13.8134i	−0.272642	+	0.839107i	−0.989834	+	0.142230i	$0.954573\pi$
$272$	0.0515007	+	0.0167336i	0.00312269	+	0.00101462i
$273$	1.66575	+	2.29270i	0.100816	+	0.138761i
$274$	−40.6796			−2.45754
$275$	−0.981143	−	24.2486i	−0.0591652	−	1.46225i
$276$	−23.3882			−1.40780
$277$	−12.5895	−	17.3280i	−0.756431	−	1.04114i	−0.997503	−	0.0706311i	$-0.977499\pi$
$277$	−12.5895	−	17.3280i	−0.756431	−	1.04114i	0.241071	−	0.970507i	$-0.422501\pi$
$278$	45.0019	+	14.6220i	2.69903	+	0.876969i
$279$	1.88158	−	5.79091i	0.112647	−	0.346693i
$280$	−3.31557	−	3.18413i	−0.198143	−	0.190288i
$281$	8.18996	+	25.2061i	0.488572	+	1.50367i	0.826740	+	0.562584i	$0.190193\pi$
$281$	8.18996	+	25.2061i	0.488572	+	1.50367i	−0.338168	+	0.941086i	$0.609807\pi$
$282$		−	13.9653i		−	0.831622i
$283$	−2.14960	+	0.698448i	−0.127781	+	0.0415184i	−0.372209	−	0.928149i	$-0.621400\pi$
$283$	−2.14960	+	0.698448i	−0.127781	+	0.0415184i	0.244429	+	0.969667i	$0.421400\pi$
$284$	−11.7364	−	8.52702i	−0.696430	−	0.505986i
$285$	−4.42241	−	8.26212i	−0.261961	−	0.489406i
$286$	24.6989	−	17.9448i	1.46048	−	1.06110i
$287$	−2.63070	+	3.62085i	−0.155285	+	0.213732i
$288$	4.09914	−	5.64199i	0.241544	−	0.332457i
$289$	−13.7519	+	9.99131i	−0.808933	+	0.587724i
$290$	−23.0410	+	23.9922i	−1.35302	+	1.40887i
$291$	13.8572	+	10.0678i	0.812323	+	0.590187i
$292$	32.9010	−	10.6902i	1.92538	−	0.625595i
$293$		−	8.22291i		−	0.480388i	−0.970725	−	0.240194i	$-0.922789\pi$
$293$		−	8.22291i		−	0.480388i	0.970725	−	0.240194i	$-0.0772110\pi$
$294$	0.685868	+	2.11088i	0.0400006	+	0.123109i
$295$	15.6599	+	2.15669i	0.911753	+	0.125567i
$296$	−3.70623	+	11.4066i	−0.215420	+	0.662995i
$297$	4.61613	+	1.49987i	0.267855	+	0.0870314i
$298$	−18.6118	−	25.6169i	−1.07815	−	1.48395i
$299$	−22.6505			−1.30991
$300$	5.08017	+	13.7209i	0.293304	+	0.792179i
$301$	−1.64437			−0.0947799
$302$	−21.4482	−	29.5210i	−1.23421	−	1.69874i
$303$	5.25839	+	1.70855i	0.302087	+	0.0981539i
$304$	1.67012	−	5.14009i	0.0957877	−	0.294804i
$305$	−0.185104	+	0.382201i	−0.0105991	+	0.0218847i
$306$	−0.0288002	−	0.0886379i	−0.00164640	−	0.00506709i
$307$		−	17.7141i		−	1.01100i	−0.862827	−	0.505499i	$-0.831308\pi$
$307$		−	17.7141i		−	1.01100i	0.862827	−	0.505499i	$-0.168692\pi$
$308$	13.5079	−	4.38899i	0.769685	−	0.250086i
$309$	0.509177	+	0.369939i	0.0289661	+	0.0210451i
$310$	−4.12289	+	29.9366i	−0.234165	+	1.70029i
$311$	16.8495	−	12.2419i	0.955446	−	0.694172i	0.00335763	−	0.999994i	$-0.498931\pi$
$311$	16.8495	−	12.2419i	0.955446	−	0.694172i	0.952089	+	0.305822i	$0.0989312\pi$
$312$	−3.42446	+	4.71336i	−0.193872	+	0.266842i
$313$	16.0962	−	22.1545i	0.909809	−	1.25224i	−0.0574228	−	0.998350i	$-0.518288\pi$
$313$	16.0962	−	22.1545i	0.909809	−	1.25224i	0.967232	−	0.253895i	$-0.0817117\pi$
$314$	8.95761	−	6.50809i	0.505507	−	0.367273i
$315$	0.305073	−	2.21516i	0.0171889	−	0.124810i
$316$	−25.4177	−	18.4670i	−1.42986	−	1.03885i
$317$	−4.11376	+	1.33664i	−0.231052	+	0.0750733i	−0.422255	−	0.906477i	$-0.638761\pi$
$317$	−4.11376	+	1.33664i	−0.231052	+	0.0750733i	0.191203	+	0.981551i	$0.438761\pi$
$318$			13.7364i			0.770297i
$319$	−10.0529	−	30.9395i	−0.562852	−	1.73228i
$320$	−12.5726	+	25.9597i	−0.702831	+	1.45119i
$321$	1.37322	−	4.22634i	0.0766457	−	0.235891i
$322$	−16.8714	−	5.48185i	−0.940206	−	0.305491i
$323$	−0.103440	−	0.142372i	−0.00575553	−	0.00792181i
$324$	−2.92624			−0.162569
$325$	4.91992	+	13.2881i	0.272908	+	0.737093i
$326$	40.0381			2.21750
$327$	8.72310	+	12.0063i	0.482389	+	0.663951i
$328$	−8.75069	−	2.84327i	−0.483176	−	0.156993i
$329$	1.94435	−	5.98410i	0.107196	−	0.329914i
$330$	−23.8635	−	3.28650i	−1.31364	−	0.180916i
$331$	1.24406	+	3.82881i	0.0683795	+	0.210450i	0.979407	−	0.201895i	$-0.0647098\pi$
$331$	1.24406	+	3.82881i	0.0683795	+	0.210450i	−0.911028	+	0.412345i	$0.864710\pi$
$332$		−	8.80483i		−	0.483228i
$333$	−5.54847	+	1.80281i	−0.304054	+	0.0987932i
$334$	25.6878	+	18.6632i	1.40557	+	1.02121i
$335$	−20.9599	+	21.8252i	−1.14516	+	1.19244i
$336$	1.04330	−	0.758002i	0.0569167	−	0.0413524i
$337$	−8.32339	+	11.4562i	−0.453404	+	0.624057i	−0.973125	−	0.230279i	$-0.926036\pi$
$337$	−8.32339	+	11.4562i	−0.453404	+	0.624057i	0.519721	+	0.854336i	$0.326036\pi$
$338$	6.48227	−	8.92208i	0.352589	−	0.485297i
$339$	0.332069	−	0.241262i	0.0180355	−	0.0131036i
$340$	0.129662	+	0.242239i	0.00703190	+	0.0131373i
$341$	−23.9095	−	17.3712i	−1.29477	−	0.940705i
$342$	−8.84661	+	2.87444i	−0.478370	+	0.155432i
$343$			1.00000i			0.0539949i
$344$	−1.04463	−	3.21505i	−0.0563229	−	0.173344i
$345$	12.8903	+	12.3793i	0.693990	+	0.666478i
$346$	−0.863632	+	2.65799i	−0.0464292	+	0.142894i
$347$	8.75525	+	2.84475i	0.470006	+	0.152714i	0.534438	−	0.845208i	$-0.320523\pi$
$347$	8.75525	+	2.84475i	0.470006	+	0.152714i	−0.0644314	+	0.997922i	$0.520523\pi$
$348$	11.5283	+	15.8673i	0.617981	+	0.850577i
$349$	2.84197			0.152127			0.0760637	−	0.997103i	$-0.475765\pi$
$349$	2.84197			0.152127			0.0760637	+	0.997103i	$0.475765\pi$
$350$	0.448661	+	11.0885i	0.0239819	+	0.592705i
$351$	−2.83394			−0.151264
$352$	−19.8960	−	27.3844i	−1.06046	−	1.45960i
$353$	−33.7774	−	10.9749i	−1.79779	−	0.584138i	−0.797963	−	0.602706i	$-0.794089\pi$
$353$	−33.7774	−	10.9749i	−1.79779	−	0.584138i	−0.999828	+	0.0185688i	$0.994089\pi$
$354$	4.84868	−	14.9227i	0.257704	−	0.793133i
$355$	1.95516	+	10.9117i	0.103769	+	0.579132i
$356$	0.577571	+	1.77758i	0.0306112	+	0.0942116i
$357$		−	0.0419909i		−	0.00222239i
$358$	44.1069	−	14.3312i	2.33112	−	0.757427i
$359$	18.0024	+	13.0795i	0.950130	+	0.690310i	0.950838	−	0.309690i	$-0.100225\pi$
$359$	18.0024	+	13.0795i	0.950130	+	0.690310i	−0.000707700		1.00000i	$0.500225\pi$
$360$	4.52486	−	0.810770i	0.238481	−	0.0427313i
$361$	1.16168	−	0.844012i	0.0611412	−	0.0444217i
$362$	27.7237	−	38.1584i	1.45713	−	2.00556i
$363$	7.38157	−	10.1599i	0.387432	−	0.533254i
$364$	−6.70901	+	4.87438i	−0.351648	+	0.255487i
$365$	−23.7915	−	11.5225i	−1.24530	−	0.603116i
$366$	0.341018	+	0.247764i	0.0178253	+	0.0129508i
$367$	15.8641	−	5.15457i	0.828102	−	0.269067i	0.135856	−	0.990729i	$-0.456622\pi$
$367$	15.8641	−	5.15457i	0.828102	−	0.269067i	0.692246	+	0.721662i	$0.256622\pi$
$368$			10.3071i			0.537297i
$369$	−1.38304	−	4.25657i	−0.0719983	−	0.221588i
$370$	25.5272	−	13.6638i	1.32710	−	0.710347i
$371$	−1.91248	+	5.88600i	−0.0992908	+	0.305586i
$372$	16.9456	+	5.50596i	0.878588	+	0.285471i
$373$	1.17730	+	1.62041i	0.0609582	+	0.0839018i	0.838408	−	0.545044i	$-0.183487\pi$
$373$	1.17730	+	1.62041i	0.0609582	+	0.0839018i	−0.777449	+	0.628945i	$0.783487\pi$
$374$	−0.452361			−0.0233910
$375$	4.46253	−	10.2511i	0.230444	−	0.529367i
$376$	12.9353			0.667085
$377$	11.1646	+	15.3668i	0.575008	+	0.791431i
$378$	−2.11088	−	0.685868i	−0.108572	−	0.0352772i
$379$	−11.1710	+	34.3809i	−0.573817	+	1.76603i	0.0663543	+	0.997796i	$0.478863\pi$
$379$	−11.1710	+	34.3809i	−0.573817	+	1.76603i	−0.640172	+	0.768232i	$0.721137\pi$
$380$	24.1770	−	12.9411i	1.24025	−	0.663862i
$381$	5.89551	+	18.1445i	0.302036	+	0.929572i
$382$			38.7952i			1.98493i
$383$	−22.0990	+	7.18039i	−1.12920	+	0.366901i	−0.813274	−	0.581881i	$-0.802317\pi$
$383$	−22.0990	+	7.18039i	−1.12920	+	0.366901i	−0.315931	+	0.948782i	$0.602317\pi$
$384$	11.8786	+	8.63030i	0.606176	+	0.440413i
$385$	−9.76789	−	4.73071i	−0.497818	−	0.241099i
$386$	11.2636	−	8.18348i	0.573302	−	0.416528i
$387$	0.966536	−	1.33032i	0.0491318	−	0.0676241i
$388$	−29.4610	+	40.5495i	−1.49565	+	2.05859i
$389$	−8.77380	+	6.37454i	−0.444849	+	0.323202i	−0.787559	−	0.616240i	$-0.788655\pi$
$389$	−8.77380	+	6.37454i	−0.444849	+	0.323202i	0.342710	+	0.939441i	$0.388655\pi$
$390$	13.8443	−	2.48064i	0.701034	−	0.125612i
$391$	0.271518	+	0.197270i	0.0137313	+	0.00997636i
$392$	−1.95519	+	0.635280i	−0.0987520	+	0.0320865i
$393$		−	2.25908i		−	0.113955i
$394$	−5.52889	−	17.0162i	−0.278542	−	0.857263i
$395$	4.23431	+	23.6315i	0.213051	+	1.18903i
$396$	−4.38899	+	13.5079i	−0.220555	+	0.678798i
$397$	4.17999	+	1.35816i	0.209788	+	0.0681642i	0.412026	−	0.911172i	$-0.364821\pi$
$397$	4.17999	+	1.35816i	0.209788	+	0.0681642i	−0.202238	+	0.979336i	$0.564821\pi$
$398$	21.3077	+	29.3276i	1.06806	+	1.47006i
$399$	−4.19095			−0.209810
$400$	6.04679	−	2.23882i	0.302340	−	0.111941i
$401$	−11.0909			−0.553853			−0.276927	−	0.960891i	$-0.589316\pi$
$401$	−11.0909			−0.553853			−0.276927	+	0.960891i	$0.589316\pi$
$402$	17.6546	+	24.2995i	0.880532	+	1.21195i
$403$	16.4111	+	5.33228i	0.817494	+	0.265620i
$404$	−4.99964	+	15.3873i	−0.248742	+	0.765548i
$405$	1.61278	+	1.54885i	0.0801399	+	0.0769628i
$406$	4.59701	+	14.1482i	0.228146	+	0.702161i
$407$			28.3164i			1.40359i
$408$	0.0821002	−	0.0266760i	0.00406456	−	0.00132066i
$409$	−7.04917	−	5.12152i	−0.348559	−	0.253243i	0.399705	−	0.916644i	$-0.369112\pi$
$409$	−7.04917	−	5.12152i	−0.348559	−	0.253243i	−0.748264	+	0.663401i	$0.769112\pi$
$410$	10.4823	+	19.5835i	0.517685	+	0.967159i
$411$	14.8278	−	10.7730i	0.731401	−	0.531394i
$412$	−1.08253	+	1.48998i	−0.0533325	+	0.0734059i
$413$	4.15530	−	5.71928i	0.204469	−	0.281427i
$414$	14.3517	−	10.4271i	0.705346	−	0.512464i
$415$	−4.66036	+	4.85274i	−0.228768	+	0.238212i
$416$	15.9890	+	11.6167i	0.783927	+	0.569557i
$417$	−20.2755	+	6.58792i	−0.992898	+	0.322612i
$418$			45.1484i			2.20828i
$419$	−6.15870	−	18.9545i	−0.300872	−	0.925990i	−0.981185	−	0.193068i	$-0.938156\pi$
$419$	−6.15870	−	18.9545i	−0.300872	−	0.925990i	0.680313	−	0.732922i	$-0.261844\pi$
$420$	6.48209	+	0.892718i	0.316294	+	0.0435602i
$421$	10.1021	−	31.0909i	0.492344	−	1.51528i	−0.328711	−	0.944431i	$-0.606614\pi$
$421$	10.1021	−	31.0909i	0.492344	−	1.51528i	0.821055	−	0.570849i	$-0.193386\pi$
$422$	35.1008	+	11.4049i	1.70868	+	0.555184i
$423$	3.69838	+	5.09038i	0.179821	+	0.247503i
$424$	−12.7232			−0.617893
$425$	0.0567537	−	0.202138i	0.00275296	−	0.00980515i
$426$	11.0034			0.533116
$427$	0.111630	+	0.153645i	0.00540215	+	0.00743543i
$428$	12.3673	+	4.01838i	0.597796	+	0.194236i
$429$	−4.25054	+	13.0818i	−0.205218	+	0.631597i
$430$	−3.55723	+	7.34491i	−0.171545	+	0.354203i
$431$	−3.75400	−	11.5536i	−0.180824	−	0.556518i	0.819028	−	0.573754i	$-0.194513\pi$
$431$	−3.75400	−	11.5536i	−0.180824	−	0.556518i	−0.999851	+	0.0172359i	$0.994513\pi$
$432$			1.28959i			0.0620454i
$433$	7.56375	−	2.45761i	0.363491	−	0.118105i	−0.121577	−	0.992582i	$-0.538795\pi$
$433$	7.56375	−	2.45761i	0.363491	−	0.118105i	0.485067	+	0.874477i	$0.338795\pi$
$434$	10.9334	+	7.94359i	0.524821	+	0.381305i
$435$	2.04475	−	14.8471i	0.0980381	−	0.711862i
$436$	−35.1334	+	25.5259i	−1.68259	+	1.22247i
$437$	19.6887	−	27.0992i	0.941840	−	1.29633i
$438$	−15.4230	+	21.2279i	−0.736940	+	1.01431i
$439$	−17.4969	+	12.7122i	−0.835079	+	0.606721i	−0.920992	−	0.389582i	$-0.872619\pi$
$439$	−17.4969	+	12.7122i	−0.835079	+	0.606721i	0.0859125	+	0.996303i	$0.472619\pi$
$440$	3.04410	−	22.1034i	0.145122	−	1.05374i
$441$	−0.809017	−	0.587785i	−0.0385246	−	0.0279898i
$442$	0.251194	−	0.0816180i	0.0119481	−	0.00388217i
$443$			5.53895i			0.263163i	0.991305	+	0.131582i	$0.0420056\pi$
$443$			5.53895i			0.263163i	−0.991305	+	0.131582i	$0.957994\pi$
$444$	−5.27545	−	16.2362i	−0.250362	−	0.770535i
$445$	0.622541	−	1.28541i	0.0295113	−	0.0609343i
$446$	−8.03301	+	24.7231i	−0.380374	+	1.17067i
$447$	13.5681	+	4.40853i	0.641747	+	0.208516i
$448$	7.58210	+	10.4359i	0.358221	+	0.493048i
$449$	−17.3381			−0.818237			−0.409119	−	0.912481i	$-0.634164\pi$
$449$	−17.3381			−0.818237			−0.409119	+	0.912481i	$0.634164\pi$
$450$	−9.23450	−	6.15468i	−0.435318	−	0.290134i
$451$	−21.7233			−1.02291
$452$	0.705992	+	0.971714i	0.0332071	+	0.0457056i
$453$	15.6358	+	5.08039i	0.734636	+	0.238698i
$454$	16.8196	−	51.7653i	0.789382	−	2.42947i
$455$	6.27763	+	0.864559i	0.294300	+	0.0405311i
$456$	−2.66243	−	8.19411i	−0.124680	−	0.383724i
$457$		−	15.6176i		−	0.730560i	−0.930898	−	0.365280i	$-0.880973\pi$
$457$		−	15.6176i		−	0.730560i	0.930898	−	0.365280i	$-0.119027\pi$
$458$	−23.7368	+	7.71256i	−1.10915	+	0.360384i
$459$	0.0339714	+	0.0246816i	0.00158565	+	0.00115204i
$460$	−36.2248	+	37.7201i	−1.68899	+	1.75871i
$461$	4.06052	−	2.95014i	0.189117	−	0.137402i	−0.489198	−	0.872173i	$-0.662710\pi$
$461$	4.06052	−	2.95014i	0.189117	−	0.137402i	0.678315	+	0.734771i	$0.262710\pi$
$462$	−6.33211	+	8.71540i	−0.294596	+	0.405477i
$463$	14.6924	−	20.2224i	0.682814	−	0.939813i	−0.317149	−	0.948376i	$-0.602726\pi$
$463$	14.6924	−	20.2224i	0.682814	−	0.939813i	0.999963	+	0.00856254i	$0.00272557\pi$
$464$	6.99270	−	5.08049i	0.324628	−	0.235856i
$465$	−6.42520	−	12.0038i	−0.297962	−	0.556663i
$466$	28.2861	+	20.5511i	1.31033	+	0.952011i
$467$	−7.95790	+	2.58568i	−0.368248	+	0.119651i	−0.487295	−	0.873238i	$-0.662016\pi$
$467$	−7.95790	+	2.58568i	−0.368248	+	0.119651i	0.119047	+	0.992889i	$0.462016\pi$
$468$		−	8.29279i		−	0.383334i
$469$	4.18181	+	12.8703i	0.193098	+	0.594294i
$470$	−22.5230	−	21.6301i	−1.03891	−	0.997723i
$471$	−1.54156	+	4.74442i	−0.0710311	+	0.218611i
$472$	13.8220	+	4.49105i	0.636211	+	0.206718i
$473$	−4.69126	−	6.45697i	−0.215705	−	0.296892i
$474$	23.8301			1.09455
$475$	−20.1747	−	5.66437i	−0.925677	−	0.259899i
$476$	0.122876			0.00563199
$477$	−3.63775	−	5.00693i	−0.166561	−	0.229252i
$478$	−34.8923	−	11.3372i	−1.59594	−	0.518552i
$479$	8.54262	−	26.2915i	0.390322	−	1.20129i	−0.542222	−	0.840235i	$-0.682417\pi$
$479$	8.54262	−	26.2915i	0.390322	−	1.20129i	0.932545	−	0.361054i	$-0.117583\pi$
$480$	−2.75036	−	15.3496i	−0.125536	−	0.700611i
$481$	−5.10905	−	15.7240i	−0.232952	−	0.716954i
$482$			40.1650i			1.82946i
$483$	7.60139	−	2.46984i	0.345875	−	0.112382i
$484$	29.7302	+	21.6003i	1.35137	+	0.981830i
$485$	37.6999	−	6.75511i	1.71187	−	0.306734i
$486$	1.79562	−	1.30460i	0.0814512	−	0.0591777i
$487$	9.33058	−	12.8424i	0.422809	−	0.581946i	−0.543475	−	0.839425i	$-0.682892\pi$
$487$	9.33058	−	12.8424i	0.422809	−	0.581946i	0.966284	+	0.257479i	$0.0828918\pi$
$488$	−0.229490	+	0.315866i	−0.0103885	+	0.0142986i
$489$	−14.5939	+	10.6031i	−0.659961	+	0.479490i
$490$	4.46670	+	2.16328i	0.201785	+	0.0977270i
$491$	−29.7635	−	21.6244i	−1.34321	−	0.975897i	−0.999319	−	0.0368863i	$-0.988256\pi$
$491$	−29.7635	−	21.6244i	−1.34321	−	0.975897i	−0.343888	−	0.939011i	$-0.611744\pi$
$492$	12.4557	−	4.04712i	0.561548	−	0.182458i
$493$		−	0.281443i		−	0.0126756i
$494$	−8.14598	−	25.0708i	−0.366505	−	1.12799i
$495$	9.56865	−	5.12175i	0.430079	−	0.230205i
$496$	2.42647	−	7.46789i	0.108952	−	0.335318i
$497$	4.71493	+	1.53197i	0.211493	+	0.0687183i
$498$	3.92543	+	5.40289i	0.175903	+	0.242109i
$499$	12.6827			0.567756			0.283878	−	0.958860i	$-0.408379\pi$
$499$	12.6827			0.567756			0.283878	+	0.958860i	$0.408379\pi$
$500$	29.9973	+	13.0584i	1.34152	+	0.583991i
$501$	−14.3058			−0.639134
$502$	−15.3165	−	21.0813i	−0.683608	−	0.940905i
$503$	−15.5903	−	5.06559i	−0.695136	−	0.225863i	−0.0599260	−	0.998203i	$-0.519086\pi$
$503$	−15.5903	−	5.06559i	−0.695136	−	0.225863i	−0.635210	+	0.772339i	$0.719086\pi$
$504$	0.635280	−	1.95519i	0.0282976	−	0.0870911i
$505$	10.9000	−	5.83436i	0.485042	−	0.259625i
$506$	−26.6072	−	81.8884i	−1.18283	−	3.64038i
$507$			4.96879i			0.220672i
$508$	−53.0952	+	17.2517i	−2.35572	+	0.765420i
$509$	−0.606707	−	0.440798i	−0.0268918	−	0.0195380i	0.574258	−	0.818674i	$-0.305291\pi$
$509$	−0.606707	−	0.440798i	−0.0268918	−	0.0195380i	−0.601150	+	0.799136i	$0.705291\pi$
$510$	−0.187561	−	0.0908381i	−0.00830533	−	0.00402238i
$511$	−9.56423	+	6.94882i	−0.423097	+	0.307398i
$512$	8.40282	−	11.5655i	0.371356	−	0.511128i
$513$	2.46338	−	3.39055i	0.108761	−	0.149697i
$514$	29.1364	−	21.1688i	1.28515	−	0.933717i
$515$	1.38527	−	0.248214i	0.0610423	−	0.0109376i
$516$	3.89285	+	2.82832i	0.171373	+	0.124510i
$517$	29.0449	−	9.43727i	1.27740	−	0.415051i
$518$		−	12.9487i		−	0.568931i
$519$	−0.389109	−	1.19755i	−0.0170800	−	0.0525668i
$520$	2.29767	+	12.8232i	0.100760	+	0.562334i
$521$	2.17610	−	6.69735i	0.0953367	−	0.293416i	−0.892005	−	0.452026i	$-0.850701\pi$
$521$	2.17610	−	6.69735i	0.0953367	−	0.293416i	0.987341	+	0.158610i	$0.0507013\pi$
$522$	−14.1482	−	4.59701i	−0.619248	−	0.201206i
$523$	−7.82888	−	10.7755i	−0.342333	−	0.471181i	0.602788	−	0.797901i	$-0.294056\pi$
$523$	−7.82888	−	10.7755i	−0.342333	−	0.471181i	−0.945121	+	0.326720i	$0.894056\pi$
$524$	6.61060			0.288786
$525$	−3.10006	−	3.92296i	−0.135298	−	0.171212i
$526$	11.9055			0.519103
$527$	−0.150284	−	0.206849i	−0.00654649	−	0.00901048i
$528$	5.95291	+	1.93422i	0.259067	+	0.0841761i
$529$	−12.6330	+	38.8803i	−0.549260	+	1.69045i
$530$	22.1538	+	21.2755i	0.962299	+	0.924150i
$531$	2.18457	+	6.72341i	0.0948022	+	0.291771i
$532$		−	12.2637i		−	0.531701i
$533$	12.0628	−	3.91946i	0.522500	−	0.169771i
$534$	−1.14691	−	0.833277i	−0.0496315	−	0.0360594i
$535$	−4.68926	−	8.76067i	−0.202735	−	0.378757i
$536$	−22.5072	+	16.3525i	−0.972164	+	0.706318i
$537$	−12.2818	+	16.9044i	−0.529997	+	0.729479i
$538$	−24.1829	+	33.2849i	−1.04260	+	1.43501i
$539$	−3.92672	+	2.85293i	−0.169136	+	0.122884i
$540$	−4.53230	+	4.71940i	−0.195039	+	0.203091i
$541$	6.12488	+	4.44999i	0.263329	+	0.191320i	0.711613	−	0.702571i	$-0.247965\pi$
$541$	6.12488	+	4.44999i	0.263329	+	0.191320i	−0.448284	+	0.893891i	$0.647965\pi$
$542$	30.6591	−	9.96175i	1.31692	−	0.427894i
$543$			21.2508i			0.911958i
$544$	−0.0904924	−	0.278507i	−0.00387983	−	0.0119409i
$545$	32.8744	+	4.52748i	1.40818	+	0.193936i
$546$	1.94371	−	5.98211i	0.0831830	−	0.256011i
$547$	−11.3522	−	3.68855i	−0.485384	−	0.157711i	0.0560943	−	0.998425i	$-0.482135\pi$
$547$	−11.3522	−	3.68855i	−0.485384	−	0.157711i	−0.541479	+	0.840715i	$0.682135\pi$
$548$	31.5245	+	43.3897i	1.34666	+	1.85352i
$549$	−0.189916			−0.00810543
$550$	−42.2614	+	33.3964i	−1.80203	+	1.42403i
$551$	−28.0898			−1.19666
$552$	9.65802	+	13.2931i	0.411072	+	0.565793i
$553$	10.2111	+	3.31780i	0.434222	+	0.141087i
$554$	−14.6903	+	45.2121i	−0.624132	+	1.92088i
$555$	−5.68619	+	11.7408i	−0.241366	+	0.498367i
$556$	−19.2779	−	59.3312i	−0.817564	−	2.51620i
$557$			1.37561i			0.0582865i	0.999575	+	0.0291433i	$0.00927790\pi$
$557$			1.37561i			0.0582865i	−0.999575	+	0.0291433i	$0.990722\pi$
$558$	−12.8530	+	4.17619i	−0.544111	+	0.176792i
$559$	3.77005	+	2.73910i	0.159456	+	0.115852i
$560$	0.393419	−	2.85665i	0.0166250	−	0.120715i
$561$	0.164886	−	0.119797i	0.00696151	−	0.00505783i
$562$	34.5761	−	47.5899i	1.45850	−	2.00746i
$563$	−20.8503	+	28.6980i	−0.878737	+	1.20948i	0.0980321	+	0.995183i	$0.468745\pi$
$563$	−20.8503	+	28.6980i	−0.878737	+	1.20948i	−0.976769	+	0.214294i	$0.931255\pi$
$564$	−14.8957	+	10.8223i	−0.627221	+	0.455703i
$565$	0.125220	−	0.909234i	0.00526806	−	0.0382518i
$566$	4.05852	+	2.94868i	0.170592	+	0.123942i
$567$	0.951057	−	0.309017i	0.0399406	−	0.0129775i
$568$			10.1918i			0.427639i
$569$	−6.64887	−	20.4631i	−0.278735	−	0.857859i	−0.988207	−	0.153125i	$-0.951066\pi$
$569$	−6.64887	−	20.4631i	−0.278735	−	0.857859i	0.709472	−	0.704734i	$-0.248934\pi$
$570$	−9.06620	+	18.7197i	−0.379741	+	0.784084i
$571$	5.98348	−	18.4153i	0.250401	−	0.770654i	−0.744300	−	0.667845i	$-0.767217\pi$
$571$	5.98348	−	18.4153i	0.250401	−	0.770654i	0.994701	−	0.102809i	$-0.0327831\pi$
$572$	−38.2806	−	12.4381i	−1.60059	−	0.520064i
$573$	−10.2740	−	14.1409i	−0.429202	−	0.590745i
$574$	9.93370			0.414625
$575$	39.9302	−	1.61565i	1.66520	−	0.0673772i
$576$	−12.8994			−0.537477
$577$	−12.5068	−	17.2141i	−0.520663	−	0.716631i	0.465009	−	0.885306i	$-0.346051\pi$
$577$	−12.5068	−	17.2141i	−0.520663	−	0.716631i	−0.985672	+	0.168675i	$0.946051\pi$
$578$	35.8813	+	11.6585i	1.49247	+	0.484931i
$579$	−1.93840	+	5.96579i	−0.0805572	+	0.247930i
$580$	43.4461	+	5.98343i	1.80400	+	0.248448i
$581$	0.929807	+	2.86165i	0.0385749	+	0.118721i
$582$		−	38.0168i		−	1.57585i
$583$	−28.5688	+	9.28256i	−1.18320	+	0.384444i
$584$	−19.6622	−	14.2854i	−0.813629	−	0.591136i
$585$	−4.38934	+	4.57053i	−0.181477	+	0.188968i
$586$	−14.7653	+	10.7276i	−0.609947	+	0.443153i
$587$	−25.3289	+	34.8622i	−1.04544	+	1.43892i	−0.152735	+	0.988267i	$0.548808\pi$
$587$	−25.3289	+	34.8622i	−1.04544	+	1.43892i	−0.892700	+	0.450651i	$0.851192\pi$
$588$	1.72000	−	2.36738i	0.0709317	−	0.0976291i
$589$	−20.6448	+	14.9993i	−0.850654	+	0.618036i
$590$	−16.5572	−	30.9329i	−0.681650	−	1.27349i
$591$	6.52162	+	4.73824i	0.268264	+	0.194905i
$592$	−7.15525	+	2.32488i	−0.294079	+	0.0955520i
$593$		−	46.6044i		−	1.91381i	−0.290396	−	0.956906i	$-0.593787\pi$
$593$		−	46.6044i		−	1.91381i	0.290396	−	0.956906i	$-0.406213\pi$
$594$	−3.32899	−	10.2456i	−0.136590	−	0.420381i
$595$	−0.0677222	−	0.0650375i	−0.00277634	−	0.00266628i
$596$	−12.9004	+	39.7034i	−0.528422	+	1.62632i
$597$	−15.5334	−	5.04711i	−0.635740	−	0.206564i
$598$	29.5497	+	40.6717i	1.20838	+	1.66319i
$599$	33.3360			1.36207			0.681036	−	0.732250i	$-0.261530\pi$
$599$	33.3360			1.36207			0.681036	+	0.732250i	$0.261530\pi$
$600$	5.70073	−	8.55339i	0.232731	−	0.349191i
$601$	−0.186266			−0.00759796			−0.00379898	−	0.999993i	$-0.501209\pi$
$601$	−0.186266			−0.00759796			−0.00379898	+	0.999993i	$0.501209\pi$
$602$	2.14524	+	2.95267i	0.0874335	+	0.120342i
$603$	−12.8703	−	4.18181i	−0.524118	−	0.170296i
$604$	−14.8665	+	45.7543i	−0.604908	+	1.86172i
$605$	−4.95273	−	27.6409i	−0.201357	−	1.12376i
$606$	−3.79216	−	11.6711i	−0.154046	−	0.474105i
$607$		−	1.31479i		−	0.0533657i	−0.999644	−	0.0266829i	$-0.991506\pi$
$607$		−	1.31479i		−	0.0533657i	0.999644	−	0.0266829i	$-0.00849442\pi$
$608$	−27.7967	+	9.03170i	−1.12731	+	0.366284i
$609$	−5.42242	−	3.93962i	−0.219728	−	0.159641i
$610$	0.927776	−	0.166240i	0.0375645	−	0.00673085i
$611$	−14.4258	+	10.4810i	−0.583606	+	0.424015i
$612$	−0.0722244	+	0.0994084i	−0.00291950	+	0.00401835i
$613$	7.08453	−	9.75103i	0.286142	−	0.393840i	−0.641614	−	0.767027i	$-0.721735\pi$
$613$	7.08453	−	9.75103i	0.286142	−	0.393840i	0.927756	+	0.373187i	$0.121735\pi$
$614$	−31.8079	+	23.1098i	−1.28366	+	0.932636i
$615$	−9.00704	−	4.36222i	−0.363199	−	0.175902i
$616$	−8.07257	−	5.86507i	−0.325253	−	0.236310i
$617$	17.2801	−	5.61465i	0.695671	−	0.226037i	0.0602276	−	0.998185i	$-0.480817\pi$
$617$	17.2801	−	5.61465i	0.695671	−	0.226037i	0.635443	+	0.772147i	$0.280817\pi$
$618$		−	1.39691i		−	0.0561921i
$619$	5.00247	+	15.3960i	0.201066	+	0.618818i	0.999852	+	0.0172026i	$0.00547602\pi$
$619$	5.00247	+	15.3960i	0.201066	+	0.618818i	−0.798786	+	0.601615i	$0.794524\pi$
$620$	35.1261	−	18.8017i	1.41070	−	0.755094i
$621$	−2.46984	+	7.60139i	−0.0991113	+	0.305033i
$622$	−43.9636	−	14.2846i	−1.76278	−	0.572762i
$623$	−0.375432	−	0.516738i	−0.0150414	−	0.0207027i
$624$	−3.65462			−0.146302
$625$	−9.62110	−	23.0745i	−0.384844	−	0.922982i
$626$	−60.7801			−2.42926
$627$	−11.9565	−	16.4567i	−0.477496	−	0.657216i
$628$	−13.8833	−	4.51097i	−0.554005	−	0.180007i
$629$	−0.0757015	+	0.232985i	−0.00301842	+	0.00928973i
$630$	−4.37559	+	2.34209i	−0.174328	+	0.0933113i
$631$	2.62113	+	8.06701i	0.104346	+	0.321143i	0.989576	−	0.144010i	$-0.0459996\pi$
$631$	2.62113	+	8.06701i	0.104346	+	0.321143i	−0.885231	+	0.465152i	$0.846000\pi$
$632$			22.0725i			0.877996i
$633$	−15.8146	+	5.13849i	−0.628576	+	0.204237i
$634$	7.76691	+	5.64299i	0.308463	+	0.224112i
$635$	38.3944	+	18.5949i	1.52364	+	0.737916i
$636$	14.6515	−	10.6449i	0.580969	−	0.422099i
$637$	1.66575	−	2.29270i	0.0659993	−	0.0908403i
$638$	−42.4408	+	58.4148i	−1.68025	+	2.31266i
$639$	−4.01076	+	2.91398i	−0.158663	+	0.115275i
$640$	32.3169	−	5.79058i	1.27744	−	0.228893i
$641$	23.8934	+	17.3596i	0.943732	+	0.685661i	0.949316	−	0.314323i	$-0.101778\pi$
$641$	23.8934	+	17.3596i	0.943732	+	0.685661i	−0.00558446	+	0.999984i	$0.501778\pi$
$642$	−9.38042	+	3.04788i	−0.370216	+	0.120290i
$643$			22.1880i			0.875009i	0.899216	+	0.437504i	$0.144138\pi$
$643$			22.1880i			0.875009i	−0.899216	+	0.437504i	$0.855862\pi$
$644$	7.22735	+	22.2435i	0.284798	+	0.876517i
$645$	−0.648506	−	3.61928i	−0.0255349	−	0.142509i
$646$	−0.120700	+	0.371477i	−0.00474889	+	0.0146156i
$647$	15.0383	+	4.88625i	0.591218	+	0.192098i	0.589320	−	0.807900i	$-0.299396\pi$
$647$	15.0383	+	4.88625i	0.591218	+	0.192098i	0.00189789	+	0.999998i	$0.499396\pi$
$648$	1.20837	+	1.66318i	0.0474694	+	0.0653360i
$649$	34.3127			1.34689
$650$	17.4420	−	26.1700i	0.684131	−	1.02647i
$651$	−6.08892			−0.238644
$652$	−31.0273	−	42.7054i	−1.21512	−	1.67247i
$653$	3.91409	+	1.27176i	0.153170	+	0.0497680i	0.384598	−	0.923084i	$-0.374340\pi$
$653$	3.91409	+	1.27176i	0.153170	+	0.0497680i	−0.231428	+	0.972852i	$0.574340\pi$
$654$	10.1787	−	31.3268i	0.398019	−	1.22498i
$655$	−3.64340	−	3.49896i	−0.142359	−	0.136716i
$656$	−1.78356	−	5.48922i	−0.0696362	−	0.214318i
$657$		−	11.8220i		−	0.461222i
$658$	−13.2818	+	4.31552i	−0.517778	+	0.168236i
$659$	1.65171	+	1.20004i	0.0643414	+	0.0467468i	0.619491	−	0.785004i	$-0.287339\pi$
$659$	1.65171	+	1.20004i	0.0643414	+	0.0467468i	−0.555150	+	0.831750i	$0.687339\pi$
$660$	14.9875	+	28.0002i	0.583387	+	1.08991i
$661$	−10.8315	+	7.86957i	−0.421298	+	0.306091i	−0.778160	−	0.628066i	$-0.783847\pi$
$661$	−10.8315	+	7.86957i	−0.421298	+	0.306091i	0.356862	+	0.934157i	$0.383847\pi$
$662$	5.25211	−	7.22891i	0.204129	−	0.280960i
$663$	−0.0699462	+	0.0962727i	−0.00271649	+	0.00373892i
$664$	−5.00439	+	3.63590i	−0.194208	+	0.141100i
$665$	−6.49115	+	6.75910i	−0.251716	+	0.262107i
$666$	10.4757	+	7.61103i	0.405925	+	0.294921i
$667$	50.9481	−	16.5541i	1.97272	−	0.640976i
$668$		−	41.8621i		−	1.61969i
$669$	−3.61926	−	11.1389i	−0.139929	−	0.430657i
$670$	66.5341	+	9.16312i	2.57044	+	0.354002i
$671$	−0.284850	+	0.876678i	−0.0109965	+	0.0338438i
$672$	−6.63255	−	2.15505i	−0.255856	−	0.0831327i
$673$	−18.7354	−	25.7871i	−0.722197	−	0.994019i	−0.999448	−	0.0332213i	$-0.989423\pi$
$673$	−18.7354	−	25.7871i	−0.722197	−	0.994019i	0.277251	−	0.960798i	$-0.410577\pi$
$674$	31.4296			1.21062
$675$	4.99591	−	0.202144i	0.192293	−	0.00778052i
$676$	−14.5399			−0.559227
$677$	−0.245902	−	0.338455i	−0.00945078	−	0.0130079i	0.804265	−	0.594270i	$-0.202559\pi$
$677$	−0.245902	−	0.338455i	−0.00945078	−	0.0130079i	−0.813716	+	0.581262i	$0.802559\pi$
$678$	−0.866433	−	0.281521i	−0.0332752	−	0.0108118i
$679$	5.29298	−	16.2901i	0.203126	−	0.625157i
$680$	0.0841381	−	0.173727i	0.00322655	−	0.00666212i
$681$	7.57804	+	23.3228i	0.290391	+	0.893732i
$682$			65.5949i			2.51176i
$683$	−8.31108	+	2.70043i	−0.318015	+	0.103329i	−0.463675	−	0.886005i	$-0.653469\pi$
$683$	−8.31108	+	2.70043i	−0.318015	+	0.103329i	0.145660	+	0.989335i	$0.453469\pi$
$684$	9.92158	+	7.20845i	0.379361	+	0.275622i
$685$	5.59143	−	40.5998i	0.213637	−	1.55124i
$686$	1.79562	−	1.30460i	0.0685573	−	0.0498098i
$687$	6.60963	−	9.09737i	0.252173	−	0.347086i
$688$	1.24643	−	1.71557i	0.0475199	−	0.0654055i
$689$	14.1893	−	10.3092i	0.540570	−	0.392747i
$690$	5.41188	−	39.2961i	0.206027	−	1.49598i
$691$	−21.9464	−	15.9450i	−0.834879	−	0.606575i	0.0860562	−	0.996290i	$-0.472574\pi$
$691$	−21.9464	−	15.9450i	−0.834879	−	0.606575i	−0.920936	+	0.389715i	$0.872574\pi$
$692$	3.50433	−	1.13863i	0.133215	−	0.0432841i
$693$		−	4.85369i		−	0.184376i
$694$	−6.31397	−	19.4324i	−0.239675	−	0.737644i
$695$	−20.7788	+	42.9038i	−0.788186	+	1.62743i
$696$	4.25795	−	13.1046i	0.161397	−	0.496729i
$697$	−0.178737	−	0.0580752i	−0.00677015	−	0.00219975i
$698$	−3.70763	−	5.10312i	−0.140336	−	0.193156i
$699$	−15.7528			−0.595826
$700$	11.4795	−	9.07153i	0.433886	−	0.342872i
$701$	−18.4884			−0.698298			−0.349149	−	0.937067i	$-0.613529\pi$
$701$	−18.4884			−0.698298			−0.349149	+	0.937067i	$0.613529\pi$
$702$	3.69715	+	5.08869i	0.139540	+	0.192060i
$703$	23.2534	+	7.55548i	0.877018	+	0.284960i
$704$	−19.3475	+	59.5455i	−0.729187	+	2.24421i
$705$	13.9379	+	1.91954i	0.524932	+	0.0722939i
$706$	24.3591	+	74.9695i	0.916765	+	2.82151i
$707$		−	5.52900i		−	0.207939i
$708$	−19.6743	+	6.39258i	−0.739407	+	0.240248i
$709$	5.04666	+	3.66662i	0.189531	+	0.137703i	0.678505	−	0.734596i	$-0.262628\pi$
$709$	5.04666	+	3.66662i	0.189531	+	0.137703i	−0.488973	+	0.872299i	$0.662628\pi$
$710$	17.0426	−	17.7461i	0.639596	−	0.665999i
$711$	−8.68612	+	6.31084i	−0.325755	+	0.236675i
$712$	0.771817	−	1.06231i	0.0289251	−	0.0398119i
$713$	28.6052	−	39.3717i	1.07127	−	1.47448i
$714$	−0.0753999	+	0.0547812i	−0.00282177	+	0.00205014i
$715$	14.5147	+	27.1170i	0.542820	+	1.01412i
$716$	−49.4664	−	35.9394i	−1.84865	−	1.34312i
$717$	15.7207	−	5.10797i	0.587101	−	0.190761i
$718$		−	49.3890i		−	1.84318i
$719$	12.1228	+	37.3102i	0.452105	+	1.39144i	0.874501	+	0.485024i	$0.161189\pi$
$719$	12.1228	+	37.3102i	0.452105	+	1.39144i	−0.422396	+	0.906411i	$0.638811\pi$
$720$	2.07983	+	1.99738i	0.0775107	+	0.0744379i
$721$	0.194488	−	0.598574i	0.00724313	−	0.0222921i
$722$	−3.03106	−	0.984851i	−0.112804	−	0.0366524i
$723$	−10.6367	−	14.6402i	−0.395584	−	0.544475i
$724$	−62.1849			−2.31109
$725$	−20.7781	−	26.2936i	−0.771679	−	0.976518i
$726$	−27.8733			−1.03447
$727$	−11.3554	−	15.6294i	−0.421149	−	0.579662i	0.544744	−	0.838602i	$-0.316627\pi$
$727$	−11.3554	−	15.6294i	−0.421149	−	0.579662i	−0.965893	+	0.258940i	$0.916627\pi$
$728$	5.54089	+	1.80034i	0.205359	+	0.0667252i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	10.3482	+	57.7528i	0.383004	+	2.13753i
$731$	−0.0213372	−	0.0656691i	−0.000789184	−	0.00242886i
$732$		−	0.555741i		−	0.0205408i
$733$	−36.1754	+	11.7541i	−1.33617	+	0.434147i	−0.888017	−	0.459810i	$-0.847917\pi$
$733$	−36.1754	+	11.7541i	−1.33617	+	0.434147i	−0.448151	+	0.893958i	$0.647917\pi$
$734$	−29.9520	−	21.7614i	−1.10555	−	0.803228i
$735$	−2.20101	+	0.394380i	−0.0811856	+	0.0145469i
$736$	45.0940	−	32.7627i	1.66219	−	1.20765i
$737$	−38.6075	+	53.1387i	−1.42213	+	1.95739i
$738$	−5.83888	+	8.03653i	−0.214932	+	0.295829i
$739$	24.2062	−	17.5868i	0.890438	−	0.646941i	−0.0455540	−	0.998962i	$-0.514505\pi$
$739$	24.2062	−	17.5868i	0.890438	−	0.646941i	0.935992	+	0.352021i	$0.114505\pi$
$740$	−34.3563	−	16.6392i	−1.26296	−	0.611669i
$741$	9.60862	+	6.98107i	0.352981	+	0.256456i
$742$	13.0641	−	4.24477i	0.479597	−	0.155830i
$743$			29.2631i			1.07356i	0.843722	+	0.536780i	$0.180360\pi$
$743$			29.2631i			1.07356i	−0.843722	+	0.536780i	$0.819640\pi$
$744$	−3.86817	−	11.9050i	−0.141814	−	0.436458i
$745$	28.1249	−	15.0542i	1.03041	−	0.551543i
$746$	1.37375	−	4.22797i	0.0502966	−	0.154797i
$747$	−2.86165	−	0.929807i	−0.104702	−	0.0340199i
$748$	0.350555	+	0.482497i	0.0128176	+	0.0176418i
$749$	−4.44384			−0.162374
$750$	−24.2290	+	5.36059i	−0.884718	+	0.195741i
$751$	19.6650			0.717585			0.358792	−	0.933417i	$-0.383189\pi$
$751$	19.6650			0.717585			0.358792	+	0.933417i	$0.383189\pi$
$752$	4.76939	+	6.56450i	0.173922	+	0.239383i
$753$	11.1658	+	3.62798i	0.406903	+	0.132211i
$754$	13.0277	−	40.0950i	0.474439	−	1.46017i
$755$	32.4111	−	17.3485i	1.17956	−	0.631376i
$756$	0.904259	+	2.78302i	0.0328876	+	0.101218i
$757$			24.4409i			0.888319i	0.895948	+	0.444160i	$0.146498\pi$
$757$			24.4409i			0.888319i	−0.895948	+	0.444160i	$0.853502\pi$
$758$	76.3089	−	24.7943i	2.77166	−	0.900568i
$759$	31.3846	+	22.8022i	1.13919	+	0.827668i
$760$	−17.3390	−	8.39750i	−0.628952	−	0.304609i
$761$	18.4509	−	13.4054i	0.668844	−	0.485944i	−0.200794	−	0.979634i	$-0.564352\pi$
$761$	18.4509	−	13.4054i	0.668844	−	0.485944i	0.869638	+	0.493690i	$0.164352\pi$
$762$	24.8895	−	34.2574i	0.901650	−	1.24101i
$763$	8.72310	−	12.0063i	0.315798	−	0.434658i
$764$	41.3798	−	30.0642i	1.49707	−	1.08768i
$765$	0.0924226	−	0.0165604i	0.00334155	−	0.000598741i
$766$	41.7235	+	30.3139i	1.50753	+	1.09529i
$767$	−19.0537	+	6.19093i	−0.687990	+	0.223542i
$768$		−	6.78966i		−	0.245001i
$769$	11.4605	+	35.2718i	0.413276	+	1.27193i	0.913784	+	0.406201i	$0.133147\pi$
$769$	11.4605	+	35.2718i	0.413276	+	1.27193i	−0.500508	+	0.865732i	$0.666853\pi$
$770$	4.24859	+	23.7111i	0.153108	+	0.854490i
$771$	−5.01421	+	15.4322i	−0.180582	+	0.555776i
$772$	−17.4573	−	5.67223i	−0.628304	−	0.204148i
$773$	−17.8618	−	24.5847i	−0.642444	−	0.884249i	0.356299	−	0.934372i	$-0.384039\pi$
$773$	−17.8618	−	24.5847i	−0.642444	−	0.884249i	−0.998743	+	0.0501232i	$0.984039\pi$
$774$	−3.64970			−0.131186
$775$	−29.3112	−	8.22961i	−1.05289	−	0.295616i
$776$	35.2128			1.26407
$777$	3.42914	+	4.71981i	0.123020	+	0.169322i
$778$	22.8925	+	7.43824i	0.820738	+	0.266674i
$779$	−5.79626	+	17.8391i	−0.207673	+	0.639151i
$780$	−13.3745	−	12.8443i	−0.478883	−	0.459899i
$781$	7.43571	+	22.8848i	0.266071	+	0.818882i
$782$		−	0.744903i		−	0.0266377i
$783$	6.37444	−	2.07118i	0.227804	−	0.0740179i
$784$	−1.04330	−	0.758002i	−0.0372607	−	0.0270715i
$785$	5.26409	+	9.83458i	0.187883	+	0.351011i
$786$	−4.05645	+	2.94718i	−0.144689	+	0.105123i
$787$	21.7687	−	29.9621i	0.775971	−	1.06803i	−0.219744	−	0.975558i	$-0.570522\pi$
$787$	21.7687	−	29.9621i	0.775971	−	1.06803i	0.995715	−	0.0924751i	$-0.0294778\pi$
$788$	−13.8652	+	19.0838i	−0.493928	+	0.679834i
$789$	−4.33956	+	3.15288i	−0.154493	+	0.112245i
$790$	36.9092	−	38.4328i	1.31317	−	1.36738i
$791$	−0.332069	−	0.241262i	−0.0118070	−	0.00857830i
$792$	9.48988	−	3.08345i	0.337208	−	0.109566i
$793$		−	0.538211i		−	0.0191124i
$794$	−3.01446	−	9.27755i	−0.106979	−	0.329248i
$795$	−13.7094	−	1.88807i	−0.486223	−	0.0669629i
$796$	14.7691	−	45.4545i	0.523476	−	1.61109i
$797$	−33.4869	−	10.8805i	−1.18617	−	0.385409i	−0.351512	−	0.936183i	$-0.614332\pi$
$797$	−33.4869	−	10.8805i	−1.18617	−	0.385409i	−0.834654	+	0.550775i	$0.814332\pi$
$798$	5.46751	+	7.52538i	0.193548	+	0.266395i
$799$	0.264209			0.00934704
$800$	−29.0155	−	19.3385i	−1.02585	−	0.683718i
$801$	0.638723			0.0225682
$802$	14.4692	+	19.9151i	0.510924	+	0.703227i
$803$	−54.5721	−	17.7315i	−1.92581	−	0.625732i
$804$	12.2370	−	37.6616i	0.431565	−	1.32822i
$805$	7.79007	−	16.0848i	0.274564	−	0.566915i
$806$	−11.8351	−	36.4246i	−0.416873	−	1.28300i
$807$		−	18.5367i		−	0.652522i
$808$	10.8102	−	3.51246i	0.380303	−	0.123568i
$809$	−8.43852	−	6.13094i	−0.296682	−	0.215552i	0.429479	−	0.903077i	$-0.358697\pi$
$809$	−8.43852	−	6.13094i	−0.296682	−	0.215552i	−0.726161	+	0.687525i	$0.758697\pi$
$810$	0.677114	−	4.91658i	0.0237914	−	0.172751i
$811$	9.32798	−	6.77717i	0.327550	−	0.237979i	−0.411841	−	0.911256i	$-0.635114\pi$
$811$	9.32798	−	6.77717i	0.327550	−	0.237979i	0.739390	+	0.673277i	$0.235114\pi$
$812$	11.5283	−	15.8673i	0.404563	−	0.556834i
$813$	−8.53717	+	11.7504i	−0.299412	+	0.412105i
$814$	50.8457	−	36.9416i	1.78214	−	1.29480i
$815$	−5.50325	+	39.9595i	−0.192770	+	1.39972i
$816$	0.0438091	+	0.0318292i	0.00153363	+	0.00111424i
$817$	−6.55418	+	2.12958i	−0.229302	+	0.0745047i
$818$			19.3392i			0.676178i
$819$	0.875735	+	2.69524i	0.0306007	+	0.0941792i
$820$	12.7649	−	26.3568i	0.445771	−	0.920419i
$821$	−10.4029	+	32.0168i	−0.363064	+	1.11739i	0.588121	+	0.808773i	$0.299868\pi$
$821$	−10.4029	+	32.0168i	−0.363064	+	1.11739i	−0.951185	+	0.308622i	$0.900132\pi$
$822$	−38.6886	−	12.5707i	−1.34942	−	0.438453i
$823$	22.3465	+	30.7573i	0.778950	+	1.07213i	0.995397	+	0.0958381i	$0.0305531\pi$
$823$	22.3465	+	30.7573i	0.778950	+	1.07213i	−0.216447	+	0.976294i	$0.569447\pi$
$824$	1.29388			0.0450745
$825$	6.56010	−	23.3650i	0.228394	−	0.813464i
$826$	−15.6907			−0.545948
$827$	13.3628	+	18.3923i	0.464669	+	0.639562i	0.975469	−	0.220138i	$-0.0706507\pi$
$827$	13.3628	+	18.3923i	0.464669	+	0.639562i	−0.510800	+	0.859700i	$0.670651\pi$
$828$	−22.2435	−	7.22735i	−0.773015	−	0.251168i
$829$	13.9506	−	42.9354i	0.484523	−	1.49121i	−0.348148	−	0.937440i	$-0.613189\pi$
$829$	13.9506	−	42.9354i	0.484523	−	1.49121i	0.832671	−	0.553768i	$-0.186811\pi$
$830$	14.7936	+	2.03738i	0.513493	+	0.0707186i
$831$	−6.61871	−	20.3703i	−0.229600	−	0.706637i
$832$		−	36.5562i		−	1.26736i
$833$	−0.0399357	+	0.0129759i	−0.00138369	+	0.000449588i
$834$	38.2809	+	27.8127i	1.32556	+	0.963074i
$835$	−22.1574	+	23.0721i	−0.766789	+	0.798442i
$836$	48.1562	−	34.9875i	1.66552	−	1.21007i
$837$	3.57898	−	4.92604i	0.123708	−	0.170269i
$838$	−26.0006	+	35.7868i	−0.898176	+	1.23623i
$839$	17.9052	−	13.0089i	0.618157	−	0.449118i	−0.234120	−	0.972208i	$-0.575221\pi$
$839$	17.9052	−	13.0089i	0.618157	−	0.449118i	0.852277	+	0.523090i	$0.175221\pi$
$840$	−2.16935	−	4.05286i	−0.0748496	−	0.139837i
$841$	−12.8822	−	9.35944i	−0.444212	−	0.322739i
$842$	−69.0068	+	22.4217i	−2.37813	+	0.772702i
$843$			26.5033i			0.912821i
$844$	−15.0365	−	46.2775i	−0.517576	−	1.59294i
$845$	8.01359	+	7.69590i	0.275676	+	0.264747i
$846$	4.31552	−	13.2818i	0.148370	−	0.456637i
$847$	−11.9436	−	3.88072i	−0.410388	−	0.133343i
$848$	−4.69120	−	6.45688i	−0.161096	−	0.221730i
$849$	−2.26023			−0.0775707
$850$	−0.437005	+	0.161801i	−0.0149892	+	0.00554972i
$851$	−46.6287			−1.59841
$852$	−8.52702	−	11.7364i	−0.292131	−	0.402084i
$853$	4.04516	+	1.31435i	0.138504	+	0.0450026i	0.377449	−	0.926031i	$-0.376802\pi$
$853$	4.04516	+	1.31435i	0.138504	+	0.0450026i	−0.238945	+	0.971033i	$0.576802\pi$
$854$	0.130257	−	0.400891i	0.00445732	−	0.0137182i
$855$	−1.65283	−	9.22435i	−0.0565255	−	0.315466i
$856$	−2.82308	−	8.68855i	−0.0964909	−	0.296968i
$857$		−	33.0610i		−	1.12934i	−0.825316	−	0.564671i	$-0.809003\pi$
$857$		−	33.0610i		−	1.12934i	0.825316	−	0.564671i	$-0.190997\pi$
$858$	29.0353	−	9.43414i	0.991249	−	0.322076i
$859$	−18.1432	−	13.1818i	−0.619038	−	0.449757i	0.233547	−	0.972345i	$-0.424967\pi$
$859$	−18.1432	−	13.1818i	−0.619038	−	0.449757i	−0.852585	+	0.522588i	$0.824967\pi$
$860$	10.5909	−	1.89769i	0.361146	−	0.0647106i
$861$	−3.62085	+	2.63070i	−0.123398	+	0.0896541i
$862$	−15.8485	+	21.8136i	−0.539802	+	0.742974i
$863$	−23.2469	+	31.9966i	−0.791333	+	1.08918i	0.202608	+	0.979260i	$0.435058\pi$
$863$	−23.2469	+	31.9966i	−0.791333	+	1.08918i	−0.993941	+	0.109916i	$0.964942\pi$
$864$	5.64199	−	4.09914i	0.191944	−	0.139456i
$865$	−2.53407	−	1.22728i	−0.0861608	−	0.0417288i
$866$	−14.2806	−	10.3755i	−0.485275	−	0.352573i
$867$	−16.1663	+	5.25274i	−0.549036	+	0.178393i
$868$		−	17.8177i		−	0.604771i
$869$	16.1036	+	49.5617i	0.546276	+	1.68127i
$870$	−29.3273	+	15.6978i	−0.994289	+	0.532207i
$871$	11.8510	−	36.4736i	0.401555	−	1.23586i
$872$	29.0163	+	9.42795i	0.982614	+	0.319271i
$873$	10.0678	+	13.8572i	0.340745	+	0.468995i
$874$	−74.3459			−2.51479
$875$	−11.1284	−	1.07634i	−0.376209	−	0.0363869i
$876$	34.5941			1.16883
$877$	−21.6877	−	29.8505i	−0.732340	−	1.00798i	−0.999023	−	0.0441954i	$-0.985928\pi$
$877$	−21.6877	−	29.8505i	−0.732340	−	1.00798i	0.266683	−	0.963784i	$-0.414072\pi$
$878$	45.6527	+	14.8335i	1.54070	+	0.500605i
$879$	2.54102	−	7.82046i	0.0857065	−	0.263777i
$880$	12.3396	−	6.60495i	0.415969	−	0.222653i
$881$	−10.2388	−	31.5117i	−0.344954	−	1.06166i	−0.961609	−	0.274424i	$-0.911513\pi$
$881$	−10.2388	−	31.5117i	−0.344954	−	1.06166i	0.616655	−	0.787233i	$-0.288487\pi$
$882$			2.21951i			0.0747349i
$883$	17.3663	−	5.64266i	0.584424	−	0.189891i	−0.00185763	−	0.999998i	$-0.500591\pi$
$883$	17.3663	−	5.64266i	0.584424	−	0.189891i	0.586281	+	0.810107i	$0.300591\pi$
$884$	−0.281717	−	0.204680i	−0.00947518	−	0.00688412i
$885$	14.2270	+	6.89030i	0.478234	+	0.231615i
$886$	9.94587	−	7.22610i	0.334138	−	0.242766i
$887$	12.7070	−	17.4897i	0.426661	−	0.587248i	−0.540522	−	0.841330i	$-0.681773\pi$
$887$	12.7070	−	17.4897i	0.426661	−	0.587248i	0.967183	+	0.254082i	$0.0817732\pi$
$888$	−7.04966	+	9.70303i	−0.236571	+	0.325612i
$889$	15.4346	−	11.2139i	0.517661	−	0.376103i
$890$	−3.12028	+	0.559095i	−0.104592	+	0.0187409i
$891$	3.92672	+	2.85293i	0.131550	+	0.0955766i
$892$	32.5953	−	10.5908i	1.09137	−	0.354608i
$893$		−	26.3697i		−	0.882428i
$894$	−9.78479	−	30.1145i	−0.327252	−	1.00718i
$895$	8.24057	+	45.9902i	0.275452	+	1.53728i
$896$	4.53722	−	13.9641i	0.151578	−	0.466508i
$897$	−21.5419	−	6.99938i	−0.719262	−	0.233702i
$898$	22.6193	+	31.1328i	0.754815	+	1.03891i
$899$	−40.8109			−1.36112
$900$	0.591522	+	14.6193i	0.0197174	+	0.487308i
$901$	−0.259878			−0.00865778
$902$	28.3401	+	39.0068i	0.943622	+	1.29878i
$903$	−1.56389	−	0.508138i	−0.0520429	−	0.0169098i
$904$	0.260757	−	0.802527i	0.00867264	−	0.0266916i
$905$	34.2729	+	32.9142i	1.13927	+	1.09411i
$906$	−11.2760	−	34.7040i	−0.374620	−	1.15296i
$907$			49.8759i			1.65610i	0.560653	+	0.828051i	$0.310550\pi$
$907$			49.8759i			1.65610i	−0.560653	+	0.828051i	$0.689450\pi$
$908$	−68.2482	+	22.1752i	−2.26490	+	0.735910i
$909$	4.47305	+	3.24986i	0.148362	+	0.107791i
$910$	−6.63735	−	12.4002i	−0.220026	−	0.411061i
$911$	−9.03148	+	6.56175i	−0.299226	+	0.217401i	−0.727260	−	0.686362i	$-0.759206\pi$
$911$	−9.03148	+	6.56175i	−0.299226	+	0.217401i	0.428034	+	0.903763i	$0.359206\pi$
$912$	3.17675	−	4.37242i	0.105193	−	0.144785i
$913$	−8.58423	+	11.8152i	−0.284096	+	0.391025i
$914$	−28.0433	+	20.3747i	−0.927591	+	0.673934i
$915$	−0.294151	+	0.306294i	−0.00972434	+	0.0101258i
$916$	26.6211	+	19.3414i	0.879586	+	0.639057i
$917$	−2.14851	+	0.698093i	−0.0709500	+	0.0230531i
$918$		−	0.0931994i		−	0.00307604i
$919$	6.89150	+	21.2099i	0.227330	+	0.699649i	0.998047	+	0.0624714i	$0.0198982\pi$
$919$	6.89150	+	21.2099i	0.227330	+	0.699649i	−0.770717	+	0.637178i	$0.780102\pi$
$920$	36.3977	+	5.01272i	1.20000	+	0.165264i
$921$	5.47397	−	16.8471i	0.180373	−	0.555132i
$922$	−10.5947	−	3.44242i	−0.348918	−	0.113370i
$923$	−8.25805	−	11.3662i	−0.271817	−	0.374124i
$924$	14.2031			0.467247
$925$	10.1283	+	27.3552i	0.333015	+	0.899435i
$926$	−55.4795			−1.82317
$927$	0.369939	+	0.509177i	0.0121504	+	0.0167236i
$928$	−44.4545	−	14.4442i	−1.45929	−	0.474153i
$929$	−15.0708	+	46.3831i	−0.494456	+	1.52178i	0.323346	+	0.946281i	$0.395192\pi$
$929$	−15.0708	+	46.3831i	−0.494456	+	1.52178i	−0.817802	+	0.575499i	$0.804808\pi$
$930$	−13.1720	+	27.1974i	−0.431928	+	0.891838i
$931$	1.29508	+	3.98583i	0.0424444	+	0.130630i
$932$		−	46.0966i		−	1.50994i
$933$	19.8078	−	6.43593i	0.648477	−	0.210703i
$934$	15.0248	+	10.9161i	0.491625	+	0.357187i
$935$	0.0621772	−	0.451473i	0.00203341	−	0.0147647i
$936$	−4.71336	+	3.42446i	−0.154061	+	0.111932i
$937$	−24.9736	+	34.3733i	−0.815853	+	1.12293i	0.174541	+	0.984650i	$0.444156\pi$
$937$	−24.9736	+	34.3733i	−0.815853	+	1.12293i	−0.990394	+	0.138276i	$0.955844\pi$
$938$	17.6546	−	24.2995i	0.576443	−	0.793406i
$939$	22.1545	−	16.0962i	0.722984	−	0.525278i
$940$	−5.61703	+	40.7857i	−0.183207	+	1.33028i
$941$	23.0777	+	16.7670i	0.752313	+	0.546587i	0.896543	−	0.442957i	$-0.146070\pi$
$941$	23.0777	+	16.7670i	0.752313	+	0.546587i	−0.144230	+	0.989544i	$0.546070\pi$
$942$	10.5303	−	3.42150i	0.343096	−	0.111479i
$943$		−	35.7717i		−	1.16489i
$944$	2.81720	+	8.67044i	0.0916919	+	0.282199i
$945$	0.974664	−	2.01247i	0.0317058	−	0.0654656i
$946$	−5.47408	+	16.8475i	−0.177978	+	0.547759i
$947$	42.2696	+	13.7342i	1.37358	+	0.446302i	0.900553	−	0.434747i	$-0.143162\pi$
$947$	42.2696	+	13.7342i	1.37358	+	0.446302i	0.473024	+	0.881049i	$0.343162\pi$
$948$	−18.4670	−	25.4177i	−0.599782	−	0.825529i
$949$	33.5029			1.08755
$950$	16.1487	+	43.6158i	0.523934	+	1.41508i
$951$	−4.32546			−0.140263
$952$	−0.0507407	−	0.0698386i	−0.00164452	−	0.00226348i
$953$	36.9097	+	11.9927i	1.19562	+	0.388481i	0.838148	−	0.545442i	$-0.183638\pi$
$953$	36.9097	+	11.9927i	1.19562	+	0.388481i	0.357473	+	0.933923i	$0.383638\pi$
$954$	−4.24477	+	13.0641i	−0.137429	+	0.422964i
$955$	−38.7191	−	5.33242i	−1.25292	−	0.172553i
$956$	14.9472	+	46.0026i	0.483426	+	1.48783i
$957$		−	32.5317i		−	1.05160i
$958$	−58.3543	+	18.9605i	−1.88534	+	0.612585i
$959$	−14.8278	−	10.7730i	−0.478814	−	0.347879i
$960$	−19.9793	+	20.8040i	−0.644828	+	0.671447i
$961$	−4.91473	+	3.57076i	−0.158540	+	0.115186i
$962$	−21.5692	+	29.6875i	−0.695419	+	0.957162i
$963$	2.61202	−	3.59514i	0.0841712	−	0.115852i
$964$	42.8408	−	31.1257i	1.37981	−	1.00249i
$965$	6.61924	+	12.3663i	0.213081	+	0.398086i
$966$	−14.3517	−	10.4271i	−0.461757	−	0.335486i
$967$	57.7072	−	18.7502i	1.85574	−	0.602966i	0.860050	−	0.510210i	$-0.170432\pi$
$967$	57.7072	−	18.7502i	1.85574	−	0.602966i	0.995689	−	0.0927557i	$-0.0295676\pi$
$968$		−	25.8174i		−	0.829803i
$969$	−0.0543814	−	0.167369i	−0.00174698	−	0.00537666i
$970$	−61.3129	−	58.8822i	−1.96864	−	1.89059i
$971$	11.0196	−	33.9149i	0.353637	−	1.08838i	−0.603159	−	0.797621i	$-0.706091\pi$
$971$	11.0196	−	33.9149i	0.353637	−	1.08838i	0.956796	−	0.290761i	$-0.0939085\pi$
$972$	−2.78302	−	0.904259i	−0.0892655	−	0.0290041i
$973$	12.5310	+	17.2474i	0.401725	+	0.552927i
$974$	−35.2328			−1.12893
$975$	0.572863	+	14.1581i	0.0183463	+	0.453422i
$976$	−0.244914			−0.00783951
$977$	2.68285	+	3.69263i	0.0858321	+	0.118138i	0.849774	−	0.527148i	$-0.176739\pi$
$977$	2.68285	+	3.69263i	0.0858321	+	0.118138i	−0.763942	+	0.645285i	$0.776739\pi$
$978$	38.0785	+	12.3724i	1.21761	+	0.395627i
$979$	0.958003	−	2.94843i	0.0306179	−	0.0942322i
$980$	−1.15405	−	6.44070i	−0.0368648	−	0.205741i
$981$	4.58601	+	14.1143i	0.146420	+	0.450634i
$982$			81.6552i			2.60572i
$983$	42.8748	−	13.9309i	1.36749	−	0.444326i	0.468957	−	0.883221i	$-0.344630\pi$
$983$	42.8748	−	13.9309i	1.36749	−	0.444326i	0.898538	+	0.438895i	$0.144630\pi$
$984$	−7.44378	−	5.40822i	−0.237299	−	0.172408i
$985$	17.7427	−	3.17916i	0.565331	−	0.101297i
$986$	−0.505366	+	0.367170i	−0.0160941	+	0.0116931i
$987$	3.69838	−	5.09038i	0.117721	−	0.162029i
$988$	−20.4283	+	28.1171i	−0.649911	+	0.894525i
$989$	10.6327	−	7.72511i	0.338100	−	0.245644i
$990$	−21.6800	−	10.4999i	−0.689035	−	0.333708i
$991$	−23.5488	−	17.1092i	−0.748052	−	0.543491i	0.147171	−	0.989111i	$-0.452983\pi$
$991$	−23.5488	−	17.1092i	−0.748052	−	0.543491i	−0.895222	+	0.445620i	$0.852983\pi$
$992$	−40.3851	+	13.1219i	−1.28223	+	0.416621i
$993$			4.02585i			0.127756i
$994$	−3.40023	−	10.4648i	−0.107849	−	0.331925i
$995$	−32.1988	+	17.2348i	−1.02077	+	0.546381i
$996$	2.72084	−	8.37389i	0.0862132	−	0.265337i
$997$	−56.9442	−	18.5023i	−1.80344	−	0.585974i	−0.803485	−	0.595325i	$-0.797023\pi$
$997$	−56.9442	−	18.5023i	−1.80344	−	0.585974i	−0.999956	+	0.00935120i	$0.997023\pi$
$998$	−16.5458	−	22.7734i	−0.523749	−	0.720879i
$999$	−5.83401			−0.184580

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.z.b.64.4	✓	72
25.9	even	10	inner	525.2.z.b.484.4	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.z.b.64.4	✓	72	1.1	even	1	trivial
525.2.z.b.484.4	yes	72	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.z (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30460 - 1.79562i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.904259 + 2.78302i) q^{4} +(1.97142 - 1.05523i) q^{5} +(-0.685868 - 2.11088i) q^{6} -1.00000i q^{7} +(1.95519 - 0.635280i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-1.30460 - 1.79562i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.904259 + 2.78302i) q^{4} +(1.97142 - 1.05523i) q^{5} +(-0.685868 - 2.11088i) q^{6} -1.00000i q^{7} +(1.95519 - 0.635280i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-4.46670 - 2.16328i) q^{10} +(3.92672 - 2.85293i) q^{11} +(-1.72000 + 2.36738i) q^{12} +(-1.66575 + 2.29270i) q^{13} +(-1.79562 + 1.30460i) q^{14} +(2.20101 - 0.394380i) q^{15} +(1.04330 + 0.758002i) q^{16} +(0.0399357 - 0.0129759i) q^{17} -2.21951i q^{18} +(-1.29508 - 3.98583i) q^{19} +(1.15405 + 6.44070i) q^{20} +(0.309017 - 0.951057i) q^{21} +(-10.2456 - 3.32899i) q^{22} +(4.69792 + 6.46613i) q^{23} +2.05581 q^{24} +(2.77299 - 4.16059i) q^{25} +6.28997 q^{26} +(0.587785 + 0.809017i) q^{27} +(2.78302 + 0.904259i) q^{28} +(2.07118 - 6.37444i) q^{29} +(-3.57960 - 3.43769i) q^{30} +(-1.88158 - 5.79091i) q^{31} -6.97388i q^{32} +(4.61613 - 1.49987i) q^{33} +(-0.0753999 - 0.0547812i) q^{34} +(-1.05523 - 1.97142i) q^{35} +(-2.36738 + 1.72000i) q^{36} +(-3.42914 + 4.71981i) q^{37} +(-5.46751 + 7.52538i) q^{38} +(-2.29270 + 1.66575i) q^{39} +(3.18413 - 3.31557i) q^{40} +(-3.62085 - 2.63070i) q^{41} +(-2.11088 + 0.685868i) q^{42} -1.64437i q^{43} +(4.38899 + 13.5079i) q^{44} +(2.21516 + 0.305073i) q^{45} +(5.48185 - 16.8714i) q^{46} +(5.98410 + 1.94435i) q^{47} +(0.758002 + 1.04330i) q^{48} -1.00000 q^{49} +(-11.0885 + 0.448661i) q^{50} +0.0419909 q^{51} +(-4.87438 - 6.70901i) q^{52} +(-5.88600 - 1.91248i) q^{53} +(0.685868 - 2.11088i) q^{54} +(4.73071 - 9.76789i) q^{55} +(-0.635280 - 1.95519i) q^{56} -4.19095i q^{57} +(-14.1482 + 4.59701i) q^{58} +(5.71928 + 4.15530i) q^{59} +(-0.892718 + 6.48209i) q^{60} +(-0.153645 + 0.111630i) q^{61} +(-7.94359 + 10.9334i) q^{62} +(0.587785 - 0.809017i) q^{63} +(-10.4359 + 7.58210i) q^{64} +(-0.864559 + 6.27763i) q^{65} +(-8.71540 - 6.33211i) q^{66} +(-12.8703 + 4.18181i) q^{67} +0.122876i q^{68} +(2.46984 + 7.60139i) q^{69} +(-2.16328 + 4.46670i) q^{70} +(-1.53197 + 4.71493i) q^{71} +(1.95519 + 0.635280i) q^{72} +(-6.94882 - 9.56423i) q^{73} +12.9487 q^{74} +(3.92296 - 3.10006i) q^{75} +12.2637 q^{76} +(-2.85293 - 3.92672i) q^{77} +(5.98211 + 1.94371i) q^{78} +(-3.31780 + 10.2111i) q^{79} +(2.85665 + 0.393419i) q^{80} +(0.309017 + 0.951057i) q^{81} +9.93370i q^{82} +(-2.86165 + 0.929807i) q^{83} +(2.36738 + 1.72000i) q^{84} +(0.0650375 - 0.0677222i) q^{85} +(-2.95267 + 2.14524i) q^{86} +(3.93962 - 5.42242i) q^{87} +(5.86507 - 8.07257i) q^{88} +(0.516738 - 0.375432i) q^{89} +(-2.34209 - 4.37559i) q^{90} +(2.29270 + 1.66575i) q^{91} +(-22.2435 + 7.22735i) q^{92} -6.08892i q^{93} +(-4.31552 - 13.2818i) q^{94} +(-6.75910 - 6.49115i) q^{95} +(2.15505 - 6.63255i) q^{96} +(16.2901 + 5.29298i) q^{97} +(1.30460 + 1.79562i) q^{98} +4.85369 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 24 q^{4} - 2 q^{5} + 18 q^{9}+O(q^{10}) \) 72 * q + 24 * q^4 - 2 * q^5 + 18 * q^9	\( 72 q + 24 q^{4} - 2 q^{5} + 18 q^{9} - 28 q^{10} - 12 q^{11} - 20 q^{13} - 24 q^{16} + 10 q^{19} + 10 q^{20} - 18 q^{21} + 50 q^{22} - 10 q^{23} + 12 q^{25} + 36 q^{26} + 20 q^{28} - 2 q^{29} + 10 q^{30} - 16 q^{31} - 10 q^{33} + 24 q^{34} - 10 q^{35} - 24 q^{36} + 10 q^{37} - 100 q^{38} + 16 q^{39} - 14 q^{40} - 16 q^{41} - 18 q^{44} + 2 q^{45} - 44 q^{46} + 20 q^{47} - 72 q^{49} + 86 q^{50} + 32 q^{51} - 80 q^{52} + 70 q^{53} + 46 q^{55} - 40 q^{58} + 44 q^{59} - 62 q^{60} + 4 q^{61} - 50 q^{62} + 48 q^{64} + 38 q^{65} - 16 q^{66} - 20 q^{67} + 4 q^{69} + 10 q^{70} - 8 q^{71} - 20 q^{73} - 116 q^{74} - 8 q^{75} + 92 q^{76} + 20 q^{77} + 90 q^{78} + 28 q^{79} + 114 q^{80} - 18 q^{81} + 30 q^{83} + 24 q^{84} - 122 q^{85} + 40 q^{86} - 40 q^{87} - 270 q^{88} + 2 q^{89} - 12 q^{90} - 16 q^{91} - 100 q^{92} + 22 q^{94} + 116 q^{95} + 10 q^{96} + 190 q^{97} - 48 q^{99}+O(q^{100}) \) 72 * q + 24 * q^4 - 2 * q^5 + 18 * q^9 - 28 * q^10 - 12 * q^11 - 20 * q^13 - 24 * q^16 + 10 * q^19 + 10 * q^20 - 18 * q^21 + 50 * q^22 - 10 * q^23 + 12 * q^25 + 36 * q^26 + 20 * q^28 - 2 * q^29 + 10 * q^30 - 16 * q^31 - 10 * q^33 + 24 * q^34 - 10 * q^35 - 24 * q^36 + 10 * q^37 - 100 * q^38 + 16 * q^39 - 14 * q^40 - 16 * q^41 - 18 * q^44 + 2 * q^45 - 44 * q^46 + 20 * q^47 - 72 * q^49 + 86 * q^50 + 32 * q^51 - 80 * q^52 + 70 * q^53 + 46 * q^55 - 40 * q^58 + 44 * q^59 - 62 * q^60 + 4 * q^61 - 50 * q^62 + 48 * q^64 + 38 * q^65 - 16 * q^66 - 20 * q^67 + 4 * q^69 + 10 * q^70 - 8 * q^71 - 20 * q^73 - 116 * q^74 - 8 * q^75 + 92 * q^76 + 20 * q^77 + 90 * q^78 + 28 * q^79 + 114 * q^80 - 18 * q^81 + 30 * q^83 + 24 * q^84 - 122 * q^85 + 40 * q^86 - 40 * q^87 - 270 * q^88 + 2 * q^89 - 12 * q^90 - 16 * q^91 - 100 * q^92 + 22 * q^94 + 116 * q^95 + 10 * q^96 + 190 * q^97 - 48 * q^99

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