LMFDB - Embedded newform 287.2.e.d.165.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(165,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("287.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.e (of order $3$, degree $2$, 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:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			165.8
Character	$\chi$	$=$	287.165
Dual form			287.2.e.d.247.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.557713 - 0.965987i) q^{2} +(1.37705 - 2.38511i) q^{3} +(0.377913 - 0.654564i) q^{4} +(0.672309 + 1.16447i) q^{5} -3.07199 q^{6} +(-2.64555 + 0.0328867i) q^{7} -3.07392 q^{8} +(-2.29251 - 3.97075i) q^{9} +O(q^{10})$	\(q+(-0.557713 - 0.965987i) q^{2} +(1.37705 - 2.38511i) q^{3} +(0.377913 - 0.654564i) q^{4} +(0.672309 + 1.16447i) q^{5} -3.07199 q^{6} +(-2.64555 + 0.0328867i) q^{7} -3.07392 q^{8} +(-2.29251 - 3.97075i) q^{9} +(0.749910 - 1.29888i) q^{10} +(0.538640 - 0.932951i) q^{11} +(-1.04081 - 1.80273i) q^{12} -0.966204 q^{13} +(1.50722 + 2.53722i) q^{14} +3.70320 q^{15} +(0.958539 + 1.66024i) q^{16} +(3.26440 - 5.65411i) q^{17} +(-2.55713 + 4.42908i) q^{18} +(3.53971 + 6.13096i) q^{19} +1.01630 q^{20} +(-3.56460 + 6.35522i) q^{21} -1.20163 q^{22} +(-0.449123 - 0.777904i) q^{23} +(-4.23293 + 7.33165i) q^{24} +(1.59600 - 2.76436i) q^{25} +(0.538864 + 0.933340i) q^{26} -4.36532 q^{27} +(-0.978259 + 1.74411i) q^{28} +2.82453 q^{29} +(-2.06532 - 3.57724i) q^{30} +(0.694642 - 1.20315i) q^{31} +(-2.00474 + 3.47231i) q^{32} +(-1.48346 - 2.56943i) q^{33} -7.28240 q^{34} +(-1.81692 - 3.05856i) q^{35} -3.46548 q^{36} +(3.56253 + 6.17048i) q^{37} +(3.94829 - 6.83863i) q^{38} +(-1.33051 + 2.30451i) q^{39} +(-2.06662 - 3.57949i) q^{40} +1.00000 q^{41} +(8.12708 - 0.101027i) q^{42} +1.23495 q^{43} +(-0.407117 - 0.705148i) q^{44} +(3.08255 - 5.33914i) q^{45} +(-0.500964 + 0.867695i) q^{46} +(-3.92655 - 6.80098i) q^{47} +5.27981 q^{48} +(6.99784 - 0.174006i) q^{49} -3.56044 q^{50} +(-8.99047 - 15.5719i) q^{51} +(-0.365141 + 0.632442i) q^{52} +(-3.29469 + 5.70658i) q^{53} +(2.43459 + 4.21684i) q^{54} +1.44853 q^{55} +(8.13220 - 0.101091i) q^{56} +19.4974 q^{57} +(-1.57528 - 2.72846i) q^{58} +(-1.36053 + 2.35651i) q^{59} +(1.39949 - 2.42398i) q^{60} +(5.52445 + 9.56863i) q^{61} -1.54964 q^{62} +(6.19554 + 10.4294i) q^{63} +8.30643 q^{64} +(-0.649587 - 1.12512i) q^{65} +(-1.65469 + 2.86601i) q^{66} +(-1.22837 + 2.12759i) q^{67} +(-2.46732 - 4.27352i) q^{68} -2.47385 q^{69} +(-1.94121 + 3.46092i) q^{70} +2.40706 q^{71} +(7.04700 + 12.2058i) q^{72} +(-4.06039 + 7.03280i) q^{73} +(3.97373 - 6.88271i) q^{74} +(-4.39554 - 7.61330i) q^{75} +5.35081 q^{76} +(-1.39431 + 2.48588i) q^{77} +2.96816 q^{78} +(0.980663 + 1.69856i) q^{79} +(-1.28887 + 2.23238i) q^{80} +(0.866298 - 1.50047i) q^{81} +(-0.557713 - 0.965987i) q^{82} -9.30225 q^{83} +(2.81279 + 4.73498i) q^{84} +8.77874 q^{85} +(-0.688749 - 1.19295i) q^{86} +(3.88951 - 6.73683i) q^{87} +(-1.65573 + 2.86782i) q^{88} +(-6.39763 - 11.0810i) q^{89} -6.87672 q^{90} +(2.55614 - 0.0317752i) q^{91} -0.678918 q^{92} +(-1.91311 - 3.31360i) q^{93} +(-4.37977 + 7.58599i) q^{94} +(-4.75956 + 8.24380i) q^{95} +(5.52124 + 9.56307i) q^{96} +18.4064 q^{97} +(-4.07087 - 6.66277i) q^{98} -4.93936 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 3 q^{2} - q^{3} - 25 q^{4} + q^{5} + 4 q^{6} - 2 q^{7} + 18 q^{8} - 26 q^{9}+O(q^{10}) $ 34 * q - 3 * q^2 - q^3 - 25 * q^4 + q^5 + 4 * q^6 - 2 * q^7 + 18 * q^8 - 26 * q^9	\( 34 q - 3 q^{2} - q^{3} - 25 q^{4} + q^{5} + 4 q^{6} - 2 q^{7} + 18 q^{8} - 26 q^{9} + 2 q^{10} - 15 q^{11} - 4 q^{12} - 10 q^{13} + 21 q^{14} + 48 q^{15} - 33 q^{16} - 4 q^{17} - 10 q^{18} - 5 q^{19} - 52 q^{20} + 12 q^{21} + 32 q^{22} - 12 q^{23} - 16 q^{24} - 24 q^{25} - 31 q^{26} - 22 q^{27} + 60 q^{28} + 28 q^{29} + 33 q^{30} + 3 q^{31} - 16 q^{32} - 4 q^{33} - 48 q^{34} + 45 q^{35} + 114 q^{36} - 24 q^{37} - 45 q^{39} - 36 q^{40} + 34 q^{41} + 65 q^{42} + 28 q^{43} + 9 q^{44} + 21 q^{45} - 44 q^{46} - 19 q^{47} - 120 q^{48} - 10 q^{49} - 8 q^{50} - 2 q^{51} + 25 q^{52} - 4 q^{53} - 68 q^{54} + 18 q^{55} + 25 q^{56} - 24 q^{57} + q^{58} + 27 q^{59} - 66 q^{60} + q^{61} - 46 q^{62} + 37 q^{63} + 150 q^{64} - 22 q^{65} + 16 q^{66} - 49 q^{67} - 45 q^{68} + 24 q^{69} + 73 q^{70} + 80 q^{71} + 23 q^{72} + 14 q^{73} - 33 q^{74} - 27 q^{75} - 18 q^{76} - 20 q^{77} - 24 q^{78} - 61 q^{79} + 82 q^{80} - 53 q^{81} - 3 q^{82} - 36 q^{83} + 188 q^{84} - 26 q^{85} + 4 q^{86} + 17 q^{87} - 74 q^{88} - 18 q^{89} - 40 q^{90} + 7 q^{91} + 56 q^{92} + 36 q^{93} + 5 q^{94} - 20 q^{95} - 148 q^{96} + 52 q^{97} + 142 q^{98} + 76 q^{99}+O(q^{100}) \) 34 * q - 3 * q^2 - q^3 - 25 * q^4 + q^5 + 4 * q^6 - 2 * q^7 + 18 * q^8 - 26 * q^9 + 2 * q^10 - 15 * q^11 - 4 * q^12 - 10 * q^13 + 21 * q^14 + 48 * q^15 - 33 * q^16 - 4 * q^17 - 10 * q^18 - 5 * q^19 - 52 * q^20 + 12 * q^21 + 32 * q^22 - 12 * q^23 - 16 * q^24 - 24 * q^25 - 31 * q^26 - 22 * q^27 + 60 * q^28 + 28 * q^29 + 33 * q^30 + 3 * q^31 - 16 * q^32 - 4 * q^33 - 48 * q^34 + 45 * q^35 + 114 * q^36 - 24 * q^37 - 45 * q^39 - 36 * q^40 + 34 * q^41 + 65 * q^42 + 28 * q^43 + 9 * q^44 + 21 * q^45 - 44 * q^46 - 19 * q^47 - 120 * q^48 - 10 * q^49 - 8 * q^50 - 2 * q^51 + 25 * q^52 - 4 * q^53 - 68 * q^54 + 18 * q^55 + 25 * q^56 - 24 * q^57 + q^58 + 27 * q^59 - 66 * q^60 + q^61 - 46 * q^62 + 37 * q^63 + 150 * q^64 - 22 * q^65 + 16 * q^66 - 49 * q^67 - 45 * q^68 + 24 * q^69 + 73 * q^70 + 80 * q^71 + 23 * q^72 + 14 * q^73 - 33 * q^74 - 27 * q^75 - 18 * q^76 - 20 * q^77 - 24 * q^78 - 61 * q^79 + 82 * q^80 - 53 * q^81 - 3 * q^82 - 36 * q^83 + 188 * q^84 - 26 * q^85 + 4 * q^86 + 17 * q^87 - 74 * q^88 - 18 * q^89 - 40 * q^90 + 7 * q^91 + 56 * q^92 + 36 * q^93 + 5 * q^94 - 20 * q^95 - 148 * q^96 + 52 * q^97 + 142 * q^98 + 76 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.557713	−	0.965987i	−0.394363	−	0.683056i	0.598657	−	0.801005i	$-0.295701\pi$
$2$	−0.557713	−	0.965987i	−0.394363	−	0.683056i	−0.993020	+	0.117949i	$0.962368\pi$
$3$	1.37705	−	2.38511i	0.795038	−	1.37705i	−0.127777	−	0.991803i	$-0.540784\pi$
$3$	1.37705	−	2.38511i	0.795038	−	1.37705i	0.922815	−	0.385244i	$-0.125883\pi$
$4$	0.377913	−	0.654564i	0.188956	−	0.327282i
$5$	0.672309	+	1.16447i	0.300666	+	0.520768i	0.976287	−	0.216481i	$-0.0694579\pi$
$5$	0.672309	+	1.16447i	0.300666	+	0.520768i	−0.675621	+	0.737249i	$0.736125\pi$
$6$	−3.07199			−1.25413
$7$	−2.64555	+	0.0328867i	−0.999923	+	0.0124300i
$7$	−2.64555	+	0.0328867i	−0.999923	+	0.0124300i
$8$	−3.07392			−1.08679
$9$	−2.29251	−	3.97075i	−0.764172	−	1.32358i
$10$	0.749910	−	1.29888i	0.237143	−	0.410743i
$11$	0.538640	−	0.932951i	0.162406	−	0.281295i	−0.773325	−	0.634010i	$-0.781408\pi$
$11$	0.538640	−	0.932951i	0.162406	−	0.281295i	0.935731	+	0.352714i	$0.114741\pi$
$12$	−1.04081	−	1.80273i	−0.300455	−	0.520403i
$13$	−0.966204			−0.267977			−0.133988	−	0.990983i	$-0.542778\pi$
$13$	−0.966204			−0.267977			−0.133988	+	0.990983i	$0.542778\pi$
$14$	1.50722	+	2.53722i	0.402822	+	0.678101i
$15$	3.70320			0.956163
$16$	0.958539	+	1.66024i	0.239635	+	0.415059i
$17$	3.26440	−	5.65411i	0.791734	−	1.37132i	−0.133159	−	0.991095i	$-0.542512\pi$
$17$	3.26440	−	5.65411i	0.791734	−	1.37132i	0.924893	−	0.380228i	$-0.124155\pi$
$18$	−2.55713	+	4.42908i	−0.602721	+	1.04394i
$19$	3.53971	+	6.13096i	0.812065	+	1.40654i	0.911416	+	0.411486i	$0.134990\pi$
$19$	3.53971	+	6.13096i	0.812065	+	1.40654i	−0.0993505	+	0.995052i	$0.531677\pi$
$20$	1.01630			0.227251
$21$	−3.56460	+	6.35522i	−0.777860	+	1.38682i
$22$	−1.20163			−0.256187
$23$	−0.449123	−	0.777904i	−0.0936487	−	0.162204i	0.815395	−	0.578905i	$-0.196520\pi$
$23$	−0.449123	−	0.777904i	−0.0936487	−	0.162204i	−0.909044	+	0.416701i	$0.863186\pi$
$24$	−4.23293	+	7.33165i	−0.864043	+	1.49657i
$25$	1.59600	−	2.76436i	0.319200	−	0.552871i
$26$	0.538864	+	0.933340i	0.105680	+	0.183043i
$27$	−4.36532			−0.840106
$28$	−0.978259	+	1.74411i	−0.184874	+	0.329605i
$29$	2.82453			0.524502			0.262251	−	0.965000i	$-0.415535\pi$
$29$	2.82453			0.524502			0.262251	+	0.965000i	$0.415535\pi$
$30$	−2.06532	−	3.57724i	−0.377075	−	0.653113i
$31$	0.694642	−	1.20315i	0.124761	−	0.216093i	−0.796878	−	0.604140i	$-0.793517\pi$
$31$	0.694642	−	1.20315i	0.124761	−	0.216093i	0.921640	+	0.388047i	$0.126850\pi$
$32$	−2.00474	+	3.47231i	−0.354391	+	0.613824i
$33$	−1.48346	−	2.56943i	−0.258238	−	0.447281i
$34$	−7.28240			−1.24892
$35$	−1.81692	−	3.05856i	−0.307116	−	0.516991i
$36$	−3.46548			−0.577580
$37$	3.56253	+	6.17048i	0.585676	+	1.01442i	0.994791	+	0.101937i	$0.0325042\pi$
$37$	3.56253	+	6.17048i	0.585676	+	1.01442i	−0.409115	+	0.912483i	$0.634162\pi$
$38$	3.94829	−	6.83863i	0.640496	−	1.10937i
$39$	−1.33051	+	2.30451i	−0.213052	+	0.369016i
$40$	−2.06662	−	3.57949i	−0.326762	−	0.565968i
$41$	1.00000			0.156174
$41$	1.00000			0.156174
$42$	8.12708	−	0.101027i	1.25404	−	0.0155889i
$43$	1.23495			0.188328			0.0941642	−	0.995557i	$-0.469982\pi$
$43$	1.23495			0.188328			0.0941642	+	0.995557i	$0.469982\pi$
$44$	−0.407117	−	0.705148i	−0.0613753	−	0.106305i
$45$	3.08255	−	5.33914i	0.459520	−	0.795912i
$46$	−0.500964	+	0.867695i	−0.0738631	+	0.127935i
$47$	−3.92655	−	6.80098i	−0.572746	−	0.992025i	−0.996283	−	0.0861460i	$-0.972545\pi$
$47$	−3.92655	−	6.80098i	−0.572746	−	0.992025i	0.423537	−	0.905879i	$-0.360789\pi$
$48$	5.27981			0.762075
$49$	6.99784	−	0.174006i	0.999691	−	0.0248581i
$50$	−3.56044			−0.503523
$51$	−8.99047	−	15.5719i	−1.25892	−	2.18051i
$52$	−0.365141	+	0.632442i	−0.0506359	+	0.0877039i
$53$	−3.29469	+	5.70658i	−0.452561	+	0.783859i	−0.998544	−	0.0539374i	$-0.982823\pi$
$53$	−3.29469	+	5.70658i	−0.452561	+	0.783859i	0.545983	+	0.837796i	$0.316156\pi$
$54$	2.43459	+	4.21684i	0.331306	+	0.573839i
$55$	1.44853			0.195320
$56$	8.13220	−	0.101091i	1.08671	−	0.0135088i
$57$	19.4974			2.58249
$58$	−1.57528	−	2.72846i	−0.206844	−	0.358264i
$59$	−1.36053	+	2.35651i	−0.177126	+	0.306792i	−0.940895	−	0.338698i	$-0.890014\pi$
$59$	−1.36053	+	2.35651i	−0.177126	+	0.306792i	0.763769	+	0.645490i	$0.223347\pi$
$60$	1.39949	−	2.42398i	0.180673	−	0.312935i
$61$	5.52445	+	9.56863i	0.707334	+	1.22514i	0.965843	+	0.259129i	$0.0834356\pi$
$61$	5.52445	+	9.56863i	0.707334	+	1.22514i	−0.258509	+	0.966009i	$0.583231\pi$
$62$	−1.54964			−0.196805
$63$	6.19554	+	10.4294i	0.780565	+	1.31398i
$64$	8.30643			1.03830
$65$	−0.649587	−	1.12512i	−0.0805714	−	0.139554i
$66$	−1.65469	+	2.86601i	−0.203679	+	0.352782i
$67$	−1.22837	+	2.12759i	−0.150069	+	0.259927i	−0.931253	−	0.364374i	$-0.881283\pi$
$67$	−1.22837	+	2.12759i	−0.150069	+	0.259927i	0.781184	+	0.624301i	$0.214616\pi$
$68$	−2.46732	−	4.27352i	−0.299206	−	0.518240i
$69$	−2.47385			−0.297817
$70$	−1.94121	+	3.46092i	−0.232019	+	0.413659i
$71$	2.40706			0.285666			0.142833	−	0.989747i	$-0.454379\pi$
$71$	2.40706			0.285666			0.142833	+	0.989747i	$0.454379\pi$
$72$	7.04700	+	12.2058i	0.830497	+	1.43846i
$73$	−4.06039	+	7.03280i	−0.475232	+	0.823127i	−0.999598	−	0.0283668i	$-0.990969\pi$
$73$	−4.06039	+	7.03280i	−0.475232	+	0.823127i	0.524365	+	0.851494i	$0.324303\pi$
$74$	3.97373	−	6.88271i	0.461937	−	0.800099i
$75$	−4.39554	−	7.61330i	−0.507553	−	0.879108i
$76$	5.35081			0.613780
$77$	−1.39431	+	2.48588i	−0.158897	+	0.283292i
$78$	2.96816			0.336078
$79$	0.980663	+	1.69856i	0.110333	+	0.191103i	0.915905	−	0.401396i	$-0.131475\pi$
$79$	0.980663	+	1.69856i	0.110333	+	0.191103i	−0.805571	+	0.592499i	$0.798142\pi$
$80$	−1.28887	+	2.23238i	−0.144100	+	0.249588i
$81$	0.866298	−	1.50047i	0.0962553	−	0.166719i
$82$	−0.557713	−	0.965987i	−0.0615891	−	0.106675i
$83$	−9.30225			−1.02105			−0.510527	−	0.859862i	$-0.670550\pi$
$83$	−9.30225			−1.02105			−0.510527	+	0.859862i	$0.670550\pi$
$84$	2.81279	+	4.73498i	0.306900	+	0.516628i
$85$	8.77874			0.952188
$86$	−0.688749	−	1.19295i	−0.0742697	−	0.128639i
$87$	3.88951	−	6.73683i	0.416999	−	0.722264i
$88$	−1.65573	+	2.86782i	−0.176502	+	0.305710i
$89$	−6.39763	−	11.0810i	−0.678147	−	1.17459i	−0.975538	−	0.219830i	$-0.929450\pi$
$89$	−6.39763	−	11.0810i	−0.678147	−	1.17459i	0.297391	−	0.954756i	$-0.403884\pi$
$90$	−6.87672			−0.724870
$91$	2.55614	−	0.0317752i	0.267956	−	0.00333095i
$92$	−0.678918			−0.0707820
$93$	−1.91311	−	3.31360i	−0.198380	−	0.343604i
$94$	−4.37977	+	7.58599i	−0.451739	+	0.782435i
$95$	−4.75956	+	8.24380i	−0.488320	+	0.845796i
$96$	5.52124	+	9.56307i	0.563509	+	0.976027i
$97$	18.4064			1.86888			0.934442	−	0.356117i	$-0.115899\pi$
$97$	18.4064			1.86888			0.934442	+	0.356117i	$0.115899\pi$
$98$	−4.07087	−	6.66277i	−0.411220	−	0.673042i
$99$	−4.93936			−0.496424
$100$	−1.20630	−	2.08937i	−0.120630	−	0.208937i
$101$	3.63158	−	6.29008i	0.361356	−	0.625886i	−0.626829	−	0.779157i	$-0.715647\pi$
$101$	3.63158	−	6.29008i	0.361356	−	0.625886i	0.988184	+	0.153271i	$0.0489807\pi$
$102$	−10.0282	+	17.3693i	−0.992939	+	1.71982i
$103$	−9.54333	−	16.5295i	−0.940332	−	1.62870i	−0.764838	−	0.644223i	$-0.777181\pi$
$103$	−9.54333	−	16.5295i	−0.940332	−	1.62870i	−0.175495	−	0.984480i	$-0.556153\pi$
$104$	2.97003			0.291236
$105$	−9.79699	+	0.121786i	−0.956089	+	0.0118851i
$106$	7.34997			0.713892
$107$	5.83474	+	10.1061i	0.564065	+	0.976990i	0.997136	+	0.0756297i	$0.0240967\pi$
$107$	5.83474	+	10.1061i	0.564065	+	0.976990i	−0.433071	+	0.901360i	$0.642570\pi$
$108$	−1.64971	+	2.85738i	−0.158743	+	0.274951i
$109$	−8.52222	+	14.7609i	−0.816281	+	1.41384i	0.0921241	+	0.995748i	$0.470634\pi$
$109$	−8.52222	+	14.7609i	−0.816281	+	1.41384i	−0.908405	+	0.418092i	$0.862699\pi$
$110$	−0.807863	−	1.39926i	−0.0770267	−	0.133414i
$111$	19.6231			1.86254
$112$	−2.59046	−	4.36071i	−0.244775	−	0.412049i
$113$	−4.74418			−0.446295			−0.223147	−	0.974785i	$-0.571633\pi$
$113$	−4.74418			−0.446295			−0.223147	+	0.974785i	$0.571633\pi$
$114$	−10.8739	−	18.8342i	−1.01844	−	1.76399i
$115$	0.603899	−	1.04598i	0.0563139	−	0.0975385i
$116$	1.06743	−	1.84884i	0.0991080	−	0.171660i
$117$	2.21504	+	3.83656i	0.204780	+	0.354690i
$118$	3.03515			0.279408
$119$	−8.45018	+	15.0656i	−0.774627	+	1.38106i
$120$	−11.3833			−1.03915
$121$	4.91973	+	8.52123i	0.447249	+	0.774657i
$122$	6.16212	−	10.6731i	0.557892	−	0.966297i
$123$	1.37705	−	2.38511i	0.124164	−	0.215059i
$124$	−0.525028	−	0.909375i	−0.0471489	−	0.0816643i
$125$	11.0151			0.985222
$126$	6.61935	−	11.8014i	0.589698	−	1.05136i
$127$	−9.95232			−0.883126			−0.441563	−	0.897230i	$-0.645576\pi$
$127$	−9.95232			−0.883126			−0.441563	+	0.897230i	$0.645576\pi$
$128$	−0.623125	−	1.07928i	−0.0550770	−	0.0953961i
$129$	1.70059	−	2.94550i	0.149728	−	0.259337i
$130$	−0.724566	+	1.25499i	−0.0635487	+	0.110070i
$131$	−10.5469	−	18.2677i	−0.921484	−	1.59606i	−0.797120	−	0.603821i	$-0.793644\pi$
$131$	−10.5469	−	18.2677i	−0.921484	−	1.59606i	−0.124364	−	0.992237i	$-0.539689\pi$
$132$	−2.24248			−0.195183
$133$	−9.56610	−	16.1033i	−0.829486	−	1.39634i
$134$	2.74030			0.236726
$135$	−2.93484	−	5.08329i	−0.252591	−	0.437500i
$136$	−10.0345	+	17.3803i	−0.860452	+	1.49035i
$137$	4.00076	−	6.92951i	0.341808	−	0.592028i	−0.642961	−	0.765899i	$-0.722294\pi$
$137$	4.00076	−	6.92951i	0.341808	−	0.592028i	0.984768	+	0.173871i	$0.0556275\pi$
$138$	1.37970	+	2.38971i	0.117448	+	0.203426i
$139$	−7.13603			−0.605270			−0.302635	−	0.953107i	$-0.597866\pi$
$139$	−7.13603			−0.605270			−0.302635	+	0.953107i	$0.597866\pi$
$140$	−2.68866	+	0.0334226i	−0.227233	+	0.00282472i
$141$	−21.6282			−1.82142
$142$	−1.34245	−	2.32519i	−0.112656	−	0.195126i
$143$	−0.520436	+	0.901421i	−0.0435210	+	0.0753806i
$144$	4.39493	−	7.61224i	0.366244	−	0.634353i
$145$	1.89896	+	3.28909i	0.157700	+	0.273144i
$146$	9.05812			0.749656
$147$	9.22132	−	16.9303i	0.760562	−	1.39638i
$148$	5.38530			0.442669
$149$	5.48905	+	9.50731i	0.449680	+	0.778869i	0.998365	−	0.0571601i	$-0.0182045\pi$
$149$	5.48905	+	9.50731i	0.449680	+	0.778869i	−0.548685	+	0.836029i	$0.684871\pi$
$150$	−4.90290	+	8.49207i	−0.400320	+	0.693374i
$151$	−9.91796	+	17.1784i	−0.807112	+	1.39796i	0.107744	+	0.994179i	$0.465637\pi$
$151$	−9.91796	+	17.1784i	−0.807112	+	1.39796i	−0.914856	+	0.403780i	$0.867696\pi$
$152$	−10.8808	−	18.8461i	−0.882548	−	1.52862i
$153$	−29.9348			−2.42008
$154$	3.17896	−	0.0395175i	0.256168	−	0.00318441i
$155$	1.86806			0.150046
$156$	1.00563	+	1.74180i	0.0805149	+	0.139456i
$157$	4.81072	−	8.33241i	0.383937	−	0.664999i	−0.607684	−	0.794179i	$-0.707901\pi$
$157$	4.81072	−	8.33241i	0.383937	−	0.664999i	0.991621	+	0.129180i	$0.0412345\pi$
$158$	1.09386	−	1.89462i	0.0870226	−	0.150728i
$159$	9.07389	+	15.7164i	0.719607	+	1.24640i
$160$	−5.39122			−0.426213
$161$	1.21376	+	2.04321i	0.0956577	+	0.161028i
$162$	−1.93258			−0.151838
$163$	−0.166853	−	0.288997i	−0.0130689	−	0.0226360i	0.859417	−	0.511275i	$-0.170827\pi$
$163$	−0.166853	−	0.288997i	−0.0130689	−	0.0226360i	−0.872486	+	0.488639i	$0.837493\pi$
$164$	0.377913	−	0.654564i	0.0295100	−	0.0511129i
$165$	1.99469	−	3.45491i	0.155287	−	0.268964i
$166$	5.18799	+	8.98585i	0.402666	+	0.697438i
$167$	−16.6780			−1.29058			−0.645290	−	0.763938i	$-0.723263\pi$
$167$	−16.6780			−1.29058			−0.645290	+	0.763938i	$0.723263\pi$
$168$	10.9573	−	19.5354i	0.845374	−	1.50719i
$169$	−12.0665			−0.928188
$170$	−4.89602	−	8.48015i	−0.375507	−	0.650398i
$171$	16.2297	−	28.1106i	1.24111	−	2.14967i
$172$	0.466704	−	0.808355i	0.0355859	−	0.0616365i
$173$	6.47290	+	11.2114i	0.492125	+	0.852386i	0.999959	−	0.00906937i	$-0.00288691\pi$
$173$	6.47290	+	11.2114i	0.492125	+	0.852386i	−0.507834	+	0.861455i	$0.669554\pi$
$174$	−8.67692			−0.657796
$175$	−4.13139	+	7.36572i	−0.312304	+	0.556796i
$176$	2.06523			0.155672
$177$	3.74704	+	6.49006i	0.281645	+	0.487823i
$178$	−7.13608	+	12.3601i	−0.534872	+	0.926425i
$179$	−8.53291	+	14.7794i	−0.637779	+	1.10467i	0.348140	+	0.937443i	$0.386814\pi$
$179$	−8.53291	+	14.7794i	−0.637779	+	1.10467i	−0.985919	+	0.167224i	$0.946520\pi$
$180$	−2.32987	−	4.03546i	−0.173658	−	0.300785i
$181$	−0.402992			−0.0299541			−0.0149771	−	0.999888i	$-0.504768\pi$
$181$	−0.402992			−0.0299541			−0.0149771	+	0.999888i	$0.504768\pi$
$182$	−1.45629	−	2.45147i	−0.107947	−	0.181715i
$183$	30.4297			2.24943
$184$	1.38057	+	2.39121i	0.101777	+	0.176283i
$185$	−4.79024	+	8.29693i	−0.352185	+	0.610003i
$186$	−2.13393	+	3.69608i	−0.156467	+	0.271009i
$187$	−3.51667	−	6.09105i	−0.257165	−	0.445422i
$188$	−5.93557			−0.432896
$189$	11.5487	−	0.143561i	0.840041	−	0.0104425i
$190$	10.6179			0.770301
$191$	6.80344	+	11.7839i	0.492280	+	0.852654i	0.999960	−	0.00889176i	$-0.00283037\pi$
$191$	6.80344	+	11.7839i	0.492280	+	0.852654i	−0.507681	+	0.861545i	$0.669497\pi$
$192$	11.4383	−	19.8118i	0.825491	−	1.42979i
$193$	3.19843	−	5.53984i	0.230228	−	0.398766i	−0.727647	−	0.685952i	$-0.759386\pi$
$193$	3.19843	−	5.53984i	0.230228	−	0.398766i	0.957875	+	0.287185i	$0.0927195\pi$
$194$	−10.2655	−	17.7803i	−0.737018	−	1.27655i
$195$	−3.57805			−0.256229
$196$	2.53067	−	4.64629i	0.180762	−	0.331878i
$197$	−21.8587			−1.55737			−0.778684	−	0.627416i	$-0.784113\pi$
$197$	−21.8587			−1.55737			−0.778684	+	0.627416i	$0.784113\pi$
$198$	2.75474	+	4.77136i	0.195771	+	0.339085i
$199$	−11.0880	+	19.2049i	−0.786005	+	1.36140i	0.142391	+	0.989810i	$0.454521\pi$
$199$	−11.0880	+	19.2049i	−0.786005	+	1.36140i	−0.928397	+	0.371591i	$0.878812\pi$
$200$	−4.90598	+	8.49741i	−0.346905	+	0.600857i
$201$	3.38304	+	5.85959i	0.238621	+	0.413304i
$202$	−8.10151			−0.570020
$203$	−7.47243	+	0.0928894i	−0.524462	+	0.00651956i
$204$	−13.5904			−0.951521
$205$	0.672309	+	1.16447i	0.0469561	+	0.0813303i
$206$	−10.6449	+	18.4375i	−0.741664	+	1.28460i
$207$	−2.05924	+	3.56671i	−0.143127	+	0.247904i
$208$	−0.926144	−	1.60413i	−0.0642165	−	0.111226i
$209$	7.62652			0.527537
$210$	5.58155	+	9.39585i	0.385164	+	0.648375i
$211$	16.8283			1.15851			0.579254	−	0.815147i	$-0.303344\pi$
$211$	16.8283			1.15851			0.579254	+	0.815147i	$0.303344\pi$
$212$	2.49021	+	4.31318i	0.171029	+	0.296230i
$213$	3.31464	−	5.74112i	0.227115	−	0.393375i
$214$	6.50822	−	11.2726i	0.444892	−	0.770576i
$215$	0.830269	+	1.43807i	0.0566239	+	0.0980754i
$216$	13.4186			0.913022
$217$	−1.79814	+	3.20585i	−0.122066	+	0.217627i
$218$	19.0118			1.28764
$219$	11.1827	+	19.3690i	0.755656	+	1.30883i
$220$	0.547417	−	0.948155i	0.0369069	−	0.0639246i
$221$	−3.15408	+	5.46302i	−0.212166	+	0.367483i
$222$	−10.9440	−	18.9556i	−0.734516	−	1.27222i
$223$	3.85768			0.258329			0.129165	−	0.991623i	$-0.458770\pi$
$223$	3.85768			0.258329			0.129165	+	0.991623i	$0.458770\pi$
$224$	5.18944	−	9.25209i	0.346734	−	0.618181i
$225$	−14.6354			−0.975695
$226$	2.64589	+	4.58281i	0.176002	+	0.304844i
$227$	14.0959	−	24.4148i	0.935576	−	1.62046i	0.161972	−	0.986795i	$-0.448215\pi$
$227$	14.0959	−	24.4148i	0.935576	−	1.62046i	0.773604	−	0.633669i	$-0.218452\pi$
$228$	7.36831	−	12.7623i	0.487978	−	0.845203i
$229$	7.61182	+	13.1841i	0.503003	+	0.871227i	0.999994	+	0.00347094i	$0.00110484\pi$
$229$	7.61182	+	13.1841i	0.503003	+	0.871227i	−0.496991	+	0.867756i	$0.665562\pi$
$230$	−1.34721			−0.0888323
$231$	4.00907	+	6.74877i	0.263778	+	0.444037i
$232$	−8.68238			−0.570026
$233$	14.5088	+	25.1299i	0.950501	+	1.64632i	0.744343	+	0.667797i	$0.232763\pi$
$233$	14.5088	+	25.1299i	0.950501	+	1.64632i	0.206158	+	0.978519i	$0.433904\pi$
$234$	2.47071	−	4.27939i	0.161515	−	0.279753i
$235$	5.27971	−	9.14472i	0.344410	−	0.596536i
$236$	1.02833	+	1.78111i	0.0669383	+	0.115941i
$237$	5.40168			0.350877
$238$	19.2659	−	0.239494i	1.24882	−	0.0155241i
$239$	25.0381			1.61958			0.809792	−	0.586718i	$-0.199580\pi$
$239$	25.0381			1.61958			0.809792	+	0.586718i	$0.199580\pi$
$240$	3.54966	+	6.14820i	0.229130	+	0.396864i
$241$	0.556910	−	0.964596i	0.0358737	−	0.0621351i	−0.847531	−	0.530746i	$-0.821912\pi$
$241$	0.556910	−	0.964596i	0.0358737	−	0.0621351i	0.883405	+	0.468611i	$0.155245\pi$
$242$	5.48760	−	9.50480i	0.352756	−	0.610992i
$243$	−8.93384	−	15.4739i	−0.573106	−	0.992649i
$244$	8.35104			0.534621
$245$	4.90733	+	8.03181i	0.313518	+	0.513133i
$246$	−3.07199			−0.195863
$247$	−3.42008	−	5.92376i	−0.217615	−	0.376920i
$248$	−2.13527	+	3.69840i	−0.135590	+	0.234849i
$249$	−12.8096	+	22.1869i	−0.811778	+	1.40604i
$250$	−6.14327	−	10.6405i	−0.388534	−	0.672961i
$251$	7.27825			0.459399			0.229700	−	0.973262i	$-0.426226\pi$
$251$	7.27825			0.459399			0.229700	+	0.973262i	$0.426226\pi$
$252$	9.16809	−	0.113968i	0.577536	−	0.00717932i
$253$	−0.967663			−0.0608364
$254$	5.55054	+	9.61382i	0.348272	+	0.603224i
$255$	12.0887	−	20.9383i	0.757026	−	1.31121i
$256$	7.61138	−	13.1833i	0.475711	−	0.823956i
$257$	4.44971	+	7.70712i	0.277565	+	0.480757i	0.970779	−	0.239975i	$-0.0771392\pi$
$257$	4.44971	+	7.70712i	0.277565	+	0.480757i	−0.693214	+	0.720732i	$0.743806\pi$
$258$	−3.79376			−0.236189
$259$	−9.62776	−	16.2071i	−0.598240	−	1.00706i
$260$	−0.981949			−0.0608979
$261$	−6.47528	−	11.2155i	−0.400810	−	0.694223i
$262$	−11.7642	+	20.3763i	−0.726798	+	1.25885i
$263$	2.94935	−	5.10842i	0.181865	−	0.314999i	−0.760651	−	0.649161i	$-0.775120\pi$
$263$	2.94935	−	5.10842i	0.181865	−	0.314999i	0.942516	+	0.334162i	$0.108453\pi$
$264$	4.56005	+	7.89823i	0.280651	+	0.486103i
$265$	−8.86021			−0.544278
$266$	−10.2205	+	18.2218i	−0.626657	+	1.11725i
$267$	−35.2393			−2.15661
$268$	0.928430	+	1.60809i	0.0567129	+	0.0982296i
$269$	−2.09366	+	3.62633i	−0.127653	+	0.221101i	−0.922767	−	0.385359i	$-0.874078\pi$
$269$	−2.09366	+	3.62633i	−0.127653	+	0.221101i	0.795114	+	0.606460i	$0.207411\pi$
$270$	−3.27360	+	5.67004i	−0.199225	+	0.345067i
$271$	−5.02504	−	8.70363i	−0.305250	−	0.528708i	0.672067	−	0.740490i	$-0.265407\pi$
$271$	−5.02504	−	8.70363i	−0.305250	−	0.528708i	−0.977317	+	0.211782i	$0.932073\pi$
$272$	12.5162			0.758907
$273$	3.44413	−	6.14044i	0.208448	−	0.371636i
$274$	−8.92510			−0.539185
$275$	−1.71934	−	2.97798i	−0.103680	−	0.179579i
$276$	−0.934901	+	1.61930i	−0.0562744	+	0.0974702i
$277$	3.08304	−	5.33998i	0.185242	−	0.320848i	−0.758416	−	0.651771i	$-0.774027\pi$
$277$	3.08304	−	5.33998i	0.185242	−	0.320848i	0.943658	+	0.330922i	$0.107360\pi$
$278$	3.97986	+	6.89331i	0.238696	+	0.413433i
$279$	−6.36991			−0.381356
$280$	5.58506	+	9.40176i	0.333771	+	0.561862i
$281$	−6.64050			−0.396139			−0.198069	−	0.980188i	$-0.563467\pi$
$281$	−6.64050			−0.396139			−0.198069	+	0.980188i	$0.563467\pi$
$282$	12.0623	+	20.8925i	0.718300	+	1.24413i
$283$	−16.2209	+	28.0954i	−0.964232	+	1.67010i	−0.252566	+	0.967580i	$0.581275\pi$
$283$	−16.2209	+	28.0954i	−0.964232	+	1.67010i	−0.711665	+	0.702518i	$0.752059\pi$
$284$	0.909659	−	1.57558i	0.0539784	−	0.0934932i
$285$	13.1083	+	22.7042i	0.776467	+	1.34488i
$286$	1.16101			0.0686522
$287$	−2.64555	+	0.0328867i	−0.156162	+	0.00194124i
$288$	18.3836			1.08326
$289$	−12.8126	−	22.1921i	−0.753684	−	1.30542i
$290$	2.11815	−	3.66874i	0.124382	−	0.215436i
$291$	25.3464	−	43.9013i	1.48583	−	2.57354i
$292$	3.06894	+	5.31557i	0.179596	+	0.311070i
$293$	3.63051			0.212097			0.106048	−	0.994361i	$-0.466180\pi$
$293$	3.63051			0.212097			0.106048	+	0.994361i	$0.466180\pi$
$294$	−21.4973	+	0.534546i	−1.25375	+	0.0311753i
$295$	−3.65880			−0.213023
$296$	−10.9509	−	18.9675i	−0.636509	−	1.10247i
$297$	−2.35133	+	4.07263i	−0.136438	+	0.236318i
$298$	6.12263	−	10.6047i	0.354674	−	0.614314i
$299$	0.433945	+	0.751614i	0.0250957	+	0.0434670i
$300$	−6.64452			−0.383621
$301$	−3.26712	+	0.0406135i	−0.188314	+	0.00234092i
$302$	22.1255			1.27318
$303$	−10.0017	−	17.3235i	−0.574583	−	0.995207i
$304$	−6.78590	+	11.7535i	−0.389198	+	0.674111i
$305$	−7.42828	+	12.8662i	−0.425342	+	0.736714i
$306$	16.6950	+	28.9166i	0.954389	+	1.65305i
$307$	−0.641523			−0.0366136			−0.0183068	−	0.999832i	$-0.505828\pi$
$307$	−0.641523			−0.0366136			−0.0183068	+	0.999832i	$0.505828\pi$
$308$	1.10024	+	1.85211i	0.0626919	+	0.105534i
$309$	−52.5664			−2.99040
$310$	−1.04184	−	1.80452i	−0.0591724	−	0.102490i
$311$	5.92088	−	10.2553i	0.335743	−	0.581523i	−0.647885	−	0.761738i	$-0.724346\pi$
$311$	5.92088	−	10.2553i	0.335743	−	0.581523i	0.983627	+	0.180215i	$0.0576795\pi$
$312$	4.08987	−	7.08387i	0.231543	−	0.401045i
$313$	−9.86517	−	17.0870i	−0.557612	−	0.965813i	−0.997695	−	0.0678556i	$-0.978384\pi$
$313$	−9.86517	−	17.0870i	−0.557612	−	0.965813i	0.440083	−	0.897957i	$-0.354949\pi$
$314$	−10.7320			−0.605642
$315$	−7.97946	+	14.2263i	−0.449591	+	0.801563i
$316$	1.48242			0.0833926
$317$	−12.2533	−	21.2233i	−0.688211	−	1.19202i	−0.972416	−	0.233253i	$-0.925063\pi$
$317$	−12.2533	−	21.2233i	−0.688211	−	1.19202i	0.284205	−	0.958764i	$-0.408270\pi$
$318$	10.1213	−	17.5305i	0.567572	−	0.983063i
$319$	1.52140	−	2.63515i	0.0851823	−	0.147540i
$320$	5.58449	+	9.67261i	0.312182	+	0.540716i
$321$	32.1388			1.79381
$322$	1.29679	−	2.31200i	0.0722671	−	0.128843i
$323$	46.2202			2.57176
$324$	−0.654770	−	1.13409i	−0.0363761	−	0.0630053i
$325$	−1.54206	+	2.67093i	−0.0855383	+	0.148157i
$326$	−0.186112	+	0.322355i	−0.0103078	+	0.0178536i
$327$	23.4710	+	40.6529i	1.29795	+	2.24811i
$328$	−3.07392			−0.169729
$329$	10.6115	+	17.8632i	0.585033	+	0.984829i
$330$	−4.44986			−0.244957
$331$	−13.9151	−	24.1016i	−0.764841	−	1.32474i	−0.940331	−	0.340262i	$-0.889484\pi$
$331$	−13.9151	−	24.1016i	−0.764841	−	1.32474i	0.175489	−	0.984481i	$-0.443849\pi$
$332$	−3.51544	+	6.08892i	−0.192935	+	0.334173i
$333$	16.3343	−	28.2918i	0.895114	−	1.55038i
$334$	9.30151	+	16.1107i	0.508956	+	0.881538i
$335$	−3.30337			−0.180482
$336$	−13.9680	+	0.173635i	−0.762016	+	0.00947259i
$337$	0.235392			0.0128226			0.00641130	−	0.999979i	$-0.497959\pi$
$337$	0.235392			0.0128226			0.00641130	+	0.999979i	$0.497959\pi$
$338$	6.72962	+	11.6560i	0.366043	+	0.634005i
$339$	−6.53295	+	11.3154i	−0.354821	+	0.614569i
$340$	3.31760	−	5.74625i	0.179922	−	0.311634i
$341$	−0.748323	−	1.29613i	−0.0405240	−	0.0701896i
$342$	−36.2060			−1.95780
$343$	−18.5074	+	0.690478i	−0.999305	+	0.0372823i
$344$	−3.79614			−0.204674
$345$	−1.66319	−	2.88074i	−0.0895434	−	0.155094i
$346$	7.22003	−	12.5055i	0.388151	−	0.672298i
$347$	0.254504	−	0.440814i	0.0136625	−	0.0236641i	−0.859113	−	0.511785i	$-0.828984\pi$
$347$	0.254504	−	0.440814i	0.0136625	−	0.0236641i	0.872776	+	0.488121i	$0.162318\pi$
$348$	−2.93979	−	5.09187i	−0.157589	−	0.272953i
$349$	−23.8662			−1.27753			−0.638764	−	0.769403i	$-0.720554\pi$
$349$	−23.8662			−1.27753			−0.638764	+	0.769403i	$0.720554\pi$
$350$	9.41932	−	0.117091i	0.503484	−	0.00625879i
$351$	4.21779			0.225129
$352$	2.15966	+	3.74065i	0.115111	+	0.199377i
$353$	−6.80152	+	11.7806i	−0.362008	+	0.627017i	−0.988291	−	0.152579i	$-0.951242\pi$
$353$	−6.80152	+	11.7806i	−0.362008	+	0.627017i	0.626283	+	0.779596i	$0.284575\pi$
$354$	4.17954	−	7.23918i	0.222140	−	0.384758i
$355$	1.61829	+	2.80296i	0.0858899	+	0.148766i
$356$	−9.67098			−0.512561
$357$	24.2968	+	40.9006i	1.28592	+	2.16469i
$358$	19.0356			1.00607
$359$	2.42448	+	4.19933i	0.127959	+	0.221632i	0.922886	−	0.385074i	$-0.125824\pi$
$359$	2.42448	+	4.19933i	0.127959	+	0.221632i	−0.794926	+	0.606706i	$0.792491\pi$
$360$	−9.47552	+	16.4121i	−0.499404	+	0.864993i
$361$	−15.5591	+	26.9492i	−0.818901	+	1.41838i
$362$	0.224754	+	0.389285i	0.0118128	+	0.0204604i
$363$	27.0988			1.42232
$364$	0.945198	−	1.68516i	0.0495418	−	0.0883266i
$365$	−10.9193			−0.571544
$366$	−16.9710	−	29.3947i	−0.887091	−	1.53649i
$367$	10.1177	−	17.5243i	0.528139	−	0.914764i	−0.471323	−	0.881961i	$-0.656223\pi$
$367$	10.1177	−	17.5243i	0.528139	−	0.914764i	0.999462	−	0.0328028i	$-0.0104433\pi$
$368$	0.861004	−	1.49130i	0.0448829	−	0.0777395i
$369$	−2.29251	−	3.97075i	−0.119344	−	0.206709i
$370$	10.6863			0.555555
$371$	8.52860	−	15.2054i	0.442783	−	0.789423i
$372$	−2.89195			−0.149941
$373$	7.04352	+	12.1997i	0.364700	+	0.631678i	0.988728	−	0.149724i	$-0.0478384\pi$
$373$	7.04352	+	12.1997i	0.364700	+	0.631678i	−0.624028	+	0.781402i	$0.714505\pi$
$374$	−3.92259	+	6.79412i	−0.202832	+	0.351316i
$375$	15.1683	−	26.2723i	0.783289	−	1.35670i
$376$	12.0699	+	20.9057i	0.622457	+	1.07813i
$377$	−2.72907			−0.140554
$378$	−6.57951	−	11.0758i	−0.338413	−	0.569677i
$379$	−2.35252			−0.120841			−0.0604205	−	0.998173i	$-0.519244\pi$
$379$	−2.35252			−0.120841			−0.0604205	+	0.998173i	$0.519244\pi$
$380$	3.59739	+	6.23087i	0.184542	+	0.319637i
$381$	−13.7048	+	23.7374i	−0.702119	+	1.21611i
$382$	7.58873	−	13.1441i	0.388273	−	0.672509i
$383$	5.92517	+	10.2627i	0.302762	+	0.524399i	0.976761	−	0.214333i	$-0.0687579\pi$
$383$	5.92517	+	10.2627i	0.302762	+	0.524399i	−0.673998	+	0.738733i	$0.735425\pi$
$384$	−3.43229			−0.175153
$385$	−3.83215	+	0.0476373i	−0.195304	+	0.00242782i
$386$	−7.13522			−0.363173
$387$	−2.83115	−	4.90369i	−0.143915	−	0.249269i
$388$	6.95600	−	12.0481i	0.353137	−	0.611652i
$389$	4.11552	−	7.12829i	0.208665	−	0.361419i	−0.742629	−	0.669703i	$-0.766421\pi$
$389$	4.11552	−	7.12829i	0.208665	−	0.361419i	0.951294	+	0.308284i	$0.0997548\pi$
$390$	1.99552	+	3.45635i	0.101047	+	0.175019i
$391$	−5.86448			−0.296579
$392$	−21.5108	+	0.534882i	−1.08646	+	0.0270156i
$393$	−58.0941			−2.93046
$394$	12.1909	+	21.1152i	0.614168	+	1.06377i
$395$	−1.31862	+	2.28391i	−0.0663468	+	0.114916i
$396$	−1.86665	+	3.23312i	−0.0938025	+	0.162471i
$397$	3.52778	+	6.11029i	0.177054	+	0.306666i	0.940870	−	0.338767i	$-0.110010\pi$
$397$	3.52778	+	6.11029i	0.177054	+	0.306666i	−0.763816	+	0.645434i	$0.776677\pi$
$398$	24.7356			1.23988
$399$	−51.5813	+	0.641204i	−2.58229	+	0.0321004i
$400$	6.11932			0.305966
$401$	−16.2698	−	28.1802i	−0.812477	−	1.40725i	−0.911125	−	0.412130i	$-0.864785\pi$
$401$	−16.2698	−	28.1802i	−0.812477	−	1.40725i	0.0986477	−	0.995122i	$-0.468548\pi$
$402$	3.77352	−	6.53594i	0.188206	−	0.325983i
$403$	−0.671166	+	1.16249i	−0.0334331	+	0.0579079i
$404$	−2.74484	−	4.75420i	−0.136561	−	0.236530i
$405$	2.32968			0.115763
$406$	4.25720	+	7.16646i	0.211281	+	0.355666i
$407$	7.67567			0.380469
$408$	27.6360	+	47.8669i	1.36818	+	2.36976i
$409$	2.31177	−	4.00411i	0.114310	−	0.197990i	−0.803194	−	0.595718i	$-0.796868\pi$
$409$	2.31177	−	4.00411i	0.114310	−	0.197990i	0.917504	+	0.397727i	$0.130201\pi$
$410$	0.749910	−	1.29888i	0.0370354	−	0.0641473i
$411$	−11.0185	−	19.0845i	−0.543500	−	0.941370i
$412$	−14.4262			−0.710727
$413$	3.52186	−	6.27901i	0.173299	−	0.308970i
$414$	4.59387			0.225776
$415$	−6.25398	−	10.8322i	−0.306996	−	0.531733i
$416$	1.93699	−	3.35496i	0.0949686	−	0.164490i
$417$	−9.82665	+	17.0202i	−0.481213	+	0.833485i
$418$	−4.25341	−	7.36712i	−0.208041	−	0.360337i
$419$	−13.1741			−0.643598			−0.321799	−	0.946808i	$-0.604288\pi$
$419$	−13.1741			−0.643598			−0.321799	+	0.946808i	$0.604288\pi$
$420$	−3.62269	+	6.45878i	−0.176769	+	0.315156i
$421$	30.1903			1.47139			0.735693	−	0.677316i	$-0.236857\pi$
$421$	30.1903			1.47139			0.735693	+	0.677316i	$0.236857\pi$
$422$	−9.38537	−	16.2559i	−0.456873	−	0.791326i
$423$	−18.0033	+	31.1827i	−0.875352	+	1.51615i
$424$	10.1276	−	17.5416i	0.491841	−	0.851893i
$425$	−10.4200	−	18.0479i	−0.505443	−	0.875454i
$426$	−7.39446			−0.358263
$427$	−14.9299	−	25.1326i	−0.722508	−	1.21625i
$428$	8.82008			0.426335
$429$	1.43333	+	2.48260i	0.0692017	+	0.119861i
$430$	0.926104	−	1.60406i	0.0446607	−	0.0773546i
$431$	2.97474	−	5.15240i	0.143288	−	0.248182i	−0.785445	−	0.618932i	$-0.787566\pi$
$431$	2.97474	−	5.15240i	0.143288	−	0.248182i	0.928733	+	0.370749i	$0.120899\pi$
$432$	−4.18433	−	7.24747i	−0.201318	−	0.348694i
$433$	27.8876			1.34019			0.670096	−	0.742274i	$-0.266253\pi$
$433$	27.8876			1.34019			0.670096	+	0.742274i	$0.266253\pi$
$434$	4.09965	−	0.0509626i	0.196790	−	0.00244628i
$435$	10.4598			0.501509
$436$	6.44131	+	11.1567i	0.308483	+	0.534308i
$437$	3.17953	−	5.50711i	0.152098	−	0.263441i
$438$	12.4735	−	21.6047i	0.596005	−	1.03231i
$439$	−12.7240	−	22.0385i	−0.607281	−	1.05184i	−0.991687	−	0.128677i	$-0.958927\pi$
$439$	−12.7240	−	22.0385i	−0.607281	−	1.05184i	0.384405	−	0.923164i	$-0.374406\pi$
$440$	−4.45266			−0.212272
$441$	−16.7336	−	27.3878i	−0.796837	−	1.30418i
$442$	7.03628			0.334682
$443$	−4.71018	−	8.15827i	−0.223787	−	0.387611i	0.732168	−	0.681124i	$-0.238509\pi$
$443$	−4.71018	−	8.15827i	−0.223787	−	0.387611i	−0.955955	+	0.293514i	$0.905175\pi$
$444$	7.41580	−	12.8445i	0.351938	−	0.609575i
$445$	8.60236	−	14.8997i	0.407791	−	0.706315i
$446$	−2.15148	−	3.72647i	−0.101875	−	0.176453i
$447$	30.2347			1.43005
$448$	−21.9751	+	0.273171i	−1.03822	+	0.0129061i
$449$	−23.2678			−1.09808			−0.549038	−	0.835798i	$-0.685006\pi$
$449$	−23.2678			−1.09808			−0.549038	+	0.835798i	$0.685006\pi$
$450$	8.16237	+	14.1376i	0.384778	+	0.666455i
$451$	0.538640	−	0.932951i	0.0253636	−	0.0439310i
$452$	−1.79288	+	3.10537i	−0.0843302	+	0.146064i
$453$	27.3150	+	47.3109i	1.28337	+	2.22286i
$454$	−31.4458			−1.47582
$455$	1.75551	+	2.95519i	0.0822998	+	0.138541i
$456$	−59.9334			−2.80664
$457$	−2.43398	−	4.21577i	−0.113857	−	0.197206i	0.803465	−	0.595351i	$-0.202987\pi$
$457$	−2.43398	−	4.21577i	−0.113857	−	0.197206i	−0.917322	+	0.398146i	$0.869654\pi$
$458$	8.49042	−	14.7058i	0.396731	−	0.687158i
$459$	−14.2501	+	24.6820i	−0.665140	+	1.15206i
$460$	−0.456442	−	0.790581i	−0.0212817	−	0.0368610i
$461$	16.1888			0.753987			0.376993	−	0.926216i	$-0.376958\pi$
$461$	16.1888			0.753987			0.376993	+	0.926216i	$0.376958\pi$
$462$	4.28332	−	7.63659i	0.199278	−	0.355286i
$463$	−12.0971			−0.562200			−0.281100	−	0.959679i	$-0.590699\pi$
$463$	−12.0971			−0.562200			−0.281100	+	0.959679i	$0.590699\pi$
$464$	2.70742	+	4.68939i	0.125689	+	0.217700i
$465$	2.57240	−	4.45553i	0.119292	−	0.206620i
$466$	16.1835	−	28.0306i	0.749684	−	1.29849i
$467$	−1.61757	−	2.80171i	−0.0748521	−	0.129648i	0.826170	−	0.563421i	$-0.190515\pi$
$467$	−1.61757	−	2.80171i	−0.0748521	−	0.129648i	−0.901022	+	0.433773i	$0.857182\pi$
$468$	3.34836			0.154778
$469$	3.17973	−	5.66904i	0.146826	−	0.261772i
$470$	−11.7782			−0.543290
$471$	−13.2492	−	22.9482i	−0.610490	−	1.05740i
$472$	4.18217	−	7.24373i	0.192500	−	0.333420i
$473$	0.665194	−	1.15215i	0.0305857	−	0.0529759i
$474$	−3.01258	−	5.21795i	−0.138373	−	0.239668i
$475$	22.5975			1.03685
$476$	6.66795	+	11.2247i	0.305625	+	0.514481i
$477$	30.2125			1.38334
$478$	−13.9641	−	24.1865i	−0.638703	−	1.10627i
$479$	6.11284	−	10.5877i	0.279303	−	0.483766i	−0.691909	−	0.721985i	$-0.743230\pi$
$479$	6.11284	−	10.5877i	0.279303	−	0.483766i	0.971212	+	0.238218i	$0.0765634\pi$
$480$	−7.42396	+	12.8587i	−0.338856	+	0.586915i
$481$	−3.44213	−	5.96194i	−0.156947	−	0.271841i
$482$	−1.24238			−0.0565890
$483$	6.54470	−	0.0813569i	0.297794	−	0.00370187i
$484$	7.43692			0.338042
$485$	12.3748	+	21.4337i	0.561909	+	0.973255i
$486$	−9.96504	+	17.2600i	−0.452023	+	0.782927i
$487$	−1.68369	+	2.91623i	−0.0762951	+	0.132147i	−0.901649	−	0.432469i	$-0.857642\pi$
$487$	−1.68369	+	2.91623i	−0.0762951	+	0.132147i	0.825354	+	0.564616i	$0.190976\pi$
$488$	−16.9817	−	29.4132i	−0.768726	−	1.33147i
$489$	−0.919055			−0.0415611
$490$	5.02174	−	9.21986i	0.226859	−	0.416511i
$491$	−1.58497			−0.0715286			−0.0357643	−	0.999360i	$-0.511387\pi$
$491$	−1.58497			−0.0715286			−0.0357643	+	0.999360i	$0.511387\pi$
$492$	−1.04081	−	1.80273i	−0.0469232	−	0.0812733i
$493$	9.22040	−	15.9702i	0.415266	−	0.719262i
$494$	−3.81485	+	6.60751i	−0.171638	+	0.297286i
$495$	−3.32077	−	5.75175i	−0.149258	−	0.258522i
$496$	2.66336			0.119589
$497$	−6.36800	+	0.0791603i	−0.285644	+	0.00355082i
$498$	28.5764			1.28054
$499$	13.7985	+	23.8997i	0.617706	+	1.06990i	0.989903	+	0.141745i	$0.0452713\pi$
$499$	13.7985	+	23.8997i	0.617706	+	1.06990i	−0.372197	+	0.928154i	$0.621395\pi$
$500$	4.16275	−	7.21009i	0.186164	−	0.322445i
$501$	−22.9663	+	39.7788i	−1.02606	+	1.77719i
$502$	−4.05917	−	7.03070i	−0.181170	−	0.313795i
$503$	−0.387957			−0.0172982			−0.00864908	−	0.999963i	$-0.502753\pi$
$503$	−0.387957			−0.0172982			−0.00864908	+	0.999963i	$0.502753\pi$
$504$	−19.0446	−	32.0592i	−0.848313	−	1.42803i
$505$	9.76617			0.434589
$506$	0.539678	+	0.934750i	0.0239916	+	0.0415547i
$507$	−16.6161	+	28.7799i	−0.737945	+	1.27816i
$508$	−3.76111	+	6.51443i	−0.166872	+	0.289031i
$509$	19.3833	+	33.5729i	0.859151	+	1.48809i	0.872740	+	0.488186i	$0.162341\pi$
$509$	19.3833	+	33.5729i	0.859151	+	1.48809i	−0.0135882	+	0.999908i	$0.504325\pi$
$510$	−26.9682			−1.19417
$511$	10.5107	−	18.7391i	0.464964	−	0.828970i
$512$	−19.4724			−0.860565
$513$	−15.4520	−	26.7636i	−0.682221	−	1.18164i
$514$	4.96332	−	8.59672i	0.218923	−	0.379185i
$515$	12.8321	−	22.2259i	0.565451	−	0.979390i
$516$	−1.28535	−	2.22629i	−0.0565842	−	0.0980067i
$517$	−8.45998			−0.372069
$518$	−10.2864	+	18.3392i	−0.451956	+	0.805779i
$519$	35.6539			1.56503
$520$	1.99678	+	3.45852i	0.0875645	+	0.151666i
$521$	0.309525	−	0.536112i	0.0135605	−	0.0234875i	−0.859166	−	0.511698i	$-0.829017\pi$
$521$	0.309525	−	0.536112i	0.0135605	−	0.0234875i	0.872726	+	0.488210i	$0.162350\pi$
$522$	−7.22269	+	12.5101i	−0.316129	+	0.547551i
$523$	0.516090	+	0.893894i	0.0225670	+	0.0390872i	0.877088	−	0.480329i	$-0.159483\pi$
$523$	0.516090	+	0.893894i	0.0225670	+	0.0390872i	−0.854521	+	0.519416i	$0.826149\pi$
$524$	−15.9432			−0.696481
$525$	11.8790	+	19.9968i	0.518441	+	0.872731i
$526$	−6.57956			−0.286883
$527$	−4.53518	−	7.85516i	−0.197556	−	0.342176i
$528$	2.84392	−	4.92581i	0.123766	−	0.214368i
$529$	11.0966	−	19.2198i	0.482460	−	0.835645i
$530$	4.94145	+	8.55884i	0.214643	+	0.371772i
$531$	12.4762			0.541420
$532$	−14.1558	+	0.175970i	−0.613732	+	0.00762928i
$533$	−0.966204			−0.0418509
$534$	19.6534	+	34.0407i	0.850487	+	1.47309i
$535$	−7.84549	+	13.5888i	−0.339190	+	0.587494i
$536$	3.77590	−	6.54005i	0.163094	−	0.282487i
$537$	23.5004	+	40.7039i	1.01412	+	1.75650i
$538$	4.67065			0.201366
$539$	3.60697	−	6.62237i	0.155363	−	0.285246i
$540$	−4.43645			−0.190915
$541$	−19.1659	−	33.1963i	−0.824007	−	1.42722i	−0.902676	−	0.430321i	$-0.858400\pi$
$541$	−19.1659	−	33.1963i	−0.824007	−	1.42722i	0.0786692	−	0.996901i	$-0.474933\pi$
$542$	−5.60506	+	9.70825i	−0.240758	+	0.417005i
$543$	−0.554938	+	0.961181i	−0.0238147	+	0.0412482i
$544$	13.0886	+	22.6700i	0.561167	+	0.971970i
$545$	−22.9183			−0.981710
$546$	−7.85242	+	0.0976131i	−0.336053	+	0.00417745i
$547$	1.37593			0.0588306			0.0294153	−	0.999567i	$-0.490635\pi$
$547$	1.37593			0.0588306			0.0294153	+	0.999567i	$0.490635\pi$
$548$	−3.02387	−	5.23750i	−0.129173	−	0.223735i
$549$	25.3298	−	43.8725i	1.08105	−	1.87243i
$550$	−1.91780	+	3.32172i	−0.0817751	+	0.141639i
$551$	9.99802	+	17.3171i	0.425930	+	0.737733i
$552$	7.60443			0.323666
$553$	−2.65025	−	4.46137i	−0.112700	−	0.189717i
$554$	−6.87780			−0.292210
$555$	13.1928	+	22.8505i	0.560001	+	0.969951i
$556$	−2.69680	+	4.67099i	−0.114370	+	0.198094i
$557$	7.40092	−	12.8188i	0.313587	−	0.543148i	−0.665549	−	0.746354i	$-0.731803\pi$
$557$	7.40092	−	12.8188i	0.313587	−	0.543148i	0.979136	+	0.203206i	$0.0651360\pi$
$558$	3.55258	+	6.15325i	0.150393	+	0.260488i
$559$	−1.19322			−0.0504676
$560$	3.33634	−	5.94827i	0.140986	−	0.251360i
$561$	−19.3705			−0.817823
$562$	3.70349	+	6.41463i	0.156222	+	0.270585i
$563$	−16.3995	+	28.4048i	−0.691158	+	1.19712i	0.280301	+	0.959912i	$0.409566\pi$
$563$	−16.3995	+	28.4048i	−0.691158	+	1.19712i	−0.971459	+	0.237208i	$0.923768\pi$
$564$	−8.17355	+	14.1570i	−0.344169	+	0.596118i
$565$	−3.18955	−	5.52447i	−0.134185	−	0.232416i
$566$	36.1864			1.52103
$567$	−2.24249	+	3.99806i	−0.0941756	+	0.167903i
$568$	−7.39911			−0.310460
$569$	−6.36372	−	11.0223i	−0.266781	−	0.462078i	0.701248	−	0.712918i	$-0.252627\pi$
$569$	−6.36372	−	11.0223i	−0.266781	−	0.462078i	−0.968029	+	0.250840i	$0.919293\pi$
$570$	14.6213	−	25.3248i	0.612419	−	1.06074i
$571$	−12.9452	+	22.4218i	−0.541740	+	0.938321i	0.457064	+	0.889434i	$0.348901\pi$
$571$	−12.9452	+	22.4218i	−0.541740	+	0.938321i	−0.998804	+	0.0488875i	$0.984432\pi$
$572$	0.393358	+	0.681317i	0.0164471	+	0.0284873i
$573$	37.4746			1.56552
$574$	1.50722	+	2.53722i	0.0629103	+	0.105902i
$575$	−2.86721			−0.119571
$576$	−19.0426	−	32.9828i	−0.793442	−	1.37428i
$577$	7.85221	−	13.6004i	0.326892	−	0.566193i	−0.655001	−	0.755628i	$-0.727332\pi$
$577$	7.85221	−	13.6004i	0.326892	−	0.566193i	0.981893	+	0.189434i	$0.0606653\pi$
$578$	−14.2915	+	24.7537i	−0.594450	+	1.02962i
$579$	−8.80877	−	15.2572i	−0.366080	−	0.634069i
$580$	2.87056			0.119193
$581$	24.6095	−	0.305920i	1.02098	−	0.0126917i
$582$	−56.5441			−2.34383
$583$	3.54931	+	6.14758i	0.146997	+	0.254607i
$584$	12.4813	−	21.6182i	0.516480	−	0.894569i
$585$	−2.97838	+	5.15870i	−0.123141	+	0.213286i
$586$	−2.02478	−	3.50703i	−0.0836431	−	0.144874i
$587$	−11.2577			−0.464653			−0.232327	−	0.972638i	$-0.574634\pi$
$587$	−11.2577			−0.464653			−0.232327	+	0.972638i	$0.574634\pi$
$588$	−7.59708	−	12.4341i	−0.313298	−	0.512774i
$589$	9.83533			0.405258
$590$	2.04056	+	3.53435i	0.0840084	+	0.145507i
$591$	−30.1005	+	52.1355i	−1.23817	+	2.14457i
$592$	−6.82964	+	11.8293i	−0.280697	+	0.486181i
$593$	1.88605	+	3.26673i	0.0774508	+	0.134149i	0.902149	−	0.431424i	$-0.141989\pi$
$593$	1.88605	+	3.26673i	0.0774508	+	0.134149i	−0.824699	+	0.565572i	$0.808655\pi$
$594$	5.24548			0.215224
$595$	−23.2246	+	0.288704i	−0.952115	+	0.0118357i
$596$	8.29752			0.339880
$597$	30.5373	+	52.8922i	1.24981	+	2.16473i
$598$	0.484033	−	0.838370i	0.0197936	−	0.0342835i
$599$	−11.0659	+	19.1666i	−0.452139	+	0.783128i	−0.998519	−	0.0544097i	$-0.982672\pi$
$599$	−11.0659	+	19.1666i	−0.452139	+	0.783128i	0.546380	+	0.837538i	$0.316006\pi$
$600$	13.5115	+	23.4027i	0.551606	+	0.955409i
$601$	16.4817			0.672301			0.336151	−	0.941808i	$-0.390875\pi$
$601$	16.4817			0.672301			0.336151	+	0.941808i	$0.390875\pi$
$602$	1.86135	+	3.13335i	0.0758629	+	0.127706i
$603$	11.2642			0.458713
$604$	7.49624	+	12.9839i	0.305018	+	0.528306i
$605$	−6.61516	+	11.4578i	−0.268945	+	0.465826i
$606$	−11.1562	+	19.3230i	−0.453188	+	0.784945i
$607$	−7.02829	−	12.1734i	−0.285270	−	0.494101i	0.687405	−	0.726274i	$-0.258750\pi$
$607$	−7.02829	−	12.1734i	−0.285270	−	0.494101i	−0.972675	+	0.232173i	$0.925416\pi$
$608$	−28.3848			−1.15116
$609$	−10.0683	+	17.9505i	−0.407989	+	0.727391i
$610$	16.5714			0.670956
$611$	3.79385	+	6.57113i	0.153483	+	0.265840i
$612$	−11.3127	+	19.5942i	−0.457290	+	0.792049i
$613$	18.4378	−	31.9352i	0.744697	−	1.28985i	−0.205640	−	0.978628i	$-0.565927\pi$
$613$	18.4378	−	31.9352i	0.744697	−	1.28985i	0.950336	−	0.311225i	$-0.100739\pi$
$614$	0.357786	+	0.619703i	0.0144390	+	0.0250092i
$615$	3.70320			0.149328
$616$	4.28601	−	7.64139i	0.172688	−	0.307881i
$617$	7.53517			0.303354			0.151677	−	0.988430i	$-0.451533\pi$
$617$	7.53517			0.303354			0.151677	+	0.988430i	$0.451533\pi$
$618$	29.3170	+	50.7785i	1.17930	+	2.04261i
$619$	−11.2501	+	19.4857i	−0.452179	+	0.783197i	−0.998521	−	0.0543649i	$-0.982687\pi$
$619$	−11.2501	+	19.4857i	−0.452179	+	0.783197i	0.546342	+	0.837562i	$0.316020\pi$
$620$	0.705962	−	1.22276i	0.0283521	−	0.0491073i
$621$	1.96057	+	3.39580i	0.0786748	+	0.136269i
$622$	−13.2086			−0.529617
$623$	17.2896	+	29.1050i	0.692695	+	1.16607i
$624$	−5.10137			−0.204218
$625$	−0.574454	−	0.994984i	−0.0229782	−	0.0397994i
$626$	−11.0039	+	19.0593i	−0.439803	+	0.761761i
$627$	10.5021	−	18.1901i	0.419412	−	0.726443i
$628$	−3.63606	−	6.29785i	−0.145095	−	0.251311i
$629$	46.5181			1.85480
$630$	18.1927	−	0.226153i	0.724814	−	0.00901013i
$631$	25.4663			1.01380			0.506899	−	0.862005i	$-0.330792\pi$
$631$	25.4663			1.01380			0.506899	+	0.862005i	$0.330792\pi$
$632$	−3.01448	−	5.22123i	−0.119910	−	0.207689i
$633$	23.1734	−	40.1375i	0.921059	−	1.59532i
$634$	−13.6676	+	23.6730i	−0.542809	+	0.940174i
$635$	−6.69103	−	11.5892i	−0.265526	−	0.459904i
$636$	13.7166			0.543897
$637$	−6.76134	+	0.168126i	−0.267894	+	0.00666138i
$638$	−3.39403			−0.134371
$639$	−5.51823	−	9.55785i	−0.218298	−	0.378103i
$640$	0.837864	−	1.45122i	0.0331195	−	0.0573647i
$641$	−22.6035	+	39.1504i	−0.892785	+	1.54635i	−0.0562631	+	0.998416i	$0.517919\pi$
$641$	−22.6035	+	39.1504i	−0.892785	+	1.54635i	−0.836522	+	0.547933i	$0.815415\pi$
$642$	−17.9242	−	31.0457i	−0.707413	−	1.22528i
$643$	7.05984			0.278413			0.139206	−	0.990263i	$-0.455545\pi$
$643$	7.05984			0.278413			0.139206	+	0.990263i	$0.455545\pi$
$644$	1.79611	−	0.0223273i	0.0707766	−	0.000879820i
$645$	4.57328			0.180073
$646$	−25.7776	−	44.6481i	−1.01421	−	1.75665i
$647$	0.341586	−	0.591644i	0.0134291	−	0.0232599i	−0.859233	−	0.511585i	$-0.829059\pi$
$647$	0.341586	−	0.591644i	0.0134291	−	0.0232599i	0.872662	+	0.488325i	$0.162392\pi$
$648$	−2.66293	+	4.61233i	−0.104610	+	0.181189i
$649$	1.46568	+	2.53862i	0.0575328	+	0.0996497i
$650$	3.44011			0.134932
$651$	5.17019	+	8.70337i	0.202636	+	0.341112i
$652$	−0.252223			−0.00987780
$653$	8.59146	+	14.8808i	0.336210	+	0.582332i	0.983716	−	0.179727i	$-0.0575216\pi$
$653$	8.59146	+	14.8808i	0.336210	+	0.582332i	−0.647507	+	0.762060i	$0.724188\pi$
$654$	26.1801	−	45.3453i	1.02372	−	1.77314i
$655$	14.1815	−	24.5631i	0.554117	−	0.959759i
$656$	0.958539	+	1.66024i	0.0374247	+	0.0648214i
$657$	37.2340			1.45264
$658$	11.3374	−	20.2131i	0.441979	−	0.787990i
$659$	−7.11888			−0.277312			−0.138656	−	0.990341i	$-0.544278\pi$
$659$	−7.11888			−0.277312			−0.138656	+	0.990341i	$0.544278\pi$
$660$	−1.50764	−	2.61131i	−0.0586847	−	0.101645i
$661$	12.1760	−	21.0894i	0.473590	−	0.820282i	−0.525953	−	0.850514i	$-0.676291\pi$
$661$	12.1760	−	21.0894i	0.473590	−	0.820282i	0.999543	+	0.0302316i	$0.00962450\pi$
$662$	−15.5212	+	26.8835i	−0.603249	+	1.04486i
$663$	8.68662	+	15.0457i	0.337360	+	0.584325i
$664$	28.5944			1.10968
$665$	12.3205	−	21.9659i	0.477769	−	0.851800i
$666$	−36.4394			−1.41200
$667$	−1.26856	−	2.19722i	−0.0491189	−	0.0850765i
$668$	−6.30281	+	10.9168i	−0.243863	+	0.422383i
$669$	5.31220	−	9.20100i	0.205382	−	0.355731i
$670$	1.84233	+	3.19101i	0.0711754	+	0.123279i
$671$	11.9028			0.459501
$672$	−14.9212	−	25.1180i	−0.575598	−	0.968947i
$673$	45.7116			1.76205			0.881027	−	0.473066i	$-0.156853\pi$
$673$	45.7116			1.76205			0.881027	+	0.473066i	$0.156853\pi$
$674$	−0.131281	−	0.227385i	−0.00505675	−	0.00875855i
$675$	−6.96706	+	12.0673i	−0.268162	+	0.464470i
$676$	−4.56006	+	7.89826i	−0.175387	+	0.303779i
$677$	−11.0992	−	19.2243i	−0.426576	−	0.738851i	0.569991	−	0.821651i	$-0.306947\pi$
$677$	−11.0992	−	19.2243i	−0.426576	−	0.738851i	−0.996566	+	0.0828007i	$0.973614\pi$
$678$	14.5740			0.559713
$679$	−48.6949	+	0.605324i	−1.86874	+	0.0232302i
$680$	−26.9851			−1.03483
$681$	−38.8213	−	67.2405i	−1.48764	−	2.57666i
$682$	−0.834699	+	1.44574i	−0.0319623	+	0.0553603i
$683$	−5.69102	+	9.85713i	−0.217761	+	0.377173i	−0.954123	−	0.299415i	$-0.903209\pi$
$683$	−5.69102	+	9.85713i	−0.217761	+	0.377173i	0.736362	+	0.676587i	$0.236542\pi$
$684$	−12.2668	−	21.2467i	−0.469033	−	0.812389i
$685$	10.7590			0.411079
$686$	10.9888	+	17.4928i	0.419554	+	0.667878i
$687$	41.9273			1.59963
$688$	1.18375	+	2.05031i	0.0451300	+	0.0781675i
$689$	3.18335	−	5.51372i	0.121276	−	0.210056i
$690$	−1.85517	+	3.21325i	−0.0706251	+	0.122326i
$691$	19.1548	+	33.1772i	0.728685	+	1.26212i	0.957439	+	0.288635i	$0.0932013\pi$
$691$	19.1548	+	33.1772i	0.728685	+	1.26212i	−0.228755	+	0.973484i	$0.573465\pi$
$692$	9.78476			0.371961
$693$	13.0673	−	0.162439i	0.496386	−	0.00617055i
$694$	−0.567761			−0.0215519
$695$	−4.79762	−	8.30971i	−0.181984	−	0.315205i
$696$	−11.9560	+	20.7085i	−0.453192	+	0.784952i
$697$	3.26440	−	5.65411i	0.123648	−	0.214165i
$698$	13.3105	+	23.0544i	0.503809	+	0.872623i
$699$	79.9170			3.02274
$700$	3.26003	+	5.48786i	0.123218	+	0.207421i
$701$	−31.1871			−1.17792			−0.588961	−	0.808162i	$-0.700463\pi$
$701$	−31.1871			−1.17792			−0.588961	+	0.808162i	$0.700463\pi$
$702$	−2.35231	−	4.07433i	−0.0887824	−	0.153776i
$703$	−25.2206	+	43.6834i	−0.951214	+	1.64755i
$704$	4.47417	−	7.74950i	0.168627	−	0.292070i
$705$	−14.5408	−	25.1854i	−0.547638	−	0.948537i
$706$	15.1732			0.571050
$707$	−9.40065	+	16.7601i	−0.353548	+	0.630329i
$708$	5.66421			0.212874
$709$	−12.4579	−	21.5777i	−0.467867	−	0.810369i	0.531459	−	0.847084i	$-0.321644\pi$
$709$	−12.4579	−	21.5777i	−0.467867	−	0.810369i	−0.999326	+	0.0367152i	$0.988311\pi$
$710$	1.80508	−	3.12649i	0.0677435	−	0.117335i
$711$	4.49637	−	7.78794i	0.168627	−	0.292071i
$712$	19.6658	+	34.0622i	0.737007	+	1.27653i
$713$	−1.24792			−0.0467349
$714$	25.9588	−	46.2812i	0.971485	−	1.73203i
$715$	−1.39957			−0.0523411
$716$	6.44939	+	11.1707i	0.241025	+	0.417467i
$717$	34.4787	−	59.7189i	1.28763	−	2.23024i
$718$	2.70433	−	4.68404i	0.100925	−	0.174807i
$719$	−20.5854	−	35.6549i	−0.767704	−	1.32970i	−0.938805	−	0.344449i	$-0.888066\pi$
$719$	−20.5854	−	35.6549i	−0.767704	−	1.32970i	0.171101	−	0.985254i	$-0.445268\pi$
$720$	11.8190			0.440468
$721$	25.7909	+	43.4158i	0.960505	+	1.61689i
$722$	34.7101			1.29178
$723$	−1.53378	−	2.65659i	−0.0570420	−	0.0987996i
$724$	−0.152296	+	0.263784i	−0.00566002	+	0.00980345i
$725$	4.50796	−	7.80801i	0.167421	−	0.289982i
$726$	−15.1134	−	26.1771i	−0.560909	−	0.971523i
$727$	−2.84985			−0.105695			−0.0528475	−	0.998603i	$-0.516830\pi$
$727$	−2.84985			−0.105695			−0.0528475	+	0.998603i	$0.516830\pi$
$728$	−7.85736	+	0.0976745i	−0.291213	+	0.00362006i
$729$	−44.0115			−1.63005
$730$	6.08985	+	10.5479i	0.225396	+	0.390397i
$731$	4.03138	−	6.98255i	0.149106	−	0.258259i
$732$	11.4998	−	19.9182i	0.425044	−	0.736198i
$733$	−18.0033	−	31.1827i	−0.664968	−	1.15176i	−0.979294	−	0.202443i	$-0.935112\pi$
$733$	−18.0033	−	31.1827i	−0.664968	−	1.15176i	0.314326	−	0.949315i	$-0.398222\pi$
$734$	−22.5711			−0.833113
$735$	25.9144	−	0.644381i	0.955867	−	0.0237684i
$736$	3.60150			0.132753
$737$	1.32329	+	2.29201i	0.0487441	+	0.0844273i
$738$	−2.55713	+	4.42908i	−0.0941292	+	0.163037i
$739$	2.95316	−	5.11501i	0.108634	−	0.188159i	−0.806583	−	0.591120i	$-0.798686\pi$
$739$	2.95316	−	5.11501i	0.108634	−	0.188159i	0.915217	+	0.402962i	$0.132019\pi$
$740$	3.62058	+	6.27103i	0.133095	+	0.230528i
$741$	−18.8385			−0.692048
$742$	−19.4447	+	0.241716i	−0.713837	+	0.00887368i
$743$	−47.1256			−1.72887			−0.864436	−	0.502744i	$-0.832324\pi$
$743$	−47.1256			−1.72887			−0.864436	+	0.502744i	$0.832324\pi$
$744$	5.88074	+	10.1857i	0.215598	+	0.373427i
$745$	−7.38067	+	12.7837i	−0.270407	+	0.468358i
$746$	7.85652	−	13.6079i	0.287648	−	0.498220i
$747$	21.3255	+	36.9369i	0.780261	+	1.35145i
$748$	−5.31598			−0.194371
$749$	−15.7684	−	26.5442i	−0.576166	−	0.969903i
$750$	−33.8383			−1.23560
$751$	1.99714	+	3.45915i	0.0728768	+	0.126226i	0.900161	−	0.435557i	$-0.143449\pi$
$751$	1.99714	+	3.45915i	0.0728768	+	0.126226i	−0.827284	+	0.561784i	$0.810115\pi$
$752$	7.52750	−	13.0380i	0.274500	−	0.475447i
$753$	10.0225	−	17.3595i	0.365240	−	0.632614i
$754$	1.52204	+	2.63625i	0.0554294	+	0.0960065i
$755$	−26.6717			−0.970683
$756$	4.27041	−	7.61358i	0.155313	−	0.276903i
$757$	0.0523804			0.00190380			0.000951899	−	1.00000i	$-0.499697\pi$
$757$	0.0523804			0.00190380			0.000951899		1.00000i	$0.499697\pi$
$758$	1.31203	+	2.27251i	0.0476552	+	0.0825412i
$759$	−1.33252	+	2.30799i	−0.0483673	+	0.0837746i
$760$	14.6305	−	25.3408i	0.530704	−	0.919206i
$761$	−23.7108	−	41.0683i	−0.859515	−	1.48872i	−0.872393	−	0.488806i	$-0.837433\pi$
$761$	−23.7108	−	41.0683i	−0.859515	−	1.48872i	0.0128780	−	0.999917i	$-0.495901\pi$
$762$	30.5734			1.10756
$763$	22.0605	−	39.3310i	0.798644	−	1.42388i
$764$	10.2844			0.372077
$765$	−20.1254	−	34.8582i	−0.727635	−	1.26030i
$766$	6.60909	−	11.4473i	0.238796	−	0.413607i
$767$	1.31455	−	2.27687i	0.0474658	−	0.0822131i
$768$	−20.9625	−	36.3080i	−0.756417	−	1.31015i
$769$	−24.0845			−0.868508			−0.434254	−	0.900790i	$-0.642988\pi$
$769$	−24.0845			−0.868508			−0.434254	+	0.900790i	$0.642988\pi$
$770$	2.18326	+	3.67524i	0.0786791	+	0.132446i
$771$	24.5098			0.882700
$772$	−2.41745	−	4.18715i	−0.0870060	−	0.150699i
$773$	−12.8769	+	22.3034i	−0.463148	+	0.802197i	−0.999116	−	0.0420420i	$-0.986614\pi$
$773$	−12.8769	+	22.3034i	−0.463148	+	0.802197i	0.535967	+	0.844239i	$0.319947\pi$
$774$	−3.15793	+	5.46970i	−0.113510	+	0.196604i
$775$	−2.21730	−	3.84048i	−0.0796477	−	0.137954i
$776$	−56.5797			−2.03109
$777$	−51.9137	+	0.645337i	−1.86239	+	0.0231513i
$778$	−9.18111			−0.329159
$779$	3.53971	+	6.13096i	0.126823	+	0.219664i
$780$	−1.35219	+	2.34206i	−0.0484161	+	0.0838592i
$781$	1.29654	−	2.24567i	0.0463938	−	0.0803565i
$782$	3.27069	+	5.66501i	0.116960	+	0.202580i
$783$	−12.3300			−0.440637
$784$	6.99659	+	11.4513i	0.249878	+	0.408974i
$785$	12.9372			0.461747
$786$	32.3998	+	56.1182i	1.15566	+	2.00167i
$787$	15.4513	−	26.7624i	0.550780	−	0.953978i	−0.447439	−	0.894314i	$-0.647664\pi$
$787$	15.4513	−	26.7624i	0.550780	−	0.953978i	0.998219	−	0.0596637i	$-0.0190028\pi$
$788$	−8.26068	+	14.3079i	−0.294275	+	0.509699i
$789$	−8.12278	−	14.0691i	−0.289179	−	0.500872i
$790$	2.94164			0.104659
$791$	12.5509	−	0.156020i	0.446260	−	0.00554744i
$792$	15.1832			0.539511
$793$	−5.33775	−	9.24525i	−0.189549	−	0.328308i
$794$	3.93497	−	6.81557i	0.139647	−	0.241876i
$795$	−12.2009	+	21.1326i	−0.432722	+	0.749496i
$796$	8.38057	+	14.5156i	0.297041	+	0.514491i
$797$	−39.1277			−1.38598			−0.692988	−	0.720949i	$-0.743706\pi$
$797$	−39.1277			−1.38598			−0.692988	+	0.720949i	$0.743706\pi$
$798$	29.3869	+	49.4692i	1.04029	+	1.75119i
$799$	−51.2713			−1.81385
$800$	6.39914	+	11.0836i	0.226244	+	0.391866i
$801$	−29.3333	+	50.8068i	−1.03644	+	1.79517i
$802$	−18.1478	+	31.4329i	−0.640821	+	1.10994i
$803$	4.37417	+	7.57629i	0.154361	+	0.267361i
$804$	5.11397			0.180356
$805$	−1.56324	+	2.78706i	−0.0550971	+	0.0982309i
$806$	1.49727			0.0527391
$807$	5.76615	+	9.98726i	0.202978	+	0.351568i
$808$	−11.1632	+	19.3352i	−0.392719	+	0.680210i
$809$	−7.88160	+	13.6513i	−0.277102	+	0.479955i	−0.970663	−	0.240443i	$-0.922707\pi$
$809$	−7.88160	+	13.6513i	−0.277102	+	0.479955i	0.693561	+	0.720398i	$0.256041\pi$
$810$	−1.29929	−	2.25044i	−0.0456525	−	0.0790724i
$811$	−32.9193			−1.15595			−0.577976	−	0.816054i	$-0.696157\pi$
$811$	−32.9193			−1.15595			−0.577976	+	0.816054i	$0.696157\pi$
$812$	−2.76312	+	4.92629i	−0.0969666	+	0.172879i
$813$	−27.6789			−0.970740
$814$	−4.28082	−	7.41460i	−0.150043	−	0.259882i
$815$	0.224353	−	0.388590i	0.00785874	−	0.0136117i
$816$	17.2354	−	29.8526i	0.603360	−	1.04505i
$817$	4.37137	+	7.57144i	0.152935	+	0.264891i
$818$	−5.15722			−0.180318
$819$	−5.98615	−	10.0769i	−0.209173	−	0.352117i
$820$	1.01630			0.0354906
$821$	20.8919	+	36.1857i	0.729131	+	1.26289i	0.957251	+	0.289258i	$0.0934087\pi$
$821$	20.8919	+	36.1857i	0.729131	+	1.26289i	−0.228120	+	0.973633i	$0.573258\pi$
$822$	−12.2903	+	21.2874i	−0.428672	+	0.742483i
$823$	−17.5023	+	30.3148i	−0.610091	+	1.05671i	0.381134	+	0.924520i	$0.375534\pi$
$823$	−17.5023	+	30.3148i	−0.610091	+	1.05671i	−0.991225	+	0.132189i	$0.957800\pi$
$824$	29.3354	+	50.8104i	1.02195	+	1.77007i
$825$	−9.47044			−0.329719
$826$	−8.02963	+	0.0998160i	−0.279387	+	0.00347304i
$827$	16.3017			0.566866			0.283433	−	0.958992i	$-0.408527\pi$
$827$	16.3017			0.566866			0.283433	+	0.958992i	$0.408527\pi$
$828$	1.55643	+	2.69581i	0.0540896	+	0.0936860i
$829$	−10.5980	+	18.3564i	−0.368085	+	0.637543i	−0.989266	−	0.146125i	$-0.953320\pi$
$829$	−10.5980	+	18.3564i	−0.368085	+	0.637543i	0.621181	+	0.783667i	$0.286653\pi$
$830$	−6.97586	+	12.0825i	−0.242135	+	0.419391i
$831$	−8.49097	−	14.7068i	−0.294548	−	0.510173i
$832$	−8.02571			−0.278241
$833$	21.8599	−	40.1346i	0.757401	−	1.39058i
$834$	21.9218			0.759089
$835$	−11.2127	−	19.4210i	−0.388033	−	0.672092i
$836$	2.88216	−	4.99204i	0.0996815	−	0.172653i
$837$	−3.03233	+	5.25215i	−0.104813	+	0.181541i
$838$	7.34738	+	12.7260i	0.253811	+	0.439614i
$839$	33.6120			1.16042			0.580208	−	0.814468i	$-0.302971\pi$
$839$	33.6120			1.16042			0.580208	+	0.814468i	$0.302971\pi$
$840$	30.1152	−	0.374360i	1.03907	−	0.0129167i
$841$	−21.0220			−0.724897
$842$	−16.8375	−	29.1634i	−0.580259	−	1.00504i
$843$	−9.14427	+	15.8383i	−0.314945	+	0.545502i
$844$	6.35963	−	11.0152i	0.218908	−	0.379159i
$845$	−8.11238	−	14.0511i	−0.279074	−	0.483371i
$846$	40.1628			1.38082
$847$	−13.2956	−	22.3815i	−0.456843	−	0.769038i
$848$	−12.6324			−0.433797
$849$	44.6738	+	77.3773i	1.53320	+	2.65558i
$850$	−11.6227	+	20.1311i	−0.398656	+	0.690492i
$851$	3.20003	−	5.54261i	0.109696	−	0.189998i
$852$	−2.50529	−	4.33928i	−0.0858297	−	0.148661i
$853$	−49.5839			−1.69772			−0.848860	−	0.528618i	$-0.822711\pi$
$853$	−49.5839			−1.69772			−0.848860	+	0.528618i	$0.822711\pi$
$854$	−15.9512	+	28.4388i	−0.545838	+	0.973157i
$855$	43.6454			1.49264
$856$	−17.9355	−	31.0652i	−0.613023	−	1.06179i
$857$	20.4146	−	35.3591i	0.697348	−	1.20784i	−0.272034	−	0.962288i	$-0.587696\pi$
$857$	20.4146	−	35.3591i	0.697348	−	1.20784i	0.969383	−	0.245555i	$-0.0789702\pi$
$858$	1.59877	−	2.76915i	0.0545812	−	0.0945373i
$859$	2.87748	+	4.98394i	0.0981782	+	0.170050i	0.910931	−	0.412560i	$-0.135365\pi$
$859$	2.87748	+	4.98394i	0.0981782	+	0.170050i	−0.812752	+	0.582609i	$0.802032\pi$
$860$	1.25508			0.0427978
$861$	−3.56460	+	6.35522i	−0.121481	+	0.216585i
$862$	−6.63621			−0.226030
$863$	2.72157	+	4.71389i	0.0926432	+	0.160463i	0.908623	−	0.417618i	$-0.137135\pi$
$863$	2.72157	+	4.71389i	0.0926432	+	0.160463i	−0.815979	+	0.578081i	$0.803802\pi$
$864$	8.75133	−	15.1577i	0.297726	−	0.515677i
$865$	−8.70357	+	15.0750i	−0.295930	+	0.512566i
$866$	−15.5533	−	26.9391i	−0.528522	−	0.915427i
$867$	−70.5744			−2.39683
$868$	1.41889	+	2.38853i	0.0481603	+	0.0810719i
$869$	2.11290			0.0716751
$870$	−5.83357	−	10.1040i	−0.197777	−	0.342559i
$871$	1.18685	−	2.05569i	0.0402150	−	0.0696543i
$872$	26.1966	−	45.3739i	0.887129	−	1.53655i
$873$	−42.1969	−	73.0871i	−1.42815	−	2.47362i
$874$	−7.09307			−0.239927
$875$	−29.1410	+	0.362250i	−0.985145	+	0.0122463i
$876$	16.9043			0.571144
$877$	0.0188680	+	0.0326804i	0.000637128	+	0.00110354i	0.866344	−	0.499448i	$-0.166464\pi$
$877$	0.0188680	+	0.0326804i	0.000637128	+	0.00110354i	−0.865707	+	0.500552i	$0.833131\pi$
$878$	−14.1926	+	24.5823i	−0.478978	+	0.829614i
$879$	4.99939	−	8.65919i	0.168625	−	0.292067i
$880$	1.38847	+	2.40490i	0.0468053	+	0.0810692i
$881$	43.4095			1.46250			0.731252	−	0.682108i	$-0.238936\pi$
$881$	43.4095			1.46250			0.731252	+	0.682108i	$0.238936\pi$
$882$	−17.1237	+	31.4389i	−0.576585	+	1.05860i
$883$	29.9703			1.00858			0.504291	−	0.863534i	$-0.331754\pi$
$883$	29.9703			1.00858			0.504291	+	0.863534i	$0.331754\pi$
$884$	2.38393	+	4.12909i	0.0801803	+	0.138876i
$885$	−5.03833	+	8.72665i	−0.169362	+	0.293343i
$886$	−5.25385	+	9.09994i	−0.176507	+	0.305718i
$887$	9.75466	+	16.8956i	0.327529	+	0.567298i	0.982021	−	0.188772i	$-0.0604506\pi$
$887$	9.75466	+	16.8956i	0.327529	+	0.567298i	−0.654492	+	0.756069i	$0.727117\pi$
$888$	−60.3197			−2.02420
$889$	26.3293	−	0.327299i	0.883058	−	0.0109773i
$890$	−19.1906			−0.643270
$891$	−0.933245	−	1.61643i	−0.0312649	−	0.0541524i
$892$	1.45787	−	2.52510i	0.0488129	−	0.0845465i
$893$	27.7977	−	48.1470i	0.930214	−	1.61118i
$894$	−16.8623	−	29.2063i	−0.563959	−	0.976806i
$895$	−22.9470			−0.767033
$896$	1.68400	+	2.83480i	0.0562585	+	0.0947041i
$897$	2.39025			0.0798081
$898$	12.9768	+	22.4764i	0.433040	+	0.750047i
$899$	1.96204	−	3.39835i	0.0654376	−	0.113341i
$900$	−5.53091	+	9.57982i	−0.184364	+	0.319327i
$901$	21.5104	+	37.2571i	0.716615	+	1.24121i
$902$	−1.20163			−0.0400097
$903$	−4.40211	+	7.84839i	−0.146493	+	0.261178i
$904$	14.5832			0.485031
$905$	−0.270935	−	0.469273i	−0.00900618	−	0.0155992i
$906$	30.4678	−	52.7718i	1.01223	−	1.75323i
$907$	−17.6394	+	30.5524i	−0.585707	+	1.01447i	0.409080	+	0.912499i	$0.365850\pi$
$907$	−17.6394	+	30.5524i	−0.585707	+	1.01447i	−0.994787	+	0.101976i	$0.967484\pi$
$908$	−10.6540	−	18.4533i	−0.353566	−	0.612394i
$909$	−33.3018			−1.10455
$910$	1.87560	−	3.34395i	0.0621756	−	0.110851i
$911$	15.2689			0.505882			0.252941	−	0.967482i	$-0.418602\pi$
$911$	15.2689			0.505882			0.252941	+	0.967482i	$0.418602\pi$
$912$	18.6890	+	32.3703i	0.618855	+	1.07189i
$913$	−5.01056	+	8.67855i	−0.165825	+	0.287218i
$914$	−2.71492	+	4.70238i	−0.0898016	+	0.155541i
$915$	20.4582	+	35.4346i	0.676326	+	1.17143i
$916$	11.5064			0.380182
$917$	28.5030	+	47.9812i	0.941252	+	1.58448i
$918$	31.7900			1.04923
$919$	−26.1806	−	45.3462i	−0.863619	−	1.49583i	−0.868412	−	0.495843i	$-0.834859\pi$
$919$	−26.1806	−	45.3462i	−0.863619	−	1.49583i	0.00479325	−	0.999989i	$-0.498474\pi$
$920$	−1.85634	+	3.21527i	−0.0612016	+	0.106004i
$921$	−0.883407	+	1.53011i	−0.0291092	+	0.0504187i
$922$	−9.02869	−	15.6382i	−0.297344	−	0.515015i
$923$	−2.32571			−0.0765518
$924$	5.93258	−	0.0737477i	0.195168	−	0.00242612i
$925$	22.7432			0.747792
$926$	6.74671	+	11.6856i	0.221710	+	0.384014i
$927$	−43.7565	+	75.7884i	−1.43715	+	2.48922i
$928$	−5.66245	+	9.80765i	−0.185879	+	0.321952i
$929$	−23.0443	−	39.9139i	−0.756060	−	1.30953i	−0.944846	−	0.327516i	$-0.893789\pi$
$929$	−23.0443	−	39.9139i	−0.756060	−	1.30953i	0.188786	−	0.982018i	$-0.439545\pi$
$930$	−5.73864			−0.188177
$931$	25.8371	+	42.2875i	0.846778	+	1.38592i
$932$	21.9322			0.718413
$933$	−16.3067	−	28.2440i	−0.533856	−	0.924666i
$934$	−1.80428	+	3.12510i	−0.0590378	+	0.102256i
$935$	4.72858	−	8.19014i	0.154641	−	0.267846i
$936$	−6.80884	−	11.7933i	−0.222554	−	0.385475i
$937$	−33.6725			−1.10003			−0.550016	−	0.835154i	$-0.685378\pi$
$937$	−33.6725			−1.10003			−0.550016	+	0.835154i	$0.685378\pi$
$938$	−7.24960	+	0.0901195i	−0.236708	+	0.00294250i
$939$	−54.3392			−1.77329
$940$	−3.99053	−	6.91181i	−0.130157	−	0.225438i
$941$	4.72135	−	8.17761i	0.153911	−	0.266582i	−0.778751	−	0.627334i	$-0.784146\pi$
$941$	4.72135	−	8.17761i	0.153911	−	0.266582i	0.932662	+	0.360751i	$0.117480\pi$
$942$	−14.7785	+	25.5971i	−0.481509	+	0.833997i
$943$	−0.449123	−	0.777904i	−0.0146255	−	0.0253321i
$944$	−5.21650			−0.169783
$945$	7.93143	+	13.3516i	0.258010	+	0.434327i
$946$	−1.48395			−0.0482474
$947$	15.2459	+	26.4067i	0.495427	+	0.858104i	0.999986	−	0.00527297i	$-0.00167844\pi$
$947$	15.2459	+	26.4067i	0.495427	+	0.858104i	−0.504560	+	0.863377i	$0.668345\pi$
$948$	2.04136	−	3.53574i	0.0663003	−	0.114836i
$949$	3.92316	−	6.79512i	0.127351	−	0.220579i
$950$	−12.6029	−	21.8289i	−0.408893	−	0.708224i
$951$	−67.4932			−2.18862
$952$	25.9752	−	46.3103i	0.841860	−	1.50093i
$953$	−60.9536			−1.97448			−0.987241	−	0.159235i	$-0.949097\pi$
$953$	−60.9536			−1.97448			−0.987241	+	0.159235i	$0.949097\pi$
$954$	−16.8499	−	29.1849i	−0.545536	−	0.944897i
$955$	−9.14803	+	15.8448i	−0.296023	+	0.512727i
$956$	9.46223	−	16.3891i	0.306030	−	0.530060i
$957$	−4.19009	−	7.25745i	−0.135446	−	0.234600i
$958$	−13.6368			−0.440586
$959$	−10.3563	+	18.4639i	−0.334422	+	0.596231i
$960$	30.7604			0.992787
$961$	14.5349	+	25.1753i	0.468869	+	0.812105i
$962$	−3.83944	+	6.65010i	−0.123788	+	0.214408i
$963$	26.7524	−	46.3366i	0.862085	−	1.49318i
$964$	−0.420927	−	0.729066i	−0.0135571	−	0.0234816i
$965$	8.60132			0.276886
$966$	−3.72865	−	6.27672i	−0.119967	−	0.201950i
$967$	13.3405			0.429001			0.214501	−	0.976724i	$-0.431188\pi$
$967$	13.3405			0.429001			0.214501	+	0.976724i	$0.431188\pi$
$968$	−15.1229	−	26.1936i	−0.486067	−	0.841893i
$969$	63.6473	−	110.240i	2.04465	−	3.54143i
$970$	13.8031	−	23.9077i	0.443192	−	0.767630i
$971$	−7.16954	−	12.4180i	−0.230081	−	0.398513i	0.727750	−	0.685842i	$-0.240566\pi$
$971$	−7.16954	−	12.4180i	−0.230081	−	0.398513i	−0.957832	+	0.287329i	$0.907233\pi$
$972$	−13.5048			−0.433168
$973$	18.8787	−	0.234680i	0.605223	−	0.00752351i
$974$	3.75605			0.120352
$975$	4.24699	+	7.35599i	0.136012	+	0.235580i
$976$	−10.5908	+	18.3438i	−0.339003	+	0.587171i
$977$	−23.2574	+	40.2830i	−0.744069	+	1.28877i	0.206559	+	0.978434i	$0.433773\pi$
$977$	−23.2574	+	40.2830i	−0.744069	+	1.28877i	−0.950628	+	0.310332i	$0.899560\pi$
$978$	0.512569	+	0.887795i	0.0163901	+	0.0283886i
$979$	−13.7841			−0.440541
$980$	7.11187	−	0.176842i	0.227180	−	0.00564901i
$981$	78.1493			2.49511
$982$	0.883957	+	1.53106i	0.0282082	+	0.0488580i
$983$	21.8938	−	37.9211i	0.698303	−	1.20950i	−0.270751	−	0.962649i	$-0.587272\pi$
$983$	21.8938	−	37.9211i	0.698303	−	1.20950i	0.969054	−	0.246847i	$-0.0793945\pi$
$984$	−4.23293	+	7.33165i	−0.134941	+	0.233724i
$985$	−14.6958	−	25.4539i	−0.468247	−	0.811028i
$986$	−20.5693			−0.655062
$987$	57.2183	−	0.711278i	1.82128	−	0.0226402i
$988$	−5.16997			−0.164479
$989$	−0.554646	−	0.960675i	−0.0176367	−	0.0305477i
$990$	−3.70408	+	6.41565i	−0.117723	+	0.203903i
$991$	4.08397	−	7.07365i	0.129732	−	0.224702i	−0.793841	−	0.608126i	$-0.791922\pi$
$991$	4.08397	−	7.07365i	0.129732	−	0.224702i	0.923573	+	0.383424i	$0.125255\pi$
$992$	2.78515	+	4.82403i	0.0884287	+	0.153163i
$993$	−76.6468			−2.43231
$994$	3.62798	+	6.10725i	0.115073	+	0.193710i
$995$	−29.8182			−0.945299
$996$	9.68184	+	16.7694i	0.306781	+	0.531360i
$997$	22.1907	−	38.4354i	0.702786	−	1.21726i	−0.264699	−	0.964331i	$-0.585273\pi$
$997$	22.1907	−	38.4354i	0.702786	−	1.21726i	0.967485	−	0.252929i	$-0.0813940\pi$
$998$	15.3912	−	26.6584i	0.487201	−	0.843856i
$999$	−15.5516	−	26.9361i	−0.492030	−	0.852220i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.e.d.165.8	✓	34
7.2	even	3	inner	287.2.e.d.247.8	yes	34
7.3	odd	6		2009.2.a.r.1.10		17
7.4	even	3		2009.2.a.s.1.10		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.e.d.165.8	✓	34	1.1	even	1	trivial
287.2.e.d.247.8	yes	34	7.2	even	3	inner
2009.2.a.r.1.10		17	7.3	odd	6
2009.2.a.s.1.10		17	7.4	even	3

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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.557713 - 0.965987i) q^{2} +(1.37705 - 2.38511i) q^{3} +(0.377913 - 0.654564i) q^{4} +(0.672309 + 1.16447i) q^{5} -3.07199 q^{6} +(-2.64555 + 0.0328867i) q^{7} -3.07392 q^{8} +(-2.29251 - 3.97075i) q^{9} +O(q^{10})\)	\(q+(-0.557713 - 0.965987i) q^{2} +(1.37705 - 2.38511i) q^{3} +(0.377913 - 0.654564i) q^{4} +(0.672309 + 1.16447i) q^{5} -3.07199 q^{6} +(-2.64555 + 0.0328867i) q^{7} -3.07392 q^{8} +(-2.29251 - 3.97075i) q^{9} +(0.749910 - 1.29888i) q^{10} +(0.538640 - 0.932951i) q^{11} +(-1.04081 - 1.80273i) q^{12} -0.966204 q^{13} +(1.50722 + 2.53722i) q^{14} +3.70320 q^{15} +(0.958539 + 1.66024i) q^{16} +(3.26440 - 5.65411i) q^{17} +(-2.55713 + 4.42908i) q^{18} +(3.53971 + 6.13096i) q^{19} +1.01630 q^{20} +(-3.56460 + 6.35522i) q^{21} -1.20163 q^{22} +(-0.449123 - 0.777904i) q^{23} +(-4.23293 + 7.33165i) q^{24} +(1.59600 - 2.76436i) q^{25} +(0.538864 + 0.933340i) q^{26} -4.36532 q^{27} +(-0.978259 + 1.74411i) q^{28} +2.82453 q^{29} +(-2.06532 - 3.57724i) q^{30} +(0.694642 - 1.20315i) q^{31} +(-2.00474 + 3.47231i) q^{32} +(-1.48346 - 2.56943i) q^{33} -7.28240 q^{34} +(-1.81692 - 3.05856i) q^{35} -3.46548 q^{36} +(3.56253 + 6.17048i) q^{37} +(3.94829 - 6.83863i) q^{38} +(-1.33051 + 2.30451i) q^{39} +(-2.06662 - 3.57949i) q^{40} +1.00000 q^{41} +(8.12708 - 0.101027i) q^{42} +1.23495 q^{43} +(-0.407117 - 0.705148i) q^{44} +(3.08255 - 5.33914i) q^{45} +(-0.500964 + 0.867695i) q^{46} +(-3.92655 - 6.80098i) q^{47} +5.27981 q^{48} +(6.99784 - 0.174006i) q^{49} -3.56044 q^{50} +(-8.99047 - 15.5719i) q^{51} +(-0.365141 + 0.632442i) q^{52} +(-3.29469 + 5.70658i) q^{53} +(2.43459 + 4.21684i) q^{54} +1.44853 q^{55} +(8.13220 - 0.101091i) q^{56} +19.4974 q^{57} +(-1.57528 - 2.72846i) q^{58} +(-1.36053 + 2.35651i) q^{59} +(1.39949 - 2.42398i) q^{60} +(5.52445 + 9.56863i) q^{61} -1.54964 q^{62} +(6.19554 + 10.4294i) q^{63} +8.30643 q^{64} +(-0.649587 - 1.12512i) q^{65} +(-1.65469 + 2.86601i) q^{66} +(-1.22837 + 2.12759i) q^{67} +(-2.46732 - 4.27352i) q^{68} -2.47385 q^{69} +(-1.94121 + 3.46092i) q^{70} +2.40706 q^{71} +(7.04700 + 12.2058i) q^{72} +(-4.06039 + 7.03280i) q^{73} +(3.97373 - 6.88271i) q^{74} +(-4.39554 - 7.61330i) q^{75} +5.35081 q^{76} +(-1.39431 + 2.48588i) q^{77} +2.96816 q^{78} +(0.980663 + 1.69856i) q^{79} +(-1.28887 + 2.23238i) q^{80} +(0.866298 - 1.50047i) q^{81} +(-0.557713 - 0.965987i) q^{82} -9.30225 q^{83} +(2.81279 + 4.73498i) q^{84} +8.77874 q^{85} +(-0.688749 - 1.19295i) q^{86} +(3.88951 - 6.73683i) q^{87} +(-1.65573 + 2.86782i) q^{88} +(-6.39763 - 11.0810i) q^{89} -6.87672 q^{90} +(2.55614 - 0.0317752i) q^{91} -0.678918 q^{92} +(-1.91311 - 3.31360i) q^{93} +(-4.37977 + 7.58599i) q^{94} +(-4.75956 + 8.24380i) q^{95} +(5.52124 + 9.56307i) q^{96} +18.4064 q^{97} +(-4.07087 - 6.66277i) q^{98} -4.93936 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 3 q^{2} - q^{3} - 25 q^{4} + q^{5} + 4 q^{6} - 2 q^{7} + 18 q^{8} - 26 q^{9}+O(q^{10}) \) 34 * q - 3 * q^2 - q^3 - 25 * q^4 + q^5 + 4 * q^6 - 2 * q^7 + 18 * q^8 - 26 * q^9	\( 34 q - 3 q^{2} - q^{3} - 25 q^{4} + q^{5} + 4 q^{6} - 2 q^{7} + 18 q^{8} - 26 q^{9} + 2 q^{10} - 15 q^{11} - 4 q^{12} - 10 q^{13} + 21 q^{14} + 48 q^{15} - 33 q^{16} - 4 q^{17} - 10 q^{18} - 5 q^{19} - 52 q^{20} + 12 q^{21} + 32 q^{22} - 12 q^{23} - 16 q^{24} - 24 q^{25} - 31 q^{26} - 22 q^{27} + 60 q^{28} + 28 q^{29} + 33 q^{30} + 3 q^{31} - 16 q^{32} - 4 q^{33} - 48 q^{34} + 45 q^{35} + 114 q^{36} - 24 q^{37} - 45 q^{39} - 36 q^{40} + 34 q^{41} + 65 q^{42} + 28 q^{43} + 9 q^{44} + 21 q^{45} - 44 q^{46} - 19 q^{47} - 120 q^{48} - 10 q^{49} - 8 q^{50} - 2 q^{51} + 25 q^{52} - 4 q^{53} - 68 q^{54} + 18 q^{55} + 25 q^{56} - 24 q^{57} + q^{58} + 27 q^{59} - 66 q^{60} + q^{61} - 46 q^{62} + 37 q^{63} + 150 q^{64} - 22 q^{65} + 16 q^{66} - 49 q^{67} - 45 q^{68} + 24 q^{69} + 73 q^{70} + 80 q^{71} + 23 q^{72} + 14 q^{73} - 33 q^{74} - 27 q^{75} - 18 q^{76} - 20 q^{77} - 24 q^{78} - 61 q^{79} + 82 q^{80} - 53 q^{81} - 3 q^{82} - 36 q^{83} + 188 q^{84} - 26 q^{85} + 4 q^{86} + 17 q^{87} - 74 q^{88} - 18 q^{89} - 40 q^{90} + 7 q^{91} + 56 q^{92} + 36 q^{93} + 5 q^{94} - 20 q^{95} - 148 q^{96} + 52 q^{97} + 142 q^{98} + 76 q^{99}+O(q^{100}) \) 34 * q - 3 * q^2 - q^3 - 25 * q^4 + q^5 + 4 * q^6 - 2 * q^7 + 18 * q^8 - 26 * q^9 + 2 * q^10 - 15 * q^11 - 4 * q^12 - 10 * q^13 + 21 * q^14 + 48 * q^15 - 33 * q^16 - 4 * q^17 - 10 * q^18 - 5 * q^19 - 52 * q^20 + 12 * q^21 + 32 * q^22 - 12 * q^23 - 16 * q^24 - 24 * q^25 - 31 * q^26 - 22 * q^27 + 60 * q^28 + 28 * q^29 + 33 * q^30 + 3 * q^31 - 16 * q^32 - 4 * q^33 - 48 * q^34 + 45 * q^35 + 114 * q^36 - 24 * q^37 - 45 * q^39 - 36 * q^40 + 34 * q^41 + 65 * q^42 + 28 * q^43 + 9 * q^44 + 21 * q^45 - 44 * q^46 - 19 * q^47 - 120 * q^48 - 10 * q^49 - 8 * q^50 - 2 * q^51 + 25 * q^52 - 4 * q^53 - 68 * q^54 + 18 * q^55 + 25 * q^56 - 24 * q^57 + q^58 + 27 * q^59 - 66 * q^60 + q^61 - 46 * q^62 + 37 * q^63 + 150 * q^64 - 22 * q^65 + 16 * q^66 - 49 * q^67 - 45 * q^68 + 24 * q^69 + 73 * q^70 + 80 * q^71 + 23 * q^72 + 14 * q^73 - 33 * q^74 - 27 * q^75 - 18 * q^76 - 20 * q^77 - 24 * q^78 - 61 * q^79 + 82 * q^80 - 53 * q^81 - 3 * q^82 - 36 * q^83 + 188 * q^84 - 26 * q^85 + 4 * q^86 + 17 * q^87 - 74 * q^88 - 18 * q^89 - 40 * q^90 + 7 * q^91 + 56 * q^92 + 36 * q^93 + 5 * q^94 - 20 * q^95 - 148 * q^96 + 52 * q^97 + 142 * q^98 + 76 * q^99

Introduction

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