LMFDB - Embedded newform 285.2.i.f.121.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [285,2,Mod(106,285)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(285, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("285.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 285 = 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	285.i (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:	$2.27573645761$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 9x^{8} - 2x^{7} + 56x^{6} - 18x^{5} + 125x^{4} + x^{3} + 189x^{2} - 52x + 16 $ x^10 - x^9 + 9x^8 - 2x^7 + 56x^6 - 18x^5 + 125x^4 + x^3 + 189x^2 - 52*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.5
Root			$1.34580 - 2.33099i$ of defining polynomial
Character	$\chi$	$=$	285.121
Dual form			285.2.i.f.106.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.34580 + 2.33099i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-2.62233 + 4.54201i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.34580 + 2.33099i) q^{6} -0.797044 q^{7} -8.73329 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.34580 - 2.33099i) q^{10} +2.59225 q^{11} -5.24466 q^{12} +(1.39852 - 2.42231i) q^{13} +(-1.07266 - 1.85790i) q^{14} +(0.500000 - 0.866025i) q^{15} +(-6.50857 - 11.2732i) q^{16} +(2.88624 + 4.99911i) q^{17} -2.69159 q^{18} +(2.45159 + 3.60412i) q^{19} +5.24466 q^{20} +(-0.398522 - 0.690261i) q^{21} +(3.48863 + 6.04249i) q^{22} +(1.55307 - 2.68999i) q^{23} +(-4.36665 - 7.56325i) q^{24} +(-0.500000 + 0.866025i) q^{25} +7.52850 q^{26} -1.00000 q^{27} +(2.09011 - 3.62018i) q^{28} +(2.39547 - 4.14907i) q^{29} +2.69159 q^{30} -9.48932 q^{31} +(8.78510 - 15.2162i) q^{32} +(1.29612 + 2.24495i) q^{33} +(-7.76857 + 13.4556i) q^{34} +(0.398522 + 0.690261i) q^{35} +(-2.62233 - 4.54201i) q^{36} +7.69227 q^{37} +(-5.10182 + 10.5650i) q^{38} +2.79704 q^{39} +(4.36665 + 7.56325i) q^{40} +(-3.69159 - 6.39402i) q^{41} +(1.07266 - 1.85790i) q^{42} +(1.39852 + 2.42231i) q^{43} +(-6.79773 + 11.7740i) q^{44} +1.00000 q^{45} +8.36045 q^{46} +(5.53865 - 9.59322i) q^{47} +(6.50857 - 11.2732i) q^{48} -6.36472 q^{49} -2.69159 q^{50} +(-2.88624 + 4.99911i) q^{51} +(7.33477 + 12.7042i) q^{52} +(4.43931 - 7.68910i) q^{53} +(-1.34580 - 2.33099i) q^{54} +(-1.29612 - 2.24495i) q^{55} +6.96082 q^{56} +(-1.89547 + 3.92520i) q^{57} +12.8952 q^{58} +(-0.540099 - 0.935479i) q^{59} +(2.62233 + 4.54201i) q^{60} +(-2.03612 + 3.52667i) q^{61} +(-12.7707 - 22.1195i) q^{62} +(0.398522 - 0.690261i) q^{63} +21.2575 q^{64} -2.79704 q^{65} +(-3.48863 + 6.04249i) q^{66} +(-6.88784 + 11.9301i) q^{67} -30.2747 q^{68} +3.10614 q^{69} +(-1.07266 + 1.85790i) q^{70} +(5.98771 + 10.3710i) q^{71} +(4.36665 - 7.56325i) q^{72} +(-4.25389 - 7.36795i) q^{73} +(10.3522 + 17.9306i) q^{74} -1.00000 q^{75} +(-22.7988 + 1.68395i) q^{76} -2.06614 q^{77} +(3.76425 + 6.51987i) q^{78} +(-3.24092 - 5.61344i) q^{79} +(-6.50857 + 11.2732i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(9.93625 - 17.2101i) q^{82} -2.79520 q^{83} +4.18023 q^{84} +(2.88624 - 4.99911i) q^{85} +(-3.76425 + 6.51987i) q^{86} +4.79093 q^{87} -22.6389 q^{88} +(6.67930 - 11.5689i) q^{89} +(1.34580 + 2.33099i) q^{90} +(-1.11468 + 1.93069i) q^{91} +(8.14532 + 14.1081i) q^{92} +(-4.74466 - 8.21799i) q^{93} +29.8155 q^{94} +(1.89547 - 3.92520i) q^{95} +17.5702 q^{96} +(-1.00000 - 1.73205i) q^{97} +(-8.56561 - 14.8361i) q^{98} +(-1.29612 + 2.24495i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} + 5 q^{3} - 7 q^{4} - 5 q^{5} - q^{6} + 4 q^{7} - 12 q^{8} - 5 q^{9} + q^{10} + 10 q^{11} - 14 q^{12} + 8 q^{13} + 4 q^{14} + 5 q^{15} - 7 q^{16} - 10 q^{17} - 2 q^{18} + 5 q^{19} + 14 q^{20}+ \cdots - 5 q^{99}+O(q^{100}) $ 10 * q + q^2 + 5 * q^3 - 7 * q^4 - 5 * q^5 - q^6 + 4 * q^7 - 12 * q^8 - 5 * q^9 + q^10 + 10 * q^11 - 14 * q^12 + 8 * q^13 + 4 * q^14 + 5 * q^15 - 7 * q^16 - 10 * q^17 - 2 * q^18 + 5 * q^19 + 14 * q^20 + 2 * q^21 - 2 * q^22 + 2 * q^23 - 6 * q^24 - 5 * q^25 - 4 * q^26 - 10 * q^27 - 10 * q^28 + 7 * q^29 + 2 * q^30 - 18 * q^31 + 23 * q^32 + 5 * q^33 - 25 * q^34 - 2 * q^35 - 7 * q^36 + 12 * q^37 - 37 * q^38 + 16 * q^39 + 6 * q^40 - 12 * q^41 - 4 * q^42 + 8 * q^43 - 16 * q^44 + 10 * q^45 - 40 * q^46 - 6 * q^47 + 7 * q^48 + 30 * q^49 - 2 * q^50 + 10 * q^51 + 4 * q^52 - 8 * q^53 - q^54 - 5 * q^55 + 72 * q^56 - 2 * q^57 + 76 * q^58 + q^59 + 7 * q^60 - 7 * q^61 - 15 * q^62 - 2 * q^63 + 28 * q^64 - 16 * q^65 + 2 * q^66 + 14 * q^67 - 2 * q^68 + 4 * q^69 + 4 * q^70 + 27 * q^71 + 6 * q^72 - 26 * q^73 + 18 * q^74 - 10 * q^75 - 56 * q^76 + 28 * q^77 - 2 * q^78 - 23 * q^79 - 7 * q^80 - 5 * q^81 + 36 * q^82 - 24 * q^83 - 20 * q^84 - 10 * q^85 + 2 * q^86 + 14 * q^87 + 9 * q^89 + q^90 - 46 * q^91 + 52 * q^92 - 9 * q^93 + 90 * q^94 + 2 * q^95 + 46 * q^96 - 10 * q^97 - 21 * q^98 - 5 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/285\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	1.34580	+	2.33099i	0.951621	+	1.64826i	0.741918	+	0.670491i	$0.233916\pi$
$2$	1.34580	+	2.33099i	0.951621	+	1.64826i	0.209703	+	0.977765i	$0.432750\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−2.62233	+	4.54201i	−1.31116	+	2.27100i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−1.34580	+	2.33099i	−0.549419	+	0.951621i
$7$	−0.797044			−0.301254			−0.150627	−	0.988591i	$-0.548129\pi$
$7$	−0.797044			−0.301254			−0.150627	+	0.988591i	$0.548129\pi$
$8$	−8.73329			−3.08769
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.34580	−	2.33099i	0.425578	−	0.737122i
$11$	2.59225			0.781592			0.390796	−	0.920477i	$-0.372200\pi$
$11$	2.59225			0.781592			0.390796	+	0.920477i	$0.372200\pi$
$12$	−5.24466			−1.51400
$13$	1.39852	−	2.42231i	0.387880	−	0.671828i	−0.604284	−	0.796769i	$-0.706541\pi$
$13$	1.39852	−	2.42231i	0.387880	−	0.671828i	0.992164	+	0.124941i	$0.0398741\pi$
$14$	−1.07266	−	1.85790i	−0.286680	−	0.496544i
$15$	0.500000	−	0.866025i	0.129099	−	0.223607i
$16$	−6.50857	−	11.2732i	−1.62714	−	2.81829i
$17$	2.88624	+	4.99911i	0.700015	+	1.21246i	0.968461	+	0.249167i	$0.0801568\pi$
$17$	2.88624	+	4.99911i	0.700015	+	1.21246i	−0.268445	+	0.963295i	$0.586510\pi$
$18$	−2.69159			−0.634414
$19$	2.45159	+	3.60412i	0.562434	+	0.826843i
$19$	2.45159	+	3.60412i	0.562434	+	0.826843i
$20$	5.24466			1.17274
$21$	−0.398522	−	0.690261i	−0.0869646	−	0.150627i
$22$	3.48863	+	6.04249i	0.743779	+	1.28826i
$23$	1.55307	−	2.68999i	0.323837	−	0.560903i	−0.657439	−	0.753508i	$-0.728360\pi$
$23$	1.55307	−	2.68999i	0.323837	−	0.560903i	0.981276	+	0.192605i	$0.0616936\pi$
$24$	−4.36665	−	7.56325i	−0.891338	−	1.54384i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	7.52850			1.47646
$27$	−1.00000			−0.192450
$28$	2.09011	−	3.62018i	0.394994	−	0.684150i
$29$	2.39547	−	4.14907i	0.444827	−	0.770463i	−0.553213	−	0.833040i	$-0.686599\pi$
$29$	2.39547	−	4.14907i	0.444827	−	0.770463i	0.998040	+	0.0625768i	$0.0199318\pi$
$30$	2.69159			0.491415
$31$	−9.48932			−1.70433			−0.852166	−	0.523272i	$-0.824711\pi$
$31$	−9.48932			−1.70433			−0.852166	+	0.523272i	$0.824711\pi$
$32$	8.78510	−	15.2162i	1.55300	−	2.68988i
$33$	1.29612	+	2.24495i	0.225626	+	0.390796i
$34$	−7.76857	+	13.4556i	−1.33230	+	2.30761i
$35$	0.398522	+	0.690261i	0.0673625	+	0.116675i
$36$	−2.62233	−	4.54201i	−0.437055	−	0.757001i
$37$	7.69227			1.26460			0.632301	−	0.774723i	$-0.282111\pi$
$37$	7.69227			1.26460			0.632301	+	0.774723i	$0.282111\pi$
$38$	−5.10182	+	10.5650i	−0.827624	+	1.71387i
$39$	2.79704			0.447886
$40$	4.36665	+	7.56325i	0.690428	+	1.19586i
$41$	−3.69159	−	6.39402i	−0.576530	−	0.998579i	−0.995874	−	0.0907511i	$-0.971073\pi$
$41$	−3.69159	−	6.39402i	−0.576530	−	0.998579i	0.419344	−	0.907827i	$-0.362260\pi$
$42$	1.07266	−	1.85790i	0.165515	−	0.286680i
$43$	1.39852	+	2.42231i	0.213273	+	0.369399i	0.952737	−	0.303797i	$-0.0982544\pi$
$43$	1.39852	+	2.42231i	0.213273	+	0.369399i	−0.739464	+	0.673196i	$0.764921\pi$
$44$	−6.79773	+	11.7740i	−1.02480	+	1.77500i
$45$	1.00000			0.149071
$46$	8.36045			1.23268
$47$	5.53865	−	9.59322i	0.807895	−	1.39931i	−0.106424	−	0.994321i	$-0.533940\pi$
$47$	5.53865	−	9.59322i	0.807895	−	1.39931i	0.914319	−	0.404994i	$-0.132726\pi$
$48$	6.50857	−	11.2732i	0.939431	−	1.62714i
$49$	−6.36472			−0.909246
$50$	−2.69159			−0.380648
$51$	−2.88624	+	4.99911i	−0.404154	+	0.700015i
$52$	7.33477	+	12.7042i	1.01715	+	1.76176i
$53$	4.43931	−	7.68910i	0.609785	−	1.05618i	−0.381490	−	0.924373i	$-0.624589\pi$
$53$	4.43931	−	7.68910i	0.609785	−	1.05618i	0.991275	−	0.131806i	$-0.0420777\pi$
$54$	−1.34580	−	2.33099i	−0.183140	−	0.317207i
$55$	−1.29612	−	2.24495i	−0.174769	−	0.302709i
$56$	6.96082			0.930179
$57$	−1.89547	+	3.92520i	−0.251061	+	0.519906i
$58$	12.8952			1.69323
$59$	−0.540099	−	0.935479i	−0.0703149	−	0.121789i	0.828724	−	0.559657i	$-0.189067\pi$
$59$	−0.540099	−	0.935479i	−0.0703149	−	0.121789i	−0.899039	+	0.437868i	$0.855734\pi$
$60$	2.62233	+	4.54201i	0.338541	+	0.586371i
$61$	−2.03612	+	3.52667i	−0.260699	+	0.451544i	−0.966428	−	0.256938i	$-0.917286\pi$
$61$	−2.03612	+	3.52667i	−0.260699	+	0.451544i	0.705729	+	0.708482i	$0.250620\pi$
$62$	−12.7707	−	22.1195i	−1.62188	−	2.80917i
$63$	0.398522	−	0.690261i	0.0502091	−	0.0869646i
$64$	21.2575			2.65719
$65$	−2.79704			−0.346931
$66$	−3.48863	+	6.04249i	−0.429421	+	0.743779i
$67$	−6.88784	+	11.9301i	−0.841484	+	1.45749i	0.0471566	+	0.998888i	$0.484984\pi$
$67$	−6.88784	+	11.9301i	−0.841484	+	1.45749i	−0.888640	+	0.458605i	$0.848349\pi$
$68$	−30.2747			−3.67134
$69$	3.10614			0.373935
$70$	−1.07266	+	1.85790i	−0.128207	+	0.222061i
$71$	5.98771	+	10.3710i	0.710611	+	1.23081i	0.964628	+	0.263615i	$0.0849147\pi$
$71$	5.98771	+	10.3710i	0.710611	+	1.23081i	−0.254017	+	0.967200i	$0.581752\pi$
$72$	4.36665	−	7.56325i	0.514614	−	0.891338i
$73$	−4.25389	−	7.36795i	−0.497880	−	0.862354i	0.502117	−	0.864800i	$-0.332555\pi$
$73$	−4.25389	−	7.36795i	−0.497880	−	0.862354i	−0.999997	+	0.00244612i	$0.999221\pi$
$74$	10.3522	+	17.9306i	1.20342	+	2.08439i
$75$	−1.00000			−0.115470
$76$	−22.7988	+	1.68395i	−2.61521	+	0.193162i
$77$	−2.06614			−0.235458
$78$	3.76425	+	6.51987i	0.426217	+	0.738230i
$79$	−3.24092	−	5.61344i	−0.364632	−	0.631561i	0.624085	−	0.781356i	$-0.285472\pi$
$79$	−3.24092	−	5.61344i	−0.364632	−	0.631561i	−0.988717	+	0.149795i	$0.952139\pi$
$80$	−6.50857	+	11.2732i	−0.727680	+	1.26038i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	9.93625	−	17.2101i	1.09728	−	1.90054i
$83$	−2.79520			−0.306813			−0.153407	−	0.988163i	$-0.549024\pi$
$83$	−2.79520			−0.306813			−0.153407	+	0.988163i	$0.549024\pi$
$84$	4.18023			0.456100
$85$	2.88624	−	4.99911i	0.313056	−	0.542229i
$86$	−3.76425	+	6.51987i	−0.405909	+	0.703056i
$87$	4.79093			0.513642
$88$	−22.6389			−2.41331
$89$	6.67930	−	11.5689i	0.708005	−	1.22630i	−0.257591	−	0.966254i	$-0.582929\pi$
$89$	6.67930	−	11.5689i	0.708005	−	1.22630i	0.965596	−	0.260046i	$-0.0837379\pi$
$90$	1.34580	+	2.33099i	0.141859	+	0.245707i
$91$	−1.11468	+	1.93069i	−0.116851	+	0.202391i
$92$	8.14532	+	14.1081i	0.849208	+	1.47087i
$93$	−4.74466	−	8.21799i	−0.491998	−	0.852166i
$94$	29.8155			3.07524
$95$	1.89547	−	3.92520i	0.194471	−	0.402717i
$96$	17.5702			1.79325
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	0.810782	−	0.585348i	$-0.199042\pi$
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	−0.912317	+	0.409484i	$0.865709\pi$
$98$	−8.56561	−	14.8361i	−0.865257	−	1.49867i
$99$	−1.29612	+	2.24495i	−0.130265	+	0.225626i
$100$	−2.62233	−	4.54201i	−0.262233	−	0.454201i
$101$	−6.54078	+	11.3290i	−0.650832	+	1.12727i	0.332089	+	0.943248i	$0.392247\pi$
$101$	−6.54078	+	11.3290i	−0.650832	+	1.12727i	−0.982921	+	0.184026i	$0.941087\pi$
$102$	−15.5371			−1.53841
$103$	14.4586			1.42465			0.712326	−	0.701849i	$-0.247642\pi$
$103$	14.4586			1.42465			0.712326	+	0.701849i	$0.247642\pi$
$104$	−12.2137	+	21.1548i	−1.19765	+	2.07439i
$105$	−0.398522	+	0.690261i	−0.0388918	+	0.0673625i
$106$	23.8976			2.32114
$107$	3.20480			0.309819			0.154910	−	0.987929i	$-0.450491\pi$
$107$	3.20480			0.309819			0.154910	+	0.987929i	$0.450491\pi$
$108$	2.62233	−	4.54201i	0.252334	−	0.437055i
$109$	−3.89921	−	6.75362i	−0.373476	−	0.646880i	0.616622	−	0.787260i	$-0.288501\pi$
$109$	−3.89921	−	6.75362i	−0.373476	−	0.646880i	−0.990098	+	0.140380i	$0.955168\pi$
$110$	3.48863	−	6.04249i	0.332628	−	0.576129i
$111$	3.84614	+	6.66170i	0.365059	+	0.632301i
$112$	5.18761	+	8.98521i	0.490184	+	0.849023i
$113$	8.26042			0.777075			0.388538	−	0.921433i	$-0.372980\pi$
$113$	8.26042			0.777075			0.388538	+	0.921433i	$0.372980\pi$
$114$	−11.7005	+	0.864212i	−1.09585	+	0.0809409i
$115$	−3.10614			−0.289649
$116$	12.5634	+	21.7605i	1.16648	+	2.02041i
$117$	1.39852	+	2.42231i	0.129293	+	0.223943i
$118$	1.45373	−	2.51793i	0.133826	−	0.231794i
$119$	−2.30046	−	3.98451i	−0.210883	−	0.365259i
$120$	−4.36665	+	7.56325i	−0.398619	+	0.690428i
$121$	−4.28025			−0.389114
$122$	−10.9608			−0.992346
$123$	3.69159	−	6.39402i	0.332860	−	0.576530i
$124$	24.8841	−	43.1006i	2.23466	−	3.87054i
$125$	1.00000			0.0894427
$126$	2.14532			0.191120
$127$	−2.24466	+	3.88786i	−0.199181	+	0.344992i	−0.948263	−	0.317485i	$-0.897162\pi$
$127$	−2.24466	+	3.88786i	−0.199181	+	0.344992i	0.749082	+	0.662477i	$0.230495\pi$
$128$	11.0381	+	19.1185i	0.975637	+	1.68985i
$129$	−1.39852	+	2.42231i	−0.123133	+	0.213273i
$130$	−3.76425	−	6.51987i	−0.330146	−	0.571830i
$131$	−9.73940	−	16.8691i	−0.850936	−	1.47386i	−0.880365	−	0.474297i	$-0.842702\pi$
$131$	−9.73940	−	16.8691i	−0.850936	−	1.47386i	0.0294291	−	0.999567i	$-0.490631\pi$
$132$	−13.5955			−1.18333
$133$	−1.95403	−	2.87265i	−0.169436	−	0.249090i
$134$	−37.0785			−3.20309
$135$	0.500000	+	0.866025i	0.0430331	+	0.0745356i
$136$	−25.2064	−	43.6587i	−2.16143	−	3.74370i
$137$	−2.11376	+	3.66115i	−0.180591	+	0.312793i	−0.942082	−	0.335383i	$-0.891134\pi$
$137$	−2.11376	+	3.66115i	−0.180591	+	0.312793i	0.761491	+	0.648176i	$0.224468\pi$
$138$	4.18023	+	7.24036i	0.355844	+	0.616341i
$139$	−3.89547	+	6.74715i	−0.330409	+	0.572285i	−0.982592	−	0.185776i	$-0.940520\pi$
$139$	−3.89547	+	6.74715i	−0.330409	+	0.572285i	0.652183	+	0.758062i	$0.273853\pi$
$140$	−4.18023			−0.353294
$141$	11.0773			0.932877
$142$	−16.1165	+	27.9146i	−1.35246	+	2.34254i
$143$	3.62532	−	6.27923i	0.303164	−	0.525096i
$144$	13.0171			1.08476
$145$	−4.79093			−0.397865
$146$	11.4497	−	19.8315i	0.947586	−	1.64127i
$147$	−3.18236	−	5.51201i	−0.262477	−	0.454623i
$148$	−20.1717	+	34.9384i	−1.65810	+	2.87192i
$149$	0.0453536	+	0.0785548i	0.00371552	+	0.00643546i	0.867877	−	0.496779i	$-0.165484\pi$
$149$	0.0453536	+	0.0785548i	0.00371552	+	0.00643546i	−0.864162	+	0.503214i	$0.832151\pi$
$150$	−1.34580	−	2.33099i	−0.109884	−	0.190324i
$151$	−4.49727			−0.365983			−0.182991	−	0.983115i	$-0.558578\pi$
$151$	−4.49727			−0.365983			−0.182991	+	0.983115i	$0.558578\pi$
$152$	−21.4105	−	31.4759i	−1.73662	−	2.55303i
$153$	−5.77247			−0.466677
$154$	−2.78060	−	4.81613i	−0.224067	−	0.388095i
$155$	4.74466	+	8.21799i	0.381100	+	0.660085i
$156$	−7.33477	+	12.7042i	−0.587252	+	1.01715i
$157$	−8.82341	−	15.2826i	−0.704184	−	1.21968i	−0.966985	−	0.254833i	$-0.917979\pi$
$157$	−8.82341	−	15.2826i	−0.704184	−	1.21968i	0.262801	−	0.964850i	$-0.415354\pi$
$158$	8.72323	−	15.1091i	0.693983	−	1.20201i
$159$	8.87861			0.704120
$160$	−17.5702			−1.38905
$161$	−1.23786	+	2.14404i	−0.0975574	+	0.168974i
$162$	1.34580	−	2.33099i	0.105736	−	0.183140i
$163$	4.25858			0.333558			0.166779	−	0.985994i	$-0.446663\pi$
$163$	4.25858			0.333558			0.166779	+	0.985994i	$0.446663\pi$
$164$	38.7223			3.02370
$165$	1.29612	−	2.24495i	0.100903	−	0.174769i
$166$	−3.76177	−	6.51558i	−0.291970	−	0.505707i
$167$	−1.98985	+	3.44652i	−0.153979	+	0.266700i	−0.932687	−	0.360687i	$-0.882542\pi$
$167$	−1.98985	+	3.44652i	−0.153979	+	0.266700i	0.778708	+	0.627387i	$0.215876\pi$
$168$	3.48041	+	6.02825i	0.268520	+	0.465089i
$169$	2.58827	+	4.48302i	0.199098	+	0.344848i
$170$	15.5371			1.19164
$171$	−4.34706	+	0.321078i	−0.332428	+	0.0245535i
$172$	−14.6695			−1.11854
$173$	−5.58614	−	9.67547i	−0.424706	−	0.735613i	0.571687	−	0.820472i	$-0.306289\pi$
$173$	−5.58614	−	9.67547i	−0.424706	−	0.735613i	−0.996393	+	0.0848594i	$0.972956\pi$
$174$	6.44762	+	11.1676i	0.488792	+	0.846613i
$175$	0.398522	−	0.690261i	0.0301254	−	0.0521788i
$176$	−16.8718	−	29.2228i	−1.27176	−	2.20275i
$177$	0.540099	−	0.935479i	0.0405963	−	0.0703149i
$178$	35.9559			2.69501
$179$	9.63565			0.720203			0.360101	−	0.932913i	$-0.382742\pi$
$179$	9.63565			0.720203			0.360101	+	0.932913i	$0.382742\pi$
$180$	−2.62233	+	4.54201i	−0.195457	+	0.338541i
$181$	−2.05001	+	3.55073i	−0.152376	+	0.263923i	−0.932101	−	0.362200i	$-0.882026\pi$
$181$	−2.05001	+	3.55073i	−0.152376	+	0.263923i	0.779724	+	0.626123i	$0.215359\pi$
$182$	−6.00055			−0.444790
$183$	−4.07225			−0.301029
$184$	−13.5634	+	23.4925i	−0.999908	+	1.73189i
$185$	−3.84614	−	6.66170i	−0.282774	−	0.489778i
$186$	12.7707	−	22.1195i	0.936392	−	1.62188i
$187$	7.48184	+	12.9589i	0.547126	+	0.947651i
$188$	29.0483	+	50.3132i	2.11857	+	3.66946i
$189$	0.797044			0.0579764
$190$	11.7005	−	0.864212i	0.848843	−	0.0626965i
$191$	−22.6143			−1.63631			−0.818156	−	0.574996i	$-0.805004\pi$
$191$	−22.6143			−1.63631			−0.818156	+	0.574996i	$0.805004\pi$
$192$	10.6288	+	18.4096i	0.767065	+	1.32860i
$193$	−8.30170	−	14.3790i	−0.597570	−	1.03502i	−0.993179	−	0.116602i	$-0.962800\pi$
$193$	−8.30170	−	14.3790i	−0.597570	−	1.03502i	0.395609	−	0.918419i	$-0.370534\pi$
$194$	2.69159	−	4.66197i	0.193245	−	0.334710i
$195$	−1.39852	−	2.42231i	−0.100150	−	0.173465i
$196$	16.6904	−	28.9086i	1.19217	−	2.06490i
$197$	−17.6450			−1.25715			−0.628576	−	0.777748i	$-0.716362\pi$
$197$	−17.6450			−1.25715			−0.628576	+	0.777748i	$0.716362\pi$
$198$	−6.97727			−0.495853
$199$	−9.53155	+	16.5091i	−0.675674	+	1.17030i	0.300598	+	0.953751i	$0.402814\pi$
$199$	−9.53155	+	16.5091i	−0.675674	+	1.17030i	−0.976271	+	0.216550i	$0.930519\pi$
$200$	4.36665	−	7.56325i	0.308769	−	0.534803i
$201$	−13.7757			−0.971662
$202$	−35.2102			−2.47738
$203$	−1.90929	+	3.30699i	−0.134006	+	0.232105i
$204$	−15.1373	−	26.2186i	−1.05982	−	1.83567i
$205$	−3.69159	+	6.39402i	−0.257832	+	0.446578i
$206$	19.4584	+	33.7029i	1.35573	+	2.34819i
$207$	1.55307	+	2.68999i	0.107946	+	0.186968i
$208$	−36.4095			−2.52454
$209$	6.35513	+	9.34278i	0.439594	+	0.646254i
$210$	−2.14532			−0.148041
$211$	7.02170	+	12.1619i	0.483394	+	0.837263i	0.999818	−	0.0190700i	$-0.00607055\pi$
$211$	7.02170	+	12.1619i	0.483394	+	0.837263i	−0.516424	+	0.856333i	$0.672737\pi$
$212$	23.2826	+	40.3267i	1.59906	+	2.76965i
$213$	−5.98771	+	10.3710i	−0.410271	+	0.710611i
$214$	4.31300	+	7.47033i	0.294831	+	0.510662i
$215$	1.39852	−	2.42231i	0.0953784	−	0.165200i
$216$	8.73329			0.594225
$217$	7.56341			0.513437
$218$	10.4951	−	18.1780i	0.710816	−	1.23117i
$219$	4.25389	−	7.36795i	0.287451	−	0.497880i
$220$	13.5955			0.916605
$221$	16.1459			1.08609
$222$	−10.3522	+	17.9306i	−0.694796	+	1.20342i
$223$	12.0926	+	20.9451i	0.809783	+	1.40259i	0.913014	+	0.407928i	$0.133748\pi$
$223$	12.0926	+	20.9451i	0.809783	+	1.40259i	−0.103231	+	0.994657i	$0.532918\pi$
$224$	−7.00211	+	12.1280i	−0.467848	+	0.810337i
$225$	−0.500000	−	0.866025i	−0.0333333	−	0.0577350i
$226$	11.1168	+	19.2549i	0.739481	+	1.28082i
$227$	3.38455			0.224640			0.112320	−	0.993672i	$-0.464172\pi$
$227$	3.38455			0.224640			0.112320	+	0.993672i	$0.464172\pi$
$228$	−12.8578	−	18.9024i	−0.851526	−	1.25184i
$229$	−25.9664			−1.71591			−0.857955	−	0.513726i	$-0.828265\pi$
$229$	−25.9664			−1.71591			−0.857955	+	0.513726i	$0.828265\pi$
$230$	−4.18023	−	7.24036i	−0.275636	−	0.477415i
$231$	−1.03307	−	1.78933i	−0.0679709	−	0.117729i
$232$	−20.9203	+	36.2350i	−1.37349	+	2.37895i
$233$	3.35911	+	5.81814i	0.220062	+	0.381159i	0.954827	−	0.297163i	$-0.0960406\pi$
$233$	3.35911	+	5.81814i	0.220062	+	0.381159i	−0.734764	+	0.678323i	$0.762707\pi$
$234$	−3.76425	+	6.51987i	−0.246077	+	0.426217i
$235$	−11.0773			−0.722603
$236$	5.66527			0.368778
$237$	3.24092	−	5.61344i	0.210520	−	0.364632i
$238$	6.19189	−	10.7247i	0.401361	−	0.695177i
$239$	25.7818			1.66769			0.833843	−	0.552002i	$-0.186136\pi$
$239$	25.7818			1.66769			0.833843	+	0.552002i	$0.186136\pi$
$240$	−13.0171			−0.840252
$241$	3.88929	−	6.73645i	0.250531	−	0.433933i	−0.713141	−	0.701021i	$-0.752728\pi$
$241$	3.88929	−	6.73645i	0.250531	−	0.433933i	0.963672	+	0.267088i	$0.0860614\pi$
$242$	−5.76034	−	9.97721i	−0.370289	−	0.641359i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−10.6788	−	18.4962i	−0.683638	−	1.18410i
$245$	3.18236	+	5.51201i	0.203314	+	0.352149i
$246$	19.8725			1.26702
$247$	12.1589	−	0.898071i	0.773653	−	0.0571429i
$248$	82.8730			5.26244
$249$	−1.39760	−	2.42072i	−0.0885694	−	0.153407i
$250$	1.34580	+	2.33099i	0.0851156	+	0.147424i
$251$	−5.43717	+	9.41745i	−0.343191	+	0.594424i	−0.985023	−	0.172421i	$-0.944841\pi$
$251$	−5.43717	+	9.41745i	−0.343191	+	0.594424i	0.641832	+	0.766845i	$0.278175\pi$
$252$	2.09011	+	3.62018i	0.131665	+	0.228050i
$253$	4.02594	−	6.97313i	0.253109	−	0.438397i
$254$	−12.0834			−0.758180
$255$	5.77247			0.361486
$256$	−8.45244	+	14.6401i	−0.528278	+	0.915004i
$257$	−5.62716	+	9.74652i	−0.351012	+	0.607971i	−0.986427	−	0.164200i	$-0.947496\pi$
$257$	−5.62716	+	9.74652i	−0.351012	+	0.607971i	0.635415	+	0.772171i	$0.280829\pi$
$258$	−7.52850			−0.468704
$259$	−6.13108			−0.380967
$260$	7.33477	−	12.7042i	0.454883	−	0.787881i
$261$	2.39547	+	4.14907i	0.148276	+	0.256821i
$262$	26.2145	−	45.4048i	1.61954	−	2.80512i
$263$	6.66936	+	11.5517i	0.411250	+	0.712306i	0.995027	−	0.0996082i	$-0.0317589\pi$
$263$	6.66936	+	11.5517i	0.411250	+	0.712306i	−0.583777	+	0.811914i	$0.698426\pi$
$264$	−11.3194	−	19.6058i	−0.696663	−	1.20666i
$265$	−8.87861			−0.545409
$266$	4.06638	−	8.42080i	0.249325	−	0.516312i
$267$	13.3586			0.817534
$268$	−36.1244	−	62.5693i	−2.20665	−	3.82203i
$269$	3.53399	+	6.12105i	0.215471	+	0.373207i	0.953418	−	0.301652i	$-0.0975380\pi$
$269$	3.53399	+	6.12105i	0.215471	+	0.373207i	−0.737947	+	0.674859i	$0.764205\pi$
$270$	−1.34580	+	2.33099i	−0.0819025	+	0.141859i
$271$	11.5289	+	19.9686i	0.700330	+	1.21301i	0.968351	+	0.249594i	$0.0802971\pi$
$271$	11.5289	+	19.9686i	0.700330	+	1.21301i	−0.268021	+	0.963413i	$0.586370\pi$
$272$	37.5705	−	65.0741i	2.27805	−	3.94569i
$273$	−2.22937			−0.134927
$274$	−11.3788			−0.687417
$275$	−1.29612	+	2.24495i	−0.0781592	+	0.135376i
$276$	−8.14532	+	14.1081i	−0.490290	+	0.849208i
$277$	18.8461			1.13235			0.566176	−	0.824284i	$-0.308422\pi$
$277$	18.8461			1.13235			0.566176	+	0.824284i	$0.308422\pi$
$278$	−20.9700			−1.25770
$279$	4.74466	−	8.21799i	0.284055	−	0.491998i
$280$	−3.48041	−	6.02825i	−0.207994	−	0.360257i
$281$	−8.32486	+	14.4191i	−0.496619	+	0.860170i	−0.999992	−	0.00389922i	$-0.998759\pi$
$281$	−8.32486	+	14.4191i	−0.496619	+	0.860170i	0.503373	+	0.864069i	$0.332092\pi$
$282$	14.9078	+	25.8210i	0.887745	+	1.53762i
$283$	−6.52597	−	11.3033i	−0.387929	−	0.671912i	0.604242	−	0.796801i	$-0.293476\pi$
$283$	−6.52597	−	11.3033i	−0.387929	−	0.671912i	−0.992171	+	0.124888i	$0.960143\pi$
$284$	−62.8070			−3.72691
$285$	4.34706	−	0.321078i	0.257497	−	0.0190190i
$286$	19.5157			1.15399
$287$	2.94236	+	5.09632i	0.173682	+	0.300826i
$288$	8.78510	+	15.2162i	0.517667	+	0.896626i
$289$	−8.16072	+	14.1348i	−0.480042	+	0.831458i
$290$	−6.44762	−	11.1676i	−0.378617	−	0.655784i
$291$	1.00000	−	1.73205i	0.0586210	−	0.101535i
$292$	44.6204			2.61121
$293$	−3.07225			−0.179483			−0.0897413	−	0.995965i	$-0.528604\pi$
$293$	−3.07225			−0.179483			−0.0897413	+	0.995965i	$0.528604\pi$
$294$	8.56561	−	14.8361i	0.499557	−	0.865257i
$295$	−0.540099	+	0.935479i	−0.0314458	+	0.0544657i
$296$	−67.1789			−3.90469
$297$	−2.59225			−0.150417
$298$	−0.122073	+	0.211437i	−0.00707152	+	0.0122482i
$299$	−4.34400	−	7.52403i	−0.251220	−	0.435126i
$300$	2.62233	−	4.54201i	0.151400	−	0.262233i
$301$	−1.11468	−	1.93069i	−0.0642493	−	0.111283i
$302$	−6.05240	−	10.4831i	−0.348277	−	0.603233i
$303$	−13.0816			−0.751516
$304$	24.6735	−	51.0949i	1.41512	−	2.93049i
$305$	4.07225			0.233176
$306$	−7.76857	−	13.4556i	−0.444099	−	0.769203i
$307$	−11.7308	−	20.3183i	−0.669510	−	1.15963i	−0.978041	−	0.208412i	$-0.933171\pi$
$307$	−11.7308	−	20.3183i	−0.669510	−	1.15963i	0.308531	−	0.951214i	$-0.400163\pi$
$308$	5.41809	−	9.38441i	0.308724	−	0.534726i
$309$	7.22932	+	12.5215i	0.411262	+	0.712326i
$310$	−12.7707	+	22.1195i	−0.725326	+	1.25630i
$311$	−5.59041			−0.317003			−0.158501	−	0.987359i	$-0.550666\pi$
$311$	−5.59041			−0.317003			−0.158501	+	0.987359i	$0.550666\pi$
$312$	−24.4274			−1.38293
$313$	14.2140	−	24.6193i	0.803421	−	1.39157i	−0.113930	−	0.993489i	$-0.536344\pi$
$313$	14.2140	−	24.6193i	0.803421	−	1.39157i	0.917352	−	0.398078i	$-0.130323\pi$
$314$	23.7490	−	41.1345i	1.34023	−	2.32135i
$315$	−0.797044			−0.0449084
$316$	33.9950			1.91237
$317$	5.25481	−	9.10160i	0.295140	−	0.511197i	−0.679878	−	0.733325i	$-0.737967\pi$
$317$	5.25481	−	9.10160i	0.295140	−	0.511197i	0.975017	+	0.222129i	$0.0713005\pi$
$318$	11.9488	+	20.6959i	0.670055	+	1.16057i
$319$	6.20964	−	10.7554i	0.347673	−	0.602188i
$320$	−10.6288	−	18.4096i	−0.594166	−	1.02913i
$321$	1.60240	+	2.77544i	0.0894371	+	0.154910i
$322$	−6.66365			−0.371351
$323$	−10.9415	+	22.6581i	−0.608803	+	1.26073i
$324$	5.24466			0.291370
$325$	1.39852	+	2.42231i	0.0775760	+	0.134366i
$326$	5.73118	+	9.92670i	0.317421	+	0.549789i
$327$	3.89921	−	6.75362i	0.215627	−	0.373476i
$328$	32.2397	+	55.8409i	1.78014	+	3.08330i
$329$	−4.41455	+	7.64622i	−0.243382	+	0.421550i
$330$	6.97727			0.384086
$331$	−6.39618			−0.351566			−0.175783	−	0.984429i	$-0.556246\pi$
$331$	−6.39618			−0.351566			−0.175783	+	0.984429i	$0.556246\pi$
$332$	7.32995	−	12.6958i	0.402283	−	0.696775i
$333$	−3.84614	+	6.66170i	−0.210767	+	0.365059i
$334$	−10.7117			−0.586119
$335$	13.7757			0.752646
$336$	−5.18761	+	8.98521i	−0.283008	+	0.490184i
$337$	9.13861	+	15.8285i	0.497812	+	0.862235i	0.999997	−	0.00252482i	$-0.000803675\pi$
$337$	9.13861	+	15.8285i	0.497812	+	0.862235i	−0.502185	+	0.864760i	$0.667470\pi$
$338$	−6.96657	+	12.0664i	−0.378931	+	0.656328i
$339$	4.13021	+	7.15374i	0.224322	+	0.388538i
$340$	15.1373	+	26.2186i	0.820937	+	1.42190i
$341$	−24.5987			−1.33209
$342$	−6.59868	−	9.70082i	−0.356816	−	0.524560i
$343$	10.6523			0.575169
$344$	−12.2137	−	21.1548i	−0.658519	−	1.14059i
$345$	−1.55307	−	2.68999i	−0.0836144	−	0.144824i
$346$	15.0356	−	26.0424i	0.808318	−	1.40005i
$347$	15.8293	+	27.4171i	0.849760	+	1.47183i	0.881422	+	0.472329i	$0.156587\pi$
$347$	15.8293	+	27.4171i	0.849760	+	1.47183i	−0.0316618	+	0.999499i	$0.510080\pi$
$348$	−12.5634	+	21.7605i	−0.673469	+	1.16648i
$349$	12.0802			0.646638			0.323319	−	0.946290i	$-0.395201\pi$
$349$	12.0802			0.646638			0.323319	+	0.946290i	$0.395201\pi$
$350$	2.14532			0.114672
$351$	−1.39852	+	2.42231i	−0.0746476	+	0.129293i
$352$	22.7732	−	39.4443i	1.21381	−	2.10239i
$353$	3.63101			0.193259			0.0966296	−	0.995320i	$-0.469194\pi$
$353$	3.63101			0.193259			0.0966296	+	0.995320i	$0.469194\pi$
$354$	2.90745			0.154529
$355$	5.98771	−	10.3710i	0.317795	−	0.550437i
$356$	35.0307	+	60.6749i	1.85662	+	3.21576i
$357$	2.30046	−	3.98451i	0.121753	−	0.210883i
$358$	12.9676	+	22.4606i	0.685360	+	1.18708i
$359$	2.95898	+	5.12510i	0.156169	+	0.270493i	0.933484	−	0.358619i	$-0.116752\pi$
$359$	2.95898	+	5.12510i	0.156169	+	0.270493i	−0.777315	+	0.629112i	$0.783419\pi$
$360$	−8.73329			−0.460285
$361$	−6.97940	+	17.6717i	−0.367337	+	0.930088i
$362$	−11.0356			−0.580018
$363$	−2.14013	−	3.70681i	−0.112327	−	0.194557i
$364$	−5.84614	−	10.1258i	−0.306421	−	0.530736i
$365$	−4.25389	+	7.36795i	−0.222659	+	0.385656i
$366$	−5.48041	−	9.49235i	−0.286466	−	0.496173i
$367$	−3.09080	+	5.35342i	−0.161338	+	0.279446i	−0.935349	−	0.353727i	$-0.884914\pi$
$367$	−3.09080	+	5.35342i	−0.161338	+	0.279446i	0.774011	+	0.633173i	$0.218248\pi$
$368$	−40.4330			−2.10772
$369$	7.38318			0.384353
$370$	10.3522	−	17.9306i	0.538187	−	0.932167i
$371$	−3.53832	+	6.12855i	−0.183701	+	0.318179i
$372$	49.7682			2.58036
$373$	−7.24346			−0.375052			−0.187526	−	0.982260i	$-0.560047\pi$
$373$	−7.24346			−0.375052			−0.187526	+	0.982260i	$0.560047\pi$
$374$	−20.1380	+	34.8801i	−1.04131	+	1.80361i
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$	−48.3706	+	83.7804i	−2.49453	+	4.32064i
$377$	−6.70023	−	11.6051i	−0.345079	−	0.597695i
$378$	1.07266	+	1.85790i	0.0551716	+	0.0955600i
$379$	15.4483			0.793524			0.396762	−	0.917922i	$-0.370134\pi$
$379$	15.4483			0.793524			0.396762	+	0.917922i	$0.370134\pi$
$380$	12.8578	+	18.9024i	0.659589	+	0.969672i
$381$	−4.48932			−0.229995
$382$	−30.4342	−	52.7136i	−1.55715	−	2.69706i
$383$	9.75805	+	16.9014i	0.498613	+	0.863623i	0.999999	−	0.00160064i	$-0.000509500\pi$
$383$	9.75805	+	16.9014i	0.498613	+	0.863623i	−0.501386	+	0.865224i	$0.667176\pi$
$384$	−11.0381	+	19.1185i	−0.563284	+	0.975637i
$385$	1.03307	+	1.78933i	0.0526500	+	0.0911925i
$386$	22.3448	−	38.7023i	1.13732	−	1.96990i
$387$	−2.79704			−0.142182
$388$	10.4893			0.532514
$389$	−7.12876	+	12.3474i	−0.361443	+	0.626037i	−0.988198	−	0.153179i	$-0.951049\pi$
$389$	−7.12876	+	12.3474i	−0.361443	+	0.626037i	0.626756	+	0.779216i	$0.284382\pi$
$390$	3.76425	−	6.51987i	0.190610	−	0.330146i
$391$	17.9301			0.906764
$392$	55.5850			2.80747
$393$	9.73940	−	16.8691i	0.491288	−	0.850936i
$394$	−23.7465	−	41.1302i	−1.19633	−	2.07211i
$395$	−3.24092	+	5.61344i	−0.163068	+	0.282443i
$396$	−6.79773	−	11.7740i	−0.341599	−	0.591666i
$397$	−13.9540	−	24.1690i	−0.700330	−	1.21301i	−0.968351	−	0.249594i	$-0.919703\pi$
$397$	−13.9540	−	24.1690i	−0.700330	−	1.21301i	0.268021	−	0.963413i	$-0.413630\pi$
$398$	−51.3101			−2.57194
$399$	1.51077	−	3.12856i	0.0756331	−	0.156624i
$400$	13.0171			0.650857
$401$	−9.86205	−	17.0816i	−0.492487	−	0.853013i	0.507475	−	0.861666i	$-0.330579\pi$
$401$	−9.86205	−	17.0816i	−0.492487	−	0.853013i	−0.999963	+	0.00865308i	$0.997246\pi$
$402$	−18.5392	−	32.1109i	−0.924654	−	1.60155i
$403$	−13.2710	+	22.9861i	−0.661077	+	1.14502i
$404$	−34.3042	−	59.4166i	−1.70670	−	2.95609i
$405$	−0.500000	+	0.866025i	−0.0248452	+	0.0430331i
$406$	−10.2781			−0.510092
$407$	19.9403			0.988403
$408$	25.2064	−	43.6587i	1.24790	−	2.16143i
$409$	−9.61555	+	16.6546i	−0.475459	+	0.823518i	−0.999605	−	0.0281099i	$-0.991051\pi$
$409$	−9.61555	+	16.6546i	−0.475459	+	0.823518i	0.524146	+	0.851628i	$0.324385\pi$
$410$	−19.8725			−0.981433
$411$	−4.22753			−0.208529
$412$	−37.9153	+	65.6712i	−1.86795	+	3.23539i
$413$	0.430483	+	0.745618i	0.0211827	+	0.0366895i
$414$	−4.18023	+	7.24036i	−0.205447	+	0.355844i
$415$	1.39760	+	2.42072i	0.0686056	+	0.118828i
$416$	−24.5723	−	42.5605i	−1.20476	−	2.08670i
$417$	−7.79093			−0.381524
$418$	−13.2252	+	27.3872i	−0.646865	+	1.33955i
$419$	−4.45253			−0.217520			−0.108760	−	0.994068i	$-0.534688\pi$
$419$	−4.45253			−0.217520			−0.108760	+	0.994068i	$0.534688\pi$
$420$	−2.09011	−	3.62018i	−0.101987	−	0.176647i
$421$	−6.04467	−	10.4697i	−0.294599	−	0.510261i	0.680292	−	0.732941i	$-0.261853\pi$
$421$	−6.04467	−	10.4697i	−0.294599	−	0.510261i	−0.974892	+	0.222680i	$0.928519\pi$
$422$	−18.8995	+	32.7350i	−0.920016	+	1.59351i
$423$	5.53865	+	9.59322i	0.269298	+	0.466438i
$424$	−38.7698	+	67.1512i	−1.88283	+	3.26115i
$425$	−5.77247			−0.280006
$426$	−32.2329			−1.56169
$427$	1.62288	−	2.81091i	0.0785367	−	0.136030i
$428$	−8.40403	+	14.5562i	−0.406224	+	0.703601i
$429$	7.25063			0.350064
$430$	7.52850			0.363056
$431$	10.2716	−	17.7909i	0.494763	−	0.856955i	−0.505219	−	0.862991i	$-0.668588\pi$
$431$	10.2716	−	17.7909i	0.494763	−	0.856955i	0.999982	+	0.00603633i	$0.00192143\pi$
$432$	6.50857	+	11.2732i	0.313144	+	0.542381i
$433$	9.68673	−	16.7779i	0.465514	−	0.806294i	−0.533710	−	0.845667i	$-0.679203\pi$
$433$	9.68673	−	16.7779i	0.465514	−	0.806294i	0.999225	+	0.0393730i	$0.0125360\pi$
$434$	10.1788	+	17.6302i	0.488598	+	0.846276i
$435$	−2.39547	−	4.14907i	−0.114854	−	0.198933i
$436$	40.9000			1.95876
$437$	13.5026	−	0.997314i	0.645915	−	0.0477080i
$438$	22.8995			1.09418
$439$	−8.61579	−	14.9230i	−0.411209	−	0.712235i	0.583813	−	0.811888i	$-0.301560\pi$
$439$	−8.61579	−	14.9230i	−0.411209	−	0.712235i	−0.995022	+	0.0996528i	$0.968227\pi$
$440$	11.3194	+	19.6058i	0.539633	+	0.934671i
$441$	3.18236	−	5.51201i	0.151541	−	0.262477i
$442$	21.7290	+	37.6358i	1.03354	+	1.79015i
$443$	−8.32774	+	14.4241i	−0.395663	+	0.685308i	−0.993186	−	0.116544i	$-0.962818\pi$
$443$	−8.32774	+	14.4241i	−0.395663	+	0.685308i	0.597523	+	0.801852i	$0.296152\pi$
$444$	−40.3434			−1.91461
$445$	−13.3586			−0.633259
$446$	−32.5484	+	56.3755i	−1.54121	+	2.66946i
$447$	−0.0453536	+	0.0785548i	−0.00214515	+	0.00371552i
$448$	−16.9432			−0.800490
$449$	−18.4698			−0.871644			−0.435822	−	0.900033i	$-0.643542\pi$
$449$	−18.4698			−0.871644			−0.435822	+	0.900033i	$0.643542\pi$
$450$	1.34580	−	2.33099i	0.0634414	−	0.109884i
$451$	−9.56952	−	16.5749i	−0.450611	−	0.780481i
$452$	−21.6616	+	37.5189i	−1.01887	+	1.76474i
$453$	−2.24864	−	3.89475i	−0.105650	−	0.182991i
$454$	4.55491	+	7.88933i	0.213772	+	0.370265i
$455$	2.22937			0.104514
$456$	16.5537	−	34.2799i	0.775196	−	1.60531i
$457$	3.40669			0.159358			0.0796791	−	0.996821i	$-0.474610\pi$
$457$	3.40669			0.159358			0.0796791	+	0.996821i	$0.474610\pi$
$458$	−34.9455	−	60.5273i	−1.63289	−	2.82826i
$459$	−2.88624	−	4.99911i	−0.134718	−	0.233338i
$460$	8.14532	−	14.1081i	0.379777	−	0.657794i
$461$	−20.2028	−	34.9924i	−0.940940	−	1.62976i	−0.763682	−	0.645592i	$-0.776611\pi$
$461$	−20.2028	−	34.9924i	−0.940940	−	1.62976i	−0.177258	−	0.984164i	$-0.556723\pi$
$462$	2.78060	−	4.81613i	0.129365	−	0.224067i
$463$	−22.9724			−1.06762			−0.533809	−	0.845605i	$-0.679240\pi$
$463$	−22.9724			−1.06762			−0.533809	+	0.845605i	$0.679240\pi$
$464$	−62.3642			−2.89519
$465$	−4.74466	+	8.21799i	−0.220028	+	0.381100i
$466$	−9.04134	+	15.6601i	−0.418832	+	0.725438i
$467$	7.02174			0.324927			0.162464	−	0.986715i	$-0.448056\pi$
$467$	7.02174			0.324927			0.162464	+	0.986715i	$0.448056\pi$
$468$	−14.6695			−0.678100
$469$	5.48991	−	9.50881i	0.253501	−	0.439076i
$470$	−14.9078	−	25.8210i	−0.687644	−	1.19103i
$471$	8.82341	−	15.2826i	0.406561	−	0.704184i
$472$	4.71685	+	8.16982i	0.217110	+	0.376046i
$473$	3.62532	+	6.27923i	0.166692	+	0.288719i
$474$	17.4465			0.801342
$475$	−4.34706	+	0.321078i	−0.199457	+	0.0147321i
$476$	24.1302			1.10601
$477$	4.43931	+	7.68910i	0.203262	+	0.352060i
$478$	34.6970	+	60.0970i	1.58700	+	2.74877i
$479$	1.46058	−	2.52981i	0.0667358	−	0.115590i	−0.830727	−	0.556680i	$-0.812075\pi$
$479$	1.46058	−	2.52981i	0.0667358	−	0.115590i	0.897463	+	0.441090i	$0.145408\pi$
$480$	−8.78510	−	15.2162i	−0.400983	−	0.694523i
$481$	10.7578	−	18.6331i	0.490514	−	0.849595i
$482$	20.9368			0.953643
$483$	−2.47573			−0.112650
$484$	11.2242	−	19.4409i	0.510192	−	0.883679i
$485$	−1.00000	+	1.73205i	−0.0454077	+	0.0786484i
$486$	2.69159			0.122093
$487$	19.2038			0.870207			0.435104	−	0.900380i	$-0.356712\pi$
$487$	19.2038			0.870207			0.435104	+	0.900380i	$0.356712\pi$
$488$	17.7821	−	30.7994i	0.804956	−	1.39423i
$489$	2.12929	+	3.68804i	0.0962899	+	0.166779i
$490$	−8.56561	+	14.8361i	−0.386955	+	0.670225i
$491$	−5.21845	−	9.03862i	−0.235505	−	0.407907i	0.723914	−	0.689890i	$-0.242341\pi$
$491$	−5.21845	−	9.03862i	−0.235505	−	0.407907i	−0.959419	+	0.281983i	$0.909008\pi$
$492$	19.3611	+	33.5345i	0.872867	+	1.51185i
$493$	27.6555			1.24554
$494$	18.4568	+	27.1336i	0.830410	+	1.22080i
$495$	2.59225			0.116513
$496$	61.7619	+	106.975i	2.77319	+	4.80330i
$497$	−4.77247	−	8.26617i	−0.214075	−	0.370788i
$498$	3.76177	−	6.51558i	0.168569	−	0.291970i
$499$	−13.0850	−	22.6639i	−0.585766	−	1.01458i	−0.994780	−	0.102048i	$-0.967461\pi$
$499$	−13.0850	−	22.6639i	−0.585766	−	1.01458i	0.409014	−	0.912528i	$-0.365873\pi$
$500$	−2.62233	+	4.54201i	−0.117274	+	0.203125i
$501$	−3.97970			−0.177800
$502$	−29.2693			−1.30635
$503$	−2.67547	+	4.63405i	−0.119293	+	0.206622i	−0.919488	−	0.393119i	$-0.871396\pi$
$503$	−2.67547	+	4.63405i	−0.119293	+	0.206622i	0.800195	+	0.599740i	$0.204730\pi$
$504$	−3.48041	+	6.02825i	−0.155030	+	0.268520i
$505$	13.0816			0.582122
$506$	21.6724			0.963454
$507$	−2.58827	+	4.48302i	−0.114949	+	0.199098i
$508$	−11.7725	−	20.3905i	−0.522319	−	0.904683i
$509$	−4.89455	+	8.47760i	−0.216947	+	0.375763i	−0.953873	−	0.300210i	$-0.902943\pi$
$509$	−4.89455	+	8.47760i	−0.216947	+	0.375763i	0.736926	+	0.675973i	$0.236277\pi$
$510$	7.76857	+	13.4556i	0.343998	+	0.595822i
$511$	3.39054	+	5.87258i	0.149989	+	0.259788i
$512$	−1.34875			−0.0596067
$513$	−2.45159	−	3.60412i	−0.108240	−	0.159126i
$514$	−30.2920			−1.33612
$515$	−7.22932	−	12.5215i	−0.318562	−	0.551765i
$516$	−7.33477	−	12.7042i	−0.322895	−	0.559271i
$517$	14.3575	−	24.8680i	0.631444	−	1.09369i
$518$	−8.25118	−	14.2915i	−0.362536	−	0.627931i
$519$	5.58614	−	9.67547i	0.245204	−	0.424706i
$520$	24.4274			1.07121
$521$	26.4315			1.15799			0.578993	−	0.815333i	$-0.303446\pi$
$521$	26.4315			1.15799			0.578993	+	0.815333i	$0.303446\pi$
$522$	−6.44762	+	11.1676i	−0.282204	+	0.488792i
$523$	−14.3312	+	24.8223i	−0.626659	+	1.08541i	0.361559	+	0.932349i	$0.382245\pi$
$523$	−14.3312	+	24.8223i	−0.626659	+	1.08541i	−0.988218	+	0.153056i	$0.951089\pi$
$524$	102.160			4.46287
$525$	0.797044			0.0347859
$526$	−17.9512	+	31.0924i	−0.782709	+	1.35569i
$527$	−27.3884	−	47.4381i	−1.19306	−	2.06644i
$528$	16.8718	−	29.2228i	0.734252	−	1.27176i
$529$	6.67595	+	11.5631i	0.290259	+	0.502743i
$530$	−11.9488	−	20.6959i	−0.519022	−	0.898973i
$531$	1.08020			0.0468766
$532$	18.1717	−	1.34218i	0.787842	−	0.0581909i
$533$	−20.6511			−0.894498
$534$	17.9780	+	31.1387i	0.777982	+	1.34750i
$535$	−1.60240	−	2.77544i	−0.0692777	−	0.119993i
$536$	60.1535	−	104.189i	2.59824	−	4.50028i
$537$	4.81783	+	8.34472i	0.207905	+	0.360101i
$538$	−9.51205	+	16.4754i	−0.410094	+	0.710303i
$539$	−16.4989			−0.710659
$540$	−5.24466			−0.225694
$541$	12.0973	−	20.9531i	0.520103	−	0.900846i	−0.479623	−	0.877474i	$-0.659227\pi$
$541$	12.0973	−	20.9531i	0.520103	−	0.900846i	0.999727	−	0.0233711i	$-0.00743993\pi$
$542$	−31.0310	+	53.7473i	−1.33290	+	2.30865i
$543$	−4.10003			−0.175949
$544$	101.424			4.34850
$545$	−3.89921	+	6.75362i	−0.167024	+	0.289293i
$546$	−3.00027	−	5.19662i	−0.128400	−	0.222395i
$547$	−15.4959	+	26.8396i	−0.662555	+	1.14758i	0.317387	+	0.948296i	$0.397195\pi$
$547$	−15.4959	+	26.8396i	−0.662555	+	1.14758i	−0.979942	+	0.199283i	$0.936139\pi$
$548$	−11.0860	−	19.2015i	−0.473569	−	0.820246i
$549$	−2.03612	−	3.52667i	−0.0868996	−	0.150515i
$550$	−6.97727			−0.297512
$551$	20.8265	−	1.53827i	0.887237	−	0.0655323i
$552$	−27.1268			−1.15459
$553$	2.58316	+	4.47416i	0.109847	+	0.190261i
$554$	25.3630	+	43.9300i	1.07757	+	1.86641i
$555$	3.84614	−	6.66170i	0.163259	−	0.282774i
$556$	−20.4304	−	35.3865i	−0.866442	−	1.50072i
$557$	−6.38318	+	11.0560i	−0.270464	+	0.468457i	−0.968981	−	0.247136i	$-0.920510\pi$
$557$	−6.38318	+	11.0560i	−0.270464	+	0.468457i	0.698517	+	0.715594i	$0.253844\pi$
$558$	25.5414			1.08125
$559$	7.82346			0.330897
$560$	5.18761	−	8.98521i	0.219217	−	0.379695i
$561$	−7.48184	+	12.9589i	−0.315884	+	0.547126i
$562$	−44.8142			−1.89037
$563$	−8.11088			−0.341833			−0.170916	−	0.985286i	$-0.554673\pi$
$563$	−8.11088			−0.341833			−0.170916	+	0.985286i	$0.554673\pi$
$564$	−29.0483	+	50.3132i	−1.22315	+	2.11857i
$565$	−4.13021	−	7.15374i	−0.173759	−	0.300960i
$566$	17.5652	−	30.4239i	0.738322	−	1.27881i
$567$	0.398522	+	0.690261i	0.0167364	+	0.0289882i
$568$	−52.2925	−	90.5732i	−2.19414	−	3.80037i
$569$	21.0412			0.882091			0.441046	−	0.897485i	$-0.354608\pi$
$569$	21.0412			0.882091			0.441046	+	0.897485i	$0.354608\pi$
$570$	6.59868	+	9.70082i	0.276388	+	0.406323i
$571$	−8.45300			−0.353747			−0.176873	−	0.984234i	$-0.556598\pi$
$571$	−8.45300			−0.353747			−0.176873	+	0.984234i	$0.556598\pi$
$572$	19.0135	+	32.9324i	0.794996	+	1.37697i
$573$	−11.3071	−	19.5845i	−0.472363	−	0.818156i
$574$	−7.91963	+	13.7172i	−0.330559	+	0.572545i
$575$	1.55307	+	2.68999i	0.0647674	+	0.112181i
$576$	−10.6288	+	18.4096i	−0.442865	+	0.767065i
$577$	23.4005			0.974174			0.487087	−	0.873354i	$-0.338060\pi$
$577$	23.4005			0.974174			0.487087	+	0.873354i	$0.338060\pi$
$578$	−43.9306			−1.82727
$579$	8.30170	−	14.3790i	0.345007	−	0.597570i
$580$	12.5634	−	21.7605i	0.521667	−	0.903554i
$581$	2.22790			0.0924289
$582$	5.38318			0.223140
$583$	11.5078	−	19.9321i	0.476604	−	0.825501i
$584$	37.1505	+	64.3465i	1.53730	+	2.66268i
$585$	1.39852	−	2.42231i	0.0578218	−	0.100150i
$586$	−4.13462	−	7.16136i	−0.170799	−	0.295833i
$587$	−15.0838	−	26.1258i	−0.622574	−	1.07833i	−0.989005	−	0.147884i	$-0.952754\pi$
$587$	−15.0838	−	26.1258i	−0.622574	−	1.07833i	0.366431	−	0.930445i	$-0.380580\pi$
$588$	33.3808			1.37660
$589$	−23.2639	−	34.2007i	−0.958573	−	1.40921i
$590$	−2.90745			−0.119698
$591$	−8.82249	−	15.2810i	−0.362909	−	0.628576i
$592$	−50.0657	−	86.7163i	−2.05769	−	3.56402i
$593$	−11.3496	+	19.6581i	−0.466073	+	0.807262i	−0.999249	−	0.0387422i	$-0.987665\pi$
$593$	−11.3496	+	19.6581i	−0.466073	+	0.807262i	0.533176	+	0.846004i	$0.320998\pi$
$594$	−3.48863	−	6.04249i	−0.143140	−	0.247926i
$595$	−2.30046	+	3.98451i	−0.0943096	+	0.163349i
$596$	−0.475729			−0.0194866
$597$	−19.0631			−0.780201
$598$	11.6923	−	20.2516i	0.478133	−	0.828150i
$599$	9.96335	−	17.2570i	0.407091	−	0.705103i	−0.587471	−	0.809245i	$-0.699876\pi$
$599$	9.96335	−	17.2570i	0.407091	−	0.705103i	0.994562	+	0.104142i	$0.0332098\pi$
$600$	8.73329			0.356535
$601$	24.8942			1.01545			0.507727	−	0.861518i	$-0.330486\pi$
$601$	24.8942			1.01545			0.507727	+	0.861518i	$0.330486\pi$
$602$	3.00027	−	5.19662i	0.122282	−	0.211799i
$603$	−6.88784	−	11.9301i	−0.280495	−	0.485831i
$604$	11.7933	−	20.4266i	0.479864	−	0.831148i
$605$	2.14013	+	3.70681i	0.0870085	+	0.150703i
$606$	−17.6051	−	30.4929i	−0.715159	−	1.23869i
$607$	−11.3318			−0.459945			−0.229972	−	0.973197i	$-0.573864\pi$
$607$	−11.3318			−0.459945			−0.229972	+	0.973197i	$0.573864\pi$
$608$	76.3787	−	5.64141i	3.09756	−	0.228790i
$609$	−3.81859			−0.154737
$610$	5.48041	+	9.49235i	0.221895	+	0.384334i
$611$	−15.4918	−	26.8327i	−0.626733	−	1.08553i
$612$	15.1373	−	26.2186i	0.611890	−	1.05982i
$613$	3.48427	+	6.03493i	0.140728	+	0.243749i	0.927771	−	0.373150i	$-0.121722\pi$
$613$	3.48427	+	6.03493i	0.140728	+	0.243749i	−0.787043	+	0.616898i	$0.788389\pi$
$614$	31.5744	−	54.6885i	1.27424	−	2.20705i
$615$	−7.38318			−0.297719
$616$	18.0442			0.727020
$617$	2.46999	−	4.27814i	0.0994380	−	0.172232i	−0.812014	−	0.583638i	$-0.801629\pi$
$617$	2.46999	−	4.27814i	0.0994380	−	0.172232i	0.911452	+	0.411406i	$0.134962\pi$
$618$	−19.4584	+	33.7029i	−0.782730	+	1.35573i
$619$	−17.7750			−0.714439			−0.357219	−	0.934021i	$-0.616275\pi$
$619$	−17.7750			−0.714439			−0.357219	+	0.934021i	$0.616275\pi$
$620$	−49.7682			−1.99874
$621$	−1.55307	+	2.68999i	−0.0623225	+	0.107946i
$622$	−7.52354	−	13.0312i	−0.301667	−	0.522502i
$623$	−5.32370	+	9.22092i	−0.213290	+	0.369428i
$624$	−18.2047	−	31.5315i	−0.728773	−	1.26227i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	76.5164			3.05821
$627$	−4.91352	+	10.1751i	−0.196227	+	0.406354i
$628$	92.5515			3.69321
$629$	22.2017	+	38.4545i	0.885241	+	1.53328i
$630$	−1.07266	−	1.85790i	−0.0427357	−	0.0740205i
$631$	5.14920	−	8.91868i	0.204987	−	0.355047i	−0.745142	−	0.666906i	$-0.767618\pi$
$631$	5.14920	−	8.91868i	0.204987	−	0.355047i	0.950128	+	0.311859i	$0.100952\pi$
$632$	28.3039	+	49.0238i	1.12587	+	1.95006i
$633$	−7.02170	+	12.1619i	−0.279088	+	0.483394i
$634$	28.2876			1.12344
$635$	4.48932			0.178153
$636$	−23.2826	+	40.3267i	−0.923217	+	1.59906i
$637$	−8.90120	+	15.4173i	−0.352678	+	0.610857i
$638$	33.4276			1.32341
$639$	−11.9754			−0.473741
$640$	11.0381	−	19.1185i	0.436318	−	0.755725i
$641$	−12.4745	−	21.6065i	−0.492713	−	0.853405i	0.507251	−	0.861798i	$-0.330662\pi$
$641$	−12.4745	−	21.6065i	−0.492713	−	0.853405i	−0.999965	+	0.00839344i	$0.997328\pi$
$642$	−4.31300	+	7.47033i	−0.170221	+	0.294831i
$643$	2.84614	+	4.92965i	0.112241	+	0.194407i	0.916673	−	0.399637i	$-0.130864\pi$
$643$	2.84614	+	4.92965i	0.112241	+	0.194407i	−0.804433	+	0.594044i	$0.797531\pi$
$644$	−6.49218	−	11.2448i	−0.255828	−	0.443106i
$645$	2.79704			0.110134
$646$	−67.5408	+	4.98864i	−2.65736	+	0.196275i
$647$	−19.9379			−0.783840			−0.391920	−	0.919999i	$-0.628189\pi$
$647$	−19.9379			−0.783840			−0.391920	+	0.919999i	$0.628189\pi$
$648$	4.36665	+	7.56325i	0.171538	+	0.297113i
$649$	−1.40007	−	2.42499i	−0.0549576	−	0.0951894i
$650$	−3.76425	+	6.51987i	−0.147646	+	0.255730i
$651$	3.78170	+	6.55010i	0.148217	+	0.256719i
$652$	−11.1674	+	19.3425i	−0.437349	+	0.757511i
$653$	21.5636			0.843848			0.421924	−	0.906631i	$-0.361355\pi$
$653$	21.5636			0.843848			0.421924	+	0.906631i	$0.361355\pi$
$654$	20.9901			0.820779
$655$	−9.73940	+	16.8691i	−0.380550	+	0.659132i
$656$	−48.0539	+	83.2318i	−1.87619	+	3.24966i
$657$	8.50778			0.331920
$658$	−23.7643			−0.926429
$659$	20.3255	−	35.2049i	0.791771	−	1.37139i	−0.133099	−	0.991103i	$-0.542493\pi$
$659$	20.3255	−	35.2049i	0.791771	−	1.37139i	0.924870	−	0.380284i	$-0.124174\pi$
$660$	6.79773	+	11.7740i	0.264601	+	0.458303i
$661$	19.7551	−	34.2168i	0.768384	−	1.33088i	−0.170055	−	0.985435i	$-0.554395\pi$
$661$	19.7551	−	34.2168i	0.768384	−	1.33088i	0.938439	−	0.345445i	$-0.112272\pi$
$662$	−8.60795	−	14.9094i	−0.334557	−	0.579471i
$663$	8.07293	+	13.9827i	0.313527	+	0.543044i
$664$	24.4113			0.947343
$665$	−1.51077	+	3.12856i	−0.0585852	+	0.121320i
$666$	−20.7045			−0.802281
$667$	−7.44065	−	12.8876i	−0.288103	−	0.499009i
$668$	−10.4361	−	18.0758i	−0.403784	−	0.699375i
$669$	−12.0926	+	20.9451i	−0.467528	+	0.809783i
$670$	18.5392	+	32.1109i	0.716234	+	1.24055i
$671$	−5.27814	+	9.14200i	−0.203760	+	0.352923i
$672$	−14.0042			−0.540225
$673$	6.47351			0.249536			0.124768	−	0.992186i	$-0.460181\pi$
$673$	6.47351			0.249536			0.124768	+	0.992186i	$0.460181\pi$
$674$	−24.5974	+	42.6039i	−0.947456	+	1.64104i
$675$	0.500000	−	0.866025i	0.0192450	−	0.0333333i
$676$	−27.1492			−1.04420
$677$	45.8593			1.76252			0.881258	−	0.472636i	$-0.156697\pi$
$677$	45.8593			1.76252			0.881258	+	0.472636i	$0.156697\pi$
$678$	−11.1168	+	19.2549i	−0.426940	+	0.739481i
$679$	0.797044	+	1.38052i	0.0305877	+	0.0529795i
$680$	−25.2064	+	43.6587i	−0.966619	+	1.67423i
$681$	1.69227	+	2.93111i	0.0648481	+	0.112320i
$682$	−33.1048	−	57.3391i	−1.26765	−	2.19563i
$683$	−7.04406			−0.269533			−0.134767	−	0.990877i	$-0.543028\pi$
$683$	−7.04406			−0.269533			−0.134767	+	0.990877i	$0.543028\pi$
$684$	9.94108	−	20.5863i	0.380107	−	0.787139i
$685$	4.22753			0.161526
$686$	14.3358	+	24.8303i	0.547343	+	0.948025i
$687$	−12.9832	−	22.4876i	−0.495340	−	0.857955i
$688$	18.2047	−	31.5315i	0.694049	−	1.20213i
$689$	−12.4169	−	21.5068i	−0.473047	−	0.819342i
$690$	4.18023	−	7.24036i	0.159138	−	0.275636i
$691$	6.01990			0.229008			0.114504	−	0.993423i	$-0.463472\pi$
$691$	6.01990			0.229008			0.114504	+	0.993423i	$0.463472\pi$
$692$	58.5948			2.22744
$693$	1.03307	−	1.78933i	0.0392430	−	0.0679709i
$694$	−42.6059	+	73.7957i	−1.61730	+	2.80124i
$695$	7.79093			0.295527
$696$	−41.8406			−1.58596
$697$	21.3096	−	36.9093i	0.807159	−	1.39804i
$698$	16.2575	+	28.1588i	0.615354	+	1.06583i
$699$	−3.35911	+	5.81814i	−0.127053	+	0.220062i
$700$	2.09011	+	3.62018i	0.0789988	+	0.136830i
$701$	−0.268547	−	0.465137i	−0.0101429	−	0.0175680i	0.860909	−	0.508758i	$-0.169895\pi$
$701$	−0.268547	−	0.465137i	−0.0101429	−	0.0175680i	−0.871052	+	0.491190i	$0.836562\pi$
$702$	−7.52850			−0.284145
$703$	18.8583	+	27.7239i	0.711255	+	1.04563i
$704$	55.1048			2.07684
$705$	−5.53865	−	9.59322i	−0.208598	−	0.361302i
$706$	4.88659	+	8.46383i	0.183909	+	0.318540i
$707$	5.21329	−	9.02969i	0.196066	−	0.339596i
$708$	2.83264	+	4.90627i	0.106457	+	0.184389i
$709$	−11.3786	+	19.7083i	−0.427333	+	0.740162i	−0.996635	−	0.0819663i	$-0.973880\pi$
$709$	−11.3786	+	19.7083i	−0.427333	+	0.740162i	0.569302	+	0.822128i	$0.307213\pi$
$710$	32.2329			1.20968
$711$	6.48184			0.243088
$712$	−58.3323	+	101.035i	−2.18610	+	3.78643i
$713$	−14.7376	+	25.5262i	−0.551926	+	0.955964i
$714$	12.3838			0.463451
$715$	−7.25063			−0.271158
$716$	−25.2679	+	43.7652i	−0.944304	+	1.63558i
$717$	12.8909	+	22.3277i	0.481419	+	0.833843i
$718$	−7.96436	+	13.7947i	−0.297227	+	0.514813i
$719$	−1.29796	−	2.24814i	−0.0484059	−	0.0838415i	0.840807	−	0.541335i	$-0.182081\pi$
$719$	−1.29796	−	2.24814i	−0.0484059	−	0.0838415i	−0.889213	+	0.457493i	$0.848747\pi$
$720$	−6.50857	−	11.2732i	−0.242560	−	0.420126i
$721$	−11.5242			−0.429183
$722$	−50.5853	+	7.51356i	−1.88259	+	0.279626i
$723$	7.77858			0.289289
$724$	−10.7516	−	18.6224i	−0.399581	−	0.692094i
$725$	2.39547	+	4.14907i	0.0889654	+	0.154093i
$726$	5.76034	−	9.97721i	0.213786	−	0.370289i
$727$	−12.0755	−	20.9155i	−0.447857	−	0.775711i	0.550389	−	0.834908i	$-0.314479\pi$
$727$	−12.0755	−	20.9155i	−0.447857	−	0.775711i	−0.998246	+	0.0591969i	$0.981146\pi$
$728$	9.73486	−	16.8613i	0.360798	−	0.624920i
$729$	1.00000			0.0370370
$730$	−22.8995			−0.847547
$731$	−8.07293	+	13.9827i	−0.298588	+	0.517170i
$732$	10.6788	−	18.4962i	0.394699	−	0.683638i
$733$	0.0870881			0.00321667			0.00160834	−	0.999999i	$-0.499488\pi$
$733$	0.0870881			0.00321667			0.00160834	+	0.999999i	$0.499488\pi$
$734$	−16.6383			−0.614131
$735$	−3.18236	+	5.51201i	−0.117383	+	0.203314i
$736$	−27.2877	−	47.2637i	−1.00584	−	1.74216i
$737$	−17.8550	+	30.9257i	−0.657697	+	1.13916i
$738$	9.93625	+	17.2101i	0.365758	+	0.633512i
$739$	10.6880	+	18.5122i	0.393166	+	0.680983i	0.992865	−	0.119242i	$-0.0380465\pi$
$739$	10.6880	+	18.5122i	0.393166	+	0.680983i	−0.599699	+	0.800225i	$0.704713\pi$
$740$	40.3434			1.48305
$741$	6.85721	+	10.0809i	0.251906	+	0.370331i
$742$	−19.0474			−0.699253
$743$	10.3616	+	17.9469i	0.380131	+	0.658407i	0.991081	−	0.133263i	$-0.0425454\pi$
$743$	10.3616	+	17.9469i	0.380131	+	0.658407i	−0.610949	+	0.791670i	$0.709212\pi$
$744$	41.4365	+	71.7701i	1.51914	+	2.63122i
$745$	0.0453536	−	0.0785548i	0.00166163	−	0.00287803i
$746$	−9.74821	−	16.8844i	−0.356907	−	0.618182i
$747$	1.39760	−	2.42072i	0.0511356	−	0.0885694i
$748$	−78.4794			−2.86949
$749$	−2.55436			−0.0933344
$750$	−1.34580	+	2.33099i	−0.0491415	+	0.0851156i
$751$	−6.81691	+	11.8072i	−0.248752	+	0.430852i	−0.963180	−	0.268858i	$-0.913354\pi$
$751$	−6.81691	+	11.8072i	−0.248752	+	0.430852i	0.714427	+	0.699709i	$0.246687\pi$
$752$	−144.195			−5.25824
$753$	−10.8743			−0.396283
$754$	18.0343	−	31.2363i	0.656769	−	1.13756i
$755$	2.24864	+	3.89475i	0.0818362	+	0.141744i
$756$	−2.09011	+	3.62018i	−0.0760167	+	0.131665i
$757$	4.40600	+	7.63142i	0.160139	+	0.277369i	0.934918	−	0.354863i	$-0.115472\pi$
$757$	4.40600	+	7.63142i	0.160139	+	0.277369i	−0.774780	+	0.632232i	$0.782139\pi$
$758$	20.7902	+	36.0097i	0.755134	+	1.30793i
$759$	8.05188			0.292265
$760$	−16.5537	+	34.2799i	−0.600465	+	1.24346i
$761$	36.5972			1.32665			0.663323	−	0.748333i	$-0.269145\pi$
$761$	36.5972			1.32665			0.663323	+	0.748333i	$0.269145\pi$
$762$	−6.04170	−	10.4645i	−0.218868	−	0.379090i
$763$	3.10784	+	5.38294i	0.112511	+	0.194875i
$764$	59.3021	−	102.714i	2.14548	−	3.71607i
$765$	2.88624	+	4.99911i	0.104352	+	0.180743i
$766$	−26.2647	+	45.4918i	−0.948981	+	1.64368i
$767$	−3.02136			−0.109095
$768$	−16.9049			−0.610002
$769$	−5.91386	+	10.2431i	−0.213259	+	0.369376i	−0.952733	−	0.303810i	$-0.901741\pi$
$769$	−5.91386	+	10.2431i	−0.213259	+	0.369376i	0.739473	+	0.673186i	$0.235075\pi$
$770$	−2.78060	+	4.81613i	−0.100206	+	0.173561i
$771$	−11.2543			−0.405314
$772$	87.0792			3.13405
$773$	6.57819	−	11.3938i	0.236601	−	0.409805i	−0.723136	−	0.690706i	$-0.757300\pi$
$773$	6.57819	−	11.3938i	0.236601	−	0.409805i	0.959737	+	0.280901i	$0.0906333\pi$
$774$	−3.76425	−	6.51987i	−0.135303	−	0.234352i
$775$	4.74466	−	8.21799i	0.170433	−	0.295199i
$776$	8.73329	+	15.1265i	0.313507	+	0.543010i
$777$	−3.06554	−	5.30967i	−0.109976	−	0.190483i
$778$	−38.3754			−1.37583
$779$	13.9946	−	28.9805i	0.501408	−	1.03833i
$780$	14.6695			0.525254
$781$	15.5216	+	26.8843i	0.555408	+	0.961995i
$782$	24.1302	+	41.7948i	0.862895	+	1.49458i
$783$	−2.39547	+	4.14907i	−0.0856070	+	0.148276i
$784$	41.4252	+	71.7506i	1.47947	+	2.56252i
$785$	−8.82341	+	15.2826i	−0.314921	+	0.545459i
$786$	52.4290			1.87008
$787$	4.59331			0.163734			0.0818669	−	0.996643i	$-0.473912\pi$
$787$	4.59331			0.163734			0.0818669	+	0.996643i	$0.473912\pi$
$788$	46.2709	−	80.1436i	1.64833	−	2.85500i
$789$	−6.66936	+	11.5517i	−0.237435	+	0.411250i
$790$	−17.4465			−0.620717
$791$	−6.58392			−0.234097
$792$	11.3194	−	19.6058i	0.402218	−	0.696663i
$793$	5.69513	+	9.86425i	0.202240	+	0.350290i
$794$	37.5584	−	65.0530i	1.33290	−	2.30865i
$795$	−4.43931	−	7.68910i	−0.157446	−	0.272704i
$796$	−49.9897	−	86.5848i	−1.77184	−	3.06892i
$797$	10.1848			0.360764			0.180382	−	0.983597i	$-0.442267\pi$
$797$	10.1848			0.360764			0.180382	+	0.983597i	$0.442267\pi$
$798$	9.32581	−	0.688815i	0.330130	−	0.0243838i
$799$	63.9434			2.26215
$800$	8.78510	+	15.2162i	0.310600	+	0.537975i
$801$	6.67930	+	11.5689i	0.236002	+	0.408767i
$802$	26.5446	−	45.9766i	0.937323	−	1.62349i
$803$	−11.0271	−	19.0996i	−0.389139	−	0.674009i
$804$	36.1244	−	62.5693i	1.27401	−	2.20665i
$805$	2.47573			0.0872580
$806$	−71.4403			−2.51638
$807$	−3.53399	+	6.12105i	−0.124402	+	0.215471i
$808$	57.1226	−	98.9392i	2.00957	−	3.48067i
$809$	31.9669			1.12390			0.561948	−	0.827173i	$-0.310052\pi$
$809$	31.9669			1.12390			0.561948	+	0.827173i	$0.310052\pi$
$810$	−2.69159			−0.0945728
$811$	−11.1179	+	19.2568i	−0.390403	+	0.676198i	−0.992503	−	0.122223i	$-0.960998\pi$
$811$	−11.1179	+	19.2568i	−0.390403	+	0.676198i	0.602099	+	0.798421i	$0.294331\pi$
$812$	−10.0136	−	17.3440i	−0.351408	−	0.608657i
$813$	−11.5289	+	19.9686i	−0.404336	+	0.700330i
$814$	26.8355	+	46.4805i	0.940585	+	1.62914i
$815$	−2.12929	−	3.68804i	−0.0745858	−	0.129186i
$816$	75.1410			2.63046
$817$	−5.30170	+	10.9790i	−0.185483	+	0.384105i
$818$	−51.7623			−1.80983
$819$	−1.11468	−	1.93069i	−0.0389502	−	0.0674637i
$820$	−19.3611	−	33.5345i	−0.676120	−	1.17107i
$821$	−25.5604	+	44.2720i	−0.892065	+	1.54510i	−0.0546706	+	0.998504i	$0.517411\pi$
$821$	−25.5604	+	44.2720i	−0.892065	+	1.54510i	−0.837395	+	0.546598i	$0.815922\pi$
$822$	−5.68939	−	9.85431i	−0.198440	−	0.343708i
$823$	17.1145	−	29.6431i	0.596573	−	1.03329i	−0.396750	−	0.917927i	$-0.629862\pi$
$823$	17.1145	−	29.6431i	0.596573	−	1.03329i	0.993323	−	0.115368i	$-0.0368046\pi$
$824$	−126.272			−4.39888
$825$	−2.59225			−0.0902505
$826$	−1.15868	+	2.00690i	−0.0403158	+	0.0698290i
$827$	−4.28856	+	7.42801i	−0.149128	+	0.258297i	−0.930905	−	0.365260i	$-0.880980\pi$
$827$	−4.28856	+	7.42801i	−0.149128	+	0.258297i	0.781777	+	0.623558i	$0.214313\pi$
$828$	−16.2906			−0.566139
$829$	−13.4230			−0.466199			−0.233099	−	0.972453i	$-0.574887\pi$
$829$	−13.4230			−0.466199			−0.233099	+	0.972453i	$0.574887\pi$
$830$	−3.76177	+	6.51558i	−0.130573	+	0.226159i
$831$	9.42304	+	16.3212i	0.326882	+	0.566176i
$832$	29.7291	−	51.4923i	1.03067	−	1.78518i
$833$	−18.3701	−	31.8179i	−0.636486	−	1.10243i
$834$	−10.4850	−	18.1606i	−0.363066	−	0.628849i
$835$	3.97970			0.137723
$836$	−59.1002	+	4.36521i	−2.04402	+	0.150974i
$837$	9.48932			0.327999
$838$	−5.99219	−	10.3788i	−0.206997	−	0.358529i
$839$	−19.8194	−	34.3282i	−0.684242	−	1.18514i	−0.973675	−	0.227943i	$-0.926800\pi$
$839$	−19.8194	−	34.3282i	−0.684242	−	1.18514i	0.289433	−	0.957198i	$-0.406533\pi$
$840$	3.48041	−	6.02825i	0.120086	−	0.207994i
$841$	3.02348	+	5.23682i	0.104258	+	0.180580i
$842$	16.2698	−	28.1801i	0.560693	−	0.971150i
$843$	−16.6497			−0.573447
$844$	−73.6529			−2.53524
$845$	2.58827	−	4.48302i	0.0890393	−	0.154221i
$846$	−14.9078	+	25.8210i	−0.512540	+	0.887745i
$847$	3.41155			0.117222
$848$	−115.574			−3.96883
$849$	6.52597	−	11.3033i	0.223971	−	0.387929i
$850$	−7.76857	−	13.4556i	−0.266460	−	0.461522i
$851$	11.9466	−	20.6922i	0.409525	−	0.709319i
$852$	−31.4035	−	54.3925i	−1.07587	−	1.86346i
$853$	3.02452	+	5.23863i	0.103558	+	0.179367i	0.913148	−	0.407628i	$-0.133644\pi$
$853$	3.02452	+	5.23863i	0.103558	+	0.179367i	−0.809590	+	0.586995i	$0.800311\pi$
$854$	8.73626			0.298949
$855$	2.45159	+	3.60412i	0.0838426	+	0.123258i
$856$	−27.9884			−0.956625
$857$	−25.6680	−	44.4583i	−0.876803	−	1.51867i	−0.854829	−	0.518909i	$-0.826338\pi$
$857$	−25.6680	−	44.4583i	−0.876803	−	1.51867i	−0.0219737	−	0.999759i	$-0.506995\pi$
$858$	9.75787	+	16.9011i	0.333128	+	0.576995i
$859$	−6.03713	+	10.4566i	−0.205984	+	0.356775i	−0.950446	−	0.310890i	$-0.899373\pi$
$859$	−6.03713	+	10.4566i	−0.205984	+	0.356775i	0.744462	+	0.667665i	$0.232706\pi$
$860$	7.33477	+	12.7042i	0.250114	+	0.433210i
$861$	−2.94236	+	5.09632i	−0.100275	+	0.173682i
$862$	55.2936			1.88331
$863$	−12.8023			−0.435797			−0.217898	−	0.975971i	$-0.569920\pi$
$863$	−12.8023			−0.435797			−0.217898	+	0.975971i	$0.569920\pi$
$864$	−8.78510	+	15.2162i	−0.298875	+	0.517667i
$865$	−5.58614	+	9.67547i	−0.189934	+	0.328976i
$866$	52.1454			1.77197
$867$	−16.3214			−0.554305
$868$	−19.8337	+	34.3531i	−0.673201	+	1.16602i
$869$	−8.40127	−	14.5514i	−0.284993	−	0.493623i
$870$	6.44762	−	11.1676i	0.218595	−	0.378617i
$871$	19.2656	+	33.3690i	0.652790	+	1.13067i
$872$	34.0529	+	58.9814i	1.15318	+	1.99736i
$873$	2.00000			0.0676897
$874$	20.4964	+	30.1321i	0.693301	+	1.01923i
$875$	−0.797044			−0.0269450
$876$	22.3102	+	38.6424i	0.753792	+	1.30561i
$877$	15.2683	+	26.4455i	0.515575	+	0.893002i	0.999837	+	0.0180785i	$0.00575488\pi$
$877$	15.2683	+	26.4455i	0.515575	+	0.893002i	−0.484262	+	0.874923i	$0.660912\pi$
$878$	23.1902	−	40.1666i	0.782631	−	1.35556i
$879$	−1.53612	−	2.66064i	−0.0518122	−	0.0897413i
$880$	−16.8718	+	29.2228i	−0.568749	+	0.985102i
$881$	−6.79947			−0.229080			−0.114540	−	0.993419i	$-0.536539\pi$
$881$	−6.79947			−0.229080			−0.114540	+	0.993419i	$0.536539\pi$
$882$	17.1312			0.576838
$883$	−13.5370	+	23.4468i	−0.455558	+	0.789049i	−0.998720	−	0.0505785i	$-0.983893\pi$
$883$	−13.5370	+	23.4468i	−0.455558	+	0.789049i	0.543162	+	0.839628i	$0.317227\pi$
$884$	−42.3398	+	73.3346i	−1.42404	+	2.46651i
$885$	−1.08020			−0.0363105
$886$	−44.8297			−1.50608
$887$	5.62312	−	9.73952i	0.188806	−	0.327021i	−0.756047	−	0.654518i	$-0.772872\pi$
$887$	5.62312	−	9.73952i	0.188806	−	0.327021i	0.944852	+	0.327497i	$0.106205\pi$
$888$	−33.5894	−	58.1786i	−1.12719	−	1.95235i
$889$	1.78909	−	3.09880i	0.0600042	−	0.103930i
$890$	−17.9780	−	31.1387i	−0.602622	−	1.04377i
$891$	−1.29612	−	2.24495i	−0.0434218	−	0.0752087i
$892$	−126.844			−4.24704
$893$	48.1536	−	3.55668i	1.61140	−	0.119020i
$894$	−0.244147			−0.00816549
$895$	−4.81783	−	8.34472i	−0.161042	−	0.278933i
$896$	−8.79783	−	15.2383i	−0.293915	−	0.509075i
$897$	4.34400	−	7.52403i	0.145042	−	0.251220i
$898$	−24.8566	−	43.0528i	−0.829474	−	1.43669i
$899$	−22.7313	+	39.3718i	−0.758133	+	1.31312i
$900$	5.24466			0.174822
$901$	51.2515			1.70744
$902$	25.7572	−	44.6128i	0.857622	−	1.48544i
$903$	1.11468	−	1.93069i	0.0370944	−	0.0642493i
$904$	−72.1407			−2.39936
$905$	4.10003			0.136289
$906$	6.05240	−	10.4831i	0.201078	−	0.348277i
$907$	21.4377	+	37.1313i	0.711829	+	1.23292i	0.964170	+	0.265285i	$0.0854661\pi$
$907$	21.4377	+	37.1313i	0.711829	+	1.23292i	−0.252341	+	0.967638i	$0.581201\pi$
$908$	−8.87540	+	15.3726i	−0.294541	+	0.510159i
$909$	−6.54078	−	11.3290i	−0.216944	−	0.375758i
$910$	3.00027	+	5.19662i	0.0994581	+	0.172266i
$911$	39.7951			1.31847			0.659235	−	0.751937i	$-0.270880\pi$
$911$	39.7951			1.31847			0.659235	+	0.751937i	$0.270880\pi$
$912$	56.5862	−	4.17952i	1.87376	−	0.138398i
$913$	−7.24586			−0.239803
$914$	4.58471	+	7.94095i	0.151649	+	0.262663i
$915$	2.03612	+	3.52667i	0.0673122	+	0.116588i
$916$	68.0925	−	117.940i	2.24984	−	3.89684i
$917$	7.76274	+	13.4455i	0.256348	+	0.444008i
$918$	7.76857	−	13.4556i	0.256401	−	0.444099i
$919$	−51.8927			−1.71178			−0.855891	−	0.517156i	$-0.826991\pi$
$919$	−51.8927			−1.71178			−0.855891	+	0.517156i	$0.826991\pi$
$920$	27.1268			0.894345
$921$	11.7308	−	20.3183i	0.386542	−	0.669510i
$922$	54.3778	−	94.1851i	1.79084	−	3.10182i
$923$	33.4958			1.10253
$924$	10.8362			0.356484
$925$	−3.84614	+	6.66170i	−0.126460	+	0.219036i
$926$	−30.9161	−	53.5483i	−1.01597	−	1.75971i
$927$	−7.22932	+	12.5215i	−0.237442	+	0.411262i
$928$	−42.0888	−	72.9000i	−1.38163	−	2.39306i
$929$	13.0662	+	22.6313i	0.428687	+	0.742508i	0.996757	−	0.0804727i	$-0.0256430\pi$
$929$	13.0662	+	22.6313i	0.428687	+	0.742508i	−0.568070	+	0.822980i	$0.692310\pi$
$930$	−25.5414			−0.837534
$931$	−15.6037	−	22.9392i	−0.511390	−	0.751803i
$932$	−35.2347			−1.15415
$933$	−2.79520	−	4.84143i	−0.0915109	−	0.158501i
$934$	9.44982	+	16.3676i	0.309208	+	0.535563i
$935$	7.48184	−	12.9589i	0.244682	−	0.423802i
$936$	−12.2137	−	21.1548i	−0.399217	−	0.691465i
$937$	−16.1159	+	27.9135i	−0.526483	+	0.911895i	0.473041	+	0.881040i	$0.343156\pi$
$937$	−16.1159	+	27.9135i	−0.526483	+	0.911895i	−0.999524	+	0.0308547i	$0.990177\pi$
$938$	29.5532			0.964946
$939$	28.4280			0.927711
$940$	29.0483	−	50.3132i	0.947452	−	1.64103i
$941$	16.9670	−	29.3878i	0.553110	−	0.958014i	−0.444938	−	0.895561i	$-0.646774\pi$
$941$	16.9670	−	29.3878i	0.553110	−	0.958014i	0.998048	−	0.0624526i	$-0.0198922\pi$
$942$	47.4980			1.54757
$943$	−22.9332			−0.746807
$944$	−7.03054	+	12.1773i	−0.228825	+	0.396336i
$945$	−0.398522	−	0.690261i	−0.0129639	−	0.0224542i
$946$	−9.75787	+	16.9011i	−0.317256	+	0.549503i
$947$	−0.448299	−	0.776476i	−0.0145678	−	0.0252321i	0.858650	−	0.512563i	$-0.171304\pi$
$947$	−0.448299	−	0.776476i	−0.0145678	−	0.0252321i	−0.873217	+	0.487331i	$0.837971\pi$
$948$	16.9975	+	29.4406i	0.552054	+	0.956185i
$949$	−23.7966			−0.772471
$950$	−6.59868	−	9.70082i	−0.214089	−	0.314736i
$951$	10.5096			0.340798
$952$	20.0906	+	34.7979i	0.651139	+	1.12781i
$953$	15.3609	+	26.6059i	0.497590	+	0.861851i	0.999996	−	0.00278072i	$-0.000885133\pi$
$953$	15.3609	+	26.6059i	0.497590	+	0.861851i	−0.502406	+	0.864632i	$0.667552\pi$
$954$	−11.9488	+	20.6959i	−0.386856	+	0.670055i
$955$	11.3071	+	19.5845i	0.365891	+	0.633741i
$956$	−67.6084	+	117.101i	−2.18661	+	3.78732i
$957$	12.4193			0.401458
$958$	7.86259			0.254029
$959$	1.68476	−	2.91810i	0.0544038	−	0.0942302i
$960$	10.6288	−	18.4096i	0.343042	−	0.594166i
$961$	59.0472			1.90475
$962$	57.9113			1.86713
$963$	−1.60240	+	2.77544i	−0.0516366	+	0.0894371i
$964$	20.3980	+	35.3304i	0.656976	+	1.13792i
$965$	−8.30170	+	14.3790i	−0.267241	+	0.462876i
$966$	−3.33182	−	5.77089i	−0.107200	−	0.185675i
$967$	6.82768	+	11.8259i	0.219563	+	0.380295i	0.954675	−	0.297652i	$-0.0962034\pi$
$967$	6.82768	+	11.8259i	0.219563	+	0.380295i	−0.735111	+	0.677947i	$0.762870\pi$
$968$	37.3807			1.20146
$969$	−25.0933	+	1.85342i	−0.806112	+	0.0595403i
$970$	−5.38318			−0.172844
$971$	−19.1657	−	33.1959i	−0.615055	−	1.06531i	−0.990375	−	0.138411i	$-0.955800\pi$
$971$	−19.1657	−	33.1959i	−0.615055	−	1.06531i	0.375320	−	0.926895i	$-0.377533\pi$
$972$	2.62233	+	4.54201i	0.0841113	+	0.145685i
$973$	3.10486	−	5.37777i	0.0995372	−	0.172404i
$974$	25.8444	+	44.7638i	0.828108	+	1.43432i
$975$	−1.39852	+	2.42231i	−0.0447886	+	0.0775760i
$976$	53.0090			1.69678
$977$	−57.0555			−1.82537			−0.912684	−	0.408666i	$-0.865994\pi$
$977$	−57.0555			−1.82537			−0.912684	+	0.408666i	$0.865994\pi$
$978$	−5.73118	+	9.92670i	−0.183263	+	0.317421i
$979$	17.3144	−	29.9894i	0.553371	−	0.958467i
$980$	−33.3808			−1.06631
$981$	7.79841			0.248984
$982$	14.0459	−	24.3283i	0.448224	−	0.776346i
$983$	14.4625	+	25.0499i	0.461284	+	0.798967i	0.999025	−	0.0441430i	$-0.0140557\pi$
$983$	14.4625	+	25.0499i	0.461284	+	0.798967i	−0.537742	+	0.843110i	$0.680722\pi$
$984$	−32.2397	+	55.8409i	−1.02777	+	1.78014i
$985$	8.82249	+	15.2810i	0.281108	+	0.486893i
$986$	37.2187	+	64.4646i	1.18528	+	2.05297i
$987$	−8.82909			−0.281033
$988$	−27.8056	+	57.5809i	−0.884615	+	1.83189i
$989$	8.68800			0.276262
$990$	3.48863	+	6.04249i	0.110876	+	0.192043i
$991$	−4.07064	−	7.05056i	−0.129308	−	0.223968i	0.794101	−	0.607786i	$-0.207942\pi$
$991$	−4.07064	−	7.05056i	−0.129308	−	0.223968i	−0.923409	+	0.383818i	$0.874609\pi$
$992$	−83.3646	+	144.392i	−2.64683	+	4.58444i
$993$	−3.19809	−	5.53926i	−0.101488	−	0.175783i
$994$	12.8455	−	22.2491i	0.407436	−	0.705700i
$995$	19.0631			0.604341
$996$	14.6599			0.464516
$997$	−21.8847	+	37.9054i	−0.693095	+	1.20047i	0.277724	+	0.960661i	$0.410420\pi$
$997$	−21.8847	+	37.9054i	−0.693095	+	1.20047i	−0.970819	+	0.239814i	$0.922914\pi$
$998$	35.2195	−	61.0019i	1.11485	−	1.93098i
$999$	−7.69227			−0.243373

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.2.i.f.121.5	yes	10
3.2	odd	2		855.2.k.i.406.1		10
19.7	even	3		5415.2.a.y.1.1		5
19.11	even	3	inner	285.2.i.f.106.5	✓	10
19.12	odd	6		5415.2.a.z.1.5		5
57.11	odd	6		855.2.k.i.676.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.i.f.106.5	✓	10	19.11	even	3	inner
285.2.i.f.121.5	yes	10	1.1	even	1	trivial
855.2.k.i.406.1		10	3.2	odd	2
855.2.k.i.676.1		10	57.11	odd	6
5415.2.a.y.1.1		5	19.7	even	3
5415.2.a.z.1.5		5	19.12	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 285 = 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	285.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34580 + 2.33099i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-2.62233 + 4.54201i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.34580 + 2.33099i) q^{6} -0.797044 q^{7} -8.73329 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.34580 - 2.33099i) q^{10} +2.59225 q^{11} -5.24466 q^{12} +(1.39852 - 2.42231i) q^{13} +(-1.07266 - 1.85790i) q^{14} +(0.500000 - 0.866025i) q^{15} +(-6.50857 - 11.2732i) q^{16} +(2.88624 + 4.99911i) q^{17} -2.69159 q^{18} +(2.45159 + 3.60412i) q^{19} +5.24466 q^{20} +(-0.398522 - 0.690261i) q^{21} +(3.48863 + 6.04249i) q^{22} +(1.55307 - 2.68999i) q^{23} +(-4.36665 - 7.56325i) q^{24} +(-0.500000 + 0.866025i) q^{25} +7.52850 q^{26} -1.00000 q^{27} +(2.09011 - 3.62018i) q^{28} +(2.39547 - 4.14907i) q^{29} +2.69159 q^{30} -9.48932 q^{31} +(8.78510 - 15.2162i) q^{32} +(1.29612 + 2.24495i) q^{33} +(-7.76857 + 13.4556i) q^{34} +(0.398522 + 0.690261i) q^{35} +(-2.62233 - 4.54201i) q^{36} +7.69227 q^{37} +(-5.10182 + 10.5650i) q^{38} +2.79704 q^{39} +(4.36665 + 7.56325i) q^{40} +(-3.69159 - 6.39402i) q^{41} +(1.07266 - 1.85790i) q^{42} +(1.39852 + 2.42231i) q^{43} +(-6.79773 + 11.7740i) q^{44} +1.00000 q^{45} +8.36045 q^{46} +(5.53865 - 9.59322i) q^{47} +(6.50857 - 11.2732i) q^{48} -6.36472 q^{49} -2.69159 q^{50} +(-2.88624 + 4.99911i) q^{51} +(7.33477 + 12.7042i) q^{52} +(4.43931 - 7.68910i) q^{53} +(-1.34580 - 2.33099i) q^{54} +(-1.29612 - 2.24495i) q^{55} +6.96082 q^{56} +(-1.89547 + 3.92520i) q^{57} +12.8952 q^{58} +(-0.540099 - 0.935479i) q^{59} +(2.62233 + 4.54201i) q^{60} +(-2.03612 + 3.52667i) q^{61} +(-12.7707 - 22.1195i) q^{62} +(0.398522 - 0.690261i) q^{63} +21.2575 q^{64} -2.79704 q^{65} +(-3.48863 + 6.04249i) q^{66} +(-6.88784 + 11.9301i) q^{67} -30.2747 q^{68} +3.10614 q^{69} +(-1.07266 + 1.85790i) q^{70} +(5.98771 + 10.3710i) q^{71} +(4.36665 - 7.56325i) q^{72} +(-4.25389 - 7.36795i) q^{73} +(10.3522 + 17.9306i) q^{74} -1.00000 q^{75} +(-22.7988 + 1.68395i) q^{76} -2.06614 q^{77} +(3.76425 + 6.51987i) q^{78} +(-3.24092 - 5.61344i) q^{79} +(-6.50857 + 11.2732i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(9.93625 - 17.2101i) q^{82} -2.79520 q^{83} +4.18023 q^{84} +(2.88624 - 4.99911i) q^{85} +(-3.76425 + 6.51987i) q^{86} +4.79093 q^{87} -22.6389 q^{88} +(6.67930 - 11.5689i) q^{89} +(1.34580 + 2.33099i) q^{90} +(-1.11468 + 1.93069i) q^{91} +(8.14532 + 14.1081i) q^{92} +(-4.74466 - 8.21799i) q^{93} +29.8155 q^{94} +(1.89547 - 3.92520i) q^{95} +17.5702 q^{96} +(-1.00000 - 1.73205i) q^{97} +(-8.56561 - 14.8361i) q^{98} +(-1.29612 + 2.24495i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} + 5 q^{3} - 7 q^{4} - 5 q^{5} - q^{6} + 4 q^{7} - 12 q^{8} - 5 q^{9} + q^{10} + 10 q^{11} - 14 q^{12} + 8 q^{13} + 4 q^{14} + 5 q^{15} - 7 q^{16} - 10 q^{17} - 2 q^{18} + 5 q^{19} + 14 q^{20}+ \cdots - 5 q^{99}+O(q^{100}) \) 10 * q + q^2 + 5 * q^3 - 7 * q^4 - 5 * q^5 - q^6 + 4 * q^7 - 12 * q^8 - 5 * q^9 + q^10 + 10 * q^11 - 14 * q^12 + 8 * q^13 + 4 * q^14 + 5 * q^15 - 7 * q^16 - 10 * q^17 - 2 * q^18 + 5 * q^19 + 14 * q^20 + 2 * q^21 - 2 * q^22 + 2 * q^23 - 6 * q^24 - 5 * q^25 - 4 * q^26 - 10 * q^27 - 10 * q^28 + 7 * q^29 + 2 * q^30 - 18 * q^31 + 23 * q^32 + 5 * q^33 - 25 * q^34 - 2 * q^35 - 7 * q^36 + 12 * q^37 - 37 * q^38 + 16 * q^39 + 6 * q^40 - 12 * q^41 - 4 * q^42 + 8 * q^43 - 16 * q^44 + 10 * q^45 - 40 * q^46 - 6 * q^47 + 7 * q^48 + 30 * q^49 - 2 * q^50 + 10 * q^51 + 4 * q^52 - 8 * q^53 - q^54 - 5 * q^55 + 72 * q^56 - 2 * q^57 + 76 * q^58 + q^59 + 7 * q^60 - 7 * q^61 - 15 * q^62 - 2 * q^63 + 28 * q^64 - 16 * q^65 + 2 * q^66 + 14 * q^67 - 2 * q^68 + 4 * q^69 + 4 * q^70 + 27 * q^71 + 6 * q^72 - 26 * q^73 + 18 * q^74 - 10 * q^75 - 56 * q^76 + 28 * q^77 - 2 * q^78 - 23 * q^79 - 7 * q^80 - 5 * q^81 + 36 * q^82 - 24 * q^83 - 20 * q^84 - 10 * q^85 + 2 * q^86 + 14 * q^87 + 9 * q^89 + q^90 - 46 * q^91 + 52 * q^92 - 9 * q^93 + 90 * q^94 + 2 * q^95 + 46 * q^96 - 10 * q^97 - 21 * q^98 - 5 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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