LMFDB - Embedded newform 585.2.i.g.391.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(196,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("585.196");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$26$
Relative dimension:	$13$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			391.4
Character	$\chi$	$=$	585.391
Dual form			585.2.i.g.196.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.780853 - 1.35248i) q^{2} +(0.0458444 - 1.73144i) q^{3} +(-0.219464 + 0.380123i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-2.37754 + 1.29000i) q^{6} +(-2.47307 - 4.28349i) q^{7} -2.43794 q^{8} +(-2.99580 - 0.158754i) q^{9} +O(q^{10})$	\(q+(-0.780853 - 1.35248i) q^{2} +(0.0458444 - 1.73144i) q^{3} +(-0.219464 + 0.380123i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-2.37754 + 1.29000i) q^{6} +(-2.47307 - 4.28349i) q^{7} -2.43794 q^{8} +(-2.99580 - 0.158754i) q^{9} +1.56171 q^{10} +(0.149658 + 0.259215i) q^{11} +(0.648101 + 0.397417i) q^{12} +(0.500000 - 0.866025i) q^{13} +(-3.86221 + 6.68955i) q^{14} +(1.47655 + 0.905424i) q^{15} +(2.34260 + 4.05750i) q^{16} +8.20364 q^{17} +(2.12457 + 4.17571i) q^{18} -3.11389 q^{19} +(-0.219464 - 0.380123i) q^{20} +(-7.53000 + 4.08561i) q^{21} +(0.233722 - 0.404818i) q^{22} +(-0.916153 + 1.58682i) q^{23} +(-0.111766 + 4.22115i) q^{24} +(-0.500000 - 0.866025i) q^{25} -1.56171 q^{26} +(-0.412215 + 5.17978i) q^{27} +2.17101 q^{28} +(-0.905640 - 1.56861i) q^{29} +(0.0715956 - 2.70401i) q^{30} +(-0.503860 + 0.872711i) q^{31} +(1.22052 - 2.11400i) q^{32} +(0.455678 - 0.247241i) q^{33} +(-6.40584 - 11.0952i) q^{34} +4.94615 q^{35} +(0.717817 - 1.10393i) q^{36} -4.66095 q^{37} +(2.43149 + 4.21146i) q^{38} +(-1.47655 - 0.905424i) q^{39} +(1.21897 - 2.11131i) q^{40} +(-0.897469 + 1.55446i) q^{41} +(11.4055 + 6.99389i) q^{42} +(-5.48520 - 9.50064i) q^{43} -0.131378 q^{44} +(1.63538 - 2.51506i) q^{45} +2.86152 q^{46} +(2.79002 + 4.83245i) q^{47} +(7.13273 - 3.87007i) q^{48} +(-8.73218 + 15.1246i) q^{49} +(-0.780853 + 1.35248i) q^{50} +(0.376091 - 14.2041i) q^{51} +(0.219464 + 0.380123i) q^{52} -0.636520 q^{53} +(7.32741 - 3.48713i) q^{54} -0.299316 q^{55} +(6.02919 + 10.4429i) q^{56} +(-0.142754 + 5.39152i) q^{57} +(-1.41434 + 2.44972i) q^{58} +(0.367629 - 0.636752i) q^{59} +(-0.668224 + 0.362564i) q^{60} +(1.66731 + 2.88786i) q^{61} +1.57376 q^{62} +(6.72880 + 13.2251i) q^{63} +5.55821 q^{64} +(0.500000 + 0.866025i) q^{65} +(-0.690205 - 0.423235i) q^{66} +(5.07151 - 8.78411i) q^{67} +(-1.80041 + 3.11839i) q^{68} +(2.70549 + 1.65901i) q^{69} +(-3.86221 - 6.68955i) q^{70} -0.479551 q^{71} +(7.30356 + 0.387033i) q^{72} +8.42735 q^{73} +(3.63952 + 6.30384i) q^{74} +(-1.52240 + 0.826020i) q^{75} +(0.683387 - 1.18366i) q^{76} +(0.740230 - 1.28212i) q^{77} +(-0.0715956 + 2.70401i) q^{78} +(-7.32823 - 12.6929i) q^{79} -4.68520 q^{80} +(8.94959 + 0.951190i) q^{81} +2.80317 q^{82} +(-8.26172 - 14.3097i) q^{83} +(0.0995285 - 3.75897i) q^{84} +(-4.10182 + 7.10456i) q^{85} +(-8.56627 + 14.8372i) q^{86} +(-2.75749 + 1.49615i) q^{87} +(-0.364857 - 0.631950i) q^{88} -13.5058 q^{89} +(-4.67856 - 0.247928i) q^{90} -4.94615 q^{91} +(-0.402126 - 0.696502i) q^{92} +(1.48795 + 0.912414i) q^{93} +(4.35719 - 7.54687i) q^{94} +(1.55694 - 2.69670i) q^{95} +(-3.60432 - 2.21017i) q^{96} +(-7.11278 - 12.3197i) q^{97} +27.2742 q^{98} +(-0.407194 - 0.800315i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q + q^{2} + q^{3} - 15 q^{4} - 13 q^{5} + 7 q^{6} - 10 q^{7} - 12 q^{8} + 7 q^{9}+O(q^{10}) $ 26 * q + q^2 + q^3 - 15 * q^4 - 13 * q^5 + 7 * q^6 - 10 * q^7 - 12 * q^8 + 7 * q^9	\( 26 q + q^{2} + q^{3} - 15 q^{4} - 13 q^{5} + 7 q^{6} - 10 q^{7} - 12 q^{8} + 7 q^{9} - 2 q^{10} - 11 q^{11} - 20 q^{12} + 13 q^{13} - 15 q^{14} - 2 q^{15} - 19 q^{16} + 6 q^{17} - 13 q^{18} + 30 q^{19} - 15 q^{20} - q^{21} - 12 q^{22} - 6 q^{23} + 20 q^{24} - 13 q^{25} + 2 q^{26} - 2 q^{27} + 10 q^{28} - 14 q^{29} - 2 q^{30} - 30 q^{31} + 43 q^{32} + 6 q^{33} - 19 q^{34} + 20 q^{35} - 39 q^{36} + 32 q^{37} + 2 q^{38} + 2 q^{39} + 6 q^{40} - 17 q^{41} + 83 q^{42} - 6 q^{43} + 46 q^{44} - 5 q^{45} + 46 q^{46} + 21 q^{47} - 7 q^{48} - 29 q^{49} + q^{50} + 55 q^{51} + 15 q^{52} + 2 q^{53} - 6 q^{54} + 22 q^{55} - 37 q^{56} + 33 q^{57} - 14 q^{58} - 13 q^{59} + 25 q^{60} - 22 q^{61} - 114 q^{62} - 44 q^{63} + 84 q^{64} + 13 q^{65} - 68 q^{66} - 35 q^{67} + 4 q^{68} - 38 q^{69} - 15 q^{70} + 24 q^{71} - 24 q^{72} + 64 q^{73} + 28 q^{74} + q^{75} - 54 q^{76} - 4 q^{77} + 2 q^{78} - 12 q^{79} + 38 q^{80} + 15 q^{81} + 46 q^{82} + 3 q^{83} + 27 q^{84} - 3 q^{85} + 40 q^{86} - 12 q^{87} - 29 q^{88} + 12 q^{89} - 10 q^{90} - 20 q^{91} + 16 q^{92} - 9 q^{93} - 44 q^{94} - 15 q^{95} + 51 q^{96} - 33 q^{97} + 70 q^{98} - 22 q^{99}+O(q^{100}) \) 26 * q + q^2 + q^3 - 15 * q^4 - 13 * q^5 + 7 * q^6 - 10 * q^7 - 12 * q^8 + 7 * q^9 - 2 * q^10 - 11 * q^11 - 20 * q^12 + 13 * q^13 - 15 * q^14 - 2 * q^15 - 19 * q^16 + 6 * q^17 - 13 * q^18 + 30 * q^19 - 15 * q^20 - q^21 - 12 * q^22 - 6 * q^23 + 20 * q^24 - 13 * q^25 + 2 * q^26 - 2 * q^27 + 10 * q^28 - 14 * q^29 - 2 * q^30 - 30 * q^31 + 43 * q^32 + 6 * q^33 - 19 * q^34 + 20 * q^35 - 39 * q^36 + 32 * q^37 + 2 * q^38 + 2 * q^39 + 6 * q^40 - 17 * q^41 + 83 * q^42 - 6 * q^43 + 46 * q^44 - 5 * q^45 + 46 * q^46 + 21 * q^47 - 7 * q^48 - 29 * q^49 + q^50 + 55 * q^51 + 15 * q^52 + 2 * q^53 - 6 * q^54 + 22 * q^55 - 37 * q^56 + 33 * q^57 - 14 * q^58 - 13 * q^59 + 25 * q^60 - 22 * q^61 - 114 * q^62 - 44 * q^63 + 84 * q^64 + 13 * q^65 - 68 * q^66 - 35 * q^67 + 4 * q^68 - 38 * q^69 - 15 * q^70 + 24 * q^71 - 24 * q^72 + 64 * q^73 + 28 * q^74 + q^75 - 54 * q^76 - 4 * q^77 + 2 * q^78 - 12 * q^79 + 38 * q^80 + 15 * q^81 + 46 * q^82 + 3 * q^83 + 27 * q^84 - 3 * q^85 + 40 * q^86 - 12 * q^87 - 29 * q^88 + 12 * q^89 - 10 * q^90 - 20 * q^91 + 16 * q^92 - 9 * q^93 - 44 * q^94 - 15 * q^95 + 51 * q^96 - 33 * q^97 + 70 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.780853	−	1.35248i	−0.552147	−	0.956346i	−0.998119	−	0.0612997i	$-0.980475\pi$
$2$	−0.780853	−	1.35248i	−0.552147	−	0.956346i	0.445973	−	0.895047i	$-0.352858\pi$
$3$	0.0458444	−	1.73144i	0.0264683	−	0.999650i
$3$	0.0458444	−	1.73144i	0.0264683	−	0.999650i
$4$	−0.219464	+	0.380123i	−0.109732	+	0.190062i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	−2.37754	+	1.29000i	−0.970626	+	0.526640i
$7$	−2.47307	−	4.28349i	−0.934734	−	1.61901i	−0.775108	−	0.631828i	$-0.782305\pi$
$7$	−2.47307	−	4.28349i	−0.934734	−	1.61901i	−0.159625	−	0.987178i	$-0.551029\pi$
$8$	−2.43794			−0.861941
$9$	−2.99580	−	0.158754i	−0.998599	−	0.0529181i
$10$	1.56171			0.493855
$11$	0.149658	+	0.259215i	0.0451236	+	0.0781564i	0.887705	−	0.460413i	$-0.152299\pi$
$11$	0.149658	+	0.259215i	0.0451236	+	0.0781564i	−0.842581	+	0.538569i	$0.818965\pi$
$12$	0.648101	+	0.397417i	0.187091	+	0.114724i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$14$	−3.86221	+	6.68955i	−1.03222	+	1.78786i
$15$	1.47655	+	0.905424i	0.381244	+	0.233780i
$16$	2.34260	+	4.05750i	0.585650	+	1.01438i
$17$	8.20364			1.98967			0.994837	−	0.101484i	$-0.0323591\pi$
$17$	8.20364			1.98967			0.994837	+	0.101484i	$0.0323591\pi$
$18$	2.12457	+	4.17571i	0.500765	+	0.984225i
$19$	−3.11389			−0.714375			−0.357187	−	0.934033i	$-0.616264\pi$
$19$	−3.11389			−0.714375			−0.357187	+	0.934033i	$0.616264\pi$
$20$	−0.219464	−	0.380123i	−0.0490737	−	0.0849982i
$21$	−7.53000	+	4.08561i	−1.64318	+	0.891554i
$22$	0.233722	−	0.404818i	0.0498297	−	0.0863076i
$23$	−0.916153	+	1.58682i	−0.191031	+	0.330875i	−0.945592	−	0.325354i	$-0.894516\pi$
$23$	−0.916153	+	1.58682i	−0.191031	+	0.330875i	0.754561	+	0.656230i	$0.227850\pi$
$24$	−0.111766	+	4.22115i	−0.0228141	+	0.861639i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−1.56171			−0.306276
$27$	−0.412215	+	5.17978i	−0.0793307	+	0.996848i
$28$	2.17101			0.410281
$29$	−0.905640	−	1.56861i	−0.168173	−	0.291284i	0.769604	−	0.638521i	$-0.220453\pi$
$29$	−0.905640	−	1.56861i	−0.168173	−	0.291284i	−0.937778	+	0.347237i	$0.887120\pi$
$30$	0.0715956	−	2.70401i	0.0130715	−	0.493682i
$31$	−0.503860	+	0.872711i	−0.0904959	+	0.156744i	−0.907720	−	0.419577i	$-0.862179\pi$
$31$	−0.503860	+	0.872711i	−0.0904959	+	0.156744i	0.817224	+	0.576320i	$0.195512\pi$
$32$	1.22052	−	2.11400i	0.215759	−	0.373706i
$33$	0.455678	−	0.247241i	0.0793233	−	0.0430391i
$34$	−6.40584	−	11.0952i	−1.09859	−	1.90282i
$35$	4.94615			0.836051
$36$	0.717817	−	1.10393i	0.119636	−	0.183989i
$37$	−4.66095			−0.766256			−0.383128	−	0.923695i	$-0.625153\pi$
$37$	−4.66095			−0.766256			−0.383128	+	0.923695i	$0.625153\pi$
$38$	2.43149	+	4.21146i	0.394440	+	0.683189i
$39$	−1.47655	−	0.905424i	−0.236438	−	0.144984i
$40$	1.21897	−	2.11131i	0.192736	−	0.333828i
$41$	−0.897469	+	1.55446i	−0.140161	+	0.242766i	−0.927557	−	0.373681i	$-0.878095\pi$
$41$	−0.897469	+	1.55446i	−0.140161	+	0.242766i	0.787396	+	0.616447i	$0.211429\pi$
$42$	11.4055	+	6.99389i	1.75991	+	1.07918i
$43$	−5.48520	−	9.50064i	−0.836485	−	1.44883i	−0.892816	−	0.450422i	$-0.851273\pi$
$43$	−5.48520	−	9.50064i	−0.836485	−	1.44883i	0.0563307	−	0.998412i	$-0.482060\pi$
$44$	−0.131378			−0.0198060
$45$	1.63538	−	2.51506i	0.243789	−	0.374923i
$46$	2.86152			0.421909
$47$	2.79002	+	4.83245i	0.406966	+	0.704885i	0.994548	−	0.104279i	$-0.0332536\pi$
$47$	2.79002	+	4.83245i	0.406966	+	0.704885i	−0.587582	+	0.809164i	$0.699920\pi$
$48$	7.13273	−	3.87007i	1.02952	−	0.558596i
$49$	−8.73218	+	15.1246i	−1.24745	+	2.16065i
$50$	−0.780853	+	1.35248i	−0.110429	+	0.191269i
$51$	0.376091	−	14.2041i	0.0526633	−	1.98898i
$52$	0.219464	+	0.380123i	0.0304342	+	0.0527136i
$53$	−0.636520			−0.0874327			−0.0437164	−	0.999044i	$-0.513920\pi$
$53$	−0.636520			−0.0874327			−0.0437164	+	0.999044i	$0.513920\pi$
$54$	7.32741	−	3.48713i	0.997134	−	0.474539i
$55$	−0.299316			−0.0403598
$56$	6.02919	+	10.4429i	0.805685	+	1.39549i
$57$	−0.142754	+	5.39152i	−0.0189083	+	0.714124i
$58$	−1.41434	+	2.44972i	−0.185712	+	0.321663i
$59$	0.367629	−	0.636752i	0.0478612	−	0.0828980i	−0.841102	−	0.540876i	$-0.818093\pi$
$59$	0.367629	−	0.636752i	0.0478612	−	0.0828980i	0.888964	+	0.457978i	$0.151426\pi$
$60$	−0.668224	+	0.362564i	−0.0862673	+	0.0468068i
$61$	1.66731	+	2.88786i	0.213477	+	0.369753i	0.952800	−	0.303598i	$-0.0981879\pi$
$61$	1.66731	+	2.88786i	0.213477	+	0.369753i	−0.739324	+	0.673350i	$0.764855\pi$
$62$	1.57376			0.199868
$63$	6.72880	+	13.2251i	0.847749	+	1.66620i
$64$	5.55821			0.694777
$65$	0.500000	+	0.866025i	0.0620174	+	0.107417i
$66$	−0.690205	−	0.423235i	−0.0849584	−	0.0520967i
$67$	5.07151	−	8.78411i	0.619584	−	1.07315i	−0.369978	−	0.929041i	$-0.620635\pi$
$67$	5.07151	−	8.78411i	0.619584	−	1.07315i	0.989562	−	0.144110i	$-0.0460319\pi$
$68$	−1.80041	+	3.11839i	−0.218331	+	0.378161i
$69$	2.70549	+	1.65901i	0.325703	+	0.199722i
$70$	−3.86221	−	6.68955i	−0.461623	−	0.799554i
$71$	−0.479551			−0.0569122			−0.0284561	−	0.999595i	$-0.509059\pi$
$71$	−0.479551			−0.0569122			−0.0284561	+	0.999595i	$0.509059\pi$
$72$	7.30356	+	0.387033i	0.860733	+	0.0456122i
$73$	8.42735			0.986347			0.493173	−	0.869931i	$-0.335837\pi$
$73$	8.42735			0.986347			0.493173	+	0.869931i	$0.335837\pi$
$74$	3.63952	+	6.30384i	0.423086	+	0.732806i
$75$	−1.52240	+	0.826020i	−0.175791	+	0.0953805i
$76$	0.683387	−	1.18366i	0.0783899	−	0.135775i
$77$	0.740230	−	1.28212i	0.0843571	−	0.146111i
$78$	−0.0715956	+	2.70401i	−0.00810660	+	0.306169i
$79$	−7.32823	−	12.6929i	−0.824490	−	1.42806i	−0.902308	−	0.431091i	$-0.858129\pi$
$79$	−7.32823	−	12.6929i	−0.824490	−	1.42806i	0.0778182	−	0.996968i	$-0.475205\pi$
$80$	−4.68520			−0.523821
$81$	8.94959	+	0.951190i	0.994399	+	0.105688i
$82$	2.80317			0.309558
$83$	−8.26172	−	14.3097i	−0.906841	−	1.57069i	−0.818426	−	0.574611i	$-0.805153\pi$
$83$	−8.26172	−	14.3097i	−0.906841	−	1.57069i	−0.0884147	−	0.996084i	$-0.528180\pi$
$84$	0.0995285	−	3.75897i	0.0108595	−	0.410138i
$85$	−4.10182	+	7.10456i	−0.444905	+	0.770598i
$86$	−8.56627	+	14.8372i	−0.923725	+	1.59994i
$87$	−2.75749	+	1.49615i	−0.295634	+	0.160404i
$88$	−0.364857	−	0.631950i	−0.0388939	−	0.0673661i
$89$	−13.5058			−1.43161			−0.715807	−	0.698298i	$-0.753941\pi$
$89$	−13.5058			−1.43161			−0.715807	+	0.698298i	$0.753941\pi$
$90$	−4.67856	−	0.247928i	−0.493163	−	0.0261339i
$91$	−4.94615			−0.518497
$92$	−0.402126	−	0.696502i	−0.0419245	−	0.0726154i
$93$	1.48795	+	0.912414i	0.154293	+	0.0946130i
$94$	4.35719	−	7.54687i	0.449409	−	0.778400i
$95$	1.55694	−	2.69670i	0.159739	−	0.276676i
$96$	−3.60432	−	2.21017i	−0.367864	−	0.225575i
$97$	−7.11278	−	12.3197i	−0.722194	−	1.25088i	−0.960119	−	0.279593i	$-0.909801\pi$
$97$	−7.11278	−	12.3197i	−0.722194	−	1.25088i	0.237925	−	0.971284i	$-0.423533\pi$
$98$	27.2742			2.75511
$99$	−0.407194	−	0.800315i	−0.0409245	−	0.0804347i
$100$	0.438929			0.0438929
$101$	7.95682	+	13.7816i	0.791733	+	1.37132i	0.924893	+	0.380227i	$0.124154\pi$
$101$	7.95682	+	13.7816i	0.791733	+	1.37132i	−0.133160	+	0.991094i	$0.542513\pi$
$102$	−19.5045	+	10.5827i	−1.93123	+	1.04784i
$103$	−3.53280	+	6.11899i	−0.348097	+	0.602922i	−0.985911	−	0.167268i	$-0.946505\pi$
$103$	−3.53280	+	6.11899i	−0.348097	+	0.602922i	0.637814	+	0.770190i	$0.279839\pi$
$104$	−1.21897	+	2.11131i	−0.119530	+	0.207031i
$105$	0.226753	−	8.56397i	0.0221289	−	0.835758i
$106$	0.497029	+	0.860879i	0.0482757	+	0.0836159i
$107$	−15.7716			−1.52470			−0.762350	−	0.647165i	$-0.775954\pi$
$107$	−15.7716			−1.52470			−0.762350	+	0.647165i	$0.775954\pi$
$108$	−1.87849	−	1.29347i	−0.180758	−	0.124464i
$109$	−1.01935			−0.0976362			−0.0488181	−	0.998808i	$-0.515545\pi$
$109$	−1.01935			−0.0976362			−0.0488181	+	0.998808i	$0.515545\pi$
$110$	0.233722	+	0.404818i	0.0222845	+	0.0385979i
$111$	−0.213679	+	8.07018i	−0.0202815	+	0.765987i
$112$	11.5868	−	20.0690i	1.09485	−	1.89634i
$113$	−4.18327	+	7.24564i	−0.393529	+	0.681613i	−0.992912	−	0.118850i	$-0.962079\pi$
$113$	−4.18327	+	7.24564i	−0.393529	+	0.681613i	0.599383	+	0.800462i	$0.295413\pi$
$114$	7.40338	−	4.01691i	0.693390	−	0.376219i
$115$	−0.916153	−	1.58682i	−0.0854317	−	0.147972i
$116$	0.795023			0.0738160
$117$	−1.63538	+	2.51506i	−0.151191	+	0.232517i
$118$	−1.14826			−0.105706
$119$	−20.2882	−	35.1402i	−1.85982	−	3.22129i
$120$	−3.59974	−	2.20737i	−0.328610	−	0.201504i
$121$	5.45520	−	9.44869i	0.495928	−	0.858972i
$122$	2.60384	−	4.50999i	0.235741	−	0.408315i
$123$	2.65032	+	1.62518i	0.238971	+	0.146538i
$124$	−0.221159	−	0.383058i	−0.0198606	−	0.0343996i
$125$	1.00000			0.0894427
$126$	12.6324	−	19.4274i	1.12538	−	1.73073i
$127$	2.19173			0.194485			0.0972424	−	0.995261i	$-0.468998\pi$
$127$	2.19173			0.194485			0.0972424	+	0.995261i	$0.468998\pi$
$128$	−6.78119	−	11.7454i	−0.599378	−	1.03815i
$129$	−16.7013	+	9.06176i	−1.47047	+	0.797844i
$130$	0.780853	−	1.35248i	0.0684854	−	0.118620i
$131$	6.66518	−	11.5444i	0.582340	−	1.00864i	−0.412862	−	0.910794i	$-0.635471\pi$
$131$	6.66518	−	11.5444i	0.582340	−	1.00864i	0.995201	−	0.0978481i	$-0.0311959\pi$
$132$	−0.00602297	+	0.227474i	−0.000524232	+	0.0197991i
$133$	7.70087	+	13.3383i	0.667750	+	1.15658i
$134$	−15.8404			−1.36840
$135$	−4.27971	−	2.94688i	−0.368339	−	0.253627i
$136$	−19.9999			−1.71498
$137$	−5.08188	−	8.80208i	−0.434174	−	0.752012i	0.563053	−	0.826420i	$-0.309626\pi$
$137$	−5.08188	−	8.80208i	−0.434174	−	0.752012i	−0.997228	+	0.0744084i	$0.976293\pi$
$138$	0.131185	−	4.95457i	0.0111672	−	0.421761i
$139$	2.74257	−	4.75028i	0.232622	−	0.402913i	−0.725957	−	0.687740i	$-0.758603\pi$
$139$	2.74257	−	4.75028i	0.232622	−	0.402913i	0.958579	+	0.284827i	$0.0919362\pi$
$140$	−1.08550	+	1.88015i	−0.0917417	+	0.158901i
$141$	8.49502	−	4.60921i	0.715410	−	0.388166i
$142$	0.374459	+	0.648582i	0.0314239	+	0.0544278i
$143$	0.299316			0.0250301
$144$	−6.37381	−	12.5273i	−0.531151	−	1.04395i
$145$	1.81128			0.150419
$146$	−6.58053	−	11.3978i	−0.544608	−	0.943289i
$147$	25.7870	+	15.8127i	2.12688	+	1.30421i
$148$	1.02291	−	1.77174i	0.0840829	−	0.145636i
$149$	6.79858	−	11.7755i	0.556961	−	0.964685i	−0.440787	−	0.897612i	$-0.645300\pi$
$149$	6.79858	−	11.7755i	0.556961	−	0.964685i	0.997748	−	0.0670735i	$-0.0213662\pi$
$150$	2.30594	+	1.41401i	0.188279	+	0.115453i
$151$	2.75879	+	4.77837i	0.224507	+	0.388858i	0.956172	−	0.292807i	$-0.0945893\pi$
$151$	2.75879	+	4.77837i	0.224507	+	0.388858i	−0.731664	+	0.681665i	$0.761256\pi$
$152$	7.59146			0.615748
$153$	−24.5764	−	1.30236i	−1.98689	−	0.105290i
$154$	−2.31205			−0.186310
$155$	−0.503860	−	0.872711i	−0.0404710	−	0.0700978i
$156$	0.668224	−	0.362564i	0.0535007	−	0.0290283i
$157$	−3.18559	+	5.51760i	−0.254237	+	0.440352i	−0.964688	−	0.263395i	$-0.915158\pi$
$157$	−3.18559	+	5.51760i	−0.254237	+	0.440352i	0.710451	+	0.703747i	$0.248491\pi$
$158$	−11.4445	+	19.8225i	−0.910479	+	1.57700i
$159$	−0.0291809	+	1.10210i	−0.00231420	+	0.0874021i
$160$	1.22052	+	2.11400i	0.0964904	+	0.167126i
$161$	9.06285			0.714253
$162$	−5.70186	−	12.8469i	−0.447980	−	1.00935i
$163$	18.9059			1.48082			0.740411	−	0.672155i	$-0.234631\pi$
$163$	18.9059			1.48082			0.740411	+	0.672155i	$0.234631\pi$
$164$	−0.393925	−	0.682298i	−0.0307604	−	0.0532785i
$165$	−0.0137220	+	0.518249i	−0.00106825	+	0.0403456i
$166$	−12.9024	+	22.3476i	−1.00142	+	1.73451i
$167$	−8.66727	+	15.0122i	−0.670694	+	1.16168i	0.307014	+	0.951705i	$0.400670\pi$
$167$	−8.66727	+	15.0122i	−0.670694	+	1.16168i	−0.977708	+	0.209970i	$0.932663\pi$
$168$	18.3576	−	9.96046i	1.41632	−	0.768466i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	12.8117			0.982611
$171$	9.32857	+	0.494342i	0.713374	+	0.0378033i
$172$	4.81522			0.367157
$173$	−1.92897	−	3.34107i	−0.146657	−	0.254017i	0.783333	−	0.621602i	$-0.213518\pi$
$173$	−1.92897	−	3.34107i	−0.146657	−	0.254017i	−0.929990	+	0.367585i	$0.880185\pi$
$174$	4.17671	+	2.56116i	0.316635	+	0.194161i
$175$	−2.47307	+	4.28349i	−0.186947	+	0.323801i
$176$	−0.701178	+	1.21448i	−0.0528533	+	0.0915445i
$177$	−1.08565	−	0.665720i	−0.0816021	−	0.0500386i
$178$	10.5461	+	18.2663i	0.790461	+	1.36912i
$179$	−7.16667			−0.535662			−0.267831	−	0.963466i	$-0.586307\pi$
$179$	−7.16667			−0.535662			−0.267831	+	0.963466i	$0.586307\pi$
$180$	0.597124	+	1.17361i	0.0445070	+	0.0874760i
$181$	−1.35903			−0.101016			−0.0505078	−	0.998724i	$-0.516084\pi$
$181$	−1.35903			−0.101016			−0.0505078	+	0.998724i	$0.516084\pi$
$182$	3.86221	+	6.68955i	0.286286	+	0.495863i
$183$	5.07660	−	2.75446i	0.375273	−	0.203615i
$184$	2.23352	−	3.86857i	0.164657	−	0.285195i
$185$	2.33048	−	4.03650i	0.171340	−	0.296770i
$186$	0.0721483	−	2.72488i	0.00529017	−	0.199798i
$187$	1.22774	+	2.12651i	0.0897813	+	0.155506i
$188$	−2.44924			−0.178629
$189$	23.2069	−	11.0442i	1.68806	−	0.803351i
$190$	−4.86298			−0.352798
$191$	−1.83779	−	3.18315i	−0.132978	−	0.230324i	0.791845	−	0.610722i	$-0.209121\pi$
$191$	−1.83779	−	3.18315i	−0.132978	−	0.230324i	−0.924823	+	0.380397i	$0.875787\pi$
$192$	0.254813	−	9.62374i	0.0183896	−	0.694533i
$193$	−2.03296	+	3.52120i	−0.146336	+	0.253461i	−0.929871	−	0.367887i	$-0.880081\pi$
$193$	−2.03296	+	3.52120i	−0.146336	+	0.253461i	0.783535	+	0.621348i	$0.213415\pi$
$194$	−11.1081	+	19.2398i	−0.797514	+	1.38133i
$195$	1.52240	−	0.826020i	0.109021	−	0.0591525i
$196$	−3.83280	−	6.63861i	−0.273772	−	0.474186i
$197$	−3.56542			−0.254025			−0.127013	−	0.991901i	$-0.540539\pi$
$197$	−3.56542			−0.254025			−0.127013	+	0.991901i	$0.540539\pi$
$198$	−0.764450	+	1.17565i	−0.0543271	+	0.0835497i
$199$	5.37399			0.380952			0.190476	−	0.981692i	$-0.438997\pi$
$199$	5.37399			0.380952			0.190476	+	0.981692i	$0.438997\pi$
$200$	1.21897	+	2.11131i	0.0861941	+	0.149292i
$201$	−14.9767	−	9.18374i	−1.05638	−	0.647771i
$202$	12.4262	−	21.5228i	0.874305	−	1.51434i
$203$	−4.47943	+	7.75859i	−0.314394	+	0.544547i
$204$	5.31679	+	3.26026i	0.372250	+	0.228264i
$205$	−0.897469	−	1.55446i	−0.0626819	−	0.108568i
$206$	11.0344			0.768803
$207$	2.99652	−	4.60836i	0.208273	−	0.320303i
$208$	4.68520			0.324860
$209$	−0.466018	−	0.807167i	−0.0322351	−	0.0558329i
$210$	−11.7596	+	6.38053i	−0.811493	+	0.440298i
$211$	10.9870	−	19.0300i	0.756375	−	1.31008i	−0.188313	−	0.982109i	$-0.560302\pi$
$211$	10.9870	−	19.0300i	0.756375	−	1.31008i	0.944688	−	0.327971i	$-0.106365\pi$
$212$	0.139693	−	0.241956i	0.00959418	−	0.0166176i
$213$	−0.0219847	+	0.830315i	−0.00150637	+	0.0568923i
$214$	12.3153	+	21.3308i	0.841858	+	1.45814i
$215$	10.9704			0.748175
$216$	1.00495	−	12.6280i	0.0683784	−	0.859224i
$217$	4.98433			0.338358
$218$	0.795964	+	1.37865i	0.0539095	+	0.0933740i
$219$	0.386347	−	14.5915i	0.0261069	−	0.986001i
$220$	0.0656892	−	0.113777i	0.00442877	−	0.00767085i
$221$	4.10182	−	7.10456i	0.275918	−	0.477904i
$222$	11.0816	−	6.01263i	0.743748	−	0.403541i
$223$	−14.5800	−	25.2533i	−0.976349	−	1.69109i	−0.675408	−	0.737444i	$-0.736033\pi$
$223$	−14.5800	−	25.2533i	−0.976349	−	1.69109i	−0.300941	−	0.953643i	$-0.597301\pi$
$224$	−12.0737			−0.806709
$225$	1.36041	+	2.67381i	0.0906942	+	0.178254i
$226$	13.0661			0.869144
$227$	2.94773	+	5.10561i	0.195648	+	0.338871i	0.947113	−	0.320901i	$-0.103986\pi$
$227$	2.94773	+	5.10561i	0.195648	+	0.338871i	−0.751465	+	0.659773i	$0.770652\pi$
$228$	−2.01811	−	1.23751i	−0.133653	−	0.0819562i
$229$	−10.0410	+	17.3915i	−0.663526	+	1.14926i	0.316157	+	0.948707i	$0.397607\pi$
$229$	−10.0410	+	17.3915i	−0.663526	+	1.14926i	−0.979683	+	0.200554i	$0.935726\pi$
$230$	−1.43076	+	2.47815i	−0.0943417	+	0.163405i
$231$	−2.18598	−	1.34045i	−0.143827	−	0.0881948i
$232$	2.20789	+	3.82418i	0.144955	+	0.251070i
$233$	−6.10344			−0.399850			−0.199925	−	0.979811i	$-0.564070\pi$
$233$	−6.10344			−0.399850			−0.199925	+	0.979811i	$0.564070\pi$
$234$	4.67856	+	0.247928i	0.305847	+	0.0162075i
$235$	−5.58003			−0.364001
$236$	0.161363	+	0.279489i	0.0105038	+	0.0181932i
$237$	−22.3129	+	12.1065i	−1.44938	+	0.786403i
$238$	−31.6842	+	54.8787i	−2.05378	+	3.55726i
$239$	−8.41550	+	14.5761i	−0.544354	+	0.942848i	0.454294	+	0.890852i	$0.349892\pi$
$239$	−8.41550	+	14.5761i	−0.544354	+	0.942848i	−0.998647	+	0.0519961i	$0.983442\pi$
$240$	−0.214790	+	8.11216i	−0.0138647	+	0.523638i
$241$	3.33888	+	5.78311i	0.215076	+	0.372523i	0.953296	−	0.302037i	$-0.0976667\pi$
$241$	3.33888	+	5.78311i	0.215076	+	0.372523i	−0.738220	+	0.674560i	$0.764333\pi$
$242$	−17.0389			−1.09530
$243$	2.05722	−	15.4521i	0.131971	−	0.991254i
$244$	−1.46366			−0.0937011
$245$	−8.73218	−	15.1246i	−0.557878	−	0.966274i
$246$	0.128510	−	4.85352i	0.00819347	−	0.309449i
$247$	−1.55694	+	2.69670i	−0.0990659	+	0.171587i
$248$	1.22838	−	2.12761i	0.0780021	−	0.135104i
$249$	−25.1552	+	13.6487i	−1.59415	+	0.864950i
$250$	−0.780853	−	1.35248i	−0.0493855	−	0.0855382i
$251$	13.2018			0.833293			0.416646	−	0.909069i	$-0.363205\pi$
$251$	13.2018			0.833293			0.416646	+	0.909069i	$0.363205\pi$
$252$	−6.50389	−	0.344656i	−0.409707	−	0.0217113i
$253$	−0.548438			−0.0344800
$254$	−1.71142	−	2.96427i	−0.107384	−	0.185995i
$255$	12.1131	+	7.42777i	0.758552	+	0.465145i
$256$	−5.03201	+	8.71570i	−0.314501	+	0.544731i
$257$	9.36390	−	16.2187i	0.584104	−	1.01170i	−0.410883	−	0.911688i	$-0.634779\pi$
$257$	9.36390	−	16.2187i	0.584104	−	1.01170i	0.994987	−	0.100009i	$-0.0318872\pi$
$258$	25.2971	+	15.5122i	1.57493	+	0.965749i
$259$	11.5269	+	19.9651i	0.716245	+	1.24057i
$260$	−0.438929			−0.0272212
$261$	2.46409	+	4.84302i	0.152523	+	0.299776i
$262$	−20.8181			−1.28615
$263$	9.14966	+	15.8477i	0.564192	+	0.977209i	0.997124	+	0.0757830i	$0.0241456\pi$
$263$	9.14966	+	15.8477i	0.564192	+	0.977209i	−0.432932	+	0.901426i	$0.642521\pi$
$264$	−1.11091	+	0.602758i	−0.0683720	+	0.0370972i
$265$	0.318260	−	0.551242i	0.0195505	−	0.0338625i
$266$	12.0265	−	20.8305i	0.737392	−	1.27720i
$267$	−0.619167	+	23.3846i	−0.0378924	+	1.43111i
$268$	2.22603	+	3.85560i	0.135977	+	0.235518i
$269$	−3.65867			−0.223073			−0.111537	−	0.993760i	$-0.535577\pi$
$269$	−3.65867			−0.223073			−0.111537	+	0.993760i	$0.535577\pi$
$270$	−0.643758	+	8.08929i	−0.0391779	+	0.492299i
$271$	−9.16288			−0.556605			−0.278303	−	0.960493i	$-0.589772\pi$
$271$	−9.16288			−0.556605			−0.278303	+	0.960493i	$0.589772\pi$
$272$	19.2178	+	33.2863i	1.16525	+	2.01828i
$273$	−0.226753	+	8.56397i	−0.0137237	+	0.518315i
$274$	−7.93641	+	13.7463i	−0.479456	+	0.830442i
$275$	0.149658	−	0.259215i	0.00902472	−	0.0156313i
$276$	−1.22439	+	0.664327i	−0.0736996	+	0.0399878i
$277$	−9.76171	−	16.9078i	−0.586524	−	1.01589i	−0.994684	−	0.102979i	$-0.967163\pi$
$277$	−9.76171	−	16.9078i	−0.586524	−	1.01589i	0.408159	−	0.912911i	$-0.366171\pi$
$278$	−8.56619			−0.513766
$279$	1.64801	−	2.53448i	0.0986637	−	0.151735i
$280$	−12.0584			−0.720626
$281$	8.45559	+	14.6455i	0.504418	+	0.873678i	0.999987	+	0.00510940i	$0.00162638\pi$
$281$	8.45559	+	14.6455i	0.504418	+	0.873678i	−0.495569	+	0.868569i	$0.665040\pi$
$282$	−12.8672	−	7.89021i	−0.766232	−	0.469855i
$283$	10.3049	−	17.8486i	0.612561	−	1.06099i	−0.378246	−	0.925705i	$-0.623473\pi$
$283$	10.3049	−	17.8486i	0.612561	−	1.06099i	0.990807	−	0.135282i	$-0.0431941\pi$
$284$	0.105244	−	0.182288i	0.00624510	−	0.0108168i
$285$	−4.59782	−	2.81939i	−0.272351	−	0.167006i
$286$	−0.233722	−	0.404818i	−0.0138203	−	0.0239374i
$287$	8.87802			0.524053
$288$	−3.99203	+	6.13935i	−0.235233	+	0.361765i
$289$	50.2997			2.95880
$290$	−1.41434	−	2.44972i	−0.0830532	−	0.143852i
$291$	−21.6570	+	11.7506i	−1.26955	+	0.688832i
$292$	−1.84950	+	3.20343i	−0.108234	+	0.187467i
$293$	7.89823	−	13.6801i	0.461420	−	0.799202i	−0.537612	−	0.843192i	$-0.680674\pi$
$293$	7.89823	−	13.6801i	0.461420	−	0.799202i	0.999032	+	0.0439898i	$0.0140069\pi$
$294$	1.25037	−	47.2238i	0.0729231	−	2.75415i
$295$	0.367629	+	0.636752i	0.0214042	+	0.0370731i
$296$	11.3631			0.660467
$297$	−1.40437	+	0.668343i	−0.0814897	+	0.0387812i
$298$	−21.2348			−1.23010
$299$	0.916153	+	1.58682i	0.0529825	+	0.0917683i
$300$	0.0201224	−	0.759980i	0.00116177	−	0.0438775i
$301$	−27.1306	+	46.9916i	−1.56378	+	2.70855i
$302$	4.30843	−	7.46242i	0.247922	−	0.429414i
$303$	24.2269	−	13.1450i	1.39180	−	0.755159i
$304$	−7.29459	−	12.6346i	−0.418373	−	0.724644i
$305$	−3.33461			−0.190939
$306$	17.4292	+	34.2560i	0.996360	+	1.95829i
$307$	16.1441			0.921392			0.460696	−	0.887558i	$-0.347600\pi$
$307$	16.1441			0.921392			0.460696	+	0.887558i	$0.347600\pi$
$308$	0.324908	+	0.562758i	0.0185134	+	0.0320661i
$309$	10.4327	+	6.39737i	0.593497	+	0.363934i
$310$	−0.786882	+	1.36292i	−0.0446919	+	0.0774086i
$311$	8.77189	−	15.1934i	0.497408	−	0.861536i	−0.502588	−	0.864526i	$-0.667619\pi$
$311$	8.77189	−	15.1934i	0.497408	−	0.861536i	0.999996	+	0.00299040i	$0.000951877\pi$
$312$	3.59974	+	2.20737i	0.203795	+	0.124968i
$313$	−9.51408	−	16.4789i	−0.537768	−	0.931441i	−0.999024	−	0.0441738i	$-0.985934\pi$
$313$	−9.51408	−	16.4789i	−0.537768	−	0.931441i	0.461256	−	0.887267i	$-0.347399\pi$
$314$	9.94990			0.561505
$315$	−14.8176	−	0.785221i	−0.834880	−	0.0442422i
$316$	6.43314			0.361892
$317$	1.72409	+	2.98622i	0.0968347	+	0.167723i	0.910373	−	0.413789i	$-0.135795\pi$
$317$	1.72409	+	2.98622i	0.0968347	+	0.167723i	−0.813538	+	0.581512i	$0.802462\pi$
$318$	1.51335	−	0.821111i	0.0848644	−	0.0460456i
$319$	0.271073	−	0.469511i	0.0151772	−	0.0262876i
$320$	−2.77911	+	4.81356i	−0.155357	+	0.269086i
$321$	−0.723041	+	27.3077i	−0.0403562	+	1.52417i
$322$	−7.07676	−	12.2573i	−0.394372	−	0.683073i
$323$	−25.5452			−1.42137
$324$	−2.32569	+	3.19320i	−0.129205	+	0.177400i
$325$	−1.00000			−0.0554700
$326$	−14.7627	−	25.5698i	−0.817631	−	1.41618i
$327$	−0.0467316	+	1.76495i	−0.00258426	+	0.0976020i
$328$	2.18797	−	3.78968i	0.120810	−	0.209250i
$329$	13.7998	−	23.9020i	0.760809	−	1.31776i
$330$	0.711635	−	0.386118i	0.0391742	−	0.0212551i
$331$	9.35846	+	16.2093i	0.514388	+	0.890946i	0.999861	+	0.0166940i	$0.00531410\pi$
$331$	9.35846	+	16.2093i	0.514388	+	0.890946i	−0.485473	+	0.874252i	$0.661353\pi$
$332$	7.25261			0.398039
$333$	13.9633	+	0.739946i	0.765182	+	0.0405488i
$334$	27.0715			1.48129
$335$	5.07151	+	8.78411i	0.277086	+	0.479927i
$336$	−34.2171	−	20.9820i	−1.86670	−	1.14466i
$337$	−10.5023	+	18.1905i	−0.572097	+	0.990901i	0.424253	+	0.905544i	$0.360537\pi$
$337$	−10.5023	+	18.1905i	−0.572097	+	0.990901i	−0.996350	+	0.0853578i	$0.972797\pi$
$338$	−0.780853	+	1.35248i	−0.0424728	+	0.0735651i
$339$	12.3536	+	7.57528i	0.670958	+	0.411433i
$340$	−1.80041	−	3.11839i	−0.0976407	−	0.169119i
$341$	−0.301627			−0.0163340
$342$	−6.61566	−	13.0027i	−0.357734	−	0.703105i
$343$	51.7582			2.79468
$344$	13.3726	+	23.1620i	0.721000	+	1.24881i
$345$	−2.78950	+	1.51352i	−0.150181	+	0.0814852i
$346$	−3.01248	+	5.21777i	−0.161952	+	0.280509i
$347$	−10.1906	+	17.6507i	−0.547061	+	0.947537i	0.451413	+	0.892315i	$0.350920\pi$
$347$	−10.1906	+	17.6507i	−0.547061	+	0.947537i	−0.998474	+	0.0552220i	$0.982413\pi$
$348$	0.0364474	−	1.37654i	0.00195378	−	0.0737901i
$349$	6.44252	+	11.1588i	0.344860	+	0.597315i	0.985328	−	0.170670i	$-0.0545930\pi$
$349$	6.44252	+	11.1588i	0.344860	+	0.597315i	−0.640468	+	0.767985i	$0.721260\pi$
$350$	7.72443			0.412888
$351$	4.27971	+	2.94688i	0.228434	+	0.157293i
$352$	0.730641			0.0389433
$353$	12.9441	+	22.4198i	0.688943	+	1.19328i	0.972180	+	0.234234i	$0.0752583\pi$
$353$	12.9441	+	22.4198i	0.688943	+	1.19328i	−0.283237	+	0.959050i	$0.591408\pi$
$354$	−0.0526412	+	1.98814i	−0.00279785	+	0.105669i
$355$	0.239775	−	0.415303i	0.0127260	−	0.0220420i
$356$	2.96405	−	5.13388i	0.157094	−	0.272095i
$357$	−61.7733	+	33.5169i	−3.26939	+	1.77390i
$358$	5.59612	+	9.69276i	0.295764	+	0.512278i
$359$	−18.3277			−0.967299			−0.483650	−	0.875262i	$-0.660689\pi$
$359$	−18.3277			−0.967299			−0.483650	+	0.875262i	$0.660689\pi$
$360$	−3.98696	+	6.13155i	−0.210131	+	0.323161i
$361$	−9.30371			−0.489669
$362$	1.06120	+	1.83805i	0.0557754	+	0.0966059i
$363$	−16.1098	−	9.87855i	−0.845545	−	0.518490i
$364$	1.08550	−	1.88015i	0.0568958	−	0.0985464i
$365$	−4.21367	+	7.29830i	−0.220554	+	0.382010i
$366$	−7.68942	−	4.71517i	−0.401933	−	0.246466i
$367$	6.84883	+	11.8625i	0.357506	+	0.619218i	0.987543	−	0.157346i	$-0.0502939\pi$
$367$	6.84883	+	11.8625i	0.357506	+	0.619218i	−0.630038	+	0.776565i	$0.716961\pi$
$368$	−8.58472			−0.447509
$369$	2.93541	−	4.51437i	0.152811	−	0.235009i
$370$	−7.27904			−0.378419
$371$	1.57416	+	2.72652i	0.0817263	+	0.141554i
$372$	−0.673382	+	0.365363i	−0.0349132	+	0.0189432i
$373$	11.2628	−	19.5078i	0.583168	−	1.01008i	−0.411934	−	0.911214i	$-0.635146\pi$
$373$	11.2628	−	19.5078i	0.583168	−	1.01008i	0.995101	−	0.0988620i	$-0.0315203\pi$
$374$	1.91737	−	3.32098i	0.0991449	−	0.171724i
$375$	0.0458444	−	1.73144i	0.00236740	−	0.0894114i
$376$	−6.80188	−	11.7812i	−0.350780	−	0.607569i
$377$	−1.81128			−0.0932857
$378$	−33.0583	−	22.7629i	−1.70034	−	1.17080i
$379$	0.374919			0.0192583			0.00962915	−	0.999954i	$-0.496935\pi$
$379$	0.374919			0.0192583			0.00962915	+	0.999954i	$0.496935\pi$
$380$	0.683387	+	1.18366i	0.0350570	+	0.0607205i
$381$	0.100479	−	3.79486i	0.00514768	−	0.194417i
$382$	−2.87009	+	4.97114i	−0.146847	+	0.254346i
$383$	7.09474	−	12.2884i	0.362524	−	0.627910i	−0.625851	−	0.779942i	$-0.715248\pi$
$383$	7.09474	−	12.2884i	0.362524	−	0.627910i	0.988376	+	0.152032i	$0.0485817\pi$
$384$	−20.6473	+	11.2028i	−1.05365	+	0.571690i
$385$	0.740230	+	1.28212i	0.0377256	+	0.0653427i
$386$	6.34979			0.323196
$387$	14.9243	+	29.3328i	0.758643	+	1.49107i
$388$	6.24401			0.316992
$389$	−11.3583	−	19.6732i	−0.575890	−	0.997470i	−0.995944	−	0.0899713i	$-0.971322\pi$
$389$	−11.3583	−	19.6732i	−0.575890	−	0.997470i	0.420055	−	0.907499i	$-0.362011\pi$
$390$	−2.30594	−	1.41401i	−0.116766	−	0.0716011i
$391$	−7.51578	+	13.0177i	−0.380090	+	0.658334i
$392$	21.2885	−	36.8727i	1.07523	−	1.86235i
$393$	−19.6830	−	12.0696i	−0.992875	−	0.608833i
$394$	2.78407	+	4.82215i	0.140259	+	0.242936i
$395$	14.6565			0.737446
$396$	0.393583	+	0.0208569i	0.0197783	+	0.00104810i
$397$	4.67179			0.234470			0.117235	−	0.993104i	$-0.462597\pi$
$397$	4.67179			0.234470			0.117235	+	0.993104i	$0.462597\pi$
$398$	−4.19630	−	7.26820i	−0.210341	−	0.364322i
$399$	23.4475	−	12.7221i	1.17385	−	0.636903i
$400$	2.34260	−	4.05750i	0.117130	−	0.202875i
$401$	6.73024	−	11.6571i	0.336092	−	0.582128i	−0.647602	−	0.761979i	$-0.724228\pi$
$401$	6.73024	−	11.6571i	0.336092	−	0.582128i	0.983694	+	0.179850i	$0.0575614\pi$
$402$	−0.726196	+	27.4268i	−0.0362193	+	1.36793i
$403$	0.503860	+	0.872711i	0.0250991	+	0.0434728i
$404$	−6.98495			−0.347514
$405$	−5.29855	+	7.27498i	−0.263287	+	0.361497i
$406$	13.9911			0.694367
$407$	−0.697549	−	1.20819i	−0.0345762	−	0.0598878i
$408$	−0.916886	+	34.6288i	−0.0453926	+	1.71438i
$409$	18.1342	−	31.4094i	0.896679	−	1.55309i	0.0649668	−	0.997887i	$-0.479306\pi$
$409$	18.1342	−	31.4094i	0.896679	−	1.55309i	0.831712	−	0.555207i	$-0.187361\pi$
$410$	−1.40158	+	2.42761i	−0.0692192	+	0.119891i
$411$	−15.4733	+	8.39547i	−0.763240	+	0.414118i
$412$	−1.55065	−	2.68580i	−0.0763949	−	0.132320i
$413$	−3.63669			−0.178950
$414$	−8.57254	−	0.454279i	−0.421318	−	0.0223266i
$415$	16.5234			0.811103
$416$	−1.22052	−	2.11400i	−0.0598408	−	0.103647i
$417$	−8.09910	−	4.96639i	−0.396615	−	0.243205i
$418$	−0.727784	+	1.26056i	−0.0355971	+	0.0616559i
$419$	8.66930	−	15.0157i	0.423523	−	0.733563i	−0.572758	−	0.819724i	$-0.694127\pi$
$419$	8.66930	−	15.0157i	0.423523	−	0.733563i	0.996281	+	0.0861610i	$0.0274600\pi$
$420$	3.20560	+	1.96568i	0.156417	+	0.0959154i
$421$	0.0523236	+	0.0906271i	0.00255009	+	0.00441689i	0.867298	−	0.497790i	$-0.165855\pi$
$421$	0.0523236	+	0.0906271i	0.00255009	+	0.00441689i	−0.864748	+	0.502207i	$0.832522\pi$
$422$	−34.3169			−1.67052
$423$	−7.59115	−	14.9200i	−0.369094	−	0.725433i
$424$	1.55179			0.0753618
$425$	−4.10182	−	7.10456i	−0.198967	−	0.344622i
$426$	1.14015	−	0.618621i	0.0552404	−	0.0299723i
$427$	8.24674	−	14.2838i	0.399088	−	0.691240i
$428$	3.46131	−	5.99516i	0.167309	−	0.289787i
$429$	0.0137220	−	0.518249i	0.000662503	−	0.0250213i
$430$	−8.56627	−	14.8372i	−0.413102	−	0.715514i
$431$	20.0732			0.966891			0.483445	−	0.875375i	$-0.339385\pi$
$431$	20.0732			0.966891			0.483445	+	0.875375i	$0.339385\pi$
$432$	−21.9826	+	10.4616i	−1.05764	+	0.503333i
$433$	−13.8238			−0.664329			−0.332164	−	0.943221i	$-0.607779\pi$
$433$	−13.8238			−0.664329			−0.332164	+	0.943221i	$0.607779\pi$
$434$	−3.89203	−	6.74120i	−0.186823	−	0.323588i
$435$	0.0830371	−	3.13613i	0.00398133	−	0.150366i
$436$	0.223711	−	0.387479i	0.0107138	−	0.0185569i
$437$	2.85280	−	4.94119i	0.136468	−	0.236369i
$438$	−20.0363	+	10.8713i	−0.957373	+	0.519450i
$439$	16.0505	+	27.8003i	0.766048	+	1.32683i	0.939691	+	0.342025i	$0.111113\pi$
$439$	16.0505	+	27.8003i	0.766048	+	1.32683i	−0.173643	+	0.984809i	$0.555554\pi$
$440$	0.729713			0.0347877
$441$	28.5609	−	43.9239i	1.36004	−	2.09161i
$442$	−12.8117			−0.609389
$443$	−3.50669	−	6.07377i	−0.166608	−	0.288574i	0.770617	−	0.637298i	$-0.219948\pi$
$443$	−3.50669	−	6.07377i	−0.166608	−	0.288574i	−0.937225	+	0.348725i	$0.886615\pi$
$444$	−3.02077	−	1.85234i	−0.143359	−	0.0879082i
$445$	6.75291	−	11.6964i	0.320119	−	0.554462i
$446$	−22.7697	+	39.4383i	−1.07818	+	1.86746i
$447$	−20.0769	−	12.3112i	−0.949606	−	0.582300i
$448$	−13.7459	−	23.8085i	−0.649431	−	1.12485i
$449$	38.8180			1.83194			0.915968	−	0.401250i	$-0.131424\pi$
$449$	38.8180			1.83194			0.915968	+	0.401250i	$0.131424\pi$
$450$	2.55399	−	3.92778i	0.120396	−	0.185158i
$451$	−0.537254			−0.0252983
$452$	−1.83616	−	3.18032i	−0.0863657	−	0.149590i
$453$	8.39996	−	4.55764i	0.394664	−	0.214136i
$454$	4.60349	−	7.97347i	0.216052	−	0.374214i
$455$	2.47307	−	4.28349i	0.115939	−	0.200813i
$456$	0.348026	−	13.1442i	0.0162978	−	0.615533i
$457$	−10.5153	−	18.2131i	−0.491887	−	0.851973i	0.508070	−	0.861316i	$-0.330359\pi$
$457$	−10.5153	−	18.2131i	−0.491887	−	0.851973i	−0.999956	+	0.00934308i	$0.997026\pi$
$458$	31.3621			1.46546
$459$	−3.38166	+	42.4930i	−0.157842	+	1.98340i
$460$	0.804251			0.0374984
$461$	−12.1990	−	21.1293i	−0.568163	−	0.984088i	−0.996748	−	0.0805860i	$-0.974321\pi$
$461$	−12.1990	−	21.1293i	−0.568163	−	0.984088i	0.428584	−	0.903502i	$-0.359013\pi$
$462$	−0.105994	+	4.00318i	−0.00493131	+	0.186245i
$463$	−7.42545	+	12.8612i	−0.345090	+	0.597713i	−0.985370	−	0.170428i	$-0.945485\pi$
$463$	−7.42545	+	12.8612i	−0.345090	+	0.597713i	0.640280	+	0.768141i	$0.278818\pi$
$464$	4.24310	−	7.34927i	0.196981	−	0.341181i
$465$	−1.53415	+	0.832396i	−0.0711445	+	0.0386015i
$466$	4.76589	+	8.25477i	0.220776	+	0.382395i
$467$	0.149468			0.00691656			0.00345828	−	0.999994i	$-0.498899\pi$
$467$	0.149468			0.00691656			0.00345828	+	0.999994i	$0.498899\pi$
$468$	−0.597124	−	1.17361i	−0.0276021	−	0.0542503i
$469$	−50.1689			−2.31658
$470$	4.35719	+	7.54687i	0.200982	+	0.348111i
$471$	9.40737	+	5.76861i	0.433469	+	0.265804i
$472$	−0.896255	+	1.55236i	−0.0412535	+	0.0714531i
$473$	1.64181	−	2.84370i	0.0754904	−	0.130753i
$474$	33.7969	+	20.7243i	1.55234	+	0.951901i
$475$	1.55694	+	2.69670i	0.0714375	+	0.123733i
$476$	17.8101			0.816326
$477$	1.90688	+	0.101050i	0.0873102	+	0.00462677i
$478$	26.2851			1.20225
$479$	1.01615	+	1.76002i	0.0464291	+	0.0804176i	0.888306	−	0.459252i	$-0.151883\pi$
$479$	1.01615	+	1.76002i	0.0464291	+	0.0804176i	−0.841877	+	0.539670i	$0.818549\pi$
$480$	3.71623	−	2.01634i	0.169622	−	0.0920331i
$481$	−2.33048	+	4.03650i	−0.106261	+	0.184049i
$482$	5.21435	−	9.03152i	0.237507	−	0.411375i
$483$	0.415481	−	15.6918i	0.0189051	−	0.714002i
$484$	2.39445	+	4.14730i	0.108838	+	0.188514i
$485$	14.2256			0.645950
$486$	−22.5050	+	9.28349i	−1.02085	+	0.421108i
$487$	−7.09536			−0.321522			−0.160761	−	0.986993i	$-0.551395\pi$
$487$	−7.09536			−0.321522			−0.160761	+	0.986993i	$0.551395\pi$
$488$	−4.06479	−	7.04042i	−0.184004	−	0.318705i
$489$	0.866729	−	32.7344i	0.0391948	−	1.48030i
$490$	−13.6371	+	23.6202i	−0.616061	+	1.06705i
$491$	4.24817	−	7.35805i	0.191717	−	0.332064i	−0.754102	−	0.656757i	$-0.771928\pi$
$491$	4.24817	−	7.35805i	0.191717	−	0.332064i	0.945819	+	0.324693i	$0.105261\pi$
$492$	−1.19942	+	0.650779i	−0.0540740	+	0.0293394i
$493$	−7.42954	−	12.8683i	−0.334610	−	0.579561i
$494$	4.86298			0.218796
$495$	0.896690	+	0.0475177i	0.0403032	+	0.00213576i
$496$	−4.72137			−0.211996
$497$	1.18596	+	2.05415i	0.0531977	+	0.0921412i
$498$	38.1021	+	23.3643i	1.70739	+	1.04698i
$499$	−19.1670	+	33.1983i	−0.858034	+	1.48616i	0.0157672	+	0.999876i	$0.494981\pi$
$499$	−19.1670	+	33.1983i	−0.858034	+	1.48616i	−0.873801	+	0.486283i	$0.838352\pi$
$500$	−0.219464	+	0.380123i	−0.00981474	+	0.0169996i
$501$	25.5954	+	15.6951i	1.14352	+	0.701206i
$502$	−10.3087	−	17.8552i	−0.460100	−	0.796917i
$503$	−2.24133			−0.0999358			−0.0499679	−	0.998751i	$-0.515912\pi$
$503$	−2.24133			−0.0999358			−0.0499679	+	0.998751i	$0.515912\pi$
$504$	−16.4044	−	32.2419i	−0.730709	−	1.43617i
$505$	−15.9136			−0.708147
$506$	0.428250	+	0.741751i	0.0190380	+	0.0329749i
$507$	−1.52240	+	0.826020i	−0.0676120	+	0.0366848i
$508$	−0.481007	+	0.833129i	−0.0213412	+	0.0369641i
$509$	16.9511	−	29.3601i	0.751343	−	1.30136i	−0.195828	−	0.980638i	$-0.562740\pi$
$509$	16.9511	−	29.3601i	0.751343	−	1.30136i	0.947172	−	0.320727i	$-0.103927\pi$
$510$	0.587344	−	22.1827i	0.0260080	−	0.982267i
$511$	−20.8414	−	36.0984i	−0.921971	−	1.59690i
$512$	−11.4077			−0.504153
$513$	1.28359	−	16.1292i	0.0566719	−	0.712123i
$514$	−29.2473			−1.29004
$515$	−3.53280	−	6.11899i	−0.155674	−	0.269635i
$516$	0.220751	−	8.33729i	0.00971803	−	0.367029i
$517$	−0.835096	+	1.44643i	−0.0367275	+	0.0636139i
$518$	18.0016	−	31.1797i	0.790945	−	1.36996i
$519$	−5.87330	+	3.18673i	−0.257809	+	0.139882i
$520$	−1.21897	−	2.11131i	−0.0534553	−	0.0925873i
$521$	−16.9160			−0.741103			−0.370551	−	0.928812i	$-0.620831\pi$
$521$	−16.9160			−0.741103			−0.370551	+	0.928812i	$0.620831\pi$
$522$	4.62599	−	7.11432i	0.202474	−	0.311385i
$523$	16.5434			0.723393			0.361696	−	0.932296i	$-0.382198\pi$
$523$	16.5434			0.723393			0.361696	+	0.932296i	$0.382198\pi$
$524$	2.92554	+	5.06718i	0.127803	+	0.221361i
$525$	7.30324	+	4.47836i	0.318740	+	0.195452i
$526$	14.2891	−	24.7494i	0.623034	−	1.07913i
$527$	−4.13348	+	7.15941i	−0.180057	+	0.311869i
$528$	2.07065	+	1.26973i	0.0901135	+	0.0552578i
$529$	9.82133	+	17.0110i	0.427014	+	0.739610i
$530$	−0.994057			−0.0431791
$531$	−1.20243	+	1.84922i	−0.0521809	+	0.0802491i
$532$	−6.76026			−0.293095
$533$	0.897469	+	1.55446i	0.0388737	+	0.0673312i
$534$	32.1106	−	17.4225i	1.38956	−	0.753946i
$535$	7.88581	−	13.6586i	0.340933	−	0.590513i
$536$	−12.3640	+	21.4151i	−0.534044	+	0.924992i
$537$	−0.328552	+	12.4087i	−0.0141781	+	0.535474i
$538$	2.85689	+	4.94827i	0.123169	+	0.213335i
$539$	−5.22736			−0.225158
$540$	2.05942	−	0.980084i	0.0886234	−	0.0421761i
$541$	9.88539			0.425006			0.212503	−	0.977160i	$-0.431838\pi$
$541$	9.88539			0.425006			0.212503	+	0.977160i	$0.431838\pi$
$542$	7.15487	+	12.3926i	0.307328	+	0.532307i
$543$	−0.0623038	+	2.35308i	−0.00267371	+	0.100980i
$544$	10.0127	−	17.3425i	0.429290	−	0.743553i
$545$	0.509676	−	0.882784i	0.0218321	−	0.0378143i
$546$	11.7596	−	6.38053i	0.503266	−	0.273061i
$547$	2.44366	+	4.23254i	0.104483	+	0.180970i	0.913527	−	0.406778i	$-0.133348\pi$
$547$	2.44366	+	4.23254i	0.104483	+	0.180970i	−0.809044	+	0.587749i	$0.800014\pi$
$548$	4.46117			0.190572
$549$	−4.53645	−	8.91613i	−0.193611	−	0.380531i
$550$	−0.467444			−0.0199319
$551$	2.82006	+	4.88449i	0.120139	+	0.208086i
$552$	−6.59582	−	4.04457i	−0.280737	−	0.172148i
$553$	−36.2465	+	62.7808i	−1.54136	+	2.66971i
$554$	−15.2449	+	26.4050i	−0.647695	+	1.12184i
$555$	−6.88214	−	4.22014i	−0.292131	−	0.179135i
$556$	1.20379	+	2.08503i	0.0510522	+	0.0884251i
$557$	44.4556			1.88364			0.941822	−	0.336112i	$-0.109112\pi$
$557$	44.4556			1.88364			0.941822	+	0.336112i	$0.109112\pi$
$558$	−4.71468	−	0.249842i	−0.199588	−	0.0105766i
$559$	−10.9704			−0.463998
$560$	11.5868	+	20.0690i	0.489633	+	0.848070i
$561$	3.73822	−	2.02827i	0.157828	−	0.0856338i
$562$	13.2052	−	22.8720i	0.557026	−	0.964797i
$563$	20.4551	−	35.4293i	0.862081	−	1.49317i	−0.00783651	−	0.999969i	$-0.502494\pi$
$563$	20.4551	−	35.4293i	0.862081	−	1.49317i	0.869917	−	0.493198i	$-0.164172\pi$
$564$	−0.112284	+	4.24071i	−0.00472800	+	0.178566i
$565$	−4.18327	−	7.24564i	−0.175992	−	0.304826i
$566$	−32.1864			−1.35290
$567$	−18.0586	−	40.6878i	−0.758389	−	1.70873i
$568$	1.16911			0.0490549
$569$	22.3501	+	38.7115i	0.936965	+	1.62287i	0.771091	+	0.636724i	$0.219711\pi$
$569$	22.3501	+	38.7115i	0.936965	+	1.62287i	0.165874	+	0.986147i	$0.446956\pi$
$570$	−0.222941	+	8.41997i	−0.00933795	+	0.352674i
$571$	22.4933	−	38.9596i	0.941316	−	1.63041i	0.178352	−	0.983967i	$-0.442923\pi$
$571$	22.4933	−	38.9596i	0.941316	−	1.63041i	0.762964	−	0.646441i	$-0.223743\pi$
$572$	−0.0656892	+	0.113777i	−0.00274660	+	0.00475726i
$573$	−5.59569	+	3.03610i	−0.233763	+	0.126835i
$574$	−6.93243	−	12.0073i	−0.289354	−	0.501176i
$575$	1.83231			0.0764124
$576$	−16.6513	−	0.882390i	−0.693803	−	0.0367662i
$577$	13.9526			0.580855			0.290427	−	0.956897i	$-0.406203\pi$
$577$	13.9526			0.580855			0.290427	+	0.956897i	$0.406203\pi$
$578$	−39.2767	−	68.0292i	−1.63369	−	2.82964i
$579$	6.00356	+	3.68139i	0.249499	+	0.152993i
$580$	−0.397511	+	0.688510i	−0.0165058	+	0.0285888i
$581$	−40.8636	+	70.7779i	−1.69531	+	2.93636i
$582$	32.8033	+	20.1151i	1.35974	+	0.833796i
$583$	−0.0952603	−	0.164996i	−0.00394528	−	0.00683342i
$584$	−20.5453			−0.850172
$585$	−1.36041	−	2.67381i	−0.0562462	−	0.110549i
$586$	−24.6695			−1.01909
$587$	−9.24560	−	16.0139i	−0.381607	−	0.660962i	0.609685	−	0.792644i	$-0.291296\pi$
$587$	−9.24560	−	16.0139i	−0.381607	−	0.660962i	−0.991292	+	0.131681i	$0.957963\pi$
$588$	−11.6701	+	6.33194i	−0.481267	+	0.261125i
$589$	1.56896	−	2.71752i	0.0646480	−	0.111974i
$590$	0.574128	−	0.994419i	0.0236365	−	0.0409396i
$591$	−0.163455	+	6.17332i	−0.00672362	+	0.253936i
$592$	−10.9187	−	18.9118i	−0.448758	−	0.777271i
$593$	−20.1399			−0.827045			−0.413522	−	0.910494i	$-0.635702\pi$
$593$	−20.1399			−0.827045			−0.413522	+	0.910494i	$0.635702\pi$
$594$	2.00052	+	1.37750i	0.0820825	+	0.0565195i
$595$	40.5764			1.66347
$596$	2.98409	+	5.16860i	0.122233	+	0.211714i
$597$	0.246368	−	9.30476i	0.0100832	−	0.380819i
$598$	1.43076	−	2.47815i	0.0585082	−	0.101339i
$599$	−17.7769	+	30.7904i	−0.726342	+	1.25806i	0.232077	+	0.972698i	$0.425448\pi$
$599$	−17.7769	+	30.7904i	−0.726342	+	1.25806i	−0.958419	+	0.285365i	$0.907885\pi$
$600$	3.71151	−	2.01378i	0.151522	−	0.0822123i
$601$	8.61356	+	14.9191i	0.351354	+	0.608564i	0.986487	−	0.163839i	$-0.0523879\pi$
$601$	8.61356	+	14.9191i	0.351354	+	0.608564i	−0.635133	+	0.772403i	$0.719055\pi$
$602$	84.7401			3.45375
$603$	−16.5877	+	25.5103i	−0.675505	+	1.03886i
$604$	−2.42183			−0.0985428
$605$	5.45520	+	9.44869i	0.221786	+	0.384144i
$606$	−36.6959	−	22.5020i	−1.49067	−	0.914081i
$607$	9.07357	−	15.7159i	0.368285	−	0.637888i	−0.621013	−	0.783801i	$-0.713278\pi$
$607$	9.07357	−	15.7159i	0.368285	−	0.637888i	0.989298	+	0.145912i	$0.0466118\pi$
$608$	−3.80055	+	6.58275i	−0.154133	+	0.266966i
$609$	13.2282	+	8.11156i	0.536034	+	0.328697i
$610$	2.60384	+	4.50999i	0.105427	+	0.182604i
$611$	5.58003			0.225744
$612$	5.88871	−	9.05625i	0.238037	−	0.366077i
$613$	7.25864			0.293174			0.146587	−	0.989198i	$-0.453171\pi$
$613$	7.25864			0.293174			0.146587	+	0.989198i	$0.453171\pi$
$614$	−12.6062	−	21.8345i	−0.508743	−	0.881169i
$615$	−2.73261	+	1.48265i	−0.110189	+	0.0597863i
$616$	−1.80463	+	3.12572i	−0.0727108	+	0.125939i
$617$	9.96059	−	17.2523i	0.400998	−	0.694549i	−0.592848	−	0.805314i	$-0.701997\pi$
$617$	9.96059	−	17.2523i	0.400998	−	0.694549i	0.993847	+	0.110765i	$0.0353300\pi$
$618$	0.505866	−	19.1054i	0.0203489	−	0.768534i
$619$	−5.31777	−	9.21065i	−0.213739	−	0.370207i	0.739143	−	0.673549i	$-0.235231\pi$
$619$	−5.31777	−	9.21065i	−0.213739	−	0.370207i	−0.952882	+	0.303342i	$0.901898\pi$
$620$	0.442317			0.0177639
$621$	−7.84174	−	5.39958i	−0.314678	−	0.216678i
$622$	−27.3982			−1.09857
$623$	33.4009	+	57.8520i	1.33818	+	2.31779i
$624$	0.214790	−	8.11216i	0.00859850	−	0.324746i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−14.8582	+	25.7352i	−0.593853	+	1.02858i
$627$	−1.41893	+	0.769880i	−0.0566666	+	0.0307461i
$628$	−1.39824	−	2.42183i	−0.0557960	−	0.0966416i
$629$	−38.2368			−1.52460
$630$	10.5084	+	20.6537i	0.418665	+	0.822862i
$631$	−30.9722			−1.23298			−0.616491	−	0.787362i	$-0.711446\pi$
$631$	−30.9722			−1.23298			−0.616491	+	0.787362i	$0.711446\pi$
$632$	17.8658	+	30.9444i	0.710661	+	1.23090i
$633$	−32.4457	−	19.8958i	−1.28960	−	0.790785i
$634$	2.69253	−	4.66359i	0.106934	−	0.185215i
$635$	−1.09587	+	1.89810i	−0.0434881	+	0.0753236i
$636$	−0.412529	−	0.252964i	−0.0163578	−	0.0100307i
$637$	8.73218	+	15.1246i	0.345981	+	0.599257i
$638$	−0.846672			−0.0335201
$639$	1.43664	+	0.0761307i	0.0568325	+	0.00301168i
$640$	13.5624			0.536100
$641$	13.9115	+	24.0955i	0.549473	+	0.951715i	0.998311	+	0.0581019i	$0.0185048\pi$
$641$	13.9115	+	24.0955i	0.549473	+	0.951715i	−0.448838	+	0.893613i	$0.648162\pi$
$642$	37.4976	−	20.3454i	1.47991	−	0.802968i
$643$	17.0650	−	29.5574i	0.672978	−	1.16563i	−0.304078	−	0.952647i	$-0.598348\pi$
$643$	17.0650	−	29.5574i	0.672978	−	1.16563i	0.977056	−	0.212985i	$-0.0683184\pi$
$644$	−1.98897	+	3.44500i	−0.0783765	+	0.135752i
$645$	0.502932	−	18.9946i	0.0198029	−	0.747913i
$646$	19.9471	+	34.5493i	0.784806	+	1.35932i
$647$	−27.3242			−1.07422			−0.537112	−	0.843511i	$-0.680485\pi$
$647$	−27.3242			−1.07422			−0.537112	+	0.843511i	$0.680485\pi$
$648$	−21.8185	−	2.31894i	−0.857113	−	0.0910966i
$649$	0.220074			0.00863867
$650$	0.780853	+	1.35248i	0.0306276	+	0.0530485i
$651$	0.228504	−	8.63009i	0.00895577	−	0.338240i
$652$	−4.14916	+	7.18656i	−0.162494	+	0.281447i
$653$	−4.42268	+	7.66031i	−0.173073	+	0.299771i	−0.939493	−	0.342569i	$-0.888703\pi$
$653$	−4.42268	+	7.66031i	−0.173073	+	0.299771i	0.766420	+	0.642340i	$0.222036\pi$
$654$	2.42355	−	1.31496i	0.0947682	−	0.0514192i
$655$	6.66518	+	11.5444i	0.260430	+	0.451078i
$656$	−8.40964			−0.328341
$657$	−25.2466	−	1.33788i	−0.984965	−	0.0521956i
$658$	−43.1026			−1.68031
$659$	2.69251	+	4.66357i	0.104885	+	0.181667i	0.913691	−	0.406409i	$-0.133219\pi$
$659$	2.69251	+	4.66357i	0.104885	+	0.181667i	−0.808806	+	0.588076i	$0.799886\pi$
$660$	−0.193987	−	0.118953i	−0.00755094	−	0.00463025i
$661$	20.1739	−	34.9422i	0.784672	−	1.35909i	−0.144522	−	0.989502i	$-0.546164\pi$
$661$	20.1739	−	34.9422i	0.784672	−	1.35909i	0.929195	−	0.369591i	$-0.120502\pi$
$662$	14.6152	−	25.3142i	0.568035	−	0.983866i
$663$	−12.1131	−	7.42777i	−0.470434	−	0.288471i
$664$	20.1415	+	34.8862i	0.781643	+	1.35385i
$665$	−15.4017			−0.597254
$666$	−9.90250	−	19.4628i	−0.383714	−	0.754168i
$667$	3.31882			0.128505
$668$	−3.80431	−	6.58926i	−0.147193	−	0.254946i
$669$	−44.3931	+	24.0867i	−1.71634	+	0.931247i
$670$	7.92021	−	13.7182i	0.305985	−	0.529981i
$671$	−0.499052	+	0.864383i	−0.0192657	+	0.0333691i
$672$	−0.553513	+	20.9050i	−0.0213522	+	0.806427i
$673$	−8.74409	−	15.1452i	−0.337060	−	0.583805i	0.646819	−	0.762644i	$-0.276099\pi$
$673$	−8.74409	−	15.1452i	−0.337060	−	0.583805i	−0.983878	+	0.178839i	$0.942766\pi$
$674$	32.8031			1.26353
$675$	4.69192	−	2.23290i	0.180592	−	0.0859443i
$676$	0.438929			0.0168819
$677$	8.44186	+	14.6217i	0.324447	+	0.561959i	0.981400	−	0.191972i	$-0.0614884\pi$
$677$	8.44186	+	14.6217i	0.324447	+	0.561959i	−0.656953	+	0.753931i	$0.728155\pi$
$678$	0.599008	−	22.6232i	0.0230048	−	0.868839i
$679$	−35.1809	+	60.9350i	−1.35012	+	2.33847i
$680$	9.99997	−	17.3205i	0.383481	−	0.664209i
$681$	8.97522	−	4.86976i	0.343931	−	0.186610i
$682$	0.235526	+	0.407944i	0.00901877	+	0.0156210i
$683$	−35.5062			−1.35861			−0.679303	−	0.733858i	$-0.737718\pi$
$683$	−35.5062			−1.35861			−0.679303	+	0.733858i	$0.737718\pi$
$684$	−2.23520	+	3.43752i	−0.0854650	+	0.131437i
$685$	10.1638			0.388337
$686$	−40.4156	−	70.0018i	−1.54307	−	2.67268i
$687$	29.6520	+	18.1827i	1.13130	+	0.693713i
$688$	25.6992	−	44.5124i	0.979775	−	1.69702i
$689$	−0.318260	+	0.551242i	−0.0121247	+	0.0210007i
$690$	4.22519	+	2.59089i	0.160850	+	0.0986337i
$691$	19.5028	+	33.7799i	0.741922	+	1.28505i	0.951619	+	0.307281i	$0.0994191\pi$
$691$	19.5028	+	33.7799i	0.741922	+	1.28505i	−0.209696	+	0.977767i	$0.567248\pi$
$692$	1.69336			0.0643718
$693$	−2.42112	+	3.72345i	−0.0919708	+	0.141442i
$694$	31.8295			1.20823
$695$	2.74257	+	4.75028i	0.104032	+	0.180188i
$696$	6.72258	−	3.64752i	0.254819	−	0.138259i
$697$	−7.36251	+	12.7522i	−0.278875	+	0.483025i
$698$	10.0613	−	17.4267i	0.380827	−	0.659611i
$699$	−0.279809	+	10.5678i	−0.0105833	+	0.399710i
$700$	−1.08550	−	1.88015i	−0.0410281	−	0.0710628i
$701$	−19.5418			−0.738082			−0.369041	−	0.929413i	$-0.620314\pi$
$701$	−19.5418			−0.738082			−0.369041	+	0.929413i	$0.620314\pi$
$702$	0.643758	−	8.08929i	0.0242971	−	0.305311i
$703$	14.5137			0.547394
$704$	0.831831	+	1.44077i	0.0313508	+	0.0543012i
$705$	−0.255813	+	9.66151i	−0.00963449	+	0.363874i
$706$	20.2148	−	35.0131i	0.760795	−	1.31774i
$707$	39.3556	−	68.1658i	1.48012	−	2.56364i
$708$	0.491316	−	0.266578i	0.0184648	−	0.0100186i
$709$	−2.31562	−	4.01078i	−0.0869650	−	0.150628i	0.819262	−	0.573420i	$-0.194384\pi$
$709$	−2.31562	−	4.01078i	−0.0869650	−	0.150628i	−0.906227	+	0.422792i	$0.861050\pi$
$710$	−0.748918			−0.0281064
$711$	19.9388	+	39.1886i	0.747765	+	1.46969i
$712$	32.9263			1.23397
$713$	−0.923225	−	1.59907i	−0.0345751	−	0.0598858i
$714$	93.5668	+	57.3753i	3.50165	+	2.14722i
$715$	−0.149658	+	0.259215i	−0.00559689	+	0.00969410i
$716$	1.57283	−	2.72422i	0.0587793	−	0.101809i
$717$	24.8519	+	15.2392i	0.928110	+	0.569118i
$718$	14.3113	+	24.7878i	0.534091	+	0.925073i
$719$	−7.26258			−0.270849			−0.135424	−	0.990788i	$-0.543240\pi$
$719$	−7.26258			−0.270849			−0.135424	+	0.990788i	$0.543240\pi$
$720$	14.0359	+	0.743795i	0.523087	+	0.0277196i
$721$	34.9475			1.30151
$722$	7.26484	+	12.5831i	0.270369	+	0.468293i
$723$	10.1662	−	5.51596i	0.378085	−	0.205141i
$724$	0.298258	−	0.516598i	0.0110847	−	0.0191992i
$725$	−0.905640	+	1.56861i	−0.0336346	+	0.0582569i
$726$	−0.781137	+	29.5018i	−0.0289907	+	1.09492i
$727$	−18.4428	−	31.9440i	−0.684007	−	1.18474i	−0.973748	−	0.227630i	$-0.926902\pi$
$727$	−18.4428	−	31.9440i	−0.684007	−	1.18474i	0.289740	−	0.957105i	$-0.406431\pi$
$728$	12.0584			0.446913
$729$	−26.6602	−	4.27036i	−0.987413	−	0.158161i
$730$	13.1611			0.487112
$731$	−44.9986	−	77.9398i	−1.66433	−	2.88271i
$732$	−0.0671006	+	2.53424i	−0.00248011	+	0.0936682i
$733$	−13.6739	+	23.6839i	−0.505058	+	0.874785i	0.494925	+	0.868935i	$0.335195\pi$
$733$	−13.6739	+	23.6839i	−0.505058	+	0.874785i	−0.999983	+	0.00584983i	$0.998138\pi$
$734$	10.6959	−	18.5258i	0.394791	−	0.683799i
$735$	−26.5877	+	14.4259i	−0.980701	+	0.532107i
$736$	2.23636	+	3.87349i	0.0824334	+	0.142779i
$737$	3.03597			0.111831
$738$	−8.39771	−	0.445014i	−0.309124	−	0.0163812i
$739$	35.8594			1.31911			0.659555	−	0.751656i	$-0.270745\pi$
$739$	35.8594			1.31911			0.659555	+	0.751656i	$0.270745\pi$
$740$	1.02291	+	1.77174i	0.0376030	+	0.0651304i
$741$	4.59782	+	2.81939i	0.168905	+	0.103573i
$742$	2.45838	−	4.25803i	0.0902498	−	0.156317i
$743$	−0.881101	+	1.52611i	−0.0323245	+	0.0559876i	−0.881735	−	0.471745i	$-0.843624\pi$
$743$	−0.881101	+	1.52611i	−0.0323245	+	0.0559876i	0.849411	+	0.527733i	$0.176958\pi$
$744$	−3.62753	−	2.22441i	−0.132992	−	0.0815507i
$745$	6.79858	+	11.7755i	0.249081	+	0.431420i
$746$	−35.1785			−1.28798
$747$	22.4787	+	44.1806i	0.822452	+	1.61648i
$748$	−1.07778			−0.0394076
$749$	39.0043	+	67.5575i	1.42519	+	2.46850i
$750$	−2.37754	+	1.29000i	−0.0868154	+	0.0471042i
$751$	17.2540	−	29.8847i	0.629606	−	1.09051i	−0.358025	−	0.933712i	$-0.616550\pi$
$751$	17.2540	−	29.8847i	0.629606	−	1.09051i	0.987631	−	0.156798i	$-0.0501171\pi$
$752$	−13.0718	+	22.6410i	−0.476679	+	0.825632i
$753$	0.605231	−	22.8582i	0.0220558	−	0.833001i
$754$	1.41434	+	2.44972i	0.0515074	+	0.0892134i
$755$	−5.51759			−0.200806
$756$	−0.894920	+	11.2453i	−0.0325479	+	0.408988i
$757$	−45.1803			−1.64210			−0.821052	−	0.570853i	$-0.806613\pi$
$757$	−45.1803			−1.64210			−0.821052	+	0.570853i	$0.806613\pi$
$758$	−0.292757	−	0.507070i	−0.0106334	−	0.0184176i
$759$	−0.0251429	+	0.949590i	−0.000912628	+	0.0344680i
$760$	−3.79573	+	6.57439i	−0.137686	+	0.238478i
$761$	14.7789	−	25.5978i	0.535735	−	0.927921i	−0.463392	−	0.886153i	$-0.653368\pi$
$761$	14.7789	−	25.5978i	0.535735	−	0.927921i	0.999127	−	0.0417676i	$-0.0132989\pi$
$762$	−5.21093	+	2.82734i	−0.188772	+	0.102424i
$763$	2.52093	+	4.36638i	0.0912638	+	0.158074i
$764$	1.61332			0.0583678
$765$	13.4161	−	20.6326i	0.485060	−	0.745974i
$766$	−22.1598			−0.800666
$767$	−0.367629	−	0.636752i	−0.0132743	−	0.0229918i
$768$	14.8601	+	9.11222i	0.536216	+	0.328809i
$769$	−7.87546	+	13.6407i	−0.283996	+	0.491896i	−0.972365	−	0.233465i	$-0.924994\pi$
$769$	−7.87546	+	13.6407i	−0.283996	+	0.491896i	0.688369	+	0.725361i	$0.258327\pi$
$770$	1.15602	−	2.00229i	0.0416602	−	0.0721575i
$771$	−27.6526	−	16.9566i	−0.995883	−	0.610677i
$772$	−0.892327	−	1.54555i	−0.0321155	−	0.0556257i
$773$	−41.4251			−1.48996			−0.744979	−	0.667088i	$-0.767540\pi$
$773$	−41.4251			−1.48996			−0.744979	+	0.667088i	$0.767540\pi$
$774$	28.0183	−	43.0894i	1.00710	−	1.54882i
$775$	1.00772			0.0361984
$776$	17.3405	+	30.0346i	0.622488	+	1.07818i
$777$	35.0969	−	19.0428i	1.25910	−	0.683158i
$778$	−17.7384	+	30.7238i	−0.635951	+	1.10150i
$779$	2.79462	−	4.84042i	0.100127	−	0.173426i
$780$	−0.0201224	+	0.759980i	−0.000720499	+	0.0272117i
$781$	−0.0717686	−	0.124307i	−0.00256808	−	0.00444805i
$782$	23.4749			0.839461
$783$	8.49839	−	4.04441i	0.303708	−	0.144535i
$784$	−81.8240			−2.92228
$785$	−3.18559	−	5.51760i	−0.113698	−	0.196931i
$786$	−0.954395	+	36.0454i	−0.0340422	+	1.28570i
$787$	−13.9735	+	24.2028i	−0.498100	+	0.862735i	−0.999998	−	0.00219222i	$-0.999302\pi$
$787$	−13.9735	+	24.2028i	−0.498100	+	0.862735i	0.501897	+	0.864927i	$0.332636\pi$
$788$	0.782482	−	1.35530i	0.0278748	−	0.0482805i
$789$	27.8588	−	15.1156i	0.991800	−	0.538129i
$790$	−11.4445	−	19.8225i	−0.407179	−	0.705254i
$791$	41.3822			1.47138
$792$	0.992712	+	1.95112i	0.0352745	+	0.0693299i
$793$	3.33461			0.118416
$794$	−3.64798	−	6.31849i	−0.129462	−	0.224235i
$795$	−0.939855	−	0.576320i	−0.0333332	−	0.0204400i
$796$	−1.17940	+	2.04278i	−0.0418027	+	0.0724044i
$797$	−14.4943	+	25.1049i	−0.513415	+	0.889261i	0.486464	+	0.873701i	$0.338287\pi$
$797$	−14.4943	+	25.1049i	−0.513415	+	0.889261i	−0.999879	+	0.0155603i	$0.995047\pi$
$798$	−35.5155	−	21.7782i	−1.25724	−	0.770939i
$799$	22.8883	+	39.6437i	0.809729	+	1.40249i
$800$	−2.44104			−0.0863037
$801$	40.4607	+	2.14411i	1.42961	+	0.0757582i
$802$	−21.0213			−0.742288
$803$	1.26122	+	2.18450i	0.0445075	+	0.0770893i
$804$	6.77781	−	3.67749i	0.239035	−	0.129695i
$805$	−4.53142	+	7.84866i	−0.159712	+	0.276629i
$806$	0.786882	−	1.36292i	0.0277167	−	0.0480068i
$807$	−0.167730	+	6.33479i	−0.00590437	+	0.222995i
$808$	−19.3982	−	33.5987i	−0.682427	−	1.18200i
$809$	−27.4686			−0.965746			−0.482873	−	0.875690i	$-0.660407\pi$
$809$	−27.4686			−0.965746			−0.482873	+	0.875690i	$0.660407\pi$
$810$	13.9766	+	1.48548i	0.491089	+	0.0521945i
$811$	−6.38660			−0.224264			−0.112132	−	0.993693i	$-0.535768\pi$
$811$	−6.38660			−0.224264			−0.112132	+	0.993693i	$0.535768\pi$
$812$	−1.96615	−	3.40547i	−0.0689983	−	0.119509i
$813$	−0.420067	+	15.8650i	−0.0147324	+	0.556410i
$814$	−1.08937	+	1.88684i	−0.0381823	+	0.0661337i
$815$	−9.45293	+	16.3730i	−0.331122	+	0.573520i
$816$	58.5143	−	31.7486i	2.04841	−	1.11142i
$817$	17.0803	+	29.5839i	0.597564	+	1.03501i
$818$	−56.6407			−1.98039
$819$	14.8176	+	0.785221i	0.517770	+	0.0274379i
$820$	0.787849			0.0275129
$821$	−12.5386	−	21.7175i	−0.437601	−	0.757947i	0.559903	−	0.828558i	$-0.310838\pi$
$821$	−12.5386	−	21.7175i	−0.437601	−	0.757947i	−0.997504	+	0.0706112i	$0.977505\pi$
$822$	23.4370	+	14.3716i	0.817461	+	0.501268i
$823$	−12.5477	+	21.7333i	−0.437386	+	0.757574i	−0.997487	−	0.0708497i	$-0.977429\pi$
$823$	−12.5477	+	21.7333i	−0.437386	+	0.757574i	0.560101	+	0.828424i	$0.310762\pi$
$824$	8.61274	−	14.9177i	0.300039	−	0.519683i
$825$	−0.441956	−	0.271008i	−0.0153869	−	0.00943529i
$826$	2.83972	+	4.91854i	0.0988066	+	0.171138i
$827$	6.89156			0.239643			0.119821	−	0.992795i	$-0.461768\pi$
$827$	6.89156			0.239643			0.119821	+	0.992795i	$0.461768\pi$
$828$	1.09411	+	2.15042i	0.0380231	+	0.0747322i
$829$	−15.3569			−0.533367			−0.266683	−	0.963784i	$-0.585928\pi$
$829$	−15.3569			−0.533367			−0.266683	+	0.963784i	$0.585928\pi$
$830$	−12.9024	−	22.3476i	−0.447848	−	0.775696i
$831$	−29.7224	+	16.1267i	−1.03106	+	0.559430i
$832$	2.77911	−	4.81356i	0.0963482	−	0.166880i
$833$	−71.6356	+	124.077i	−2.48203	+	4.29900i
$834$	−0.392712	+	14.8319i	−0.0135985	+	0.513586i
$835$	−8.66727	−	15.0122i	−0.299943	−	0.519517i
$836$	0.409097			0.0141489
$837$	−4.31275	−	2.96963i	−0.149070	−	0.102645i
$838$	−27.0778			−0.935387
$839$	11.3154	+	19.5989i	0.390651	+	0.676628i	0.992536	−	0.121955i	$-0.0389165\pi$
$839$	11.3154	+	19.5989i	0.390651	+	0.676628i	−0.601884	+	0.798583i	$0.705583\pi$
$840$	−0.552810	+	20.8784i	−0.0190738	+	0.720374i
$841$	12.8596	−	22.2735i	0.443436	−	0.768053i
$842$	0.0817141	−	0.141533i	0.00281605	−	0.00487755i
$843$	25.7455	−	13.9690i	0.886723	−	0.481117i
$844$	4.82250	+	8.35282i	0.165997	+	0.287516i
$845$	1.00000			0.0344010
$846$	−14.2513	+	21.9172i	−0.489971	+	0.753528i
$847$	−53.9645			−1.85424
$848$	−1.49111	−	2.58268i	−0.0512050	−	0.0886896i
$849$	−30.4314	−	18.6606i	−1.04440	−	0.640429i
$850$	−6.40584	+	11.0952i	−0.219718	+	0.380564i
$851$	4.27014	−	7.39611i	0.146379	−	0.253535i
$852$	−0.310797	−	0.190582i	−0.0106477	−	0.00652921i
$853$	12.7936	+	22.1592i	0.438045	+	0.758716i	0.997539	−	0.0701185i	$-0.0223377\pi$
$853$	12.7936	+	22.1592i	0.438045	+	0.758716i	−0.559494	+	0.828835i	$0.689004\pi$
$854$	−25.7580			−0.881420
$855$	−5.09240	+	7.83161i	−0.174156	+	0.267835i
$856$	38.4502			1.31420
$857$	5.53224	+	9.58212i	0.188978	+	0.327319i	0.944910	−	0.327331i	$-0.106149\pi$
$857$	5.53224	+	9.58212i	0.188978	+	0.327319i	−0.755932	+	0.654650i	$0.772816\pi$
$858$	−0.711635	+	0.386118i	−0.0242948	+	0.0131818i
$859$	15.9113	−	27.5592i	0.542888	−	0.940309i	−0.455849	−	0.890057i	$-0.650664\pi$
$859$	15.9113	−	27.5592i	0.542888	−	0.940309i	0.998737	−	0.0502519i	$-0.0160024\pi$
$860$	−2.40761	+	4.17010i	−0.0820989	+	0.142199i
$861$	0.407008	−	15.3718i	0.0138708	−	0.523869i
$862$	−15.6742	−	27.1485i	−0.533866	−	0.924682i
$863$	−44.3431			−1.50946			−0.754728	−	0.656038i	$-0.772231\pi$
$863$	−44.3431			−1.50946			−0.754728	+	0.656038i	$0.772231\pi$
$864$	10.4469	+	7.19343i	0.355412	+	0.244726i
$865$	3.85793			0.131174
$866$	10.7944	+	18.6964i	0.366807	+	0.635328i
$867$	2.30596	−	87.0911i	0.0783145	−	2.95777i
$868$	−1.09388	+	1.89466i	−0.0371288	+	0.0643090i
$869$	2.19346	−	3.79918i	0.0744079	−	0.128878i
$870$	−4.30639	+	2.33655i	−0.146000	+	0.0792165i
$871$	−5.07151	−	8.78411i	−0.171842	−	0.297638i
$872$	2.48511			0.0841566
$873$	19.3526	+	38.0365i	0.654988	+	1.28734i
$874$	−8.91046			−0.301401
$875$	−2.47307	−	4.28349i	−0.0836051	−	0.144808i
$876$	5.46178	+	3.34917i	0.184536	+	0.113158i
$877$	−1.78174	+	3.08606i	−0.0601650	+	0.104209i	−0.894539	−	0.446990i	$-0.852496\pi$
$877$	−1.78174	+	3.08606i	−0.0601650	+	0.104209i	0.834374	+	0.551199i	$0.185829\pi$
$878$	25.0662	−	43.4159i	0.845942	−	1.46521i
$879$	−23.3243	−	14.3025i	−0.786709	−	0.482412i
$880$	−0.701178	−	1.21448i	−0.0236367	−	0.0409400i
$881$	−41.6512			−1.40326			−0.701632	−	0.712540i	$-0.747545\pi$
$881$	−41.6512			−1.40326			−0.701632	+	0.712540i	$0.747545\pi$
$882$	−81.7080	−	4.32989i	−2.75125	−	0.145795i
$883$	13.6678			0.459958			0.229979	−	0.973196i	$-0.426134\pi$
$883$	13.6678			0.459958			0.229979	+	0.973196i	$0.426134\pi$
$884$	1.80041	+	3.11839i	0.0605542	+	0.104883i
$885$	1.11935	−	0.607337i	0.0376267	−	0.0204154i
$886$	−5.47643	+	9.48545i	−0.183984	+	0.318670i
$887$	−7.22380	+	12.5120i	−0.242552	+	0.420112i	−0.961440	−	0.275013i	$-0.911318\pi$
$887$	−7.22380	+	12.5120i	−0.242552	+	0.420112i	0.718889	+	0.695125i	$0.244651\pi$
$888$	0.520935	−	19.6746i	0.0174814	−	0.660236i
$889$	−5.42031	−	9.38826i	−0.181791	−	0.314872i
$890$	−21.0921			−0.707010
$891$	1.09282	+	2.46223i	0.0366107	+	0.0824876i
$892$	12.7992			0.428548
$893$	−8.68779	−	15.0477i	−0.290726	−	0.503552i
$894$	−0.973497	+	36.7668i	−0.0325586	+	1.22967i
$895$	3.58333	−	6.20652i	0.119778	−	0.207461i
$896$	−33.5407	+	58.0943i	−1.12052	+	1.94079i
$897$	2.78950	−	1.51352i	0.0931386	−	0.0505350i
$898$	−30.3112	−	52.5006i	−1.01150	−	1.75197i
$899$	1.82526			0.0608759
$900$	−1.31494	−	0.0696818i	−0.0438314	−	0.00232273i
$901$	−5.22178			−0.173963
$902$	0.419516	+	0.726624i	0.0139684	+	0.0241939i
$903$	80.1195	+	49.1294i	2.66621	+	1.63492i
$904$	10.1986	−	17.6644i	0.339199	−	0.587510i
$905$	0.679513	−	1.17695i	0.0225878	−	0.0391232i
$906$	−12.7232	−	7.80191i	−0.422701	−	0.259201i
$907$	5.03453	+	8.72006i	0.167169	+	0.289545i	0.937423	−	0.348192i	$-0.113204\pi$
$907$	5.03453	+	8.72006i	0.167169	+	0.289545i	−0.770255	+	0.637736i	$0.779871\pi$
$908$	−2.58768			−0.0858753
$909$	−21.6491	−	42.5501i	−0.718056	−	1.41130i
$910$	−7.72443			−0.256062
$911$	−3.72430	−	6.45068i	−0.123392	−	0.213720i	0.797712	−	0.603039i	$-0.206044\pi$
$911$	−3.72430	−	6.45068i	−0.123392	−	0.213720i	−0.921103	+	0.389319i	$0.872710\pi$
$912$	−22.2105	+	12.0509i	−0.735464	+	0.399047i
$913$	2.47286	−	4.28313i	0.0818399	−	0.141751i
$914$	−16.4219	+	28.4435i	−0.543187	+	0.940828i
$915$	−0.152873	+	5.77370i	−0.00505384	+	0.190872i
$916$	−4.40727	−	7.63362i	−0.145620	−	0.252222i
$917$	−65.9339			−2.17733
$918$	60.1114	−	28.6072i	1.98397	−	0.944178i
$919$	31.5254			1.03993			0.519963	−	0.854189i	$-0.325946\pi$
$919$	31.5254			1.03993			0.519963	+	0.854189i	$0.325946\pi$
$920$	2.23352	+	3.86857i	0.0736370	+	0.127543i
$921$	0.740117	−	27.9526i	0.0243877	−	0.921069i
$922$	−19.0512	+	32.9977i	−0.627419	+	1.08672i
$923$	−0.239775	+	0.415303i	−0.00789230	+	0.0136699i
$924$	0.989279	−	0.536761i	0.0325449	−	0.0176582i
$925$	2.33048	+	4.03650i	0.0766256	+	0.132719i
$926$	23.1927			0.762161
$927$	11.5550	−	17.7704i	0.379515	−	0.583657i
$928$	−4.42140			−0.145140
$929$	−14.0586	−	24.3503i	−0.461249	−	0.798907i	0.537774	−	0.843089i	$-0.319265\pi$
$929$	−14.0586	−	24.3503i	−0.461249	−	0.798907i	−0.999024	+	0.0441819i	$0.985932\pi$
$930$	2.32374	+	1.42492i	0.0761986	+	0.0467251i
$931$	27.1910	−	47.0962i	0.891149	−	1.54352i
$932$	1.33949	−	2.32006i	0.0438764	−	0.0759961i
$933$	−25.9043	−	15.8846i	−0.848069	−	0.520037i
$934$	−0.116713	−	0.202152i	−0.00381896	−	0.00661463i
$935$	−2.45548			−0.0803028
$936$	3.98696	−	6.13155i	0.130318	−	0.200416i
$937$	−17.2669			−0.564086			−0.282043	−	0.959402i	$-0.591012\pi$
$937$	−17.2669			−0.564086			−0.282043	+	0.959402i	$0.591012\pi$
$938$	39.1745	+	67.8523i	1.27909	+	2.21546i
$939$	−28.9684	+	15.7176i	−0.945348	+	0.512926i
$940$	1.22462	−	2.12110i	0.0399426	−	0.0691827i
$941$	8.68548	−	15.0437i	0.283139	−	0.490410i	−0.689018	−	0.724745i	$-0.741958\pi$
$941$	8.68548	−	15.0437i	0.283139	−	0.490410i	0.972156	+	0.234334i	$0.0752910\pi$
$942$	0.456148	−	17.2277i	0.0148621	−	0.561309i
$943$	−1.64444	−	2.84825i	−0.0535502	−	0.0927517i
$944$	3.44483			0.112120
$945$	−2.03887	+	25.6199i	−0.0663246	+	0.833416i
$946$	−5.12805			−0.166727
$947$	4.00127	+	6.93041i	0.130024	+	0.225208i	0.923686	−	0.383151i	$-0.125161\pi$
$947$	4.00127	+	6.93041i	0.130024	+	0.225208i	−0.793662	+	0.608359i	$0.791828\pi$
$948$	0.294924	−	11.1386i	0.00957868	−	0.361766i
$949$	4.21367	−	7.29830i	0.136782	−	0.236913i
$950$	2.43149	−	4.21146i	0.0788879	−	0.136638i
$951$	5.24951	−	2.84827i	0.170227	−	0.0923614i
$952$	49.4613	+	85.6695i	1.60305	+	2.77656i
$953$	16.3425			0.529386			0.264693	−	0.964333i	$-0.414729\pi$
$953$	16.3425			0.529386			0.264693	+	0.964333i	$0.414729\pi$
$954$	−1.35233	−	2.65792i	−0.0437833	−	0.0860534i
$955$	3.67558			0.118939
$956$	−3.69381	−	6.39786i	−0.119466	−	0.206922i
$957$	−0.800506	−	0.490871i	−0.0258767	−	0.0158676i
$958$	1.58693	−	2.74864i	0.0512714	−	0.0888046i
$959$	−25.1357	+	43.5363i	−0.811675	+	1.40586i
$960$	8.20699	+	5.03254i	0.264880	+	0.162425i
$961$	14.9923	+	25.9673i	0.483621	+	0.837656i
$962$	7.27904			0.234686
$963$	47.2485	+	2.50381i	1.52256	+	0.0806841i
$964$	−2.93106			−0.0944031
$965$	−2.03296	−	3.52120i	−0.0654434	−	0.113351i
$966$	−21.5473	+	11.6911i	−0.693272	+	0.376154i
$967$	27.1847	−	47.0852i	0.874200	−	1.51416i	0.0165884	−	0.999862i	$-0.494720\pi$
$967$	27.1847	−	47.0852i	0.874200	−	1.51416i	0.857612	−	0.514297i	$-0.171947\pi$
$968$	−13.2994	+	23.0353i	−0.427460	+	0.740383i
$969$	−1.17111	+	44.2301i	−0.0376213	+	1.42087i
$970$	−11.1081	−	19.2398i	−0.356659	−	0.617752i
$971$	−20.5742			−0.660257			−0.330128	−	0.943936i	$-0.607092\pi$
$971$	−20.5742			−0.660257			−0.330128	+	0.943936i	$0.607092\pi$
$972$	5.42222	+	4.17319i	0.173918	+	0.133855i
$973$	−27.1303			−0.869758
$974$	5.54044	+	9.59632i	0.177527	+	0.307486i
$975$	−0.0458444	+	1.73144i	−0.00146820	+	0.0554506i
$976$	−7.81166	+	13.5302i	−0.250045	+	0.433091i
$977$	18.1836	−	31.4949i	0.581745	−	1.00761i	−0.413528	−	0.910491i	$-0.635704\pi$
$977$	18.1836	−	31.4949i	0.581745	−	1.00761i	0.995273	−	0.0971197i	$-0.0309630\pi$
$978$	−44.9494	+	24.3886i	−1.43732	+	0.779861i
$979$	−2.02125	−	3.50092i	−0.0645996	−	0.111890i
$980$	7.66561			0.244869
$981$	3.05377	+	0.161826i	0.0974994	+	0.00516672i
$982$	−13.2688			−0.423425
$983$	10.9862	+	19.0286i	0.350405	+	0.606919i	0.986320	−	0.164840i	$-0.0527108\pi$
$983$	10.9862	+	19.0286i	0.350405	+	0.606919i	−0.635916	+	0.771758i	$0.719377\pi$
$984$	−6.46131	−	3.96208i	−0.205979	−	0.126307i
$985$	1.78271	−	3.08774i	0.0568018	−	0.0983836i
$986$	−11.6028	+	20.0966i	−0.369507	+	0.640006i
$987$	−40.7523	−	24.9894i	−1.29716	−	0.795421i
$988$	−0.683387	−	1.18366i	−0.0217414	−	0.0376573i
$989$	20.1011			0.639178
$990$	−0.635917	−	1.24986i	−0.0202108	−	0.0397231i
$991$	−3.05592			−0.0970744			−0.0485372	−	0.998821i	$-0.515456\pi$
$991$	−3.05592			−0.0970744			−0.0485372	+	0.998821i	$0.515456\pi$
$992$	1.22994	+	2.13032i	0.0390507	+	0.0676377i
$993$	28.4946	−	15.4605i	0.904249	−	0.490626i
$994$	1.85213	−	3.20798i	0.0587459	−	0.101751i
$995$	−2.68700	+	4.65401i	−0.0851835	+	0.147542i
$996$	0.332492	−	12.5575i	0.0105354	−	0.397899i
$997$	−21.6821	−	37.5545i	−0.686679	−	1.18936i	−0.972906	−	0.231201i	$-0.925734\pi$
$997$	−21.6821	−	37.5545i	−0.686679	−	1.18936i	0.286227	−	0.958162i	$-0.407599\pi$
$998$	59.8666			1.89504
$999$	1.92131	−	24.1427i	0.0607876	−	0.763841i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.i.g.391.4	yes	26
3.2	odd	2		1755.2.i.g.1171.10		26
9.2	odd	6		1755.2.i.g.586.10		26
9.4	even	3		5265.2.a.bg.1.10		13
9.5	odd	6		5265.2.a.bh.1.4		13
9.7	even	3	inner	585.2.i.g.196.4	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.g.196.4	✓	26	9.7	even	3	inner
585.2.i.g.391.4	yes	26	1.1	even	1	trivial
1755.2.i.g.586.10		26	9.2	odd	6
1755.2.i.g.1171.10		26	3.2	odd	2
5265.2.a.bg.1.10		13	9.4	even	3
5265.2.a.bh.1.4		13	9.5	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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.780853 - 1.35248i) q^{2} +(0.0458444 - 1.73144i) q^{3} +(-0.219464 + 0.380123i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-2.37754 + 1.29000i) q^{6} +(-2.47307 - 4.28349i) q^{7} -2.43794 q^{8} +(-2.99580 - 0.158754i) q^{9} +O(q^{10})\)	\(q+(-0.780853 - 1.35248i) q^{2} +(0.0458444 - 1.73144i) q^{3} +(-0.219464 + 0.380123i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-2.37754 + 1.29000i) q^{6} +(-2.47307 - 4.28349i) q^{7} -2.43794 q^{8} +(-2.99580 - 0.158754i) q^{9} +1.56171 q^{10} +(0.149658 + 0.259215i) q^{11} +(0.648101 + 0.397417i) q^{12} +(0.500000 - 0.866025i) q^{13} +(-3.86221 + 6.68955i) q^{14} +(1.47655 + 0.905424i) q^{15} +(2.34260 + 4.05750i) q^{16} +8.20364 q^{17} +(2.12457 + 4.17571i) q^{18} -3.11389 q^{19} +(-0.219464 - 0.380123i) q^{20} +(-7.53000 + 4.08561i) q^{21} +(0.233722 - 0.404818i) q^{22} +(-0.916153 + 1.58682i) q^{23} +(-0.111766 + 4.22115i) q^{24} +(-0.500000 - 0.866025i) q^{25} -1.56171 q^{26} +(-0.412215 + 5.17978i) q^{27} +2.17101 q^{28} +(-0.905640 - 1.56861i) q^{29} +(0.0715956 - 2.70401i) q^{30} +(-0.503860 + 0.872711i) q^{31} +(1.22052 - 2.11400i) q^{32} +(0.455678 - 0.247241i) q^{33} +(-6.40584 - 11.0952i) q^{34} +4.94615 q^{35} +(0.717817 - 1.10393i) q^{36} -4.66095 q^{37} +(2.43149 + 4.21146i) q^{38} +(-1.47655 - 0.905424i) q^{39} +(1.21897 - 2.11131i) q^{40} +(-0.897469 + 1.55446i) q^{41} +(11.4055 + 6.99389i) q^{42} +(-5.48520 - 9.50064i) q^{43} -0.131378 q^{44} +(1.63538 - 2.51506i) q^{45} +2.86152 q^{46} +(2.79002 + 4.83245i) q^{47} +(7.13273 - 3.87007i) q^{48} +(-8.73218 + 15.1246i) q^{49} +(-0.780853 + 1.35248i) q^{50} +(0.376091 - 14.2041i) q^{51} +(0.219464 + 0.380123i) q^{52} -0.636520 q^{53} +(7.32741 - 3.48713i) q^{54} -0.299316 q^{55} +(6.02919 + 10.4429i) q^{56} +(-0.142754 + 5.39152i) q^{57} +(-1.41434 + 2.44972i) q^{58} +(0.367629 - 0.636752i) q^{59} +(-0.668224 + 0.362564i) q^{60} +(1.66731 + 2.88786i) q^{61} +1.57376 q^{62} +(6.72880 + 13.2251i) q^{63} +5.55821 q^{64} +(0.500000 + 0.866025i) q^{65} +(-0.690205 - 0.423235i) q^{66} +(5.07151 - 8.78411i) q^{67} +(-1.80041 + 3.11839i) q^{68} +(2.70549 + 1.65901i) q^{69} +(-3.86221 - 6.68955i) q^{70} -0.479551 q^{71} +(7.30356 + 0.387033i) q^{72} +8.42735 q^{73} +(3.63952 + 6.30384i) q^{74} +(-1.52240 + 0.826020i) q^{75} +(0.683387 - 1.18366i) q^{76} +(0.740230 - 1.28212i) q^{77} +(-0.0715956 + 2.70401i) q^{78} +(-7.32823 - 12.6929i) q^{79} -4.68520 q^{80} +(8.94959 + 0.951190i) q^{81} +2.80317 q^{82} +(-8.26172 - 14.3097i) q^{83} +(0.0995285 - 3.75897i) q^{84} +(-4.10182 + 7.10456i) q^{85} +(-8.56627 + 14.8372i) q^{86} +(-2.75749 + 1.49615i) q^{87} +(-0.364857 - 0.631950i) q^{88} -13.5058 q^{89} +(-4.67856 - 0.247928i) q^{90} -4.94615 q^{91} +(-0.402126 - 0.696502i) q^{92} +(1.48795 + 0.912414i) q^{93} +(4.35719 - 7.54687i) q^{94} +(1.55694 - 2.69670i) q^{95} +(-3.60432 - 2.21017i) q^{96} +(-7.11278 - 12.3197i) q^{97} +27.2742 q^{98} +(-0.407194 - 0.800315i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + q^{2} + q^{3} - 15 q^{4} - 13 q^{5} + 7 q^{6} - 10 q^{7} - 12 q^{8} + 7 q^{9}+O(q^{10}) \) 26 * q + q^2 + q^3 - 15 * q^4 - 13 * q^5 + 7 * q^6 - 10 * q^7 - 12 * q^8 + 7 * q^9	\( 26 q + q^{2} + q^{3} - 15 q^{4} - 13 q^{5} + 7 q^{6} - 10 q^{7} - 12 q^{8} + 7 q^{9} - 2 q^{10} - 11 q^{11} - 20 q^{12} + 13 q^{13} - 15 q^{14} - 2 q^{15} - 19 q^{16} + 6 q^{17} - 13 q^{18} + 30 q^{19} - 15 q^{20} - q^{21} - 12 q^{22} - 6 q^{23} + 20 q^{24} - 13 q^{25} + 2 q^{26} - 2 q^{27} + 10 q^{28} - 14 q^{29} - 2 q^{30} - 30 q^{31} + 43 q^{32} + 6 q^{33} - 19 q^{34} + 20 q^{35} - 39 q^{36} + 32 q^{37} + 2 q^{38} + 2 q^{39} + 6 q^{40} - 17 q^{41} + 83 q^{42} - 6 q^{43} + 46 q^{44} - 5 q^{45} + 46 q^{46} + 21 q^{47} - 7 q^{48} - 29 q^{49} + q^{50} + 55 q^{51} + 15 q^{52} + 2 q^{53} - 6 q^{54} + 22 q^{55} - 37 q^{56} + 33 q^{57} - 14 q^{58} - 13 q^{59} + 25 q^{60} - 22 q^{61} - 114 q^{62} - 44 q^{63} + 84 q^{64} + 13 q^{65} - 68 q^{66} - 35 q^{67} + 4 q^{68} - 38 q^{69} - 15 q^{70} + 24 q^{71} - 24 q^{72} + 64 q^{73} + 28 q^{74} + q^{75} - 54 q^{76} - 4 q^{77} + 2 q^{78} - 12 q^{79} + 38 q^{80} + 15 q^{81} + 46 q^{82} + 3 q^{83} + 27 q^{84} - 3 q^{85} + 40 q^{86} - 12 q^{87} - 29 q^{88} + 12 q^{89} - 10 q^{90} - 20 q^{91} + 16 q^{92} - 9 q^{93} - 44 q^{94} - 15 q^{95} + 51 q^{96} - 33 q^{97} + 70 q^{98} - 22 q^{99}+O(q^{100}) \) 26 * q + q^2 + q^3 - 15 * q^4 - 13 * q^5 + 7 * q^6 - 10 * q^7 - 12 * q^8 + 7 * q^9 - 2 * q^10 - 11 * q^11 - 20 * q^12 + 13 * q^13 - 15 * q^14 - 2 * q^15 - 19 * q^16 + 6 * q^17 - 13 * q^18 + 30 * q^19 - 15 * q^20 - q^21 - 12 * q^22 - 6 * q^23 + 20 * q^24 - 13 * q^25 + 2 * q^26 - 2 * q^27 + 10 * q^28 - 14 * q^29 - 2 * q^30 - 30 * q^31 + 43 * q^32 + 6 * q^33 - 19 * q^34 + 20 * q^35 - 39 * q^36 + 32 * q^37 + 2 * q^38 + 2 * q^39 + 6 * q^40 - 17 * q^41 + 83 * q^42 - 6 * q^43 + 46 * q^44 - 5 * q^45 + 46 * q^46 + 21 * q^47 - 7 * q^48 - 29 * q^49 + q^50 + 55 * q^51 + 15 * q^52 + 2 * q^53 - 6 * q^54 + 22 * q^55 - 37 * q^56 + 33 * q^57 - 14 * q^58 - 13 * q^59 + 25 * q^60 - 22 * q^61 - 114 * q^62 - 44 * q^63 + 84 * q^64 + 13 * q^65 - 68 * q^66 - 35 * q^67 + 4 * q^68 - 38 * q^69 - 15 * q^70 + 24 * q^71 - 24 * q^72 + 64 * q^73 + 28 * q^74 + q^75 - 54 * q^76 - 4 * q^77 + 2 * q^78 - 12 * q^79 + 38 * q^80 + 15 * q^81 + 46 * q^82 + 3 * q^83 + 27 * q^84 - 3 * q^85 + 40 * q^86 - 12 * q^87 - 29 * q^88 + 12 * q^89 - 10 * q^90 - 20 * q^91 + 16 * q^92 - 9 * q^93 - 44 * q^94 - 15 * q^95 + 51 * q^96 - 33 * q^97 + 70 * q^98 - 22 * q^99

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