LMFDB - Embedded newform 585.2.i.g.196.9

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			196.9
Character	$\chi$	$=$	585.196
Dual form			585.2.i.g.391.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.669930 - 1.16035i) q^{2} +(0.478101 - 1.66476i) q^{3} +(0.102389 + 0.177343i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.61141 - 1.67004i) q^{6} +(-0.186958 + 0.323821i) q^{7} +2.95409 q^{8} +(-2.54284 - 1.59184i) q^{9} +O(q^{10})$	\(q+(0.669930 - 1.16035i) q^{2} +(0.478101 - 1.66476i) q^{3} +(0.102389 + 0.177343i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.61141 - 1.67004i) q^{6} +(-0.186958 + 0.323821i) q^{7} +2.95409 q^{8} +(-2.54284 - 1.59184i) q^{9} -1.33986 q^{10} +(2.53321 - 4.38765i) q^{11} +(0.344185 - 0.0856650i) q^{12} +(0.500000 + 0.866025i) q^{13} +(0.250497 + 0.433874i) q^{14} +(-1.68077 + 0.418332i) q^{15} +(1.77426 - 3.07310i) q^{16} -0.733484 q^{17} +(-3.55062 + 1.88417i) q^{18} -3.65108 q^{19} +(0.102389 - 0.177343i) q^{20} +(0.449699 + 0.466059i) q^{21} +(-3.39414 - 5.87883i) q^{22} +(-0.697881 - 1.20877i) q^{23} +(1.41235 - 4.91785i) q^{24} +(-0.500000 + 0.866025i) q^{25} +1.33986 q^{26} +(-3.86577 + 3.47215i) q^{27} -0.0765697 q^{28} +(1.02349 - 1.77274i) q^{29} +(-0.640587 + 2.23054i) q^{30} +(-0.541514 - 0.937930i) q^{31} +(0.576839 + 0.999115i) q^{32} +(-6.09324 - 6.31492i) q^{33} +(-0.491383 + 0.851099i) q^{34} +0.373916 q^{35} +(0.0219434 - 0.613941i) q^{36} +2.03066 q^{37} +(-2.44597 + 4.23654i) q^{38} +(1.68077 - 0.418332i) q^{39} +(-1.47705 - 2.55832i) q^{40} +(3.99634 + 6.92187i) q^{41} +(0.842059 - 0.209582i) q^{42} +(0.227676 - 0.394347i) q^{43} +1.03749 q^{44} +(-0.107157 + 2.99809i) q^{45} -1.87012 q^{46} +(-1.83933 + 3.18582i) q^{47} +(-4.26770 - 4.42296i) q^{48} +(3.43009 + 5.94110i) q^{49} +(0.669930 + 1.16035i) q^{50} +(-0.350679 + 1.22107i) q^{51} +(-0.102389 + 0.177343i) q^{52} -0.225888 q^{53} +(1.43913 + 6.81175i) q^{54} -5.06642 q^{55} +(-0.552291 + 0.956596i) q^{56} +(-1.74558 + 6.07817i) q^{57} +(-1.37134 - 2.37522i) q^{58} +(3.71136 + 6.42826i) q^{59} +(-0.246281 - 0.255240i) q^{60} +(0.283754 - 0.491476i) q^{61} -1.45111 q^{62} +(0.990877 - 0.525817i) q^{63} +8.64279 q^{64} +(0.500000 - 0.866025i) q^{65} +(-11.4096 + 2.83976i) q^{66} +(-5.39166 - 9.33863i) q^{67} +(-0.0751006 - 0.130078i) q^{68} +(-2.34596 + 0.583892i) q^{69} +(0.250497 - 0.433874i) q^{70} +14.0647 q^{71} +(-7.51178 - 4.70245i) q^{72} +3.36196 q^{73} +(1.36040 - 2.35628i) q^{74} +(1.20267 + 1.24643i) q^{75} +(-0.373830 - 0.647492i) q^{76} +(0.947208 + 1.64061i) q^{77} +(0.640587 - 2.23054i) q^{78} +(-6.20057 + 10.7397i) q^{79} -3.54851 q^{80} +(3.93207 + 8.09561i) q^{81} +10.7091 q^{82} +(2.84151 - 4.92164i) q^{83} +(-0.0366080 + 0.127470i) q^{84} +(0.366742 + 0.635216i) q^{85} +(-0.305054 - 0.528369i) q^{86} +(-2.46185 - 2.55142i) q^{87} +(7.48333 - 12.9615i) q^{88} +8.89766 q^{89} +(3.40705 + 2.13285i) q^{90} -0.373916 q^{91} +(0.142910 - 0.247528i) q^{92} +(-1.82033 + 0.453065i) q^{93} +(2.46445 + 4.26854i) q^{94} +(1.82554 + 3.16193i) q^{95} +(1.93907 - 0.482621i) q^{96} +(-8.79576 + 15.2347i) q^{97} +9.19168 q^{98} +(-13.4260 + 7.12461i) 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 $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$	0.669930	−	1.16035i	0.473712	−	0.820493i	−0.525835	−	0.850586i	$-0.676247\pi$
$2$	0.669930	−	1.16035i	0.473712	−	0.820493i	0.999547	+	0.0300936i	$0.00958054\pi$
$3$	0.478101	−	1.66476i	0.276031	−	0.961149i
$3$	0.478101	−	1.66476i	0.276031	−	0.961149i
$4$	0.102389	+	0.177343i	0.0511944	+	0.0886713i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−1.61141	−	1.67004i	−0.657856	−	0.681789i
$7$	−0.186958	+	0.323821i	−0.0706635	+	0.122393i	−0.899192	−	0.437554i	$-0.855845\pi$
$7$	−0.186958	+	0.323821i	−0.0706635	+	0.122393i	0.828529	+	0.559946i	$0.189178\pi$
$8$	2.95409			1.04443
$9$	−2.54284	−	1.59184i	−0.847613	−	0.530615i
$10$	−1.33986			−0.423701
$11$	2.53321	−	4.38765i	0.763791	−	1.32293i	−0.177092	−	0.984194i	$-0.556669\pi$
$11$	2.53321	−	4.38765i	0.763791	−	1.32293i	0.940883	−	0.338731i	$-0.109998\pi$
$12$	0.344185	−	0.0856650i	0.0993576	−	0.0247294i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$14$	0.250497	+	0.433874i	0.0669483	+	0.115958i
$15$	−1.68077	+	0.418332i	−0.433974	+	0.108013i
$16$	1.77426	−	3.07310i	0.443564	−	0.768275i
$17$	−0.733484			−0.177896			−0.0889480	−	0.996036i	$-0.528350\pi$
$17$	−0.733484			−0.177896			−0.0889480	+	0.996036i	$0.528350\pi$
$18$	−3.55062	+	1.88417i	−0.836890	+	0.444102i
$19$	−3.65108			−0.837615			−0.418808	−	0.908075i	$-0.637552\pi$
$19$	−3.65108			−0.837615			−0.418808	+	0.908075i	$0.637552\pi$
$20$	0.102389	−	0.177343i	0.0228948	−	0.0396550i
$21$	0.449699	+	0.466059i	0.0981323	+	0.101702i
$22$	−3.39414	−	5.87883i	−0.723634	−	1.25337i
$23$	−0.697881	−	1.20877i	−0.145518	−	0.252045i	0.784048	−	0.620700i	$-0.213152\pi$
$23$	−0.697881	−	1.20877i	−0.145518	−	0.252045i	−0.929566	+	0.368655i	$0.879818\pi$
$24$	1.41235	−	4.91785i	0.288295	−	1.00385i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	1.33986			0.262768
$27$	−3.86577	+	3.47215i	−0.743967	+	0.668216i
$28$	−0.0765697			−0.0144703
$29$	1.02349	−	1.77274i	0.190058	−	0.329190i	−0.755211	−	0.655481i	$-0.772466\pi$
$29$	1.02349	−	1.77274i	0.190058	−	0.329190i	0.945269	+	0.326291i	$0.105799\pi$
$30$	−0.640587	+	2.23054i	−0.116955	+	0.407239i
$31$	−0.541514	−	0.937930i	−0.0972588	−	0.168457i	0.813290	−	0.581858i	$-0.197674\pi$
$31$	−0.541514	−	0.937930i	−0.0972588	−	0.168457i	−0.910549	+	0.413401i	$0.864341\pi$
$32$	0.576839	+	0.999115i	0.101972	+	0.176620i
$33$	−6.09324	−	6.31492i	−1.06070	−	1.09929i
$34$	−0.491383	+	0.851099i	−0.0842714	+	0.145962i
$35$	0.373916			0.0632034
$36$	0.0219434	−	0.613941i	0.00365723	−	0.102324i
$37$	2.03066			0.333838			0.166919	−	0.985971i	$-0.446618\pi$
$37$	2.03066			0.333838			0.166919	+	0.985971i	$0.446618\pi$
$38$	−2.44597	+	4.23654i	−0.396788	+	0.687257i
$39$	1.68077	−	0.418332i	0.269139	−	0.0669867i
$40$	−1.47705	−	2.55832i	−0.233541	−	0.404506i
$41$	3.99634	+	6.92187i	0.624124	+	1.08101i	0.988710	+	0.149844i	$0.0478772\pi$
$41$	3.99634	+	6.92187i	0.624124	+	1.08101i	−0.364586	+	0.931170i	$0.618789\pi$
$42$	0.842059	−	0.209582i	0.129932	−	0.0323392i
$43$	0.227676	−	0.394347i	0.0347203	−	0.0601373i	−0.848143	−	0.529767i	$-0.822279\pi$
$43$	0.227676	−	0.394347i	0.0347203	−	0.0601373i	0.882863	+	0.469630i	$0.155613\pi$
$44$	1.03749			0.156407
$45$	−0.107157	+	2.99809i	−0.0159740	+	0.446928i
$46$	−1.87012			−0.275735
$47$	−1.83933	+	3.18582i	−0.268294	+	0.464699i	−0.968421	−	0.249319i	$-0.919793\pi$
$47$	−1.83933	+	3.18582i	−0.268294	+	0.464699i	0.700127	+	0.714018i	$0.253127\pi$
$48$	−4.26770	−	4.42296i	−0.615989	−	0.638399i
$49$	3.43009	+	5.94110i	0.490013	+	0.848728i
$50$	0.669930	+	1.16035i	0.0947423	+	0.164099i
$51$	−0.350679	+	1.22107i	−0.0491049	+	0.170984i
$52$	−0.102389	+	0.177343i	−0.0141988	+	0.0245930i
$53$	−0.225888			−0.0310281			−0.0155140	−	0.999880i	$-0.504938\pi$
$53$	−0.225888			−0.0310281			−0.0155140	+	0.999880i	$0.504938\pi$
$54$	1.43913	+	6.81175i	0.195840	+	0.926962i
$55$	−5.06642			−0.683156
$56$	−0.552291	+	0.956596i	−0.0738030	+	0.127831i
$57$	−1.74558	+	6.07817i	−0.231208	+	0.805073i
$58$	−1.37134	−	2.37522i	−0.180065	−	0.311882i
$59$	3.71136	+	6.42826i	0.483178	+	0.836888i	0.999813	−	0.0193171i	$-0.00614920\pi$
$59$	3.71136	+	6.42826i	0.483178	+	0.836888i	−0.516636	+	0.856205i	$0.672816\pi$
$60$	−0.246281	−	0.255240i	−0.0317947	−	0.0329514i
$61$	0.283754	−	0.491476i	0.0363310	−	0.0629271i	−0.847288	−	0.531133i	$-0.821766\pi$
$61$	0.283754	−	0.491476i	0.0363310	−	0.0629271i	0.883619	+	0.468206i	$0.155100\pi$
$62$	−1.45111			−0.184291
$63$	0.990877	−	0.525817i	0.124839	−	0.0662467i
$64$	8.64279			1.08035
$65$	0.500000	−	0.866025i	0.0620174	−	0.107417i
$66$	−11.4096	+	2.83976i	−1.40442	+	0.349550i
$67$	−5.39166	−	9.33863i	−0.658696	−	1.14090i	−0.980953	−	0.194243i	$-0.937775\pi$
$67$	−5.39166	−	9.33863i	−0.658696	−	1.14090i	0.322257	−	0.946652i	$-0.395558\pi$
$68$	−0.0751006	−	0.130078i	−0.00910728	−	0.0157743i
$69$	−2.34596	+	0.583892i	−0.282420	+	0.0702923i
$70$	0.250497	−	0.433874i	0.0299402	−	0.0518579i
$71$	14.0647			1.66917			0.834585	−	0.550880i	$-0.185708\pi$
$71$	14.0647			1.66917			0.834585	+	0.550880i	$0.185708\pi$
$72$	−7.51178	−	4.70245i	−0.885272	−	0.554189i
$73$	3.36196			0.393488			0.196744	−	0.980455i	$-0.436963\pi$
$73$	3.36196			0.393488			0.196744	+	0.980455i	$0.436963\pi$
$74$	1.36040	−	2.35628i	0.158143	−	0.273911i
$75$	1.20267	+	1.24643i	0.138873	+	0.143925i
$76$	−0.373830	−	0.647492i	−0.0428812	−	0.0742725i
$77$	0.947208	+	1.64061i	0.107944	+	0.186965i
$78$	0.640587	−	2.23054i	0.0725322	−	0.252559i
$79$	−6.20057	+	10.7397i	−0.697618	+	1.20831i	0.271672	+	0.962390i	$0.412423\pi$
$79$	−6.20057	+	10.7397i	−0.697618	+	1.20831i	−0.969290	+	0.245920i	$0.920910\pi$
$80$	−3.54851			−0.396736
$81$	3.93207	+	8.09561i	0.436896	+	0.899512i
$82$	10.7091			1.18262
$83$	2.84151	−	4.92164i	0.311896	−	0.540220i	−0.666877	−	0.745168i	$-0.732369\pi$
$83$	2.84151	−	4.92164i	0.311896	−	0.540220i	0.978773	+	0.204948i	$0.0657026\pi$
$84$	−0.0366080	+	0.127470i	−0.00399426	+	0.0139081i
$85$	0.366742	+	0.635216i	0.0397787	+	0.0688988i
$86$	−0.305054	−	0.528369i	−0.0328948	−	0.0569755i
$87$	−2.46185	−	2.55142i	−0.263939	−	0.273541i
$88$	7.48333	−	12.9615i	0.797726	−	1.38170i
$89$	8.89766			0.943150			0.471575	−	0.881826i	$-0.343686\pi$
$89$	8.89766			0.943150			0.471575	+	0.881826i	$0.343686\pi$
$90$	3.40705	+	2.13285i	0.359134	+	0.224822i
$91$	−0.373916			−0.0391971
$92$	0.142910	−	0.247528i	0.0148994	−	0.0258066i
$93$	−1.82033	+	0.453065i	−0.188759	+	0.0469807i
$94$	2.46445	+	4.26854i	0.254188	+	0.440267i
$95$	1.82554	+	3.16193i	0.187296	+	0.324407i
$96$	1.93907	−	0.482621i	0.197906	−	0.0492572i
$97$	−8.79576	+	15.2347i	−0.893075	+	1.54685i	−0.0569051	+	0.998380i	$0.518123\pi$
$97$	−8.79576	+	15.2347i	−0.893075	+	1.54685i	−0.836170	+	0.548471i	$0.815210\pi$
$98$	9.19168			0.928500
$99$	−13.4260	+	7.12461i	−1.34936	+	0.716050i
$100$	−0.204778			−0.0204778
$101$	4.66736	−	8.08410i	0.464420	−	0.804398i	−0.534755	−	0.845007i	$-0.679596\pi$
$101$	4.66736	−	8.08410i	0.464420	−	0.804398i	0.999175	+	0.0406084i	$0.0129296\pi$
$102$	1.18194	+	1.22494i	0.117030	+	0.121288i
$103$	−4.18303	−	7.24523i	−0.412166	−	0.713893i	0.582960	−	0.812501i	$-0.301894\pi$
$103$	−4.18303	−	7.24523i	−0.412166	−	0.713893i	−0.995126	+	0.0986077i	$0.968561\pi$
$104$	1.47705	+	2.55832i	0.144836	+	0.250864i
$105$	0.178769	−	0.622480i	0.0174461	−	0.0607478i
$106$	−0.151329	+	0.262109i	−0.0146984	+	0.0254583i
$107$	−13.0696			−1.26348			−0.631742	−	0.775179i	$-0.717660\pi$
$107$	−13.0696			−1.26348			−0.631742	+	0.775179i	$0.717660\pi$
$108$	−1.01157	−	0.330056i	−0.0973386	−	0.0317597i
$109$	4.16014			0.398469			0.199235	−	0.979952i	$-0.436154\pi$
$109$	4.16014			0.398469			0.199235	+	0.979952i	$0.436154\pi$
$110$	−3.39414	+	5.87883i	−0.323619	+	0.560524i
$111$	0.970858	−	3.38055i	0.0921497	−	0.320868i
$112$	0.663423	+	1.14908i	0.0626876	+	0.108578i
$113$	−2.70551	−	4.68608i	−0.254513	−	0.440829i	0.710250	−	0.703949i	$-0.248582\pi$
$113$	−2.70551	−	4.68608i	−0.254513	−	0.440829i	−0.964763	+	0.263120i	$0.915248\pi$
$114$	5.88339	+	6.09743i	0.551030	+	0.571077i
$115$	−0.697881	+	1.20877i	−0.0650777	+	0.112718i
$116$	0.419177			0.0389196
$117$	0.107157	−	2.99809i	0.00990668	−	0.277173i
$118$	9.94539			0.915548
$119$	0.137131	−	0.237517i	0.0125708	−	0.0217732i
$120$	−4.96516	+	1.23579i	−0.453255	+	0.112812i
$121$	−7.33430	−	12.7034i	−0.666755	−	1.15485i
$122$	−0.380190	−	0.658509i	−0.0344208	−	0.0596186i
$123$	13.4339	−	3.34359i	1.21129	−	0.301482i
$124$	0.110890	−	0.192067i	0.00995822	−	0.0172481i
$125$	1.00000			0.0894427
$126$	0.0536852	−	1.50203i	0.00478265	−	0.133811i
$127$	18.7160			1.66078			0.830388	−	0.557185i	$-0.188119\pi$
$127$	18.7160			1.66078			0.830388	+	0.557185i	$0.188119\pi$
$128$	4.63638	−	8.03045i	0.409802	−	0.709798i
$129$	−0.547640	−	0.567563i	−0.0482170	−	0.0499712i
$130$	−0.669930	−	1.16035i	−0.0587567	−	0.101770i
$131$	3.72218	+	6.44701i	0.325209	+	0.563278i	0.981555	−	0.191182i	$-0.0612321\pi$
$131$	3.72218	+	6.44701i	0.325209	+	0.563278i	−0.656346	+	0.754460i	$0.727899\pi$
$132$	0.496024	−	1.72717i	0.0431734	−	0.150331i
$133$	0.682599	−	1.18230i	0.0591888	−	0.102518i
$134$	−14.4481			−1.24813
$135$	4.93986	+	1.61178i	0.425155	+	0.138720i
$136$	−2.16678			−0.185800
$137$	−7.82957	+	13.5612i	−0.668926	+	1.15861i	0.309279	+	0.950971i	$0.399912\pi$
$137$	−7.82957	+	13.5612i	−0.668926	+	1.15861i	−0.978205	+	0.207642i	$0.933421\pi$
$138$	−0.894107	+	3.11330i	−0.0761115	+	0.265022i
$139$	2.11827	+	3.66895i	0.179669	+	0.311197i	0.941767	−	0.336265i	$-0.109164\pi$
$139$	2.11827	+	3.66895i	0.179669	+	0.311197i	−0.762098	+	0.647462i	$0.775831\pi$
$140$	0.0382848	+	0.0663113i	0.00323566	+	0.00560433i
$141$	4.42423	+	4.58518i	0.372587	+	0.386142i
$142$	9.42234	−	16.3200i	0.790705	−	1.36954i
$143$	5.06642			0.423675
$144$	−9.40354	+	4.99006i	−0.783629	+	0.415839i
$145$	−2.04699			−0.169993
$146$	2.25228	−	3.90106i	0.186400	−	0.322854i
$147$	11.5304	−	2.86983i	0.951013	−	0.236700i
$148$	0.207917	+	0.360122i	0.0170906	+	0.0296018i
$149$	3.51144	+	6.08199i	0.287668	+	0.498256i	0.973253	−	0.229737i	$-0.0737866\pi$
$149$	3.51144	+	6.08199i	0.287668	+	0.498256i	−0.685584	+	0.727993i	$0.740453\pi$
$150$	2.25200	−	0.560506i	0.183875	−	0.0457651i
$151$	4.09510	−	7.09293i	0.333255	−	0.577214i	−0.649893	−	0.760026i	$-0.725186\pi$
$151$	4.09510	−	7.09293i	0.333255	−	0.577214i	0.983148	+	0.182811i	$0.0585197\pi$
$152$	−10.7856			−0.874830
$153$	1.86513	+	1.16759i	0.150787	+	0.0943942i
$154$	2.53825			0.204538
$155$	−0.541514	+	0.937930i	−0.0434955	+	0.0753364i
$156$	0.246281	+	0.255240i	0.0197182	+	0.0204356i
$157$	−1.78303	−	3.08830i	−0.142301	−	0.246473i	0.786062	−	0.618148i	$-0.212117\pi$
$157$	−1.78303	−	3.08830i	−0.142301	−	0.246473i	−0.928363	+	0.371675i	$0.878783\pi$
$158$	8.30789	+	14.3897i	0.660940	+	1.14478i
$159$	−0.107997	+	0.376049i	−0.00856473	+	0.0298226i
$160$	0.576839	−	0.999115i	0.0456031	−	0.0789870i
$161$	0.521898			0.0411313
$162$	12.0280	+	0.860903i	0.945006	+	0.0676389i
$163$	−16.9173			−1.32507			−0.662533	−	0.749033i	$-0.730518\pi$
$163$	−16.9173			−1.32507			−0.662533	+	0.749033i	$0.730518\pi$
$164$	−0.818362	+	1.41744i	−0.0639033	+	0.110684i
$165$	−2.42226	+	8.43436i	−0.188573	+	0.656614i
$166$	−3.80722	−	6.59430i	−0.295498	−	0.511817i
$167$	10.0973	+	17.4890i	0.781351	+	1.35334i	0.931155	+	0.364623i	$0.118802\pi$
$167$	10.0973	+	17.4890i	0.781351	+	1.35334i	−0.149804	+	0.988716i	$0.547864\pi$
$168$	1.32845	+	1.37678i	0.102492	+	0.106221i
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	0.982765			0.0753746
$171$	9.28411	+	5.81195i	0.709974	+	0.444451i
$172$	0.0932460			0.00710994
$173$	2.52778	−	4.37825i	0.192184	−	0.332872i	−0.753790	−	0.657115i	$-0.771776\pi$
$173$	2.52778	−	4.37825i	0.192184	−	0.332872i	0.945974	+	0.324244i	$0.105110\pi$
$174$	−4.60981	+	1.14735i	−0.349469	+	0.0869802i
$175$	−0.186958	−	0.323821i	−0.0141327	−	0.0244786i
$176$	−8.98912	−	15.5696i	−0.677581	−	1.17360i
$177$	12.4759	−	3.10516i	0.937746	−	0.233398i
$178$	5.96080	−	10.3244i	0.446781	−	0.773848i
$179$	14.9077			1.11426			0.557128	−	0.830427i	$-0.311903\pi$
$179$	14.9077			1.11426			0.557128	+	0.830427i	$0.311903\pi$
$180$	−0.542660	+	0.287967i	−0.0404475	+	0.0214638i
$181$	−1.13779			−0.0845710			−0.0422855	−	0.999106i	$-0.513464\pi$
$181$	−1.13779			−0.0845710			−0.0422855	+	0.999106i	$0.513464\pi$
$182$	−0.250497	+	0.433874i	−0.0185681	+	0.0321609i
$183$	−0.682526	−	0.707356i	−0.0504538	−	0.0522893i
$184$	−2.06160	−	3.57080i	−0.151983	−	0.263243i
$185$	−1.01533	−	1.75860i	−0.0746484	−	0.129295i
$186$	−0.693774	+	2.41574i	−0.0508700	+	0.177131i
$187$	−1.85807	+	3.21827i	−0.135875	+	0.235343i
$188$	−0.753308			−0.0549406
$189$	−0.401619	−	1.90096i	−0.0292135	−	0.138275i
$190$	4.89193			0.354898
$191$	7.57728	−	13.1242i	0.548273	−	0.949636i	−0.450120	−	0.892968i	$-0.648619\pi$
$191$	7.57728	−	13.1242i	0.548273	−	0.949636i	0.998393	−	0.0566684i	$-0.0180478\pi$
$192$	4.13212	−	14.3882i	0.298210	−	1.03838i
$193$	7.27580	+	12.6021i	0.523724	+	0.907116i	0.999619	+	0.0276140i	$0.00879094\pi$
$193$	7.27580	+	12.6021i	0.523724	+	0.907116i	−0.475895	+	0.879502i	$0.657876\pi$
$194$	11.7851	+	20.4124i	0.846120	+	1.46552i
$195$	−1.20267	−	1.24643i	−0.0861252	−	0.0892584i
$196$	−0.702407	+	1.21660i	−0.0501719	+	0.0869003i
$197$	−24.9212			−1.77556			−0.887782	−	0.460265i	$-0.847755\pi$
$197$	−24.9212			−1.77556			−0.887782	+	0.460265i	$0.847755\pi$
$198$	−0.727413	+	20.3519i	−0.0516950	+	1.44634i
$199$	−7.11441			−0.504327			−0.252163	−	0.967685i	$-0.581142\pi$
$199$	−7.11441			−0.504327			−0.252163	+	0.967685i	$0.581142\pi$
$200$	−1.47705	+	2.55832i	−0.104443	+	0.180900i
$201$	−18.1243	+	4.51101i	−1.27839	+	0.318182i
$202$	−6.25360	−	10.8316i	−0.440002	−	0.762106i
$203$	0.382701	+	0.662857i	0.0268603	+	0.0465234i
$204$	−0.252454	+	0.0628339i	−0.0176753	+	0.00439925i
$205$	3.99634	−	6.92187i	0.279117	−	0.483444i
$206$	−11.2093			−0.780992
$207$	−0.149566	+	4.18461i	−0.0103955	+	0.290851i
$208$	3.54851			0.246045
$209$	−9.24895	+	16.0197i	−0.639763	+	1.10810i
$210$	−0.602533	−	0.624453i	−0.0415787	−	0.0430914i
$211$	−9.80151	−	16.9767i	−0.674764	−	1.16873i	−0.976538	−	0.215346i	$-0.930912\pi$
$211$	−9.80151	−	16.9767i	−0.674764	−	1.16873i	0.301774	−	0.953380i	$-0.402421\pi$
$212$	−0.0231284	−	0.0400595i	−0.00158846	−	0.00275130i
$213$	6.72433	−	23.4143i	0.460743	−	1.60432i
$214$	−8.75570	+	15.1653i	−0.598527	+	1.03668i
$215$	−0.455353			−0.0310548
$216$	−11.4198	+	10.2571i	−0.777021	+	0.697904i
$217$	0.404962			0.0274906
$218$	2.78700	−	4.82723i	0.188760	−	0.326941i
$219$	1.60736	−	5.59685i	0.108615	−	0.378200i
$220$	−0.518745	−	0.898492i	−0.0349738	−	0.0605763i
$221$	−0.366742	−	0.635216i	−0.0246697	−	0.0427292i
$222$	−3.27222	−	3.39127i	−0.219617	−	0.227607i
$223$	−14.4848	+	25.0884i	−0.969975	+	1.68005i	−0.274367	+	0.961625i	$0.588468\pi$
$223$	−14.4848	+	25.0884i	−0.969975	+	1.68005i	−0.695608	+	0.718421i	$0.744865\pi$
$224$	−0.431379			−0.0288227
$225$	2.65000	−	1.40624i	0.176666	−	0.0937495i
$226$	−7.25000			−0.482263
$227$	−8.41464	+	14.5746i	−0.558499	+	0.967349i	0.439123	+	0.898427i	$0.355289\pi$
$227$	−8.41464	+	14.5746i	−0.558499	+	0.967349i	−0.997622	+	0.0689217i	$0.978044\pi$
$228$	−1.25665	+	0.312770i	−0.0832235	+	0.0207137i
$229$	−2.66521	−	4.61628i	−0.176122	−	0.305052i	0.764427	−	0.644710i	$-0.223022\pi$
$229$	−2.66521	−	4.61628i	−0.176122	−	0.305052i	−0.940549	+	0.339658i	$0.889689\pi$
$230$	0.935062	+	1.61958i	0.0616562	+	0.106792i
$231$	3.18408	−	0.792495i	0.209497	−	0.0521423i
$232$	3.02349	−	5.23684i	0.198502	−	0.343816i
$233$	−21.0852			−1.38134			−0.690669	−	0.723171i	$-0.742684\pi$
$233$	−21.0852			−1.38134			−0.690669	+	0.723171i	$0.742684\pi$
$234$	−3.40705	−	2.13285i	−0.222726	−	0.139429i
$235$	3.67866			0.239970
$236$	−0.760003	+	1.31636i	−0.0494720	+	0.0856880i
$237$	14.9145	+	15.4571i	0.968801	+	1.00405i
$238$	−0.183736	−	0.318240i	−0.0119098	−	0.0206284i
$239$	−10.6282	−	18.4085i	−0.687479	−	1.19075i	−0.972651	−	0.232272i	$-0.925384\pi$
$239$	−10.6282	−	18.4085i	−0.687479	−	1.19075i	0.285172	−	0.958476i	$-0.407949\pi$
$240$	−1.69654	+	5.90741i	−0.109512	+	0.381322i
$241$	−14.3571	+	24.8672i	−0.924821	+	1.60184i	−0.132971	+	0.991120i	$0.542452\pi$
$241$	−14.3571	+	24.8672i	−0.924821	+	1.60184i	−0.791850	+	0.610716i	$0.790882\pi$
$242$	−19.6539			−1.26340
$243$	15.3572	−	2.67543i	0.985162	−	0.171629i
$244$	0.116213			0.00743977
$245$	3.43009	−	5.94110i	0.219141	−	0.379563i
$246$	5.12001	−	17.8280i	0.326440	−	1.13667i
$247$	−1.82554	−	3.16193i	−0.116156	−	0.201189i
$248$	−1.59968	−	2.77073i	−0.101580	−	0.175942i
$249$	−6.83481	−	7.08346i	−0.433138	−	0.448896i
$250$	0.669930	−	1.16035i	0.0423701	−	0.0733871i
$251$	19.0692			1.20364			0.601818	−	0.798633i	$-0.294443\pi$
$251$	19.0692			1.20364			0.601818	+	0.798633i	$0.294443\pi$
$252$	0.194704	+	0.121887i	0.0122652	+	0.00767816i
$253$	−7.07152			−0.444582
$254$	12.5384	−	21.7171i	0.786729	−	1.36266i
$255$	1.23282	−	0.306840i	0.0772022	−	0.0192150i
$256$	2.43069	+	4.21008i	0.151918	+	0.263130i
$257$	−3.70076	−	6.40991i	−0.230847	−	0.399839i	0.727210	−	0.686415i	$-0.240816\pi$
$257$	−3.70076	−	6.40991i	−0.230847	−	0.399839i	−0.958058	+	0.286575i	$0.907483\pi$
$258$	−1.02545	+	0.255228i	−0.0638419	+	0.0158898i
$259$	−0.379648	+	0.657569i	−0.0235901	+	0.0408593i
$260$	0.204778			0.0126998
$261$	−5.42451	+	2.87856i	−0.335769	+	0.178178i
$262$	9.97440			0.616221
$263$	10.8547	−	18.8010i	0.669332	−	1.15932i	−0.308759	−	0.951140i	$-0.599914\pi$
$263$	10.8547	−	18.8010i	0.669332	−	1.15932i	0.978091	−	0.208177i	$-0.0667532\pi$
$264$	−18.0000	−	18.6548i	−1.10782	−	1.14813i
$265$	0.112944	+	0.195625i	0.00693809	+	0.0120171i
$266$	−0.914586	−	1.58411i	−0.0560769	−	0.0971280i
$267$	4.25398	−	14.8124i	0.260339	−	0.906507i
$268$	1.10409	−	1.91234i	0.0674431	−	0.116815i
$269$	−21.5429			−1.31350			−0.656748	−	0.754110i	$-0.728068\pi$
$269$	−21.5429			−1.31350			−0.656748	+	0.754110i	$0.728068\pi$
$270$	5.17958	−	4.65219i	0.315219	−	0.283124i
$271$	4.72843			0.287232			0.143616	−	0.989634i	$-0.454127\pi$
$271$	4.72843			0.287232			0.143616	+	0.989634i	$0.454127\pi$
$272$	−1.30139	+	2.25407i	−0.0789082	+	0.136673i
$273$	−0.178769	+	0.622480i	−0.0108196	+	0.0376742i
$274$	10.4905	+	18.1701i	0.633756	+	1.09770i
$275$	2.53321	+	4.38765i	0.152758	+	0.264585i
$276$	−0.343749	−	0.356255i	−0.0206913	−	0.0214440i
$277$	3.37475	−	5.84524i	0.202769	−	0.351206i	−0.746651	−	0.665216i	$-0.768339\pi$
$277$	3.37475	−	5.84524i	0.202769	−	0.351206i	0.949420	+	0.314010i	$0.101673\pi$
$278$	5.67637			0.340446
$279$	−0.116054	+	3.24701i	−0.00694798	+	0.194394i
$280$	1.10458			0.0660114
$281$	−8.23651	+	14.2661i	−0.491349	+	0.851041i	−0.999950	−	0.00996079i	$-0.996829\pi$
$281$	−8.23651	+	14.2661i	−0.491349	+	0.851041i	0.508601	+	0.861002i	$0.330163\pi$
$282$	8.28435	−	2.06191i	0.493326	−	0.122785i
$283$	−2.52813	−	4.37884i	−0.150281	−	0.260295i	0.781049	−	0.624469i	$-0.214685\pi$
$283$	−2.52813	−	4.37884i	−0.150281	−	0.260295i	−0.931331	+	0.364174i	$0.881351\pi$
$284$	1.44007	+	2.49427i	0.0854522	+	0.148007i
$285$	6.13664	−	1.52736i	0.363503	−	0.0904732i
$286$	3.39414	−	5.87883i	0.200700	−	0.347623i
$287$	−2.98859			−0.176411
$288$	0.123625	−	3.45883i	0.00728466	−	0.203813i
$289$	−16.4620			−0.968353
$290$	−1.37134	+	2.37522i	−0.0805277	+	0.139478i
$291$	21.1569	+	21.9265i	1.24024	+	1.28536i
$292$	0.344227	+	0.596219i	0.0201444	+	0.0348911i
$293$	−0.139466	−	0.241562i	−0.00814768	−	0.0141122i	0.861923	−	0.507040i	$-0.169260\pi$
$293$	−0.139466	−	0.241562i	−0.00814768	−	0.0141122i	−0.870070	+	0.492927i	$0.835927\pi$
$294$	4.39455	−	15.3019i	0.256295	−	0.892427i
$295$	3.71136	−	6.42826i	0.216084	−	0.374268i
$296$	5.99874			0.348670
$297$	5.44178	+	25.7573i	0.315764	+	1.49459i
$298$	9.40967			0.545088
$299$	0.697881	−	1.20877i	0.0403595	−	0.0699047i
$300$	−0.0979043	+	0.340905i	−0.00565251	+	0.0196822i
$301$	0.0851318	+	0.147453i	0.00490692	+	0.00849903i
$302$	−5.48686	−	9.50352i	−0.315733	−	0.546866i
$303$	−11.2266	−	11.6350i	−0.644952	−	0.668416i
$304$	−6.47795	+	11.2201i	−0.371536	+	0.643519i
$305$	−0.567508			−0.0324954
$306$	2.60432	−	1.38201i	0.148879	−	0.0790040i
$307$	27.7910			1.58612			0.793059	−	0.609145i	$-0.208487\pi$
$307$	27.7910			1.58612			0.793059	+	0.609145i	$0.208487\pi$
$308$	−0.193967	+	0.335961i	−0.0110523	+	0.0191431i
$309$	−14.0615	+	3.49979i	−0.799928	+	0.199096i
$310$	0.725553	+	1.25669i	0.0412086	+	0.0713755i
$311$	−16.1972	−	28.0544i	−0.918459	−	1.59082i	−0.801756	−	0.597652i	$-0.796101\pi$
$311$	−16.1972	−	28.0544i	−0.918459	−	1.59082i	−0.116704	−	0.993167i	$-0.537233\pi$
$312$	4.96516	−	1.23579i	0.281097	−	0.0699629i
$313$	−13.3485	+	23.1203i	−0.754503	+	1.30684i	0.191118	+	0.981567i	$0.438789\pi$
$313$	−13.3485	+	23.1203i	−0.754503	+	1.30684i	−0.945621	+	0.325270i	$0.894545\pi$
$314$	−4.77801			−0.269639
$315$	−0.950809	−	0.595216i	−0.0535720	−	0.0335366i
$316$	−2.53948			−0.142857
$317$	7.63673	−	13.2272i	0.428922	−	0.742914i	−0.567856	−	0.823128i	$-0.692227\pi$
$317$	7.63673	−	13.2272i	0.428922	−	0.742914i	0.996778	+	0.0802137i	$0.0255603\pi$
$318$	0.363998	+	0.377241i	0.0204120	+	0.0211546i
$319$	−5.18545	−	8.98146i	−0.290329	−	0.502865i
$320$	−4.32139	−	7.48487i	−0.241573	−	0.418417i
$321$	−6.24857	+	21.7577i	−0.348761	+	1.21440i
$322$	0.349635	−	0.605585i	0.0194844	−	0.0337479i
$323$	2.67801			0.149008
$324$	−1.03310	+	1.52622i	−0.0573943	+	0.0847902i
$325$	−1.00000			−0.0554700
$326$	−11.3334	+	19.6300i	−0.627699	+	1.08721i
$327$	1.98897	−	6.92563i	0.109990	−	0.382988i
$328$	11.8056	+	20.4478i	0.651853	+	1.12904i
$329$	−0.687756	−	1.19123i	−0.0379172	−	0.0656745i
$330$	8.16409	+	8.46110i	0.449418	+	0.465768i
$331$	−1.89026	+	3.27402i	−0.103898	+	0.179957i	−0.913287	−	0.407316i	$-0.866465\pi$
$331$	−1.89026	+	3.27402i	−0.103898	+	0.179957i	0.809389	+	0.587272i	$0.199798\pi$
$332$	1.16375			0.0638693
$333$	−5.16363	−	3.23249i	−0.282965	−	0.177139i
$334$	27.0579			1.48054
$335$	−5.39166	+	9.33863i	−0.294578	+	0.510224i
$336$	2.23013	−	0.555062i	0.121663	−	0.0302811i
$337$	−6.97747	−	12.0853i	−0.380087	−	0.658330i	0.610987	−	0.791641i	$-0.290773\pi$
$337$	−6.97747	−	12.0853i	−0.380087	−	0.658330i	−0.991074	+	0.133310i	$0.957439\pi$
$338$	0.669930	+	1.16035i	0.0364394	+	0.0631148i
$339$	−9.09469	+	2.26360i	−0.493956	+	0.122942i
$340$	−0.0751006	+	0.130078i	−0.00407290	+	0.00705447i
$341$	−5.48708			−0.297142
$342$	12.9636	−	6.87924i	0.700992	−	0.371987i
$343$	−5.18255			−0.279831
$344$	0.672576	−	1.16494i	0.0362629	−	0.0628092i
$345$	1.67864	+	1.73971i	0.0903752	+	0.0936631i
$346$	−3.38687	−	5.86623i	−0.182079	−	0.315371i
$347$	−15.4676	−	26.7908i	−0.830347	−	1.43820i	−0.897763	−	0.440478i	$-0.854809\pi$
$347$	−15.4676	−	26.7908i	−0.830347	−	1.43820i	0.0674164	−	0.997725i	$-0.478524\pi$
$348$	0.200409	−	0.697829i	0.0107430	−	0.0374075i
$349$	0.572219	−	0.991113i	0.0306302	−	0.0530530i	−0.850304	−	0.526292i	$-0.823582\pi$
$349$	0.572219	−	0.991113i	0.0306302	−	0.0530530i	0.880934	+	0.473239i	$0.156915\pi$
$350$	−0.500995			−0.0267793
$351$	−4.93986	−	1.61178i	−0.263670	−	0.0860303i
$352$	5.84502			0.311541
$353$	4.41753	−	7.65138i	0.235121	−	0.407242i	−0.724187	−	0.689604i	$-0.757785\pi$
$353$	4.41753	−	7.65138i	0.235121	−	0.407242i	0.959308	+	0.282362i	$0.0911179\pi$
$354$	4.75490	−	16.5567i	0.252720	−	0.879977i
$355$	−7.03234	−	12.1804i	−0.373238	−	0.646467i
$356$	0.911021	+	1.57793i	0.0482840	+	0.0836304i
$357$	−0.329847	−	0.341847i	−0.0174573	−	0.0180924i
$358$	9.98713	−	17.2982i	0.527836	−	0.914239i
$359$	−4.59322			−0.242421			−0.121210	−	0.992627i	$-0.538678\pi$
$359$	−4.59322			−0.242421			−0.121210	+	0.992627i	$0.538678\pi$
$360$	−0.316552	+	8.85662i	−0.0166837	+	0.466785i
$361$	−5.66961			−0.298401
$362$	−0.762237	+	1.32023i	−0.0400623	+	0.0693899i
$363$	−24.6546	+	6.13635i	−1.29403	+	0.322075i
$364$	−0.0382848	−	0.0663113i	−0.00200667	−	0.00347566i
$365$	−1.68098	−	2.91154i	−0.0879865	−	0.152397i
$366$	−1.27803	+	0.318091i	−0.0668035	+	0.0166269i
$367$	−7.03476	+	12.1846i	−0.367211	+	0.636029i	−0.989128	−	0.147054i	$-0.953021\pi$
$367$	−7.03476	+	12.1846i	−0.367211	+	0.636029i	0.621917	+	0.783083i	$0.286354\pi$
$368$	−4.95288			−0.258187
$369$	0.856473	−	23.9627i	0.0445862	−	1.24745i
$370$	−2.72079			−0.141447
$371$	0.0422315	−	0.0731472i	0.00219255	−	0.00379761i
$372$	−0.266729	−	0.276433i	−0.0138292	−	0.0143324i
$373$	−5.68737	−	9.85081i	−0.294481	−	0.510055i	0.680383	−	0.732856i	$-0.261813\pi$
$373$	−5.68737	−	9.85081i	−0.294481	−	0.510055i	−0.974864	+	0.222801i	$0.928480\pi$
$374$	2.48955	+	4.31203i	0.128732	+	0.222970i
$375$	0.478101	−	1.66476i	0.0246890	−	0.0859677i
$376$	−5.43355	+	9.41119i	−0.280214	+	0.485345i
$377$	2.04699			0.105425
$378$	−2.47484	−	0.807492i	−0.127292	−	0.0415329i
$379$	3.70193			0.190156			0.0950778	−	0.995470i	$-0.469690\pi$
$379$	3.70193			0.190156			0.0950778	+	0.995470i	$0.469690\pi$
$380$	−0.373830	+	0.647492i	−0.0191771	+	0.0332157i
$381$	8.94813	−	31.1576i	0.458427	−	1.59625i
$382$	−10.1525	−	17.5846i	−0.519447	−	0.899708i
$383$	−17.8321	−	30.8861i	−0.911179	−	1.57821i	−0.812402	−	0.583098i	$-0.801840\pi$
$383$	−17.8321	−	30.8861i	−0.911179	−	1.57821i	−0.0987766	−	0.995110i	$-0.531493\pi$
$384$	−11.1521	−	11.5578i	−0.569103	−	0.589807i
$385$	0.947208	−	1.64061i	0.0482742	−	0.0836133i
$386$	19.4971			0.992376
$387$	−1.20668	+	0.640336i	−0.0613391	+	0.0325501i
$388$	−3.60235			−0.182882
$389$	−4.14304	+	7.17595i	−0.210060	+	0.363835i	−0.951733	−	0.306927i	$-0.900699\pi$
$389$	−4.14304	+	7.17595i	−0.210060	+	0.363835i	0.741673	+	0.670762i	$0.234033\pi$
$390$	−2.25200	+	0.560506i	−0.114034	+	0.0283823i
$391$	0.511884	+	0.886610i	0.0258871	+	0.0448378i
$392$	10.1328	+	17.5505i	0.511784	+	0.886436i
$393$	12.5123	−	3.11422i	0.631162	−	0.157091i
$394$	−16.6955	+	28.9174i	−0.841105	+	1.45684i
$395$	12.4011			0.623969
$396$	−2.63817	−	1.65152i	−0.132573	−	0.0829921i
$397$	−6.91135			−0.346871			−0.173435	−	0.984845i	$-0.555487\pi$
$397$	−6.91135			−0.346871			−0.173435	+	0.984845i	$0.555487\pi$
$398$	−4.76615	+	8.25522i	−0.238906	+	0.413797i
$399$	−1.64189	−	1.70162i	−0.0821971	−	0.0851875i
$400$	1.77426	+	3.07310i	0.0887128	+	0.153655i
$401$	−13.8559	−	23.9991i	−0.691931	−	1.19846i	−0.971204	−	0.238248i	$-0.923427\pi$
$401$	−13.8559	−	23.9991i	−0.691931	−	1.19846i	0.279274	−	0.960212i	$-0.409906\pi$
$402$	−6.90766	+	24.0526i	−0.344523	+	1.19964i
$403$	0.541514	−	0.937930i	0.0269748	−	0.0467216i
$404$	1.91154			0.0951028
$405$	5.04497	−	7.45307i	0.250686	−	0.370346i
$406$	1.02553			0.0508962
$407$	5.14408	−	8.90980i	0.254982	−	0.441643i
$408$	−1.03594	+	3.60716i	−0.0512866	+	0.178581i
$409$	14.7913	+	25.6192i	0.731381	+	1.26679i	0.956293	+	0.292411i	$0.0944574\pi$
$409$	14.7913	+	25.6192i	0.731381	+	1.26679i	−0.224911	+	0.974379i	$0.572209\pi$
$410$	−5.35453	−	9.27432i	−0.264442	−	0.458026i
$411$	18.8328	+	19.5180i	0.928955	+	0.962751i
$412$	0.856592	−	1.48366i	0.0422012	−	0.0730947i
$413$	−2.77547			−0.136572
$414$	4.75543	+	2.97695i	0.233716	+	0.146309i
$415$	−5.68302			−0.278968
$416$	−0.576839	+	0.999115i	−0.0282819	+	0.0489856i
$417$	7.12067	−	1.77228i	0.348701	−	0.0867890i
$418$	12.3923	+	21.4641i	0.606127	+	1.04984i
$419$	−16.7706	−	29.0475i	−0.819297	−	1.41906i	−0.906201	−	0.422847i	$-0.861031\pi$
$419$	−16.7706	−	29.0475i	−0.819297	−	1.41906i	0.0869045	−	0.996217i	$-0.472302\pi$
$420$	0.128696	−	0.0320315i	0.00627973	−	0.00156298i
$421$	−12.8254	+	22.2142i	−0.625071	+	1.08265i	0.363457	+	0.931611i	$0.381596\pi$
$421$	−12.8254	+	22.2142i	−0.625071	+	1.08265i	−0.988527	+	0.151043i	$0.951737\pi$
$422$	−26.2653			−1.27857
$423$	9.74845	−	5.17309i	0.473986	−	0.251524i
$424$	−0.667293			−0.0324066
$425$	0.366742	−	0.635216i	0.0177896	−	0.0308125i
$426$	−22.6640	−	23.4885i	−1.09807	−	1.13802i
$427$	0.106100	+	0.183771i	0.00513454	+	0.00889329i
$428$	−1.33818	−	2.31779i	−0.0646833	−	0.112035i
$429$	2.42226	−	8.43436i	0.116948	−	0.407215i
$430$	−0.305054	+	0.528369i	−0.0147110	+	0.0254802i
$431$	34.6003			1.66664			0.833318	−	0.552794i	$-0.186438\pi$
$431$	34.6003			1.66664			0.833318	+	0.552794i	$0.186438\pi$
$432$	3.81141	+	18.0404i	0.183377	+	0.867968i
$433$	−5.78144			−0.277838			−0.138919	−	0.990304i	$-0.544363\pi$
$433$	−5.78144			−0.277838			−0.138919	+	0.990304i	$0.544363\pi$
$434$	0.271296	−	0.469898i	0.0130226	−	0.0225558i
$435$	−0.978665	+	3.40774i	−0.0469234	+	0.163389i
$436$	0.425952	+	0.737771i	0.0203994	+	0.0353328i
$437$	2.54802	+	4.41330i	0.121888	+	0.211117i
$438$	−5.41750	−	5.61459i	−0.258858	−	0.268276i
$439$	−12.7969	+	22.1648i	−0.610761	+	1.05787i	0.380352	+	0.924842i	$0.375803\pi$
$439$	−12.7969	+	22.1648i	−0.610761	+	1.05787i	−0.991112	+	0.133027i	$0.957530\pi$
$440$	−14.9667			−0.713508
$441$	0.735118	−	20.5674i	0.0350056	−	0.979401i
$442$	−0.982765			−0.0467454
$443$	−16.1855	+	28.0342i	−0.768997	+	1.33194i	0.169110	+	0.985597i	$0.445911\pi$
$443$	−16.1855	+	28.0342i	−0.768997	+	1.33194i	−0.938107	+	0.346345i	$0.887423\pi$
$444$	0.698921	−	0.173956i	0.0331693	−	0.00825560i
$445$	−4.44883	−	7.70560i	−0.210895	−	0.365280i
$446$	19.4076	+	33.6150i	0.918977	+	1.59172i
$447$	11.8039	−	2.93789i	0.558304	−	0.138958i
$448$	−1.61584	+	2.79872i	−0.0763412	+	0.132227i
$449$	28.1593			1.32892			0.664460	−	0.747324i	$-0.268662\pi$
$449$	28.1593			1.32892			0.664460	+	0.747324i	$0.268662\pi$
$450$	0.143575	−	4.01701i	0.00676821	−	0.189364i
$451$	40.4943			1.90680
$452$	0.554028	−	0.959604i	0.0260593	−	0.0451360i
$453$	−9.85014	−	10.2085i	−0.462800	−	0.479637i
$454$	11.2744	+	19.5279i	0.529135	+	0.916489i
$455$	0.186958	+	0.323821i	0.00876473	+	0.0151810i
$456$	−5.15661	+	17.9555i	−0.241481	+	0.840841i
$457$	−0.331641	+	0.574419i	−0.0155135	+	0.0268702i	−0.873678	−	0.486505i	$-0.838272\pi$
$457$	−0.331641	+	0.574419i	−0.0155135	+	0.0268702i	0.858164	+	0.513375i	$0.171605\pi$
$458$	−7.14201			−0.333724
$459$	2.83548	−	2.54677i	0.132349	−	0.118873i
$460$	−0.285821			−0.0133265
$461$	2.32291	−	4.02339i	0.108189	−	0.187388i	−0.806848	−	0.590759i	$-0.798828\pi$
$461$	2.32291	−	4.02339i	0.108189	−	0.187388i	0.915036	+	0.403371i	$0.132162\pi$
$462$	1.21354	−	4.22557i	0.0564589	−	0.196591i
$463$	16.6792	+	28.8892i	0.775148	+	1.34260i	0.934711	+	0.355408i	$0.115658\pi$
$463$	16.6792	+	28.8892i	0.775148	+	1.34260i	−0.159564	+	0.987188i	$0.551009\pi$
$464$	−3.63188	−	6.29059i	−0.168606	−	0.292034i
$465$	1.30253	+	1.34992i	0.0604033	+	0.0626008i
$466$	−14.1256	+	24.4662i	−0.654356	+	1.13338i
$467$	23.5649			1.09045			0.545227	−	0.838289i	$-0.316444\pi$
$467$	23.5649			1.09045			0.545227	+	0.838289i	$0.316444\pi$
$468$	0.542660	−	0.287967i	0.0250845	−	0.0133113i
$469$	4.03206			0.186183
$470$	2.46445	−	4.26854i	0.113676	−	0.196893i
$471$	−5.99373	+	1.49180i	−0.276177	+	0.0687383i
$472$	10.9637	+	18.9897i	0.504645	+	0.874070i
$473$	−1.15350	−	1.99793i	−0.0530381	−	0.0918648i
$474$	27.9273	−	6.95091i	1.28275	−	0.319266i
$475$	1.82554	−	3.16193i	0.0837615	−	0.145079i
$476$	0.0561626			0.00257421
$477$	0.574396	+	0.359578i	0.0262998	+	0.0164639i
$478$	−28.4805			−1.30267
$479$	18.2570	−	31.6220i	0.834182	−	1.44485i	−0.0605126	−	0.998167i	$-0.519274\pi$
$479$	18.2570	−	31.6220i	0.834182	−	1.44485i	0.894695	−	0.446678i	$-0.147393\pi$
$480$	−1.38750	−	1.43798i	−0.0633303	−	0.0656343i
$481$	1.01533	+	1.75860i	0.0462950	+	0.0801852i
$482$	19.2365	+	33.3185i	0.876197	+	1.51762i
$483$	0.249520	−	0.868834i	0.0113535	−	0.0395333i
$484$	1.50190	−	2.60137i	0.0682683	−	0.118244i
$485$	17.5915			0.798790
$486$	7.18377	−	19.6120i	0.325862	−	0.889621i
$487$	−32.6886			−1.48126			−0.740631	−	0.671912i	$-0.765473\pi$
$487$	−32.6886			−1.48126			−0.740631	+	0.671912i	$0.765473\pi$
$488$	0.838235	−	1.45187i	0.0379451	−	0.0657228i
$489$	−8.08817	+	28.1632i	−0.365760	+	1.27358i
$490$	−4.59584	−	7.96023i	−0.207619	−	0.359607i
$491$	−9.30588	−	16.1183i	−0.419969	−	0.727407i	0.575967	−	0.817473i	$-0.304626\pi$
$491$	−9.30588	−	16.1183i	−0.419969	−	0.727407i	−0.995936	+	0.0900659i	$0.971292\pi$
$492$	1.96844	+	2.04005i	0.0887442	+	0.0919728i
$493$	−0.750716	+	1.30028i	−0.0338105	+	0.0585616i
$494$	−4.89193			−0.220098
$495$	12.8831	+	8.06495i	0.579052	+	0.362492i
$496$	−3.84314			−0.172562
$497$	−2.62950	+	4.55443i	−0.117949	+	0.204294i
$498$	−12.7981	+	3.18536i	−0.573499	+	0.142740i
$499$	−2.06211	−	3.57168i	−0.0923128	−	0.159890i	0.816171	−	0.577810i	$-0.196093\pi$
$499$	−2.06211	−	3.57168i	−0.0923128	−	0.159890i	−0.908484	+	0.417920i	$0.862759\pi$
$500$	0.102389	+	0.177343i	0.00457897	+	0.00793101i
$501$	33.9425	−	8.44803i	1.51644	−	0.377430i
$502$	12.7750	−	22.1270i	0.570177	−	0.987575i
$503$	17.4032			0.775971			0.387986	−	0.921665i	$-0.373171\pi$
$503$	17.4032			0.775971			0.387986	+	0.921665i	$0.373171\pi$
$504$	2.92714	−	1.55331i	0.130385	−	0.0691899i
$505$	−9.33472			−0.415390
$506$	−4.73742	+	8.20545i	−0.210604	+	0.364777i
$507$	1.20267	+	1.24643i	0.0534126	+	0.0553557i
$508$	1.91631	+	3.31915i	0.0850225	+	0.147263i
$509$	−0.749250	−	1.29774i	−0.0332099	−	0.0575213i	0.848943	−	0.528485i	$-0.177240\pi$
$509$	−0.749250	−	1.29774i	−0.0332099	−	0.0575213i	−0.882153	+	0.470964i	$0.843906\pi$
$510$	0.469860	−	1.63607i	0.0208058	−	0.0724462i
$511$	−0.628546	+	1.08867i	−0.0278052	+	0.0481601i
$512$	25.0591			1.10747
$513$	14.1142	−	12.6771i	0.623158	−	0.559708i
$514$	−9.91700			−0.437420
$515$	−4.18303	+	7.24523i	−0.184326	+	0.319263i
$516$	0.0445810	−	0.155232i	0.00196257	−	0.00683371i
$517$	9.31883	+	16.1407i	0.409841	+	0.709866i
$518$	0.508674	+	0.881050i	0.0223499	+	0.0387111i
$519$	−6.08019	−	6.30139i	−0.266891	−	0.276600i
$520$	1.47705	−	2.55832i	0.0647727	−	0.112190i
$521$	−1.71625			−0.0751904			−0.0375952	−	0.999293i	$-0.511970\pi$
$521$	−1.71625			−0.0751904			−0.0375952	+	0.999293i	$0.511970\pi$
$522$	−0.293897	+	8.22277i	−0.0128635	+	0.359901i
$523$	−12.3293			−0.539121			−0.269560	−	0.962984i	$-0.586878\pi$
$523$	−12.3293			−0.539121			−0.269560	+	0.962984i	$0.586878\pi$
$524$	−0.762220	+	1.32020i	−0.0332977	+	0.0576734i
$525$	−0.628468	+	0.156421i	−0.0274286	+	0.00682677i
$526$	−14.5438	−	25.1907i	−0.634141	−	1.09836i
$527$	0.397192	+	0.687957i	0.0173020	+	0.0299679i
$528$	−30.2174	+	7.52087i	−1.31504	+	0.327304i
$529$	10.5259	−	18.2314i	0.457649	−	0.792671i
$530$	0.302658			0.0131466
$531$	0.795397	−	22.2539i	0.0345173	−	0.965739i
$532$	0.279562			0.0121206
$533$	−3.99634	+	6.92187i	−0.173101	+	0.299819i
$534$	−14.3378	−	14.8594i	−0.620457	−	0.643029i
$535$	6.53479	+	11.3186i	0.282524	+	0.489345i
$536$	−15.9275	−	27.5872i	−0.687961	−	1.19158i
$537$	7.12739	−	24.8178i	0.307570	−	1.07097i
$538$	−14.4322	+	24.9974i	−0.622218	+	1.07771i
$539$	34.7566			1.49707
$540$	0.219949	+	1.04108i	0.00946511	+	0.0448007i
$541$	40.1458			1.72600			0.863002	−	0.505201i	$-0.168581\pi$
$541$	40.1458			1.72600			0.863002	+	0.505201i	$0.168581\pi$
$542$	3.16772	−	5.48664i	0.136065	−	0.235672i
$543$	−0.543976	+	1.89414i	−0.0233443	+	0.0812853i
$544$	−0.423102	−	0.732835i	−0.0181404	−	0.0314200i
$545$	−2.08007	−	3.60279i	−0.0891005	−	0.154327i
$546$	0.602533	+	0.624453i	0.0257860	+	0.0267241i
$547$	11.1426	−	19.2995i	0.476423	−	0.825189i	−0.523212	−	0.852202i	$-0.675266\pi$
$547$	11.1426	−	19.2995i	0.476423	−	0.825189i	0.999635	+	0.0270139i	$0.00859983\pi$
$548$	−3.20664			−0.136981
$549$	−1.50389	+	0.798053i	−0.0641846	+	0.0340601i
$550$	6.78829			0.289454
$551$	−3.73686	+	6.47242i	−0.159195	+	0.275735i
$552$	−6.93018	+	1.72487i	−0.294968	+	0.0734153i
$553$	−2.31849	−	4.01575i	−0.0985923	−	0.170767i
$554$	−4.52169	−	7.83180i	−0.192108	−	0.332741i
$555$	−3.41307	+	0.849488i	−0.144877	+	0.0360588i
$556$	−0.433775	+	0.751320i	−0.0183961	+	0.0318631i
$557$	−36.2726			−1.53692			−0.768460	−	0.639897i	$-0.778977\pi$
$557$	−36.2726			−1.53692			−0.768460	+	0.639897i	$0.778977\pi$
$558$	3.68993	+	2.30993i	0.156207	+	0.0977873i
$559$	0.455353			0.0192594
$560$	0.663423	−	1.14908i	0.0280347	−	0.0485576i
$561$	4.46930	+	4.63189i	0.188694	+	0.195559i
$562$	11.0358	+	19.1145i	0.465515	+	0.806296i
$563$	21.7913	+	37.7436i	0.918392	+	1.59070i	0.801858	+	0.597515i	$0.203845\pi$
$563$	21.7913	+	37.7436i	0.918392	+	1.59070i	0.116534	+	0.993187i	$0.462822\pi$
$564$	−0.360157	+	1.25408i	−0.0151653	+	0.0528061i
$565$	−2.70551	+	4.68608i	−0.113822	+	0.197145i
$566$	−6.77466			−0.284760
$567$	−3.35666	−	0.240253i	−0.140966	−	0.0100897i
$568$	41.5483			1.74333
$569$	1.27682	−	2.21151i	0.0535269	−	0.0927114i	−0.838020	−	0.545639i	$-0.816287\pi$
$569$	1.27682	−	2.21151i	0.0535269	−	0.0927114i	0.891547	+	0.452928i	$0.149620\pi$
$570$	2.33884	−	8.14389i	0.0979631	−	0.341110i
$571$	15.6382	+	27.0861i	0.654438	+	1.13352i	0.982034	+	0.188702i	$0.0604281\pi$
$571$	15.6382	+	27.0861i	0.654438	+	1.13352i	−0.327596	+	0.944818i	$0.606239\pi$
$572$	0.518745	+	0.898492i	0.0216898	+	0.0375679i
$573$	−18.2260	−	18.8890i	−0.761401	−	0.789101i
$574$	−2.00215	+	3.46782i	−0.0835680	+	0.144744i
$575$	1.39576			0.0582073
$576$	−21.9772	−	13.7580i	−0.915718	−	0.573249i
$577$	−8.17276			−0.340237			−0.170118	−	0.985424i	$-0.554415\pi$
$577$	−8.17276			−0.340237			−0.170118	+	0.985424i	$0.554415\pi$
$578$	−11.0284	+	19.1017i	−0.458720	+	0.794527i
$579$	24.4579	−	6.08740i	1.01644	−	0.252984i
$580$	−0.209589	−	0.363018i	−0.00870269	−	0.0150735i
$581$	1.06249	+	1.84028i	0.0440793	+	0.0763476i
$582$	39.6161	−	9.86015i	1.64214	−	0.408717i
$583$	−0.572221	+	0.991116i	−0.0236990	+	0.0410478i
$584$	9.93154			0.410970
$585$	−2.65000	+	1.40624i	−0.109564	+	0.0581410i
$586$	−0.373729			−0.0154386
$587$	−1.66527	+	2.88434i	−0.0687332	+	0.119049i	−0.898344	−	0.439293i	$-0.855229\pi$
$587$	−1.66527	+	2.88434i	−0.0687332	+	0.119049i	0.829611	+	0.558342i	$0.188562\pi$
$588$	1.68953	+	1.75100i	0.0696751	+	0.0722099i
$589$	1.97711	+	3.42446i	0.0814655	+	0.141102i
$590$	−4.97270	−	8.61296i	−0.204723	−	0.354590i
$591$	−11.9149	+	41.4878i	−0.490111	+	1.70658i
$592$	3.60290	−	6.24041i	0.148078	−	0.256479i
$593$	−6.57804			−0.270128			−0.135064	−	0.990837i	$-0.543124\pi$
$593$	−6.57804			−0.270128			−0.135064	+	0.990837i	$0.543124\pi$
$594$	33.5332	+	10.9412i	1.37588	+	0.448923i
$595$	−0.274261			−0.0112436
$596$	−0.719065	+	1.24546i	−0.0294540	+	0.0510159i
$597$	−3.40140	+	11.8438i	−0.139210	+	0.484733i
$598$	−0.935062	−	1.61958i	−0.0382375	−	0.0662294i
$599$	12.3336	+	21.3623i	0.503936	+	0.872842i	0.999990	+	0.00455031i	$0.00144841\pi$
$599$	12.3336	+	21.3623i	0.503936	+	0.872842i	−0.496054	+	0.868292i	$0.665218\pi$
$600$	3.55280	+	3.68206i	0.145043	+	0.150319i
$601$	−7.17479	+	12.4271i	−0.292666	+	0.506912i	−0.974439	−	0.224651i	$-0.927876\pi$
$601$	−7.17479	+	12.4271i	−0.292666	+	0.506912i	0.681773	+	0.731563i	$0.261209\pi$
$602$	0.228129			0.00929786
$603$	−1.15551	+	32.3293i	−0.0470560	+	1.31655i
$604$	1.67717			0.0682431
$605$	−7.33430	+	12.7034i	−0.298182	+	0.516466i
$606$	−21.0218	+	5.23216i	−0.853951	+	0.212542i
$607$	−19.1706	−	33.2044i	−0.778110	−	1.34773i	−0.933030	−	0.359799i	$-0.882845\pi$
$607$	−19.1706	−	33.2044i	−0.778110	−	1.34773i	0.154919	−	0.987927i	$-0.450488\pi$
$608$	−2.10609	−	3.64785i	−0.0854131	−	0.147940i
$609$	1.28647	−	0.320192i	0.0521302	−	0.0129748i
$610$	−0.380190	+	0.658509i	−0.0153934	+	0.0266622i
$611$	−3.67866			−0.148823
$612$	−0.0160951	+	0.450316i	−0.000650607	+	0.0182029i
$613$	−20.1756			−0.814885			−0.407443	−	0.913231i	$-0.633579\pi$
$613$	−20.1756			−0.814885			−0.407443	+	0.913231i	$0.633579\pi$
$614$	18.6180	−	32.2474i	0.751362	−	1.30140i
$615$	−9.61258	−	9.96229i	−0.387617	−	0.401718i
$616$	2.79814	+	4.84652i	0.112740	+	0.195272i
$617$	−6.52956	−	11.3095i	−0.262870	−	0.455305i	0.704133	−	0.710068i	$-0.251336\pi$
$617$	−6.52956	−	11.3095i	−0.262870	−	0.455305i	−0.967003	+	0.254763i	$0.918002\pi$
$618$	−5.35920	+	18.6609i	−0.215578	+	0.750650i
$619$	11.4634	−	19.8552i	0.460752	−	0.798047i	−0.538246	−	0.842788i	$-0.680913\pi$
$619$	11.4634	−	19.8552i	0.460752	−	0.798047i	0.998999	+	0.0447410i	$0.0142463\pi$
$620$	−0.221780			−0.00890690
$621$	6.89486	+	2.24966i	0.276681	+	0.0902756i
$622$	−43.4040			−1.74034
$623$	−1.66349	+	2.88125i	−0.0666463	+	0.115435i
$624$	1.69654	−	5.90741i	0.0679161	−	0.236486i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	17.8851	+	30.9780i	0.714834	+	1.23813i
$627$	22.2469	+	23.0563i	0.888457	+	0.920779i
$628$	0.365124	−	0.632414i	0.0145700	−	0.0252361i
$629$	−1.48945			−0.0593884
$630$	−1.32763	+	0.704520i	−0.0528942	+	0.0280688i
$631$	48.3336			1.92413			0.962064	−	0.272823i	$-0.0879573\pi$
$631$	48.3336			1.92413			0.962064	+	0.272823i	$0.0879573\pi$
$632$	−18.3170	+	31.7260i	−0.728613	+	1.26199i
$633$	−32.9482	+	8.20057i	−1.30957	+	0.325943i
$634$	−10.2321	−	17.7226i	−0.406370	−	0.703854i
$635$	−9.35800	−	16.2085i	−0.371361	−	0.643216i
$636$	−0.0777472	+	0.0193507i	−0.00308288	+	0.000767305i
$637$	−3.43009	+	5.94110i	−0.135905	+	0.235395i
$638$	−13.8955			−0.550129
$639$	−35.7642	−	22.3888i	−1.41481	−	0.885686i
$640$	−9.27276			−0.366538
$641$	−11.2494	+	19.4845i	−0.444323	+	0.769591i	−0.998005	−	0.0631378i	$-0.979889\pi$
$641$	−11.2494	+	19.4845i	−0.444323	+	0.769591i	0.553681	+	0.832729i	$0.313223\pi$
$642$	21.0605	+	21.8267i	0.831191	+	0.861430i
$643$	13.3442	+	23.1129i	0.526245	+	0.911484i	0.999532	+	0.0305755i	$0.00973399\pi$
$643$	13.3442	+	23.1129i	0.526245	+	0.911484i	−0.473287	+	0.880908i	$0.656933\pi$
$644$	0.0534365	+	0.0925548i	0.00210569	+	0.00364717i
$645$	−0.217704	+	0.758052i	−0.00857210	+	0.0298483i
$646$	1.79408	−	3.10743i	0.0705870	−	0.122260i
$647$	−20.2081			−0.794462			−0.397231	−	0.917719i	$-0.630029\pi$
$647$	−20.2081			−0.794462			−0.397231	+	0.917719i	$0.630029\pi$
$648$	11.6157	+	23.9152i	0.456307	+	0.939476i
$649$	37.6066			1.47619
$650$	−0.669930	+	1.16035i	−0.0262768	+	0.0455127i
$651$	0.193612	−	0.674164i	0.00758827	−	0.0264226i
$652$	−1.73214	−	3.00016i	−0.0678360	−	0.117495i
$653$	2.99361	+	5.18508i	0.117149	+	0.202908i	0.918637	−	0.395103i	$-0.129291\pi$
$653$	2.99361	+	5.18508i	0.117149	+	0.202908i	−0.801488	+	0.598011i	$0.795958\pi$
$654$	−6.70370	−	6.94759i	−0.262136	−	0.271672i
$655$	3.72218	−	6.44701i	0.145438	−	0.251906i
$656$	28.3621			1.10735
$657$	−8.54893	−	5.35171i	−0.333525	−	0.208790i
$658$	−1.84299			−0.0718473
$659$	18.7977	−	32.5586i	0.732256	−	1.26830i	−0.223661	−	0.974667i	$-0.571801\pi$
$659$	18.7977	−	32.5586i	0.732256	−	1.26830i	0.955917	−	0.293637i	$-0.0948657\pi$
$660$	−1.74378	+	0.434015i	−0.0678767	+	0.0168940i
$661$	−4.08338	−	7.07262i	−0.158825	−	0.275093i	0.775620	−	0.631200i	$-0.217437\pi$
$661$	−4.08338	−	7.07262i	−0.158825	−	0.275093i	−0.934445	+	0.356107i	$0.884104\pi$
$662$	2.53268	+	4.38673i	0.0984354	+	0.170495i
$663$	−1.23282	+	0.306840i	−0.0478788	+	0.0119167i
$664$	8.39407	−	14.5390i	0.325753	−	0.564221i
$665$	−1.36520			−0.0529401
$666$	−7.21009	+	3.82609i	−0.279385	+	0.148258i
$667$	−2.85711			−0.110628
$668$	−2.06770	+	3.58136i	−0.0800016	+	0.138567i
$669$	34.8410	+	36.1085i	1.34703	+	1.39604i
$670$	7.22406	+	12.5124i	0.279090	+	0.483398i
$671$	−1.43762	−	2.49002i	−0.0554985	−	0.0961263i
$672$	−0.206243	+	0.718142i	−0.00795598	+	0.0277029i
$673$	10.0476	−	17.4030i	0.387308	−	0.670836i	−0.604779	−	0.796393i	$-0.706738\pi$
$673$	10.0476	−	17.4030i	0.387308	−	0.670836i	0.992086	+	0.125557i	$0.0400718\pi$
$674$	−18.6977			−0.720207
$675$	−1.07409	−	5.08393i	−0.0413417	−	0.195681i
$676$	−0.204778			−0.00787606
$677$	3.41643	−	5.91743i	0.131304	−	0.227425i	−0.792876	−	0.609384i	$-0.791417\pi$
$677$	3.41643	−	5.91743i	0.131304	−	0.227425i	0.924179	+	0.381959i	$0.124750\pi$
$678$	−3.46623	+	12.0695i	−0.133120	+	0.463526i
$679$	−3.28888	−	5.69650i	−0.126216	−	0.218612i
$680$	1.08339	+	1.87649i	0.0415461	+	0.0719599i
$681$	20.2401	+	20.9764i	0.775602	+	0.803819i
$682$	−3.67596	+	6.36694i	−0.140760	+	0.243803i
$683$	43.0486			1.64721			0.823604	−	0.567166i	$-0.191960\pi$
$683$	43.0486			1.64721			0.823604	+	0.567166i	$0.191960\pi$
$684$	−0.0801171	+	2.24155i	−0.00306335	+	0.0857077i
$685$	15.6591			0.598305
$686$	−3.47194	+	6.01358i	−0.132559	+	0.229600i
$687$	−8.95923	+	2.22989i	−0.341816	+	0.0850754i
$688$	−0.807912	−	1.39934i	−0.0308013	−	0.0533495i
$689$	−0.112944	−	0.195625i	−0.00430282	−	0.00745270i
$690$	3.14325	−	0.782333i	0.119662	−	0.0297829i
$691$	−24.0325	+	41.6255i	−0.914239	+	1.58351i	−0.106228	+	0.994342i	$0.533877\pi$
$691$	−24.0325	+	41.6255i	−0.914239	+	1.58351i	−0.808011	+	0.589167i	$0.799456\pi$
$692$	1.03527			0.0393549
$693$	0.203000	−	5.67962i	0.00771134	−	0.215751i
$694$	−41.4489			−1.57338
$695$	2.11827	−	3.66895i	0.0803506	−	0.139171i
$696$	−7.27254	−	7.53712i	−0.275665	−	0.285694i
$697$	−2.93125	−	5.07708i	−0.111029	−	0.192308i
$698$	−0.766693	−	1.32795i	−0.0290198	−	0.0502637i
$699$	−10.0808	+	35.1018i	−0.381293	+	1.32767i
$700$	0.0382848	−	0.0663113i	0.00144703	−	0.00250633i
$701$	−8.26280			−0.312082			−0.156041	−	0.987751i	$-0.549873\pi$
$701$	−8.26280			−0.312082			−0.156041	+	0.987751i	$0.549873\pi$
$702$	−5.17958	+	4.65219i	−0.195491	+	0.175586i
$703$	−7.41409			−0.279628
$704$	21.8940	−	37.9215i	0.825161	−	1.42922i
$705$	1.75877	−	6.12408i	0.0662391	−	0.230646i
$706$	−5.91887	−	10.2518i	−0.222759	−	0.385831i
$707$	1.74520	+	3.02278i	0.0656350	+	0.113683i
$708$	1.82807	+	1.89458i	0.0687031	+	0.0712025i
$709$	−0.884725	+	1.53239i	−0.0332266	+	0.0575501i	−0.882161	−	0.470949i	$-0.843912\pi$
$709$	−0.884725	+	1.53239i	−0.0332266	+	0.0575501i	0.848934	+	0.528499i	$0.177245\pi$
$710$	−18.8447			−0.707228
$711$	32.8630	−	17.4390i	1.23246	−	0.654013i
$712$	26.2845			0.985053
$713$	−0.755825	+	1.30913i	−0.0283059	+	0.0490272i
$714$	−0.617637	+	0.153725i	−0.0231145	+	0.00575302i
$715$	−2.53321	−	4.38765i	−0.0947367	−	0.164089i
$716$	1.52638	+	2.64378i	0.0570437	+	0.0988026i
$717$	−35.7271	+	8.89220i	−1.33425	+	0.332085i
$718$	−3.07713	+	5.32975i	−0.114838	+	0.198904i
$719$	30.5440			1.13910			0.569549	−	0.821957i	$-0.307118\pi$
$719$	30.5440			1.13910			0.569549	+	0.821957i	$0.307118\pi$
$720$	9.02329	+	5.64867i	0.336278	+	0.210514i
$721$	3.12821			0.116501
$722$	−3.79824	+	6.57874i	−0.141356	+	0.244835i
$723$	34.5337	+	35.7901i	1.28432	+	1.33105i
$724$	−0.116497	−	0.201778i	−0.00432956	−	0.00749902i
$725$	1.02349	+	1.77274i	0.0380116	+	0.0658380i
$726$	−9.39652	+	32.7189i	−0.348738	+	1.21431i
$727$	19.4927	−	33.7624i	0.722945	−	1.25218i	−0.236870	−	0.971541i	$-0.576121\pi$
$727$	19.4927	−	33.7624i	0.722945	−	1.25218i	0.959814	−	0.280635i	$-0.0905452\pi$
$728$	−1.10458			−0.0409385
$729$	2.88832	−	26.8451i	0.106975	−	0.994262i
$730$	−4.50455			−0.166721
$731$	−0.166997	+	0.289247i	−0.00617660	+	0.0106982i
$732$	0.0555614	−	0.193466i	0.00205361	−	0.00715072i
$733$	−4.63822	−	8.03363i	−0.171316	−	0.296729i	0.767564	−	0.640972i	$-0.221469\pi$
$733$	−4.63822	−	8.03363i	−0.171316	−	0.296729i	−0.938880	+	0.344244i	$0.888135\pi$
$734$	9.42559	+	16.3256i	0.347905	+	0.602589i
$735$	−8.25056	−	8.55072i	−0.304326	−	0.315398i
$736$	0.805130	−	1.39453i	0.0296775	−	0.0514029i
$737$	−54.6328			−2.01243
$738$	−27.2314	−	17.0472i	−1.00240	−	0.627515i
$739$	−23.4219			−0.861590			−0.430795	−	0.902450i	$-0.641767\pi$
$739$	−23.4219			−0.861590			−0.430795	+	0.902450i	$0.641767\pi$
$740$	0.207917	−	0.360122i	0.00764316	−	0.0132383i
$741$	−6.13664	+	1.52736i	−0.225435	+	0.0561091i
$742$	−0.0565843	−	0.0980069i	−0.00207728	−	0.00359795i
$743$	1.57262	+	2.72386i	0.0576939	+	0.0999288i	0.893430	−	0.449203i	$-0.148292\pi$
$743$	1.57262	+	2.72386i	0.0576939	+	0.0999288i	−0.835736	+	0.549132i	$0.814959\pi$
$744$	−5.37741	+	1.33840i	−0.197145	+	0.0490680i
$745$	3.51144	−	6.08199i	0.128649	−	0.222827i
$746$	−15.2405			−0.557996
$747$	−15.0600	+	7.99170i	−0.551016	+	0.292401i
$748$	−0.760982			−0.0278243
$749$	2.44346	−	4.23220i	0.0892822	−	0.154641i
$750$	−1.61141	−	1.67004i	−0.0588404	−	0.0609811i
$751$	−12.8508	−	22.2582i	−0.468932	−	0.812214i	0.530437	−	0.847724i	$-0.322028\pi$
$751$	−12.8508	−	22.2582i	−0.468932	−	0.812214i	−0.999369	+	0.0355100i	$0.988694\pi$
$752$	6.52689	+	11.3049i	0.238011	+	0.412247i
$753$	9.11699	−	31.7456i	0.332242	−	1.15687i
$754$	1.37134	−	2.37522i	0.0499411	−	0.0865006i
$755$	−8.19021			−0.298072
$756$	0.296001	−	0.265862i	0.0107654	−	0.00966929i
$757$	12.7247			0.462486			0.231243	−	0.972896i	$-0.425721\pi$
$757$	12.7247			0.462486			0.231243	+	0.972896i	$0.425721\pi$
$758$	2.48003	−	4.29555i	0.0900789	−	0.156021i
$759$	−3.38090	+	11.7724i	−0.122719	+	0.427310i
$760$	5.39281	+	9.34063i	0.195618	+	0.338820i
$761$	−2.16390	−	3.74799i	−0.0784414	−	0.135864i	0.824136	−	0.566392i	$-0.191661\pi$
$761$	−2.16390	−	3.74799i	−0.0784414	−	0.135864i	−0.902578	+	0.430527i	$0.858328\pi$
$762$	−30.1592	−	31.2564i	−1.09255	−	1.13230i
$763$	−0.777772	+	1.34714i	−0.0281572	+	0.0487698i
$764$	3.10332			0.112274
$765$	0.0785980	−	2.19905i	0.00284172	−	0.0795067i
$766$	−47.7850			−1.72654
$767$	−3.71136	+	6.42826i	−0.134009	+	0.232111i
$768$	8.17088	−	2.03367i	0.294841	−	0.0733838i
$769$	−24.0104	−	41.5872i	−0.865837	−	1.49967i	−0.866213	−	0.499674i	$-0.833453\pi$
$769$	−24.0104	−	41.5872i	−0.865837	−	1.49967i	0.000376282	−	1.00000i	$-0.499880\pi$
$770$	−1.26913	−	2.19819i	−0.0457361	−	0.0792172i
$771$	−12.4403	+	3.09629i	−0.448026	+	0.111510i
$772$	−1.48992	+	2.58062i	−0.0536235	+	0.0928786i
$773$	38.8366			1.39685			0.698427	−	0.715681i	$-0.253884\pi$
$773$	38.8366			1.39685			0.698427	+	0.715681i	$0.253884\pi$
$774$	−0.0653774	+	1.82916i	−0.00234994	+	0.0657477i
$775$	1.08303			0.0389035
$776$	−25.9835	+	45.0047i	−0.932753	+	1.61558i
$777$	0.913183	+	0.946405i	0.0327603	+	0.0339521i
$778$	5.55108	+	9.61476i	0.199016	+	0.344706i
$779$	−14.5910	−	25.2723i	−0.522776	−	0.905474i
$780$	0.0979043	−	0.340905i	0.00350554	−	0.0122064i
$781$	35.6288	−	61.7108i	1.27490	−	2.20819i
$782$	1.37171			0.0490521
$783$	2.19864	+	10.4067i	0.0785731	+	0.371906i
$784$	24.3434			0.869409
$785$	−1.78303	+	3.08830i	−0.0636390	+	0.110226i
$786$	4.76877	−	16.6050i	0.170096	−	0.592280i
$787$	−3.19755	−	5.53832i	−0.113980	−	0.197420i	0.803391	−	0.595451i	$-0.203027\pi$
$787$	−3.19755	−	5.53832i	−0.113980	−	0.197420i	−0.917372	+	0.398032i	$0.869693\pi$
$788$	−2.55166	−	4.41960i	−0.0908990	−	0.157442i
$789$	−26.1094	−	27.0593i	−0.929520	−	0.963336i
$790$	8.30789	−	14.3897i	0.295581	−	0.511962i
$791$	2.02327			0.0719391
$792$	−39.6616	+	21.0468i	−1.40931	+	0.747864i
$793$	0.567508			0.0201528
$794$	−4.63012	+	8.01960i	−0.164317	+	0.284605i
$795$	0.379666	−	0.0944961i	0.0134654	−	0.00335143i
$796$	−0.728436	−	1.26169i	−0.0258187	−	0.0447193i
$797$	−14.2318	−	24.6502i	−0.504116	−	0.873155i	−0.999989	−	0.00475956i	$-0.998485\pi$
$797$	−14.2318	−	24.6502i	−0.504116	−	0.873155i	0.495872	−	0.868395i	$-0.334848\pi$
$798$	−3.07442	+	0.765201i	−0.108833	+	0.0270878i
$799$	1.34912	−	2.33674i	0.0477284	−	0.0826681i
$800$	−1.15368			−0.0407887
$801$	−22.6253	−	14.1637i	−0.799426	−	0.500449i
$802$	−37.1299			−1.31110
$803$	8.51655	−	14.7511i	0.300543	−	0.520555i
$804$	−2.65572	−	2.75234i	−0.0936601	−	0.0970675i
$805$	−0.260949	−	0.451977i	−0.00919724	−	0.0159301i
$806$	−0.725553	−	1.25669i	−0.0255565	−	0.0442652i
$807$	−10.2997	+	35.8638i	−0.362566	+	1.26246i
$808$	13.7878	−	23.8812i	0.485053	−	0.840137i
$809$	−11.4245			−0.401664			−0.200832	−	0.979626i	$-0.564364\pi$
$809$	−11.4245			−0.401664			−0.200832	+	0.979626i	$0.564364\pi$
$810$	−5.26842	−	10.8470i	−0.185113	−	0.381124i
$811$	29.7895			1.04605			0.523026	−	0.852317i	$-0.324803\pi$
$811$	29.7895			1.04605			0.523026	+	0.852317i	$0.324803\pi$
$812$	−0.0783685	+	0.135738i	−0.00275020	+	0.00476348i
$813$	2.26067	−	7.87169i	0.0792850	−	0.276072i
$814$	−6.89234	−	11.9379i	−0.241576	−	0.418423i
$815$	8.45865	+	14.6508i	0.296294	+	0.513196i
$816$	3.13029	+	3.24417i	0.109582	+	0.113569i
$817$	−0.831264	+	1.43979i	−0.0290823	+	0.0503720i
$818$	39.6364			1.38586
$819$	0.950809	+	0.595216i	0.0332239	+	0.0207985i
$820$	1.63672			0.0571568
$821$	−22.3237	+	38.6658i	−0.779103	+	1.34945i	0.153357	+	0.988171i	$0.450992\pi$
$821$	−22.3237	+	38.6658i	−0.779103	+	1.34945i	−0.932459	+	0.361275i	$0.882342\pi$
$822$	35.2644	−	8.77704i	1.22999	−	0.306135i
$823$	9.50630	+	16.4654i	0.331369	+	0.573947i	0.982780	−	0.184777i	$-0.0591563\pi$
$823$	9.50630	+	16.4654i	0.331369	+	0.573947i	−0.651412	+	0.758724i	$0.725823\pi$
$824$	−12.3571	−	21.4031i	−0.430479	−	0.745611i
$825$	8.51550	−	2.11944i	0.296472	−	0.0737896i
$826$	−1.85937	+	3.22053i	−0.0646958	+	0.112056i
$827$	0.00835178			0.000290420			0.000145210	−	1.00000i	$-0.499954\pi$
$827$	0.00835178			0.000290420			0.000145210		1.00000i	$0.499954\pi$
$828$	−0.757424	+	0.401933i	−0.0263223	+	0.0139681i
$829$	−25.2464			−0.876843			−0.438421	−	0.898770i	$-0.644462\pi$
$829$	−25.2464			−0.876843			−0.438421	+	0.898770i	$0.644462\pi$
$830$	−3.80722	+	6.59430i	−0.132151	+	0.228891i
$831$	−8.11744	−	8.41276i	−0.281591	−	0.291835i
$832$	4.32139	+	7.48487i	0.149817	+	0.259491i
$833$	−2.51592	−	4.35770i	−0.0871714	−	0.150985i
$834$	2.71388	−	9.44979i	0.0939738	−	0.327219i
$835$	10.0973	−	17.4890i	0.349431	−	0.605232i
$836$	−3.78796			−0.131009
$837$	5.35001	+	1.74560i	0.184923	+	0.0603368i
$838$	−44.9404			−1.55244
$839$	−1.51371	+	2.62182i	−0.0522591	+	0.0905154i	−0.890972	−	0.454059i	$-0.849976\pi$
$839$	−1.51371	+	2.62182i	−0.0522591	+	0.0905154i	0.838712	+	0.544574i	$0.183309\pi$
$840$	0.528101	−	1.83886i	0.0182212	−	0.0634468i
$841$	12.4049	+	21.4860i	0.427756	+	0.740895i
$842$	17.1842	+	29.7639i	0.592207	+	1.02573i
$843$	19.8116	+	20.5324i	0.682349	+	0.707173i
$844$	2.00713	−	3.47645i	0.0690883	−	0.119664i
$845$	1.00000			0.0344010
$846$	0.528166	−	14.7772i	0.0181587	−	0.508052i
$847$	5.48483			0.188461
$848$	−0.400783	+	0.694176i	−0.0137629	+	0.0238381i
$849$	−8.49841	+	2.11519i	−0.291665	+	0.0725932i
$850$	−0.491383	−	0.851099i	−0.0168543	−	0.0291925i
$851$	−1.41716	−	2.45459i	−0.0485795	−	0.0841421i
$852$	4.84085	−	1.20485i	0.165845	−	0.0412775i
$853$	17.9390	−	31.0713i	0.614220	−	1.06386i	−0.376301	−	0.926498i	$-0.622804\pi$
$853$	17.9390	−	31.0713i	0.614220	−	1.06386i	0.990521	−	0.137363i	$-0.0438626\pi$
$854$	0.284318			0.00972918
$855$	0.391239	−	10.9463i	0.0133801	−	0.374354i
$856$	−38.6087			−1.31962
$857$	−6.26938	+	10.8589i	−0.214158	+	0.370933i	−0.953012	−	0.302933i	$-0.902034\pi$
$857$	−6.26938	+	10.8589i	−0.214158	+	0.370933i	0.738854	+	0.673866i	$0.235367\pi$
$858$	−8.16409	−	8.46110i	−0.278717	−	0.288857i
$859$	−12.5010	−	21.6524i	−0.426529	−	0.738770i	0.570033	−	0.821622i	$-0.306930\pi$
$859$	−12.5010	−	21.6524i	−0.426529	−	0.738770i	−0.996562	+	0.0828519i	$0.973597\pi$
$860$	−0.0466230	−	0.0807534i	−0.00158983	−	0.00275367i
$861$	−1.42885	+	4.97528i	−0.0486950	+	0.169557i
$862$	23.1797	−	40.1485i	0.789505	−	1.36746i
$863$	−32.6989			−1.11308			−0.556541	−	0.830820i	$-0.687872\pi$
$863$	−32.6989			−1.11308			−0.556541	+	0.830820i	$0.687872\pi$
$864$	−5.69901	−	1.85947i	−0.193884	−	0.0632605i
$865$	−5.05556			−0.171894
$866$	−3.87316	+	6.70851i	−0.131615	+	0.227964i
$867$	−7.87049	+	27.4053i	−0.267296	+	0.930731i
$868$	0.0414636	+	0.0718170i	0.00140737	+	0.00243763i
$869$	31.4147	+	54.4118i	1.06567	+	1.84579i
$870$	3.29854	+	3.41854i	0.111831	+	0.115899i
$871$	5.39166	−	9.33863i	0.182689	−	0.316427i
$872$	12.2894			0.416173
$873$	46.6175	−	24.7379i	1.57776	−	0.837253i
$874$	6.82797			0.230960
$875$	−0.186958	+	0.323821i	−0.00632034	+	0.0109471i
$876$	1.15714	−	0.288002i	0.0390960	−	0.00973070i
$877$	−9.28493	−	16.0820i	−0.313530	−	0.543050i	0.665594	−	0.746314i	$-0.268178\pi$
$877$	−9.28493	−	16.0820i	−0.313530	−	0.543050i	−0.979124	+	0.203264i	$0.934845\pi$
$878$	17.1460	+	29.6977i	0.578649	+	1.00225i
$879$	−0.468821	+	0.116686i	−0.0158129	+	0.00393572i
$880$	−8.98912	+	15.5696i	−0.303023	+	0.524852i
$881$	−54.6862			−1.84242			−0.921212	−	0.389061i	$-0.872800\pi$
$881$	−54.6862			−1.84242			−0.921212	+	0.389061i	$0.872800\pi$
$882$	−23.3730	−	14.6317i	−0.787009	−	0.492676i
$883$	23.9427			0.805735			0.402868	−	0.915258i	$-0.368014\pi$
$883$	23.9427			0.805735			0.402868	+	0.915258i	$0.368014\pi$
$884$	0.0751006	−	0.130078i	0.00252591	−	0.00437500i
$885$	−8.92710	−	9.25187i	−0.300081	−	0.310998i
$886$	21.6863	+	37.5618i	0.728566	+	1.26191i
$887$	−5.57131	−	9.64979i	−0.187066	−	0.324008i	0.757205	−	0.653178i	$-0.226565\pi$
$887$	−5.57131	−	9.64979i	−0.187066	−	0.324008i	−0.944271	+	0.329170i	$0.893231\pi$
$888$	2.86800	−	9.98646i	0.0962439	−	0.335124i
$889$	−3.49911	+	6.06063i	−0.117356	+	0.203267i
$890$	−11.9216			−0.399613
$891$	45.4814	+	3.25534i	1.52369	+	0.109058i
$892$	−5.93234			−0.198629
$893$	6.71555	−	11.6317i	0.224727	−	0.389239i
$894$	4.49877	−	15.6648i	0.150461	−	0.523910i
$895$	−7.45386	−	12.9105i	−0.249155	−	0.431549i
$896$	1.73362	+	3.00271i	0.0579161	+	0.100314i
$897$	−1.67864	−	1.73971i	−0.0560483	−	0.0580874i
$898$	18.8648	−	32.6747i	0.629525	−	1.09037i
$899$	−2.21694			−0.0739393
$900$	0.520717	+	0.325974i	0.0173572	+	0.0108658i
$901$	0.165685			0.00551977
$902$	27.1283	−	46.9876i	0.903274	−	1.56452i
$903$	0.286175	−	0.0712267i	0.00952329	−	0.00237028i
$904$	−7.99232	−	13.8431i	−0.265821	−	0.460415i
$905$	0.568893	+	0.985352i	0.0189106	+	0.0327542i
$906$	−18.4443	+	4.59066i	−0.612772	+	0.152514i
$907$	−5.48700	+	9.50377i	−0.182193	+	0.315568i	−0.942627	−	0.333848i	$-0.891653\pi$
$907$	−5.48700	+	9.50377i	−0.182193	+	0.315568i	0.760434	+	0.649415i	$0.224986\pi$
$908$	−3.44626			−0.114368
$909$	−24.7370	+	13.1269i	−0.820474	+	0.435391i
$910$	0.500995			0.0166078
$911$	9.91091	−	17.1662i	0.328363	−	0.568742i	−0.653824	−	0.756647i	$-0.726836\pi$
$911$	9.91091	−	17.1662i	0.328363	−	0.568742i	0.982187	+	0.187905i	$0.0601697\pi$
$912$	15.5817	+	16.1486i	0.515962	+	0.534733i
$913$	−14.3963	−	24.9351i	−0.476447	−	0.825231i
$914$	0.444352	+	0.769641i	0.0146979	+	0.0254575i
$915$	−0.271326	+	0.944763i	−0.00896975	+	0.0312329i
$916$	0.545776	−	0.945311i	0.0180329	−	0.0312340i
$917$	−2.78357			−0.0919216
$918$	−1.05558	−	4.99631i	−0.0348392	−	0.164903i
$919$	20.9902			0.692403			0.346202	−	0.938160i	$-0.387471\pi$
$919$	20.9902			0.692403			0.346202	+	0.938160i	$0.387471\pi$
$920$	−2.06160	+	3.57080i	−0.0679691	+	0.117726i
$921$	13.2869	−	46.2653i	0.437818	−	1.52449i
$922$	−3.11237	−	5.39078i	−0.102500	−	0.177536i
$923$	7.03234	+	12.1804i	0.231472	+	0.400922i
$924$	0.466558	+	0.483531i	0.0153486	+	0.0159070i
$925$	−1.01533	+	1.75860i	−0.0333838	+	0.0578224i
$926$	44.6955			1.46879
$927$	−0.896483	+	25.0822i	−0.0294444	+	0.823807i
$928$	2.36156			0.0775221
$929$	15.6388	−	27.0872i	0.513093	−	0.888703i	−0.486792	−	0.873518i	$-0.661833\pi$
$929$	15.6388	−	27.0872i	0.513093	−	0.888703i	0.999885	−	0.0151851i	$-0.00483375\pi$
$930$	2.43898	−	0.607044i	0.0799773	−	0.0199058i
$931$	−12.5235	−	21.6914i	−0.410443	−	0.710908i
$932$	−2.15889	−	3.73931i	−0.0707168	−	0.122485i
$933$	−54.4477	+	13.5516i	−1.78254	+	0.443660i
$934$	15.7868	−	27.3436i	0.516561	−	0.894709i
$935$	3.71614			0.121531
$936$	0.316552	−	8.85662i	0.0103468	−	0.289488i
$937$	1.63068			0.0532718			0.0266359	−	0.999645i	$-0.491521\pi$
$937$	1.63068			0.0532718			0.0266359	+	0.999645i	$0.491521\pi$
$938$	2.70119	−	4.67861i	0.0881971	−	0.152762i
$939$	32.1078	+	33.2759i	1.04780	+	1.08592i
$940$	0.376654	+	0.652384i	0.0122851	+	0.0212784i
$941$	−22.1374	−	38.3431i	−0.721659	−	1.24995i	−0.960334	−	0.278851i	$-0.910047\pi$
$941$	−22.1374	−	38.3431i	−0.721659	−	1.24995i	0.238675	−	0.971099i	$-0.423287\pi$
$942$	−2.28437	+	7.95424i	−0.0744288	+	0.259163i
$943$	5.57794	−	9.66128i	0.181643	−	0.314614i
$944$	26.3396			0.857280
$945$	−1.44547	+	1.29829i	−0.0470212	+	0.0422335i
$946$	−3.09106			−0.100499
$947$	7.35789	−	12.7442i	0.239099	−	0.414132i	−0.721357	−	0.692564i	$-0.756481\pi$
$947$	7.35789	−	12.7442i	0.239099	−	0.414132i	0.960456	+	0.278432i	$0.0898146\pi$
$948$	−1.21412	+	4.22761i	−0.0394329	+	0.137306i
$949$	1.68098	+	2.91154i	0.0545669	+	0.0945127i
$950$	−2.44597	−	4.23654i	−0.0793576	−	0.137451i
$951$	−18.3690	−	19.0373i	−0.595655	−	0.617325i
$952$	0.405097	−	0.701648i	0.0131293	−	0.0227405i
$953$	−3.63206			−0.117654			−0.0588270	−	0.998268i	$-0.518736\pi$
$953$	−3.63206			−0.117654			−0.0588270	+	0.998268i	$0.518736\pi$
$954$	0.802042	−	0.425610i	0.0259671	−	0.0137796i
$955$	−15.1546			−0.490390
$956$	2.17641	−	3.76965i	0.0703902	−	0.121919i
$957$	−17.4311	+	4.33847i	−0.563468	+	0.140243i
$958$	−24.4618	−	42.3690i	−0.790324	−	1.36888i
$959$	−2.92760	−	5.07076i	−0.0945373	−	0.163743i
$960$	−14.5266	+	3.61555i	−0.468843	+	0.116691i
$961$	14.9135	−	25.8310i	0.481081	−	0.833257i
$962$	2.72079			0.0877219
$963$	33.2338	+	20.8047i	1.07095	+	0.670423i
$964$	−5.88002			−0.189383
$965$	7.27580	−	12.6021i	0.234216	−	0.405675i
$966$	−0.840992	−	0.871588i	−0.0270585	−	0.0280429i
$967$	−23.2187	−	40.2160i	−0.746664	−	1.29326i	−0.949413	−	0.314029i	$-0.898321\pi$
$967$	−23.2187	−	40.2160i	−0.746664	−	1.29326i	0.202750	−	0.979231i	$-0.435012\pi$
$968$	−21.6662	−	37.5270i	−0.696378	−	1.20616i
$969$	1.28036	−	4.45824i	0.0411310	−	0.143219i
$970$	11.7851	−	20.4124i	0.378396	−	0.655402i
$971$	−27.7058			−0.889121			−0.444561	−	0.895749i	$-0.646640\pi$
$971$	−27.7058			−0.889121			−0.444561	+	0.895749i	$0.646640\pi$
$972$	2.04687	+	2.44954i	0.0656533	+	0.0785692i
$973$	−1.58411			−0.0507843
$974$	−21.8991	+	37.9303i	−0.701691	+	1.21536i
$975$	−0.478101	+	1.66476i	−0.0153115	+	0.0533149i
$976$	−1.00690	−	1.74401i	−0.0322302	−	0.0558243i
$977$	−17.6374	−	30.5489i	−0.564271	−	0.977347i	−0.997117	−	0.0758787i	$-0.975824\pi$
$977$	−17.6374	−	30.5489i	−0.564271	−	0.977347i	0.432846	−	0.901468i	$-0.357510\pi$
$978$	27.2607	+	28.2525i	0.871702	+	0.903415i
$979$	22.5396	−	39.0398i	0.720370	−	1.24772i
$980$	1.40481			0.0448751
$981$	−10.5786	−	6.62230i	−0.337748	−	0.211434i
$982$	−24.9371			−0.795776
$983$	−10.0457	+	17.3997i	−0.320409	+	0.554964i	−0.980572	−	0.196158i	$-0.937154\pi$
$983$	−10.0457	+	17.3997i	−0.320409	+	0.554964i	0.660164	+	0.751122i	$0.270487\pi$
$984$	39.6849	−	9.87728i	1.26511	−	0.314876i
$985$	12.4606	+	21.5824i	0.397028	+	0.687673i
$986$	1.00585	+	1.74219i	0.0320329	+	0.0554826i
$987$	−2.31192	+	0.575420i	−0.0735893	+	0.0183158i
$988$	0.373830	−	0.647492i	0.0118931	−	0.0205995i
$989$	−0.635564			−0.0202097
$990$	17.9889	−	9.54598i	0.571726	−	0.303391i
$991$	−42.6330			−1.35428			−0.677141	−	0.735853i	$-0.736781\pi$
$991$	−42.6330			−1.35428			−0.677141	+	0.735853i	$0.736781\pi$
$992$	0.624733	−	1.08207i	0.0198353	−	0.0343558i
$993$	4.54672	+	4.71213i	0.144286	+	0.149535i
$994$	3.52316	+	6.10230i	0.111748	+	0.193553i
$995$	3.55720	+	6.16126i	0.112771	+	0.195325i
$996$	0.556392	−	1.93737i	0.0176300	−	0.0613879i
$997$	−9.74942	+	16.8865i	−0.308767	+	0.534800i	−0.978093	−	0.208169i	$-0.933250\pi$
$997$	−9.74942	+	16.8865i	−0.308767	+	0.534800i	0.669326	+	0.742969i	$0.266583\pi$
$998$	−5.52588			−0.174919
$999$	−7.85004	+	7.05075i	−0.248364	+	0.223076i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.i.g.196.9	✓	26
3.2	odd	2		1755.2.i.g.586.5		26
9.2	odd	6		5265.2.a.bh.1.9		13
9.4	even	3	inner	585.2.i.g.391.9	yes	26
9.5	odd	6		1755.2.i.g.1171.5		26
9.7	even	3		5265.2.a.bg.1.5		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.g.196.9	✓	26	1.1	even	1	trivial
585.2.i.g.391.9	yes	26	9.4	even	3	inner
1755.2.i.g.586.5		26	3.2	odd	2
1755.2.i.g.1171.5		26	9.5	odd	6
5265.2.a.bg.1.5		13	9.7	even	3
5265.2.a.bh.1.9		13	9.2	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)

\(f(q)\)	\(=\)	\(q+(0.669930 - 1.16035i) q^{2} +(0.478101 - 1.66476i) q^{3} +(0.102389 + 0.177343i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.61141 - 1.67004i) q^{6} +(-0.186958 + 0.323821i) q^{7} +2.95409 q^{8} +(-2.54284 - 1.59184i) q^{9} +O(q^{10})\)	\(q+(0.669930 - 1.16035i) q^{2} +(0.478101 - 1.66476i) q^{3} +(0.102389 + 0.177343i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.61141 - 1.67004i) q^{6} +(-0.186958 + 0.323821i) q^{7} +2.95409 q^{8} +(-2.54284 - 1.59184i) q^{9} -1.33986 q^{10} +(2.53321 - 4.38765i) q^{11} +(0.344185 - 0.0856650i) q^{12} +(0.500000 + 0.866025i) q^{13} +(0.250497 + 0.433874i) q^{14} +(-1.68077 + 0.418332i) q^{15} +(1.77426 - 3.07310i) q^{16} -0.733484 q^{17} +(-3.55062 + 1.88417i) q^{18} -3.65108 q^{19} +(0.102389 - 0.177343i) q^{20} +(0.449699 + 0.466059i) q^{21} +(-3.39414 - 5.87883i) q^{22} +(-0.697881 - 1.20877i) q^{23} +(1.41235 - 4.91785i) q^{24} +(-0.500000 + 0.866025i) q^{25} +1.33986 q^{26} +(-3.86577 + 3.47215i) q^{27} -0.0765697 q^{28} +(1.02349 - 1.77274i) q^{29} +(-0.640587 + 2.23054i) q^{30} +(-0.541514 - 0.937930i) q^{31} +(0.576839 + 0.999115i) q^{32} +(-6.09324 - 6.31492i) q^{33} +(-0.491383 + 0.851099i) q^{34} +0.373916 q^{35} +(0.0219434 - 0.613941i) q^{36} +2.03066 q^{37} +(-2.44597 + 4.23654i) q^{38} +(1.68077 - 0.418332i) q^{39} +(-1.47705 - 2.55832i) q^{40} +(3.99634 + 6.92187i) q^{41} +(0.842059 - 0.209582i) q^{42} +(0.227676 - 0.394347i) q^{43} +1.03749 q^{44} +(-0.107157 + 2.99809i) q^{45} -1.87012 q^{46} +(-1.83933 + 3.18582i) q^{47} +(-4.26770 - 4.42296i) q^{48} +(3.43009 + 5.94110i) q^{49} +(0.669930 + 1.16035i) q^{50} +(-0.350679 + 1.22107i) q^{51} +(-0.102389 + 0.177343i) q^{52} -0.225888 q^{53} +(1.43913 + 6.81175i) q^{54} -5.06642 q^{55} +(-0.552291 + 0.956596i) q^{56} +(-1.74558 + 6.07817i) q^{57} +(-1.37134 - 2.37522i) q^{58} +(3.71136 + 6.42826i) q^{59} +(-0.246281 - 0.255240i) q^{60} +(0.283754 - 0.491476i) q^{61} -1.45111 q^{62} +(0.990877 - 0.525817i) q^{63} +8.64279 q^{64} +(0.500000 - 0.866025i) q^{65} +(-11.4096 + 2.83976i) q^{66} +(-5.39166 - 9.33863i) q^{67} +(-0.0751006 - 0.130078i) q^{68} +(-2.34596 + 0.583892i) q^{69} +(0.250497 - 0.433874i) q^{70} +14.0647 q^{71} +(-7.51178 - 4.70245i) q^{72} +3.36196 q^{73} +(1.36040 - 2.35628i) q^{74} +(1.20267 + 1.24643i) q^{75} +(-0.373830 - 0.647492i) q^{76} +(0.947208 + 1.64061i) q^{77} +(0.640587 - 2.23054i) q^{78} +(-6.20057 + 10.7397i) q^{79} -3.54851 q^{80} +(3.93207 + 8.09561i) q^{81} +10.7091 q^{82} +(2.84151 - 4.92164i) q^{83} +(-0.0366080 + 0.127470i) q^{84} +(0.366742 + 0.635216i) q^{85} +(-0.305054 - 0.528369i) q^{86} +(-2.46185 - 2.55142i) q^{87} +(7.48333 - 12.9615i) q^{88} +8.89766 q^{89} +(3.40705 + 2.13285i) q^{90} -0.373916 q^{91} +(0.142910 - 0.247528i) q^{92} +(-1.82033 + 0.453065i) q^{93} +(2.46445 + 4.26854i) q^{94} +(1.82554 + 3.16193i) q^{95} +(1.93907 - 0.482621i) q^{96} +(-8.79576 + 15.2347i) q^{97} +9.19168 q^{98} +(-13.4260 + 7.12461i) 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

Introduction

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