LMFDB - Embedded newform 585.2.i.g.196.11

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			196.11
Character	$\chi$	$=$	585.196
Dual form			585.2.i.g.391.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.853509 - 1.47832i) q^{2} +(0.733344 + 1.56914i) q^{3} +(-0.456955 - 0.791470i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.94561 + 0.255158i) q^{6} +(1.35209 - 2.34188i) q^{7} +1.85397 q^{8} +(-1.92441 + 2.30144i) q^{9} +O(q^{10})$	\(q+(0.853509 - 1.47832i) q^{2} +(0.733344 + 1.56914i) q^{3} +(-0.456955 - 0.791470i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.94561 + 0.255158i) q^{6} +(1.35209 - 2.34188i) q^{7} +1.85397 q^{8} +(-1.92441 + 2.30144i) q^{9} -1.70702 q^{10} +(0.781129 - 1.35295i) q^{11} +(0.906822 - 1.29745i) q^{12} +(0.500000 + 0.866025i) q^{13} +(-2.30804 - 3.99764i) q^{14} +(0.992244 - 1.41967i) q^{15} +(2.49629 - 4.32371i) q^{16} -1.05862 q^{17} +(1.75977 + 4.80920i) q^{18} +5.32455 q^{19} +(-0.456955 + 0.791470i) q^{20} +(4.66630 + 0.404209i) q^{21} +(-1.33340 - 2.30952i) q^{22} +(0.295081 + 0.511096i) q^{23} +(1.35960 + 2.90915i) q^{24} +(-0.500000 + 0.866025i) q^{25} +1.70702 q^{26} +(-5.02255 - 1.33193i) q^{27} -2.47137 q^{28} +(-2.16555 + 3.75085i) q^{29} +(-1.25183 - 2.67855i) q^{30} +(1.16135 + 2.01151i) q^{31} +(-2.40724 - 4.16947i) q^{32} +(2.69581 + 0.233520i) q^{33} +(-0.903544 + 1.56498i) q^{34} -2.70418 q^{35} +(2.70089 + 0.471457i) q^{36} -0.158846 q^{37} +(4.54455 - 7.87139i) q^{38} +(-0.992244 + 1.41967i) q^{39} +(-0.926987 - 1.60559i) q^{40} +(-0.609700 - 1.05603i) q^{41} +(4.58028 - 6.55329i) q^{42} +(0.0815831 - 0.141306i) q^{43} -1.42776 q^{44} +(2.95531 + 0.515868i) q^{45} +1.00742 q^{46} +(3.73480 - 6.46886i) q^{47} +(8.61516 + 0.746272i) q^{48} +(-0.156283 - 0.270690i) q^{49} +(0.853509 + 1.47832i) q^{50} +(-0.776335 - 1.66113i) q^{51} +(0.456955 - 0.791470i) q^{52} -12.3871 q^{53} +(-6.25580 + 6.28813i) q^{54} -1.56226 q^{55} +(2.50674 - 4.34179i) q^{56} +(3.90473 + 8.35497i) q^{57} +(3.69664 + 6.40276i) q^{58} +(-2.45185 - 4.24674i) q^{59} +(-1.57703 - 0.136608i) q^{60} +(-3.71783 + 6.43947i) q^{61} +3.96488 q^{62} +(2.78774 + 7.61850i) q^{63} +1.76676 q^{64} +(0.500000 - 0.866025i) q^{65} +(2.64612 - 3.78597i) q^{66} +(-0.676472 - 1.17168i) q^{67} +(0.483743 + 0.837867i) q^{68} +(-0.585586 + 0.837834i) q^{69} +(-2.30804 + 3.99764i) q^{70} -15.9401 q^{71} +(-3.56781 + 4.26682i) q^{72} +2.78604 q^{73} +(-0.135577 + 0.234826i) q^{74} +(-1.72559 - 0.149476i) q^{75} +(-2.43308 - 4.21422i) q^{76} +(-2.11231 - 3.65863i) q^{77} +(1.25183 + 2.67855i) q^{78} +(-3.90562 + 6.76474i) q^{79} -4.99259 q^{80} +(-1.59328 - 8.85785i) q^{81} -2.08154 q^{82} +(-6.74274 + 11.6788i) q^{83} +(-1.81237 - 3.87794i) q^{84} +(0.529311 + 0.916794i) q^{85} +(-0.139264 - 0.241212i) q^{86} +(-7.47371 - 0.647396i) q^{87} +(1.44819 - 2.50834i) q^{88} -8.37469 q^{89} +(3.28501 - 3.92860i) q^{90} +2.70418 q^{91} +(0.269678 - 0.467096i) q^{92} +(-2.30468 + 3.29745i) q^{93} +(-6.37537 - 11.0425i) q^{94} +(-2.66228 - 4.61120i) q^{95} +(4.77715 - 6.83497i) q^{96} +(-6.15231 + 10.6561i) q^{97} -0.533556 q^{98} +(1.61053 + 4.40136i) 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 $

$2$	0.853509	−	1.47832i	0.603522	−	1.04533i	−0.388761	−	0.921339i	$-0.627097\pi$
$2$	0.853509	−	1.47832i	0.603522	−	1.04533i	0.992283	−	0.123992i	$-0.0395698\pi$
$3$	0.733344	+	1.56914i	0.423397	+	0.905944i
$3$	0.733344	+	1.56914i	0.423397	+	0.905944i
$4$	−0.456955	−	0.791470i	−0.228478	−	0.395735i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	2.94561	+	0.255158i	1.20254	+	0.104168i
$7$	1.35209	−	2.34188i	0.511041	−	0.885149i	−0.488877	−	0.872353i	$-0.662593\pi$
$7$	1.35209	−	2.34188i	0.511041	−	0.885149i	0.999918	−	0.0127965i	$-0.00407337\pi$
$8$	1.85397			0.655479
$9$	−1.92441	+	2.30144i	−0.641471	+	0.767148i
$10$	−1.70702			−0.539806
$11$	0.781129	−	1.35295i	0.235519	−	0.407931i	−0.723904	−	0.689900i	$-0.757654\pi$
$11$	0.781129	−	1.35295i	0.235519	−	0.407931i	0.959423	+	0.281969i	$0.0909876\pi$
$12$	0.906822	−	1.29745i	0.261777	−	0.374541i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$14$	−2.30804	−	3.99764i	−0.616849	−	1.06841i
$15$	0.992244	−	1.41967i	0.256196	−	0.366556i
$16$	2.49629	−	4.32371i	0.624074	−	1.08093i
$17$	−1.05862			−0.256754			−0.128377	−	0.991725i	$-0.540977\pi$
$17$	−1.05862			−0.256754			−0.128377	+	0.991725i	$0.540977\pi$
$18$	1.75977	+	4.80920i	0.414781	+	1.13354i
$19$	5.32455			1.22154			0.610768	−	0.791810i	$-0.290861\pi$
$19$	5.32455			1.22154			0.610768	+	0.791810i	$0.290861\pi$
$20$	−0.456955	+	0.791470i	−0.102178	+	0.176978i
$21$	4.66630	+	0.404209i	1.01827	+	0.0882057i
$22$	−1.33340	−	2.30952i	−0.284282	−	0.492391i
$23$	0.295081	+	0.511096i	0.0615287	+	0.106571i	0.895149	−	0.445767i	$-0.147069\pi$
$23$	0.295081	+	0.511096i	0.0615287	+	0.106571i	−0.833620	+	0.552338i	$0.813736\pi$
$24$	1.35960	+	2.90915i	0.277528	+	0.593828i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	1.70702			0.334774
$27$	−5.02255	−	1.33193i	−0.966590	−	0.256329i
$28$	−2.47137			−0.467046
$29$	−2.16555	+	3.75085i	−0.402133	+	0.696515i	−0.993983	−	0.109533i	$-0.965064\pi$
$29$	−2.16555	+	3.75085i	−0.402133	+	0.696515i	0.591850	+	0.806048i	$0.298398\pi$
$30$	−1.25183	−	2.67855i	−0.228552	−	0.489035i
$31$	1.16135	+	2.01151i	0.208584	+	0.361278i	0.951269	−	0.308363i	$-0.0997812\pi$
$31$	1.16135	+	2.01151i	0.208584	+	0.361278i	−0.742685	+	0.669641i	$0.766448\pi$
$32$	−2.40724	−	4.16947i	−0.425545	−	0.737065i
$33$	2.69581	+	0.233520i	0.469281	+	0.0406506i
$34$	−0.903544	+	1.56498i	−0.154956	+	0.268392i
$35$	−2.70418			−0.457089
$36$	2.70089	+	0.471457i	0.450149	+	0.0785762i
$37$	−0.158846			−0.0261142			−0.0130571	−	0.999915i	$-0.504156\pi$
$37$	−0.158846			−0.0261142			−0.0130571	+	0.999915i	$0.504156\pi$
$38$	4.54455	−	7.87139i	0.737224	−	1.27691i
$39$	−0.992244	+	1.41967i	−0.158886	+	0.227328i
$40$	−0.926987	−	1.60559i	−0.146570	−	0.253866i
$41$	−0.609700	−	1.05603i	−0.0952191	−	0.164924i	0.814481	−	0.580190i	$-0.197022\pi$
$41$	−0.609700	−	1.05603i	−0.0952191	−	0.164924i	−0.909700	+	0.415266i	$0.863689\pi$
$42$	4.58028	−	6.55329i	0.706752	−	1.01119i
$43$	0.0815831	−	0.141306i	0.0124413	−	0.0215490i	−0.859738	−	0.510736i	$-0.829373\pi$
$43$	0.0815831	−	0.141306i	0.0124413	−	0.0215490i	0.872179	+	0.489187i	$0.162706\pi$
$44$	−1.42776			−0.215243
$45$	2.95531	+	0.515868i	0.440552	+	0.0769011i
$46$	1.00742			0.148536
$47$	3.73480	−	6.46886i	0.544776	−	0.943580i	−0.453844	−	0.891081i	$-0.649948\pi$
$47$	3.73480	−	6.46886i	0.544776	−	0.943580i	0.998621	−	0.0524996i	$-0.0167188\pi$
$48$	8.61516	+	0.746272i	1.24349	+	0.107715i
$49$	−0.156283	−	0.270690i	−0.0223261	−	0.0386700i
$50$	0.853509	+	1.47832i	0.120704	+	0.209066i
$51$	−0.776335	−	1.66113i	−0.108709	−	0.232605i
$52$	0.456955	−	0.791470i	0.0633683	−	0.109757i
$53$	−12.3871			−1.70150			−0.850751	−	0.525568i	$-0.823853\pi$
$53$	−12.3871			−1.70150			−0.850751	+	0.525568i	$0.823853\pi$
$54$	−6.25580	+	6.28813i	−0.851307	+	0.855706i
$55$	−1.56226			−0.210655
$56$	2.50674	−	4.34179i	0.334977	−	0.580197i
$57$	3.90473	+	8.35497i	0.517194	+	1.10664i
$58$	3.69664	+	6.40276i	0.485392	+	0.840724i
$59$	−2.45185	−	4.24674i	−0.319204	−	0.552878i	0.661118	−	0.750282i	$-0.270082\pi$
$59$	−2.45185	−	4.24674i	−0.319204	−	0.552878i	−0.980322	+	0.197404i	$0.936749\pi$
$60$	−1.57703	−	0.136608i	−0.203594	−	0.0176360i
$61$	−3.71783	+	6.43947i	−0.476020	+	0.824490i	−0.999623	−	0.0274724i	$-0.991254\pi$
$61$	−3.71783	+	6.43947i	−0.476020	+	0.824490i	0.523603	+	0.851962i	$0.324588\pi$
$62$	3.96488			0.503540
$63$	2.78774	+	7.61850i	0.351222	+	0.959841i
$64$	1.76676			0.220845
$65$	0.500000	−	0.866025i	0.0620174	−	0.107417i
$66$	2.64612	−	3.78597i	0.325715	−	0.466020i
$67$	−0.676472	−	1.17168i	−0.0826442	−	0.143144i	0.821741	−	0.569862i	$-0.193003\pi$
$67$	−0.676472	−	1.17168i	−0.0826442	−	0.143144i	−0.904385	+	0.426718i	$0.859670\pi$
$68$	0.483743	+	0.837867i	0.0586624	+	0.101606i
$69$	−0.585586	+	0.837834i	−0.0704963	+	0.100863i
$70$	−2.30804	+	3.99764i	−0.275863	+	0.477809i
$71$	−15.9401			−1.89174			−0.945871	−	0.324544i	$-0.894789\pi$
$71$	−15.9401			−1.89174			−0.945871	+	0.324544i	$0.894789\pi$
$72$	−3.56781	+	4.26682i	−0.420471	+	0.502849i
$73$	2.78604			0.326082			0.163041	−	0.986619i	$-0.447870\pi$
$73$	2.78604			0.326082			0.163041	+	0.986619i	$0.447870\pi$
$74$	−0.135577	+	0.234826i	−0.0157605	+	0.0272980i
$75$	−1.72559	−	0.149476i	−0.199254	−	0.0172600i
$76$	−2.43308	−	4.21422i	−0.279094	−	0.483404i
$77$	−2.11231	−	3.65863i	−0.240720	−	0.416939i
$78$	1.25183	+	2.67855i	0.141742	+	0.303286i
$79$	−3.90562	+	6.76474i	−0.439417	+	0.761092i	−0.997645	−	0.0685955i	$-0.978148\pi$
$79$	−3.90562	+	6.76474i	−0.439417	+	0.761092i	0.558228	+	0.829688i	$0.311482\pi$
$80$	−4.99259			−0.558188
$81$	−1.59328	−	8.85785i	−0.177031	−	0.984205i
$82$	−2.08154			−0.229867
$83$	−6.74274	+	11.6788i	−0.740112	+	1.28191i	0.212332	+	0.977198i	$0.431894\pi$
$83$	−6.74274	+	11.6788i	−0.740112	+	1.28191i	−0.952444	+	0.304714i	$0.901439\pi$
$84$	−1.81237	−	3.87794i	−0.197746	−	0.423118i
$85$	0.529311	+	0.916794i	0.0574119	+	0.0994403i
$86$	−0.139264	−	0.241212i	−0.0150172	−	0.0260106i
$87$	−7.47371	−	0.647396i	−0.801265	−	0.0694082i
$88$	1.44819	−	2.50834i	0.154378	−	0.267390i
$89$	−8.37469			−0.887716			−0.443858	−	0.896097i	$-0.646390\pi$
$89$	−8.37469			−0.887716			−0.443858	+	0.896097i	$0.646390\pi$
$90$	3.28501	−	3.92860i	0.346270	−	0.414111i
$91$	2.70418			0.283475
$92$	0.269678	−	0.467096i	0.0281159	−	0.0486981i
$93$	−2.30468	+	3.29745i	−0.238984	+	0.341929i
$94$	−6.37537	−	11.0425i	−0.657569	−	1.13894i
$95$	−2.66228	−	4.61120i	−0.273144	−	0.473099i
$96$	4.77715	−	6.83497i	0.487566	−	0.697591i
$97$	−6.15231	+	10.6561i	−0.624673	+	1.08196i	0.363931	+	0.931426i	$0.381434\pi$
$97$	−6.15231	+	10.6561i	−0.624673	+	1.08196i	−0.988604	+	0.150539i	$0.951899\pi$
$98$	−0.533556			−0.0538973
$99$	1.61053	+	4.40136i	0.161865	+	0.442354i
$100$	0.913910			0.0913910
$101$	0.955852	−	1.65559i	0.0951109	−	0.164737i	−0.814544	−	0.580102i	$-0.803013\pi$
$101$	0.955852	−	1.65559i	0.0951109	−	0.164737i	0.909655	+	0.415365i	$0.136346\pi$
$102$	−3.11829	−	0.270116i	−0.308757	−	0.0267455i
$103$	−3.10383	−	5.37599i	−0.305829	−	0.529712i	0.671616	−	0.740899i	$-0.265600\pi$
$103$	−3.10383	−	5.37599i	−0.305829	−	0.529712i	−0.977446	+	0.211187i	$0.932267\pi$
$104$	0.926987	+	1.60559i	0.0908986	+	0.157441i
$105$	−1.98309	−	4.24324i	−0.193530	−	0.414097i
$106$	−10.5725	+	18.3121i	−1.02689	+	1.77863i
$107$	5.06748			0.489892			0.244946	−	0.969537i	$-0.421230\pi$
$107$	5.06748			0.489892			0.244946	+	0.969537i	$0.421230\pi$
$108$	1.24090	+	4.58382i	0.119406	+	0.441079i
$109$	−4.95400			−0.474507			−0.237254	−	0.971448i	$-0.576247\pi$
$109$	−4.95400			−0.474507			−0.237254	+	0.971448i	$0.576247\pi$
$110$	−1.33340	+	2.30952i	−0.127135	+	0.220204i
$111$	−0.116489	−	0.249252i	−0.0110567	−	0.0236580i
$112$	−6.75042	−	11.6921i	−0.637855	−	1.10480i
$113$	4.87070	+	8.43630i	0.458197	+	0.793620i	0.998866	−	0.0476155i	$-0.0151622\pi$
$113$	4.87070	+	8.43630i	0.458197	+	0.793620i	−0.540669	+	0.841235i	$0.681829\pi$
$114$	15.6841	+	1.35860i	1.46895	+	0.127245i
$115$	0.295081	−	0.511096i	0.0275165	−	0.0476600i
$116$	3.95824			0.367513
$117$	−2.95531	−	0.515868i	−0.273219	−	0.0476920i
$118$	−8.37072			−0.770587
$119$	−1.43135	+	2.47917i	−0.131212	+	0.227265i
$120$	1.83960	−	2.63202i	0.167931	−	0.240270i
$121$	4.27968	+	7.41262i	0.389061	+	0.673874i
$122$	6.34640	+	10.9923i	0.574576	+	0.995196i
$123$	1.20994	−	1.73114i	0.109097	−	0.156092i
$124$	1.06137	−	1.83834i	0.0953135	−	0.165088i
$125$	1.00000			0.0894427
$126$	13.6420	+	2.38129i	1.21532	+	0.212142i
$127$	7.25051			0.643379			0.321690	−	0.946845i	$-0.395749\pi$
$127$	7.25051			0.643379			0.321690	+	0.946845i	$0.395749\pi$
$128$	6.32243	−	10.9508i	0.558829	−	0.967921i
$129$	0.281558	+	0.0243894i	0.0247898	+	0.00214737i
$130$	−0.853509	−	1.47832i	−0.0748577	−	0.129657i
$131$	−3.09607	−	5.36255i	−0.270505	−	0.468529i	0.698486	−	0.715624i	$-0.253857\pi$
$131$	−3.09607	−	5.36255i	−0.270505	−	0.468529i	−0.968991	+	0.247095i	$0.920524\pi$
$132$	−1.04704	−	2.24036i	−0.0911333	−	0.194999i
$133$	7.19926	−	12.4695i	0.624255	−	1.08124i
$134$	−2.30950			−0.199510
$135$	1.35779	+	5.01562i	0.116860	+	0.431675i
$136$	−1.96266			−0.168297
$137$	10.4432	−	18.0882i	0.892225	−	1.54538i	0.0550238	−	0.998485i	$-0.482477\pi$
$137$	10.4432	−	18.0882i	0.892225	−	1.54538i	0.837202	−	0.546895i	$-0.184190\pi$
$138$	0.738785	+	1.58078i	0.0628895	+	0.134565i
$139$	0.396317	+	0.686442i	0.0336152	+	0.0582232i	0.882344	−	0.470606i	$-0.155965\pi$
$139$	0.396317	+	0.686442i	0.0336152	+	0.0582232i	−0.848728	+	0.528829i	$0.822631\pi$
$140$	1.23569	+	2.14027i	0.104435	+	0.180886i
$141$	12.8895	+	1.11653i	1.08549	+	0.0940284i
$142$	−13.6050	+	23.5646i	−1.14171	+	1.97750i
$143$	1.56226			0.130643
$144$	5.14687	+	14.0657i	0.428906	+	1.17214i
$145$	4.33111			0.359679
$146$	2.37791	−	4.11867i	0.196797	−	0.340863i
$147$	0.310142	−	0.443739i	0.0255801	−	0.0365990i
$148$	0.0725857	+	0.125722i	0.00596650	+	0.0103343i
$149$	−4.44412	−	7.69743i	−0.364076	−	0.630598i	0.624551	−	0.780984i	$-0.285282\pi$
$149$	−4.44412	−	7.69743i	−0.364076	−	0.630598i	−0.988627	+	0.150385i	$0.951949\pi$
$150$	−1.69378	+	2.42339i	−0.138296	+	0.197869i
$151$	−11.8295	+	20.4893i	−0.962672	+	1.66740i	−0.246929	+	0.969033i	$0.579422\pi$
$151$	−11.8295	+	20.4893i	−0.962672	+	1.66740i	−0.715743	+	0.698364i	$0.753912\pi$
$152$	9.87158			0.800691
$153$	2.03723	−	2.43636i	0.164700	−	0.196968i
$154$	−7.21150			−0.581119
$155$	1.16135	−	2.01151i	0.0932816	−	0.161568i
$156$	1.57703	+	0.136608i	0.126264	+	0.0109374i
$157$	−8.61164	−	14.9158i	−0.687284	−	1.19041i	−0.972713	−	0.232011i	$-0.925470\pi$
$157$	−8.61164	−	14.9158i	−0.687284	−	1.19041i	0.285429	−	0.958400i	$-0.407864\pi$
$158$	6.66697	+	11.5475i	0.530395	+	0.918672i
$159$	−9.08403	−	19.4372i	−0.720410	−	1.54147i
$160$	−2.40724	+	4.16947i	−0.190309	+	0.329626i
$161$	1.59590			0.125775
$162$	−14.4546	−	5.20488i	−1.13566	−	0.408934i
$163$	15.0205			1.17649			0.588247	−	0.808681i	$-0.299818\pi$
$163$	15.0205			1.17649			0.588247	+	0.808681i	$0.299818\pi$
$164$	−0.557211	+	0.965118i	−0.0435109	+	0.0753630i
$165$	−1.14567	−	2.45140i	−0.0891905	−	0.190841i
$166$	11.5100	+	19.9359i	0.893348	+	1.54732i
$167$	7.47594	+	12.9487i	0.578505	+	1.00200i	0.995651	+	0.0931612i	$0.0296972\pi$
$167$	7.47594	+	12.9487i	0.578505	+	1.00200i	−0.417146	+	0.908840i	$0.636969\pi$
$168$	8.65119	+	0.749394i	0.667454	+	0.0578170i
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	1.80709			0.138597
$171$	−10.2466	+	12.2541i	−0.783579	+	0.937098i
$172$	−0.149119			−0.0113702
$173$	12.0329	−	20.8417i	0.914848	−	1.58456i	0.107725	−	0.994181i	$-0.465643\pi$
$173$	12.0329	−	20.8417i	0.914848	−	1.58456i	0.807123	−	0.590383i	$-0.201023\pi$
$174$	−7.33594	+	10.4960i	−0.556136	+	0.795698i
$175$	1.35209	+	2.34188i	0.102208	+	0.177030i
$176$	−3.89985	−	6.75474i	−0.293963	−	0.509158i
$177$	4.86568	−	6.96163i	0.365727	−	0.523268i
$178$	−7.14788	+	12.3805i	−0.535756	+	0.927956i
$179$	−3.97560			−0.297150			−0.148575	−	0.988901i	$-0.547469\pi$
$179$	−3.97560			−0.297150			−0.148575	+	0.988901i	$0.547469\pi$
$180$	−0.942152	−	2.57477i	−0.0702238	−	0.191912i
$181$	3.55107			0.263949			0.131975	−	0.991253i	$-0.457868\pi$
$181$	3.55107			0.263949			0.131975	+	0.991253i	$0.457868\pi$
$182$	2.30804	−	3.99764i	0.171083	−	0.296325i
$183$	−12.8309	−	1.11145i	−0.948487	−	0.0821610i
$184$	0.547074	+	0.947559i	0.0403308	+	0.0698550i
$185$	0.0794232	+	0.137565i	0.00583931	+	0.0101140i
$186$	2.90762	+	6.22146i	0.213197	+	0.456179i
$187$	−0.826920	+	1.43227i	−0.0604704	+	0.104738i
$188$	−6.82654			−0.497877
$189$	−9.91014	+	9.96135i	−0.720857	+	0.724581i
$190$	−9.08910			−0.659393
$191$	−12.8791	+	22.3073i	−0.931902	+	1.61410i	−0.151835	+	0.988406i	$0.548518\pi$
$191$	−12.8791	+	22.3073i	−0.931902	+	1.61410i	−0.780067	+	0.625696i	$0.784815\pi$
$192$	1.29564	+	2.77229i	0.0935049	+	0.200073i
$193$	3.63729	+	6.29996i	0.261818	+	0.453481i	0.966725	−	0.255818i	$-0.0823448\pi$
$193$	3.63729	+	6.29996i	0.261818	+	0.453481i	−0.704907	+	0.709299i	$0.749011\pi$
$194$	10.5021	+	18.1902i	0.754007	+	1.30598i
$195$	1.72559	+	0.149476i	0.123572	+	0.0107042i
$196$	−0.142829	+	0.247386i	−0.0102020	+	0.0176705i
$197$	17.6280			1.25594			0.627970	−	0.778238i	$-0.283886\pi$
$197$	17.6280			1.25594			0.627970	+	0.778238i	$0.283886\pi$
$198$	7.88123	+	1.37572i	0.560095	+	0.0977680i
$199$	−1.42431			−0.100967			−0.0504834	−	0.998725i	$-0.516076\pi$
$199$	−1.42431			−0.100967			−0.0504834	+	0.998725i	$0.516076\pi$
$200$	−0.926987	+	1.60559i	−0.0655479	+	0.113532i
$201$	1.34245	−	1.92073i	0.0946892	−	0.135478i
$202$	−1.63166	−	2.82611i	−0.114803	−	0.198845i
$203$	5.85603	+	10.1429i	0.411013	+	0.711895i
$204$	−0.959983	+	1.37351i	−0.0672122	+	0.0961647i
$205$	−0.609700	+	1.05603i	−0.0425833	+	0.0737564i
$206$	−10.5966			−0.738299
$207$	−1.74412	−	0.304446i	−0.121224	−	0.0211605i
$208$	4.99259			0.346174
$209$	4.15916	−	7.20387i	0.287695	−	0.498302i
$210$	−7.96545	−	0.689993i	−0.549668	−	0.0476140i
$211$	4.54860	+	7.87840i	0.313138	+	0.542372i	0.979040	−	0.203668i	$-0.0652863\pi$
$211$	4.54860	+	7.87840i	0.313138	+	0.542372i	−0.665902	+	0.746040i	$0.731953\pi$
$212$	5.66036	+	9.80403i	0.388755	+	0.673344i
$213$	−11.6896	−	25.0123i	−0.800957	−	1.71381i
$214$	4.32514	−	7.49136i	0.295660	−	0.512099i
$215$	−0.163166			−0.0111278
$216$	−9.31167	−	2.46936i	−0.633579	−	0.168018i
$217$	6.28097			0.426380
$218$	−4.22828	+	7.32360i	−0.286376	+	0.496017i
$219$	2.04313	+	4.37170i	0.138062	+	0.295412i
$220$	0.713881	+	1.23648i	0.0481299	+	0.0833634i
$221$	−0.529311	−	0.916794i	−0.0356053	−	0.0616702i
$222$	−0.467900	−	0.0405310i	−0.0314034	−	0.00272026i
$223$	11.3374	−	19.6369i	0.759207	−	1.31498i	−0.184049	−	0.982917i	$-0.558921\pi$
$223$	11.3374	−	19.6369i	0.759207	−	1.31498i	0.943256	−	0.332067i	$-0.107746\pi$
$224$	−13.0192			−0.869884
$225$	−1.03090	−	2.81731i	−0.0687268	−	0.187821i
$226$	16.6287			1.10613
$227$	−3.92628	+	6.80051i	−0.260596	+	0.451366i	−0.966400	−	0.257041i	$-0.917252\pi$
$227$	−3.92628	+	6.80051i	−0.260596	+	0.451366i	0.705804	+	0.708407i	$0.250586\pi$
$228$	4.82842	−	6.90832i	0.319770	−	0.457515i
$229$	−7.94194	−	13.7558i	−0.524818	−	0.909011i	−0.999582	−	0.0288984i	$-0.990800\pi$
$229$	−7.94194	−	13.7558i	−0.524818	−	0.909011i	0.474764	−	0.880113i	$-0.342533\pi$
$230$	−0.503709	−	0.872450i	−0.0332136	−	0.0575277i
$231$	4.19185	−	5.99755i	0.275804	−	0.394609i
$232$	−4.01488	+	6.95398i	−0.263590	+	0.456551i
$233$	4.64530			0.304323			0.152162	−	0.988356i	$-0.451377\pi$
$233$	4.64530			0.304323			0.152162	+	0.988356i	$0.451377\pi$
$234$	−3.28501	+	3.92860i	−0.214748	+	0.256821i
$235$	−7.46960			−0.487263
$236$	−2.24077	+	3.88114i	−0.145862	+	0.252640i
$237$	−13.4790	−	1.16759i	−0.875555	−	0.0758434i
$238$	2.44334	+	4.23199i	0.158378	+	0.274319i
$239$	−12.6872	−	21.9749i	−0.820669	−	1.42144i	−0.905185	−	0.425018i	$-0.860268\pi$
$239$	−12.6872	−	21.9749i	−0.820669	−	1.42144i	0.0845161	−	0.996422i	$-0.473066\pi$
$240$	−3.66129	−	7.83408i	−0.236335	−	0.505688i
$241$	6.74908	−	11.6897i	0.434746	−	0.753003i	−0.562529	−	0.826778i	$-0.690171\pi$
$241$	6.74908	−	11.6897i	0.434746	−	0.753003i	0.997275	+	0.0737750i	$0.0235047\pi$
$242$	14.6110			0.939229
$243$	12.7308	−	8.99593i	0.816681	−	0.577089i
$244$	6.79553			0.435039
$245$	−0.156283	+	0.270690i	−0.00998455	+	0.0172938i
$246$	−1.52648	−	3.26623i	−0.0973250	−	0.208247i
$247$	2.66228	+	4.61120i	0.169397	+	0.293403i
$248$	2.15311	+	3.72929i	0.136722	+	0.236810i
$249$	−23.2704	−	2.01576i	−1.47470	−	0.127743i
$250$	0.853509	−	1.47832i	0.0539806	−	0.0934972i
$251$	10.1921			0.643323			0.321661	−	0.946855i	$-0.395759\pi$
$251$	10.1921			0.643323			0.321661	+	0.946855i	$0.395759\pi$
$252$	4.75594	−	5.68773i	0.299596	−	0.358293i
$253$	0.921986			0.0579648
$254$	6.18838	−	10.7186i	0.388293	−	0.672544i
$255$	−1.05041	+	1.50289i	−0.0657794	+	0.0941146i
$256$	−9.02575	−	15.6331i	−0.564109	−	0.977066i
$257$	14.5887	+	25.2683i	0.910016	+	1.57619i	0.814039	+	0.580810i	$0.197264\pi$
$257$	14.5887	+	25.2683i	0.910016	+	1.57619i	0.0959766	+	0.995384i	$0.469403\pi$
$258$	0.276367	−	0.395416i	0.0172059	−	0.0246175i
$259$	−0.214774	+	0.372000i	−0.0133454	+	0.0231149i
$260$	−0.913910			−0.0566783
$261$	−4.46494	−	12.2021i	−0.276373	−	0.755289i
$262$	−10.5701			−0.653023
$263$	2.36727	−	4.10024i	0.145972	−	0.252832i	−0.783763	−	0.621060i	$-0.786702\pi$
$263$	2.36727	−	4.10024i	0.145972	−	0.252832i	0.929735	+	0.368229i	$0.120036\pi$
$264$	4.99797	+	0.432940i	0.307604	+	0.0266456i
$265$	6.19356	+	10.7276i	0.380468	+	0.658989i
$266$	−12.2893	−	21.2856i	−0.753503	−	1.30511i
$267$	−6.14153	−	13.1411i	−0.375856	−	0.804221i
$268$	−0.618235	+	1.07081i	−0.0377647	+	0.0654104i
$269$	11.5638			0.705058			0.352529	−	0.935801i	$-0.385322\pi$
$269$	11.5638			0.705058			0.352529	+	0.935801i	$0.385322\pi$
$270$	8.57358	+	2.27362i	0.521771	+	0.138368i
$271$	29.2660			1.77779			0.888893	−	0.458116i	$-0.151475\pi$
$271$	29.2660			1.77779			0.888893	+	0.458116i	$0.151475\pi$
$272$	−2.64263	+	4.57717i	−0.160233	+	0.277532i
$273$	1.98309	+	4.24324i	0.120022	+	0.256812i
$274$	−17.8268	−	30.8769i	−1.07696	−	1.86534i
$275$	0.781129	+	1.35295i	0.0471038	+	0.0815862i
$276$	0.930707	+	0.0806208i	0.0560220	+	0.00485280i
$277$	2.15795	−	3.73769i	0.129659	−	0.224576i	−0.793886	−	0.608067i	$-0.791945\pi$
$277$	2.15795	−	3.73769i	0.129659	−	0.224576i	0.923544	+	0.383491i	$0.125278\pi$
$278$	1.35304			0.0811500
$279$	−6.86429	−	1.19820i	−0.410954	−	0.0717346i
$280$	−5.01347			−0.299612
$281$	−10.6990	+	18.5312i	−0.638249	+	1.10548i	0.347568	+	0.937655i	$0.387007\pi$
$281$	−10.6990	+	18.5312i	−0.638249	+	1.10548i	−0.985817	+	0.167824i	$0.946326\pi$
$282$	12.6518	−	18.1018i	0.753407	−	1.07795i
$283$	2.35631	+	4.08125i	0.140068	+	0.242605i	0.927522	−	0.373768i	$-0.121935\pi$
$283$	2.35631	+	4.08125i	0.140068	+	0.242605i	−0.787454	+	0.616373i	$0.788601\pi$
$284$	7.28391	+	12.6161i	0.432220	+	0.748628i
$285$	5.28326	−	7.55908i	0.312953	−	0.447761i
$286$	1.33340	−	2.30952i	0.0788456	−	0.136565i
$287$	−3.29747			−0.194644
$288$	14.2283	+	2.48364i	0.838412	+	0.146350i
$289$	−15.8793			−0.934078
$290$	3.69664	−	6.40276i	0.217074	−	0.375983i
$291$	−21.2327	−	1.83925i	−1.24468	−	0.107819i
$292$	−1.27310	−	2.20507i	−0.0745023	−	0.129042i
$293$	−13.4588	−	23.3114i	−0.786274	−	1.36187i	−0.928235	−	0.371994i	$-0.878674\pi$
$293$	−13.4588	−	23.3114i	−0.786274	−	1.36187i	0.141962	−	0.989872i	$-0.454659\pi$
$294$	−0.391280	−	0.837225i	−0.0228199	−	0.0488279i
$295$	−2.45185	+	4.24674i	−0.142752	+	0.247255i
$296$	−0.294497			−0.0171173
$297$	−5.72529	+	5.75487i	−0.332215	+	0.333932i
$298$	−15.1724			−0.878912
$299$	−0.295081	+	0.511096i	−0.0170650	+	0.0295574i
$300$	0.670211	+	1.43405i	0.0386946	+	0.0827952i
$301$	−0.220615	−	0.382116i	−0.0127160	−	0.0220248i
$302$	20.1932	+	34.9756i	1.16199	+	2.01262i
$303$	3.29882	+	0.285754i	0.189512	+	0.0164161i
$304$	13.2916	−	23.0218i	0.762328	−	1.32039i
$305$	7.43566			0.425765
$306$	−1.86293	−	5.09113i	−0.106497	−	0.291040i
$307$	−32.9463			−1.88034			−0.940172	−	0.340701i	$-0.889336\pi$
$307$	−32.9463			−1.88034			−0.940172	+	0.340701i	$0.889336\pi$
$308$	−1.93046	+	3.34366i	−0.109998	+	0.190522i
$309$	6.15951	−	8.81280i	0.350402	−	0.501342i
$310$	−1.98244	−	3.43369i	−0.112595	−	0.195020i
$311$	−11.5192	−	19.9518i	−0.653192	−	1.13136i	−0.982344	−	0.187085i	$-0.940096\pi$
$311$	−11.5192	−	19.9518i	−0.653192	−	1.13136i	0.329152	−	0.944277i	$-0.393237\pi$
$312$	−1.83960	+	2.63202i	−0.104147	+	0.149009i
$313$	15.5405	−	26.9169i	0.878399	−	1.52143i	0.0253009	−	0.999680i	$-0.491946\pi$
$313$	15.5405	−	26.9169i	0.878399	−	1.52143i	0.853098	−	0.521751i	$-0.174721\pi$
$314$	−29.4005			−1.65916
$315$	5.20395	−	6.22351i	0.293209	−	0.350655i
$316$	7.13878			0.401588
$317$	−8.00124	+	13.8585i	−0.449394	+	0.778374i	−0.998347	−	0.0574800i	$-0.981693\pi$
$317$	−8.00124	+	13.8585i	−0.449394	+	0.778374i	0.548952	+	0.835854i	$0.315027\pi$
$318$	−36.4877	−	3.16068i	−2.04613	−	0.177242i
$319$	3.38315	+	5.85979i	0.189420	+	0.328085i
$320$	−0.883379	−	1.53006i	−0.0493824	−	0.0855328i
$321$	3.71621	+	7.95159i	0.207418	+	0.443815i
$322$	1.36212	−	2.35926i	0.0759079	−	0.131476i
$323$	−5.63669			−0.313634
$324$	−6.28266	+	5.30867i	−0.349037	+	0.294926i
$325$	−1.00000			−0.0554700
$326$	12.8201	−	22.2051i	0.710040	−	1.22983i
$327$	−3.63299	−	7.77353i	−0.200905	−	0.429877i
$328$	−1.13037	−	1.95785i	−0.0624141	−	0.108104i
$329$	−10.0996	−	17.4929i	−0.556806	−	0.964417i
$330$	−4.60180	−	0.398623i	−0.253321	−	0.0219435i
$331$	−3.56797	+	6.17990i	−0.196113	+	0.339678i	−0.947265	−	0.320452i	$-0.896165\pi$
$331$	−3.56797	+	6.17990i	−0.196113	+	0.339678i	0.751152	+	0.660130i	$0.229499\pi$
$332$	12.3245			0.676396
$333$	0.305686	−	0.365576i	0.0167515	−	0.0200334i
$334$	25.5231			1.39656
$335$	−0.676472	+	1.17168i	−0.0369596	+	0.0640159i
$336$	13.3961	−	19.1667i	0.730819	−	1.04563i
$337$	−17.3856	−	30.1127i	−0.947054	−	1.64035i	−0.751585	−	0.659636i	$-0.770710\pi$
$337$	−17.3856	−	30.1127i	−0.947054	−	1.64035i	−0.195469	−	0.980710i	$-0.562623\pi$
$338$	0.853509	+	1.47832i	0.0464248	+	0.0804101i
$339$	−9.66584	+	13.8295i	−0.524977	+	0.751117i
$340$	0.483743	−	0.837867i	0.0262346	−	0.0454397i
$341$	3.62864			0.196502
$342$	9.36997	+	25.6068i	0.506670	+	1.38466i
$343$	18.0840			0.976444
$344$	0.151253	−	0.261978i	0.00815501	−	0.0141249i
$345$	1.01838	+	0.0882152i	0.0548277	+	0.00474935i
$346$	−20.5405	−	35.5771i	−1.10426	−	1.91264i
$347$	8.80403	+	15.2490i	0.472625	+	0.818611i	0.999509	−	0.0313264i	$-0.00997312\pi$
$347$	8.80403	+	15.2490i	0.472625	+	0.818611i	−0.526884	+	0.849937i	$0.676640\pi$
$348$	2.90275	+	6.21104i	0.155604	+	0.332947i
$349$	−0.0897091	+	0.155381i	−0.00480202	+	0.00831734i	−0.868416	−	0.495836i	$-0.834862\pi$
$349$	−0.0897091	+	0.155381i	−0.00480202	+	0.00831734i	0.863614	+	0.504153i	$0.168195\pi$
$350$	4.61608			0.246740
$351$	−1.35779	−	5.01562i	−0.0724736	−	0.267714i
$352$	−7.52147			−0.400896
$353$	8.63759	−	14.9607i	0.459733	−	0.796280i	−0.539214	−	0.842169i	$-0.681279\pi$
$353$	8.63759	−	14.9607i	0.459733	−	0.796280i	0.998947	+	0.0458885i	$0.0146119\pi$
$354$	−6.13862	−	13.1348i	−0.326264	−	0.698109i
$355$	7.97005	+	13.8045i	0.423006	+	0.732668i
$356$	3.82686	+	6.62831i	0.202823	+	0.351300i
$357$	−4.93984	−	0.427905i	−0.261444	−	0.0226471i
$358$	−3.39321	+	5.87721i	−0.179337	+	0.310620i
$359$	−2.99658			−0.158153			−0.0790767	−	0.996869i	$-0.525197\pi$
$359$	−2.99658			−0.158153			−0.0790767	+	0.996869i	$0.525197\pi$
$360$	5.47908	+	0.956407i	0.288773	+	0.0504071i
$361$	9.35084			0.492149
$362$	3.03087	−	5.24962i	0.159299	−	0.275914i
$363$	−8.49297	+	12.1514i	−0.445765	+	0.637784i
$364$	−1.23569	−	2.14027i	−0.0647676	−	0.112181i
$365$	−1.39302	−	2.41278i	−0.0729141	−	0.126291i
$366$	−12.5944	+	18.0195i	−0.658318	+	0.941897i
$367$	−7.16366	+	12.4078i	−0.373940	+	0.647683i	−0.990168	−	0.139885i	$-0.955327\pi$
$367$	−7.16366	+	12.4078i	−0.373940	+	0.647683i	0.616228	+	0.787568i	$0.288660\pi$
$368$	2.94644			0.153594
$369$	3.60371	+	0.629050i	0.187602	+	0.0327470i
$370$	0.271154			0.0140966
$371$	−16.7485	+	29.0092i	−0.869538	+	1.50608i
$372$	3.66296	+	0.317298i	0.189916	+	0.0164511i
$373$	−11.0304	−	19.1053i	−0.571135	−	0.989235i	−0.996450	−	0.0841891i	$-0.973170\pi$
$373$	−11.0304	−	19.1053i	−0.571135	−	0.989235i	0.425315	−	0.905045i	$-0.360163\pi$
$374$	1.41157	+	2.44491i	0.0729904	+	0.126423i
$375$	0.733344	+	1.56914i	0.0378697	+	0.0810301i
$376$	6.92422	−	11.9931i	0.357090	−	0.618497i
$377$	−4.33111			−0.223063
$378$	6.26767	+	23.1525i	0.322374	+	1.19083i
$379$	36.8934			1.89509			0.947543	−	0.319628i	$-0.103558\pi$
$379$	36.8934			1.89509			0.947543	+	0.319628i	$0.103558\pi$
$380$	−2.43308	+	4.21422i	−0.124814	+	0.216185i
$381$	5.31712	+	11.3771i	0.272405	+	0.582866i
$382$	21.9849	+	38.0790i	1.12485	+	1.94829i
$383$	−2.42126	−	4.19374i	−0.123721	−	0.214290i	0.797512	−	0.603304i	$-0.206149\pi$
$383$	−2.42126	−	4.19374i	−0.123721	−	0.214290i	−0.921232	+	0.389013i	$0.872816\pi$
$384$	21.8198	+	1.89010i	1.11349	+	0.0964540i
$385$	−2.11231	+	3.65863i	−0.107653	+	0.186461i
$386$	12.4178			0.632051
$387$	0.168208	+	0.459690i	0.00855051	+	0.0233673i
$388$	11.2453			0.570895
$389$	−8.88124	+	15.3828i	−0.450297	+	0.779937i	−0.998404	−	0.0564711i	$-0.982015\pi$
$389$	−8.88124	+	15.3828i	−0.450297	+	0.779937i	0.548108	+	0.836408i	$0.315348\pi$
$390$	1.69378	−	2.42339i	0.0857678	−	0.122713i
$391$	−0.312380	−	0.541058i	−0.0157977	−	0.0273625i
$392$	−0.289745	−	0.501852i	−0.0146343	−	0.0253474i
$393$	6.14412	−	8.79078i	0.309930	−	0.443436i
$394$	15.0456	−	26.0598i	0.757987	−	1.31287i
$395$	7.81124			0.393026
$396$	2.74760	−	3.28591i	0.138072	−	0.165123i
$397$	33.8244			1.69760			0.848800	−	0.528714i	$-0.177326\pi$
$397$	33.8244			1.69760			0.848800	+	0.528714i	$0.177326\pi$
$398$	−1.21566	+	2.10559i	−0.0609357	+	0.105544i
$399$	24.8459	+	2.15223i	1.24385	+	0.107746i
$400$	2.49629	+	4.32371i	0.124815	+	0.216185i
$401$	5.90685	+	10.2310i	0.294974	+	0.510910i	0.974979	−	0.222298i	$-0.0713557\pi$
$401$	5.90685	+	10.2310i	0.294974	+	0.510910i	−0.680005	+	0.733208i	$0.738022\pi$
$402$	−1.69366	−	3.62393i	−0.0844720	−	0.180745i
$403$	−1.16135	+	2.01151i	−0.0578508	+	0.100201i
$404$	−1.74713			−0.0869228
$405$	−6.87448	+	5.80874i	−0.341596	+	0.288639i
$406$	19.9927			0.992222
$407$	−0.124079	+	0.214912i	−0.00615039	+	0.0106528i
$408$	−1.43930	−	3.07969i	−0.0712562	−	0.152467i
$409$	6.94911	+	12.0362i	0.343611	+	0.595152i	0.985100	−	0.171980i	$-0.0550164\pi$
$409$	6.94911	+	12.0362i	0.343611	+	0.595152i	−0.641489	+	0.767132i	$0.721683\pi$
$410$	1.04077	+	1.80266i	0.0513999	+	0.0890272i
$411$	36.0414	+	3.12202i	1.77779	+	0.153998i
$412$	−2.83662	+	4.91317i	−0.139750	+	0.242055i
$413$	−13.2605			−0.652506
$414$	−1.93869	+	2.31852i	−0.0952813	+	0.113949i
$415$	13.4855			0.661976
$416$	2.40724	−	4.16947i	0.118025	−	0.204425i
$417$	−0.786487	+	1.12528i	−0.0385144	+	0.0551050i
$418$	−7.09976	−	12.2971i	−0.347261	−	0.601473i
$419$	4.47629	+	7.75315i	0.218681	+	0.378766i	0.954405	−	0.298515i	$-0.0964913\pi$
$419$	4.47629	+	7.75315i	0.218681	+	0.378766i	−0.735724	+	0.677281i	$0.763158\pi$
$420$	−2.45221	+	3.50853i	−0.119655	+	0.171198i
$421$	−13.1135	+	22.7132i	−0.639111	+	1.10697i	0.346517	+	0.938044i	$0.387364\pi$
$421$	−13.1135	+	22.7132i	−0.639111	+	1.10697i	−0.985628	+	0.168929i	$0.945969\pi$
$422$	15.5291			0.755944
$423$	7.70042	+	21.0442i	0.374407	+	1.02320i
$424$	−22.9654			−1.11530
$425$	0.529311	−	0.916794i	0.0256754	−	0.0444710i
$426$	−46.9533	−	4.06725i	−2.27490	−	0.197059i
$427$	10.0537	+	17.4135i	0.486531	+	0.842697i
$428$	−2.31561	−	4.01076i	−0.111929	−	0.193867i
$429$	1.14567	+	2.45140i	0.0553136	+	0.118355i
$430$	−0.139264	+	0.241212i	−0.00671590	+	0.0116323i
$431$	1.07839			0.0519443			0.0259721	−	0.999663i	$-0.491732\pi$
$431$	1.07839			0.0519443			0.0259721	+	0.999663i	$0.491732\pi$
$432$	−18.2966	+	18.3912i	−0.880296	+	0.884845i
$433$	3.51862			0.169094			0.0845471	−	0.996419i	$-0.473056\pi$
$433$	3.51862			0.169094			0.0845471	+	0.996419i	$0.473056\pi$
$434$	5.36086	−	9.28529i	0.257330	−	0.445708i
$435$	3.17619	+	6.79612i	0.152287	+	0.325849i
$436$	2.26376	+	3.92094i	0.108414	+	0.187779i
$437$	1.57118	+	2.72136i	0.0751595	+	0.130180i
$438$	8.20660	+	0.710882i	0.392126	+	0.0339672i
$439$	14.3877	−	24.9203i	0.686689	−	1.18938i	−0.286214	−	0.958166i	$-0.592397\pi$
$439$	14.3877	−	24.9203i	0.686689	−	1.18938i	0.972903	−	0.231214i	$-0.0742698\pi$
$440$	−2.89639			−0.138080
$441$	0.923730	+	0.161243i	0.0439872	+	0.00767823i
$442$	−1.80709			−0.0859544
$443$	−16.9355	+	29.3332i	−0.804630	+	1.39366i	0.111910	+	0.993718i	$0.464303\pi$
$443$	−16.9355	+	29.3332i	−0.804630	+	1.39366i	−0.916540	+	0.399943i	$0.869030\pi$
$444$	−0.144045	+	0.206095i	−0.00683609	+	0.00978082i
$445$	4.18735	+	7.25270i	0.198499	+	0.343811i
$446$	−19.3531	−	33.5205i	−0.916396	−	1.58724i
$447$	8.81930	−	12.6183i	0.417138	−	0.596826i
$448$	2.38881	−	4.13754i	0.112861	−	0.195481i
$449$	16.9364			0.799276			0.399638	−	0.916673i	$-0.369136\pi$
$449$	16.9364			0.799276			0.399638	+	0.916673i	$0.369136\pi$
$450$	−5.04477	−	0.880597i	−0.237813	−	0.0415117i
$451$	−1.90502			−0.0897037
$452$	4.45138	−	7.71002i	0.209375	−	0.362649i
$453$	−40.8258	−	3.53646i	−1.91816	−	0.166157i
$454$	6.70222	+	11.6086i	0.314551	+	0.544818i
$455$	−1.35209	−	2.34188i	−0.0633869	−	0.109789i
$456$	7.23927	+	15.4899i	0.339010	+	0.725382i
$457$	1.82793	−	3.16607i	0.0855069	−	0.148102i	−0.820100	−	0.572220i	$-0.806082\pi$
$457$	1.82793	−	3.16607i	0.0855069	−	0.148102i	0.905607	+	0.424118i	$0.139416\pi$
$458$	−27.1141			−1.26696
$459$	5.31698	+	1.41001i	0.248175	+	0.0658134i
$460$	−0.539356			−0.0251476
$461$	−12.5092	+	21.6666i	−0.582612	+	1.00911i	0.412557	+	0.910932i	$0.364636\pi$
$461$	−12.5092	+	21.6666i	−0.582612	+	1.00911i	−0.995169	+	0.0981815i	$0.968697\pi$
$462$	−5.28851	−	11.3159i	−0.246044	−	0.526462i
$463$	10.7557	+	18.6293i	0.499858	+	0.865779i	1.00000		0.000164262i	$-5.22863e-5\pi$
$463$	10.7557	+	18.6293i	0.499858	+	0.865779i	−0.500142	+	0.865943i	$0.666719\pi$
$464$	10.8117	+	18.7264i	0.501921	+	0.869353i
$465$	4.00801	+	0.347187i	0.185867	+	0.0161004i
$466$	3.96480	−	6.86724i	0.183666	−	0.318119i
$467$	2.10527			0.0974205			0.0487102	−	0.998813i	$-0.484489\pi$
$467$	2.10527			0.0974205			0.0487102	+	0.998813i	$0.484489\pi$
$468$	0.942152	+	2.57477i	0.0435510	+	0.119019i
$469$	−3.65860			−0.168938
$470$	−6.37537	+	11.0425i	−0.294074	+	0.509351i
$471$	17.0897	−	24.4513i	0.787452	−	1.12666i
$472$	−4.54567	−	7.87334i	−0.209232	−	0.362400i
$473$	−0.127454	−	0.220756i	−0.00586033	−	0.0101504i
$474$	−13.2305	+	18.9297i	−0.607698	+	0.869471i
$475$	−2.66228	+	4.61120i	−0.122154	+	0.211576i
$476$	2.61625			0.119916
$477$	23.8379	−	28.5083i	1.09146	−	1.30530i
$478$	−43.3147			−1.98117
$479$	−1.54095	+	2.66900i	−0.0704077	+	0.121950i	−0.899080	−	0.437784i	$-0.855763\pi$
$479$	−1.54095	+	2.66900i	−0.0704077	+	0.121950i	0.828672	+	0.559734i	$0.189097\pi$
$480$	−8.30783	−	0.719651i	−0.379199	−	0.0328474i
$481$	−0.0794232	−	0.137565i	−0.00362138	−	0.00627242i
$482$	−11.5208	−	19.9546i	−0.524758	−	0.908908i
$483$	1.17035	+	2.50420i	0.0532526	+	0.113945i
$484$	3.91124	−	6.77447i	0.177784	−	0.307930i
$485$	12.3046			0.558724
$486$	−2.43302	−	26.4983i	−0.110364	−	1.20199i
$487$	20.7167			0.938762			0.469381	−	0.882996i	$-0.344477\pi$
$487$	20.7167			0.938762			0.469381	+	0.882996i	$0.344477\pi$
$488$	−6.89276	+	11.9386i	−0.312021	+	0.540436i
$489$	11.0152	+	23.5693i	0.498124	+	1.06584i
$490$	0.266778	+	0.462073i	0.0120518	+	0.0208743i
$491$	3.84747	+	6.66402i	0.173634	+	0.300743i	0.939688	−	0.342034i	$-0.111116\pi$
$491$	3.84747	+	6.66402i	0.173634	+	0.300743i	−0.766054	+	0.642777i	$0.777782\pi$
$492$	−1.92303	−	0.166579i	−0.0866971	−	0.00750998i
$493$	2.29250	−	3.97073i	0.103249	−	0.178833i
$494$	9.08910			0.408938
$495$	3.00643	−	3.59545i	0.135129	−	0.161603i
$496$	11.5963			0.520687
$497$	−21.5524	+	37.3299i	−0.966758	+	1.67447i
$498$	−22.8414	+	32.6806i	−1.02355	+	1.46445i
$499$	−12.2279	−	21.1793i	−0.547395	−	0.948116i	−0.998452	−	0.0556210i	$-0.982286\pi$
$499$	−12.2279	−	21.1793i	−0.547395	−	0.948116i	0.451057	−	0.892495i	$-0.351047\pi$
$500$	−0.456955	−	0.791470i	−0.0204357	−	0.0353956i
$501$	−14.8359	+	21.2267i	−0.662820	+	0.948338i
$502$	8.69909	−	15.0673i	0.388259	−	0.672485i
$503$	−3.94139			−0.175738			−0.0878690	−	0.996132i	$-0.528006\pi$
$503$	−3.94139			−0.175738			−0.0878690	+	0.996132i	$0.528006\pi$
$504$	5.16840	+	14.1245i	0.230219	+	0.629156i
$505$	−1.91170			−0.0850698
$506$	0.786923	−	1.36299i	0.0349830	−	0.0605924i
$507$	−1.72559	−	0.149476i	−0.0766361	−	0.00663846i
$508$	−3.31316	−	5.73856i	−0.146998	−	0.254607i
$509$	−19.0668	−	33.0247i	−0.845122	−	1.46379i	−0.885515	−	0.464611i	$-0.846194\pi$
$509$	−19.0668	−	33.0247i	−0.845122	−	1.46379i	0.0403926	−	0.999184i	$-0.487139\pi$
$510$	1.32522	+	2.83558i	0.0586816	+	0.125561i
$511$	3.76697	−	6.52459i	0.166641	−	0.288631i
$512$	−5.52450			−0.244151
$513$	−26.7428	−	7.09190i	−1.18072	−	0.313115i
$514$	49.8062			2.19686
$515$	−3.10383	+	5.37599i	−0.136771	+	0.236894i
$516$	−0.109356	−	0.233989i	−0.00481412	−	0.0103008i
$517$	−5.83472	−	10.1060i	−0.256611	−	0.444462i
$518$	0.366623	+	0.635010i	0.0161085	+	0.0279008i
$519$	41.5278	+	3.59727i	1.82287	+	0.157903i
$520$	0.926987	−	1.60559i	0.0406511	−	0.0704097i
$521$	−7.46068			−0.326858			−0.163429	−	0.986555i	$-0.552255\pi$
$521$	−7.46068			−0.326858			−0.163429	+	0.986555i	$0.552255\pi$
$522$	−21.8494	−	3.81396i	−0.956324	−	0.166932i
$523$	20.1819			0.882492			0.441246	−	0.897386i	$-0.354537\pi$
$523$	20.1819			0.882492			0.441246	+	0.897386i	$0.354537\pi$
$524$	−2.82953	+	4.90089i	−0.123609	+	0.214097i
$525$	−2.68320	+	3.83903i	−0.117105	+	0.167549i
$526$	−4.04098	−	6.99918i	−0.176195	−	0.305179i
$527$	−1.22943	−	2.12943i	−0.0535547	−	0.0927595i
$528$	7.73922	−	11.0730i	0.336806	−	0.481889i
$529$	11.3259	−	19.6170i	0.492428	−	0.852911i
$530$	21.1450			0.918482
$531$	14.4920	+	2.52967i	0.628899	+	0.109778i
$532$	−13.1590			−0.570513
$533$	0.609700	−	1.05603i	0.0264090	−	0.0457418i
$534$	−24.6686	−	2.13687i	−1.06751	−	0.0924715i
$535$	−2.53374	−	4.38857i	−0.109543	−	0.189734i
$536$	−1.25416	−	2.17227i	−0.0541716	−	0.0938279i
$537$	−2.91548	−	6.23828i	−0.125812	−	0.269201i
$538$	9.86982	−	17.0950i	0.425518	−	0.737019i
$539$	−0.488308			−0.0210329
$540$	3.34926	−	3.36656i	0.144129	−	0.144874i
$541$	−22.2316			−0.955812			−0.477906	−	0.878411i	$-0.658604\pi$
$541$	−22.2316			−0.955812			−0.477906	+	0.878411i	$0.658604\pi$
$542$	24.9788	−	43.2646i	1.07293	−	1.85837i
$543$	2.60416	+	5.57213i	0.111755	+	0.239123i
$544$	2.54836	+	4.41389i	0.109260	+	0.189244i
$545$	2.47700	+	4.29029i	0.106103	+	0.183776i
$546$	7.96545	+	0.689993i	0.340890	+	0.0295290i
$547$	−20.2834	+	35.1319i	−0.867256	+	1.50213i	−0.00246674	+	0.999997i	$0.500785\pi$
$547$	−20.2834	+	35.1319i	−0.867256	+	1.50213i	−0.864789	+	0.502135i	$0.832548\pi$
$548$	−19.0884			−0.815414
$549$	−7.66544	−	20.9486i	−0.327153	−	0.894063i
$550$	2.66680			0.113713
$551$	−11.5306	+	19.9716i	−0.491220	+	0.850818i
$552$	−1.08566	+	1.55332i	−0.0462088	+	0.0661138i
$553$	10.5615	+	18.2930i	0.449120	+	0.777899i
$554$	−3.68367	−	6.38030i	−0.156504	−	0.271073i
$555$	−0.157614	+	0.225509i	−0.00669036	+	0.00957231i
$556$	0.362198	−	0.627346i	0.0153606	−	0.0266054i
$557$	−29.9682			−1.26979			−0.634896	−	0.772597i	$-0.718957\pi$
$557$	−29.9682			−1.26979			−0.634896	+	0.772597i	$0.718957\pi$
$558$	−7.63006	+	9.12494i	−0.323006	+	0.386290i
$559$	0.163166			0.00690119
$560$	−6.75042	+	11.6921i	−0.285257	+	0.494080i
$561$	−2.85385	−	0.247209i	−0.120490	−	0.0104372i
$562$	18.2634	+	31.6331i	0.770394	+	1.33436i
$563$	−12.7552	−	22.0927i	−0.537569	−	0.931097i	−0.999034	−	0.0439384i	$-0.986009\pi$
$563$	−12.7552	−	22.0927i	−0.537569	−	0.931097i	0.461465	−	0.887158i	$-0.347324\pi$
$564$	−5.00621	−	10.7118i	−0.210799	−	0.451049i
$565$	4.87070	−	8.43630i	0.204912	−	0.354918i
$566$	8.04453			0.338137
$567$	−22.8983	−	8.24532i	−0.961639	−	0.346271i
$568$	−29.5525			−1.24000
$569$	−5.96086	+	10.3245i	−0.249892	+	0.432826i	−0.963496	−	0.267724i	$-0.913729\pi$
$569$	−5.96086	+	10.3245i	−0.249892	+	0.432826i	0.713603	+	0.700550i	$0.247062\pi$
$570$	−6.66544	−	14.2621i	−0.279185	−	0.597373i
$571$	−9.13648	−	15.8248i	−0.382350	−	0.662249i	0.609048	−	0.793133i	$-0.291552\pi$
$571$	−9.13648	−	15.8248i	−0.382350	−	0.662249i	−0.991398	+	0.130884i	$0.958218\pi$
$572$	−0.713881	−	1.23648i	−0.0298489	−	0.0516998i
$573$	−44.4482	−	3.85025i	−1.85685	−	0.160846i
$574$	−2.81442	+	4.87472i	−0.117472	+	0.203467i
$575$	−0.590163			−0.0246115
$576$	−3.39997	+	4.06609i	−0.141665	+	0.169420i
$577$	21.5503			0.897150			0.448575	−	0.893745i	$-0.351932\pi$
$577$	21.5503			0.897150			0.448575	+	0.893745i	$0.351932\pi$
$578$	−13.5531	+	23.4747i	−0.563736	+	0.976420i
$579$	−7.21815	+	10.3275i	−0.299976	+	0.429195i
$580$	−1.97912	−	3.42794i	−0.0821785	−	0.142337i
$581$	18.2336	+	31.5814i	0.756455	+	1.31022i
$582$	−20.8413	+	29.8190i	−0.863900	+	1.23604i
$583$	−9.67594	+	16.7592i	−0.400736	+	0.694096i
$584$	5.16525			0.213740
$585$	1.03090	+	2.81731i	0.0426225	+	0.116481i
$586$	−45.9489			−1.89813
$587$	18.0974	−	31.3456i	0.746960	−	1.29377i	−0.202313	−	0.979321i	$-0.564846\pi$
$587$	18.0974	−	31.3456i	0.746960	−	1.29377i	0.949273	−	0.314452i	$-0.101821\pi$
$588$	−0.492927	−	0.0426989i	−0.0203280	−	0.00176087i
$589$	6.18365	+	10.7104i	0.254793	+	0.441314i
$590$	4.18536	+	7.24925i	0.172308	+	0.298447i
$591$	12.9274	+	27.6608i	0.531761	+	1.13781i
$592$	−0.396527	+	0.686805i	−0.0162972	+	0.0282275i
$593$	33.4499			1.37362			0.686811	−	0.726836i	$-0.259010\pi$
$593$	33.4499			1.37362			0.686811	+	0.726836i	$0.259010\pi$
$594$	3.62096	+	13.3756i	0.148570	+	0.548810i
$595$	2.86270			0.117359
$596$	−4.06152	+	7.03476i	−0.166366	+	0.288155i
$597$	−1.04451	−	2.23495i	−0.0427490	−	0.0914703i
$598$	0.503709	+	0.872450i	0.0205982	+	0.0356771i
$599$	10.5927	+	18.3472i	0.432808	+	0.749645i	0.997114	−	0.0759206i	$-0.0241896\pi$
$599$	10.5927	+	18.3472i	0.432808	+	0.749645i	−0.564306	+	0.825566i	$0.690856\pi$
$600$	−3.19920	−	0.277125i	−0.130607	−	0.0113136i
$601$	5.91505	−	10.2452i	0.241280	−	0.417909i	−0.719799	−	0.694182i	$-0.755766\pi$
$601$	5.91505	−	10.2452i	0.241280	−	0.417909i	0.961079	+	0.276273i	$0.0890995\pi$
$602$	−0.753188			−0.0306976
$603$	3.99838	+	0.697941i	0.162826	+	0.0284224i
$604$	21.6222			0.879796
$605$	4.27968	−	7.41262i	0.173994	−	0.301366i
$606$	3.23801	−	4.63282i	0.131535	−	0.188195i
$607$	−22.7324	−	39.3737i	−0.922680	−	1.59813i	−0.795251	−	0.606281i	$-0.792661\pi$
$607$	−22.7324	−	39.3737i	−0.922680	−	1.59813i	−0.127429	−	0.991848i	$-0.540673\pi$
$608$	−12.8175	−	22.2006i	−0.519818	−	0.900351i
$609$	−11.6212	+	16.6272i	−0.470916	+	0.673769i
$610$	6.34640	−	10.9923i	0.256958	−	0.445065i
$611$	7.46960			0.302188
$612$	−2.85922	−	0.499095i	−0.115577	−	0.0201747i
$613$	0.857091			0.0346176			0.0173088	−	0.999850i	$-0.494490\pi$
$613$	0.857091			0.0346176			0.0173088	+	0.999850i	$0.494490\pi$
$614$	−28.1199	+	48.7052i	−1.13483	+	1.96558i
$615$	−2.10418	−	0.182271i	−0.0848488	−	0.00734988i
$616$	−3.91617	−	6.78300i	−0.157787	−	0.273295i
$617$	−16.5193	−	28.6123i	−0.665043	−	1.15189i	−0.979274	−	0.202542i	$-0.935080\pi$
$617$	−16.5193	−	28.6123i	−0.665043	−	1.15189i	0.314230	−	0.949347i	$-0.398254\pi$
$618$	−7.77094	−	16.6275i	−0.312593	−	0.668858i
$619$	−13.8394	+	23.9705i	−0.556252	+	0.963457i	0.441553	+	0.897235i	$0.354428\pi$
$619$	−13.8394	+	23.9705i	−0.556252	+	0.963457i	−0.997805	+	0.0662218i	$0.978906\pi$
$620$	−2.12273			−0.0852510
$621$	−0.801319	−	2.96003i	−0.0321558	−	0.118782i
$622$	−39.3269			−1.57686
$623$	−11.3233	+	19.6126i	−0.453659	+	0.785761i
$624$	3.66129	+	7.83408i	0.146569	+	0.313614i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−26.5278	−	45.9476i	−1.06027	−	1.83643i
$627$	14.3540	+	1.24339i	0.573243	+	0.0496562i
$628$	−7.87027	+	13.6317i	−0.314058	+	0.543964i
$629$	0.168158			0.00670491
$630$	−4.75872	−	13.0049i	−0.189592	−	0.518129i
$631$	39.1686			1.55928			0.779639	−	0.626229i	$-0.215403\pi$
$631$	39.1686			1.55928			0.779639	+	0.626229i	$0.215403\pi$
$632$	−7.24092	+	12.5416i	−0.288028	+	0.498880i
$633$	−9.02664	+	12.9150i	−0.358777	+	0.513324i
$634$	13.6583	+	23.6568i	0.542439	+	0.939531i
$635$	−3.62526	−	6.27913i	−0.143864	−	0.249180i
$636$	−11.2329	+	16.0716i	−0.445414	+	0.637282i
$637$	0.156283	−	0.270690i	0.00619216	−	0.0107251i
$638$	11.5502			0.457277
$639$	30.6753	−	36.6852i	1.21350	−	1.45124i
$640$	−12.6449			−0.499832
$641$	−1.07166	+	1.85617i	−0.0423281	+	0.0733144i	−0.886413	−	0.462895i	$-0.846811\pi$
$641$	−1.07166	+	1.85617i	−0.0423281	+	0.0733144i	0.844085	+	0.536209i	$0.180144\pi$
$642$	14.9268	+	1.29301i	0.589115	+	0.0510310i
$643$	2.22966	+	3.86188i	0.0879292	+	0.152298i	0.906636	−	0.421914i	$-0.138642\pi$
$643$	2.22966	+	3.86188i	0.0879292	+	0.152298i	−0.818706	+	0.574212i	$0.805308\pi$
$644$	−0.729257	−	1.26311i	−0.0287367	−	0.0497735i
$645$	−0.119657	−	0.256031i	−0.00471149	−	0.0100812i
$646$	−4.81096	+	8.33283i	−0.189285	+	0.327851i
$647$	−4.30783			−0.169358			−0.0846792	−	0.996408i	$-0.526987\pi$
$647$	−4.30783			−0.169358			−0.0846792	+	0.996408i	$0.526987\pi$
$648$	−2.95389	−	16.4222i	−0.116040	−	0.645126i
$649$	−7.66085			−0.300715
$650$	−0.853509	+	1.47832i	−0.0334774	+	0.0579845i
$651$	4.60611	+	9.85573i	0.180528	+	0.386277i
$652$	−6.86368	−	11.8882i	−0.268803	−	0.465580i
$653$	9.17785	+	15.8965i	0.359157	+	0.622078i	0.987820	−	0.155600i	$-0.0497310\pi$
$653$	9.17785	+	15.8965i	0.359157	+	0.622078i	−0.628663	+	0.777678i	$0.716398\pi$
$654$	−14.5926	−	1.26405i	−0.570614	−	0.0494284i
$655$	−3.09607	+	5.36255i	−0.120974	+	0.209532i
$656$	−6.08796			−0.237695
$657$	−5.36149	+	6.41192i	−0.209172	+	0.250153i
$658$	−34.4802			−1.34418
$659$	3.72555	−	6.45284i	0.145127	−	0.251367i	−0.784293	−	0.620390i	$-0.786974\pi$
$659$	3.72555	−	6.45284i	0.145127	−	0.251367i	0.929420	+	0.369023i	$0.120308\pi$
$660$	−1.41669	+	2.02695i	−0.0551446	+	0.0788988i
$661$	−21.5188	−	37.2717i	−0.836985	−	1.44970i	−0.892404	−	0.451238i	$-0.850983\pi$
$661$	−21.5188	−	37.2717i	−0.836985	−	1.44970i	0.0554182	−	0.998463i	$-0.482351\pi$
$662$	6.09058	+	10.5492i	0.236717	+	0.410006i
$663$	1.05041	−	1.50289i	0.0407946	−	0.0583674i
$664$	−12.5009	+	21.6521i	−0.485128	+	0.840266i
$665$	−14.3985			−0.558351
$666$	−0.279533	−	0.763924i	−0.0108317	−	0.0296015i
$667$	−2.55606			−0.0989709
$668$	6.83234	−	11.8340i	0.264351	−	0.457869i
$669$	39.1273	+	3.38933i	1.51275	+	0.131039i
$670$	1.15475	+	2.00009i	0.0446119	+	0.0772701i
$671$	5.80821	+	10.0601i	0.224223	+	0.388366i
$672$	−9.54758	−	20.4290i	−0.368306	−	0.788066i
$673$	8.58622	−	14.8718i	0.330974	−	0.573265i	−0.651729	−	0.758452i	$-0.725956\pi$
$673$	8.58622	−	14.8718i	0.330974	−	0.573265i	0.982703	+	0.185188i	$0.0592893\pi$
$674$	−59.3551			−2.28627
$675$	3.66475	−	3.68369i	0.141056	−	0.141785i
$676$	0.913910			0.0351504
$677$	13.4214	−	23.2465i	0.515825	−	0.893435i	−0.484006	−	0.875065i	$-0.660819\pi$
$677$	13.4214	−	23.2465i	0.515825	−	0.893435i	0.999831	−	0.0183705i	$-0.00584785\pi$
$678$	12.1946	+	26.0928i	0.468330	+	1.00209i
$679$	16.6369	+	28.8160i	0.638467	+	1.10586i
$680$	0.981329	+	1.69971i	0.0376323	+	0.0651810i
$681$	−13.5503	−	1.17377i	−0.519248	−	0.0449789i
$682$	3.09708	−	5.36430i	0.118593	−	0.205410i
$683$	4.73852			0.181314			0.0906572	−	0.995882i	$-0.471103\pi$
$683$	4.73852			0.181314			0.0906572	+	0.995882i	$0.471103\pi$
$684$	14.3810	+	2.51030i	0.549873	+	0.0959837i
$685$	−20.8865			−0.798031
$686$	15.4349	−	26.7340i	0.589305	−	1.02071i
$687$	15.7607	−	22.5498i	0.601308	−	0.860328i
$688$	−0.407311	−	0.705483i	−0.0155286	−	0.0268963i
$689$	−6.19356	−	10.7276i	−0.235956	−	0.408688i
$690$	0.999606	−	1.43020i	0.0380543	−	0.0544467i
$691$	−13.1432	+	22.7646i	−0.499989	+	0.866007i	−1.00000		1.22854e-5i	$-0.999996\pi$
$691$	−13.1432	+	22.7646i	−0.499989	+	0.866007i	0.500011	+	0.866019i	$0.333329\pi$
$692$	−21.9941			−0.836089
$693$	12.4851	+	2.17935i	0.474269	+	0.0827865i
$694$	30.0573			1.14096
$695$	0.396317	−	0.686442i	0.0150332	−	0.0260382i
$696$	−13.8561	−	1.20026i	−0.525213	−	0.0454956i
$697$	0.645442	+	1.11794i	0.0244478	+	0.0423449i
$698$	0.153135	+	0.265238i	0.00579625	+	0.0100394i
$699$	3.40660	+	7.28913i	0.128849	+	0.275700i
$700$	1.23569	−	2.14027i	0.0467046	−	0.0808947i
$701$	51.8206			1.95724			0.978618	−	0.205687i	$-0.0659429\pi$
$701$	51.8206			1.95724			0.978618	+	0.205687i	$0.0659429\pi$
$702$	−8.57358	−	2.27362i	−0.323589	−	0.0858123i
$703$	−0.845785			−0.0318994
$704$	1.38006	−	2.39034i	0.0520132	−	0.0900894i
$705$	−5.47779	−	11.7209i	−0.206305	−	0.441433i
$706$	−14.7445	−	25.5383i	−0.554918	−	0.961145i
$707$	−2.58479	−	4.47699i	−0.0972111	−	0.168375i
$708$	−7.73331	−	0.669884i	−0.290636	−	0.0251758i
$709$	−20.6347	+	35.7403i	−0.774952	+	1.34226i	0.159870	+	0.987138i	$0.448893\pi$
$709$	−20.6347	+	35.7403i	−0.774952	+	1.34226i	−0.934822	+	0.355118i	$0.884441\pi$
$710$	27.2100			1.02117
$711$	−8.05263	−	22.0067i	−0.301997	−	0.825316i
$712$	−15.5265			−0.581879
$713$	−0.685384	+	1.18712i	−0.0256678	+	0.0444580i
$714$	−4.84878	+	6.93745i	−0.181461	+	0.259628i
$715$	−0.781129	−	1.35295i	−0.0292126	−	0.0505976i
$716$	1.81667	+	3.14656i	0.0678921	+	0.117593i
$717$	25.1777	−	36.0233i	0.940277	−	1.34531i
$718$	−2.55761	+	4.42990i	−0.0954490	+	0.165323i
$719$	17.5626			0.654975			0.327487	−	0.944856i	$-0.393798\pi$
$719$	17.5626			0.654975			0.327487	+	0.944856i	$0.393798\pi$
$720$	9.60780	−	11.4902i	0.358061	−	0.428213i
$721$	−16.7866			−0.625165
$722$	7.98102	−	13.8235i	0.297023	−	0.514459i
$723$	23.2923	+	2.01765i	0.866249	+	0.0750373i
$724$	−1.62268	−	2.81056i	−0.0603064	−	0.104454i
$725$	−2.16555	−	3.75085i	−0.0804266	−	0.139303i
$726$	10.7149	+	22.9267i	0.397666	+	0.850889i
$727$	−9.67687	+	16.7608i	−0.358895	+	0.621625i	−0.987777	−	0.155876i	$-0.950180\pi$
$727$	−9.67687	+	16.7608i	−0.358895	+	0.621625i	0.628881	+	0.777501i	$0.283513\pi$
$728$	5.01347			0.185812
$729$	23.4520	+	13.3793i	0.868591	+	0.495530i
$730$	−4.75582			−0.176021
$731$	−0.0863657	+	0.149590i	−0.00319435	+	0.00553278i
$732$	4.98346	+	10.6631i	0.184194	+	0.394121i
$733$	−2.53978	−	4.39903i	−0.0938090	−	0.162482i	0.815302	−	0.579036i	$-0.196571\pi$
$733$	−2.53978	−	4.39903i	−0.0938090	−	0.162482i	−0.909111	+	0.416554i	$0.863238\pi$
$734$	12.2285	+	21.1804i	0.451362	+	0.781782i
$735$	−0.539360	−	0.0467211i	−0.0198946	−	0.00172333i
$736$	1.42067	−	2.46067i	0.0523665	−	0.0907014i
$737$	−2.11365			−0.0778572
$738$	4.00573	−	4.79054i	0.147453	−	0.176342i
$739$	15.9401			0.586366			0.293183	−	0.956056i	$-0.405286\pi$
$739$	15.9401			0.586366			0.293183	+	0.956056i	$0.405286\pi$
$740$	0.0725857	−	0.125722i	0.00266830	−	0.00462163i
$741$	−5.28326	+	7.55908i	−0.194085	+	0.277690i
$742$	28.5900	+	49.5193i	1.04957	+	1.81791i
$743$	12.0016	+	20.7873i	0.440294	+	0.762612i	0.997711	−	0.0676207i	$-0.0215408\pi$
$743$	12.0016	+	20.7873i	0.440294	+	0.762612i	−0.557417	+	0.830233i	$0.688207\pi$
$744$	−4.27282	+	6.11338i	−0.156649	+	0.224128i
$745$	−4.44412	+	7.69743i	−0.162820	+	0.282012i
$746$	−37.6583			−1.37877
$747$	−13.9022	−	37.9928i	−0.508655	−	1.39008i
$748$	1.51146			0.0552645
$749$	6.85168	−	11.8675i	0.250355	−	0.433627i
$750$	2.94561	+	0.255158i	0.107559	+	0.00931706i
$751$	−24.4746	−	42.3912i	−0.893090	−	1.54688i	−0.836151	−	0.548500i	$-0.815199\pi$
$751$	−24.4746	−	42.3912i	−0.893090	−	1.54688i	−0.0569392	−	0.998378i	$-0.518134\pi$
$752$	−18.6463	−	32.2964i	−0.679961	−	1.17773i
$753$	7.47435	+	15.9929i	0.272381	+	0.582814i
$754$	−3.69664	+	6.40276i	−0.134624	+	0.233175i
$755$	23.6590			0.861040
$756$	12.4126	+	3.29169i	0.451442	+	0.119717i
$757$	−21.3970			−0.777689			−0.388844	−	0.921303i	$-0.627126\pi$
$757$	−21.3970			−0.777689			−0.388844	+	0.921303i	$0.627126\pi$
$758$	31.4888	−	54.5403i	1.14373	−	1.98099i
$759$	0.676133	+	1.44673i	0.0245421	+	0.0525129i
$760$	−4.93579	−	8.54904i	−0.179040	−	0.310106i
$761$	24.4305	+	42.3148i	0.885604	+	1.53391i	0.845019	+	0.534736i	$0.179589\pi$
$761$	24.4305	+	42.3148i	0.885604	+	1.53391i	0.0405853	+	0.999176i	$0.487078\pi$
$762$	21.3572	+	1.85003i	0.773690	+	0.0670195i
$763$	−6.69825	+	11.6017i	−0.242493	+	0.420010i
$764$	23.5408			0.851675
$765$	−3.12856	−	0.546110i	−0.113113	−	0.0197446i
$766$	−8.26627			−0.298672
$767$	2.45185	−	4.24674i	0.0885313	−	0.153341i
$768$	17.9115	−	25.6271i	0.646326	−	0.924738i
$769$	−13.8909	−	24.0597i	−0.500918	−	0.867615i	−0.999999	−	0.00106036i	$-0.999662\pi$
$769$	−13.8909	−	24.0597i	−0.500918	−	0.867615i	0.499081	−	0.866555i	$-0.333671\pi$
$770$	3.60575	+	6.24534i	0.129942	+	0.225066i
$771$	−28.9510	+	41.4221i	−1.04265	+	1.49178i
$772$	3.32415	−	5.75760i	0.119639	−	0.207221i
$773$	−9.46245			−0.340341			−0.170170	−	0.985415i	$-0.554432\pi$
$773$	−9.46245			−0.340341			−0.170170	+	0.985415i	$0.554432\pi$
$774$	0.823136	+	0.143684i	0.0295870	+	0.00516460i
$775$	−2.32269			−0.0834336
$776$	−11.4062	+	19.7562i	−0.409460	+	0.709205i
$777$	−0.741224	−	0.0642072i	−0.0265913	−	0.00230342i
$778$	15.1604	+	26.2586i	0.543528	+	0.941418i
$779$	−3.24638	−	5.62289i	−0.116314	−	0.201461i
$780$	−0.670211	−	1.43405i	−0.0239974	−	0.0513474i
$781$	−12.4513	+	21.5662i	−0.445541	+	0.771700i
$782$	−1.06648			−0.0381371
$783$	15.8724	−	15.9545i	0.567235	−	0.570166i
$784$	−1.56051			−0.0557326
$785$	−8.61164	+	14.9158i	−0.307363	+	0.532368i
$786$	−7.75153	−	16.5860i	−0.276488	−	0.591603i
$787$	−7.46889	−	12.9365i	−0.266237	−	0.461136i	0.701650	−	0.712522i	$-0.252447\pi$
$787$	−7.46889	−	12.9365i	−0.266237	−	0.461136i	−0.967887	+	0.251386i	$0.919114\pi$
$788$	−8.05519	−	13.9520i	−0.286954	−	0.497019i
$789$	8.16988	+	0.707701i	0.290856	+	0.0251948i
$790$	6.66697	−	11.5475i	0.237200	−	0.410843i
$791$	26.3424			0.936629
$792$	2.98589	+	8.16002i	0.106099	+	0.289954i
$793$	−7.43566			−0.264048
$794$	28.8695	−	50.0034i	1.02454	−	1.77455i
$795$	−12.2911	+	17.5856i	−0.435919	+	0.623696i
$796$	0.650847	+	1.12730i	0.0230687	+	0.0399561i
$797$	21.2280	+	36.7680i	0.751936	+	1.30239i	0.946883	+	0.321577i	$0.104213\pi$
$797$	21.2280	+	36.7680i	0.751936	+	1.30239i	−0.194948	+	0.980814i	$0.562454\pi$
$798$	24.3879	−	34.8933i	0.863323	−	1.23521i
$799$	−3.95374	+	6.84808i	−0.139873	+	0.242268i
$800$	4.81449			0.170218
$801$	16.1164	−	19.2739i	0.569444	−	0.681009i
$802$	20.1662			0.712093
$803$	2.17626	−	3.76939i	0.0767985	−	0.133019i
$804$	−2.13364	−	0.184823i	−0.0752476	−	0.00651819i
$805$	−0.797952	−	1.38209i	−0.0281241	−	0.0487124i
$806$	1.98244	+	3.43369i	0.0698284	+	0.120946i
$807$	8.48026	+	18.1453i	0.298519	+	0.638744i
$808$	1.77213	−	3.06941i	0.0623432	−	0.107982i
$809$	1.52951			0.0537749			0.0268874	−	0.999638i	$-0.491440\pi$
$809$	1.52951			0.0537749			0.0268874	+	0.999638i	$0.491440\pi$
$810$	2.71975	+	15.1205i	0.0955624	+	0.531280i
$811$	−30.2267			−1.06140			−0.530701	−	0.847559i	$-0.678071\pi$
$811$	−30.2267			−1.06140			−0.530701	+	0.847559i	$0.678071\pi$
$812$	5.35189	−	9.26975i	0.187815	−	0.325304i
$813$	21.4621	+	45.9226i	0.752708	+	1.61057i
$814$	0.211806	+	0.366858i	0.00742379	+	0.0128584i
$815$	−7.51024	−	13.0081i	−0.263072	−	0.455654i
$816$	−9.12020	−	0.790021i	−0.319271	−	0.0276563i
$817$	0.434393	−	0.752391i	0.0151975	−	0.0263228i
$818$	23.7245			0.829508
$819$	−5.20395	+	6.22351i	−0.181841	+	0.217467i
$820$	1.11442			0.0389173
$821$	7.30433	−	12.6515i	0.254923	−	0.441540i	−0.709952	−	0.704250i	$-0.751283\pi$
$821$	7.30433	−	12.6515i	0.254923	−	0.441540i	0.964875	+	0.262711i	$0.0846166\pi$
$822$	35.3770	−	50.6161i	1.23392	−	1.76544i
$823$	22.9727	+	39.7898i	0.800777	+	1.38699i	0.919106	+	0.394011i	$0.128913\pi$
$823$	22.9727	+	39.7898i	0.800777	+	1.38699i	−0.118329	+	0.992974i	$0.537754\pi$
$824$	−5.75442	−	9.96694i	−0.200465	−	0.347215i
$825$	−1.55014	+	2.21788i	−0.0539690	+	0.0772168i
$826$	−11.3179	+	19.6033i	−0.393802	+	0.682084i
$827$	22.7043			0.789505			0.394752	−	0.918788i	$-0.370830\pi$
$827$	22.7043			0.789505			0.394752	+	0.918788i	$0.370830\pi$
$828$	0.556023	+	1.51953i	0.0193231	+	0.0528074i
$829$	−8.07414			−0.280427			−0.140213	−	0.990121i	$-0.544779\pi$
$829$	−8.07414			−0.280427			−0.140213	+	0.990121i	$0.544779\pi$
$830$	11.5100	−	19.9359i	0.399517	−	0.691984i
$831$	7.44748	+	0.645125i	0.258350	+	0.0223791i
$832$	0.883379	+	1.53006i	0.0306257	+	0.0530452i
$833$	0.165445	+	0.286559i	0.00573232	+	0.00992866i
$834$	0.992245	+	2.12311i	0.0343586	+	0.0735174i
$835$	7.47594	−	12.9487i	0.258716	−	0.448108i
$836$	−7.60220			−0.262927
$837$	−3.15373	−	11.6497i	−0.109009	−	0.402674i
$838$	15.2822			0.527915
$839$	3.47148	−	6.01278i	0.119849	−	0.207584i	−0.799859	−	0.600188i	$-0.795092\pi$
$839$	3.47148	−	6.01278i	0.119849	−	0.207584i	0.919708	+	0.392604i	$0.128426\pi$
$840$	−3.67660	−	7.86685i	−0.126855	−	0.271432i
$841$	5.12076	+	8.86942i	0.176578	+	0.305842i
$842$	22.3849	+	38.7718i	0.771435	+	1.33617i
$843$	−36.9241	−	3.19849i	−1.27173	−	0.110162i
$844$	4.15701	−	7.20016i	0.143090	−	0.247840i
$845$	1.00000			0.0344010
$846$	37.6824	+	6.57770i	1.29555	+	0.226146i
$847$	23.1460			0.795306
$848$	−30.9219	+	53.5583i	−1.06186	+	1.83920i
$849$	−4.67607	+	6.69034i	−0.160482	+	0.229612i
$850$	−0.903544	−	1.56498i	−0.0309913	−	0.0536785i
$851$	−0.0468726	−	0.0811857i	−0.00160677	−	0.00278301i
$852$	−14.4548	+	20.6814i	−0.495214	+	0.708534i
$853$	7.29683	−	12.6385i	0.249839	−	0.432733i	−0.713642	−	0.700510i	$-0.752956\pi$
$853$	7.29683	−	12.6385i	0.249839	−	0.432733i	0.963481	+	0.267777i	$0.0862890\pi$
$854$	34.3236			1.17453
$855$	15.7357	+	2.74677i	0.538150	+	0.0939375i
$856$	9.39498			0.321114
$857$	−6.16769	+	10.6827i	−0.210684	+	0.364916i	−0.951929	−	0.306319i	$-0.900902\pi$
$857$	−6.16769	+	10.6827i	−0.210684	+	0.364916i	0.741245	+	0.671235i	$0.234236\pi$
$858$	4.60180	+	0.398623i	0.157103	+	0.0136088i
$859$	7.46588	+	12.9313i	0.254732	+	0.441209i	0.964823	−	0.262901i	$-0.0846793\pi$
$859$	7.46588	+	12.9313i	0.254732	+	0.441209i	−0.710090	+	0.704111i	$0.751346\pi$
$860$	0.0745596	+	0.129141i	0.00254246	+	0.00440367i
$861$	−2.41818	−	5.17420i	−0.0824114	−	0.176336i
$862$	0.920417	−	1.59421i	0.0313495	−	0.0542990i
$863$	3.39276			0.115491			0.0577455	−	0.998331i	$-0.481609\pi$
$863$	3.39276			0.115491			0.0577455	+	0.998331i	$0.481609\pi$
$864$	6.53708	+	24.1476i	0.222396	+	0.821519i
$865$	−24.0659			−0.818265
$866$	3.00318	−	5.20165i	0.102052	−	0.176759i
$867$	−11.6450	−	24.9169i	−0.395485	−	0.846222i
$868$	−2.87012	−	4.97120i	−0.0974183	−	0.168733i
$869$	6.10159	+	10.5683i	0.206982	+	0.358504i
$870$	12.7578	+	1.10512i	0.432528	+	0.0374670i
$871$	0.676472	−	1.17168i	0.0229214	−	0.0397010i
$872$	−9.18459			−0.311030
$873$	−12.6849	−	34.6660i	−0.429317	−	1.17326i
$874$	5.36405			0.181442
$875$	1.35209	−	2.34188i	0.0457089	−	0.0791702i
$876$	2.52645	−	3.61474i	0.0853607	−	0.122131i
$877$	−16.3939	−	28.3951i	−0.553584	−	0.958836i	−0.998012	−	0.0630213i	$-0.979926\pi$
$877$	−16.3939	−	28.3951i	−0.553584	−	0.958836i	0.444428	−	0.895815i	$-0.353407\pi$
$878$	−24.5601	−	42.5394i	−0.828863	−	1.43563i
$879$	26.7089	−	38.2141i	0.900869	−	1.28893i
$880$	−3.89985	+	6.75474i	−0.131464	+	0.227702i
$881$	45.5037			1.53306			0.766530	−	0.642208i	$-0.221982\pi$
$881$	45.5037			1.53306			0.766530	+	0.642208i	$0.221982\pi$
$882$	1.02678	−	1.22795i	0.0345735	−	0.0413472i
$883$	−46.2039			−1.55489			−0.777443	−	0.628953i	$-0.783484\pi$
$883$	−46.2039			−1.55489			−0.777443	+	0.628953i	$0.783484\pi$
$884$	−0.483743	+	0.837867i	−0.0162700	+	0.0281805i
$885$	−8.46178	−	0.732987i	−0.284440	−	0.0246391i
$886$	28.9092	+	50.0722i	0.971224	+	1.68221i
$887$	−13.9620	−	24.1830i	−0.468800	−	0.811985i	0.530564	−	0.847645i	$-0.321980\pi$
$887$	−13.9620	−	24.1830i	−0.468800	−	0.811985i	−0.999364	+	0.0356600i	$0.988647\pi$
$888$	−0.215968	−	0.462108i	−0.00724740	−	0.0155073i
$889$	9.80333	−	16.9799i	0.328793	−	0.569487i
$890$	14.2958			0.479195
$891$	−13.2288	−	4.76349i	−0.443182	−	0.159583i
$892$	−20.7227			−0.693847
$893$	19.8861	−	34.4438i	0.665464	−	1.15262i
$894$	−11.1266	−	23.8076i	−0.372128	−	0.796245i
$895$	1.98780	+	3.44297i	0.0664448	+	0.115086i
$896$	−17.0970	−	29.6128i	−0.571170	−	0.989295i
$897$	−1.01838	−	0.0882152i	−0.0340027	−	0.00294542i
$898$	14.4553	−	25.0374i	0.482381	−	0.835508i
$899$	−10.0598			−0.335514
$900$	−1.75874	+	2.10331i	−0.0586247	+	0.0701104i
$901$	13.1133			0.436867
$902$	−1.62595	+	2.81622i	−0.0541381	+	0.0937700i
$903$	0.437808	−	0.626399i	0.0145693	−	0.0208453i
$904$	9.03015	+	15.6407i	0.300338	+	0.520201i
$905$	−1.77554	−	3.07532i	−0.0590208	−	0.102227i
$906$	−40.0732	+	57.3352i	−1.33134	+	1.90483i
$907$	−28.8177	+	49.9137i	−0.956876	+	1.65736i	−0.226860	+	0.973927i	$0.572846\pi$
$907$	−28.8177	+	49.9137i	−0.956876	+	1.65736i	−0.730016	+	0.683430i	$0.760487\pi$
$908$	7.17653			0.238161
$909$	1.97078	+	5.38587i	0.0653666	+	0.178638i
$910$	−4.61608			−0.153021
$911$	14.6236	−	25.3288i	0.484501	−	0.839180i	−0.515341	−	0.856985i	$-0.672335\pi$
$911$	14.6236	−	25.3288i	0.484501	−	0.839180i	0.999841	+	0.0178054i	$0.00566792\pi$
$912$	45.8718	+	3.97356i	1.51897	+	0.131578i
$913$	10.5339	+	18.2452i	0.348621	+	0.603829i
$914$	−3.12031	−	5.40453i	−0.103211	−	0.178766i
$915$	5.45290	+	11.6676i	0.180267	+	0.385719i
$916$	−7.25822	+	12.5716i	−0.239818	+	0.415377i
$917$	−16.7446			−0.552957
$918$	6.62253	−	6.65675i	0.218576	−	0.219706i
$919$	−12.6561			−0.417485			−0.208743	−	0.977971i	$-0.566937\pi$
$919$	−12.6561			−0.417485			−0.208743	+	0.977971i	$0.566937\pi$
$920$	0.547074	−	0.947559i	0.0180365	−	0.0312401i
$921$	−24.1610	−	51.6974i	−0.796131	−	1.70349i
$922$	21.3534	+	36.9852i	0.703238	+	1.21804i
$923$	−7.97005	−	13.8045i	−0.262337	−	0.454382i
$924$	−6.66236	−	0.577115i	−0.219176	−	0.0189857i
$925$	0.0794232	−	0.137565i	0.00261142	−	0.00452311i
$926$	36.7202			1.20670
$927$	18.3456	+	3.20233i	0.602548	+	0.105178i
$928$	20.8521			0.684502
$929$	−10.8576	+	18.8058i	−0.356225	+	0.617000i	−0.987327	−	0.158700i	$-0.949270\pi$
$929$	−10.8576	+	18.8058i	−0.356225	+	0.617000i	0.631102	+	0.775700i	$0.282603\pi$
$930$	3.93413	−	5.62880i	0.129005	−	0.184576i
$931$	−0.832137	−	1.44130i	−0.0272722	−	0.0472368i
$932$	−2.12269	−	3.67661i	−0.0695311	−	0.120431i
$933$	22.8597	−	32.7067i	0.748392	−	1.07077i
$934$	1.79687	−	3.11227i	0.0587954	−	0.101837i
$935$	1.65384			0.0540864
$936$	−5.47908	−	0.956407i	−0.179089	−	0.0312611i
$937$	−31.5757			−1.03153			−0.515767	−	0.856729i	$-0.672493\pi$
$937$	−31.5757			−1.03153			−0.515767	+	0.856729i	$0.672493\pi$
$938$	−3.12265	+	5.40858i	−0.101958	+	0.176597i
$939$	53.6329	+	4.64585i	1.75024	+	0.151612i
$940$	3.41327	+	5.91196i	0.111329	+	0.192827i
$941$	15.6477	+	27.1026i	0.510101	+	0.883520i	0.999932	+	0.0117027i	$0.00372517\pi$
$941$	15.6477	+	27.1026i	0.510101	+	0.883520i	−0.489831	+	0.871817i	$0.662941\pi$
$942$	−21.5607	−	46.1335i	−0.702484	−	1.50311i
$943$	0.359822	−	0.623230i	0.0117174	−	0.0202952i
$944$	−24.4822			−0.796828
$945$	13.5818	+	3.60176i	0.441818	+	0.117165i
$946$	−0.435132			−0.0141474
$947$	2.63072	−	4.55655i	0.0854871	−	0.148068i	−0.820112	−	0.572204i	$-0.806089\pi$
$947$	2.63072	−	4.55655i	0.0854871	−	0.148068i	0.905599	+	0.424136i	$0.139422\pi$
$948$	5.23518	+	11.2018i	0.170031	+	0.363816i
$949$	1.39302	+	2.41278i	0.0452194	+	0.0783223i
$950$	4.54455	+	7.87139i	0.147445	+	0.255382i
$951$	−27.6137	−	2.39199i	−0.895435	−	0.0775655i
$952$	−2.65369	+	4.59632i	−0.0860065	+	0.148968i
$953$	−10.0213			−0.324621			−0.162310	−	0.986740i	$-0.551895\pi$
$953$	−10.0213			−0.324621			−0.162310	+	0.986740i	$0.551895\pi$
$954$	−21.7985	−	59.5722i	−0.705751	−	1.92872i
$955$	25.7583			0.833519
$956$	−11.5950	+	20.0831i	−0.375009	+	0.649534i
$957$	−6.71382	+	9.60588i	−0.217027	+	0.310514i
$958$	2.63042	+	4.55603i	0.0849852	+	0.147199i
$959$	−28.2403	−	48.9137i	−0.911928	−	1.57951i
$960$	1.75306	−	2.50821i	0.0565796	−	0.0809520i
$961$	12.8025	−	22.1747i	0.412985	−	0.715312i
$962$	−0.271154			−0.00874234
$963$	−9.75192	+	11.6625i	−0.314251	+	0.375819i
$964$	−12.3361			−0.397319
$965$	3.63729	−	6.29996i	0.117088	−	0.202803i
$966$	4.70091	+	0.407208i	0.151249	+	0.0131017i
$967$	1.98064	+	3.43057i	0.0636931	+	0.110320i	0.896114	−	0.443825i	$-0.146379\pi$
$967$	1.98064	+	3.43057i	0.0636931	+	0.110320i	−0.832420	+	0.554145i	$0.813045\pi$
$968$	7.93441	+	13.7428i	0.255022	+	0.441710i
$969$	−4.13363	−	8.84476i	−0.132791	−	0.284135i
$970$	10.5021	−	18.1902i	0.337202	−	0.584052i
$971$	−43.5118			−1.39636			−0.698179	−	0.715923i	$-0.746006\pi$
$971$	−43.5118			−1.39636			−0.698179	+	0.715923i	$0.746006\pi$
$972$	−12.9374	−	5.96530i	−0.414968	−	0.191337i
$973$	2.14342			0.0687150
$974$	17.6819	−	30.6259i	0.566563	−	0.981316i
$975$	−0.733344	−	1.56914i	−0.0234858	−	0.0502528i
$976$	18.5616	+	32.1496i	0.594142	+	1.02908i
$977$	−17.9017	−	31.0066i	−0.572725	−	0.991988i	−0.996285	−	0.0861202i	$-0.972553\pi$
$977$	−17.9017	−	31.0066i	−0.572725	−	0.991988i	0.423560	−	0.905868i	$-0.360780\pi$
$978$	44.2445	+	3.83260i	1.41478	+	0.122553i
$979$	−6.54171	+	11.3306i	−0.209074	+	0.362127i
$980$	0.285657			0.00912499
$981$	9.53354	−	11.4014i	0.304383	−	0.364017i
$982$	13.1354			0.419168
$983$	6.58004	−	11.3970i	0.209871	−	0.363506i	−0.741803	−	0.670618i	$-0.766029\pi$
$983$	6.58004	−	11.3970i	0.209871	−	0.363506i	0.951674	+	0.307111i	$0.0993624\pi$
$984$	2.24320	−	3.20949i	0.0715107	−	0.102315i
$985$	−8.81398	−	15.2663i	−0.280837	−	0.486423i
$986$	−3.91334	−	6.77811i	−0.124626	−	0.215859i
$987$	20.0425	−	28.6760i	0.637958	−	0.912766i
$988$	2.43308	−	4.21422i	0.0774066	−	0.134072i
$989$	0.0962946			0.00306199
$990$	−2.74921	−	7.51321i	−0.0873756	−	0.238785i
$991$	23.8623			0.758010			0.379005	−	0.925395i	$-0.376266\pi$
$991$	23.8623			0.758010			0.379005	+	0.925395i	$0.376266\pi$
$992$	5.59129	−	9.68440i	0.177524	−	0.307480i
$993$	−12.3137	−	1.06665i	−0.390763	−	0.0338491i
$994$	36.7903	+	63.7227i	1.16692	+	2.02116i
$995$	0.712156	+	1.23349i	0.0225769	+	0.0391043i
$996$	9.03812	+	19.3389i	0.286384	+	0.612777i
$997$	12.8874	−	22.3216i	0.408148	−	0.706934i	−0.586534	−	0.809925i	$-0.699508\pi$
$997$	12.8874	−	22.3216i	0.408148	−	0.706934i	0.994682	+	0.102991i	$0.0328413\pi$
$998$	−41.7464			−1.32146
$999$	0.797813	+	0.211571i	0.0252417	+	0.00669382i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.i.g.196.11	✓	26
3.2	odd	2		1755.2.i.g.586.3		26
9.2	odd	6		5265.2.a.bh.1.11		13
9.4	even	3	inner	585.2.i.g.391.11	yes	26
9.5	odd	6		1755.2.i.g.1171.3		26
9.7	even	3		5265.2.a.bg.1.3		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.g.196.11	✓	26	1.1	even	1	trivial
585.2.i.g.391.11	yes	26	9.4	even	3	inner
1755.2.i.g.586.3		26	3.2	odd	2
1755.2.i.g.1171.3		26	9.5	odd	6
5265.2.a.bg.1.3		13	9.7	even	3
5265.2.a.bh.1.11		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)

\(f(q)\)	\(=\)	\(q+(0.853509 - 1.47832i) q^{2} +(0.733344 + 1.56914i) q^{3} +(-0.456955 - 0.791470i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.94561 + 0.255158i) q^{6} +(1.35209 - 2.34188i) q^{7} +1.85397 q^{8} +(-1.92441 + 2.30144i) q^{9} +O(q^{10})\)	\(q+(0.853509 - 1.47832i) q^{2} +(0.733344 + 1.56914i) q^{3} +(-0.456955 - 0.791470i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.94561 + 0.255158i) q^{6} +(1.35209 - 2.34188i) q^{7} +1.85397 q^{8} +(-1.92441 + 2.30144i) q^{9} -1.70702 q^{10} +(0.781129 - 1.35295i) q^{11} +(0.906822 - 1.29745i) q^{12} +(0.500000 + 0.866025i) q^{13} +(-2.30804 - 3.99764i) q^{14} +(0.992244 - 1.41967i) q^{15} +(2.49629 - 4.32371i) q^{16} -1.05862 q^{17} +(1.75977 + 4.80920i) q^{18} +5.32455 q^{19} +(-0.456955 + 0.791470i) q^{20} +(4.66630 + 0.404209i) q^{21} +(-1.33340 - 2.30952i) q^{22} +(0.295081 + 0.511096i) q^{23} +(1.35960 + 2.90915i) q^{24} +(-0.500000 + 0.866025i) q^{25} +1.70702 q^{26} +(-5.02255 - 1.33193i) q^{27} -2.47137 q^{28} +(-2.16555 + 3.75085i) q^{29} +(-1.25183 - 2.67855i) q^{30} +(1.16135 + 2.01151i) q^{31} +(-2.40724 - 4.16947i) q^{32} +(2.69581 + 0.233520i) q^{33} +(-0.903544 + 1.56498i) q^{34} -2.70418 q^{35} +(2.70089 + 0.471457i) q^{36} -0.158846 q^{37} +(4.54455 - 7.87139i) q^{38} +(-0.992244 + 1.41967i) q^{39} +(-0.926987 - 1.60559i) q^{40} +(-0.609700 - 1.05603i) q^{41} +(4.58028 - 6.55329i) q^{42} +(0.0815831 - 0.141306i) q^{43} -1.42776 q^{44} +(2.95531 + 0.515868i) q^{45} +1.00742 q^{46} +(3.73480 - 6.46886i) q^{47} +(8.61516 + 0.746272i) q^{48} +(-0.156283 - 0.270690i) q^{49} +(0.853509 + 1.47832i) q^{50} +(-0.776335 - 1.66113i) q^{51} +(0.456955 - 0.791470i) q^{52} -12.3871 q^{53} +(-6.25580 + 6.28813i) q^{54} -1.56226 q^{55} +(2.50674 - 4.34179i) q^{56} +(3.90473 + 8.35497i) q^{57} +(3.69664 + 6.40276i) q^{58} +(-2.45185 - 4.24674i) q^{59} +(-1.57703 - 0.136608i) q^{60} +(-3.71783 + 6.43947i) q^{61} +3.96488 q^{62} +(2.78774 + 7.61850i) q^{63} +1.76676 q^{64} +(0.500000 - 0.866025i) q^{65} +(2.64612 - 3.78597i) q^{66} +(-0.676472 - 1.17168i) q^{67} +(0.483743 + 0.837867i) q^{68} +(-0.585586 + 0.837834i) q^{69} +(-2.30804 + 3.99764i) q^{70} -15.9401 q^{71} +(-3.56781 + 4.26682i) q^{72} +2.78604 q^{73} +(-0.135577 + 0.234826i) q^{74} +(-1.72559 - 0.149476i) q^{75} +(-2.43308 - 4.21422i) q^{76} +(-2.11231 - 3.65863i) q^{77} +(1.25183 + 2.67855i) q^{78} +(-3.90562 + 6.76474i) q^{79} -4.99259 q^{80} +(-1.59328 - 8.85785i) q^{81} -2.08154 q^{82} +(-6.74274 + 11.6788i) q^{83} +(-1.81237 - 3.87794i) q^{84} +(0.529311 + 0.916794i) q^{85} +(-0.139264 - 0.241212i) q^{86} +(-7.47371 - 0.647396i) q^{87} +(1.44819 - 2.50834i) q^{88} -8.37469 q^{89} +(3.28501 - 3.92860i) q^{90} +2.70418 q^{91} +(0.269678 - 0.467096i) q^{92} +(-2.30468 + 3.29745i) q^{93} +(-6.37537 - 11.0425i) q^{94} +(-2.66228 - 4.61120i) q^{95} +(4.77715 - 6.83497i) q^{96} +(-6.15231 + 10.6561i) q^{97} -0.533556 q^{98} +(1.61053 + 4.40136i) 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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