LMFDB - Embedded newform 585.2.k.a.61.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(61,585)]

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, 4]))

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

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

chi := DirichletCharacter("585.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.k (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:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			61.2
Character	$\chi$	$=$	585.61
Dual form			585.2.k.a.211.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30568 - 2.26150i) q^{2} +(1.68776 - 0.389194i) q^{3} +(-2.40958 + 4.17352i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-3.08383 - 3.30870i) q^{6} -1.51841 q^{7} +7.36184 q^{8} +(2.69706 - 1.31373i) q^{9} +O(q^{10})$	\(q+(-1.30568 - 2.26150i) q^{2} +(1.68776 - 0.389194i) q^{3} +(-2.40958 + 4.17352i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-3.08383 - 3.30870i) q^{6} -1.51841 q^{7} +7.36184 q^{8} +(2.69706 - 1.31373i) q^{9} +(1.30568 - 2.26150i) q^{10} +(1.10811 + 1.91931i) q^{11} +(-2.44248 + 7.98169i) q^{12} +(1.72140 - 3.16809i) q^{13} +(1.98255 + 3.43388i) q^{14} +(1.18093 + 1.26704i) q^{15} +(-4.79302 - 8.30176i) q^{16} +(3.89453 + 6.74552i) q^{17} +(-6.49248 - 4.38408i) q^{18} +(1.35650 + 2.34953i) q^{19} -4.81917 q^{20} +(-2.56271 + 0.590956i) q^{21} +(2.89367 - 5.01199i) q^{22} +4.82428 q^{23} +(12.4250 - 2.86519i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-9.41222 + 0.243552i) q^{26} +(4.04068 - 3.26694i) q^{27} +(3.65874 - 6.33712i) q^{28} +(-2.73933 - 4.74467i) q^{29} +(1.32350 - 4.32502i) q^{30} +(-3.21109 - 5.56177i) q^{31} +(-5.15443 + 8.92773i) q^{32} +(2.61721 + 2.80805i) q^{33} +(10.1700 - 17.6149i) q^{34} +(-0.759205 - 1.31498i) q^{35} +(-1.01590 + 14.4218i) q^{36} +(3.67149 - 6.35920i) q^{37} +(3.54230 - 6.13545i) q^{38} +(1.67231 - 6.01692i) q^{39} +(3.68092 + 6.37554i) q^{40} +0.650503 q^{41} +(4.68252 + 5.02396i) q^{42} +4.61852 q^{43} -10.6804 q^{44} +(2.48625 + 1.67885i) q^{45} +(-6.29896 - 10.9101i) q^{46} +(-5.92305 + 10.2590i) q^{47} +(-11.3205 - 12.1459i) q^{48} -4.69443 q^{49} +2.61135 q^{50} +(9.19834 + 9.86908i) q^{51} +(9.07422 + 14.8181i) q^{52} +10.3886 q^{53} +(-12.6640 - 4.87243i) q^{54} +(-1.10811 + 1.91931i) q^{55} -11.1783 q^{56} +(3.20387 + 3.43749i) q^{57} +(-7.15337 + 12.3900i) q^{58} +(2.82979 - 4.90134i) q^{59} +(-8.13359 + 1.87559i) q^{60} +3.88662 q^{61} +(-8.38529 + 14.5238i) q^{62} +(-4.09524 + 1.99478i) q^{63} +7.74799 q^{64} +(3.60434 - 0.0932665i) q^{65} +(2.93318 - 9.58522i) q^{66} -8.97657 q^{67} -37.5368 q^{68} +(8.14223 - 1.87758i) q^{69} +(-1.98255 + 3.43388i) q^{70} +(-4.14295 - 7.17580i) q^{71} +(19.8553 - 9.67148i) q^{72} -0.623359 q^{73} -19.1751 q^{74} +(-0.506827 + 1.65624i) q^{75} -13.0744 q^{76} +(-1.68257 - 2.91429i) q^{77} +(-15.7908 + 4.07424i) q^{78} +(-4.98663 + 8.63709i) q^{79} +(4.79302 - 8.30176i) q^{80} +(5.54822 - 7.08641i) q^{81} +(-0.849347 - 1.47111i) q^{82} +(3.10033 - 5.36992i) q^{83} +(3.70869 - 12.1195i) q^{84} +(-3.89453 + 6.74552i) q^{85} +(-6.03030 - 10.4448i) q^{86} +(-6.46993 - 6.94172i) q^{87} +(8.15775 + 14.1296i) q^{88} +(-4.35969 + 7.55120i) q^{89} +(0.550482 - 7.81470i) q^{90} +(-2.61379 + 4.81046i) q^{91} +(-11.6245 + 20.1343i) q^{92} +(-7.58416 - 8.13719i) q^{93} +30.9344 q^{94} +(-1.35650 + 2.34953i) q^{95} +(-5.22481 + 17.0739i) q^{96} +5.36548 q^{97} +(6.12941 + 10.6164i) q^{98} +(5.51009 + 3.72072i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - q^{3} - 28 q^{4} + 28 q^{5} + 2 q^{6} - 12 q^{7} + 6 q^{8} + 5 q^{9}+O(q^{10}) $ 56 * q - q^3 - 28 * q^4 + 28 * q^5 + 2 * q^6 - 12 * q^7 + 6 * q^8 + 5 * q^9	\( 56 q - q^{3} - 28 q^{4} + 28 q^{5} + 2 q^{6} - 12 q^{7} + 6 q^{8} + 5 q^{9} + 2 q^{11} - 10 q^{12} - 2 q^{13} - 2 q^{15} - 36 q^{16} - 5 q^{17} - 7 q^{18} + 19 q^{19} - 56 q^{20} + 17 q^{21} + 24 q^{23} + 12 q^{24} - 28 q^{25} + 2 q^{26} - 16 q^{27} + 21 q^{28} - q^{29} + q^{30} + 20 q^{31} - 6 q^{32} - 12 q^{33} + 2 q^{34} - 6 q^{35} - 20 q^{36} + 17 q^{37} - 2 q^{38} + 3 q^{39} + 3 q^{40} + 4 q^{41} - 11 q^{42} - 8 q^{43} - 56 q^{44} + 7 q^{45} + 20 q^{46} - 15 q^{47} + 86 q^{48} + 48 q^{49} + 10 q^{51} + 43 q^{52} + 32 q^{53} + 50 q^{54} - 2 q^{55} + 40 q^{56} + 5 q^{57} + 48 q^{58} + 10 q^{59} + q^{60} - 14 q^{61} - 25 q^{62} - 51 q^{63} + 106 q^{64} - q^{65} + 7 q^{66} - 96 q^{67} + 50 q^{68} + 14 q^{69} - 6 q^{71} - 21 q^{72} - 62 q^{73} + 20 q^{74} - q^{75} - 88 q^{76} - 34 q^{77} - 2 q^{78} + 10 q^{79} + 36 q^{80} - 7 q^{81} - q^{82} + 9 q^{83} - 51 q^{84} + 5 q^{85} - 69 q^{86} - 61 q^{87} + 19 q^{88} + 10 q^{89} + 19 q^{90} - 26 q^{91} + 14 q^{92} - 59 q^{93} + 52 q^{94} - 19 q^{95} - 76 q^{96} - 34 q^{97} + 24 q^{98} + q^{99}+O(q^{100}) \) 56 * q - q^3 - 28 * q^4 + 28 * q^5 + 2 * q^6 - 12 * q^7 + 6 * q^8 + 5 * q^9 + 2 * q^11 - 10 * q^12 - 2 * q^13 - 2 * q^15 - 36 * q^16 - 5 * q^17 - 7 * q^18 + 19 * q^19 - 56 * q^20 + 17 * q^21 + 24 * q^23 + 12 * q^24 - 28 * q^25 + 2 * q^26 - 16 * q^27 + 21 * q^28 - q^29 + q^30 + 20 * q^31 - 6 * q^32 - 12 * q^33 + 2 * q^34 - 6 * q^35 - 20 * q^36 + 17 * q^37 - 2 * q^38 + 3 * q^39 + 3 * q^40 + 4 * q^41 - 11 * q^42 - 8 * q^43 - 56 * q^44 + 7 * q^45 + 20 * q^46 - 15 * q^47 + 86 * q^48 + 48 * q^49 + 10 * q^51 + 43 * q^52 + 32 * q^53 + 50 * q^54 - 2 * q^55 + 40 * q^56 + 5 * q^57 + 48 * q^58 + 10 * q^59 + q^60 - 14 * q^61 - 25 * q^62 - 51 * q^63 + 106 * q^64 - q^65 + 7 * q^66 - 96 * q^67 + 50 * q^68 + 14 * q^69 - 6 * q^71 - 21 * q^72 - 62 * q^73 + 20 * q^74 - q^75 - 88 * q^76 - 34 * q^77 - 2 * q^78 + 10 * q^79 + 36 * q^80 - 7 * q^81 - q^82 + 9 * q^83 - 51 * q^84 + 5 * q^85 - 69 * q^86 - 61 * q^87 + 19 * q^88 + 10 * q^89 + 19 * q^90 - 26 * q^91 + 14 * q^92 - 59 * q^93 + 52 * q^94 - 19 * q^95 - 76 * q^96 - 34 * q^97 + 24 * q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.30568	−	2.26150i	−0.923253	−	1.59912i	−0.794347	−	0.607464i	$-0.792187\pi$
$2$	−1.30568	−	2.26150i	−0.923253	−	1.59912i	−0.128906	−	0.991657i	$-0.541146\pi$
$3$	1.68776	−	0.389194i	0.974428	−	0.224701i
$3$	1.68776	−	0.389194i	0.974428	−	0.224701i
$4$	−2.40958	+	4.17352i	−1.20479	+	2.08676i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−3.08383	−	3.30870i	−1.25897	−	1.35077i
$7$	−1.51841			−0.573905			−0.286953	−	0.957945i	$-0.592642\pi$
$7$	−1.51841			−0.573905			−0.286953	+	0.957945i	$0.592642\pi$
$8$	7.36184			2.60280
$9$	2.69706	−	1.31373i	0.899019	−	0.437910i
$10$	1.30568	−	2.26150i	0.412891	−	0.715149i
$11$	1.10811	+	1.91931i	0.334108	+	0.578693i	0.983313	−	0.181921i	$-0.0582315\pi$
$11$	1.10811	+	1.91931i	0.334108	+	0.578693i	−0.649205	+	0.760614i	$0.724898\pi$
$12$	−2.44248	+	7.98169i	−0.705085	+	2.30412i
$13$	1.72140	−	3.16809i	0.477431	−	0.878669i
$13$	1.72140	−	3.16809i	0.477431	−	0.878669i
$14$	1.98255	+	3.43388i	0.529860	+	0.917744i
$15$	1.18093	+	1.26704i	0.304915	+	0.327149i
$16$	−4.79302	−	8.30176i	−1.19826	−	2.07544i
$17$	3.89453	+	6.74552i	0.944562	+	1.63603i	0.756625	+	0.653849i	$0.226847\pi$
$17$	3.89453	+	6.74552i	0.944562	+	1.63603i	0.187937	+	0.982181i	$0.439820\pi$
$18$	−6.49248	−	4.38408i	−1.53029	−	1.03334i
$19$	1.35650	+	2.34953i	0.311203	+	0.539019i	0.978623	−	0.205662i	$-0.0659348\pi$
$19$	1.35650	+	2.34953i	0.311203	+	0.539019i	−0.667420	+	0.744681i	$0.732602\pi$
$20$	−4.81917			−1.07760
$21$	−2.56271	+	0.590956i	−0.559229	+	0.128957i
$22$	2.89367	−	5.01199i	0.616933	−	1.06856i
$23$	4.82428			1.00593			0.502966	−	0.864306i	$-0.332242\pi$
$23$	4.82428			1.00593			0.502966	+	0.864306i	$0.332242\pi$
$24$	12.4250	−	2.86519i	2.53625	−	0.584854i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−9.41222	+	0.243552i	−1.84589	+	0.0477644i
$27$	4.04068	−	3.26694i	0.777630	−	0.628723i
$28$	3.65874	−	6.33712i	0.691436	−	1.19760i
$29$	−2.73933	−	4.74467i	−0.508682	−	0.881062i	−0.999949	−	0.0100538i	$-0.996800\pi$
$29$	−2.73933	−	4.74467i	−0.508682	−	0.881062i	0.491268	−	0.871009i	$-0.336534\pi$
$30$	1.32350	−	4.32502i	0.241638	−	0.789638i
$31$	−3.21109	−	5.56177i	−0.576729	−	0.998924i	−0.995851	−	0.0909942i	$-0.970996\pi$
$31$	−3.21109	−	5.56177i	−0.576729	−	0.998924i	0.419122	−	0.907930i	$-0.362338\pi$
$32$	−5.15443	+	8.92773i	−0.911183	+	1.57822i
$33$	2.61721	+	2.80805i	0.455597	+	0.488820i
$34$	10.1700	−	17.6149i	1.74414	−	3.02094i
$35$	−0.759205	−	1.31498i	−0.128329	−	0.222272i
$36$	−1.01590	+	14.4218i	−0.169316	+	2.40363i
$37$	3.67149	−	6.35920i	0.603589	−	1.04545i	−0.388684	−	0.921371i	$-0.627070\pi$
$37$	3.67149	−	6.35920i	0.603589	−	1.04545i	0.992273	−	0.124075i	$-0.0395965\pi$
$38$	3.54230	−	6.13545i	0.574638	−	0.995302i
$39$	1.67231	−	6.01692i	0.267784	−	0.963479i
$40$	3.68092	+	6.37554i	0.582005	+	1.00806i
$41$	0.650503			0.101591			0.0507957	−	0.998709i	$-0.483824\pi$
$41$	0.650503			0.101591			0.0507957	+	0.998709i	$0.483824\pi$
$42$	4.68252	+	5.02396i	0.722528	+	0.775215i
$43$	4.61852			0.704318			0.352159	−	0.935940i	$-0.385448\pi$
$43$	4.61852			0.704318			0.352159	+	0.935940i	$0.385448\pi$
$44$	−10.6804			−1.61012
$45$	2.48625	+	1.67885i	0.370629	+	0.250269i
$46$	−6.29896	−	10.9101i	−0.928730	−	1.60861i
$47$	−5.92305	+	10.2590i	−0.863966	+	1.49643i	0.00410421	+	0.999992i	$0.498694\pi$
$47$	−5.92305	+	10.2590i	−0.863966	+	1.49643i	−0.868070	+	0.496441i	$0.834640\pi$
$48$	−11.3205	−	12.1459i	−1.63397	−	1.75312i
$49$	−4.69443			−0.670633
$50$	2.61135			0.369301
$51$	9.19834	+	9.86908i	1.28803	+	1.38195i
$52$	9.07422	+	14.8181i	1.25837	+	2.05490i
$53$	10.3886			1.42699			0.713494	−	0.700661i	$-0.247111\pi$
$53$	10.3886			1.42699			0.713494	+	0.700661i	$0.247111\pi$
$54$	−12.6640	−	4.87243i	−1.72335	−	0.663054i
$55$	−1.10811	+	1.91931i	−0.149418	+	0.258799i
$56$	−11.1783			−1.49376
$57$	3.20387	+	3.43749i	0.424363	+	0.455307i
$58$	−7.15337	+	12.3900i	−0.939284	+	1.62689i
$59$	2.82979	−	4.90134i	0.368407	−	0.638100i	−0.620910	−	0.783882i	$-0.713237\pi$
$59$	2.82979	−	4.90134i	0.368407	−	0.638100i	0.989317	+	0.145782i	$0.0465699\pi$
$60$	−8.13359	+	1.87559i	−1.05004	+	0.242138i
$61$	3.88662			0.497631			0.248815	−	0.968551i	$-0.419959\pi$
$61$	3.88662			0.497631			0.248815	+	0.968551i	$0.419959\pi$
$62$	−8.38529	+	14.5238i	−1.06493	+	1.84452i
$63$	−4.09524	+	1.99478i	−0.515951	+	0.251319i
$64$	7.74799			0.968499
$65$	3.60434	−	0.0932665i	0.447064	−	0.0115683i
$66$	2.93318	−	9.58522i	0.361050	−	1.17986i
$67$	−8.97657			−1.09666			−0.548331	−	0.836261i	$-0.684737\pi$
$67$	−8.97657			−1.09666			−0.548331	+	0.836261i	$0.684737\pi$
$68$	−37.5368			−4.55200
$69$	8.14223	−	1.87758i	0.980209	−	0.226034i
$70$	−1.98255	+	3.43388i	−0.236960	+	0.410427i
$71$	−4.14295	−	7.17580i	−0.491678	−	0.851611i	0.508276	−	0.861194i	$-0.330283\pi$
$71$	−4.14295	−	7.17580i	−0.491678	−	0.851611i	−0.999954	+	0.00958321i	$0.996950\pi$
$72$	19.8553	−	9.67148i	2.33997	−	1.13980i
$73$	−0.623359			−0.0729586			−0.0364793	−	0.999334i	$-0.511614\pi$
$73$	−0.623359			−0.0729586			−0.0364793	+	0.999334i	$0.511614\pi$
$74$	−19.1751			−2.22906
$75$	−0.506827	+	1.65624i	−0.0585234	+	0.191246i
$76$	−13.0744			−1.49974
$77$	−1.68257	−	2.91429i	−0.191746	−	0.332115i
$78$	−15.7908	+	4.07424i	−1.78795	+	0.461317i
$79$	−4.98663	+	8.63709i	−0.561039	+	0.971748i	0.436367	+	0.899769i	$0.356265\pi$
$79$	−4.98663	+	8.63709i	−0.561039	+	0.971748i	−0.997406	+	0.0719796i	$0.977068\pi$
$80$	4.79302	−	8.30176i	0.535876	−	0.928165i
$81$	5.54822	−	7.08641i	0.616469	−	0.787379i
$82$	−0.849347	−	1.47111i	−0.0937946	−	0.162457i
$83$	3.10033	−	5.36992i	0.340305	−	0.589426i	−0.644184	−	0.764870i	$-0.722803\pi$
$83$	3.10033	−	5.36992i	0.340305	−	0.589426i	0.984489	+	0.175445i	$0.0561363\pi$
$84$	3.70869	−	12.1195i	0.404652	−	1.32234i
$85$	−3.89453	+	6.74552i	−0.422421	+	0.731655i
$86$	−6.03030	−	10.4448i	−0.650264	−	1.12629i
$87$	−6.46993	−	6.94172i	−0.693649	−	0.744230i
$88$	8.15775	+	14.1296i	0.869619	+	1.50622i
$89$	−4.35969	+	7.55120i	−0.462126	+	0.800426i	−0.999067	−	0.0431941i	$-0.986247\pi$
$89$	−4.35969	+	7.55120i	−0.462126	+	0.800426i	0.536941	+	0.843620i	$0.319580\pi$
$90$	0.550482	−	7.81470i	0.0580259	−	0.823741i
$91$	−2.61379	+	4.81046i	−0.274000	+	0.504273i
$92$	−11.6245	+	20.1343i	−1.21194	+	2.09914i
$93$	−7.58416	−	8.13719i	−0.786440	−	0.843787i
$94$	30.9344			3.19064
$95$	−1.35650	+	2.34953i	−0.139174	+	0.241057i
$96$	−5.22481	+	17.0739i	−0.533255	+	1.74260i
$97$	5.36548			0.544782			0.272391	−	0.962187i	$-0.412186\pi$
$97$	5.36548			0.544782			0.272391	+	0.962187i	$0.412186\pi$
$98$	6.12941	+	10.6164i	0.619164	+	1.07242i
$99$	5.51009	+	3.72072i	0.553785	+	0.373946i
$100$	−2.40958	−	4.17352i	−0.240958	−	0.417352i
$101$	8.61787	+	14.9266i	0.857510	+	1.48525i	0.874297	+	0.485392i	$0.161323\pi$
$101$	8.61787	+	14.9266i	0.857510	+	1.48525i	−0.0167863	+	0.999859i	$0.505344\pi$
$102$	10.3089	−	33.6879i	1.02073	−	3.33560i
$103$	0.886219	+	1.53498i	0.0873218	+	0.151246i	0.906378	−	0.422467i	$-0.138836\pi$
$103$	0.886219	+	1.53498i	0.0873218	+	0.151246i	−0.819056	+	0.573713i	$0.805503\pi$
$104$	12.6727	−	23.3230i	1.24266	−	2.28700i
$105$	−1.79314	−	1.92389i	−0.174992	−	0.187753i
$106$	−13.5642	−	23.4939i	−1.31747	−	2.28193i
$107$	−3.42653	+	5.93492i	−0.331255	+	0.573750i	−0.982758	−	0.184896i	$-0.940805\pi$
$107$	−3.42653	+	5.93492i	−0.331255	+	0.573750i	0.651503	+	0.758646i	$0.274139\pi$
$108$	3.89828	+	24.7358i	0.375112	+	2.38021i
$109$	−10.0955			−0.966972			−0.483486	−	0.875352i	$-0.660630\pi$
$109$	−10.0955			−0.966972			−0.483486	+	0.875352i	$0.660630\pi$
$110$	5.78734			0.551802
$111$	3.72162	−	12.1617i	0.353240	−	1.15434i
$112$	7.27777	+	12.6055i	0.687685	+	1.19110i
$113$	−0.450054	+	0.779517i	−0.0423376	+	0.0733308i	−0.886418	−	0.462886i	$-0.846814\pi$
$113$	−0.450054	+	0.779517i	−0.0423376	+	0.0733308i	0.844080	+	0.536217i	$0.180147\pi$
$114$	3.59067	−	11.7338i	0.336297	−	1.09897i
$115$	2.41214	+	4.17795i	0.224933	+	0.389596i
$116$	26.4026			2.45142
$117$	0.480700	−	10.8060i	0.0444407	−	0.999012i
$118$	−14.7792			−1.36053
$119$	−5.91349	−	10.2425i	−0.542089	−	0.938926i
$120$	8.69383	+	9.32778i	0.793635	+	0.851506i
$121$	3.04418	−	5.27267i	0.276743	−	0.479333i
$122$	−5.07467	−	8.78959i	−0.459439	−	0.795772i
$123$	1.09789	−	0.253172i	0.0989936	−	0.0228277i
$124$	30.9496			2.77935
$125$	−1.00000			−0.0894427
$126$	9.85825	+	6.65683i	0.878243	+	0.593038i
$127$	0.852752	−	1.47701i	0.0756695	−	0.131063i	−0.825708	−	0.564098i	$-0.809224\pi$
$127$	0.852752	−	1.47701i	0.0756695	−	0.131063i	0.901377	+	0.433035i	$0.142557\pi$
$128$	0.192485	+	0.333394i	0.0170135	+	0.0294682i
$129$	7.79495	−	1.79750i	0.686307	−	0.158261i
$130$	−4.91703	−	8.02944i	−0.431252	−	0.704229i
$131$	8.45193	+	14.6392i	0.738448	+	1.27903i	0.953194	+	0.302360i	$0.0977745\pi$
$131$	8.45193	+	14.6392i	0.738448	+	1.27903i	−0.214746	+	0.976670i	$0.568892\pi$
$132$	−18.0259	+	4.15673i	−1.56895	+	0.361797i
$133$	−2.05973	−	3.56755i	−0.178601	−	0.309346i
$134$	11.7205	+	20.3005i	1.01250	+	1.75370i
$135$	4.84959	+	1.86586i	0.417387	+	0.160588i
$136$	28.6709	+	49.6595i	2.45851	+	4.25827i
$137$	−12.7126			−1.08611			−0.543054	−	0.839698i	$-0.682732\pi$
$137$	−12.7126			−1.08611			−0.543054	+	0.839698i	$0.682732\pi$
$138$	−14.8773	−	15.9621i	−1.26644	−	1.35879i
$139$	−3.96645	+	6.87009i	−0.336430	+	0.582714i	−0.983758	−	0.179497i	$-0.942553\pi$
$139$	−3.96645	+	6.87009i	−0.336430	+	0.582714i	0.647329	+	0.762211i	$0.275886\pi$
$140$	7.31747			0.618439
$141$	−6.00393	+	19.6200i	−0.505622	+	1.65230i
$142$	−10.8187	+	18.7386i	−0.907886	+	1.57250i
$143$	7.98804	−	0.206699i	0.667993	−	0.0172851i
$144$	−23.8333	−	16.0936i	−1.98611	−	1.34113i
$145$	2.73933	−	4.74467i	0.227489	−	0.394023i
$146$	0.813905	+	1.40972i	0.0673593	+	0.116670i
$147$	−7.92306	+	1.82705i	−0.653483	+	0.150692i
$148$	17.6935	+	30.6461i	1.45440	+	2.51909i
$149$	4.82098	−	8.35019i	0.394950	−	0.684074i	−0.598144	−	0.801388i	$-0.704095\pi$
$149$	4.82098	−	8.35019i	0.394950	−	0.684074i	0.993095	+	0.117314i	$0.0374284\pi$
$150$	4.40733	−	1.01632i	0.359857	−	0.0829825i
$151$	−0.0663036	+	0.114841i	−0.00539571	+	0.00934565i	−0.868711	−	0.495320i	$-0.835051\pi$
$151$	−0.0663036	+	0.114841i	−0.00539571	+	0.00934565i	0.863315	+	0.504666i	$0.168384\pi$
$152$	9.98635	+	17.2969i	0.810000	+	1.40296i
$153$	19.3656	+	13.0767i	1.56561	+	1.05719i
$154$	−4.39378	+	7.61025i	−0.354061	+	0.613252i
$155$	3.21109	−	5.56177i	0.257921	−	0.446732i
$156$	21.0822	+	21.4777i	1.68793	+	1.71959i
$157$	−7.97470	−	13.8126i	−0.636450	−	1.10236i	−0.986206	−	0.165523i	$-0.947069\pi$
$157$	−7.97470	−	13.8126i	−0.636450	−	1.10236i	0.349756	−	0.936841i	$-0.386265\pi$
$158$	26.0437			2.07192
$159$	17.5335	−	4.04320i	1.39050	−	0.320646i
$160$	−10.3089			−0.814987
$161$	−7.32524			−0.577310
$162$	−23.2701	−	3.29473i	−1.82827	−	0.258858i
$163$	6.42632	+	11.1307i	0.503348	+	0.871824i	0.999993	+	0.00387008i	$0.00123189\pi$
$163$	6.42632	+	11.1307i	0.503348	+	0.871824i	−0.496645	+	0.867954i	$0.665435\pi$
$164$	−1.56744	+	2.71489i	−0.122397	+	0.211997i
$165$	−1.12324	+	3.67060i	−0.0874443	+	0.285756i
$166$	−16.1921			−1.25675
$167$	10.5438			0.815900			0.407950	−	0.913004i	$-0.366244\pi$
$167$	10.5438			0.815900			0.407950	+	0.913004i	$0.366244\pi$
$168$	−18.8663	+	4.35053i	−1.45556	+	0.335651i
$169$	−7.07356	−	10.9071i	−0.544120	−	0.839008i
$170$	20.3400			1.56001
$171$	6.74521	+	4.55473i	0.515819	+	0.348309i
$172$	−11.1287	+	19.2755i	−0.848557	+	1.46974i
$173$	−16.2583			−1.23609			−0.618047	−	0.786141i	$-0.712076\pi$
$173$	−16.2583			−1.23609			−0.618047	+	0.786141i	$0.712076\pi$
$174$	−7.25104	+	23.6954i	−0.549700	+	1.79634i
$175$	0.759205	−	1.31498i	0.0573905	−	0.0994033i
$176$	10.6224	−	18.3986i	0.800694	−	1.38684i
$177$	2.86843	−	9.37361i	0.215604	−	0.704564i
$178$	22.7694			1.70664
$179$	3.44039	−	5.95893i	0.257147	−	0.445391i	−0.708330	−	0.705882i	$-0.750551\pi$
$179$	3.44039	−	5.95893i	0.257147	−	0.445391i	0.965476	+	0.260490i	$0.0838843\pi$
$180$	−12.9976	+	6.33109i	−0.968781	+	0.471892i
$181$	1.95012			0.144951			0.0724757	−	0.997370i	$-0.476910\pi$
$181$	1.95012			0.144951			0.0724757	+	0.997370i	$0.476910\pi$
$182$	14.2916	−	0.369811i	1.05936	−	0.0274123i
$183$	6.55968	−	1.51265i	0.484905	−	0.111818i
$184$	35.5156			2.61825
$185$	7.34298			0.539866
$186$	−8.49979	+	27.7761i	−0.623235	+	2.03664i
$187$	−8.63115	+	14.9496i	−0.631172	+	1.09322i
$188$	−28.5442	−	49.4400i	−2.08180	−	3.60578i
$189$	−6.13541	+	4.96055i	−0.446286	+	0.360827i
$190$	7.08461			0.513972
$191$	−21.5402			−1.55859			−0.779297	−	0.626655i	$-0.784424\pi$
$191$	−21.5402			−1.55859			−0.779297	+	0.626655i	$0.784424\pi$
$192$	13.0767	−	3.01547i	0.943732	−	0.217623i
$193$	−5.00867			−0.360532			−0.180266	−	0.983618i	$-0.557696\pi$
$193$	−5.00867			−0.360532			−0.180266	+	0.983618i	$0.557696\pi$
$194$	−7.00559	−	12.1340i	−0.502972	−	0.871173i
$195$	6.04696	−	1.56020i	0.433032	−	0.111728i
$196$	11.3116	−	19.5923i	0.807973	−	1.39945i
$197$	12.6479	−	21.9068i	0.901127	−	1.56080i	0.0750929	−	0.997177i	$-0.476075\pi$
$197$	12.6479	−	21.9068i	0.901127	−	1.56080i	0.826034	−	0.563621i	$-0.190592\pi$
$198$	1.21999	−	17.3191i	0.0867010	−	1.23082i
$199$	−7.83148	−	13.5645i	−0.555159	−	0.961563i	−0.997891	−	0.0649096i	$-0.979324\pi$
$199$	−7.83148	−	13.5645i	−0.555159	−	0.961563i	0.442732	−	0.896654i	$-0.354009\pi$
$200$	−3.68092	+	6.37554i	−0.260280	+	0.450819i
$201$	−15.1503	+	3.49363i	−1.06862	+	0.246422i
$202$	22.5043	−	38.9786i	1.58340	−	2.74253i
$203$	4.15943	+	7.20435i	0.291935	+	0.505646i
$204$	−63.3530	+	14.6091i	−4.43560	+	1.02284i
$205$	0.325251	+	0.563352i	0.0227165	+	0.0393462i
$206$	2.31423	−	4.00837i	0.161240	−	0.279276i
$207$	13.0114	−	6.33781i	0.904352	−	0.440508i
$208$	−34.5514	+	0.894057i	−2.39571	+	0.0619917i
$209$	−3.00631	+	5.20708i	−0.207951	+	0.360181i
$210$	−2.00962	+	6.56716i	−0.138677	+	0.453177i
$211$	−16.2810			−1.12083			−0.560414	−	0.828212i	$-0.689358\pi$
$211$	−16.2810			−1.12083			−0.560414	+	0.828212i	$0.689358\pi$
$212$	−25.0323	+	43.3572i	−1.71922	+	2.97778i
$213$	−9.78508	−	10.4986i	−0.670462	−	0.719353i
$214$	17.8957			1.22333
$215$	2.30926	+	3.99976i	0.157490	+	0.272781i
$216$	29.7469	−	24.0507i	2.02402	−	1.63644i
$217$	4.87575	+	8.44505i	0.330988	+	0.573287i
$218$	13.1814	+	22.8309i	0.892760	+	1.54631i
$219$	−1.05208	+	0.242608i	−0.0710929	+	0.0163939i
$220$	−5.34018	−	9.24946i	−0.360035	−	0.623598i
$221$	28.0745	−	0.726458i	1.88849	−	0.0488669i
$222$	−32.3629	+	7.46284i	−2.17206	+	0.500873i
$223$	2.20096	+	3.81217i	0.147387	+	0.255282i	0.930261	−	0.366898i	$-0.119580\pi$
$223$	2.20096	+	3.81217i	0.147387	+	0.255282i	−0.782874	+	0.622180i	$0.786247\pi$
$224$	7.82654	−	13.5560i	0.522933	−	0.905746i
$225$	−0.210803	+	2.99258i	−0.0140536	+	0.199506i
$226$	2.35050			0.156353
$227$	−11.1168			−0.737847			−0.368923	−	0.929460i	$-0.620274\pi$
$227$	−11.1168			−0.737847			−0.368923	+	0.929460i	$0.620274\pi$
$228$	−22.0665	+	5.08849i	−1.46139	+	0.336993i
$229$	−9.46002	−	16.3852i	−0.625136	−	1.08277i	−0.988515	−	0.151125i	$-0.951710\pi$
$229$	−9.46002	−	16.3852i	−0.625136	−	1.08277i	0.363379	−	0.931641i	$-0.381623\pi$
$230$	6.29896	−	10.9101i	0.415341	−	0.719392i
$231$	−3.97399	−	4.26378i	−0.261470	−	0.280536i
$232$	−20.1666	−	34.9295i	−1.32400	−	2.29323i
$233$	−8.68243			−0.568805			−0.284402	−	0.958705i	$-0.591795\pi$
$233$	−8.68243			−0.568805			−0.284402	+	0.958705i	$0.591795\pi$
$234$	−25.0653	+	13.0220i	−1.63857	+	0.851275i
$235$	−11.8461			−0.772755
$236$	13.6372	+	23.6204i	0.887708	+	1.53755i
$237$	−5.05471	+	16.5181i	−0.328339	+	1.07296i
$238$	−15.4422	+	26.7467i	−1.00097	+	1.73373i
$239$	12.3481	+	21.3875i	0.798730	+	1.38344i	0.920443	+	0.390876i	$0.127828\pi$
$239$	12.3481	+	21.3875i	0.798730	+	1.38344i	−0.121713	+	0.992565i	$0.538839\pi$
$240$	4.85847	−	15.8768i	0.313613	−	1.02484i
$241$	−21.5308			−1.38692			−0.693461	−	0.720494i	$-0.743915\pi$
$241$	−21.5308			−1.38692			−0.693461	+	0.720494i	$0.743915\pi$
$242$	−15.8988			−1.02202
$243$	6.60606	−	14.1195i	0.423779	−	0.905766i
$244$	−9.36514	+	16.2209i	−0.599542	+	1.03844i
$245$	−2.34722	−	4.06550i	−0.149958	−	0.259735i
$246$	−2.00604	−	2.15232i	−0.127900	−	0.137227i
$247$	9.77860	−	0.253032i	0.622197	−	0.0161001i
$248$	−23.6396	−	40.9449i	−1.50111	−	2.60000i
$249$	3.14266	−	10.2698i	0.199158	−	0.650820i
$250$	1.30568	+	2.26150i	0.0825783	+	0.143030i
$251$	−11.8610	−	20.5439i	−0.748660	−	1.29672i	−0.948465	−	0.316881i	$-0.897364\pi$
$251$	−11.8610	−	20.5439i	−0.748660	−	1.29672i	0.199805	−	0.979836i	$-0.435969\pi$
$252$	1.54255	−	21.8982i	0.0971713	−	1.37945i
$253$	5.34585	+	9.25928i	0.336091	+	0.582126i
$254$	−4.45367			−0.279448
$255$	−3.94771	+	12.9005i	−0.247215	+	0.807863i
$256$	8.25064	−	14.2905i	0.515665	−	0.893158i
$257$	−14.7553			−0.920407			−0.460204	−	0.887813i	$-0.652224\pi$
$257$	−14.7553			−0.920407			−0.460204	+	0.887813i	$0.652224\pi$
$258$	−14.2427	−	15.2813i	−0.886714	−	0.951373i
$259$	−5.57482	+	9.65588i	−0.346403	+	0.599987i
$260$	−8.29572	+	15.2675i	−0.514479	+	0.946853i
$261$	−13.6214	−	9.19788i	−0.843141	−	0.569335i
$262$	22.0710	−	38.2280i	1.36355	−	2.36174i
$263$	1.15065	+	1.99299i	0.0709524	+	0.122893i	0.899319	−	0.437293i	$-0.144063\pi$
$263$	1.15065	+	1.99299i	0.0709524	+	0.122893i	−0.828367	+	0.560186i	$0.810729\pi$
$264$	19.2675	+	20.6725i	1.18583	+	1.27230i
$265$	5.19432	+	8.99682i	0.319084	+	0.552670i
$266$	−5.37867	+	9.31613i	−0.329787	+	0.571209i
$267$	−4.41922	+	14.4414i	−0.270452	+	0.883798i
$268$	21.6298	−	37.4639i	1.32125	−	2.28847i
$269$	11.3541	+	19.6658i	0.692269	+	1.19905i	0.971093	+	0.238703i	$0.0767223\pi$
$269$	11.3541	+	19.6658i	0.692269	+	1.19905i	−0.278823	+	0.960342i	$0.589944\pi$
$270$	−2.11235	−	13.4036i	−0.128554	−	0.815715i
$271$	−7.18044	+	12.4369i	−0.436181	+	0.755487i	−0.997391	−	0.0721858i	$-0.977003\pi$
$271$	−7.18044	+	12.4369i	−0.436181	+	0.755487i	0.561210	+	0.827673i	$0.310336\pi$
$272$	37.3331	−	64.6629i	2.26365	−	3.92076i
$273$	−2.53925	+	9.13616i	−0.153682	+	0.552945i
$274$	16.5985	+	28.7495i	1.00275	+	1.73682i
$275$	−2.21622			−0.133643
$276$	−11.7832	+	38.5060i	−0.709268	+	2.31779i
$277$	4.95002			0.297418			0.148709	−	0.988881i	$-0.452488\pi$
$277$	4.95002			0.297418			0.148709	+	0.988881i	$0.452488\pi$
$278$	20.7156			1.24244
$279$	−15.9672	−	10.7819i	−0.955929	−	0.645496i
$280$	−5.58915	−	9.68069i	−0.334016	−	0.578532i
$281$	−2.56975	+	4.45094i	−0.153298	+	0.265521i	−0.932438	−	0.361330i	$-0.882323\pi$
$281$	−2.56975	+	4.45094i	−0.153298	+	0.265521i	0.779140	+	0.626850i	$0.215656\pi$
$282$	52.2097	−	12.0395i	3.10904	−	0.716940i
$283$	7.93360			0.471603			0.235802	−	0.971801i	$-0.424228\pi$
$283$	7.93360			0.471603			0.235802	+	0.971801i	$0.424228\pi$
$284$	39.9311			2.36948
$285$	−1.37502	+	4.49338i	−0.0814494	+	0.266165i
$286$	−10.8972	−	17.7950i	−0.644368	−	1.05224i
$287$	−0.987730			−0.0583039
$288$	−2.17314	+	30.8501i	−0.128054	+	1.81786i
$289$	−21.8347	+	37.8189i	−1.28440	+	2.22464i
$290$	−14.3067			−0.840121
$291$	9.05564	−	2.08821i	0.530851	−	0.122413i
$292$	1.50204	−	2.60160i	0.0879000	−	0.152247i
$293$	−4.61817	+	7.99890i	−0.269796	+	0.467301i	−0.968809	−	0.247808i	$-0.920290\pi$
$293$	−4.61817	+	7.99890i	−0.269796	+	0.467301i	0.699013	+	0.715109i	$0.253623\pi$
$294$	14.4768	+	15.5325i	0.844305	+	0.905872i
$295$	5.65958			0.329513
$296$	27.0289	−	46.8155i	1.57102	−	2.72109i
$297$	10.7478	+	4.13517i	0.623650	+	0.239947i
$298$	−25.1786			−1.45856
$299$	8.30453	−	15.2838i	0.480263	−	0.883882i
$300$	−5.69111	−	6.10610i	−0.328576	−	0.352536i
$301$	−7.01281			−0.404212
$302$	0.346285			0.0199264
$303$	20.3542	+	21.8385i	1.16932	+	1.25459i
$304$	13.0035	−	22.5227i	0.745801	−	1.29176i
$305$	1.94331	+	3.36591i	0.111274	+	0.192732i
$306$	4.28774	−	60.8691i	0.245114	−	3.47966i
$307$	−17.4742			−0.997307			−0.498653	−	0.866801i	$-0.666172\pi$
$307$	−17.4742			−0.997307			−0.498653	+	0.866801i	$0.666172\pi$
$308$	16.2172			0.924058
$309$	2.09313	+	2.24576i	0.119074	+	0.127757i
$310$	−16.7706			−0.952505
$311$	−7.40231	−	12.8212i	−0.419746	−	0.727022i	0.576167	−	0.817332i	$-0.304548\pi$
$311$	−7.40231	−	12.8212i	−0.419746	−	0.727022i	−0.995914	+	0.0903097i	$0.971214\pi$
$312$	12.3113	−	44.2957i	0.696989	−	2.50775i
$313$	9.56555	−	16.5680i	0.540677	−	0.936480i	−0.458189	−	0.888855i	$-0.651502\pi$
$313$	9.56555	−	16.5680i	0.540677	−	0.936480i	0.998865	−	0.0476246i	$-0.0151651\pi$
$314$	−20.8248	+	36.0695i	−1.17521	+	2.03552i
$315$	−3.77515	−	2.54919i	−0.212706	−	0.143630i
$316$	−24.0314	−	41.6236i	−1.35187	−	2.34151i
$317$	14.2923	−	24.7550i	0.802737	−	1.39038i	−0.115071	−	0.993357i	$-0.536709\pi$
$317$	14.2923	−	24.7550i	0.802737	−	1.39038i	0.917808	−	0.397025i	$-0.129957\pi$
$318$	−32.0368	−	34.3729i	−1.79653	−	1.92754i
$319$	6.07098	−	10.5152i	0.339910	−	0.588741i
$320$	3.87400	+	6.70996i	0.216563	+	0.375098i
$321$	−3.47331	+	11.3503i	−0.193861	+	0.633511i
$322$	9.56440	+	16.5660i	0.533003	+	0.923188i
$323$	−10.5659	+	18.3006i	−0.587901	+	1.01827i
$324$	16.2064	+	40.2309i	0.900355	+	2.23505i
$325$	1.88294	+	3.07482i	0.104447	+	0.170560i
$326$	16.7814	−	29.0662i	0.929435	−	1.60983i
$327$	−17.0387	+	3.92910i	−0.942244	+	0.217280i
$328$	4.78890			0.264423
$329$	8.99362	−	15.5774i	0.495834	−	0.858810i
$330$	9.76764	−	2.25240i	0.537691	−	0.123991i
$331$	−27.4292			−1.50764			−0.753822	−	0.657078i	$-0.771792\pi$
$331$	−27.4292			−1.50764			−0.753822	+	0.657078i	$0.771792\pi$
$332$	14.9410	+	25.8786i	0.819994	+	1.42027i
$333$	1.54792	−	21.9745i	0.0848257	−	1.20419i
$334$	−13.7667	−	23.8447i	−0.753282	−	1.30472i
$335$	−4.48829	−	7.77394i	−0.245221	−	0.424736i
$336$	17.1891	+	18.4425i	0.937742	+	1.00612i
$337$	1.34610	+	2.33152i	0.0733268	+	0.127006i	0.900357	−	0.435151i	$-0.143305\pi$
$337$	1.34610	+	2.33152i	0.0733268	+	0.127006i	−0.827031	+	0.562157i	$0.809972\pi$
$338$	−15.4306	+	30.2380i	−0.839315	+	1.64473i
$339$	−0.456200	+	1.49080i	−0.0247774	+	0.0809689i
$340$	−18.7684	−	32.5078i	−1.01786	−	1.76298i
$341$	7.11650	−	12.3261i	0.385380	−	0.667498i
$342$	1.49346	−	21.2013i	0.0807570	−	1.14643i
$343$	17.7569			0.958785
$344$	34.0008			1.83320
$345$	5.69715	+	6.11258i	0.306724	+	0.329090i
$346$	21.2281	+	36.7681i	1.14123	+	1.97666i
$347$	−3.77332	+	6.53558i	−0.202562	+	0.350848i	−0.949353	−	0.314211i	$-0.898260\pi$
$347$	−3.77332	+	6.53558i	−0.202562	+	0.350848i	0.746791	+	0.665059i	$0.231594\pi$
$348$	44.5612	−	10.2757i	2.38873	−	0.550838i
$349$	1.30705	+	2.26388i	0.0699648	+	0.121183i	0.898886	−	0.438183i	$-0.144378\pi$
$349$	1.30705	+	2.26388i	0.0699648	+	0.121183i	−0.828921	+	0.559366i	$0.811045\pi$
$350$	−3.96511			−0.211944
$351$	−3.39431	−	18.4249i	−0.181175	−	0.983451i
$352$	−22.8467			−1.21774
$353$	5.51962	+	9.56026i	0.293780	+	0.508841i	0.974700	−	0.223516i	$-0.0717535\pi$
$353$	5.51962	+	9.56026i	0.293780	+	0.508841i	−0.680921	+	0.732357i	$0.738420\pi$
$354$	−24.9436	+	5.75196i	−1.32574	+	0.305713i
$355$	4.14295	−	7.17580i	0.219885	−	0.380852i
$356$	−21.0101	−	36.3905i	−1.11353	−	1.92869i
$357$	−13.9669	−	14.9853i	−0.739204	−	0.793107i
$358$	−17.9682			−0.949646
$359$	−20.8092			−1.09827			−0.549134	−	0.835734i	$-0.685042\pi$
$359$	−20.8092			−1.09827			−0.549134	+	0.835734i	$0.685042\pi$
$360$	18.3034	+	12.3595i	0.964674	+	0.651401i
$361$	5.81981	−	10.0802i	0.306306	−	0.530537i
$362$	−2.54623	−	4.41019i	−0.133827	−	0.231795i
$363$	3.08574	−	10.0838i	0.161959	−	0.529260i
$364$	−13.7784	−	22.4999i	−0.722184	−	1.17932i
$365$	−0.311679	−	0.539844i	−0.0163140	−	0.0282568i
$366$	−11.9857	−	12.8597i	−0.626501	−	0.672186i
$367$	−13.9798	−	24.2138i	−0.729741	−	1.26395i	−0.956993	−	0.290112i	$-0.906308\pi$
$367$	−13.9798	−	24.2138i	−0.729741	−	1.26395i	0.227252	−	0.973836i	$-0.427026\pi$
$368$	−23.1229	−	40.0500i	−1.20536	−	2.08775i
$369$	1.75444	−	0.854586i	0.0913326	−	0.0444880i
$370$	−9.58755	−	16.6061i	−0.498433	−	0.863312i
$371$	−15.7742			−0.818956
$372$	52.2354	−	12.0454i	2.70828	−	0.624525i
$373$	6.18601	−	10.7145i	0.320299	−	0.554775i	−0.660250	−	0.751045i	$-0.729550\pi$
$373$	6.18601	−	10.7145i	0.320299	−	0.554775i	0.980550	+	0.196271i	$0.0628832\pi$
$374$	45.0780			2.33093
$375$	−1.68776	+	0.389194i	−0.0871555	+	0.0200979i
$376$	−43.6046	+	75.5254i	−2.24874	+	3.89492i
$377$	−19.7470	+	0.510976i	−1.01702	+	0.0263166i
$378$	19.2291	+	7.39835i	0.989041	+	0.380530i
$379$	5.29558	−	9.17221i	0.272016	−	0.471145i	−0.697362	−	0.716719i	$-0.745643\pi$
$379$	5.29558	−	9.17221i	0.272016	−	0.471145i	0.969378	+	0.245574i	$0.0789764\pi$
$380$	−6.53721	−	11.3228i	−0.335352	−	0.580846i
$381$	0.864396	−	2.82472i	0.0442843	−	0.144715i
$382$	28.1245	+	48.7131i	1.43898	+	2.49238i
$383$	−9.93697	+	17.2113i	−0.507755	+	0.879458i	0.492204	+	0.870480i	$0.336191\pi$
$383$	−9.93697	+	17.2113i	−0.507755	+	0.879458i	−0.999960	+	0.00897845i	$0.997142\pi$
$384$	0.454624	+	0.487775i	0.0231999	+	0.0248917i
$385$	1.68257	−	2.91429i	0.0857516	−	0.148526i
$386$	6.53970	+	11.3271i	0.332862	+	0.576534i
$387$	12.4564	−	6.06750i	0.633195	−	0.308428i
$388$	−12.9286	+	22.3930i	−0.656349	+	1.13683i
$389$	13.5377	−	23.4481i	0.686391	−	1.18886i	−0.286606	−	0.958048i	$-0.592527\pi$
$389$	13.5377	−	23.4481i	0.686391	−	1.18886i	0.972997	−	0.230816i	$-0.0741395\pi$
$390$	−11.4238	−	11.6381i	−0.578465	−	0.589317i
$391$	18.7883	+	32.5423i	0.950166	+	1.64574i
$392$	−34.5597			−1.74553
$393$	19.9623	+	21.4179i	1.00696	+	1.08039i
$394$	−66.0564			−3.32787
$395$	−9.97325			−0.501809
$396$	−28.8055	+	14.0311i	−1.44753	+	0.705090i
$397$	19.0723	+	33.0342i	0.957211	+	1.65794i	0.729225	+	0.684274i	$0.239881\pi$
$397$	19.0723	+	33.0342i	0.957211	+	1.65794i	0.227986	+	0.973664i	$0.426786\pi$
$398$	−20.4508	+	35.4218i	−1.02510	+	1.77553i
$399$	−4.86479	−	5.21953i	−0.243544	−	0.261303i
$400$	9.58604			0.479302
$401$	31.1625			1.55618			0.778092	−	0.628151i	$-0.216188\pi$
$401$	31.1625			1.55618			0.778092	+	0.628151i	$0.216188\pi$
$402$	27.6822	+	29.7008i	1.38066	+	1.48134i
$403$	−23.1478	+	0.598974i	−1.15307	+	0.0298370i
$404$	−83.0619			−4.13249
$405$	8.91112	+	1.26169i	0.442797	+	0.0626940i
$406$	10.8617	−	18.8131i	0.539060	−	0.933679i
$407$	16.2737			0.806656
$408$	67.7168	+	72.6547i	3.35248	+	3.59694i
$409$	0.413863	−	0.716831i	0.0204642	−	0.0354450i	−0.855612	−	0.517618i	$-0.826819\pi$
$409$	0.413863	−	0.716831i	0.0204642	−	0.0354450i	0.876076	+	0.482173i	$0.160152\pi$
$410$	0.849347	−	1.47111i	0.0419462	−	0.0726530i
$411$	−21.4557	+	4.94766i	−1.05833	+	0.244050i
$412$	−8.54168			−0.420818
$413$	−4.29678	+	7.44224i	−0.211431	+	0.366209i
$414$	−31.3216	−	21.1500i	−1.53937	−	1.03947i
$415$	6.20065			0.304378
$416$	19.4110	+	31.6979i	0.951703	+	1.55412i
$417$	−4.02061	+	13.1388i	−0.196890	+	0.643409i
$418$	15.7011			0.767965
$419$	−33.6746			−1.64511			−0.822556	−	0.568685i	$-0.807452\pi$
$419$	−33.6746			−1.64511			−0.822556	+	0.568685i	$0.807452\pi$
$420$	12.3501	−	2.84792i	0.602624	−	0.138964i
$421$	4.75864	−	8.24220i	0.231922	−	0.401700i	−0.726452	−	0.687217i	$-0.758832\pi$
$421$	4.75864	−	8.24220i	0.231922	−	0.401700i	0.958374	+	0.285517i	$0.0921653\pi$
$422$	21.2577	+	36.8194i	1.03481	+	1.79234i
$423$	−2.49720	+	35.4505i	−0.121418	+	1.72366i
$424$	76.4795			3.71417
$425$	−7.78906			−0.377825
$426$	−10.9664	+	35.8367i	−0.531325	+	1.73629i
$427$	−5.90148			−0.285593
$428$	−16.5130	−	28.6014i	−0.798186	−	1.38250i
$429$	13.4014	−	3.45776i	0.647027	−	0.166942i
$430$	6.03030	−	10.4448i	0.290807	−	0.503692i
$431$	−12.3943	+	21.4675i	−0.597012	+	1.03406i	0.396247	+	0.918144i	$0.370312\pi$
$431$	−12.3943	+	21.4675i	−0.597012	+	1.03406i	−0.993260	+	0.115912i	$0.963021\pi$
$432$	−46.4884	−	17.8862i	−2.23667	−	0.860552i
$433$	−2.02166	−	3.50162i	−0.0971548	−	0.168277i	0.813351	−	0.581773i	$-0.197641\pi$
$433$	−2.02166	−	3.50162i	−0.0971548	−	0.168277i	−0.910506	+	0.413496i	$0.864308\pi$
$434$	12.7323	−	22.0530i	0.611171	−	1.05858i
$435$	2.77674	−	9.07398i	0.133134	−	0.435064i
$436$	24.3259	−	42.1337i	1.16500	−	2.01784i
$437$	6.54415	+	11.3348i	0.313049	+	0.542217i
$438$	1.92233	+	2.06251i	0.0918526	+	0.0985504i
$439$	16.6737	+	28.8797i	0.795792	+	1.37835i	0.922335	+	0.386391i	$0.126279\pi$
$439$	16.6737	+	28.8797i	0.795792	+	1.37835i	−0.126543	+	0.991961i	$0.540388\pi$
$440$	−8.15775	+	14.1296i	−0.388905	+	0.673604i
$441$	−12.6611	+	6.16722i	−0.602912	+	0.293677i
$442$	−38.2991	−	62.5418i	−1.82170	−	2.97481i
$443$	−8.45494	+	14.6444i	−0.401706	+	0.695776i	−0.993932	−	0.109996i	$-0.964916\pi$
$443$	−8.45494	+	14.6444i	−0.401706	+	0.695776i	0.592226	+	0.805772i	$0.298249\pi$
$444$	41.7896	+	44.8369i	1.98325	+	2.12787i
$445$	−8.71938			−0.413338
$446$	5.74749	−	9.95494i	0.272151	−	0.471380i
$447$	4.88681	−	15.9694i	0.231138	−	0.755327i
$448$	−11.7646			−0.555827
$449$	−6.57032	−	11.3801i	−0.310072	−	0.537061i	0.668305	−	0.743887i	$-0.267020\pi$
$449$	−6.57032	−	11.3801i	−0.310072	−	0.537061i	−0.978378	+	0.206826i	$0.933687\pi$
$450$	7.04297	−	3.43062i	0.332009	−	0.161721i
$451$	0.720830	+	1.24851i	0.0339426	+	0.0587903i
$452$	−2.16889	−	3.75662i	−0.102016	−	0.176697i
$453$	−0.0672090	+	0.219629i	−0.00315775	+	0.0103191i
$454$	14.5149	+	25.1406i	0.681219	+	1.17991i
$455$	−5.47287	+	0.141617i	−0.256572	+	0.00663910i
$456$	23.5864	+	25.3063i	1.10453	+	1.18508i
$457$	5.11881	+	8.86604i	0.239448	+	0.414736i	0.960556	−	0.278087i	$-0.0897003\pi$
$457$	5.11881	+	8.86604i	0.239448	+	0.414736i	−0.721108	+	0.692823i	$0.756367\pi$
$458$	−24.7035	+	42.7876i	−1.15432	+	1.99933i
$459$	37.7738	+	14.5333i	1.76313	+	0.678357i
$460$	−23.2490			−1.08399
$461$	−24.8222			−1.15608			−0.578042	−	0.816007i	$-0.696183\pi$
$461$	−24.8222			−1.15608			−0.578042	+	0.816007i	$0.696183\pi$
$462$	−4.45377	+	14.5543i	−0.207208	+	0.677127i
$463$	−1.66549	−	2.88471i	−0.0774018	−	0.134064i	0.824726	−	0.565532i	$-0.191329\pi$
$463$	−1.66549	−	2.88471i	−0.0774018	−	0.134064i	−0.902128	+	0.431468i	$0.857996\pi$
$464$	−26.2594	+	45.4826i	−1.21906	+	2.11148i
$465$	3.25494	−	10.6367i	0.150944	−	0.493264i
$466$	11.3364	+	19.6353i	0.525151	+	0.909588i
$467$	9.81015			0.453959			0.226980	−	0.973899i	$-0.427115\pi$
$467$	9.81015			0.453959			0.226980	+	0.973899i	$0.427115\pi$
$468$	43.9407	+	28.0441i	2.03116	+	1.29634i
$469$	13.6301			0.629380
$470$	15.4672	+	26.7899i	0.713448	+	1.23573i
$471$	−18.8351	−	20.2086i	−0.867877	−	0.931163i
$472$	20.8325	−	36.0829i	0.958892	−	1.66085i
$473$	5.11784	+	8.86436i	0.235319	+	0.407584i
$474$	43.9554	−	10.1361i	2.01894	−	0.465564i
$475$	−2.71300			−0.124481
$476$	56.9962			2.61242
$477$	28.0187	−	13.6479i	1.28289	−	0.624893i
$478$	32.2452	−	55.8503i	1.47486	−	2.55453i
$479$	−10.4517	−	18.1028i	−0.477549	−	0.827139i	0.522120	−	0.852872i	$-0.325141\pi$
$479$	−10.4517	−	18.1028i	−0.477549	−	0.827139i	−0.999669	+	0.0257329i	$0.991808\pi$
$480$	−17.3989	+	4.01215i	−0.794146	+	0.183129i
$481$	−13.8264	−	22.5783i	−0.630430	−	1.02948i
$482$	28.1123	+	48.6919i	1.28048	+	2.21786i
$483$	−12.3632	+	2.85094i	−0.562547	+	0.129722i
$484$	14.6704	+	25.4099i	0.666836	+	1.15499i
$485$	2.68274	+	4.64664i	0.121817	+	0.210993i
$486$	−40.5566	+	3.49588i	−1.83968	+	0.158576i
$487$	7.91472	+	13.7087i	0.358650	+	0.621200i	0.987736	−	0.156136i	$-0.0499038\pi$
$487$	7.91472	+	13.7087i	0.358650	+	0.621200i	−0.629086	+	0.777336i	$0.716570\pi$
$488$	28.6127			1.29524
$489$	15.1781	+	16.2849i	0.686376	+	0.736427i
$490$	−6.12941	+	10.6164i	−0.276899	+	0.479602i
$491$	−28.8861			−1.30361			−0.651805	−	0.758386i	$-0.725988\pi$
$491$	−28.8861			−1.30361			−0.651805	+	0.758386i	$0.725988\pi$
$492$	−1.58884	+	5.19211i	−0.0716306	+	0.234079i
$493$	21.3368	−	36.9565i	0.960963	−	1.66444i
$494$	−13.3399	−	21.7839i	−0.600191	−	0.980104i
$495$	−0.467187	+	6.63224i	−0.0209985	+	0.298097i
$496$	−30.7817	+	53.3154i	−1.38214	+	2.39393i
$497$	6.29070	+	10.8958i	0.282176	+	0.488744i
$498$	−27.3284	+	6.30187i	−1.22461	+	0.282394i
$499$	3.64275	+	6.30943i	0.163072	+	0.282449i	0.935969	−	0.352083i	$-0.114526\pi$
$499$	3.64275	+	6.30943i	0.163072	+	0.282449i	−0.772897	+	0.634531i	$0.781193\pi$
$500$	2.40958	−	4.17352i	0.107760	−	0.186646i
$501$	17.7953	−	4.10357i	0.795036	−	0.183334i
$502$	−30.9733	+	53.6473i	−1.38241	+	2.39440i
$503$	−15.7003	−	27.1938i	−0.700044	−	1.21251i	−0.968451	−	0.249205i	$-0.919831\pi$
$503$	−15.7003	−	27.1938i	−0.700044	−	1.21251i	0.268407	−	0.963306i	$-0.413503\pi$
$504$	−30.1485	+	14.6853i	−1.34292	+	0.654134i
$505$	−8.61787	+	14.9266i	−0.383490	+	0.664225i
$506$	13.9599	−	24.1793i	0.620593	−	1.07490i
$507$	−16.1834	−	15.6556i	−0.718731	−	0.695288i
$508$	4.10956	+	7.11796i	0.182332	+	0.315808i
$509$	−23.5807			−1.04520			−0.522599	−	0.852579i	$-0.675037\pi$
$509$	−23.5807			−1.04520			−0.522599	+	0.852579i	$0.675037\pi$
$510$	34.3290	−	7.91620i	1.52011	−	0.350535i
$511$	0.946514			0.0418713
$512$	−42.3207			−1.87033
$513$	13.1570	+	5.06209i	0.580894	+	0.223497i
$514$	19.2656	+	33.3690i	0.849769	+	1.47184i
$515$	−0.886219	+	1.53498i	−0.0390515	+	0.0676391i
$516$	−11.2807	+	36.8636i	−0.496604	+	1.62283i
$517$	−26.2536			−1.15463
$518$	29.1157			1.27927
$519$	−27.4400	+	6.32763i	−1.20448	+	0.277752i
$520$	26.5346	−	0.686613i	1.16362	−	0.0301100i
$521$	30.9740			1.35699			0.678497	−	0.734603i	$-0.262632\pi$
$521$	30.9740			1.35699			0.678497	+	0.734603i	$0.262632\pi$
$522$	−3.01591	+	42.8141i	−0.132003	+	1.87392i
$523$	−5.43961	+	9.42167i	−0.237857	+	0.411981i	−0.960099	−	0.279660i	$-0.909778\pi$
$523$	−5.43961	+	9.42167i	−0.237857	+	0.411981i	0.722242	+	0.691641i	$0.243112\pi$
$524$	−81.4625			−3.55871
$525$	0.769571	−	2.51485i	0.0335868	−	0.109757i
$526$	3.00477	−	5.20441i	0.131014	−	0.226923i
$527$	25.0114	−	43.3210i	1.08951	−	1.88709i
$528$	10.7675	−	35.1865i	0.468593	−	1.53130i
$529$	0.273722			0.0119010
$530$	13.5642	−	23.4939i	0.589191	−	1.02051i
$531$	1.19306	−	16.9368i	0.0517743	−	0.734993i
$532$	19.8523			0.860707
$533$	1.11978	−	2.06085i	0.0485029	−	0.0892653i
$534$	38.4292	−	8.86171i	1.66299	−	0.383484i
$535$	−6.85305			−0.296283
$536$	−66.0841			−2.85440
$537$	3.48737	−	11.3962i	0.150491	−	0.491783i
$538$	29.6495	−	51.3544i	1.27828	−	2.21404i
$539$	−5.20196	−	9.01005i	−0.224064	−	0.388090i
$540$	−19.4727	+	15.7439i	−0.837973	+	0.677511i
$541$	−16.6842			−0.717308			−0.358654	−	0.933471i	$-0.616764\pi$
$541$	−16.6842			−0.717308			−0.358654	+	0.933471i	$0.616764\pi$
$542$	37.5014			1.61082
$543$	3.29133	−	0.758975i	0.141245	−	0.0325708i
$544$	−80.2963			−3.44268
$545$	−5.04774	−	8.74295i	−0.216222	−	0.374507i
$546$	23.9768	−	6.18636i	1.02611	−	0.264752i
$547$	19.3482	−	33.5121i	0.827271	−	1.43287i	−0.0729008	−	0.997339i	$-0.523226\pi$
$547$	19.3482	−	33.5121i	0.827271	−	1.43287i	0.900171	−	0.435536i	$-0.143441\pi$
$548$	30.6320	−	53.0562i	1.30853	−	2.26645i
$549$	10.4824	−	5.10598i	0.447379	−	0.217918i
$550$	2.89367	+	5.01199i	0.123387	+	0.213712i
$551$	7.43182	−	12.8723i	0.316606	−	0.548378i
$552$	59.9418	−	13.8225i	2.55129	−	0.588324i
$553$	7.57174	−	13.1146i	0.321983	−	0.557691i
$554$	−6.46313	−	11.1945i	−0.274592	−	0.475608i
$555$	12.3932	−	2.85784i	0.526061	−	0.121309i
$556$	−19.1150	−	33.1081i	−0.810656	−	1.40410i
$557$	−4.33443	+	7.50745i	−0.183656	+	0.318101i	−0.943123	−	0.332445i	$-0.892126\pi$
$557$	−4.33443	+	7.50745i	−0.183656	+	0.318101i	0.759467	+	0.650546i	$0.225460\pi$
$558$	−3.53530	+	50.1874i	−0.149661	+	2.12460i
$559$	7.95033	−	14.6319i	0.336263	−	0.618863i
$560$	−7.27777	+	12.6055i	−0.307542	+	0.532678i
$561$	−8.74900	+	28.5905i	−0.369383	+	1.20709i
$562$	13.4211			0.566133
$563$	8.34729	−	14.4579i	0.351796	−	0.609329i	−0.634768	−	0.772703i	$-0.718904\pi$
$563$	8.34729	−	14.4579i	0.351796	−	0.609329i	0.986564	+	0.163374i	$0.0522376\pi$
$564$	−67.4174	−	72.3335i	−2.83879	−	3.04579i
$565$	−0.900109			−0.0378679
$566$	−10.3587	−	17.9418i	−0.435409	−	0.754151i
$567$	−8.42447	+	10.7601i	−0.353795	+	0.451881i
$568$	−30.4998	−	52.8271i	−1.27974	−	2.21658i
$569$	0.118747	+	0.205676i	0.00497815	+	0.00862240i	0.868504	−	0.495683i	$-0.165082\pi$
$569$	0.118747	+	0.205676i	0.00497815	+	0.00862240i	−0.863526	+	0.504305i	$0.831749\pi$
$570$	11.9571	−	2.75729i	0.500828	−	0.115490i
$571$	7.10342	+	12.3035i	0.297269	+	0.514885i	0.975510	−	0.219954i	$-0.0705909\pi$
$571$	7.10342	+	12.3035i	0.297269	+	0.514885i	−0.678241	+	0.734839i	$0.737258\pi$
$572$	−18.3852	+	33.8363i	−0.768723	+	1.41477i
$573$	−36.3547	+	8.38332i	−1.51874	+	0.350218i
$574$	1.28966	+	2.23375i	0.0538292	+	0.0932349i
$575$	−2.41214	+	4.17795i	−0.100593	+	0.174233i
$576$	20.8968	−	10.1788i	0.870699	−	0.424116i
$577$	−8.91083			−0.370963			−0.185481	−	0.982648i	$-0.559384\pi$
$577$	−8.91083			−0.370963			−0.185481	+	0.982648i	$0.559384\pi$
$578$	114.036			4.74329
$579$	−8.45342	+	1.94934i	−0.351312	+	0.0810120i
$580$	13.2013	+	22.8653i	0.548155	+	0.949432i
$581$	−4.70757	+	8.15375i	−0.195303	+	0.338274i
$582$	−16.5462	−	17.7528i	−0.685863	−	0.735876i
$583$	11.5118	+	19.9390i	0.476769	+	0.825788i
$584$	−4.58907			−0.189897
$585$	9.59859	−	4.98669i	0.396853	−	0.206174i
$586$	24.1193			0.996360
$587$	−6.91359	−	11.9747i	−0.285354	−	0.494248i	0.687341	−	0.726335i	$-0.258778\pi$
$587$	−6.91359	−	11.9747i	−0.285354	−	0.494248i	−0.972695	+	0.232087i	$0.925445\pi$
$588$	11.4661	−	37.4695i	0.472853	−	1.54522i
$589$	8.71170	−	15.0891i	0.358959	−	0.621736i
$590$	−7.38958	−	12.7991i	−0.304224	−	0.526932i
$591$	12.8206	−	41.8959i	0.527370	−	1.72337i
$592$	−70.3901			−2.89301
$593$	26.8894			1.10422			0.552108	−	0.833773i	$-0.313824\pi$
$593$	26.8894			1.10422			0.552108	+	0.833773i	$0.313824\pi$
$594$	−4.68145	−	29.7053i	−0.192082	−	1.21882i
$595$	5.91349	−	10.2425i	0.242430	−	0.419900i
$596$	23.2331	+	40.2410i	0.951666	+	1.64833i
$597$	−18.4969	−	19.8457i	−0.757027	−	0.812229i
$598$	−45.4072	+	1.17496i	−1.85684	+	0.0480478i
$599$	−14.1910	−	24.5795i	−0.579828	−	1.00429i	−0.995499	−	0.0947765i	$-0.969786\pi$
$599$	−14.1910	−	24.5795i	−0.579828	−	1.00429i	0.415670	−	0.909515i	$-0.363547\pi$
$600$	−3.73118	+	12.1930i	−0.152325	+	0.497776i
$601$	10.8784	+	18.8419i	0.443738	+	0.768576i	0.997963	−	0.0637904i	$-0.0203189\pi$
$601$	10.8784	+	18.8419i	0.443738	+	0.768576i	−0.554226	+	0.832366i	$0.686986\pi$
$602$	9.15646	+	15.8595i	0.373190	+	0.646383i
$603$	−24.2103	+	11.7928i	−0.985920	+	0.480240i
$604$	−0.319528	−	0.553439i	−0.0130014	−	0.0225191i
$605$	6.08835			0.247527
$606$	22.8116	−	74.5450i	0.926657	−	3.02818i
$607$	0.0344775	−	0.0597168i	0.00139940	−	0.00242383i	−0.865325	−	0.501211i	$-0.832888\pi$
$607$	0.0344775	−	0.0597168i	0.00139940	−	0.00242383i	0.866724	+	0.498788i	$0.166221\pi$
$608$	−27.9680			−1.13425
$609$	9.82401	+	10.5404i	0.398089	+	0.427117i
$610$	5.07467	−	8.78959i	0.205467	−	0.355880i
$611$	22.3055	+	36.4247i	0.902386	+	1.47358i
$612$	−101.239	+	49.3132i	−4.09234	+	1.99337i
$613$	19.4119	−	33.6224i	0.784039	−	1.35800i	−0.145532	−	0.989353i	$-0.546490\pi$
$613$	19.4119	−	33.6224i	0.784039	−	1.35800i	0.929571	−	0.368642i	$-0.120177\pi$
$614$	22.8157	+	39.5179i	0.920767	+	1.59481i
$615$	0.768199	+	0.824216i	0.0309768	+	0.0332356i
$616$	−12.3868	−	21.4546i	−0.499079	−	0.864430i
$617$	8.57087	−	14.8452i	0.345050	−	0.597645i	−0.640313	−	0.768114i	$-0.721195\pi$
$617$	8.57087	−	14.8452i	0.345050	−	0.597645i	0.985363	+	0.170470i	$0.0545285\pi$
$618$	2.34583	−	7.66584i	0.0943631	−	0.308365i
$619$	−9.48341	+	16.4258i	−0.381171	+	0.660207i	−0.991230	−	0.132149i	$-0.957812\pi$
$619$	−9.48341	+	16.4258i	−0.381171	+	0.660207i	0.610059	+	0.792356i	$0.291146\pi$
$620$	15.4748	+	26.8031i	0.621482	+	1.07644i
$621$	19.4934	−	15.7606i	0.782243	−	0.632453i
$622$	−19.3300	+	33.4806i	−0.775064	+	1.34245i
$623$	6.61980	−	11.4658i	0.265217	−	0.459368i
$624$	−57.9665	+	14.9562i	−2.32052	+	0.598725i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−49.9581			−1.99673
$627$	−3.04736	+	9.95834i	−0.121700	+	0.397698i
$628$	76.8628			3.06716
$629$	57.1949			2.28051
$630$	−0.835857	+	11.8659i	−0.0333013	+	0.472749i
$631$	0.0473814	+	0.0820669i	0.00188622	+	0.00326703i	0.866967	−	0.498366i	$-0.166066\pi$
$631$	0.0473814	+	0.0820669i	0.00188622	+	0.00326703i	−0.865081	+	0.501633i	$0.832733\pi$
$632$	−36.7108	+	63.5849i	−1.46028	+	2.52927i
$633$	−27.4783	+	6.33646i	−1.09217	+	0.251852i
$634$	−74.6447			−2.96452
$635$	1.70550			0.0676809
$636$	−25.3741	+	82.9189i	−1.00615	+	3.28795i
$637$	−8.08100	+	14.8724i	−0.320181	+	0.589265i
$638$	−31.7069			−1.25529
$639$	−20.6008	−	13.9108i	−0.814957	−	0.550303i
$640$	−0.192485	+	0.333394i	−0.00760865	+	0.0131786i
$641$	27.3779			1.08136			0.540680	−	0.841228i	$-0.318167\pi$
$641$	27.3779			1.08136			0.540680	+	0.841228i	$0.318167\pi$
$642$	30.2037	−	6.96492i	1.19204	−	0.274883i
$643$	0.729225	−	1.26305i	0.0287578	−	0.0498100i	−0.851288	−	0.524698i	$-0.824178\pi$
$643$	0.729225	−	1.26305i	0.0287578	−	0.0498100i	0.880046	+	0.474888i	$0.157512\pi$
$644$	17.6508	−	30.5721i	0.695538	−	1.20471i
$645$	5.45416	+	5.85187i	0.214757	+	0.230417i
$646$	55.1824			2.17112
$647$	−2.87909	+	4.98673i	−0.113189	+	0.196049i	−0.917054	−	0.398762i	$-0.869440\pi$
$647$	−2.87909	+	4.98673i	−0.113189	+	0.196049i	0.803866	+	0.594811i	$0.202773\pi$
$648$	40.8451	−	52.1691i	1.60455	−	2.04939i
$649$	12.5429			0.492352
$650$	4.49519	−	8.27300i	0.176316	−	0.324494i
$651$	11.5159	+	12.3556i	0.451342	+	0.484254i
$652$	−61.9390			−2.42572
$653$	−9.29890			−0.363894			−0.181947	−	0.983308i	$-0.558240\pi$
$653$	−9.29890			−0.363894			−0.181947	+	0.983308i	$0.558240\pi$
$654$	31.1327	+	33.4029i	1.21739	+	1.30616i
$655$	−8.45193	+	14.6392i	−0.330244	+	0.572000i
$656$	−3.11787	−	5.40032i	−0.121733	−	0.210847i
$657$	−1.68123	+	0.818926i	−0.0655912	+	0.0319493i
$658$	−46.9711			−1.83112
$659$	−7.54198			−0.293794			−0.146897	−	0.989152i	$-0.546929\pi$
$659$	−7.54198			−0.293794			−0.146897	+	0.989152i	$0.546929\pi$
$660$	−12.6128	−	13.5325i	−0.490951	−	0.526751i
$661$	37.4941			1.45835			0.729175	−	0.684327i	$-0.239904\pi$
$661$	37.4941			1.45835			0.729175	+	0.684327i	$0.239904\pi$
$662$	35.8137	+	62.0311i	1.39194	+	2.41091i
$663$	47.1002	−	12.1525i	1.82922	−	0.471964i
$664$	22.8241	−	39.5325i	0.885748	−	1.53416i
$665$	2.05973	−	3.56755i	0.0798727	−	0.138344i
$666$	−51.7163	+	25.1909i	−2.00397	+	0.976129i
$667$	−13.2153	−	22.8896i	−0.511700	−	0.886290i
$668$	−25.4061	+	44.0046i	−0.982990	+	1.70259i
$669$	5.19836	+	5.57743i	0.200980	+	0.215636i
$670$	−11.7205	+	20.3005i	−0.452802	+	0.784277i
$671$	4.30681	+	7.45962i	0.166263	+	0.287975i
$672$	7.93340	−	25.9252i	0.306038	−	1.00009i
$673$	−24.0003	−	41.5698i	−0.925145	−	1.60240i	−0.791328	−	0.611392i	$-0.790610\pi$
$673$	−24.0003	−	41.5698i	−0.925145	−	1.60240i	−0.133817	−	0.991006i	$-0.542723\pi$
$674$	3.51515	−	6.08842i	0.135398	−	0.234517i
$675$	0.808911	+	5.13280i	0.0311350	+	0.197562i
$676$	62.5653	−	3.24007i	2.40636	−	0.124618i
$677$	10.7632	−	18.6425i	0.413665	−	0.716488i	−0.581622	−	0.813459i	$-0.697582\pi$
$677$	10.7632	−	18.6425i	0.413665	−	0.716488i	0.995287	+	0.0969704i	$0.0309152\pi$
$678$	3.96708	−	0.914802i	0.152355	−	0.0351328i
$679$	−8.14700			−0.312653
$680$	−28.6709	+	49.6595i	−1.09948	+	1.90435i
$681$	−18.7624	+	4.32659i	−0.718978	+	0.165795i
$682$	−37.1674			−1.42321
$683$	18.2668	+	31.6390i	0.698960	+	1.21063i	0.968827	+	0.247736i	$0.0796867\pi$
$683$	18.2668	+	31.6390i	0.698960	+	1.21063i	−0.269868	+	0.962897i	$0.586980\pi$
$684$	−35.2624	+	17.1763i	−1.34829	+	0.656751i
$685$	−6.35628	−	11.0094i	−0.242861	−	0.420648i
$686$	−23.1848	−	40.1573i	−0.885201	−	1.53321i
$687$	−22.3433	−	23.9725i	−0.852449	−	0.914609i
$688$	−22.1367	−	38.3418i	−0.843953	−	1.46177i
$689$	17.8830	−	32.9121i	0.681289	−	1.25385i
$690$	6.38496	−	20.8652i	0.243071	−	0.794323i
$691$	11.0869	+	19.2031i	0.421765	+	0.730519i	0.996112	−	0.0880929i	$-0.0280772\pi$
$691$	11.0869	+	19.2031i	0.421765	+	0.730519i	−0.574347	+	0.818612i	$0.694744\pi$
$692$	39.1757	−	67.8543i	1.48924	−	2.57943i
$693$	−8.36658	−	5.64957i	−0.317820	−	0.214609i
$694$	19.7069			0.748065
$695$	−7.93290			−0.300912
$696$	−47.6306	−	51.1038i	−1.80543	−	1.93709i
$697$	2.53340	+	4.38798i	0.0959595	+	0.166207i
$698$	3.41317	−	5.91178i	0.129190	−	0.223764i
$699$	−14.6538	+	3.37915i	−0.554259	+	0.127811i
$700$	3.65874	+	6.33712i	0.138287	+	0.239521i
$701$	−14.9607			−0.565058			−0.282529	−	0.959259i	$-0.591173\pi$
$701$	−14.9607			−0.565058			−0.282529	+	0.959259i	$0.591173\pi$
$702$	−37.2361	+	31.7333i	−1.40539	+	1.19769i
$703$	19.9215			0.751354
$704$	8.58564	+	14.8708i	0.323584	+	0.560463i
$705$	−19.9934	+	4.61043i	−0.752994	+	0.173639i
$706$	14.4137	−	24.9652i	0.542466	−	0.939578i
$707$	−13.0855	−	22.6647i	−0.492129	−	0.852393i
$708$	32.2092	+	34.5579i	1.21050	+	1.29877i
$709$	14.6803			0.551329			0.275664	−	0.961254i	$-0.411102\pi$
$709$	14.6803			0.551329			0.275664	+	0.961254i	$0.411102\pi$
$710$	−21.6374			−0.812038
$711$	−2.10239	+	29.8458i	−0.0788459	+	1.11930i
$712$	−32.0954	+	55.5908i	−1.20282	+	2.08335i
$713$	−15.4912	−	26.8316i	−0.580151	−	1.00485i
$714$	−15.6531	+	51.1520i	−0.585802	+	1.91432i
$715$	4.17302	+	6.81449i	0.156062	+	0.254848i
$716$	16.5798	+	28.7171i	0.619617	+	1.07321i
$717$	29.1644	+	31.2911i	1.08917	+	1.16859i
$718$	27.1701	+	47.0600i	1.01398	+	1.75626i
$719$	−5.45911	−	9.45545i	−0.203590	−	0.352629i	0.746092	−	0.665842i	$-0.231928\pi$
$719$	−5.45911	−	9.45545i	−0.203590	−	0.352629i	−0.949683	+	0.313214i	$0.898594\pi$
$720$	2.02077	−	28.6870i	0.0753096	−	1.06910i
$721$	−1.34564	−	2.33072i	−0.0501144	−	0.0868007i
$722$	−30.3952			−1.13119
$723$	−36.3388	+	8.37967i	−1.35146	+	0.311643i
$724$	−4.69898	+	8.13887i	−0.174636	+	0.302479i
$725$	5.47867			0.203473
$726$	−26.8334	+	6.18773i	−0.995881	+	0.229648i
$727$	14.8068	−	25.6461i	0.549153	−	0.951161i	−0.449180	−	0.893441i	$-0.648284\pi$
$727$	14.8068	−	25.6461i	0.549153	−	0.951161i	0.998333	−	0.0577195i	$-0.0183829\pi$
$728$	−19.2423	+	35.4138i	−0.713168	+	1.31252i
$729$	5.65422	−	26.4013i	0.209415	−	0.977827i
$730$	−0.813905	+	1.40972i	−0.0301240	+	0.0521763i
$731$	17.9870	+	31.1543i	0.665272	+	1.15229i
$732$	−9.49301	+	31.0218i	−0.350872	+	1.14660i
$733$	3.48671	+	6.03916i	0.128785	+	0.223061i	0.923206	−	0.384306i	$-0.125559\pi$
$733$	3.48671	+	6.03916i	0.128785	+	0.223061i	−0.794421	+	0.607367i	$0.792226\pi$
$734$	−36.5062	+	63.2307i	−1.34747	+	2.33389i
$735$	−5.54380	−	5.94805i	−0.204486	−	0.219397i
$736$	−24.8664	+	43.0699i	−0.916589	+	1.58758i
$737$	−9.94705	−	17.2288i	−0.366404	−	0.634631i
$738$	−4.22338	−	2.85186i	−0.155465	−	0.104978i
$739$	−22.7924	+	39.4776i	−0.838433	+	1.45221i	0.0527713	+	0.998607i	$0.483195\pi$
$739$	−22.7924	+	39.4776i	−0.838433	+	1.45221i	−0.891204	+	0.453602i	$0.850139\pi$
$740$	−17.6935	+	30.6461i	−0.650427	+	1.12657i
$741$	16.4054	−	4.23283i	0.602668	−	0.155497i
$742$	20.5960	+	35.6734i	0.756104	+	1.30961i
$743$	38.5886			1.41568			0.707839	−	0.706374i	$-0.249670\pi$
$743$	38.5886			1.41568			0.707839	+	0.706374i	$0.249670\pi$
$744$	−55.8334	−	59.9047i	−2.04695	−	2.19621i
$745$	9.64197			0.353254
$746$	−32.3077			−1.18287
$747$	1.30712	−	18.5560i	0.0478250	−	0.678928i
$748$	−41.5950	−	72.0446i	−1.52086	−	2.63421i
$749$	5.20287	−	9.01164i	0.190109	−	0.329278i
$750$	3.08383	+	3.30870i	0.112606	+	0.120817i
$751$	−31.7736			−1.15944			−0.579718	−	0.814817i	$-0.696837\pi$
$751$	−31.7736			−1.15944			−0.579718	+	0.814817i	$0.696837\pi$
$752$	113.557			4.14101
$753$	−28.0141	−	30.0568i	−1.02089	−	1.09533i
$754$	26.9388	+	43.9907i	0.981053	+	1.60205i
$755$	−0.132607			−0.00482607
$756$	−5.91919	−	37.5591i	−0.215279	−	1.36601i
$757$	21.8063	−	37.7697i	0.792564	−	1.37276i	−0.131810	−	0.991275i	$-0.542079\pi$
$757$	21.8063	−	37.7697i	0.792564	−	1.37276i	0.924374	−	0.381486i	$-0.124588\pi$
$758$	−27.6573			−1.00456
$759$	12.6262	+	13.5469i	0.458300	+	0.491720i
$760$	−9.98635	+	17.2969i	−0.362243	+	0.627423i
$761$	3.52276	−	6.10159i	0.127700	−	0.221183i	−0.795085	−	0.606498i	$-0.792574\pi$
$761$	3.52276	−	6.10159i	0.127700	−	0.221183i	0.922785	+	0.385315i	$0.125907\pi$
$762$	−7.51673	+	1.73334i	−0.272302	+	0.0627924i
$763$	15.3291			0.554950
$764$	51.9029	−	89.8985i	1.87778	−	3.25241i
$765$	−1.64196	+	23.3094i	−0.0593652	+	0.842754i
$766$	51.8979			1.87515
$767$	−10.6567	−	17.4022i	−0.384790	−	0.628356i
$768$	8.36330	−	27.3301i	0.301784	−	0.986188i
$769$	18.2259			0.657243			0.328622	−	0.944462i	$-0.393416\pi$
$769$	18.2259			0.657243			0.328622	+	0.944462i	$0.393416\pi$
$770$	−8.78756			−0.316682
$771$	−24.9033	+	5.74266i	−0.896870	+	0.206817i
$772$	12.0688	−	20.9038i	0.434366	−	0.752344i
$773$	−24.8841	−	43.1005i	−0.895018	−	1.55022i	−0.833783	−	0.552093i	$-0.813829\pi$
$773$	−24.8841	−	43.1005i	−0.895018	−	1.55022i	−0.0612350	−	0.998123i	$-0.519504\pi$
$774$	−29.9857	−	20.2480i	−1.07781	−	0.727798i
$775$	6.42218			0.230692
$776$	39.4998			1.41796
$777$	−5.65094	+	18.4665i	−0.202726	+	0.662481i
$778$	−70.7037			−2.53485
$779$	0.882408	+	1.52838i	0.0316156	+	0.0547597i
$780$	−8.05913	+	28.9966i	−0.288563	+	1.03824i
$781$	9.18171	−	15.9032i	0.328547	−	0.569061i
$782$	49.0629	−	84.9795i	1.75449	−	3.03886i
$783$	−26.5693	−	10.2224i	−0.949510	−	0.365320i
$784$	22.5005	+	38.9720i	0.803590	+	1.39186i
$785$	7.97470	−	13.8126i	0.284629	−	0.492992i
$786$	22.3723	−	73.1096i	0.797995	−	2.60773i
$787$	−8.32284	+	14.4156i	−0.296677	+	0.513860i	−0.975374	−	0.220559i	$-0.929212\pi$
$787$	−8.32284	+	14.4156i	−0.296677	+	0.513860i	0.678696	+	0.734419i	$0.262545\pi$
$788$	60.9524	+	105.573i	2.17134	+	3.76087i
$789$	2.71769	+	2.91586i	0.0967523	+	0.103807i
$790$	13.0218	+	22.5545i	0.463296	+	0.802453i
$791$	0.683367	−	1.18363i	0.0242977	−	0.0420849i
$792$	40.5644	+	27.3913i	1.44139	+	0.973308i
$793$	6.69043	−	12.3132i	0.237584	−	0.437253i
$794$	49.8045	−	86.2639i	1.76750	−	3.06139i
$795$	12.2683	+	13.1629i	0.435111	+	0.466839i
$796$	75.4824			2.67540
$797$	−15.9465	+	27.6202i	−0.564854	+	0.978356i	0.432209	+	0.901773i	$0.357734\pi$
$797$	−15.9465	+	27.6202i	−0.564854	+	0.978356i	−0.997063	+	0.0765828i	$0.975599\pi$
$798$	−5.45211	+	17.8167i	−0.193003	+	0.630705i
$799$	−92.2700			−3.26428
$800$	−5.15443	−	8.92773i	−0.182237	−	0.315643i
$801$	−1.83807	+	26.0935i	−0.0649451	+	0.921968i
$802$	−40.6882	−	70.4740i	−1.43675	−	2.48853i
$803$	−0.690751	−	1.19642i	−0.0243761	−	0.0422206i
$804$	21.9251	−	71.6482i	0.773240	−	2.52684i
$805$	−3.66262	−	6.34385i	−0.129090	−	0.223591i
$806$	31.5781	+	51.5666i	1.11229	+	1.81635i
$807$	26.8167	+	28.7722i	0.943993	+	1.01283i
$808$	63.4434	+	109.887i	2.23193	+	3.86582i
$809$	−10.2607	+	17.7721i	−0.360747	+	0.624833i	−0.988084	−	0.153915i	$-0.950812\pi$
$809$	−10.2607	+	17.7721i	−0.360747	+	0.624833i	0.627337	+	0.778748i	$0.284145\pi$
$810$	−8.78173	−	21.7999i	−0.308559	−	0.765969i
$811$	17.8609			0.627181			0.313590	−	0.949558i	$-0.398468\pi$
$811$	17.8609			0.627181			0.313590	+	0.949558i	$0.398468\pi$
$812$	−40.0900			−1.40688
$813$	−7.27849	+	23.7851i	−0.255268	+	0.834178i
$814$	−21.2482	−	36.8029i	−0.744748	−	1.28994i
$815$	−6.42632	+	11.1307i	−0.225104	+	0.389892i
$816$	37.8429	−	123.665i	1.32477	−	4.32915i
$817$	6.26503	+	10.8514i	0.219186	+	0.379641i
$818$	−2.16148			−0.0755745
$819$	−0.729899	+	16.4079i	−0.0255047	+	0.573338i
$820$	−3.13488			−0.109475
$821$	−0.367023	−	0.635703i	−0.0128092	−	0.0221862i	0.859550	−	0.511052i	$-0.170744\pi$
$821$	−0.367023	−	0.635703i	−0.0128092	−	0.0221862i	−0.872359	+	0.488866i	$0.837411\pi$
$822$	39.2034	+	42.0621i	1.36738	+	1.46708i
$823$	−14.4636	+	25.0517i	−0.504170	+	0.873248i	0.495818	+	0.868426i	$0.334868\pi$
$823$	−14.4636	+	25.0517i	−0.504170	+	0.873248i	−0.999988	+	0.00482168i	$0.998465\pi$
$824$	6.52421	+	11.3003i	0.227282	+	0.393663i
$825$	−3.74045	+	0.862541i	−0.130226	+	0.0300298i
$826$	22.4408			0.780816
$827$	−17.4090			−0.605370			−0.302685	−	0.953091i	$-0.597883\pi$
$827$	−17.4090			−0.605370			−0.302685	+	0.953091i	$0.597883\pi$
$828$	−4.90097	+	69.5747i	−0.170321	+	2.41789i
$829$	−25.3663	+	43.9358i	−0.881010	+	1.52595i	−0.0307899	+	0.999526i	$0.509802\pi$
$829$	−25.3663	+	43.9358i	−0.881010	+	1.52595i	−0.850220	+	0.526428i	$0.823531\pi$
$830$	−8.09605	−	14.0228i	−0.281018	−	0.486738i
$831$	8.35444	−	1.92652i	0.289812	−	0.0668303i
$832$	13.3374	−	24.5463i	0.462391	−	0.850990i
$833$	−18.2826	−	31.6664i	−0.633455	−	1.09718i
$834$	34.9629	−	8.06239i	1.21067	−	0.279178i
$835$	5.27188	+	9.13116i	0.182441	+	0.315997i
$836$	−14.4879	−	25.0938i	−0.501075	−	0.867888i
$837$	−31.1450	−	11.9829i	−1.07653	−	0.414190i
$838$	43.9681	+	76.1550i	1.51885	+	2.63073i
$839$	−3.15817			−0.109032			−0.0545161	−	0.998513i	$-0.517362\pi$
$839$	−3.15817			−0.109032			−0.0545161	+	0.998513i	$0.517362\pi$
$840$	−13.2008	−	14.1634i	−0.455471	−	0.488684i
$841$	−0.507905	+	0.879717i	−0.0175140	+	0.0303351i
$842$	−24.8530			−0.856490
$843$	−2.60484	+	8.51224i	−0.0897154	+	0.293177i
$844$	39.2304	−	67.9490i	1.35037	−	2.33890i
$845$	5.90905	−	11.5794i	0.203277	−	0.398344i
$846$	83.4317	−	40.6394i	2.86844	−	1.39721i
$847$	−4.62231	+	8.00607i	−0.158824	+	0.275092i
$848$	−49.7930	−	86.2439i	−1.70990	−	2.96163i
$849$	13.3900	−	3.08771i	0.459543	−	0.105970i
$850$	10.1700	+	17.6149i	0.348828	+	0.604188i
$851$	17.7123	−	30.6786i	0.607170	−	1.05165i
$852$	67.3941	−	15.5410i	2.30888	−	0.532425i
$853$	−4.05291	+	7.01985i	−0.138769	+	0.240355i	−0.927031	−	0.374985i	$-0.877648\pi$
$853$	−4.05291	+	7.01985i	−0.138769	+	0.240355i	0.788262	+	0.615340i	$0.210981\pi$
$854$	7.70543	+	13.3462i	0.263674	+	0.456697i
$855$	−0.571910	+	8.11889i	−0.0195589	+	0.277660i
$856$	−25.2256	+	43.6919i	−0.862192	+	1.49336i
$857$	−1.99817	+	3.46093i	−0.0682562	+	0.118223i	−0.898134	−	0.439722i	$-0.855077\pi$
$857$	−1.99817	+	3.46093i	−0.0682562	+	0.118223i	0.829878	+	0.557946i	$0.188410\pi$
$858$	−25.3176	−	25.7926i	−0.864330	−	0.880545i
$859$	−13.4957	−	23.3752i	−0.460467	−	0.797552i	0.538518	−	0.842614i	$-0.318985\pi$
$859$	−13.4957	−	23.3752i	−0.460467	−	0.797552i	−0.998984	+	0.0450627i	$0.985651\pi$
$860$	−22.2574			−0.758972
$861$	−1.66705	+	0.384419i	−0.0568129	+	0.0131010i
$862$	64.7318			2.20477
$863$	−26.2622			−0.893976			−0.446988	−	0.894540i	$-0.647503\pi$
$863$	−26.2622			−0.893976			−0.446988	+	0.894540i	$0.647503\pi$
$864$	8.33895	+	52.9133i	0.283697	+	1.80015i
$865$	−8.12914	−	14.0801i	−0.276399	−	0.478737i
$866$	−5.27927	+	9.14396i	−0.179397	+	0.310724i
$867$	−22.1329	+	72.3270i	−0.751671	+	2.45635i
$868$	−46.9941			−1.59509
$869$	−22.1030			−0.749792
$870$	−24.1463	+	5.56810i	−0.818637	+	0.188776i
$871$	−15.4523	+	28.4386i	−0.523581	+	0.963604i
$872$	−74.3214			−2.51684
$873$	14.4710	−	7.04880i	0.489769	−	0.238566i
$874$	17.0891	−	29.5992i	0.578047	−	1.00121i
$875$	1.51841			0.0513316
$876$	1.52254	−	4.97546i	0.0514420	−	0.168105i
$877$	19.4001	−	33.6020i	0.655096	−	1.13466i	−0.326773	−	0.945103i	$-0.605961\pi$
$877$	19.4001	−	33.6020i	0.655096	−	1.13466i	0.981870	−	0.189557i	$-0.0607053\pi$
$878$	43.5409	−	75.4151i	1.46943	−	2.54514i
$879$	−4.68122	+	15.2976i	−0.157894	+	0.515974i
$880$	21.2448			0.716163
$881$	−14.5303	+	25.1672i	−0.489538	+	0.847904i	−0.999928	−	0.0120389i	$-0.996168\pi$
$881$	−14.5303	+	25.1672i	−0.489538	+	0.847904i	0.510390	+	0.859943i	$0.329501\pi$
$882$	30.4785	+	20.5808i	1.02627	+	0.692990i
$883$	29.1018			0.979355			0.489677	−	0.871904i	$-0.337115\pi$
$883$	29.1018			0.979355			0.489677	+	0.871904i	$0.337115\pi$
$884$	−64.6159	+	118.920i	−2.17327	+	3.99971i
$885$	9.55200	−	2.20267i	0.321087	−	0.0740421i
$886$	44.1577			1.48351
$887$	9.27217			0.311329			0.155664	−	0.987810i	$-0.450248\pi$
$887$	9.27217			0.311329			0.155664	+	0.987810i	$0.450248\pi$
$888$	27.3980	−	89.5327i	0.919416	−	3.00452i
$889$	−1.29483	+	2.24271i	−0.0434271	+	0.0752180i
$890$	11.3847	+	19.7189i	0.381616	+	0.660978i
$891$	19.7490	+	2.79619i	0.661618	+	0.0936761i
$892$	−21.2136			−0.710284
$893$	−32.1385			−1.07547
$894$	−42.4954	+	9.79936i	−1.42126	+	0.327740i
$895$	6.88078			0.229999
$896$	−0.292272	−	0.506229i	−0.00976411	−	0.0169119i
$897$	8.06769	−	29.0274i	0.269372	−	0.969195i
$898$	−17.1574	+	29.7175i	−0.572550	+	0.991687i
$899$	−17.5925	+	30.4711i	−0.586743	+	1.01627i
$900$	−11.9817	−	8.09068i	−0.399389	−	0.269689i
$901$	40.4589	+	70.0768i	1.34788	+	2.33460i
$902$	1.88234	−	3.26031i	0.0626752	−	0.108557i
$903$	−11.8359	+	2.72934i	−0.393875	+	0.0908269i
$904$	−3.31323	+	5.73868i	−0.110196	+	0.190866i
$905$	0.975060	+	1.68885i	0.0324121	+	0.0561394i
$906$	0.584445	−	0.134772i	0.0194169	−	0.00447750i
$907$	18.7827	+	32.5326i	0.623669	+	1.08023i	0.988797	+	0.149269i	$0.0476921\pi$
$907$	18.7827	+	32.5326i	0.623669	+	1.08023i	−0.365127	+	0.930958i	$0.618975\pi$
$908$	26.7868	−	46.3961i	0.888952	−	1.53971i
$909$	42.8524	+	28.9363i	1.42132	+	0.959756i
$910$	7.46607	+	12.1920i	0.247498	+	0.404161i
$911$	12.0750	−	20.9146i	0.400064	−	0.692931i	−0.593669	−	0.804709i	$-0.702321\pi$
$911$	12.0750	−	20.9146i	0.400064	−	0.692931i	0.993733	+	0.111778i	$0.0356546\pi$
$912$	13.1810	−	43.0737i	0.436468	−	1.42631i
$913$	13.7420			0.454795
$914$	13.3670	−	23.1524i	0.442142	−	0.765812i
$915$	4.58983	+	4.92452i	0.151735	+	0.162800i
$916$	91.1788			3.01263
$917$	−12.8335	−	22.2283i	−0.423799	−	0.734042i
$918$	−16.4532	−	104.401i	−0.543038	−	3.44575i
$919$	−7.35962	−	12.7472i	−0.242771	−	0.420492i	0.718731	−	0.695288i	$-0.244723\pi$
$919$	−7.35962	−	12.7472i	−0.242771	−	0.420492i	−0.961503	+	0.274796i	$0.911390\pi$
$920$	17.7578	+	30.7574i	0.585458	+	1.01404i
$921$	−29.4923	+	6.80087i	−0.971803	+	0.224096i
$922$	32.4098	+	56.1354i	1.06736	+	1.84872i
$923$	−29.8652	+	0.772797i	−0.983026	+	0.0254369i
$924$	27.3706	−	6.31162i	0.900428	−	0.207637i
$925$	3.67149	+	6.35920i	0.120718	+	0.209089i
$926$	−4.34918	+	7.53300i	−0.142923	+	0.247550i
$927$	4.40673	+	2.97566i	0.144736	+	0.0977336i
$928$	56.4788			1.85401
$929$	25.8981			0.849688			0.424844	−	0.905267i	$-0.360329\pi$
$929$	25.8981			0.849688			0.424844	+	0.905267i	$0.360329\pi$
$930$	−28.3047	+	6.52702i	−0.928148	+	0.214029i
$931$	−6.36800	−	11.0297i	−0.208703	−	0.361484i
$932$	20.9210	−	36.2363i	0.685292	−	1.18696i
$933$	−17.4832	−	18.7581i	−0.572375	−	0.614113i
$934$	−12.8089	−	22.1856i	−0.419119	−	0.725936i
$935$	−17.2623			−0.564538
$936$	3.53884	−	79.5518i	0.115671	−	2.60023i
$937$	21.1191			0.689931			0.344965	−	0.938615i	$-0.387891\pi$
$937$	21.1191			0.689931			0.344965	+	0.938615i	$0.387891\pi$
$938$	−17.7965	−	30.8245i	−0.581077	−	1.00646i
$939$	9.69616	−	31.6857i	0.316422	−	1.03402i
$940$	28.5442	−	49.4400i	0.931009	−	1.61255i
$941$	8.40481	+	14.5576i	0.273989	+	0.474563i	0.969880	−	0.243585i	$-0.0783235\pi$
$941$	8.40481	+	14.5576i	0.273989	+	0.474563i	−0.695891	+	0.718148i	$0.744990\pi$
$942$	−21.1091	+	68.9815i	−0.687772	+	2.24754i
$943$	3.13821			0.102194
$944$	−54.2529			−1.76578
$945$	−7.36367	−	2.83315i	−0.239540	−	0.0921622i
$946$	13.3645	−	23.1480i	0.434517	−	0.752606i
$947$	−6.80091	−	11.7795i	−0.221000	−	0.382783i	0.734112	−	0.679028i	$-0.237599\pi$
$947$	−6.80091	−	11.7795i	−0.221000	−	0.382783i	−0.955112	+	0.296245i	$0.904265\pi$
$948$	−56.7588	−	60.8977i	−1.84344	−	1.97786i
$949$	−1.07305	+	1.97485i	−0.0348327	+	0.0641065i
$950$	3.54230	+	6.13545i	0.114928	+	0.199060i
$951$	14.4875	−	47.3430i	0.469789	−	1.53520i
$952$	−43.5342	−	75.4035i	−1.41095	−	2.44384i
$953$	16.7114	+	28.9450i	0.541335	+	0.937619i	0.998828	+	0.0484061i	$0.0154142\pi$
$953$	16.7114	+	28.9450i	0.541335	+	0.937619i	−0.457493	+	0.889213i	$0.651253\pi$
$954$	−67.4481	−	45.5446i	−2.18371	−	1.47456i
$955$	−10.7701	−	18.6544i	−0.348512	−	0.603641i
$956$	−119.015			−3.84922
$957$	6.15387	−	20.1100i	0.198926	−	0.650063i
$958$	−27.2930	+	47.2729i	−0.881797	+	1.52732i
$959$	19.3029			0.623323
$960$	9.14985	+	9.81705i	0.295310	+	0.316844i
$961$	−5.12221	+	8.87193i	−0.165233	+	0.286191i
$962$	−33.0081	+	60.7484i	−1.06422	+	1.95861i
$963$	−1.44465	+	20.5083i	−0.0465531	+	0.660872i
$964$	51.8803	−	89.8594i	1.67095	−	2.89418i
$965$	−2.50433	−	4.33763i	−0.0806174	−	0.139633i
$966$	22.5898	+	24.2370i	0.726815	+	0.779814i
$967$	15.9169	+	27.5689i	0.511854	+	0.886557i	0.999906	+	0.0137423i	$0.00437446\pi$
$967$	15.9169	+	27.5689i	0.511854	+	0.886557i	−0.488052	+	0.872815i	$0.662292\pi$
$968$	22.4107	−	38.8165i	0.720309	−	1.24761i
$969$	−10.7101	+	34.9992i	−0.344059	+	1.12434i
$970$	7.00559	−	12.1340i	0.224936	−	0.389600i
$971$	4.17466	+	7.23072i	0.133971	+	0.232045i	0.925204	−	0.379470i	$-0.123894\pi$
$971$	4.17466	+	7.23072i	0.133971	+	0.232045i	−0.791233	+	0.611515i	$0.790560\pi$
$972$	43.0101	+	61.5926i	1.37955	+	1.97558i
$973$	6.02270	−	10.4316i	0.193079	−	0.334422i
$974$	20.6681	−	35.7982i	0.662249	−	1.14705i
$975$	4.37466	+	4.45672i	0.140101	+	0.142729i
$976$	−18.6287	−	32.2658i	−0.596289	−	1.03280i
$977$	28.0990			0.898967			0.449484	−	0.893289i	$-0.351608\pi$
$977$	28.0990			0.898967			0.449484	+	0.893289i	$0.351608\pi$
$978$	17.0105	−	55.5879i	0.543936	−	1.77751i
$979$	−19.3241			−0.617601
$980$	22.6233			0.722673
$981$	−27.2281	+	13.2628i	−0.869326	+	0.423447i
$982$	37.7159	+	65.3258i	1.20356	+	2.08463i
$983$	−12.2726	+	21.2567i	−0.391434	+	0.677984i	−0.992639	−	0.121111i	$-0.961354\pi$
$983$	−12.2726	+	21.2567i	−0.391434	+	0.677984i	0.601205	+	0.799095i	$0.294688\pi$
$984$	8.08251	−	1.86381i	0.257661	−	0.0594162i
$985$	25.2958			0.805992
$986$	−111.436			−3.54885
$987$	9.11642	−	29.7912i	0.290179	−	0.948263i
$988$	−22.5063	+	41.4209i	−0.716021	+	1.31777i
$989$	22.2811			0.708497
$990$	15.6088	−	7.60302i	0.496080	−	0.241640i
$991$	14.1676	−	24.5389i	0.450047	−	0.779505i	−0.548341	−	0.836255i	$-0.684740\pi$
$991$	14.1676	−	24.5389i	0.450047	−	0.779505i	0.998388	+	0.0567498i	$0.0180737\pi$
$992$	66.2054			2.10202
$993$	−46.2939	+	10.6753i	−1.46909	+	0.338770i
$994$	16.4272	−	28.4528i	0.521040	−	0.902468i
$995$	7.83148	−	13.5645i	0.248275	−	0.430024i
$996$	35.2886	+	37.8618i	1.11816	+	1.19970i
$997$	−10.4067			−0.329583			−0.164792	−	0.986328i	$-0.552695\pi$
$997$	−10.4067			−0.329583			−0.164792	+	0.986328i	$0.552695\pi$
$998$	9.51250	−	16.4761i	0.301113	−	0.521543i
$999$	−5.93982	−	37.6900i	−0.187927	−	1.19246i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.k.a.61.2	✓	56
9.4	even	3		585.2.l.a.256.27	yes	56
13.3	even	3		585.2.l.a.16.27	yes	56
117.94	even	3	inner	585.2.k.a.211.2	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.k.a.61.2	✓	56	1.1	even	1	trivial
585.2.k.a.211.2	yes	56	117.94	even	3	inner
585.2.l.a.16.27	yes	56	13.3	even	3
585.2.l.a.256.27	yes	56	9.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30568 - 2.26150i) q^{2} +(1.68776 - 0.389194i) q^{3} +(-2.40958 + 4.17352i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-3.08383 - 3.30870i) q^{6} -1.51841 q^{7} +7.36184 q^{8} +(2.69706 - 1.31373i) q^{9} +O(q^{10})\)	\(q+(-1.30568 - 2.26150i) q^{2} +(1.68776 - 0.389194i) q^{3} +(-2.40958 + 4.17352i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-3.08383 - 3.30870i) q^{6} -1.51841 q^{7} +7.36184 q^{8} +(2.69706 - 1.31373i) q^{9} +(1.30568 - 2.26150i) q^{10} +(1.10811 + 1.91931i) q^{11} +(-2.44248 + 7.98169i) q^{12} +(1.72140 - 3.16809i) q^{13} +(1.98255 + 3.43388i) q^{14} +(1.18093 + 1.26704i) q^{15} +(-4.79302 - 8.30176i) q^{16} +(3.89453 + 6.74552i) q^{17} +(-6.49248 - 4.38408i) q^{18} +(1.35650 + 2.34953i) q^{19} -4.81917 q^{20} +(-2.56271 + 0.590956i) q^{21} +(2.89367 - 5.01199i) q^{22} +4.82428 q^{23} +(12.4250 - 2.86519i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-9.41222 + 0.243552i) q^{26} +(4.04068 - 3.26694i) q^{27} +(3.65874 - 6.33712i) q^{28} +(-2.73933 - 4.74467i) q^{29} +(1.32350 - 4.32502i) q^{30} +(-3.21109 - 5.56177i) q^{31} +(-5.15443 + 8.92773i) q^{32} +(2.61721 + 2.80805i) q^{33} +(10.1700 - 17.6149i) q^{34} +(-0.759205 - 1.31498i) q^{35} +(-1.01590 + 14.4218i) q^{36} +(3.67149 - 6.35920i) q^{37} +(3.54230 - 6.13545i) q^{38} +(1.67231 - 6.01692i) q^{39} +(3.68092 + 6.37554i) q^{40} +0.650503 q^{41} +(4.68252 + 5.02396i) q^{42} +4.61852 q^{43} -10.6804 q^{44} +(2.48625 + 1.67885i) q^{45} +(-6.29896 - 10.9101i) q^{46} +(-5.92305 + 10.2590i) q^{47} +(-11.3205 - 12.1459i) q^{48} -4.69443 q^{49} +2.61135 q^{50} +(9.19834 + 9.86908i) q^{51} +(9.07422 + 14.8181i) q^{52} +10.3886 q^{53} +(-12.6640 - 4.87243i) q^{54} +(-1.10811 + 1.91931i) q^{55} -11.1783 q^{56} +(3.20387 + 3.43749i) q^{57} +(-7.15337 + 12.3900i) q^{58} +(2.82979 - 4.90134i) q^{59} +(-8.13359 + 1.87559i) q^{60} +3.88662 q^{61} +(-8.38529 + 14.5238i) q^{62} +(-4.09524 + 1.99478i) q^{63} +7.74799 q^{64} +(3.60434 - 0.0932665i) q^{65} +(2.93318 - 9.58522i) q^{66} -8.97657 q^{67} -37.5368 q^{68} +(8.14223 - 1.87758i) q^{69} +(-1.98255 + 3.43388i) q^{70} +(-4.14295 - 7.17580i) q^{71} +(19.8553 - 9.67148i) q^{72} -0.623359 q^{73} -19.1751 q^{74} +(-0.506827 + 1.65624i) q^{75} -13.0744 q^{76} +(-1.68257 - 2.91429i) q^{77} +(-15.7908 + 4.07424i) q^{78} +(-4.98663 + 8.63709i) q^{79} +(4.79302 - 8.30176i) q^{80} +(5.54822 - 7.08641i) q^{81} +(-0.849347 - 1.47111i) q^{82} +(3.10033 - 5.36992i) q^{83} +(3.70869 - 12.1195i) q^{84} +(-3.89453 + 6.74552i) q^{85} +(-6.03030 - 10.4448i) q^{86} +(-6.46993 - 6.94172i) q^{87} +(8.15775 + 14.1296i) q^{88} +(-4.35969 + 7.55120i) q^{89} +(0.550482 - 7.81470i) q^{90} +(-2.61379 + 4.81046i) q^{91} +(-11.6245 + 20.1343i) q^{92} +(-7.58416 - 8.13719i) q^{93} +30.9344 q^{94} +(-1.35650 + 2.34953i) q^{95} +(-5.22481 + 17.0739i) q^{96} +5.36548 q^{97} +(6.12941 + 10.6164i) q^{98} +(5.51009 + 3.72072i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - q^{3} - 28 q^{4} + 28 q^{5} + 2 q^{6} - 12 q^{7} + 6 q^{8} + 5 q^{9}+O(q^{10}) \) 56 * q - q^3 - 28 * q^4 + 28 * q^5 + 2 * q^6 - 12 * q^7 + 6 * q^8 + 5 * q^9	\( 56 q - q^{3} - 28 q^{4} + 28 q^{5} + 2 q^{6} - 12 q^{7} + 6 q^{8} + 5 q^{9} + 2 q^{11} - 10 q^{12} - 2 q^{13} - 2 q^{15} - 36 q^{16} - 5 q^{17} - 7 q^{18} + 19 q^{19} - 56 q^{20} + 17 q^{21} + 24 q^{23} + 12 q^{24} - 28 q^{25} + 2 q^{26} - 16 q^{27} + 21 q^{28} - q^{29} + q^{30} + 20 q^{31} - 6 q^{32} - 12 q^{33} + 2 q^{34} - 6 q^{35} - 20 q^{36} + 17 q^{37} - 2 q^{38} + 3 q^{39} + 3 q^{40} + 4 q^{41} - 11 q^{42} - 8 q^{43} - 56 q^{44} + 7 q^{45} + 20 q^{46} - 15 q^{47} + 86 q^{48} + 48 q^{49} + 10 q^{51} + 43 q^{52} + 32 q^{53} + 50 q^{54} - 2 q^{55} + 40 q^{56} + 5 q^{57} + 48 q^{58} + 10 q^{59} + q^{60} - 14 q^{61} - 25 q^{62} - 51 q^{63} + 106 q^{64} - q^{65} + 7 q^{66} - 96 q^{67} + 50 q^{68} + 14 q^{69} - 6 q^{71} - 21 q^{72} - 62 q^{73} + 20 q^{74} - q^{75} - 88 q^{76} - 34 q^{77} - 2 q^{78} + 10 q^{79} + 36 q^{80} - 7 q^{81} - q^{82} + 9 q^{83} - 51 q^{84} + 5 q^{85} - 69 q^{86} - 61 q^{87} + 19 q^{88} + 10 q^{89} + 19 q^{90} - 26 q^{91} + 14 q^{92} - 59 q^{93} + 52 q^{94} - 19 q^{95} - 76 q^{96} - 34 q^{97} + 24 q^{98} + q^{99}+O(q^{100}) \) 56 * q - q^3 - 28 * q^4 + 28 * q^5 + 2 * q^6 - 12 * q^7 + 6 * q^8 + 5 * q^9 + 2 * q^11 - 10 * q^12 - 2 * q^13 - 2 * q^15 - 36 * q^16 - 5 * q^17 - 7 * q^18 + 19 * q^19 - 56 * q^20 + 17 * q^21 + 24 * q^23 + 12 * q^24 - 28 * q^25 + 2 * q^26 - 16 * q^27 + 21 * q^28 - q^29 + q^30 + 20 * q^31 - 6 * q^32 - 12 * q^33 + 2 * q^34 - 6 * q^35 - 20 * q^36 + 17 * q^37 - 2 * q^38 + 3 * q^39 + 3 * q^40 + 4 * q^41 - 11 * q^42 - 8 * q^43 - 56 * q^44 + 7 * q^45 + 20 * q^46 - 15 * q^47 + 86 * q^48 + 48 * q^49 + 10 * q^51 + 43 * q^52 + 32 * q^53 + 50 * q^54 - 2 * q^55 + 40 * q^56 + 5 * q^57 + 48 * q^58 + 10 * q^59 + q^60 - 14 * q^61 - 25 * q^62 - 51 * q^63 + 106 * q^64 - q^65 + 7 * q^66 - 96 * q^67 + 50 * q^68 + 14 * q^69 - 6 * q^71 - 21 * q^72 - 62 * q^73 + 20 * q^74 - q^75 - 88 * q^76 - 34 * q^77 - 2 * q^78 + 10 * q^79 + 36 * q^80 - 7 * q^81 - q^82 + 9 * q^83 - 51 * q^84 + 5 * q^85 - 69 * q^86 - 61 * q^87 + 19 * q^88 + 10 * q^89 + 19 * q^90 - 26 * q^91 + 14 * q^92 - 59 * q^93 + 52 * q^94 - 19 * q^95 - 76 * q^96 - 34 * q^97 + 24 * q^98 + q^99

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