LMFDB - Embedded newform 585.2.i.f.391.1

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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 11 x^{14} - 4 x^{13} + 74 x^{12} - 18 x^{11} + 289 x^{10} - 4 x^{9} + 784 x^{8} + \cdots + 81 $ x^16 - x^15 + 11x^14 - 4x^13 + 74x^12 - 18x^11 + 289x^10 - 4x^9 + 784x^8 - 9x^7 + 1221x^6 + 133x^5 + 1245x^4 - 14x^3 + 391x^2 + 63x + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			391.1
Root			$-0.947115 - 1.64045i$ of defining polynomial
Character	$\chi$	$=$	585.391
Dual form			585.2.i.f.196.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.947115 - 1.64045i) q^{2} +(1.31847 + 1.12323i) q^{3} +(-0.794055 + 1.37534i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.593868 - 3.22671i) q^{6} +(-0.837925 - 1.45133i) q^{7} -0.780216 q^{8} +(0.476703 + 2.96188i) q^{9} +O(q^{10})$	\(q+(-0.947115 - 1.64045i) q^{2} +(1.31847 + 1.12323i) q^{3} +(-0.794055 + 1.37534i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.593868 - 3.22671i) q^{6} +(-0.837925 - 1.45133i) q^{7} -0.780216 q^{8} +(0.476703 + 2.96188i) q^{9} +1.89423 q^{10} +(3.21299 + 5.56505i) q^{11} +(-2.59176 + 0.921436i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(-1.58722 + 2.74915i) q^{14} +(-1.63198 + 0.580209i) q^{15} +(2.32706 + 4.03059i) q^{16} +1.05707 q^{17} +(4.40733 - 3.58725i) q^{18} -3.65865 q^{19} +(-0.794055 - 1.37534i) q^{20} +(0.525402 - 2.85471i) q^{21} +(6.08613 - 10.5415i) q^{22} +(-0.680383 + 1.17846i) q^{23} +(-1.02869 - 0.876363i) q^{24} +(-0.500000 - 0.866025i) q^{25} +1.89423 q^{26} +(-2.69836 + 4.44059i) q^{27} +2.66143 q^{28} +(3.77283 + 6.53474i) q^{29} +(2.49748 + 2.12766i) q^{30} +(3.43234 - 5.94499i) q^{31} +(3.62778 - 6.28350i) q^{32} +(-2.01463 + 10.9463i) q^{33} +(-1.00117 - 1.73408i) q^{34} +1.67585 q^{35} +(-4.45213 - 1.69627i) q^{36} +1.00252 q^{37} +(3.46517 + 6.00184i) q^{38} +(-1.63198 + 0.580209i) q^{39} +(0.390108 - 0.675687i) q^{40} +(-4.24719 + 7.35635i) q^{41} +(-5.18063 + 1.84184i) q^{42} +(4.06159 + 7.03488i) q^{43} -10.2051 q^{44} +(-2.80342 - 1.06810i) q^{45} +2.57760 q^{46} +(1.19645 + 2.07231i) q^{47} +(-1.45913 + 7.92803i) q^{48} +(2.09576 - 3.62997i) q^{49} +(-0.947115 + 1.64045i) q^{50} +(1.39372 + 1.18734i) q^{51} +(-0.794055 - 1.37534i) q^{52} +8.53534 q^{53} +(9.84023 + 0.220784i) q^{54} -6.42597 q^{55} +(0.653762 + 1.13235i) q^{56} +(-4.82381 - 4.10951i) q^{57} +(7.14661 - 12.3783i) q^{58} +(-1.08646 + 1.88181i) q^{59} +(0.497894 - 2.70525i) q^{60} +(-3.43982 - 5.95795i) q^{61} -13.0033 q^{62} +(3.89922 - 3.17369i) q^{63} -4.43545 q^{64} +(-0.500000 - 0.866025i) q^{65} +(19.8649 - 7.06246i) q^{66} +(7.61479 - 13.1892i) q^{67} +(-0.839375 + 1.45384i) q^{68} +(-2.22074 + 0.789528i) q^{69} +(-1.58722 - 2.74915i) q^{70} -2.39189 q^{71} +(-0.371932 - 2.31091i) q^{72} -15.4370 q^{73} +(-0.949498 - 1.64458i) q^{74} +(0.313514 - 1.70344i) q^{75} +(2.90517 - 5.03190i) q^{76} +(5.38448 - 9.32619i) q^{77} +(2.49748 + 2.12766i) q^{78} +(8.52960 + 14.7737i) q^{79} -4.65413 q^{80} +(-8.54551 + 2.82388i) q^{81} +16.0903 q^{82} +(-6.10235 - 10.5696i) q^{83} +(3.50901 + 2.98940i) q^{84} +(-0.528537 + 0.915454i) q^{85} +(7.69359 - 13.3257i) q^{86} +(-2.36567 + 12.8536i) q^{87} +(-2.50682 - 4.34194i) q^{88} +5.02045 q^{89} +(0.902986 + 5.61049i) q^{90} +1.67585 q^{91} +(-1.08052 - 1.87152i) q^{92} +(11.2030 - 3.98295i) q^{93} +(2.26635 - 3.92543i) q^{94} +(1.82933 - 3.16849i) q^{95} +(11.8409 - 4.20974i) q^{96} +(0.432165 + 0.748531i) q^{97} -7.93972 q^{98} +(-14.9514 + 12.1694i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{2} - 2 q^{3} - 5 q^{4} - 8 q^{5} - 13 q^{6} + 6 q^{7} - 12 q^{8} + 4 q^{9}+O(q^{10}) $ 16 * q + q^2 - 2 * q^3 - 5 * q^4 - 8 * q^5 - 13 * q^6 + 6 * q^7 - 12 * q^8 + 4 * q^9	\( 16 q + q^{2} - 2 q^{3} - 5 q^{4} - 8 q^{5} - 13 q^{6} + 6 q^{7} - 12 q^{8} + 4 q^{9} - 2 q^{10} + 9 q^{11} - 16 q^{12} - 8 q^{13} - 3 q^{14} + q^{15} + 13 q^{16} + 12 q^{17} + 23 q^{18} - 22 q^{19} - 5 q^{20} + 15 q^{21} + 4 q^{22} + 3 q^{23} - 12 q^{24} - 8 q^{25} - 2 q^{26} + 22 q^{27} - 26 q^{28} + 8 q^{29} + 8 q^{30} + 18 q^{31} + 3 q^{32} - 26 q^{33} + 9 q^{34} - 12 q^{35} + 5 q^{36} - 36 q^{37} - 8 q^{38} + q^{39} + 6 q^{40} - 17 q^{41} - 45 q^{42} + 17 q^{43} + 10 q^{44} + q^{45} + 6 q^{46} + 11 q^{47} + 35 q^{48} + 16 q^{49} + q^{50} - 16 q^{51} - 5 q^{52} + 20 q^{53} + 44 q^{54} - 18 q^{55} - q^{56} - 25 q^{57} + 10 q^{58} + 7 q^{59} + 5 q^{60} + 21 q^{61} - 58 q^{62} - 30 q^{63} - 20 q^{64} - 8 q^{65} + 68 q^{66} + 13 q^{67} - 16 q^{68} - 13 q^{69} - 3 q^{70} - 68 q^{71} + 36 q^{72} - 32 q^{73} - 4 q^{74} + q^{75} + 2 q^{76} + 18 q^{77} + 8 q^{78} + 37 q^{79} - 26 q^{80} - 32 q^{81} + 2 q^{82} + 3 q^{83} + 27 q^{84} - 6 q^{85} - 2 q^{86} - 20 q^{87} + 19 q^{88} + 28 q^{89} - 16 q^{90} - 12 q^{91} - 14 q^{92} + 19 q^{93} + 44 q^{94} + 11 q^{95} - 35 q^{96} + 17 q^{97} + 90 q^{98} - 44 q^{99}+O(q^{100}) \) 16 * q + q^2 - 2 * q^3 - 5 * q^4 - 8 * q^5 - 13 * q^6 + 6 * q^7 - 12 * q^8 + 4 * q^9 - 2 * q^10 + 9 * q^11 - 16 * q^12 - 8 * q^13 - 3 * q^14 + q^15 + 13 * q^16 + 12 * q^17 + 23 * q^18 - 22 * q^19 - 5 * q^20 + 15 * q^21 + 4 * q^22 + 3 * q^23 - 12 * q^24 - 8 * q^25 - 2 * q^26 + 22 * q^27 - 26 * q^28 + 8 * q^29 + 8 * q^30 + 18 * q^31 + 3 * q^32 - 26 * q^33 + 9 * q^34 - 12 * q^35 + 5 * q^36 - 36 * q^37 - 8 * q^38 + q^39 + 6 * q^40 - 17 * q^41 - 45 * q^42 + 17 * q^43 + 10 * q^44 + q^45 + 6 * q^46 + 11 * q^47 + 35 * q^48 + 16 * q^49 + q^50 - 16 * q^51 - 5 * q^52 + 20 * q^53 + 44 * q^54 - 18 * q^55 - q^56 - 25 * q^57 + 10 * q^58 + 7 * q^59 + 5 * q^60 + 21 * q^61 - 58 * q^62 - 30 * q^63 - 20 * q^64 - 8 * q^65 + 68 * q^66 + 13 * q^67 - 16 * q^68 - 13 * q^69 - 3 * q^70 - 68 * q^71 + 36 * q^72 - 32 * q^73 - 4 * q^74 + q^75 + 2 * q^76 + 18 * q^77 + 8 * q^78 + 37 * q^79 - 26 * q^80 - 32 * q^81 + 2 * q^82 + 3 * q^83 + 27 * q^84 - 6 * q^85 - 2 * q^86 - 20 * q^87 + 19 * q^88 + 28 * q^89 - 16 * q^90 - 12 * q^91 - 14 * q^92 + 19 * q^93 + 44 * q^94 + 11 * q^95 - 35 * q^96 + 17 * q^97 + 90 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.947115	−	1.64045i	−0.669712	−	1.15997i	−0.977985	−	0.208677i	$-0.933084\pi$
$2$	−0.947115	−	1.64045i	−0.669712	−	1.15997i	0.308273	−	0.951298i	$-0.400249\pi$
$3$	1.31847	+	1.12323i	0.761217	+	0.648498i
$3$	1.31847	+	1.12323i	0.761217	+	0.648498i
$4$	−0.794055	+	1.37534i	−0.397027	+	0.687672i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	0.593868	−	3.22671i	0.242445	−	1.31730i
$7$	−0.837925	−	1.45133i	−0.316706	−	0.548551i	0.663093	−	0.748537i	$-0.269243\pi$
$7$	−0.837925	−	1.45133i	−0.316706	−	0.548551i	−0.979799	+	0.199987i	$0.935910\pi$
$8$	−0.780216			−0.275848
$9$	0.476703	+	2.96188i	0.158901	+	0.987295i
$10$	1.89423			0.599008
$11$	3.21299	+	5.56505i	0.968751	+	1.67793i	0.699179	+	0.714947i	$0.253549\pi$
$11$	3.21299	+	5.56505i	0.968751	+	1.67793i	0.269573	+	0.962980i	$0.413118\pi$
$12$	−2.59176	+	0.921436i	−0.748177	+	0.265996i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$14$	−1.58722	+	2.74915i	−0.424203	+	0.734741i
$15$	−1.63198	+	0.580209i	−0.421375	+	0.149809i
$16$	2.32706	+	4.03059i	0.581766	+	1.00765i
$17$	1.05707			0.256378			0.128189	−	0.991750i	$-0.459084\pi$
$17$	1.05707			0.256378			0.128189	+	0.991750i	$0.459084\pi$
$18$	4.40733	−	3.58725i	1.03882	−	0.845524i
$19$	−3.65865			−0.839353			−0.419676	−	0.907674i	$-0.637856\pi$
$19$	−3.65865			−0.839353			−0.419676	+	0.907674i	$0.637856\pi$
$20$	−0.794055	−	1.37534i	−0.177556	−	0.307536i
$21$	0.525402	−	2.85471i	0.114652	−	0.622949i
$22$	6.08613	−	10.5415i	1.29757	−	2.24745i
$23$	−0.680383	+	1.17846i	−0.141870	+	0.245725i	−0.928201	−	0.372080i	$-0.878645\pi$
$23$	−0.680383	+	1.17846i	−0.141870	+	0.245725i	0.786331	+	0.617805i	$0.211978\pi$
$24$	−1.02869	−	0.876363i	−0.209980	−	0.178887i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	1.89423			0.371489
$27$	−2.69836	+	4.44059i	−0.519300	+	0.854592i
$28$	2.66143			0.502964
$29$	3.77283	+	6.53474i	0.700597	+	1.21347i	0.968257	+	0.249957i	$0.0804164\pi$
$29$	3.77283	+	6.53474i	0.700597	+	1.21347i	−0.267660	+	0.963514i	$0.586250\pi$
$30$	2.49748	+	2.12766i	0.455975	+	0.388456i
$31$	3.43234	−	5.94499i	0.616467	−	1.06775i	−0.373658	−	0.927566i	$-0.621897\pi$
$31$	3.43234	−	5.94499i	0.616467	−	1.06775i	0.990125	−	0.140186i	$-0.0447699\pi$
$32$	3.62778	−	6.28350i	0.641307	−	1.11078i
$33$	−2.01463	+	10.9463i	−0.350702	+	1.90550i
$34$	−1.00117	−	1.73408i	−0.171700	−	0.297392i
$35$	1.67585			0.283270
$36$	−4.45213	−	1.69627i	−0.742022	−	0.282711i
$37$	1.00252			0.164813			0.0824063	−	0.996599i	$-0.473739\pi$
$37$	1.00252			0.164813			0.0824063	+	0.996599i	$0.473739\pi$
$38$	3.46517	+	6.00184i	0.562124	+	0.973628i
$39$	−1.63198	+	0.580209i	−0.261326	+	0.0929078i
$40$	0.390108	−	0.675687i	0.0616815	−	0.106835i
$41$	−4.24719	+	7.35635i	−0.663299	+	1.14887i	0.316444	+	0.948611i	$0.397511\pi$
$41$	−4.24719	+	7.35635i	−0.663299	+	1.14887i	−0.979743	+	0.200257i	$0.935822\pi$
$42$	−5.18063	+	1.84184i	−0.799389	+	0.284202i
$43$	4.06159	+	7.03488i	0.619387	+	1.07281i	0.989598	+	0.143861i	$0.0459519\pi$
$43$	4.06159	+	7.03488i	0.619387	+	1.07281i	−0.370211	+	0.928948i	$0.620715\pi$
$44$	−10.2051			−1.53848
$45$	−2.80342	−	1.06810i	−0.417909	−	0.159224i
$46$	2.57760			0.380047
$47$	1.19645	+	2.07231i	0.174520	+	0.302277i	0.939995	−	0.341188i	$-0.110829\pi$
$47$	1.19645	+	2.07231i	0.174520	+	0.302277i	−0.765475	+	0.643465i	$0.777496\pi$
$48$	−1.45913	+	7.92803i	−0.210608	+	1.14431i
$49$	2.09576	−	3.62997i	0.299395	−	0.518567i
$50$	−0.947115	+	1.64045i	−0.133942	+	0.231995i
$51$	1.39372	+	1.18734i	0.195159	+	0.166261i
$52$	−0.794055	−	1.37534i	−0.110116	−	0.190726i
$53$	8.53534			1.17242			0.586210	−	0.810159i	$-0.300619\pi$
$53$	8.53534			1.17242			0.586210	+	0.810159i	$0.300619\pi$
$54$	9.84023	+	0.220784i	1.33909	+	0.0300449i
$55$	−6.42597			−0.866478
$56$	0.653762	+	1.13235i	0.0873627	+	0.151317i
$57$	−4.82381	−	4.10951i	−0.638929	−	0.544318i
$58$	7.14661	−	12.3783i	0.938396	−	1.62535i
$59$	−1.08646	+	1.88181i	−0.141445	+	0.244990i	−0.928041	−	0.372478i	$-0.878508\pi$
$59$	−1.08646	+	1.88181i	−0.141445	+	0.244990i	0.786596	+	0.617468i	$0.211842\pi$
$60$	0.497894	−	2.70525i	0.0642779	−	0.349246i
$61$	−3.43982	−	5.95795i	−0.440424	−	0.762837i	0.557297	−	0.830313i	$-0.311839\pi$
$61$	−3.43982	−	5.95795i	−0.440424	−	0.762837i	−0.997721	+	0.0674765i	$0.978505\pi$
$62$	−13.0033			−1.65142
$63$	3.89922	−	3.17369i	0.491256	−	0.399847i
$64$	−4.43545			−0.554431
$65$	−0.500000	−	0.866025i	−0.0620174	−	0.107417i
$66$	19.8649	−	7.06246i	2.44520	−	0.869329i
$67$	7.61479	−	13.1892i	0.930295	−	1.61132i	0.147478	−	0.989065i	$-0.452885\pi$
$67$	7.61479	−	13.1892i	0.930295	−	1.61132i	0.782817	−	0.622252i	$-0.213782\pi$
$68$	−0.839375	+	1.45384i	−0.101789	+	0.176304i
$69$	−2.22074	+	0.789528i	−0.267346	+	0.0950480i
$70$	−1.58722	−	2.74915i	−0.189709	−	0.328586i
$71$	−2.39189			−0.283865			−0.141932	−	0.989876i	$-0.545332\pi$
$71$	−2.39189			−0.283865			−0.141932	+	0.989876i	$0.545332\pi$
$72$	−0.371932	−	2.31091i	−0.0438326	−	0.272343i
$73$	−15.4370			−1.80676			−0.903380	−	0.428840i	$-0.858922\pi$
$73$	−15.4370			−1.80676			−0.903380	+	0.428840i	$0.858922\pi$
$74$	−0.949498	−	1.64458i	−0.110377	−	0.191178i
$75$	0.313514	−	1.70344i	0.0362015	−	0.196696i
$76$	2.90517	−	5.03190i	0.333246	−	0.577199i
$77$	5.38448	−	9.32619i	0.613619	−	1.06282i
$78$	2.49748	+	2.12766i	0.282784	+	0.240910i
$79$	8.52960	+	14.7737i	0.959655	+	1.66217i	0.723337	+	0.690495i	$0.242607\pi$
$79$	8.52960	+	14.7737i	0.959655	+	1.66217i	0.236317	+	0.971676i	$0.424060\pi$
$80$	−4.65413			−0.520347
$81$	−8.54551	+	2.82388i	−0.949501	+	0.313764i
$82$	16.0903			1.77688
$83$	−6.10235	−	10.5696i	−0.669820	−	1.16016i	−0.977954	−	0.208819i	$-0.933038\pi$
$83$	−6.10235	−	10.5696i	−0.669820	−	1.16016i	0.308134	−	0.951343i	$-0.400295\pi$
$84$	3.50901	+	2.98940i	0.382864	+	0.326171i
$85$	−0.528537	+	0.915454i	−0.0573279	+	0.0992949i
$86$	7.69359	−	13.3257i	0.829621	−	1.43695i
$87$	−2.36567	+	12.8536i	−0.253627	+	1.37805i
$88$	−2.50682	−	4.34194i	−0.267228	−	0.462853i
$89$	5.02045			0.532166			0.266083	−	0.963950i	$-0.414270\pi$
$89$	5.02045			0.532166			0.266083	+	0.963950i	$0.414270\pi$
$90$	0.902986	+	5.61049i	0.0951831	+	0.591398i
$91$	1.67585			0.175677
$92$	−1.08052	−	1.87152i	−0.112652	−	0.195119i
$93$	11.2030	−	3.98295i	1.16170	−	0.413013i
$94$	2.26635	−	3.92543i	0.233756	−	0.404877i
$95$	1.82933	−	3.16849i	0.187685	−	0.325080i
$96$	11.8409	−	4.20974i	1.20851	−	0.429655i
$97$	0.432165	+	0.748531i	0.0438797	+	0.0760018i	0.887131	−	0.461518i	$-0.152695\pi$
$97$	0.432165	+	0.748531i	0.0438797	+	0.0760018i	−0.843251	+	0.537519i	$0.819362\pi$
$98$	−7.93972			−0.802033
$99$	−14.9514	+	12.1694i	−1.50267	+	1.22307i
$100$	1.58811			0.158811
$101$	−5.97502	−	10.3490i	−0.594536	−	1.02977i	−0.993612	−	0.112849i	$-0.964002\pi$
$101$	−5.97502	−	10.3490i	−0.594536	−	1.02977i	0.399076	−	0.916918i	$-0.369331\pi$
$102$	0.627762	−	3.41087i	0.0621577	−	0.337727i
$103$	1.89744	−	3.28646i	0.186960	−	0.323825i	−0.757275	−	0.653096i	$-0.773470\pi$
$103$	1.89744	−	3.28646i	0.186960	−	0.323825i	0.944235	+	0.329271i	$0.106803\pi$
$104$	0.390108	−	0.675687i	0.0382532	−	0.0662565i
$105$	2.20955	+	1.88237i	0.215630	+	0.183700i
$106$	−8.08395	−	14.0018i	−0.785183	−	1.35998i
$107$	−13.3872			−1.29419			−0.647097	−	0.762408i	$-0.724017\pi$
$107$	−13.3872			−1.29419			−0.647097	+	0.762408i	$0.724017\pi$
$108$	−3.96469	−	7.23725i	−0.381502	−	0.696404i
$109$	5.97983			0.572764			0.286382	−	0.958116i	$-0.407547\pi$
$109$	5.97983			0.572764			0.286382	+	0.958116i	$0.407547\pi$
$110$	6.08613	+	10.5415i	0.580290	+	1.00509i
$111$	1.32178	+	1.12606i	0.125458	+	0.106881i
$112$	3.89981	−	6.75467i	0.368497	−	0.638256i
$113$	4.72340	−	8.18116i	0.444340	−	0.769619i	−0.553666	−	0.832739i	$-0.686772\pi$
$113$	4.72340	−	8.18116i	0.444340	−	0.769619i	0.998006	+	0.0631196i	$0.0201050\pi$
$114$	−2.17276	+	11.8054i	−0.203497	+	1.10568i
$115$	−0.680383	−	1.17846i	−0.0634460	−	0.109892i
$116$	−11.9833			−1.11263
$117$	−2.80342	−	1.06810i	−0.259176	−	0.0987463i
$118$	4.11602			0.378910
$119$	−0.885749	−	1.53416i	−0.0811965	−	0.140636i
$120$	1.27330	−	0.452688i	0.116236	−	0.0413246i
$121$	−15.1465	+	26.2346i	−1.37696	+	2.38496i
$122$	−6.51582	+	11.2857i	−0.589914	+	1.02176i
$123$	−13.8627	+	4.92852i	−1.24995	+	0.444389i
$124$	5.45094	+	9.44130i	0.489508	+	0.847853i
$125$	1.00000			0.0894427
$126$	−8.89930	−	3.39064i	−0.792813	−	0.302062i
$127$	5.67216			0.503322			0.251661	−	0.967815i	$-0.419023\pi$
$127$	5.67216			0.503322			0.251661	+	0.967815i	$0.419023\pi$
$128$	−3.05468	−	5.29086i	−0.269998	−	0.467650i
$129$	−2.54673	+	13.8373i	−0.224227	+	1.21831i
$130$	−0.947115	+	1.64045i	−0.0830675	+	0.143877i
$131$	−2.02847	+	3.51341i	−0.177228	+	0.306968i	−0.940930	−	0.338601i	$-0.890046\pi$
$131$	−2.02847	+	3.51341i	−0.177228	+	0.306968i	0.763702	+	0.645569i	$0.223380\pi$
$132$	−13.4551	−	11.4627i	−1.17112	−	0.997703i
$133$	3.06568	+	5.30991i	0.265828	+	0.460427i
$134$	−28.8483			−2.49212
$135$	−2.49648	−	4.55715i	−0.214863	−	0.392217i
$136$	−0.824746			−0.0707214
$137$	3.37495	+	5.84559i	0.288342	+	0.499422i	0.973414	−	0.229053i	$-0.0735628\pi$
$137$	3.37495	+	5.84559i	0.288342	+	0.499422i	−0.685072	+	0.728475i	$0.740229\pi$
$138$	3.39848	+	2.89524i	0.289298	+	0.246460i
$139$	−5.86074	+	10.1511i	−0.497101	+	0.861005i	−0.999994	−	0.00334400i	$-0.998936\pi$
$139$	−5.86074	+	10.1511i	−0.497101	+	0.861005i	0.502893	+	0.864349i	$0.332269\pi$
$140$	−1.33072	+	2.30487i	−0.112466	+	0.194797i
$141$	−0.750206	+	4.07615i	−0.0631787	+	0.343274i
$142$	2.26539	+	3.92378i	0.190108	+	0.329276i
$143$	−6.42597			−0.537367
$144$	−10.8288	+	8.81389i	−0.902402	+	0.734491i
$145$	−7.54566			−0.626633
$146$	14.6206	+	25.3236i	1.21001	+	2.09580i
$147$	6.84049	−	2.43196i	0.564194	−	0.200585i
$148$	−0.796053	+	1.37880i	−0.0654351	+	0.113337i
$149$	1.46788	−	2.54245i	0.120254	−	0.208285i	−0.799614	−	0.600514i	$-0.794963\pi$
$149$	1.46788	−	2.54245i	0.120254	−	0.208285i	0.919868	+	0.392229i	$0.128296\pi$
$150$	−3.09135	+	1.09905i	−0.252407	+	0.0897370i
$151$	−8.84729	−	15.3240i	−0.719982	−	1.24705i	−0.961006	−	0.276526i	$-0.910817\pi$
$151$	−8.84729	−	15.3240i	−0.719982	−	1.24705i	0.241024	−	0.970519i	$-0.422517\pi$
$152$	2.85454			0.231534
$153$	0.503911	+	3.13093i	0.0407388	+	0.253121i
$154$	−20.3989			−1.64379
$155$	3.43234	+	5.94499i	0.275692	+	0.477513i
$156$	0.497894	−	2.70525i	0.0398635	−	0.216593i
$157$	6.50312	−	11.2637i	0.519005	−	0.898943i	−0.480751	−	0.876857i	$-0.659636\pi$
$157$	6.50312	−	11.2637i	0.519005	−	0.898943i	0.999756	−	0.0220861i	$-0.00703079\pi$
$158$	16.1570	−	27.9848i	1.28538	−	2.22635i
$159$	11.2536	+	9.58716i	0.892465	+	0.760312i
$160$	3.62778	+	6.28350i	0.286801	+	0.496754i
$161$	2.28044			0.179724
$162$	12.7260	+	11.3440i	0.999851	+	0.891265i
$163$	−1.00255			−0.0785254			−0.0392627	−	0.999229i	$-0.512501\pi$
$163$	−1.00255			−0.0785254			−0.0392627	+	0.999229i	$0.512501\pi$
$164$	−6.74500	−	11.6827i	−0.526696	−	0.912264i
$165$	−8.47242	−	7.21785i	−0.659577	−	0.561909i
$166$	−11.5593	+	20.0212i	−0.897172	+	1.55395i
$167$	0.260742	−	0.451619i	0.0201768	−	0.0349473i	−0.855761	−	0.517372i	$-0.826910\pi$
$167$	0.260742	−	0.451619i	0.0201768	−	0.0349473i	0.875938	+	0.482425i	$0.160244\pi$
$168$	−0.409927	+	2.22729i	−0.0316266	+	0.171839i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	2.00234			0.153573
$171$	−1.74409	−	10.8365i	−0.133374	−	0.828688i
$172$	−12.9005			−0.983654
$173$	−2.02836	−	3.51322i	−0.154213	−	0.267105i	0.778559	−	0.627571i	$-0.215951\pi$
$173$	−2.02836	−	3.51322i	−0.154213	−	0.267105i	−0.932772	+	0.360466i	$0.882618\pi$
$174$	23.3263	−	8.29306i	1.76836	−	0.628695i
$175$	−0.837925	+	1.45133i	−0.0633412	+	0.109710i
$176$	−14.9536	+	25.9005i	−1.12717	+	1.95232i
$177$	−3.54617	+	1.26075i	−0.266546	+	0.0947637i
$178$	−4.75494	−	8.23580i	−0.356398	−	0.617299i
$179$	−9.05967			−0.677151			−0.338576	−	0.940939i	$-0.609945\pi$
$179$	−9.05967			−0.677151			−0.338576	+	0.940939i	$0.609945\pi$
$180$	3.69508	−	3.00753i	0.275415	−	0.224168i
$181$	5.42340			0.403118			0.201559	−	0.979476i	$-0.435399\pi$
$181$	5.42340			0.403118			0.201559	+	0.979476i	$0.435399\pi$
$182$	−1.58722	−	2.74915i	−0.117653	−	0.203781i
$183$	2.15686	−	11.7191i	0.159440	−	0.866298i
$184$	0.530845	−	0.919451i	0.0391344	−	0.0677828i
$185$	−0.501258	+	0.868204i	−0.0368532	+	0.0638317i
$186$	−17.1444	−	14.6057i	−1.25709	−	1.07094i
$187$	3.39637	+	5.88268i	0.248367	+	0.430184i
$188$	−3.80018			−0.277156
$189$	8.70578	+	0.195330i	0.633252	+	0.0142082i
$190$	−6.93033			−0.502779
$191$	1.01861	+	1.76428i	0.0737039	+	0.127659i	0.900522	−	0.434811i	$-0.143185\pi$
$191$	1.01861	+	1.76428i	0.0737039	+	0.127659i	−0.826818	+	0.562470i	$0.809851\pi$
$192$	−5.84798	−	4.98203i	−0.422042	−	0.359547i
$193$	−2.22435	+	3.85268i	−0.160112	+	0.277322i	−0.934909	−	0.354888i	$-0.884519\pi$
$193$	−2.22435	+	3.85268i	−0.160112	+	0.277322i	0.774797	+	0.632210i	$0.217852\pi$
$194$	0.818619	−	1.41789i	0.0587734	−	0.101799i
$195$	0.313514	−	1.70344i	0.0224512	−	0.121986i
$196$	3.32830	+	5.76479i	0.237736	+	0.411771i
$197$	0.420010			0.0299245			0.0149622	−	0.999888i	$-0.495237\pi$
$197$	0.420010			0.0299245			0.0149622	+	0.999888i	$0.495237\pi$
$198$	34.1240	+	13.0013i	2.42508	+	0.923959i
$199$	−4.01722			−0.284773			−0.142387	−	0.989811i	$-0.545478\pi$
$199$	−4.01722			−0.284773			−0.142387	+	0.989811i	$0.545478\pi$
$200$	0.390108	+	0.675687i	0.0275848	+	0.0477783i
$201$	24.8544	−	8.83634i	1.75309	−	0.623267i
$202$	−11.3181	+	19.6035i	−0.796336	+	1.37929i
$203$	6.32270	−	10.9512i	0.443767	−	0.768626i
$204$	−2.73969	+	0.974026i	−0.191816	+	0.0681955i
$205$	−4.24719	−	7.35635i	−0.296637	−	0.513790i
$206$	−7.18838			−0.500838
$207$	−3.81479	−	1.45344i	−0.265146	−	0.101021i
$208$	−4.65413			−0.322706
$209$	−11.7552	−	20.3606i	−0.813124	−	1.40837i
$210$	0.995233	−	5.40748i	0.0686776	−	0.373152i
$211$	11.0551	−	19.1481i	0.761068	−	1.31821i	−0.181233	−	0.983440i	$-0.558009\pi$
$211$	11.0551	−	19.1481i	0.761068	−	1.31821i	0.942301	−	0.334768i	$-0.108658\pi$
$212$	−6.77753	+	11.7390i	−0.465483	+	0.806240i
$213$	−3.15362	−	2.68664i	−0.216083	−	0.184086i
$214$	12.6793	+	21.9611i	0.866736	+	1.50123i
$215$	−8.12318			−0.553996
$216$	2.10531	−	3.46462i	0.143248	−	0.235737i
$217$	−11.5042			−0.780955
$218$	−5.66359	−	9.80962i	−0.383587	−	0.664392i
$219$	−20.3531	−	17.3393i	−1.37534	−	1.17168i
$220$	5.10257	−	8.83791i	0.344015	−	0.595852i
$221$	−0.528537	+	0.915454i	−0.0355533	+	0.0615801i
$222$	0.595362	−	3.23483i	0.0399581	−	0.217107i
$223$	9.41584	+	16.3087i	0.630531	+	1.09211i	0.987443	+	0.157974i	$0.0504962\pi$
$223$	9.41584	+	16.3087i	0.630531	+	1.09211i	−0.356912	+	0.934138i	$0.616170\pi$
$224$	−12.1592			−0.812422
$225$	2.32671	−	1.89378i	0.155114	−	0.126252i
$226$	−17.8944			−1.19032
$227$	−8.44001	−	14.6185i	−0.560183	−	0.970265i	−0.997480	−	0.0709482i	$-0.977398\pi$
$227$	−8.44001	−	14.6185i	−0.560183	−	0.970265i	0.437297	−	0.899317i	$-0.355936\pi$
$228$	9.48236	−	3.37121i	0.627985	−	0.223264i
$229$	−3.14514	+	5.44754i	−0.207836	+	0.359983i	−0.951033	−	0.309090i	$-0.899976\pi$
$229$	−3.14514	+	5.44754i	−0.207836	+	0.359983i	0.743196	+	0.669073i	$0.233309\pi$
$230$	−1.28880	+	2.23227i	−0.0849810	+	0.147191i
$231$	17.5747	−	6.24825i	1.15633	−	0.411105i
$232$	−2.94362	−	5.09851i	−0.193258	−	0.334733i
$233$	−4.62703			−0.303127			−0.151563	−	0.988448i	$-0.548431\pi$
$233$	−4.62703			−0.303127			−0.151563	+	0.988448i	$0.548431\pi$
$234$	0.902986	+	5.61049i	0.0590300	+	0.366769i
$235$	−2.39289			−0.156095
$236$	−1.72542	−	2.98851i	−0.112315	−	0.194536i
$237$	−5.34829	+	29.0593i	−0.347409	+	1.88761i
$238$	−1.67781	+	2.90606i	−0.108756	+	0.188372i
$239$	12.5888	−	21.8044i	0.814300	−	1.41041i	−0.0955287	−	0.995427i	$-0.530454\pi$
$239$	12.5888	−	21.8044i	0.814300	−	1.41041i	0.909829	−	0.414983i	$-0.136212\pi$
$240$	−6.13631	−	5.22766i	−0.396097	−	0.337444i
$241$	−1.00234	−	1.73610i	−0.0645662	−	0.111832i	0.831935	−	0.554873i	$-0.187233\pi$
$241$	−1.00234	−	1.73610i	−0.0645662	−	0.111832i	−0.896501	+	0.443041i	$0.853900\pi$
$242$	57.3821			3.68866
$243$	−14.4388	−	5.87539i	−0.926251	−	0.376907i
$244$	10.9256			0.699442
$245$	2.09576	+	3.62997i	0.133893	+	0.231910i
$246$	21.2145	+	18.0731i	1.35259	+	1.15230i
$247$	1.82933	−	3.16849i	0.116397	−	0.201606i
$248$	−2.67797	+	4.63838i	−0.170051	+	0.294537i
$249$	3.82634	−	20.7900i	0.242485	−	1.31751i
$250$	−0.947115	−	1.64045i	−0.0599008	−	0.103751i
$251$	27.2400			1.71938			0.859688	−	0.510820i	$-0.170658\pi$
$251$	27.2400			1.71938			0.859688	+	0.510820i	$0.170658\pi$
$252$	1.26871	+	7.88285i	0.0799215	+	0.496573i
$253$	−8.74424			−0.549745
$254$	−5.37219	−	9.30490i	−0.337081	−	0.583841i
$255$	−1.72512	+	0.613324i	−0.108031	+	0.0384079i
$256$	−10.2217	+	17.7045i	−0.638857	+	1.10653i
$257$	−3.10679	+	5.38111i	−0.193796	+	0.335665i	−0.946505	−	0.322689i	$-0.895413\pi$
$257$	−3.10679	+	5.38111i	−0.193796	+	0.335665i	0.752709	+	0.658353i	$0.228747\pi$
$258$	25.1115	−	8.92778i	1.56338	−	0.555819i
$259$	−0.840033	−	1.45498i	−0.0521971	−	0.0904081i
$260$	1.58811			0.0984904
$261$	−17.5566	+	14.2898i	−1.08673	+	0.884518i
$262$	7.68477			0.474767
$263$	−3.14447	−	5.44639i	−0.193897	−	0.335839i	0.752642	−	0.658430i	$-0.228779\pi$
$263$	−3.14447	−	5.44639i	−0.193897	−	0.335839i	−0.946538	+	0.322592i	$0.895446\pi$
$264$	1.57185	−	8.54044i	0.0967405	−	0.525628i
$265$	−4.26767	+	7.39182i	−0.262161	+	0.454076i
$266$	5.80710	−	10.0582i	0.356056	−	0.616707i
$267$	6.61929	+	5.63912i	0.405094	+	0.345109i
$268$	12.0931	+	20.9459i	0.738705	+	1.27947i
$269$	18.7900			1.14565			0.572823	−	0.819679i	$-0.305848\pi$
$269$	18.7900			1.14565			0.572823	+	0.819679i	$0.305848\pi$
$270$	−5.11132	+	8.41150i	−0.311065	+	0.511908i
$271$	14.2230			0.863987			0.431994	−	0.901877i	$-0.357810\pi$
$271$	14.2230			0.863987			0.431994	+	0.901877i	$0.357810\pi$
$272$	2.45988	+	4.26064i	0.149152	+	0.258339i
$273$	2.20955	+	1.88237i	0.133728	+	0.113926i
$274$	6.39294	−	11.0729i	0.386211	−	0.668938i
$275$	3.21299	−	5.56505i	0.193750	−	0.335585i
$276$	0.677517	−	3.68121i	0.0407817	−	0.221583i
$277$	11.7549	+	20.3602i	0.706286	+	1.22332i	0.966225	+	0.257698i	$0.0829640\pi$
$277$	11.7549	+	20.3602i	0.706286	+	1.22332i	−0.259940	+	0.965625i	$0.583703\pi$
$278$	22.2032			1.33166
$279$	19.2446	+	7.33220i	1.15214	+	0.438967i
$280$	−1.30752			−0.0781395
$281$	12.4921	+	21.6369i	0.745216	+	1.29075i	0.950094	+	0.311965i	$0.100987\pi$
$281$	12.4921	+	21.6369i	0.745216	+	1.29075i	−0.204878	+	0.978788i	$0.565680\pi$
$282$	7.39726	−	2.62991i	0.440501	−	0.156609i
$283$	16.1618	−	27.9931i	0.960720	−	1.66402i	0.240022	−	0.970767i	$-0.422845\pi$
$283$	16.1618	−	27.9931i	0.960720	−	1.66402i	0.720698	−	0.693249i	$-0.243821\pi$
$284$	1.89929	−	3.28967i	0.112702	−	0.195206i
$285$	5.97085	−	2.12278i	0.353683	−	0.125743i
$286$	6.08613	+	10.5415i	0.359881	+	0.623332i
$287$	14.2353			0.840283
$288$	20.3404	+	7.74969i	1.19857	+	0.456655i
$289$	−15.8826			−0.934270
$290$	7.14661	+	12.3783i	0.419664	+	0.726879i
$291$	−0.270979	+	1.47233i	−0.0158851	+	0.0863097i
$292$	12.2578	−	21.2311i	0.717333	−	1.24246i
$293$	−10.9827	+	19.0225i	−0.641614	+	1.11131i	0.343458	+	0.939168i	$0.388402\pi$
$293$	−10.9827	+	19.0225i	−0.641614	+	1.11131i	−0.985072	+	0.172140i	$0.944932\pi$
$294$	−10.4682	−	8.91814i	−0.610521	−	0.520117i
$295$	−1.08646	−	1.88181i	−0.0632562	−	0.109563i
$296$	−0.782179			−0.0454632
$297$	−33.3819	−	0.748985i	−1.93702	−	0.0434605i
$298$	−5.56101			−0.322141
$299$	−0.680383	−	1.17846i	−0.0393475	−	0.0681519i
$300$	2.09387	+	1.78381i	0.120890	+	0.102989i
$301$	6.80661	−	11.7894i	0.392327	−	0.679530i
$302$	−16.7588	+	29.0271i	−0.964361	+	1.67032i
$303$	3.74650	−	20.3562i	0.215231	−	1.16943i
$304$	−8.51392	−	14.7465i	−0.488307	−	0.845772i
$305$	6.87964			0.393927
$306$	4.65888	−	3.79200i	0.266331	−	0.216774i
$307$	28.3862			1.62009			0.810044	−	0.586369i	$-0.199443\pi$
$307$	28.3862			1.62009			0.810044	+	0.586369i	$0.199443\pi$
$308$	8.55114	+	14.8110i	0.487247	+	0.843936i
$309$	6.19317	−	2.20182i	0.352317	−	0.125257i
$310$	6.50165	−	11.2612i	0.369269	−	0.639592i
$311$	16.3025	−	28.2368i	0.924433	−	1.60116i	0.131962	−	0.991255i	$-0.457872\pi$
$311$	16.3025	−	28.2368i	0.924433	−	1.60116i	0.792471	−	0.609909i	$-0.208794\pi$
$312$	1.27330	−	0.452688i	0.0720862	−	0.0256284i
$313$	−0.361137	−	0.625508i	−0.0204127	−	0.0353558i	0.855639	−	0.517574i	$-0.173165\pi$
$313$	−0.361137	−	0.625508i	−0.0204127	−	0.0353558i	−0.876051	+	0.482218i	$0.839831\pi$
$314$	−24.6368			−1.39034
$315$	0.798883	+	4.96367i	0.0450120	+	0.279671i
$316$	−27.0919			−1.52404
$317$	5.91392	+	10.2432i	0.332159	+	0.575316i	0.982935	−	0.183954i	$-0.0588896\pi$
$317$	5.91392	+	10.2432i	0.332159	+	0.575316i	−0.650776	+	0.759270i	$0.725556\pi$
$318$	5.06886	−	27.5411i	0.284248	−	1.54443i
$319$	−24.2441	+	41.9920i	−1.35741	+	2.35110i
$320$	2.21772	−	3.84121i	0.123974	−	0.214730i
$321$	−17.6506	−	15.0370i	−0.985161	−	0.839282i
$322$	−2.15984	−	3.74095i	−0.120363	−	0.208475i
$323$	−3.86747			−0.215192
$324$	2.90180	−	13.9953i	0.161211	−	0.777518i
$325$	1.00000			0.0554700
$326$	0.949526	+	1.64463i	0.0525894	+	0.0910875i
$327$	7.88420	+	6.71673i	0.435997	+	0.371436i
$328$	3.31372	−	5.73954i	0.182970	−	0.316913i
$329$	2.00507	−	3.47288i	0.110543	−	0.191466i
$330$	−3.81618	+	20.7347i	−0.210074	+	1.14141i
$331$	4.29469	+	7.43863i	0.236058	+	0.408864i	0.959580	−	0.281438i	$-0.0908112\pi$
$331$	4.29469	+	7.43863i	0.236058	+	0.408864i	−0.723522	+	0.690301i	$0.757478\pi$
$332$	19.3824			1.06375
$333$	0.477903	+	2.96934i	0.0261889	+	0.162719i
$334$	−0.987812			−0.0540507
$335$	7.61479	+	13.1892i	0.416040	+	0.720603i
$336$	12.7288	−	4.52541i	0.694414	−	0.246881i
$337$	−7.03256	+	12.1807i	−0.383088	+	0.663527i	−0.991502	−	0.130092i	$-0.958473\pi$
$337$	−7.03256	+	12.1807i	−0.383088	+	0.663527i	0.608414	+	0.793620i	$0.291806\pi$
$338$	−0.947115	+	1.64045i	−0.0515163	+	0.0892288i
$339$	15.4170	−	5.48112i	0.837335	−	0.297693i
$340$	−0.839375	−	1.45384i	−0.0455215	−	0.0788456i
$341$	44.1123			2.38881
$342$	−16.1249	+	13.1245i	−0.871935	+	0.709693i
$343$	−18.7553			−1.01269
$344$	−3.16892	−	5.48872i	−0.170857	−	0.295932i
$345$	0.426619	−	2.31798i	0.0229684	−	0.124796i
$346$	−3.84218	+	6.65485i	−0.206557	+	0.357767i
$347$	−3.75358	+	6.50139i	−0.201503	+	0.349013i	−0.949013	−	0.315237i	$-0.897916\pi$
$347$	−3.75358	+	6.50139i	−0.201503	+	0.349013i	0.747510	+	0.664250i	$0.231249\pi$
$348$	−15.7996	−	13.4601i	−0.846949	−	0.721535i
$349$	1.51651	+	2.62668i	0.0811770	+	0.140603i	0.903756	−	0.428048i	$-0.140799\pi$
$349$	1.51651	+	2.62668i	0.0811770	+	0.140603i	−0.822579	+	0.568651i	$0.807465\pi$
$350$	3.17445			0.169681
$351$	−2.49648	−	4.55715i	−0.133252	−	0.243242i
$352$	46.6240			2.48507
$353$	1.32903	+	2.30194i	0.0707369	+	0.122520i	0.899224	−	0.437488i	$-0.144132\pi$
$353$	1.32903	+	2.30194i	0.0707369	+	0.122520i	−0.828488	+	0.560007i	$0.810798\pi$
$354$	5.42683	+	4.62324i	0.288433	+	0.245722i
$355$	1.19594	−	2.07144i	0.0634741	−	0.109940i
$356$	−3.98651	+	6.90484i	−0.211285	+	0.365956i
$357$	0.555389	−	3.01764i	0.0293943	−	0.159711i
$358$	8.58055	+	14.8620i	0.453496	+	0.785479i
$359$	18.6320			0.983360			0.491680	−	0.870776i	$-0.336383\pi$
$359$	18.6320			0.983360			0.491680	+	0.870776i	$0.336383\pi$
$360$	2.18727	+	0.833352i	0.115279	+	0.0439215i
$361$	−5.61425			−0.295487
$362$	−5.13659	−	8.89683i	−0.269973	−	0.467607i
$363$	−49.4377	+	17.5763i	−2.59481	+	0.922518i
$364$	−1.33072	+	2.30487i	−0.0697485	+	0.120808i
$365$	7.71848	−	13.3688i	0.404004	−	0.699755i
$366$	−21.2674	+	7.56107i	−1.11166	+	0.395224i
$367$	−15.6616	−	27.1268i	−0.817531	−	1.41601i	−0.907496	−	0.420060i	$-0.862009\pi$
$367$	−15.6616	−	27.1268i	−0.817531	−	1.41601i	0.0899651	−	0.995945i	$-0.471324\pi$
$368$	−6.33317			−0.330140
$369$	−23.8133	−	9.07288i	−1.23967	−	0.472315i
$370$	1.89900			0.0987241
$371$	−7.15198	−	12.3876i	−0.371312	−	0.643132i
$372$	−3.41789	+	18.5707i	−0.177209	+	0.962845i
$373$	15.1332	−	26.2115i	0.783568	−	1.35718i	−0.146282	−	0.989243i	$-0.546731\pi$
$373$	15.1332	−	26.2115i	0.783568	−	1.35718i	0.929851	−	0.367937i	$-0.119936\pi$
$374$	6.43350	−	11.1431i	0.332668	−	0.576198i
$375$	1.31847	+	1.12323i	0.0680853	+	0.0580034i
$376$	−0.933487	−	1.61685i	−0.0481409	−	0.0833825i
$377$	−7.54566			−0.388622
$378$	−7.92495	−	14.4664i	−0.407615	−	0.744072i
$379$	28.6882			1.47361			0.736806	−	0.676104i	$-0.236333\pi$
$379$	28.6882			1.47361			0.736806	+	0.676104i	$0.236333\pi$
$380$	2.90517	+	5.03190i	0.149032	+	0.258131i
$381$	7.47854	+	6.37114i	0.383137	+	0.326403i
$382$	1.92948	−	3.34196i	0.0987207	−	0.170989i
$383$	−5.44836	+	9.43683i	−0.278398	+	0.482200i	−0.970987	−	0.239133i	$-0.923137\pi$
$383$	−5.44836	+	9.43683i	−0.278398	+	0.482200i	0.692589	+	0.721333i	$0.256470\pi$
$384$	1.91537	−	10.4069i	0.0977433	−	0.531076i
$385$	5.38448	+	9.32619i	0.274419	+	0.475307i
$386$	8.42685			0.428915
$387$	−18.9003	+	15.3835i	−0.960757	+	0.781987i
$388$	−1.37265			−0.0696857
$389$	2.65382	+	4.59655i	0.134554	+	0.233054i	0.925427	−	0.378926i	$-0.123707\pi$
$389$	2.65382	+	4.59655i	0.134554	+	0.233054i	−0.790873	+	0.611980i	$0.790373\pi$
$390$	−3.09135	+	1.09905i	−0.156536	+	0.0556526i
$391$	−0.719215	+	1.24572i	−0.0363723	+	0.0629986i
$392$	−1.63515	+	2.83216i	−0.0825875	+	0.143046i
$393$	−6.62083	+	2.35387i	−0.333977	+	0.118737i
$394$	−0.397798	−	0.689006i	−0.0200408	−	0.0347116i
$395$	−17.0592			−0.858341
$396$	−4.86483	−	30.2264i	−0.244467	−	1.51894i
$397$	18.8514			0.946122			0.473061	−	0.881030i	$-0.343149\pi$
$397$	18.8514			0.946122			0.473061	+	0.881030i	$0.343149\pi$
$398$	3.80477	+	6.59006i	0.190716	+	0.330330i
$399$	−1.92226	+	10.4444i	−0.0962336	+	0.522874i
$400$	2.32706	−	4.03059i	0.116353	−	0.201530i
$401$	−7.62772	+	13.2116i	−0.380910	+	0.659756i	−0.991193	−	0.132428i	$-0.957723\pi$
$401$	−7.62772	+	13.2116i	−0.380910	+	0.659756i	0.610282	+	0.792184i	$0.291056\pi$
$402$	−38.0355	−	32.4033i	−1.89704	−	1.61613i
$403$	3.43234	+	5.94499i	0.170977	+	0.296141i
$404$	18.9780			0.944189
$405$	1.82720	−	8.81257i	0.0907944	−	0.437900i
$406$	−23.9533			−1.18878
$407$	3.22107	+	5.57906i	0.159662	+	0.276544i
$408$	−1.08740	−	0.926381i	−0.0538343	−	0.0458627i
$409$	8.94473	−	15.4927i	0.442288	−	0.766066i	−0.555571	−	0.831469i	$-0.687500\pi$
$409$	8.94473	−	15.4927i	0.442288	−	0.766066i	0.997859	+	0.0654035i	$0.0208334\pi$
$410$	−8.04515	+	13.9346i	−0.397322	+	0.688182i
$411$	−2.11619	+	11.4981i	−0.104384	+	0.567157i
$412$	3.01334	+	5.21926i	0.148457	+	0.257135i
$413$	3.64149			0.179186
$414$	1.22875	+	7.63456i	0.0603899	+	0.375218i
$415$	12.2047			0.599105
$416$	3.62778	+	6.28350i	0.177867	+	0.308074i
$417$	−19.1292	+	6.80091i	−0.936761	+	0.333042i
$418$	−22.2671	+	38.5677i	−1.08912	+	1.88641i
$419$	9.41619	−	16.3093i	0.460011	−	0.796762i	−0.538950	−	0.842338i	$-0.681179\pi$
$419$	9.41619	−	16.3093i	0.460011	−	0.796762i	0.998961	+	0.0455757i	$0.0145122\pi$
$420$	−4.34340	+	1.54419i	−0.211936	+	0.0753486i
$421$	−15.4624	−	26.7816i	−0.753589	−	1.30526i	−0.946073	−	0.323955i	$-0.894987\pi$
$421$	−15.4624	−	26.7816i	−0.753589	−	1.30526i	0.192483	−	0.981300i	$-0.438346\pi$
$422$	−41.8820			−2.03878
$423$	−5.56758	+	4.53161i	−0.270705	+	0.220335i
$424$	−6.65941			−0.323410
$425$	−0.528537	−	0.915454i	−0.0256378	−	0.0444060i
$426$	−1.42046	+	7.71793i	−0.0688217	+	0.373935i
$427$	−5.76462	+	9.98462i	−0.278970	+	0.483190i
$428$	10.6302	−	18.4120i	0.513830	−	0.889980i
$429$	−8.47242	−	7.21785i	−0.409052	−	0.348481i
$430$	7.69359	+	13.3257i	0.371018	+	0.642621i
$431$	−16.8500			−0.811636			−0.405818	−	0.913954i	$-0.633013\pi$
$431$	−16.8500			−0.811636			−0.405818	+	0.913954i	$0.633013\pi$
$432$	−24.1775	−	0.542466i	−1.16324	−	0.0260994i
$433$	17.9932			0.864696			0.432348	−	0.901707i	$-0.357685\pi$
$433$	17.9932			0.864696			0.432348	+	0.901707i	$0.357685\pi$
$434$	10.8958	+	18.8721i	0.523014	+	0.905888i
$435$	−9.94870	−	8.47553i	−0.477004	−	0.406370i
$436$	−4.74831	+	8.22432i	−0.227403	+	0.393873i
$437$	2.48928	−	4.31157i	0.119079	−	0.206250i
$438$	−9.16752	+	49.8106i	−0.438041	+	2.38004i
$439$	3.33331	+	5.77346i	0.159090	+	0.275552i	0.934541	−	0.355856i	$-0.115811\pi$
$439$	3.33331	+	5.77346i	0.159090	+	0.275552i	−0.775451	+	0.631408i	$0.782477\pi$
$440$	5.01364			0.239016
$441$	11.7506	+	4.47699i	0.559553	+	0.213190i
$442$	2.00234			0.0952418
$443$	−18.8749	−	32.6923i	−0.896775	−	1.55326i	−0.831592	−	0.555387i	$-0.812570\pi$
$443$	−18.8749	−	32.6923i	−0.896775	−	1.55326i	−0.0651831	−	0.997873i	$-0.520763\pi$
$444$	−2.59828	+	0.923754i	−0.123309	+	0.0438394i
$445$	−2.51022	+	4.34783i	−0.118996	+	0.206107i
$446$	17.8358	−	30.8925i	0.844548	−	1.46280i
$447$	4.79111	−	1.70336i	0.226612	−	0.0805660i
$448$	3.71657	+	6.43729i	0.175591	+	0.304133i
$449$	2.90874			0.137272			0.0686359	−	0.997642i	$-0.478135\pi$
$449$	2.90874			0.137272			0.0686359	+	0.997642i	$0.478135\pi$
$450$	−5.31032	−	2.02324i	−0.250331	−	0.0953763i
$451$	−54.5846			−2.57029
$452$	7.50127	+	12.9926i	0.352830	+	0.611120i
$453$	5.54750	−	30.1417i	0.260644	−	1.41618i
$454$	−15.9873	+	27.6908i	−0.750322	+	1.29960i
$455$	−0.837925	+	1.45133i	−0.0392825	+	0.0680393i
$456$	3.76361	+	3.20631i	0.176247	+	0.150149i
$457$	19.6973	+	34.1167i	0.921401	+	1.59591i	0.797250	+	0.603649i	$0.206287\pi$
$457$	19.6973	+	34.1167i	0.921401	+	1.59591i	0.124150	+	0.992263i	$0.460379\pi$
$458$	11.9152			0.556762
$459$	−2.85237	+	4.69404i	−0.133137	+	0.219099i
$460$	2.16104			0.100759
$461$	2.38035	+	4.12289i	0.110864	+	0.192022i	0.916119	−	0.400907i	$-0.131305\pi$
$461$	2.38035	+	4.12289i	0.110864	+	0.192022i	−0.805255	+	0.592929i	$0.797972\pi$
$462$	−26.8952	−	22.9127i	−1.25128	−	1.06599i
$463$	2.57482	−	4.45972i	0.119662	−	0.207261i	−0.799972	−	0.600038i	$-0.795152\pi$
$463$	2.57482	−	4.45972i	0.119662	−	0.207261i	0.919634	+	0.392777i	$0.128486\pi$
$464$	−17.5592	+	30.4135i	−0.815167	+	1.41191i
$465$	−2.15217	+	11.6936i	−0.0998047	+	0.542277i
$466$	4.38233	+	7.59042i	0.203007	+	0.351619i
$467$	11.4529			0.529978			0.264989	−	0.964251i	$-0.414632\pi$
$467$	11.4529			0.529978			0.264989	+	0.964251i	$0.414632\pi$
$468$	3.69508	−	3.00753i	0.170805	−	0.139023i
$469$	−25.5225			−1.17852
$470$	2.26635	+	3.92543i	0.104539	+	0.181066i
$471$	21.2259	−	7.54633i	0.978038	−	0.347717i
$472$	0.847674	−	1.46821i	0.0390174	−	0.0675801i
$473$	−26.0997	+	45.2059i	−1.20006	+	2.07857i
$474$	52.7359	−	18.7489i	2.42224	−	0.861166i
$475$	1.82933	+	3.16849i	0.0839353	+	0.145380i
$476$	2.81333			0.128949
$477$	4.06883	+	25.2807i	0.186299	+	1.15752i
$478$	−47.6921			−2.18139
$479$	−9.16898	−	15.8811i	−0.418941	−	0.725628i	0.576892	−	0.816820i	$-0.304265\pi$
$479$	−9.16898	−	15.8811i	−0.418941	−	0.725628i	−0.995833	+	0.0911928i	$0.970932\pi$
$480$	−2.27472	+	12.3594i	−0.103826	+	0.564127i
$481$	−0.501258	+	0.868204i	−0.0228554	+	0.0395867i
$482$	−1.89866	+	3.28857i	−0.0864814	+	0.149790i
$483$	3.00668	+	2.56146i	0.136809	+	0.116550i
$484$	−24.0544	−	41.6634i	−1.09338	−	1.89379i
$485$	−0.864329			−0.0392472
$486$	4.03694	+	29.2509i	0.183119	+	1.32685i
$487$	−12.9479			−0.586724			−0.293362	−	0.956001i	$-0.594774\pi$
$487$	−12.9479			−0.586724			−0.293362	+	0.956001i	$0.594774\pi$
$488$	2.68380	+	4.64848i	0.121490	+	0.210427i
$489$	−1.32182	−	1.12609i	−0.0597748	−	0.0509236i
$490$	3.96986	−	6.87600i	0.179340	−	0.310626i
$491$	9.27909	−	16.0719i	0.418760	−	0.725313i	−0.577055	−	0.816705i	$-0.695798\pi$
$491$	9.27909	−	16.0719i	0.418760	−	0.725313i	0.995815	+	0.0913922i	$0.0291317\pi$
$492$	4.22930	−	22.9794i	0.190672	−	1.03599i
$493$	3.98817	+	6.90771i	0.179618	+	0.311107i
$494$	−6.93033			−0.311810
$495$	−3.06328	−	19.0330i	−0.137684	−	0.855469i
$496$	31.9491			1.43456
$497$	2.00422	+	3.47141i	0.0899017	+	0.155714i
$498$	−37.7289	+	13.4136i	−1.69067	+	0.601077i
$499$	8.30155	−	14.3787i	0.371629	−	0.643680i	−0.618188	−	0.786031i	$-0.712133\pi$
$499$	8.30155	−	14.3787i	0.371629	−	0.643680i	0.989816	+	0.142351i	$0.0454662\pi$
$500$	−0.794055	+	1.37534i	−0.0355112	+	0.0615072i
$501$	0.851052	−	0.302570i	0.0380222	−	0.0135178i
$502$	−25.7995	−	44.6860i	−1.15149	−	1.99443i
$503$	−20.3977			−0.909489			−0.454745	−	0.890622i	$-0.650269\pi$
$503$	−20.3977			−0.909489			−0.454745	+	0.890622i	$0.650269\pi$
$504$	−3.04224	+	2.47616i	−0.135512	+	0.110297i
$505$	11.9500			0.531770
$506$	8.28180	+	14.3445i	0.368171	+	0.637691i
$507$	0.313514	−	1.70344i	0.0139236	−	0.0756524i
$508$	−4.50400	+	7.80116i	−0.199833	+	0.346120i
$509$	−9.42780	+	16.3294i	−0.417880	+	0.723789i	−0.995726	−	0.0923565i	$-0.970560\pi$
$509$	−9.42780	+	16.3294i	−0.417880	+	0.723789i	0.577846	+	0.816146i	$0.303893\pi$
$510$	2.64002	+	2.24909i	0.116902	+	0.0995916i
$511$	12.9350	+	22.4041i	0.572212	+	0.991100i
$512$	26.5058			1.17140
$513$	9.87238	−	16.2466i	0.435876	−	0.717304i
$514$	11.7699			0.519150
$515$	1.89744	+	3.28646i	0.0836112	+	0.144819i
$516$	−17.0089	−	14.4902i	−0.748773	−	0.637897i
$517$	−7.68833	+	13.3166i	−0.338132	+	0.585663i
$518$	−1.59122	+	2.75607i	−0.0699140	+	0.121095i
$519$	1.27184	−	6.91038i	0.0558275	−	0.303332i
$520$	0.390108	+	0.675687i	0.0171074	+	0.0296308i
$521$	−18.6463			−0.816908			−0.408454	−	0.912779i	$-0.633932\pi$
$521$	−18.6463			−0.816908			−0.408454	+	0.912779i	$0.633932\pi$
$522$	40.0699	+	15.2667i	1.75381	+	0.668204i
$523$	−17.7265			−0.775127			−0.387563	−	0.921843i	$-0.626683\pi$
$523$	−17.7265			−0.775127			−0.387563	+	0.921843i	$0.626683\pi$
$524$	−3.22143	−	5.57968i	−0.140729	−	0.243749i
$525$	−2.73495	+	0.972343i	−0.119363	+	0.0424365i
$526$	−5.95636	+	10.3167i	−0.259710	+	0.449830i
$527$	3.62824	−	6.28430i	0.158049	−	0.273748i
$528$	−48.8081	+	17.3525i	−2.12410	+	0.755170i
$529$	10.5742	+	18.3150i	0.459746	+	0.796304i
$530$	16.1679			0.702289
$531$	−6.09161	−	2.32091i	−0.264353	−	0.100719i
$532$	−9.73726			−0.422164
$533$	−4.24719	−	7.35635i	−0.183966	−	0.318639i
$534$	2.98148	−	16.1995i	0.129021	−	0.701022i
$535$	6.69362	−	11.5937i	0.289390	−	0.501239i
$536$	−5.94118	+	10.2904i	−0.256620	+	0.444479i
$537$	−11.9449	−	10.1761i	−0.515459	−	0.439131i
$538$	−17.7963	−	30.8241i	−0.767252	−	1.32892i
$539$	26.9346			1.16016
$540$	8.24998	+	0.185104i	0.355023	+	0.00796559i
$541$	19.6344			0.844150			0.422075	−	0.906561i	$-0.361302\pi$
$541$	19.6344			0.844150			0.422075	+	0.906561i	$0.361302\pi$
$542$	−13.4708	−	23.3322i	−0.578622	−	1.00220i
$543$	7.15057	+	6.09174i	0.306860	+	0.261421i
$544$	3.83483	−	6.64213i	0.164417	−	0.284779i
$545$	−2.98992	+	5.17869i	−0.128074	+	0.221831i
$546$	0.995233	−	5.40748i	0.0425920	−	0.231419i
$547$	−12.1002	−	20.9582i	−0.517368	−	0.896107i	−0.999797	−	0.0201722i	$-0.993579\pi$
$547$	−12.1002	−	20.9582i	−0.517368	−	0.896107i	0.482429	−	0.875935i	$-0.339755\pi$
$548$	−10.7196			−0.457918
$549$	16.0070	−	13.0285i	0.683161	−	0.556044i
$550$	−12.1723			−0.519027
$551$	−13.8035	−	23.9083i	−0.588048	−	1.01853i
$552$	1.73266	−	0.616003i	0.0737468	−	0.0262188i
$553$	14.2943	−	24.7585i	0.607856	−	1.05284i
$554$	22.2666	−	38.5668i	0.946016	−	1.63855i
$555$	−1.63609	+	0.581669i	−0.0694480	+	0.0246905i
$556$	−9.30749	−	16.1210i	−0.394726	−	0.683685i
$557$	24.7783			1.04989			0.524946	−	0.851136i	$-0.324085\pi$
$557$	24.7783			1.04989			0.524946	+	0.851136i	$0.324085\pi$
$558$	−6.19872	−	38.5142i	−0.262413	−	1.63044i
$559$	−8.12318			−0.343574
$560$	3.89981	+	6.75467i	0.164797	+	0.285437i
$561$	−2.12962	+	11.5710i	−0.0899124	+	0.488529i
$562$	23.6629	−	40.9854i	0.998160	−	1.72886i
$563$	−14.4910	+	25.0991i	−0.610722	+	1.05780i	0.380397	+	0.924823i	$0.375787\pi$
$563$	−14.4910	+	25.0991i	−0.610722	+	1.05780i	−0.991119	+	0.132978i	$0.957546\pi$
$564$	−5.01040	−	4.26848i	−0.210976	−	0.179735i
$565$	4.72340	+	8.18116i	0.198715	+	0.344184i
$566$	−61.2284			−2.57362
$567$	11.2589	+	10.0361i	0.472828	+	0.421478i
$568$	1.86619			0.0783035
$569$	16.9488	+	29.3562i	0.710532	+	1.23068i	0.964658	+	0.263506i	$0.0848788\pi$
$569$	16.9488	+	29.3562i	0.710532	+	1.23068i	−0.254126	+	0.967171i	$0.581788\pi$
$570$	−9.13741	−	7.78437i	−0.382724	−	0.326051i
$571$	23.3174	−	40.3868i	0.975801	−	1.69014i	0.298534	−	0.954399i	$-0.403502\pi$
$571$	23.3174	−	40.3868i	0.975801	−	1.69014i	0.677266	−	0.735738i	$-0.263164\pi$
$572$	5.10257	−	8.83791i	0.213349	−	0.369532i
$573$	−0.638696	+	3.47028i	−0.0266819	+	0.144973i
$574$	−13.4825	−	23.3523i	−0.562747	−	0.974707i
$575$	1.36077			0.0567478
$576$	−2.11439	−	13.1373i	−0.0880997	−	0.547386i
$577$	9.64774			0.401641			0.200820	−	0.979628i	$-0.435639\pi$
$577$	9.64774			0.401641			0.200820	+	0.979628i	$0.435639\pi$
$578$	15.0426	+	26.0546i	0.625692	+	1.08373i
$579$	−7.26017	+	2.58117i	−0.301722	+	0.107270i
$580$	5.99167	−	10.3779i	0.248791	−	0.430918i
$581$	−10.2266	+	17.7130i	−0.424272	+	0.734860i
$582$	2.67194	−	0.949941i	0.110755	−	0.0393763i
$583$	27.4239	+	47.4996i	1.13578	+	1.96723i
$584$	12.0442			0.498391
$585$	2.32671	−	1.89378i	0.0961978	−	0.0782981i
$586$	41.6074			1.71879
$587$	13.3146	+	23.0615i	0.549551	+	0.951851i	0.998305	+	0.0581955i	$0.0185347\pi$
$587$	13.3146	+	23.0615i	0.549551	+	0.951851i	−0.448754	+	0.893655i	$0.648132\pi$
$588$	−2.08694	+	11.3391i	−0.0860639	+	0.467618i
$589$	−12.5578	+	21.7507i	−0.517433	+	0.896221i
$590$	−2.05801	+	3.56457i	−0.0847268	+	0.146751i
$591$	0.553768	+	0.471768i	0.0227790	+	0.0194059i
$592$	2.33292	+	4.04073i	0.0958824	+	0.166073i
$593$	17.5176			0.719360			0.359680	−	0.933076i	$-0.382886\pi$
$593$	17.5176			0.719360			0.359680	+	0.933076i	$0.382886\pi$
$594$	30.3879	+	55.4708i	1.24683	+	2.27599i
$595$	1.77150			0.0726244
$596$	2.33116	+	4.03768i	0.0954879	+	0.165390i
$597$	−5.29657	−	4.51227i	−0.216774	−	0.184675i
$598$	−1.28880	+	2.23227i	−0.0527030	+	0.0912843i
$599$	10.7226	−	18.5720i	0.438112	−	0.758832i	−0.559432	−	0.828876i	$-0.688981\pi$
$599$	10.7226	−	18.5720i	0.438112	−	0.758832i	0.997544	+	0.0700441i	$0.0223140\pi$
$600$	−0.244609	+	1.32905i	−0.00998610	+	0.0542583i
$601$	6.63224	+	11.4874i	0.270535	+	0.468580i	0.968999	−	0.247065i	$-0.0794662\pi$
$601$	6.63224	+	11.4874i	0.270535	+	0.468580i	−0.698464	+	0.715645i	$0.746133\pi$
$602$	−25.7866			−1.05098
$603$	42.6949	+	16.2668i	1.73867	+	0.662435i
$604$	28.1009			1.14341
$605$	−15.1465	−	26.2346i	−0.615795	−	1.06659i
$606$	−36.9417	+	13.1337i	−1.50065	+	0.533519i
$607$	4.79268	−	8.30117i	0.194529	−	0.336934i	−0.752217	−	0.658915i	$-0.771015\pi$
$607$	4.79268	−	8.30117i	0.194529	−	0.336934i	0.946746	+	0.321981i	$0.104349\pi$
$608$	−13.2728	+	22.9891i	−0.538283	+	0.932333i
$609$	20.6370	−	7.33698i	0.836255	−	0.297309i
$610$	−6.51582	−	11.2857i	−0.263818	−	0.456946i
$611$	−2.39289			−0.0968061
$612$	−4.70624	−	1.79308i	−0.190238	−	0.0724810i
$613$	7.37890			0.298031			0.149015	−	0.988835i	$-0.452390\pi$
$613$	7.37890			0.298031			0.149015	+	0.988835i	$0.452390\pi$
$614$	−26.8850	−	46.5662i	−1.08499	−	1.87926i
$615$	2.66311	−	14.4697i	0.107387	−	0.583473i
$616$	−4.20106	+	7.27644i	−0.169265	+	0.293176i
$617$	−7.72473	+	13.3796i	−0.310986	+	0.538643i	−0.978576	−	0.205886i	$-0.933992\pi$
$617$	−7.72473	+	13.3796i	−0.310986	+	0.538643i	0.667590	+	0.744529i	$0.267326\pi$
$618$	−9.47763	−	8.07421i	−0.381246	−	0.324792i
$619$	−5.56743	−	9.64307i	−0.223774	−	0.387588i	0.732177	−	0.681114i	$-0.238504\pi$
$619$	−5.56743	−	9.64307i	−0.223774	−	0.387588i	−0.955951	+	0.293527i	$0.905171\pi$
$620$	−10.9019			−0.437830
$621$	−3.39713	−	6.20120i	−0.136322	−	0.248846i
$622$	−61.7616			−2.47641
$623$	−4.20676	−	7.28632i	−0.168540	−	0.291920i
$624$	−6.13631	−	5.22766i	−0.245649	−	0.209274i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−0.684078	+	1.18486i	−0.0273412	+	0.0473564i
$627$	7.37084	−	40.0486i	0.294363	−	1.59939i
$628$	10.3277	+	17.8880i	0.412118	+	0.713810i
$629$	1.05973			0.0422544
$630$	7.38603	−	6.01170i	0.294266	−	0.239512i
$631$	15.2967			0.608950			0.304475	−	0.952520i	$-0.401519\pi$
$631$	15.2967			0.608950			0.304475	+	0.952520i	$0.401519\pi$
$632$	−6.65493	−	11.5267i	−0.264719	−	0.458506i
$633$	36.0836	−	12.8286i	1.43419	−	0.509891i
$634$	11.2023	−	19.4030i	0.444901	−	0.770592i
$635$	−2.83608	+	4.91223i	−0.112546	+	0.194936i
$636$	−22.1216	+	7.86477i	−0.877178	+	0.311858i
$637$	2.09576	+	3.62997i	0.0830372	+	0.143825i
$638$	91.8479			3.63629
$639$	−1.14022	−	7.08449i	−0.0451064	−	0.280258i
$640$	6.10936			0.241494
$641$	−6.99410	−	12.1141i	−0.276250	−	0.478479i	0.694200	−	0.719783i	$-0.255759\pi$
$641$	−6.99410	−	12.1141i	−0.276250	−	0.478479i	−0.970450	+	0.241303i	$0.922425\pi$
$642$	−7.95025	+	43.1967i	−0.313771	+	1.70484i
$643$	−16.3550	+	28.3277i	−0.644977	+	1.11713i	0.339329	+	0.940668i	$0.389800\pi$
$643$	−16.3550	+	28.3277i	−0.644977	+	1.11713i	−0.984307	+	0.176466i	$0.943533\pi$
$644$	−1.81079	+	3.13638i	−0.0713552	+	0.123591i
$645$	−10.7101	−	9.12421i	−0.421711	−	0.359265i
$646$	3.66294	+	6.34440i	0.144116	+	0.249617i
$647$	26.7392			1.05123			0.525613	−	0.850724i	$-0.323836\pi$
$647$	26.7392			1.05123			0.525613	+	0.850724i	$0.323836\pi$
$648$	6.66734	−	2.20324i	0.261918	−	0.0865513i
$649$	−13.9631			−0.548101
$650$	−0.947115	−	1.64045i	−0.0371489	−	0.0643438i
$651$	−15.1679	−	12.9219i	−0.594476	−	0.506447i
$652$	0.796076	−	1.37884i	0.0311767	−	0.0539997i
$653$	−7.78371	+	13.4818i	−0.304600	+	0.527583i	−0.977172	−	0.212449i	$-0.931856\pi$
$653$	−7.78371	+	13.4818i	−0.304600	+	0.527583i	0.672572	+	0.740032i	$0.265190\pi$
$654$	3.55123	−	19.2952i	0.138864	−	0.754501i
$655$	−2.02847	−	3.51341i	−0.0792588	−	0.137280i
$656$	−39.5339			−1.54354
$657$	−7.35886	−	45.7225i	−0.287096	−	1.78380i
$658$	−7.59611			−0.296127
$659$	3.74338	+	6.48373i	0.145821	+	0.252570i	0.929679	−	0.368370i	$-0.120084\pi$
$659$	3.74338	+	6.48373i	0.145821	+	0.252570i	−0.783858	+	0.620941i	$0.786751\pi$
$660$	16.6546	−	5.92112i	0.648279	−	0.230479i
$661$	−2.00130	+	3.46635i	−0.0778415	+	0.134825i	−0.902318	−	0.431070i	$-0.858136\pi$
$661$	−2.00130	+	3.46635i	−0.0778415	+	0.134825i	0.824477	+	0.565896i	$0.191469\pi$
$662$	8.13514	−	14.0905i	0.316181	−	0.547642i
$663$	−1.72512	+	0.613324i	−0.0669983	+	0.0238195i
$664$	4.76115	+	8.24655i	0.184768	+	0.320028i
$665$	−6.13135			−0.237764
$666$	4.41842	−	3.59628i	0.171210	−	0.139353i
$667$	−10.2679			−0.397574
$668$	0.414087	+	0.717220i	0.0160215	+	0.0277501i
$669$	−5.90399	+	32.0786i	−0.228262	+	1.24023i
$670$	14.4242	−	24.9834i	0.557254	−	0.965192i
$671$	22.1042	−	38.2856i	0.853323	−	1.47800i
$672$	−16.0315	−	13.6576i	−0.618429	−	0.526854i
$673$	21.4189	+	37.0987i	0.825639	+	1.43005i	0.901430	+	0.432925i	$0.142519\pi$
$673$	21.4189	+	37.0987i	0.825639	+	1.43005i	−0.0757907	+	0.997124i	$0.524148\pi$
$674$	26.6426			1.02623
$675$	5.19485	+	0.116556i	0.199950	+	0.00448624i
$676$	1.58811			0.0610811
$677$	2.05786	+	3.56431i	0.0790898	+	0.136988i	0.902857	−	0.429940i	$-0.141465\pi$
$677$	2.05786	+	3.56431i	0.0790898	+	0.136988i	−0.823768	+	0.566928i	$0.808132\pi$
$678$	−23.5932	−	20.0996i	−0.906090	−	0.771919i
$679$	0.724243	−	1.25443i	0.0277939	−	0.0481404i
$680$	0.412373	−	0.714251i	0.0158138	−	0.0273903i
$681$	5.29212	−	28.7541i	0.202794	−	1.10186i
$682$	−41.7794	−	72.3640i	−1.59982	−	2.77096i
$683$	−29.0175			−1.11032			−0.555162	−	0.831742i	$-0.687344\pi$
$683$	−29.0175			−1.11032			−0.555162	+	0.831742i	$0.687344\pi$
$684$	16.2888	+	6.20605i	0.622819	+	0.237294i
$685$	−6.74990			−0.257901
$686$	17.7634	+	30.7672i	0.678212	+	1.17470i
$687$	−10.2656	+	3.64967i	−0.391657	+	0.139244i
$688$	−18.9032	+	32.7412i	−0.720676	+	1.24825i
$689$	−4.26767	+	7.39182i	−0.162585	+	0.281606i
$690$	−4.20659	+	1.49555i	−0.160142	+	0.0569346i
$691$	−9.16630	−	15.8765i	−0.348702	−	0.603970i	0.637317	−	0.770602i	$-0.280044\pi$
$691$	−9.16630	−	15.8765i	−0.348702	−	0.603970i	−0.986019	+	0.166632i	$0.946711\pi$
$692$	6.44252			0.244908
$693$	30.1899	+	11.5024i	1.14682	+	0.436939i
$694$	14.2203			0.539795
$695$	−5.86074	−	10.1511i	−0.222310	−	0.385053i
$696$	1.84573	−	10.0286i	0.0699624	−	0.380132i
$697$	−4.48960	+	7.77621i	−0.170056	+	0.294545i
$698$	2.87262	−	4.97553i	0.108730	−	0.188327i
$699$	−6.10058	−	5.19722i	−0.230745	−	0.196577i
$700$	−1.33072	−	2.30487i	−0.0502964	−	0.0871158i
$701$	−1.22938			−0.0464330			−0.0232165	−	0.999730i	$-0.507391\pi$
$701$	−1.22938			−0.0464330			−0.0232165	+	0.999730i	$0.507391\pi$
$702$	−5.11132	+	8.41150i	−0.192914	+	0.317472i
$703$	−3.66786			−0.138336
$704$	−14.2510	−	24.6835i	−0.537106	−	0.930294i
$705$	−3.15495	−	2.68777i	−0.118822	−	0.101227i
$706$	2.51748	−	4.36040i	0.0947466	−	0.164106i
$707$	−10.0132	+	17.3434i	−0.376586	+	0.652267i
$708$	1.08189	−	5.87830i	0.0406598	−	0.220920i
$709$	12.4520	+	21.5676i	0.467647	+	0.809988i	0.999317	−	0.0369640i	$-0.0117687\pi$
$709$	12.4520	+	21.5676i	0.467647	+	0.809988i	−0.531670	+	0.846952i	$0.678435\pi$
$710$	−4.53079			−0.170037
$711$	−39.6919	+	32.3063i	−1.48856	+	1.21158i
$712$	−3.91703			−0.146797
$713$	4.67061	+	8.08974i	0.174916	+	0.302963i
$714$	−5.47631	+	1.94697i	−0.204946	+	0.0728633i
$715$	3.21299	−	5.56505i	0.120159	−	0.208121i
$716$	7.19387	−	12.4602i	0.268848	−	0.465658i
$717$	41.0893	−	14.6082i	1.53451	−	0.545555i
$718$	−17.6467	−	30.5649i	−0.658567	−	1.14067i
$719$	−15.4428			−0.575919			−0.287959	−	0.957643i	$-0.592977\pi$
$719$	−15.4428			−0.575919			−0.287959	+	0.957643i	$0.592977\pi$
$720$	−2.21864	−	13.7850i	−0.0826838	−	0.513736i
$721$	−6.35965			−0.236846
$722$	5.31734	+	9.20991i	0.197891	+	0.342757i
$723$	0.628493	−	3.41484i	0.0233739	−	0.126999i
$724$	−4.30648	+	7.45904i	−0.160049	+	0.277213i
$725$	3.77283	−	6.53474i	0.140119	−	0.242694i
$726$	75.6563	+	64.4534i	2.80787	+	2.39209i
$727$	−1.09304	−	1.89320i	−0.0405386	−	0.0702149i	0.845044	−	0.534696i	$-0.179574\pi$
$727$	−1.09304	−	1.89320i	−0.0405386	−	0.0702149i	−0.885583	+	0.464482i	$0.846241\pi$
$728$	−1.30752			−0.0484601
$729$	−12.4377	−	23.9646i	−0.460655	−	0.887579i
$730$	−29.2412			−1.08226
$731$	4.29340	+	7.43639i	0.158797	+	0.275045i
$732$	14.4051	+	12.2720i	0.532426	+	0.453586i
$733$	−9.44673	+	16.3622i	−0.348923	+	0.604352i	−0.986058	−	0.166400i	$-0.946786\pi$
$733$	−9.44673	+	16.3622i	−0.348923	+	0.604352i	0.637135	+	0.770752i	$0.280119\pi$
$734$	−29.6668	+	51.3843i	−1.09502	+	1.89663i
$735$	−1.31410	+	7.14002i	−0.0484714	+	0.263363i
$736$	4.93656	+	8.55036i	0.181964	+	0.315171i
$737$	97.8648			3.60490
$738$	7.67030	+	47.6576i	0.282348	+	1.75430i
$739$	26.3288			0.968521			0.484260	−	0.874924i	$-0.339089\pi$
$739$	26.3288			0.968521			0.484260	+	0.874924i	$0.339089\pi$
$740$	−0.796053	−	1.37880i	−0.0292635	−	0.0506858i
$741$	5.97085	−	2.12278i	0.219345	−	0.0779824i
$742$	−13.5475	+	23.4649i	−0.497344	+	0.861425i
$743$	−3.99783	+	6.92445i	−0.146666	+	0.254034i	−0.929993	−	0.367576i	$-0.880188\pi$
$743$	−3.99783	+	6.92445i	−0.146666	+	0.254034i	0.783327	+	0.621610i	$0.213521\pi$
$744$	−8.74078	+	3.10756i	−0.320452	+	0.113929i
$745$	1.46788	+	2.54245i	0.0537790	+	0.0931480i
$746$	−57.3316			−2.09906
$747$	28.3969	−	23.1130i	1.03899	−	0.845661i
$748$	−10.7876			−0.394434
$749$	11.2175	+	19.4293i	0.409879	+	0.709931i
$750$	0.593868	−	3.22671i	0.0216850	−	0.117823i
$751$	−14.1073	+	24.4346i	−0.514783	+	0.891630i	0.485070	+	0.874475i	$0.338794\pi$
$751$	−14.1073	+	24.4346i	−0.514783	+	0.891630i	−0.999853	+	0.0171547i	$0.994539\pi$
$752$	−5.56842	+	9.64478i	−0.203059	+	0.351709i
$753$	35.9151	+	30.5969i	1.30882	+	1.11501i
$754$	7.14661	+	12.3783i	0.260264	+	0.450791i
$755$	17.6946			0.643971
$756$	−7.18151	+	11.8183i	−0.261189	+	0.429829i
$757$	−4.89400			−0.177875			−0.0889377	−	0.996037i	$-0.528347\pi$
$757$	−4.89400			−0.177875			−0.0889377	+	0.996037i	$0.528347\pi$
$758$	−27.1710	−	47.0615i	−0.986895	−	1.70935i
$759$	−11.5290	−	9.82180i	−0.418475	−	0.356509i
$760$	−1.42727	+	2.47210i	−0.0517725	+	0.0896726i
$761$	12.6934	−	21.9856i	0.460134	−	0.796976i	−0.538833	−	0.842413i	$-0.681135\pi$
$761$	12.6934	−	21.9856i	0.460134	−	0.796976i	0.998967	+	0.0454369i	$0.0144680\pi$
$762$	3.36851	−	18.3024i	0.122028	−	0.663026i
$763$	−5.01065	−	8.67870i	−0.181398	−	0.314190i
$764$	−3.23532			−0.117050
$765$	−2.96342	−	1.12907i	−0.107143	−	0.0408215i
$766$	20.6409			0.745786
$767$	−1.08646	−	1.88181i	−0.0392298	−	0.0679481i
$768$	−33.3633	+	11.8615i	−1.20389	+	0.428014i
$769$	−15.7212	+	27.2299i	−0.566920	+	0.981934i	0.429948	+	0.902853i	$0.358532\pi$
$769$	−15.7212	+	27.2299i	−0.566920	+	0.981934i	−0.996868	+	0.0790805i	$0.974802\pi$
$770$	10.1994	−	17.6660i	0.367563	−	0.636637i
$771$	−10.1404	+	3.60517i	−0.365198	+	0.129837i
$772$	−3.53250	−	6.11848i	−0.127138	−	0.220209i
$773$	−3.16918			−0.113987			−0.0569937	−	0.998375i	$-0.518151\pi$
$773$	−3.16918			−0.113987			−0.0569937	+	0.998375i	$0.518151\pi$
$774$	43.1367	+	16.4351i	1.55052	+	0.590748i
$775$	−6.86468			−0.246587
$776$	−0.337182	−	0.584016i	−0.0121041	−	0.0209649i
$777$	0.526724	−	2.86189i	0.0188961	−	0.102670i
$778$	5.02694	−	8.70692i	0.180225	−	0.312158i
$779$	15.5390	−	26.9143i	0.556742	−	0.964306i
$780$	2.09387	+	1.78381i	0.0749725	+	0.0638708i
$781$	−7.68510	−	13.3110i	−0.274995	−	0.476304i
$782$	2.72472			0.0974357
$783$	−39.1986	−	0.879492i	−1.40084	−	0.0314305i
$784$	19.5079			0.696711
$785$	6.50312	+	11.2637i	0.232106	+	0.402020i
$786$	10.1321	+	8.63177i	0.361400	+	0.307885i
$787$	−7.57256	+	13.1161i	−0.269933	+	0.467537i	−0.968844	−	0.247671i	$-0.920335\pi$
$787$	−7.57256	+	13.1161i	−0.269933	+	0.467537i	0.698912	+	0.715208i	$0.253668\pi$
$788$	−0.333511	+	0.577657i	−0.0118808	+	0.0205782i
$789$	1.97167	−	10.7129i	0.0701934	−	0.381388i
$790$	16.1570	+	27.9848i	0.574841	+	0.995654i
$791$	−15.8314			−0.562900
$792$	11.6653	−	9.49473i	0.414509	−	0.337381i
$793$	6.87964			0.244303
$794$	−17.8544	−	30.9247i	−0.633629	−	1.09748i
$795$	−13.9295	+	4.95228i	−0.494029	+	0.175639i
$796$	3.18990	−	5.52506i	0.113063	−	0.195831i
$797$	−10.5844	+	18.3328i	−0.374919	+	0.649379i	−0.990315	−	0.138839i	$-0.955663\pi$
$797$	−10.5844	+	18.3328i	−0.374919	+	0.649379i	0.615396	+	0.788218i	$0.288996\pi$
$798$	18.9541	−	6.73866i	0.670969	−	0.238546i
$799$	1.26473	+	2.19058i	0.0447431	+	0.0774973i
$800$	−7.25556			−0.256523
$801$	2.39326	+	14.8700i	0.0845618	+	0.525405i
$802$	28.8973			1.02040
$803$	−49.5988	−	85.9076i	−1.75030	−	3.03161i
$804$	−7.58272	+	41.1998i	−0.267422	+	1.45301i
$805$	−1.14022	+	1.97492i	−0.0401874	+	0.0696067i
$806$	6.50165	−	11.2612i	0.229011	−	0.396658i
$807$	24.7739	+	21.1055i	0.872084	+	0.742949i
$808$	4.66180	+	8.07448i	0.164002	+	0.284059i
$809$	−47.6345			−1.67474			−0.837371	−	0.546635i	$-0.815908\pi$
$809$	−47.6345			−1.67474			−0.837371	+	0.546635i	$0.815908\pi$
$810$	−16.1872	+	5.34908i	−0.568759	+	0.187947i
$811$	−1.63492			−0.0574097			−0.0287048	−	0.999588i	$-0.509138\pi$
$811$	−1.63492			−0.0574097			−0.0287048	+	0.999588i	$0.509138\pi$
$812$	10.0411	+	17.3918i	0.352375	+	0.610331i
$813$	18.7526	+	15.9757i	0.657682	+	0.560294i
$814$	6.10145	−	10.5680i	0.213856	−	0.370409i
$815$	0.501273	−	0.868230i	0.0175588	−	0.0304128i
$816$	−1.54241	+	8.38052i	−0.0539953	+	0.293377i
$817$	−14.8599	−	25.7382i	−0.519884	−	0.900465i
$818$	−33.8868			−1.18482
$819$	0.798883	+	4.96367i	0.0279152	+	0.173445i
$820$	13.4900			0.471091
$821$	−26.8283	−	46.4679i	−0.936313	−	1.62174i	−0.772276	−	0.635288i	$-0.780882\pi$
$821$	−26.8283	−	46.4679i	−0.936313	−	1.62174i	−0.164038	−	0.986454i	$-0.552452\pi$
$822$	20.8663	−	7.41848i	0.727795	−	0.258749i
$823$	18.1569	−	31.4487i	0.632911	−	1.09623i	−0.354042	−	0.935229i	$-0.615193\pi$
$823$	18.1569	−	31.4487i	0.632911	−	1.09623i	0.986954	−	0.161005i	$-0.0514735\pi$
$824$	−1.48041	+	2.56415i	−0.0515726	+	0.0893264i
$825$	10.4871	−	3.72841i	0.365112	−	0.129806i
$826$	−3.44891	−	5.97369i	−0.120003	−	0.207851i
$827$	−55.2893			−1.92260			−0.961299	−	0.275508i	$-0.911154\pi$
$827$	−55.2893			−1.92260			−0.961299	+	0.275508i	$0.911154\pi$
$828$	5.02813	−	4.09254i	0.174740	−	0.142226i
$829$	−31.3443			−1.08863			−0.544317	−	0.838880i	$-0.683211\pi$
$829$	−31.3443			−1.08863			−0.544317	+	0.838880i	$0.683211\pi$
$830$	−11.5593	−	20.0212i	−0.401228	−	0.694947i
$831$	−7.37067	+	40.0477i	−0.255686	+	1.38924i
$832$	2.21772	−	3.84121i	0.0768857	−	0.133170i
$833$	2.21538	−	3.83715i	0.0767583	−	0.132949i
$834$	29.2741	+	24.9393i	1.01368	+	0.863577i
$835$	0.260742	+	0.451619i	0.00902336	+	0.0156289i
$836$	37.3371			1.29133
$837$	17.1376	+	31.2834i	0.592361	+	1.08131i
$838$	−35.6729			−1.23230
$839$	−27.6351	−	47.8654i	−0.954069	−	1.65250i	−0.736483	−	0.676456i	$-0.763515\pi$
$839$	−27.6351	−	47.8654i	−0.954069	−	1.65250i	−0.217586	−	0.976041i	$-0.569818\pi$
$840$	−1.72393	−	1.46865i	−0.0594811	−	0.0506733i
$841$	−13.9685	+	24.1942i	−0.481673	+	0.834283i
$842$	−29.2893	+	50.7305i	−1.00938	+	1.74829i
$843$	−7.83289	+	42.5591i	−0.269779	+	1.46581i
$844$	17.5568	+	30.4092i	0.604329	+	1.04673i
$845$	1.00000			0.0344010
$846$	12.7070	+	4.84139i	0.436877	+	0.166450i
$847$	50.7667			1.74436
$848$	19.8623	+	34.4025i	0.682074	+	1.18139i
$849$	52.7515	−	18.7545i	1.81043	−	0.643652i
$850$	−1.00117	+	1.73408i	−0.0343399	+	0.0594785i
$851$	−0.682094	+	1.18142i	−0.0233819	+	0.0404986i
$852$	6.19920	−	2.20397i	0.212381	−	0.0755068i
$853$	3.46278	+	5.99771i	0.118563	+	0.205358i	0.919199	−	0.393794i	$-0.128838\pi$
$853$	3.46278	+	5.99771i	0.118563	+	0.205358i	−0.800635	+	0.599152i	$0.795504\pi$
$854$	21.8391			0.747317
$855$	10.2567	+	3.90782i	0.350773	+	0.133645i
$856$	10.4449			0.357001
$857$	−18.7232	−	32.4295i	−0.639572	−	1.10777i	−0.985527	−	0.169520i	$-0.945778\pi$
$857$	−18.7232	−	32.4295i	−0.639572	−	1.10777i	0.345955	−	0.938251i	$-0.387555\pi$
$858$	−3.81618	+	20.7347i	−0.130282	+	0.707872i
$859$	−4.98459	+	8.63356i	−0.170072	+	0.294573i	−0.938445	−	0.345429i	$-0.887733\pi$
$859$	−4.98459	+	8.63356i	−0.170072	+	0.294573i	0.768373	+	0.640003i	$0.221067\pi$
$860$	6.45025	−	11.1722i	0.219952	−	0.380967i
$861$	18.7688	+	15.9895i	0.639637	+	0.544922i
$862$	15.9589	+	27.6416i	0.543562	+	0.941477i
$863$	−55.1823			−1.87843			−0.939213	−	0.343335i	$-0.888443\pi$
$863$	−55.1823			−1.87843			−0.939213	+	0.343335i	$0.888443\pi$
$864$	18.1134	+	33.0646i	0.616229	+	1.12488i
$865$	4.05672			0.137933
$866$	−17.0416	−	29.5169i	−0.579097	−	1.00303i
$867$	−20.9407	−	17.8398i	−0.711182	−	0.605872i
$868$	9.13495	−	15.8222i	0.310060	−	0.537040i
$869$	−54.8109	+	94.9353i	−1.85933	+	3.22046i
$870$	−4.48113	+	24.3477i	−0.151924	+	0.825463i
$871$	7.61479	+	13.1892i	0.258017	+	0.446899i
$872$	−4.66556			−0.157996
$873$	−2.01105	+	1.63685i	−0.0680636	+	0.0553989i
$874$	−9.43056			−0.318993
$875$	−0.837925	−	1.45133i	−0.0283270	−	0.0490639i
$876$	40.0089	−	14.2242i	1.35178	−	0.480590i
$877$	8.98331	−	15.5596i	0.303345	−	0.525409i	−0.673547	−	0.739145i	$-0.735230\pi$
$877$	8.98331	−	15.5596i	0.303345	−	0.525409i	0.976891	+	0.213736i	$0.0685632\pi$
$878$	6.31405	−	10.9363i	0.213089	−	0.369081i
$879$	−35.8470	+	12.7445i	−1.20909	+	0.429861i
$880$	−14.9536	−	25.9005i	−0.504087	−	0.873105i
$881$	3.77696			0.127249			0.0636245	−	0.997974i	$-0.479734\pi$
$881$	3.77696			0.127249			0.0636245	+	0.997974i	$0.479734\pi$
$882$	−3.78489	−	23.5165i	−0.127444	−	0.791843i
$883$	−2.58683			−0.0870539			−0.0435269	−	0.999052i	$-0.513859\pi$
$883$	−2.58683			−0.0870539			−0.0435269	+	0.999052i	$0.513859\pi$
$884$	−0.839375	−	1.45384i	−0.0282312	−	0.0488979i
$885$	0.681241	−	3.70144i	0.0228997	−	0.124423i
$886$	−35.7535	+	61.9268i	−1.20116	+	2.08047i
$887$	−12.3953	+	21.4692i	−0.416192	+	0.720866i	−0.995553	−	0.0942051i	$-0.969969\pi$
$887$	−12.3953	+	21.4692i	−0.416192	+	0.720866i	0.579360	+	0.815071i	$0.303302\pi$
$888$	−1.03128	−	0.878568i	−0.0346074	−	0.0294828i
$889$	−4.75284	−	8.23216i	−0.159405	−	0.276098i
$890$	9.50988			0.318772
$891$	−43.1716	−	38.4831i	−1.44630	−	1.28923i
$892$	−29.9068			−1.00135
$893$	−4.37739	−	7.58185i	−0.146484	−	0.253717i
$894$	−7.33201	−	6.24630i	−0.245219	−	0.208908i
$895$	4.52983	−	7.84590i	0.151416	−	0.262260i
$896$	−5.11919	+	8.86669i	−0.171020	+	0.296215i
$897$	0.426619	−	2.31798i	0.0142444	−	0.0773952i
$898$	−2.75491	−	4.77164i	−0.0919325	−	0.159232i
$899$	51.7986			1.72758
$900$	0.757057	+	4.70379i	0.0252352	+	0.156793i
$901$	9.02250			0.300583
$902$	51.6979	+	89.5434i	1.72135	+	2.98147i
$903$	22.2165	−	7.89852i	0.739319	−	0.262846i
$904$	−3.68527	+	6.38307i	−0.122570	+	0.212298i
$905$	−2.71170	+	4.69681i	−0.0901400	+	0.156127i
$906$	−54.7000	+	19.4472i	−1.81729	+	0.646091i
$907$	−5.31792	−	9.21090i	−0.176579	−	0.305843i	0.764128	−	0.645065i	$-0.223170\pi$
$907$	−5.31792	−	9.21090i	−0.176579	−	0.305843i	−0.940706	+	0.339222i	$0.889836\pi$
$908$	26.8073			0.889632
$909$	27.8043	−	22.6307i	0.922211	−	0.750614i
$910$	3.17445			0.105232
$911$	−22.3023	−	38.6286i	−0.738907	−	1.27982i	−0.952988	−	0.303008i	$-0.902009\pi$
$911$	−22.3023	−	38.6286i	−0.738907	−	1.27982i	0.214081	−	0.976816i	$-0.431324\pi$
$912$	5.33846	−	29.0059i	0.176774	−	0.960482i
$913$	39.2135	−	67.9198i	1.29778	−	2.24782i
$914$	37.3112	−	64.6249i	1.23415	−	2.13760i
$915$	9.07057	+	7.72743i	0.299864	+	0.255461i
$916$	−4.99482	−	8.65128i	−0.165034	−	0.285846i
$917$	6.79881			0.224517
$918$	10.4019	+	0.233385i	0.343313	+	0.00770285i
$919$	35.3363			1.16564			0.582819	−	0.812602i	$-0.301950\pi$
$919$	35.3363			1.16564			0.582819	+	0.812602i	$0.301950\pi$
$920$	0.530845	+	0.919451i	0.0175014	+	0.0303134i
$921$	37.4263	+	31.8843i	1.23324	+	1.05062i
$922$	4.50893	−	7.80970i	0.148494	−	0.257199i
$923$	1.19594	−	2.07144i	0.0393650	−	0.0681821i
$924$	−5.36181	+	29.1327i	−0.176390	+	0.958396i
$925$	−0.501258	−	0.868204i	−0.0164813	−	0.0285464i
$926$	−9.75461			−0.320556
$927$	10.6386	+	4.05333i	0.349419	+	0.133129i
$928$	54.7480			1.79719
$929$	17.8306	+	30.8835i	0.585003	+	1.01325i	0.994875	+	0.101112i	$0.0322400\pi$
$929$	17.8306	+	30.8835i	0.585003	+	1.01325i	−0.409872	+	0.912143i	$0.634427\pi$
$930$	21.2211	−	7.54463i	0.695868	−	0.247398i
$931$	−7.66767	+	13.2808i	−0.251298	+	0.435261i
$932$	3.67411	−	6.36375i	0.120350	−	0.208452i
$933$	53.2108	−	18.9178i	1.74204	−	0.619340i
$934$	−10.8472	−	18.7879i	−0.354932	−	0.614760i
$935$	−6.79273			−0.222146
$936$	2.18727	+	0.833352i	0.0714932	+	0.0272390i
$937$	−44.3484			−1.44880			−0.724399	−	0.689380i	$-0.757883\pi$
$937$	−44.3484			−1.44880			−0.724399	+	0.689380i	$0.757883\pi$
$938$	24.1727	+	41.8684i	0.789268	+	1.36705i
$939$	0.226443	−	1.23035i	0.00738970	−	0.0401510i
$940$	1.90009	−	3.29105i	0.0619741	−	0.107342i
$941$	−3.21016	+	5.56016i	−0.104648	+	0.181256i	−0.913594	−	0.406627i	$-0.866705\pi$
$941$	−3.21016	+	5.56016i	−0.104648	+	0.181256i	0.808946	+	0.587883i	$0.200038\pi$
$942$	−32.4828	−	27.6728i	−1.05835	−	0.901629i
$943$	−5.77943	−	10.0103i	−0.188204	−	0.325979i
$944$	−10.1131			−0.329152
$945$	−4.52205	+	7.44176i	−0.147102	+	0.242081i
$946$	98.8775			3.21479
$947$	−16.0725	−	27.8383i	−0.522285	−	0.904624i	−0.999664	−	0.0259262i	$-0.991747\pi$
$947$	−16.0725	−	27.8383i	−0.522285	−	0.904624i	0.477379	−	0.878697i	$-0.341587\pi$
$948$	−35.7197	−	30.4304i	−1.16012	−	0.988334i
$949$	7.71848	−	13.3688i	0.250553	−	0.433970i
$950$	3.46517	−	6.00184i	0.112425	−	0.194726i
$951$	−3.70819	+	20.1480i	−0.120246	+	0.653345i
$952$	0.691076	+	1.19698i	0.0223979	+	0.0387943i
$953$	−37.7003			−1.22123			−0.610617	−	0.791926i	$-0.709078\pi$
$953$	−37.7003			−1.22123			−0.610617	+	0.791926i	$0.709078\pi$
$954$	37.6181	−	30.6184i	1.21793	−	0.991309i
$955$	−2.03722			−0.0659228
$956$	19.9924	+	34.6278i	0.646599	+	1.11994i
$957$	−79.1318	+	28.1333i	−2.55797	+	0.909421i
$958$	−17.3682	+	30.0825i	−0.561140	+	0.971923i
$959$	5.65591	−	9.79633i	0.182639	−	0.316340i
$960$	7.23856	−	2.57349i	0.233623	−	0.0830589i
$961$	−8.06195	−	13.9637i	−0.260063	−	0.450442i
$962$	1.89900			0.0612261
$963$	−6.38174	−	39.6514i	−0.205649	−	1.27775i
$964$	3.18364			0.102538
$965$	−2.22435	−	3.85268i	−0.0716042	−	0.124022i
$966$	1.35428	−	7.35831i	0.0435732	−	0.236750i
$967$	−15.9822	+	27.6820i	−0.513952	+	0.890192i	0.485917	+	0.874005i	$0.338486\pi$
$967$	−15.9822	+	27.6820i	−0.513952	+	0.890192i	−0.999869	+	0.0161864i	$0.994847\pi$
$968$	11.8176	−	20.4686i	0.379831	−	0.657887i
$969$	−5.09913	−	4.34406i	−0.163808	−	0.139551i
$970$	0.818619	+	1.41789i	0.0262843	+	0.0455257i
$971$	0.748771			0.0240292			0.0120146	−	0.999928i	$-0.496176\pi$
$971$	0.748771			0.0240292			0.0120146	+	0.999928i	$0.496176\pi$
$972$	19.5459	−	15.1930i	0.626935	−	0.487314i
$973$	19.6434			0.629739
$974$	12.2631	+	21.2404i	0.392936	+	0.680585i
$975$	1.31847	+	1.12323i	0.0422247	+	0.0359722i
$976$	16.0094	−	27.7290i	0.512447	−	0.887585i
$977$	−3.62819	+	6.28422i	−0.116076	+	0.201050i	−0.918209	−	0.396095i	$-0.870365\pi$
$977$	−3.62819	+	6.28422i	−0.116076	+	0.201050i	0.802133	+	0.597145i	$0.203698\pi$
$978$	−0.595379	+	3.23492i	−0.0190381	+	0.103441i
$979$	16.1306	+	27.9391i	0.515537	+	0.892936i
$980$	−6.65660			−0.212637
$981$	2.85061	+	17.7116i	0.0910128	+	0.565487i
$982$	−35.1535			−1.12179
$983$	22.4473	+	38.8799i	0.715958	+	1.24008i	0.962589	+	0.270966i	$0.0873431\pi$
$983$	22.4473	+	38.8799i	0.715958	+	1.24008i	−0.246631	+	0.969109i	$0.579324\pi$
$984$	10.8159	−	3.84531i	0.344797	−	0.122584i
$985$	−0.210005	+	0.363739i	−0.00669131	+	0.0115897i
$986$	7.55451	−	13.0848i	0.240584	−	0.416705i
$987$	6.54445	−	2.32671i	0.208312	−	0.0740601i
$988$	2.90517	+	5.03190i	0.0924258	+	0.160086i
$989$	−11.0537			−0.351488
$990$	−28.3214	+	23.0516i	−0.900113	+	0.732628i
$991$	34.5767			1.09836			0.549182	−	0.835703i	$-0.314939\pi$
$991$	34.5767			1.09836			0.549182	+	0.835703i	$0.314939\pi$
$992$	−24.9036	−	43.1342i	−0.790689	−	1.36951i
$993$	−2.69289	+	14.6315i	−0.0854563	+	0.464317i
$994$	3.79646	−	6.57566i	0.120416	−	0.208567i
$995$	2.00861	−	3.47902i	0.0636773	−	0.110292i
$996$	25.5550	+	21.7709i	0.809742	+	0.689838i
$997$	−22.3003	−	38.6252i	−0.706257	−	1.22327i	−0.966236	−	0.257658i	$-0.917049\pi$
$997$	−22.3003	−	38.6252i	−0.706257	−	1.22327i	0.259979	−	0.965614i	$-0.416284\pi$
$998$	−31.4501			−0.995536
$999$	−2.70515	+	4.45176i	−0.0855872	+	0.140848i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.i.f.391.1	yes	16
3.2	odd	2		1755.2.i.e.1171.8		16
9.2	odd	6		1755.2.i.e.586.8		16
9.4	even	3		5265.2.a.bb.1.8		8
9.5	odd	6		5265.2.a.be.1.1		8
9.7	even	3	inner	585.2.i.f.196.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.f.196.1	✓	16	9.7	even	3	inner
585.2.i.f.391.1	yes	16	1.1	even	1	trivial
1755.2.i.e.586.8		16	9.2	odd	6
1755.2.i.e.1171.8		16	3.2	odd	2
5265.2.a.bb.1.8		8	9.4	even	3
5265.2.a.be.1.1		8	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.947115 - 1.64045i) q^{2} +(1.31847 + 1.12323i) q^{3} +(-0.794055 + 1.37534i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.593868 - 3.22671i) q^{6} +(-0.837925 - 1.45133i) q^{7} -0.780216 q^{8} +(0.476703 + 2.96188i) q^{9} +O(q^{10})\)	\(q+(-0.947115 - 1.64045i) q^{2} +(1.31847 + 1.12323i) q^{3} +(-0.794055 + 1.37534i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.593868 - 3.22671i) q^{6} +(-0.837925 - 1.45133i) q^{7} -0.780216 q^{8} +(0.476703 + 2.96188i) q^{9} +1.89423 q^{10} +(3.21299 + 5.56505i) q^{11} +(-2.59176 + 0.921436i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(-1.58722 + 2.74915i) q^{14} +(-1.63198 + 0.580209i) q^{15} +(2.32706 + 4.03059i) q^{16} +1.05707 q^{17} +(4.40733 - 3.58725i) q^{18} -3.65865 q^{19} +(-0.794055 - 1.37534i) q^{20} +(0.525402 - 2.85471i) q^{21} +(6.08613 - 10.5415i) q^{22} +(-0.680383 + 1.17846i) q^{23} +(-1.02869 - 0.876363i) q^{24} +(-0.500000 - 0.866025i) q^{25} +1.89423 q^{26} +(-2.69836 + 4.44059i) q^{27} +2.66143 q^{28} +(3.77283 + 6.53474i) q^{29} +(2.49748 + 2.12766i) q^{30} +(3.43234 - 5.94499i) q^{31} +(3.62778 - 6.28350i) q^{32} +(-2.01463 + 10.9463i) q^{33} +(-1.00117 - 1.73408i) q^{34} +1.67585 q^{35} +(-4.45213 - 1.69627i) q^{36} +1.00252 q^{37} +(3.46517 + 6.00184i) q^{38} +(-1.63198 + 0.580209i) q^{39} +(0.390108 - 0.675687i) q^{40} +(-4.24719 + 7.35635i) q^{41} +(-5.18063 + 1.84184i) q^{42} +(4.06159 + 7.03488i) q^{43} -10.2051 q^{44} +(-2.80342 - 1.06810i) q^{45} +2.57760 q^{46} +(1.19645 + 2.07231i) q^{47} +(-1.45913 + 7.92803i) q^{48} +(2.09576 - 3.62997i) q^{49} +(-0.947115 + 1.64045i) q^{50} +(1.39372 + 1.18734i) q^{51} +(-0.794055 - 1.37534i) q^{52} +8.53534 q^{53} +(9.84023 + 0.220784i) q^{54} -6.42597 q^{55} +(0.653762 + 1.13235i) q^{56} +(-4.82381 - 4.10951i) q^{57} +(7.14661 - 12.3783i) q^{58} +(-1.08646 + 1.88181i) q^{59} +(0.497894 - 2.70525i) q^{60} +(-3.43982 - 5.95795i) q^{61} -13.0033 q^{62} +(3.89922 - 3.17369i) q^{63} -4.43545 q^{64} +(-0.500000 - 0.866025i) q^{65} +(19.8649 - 7.06246i) q^{66} +(7.61479 - 13.1892i) q^{67} +(-0.839375 + 1.45384i) q^{68} +(-2.22074 + 0.789528i) q^{69} +(-1.58722 - 2.74915i) q^{70} -2.39189 q^{71} +(-0.371932 - 2.31091i) q^{72} -15.4370 q^{73} +(-0.949498 - 1.64458i) q^{74} +(0.313514 - 1.70344i) q^{75} +(2.90517 - 5.03190i) q^{76} +(5.38448 - 9.32619i) q^{77} +(2.49748 + 2.12766i) q^{78} +(8.52960 + 14.7737i) q^{79} -4.65413 q^{80} +(-8.54551 + 2.82388i) q^{81} +16.0903 q^{82} +(-6.10235 - 10.5696i) q^{83} +(3.50901 + 2.98940i) q^{84} +(-0.528537 + 0.915454i) q^{85} +(7.69359 - 13.3257i) q^{86} +(-2.36567 + 12.8536i) q^{87} +(-2.50682 - 4.34194i) q^{88} +5.02045 q^{89} +(0.902986 + 5.61049i) q^{90} +1.67585 q^{91} +(-1.08052 - 1.87152i) q^{92} +(11.2030 - 3.98295i) q^{93} +(2.26635 - 3.92543i) q^{94} +(1.82933 - 3.16849i) q^{95} +(11.8409 - 4.20974i) q^{96} +(0.432165 + 0.748531i) q^{97} -7.93972 q^{98} +(-14.9514 + 12.1694i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{2} - 2 q^{3} - 5 q^{4} - 8 q^{5} - 13 q^{6} + 6 q^{7} - 12 q^{8} + 4 q^{9}+O(q^{10}) \) 16 * q + q^2 - 2 * q^3 - 5 * q^4 - 8 * q^5 - 13 * q^6 + 6 * q^7 - 12 * q^8 + 4 * q^9	\( 16 q + q^{2} - 2 q^{3} - 5 q^{4} - 8 q^{5} - 13 q^{6} + 6 q^{7} - 12 q^{8} + 4 q^{9} - 2 q^{10} + 9 q^{11} - 16 q^{12} - 8 q^{13} - 3 q^{14} + q^{15} + 13 q^{16} + 12 q^{17} + 23 q^{18} - 22 q^{19} - 5 q^{20} + 15 q^{21} + 4 q^{22} + 3 q^{23} - 12 q^{24} - 8 q^{25} - 2 q^{26} + 22 q^{27} - 26 q^{28} + 8 q^{29} + 8 q^{30} + 18 q^{31} + 3 q^{32} - 26 q^{33} + 9 q^{34} - 12 q^{35} + 5 q^{36} - 36 q^{37} - 8 q^{38} + q^{39} + 6 q^{40} - 17 q^{41} - 45 q^{42} + 17 q^{43} + 10 q^{44} + q^{45} + 6 q^{46} + 11 q^{47} + 35 q^{48} + 16 q^{49} + q^{50} - 16 q^{51} - 5 q^{52} + 20 q^{53} + 44 q^{54} - 18 q^{55} - q^{56} - 25 q^{57} + 10 q^{58} + 7 q^{59} + 5 q^{60} + 21 q^{61} - 58 q^{62} - 30 q^{63} - 20 q^{64} - 8 q^{65} + 68 q^{66} + 13 q^{67} - 16 q^{68} - 13 q^{69} - 3 q^{70} - 68 q^{71} + 36 q^{72} - 32 q^{73} - 4 q^{74} + q^{75} + 2 q^{76} + 18 q^{77} + 8 q^{78} + 37 q^{79} - 26 q^{80} - 32 q^{81} + 2 q^{82} + 3 q^{83} + 27 q^{84} - 6 q^{85} - 2 q^{86} - 20 q^{87} + 19 q^{88} + 28 q^{89} - 16 q^{90} - 12 q^{91} - 14 q^{92} + 19 q^{93} + 44 q^{94} + 11 q^{95} - 35 q^{96} + 17 q^{97} + 90 q^{98} - 44 q^{99}+O(q^{100}) \) 16 * q + q^2 - 2 * q^3 - 5 * q^4 - 8 * q^5 - 13 * q^6 + 6 * q^7 - 12 * q^8 + 4 * q^9 - 2 * q^10 + 9 * q^11 - 16 * q^12 - 8 * q^13 - 3 * q^14 + q^15 + 13 * q^16 + 12 * q^17 + 23 * q^18 - 22 * q^19 - 5 * q^20 + 15 * q^21 + 4 * q^22 + 3 * q^23 - 12 * q^24 - 8 * q^25 - 2 * q^26 + 22 * q^27 - 26 * q^28 + 8 * q^29 + 8 * q^30 + 18 * q^31 + 3 * q^32 - 26 * q^33 + 9 * q^34 - 12 * q^35 + 5 * q^36 - 36 * q^37 - 8 * q^38 + q^39 + 6 * q^40 - 17 * q^41 - 45 * q^42 + 17 * q^43 + 10 * q^44 + q^45 + 6 * q^46 + 11 * q^47 + 35 * q^48 + 16 * q^49 + q^50 - 16 * q^51 - 5 * q^52 + 20 * q^53 + 44 * q^54 - 18 * q^55 - q^56 - 25 * q^57 + 10 * q^58 + 7 * q^59 + 5 * q^60 + 21 * q^61 - 58 * q^62 - 30 * q^63 - 20 * q^64 - 8 * q^65 + 68 * q^66 + 13 * q^67 - 16 * q^68 - 13 * q^69 - 3 * q^70 - 68 * q^71 + 36 * q^72 - 32 * q^73 - 4 * q^74 + q^75 + 2 * q^76 + 18 * q^77 + 8 * q^78 + 37 * q^79 - 26 * q^80 - 32 * q^81 + 2 * q^82 + 3 * q^83 + 27 * q^84 - 6 * q^85 - 2 * q^86 - 20 * q^87 + 19 * q^88 + 28 * q^89 - 16 * q^90 - 12 * q^91 - 14 * q^92 + 19 * q^93 + 44 * q^94 + 11 * q^95 - 35 * q^96 + 17 * q^97 + 90 * q^98 - 44 * q^99

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