LMFDB - Embedded newform 322.2.g.a.229.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(45,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("322.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.g (of order $6$, 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:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} + 18x^{14} + 226x^{12} + 1434x^{10} + 6585x^{8} + 14406x^{6} + 22423x^{4} + 8085x^{2} + 2401 $ x^16 + 18x^14 + 226x^12 + 1434x^10 + 6585x^8 + 14406x^6 + 22423x^4 + 8085*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			229.2
Root			$-1.52769 + 2.64604i$ of defining polynomial
Character	$\chi$	$=$	322.229
Dual form			322.2.g.a.45.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-1.86037 + 1.07408i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.264227 - 0.457654i) q^{5} -2.14817i q^{6} +(1.26346 - 2.32458i) q^{7} +1.00000 q^{8} +(0.807314 - 1.39831i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.86037 + 1.07408i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.264227 - 0.457654i) q^{5} -2.14817i q^{6} +(1.26346 - 2.32458i) q^{7} +1.00000 q^{8} +(0.807314 - 1.39831i) q^{9} +(0.264227 + 0.457654i) q^{10} +(1.77580 - 1.02526i) q^{11} +(1.86037 + 1.07408i) q^{12} -3.70082i q^{13} +(1.38141 + 2.25648i) q^{14} +1.13521i q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.44977 + 5.97518i) q^{17} +(0.807314 + 1.39831i) q^{18} +(0.264227 - 0.457654i) q^{19} -0.528453 q^{20} +(0.146281 + 5.68164i) q^{21} +2.05052i q^{22} +(3.94348 - 2.72928i) q^{23} +(-1.86037 + 1.07408i) q^{24} +(2.36037 + 4.08828i) q^{25} +(3.20501 + 1.85041i) q^{26} -2.97601i q^{27} +(-2.64487 + 0.0680958i) q^{28} +3.68928 q^{29} +(-0.983118 - 0.567604i) q^{30} +(-4.28231 + 2.47239i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.20243 + 3.81471i) q^{33} -6.89954 q^{34} +(-0.730011 - 1.19245i) q^{35} -1.61463 q^{36} +(7.50830 + 4.33492i) q^{37} +(0.264227 + 0.457654i) q^{38} +(3.97500 + 6.88490i) q^{39} +(0.264227 - 0.457654i) q^{40} -3.70082i q^{41} +(-4.99358 - 2.71414i) q^{42} -8.98453i q^{43} +(-1.77580 - 1.02526i) q^{44} +(-0.426628 - 0.738941i) q^{45} +(0.391884 + 4.77979i) q^{46} +(-1.70501 - 0.984386i) q^{47} -2.14817i q^{48} +(-3.80731 - 5.87404i) q^{49} -4.72074 q^{50} +(-12.8357 - 7.41069i) q^{51} +(-3.20501 + 1.85041i) q^{52} +(11.8526 - 6.84309i) q^{53} +(2.57730 + 1.48801i) q^{54} -1.08360i q^{55} +(1.26346 - 2.32458i) q^{56} +1.13521i q^{57} +(-1.84464 + 3.19501i) q^{58} +(-5.00305 + 2.88851i) q^{59} +(0.983118 - 0.567604i) q^{60} +(2.92132 - 5.05987i) q^{61} -4.94479i q^{62} +(-2.23046 - 3.64338i) q^{63} +1.00000 q^{64} +(-1.69370 - 0.977857i) q^{65} +(-2.20243 - 3.81471i) q^{66} +(-0.710579 + 0.410253i) q^{67} +(3.44977 - 5.97518i) q^{68} +(-4.40485 + 9.31309i) q^{69} +(1.39769 - 0.0359855i) q^{70} +1.03146 q^{71} +(0.807314 - 1.39831i) q^{72} +(-4.28231 + 2.47239i) q^{73} +(-7.50830 + 4.33492i) q^{74} +(-8.78231 - 5.07047i) q^{75} -0.528453 q^{76} +(-0.139632 - 5.42336i) q^{77} -7.94999 q^{78} +(-10.3493 - 5.97518i) q^{79} +(0.264227 + 0.457654i) q^{80} +(5.61843 + 9.73141i) q^{81} +(3.20501 + 1.85041i) q^{82} +16.4544 q^{83} +(4.84730 - 2.96750i) q^{84} +3.64609 q^{85} +(7.78083 + 4.49227i) q^{86} +(-6.86342 + 3.96259i) q^{87} +(1.77580 - 1.02526i) q^{88} +(-3.81582 + 6.60920i) q^{89} +0.853256 q^{90} +(-8.60285 - 4.67586i) q^{91} +(-4.33536 - 2.05052i) q^{92} +(5.31112 - 9.19912i) q^{93} +(1.70501 - 0.984386i) q^{94} +(-0.139632 - 0.241849i) q^{95} +(1.86037 + 1.07408i) q^{96} -11.1402 q^{97} +(6.99073 - 0.360210i) q^{98} -3.31082i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} + 6 q^{3} - 8 q^{4} + 16 q^{8} + 10 q^{9}+O(q^{10}) $ 16 * q - 8 * q^2 + 6 * q^3 - 8 * q^4 + 16 * q^8 + 10 * q^9	$ 16 q - 8 q^{2} + 6 q^{3} - 8 q^{4} + 16 q^{8} + 10 q^{9} - 6 q^{12} - 8 q^{16} + 10 q^{18} - 4 q^{23} + 6 q^{24} + 2 q^{25} - 6 q^{26} + 16 q^{29} - 24 q^{31} - 8 q^{32} + 4 q^{35} - 20 q^{36} + 22 q^{39} - 4 q^{46} + 30 q^{47} - 58 q^{49} - 4 q^{50} + 6 q^{52} + 54 q^{54} - 8 q^{58} + 36 q^{59} + 16 q^{64} - 32 q^{70} - 12 q^{71} + 10 q^{72} - 24 q^{73} - 96 q^{75} - 38 q^{77} - 44 q^{78} - 36 q^{81} - 6 q^{82} + 24 q^{85} + 42 q^{87} + 8 q^{92} - 38 q^{93} - 30 q^{94} - 38 q^{95} - 6 q^{96} + 56 q^{98}+O(q^{100}) $ 16 * q - 8 * q^2 + 6 * q^3 - 8 * q^4 + 16 * q^8 + 10 * q^9 - 6 * q^12 - 8 * q^16 + 10 * q^18 - 4 * q^23 + 6 * q^24 + 2 * q^25 - 6 * q^26 + 16 * q^29 - 24 * q^31 - 8 * q^32 + 4 * q^35 - 20 * q^36 + 22 * q^39 - 4 * q^46 + 30 * q^47 - 58 * q^49 - 4 * q^50 + 6 * q^52 + 54 * q^54 - 8 * q^58 + 36 * q^59 + 16 * q^64 - 32 * q^70 - 12 * q^71 + 10 * q^72 - 24 * q^73 - 96 * q^75 - 38 * q^77 - 44 * q^78 - 36 * q^81 - 6 * q^82 + 24 * q^85 + 42 * q^87 + 8 * q^92 - 38 * q^93 - 30 * q^94 - 38 * q^95 - 6 * q^96 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−1.86037	+	1.07408i	−1.07408	+	0.620123i	−0.929294	−	0.369340i	$-0.879584\pi$
$3$	−1.86037	+	1.07408i	−1.07408	+	0.620123i	−0.144790	+	0.989462i	$0.546251\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.264227	−	0.457654i	0.118166	−	0.204669i	−0.800875	−	0.598832i	$-0.795632\pi$
$5$	0.264227	−	0.457654i	0.118166	−	0.204669i	0.919041	+	0.394162i	$0.128965\pi$
$6$		−	2.14817i		−	0.876986i
$7$	1.26346	−	2.32458i	0.477545	−	0.878607i
$7$	1.26346	−	2.32458i	0.477545	−	0.878607i
$8$	1.00000			0.353553
$9$	0.807314	−	1.39831i	0.269105	−	0.466103i
$10$	0.264227	+	0.457654i	0.0835558	+	0.144723i
$11$	1.77580	−	1.02526i	0.535423	−	0.309127i	−0.207799	−	0.978172i	$-0.566630\pi$
$11$	1.77580	−	1.02526i	0.535423	−	0.309127i	0.743222	+	0.669045i	$0.233297\pi$
$12$	1.86037	+	1.07408i	0.537042	+	0.310061i
$13$		−	3.70082i		−	1.02642i	−0.858262	−	0.513212i	$-0.828456\pi$
$13$		−	3.70082i		−	1.02642i	0.858262	−	0.513212i	$-0.171544\pi$
$14$	1.38141	+	2.25648i	0.369197	+	0.603070i
$15$			1.13521i			0.293109i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.44977	+	5.97518i	0.836692	+	1.44919i	0.892645	+	0.450760i	$0.148847\pi$
$17$	3.44977	+	5.97518i	0.836692	+	1.44919i	−0.0559526	+	0.998433i	$0.517820\pi$
$18$	0.807314	+	1.39831i	0.190286	+	0.329585i
$19$	0.264227	−	0.457654i	0.0606178	−	0.104993i	−0.834124	−	0.551577i	$-0.814026\pi$
$19$	0.264227	−	0.457654i	0.0606178	−	0.104993i	0.894742	+	0.446584i	$0.147360\pi$
$20$	−0.528453			−0.118166
$21$	0.146281	+	5.68164i	0.0319212	+	1.23983i
$22$			2.05052i			0.437171i
$23$	3.94348	−	2.72928i	0.822273	−	0.569094i
$23$	3.94348	−	2.72928i	0.822273	−	0.569094i
$24$	−1.86037	+	1.07408i	−0.379746	+	0.219247i
$25$	2.36037	+	4.08828i	0.472074	+	0.817656i
$26$	3.20501	+	1.85041i	0.628554	+	0.362896i
$27$		−	2.97601i		−	0.572734i
$28$	−2.64487	+	0.0680958i	−0.499834	+	0.0128689i
$29$	3.68928			0.685082			0.342541	−	0.939503i	$-0.388713\pi$
$29$	3.68928			0.685082			0.342541	+	0.939503i	$0.388713\pi$
$30$	−0.983118	−	0.567604i	−0.179492	−	0.103630i
$31$	−4.28231	+	2.47239i	−0.769126	+	0.444055i	−0.832563	−	0.553931i	$-0.813127\pi$
$31$	−4.28231	+	2.47239i	−0.769126	+	0.444055i	0.0634370	+	0.997986i	$0.479794\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−2.20243	+	3.81471i	−0.383393	+	0.664056i
$34$	−6.89954			−1.18326
$35$	−0.730011	−	1.19245i	−0.123394	−	0.201560i
$36$	−1.61463			−0.269105
$37$	7.50830	+	4.33492i	1.23436	+	0.712656i	0.967935	−	0.251201i	$-0.0808255\pi$
$37$	7.50830	+	4.33492i	1.23436	+	0.712656i	0.266421	+	0.963857i	$0.414159\pi$
$38$	0.264227	+	0.457654i	0.0428632	+	0.0742413i
$39$	3.97500	+	6.88490i	0.636509	+	1.10247i
$40$	0.264227	−	0.457654i	0.0417779	−	0.0723615i
$41$		−	3.70082i		−	0.577972i	−0.957333	−	0.288986i	$-0.906682\pi$
$41$		−	3.70082i		−	0.577972i	0.957333	−	0.288986i	$-0.0933180\pi$
$42$	−4.99358	−	2.71414i	−0.770526	−	0.418800i
$43$		−	8.98453i		−	1.37013i	−0.728483	−	0.685064i	$-0.759774\pi$
$43$		−	8.98453i		−	1.37013i	0.728483	−	0.685064i	$-0.240226\pi$
$44$	−1.77580	−	1.02526i	−0.267712	−	0.154563i
$45$	−0.426628	−	0.738941i	−0.0635979	−	0.110155i
$46$	0.391884	+	4.77979i	0.0577801	+	0.704742i
$47$	−1.70501	−	0.984386i	−0.248701	−	0.143588i	0.370468	−	0.928845i	$-0.379197\pi$
$47$	−1.70501	−	0.984386i	−0.248701	−	0.143588i	−0.619169	+	0.785258i	$0.712531\pi$
$48$		−	2.14817i		−	0.310061i
$49$	−3.80731	−	5.87404i	−0.543902	−	0.839149i
$50$	−4.72074			−0.667613
$51$	−12.8357	−	7.41069i	−1.79736	−	1.03770i
$52$	−3.20501	+	1.85041i	−0.444455	+	0.256606i
$53$	11.8526	−	6.84309i	1.62808	−	0.939970i	0.643410	−	0.765522i	$-0.277519\pi$
$53$	11.8526	−	6.84309i	1.62808	−	0.939970i	0.984666	−	0.174448i	$-0.0558141\pi$
$54$	2.57730	+	1.48801i	0.350726	+	0.202492i
$55$		−	1.08360i		−	0.146113i
$56$	1.26346	−	2.32458i	0.168838	−	0.310635i
$57$			1.13521i			0.150362i
$58$	−1.84464	+	3.19501i	−0.242213	+	0.419525i
$59$	−5.00305	+	2.88851i	−0.651341	+	0.376052i	−0.788970	−	0.614432i	$-0.789385\pi$
$59$	−5.00305	+	2.88851i	−0.651341	+	0.376052i	0.137629	+	0.990484i	$0.456052\pi$
$60$	0.983118	−	0.567604i	0.126920	−	0.0732773i
$61$	2.92132	−	5.05987i	0.374036	−	0.647850i	−0.616146	−	0.787632i	$-0.711307\pi$
$61$	2.92132	−	5.05987i	0.374036	−	0.647850i	0.990182	+	0.139782i	$0.0446402\pi$
$62$		−	4.94479i		−	0.627988i
$63$	−2.23046	−	3.64338i	−0.281012	−	0.459022i
$64$	1.00000			0.125000
$65$	−1.69370	−	0.977857i	−0.210077	−	0.121288i
$66$	−2.20243	−	3.81471i	−0.271100	−	0.469559i
$67$	−0.710579	+	0.410253i	−0.0868110	+	0.0501204i	−0.542777	−	0.839877i	$-0.682627\pi$
$67$	−0.710579	+	0.410253i	−0.0868110	+	0.0501204i	0.455966	+	0.889997i	$0.349294\pi$
$68$	3.44977	−	5.97518i	0.418346	−	0.724597i
$69$	−4.40485	+	9.31309i	−0.530282	+	1.12116i
$70$	1.39769	−	0.0359855i	0.167056	−	0.00430109i
$71$	1.03146			0.122412			0.0612059	−	0.998125i	$-0.480505\pi$
$71$	1.03146			0.122412			0.0612059	+	0.998125i	$0.480505\pi$
$72$	0.807314	−	1.39831i	0.0951429	−	0.164792i
$73$	−4.28231	+	2.47239i	−0.501206	+	0.289372i	−0.729212	−	0.684288i	$-0.760113\pi$
$73$	−4.28231	+	2.47239i	−0.501206	+	0.289372i	0.228005	+	0.973660i	$0.426780\pi$
$74$	−7.50830	+	4.33492i	−0.872822	+	0.503924i
$75$	−8.78231	−	5.07047i	−1.01409	−	0.585487i
$76$	−0.528453			−0.0606178
$77$	−0.139632	−	5.42336i	−0.0159125	−	0.618049i
$78$	−7.94999			−0.900159
$79$	−10.3493	−	5.97518i	−1.16439	−	0.672260i	−0.212037	−	0.977262i	$-0.568010\pi$
$79$	−10.3493	−	5.97518i	−1.16439	−	0.672260i	−0.952352	+	0.305002i	$0.901343\pi$
$80$	0.264227	+	0.457654i	0.0295414	+	0.0511673i
$81$	5.61843	+	9.73141i	0.624270	+	1.08127i
$82$	3.20501	+	1.85041i	0.353934	+	0.204344i
$83$	16.4544			1.80610			0.903051	−	0.429533i	$-0.141322\pi$
$83$	16.4544			1.80610			0.903051	+	0.429533i	$0.141322\pi$
$84$	4.84730	−	2.96750i	0.528884	−	0.323781i
$85$	3.64609			0.395474
$86$	7.78083	+	4.49227i	0.839029	+	0.484414i
$87$	−6.86342	+	3.96259i	−0.735835	+	0.424835i
$88$	1.77580	−	1.02526i	0.189301	−	0.109293i
$89$	−3.81582	+	6.60920i	−0.404476	+	0.700574i	−0.994260	−	0.106987i	$-0.965880\pi$
$89$	−3.81582	+	6.60920i	−0.404476	+	0.700574i	0.589784	+	0.807561i	$0.299213\pi$
$90$	0.853256			0.0899410
$91$	−8.60285	−	4.67586i	−0.901824	−	0.490163i
$92$	−4.33536	−	2.05052i	−0.451993	−	0.213781i
$93$	5.31112	−	9.19912i	0.550737	−	0.953905i
$94$	1.70501	−	0.984386i	0.175858	−	0.101532i
$95$	−0.139632	−	0.241849i	−0.0143259	−	0.0248132i
$96$	1.86037	+	1.07408i	0.189873	+	0.109623i
$97$	−11.1402			−1.13112			−0.565558	−	0.824709i	$-0.691339\pi$
$97$	−11.1402			−1.13112			−0.565558	+	0.824709i	$0.691339\pi$
$98$	6.99073	−	0.360210i	0.706170	−	0.0363867i
$99$		−	3.31082i		−	0.332750i
$100$	2.36037	−	4.08828i	0.236037	−	0.408828i
$101$	−2.58111	+	1.49020i	−0.256830	+	0.148281i	−0.622887	−	0.782311i	$-0.714041\pi$
$101$	−2.58111	+	1.49020i	−0.256830	+	0.148281i	0.366058	+	0.930592i	$0.380707\pi$
$102$	12.8357	−	7.41069i	1.27092	−	0.733768i
$103$	0.881293	−	1.52644i	0.0868363	−	0.150405i	−0.819336	−	0.573314i	$-0.805658\pi$
$103$	0.881293	−	1.52644i	0.0868363	−	0.150405i	0.906172	+	0.422909i	$0.138991\pi$
$104$		−	3.70082i		−	0.362896i
$105$	2.63888	+	1.43429i	0.257528	+	0.139973i
$106$			13.6862i			1.32932i
$107$	7.69873	+	4.44487i	0.744265	+	0.429701i	0.823618	−	0.567145i	$-0.191952\pi$
$107$	7.69873	+	4.44487i	0.744265	+	0.429701i	−0.0793532	+	0.996847i	$0.525285\pi$
$108$	−2.57730	+	1.48801i	−0.248001	+	0.143183i
$109$	−6.00504	+	3.46701i	−0.575178	+	0.332079i	−0.759215	−	0.650840i	$-0.774417\pi$
$109$	−6.00504	+	3.46701i	−0.575178	+	0.332079i	0.184037	+	0.982919i	$0.441083\pi$
$110$	0.938427	+	0.541801i	0.0894755	+	0.0516587i
$111$	−18.6243			−1.76774
$112$	1.38141	+	2.25648i	0.130531	+	0.213217i
$113$			5.00860i			0.471169i	0.971854	+	0.235585i	$0.0757005\pi$
$113$			5.00860i			0.471169i	−0.971854	+	0.235585i	$0.924299\pi$
$114$	−0.983118	−	0.567604i	−0.0920775	−	0.0531609i
$115$	−0.207092	−	2.52590i	−0.0193115	−	0.235541i
$116$	−1.84464	−	3.19501i	−0.171270	−	0.296649i
$117$	−5.17489	−	2.98773i	−0.478419	−	0.276215i
$118$		−	5.77702i		−	0.531818i
$119$	18.2484	−	0.469830i	1.67283	−	0.0430692i
$120$			1.13521i			0.103630i
$121$	−3.39769	+	5.88498i	−0.308881	+	0.534998i
$122$	2.92132	+	5.05987i	0.264484	+	0.458099i
$123$	3.97500	+	6.88490i	0.358413	+	0.620790i
$124$	4.28231	+	2.47239i	0.384563	+	0.222027i
$125$	5.13696			0.459463
$126$	4.27049	−	0.109949i	0.380445	−	0.00979507i
$127$	−3.31072			−0.293779			−0.146890	−	0.989153i	$-0.546926\pi$
$127$	−3.31072			−0.293779			−0.146890	+	0.989153i	$0.546926\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	9.65015	+	16.7145i	0.849648	+	1.47163i
$130$	1.69370	−	0.977857i	0.148547	−	0.0857637i
$131$	−14.1457	−	8.16704i	−1.23592	−	0.713557i	−0.267661	−	0.963513i	$-0.586251\pi$
$131$	−14.1457	−	8.16704i	−1.23592	−	0.713557i	−0.968257	+	0.249956i	$0.919584\pi$
$132$	4.40485			0.383393
$133$	−0.730011	−	1.19245i	−0.0633000	−	0.103398i
$134$		−	0.820506i		−	0.0708809i
$135$	−1.36198	−	0.786342i	−0.117221	−	0.0676776i
$136$	3.44977	+	5.97518i	0.295815	+	0.512367i
$137$	−8.49141	+	4.90252i	−0.725470	+	0.418851i	−0.816763	−	0.576974i	$-0.804234\pi$
$137$	−8.49141	+	4.90252i	−0.725470	+	0.418851i	0.0912924	+	0.995824i	$0.470900\pi$
$138$	−5.86295	−	8.47126i	−0.499087	−	0.721122i
$139$			18.4468i			1.56464i	0.622879	+	0.782318i	$0.285963\pi$
$139$			18.4468i			1.56464i	−0.622879	+	0.782318i	$0.714037\pi$
$140$	−0.667682	+	1.22843i	−0.0564295	+	0.103821i
$141$	4.22926			0.356168
$142$	−0.515730	+	0.893270i	−0.0432791	+	0.0749616i
$143$	−3.79430	−	6.57192i	−0.317295	−	0.549571i
$144$	0.807314	+	1.39831i	0.0672762	+	0.116526i
$145$	0.974806	−	1.68841i	0.0809532	−	0.140215i
$146$		−	4.94479i		−	0.409233i
$147$	13.3922	+	6.83851i	1.10457	+	0.564030i
$148$		−	8.66983i		−	0.712656i
$149$	3.55160	+	2.05052i	0.290958	+	0.167985i	0.638374	−	0.769726i	$-0.279607\pi$
$149$	3.55160	+	2.05052i	0.290958	+	0.167985i	−0.347416	+	0.937711i	$0.612941\pi$
$150$	8.78231	−	5.07047i	0.717073	−	0.414002i
$151$	−0.885372	−	1.53351i	−0.0720506	−	0.124795i	0.827749	−	0.561098i	$-0.189621\pi$
$151$	−0.885372	−	1.53351i	−0.0720506	−	0.124795i	−0.899800	+	0.436303i	$0.856288\pi$
$152$	0.264227	−	0.457654i	0.0214316	−	0.0371207i
$153$	11.1402			0.900631
$154$	4.76658	+	2.59075i	0.384102	+	0.208769i
$155$			2.61309i			0.209888i
$156$	3.97500	−	6.88490i	0.318254	−	0.551233i
$157$	−3.73372	−	6.46700i	−0.297983	−	0.516123i	0.677691	−	0.735347i	$-0.262981\pi$
$157$	−3.73372	−	6.46700i	−0.297983	−	0.516123i	−0.975675	+	0.219224i	$0.929647\pi$
$158$	10.3493	−	5.97518i	0.823347	−	0.475360i
$159$	−14.7001	+	25.4613i	−1.16579	+	2.01921i
$160$	−0.528453			−0.0417779
$161$	−1.36197	−	12.6153i	−0.107338	−	0.994223i
$162$	−11.2369			−0.882851
$163$	2.80731	−	4.86241i	0.219886	−	0.380853i	−0.734887	−	0.678189i	$-0.762765\pi$
$163$	2.80731	−	4.86241i	0.219886	−	0.380853i	0.954773	+	0.297336i	$0.0960982\pi$
$164$	−3.20501	+	1.85041i	−0.250269	+	0.144493i
$165$	1.16388	+	2.01590i	0.0906079	+	0.156938i
$166$	−8.22719	+	14.2499i	−0.638554	+	1.10601i
$167$			4.65513i			0.360225i	0.983646	+	0.180112i	$0.0576461\pi$
$167$			4.65513i			0.360225i	−0.983646	+	0.180112i	$0.942354\pi$
$168$	0.146281	+	5.68164i	0.0112858	+	0.438348i
$169$	−0.696095			−0.0535458
$170$	−1.82304	+	3.15760i	−0.139821	+	0.242177i
$171$	−0.426628	−	0.738941i	−0.0326250	−	0.0565082i
$172$	−7.78083	+	4.49227i	−0.593283	+	0.342532i
$173$	−12.8049	−	7.39291i	−0.973538	−	0.562072i	−0.0732248	−	0.997315i	$-0.523329\pi$
$173$	−12.8049	−	7.39291i	−0.973538	−	0.562072i	−0.900313	+	0.435243i	$0.856662\pi$
$174$		−	7.92519i		−	0.600807i
$175$	12.4858	−	0.321462i	0.943835	−	0.0243003i
$176$			2.05052i			0.154563i
$177$	6.20501	−	10.7474i	0.466397	−	0.807823i
$178$	−3.81582	−	6.60920i	−0.286008	−	0.495381i
$179$	−1.69269	−	2.93182i	−0.126517	−	0.219134i	0.795808	−	0.605549i	$-0.207047\pi$
$179$	−1.69269	−	2.93182i	−0.126517	−	0.219134i	−0.922325	+	0.386415i	$0.873713\pi$
$180$	−0.426628	+	0.738941i	−0.0317990	+	0.0550774i
$181$	10.2869			0.764622			0.382311	−	0.924034i	$-0.375128\pi$
$181$	10.2869			0.764622			0.382311	+	0.924034i	$0.375128\pi$
$182$	8.35084	−	5.11236i	0.619005	−	0.378953i
$183$			12.5510i			0.927794i
$184$	3.94348	−	2.72928i	0.290717	−	0.201205i
$185$	3.96779	−	2.29080i	0.291717	−	0.168423i
$186$	5.31112	+	9.19912i	0.389430	+	0.674512i
$187$	12.2522	+	7.07381i	0.895969	+	0.517288i
$188$			1.96877i			0.143588i
$189$	−6.91797	−	3.76009i	−0.503208	−	0.273506i
$190$	0.279263			0.0202599
$191$	3.36116	+	1.94057i	0.243205	+	0.140414i	0.616649	−	0.787238i	$-0.288490\pi$
$191$	3.36116	+	1.94057i	0.243205	+	0.140414i	−0.373444	+	0.927653i	$0.621823\pi$
$192$	−1.86037	+	1.07408i	−0.134261	+	0.0775154i
$193$	−6.84769	−	11.8605i	−0.492907	−	0.853740i	0.507059	−	0.861911i	$-0.330732\pi$
$193$	−6.84769	−	11.8605i	−0.492907	−	0.853740i	−0.999967	+	0.00817078i	$0.997399\pi$
$194$	5.57010	−	9.64769i	0.399910	−	0.692664i
$195$	4.20120			0.300854
$196$	−3.18341	+	6.23425i	−0.227387	+	0.445304i
$197$	20.4976			1.46039			0.730196	−	0.683238i	$-0.239429\pi$
$197$	20.4976			1.46039			0.730196	+	0.683238i	$0.239429\pi$
$198$	2.86725	+	1.65541i	0.203767	+	0.117645i
$199$	10.4428	+	18.0875i	0.740272	+	1.28219i	0.952371	+	0.304941i	$0.0986368\pi$
$199$	10.4428	+	18.0875i	0.740272	+	1.28219i	−0.212099	+	0.977248i	$0.568030\pi$
$200$	2.36037	+	4.08828i	0.166903	+	0.289085i
$201$	0.881293	−	1.52644i	0.0621616	−	0.107667i
$202$		−	2.98040i		−	0.209700i
$203$	4.66127	−	8.57601i	0.327157	−	0.601918i
$204$			14.8214i			1.03770i
$205$	−1.69370	−	0.977857i	−0.118293	−	0.0682965i
$206$	0.881293	+	1.52644i	0.0614026	+	0.106352i
$207$	−0.632747	−	7.71759i	−0.0439789	−	0.536409i
$208$	3.20501	+	1.85041i	0.222227	+	0.128303i
$209$		−	1.08360i		−	0.0749543i
$210$	−2.56157	+	1.56819i	−0.176765	+	0.108215i
$211$	−26.0807			−1.79547			−0.897736	−	0.440533i	$-0.854789\pi$
$211$	−26.0807			−1.79547			−0.897736	+	0.440533i	$0.854789\pi$
$212$	−11.8526	−	6.84309i	−0.814038	−	0.469985i
$213$	−1.91889	+	1.10787i	−0.131480	+	0.0759103i
$214$	−7.69873	+	4.44487i	−0.526275	+	0.303845i
$215$	−4.11181	−	2.37395i	−0.280423	−	0.161902i
$216$		−	2.97601i		−	0.202492i
$217$	0.336719	+	13.0783i	0.0228580	+	0.887816i
$218$		−	6.93402i		−	0.469631i
$219$	5.31112	−	9.19912i	0.358892	−	0.621619i
$220$	−0.938427	+	0.541801i	−0.0632687	+	0.0365282i
$221$	22.1131	−	12.7670i	1.48749	−	0.858801i
$222$	9.31213	−	16.1291i	0.624989	−	1.08251i
$223$		−	3.15541i		−	0.211302i	−0.994403	−	0.105651i	$-0.966307\pi$
$223$		−	3.15541i		−	0.211302i	0.994403	−	0.105651i	$-0.0336926\pi$
$224$	−2.64487	+	0.0680958i	−0.176718	+	0.00454984i
$225$	7.62223			0.508149
$226$	−4.33757	−	2.50430i	−0.288531	−	0.166584i
$227$	3.89612	+	6.74828i	0.258595	+	0.447899i	0.965866	−	0.259043i	$-0.0834072\pi$
$227$	3.89612	+	6.74828i	0.258595	+	0.447899i	−0.707271	+	0.706943i	$0.750074\pi$
$228$	0.983118	−	0.567604i	0.0651086	−	0.0375905i
$229$	−2.83922	+	4.91767i	−0.187621	+	0.324969i	−0.944456	−	0.328636i	$-0.893411\pi$
$229$	−2.83922	+	4.91767i	−0.187621	+	0.324969i	0.756836	+	0.653605i	$0.226744\pi$
$230$	2.29104	+	1.08360i	0.151067	+	0.0714506i
$231$	6.08491	+	9.93947i	0.400358	+	0.653969i
$232$	3.68928			0.242213
$233$	−14.2518	+	24.6849i	−0.933669	+	1.61716i	−0.156678	+	0.987650i	$0.550078\pi$
$233$	−14.2518	+	24.6849i	−0.933669	+	1.61716i	−0.776991	+	0.629512i	$0.783255\pi$
$234$	5.17489	−	2.98773i	0.338293	−	0.195314i
$235$	−0.901017	+	0.520202i	−0.0587759	+	0.0339343i
$236$	5.00305	+	2.88851i	0.325671	+	0.188026i
$237$	25.6714			1.66754
$238$	−8.71733	+	16.0385i	−0.565060	+	1.03962i
$239$	2.10460			0.136135			0.0680676	−	0.997681i	$-0.478317\pi$
$239$	2.10460			0.136135			0.0680676	+	0.997681i	$0.478317\pi$
$240$	−0.983118	−	0.567604i	−0.0634600	−	0.0366387i
$241$	−7.60361	−	13.1698i	−0.489792	−	0.848344i	0.510139	−	0.860092i	$-0.329594\pi$
$241$	−7.60361	−	13.1698i	−0.489792	−	0.848344i	−0.999931	+	0.0117478i	$0.996260\pi$
$242$	−3.39769	−	5.88498i	−0.218412	−	0.378301i
$243$	−13.1728	−	7.60532i	−0.845035	−	0.487881i
$244$	−5.84264			−0.374036
$245$	−3.69427	+	0.190354i	−0.236018	+	0.0121613i
$246$	−7.94999			−0.506873
$247$	−1.69370	−	0.977857i	−0.107767	−	0.0622195i
$248$	−4.28231	+	2.47239i	−0.271927	+	0.156997i
$249$	−30.6112	+	17.6734i	−1.93991	+	1.12001i
$250$	−2.56848	+	4.44874i	−0.162445	+	0.281363i
$251$	−21.0463			−1.32843			−0.664214	−	0.747543i	$-0.731234\pi$
$251$	−21.0463			−1.32843			−0.664214	+	0.747543i	$0.731234\pi$
$252$	−2.04003	+	3.75333i	−0.128510	+	0.236437i
$253$	4.20461	−	8.88973i	0.264342	−	0.558893i
$254$	1.65536	−	2.86717i	0.103867	−	0.179902i
$255$	−6.78307	+	3.91620i	−0.424772	+	0.245242i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	19.3956	+	11.1981i	1.20987	+	0.698517i	0.962730	−	0.270464i	$-0.0871772\pi$
$257$	19.3956	+	11.1981i	1.20987	+	0.698517i	0.247136	+	0.968981i	$0.420511\pi$
$258$	−19.3003			−1.20158
$259$	19.5633	−	11.9766i	1.21561	−	0.744189i
$260$			1.95571i			0.121288i
$261$	2.97840	−	5.15875i	0.184359	−	0.319319i
$262$	14.1457	−	8.16704i	0.873926	−	0.504561i
$263$	−8.30098	+	4.79257i	−0.511860	+	0.295523i	−0.733598	−	0.679584i	$-0.762160\pi$
$263$	−8.30098	+	4.79257i	−0.511860	+	0.295523i	0.221738	+	0.975106i	$0.428827\pi$
$264$	−2.20243	+	3.81471i	−0.135550	+	0.234779i
$265$		−	7.23251i		−	0.444289i
$266$	1.39769	−	0.0359855i	0.0856981	−	0.00220641i
$267$		−	16.3941i		−	1.00330i
$268$	0.710579	+	0.410253i	0.0434055	+	0.0250602i
$269$	−14.7823	+	8.53457i	−0.901293	+	0.520362i	−0.877620	−	0.479358i	$-0.840870\pi$
$269$	−14.7823	+	8.53457i	−0.901293	+	0.520362i	−0.0236738	+	0.999720i	$0.507536\pi$
$270$	1.36198	−	0.786342i	0.0828877	−	0.0478553i
$271$	12.9093	+	7.45316i	0.784182	+	0.452747i	0.837910	−	0.545808i	$-0.183777\pi$
$271$	12.9093	+	7.45316i	0.784182	+	0.452747i	−0.0537286	+	0.998556i	$0.517111\pi$
$272$	−6.89954			−0.418346
$273$	21.0267	−	0.541361i	1.27260	−	0.0327647i
$274$		−	9.80504i		−	0.592344i
$275$	8.38308	+	4.83997i	0.505519	+	0.291861i
$276$	10.2678	−	0.841833i	0.618049	−	0.0506724i
$277$	−14.9407	−	25.8781i	−0.897701	−	1.55486i	−0.830426	−	0.557129i	$-0.811903\pi$
$277$	−14.9407	−	25.8781i	−0.897701	−	1.55486i	−0.0672747	−	0.997734i	$-0.521430\pi$
$278$	−15.9754	−	9.22340i	−0.958140	−	0.553183i
$279$			7.98399i			0.477989i
$280$	−0.730011	−	1.19245i	−0.0436265	−	0.0712622i
$281$		−	21.7934i		−	1.30009i	−0.759897	−	0.650044i	$-0.774751\pi$
$281$		−	21.7934i		−	1.30009i	0.759897	−	0.650044i	$-0.225249\pi$
$282$	−2.11463	+	3.66264i	−0.125924	+	0.218107i
$283$	−13.3641	−	23.1474i	−0.794416	−	1.37597i	−0.923209	−	0.384297i	$-0.874444\pi$
$283$	−13.3641	−	23.1474i	−0.794416	−	1.37597i	0.128793	−	0.991671i	$-0.458890\pi$
$284$	−0.515730	−	0.893270i	−0.0306029	−	0.0530058i
$285$	0.519532	+	0.299952i	0.0307744	+	0.0177676i
$286$	7.58860			0.448723
$287$	−8.60285	−	4.67586i	−0.507810	−	0.276007i
$288$	−1.61463			−0.0951429
$289$	−15.3018	+	26.5036i	−0.900108	+	1.55903i
$290$	0.974806	+	1.68841i	0.0572426	+	0.0991470i
$291$	20.7249	−	11.9655i	1.21491	−	0.701430i
$292$	4.28231	+	2.47239i	0.250603	+	0.144686i
$293$	−21.3877			−1.24948			−0.624741	−	0.780832i	$-0.714795\pi$
$293$	−21.3877			−1.24948			−0.624741	+	0.780832i	$0.714795\pi$
$294$	−12.6184	+	8.17875i	−0.735922	+	0.476994i
$295$			3.05289i			0.177746i
$296$	7.50830	+	4.33492i	0.436411	+	0.251962i
$297$	−3.05118	−	5.28480i	−0.177047	−	0.306655i
$298$	−3.55160	+	2.05052i	−0.205738	+	0.118783i
$299$	−10.1006	−	14.5941i	−0.584131	−	0.844000i
$300$			10.1409i			0.585487i
$301$	−20.8852	−	11.3516i	−1.20381	−	0.654298i
$302$	1.77074			0.101895
$303$	3.20120	−	5.54465i	0.183904	−	0.318532i
$304$	0.264227	+	0.457654i	0.0151544	+	0.0262483i
$305$	−1.54378	−	2.67391i	−0.0883966	−	0.153107i
$306$	−5.57010	+	9.64769i	−0.318421	+	0.551522i
$307$		−	2.16565i		−	0.123600i	−0.998089	−	0.0618001i	$-0.980316\pi$
$307$		−	2.16565i		−	0.123600i	0.998089	−	0.0618001i	$-0.0196841\pi$
$308$	−4.62695	+	2.83260i	−0.263645	+	0.161403i
$309$			3.78633i			0.215397i
$310$	−2.26300	−	1.30654i	−0.128530	−	0.0742067i
$311$	16.2365	−	9.37413i	0.920686	−	0.531558i	0.0368318	−	0.999321i	$-0.488273\pi$
$311$	16.2365	−	9.37413i	0.920686	−	0.531558i	0.883854	+	0.467763i	$0.154940\pi$
$312$	3.97500	+	6.88490i	0.225040	+	0.389780i
$313$	15.6552	−	27.1156i	0.884883	−	1.53266i	0.0390359	−	0.999238i	$-0.487571\pi$
$313$	15.6552	−	27.1156i	0.884883	−	1.53266i	0.845847	−	0.533425i	$-0.179095\pi$
$314$	7.46744			0.421412
$315$	−2.25675	+	0.0581031i	−0.127154	+	0.00327374i
$316$			11.9504i			0.672260i
$317$	−14.3234	+	24.8089i	−0.804484	+	1.39341i	0.112154	+	0.993691i	$0.464225\pi$
$317$	−14.3234	+	24.8089i	−0.804484	+	1.39341i	−0.916639	+	0.399717i	$0.869108\pi$
$318$	−14.7001	−	25.4613i	−0.824341	−	1.42780i
$319$	6.55141	−	3.78246i	0.366809	−	0.211777i
$320$	0.264227	−	0.457654i	0.0147707	−	0.0255836i
$321$	−19.0966			−1.06587
$322$	11.6061	+	5.12814i	0.646784	+	0.285780i
$323$	3.64609			0.202874
$324$	5.61843	−	9.73141i	0.312135	−	0.540634i
$325$	15.1300	−	8.73531i	0.839261	−	0.484548i
$326$	2.80731	+	4.86241i	0.155483	+	0.269304i
$327$	7.44772	−	12.8998i	0.411860	−	0.713362i
$328$		−	3.70082i		−	0.204344i
$329$	−4.44250	+	2.71968i	−0.244923	+	0.149941i
$330$	−2.32776			−0.128139
$331$	−13.6550	+	23.6512i	−0.750547	+	1.29998i	0.197011	+	0.980401i	$0.436876\pi$
$331$	−13.6550	+	23.6512i	−0.750547	+	1.29998i	−0.947558	+	0.319584i	$0.896457\pi$
$332$	−8.22719	−	14.2499i	−0.451526	−	0.782065i
$333$	12.1231	−	6.99928i	0.664342	−	0.383558i
$334$	−4.03146	−	2.32756i	−0.220592	−	0.127359i
$335$			0.433599i			0.0236901i
$336$	−4.99358	−	2.71414i	−0.272422	−	0.148068i
$337$			3.09092i			0.168373i	0.996450	+	0.0841866i	$0.0268292\pi$
$337$			3.09092i			0.168373i	−0.996450	+	0.0841866i	$0.973171\pi$
$338$	0.348047	−	0.602836i	0.0189313	−	0.0327899i
$339$	−5.37966	−	9.31784i	−0.292183	−	0.506076i
$340$	−1.82304	−	3.15760i	−0.0988684	−	0.171245i
$341$	−5.06968	+	8.78094i	−0.274539	+	0.475515i
$342$	0.853256			0.0461388
$343$	−18.4651	+	1.42875i	−0.997020	+	0.0771452i
$344$		−	8.98453i		−	0.484414i
$345$	3.09830	+	4.47667i	0.166807	+	0.241016i
$346$	12.8049	−	7.39291i	0.688395	−	0.397445i
$347$	2.72415	+	4.71836i	0.146240	+	0.253295i	0.929835	−	0.367977i	$-0.119950\pi$
$347$	2.72415	+	4.71836i	0.146240	+	0.253295i	−0.783595	+	0.621272i	$0.786616\pi$
$348$	6.86342	+	3.96259i	0.367918	+	0.212417i
$349$		−	7.05311i		−	0.377544i	−0.982021	−	0.188772i	$-0.939549\pi$
$349$		−	7.05311i		−	0.377544i	0.982021	−	0.188772i	$-0.0604508\pi$
$350$	−5.96448	+	10.9737i	−0.318815	+	0.586570i
$351$	−11.0137			−0.587868
$352$	−1.77580	−	1.02526i	−0.0946504	−	0.0546464i
$353$	7.67718	−	4.43242i	0.408615	−	0.235914i	−0.281579	−	0.959538i	$-0.590858\pi$
$353$	7.67718	−	4.43242i	0.408615	−	0.235914i	0.690195	+	0.723624i	$0.257525\pi$
$354$	6.20501	+	10.7474i	0.329792	+	0.571217i
$355$	0.272539	−	0.472052i	0.0144649	−	0.0250539i
$356$	7.63165			0.404476
$357$	−33.4442	+	20.4744i	−1.77005	+	1.08362i
$358$	3.38537			0.178922
$359$	8.33391	+	4.81159i	0.439847	+	0.253946i	0.703533	−	0.710663i	$-0.251605\pi$
$359$	8.33391	+	4.81159i	0.439847	+	0.253946i	−0.263686	+	0.964609i	$0.584938\pi$
$360$	−0.426628	−	0.738941i	−0.0224853	−	0.0389456i
$361$	9.36037	+	16.2126i	0.492651	+	0.853297i
$362$	−5.14347	+	8.90875i	−0.270335	+	0.468233i
$363$		−	14.5976i		−	0.766177i
$364$	0.252011	+	9.78822i	0.0132089	+	0.513042i
$365$			2.61309i			0.136775i
$366$	−10.8695	−	6.27548i	−0.568155	−	0.328025i
$367$	12.1036	+	20.9640i	0.631802	+	1.09431i	0.987183	+	0.159592i	$0.0510178\pi$
$367$	12.1036	+	20.9640i	0.631802	+	1.09431i	−0.355381	+	0.934722i	$0.615649\pi$
$368$	0.391884	+	4.77979i	0.0204284	+	0.249164i
$369$	−5.17489	−	2.98773i	−0.269394	−	0.155535i
$370$			4.58160i			0.238186i
$371$	−0.931971	−	36.1982i	−0.0483855	−	1.87932i
$372$	−10.6222			−0.550737
$373$	0.0491634	+	0.0283845i	0.00254558	+	0.00146969i	0.501272	−	0.865290i	$-0.332866\pi$
$373$	0.0491634	+	0.0283845i	0.00254558	+	0.00146969i	−0.498727	+	0.866759i	$0.666199\pi$
$374$	−12.2522	+	7.07381i	−0.633546	+	0.365778i
$375$	−9.55663	+	5.51752i	−0.493502	+	0.284924i
$376$	−1.70501	−	0.984386i	−0.0879290	−	0.0507659i
$377$		−	13.6534i		−	0.703184i
$378$	6.71532	−	4.11109i	0.345399	−	0.211452i
$379$			20.4003i			1.04789i	0.851751	+	0.523946i	$0.175541\pi$
$379$			20.4003i			1.04789i	−0.851751	+	0.523946i	$0.824459\pi$
$380$	−0.139632	+	0.241849i	−0.00716295	+	0.0124066i
$381$	6.15916	−	3.55599i	0.315544	−	0.182179i
$382$	−3.36116	+	1.94057i	−0.171972	+	0.0992880i
$383$	−6.47291	+	11.2114i	−0.330750	+	0.572877i	−0.982659	−	0.185421i	$-0.940635\pi$
$383$	−6.47291	+	11.2114i	−0.330750	+	0.572877i	0.651909	+	0.758297i	$0.273969\pi$
$384$		−	2.14817i		−	0.109623i
$385$	−2.51892	−	1.36909i	−0.128376	−	0.0697754i
$386$	13.6954			0.697076
$387$	−12.5632	−	7.25334i	−0.638621	−	0.368708i
$388$	5.57010	+	9.64769i	0.282779	+	0.489787i
$389$	−30.9988	+	17.8972i	−1.57170	+	0.907422i	−0.575740	+	0.817633i	$0.695286\pi$
$389$	−30.9988	+	17.8972i	−1.57170	+	0.907422i	−0.995961	+	0.0897885i	$0.971381\pi$
$390$	−2.10060	+	3.63835i	−0.106368	+	0.184235i
$391$	29.9120	+	14.1476i	1.51272	+	0.715476i
$392$	−3.80731	−	5.87404i	−0.192298	−	0.296684i
$393$	35.0883			1.76997
$394$	−10.2488	+	17.7514i	−0.516326	+	0.894304i
$395$	−5.46913	+	3.15760i	−0.275182	+	0.158876i
$396$	−2.86725	+	1.65541i	−0.144085	+	0.0831875i
$397$	18.9349	+	10.9321i	0.950315	+	0.548664i	0.893179	−	0.449702i	$-0.148470\pi$
$397$	18.9349	+	10.9321i	0.950315	+	0.548664i	0.0571360	+	0.998366i	$0.481803\pi$
$398$	−20.8857			−1.04690
$399$	2.63888	+	1.43429i	0.132109	+	0.0718045i
$400$	−4.72074			−0.236037
$401$	15.0987	+	8.71723i	0.753993	+	0.435318i	0.827135	−	0.562004i	$-0.189969\pi$
$401$	15.0987	+	8.71723i	0.753993	+	0.435318i	−0.0731420	+	0.997322i	$0.523303\pi$
$402$	0.881293	+	1.52644i	0.0439549	+	0.0761321i
$403$	9.14989	+	15.8481i	0.455788	+	0.789449i
$404$	2.58111	+	1.49020i	0.128415	+	0.0741403i
$405$	5.93816			0.295069
$406$	5.09641	+	8.32478i	0.252930	+	0.413152i
$407$	17.7776			0.881204
$408$	−12.8357	−	7.41069i	−0.635461	−	0.366884i
$409$	28.6772	−	16.5568i	1.41800	−	0.818680i	0.421873	−	0.906655i	$-0.361373\pi$
$409$	28.6772	−	16.5568i	1.41800	−	0.818680i	0.996123	+	0.0879749i	$0.0280395\pi$
$410$	1.69370	−	0.977857i	0.0836457	−	0.0482929i
$411$	10.5314	−	18.2410i	0.519478	−	0.899762i
$412$	−1.76259			−0.0868363
$413$	0.393391	+	15.2795i	0.0193575	+	0.751855i
$414$	7.00000	+	3.31082i	0.344031	+	0.162718i
$415$	4.34769	−	7.53041i	0.213419	−	0.369653i
$416$	−3.20501	+	1.85041i	−0.157138	+	0.0907239i
$417$	−19.8134	−	34.3178i	−0.970267	−	1.68055i
$418$	0.938427	+	0.541801i	0.0459000	+	0.0265004i
$419$	22.9995			1.12360			0.561799	−	0.827274i	$-0.310110\pi$
$419$	22.9995			1.12360			0.561799	+	0.827274i	$0.310110\pi$
$420$	−0.0773029	−	3.00248i	−0.00377199	−	0.146506i
$421$		−	13.9931i		−	0.681984i	−0.940066	−	0.340992i	$-0.889237\pi$
$421$		−	13.9931i		−	0.681984i	0.940066	−	0.340992i	$-0.110763\pi$
$422$	13.0404	−	22.5866i	0.634795	−	1.09950i
$423$	−2.75295	+	1.58942i	−0.133853	+	0.0772801i
$424$	11.8526	−	6.84309i	0.575612	−	0.332330i
$425$	−16.2855	+	28.2072i	−0.789961	+	1.36825i
$426$		−	2.21575i		−	0.107353i
$427$	−8.07108	−	13.1838i	−0.390587	−	0.638009i
$428$		−	8.88973i		−	0.429701i
$429$	14.1176	+	8.15079i	0.681603	+	0.393524i
$430$	4.11181	−	2.37395i	0.198289	−	0.114482i
$431$	−13.0194	+	7.51677i	−0.627124	+	0.362070i	−0.779637	−	0.626231i	$-0.784597\pi$
$431$	−13.0194	+	7.51677i	−0.627124	+	0.362070i	0.152514	+	0.988301i	$0.451263\pi$
$432$	2.57730	+	1.48801i	0.124001	+	0.0715917i
$433$	8.50153			0.408557			0.204279	−	0.978913i	$-0.434515\pi$
$433$	8.50153			0.408557			0.204279	+	0.978913i	$0.434515\pi$
$434$	−11.4945	−	6.24756i	−0.551755	−	0.299893i
$435$			4.18809i			0.200804i
$436$	6.00504	+	3.46701i	0.287589	+	0.166040i
$437$	−0.207092	−	2.52590i	−0.00990657	−	0.120830i
$438$	5.31112	+	9.19912i	0.253775	+	0.439551i
$439$	1.54965	+	0.894688i	0.0739606	+	0.0427012i	0.536524	−	0.843885i	$-0.319737\pi$
$439$	1.54965	+	0.894688i	0.0739606	+	0.0427012i	−0.462564	+	0.886586i	$0.653070\pi$
$440$		−	1.08360i		−	0.0516587i
$441$	−11.2874	+	0.581605i	−0.537496	+	0.0276955i
$442$			25.5340i			1.21453i
$443$	−7.21146	+	12.4906i	−0.342627	+	0.593447i	−0.984920	−	0.173012i	$-0.944650\pi$
$443$	−7.21146	+	12.4906i	−0.342627	+	0.593447i	0.642293	+	0.766459i	$0.277983\pi$
$444$	9.31213	+	16.1291i	0.441934	+	0.765452i
$445$	2.01649	+	3.49265i	0.0955906	+	0.165568i
$446$	2.73266	+	1.57770i	0.129395	+	0.0747065i
$447$	−8.80970			−0.416685
$448$	1.26346	−	2.32458i	0.0596931	−	0.109826i
$449$	9.65218			0.455515			0.227757	−	0.973718i	$-0.426861\pi$
$449$	9.65218			0.455515			0.227757	+	0.973718i	$0.426861\pi$
$450$	−3.81112	+	6.60105i	−0.179658	+	0.311176i
$451$	−3.79430	−	6.57192i	−0.178667	−	0.309459i
$452$	4.33757	−	2.50430i	0.204022	−	0.117792i
$453$	3.29424	+	1.90193i	0.154777	+	0.0893604i
$454$	−7.79225			−0.365708
$455$	−4.41303	+	2.70164i	−0.206886	+	0.126655i
$456$			1.13521i			0.0531609i
$457$	31.2955	+	18.0685i	1.46394	+	0.845208i	0.999190	−	0.0402319i	$-0.0128097\pi$
$457$	31.2955	+	18.0685i	1.46394	+	0.845208i	0.464753	+	0.885440i	$0.346143\pi$
$458$	−2.83922	−	4.91767i	−0.132668	−	0.229787i
$459$	17.7822	−	10.2666i	0.830002	−	0.479202i
$460$	−2.08395	+	1.44230i	−0.0971645	+	0.0672474i
$461$			27.5367i			1.28251i	0.767326	+	0.641257i	$0.221587\pi$
$461$			27.5367i			1.28251i	−0.767326	+	0.641257i	$0.778413\pi$
$462$	−11.6503	+	0.299952i	−0.542020	+	0.0139550i
$463$	−0.186065			−0.00864718			−0.00432359	−	0.999991i	$-0.501376\pi$
$463$	−0.186065			−0.00864718			−0.00432359	+	0.999991i	$0.501376\pi$
$464$	−1.84464	+	3.19501i	−0.0856352	+	0.148325i
$465$	−2.80668	−	4.86131i	−0.130157	−	0.225438i
$466$	−14.2518	−	24.6849i	−0.660203	−	1.14351i
$467$	8.66213	−	15.0032i	0.400835	−	0.694267i	−0.592992	−	0.805209i	$-0.702053\pi$
$467$	8.66213	−	15.0032i	0.400835	−	0.694267i	0.993827	+	0.110941i	$0.0353866\pi$
$468$			5.97545i			0.276215i
$469$	0.0558730	+	2.17014i	0.00257998	+	0.100208i
$470$		−	1.04040i		−	0.0479903i
$471$	13.8922	+	8.02066i	0.640119	+	0.369573i
$472$	−5.00305	+	2.88851i	−0.230284	+	0.132954i
$473$	−9.21146	−	15.9547i	−0.423544	−	0.733599i
$474$	−12.8357	+	22.2321i	−0.589563	+	1.02115i
$475$	2.49469			0.114464
$476$	−9.53110	−	15.5687i	−0.436857	−	0.713590i
$477$		−	22.0981i		−	1.01180i
$478$	−1.05230	+	1.82264i	−0.0481310	+	0.0833654i
$479$	16.1836	+	28.0309i	0.739449	+	1.28076i	0.952744	+	0.303776i	$0.0982473\pi$
$479$	16.1836	+	28.0309i	0.739449	+	1.28076i	−0.213294	+	0.976988i	$0.568419\pi$
$480$	0.983118	−	0.567604i	0.0448730	−	0.0259074i
$481$	16.0428	−	27.7869i	0.731487	−	1.26697i
$482$	15.2072			0.692670
$483$	16.0836	+	22.0062i	0.731830	+	1.00132i
$484$	6.79539			0.308881
$485$	−2.94354	+	5.09836i	−0.133659	+	0.231504i
$486$	13.1728	−	7.60532i	0.597530	−	0.344984i
$487$	−15.0010	−	25.9825i	−0.679759	−	1.17738i	−0.975053	−	0.221971i	$-0.928751\pi$
$487$	−15.0010	−	25.9825i	−0.679759	−	1.17738i	0.295294	−	0.955407i	$-0.404583\pi$
$488$	2.92132	−	5.05987i	0.132242	−	0.229050i
$489$			12.0612i			0.545425i
$490$	1.68229	−	3.29451i	0.0759979	−	0.148831i
$491$	−11.9761			−0.540476			−0.270238	−	0.962794i	$-0.587102\pi$
$491$	−11.9761			−0.540476			−0.270238	+	0.962794i	$0.587102\pi$
$492$	3.97500	−	6.88490i	0.179207	−	0.310395i
$493$	12.7272	+	22.0441i	0.573203	+	0.992816i
$494$	1.69370	−	0.977857i	0.0762030	−	0.0439958i
$495$	−1.51521	−	0.874807i	−0.0681036	−	0.0393196i
$496$		−	4.94479i		−	0.222027i
$497$	1.30321	−	2.39771i	0.0584571	−	0.107552i
$498$		−	35.3468i		−	1.58393i
$499$	20.1372	−	34.8787i	0.901465	−	1.56138i	0.0758721	−	0.997118i	$-0.475826\pi$
$499$	20.1372	−	34.8787i	0.901465	−	1.56138i	0.825593	−	0.564266i	$-0.190841\pi$
$500$	−2.56848	−	4.44874i	−0.114866	−	0.198953i
$501$	−5.00000	−	8.66025i	−0.223384	−	0.386912i
$502$	10.5231	−	18.2266i	0.469670	−	0.813493i
$503$	19.6812			0.877540			0.438770	−	0.898599i	$-0.355414\pi$
$503$	19.6812			0.877540			0.438770	+	0.898599i	$0.355414\pi$
$504$	−2.23046	−	3.64338i	−0.0993527	−	0.162289i
$505$			1.57500i			0.0700868i
$506$	5.59643	+	8.08617i	0.248792	+	0.359474i
$507$	1.29499	−	0.747664i	0.0575126	−	0.0332049i
$508$	1.65536	+	2.86717i	0.0734448	+	0.127210i
$509$	25.0722	+	14.4755i	1.11131	+	0.641613i	0.939168	−	0.343459i	$-0.111599\pi$
$509$	25.0722	+	14.4755i	1.11131	+	0.641613i	0.172139	+	0.985073i	$0.444932\pi$
$510$		−	7.83241i		−	0.346825i
$511$	0.336719	+	13.0783i	0.0148956	+	0.578552i
$512$	1.00000			0.0441942
$513$	−1.36198	−	0.786342i	−0.0601331	−	0.0347179i
$514$	−19.3956	+	11.1981i	−0.855505	+	0.493926i
$515$	−0.465722	−	0.806654i	−0.0205222	−	0.0355454i
$516$	9.65015	−	16.7145i	0.424824	−	0.735817i
$517$	−4.03700			−0.177547
$518$	0.590379	+	22.9306i	0.0259398	+	1.00751i
$519$	31.7624			1.39422
$520$	−1.69370	−	0.977857i	−0.0742735	−	0.0428818i
$521$	−14.5786	−	25.2508i	−0.638698	−	1.10626i	−0.985719	−	0.168400i	$-0.946140\pi$
$521$	−14.5786	−	25.2508i	−0.638698	−	1.10626i	0.347021	−	0.937857i	$-0.387193\pi$
$522$	2.97840	+	5.15875i	0.130361	+	0.225792i
$523$	−8.36986	+	14.4970i	−0.365989	+	0.633911i	−0.988934	−	0.148354i	$-0.952602\pi$
$523$	−8.36986	+	14.4970i	−0.365989	+	0.633911i	0.622946	+	0.782265i	$0.285936\pi$
$524$			16.3341i			0.713557i
$525$	−22.8828	+	14.0088i	−0.998689	+	0.611394i
$526$		−	9.58514i		−	0.417932i
$527$	−29.5460	−	17.0584i	−1.28704	−	0.743075i
$528$	−2.20243	−	3.81471i	−0.0958483	−	0.166014i
$529$	8.10208	−	21.5257i	0.352264	−	0.935901i
$530$	6.26353	+	3.61625i	0.272071	+	0.157080i
$531$			9.32774i			0.404789i
$532$	−0.667682	+	1.22843i	−0.0289477	+	0.0532592i
$533$	−13.6961			−0.593244
$534$	14.1977	+	8.19703i	0.614394	+	0.354720i
$535$	4.06842	−	2.34890i	0.175893	−	0.101552i
$536$	−0.710579	+	0.410253i	−0.0306923	+	0.0177202i
$537$	6.29804	+	3.63617i	0.271780	+	0.156913i
$538$		−	17.0691i		−	0.735903i
$539$	−12.7834	−	6.52764i	−0.550621	−	0.281165i
$540$			1.57268i			0.0676776i
$541$	13.9445	−	24.1526i	0.599522	−	1.03840i	−0.393370	−	0.919380i	$-0.628691\pi$
$541$	13.9445	−	24.1526i	0.599522	−	1.03840i	0.992892	−	0.119022i	$-0.0379759\pi$
$542$	−12.9093	+	7.45316i	−0.554500	+	0.320141i
$543$	−19.1375	+	11.0490i	−0.821268	+	0.474160i
$544$	3.44977	−	5.97518i	0.147908	−	0.256184i
$545$			3.66431i			0.156962i
$546$	−10.0445	+	18.4804i	−0.429866	+	0.790887i
$547$	−29.2861			−1.25219			−0.626093	−	0.779749i	$-0.715347\pi$
$547$	−29.2861			−1.25219			−0.626093	+	0.779749i	$0.715347\pi$
$548$	8.49141	+	4.90252i	0.362735	+	0.209425i
$549$	−4.71684	−	8.16981i	−0.201310	−	0.348679i
$550$	−8.38308	+	4.83997i	−0.357456	+	0.206377i
$551$	0.974806	−	1.68841i	0.0415281	−	0.0719288i
$552$	−4.40485	+	9.31309i	−0.187483	+	0.396392i
$553$	−26.9658	+	16.5083i	−1.14670	+	0.702006i
$554$	29.8814			1.26954
$555$	−4.92103	+	8.52347i	−0.208886	+	0.361801i
$556$	15.9754	−	9.22340i	0.677507	−	0.391159i
$557$	−22.9683	+	13.2608i	−0.973199	+	0.561877i	−0.900210	−	0.435456i	$-0.856587\pi$
$557$	−22.9683	+	13.2608i	−0.973199	+	0.561877i	−0.0729893	+	0.997333i	$0.523254\pi$
$558$	−6.91434	−	3.99199i	−0.292707	−	0.168995i
$559$	−33.2502			−1.40633
$560$	1.39769	−	0.0359855i	0.0590633	−	0.00152066i
$561$	−30.3915			−1.28313
$562$	18.8737	+	10.8967i	0.796138	+	0.459650i
$563$	11.2503	+	19.4861i	0.474145	+	0.821243i	0.999562	−	0.0296019i	$-0.00942395\pi$
$563$	11.2503	+	19.4861i	0.474145	+	0.821243i	−0.525417	+	0.850845i	$0.676091\pi$
$564$	−2.11463	−	3.66264i	−0.0890419	−	0.154225i
$565$	2.29221	+	1.32341i	0.0964339	+	0.0556761i
$566$	26.7283			1.12347
$567$	29.7201	−	0.765183i	1.24813	−	0.0321347i
$568$	1.03146			0.0432791
$569$	−39.9445	−	23.0619i	−1.67456	−	0.966807i	−0.965033	−	0.262127i	$-0.915576\pi$
$569$	−39.9445	−	23.0619i	−1.67456	−	0.966807i	−0.709525	−	0.704680i	$-0.751091\pi$
$570$	−0.519532	+	0.299952i	−0.0217608	+	0.0125636i
$571$	8.35014	−	4.82096i	0.349442	−	0.201751i	−0.314997	−	0.949093i	$-0.602004\pi$
$571$	8.35014	−	4.82096i	0.349442	−	0.201751i	0.664440	+	0.747342i	$0.268670\pi$
$572$	−3.79430	+	6.57192i	−0.158648	+	0.274786i
$573$	−8.33733			−0.348297
$574$	8.35084	−	5.11236i	0.348557	−	0.213386i
$575$	20.4661	+	9.67994i	0.853496	+	0.403682i
$576$	0.807314	−	1.39831i	0.0336381	−	0.0582629i
$577$	−5.57577	+	3.21917i	−0.232122	+	0.134016i	−0.611551	−	0.791205i	$-0.709454\pi$
$577$	−5.57577	+	3.21917i	−0.232122	+	0.134016i	0.379428	+	0.925221i	$0.376121\pi$
$578$	−15.3018	−	26.5036i	−0.636473	−	1.10240i
$579$	25.4784	+	14.7100i	1.05885	+	0.611326i
$580$	−1.94961			−0.0809532
$581$	20.7895	−	38.2495i	0.862495	−	1.58685i
$582$			23.9310i			0.991972i
$583$	14.0319	−	24.3039i	0.581140	−	1.00656i
$584$	−4.28231	+	2.47239i	−0.177203	+	0.102308i
$585$	−2.73469	+	1.57887i	−0.113066	+	0.0652784i
$586$	10.6938	−	18.5223i	0.441758	−	0.765148i
$587$			23.4844i			0.969303i	0.874707	+	0.484652i	$0.161054\pi$
$587$			23.4844i			0.969303i	−0.874707	+	0.484652i	$0.838946\pi$
$588$	−0.773792	−	15.0173i	−0.0319106	−	0.619301i
$589$			2.61309i			0.107670i
$590$	−2.64388	−	1.52644i	−0.108847	−	0.0628427i
$591$	−38.1330	+	22.0161i	−1.56858	+	0.905622i
$592$	−7.50830	+	4.33492i	−0.308589	+	0.178164i
$593$	−4.62619	−	2.67093i	−0.189975	−	0.109682i	0.401996	−	0.915641i	$-0.368317\pi$
$593$	−4.62619	−	2.67093i	−0.189975	−	0.109682i	−0.591971	+	0.805959i	$0.701650\pi$
$594$	6.10236			0.250383
$595$	4.60670	−	8.47561i	0.188856	−	0.347466i
$596$		−	4.10103i		−	0.167985i
$597$	−38.8550	−	22.4330i	−1.59023	−	0.918120i
$598$	17.6892	−	1.45029i	0.723364	−	0.0593069i
$599$	−7.02881	−	12.1742i	−0.287189	−	0.497426i	0.685948	−	0.727650i	$-0.259388\pi$
$599$	−7.02881	−	12.1742i	−0.287189	−	0.497426i	−0.973138	+	0.230224i	$0.926054\pi$
$600$	−8.78231	−	5.07047i	−0.358536	−	0.207001i
$601$			13.0270i			0.531383i	0.964058	+	0.265691i	$0.0856002\pi$
$601$			13.0270i			0.531383i	−0.964058	+	0.265691i	$0.914400\pi$
$602$	20.2734	−	12.4113i	0.826283	−	0.505848i
$603$			1.32481i			0.0539505i
$604$	−0.885372	+	1.53351i	−0.0360253	+	0.0623976i
$605$	1.79552	+	3.10994i	0.0729984	+	0.126437i
$606$	3.20120	+	5.54465i	0.130040	+	0.225236i
$607$	34.3614	+	19.8386i	1.39469	+	0.805222i	0.993829	−	0.110919i	$-0.0353794\pi$
$607$	34.3614	+	19.8386i	1.39469	+	0.805222i	0.400856	+	0.916141i	$0.368713\pi$
$608$	−0.528453			−0.0214316
$609$	0.539672	+	20.9611i	0.0218686	+	0.849388i
$610$	3.08756			0.125012
$611$	−3.64304	+	6.30993i	−0.147382	+	0.255272i
$612$	−5.57010	−	9.64769i	−0.225158	−	0.389985i
$613$	−22.8371	+	13.1850i	−0.922380	+	0.532537i	−0.884394	−	0.466742i	$-0.845428\pi$
$613$	−22.8371	+	13.1850i	−0.922380	+	0.532537i	−0.0379867	+	0.999278i	$0.512094\pi$
$614$	1.87551	+	1.08283i	0.0756893	+	0.0436993i
$615$	4.20120			0.169409
$616$	−0.139632	−	5.42336i	−0.00562592	−	0.218513i
$617$		−	10.7491i		−	0.432744i	−0.976311	−	0.216372i	$-0.930578\pi$
$617$		−	10.7491i		−	0.432744i	0.976311	−	0.216372i	$-0.0694224\pi$
$618$	−3.27906	−	1.89316i	−0.131903	−	0.0761543i
$619$	−17.9379	−	31.0694i	−0.720985	−	1.24878i	−0.960605	−	0.277917i	$-0.910356\pi$
$619$	−17.9379	−	31.0694i	−0.720985	−	1.24878i	0.239620	−	0.970867i	$-0.422977\pi$
$620$	2.26300	−	1.30654i	0.0908843	−	0.0524721i
$621$	−8.12237	−	11.7358i	−0.325939	−	0.470943i
$622$			18.7483i			0.751737i
$623$	10.5424	+	17.2207i	0.422374	+	0.689931i
$624$	−7.94999			−0.318254
$625$	−10.4445	+	18.0904i	−0.417781	+	0.723618i
$626$	15.6552	+	27.1156i	0.625707	+	1.08376i
$627$	1.16388	+	2.01590i	0.0464809	+	0.0805073i
$628$	−3.73372	+	6.46700i	−0.148992	+	0.258061i
$629$			59.8179i			2.38510i
$630$	1.07806	−	1.98346i	0.0429509	−	0.0790229i
$631$			33.2092i			1.32204i	0.750370	+	0.661018i	$0.229876\pi$
$631$			33.2092i			1.32204i	−0.750370	+	0.661018i	$0.770124\pi$
$632$	−10.3493	−	5.97518i	−0.411674	−	0.237680i
$633$	48.5198	−	28.0129i	1.92849	−	1.11341i
$634$	−14.3234	−	24.8089i	−0.568856	−	0.985288i
$635$	−0.874781	+	1.51517i	−0.0347146	+	0.0601275i
$636$	29.4002			1.16579
$637$	−21.7388	+	14.0902i	−0.861322	+	0.558274i
$638$			7.56492i			0.299498i
$639$	0.832712	−	1.44230i	0.0329416	−	0.0570565i
$640$	0.264227	+	0.457654i	0.0104445	+	0.0180904i
$641$	−4.72515	+	2.72807i	−0.186632	+	0.107752i	−0.590405	−	0.807107i	$-0.701032\pi$
$641$	−4.72515	+	2.72807i	−0.186632	+	0.107752i	0.403773	+	0.914859i	$0.367699\pi$
$642$	9.54832	−	16.5382i	0.376842	−	0.652710i
$643$	19.3950			0.764865			0.382432	−	0.923983i	$-0.375086\pi$
$643$	19.3950			0.764865			0.382432	+	0.923983i	$0.375086\pi$
$644$	−10.2442	+	7.48713i	−0.403676	+	0.295034i
$645$	10.1993			0.401597
$646$	−1.82304	+	3.15760i	−0.0717267	+	0.124234i
$647$	−32.8996	+	18.9946i	−1.29342	+	0.746755i	−0.979258	−	0.202615i	$-0.935056\pi$
$647$	−32.8996	+	18.9946i	−1.29342	+	0.746755i	−0.314159	+	0.949370i	$0.601723\pi$
$648$	5.61843	+	9.73141i	0.220713	+	0.382286i
$649$	−5.92294	+	10.2588i	−0.232496	+	0.402694i
$650$			17.4706i			0.685254i
$651$	−14.6737	−	23.9689i	−0.575106	−	0.939414i
$652$	−5.61463			−0.219886
$653$	3.32891	−	5.76584i	0.130270	−	0.225635i	−0.793510	−	0.608557i	$-0.791749\pi$
$653$	3.32891	−	5.76584i	0.130270	−	0.225635i	0.923781	+	0.382922i	$0.125082\pi$
$654$	7.44772	+	12.8998i	0.291229	+	0.504423i
$655$	−7.47536	+	4.31590i	−0.292086	+	0.168636i
$656$	3.20501	+	1.85041i	0.125135	+	0.0722464i
$657$			7.98399i			0.311485i
$658$	−0.134065	−	5.20716i	−0.00522641	−	0.202996i
$659$			7.65972i			0.298380i	0.988809	+	0.149190i	$0.0476667\pi$
$659$			7.65972i			0.298380i	−0.988809	+	0.149190i	$0.952333\pi$
$660$	1.16388	−	2.01590i	0.0453040	−	0.0784688i
$661$	−11.6853	−	20.2395i	−0.454504	−	0.787225i	0.544155	−	0.838985i	$-0.316850\pi$
$661$	−11.6853	−	20.2395i	−0.454504	−	0.787225i	−0.998660	+	0.0517599i	$0.983517\pi$
$662$	−13.6550	−	23.6512i	−0.530717	−	0.919228i
$663$	−27.4257	+	47.5026i	−1.06512	+	1.84485i
$664$	16.4544			0.638554
$665$	−0.738616	+	0.0190167i	−0.0286423	+	0.000737434i
$666$			13.9986i			0.542433i
$667$	14.5486	−	10.0691i	0.563324	−	0.389876i
$668$	4.03146	−	2.32756i	0.155982	−	0.0900562i
$669$	3.38917	+	5.87022i	0.131033	+	0.226956i
$670$	−0.375508	−	0.216800i	−0.0145071	−	0.00837570i
$671$		−	11.9804i		−	0.462499i
$672$	4.84730	−	2.96750i	0.186989	−	0.114474i
$673$	−32.0944			−1.23715			−0.618575	−	0.785726i	$-0.712290\pi$
$673$	−32.0944			−1.23715			−0.618575	+	0.785726i	$0.712290\pi$
$674$	−2.67682	−	1.54546i	−0.103107	−	0.0595289i
$675$	12.1668	−	7.02449i	0.468299	−	0.270373i
$676$	0.348047	+	0.602836i	0.0133864	+	0.0231860i
$677$	−5.30587	+	9.19004i	−0.203921	+	0.353202i	−0.949788	−	0.312893i	$-0.898702\pi$
$677$	−5.30587	+	9.19004i	−0.203921	+	0.353202i	0.745867	+	0.666095i	$0.232035\pi$
$678$	10.7593			0.413209
$679$	−14.0752	+	25.8962i	−0.540158	+	0.993806i
$680$	3.64609			0.139821
$681$	−14.4965	−	8.36953i	−0.555505	−	0.320721i
$682$	−5.06968	−	8.78094i	−0.194128	−	0.336240i
$683$	20.7369	+	35.9173i	0.793474	+	1.37434i	0.923804	+	0.382866i	$0.125063\pi$
$683$	20.7369	+	35.9173i	0.793474	+	1.37434i	−0.130330	+	0.991471i	$0.541604\pi$
$684$	−0.426628	+	0.738941i	−0.0163125	+	0.0282541i
$685$			5.18151i			0.197975i
$686$	7.99520	−	16.7056i	0.305258	−	0.637822i
$687$		−	12.1982i		−	0.465392i
$688$	7.78083	+	4.49227i	0.296642	+	0.171266i
$689$	−25.3251	−	43.8643i	−0.964808	−	1.67110i
$690$	−5.42606	+	0.444869i	−0.206566	+	0.0169359i
$691$	−3.74856	−	2.16423i	−0.142602	−	0.0823313i	0.427002	−	0.904251i	$-0.359570\pi$
$691$	−3.74856	−	2.16423i	−0.142602	−	0.0823313i	−0.569603	+	0.821920i	$0.692903\pi$
$692$			14.7858i			0.562072i
$693$	−7.69625	−	4.18310i	−0.292356	−	0.158903i
$694$	−5.44829			−0.206814
$695$	8.44225	+	4.87414i	0.320233	+	0.184887i
$696$	−6.86342	+	3.96259i	−0.260157	+	0.150202i
$697$	22.1131	−	12.7670i	0.837593	−	0.483584i
$698$	6.10817	+	3.52655i	0.231198	+	0.133482i
$699$		−	61.2307i		−	2.31596i
$700$	−6.52127	−	10.6523i	−0.246481	−	0.402617i
$701$		−	4.85553i		−	0.183391i	−0.995787	−	0.0916954i	$-0.970771\pi$
$701$		−	4.85553i		−	0.183391i	0.995787	−	0.0916954i	$-0.0292286\pi$
$702$	5.50685	−	9.53814i	0.207843	−	0.359994i
$703$	3.96779	−	2.29080i	0.149648	−	0.0863992i
$704$	1.77580	−	1.02526i	0.0669279	−	0.0386409i
$705$	1.11748	−	1.93554i	0.0420868	−	0.0728965i
$706$			8.86485i			0.333633i
$707$	0.202953	+	7.88279i	0.00763284	+	0.296463i
$708$	−12.4100			−0.466397
$709$	−12.1318	−	7.00431i	−0.455620	−	0.263052i	0.254581	−	0.967051i	$-0.418062\pi$
$709$	−12.1318	−	7.00431i	−0.455620	−	0.263052i	−0.710201	+	0.703999i	$0.751396\pi$
$710$	0.272539	+	0.472052i	0.0102282	+	0.0177158i
$711$	−16.7103	+	9.64769i	−0.626685	+	0.361817i
$712$	−3.81582	+	6.60920i	−0.143004	+	0.247690i
$713$	−10.1394	+	21.4374i	−0.379722	+	0.802839i
$714$	−1.00927	−	39.2007i	−0.0377711	−	1.46705i
$715$	−4.01022			−0.149974
$716$	−1.69269	+	2.93182i	−0.0632587	+	0.109567i
$717$	−3.91533	+	2.26052i	−0.146221	+	0.0844205i
$718$	−8.33391	+	4.81159i	−0.311019	+	0.179567i
$719$	−29.9439	−	17.2881i	−1.11672	−	0.644739i	−0.176159	−	0.984362i	$-0.556367\pi$
$719$	−29.9439	−	17.2881i	−1.11672	−	0.644739i	−0.940562	+	0.339623i	$0.889700\pi$
$720$	0.853256			0.0317990
$721$	−2.43485	−	3.97724i	−0.0906787	−	0.148120i
$722$	−18.7207			−0.696714
$723$	28.2910	+	16.3338i	1.05215	+	0.607462i
$724$	−5.14347	−	8.90875i	−0.191155	−	0.331091i
$725$	8.70805	+	15.0828i	0.323409	+	0.560161i
$726$	12.6419	+	7.29882i	0.469186	+	0.270885i
$727$	−29.9681			−1.11146			−0.555728	−	0.831364i	$-0.687560\pi$
$727$	−29.9681			−1.11146			−0.555728	+	0.831364i	$0.687560\pi$
$728$	−8.60285	−	4.67586i	−0.318843	−	0.173299i
$729$	−1.03559			−0.0383550
$730$	−2.26300	−	1.30654i	−0.0837574	−	0.0483574i
$731$	53.6842	−	30.9946i	1.98558	−	1.14638i
$732$	10.8695	−	6.27548i	0.401747	−	0.231949i
$733$	23.8350	−	41.2834i	0.880366	−	1.52484i	0.0294318	−	0.999567i	$-0.490630\pi$
$733$	23.8350	−	41.2834i	0.880366	−	1.52484i	0.850934	−	0.525272i	$-0.176036\pi$
$734$	−24.2072			−0.893503
$735$	6.66825	−	4.32209i	0.245962	−	0.159423i
$736$	−4.33536	−	2.05052i	−0.159804	−	0.0755830i
$737$	−0.841230	+	1.45705i	−0.0309871	+	0.0536712i
$738$	5.17489	−	2.98773i	0.190490	−	0.109980i
$739$	0.172792	+	0.299285i	0.00635626	+	0.0110094i	0.869186	−	0.494485i	$-0.164643\pi$
$739$	0.172792	+	0.299285i	0.00635626	+	0.0110094i	−0.862830	+	0.505495i	$0.831310\pi$
$740$	−3.96779	−	2.29080i	−0.145859	−	0.0842115i
$741$	4.20120			0.154335
$742$	31.8146	+	17.2920i	1.16795	+	0.634809i
$743$			14.5735i			0.534650i	0.963606	+	0.267325i	$0.0861397\pi$
$743$			14.5735i			0.534650i	−0.963606	+	0.267325i	$0.913860\pi$
$744$	5.31112	−	9.19912i	0.194715	−	0.337256i
$745$	1.87685	−	1.08360i	0.0687626	−	0.0397001i
$746$	−0.0491634	+	0.0283845i	−0.00180000	+	0.00103923i
$747$	13.2838	−	23.0083i	0.486030	−	0.841829i
$748$		−	14.1476i		−	0.517288i
$749$	20.0595	−	12.2804i	0.732959	−	0.448715i
$750$		−	11.0350i		−	0.402943i
$751$	−40.0662	−	23.1322i	−1.46204	−	0.844107i	−0.462931	−	0.886394i	$-0.653202\pi$
$751$	−40.0662	−	23.1322i	−1.46204	−	0.844107i	−0.999105	+	0.0422873i	$0.986536\pi$
$752$	1.70501	−	0.984386i	0.0621752	−	0.0358969i
$753$	39.1538	−	22.6054i	1.42684	−	0.823788i
$754$	11.8242	+	6.82668i	0.430611	+	0.248613i
$755$	−0.935756			−0.0340557
$756$	0.202654	+	7.87118i	0.00737046	+	0.286272i
$757$			5.74054i			0.208644i	0.994544	+	0.104322i	$0.0332672\pi$
$757$			5.74054i			0.208644i	−0.994544	+	0.104322i	$0.966733\pi$
$758$	−17.6672	−	10.2001i	−0.641701	−	0.370486i
$759$	1.72619	+	21.0543i	0.0626568	+	0.764222i
$760$	−0.139632	−	0.241849i	−0.00506497	−	0.00877278i
$761$	−38.7314	−	22.3616i	−1.40401	−	0.810607i	−0.409210	−	0.912440i	$-0.634196\pi$
$761$	−38.7314	−	22.3616i	−1.40401	−	0.810607i	−0.994801	+	0.101834i	$0.967529\pi$
$762$			7.11199i			0.257640i
$763$	0.472178	+	18.3396i	0.0170940	+	0.663939i
$764$		−	3.88113i		−	0.140414i
$765$	2.94354	−	5.09836i	0.106424	−	0.184331i
$766$	−6.47291	−	11.2114i	−0.233876	−	0.405085i
$767$	10.6899	+	18.5154i	0.385989	+	0.668552i
$768$	1.86037	+	1.07408i	0.0671303	+	0.0387577i
$769$	30.7425			1.10860			0.554301	−	0.832316i	$-0.312986\pi$
$769$	30.7425			1.10860			0.554301	+	0.832316i	$0.312986\pi$
$770$	2.44513	−	1.49690i	0.0881163	−	0.0539445i
$771$	−48.1107			−1.73266
$772$	−6.84769	+	11.8605i	−0.246454	+	0.426870i
$773$	−14.1519	−	24.5119i	−0.509009	−	0.881630i	−0.999946	−	0.0104345i	$-0.996679\pi$
$773$	−14.1519	−	24.5119i	−0.509009	−	0.881630i	0.490936	−	0.871196i	$-0.336655\pi$
$774$	12.5632	−	7.25334i	0.451573	−	0.260716i
$775$	−20.2157	−	11.6715i	−0.726168	−	0.419253i
$776$	−11.1402			−0.399910
$777$	−23.5311	+	43.2935i	−0.844173	+	1.55315i
$778$		−	35.7943i		−	1.28329i
$779$	−1.69370	−	0.977857i	−0.0606830	−	0.0350353i
$780$	−2.10060	−	3.63835i	−0.0752136	−	0.130274i
$781$	1.83166	−	1.05751i	0.0655421	−	0.0378407i
$782$	−27.2082	+	18.8308i	−0.972964	+	0.673387i
$783$		−	10.9793i		−	0.392370i
$784$	6.99073	−	0.360210i	0.249669	−	0.0128646i
$785$	−3.94620			−0.140846
$786$	−17.5442	+	30.3874i	−0.625780	+	1.08388i
$787$	1.87582	+	3.24902i	0.0668659	+	0.115815i	0.897520	−	0.440973i	$-0.145367\pi$
$787$	1.87582	+	3.24902i	0.0668659	+	0.115815i	−0.830654	+	0.556789i	$0.812033\pi$
$788$	−10.2488	−	17.7514i	−0.365098	−	0.632368i
$789$	10.2952	−	17.8319i	0.366521	−	0.634832i
$790$		−	6.31521i		−	0.224685i
$791$	11.6429	+	6.32819i	0.413973	+	0.225005i
$792$		−	3.31082i		−	0.117645i
$793$	−18.7257	−	10.8113i	−0.664969	−	0.383920i
$794$	−18.9349	+	10.9321i	−0.671974	+	0.387964i
$795$	7.76832	+	13.4551i	0.275514	+	0.477204i
$796$	10.4428	−	18.0875i	0.370136	−	0.641095i
$797$	−14.8394			−0.525637			−0.262819	−	0.964845i	$-0.584652\pi$
$797$	−14.8394			−0.525637			−0.262819	+	0.964845i	$0.584652\pi$
$798$	−2.56157	+	1.56819i	−0.0906787	+	0.0555132i
$799$		−	13.5836i		−	0.480554i
$800$	2.36037	−	4.08828i	0.0834516	−	0.144542i
$801$	6.16113	+	10.6714i	0.217693	+	0.377055i
$802$	−15.0987	+	8.71723i	−0.533153	+	0.307816i
$803$	−5.06968	+	8.78094i	−0.178905	+	0.309873i
$804$	−1.76259			−0.0621616
$805$	−6.13330	−	2.70998i	−0.216170	−	0.0955143i
$806$	−18.2998			−0.644582
$807$	18.3337	−	31.7549i	0.645377	−	1.11783i
$808$	−2.58111	+	1.49020i	−0.0908030	+	0.0524251i
$809$	−23.3360	−	40.4191i	−0.820450	−	1.42106i	−0.905348	−	0.424671i	$-0.860390\pi$
$809$	−23.3360	−	40.4191i	−0.820450	−	1.42106i	0.0848982	−	0.996390i	$-0.472943\pi$
$810$	−2.96908	+	5.14260i	−0.104323	+	0.180692i
$811$			10.5200i			0.369409i	0.982794	+	0.184704i	$0.0591328\pi$
$811$			10.5200i			0.369409i	−0.982794	+	0.184704i	$0.940867\pi$
$812$	−9.75768	+	0.251224i	−0.342427	+	0.00881625i
$813$	−32.0213			−1.12304
$814$	−8.88881	+	15.3959i	−0.311553	+	0.539625i
$815$	−1.48353	−	2.56956i	−0.0519660	−	0.0900077i
$816$	12.8357	−	7.41069i	0.449339	−	0.259426i
$817$	−4.11181	−	2.37395i	−0.143854	−	0.0830541i
$818$			33.1136i			1.15779i
$819$	−13.4835	+	8.25455i	−0.471151	+	0.288437i
$820$			1.95571i			0.0682965i
$821$	7.02805	−	12.1729i	0.245281	−	0.424839i	−0.716930	−	0.697145i	$-0.754453\pi$
$821$	7.02805	−	12.1729i	0.245281	−	0.424839i	0.962210	+	0.272307i	$0.0877866\pi$
$822$	10.5314	+	18.2410i	0.367326	+	0.636228i
$823$	3.49718	+	6.05730i	0.121904	+	0.211144i	0.920519	−	0.390699i	$-0.127767\pi$
$823$	3.49718	+	6.05730i	0.121904	+	0.211144i	−0.798614	+	0.601843i	$0.794433\pi$
$824$	0.881293	−	1.52644i	0.0307013	−	0.0531762i
$825$	−20.7941			−0.723959
$826$	−13.4291	−	7.29906i	−0.467259	−	0.253967i
$827$		−	36.9598i		−	1.28522i	−0.766194	−	0.642609i	$-0.777852\pi$
$827$		−	36.9598i		−	1.28522i	0.766194	−	0.642609i	$-0.222148\pi$
$828$	−6.36725	+	4.40677i	−0.221277	+	0.153146i
$829$	3.07501	−	1.77536i	0.106800	−	0.0616608i	−0.445649	−	0.895208i	$-0.647027\pi$
$829$	3.07501	−	1.77536i	0.106800	−	0.0616608i	0.552448	+	0.833547i	$0.313694\pi$
$830$	4.34769	+	7.53041i	0.150910	+	0.261384i
$831$	55.5905	+	32.0952i	1.92841	+	1.11337i
$832$		−	3.70082i		−	0.128303i
$833$	21.9641	−	43.0135i	0.761010	−	1.49033i
$834$	39.6268			1.37216
$835$	2.13044	+	1.23001i	0.0737269	+	0.0425662i
$836$	−0.938427	+	0.541801i	−0.0324562	+	0.0187386i
$837$	7.35787	+	12.7442i	0.254325	+	0.440504i
$838$	−11.4997	+	19.9181i	−0.397252	+	0.688060i
$839$	−4.89386			−0.168955			−0.0844774	−	0.996425i	$-0.526922\pi$
$839$	−4.89386			−0.168955			−0.0844774	+	0.996425i	$0.526922\pi$
$840$	2.63888	+	1.43429i	0.0910499	+	0.0494878i
$841$	−15.3892			−0.530663
$842$	12.1184	+	6.99657i	0.417628	+	0.241118i
$843$	23.4080	+	40.5438i	0.806214	+	1.39640i
$844$	13.0404	+	22.5866i	0.448868	+	0.777462i
$845$	−0.183927	+	0.318571i	−0.00632728	+	0.0109592i
$846$		−	3.17884i		−	0.109291i
$847$	9.38722	+	15.3337i	0.322549	+	0.526871i
$848$			13.6862i			0.469985i
$849$	49.7245	+	28.7084i	1.70654	+	0.985271i
$850$	−16.2855	−	28.2072i	−0.558587	−	0.967501i
$851$	41.4400	−	3.39757i	1.42055	−	0.116467i
$852$	1.91889	+	1.10787i	0.0657402	+	0.0379551i
$853$		−	15.0374i		−	0.514871i	−0.966296	−	0.257435i	$-0.917123\pi$
$853$		−	15.0374i		−	0.514871i	0.966296	−	0.257435i	$-0.0828774\pi$
$854$	15.4530	−	0.397859i	0.528792	−	0.0136145i
$855$	−0.450906			−0.0154207
$856$	7.69873	+	4.44487i	0.263137	+	0.151922i
$857$	−21.1705	+	12.2228i	−0.723171	+	0.417523i	−0.815919	−	0.578167i	$-0.803768\pi$
$857$	−21.1705	+	12.2228i	−0.723171	+	0.417523i	0.0927480	+	0.995690i	$0.470435\pi$
$858$	−14.1176	+	8.15079i	−0.481966	+	0.278263i
$859$	−39.3337	−	22.7093i	−1.34205	−	0.774833i	−0.354942	−	0.934889i	$-0.615499\pi$
$859$	−39.3337	−	22.7093i	−1.34205	−	0.774833i	−0.987108	+	0.160056i	$0.948833\pi$
$860$			4.74791i			0.161902i
$861$	21.0267	−	0.541361i	0.716589	−	0.0184495i
$862$		−	15.0335i		−	0.512044i
$863$	15.5188	−	26.8793i	0.528265	−	0.914982i	−0.471192	−	0.882031i	$-0.656176\pi$
$863$	15.5188	−	26.8793i	0.528265	−	0.914982i	0.999457	−	0.0329515i	$-0.0104907\pi$
$864$	−2.57730	+	1.48801i	−0.0876816	+	0.0506230i
$865$	−6.76679	+	3.90681i	−0.230078	+	0.132835i
$866$	−4.25076	+	7.36254i	−0.144447	+	0.250189i
$867$		−	65.7419i		−	2.23271i
$868$	11.1578	−	6.83078i	0.378721	−	0.231852i
$869$	−24.5044			−0.831255
$870$	−3.62700	−	2.09405i	−0.122967	−	0.0709948i
$871$	1.51827	+	2.62973i	0.0514447	+	0.0891049i
$872$	−6.00504	+	3.46701i	−0.203356	+	0.117408i
$873$	−8.99363	+	15.5774i	−0.304388	+	0.527216i
$874$	2.29104	+	1.08360i	0.0774955	+	0.0366534i
$875$	6.49036	−	11.9413i	0.219414	−	0.403688i
$876$	−10.6222			−0.358892
$877$	13.4970	−	23.3775i	0.455761	−	0.789401i	−0.542971	−	0.839752i	$-0.682701\pi$
$877$	13.4970	−	23.3775i	0.455761	−	0.789401i	0.998732	+	0.0503507i	$0.0160339\pi$
$878$	−1.54965	+	0.894688i	−0.0522980	+	0.0301943i
$879$	39.7890	−	22.9722i	1.34205	−	0.774832i
$880$	0.938427	+	0.541801i	0.0316344	+	0.0182641i
$881$	41.9616			1.41372			0.706860	−	0.707353i	$-0.250111\pi$
$881$	41.9616			1.41372			0.706860	+	0.707353i	$0.250111\pi$
$882$	5.14003	−	10.0660i	0.173074	−	0.338940i
$883$	−10.3346			−0.347786			−0.173893	−	0.984765i	$-0.555635\pi$
$883$	−10.3346			−0.347786			−0.173893	+	0.984765i	$0.555635\pi$
$884$	−22.1131	−	12.7670i	−0.743743	−	0.429400i
$885$	−3.27906	−	5.67949i	−0.110224	−	0.190914i
$886$	−7.21146	−	12.4906i	−0.242274	−	0.419631i
$887$	−30.0510	−	17.3499i	−1.00901	−	0.582554i	−0.0981109	−	0.995175i	$-0.531280\pi$
$887$	−30.0510	−	17.3499i	−1.00901	−	0.582554i	−0.910903	+	0.412621i	$0.864613\pi$
$888$	−18.6243			−0.624989
$889$	−4.18298	+	7.69603i	−0.140293	+	0.258117i
$890$	−4.03297			−0.135185
$891$	19.9544	+	11.5207i	0.668498	+	0.385957i
$892$	−2.73266	+	1.57770i	−0.0914964	+	0.0528254i
$893$	−0.901017	+	0.520202i	−0.0301514	+	0.0174079i
$894$	4.40485	−	7.62943i	0.147320	−	0.255166i
$895$	−1.78901			−0.0598001
$896$	1.38141	+	2.25648i	0.0461497	+	0.0753837i
$897$	34.4661	+	16.3016i	1.15079	+	0.544294i
$898$	−4.82609	+	8.35903i	−0.161049	+	0.278945i
$899$	−15.7986	+	9.12134i	−0.526914	+	0.304214i
$900$	−3.81112	−	6.60105i	−0.127037	−	0.220035i
$901$	81.7773	+	47.2142i	2.72440	+	1.57293i
$902$	7.58860			0.252673
$903$	51.0469	−	1.31427i	1.69873	−	0.0437361i
$904$			5.00860i			0.166584i
$905$	2.71808	−	4.70786i	0.0903522	−	0.156495i
$906$	−3.29424	+	1.90193i	−0.109444	+	0.0631874i
$907$	−27.5555	+	15.9092i	−0.914966	+	0.528256i	−0.882026	−	0.471201i	$-0.843820\pi$
$907$	−27.5555	+	15.9092i	−0.914966	+	0.528256i	−0.0329403	+	0.999457i	$0.510487\pi$
$908$	3.89612	−	6.74828i	0.129297	−	0.223950i
$909$			4.81224i			0.159612i
$910$	−0.133176	−	5.17262i	−0.00441474	−	0.171471i
$911$			3.68229i			0.122000i	0.998138	+	0.0609998i	$0.0194289\pi$
$911$			3.68229i			0.122000i	−0.998138	+	0.0609998i	$0.980571\pi$
$912$	−0.983118	−	0.567604i	−0.0325543	−	0.0187952i
$913$	29.2197	−	16.8700i	0.967029	−	0.558315i
$914$	−31.2955	+	18.0685i	−1.03516	+	0.597653i
$915$	5.74400	+	3.31630i	0.189891	+	0.109634i
$916$	5.67843			0.187621
$917$	−36.8575	+	22.5641i	−1.21714	+	0.745131i
$918$			20.5331i			0.677694i
$919$	45.3869	+	26.2041i	1.49718	+	0.864395i	0.999995	−	0.00325243i	$-0.00103528\pi$
$919$	45.3869	+	26.2041i	1.49718	+	0.864395i	0.497181	+	0.867647i	$0.334369\pi$
$920$	−0.207092	−	2.52590i	−0.00682763	−	0.0832764i
$921$	2.32609	+	4.02891i	0.0766473	+	0.132757i
$922$	−23.8475	−	13.7684i	−0.785376	−	0.453437i
$923$		−	3.81725i		−	0.125646i
$924$	5.56538	−	10.2394i	0.183087	−	0.336852i
$925$			40.9280i			1.34570i
$926$	0.0930326	−	0.161137i	0.00305724	−	0.00529530i
$927$	−1.42296	−	2.46464i	−0.0467361	−	0.0809493i
$928$	−1.84464	−	3.19501i	−0.0605532	−	0.104881i
$929$	−1.47463	−	0.851381i	−0.0483812	−	0.0279329i	0.475614	−	0.879654i	$-0.342226\pi$
$929$	−1.47463	−	0.851381i	−0.0483812	−	0.0279329i	−0.523995	+	0.851721i	$0.675559\pi$
$930$	5.61336			0.184069
$931$	−3.69427	+	0.190354i	−0.121075	+	0.00623861i
$932$	28.5037			0.933669
$933$	−20.1372	+	34.8787i	−0.659263	+	1.14188i
$934$	8.66213	+	15.0032i	0.283433	+	0.490921i
$935$	6.47472	−	3.73818i	0.211746	−	0.122252i
$936$	−5.17489	−	2.98773i	−0.169147	−	0.0976569i
$937$	17.8589			0.583425			0.291713	−	0.956506i	$-0.405775\pi$
$937$	17.8589			0.583425			0.291713	+	0.956506i	$0.405775\pi$
$938$	−1.90733	−	1.03668i	−0.0622765	−	0.0338488i
$939$			67.2599i			2.19495i
$940$	0.901017	+	0.520202i	0.0293879	+	0.0169671i
$941$	28.6616	+	49.6433i	0.934341	+	1.61833i	0.775805	+	0.630973i	$0.217344\pi$
$941$	28.6616	+	49.6433i	0.934341	+	1.61833i	0.158536	+	0.987353i	$0.449323\pi$
$942$	−13.8922	+	8.02066i	−0.452632	+	0.261327i
$943$	−10.1006	−	14.5941i	−0.328920	−	0.475250i
$944$		−	5.77702i		−	0.188026i
$945$	−3.54873	+	2.17252i	−0.115440	+	0.0706722i
$946$	18.4229			0.598981
$947$	−1.22926	+	2.12913i	−0.0399454	+	0.0691875i	−0.885307	−	0.465007i	$-0.846052\pi$
$947$	−1.22926	+	2.12913i	−0.0399454	+	0.0691875i	0.845361	+	0.534195i	$0.179385\pi$
$948$	−12.8357	−	22.2321i	−0.416884	−	0.722064i
$949$	9.14989	+	15.8481i	0.297018	+	0.514450i
$950$	−1.24734	+	2.16046i	−0.0404692	+	0.0700947i
$951$		−	61.5383i		−	1.99552i
$952$	18.2484	−	0.469830i	0.591435	−	0.0152273i
$953$			22.3180i			0.722950i	0.932382	+	0.361475i	$0.117727\pi$
$953$			22.3180i			0.722950i	−0.932382	+	0.361475i	$0.882273\pi$
$954$	19.1375	+	11.0490i	0.619599	+	0.357726i
$955$	1.77622	−	1.02550i	0.0574770	−	0.0331844i
$956$	−1.05230	−	1.82264i	−0.0340338	−	0.0589482i
$957$	−8.12536	+	14.0735i	−0.262656	+	0.454933i
$958$	−32.3673			−1.04574
$959$	0.667682	+	25.9331i	0.0215606	+	0.837424i
$960$			1.13521i			0.0366387i
$961$	−3.27455	+	5.67168i	−0.105631	+	0.182957i
$962$	16.0428	+	27.7869i	0.517239	+	0.895885i
$963$	12.4306	−	7.17680i	0.400570	−	0.231269i
$964$	−7.60361	+	13.1698i	−0.244896	+	0.424172i
$965$	−7.23737			−0.232979
$966$	−27.0997	+	2.92574i	−0.871919	+	0.0941340i
$967$	52.7700			1.69697			0.848485	−	0.529220i	$-0.177515\pi$
$967$	52.7700			1.69697			0.848485	+	0.529220i	$0.177515\pi$
$968$	−3.39769	+	5.88498i	−0.109206	+	0.189150i
$969$	−6.78307	+	3.91620i	−0.217903	+	0.125807i
$970$	−2.94354	−	5.09836i	−0.0945113	−	0.163698i
$971$	−1.75446	+	3.03882i	−0.0563034	+	0.0975204i	−0.892803	−	0.450447i	$-0.851265\pi$
$971$	−1.75446	+	3.03882i	−0.0563034	+	0.0975204i	0.836500	+	0.547967i	$0.184598\pi$
$972$			15.2106i			0.487881i
$973$	42.8810	+	23.3069i	1.37470	+	0.747184i
$974$	30.0020			0.961325
$975$	−18.7649	+	32.5018i	−0.600958	+	1.04089i
$976$	2.92132	+	5.05987i	0.0935091	+	0.161963i
$977$	−26.1586	+	15.1027i	−0.836887	+	0.483177i	−0.856205	−	0.516636i	$-0.827184\pi$
$977$	−26.1586	+	15.1027i	−0.836887	+	0.483177i	0.0193177	+	0.999813i	$0.493851\pi$
$978$	−10.4453	−	6.03058i	−0.334003	−	0.192837i
$979$			15.6488i			0.500138i
$980$	2.01199	+	3.10416i	0.0642706	+	0.0991587i
$981$			11.1959i			0.357456i
$982$	5.98807	−	10.3716i	0.191087	−	0.330973i
$983$	10.5938	+	18.3490i	0.337890	+	0.585243i	0.984036	−	0.177971i	$-0.0569534\pi$
$983$	10.5938	+	18.3490i	0.337890	+	0.585243i	−0.646145	+	0.763214i	$0.723620\pi$
$984$	3.97500	+	6.88490i	0.126718	+	0.219482i
$985$	5.41601	−	9.38080i	0.172568	−	0.298897i
$986$	−25.4543			−0.810631
$987$	5.34352	−	9.83123i	0.170086	−	0.312931i
$988$			1.95571i			0.0622195i
$989$	−24.5213	−	35.4303i	−0.779732	−	1.12662i
$990$	1.51521	−	0.874807i	0.0481565	−	0.0278032i
$991$	27.8066	+	48.1624i	0.883305	+	1.52993i	0.847644	+	0.530566i	$0.178021\pi$
$991$	27.8066	+	48.1624i	0.883305	+	1.52993i	0.0356618	+	0.999364i	$0.488646\pi$
$992$	4.28231	+	2.47239i	0.135963	+	0.0784986i
$993$		−	58.6665i		−	1.86172i
$994$	1.42487	+	2.32747i	0.0451941	+	0.0738228i
$995$	11.0371			0.349899
$996$	30.6112	+	17.6734i	0.969953	+	0.560003i
$997$	5.61807	−	3.24359i	0.177926	−	0.102726i	−0.408392	−	0.912807i	$-0.633910\pi$
$997$	5.61807	−	3.24359i	0.177926	−	0.102726i	0.586318	+	0.810081i	$0.300577\pi$
$998$	20.1372	+	34.8787i	0.637432	+	1.10406i
$999$	12.9008	−	22.3448i	0.408162	−	0.706958i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.g.a.229.2	yes	16
7.2	even	3		2254.2.c.c.2253.3		16
7.3	odd	6	inner	322.2.g.a.45.1	✓	16
7.5	odd	6		2254.2.c.c.2253.14		16
23.22	odd	2	inner	322.2.g.a.229.1	yes	16
161.45	even	6	inner	322.2.g.a.45.2	yes	16
161.68	even	6		2254.2.c.c.2253.13		16
161.114	odd	6		2254.2.c.c.2253.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.g.a.45.1	✓	16	7.3	odd	6	inner
322.2.g.a.45.2	yes	16	161.45	even	6	inner
322.2.g.a.229.1	yes	16	23.22	odd	2	inner
322.2.g.a.229.2	yes	16	1.1	even	1	trivial
2254.2.c.c.2253.3		16	7.2	even	3
2254.2.c.c.2253.4		16	161.114	odd	6
2254.2.c.c.2253.13		16	161.68	even	6
2254.2.c.c.2253.14		16	7.5	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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.86037 + 1.07408i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.264227 - 0.457654i) q^{5} -2.14817i q^{6} +(1.26346 - 2.32458i) q^{7} +1.00000 q^{8} +(0.807314 - 1.39831i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.86037 + 1.07408i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.264227 - 0.457654i) q^{5} -2.14817i q^{6} +(1.26346 - 2.32458i) q^{7} +1.00000 q^{8} +(0.807314 - 1.39831i) q^{9} +(0.264227 + 0.457654i) q^{10} +(1.77580 - 1.02526i) q^{11} +(1.86037 + 1.07408i) q^{12} -3.70082i q^{13} +(1.38141 + 2.25648i) q^{14} +1.13521i q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.44977 + 5.97518i) q^{17} +(0.807314 + 1.39831i) q^{18} +(0.264227 - 0.457654i) q^{19} -0.528453 q^{20} +(0.146281 + 5.68164i) q^{21} +2.05052i q^{22} +(3.94348 - 2.72928i) q^{23} +(-1.86037 + 1.07408i) q^{24} +(2.36037 + 4.08828i) q^{25} +(3.20501 + 1.85041i) q^{26} -2.97601i q^{27} +(-2.64487 + 0.0680958i) q^{28} +3.68928 q^{29} +(-0.983118 - 0.567604i) q^{30} +(-4.28231 + 2.47239i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.20243 + 3.81471i) q^{33} -6.89954 q^{34} +(-0.730011 - 1.19245i) q^{35} -1.61463 q^{36} +(7.50830 + 4.33492i) q^{37} +(0.264227 + 0.457654i) q^{38} +(3.97500 + 6.88490i) q^{39} +(0.264227 - 0.457654i) q^{40} -3.70082i q^{41} +(-4.99358 - 2.71414i) q^{42} -8.98453i q^{43} +(-1.77580 - 1.02526i) q^{44} +(-0.426628 - 0.738941i) q^{45} +(0.391884 + 4.77979i) q^{46} +(-1.70501 - 0.984386i) q^{47} -2.14817i q^{48} +(-3.80731 - 5.87404i) q^{49} -4.72074 q^{50} +(-12.8357 - 7.41069i) q^{51} +(-3.20501 + 1.85041i) q^{52} +(11.8526 - 6.84309i) q^{53} +(2.57730 + 1.48801i) q^{54} -1.08360i q^{55} +(1.26346 - 2.32458i) q^{56} +1.13521i q^{57} +(-1.84464 + 3.19501i) q^{58} +(-5.00305 + 2.88851i) q^{59} +(0.983118 - 0.567604i) q^{60} +(2.92132 - 5.05987i) q^{61} -4.94479i q^{62} +(-2.23046 - 3.64338i) q^{63} +1.00000 q^{64} +(-1.69370 - 0.977857i) q^{65} +(-2.20243 - 3.81471i) q^{66} +(-0.710579 + 0.410253i) q^{67} +(3.44977 - 5.97518i) q^{68} +(-4.40485 + 9.31309i) q^{69} +(1.39769 - 0.0359855i) q^{70} +1.03146 q^{71} +(0.807314 - 1.39831i) q^{72} +(-4.28231 + 2.47239i) q^{73} +(-7.50830 + 4.33492i) q^{74} +(-8.78231 - 5.07047i) q^{75} -0.528453 q^{76} +(-0.139632 - 5.42336i) q^{77} -7.94999 q^{78} +(-10.3493 - 5.97518i) q^{79} +(0.264227 + 0.457654i) q^{80} +(5.61843 + 9.73141i) q^{81} +(3.20501 + 1.85041i) q^{82} +16.4544 q^{83} +(4.84730 - 2.96750i) q^{84} +3.64609 q^{85} +(7.78083 + 4.49227i) q^{86} +(-6.86342 + 3.96259i) q^{87} +(1.77580 - 1.02526i) q^{88} +(-3.81582 + 6.60920i) q^{89} +0.853256 q^{90} +(-8.60285 - 4.67586i) q^{91} +(-4.33536 - 2.05052i) q^{92} +(5.31112 - 9.19912i) q^{93} +(1.70501 - 0.984386i) q^{94} +(-0.139632 - 0.241849i) q^{95} +(1.86037 + 1.07408i) q^{96} -11.1402 q^{97} +(6.99073 - 0.360210i) q^{98} -3.31082i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} + 6 q^{3} - 8 q^{4} + 16 q^{8} + 10 q^{9}+O(q^{10}) \) 16 * q - 8 * q^2 + 6 * q^3 - 8 * q^4 + 16 * q^8 + 10 * q^9	\( 16 q - 8 q^{2} + 6 q^{3} - 8 q^{4} + 16 q^{8} + 10 q^{9} - 6 q^{12} - 8 q^{16} + 10 q^{18} - 4 q^{23} + 6 q^{24} + 2 q^{25} - 6 q^{26} + 16 q^{29} - 24 q^{31} - 8 q^{32} + 4 q^{35} - 20 q^{36} + 22 q^{39} - 4 q^{46} + 30 q^{47} - 58 q^{49} - 4 q^{50} + 6 q^{52} + 54 q^{54} - 8 q^{58} + 36 q^{59} + 16 q^{64} - 32 q^{70} - 12 q^{71} + 10 q^{72} - 24 q^{73} - 96 q^{75} - 38 q^{77} - 44 q^{78} - 36 q^{81} - 6 q^{82} + 24 q^{85} + 42 q^{87} + 8 q^{92} - 38 q^{93} - 30 q^{94} - 38 q^{95} - 6 q^{96} + 56 q^{98}+O(q^{100}) \) 16 * q - 8 * q^2 + 6 * q^3 - 8 * q^4 + 16 * q^8 + 10 * q^9 - 6 * q^12 - 8 * q^16 + 10 * q^18 - 4 * q^23 + 6 * q^24 + 2 * q^25 - 6 * q^26 + 16 * q^29 - 24 * q^31 - 8 * q^32 + 4 * q^35 - 20 * q^36 + 22 * q^39 - 4 * q^46 + 30 * q^47 - 58 * q^49 - 4 * q^50 + 6 * q^52 + 54 * q^54 - 8 * q^58 + 36 * q^59 + 16 * q^64 - 32 * q^70 - 12 * q^71 + 10 * q^72 - 24 * q^73 - 96 * q^75 - 38 * q^77 - 44 * q^78 - 36 * q^81 - 6 * q^82 + 24 * q^85 + 42 * q^87 + 8 * q^92 - 38 * q^93 - 30 * q^94 - 38 * q^95 - 6 * q^96 + 56 * q^98

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