LMFDB - Embedded newform 546.2.z.a.131.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(131,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("546.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.z (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.16
Character	$\chi$	$=$	546.131
Dual form			546.2.z.a.521.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{2} +(1.67937 - 0.423929i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.33293 - 2.30870i) q^{5} +(1.66634 + 0.472552i) q^{6} +(-2.41436 - 1.08207i) q^{7} +1.00000i q^{8} +(2.64057 - 1.42387i) q^{9} +(2.30870 - 1.33293i) q^{10} +(0.470358 - 0.271562i) q^{11} +(1.20682 + 1.24241i) q^{12} -1.00000i q^{13} +(-1.54986 - 2.14428i) q^{14} +(1.25975 - 4.44223i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.17473 + 5.49879i) q^{17} +(2.99873 + 0.0871789i) q^{18} +(-5.41050 - 3.12375i) q^{19} +2.66585 q^{20} +(-4.51332 - 0.793672i) q^{21} +0.543123 q^{22} +(2.03823 + 1.17677i) q^{23} +(0.423929 + 1.67937i) q^{24} +(-1.05339 - 1.82453i) q^{25} +(0.500000 - 0.866025i) q^{26} +(3.83087 - 3.51061i) q^{27} +(-0.270084 - 2.63193i) q^{28} +5.75382i q^{29} +(3.31209 - 3.21720i) q^{30} +(5.60990 - 3.23888i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.674783 - 0.655451i) q^{33} +6.34946i q^{34} +(-5.71633 + 4.13171i) q^{35} +(2.55339 + 1.57487i) q^{36} +(-4.73565 + 8.20238i) q^{37} +(-3.12375 - 5.41050i) q^{38} +(-0.423929 - 1.67937i) q^{39} +(2.30870 + 1.33293i) q^{40} -6.50568 q^{41} +(-3.51182 - 2.94400i) q^{42} -9.79478 q^{43} +(0.470358 + 0.271562i) q^{44} +(0.232406 - 7.99419i) q^{45} +(1.17677 + 2.03823i) q^{46} +(3.16636 - 5.48430i) q^{47} +(-0.472552 + 1.66634i) q^{48} +(4.65827 + 5.22499i) q^{49} -2.10678i q^{50} +(7.66264 + 7.88865i) q^{51} +(0.866025 - 0.500000i) q^{52} +(-6.39787 + 3.69381i) q^{53} +(5.07294 - 1.12484i) q^{54} -1.44789i q^{55} +(1.08207 - 2.41436i) q^{56} +(-10.4105 - 2.95227i) q^{57} +(-2.87691 + 4.98295i) q^{58} +(5.14321 + 8.90831i) q^{59} +(4.47696 - 1.13013i) q^{60} +(5.27061 + 3.04299i) q^{61} +6.47776 q^{62} +(-7.91600 + 0.580460i) q^{63} -1.00000 q^{64} +(-2.30870 - 1.33293i) q^{65} +(0.912105 - 0.230246i) q^{66} +(2.29391 + 3.97316i) q^{67} +(-3.17473 + 5.49879i) q^{68} +(3.92182 + 1.11217i) q^{69} +(-7.01634 + 0.720004i) q^{70} -10.3944i q^{71} +(1.42387 + 2.64057i) q^{72} +(-1.57792 + 0.911014i) q^{73} +(-8.20238 + 4.73565i) q^{74} +(-2.54250 - 2.61749i) q^{75} -6.24751i q^{76} +(-1.42946 + 0.146689i) q^{77} +(0.472552 - 1.66634i) q^{78} +(3.20588 - 5.55275i) q^{79} +(1.33293 + 2.30870i) q^{80} +(4.94520 - 7.51964i) q^{81} +(-5.63408 - 3.25284i) q^{82} +6.54629 q^{83} +(-1.56932 - 4.30549i) q^{84} +16.9267 q^{85} +(-8.48253 - 4.89739i) q^{86} +(2.43921 + 9.66279i) q^{87} +(0.271562 + 0.470358i) q^{88} +(-6.59265 + 11.4188i) q^{89} +(4.19836 - 6.80697i) q^{90} +(-1.08207 + 2.41436i) q^{91} +2.35355i q^{92} +(8.04805 - 7.81748i) q^{93} +(5.48430 - 3.16636i) q^{94} +(-14.4236 + 8.32748i) q^{95} +(-1.24241 + 1.20682i) q^{96} +3.22151i q^{97} +(1.42168 + 6.85411i) q^{98} +(0.855346 - 1.38680i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9} + 6 q^{10} - 24 q^{11} + 4 q^{14} - 12 q^{15} - 16 q^{16} + 4 q^{17} + 24 q^{18} - 12 q^{21} - 12 q^{22} - 6 q^{24} - 18 q^{25} + 16 q^{26} - 6 q^{27} - 2 q^{28} + 10 q^{30}+ \cdots + 32 q^{98}+O(q^{100}) $ 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9 + 6 * q^10 - 24 * q^11 + 4 * q^14 - 12 * q^15 - 16 * q^16 + 4 * q^17 + 24 * q^18 - 12 * q^21 - 12 * q^22 - 6 * q^24 - 18 * q^25 + 16 * q^26 - 6 * q^27 - 2 * q^28 + 10 * q^30 - 6 * q^31 - 14 * q^33 + 48 * q^35 + 4 * q^36 + 16 * q^38 + 6 * q^39 + 6 * q^40 + 16 * q^41 - 18 * q^42 + 32 * q^43 - 24 * q^44 - 20 * q^45 + 16 * q^46 + 20 * q^47 - 26 * q^49 + 44 * q^51 - 60 * q^53 - 6 * q^54 + 8 * q^56 - 8 * q^57 - 10 * q^58 + 8 * q^59 - 6 * q^60 + 36 * q^61 + 36 * q^62 - 28 * q^63 - 32 * q^64 - 6 * q^65 + 12 * q^66 - 4 * q^68 - 36 * q^69 - 18 * q^70 + 24 * q^72 - 48 * q^73 - 84 * q^74 + 14 * q^75 + 52 * q^77 + 18 * q^79 + 70 * q^81 + 24 * q^83 - 24 * q^84 - 32 * q^85 - 24 * q^86 - 26 * q^87 - 6 * q^88 - 20 * q^89 - 6 * q^90 - 8 * q^91 + 92 * q^93 - 72 * q^95 - 6 * q^96 + 32 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	1.67937	−	0.423929i	0.969585	−	0.244756i
$3$	1.67937	−	0.423929i	0.969585	−	0.244756i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.33293	−	2.30870i	0.596103	−	1.03248i	−0.397287	−	0.917694i	$-0.630048\pi$
$5$	1.33293	−	2.30870i	0.596103	−	1.03248i	0.993390	−	0.114787i	$-0.0366185\pi$
$6$	1.66634	+	0.472552i	0.680281	+	0.192918i
$7$	−2.41436	−	1.08207i	−0.912542	−	0.408982i
$7$	−2.41436	−	1.08207i	−0.912542	−	0.408982i
$8$			1.00000i			0.353553i
$9$	2.64057	−	1.42387i	0.880189	−	0.474622i
$10$	2.30870	−	1.33293i	0.730074	−	0.421509i
$11$	0.470358	−	0.271562i	0.141818	−	0.0818789i	−0.427412	−	0.904057i	$-0.640575\pi$
$11$	0.470358	−	0.271562i	0.141818	−	0.0818789i	0.569230	+	0.822178i	$0.307241\pi$
$12$	1.20682	+	1.24241i	0.348378	+	0.358654i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	−1.54986	−	2.14428i	−0.414219	−	0.573082i
$15$	1.25975	−	4.44223i	0.325267	−	1.14698i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.17473	+	5.49879i	0.769985	+	1.33365i	0.937571	+	0.347795i	$0.113070\pi$
$17$	3.17473	+	5.49879i	0.769985	+	1.33365i	−0.167586	+	0.985857i	$0.553597\pi$
$18$	2.99873	+	0.0871789i	0.706808	+	0.0205483i
$19$	−5.41050	−	3.12375i	−1.24125	−	0.716638i	−0.271905	−	0.962324i	$-0.587654\pi$
$19$	−5.41050	−	3.12375i	−1.24125	−	0.716638i	−0.969350	+	0.245686i	$0.920987\pi$
$20$	2.66585			0.596103
$21$	−4.51332	−	0.793672i	−0.984888	−	0.173193i
$22$	0.543123			0.115794
$23$	2.03823	+	1.17677i	0.425001	+	0.245375i	0.697215	−	0.716862i	$-0.254422\pi$
$23$	2.03823	+	1.17677i	0.425001	+	0.245375i	−0.272214	+	0.962237i	$0.587756\pi$
$24$	0.423929	+	1.67937i	0.0865341	+	0.342800i
$25$	−1.05339	−	1.82453i	−0.210678	−	0.364905i
$26$	0.500000	−	0.866025i	0.0980581	−	0.169842i
$27$	3.83087	−	3.51061i	0.737252	−	0.675618i
$28$	−0.270084	−	2.63193i	−0.0510410	−	0.497388i
$29$			5.75382i			1.06846i	0.845340	+	0.534228i	$0.179398\pi$
$29$			5.75382i			1.06846i	−0.845340	+	0.534228i	$0.820602\pi$
$30$	3.31209	−	3.21720i	0.604703	−	0.587378i
$31$	5.60990	−	3.23888i	1.00757	−	0.581720i	0.0970894	−	0.995276i	$-0.469047\pi$
$31$	5.60990	−	3.23888i	1.00757	−	0.581720i	0.910479	+	0.413556i	$0.135713\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	0.674783	−	0.655451i	0.117465	−	0.114099i
$34$			6.34946i			1.08892i
$35$	−5.71633	+	4.13171i	−0.966236	+	0.698387i
$36$	2.55339	+	1.57487i	0.425565	+	0.262478i
$37$	−4.73565	+	8.20238i	−0.778536	+	1.34846i	0.154250	+	0.988032i	$0.450704\pi$
$37$	−4.73565	+	8.20238i	−0.778536	+	1.34846i	−0.932786	+	0.360432i	$0.882629\pi$
$38$	−3.12375	−	5.41050i	−0.506740	−	0.877699i
$39$	−0.423929	−	1.67937i	−0.0678830	−	0.268914i
$40$	2.30870	+	1.33293i	0.365037	+	0.210754i
$41$	−6.50568			−1.01602			−0.508008	−	0.861352i	$-0.669618\pi$
$41$	−6.50568			−1.01602			−0.508008	+	0.861352i	$0.669618\pi$
$42$	−3.51182	−	2.94400i	−0.541885	−	0.454269i
$43$	−9.79478			−1.49369			−0.746845	−	0.664998i	$-0.768432\pi$
$43$	−9.79478			−1.49369			−0.746845	+	0.664998i	$0.768432\pi$
$44$	0.470358	+	0.271562i	0.0709092	+	0.0409394i
$45$	0.232406	−	7.99419i	0.0346451	−	1.19170i
$46$	1.17677	+	2.03823i	0.173506	+	0.300521i
$47$	3.16636	−	5.48430i	0.461861	−	0.799968i	−0.537192	−	0.843460i	$-0.680515\pi$
$47$	3.16636	−	5.48430i	0.461861	−	0.799968i	0.999054	+	0.0434923i	$0.0138484\pi$
$48$	−0.472552	+	1.66634i	−0.0682070	+	0.240516i
$49$	4.65827	+	5.22499i	0.665467	+	0.746427i
$50$		−	2.10678i		−	0.297944i
$51$	7.66264	+	7.88865i	1.07298	+	1.10463i
$52$	0.866025	−	0.500000i	0.120096	−	0.0693375i
$53$	−6.39787	+	3.69381i	−0.878815	+	0.507384i	−0.870267	−	0.492579i	$-0.836054\pi$
$53$	−6.39787	+	3.69381i	−0.878815	+	0.507384i	−0.00854737	+	0.999963i	$0.502721\pi$
$54$	5.07294	−	1.12484i	0.690340	−	0.153072i
$55$		−	1.44789i		−	0.195233i
$56$	1.08207	−	2.41436i	0.144597	−	0.322632i
$57$	−10.4105	−	2.95227i	−1.37890	−	0.391038i
$58$	−2.87691	+	4.98295i	−0.377757	+	0.654294i
$59$	5.14321	+	8.90831i	0.669589	+	1.15976i	0.978019	+	0.208515i	$0.0668632\pi$
$59$	5.14321	+	8.90831i	0.669589	+	1.15976i	−0.308430	+	0.951247i	$0.599804\pi$
$60$	4.47696	−	1.13013i	0.577973	−	0.145900i
$61$	5.27061	+	3.04299i	0.674833	+	0.389615i	0.797905	−	0.602783i	$-0.205941\pi$
$61$	5.27061	+	3.04299i	0.674833	+	0.389615i	−0.123073	+	0.992398i	$0.539275\pi$
$62$	6.47776			0.822676
$63$	−7.91600	+	0.580460i	−0.997322	+	0.0731311i
$64$	−1.00000			−0.125000
$65$	−2.30870	−	1.33293i	−0.286359	−	0.165329i
$66$	0.912105	−	0.230246i	0.112272	−	0.0283413i
$67$	2.29391	+	3.97316i	0.280245	+	0.485399i	0.971445	−	0.237265i	$-0.0762508\pi$
$67$	2.29391	+	3.97316i	0.280245	+	0.485399i	−0.691200	+	0.722664i	$0.742918\pi$
$68$	−3.17473	+	5.49879i	−0.384992	+	0.666826i
$69$	3.92182	+	1.11217i	0.472131	+	0.133890i
$70$	−7.01634	+	0.720004i	−0.838613	+	0.0860569i
$71$		−	10.3944i		−	1.23359i	−0.787125	−	0.616794i	$-0.788431\pi$
$71$		−	10.3944i		−	1.23359i	0.787125	−	0.616794i	$-0.211569\pi$
$72$	1.42387	+	2.64057i	0.167804	+	0.311194i
$73$	−1.57792	+	0.911014i	−0.184682	+	0.106626i	−0.589491	−	0.807775i	$-0.700671\pi$
$73$	−1.57792	+	0.911014i	−0.184682	+	0.106626i	0.404809	+	0.914401i	$0.367338\pi$
$74$	−8.20238	+	4.73565i	−0.953508	+	0.550508i
$75$	−2.54250	−	2.61749i	−0.293583	−	0.302242i
$76$		−	6.24751i		−	0.716638i
$77$	−1.42946	+	0.146689i	−0.162902	+	0.0167167i
$78$	0.472552	−	1.66634i	0.0535060	−	0.188676i
$79$	3.20588	−	5.55275i	0.360690	−	0.624734i	−0.627384	−	0.778710i	$-0.715875\pi$
$79$	3.20588	−	5.55275i	0.360690	−	0.624734i	0.988075	+	0.153976i	$0.0492079\pi$
$80$	1.33293	+	2.30870i	0.149026	+	0.258120i
$81$	4.94520	−	7.51964i	0.549467	−	0.835515i
$82$	−5.63408	−	3.25284i	−0.622180	−	0.359216i
$83$	6.54629			0.718549			0.359274	−	0.933232i	$-0.383024\pi$
$83$	6.54629			0.718549			0.359274	+	0.933232i	$0.383024\pi$
$84$	−1.56932	−	4.30549i	−0.171227	−	0.469767i
$85$	16.9267			1.83596
$86$	−8.48253	−	4.89739i	−0.914695	−	0.528099i
$87$	2.43921	+	9.66279i	0.261511	+	1.03596i
$88$	0.271562	+	0.470358i	0.0289486	+	0.0501404i
$89$	−6.59265	+	11.4188i	−0.698819	+	1.21039i	0.270057	+	0.962844i	$0.412958\pi$
$89$	−6.59265	+	11.4188i	−0.698819	+	1.21039i	−0.968876	+	0.247546i	$0.920376\pi$
$90$	4.19836	−	6.80697i	0.442546	−	0.717517i
$91$	−1.08207	+	2.41436i	−0.113431	+	0.253094i
$92$			2.35355i			0.245375i
$93$	8.04805	−	7.81748i	0.834544	−	0.810634i
$94$	5.48430	−	3.16636i	0.565662	−	0.326585i
$95$	−14.4236	+	8.32748i	−1.47983	+	0.854381i
$96$	−1.24241	+	1.20682i	−0.126803	+	0.123170i
$97$			3.22151i			0.327095i	0.986535	+	0.163547i	$0.0522936\pi$
$97$			3.22151i			0.327095i	−0.986535	+	0.163547i	$0.947706\pi$
$98$	1.42168	+	6.85411i	0.143612	+	0.692370i
$99$	0.855346	−	1.38680i	0.0859655	−	0.139379i
$100$	1.05339	−	1.82453i	0.105339	−	0.182453i
$101$	−7.33394	−	12.7028i	−0.729754	−	1.26397i	−0.956987	−	0.290131i	$-0.906301\pi$
$101$	−7.33394	−	12.7028i	−0.729754	−	1.26397i	0.227233	−	0.973841i	$-0.427032\pi$
$102$	2.69172	+	10.6631i	0.266520	+	1.05580i
$103$	−8.19166	−	4.72946i	−0.807148	−	0.466007i	0.0388166	−	0.999246i	$-0.487641\pi$
$103$	−8.19166	−	4.72946i	−0.807148	−	0.466007i	−0.845964	+	0.533239i	$0.820975\pi$
$104$	1.00000			0.0980581
$105$	−7.84828	+	9.36199i	−0.765914	+	0.913637i
$106$	−7.38762			−0.717549
$107$	−0.0653711	−	0.0377420i	−0.00631967	−	0.00364866i	0.496837	−	0.867844i	$-0.334495\pi$
$107$	−0.0653711	−	0.0377420i	−0.00631967	−	0.00364866i	−0.503157	+	0.864195i	$0.667828\pi$
$108$	4.95572	+	1.56233i	0.476864	+	0.150335i
$109$	−7.71263	−	13.3587i	−0.738736	−	1.27953i	−0.953065	−	0.302766i	$-0.902090\pi$
$109$	−7.71263	−	13.3587i	−0.738736	−	1.27953i	0.214329	−	0.976762i	$-0.431243\pi$
$110$	0.723944	−	1.25391i	0.0690253	−	0.119555i
$111$	−4.47568	+	15.7824i	−0.424813	+	1.49800i
$112$	2.14428	−	1.54986i	0.202615	−	0.146448i
$113$		−	12.7346i		−	1.19797i	−0.800761	−	0.598984i	$-0.795571\pi$
$113$		−	12.7346i		−	1.19797i	0.800761	−	0.598984i	$-0.204429\pi$
$114$	−7.53961	−	7.76198i	−0.706149	−	0.726976i
$115$	5.43364	−	3.13711i	0.506689	−	0.292537i
$116$	−4.98295	+	2.87691i	−0.462655	+	0.267114i
$117$	−1.42387	−	2.64057i	−0.131637	−	0.244121i
$118$			10.2864i			0.946942i
$119$	−1.71488	−	16.7113i	−0.157203	−	1.53192i
$120$	4.44223	+	1.25975i	0.405518	+	0.114999i
$121$	−5.35251	+	9.27082i	−0.486592	+	0.842802i
$122$	3.04299	+	5.27061i	0.275499	+	0.477179i
$123$	−10.9254	+	2.75794i	−0.985114	+	0.248675i
$124$	5.60990	+	3.23888i	0.503784	+	0.290860i
$125$	7.71290			0.689863
$126$	−7.14569	−	3.45531i	−0.636588	−	0.307823i
$127$	8.21499			0.728963			0.364481	−	0.931211i	$-0.381246\pi$
$127$	8.21499			0.728963			0.364481	+	0.931211i	$0.381246\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−16.4491	+	4.15229i	−1.44826	+	0.365589i
$130$	−1.33293	−	2.30870i	−0.116905	−	0.202486i
$131$	−10.3512	+	17.9289i	−0.904391	+	1.56645i	−0.0826587	+	0.996578i	$0.526341\pi$
$131$	−10.3512	+	17.9289i	−0.904391	+	1.56645i	−0.821732	+	0.569873i	$0.806992\pi$
$132$	0.905029	+	0.256654i	0.0787726	+	0.0223388i
$133$	9.68279	+	13.3964i	0.839604	+	1.16161i
$134$			4.58781i			0.396327i
$135$	−2.99867	−	13.5237i	−0.258085	−	1.16394i
$136$	−5.49879	+	3.17473i	−0.471517	+	0.272231i
$137$	−8.60998	+	4.97097i	−0.735600	+	0.424699i	−0.820467	−	0.571693i	$-0.806287\pi$
$137$	−8.60998	+	4.97097i	−0.735600	+	0.424699i	0.0848672	+	0.996392i	$0.472953\pi$
$138$	2.84031	+	2.92408i	0.241783	+	0.248914i
$139$		−	10.2922i		−	0.872973i	−0.899711	−	0.436486i	$-0.856223\pi$
$139$		−	10.2922i		−	0.872973i	0.899711	−	0.436486i	$-0.143777\pi$
$140$	−6.43633	−	2.88463i	−0.543969	−	0.243796i
$141$	2.99254	−	10.5525i	0.252017	−	0.888680i
$142$	5.19720	−	9.00181i	0.436139	−	0.755415i
$143$	−0.271562	−	0.470358i	−0.0227091	−	0.0393333i
$144$	−0.0871789	+	2.99873i	−0.00726491	+	0.249894i
$145$	13.2838	+	7.66942i	1.10316	+	0.636911i
$146$	−1.82203			−0.150792
$147$	10.0380	+	6.79992i	0.827919	+	0.560848i
$148$	−9.47130			−0.778536
$149$	−1.04576	−	0.603773i	−0.0856724	−	0.0494630i	0.456552	−	0.889697i	$-0.349084\pi$
$149$	−1.04576	−	0.603773i	−0.0856724	−	0.0494630i	−0.542224	+	0.840234i	$0.682418\pi$
$150$	−0.893126	−	3.53807i	−0.0729234	−	0.288882i
$151$	−1.52088	−	2.63424i	−0.123768	−	0.214372i	0.797483	−	0.603341i	$-0.206164\pi$
$151$	−1.52088	−	2.63424i	−0.123768	−	0.214372i	−0.921251	+	0.388970i	$0.872831\pi$
$152$	3.12375	−	5.41050i	0.253370	−	0.438850i
$153$	16.2126	+	9.99954i	1.31071	+	0.808415i
$154$	−1.31129	−	0.587695i	−0.105667	−	0.0473578i
$155$		−	17.2688i		−	1.38706i
$156$	1.24241	−	1.20682i	0.0994726	−	0.0966228i
$157$	13.6557	−	7.88410i	1.08984	−	0.629220i	0.156306	−	0.987709i	$-0.450041\pi$
$157$	13.6557	−	7.88410i	1.08984	−	0.629220i	0.933534	+	0.358489i	$0.116708\pi$
$158$	5.55275	−	3.20588i	0.441753	−	0.255046i
$159$	−9.17848	+	8.91552i	−0.727900	+	0.707047i
$160$			2.66585i			0.210754i
$161$	−3.64768	−	5.04666i	−0.287478	−	0.397733i
$162$	8.04249	−	4.03960i	0.631878	−	0.317381i
$163$	0.865470	−	1.49904i	0.0677889	−	0.117414i	−0.830139	−	0.557557i	$-0.811739\pi$
$163$	0.865470	−	1.49904i	0.0677889	−	0.117414i	0.897928	+	0.440143i	$0.145072\pi$
$164$	−3.25284	−	5.63408i	−0.254004	−	0.439948i
$165$	−0.613801	−	2.43154i	−0.0477844	−	0.189295i
$166$	5.66925	+	3.27315i	0.440019	+	0.254045i
$167$	−6.68559			−0.517346			−0.258673	−	0.965965i	$-0.583285\pi$
$167$	−6.68559			−0.517346			−0.258673	+	0.965965i	$0.583285\pi$
$168$	0.793672	−	4.51332i	0.0612331	−	0.348210i
$169$	−1.00000			−0.0769231
$170$	14.6590	+	8.46336i	1.12429	+	0.649110i
$171$	−18.7346	−	0.544651i	−1.43267	−	0.0416505i
$172$	−4.89739	−	8.48253i	−0.373423	−	0.646787i
$173$	1.14785	−	1.98813i	0.0872691	−	0.151155i	−0.819087	−	0.573670i	$-0.805519\pi$
$173$	1.14785	−	1.98813i	0.0872691	−	0.151155i	0.906356	+	0.422515i	$0.138853\pi$
$174$	−2.71898	+	9.58782i	−0.206125	+	0.726851i
$175$	0.569007	+	5.54490i	0.0430129	+	0.419155i
$176$			0.543123i			0.0409394i
$177$	12.4138	+	12.7800i	0.933082	+	0.960603i
$178$	−11.4188	+	6.59265i	−0.855876	+	0.494140i
$179$	−1.83137	+	1.05734i	−0.136883	+	0.0790295i	−0.566878	−	0.823802i	$-0.691849\pi$
$179$	−1.83137	+	1.05734i	−0.136883	+	0.0790295i	0.429995	+	0.902831i	$0.358515\pi$
$180$	7.03937	−	3.79582i	0.524684	−	0.282924i
$181$		−	12.7279i		−	0.946056i	−0.881047	−	0.473028i	$-0.843161\pi$
$181$		−	12.7279i		−	0.946056i	0.881047	−	0.473028i	$-0.156839\pi$
$182$	−2.14428	+	1.54986i	−0.158944	+	0.114884i
$183$	10.1413	+	2.87594i	0.749668	+	0.212596i
$184$	−1.17677	+	2.03823i	−0.0867530	+	0.150261i
$185$	12.6246	+	21.8664i	0.928175	+	1.60765i
$186$	10.8786	−	2.74611i	0.797654	−	0.201354i
$187$	2.98652	+	1.72427i	0.218396	+	0.126091i
$188$	6.33273			0.461861
$189$	−13.0478	+	4.33063i	−0.949089	+	0.315007i
$190$	−16.6550			−1.20828
$191$	−9.50195	−	5.48596i	−0.687537	−	0.396950i	0.115151	−	0.993348i	$-0.463265\pi$
$191$	−9.50195	−	5.48596i	−0.687537	−	0.396950i	−0.802689	+	0.596398i	$0.796598\pi$
$192$	−1.67937	+	0.423929i	−0.121198	+	0.0305944i
$193$	−6.98800	−	12.1036i	−0.503007	−	0.871234i	−0.999994	−	0.00347612i	$-0.998894\pi$
$193$	−6.98800	−	12.1036i	−0.503007	−	0.871234i	0.496987	−	0.867758i	$-0.334440\pi$
$194$	−1.61075	+	2.78991i	−0.115645	+	0.200304i
$195$	−4.44223	−	1.25975i	−0.318114	−	0.0902129i
$196$	−2.19584	+	6.64667i	−0.156846	+	0.474762i
$197$			12.0670i			0.859741i	0.902891	+	0.429871i	$0.141441\pi$
$197$			12.0670i			0.859741i	−0.902891	+	0.429871i	$0.858559\pi$
$198$	1.43415	−	0.773335i	0.101921	−	0.0549585i
$199$	10.0679	−	5.81272i	0.713697	−	0.412053i	−0.0987317	−	0.995114i	$-0.531479\pi$
$199$	10.0679	−	5.81272i	0.713697	−	0.412053i	0.812428	+	0.583061i	$0.198145\pi$
$200$	1.82453	−	1.05339i	0.129014	−	0.0744860i
$201$	5.53666	+	5.69996i	0.390526	+	0.402044i
$202$		−	14.6679i		−	1.03203i
$203$	6.22601	−	13.8918i	0.436980	−	0.975012i
$204$	−3.00045	+	10.5804i	−0.210073	+	0.740774i
$205$	−8.67159	+	15.0196i	−0.605650	+	1.04902i
$206$	−4.72946	−	8.19166i	−0.329517	−	0.570740i
$207$	7.05767	+	0.205180i	0.490542	+	0.0142610i
$208$	0.866025	+	0.500000i	0.0600481	+	0.0346688i
$209$	−3.39317			−0.234710
$210$	−11.4778	+	4.18358i	−0.792044	+	0.288695i
$211$	−0.531537			−0.0365925			−0.0182962	−	0.999833i	$-0.505824\pi$
$211$	−0.531537			−0.0365925			−0.0182962	+	0.999833i	$0.505824\pi$
$212$	−6.39787	−	3.69381i	−0.439407	−	0.253692i
$213$	−4.40648	−	17.4560i	−0.301927	−	1.19607i
$214$	−0.0377420	−	0.0653711i	−0.00257999	−	0.00446868i
$215$	−13.0557	+	22.6132i	−0.890394	+	1.54221i
$216$	3.51061	+	3.83087i	0.238867	+	0.260658i
$217$	−17.0490	+	1.74954i	−1.15736	+	0.118766i
$218$		−	15.4253i		−	1.04473i
$219$	−2.26371	+	2.19886i	−0.152967	+	0.148585i
$220$	1.25391	−	0.723944i	0.0845384	−	0.0488083i
$221$	5.49879	−	3.17473i	0.369889	−	0.213555i
$222$	−11.7673	+	11.4301i	−0.789767	+	0.767140i
$223$		−	19.6780i		−	1.31774i	−0.752258	−	0.658869i	$-0.771035\pi$
$223$		−	19.6780i		−	1.31774i	0.752258	−	0.658869i	$-0.228965\pi$
$224$	2.63193	−	0.270084i	0.175853	−	0.0180457i
$225$	−5.37944	−	3.31790i	−0.358629	−	0.221193i
$226$	6.36729	−	11.0285i	0.423546	−	0.733603i
$227$	12.2736	+	21.2585i	0.814627	+	1.41098i	0.909596	+	0.415495i	$0.136392\pi$
$227$	12.2736	+	21.2585i	0.814627	+	1.41098i	−0.0949686	+	0.995480i	$0.530275\pi$
$228$	−2.64850	−	10.4919i	−0.175401	−	0.694842i
$229$	7.32264	+	4.22773i	0.483894	+	0.279376i	0.722038	−	0.691854i	$-0.243206\pi$
$229$	7.32264	+	4.22773i	0.483894	+	0.279376i	−0.238144	+	0.971230i	$0.576539\pi$
$230$	6.27422			0.413710
$231$	−2.33841	+	0.852335i	−0.153856	+	0.0560795i
$232$	−5.75382			−0.377757
$233$	0.779673	+	0.450144i	0.0510781	+	0.0294899i	0.525322	−	0.850904i	$-0.323945\pi$
$233$	0.779673	+	0.450144i	0.0510781	+	0.0294899i	−0.474244	+	0.880394i	$0.657278\pi$
$234$	0.0871789	−	2.99873i	0.00569906	−	0.196033i
$235$	−8.44106	−	14.6204i	−0.550634	−	0.953727i
$236$	−5.14321	+	8.90831i	−0.334795	+	0.579881i
$237$	3.02989	−	10.6842i	0.196813	−	0.694013i
$238$	6.87053	−	15.3299i	0.445350	−	0.993688i
$239$		−	17.1152i		−	1.10709i	−0.832820	−	0.553544i	$-0.813275\pi$
$239$		−	17.1152i		−	1.10709i	0.832820	−	0.553544i	$-0.186725\pi$
$240$	3.21720	+	3.31209i	0.207670	+	0.213795i
$241$	−3.53532	+	2.04112i	−0.227730	+	0.131480i	−0.609524	−	0.792767i	$-0.708640\pi$
$241$	−3.53532	+	2.04112i	−0.227730	+	0.131480i	0.381794	+	0.924247i	$0.375306\pi$
$242$	−9.27082	+	5.35251i	−0.595951	+	0.344072i
$243$	5.11703	−	14.7247i	0.328258	−	0.944588i
$244$			6.08598i			0.389615i
$245$	18.2721	−	3.79000i	1.16736	−	0.242134i
$246$	−10.8407	−	3.07427i	−0.691177	−	0.196008i
$247$	−3.12375	+	5.41050i	−0.198760	+	0.344262i
$248$	3.23888	+	5.60990i	0.205669	+	0.356229i
$249$	10.9936	−	2.77516i	0.696694	−	0.175869i
$250$	6.67957	+	3.85645i	0.422453	+	0.243903i
$251$	21.0662			1.32968			0.664842	−	0.746984i	$-0.268499\pi$
$251$	21.0662			1.32968			0.664842	+	0.746984i	$0.268499\pi$
$252$	−4.46069	−	6.56523i	−0.280997	−	0.413570i
$253$	1.27827			0.0803640
$254$	7.11439	+	4.10750i	0.446397	+	0.257727i
$255$	28.4262	−	7.17573i	1.78012	−	0.449362i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	8.06193	−	13.9637i	0.502889	−	0.871030i	−0.497105	−	0.867690i	$-0.665604\pi$
$257$	8.06193	−	13.9637i	0.502889	−	0.871030i	0.999994	−	0.00333939i	$-0.00106296\pi$
$258$	−16.3215	−	4.62854i	−1.01613	−	0.288161i
$259$	20.3091	−	14.6792i	1.26194	−	0.912123i
$260$		−	2.66585i		−	0.165329i
$261$	8.19267	+	15.1933i	0.507114	+	0.940445i
$262$	−17.9289	+	10.3512i	−1.10765	+	0.639501i
$263$	1.37601	−	0.794440i	0.0848485	−	0.0489873i	−0.456975	−	0.889479i	$-0.651067\pi$
$263$	1.37601	−	0.794440i	0.0848485	−	0.0489873i	0.541824	+	0.840492i	$0.317734\pi$
$264$	0.655451	+	0.674783i	0.0403402	+	0.0415300i
$265$			19.6943i			1.20981i
$266$	1.68735	+	16.4430i	0.103458	+	1.00819i
$267$	−6.23074	+	21.9712i	−0.381315	+	1.34462i
$268$	−2.29391	+	3.97316i	−0.140123	+	0.242700i
$269$	4.86980	+	8.43474i	0.296917	+	0.514275i	0.975429	−	0.220314i	$-0.0707082\pi$
$269$	4.86980	+	8.43474i	0.296917	+	0.514275i	−0.678512	+	0.734589i	$0.737375\pi$
$270$	4.16494	−	13.2112i	0.253470	−	0.804009i
$271$	7.36747	+	4.25361i	0.447542	+	0.258389i	0.706792	−	0.707422i	$-0.250142\pi$
$271$	7.36747	+	4.25361i	0.447542	+	0.258389i	−0.259249	+	0.965810i	$0.583475\pi$
$272$	−6.34946			−0.384992
$273$	−0.793672	+	4.51332i	−0.0480352	+	0.273159i
$274$	−9.94195			−0.600615
$275$	−0.990943	−	0.572121i	−0.0597561	−	0.0345002i
$276$	0.997738	+	3.95248i	0.0600568	+	0.237911i
$277$	15.4290	+	26.7239i	0.927041	+	1.60568i	0.788245	+	0.615362i	$0.210990\pi$
$277$	15.4290	+	26.7239i	0.927041	+	1.60568i	0.138797	+	0.990321i	$0.455677\pi$
$278$	5.14610	−	8.91330i	0.308642	−	0.534584i
$279$	10.2016	−	16.5402i	0.610754	−	0.990238i
$280$	−4.13171	−	5.71633i	−0.246917	−	0.341616i
$281$		−	18.0593i		−	1.07733i	−0.842521	−	0.538663i	$-0.818930\pi$
$281$		−	18.0593i		−	1.07733i	0.842521	−	0.538663i	$-0.181070\pi$
$282$	7.86786	−	7.64245i	0.468524	−	0.455101i
$283$	−13.6603	+	7.88679i	−0.812022	+	0.468821i	−0.847658	−	0.530544i	$-0.821988\pi$
$283$	−13.6603	+	7.88679i	−0.812022	+	0.468821i	0.0356354	+	0.999365i	$0.488655\pi$
$284$	9.00181	−	5.19720i	0.534159	−	0.308397i
$285$	−20.6923	+	20.0995i	−1.22571	+	1.19059i
$286$		−	0.543123i		−	0.0321155i
$287$	15.7070	+	7.03957i	0.927158	+	0.415533i
$288$	−1.57487	+	2.55339i	−0.0927998	+	0.150460i
$289$	−11.6578	+	20.1919i	−0.685753	+	1.18776i
$290$	7.66942	+	13.2838i	0.450364	+	0.780053i
$291$	1.36569	+	5.41010i	0.0800582	+	0.317146i
$292$	−1.57792	−	0.911014i	−0.0923409	−	0.0533131i
$293$	29.8861			1.74597			0.872983	−	0.487750i	$-0.162182\pi$
$293$	29.8861			1.74597			0.872983	+	0.487750i	$0.162182\pi$
$294$	5.29319	+	10.9079i	0.308705	+	0.636161i
$295$	27.4221			1.59658
$296$	−8.20238	−	4.73565i	−0.476754	−	0.275254i
$297$	0.848536	−	2.69156i	0.0492370	−	0.156180i
$298$	−0.603773	−	1.04576i	−0.0349756	−	0.0605795i
$299$	1.17677	−	2.03823i	0.0680546	−	0.117874i
$300$	0.995564	−	3.51062i	0.0574789	−	0.202686i
$301$	23.6481	+	10.5986i	1.36306	+	0.610893i
$302$		−	3.04176i		−	0.175034i
$303$	−17.7015	−	18.2236i	−1.01692	−	1.04692i
$304$	5.41050	−	3.12375i	0.310314	−	0.179160i
$305$	14.0507	−	8.11217i	0.804540	−	0.464501i
$306$	9.04078	+	16.7662i	0.516827	+	0.958458i
$307$		−	15.7500i		−	0.898902i	−0.893305	−	0.449451i	$-0.851620\pi$
$307$		−	15.7500i		−	0.898902i	0.893305	−	0.449451i	$-0.148380\pi$
$308$	−0.841767	−	1.16461i	−0.0479641	−	0.0663596i
$309$	−15.7618	−	4.46983i	−0.896656	−	0.254279i
$310$	8.63438	−	14.9552i	0.490400	−	0.849397i
$311$	6.94368	+	12.0268i	0.393740	+	0.681977i	0.992939	−	0.118622i	$-0.0378478\pi$
$311$	6.94368	+	12.0268i	0.393740	+	0.681977i	−0.599200	+	0.800600i	$0.704514\pi$
$312$	1.67937	−	0.423929i	0.0950756	−	0.0240003i
$313$	6.92272	+	3.99684i	0.391296	+	0.225915i	0.682721	−	0.730679i	$-0.260796\pi$
$313$	6.92272	+	3.99684i	0.391296	+	0.225915i	−0.291426	+	0.956593i	$0.594130\pi$
$314$	15.7682			0.889851
$315$	−9.21135	+	19.0494i	−0.519001	+	1.07331i
$316$	6.41177			0.360690
$317$	20.3402	+	11.7434i	1.14242	+	0.659575i	0.947028	−	0.321150i	$-0.104069\pi$
$317$	20.3402	+	11.7434i	1.14242	+	0.659575i	0.195390	+	0.980726i	$0.437403\pi$
$318$	−12.4066	+	3.13183i	−0.695725	+	0.175624i
$319$	1.56252	+	2.70636i	0.0874841	+	0.151527i
$320$	−1.33293	+	2.30870i	−0.0745129	+	0.129060i
$321$	−0.125782	−	0.0356701i	−0.00702048	−	0.00199091i
$322$	−0.635655	−	6.19438i	−0.0354237	−	0.345199i
$323$		−	39.6683i		−	2.20720i
$324$	8.98480	+	0.522853i	0.499156	+	0.0290474i
$325$	−1.82453	+	1.05339i	−0.101207	+	0.0584316i
$326$	1.49904	−	0.865470i	0.0830241	−	0.0479340i
$327$	−18.6155	−	19.1645i	−1.02944	−	1.05980i
$328$		−	6.50568i		−	0.359216i
$329$	−13.5791	+	9.81486i	−0.748641	+	0.541111i
$330$	0.684202	−	2.41268i	0.0376641	−	0.132813i
$331$	6.73452	−	11.6645i	0.370163	−	0.641141i	−0.619428	−	0.785054i	$-0.712635\pi$
$331$	6.73452	−	11.6645i	0.370163	−	0.641141i	0.989590	+	0.143913i	$0.0459686\pi$
$332$	3.27315	+	5.66925i	0.179637	+	0.311141i
$333$	−0.825697	+	28.4019i	−0.0452479	+	1.55641i
$334$	−5.78989	−	3.34279i	−0.316808	−	0.182909i
$335$	12.2304			0.668221
$336$	2.94400	−	3.51182i	0.160608	−	0.191585i
$337$	−4.88966			−0.266357			−0.133178	−	0.991092i	$-0.542518\pi$
$337$	−4.88966			−0.266357			−0.133178	+	0.991092i	$0.542518\pi$
$338$	−0.866025	−	0.500000i	−0.0471056	−	0.0271964i
$339$	−5.39855	−	21.3861i	−0.293209	−	1.16153i
$340$	8.46336	+	14.6590i	0.458990	+	0.794995i
$341$	1.75911	−	3.04687i	0.0952611	−	0.164997i
$342$	−15.9523	−	9.83899i	−0.862603	−	0.532031i
$343$	−5.59295	−	17.6556i	−0.301991	−	0.953311i
$344$		−	9.79478i		−	0.528099i
$345$	7.79517	−	7.57185i	0.419678	−	0.407655i
$346$	1.98813	−	1.14785i	0.106882	−	0.0617086i
$347$	9.10626	−	5.25750i	0.488850	−	0.282237i	−0.235247	−	0.971935i	$-0.575590\pi$
$347$	9.10626	−	5.25750i	0.488850	−	0.282237i	0.724097	+	0.689698i	$0.242257\pi$
$348$	−7.14862	+	6.94381i	−0.383206	+	0.372227i
$349$		−	10.1009i		−	0.540689i	−0.962764	−	0.270345i	$-0.912862\pi$
$349$		−	10.1009i		−	0.540689i	0.962764	−	0.270345i	$-0.0871376\pi$
$350$	−2.27968	+	5.08653i	−0.121854	+	0.271887i
$351$	−3.51061	−	3.83087i	−0.187383	−	0.204477i
$352$	−0.271562	+	0.470358i	−0.0144743	+	0.0250702i
$353$	−5.66463	−	9.81143i	−0.301498	−	0.522210i	0.674977	−	0.737838i	$-0.264153\pi$
$353$	−5.66463	−	9.81143i	−0.301498	−	0.522210i	−0.976475	+	0.215628i	$0.930820\pi$
$354$	4.36071	+	17.2747i	0.231769	+	0.918141i
$355$	−23.9975	−	13.8550i	−1.27366	−	0.735346i
$356$	−13.1853			−0.698819
$357$	−9.96434	−	27.3375i	−0.527369	−	1.44685i
$358$	−2.11469			−0.111765
$359$	−23.1736	−	13.3793i	−1.22306	−	0.706132i	−0.257488	−	0.966282i	$-0.582895\pi$
$359$	−23.1736	−	13.3793i	−1.22306	−	0.706132i	−0.965568	+	0.260150i	$0.916228\pi$
$360$	7.99419	+	0.232406i	0.421331	+	0.0122489i
$361$	10.0157	+	17.3477i	0.527141	+	0.913035i
$362$	6.36394	−	11.0227i	0.334481	−	0.579338i
$363$	−5.05868	+	17.8382i	−0.265512	+	0.936264i
$364$	−2.63193	+	0.270084i	−0.137951	+	0.0141562i
$365$			4.85726i			0.254241i
$366$	7.34467	+	7.56130i	0.383912	+	0.395235i
$367$	−9.72928	+	5.61720i	−0.507864	+	0.293216i	−0.731955	−	0.681353i	$-0.761392\pi$
$367$	−9.72928	+	5.61720i	−0.507864	+	0.293216i	0.224091	+	0.974568i	$0.428059\pi$
$368$	−2.03823	+	1.17677i	−0.106250	+	0.0613436i
$369$	−17.1787	+	9.26322i	−0.894287	+	0.482224i
$370$			25.2491i			1.31264i
$371$	19.4437	−	1.99528i	1.00947	−	0.103590i
$372$	10.7942	+	3.06108i	0.559651	+	0.158709i
$373$	−17.1657	+	29.7318i	−0.888804	+	1.53945i	−0.0475138	+	0.998871i	$0.515130\pi$
$373$	−17.1657	+	29.7318i	−0.888804	+	1.53945i	−0.841290	+	0.540583i	$0.818204\pi$
$374$	1.72427	+	2.98652i	0.0891598	+	0.154429i
$375$	12.9528	−	3.26972i	0.668880	−	0.168848i
$376$	5.48430	+	3.16636i	0.282831	+	0.163293i
$377$	5.75382			0.296337
$378$	−13.4651	−	2.77348i	−0.692568	−	0.142652i
$379$	−6.38618			−0.328036			−0.164018	−	0.986457i	$-0.552446\pi$
$379$	−6.38618			−0.328036			−0.164018	+	0.986457i	$0.552446\pi$
$380$	−14.4236	−	8.32748i	−0.739916	−	0.427191i
$381$	13.7960	−	3.48257i	0.706791	−	0.178418i
$382$	−5.48596	−	9.50195i	−0.280686	−	0.486162i
$383$	−6.63103	+	11.4853i	−0.338830	+	0.586871i	−0.984213	−	0.176988i	$-0.943364\pi$
$383$	−6.63103	+	11.4853i	−0.338830	+	0.586871i	0.645383	+	0.763859i	$0.276698\pi$
$384$	−1.66634	−	0.472552i	−0.0850351	−	0.0241148i
$385$	−1.56671	+	3.49572i	−0.0798469	+	0.178158i
$386$		−	13.9760i		−	0.711360i
$387$	−25.8638	+	13.9465i	−1.31473	+	0.708939i
$388$	−2.78991	+	1.61075i	−0.141636	+	0.0817737i
$389$	4.66329	−	2.69235i	0.236438	−	0.136508i	−0.377100	−	0.926172i	$-0.623079\pi$
$389$	4.66329	−	2.69235i	0.236438	−	0.136508i	0.613539	+	0.789665i	$0.289746\pi$
$390$	−3.21720	−	3.31209i	−0.162909	−	0.167714i
$391$			14.9438i			0.755739i
$392$	−5.22499	+	4.65827i	−0.263902	+	0.235278i
$393$	−9.78299	+	34.4974i	−0.493486	+	1.74016i
$394$	−6.03352	+	10.4504i	−0.303964	+	0.526482i
$395$	−8.54642	−	14.8028i	−0.430017	−	0.744812i
$396$	1.62868	+	0.0473489i	0.0818443	+	0.00237937i
$397$	19.9098	+	11.4949i	0.999244	+	0.576914i	0.908025	−	0.418917i	$-0.137590\pi$
$397$	19.9098	+	11.4949i	0.999244	+	0.576914i	0.0912198	+	0.995831i	$0.470923\pi$
$398$	11.6254			0.582731
$399$	21.9401	+	18.3927i	1.09838	+	0.920785i
$400$	2.10678			0.105339
$401$	−2.52081	−	1.45539i	−0.125883	−	0.0726788i	0.435736	−	0.900074i	$-0.356488\pi$
$401$	−2.52081	−	1.45539i	−0.125883	−	0.0726788i	−0.561619	+	0.827396i	$0.689821\pi$
$402$	1.94491	+	7.70464i	0.0970032	+	0.384272i
$403$	−3.23888	−	5.60990i	−0.161340	−	0.279449i
$404$	7.33394	−	12.7028i	0.364877	−	0.631986i
$405$	−10.7690	−	21.4401i	−0.535115	−	1.06537i
$406$	12.3378	−	8.91763i	0.612313	−	0.442575i
$407$			5.14408i			0.254983i
$408$	−7.88865	+	7.66264i	−0.390546	+	0.379357i
$409$	12.3943	−	7.15586i	0.612859	−	0.353835i	−0.161224	−	0.986918i	$-0.551544\pi$
$409$	12.3943	−	7.15586i	0.612859	−	0.353835i	0.774084	+	0.633083i	$0.218211\pi$
$410$	−15.0196	+	8.67159i	−0.741767	+	0.428260i
$411$	−12.3520	+	11.9981i	−0.609279	+	0.591824i
$412$		−	9.45891i		−	0.466007i
$413$	−2.77819	−	27.0731i	−0.136706	−	1.33218i
$414$	6.00953	+	3.70652i	0.295352	+	0.182166i
$415$	8.72573	−	15.1134i	0.428329	−	0.741888i
$416$	0.500000	+	0.866025i	0.0245145	+	0.0424604i
$417$	−4.36316	−	17.2844i	−0.213665	−	0.846421i
$418$	−2.93857	−	1.69658i	−0.143730	−	0.0829826i
$419$	−19.1891			−0.937450			−0.468725	−	0.883344i	$-0.655286\pi$
$419$	−19.1891			−0.937450			−0.468725	+	0.883344i	$0.655286\pi$
$420$	−12.0319	−	2.11581i	−0.587095	−	0.103241i
$421$	−12.9380			−0.630558			−0.315279	−	0.948999i	$-0.602098\pi$
$421$	−12.9380			−0.630558			−0.315279	+	0.948999i	$0.602098\pi$
$422$	−0.460324	−	0.265768i	−0.0224082	−	0.0129374i
$423$	0.552080	−	18.9902i	0.0268431	−	0.923333i
$424$	−3.69381	−	6.39787i	−0.179387	−	0.310708i
$425$	6.68846	−	11.5848i	0.324438	−	0.561943i
$426$	4.91189	−	17.3206i	0.237982	−	0.839186i
$427$	−9.43244	−	13.0500i	−0.456468	−	0.631535i
$428$		−	0.0754841i		−	0.00364866i
$429$	−0.655451	−	0.674783i	−0.0316455	−	0.0325788i
$430$	−22.6132	+	13.0557i	−1.09051	+	0.629604i
$431$	−3.56091	+	2.05589i	−0.171523	+	0.0990289i	−0.583304	−	0.812254i	$-0.698240\pi$
$431$	−3.56091	+	2.05589i	−0.171523	+	0.0990289i	0.411781	+	0.911283i	$0.364907\pi$
$432$	1.12484	+	5.07294i	0.0541191	+	0.244072i
$433$		−	38.0396i		−	1.82807i	−0.405640	−	0.914033i	$-0.632951\pi$
$433$		−	38.0396i		−	1.82807i	0.405640	−	0.914033i	$-0.367049\pi$
$434$	−15.6396	−	7.00936i	−0.750727	−	0.336460i
$435$	25.5598	+	7.24840i	1.22550	+	0.347534i
$436$	7.71263	−	13.3587i	0.369368	−	0.639764i
$437$	−7.35191	−	12.7339i	−0.351690	−	0.609144i
$438$	−3.05986	+	0.772410i	−0.146206	+	0.0369072i
$439$	−21.6324	−	12.4895i	−1.03246	−	0.596089i	−0.114769	−	0.993392i	$-0.536613\pi$
$439$	−21.6324	−	12.4895i	−1.03246	−	0.596089i	−0.917687	+	0.397303i	$0.869946\pi$
$440$	1.44789			0.0690253
$441$	19.7402	+	7.16419i	0.940008	+	0.341152i
$442$	6.34946			0.302013
$443$	−0.136784	−	0.0789726i	−0.00649883	−	0.00375210i	0.496747	−	0.867895i	$-0.334528\pi$
$443$	−0.136784	−	0.0789726i	−0.00649883	−	0.00375210i	−0.503246	+	0.864143i	$0.667861\pi$
$444$	−15.9058	+	4.01516i	−0.754856	+	0.190551i
$445$	17.5750	+	30.4409i	0.833137	+	1.44304i
$446$	9.83901	−	17.0417i	0.465891	−	0.806946i
$447$	−2.01218	−	0.570628i	−0.0951730	−	0.0269898i
$448$	2.41436	+	1.08207i	0.114068	+	0.0511228i
$449$			33.2051i			1.56705i	0.621363	+	0.783523i	$0.286579\pi$
$449$			33.2051i			1.56705i	−0.621363	+	0.783523i	$0.713421\pi$
$450$	−2.99978	−	5.56310i	−0.141411	−	0.262247i
$451$	−3.06000	+	1.76669i	−0.144090	+	0.0831902i
$452$	11.0285	−	6.36729i	0.518735	−	0.299492i
$453$	−3.67086	−	3.77913i	−0.172472	−	0.177559i
$454$			24.5472i			1.15206i
$455$	4.13171	+	5.71633i	0.193698	+	0.267986i
$456$	2.95227	−	10.4105i	0.138253	−	0.487516i
$457$	7.61724	−	13.1934i	0.356319	−	0.617163i	−0.631024	−	0.775764i	$-0.717365\pi$
$457$	7.61724	−	13.1934i	0.356319	−	0.617163i	0.987343	+	0.158601i	$0.0506982\pi$
$458$	4.22773	+	7.32264i	0.197549	+	0.342164i
$459$	31.4661	+	9.91993i	1.46871	+	0.463022i
$460$	5.43364	+	3.13711i	0.253345	+	0.146269i
$461$	−5.44421			−0.253562			−0.126781	−	0.991931i	$-0.540465\pi$
$461$	−5.44421			−0.253562			−0.126781	+	0.991931i	$0.540465\pi$
$462$	−2.45129	−	0.431061i	−0.114044	−	0.0200548i
$463$	6.10504			0.283725			0.141863	−	0.989886i	$-0.454691\pi$
$463$	6.10504			0.283725			0.141863	+	0.989886i	$0.454691\pi$
$464$	−4.98295	−	2.87691i	−0.231328	−	0.133557i
$465$	−7.32073	−	29.0006i	−0.339491	−	1.34487i
$466$	0.450144	+	0.779673i	0.0208525	+	0.0361176i
$467$	−14.8469	+	25.7156i	−0.687034	+	1.18998i	0.285759	+	0.958302i	$0.407754\pi$
$467$	−14.8469	+	25.7156i	−0.687034	+	1.18998i	−0.972793	+	0.231676i	$0.925579\pi$
$468$	1.57487	−	2.55339i	0.0727982	−	0.118030i
$469$	−1.23909	−	12.0748i	−0.0572160	−	0.557563i
$470$		−	16.8821i		−	0.778714i
$471$	19.5906	−	19.0294i	0.902688	−	0.876826i
$472$	−8.90831	+	5.14321i	−0.410038	+	0.236736i
$473$	−4.60706	+	2.65989i	−0.211833	+	0.122302i
$474$	7.96606	−	7.73784i	0.365893	−	0.355411i
$475$			13.1621i			0.603921i
$476$	13.6150	−	9.84080i	0.624042	−	0.451052i
$477$	−11.6345	+	18.8635i	−0.532708	+	0.863699i
$478$	8.55758	−	14.8222i	0.391414	−	0.677950i
$479$	−11.0429	−	19.1269i	−0.504563	−	0.873930i	−0.999986	−	0.00527748i	$-0.998320\pi$
$479$	−11.0429	−	19.1269i	−0.504563	−	0.873930i	0.495423	−	0.868652i	$-0.335013\pi$
$480$	1.13013	+	4.47696i	0.0515833	+	0.204344i
$481$	8.20238	+	4.73565i	0.373996	+	0.215927i
$482$	−4.08224			−0.185941
$483$	−8.26524	−	6.92885i	−0.376081	−	0.315274i
$484$	−10.7050			−0.486592
$485$	7.43749	+	4.29404i	0.337719	+	0.194982i
$486$	11.7938	−	10.1934i	0.534978	−	0.462383i
$487$	−10.9307	−	18.9325i	−0.495317	−	0.857914i	0.504669	−	0.863313i	$-0.331615\pi$
$487$	−10.9307	−	18.9325i	−0.495317	−	0.857914i	−0.999985	+	0.00539928i	$0.998281\pi$
$488$	−3.04299	+	5.27061i	−0.137750	+	0.238589i
$489$	0.817959	−	2.88434i	0.0369894	−	0.130434i
$490$	17.7191	+	5.85380i	0.800466	+	0.264448i
$491$			25.6590i			1.15797i	0.815336	+	0.578987i	$0.196552\pi$
$491$			25.6590i			1.15797i	−0.815336	+	0.578987i	$0.803448\pi$
$492$	−7.85117	−	8.08274i	−0.353958	−	0.364398i
$493$	−31.6390	+	18.2668i	−1.42495	+	0.822695i
$494$	−5.41050	+	3.12375i	−0.243430	+	0.140544i
$495$	−2.06160	−	3.82325i	−0.0926620	−	0.171842i
$496$			6.47776i			0.290860i
$497$	−11.2474	+	25.0958i	−0.504516	+	1.12570i
$498$	10.9084	+	3.09346i	0.488815	+	0.138621i
$499$	−20.9643	+	36.3113i	−0.938492	+	1.62552i	−0.170206	+	0.985409i	$0.554443\pi$
$499$	−20.9643	+	36.3113i	−0.938492	+	1.62552i	−0.768286	+	0.640107i	$0.778890\pi$
$500$	3.85645	+	6.67957i	0.172466	+	0.298719i
$501$	−11.2276	+	2.83421i	−0.501611	+	0.126623i
$502$	18.2438	+	10.5331i	0.814262	+	0.470114i
$503$	−26.6243			−1.18712			−0.593559	−	0.804790i	$-0.702278\pi$
$503$	−26.6243			−1.18712			−0.593559	+	0.804790i	$0.702278\pi$
$504$	−0.580460	−	7.91600i	−0.0258557	−	0.352607i
$505$	−39.1024			−1.74004
$506$	1.10701	+	0.639134i	0.0492127	+	0.0284130i
$507$	−1.67937	+	0.423929i	−0.0745834	+	0.0188273i
$508$	4.10750	+	7.11439i	0.182241	+	0.315650i
$509$	15.1428	−	26.2281i	0.671192	−	1.16254i	−0.306375	−	0.951911i	$-0.599116\pi$
$509$	15.1428	−	26.2281i	0.671192	−	1.16254i	0.977566	−	0.210627i	$-0.0675506\pi$
$510$	28.2057	+	7.99876i	1.24897	+	0.354191i
$511$	4.79545	−	0.492100i	0.212138	−	0.0217692i
$512$		−	1.00000i		−	0.0441942i
$513$	−31.6932	+	7.02747i	−1.39929	+	0.310271i
$514$	13.9637	−	8.06193i	0.615911	−	0.355596i
$515$	−21.8378	+	12.6080i	−0.962287	+	0.555577i
$516$	−11.8205	−	12.1692i	−0.520370	−	0.535718i
$517$		−	3.43945i		−	0.151267i
$518$	24.9278	−	2.55804i	1.09526	−	0.112394i
$519$	1.08483	−	3.82541i	0.0476189	−	0.167917i
$520$	1.33293	−	2.30870i	0.0584527	−	0.101243i
$521$	−0.158831	−	0.275103i	−0.00695850	−	0.0120525i	0.862525	−	0.506014i	$-0.168882\pi$
$521$	−0.158831	−	0.275103i	−0.00695850	−	0.0120525i	−0.869484	+	0.493962i	$0.835548\pi$
$522$	−0.501612	+	17.2542i	−0.0219549	+	0.755194i
$523$	9.84436	+	5.68364i	0.430464	+	0.248528i	0.699544	−	0.714589i	$-0.253386\pi$
$523$	9.84436	+	5.68364i	0.430464	+	0.248528i	−0.269080	+	0.963118i	$0.586720\pi$
$524$	−20.7025			−0.904391
$525$	3.30622	+	9.07073i	0.144295	+	0.395879i
$526$	1.58888			0.0692785
$527$	35.6198	+	20.5651i	1.55162	+	0.895831i
$528$	0.230246	+	0.912105i	0.0100202	+	0.0396943i
$529$	−8.73040	−	15.1215i	−0.379583	−	0.657456i
$530$	−9.84716	+	17.0558i	−0.427733	+	0.740856i
$531$	26.2652	+	16.1997i	1.13981	+	0.703009i
$532$	−6.76021	+	15.0837i	−0.293092	+	0.653963i
$533$			6.50568i			0.281792i
$534$	−16.3816	+	15.9123i	−0.708900	+	0.688591i
$535$	−0.174270	+	0.100615i	−0.00753435	+	0.00434996i
$536$	−3.97316	+	2.29391i	−0.171615	+	0.0990817i
$537$	−2.62731	+	2.55204i	−0.113377	+	0.110129i
$538$			9.73960i			0.419904i
$539$	3.60996	+	1.19261i	0.155492	+	0.0513695i
$540$	10.2126	−	9.35879i	0.439478	−	0.402738i
$541$	1.84998	−	3.20426i	0.0795370	−	0.137762i	−0.823513	−	0.567297i	$-0.807989\pi$
$541$	1.84998	−	3.20426i	0.0795370	−	0.137762i	0.903050	+	0.429535i	$0.141322\pi$
$542$	4.25361	+	7.36747i	0.182708	+	0.316460i
$543$	−5.39572	−	21.3748i	−0.231552	−	0.917281i
$544$	−5.49879	−	3.17473i	−0.235759	−	0.136115i
$545$	−41.1215			−1.76145
$546$	−2.94400	+	3.51182i	−0.125992	+	0.150292i
$547$	8.88169			0.379754			0.189877	−	0.981808i	$-0.439191\pi$
$547$	8.88169			0.379754			0.189877	+	0.981808i	$0.439191\pi$
$548$	−8.60998	−	4.97097i	−0.367800	−	0.212350i
$549$	18.2502	+	0.530569i	0.778900	+	0.0226441i
$550$	−0.572121	−	0.990943i	−0.0243953	−	0.0422539i
$551$	17.9735	−	31.1310i	0.765697	−	1.32623i
$552$	−1.11217	+	3.92182i	−0.0473373	+	0.166924i
$553$	−13.7486	+	9.93737i	−0.584650	+	0.422580i
$554$			30.8581i			1.31103i
$555$	30.4711	+	31.3698i	1.29343	+	1.33157i
$556$	8.91330	−	5.14610i	0.378008	−	0.218243i
$557$	−21.3372	+	12.3191i	−0.904088	+	0.521975i	−0.878524	−	0.477698i	$-0.841471\pi$
$557$	−21.3372	+	12.3191i	−0.904088	+	0.521975i	−0.0255637	+	0.999673i	$0.508138\pi$
$558$	17.1050	−	9.22347i	0.724111	−	0.390460i
$559$			9.79478i			0.414275i
$560$	−0.720004	−	7.01634i	−0.0304257	−	0.296495i
$561$	5.74644	+	1.62961i	0.242615	+	0.0688023i
$562$	9.02964	−	15.6398i	0.380892	−	0.659725i
$563$	20.8839	+	36.1720i	0.880153	+	1.52447i	0.851170	+	0.524890i	$0.175894\pi$
$563$	20.8839	+	36.1720i	0.880153	+	1.52447i	0.0289833	+	0.999580i	$0.490773\pi$
$564$	10.6350	−	2.68463i	0.447814	−	0.113043i
$565$	−29.4003	−	16.9743i	−1.23688	−	0.714113i
$566$	−15.7736			−0.663013
$567$	−20.0762	+	12.8041i	−0.843123	+	0.537721i
$568$	10.3944			0.436139
$569$	−26.4189	−	15.2530i	−1.10754	−	0.639438i	−0.169348	−	0.985556i	$-0.554166\pi$
$569$	−26.4189	−	15.2530i	−1.10754	−	0.639438i	−0.938191	+	0.346118i	$0.887500\pi$
$570$	−27.9698	+	7.06052i	−1.17153	+	0.295733i
$571$	18.7148	+	32.4149i	0.783189	+	1.35652i	0.930075	+	0.367370i	$0.119742\pi$
$571$	18.7148	+	32.4149i	0.783189	+	1.35652i	−0.146886	+	0.989153i	$0.546925\pi$
$572$	0.271562	−	0.470358i	0.0113546	−	0.0196667i
$573$	−18.2830	−	5.18480i	−0.763781	−	0.216598i
$574$	10.0829	+	13.9500i	0.420853	+	0.582260i
$575$		−	4.95842i		−	0.206780i
$576$	−2.64057	+	1.42387i	−0.110024	+	0.0593278i
$577$	31.5630	−	18.2229i	1.31399	−	0.758630i	0.331232	−	0.943549i	$-0.392536\pi$
$577$	31.5630	−	18.2229i	1.31399	−	0.758630i	0.982754	+	0.184919i	$0.0592024\pi$
$578$	−20.1919	+	11.6578i	−0.839872	+	0.484900i
$579$	−16.8665	−	17.3640i	−0.700948	−	0.721622i
$580$			15.3388i			0.636911i
$581$	−15.8051	−	7.08352i	−0.655706	−	0.293874i
$582$	−1.52233	+	5.36813i	−0.0631026	+	0.222516i
$583$	−2.00619	+	3.47483i	−0.0830881	+	0.143913i
$584$	−0.911014	−	1.57792i	−0.0376980	−	0.0652949i
$585$	−7.99419	−	0.232406i	−0.330519	−	0.00960882i
$586$	25.8822	+	14.9431i	1.06918	+	0.617292i
$587$	−13.3923			−0.552759			−0.276379	−	0.961049i	$-0.589135\pi$
$587$	−13.3923			−0.552759			−0.276379	+	0.961049i	$0.589135\pi$
$588$	−0.869914	+	12.0931i	−0.0358746	+	0.498711i
$589$	−40.4698			−1.66753
$590$	23.7482	+	13.7111i	0.977700	+	0.564475i
$591$	5.11557	+	20.2650i	0.210426	+	0.833592i
$592$	−4.73565	−	8.20238i	−0.194634	−	0.337116i
$593$	4.29637	−	7.44153i	0.176431	−	0.305587i	−0.764225	−	0.644950i	$-0.776878\pi$
$593$	4.29637	−	7.44153i	0.176431	−	0.305587i	0.940655	+	0.339363i	$0.110212\pi$
$594$	2.08064	−	1.90670i	0.0853695	−	0.0782327i
$595$	−40.8672	−	18.3158i	−1.67539	−	0.750876i
$596$		−	1.20755i		−	0.0494630i
$597$	14.4436	−	14.0298i	0.591137	−	0.574201i
$598$	2.03823	−	1.17677i	0.0833496	−	0.0481219i
$599$	−1.98864	+	1.14814i	−0.0812535	+	0.0469117i	−0.540076	−	0.841616i	$-0.681605\pi$
$599$	−1.98864	+	1.14814i	−0.0812535	+	0.0469117i	0.458823	+	0.888528i	$0.348271\pi$
$600$	2.61749	−	2.54250i	0.106859	−	0.103797i
$601$		−	39.8966i		−	1.62741i	−0.581275	−	0.813707i	$-0.697446\pi$
$601$		−	39.8966i		−	1.62741i	0.581275	−	0.813707i	$-0.302554\pi$
$602$	15.1806	+	21.0027i	0.618714	+	0.856007i
$603$	11.7145	+	7.22519i	0.477050	+	0.294233i
$604$	1.52088	−	2.63424i	0.0618838	−	0.107186i
$605$	14.2690	+	24.7147i	0.580118	+	1.00479i
$606$	−6.21814	−	24.6328i	−0.252595	−	1.00064i
$607$	−29.5830	−	17.0798i	−1.20074	−	0.693246i	−0.240018	−	0.970768i	$-0.577153\pi$
$607$	−29.5830	−	17.0798i	−1.20074	−	0.693246i	−0.960719	+	0.277522i	$0.910487\pi$
$608$	6.24751			0.253370
$609$	4.56664	−	25.9688i	0.185050	−	1.05231i
$610$	16.2243			0.656904
$611$	−5.48430	−	3.16636i	−0.221871	−	0.128097i
$612$	−0.553539	+	19.0403i	−0.0223755	+	0.769660i
$613$	−5.94566	−	10.2982i	−0.240143	−	0.415940i	0.720612	−	0.693339i	$-0.243861\pi$
$613$	−5.94566	−	10.2982i	−0.240143	−	0.415940i	−0.960755	+	0.277399i	$0.910528\pi$
$614$	7.87501	−	13.6399i	0.317810	−	0.550463i
$615$	−8.19556	+	28.8997i	−0.330477	+	1.16535i
$616$	−0.146689	−	1.42946i	−0.00591025	−	0.0575947i
$617$			17.2228i			0.693364i	0.937983	+	0.346682i	$0.112692\pi$
$617$			17.2228i			0.693364i	−0.937983	+	0.346682i	$0.887308\pi$
$618$	−11.4152	−	11.7519i	−0.459186	−	0.472730i
$619$	−10.6860	+	6.16958i	−0.429508	+	0.247976i	−0.699137	−	0.714988i	$-0.746432\pi$
$619$	−10.6860	+	6.16958i	−0.429508	+	0.247976i	0.269629	+	0.962964i	$0.413099\pi$
$620$	14.9552	−	8.63438i	0.600615	−	0.346765i
$621$	11.9394	−	2.64738i	0.479112	−	0.106236i
$622$			13.8874i			0.556832i
$623$	28.2729	−	20.4354i	1.13273	−	0.818728i
$624$	1.66634	+	0.472552i	0.0667071	+	0.0189172i
$625$	15.5477	−	26.9294i	0.621908	−	1.07718i
$626$	3.99684	+	6.92272i	0.159746	+	0.276688i
$627$	−5.69838	+	1.43846i	−0.227571	+	0.0574466i
$628$	13.6557	+	7.88410i	0.544920	+	0.314610i
$629$	−60.1376			−2.39784
$630$	−17.5019	+	11.8916i	−0.697294	+	0.473771i
$631$	−13.3971			−0.533328			−0.266664	−	0.963789i	$-0.585921\pi$
$631$	−13.3971			−0.533328			−0.266664	+	0.963789i	$0.585921\pi$
$632$	5.55275	+	3.20588i	0.220877	+	0.127523i
$633$	−0.892647	+	0.225334i	−0.0354795	+	0.00895621i
$634$	11.7434	+	20.3402i	0.466390	+	0.807812i
$635$	10.9500	−	18.9659i	0.434537	−	0.752640i
$636$	−12.3103	−	3.49103i	−0.488135	−	0.138429i
$637$	5.22499	−	4.65827i	0.207022	−	0.184567i
$638$			3.12503i			0.123721i
$639$	−14.8002	−	27.4471i	−0.585488	−	1.08579i
$640$	−2.30870	+	1.33293i	−0.0912593	+	0.0526886i
$641$	1.35911	−	0.784681i	0.0536815	−	0.0309930i	−0.472919	−	0.881106i	$-0.656800\pi$
$641$	1.35911	−	0.784681i	0.0536815	−	0.0309930i	0.526601	+	0.850113i	$0.323466\pi$
$642$	−0.0910956	−	0.0937824i	−0.00359526	−	0.00370130i
$643$			2.35306i			0.0927957i	0.998923	+	0.0463979i	$0.0147742\pi$
$643$			2.35306i			0.0927957i	−0.998923	+	0.0463979i	$0.985226\pi$
$644$	2.54670	−	5.68232i	0.100354	−	0.223915i
$645$	−12.3390	+	43.5106i	−0.485849	+	1.71323i
$646$	19.8341	−	34.3537i	0.780364	−	1.35163i
$647$	12.1063	+	20.9686i	0.475946	+	0.824362i	0.999620	−	0.0275561i	$-0.00877248\pi$
$647$	12.1063	+	20.9686i	0.475946	+	0.824362i	−0.523674	+	0.851919i	$0.675439\pi$
$648$	7.51964	+	4.94520i	0.295399	+	0.194266i
$649$	4.83831	+	2.79340i	0.189920	+	0.109650i
$650$	−2.10678			−0.0826348
$651$	−27.8899	+	10.1657i	−1.09309	+	0.398425i
$652$	1.73094			0.0677889
$653$	−23.4125	−	13.5172i	−0.916202	−	0.528969i	−0.0337804	−	0.999429i	$-0.510755\pi$
$653$	−23.4125	−	13.5172i	−0.916202	−	0.528969i	−0.882421	+	0.470460i	$0.844088\pi$
$654$	−6.53921	−	25.9047i	−0.255703	−	1.01295i
$655$	27.5949	+	47.7957i	1.07822	+	1.86753i
$656$	3.25284	−	5.63408i	0.127002	−	0.219974i
$657$	−2.86945	+	4.65235i	−0.111948	+	0.181505i
$658$	−16.6673	+	1.71037i	−0.649759	+	0.0666770i
$659$		−	34.8159i		−	1.35623i	−0.734954	−	0.678117i	$-0.762796\pi$
$659$		−	34.8159i		−	1.35623i	0.734954	−	0.678117i	$-0.237204\pi$
$660$	1.79887	−	1.74734i	0.0700211	−	0.0680150i
$661$	−44.3846	+	25.6254i	−1.72636	+	0.996714i	−0.822679	+	0.568506i	$0.807521\pi$
$661$	−44.3846	+	25.6254i	−1.72636	+	0.996714i	−0.903680	+	0.428208i	$0.859145\pi$
$662$	11.6645	−	6.73452i	0.453355	−	0.261745i
$663$	7.88865	−	7.66264i	0.306370	−	0.297592i
$664$			6.54629i			0.254045i
$665$	43.8347	−	4.49823i	1.69984	−	0.174434i
$666$	−14.9160	+	24.1839i	−0.577984	+	0.937107i
$667$	−6.77095	+	11.7276i	−0.262172	+	0.454095i
$668$	−3.34279	−	5.78989i	−0.129337	−	0.224017i
$669$	−8.34208	−	33.0467i	−0.322524	−	1.27766i
$670$	10.5919	+	6.11522i	0.409200	+	0.236252i
$671$	3.30543			0.127605
$672$	4.30549	−	1.56932i	0.166088	−	0.0605379i
$673$	40.4524			1.55933			0.779663	−	0.626199i	$-0.215390\pi$
$673$	40.4524			1.55933			0.779663	+	0.626199i	$0.215390\pi$
$674$	−4.23457	−	2.44483i	−0.163110	−	0.0941714i
$675$	−10.4406	−	3.29148i	−0.401860	−	0.126689i
$676$	−0.500000	−	0.866025i	−0.0192308	−	0.0333087i
$677$	19.5486	−	33.8592i	0.751315	−	1.30132i	−0.195871	−	0.980630i	$-0.562753\pi$
$677$	19.5486	−	33.8592i	0.751315	−	1.30132i	0.947186	−	0.320686i	$-0.103913\pi$
$678$	6.01775	−	21.2202i	0.231110	−	0.814955i
$679$	3.48588	−	7.77788i	0.133776	−	0.298488i
$680$			16.9267i			0.649110i
$681$	29.6240	+	30.4977i	1.13519	+	1.16868i
$682$	3.04687	−	1.75911i	0.116671	−	0.0673598i
$683$	−24.3692	+	14.0696i	−0.932462	+	0.538357i	−0.887589	−	0.460635i	$-0.847622\pi$
$683$	−24.3692	+	14.0696i	−0.932462	+	0.538357i	−0.0448727	+	0.998993i	$0.514288\pi$
$684$	−8.89562	−	16.4970i	−0.340133	−	0.630778i
$685$			26.5038i			1.01266i
$686$	3.98414	−	18.0866i	0.152115	−	0.690551i
$687$	14.0897	+	3.99564i	0.537555	+	0.152443i
$688$	4.89739	−	8.48253i	0.186711	−	0.323394i
$689$	3.69381	+	6.39787i	0.140723	+	0.243739i
$690$	10.5367	−	2.65982i	0.401127	−	0.101258i
$691$	−30.2824	−	17.4836i	−1.15200	−	0.665106i	−0.202624	−	0.979257i	$-0.564947\pi$
$691$	−30.2824	−	17.4836i	−1.15200	−	0.665106i	−0.949373	+	0.314151i	$0.898280\pi$
$692$	2.29569			0.0872691
$693$	−3.56573	+	2.42271i	−0.135451	+	0.0920310i
$694$	10.5150			0.399144
$695$	−23.7616	−	13.7188i	−0.901328	−	0.520382i
$696$	−9.66279	+	2.43921i	−0.366267	+	0.0924580i
$697$	−20.6538	−	35.7734i	−0.782317	−	1.35501i
$698$	5.05045	−	8.74764i	0.191162	−	0.331103i
$699$	1.50019	+	0.425433i	0.0567423	+	0.0160914i
$700$	−4.51752	+	3.26523i	−0.170746	+	0.123414i
$701$		−	19.3351i		−	0.730276i	−0.930953	−	0.365138i	$-0.881022\pi$
$701$		−	19.3351i		−	0.730276i	0.930953	−	0.365138i	$-0.118978\pi$
$702$	−1.12484	−	5.07294i	−0.0424545	−	0.191466i
$703$	51.2445	−	29.5860i	1.93272	−	1.11586i
$704$	−0.470358	+	0.271562i	−0.0177273	+	0.0102349i
$705$	−20.3737	−	20.9746i	−0.767316	−	0.789948i
$706$		−	11.3293i		−	0.426383i
$707$	3.96155	+	38.6048i	0.148990	+	1.45188i
$708$	−4.86087	+	17.1407i	−0.182683	+	0.644187i
$709$	−4.54865	+	7.87849i	−0.170828	+	0.295883i	−0.938710	−	0.344709i	$-0.887978\pi$
$709$	−4.54865	+	7.87849i	−0.170828	+	0.295883i	0.767882	+	0.640592i	$0.221311\pi$
$710$	−13.8550	−	23.9975i	−0.519968	−	0.900611i
$711$	0.558971	−	19.2272i	0.0209631	−	0.721076i
$712$	−11.4188	−	6.59265i	−0.427938	−	0.247070i
$713$	15.2457			0.570957
$714$	5.03938	−	28.6571i	0.188594	−	1.07247i
$715$	−1.44789			−0.0541479
$716$	−1.83137	−	1.05734i	−0.0684416	−	0.0395148i
$717$	−7.25561	−	28.7427i	−0.270966	−	1.07342i
$718$	−13.3793	−	23.1736i	−0.499311	−	0.864831i
$719$	−1.39766	+	2.42081i	−0.0521238	+	0.0902811i	−0.890910	−	0.454180i	$-0.849932\pi$
$719$	−1.39766	+	2.42081i	−0.0521238	+	0.0902811i	0.838786	+	0.544461i	$0.183266\pi$
$720$	6.80697	+	4.19836i	0.253681	+	0.156464i
$721$	14.6600	+	20.2825i	0.545968	+	0.755360i
$722$			20.0314i			0.745490i
$723$	−5.07182	+	4.92652i	−0.188623	+	0.183219i
$724$	11.0227	−	6.36394i	0.409654	−	0.236514i
$725$	10.4980	−	6.06102i	0.389886	−	0.225101i
$726$	−13.3001	+	12.9190i	−0.493611	+	0.479469i
$727$			16.6241i			0.616553i	0.951297	+	0.308277i	$0.0997523\pi$
$727$			16.6241i			0.616553i	−0.951297	+	0.308277i	$0.900248\pi$
$728$	−2.41436	−	1.08207i	−0.0894821	−	0.0401040i
$729$	2.35118	−	26.8974i	0.0870808	−	0.996201i
$730$	−2.42863	+	4.20651i	−0.0898877	+	0.155690i
$731$	−31.0958	−	53.8595i	−1.15012	−	1.99206i
$732$	2.58002	+	10.2206i	0.0953604	+	0.377765i
$733$	7.55816	+	4.36371i	0.279167	+	0.161177i	0.633046	−	0.774114i	$-0.281804\pi$
$733$	7.55816	+	4.36371i	0.279167	+	0.161177i	−0.353879	+	0.935291i	$0.615138\pi$
$734$	−11.2344			−0.414669
$735$	29.0789	−	14.1109i	1.07259	−	0.520487i
$736$	−2.35355			−0.0867530
$737$	2.15792	+	1.24587i	0.0794879	+	0.0458924i
$738$	−19.5088	−	0.567158i	−0.718128	−	0.0208774i
$739$	−14.1965	−	24.5890i	−0.522225	−	0.904521i	−0.999666	−	0.0258565i	$-0.991769\pi$
$739$	−14.1965	−	24.5890i	−0.522225	−	0.904521i	0.477440	−	0.878664i	$-0.341565\pi$
$740$	−12.6246	+	21.8664i	−0.464088	+	0.803824i
$741$	−2.95227	+	10.4105i	−0.108454	+	0.382439i
$742$	17.8364	+	7.99389i	0.654794	+	0.293465i
$743$			43.4836i			1.59526i	0.603147	+	0.797630i	$0.293913\pi$
$743$			43.4836i			1.59526i	−0.603147	+	0.797630i	$0.706087\pi$
$744$	7.81748	+	8.04805i	0.286603	+	0.295056i
$745$	−2.78786	+	1.60957i	−0.102139	+	0.0589701i
$746$	−29.7318	+	17.1657i	−1.08856	+	0.628479i
$747$	17.2859	−	9.32105i	0.632459	−	0.341039i
$748$			3.44854i			0.126091i
$749$	0.116990	+	0.161859i	0.00427472	+	0.00591419i
$750$	12.8523	+	3.64474i	0.469301	+	0.133087i
$751$	−0.0418239	+	0.0724412i	−0.00152618	+	0.00264342i	−0.866787	−	0.498678i	$-0.833819\pi$
$751$	−0.0418239	+	0.0724412i	−0.00152618	+	0.00264342i	0.865261	+	0.501321i	$0.167152\pi$
$752$	3.16636	+	5.48430i	0.115465	+	0.199992i
$753$	35.3779	−	8.93056i	1.28924	−	0.325448i
$754$	4.98295	+	2.87691i	0.181468	+	0.104771i
$755$	−8.10890			−0.295113
$756$	−10.2743	−	9.13443i	−0.373674	−	0.332216i
$757$	37.2848			1.35514			0.677569	−	0.735459i	$-0.263034\pi$
$757$	37.2848			1.35514			0.677569	+	0.735459i	$0.263034\pi$
$758$	−5.53060	−	3.19309i	−0.200880	−	0.115978i
$759$	2.14668	−	0.541894i	0.0779197	−	0.0196695i
$760$	−8.32748	−	14.4236i	−0.302069	−	0.523199i
$761$	−16.3939	+	28.3951i	−0.594280	+	1.02932i	0.399368	+	0.916791i	$0.369230\pi$
$761$	−16.3939	+	28.3951i	−0.594280	+	1.02932i	−0.993648	+	0.112533i	$0.964104\pi$
$762$	13.6890	+	3.88201i	0.495900	+	0.140630i
$763$	4.16611	+	40.5982i	0.150823	+	1.46975i
$764$		−	10.9719i		−	0.396950i
$765$	44.6962	−	24.1014i	1.61599	−	0.871389i
$766$	−11.4853	+	6.63103i	−0.414980	+	0.239589i
$767$	8.90831	−	5.14321i	0.321660	−	0.185711i
$768$	−1.20682	−	1.24241i	−0.0435473	−	0.0448317i
$769$		−	10.3239i		−	0.372290i	−0.982522	−	0.186145i	$-0.940401\pi$
$769$		−	10.3239i		−	0.372290i	0.982522	−	0.186145i	$-0.0595994\pi$
$770$	−3.10467	+	2.24403i	−0.111885	+	0.0808692i
$771$	7.61936	−	26.8679i	0.274404	−	0.967622i
$772$	6.98800	−	12.1036i	0.251504	−	0.435617i
$773$	2.64824	+	4.58689i	0.0952505	+	0.164979i	0.909713	−	0.415237i	$-0.136301\pi$
$773$	2.64824	+	4.58689i	0.0952505	+	0.164979i	−0.814463	+	0.580216i	$0.802968\pi$
$774$	−29.3719	−	0.853899i	−1.05575	−	0.0306928i
$775$	−11.8188	−	6.82361i	−0.424545	−	0.245111i
$776$	−3.22151			−0.115645
$777$	27.8835	−	33.2615i	1.00032	−	1.19325i
$778$	5.38470			0.193051
$779$	35.1990	+	20.3221i	1.26113	+	0.728116i
$780$	−1.13013	−	4.47696i	−0.0404653	−	0.160301i
$781$	−2.82272	−	4.88909i	−0.101005	−	0.174945i
$782$	−7.47188	+	12.9417i	−0.267194	+	0.462793i
$783$	20.1994	+	22.0421i	0.721869	+	0.787722i
$784$	−6.85411	+	1.42168i	−0.244790	+	0.0507744i
$785$		−	42.0357i		−	1.50032i
$786$	−25.7210	+	24.9841i	−0.917438	+	0.891154i
$787$	−35.5909	+	20.5484i	−1.26868	+	0.732472i	−0.974738	−	0.223351i	$-0.928300\pi$
$787$	−35.5909	+	20.5484i	−1.26868	+	0.732472i	−0.293941	+	0.955824i	$0.594967\pi$
$788$	−10.4504	+	6.03352i	−0.372279	+	0.214935i
$789$	1.97405	−	1.91749i	0.0702779	−	0.0682645i
$790$		−	17.0928i		−	0.608136i
$791$	−13.7796	+	30.7458i	−0.489948	+	1.09320i
$792$	1.38680	+	0.855346i	0.0492780	+	0.0303934i
$793$	3.04299	−	5.27061i	0.108060	−	0.187165i
$794$	11.4949	+	19.9098i	0.407940	+	0.706573i
$795$	8.34900	+	33.0741i	0.296108	+	1.17302i
$796$	10.0679	+	5.81272i	0.356848	+	0.206026i
$797$	33.9818			1.20370			0.601849	−	0.798610i	$-0.294431\pi$
$797$	33.9818			1.20370			0.601849	+	0.798610i	$0.294431\pi$
$798$	9.80435	+	26.8986i	0.347070	+	0.952199i
$799$	40.2094			1.42251
$800$	1.82453	+	1.05339i	0.0645068	+	0.0372430i
$801$	−1.14948	+	39.5392i	−0.0406149	+	1.39705i
$802$	−1.45539	−	2.52081i	−0.0513916	−	0.0890129i
$803$	−0.494793	+	0.857006i	−0.0174609	+	0.0302431i
$804$	−2.16798	+	7.64487i	−0.0764588	+	0.269614i
$805$	−16.5133	+	1.69456i	−0.582018	+	0.0597256i
$806$		−	6.47776i		−	0.228169i
$807$	11.7539	+	12.1006i	0.413758	+	0.425961i
$808$	12.7028	−	7.33394i	0.446881	−	0.258007i
$809$	25.4404	−	14.6880i	0.894438	−	0.516404i	0.0190467	−	0.999819i	$-0.493937\pi$
$809$	25.4404	−	14.6880i	0.894438	−	0.516404i	0.875392	+	0.483414i	$0.160604\pi$
$810$	1.39385	−	23.9522i	0.0489749	−	0.841594i
$811$			6.67053i			0.234234i	0.993118	+	0.117117i	$0.0373652\pi$
$811$			6.67053i			0.234234i	−0.993118	+	0.117117i	$0.962635\pi$
$812$	15.1436	−	1.55401i	0.531438	−	0.0545351i
$813$	14.1759	+	4.02011i	0.497172	+	0.140991i
$814$	−2.57204	+	4.45490i	−0.0901499	+	0.156144i
$815$	−2.30722	−	3.99622i	−0.0808183	−	0.139981i
$816$	−10.6631	+	2.69172i	−0.373283	+	0.0942290i
$817$	52.9947	+	30.5965i	1.85405	+	1.07044i
$818$	14.3117			0.500398
$819$	0.580460	+	7.91600i	0.0202829	+	0.276607i
$820$	−17.3432			−0.605650
$821$	21.4941	+	12.4096i	0.750148	+	0.433098i	0.825748	−	0.564040i	$-0.190754\pi$
$821$	21.4941	+	12.4096i	0.750148	+	0.433098i	−0.0755992	+	0.997138i	$0.524087\pi$
$822$	−16.6962	+	4.21468i	−0.582347	+	0.147004i
$823$	2.24676	+	3.89150i	0.0783170	+	0.135649i	0.902524	−	0.430640i	$-0.141712\pi$
$823$	2.24676	+	3.89150i	0.0783170	+	0.135649i	−0.824207	+	0.566289i	$0.808379\pi$
$824$	4.72946	−	8.19166i	0.164758	−	0.285370i
$825$	−1.90670	−	0.540714i	−0.0663827	−	0.0188252i
$826$	11.1306	−	24.8351i	0.387283	−	0.864125i
$827$			24.1857i			0.841018i	0.907288	+	0.420509i	$0.138148\pi$
$827$			24.1857i			0.841018i	−0.907288	+	0.420509i	$0.861852\pi$
$828$	3.35114	+	6.21471i	0.116460	+	0.215976i
$829$	31.0238	−	17.9116i	1.07750	−	0.622095i	0.147279	−	0.989095i	$-0.452949\pi$
$829$	31.0238	−	17.9116i	1.07750	−	0.622095i	0.930221	+	0.367000i	$0.119615\pi$
$830$	15.1134	−	8.72573i	0.524594	−	0.302875i
$831$	37.2401	+	38.3385i	1.29184	+	1.32995i
$832$			1.00000i			0.0346688i
$833$	−13.9424	+	42.2028i	−0.483076	+	1.46224i
$834$	4.86360	−	17.1503i	0.168413	−	0.593867i
$835$	−8.91140	+	15.4350i	−0.308392	+	0.534150i
$836$	−1.69658	−	2.93857i	−0.0586776	−	0.101632i
$837$	10.1204	−	32.1019i	0.349811	−	1.10961i
$838$	−16.6183	−	9.59456i	−0.574068	−	0.331439i
$839$	−16.5566			−0.571598			−0.285799	−	0.958290i	$-0.592259\pi$
$839$	−16.5566			−0.571598			−0.285799	+	0.958290i	$0.592259\pi$
$840$	−9.36199	−	7.84828i	−0.323019	−	0.270791i
$841$	−4.10641			−0.141600
$842$	−11.2046	−	6.46899i	−0.386137	−	0.222936i
$843$	−7.65585	−	30.3282i	−0.263682	−	1.04456i
$844$	−0.265768	−	0.460324i	−0.00914812	−	0.0158450i
$845$	−1.33293	+	2.30870i	−0.0458541	+	0.0794216i
$846$	9.97319	−	16.1699i	0.342885	−	0.555933i
$847$	22.9545	−	16.5913i	0.788726	−	0.570085i
$848$		−	7.38762i		−	0.253692i
$849$	−19.5973	+	19.0359i	−0.672578	+	0.653309i
$850$	11.5848	−	6.68846i	0.397354	−	0.229412i
$851$	−19.3047	+	11.1456i	−0.661757	+	0.382066i
$852$	12.9141	−	12.5441i	0.442431	−	0.429755i
$853$		−	28.7173i		−	0.983262i	−0.870804	−	0.491631i	$-0.836401\pi$
$853$		−	28.7173i		−	0.983262i	0.870804	−	0.491631i	$-0.163599\pi$
$854$	−1.64372	−	16.0179i	−0.0562470	−	0.548120i
$855$	−26.2293	+	42.5266i	−0.897024	+	1.45438i
$856$	0.0377420	−	0.0653711i	0.00129000	−	0.00223434i
$857$	−7.66767	−	13.2808i	−0.261922	−	0.453663i	0.704830	−	0.709376i	$-0.251023\pi$
$857$	−7.66767	−	13.2808i	−0.261922	−	0.453663i	−0.966753	+	0.255713i	$0.917690\pi$
$858$	−0.230246	−	0.912105i	−0.00786046	−	0.0311387i
$859$	−7.66211	−	4.42372i	−0.261428	−	0.150935i	0.363558	−	0.931572i	$-0.381562\pi$
$859$	−7.66211	−	4.42372i	−0.261428	−	0.150935i	−0.624986	+	0.780636i	$0.714895\pi$
$860$	−26.1115			−0.890394
$861$	29.3622	+	5.16337i	1.00066	+	0.175967i
$862$	−4.11179			−0.140048
$863$	26.2412	+	15.1503i	0.893260	+	0.515724i	0.875007	−	0.484110i	$-0.160856\pi$
$863$	26.2412	+	15.1503i	0.893260	+	0.515724i	0.0182525	+	0.999833i	$0.494190\pi$
$864$	−1.56233	+	4.95572i	−0.0531514	+	0.168597i
$865$	−3.05999	−	5.30006i	−0.104043	−	0.180207i
$866$	19.0198	−	32.9432i	0.646319	−	1.11946i
$867$	−11.0178	+	38.8518i	−0.374185	+	1.31947i
$868$	−10.0396	−	13.8901i	−0.340768	−	0.471461i
$869$		−	3.48238i		−	0.118132i
$870$	18.5112	+	19.0572i	0.627588	+	0.646099i
$871$	3.97316	−	2.29391i	0.134626	−	0.0777261i
$872$	13.3587	−	7.71263i	0.452381	−	0.261183i
$873$	4.58700	+	8.50661i	0.155246	+	0.287905i
$874$		−	14.7038i		−	0.497364i
$875$	−18.6217	−	8.34586i	−0.629529	−	0.282142i
$876$	−3.03612	−	0.861003i	−0.102581	−	0.0290906i
$877$	25.5869	−	44.3178i	0.864008	−	1.49651i	−0.00402120	−	0.999992i	$-0.501280\pi$
$877$	25.5869	−	44.3178i	0.864008	−	1.49651i	0.868029	−	0.496513i	$-0.165387\pi$
$878$	−12.4895	−	21.6324i	−0.421499	−	0.730057i
$879$	50.1899	−	12.6696i	1.69286	−	0.427335i
$880$	1.25391	+	0.723944i	0.0422692	+	0.0244041i
$881$	−8.62018			−0.290421			−0.145211	−	0.989401i	$-0.546386\pi$
$881$	−8.62018			−0.290421			−0.145211	+	0.989401i	$0.546386\pi$
$882$	13.5134	+	16.0745i	0.455020	+	0.541255i
$883$	17.5377			0.590189			0.295095	−	0.955468i	$-0.404649\pi$
$883$	17.5377			0.590189			0.295095	+	0.955468i	$0.404649\pi$
$884$	5.49879	+	3.17473i	0.184944	+	0.106778i
$885$	46.0519	−	11.6250i	1.54802	−	0.390771i
$886$	−0.0789726	−	0.136784i	−0.00265313	−	0.00459536i
$887$	3.86176	−	6.68876i	0.129665	−	0.224587i	−0.793882	−	0.608072i	$-0.791943\pi$
$887$	3.86176	−	6.68876i	0.129665	−	0.224587i	0.923547	+	0.383486i	$0.125276\pi$
$888$	−15.7824	−	4.47568i	−0.529623	−	0.150194i
$889$	−19.8340	−	8.88916i	−0.665209	−	0.298133i
$890$			35.1501i			1.17823i
$891$	0.283973	−	4.87985i	0.00951346	−	0.163481i
$892$	17.0417	−	9.83901i	0.570597	−	0.329434i
$893$	−34.2632	+	19.7819i	−1.14657	+	0.661975i
$894$	−1.45729	−	1.50027i	−0.0487390	−	0.0501765i
$895$			5.63745i			0.188439i
$896$	1.54986	+	2.14428i	0.0517773	+	0.0716352i
$897$	1.11217	−	3.92182i	0.0371344	−	0.130946i
$898$	−16.6025	+	28.7565i	−0.554034	+	0.959615i
$899$	18.6359	+	32.2783i	0.621542	+	1.07654i
$900$	0.183667	−	6.31768i	0.00612223	−	0.210589i
$901$	−40.6230	−	23.4537i	−1.35335	−	0.781356i
$902$	−3.53338			−0.117649
$903$	44.2070	+	7.77384i	1.47112	+	0.258697i
$904$	12.7346			0.423546
$905$	−29.3848	−	16.9653i	−0.976785	−	0.563947i
$906$	−1.28949	−	5.10825i	−0.0428405	−	0.169710i
$907$	−16.0641	−	27.8238i	−0.533399	−	0.923874i	−0.999239	−	0.0390051i	$-0.987581\pi$
$907$	−16.0641	−	27.8238i	−0.533399	−	0.923874i	0.465840	−	0.884869i	$-0.345752\pi$
$908$	−12.2736	+	21.2585i	−0.407313	+	0.705488i
$909$	−37.4528	−	23.0999i	−1.24223	−	0.766177i
$910$	0.720004	+	7.01634i	0.0238679	+	0.232590i
$911$			23.6889i			0.784847i	0.919785	+	0.392424i	$0.128363\pi$
$911$			23.6889i			0.784847i	−0.919785	+	0.392424i	$0.871637\pi$
$912$	7.76198	−	7.53961i	0.257025	−	0.249661i
$913$	3.07910	−	1.77772i	0.101903	−	0.0588340i
$914$	13.1934	−	7.61724i	0.436400	−	0.251956i
$915$	20.1573	−	19.5798i	0.666380	−	0.647289i
$916$			8.45545i			0.279376i
$917$	44.3918	−	32.0860i	1.46595	−	1.05957i
$918$	22.2905	+	24.3240i	0.735696	+	0.802810i
$919$	9.12036	−	15.7969i	0.300853	−	0.521093i	−0.675476	−	0.737382i	$-0.736062\pi$
$919$	9.12036	−	15.7969i	0.300853	−	0.521093i	0.976329	+	0.216289i	$0.0693953\pi$
$920$	3.13711	+	5.43364i	0.103427	+	0.179142i
$921$	−6.67689	−	26.4501i	−0.220011	−	0.871561i
$922$	−4.71482	−	2.72211i	−0.155274	−	0.0896478i
$923$	−10.3944			−0.342136
$924$	−1.90735	−	1.59896i	−0.0627472	−	0.0526018i
$925$	19.9540			0.656082
$926$	5.28712	+	3.05252i	0.173745	+	0.100312i
$927$	−28.3647	−	0.824618i	−0.931621	−	0.0270840i
$928$	−2.87691	−	4.98295i	−0.0944391	−	0.163573i
$929$	22.1670	−	38.3944i	0.727276	−	1.25968i	−0.230754	−	0.973012i	$-0.574119\pi$
$929$	22.1670	−	38.3944i	0.727276	−	1.25968i	0.958030	−	0.286668i	$-0.0925475\pi$
$930$	8.16038	−	28.7757i	0.267590	−	0.943591i
$931$	−8.88197	−	42.8211i	−0.291095	−	1.40341i
$932$			0.900289i			0.0294899i
$933$	16.7595	+	17.2538i	0.548682	+	0.564865i
$934$	−25.7156	+	14.8469i	−0.841442	+	0.485806i
$935$	7.96163	−	4.59665i	0.260373	−	0.150326i
$936$	2.64057	−	1.42387i	0.0863097	−	0.0465406i
$937$			14.9915i			0.489750i	0.969555	+	0.244875i	$0.0787470\pi$
$937$			14.9915i			0.489750i	−0.969555	+	0.244875i	$0.921253\pi$
$938$	4.96432	−	11.0766i	0.162091	−	0.361665i
$939$	13.3202	+	3.77743i	0.434688	+	0.123272i
$940$	8.44106	−	14.6204i	0.275317	−	0.476863i
$941$	18.9207	+	32.7717i	0.616798	+	1.06833i	0.990066	+	0.140602i	$0.0449038\pi$
$941$	18.9207	+	32.7717i	0.616798	+	1.06833i	−0.373268	+	0.927723i	$0.621763\pi$
$942$	26.4806	−	6.68460i	0.862786	−	0.217796i
$943$	−13.2601	−	7.65572i	−0.431808	−	0.249304i
$944$	−10.2864			−0.334795
$945$	−7.39369	+	35.8959i	−0.240517	+	1.16769i
$946$	−5.31977			−0.172961
$947$	10.6692	+	6.15986i	0.346702	+	0.200169i	0.663232	−	0.748414i	$-0.269184\pi$
$947$	10.6692	+	6.15986i	0.346702	+	0.200169i	−0.316530	+	0.948583i	$0.602518\pi$
$948$	10.7677	−	2.71813i	0.349720	−	0.0882809i
$949$	0.911014	+	1.57792i	0.0295728	+	0.0512215i
$950$	−6.58107	+	11.3987i	−0.213518	+	0.369824i
$951$	39.1371	+	11.0987i	1.26911	+	0.359901i
$952$	16.7113	−	1.71488i	0.541617	−	0.0555797i
$953$			39.8703i			1.29153i	0.763538	+	0.645763i	$0.223461\pi$
$953$			39.8703i			1.29153i	−0.763538	+	0.645763i	$0.776539\pi$
$954$	−19.5075	+	10.5190i	−0.631579	+	0.340565i
$955$	−25.3308	+	14.6248i	−0.819686	+	0.473246i
$956$	14.8222	−	8.55758i	0.479383	−	0.276772i
$957$	3.77134	+	3.88258i	0.121910	+	0.125506i
$958$		−	22.0858i		−	0.713561i
$959$	26.1665	−	2.68516i	0.844961	−	0.0867083i
$960$	−1.25975	+	4.44223i	−0.0406584	+	0.143372i
$961$	5.48066	−	9.49279i	0.176796	−	0.306219i
$962$	4.73565	+	8.20238i	0.152683	+	0.264455i
$963$	−0.226357	−	0.00658062i	−0.00729424	−	0.000212058i
$964$	−3.53532	−	2.04112i	−0.113865	−	0.0657400i
$965$	−37.2580			−1.19938
$966$	−3.69348	−	10.1332i	−0.118836	−	0.326030i
$967$	−32.8523			−1.05646			−0.528229	−	0.849102i	$-0.677144\pi$
$967$	−32.8523			−1.05646			−0.528229	+	0.849102i	$0.677144\pi$
$968$	−9.27082	−	5.35251i	−0.297975	−	0.172036i
$969$	−16.8165	−	66.6177i	−0.540225	−	2.14007i
$970$	4.29404	+	7.43749i	0.137873	+	0.238803i
$971$	11.6929	−	20.2526i	0.375242	−	0.649938i	−0.615122	−	0.788432i	$-0.710893\pi$
$971$	11.6929	−	20.2526i	0.375242	−	0.649938i	0.990363	+	0.138495i	$0.0442264\pi$
$972$	15.3105	−	2.93085i	0.491083	−	0.0940072i
$973$	−11.1368	+	24.8491i	−0.357030	+	0.796624i
$974$		−	21.8614i		−	0.700484i
$975$	−2.61749	+	2.54250i	−0.0838269	+	0.0814253i
$976$	−5.27061	+	3.04299i	−0.168708	+	0.0974037i
$977$	−35.8303	+	20.6866i	−1.14631	+	0.661825i	−0.947986	−	0.318311i	$-0.896884\pi$
$977$	−35.8303	+	20.6866i	−1.14631	+	0.661825i	−0.198327	+	0.980136i	$0.563551\pi$
$978$	2.15054	−	2.08893i	0.0687668	−	0.0667967i
$979$			7.16124i			0.228874i
$980$	12.4183	+	13.9291i	0.396687	+	0.444948i
$981$	−39.3867	−	24.2927i	−1.25752	−	0.775606i
$982$	−12.8295	+	22.2214i	−0.409406	+	0.709112i
$983$	−26.0249	−	45.0764i	−0.830064	−	1.43771i	−0.897986	−	0.440023i	$-0.854970\pi$
$983$	−26.0249	−	45.0764i	−0.830064	−	1.43771i	0.0679220	−	0.997691i	$-0.478363\pi$
$984$	−2.75794	−	10.9254i	−0.0879201	−	0.348290i
$985$	27.8592	+	16.0845i	0.887667	+	0.512495i
$986$	−36.5336			−1.16347
$987$	−18.6436	+	22.2394i	−0.593431	+	0.707887i
$988$	−6.24751			−0.198760
$989$	−19.9641	−	11.5263i	−0.634820	−	0.366514i
$990$	0.126225	−	4.34183i	0.00401170	−	0.137992i
$991$	1.92081	+	3.32694i	0.0610165	+	0.105684i	0.894920	−	0.446227i	$-0.147232\pi$
$991$	1.92081	+	3.32694i	0.0610165	+	0.105684i	−0.833904	+	0.551910i	$0.813899\pi$
$992$	−3.23888	+	5.60990i	−0.102834	+	0.178115i
$993$	6.36482	−	22.4440i	0.201981	−	0.712239i
$994$	−22.2884	+	16.1099i	−0.706947	+	0.510975i
$995$		−	30.9917i		−	0.982504i
$996$	7.90018	+	8.13319i	0.250327	+	0.257710i
$997$	−6.09299	+	3.51779i	−0.192967	+	0.111410i	−0.593371	−	0.804929i	$-0.702203\pi$
$997$	−6.09299	+	3.51779i	−0.192967	+	0.111410i	0.400404	+	0.916339i	$0.368870\pi$
$998$	−36.3113	+	20.9643i	−1.14941	+	0.663614i
$999$	10.6537	+	48.0473i	0.337069	+	1.52015i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.z.a.131.16	✓	32
3.2	odd	2		546.2.z.b.131.6	yes	32
7.3	odd	6		546.2.z.b.521.6	yes	32
21.17	even	6	inner	546.2.z.a.521.16	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.z.a.131.16	✓	32	1.1	even	1	trivial
546.2.z.a.521.16	yes	32	21.17	even	6	inner
546.2.z.b.131.6	yes	32	3.2	odd	2
546.2.z.b.521.6	yes	32	7.3	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(1.67937 - 0.423929i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.33293 - 2.30870i) q^{5} +(1.66634 + 0.472552i) q^{6} +(-2.41436 - 1.08207i) q^{7} +1.00000i q^{8} +(2.64057 - 1.42387i) q^{9} +(2.30870 - 1.33293i) q^{10} +(0.470358 - 0.271562i) q^{11} +(1.20682 + 1.24241i) q^{12} -1.00000i q^{13} +(-1.54986 - 2.14428i) q^{14} +(1.25975 - 4.44223i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.17473 + 5.49879i) q^{17} +(2.99873 + 0.0871789i) q^{18} +(-5.41050 - 3.12375i) q^{19} +2.66585 q^{20} +(-4.51332 - 0.793672i) q^{21} +0.543123 q^{22} +(2.03823 + 1.17677i) q^{23} +(0.423929 + 1.67937i) q^{24} +(-1.05339 - 1.82453i) q^{25} +(0.500000 - 0.866025i) q^{26} +(3.83087 - 3.51061i) q^{27} +(-0.270084 - 2.63193i) q^{28} +5.75382i q^{29} +(3.31209 - 3.21720i) q^{30} +(5.60990 - 3.23888i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.674783 - 0.655451i) q^{33} +6.34946i q^{34} +(-5.71633 + 4.13171i) q^{35} +(2.55339 + 1.57487i) q^{36} +(-4.73565 + 8.20238i) q^{37} +(-3.12375 - 5.41050i) q^{38} +(-0.423929 - 1.67937i) q^{39} +(2.30870 + 1.33293i) q^{40} -6.50568 q^{41} +(-3.51182 - 2.94400i) q^{42} -9.79478 q^{43} +(0.470358 + 0.271562i) q^{44} +(0.232406 - 7.99419i) q^{45} +(1.17677 + 2.03823i) q^{46} +(3.16636 - 5.48430i) q^{47} +(-0.472552 + 1.66634i) q^{48} +(4.65827 + 5.22499i) q^{49} -2.10678i q^{50} +(7.66264 + 7.88865i) q^{51} +(0.866025 - 0.500000i) q^{52} +(-6.39787 + 3.69381i) q^{53} +(5.07294 - 1.12484i) q^{54} -1.44789i q^{55} +(1.08207 - 2.41436i) q^{56} +(-10.4105 - 2.95227i) q^{57} +(-2.87691 + 4.98295i) q^{58} +(5.14321 + 8.90831i) q^{59} +(4.47696 - 1.13013i) q^{60} +(5.27061 + 3.04299i) q^{61} +6.47776 q^{62} +(-7.91600 + 0.580460i) q^{63} -1.00000 q^{64} +(-2.30870 - 1.33293i) q^{65} +(0.912105 - 0.230246i) q^{66} +(2.29391 + 3.97316i) q^{67} +(-3.17473 + 5.49879i) q^{68} +(3.92182 + 1.11217i) q^{69} +(-7.01634 + 0.720004i) q^{70} -10.3944i q^{71} +(1.42387 + 2.64057i) q^{72} +(-1.57792 + 0.911014i) q^{73} +(-8.20238 + 4.73565i) q^{74} +(-2.54250 - 2.61749i) q^{75} -6.24751i q^{76} +(-1.42946 + 0.146689i) q^{77} +(0.472552 - 1.66634i) q^{78} +(3.20588 - 5.55275i) q^{79} +(1.33293 + 2.30870i) q^{80} +(4.94520 - 7.51964i) q^{81} +(-5.63408 - 3.25284i) q^{82} +6.54629 q^{83} +(-1.56932 - 4.30549i) q^{84} +16.9267 q^{85} +(-8.48253 - 4.89739i) q^{86} +(2.43921 + 9.66279i) q^{87} +(0.271562 + 0.470358i) q^{88} +(-6.59265 + 11.4188i) q^{89} +(4.19836 - 6.80697i) q^{90} +(-1.08207 + 2.41436i) q^{91} +2.35355i q^{92} +(8.04805 - 7.81748i) q^{93} +(5.48430 - 3.16636i) q^{94} +(-14.4236 + 8.32748i) q^{95} +(-1.24241 + 1.20682i) q^{96} +3.22151i q^{97} +(1.42168 + 6.85411i) q^{98} +(0.855346 - 1.38680i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9} + 6 q^{10} - 24 q^{11} + 4 q^{14} - 12 q^{15} - 16 q^{16} + 4 q^{17} + 24 q^{18} - 12 q^{21} - 12 q^{22} - 6 q^{24} - 18 q^{25} + 16 q^{26} - 6 q^{27} - 2 q^{28} + 10 q^{30}+ \cdots + 32 q^{98}+O(q^{100}) \) 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9 + 6 * q^10 - 24 * q^11 + 4 * q^14 - 12 * q^15 - 16 * q^16 + 4 * q^17 + 24 * q^18 - 12 * q^21 - 12 * q^22 - 6 * q^24 - 18 * q^25 + 16 * q^26 - 6 * q^27 - 2 * q^28 + 10 * q^30 - 6 * q^31 - 14 * q^33 + 48 * q^35 + 4 * q^36 + 16 * q^38 + 6 * q^39 + 6 * q^40 + 16 * q^41 - 18 * q^42 + 32 * q^43 - 24 * q^44 - 20 * q^45 + 16 * q^46 + 20 * q^47 - 26 * q^49 + 44 * q^51 - 60 * q^53 - 6 * q^54 + 8 * q^56 - 8 * q^57 - 10 * q^58 + 8 * q^59 - 6 * q^60 + 36 * q^61 + 36 * q^62 - 28 * q^63 - 32 * q^64 - 6 * q^65 + 12 * q^66 - 4 * q^68 - 36 * q^69 - 18 * q^70 + 24 * q^72 - 48 * q^73 - 84 * q^74 + 14 * q^75 + 52 * q^77 + 18 * q^79 + 70 * q^81 + 24 * q^83 - 24 * q^84 - 32 * q^85 - 24 * q^86 - 26 * q^87 - 6 * q^88 - 20 * q^89 - 6 * q^90 - 8 * q^91 + 92 * q^93 - 72 * q^95 - 6 * q^96 + 32 * q^98

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