LMFDB - Embedded newform 273.2.l.c.256.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(16,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 2]))

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

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

chi := DirichletCharacter("273.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.l (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 18 x^{18} - 4 x^{17} + 211 x^{16} - 59 x^{15} + 1458 x^{14} - 526 x^{13} + 7324 x^{12} + \cdots + 1369 $ x^20 + 18x^18 - 4x^17 + 211x^16 - 59x^15 + 1458x^14 - 526x^13 + 7324x^12 - 2645x^11 + 23428x^10 - 8506x^9 + 54235x^8 - 18801x^7 + 74141x^6 - 25533x^5 + 68867x^4 - 16327x^3 + 16588x^2 + 2997x + 1369
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			256.4
Root			$-0.707433 + 1.22531i$ of defining polynomial
Character	$\chi$	$=$	273.256
Dual form			273.2.l.c.16.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41487 q^{2} +(-0.500000 - 0.866025i) q^{3} +0.00184802 q^{4} +(-1.42962 - 2.47618i) q^{5} +(0.707433 + 1.22531i) q^{6} +(2.56093 - 0.664549i) q^{7} +2.82712 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q-1.41487 q^{2} +(-0.500000 - 0.866025i) q^{3} +0.00184802 q^{4} +(-1.42962 - 2.47618i) q^{5} +(0.707433 + 1.22531i) q^{6} +(2.56093 - 0.664549i) q^{7} +2.82712 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.02273 + 3.50347i) q^{10} +(-1.15352 - 1.99796i) q^{11} +(-0.000924008 - 0.00160043i) q^{12} +(-3.12586 + 1.79694i) q^{13} +(-3.62338 + 0.940248i) q^{14} +(-1.42962 + 2.47618i) q^{15} -4.00369 q^{16} -7.45162 q^{17} +(0.707433 - 1.22531i) q^{18} +(-0.282836 + 0.489887i) q^{19} +(-0.00264197 - 0.00457603i) q^{20} +(-1.85598 - 1.88556i) q^{21} +(1.63208 + 2.82685i) q^{22} -0.797888 q^{23} +(-1.41356 - 2.44836i) q^{24} +(-1.58765 + 2.74989i) q^{25} +(4.42268 - 2.54243i) q^{26} +1.00000 q^{27} +(0.00473265 - 0.00122810i) q^{28} +(3.00672 - 5.20778i) q^{29} +(2.02273 - 3.50347i) q^{30} +(-3.80370 + 6.58820i) q^{31} +0.0104540 q^{32} +(-1.15352 + 1.99796i) q^{33} +10.5431 q^{34} +(-5.30672 - 5.39128i) q^{35} +(-0.000924008 + 0.00160043i) q^{36} +2.30147 q^{37} +(0.400176 - 0.693125i) q^{38} +(3.11913 + 1.80861i) q^{39} +(-4.04172 - 7.00046i) q^{40} +(-5.68100 + 9.83978i) q^{41} +(2.62597 + 2.66781i) q^{42} +(-3.76945 - 6.52888i) q^{43} +(-0.00213173 - 0.00369227i) q^{44} +2.85925 q^{45} +1.12890 q^{46} +(0.134822 + 0.233518i) q^{47} +(2.00185 + 3.46730i) q^{48} +(6.11675 - 3.40373i) q^{49} +(2.24632 - 3.89073i) q^{50} +(3.72581 + 6.45329i) q^{51} +(-0.00577664 + 0.00332077i) q^{52} +(2.35993 - 4.08751i) q^{53} -1.41487 q^{54} +(-3.29821 + 5.71267i) q^{55} +(7.24006 - 1.87876i) q^{56} +0.565673 q^{57} +(-4.25410 + 7.36832i) q^{58} -5.82180 q^{59} +(-0.00264197 + 0.00457603i) q^{60} +(1.46702 - 2.54094i) q^{61} +(5.38172 - 9.32142i) q^{62} +(-0.704950 + 2.55011i) q^{63} +7.99259 q^{64} +(8.91836 + 5.17125i) q^{65} +(1.63208 - 2.82685i) q^{66} +(-1.58734 - 2.74935i) q^{67} -0.0137707 q^{68} +(0.398944 + 0.690991i) q^{69} +(7.50830 + 7.62794i) q^{70} +(-3.01045 - 5.21425i) q^{71} +(-1.41356 + 2.44836i) q^{72} +(5.31799 - 9.21103i) q^{73} -3.25627 q^{74} +3.17530 q^{75} +(-0.000522686 + 0.000905319i) q^{76} +(-4.28184 - 4.35007i) q^{77} +(-4.41315 - 2.55894i) q^{78} +(-2.01404 - 3.48841i) q^{79} +(5.72378 + 9.91387i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(8.03786 - 13.9220i) q^{82} +16.2573 q^{83} +(-0.00342989 - 0.00348454i) q^{84} +(10.6530 + 18.4516i) q^{85} +(5.33327 + 9.23749i) q^{86} -6.01343 q^{87} +(-3.26115 - 5.64848i) q^{88} -1.41839 q^{89} -4.04546 q^{90} +(-6.81097 + 6.67913i) q^{91} -0.00147451 q^{92} +7.60739 q^{93} +(-0.190755 - 0.330397i) q^{94} +1.61740 q^{95} +(-0.00522698 - 0.00905339i) q^{96} +(-5.23049 - 9.05948i) q^{97} +(-8.65439 + 4.81582i) q^{98} +2.30705 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 10 q^{3} + 32 q^{4} + 3 q^{7} - 12 q^{8} - 10 q^{9}+O(q^{10}) $ 20 * q - 10 * q^3 + 32 * q^4 + 3 * q^7 - 12 * q^8 - 10 * q^9	$ 20 q - 10 q^{3} + 32 q^{4} + 3 q^{7} - 12 q^{8} - 10 q^{9} - 4 q^{10} - 8 q^{11} - 16 q^{12} - 5 q^{13} - 9 q^{14} + 40 q^{16} + 7 q^{19} + 12 q^{20} - 9 q^{21} - 9 q^{22} + 28 q^{23} + 6 q^{24} - 32 q^{25} + 13 q^{26} + 20 q^{27} - 23 q^{28} - 9 q^{29} - 4 q^{30} - 9 q^{31} - 34 q^{32} - 8 q^{33} + 12 q^{34} + 10 q^{35} - 16 q^{36} - 36 q^{37} + 22 q^{38} + 4 q^{39} - 9 q^{40} - q^{41} + 3 q^{42} - 11 q^{43} + 8 q^{44} + 20 q^{46} + 13 q^{47} - 20 q^{48} - 3 q^{49} + 5 q^{50} - 44 q^{52} - 6 q^{53} - 19 q^{55} - 23 q^{56} - 14 q^{57} + 30 q^{59} + 12 q^{60} + 22 q^{62} + 6 q^{63} + 72 q^{64} - 6 q^{65} - 9 q^{66} - 22 q^{67} - 78 q^{68} - 14 q^{69} + 30 q^{70} - 11 q^{71} + 6 q^{72} + 6 q^{74} + 64 q^{75} + 6 q^{76} + 56 q^{77} + 4 q^{78} - 36 q^{79} + 48 q^{80} - 10 q^{81} - 13 q^{82} + 40 q^{83} + 10 q^{84} - 16 q^{85} + 4 q^{86} + 18 q^{87} - 12 q^{88} - 4 q^{89} + 8 q^{90} + 30 q^{91} + 66 q^{92} + 18 q^{93} - 44 q^{94} + 72 q^{95} + 17 q^{96} + 21 q^{97} - 76 q^{98} + 16 q^{99}+O(q^{100}) $ 20 * q - 10 * q^3 + 32 * q^4 + 3 * q^7 - 12 * q^8 - 10 * q^9 - 4 * q^10 - 8 * q^11 - 16 * q^12 - 5 * q^13 - 9 * q^14 + 40 * q^16 + 7 * q^19 + 12 * q^20 - 9 * q^21 - 9 * q^22 + 28 * q^23 + 6 * q^24 - 32 * q^25 + 13 * q^26 + 20 * q^27 - 23 * q^28 - 9 * q^29 - 4 * q^30 - 9 * q^31 - 34 * q^32 - 8 * q^33 + 12 * q^34 + 10 * q^35 - 16 * q^36 - 36 * q^37 + 22 * q^38 + 4 * q^39 - 9 * q^40 - q^41 + 3 * q^42 - 11 * q^43 + 8 * q^44 + 20 * q^46 + 13 * q^47 - 20 * q^48 - 3 * q^49 + 5 * q^50 - 44 * q^52 - 6 * q^53 - 19 * q^55 - 23 * q^56 - 14 * q^57 + 30 * q^59 + 12 * q^60 + 22 * q^62 + 6 * q^63 + 72 * q^64 - 6 * q^65 - 9 * q^66 - 22 * q^67 - 78 * q^68 - 14 * q^69 + 30 * q^70 - 11 * q^71 + 6 * q^72 + 6 * q^74 + 64 * q^75 + 6 * q^76 + 56 * q^77 + 4 * q^78 - 36 * q^79 + 48 * q^80 - 10 * q^81 - 13 * q^82 + 40 * q^83 + 10 * q^84 - 16 * q^85 + 4 * q^86 + 18 * q^87 - 12 * q^88 - 4 * q^89 + 8 * q^90 + 30 * q^91 + 66 * q^92 + 18 * q^93 - 44 * q^94 + 72 * q^95 + 17 * q^96 + 21 * q^97 - 76 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.41487			−1.00046			−0.500231	−	0.865892i	$-0.666752\pi$
$2$	−1.41487			−1.00046			−0.500231	+	0.865892i	$0.666752\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.00184802			0.000924008
$5$	−1.42962	−	2.47618i	−0.639347	−	1.10738i	−0.985576	−	0.169232i	$-0.945871\pi$
$5$	−1.42962	−	2.47618i	−0.639347	−	1.10738i	0.346229	−	0.938150i	$-0.387462\pi$
$6$	0.707433	+	1.22531i	0.288808	+	0.500231i
$7$	2.56093	−	0.664549i	0.967941	−	0.251176i
$7$	2.56093	−	0.664549i	0.967941	−	0.251176i
$8$	2.82712			0.999537
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	2.02273	+	3.50347i	0.639643	+	1.10789i
$11$	−1.15352	−	1.99796i	−0.347801	−	0.602408i	0.638058	−	0.769988i	$-0.279738\pi$
$11$	−1.15352	−	1.99796i	−0.347801	−	0.602408i	−0.985858	+	0.167580i	$0.946405\pi$
$12$	−0.000924008	−	0.00160043i	−0.000266738	−	0.000462004i
$13$	−3.12586	+	1.79694i	−0.866958	+	0.498381i
$13$	−3.12586	+	1.79694i	−0.866958	+	0.498381i
$14$	−3.62338	+	0.940248i	−0.968389	+	0.251292i
$15$	−1.42962	+	2.47618i	−0.369127	+	0.639347i
$16$	−4.00369			−1.00092
$17$	−7.45162			−1.80728			−0.903642	−	0.428289i	$-0.859117\pi$
$17$	−7.45162			−1.80728			−0.903642	+	0.428289i	$0.859117\pi$
$18$	0.707433	−	1.22531i	0.166744	−	0.288808i
$19$	−0.282836	+	0.489887i	−0.0648871	+	0.112388i	−0.896644	−	0.442752i	$-0.854002\pi$
$19$	−0.282836	+	0.489887i	−0.0648871	+	0.112388i	0.831757	+	0.555140i	$0.187335\pi$
$20$	−0.00264197	−	0.00457603i	−0.000590762	−	0.00102323i
$21$	−1.85598	−	1.88556i	−0.405009	−	0.411463i
$22$	1.63208	+	2.82685i	0.347961	+	0.602686i
$23$	−0.797888			−0.166371			−0.0831855	−	0.996534i	$-0.526509\pi$
$23$	−0.797888			−0.166371			−0.0831855	+	0.996534i	$0.526509\pi$
$24$	−1.41356	−	2.44836i	−0.288542	−	0.499769i
$25$	−1.58765	+	2.74989i	−0.317530	+	0.549979i
$26$	4.42268	−	2.54243i	0.867358	−	0.498611i
$27$	1.00000			0.192450
$28$	0.00473265	−	0.00122810i	0.000894386	−	0.000232089i
$29$	3.00672	−	5.20778i	0.558333	−	0.967061i	−0.439303	−	0.898339i	$-0.644775\pi$
$29$	3.00672	−	5.20778i	0.558333	−	0.967061i	0.997636	−	0.0687221i	$-0.0218922\pi$
$30$	2.02273	−	3.50347i	0.369298	−	0.639643i
$31$	−3.80370	+	6.58820i	−0.683164	+	1.18328i	0.290846	+	0.956770i	$0.406063\pi$
$31$	−3.80370	+	6.58820i	−0.683164	+	1.18328i	−0.974010	+	0.226505i	$0.927270\pi$
$32$	0.0104540			0.00184802
$33$	−1.15352	+	1.99796i	−0.200803	+	0.347801i
$34$	10.5431			1.80812
$35$	−5.30672	−	5.39128i	−0.896999	−	0.911293i
$36$	−0.000924008		0.00160043i	−0.000154001		0.000266738i
$37$	2.30147			0.378359			0.189179	−	0.981943i	$-0.439417\pi$
$37$	2.30147			0.378359			0.189179	+	0.981943i	$0.439417\pi$
$38$	0.400176	−	0.693125i	0.0649171	−	0.112440i
$39$	3.11913	+	1.80861i	0.499460	+	0.289609i
$40$	−4.04172	−	7.00046i	−0.639052	−	1.10687i
$41$	−5.68100	+	9.83978i	−0.887223	+	1.53672i	−0.0440794	+	0.999028i	$0.514035\pi$
$41$	−5.68100	+	9.83978i	−0.887223	+	1.53672i	−0.843144	+	0.537688i	$0.819298\pi$
$42$	2.62597	+	2.66781i	0.405196	+	0.411653i
$43$	−3.76945	−	6.52888i	−0.574835	−	0.995644i	−0.996059	−	0.0886876i	$-0.971733\pi$
$43$	−3.76945	−	6.52888i	−0.574835	−	0.995644i	0.421224	−	0.906957i	$-0.361601\pi$
$44$	−0.00213173	−	0.00369227i	−0.000321371	−	0.000556630i
$45$	2.85925			0.426232
$46$	1.12890			0.166448
$47$	0.134822	+	0.233518i	0.0196658	+	0.0340621i	0.875691	−	0.482872i	$-0.160406\pi$
$47$	0.134822	+	0.233518i	0.0196658	+	0.0340621i	−0.856025	+	0.516934i	$0.827073\pi$
$48$	2.00185	+	3.46730i	0.288942	+	0.500462i
$49$	6.11675	−	3.40373i	0.873821	−	0.486247i
$50$	2.24632	−	3.89073i	0.317677	−	0.550233i
$51$	3.72581	+	6.45329i	0.521718	+	0.903642i
$52$	−0.00577664	+	0.00332077i	−0.000801076	+	0.000460508i
$53$	2.35993	−	4.08751i	0.324161	−	0.561463i	−0.657181	−	0.753733i	$-0.728251\pi$
$53$	2.35993	−	4.08751i	0.324161	−	0.561463i	0.981342	+	0.192269i	$0.0615847\pi$
$54$	−1.41487			−0.192539
$55$	−3.29821	+	5.71267i	−0.444731	+	0.770296i
$56$	7.24006	−	1.87876i	0.967494	−	0.251060i
$57$	0.565673			0.0749252
$58$	−4.25410	+	7.36832i	−0.558591	+	0.967508i
$59$	−5.82180			−0.757934			−0.378967	−	0.925410i	$-0.623721\pi$
$59$	−5.82180			−0.757934			−0.378967	+	0.925410i	$0.623721\pi$
$60$	−0.00264197	+	0.00457603i	−0.000341077	+	0.000590762i
$61$	1.46702	−	2.54094i	0.187832	−	0.325335i	−0.756695	−	0.653768i	$-0.773187\pi$
$61$	1.46702	−	2.54094i	0.187832	−	0.325335i	0.944527	+	0.328433i	$0.106521\pi$
$62$	5.38172	−	9.32142i	0.683480	−	1.18382i
$63$	−0.704950	+	2.55011i	−0.0888154	+	0.321283i
$64$	7.99259			0.999074
$65$	8.91836	+	5.17125i	1.10619	+	0.641415i
$66$	1.63208	−	2.82685i	0.200895	−	0.347961i
$67$	−1.58734	−	2.74935i	−0.193924	−	0.335887i	0.752623	−	0.658452i	$-0.228788\pi$
$67$	−1.58734	−	2.74935i	−0.193924	−	0.335887i	−0.946547	+	0.322565i	$0.895455\pi$
$68$	−0.0137707			−0.00166995
$69$	0.398944	+	0.690991i	0.0480272	+	0.0831855i
$70$	7.50830	+	7.62794i	0.897413	+	0.911714i
$71$	−3.01045	−	5.21425i	−0.357275	−	0.618818i	0.630230	−	0.776409i	$-0.282961\pi$
$71$	−3.01045	−	5.21425i	−0.357275	−	0.618818i	−0.987505	+	0.157591i	$0.949627\pi$
$72$	−1.41356	+	2.44836i	−0.166590	+	0.288542i
$73$	5.31799	−	9.21103i	0.622424	−	1.07807i	−0.366609	−	0.930375i	$-0.619481\pi$
$73$	5.31799	−	9.21103i	0.622424	−	1.07807i	0.989033	−	0.147694i	$-0.0471852\pi$
$74$	−3.25627			−0.378533
$75$	3.17530			0.366652
$76$	−0.000522686	0	0.000905319i	−5.99562e−5	0	0.000103847i
$77$	−4.28184	−	4.35007i	−0.487961	−	0.495737i
$78$	−4.41315	−	2.55894i	−0.499691	−	0.289743i
$79$	−2.01404	−	3.48841i	−0.226597	−	0.392477i	0.730201	−	0.683233i	$-0.239427\pi$
$79$	−2.01404	−	3.48841i	−0.226597	−	0.392477i	−0.956797	+	0.290756i	$0.906093\pi$
$80$	5.72378	+	9.91387i	0.639938	+	1.10840i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	8.03786	−	13.9220i	0.887633	−	1.53743i
$83$	16.2573			1.78447			0.892237	−	0.451567i	$-0.149135\pi$
$83$	16.2573			1.78447			0.892237	+	0.451567i	$0.149135\pi$
$84$	−0.00342989	−	0.00348454i	−0.000374231	−	0.000380195i
$85$	10.6530	+	18.4516i	1.15548	+	2.00135i
$86$	5.33327	+	9.23749i	0.575101	+	0.996104i
$87$	−6.01343			−0.644707
$88$	−3.26115	−	5.64848i	−0.347640	−	0.602130i
$89$	−1.41839			−0.150349			−0.0751745	−	0.997170i	$-0.523951\pi$
$89$	−1.41839			−0.150349			−0.0751745	+	0.997170i	$0.523951\pi$
$90$	−4.04546			−0.426429
$91$	−6.81097	+	6.67913i	−0.713983	+	0.700163i
$92$	−0.00147451			−0.000153728
$93$	7.60739			0.788850
$94$	−0.190755	−	0.330397i	−0.0196748	−	0.0340778i
$95$	1.61740			0.165942
$96$	−0.00522698	−	0.00905339i	−0.000533476	−	0.000924008i
$97$	−5.23049	−	9.05948i	−0.531076	−	0.919851i	−0.999342	−	0.0362635i	$-0.988454\pi$
$97$	−5.23049	−	9.05948i	−0.531076	−	0.919851i	0.468266	−	0.883588i	$-0.344879\pi$
$98$	−8.65439	+	4.81582i	−0.874225	+	0.486472i
$99$	2.30705			0.231867
$100$	−0.00293401	+	0.00508185i	−0.000293401	+	0.000508185i
$101$	4.73742	+	8.20545i	0.471391	+	0.816473i	0.999464	−	0.0327260i	$-0.0104189\pi$
$101$	4.73742	+	8.20545i	0.471391	+	0.816473i	−0.528074	+	0.849199i	$0.677086\pi$
$102$	−5.27153	−	9.13055i	−0.521959	−	0.904059i
$103$	−10.1433	−	17.5686i	−0.999444	−	1.73109i	−0.528588	−	0.848879i	$-0.677278\pi$
$103$	−10.1433	−	17.5686i	−0.999444	−	1.73109i	−0.470857	−	0.882210i	$-0.656055\pi$
$104$	−8.83718	+	5.08016i	−0.866557	+	0.498151i
$105$	−2.01563	+	7.29139i	−0.196705	+	0.711567i
$106$	−3.33898	+	5.78329i	−0.324311	+	0.561723i
$107$	−13.3661			−1.29215			−0.646075	−	0.763274i	$-0.723591\pi$
$107$	−13.3661			−1.29215			−0.646075	+	0.763274i	$0.723591\pi$
$108$	0.00184802			0.000177825
$109$	−0.471097	+	0.815964i	−0.0451229	+	0.0781551i	−0.887705	−	0.460413i	$-0.847701\pi$
$109$	−0.471097	+	0.815964i	−0.0451229	+	0.0781551i	0.842582	+	0.538568i	$0.181035\pi$
$110$	4.66653	−	8.08267i	0.444936	−	0.770652i
$111$	−1.15073	−	1.99313i	−0.109223	−	0.189179i
$112$	−10.2532	+	2.66065i	−0.968835	+	0.251408i
$113$	−1.28957	−	2.23360i	−0.121313	−	0.210120i	0.798973	−	0.601367i	$-0.205377\pi$
$113$	−1.28957	−	2.23360i	−0.121313	−	0.210120i	−0.920286	+	0.391247i	$0.872044\pi$
$114$	−0.800352			−0.0749598
$115$	1.14068	+	1.97572i	0.106369	+	0.184236i
$116$	0.00555646	−	0.00962407i	0.000515904	−	0.000893572i
$117$	0.00673603	−	3.60554i	0.000622746	−	0.333333i
$118$	8.23707			0.758284
$119$	−19.0831	+	4.95197i	−1.74934	+	0.453946i
$120$	−4.04172	+	7.00046i	−0.368957	+	0.639052i
$121$	2.83876	−	4.91689i	0.258070	−	0.446990i
$122$	−2.07563	+	3.59510i	−0.187919	+	0.325485i
$123$	11.3620			1.02448
$124$	−0.00702930	+	0.0121751i	−0.000631249	+	0.00109336i
$125$	−5.21726			−0.466646
$126$	0.997410	−	3.60806i	0.0888564	−	0.321432i
$127$	−2.06314	+	3.57347i	−0.183074	+	0.317094i	−0.942926	−	0.333003i	$-0.891938\pi$
$127$	−2.06314	+	3.57347i	−0.183074	+	0.317094i	0.759852	+	0.650097i	$0.225272\pi$
$128$	−11.3294			−1.00138
$129$	−3.76945	+	6.52888i	−0.331881	+	0.574835i
$130$	−12.6183	−	7.31664i	−1.10670	−	0.641711i
$131$	3.77229	+	6.53379i	0.329586	+	0.570860i	0.982430	−	0.186633i	$-0.0597574\pi$
$131$	3.77229	+	6.53379i	0.329586	+	0.570860i	−0.652844	+	0.757493i	$0.726424\pi$
$132$	−0.00213173	+	0.00369227i	−0.000185543	+	0.000321371i
$133$	−0.398771	+	1.44253i	−0.0345778	+	0.125083i
$134$	2.24588	+	3.88997i	0.194014	+	0.336042i
$135$	−1.42962	−	2.47618i	−0.123042	−	0.213116i
$136$	−21.0666			−1.80645
$137$	16.6998			1.42676			0.713381	−	0.700776i	$-0.247163\pi$
$137$	16.6998			1.42676			0.713381	+	0.700776i	$0.247163\pi$
$138$	−0.564452	−	0.977660i	−0.0480494	−	0.0832240i
$139$	−5.17295	−	8.95981i	−0.438764	−	0.759961i	0.558831	−	0.829282i	$-0.311250\pi$
$139$	−5.17295	−	8.95981i	−0.438764	−	0.759961i	−0.997594	+	0.0693207i	$0.977917\pi$
$140$	−0.00980690	−	0.00996317i	−0.000828834	−	0.000842042i
$141$	0.134822	−	0.233518i	0.0113540	−	0.0196658i
$142$	4.25939	+	7.37747i	0.357440	+	0.619104i
$143$	7.19597	+	4.17254i	0.601757	+	0.348925i
$144$	2.00185	−	3.46730i	0.166821	−	0.288942i
$145$	−17.1939			−1.42788
$146$	−7.52425	+	13.0324i	−0.622711	+	1.07857i
$147$	−6.00609	−	3.59540i	−0.495374	−	0.296543i
$148$	0.00425315			0.000349606
$149$	6.12229	−	10.6041i	0.501558	−	0.868724i	−0.498440	−	0.866924i	$-0.666094\pi$
$149$	6.12229	−	10.6041i	0.501558	−	0.868724i	0.999998	−	0.00179987i	$-0.000572918\pi$
$150$	−4.49263			−0.366822
$151$	−9.04334	+	15.6635i	−0.735936	+	1.27468i	0.218375	+	0.975865i	$0.429924\pi$
$151$	−9.04334	+	15.6635i	−0.735936	+	1.27468i	−0.954311	+	0.298814i	$0.903409\pi$
$152$	−0.799612	+	1.38497i	−0.0648571	+	0.112336i
$153$	3.72581	−	6.45329i	0.301214	−	0.521718i
$154$	6.05823	+	6.15477i	0.488186	+	0.495966i
$155$	21.7514			1.74712
$156$	0.00576420	+	0.00334233i	0.000461505	+	0.000267601i
$157$	10.9151	−	18.9055i	0.871120	−	1.50882i	0.0102810	−	0.999947i	$-0.496727\pi$
$157$	10.9151	−	18.9055i	0.871120	−	1.50882i	0.860839	−	0.508877i	$-0.169939\pi$
$158$	2.84959	+	4.93564i	0.226701	+	0.392658i
$159$	−4.71985			−0.374309
$160$	−0.0149452	−	0.0258859i	−0.00118152	−	0.00204646i
$161$	−2.04334	+	0.530235i	−0.161037	+	0.0417884i
$162$	0.707433	+	1.22531i	0.0555812	+	0.0962695i
$163$	5.68715	−	9.85044i	0.445452	−	0.771546i	−0.552631	−	0.833426i	$-0.686376\pi$
$163$	5.68715	−	9.85044i	0.445452	−	0.771546i	0.998084	+	0.0618799i	$0.0197096\pi$
$164$	−0.0104986	+	0.0181841i	−0.000819802	+	0.00141994i
$165$	6.59642			0.513531
$166$	−23.0020			−1.78530
$167$	0.262814	−	0.455207i	0.0203372	−	0.0352250i	−0.855678	−	0.517509i	$-0.826859\pi$
$167$	0.262814	−	0.455207i	0.0203372	−	0.0352250i	0.876015	+	0.482284i	$0.160193\pi$
$168$	−5.24708	−	5.33070i	−0.404821	−	0.411272i
$169$	6.54202	−	11.2340i	0.503232	−	0.864151i
$170$	−15.0726	−	26.1065i	−1.15602	−	2.00228i
$171$	−0.282836	−	0.489887i	−0.0216290	−	0.0374626i
$172$	−0.00696600	−	0.0120655i	−0.000531153	−	0.000919984i
$173$	4.57259	−	7.91995i	0.347647	−	0.602143i	−0.638184	−	0.769884i	$-0.720314\pi$
$173$	4.57259	−	7.91995i	0.347647	−	0.602143i	0.985831	+	0.167741i	$0.0536473\pi$
$174$	8.50820			0.645005
$175$	−2.23843	+	8.09736i	−0.169209	+	0.612103i
$176$	4.61836	+	7.99923i	0.348122	+	0.602964i
$177$	2.91090	+	5.04183i	0.218797	+	0.378967i
$178$	2.00683			0.150418
$179$	0.861430	+	1.49204i	0.0643863	+	0.111520i	0.896422	−	0.443202i	$-0.146158\pi$
$179$	0.861430	+	1.49204i	0.0643863	+	0.111520i	−0.832035	+	0.554723i	$0.812824\pi$
$180$	0.00528394			0.000393842
$181$	−3.97723			−0.295625			−0.147813	−	0.989015i	$-0.547223\pi$
$181$	−3.97723			−0.295625			−0.147813	+	0.989015i	$0.547223\pi$
$182$	9.63661	−	9.45007i	0.714313	−	0.700486i
$183$	−2.93403			−0.216890
$184$	−2.25572			−0.166294
$185$	−3.29023	−	5.69885i	−0.241903	−	0.418988i
$186$	−10.7634			−0.789214
$187$	8.59562	+	14.8881i	0.628574	+	1.08872i
$188$	0.000249153	0	0.000431545i	1.81713e−5	0	3.14737e-5i
$189$	2.56093	−	0.664549i	0.186280	−	0.0483388i
$190$	−2.28840			−0.166018
$191$	−12.5767	+	21.7835i	−0.910019	+	1.57620i	−0.0959855	+	0.995383i	$0.530600\pi$
$191$	−12.5767	+	21.7835i	−0.910019	+	1.57620i	−0.814034	+	0.580817i	$0.802733\pi$
$192$	−3.99630	−	6.92179i	−0.288408	−	0.499537i
$193$	9.07766	+	15.7230i	0.653425	+	1.13176i	0.982286	+	0.187386i	$0.0600017\pi$
$193$	9.07766	+	15.7230i	0.653425	+	1.13176i	−0.328862	+	0.944378i	$0.606665\pi$
$194$	7.40045	+	12.8180i	0.531322	+	0.920276i
$195$	0.0192600	−	10.3091i	0.00137924	−	0.738254i
$196$	0.0113039	−	0.00629015i	0.000807418	−	0.000449296i
$197$	0.782504	−	1.35534i	0.0557511	−	0.0965638i	−0.836803	−	0.547504i	$-0.815578\pi$
$197$	0.782504	−	1.35534i	0.0557511	−	0.0965638i	0.892554	+	0.450940i	$0.148911\pi$
$198$	−3.26417			−0.231974
$199$	−15.1161			−1.07155			−0.535776	−	0.844360i	$-0.679981\pi$
$199$	−15.1161			−1.07155			−0.535776	+	0.844360i	$0.679981\pi$
$200$	−4.48848	+	7.77427i	−0.317383	+	0.549724i
$201$	−1.58734	+	2.74935i	−0.111962	+	0.193924i
$202$	−6.70281	−	11.6096i	−0.471608	−	0.816850i
$203$	4.23917	−	15.3349i	0.297531	−	1.07630i
$204$	0.00688536	+	0.0119258i	0.000482072	+	0.000834973i
$205$	32.4868			2.26898
$206$	14.3514	+	24.8573i	0.999906	+	1.73189i
$207$	0.398944	−	0.690991i	0.0277285	−	0.0480272i
$208$	12.5150	−	7.19439i	0.867758	−	0.498841i
$209$	1.30503			0.0902711
$210$	2.85184	−	10.3163i	0.196796	−	0.711895i
$211$	−8.28852	+	14.3561i	−0.570606	+	0.988318i	0.425898	+	0.904771i	$0.359958\pi$
$211$	−8.28852	+	14.3561i	−0.570606	+	0.988318i	−0.996504	+	0.0835467i	$0.973375\pi$
$212$	0.00436118	−	0.00755379i	0.000299527	−	0.000518797i
$213$	−3.01045	+	5.21425i	−0.206273	+	0.357275i
$214$	18.9112			1.29275
$215$	−10.7778	+	18.6677i	−0.735039	+	1.27313i
$216$	2.82712			0.192361
$217$	−5.36283	+	19.3997i	−0.364053	+	1.31694i
$218$	0.666539	−	1.15448i	0.0451437	−	0.0781912i
$219$	−10.6360			−0.718713
$220$	−0.00609515	+	0.0105571i	−0.000410935	+	0.000711760i
$221$	23.2927	−	13.3901i	1.56684	−	0.900716i
$222$	1.62813	+	2.82001i	0.109273	+	0.189267i
$223$	3.10234	−	5.37341i	0.207748	−	0.359830i	−0.743257	−	0.669006i	$-0.766720\pi$
$223$	3.10234	−	5.37341i	0.207748	−	0.359830i	0.951005	+	0.309176i	$0.100053\pi$
$224$	0.0267719	−	0.00694716i	0.00178877	−	0.000464177i
$225$	−1.58765	−	2.74989i	−0.105843	−	0.183326i
$226$	1.82457	+	3.16025i	0.121369	+	0.210217i
$227$	−1.54064			−0.102256			−0.0511278	−	0.998692i	$-0.516282\pi$
$227$	−1.54064			−0.102256			−0.0511278	+	0.998692i	$0.516282\pi$
$228$	0.00104537			6.92315e−5
$229$	10.6720	+	18.4845i	0.705227	+	1.22149i	0.966610	+	0.256253i	$0.0824880\pi$
$229$	10.6720	+	18.4845i	0.705227	+	1.22149i	−0.261383	+	0.965235i	$0.584179\pi$
$230$	−1.61391	−	2.79537i	−0.106418	−	0.184321i
$231$	−1.62635	+	5.88322i	−0.107006	+	0.387087i
$232$	8.50034	−	14.7230i	0.558075	−	0.966614i
$233$	−4.31457	−	7.47305i	−0.282657	−	0.489576i	0.689381	−	0.724399i	$-0.257882\pi$
$233$	−4.31457	−	7.47305i	−0.282657	−	0.489576i	−0.972038	+	0.234823i	$0.924549\pi$
$234$	−0.00953058	+	5.10137i	−0.000623034	+	0.333487i
$235$	0.385489	−	0.667686i	0.0251465	−	0.0435550i
$236$	−0.0107588			−0.000700337
$237$	−2.01404	+	3.48841i	−0.130826	+	0.226597i
$238$	27.0000	−	7.00637i	1.75015	−	0.454156i
$239$	20.3222			1.31454			0.657268	−	0.753657i	$-0.271712\pi$
$239$	20.3222			1.31454			0.657268	+	0.753657i	$0.271712\pi$
$240$	5.72378	−	9.91387i	0.369468	−	0.639938i
$241$	26.1153			1.68224			0.841119	−	0.540851i	$-0.181898\pi$
$241$	26.1153			1.68224			0.841119	+	0.540851i	$0.181898\pi$
$242$	−4.01647	+	6.95674i	−0.258189	+	0.447196i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	0.00271107	−	0.00469571i	0.000173558	−	0.000300612i
$245$	−17.1729	−	10.2801i	−1.09714	−	0.656773i
$246$	−16.0757			−1.02495
$247$	0.00381039	−	2.03956i	0.000242449	−	0.129774i
$248$	−10.7535	+	18.6256i	−0.682848	+	1.18273i
$249$	−8.12867	−	14.0793i	−0.515133	−	0.892237i
$250$	7.38173			0.466862
$251$	−11.2757	−	19.5301i	−0.711718	−	1.23273i	−0.964212	−	0.265133i	$-0.914584\pi$
$251$	−11.2757	−	19.5301i	−0.711718	−	1.23273i	0.252494	−	0.967599i	$-0.418749\pi$
$252$	−0.00130276	+	0.00471264i	−8.20661e−5	+	0.000296868i
$253$	0.920383	+	1.59415i	0.0578640	+	0.100223i
$254$	2.91907	−	5.05598i	0.183159	−	0.317240i
$255$	10.6530	−	18.4516i	0.667118	−	1.15548i
$256$	0.0443524			0.00277202
$257$	−1.07243			−0.0668965			−0.0334483	−	0.999440i	$-0.510649\pi$
$257$	−1.07243			−0.0668965			−0.0334483	+	0.999440i	$0.510649\pi$
$258$	5.33327	−	9.23749i	0.332035	−	0.575101i
$259$	5.89390	−	1.52944i	0.366229	−	0.0950345i
$260$	0.0164813	+	0.00955656i	0.00102212	+	0.000592673i
$261$	3.00672	+	5.20778i	0.186111	+	0.322354i
$262$	−5.33728	−	9.24445i	−0.329738	−	0.571124i
$263$	−7.73455	−	13.3966i	−0.476933	−	0.826072i	0.522718	−	0.852506i	$-0.324918\pi$
$263$	−7.73455	−	13.3966i	−0.476933	−	0.826072i	−0.999651	+	0.0264339i	$0.991585\pi$
$264$	−3.26115	+	5.64848i	−0.200710	+	0.347640i
$265$	−13.4952			−0.829006
$266$	0.564208	−	2.04098i	0.0345938	−	0.125141i
$267$	0.709194	+	1.22836i	0.0434020	+	0.0751745i
$268$	−0.00293343	−	0.00508085i	−0.000179188	−	0.000310362i
$269$	2.23782			0.136442			0.0682212	−	0.997670i	$-0.478268\pi$
$269$	2.23782			0.136442			0.0682212	+	0.997670i	$0.478268\pi$
$270$	2.02273	+	3.50347i	0.123099	+	0.213214i
$271$	6.14439			0.373245			0.186623	−	0.982432i	$-0.440246\pi$
$271$	6.14439			0.373245			0.186623	+	0.982432i	$0.440246\pi$
$272$	29.8340			1.80895
$273$	9.18978	+	2.55891i	0.556191	+	0.154872i
$274$	−23.6280			−1.42742
$275$	7.32558			0.441749
$276$	0.000737255		0.00127696i	4.43775e−5		7.68641e-5i
$277$	−3.34827			−0.201178			−0.100589	−	0.994928i	$-0.532073\pi$
$277$	−3.34827			−0.201178			−0.100589	+	0.994928i	$0.532073\pi$
$278$	7.31903	+	12.6769i	0.438966	+	0.760312i
$279$	−3.80370	−	6.58820i	−0.227721	−	0.394425i
$280$	−15.0027	−	15.2418i	−0.896584	−	0.910871i
$281$	−14.2117			−0.847800			−0.423900	−	0.905709i	$-0.639339\pi$
$281$	−14.2117			−0.847800			−0.423900	+	0.905709i	$0.639339\pi$
$282$	−0.190755	+	0.330397i	−0.0113593	+	0.0196748i
$283$	−7.31417	−	12.6685i	−0.434782	−	0.753065i	0.562495	−	0.826800i	$-0.309841\pi$
$283$	−7.31417	−	12.6685i	−0.434782	−	0.753065i	−0.997278	+	0.0737351i	$0.976508\pi$
$284$	−0.00556336	−	0.00963602i	−0.000330125	−	0.000571793i
$285$	−0.808700	−	1.40071i	−0.0479032	−	0.0829708i
$286$	−10.1813	−	5.90359i	−0.602035	−	0.349087i
$287$	−8.00964	+	28.9743i	−0.472794	+	1.71030i
$288$	−0.00522698	+	0.00905339i	−0.000308003	+	0.000533476i
$289$	38.5267			2.26627
$290$	24.3271			1.42853
$291$	−5.23049	+	9.05948i	−0.306617	+	0.531076i
$292$	0.00982773	−	0.0170221i	0.000575125	−	0.000996145i
$293$	−10.7723	−	18.6582i	−0.629324	−	1.09002i	−0.987688	−	0.156439i	$-0.949998\pi$
$293$	−10.7723	−	18.6582i	−0.629324	−	1.09002i	0.358363	−	0.933582i	$-0.383335\pi$
$294$	8.49782	+	5.08701i	0.495603	+	0.296680i
$295$	8.32299	+	14.4158i	0.484583	+	0.839323i
$296$	6.50652			0.378184
$297$	−1.15352	−	1.99796i	−0.0669342	−	0.115934i
$298$	−8.66223	+	15.0034i	−0.501790	+	0.869125i
$299$	2.49409	−	1.43376i	0.144237	−	0.0829162i
$300$	0.00586801			0.000338790
$301$	−13.9921	−	14.2150i	−0.806489	−	0.819341i
$302$	12.7951	−	22.1618i	0.736276	−	1.27527i
$303$	4.73742	−	8.20545i	0.272158	−	0.471391i
$304$	1.13239	−	1.96136i	0.0649470	−	0.112492i
$305$	−8.38912			−0.480360
$306$	−5.27153	+	9.13055i	−0.301353	+	0.521959i
$307$	18.6457			1.06416			0.532082	−	0.846693i	$-0.321410\pi$
$307$	18.6457			1.06416			0.532082	+	0.846693i	$0.321410\pi$
$308$	−0.00791291	−	0.00803901i	−0.000450880	−	0.000458065i
$309$	−10.1433	+	17.5686i	−0.577029	+	0.999444i
$310$	−30.7754			−1.74792
$311$	−0.578424	+	1.00186i	−0.0327994	+	0.0568103i	−0.881959	−	0.471326i	$-0.843776\pi$
$311$	−0.578424	+	1.00186i	−0.0327994	+	0.0568103i	0.849160	+	0.528136i	$0.177109\pi$
$312$	8.81814	+	5.11314i	0.499229	+	0.289475i
$313$	−6.86004	−	11.8819i	−0.387752	−	0.671607i	0.604394	−	0.796685i	$-0.293415\pi$
$313$	−6.86004	−	11.8819i	−0.387752	−	0.671607i	−0.992147	+	0.125078i	$0.960082\pi$
$314$	−15.4434	+	26.7488i	−0.871523	+	1.50952i
$315$	7.32234	−	1.90011i	0.412567	−	0.107059i
$316$	−0.00372197	−	0.00644664i	−0.000209377	−	0.000362652i
$317$	−2.13847	−	3.70393i	−0.120108	−	0.208034i	0.799702	−	0.600397i	$-0.204991\pi$
$317$	−2.13847	−	3.70393i	−0.120108	−	0.208034i	−0.919810	+	0.392364i	$0.871658\pi$
$318$	6.67796			0.374482
$319$	−13.8733			−0.776754
$320$	−11.4264	−	19.7911i	−0.638756	−	1.10636i
$321$	6.68305	+	11.5754i	0.373011	+	0.646075i
$322$	2.89105	−	0.750212i	0.161112	−	0.0418077i
$323$	2.10759	−	3.65045i	0.117269	−	0.203117i
$324$	−0.000924008	−	0.00160043i	−5.13338e−5	−	8.89127e-5i
$325$	0.0213889	−	11.4487i	0.00118644	−	0.635060i
$326$	−8.04657	+	13.9371i	−0.445658	+	0.771902i
$327$	0.942194			0.0521034
$328$	−16.0609	+	27.8182i	−0.886813	+	1.53601i
$329$	0.500453	+	0.508428i	0.0275909	+	0.0280306i
$330$	−9.33306			−0.513768
$331$	−5.83057	+	10.0988i	−0.320477	+	0.555083i	−0.980587	−	0.196087i	$-0.937177\pi$
$331$	−5.83057	+	10.0988i	−0.320477	+	0.555083i	0.660109	+	0.751170i	$0.270510\pi$
$332$	0.0300438			0.00164887
$333$	−1.15073	+	1.99313i	−0.0630598	+	0.109223i
$334$	−0.371847	+	0.644057i	−0.0203465	+	0.0352412i
$335$	−4.53860	+	7.86109i	−0.247970	+	0.429497i
$336$	7.43078	+	7.54920i	0.405382	+	0.411842i
$337$	−16.2903			−0.887387			−0.443693	−	0.896179i	$-0.646332\pi$
$337$	−16.2903			−0.887387			−0.443693	+	0.896179i	$0.646332\pi$
$338$	−9.25609	+	15.8946i	−0.503465	+	0.864550i
$339$	−1.28957	+	2.23360i	−0.0700400	+	0.121313i
$340$	0.0196870	+	0.0340988i	0.00106768	+	0.00184927i
$341$	17.5506			0.950420
$342$	0.400176	+	0.693125i	0.0216390	+	0.0374799i
$343$	13.4026	−	12.7816i	0.723674	−	0.690142i
$344$	−10.6567	−	18.4579i	−0.574570	−	0.995184i
$345$	1.14068	−	1.97572i	0.0614121	−	0.106369i
$346$	−6.46960	+	11.2057i	−0.347808	+	0.602421i
$347$	25.7112			1.38025			0.690126	−	0.723689i	$-0.257555\pi$
$347$	25.7112			1.38025			0.690126	+	0.723689i	$0.257555\pi$
$348$	−0.0111129			−0.000595715
$349$	−0.908371	+	1.57334i	−0.0486240	+	0.0842192i	−0.889313	−	0.457299i	$-0.848817\pi$
$349$	−0.908371	+	1.57334i	−0.0486240	+	0.0842192i	0.840689	+	0.541518i	$0.182150\pi$
$350$	3.16708	−	11.4567i	0.169288	−	0.612386i
$351$	−3.12586	+	1.79694i	−0.166846	+	0.0959135i
$352$	−0.0120589	−	0.0208866i	−0.000642741	−	0.00111326i
$353$	0.0312072	+	0.0540524i	0.00166099	+	0.00287692i	0.866855	−	0.498561i	$-0.166138\pi$
$353$	0.0312072	+	0.0540524i	0.00166099	+	0.00287692i	−0.865194	+	0.501438i	$0.832805\pi$
$354$	−4.11854	−	7.13352i	−0.218898	−	0.379142i
$355$	−8.60762	+	14.9088i	−0.456845	+	0.791279i
$356$	−0.00262121			−0.000138924
$357$	13.8301	+	14.0505i	0.731965	+	0.743629i
$358$	−1.21881	−	2.11104i	−0.0644160	−	0.111572i
$359$	−6.71414	−	11.6292i	−0.354359	−	0.613767i	0.632649	−	0.774438i	$-0.281967\pi$
$359$	−6.71414	−	11.6292i	−0.354359	−	0.613767i	−0.987008	+	0.160671i	$0.948634\pi$
$360$	8.08344			0.426034
$361$	9.34001	+	16.1774i	0.491579	+	0.851440i
$362$	5.62725			0.295762
$363$	−5.67753			−0.297993
$364$	−0.0125868	+	0.0123431i	−0.000659726	+	0.000646956i
$365$	−30.4109			−1.59178
$366$	4.15126			0.216990
$367$	−10.6716	−	18.4837i	−0.557052	−	0.964843i	−0.997741	−	0.0671828i	$-0.978599\pi$
$367$	−10.6716	−	18.4837i	−0.557052	−	0.964843i	0.440688	−	0.897660i	$-0.354734\pi$
$368$	3.19450			0.166525
$369$	−5.68100	−	9.83978i	−0.295741	−	0.512239i
$370$	4.65524	+	8.06311i	0.242014	+	0.419181i
$371$	3.32726	−	12.0361i	0.172743	−	0.624885i
$372$	0.0140586			0.000728904
$373$	−14.3838	+	24.9135i	−0.744767	+	1.28997i	0.205537	+	0.978649i	$0.434106\pi$
$373$	−14.3838	+	24.9135i	−0.744767	+	1.28997i	−0.950304	+	0.311325i	$0.899227\pi$
$374$	−12.1617	−	21.0646i	−0.628865	−	1.08923i
$375$	2.60863	+	4.51828i	0.134709	+	0.233323i
$376$	0.381157	+	0.660183i	0.0196567	+	0.0340463i
$377$	−0.0405066	+	21.6817i	−0.00208620	+	1.11666i
$378$	−3.62338	+	0.940248i	−0.186366	+	0.0483611i
$379$	9.71923	−	16.8342i	0.499244	−	0.864715i	−0.500756	−	0.865588i	$-0.666945\pi$
$379$	9.71923	−	16.8342i	0.499244	−	0.864715i	1.00000		0.000873266i	$0.000277969\pi$
$380$	0.00298898			0.000153331
$381$	4.12629			0.211396
$382$	17.7944	−	30.8208i	0.910440	−	1.57693i
$383$	−15.1306	+	26.2069i	−0.773137	+	1.33911i	0.162699	+	0.986676i	$0.447980\pi$
$383$	−15.1306	+	26.2069i	−0.773137	+	1.33911i	−0.935836	+	0.352437i	$0.885353\pi$
$384$	5.66468	+	9.81152i	0.289075	+	0.500692i
$385$	−4.65015	+	16.8216i	−0.236994	+	0.857307i
$386$	−12.8437	−	22.2459i	−0.653726	−	1.13229i
$387$	7.53890			0.383224
$388$	−0.00966604	−	0.0167421i	−0.000490719	−	0.000849950i
$389$	0.308324	−	0.534034i	0.0156327	−	0.0270766i	−0.858103	−	0.513477i	$-0.828357\pi$
$389$	0.308324	−	0.534034i	0.0156327	−	0.0270766i	0.873736	+	0.486401i	$0.161690\pi$
$390$	−0.0272503	+	14.5861i	−0.00137987	+	0.738595i
$391$	5.94556			0.300680
$392$	17.2928	−	9.62275i	0.873417	−	0.486022i
$393$	3.77229	−	6.53379i	0.190287	−	0.329586i
$394$	−1.10714	+	1.91762i	−0.0557769	+	0.0966084i
$395$	−5.75863	+	9.97424i	−0.289748	+	0.501858i
$396$	0.00426346			0.000214247
$397$	−14.7888	+	25.6149i	−0.742227	+	1.28557i	0.209252	+	0.977862i	$0.432897\pi$
$397$	−14.7888	+	25.6149i	−0.742227	+	1.28557i	−0.951479	+	0.307713i	$0.900436\pi$
$398$	21.3873			1.07205
$399$	1.44865	−	0.375917i	0.0725232	−	0.0188194i
$400$	6.35647	−	11.0097i	0.317823	−	0.550486i
$401$	−19.8474			−0.991130			−0.495565	−	0.868571i	$-0.665039\pi$
$401$	−19.8474			−0.991130			−0.495565	+	0.868571i	$0.665039\pi$
$402$	2.24588	−	3.88997i	0.112014	−	0.194014i
$403$	0.0512436	−	27.4288i	0.00255263	−	1.36633i
$404$	0.00875483	+	0.0151638i	0.000435569	+	0.000754427i
$405$	−1.42962	+	2.47618i	−0.0710386	+	0.123042i
$406$	−5.99786	+	21.6968i	−0.297669	+	1.07680i
$407$	−2.65480	−	4.59824i	−0.131593	−	0.227926i
$408$	10.5333	+	18.2442i	0.521477	+	0.903224i
$409$	23.5323			1.16360			0.581800	−	0.813332i	$-0.302349\pi$
$409$	23.5323			1.16360			0.581800	+	0.813332i	$0.302349\pi$
$410$	−45.9645			−2.27002
$411$	−8.34991	−	14.4625i	−0.411871	−	0.713381i
$412$	−0.0187449	−	0.0324671i	−0.000923495	−	0.00159954i
$413$	−14.9092	+	3.86887i	−0.733636	+	0.190375i
$414$	−0.564452	+	0.977660i	−0.0277413	+	0.0480494i
$415$	−23.2419	−	40.2561i	−1.14090	−	1.97610i
$416$	−0.0326776	+	0.0187851i	−0.00160215	+	0.000921016i
$417$	−5.17295	+	8.95981i	−0.253320	+	0.438764i
$418$	−1.84645			−0.0903128
$419$	17.6833	−	30.6285i	0.863888	−	1.49630i	−0.00425910	−	0.999991i	$-0.501356\pi$
$419$	17.6833	−	30.6285i	0.863888	−	1.49630i	0.868147	−	0.496307i	$-0.165311\pi$
$420$	−0.00372491	+	0.0134746i	−0.000181757	+	0.000657494i
$421$	−10.1261			−0.493514			−0.246757	−	0.969077i	$-0.579365\pi$
$421$	−10.1261			−0.493514			−0.246757	+	0.969077i	$0.579365\pi$
$422$	11.7272	−	20.3120i	0.570869	−	0.988774i
$423$	−0.269643			−0.0131105
$424$	6.67179	−	11.5559i	0.324011	−	0.561203i
$425$	11.8306	−	20.4912i	0.573867	−	0.993967i
$426$	4.25939	−	7.37747i	0.206368	−	0.357440i
$427$	2.06834	−	7.48209i	0.100094	−	0.362084i
$428$	−0.0247008			−0.00119396
$429$	0.0155403	−	8.31817i	0.000750295	−	0.401605i
$430$	15.2491	−	26.4123i	0.735379	−	1.27371i
$431$	3.12150	+	5.40659i	0.150357	+	0.260426i	0.931359	−	0.364103i	$-0.118624\pi$
$431$	3.12150	+	5.40659i	0.150357	+	0.260426i	−0.781002	+	0.624529i	$0.785291\pi$
$432$	−4.00369			−0.192628
$433$	16.9222	+	29.3101i	0.813229	+	1.40855i	0.910593	+	0.413305i	$0.135626\pi$
$433$	16.9222	+	29.3101i	0.813229	+	1.40855i	−0.0973634	+	0.995249i	$0.531041\pi$
$434$	7.58769	−	27.4479i	0.364221	−	1.31754i
$435$	8.59695	+	14.8903i	0.412192	+	0.713938i
$436$	−0.000870595		0.00150791i	−4.16939e−5		7.22160e-5i
$437$	0.225672	−	0.390875i	0.0107953	−	0.0186981i
$438$	15.0485			0.719045
$439$	8.87482			0.423572			0.211786	−	0.977316i	$-0.432072\pi$
$439$	8.87482			0.423572			0.211786	+	0.977316i	$0.432072\pi$
$440$	−9.32444	+	16.1504i	−0.444525	+	0.769940i
$441$	−0.110659	+	6.99913i	−0.00526947	+	0.333292i
$442$	−32.9561	+	18.9452i	−1.56756	+	0.901132i
$443$	5.95160	+	10.3085i	0.282769	+	0.489770i	0.972066	−	0.234709i	$-0.0754136\pi$
$443$	5.95160	+	10.3085i	0.282769	+	0.489770i	−0.689297	+	0.724479i	$0.742080\pi$
$444$	−0.00212657	−	0.00368333i	−0.000100923	−	0.000174803i
$445$	2.02776	+	3.51219i	0.0961252	+	0.166494i
$446$	−4.38940	+	7.60266i	−0.207844	+	0.359996i
$447$	−12.2446			−0.579149
$448$	20.4685	−	5.31147i	0.967045	−	0.250943i
$449$	2.97292	+	5.14925i	0.140301	+	0.243008i	0.927610	−	0.373550i	$-0.121860\pi$
$449$	2.97292	+	5.14925i	0.140301	+	0.243008i	−0.787309	+	0.616558i	$0.788526\pi$
$450$	2.24632	+	3.89073i	0.105892	+	0.183411i
$451$	26.2127			1.23431
$452$	−0.00238315	−	0.00412774i	−0.000112094	−	0.000194153i
$453$	18.0867			0.849786
$454$	2.17980			0.102303
$455$	26.2759	+	7.31655i	1.23183	+	0.343005i
$456$	1.59922			0.0748905
$457$	12.1123			0.566588			0.283294	−	0.959033i	$-0.408573\pi$
$457$	12.1123			0.566588			0.283294	+	0.959033i	$0.408573\pi$
$458$	−15.0995	−	26.1531i	−0.705552	−	1.22205i
$459$	−7.45162			−0.347812
$460$	0.00210800	+	0.00365115i	9.82858e−5	+	0.000170236i
$461$	−2.55673	−	4.42839i	−0.119079	−	0.206251i	0.800324	−	0.599568i	$-0.204661\pi$
$461$	−2.55673	−	4.42839i	−0.119079	−	0.206251i	−0.919403	+	0.393317i	$0.871327\pi$
$462$	2.30107	−	8.32397i	0.107056	−	0.387266i
$463$	−38.9344			−1.80944			−0.904718	−	0.426010i	$-0.859919\pi$
$463$	−38.9344			−1.80944			−0.904718	+	0.426010i	$0.859919\pi$
$464$	−12.0380	+	20.8504i	−0.558848	+	0.967954i
$465$	−10.8757	−	18.8373i	−0.504349	−	0.873559i
$466$	6.10454	+	10.5734i	0.282787	+	0.489802i
$467$	7.02626	+	12.1698i	0.325136	+	0.563153i	0.981540	−	0.191257i	$-0.0612564\pi$
$467$	7.02626	+	12.1698i	0.325136	+	0.563153i	−0.656404	+	0.754410i	$0.727923\pi$
$468$	1.24483e−5	−	0.00666311i	5.75423e−7	−	0.000308002i
$469$	−5.89215	−	5.98604i	−0.272074	−	0.276410i
$470$	−0.545415	+	0.944687i	−0.0251581	+	0.0435752i
$471$	−21.8302			−1.00588
$472$	−16.4589			−0.757584
$473$	−8.69630	+	15.0624i	−0.399856	+	0.692571i
$474$	2.84959	−	4.93564i	0.130886	−	0.226701i
$475$	−0.898091	−	1.55554i	−0.0412073	−	0.0713731i
$476$	−0.0352659	+	0.00915132i	−0.00161641	+	0.000419450i
$477$	2.35993	+	4.08751i	0.108054	+	0.187154i
$478$	−28.7533			−1.31514
$479$	16.1368	+	27.9497i	0.737308	+	1.27705i	0.953703	+	0.300749i	$0.0972366\pi$
$479$	16.1368	+	27.9497i	0.737308	+	1.27705i	−0.216395	+	0.976306i	$0.569430\pi$
$480$	−0.0149452	+	0.0258859i	−0.000682153	+	0.00118152i
$481$	−7.19406	+	4.13559i	−0.328021	+	0.188567i
$482$	−36.9497			−1.68301
$483$	1.48087	+	1.50446i	0.0673817	+	0.0684555i
$484$	0.00524608	−	0.00908648i	0.000238458	−	0.000413022i
$485$	−14.9553	+	25.9033i	−0.679084	+	1.17621i
$486$	0.707433	−	1.22531i	0.0320898	−	0.0555812i
$487$	−12.2816			−0.556533			−0.278266	−	0.960504i	$-0.589760\pi$
$487$	−12.2816			−0.556533			−0.278266	+	0.960504i	$0.589760\pi$
$488$	4.14743	−	7.18355i	0.187745	−	0.325184i
$489$	−11.3743			−0.514364
$490$	24.2974	+	14.5450i	1.09764	+	0.657077i
$491$	−10.8531	+	18.7981i	−0.489792	+	0.848345i	−0.999931	−	0.0117472i	$-0.996261\pi$
$491$	−10.8531	+	18.7981i	−0.489792	+	0.848345i	0.510139	+	0.860092i	$0.329594\pi$
$492$	0.0209972			0.000946625
$493$	−22.4049	+	38.8064i	−1.00907	+	1.74775i
$494$	−0.00539119	+	2.88570i	−0.000242561	+	0.129834i
$495$	−3.29821	−	5.71267i	−0.148244	−	0.256765i
$496$	15.2288	−	26.3771i	0.683795	−	1.18437i
$497$	−11.1747	−	11.3528i	−0.501253	−	0.509241i
$498$	11.5010	+	19.9203i	0.515371	+	0.892649i
$499$	−4.93997	−	8.55628i	−0.221143	−	0.383032i	0.734012	−	0.679136i	$-0.237646\pi$
$499$	−4.93997	−	8.55628i	−0.221143	−	0.383032i	−0.955155	+	0.296105i	$0.904312\pi$
$500$	−0.00964159			−0.000431185
$501$	−0.525628			−0.0234833
$502$	15.9537	+	27.6326i	0.712047	+	1.23330i
$503$	−17.2279	−	29.8396i	−0.768155	−	1.33048i	−0.938562	−	0.345110i	$-0.887842\pi$
$503$	−17.2279	−	29.8396i	−0.768155	−	1.33048i	0.170407	−	0.985374i	$-0.445492\pi$
$504$	−1.99298	+	7.20946i	−0.0887743	+	0.321135i
$505$	13.5455	−	23.4614i	0.602765	−	1.04402i
$506$	−1.30222	−	2.25551i	−0.0578907	−	0.100270i
$507$	−12.9999	−	0.0485741i	−0.577346	−	0.00215725i
$508$	−0.00381272	+	0.00660383i	−0.000169162	+	0.000292998i
$509$	10.8665			0.481648			0.240824	−	0.970569i	$-0.422582\pi$
$509$	10.8665			0.481648			0.240824	+	0.970569i	$0.422582\pi$
$510$	−15.0726	+	26.1065i	−0.667426	+	1.15602i
$511$	7.49784	−	27.1229i	0.331685	−	1.19985i
$512$	22.5960			0.998610
$513$	−0.282836	+	0.489887i	−0.0124875	+	0.0216290i
$514$	1.51735			0.0669274
$515$	−29.0021	+	50.2331i	−1.27798	+	2.21353i
$516$	−0.00696600	+	0.0120655i	−0.000306661	+	0.000531153i
$517$	0.311040	−	0.538737i	0.0136795	−	0.0236936i
$518$	−8.33908	+	2.16395i	−0.366398	+	0.0950784i
$519$	−9.14517			−0.401429
$520$	25.2133	+	14.6198i	1.10567	+	0.641119i
$521$	19.0141	−	32.9334i	0.833024	−	1.44284i	−0.0626059	−	0.998038i	$-0.519941\pi$
$521$	19.0141	−	32.9334i	0.833024	−	1.44284i	0.895630	−	0.444801i	$-0.146726\pi$
$522$	−4.25410	−	7.36832i	−0.186197	−	0.322503i
$523$	27.2284			1.19061			0.595307	−	0.803498i	$-0.297030\pi$
$523$	27.2284			1.19061			0.595307	+	0.803498i	$0.297030\pi$
$524$	0.00697125	+	0.0120746i	0.000304540	+	0.000527479i
$525$	8.13174	−	2.11014i	0.354898	−	0.0920942i
$526$	10.9434	+	18.9545i	0.477153	+	0.826453i
$527$	28.3437	−	49.0927i	1.23467	−	2.13851i
$528$	4.61836	−	7.99923i	0.200988	−	0.348122i
$529$	−22.3634			−0.972321
$530$	19.0940			0.829389
$531$	2.91090	−	5.04183i	0.126322	−	0.218797i
$532$	−0.000736936		0.00266581i	−3.19502e−5		0.000115578i
$533$	0.0765348	−	40.9662i	0.00331509	−	1.77444i
$534$	−1.00342	−	1.73797i	−0.0434220	−	0.0752092i
$535$	19.1085	+	33.0969i	0.826132	+	1.43090i
$536$	−4.48760	−	7.77275i	−0.193835	−	0.335732i
$537$	0.861430	−	1.49204i	0.0371734	−	0.0643863i
$538$	−3.16622			−0.136505
$539$	−13.8563	−	8.29475i	−0.596835	−	0.357280i
$540$	−0.00264197	−	0.00457603i	−0.000113692	−	0.000196921i
$541$	−19.4083	−	33.6162i	−0.834430	−	1.44528i	−0.894494	−	0.447081i	$-0.852464\pi$
$541$	−19.4083	−	33.6162i	−0.834430	−	1.44528i	0.0600635	−	0.998195i	$-0.480870\pi$
$542$	−8.69350			−0.373418
$543$	1.98862	+	3.44438i	0.0853397	+	0.147813i
$544$	−0.0778989			−0.00333989
$545$	2.69397			0.115397
$546$	−13.0023	−	3.62051i	−0.556447	−	0.154944i
$547$	−8.34899			−0.356977			−0.178489	−	0.983942i	$-0.557121\pi$
$547$	−8.34899			−0.356977			−0.178489	+	0.983942i	$0.557121\pi$
$548$	0.0308616			0.00131834
$549$	1.46702	+	2.54094i	0.0626107	+	0.108445i
$550$	−10.3647			−0.441953
$551$	1.70082	+	2.94590i	0.0724572	+	0.125500i
$552$	1.12786	+	1.95351i	0.0480050	+	0.0831471i
$553$	−7.47603	−	7.59516i	−0.317913	−	0.322979i
$554$	4.73736			0.201271
$555$	−3.29023	+	5.69885i	−0.139663	+	0.241903i
$556$	−0.00955969	−	0.0165579i	−0.000405421	−	0.000702210i
$557$	−10.1701	−	17.6151i	−0.430921	−	0.746377i	0.566032	−	0.824383i	$-0.308478\pi$
$557$	−10.1701	−	17.6151i	−0.430921	−	0.746377i	−0.996953	+	0.0780065i	$0.975145\pi$
$558$	5.38172	+	9.32142i	0.227827	+	0.394607i
$559$	23.5148	+	13.6349i	0.994569	+	0.576695i
$560$	21.2465	+	21.5850i	0.897827	+	0.912134i
$561$	8.59562	−	14.8881i	0.362908	−	0.628574i
$562$	20.1077			0.848191
$563$	−3.65384			−0.153991			−0.0769955	−	0.997031i	$-0.524533\pi$
$563$	−3.65384			−0.153991			−0.0769955	+	0.997031i	$0.524533\pi$
$564$	0.000249153	0	0.000431545i	1.04912e−5	0	1.81713e-5i
$565$	−3.68721	+	6.38643i	−0.155122	+	0.268679i
$566$	10.3486	+	17.9243i	0.434983	+	0.753413i
$567$	−1.85598	−	1.88556i	−0.0779439	−	0.0791860i
$568$	−8.51090	−	14.7413i	−0.357109	−	0.618532i
$569$	5.38814			0.225883			0.112941	−	0.993602i	$-0.463973\pi$
$569$	5.38814			0.225883			0.112941	+	0.993602i	$0.463973\pi$
$570$	1.14420	+	1.98182i	0.0479254	+	0.0830092i
$571$	−3.46902	+	6.00851i	−0.145174	+	0.251448i	−0.929438	−	0.368979i	$-0.879707\pi$
$571$	−3.46902	+	6.00851i	−0.145174	+	0.251448i	0.784264	+	0.620427i	$0.213041\pi$
$572$	0.0132983	+	0.00771092i	0.000556029	+	0.000322410i
$573$	25.1534			1.05080
$574$	11.3326	−	40.9948i	0.473013	−	1.71109i
$575$	1.26677	−	2.19411i	0.0528279	−	0.0915005i
$576$	−3.99630	+	6.92179i	−0.166512	+	0.288408i
$577$	−4.66974	+	8.08823i	−0.194404	+	0.336718i	−0.946705	−	0.322102i	$-0.895611\pi$
$577$	−4.66974	+	8.08823i	−0.194404	+	0.336718i	0.752301	+	0.658820i	$0.228944\pi$
$578$	−54.5101			−2.26732
$579$	9.07766	−	15.7230i	0.377255	−	0.653425i
$580$	−0.0317746			−0.00131937
$581$	41.6339	−	10.8038i	1.72727	−	0.448217i
$582$	7.40045	−	12.8180i	0.306759	−	0.531322i
$583$	−10.8889			−0.450973
$584$	15.0346	−	26.0407i	0.622136	−	1.07757i
$585$	−8.93762	+	5.13790i	−0.369525	+	0.212426i
$586$	15.2414	+	26.3988i	0.629615	+	1.09053i
$587$	−11.8226	+	20.4774i	−0.487972	+	0.845192i	−0.999904	−	0.0138340i	$-0.995596\pi$
$587$	−11.8226	+	20.4774i	−0.487972	+	0.845192i	0.511933	+	0.859026i	$0.328930\pi$
$588$	−0.0110994	−	0.00664435i	−0.000457730	−	0.000274008i
$589$	−2.15165	−	3.72676i	−0.0886571	−	0.153559i
$590$	−11.7759	−	20.3965i	−0.484807	−	0.839710i
$591$	−1.56501			−0.0643758
$592$	−9.21436			−0.378708
$593$	6.02330	+	10.4327i	0.247347	+	0.428418i	0.962789	−	0.270254i	$-0.0871078\pi$
$593$	6.02330	+	10.4327i	0.247347	+	0.428418i	−0.715442	+	0.698673i	$0.753774\pi$
$594$	1.63208	+	2.82685i	0.0669652	+	0.115987i
$595$	39.5436	+	40.1738i	1.62113	+	1.64696i
$596$	0.0113141	−	0.0195966i	0.000463444	−	0.000802708i
$597$	7.55805	+	13.0909i	0.309330	+	0.535776i
$598$	−3.52880	+	2.02857i	−0.144303	+	0.0829545i
$599$	3.07545	−	5.32684i	0.125660	−	0.217649i	−0.796331	−	0.604861i	$-0.793229\pi$
$599$	3.07545	−	5.32684i	0.125660	−	0.217649i	0.921991	+	0.387212i	$0.126562\pi$
$600$	8.97696			0.366483
$601$	2.33860	−	4.05057i	0.0953934	−	0.165226i	−0.814379	−	0.580333i	$-0.802922\pi$
$601$	2.33860	−	4.05057i	0.0953934	−	0.165226i	0.909773	+	0.415107i	$0.136256\pi$
$602$	19.7969	+	20.1124i	0.806861	+	0.819719i
$603$	3.17468			0.129283
$604$	−0.0167122	+	0.0289464i	−0.000680011	+	0.00117781i
$605$	−16.2335			−0.659984
$606$	−6.70281	+	11.6096i	−0.272283	+	0.471608i
$607$	7.65004	−	13.2502i	0.310505	−	0.537811i	−0.667967	−	0.744191i	$-0.732835\pi$
$607$	7.65004	−	13.2502i	0.310505	−	0.537811i	0.978472	+	0.206380i	$0.0661684\pi$
$608$	−0.00295676	+	0.00512126i	−0.000119912	+	0.000207694i
$609$	−15.4000	+	3.99622i	−0.624039	+	0.161935i
$610$	11.8695			0.480582
$611$	−0.841051	−	0.487679i	−0.0340253	−	0.0197294i
$612$	0.00688536	−	0.0119258i	0.000278324	−	0.000482072i
$613$	−5.76413	−	9.98376i	−0.232811	−	0.403240i	0.725823	−	0.687881i	$-0.241459\pi$
$613$	−5.76413	−	9.98376i	−0.232811	−	0.403240i	−0.958634	+	0.284641i	$0.908126\pi$
$614$	−26.3811			−1.06466
$615$	−16.2434	−	28.1344i	−0.654997	−	1.13449i
$616$	−12.1053	−	12.2982i	−0.487735	−	0.495508i
$617$	10.2940	+	17.8298i	0.414423	+	0.717801i	0.995368	−	0.0961418i	$-0.0306502\pi$
$617$	10.2940	+	17.8298i	0.414423	+	0.717801i	−0.580945	+	0.813943i	$0.697317\pi$
$618$	14.3514	−	24.8573i	0.577296	−	0.999906i
$619$	−9.83404	+	17.0331i	−0.395263	+	0.684616i	−0.993135	−	0.116976i	$-0.962680\pi$
$619$	−9.83404	+	17.0331i	−0.395263	+	0.684616i	0.597871	+	0.801592i	$0.296013\pi$
$620$	0.0401970			0.00161435
$621$	−0.797888			−0.0320181
$622$	0.818393	−	1.41750i	0.0328146	−	0.0568365i
$623$	−3.63240	+	0.942589i	−0.145529	+	0.0377640i
$624$	−12.4880	−	7.24110i	−0.499921	−	0.289876i
$625$	15.3970	+	26.6684i	0.615879	+	1.06673i
$626$	9.70605	+	16.8114i	0.387932	+	0.671917i
$627$	−0.652517	−	1.13019i	−0.0260590	−	0.0451356i
$628$	0.0201713	−	0.0349377i	0.000804922	−	0.00139417i
$629$	−17.1496			−0.683801
$630$	−10.3601	+	2.68840i	−0.412758	+	0.107109i
$631$	21.7095	+	37.6019i	0.864241	+	1.49691i	0.867799	+	0.496916i	$0.165534\pi$
$631$	21.7095	+	37.6019i	0.864241	+	1.49691i	−0.00355775	+	0.999994i	$0.501132\pi$
$632$	−5.69392	−	9.86215i	−0.226492	−	0.392295i
$633$	16.5770			0.658878
$634$	3.02565	+	5.24057i	0.120164	+	0.208130i
$635$	11.7981			0.468192
$636$	−0.00872237			−0.000345864
$637$	−13.0038	+	21.6310i	−0.515230	+	0.857052i
$638$	19.6288			0.777113
$639$	6.02090			0.238183
$640$	16.1967	+	28.0536i	0.640232	+	1.10891i
$641$	26.9811			1.06569			0.532844	−	0.846214i	$-0.321123\pi$
$641$	26.9811			1.06569			0.532844	+	0.846214i	$0.321123\pi$
$642$	−9.45562	−	16.3776i	−0.373184	−	0.646373i
$643$	−2.55705	−	4.42895i	−0.100840	−	0.174661i	0.811191	−	0.584782i	$-0.198820\pi$
$643$	−2.55705	−	4.42895i	−0.100840	−	0.174661i	−0.912031	+	0.410121i	$0.865486\pi$
$644$	−0.00377612		0.000979884i	−0.000148800		3.86128e-5i
$645$	21.5556			0.848750
$646$	−2.98196	+	5.16490i	−0.117324	+	0.203210i
$647$	−9.77239	−	16.9263i	−0.384192	−	0.665440i	0.607465	−	0.794347i	$-0.292187\pi$
$647$	−9.77239	−	16.9263i	−0.384192	−	0.665440i	−0.991657	+	0.128906i	$0.958853\pi$
$648$	−1.41356	−	2.44836i	−0.0555299	−	0.0961805i
$649$	6.71559	+	11.6317i	0.263610	+	0.456586i
$650$	−0.0302625	+	16.1984i	−0.00118699	+	0.635353i
$651$	19.4820	−	5.05548i	0.763561	−	0.198140i
$652$	0.0105100	−	0.0182038i	0.000411602	−	0.000712915i
$653$	15.3626			0.601186			0.300593	−	0.953753i	$-0.402815\pi$
$653$	15.3626			0.601186			0.300593	+	0.953753i	$0.402815\pi$
$654$	−1.33308			−0.0521275
$655$	10.7859	−	18.6817i	0.421440	−	0.729956i
$656$	22.7450	−	39.3955i	0.888042	−	1.53813i
$657$	5.31799	+	9.21103i	0.207475	+	0.359356i
$658$	−0.708075	−	0.719358i	−0.0276036	−	0.0280435i
$659$	−8.71206	−	15.0897i	−0.339374	−	0.587813i	0.644941	−	0.764232i	$-0.276882\pi$
$659$	−8.71206	−	15.0897i	−0.339374	−	0.587813i	−0.984315	+	0.176420i	$0.943548\pi$
$660$	0.0121903			0.000474507
$661$	−8.35831	−	14.4770i	−0.325101	−	0.563091i	0.656432	−	0.754385i	$-0.272065\pi$
$661$	−8.35831	−	14.4770i	−0.325101	−	0.563091i	−0.981533	+	0.191294i	$0.938732\pi$
$662$	8.24948	−	14.2885i	0.320625	−	0.555339i
$663$	−23.2425	−	13.4770i	−0.902666	−	0.523405i
$664$	45.9614			1.78365
$665$	4.14205	−	1.07484i	0.160622	−	0.0416805i
$666$	1.62813	−	2.82001i	0.0630889	−	0.109273i
$667$	−2.39902	+	4.15523i	−0.0928905	+	0.160891i
$668$	0.000485684	0	0.000841230i	1.87917e−5	0	3.25482e-5i
$669$	−6.20468			−0.239887
$670$	6.42152	−	11.1224i	0.248085	−	0.429695i
$671$	−6.76895			−0.261312
$672$	−0.0194024	−	0.0197115i	−0.000748462	−	0.000760389i
$673$	−15.0178	+	26.0116i	−0.578894	+	1.00267i	0.416713	+	0.909038i	$0.363182\pi$
$673$	−15.0178	+	26.0116i	−0.578894	+	1.00267i	−0.995607	+	0.0936354i	$0.970151\pi$
$674$	23.0485			0.887797
$675$	−1.58765	+	2.74989i	−0.0611087	+	0.105843i
$676$	0.0120898	−	0.0207606i	0.000464991	−	0.000798483i
$677$	1.91898	+	3.32377i	0.0737525	+	0.127743i	0.900543	−	0.434767i	$-0.143169\pi$
$677$	1.91898	+	3.32377i	0.0737525	+	0.127743i	−0.826791	+	0.562510i	$0.809836\pi$
$678$	1.82457	−	3.16025i	0.0700723	−	0.121369i
$679$	−19.4154	−	19.7248i	−0.745095	−	0.756968i
$680$	30.1174	+	52.1648i	1.15495	+	2.00043i
$681$	0.770318	+	1.33423i	0.0295187	+	0.0511278i
$682$	−24.8318			−0.950859
$683$	27.9568			1.06974			0.534868	−	0.844935i	$-0.320361\pi$
$683$	27.9568			1.06974			0.534868	+	0.844935i	$0.320361\pi$
$684$	−0.000522686	0	0.000905319i	−1.99854e−5	0	3.46157e-5i
$685$	−23.8745	−	41.3518i	−0.912197	−	1.57997i
$686$	−18.9629	+	18.0843i	−0.724009	+	0.690460i
$687$	10.6720	−	18.4845i	0.407163	−	0.705227i
$688$	15.0917	+	26.1396i	0.575366	+	0.996563i
$689$	−0.0317931	+	17.0176i	−0.00121122	+	0.648321i
$690$	−1.61391	+	2.79537i	−0.0614405	+	0.106418i
$691$	−17.9471			−0.682738			−0.341369	−	0.939929i	$-0.610891\pi$
$691$	−17.9471			−0.682738			−0.341369	+	0.939929i	$0.610891\pi$
$692$	0.00845022	−	0.0146362i	0.000321229	−	0.000556385i
$693$	5.90819	−	1.53315i	0.224434	−	0.0582394i
$694$	−36.3780			−1.38089
$695$	−14.7907	+	25.6183i	−0.561045	+	0.971758i
$696$	−17.0007			−0.644409
$697$	42.3327	−	73.3223i	1.60346	−	2.77728i
$698$	1.28522	−	2.22607i	0.0486464	−	0.0842581i
$699$	−4.31457	+	7.47305i	−0.163192	+	0.282657i
$700$	−0.00413666	+	0.0149641i	−0.000156351	+	0.000565588i
$701$	35.0636			1.32433			0.662167	−	0.749356i	$-0.269637\pi$
$701$	35.0636			1.32433			0.662167	+	0.749356i	$0.269637\pi$
$702$	4.42268	−	2.54243i	0.166923	−	0.0959578i
$703$	−0.650938	+	1.12746i	−0.0245506	+	0.0425229i
$704$	−9.21965	−	15.9689i	−0.347479	−	0.601851i
$705$	−0.770977			−0.0290367
$706$	−0.0441540	−	0.0764769i	−0.00166176	−	0.00287825i
$707$	17.5851	+	17.8654i	0.661357	+	0.671896i
$708$	0.00537939	+	0.00931738i	0.000202170	+	0.000350169i
$709$	3.82252	−	6.62079i	0.143558	−	0.248649i	−0.785276	−	0.619146i	$-0.787479\pi$
$709$	3.82252	−	6.62079i	0.143558	−	0.248649i	0.928834	+	0.370496i	$0.120812\pi$
$710$	12.1786	−	21.0940i	0.457056	−	0.791645i
$711$	4.02807			0.151064
$712$	−4.00995			−0.150279
$713$	3.03492	−	5.25664i	0.113659	−	0.196863i
$714$	−19.5677	−	19.8795i	−0.732303	−	0.743973i
$715$	0.0444337	−	23.7837i	0.00166173	−	0.889460i
$716$	0.00159194	+	0.00275732i	5.94935e−5	+	0.000103046i
$717$	−10.1611	−	17.5996i	−0.379474	−	0.657268i
$718$	9.49961	+	16.4538i	0.354522	+	0.614051i
$719$	−13.9765	+	24.2081i	−0.521237	+	0.902809i	0.478458	+	0.878111i	$0.341196\pi$
$719$	−13.9765	+	24.2081i	−0.521237	+	0.902809i	−0.999695	+	0.0246986i	$0.992137\pi$
$720$	−11.4476			−0.426625
$721$	−37.6514	−	38.2514i	−1.40221	−	1.42456i
$722$	−13.2149	−	22.8888i	−0.491806	−	0.851834i
$723$	−13.0577	−	22.6166i	−0.485620	−	0.841119i
$724$	−0.00734999			−0.000273160
$725$	9.54723	+	16.5363i	0.354575	+	0.614142i
$726$	8.03295			0.298131
$727$	−9.94798			−0.368950			−0.184475	−	0.982837i	$-0.559058\pi$
$727$	−9.94798			−0.368950			−0.184475	+	0.982837i	$0.559058\pi$
$728$	−19.2554	+	18.8827i	−0.713653	+	0.699839i
$729$	1.00000			0.0370370
$730$	43.0274			1.59252
$731$	28.0885	+	48.6507i	1.03889	+	1.79941i
$732$	−0.00542214			−0.000200408
$733$	−15.9308	−	27.5929i	−0.588416	−	1.01917i	−0.994440	−	0.105304i	$-0.966418\pi$
$733$	−15.9308	−	27.5929i	−0.588416	−	1.01917i	0.406024	−	0.913863i	$-0.366915\pi$
$734$	15.0989	+	26.1520i	0.557310	+	0.965289i
$735$	−0.316401	+	20.0122i	−0.0116706	+	0.738163i
$736$	−0.00834108			−0.000307456
$737$	−3.66207	+	6.34289i	−0.134894	+	0.233643i
$738$	8.03786	+	13.9220i	0.295878	+	0.512475i
$739$	9.07418	+	15.7169i	0.333799	+	0.578157i	0.983253	−	0.182244i	$-0.0583359\pi$
$739$	9.07418	+	15.7169i	0.333799	+	0.578157i	−0.649454	+	0.760401i	$0.725003\pi$
$740$	−0.00608040	−	0.0105316i	−0.000223520	−	0.000387148i
$741$	−1.76821	+	1.01648i	−0.0649570	+	0.0373413i
$742$	−4.70763	+	17.0295i	−0.172823	+	0.625174i
$743$	−12.8238	+	22.2115i	−0.470460	+	0.814861i	−0.999429	−	0.0337802i	$-0.989245\pi$
$743$	−12.8238	+	22.2115i	−0.470460	+	0.814861i	0.528969	+	0.848641i	$0.322579\pi$
$744$	21.5070			0.788485
$745$	−35.0103			−1.28268
$746$	20.3512	−	35.2493i	0.745111	−	1.29057i
$747$	−8.12867	+	14.0793i	−0.297412	+	0.515133i
$748$	0.0158849	+	0.0275134i	0.000580808	+	0.00100599i
$749$	−34.2297	+	8.88242i	−1.25072	+	0.324557i
$750$	−3.69087	−	6.39277i	−0.134771	−	0.233431i
$751$	−50.5739			−1.84547			−0.922734	−	0.385438i	$-0.874050\pi$
$751$	−50.5739			−1.84547			−0.922734	+	0.385438i	$0.874050\pi$
$752$	−0.539785	−	0.934934i	−0.0196839	−	0.0340935i
$753$	−11.2757	+	19.5301i	−0.410911	+	0.711718i
$754$	0.0573115	−	30.6767i	0.00208716	−	1.11718i
$755$	51.7143			1.88208
$756$	0.00473265	−	0.00122810i	0.000172125	−	4.46655e-5i
$757$	0.651718	−	1.12881i	0.0236871	−	0.0410272i	−0.853939	−	0.520373i	$-0.825793\pi$
$757$	0.651718	−	1.12881i	0.0236871	−	0.0410272i	0.877626	+	0.479346i	$0.159126\pi$
$758$	−13.7514	+	23.8182i	−0.499474	+	0.865115i
$759$	0.920383	−	1.59415i	0.0334078	−	0.0578640i
$760$	4.57258			0.165865
$761$	−7.67600	+	13.2952i	−0.278255	+	0.481952i	−0.970951	−	0.239278i	$-0.923089\pi$
$761$	−7.67600	+	13.2952i	−0.278255	+	0.481952i	0.692696	+	0.721229i	$0.256423\pi$
$762$	−5.83814			−0.211494
$763$	−0.664199	+	2.40269i	−0.0240456	+	0.0869834i
$764$	−0.0232420	+	0.0402563i	−0.000840866	+	0.00145642i
$765$	−21.3060			−0.770321
$766$	21.4078	−	37.0793i	0.773494	−	1.33973i
$767$	18.1981	−	10.4614i	0.657097	−	0.377740i
$768$	−0.0221762	−	0.0384103i	−0.000800214	−	0.00138601i
$769$	−9.84042	+	17.0441i	−0.354855	+	0.614626i	−0.987093	−	0.160148i	$-0.948803\pi$
$769$	−9.84042	+	17.0441i	−0.354855	+	0.614626i	0.632239	+	0.774774i	$0.282136\pi$
$770$	6.57934	−	23.8003i	0.237103	−	0.857703i
$771$	0.536216	+	0.928754i	0.0193114	+	0.0334483i
$772$	0.0167757	+	0.0290563i	0.000603770	+	0.00104576i
$773$	−18.3611			−0.660402			−0.330201	−	0.943911i	$-0.607117\pi$
$773$	−18.3611			−0.660402			−0.330201	+	0.943911i	$0.607117\pi$
$774$	−10.6665			−0.383401
$775$	−12.0779	−	20.9195i	−0.433851	−	0.751451i
$776$	−14.7872	−	25.6122i	−0.530831	−	0.919426i
$777$	−4.27148	−	4.33955i	−0.153238	−	0.155680i
$778$	−0.436238	+	0.755586i	−0.0156399	+	0.0270891i
$779$	−3.21359	−	5.56610i	−0.115139	−	0.199426i
$780$	3.55928e−5	−	0.0190515i	1.27443e−6	−	0.000682152i
$781$	−6.94525	+	12.0295i	−0.248521	+	0.430450i
$782$	−8.41217			−0.300819
$783$	3.00672	−	5.20778i	0.107451	−	0.186111i
$784$	−24.4896	+	13.6275i	−0.874628	+	0.486696i
$785$	−62.4180			−2.22779
$786$	−5.33728	+	9.24445i	−0.190375	+	0.329738i
$787$	−3.22399			−0.114923			−0.0574615	−	0.998348i	$-0.518301\pi$
$787$	−3.22399			−0.114923			−0.0574615	+	0.998348i	$0.518301\pi$
$788$	0.00144608	−	0.00250469i	5.15145e−5	−	8.92257e-5i
$789$	−7.73455	+	13.3966i	−0.275357	+	0.476933i
$790$	8.14769	−	14.1122i	0.289882	−	0.502090i
$791$	−4.78685	−	4.86313i	−0.170201	−	0.172913i
$792$	6.52230			0.231760
$793$	−0.0197637	+	10.5788i	−0.000701830	+	0.375663i
$794$	20.9241	−	36.2417i	0.742570	−	1.28617i
$795$	6.74762	+	11.6872i	0.239313	+	0.414503i
$796$	−0.0279348			−0.000990123
$797$	−7.59673	−	13.1579i	−0.269090	−	0.466078i	0.699537	−	0.714596i	$-0.253390\pi$
$797$	−7.59673	−	13.1579i	−0.269090	−	0.466078i	−0.968627	+	0.248519i	$0.920056\pi$
$798$	−2.04965	+	0.531873i	−0.0725567	+	0.0188281i
$799$	−1.00464	−	1.74009i	−0.0355416	−	0.0615599i
$800$	−0.0165972	+	0.0287473i	−0.000586801	+	0.00101637i
$801$	0.709194	−	1.22836i	0.0250582	−	0.0434020i
$802$	28.0814			0.991588
$803$	−24.5377			−0.865917
$804$	−0.00293343	+	0.00508085i	−0.000103454	+	0.000179188i
$805$	4.23416	+	4.30164i	0.149235	+	0.151613i
$806$	−0.0725029	+	38.8081i	−0.00255381	+	1.36696i
$807$	−1.11891	−	1.93801i	−0.0393875	−	0.0682212i
$808$	13.3932	+	23.1978i	0.471173	+	0.816095i
$809$	14.5054	+	25.1242i	0.509984	+	0.883319i	0.999933	+	0.0115675i	$0.00368212\pi$
$809$	14.5054	+	25.1242i	0.509984	+	0.883319i	−0.489949	+	0.871751i	$0.662985\pi$
$810$	2.02273	−	3.50347i	0.0710714	−	0.123099i
$811$	−20.5902			−0.723020			−0.361510	−	0.932368i	$-0.617739\pi$
$811$	−20.5902			−0.723020			−0.361510	+	0.932368i	$0.617739\pi$
$812$	0.00783405	−	0.0283391i	0.000274921	−	0.000994508i
$813$	−3.07220	−	5.32120i	−0.107747	−	0.186623i
$814$	3.75618	+	6.50590i	0.131654	+	0.228032i
$815$	−32.5220			−1.13920
$816$	−14.9170	−	25.8370i	−0.522199	−	0.904476i
$817$	4.26455			0.149198
$818$	−33.2951			−1.16414
$819$	−2.37881	−	9.23803i	−0.0831224	−	0.322803i
$820$	0.0600361			0.00209655
$821$	0.286058			0.00998349			0.00499174	−	0.999988i	$-0.498411\pi$
$821$	0.286058			0.00998349			0.00499174	+	0.999988i	$0.498411\pi$
$822$	11.8140	+	20.4625i	0.412061	+	0.713711i
$823$	22.5814			0.787137			0.393568	−	0.919295i	$-0.371240\pi$
$823$	22.5814			0.787137			0.393568	+	0.919295i	$0.371240\pi$
$824$	−28.6762	−	49.6686i	−0.998982	−	1.73029i
$825$	−3.66279	−	6.34414i	−0.127522	−	0.220874i
$826$	21.0946	−	5.47394i	0.733975	−	0.190463i
$827$	27.6090			0.960060			0.480030	−	0.877252i	$-0.340626\pi$
$827$	27.6090			0.960060			0.480030	+	0.877252i	$0.340626\pi$
$828$	0.000737255	−	0.00127696i	2.56214e−5	−	4.43775e-5i
$829$	−15.0977	−	26.1500i	−0.524366	−	0.908228i	−0.999598	−	0.0283673i	$-0.990969\pi$
$829$	−15.0977	−	26.1500i	−0.524366	−	0.908228i	0.475232	−	0.879861i	$-0.342364\pi$
$830$	32.8842	+	56.9570i	1.14143	+	1.97701i
$831$	1.67414	+	2.89969i	0.0580752	+	0.100589i
$832$	−24.9837	+	14.3622i	−0.866155	+	0.497920i
$833$	−45.5797	+	25.3633i	−1.57924	+	0.878786i
$834$	7.31903	−	12.6769i	0.253437	−	0.438966i
$835$	−1.50290			−0.0520100
$836$	0.00241172			8.34113e−5
$837$	−3.80370	+	6.58820i	−0.131475	+	0.227721i
$838$	−25.0196	+	43.3352i	−0.864287	+	1.49699i
$839$	25.9928	+	45.0209i	0.897372	+	1.55429i	0.830841	+	0.556509i	$0.187860\pi$
$839$	25.9928	+	45.0209i	0.897372	+	1.55429i	0.0665306	+	0.997784i	$0.478807\pi$
$840$	−5.69842	+	20.6136i	−0.196614	+	0.711238i
$841$	−3.58067	−	6.20190i	−0.123471	−	0.213859i
$842$	14.3270			0.493742
$843$	7.10586	+	12.3077i	0.244739	+	0.423900i
$844$	−0.0153173	+	0.0265304i	−0.000527244	+	0.000913214i
$845$	−37.1700	−	0.138885i	−1.27869	−	0.00477781i
$846$	0.381509			0.0131166
$847$	4.00237	−	14.4783i	0.137523	−	0.497481i
$848$	−9.44842	+	16.3651i	−0.324460	+	0.561981i
$849$	−7.31417	+	12.6685i	−0.251022	+	0.434782i
$850$	−16.7387	+	28.9923i	−0.574132	+	0.994427i
$851$	−1.83631			−0.0629479
$852$	−0.00556336	+	0.00963602i	−0.000190598	+	0.000330125i
$853$	11.5389			0.395085			0.197542	−	0.980294i	$-0.436704\pi$
$853$	11.5389			0.395085			0.197542	+	0.980294i	$0.436704\pi$
$854$	−2.92643	+	10.5862i	−0.100140	+	0.362251i
$855$	−0.808700	+	1.40071i	−0.0276569	+	0.0479032i
$856$	−37.7875			−1.29155
$857$	3.43142	−	5.94339i	0.117215	−	0.203022i	−0.801448	−	0.598064i	$-0.795937\pi$
$857$	3.43142	−	5.94339i	0.117215	−	0.203022i	0.918663	+	0.395042i	$0.129270\pi$
$858$	−0.0219875	+	11.7691i	−0.000750641	+	0.401790i
$859$	−6.60534	−	11.4408i	−0.225371	−	0.390355i	0.731059	−	0.682314i	$-0.239026\pi$
$859$	−6.60534	−	11.4408i	−0.225371	−	0.390355i	−0.956431	+	0.291959i	$0.905693\pi$
$860$	−0.0199175	+	0.0344982i	−0.000679182	+	0.00117638i
$861$	29.0973	−	7.55061i	0.991634	−	0.257324i
$862$	−4.41650	−	7.64961i	−0.150427	−	0.260547i
$863$	11.4551	+	19.8408i	0.389937	+	0.675390i	0.992441	−	0.122726i	$-0.0391635\pi$
$863$	11.4551	+	19.8408i	0.389937	+	0.675390i	−0.602504	+	0.798116i	$0.705830\pi$
$864$	0.0104540			0.000355651
$865$	−26.1483			−0.889070
$866$	−23.9427	−	41.4699i	−0.813605	−	1.40920i
$867$	−19.2633	−	33.3651i	−0.654217	−	1.13314i
$868$	−0.00991060	+	0.0358509i	−0.000336388	+	0.00121686i
$869$	−4.64648	+	8.04793i	−0.157621	+	0.273007i
$870$	−12.1635	−	21.0679i	−0.412382	−	0.714267i
$871$	9.90223	+	5.74175i	0.335524	+	0.194552i
$872$	−1.33185	+	2.30683i	−0.0451020	+	0.0781190i
$873$	10.4610			0.354051
$874$	−0.319295	+	0.553036i	−0.0108003	+	0.0187067i
$875$	−13.3611	+	3.46713i	−0.451686	+	0.117210i
$876$	−0.0196555			−0.000664097
$877$	14.2509	−	24.6834i	0.481220	−	0.833498i	−0.518548	−	0.855049i	$-0.673527\pi$
$877$	14.2509	−	24.6834i	0.481220	−	0.833498i	0.999768	+	0.0215511i	$0.00686045\pi$
$878$	−12.5567			−0.423767
$879$	−10.7723	+	18.6582i	−0.363341	+	0.629324i
$880$	13.2050	−	22.8718i	0.445141	−	0.771007i
$881$	15.9035	−	27.5457i	0.535804	−	0.928039i	−0.463320	−	0.886191i	$-0.653342\pi$
$881$	15.9035	−	27.5457i	0.535804	−	0.928039i	0.999124	−	0.0418483i	$-0.0133246\pi$
$882$	0.156568	−	9.90283i	0.00527190	−	0.333446i
$883$	11.0073			0.370427			0.185213	−	0.982698i	$-0.440702\pi$
$883$	11.0073			0.370427			0.185213	+	0.982698i	$0.440702\pi$
$884$	0.0430454	−	0.0247451i	0.00144777	−	0.000832269i
$885$	8.32299	−	14.4158i	0.279774	−	0.484583i
$886$	−8.42072	−	14.5851i	−0.282900	−	0.489997i
$887$	−22.2051			−0.745574			−0.372787	−	0.927917i	$-0.621598\pi$
$887$	−22.2051			−0.745574			−0.372787	+	0.927917i	$0.621598\pi$
$888$	−3.25326	−	5.63481i	−0.109172	−	0.189092i
$889$	−2.90883	+	10.5225i	−0.0975589	+	0.352912i
$890$	−2.86901	−	4.96928i	−0.0961696	−	0.166571i
$891$	−1.15352	+	1.99796i	−0.0386445	+	0.0669342i
$892$	0.00573317	−	0.00993015i	0.000191961	−	0.000332486i
$893$	−0.152530			−0.00510422
$894$	17.3245			0.579417
$895$	2.46304	−	4.26611i	0.0823304	−	0.142600i
$896$	−29.0137	+	7.52892i	−0.969281	+	0.251523i
$897$	−2.48871	−	1.44306i	−0.0830957	−	0.0481825i
$898$	−4.20628	−	7.28550i	−0.140366	−	0.243120i
$899$	22.8733	+	39.6177i	0.762866	+	1.32132i
$900$	−0.00293401	−	0.00508185i	−9.78002e−5	−	0.000169395i
$901$	−17.5853	+	30.4586i	−0.585851	+	1.01472i
$902$	−37.0875			−1.23488
$903$	−5.31455	+	19.2250i	−0.176857	+	0.639768i
$904$	−3.64577	−	6.31467i	−0.121257	−	0.210023i
$905$	5.68595	+	9.84835i	0.189007	+	0.327370i
$906$	−25.5902			−0.850178
$907$	−0.795213	−	1.37735i	−0.0264046	−	0.0457341i	0.852521	−	0.522693i	$-0.175072\pi$
$907$	−0.795213	−	1.37735i	−0.0264046	−	0.0457341i	−0.878926	+	0.476959i	$0.841739\pi$
$908$	−0.00284712			−9.44850e−5
$909$	−9.47483			−0.314260
$910$	−37.1768	−	10.3519i	−1.23240	−	0.343164i
$911$	−2.61896			−0.0867699			−0.0433849	−	0.999058i	$-0.513814\pi$
$911$	−2.61896			−0.0867699			−0.0433849	+	0.999058i	$0.513814\pi$
$912$	−2.26478			−0.0749944
$913$	−18.7532	−	32.4815i	−0.620641	−	1.07498i
$914$	−17.1372			−0.566849
$915$	4.19456	+	7.26519i	0.138668	+	0.240180i
$916$	0.0197221	+	0.0341596i	0.000651635	+	0.00112867i
$917$	14.0026	+	14.2257i	0.462406	+	0.469775i
$918$	10.5431			0.347973
$919$	−10.0892	+	17.4750i	−0.332811	+	0.576446i	−0.983062	−	0.183274i	$-0.941331\pi$
$919$	−10.0892	+	17.4750i	−0.332811	+	0.576446i	0.650251	+	0.759720i	$0.274664\pi$
$920$	3.22484	+	5.58558i	0.106320	+	0.184151i
$921$	−9.32283	−	16.1476i	−0.307198	−	0.532082i
$922$	3.61743	+	6.26558i	0.119134	+	0.206346i
$923$	18.7799	+	10.8894i	0.618149	+	0.358430i
$924$	−0.00300553	+	0.0108723i	−9.88746e−5	+	0.000357672i
$925$	−3.65392	+	6.32878i	−0.120140	+	0.208089i
$926$	55.0870			1.81027
$927$	20.2865			0.666296
$928$	0.0314321	−	0.0544419i	0.00103181	−	0.00178714i
$929$	16.4051	−	28.4145i	0.538234	−	0.932248i	−0.460765	−	0.887522i	$-0.652425\pi$
$929$	16.4051	−	28.4145i	0.538234	−	0.932248i	0.998999	−	0.0447264i	$-0.0142416\pi$
$930$	15.3877	+	26.6523i	0.504582	+	0.873962i
$931$	−0.0625967	+	3.95921i	−0.00205152	+	0.129758i
$932$	−0.00797339	−	0.0138103i	−0.000261177	−	0.000452372i
$933$	1.15685			0.0378735
$934$	−9.94122	−	17.2187i	−0.325287	−	0.563413i
$935$	24.5770	−	42.5687i	0.803755	−	1.39214i
$936$	0.0190436	−	10.1933i	0.000622458	−	0.333179i
$937$	48.1088			1.57165			0.785823	−	0.618452i	$-0.212240\pi$
$937$	48.1088			1.57165			0.785823	+	0.618452i	$0.212240\pi$
$938$	8.33661	+	8.46946i	0.272200	+	0.276538i
$939$	−6.86004	+	11.8819i	−0.223869	+	0.387752i
$940$	0.000712390	−	0.00123389i	2.32356e−5	−	4.02452e-5i
$941$	5.25163	−	9.09609i	0.171198	−	0.296524i	−0.767641	−	0.640880i	$-0.778569\pi$
$941$	5.25163	−	9.09609i	0.171198	−	0.296524i	0.938839	+	0.344356i	$0.111903\pi$
$942$	30.8868			1.00635
$943$	4.53280	−	7.85104i	0.147608	−	0.255665i
$944$	23.3087			0.758634
$945$	−5.30672	−	5.39128i	−0.172627	−	0.175378i
$946$	12.3041	−	21.3113i	0.400041	−	0.692891i
$947$	−0.629609			−0.0204595			−0.0102298	−	0.999948i	$-0.503256\pi$
$947$	−0.629609			−0.0204595			−0.0102298	+	0.999948i	$0.503256\pi$
$948$	−0.00372197	+	0.00644664i	−0.000120884	+	0.000209377i
$949$	−0.0716443	+	38.3485i	−0.00232567	+	1.24485i
$950$	1.27068	+	2.20088i	0.0412263	+	0.0714060i
$951$	−2.13847	+	3.70393i	−0.0693446	+	0.120108i
$952$	−53.9502	+	13.9998i	−1.74854	+	0.453736i
$953$	10.6206	+	18.3954i	0.344034	+	0.595885i	0.985178	−	0.171536i	$-0.0548730\pi$
$953$	10.6206	+	18.3954i	0.344034	+	0.595885i	−0.641144	+	0.767421i	$0.721540\pi$
$954$	−3.33898	−	5.78329i	−0.108104	−	0.187241i
$955$	71.9199			2.32727
$956$	0.0375558			0.00121464
$957$	6.93664	+	12.0146i	0.224230	+	0.388377i
$958$	−22.8314	−	39.5451i	−0.737648	−	1.27764i
$959$	42.7671	−	11.0979i	1.38102	−	0.358368i
$960$	−11.4264	+	19.7911i	−0.368786	+	0.638756i
$961$	−13.4362	−	23.2722i	−0.433427	−	0.750717i
$962$	10.1786	−	5.85131i	0.328173	−	0.188654i
$963$	6.68305	−	11.5754i	0.215358	−	0.373011i
$964$	0.0482616			0.00155440
$965$	25.9553	−	44.9559i	0.835531	−	1.44718i
$966$	−2.09523	−	2.12862i	−0.0674128	−	0.0684871i
$967$	15.0353			0.483502			0.241751	−	0.970338i	$-0.422278\pi$
$967$	15.0353			0.483502			0.241751	+	0.970338i	$0.422278\pi$
$968$	8.02553	−	13.9006i	0.257950	−	0.446783i
$969$	−4.21518			−0.135411
$970$	21.1597	−	36.6497i	0.679398	−	1.17675i
$971$	3.94070	−	6.82549i	0.126463	−	0.219040i	−0.795841	−	0.605506i	$-0.792971\pi$
$971$	3.94070	−	6.82549i	0.126463	−	0.219040i	0.922304	+	0.386465i	$0.126304\pi$
$972$	−0.000924008		0.00160043i	−2.96376e−5		5.13338e-5i
$973$	−19.2018	−	19.5078i	−0.615582	−	0.625391i
$974$	17.3768			0.556790
$975$	−9.92556	+	5.70583i	−0.317872	+	0.182733i
$976$	−5.87348	+	10.1732i	−0.188005	+	0.325635i
$977$	−8.97409	−	15.5436i	−0.287107	−	0.497283i	0.686011	−	0.727591i	$-0.259360\pi$
$977$	−8.97409	−	15.5436i	−0.287107	−	0.497283i	−0.973118	+	0.230308i	$0.926027\pi$
$978$	16.0931			0.514602
$979$	1.63615	+	2.83389i	0.0522914	+	0.0905714i
$980$	−0.0317358	−	0.0189979i	−0.00101376	−	0.000606864i
$981$	−0.471097	−	0.815964i	−0.0150410	−	0.0260517i
$982$	15.3556	−	26.5968i	0.490018	−	0.848737i
$983$	2.92791	−	5.07129i	0.0933858	−	0.161749i	−0.815548	−	0.578689i	$-0.803564\pi$
$983$	2.92791	−	5.07129i	0.0933858	−	0.161749i	0.908934	+	0.416941i	$0.136898\pi$
$984$	32.1217			1.02400
$985$	−4.47475			−0.142577
$986$	31.7000	−	54.9059i	1.00953	−	1.74856i
$987$	0.190085	−	0.687619i	0.00605048	−	0.0218872i
$988$	7.04166e−6	−	0.00376914i	2.24025e−7	−	0.000119912i
$989$	3.00760	+	5.20931i	0.0956360	+	0.165646i
$990$	4.66653	+	8.08267i	0.148312	+	0.256884i
$991$	−25.6014	−	44.3429i	−0.813255	−	1.40860i	−0.910574	−	0.413345i	$-0.864360\pi$
$991$	−25.6014	−	44.3429i	−0.813255	−	1.40860i	0.0973198	−	0.995253i	$-0.468973\pi$
$992$	−0.0397637	+	0.0688727i	−0.00126250	+	0.00218671i
$993$	11.6611			0.370055
$994$	15.8107	+	16.0626i	0.501485	+	0.509476i
$995$	21.6104	+	37.4302i	0.685094	+	1.18662i
$996$	−0.0150219	−	0.0260187i	−0.000475987	−	0.000824434i
$997$	5.05724			0.160164			0.0800822	−	0.996788i	$-0.474482\pi$
$997$	5.05724			0.160164			0.0800822	+	0.996788i	$0.474482\pi$
$998$	6.98940	+	12.1060i	0.221246	+	0.383208i
$999$	2.30147			0.0728151

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.l.c.256.4	yes	20
3.2	odd	2		819.2.s.f.802.7		20
7.2	even	3		273.2.j.c.100.7	✓	20
13.3	even	3		273.2.j.c.172.7	yes	20
21.2	odd	6		819.2.n.f.100.4		20
39.29	odd	6		819.2.n.f.172.4		20
91.16	even	3	inner	273.2.l.c.16.4	yes	20
273.107	odd	6		819.2.s.f.289.7		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.c.100.7	✓	20	7.2	even	3
273.2.j.c.172.7	yes	20	13.3	even	3
273.2.l.c.16.4	yes	20	91.16	even	3	inner
273.2.l.c.256.4	yes	20	1.1	even	1	trivial
819.2.n.f.100.4		20	21.2	odd	6
819.2.n.f.172.4		20	39.29	odd	6
819.2.s.f.289.7		20	273.107	odd	6
819.2.s.f.802.7		20	3.2	odd	2

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.41487 q^{2} +(-0.500000 - 0.866025i) q^{3} +0.00184802 q^{4} +(-1.42962 - 2.47618i) q^{5} +(0.707433 + 1.22531i) q^{6} +(2.56093 - 0.664549i) q^{7} +2.82712 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q-1.41487 q^{2} +(-0.500000 - 0.866025i) q^{3} +0.00184802 q^{4} +(-1.42962 - 2.47618i) q^{5} +(0.707433 + 1.22531i) q^{6} +(2.56093 - 0.664549i) q^{7} +2.82712 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.02273 + 3.50347i) q^{10} +(-1.15352 - 1.99796i) q^{11} +(-0.000924008 - 0.00160043i) q^{12} +(-3.12586 + 1.79694i) q^{13} +(-3.62338 + 0.940248i) q^{14} +(-1.42962 + 2.47618i) q^{15} -4.00369 q^{16} -7.45162 q^{17} +(0.707433 - 1.22531i) q^{18} +(-0.282836 + 0.489887i) q^{19} +(-0.00264197 - 0.00457603i) q^{20} +(-1.85598 - 1.88556i) q^{21} +(1.63208 + 2.82685i) q^{22} -0.797888 q^{23} +(-1.41356 - 2.44836i) q^{24} +(-1.58765 + 2.74989i) q^{25} +(4.42268 - 2.54243i) q^{26} +1.00000 q^{27} +(0.00473265 - 0.00122810i) q^{28} +(3.00672 - 5.20778i) q^{29} +(2.02273 - 3.50347i) q^{30} +(-3.80370 + 6.58820i) q^{31} +0.0104540 q^{32} +(-1.15352 + 1.99796i) q^{33} +10.5431 q^{34} +(-5.30672 - 5.39128i) q^{35} +(-0.000924008 + 0.00160043i) q^{36} +2.30147 q^{37} +(0.400176 - 0.693125i) q^{38} +(3.11913 + 1.80861i) q^{39} +(-4.04172 - 7.00046i) q^{40} +(-5.68100 + 9.83978i) q^{41} +(2.62597 + 2.66781i) q^{42} +(-3.76945 - 6.52888i) q^{43} +(-0.00213173 - 0.00369227i) q^{44} +2.85925 q^{45} +1.12890 q^{46} +(0.134822 + 0.233518i) q^{47} +(2.00185 + 3.46730i) q^{48} +(6.11675 - 3.40373i) q^{49} +(2.24632 - 3.89073i) q^{50} +(3.72581 + 6.45329i) q^{51} +(-0.00577664 + 0.00332077i) q^{52} +(2.35993 - 4.08751i) q^{53} -1.41487 q^{54} +(-3.29821 + 5.71267i) q^{55} +(7.24006 - 1.87876i) q^{56} +0.565673 q^{57} +(-4.25410 + 7.36832i) q^{58} -5.82180 q^{59} +(-0.00264197 + 0.00457603i) q^{60} +(1.46702 - 2.54094i) q^{61} +(5.38172 - 9.32142i) q^{62} +(-0.704950 + 2.55011i) q^{63} +7.99259 q^{64} +(8.91836 + 5.17125i) q^{65} +(1.63208 - 2.82685i) q^{66} +(-1.58734 - 2.74935i) q^{67} -0.0137707 q^{68} +(0.398944 + 0.690991i) q^{69} +(7.50830 + 7.62794i) q^{70} +(-3.01045 - 5.21425i) q^{71} +(-1.41356 + 2.44836i) q^{72} +(5.31799 - 9.21103i) q^{73} -3.25627 q^{74} +3.17530 q^{75} +(-0.000522686 + 0.000905319i) q^{76} +(-4.28184 - 4.35007i) q^{77} +(-4.41315 - 2.55894i) q^{78} +(-2.01404 - 3.48841i) q^{79} +(5.72378 + 9.91387i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(8.03786 - 13.9220i) q^{82} +16.2573 q^{83} +(-0.00342989 - 0.00348454i) q^{84} +(10.6530 + 18.4516i) q^{85} +(5.33327 + 9.23749i) q^{86} -6.01343 q^{87} +(-3.26115 - 5.64848i) q^{88} -1.41839 q^{89} -4.04546 q^{90} +(-6.81097 + 6.67913i) q^{91} -0.00147451 q^{92} +7.60739 q^{93} +(-0.190755 - 0.330397i) q^{94} +1.61740 q^{95} +(-0.00522698 - 0.00905339i) q^{96} +(-5.23049 - 9.05948i) q^{97} +(-8.65439 + 4.81582i) q^{98} +2.30705 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 10 q^{3} + 32 q^{4} + 3 q^{7} - 12 q^{8} - 10 q^{9}+O(q^{10}) \) 20 * q - 10 * q^3 + 32 * q^4 + 3 * q^7 - 12 * q^8 - 10 * q^9	\( 20 q - 10 q^{3} + 32 q^{4} + 3 q^{7} - 12 q^{8} - 10 q^{9} - 4 q^{10} - 8 q^{11} - 16 q^{12} - 5 q^{13} - 9 q^{14} + 40 q^{16} + 7 q^{19} + 12 q^{20} - 9 q^{21} - 9 q^{22} + 28 q^{23} + 6 q^{24} - 32 q^{25} + 13 q^{26} + 20 q^{27} - 23 q^{28} - 9 q^{29} - 4 q^{30} - 9 q^{31} - 34 q^{32} - 8 q^{33} + 12 q^{34} + 10 q^{35} - 16 q^{36} - 36 q^{37} + 22 q^{38} + 4 q^{39} - 9 q^{40} - q^{41} + 3 q^{42} - 11 q^{43} + 8 q^{44} + 20 q^{46} + 13 q^{47} - 20 q^{48} - 3 q^{49} + 5 q^{50} - 44 q^{52} - 6 q^{53} - 19 q^{55} - 23 q^{56} - 14 q^{57} + 30 q^{59} + 12 q^{60} + 22 q^{62} + 6 q^{63} + 72 q^{64} - 6 q^{65} - 9 q^{66} - 22 q^{67} - 78 q^{68} - 14 q^{69} + 30 q^{70} - 11 q^{71} + 6 q^{72} + 6 q^{74} + 64 q^{75} + 6 q^{76} + 56 q^{77} + 4 q^{78} - 36 q^{79} + 48 q^{80} - 10 q^{81} - 13 q^{82} + 40 q^{83} + 10 q^{84} - 16 q^{85} + 4 q^{86} + 18 q^{87} - 12 q^{88} - 4 q^{89} + 8 q^{90} + 30 q^{91} + 66 q^{92} + 18 q^{93} - 44 q^{94} + 72 q^{95} + 17 q^{96} + 21 q^{97} - 76 q^{98} + 16 q^{99}+O(q^{100}) \) 20 * q - 10 * q^3 + 32 * q^4 + 3 * q^7 - 12 * q^8 - 10 * q^9 - 4 * q^10 - 8 * q^11 - 16 * q^12 - 5 * q^13 - 9 * q^14 + 40 * q^16 + 7 * q^19 + 12 * q^20 - 9 * q^21 - 9 * q^22 + 28 * q^23 + 6 * q^24 - 32 * q^25 + 13 * q^26 + 20 * q^27 - 23 * q^28 - 9 * q^29 - 4 * q^30 - 9 * q^31 - 34 * q^32 - 8 * q^33 + 12 * q^34 + 10 * q^35 - 16 * q^36 - 36 * q^37 + 22 * q^38 + 4 * q^39 - 9 * q^40 - q^41 + 3 * q^42 - 11 * q^43 + 8 * q^44 + 20 * q^46 + 13 * q^47 - 20 * q^48 - 3 * q^49 + 5 * q^50 - 44 * q^52 - 6 * q^53 - 19 * q^55 - 23 * q^56 - 14 * q^57 + 30 * q^59 + 12 * q^60 + 22 * q^62 + 6 * q^63 + 72 * q^64 - 6 * q^65 - 9 * q^66 - 22 * q^67 - 78 * q^68 - 14 * q^69 + 30 * q^70 - 11 * q^71 + 6 * q^72 + 6 * q^74 + 64 * q^75 + 6 * q^76 + 56 * q^77 + 4 * q^78 - 36 * q^79 + 48 * q^80 - 10 * q^81 - 13 * q^82 + 40 * q^83 + 10 * q^84 - 16 * q^85 + 4 * q^86 + 18 * q^87 - 12 * q^88 - 4 * q^89 + 8 * q^90 + 30 * q^91 + 66 * q^92 + 18 * q^93 - 44 * q^94 + 72 * q^95 + 17 * q^96 + 21 * q^97 - 76 * q^98 + 16 * q^99

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