LMFDB - Embedded newform 273.2.k.a.211.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(22,273)]

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, 0, 4]))

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

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

chi := DirichletCharacter("273.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
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			211.1
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	273.211
Dual form			273.2.k.a.22.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 - 1.32683i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.173648 + 0.300767i) q^{4} +0.120615 q^{5} +(-0.766044 + 1.32683i) q^{6} +(0.500000 - 0.866025i) q^{7} -2.53209 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.766044 - 1.32683i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.173648 + 0.300767i) q^{4} +0.120615 q^{5} +(-0.766044 + 1.32683i) q^{6} +(0.500000 - 0.866025i) q^{7} -2.53209 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.0923963 - 0.160035i) q^{10} +(-2.28699 - 3.96118i) q^{11} +0.347296 q^{12} +(-0.245100 - 3.59721i) q^{13} -1.53209 q^{14} +(-0.0603074 - 0.104455i) q^{15} +(2.28699 + 3.96118i) q^{16} +(-2.46064 + 4.26195i) q^{17} +1.53209 q^{18} +(0.379385 - 0.657115i) q^{19} +(-0.0209445 + 0.0362770i) q^{20} -1.00000 q^{21} +(-3.50387 + 6.06888i) q^{22} +(2.73783 + 4.74205i) q^{23} +(1.26604 + 2.19285i) q^{24} -4.98545 q^{25} +(-4.58512 + 3.08083i) q^{26} +1.00000 q^{27} +(0.173648 + 0.300767i) q^{28} +(-5.33022 - 9.23222i) q^{29} +(-0.0923963 + 0.160035i) q^{30} +8.63816 q^{31} +(0.971782 - 1.68317i) q^{32} +(-2.28699 + 3.96118i) q^{33} +7.53983 q^{34} +(0.0603074 - 0.104455i) q^{35} +(-0.173648 - 0.300767i) q^{36} +(2.35117 + 4.07234i) q^{37} -1.16250 q^{38} +(-2.99273 + 2.01087i) q^{39} -0.305407 q^{40} +(-5.45336 - 9.44550i) q^{41} +(0.766044 + 1.32683i) q^{42} +(-0.631759 + 1.09424i) q^{43} +1.58853 q^{44} +(-0.0603074 + 0.104455i) q^{45} +(4.19459 - 7.26525i) q^{46} +5.94356 q^{47} +(2.28699 - 3.96118i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(3.81908 + 6.61484i) q^{50} +4.92127 q^{51} +(1.12449 + 0.550931i) q^{52} +9.49794 q^{53} +(-0.766044 - 1.32683i) q^{54} +(-0.275845 - 0.477777i) q^{55} +(-1.26604 + 2.19285i) q^{56} -0.758770 q^{57} +(-8.16637 + 14.1446i) q^{58} +(4.49660 - 7.78833i) q^{59} +0.0418891 q^{60} +(4.72668 - 8.18685i) q^{61} +(-6.61721 - 11.4613i) q^{62} +(0.500000 + 0.866025i) q^{63} +6.17024 q^{64} +(-0.0295627 - 0.433877i) q^{65} +7.00774 q^{66} +(-6.51501 - 11.2843i) q^{67} +(-0.854570 - 1.48016i) q^{68} +(2.73783 - 4.74205i) q^{69} -0.184793 q^{70} +(-1.23783 + 2.14398i) q^{71} +(1.26604 - 2.19285i) q^{72} +5.89393 q^{73} +(3.60220 - 6.23919i) q^{74} +(2.49273 + 4.31753i) q^{75} +(0.131759 + 0.228213i) q^{76} -4.57398 q^{77} +(4.96064 + 2.43042i) q^{78} -8.18479 q^{79} +(0.275845 + 0.477777i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-8.35504 + 14.4713i) q^{82} +12.2490 q^{83} +(0.173648 - 0.300767i) q^{84} +(-0.296789 + 0.514054i) q^{85} +1.93582 q^{86} +(-5.33022 + 9.23222i) q^{87} +(5.79086 + 10.0301i) q^{88} +(3.37939 + 5.85327i) q^{89} +0.184793 q^{90} +(-3.23783 - 1.58634i) q^{91} -1.90167 q^{92} +(-4.31908 - 7.48086i) q^{93} +(-4.55303 - 7.88609i) q^{94} +(0.0457595 - 0.0792577i) q^{95} -1.94356 q^{96} +(5.03596 - 8.72254i) q^{97} +(-0.766044 + 1.32683i) q^{98} +4.57398 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{3} + 12 q^{5} + 3 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - 3 * q^3 + 12 * q^5 + 3 * q^7 - 6 * q^8 - 3 * q^9	$ 6 q - 3 q^{3} + 12 q^{5} + 3 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{10} - 6 q^{11} - 6 q^{15} + 6 q^{16} - 6 q^{17} - 9 q^{19} + 3 q^{20} - 6 q^{21} + 3 q^{22} - 3 q^{23} + 3 q^{24} + 6 q^{25} - 6 q^{26} + 6 q^{27} - 9 q^{29} + 3 q^{30} + 18 q^{31} - 9 q^{32} - 6 q^{33} - 12 q^{34} + 6 q^{35} - 12 q^{37} - 12 q^{38} - 6 q^{40} - 6 q^{41} - 9 q^{43} + 30 q^{44} - 6 q^{45} + 21 q^{46} + 6 q^{47} + 6 q^{48} - 3 q^{49} + 6 q^{50} + 12 q^{51} - 6 q^{52} + 6 q^{53} - 3 q^{56} + 18 q^{57} - 30 q^{58} - 15 q^{59} - 6 q^{60} + 15 q^{61} - 9 q^{62} + 3 q^{63} - 6 q^{64} - 6 q^{65} - 6 q^{66} - 9 q^{67} - 21 q^{68} - 3 q^{69} + 6 q^{70} + 12 q^{71} + 3 q^{72} + 60 q^{73} + 21 q^{74} - 3 q^{75} + 6 q^{76} - 12 q^{77} + 21 q^{78} - 42 q^{79} - 3 q^{81} + 48 q^{83} + 3 q^{85} + 30 q^{86} - 9 q^{87} + 3 q^{88} + 9 q^{89} - 6 q^{90} + 12 q^{92} - 9 q^{93} - 15 q^{94} - 30 q^{95} + 18 q^{96} - 3 q^{97} + 12 q^{99}+O(q^{100}) $ 6 * q - 3 * q^3 + 12 * q^5 + 3 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^10 - 6 * q^11 - 6 * q^15 + 6 * q^16 - 6 * q^17 - 9 * q^19 + 3 * q^20 - 6 * q^21 + 3 * q^22 - 3 * q^23 + 3 * q^24 + 6 * q^25 - 6 * q^26 + 6 * q^27 - 9 * q^29 + 3 * q^30 + 18 * q^31 - 9 * q^32 - 6 * q^33 - 12 * q^34 + 6 * q^35 - 12 * q^37 - 12 * q^38 - 6 * q^40 - 6 * q^41 - 9 * q^43 + 30 * q^44 - 6 * q^45 + 21 * q^46 + 6 * q^47 + 6 * q^48 - 3 * q^49 + 6 * q^50 + 12 * q^51 - 6 * q^52 + 6 * q^53 - 3 * q^56 + 18 * q^57 - 30 * q^58 - 15 * q^59 - 6 * q^60 + 15 * q^61 - 9 * q^62 + 3 * q^63 - 6 * q^64 - 6 * q^65 - 6 * q^66 - 9 * q^67 - 21 * q^68 - 3 * q^69 + 6 * q^70 + 12 * q^71 + 3 * q^72 + 60 * q^73 + 21 * q^74 - 3 * q^75 + 6 * q^76 - 12 * q^77 + 21 * q^78 - 42 * q^79 - 3 * q^81 + 48 * q^83 + 3 * q^85 + 30 * q^86 - 9 * q^87 + 3 * q^88 + 9 * q^89 - 6 * q^90 + 12 * q^92 - 9 * q^93 - 15 * q^94 - 30 * q^95 + 18 * q^96 - 3 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.766044	−	1.32683i	−0.541675	−	0.938209i	−0.998808	−	0.0488106i	$-0.984457\pi$
$2$	−0.766044	−	1.32683i	−0.541675	−	0.938209i	0.457133	−	0.889398i	$-0.348876\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.173648	+	0.300767i	−0.0868241	+	0.150384i
$5$	0.120615			0.0539406			0.0269703	−	0.999636i	$-0.491414\pi$
$5$	0.120615			0.0539406			0.0269703	+	0.999636i	$0.491414\pi$
$6$	−0.766044	+	1.32683i	−0.312736	+	0.541675i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$	−2.53209			−0.895229
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.0923963	−	0.160035i	−0.0292183	−	0.0506075i
$11$	−2.28699	−	3.96118i	−0.689553	−	1.19434i	−0.971983	−	0.235053i	$-0.924474\pi$
$11$	−2.28699	−	3.96118i	−0.689553	−	1.19434i	0.282429	−	0.959288i	$-0.408860\pi$
$12$	0.347296			0.100256
$13$	−0.245100	−	3.59721i	−0.0679785	−	0.997687i
$13$	−0.245100	−	3.59721i	−0.0679785	−	0.997687i
$14$	−1.53209			−0.409468
$15$	−0.0603074	−	0.104455i	−0.0155713	−	0.0269703i
$16$	2.28699	+	3.96118i	0.571747	+	0.990295i
$17$	−2.46064	+	4.26195i	−0.596792	+	1.03367i	0.396499	+	0.918035i	$0.370225\pi$
$17$	−2.46064	+	4.26195i	−0.596792	+	1.03367i	−0.993291	+	0.115639i	$0.963108\pi$
$18$	1.53209			0.361117
$19$	0.379385	−	0.657115i	0.0870369	−	0.150752i	−0.819220	−	0.573479i	$-0.805594\pi$
$19$	0.379385	−	0.657115i	0.0870369	−	0.150752i	0.906257	+	0.422726i	$0.138927\pi$
$20$	−0.0209445	+	0.0362770i	−0.00468334	+	0.00811178i
$21$	−1.00000			−0.218218
$22$	−3.50387	+	6.06888i	−0.747028	+	1.29389i
$23$	2.73783	+	4.74205i	0.570876	+	0.988787i	0.996476	+	0.0838752i	$0.0267297\pi$
$23$	2.73783	+	4.74205i	0.570876	+	0.988787i	−0.425600	+	0.904911i	$0.639937\pi$
$24$	1.26604	+	2.19285i	0.258430	+	0.447614i
$25$	−4.98545			−0.997090
$26$	−4.58512	+	3.08083i	−0.899216	+	0.604200i
$27$	1.00000			0.192450
$28$	0.173648	+	0.300767i	0.0328164	+	0.0568397i
$29$	−5.33022	−	9.23222i	−0.989797	−	1.71438i	−0.618292	−	0.785949i	$-0.712175\pi$
$29$	−5.33022	−	9.23222i	−0.989797	−	1.71438i	−0.371506	−	0.928431i	$-0.621158\pi$
$30$	−0.0923963	+	0.160035i	−0.0168692	+	0.0292183i
$31$	8.63816			1.55146			0.775729	−	0.631066i	$-0.217382\pi$
$31$	8.63816			1.55146			0.775729	+	0.631066i	$0.217382\pi$
$32$	0.971782	−	1.68317i	0.171788	−	0.297546i
$33$	−2.28699	+	3.96118i	−0.398114	+	0.689553i
$34$	7.53983			1.29307
$35$	0.0603074	−	0.104455i	0.0101938	−	0.0176562i
$36$	−0.173648	−	0.300767i	−0.0289414	−	0.0501279i
$37$	2.35117	+	4.07234i	0.386529	+	0.669489i	0.991980	−	0.126394i	$-0.0403404\pi$
$37$	2.35117	+	4.07234i	0.386529	+	0.669489i	−0.605451	+	0.795883i	$0.707007\pi$
$38$	−1.16250			−0.188583
$39$	−2.99273	+	2.01087i	−0.479220	+	0.321997i
$40$	−0.305407			−0.0482891
$41$	−5.45336	−	9.44550i	−0.851672	−	1.47514i	−0.879698	−	0.475532i	$-0.842255\pi$
$41$	−5.45336	−	9.44550i	−0.851672	−	1.47514i	0.0280260	−	0.999607i	$-0.491078\pi$
$42$	0.766044	+	1.32683i	0.118203	+	0.204734i
$43$	−0.631759	+	1.09424i	−0.0963424	+	0.166870i	−0.910168	−	0.414239i	$-0.864048\pi$
$43$	−0.631759	+	1.09424i	−0.0963424	+	0.166870i	0.813826	+	0.581109i	$0.197381\pi$
$44$	1.58853			0.239479
$45$	−0.0603074	+	0.104455i	−0.00899009	+	0.0155713i
$46$	4.19459	−	7.26525i	0.618459	−	1.07120i
$47$	5.94356			0.866958			0.433479	−	0.901164i	$-0.357286\pi$
$47$	5.94356			0.866958			0.433479	+	0.901164i	$0.357286\pi$
$48$	2.28699	−	3.96118i	0.330098	−	0.571747i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	3.81908	+	6.61484i	0.540099	+	0.935479i
$51$	4.92127			0.689116
$52$	1.12449	+	0.550931i	0.155938	+	0.0764004i
$53$	9.49794			1.30464			0.652321	−	0.757943i	$-0.273795\pi$
$53$	9.49794			1.30464			0.652321	+	0.757943i	$0.273795\pi$
$54$	−0.766044	−	1.32683i	−0.104245	−	0.180558i
$55$	−0.275845	−	0.477777i	−0.0371949	−	0.0644234i
$56$	−1.26604	+	2.19285i	−0.169182	+	0.293032i
$57$	−0.758770			−0.100502
$58$	−8.16637	+	14.1446i	−1.07230	+	1.85727i
$59$	4.49660	−	7.78833i	0.585407	−	1.01395i	−0.409418	−	0.912347i	$-0.634268\pi$
$59$	4.49660	−	7.78833i	0.585407	−	1.01395i	0.994825	−	0.101608i	$-0.0323986\pi$
$60$	0.0418891			0.00540786
$61$	4.72668	−	8.18685i	0.605190	−	1.04822i	−0.386832	−	0.922150i	$-0.626431\pi$
$61$	4.72668	−	8.18685i	0.605190	−	1.04822i	0.992021	−	0.126069i	$-0.0402360\pi$
$62$	−6.61721	−	11.4613i	−0.840387	−	1.45559i
$63$	0.500000	+	0.866025i	0.0629941	+	0.109109i
$64$	6.17024			0.771281
$65$	−0.0295627	−	0.433877i	−0.00366680	−	0.0538158i
$66$	7.00774			0.862593
$67$	−6.51501	−	11.2843i	−0.795936	−	1.37860i	−0.922243	−	0.386610i	$-0.873646\pi$
$67$	−6.51501	−	11.2843i	−0.795936	−	1.37860i	0.126308	−	0.991991i	$-0.459687\pi$
$68$	−0.854570	−	1.48016i	−0.103632	−	0.179496i
$69$	2.73783	−	4.74205i	0.329596	−	0.570876i
$70$	−0.184793			−0.0220869
$71$	−1.23783	+	2.14398i	−0.146903	+	0.254443i	−0.930081	−	0.367354i	$-0.880264\pi$
$71$	−1.23783	+	2.14398i	−0.146903	+	0.254443i	0.783178	+	0.621797i	$0.213597\pi$
$72$	1.26604	−	2.19285i	0.149205	−	0.258430i
$73$	5.89393			0.689833			0.344916	−	0.938633i	$-0.387907\pi$
$73$	5.89393			0.689833			0.344916	+	0.938633i	$0.387907\pi$
$74$	3.60220	−	6.23919i	0.418747	−	0.725291i
$75$	2.49273	+	4.31753i	0.287835	+	0.498545i
$76$	0.131759	+	0.228213i	0.0151138	+	0.0261779i
$77$	−4.57398			−0.521253
$78$	4.96064	+	2.43042i	0.561682	+	0.275191i
$79$	−8.18479			−0.920861			−0.460431	−	0.887696i	$-0.652305\pi$
$79$	−8.18479			−0.920861			−0.460431	+	0.887696i	$0.652305\pi$
$80$	0.275845	+	0.477777i	0.0308404	+	0.0534171i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−8.35504	+	14.4713i	−0.922660	+	1.59809i
$83$	12.2490			1.34450			0.672250	−	0.740325i	$-0.265328\pi$
$83$	12.2490			1.34450			0.672250	+	0.740325i	$0.265328\pi$
$84$	0.173648	−	0.300767i	0.0189466	−	0.0328164i
$85$	−0.296789	+	0.514054i	−0.0321913	+	0.0557570i
$86$	1.93582			0.208745
$87$	−5.33022	+	9.23222i	−0.571460	+	0.989797i
$88$	5.79086	+	10.0301i	0.617308	+	1.06921i
$89$	3.37939	+	5.85327i	0.358214	+	0.620445i	0.987663	−	0.156597i	$-0.0500524\pi$
$89$	3.37939	+	5.85327i	0.358214	+	0.620445i	−0.629448	+	0.777042i	$0.716719\pi$
$90$	0.184793			0.0194788
$91$	−3.23783	−	1.58634i	−0.339416	−	0.166294i
$92$	−1.90167			−0.198263
$93$	−4.31908	−	7.48086i	−0.447868	−	0.775729i
$94$	−4.55303	−	7.88609i	−0.469610	−	0.813388i
$95$	0.0457595	−	0.0792577i	0.00469482	−	0.00813167i
$96$	−1.94356			−0.198364
$97$	5.03596	−	8.72254i	0.511324	−	0.885639i	−0.488590	−	0.872514i	$-0.662488\pi$
$97$	5.03596	−	8.72254i	0.511324	−	0.885639i	0.999914	−	0.0131258i	$-0.00417819\pi$
$98$	−0.766044	+	1.32683i	−0.0773822	+	0.134030i
$99$	4.57398			0.459702
$100$	0.865715	−	1.49946i	0.0865715	−	0.149946i
$101$	2.97906	+	5.15988i	0.296427	+	0.513427i	0.975316	−	0.220814i	$-0.0708715\pi$
$101$	2.97906	+	5.15988i	0.296427	+	0.513427i	−0.678889	+	0.734241i	$0.737538\pi$
$102$	−3.76991	−	6.52968i	−0.373277	−	0.646535i
$103$	−2.75877			−0.271830			−0.135915	−	0.990721i	$-0.543397\pi$
$103$	−2.75877			−0.271830			−0.135915	+	0.990721i	$0.543397\pi$
$104$	0.620615	+	9.10846i	0.0608563	+	0.893158i
$105$	−0.120615			−0.0117708
$106$	−7.27584	−	12.6021i	−0.706693	−	1.22403i
$107$	1.93242	+	3.34705i	0.186814	+	0.323571i	0.944186	−	0.329412i	$-0.106851\pi$
$107$	1.93242	+	3.34705i	0.186814	+	0.323571i	−0.757372	+	0.652983i	$0.773517\pi$
$108$	−0.173648	+	0.300767i	−0.0167093	+	0.0289414i
$109$	−12.0496			−1.15415			−0.577073	−	0.816693i	$-0.695805\pi$
$109$	−12.0496			−1.15415			−0.577073	+	0.816693i	$0.695805\pi$
$110$	−0.422618	+	0.731997i	−0.0402951	+	0.0697931i
$111$	2.35117	−	4.07234i	0.223163	−	0.386529i
$112$	4.57398			0.432200
$113$	−3.78699	+	6.55926i	−0.356250	+	0.617043i	−0.987331	−	0.158674i	$-0.949278\pi$
$113$	−3.78699	+	6.55926i	−0.356250	+	0.617043i	0.631081	+	0.775717i	$0.282612\pi$
$114$	0.581252	+	1.00676i	0.0544392	+	0.0942915i
$115$	0.330222	+	0.571962i	0.0307934	+	0.0533357i
$116$	3.70233			0.343753
$117$	3.23783	+	1.58634i	0.299337	+	0.146657i
$118$	−13.7784			−1.26840
$119$	2.46064	+	4.26195i	0.225566	+	0.390692i
$120$	0.152704	+	0.264490i	0.0139399	+	0.0241446i
$121$	−4.96064	+	8.59208i	−0.450967	+	0.781098i
$122$	−14.4834			−1.31126
$123$	−5.45336	+	9.44550i	−0.491713	+	0.851672i
$124$	−1.50000	+	2.59808i	−0.134704	+	0.233314i
$125$	−1.20439			−0.107724
$126$	0.766044	−	1.32683i	0.0682447	−	0.118203i
$127$	4.93969	+	8.55580i	0.438327	+	0.759204i	0.997561	−	0.0698056i	$-0.0222379\pi$
$127$	4.93969	+	8.55580i	0.438327	+	0.759204i	−0.559234	+	0.829010i	$0.688905\pi$
$128$	−6.67024	−	11.5532i	−0.589572	−	1.02117i
$129$	1.26352			0.111247
$130$	−0.553033	+	0.371593i	−0.0485042	+	0.0325909i
$131$	15.5253			1.35645			0.678225	−	0.734854i	$-0.262749\pi$
$131$	15.5253			1.35645			0.678225	+	0.734854i	$0.262749\pi$
$132$	−0.794263	−	1.37570i	−0.0691317	−	0.119740i
$133$	−0.379385	−	0.657115i	−0.0328969	−	0.0569791i
$134$	−9.98158	+	17.2886i	−0.862277	+	1.49351i
$135$	0.120615			0.0103809
$136$	6.23055	−	10.7916i	0.534265	−	0.925375i
$137$	0.783119	−	1.35640i	0.0669063	−	0.115885i	−0.830632	−	0.556822i	$-0.812020\pi$
$137$	0.783119	−	1.35640i	0.0669063	−	0.115885i	0.897538	+	0.440937i	$0.145354\pi$
$138$	−8.38919			−0.714135
$139$	−5.25150	+	9.09586i	−0.445426	+	0.771501i	−0.998082	−	0.0619090i	$-0.980281\pi$
$139$	−5.25150	+	9.09586i	−0.445426	+	0.771501i	0.552656	+	0.833410i	$0.313614\pi$
$140$	0.0209445	+	0.0362770i	0.00177014	+	0.00306597i
$141$	−2.97178	−	5.14728i	−0.250269	−	0.433479i
$142$	3.79292			0.318295
$143$	−13.6887	+	9.19767i	−1.14470	+	0.769148i
$144$	−4.57398			−0.381165
$145$	−0.642903	−	1.11354i	−0.0533902	−	0.0924746i
$146$	−4.51501	−	7.82023i	−0.373665	−	0.647207i
$147$	−0.500000	+	0.866025i	−0.0412393	+	0.0714286i
$148$	−1.63310			−0.134240
$149$	−0.124485	+	0.215615i	−0.0101982	+	0.0176638i	−0.871079	−	0.491142i	$-0.836580\pi$
$149$	−0.124485	+	0.215615i	−0.0101982	+	0.0176638i	0.860881	+	0.508806i	$0.169913\pi$
$150$	3.81908	−	6.61484i	0.311826	−	0.540099i
$151$	18.9513			1.54224			0.771118	−	0.636693i	$-0.219698\pi$
$151$	18.9513			1.54224			0.771118	+	0.636693i	$0.219698\pi$
$152$	−0.960637	+	1.66387i	−0.0779180	+	0.134958i
$153$	−2.46064	−	4.26195i	−0.198931	−	0.344558i
$154$	3.50387	+	6.06888i	0.282350	+	0.489044i
$155$	1.04189			0.0836865
$156$	−0.0851223	−	1.24930i	−0.00681524	−	0.100024i
$157$	−18.6827			−1.49104			−0.745522	−	0.666481i	$-0.767800\pi$
$157$	−18.6827			−1.49104			−0.745522	+	0.666481i	$0.767800\pi$
$158$	6.26991	+	10.8598i	0.498808	+	0.863960i
$159$	−4.74897	−	8.22546i	−0.376618	−	0.652321i
$160$	0.117211	−	0.203016i	0.00926636	−	0.0160498i
$161$	5.47565			0.431542
$162$	−0.766044	+	1.32683i	−0.0601861	+	0.104245i
$163$	−10.0175	+	17.3509i	−0.784634	+	1.35903i	0.144583	+	0.989493i	$0.453816\pi$
$163$	−10.0175	+	17.3509i	−0.784634	+	1.35903i	−0.929217	+	0.369534i	$0.879517\pi$
$164$	3.78787			0.295783
$165$	−0.275845	+	0.477777i	−0.0214745	+	0.0371949i
$166$	−9.38326	−	16.2523i	−0.728282	−	1.26142i
$167$	1.00980	+	1.74903i	0.0781407	+	0.135344i	0.902448	−	0.430799i	$-0.141768\pi$
$167$	1.00980	+	1.74903i	0.0781407	+	0.135344i	−0.824307	+	0.566143i	$0.808435\pi$
$168$	2.53209			0.195355
$169$	−12.8799	+	1.76335i	−0.990758	+	0.135642i
$170$	0.909415			0.0697489
$171$	0.379385	+	0.657115i	0.0290123	+	0.0502508i
$172$	−0.219408	−	0.380025i	−0.0167297	−	0.0289766i
$173$	−1.09967	+	1.90468i	−0.0836064	+	0.144810i	−0.904797	−	0.425844i	$-0.859977\pi$
$173$	−1.09967	+	1.90468i	−0.0836064	+	0.144810i	0.821190	+	0.570655i	$0.193311\pi$
$174$	16.3327			1.23818
$175$	−2.49273	+	4.31753i	−0.188432	+	0.326374i
$176$	10.4606	−	18.1184i	0.788500	−	1.36572i
$177$	−8.99319			−0.675970
$178$	5.17752	−	8.96773i	0.388071	−	0.672159i
$179$	4.28833	+	7.42761i	0.320525	+	0.555166i	0.980596	−	0.196037i	$-0.0628073\pi$
$179$	4.28833	+	7.42761i	0.320525	+	0.555166i	−0.660071	+	0.751203i	$0.729474\pi$
$180$	−0.0209445	−	0.0362770i	−0.00156111	−	0.00270393i
$181$	11.8844			0.883363			0.441682	−	0.897172i	$-0.354382\pi$
$181$	11.8844			0.883363			0.441682	+	0.897172i	$0.354382\pi$
$182$	0.375515	+	5.51125i	0.0278350	+	0.408521i
$183$	−9.45336			−0.698813
$184$	−6.93242	−	12.0073i	−0.511065	−	0.885190i
$185$	0.283585	+	0.491184i	0.0208496	+	0.0361126i
$186$	−6.61721	+	11.4613i	−0.485197	+	0.840387i
$187$	22.5098			1.64608
$188$	−1.03209	+	1.78763i	−0.0752728	+	0.130376i
$189$	0.500000	−	0.866025i	0.0363696	−	0.0629941i
$190$	−0.140215			−0.0101723
$191$	6.90033	−	11.9517i	0.499290	−	0.864796i	−0.500709	−	0.865615i	$-0.666927\pi$
$191$	6.90033	−	11.9517i	0.499290	−	0.864796i	1.00000		0.000819252i	$0.000260776\pi$
$192$	−3.08512	−	5.34359i	−0.222650	−	0.385640i
$193$	−9.10741	−	15.7745i	−0.655566	−	1.13547i	−0.981752	−	0.190168i	$-0.939097\pi$
$193$	−9.10741	−	15.7745i	−0.655566	−	1.13547i	0.326186	−	0.945306i	$-0.394236\pi$
$194$	−15.4311			−1.10789
$195$	−0.360967	+	0.242540i	−0.0258494	+	0.0173687i
$196$	0.347296			0.0248069
$197$	−1.78446	−	3.09078i	−0.127138	−	0.220209i	0.795429	−	0.606047i	$-0.207246\pi$
$197$	−1.78446	−	3.09078i	−0.127138	−	0.220209i	−0.922567	+	0.385838i	$0.873912\pi$
$198$	−3.50387	−	6.06888i	−0.249009	−	0.431297i
$199$	4.86824	−	8.43204i	0.345100	−	0.597732i	−0.640272	−	0.768149i	$-0.721178\pi$
$199$	4.86824	−	8.43204i	0.345100	−	0.597732i	0.985372	+	0.170417i	$0.0545115\pi$
$200$	12.6236			0.892624
$201$	−6.51501	+	11.2843i	−0.459534	+	0.795936i
$202$	4.56418	−	7.90539i	0.321134	−	0.556221i
$203$	−10.6604			−0.748217
$204$	−0.854570	+	1.48016i	−0.0598319	+	0.103632i
$205$	−0.657756	−	1.13927i	−0.0459397	−	0.0795699i
$206$	2.11334	+	3.66041i	0.147243	+	0.255033i
$207$	−5.47565			−0.380584
$208$	13.6887	−	9.19767i	0.949138	−	0.637743i
$209$	−3.47060			−0.240066
$210$	0.0923963	+	0.160035i	0.00637595	+	0.0110435i
$211$	11.0287	+	19.1022i	0.759246	+	1.31505i	0.943236	+	0.332124i	$0.107765\pi$
$211$	11.0287	+	19.1022i	0.759246	+	1.31505i	−0.183990	+	0.982928i	$0.558901\pi$
$212$	−1.64930	+	2.85667i	−0.113274	+	0.196197i
$213$	2.47565			0.169629
$214$	2.96064	−	5.12797i	0.202385	−	0.350541i
$215$	−0.0761995	+	0.131981i	−0.00519676	+	0.00900105i
$216$	−2.53209			−0.172287
$217$	4.31908	−	7.48086i	0.293198	−	0.507834i
$218$	9.23055	+	15.9878i	0.625172	+	1.08283i
$219$	−2.94697	−	5.10430i	−0.199138	−	0.344916i
$220$	0.191600			0.0129176
$221$	15.9342	+	7.80683i	1.07185	+	0.525144i
$222$	−7.20439			−0.483527
$223$	1.72668	+	2.99070i	0.115627	+	0.200272i	0.918030	−	0.396510i	$-0.129779\pi$
$223$	1.72668	+	2.99070i	0.115627	+	0.200272i	−0.802403	+	0.596782i	$0.796446\pi$
$224$	−0.971782	−	1.68317i	−0.0649299	−	0.112462i
$225$	2.49273	−	4.31753i	0.166182	−	0.287835i
$226$	11.6040			0.771887
$227$	2.56031	−	4.43458i	0.169934	−	0.294334i	−0.768463	−	0.639895i	$-0.778978\pi$
$227$	2.56031	−	4.43458i	0.169934	−	0.294334i	0.938396	+	0.345561i	$0.112311\pi$
$228$	0.131759	−	0.228213i	0.00872596	−	0.0151138i
$229$	−15.3628			−1.01520			−0.507600	−	0.861593i	$-0.669467\pi$
$229$	−15.3628			−1.01520			−0.507600	+	0.861593i	$0.669467\pi$
$230$	0.505930	−	0.876296i	0.0333600	−	0.0577813i
$231$	2.28699	+	3.96118i	0.150473	+	0.260627i
$232$	13.4966	+	23.3768i	0.886095	+	1.53476i
$233$	6.23173			0.408254			0.204127	−	0.978944i	$-0.434564\pi$
$233$	6.23173			0.408254			0.204127	+	0.978944i	$0.434564\pi$
$234$	−0.375515	−	5.51125i	−0.0245482	−	0.360281i
$235$	0.716881			0.0467642
$236$	1.56165	+	2.70486i	0.101655	+	0.176071i
$237$	4.09240	+	7.08824i	0.265830	+	0.460431i
$238$	3.76991	−	6.52968i	0.244367	−	0.423257i
$239$	−4.45336			−0.288064			−0.144032	−	0.989573i	$-0.546007\pi$
$239$	−4.45336			−0.288064			−0.144032	+	0.989573i	$0.546007\pi$
$240$	0.275845	−	0.477777i	0.0178057	−	0.0308404i
$241$	4.52347	−	7.83488i	0.291382	−	0.504689i	−0.682754	−	0.730648i	$-0.739218\pi$
$241$	4.52347	−	7.83488i	0.291382	−	0.504689i	0.974137	+	0.225959i	$0.0725515\pi$
$242$	15.2003			0.977111
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	1.64156	+	2.84326i	0.105090	+	0.182021i
$245$	−0.0603074	−	0.104455i	−0.00385290	−	0.00667341i
$246$	16.7101			1.06540
$247$	−2.45677	−	1.20367i	−0.156320	−	0.0765877i
$248$	−21.8726			−1.38891
$249$	−6.12449	−	10.6079i	−0.388123	−	0.672250i
$250$	0.922618	+	1.59802i	0.0583515	+	0.101068i
$251$	0.971782	−	1.68317i	0.0613383	−	0.106241i	−0.833726	−	0.552179i	$-0.813796\pi$
$251$	0.971782	−	1.68317i	0.0613383	−	0.106241i	0.895064	+	0.445938i	$0.147130\pi$
$252$	−0.347296			−0.0218776
$253$	12.5228	−	21.6900i	0.787299	−	1.36364i
$254$	7.56805	−	13.1082i	0.474862	−	0.822484i
$255$	0.593578			0.0371713
$256$	−4.04916	+	7.01336i	−0.253073	+	0.438335i
$257$	10.2797	+	17.8050i	0.641231	+	1.11064i	0.985158	+	0.171648i	$0.0549093\pi$
$257$	10.2797	+	17.8050i	0.641231	+	1.11064i	−0.343927	+	0.938996i	$0.611757\pi$
$258$	−0.967911	−	1.67647i	−0.0602595	−	0.104373i
$259$	4.70233			0.292189
$260$	0.135630	+	0.0664504i	0.00841138	+	0.00412108i
$261$	10.6604			0.659865
$262$	−11.8931	−	20.5994i	−0.734755	−	1.27263i
$263$	−8.05303	−	13.9483i	−0.496571	−	0.860087i	0.503421	−	0.864041i	$-0.332075\pi$
$263$	−8.05303	−	13.9483i	−0.496571	−	0.860087i	−0.999992	+	0.00395459i	$0.998741\pi$
$264$	5.79086	−	10.0301i	0.356403	−	0.617308i
$265$	1.14559			0.0703731
$266$	−0.581252	+	1.00676i	−0.0356388	+	0.0617283i
$267$	3.37939	−	5.85327i	0.206815	−	0.358214i
$268$	4.52528			0.276426
$269$	2.14883	−	3.72189i	0.131017	−	0.226928i	−0.793052	−	0.609154i	$-0.791509\pi$
$269$	2.14883	−	3.72189i	0.131017	−	0.226928i	0.924069	+	0.382226i	$0.124843\pi$
$270$	−0.0923963	−	0.160035i	−0.00562306	−	0.00973942i
$271$	−5.95084	−	10.3072i	−0.361488	−	0.626115i	0.626718	−	0.779246i	$-0.284398\pi$
$271$	−5.95084	−	10.3072i	−0.361488	−	0.626115i	−0.988206	+	0.153131i	$0.951064\pi$
$272$	−22.5098			−1.36486
$273$	0.245100	+	3.59721i	0.0148341	+	0.217713i
$274$	−2.39961			−0.144966
$275$	11.4017	+	19.7483i	0.687547	+	1.19087i
$276$	0.950837	+	1.64690i	0.0572337	+	0.0991316i
$277$	−5.41147	+	9.37295i	−0.325144	+	0.563166i	−0.981541	−	0.191249i	$-0.938746\pi$
$277$	−5.41147	+	9.37295i	−0.325144	+	0.563166i	0.656398	+	0.754415i	$0.272079\pi$
$278$	16.0915			0.965105
$279$	−4.31908	+	7.48086i	−0.258576	+	0.447868i
$280$	−0.152704	+	0.264490i	−0.00912579	+	0.0158063i
$281$	6.83481			0.407730			0.203865	−	0.978999i	$-0.434650\pi$
$281$	6.83481			0.407730			0.203865	+	0.978999i	$0.434650\pi$
$282$	−4.55303	+	7.88609i	−0.271129	+	0.469610i
$283$	11.3721	+	19.6971i	0.676002	+	1.17087i	0.976175	+	0.216985i	$0.0696222\pi$
$283$	11.3721	+	19.6971i	0.676002	+	1.17087i	−0.300173	+	0.953885i	$0.597044\pi$
$284$	−0.429892	−	0.744596i	−0.0255094	−	0.0441836i
$285$	−0.0915189			−0.00542111
$286$	22.6898	+	11.1167i	1.34168	+	0.657343i
$287$	−10.9067			−0.643804
$288$	0.971782	+	1.68317i	0.0572628	+	0.0991820i
$289$	−3.60947	−	6.25179i	−0.212322	−	0.367752i
$290$	−0.984985	+	1.70604i	−0.0578403	+	0.100182i
$291$	−10.0719			−0.590426
$292$	−1.02347	+	1.77270i	−0.0598941	+	0.103740i
$293$	−10.4991	+	18.1850i	−0.613365	+	1.06238i	0.377304	+	0.926090i	$0.376851\pi$
$293$	−10.4991	+	18.1850i	−0.613365	+	1.06238i	−0.990669	+	0.136290i	$0.956482\pi$
$294$	1.53209			0.0893532
$295$	0.542356	−	0.939388i	0.0315772	−	0.0546933i
$296$	−5.95336	−	10.3115i	−0.346032	−	0.599345i
$297$	−2.28699	−	3.96118i	−0.132705	−	0.229851i
$298$	0.381445			0.0220965
$299$	16.3871	−	11.0108i	0.947692	−	0.636772i
$300$	−1.73143			−0.0999641
$301$	0.631759	+	1.09424i	0.0364140	+	0.0630709i
$302$	−14.5175	−	25.1451i	−0.835391	−	1.44694i
$303$	2.97906	−	5.15988i	0.171142	−	0.296427i
$304$	3.47060			0.199053
$305$	0.570108	−	0.987455i	0.0326443	−	0.0565415i
$306$	−3.76991	+	6.52968i	−0.215512	+	0.373277i
$307$	−15.8821			−0.906438			−0.453219	−	0.891399i	$-0.649724\pi$
$307$	−15.8821			−0.906438			−0.453219	+	0.891399i	$0.649724\pi$
$308$	0.794263	−	1.37570i	0.0452573	−	0.0783880i
$309$	1.37939	+	2.38917i	0.0784705	+	0.135915i
$310$	−0.798133	−	1.38241i	−0.0453309	−	0.0785155i
$311$	−10.1976			−0.578252			−0.289126	−	0.957291i	$-0.593365\pi$
$311$	−10.1976			−0.578252			−0.289126	+	0.957291i	$0.593365\pi$
$312$	7.57785	−	5.09170i	0.429011	−	0.288261i
$313$	−18.6578			−1.05460			−0.527299	−	0.849680i	$-0.676795\pi$
$313$	−18.6578			−1.05460			−0.527299	+	0.849680i	$0.676795\pi$
$314$	14.3118	+	24.7888i	0.807662	+	1.39891i
$315$	0.0603074	+	0.104455i	0.00339794	+	0.00588540i
$316$	1.42127	−	2.46172i	0.0799529	−	0.138483i
$317$	−15.3746			−0.863526			−0.431763	−	0.901987i	$-0.642108\pi$
$317$	−15.3746			−0.863526			−0.431763	+	0.901987i	$0.642108\pi$
$318$	−7.27584	+	12.6021i	−0.408009	+	0.706693i
$319$	−24.3803	+	42.2280i	−1.36504	+	2.36431i
$320$	0.744223			0.0416033
$321$	1.93242	−	3.34705i	0.107857	−	0.186814i
$322$	−4.19459	−	7.26525i	−0.233756	−	0.404876i
$323$	1.86706	+	3.23384i	0.103886	+	0.179936i
$324$	0.347296			0.0192942
$325$	1.22193	+	17.9337i	0.0677807	+	0.994784i
$326$	30.6955			1.70007
$327$	6.02481	+	10.4353i	0.333173	+	0.577073i
$328$	13.8084	+	23.9169i	0.762441	+	1.32059i
$329$	2.97178	−	5.14728i	0.163840	−	0.283779i
$330$	0.845237			0.0465288
$331$	3.47818	−	6.02438i	0.191178	−	0.331130i	−0.754463	−	0.656343i	$-0.772103\pi$
$331$	3.47818	−	6.02438i	0.191178	−	0.331130i	0.945641	+	0.325213i	$0.105436\pi$
$332$	−2.12701	+	3.68409i	−0.116735	+	0.202191i
$333$	−4.70233			−0.257686
$334$	1.54710	−	2.67966i	0.0846537	−	0.146625i
$335$	−0.785807	−	1.36106i	−0.0429332	−	0.0743625i
$336$	−2.28699	−	3.96118i	−0.124765	−	0.216100i
$337$	−12.1111			−0.659735			−0.329867	−	0.944027i	$-0.607004\pi$
$337$	−12.1111			−0.659735			−0.329867	+	0.944027i	$0.607004\pi$
$338$	12.2062	+	15.7385i	0.663930	+	0.856064i
$339$	7.57398			0.411362
$340$	−0.103074	−	0.178529i	−0.00558996	−	0.00968210i
$341$	−19.7554	−	34.2173i	−1.06981	−	1.85297i
$342$	0.581252	−	1.00676i	0.0314305	−	0.0544392i
$343$	−1.00000			−0.0539949
$344$	1.59967	−	2.77071i	0.0862484	−	0.149387i
$345$	0.330222	−	0.571962i	0.0177786	−	0.0307934i
$346$	3.36959			0.181150
$347$	12.4586	−	21.5789i	0.668811	−	1.15842i	−0.309425	−	0.950924i	$-0.600137\pi$
$347$	12.4586	−	21.5789i	0.668811	−	1.15842i	0.978237	−	0.207492i	$-0.0665300\pi$
$348$	−1.85117	−	3.20631i	−0.0992330	−	0.171877i
$349$	2.04710	+	3.54569i	0.109579	+	0.189796i	0.915600	−	0.402091i	$-0.131716\pi$
$349$	2.04710	+	3.54569i	0.109579	+	0.189796i	−0.806021	+	0.591887i	$0.798383\pi$
$350$	7.63816			0.408277
$351$	−0.245100	−	3.59721i	−0.0130825	−	0.192005i
$352$	−8.88981			−0.473829
$353$	3.39780	+	5.88517i	0.180847	+	0.313236i	0.942169	−	0.335138i	$-0.108783\pi$
$353$	3.39780	+	5.88517i	0.180847	+	0.313236i	−0.761322	+	0.648374i	$0.775450\pi$
$354$	6.88919	+	11.9324i	0.366156	+	0.634201i
$355$	−0.149300	+	0.258595i	−0.00792403	+	0.0137248i
$356$	−2.34730			−0.124406
$357$	2.46064	−	4.26195i	0.130231	−	0.225566i
$358$	6.57011	−	11.3798i	0.347241	−	0.601439i
$359$	−9.77425			−0.515865			−0.257933	−	0.966163i	$-0.583041\pi$
$359$	−9.77425			−0.515865			−0.257933	+	0.966163i	$0.583041\pi$
$360$	0.152704	−	0.264490i	0.00804819	−	0.0139399i
$361$	9.21213	+	15.9559i	0.484849	+	0.839783i
$362$	−9.10401	−	15.7686i	−0.478496	−	0.828779i
$363$	9.92127			0.520732
$364$	1.03936	−	0.698367i	0.0544774	−	0.0366044i
$365$	0.710895			0.0372100
$366$	7.24170	+	12.5430i	0.378530	+	0.655632i
$367$	2.70099	+	4.67825i	0.140990	+	0.244203i	0.927870	−	0.372904i	$-0.121638\pi$
$367$	2.70099	+	4.67825i	0.140990	+	0.244203i	−0.786879	+	0.617107i	$0.788305\pi$
$368$	−12.5228	+	21.6900i	−0.652794	+	1.13067i
$369$	10.9067			0.567781
$370$	0.434478	−	0.752538i	0.0225874	−	0.0391226i
$371$	4.74897	−	8.22546i	0.246554	−	0.427044i
$372$	3.00000			0.155543
$373$	17.7797	−	30.7954i	0.920599	−	1.59452i	0.122108	−	0.992517i	$-0.461035\pi$
$373$	17.7797	−	30.7954i	0.920599	−	1.59452i	0.798491	−	0.602007i	$-0.205632\pi$
$374$	−17.2435	−	29.8666i	−0.891641	−	1.54437i
$375$	0.602196	+	1.04303i	0.0310973	+	0.0538621i
$376$	−15.0496			−0.776125
$377$	−31.9038	+	21.4367i	−1.64313	+	1.10405i
$378$	−1.53209			−0.0788021
$379$	−6.16250	−	10.6738i	−0.316547	−	0.548275i	0.663218	−	0.748426i	$-0.269190\pi$
$379$	−6.16250	−	10.6738i	−0.316547	−	0.548275i	−0.979765	+	0.200151i	$0.935857\pi$
$380$	0.0158921	+	0.0275259i	0.000815247	+	0.00141205i
$381$	4.93969	−	8.55580i	0.253068	−	0.438327i
$382$	−21.1438			−1.08181
$383$	3.19253	−	5.52963i	0.163131	−	0.282551i	−0.772859	−	0.634578i	$-0.781174\pi$
$383$	3.19253	−	5.52963i	0.163131	−	0.282551i	0.935990	+	0.352027i	$0.114507\pi$
$384$	−6.67024	+	11.5532i	−0.340389	+	0.589572i
$385$	−0.551689			−0.0281167
$386$	−13.9534	+	24.1679i	−0.710207	+	1.23012i
$387$	−0.631759	−	1.09424i	−0.0321141	−	0.0556233i
$388$	1.74897	+	3.02931i	0.0887905	+	0.153790i
$389$	−23.4492			−1.18892			−0.594462	−	0.804124i	$-0.702635\pi$
$389$	−23.4492			−1.18892			−0.594462	+	0.804124i	$0.702635\pi$
$390$	0.598326	+	0.293144i	0.0302974	+	0.0148439i
$391$	−26.9472			−1.36278
$392$	1.26604	+	2.19285i	0.0639449	+	0.110756i
$393$	−7.76264	−	13.4453i	−0.391573	−	0.678225i
$394$	−2.73396	+	4.73535i	−0.137735	+	0.238563i
$395$	−0.987207			−0.0496718
$396$	−0.794263	+	1.37570i	−0.0399132	+	0.0691317i
$397$	−8.71301	+	15.0914i	−0.437293	+	0.757415i	−0.997480	−	0.0709522i	$-0.977396\pi$
$397$	−8.71301	+	15.0914i	−0.437293	+	0.757415i	0.560186	+	0.828367i	$0.310730\pi$
$398$	−14.9172			−0.747729
$399$	−0.379385	+	0.657115i	−0.0189930	+	0.0328969i
$400$	−11.4017	−	19.7483i	−0.570084	−	0.987414i
$401$	4.64068	+	8.03790i	0.231745	+	0.401393i	0.958322	−	0.285692i	$-0.0922233\pi$
$401$	4.64068	+	8.03790i	0.231745	+	0.401393i	−0.726577	+	0.687085i	$0.758890\pi$
$402$	19.9632			0.995672
$403$	−2.11721	−	31.0733i	−0.105466	−	1.54787i
$404$	−2.06923			−0.102948
$405$	−0.0603074	−	0.104455i	−0.00299670	−	0.00519043i
$406$	8.16637	+	14.1446i	0.405290	+	0.701983i
$407$	10.7542	−	18.6268i	0.533065	−	0.923296i
$408$	−12.4611			−0.616917
$409$	−7.24376	+	12.5466i	−0.358181	+	0.620387i	−0.987657	−	0.156633i	$-0.949936\pi$
$409$	−7.24376	+	12.5466i	−0.358181	+	0.620387i	0.629476	+	0.777020i	$0.283269\pi$
$410$	−1.00774	+	1.74546i	−0.0497688	+	0.0862020i
$411$	−1.56624			−0.0772568
$412$	0.479055	−	0.829748i	0.0236014	−	0.0408788i
$413$	−4.49660	−	7.78833i	−0.221263	−	0.383239i
$414$	4.19459	+	7.26525i	0.206153	+	0.357067i
$415$	1.47741			0.0725230
$416$	−6.29292	−	3.08316i	−0.308536	−	0.151164i
$417$	10.5030			0.514334
$418$	2.65863	+	4.60489i	0.130038	+	0.225232i
$419$	−2.76945	−	4.79682i	−0.135296	−	0.234340i	0.790414	−	0.612573i	$-0.209865\pi$
$419$	−2.76945	−	4.79682i	−0.135296	−	0.234340i	−0.925711	+	0.378232i	$0.876532\pi$
$420$	0.0209445	−	0.0362770i	0.00102199	−	0.00177014i
$421$	24.8949			1.21330			0.606651	−	0.794968i	$-0.292513\pi$
$421$	24.8949			1.21330			0.606651	+	0.794968i	$0.292513\pi$
$422$	16.8969	−	29.2663i	0.822529	−	1.42466i
$423$	−2.97178	+	5.14728i	−0.144493	+	0.250269i
$424$	−24.0496			−1.16795
$425$	12.2674	−	21.2477i	0.595056	−	1.03067i
$426$	−1.89646	−	3.28476i	−0.0918838	−	0.159147i
$427$	−4.72668	−	8.18685i	−0.228740	−	0.396190i
$428$	−1.34224			−0.0648798
$429$	14.8097	+	7.25590i	0.715021	+	0.350318i
$430$	0.233489			0.0112598
$431$	−8.55350	−	14.8151i	−0.412008	−	0.713618i	0.583102	−	0.812399i	$-0.301839\pi$
$431$	−8.55350	−	14.8151i	−0.412008	−	0.713618i	−0.995109	+	0.0987811i	$0.968506\pi$
$432$	2.28699	+	3.96118i	0.110033	+	0.190582i
$433$	5.94831	−	10.3028i	0.285858	−	0.495120i	−0.686959	−	0.726696i	$-0.741055\pi$
$433$	5.94831	−	10.3028i	0.285858	−	0.495120i	0.972817	+	0.231576i	$0.0743882\pi$
$434$	−13.2344			−0.635273
$435$	−0.642903	+	1.11354i	−0.0308249	+	0.0533902i
$436$	2.09240	−	3.62414i	0.100208	−	0.173565i
$437$	4.15476			0.198749
$438$	−4.51501	+	7.82023i	−0.215736	+	0.373665i
$439$	6.21735	+	10.7688i	0.296738	+	0.513965i	0.975388	−	0.220497i	$-0.0707679\pi$
$439$	6.21735	+	10.7688i	0.296738	+	0.513965i	−0.678650	+	0.734462i	$0.737435\pi$
$440$	0.698463	+	1.20977i	0.0332979	+	0.0576737i
$441$	1.00000			0.0476190
$442$	−1.84801	−	27.1224i	−0.0879009	−	1.29008i
$443$	2.27631			0.108151			0.0540754	−	0.998537i	$-0.482779\pi$
$443$	2.27631			0.108151			0.0540754	+	0.998537i	$0.482779\pi$
$444$	0.816552	+	1.41431i	0.0387518	+	0.0671201i
$445$	0.407604	+	0.705990i	0.0193223	+	0.0334672i
$446$	2.64543	−	4.58202i	0.125265	−	0.216965i
$447$	0.248970			0.0117759
$448$	3.08512	−	5.34359i	0.145758	−	0.252461i
$449$	−0.0876485	+	0.151812i	−0.00413639	+	0.00716444i	−0.868086	−	0.496414i	$-0.834650\pi$
$449$	−0.0876485	+	0.151812i	−0.00413639	+	0.00716444i	0.863950	+	0.503578i	$0.167983\pi$
$450$	−7.63816			−0.360066
$451$	−24.9436	+	43.2035i	−1.17455	+	2.03437i
$452$	−1.31521	−	2.27801i	−0.0618622	−	0.107148i
$453$	−9.47565	−	16.4123i	−0.445205	−	0.771118i
$454$	−7.84524			−0.368195
$455$	−0.390530	−	0.191336i	−0.0183083	−	0.00896999i
$456$	1.92127			0.0899719
$457$	5.75237	+	9.96340i	0.269085	+	0.466068i	0.968626	−	0.248524i	$-0.0799455\pi$
$457$	5.75237	+	9.96340i	0.269085	+	0.466068i	−0.699541	+	0.714592i	$0.746612\pi$
$458$	11.7686	+	20.3838i	0.549909	+	0.952471i
$459$	−2.46064	+	4.26195i	−0.114853	+	0.198931i
$460$	−0.229370			−0.0106944
$461$	−4.24035	+	7.34451i	−0.197493	+	0.342068i	−0.947715	−	0.319118i	$-0.896613\pi$
$461$	−4.24035	+	7.34451i	−0.197493	+	0.342068i	0.750222	+	0.661186i	$0.229947\pi$
$462$	3.50387	−	6.06888i	0.163015	−	0.282350i
$463$	−11.2790			−0.524180			−0.262090	−	0.965043i	$-0.584412\pi$
$463$	−11.2790			−0.524180			−0.262090	+	0.965043i	$0.584412\pi$
$464$	24.3803	−	42.2280i	1.13183	−	1.96038i
$465$	−0.520945	−	0.902302i	−0.0241582	−	0.0418433i
$466$	−4.77379	−	8.26844i	−0.221141	−	0.383028i
$467$	20.3063			0.939665			0.469833	−	0.882755i	$-0.344314\pi$
$467$	20.3063			0.939665			0.469833	+	0.882755i	$0.344314\pi$
$468$	−1.03936	+	0.698367i	−0.0480446	+	0.0322820i
$469$	−13.0300			−0.601671
$470$	−0.549163	−	0.951178i	−0.0253310	−	0.0438746i
$471$	9.34137	+	16.1797i	0.430427	+	0.745522i
$472$	−11.3858	+	19.7208i	−0.524073	+	0.907721i
$473$	5.77930			0.265733
$474$	6.26991	−	10.8598i	0.287987	−	0.498808i
$475$	−1.89141	+	3.27601i	−0.0867837	+	0.150314i
$476$	−1.70914			−0.0783383
$477$	−4.74897	+	8.22546i	−0.217440	+	0.376618i
$478$	3.41147	+	5.90885i	0.156037	+	0.270264i
$479$	11.5013	+	19.9209i	0.525510	+	0.910210i	0.999559	+	0.0297111i	$0.00945873\pi$
$479$	11.5013	+	19.9209i	0.525510	+	0.910210i	−0.474049	+	0.880499i	$0.657208\pi$
$480$	−0.234422			−0.0106999
$481$	14.0728	−	9.45577i	0.641664	−	0.431146i
$482$	−13.8607			−0.631338
$483$	−2.73783	−	4.74205i	−0.124575	−	0.215771i
$484$	−1.72281	−	2.98400i	−0.0783096	−	0.135636i
$485$	0.607411	−	1.05207i	0.0275811	−	0.0477719i
$486$	1.53209			0.0694970
$487$	−8.59879	+	14.8935i	−0.389648	+	0.674891i	−0.992402	−	0.123036i	$-0.960737\pi$
$487$	−8.59879	+	14.8935i	−0.389648	+	0.674891i	0.602754	+	0.797927i	$0.294070\pi$
$488$	−11.9684	+	20.7298i	−0.541783	+	0.938396i
$489$	20.0351			0.906018
$490$	−0.0923963	+	0.160035i	−0.00417404	+	0.00722965i
$491$	−20.2788	−	35.1240i	−0.915171	−	1.58512i	−0.806651	−	0.591029i	$-0.798722\pi$
$491$	−20.2788	−	35.1240i	−0.915171	−	1.58512i	−0.108521	−	0.994094i	$-0.534611\pi$
$492$	−1.89393	−	3.28039i	−0.0853851	−	0.147891i
$493$	52.4630			2.36281
$494$	0.284930	+	4.18177i	0.0128196	+	0.188147i
$495$	0.551689			0.0247966
$496$	19.7554	+	34.2173i	0.887042	+	1.53640i
$497$	1.23783	+	2.14398i	0.0555241	+	0.0961705i
$498$	−9.38326	+	16.2523i	−0.420474	+	0.728282i
$499$	−5.54757			−0.248343			−0.124172	−	0.992261i	$-0.539627\pi$
$499$	−5.54757			−0.248343			−0.124172	+	0.992261i	$0.539627\pi$
$500$	0.209141	−	0.362242i	0.00935305	−	0.0162000i
$501$	1.00980	−	1.74903i	0.0451145	−	0.0781407i
$502$	−2.97771			−0.132902
$503$	11.3794	−	19.7097i	0.507382	−	0.878811i	−0.492582	−	0.870266i	$-0.663947\pi$
$503$	11.3794	−	19.7097i	0.507382	−	0.878811i	0.999963	−	0.00854474i	$-0.00271991\pi$
$504$	−1.26604	−	2.19285i	−0.0563941	−	0.0976774i
$505$	0.359318	+	0.622357i	0.0159894	+	0.0276945i
$506$	−38.3719			−1.70584
$507$	7.96703	+	10.2726i	0.353828	+	0.456222i
$508$	−3.43107			−0.152229
$509$	12.5098	+	21.6676i	0.554487	+	0.960400i	0.997943	+	0.0641038i	$0.0204189\pi$
$509$	12.5098	+	21.6676i	0.554487	+	0.960400i	−0.443456	+	0.896296i	$0.646248\pi$
$510$	−0.454707	−	0.787576i	−0.0201348	−	0.0348745i
$511$	2.94697	−	5.10430i	0.130366	−	0.225801i
$512$	−14.2736			−0.630811
$513$	0.379385	−	0.657115i	0.0167503	−	0.0290123i
$514$	15.7494	−	27.2788i	0.694678	−	1.20322i
$515$	−0.332748			−0.0146626
$516$	−0.219408	+	0.380025i	−0.00965888	+	0.0167297i
$517$	−13.5929	−	23.5435i	−0.597813	−	1.03544i
$518$	−3.60220	−	6.23919i	−0.158271	−	0.274134i
$519$	2.19934			0.0965403
$520$	0.0748553	+	1.09861i	0.00328262	+	0.0481774i
$521$	10.0051			0.438329			0.219165	−	0.975688i	$-0.429667\pi$
$521$	10.0051			0.438329			0.219165	+	0.975688i	$0.429667\pi$
$522$	−8.16637	−	14.1446i	−0.357432	−	0.619091i
$523$	21.8025	+	37.7630i	0.953355	+	1.65126i	0.738087	+	0.674705i	$0.235729\pi$
$523$	21.8025	+	37.7630i	0.953355	+	1.65126i	0.215268	+	0.976555i	$0.430937\pi$
$524$	−2.69594	+	4.66950i	−0.117773	+	0.203988i
$525$	4.98545			0.217583
$526$	−12.3380	+	21.3700i	−0.537961	+	0.931775i
$527$	−21.2554	+	36.8154i	−0.925898	+	1.60370i
$528$	−20.9213			−0.910482
$529$	−3.49138	+	6.04725i	−0.151799	+	0.262924i
$530$	−0.877574	−	1.52000i	−0.0381194	−	0.0660247i
$531$	4.49660	+	7.78833i	0.195136	+	0.337985i
$532$	0.263518			0.0114250
$533$	−32.6408	+	21.9320i	−1.41383	+	0.949980i
$534$	−10.3550			−0.448106
$535$	0.233078	+	0.403703i	0.0100768	+	0.0174536i
$536$	16.4966	+	28.5729i	0.712544	+	1.23416i
$537$	4.28833	−	7.42761i	0.185055	−	0.320525i
$538$	−6.58441			−0.283874
$539$	−2.28699	+	3.96118i	−0.0985076	+	0.170620i
$540$	−0.0209445	+	0.0362770i	−0.000901309	+	0.00156111i
$541$	31.1002			1.33710			0.668551	−	0.743666i	$-0.266915\pi$
$541$	31.1002			1.33710			0.668551	+	0.743666i	$0.266915\pi$
$542$	−9.11721	+	15.7915i	−0.391618	+	0.678302i
$543$	−5.94222	−	10.2922i	−0.255005	−	0.441682i
$544$	4.78240	+	8.28337i	0.205044	+	0.355146i
$545$	−1.45336			−0.0622552
$546$	4.58512	−	3.08083i	0.196225	−	0.131847i
$547$	38.5827			1.64968			0.824838	−	0.565370i	$-0.191267\pi$
$547$	38.5827			1.64968			0.824838	+	0.565370i	$0.191267\pi$
$548$	0.271974	+	0.471073i	0.0116182	+	0.0201232i
$549$	4.72668	+	8.18685i	0.201730	+	0.349406i
$550$	17.4684	−	30.2561i	0.744854	−	1.29013i
$551$	−8.08883			−0.344596
$552$	−6.93242	+	12.0073i	−0.295063	+	0.511065i
$553$	−4.09240	+	7.08824i	−0.174026	+	0.301423i
$554$	16.5817			0.704490
$555$	0.283585	−	0.491184i	0.0120375	−	0.0208496i
$556$	−1.82383	−	3.15896i	−0.0773474	−	0.133970i
$557$	−20.5920	−	35.6664i	−0.872510	−	1.51123i	−0.859391	−	0.511318i	$-0.829157\pi$
$557$	−20.5920	−	35.6664i	−0.872510	−	1.51123i	−0.0131191	−	0.999914i	$-0.504176\pi$
$558$	13.2344			0.560258
$559$	4.09105	+	2.00437i	0.173033	+	0.0847759i
$560$	0.551689			0.0233131
$561$	−11.2549	−	19.4941i	−0.475182	−	0.823040i
$562$	−5.23577	−	9.06861i	−0.220857	−	0.382536i
$563$	11.3819	−	19.7140i	0.479690	−	0.830848i	−0.520038	−	0.854143i	$-0.674082\pi$
$563$	11.3819	−	19.7140i	0.479690	−	0.830848i	0.999729	+	0.0232949i	$0.00741566\pi$
$564$	2.06418			0.0869176
$565$	−0.456767	+	0.791143i	−0.0192163	+	0.0332836i
$566$	17.4231	−	30.1777i	0.732347	−	1.26846i
$567$	−1.00000			−0.0419961
$568$	3.13429	−	5.42874i	0.131512	−	0.227785i
$569$	13.1493	+	22.7753i	0.551247	+	0.954788i	0.998185	+	0.0602233i	$0.0191813\pi$
$569$	13.1493	+	22.7753i	0.551247	+	0.954788i	−0.446938	+	0.894565i	$0.647485\pi$
$570$	0.0701076	+	0.121430i	0.00293648	+	0.00508614i
$571$	13.8435			0.579332			0.289666	−	0.957128i	$-0.406456\pi$
$571$	13.8435			0.579332			0.289666	+	0.957128i	$0.406456\pi$
$572$	−0.389348	−	5.71426i	−0.0162794	−	0.238925i
$573$	−13.8007			−0.576531
$574$	8.35504	+	14.4713i	0.348733	+	0.604022i
$575$	−13.6493	−	23.6413i	−0.569215	−	0.985910i
$576$	−3.08512	+	5.34359i	−0.128547	+	0.222650i
$577$	13.9290			0.579872			0.289936	−	0.957046i	$-0.406366\pi$
$577$	13.9290			0.579872			0.289936	+	0.957046i	$0.406366\pi$
$578$	−5.53003	+	9.57829i	−0.230019	+	0.398404i
$579$	−9.10741	+	15.7745i	−0.378491	+	0.655566i
$580$	0.446556			0.0185422
$581$	6.12449	−	10.6079i	0.254086	−	0.440091i
$582$	7.71554	+	13.3637i	0.319819	+	0.553943i
$583$	−21.7217	−	37.6231i	−0.899620	−	1.55819i
$584$	−14.9240			−0.617558
$585$	0.390530	+	0.191336i	0.0161464	+	0.00791078i
$586$	32.1712			1.32898
$587$	21.6964	+	37.5793i	0.895506	+	1.55106i	0.833177	+	0.553007i	$0.186520\pi$
$587$	21.6964	+	37.5793i	0.895506	+	1.55106i	0.0623298	+	0.998056i	$0.480147\pi$
$588$	−0.173648	−	0.300767i	−0.00716113	−	0.0124034i
$589$	3.27719	−	5.67626i	0.135034	−	0.233886i
$590$	−1.66187			−0.0684183
$591$	−1.78446	+	3.09078i	−0.0734030	+	0.127138i
$592$	−10.7542	+	18.6268i	−0.441994	+	0.765557i
$593$	−2.20708			−0.0906340			−0.0453170	−	0.998973i	$-0.514430\pi$
$593$	−2.20708			−0.0906340			−0.0453170	+	0.998973i	$0.514430\pi$
$594$	−3.50387	+	6.06888i	−0.143766	+	0.249009i
$595$	0.296789	+	0.514054i	0.0121672	+	0.0210742i
$596$	−0.0432332	−	0.0748822i	−0.00177090	−	0.00306729i
$597$	−9.73648			−0.398488
$598$	−27.1627	−	13.3081i	−1.11077	−	0.544210i
$599$	33.1729			1.35541			0.677705	−	0.735334i	$-0.262975\pi$
$599$	33.1729			1.35541			0.677705	+	0.735334i	$0.262975\pi$
$600$	−6.31180	−	10.9324i	−0.257678	−	0.446312i
$601$	−9.35622	−	16.2054i	−0.381648	−	0.661034i	0.609650	−	0.792671i	$-0.291310\pi$
$601$	−9.35622	−	16.2054i	−0.381648	−	0.661034i	−0.991298	+	0.131637i	$0.957977\pi$
$602$	0.967911	−	1.67647i	0.0394491	−	0.0683279i
$603$	13.0300			0.530624
$604$	−3.29086	+	5.69994i	−0.133903	+	0.231927i
$605$	−0.598326	+	1.03633i	−0.0243254	+	0.0421329i
$606$	−9.12836			−0.370814
$607$	0.574445	−	0.994968i	0.0233160	−	0.0403845i	−0.854132	−	0.520056i	$-0.825911\pi$
$607$	0.574445	−	0.994968i	0.0233160	−	0.0403845i	0.877448	+	0.479672i	$0.159244\pi$
$608$	−0.737359	−	1.27714i	−0.0299039	−	0.0517950i
$609$	5.33022	+	9.23222i	0.215992	+	0.374108i
$610$	−1.74691			−0.0707304
$611$	−1.45677	−	21.3802i	−0.0589345	−	0.864952i
$612$	1.70914			0.0690879
$613$	6.38800	+	11.0643i	0.258009	+	0.446885i	0.965708	−	0.259629i	$-0.0836002\pi$
$613$	6.38800	+	11.0643i	0.258009	+	0.446885i	−0.707699	+	0.706514i	$0.750267\pi$
$614$	12.1664	+	21.0728i	0.490995	+	0.850428i
$615$	−0.657756	+	1.13927i	−0.0265233	+	0.0459397i
$616$	11.5817			0.466641
$617$	−3.62923	+	6.28602i	−0.146107	+	0.253065i	−0.929786	−	0.368102i	$-0.880008\pi$
$617$	−3.62923	+	6.28602i	−0.146107	+	0.253065i	0.783678	+	0.621167i	$0.213341\pi$
$618$	2.11334	−	3.66041i	0.0850110	−	0.147243i
$619$	10.8966			0.437972			0.218986	−	0.975728i	$-0.429725\pi$
$619$	10.8966			0.437972			0.218986	+	0.975728i	$0.429725\pi$
$620$	−0.180922	+	0.313366i	−0.00726601	+	0.0125851i
$621$	2.73783	+	4.74205i	0.109865	+	0.190292i
$622$	7.81180	+	13.5304i	0.313225	+	0.542521i
$623$	6.75877			0.270784
$624$	−14.8097	−	7.25590i	−0.592864	−	0.290468i
$625$	24.7820			0.991280
$626$	14.2927	+	24.7556i	0.571250	+	0.989434i
$627$	1.73530	+	3.00563i	0.0693012	+	0.120033i
$628$	3.24422	−	5.61916i	0.129459	−	0.224229i
$629$	−23.1415			−0.922711
$630$	0.0923963	−	0.160035i	0.00368116	−	0.00637595i
$631$	13.1853	−	22.8375i	0.524897	−	0.909148i	−0.474683	−	0.880157i	$-0.657437\pi$
$631$	13.1853	−	22.8375i	0.524897	−	0.909148i	0.999580	−	0.0289911i	$-0.00922946\pi$
$632$	20.7246			0.824381
$633$	11.0287	−	19.1022i	0.438351	−	0.759246i
$634$	11.7777	+	20.3995i	0.467750	+	0.810168i
$635$	0.595800	+	1.03196i	0.0236436	+	0.0409519i
$636$	3.29860			0.130798
$637$	−2.99273	+	2.01087i	−0.118576	+	0.0796735i
$638$	74.7056			2.95762
$639$	−1.23783	−	2.14398i	−0.0489676	−	0.0848144i
$640$	−0.804530	−	1.39349i	−0.0318018	−	0.0550824i
$641$	−4.78240	+	8.28337i	−0.188894	+	0.327173i	−0.944882	−	0.327412i	$-0.893823\pi$
$641$	−4.78240	+	8.28337i	−0.188894	+	0.327173i	0.755988	+	0.654585i	$0.227157\pi$
$642$	−5.92127			−0.233694
$643$	24.3803	−	42.2280i	0.961466	−	1.66531i	0.242642	−	0.970116i	$-0.421986\pi$
$643$	24.3803	−	42.2280i	0.961466	−	1.66531i	0.718824	−	0.695192i	$-0.244681\pi$
$644$	−0.950837	+	1.64690i	−0.0374682	+	0.0648969i
$645$	0.152399			0.00600070
$646$	2.86050	−	4.95453i	0.112545	−	0.194933i
$647$	9.17277	+	15.8877i	0.360619	+	0.624610i	0.988063	−	0.154052i	$-0.0492322\pi$
$647$	9.17277	+	15.8877i	0.360619	+	0.624610i	−0.627444	+	0.778662i	$0.715899\pi$
$648$	1.26604	+	2.19285i	0.0497349	+	0.0861434i
$649$	−41.1347			−1.61468
$650$	22.8589	−	15.3593i	0.896600	−	0.602442i
$651$	−8.63816			−0.338556
$652$	−3.47906	−	6.02590i	−0.136250	−	0.235992i
$653$	−1.76857	−	3.06325i	−0.0692095	−	0.119874i	0.829344	−	0.558738i	$-0.188714\pi$
$653$	−1.76857	−	3.06325i	−0.0692095	−	0.119874i	−0.898554	+	0.438864i	$0.855381\pi$
$654$	9.23055	−	15.9878i	0.360943	−	0.625172i
$655$	1.87258			0.0731677
$656$	24.9436	−	43.2035i	0.973883	−	1.68681i
$657$	−2.94697	+	5.10430i	−0.114972	+	0.199138i
$658$	−9.10607			−0.354991
$659$	−10.3755	+	17.9709i	−0.404173	+	0.700048i	−0.994225	−	0.107318i	$-0.965774\pi$
$659$	−10.3755	+	17.9709i	−0.404173	+	0.700048i	0.590052	+	0.807365i	$0.299107\pi$
$660$	−0.0957998	−	0.165930i	−0.00372900	−	0.00645882i
$661$	11.2258	+	19.4437i	0.436633	+	0.756271i	0.997427	−	0.0716844i	$-0.0228374\pi$
$661$	11.2258	+	19.4437i	0.436633	+	0.756271i	−0.560794	+	0.827955i	$0.689504\pi$
$662$	−10.6578			−0.414225
$663$	−1.20620	−	17.7029i	−0.0468451	−	0.687522i
$664$	−31.0155			−1.20363
$665$	−0.0457595	−	0.0792577i	−0.00177448	−	0.00307348i
$666$	3.60220	+	6.23919i	0.139582	+	0.241764i
$667$	29.1864	−	50.5524i	1.13010	−	1.95740i
$668$	−0.701400			−0.0271380
$669$	1.72668	−	2.99070i	0.0667574	−	0.115627i
$670$	−1.20393	+	2.08526i	−0.0465117	+	0.0805607i
$671$	−43.2395			−1.66924
$672$	−0.971782	+	1.68317i	−0.0374873	+	0.0649299i
$673$	−12.0219	−	20.8225i	−0.463409	−	0.802649i	0.535719	−	0.844396i	$-0.320041\pi$
$673$	−12.0219	−	20.8225i	−0.463409	−	0.802649i	−0.999128	+	0.0417479i	$0.986707\pi$
$674$	9.27766	+	16.0694i	0.357362	+	0.618969i
$675$	−4.98545			−0.191890
$676$	1.70620	−	4.18004i	0.0656232	−	0.160771i
$677$	−38.5321			−1.48091			−0.740454	−	0.672107i	$-0.765390\pi$
$677$	−38.5321			−1.48091			−0.740454	+	0.672107i	$0.765390\pi$
$678$	−5.80200	−	10.0494i	−0.222825	−	0.385944i
$679$	−5.03596	−	8.72254i	−0.193262	−	0.334740i
$680$	0.751497	−	1.30163i	0.0288186	−	0.0499152i
$681$	−5.12061			−0.196222
$682$	−30.2670	+	52.4239i	−1.15898	+	2.00742i
$683$	12.8097	−	22.1871i	0.490151	−	0.848967i	−0.509785	−	0.860302i	$-0.670275\pi$
$683$	12.8097	−	22.1871i	0.490151	−	0.848967i	0.999936	+	0.0113353i	$0.00360820\pi$
$684$	−0.263518			−0.0100759
$685$	0.0944557	−	0.163602i	0.00360897	−	0.00625091i
$686$	0.766044	+	1.32683i	0.0292477	+	0.0506585i
$687$	7.68139	+	13.3046i	0.293063	+	0.507600i
$688$	−5.77930			−0.220334
$689$	−2.32794	−	34.1661i	−0.0886876	−	1.30162i
$690$	−1.01186			−0.0385208
$691$	−17.1544	−	29.7122i	−0.652582	−	1.13031i	−0.982494	−	0.186294i	$-0.940352\pi$
$691$	−17.1544	−	29.7122i	−0.652582	−	1.13031i	0.329912	−	0.944012i	$-0.392981\pi$
$692$	−0.381911	−	0.661490i	−0.0145181	−	0.0251461i
$693$	2.28699	−	3.96118i	0.0868755	−	0.150473i
$694$	−38.1753			−1.44911
$695$	−0.633408	+	1.09709i	−0.0240265	+	0.0416152i
$696$	13.4966	−	23.3768i	0.511587	−	0.886095i
$697$	53.6750			2.03309
$698$	3.13634	−	5.43231i	0.118712	−	0.205616i
$699$	−3.11587	−	5.39684i	−0.117853	−	0.204127i
$700$	−0.865715	−	1.49946i	−0.0327209	−	0.0566743i
$701$	−2.03415			−0.0768287			−0.0384144	−	0.999262i	$-0.512231\pi$
$701$	−2.03415			−0.0768287			−0.0384144	+	0.999262i	$0.512231\pi$
$702$	−4.58512	+	3.08083i	−0.173054	+	0.116278i
$703$	3.56799			0.134569
$704$	−14.1113	−	24.4415i	−0.531839	−	0.921172i
$705$	−0.358441	−	0.620838i	−0.0134997	−	0.0233821i
$706$	5.20574	−	9.01660i	0.195920	−	0.339344i
$707$	5.95811			0.224078
$708$	1.56165	−	2.70486i	0.0586905	−	0.101655i
$709$	7.15136	−	12.3865i	0.268575	−	0.465185i	−0.699919	−	0.714222i	$-0.746781\pi$
$709$	7.15136	−	12.3865i	0.268575	−	0.465185i	0.968494	+	0.249037i	$0.0801140\pi$
$710$	0.457482			0.0171690
$711$	4.09240	−	7.08824i	0.153477	−	0.265830i
$712$	−8.55690	−	14.8210i	−0.320684	−	0.555440i
$713$	23.6498	+	40.9626i	0.885691	+	1.53406i
$714$	−7.53983			−0.282171
$715$	−1.65105	+	1.10937i	−0.0617459	+	0.0414882i
$716$	−2.97864			−0.111317
$717$	2.22668	+	3.85673i	0.0831569	+	0.144032i
$718$	7.48751	+	12.9688i	0.279431	+	0.483989i
$719$	−0.102663	+	0.177818i	−0.00382869	+	0.00663149i	−0.867933	−	0.496681i	$-0.834552\pi$
$719$	−0.102663	+	0.177818i	−0.00382869	+	0.00663149i	0.864105	+	0.503312i	$0.167885\pi$
$720$	−0.551689			−0.0205602
$721$	−1.37939	+	2.38917i	−0.0513710	+	0.0889772i
$722$	14.1138	−	24.4458i	0.525262	−	0.909780i
$723$	−9.04694			−0.336459
$724$	−2.06371	+	3.57445i	−0.0766972	+	0.132843i
$725$	26.5736	+	46.0268i	0.986918	+	1.70939i
$726$	−7.60014	−	13.1638i	−0.282068	−	0.488555i
$727$	18.0395			0.669049			0.334524	−	0.942387i	$-0.391424\pi$
$727$	18.0395			0.669049			0.334524	+	0.942387i	$0.391424\pi$
$728$	8.19846	+	4.01676i	0.303855	+	0.148871i
$729$	1.00000			0.0370370
$730$	−0.544577	−	0.943236i	−0.0201557	−	0.0349107i
$731$	−3.10906	−	5.38505i	−0.114993	−	0.199173i
$732$	1.64156	−	2.84326i	0.0606738	−	0.105090i
$733$	−20.9760			−0.774765			−0.387382	−	0.921919i	$-0.626621\pi$
$733$	−20.9760			−0.774765			−0.387382	+	0.921919i	$0.626621\pi$
$734$	4.13816	−	7.16750i	0.152742	−	0.264557i
$735$	−0.0603074	+	0.104455i	−0.00222447	+	0.00385290i
$736$	10.6423			0.392279
$737$	−29.7995	+	51.6143i	−1.09768	+	1.90124i
$738$	−8.35504	−	14.4713i	−0.307553	−	0.532698i
$739$	−11.0510	−	19.1408i	−0.406517	−	0.704107i	0.587980	−	0.808875i	$-0.299923\pi$
$739$	−11.0510	−	19.1408i	−0.406517	−	0.704107i	−0.994497	+	0.104768i	$0.966590\pi$
$740$	−0.196976			−0.00724099
$741$	0.185975	+	2.72946i	0.00683195	+	0.100269i
$742$	−14.5517			−0.534209
$743$	−3.06165	−	5.30294i	−0.112321	−	0.194546i	0.804385	−	0.594109i	$-0.202495\pi$
$743$	−3.06165	−	5.30294i	−0.112321	−	0.194546i	−0.916706	+	0.399563i	$0.869162\pi$
$744$	10.9363	+	18.9422i	0.400944	+	0.694455i
$745$	−0.0150147	+	0.0260063i	−0.000550098	+	0.000952797i
$746$	−54.4802			−1.99466
$747$	−6.12449	+	10.6079i	−0.224083	+	0.388123i
$748$	−3.90879	+	6.77022i	−0.142919	+	0.247544i
$749$	3.86484			0.141218
$750$	0.922618	−	1.59802i	0.0336893	−	0.0583515i
$751$	−7.12583	−	12.3423i	−0.260025	−	0.450377i	0.706223	−	0.707989i	$-0.250398\pi$
$751$	−7.12583	−	12.3423i	−0.260025	−	0.450377i	−0.966248	+	0.257612i	$0.917064\pi$
$752$	13.5929	+	23.5435i	0.495681	+	0.858544i
$753$	−1.94356			−0.0708274
$754$	52.8826	+	25.9093i	1.92587	+	0.943562i
$755$	2.28581			0.0831890
$756$	0.173648	+	0.300767i	0.00631552	+	0.0109388i
$757$	5.45471	+	9.44783i	0.198255	+	0.343387i	0.947963	−	0.318382i	$-0.103139\pi$
$757$	5.45471	+	9.44783i	0.198255	+	0.343387i	−0.749708	+	0.661769i	$0.769806\pi$
$758$	−9.44150	+	16.3532i	−0.342931	+	0.593974i
$759$	−25.0455			−0.909094
$760$	−0.115867	+	0.200688i	−0.00420294	+	0.00727970i
$761$	−25.6673	+	44.4571i	−0.930439	+	1.61157i	−0.147868	+	0.989007i	$0.547241\pi$
$761$	−25.6673	+	44.4571i	−0.930439	+	1.61157i	−0.782571	+	0.622561i	$0.786092\pi$
$762$	−15.1361			−0.548323
$763$	−6.02481	+	10.4353i	−0.218113	+	0.377783i
$764$	2.39646	+	4.15079i	0.0867009	+	0.150170i
$765$	−0.296789	−	0.514054i	−0.0107304	−	0.0185857i
$766$	−9.78249			−0.353456
$767$	−29.1184	−	14.2663i	−1.05140	−	0.515126i
$768$	8.09833			0.292223
$769$	−4.46110	−	7.72686i	−0.160872	−	0.278638i	0.774310	−	0.632807i	$-0.218097\pi$
$769$	−4.46110	−	7.72686i	−0.160872	−	0.278638i	−0.935181	+	0.354169i	$0.884764\pi$
$770$	0.422618	+	0.731997i	0.0152301	+	0.0263793i
$771$	10.2797	−	17.8050i	0.370215	−	0.641231i

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.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 - 1.32683i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.173648 + 0.300767i) q^{4} +0.120615 q^{5} +(-0.766044 + 1.32683i) q^{6} +(0.500000 - 0.866025i) q^{7} -2.53209 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.766044 - 1.32683i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.173648 + 0.300767i) q^{4} +0.120615 q^{5} +(-0.766044 + 1.32683i) q^{6} +(0.500000 - 0.866025i) q^{7} -2.53209 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.0923963 - 0.160035i) q^{10} +(-2.28699 - 3.96118i) q^{11} +0.347296 q^{12} +(-0.245100 - 3.59721i) q^{13} -1.53209 q^{14} +(-0.0603074 - 0.104455i) q^{15} +(2.28699 + 3.96118i) q^{16} +(-2.46064 + 4.26195i) q^{17} +1.53209 q^{18} +(0.379385 - 0.657115i) q^{19} +(-0.0209445 + 0.0362770i) q^{20} -1.00000 q^{21} +(-3.50387 + 6.06888i) q^{22} +(2.73783 + 4.74205i) q^{23} +(1.26604 + 2.19285i) q^{24} -4.98545 q^{25} +(-4.58512 + 3.08083i) q^{26} +1.00000 q^{27} +(0.173648 + 0.300767i) q^{28} +(-5.33022 - 9.23222i) q^{29} +(-0.0923963 + 0.160035i) q^{30} +8.63816 q^{31} +(0.971782 - 1.68317i) q^{32} +(-2.28699 + 3.96118i) q^{33} +7.53983 q^{34} +(0.0603074 - 0.104455i) q^{35} +(-0.173648 - 0.300767i) q^{36} +(2.35117 + 4.07234i) q^{37} -1.16250 q^{38} +(-2.99273 + 2.01087i) q^{39} -0.305407 q^{40} +(-5.45336 - 9.44550i) q^{41} +(0.766044 + 1.32683i) q^{42} +(-0.631759 + 1.09424i) q^{43} +1.58853 q^{44} +(-0.0603074 + 0.104455i) q^{45} +(4.19459 - 7.26525i) q^{46} +5.94356 q^{47} +(2.28699 - 3.96118i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(3.81908 + 6.61484i) q^{50} +4.92127 q^{51} +(1.12449 + 0.550931i) q^{52} +9.49794 q^{53} +(-0.766044 - 1.32683i) q^{54} +(-0.275845 - 0.477777i) q^{55} +(-1.26604 + 2.19285i) q^{56} -0.758770 q^{57} +(-8.16637 + 14.1446i) q^{58} +(4.49660 - 7.78833i) q^{59} +0.0418891 q^{60} +(4.72668 - 8.18685i) q^{61} +(-6.61721 - 11.4613i) q^{62} +(0.500000 + 0.866025i) q^{63} +6.17024 q^{64} +(-0.0295627 - 0.433877i) q^{65} +7.00774 q^{66} +(-6.51501 - 11.2843i) q^{67} +(-0.854570 - 1.48016i) q^{68} +(2.73783 - 4.74205i) q^{69} -0.184793 q^{70} +(-1.23783 + 2.14398i) q^{71} +(1.26604 - 2.19285i) q^{72} +5.89393 q^{73} +(3.60220 - 6.23919i) q^{74} +(2.49273 + 4.31753i) q^{75} +(0.131759 + 0.228213i) q^{76} -4.57398 q^{77} +(4.96064 + 2.43042i) q^{78} -8.18479 q^{79} +(0.275845 + 0.477777i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-8.35504 + 14.4713i) q^{82} +12.2490 q^{83} +(0.173648 - 0.300767i) q^{84} +(-0.296789 + 0.514054i) q^{85} +1.93582 q^{86} +(-5.33022 + 9.23222i) q^{87} +(5.79086 + 10.0301i) q^{88} +(3.37939 + 5.85327i) q^{89} +0.184793 q^{90} +(-3.23783 - 1.58634i) q^{91} -1.90167 q^{92} +(-4.31908 - 7.48086i) q^{93} +(-4.55303 - 7.88609i) q^{94} +(0.0457595 - 0.0792577i) q^{95} -1.94356 q^{96} +(5.03596 - 8.72254i) q^{97} +(-0.766044 + 1.32683i) q^{98} +4.57398 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{3} + 12 q^{5} + 3 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - 3 * q^3 + 12 * q^5 + 3 * q^7 - 6 * q^8 - 3 * q^9	\( 6 q - 3 q^{3} + 12 q^{5} + 3 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{10} - 6 q^{11} - 6 q^{15} + 6 q^{16} - 6 q^{17} - 9 q^{19} + 3 q^{20} - 6 q^{21} + 3 q^{22} - 3 q^{23} + 3 q^{24} + 6 q^{25} - 6 q^{26} + 6 q^{27} - 9 q^{29} + 3 q^{30} + 18 q^{31} - 9 q^{32} - 6 q^{33} - 12 q^{34} + 6 q^{35} - 12 q^{37} - 12 q^{38} - 6 q^{40} - 6 q^{41} - 9 q^{43} + 30 q^{44} - 6 q^{45} + 21 q^{46} + 6 q^{47} + 6 q^{48} - 3 q^{49} + 6 q^{50} + 12 q^{51} - 6 q^{52} + 6 q^{53} - 3 q^{56} + 18 q^{57} - 30 q^{58} - 15 q^{59} - 6 q^{60} + 15 q^{61} - 9 q^{62} + 3 q^{63} - 6 q^{64} - 6 q^{65} - 6 q^{66} - 9 q^{67} - 21 q^{68} - 3 q^{69} + 6 q^{70} + 12 q^{71} + 3 q^{72} + 60 q^{73} + 21 q^{74} - 3 q^{75} + 6 q^{76} - 12 q^{77} + 21 q^{78} - 42 q^{79} - 3 q^{81} + 48 q^{83} + 3 q^{85} + 30 q^{86} - 9 q^{87} + 3 q^{88} + 9 q^{89} - 6 q^{90} + 12 q^{92} - 9 q^{93} - 15 q^{94} - 30 q^{95} + 18 q^{96} - 3 q^{97} + 12 q^{99}+O(q^{100}) \) 6 * q - 3 * q^3 + 12 * q^5 + 3 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^10 - 6 * q^11 - 6 * q^15 + 6 * q^16 - 6 * q^17 - 9 * q^19 + 3 * q^20 - 6 * q^21 + 3 * q^22 - 3 * q^23 + 3 * q^24 + 6 * q^25 - 6 * q^26 + 6 * q^27 - 9 * q^29 + 3 * q^30 + 18 * q^31 - 9 * q^32 - 6 * q^33 - 12 * q^34 + 6 * q^35 - 12 * q^37 - 12 * q^38 - 6 * q^40 - 6 * q^41 - 9 * q^43 + 30 * q^44 - 6 * q^45 + 21 * q^46 + 6 * q^47 + 6 * q^48 - 3 * q^49 + 6 * q^50 + 12 * q^51 - 6 * q^52 + 6 * q^53 - 3 * q^56 + 18 * q^57 - 30 * q^58 - 15 * q^59 - 6 * q^60 + 15 * q^61 - 9 * q^62 + 3 * q^63 - 6 * q^64 - 6 * q^65 - 6 * q^66 - 9 * q^67 - 21 * q^68 - 3 * q^69 + 6 * q^70 + 12 * q^71 + 3 * q^72 + 60 * q^73 + 21 * q^74 - 3 * q^75 + 6 * q^76 - 12 * q^77 + 21 * q^78 - 42 * q^79 - 3 * q^81 + 48 * q^83 + 3 * q^85 + 30 * q^86 - 9 * q^87 + 3 * q^88 + 9 * q^89 - 6 * q^90 + 12 * q^92 - 9 * q^93 - 15 * q^94 - 30 * q^95 + 18 * q^96 - 3 * q^97 + 12 * q^99

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L-functions

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