LMFDB - Embedded newform 273.2.bd.a.127.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(43,273)]

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, 1]))

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

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

chi := DirichletCharacter("273.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bd (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 22x^{14} + 187x^{12} + 774x^{10} + 1619x^{8} + 1618x^{6} + 690x^{4} + 96x^{2} + 1 $ x^16 + 22x^14 + 187x^12 + 774x^10 + 1619x^8 + 1618x^6 + 690x^4 + 96*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.6
Root			$-1.10207i$ of defining polynomial
Character	$\chi$	$=$	273.127
Dual form			273.2.bd.a.43.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.954423 - 0.551037i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.392717 + 0.680206i) q^{4} +3.28432i q^{5} +(-0.954423 - 0.551037i) q^{6} +(0.866025 + 0.500000i) q^{7} +3.06975i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.954423 - 0.551037i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.392717 + 0.680206i) q^{4} +3.28432i q^{5} +(-0.954423 - 0.551037i) q^{6} +(0.866025 + 0.500000i) q^{7} +3.06975i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.80978 + 3.13463i) q^{10} +(-1.21979 + 0.704249i) q^{11} +0.785435 q^{12} +(3.42102 + 1.13870i) q^{13} +1.10207 q^{14} +(2.84430 - 1.64216i) q^{15} +(0.906111 + 1.56943i) q^{16} +(2.88992 - 5.00548i) q^{17} +1.10207i q^{18} +(-5.36590 - 3.09800i) q^{19} +(-2.23401 - 1.28981i) q^{20} -1.00000i q^{21} +(-0.776134 + 1.34430i) q^{22} +(1.70072 + 2.94574i) q^{23} +(2.65848 - 1.53488i) q^{24} -5.78675 q^{25} +(3.89256 - 0.798302i) q^{26} +1.00000 q^{27} +(-0.680206 + 0.392717i) q^{28} +(4.28846 + 7.42783i) q^{29} +(1.80978 - 3.13463i) q^{30} -7.64123i q^{31} +(-3.58734 - 2.07115i) q^{32} +(1.21979 + 0.704249i) q^{33} -6.36980i q^{34} +(-1.64216 + 2.84430i) q^{35} +(-0.392717 - 0.680206i) q^{36} +(4.84216 - 2.79562i) q^{37} -6.82845 q^{38} +(-0.724364 - 3.53204i) q^{39} -10.0820 q^{40} +(-0.999386 + 0.576996i) q^{41} +(-0.551037 - 0.954423i) q^{42} +(0.409497 - 0.709270i) q^{43} -1.10628i q^{44} +(-2.84430 - 1.64216i) q^{45} +(3.24642 + 1.87432i) q^{46} +3.35146i q^{47} +(0.906111 - 1.56943i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-5.52300 + 3.18871i) q^{50} -5.77983 q^{51} +(-2.11805 + 1.87981i) q^{52} +5.54281 q^{53} +(0.954423 - 0.551037i) q^{54} +(-2.31298 - 4.00619i) q^{55} +(-1.53488 + 2.65848i) q^{56} +6.19600i q^{57} +(8.18602 + 4.72620i) q^{58} +(-4.23463 - 2.44486i) q^{59} +2.57962i q^{60} +(1.48876 - 2.57860i) q^{61} +(-4.21060 - 7.29297i) q^{62} +(-0.866025 + 0.500000i) q^{63} -8.18957 q^{64} +(-3.73986 + 11.2357i) q^{65} +1.55227 q^{66} +(0.232752 - 0.134379i) q^{67} +(2.26984 + 3.93148i) q^{68} +(1.70072 - 2.94574i) q^{69} +3.61956i q^{70} +(-8.03762 - 4.64052i) q^{71} +(-2.65848 - 1.53488i) q^{72} -12.1448i q^{73} +(3.08098 - 5.33641i) q^{74} +(2.89337 + 5.01147i) q^{75} +(4.21456 - 2.43328i) q^{76} -1.40850 q^{77} +(-2.63763 - 2.97191i) q^{78} +6.00232 q^{79} +(-5.15451 + 2.97596i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.635891 + 1.10140i) q^{82} +6.02174i q^{83} +(0.680206 + 0.392717i) q^{84} +(16.4396 + 9.49140i) q^{85} -0.902592i q^{86} +(4.28846 - 7.42783i) q^{87} +(-2.16187 - 3.74447i) q^{88} +(14.3573 - 8.28917i) q^{89} -3.61956 q^{90} +(2.39334 + 2.69665i) q^{91} -2.67162 q^{92} +(-6.61750 + 3.82061i) q^{93} +(1.84678 + 3.19871i) q^{94} +(10.1748 - 17.6233i) q^{95} +4.14230i q^{96} +(-16.2251 - 9.36758i) q^{97} +(0.954423 + 0.551037i) q^{98} -1.40850i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 + 6 * q^4 - 8 * q^9	$ 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9} - 4 q^{10} - 12 q^{11} - 12 q^{12} + 4 q^{13} + 4 q^{14} - 10 q^{16} + 10 q^{17} + 6 q^{20} - 2 q^{22} - 2 q^{23} + 12 q^{25} + 20 q^{26} + 16 q^{27} + 12 q^{29} - 4 q^{30} + 30 q^{32} + 12 q^{33} - 2 q^{35} + 6 q^{36} + 18 q^{37} - 32 q^{38} - 8 q^{39} - 60 q^{40} + 18 q^{41} - 2 q^{42} - 10 q^{43} + 30 q^{46} - 10 q^{48} + 8 q^{49} - 24 q^{50} - 20 q^{51} - 26 q^{52} + 12 q^{53} + 10 q^{55} + 12 q^{56} - 54 q^{58} - 60 q^{59} - 6 q^{61} + 16 q^{62} + 16 q^{64} - 20 q^{65} + 4 q^{66} - 18 q^{67} - 20 q^{68} - 2 q^{69} + 6 q^{71} + 18 q^{74} - 6 q^{75} + 72 q^{76} - 16 q^{77} + 14 q^{78} - 4 q^{79} + 30 q^{80} - 8 q^{81} - 18 q^{82} - 24 q^{85} + 12 q^{87} - 2 q^{88} + 78 q^{89} + 8 q^{90} - 8 q^{91} - 20 q^{92} + 6 q^{93} + 16 q^{94} - 4 q^{95} - 54 q^{97}+O(q^{100}) $ 16 * q - 8 * q^3 + 6 * q^4 - 8 * q^9 - 4 * q^10 - 12 * q^11 - 12 * q^12 + 4 * q^13 + 4 * q^14 - 10 * q^16 + 10 * q^17 + 6 * q^20 - 2 * q^22 - 2 * q^23 + 12 * q^25 + 20 * q^26 + 16 * q^27 + 12 * q^29 - 4 * q^30 + 30 * q^32 + 12 * q^33 - 2 * q^35 + 6 * q^36 + 18 * q^37 - 32 * q^38 - 8 * q^39 - 60 * q^40 + 18 * q^41 - 2 * q^42 - 10 * q^43 + 30 * q^46 - 10 * q^48 + 8 * q^49 - 24 * q^50 - 20 * q^51 - 26 * q^52 + 12 * q^53 + 10 * q^55 + 12 * q^56 - 54 * q^58 - 60 * q^59 - 6 * q^61 + 16 * q^62 + 16 * q^64 - 20 * q^65 + 4 * q^66 - 18 * q^67 - 20 * q^68 - 2 * q^69 + 6 * q^71 + 18 * q^74 - 6 * q^75 + 72 * q^76 - 16 * q^77 + 14 * q^78 - 4 * q^79 + 30 * q^80 - 8 * q^81 - 18 * q^82 - 24 * q^85 + 12 * q^87 - 2 * q^88 + 78 * q^89 + 8 * q^90 - 8 * q^91 - 20 * q^92 + 6 * q^93 + 16 * q^94 - 4 * q^95 - 54 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	0.954423	−	0.551037i	0.674879	−	0.389642i	−0.123044	−	0.992401i	$-0.539266\pi$
$2$	0.954423	−	0.551037i	0.674879	−	0.389642i	0.797923	+	0.602760i	$0.205932\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.392717	+	0.680206i	−0.196359	+	0.340103i
$5$			3.28432i			1.46879i	0.678721	+	0.734396i	$0.262534\pi$
$5$			3.28432i			1.46879i	−0.678721	+	0.734396i	$0.737466\pi$
$6$	−0.954423	−	0.551037i	−0.389642	−	0.224960i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$			3.06975i			1.08532i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.80978	+	3.13463i	0.572302	+	0.991257i
$11$	−1.21979	+	0.704249i	−0.367782	+	0.212339i	−0.672489	−	0.740107i	$-0.734775\pi$
$11$	−1.21979	+	0.704249i	−0.367782	+	0.212339i	0.304707	+	0.952446i	$0.401441\pi$
$12$	0.785435			0.226735
$13$	3.42102	+	1.13870i	0.948819	+	0.315819i
$13$	3.42102	+	1.13870i	0.948819	+	0.315819i
$14$	1.10207			0.294541
$15$	2.84430	−	1.64216i	0.734396	−	0.424004i
$16$	0.906111	+	1.56943i	0.226528	+	0.392358i
$17$	2.88992	−	5.00548i	0.700907	−	1.21401i	−0.267241	−	0.963630i	$-0.586112\pi$
$17$	2.88992	−	5.00548i	0.700907	−	1.21401i	0.968148	−	0.250377i	$-0.0805547\pi$
$18$			1.10207i			0.259761i
$19$	−5.36590	−	3.09800i	−1.23102	−	0.710730i	−0.263778	−	0.964583i	$-0.584969\pi$
$19$	−5.36590	−	3.09800i	−1.23102	−	0.710730i	−0.967243	+	0.253853i	$0.918302\pi$
$20$	−2.23401	−	1.28981i	−0.499541	−	0.288410i
$21$		−	1.00000i		−	0.218218i
$22$	−0.776134	+	1.34430i	−0.165472	+	0.286606i
$23$	1.70072	+	2.94574i	0.354626	+	0.614230i	0.987054	−	0.160389i	$-0.0512750\pi$
$23$	1.70072	+	2.94574i	0.354626	+	0.614230i	−0.632428	+	0.774619i	$0.717942\pi$
$24$	2.65848	−	1.53488i	0.542661	−	0.313305i
$25$	−5.78675			−1.15735
$26$	3.89256	−	0.798302i	0.763395	−	0.156560i
$27$	1.00000			0.192450
$28$	−0.680206	+	0.392717i	−0.128547	+	0.0742166i
$29$	4.28846	+	7.42783i	0.796347	+	1.37931i	0.921980	+	0.387237i	$0.126571\pi$
$29$	4.28846	+	7.42783i	0.796347	+	1.37931i	−0.125633	+	0.992077i	$0.540096\pi$
$30$	1.80978	−	3.13463i	0.330419	−	0.572302i
$31$		−	7.64123i		−	1.37240i	−0.727411	−	0.686202i	$-0.759276\pi$
$31$		−	7.64123i		−	1.37240i	0.727411	−	0.686202i	$-0.240724\pi$
$32$	−3.58734	−	2.07115i	−0.634158	−	0.366131i
$33$	1.21979	+	0.704249i	0.212339	+	0.122594i
$34$		−	6.36980i		−	1.09241i
$35$	−1.64216	+	2.84430i	−0.277576	+	0.480775i
$36$	−0.392717	−	0.680206i	−0.0654529	−	0.113368i
$37$	4.84216	−	2.79562i	0.796046	−	0.459597i	−0.0460407	−	0.998940i	$-0.514660\pi$
$37$	4.84216	−	2.79562i	0.796046	−	0.459597i	0.842087	+	0.539342i	$0.181327\pi$
$38$	−6.82845			−1.10772
$39$	−0.724364	−	3.53204i	−0.115991	−	0.565579i
$40$	−10.0820			−1.59411
$41$	−0.999386	+	0.576996i	−0.156078	+	0.0901116i	−0.576005	−	0.817446i	$-0.695389\pi$
$41$	−0.999386	+	0.576996i	−0.156078	+	0.0901116i	0.419927	+	0.907558i	$0.362056\pi$
$42$	−0.551037	−	0.954423i	−0.0850268	−	0.147271i
$43$	0.409497	−	0.709270i	0.0624477	−	0.108163i	−0.833111	−	0.553105i	$-0.813443\pi$
$43$	0.409497	−	0.709270i	0.0624477	−	0.108163i	0.895559	+	0.444943i	$0.146776\pi$
$44$		−	1.10628i		−	0.166778i
$45$	−2.84430	−	1.64216i	−0.424004	−	0.244799i
$46$	3.24642	+	1.87432i	0.478659	+	0.276354i
$47$			3.35146i			0.488861i	0.969667	+	0.244430i	$0.0786009\pi$
$47$			3.35146i			0.488861i	−0.969667	+	0.244430i	$0.921399\pi$
$48$	0.906111	−	1.56943i	0.130786	−	0.226528i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	−5.52300	+	3.18871i	−0.781071	+	0.450951i
$51$	−5.77983			−0.809338
$52$	−2.11805	+	1.87981i	−0.293720	+	0.260683i
$53$	5.54281			0.761363			0.380682	−	0.924706i	$-0.375689\pi$
$53$	5.54281			0.761363			0.380682	+	0.924706i	$0.375689\pi$
$54$	0.954423	−	0.551037i	0.129881	−	0.0749866i
$55$	−2.31298	−	4.00619i	−0.311882	−	0.540195i
$56$	−1.53488	+	2.65848i	−0.205106	+	0.355255i
$57$			6.19600i			0.820681i
$58$	8.18602	+	4.72620i	1.07488	+	0.620580i
$59$	−4.23463	−	2.44486i	−0.551302	−	0.318294i	0.198345	−	0.980132i	$-0.436443\pi$
$59$	−4.23463	−	2.44486i	−0.551302	−	0.318294i	−0.749647	+	0.661838i	$0.769777\pi$
$60$			2.57962i			0.333027i
$61$	1.48876	−	2.57860i	0.190616	−	0.330156i	−0.754839	−	0.655910i	$-0.772285\pi$
$61$	1.48876	−	2.57860i	0.190616	−	0.330156i	0.945454	+	0.325754i	$0.105618\pi$
$62$	−4.21060	−	7.29297i	−0.534746	−	0.926208i
$63$	−0.866025	+	0.500000i	−0.109109	+	0.0629941i
$64$	−8.18957			−1.02370
$65$	−3.73986	+	11.2357i	−0.463872	+	1.39362i
$66$	1.55227			0.191071
$67$	0.232752	−	0.134379i	0.0284352	−	0.0164171i	−0.485715	−	0.874117i	$-0.661441\pi$
$67$	0.232752	−	0.134379i	0.0284352	−	0.0164171i	0.514150	+	0.857700i	$0.328107\pi$
$68$	2.26984	+	3.93148i	0.275259	+	0.476762i
$69$	1.70072	−	2.94574i	0.204743	−	0.354626i
$70$			3.61956i			0.432620i
$71$	−8.03762	−	4.64052i	−0.953890	−	0.550728i	−0.0596026	−	0.998222i	$-0.518983\pi$
$71$	−8.03762	−	4.64052i	−0.953890	−	0.550728i	−0.894287	+	0.447494i	$0.852317\pi$
$72$	−2.65848	−	1.53488i	−0.313305	−	0.180887i
$73$		−	12.1448i		−	1.42144i	−0.703474	−	0.710721i	$-0.748369\pi$
$73$		−	12.1448i		−	1.42144i	0.703474	−	0.710721i	$-0.251631\pi$
$74$	3.08098	−	5.33641i	0.358157	−	0.620345i
$75$	2.89337	+	5.01147i	0.334098	+	0.578675i
$76$	4.21456	−	2.43328i	0.483443	−	0.279116i
$77$	−1.40850			−0.160513
$78$	−2.63763	−	2.97191i	−0.298653	−	0.336502i
$79$	6.00232			0.675313			0.337657	−	0.941269i	$-0.390366\pi$
$79$	6.00232			0.675313			0.337657	+	0.941269i	$0.390366\pi$
$80$	−5.15451	+	2.97596i	−0.576292	+	0.332722i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−0.635891	+	1.10140i	−0.0702225	+	0.121629i
$83$			6.02174i			0.660972i	0.943811	+	0.330486i	$0.107213\pi$
$83$			6.02174i			0.660972i	−0.943811	+	0.330486i	$0.892787\pi$
$84$	0.680206	+	0.392717i	0.0742166	+	0.0428490i
$85$	16.4396	+	9.49140i	1.78312	+	1.02949i
$86$		−	0.902592i		−	0.0973290i
$87$	4.28846	−	7.42783i	0.459771	−	0.796347i
$88$	−2.16187	−	3.74447i	−0.230456	−	0.399162i
$89$	14.3573	−	8.28917i	1.52187	−	0.878650i	0.522201	−	0.852823i	$-0.325111\pi$
$89$	14.3573	−	8.28917i	1.52187	−	0.878650i	0.999666	−	0.0258279i	$-0.00822218\pi$
$90$	−3.61956			−0.381535
$91$	2.39334	+	2.69665i	0.250890	+	0.282686i
$92$	−2.67162			−0.278535
$93$	−6.61750	+	3.82061i	−0.686202	+	0.396179i
$94$	1.84678	+	3.19871i	0.190481	+	0.329922i
$95$	10.1748	−	17.6233i	1.04391	−	1.80811i
$96$			4.14230i			0.422772i
$97$	−16.2251	−	9.36758i	−1.64741	−	0.951134i	−0.978096	−	0.208156i	$-0.933254\pi$
$97$	−16.2251	−	9.36758i	−1.64741	−	0.951134i	−0.669316	−	0.742977i	$-0.733413\pi$
$98$	0.954423	+	0.551037i	0.0964113	+	0.0556631i
$99$		−	1.40850i		−	0.141559i
$100$	2.27256	−	3.93618i	0.227256	−	0.393618i
$101$	7.52581	+	13.0351i	0.748846	+	1.29704i	0.948376	+	0.317148i	$0.102725\pi$
$101$	7.52581	+	13.0351i	0.748846	+	1.29704i	−0.199530	+	0.979892i	$0.563942\pi$
$102$	−5.51640	+	3.18490i	−0.546205	+	0.315352i
$103$	14.0763			1.38698			0.693488	−	0.720468i	$-0.256073\pi$
$103$	14.0763			1.38698			0.693488	+	0.720468i	$0.256073\pi$
$104$	−3.49553	+	10.5017i	−0.342765	+	1.02977i
$105$	3.28432			0.320517
$106$	5.29018	−	3.05429i	0.513828	−	0.296659i
$107$	−3.67344	−	6.36259i	−0.355125	−	0.615094i	0.632014	−	0.774957i	$-0.282228\pi$
$107$	−3.67344	−	6.36259i	−0.355125	−	0.615094i	−0.987139	+	0.159862i	$0.948895\pi$
$108$	−0.392717	+	0.680206i	−0.0377892	+	0.0654529i
$109$		−	4.65621i		−	0.445984i	−0.974820	−	0.222992i	$-0.928418\pi$
$109$		−	4.65621i		−	0.445984i	0.974820	−	0.222992i	$-0.0715824\pi$
$110$	−4.41512	−	2.54907i	−0.420965	−	0.243044i
$111$	−4.84216	−	2.79562i	−0.459597	−	0.265349i
$112$			1.81222i			0.171239i
$113$	−3.58572	+	6.21066i	−0.337317	+	0.584250i	−0.983927	−	0.178571i	$-0.942853\pi$
$113$	−3.58572	+	6.21066i	−0.337317	+	0.584250i	0.646610	+	0.762820i	$0.276186\pi$
$114$	3.41422	+	5.91361i	0.319771	+	0.553860i
$115$	−9.67475	+	5.58572i	−0.902175	+	0.520871i
$116$	−6.73661			−0.625479
$117$	−2.69665	+	2.39334i	−0.249306	+	0.221264i
$118$	−5.38884			−0.496083
$119$	5.00548	−	2.88992i	0.458852	−	0.264918i
$120$	5.04102	+	8.73131i	0.460180	+	0.797056i
$121$	−4.50807	+	7.80820i	−0.409824	+	0.709837i
$122$		−	3.28143i		−	0.297087i
$123$	0.999386	+	0.576996i	0.0901116	+	0.0520259i
$124$	5.19761	+	3.00084i	0.466759	+	0.269484i
$125$		−	2.58392i		−	0.231113i
$126$	−0.551037	+	0.954423i	−0.0490902	+	0.0850268i
$127$	−5.82996	−	10.0978i	−0.517326	−	0.896034i	−0.999798	−	0.0201229i	$-0.993594\pi$
$127$	−5.82996	−	10.0978i	−0.517326	−	0.896034i	0.482472	−	0.875912i	$-0.339739\pi$
$128$	−0.641633	+	0.370447i	−0.0567129	+	0.0327432i
$129$	−0.818994			−0.0721084
$130$	2.62188	+	12.7844i	0.229954	+	1.12127i
$131$	8.68221			0.758568			0.379284	−	0.925280i	$-0.376170\pi$
$131$	8.68221			0.758568			0.379284	+	0.925280i	$0.376170\pi$
$132$	−0.958069	+	0.553141i	−0.0833892	+	0.0481448i
$133$	−3.09800	−	5.36590i	−0.268631	−	0.465282i
$134$	0.148096	−	0.256510i	0.0127935	−	0.0221591i
$135$			3.28432i			0.282669i
$136$	15.3656	+	8.87133i	1.31759	+	0.760710i
$137$	10.8923	+	6.28868i	0.930593	+	0.537278i	0.886999	−	0.461771i	$-0.152786\pi$
$137$	10.8923	+	6.28868i	0.930593	+	0.537278i	0.0435937	+	0.999049i	$0.486119\pi$
$138$		−	3.74865i		−	0.319106i
$139$	5.36634	−	9.29478i	0.455167	−	0.788373i	−0.543531	−	0.839389i	$-0.682913\pi$
$139$	5.36634	−	9.29478i	0.455167	−	0.788373i	0.998698	+	0.0510166i	$0.0162461\pi$
$140$	−1.28981	−	2.23401i	−0.109009	−	0.188809i
$141$	2.90245	−	1.67573i	0.244430	−	0.141122i
$142$	−10.2284			−0.858347
$143$	−4.97487	+	1.02027i	−0.416019	+	0.0853189i
$144$	−1.81222			−0.151019
$145$	−24.3954	+	14.0847i	−2.02593	+	1.16967i
$146$	−6.69224	−	11.5913i	−0.553853	−	0.959302i
$147$	0.500000	−	0.866025i	0.0412393	−	0.0714286i
$148$			4.39156i			0.360984i
$149$	−9.93345	−	5.73508i	−0.813780	−	0.469836i	0.0344866	−	0.999405i	$-0.489020\pi$
$149$	−9.93345	−	5.73508i	−0.813780	−	0.469836i	−0.848267	+	0.529569i	$0.822354\pi$
$150$	5.52300	+	3.18871i	0.450951	+	0.260357i
$151$			9.07431i			0.738457i	0.929339	+	0.369228i	$0.120378\pi$
$151$			9.07431i			0.738457i	−0.929339	+	0.369228i	$0.879622\pi$
$152$	9.51010	−	16.4720i	0.771371	−	1.33605i
$153$	2.88992	+	5.00548i	0.233636	+	0.404669i
$154$	−1.34430	+	0.776134i	−0.108327	+	0.0625426i
$155$	25.0962			2.01578
$156$	2.68699	+	0.894376i	0.215131	+	0.0716074i
$157$	−16.8251			−1.34279			−0.671393	−	0.741101i	$-0.734304\pi$
$157$	−16.8251			−1.34279			−0.671393	+	0.741101i	$0.734304\pi$
$158$	5.72875	−	3.30750i	0.455755	−	0.263130i
$159$	−2.77140	−	4.80021i	−0.219787	−	0.380682i
$160$	6.80232	−	11.7820i	0.537771	−	0.931446i
$161$			3.40145i			0.268072i
$162$	−0.954423	−	0.551037i	−0.0749866	−	0.0432935i
$163$	18.0424	+	10.4168i	1.41319	+	0.815905i	0.995687	−	0.0927715i	$-0.0295726\pi$
$163$	18.0424	+	10.4168i	1.41319	+	0.815905i	0.417501	+	0.908676i	$0.362906\pi$
$164$		−	0.906385i		−	0.0707768i
$165$	−2.31298	+	4.00619i	−0.180065	+	0.311882i
$166$	3.31820	+	5.74729i	0.257542	+	0.446076i
$167$	−5.37739	+	3.10464i	−0.416115	+	0.240244i	−0.693414	−	0.720540i	$-0.743894\pi$
$167$	−5.37739	+	3.10464i	−0.416115	+	0.240244i	0.277299	+	0.960784i	$0.410561\pi$
$168$	3.06975			0.236837
$169$	10.4067	+	7.79104i	0.800517	+	0.599310i
$170$	20.9204			1.60452
$171$	5.36590	−	3.09800i	0.410340	−	0.236910i
$172$	0.321633	+	0.557085i	0.0245243	+	0.0424774i
$173$	−5.27490	+	9.13639i	−0.401043	+	0.694627i	−0.993852	−	0.110716i	$-0.964686\pi$
$173$	−5.27490	+	9.13639i	−0.401043	+	0.694627i	0.592809	+	0.805343i	$0.298019\pi$
$174$		−	9.45240i		−	0.716584i
$175$	−5.01147	−	2.89337i	−0.378831	−	0.218718i
$176$	−2.21054	−	1.27626i	−0.166626	−	0.0962014i
$177$			4.88973i			0.367534i
$178$	9.13527	−	15.8228i	0.684718	−	1.18597i
$179$	−10.5029	−	18.1916i	−0.785025	−	1.35970i	−0.928984	−	0.370119i	$-0.879317\pi$
$179$	−10.5029	−	18.1916i	−0.785025	−	1.35970i	0.143960	−	0.989584i	$-0.454016\pi$
$180$	2.23401	−	1.28981i	0.166514	−	0.0961367i
$181$	14.6306			1.08748			0.543741	−	0.839253i	$-0.317007\pi$
$181$	14.6306			1.08748			0.543741	+	0.839253i	$0.317007\pi$
$182$	3.77021	+	1.25493i	0.279467	+	0.0930218i
$183$	−2.97751			−0.220104
$184$	−9.04270	+	5.22080i	−0.666637	+	0.384883i
$185$	9.18171	+	15.9032i	0.675053	+	1.16923i
$186$	−4.21060	+	7.29297i	−0.308736	+	0.534746i
$187$			8.14088i			0.595320i
$188$	−2.27968	−	1.31618i	−0.166263	−	0.0959920i
$189$	0.866025	+	0.500000i	0.0629941	+	0.0363696i
$190$		−	22.4268i		−	1.62701i
$191$	2.61431	−	4.52813i	0.189165	−	0.327644i	−0.755807	−	0.654794i	$-0.772755\pi$
$191$	2.61431	−	4.52813i	0.189165	−	0.327644i	0.944972	+	0.327151i	$0.106089\pi$
$192$	4.09478	+	7.09237i	0.295516	+	0.511848i
$193$	−20.5269	+	11.8512i	−1.47756	+	0.853069i	−0.999678	−	0.0253561i	$-0.991928\pi$
$193$	−20.5269	+	11.8512i	−1.47756	+	0.853069i	−0.477880	+	0.878425i	$0.658595\pi$
$194$	−20.6475			−1.48241
$195$	11.6003	−	2.37904i	0.830717	−	0.170367i
$196$	−0.785435			−0.0561025
$197$	−13.5273	+	7.80999i	−0.963780	+	0.556439i	−0.897334	−	0.441351i	$-0.854499\pi$
$197$	−13.5273	+	7.80999i	−0.963780	+	0.556439i	−0.0664457	+	0.997790i	$0.521166\pi$
$198$	−0.776134	−	1.34430i	−0.0551574	−	0.0955354i
$199$	−10.4174	+	18.0434i	−0.738468	+	1.27906i	0.214717	+	0.976676i	$0.431117\pi$
$199$	−10.4174	+	18.0434i	−0.738468	+	1.27906i	−0.953185	+	0.302388i	$0.902216\pi$
$200$		−	17.7639i		−	1.25610i
$201$	−0.232752	−	0.134379i	−0.0164171	−	0.00947839i
$202$	14.3656	+	8.29399i	1.01076	+	0.583563i
$203$			8.57692i			0.601982i
$204$	2.26984	−	3.93148i	0.158921	−	0.275259i
$205$	−1.89504	−	3.28230i	−0.132355	−	0.229246i
$206$	13.4347	−	7.75654i	0.936041	−	0.540424i
$207$	−3.40145			−0.236417
$208$	1.31271	+	6.40084i	0.0910200	+	0.443818i
$209$	8.72705			0.603663
$210$	3.13463	−	1.80978i	0.216310	−	0.124887i
$211$	4.48177	+	7.76266i	0.308538	+	0.534403i	0.978043	−	0.208404i	$-0.0668270\pi$
$211$	4.48177	+	7.76266i	0.308538	+	0.534403i	−0.669505	+	0.742808i	$0.733494\pi$
$212$	−2.17676	+	3.77025i	−0.149500	+	0.258942i
$213$			9.28104i			0.635926i
$214$	−7.01203	−	4.04840i	−0.479333	−	0.276743i
$215$	2.32947	+	1.34492i	0.158868	+	0.0917227i
$216$			3.06975i			0.208870i
$217$	3.82061	−	6.61750i	0.259360	−	0.449225i
$218$	−2.56574	−	4.44400i	−0.173774	−	0.300986i
$219$	−10.5177	+	6.07241i	−0.710721	+	0.410335i
$220$	3.63339			0.244963
$221$	15.5862	−	13.8331i	1.04844	−	0.930514i
$222$	−6.16196			−0.413564
$223$	2.96755	−	1.71332i	0.198722	−	0.114732i	−0.397337	−	0.917673i	$-0.630066\pi$
$223$	2.96755	−	1.71332i	0.198722	−	0.114732i	0.596059	+	0.802940i	$0.296732\pi$
$224$	−2.07115	−	3.58734i	−0.138385	−	0.239689i
$225$	2.89337	−	5.01147i	0.192892	−	0.334098i
$226$			7.90346i			0.525730i
$227$	−19.5826	−	11.3060i	−1.29974	−	0.750408i	−0.319385	−	0.947625i	$-0.603476\pi$
$227$	−19.5826	−	11.3060i	−1.29974	−	0.750408i	−0.980360	+	0.197217i	$0.936810\pi$
$228$	−4.21456	−	2.43328i	−0.279116	−	0.161148i
$229$			14.0168i			0.926253i	0.886292	+	0.463126i	$0.153272\pi$
$229$			14.0168i			0.926253i	−0.886292	+	0.463126i	$0.846728\pi$
$230$	−6.15587	+	10.6623i	−0.405906	+	0.703050i
$231$	0.704249	+	1.21979i	0.0463362	+	0.0802566i
$232$	−22.8016	+	13.1645i	−1.49700	+	0.864293i
$233$	−12.1663			−0.797043			−0.398522	−	0.917159i	$-0.630477\pi$
$233$	−12.1663			−0.797043			−0.398522	+	0.917159i	$0.630477\pi$
$234$	−1.25493	+	3.77021i	−0.0820375	+	0.246466i
$235$	−11.0073			−0.718034
$236$	3.32602	−	1.92028i	0.216506	−	0.125000i
$237$	−3.00116	−	5.19816i	−0.194946	−	0.337657i
$238$	3.18490	−	5.51640i	0.206446	−	0.357575i
$239$		−	9.34457i		−	0.604450i	−0.953237	−	0.302225i	$-0.902271\pi$
$239$		−	9.34457i		−	0.604450i	0.953237	−	0.302225i	$-0.0977294\pi$
$240$	5.15451	+	2.97596i	0.332722	+	0.192097i
$241$	−18.4239	−	10.6370i	−1.18678	−	0.685190i	−0.229210	−	0.973377i	$-0.573614\pi$
$241$	−18.4239	−	10.6370i	−1.18678	−	0.685190i	−0.957574	+	0.288186i	$0.906948\pi$
$242$			9.93644i			0.638739i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	1.16932	+	2.02532i	0.0748580	+	0.129658i
$245$	−2.84430	+	1.64216i	−0.181716	+	0.104914i
$246$	1.27178			0.0810859
$247$	−14.8291	−	16.7085i	−0.943554	−	1.06313i
$248$	23.4567			1.48950
$249$	5.21498	−	3.01087i	0.330486	−	0.190806i
$250$	−1.42384	−	2.46616i	−0.0900513	−	0.155973i
$251$	0.345368	−	0.598194i	0.0217994	−	0.0377577i	−0.854920	−	0.518760i	$-0.826394\pi$
$251$	0.345368	−	0.598194i	0.0217994	−	0.0377577i	0.876719	+	0.481002i	$0.159727\pi$
$252$		−	0.785435i		−	0.0494777i
$253$	−4.14907	−	2.39547i	−0.260850	−	0.150602i
$254$	−11.1285	−	6.42505i	−0.698265	−	0.403143i
$255$		−	18.9828i		−	1.18875i
$256$	7.78131	−	13.4776i	0.486332	−	0.842351i
$257$	−11.6700	−	20.2129i	−0.727952	−	1.26085i	−0.957748	−	0.287610i	$-0.907139\pi$
$257$	−11.6700	−	20.2129i	−0.727952	−	1.26085i	0.229796	−	0.973239i	$-0.426194\pi$
$258$	−0.781667	+	0.451296i	−0.0486645	+	0.0280965i
$259$	5.59124			0.347423
$260$	−6.17389	−	6.95633i	−0.382889	−	0.431414i
$261$	−8.57692			−0.530898
$262$	8.28651	−	4.78422i	0.511942	−	0.295570i
$263$	4.55501	+	7.88952i	0.280874	+	0.486488i	0.971600	−	0.236628i	$-0.0760423\pi$
$263$	4.55501	+	7.88952i	0.280874	+	0.486488i	−0.690726	+	0.723117i	$0.742709\pi$
$264$	−2.16187	+	3.74447i	−0.133054	+	0.230456i
$265$			18.2043i			1.11828i
$266$	−5.91361	−	3.41422i	−0.362587	−	0.209340i
$267$	−14.3573	−	8.28917i	−0.878650	−	0.507289i
$268$			0.211092i			0.0128945i
$269$	−2.20377	+	3.81704i	−0.134366	+	0.232729i	−0.925355	−	0.379101i	$-0.876233\pi$
$269$	−2.20377	+	3.81704i	−0.134366	+	0.232729i	0.790989	+	0.611831i	$0.209567\pi$
$270$	1.80978	+	3.13463i	0.110140	+	0.190767i
$271$	11.5954	−	6.69462i	0.704372	−	0.406669i	−0.104602	−	0.994514i	$-0.533357\pi$
$271$	11.5954	−	6.69462i	0.704372	−	0.406669i	0.808974	+	0.587845i	$0.200023\pi$
$272$	10.4743			0.635100
$273$	1.13870	−	3.42102i	0.0689174	−	0.207049i
$274$	13.8612			0.837383
$275$	7.05864	−	4.07531i	0.425652	−	0.245750i
$276$	1.33581	+	2.31369i	0.0804062	+	0.139268i
$277$	4.34484	−	7.52548i	0.261056	−	0.452163i	−0.705467	−	0.708743i	$-0.749263\pi$
$277$	4.34484	−	7.52548i	0.261056	−	0.452163i	0.966523	+	0.256581i	$0.0825959\pi$
$278$		−	11.8282i		−	0.709409i
$279$	6.61750	+	3.82061i	0.396179	+	0.228734i
$280$	−8.73131	−	5.04102i	−0.521795	−	0.301259i
$281$		−	21.7228i		−	1.29587i	−0.761695	−	0.647936i	$-0.775632\pi$
$281$		−	21.7228i		−	1.29587i	0.761695	−	0.647936i	$-0.224368\pi$
$282$	1.84678	−	3.19871i	0.109974	−	0.190481i
$283$	12.6879	+	21.9760i	0.754215	+	1.30634i	0.945764	+	0.324855i	$0.105316\pi$
$283$	12.6879	+	21.9760i	0.754215	+	1.30634i	−0.191549	+	0.981483i	$0.561351\pi$
$284$	6.31302	−	3.64483i	0.374609	−	0.216281i
$285$	−20.3496			−1.20541
$286$	−4.18593	+	3.71510i	−0.247519	+	0.219678i
$287$	−1.15399			−0.0681179
$288$	3.58734	−	2.07115i	0.211386	−	0.122044i
$289$	−8.20322	−	14.2084i	−0.482542	−	0.835788i
$290$	−15.5223	+	26.8855i	−0.911503	+	1.57877i
$291$			18.7352i			1.09827i
$292$	8.26098	+	4.76948i	0.483437	+	0.279113i
$293$	−22.9886	−	13.2725i	−1.34301	−	0.775387i	−0.355762	−	0.934577i	$-0.615779\pi$
$293$	−22.9886	−	13.2725i	−1.34301	−	0.775387i	−0.987248	+	0.159190i	$0.949112\pi$
$294$		−	1.10207i		−	0.0642742i
$295$	8.02971	−	13.9079i	0.467508	−	0.809747i
$296$	8.58187	+	14.8642i	0.498811	+	0.863966i
$297$	−1.21979	+	0.704249i	−0.0707797	+	0.0408647i
$298$	−12.6410			−0.732271
$299$	2.46389	+	12.0141i	0.142490	+	0.694791i
$300$	−4.54511			−0.262412
$301$	0.709270	−	0.409497i	0.0408816	−	0.0236030i
$302$	5.00028	+	8.66073i	0.287733	+	0.498369i
$303$	7.52581	−	13.0351i	0.432346	−	0.748846i
$304$		−	11.2285i		−	0.644001i
$305$	8.46894	+	4.88955i	0.484930	+	0.279975i
$306$	5.51640	+	3.18490i	0.315352	+	0.182068i
$307$			4.33093i			0.247179i	0.992333	+	0.123590i	$0.0394406\pi$
$307$			4.33093i			0.247179i	−0.992333	+	0.123590i	$0.960559\pi$
$308$	0.553141	−	0.958069i	0.0315182	−	0.0545911i
$309$	−7.03813	−	12.1904i	−0.400385	−	0.693488i
$310$	23.9524	−	13.8289i	1.36041	−	0.785431i
$311$	−14.9481			−0.847629			−0.423815	−	0.905749i	$-0.639309\pi$
$311$	−14.9481			−0.847629			−0.423815	+	0.905749i	$0.639309\pi$
$312$	10.8425	−	2.22362i	0.613835	−	0.125888i
$313$	−8.75971			−0.495128			−0.247564	−	0.968871i	$-0.579630\pi$
$313$	−8.75971			−0.495128			−0.247564	+	0.968871i	$0.579630\pi$
$314$	−16.0582	+	9.27122i	−0.906218	+	0.523205i
$315$	−1.64216	−	2.84430i	−0.0925252	−	0.160258i
$316$	−2.35721	+	4.08281i	−0.132604	+	0.229676i
$317$		−	5.46319i		−	0.306843i	−0.988161	−	0.153422i	$-0.950971\pi$
$317$		−	5.46319i		−	0.306843i	0.988161	−	0.153422i	$-0.0490293\pi$
$318$	−5.29018	−	3.05429i	−0.296659	−	0.171276i
$319$	−10.4621	−	6.04029i	−0.585764	−	0.338191i
$320$		−	26.8971i		−	1.50360i
$321$	−3.67344	+	6.36259i	−0.205031	+	0.355125i
$322$	1.87432	+	3.24642i	0.104452	+	0.180916i
$323$	−31.0140	+	17.9059i	−1.72566	+	0.996312i
$324$	0.785435			0.0436353
$325$	−19.7966	−	6.58938i	−1.09812	−	0.365513i
$326$	22.9601			1.27164
$327$	−4.03240	+	2.32811i	−0.222992	+	0.128745i
$328$	−1.77123	−	3.06787i	−0.0978000	−	0.169395i
$329$	−1.67573	+	2.90245i	−0.0923860	+	0.160017i
$330$			5.09814i			0.280643i
$331$	−7.46366	−	4.30914i	−0.410240	−	0.236852i	0.280653	−	0.959809i	$-0.409449\pi$
$331$	−7.46366	−	4.30914i	−0.410240	−	0.236852i	−0.690893	+	0.722957i	$0.742782\pi$
$332$	−4.09603	−	2.36484i	−0.224799	−	0.129788i
$333$			5.59124i			0.306398i
$334$	−3.42154	+	5.92627i	−0.187218	+	0.324271i
$335$	0.441345	+	0.764431i	0.0241132	+	0.0417653i
$336$	1.56943	−	0.906111i	0.0856195	−	0.0494324i
$337$	13.6769			0.745029			0.372515	−	0.928026i	$-0.378496\pi$
$337$	13.6769			0.745029			0.372515	+	0.928026i	$0.378496\pi$
$338$	14.2256	+	1.70146i	0.773768	+	0.0925474i
$339$	7.17145			0.389500
$340$	−12.9122	+	7.45488i	−0.700264	+	0.404297i
$341$	5.38132	+	9.32073i	0.291415	+	0.504746i
$342$	3.41422	−	5.91361i	0.184620	−	0.319771i
$343$			1.00000i			0.0539949i
$344$	2.17728	+	1.25706i	0.117391	+	0.0677759i
$345$	9.67475	+	5.58572i	0.520871	+	0.300725i
$346$			11.6266i			0.625053i
$347$	1.89779	−	3.28707i	0.101879	−	0.176459i	−0.810580	−	0.585628i	$-0.800848\pi$
$347$	1.89779	−	3.28707i	0.101879	−	0.176459i	0.912459	+	0.409169i	$0.134181\pi$
$348$	3.36831	+	5.83408i	0.180560	+	0.312739i
$349$	−9.84891	+	5.68627i	−0.527200	+	0.304379i	−0.739876	−	0.672744i	$-0.765116\pi$
$349$	−9.84891	+	5.68627i	−0.527200	+	0.304379i	0.212675	+	0.977123i	$0.431782\pi$
$350$	−6.37742			−0.340887
$351$	3.42102	+	1.13870i	0.182600	+	0.0607794i
$352$	5.83442			0.310976
$353$	−15.2156	+	8.78471i	−0.809842	+	0.467563i	−0.846901	−	0.531750i	$-0.821534\pi$
$353$	−15.2156	+	8.78471i	−0.809842	+	0.467563i	0.0370587	+	0.999313i	$0.488201\pi$
$354$	2.69442	+	4.66687i	0.143207	+	0.248041i
$355$	15.2409	−	26.3981i	0.808905	−	1.40107i
$356$			13.0212i			0.690123i
$357$	−5.00548	−	2.88992i	−0.264918	−	0.152951i
$358$	−20.0485	−	11.5750i	−1.05959	−	0.611757i
$359$		−	5.89389i		−	0.311068i	−0.987831	−	0.155534i	$-0.950290\pi$
$359$		−	5.89389i		−	0.311068i	0.987831	−	0.155534i	$-0.0497098\pi$
$360$	5.04102	−	8.73131i	0.265685	−	0.460180i
$361$	9.69523	+	16.7926i	0.510275	+	0.883822i
$362$	13.9638	−	8.06198i	0.733919	−	0.423728i
$363$	9.01613			0.473224
$364$	−2.77419	+	0.568941i	−0.145407	+	0.0298206i
$365$	39.8874			2.08780
$366$	−2.84181	+	1.64072i	−0.148544	+	0.0857617i
$367$	−8.09246	−	14.0166i	−0.422423	−	0.731658i	0.573753	−	0.819029i	$-0.305487\pi$
$367$	−8.09246	−	14.0166i	−0.422423	−	0.731658i	−0.996176	+	0.0873701i	$0.972154\pi$
$368$	−3.08209	+	5.33834i	−0.160665	+	0.278280i
$369$		−	1.15399i		−	0.0600744i
$370$	17.5265	+	10.1189i	0.911158	+	0.526057i
$371$	4.80021	+	2.77140i	0.249215	+	0.143884i
$372$		−	6.00169i		−	0.311173i
$373$	10.1223	−	17.5323i	0.524113	−	0.907790i	−0.475493	−	0.879719i	$-0.657730\pi$
$373$	10.1223	−	17.5323i	0.524113	−	0.907790i	0.999606	−	0.0280705i	$-0.00893630\pi$
$374$	4.48592	+	7.76984i	0.231961	+	0.401769i
$375$	−2.23774	+	1.29196i	−0.115556	+	0.0667166i
$376$	−10.2882			−0.530571
$377$	6.21282	+	30.2940i	0.319976	+	1.56022i
$378$	1.10207			0.0566845
$379$	14.1896	−	8.19239i	0.728872	−	0.420815i	−0.0891371	−	0.996019i	$-0.528411\pi$
$379$	14.1896	−	8.19239i	0.728872	−	0.420815i	0.818010	+	0.575205i	$0.195078\pi$
$380$	7.99166	+	13.8420i	0.409963	+	0.710078i
$381$	−5.82996	+	10.0978i	−0.298678	+	0.517326i
$382$		−	5.76233i		−	0.294827i
$383$	11.5151	+	6.64823i	0.588392	+	0.339708i	0.764462	−	0.644669i	$-0.223005\pi$
$383$	11.5151	+	6.64823i	0.588392	+	0.339708i	−0.176069	+	0.984378i	$0.556338\pi$
$384$	0.641633	+	0.370447i	0.0327432	+	0.0189043i
$385$		−	4.62595i		−	0.235760i
$386$	−13.0609	+	22.6221i	−0.664782	+	1.15144i
$387$	0.409497	+	0.709270i	0.0208159	+	0.0360542i
$388$	12.7438	−	7.35762i	0.646967	−	0.373527i
$389$	30.4724			1.54501			0.772506	−	0.635007i	$-0.219003\pi$
$389$	30.4724			1.54501			0.772506	+	0.635007i	$0.219003\pi$
$390$	9.76069	−	8.66282i	0.494252	−	0.438659i
$391$	19.6598			0.994239
$392$	−2.65848	+	1.53488i	−0.134274	+	0.0775230i
$393$	−4.34111	−	7.51902i	−0.218980	−	0.379284i
$394$	−8.60718	+	14.9081i	−0.433623	+	0.751058i
$395$			19.7135i			0.991894i
$396$	0.958069	+	0.553141i	0.0481448	+	0.0277964i
$397$	9.34001	+	5.39246i	0.468762	+	0.270640i	0.715721	−	0.698386i	$-0.246098\pi$
$397$	9.34001	+	5.39246i	0.468762	+	0.270640i	−0.246959	+	0.969026i	$0.579431\pi$
$398$			22.9614i			1.15095i
$399$	−3.09800	+	5.36590i	−0.155094	+	0.268631i
$400$	−5.24344	−	9.08190i	−0.262172	−	0.454095i
$401$	14.2073	−	8.20259i	0.709479	−	0.409618i	−0.101389	−	0.994847i	$-0.532329\pi$
$401$	14.2073	−	8.20259i	0.709479	−	0.409618i	0.810868	+	0.585229i	$0.198995\pi$
$402$	−0.296192			−0.0147727
$403$	8.70108	−	26.1408i	0.433432	−	1.30216i
$404$	−11.8221			−0.588170
$405$	2.84430	−	1.64216i	0.141335	−	0.0815995i
$406$	4.72620	+	8.18602i	0.234557	+	0.406265i
$407$	−3.93763	+	6.82017i	−0.195181	+	0.338063i
$408$		−	17.7427i		−	0.878392i
$409$	20.6891	+	11.9449i	1.02301	+	0.590636i	0.914975	−	0.403511i	$-0.132210\pi$
$409$	20.6891	+	11.9449i	1.02301	+	0.590636i	0.108037	+	0.994147i	$0.465544\pi$
$410$	−3.61734	−	2.08847i	−0.178647	−	0.103142i
$411$		−	12.5774i		−	0.620395i
$412$	−5.52799	+	9.57477i	−0.272345	+	0.471715i
$413$	−2.44486	−	4.23463i	−0.120304	−	0.208372i
$414$	−3.24642	+	1.87432i	−0.159553	+	0.0921180i
$415$	−19.7773			−0.970830
$416$	−9.91393	−	11.1704i	−0.486070	−	0.547672i
$417$	−10.7327			−0.525582
$418$	8.32930	−	4.80893i	0.407400	−	0.235212i
$419$	14.4158	+	24.9688i	0.704256	+	1.21981i	0.966959	+	0.254930i	$0.0820525\pi$
$419$	14.4158	+	24.9688i	0.704256	+	1.21981i	−0.262704	+	0.964877i	$0.584614\pi$
$420$	−1.28981	+	2.23401i	−0.0629362	+	0.109009i
$421$			13.5391i			0.659857i	0.944006	+	0.329929i	$0.107025\pi$
$421$			13.5391i			0.659857i	−0.944006	+	0.329929i	$0.892975\pi$
$422$	8.55502	+	4.93924i	0.416452	+	0.240439i
$423$	−2.90245	−	1.67573i	−0.141122	−	0.0814768i
$424$			17.0150i			0.826324i
$425$	−16.7232	+	28.9654i	−0.811194	+	1.40503i
$426$	5.11419	+	8.85804i	0.247783	+	0.429174i
$427$	2.57860	−	1.48876i	0.124787	−	0.0720459i
$428$	5.77050			0.278927
$429$	3.37101	+	3.79823i	0.162754	+	0.183380i
$430$	2.96440			0.142956
$431$	−19.3204	+	11.1546i	−0.930629	+	0.537299i	−0.887011	−	0.461749i	$-0.847222\pi$
$431$	−19.3204	+	11.1546i	−0.930629	+	0.537299i	−0.0436188	+	0.999048i	$0.513889\pi$
$432$	0.906111	+	1.56943i	0.0435953	+	0.0755093i
$433$	−5.07297	+	8.78663i	−0.243791	+	0.422259i	−0.961791	−	0.273785i	$-0.911724\pi$
$433$	−5.07297	+	8.78663i	−0.243791	+	0.422259i	0.718000	+	0.696043i	$0.245058\pi$
$434$		−	8.42119i		−	0.404230i
$435$	24.3954	+	14.0847i	1.16967	+	0.675308i
$436$	3.16719	+	1.82858i	0.151681	+	0.0875729i
$437$		−	21.0754i		−	1.00817i
$438$	−6.69224	+	11.5913i	−0.319767	+	0.553853i
$439$	−17.7570	−	30.7560i	−0.847494	−	1.46790i	−0.883437	−	0.468549i	$-0.844777\pi$
$439$	−17.7570	−	30.7560i	−0.847494	−	1.46790i	0.0359431	−	0.999354i	$-0.488556\pi$
$440$	12.2980	−	7.10027i	0.586285	−	0.338492i
$441$	−1.00000			−0.0476190
$442$	7.25330	−	21.7912i	0.345004	−	1.03650i
$443$	−25.6235			−1.21741			−0.608705	−	0.793396i	$-0.708311\pi$
$443$	−25.6235			−1.21741			−0.608705	+	0.793396i	$0.708311\pi$
$444$	3.80320	−	2.19578i	0.180492	−	0.104207i
$445$	27.2243	+	47.1538i	1.29055	+	2.23531i
$446$	1.88820	−	3.27046i	0.0894089	−	0.154861i
$447$			11.4702i			0.542520i
$448$	−7.09237	−	4.09478i	−0.335083	−	0.193460i
$449$	−1.19456	−	0.689681i	−0.0563749	−	0.0325481i	0.471548	−	0.881841i	$-0.343696\pi$
$449$	−1.19456	−	0.689681i	−0.0563749	−	0.0325481i	−0.527923	+	0.849293i	$0.677029\pi$
$450$		−	6.37742i		−	0.300634i
$451$	0.812697	−	1.40763i	0.0382684	−	0.0662828i
$452$	−2.81635	−	4.87807i	−0.132470	−	0.229445i
$453$	7.85858	−	4.53715i	0.369228	−	0.213174i
$454$	−24.9202			−1.16956
$455$	−8.85667	+	7.86048i	−0.415207	+	0.368505i
$456$	−19.0202			−0.890702
$457$	11.0804	−	6.39726i	0.518318	−	0.299251i	−0.217928	−	0.975965i	$-0.569930\pi$
$457$	11.0804	−	6.39726i	0.518318	−	0.299251i	0.736246	+	0.676714i	$0.236596\pi$
$458$	7.72374	+	13.3779i	0.360907	+	0.625109i
$459$	2.88992	−	5.00548i	0.134890	−	0.233636i
$460$		−	8.77444i		−	0.409110i
$461$	−3.69799	−	2.13504i	−0.172233	−	0.0994386i	0.411405	−	0.911452i	$-0.365038\pi$
$461$	−3.69799	−	2.13504i	−0.172233	−	0.0994386i	−0.583638	+	0.812014i	$0.698371\pi$
$462$	1.34430	+	0.776134i	0.0625426	+	0.0361090i
$463$		−	0.637577i		−	0.0296307i	−0.999890	−	0.0148154i	$-0.995284\pi$
$463$		−	0.637577i		−	0.0296307i	0.999890	−	0.0148154i	$-0.00471605\pi$
$464$	−7.77165	+	13.4609i	−0.360790	+	0.624906i
$465$	−12.5481	−	21.7340i	−0.581905	−	1.00789i
$466$	−11.6118	+	6.70410i	−0.537908	+	0.310561i
$467$	−10.3676			−0.479754			−0.239877	−	0.970803i	$-0.577107\pi$
$467$	−10.3676			−0.479754			−0.239877	+	0.970803i	$0.577107\pi$
$468$	−0.568941	−	2.77419i	−0.0262993	−	0.128237i
$469$	0.268759			0.0124101
$470$	−10.5056	+	6.06540i	−0.484587	+	0.279776i
$471$	8.41253	+	14.5709i	0.387629	+	0.671393i
$472$	7.50513	−	12.9993i	0.345452	−	0.598340i
$473$			1.15355i			0.0530404i
$474$	−5.72875	−	3.30750i	−0.263130	−	0.151918i
$475$	31.0511	+	17.9273i	1.42472	+	0.822563i
$476$			4.53968i			0.208076i
$477$	−2.77140	+	4.80021i	−0.126894	+	0.219787i
$478$	−5.14920	−	8.91868i	−0.235519	−	0.407931i
$479$	−22.1213	+	12.7717i	−1.01075	+	0.583555i	−0.911410	−	0.411498i	$-0.865006\pi$
$479$	−22.1213	+	12.7717i	−1.01075	+	0.583555i	−0.0993372	+	0.995054i	$0.531672\pi$
$480$	−13.6046			−0.620964
$481$	19.7485	−	4.05010i	0.900454	−	0.184668i
$482$	−23.4455			−1.06792
$483$	2.94574	−	1.70072i	0.134036	−	0.0773857i
$484$	−3.54079	−	6.13283i	−0.160945	−	0.278765i
$485$	30.7661	−	53.2885i	1.39702	−	2.41971i
$486$			1.10207i			0.0499911i
$487$	11.0861	+	6.40055i	0.502358	+	0.290037i	0.729687	−	0.683781i	$-0.239666\pi$
$487$	11.0861	+	6.40055i	0.502358	+	0.290037i	−0.227329	+	0.973818i	$0.572999\pi$
$488$	7.91566	+	4.57011i	0.358325	+	0.206879i
$489$		−	20.8336i		−	0.942126i
$490$	−1.80978	+	3.13463i	−0.0817575	+	0.141608i
$491$	−3.41663	−	5.91777i	−0.154190	−	0.267065i	0.778574	−	0.627553i	$-0.215944\pi$
$491$	−3.41663	−	5.91777i	−0.154190	−	0.267065i	−0.932764	+	0.360488i	$0.882610\pi$
$492$	−0.784952	+	0.453192i	−0.0353884	+	0.0204315i
$493$	49.5732			2.23266
$494$	−23.3602	−	7.77556i	−1.05103	−	0.349839i
$495$	4.62595			0.207921
$496$	11.9924	−	6.92380i	0.538474	−	0.310888i
$497$	−4.64052	−	8.03762i	−0.208156	−	0.360536i
$498$	3.31820	−	5.74729i	0.148692	−	0.257542i
$499$			29.8319i			1.33546i	0.744405	+	0.667729i	$0.232733\pi$
$499$			29.8319i			1.33546i	−0.744405	+	0.667729i	$0.767267\pi$
$500$	1.75760	+	1.01475i	0.0786023	+	0.0453810i
$501$	5.37739	+	3.10464i	0.240244	+	0.138705i
$502$		−	0.761241i		−	0.0339758i
$503$	−9.77147	+	16.9247i	−0.435688	+	0.754634i	−0.997352	−	0.0727318i	$-0.976828\pi$
$503$	−9.77147	+	16.9247i	−0.435688	+	0.754634i	0.561663	+	0.827366i	$0.310162\pi$
$504$	−1.53488	−	2.65848i	−0.0683688	−	0.118418i
$505$	−42.8114	+	24.7172i	−1.90508	+	1.09990i
$506$	−5.27996			−0.234723
$507$	1.54388	−	12.9080i	0.0685659	−	0.573264i
$508$	9.15811			0.406326
$509$	−2.03965	+	1.17759i	−0.0904058	+	0.0521958i	−0.544521	−	0.838747i	$-0.683289\pi$
$509$	−2.03965	+	1.17759i	−0.0904058	+	0.0521958i	0.454116	+	0.890943i	$0.349955\pi$
$510$	−10.4602	−	18.1176i	−0.463186	−	0.802262i
$511$	6.07241	−	10.5177i	0.268627	−	0.465276i
$512$		−	18.6329i		−	0.823467i
$513$	−5.36590	−	3.09800i	−0.236910	−	0.136780i
$514$	−22.2761	−	12.8611i	−0.982559	−	0.567281i
$515$			46.2309i			2.03718i
$516$	0.321633	−	0.557085i	0.0141591	−	0.0245243i
$517$	−2.36026	−	4.08809i	−0.103804	−	0.179794i
$518$	5.33641	−	3.08098i	0.234469	−	0.135370i
$519$	10.5498			0.463085
$520$	−34.4908	−	11.4804i	−1.51252	−	0.503451i
$521$	27.5527			1.20711			0.603553	−	0.797323i	$-0.293751\pi$
$521$	27.5527			1.20711			0.603553	+	0.797323i	$0.293751\pi$
$522$	−8.18602	+	4.72620i	−0.358292	+	0.206860i
$523$	−13.0383	−	22.5831i	−0.570127	−	0.987489i	−0.996552	−	0.0829661i	$-0.973561\pi$
$523$	−13.0383	−	22.5831i	−0.570127	−	0.987489i	0.426425	−	0.904523i	$-0.359773\pi$
$524$	−3.40966	+	5.90570i	−0.148952	+	0.257992i
$525$			5.78675i			0.252554i
$526$	8.69482	+	5.01996i	0.379112	+	0.218881i
$527$	−38.2480	−	22.0825i	−1.66611	−	0.961929i
$528$			2.55251i			0.111084i
$529$	5.71507	−	9.89879i	0.248481	−	0.430382i
$530$	10.0313	+	17.3746i	0.435730	+	0.754707i
$531$	4.23463	−	2.44486i	0.183767	−	0.106098i
$532$	4.86656			0.210992
$533$	−4.07594	+	0.835910i	−0.176549	+	0.0362073i
$534$	−18.2705			−0.790644
$535$	20.8968	−	12.0647i	0.903445	−	0.521604i
$536$	0.412511	+	0.714491i	0.0178178	+	0.0308613i
$537$	−10.5029	+	18.1916i	−0.453234	+	0.785025i
$538$			4.85744i			0.209419i
$539$	−1.21979	−	0.704249i	−0.0525403	−	0.0303341i
$540$	−2.23401	−	1.28981i	−0.0961367	−	0.0555045i
$541$			8.83112i			0.379679i	0.981815	+	0.189840i	$0.0607968\pi$
$541$			8.83112i			0.379679i	−0.981815	+	0.189840i	$0.939203\pi$
$542$	7.37796	−	12.7790i	0.316911	−	0.548905i
$543$	−7.31529	−	12.6704i	−0.313929	−	0.543741i
$544$	−20.7342	+	11.9709i	−0.888972	+	0.513248i
$545$	15.2925			0.655058
$546$	−0.798302	−	3.89256i	−0.0341642	−	0.166586i
$547$	9.61127			0.410948			0.205474	−	0.978663i	$-0.434126\pi$
$547$	9.61127			0.410948			0.205474	+	0.978663i	$0.434126\pi$
$548$	−8.55520	+	4.93935i	−0.365460	+	0.210998i
$549$	1.48876	+	2.57860i	0.0635385	+	0.110052i
$550$	4.49129	−	7.77914i	0.191509	−	0.331704i
$551$		−	53.1426i		−	2.26395i
$552$	9.04270	+	5.22080i	0.384883	+	0.222212i
$553$	5.19816	+	3.00116i	0.221048	+	0.127622i
$554$		−	9.57666i		−	0.406873i
$555$	9.18171	−	15.9032i	0.389742	−	0.675053i
$556$	4.21491	+	7.30044i	0.178752	+	0.309608i
$557$	25.3355	−	14.6275i	1.07350	−	0.619786i	0.144364	−	0.989525i	$-0.453886\pi$
$557$	25.3355	−	14.6275i	1.07350	−	0.619786i	0.929136	+	0.369739i	$0.120553\pi$
$558$	8.42119			0.356497
$559$	2.20854	−	1.96013i	0.0934114	−	0.0829046i
$560$	−5.95192			−0.251514
$561$	7.05021	−	4.07044i	0.297660	−	0.171854i
$562$	−11.9700	−	20.7327i	−0.504926	−	0.874557i
$563$	−2.28958	+	3.96567i	−0.0964943	+	0.167133i	−0.910231	−	0.414100i	$-0.864096\pi$
$563$	−2.28958	+	3.96567i	−0.0964943	+	0.167133i	0.813737	+	0.581233i	$0.197430\pi$
$564$			2.63235i			0.110842i
$565$	−20.3978	−	11.7767i	−0.858141	−	0.495448i
$566$	24.2192	+	13.9829i	1.01801	+	0.587747i
$567$		−	1.00000i		−	0.0419961i
$568$	14.2453	−	24.6735i	0.597717	−	1.03528i
$569$	−20.4112	−	35.3532i	−0.855681	−	1.48208i	−0.876012	−	0.482289i	$-0.839806\pi$
$569$	−20.4112	−	35.3532i	−0.855681	−	1.48208i	0.0203317	−	0.999793i	$-0.493528\pi$
$570$	−19.4222	+	11.2134i	−0.813505	+	0.469678i
$571$	−19.6348			−0.821692			−0.410846	−	0.911705i	$-0.634767\pi$
$571$	−19.6348			−0.821692			−0.410846	+	0.911705i	$0.634767\pi$
$572$	1.25973	−	3.78461i	0.0526718	−	0.158243i
$573$	−5.22863			−0.218429
$574$	−1.10140	+	0.635891i	−0.0459714	+	0.0265416i
$575$	−9.84166	−	17.0463i	−0.410426	−	0.710878i
$576$	4.09478	−	7.09237i	0.170616	−	0.295516i
$577$		−	35.5481i		−	1.47989i	−0.672669	−	0.739944i	$-0.734852\pi$
$577$		−	35.5481i		−	1.47989i	0.672669	−	0.739944i	$-0.265148\pi$
$578$	−15.6587	−	9.04055i	−0.651316	−	0.376037i
$579$	20.5269	+	11.8512i	0.853069	+	0.492520i
$580$		−	22.1252i		−	0.918698i
$581$	−3.01087	+	5.21498i	−0.124912	+	0.216354i
$582$	10.3238	+	17.8813i	0.427934	+	0.741203i
$583$	−6.76109	+	3.90352i	−0.280016	+	0.161667i
$584$	37.2816			1.54272
$585$	−7.86048	−	8.85667i	−0.324991	−	0.366178i
$586$	−29.2545			−1.20849
$587$	32.9428	−	19.0195i	1.35969	−	0.785020i	0.370112	−	0.928987i	$-0.379319\pi$
$587$	32.9428	−	19.0195i	1.35969	−	0.785020i	0.989582	+	0.143967i	$0.0459859\pi$
$588$	0.392717	+	0.680206i	0.0161954	+	0.0280512i
$589$	−23.6725	+	41.0020i	−0.975410	+	1.68946i
$590$		−	17.6987i		−	0.728642i
$591$	13.5273	+	7.80999i	0.556439	+	0.321260i
$592$	8.77507	+	5.06629i	0.360653	+	0.208223i
$593$			26.2586i			1.07831i	0.842207	+	0.539155i	$0.181256\pi$
$593$			26.2586i			1.07831i	−0.842207	+	0.539155i	$0.818744\pi$
$594$	−0.776134	+	1.34430i	−0.0318451	+	0.0551574i
$595$	9.49140	+	16.4396i	0.389109	+	0.673957i
$596$	7.80208	−	4.50453i	0.319586	−	0.184513i
$597$	20.8348			0.852710
$598$	8.97177	+	10.1088i	0.366883	+	0.413380i
$599$	−12.4404			−0.508299			−0.254150	−	0.967165i	$-0.581796\pi$
$599$	−12.4404			−0.508299			−0.254150	+	0.967165i	$0.581796\pi$
$600$	−15.3840	+	8.88194i	−0.628048	+	0.362604i
$601$	−9.98707	−	17.2981i	−0.407381	−	0.705605i	0.587214	−	0.809432i	$-0.300225\pi$
$601$	−9.98707	−	17.2981i	−0.407381	−	0.705605i	−0.994595	+	0.103827i	$0.966891\pi$
$602$	0.451296	−	0.781667i	0.0183934	−	0.0318584i
$603$			0.268759i			0.0109447i
$604$	−6.17240	−	3.56364i	−0.251151	−	0.145002i
$605$	−25.6446	−	14.8059i	−1.04260	−	0.601947i
$606$		−	16.5880i		−	0.673841i
$607$	−13.6931	+	23.7171i	−0.555785	+	0.962648i	0.442057	+	0.896987i	$0.354249\pi$
$607$	−13.6931	+	23.7171i	−0.555785	+	0.962648i	−0.997842	+	0.0656610i	$0.979084\pi$
$608$	12.8329	+	22.2272i	0.520441	+	0.901431i
$609$	7.42783	−	4.28846i	0.300991	−	0.173777i
$610$	10.7773			0.436359
$611$	−3.81631	+	11.4654i	−0.154391	+	0.463841i
$612$	−4.53968			−0.183506
$613$	−2.49146	+	1.43845i	−0.100629	+	0.0580983i	−0.549470	−	0.835513i	$-0.685170\pi$
$613$	−2.49146	+	1.43845i	−0.100629	+	0.0580983i	0.448841	+	0.893612i	$0.351837\pi$
$614$	2.38650	+	4.13354i	0.0963113	+	0.166816i
$615$	−1.89504	+	3.28230i	−0.0764153	+	0.132355i
$616$		−	4.32374i		−	0.174208i
$617$	25.9156	+	14.9624i	1.04332	+	0.602364i	0.920773	−	0.390098i	$-0.127559\pi$
$617$	25.9156	+	14.9624i	1.04332	+	0.602364i	0.122552	+	0.992462i	$0.460892\pi$
$618$	−13.4347	−	7.75654i	−0.540424	−	0.312014i
$619$			33.5695i			1.34927i	0.738150	+	0.674637i	$0.235700\pi$
$619$			33.5695i			1.34927i	−0.738150	+	0.674637i	$0.764300\pi$
$620$	−9.85572	+	17.0706i	−0.395815	+	0.685572i
$621$	1.70072	+	2.94574i	0.0682477	+	0.118209i
$622$	−14.2668	+	8.23695i	−0.572047	+	0.330272i
$623$	16.5783			0.664197
$624$	4.88694	−	4.33726i	0.195634	−	0.173629i
$625$	−20.4473			−0.817892
$626$	−8.36048	+	4.82692i	−0.334152	+	0.192923i
$627$	−4.36353	−	7.55785i	−0.174262	−	0.301831i
$628$	6.60749	−	11.4445i	0.263668	−	0.456686i
$629$		−	32.3164i		−	1.28854i
$630$	−3.13463	−	1.80978i	−0.124887	−	0.0721033i
$631$	−22.8988	−	13.2207i	−0.911588	−	0.526306i	−0.0306465	−	0.999530i	$-0.509757\pi$
$631$	−22.8988	−	13.2207i	−0.911588	−	0.526306i	−0.880942	+	0.473225i	$0.843090\pi$
$632$			18.4256i			0.732932i
$633$	4.48177	−	7.76266i	0.178134	−	0.308538i
$634$	−3.01042	−	5.21420i	−0.119559	−	0.207082i
$635$	33.1644	−	19.1475i	1.31609	−	0.759844i
$636$	4.35351			0.172628
$637$	0.724364	+	3.53204i	0.0287004	+	0.139944i
$638$	−13.3137			−0.527094
$639$	8.03762	−	4.64052i	0.317963	−	0.183576i
$640$	−1.21667	−	2.10733i	−0.0480929	−	0.0832994i
$641$	−12.4445	+	21.5546i	−0.491530	+	0.851354i	−0.999952	−	0.00975315i	$-0.996895\pi$
$641$	−12.4445	+	21.5546i	−0.491530	+	0.851354i	0.508423	+	0.861108i	$0.330229\pi$
$642$			8.09680i			0.319555i
$643$	−34.0297	−	19.6471i	−1.34200	−	0.774804i	−0.354899	−	0.934904i	$-0.615485\pi$
$643$	−34.0297	−	19.6471i	−1.34200	−	0.774804i	−0.987101	+	0.160100i	$0.948818\pi$
$644$	−2.31369	−	1.33581i	−0.0911721	−	0.0526382i
$645$		−	2.68984i		−	0.105912i
$646$	−19.7336	+	34.1797i	−0.776410	+	1.34478i
$647$	−14.5885	−	25.2681i	−0.573534	−	0.993390i	−0.996199	−	0.0871044i	$-0.972239\pi$
$647$	−14.5885	−	25.2681i	−0.573534	−	0.993390i	0.422665	−	0.906286i	$-0.361095\pi$
$648$	2.65848	−	1.53488i	0.104435	−	0.0602956i
$649$	6.88717			0.270345
$650$	−22.5253	+	4.61957i	−0.883514	+	0.181195i
$651$	−7.64123			−0.299483
$652$	−14.1711	+	8.18170i	−0.554984	+	0.320420i
$653$	4.03331	+	6.98589i	0.157835	+	0.273379i	0.934088	−	0.357043i	$-0.116215\pi$
$653$	4.03331	+	6.98589i	0.157835	+	0.273379i	−0.776252	+	0.630422i	$0.782882\pi$
$654$	−2.56574	+	4.44400i	−0.100329	+	0.173774i
$655$			28.5151i			1.11418i
$656$	−1.81111	−	1.04564i	−0.0707119	−	0.0408256i
$657$	10.5177	+	6.07241i	0.410335	+	0.236907i
$658$			3.69355i			0.143990i
$659$	19.5939	−	33.9377i	0.763271	−	1.32202i	−0.177884	−	0.984051i	$-0.556925\pi$
$659$	19.5939	−	33.9377i	0.763271	−	1.32202i	0.941156	−	0.337973i	$-0.109741\pi$
$660$	−1.81669	−	3.14660i	−0.0707147	−	0.122481i
$661$	−21.4769	+	12.3997i	−0.835353	+	0.482291i	−0.855682	−	0.517502i	$-0.826862\pi$
$661$	−21.4769	+	12.3997i	−0.835353	+	0.482291i	0.0203288	+	0.999793i	$0.493529\pi$
$662$	−9.49798			−0.369150
$663$	−19.7729	−	6.58150i	−0.767916	−	0.255604i
$664$	−18.4853			−0.717367
$665$	17.6233	−	10.1748i	0.683403	−	0.394563i
$666$	3.08098	+	5.33641i	0.119386	+	0.206782i
$667$	−14.5870	+	25.2654i	−0.564810	+	0.978280i
$668$		−	4.87698i		−	0.188696i
$669$	−2.96755	−	1.71332i	−0.114732	−	0.0662407i
$670$	0.842459	+	0.486394i	0.0325470	+	0.0187910i
$671$			4.19382i			0.161900i
$672$	−2.07115	+	3.58734i	−0.0798964	+	0.138385i
$673$	−14.0271	−	24.2957i	−0.540706	−	0.936530i	−0.998864	−	0.0476590i	$-0.984824\pi$
$673$	−14.0271	−	24.2957i	−0.540706	−	0.936530i	0.458158	−	0.888871i	$-0.348509\pi$
$674$	13.0536	−	7.53648i	0.502805	−	0.290294i
$675$	−5.78675			−0.222732
$676$	−9.38641	+	4.01904i	−0.361016	+	0.154579i
$677$	−17.7868			−0.683602			−0.341801	−	0.939772i	$-0.611037\pi$
$677$	−17.7868			−0.683602			−0.341801	+	0.939772i	$0.611037\pi$
$678$	6.84460	−	3.95173i	0.262865	−	0.151765i
$679$	−9.36758	−	16.2251i	−0.359495	−	0.622663i
$680$	−29.1363	+	50.4655i	−1.11732	+	1.93526i
$681$			22.6121i			0.866497i
$682$	10.2721	+	5.93061i	0.393340	+	0.227095i
$683$	6.52540	+	3.76744i	0.249687	+	0.144157i	0.619621	−	0.784901i	$-0.287286\pi$
$683$	6.52540	+	3.76744i	0.249687	+	0.144157i	−0.369934	+	0.929058i	$0.620620\pi$
$684$			4.86656i			0.186077i
$685$	−20.6540	+	35.7738i	−0.789149	+	1.36685i
$686$	0.551037	+	0.954423i	0.0210387	+	0.0364401i
$687$	12.1389	−	7.00838i	0.463126	−	0.267386i
$688$	1.48420			0.0565846
$689$	18.9620	+	6.31160i	0.722396	+	0.240453i
$690$	12.3117			0.468700
$691$	40.9443	−	23.6392i	1.55760	−	0.899278i	0.560109	−	0.828419i	$-0.310759\pi$
$691$	40.9443	−	23.6392i	1.55760	−	0.899278i	0.997486	−	0.0708592i	$-0.0225741\pi$
$692$	−4.14309	−	7.17604i	−0.157497	−	0.272792i
$693$	0.704249	−	1.21979i	0.0267522	−	0.0463362i
$694$		−	4.18301i		−	0.158785i
$695$	30.5270	+	17.6248i	1.15796	+	0.668546i
$696$	22.8016	+	13.1645i	0.864293	+	0.499000i
$697$			6.66987i			0.252639i
$698$	−6.26669	+	10.8542i	−0.237198	+	0.410838i
$699$	6.08317	+	10.5364i	0.230087	+	0.398522i
$700$	3.93618	−	2.27256i	0.148774	−	0.0858945i
$701$	5.95873			0.225058			0.112529	−	0.993648i	$-0.464105\pi$
$701$	5.95873			0.225058			0.112529	+	0.993648i	$0.464105\pi$
$702$	3.89256	−	0.798302i	0.146915	−	0.0301300i
$703$	−34.6434			−1.30660
$704$	9.98959	−	5.76749i	0.376497	−	0.217371i
$705$	5.50363	+	9.53257i	0.207279	+	0.359017i
$706$	−9.68139	+	16.7687i	−0.364364	+	0.631097i
$707$			15.0516i			0.566074i
$708$	−3.32602	−	1.92028i	−0.125000	−	0.0721686i
$709$	40.1988	+	23.2088i	1.50970	+	0.871623i	0.999936	+	0.0113067i	$0.00359911\pi$
$709$	40.1988	+	23.2088i	1.50970	+	0.871623i	0.509760	+	0.860317i	$0.329734\pi$
$710$		−	33.5933i		−	1.26073i
$711$	−3.00116	+	5.19816i	−0.112552	+	0.194946i
$712$	25.4457	+	44.0733i	0.953618	+	1.65172i
$713$	22.5091	−	12.9956i	0.842972	−	0.486690i
$714$	−6.36980			−0.238384
$715$	−3.35087	−	16.3390i	−0.125316	−	0.611046i
$716$	16.4987			0.616586
$717$	−8.09264	+	4.67229i	−0.302225	+	0.174490i
$718$	−3.24775	−	5.62527i	−0.121205	−	0.209933i
$719$	7.07044	−	12.2464i	0.263683	−	0.456712i	−0.703535	−	0.710661i	$-0.748396\pi$
$719$	7.07044	−	12.2464i	0.263683	−	0.456712i	0.967218	+	0.253949i	$0.0817294\pi$
$720$		−	5.95192i		−	0.221815i
$721$	12.1904	+	7.03813i	0.453994	+	0.262114i
$722$	18.5067	+	10.6848i	0.688748	+	0.397649i
$723$			21.2740i			0.791190i
$724$	−5.74568	+	9.95181i	−0.213537	+	0.369856i
$725$	−24.8162	−	42.9830i	−0.921652	−	1.59635i
$726$	8.60521	−	4.96822i	0.319369	−	0.184388i
$727$	−25.8145			−0.957405			−0.478703	−	0.877977i	$-0.658893\pi$
$727$	−25.8145			−0.957405			−0.478703	+	0.877977i	$0.658893\pi$
$728$	−8.27806	+	7.34695i	−0.306805	+	0.272296i
$729$	1.00000			0.0370370
$730$	38.0695	−	21.9794i	1.40901	−	0.813495i
$731$	−2.36682	−	4.09946i	−0.0875402	−	0.151624i
$732$	1.16932	−	2.02532i	0.0432193	−	0.0748580i
$733$		−	35.3926i		−	1.30725i	−0.756817	−	0.653627i	$-0.773247\pi$
$733$		−	35.3926i		−	1.30725i	0.756817	−	0.653627i	$-0.226753\pi$
$734$	−15.4473	−	8.91849i	−0.570169	−	0.329187i
$735$	2.84430	+	1.64216i	0.104914	+	0.0605719i
$736$		−	14.0898i		−	0.519358i
$737$	−0.189273	+	0.327830i	−0.00697196	+	0.0120758i
$738$	−0.635891	−	1.10140i	−0.0234075	−	0.0405430i
$739$	39.7811	−	22.9676i	1.46337	−	0.844877i	0.464204	−	0.885728i	$-0.346340\pi$
$739$	39.7811	−	22.9676i	1.46337	−	0.844877i	0.999165	+	0.0408513i	$0.0130070\pi$
$740$	−14.4233			−0.530210
$741$	−7.05540	+	21.1966i	−0.259187	+	0.778678i
$742$	6.10858			0.224253
$743$	−25.8736	+	14.9381i	−0.949210	+	0.548027i	−0.892835	−	0.450383i	$-0.851287\pi$
$743$	−25.8736	+	14.9381i	−0.949210	+	0.548027i	−0.0563746	+	0.998410i	$0.517954\pi$
$744$	−11.7283	−	20.3141i	−0.429982	−	0.744750i
$745$	18.8358	−	32.6246i	0.690092	−	1.19527i
$746$		−	22.3110i		−	0.816865i
$747$	−5.21498	−	3.01087i	−0.190806	−	0.110162i
$748$	−5.53748	−	3.19706i	−0.202470	−	0.116896i
$749$		−	7.34688i		−	0.268449i
$750$	−1.42384	+	2.46616i	−0.0519911	+	0.0900513i
$751$	17.9113	+	31.0232i	0.653591	+	1.13205i	0.982245	+	0.187603i	$0.0600717\pi$
$751$	17.9113	+	31.0232i	0.653591	+	1.13205i	−0.328654	+	0.944450i	$0.606595\pi$
$752$	−5.25988	+	3.03680i	−0.191808	+	0.110741i
$753$	−0.690735			−0.0251718
$754$	22.6228	+	25.4898i	0.823873	+	0.928285i
$755$	−29.8029			−1.08464
$756$	−0.680206	+	0.392717i	−0.0247389	+	0.0142830i
$757$	15.3033	+	26.5061i	0.556208	+	0.963381i	0.997808	+	0.0661693i	$0.0210777\pi$
$757$	15.3033	+	26.5061i	0.556208	+	0.963381i	−0.441600	+	0.897212i	$0.645589\pi$
$758$	9.02861	−	15.6380i	0.327934	−	0.567998i
$759$			4.79093i			0.173900i
$760$	54.0992	+	31.2342i	1.96238	+	1.13298i
$761$	−7.56846	−	4.36965i	−0.274356	−	0.158400i	0.356509	−	0.934292i	$-0.383967\pi$
$761$	−7.56846	−	4.36965i	−0.274356	−	0.158400i	−0.630866	+	0.775892i	$0.717300\pi$
$762$			12.8501i			0.465510i
$763$	2.32811	−	4.03240i	0.0842831	−	0.145983i
$764$	2.05337	+	3.55655i	0.0742885	+	0.128671i
$765$	−16.4396	+	9.49140i	−0.594375	+	0.343162i
$766$	14.6537			0.529458
$767$	−11.7028	−	13.1859i	−0.422562	−	0.476115i
$768$	−15.5626			−0.561567
$769$	23.7655	−	13.7210i	0.857005	−	0.494792i	−0.00600304	−	0.999982i	$-0.501911\pi$
$769$	23.7655	−	13.7210i	0.857005	−	0.494792i	0.863008	+	0.505190i	$0.168578\pi$
$770$	−2.54907	−	4.41512i	−0.0918621	−	0.159110i
$771$	−11.6700	+	20.2129i	−0.420283	+	0.727952i
$772$		−	18.6167i		−	0.670030i
$773$	−11.3594	−	6.55836i	−0.408570	−	0.235888i	0.281605	−	0.959530i	$-0.409133\pi$
$773$	−11.3594	−	6.55836i	−0.408570	−	0.235888i	−0.690175	+	0.723642i	$0.742466\pi$
$774$	0.781667	+	0.451296i	0.0280965	+	0.0162215i
$775$			44.2178i			1.58835i
$776$	28.7562	−	49.8071i	1.03229	−	1.78797i
$777$	−2.79562	−	4.84216i	−0.100292	−	0.173711i
$778$	29.0836	−	16.7914i	1.04270	−	0.602001i
$779$	7.15013			0.256180
$780$	−2.93741	+	8.82492i	−0.105176	+	0.315983i
$781$	13.0723			0.467764
$782$	18.7638	−	10.8333i	0.670991	−	0.387397i
$783$	4.28846	+	7.42783i	0.153257	+	0.265449i
$784$	−0.906111	+	1.56943i	−0.0323611	+	0.0560511i
$785$		−	55.2589i		−	1.97227i
$786$	−8.28651	−	4.78422i	−0.295570	−	0.170647i
$787$	23.0339	+	13.2986i	0.821071	+	0.474046i	0.850786	−	0.525513i	$-0.176127\pi$
$787$	23.0339	+	13.2986i	0.821071	+	0.474046i	−0.0297146	+	0.999558i	$0.509460\pi$
$788$		−	12.2685i		−	0.437046i
$789$	4.55501	−	7.88952i	0.162163	−	0.280874i
$790$	10.8629	+	18.8150i	0.386483	+	0.669409i
$791$	−6.21066	+	3.58572i	−0.220826	+	0.127494i
$792$	4.32374			0.153637
$793$	8.02931	−	7.12619i	0.285129	−	0.253058i
$794$	11.8858			0.421810
$795$	15.7654	−	9.10217i	0.559142	−	0.322821i
$796$	−8.18217	−	14.1719i	−0.290009	−	0.502311i
$797$	2.55207	−	4.42031i	0.0903988	−	0.156575i	−0.817280	−	0.576240i	$-0.804519\pi$
$797$	2.55207	−	4.42031i	0.0903988	−	0.156575i	0.907679	+	0.419665i	$0.137852\pi$
$798$			6.82845i			0.241724i
$799$	16.7757	+	9.68543i	0.593480	+	0.342646i
$800$	20.7590	+	11.9852i	0.733942	+	0.423742i
$801$			16.5783i			0.585767i
$802$	9.03986	−	15.6575i	0.319208	−	0.552885i
$803$	8.55297	+	14.8142i	0.301828	+	0.522781i
$804$	0.182811	−	0.105546i	0.00644726	−	0.00372233i
$805$	−11.1714			−0.393742
$806$	−6.10001	−	29.7440i	−0.214864	−	1.04769i
$807$	4.40754			0.155153
$808$	−40.0145	+	23.1024i	−1.40770	+	0.812739i
$809$	−0.711100	−	1.23166i	−0.0250010	−	0.0433029i	0.853254	−	0.521495i	$-0.174626\pi$
$809$	−0.711100	−	1.23166i	−0.0250010	−	0.0433029i	−0.878255	+	0.478192i	$0.841292\pi$
$810$	1.80978	−	3.13463i	0.0635892	−	0.110140i
$811$		−	4.11149i		−	0.144374i	−0.997391	−	0.0721870i	$-0.977002\pi$
$811$		−	4.11149i		−	0.144374i	0.997391	−	0.0721870i	$-0.0229978\pi$
$812$	−5.83408	−	3.36831i	−0.204736	−	0.118204i
$813$	−11.5954	−	6.69462i	−0.406669	−	0.234791i
$814$			8.67910i			0.304202i
$815$	−34.2120	+	59.2569i	−1.19839	+	2.07568i
$816$	−5.23717	−	9.07104i	−0.183338	−	0.317550i
$817$	−4.39464	+	2.53725i	−0.153749	+	0.0887670i
$818$	26.3283			0.920546
$819$	−3.53204	+	0.724364i	−0.123419	+	0.0253113i
$820$	2.97686			0.103956
$821$	−9.50662	+	5.48865i	−0.331783	+	0.191555i	−0.656633	−	0.754211i	$-0.728020\pi$
$821$	−9.50662	+	5.48865i	−0.331783	+	0.191555i	0.324849	+	0.945766i	$0.394686\pi$
$822$	−6.93058	−	12.0041i	−0.241732	−	0.418692i
$823$	19.6576	−	34.0480i	0.685221	−	1.18684i	−0.288146	−	0.957586i	$-0.593039\pi$
$823$	19.6576	−	34.0480i	0.685221	−	1.18684i	0.973367	−	0.229251i	$-0.0736277\pi$
$824$			43.2107i			1.50531i
$825$	−7.05864	−	4.07531i	−0.245750	−	0.141884i
$826$	−4.66687	−	2.69442i	−0.162381	−	0.0937508i
$827$			20.7986i			0.723238i	0.932326	+	0.361619i	$0.117776\pi$
$827$			20.7986i			0.723238i	−0.932326	+	0.361619i	$0.882224\pi$
$828$	1.33581	−	2.31369i	0.0464226	−	0.0804062i
$829$	−10.4368	−	18.0770i	−0.362484	−	0.627840i	0.625885	−	0.779915i	$-0.284738\pi$
$829$	−10.4368	−	18.0770i	−0.362484	−	0.627840i	−0.988369	+	0.152075i	$0.951405\pi$
$830$	−18.8759	+	10.8980i	−0.655193	+	0.378276i
$831$	−8.68968			−0.301442
$832$	−28.0166	−	9.32547i	−0.971303	−	0.323303i
$833$	5.77983			0.200259
$834$	−10.2435	+	5.91410i	−0.354704	+	0.204789i
$835$	−10.1966	−	17.6610i	−0.352868	−	0.611186i
$836$	−3.42727	+	5.93620i	−0.118534	+	0.205308i
$837$		−	7.64123i		−	0.264119i
$838$	27.5175	+	15.8872i	0.950575	+	0.548815i
$839$	−6.29677	−	3.63544i	−0.217389	−	0.125509i	0.387352	−	0.921932i	$-0.373390\pi$
$839$	−6.29677	−	3.63544i	−0.217389	−	0.125509i	−0.604741	+	0.796423i	$0.706723\pi$
$840$			10.0820i			0.347864i
$841$	−22.2818	+	38.5932i	−0.768338	+	1.33080i
$842$	7.46056	+	12.9221i	0.257108	+	0.445324i
$843$	−18.8125	+	10.8614i	−0.647936	+	0.374086i
$844$	−7.04028			−0.242336
$845$	−25.5882	+	34.1790i	−0.880262	+	1.17579i
$846$	−3.69355			−0.126987
$847$	−7.80820	+	4.50807i	−0.268293	+	0.154899i
$848$	5.02240	+	8.69905i	0.172470	+	0.298727i
$849$	12.6879	−	21.9760i	0.435446	−	0.754215i
$850$			36.8604i			1.26430i
$851$	16.4704	+	9.50917i	0.564597	+	0.325970i
$852$	−6.31302	−	3.64483i	−0.216281	−	0.124870i
$853$		−	25.1125i		−	0.859835i	−0.902868	−	0.429917i	$-0.858543\pi$
$853$		−	25.1125i		−	0.859835i	0.902868	−	0.429917i	$-0.141457\pi$
$854$	1.64072	−	2.84181i	0.0561442	−	0.0972446i
$855$	10.1748	+	17.6233i	0.347972	+	0.602704i
$856$	19.5316	−	11.2766i	0.667575	−	0.385425i
$857$	16.3023			0.556875			0.278438	−	0.960454i	$-0.410183\pi$
$857$	16.3023			0.556875			0.278438	+	0.960454i	$0.410183\pi$
$858$	5.31033	+	1.76757i	0.181292	+	0.0603438i
$859$	−23.6024			−0.805303			−0.402652	−	0.915353i	$-0.631911\pi$
$859$	−23.6024			−0.805303			−0.402652	+	0.915353i	$0.631911\pi$
$860$	−1.82965	+	1.05635i	−0.0623904	+	0.0360211i
$861$	0.576996	+	0.999386i	0.0196640	+	0.0340590i
$862$	−12.2932	+	21.2925i	−0.418708	+	0.725224i
$863$			6.17526i			0.210208i	0.994461	+	0.105104i	$0.0335176\pi$
$863$			6.17526i			0.210208i	−0.994461	+	0.105104i	$0.966482\pi$
$864$	−3.58734	−	2.07115i	−0.122044	−	0.0704620i
$865$	−30.0068	−	17.3244i	−1.02026	−	0.589049i
$866$			11.1816i			0.379965i
$867$	−8.20322	+	14.2084i	−0.278596	+	0.482542i
$868$	3.00084	+	5.19761i	0.101855	+	0.176418i
$869$	−7.32159	+	4.22712i	−0.248368	+	0.143395i
$870$	31.0447			1.05251
$871$	0.949266	−	0.194679i	0.0321647	−	0.00659645i
$872$	14.2934			0.484036
$873$	16.2251	−	9.36758i	0.549137	−	0.317045i
$874$	−11.6133	−	20.1148i	−0.392826	−	0.680395i
$875$	1.29196	−	2.23774i	0.0436762	−	0.0756495i
$876$		−	9.53896i		−	0.322292i
$877$	−5.66283	−	3.26944i	−0.191220	−	0.110401i	0.401333	−	0.915932i	$-0.368547\pi$
$877$	−5.66283	−	3.26944i	−0.191220	−	0.110401i	−0.592554	+	0.805531i	$0.701880\pi$
$878$	−33.8953	−	19.5695i	−1.14391	−	0.660438i
$879$			26.5450i			0.895340i
$880$	4.19163	−	7.26011i	0.141300	−	0.244738i
$881$	−5.87754	−	10.1802i	−0.198019	−	0.342980i	0.749867	−	0.661589i	$-0.230118\pi$
$881$	−5.87754	−	10.1802i	−0.198019	−	0.342980i	−0.947886	+	0.318609i	$0.896784\pi$
$882$	−0.954423	+	0.551037i	−0.0321371	+	0.0185544i
$883$	33.9878			1.14378			0.571890	−	0.820330i	$-0.306210\pi$
$883$	33.9878			1.14378			0.571890	+	0.820330i	$0.306210\pi$
$884$	3.28838	+	16.0343i	0.110600	+	0.539293i
$885$	−16.0594			−0.539832
$886$	−24.4557	+	14.1195i	−0.821605	+	0.474354i
$887$	−5.72685	−	9.91919i	−0.192289	−	0.333054i	0.753720	−	0.657196i	$-0.228258\pi$
$887$	−5.72685	−	9.91919i	−0.192289	−	0.333054i	−0.946008	+	0.324142i	$0.894924\pi$
$888$	8.58187	−	14.8642i	0.287989	−	0.498811i
$889$		−	11.6599i		−	0.391061i
$890$	51.9670	+	30.0031i	1.74194	+	1.00571i
$891$	1.21979	+	0.704249i	0.0408647	+	0.0235932i
$892$			2.69140i			0.0901147i
$893$	10.3828	−	17.9836i	0.347448	−	0.601798i
$894$	6.32048	+	10.9474i	0.211388	+	0.366136i
$895$	59.7469	−	34.4949i	1.99712	−	1.15304i
$896$	−0.740894			−0.0247515
$897$	9.17253	−	8.14082i	0.306262	−	0.271814i
$898$	−1.52016			−0.0507283
$899$	56.7578	−	32.7691i	1.89298	−	1.09291i
$900$	2.27256	+	3.93618i	0.0757519	+	0.131206i
$901$	16.0182	−	27.7444i	0.533645	−	0.924300i
$902$		−	1.79130i		−	0.0596439i
$903$	−0.709270	−	0.409497i	−0.0236030	−	0.0136272i
$904$	−19.0652	−	11.0073i	−0.634099	−	0.366097i
$905$			48.0515i			1.59728i
$906$	5.00028	−	8.66073i	0.166123	−	0.287733i
$907$	15.9352	+	27.6006i	0.529121	+	0.916464i	0.999423	+	0.0339585i	$0.0108114\pi$
$907$	15.9352	+	27.6006i	0.529121	+	0.916464i	−0.470303	+	0.882505i	$0.655855\pi$
$908$	15.3809	−	8.88015i	0.510432	−	0.294698i
$909$	−15.0516			−0.499231
$910$	−4.12160	+	12.3826i	−0.136630	+	0.410478i
$911$	19.2082			0.636395			0.318197	−	0.948024i	$-0.396923\pi$
$911$	19.2082			0.636395			0.318197	+	0.948024i	$0.396923\pi$
$912$	−9.72420	+	5.61427i	−0.322000	+	0.185907i
$913$	−4.24080	−	7.34529i	−0.140350	−	0.243093i
$914$	7.05025	−	12.2114i	0.233202	−	0.403917i
$915$		−	9.77909i		−	0.323287i
$916$	−9.53428	−	5.50462i	−0.315022	−	0.181878i
$917$	7.51902	+	4.34111i	0.248300	+	0.143356i
$918$		−	6.36980i		−	0.210235i
$919$	−27.1942	+	47.1017i	−0.897053	+	1.55374i	−0.0658107	+	0.997832i	$0.520963\pi$
$919$	−27.1942	+	47.1017i	−0.897053	+	1.55374i	−0.831243	+	0.555910i	$0.812370\pi$
$920$	−17.1468	−	29.6991i	−0.565313	−	0.979150i
$921$	3.75070	−	2.16547i	0.123590	−	0.0713545i
$922$	−4.70594			−0.154982
$923$	−22.2127	−	25.0277i	−0.731139	−	0.823798i
$924$	−1.10628			−0.0363940
$925$	−28.0203	+	16.1776i	−0.921303	+	0.531915i
$926$	−0.351328	−	0.608518i	−0.0115454	−	0.0199972i
$927$	−7.03813	+	12.1904i	−0.231163	+	0.400385i
$928$		−	35.5282i		−	1.16627i
$929$	−40.2774	−	23.2541i	−1.32146	−	0.762944i	−0.337496	−	0.941327i	$-0.609580\pi$
$929$	−40.2774	−	23.2541i	−1.32146	−	0.762944i	−0.983961	+	0.178383i	$0.942913\pi$
$930$	−23.9524	−	13.8289i	−0.785431	−	0.453469i
$931$		−	6.19600i		−	0.203066i
$932$	4.77793	−	8.27562i	0.156506	−	0.271077i
$933$	7.47405	+	12.9454i	0.244690	+	0.423815i
$934$	−9.89505	+	5.71291i	−0.323776	+	0.186932i
$935$	−26.7372			−0.874401
$936$	−7.34695	−	8.27806i	−0.240143	−	0.270577i
$937$	34.6775			1.13286			0.566432	−	0.824108i	$-0.308323\pi$
$937$	34.6775			1.13286			0.566432	+	0.824108i	$0.308323\pi$
$938$	0.256510	−	0.148096i	0.00837534	−	0.00483550i
$939$	4.37986	+	7.58614i	0.142931	+	0.247564i
$940$	4.32274	−	7.48721i	0.140992	−	0.244206i
$941$			39.8173i			1.29801i	0.760785	+	0.649004i	$0.224814\pi$
$941$			39.8173i			1.29801i	−0.760785	+	0.649004i	$0.775186\pi$
$942$	16.0582	+	9.27122i	0.523205	+	0.302073i
$943$	−3.39936	−	1.96262i	−0.110698	−	0.0639118i
$944$		−	8.86128i		−	0.288410i
$945$	−1.64216	+	2.84430i	−0.0534194	+	0.0925252i
$946$	0.635649	+	1.10098i	0.0206667	+	0.0357958i
$947$	−26.3121	+	15.1913i	−0.855027	+	0.493650i	−0.862344	−	0.506323i	$-0.831004\pi$
$947$	−26.3121	+	15.1913i	−0.855027	+	0.493650i	0.00731690	+	0.999973i	$0.497671\pi$
$948$	4.71443			0.153117
$949$	13.8293	−	41.5476i	0.448919	−	1.34869i
$950$	39.5145			1.28202
$951$	−4.73126	+	2.73159i	−0.153422	+	0.0885780i
$952$	8.87133	+	15.3656i	0.287521	+	0.498002i
$953$	−1.22107	+	2.11495i	−0.0395542	+	0.0685099i	−0.885125	−	0.465354i	$-0.845927\pi$
$953$	−1.22107	+	2.11495i	−0.0395542	+	0.0685099i	0.845571	+	0.533864i	$0.179260\pi$
$954$			6.10858i			0.197773i
$955$	14.8718	+	8.58624i	0.481240	+	0.277844i
$956$	6.35624	+	3.66978i	0.205575	+	0.118689i
$957$			12.0806i			0.390510i
$958$	−14.0754	+	24.3793i	−0.454755	+	0.787659i
$959$	6.28868	+	10.8923i	0.203072	+	0.351731i
$960$	−23.2936	+	13.4486i	−0.751798	+	0.434051i
$961$	−27.3884			−0.883495
$962$	16.6167	−	14.7476i	0.535743	−	0.475483i
$963$	7.34688			0.236750
$964$	14.4707	−	8.35468i	0.466071	−	0.269086i
$965$	−38.9231	−	67.4169i	−1.25298	−	2.17023i
$966$	1.87432	−	3.24642i	0.0603054	−	0.104452i
$967$			45.3725i			1.45908i	0.683938	+	0.729541i	$0.260266\pi$
$967$			45.3725i			1.45908i	−0.683938	+	0.729541i	$0.739734\pi$
$968$	−23.9692	−	13.8387i	−0.770401	−	0.444791i
$969$	31.0140	+	17.9059i	0.996312	+	0.575221i
$970$		−	67.8130i		−	2.17734i
$971$	−15.9568	+	27.6381i	−0.512079	+	0.886947i	0.487823	+	0.872943i	$0.337791\pi$
$971$	−15.9568	+	27.6381i	−0.512079	+	0.886947i	−0.999902	+	0.0140045i	$0.995542\pi$
$972$	−0.392717	−	0.680206i	−0.0125964	−	0.0218176i
$973$	9.29478	−	5.36634i	0.297977	−	0.172037i
$974$	14.1078			0.452042
$975$	4.19171	+	20.4390i	0.134242	+	0.654572i
$976$	5.39591			0.172719
$977$	−4.32389	+	2.49640i	−0.138334	+	0.0798669i	−0.567570	−	0.823325i	$-0.692116\pi$
$977$	−4.32389	+	2.49640i	−0.138334	+	0.0798669i	0.429236	+	0.903192i	$0.358783\pi$
$978$	−11.4800	−	19.8840i	−0.367091	−	0.635821i
$979$	−11.6753	+	20.2222i	−0.373143	+	0.646303i
$980$		−	2.57962i		−	0.0824029i
$981$	4.03240	+	2.32811i	0.128745	+	0.0743307i
$982$	−6.52182	−	3.76537i	−0.208120	−	0.120158i
$983$			18.7912i			0.599345i	0.954042	+	0.299672i	$0.0968773\pi$
$983$			18.7912i			0.599345i	−0.954042	+	0.299672i	$0.903123\pi$
$984$	−1.77123	+	3.06787i	−0.0564649	+	0.0978000i
$985$	−25.6505	−	44.4279i	−0.817292	−	1.41559i
$986$	47.3138	−	27.3166i	1.50678	−	0.869939i
$987$	3.35146			0.106678
$988$	17.1889	−	3.52516i	0.546851	−	0.112150i
$989$	2.78577			0.0885823
$990$	4.41512	−	2.54907i	0.140322	−	0.0810148i
$991$	−20.6802	−	35.8192i	−0.656929	−	1.13783i	−0.981406	−	0.191941i	$-0.938522\pi$
$991$	−20.6802	−	35.8192i	−0.656929	−	1.13783i	0.324478	−	0.945893i	$-0.394812\pi$
$992$	−15.8261	+	27.4117i	−0.502481	+	0.870322i
$993$			8.61829i			0.273493i
$994$	−8.85804	−	5.11419i	−0.280960	−	0.162212i
$995$	−59.2603	−	34.2140i	−1.87868	−	1.08466i
$996$			4.72968i			0.149866i
$997$	−6.10592	+	10.5758i	−0.193376	+	0.334938i	−0.946367	−	0.323094i	$-0.895277\pi$
$997$	−6.10592	+	10.5758i	−0.193376	+	0.334938i	0.752991	+	0.658031i	$0.228610\pi$
$998$	16.4384	+	28.4722i	0.520350	+	0.901272i
$999$	4.84216	−	2.79562i	0.153199	−	0.0884496i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bd.a.127.6	yes	16
3.2	odd	2		819.2.ct.b.127.3		16
13.2	odd	12		3549.2.a.bd.1.6		8
13.4	even	6	inner	273.2.bd.a.43.6	✓	16
13.11	odd	12		3549.2.a.bb.1.3		8
39.17	odd	6		819.2.ct.b.316.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bd.a.43.6	✓	16	13.4	even	6	inner
273.2.bd.a.127.6	yes	16	1.1	even	1	trivial
819.2.ct.b.127.3		16	3.2	odd	2
819.2.ct.b.316.3		16	39.17	odd	6
3549.2.a.bb.1.3		8	13.11	odd	12
3549.2.a.bd.1.6		8	13.2	odd	12

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.bd (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.954423 - 0.551037i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.392717 + 0.680206i) q^{4} +3.28432i q^{5} +(-0.954423 - 0.551037i) q^{6} +(0.866025 + 0.500000i) q^{7} +3.06975i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.954423 - 0.551037i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.392717 + 0.680206i) q^{4} +3.28432i q^{5} +(-0.954423 - 0.551037i) q^{6} +(0.866025 + 0.500000i) q^{7} +3.06975i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.80978 + 3.13463i) q^{10} +(-1.21979 + 0.704249i) q^{11} +0.785435 q^{12} +(3.42102 + 1.13870i) q^{13} +1.10207 q^{14} +(2.84430 - 1.64216i) q^{15} +(0.906111 + 1.56943i) q^{16} +(2.88992 - 5.00548i) q^{17} +1.10207i q^{18} +(-5.36590 - 3.09800i) q^{19} +(-2.23401 - 1.28981i) q^{20} -1.00000i q^{21} +(-0.776134 + 1.34430i) q^{22} +(1.70072 + 2.94574i) q^{23} +(2.65848 - 1.53488i) q^{24} -5.78675 q^{25} +(3.89256 - 0.798302i) q^{26} +1.00000 q^{27} +(-0.680206 + 0.392717i) q^{28} +(4.28846 + 7.42783i) q^{29} +(1.80978 - 3.13463i) q^{30} -7.64123i q^{31} +(-3.58734 - 2.07115i) q^{32} +(1.21979 + 0.704249i) q^{33} -6.36980i q^{34} +(-1.64216 + 2.84430i) q^{35} +(-0.392717 - 0.680206i) q^{36} +(4.84216 - 2.79562i) q^{37} -6.82845 q^{38} +(-0.724364 - 3.53204i) q^{39} -10.0820 q^{40} +(-0.999386 + 0.576996i) q^{41} +(-0.551037 - 0.954423i) q^{42} +(0.409497 - 0.709270i) q^{43} -1.10628i q^{44} +(-2.84430 - 1.64216i) q^{45} +(3.24642 + 1.87432i) q^{46} +3.35146i q^{47} +(0.906111 - 1.56943i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-5.52300 + 3.18871i) q^{50} -5.77983 q^{51} +(-2.11805 + 1.87981i) q^{52} +5.54281 q^{53} +(0.954423 - 0.551037i) q^{54} +(-2.31298 - 4.00619i) q^{55} +(-1.53488 + 2.65848i) q^{56} +6.19600i q^{57} +(8.18602 + 4.72620i) q^{58} +(-4.23463 - 2.44486i) q^{59} +2.57962i q^{60} +(1.48876 - 2.57860i) q^{61} +(-4.21060 - 7.29297i) q^{62} +(-0.866025 + 0.500000i) q^{63} -8.18957 q^{64} +(-3.73986 + 11.2357i) q^{65} +1.55227 q^{66} +(0.232752 - 0.134379i) q^{67} +(2.26984 + 3.93148i) q^{68} +(1.70072 - 2.94574i) q^{69} +3.61956i q^{70} +(-8.03762 - 4.64052i) q^{71} +(-2.65848 - 1.53488i) q^{72} -12.1448i q^{73} +(3.08098 - 5.33641i) q^{74} +(2.89337 + 5.01147i) q^{75} +(4.21456 - 2.43328i) q^{76} -1.40850 q^{77} +(-2.63763 - 2.97191i) q^{78} +6.00232 q^{79} +(-5.15451 + 2.97596i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.635891 + 1.10140i) q^{82} +6.02174i q^{83} +(0.680206 + 0.392717i) q^{84} +(16.4396 + 9.49140i) q^{85} -0.902592i q^{86} +(4.28846 - 7.42783i) q^{87} +(-2.16187 - 3.74447i) q^{88} +(14.3573 - 8.28917i) q^{89} -3.61956 q^{90} +(2.39334 + 2.69665i) q^{91} -2.67162 q^{92} +(-6.61750 + 3.82061i) q^{93} +(1.84678 + 3.19871i) q^{94} +(10.1748 - 17.6233i) q^{95} +4.14230i q^{96} +(-16.2251 - 9.36758i) q^{97} +(0.954423 + 0.551037i) q^{98} -1.40850i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 + 6 * q^4 - 8 * q^9	\( 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9} - 4 q^{10} - 12 q^{11} - 12 q^{12} + 4 q^{13} + 4 q^{14} - 10 q^{16} + 10 q^{17} + 6 q^{20} - 2 q^{22} - 2 q^{23} + 12 q^{25} + 20 q^{26} + 16 q^{27} + 12 q^{29} - 4 q^{30} + 30 q^{32} + 12 q^{33} - 2 q^{35} + 6 q^{36} + 18 q^{37} - 32 q^{38} - 8 q^{39} - 60 q^{40} + 18 q^{41} - 2 q^{42} - 10 q^{43} + 30 q^{46} - 10 q^{48} + 8 q^{49} - 24 q^{50} - 20 q^{51} - 26 q^{52} + 12 q^{53} + 10 q^{55} + 12 q^{56} - 54 q^{58} - 60 q^{59} - 6 q^{61} + 16 q^{62} + 16 q^{64} - 20 q^{65} + 4 q^{66} - 18 q^{67} - 20 q^{68} - 2 q^{69} + 6 q^{71} + 18 q^{74} - 6 q^{75} + 72 q^{76} - 16 q^{77} + 14 q^{78} - 4 q^{79} + 30 q^{80} - 8 q^{81} - 18 q^{82} - 24 q^{85} + 12 q^{87} - 2 q^{88} + 78 q^{89} + 8 q^{90} - 8 q^{91} - 20 q^{92} + 6 q^{93} + 16 q^{94} - 4 q^{95} - 54 q^{97}+O(q^{100}) \) 16 * q - 8 * q^3 + 6 * q^4 - 8 * q^9 - 4 * q^10 - 12 * q^11 - 12 * q^12 + 4 * q^13 + 4 * q^14 - 10 * q^16 + 10 * q^17 + 6 * q^20 - 2 * q^22 - 2 * q^23 + 12 * q^25 + 20 * q^26 + 16 * q^27 + 12 * q^29 - 4 * q^30 + 30 * q^32 + 12 * q^33 - 2 * q^35 + 6 * q^36 + 18 * q^37 - 32 * q^38 - 8 * q^39 - 60 * q^40 + 18 * q^41 - 2 * q^42 - 10 * q^43 + 30 * q^46 - 10 * q^48 + 8 * q^49 - 24 * q^50 - 20 * q^51 - 26 * q^52 + 12 * q^53 + 10 * q^55 + 12 * q^56 - 54 * q^58 - 60 * q^59 - 6 * q^61 + 16 * q^62 + 16 * q^64 - 20 * q^65 + 4 * q^66 - 18 * q^67 - 20 * q^68 - 2 * q^69 + 6 * q^71 + 18 * q^74 - 6 * q^75 + 72 * q^76 - 16 * q^77 + 14 * q^78 - 4 * q^79 + 30 * q^80 - 8 * q^81 - 18 * q^82 - 24 * q^85 + 12 * q^87 - 2 * q^88 + 78 * q^89 + 8 * q^90 - 8 * q^91 - 20 * q^92 + 6 * q^93 + 16 * q^94 - 4 * q^95 - 54 * q^97

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