LMFDB - Embedded newform 546.2.bn.f.101.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(101,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([3, 1, 5]))

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

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

chi := DirichletCharacter("546.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bn (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.13
Character	$\chi$	$=$	546.101
Dual form			546.2.bn.f.173.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(1.17271 + 1.27466i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.870413 + 0.502533i) q^{5} +(1.69024 - 0.378264i) q^{6} +(1.33597 + 2.28368i) q^{7} -1.00000 q^{8} +(-0.249516 + 2.98961i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(1.17271 + 1.27466i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.870413 + 0.502533i) q^{5} +(1.69024 - 0.378264i) q^{6} +(1.33597 + 2.28368i) q^{7} -1.00000 q^{8} +(-0.249516 + 2.98961i) q^{9} +1.00507i q^{10} -0.620619 q^{11} +(0.517534 - 1.65292i) q^{12} +(1.14202 + 3.41991i) q^{13} +(2.64571 - 0.0151415i) q^{14} +(-1.66130 - 0.520156i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.171457 - 0.296972i) q^{17} +(2.46432 + 1.71089i) q^{18} +4.33817 q^{19} +(0.870413 + 0.502533i) q^{20} +(-1.34422 + 4.38099i) q^{21} +(-0.310310 + 0.537472i) q^{22} +(-2.44412 - 1.41111i) q^{23} +(-1.17271 - 1.27466i) q^{24} +(-1.99492 + 3.45530i) q^{25} +(3.53274 + 0.720933i) q^{26} +(-4.10334 + 3.18788i) q^{27} +(1.30974 - 2.29882i) q^{28} +(8.23191 - 4.75270i) q^{29} +(-1.28112 + 1.17865i) q^{30} +(1.25167 - 2.16796i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.727805 - 0.791078i) q^{33} -0.342914 q^{34} +(-2.31047 - 1.31638i) q^{35} +(2.71383 - 1.27872i) q^{36} +(-3.76637 - 2.17451i) q^{37} +(2.16909 - 3.75697i) q^{38} +(-3.01996 + 5.46624i) q^{39} +(0.870413 - 0.502533i) q^{40} +(7.47421 - 4.31523i) q^{41} +(3.12194 + 3.35462i) q^{42} +(-0.602811 + 1.04410i) q^{43} +(0.310310 + 0.537472i) q^{44} +(-1.28519 - 2.72758i) q^{45} +(-2.44412 + 1.41111i) q^{46} +(-0.0442417 + 0.0255429i) q^{47} +(-1.69024 + 0.378264i) q^{48} +(-3.43038 + 6.10184i) q^{49} +(1.99492 + 3.45530i) q^{50} +(0.177470 - 0.566810i) q^{51} +(2.39072 - 2.69898i) q^{52} +(-4.15182 - 2.39705i) q^{53} +(0.709119 + 5.14754i) q^{54} +(0.540195 - 0.311882i) q^{55} +(-1.33597 - 2.28368i) q^{56} +(5.08741 + 5.52970i) q^{57} -9.50539i q^{58} +(-2.67570 + 1.54481i) q^{59} +(0.380181 + 1.69880i) q^{60} -6.68221i q^{61} +(-1.25167 - 2.16796i) q^{62} +(-7.16065 + 3.42420i) q^{63} +1.00000 q^{64} +(-2.71265 - 2.40283i) q^{65} +(-1.04900 + 0.234758i) q^{66} +5.48907i q^{67} +(-0.171457 + 0.296972i) q^{68} +(-1.06755 - 4.77024i) q^{69} +(-2.29525 + 1.34273i) q^{70} +(0.621982 - 1.07730i) q^{71} +(0.249516 - 2.98961i) q^{72} +(4.46154 - 7.72761i) q^{73} +(-3.76637 + 2.17451i) q^{74} +(-6.74380 + 1.50921i) q^{75} +(-2.16909 - 3.75697i) q^{76} +(-0.829127 - 1.41730i) q^{77} +(3.22393 + 5.34849i) q^{78} +(0.458065 + 0.793391i) q^{79} -1.00507i q^{80} +(-8.87548 - 1.49191i) q^{81} -8.63047i q^{82} -13.2261i q^{83} +(4.46616 - 1.02637i) q^{84} +(0.298476 + 0.172325i) q^{85} +(0.602811 + 1.04410i) q^{86} +(15.7117 + 4.91937i) q^{87} +0.620619 q^{88} +(-3.11782 - 1.80007i) q^{89} +(-3.00475 - 0.250780i) q^{90} +(-6.28427 + 7.17690i) q^{91} +2.82222i q^{92} +(4.23126 - 0.946926i) q^{93} +0.0510859i q^{94} +(-3.77600 + 2.18008i) q^{95} +(-0.517534 + 1.65292i) q^{96} +(5.10398 - 8.84035i) q^{97} +(3.56916 + 6.02172i) q^{98} +(0.154854 - 1.85541i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 17 q^{2} - 3 q^{3} - 17 q^{4} - 9 q^{5} + 3 q^{6} + 5 q^{7} - 34 q^{8} + 7 q^{9}+O(q^{10}) $ 34 * q + 17 * q^2 - 3 * q^3 - 17 * q^4 - 9 * q^5 + 3 * q^6 + 5 * q^7 - 34 * q^8 + 7 * q^9	$ 34 q + 17 q^{2} - 3 q^{3} - 17 q^{4} - 9 q^{5} + 3 q^{6} + 5 q^{7} - 34 q^{8} + 7 q^{9} + 18 q^{11} + 6 q^{12} - 8 q^{13} + 4 q^{14} - 4 q^{15} - 17 q^{16} - 6 q^{17} - 4 q^{18} - 10 q^{19} + 9 q^{20} + 7 q^{21} + 9 q^{22} - 6 q^{23} + 3 q^{24} + 16 q^{25} - 13 q^{26} - 18 q^{27} - q^{28} - 27 q^{29} + 13 q^{30} + q^{31} + 17 q^{32} + 21 q^{33} - 12 q^{34} + 3 q^{35} - 11 q^{36} + 6 q^{37} - 5 q^{38} - 2 q^{39} + 9 q^{40} - 3 q^{41} + 8 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} - 6 q^{46} + 27 q^{47} - 3 q^{48} - 5 q^{49} - 16 q^{50} - 36 q^{51} - 5 q^{52} - 21 q^{53} + 57 q^{55} - 5 q^{56} + 17 q^{57} + 6 q^{59} + 17 q^{60} - q^{62} + 34 q^{64} - 33 q^{65} - 6 q^{68} - 42 q^{69} + 3 q^{70} + 15 q^{71} - 7 q^{72} + 19 q^{73} + 6 q^{74} - 9 q^{75} + 5 q^{76} + 9 q^{77} - 7 q^{78} - 9 q^{79} - 5 q^{81} + q^{84} - 42 q^{85} + 3 q^{86} + 6 q^{87} - 18 q^{88} + 18 q^{89} + 9 q^{90} - 27 q^{91} + 8 q^{93} + 3 q^{95} - 6 q^{96} - 19 q^{97} - 7 q^{98} + 27 q^{99}+O(q^{100}) $ 34 * q + 17 * q^2 - 3 * q^3 - 17 * q^4 - 9 * q^5 + 3 * q^6 + 5 * q^7 - 34 * q^8 + 7 * q^9 + 18 * q^11 + 6 * q^12 - 8 * q^13 + 4 * q^14 - 4 * q^15 - 17 * q^16 - 6 * q^17 - 4 * q^18 - 10 * q^19 + 9 * q^20 + 7 * q^21 + 9 * q^22 - 6 * q^23 + 3 * q^24 + 16 * q^25 - 13 * q^26 - 18 * q^27 - q^28 - 27 * q^29 + 13 * q^30 + q^31 + 17 * q^32 + 21 * q^33 - 12 * q^34 + 3 * q^35 - 11 * q^36 + 6 * q^37 - 5 * q^38 - 2 * q^39 + 9 * q^40 - 3 * q^41 + 8 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 - 6 * q^46 + 27 * q^47 - 3 * q^48 - 5 * q^49 - 16 * q^50 - 36 * q^51 - 5 * q^52 - 21 * q^53 + 57 * q^55 - 5 * q^56 + 17 * q^57 + 6 * q^59 + 17 * q^60 - q^62 + 34 * q^64 - 33 * q^65 - 6 * q^68 - 42 * q^69 + 3 * q^70 + 15 * q^71 - 7 * q^72 + 19 * q^73 + 6 * q^74 - 9 * q^75 + 5 * q^76 + 9 * q^77 - 7 * q^78 - 9 * q^79 - 5 * q^81 + q^84 - 42 * q^85 + 3 * q^86 + 6 * q^87 - 18 * q^88 + 18 * q^89 + 9 * q^90 - 27 * q^91 + 8 * q^93 + 3 * q^95 - 6 * q^96 - 19 * q^97 - 7 * q^98 + 27 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	1.17271	+	1.27466i	0.677063	+	0.735925i
$3$	1.17271	+	1.27466i	0.677063	+	0.735925i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.870413	+	0.502533i	−0.389260	+	0.224740i	−0.681840	−	0.731502i	$-0.738820\pi$
$5$	−0.870413	+	0.502533i	−0.389260	+	0.224740i	0.292579	+	0.956241i	$0.405486\pi$
$6$	1.69024	−	0.378264i	0.690038	−	0.154426i
$7$	1.33597	+	2.28368i	0.504948	+	0.863150i
$7$	1.33597	+	2.28368i	0.504948	+	0.863150i
$8$	−1.00000			−0.353553
$9$	−0.249516	+	2.98961i	−0.0831719	+	0.996535i
$10$			1.00507i			0.317830i
$11$	−0.620619			−0.187124			−0.0935619	−	0.995613i	$-0.529825\pi$
$11$	−0.620619			−0.187124			−0.0935619	+	0.995613i	$0.529825\pi$
$12$	0.517534	−	1.65292i	0.149399	−	0.477158i
$13$	1.14202	+	3.41991i	0.316741	+	0.948512i
$13$	1.14202	+	3.41991i	0.316741	+	0.948512i
$14$	2.64571	−	0.0151415i	0.707095	−	0.00404675i
$15$	−1.66130	−	0.520156i	−0.428945	−	0.134304i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.171457	−	0.296972i	−0.0415844	−	0.0720263i	0.844484	−	0.535581i	$-0.179907\pi$
$17$	−0.171457	−	0.296972i	−0.0415844	−	0.0720263i	−0.886068	+	0.463554i	$0.846574\pi$
$18$	2.46432	+	1.71089i	0.580845	+	0.403261i
$19$	4.33817			0.995246			0.497623	−	0.867394i	$-0.334206\pi$
$19$	4.33817			0.995246			0.497623	+	0.867394i	$0.334206\pi$
$20$	0.870413	+	0.502533i	0.194630	+	0.112370i
$21$	−1.34422	+	4.38099i	−0.293332	+	0.956011i
$22$	−0.310310	+	0.537472i	−0.0661582	+	0.114589i
$23$	−2.44412	−	1.41111i	−0.509633	−	0.294237i	0.223050	−	0.974807i	$-0.428399\pi$
$23$	−2.44412	−	1.41111i	−0.509633	−	0.294237i	−0.732683	+	0.680570i	$0.761732\pi$
$24$	−1.17271	−	1.27466i	−0.239378	−	0.260189i
$25$	−1.99492	+	3.45530i	−0.398984	+	0.691061i
$26$	3.53274	+	0.720933i	0.692827	+	0.141387i
$27$	−4.10334	+	3.18788i	−0.789688	+	0.613509i
$28$	1.30974	−	2.29882i	0.247518	−	0.434436i
$29$	8.23191	−	4.75270i	1.52863	−	0.882553i	0.529208	−	0.848492i	$-0.322489\pi$
$29$	8.23191	−	4.75270i	1.52863	−	0.882553i	0.999420	−	0.0340609i	$-0.0108440\pi$
$30$	−1.28112	+	1.17865i	−0.233899	+	0.215191i
$31$	1.25167	−	2.16796i	0.224807	−	0.389377i	−0.731454	−	0.681890i	$-0.761158\pi$
$31$	1.25167	−	2.16796i	0.224807	−	0.389377i	0.956262	+	0.292513i	$0.0944915\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−0.727805	−	0.791078i	−0.126695	−	0.137709i
$34$	−0.342914			−0.0588092
$35$	−2.31047	−	1.31638i	−0.390540	−	0.222508i
$36$	2.71383	−	1.27872i	0.452305	−	0.213119i
$37$	−3.76637	−	2.17451i	−0.619187	−	0.357488i	0.157366	−	0.987540i	$-0.449700\pi$
$37$	−3.76637	−	2.17451i	−0.619187	−	0.357488i	−0.776552	+	0.630053i	$0.783033\pi$
$38$	2.16909	−	3.75697i	0.351872	−	0.609461i
$39$	−3.01996	+	5.46624i	−0.483581	+	0.875300i
$40$	0.870413	−	0.502533i	0.137624	−	0.0794574i
$41$	7.47421	−	4.31523i	1.16727	−	0.673926i	0.214238	−	0.976781i	$-0.431273\pi$
$41$	7.47421	−	4.31523i	1.16727	−	0.673926i	0.953037	+	0.302855i	$0.0979398\pi$
$42$	3.12194	+	3.35462i	0.481726	+	0.517629i
$43$	−0.602811	+	1.04410i	−0.0919278	+	0.159224i	−0.908322	−	0.418271i	$-0.862636\pi$
$43$	−0.602811	+	1.04410i	−0.0919278	+	0.159224i	0.816394	+	0.577495i	$0.195970\pi$
$44$	0.310310	+	0.537472i	0.0467809	+	0.0810270i
$45$	−1.28519	−	2.72758i	−0.191585	−	0.406604i
$46$	−2.44412	+	1.41111i	−0.360365	+	0.208057i
$47$	−0.0442417	+	0.0255429i	−0.00645331	+	0.00372582i	−0.503223	−	0.864156i	$-0.667853\pi$
$47$	−0.0442417	+	0.0255429i	−0.00645331	+	0.00372582i	0.496770	+	0.867882i	$0.334519\pi$
$48$	−1.69024	+	0.378264i	−0.243965	+	0.0545977i
$49$	−3.43038	+	6.10184i	−0.490055	+	0.871692i
$50$	1.99492	+	3.45530i	0.282124	+	0.488654i
$51$	0.177470	−	0.566810i	0.0248507	−	0.0793693i
$52$	2.39072	−	2.69898i	0.331533	−	0.374281i
$53$	−4.15182	−	2.39705i	−0.570296	−	0.329260i	0.186972	−	0.982365i	$-0.440133\pi$
$53$	−4.15182	−	2.39705i	−0.570296	−	0.329260i	−0.757267	+	0.653105i	$0.773466\pi$
$54$	0.709119	+	5.14754i	0.0964989	+	0.700491i
$55$	0.540195	−	0.311882i	0.0728399	−	0.0420541i
$56$	−1.33597	−	2.28368i	−0.178526	−	0.305170i
$57$	5.08741	+	5.52970i	0.673844	+	0.732426i
$58$		−	9.50539i		−	1.24812i
$59$	−2.67570	+	1.54481i	−0.348346	+	0.201118i	−0.663956	−	0.747771i	$-0.731124\pi$
$59$	−2.67570	+	1.54481i	−0.348346	+	0.201118i	0.315611	+	0.948889i	$0.397791\pi$
$60$	0.380181	+	1.69880i	0.0490811	+	0.219315i
$61$		−	6.68221i		−	0.855570i	−0.903881	−	0.427785i	$-0.859294\pi$
$61$		−	6.68221i		−	0.855570i	0.903881	−	0.427785i	$-0.140706\pi$
$62$	−1.25167	−	2.16796i	−0.158963	−	0.275331i
$63$	−7.16065	+	3.42420i	−0.902157	+	0.431409i
$64$	1.00000			0.125000
$65$	−2.71265	−	2.40283i	−0.336463	−	0.298034i
$66$	−1.04900	+	0.234758i	−0.129123	+	0.0288967i
$67$			5.48907i			0.670597i	0.942112	+	0.335298i	$0.108837\pi$
$67$			5.48907i			0.670597i	−0.942112	+	0.335298i	$0.891163\pi$
$68$	−0.171457	+	0.296972i	−0.0207922	+	0.0360131i
$69$	−1.06755	−	4.77024i	−0.128517	−	0.574269i
$70$	−2.29525	+	1.34273i	−0.274335	+	0.160488i
$71$	0.621982	−	1.07730i	0.0738157	−	0.127853i	−0.826755	−	0.562562i	$-0.809816\pi$
$71$	0.621982	−	1.07730i	0.0738157	−	0.127853i	0.900571	+	0.434710i	$0.143149\pi$
$72$	0.249516	−	2.98961i	0.0294057	−	0.352328i
$73$	4.46154	−	7.72761i	0.522183	−	0.904448i	−0.477484	−	0.878641i	$-0.658451\pi$
$73$	4.46154	−	7.72761i	0.522183	−	0.904448i	0.999667	−	0.0258074i	$-0.00821566\pi$
$74$	−3.76637	+	2.17451i	−0.437831	+	0.252782i
$75$	−6.74380	+	1.50921i	−0.778707	+	0.174269i
$76$	−2.16909	−	3.75697i	−0.248811	−	0.430954i
$77$	−0.829127	−	1.41730i	−0.0944878	−	0.161516i
$78$	3.22393	+	5.34849i	0.365038	+	0.605597i
$79$	0.458065	+	0.793391i	0.0515363	+	0.0892635i	0.890643	−	0.454704i	$-0.150255\pi$
$79$	0.458065	+	0.793391i	0.0515363	+	0.0892635i	−0.839106	+	0.543967i	$0.816922\pi$
$80$		−	1.00507i		−	0.112370i
$81$	−8.87548	−	1.49191i	−0.986165	−	0.165767i
$82$		−	8.63047i		−	0.953076i
$83$		−	13.2261i		−	1.45176i	−0.687822	−	0.725879i	$-0.741433\pi$
$83$		−	13.2261i		−	1.45176i	0.687822	−	0.725879i	$-0.258567\pi$
$84$	4.46616	−	1.02637i	0.487298	−	0.111986i
$85$	0.298476	+	0.172325i	0.0323743	+	0.0186913i
$86$	0.602811	+	1.04410i	0.0650028	+	0.112588i
$87$	15.7117	+	4.91937i	1.68447	+	0.527411i
$88$	0.620619			0.0661582
$89$	−3.11782	−	1.80007i	−0.330488	−	0.190807i	0.325570	−	0.945518i	$-0.394444\pi$
$89$	−3.11782	−	1.80007i	−0.330488	−	0.190807i	−0.656058	+	0.754711i	$0.727777\pi$
$90$	−3.00475	−	0.250780i	−0.316729	−	0.0264345i
$91$	−6.28427	+	7.17690i	−0.658771	+	0.752344i
$92$			2.82222i			0.294237i
$93$	4.23126	−	0.946926i	0.438761	−	0.0981917i
$94$			0.0510859i			0.00526910i
$95$	−3.77600	+	2.18008i	−0.387410	+	0.223671i
$96$	−0.517534	+	1.65292i	−0.0528206	+	0.168701i
$97$	5.10398	−	8.84035i	0.518231	−	0.897602i	−0.481545	−	0.876421i	$-0.659924\pi$
$97$	5.10398	−	8.84035i	0.518231	−	0.897602i	0.999776	−	0.0211806i	$-0.00674249\pi$
$98$	3.56916	+	6.02172i	0.360539	+	0.608286i
$99$	0.154854	−	1.85541i	0.0155634	−	0.186475i
$100$	3.98984			0.398984
$101$	−9.91247			−0.986328			−0.493164	−	0.869936i	$-0.664160\pi$
$101$	−9.91247			−0.986328			−0.493164	+	0.869936i	$0.664160\pi$
$102$	−0.402137	−	0.437098i	−0.0398175	−	0.0432792i
$103$	8.93253	−	5.15720i	0.880149	−	0.508154i	0.00944127	−	0.999955i	$-0.496995\pi$
$103$	8.93253	−	5.15720i	0.880149	−	0.508154i	0.870707	+	0.491801i	$0.163661\pi$
$104$	−1.14202	−	3.41991i	−0.111985	−	0.335350i
$105$	−1.03157	−	4.48878i	−0.100671	−	0.438060i
$106$	−4.15182	+	2.39705i	−0.403260	+	0.232822i
$107$	−12.7443	−	7.35793i	−1.23204	−	0.711318i	−0.264584	−	0.964363i	$-0.585235\pi$
$107$	−12.7443	−	7.35793i	−1.23204	−	0.711318i	−0.967454	+	0.253045i	$0.918568\pi$
$108$	4.81246	+	1.95965i	0.463079	+	0.188568i
$109$	15.5550	+	8.98070i	1.48990	+	0.860195i	0.999933	−	0.0115450i	$-0.00367496\pi$
$109$	15.5550	+	8.98070i	1.48990	+	0.860195i	0.489968	+	0.871740i	$0.337008\pi$
$110$		−	0.623763i		−	0.0594735i
$111$	−1.64508	−	7.35090i	−0.156144	−	0.697717i
$112$	−2.64571	+	0.0151415i	−0.249996	+	0.00143074i
$113$	−4.26195	−	2.46064i	−0.400931	−	0.231478i	0.285955	−	0.958243i	$-0.407689\pi$
$113$	−4.26195	−	2.46064i	−0.400931	−	0.231478i	−0.686886	+	0.726766i	$0.741023\pi$
$114$	7.33256	−	1.64098i	0.686757	−	0.153692i
$115$	2.83652			0.264507
$116$	−8.23191	−	4.75270i	−0.764314	−	0.441277i
$117$	−10.5091	+	2.56088i	−0.971570	+	0.236754i
$118$			3.08963i			0.284423i
$119$	0.449128	−	0.788297i	0.0411715	−	0.0722631i
$120$	1.66130	+	0.520156i	0.151655	+	0.0474835i
$121$	−10.6148			−0.964985
$122$	−5.78697	−	3.34111i	−0.523927	−	0.302490i
$123$	14.2655	+	4.46656i	1.28628	+	0.402736i
$124$	−2.50335			−0.224807
$125$		−	9.03538i		−	0.808149i
$126$	−0.614878	+	7.91340i	−0.0547777	+	0.704982i
$127$	−2.78854	−	4.82989i	−0.247443	−	0.428584i	0.715373	−	0.698743i	$-0.246257\pi$
$127$	−2.78854	−	4.82989i	−0.247443	−	0.428584i	−0.962816	+	0.270159i	$0.912924\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−2.03779	+	0.456044i	−0.179418	+	0.0401524i
$130$	−3.43723	+	1.14781i	−0.301465	+	0.100670i
$131$	9.12794	+	15.8101i	0.797512	+	1.38133i	0.921232	+	0.389014i	$0.127184\pi$
$131$	9.12794	+	15.8101i	0.797512	+	1.38133i	−0.123720	+	0.992317i	$0.539483\pi$
$132$	−0.321192	+	1.02584i	−0.0279562	+	0.0892876i
$133$	5.79566	+	9.90700i	0.502547	+	0.859046i
$134$	4.75367	+	2.74453i	0.410655	+	0.237092i
$135$	1.96958	−	4.83684i	0.169515	−	0.416289i
$136$	0.171457	+	0.296972i	0.0147023	+	0.0254651i
$137$	4.05306	+	7.02011i	0.346276	+	0.599768i	0.985585	−	0.169182i	$-0.0541126\pi$
$137$	4.05306	+	7.02011i	0.346276	+	0.599768i	−0.639308	+	0.768950i	$0.720779\pi$
$138$	−4.66492	−	1.46060i	−0.397104	−	0.124334i
$139$	16.5296	+	9.54339i	1.40203	+	0.809460i	0.994600	−	0.103779i	$-0.0330934\pi$
$139$	16.5296	+	9.54339i	1.40203	+	0.809460i	0.407425	+	0.913239i	$0.366427\pi$
$140$	0.0152182	+	2.65911i	0.00128618	+	0.224736i
$141$	−0.0844411	−	0.0264387i	−0.00711122	−	0.00222654i
$142$	−0.621982	−	1.07730i	−0.0521956	−	0.0904054i
$143$	−0.708762	−	2.12246i	−0.0592697	−	0.177489i
$144$	−2.46432	−	1.71089i	−0.205360	−	0.142574i
$145$	−4.77677	+	8.27361i	−0.396689	+	0.687086i
$146$	−4.46154	−	7.72761i	−0.369239	−	0.639541i
$147$	−11.8006	+	2.78310i	−0.973298	+	0.229546i
$148$			4.34903i			0.357488i
$149$	4.69216			0.384397			0.192198	−	0.981356i	$-0.438438\pi$
$149$	4.69216			0.384397			0.192198	+	0.981356i	$0.438438\pi$
$150$	−2.06488	+	6.59491i	−0.168597	+	0.538472i
$151$	−6.80898	−	3.93117i	−0.554107	−	0.319914i	0.196670	−	0.980470i	$-0.436987\pi$
$151$	−6.80898	−	3.93117i	−0.554107	−	0.319914i	−0.750777	+	0.660556i	$0.770321\pi$
$152$	−4.33817			−0.351872
$153$	0.930610	−	0.438489i	0.0752354	−	0.0354498i
$154$	−1.64198	+	0.00939713i	−0.132314	+	0.000757243i
$155$			2.51603i			0.202092i
$156$	6.24389	−	0.117759i	0.499911	−	0.00942827i
$157$	−19.8931	−	11.4853i	−1.58764	−	0.916627i	−0.993694	−	0.112126i	$-0.964234\pi$
$157$	−19.8931	−	11.4853i	−1.58764	−	0.916627i	−0.593951	−	0.804501i	$-0.702433\pi$
$158$	0.916129			0.0728833
$159$	−1.81344	−	8.10319i	−0.143815	−	0.642625i
$160$	−0.870413	−	0.502533i	−0.0688122	−	0.0397287i
$161$	−0.0427328	−	7.46677i	−0.00336782	−	0.588464i
$162$	−5.72977	+	6.94044i	−0.450173	+	0.545293i
$163$		−	8.84645i		−	0.692907i	−0.938067	−	0.346454i	$-0.887386\pi$
$163$		−	8.84645i		−	0.692907i	0.938067	−	0.346454i	$-0.112614\pi$
$164$	−7.47421	−	4.31523i	−0.583637	−	0.336963i
$165$	1.03103	+	0.322819i	0.0802658	+	0.0251314i
$166$	−11.4542	−	6.61307i	−0.889017	−	0.513274i
$167$	−3.95886	+	2.28565i	−0.306345	+	0.176869i	−0.645290	−	0.763938i	$-0.723263\pi$
$167$	−3.95886	+	2.28565i	−0.306345	+	0.176869i	0.338945	+	0.940806i	$0.389930\pi$
$168$	1.34422	−	4.38099i	0.103709	−	0.338001i
$169$	−10.3916	+	7.81124i	−0.799351	+	0.600864i
$170$	0.298476	−	0.172325i	0.0228921	−	0.0132168i
$171$	−1.08244	+	12.9694i	−0.0827764	+	0.991797i
$172$	1.20562			0.0919278
$173$	−13.1234			−0.997757			−0.498879	−	0.866672i	$-0.666255\pi$
$173$	−13.1234			−0.997757			−0.498879	+	0.866672i	$0.666255\pi$
$174$	12.1161	−	11.1470i	0.918522	−	0.845055i
$175$	−10.5560	+	0.0604124i	−0.797955	+	0.00456675i
$176$	0.310310	−	0.537472i	0.0233905	−	0.0405135i
$177$	−5.10692	−	1.59899i	−0.383860	−	0.120187i
$178$	−3.11782	+	1.80007i	−0.233690	+	0.134921i
$179$			19.5727i			1.46293i	0.681879	+	0.731465i	$0.261163\pi$
$179$			19.5727i			1.46293i	−0.681879	+	0.731465i	$0.738837\pi$
$180$	−1.71956	+	2.47680i	−0.128168	+	0.184610i
$181$		−	22.4310i		−	1.66728i	−0.552305	−	0.833642i	$-0.686252\pi$
$181$		−	22.4310i		−	1.66728i	0.552305	−	0.833642i	$-0.313748\pi$
$182$	3.07325	+	9.03079i	0.227804	+	0.669407i
$183$	8.51755	−	7.83628i	0.629635	−	0.579274i
$184$	2.44412	+	1.41111i	0.180183	+	0.104028i
$185$	4.37106			0.321367
$186$	1.29557	−	4.13784i	0.0949956	−	0.303401i
$187$	0.106409	+	0.184307i	0.00778143	+	0.0134778i
$188$	0.0442417	+	0.0255429i	0.00322665	+	0.00186291i
$189$	−12.7620	−	5.11180i	−0.928301	−	0.371829i
$190$			4.36015i			0.316319i
$191$			13.1414i			0.950880i	0.879748	+	0.475440i	$0.157711\pi$
$191$			13.1414i			0.950880i	−0.879748	+	0.475440i	$0.842289\pi$
$192$	1.17271	+	1.27466i	0.0846329	+	0.0919907i
$193$		−	12.6192i		−	0.908352i	−0.890912	−	0.454176i	$-0.849934\pi$
$193$		−	12.6192i		−	0.908352i	0.890912	−	0.454176i	$-0.150066\pi$
$194$	−5.10398	−	8.84035i	−0.366444	−	0.634700i
$195$	−0.118356	−	6.27552i	−0.00847562	−	0.449399i
$196$	6.99954	−	0.0801202i	0.499967	−	0.00572287i
$197$	0.693687	+	1.20150i	0.0494232	+	0.0856034i	0.889679	−	0.456587i	$-0.150928\pi$
$197$	0.693687	+	1.20150i	0.0494232	+	0.0856034i	−0.840255	+	0.542191i	$0.817595\pi$
$198$	−1.52940	−	1.06181i	−0.108690	−	0.0754596i
$199$	7.58522	−	4.37933i	0.537702	−	0.310442i	−0.206445	−	0.978458i	$-0.566190\pi$
$199$	7.58522	−	4.37933i	0.537702	−	0.310442i	0.744147	+	0.668016i	$0.232856\pi$
$200$	1.99492	−	3.45530i	0.141062	−	0.244327i
$201$	−6.99670	+	6.43707i	−0.493509	+	0.454036i
$202$	−4.95624	+	8.58446i	−0.348720	+	0.604000i
$203$	21.8512	+	12.4496i	1.53365	+	0.873791i
$204$	−0.579607	+	0.129712i	−0.0405806	+	0.00908166i
$205$	−4.33710	+	7.51207i	−0.302916	+	0.524666i
$206$		−	10.3144i		−	0.718638i
$207$	4.82851	−	6.95485i	0.335605	−	0.483395i
$208$	−3.53274	−	0.720933i	−0.244951	−	0.0499877i
$209$	−2.69235			−0.186234
$210$	−4.40318	−	1.35103i	−0.303849	−	0.0932297i
$211$	12.8567	+	22.2684i	0.885089	+	1.53302i	0.845611	+	0.533799i	$0.179236\pi$
$211$	12.8567	+	22.2684i	0.885089	+	1.53302i	0.0394776	+	0.999220i	$0.487431\pi$
$212$			4.79410i			0.329260i
$213$	2.10260	−	0.470547i	0.144068	−	0.0322414i
$214$	−12.7443	+	7.35793i	−0.871182	+	0.502977i
$215$		−	1.21173i		−	0.0826393i
$216$	4.10334	−	3.18788i	0.279197	−	0.216908i
$217$	6.62312	−	0.0379045i	0.449607	−	0.00257313i
$218$	15.5550	−	8.98070i	1.05352	−	0.608250i
$219$	15.0821	−	3.37528i	1.01916	−	0.228080i
$220$	−0.540195	−	0.311882i	−0.0364199	−	0.0210271i
$221$	0.819809	−	0.925516i	0.0551464	−	0.0622570i
$222$	−7.18861	−	2.25077i	−0.482468	−	0.151062i
$223$	4.67710	+	8.10097i	0.313201	+	0.542481i	0.979054	−	0.203603i	$-0.0652652\pi$
$223$	4.67710	+	8.10097i	0.313201	+	0.542481i	−0.665852	+	0.746084i	$0.731932\pi$
$224$	−1.30974	+	2.29882i	−0.0875108	+	0.153596i
$225$	−9.83224	−	6.82618i	−0.655482	−	0.455079i
$226$	−4.26195	+	2.46064i	−0.283501	+	0.163679i
$227$	10.2114	−	5.89553i	0.677751	−	0.391300i	−0.121256	−	0.992621i	$-0.538692\pi$
$227$	10.2114	−	5.89553i	0.677751	−	0.391300i	0.799007	+	0.601321i	$0.205359\pi$
$228$	2.24515	−	7.17067i	0.148689	−	0.474889i
$229$	5.47329	+	9.48001i	0.361685	+	0.626457i	0.988238	−	0.152922i	$-0.0488683\pi$
$229$	5.47329	+	9.48001i	0.361685	+	0.626457i	−0.626553	+	0.779379i	$0.715535\pi$
$230$	1.41826	−	2.45650i	0.0935172	−	0.161977i
$231$	0.834247	−	2.71893i	0.0548894	−	0.178892i
$232$	−8.23191	+	4.75270i	−0.540451	+	0.312030i
$233$	5.40464	−	3.12037i	0.354070	−	0.204422i	−0.312406	−	0.949949i	$-0.601135\pi$
$233$	5.40464	−	3.12037i	0.354070	−	0.204422i	0.666476	+	0.745526i	$0.267802\pi$
$234$	−3.03678	+	10.3816i	−0.198520	+	0.678668i
$235$	0.0256723	−	0.0444658i	0.00167468	−	0.00290063i
$236$	2.67570	+	1.54481i	0.174173	+	0.100559i
$237$	−0.474128	+	1.51429i	−0.0307979	+	0.0983638i
$238$	−0.458121	−	0.783105i	−0.0296956	−	0.0507612i
$239$	30.4624			1.97045			0.985225	−	0.171267i	$-0.0547862\pi$
$239$	30.4624			1.97045			0.985225	+	0.171267i	$0.0547862\pi$
$240$	1.28112	−	1.17865i	0.0826958	−	0.0760814i
$241$	2.84746	+	4.93194i	0.183421	+	0.317694i	0.943043	−	0.332670i	$-0.107950\pi$
$241$	2.84746	+	4.93194i	0.183421	+	0.317694i	−0.759622	+	0.650364i	$0.774616\pi$
$242$	−5.30742	+	9.19271i	−0.341174	+	0.590930i
$243$	−8.50667	−	13.0628i	−0.545703	−	0.837979i
$244$	−5.78697	+	3.34111i	−0.370473	+	0.213892i
$245$	−0.0805261	−	7.03500i	−0.00514462	−	0.449450i
$246$	11.0009	−	10.1210i	0.701393	−	0.645292i
$247$	4.95430	+	14.8362i	0.315235	+	0.944003i
$248$	−1.25167	+	2.16796i	−0.0794813	+	0.137666i
$249$	16.8588	−	15.5104i	1.06839	−	0.982931i
$250$	−7.82487	−	4.51769i	−0.494888	−	0.285724i
$251$	−12.0289	+	20.8346i	−0.759255	+	1.31507i	0.183976	+	0.982931i	$0.441103\pi$
$251$	−12.0289	+	20.8346i	−0.759255	+	1.31507i	−0.943231	+	0.332138i	$0.892230\pi$
$252$	6.54577	+	4.48920i	0.412345	+	0.282793i
$253$	1.51687	+	0.875762i	0.0953645	+	0.0550587i
$254$	−5.57708			−0.349937
$255$	0.130369	+	0.582543i	0.00816403	+	0.0364803i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−14.7678	+	25.5785i	−0.921189	+	1.59555i	−0.123610	+	0.992331i	$0.539447\pi$
$257$	−14.7678	+	25.5785i	−0.921189	+	1.59555i	−0.797579	+	0.603214i	$0.793886\pi$
$258$	−0.623951	+	1.99280i	−0.0388455	+	0.124066i
$259$	−0.0658509	−	11.5063i	−0.00409178	−	0.714964i
$260$	−0.724585	+	3.55064i	−0.0449369	+	0.220201i
$261$	12.1547	+	25.7960i	0.752357	+	1.59673i
$262$	18.2559			1.12785
$263$		−	22.0320i		−	1.35855i	−0.733884	−	0.679274i	$-0.762295\pi$
$263$		−	22.0320i		−	1.35855i	0.733884	−	0.679274i	$-0.237705\pi$
$264$	0.727805	+	0.791078i	0.0447933	+	0.0486875i
$265$	4.81839			0.295991
$266$	11.4775	−	0.0656867i	0.703733	−	0.00402751i
$267$	−1.36181	−	6.08512i	−0.0833412	−	0.372403i
$268$	4.75367	−	2.74453i	0.290377	−	0.167649i
$269$	−3.20777	−	5.55601i	−0.195581	−	0.338756i	0.751510	−	0.659722i	$-0.229326\pi$
$269$	−3.20777	−	5.55601i	−0.195581	−	0.338756i	−0.947091	+	0.320966i	$0.895993\pi$
$270$	−3.20403	−	4.12413i	−0.194991	−	0.250986i
$271$	10.3183	−	17.8719i	0.626794	−	1.08564i	−0.361397	−	0.932412i	$-0.617700\pi$
$271$	10.3183	−	17.8719i	0.626794	−	1.08564i	0.988191	−	0.153227i	$-0.0489664\pi$
$272$	0.342914			0.0207922
$273$	−16.5177	+	0.406098i	−0.999698	+	0.0245782i
$274$	8.10612			0.489709
$275$	1.23809	−	2.14443i	0.0746594	−	0.129314i
$276$	−3.59737	+	3.30964i	−0.216536	+	0.199217i
$277$	−6.03772	−	10.4576i	−0.362771	−	0.628338i	0.625644	−	0.780108i	$-0.284836\pi$
$277$	−6.03772	−	10.4576i	−0.362771	−	0.628338i	−0.988416	+	0.151770i	$0.951503\pi$
$278$	16.5296	−	9.54339i	0.991382	−	0.572375i
$279$	6.16904	+	4.28295i	0.369330	+	0.256413i
$280$	2.31047	+	1.31638i	0.138077	+	0.0786685i
$281$	30.4581			1.81698			0.908488	−	0.417911i	$-0.137238\pi$
$281$	30.4581			1.81698			0.908488	+	0.417911i	$0.137238\pi$
$282$	−0.0651171	+	0.0599088i	−0.00387767	+	0.00356751i
$283$			17.5980i			1.04609i	0.852304	+	0.523047i	$0.175205\pi$
$283$			17.5980i			1.04609i	−0.852304	+	0.523047i	$0.824795\pi$
$284$	−1.24396			−0.0738157
$285$	−7.20700	−	2.25653i	−0.426906	−	0.133665i
$286$	−2.19249	−	0.447425i	−0.129644	−	0.0264568i
$287$	19.8399	+	11.3037i	1.17111	+	0.667235i
$288$	−2.71383	+	1.27872i	−0.159914	+	0.0753491i
$289$	8.44121	−	14.6206i	0.496541	−	0.860035i
$290$	4.77677	+	8.27361i	0.280502	+	0.485843i
$291$	17.2539	−	3.86131i	1.01144	−	0.226354i
$292$	−8.92307			−0.522183
$293$	14.3730	+	8.29824i	0.839678	+	0.484788i	0.857155	−	0.515059i	$-0.172230\pi$
$293$	14.3730	+	8.29824i	0.839678	+	0.484788i	−0.0174766	+	0.999847i	$0.505563\pi$
$294$	−3.49007	+	11.6112i	−0.203545	+	0.677178i
$295$	1.55264	−	2.68925i	0.0903982	−	0.156574i
$296$	3.76637	+	2.17451i	0.218916	+	0.126391i
$297$	2.54661	−	1.97846i	0.147769	−	0.114802i
$298$	2.34608	−	4.06353i	0.135905	−	0.235394i
$299$	2.03463	−	9.97018i	0.117666	−	0.576590i
$300$	4.67892	+	5.08569i	0.270137	+	0.293623i
$301$	−3.18972	+	0.0182550i	−0.183853	+	0.00105220i
$302$	−6.80898	+	3.93117i	−0.391813	+	0.226213i
$303$	−11.6244	−	12.6350i	−0.667806	−	0.725864i
$304$	−2.16909	+	3.75697i	−0.124406	+	0.215477i
$305$	3.35803	+	5.81628i	0.192280	+	0.333039i
$306$	0.0855623	−	1.02518i	0.00489127	−	0.0586055i
$307$	26.3002			1.50103			0.750514	−	0.660854i	$-0.229806\pi$
$307$	26.3002			1.50103			0.750514	+	0.660854i	$0.229806\pi$
$308$	−0.812851	+	1.42669i	−0.0463165	+	0.0812934i
$309$	17.0489	+	5.33806i	0.969879	+	0.303671i
$310$	2.17894	+	1.25801i	0.123756	+	0.0714504i
$311$	6.89170	−	11.9368i	0.390793	−	0.676873i	−0.601762	−	0.798676i	$-0.705534\pi$
$311$	6.89170	−	11.9368i	0.390793	−	0.676873i	0.992554	+	0.121803i	$0.0388676\pi$
$312$	3.01996	−	5.46624i	0.170972	−	0.309465i
$313$	7.93246	−	4.57981i	0.448369	−	0.258866i	−0.258772	−	0.965938i	$-0.583318\pi$
$313$	7.93246	−	4.57981i	0.448369	−	0.258866i	0.707141	+	0.707072i	$0.249985\pi$
$314$	−19.8931	+	11.4853i	−1.12263	+	0.648153i
$315$	4.51194	−	6.57893i	0.254219	−	0.370681i
$316$	0.458065	−	0.793391i	0.0257681	−	0.0446317i
$317$	−2.37076	−	4.10628i	−0.133155	−	0.230631i	0.791736	−	0.610863i	$-0.209178\pi$
$317$	−2.37076	−	4.10628i	−0.133155	−	0.230631i	−0.924891	+	0.380232i	$0.875844\pi$
$318$	−7.92429	−	2.48111i	−0.444372	−	0.139134i
$319$	−5.10888	+	2.94961i	−0.286042	+	0.165147i
$320$	−0.870413	+	0.502533i	−0.0486575	+	0.0280924i
$321$	−5.56648	−	24.8733i	−0.310691	−	1.38829i
$322$	−6.48778	−	3.69638i	−0.361550	−	0.205991i
$323$	−0.743810	−	1.28832i	−0.0413867	−	0.0716838i
$324$	3.14571	+	8.43235i	0.174762	+	0.468464i
$325$	−14.0951	−	2.87641i	−0.781854	−	0.159554i
$326$	−7.66125	−	4.42322i	−0.424317	−	0.244980i
$327$	6.79416	+	30.3591i	0.375718	+	1.67886i
$328$	−7.47421	+	4.31523i	−0.412694	+	0.238269i
$329$	−0.117437	−	0.0669092i	−0.00647453	−	0.00368883i
$330$	0.795086	−	0.731492i	0.0437680	−	0.0402673i
$331$			24.4210i			1.34230i	0.741323	+	0.671149i	$0.234199\pi$
$331$			24.4210i			1.34230i	−0.741323	+	0.671149i	$0.765801\pi$
$332$	−11.4542	+	6.61307i	−0.628630	+	0.362940i
$333$	7.44070	−	10.7174i	0.407748	−	0.587309i
$334$			4.57129i			0.250130i
$335$	−2.75844	−	4.77776i	−0.150710	−	0.261037i
$336$	−3.12194	−	3.35462i	−0.170316	−	0.183010i
$337$	1.88882			0.102891			0.0514453	−	0.998676i	$-0.483617\pi$
$337$	1.88882			0.102891			0.0514453	+	0.998676i	$0.483617\pi$
$338$	1.56895	+	12.9050i	0.0853396	+	0.701938i
$339$	−1.86154	−	8.31815i	−0.101105	−	0.451780i
$340$		−	0.344651i		−	0.0186913i
$341$	−0.776812	+	1.34548i	−0.0420667	+	0.0728617i
$342$	10.6906	+	7.42214i	0.578083	+	0.401343i
$343$	−18.5175	+	0.317958i	−0.999853	+	0.0171681i
$344$	0.602811	−	1.04410i	0.0325014	−	0.0562940i
$345$	3.32641	+	3.61560i	0.179088	+	0.194657i
$346$	−6.56172	+	11.3652i	−0.352760	+	0.610999i
$347$	−30.0878	+	17.3712i	−1.61520	+	0.932535i	−0.627060	+	0.778971i	$0.715742\pi$
$347$	−30.0878	+	17.3712i	−1.61520	+	0.932535i	−0.988139	+	0.153564i	$0.950925\pi$
$348$	−3.59555	−	16.0664i	−0.192742	−	0.861250i
$349$	−4.20668	−	7.28618i	−0.225178	−	0.390021i	0.731195	−	0.682169i	$-0.238963\pi$
$349$	−4.20668	−	7.28618i	−0.225178	−	0.390021i	−0.956373	+	0.292148i	$0.905630\pi$
$350$	−5.22566	+	9.17193i	−0.279323	+	0.490260i
$351$	−15.5884	−	10.3924i	−0.832047	−	0.554706i
$352$	−0.310310	−	0.537472i	−0.0165396	−	0.0286474i
$353$		−	19.8207i		−	1.05495i	−0.849571	−	0.527474i	$-0.823139\pi$
$353$		−	19.8207i		−	1.05495i	0.849571	−	0.527474i	$-0.176861\pi$
$354$	−3.93822	+	3.62323i	−0.209314	+	0.192572i
$355$			1.25027i			0.0663572i
$356$			3.60015i			0.190807i
$357$	1.53151	−	0.351956i	0.0810559	−	0.0186275i
$358$	16.9504	+	9.78634i	0.895858	+	0.517224i
$359$	−0.111157	−	0.192530i	−0.00586667	−	0.0101614i	0.863077	−	0.505072i	$-0.168534\pi$
$359$	−0.111157	−	0.192530i	−0.00586667	−	0.0101614i	−0.868944	+	0.494911i	$0.835201\pi$
$360$	1.28519	+	2.72758i	0.0677357	+	0.143756i
$361$	−0.180241			−0.00948637
$362$	−19.4258	−	11.2155i	−1.02100	−	0.589474i
$363$	−12.4481	−	13.5303i	−0.653355	−	0.710157i
$364$	9.35752	+	1.85389i	0.490467	+	0.0971701i
$365$			8.96828i			0.469421i
$366$	−2.52764	−	11.2946i	−0.132122	−	0.590376i
$367$		−	13.4010i		−	0.699525i	−0.936838	−	0.349763i	$-0.886262\pi$
$367$		−	13.4010i		−	0.699525i	0.936838	−	0.349763i	$-0.113738\pi$
$368$	2.44412	−	1.41111i	0.127408	−	0.0735592i
$369$	11.0359	+	23.4216i	0.574507	+	1.21928i
$370$	2.18553	−	3.78545i	0.113620	−	0.196796i
$371$	−0.0725901	−	12.6838i	−0.00376869	−	0.658510i
$372$	−2.93569	−	3.19091i	−0.152208	−	0.165441i
$373$	−7.95557			−0.411924			−0.205962	−	0.978560i	$-0.566032\pi$
$373$	−7.95557			−0.411924			−0.205962	+	0.978560i	$0.566032\pi$
$374$	0.212819			0.0110046
$375$	11.5170	−	10.5959i	0.594738	−	0.547168i
$376$	0.0442417	−	0.0255429i	0.00228159	−	0.00131728i
$377$	25.6548	+	22.7247i	1.32129	+	1.17038i
$378$	−10.8080	+	8.49634i	−0.555902	+	0.437005i
$379$	−4.29409	+	2.47919i	−0.220572	+	0.127348i	−0.606215	−	0.795301i	$-0.707313\pi$
$379$	−4.29409	+	2.47919i	−0.220572	+	0.127348i	0.385643	+	0.922648i	$0.373980\pi$
$380$	3.77600	+	2.18008i	0.193705	+	0.111836i
$381$	2.88633	−	9.21849i	0.147871	−	0.472278i
$382$	11.3808	+	6.57071i	0.582293	+	0.336187i
$383$			10.8652i			0.555187i	0.960699	+	0.277594i	$0.0895368\pi$
$383$			10.8652i			0.555187i	−0.960699	+	0.277594i	$0.910463\pi$
$384$	1.69024	−	0.378264i	0.0862548	−	0.0193032i
$385$	1.43392	+	0.816968i	0.0730793	+	0.0416366i
$386$	−10.9286	−	6.30961i	−0.556250	−	0.321151i
$387$	−2.97103	−	2.06269i	−0.151026	−	0.104852i
$388$	−10.2080			−0.518231
$389$	−33.7632	−	19.4932i	−1.71186	−	0.988345i	−0.932048	−	0.362334i	$-0.881980\pi$
$389$	−33.7632	−	19.4932i	−1.71186	−	0.988345i	−0.779815	−	0.626011i	$-0.784687\pi$
$390$	−5.49394	−	3.03526i	−0.278196	−	0.153696i
$391$			0.967778i			0.0489427i
$392$	3.43038	−	6.10184i	0.173261	−	0.308190i
$393$	−9.44804	+	30.1756i	−0.476591	+	1.52216i
$394$	1.38737			0.0698949
$395$	−0.797410	−	0.460385i	−0.0401221	−	0.0231645i
$396$	−1.68426	+	0.793596i	−0.0846371	+	0.0398797i
$397$	−22.2075			−1.11456			−0.557282	−	0.830323i	$-0.688156\pi$
$397$	−22.2075			−1.11456			−0.557282	+	0.830323i	$0.688156\pi$
$398$		−	8.75865i		−	0.439032i
$399$	−5.83145	+	19.0055i	−0.291937	+	0.951465i
$400$	−1.99492	−	3.45530i	−0.0997461	−	0.172765i
$401$	−14.8257	+	25.6788i	−0.740358	+	1.28234i	0.211975	+	0.977275i	$0.432011\pi$
$401$	−14.8257	+	25.6788i	−0.740358	+	1.28234i	−0.952332	+	0.305062i	$0.901323\pi$
$402$	2.07632	+	9.27785i	0.103557	+	0.462737i
$403$	8.84367	+	1.80474i	0.440535	+	0.0899007i
$404$	4.95624	+	8.58446i	0.246582	+	0.427093i
$405$	8.47507	−	3.16165i	0.421129	−	0.157104i
$406$	21.7073	−	12.6989i	1.07731	−	0.630235i
$407$	2.33748	+	1.34954i	0.115865	+	0.0668944i
$408$	−0.177470	+	0.566810i	−0.00878605	+	0.0280613i
$409$	−0.530471	−	0.918802i	−0.0262301	−	0.0454318i	0.852612	−	0.522544i	$-0.175017\pi$
$409$	−0.530471	−	0.918802i	−0.0262301	−	0.0454318i	−0.878842	+	0.477112i	$0.841684\pi$
$410$	4.33710	+	7.51207i	0.214194	+	0.370995i
$411$	−4.19519	+	13.3988i	−0.206934	+	0.660914i
$412$	−8.93253	−	5.15720i	−0.440074	−	0.254077i
$413$	−7.10250	−	4.04661i	−0.349491	−	0.199121i
$414$	−3.60882	−	7.65904i	−0.177364	−	0.376421i
$415$	6.64657	+	11.5122i	0.326268	+	0.565112i
$416$	−2.39072	+	2.69898i	−0.117215	+	0.132328i
$417$	7.21985	+	32.2613i	0.353557	+	1.57984i
$418$	−1.34618	+	2.33165i	−0.0658437	+	0.114045i
$419$	2.10360	+	3.64355i	0.102768	+	0.177999i	0.912824	−	0.408353i	$-0.133897\pi$
$419$	2.10360	+	3.64355i	0.102768	+	0.177999i	−0.810056	+	0.586352i	$0.800563\pi$
$420$	−3.37162	+	3.13776i	−0.164518	+	0.153107i
$421$		−	12.1375i		−	0.591544i	−0.955259	−	0.295772i	$-0.904423\pi$
$421$		−	12.1375i		−	0.591544i	0.955259	−	0.295772i	$-0.0955768\pi$
$422$	25.7133			1.25171
$423$	−0.0653243	−	0.138638i	−0.00317618	−	0.00674083i
$424$	4.15182	+	2.39705i	0.201630	+	0.116411i
$425$	1.36817			0.0663661
$426$	0.643794	−	2.05618i	0.0311919	−	0.0996222i
$427$	15.2600	−	8.92722i	0.738485	−	0.432018i
$428$			14.7159i			0.711318i
$429$	1.87425	−	3.39246i	0.0904895	−	0.163789i
$430$	−1.04939	−	0.605865i	−0.0506060	−	0.0292174i
$431$	−6.74465			−0.324878			−0.162439	−	0.986719i	$-0.551936\pi$
$431$	−6.74465			−0.324878			−0.162439	+	0.986719i	$0.551936\pi$
$432$	−0.709119	−	5.14754i	−0.0341175	−	0.247661i
$433$	25.4298	+	14.6819i	1.22208	+	0.705566i	0.965360	−	0.260920i	$-0.0840260\pi$
$433$	25.4298	+	14.6819i	1.22208	+	0.705566i	0.256717	+	0.966487i	$0.417359\pi$
$434$	3.27873	−	5.75474i	0.157384	−	0.276236i
$435$	−16.1478	+	3.61376i	−0.774228	+	0.173267i
$436$		−	17.9614i		−	0.860195i
$437$	−10.6030	−	6.12164i	−0.507210	−	0.292838i
$438$	4.61800	−	14.7492i	0.220656	−	0.704742i
$439$	3.30932	+	1.91064i	0.157945	+	0.0911898i	0.576889	−	0.816822i	$-0.304266\pi$
$439$	3.30932	+	1.91064i	0.157945	+	0.0911898i	−0.418944	+	0.908012i	$0.637600\pi$
$440$	−0.540195	+	0.311882i	−0.0257528	+	0.0148684i
$441$	−17.3862	−	11.7780i	−0.827913	−	0.560857i
$442$	−0.391616	−	1.17273i	−0.0186273	−	0.0557813i
$443$	−20.4039	+	11.7802i	−0.969420	+	0.559695i	−0.899059	−	0.437827i	$-0.855748\pi$
$443$	−20.4039	+	11.7802i	−0.969420	+	0.559695i	−0.0703604	+	0.997522i	$0.522415\pi$
$444$	−5.54353	+	5.10013i	−0.263084	+	0.242042i
$445$	3.61839			0.171528
$446$	9.35419			0.442934
$447$	5.50253	+	5.98091i	0.260261	+	0.282887i
$448$	1.33597	+	2.28368i	0.0631185	+	0.107894i
$449$	−3.91435	+	6.77986i	−0.184730	+	0.319961i	−0.943485	−	0.331414i	$-0.892474\pi$
$449$	−3.91435	+	6.77986i	−0.184730	+	0.319961i	0.758756	+	0.651375i	$0.225808\pi$
$450$	−10.8278	+	5.10188i	−0.510426	+	0.240505i
$451$	−4.63864	+	2.67812i	−0.218425	+	0.126108i
$452$			4.92128i			0.231478i
$453$	−2.97404	−	13.2892i	−0.139733	−	0.624383i
$454$		−	11.7911i		−	0.553382i
$455$	1.86328	−	9.40492i	0.0873518	−	0.440909i
$456$	−5.08741	−	5.52970i	−0.238240	−	0.258952i
$457$	−27.5421	−	15.9014i	−1.28837	−	0.743838i	−0.310003	−	0.950736i	$-0.600330\pi$
$457$	−27.5421	−	15.9014i	−1.28837	−	0.743838i	−0.978363	+	0.206897i	$0.933663\pi$
$458$	10.9466			0.511500
$459$	1.65026	+	0.671992i	0.0770275	+	0.0313659i
$460$	−1.41826	−	2.45650i	−0.0661267	−	0.114535i
$461$	−26.9000	−	15.5307i	−1.25286	−	0.723337i	−0.281181	−	0.959655i	$-0.590726\pi$
$461$	−26.9000	−	15.5307i	−1.25286	−	0.723337i	−0.971676	+	0.236318i	$0.924059\pi$
$462$	−1.93754	−	2.08194i	−0.0901424	−	0.0968607i
$463$		−	27.0578i		−	1.25748i	−0.777614	−	0.628742i	$-0.783570\pi$
$463$		−	27.0578i		−	1.25748i	0.777614	−	0.628742i	$-0.216430\pi$
$464$			9.50539i			0.441277i
$465$	−3.20708	+	2.95056i	−0.148725	+	0.136829i
$466$		−	6.24074i		−	0.289097i
$467$	15.8112	+	27.3859i	0.731657	+	1.26727i	0.956175	+	0.292797i	$0.0945861\pi$
$467$	15.8112	+	27.3859i	0.731657	+	1.26727i	−0.224517	+	0.974470i	$0.572081\pi$
$468$	7.47235	+	7.82074i	0.345410	+	0.361514i
$469$	−12.5353	+	7.33322i	−0.578825	+	0.338616i
$470$	−0.0256723	−	0.0444658i	−0.00118418	−	0.00205105i
$471$	−8.68896	−	38.8259i	−0.400366	−	1.78900i
$472$	2.67570	−	1.54481i	0.123159	−	0.0711058i
$473$	0.374116	−	0.647988i	0.0172019	−	0.0297945i
$474$	1.07435	+	1.16775i	0.0493466	+	0.0536367i
$475$	−8.65432	+	14.9897i	−0.397087	+	0.687775i
$476$	−0.907250	+	0.00519224i	−0.0415837	+	0.000237986i
$477$	8.20218	−	11.8142i	0.375552	−	0.540935i
$478$	15.2312	−	26.3812i	0.696659	−	1.20665i
$479$			10.6459i			0.486424i	0.969973	+	0.243212i	$0.0782011\pi$
$479$			10.6459i			0.486424i	−0.969973	+	0.243212i	$0.921799\pi$
$480$	−0.380181	−	1.69880i	−0.0173528	−	0.0775394i
$481$	3.13535	−	15.3640i	0.142960	−	0.700537i
$482$	5.69491			0.259396
$483$	9.46748	−	8.81081i	0.430785	−	0.400906i
$484$	5.30742	+	9.19271i	0.241246	+	0.417851i
$485$			10.2597i			0.465868i
$486$	−15.5660	+	0.835596i	−0.706090	+	0.0379034i
$487$	−34.2885	+	19.7965i	−1.55376	+	0.897063i	−0.555928	+	0.831231i	$0.687637\pi$
$487$	−34.2885	+	19.7965i	−1.55376	+	0.897063i	−0.997831	+	0.0658322i	$0.979030\pi$
$488$			6.68221i			0.302490i
$489$	11.2762	−	10.3743i	0.509928	−	0.469142i
$490$	−6.13275	−	3.44776i	−0.277050	−	0.155754i
$491$	−27.5795	+	15.9230i	−1.24465	+	0.718597i	−0.970037	−	0.242959i	$-0.921882\pi$
$491$	−27.5795	+	15.9230i	−1.24465	+	0.718597i	−0.274610	+	0.961556i	$0.588549\pi$
$492$	−3.26460	−	14.5876i	−0.147179	−	0.657659i
$493$	−2.82283	−	1.62976i	−0.127134	−	0.0734009i
$494$	15.3256	+	3.12753i	0.689533	+	0.140714i
$495$	0.797616	+	1.69279i	0.0358502	+	0.0760852i
$496$	1.25167	+	2.16796i	0.0562018	+	0.0973443i
$497$	3.29117	−	0.0188355i	0.147629	−	0.000844889i
$498$	−5.00298	−	22.3554i	−0.224189	−	1.00177i
$499$	−7.30529	+	4.21771i	−0.327030	+	0.188811i	−0.654522	−	0.756043i	$-0.727130\pi$
$499$	−7.30529	+	4.21771i	−0.327030	+	0.188811i	0.327492	+	0.944854i	$0.393797\pi$
$500$	−7.82487	+	4.51769i	−0.349939	+	0.202037i
$501$	−7.55600	−	2.36580i	−0.337577	−	0.105696i
$502$	12.0289	+	20.8346i	0.536875	+	0.929894i
$503$	−4.21408	+	7.29900i	−0.187896	+	0.325446i	−0.944549	−	0.328371i	$-0.893500\pi$
$503$	−4.21408	+	7.29900i	−0.187896	+	0.325446i	0.756652	+	0.653818i	$0.226834\pi$
$504$	7.16065	−	3.42420i	0.318961	−	0.152526i
$505$	8.62794	−	4.98135i	0.383938	−	0.221667i
$506$	1.51687	−	0.875762i	0.0674329	−	0.0389324i
$507$	−22.1429	−	4.08541i	−0.983402	−	0.181439i
$508$	−2.78854	+	4.82989i	−0.123722	+	0.214292i
$509$	−14.1105	−	8.14669i	−0.625436	−	0.361096i	0.153546	−	0.988141i	$-0.450931\pi$
$509$	−14.1105	−	8.14669i	−0.625436	−	0.361096i	−0.778982	+	0.627046i	$0.784264\pi$
$510$	0.569682	+	0.178369i	0.0252259	+	0.00789830i
$511$	23.6078	−	0.135109i	1.04435	−	0.00597687i
$512$	−1.00000			−0.0441942
$513$	−17.8010	+	13.8296i	−0.785933	+	0.610592i
$514$	14.7678	+	25.5785i	0.651379	+	1.12822i
$515$	−5.18333	+	8.97779i	−0.228405	+	0.395609i
$516$	1.41384	+	1.53676i	0.0622409	+	0.0676520i
$517$	0.0274572	−	0.0158524i	0.00120757	−	0.000697189i
$518$	−9.99763	−	5.69610i	−0.439271	−	0.250272i
$519$	−15.3900	−	16.7279i	−0.675544	−	0.734275i
$520$	2.71265	+	2.40283i	0.118958	+	0.105371i
$521$	9.43681	−	16.3450i	0.413434	−	0.716089i	−0.581828	−	0.813312i	$-0.697662\pi$
$521$	9.43681	−	16.3450i	0.413434	−	0.716089i	0.995263	+	0.0972224i	$0.0309958\pi$
$522$	28.4174	+	2.37174i	1.24379	+	0.103808i
$523$	15.8502	+	9.15112i	0.693081	+	0.400151i	0.804765	−	0.593593i	$-0.202291\pi$
$523$	15.8502	+	9.15112i	0.693081	+	0.400151i	−0.111684	+	0.993744i	$0.535624\pi$
$524$	9.12794	−	15.8101i	0.398756	−	0.690665i
$525$	−12.4561	−	13.3844i	−0.543627	−	0.584144i
$526$	−19.0802	−	11.0160i	−0.831938	−	0.480319i
$527$	−0.858431			−0.0373939
$528$	1.04900	−	0.234758i	0.0456517	−	0.0102165i
$529$	−7.51753	−	13.0207i	−0.326849	−	0.566120i
$530$	2.40920	−	4.17285i	0.104649	−	0.181257i
$531$	−3.95076	−	8.38473i	−0.171448	−	0.363866i
$532$	5.68189	−	9.97269i	0.246341	−	0.432371i
$533$	23.2934	+	20.6330i	1.00895	+	0.893715i
$534$	−5.95077	−	1.86320i	−0.257515	−	0.0806285i
$535$	14.7904			0.639445
$536$		−	5.48907i		−	0.237092i
$537$	−24.9485	+	22.9530i	−1.07661	+	0.990496i
$538$	−6.41553			−0.276593
$539$	2.12896	−	3.78692i	0.0917009	−	0.163114i
$540$	−5.17362	+	0.712712i	−0.222637	+	0.0306702i
$541$	−1.05318	+	0.608052i	−0.0452796	+	0.0261422i	−0.522469	−	0.852658i	$-0.674989\pi$
$541$	−1.05318	+	0.608052i	−0.0452796	+	0.0261422i	0.477189	+	0.878801i	$0.341656\pi$
$542$	−10.3183	−	17.8719i	−0.443210	−	0.767662i
$543$	28.5919	−	26.3050i	1.22700	−	1.12886i
$544$	0.171457	−	0.296972i	0.00735115	−	0.0127326i
$545$	−18.0524			−0.773280
$546$	−7.90717	+	14.5078i	−0.338396	+	0.620877i
$547$	−11.3034			−0.483301			−0.241650	−	0.970363i	$-0.577689\pi$
$547$	−11.3034			−0.483301			−0.241650	+	0.970363i	$0.577689\pi$
$548$	4.05306	−	7.02011i	0.173138	−	0.299884i
$549$	19.9772	+	1.66732i	0.852605	+	0.0711593i
$550$	−1.23809	−	2.14443i	−0.0527922	−	0.0914388i
$551$	35.7115	−	20.6180i	1.52136	−	0.878357i
$552$	1.06755	+	4.77024i	0.0454378	+	0.203035i
$553$	−1.19989	+	2.10602i	−0.0510246	+	0.0895570i
$554$	−12.0754			−0.513036
$555$	5.12597	+	5.57161i	0.217585	+	0.236502i
$556$		−	19.0868i		−	0.809460i
$557$	−19.5374			−0.827825			−0.413912	−	0.910317i	$-0.635838\pi$
$557$	−19.5374			−0.827825			−0.413912	+	0.910317i	$0.635838\pi$
$558$	6.79366	−	3.20107i	0.287599	−	0.135512i
$559$	−4.25915	−	0.869172i	−0.180143	−	0.0367621i
$560$	2.29525	−	1.34273i	0.0969920	−	0.0567409i
$561$	−0.110141	+	0.351773i	−0.00465016	+	0.0148519i
$562$	15.2290	−	26.3775i	0.642398	−	1.11267i
$563$	−15.5687	−	26.9657i	−0.656141	−	1.13647i	−0.981606	−	0.190916i	$-0.938854\pi$
$563$	−15.5687	−	26.9657i	−0.656141	−	1.13647i	0.325466	−	0.945554i	$-0.394479\pi$
$564$	0.0193240	+	0.0863474i	0.000813685	+	0.00363588i
$565$	4.94621			0.208089
$566$	15.2403	+	8.79901i	0.640599	+	0.369850i
$567$	−8.45032	−	22.2619i	−0.354880	−	0.934912i
$568$	−0.621982	+	1.07730i	−0.0260978	+	0.0452027i
$569$	−1.67856	−	0.969116i	−0.0703688	−	0.0406275i	0.464403	−	0.885624i	$-0.346269\pi$
$569$	−1.67856	−	0.969116i	−0.0703688	−	0.0406275i	−0.534772	+	0.844997i	$0.679602\pi$
$570$	−5.55771	+	5.11318i	−0.232787	+	0.214168i
$571$	5.29680	−	9.17432i	0.221664	−	0.383933i	−0.733649	−	0.679528i	$-0.762185\pi$
$571$	5.29680	−	9.17432i	0.221664	−	0.383933i	0.955313	+	0.295595i	$0.0955178\pi$
$572$	−1.48372	+	1.67504i	−0.0620376	+	0.0700368i
$573$	−16.7508	+	15.4110i	−0.699776	+	0.643805i
$574$	19.7092	−	11.5300i	0.822647	−	0.481254i
$575$	9.75164	−	5.63011i	0.406671	−	0.234792i
$576$	−0.249516	+	2.98961i	−0.0103965	+	0.124567i
$577$	8.46005	−	14.6532i	0.352197	−	0.610022i	−0.634437	−	0.772974i	$-0.718768\pi$
$577$	8.46005	−	14.6532i	0.352197	−	0.610022i	0.986634	+	0.162952i	$0.0521015\pi$
$578$	−8.44121	−	14.6206i	−0.351108	−	0.608137i
$579$	16.0852	−	14.7987i	0.668479	−	0.615011i
$580$	9.55354			0.396689
$581$	30.2043	−	17.6697i	1.25308	−	0.733062i
$582$	5.28297	−	16.8730i	0.218986	−	0.699408i
$583$	2.57670	+	1.48766i	0.106716	+	0.0616124i
$584$	−4.46154	+	7.72761i	−0.184620	+	0.319771i
$585$	7.86036	−	7.51021i	0.324986	−	0.310509i
$586$	14.3730	−	8.29824i	0.593742	−	0.342797i
$587$	−17.0112	+	9.82143i	−0.702128	+	0.405374i	−0.808139	−	0.588991i	$-0.799525\pi$
$587$	−17.0112	+	9.82143i	−0.702128	+	0.405374i	0.106012	+	0.994365i	$0.466192\pi$
$588$	8.31054	+	8.82808i	0.342721	+	0.364064i
$589$	5.42997	−	9.40499i	0.223738	−	0.387526i
$590$	−1.55264	−	2.68925i	−0.0639212	−	0.110715i
$591$	−0.718014	+	2.29322i	−0.0295351	+	0.0943306i
$592$	3.76637	−	2.17451i	0.154797	−	0.0893719i
$593$	8.82193	−	5.09334i	0.362273	−	0.209158i	−0.307804	−	0.951450i	$-0.599594\pi$
$593$	8.82193	−	5.09334i	0.362273	−	0.209158i	0.670077	+	0.742291i	$0.266261\pi$
$594$	−0.440093	−	3.19466i	−0.0180572	−	0.131079i
$595$	0.00521855	+	0.911846i	0.000213940	+	0.0373820i
$596$	−2.34608	−	4.06353i	−0.0960992	−	0.166449i
$597$	14.4774	+	4.53290i	0.592520	+	0.185519i
$598$	−7.61711	−	6.74713i	−0.311487	−	0.275911i
$599$	1.11601	+	0.644326i	0.0455988	+	0.0263265i	0.522626	−	0.852562i	$-0.324952\pi$
$599$	1.11601	+	0.644326i	0.0455988	+	0.0263265i	−0.477027	+	0.878888i	$0.658286\pi$
$600$	6.74380	−	1.50921i	0.275314	−	0.0616134i
$601$	−11.6473	+	6.72456i	−0.475103	+	0.274301i	−0.718373	−	0.695658i	$-0.755113\pi$
$601$	−11.6473	+	6.72456i	−0.475103	+	0.274301i	0.243271	+	0.969958i	$0.421780\pi$
$602$	−1.57905	+	2.77151i	−0.0643574	+	0.112958i
$603$	−16.4102	−	1.36961i	−0.668273	−	0.0557748i
$604$			7.86233i			0.319914i
$605$	9.23928	−	5.33430i	0.375630	−	0.216870i
$606$	−16.7545	+	3.74954i	−0.680604	+	0.152314i
$607$		−	31.0276i		−	1.25937i	−0.776851	−	0.629685i	$-0.783184\pi$
$607$		−	31.0276i		−	1.25937i	0.776851	−	0.629685i	$-0.216816\pi$
$608$	2.16909	+	3.75697i	0.0879681	+	0.152365i
$609$	9.75605	+	42.4526i	0.395335	+	1.72027i
$610$	6.71606			0.271926
$611$	−0.137880	−	0.122132i	−0.00557801	−	0.00494092i
$612$	−0.845048	−	0.586688i	−0.0341590	−	0.0237154i
$613$			19.5668i			0.790295i	0.918618	+	0.395148i	$0.129307\pi$
$613$			19.5668i			0.790295i	−0.918618	+	0.395148i	$0.870693\pi$
$614$	13.1501	−	22.7766i	0.530694	−	0.919189i
$615$	−14.6615	+	3.28114i	−0.591208	+	0.132308i
$616$	0.829127	+	1.41730i	0.0334065	+	0.0571045i
$617$	−22.9771	+	39.7974i	−0.925022	+	1.60218i	−0.133495	+	0.991049i	$0.542620\pi$
$617$	−22.9771	+	39.7974i	−0.925022	+	1.60218i	−0.791526	+	0.611135i	$0.790713\pi$
$618$	13.1474	−	12.0958i	0.528864	−	0.486563i
$619$	−8.61313	+	14.9184i	−0.346191	+	0.599620i	−0.985569	−	0.169272i	$-0.945858\pi$
$619$	−8.61313	+	14.9184i	−0.346191	+	0.599620i	0.639378	+	0.768892i	$0.279192\pi$
$620$	2.17894	−	1.25801i	0.0875085	−	0.0505230i
$621$	14.5275	−	2.00129i	0.582968	−	0.0803091i
$622$	−6.89170	−	11.9368i	−0.276332	−	0.478621i
$623$	−0.0545118	−	9.52494i	−0.00218397	−	0.381609i
$624$	−3.22393	−	5.34849i	−0.129060	−	0.214111i
$625$	−5.43403	−	9.41201i	−0.217361	−	0.376480i
$626$		−	9.15961i		−	0.366092i
$627$	−3.15734	−	3.43184i	−0.126092	−	0.137054i
$628$			22.9706i			0.916627i
$629$			1.49134i			0.0594636i
$630$	−3.44155	−	7.19692i	−0.137115	−	0.286732i
$631$	−25.7893	−	14.8894i	−1.02665	−	0.592739i	−0.110630	−	0.993862i	$-0.535287\pi$
$631$	−25.7893	−	14.8894i	−1.02665	−	0.592739i	−0.916024	+	0.401123i	$0.868620\pi$
$632$	−0.458065	−	0.793391i	−0.0182208	−	0.0315594i
$633$	−13.3075	+	42.5022i	−0.528927	+	1.68931i
$634$	−4.74152			−0.188310
$635$	4.85436	+	2.80267i	0.192640	+	0.111220i
$636$	−6.11085	+	5.62208i	−0.242311	+	0.222930i
$637$	−24.7853	−	4.76316i	−0.982030	−	0.188723i
$638$			5.89923i			0.233553i
$639$	3.06552	+	2.12829i	0.121270	+	0.0841937i
$640$			1.00507i			0.0397287i
$641$	35.8025	−	20.6706i	1.41411	−	0.816439i	0.418341	−	0.908290i	$-0.362612\pi$
$641$	35.8025	−	20.6706i	1.41411	−	0.816439i	0.995773	+	0.0918509i	$0.0292783\pi$
$642$	−24.3242	−	7.61596i	−0.959999	−	0.300578i
$643$	−16.2778	+	28.1940i	−0.641934	+	1.11186i	0.343067	+	0.939311i	$0.388534\pi$
$643$	−16.2778	+	28.1940i	−0.641934	+	1.11186i	−0.985001	+	0.172551i	$0.944799\pi$
$644$	−6.44505	+	3.77039i	−0.253971	+	0.148574i
$645$	1.54454	−	1.42100i	0.0608163	−	0.0559520i
$646$	−1.48762			−0.0585296
$647$	−4.27122			−0.167919			−0.0839595	−	0.996469i	$-0.526757\pi$
$647$	−4.27122			−0.167919			−0.0839595	+	0.996469i	$0.526757\pi$
$648$	8.87548	+	1.49191i	0.348662	+	0.0586076i
$649$	1.66059	−	0.958741i	0.0651838	−	0.0376339i
$650$	−9.53858	+	10.7685i	−0.374134	+	0.422375i
$651$	7.81530	+	8.39778i	0.306306	+	0.329135i
$652$	−7.66125	+	4.42322i	−0.300038	+	0.173227i
$653$	11.2332	+	6.48551i	0.439590	+	0.253798i	0.703424	−	0.710771i	$-0.251654\pi$
$653$	11.2332	+	6.48551i	0.439590	+	0.253798i	−0.263834	+	0.964568i	$0.584987\pi$
$654$	29.6888	+	9.29564i	1.16093	+	0.363488i
$655$	−15.8901	−	9.17418i	−0.620879	−	0.358465i
$656$			8.63047i			0.336963i
$657$	21.9893	+	15.2664i	0.857883	+	0.595599i
$658$	−0.116664	+	0.0682490i	−0.00454803	+	0.00266062i
$659$	−31.7740	−	18.3447i	−1.23774	−	0.714609i	−0.269107	−	0.963110i	$-0.586729\pi$
$659$	−31.7740	−	18.3447i	−1.23774	−	0.714609i	−0.968631	+	0.248502i	$0.920062\pi$
$660$	−0.235947	−	1.05431i	−0.00918424	−	0.0410390i
$661$	−7.17998			−0.279269			−0.139634	−	0.990203i	$-0.544593\pi$
$661$	−7.17998			−0.279269			−0.139634	+	0.990203i	$0.544593\pi$
$662$	21.1492	+	12.2105i	0.821986	+	0.474574i
$663$	2.14111	−	0.0403812i	0.0831540	−	0.00156828i
$664$			13.2261i			0.513274i
$665$	−10.0232	−	5.71067i	−0.388683	−	0.221450i
$666$	−5.56117	−	11.8025i	−0.215491	−	0.457339i
$667$	−26.8263			−1.03872
$668$	3.95886	+	2.28565i	0.153173	+	0.0884343i
$669$	−4.84111	+	15.4618i	−0.187168	+	0.597786i
$670$	−5.51688			−0.213136
$671$			4.14711i			0.160097i
$672$	−4.46616	+	1.02637i	−0.172286	+	0.0395931i
$673$	−2.07797	−	3.59915i	−0.0800999	−	0.138737i	0.823193	−	0.567762i	$-0.192191\pi$
$673$	−2.07797	−	3.59915i	−0.0800999	−	0.138737i	−0.903293	+	0.429025i	$0.858857\pi$
$674$	0.944409	−	1.63577i	0.0363773	−	0.0630073i
$675$	−2.82927	−	20.5379i	−0.108899	−	0.790503i
$676$	11.9605	+	5.09374i	0.460020	+	0.195913i
$677$	−5.94798	−	10.3022i	−0.228599	−	0.395946i	0.728794	−	0.684733i	$-0.240081\pi$
$677$	−5.94798	−	10.3022i	−0.228599	−	0.395946i	−0.957393	+	0.288787i	$0.906748\pi$
$678$	−8.13450	−	2.54693i	−0.312404	−	0.0978143i
$679$	27.0073	−	0.154564i	1.03644	−	0.00593163i
$680$	−0.298476	−	0.172325i	−0.0114460	−	0.00660838i
$681$	19.4897	+	6.10227i	0.746848	+	0.233840i
$682$	0.776812	+	1.34548i	0.0297457	+	0.0515210i
$683$	−2.21590	−	3.83806i	−0.0847892	−	0.146859i	0.820512	−	0.571629i	$-0.193688\pi$
$683$	−2.21590	−	3.83806i	−0.0847892	−	0.146859i	−0.905301	+	0.424770i	$0.860355\pi$
$684$	11.7731	−	5.54729i	0.450155	−	0.212106i
$685$	−7.05567	−	4.07359i	−0.269583	−	0.155644i
$686$	−8.98340	+	16.1956i	−0.342988	+	0.618352i
$687$	−5.66523	+	18.0939i	−0.216142	+	0.690324i
$688$	−0.602811	−	1.04410i	−0.0229819	−	0.0398059i
$689$	3.45623	−	16.9363i	0.131672	−	0.645223i
$690$	4.79440	−	1.07295i	0.182520	−	0.0408466i
$691$	−16.8071	+	29.1108i	−0.639372	+	1.10743i	0.346198	+	0.938161i	$0.387472\pi$
$691$	−16.8071	+	29.1108i	−0.639372	+	1.10743i	−0.985571	+	0.169264i	$0.945861\pi$
$692$	6.56172	+	11.3652i	0.249439	+	0.432041i
$693$	4.44403	−	2.12512i	0.168815	−	0.0807268i
$694$			34.7424i			1.31880i
$695$	−19.1835			−0.727671
$696$	−15.7117	−	4.91937i	−0.595550	−	0.186468i
$697$	−2.56301	−	1.47975i	−0.0970808	−	0.0560496i
$698$	−8.41336			−0.318450
$699$	10.3155	+	3.22980i	0.390167	+	0.122162i
$700$	5.33030	+	9.11152i	0.201466	+	0.344383i
$701$			37.0012i			1.39751i	0.715359	+	0.698757i	$0.246263\pi$
$701$			37.0012i			1.39751i	−0.715359	+	0.698757i	$0.753737\pi$
$702$	−16.7943	+	8.30374i	−0.633859	+	0.313404i
$703$	−16.3392	−	9.43342i	−0.616243	−	0.355788i
$704$	−0.620619			−0.0233905
$705$	0.0867849	−	0.0194219i	0.00326851	−	0.000731469i
$706$	−17.1652	−	9.91033i	−0.646021	−	0.372980i
$707$	−13.2427	−	22.6369i	−0.498044	−	0.851349i
$708$	1.16870	+	5.22222i	0.0439223	+	0.196263i
$709$		−	44.1230i		−	1.65707i	−0.559934	−	0.828537i	$-0.689174\pi$
$709$		−	44.1230i		−	1.65707i	0.559934	−	0.828537i	$-0.310826\pi$
$710$	1.08276	+	0.625133i	0.0406354	+	0.0234608i
$711$	−2.48622	+	1.17147i	−0.0932406	+	0.0439335i
$712$	3.11782	+	1.80007i	0.116845	+	0.0674606i
$713$	−6.11846	+	3.53250i	−0.229138	+	0.132293i
$714$	0.460950	−	1.50230i	0.0172506	−	0.0562222i
$715$	1.68352	+	1.49124i	0.0629602	+	0.0557693i
$716$	16.9504	−	9.78634i	0.633467	−	0.365733i
$717$	35.7235	+	38.8292i	1.33412	+	1.45010i
$718$	−0.222315			−0.00829672
$719$	19.4471			0.725255			0.362627	−	0.931934i	$-0.381880\pi$
$719$	19.4471			0.725255			0.362627	+	0.931934i	$0.381880\pi$
$720$	3.00475	+	0.250780i	0.111980	+	0.00934601i
$721$	23.7110	+	13.5092i	0.883042	+	0.503109i
$722$	−0.0901205	+	0.156093i	−0.00335394	+	0.00580919i
$723$	−2.94731	+	9.41326i	−0.109612	+	0.350083i
$724$	−19.4258	+	11.2155i	−0.721955	+	0.416821i
$725$			37.9250i			1.40850i
$726$	−17.9416	+	4.01521i	−0.665876	+	0.149018i
$727$			17.7877i			0.659708i	0.944032	+	0.329854i	$0.107000\pi$
$727$			17.7877i			0.659708i	−0.944032	+	0.329854i	$0.893000\pi$
$728$	6.28427	−	7.17690i	0.232911	−	0.265994i
$729$	6.67478	−	26.1619i	0.247214	−	0.968961i
$730$	7.76676	+	4.48414i	0.287461	+	0.165965i
$731$	0.413424			0.0152910
$732$	−11.0452	−	3.45827i	−0.408242	−	0.127821i
$733$	20.9177	+	36.2305i	0.772613	+	1.33820i	0.936126	+	0.351664i	$0.114384\pi$
$733$	20.9177	+	36.2305i	0.772613	+	1.33820i	−0.163513	+	0.986541i	$0.552283\pi$
$734$	−11.6056	−	6.70049i	−0.428370	−	0.247319i
$735$	8.87280	−	8.35264i	0.327278	−	0.308092i
$736$		−	2.82222i		−	0.104028i
$737$		−	3.40662i		−	0.125485i
$738$	25.8017	+	2.15344i	0.949774	+	0.0792691i
$739$		−	18.2237i		−	0.670371i	−0.942152	−	0.335185i	$-0.891201\pi$
$739$		−	18.2237i		−	0.670371i	0.942152	−	0.335185i	$-0.108799\pi$
$740$	−2.18553	−	3.78545i	−0.0803416	−	0.139156i
$741$	−13.1011	+	23.7135i	−0.481282	+	0.871138i
$742$	−11.0208	−	6.27904i	−0.404586	−	0.230511i
$743$	−16.0336	−	27.7710i	−0.588216	−	1.01882i	−0.994466	−	0.105058i	$-0.966497\pi$
$743$	−16.0336	−	27.7710i	−0.588216	−	1.01882i	0.406250	−	0.913762i	$-0.366836\pi$
$744$	−4.23126	+	0.946926i	−0.155125	+	0.0347160i
$745$	−4.08412	+	2.35797i	−0.149631	+	0.0863892i
$746$	−3.97778	+	6.88972i	−0.145637	+	0.252251i
$747$	39.5410	+	3.30013i	1.44673	+	0.120745i
$748$	0.106409	−	0.184307i	0.00389071	−	0.00673891i
$749$	−0.222821	−	38.9338i	−0.00814169	−	1.42261i
$750$	−3.41776	−	15.2720i	−0.124799	−	0.557654i
$751$	−13.4845	+	23.3558i	−0.492055	+	0.852264i	−0.999958	−	0.00915004i	$-0.997087\pi$
$751$	−13.4845	+	23.3558i	−0.492055	+	0.852264i	0.507903	+	0.861414i	$0.330421\pi$
$752$		−	0.0510859i		−	0.00186291i
$753$	−40.6634	+	9.10018i	−1.48186	+	0.331629i
$754$	32.5076	−	10.8554i	1.18386	−	0.395330i
$755$	7.90216			0.287589
$756$	1.95406	+	13.6081i	0.0710686	+	0.494923i
$757$	−15.4821	−	26.8158i	−0.562706	−	0.974635i	−0.997259	−	0.0739889i	$-0.976427\pi$
$757$	−15.4821	−	26.8158i	−0.562706	−	0.974635i	0.434553	−	0.900646i	$-0.356906\pi$
$758$			4.95838i			0.180097i
$759$	0.662539	+	2.96050i	0.0240487	+	0.107459i
$760$	3.77600	−	2.18008i	0.136970	−	0.0790797i
$761$		−	2.42155i		−	0.0877812i	−0.999036	−	0.0438906i	$-0.986025\pi$
$761$		−	2.42155i		−	0.0877812i	0.999036	−	0.0438906i	$-0.0139753\pi$
$762$	−6.54028	−	7.10888i	−0.236930	−	0.257528i
$763$	0.271963	+	47.5206i	0.00984573	+	1.72036i
$764$	11.3808	−	6.57071i	0.411743	−	0.237720i
$765$	−0.589660	+	0.849329i	−0.0213192	+	0.0307076i
$766$	9.40956	+	5.43261i	0.339981	+	0.196288i
$767$	−8.33883	−	7.38642i	−0.301098	−	0.266708i
$768$	0.517534	−	1.65292i	0.0186749	−	0.0596448i
$769$	−4.75805	−	8.24119i	−0.171580	−	0.297185i	0.767393	−	0.641177i	$-0.221554\pi$
$769$	−4.75805	−	8.24119i	−0.171580	−	0.297185i	−0.938972	+	0.343993i	$0.888220\pi$
$770$	1.42448	−	0.833327i	0.0513345	−	0.0300310i
$771$	−49.9222	+	11.1722i	−1.79790	+	0.402359i
$772$	−10.9286	+	6.30961i	−0.393328	+	0.227088i
$773$	30.2147	−	17.4444i	1.08675	−	0.627433i	0.154037	−	0.988065i	$-0.450772\pi$
$773$	30.2147	−	17.4444i	1.08675	−	0.627433i	0.932708	+	0.360632i	$0.117439\pi$
$774$	−3.27186	+	1.54165i	−0.117604	+	0.0554134i
$775$	4.99398	+	8.64982i	0.179389	+	0.310711i
$776$	−5.10398	+	8.84035i	−0.183222	+	0.317350i
$777$	14.5893	−	13.5774i	0.523389	−	0.487087i
$778$	−33.7632	+	19.4932i	−1.21047	+	0.698865i
$779$	32.4244	−	18.7202i	1.16172	−	0.670722i
$780$	−5.37558	+	3.24026i	−0.192477	+	0.116020i
$781$	−0.386014	+	0.668596i	−0.0138127	+	0.0239243i
$782$	0.838121	+	0.483889i	0.0299711	+	0.0173038i
$783$	−18.6273	+	45.7443i	−0.665684	+	1.63477i
$784$	−3.56916	−	6.02172i	−0.127470	−	0.215061i
$785$	23.0870			0.824010
$786$	21.4088	+	23.2700i	0.763626	+	0.830015i
$787$	19.2073	+	33.2681i	0.684667	+	1.18588i	0.973541	+	0.228511i	$0.0733858\pi$
$787$	19.2073	+	33.2681i	0.684667	+	1.18588i	−0.288874	+	0.957367i	$0.593281\pi$
$788$	0.693687	−	1.20150i	0.0247116	−	0.0428017i
$789$	28.0832	−	25.8370i	0.999790	−	0.919823i
$790$	−0.797410	+	0.460385i	−0.0283706	+	0.0163798i
$791$	−0.0745158	−	13.0203i	−0.00264948	−	0.462947i
$792$	−0.154854	+	1.85541i	−0.00550250	+	0.0659290i
$793$	22.8526	−	7.63125i	0.811518	−	0.270994i
$794$	−11.1038	+	19.2323i	−0.394058	+	0.682528i
$795$	5.65056	+	6.14181i	0.200405	+	0.217828i
$796$	−7.58522	−	4.37933i	−0.268851	−	0.155221i
$797$	9.84749	−	17.0564i	0.348816	−	0.604167i	−0.637223	−	0.770679i	$-0.719917\pi$
$797$	9.84749	−	17.0564i	0.348816	−	0.604167i	0.986039	+	0.166512i	$0.0532505\pi$
$798$	13.5435	+	14.5529i	0.479436	+	0.515168i
$799$	0.0151711	+	0.00875902i	0.000536714	+	0.000309872i
$800$	−3.98984			−0.141062
$801$	6.15945	−	8.87190i	0.217634	−	0.313473i
$802$	14.8257	+	25.6788i	0.523512	+	0.906749i
$803$	−2.76892	+	4.79590i	−0.0977129	+	0.169244i
$804$	9.07302	+	2.84078i	0.319981	+	0.100187i
$805$	3.78950	+	6.47770i	0.133562	+	0.228309i
$806$	5.98479	−	6.75647i	0.210805	−	0.237987i
$807$	3.32026	−	10.6044i	0.116879	−	0.373292i
$808$	9.91247			0.348720
$809$		−	22.6813i		−	0.797432i	−0.917074	−	0.398716i	$-0.869456\pi$
$809$		−	22.6813i		−	0.797432i	0.917074	−	0.398716i	$-0.130544\pi$
$810$	1.49946	−	8.92045i	0.0526858	−	0.313433i
$811$	−17.6451			−0.619604			−0.309802	−	0.950801i	$-0.600263\pi$
$811$	−17.6451			−0.619604			−0.309802	+	0.950801i	$0.600263\pi$
$812$	−0.143926	−	25.1485i	−0.00505082	−	0.882539i
$813$	34.8809	−	7.80611i	1.22333	−	0.273772i
$814$	2.33748	−	1.34954i	0.0819286	−	0.0473015i
$815$	4.44563	+	7.70006i	0.155724	+	0.269721i
$816$	0.402137	+	0.437098i	0.0140776	+	0.0153015i
$817$	−2.61510	+	4.52948i	−0.0914907	+	0.158467i
$818$	−1.06094			−0.0370949
$819$	−19.8881	−	20.5782i	−0.694946	−	0.719062i
$820$	8.67419			0.302916
$821$	−3.13575	+	5.43128i	−0.109439	+	0.189553i	−0.915543	−	0.402220i	$-0.868239\pi$
$821$	−3.13575	+	5.43128i	−0.109439	+	0.189553i	0.806104	+	0.591773i	$0.201572\pi$
$822$	9.50611	+	10.3325i	0.331564	+	0.360389i
$823$	9.43662	+	16.3447i	0.328940	+	0.569741i	0.982302	−	0.187305i	$-0.0599753\pi$
$823$	9.43662	+	16.3447i	0.328940	+	0.569741i	−0.653362	+	0.757046i	$0.726642\pi$
$824$	−8.93253	+	5.15720i	−0.311180	+	0.179660i
$825$	4.18533	−	0.936648i	0.145714	−	0.0326099i
$826$	−7.05572	+	4.12764i	−0.245500	+	0.143619i
$827$	−37.5661			−1.30630			−0.653150	−	0.757229i	$-0.726553\pi$
$827$	−37.5661			−1.30630			−0.653150	+	0.757229i	$0.726553\pi$
$828$	−8.43733	−	0.704188i	−0.293217	−	0.0244722i
$829$			32.2784i			1.12107i	0.828129	+	0.560537i	$0.189405\pi$
$829$			32.2784i			1.12107i	−0.828129	+	0.560537i	$0.810595\pi$
$830$	13.2931			0.461412
$831$	6.24945	−	19.9598i	0.216791	−	0.692397i
$832$	1.14202	+	3.41991i	0.0395926	+	0.118564i
$833$	2.40024	−	0.0274743i	0.0831633	−	0.000951929i
$834$	31.5490	+	9.87806i	1.09245	+	0.342049i
$835$	2.29723	−	3.97891i	0.0794988	−	0.137696i
$836$	1.34618	+	2.33165i	0.0465585	+	0.0806417i
$837$	1.77517	+	12.8861i	0.0613589	+	0.445408i
$838$	4.20721			0.145336
$839$	18.1332	+	10.4692i	0.626028	+	0.361438i	0.779212	−	0.626760i	$-0.215619\pi$
$839$	18.1332	+	10.4692i	0.626028	+	0.361438i	−0.153184	+	0.988198i	$0.548953\pi$
$840$	1.03157	+	4.48878i	0.0355925	+	0.154878i
$841$	30.6762	−	53.1328i	1.05780	−	1.83216i
$842$	−10.5114	−	6.06873i	−0.362245	−	0.209142i
$843$	35.7184	+	38.8237i	1.23021	+	1.33716i
$844$	12.8567	−	22.2684i	0.442545	−	0.766510i
$845$	5.11954	−	12.0211i	0.176118	−	0.413539i
$846$	−0.152727	−	0.0127467i	−0.00525085	−	0.000438241i
$847$	−14.1811	−	24.2409i	−0.487267	−	0.832926i
$848$	4.15182	−	2.39705i	0.142574	−	0.0823151i
$849$	−22.4315	+	20.6373i	−0.769846	+	0.708271i
$850$	0.684086	−	1.18487i	0.0234640	−	0.0406408i
$851$	6.13696	+	10.6295i	0.210372	+	0.364375i
$852$	−1.45881	−	1.58563i	−0.0499779	−	0.0543228i
$853$	−24.5020			−0.838933			−0.419467	−	0.907771i	$-0.637783\pi$
$853$	−24.5020			−0.838933			−0.419467	+	0.907771i	$0.637783\pi$
$854$	−0.101179	−	17.6792i	−0.00346227	−	0.604969i
$855$	−5.57540	−	11.8327i	−0.190675	−	0.404670i
$856$	12.7443	+	7.35793i	0.435591	+	0.251489i
$857$	4.35323	−	7.54001i	0.148703	−	0.257562i	−0.782045	−	0.623222i	$-0.785823\pi$
$857$	4.35323	−	7.54001i	0.148703	−	0.257562i	0.930749	+	0.365660i	$0.119157\pi$
$858$	−2.00083	−	3.31937i	−0.0683072	−	0.113322i
$859$	31.0506	−	17.9271i	1.05943	−	0.611664i	0.134158	−	0.990960i	$-0.457167\pi$
$859$	31.0506	−	17.9271i	1.05943	−	0.611664i	0.925275	+	0.379296i	$0.123834\pi$
$860$	−1.04939	+	0.605865i	−0.0357838	+	0.0206598i
$861$	8.85805	+	38.5450i	0.301882	+	1.31361i
$862$	−3.37233	+	5.84104i	−0.114862	+	0.198947i
$863$	−5.26328	−	9.11626i	−0.179164	−	0.310321i	0.762430	−	0.647070i	$-0.224006\pi$
$863$	−5.26328	−	9.11626i	−0.179164	−	0.310321i	−0.941594	+	0.336749i	$0.890673\pi$
$864$	−4.81246	−	1.95965i	−0.163723	−	0.0666688i
$865$	11.4228	−	6.59496i	0.388387	−	0.224235i
$866$	25.4298	−	14.6819i	0.864139	−	0.498911i
$867$	28.5353	−	6.38601i	0.969111	−	0.216880i
$868$	−3.34439	−	5.71684i	−0.113516	−	0.194042i
$869$	−0.284284	−	0.492394i	−0.00964366	−	0.0167033i
$870$	−4.94429	+	15.7913i	−0.167627	+	0.535375i
$871$	−18.7721	+	6.26865i	−0.636069	+	0.212405i
$872$	−15.5550	−	8.98070i	−0.526760	−	0.304125i
$873$	25.1556	+	17.4647i	0.851390	+	0.591090i
$874$	−10.6030	+	6.12164i	−0.358652	+	0.207068i
$875$	20.6339	−	12.0710i	0.697554	−	0.408073i
$876$	−10.4642	−	11.3739i	−0.353551	−	0.384288i
$877$			52.4062i			1.76963i	0.465940	+	0.884816i	$0.345716\pi$
$877$			52.4062i			1.76963i	−0.465940	+	0.884816i	$0.654284\pi$
$878$	3.30932	−	1.91064i	0.111684	−	0.0644810i
$879$	6.27786	+	28.0521i	0.211747	+	0.946173i
$880$			0.623763i			0.0210271i
$881$	14.5503	+	25.2019i	0.490214	+	0.849075i	0.999937	−	0.0112637i	$-0.00358542\pi$
$881$	14.5503	+	25.2019i	0.490214	+	0.849075i	−0.509723	+	0.860339i	$0.670252\pi$
$882$	−18.8931	+	9.16786i	−0.636165	+	0.308698i
$883$	0.360145			0.0121199			0.00605993	−	0.999982i	$-0.498071\pi$
$883$	0.360145			0.0121199			0.00605993	+	0.999982i	$0.498071\pi$
$884$	−1.21143	−	0.247218i	−0.0407446	−	0.00831483i
$885$	5.24867	−	1.17462i	0.176432	−	0.0394843i
$886$			23.5604i			0.791528i
$887$	−7.19356	+	12.4596i	−0.241536	+	0.418353i	−0.961152	−	0.276020i	$-0.910985\pi$
$887$	−7.19356	+	12.4596i	−0.241536	+	0.418353i	0.719616	+	0.694372i	$0.244318\pi$
$888$	1.64508	+	7.35090i	0.0552053	+	0.246680i
$889$	7.30453	−	12.8207i	0.244986	−	0.429993i
$890$	1.80919	−	3.13361i	0.0606443	−	0.105039i
$891$	5.50830	+	0.925906i	0.184535	+	0.0310190i
$892$	4.67710	−	8.10097i	0.156601	−	0.271240i
$893$	−0.191928	+	0.110810i	−0.00642263	+	0.00370811i
$894$	7.93089	−	1.77488i	0.265249	−	0.0593608i
$895$	−9.83591	−	17.0363i	−0.328778	−	0.569461i
$896$	2.64571	−	0.0151415i	0.0883869	−	0.000505843i
$897$	15.0946	−	9.09863i	0.503994	−	0.303795i
$898$	3.91435	+	6.77986i	0.130624	+	0.226247i
$899$		−	23.7953i		−	0.793617i
$900$	−0.995528	+	11.9281i	−0.0331843	+	0.397602i
$901$			1.64396i			0.0547684i
$902$			5.35624i			0.178343i
$903$	−3.76388	−	4.04440i	−0.125254	−	0.134589i
$904$	4.26195	+	2.46064i	0.141750	+	0.0818397i
$905$	11.2723	+	19.5242i	0.374705	+	0.649008i
$906$	−12.9958	−	4.06903i	−0.431758	−	0.135184i
$907$	2.76947			0.0919586			0.0459793	−	0.998942i	$-0.485359\pi$
$907$	2.76947			0.0919586			0.0459793	+	0.998942i	$0.485359\pi$
$908$	−10.2114	−	5.89553i	−0.338876	−	0.195650i
$909$	2.47332	−	29.6344i	0.0820348	−	0.982911i
$910$	−7.21326	−	6.31611i	−0.239117	−	0.209377i
$911$		−	22.2089i		−	0.735813i	−0.929863	−	0.367906i	$-0.880075\pi$
$911$		−	22.2089i		−	0.735813i	0.929863	−	0.367906i	$-0.119925\pi$
$912$	−7.33256	+	1.64098i	−0.242805	+	0.0543382i
$913$			8.20840i			0.271658i
$914$	−27.5421	+	15.9014i	−0.911012	+	0.525973i
$915$	−3.47579	+	11.1011i	−0.114906	+	0.366993i
$916$	5.47329	−	9.48001i	0.180842	−	0.313228i
$917$	−23.9105	+	41.9670i	−0.789593	+	1.38587i
$918$	1.40709	−	1.09317i	0.0464409	−	0.0360800i
$919$	−31.0609			−1.02460			−0.512302	−	0.858805i	$-0.671207\pi$
$919$	−31.0609			−1.02460			−0.512302	+	0.858805i	$0.671207\pi$
$920$	−2.83652			−0.0935172
$921$	30.8424	+	33.5237i	1.01629	+	1.10465i
$922$	−26.9000	+	15.5307i	−0.885903	+	0.511477i
$923$	4.39460	+	0.896815i	0.144650	+	0.0295190i
$924$	−2.77178	+	0.636985i	−0.0911850	+	0.0209553i
$925$	15.0272	−	8.67596i	0.494092	−	0.285264i
$926$	−23.4328	−	13.5289i	−0.770048	−	0.444588i
$927$	13.1892	+	27.9916i	0.433190	+	0.919363i
$928$	8.23191	+	4.75270i	0.270226	+	0.156015i
$929$		−	52.6745i		−	1.72819i	−0.503325	−	0.864097i	$-0.667890\pi$
$929$		−	52.6745i		−	1.72819i	0.503325	−	0.864097i	$-0.332110\pi$
$930$	0.951723	+	4.25269i	0.0312082	+	0.139451i
$931$	−14.8816	+	26.4709i	−0.487725	+	0.867547i
$932$	−5.40464	−	3.12037i	−0.177035	−	0.102211i
$933$	23.2973	−	5.21377i	0.762719	−	0.170691i
$934$	31.6225			1.03472
$935$	−0.185240	−	0.106948i	−0.00605800	−	0.00349759i
$936$	10.5091	−	2.56088i	0.343502	−	0.0837050i
$937$		−	31.2959i		−	1.02239i	−0.859464	−	0.511196i	$-0.829203\pi$
$937$		−	31.2959i		−	1.02239i	0.859464	−	0.511196i	$-0.170797\pi$
$938$	0.0831130	+	14.5225i	0.00271373	+	0.474176i
$939$	15.1401	+	4.74041i	0.494080	+	0.154698i
$940$	−0.0513447			−0.00167468
$941$	46.2726	+	26.7155i	1.50844	+	0.870900i	0.999952	+	0.00983388i	$0.00313027\pi$
$941$	46.2726	+	26.7155i	1.50844	+	0.870900i	0.508492	+	0.861067i	$0.330203\pi$
$942$	−37.9687	−	11.8881i	−1.23709	−	0.387334i
$943$	−24.3571			−0.793176
$944$		−	3.08963i		−	0.100559i
$945$	13.6771	−	1.96396i	0.444916	−	0.0638877i
$946$	−0.374116	−	0.647988i	−0.0121636	−	0.0210679i
$947$	27.2913	−	47.2700i	0.886849	−	1.53607i	0.0432691	−	0.999063i	$-0.486223\pi$
$947$	27.2913	−	47.2700i	0.886849	−	1.53607i	0.843580	−	0.537004i	$-0.180444\pi$
$948$	1.54848	−	0.346539i	0.0502923	−	0.0112551i
$949$	31.5229	+	6.43294i	1.02328	+	0.208822i
$950$	8.65432	+	14.9897i	0.280783	+	0.486331i
$951$	2.45390	−	7.83737i	0.0795731	−	0.254144i
$952$	−0.449128	+	0.788297i	−0.0145563	+	0.0255489i
$953$	−0.882484	−	0.509502i	−0.0285865	−	0.0165044i	0.485639	−	0.874160i	$-0.338587\pi$
$953$	−0.882484	−	0.509502i	−0.0285865	−	0.0165044i	−0.514225	+	0.857655i	$0.671920\pi$
$954$	−6.13030	−	13.0104i	−0.198476	−	0.421227i
$955$	−6.60400	−	11.4385i	−0.213700	−	0.370140i
$956$	−15.2312	−	26.3812i	−0.492612	−	0.853230i
$957$	−9.75098	−	3.05305i	−0.315204	−	0.0986912i
$958$	9.21963	+	5.32296i	0.297873	+	0.171977i
$959$	−10.6169	+	18.6345i	−0.342838	+	0.601740i
$960$	−1.66130	−	0.520156i	−0.0536182	−	0.0167880i
$961$	12.3666	+	21.4196i	0.398924	+	0.690956i
$962$	−11.7379	−	10.3973i	−0.378446	−	0.335222i
$963$	25.1772	−	36.2645i	0.811324	−	1.16861i
$964$	2.84746	−	4.93194i	0.0917104	−	0.158847i
$965$	6.34158	+	10.9839i	0.204143	+	0.353585i
$966$	−2.89664	−	12.6045i	−0.0931979	−	0.405543i
$967$		−	31.5161i		−	1.01349i	−0.862096	−	0.506745i	$-0.830849\pi$
$967$		−	31.5161i		−	1.01349i	0.862096	−	0.506745i	$-0.169151\pi$
$968$	10.6148			0.341174
$969$	0.769894	−	2.45892i	0.0247326	−	0.0789920i
$970$	8.88514	+	5.12984i	0.285285	+	0.164709i
$971$	18.9083			0.606797			0.303399	−	0.952864i	$-0.401879\pi$
$971$	18.9083			0.606797			0.303399	+	0.952864i	$0.401879\pi$
$972$	−7.05938	+	13.8984i	−0.226430	+	0.445791i
$973$	0.289003	+	50.4980i	0.00926502	+	1.61889i
$974$			39.5929i			1.26864i
$975$	−12.8630	−	21.3396i	−0.411944	−	0.683415i
$976$	5.78697	+	3.34111i	0.185236	+	0.106946i
$977$	−50.6394			−1.62010			−0.810049	−	0.586363i	$-0.800559\pi$
$977$	−50.6394			−1.62010			−0.810049	+	0.586363i	$0.800559\pi$
$978$	−3.34630	−	14.9526i	−0.107003	−	0.478133i
$979$	1.93498	+	1.11716i	0.0618422	+	0.0357046i
$980$	−6.05223	+	3.58724i	−0.193331	+	0.114590i
$981$	−30.7300	+	44.2626i	−0.981133	+	1.41320i
$982$			31.8461i			1.01625i
$983$	−21.4061	−	12.3588i	−0.682750	−	0.394186i	0.118140	−	0.992997i	$-0.462307\pi$
$983$	−21.4061	−	12.3588i	−0.682750	−	0.394186i	−0.800890	+	0.598811i	$0.795640\pi$
$984$	−14.2655	−	4.46656i	−0.454768	−	0.142389i
$985$	−1.20759	−	0.697201i	−0.0384770	−	0.0222147i
$986$	−2.82283	+	1.62976i	−0.0898974	+	0.0519023i
$987$	−0.0524330	−	0.228158i	−0.00166896	−	0.00726233i
$988$	10.3713	−	11.7086i	0.329956	−	0.372501i
$989$	2.94668	−	1.70127i	0.0936989	−	0.0540971i
$990$	1.86481	+	0.155639i	0.0592674	+	0.00494652i
$991$	−16.6676			−0.529464			−0.264732	−	0.964322i	$-0.585284\pi$
$991$	−16.6676			−0.529464			−0.264732	+	0.964322i	$0.585284\pi$
$992$	2.50335			0.0794813
$993$	−31.1284	+	28.6386i	−0.987831	+	0.908820i
$994$	1.62927	−	2.85965i	0.0516773	−	0.0907026i
$995$	−4.40151	+	7.62364i	−0.139537	+	0.241686i
$996$	−21.8618	−	6.84498i	−0.692718	−	0.216892i
$997$	8.76275	−	5.05918i	0.277519	−	0.160226i	−0.354781	−	0.934950i	$-0.615444\pi$
$997$	8.76275	−	5.05918i	0.277519	−	0.160226i	0.632300	+	0.774724i	$0.282111\pi$
$998$			8.43543i			0.267019i
$999$	22.3868	−	3.08398i	0.708286	−	0.0975728i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bn.f.101.13	yes	34
3.2	odd	2		546.2.bn.e.101.5	yes	34
7.5	odd	6		546.2.bi.e.257.16	yes	34
13.4	even	6		546.2.bi.f.17.10	yes	34
21.5	even	6		546.2.bi.f.257.10	yes	34
39.17	odd	6		546.2.bi.e.17.16	✓	34
91.82	odd	6		546.2.bn.e.173.5	yes	34
273.173	even	6	inner	546.2.bn.f.173.13	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.16	✓	34	39.17	odd	6
546.2.bi.e.257.16	yes	34	7.5	odd	6
546.2.bi.f.17.10	yes	34	13.4	even	6
546.2.bi.f.257.10	yes	34	21.5	even	6
546.2.bn.e.101.5	yes	34	3.2	odd	2
546.2.bn.e.173.5	yes	34	91.82	odd	6
546.2.bn.f.101.13	yes	34	1.1	even	1	trivial
546.2.bn.f.173.13	yes	34	273.173	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bn (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.17271 + 1.27466i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.870413 + 0.502533i) q^{5} +(1.69024 - 0.378264i) q^{6} +(1.33597 + 2.28368i) q^{7} -1.00000 q^{8} +(-0.249516 + 2.98961i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.17271 + 1.27466i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.870413 + 0.502533i) q^{5} +(1.69024 - 0.378264i) q^{6} +(1.33597 + 2.28368i) q^{7} -1.00000 q^{8} +(-0.249516 + 2.98961i) q^{9} +1.00507i q^{10} -0.620619 q^{11} +(0.517534 - 1.65292i) q^{12} +(1.14202 + 3.41991i) q^{13} +(2.64571 - 0.0151415i) q^{14} +(-1.66130 - 0.520156i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.171457 - 0.296972i) q^{17} +(2.46432 + 1.71089i) q^{18} +4.33817 q^{19} +(0.870413 + 0.502533i) q^{20} +(-1.34422 + 4.38099i) q^{21} +(-0.310310 + 0.537472i) q^{22} +(-2.44412 - 1.41111i) q^{23} +(-1.17271 - 1.27466i) q^{24} +(-1.99492 + 3.45530i) q^{25} +(3.53274 + 0.720933i) q^{26} +(-4.10334 + 3.18788i) q^{27} +(1.30974 - 2.29882i) q^{28} +(8.23191 - 4.75270i) q^{29} +(-1.28112 + 1.17865i) q^{30} +(1.25167 - 2.16796i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.727805 - 0.791078i) q^{33} -0.342914 q^{34} +(-2.31047 - 1.31638i) q^{35} +(2.71383 - 1.27872i) q^{36} +(-3.76637 - 2.17451i) q^{37} +(2.16909 - 3.75697i) q^{38} +(-3.01996 + 5.46624i) q^{39} +(0.870413 - 0.502533i) q^{40} +(7.47421 - 4.31523i) q^{41} +(3.12194 + 3.35462i) q^{42} +(-0.602811 + 1.04410i) q^{43} +(0.310310 + 0.537472i) q^{44} +(-1.28519 - 2.72758i) q^{45} +(-2.44412 + 1.41111i) q^{46} +(-0.0442417 + 0.0255429i) q^{47} +(-1.69024 + 0.378264i) q^{48} +(-3.43038 + 6.10184i) q^{49} +(1.99492 + 3.45530i) q^{50} +(0.177470 - 0.566810i) q^{51} +(2.39072 - 2.69898i) q^{52} +(-4.15182 - 2.39705i) q^{53} +(0.709119 + 5.14754i) q^{54} +(0.540195 - 0.311882i) q^{55} +(-1.33597 - 2.28368i) q^{56} +(5.08741 + 5.52970i) q^{57} -9.50539i q^{58} +(-2.67570 + 1.54481i) q^{59} +(0.380181 + 1.69880i) q^{60} -6.68221i q^{61} +(-1.25167 - 2.16796i) q^{62} +(-7.16065 + 3.42420i) q^{63} +1.00000 q^{64} +(-2.71265 - 2.40283i) q^{65} +(-1.04900 + 0.234758i) q^{66} +5.48907i q^{67} +(-0.171457 + 0.296972i) q^{68} +(-1.06755 - 4.77024i) q^{69} +(-2.29525 + 1.34273i) q^{70} +(0.621982 - 1.07730i) q^{71} +(0.249516 - 2.98961i) q^{72} +(4.46154 - 7.72761i) q^{73} +(-3.76637 + 2.17451i) q^{74} +(-6.74380 + 1.50921i) q^{75} +(-2.16909 - 3.75697i) q^{76} +(-0.829127 - 1.41730i) q^{77} +(3.22393 + 5.34849i) q^{78} +(0.458065 + 0.793391i) q^{79} -1.00507i q^{80} +(-8.87548 - 1.49191i) q^{81} -8.63047i q^{82} -13.2261i q^{83} +(4.46616 - 1.02637i) q^{84} +(0.298476 + 0.172325i) q^{85} +(0.602811 + 1.04410i) q^{86} +(15.7117 + 4.91937i) q^{87} +0.620619 q^{88} +(-3.11782 - 1.80007i) q^{89} +(-3.00475 - 0.250780i) q^{90} +(-6.28427 + 7.17690i) q^{91} +2.82222i q^{92} +(4.23126 - 0.946926i) q^{93} +0.0510859i q^{94} +(-3.77600 + 2.18008i) q^{95} +(-0.517534 + 1.65292i) q^{96} +(5.10398 - 8.84035i) q^{97} +(3.56916 + 6.02172i) q^{98} +(0.154854 - 1.85541i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 17 q^{2} - 3 q^{3} - 17 q^{4} - 9 q^{5} + 3 q^{6} + 5 q^{7} - 34 q^{8} + 7 q^{9}+O(q^{10}) \) 34 * q + 17 * q^2 - 3 * q^3 - 17 * q^4 - 9 * q^5 + 3 * q^6 + 5 * q^7 - 34 * q^8 + 7 * q^9	\( 34 q + 17 q^{2} - 3 q^{3} - 17 q^{4} - 9 q^{5} + 3 q^{6} + 5 q^{7} - 34 q^{8} + 7 q^{9} + 18 q^{11} + 6 q^{12} - 8 q^{13} + 4 q^{14} - 4 q^{15} - 17 q^{16} - 6 q^{17} - 4 q^{18} - 10 q^{19} + 9 q^{20} + 7 q^{21} + 9 q^{22} - 6 q^{23} + 3 q^{24} + 16 q^{25} - 13 q^{26} - 18 q^{27} - q^{28} - 27 q^{29} + 13 q^{30} + q^{31} + 17 q^{32} + 21 q^{33} - 12 q^{34} + 3 q^{35} - 11 q^{36} + 6 q^{37} - 5 q^{38} - 2 q^{39} + 9 q^{40} - 3 q^{41} + 8 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} - 6 q^{46} + 27 q^{47} - 3 q^{48} - 5 q^{49} - 16 q^{50} - 36 q^{51} - 5 q^{52} - 21 q^{53} + 57 q^{55} - 5 q^{56} + 17 q^{57} + 6 q^{59} + 17 q^{60} - q^{62} + 34 q^{64} - 33 q^{65} - 6 q^{68} - 42 q^{69} + 3 q^{70} + 15 q^{71} - 7 q^{72} + 19 q^{73} + 6 q^{74} - 9 q^{75} + 5 q^{76} + 9 q^{77} - 7 q^{78} - 9 q^{79} - 5 q^{81} + q^{84} - 42 q^{85} + 3 q^{86} + 6 q^{87} - 18 q^{88} + 18 q^{89} + 9 q^{90} - 27 q^{91} + 8 q^{93} + 3 q^{95} - 6 q^{96} - 19 q^{97} - 7 q^{98} + 27 q^{99}+O(q^{100}) \) 34 * q + 17 * q^2 - 3 * q^3 - 17 * q^4 - 9 * q^5 + 3 * q^6 + 5 * q^7 - 34 * q^8 + 7 * q^9 + 18 * q^11 + 6 * q^12 - 8 * q^13 + 4 * q^14 - 4 * q^15 - 17 * q^16 - 6 * q^17 - 4 * q^18 - 10 * q^19 + 9 * q^20 + 7 * q^21 + 9 * q^22 - 6 * q^23 + 3 * q^24 + 16 * q^25 - 13 * q^26 - 18 * q^27 - q^28 - 27 * q^29 + 13 * q^30 + q^31 + 17 * q^32 + 21 * q^33 - 12 * q^34 + 3 * q^35 - 11 * q^36 + 6 * q^37 - 5 * q^38 - 2 * q^39 + 9 * q^40 - 3 * q^41 + 8 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 - 6 * q^46 + 27 * q^47 - 3 * q^48 - 5 * q^49 - 16 * q^50 - 36 * q^51 - 5 * q^52 - 21 * q^53 + 57 * q^55 - 5 * q^56 + 17 * q^57 + 6 * q^59 + 17 * q^60 - q^62 + 34 * q^64 - 33 * q^65 - 6 * q^68 - 42 * q^69 + 3 * q^70 + 15 * q^71 - 7 * q^72 + 19 * q^73 + 6 * q^74 - 9 * q^75 + 5 * q^76 + 9 * q^77 - 7 * q^78 - 9 * q^79 - 5 * q^81 + q^84 - 42 * q^85 + 3 * q^86 + 6 * q^87 - 18 * q^88 + 18 * q^89 + 9 * q^90 - 27 * q^91 + 8 * q^93 + 3 * q^95 - 6 * q^96 - 19 * q^97 - 7 * q^98 + 27 * q^99

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