LMFDB - Embedded newform 546.2.bn.e.101.5

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			101.5
Character	$\chi$	$=$	546.101
Dual form			546.2.bn.e.173.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-1.17271 + 1.27466i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.870413 - 0.502533i) q^{5} +(-0.517534 - 1.65292i) q^{6} +(1.33597 + 2.28368i) q^{7} +1.00000 q^{8} +(-0.249516 - 2.98961i) q^{9} +O(q^{10})$	\(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} +(-0.517534 - 1.65292i) 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} +(1.69024 + 0.378264i) q^{12} +(1.14202 + 3.41991i) q^{13} +(-2.64571 + 0.0151415i) q^{14} +(-0.380181 + 1.69880i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.171457 + 0.296972i) q^{17} +(2.71383 + 1.27872i) q^{18} +4.33817 q^{19} +(-0.870413 - 0.502533i) q^{20} +(-4.47761 - 0.975184i) 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} +(-2.46432 + 1.71089i) q^{36} +(-3.76637 - 2.17451i) q^{37} +(-2.16909 + 3.75697i) q^{38} +(-5.69848 - 2.55486i) q^{39} +(0.870413 - 0.502533i) q^{40} +(-7.47421 + 4.31523i) q^{41} +(3.08334 - 3.39013i) q^{42} +(-0.602811 + 1.04410i) q^{43} +(-0.310310 - 0.537472i) q^{44} +(-1.71956 - 2.47680i) q^{45} +(-2.44412 + 1.41111i) q^{46} +(0.0442417 - 0.0255429i) q^{47} +(-0.517534 - 1.65292i) q^{48} +(-3.43038 + 6.10184i) q^{49} +(-1.99492 - 3.45530i) q^{50} +(-0.579607 - 0.129712i) q^{51} +(2.39072 - 2.69898i) q^{52} +(4.15182 + 2.39705i) q^{53} +(-4.81246 + 1.95965i) 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} +(1.66130 - 0.520156i) q^{60} -6.68221i q^{61} +(1.25167 + 2.16796i) q^{62} +(6.49396 - 4.56383i) q^{63} +1.00000 q^{64} +(2.71265 + 2.40283i) q^{65} +(-0.321192 - 1.02584i) q^{66} +5.48907i q^{67} +(0.171457 - 0.296972i) q^{68} +(-4.66492 + 1.46060i) 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} +(-2.06488 - 6.59491i) q^{75} +(-2.16909 - 3.75697i) q^{76} +(0.829127 + 1.41730i) q^{77} +(5.06181 - 3.65760i) 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} +(1.39427 + 4.36532i) q^{84} +(0.298476 + 0.172325i) q^{85} +(-0.602811 - 1.04410i) q^{86} +(3.59555 - 16.0664i) 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} +(1.29557 + 4.13784i) q^{93} +0.0510859i q^{94} +(3.77600 - 2.18008i) q^{95} +(1.69024 + 0.378264i) 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} - 6 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 - 6 * 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} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9} - 18 q^{11} + 3 q^{12} - 8 q^{13} - 4 q^{14} - 17 q^{15} - 17 q^{16} + 6 q^{17} - 11 q^{18} - 10 q^{19} - 9 q^{20} - 4 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} + 4 q^{36} + 6 q^{37} + 5 q^{38} + 20 q^{39} + 9 q^{40} + 3 q^{41} + 20 q^{42} - 3 q^{43} + 9 q^{44} - 6 q^{46} - 27 q^{47} - 6 q^{48} - 5 q^{49} + 16 q^{50} + 24 q^{51} - 5 q^{52} + 21 q^{53} - 18 q^{54} + 57 q^{55} + 5 q^{56} - 17 q^{57} - 6 q^{59} + 4 q^{60} + q^{62} - 21 q^{63} + 34 q^{64} + 33 q^{65} - 21 q^{66} + 6 q^{68} - 30 q^{69} + 3 q^{70} - 15 q^{71} + 7 q^{72} + 19 q^{73} - 6 q^{74} - 63 q^{75} + 5 q^{76} - 9 q^{77} - 10 q^{78} - 9 q^{79} - 5 q^{81} - 16 q^{84} - 42 q^{85} - 3 q^{86} - 75 q^{87} - 18 q^{88} - 18 q^{89} - 9 q^{90} - 27 q^{91} + 25 q^{93} - 3 q^{95} + 3 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 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9 - 18 * q^11 + 3 * q^12 - 8 * q^13 - 4 * q^14 - 17 * q^15 - 17 * q^16 + 6 * q^17 - 11 * q^18 - 10 * q^19 - 9 * q^20 - 4 * 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 + 4 * q^36 + 6 * q^37 + 5 * q^38 + 20 * q^39 + 9 * q^40 + 3 * q^41 + 20 * q^42 - 3 * q^43 + 9 * q^44 - 6 * q^46 - 27 * q^47 - 6 * q^48 - 5 * q^49 + 16 * q^50 + 24 * q^51 - 5 * q^52 + 21 * q^53 - 18 * q^54 + 57 * q^55 + 5 * q^56 - 17 * q^57 - 6 * q^59 + 4 * q^60 + q^62 - 21 * q^63 + 34 * q^64 + 33 * q^65 - 21 * q^66 + 6 * q^68 - 30 * q^69 + 3 * q^70 - 15 * q^71 + 7 * q^72 + 19 * q^73 - 6 * q^74 - 63 * q^75 + 5 * q^76 - 9 * q^77 - 10 * q^78 - 9 * q^79 - 5 * q^81 - 16 * q^84 - 42 * q^85 - 3 * q^86 - 75 * q^87 - 18 * q^88 - 18 * q^89 - 9 * q^90 - 27 * q^91 + 25 * q^93 - 3 * q^95 + 3 * 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	−0.292579	−	0.956241i	$-0.594514\pi$
$5$	0.870413	−	0.502533i	0.389260	−	0.224740i	0.681840	+	0.731502i	$0.261180\pi$
$6$	−0.517534	−	1.65292i	−0.211282	−	0.674803i
$7$	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	$-0.470175\pi$
$11$	0.620619			0.187124			0.0935619	+	0.995613i	$0.470175\pi$
$12$	1.69024	+	0.378264i	0.487931	+	0.109195i
$13$	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
$15$	−0.380181	+	1.69880i	−0.0981622	+	0.438629i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.171457	+	0.296972i	0.0415844	+	0.0720263i	0.886068	−	0.463554i	$-0.153426\pi$
$17$	0.171457	+	0.296972i	0.0415844	+	0.0720263i	−0.844484	+	0.535581i	$0.820093\pi$
$18$	2.71383	+	1.27872i	0.639656	+	0.301396i
$19$	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
$21$	−4.47761	−	0.975184i	−0.977095	−	0.212803i
$22$	−0.310310	+	0.537472i	−0.0661582	+	0.114589i
$23$	2.44412	+	1.41111i	0.509633	+	0.294237i	0.732683	−	0.680570i	$-0.238268\pi$
$23$	2.44412	+	1.41111i	0.509633	+	0.294237i	−0.223050	+	0.974807i	$0.571601\pi$
$24$	−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	$0.677511\pi$
$29$	−8.23191	+	4.75270i	−1.52863	+	0.882553i	−0.999420	+	0.0340609i	$0.989156\pi$
$30$	−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
$36$	−2.46432	+	1.71089i	−0.410719	+	0.285148i
$37$	−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
$39$	−5.69848	−	2.55486i	−0.912487	−	0.409105i
$40$	0.870413	−	0.502533i	0.137624	−	0.0794574i
$41$	−7.47421	+	4.31523i	−1.16727	+	0.673926i	−0.953037	−	0.302855i	$-0.902060\pi$
$41$	−7.47421	+	4.31523i	−1.16727	+	0.673926i	−0.214238	+	0.976781i	$0.568727\pi$
$42$	3.08334	−	3.39013i	0.475770	−	0.523109i
$43$	−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
$45$	−1.71956	−	2.47680i	−0.256336	−	0.369220i
$46$	−2.44412	+	1.41111i	−0.360365	+	0.208057i
$47$	0.0442417	−	0.0255429i	0.00645331	−	0.00372582i	−0.496770	−	0.867882i	$-0.665481\pi$
$47$	0.0442417	−	0.0255429i	0.00645331	−	0.00372582i	0.503223	+	0.864156i	$0.332147\pi$
$48$	−0.517534	−	1.65292i	−0.0746996	−	0.238579i
$49$	−3.43038	+	6.10184i	−0.490055	+	0.871692i
$50$	−1.99492	−	3.45530i	−0.282124	−	0.488654i
$51$	−0.579607	−	0.129712i	−0.0811612	−	0.0181633i
$52$	2.39072	−	2.69898i	0.331533	−	0.374281i
$53$	4.15182	+	2.39705i	0.570296	+	0.329260i	0.757267	−	0.653105i	$-0.226534\pi$
$53$	4.15182	+	2.39705i	0.570296	+	0.329260i	−0.186972	+	0.982365i	$0.559867\pi$
$54$	−4.81246	+	1.95965i	−0.654893	+	0.266675i
$55$	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	−0.315611	−	0.948889i	$-0.602209\pi$
$59$	2.67570	−	1.54481i	0.348346	−	0.201118i	0.663956	+	0.747771i	$0.268876\pi$
$60$	1.66130	−	0.520156i	0.214473	−	0.0671519i
$61$		−	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
$63$	6.49396	−	4.56383i	0.818162	−	0.574988i
$64$	1.00000			0.125000
$65$	2.71265	+	2.40283i	0.336463	+	0.298034i
$66$	−0.321192	−	1.02584i	−0.0395360	−	0.126272i
$67$			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
$69$	−4.66492	+	1.46060i	−0.561590	+	0.175835i
$70$	−2.29525	+	1.34273i	−0.274335	+	0.160488i
$71$	−0.621982	+	1.07730i	−0.0738157	+	0.127853i	−0.900571	−	0.434710i	$-0.856851\pi$
$71$	−0.621982	+	1.07730i	−0.0738157	+	0.127853i	0.826755	+	0.562562i	$0.190184\pi$
$72$	−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
$75$	−2.06488	−	6.59491i	−0.238432	−	0.761514i
$76$	−2.16909	−	3.75697i	−0.248811	−	0.430954i
$77$	0.829127	+	1.41730i	0.0944878	+	0.161516i
$78$	5.06181	−	3.65760i	0.573138	−	0.414142i
$79$	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	$0.258567\pi$
$83$			13.2261i			1.45176i	−0.687822	+	0.725879i	$0.741433\pi$
$84$	1.39427	+	4.36532i	0.152128	+	0.476295i
$85$	0.298476	+	0.172325i	0.0323743	+	0.0186913i
$86$	−0.602811	−	1.04410i	−0.0650028	−	0.112588i
$87$	3.59555	−	16.0664i	0.385483	−	1.72250i
$88$	0.620619			0.0661582
$89$	3.11782	+	1.80007i	0.330488	+	0.190807i	0.656058	−	0.754711i	$-0.272223\pi$
$89$	3.11782	+	1.80007i	0.330488	+	0.190807i	−0.325570	+	0.945518i	$0.605556\pi$
$90$	3.00475	−	0.250780i	0.316729	−	0.0264345i
$91$	−6.28427	+	7.17690i	−0.658771	+	0.752344i
$92$		−	2.82222i		−	0.294237i
$93$	1.29557	+	4.13784i	0.134344	+	0.429074i
$94$			0.0510859i			0.00526910i
$95$	3.77600	−	2.18008i	0.387410	−	0.223671i
$96$	1.69024	+	0.378264i	0.172510	+	0.0386064i
$97$	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	$-0.335840\pi$
$101$	9.91247			0.986328			0.493164	+	0.869936i	$0.335840\pi$
$102$	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
$105$	−4.38743	+	1.40134i	−0.428170	+	0.136756i
$106$	−4.15182	+	2.39705i	−0.403260	+	0.232822i
$107$	12.7443	+	7.35793i	1.23204	+	0.711318i	0.967454	−	0.253045i	$-0.0814321\pi$
$107$	12.7443	+	7.35793i	1.23204	+	0.711318i	0.264584	+	0.964363i	$0.414765\pi$
$108$	0.709119	−	5.14754i	0.0682350	−	0.495322i
$109$	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
$111$	7.18861	−	2.25077i	0.682313	−	0.213634i
$112$	−2.64571	+	0.0151415i	−0.249996	+	0.00143074i
$113$	4.26195	+	2.46064i	0.400931	+	0.231478i	0.686886	−	0.726766i	$-0.258977\pi$
$113$	4.26195	+	2.46064i	0.400931	+	0.231478i	−0.285955	+	0.958243i	$0.592311\pi$
$114$	−2.24515	−	7.17067i	−0.210278	−	0.671595i
$115$	2.83652			0.264507
$116$	8.23191	+	4.75270i	0.764314	+	0.441277i
$117$	9.93923	−	4.26752i	0.918882	−	0.394533i
$118$			3.08963i			0.284423i
$119$	−0.449128	+	0.788297i	−0.0411715	+	0.0722631i
$120$	−0.380181	+	1.69880i	−0.0347056	+	0.155079i
$121$	−10.6148			−0.964985
$122$	5.78697	+	3.34111i	0.523927	+	0.302490i
$123$	3.26460	−	14.5876i	0.294359	−	1.31532i
$124$	−2.50335			−0.224807
$125$			9.03538i			0.808149i
$126$	0.705413	+	7.90585i	0.0628432	+	0.704309i
$127$	−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
$129$	−0.623951	−	1.99280i	−0.0549358	−	0.175456i
$130$	−3.43723	+	1.14781i	−0.301465	+	0.100670i
$131$	−9.12794	−	15.8101i	−0.797512	−	1.38133i	−0.921232	−	0.389014i	$-0.872816\pi$
$131$	−9.12794	−	15.8101i	−0.797512	−	1.38133i	0.123720	−	0.992317i	$-0.460517\pi$
$132$	1.04900	+	0.234758i	0.0913034	+	0.0204331i
$133$	5.79566	+	9.90700i	0.502547	+	0.859046i
$134$	−4.75367	−	2.74453i	−0.410655	−	0.237092i
$135$	5.17362	+	0.712712i	0.445274	+	0.0613405i
$136$	0.171457	+	0.296972i	0.0147023	+	0.0254651i
$137$	−4.05306	−	7.02011i	−0.346276	−	0.599768i	0.639308	−	0.768950i	$-0.279221\pi$
$137$	−4.05306	−	7.02011i	−0.346276	−	0.599768i	−0.985585	+	0.169182i	$0.945887\pi$
$138$	1.06755	−	4.77024i	0.0908755	−	0.406069i
$139$	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
$141$	−0.0193240	+	0.0863474i	−0.00162737	+	0.00727177i
$142$	−0.621982	−	1.07730i	−0.0521956	−	0.0904054i
$143$	0.708762	+	2.12246i	0.0592697	+	0.177489i
$144$	2.71383	+	1.27872i	0.226153	+	0.106560i
$145$	−4.77677	+	8.27361i	−0.396689	+	0.687086i
$146$	4.46154	+	7.72761i	0.369239	+	0.639541i
$147$	−3.75493	−	11.5282i	−0.309702	−	0.950834i
$148$			4.34903i			0.357488i
$149$	−4.69216			−0.384397			−0.192198	−	0.981356i	$-0.561562\pi$
$149$	−4.69216			−0.384397			−0.192198	+	0.981356i	$0.561562\pi$
$150$	6.74380	+	1.50921i	0.550629	+	0.123227i
$151$	−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
$153$	0.845048	−	0.586688i	0.0683181	−	0.0474309i
$154$	−1.64198	+	0.00939713i	−0.132314	+	0.000757243i
$155$		−	2.51603i		−	0.202092i
$156$	0.636667	+	6.21246i	0.0509741	+	0.497395i
$157$	−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
$159$	−7.92429	+	2.48111i	−0.628437	+	0.196765i
$160$	−0.870413	−	0.502533i	−0.0688122	−	0.0397287i
$161$	0.0427328	+	7.46677i	0.00336782	+	0.588464i
$162$	3.14571	−	8.43235i	0.247151	−	0.662508i
$163$		−	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
$165$	−0.235947	+	1.05431i	−0.0183685	+	0.0820780i
$166$	−11.4542	−	6.61307i	−0.889017	−	0.513274i
$167$	3.95886	−	2.28565i	0.306345	−	0.176869i	−0.338945	−	0.940806i	$-0.610070\pi$
$167$	3.95886	−	2.28565i	0.306345	−	0.176869i	0.645290	+	0.763938i	$0.276737\pi$
$168$	−4.47761	−	0.975184i	−0.345455	−	0.0752371i
$169$	−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	$-0.333745\pi$
$173$	13.1234			0.997757			0.498879	+	0.866672i	$0.333745\pi$
$174$	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
$177$	−1.16870	+	5.22222i	−0.0878445	+	0.392526i
$178$	−3.11782	+	1.80007i	−0.233690	+	0.134921i
$179$		−	19.5727i		−	1.46293i	−0.681879	−	0.731465i	$-0.738837\pi$
$179$		−	19.5727i		−	1.46293i	0.681879	−	0.731465i	$-0.261163\pi$
$180$	−1.28519	+	2.72758i	−0.0957927	+	0.203302i
$181$		−	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
$186$	−4.23126	−	0.946926i	−0.310251	−	0.0694320i
$187$	0.106409	+	0.184307i	0.00778143	+	0.0134778i
$188$	−0.0442417	−	0.0255429i	−0.00322665	−	0.00186291i
$189$	−1.79818	+	13.6296i	−0.130798	+	0.991409i
$190$			4.36015i			0.316319i
$191$		−	13.1414i		−	0.950880i	−0.879748	−	0.475440i	$-0.842289\pi$
$191$		−	13.1414i		−	0.950880i	0.879748	−	0.475440i	$-0.157711\pi$
$192$	−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
$195$	−6.24393	+	0.639892i	−0.447137	+	0.0458236i
$196$	6.99954	−	0.0801202i	0.499967	−	0.00572287i
$197$	−0.693687	−	1.20150i	−0.0494232	−	0.0856034i	0.840255	−	0.542191i	$-0.182405\pi$
$197$	−0.693687	−	1.20150i	−0.0494232	−	0.0856034i	−0.889679	+	0.456587i	$0.849072\pi$
$198$	1.68426	+	0.793596i	0.119695	+	0.0563984i
$199$	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
$204$	0.177470	+	0.566810i	0.0124254	+	0.0396847i
$205$	−4.33710	+	7.51207i	−0.302916	+	0.524666i
$206$			10.3144i			0.718638i
$207$	3.60882	−	7.65904i	0.250830	−	0.532340i
$208$	−3.53274	−	0.720933i	−0.244951	−	0.0499877i
$209$	2.69235			0.186234
$210$	0.980124	−	4.50030i	0.0676350	−	0.310550i
$211$	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
$213$	−0.643794	−	2.05618i	−0.0441121	−	0.140887i
$214$	−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
$219$	4.61800	+	14.7492i	0.312055	+	0.996656i
$220$	−0.540195	−	0.311882i	−0.0364199	−	0.0210271i
$221$	−0.819809	+	0.925516i	−0.0551464	+	0.0622570i
$222$	−1.64508	+	7.35090i	−0.110411	+	0.493360i
$223$	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
$225$	10.8278	+	5.10188i	0.721851	+	0.340125i
$226$	−4.26195	+	2.46064i	−0.283501	+	0.163679i
$227$	−10.2114	+	5.89553i	−0.677751	+	0.391300i	−0.799007	−	0.601321i	$-0.794641\pi$
$227$	−10.2114	+	5.89553i	−0.677751	+	0.391300i	0.121256	+	0.992621i	$0.461308\pi$
$228$	7.33256	+	1.64098i	0.485611	+	0.108676i
$229$	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
$231$	−2.77889	−	0.605218i	−0.182838	−	0.0398204i
$232$	−8.23191	+	4.75270i	−0.540451	+	0.312030i
$233$	−5.40464	+	3.12037i	−0.354070	+	0.204422i	−0.666476	−	0.745526i	$-0.732198\pi$
$233$	−5.40464	+	3.12037i	−0.354070	+	0.204422i	0.312406	+	0.949949i	$0.398865\pi$
$234$	−1.27383	+	10.7414i	−0.0832729	+	0.702186i
$235$	0.0256723	−	0.0444658i	0.00167468	−	0.00290063i
$236$	−2.67570	−	1.54481i	−0.174173	−	0.100559i
$237$	−1.54848	−	0.346539i	−0.100585	−	0.0225101i
$238$	−0.458121	−	0.783105i	−0.0296956	−	0.0507612i
$239$	−30.4624			−1.97045			−0.985225	−	0.171267i	$-0.945214\pi$
$239$	−30.4624			−1.97045			−0.985225	+	0.171267i	$0.945214\pi$
$240$	−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	$-0.558897\pi$
$251$	12.0289	−	20.8346i	0.759255	−	1.31507i	0.943231	−	0.332138i	$-0.107770\pi$
$252$	−7.19937	−	3.34202i	−0.453518	−	0.210527i
$253$	1.51687	+	0.875762i	0.0953645	+	0.0550587i
$254$	5.57708			0.349937
$255$	−0.569682	+	0.178369i	−0.0356749	+	0.0111699i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	14.7678	−	25.5785i	0.921189	−	1.59555i	0.123610	−	0.992331i	$-0.460553\pi$
$257$	14.7678	−	25.5785i	0.921189	−	1.59555i	0.797579	−	0.603214i	$-0.206114\pi$
$258$	2.03779	+	0.456044i	0.126867	+	0.0283920i
$259$	−0.0658509	−	11.5063i	−0.00409178	−	0.714964i
$260$	0.724585	−	3.55064i	0.0449369	−	0.220201i
$261$	16.2627	+	23.4243i	1.00663	+	1.44993i
$262$	18.2559			1.12785
$263$			22.0320i			1.35855i	0.733884	+	0.679274i	$0.237705\pi$
$263$			22.0320i			1.35855i	−0.733884	+	0.679274i	$0.762295\pi$
$264$	−0.727805	+	0.791078i	−0.0447933	+	0.0486875i
$265$	4.81839			0.295991
$266$	−11.4775	+	0.0656867i	−0.703733	+	0.00402751i
$267$	−5.95077	+	1.86320i	−0.364181	+	0.114026i
$268$	4.75367	−	2.74453i	0.290377	−	0.167649i
$269$	3.20777	+	5.55601i	0.195581	+	0.338756i	0.947091	−	0.320966i	$-0.104007\pi$
$269$	3.20777	+	5.55601i	0.195581	+	0.338756i	−0.751510	+	0.659722i	$0.770674\pi$
$270$	−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
$273$	−1.77850	−	16.4267i	−0.107640	−	0.994190i
$274$	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
$279$	−6.79366	−	3.20107i	−0.406726	−	0.191643i
$280$	2.31047	+	1.31638i	0.138077	+	0.0786685i
$281$	−30.4581			−1.81698			−0.908488	−	0.417911i	$-0.862762\pi$
$281$	−30.4581			−1.81698			−0.908488	+	0.417911i	$0.862762\pi$
$282$	−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
$285$	−1.64929	+	7.36971i	−0.0976955	+	0.436544i
$286$	−2.19249	−	0.447425i	−0.129644	−	0.0264568i
$287$	−19.8399	−	11.3037i	−1.17111	−	0.667235i
$288$	−2.46432	+	1.71089i	−0.145211	+	0.100815i
$289$	8.44121	−	14.6206i	0.496541	−	0.860035i
$290$	−4.77677	−	8.27361i	−0.280502	−	0.485843i
$291$	5.28297	+	16.8730i	0.309693	+	0.989112i
$292$	−8.92307			−0.522183
$293$	−14.3730	−	8.29824i	−0.839678	−	0.484788i	0.0174766	−	0.999847i	$-0.494437\pi$
$293$	−14.3730	−	8.29824i	−0.839678	−	0.484788i	−0.857155	+	0.515059i	$0.827770\pi$
$294$	11.8612	+	2.51225i	0.691760	+	0.146518i
$295$	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
$309$	−3.90157	+	17.4338i	−0.221953	+	0.991776i
$310$	2.17894	+	1.25801i	0.123756	+	0.0714504i
$311$	−6.89170	+	11.9368i	−0.390793	+	0.676873i	−0.992554	−	0.121803i	$-0.961132\pi$
$311$	−6.89170	+	11.9368i	−0.390793	+	0.676873i	0.601762	+	0.798676i	$0.294466\pi$
$312$	−5.69848	−	2.55486i	−0.322613	−	0.144640i
$313$	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
$315$	3.35895	−	7.23584i	0.189255	−	0.407693i
$316$	0.458065	−	0.793391i	0.0257681	−	0.0446317i
$317$	2.37076	+	4.10628i	0.133155	+	0.230631i	0.924891	−	0.380232i	$-0.124156\pi$
$317$	2.37076	+	4.10628i	0.133155	+	0.230631i	−0.791736	+	0.610863i	$0.790822\pi$
$318$	1.81344	−	8.10319i	0.101693	−	0.454405i
$319$	−5.10888	+	2.94961i	−0.286042	+	0.165147i
$320$	0.870413	−	0.502533i	0.0486575	−	0.0280924i
$321$	−24.3242	+	7.61596i	−1.35764	+	0.425081i
$322$	−6.48778	−	3.69638i	−0.361550	−	0.205991i
$323$	0.743810	+	1.28832i	0.0413867	+	0.0716838i
$324$	5.72977	+	6.94044i	0.318321	+	0.385580i
$325$	−14.0951	−	2.87641i	−0.781854	−	0.159554i
$326$	7.66125	+	4.42322i	0.424317	+	0.244980i
$327$	−29.6888	+	9.29564i	−1.64180	+	0.514050i
$328$	−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
$333$	−5.56117	+	11.8025i	−0.304750	+	0.646774i
$334$			4.57129i			0.250130i
$335$	2.75844	+	4.77776i	0.150710	+	0.261037i
$336$	3.08334	−	3.39013i	0.168210	−	0.184947i
$337$	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
$339$	−8.13450	+	2.54693i	−0.441806	+	0.138330i
$340$		−	0.344651i		−	0.0186913i
$341$	0.776812	−	1.34548i	0.0420667	−	0.0728617i
$342$	11.7731	+	5.54729i	0.636615	+	0.299963i
$343$	−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	$-0.284258\pi$
$347$	30.0878	−	17.3712i	1.61520	−	0.932535i	0.988139	−	0.153564i	$-0.0490751\pi$
$348$	−15.7117	+	4.91937i	−0.842235	+	0.263706i
$349$	−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
$351$	−6.21616	+	17.6737i	−0.331794	+	0.943352i
$352$	−0.310310	−	0.537472i	−0.0165396	−	0.0286474i
$353$			19.8207i			1.05495i	0.849571	+	0.527474i	$0.176861\pi$
$353$			19.8207i			1.05495i	−0.849571	+	0.527474i	$0.823139\pi$
$354$	−3.93822	−	3.62323i	−0.209314	−	0.192572i
$355$			1.25027i			0.0663572i
$356$		−	3.60015i		−	0.190807i
$357$	−0.478115	−	1.49693i	−0.0253045	−	0.0792258i
$358$	16.9504	+	9.78634i	0.895858	+	0.517224i
$359$	0.111157	+	0.192530i	0.00586667	+	0.0101614i	0.868944	−	0.494911i	$-0.164799\pi$
$359$	0.111157	+	0.192530i	0.00586667	+	0.0101614i	−0.863077	+	0.505072i	$0.831466\pi$
$360$	−1.71956	−	2.47680i	−0.0906286	−	0.130539i
$361$	−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
$366$	−11.0452	+	3.45827i	−0.577341	+	0.180767i
$367$		−	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
$369$	14.7658	+	21.2682i	0.768676	+	1.10718i
$370$	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
$378$	−10.9045	−	8.37208i	−0.560867	−	0.430613i
$379$	−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
$381$	9.42662	+	2.10961i	0.482940	+	0.108079i
$382$	11.3808	+	6.57071i	0.582293	+	0.336187i
$383$		−	10.8652i		−	0.555187i	−0.960699	−	0.277594i	$-0.910463\pi$
$383$		−	10.8652i		−	0.555187i	0.960699	−	0.277594i	$-0.0895368\pi$
$384$	−0.517534	−	1.65292i	−0.0264103	−	0.0843504i
$385$	1.43392	+	0.816968i	0.0730793	+	0.0416366i
$386$	10.9286	+	6.30961i	0.556250	+	0.321151i
$387$	3.27186	+	1.54165i	0.166318	+	0.0783664i
$388$	−10.2080			−0.518231
$389$	33.7632	+	19.4932i	1.71186	+	0.988345i	0.932048	+	0.362334i	$0.118020\pi$
$389$	33.7632	+	19.4932i	1.71186	+	0.988345i	0.779815	+	0.626011i	$0.215313\pi$
$390$	2.56780	−	5.72735i	0.130026	−	0.290016i
$391$			0.967778i			0.0489427i
$392$	−3.43038	+	6.10184i	−0.173261	+	0.308190i
$393$	30.8568	+	6.90555i	1.55652	+	0.348339i
$394$	1.38737			0.0698949
$395$	0.797410	+	0.460385i	0.0401221	+	0.0231645i
$396$	−1.52940	+	1.06181i	−0.0768554	+	0.0533580i
$397$	−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
$399$	−19.4247	−	4.23052i	−0.972450	−	0.211791i
$400$	−1.99492	−	3.45530i	−0.0997461	−	0.172765i
$401$	14.8257	−	25.6788i	0.740358	−	1.28234i	−0.211975	−	0.977275i	$-0.567989\pi$
$401$	14.8257	−	25.6788i	0.740358	−	1.28234i	0.952332	−	0.305062i	$-0.0986772\pi$
$402$	9.07302	−	2.84078i	0.452521	−	0.141685i
$403$	8.84367	+	1.80474i	0.440535	+	0.0899007i
$404$	−4.95624	−	8.58446i	−0.246582	−	0.427093i
$405$	−6.97560	+	5.75880i	−0.346620	+	0.286157i
$406$	21.7073	−	12.6989i	1.07731	−	0.630235i
$407$	−2.33748	−	1.34954i	−0.115865	−	0.0668944i
$408$	−0.579607	−	0.129712i	−0.0286948	−	0.00642170i
$409$	−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
$411$	13.7013	+	3.06626i	0.675835	+	0.151247i
$412$	−8.93253	−	5.15720i	−0.440074	−	0.254077i
$413$	7.10250	+	4.04661i	0.349491	+	0.199121i
$414$	4.82851	+	6.95485i	0.237308	+	0.341812i
$415$	6.64657	+	11.5122i	0.326268	+	0.565112i
$416$	2.39072	−	2.69898i	0.117215	−	0.132328i
$417$	−31.5490	+	9.87806i	−1.54496	+	0.483731i
$418$	−1.34618	+	2.33165i	−0.0658437	+	0.114045i
$419$	−2.10360	−	3.64355i	−0.102768	−	0.177999i	0.810056	−	0.586352i	$-0.199437\pi$
$419$	−2.10360	−	3.64355i	−0.102768	−	0.177999i	−0.912824	+	0.408353i	$0.866103\pi$
$420$	3.40731	+	3.09896i	0.166260	+	0.151214i
$421$		−	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
$423$	−0.0874023	−	0.125892i	−0.00424964	−	0.00612107i
$424$	4.15182	+	2.39705i	0.201630	+	0.116411i
$425$	−1.36817			−0.0663661
$426$	2.10260	+	0.470547i	0.101871	+	0.0227981i
$427$	15.2600	−	8.92722i	0.738485	−	0.432018i
$428$		−	14.7159i		−	0.711318i
$429$	−3.53659	−	1.58560i	−0.170748	−	0.0765533i
$430$	−1.04939	−	0.605865i	−0.0506060	−	0.0292174i
$431$	6.74465			0.324878			0.162439	−	0.986719i	$-0.448064\pi$
$431$	6.74465			0.324878			0.162439	+	0.986719i	$0.448064\pi$
$432$	−4.81246	+	1.95965i	−0.231540	+	0.0942839i
$433$	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
$435$	−4.94429	−	15.7913i	−0.237060	−	0.757134i
$436$		−	17.9614i		−	0.860195i
$437$	10.6030	+	6.12164i	0.507210	+	0.292838i
$438$	−15.0821	−	3.37528i	−0.720653	−	0.161277i
$439$	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
$441$	19.0980	+	8.73299i	0.909430	+	0.415857i
$442$	−0.391616	−	1.17273i	−0.0186273	−	0.0557813i
$443$	20.4039	−	11.7802i	0.969420	−	0.559695i	0.0703604	−	0.997522i	$-0.477585\pi$
$443$	20.4039	−	11.7802i	0.969420	−	0.559695i	0.899059	+	0.437827i	$0.144252\pi$
$444$	−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	−0.758756	−	0.651375i	$-0.774192\pi$
$449$	3.91435	−	6.77986i	0.184730	−	0.319961i	0.943485	+	0.331414i	$0.107526\pi$
$450$	−9.83224	+	6.82618i	−0.463496	+	0.321789i
$451$	−4.63864	+	2.67812i	−0.218425	+	0.126108i
$452$		−	4.92128i		−	0.231478i
$453$	12.9958	−	4.06903i	0.610598	−	0.191180i
$454$		−	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
$459$	−0.243167	+	1.76516i	−0.0113501	+	0.0823907i
$460$	−1.41826	−	2.45650i	−0.0661267	−	0.114535i
$461$	26.9000	+	15.5307i	1.25286	+	0.723337i	0.971676	−	0.236318i	$-0.0759406\pi$
$461$	26.9000	+	15.5307i	1.25286	+	0.723337i	0.281181	+	0.959655i	$0.409274\pi$
$462$	1.91358	−	2.10398i	0.0890278	−	0.0978861i
$463$		−	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	$-0.905414\pi$
$467$	−15.8112	−	27.3859i	−0.731657	−	1.26727i	0.224517	−	0.974470i	$-0.427919\pi$
$468$	−8.66540	−	6.47386i	−0.400558	−	0.299254i
$469$	−12.5353	+	7.33322i	−0.578825	+	0.338616i
$470$	0.0256723	+	0.0444658i	0.00118418	+	0.00205105i
$471$	37.9687	−	11.8881i	1.74950	−	0.547774i
$472$	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
$477$	6.13030	−	13.0104i	0.280687	−	0.595705i
$478$	15.2312	−	26.3812i	0.696659	−	1.20665i
$479$		−	10.6459i		−	0.486424i	−0.969973	−	0.243212i	$-0.921799\pi$
$479$		−	10.6459i		−	0.486424i	0.969973	−	0.243212i	$-0.0782011\pi$
$480$	1.66130	−	0.520156i	0.0758275	−	0.0237418i
$481$	3.13535	−	15.3640i	0.142960	−	0.700537i
$482$	−5.69491			−0.259396
$483$	−9.56771	−	8.70187i	−0.435346	−	0.395949i
$484$	5.30742	+	9.19271i	0.241246	+	0.417851i
$485$		−	10.2597i		−	0.465868i
$486$	7.05938	+	13.8984i	0.320220	+	0.630444i
$487$	−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	0.274610	−	0.961556i	$-0.411451\pi$
$491$	27.5795	−	15.9230i	1.24465	−	0.718597i	0.970037	+	0.242959i	$0.0781181\pi$
$492$	−14.2655	+	4.46656i	−0.643139	+	0.201368i
$493$	−2.82283	−	1.62976i	−0.127134	−	0.0734009i
$494$	−15.3256	−	3.12753i	−0.689533	−	0.140714i
$495$	−1.06719	−	1.53715i	−0.0479666	−	0.0690898i
$496$	1.25167	+	2.16796i	0.0562018	+	0.0973443i
$497$	−3.29117	+	0.0188355i	−0.147629	+	0.000844889i
$498$	21.8618	−	6.84498i	0.979651	−	0.306731i
$499$	−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
$501$	−1.72916	+	7.72659i	−0.0772530	+	0.345198i
$502$	12.0289	+	20.8346i	0.536875	+	0.929894i
$503$	4.21408	−	7.29900i	0.187896	−	0.325446i	−0.756652	−	0.653818i	$-0.773166\pi$
$503$	4.21408	−	7.29900i	0.187896	−	0.325446i	0.944549	+	0.328371i	$0.106500\pi$
$504$	6.49396	−	4.56383i	0.289264	−	0.203289i
$505$	8.62794	−	4.98135i	0.383938	−	0.221667i
$506$	−1.51687	+	0.875762i	−0.0674329	+	0.0389324i
$507$	2.22959	−	22.4060i	0.0990194	−	0.995085i
$508$	−2.78854	+	4.82989i	−0.123722	+	0.214292i
$509$	14.1105	+	8.14669i	0.625436	+	0.361096i	0.778982	−	0.627046i	$-0.215736\pi$
$509$	14.1105	+	8.14669i	0.625436	+	0.361096i	−0.153546	+	0.988141i	$0.549069\pi$
$510$	0.130369	−	0.582543i	0.00577284	−	0.0257954i
$511$	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	−0.995263	−	0.0972224i	$-0.969004\pi$
$521$	−9.43681	+	16.3450i	−0.413434	+	0.716089i	0.581828	+	0.813312i	$0.302338\pi$
$522$	−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
$525$	12.3020	−	13.5261i	0.536905	−	0.590327i
$526$	−19.0802	−	11.0160i	−0.831938	−	0.480319i
$527$	0.858431			0.0373939
$528$	−0.321192	−	1.02584i	−0.0139781	−	0.0446438i
$529$	−7.51753	−	13.0207i	−0.326849	−	0.566120i
$530$	−2.40920	+	4.17285i	−0.104649	+	0.181257i
$531$	−5.28601	−	7.61382i	−0.229393	−	0.330412i
$532$	5.68189	−	9.97269i	0.246341	−	0.432371i
$533$	−23.2934	−	20.6330i	−1.00895	−	0.893715i
$534$	1.36181	−	6.08512i	0.0589312	−	0.263329i
$535$	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
$540$	−1.96958	−	4.83684i	−0.0847573	−	0.208144i
$541$	−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
$546$	15.1152	+	6.67313i	0.646871	+	0.285584i
$547$	−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
$552$	−4.66492	+	1.46060i	−0.198552	+	0.0621671i
$553$	−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	$-0.364162\pi$
$557$	19.5374			0.827825			0.413912	+	0.910317i	$0.364162\pi$
$558$	6.16904	−	4.28295i	0.261156	−	0.181312i
$559$	−4.25915	−	0.869172i	−0.180143	−	0.0367621i
$560$	−2.29525	+	1.34273i	−0.0969920	+	0.0567409i
$561$	−0.359715	−	0.0805018i	−0.0151872	−	0.00339879i
$562$	15.2290	−	26.3775i	0.642398	−	1.11267i
$563$	15.5687	+	26.9657i	0.656141	+	1.13647i	0.981606	+	0.190916i	$0.0611457\pi$
$563$	15.5687	+	26.9657i	0.656141	+	1.13647i	−0.325466	+	0.945554i	$0.605521\pi$
$564$	0.0844411	−	0.0264387i	0.00355561	−	0.00111327i
$565$	4.94621			0.208089
$566$	−15.2403	−	8.79901i	−0.640599	−	0.369850i
$567$	−15.2644	−	18.2756i	−0.641044	−	0.767504i
$568$	−0.621982	+	1.07730i	−0.0260978	+	0.0452027i
$569$	1.67856	+	0.969116i	0.0703688	+	0.0406275i	0.534772	−	0.844997i	$-0.320398\pi$
$569$	1.67856	+	0.969116i	0.0703688	+	0.0406275i	−0.464403	+	0.885624i	$0.653731\pi$
$570$	−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
$582$	−17.2539	−	3.86131i	−0.715198	−	0.160056i
$583$	2.57670	+	1.48766i	0.106716	+	0.0616124i
$584$	4.46154	−	7.72761i	0.184620	−	0.319771i
$585$	6.50666	−	8.70930i	0.269017	−	0.360085i
$586$	14.3730	−	8.29824i	0.593742	−	0.342797i
$587$	17.0112	−	9.82143i	0.702128	−	0.405374i	−0.106012	−	0.994365i	$-0.533808\pi$
$587$	17.0112	−	9.82143i	0.702128	−	0.405374i	0.808139	+	0.588991i	$0.200475\pi$
$588$	−8.10629	+	9.01599i	−0.334298	+	0.371813i
$589$	5.42997	−	9.40499i	0.223738	−	0.387526i
$590$	1.55264	+	2.68925i	0.0639212	+	0.110715i
$591$	2.34500	+	0.524794i	0.0964603	+	0.0215871i
$592$	3.76637	−	2.17451i	0.154797	−	0.0893719i
$593$	−8.82193	+	5.09334i	−0.362273	+	0.209158i	−0.670077	−	0.742291i	$-0.733739\pi$
$593$	−8.82193	+	5.09334i	−0.362273	+	0.209158i	0.307804	+	0.951450i	$0.400406\pi$
$594$	−2.98670	+	1.21620i	−0.122546	+	0.0499012i
$595$	0.00521855	+	0.911846i	0.000213940	+	0.0373820i
$596$	2.34608	+	4.06353i	0.0960992	+	0.166449i
$597$	−3.31309	+	14.8042i	−0.135596	+	0.605897i
$598$	−7.61711	−	6.74713i	−0.311487	−	0.275911i
$599$	−1.11601	−	0.644326i	−0.0455988	−	0.0263265i	0.477027	−	0.878888i	$-0.341714\pi$
$599$	−1.11601	−	0.644326i	−0.0455988	−	0.0263265i	−0.522626	+	0.852562i	$0.675048\pi$
$600$	−2.06488	−	6.59491i	−0.0842984	−	0.269236i
$601$	−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
$606$	−5.13005	−	16.3846i	−0.208394	−	0.665578i
$607$		−	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
$609$	41.4941	−	13.2531i	1.68142	−	0.537043i
$610$	6.71606			0.271926
$611$	0.137880	+	0.122132i	0.00557801	+	0.00494092i
$612$	−0.930610	−	0.438489i	−0.0376177	−	0.0177249i
$613$			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
$615$	−4.48919	−	14.3378i	−0.181022	−	0.578155i
$616$	0.829127	+	1.41730i	0.0334065	+	0.0571045i
$617$	22.9771	−	39.7974i	0.925022	−	1.60218i	0.133495	−	0.991049i	$-0.457380\pi$
$617$	22.9771	−	39.7974i	0.925022	−	1.60218i	0.791526	−	0.611135i	$-0.209287\pi$
$618$	−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
$621$	5.53058	+	13.5818i	0.221934	+	0.545020i
$622$	−6.89170	−	11.9368i	−0.276332	−	0.478621i
$623$	0.0545118	+	9.52494i	0.00218397	+	0.381609i
$624$	5.06181	−	3.65760i	0.202635	−	0.146421i
$625$	−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
$630$	4.58695	+	6.52685i	0.182748	+	0.260036i
$631$	−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
$633$	−43.4617	−	9.72643i	−1.72745	−	0.386591i
$634$	−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
$639$	3.37591	+	1.59068i	0.133549	+	0.0629262i
$640$			1.00507i			0.0397287i
$641$	−35.8025	+	20.6706i	−1.41411	+	0.816439i	−0.995773	−	0.0918509i	$-0.970722\pi$
$641$	−35.8025	+	20.6706i	−1.41411	+	0.816439i	−0.418341	+	0.908290i	$0.637388\pi$
$642$	5.56648	−	24.8733i	0.219691	−	0.981673i
$643$	−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	$-0.473243\pi$
$647$	4.27122			0.167919			0.0839595	+	0.996469i	$0.473243\pi$
$648$	−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
$651$	−7.71867	+	8.48668i	−0.302518	+	0.332619i
$652$	−7.66125	+	4.42322i	−0.300038	+	0.173227i
$653$	−11.2332	−	6.48551i	−0.439590	−	0.253798i	0.263834	−	0.964568i	$-0.415013\pi$
$653$	−11.2332	−	6.48551i	−0.439590	−	0.253798i	−0.703424	+	0.710771i	$0.748346\pi$
$654$	6.79416	−	30.3591i	0.265673	−	1.18714i
$655$	−15.8901	−	9.17418i	−0.620879	−	0.358465i
$656$		−	8.63047i		−	0.336963i
$657$	−24.2157	−	11.4101i	−0.944745	−	0.445149i
$658$	−0.116664	+	0.0682490i	−0.00454803	+	0.00266062i
$659$	31.7740	+	18.3447i	1.23774	+	0.714609i	0.968631	−	0.248502i	$-0.0799381\pi$
$659$	31.7740	+	18.3447i	1.23774	+	0.714609i	0.269107	+	0.963110i	$0.413271\pi$
$660$	1.03103	−	0.322819i	0.0401329	−	0.0125657i
$661$	−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
$663$	−0.218322	−	2.13034i	−0.00847892	−	0.0827355i
$664$			13.2261i			0.513274i
$665$	10.0232	+	5.71067i	0.388683	+	0.221450i
$666$	−7.44070	−	10.7174i	−0.288321	−	0.415290i
$667$	−26.8263			−1.03872
$668$	−3.95886	−	2.28565i	−0.153173	−	0.0884343i
$669$	−15.8108	−	3.53836i	−0.611282	−	0.136801i
$670$	−5.51688			−0.213136
$671$		−	4.14711i		−	0.160097i
$672$	1.39427	+	4.36532i	0.0537852	+	0.168396i
$673$	−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
$675$	−19.2010	+	7.81871i	−0.739045	+	0.300942i
$676$	11.9605	+	5.09374i	0.460020	+	0.195913i
$677$	5.94798	+	10.3022i	0.228599	+	0.395946i	0.957393	−	0.288787i	$-0.0932521\pi$
$677$	5.94798	+	10.3022i	0.228599	+	0.395946i	−0.728794	+	0.684733i	$0.759919\pi$
$678$	1.86154	−	8.31815i	0.0714922	−	0.319457i
$679$	27.0073	−	0.154564i	1.03644	−	0.00593163i
$680$	0.298476	+	0.172325i	0.0114460	+	0.00660838i
$681$	4.46013	−	19.9297i	0.170913	−	0.763709i
$682$	0.776812	+	1.34548i	0.0297457	+	0.0515210i
$683$	2.21590	+	3.83806i	0.0847892	+	0.146859i	0.905301	−	0.424770i	$-0.139645\pi$
$683$	2.21590	+	3.83806i	0.0847892	+	0.146859i	−0.820512	+	0.571629i	$0.806312\pi$
$684$	−10.6906	+	7.42214i	−0.408767	+	0.283793i
$685$	−7.05567	−	4.07359i	−0.269583	−	0.155644i
$686$	8.98340	−	16.1956i	0.342988	−	0.618352i
$687$	−18.5024	−	4.14070i	−0.705909	−	0.157977i
$688$	−0.602811	−	1.04410i	−0.0229819	−	0.0398059i
$689$	−3.45623	+	16.9363i	−0.131672	+	0.645223i
$690$	−1.46800	−	4.68855i	−0.0558856	−	0.178490i
$691$	−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
$693$	4.03027	−	2.83240i	0.153097	−	0.107594i
$694$			34.7424i			1.31880i
$695$	19.1835			0.727671
$696$	3.59555	−	16.0664i	0.136289	−	0.608996i
$697$	−2.56301	−	1.47975i	−0.0970808	−	0.0560496i
$698$	8.41336			0.318450
$699$	2.36065	−	10.5484i	0.0892880	−	0.398976i
$700$	5.33030	+	9.11152i	0.201466	+	0.344383i
$701$		−	37.0012i		−	1.39751i	−0.715359	−	0.698757i	$-0.753737\pi$
$701$		−	37.0012i		−	1.39751i	0.715359	−	0.698757i	$-0.246263\pi$
$702$	−12.1978	−	14.2202i	−0.460376	−	0.536707i
$703$	−16.3392	−	9.43342i	−0.616243	−	0.355788i
$704$	0.620619			0.0233905
$705$	0.0265726	+	0.0848688i	0.00100078	+	0.00319635i
$706$	−17.1652	−	9.91033i	−0.646021	−	0.372980i
$707$	13.2427	+	22.6369i	0.498044	+	0.851349i
$708$	5.10692	−	1.59899i	0.191930	−	0.0600936i
$709$		−	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
$711$	2.25763	−	1.56740i	0.0846678	−	0.0587819i
$712$	3.11782	+	1.80007i	0.116845	+	0.0674606i
$713$	6.11846	−	3.53250i	0.229138	−	0.132293i
$714$	1.53543	+	0.334404i	0.0574622	+	0.0125148i
$715$	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	$-0.618120\pi$
$719$	−19.4471			−0.725255			−0.362627	+	0.931934i	$0.618120\pi$
$720$	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
$723$	−9.62578	−	2.15418i	−0.357987	−	0.0801149i
$724$	−19.4258	+	11.2155i	−0.721955	+	0.416821i
$725$		−	37.9250i		−	1.40850i
$726$	5.49354	+	17.5455i	0.203884	+	0.651175i
$727$			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
$732$	2.52764	−	11.2946i	0.0934244	−	0.417459i
$733$	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
$735$	−9.06167	−	8.14735i	−0.334245	−	0.300520i
$736$		−	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
$741$	−24.7210	−	11.0834i	−0.908149	−	0.407160i
$742$	−11.0208	−	6.27904i	−0.404586	−	0.230511i
$743$	16.0336	+	27.7710i	0.588216	+	1.01882i	0.994466	+	0.105058i	$0.0335027\pi$
$743$	16.0336	+	27.7710i	0.588216	+	1.01882i	−0.406250	+	0.913762i	$0.633164\pi$
$744$	1.29557	+	4.13784i	0.0474978	+	0.151701i
$745$	−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
$750$	14.9348	−	4.67612i	0.545342	−	0.170748i
$751$	−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
$753$	12.4507	+	39.7656i	0.453729	+	1.44914i
$754$	32.5076	−	10.8554i	1.18386	−	0.395330i
$755$	−7.90216			−0.287589
$756$	12.7027	−	5.25754i	0.461992	−	0.191215i
$757$	−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
$759$	−2.89514	+	0.906474i	−0.105087	+	0.0329029i
$760$	3.77600	−	2.18008i	0.136970	−	0.0790797i
$761$			2.42155i			0.0877812i	0.999036	+	0.0438906i	$0.0139753\pi$
$761$			2.42155i			0.0877812i	−0.999036	+	0.0438906i	$0.986025\pi$
$762$	−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
$765$	0.440711	−	0.935325i	0.0159339	−	0.0338167i
$766$	9.40956	+	5.43261i	0.339981	+	0.196288i
$767$	8.33883	+	7.38642i	0.301098	+	0.266708i
$768$	1.69024	+	0.378264i	0.0609913	+	0.0136494i
$769$	−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
$771$	15.2857	+	48.8200i	0.550500	+	1.75821i
$772$	−10.9286	+	6.30961i	−0.393328	+	0.227088i
$773$	−30.2147	+	17.4444i	−1.08675	+	0.627433i	−0.932708	−	0.360632i	$-0.882561\pi$
$773$	−30.2147	+	17.4444i	−1.08675	+	0.627433i	−0.154037	+	0.988065i	$0.549228\pi$
$774$	−2.97103	+	2.06269i	−0.106792	+	0.0741417i
$775$	4.99398	+	8.64982i	0.179389	+	0.310711i
$776$	5.10398	−	8.84035i	0.183222	−	0.317350i
$777$	14.7438	+	13.4095i	0.528930	+	0.481064i
$778$	−33.7632	+	19.4932i	−1.21047	+	0.698865i
$779$	−32.4244	+	18.7202i	−1.16172	+	0.670722i
$780$	3.67613	+	5.08746i	0.131627	+	0.182160i
$781$	−0.386014	+	0.668596i	−0.0138127	+	0.0239243i
$782$	−0.838121	−	0.483889i	−0.0299711	−	0.0173038i
$783$	−48.9294	−	6.74046i	−1.74859	−	0.240884i
$784$	−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	−0.986039	−	0.166512i	$-0.946750\pi$
$797$	−9.84749	+	17.0564i	−0.348816	+	0.604167i	0.637223	+	0.770679i	$0.280083\pi$
$798$	13.3761	−	14.7070i	0.473508	−	0.520622i
$799$	0.0151711	+	0.00875902i	0.000536714	+	0.000309872i
$800$	3.98984			0.141062
$801$	4.60357	−	9.77020i	0.162659	−	0.345213i
$802$	14.8257	+	25.6788i	0.523512	+	0.906749i
$803$	2.76892	−	4.79590i	0.0977129	−	0.169244i
$804$	−2.07632	+	9.27785i	−0.0732261	+	0.327205i
$805$	3.78950	+	6.47770i	0.133562	+	0.228309i
$806$	−5.98479	+	6.75647i	−0.210805	+	0.237987i
$807$	−10.8438	−	2.42677i	−0.381720	−	0.0854262i
$808$	9.91247			0.348720
$809$			22.6813i			0.797432i	0.917074	+	0.398716i	$0.130544\pi$
$809$			22.6813i			0.797432i	−0.917074	+	0.398716i	$0.869456\pi$
$810$	−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
$813$	10.6802	+	34.1108i	0.374570	+	1.19632i
$814$	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
$819$	23.0241	+	16.9967i	0.804528	+	0.593914i
$820$	8.67419			0.302916
$821$	3.13575	−	5.43128i	0.109439	−	0.189553i	−0.806104	−	0.591773i	$-0.798428\pi$
$821$	3.13575	−	5.43128i	0.109439	−	0.189553i	0.915543	+	0.402220i	$0.131761\pi$
$822$	−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
$825$	−1.28150	−	4.09293i	−0.0446163	−	0.142497i
$826$	−7.05572	+	4.12764i	−0.245500	+	0.143619i
$827$	37.5661			1.30630			0.653150	−	0.757229i	$-0.273447\pi$
$827$	37.5661			1.30630			0.653150	+	0.757229i	$0.273447\pi$
$828$	−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
$831$	20.4104	+	4.56771i	0.708029	+	0.158452i
$832$	1.14202	+	3.41991i	0.0395926	+	0.118564i
$833$	−2.40024	+	0.0274743i	−0.0831633	+	0.000951929i
$834$	7.21985	−	32.2613i	0.250003	−	1.11712i
$835$	2.29723	−	3.97891i	0.0794988	−	0.137696i
$836$	−1.34618	−	2.33165i	−0.0465585	−	0.0806417i
$837$	12.0472	−	4.90569i	0.416414	−	0.169565i
$838$	4.20721			0.145336
$839$	−18.1332	−	10.4692i	−0.626028	−	0.361438i	0.153184	−	0.988198i	$-0.451047\pi$
$839$	−18.1332	−	10.4692i	−0.626028	−	0.361438i	−0.779212	+	0.626760i	$0.784381\pi$
$840$	−4.38743	+	1.40134i	−0.151381	+	0.0483507i
$841$	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
$855$	−7.45974	−	10.7448i	−0.255118	−	0.367464i
$856$	12.7443	+	7.35793i	0.435591	+	0.251489i
$857$	−4.35323	+	7.54001i	−0.148703	+	0.257562i	−0.930749	−	0.365660i	$-0.880843\pi$
$857$	−4.35323	+	7.54001i	−0.148703	+	0.257562i	0.782045	+	0.623222i	$0.214177\pi$
$858$	3.14146	−	2.26998i	0.107248	−	0.0774957i
$859$	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
$861$	37.6747	−	12.0332i	1.28395	−	0.410091i
$862$	−3.37233	+	5.84104i	−0.114862	+	0.198947i
$863$	5.26328	+	9.11626i	0.179164	+	0.310321i	0.941594	−	0.336749i	$-0.109327\pi$
$863$	5.26328	+	9.11626i	0.179164	+	0.310321i	−0.762430	+	0.647070i	$0.775994\pi$
$864$	0.709119	−	5.14754i	0.0241247	−	0.175123i
$865$	11.4228	−	6.59496i	0.388387	−	0.224235i
$866$	−25.4298	+	14.6819i	−0.864139	+	0.498911i
$867$	8.73723	+	27.9053i	0.296732	+	0.947715i
$868$	−3.34439	−	5.71684i	−0.113516	−	0.194042i
$869$	0.284284	+	0.492394i	0.00964366	+	0.0167033i
$870$	16.1478	+	3.61376i	0.547462	+	0.122518i
$871$	−18.7721	+	6.26865i	−0.636069	+	0.212405i
$872$	15.5550	+	8.98070i	0.526760	+	0.304125i
$873$	−27.7027	−	13.0531i	−0.937594	−	0.441780i
$874$	−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
$879$	27.4327	−	8.58925i	0.925283	−	0.289708i
$880$			0.623763i			0.0210271i
$881$	−14.5503	−	25.2019i	−0.490214	−	0.849075i	0.509723	−	0.860339i	$-0.329748\pi$
$881$	−14.5503	−	25.2019i	−0.490214	−	0.849075i	−0.999937	+	0.0112637i	$0.996415\pi$
$882$	−17.1120	+	12.1729i	−0.576191	+	0.409882i
$883$	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
$885$	1.60709	+	5.13279i	0.0540217	+	0.172537i
$886$			23.5604i			0.791528i
$887$	7.19356	−	12.4596i	0.241536	−	0.418353i	−0.719616	−	0.694372i	$-0.755682\pi$
$887$	7.19356	−	12.4596i	0.241536	−	0.418353i	0.961152	+	0.276020i	$0.0890155\pi$
$888$	7.18861	−	2.25077i	0.241234	−	0.0755309i
$889$	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
$894$	2.42836	+	7.75579i	0.0812163	+	0.259392i
$895$	−9.83591	−	17.0363i	−0.328778	−	0.569461i
$896$	−2.64571	+	0.0151415i	−0.0883869	+	0.000505843i
$897$	−10.3226	−	14.2856i	−0.344660	−	0.476981i
$898$	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
$903$	3.71734	−	4.08722i	0.123705	−	0.136014i
$904$	4.26195	+	2.46064i	0.141750	+	0.0818397i
$905$	−11.2723	−	19.5242i	−0.374705	−	0.649008i
$906$	−2.97404	+	13.2892i	−0.0988059	+	0.441505i
$907$	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	$0.119925\pi$
$911$			22.2089i			0.735813i	−0.929863	+	0.367906i	$0.880075\pi$
$912$	−2.24515	−	7.17067i	−0.0743445	−	0.237445i
$913$			8.20840i			0.271658i
$914$	27.5421	−	15.9014i	0.911012	−	0.525973i
$915$	11.3518	+	2.54045i	0.375278	+	0.0839846i
$916$	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
$924$	0.865312	+	2.70920i	0.0284667	+	0.0891262i
$925$	15.0272	−	8.67596i	0.494092	−	0.285264i
$926$	23.4328	+	13.5289i	0.770048	+	0.444588i
$927$	−17.6468	−	25.4180i	−0.579597	−	0.834835i
$928$	8.23191	+	4.75270i	0.270226	+	0.156015i
$929$			52.6745i			1.72819i	0.503325	+	0.864097i	$0.332110\pi$
$929$			52.6745i			1.72819i	−0.503325	+	0.864097i	$0.667890\pi$
$930$	−4.15880	+	1.30213i	−0.136372	+	0.0426985i
$931$	−14.8816	+	26.4709i	−0.487725	+	0.867547i
$932$	5.40464	+	3.12037i	0.177035	+	0.102211i
$933$	−7.13339	−	22.7829i	−0.233537	−	0.745880i
$934$	31.6225			1.03472
$935$	0.185240	+	0.106948i	0.00605800	+	0.00349759i
$936$	9.93923	−	4.26752i	0.324874	−	0.139488i
$937$		−	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
$939$	−3.46476	+	15.4820i	−0.113068	+	0.505235i
$940$	−0.0513447			−0.00167468
$941$	−46.2726	−	26.7155i	−1.50844	−	0.870900i	−0.999952	−	0.00983388i	$-0.996870\pi$
$941$	−46.2726	−	26.7155i	−1.50844	−	0.870900i	−0.508492	−	0.861067i	$-0.669797\pi$
$942$	−8.68896	+	38.8259i	−0.283102	+	1.26502i
$943$	−24.3571			−0.793176
$944$			3.08963i			0.100559i
$945$	5.28417	+	12.7670i	0.171894	+	0.415312i
$946$	−0.374116	−	0.647988i	−0.0121636	−	0.0210679i
$947$	−27.2913	+	47.2700i	−0.886849	+	1.53607i	−0.0432691	+	0.999063i	$0.513777\pi$
$947$	−27.2913	+	47.2700i	−0.886849	+	1.53607i	−0.843580	+	0.537004i	$0.819556\pi$
$948$	0.474128	+	1.51429i	0.0153990	+	0.0491819i
$949$	31.5229	+	6.43294i	1.02328	+	0.208822i
$950$	−8.65432	−	14.9897i	−0.280783	−	0.486331i
$951$	−8.01431	−	1.79355i	−0.259882	−	0.0581598i
$952$	−0.449128	+	0.788297i	−0.0145563	+	0.0255489i
$953$	0.882484	+	0.509502i	0.0285865	+	0.0165044i	0.514225	−	0.857655i	$-0.328080\pi$
$953$	0.882484	+	0.509502i	0.0285865	+	0.0165044i	−0.485639	+	0.874160i	$0.661413\pi$
$954$	8.20218	+	11.8142i	0.265556	+	0.382499i
$955$	−6.60400	−	11.4385i	−0.213700	−	0.370140i
$956$	15.2312	+	26.3812i	0.492612	+	0.853230i
$957$	2.23147	−	9.97112i	0.0721331	−	0.322321i
$958$	9.21963	+	5.32296i	0.297873	+	0.171977i
$959$	10.6169	−	18.6345i	0.342838	−	0.601740i
$960$	−0.380181	+	1.69880i	−0.0122703	+	0.0548287i
$961$	12.3666	+	21.4196i	0.398924	+	0.690956i
$962$	11.7379	+	10.3973i	0.378446	+	0.335222i
$963$	18.8174	−	39.9364i	0.606382	−	1.28693i
$964$	2.84746	−	4.93194i	0.0917104	−	0.158847i
$965$	−6.34158	−	10.9839i	−0.204143	−	0.353585i
$966$	12.3199	−	3.93494i	0.396386	−	0.126605i
$967$		−	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
$969$	−2.51444	−	0.562713i	−0.0807753	−	0.0180770i
$970$	8.88514	+	5.12984i	0.285285	+	0.164709i
$971$	−18.9083			−0.606797			−0.303399	−	0.952864i	$-0.598121\pi$
$971$	−18.9083			−0.606797			−0.303399	+	0.952864i	$0.598121\pi$
$972$	−15.5660	−	0.835596i	−0.499281	−	0.0268018i
$973$	0.289003	+	50.4980i	0.00926502	+	1.61889i
$974$		−	39.5929i		−	1.26864i
$975$	20.1958	−	14.5932i	0.646785	−	0.467358i
$976$	5.78697	+	3.34111i	0.185236	+	0.106946i
$977$	50.6394			1.62010			0.810049	−	0.586363i	$-0.199441\pi$
$977$	50.6394			1.62010			0.810049	+	0.586363i	$0.199441\pi$
$978$	−14.6225	+	4.57834i	−0.467576	+	0.146399i
$979$	1.93498	+	1.11716i	0.0618422	+	0.0357046i
$980$	6.05223	−	3.58724i	0.193331	−	0.114590i
$981$	22.9675	−	48.7442i	0.733297	−	1.55628i
$982$			31.8461i			1.01625i
$983$	21.4061	+	12.3588i	0.682750	+	0.394186i	0.800890	−	0.598811i	$-0.204360\pi$
$983$	21.4061	+	12.3588i	0.682750	+	0.394186i	−0.118140	+	0.992997i	$0.537693\pi$
$984$	3.26460	−	14.5876i	0.104072	−	0.465035i
$985$	−1.20759	−	0.697201i	−0.0384770	−	0.0222147i
$986$	2.82283	−	1.62976i	0.0898974	−	0.0519023i
$987$	−0.223006	+	0.0712276i	−0.00709836	+	0.00226720i
$988$	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
$996$	−5.00298	+	22.3554i	−0.158525	+	0.708357i
$997$	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
$999$	−8.52258	−	20.9295i	−0.269643	−	0.662180i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.17271 + 1.27466i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.870413 - 0.502533i) q^{5} +(-0.517534 - 1.65292i) q^{6} +(1.33597 + 2.28368i) q^{7} +1.00000 q^{8} +(-0.249516 - 2.98961i) q^{9} +O(q^{10})\)	\(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} +(-0.517534 - 1.65292i) 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} +(1.69024 + 0.378264i) q^{12} +(1.14202 + 3.41991i) q^{13} +(-2.64571 + 0.0151415i) q^{14} +(-0.380181 + 1.69880i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.171457 + 0.296972i) q^{17} +(2.71383 + 1.27872i) q^{18} +4.33817 q^{19} +(-0.870413 - 0.502533i) q^{20} +(-4.47761 - 0.975184i) 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} +(-2.46432 + 1.71089i) q^{36} +(-3.76637 - 2.17451i) q^{37} +(-2.16909 + 3.75697i) q^{38} +(-5.69848 - 2.55486i) q^{39} +(0.870413 - 0.502533i) q^{40} +(-7.47421 + 4.31523i) q^{41} +(3.08334 - 3.39013i) q^{42} +(-0.602811 + 1.04410i) q^{43} +(-0.310310 - 0.537472i) q^{44} +(-1.71956 - 2.47680i) q^{45} +(-2.44412 + 1.41111i) q^{46} +(0.0442417 - 0.0255429i) q^{47} +(-0.517534 - 1.65292i) q^{48} +(-3.43038 + 6.10184i) q^{49} +(-1.99492 - 3.45530i) q^{50} +(-0.579607 - 0.129712i) q^{51} +(2.39072 - 2.69898i) q^{52} +(4.15182 + 2.39705i) q^{53} +(-4.81246 + 1.95965i) 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} +(1.66130 - 0.520156i) q^{60} -6.68221i q^{61} +(1.25167 + 2.16796i) q^{62} +(6.49396 - 4.56383i) q^{63} +1.00000 q^{64} +(2.71265 + 2.40283i) q^{65} +(-0.321192 - 1.02584i) q^{66} +5.48907i q^{67} +(0.171457 - 0.296972i) q^{68} +(-4.66492 + 1.46060i) 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} +(-2.06488 - 6.59491i) q^{75} +(-2.16909 - 3.75697i) q^{76} +(0.829127 + 1.41730i) q^{77} +(5.06181 - 3.65760i) 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} +(1.39427 + 4.36532i) q^{84} +(0.298476 + 0.172325i) q^{85} +(-0.602811 - 1.04410i) q^{86} +(3.59555 - 16.0664i) 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} +(1.29557 + 4.13784i) q^{93} +0.0510859i q^{94} +(3.77600 - 2.18008i) q^{95} +(1.69024 + 0.378264i) q^{96} +(5.10398 - 8.84035i) q^{97} +(-3.56916 - 6.02172i) q^{98} +(-0.154854 - 1.85541i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9}+O(q^{10}) \) 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9	\( 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9} - 18 q^{11} + 3 q^{12} - 8 q^{13} - 4 q^{14} - 17 q^{15} - 17 q^{16} + 6 q^{17} - 11 q^{18} - 10 q^{19} - 9 q^{20} - 4 q^{21} + 9 q^{22} + 6 q^{23} + 3 q^{24} + 16 q^{25} + 13 q^{26} + 18 q^{27} - q^{28} + 27 q^{29} + 13 q^{30} + q^{31} - 17 q^{32} + 21 q^{33} - 12 q^{34} - 3 q^{35} + 4 q^{36} + 6 q^{37} + 5 q^{38} + 20 q^{39} + 9 q^{40} + 3 q^{41} + 20 q^{42} - 3 q^{43} + 9 q^{44} - 6 q^{46} - 27 q^{47} - 6 q^{48} - 5 q^{49} + 16 q^{50} + 24 q^{51} - 5 q^{52} + 21 q^{53} - 18 q^{54} + 57 q^{55} + 5 q^{56} - 17 q^{57} - 6 q^{59} + 4 q^{60} + q^{62} - 21 q^{63} + 34 q^{64} + 33 q^{65} - 21 q^{66} + 6 q^{68} - 30 q^{69} + 3 q^{70} - 15 q^{71} + 7 q^{72} + 19 q^{73} - 6 q^{74} - 63 q^{75} + 5 q^{76} - 9 q^{77} - 10 q^{78} - 9 q^{79} - 5 q^{81} - 16 q^{84} - 42 q^{85} - 3 q^{86} - 75 q^{87} - 18 q^{88} - 18 q^{89} - 9 q^{90} - 27 q^{91} + 25 q^{93} - 3 q^{95} + 3 q^{96} - 19 q^{97} + 7 q^{98} - 27 q^{99}+O(q^{100}) \) 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9 - 18 * q^11 + 3 * q^12 - 8 * q^13 - 4 * q^14 - 17 * q^15 - 17 * q^16 + 6 * q^17 - 11 * q^18 - 10 * q^19 - 9 * q^20 - 4 * 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 + 4 * q^36 + 6 * q^37 + 5 * q^38 + 20 * q^39 + 9 * q^40 + 3 * q^41 + 20 * q^42 - 3 * q^43 + 9 * q^44 - 6 * q^46 - 27 * q^47 - 6 * q^48 - 5 * q^49 + 16 * q^50 + 24 * q^51 - 5 * q^52 + 21 * q^53 - 18 * q^54 + 57 * q^55 + 5 * q^56 - 17 * q^57 - 6 * q^59 + 4 * q^60 + q^62 - 21 * q^63 + 34 * q^64 + 33 * q^65 - 21 * q^66 + 6 * q^68 - 30 * q^69 + 3 * q^70 - 15 * q^71 + 7 * q^72 + 19 * q^73 - 6 * q^74 - 63 * q^75 + 5 * q^76 - 9 * q^77 - 10 * q^78 - 9 * q^79 - 5 * q^81 - 16 * q^84 - 42 * q^85 - 3 * q^86 - 75 * q^87 - 18 * q^88 - 18 * q^89 - 9 * q^90 - 27 * q^91 + 25 * q^93 - 3 * q^95 + 3 * q^96 - 19 * q^97 + 7 * q^98 - 27 * q^99

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