LMFDB - Embedded newform 546.2.bi.f.257.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(17,546)]

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, 1]))

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

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

chi := DirichletCharacter("546.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bi (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			257.10
Character	$\chi$	$=$	546.257
Dual form			546.2.bi.f.17.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(0.517534 + 1.65292i) q^{3} +1.00000 q^{4} +(0.870413 + 0.502533i) q^{5} +(0.517534 + 1.65292i) q^{6} +(2.64571 + 0.0151415i) q^{7} +1.00000 q^{8} +(-2.46432 + 1.71089i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(0.517534 + 1.65292i) q^{3} +1.00000 q^{4} +(0.870413 + 0.502533i) q^{5} +(0.517534 + 1.65292i) q^{6} +(2.64571 + 0.0151415i) q^{7} +1.00000 q^{8} +(-2.46432 + 1.71089i) q^{9} +(0.870413 + 0.502533i) q^{10} +(-0.310310 + 0.537472i) q^{11} +(0.517534 + 1.65292i) q^{12} +(-1.14202 - 3.41991i) q^{13} +(2.64571 + 0.0151415i) q^{14} +(-0.380181 + 1.69880i) q^{15} +1.00000 q^{16} +0.342914 q^{17} +(-2.46432 + 1.71089i) q^{18} +(2.16909 + 3.75697i) q^{19} +(0.870413 + 0.502533i) q^{20} +(1.34422 + 4.38099i) q^{21} +(-0.310310 + 0.537472i) q^{22} -2.82222i q^{23} +(0.517534 + 1.65292i) q^{24} +(-1.99492 - 3.45530i) q^{25} +(-1.14202 - 3.41991i) q^{26} +(-4.10334 - 3.18788i) q^{27} +(2.64571 + 0.0151415i) q^{28} +(-8.23191 + 4.75270i) q^{29} +(-0.380181 + 1.69880i) q^{30} +(-1.25167 - 2.16796i) q^{31} +1.00000 q^{32} +(-1.04900 - 0.234758i) q^{33} +0.342914 q^{34} +(2.29525 + 1.34273i) q^{35} +(-2.46432 + 1.71089i) q^{36} +4.34903i q^{37} +(2.16909 + 3.75697i) q^{38} +(5.06181 - 3.65760i) q^{39} +(0.870413 + 0.502533i) q^{40} +(7.47421 - 4.31523i) q^{41} +(1.34422 + 4.38099i) q^{42} +(-0.602811 + 1.04410i) q^{43} +(-0.310310 + 0.537472i) q^{44} +(-3.00475 + 0.250780i) q^{45} -2.82222i q^{46} +(0.0442417 + 0.0255429i) q^{47} +(0.517534 + 1.65292i) q^{48} +(6.99954 + 0.0801202i) q^{49} +(-1.99492 - 3.45530i) q^{50} +(0.177470 + 0.566810i) q^{51} +(-1.14202 - 3.41991i) q^{52} +(-4.15182 + 2.39705i) q^{53} +(-4.10334 - 3.18788i) q^{54} +(-0.540195 + 0.311882i) q^{55} +(2.64571 + 0.0151415i) q^{56} +(-5.08741 + 5.52970i) q^{57} +(-8.23191 + 4.75270i) q^{58} -3.08963i q^{59} +(-0.380181 + 1.69880i) q^{60} +(5.78697 - 3.34111i) q^{61} +(-1.25167 - 2.16796i) q^{62} +(-6.54577 + 4.48920i) q^{63} +1.00000 q^{64} +(0.724585 - 3.55064i) q^{65} +(-1.04900 - 0.234758i) q^{66} +(-4.75367 - 2.74453i) q^{67} +0.342914 q^{68} +(4.66492 - 1.46060i) q^{69} +(2.29525 + 1.34273i) q^{70} +(-0.621982 + 1.07730i) q^{71} +(-2.46432 + 1.71089i) q^{72} +(-4.46154 - 7.72761i) q^{73} +4.34903i q^{74} +(4.67892 - 5.08569i) 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} +(0.870413 + 0.502533i) q^{80} +(3.14571 - 8.43235i) q^{81} +(7.47421 - 4.31523i) q^{82} -13.2261i q^{83} +(1.34422 + 4.38099i) q^{84} +(0.298476 + 0.172325i) q^{85} +(-0.602811 + 1.04410i) q^{86} +(-12.1161 - 11.1470i) q^{87} +(-0.310310 + 0.537472i) q^{88} +3.60015i q^{89} +(-3.00475 + 0.250780i) q^{90} +(-2.96968 - 9.06537i) q^{91} -2.82222i q^{92} +(2.93569 - 3.19091i) q^{93} +(0.0442417 + 0.0255429i) q^{94} +4.36015i q^{95} +(0.517534 + 1.65292i) q^{96} +(-5.10398 + 8.84035i) q^{97} +(6.99954 + 0.0801202i) q^{98} +(-0.154854 - 1.85541i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9}+O(q^{10}) $ 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9	$ 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9} + 9 q^{10} + 9 q^{11} + 6 q^{12} + 8 q^{13} + 4 q^{14} - 17 q^{15} + 34 q^{16} + 12 q^{17} + 4 q^{18} - 5 q^{19} + 9 q^{20} - 7 q^{21} + 9 q^{22} + 6 q^{24} + 16 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} + 27 q^{29} - 17 q^{30} - q^{31} + 34 q^{32} + 12 q^{34} - 3 q^{35} + 4 q^{36} - 5 q^{38} - 10 q^{39} + 9 q^{40} - 3 q^{41} - 7 q^{42} - 3 q^{43} + 9 q^{44} + 9 q^{45} - 27 q^{47} + 6 q^{48} - 2 q^{49} + 16 q^{50} - 36 q^{51} + 8 q^{52} - 21 q^{53} - 18 q^{54} - 57 q^{55} + 4 q^{56} - 17 q^{57} + 27 q^{58} - 17 q^{60} - 51 q^{61} - q^{62} - 24 q^{63} + 34 q^{64} - 21 q^{65} - 21 q^{67} + 12 q^{68} + 30 q^{69} - 3 q^{70} - 15 q^{71} + 4 q^{72} - 19 q^{73} - 54 q^{75} - 5 q^{76} + 9 q^{77} - 10 q^{78} - 9 q^{79} + 9 q^{80} + 28 q^{81} - 3 q^{82} - 7 q^{84} - 42 q^{85} - 3 q^{86} - 81 q^{87} + 9 q^{88} + 9 q^{90} - 72 q^{91} - 17 q^{93} - 27 q^{94} + 6 q^{96} + 19 q^{97} - 2 q^{98} - 27 q^{99}+O(q^{100}) $ 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9 + 9 * q^10 + 9 * q^11 + 6 * q^12 + 8 * q^13 + 4 * q^14 - 17 * q^15 + 34 * q^16 + 12 * q^17 + 4 * q^18 - 5 * q^19 + 9 * q^20 - 7 * q^21 + 9 * q^22 + 6 * q^24 + 16 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 + 27 * q^29 - 17 * q^30 - q^31 + 34 * q^32 + 12 * q^34 - 3 * q^35 + 4 * q^36 - 5 * q^38 - 10 * q^39 + 9 * q^40 - 3 * q^41 - 7 * q^42 - 3 * q^43 + 9 * q^44 + 9 * q^45 - 27 * q^47 + 6 * q^48 - 2 * q^49 + 16 * q^50 - 36 * q^51 + 8 * q^52 - 21 * q^53 - 18 * q^54 - 57 * q^55 + 4 * q^56 - 17 * q^57 + 27 * q^58 - 17 * q^60 - 51 * q^61 - q^62 - 24 * q^63 + 34 * q^64 - 21 * q^65 - 21 * q^67 + 12 * q^68 + 30 * q^69 - 3 * q^70 - 15 * q^71 + 4 * q^72 - 19 * q^73 - 54 * q^75 - 5 * q^76 + 9 * q^77 - 10 * q^78 - 9 * q^79 + 9 * q^80 + 28 * q^81 - 3 * q^82 - 7 * q^84 - 42 * q^85 - 3 * q^86 - 81 * q^87 + 9 * q^88 + 9 * q^90 - 72 * q^91 - 17 * q^93 - 27 * q^94 + 6 * q^96 + 19 * q^97 - 2 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	0.517534	+	1.65292i	0.298799	+	0.954316i
$3$	0.517534	+	1.65292i	0.298799	+	0.954316i
$4$	1.00000			0.500000
$5$	0.870413	+	0.502533i	0.389260	+	0.224740i	0.681840	−	0.731502i	$-0.261180\pi$
$5$	0.870413	+	0.502533i	0.389260	+	0.224740i	−0.292579	+	0.956241i	$0.594514\pi$
$6$	0.517534	+	1.65292i	0.211282	+	0.674803i
$7$	2.64571	+	0.0151415i	0.999984	+	0.00572296i
$7$	2.64571	+	0.0151415i	0.999984	+	0.00572296i
$8$	1.00000			0.353553
$9$	−2.46432	+	1.71089i	−0.821439	+	0.570297i
$10$	0.870413	+	0.502533i	0.275249	+	0.158915i
$11$	−0.310310	+	0.537472i	−0.0935619	+	0.162054i	−0.909007	−	0.416780i	$-0.863159\pi$
$11$	−0.310310	+	0.537472i	−0.0935619	+	0.162054i	0.815446	+	0.578834i	$0.196492\pi$
$12$	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
$15$	−0.380181	+	1.69880i	−0.0981622	+	0.438629i
$16$	1.00000			0.250000
$17$	0.342914			0.0831688			0.0415844	−	0.999135i	$-0.486759\pi$
$17$	0.342914			0.0831688			0.0415844	+	0.999135i	$0.486759\pi$
$18$	−2.46432	+	1.71089i	−0.580845	+	0.403261i
$19$	2.16909	+	3.75697i	0.497623	+	0.861908i	0.999996	−	0.00274283i	$-0.000873072\pi$
$19$	2.16909	+	3.75697i	0.497623	+	0.861908i	−0.502373	+	0.864651i	$0.667540\pi$
$20$	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
$23$		−	2.82222i		−	0.588474i	−0.955733	−	0.294237i	$-0.904935\pi$
$23$		−	2.82222i		−	0.588474i	0.955733	−	0.294237i	$-0.0950655\pi$
$24$	0.517534	+	1.65292i	0.105641	+	0.337402i
$25$	−1.99492	−	3.45530i	−0.398984	−	0.691061i
$26$	−1.14202	−	3.41991i	−0.223969	−	0.670699i
$27$	−4.10334	−	3.18788i	−0.789688	−	0.613509i
$28$	2.64571	+	0.0151415i	0.499992	+	0.00286148i
$29$	−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	$0.989156\pi$
$30$	−0.380181	+	1.69880i	−0.0694112	+	0.310158i
$31$	−1.25167	−	2.16796i	−0.224807	−	0.389377i	0.731454	−	0.681890i	$-0.238842\pi$
$31$	−1.25167	−	2.16796i	−0.224807	−	0.389377i	−0.956262	+	0.292513i	$0.905509\pi$
$32$	1.00000			0.176777
$33$	−1.04900	−	0.234758i	−0.182607	−	0.0408661i
$34$	0.342914			0.0588092
$35$	2.29525	+	1.34273i	0.387968	+	0.226964i
$36$	−2.46432	+	1.71089i	−0.410719	+	0.285148i
$37$			4.34903i			0.714975i	0.933918	+	0.357488i	$0.116367\pi$
$37$			4.34903i			0.714975i	−0.933918	+	0.357488i	$0.883633\pi$
$38$	2.16909	+	3.75697i	0.351872	+	0.609461i
$39$	5.06181	−	3.65760i	0.810539	−	0.585685i
$40$	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	$0.0979398\pi$
$42$	1.34422	+	4.38099i	0.207417	+	0.676002i
$43$	−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
$45$	−3.00475	+	0.250780i	−0.447922	+	0.0373840i
$46$		−	2.82222i		−	0.416114i
$47$	0.0442417	+	0.0255429i	0.00645331	+	0.00372582i	0.503223	−	0.864156i	$-0.332147\pi$
$47$	0.0442417	+	0.0255429i	0.00645331	+	0.00372582i	−0.496770	+	0.867882i	$0.665481\pi$
$48$	0.517534	+	1.65292i	0.0746996	+	0.238579i
$49$	6.99954	+	0.0801202i	0.999934	+	0.0114457i
$50$	−1.99492	−	3.45530i	−0.282124	−	0.488654i
$51$	0.177470	+	0.566810i	0.0248507	+	0.0793693i
$52$	−1.14202	−	3.41991i	−0.158370	−	0.474256i
$53$	−4.15182	+	2.39705i	−0.570296	+	0.329260i	−0.757267	−	0.653105i	$-0.773466\pi$
$53$	−4.15182	+	2.39705i	−0.570296	+	0.329260i	0.186972	+	0.982365i	$0.440133\pi$
$54$	−4.10334	−	3.18788i	−0.558394	−	0.433816i
$55$	−0.540195	+	0.311882i	−0.0728399	+	0.0420541i
$56$	2.64571	+	0.0151415i	0.353548	+	0.00202337i
$57$	−5.08741	+	5.52970i	−0.673844	+	0.732426i
$58$	−8.23191	+	4.75270i	−1.08090	+	0.624059i
$59$		−	3.08963i		−	0.402235i	−0.979567	−	0.201118i	$-0.935543\pi$
$59$		−	3.08963i		−	0.402235i	0.979567	−	0.201118i	$-0.0644573\pi$
$60$	−0.380181	+	1.69880i	−0.0490811	+	0.219315i
$61$	5.78697	−	3.34111i	0.740945	−	0.427785i	−0.0814678	−	0.996676i	$-0.525961\pi$
$61$	5.78697	−	3.34111i	0.740945	−	0.427785i	0.822413	+	0.568891i	$0.192627\pi$
$62$	−1.25167	−	2.16796i	−0.158963	−	0.275331i
$63$	−6.54577	+	4.48920i	−0.824689	+	0.565586i
$64$	1.00000			0.125000
$65$	0.724585	−	3.55064i	0.0898737	−	0.440402i
$66$	−1.04900	−	0.234758i	−0.129123	−	0.0288967i
$67$	−4.75367	−	2.74453i	−0.580754	−	0.335298i	0.180679	−	0.983542i	$-0.442170\pi$
$67$	−4.75367	−	2.74453i	−0.580754	−	0.335298i	−0.761433	+	0.648244i	$0.775504\pi$
$68$	0.342914			0.0415844
$69$	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	$0.190184\pi$
$72$	−2.46432	+	1.71089i	−0.290423	+	0.201630i
$73$	−4.46154	−	7.72761i	−0.522183	−	0.904448i	−0.999667	−	0.0258074i	$-0.991784\pi$
$73$	−4.46154	−	7.72761i	−0.522183	−	0.904448i	0.477484	−	0.878641i	$-0.341549\pi$
$74$			4.34903i			0.505564i
$75$	4.67892	−	5.08569i	0.540275	−	0.587245i
$76$	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	−0.839106	−	0.543967i	$-0.816922\pi$
$79$	0.458065	−	0.793391i	0.0515363	−	0.0892635i	0.890643	+	0.454704i	$0.150255\pi$
$80$	0.870413	+	0.502533i	0.0973151	+	0.0561849i
$81$	3.14571	−	8.43235i	0.349524	−	0.936928i
$82$	7.47421	−	4.31523i	0.825388	−	0.476538i
$83$		−	13.2261i		−	1.45176i	−0.687822	−	0.725879i	$-0.741433\pi$
$83$		−	13.2261i		−	1.45176i	0.687822	−	0.725879i	$-0.258567\pi$
$84$	1.34422	+	4.38099i	0.146666	+	0.478005i
$85$	0.298476	+	0.172325i	0.0323743	+	0.0186913i
$86$	−0.602811	+	1.04410i	−0.0650028	+	0.112588i
$87$	−12.1161	−	11.1470i	−1.29899	−	1.19509i
$88$	−0.310310	+	0.537472i	−0.0330791	+	0.0572947i
$89$			3.60015i			0.381615i	0.981627	+	0.190807i	$0.0611106\pi$
$89$			3.60015i			0.381615i	−0.981627	+	0.190807i	$0.938889\pi$
$90$	−3.00475	+	0.250780i	−0.316729	+	0.0264345i
$91$	−2.96968	−	9.06537i	−0.311307	−	0.950309i
$92$		−	2.82222i		−	0.294237i
$93$	2.93569	−	3.19091i	0.304417	−	0.330882i
$94$	0.0442417	+	0.0255429i	0.00456318	+	0.00263455i
$95$			4.36015i			0.447342i
$96$	0.517534	+	1.65292i	0.0528206	+	0.168701i
$97$	−5.10398	+	8.84035i	−0.518231	+	0.897602i	0.481545	+	0.876421i	$0.340076\pi$
$97$	−5.10398	+	8.84035i	−0.518231	+	0.897602i	−0.999776	+	0.0211806i	$0.993258\pi$
$98$	6.99954	+	0.0801202i	0.707060	+	0.00809336i
$99$	−0.154854	−	1.85541i	−0.0155634	−	0.186475i
$100$	−1.99492	−	3.45530i	−0.199492	−	0.345530i
$101$	4.95624	−	8.58446i	0.493164	−	0.854185i	−0.506805	−	0.862061i	$-0.669174\pi$
$101$	4.95624	−	8.58446i	0.493164	−	0.854185i	0.999969	+	0.00787556i	$0.00250689\pi$
$102$	0.177470	+	0.566810i	0.0175721	+	0.0561226i
$103$	8.93253	+	5.15720i	0.880149	+	0.508154i	0.870707	−	0.491801i	$-0.163661\pi$
$103$	8.93253	+	5.15720i	0.880149	+	0.508154i	0.00944127	+	0.999955i	$0.496995\pi$
$104$	−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
$107$		−	14.7159i		−	1.42264i	−0.702871	−	0.711318i	$-0.748099\pi$
$107$		−	14.7159i		−	1.42264i	0.702871	−	0.711318i	$-0.251901\pi$
$108$	−4.10334	−	3.18788i	−0.394844	−	0.306754i
$109$	−15.5550	+	8.98070i	−1.48990	+	0.860195i	−0.999933	−	0.0115450i	$-0.996325\pi$
$109$	−15.5550	+	8.98070i	−1.48990	+	0.860195i	−0.489968	+	0.871740i	$0.662992\pi$
$110$	−0.540195	+	0.311882i	−0.0515056	+	0.0297367i
$111$	−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	$0.592311\pi$
$114$	−5.08741	+	5.52970i	−0.476479	+	0.517904i
$115$	1.41826	−	2.45650i	0.132253	−	0.229070i
$116$	−8.23191	+	4.75270i	−0.764314	+	0.441277i
$117$	8.66540	+	6.47386i	0.801116	+	0.598509i
$118$		−	3.08963i		−	0.284423i
$119$	0.907250	+	0.00519224i	0.0831674	+	0.000475972i
$120$	−0.380181	+	1.69880i	−0.0347056	+	0.155079i
$121$	5.30742	+	9.19271i	0.482492	+	0.835701i
$122$	5.78697	−	3.34111i	0.523927	−	0.302490i
$123$	11.0009	+	10.1210i	0.991919	+	0.912581i
$124$	−1.25167	−	2.16796i	−0.112404	−	0.194689i
$125$		−	9.03538i		−	0.808149i
$126$	−6.54577	+	4.48920i	−0.583143	+	0.399930i
$127$	−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	$0.912924\pi$
$128$	1.00000			0.0883883
$129$	−2.03779	−	0.456044i	−0.179418	−	0.0401524i
$130$	0.724585	−	3.55064i	0.0635503	−	0.311411i
$131$	9.12794	−	15.8101i	0.797512	−	1.38133i	−0.123720	−	0.992317i	$-0.539483\pi$
$131$	9.12794	−	15.8101i	0.797512	−	1.38133i	0.921232	−	0.389014i	$-0.127184\pi$
$132$	−1.04900	−	0.234758i	−0.0913034	−	0.0204331i
$133$	5.68189	+	9.97269i	0.492682	+	0.864742i
$134$	−4.75367	−	2.74453i	−0.410655	−	0.237092i
$135$	−1.96958	−	4.83684i	−0.169515	−	0.416289i
$136$	0.342914			0.0294046
$137$	8.10612			0.692553			0.346276	−	0.938133i	$-0.387446\pi$
$137$	8.10612			0.692553			0.346276	+	0.938133i	$0.387446\pi$
$138$	4.66492	−	1.46060i	0.397104	−	0.124334i
$139$	−16.5296	−	9.54339i	−1.40203	−	0.809460i	−0.407425	−	0.913239i	$-0.633573\pi$
$139$	−16.5296	−	9.54339i	−1.40203	−	0.809460i	−0.994600	+	0.103779i	$0.966907\pi$
$140$	2.29525	+	1.34273i	0.193984	+	0.113482i
$141$	−0.0193240	+	0.0863474i	−0.00162737	+	0.00727177i
$142$	−0.621982	+	1.07730i	−0.0521956	+	0.0904054i
$143$	2.19249	+	0.447425i	0.183345	+	0.0374155i
$144$	−2.46432	+	1.71089i	−0.205360	+	0.142574i
$145$	−9.55354			−0.793379
$146$	−4.46154	−	7.72761i	−0.369239	−	0.639541i
$147$	3.49007	+	11.6112i	0.287856	+	0.957674i
$148$			4.34903i			0.357488i
$149$	2.34608	+	4.06353i	0.192198	+	0.332898i	0.945979	−	0.324229i	$-0.105105\pi$
$149$	2.34608	+	4.06353i	0.192198	+	0.332898i	−0.753780	+	0.657127i	$0.771772\pi$
$150$	4.67892	−	5.08569i	0.382032	−	0.415245i
$151$	6.80898	−	3.93117i	0.554107	−	0.319914i	−0.196670	−	0.980470i	$-0.563013\pi$
$151$	6.80898	−	3.93117i	0.554107	−	0.319914i	0.750777	+	0.660556i	$0.229679\pi$
$152$	2.16909	+	3.75697i	0.175936	+	0.304730i
$153$	−0.845048	+	0.586688i	−0.0683181	+	0.0474309i
$154$	−0.829127	+	1.41730i	−0.0668129	+	0.114209i
$155$		−	2.51603i		−	0.202092i
$156$	5.06181	−	3.65760i	0.405270	−	0.292842i
$157$	−19.8931	+	11.4853i	−1.58764	+	0.916627i	−0.593951	+	0.804501i	$0.702433\pi$
$157$	−19.8931	+	11.4853i	−1.58764	+	0.916627i	−0.993694	+	0.112126i	$0.964234\pi$
$158$	0.458065	−	0.793391i	0.0364417	−	0.0631188i
$159$	−6.11085	−	5.62208i	−0.484622	−	0.445860i
$160$	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
$163$	−7.66125	+	4.42322i	−0.600075	+	0.346454i	−0.769071	−	0.639163i	$-0.779281\pi$
$163$	−7.66125	+	4.42322i	−0.600075	+	0.346454i	0.168996	+	0.985617i	$0.445948\pi$
$164$	7.47421	−	4.31523i	0.583637	−	0.336963i
$165$	−0.795086	−	0.731492i	−0.0618974	−	0.0569466i
$166$		−	13.2261i		−	1.02655i
$167$	−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
$171$	−11.7731	−	5.54729i	−0.900310	−	0.424212i
$172$	−0.602811	+	1.04410i	−0.0459639	+	0.0796118i
$173$	6.56172	+	11.3652i	0.498879	+	0.864083i	0.999999	−	0.00129451i	$-0.000412056\pi$
$173$	6.56172	+	11.3652i	0.498879	+	0.864083i	−0.501121	+	0.865377i	$0.667079\pi$
$174$	−12.1161	−	11.1470i	−0.918522	−	0.845055i
$175$	−5.22566	−	9.17193i	−0.395023	−	0.693333i
$176$	−0.310310	+	0.537472i	−0.0233905	+	0.0405135i
$177$	5.10692	−	1.59899i	0.383860	−	0.120187i
$178$			3.60015i			0.269842i
$179$	16.9504	+	9.78634i	1.26693	+	0.731465i	0.974407	−	0.224792i	$-0.0721702\pi$
$179$	16.9504	+	9.78634i	1.26693	+	0.731465i	0.292528	+	0.956257i	$0.405503\pi$
$180$	−3.00475	+	0.250780i	−0.223961	+	0.0186920i
$181$			22.4310i			1.66728i	0.552305	+	0.833642i	$0.313748\pi$
$181$			22.4310i			1.66728i	−0.552305	+	0.833642i	$0.686252\pi$
$182$	−2.96968	−	9.06537i	−0.220127	−	0.671970i
$183$	8.51755	+	7.83628i	0.629635	+	0.579274i
$184$		−	2.82222i		−	0.208057i
$185$	−2.18553	+	3.78545i	−0.160683	+	0.278312i
$186$	2.93569	−	3.19091i	0.215255	−	0.233969i
$187$	−0.106409	+	0.184307i	−0.00778143	+	0.0134778i
$188$	0.0442417	+	0.0255429i	0.00322665	+	0.00186291i
$189$	−10.8080	−	8.49634i	−0.786164	−	0.618018i
$190$			4.36015i			0.316319i
$191$	−11.3808	+	6.57071i	−0.823486	+	0.475440i	−0.851617	−	0.524164i	$-0.824378\pi$
$191$	−11.3808	+	6.57071i	−0.823486	+	0.475440i	0.0281311	+	0.999604i	$0.491044\pi$
$192$	0.517534	+	1.65292i	0.0373498	+	0.119290i
$193$	10.9286	+	6.30961i	0.786656	+	0.454176i	0.838784	−	0.544464i	$-0.183267\pi$
$193$	10.9286	+	6.30961i	0.786656	+	0.454176i	−0.0521281	+	0.998640i	$0.516600\pi$
$194$	−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	$0.849072\pi$
$198$	−0.154854	−	1.85541i	−0.0110050	−	0.131858i
$199$		−	8.75865i		−	0.620885i	−0.950592	−	0.310442i	$-0.899523\pi$
$199$		−	8.75865i		−	0.620885i	0.950592	−	0.310442i	$-0.100477\pi$
$200$	−1.99492	−	3.45530i	−0.141062	−	0.244327i
$201$	2.07632	−	9.27785i	0.146452	−	0.654409i
$202$	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
$205$	8.67419			0.605832
$206$	8.93253	+	5.15720i	0.622359	+	0.359319i
$207$	4.82851	+	6.95485i	0.335605	+	0.483395i
$208$	−1.14202	−	3.41991i	−0.0791851	−	0.237128i
$209$	−2.69235			−0.186234
$210$	−1.03157	+	4.48878i	−0.0711850	+	0.309755i
$211$	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	$0.487431\pi$
$212$	−4.15182	+	2.39705i	−0.285148	+	0.164630i
$213$	−2.10260	−	0.470547i	−0.144068	−	0.0322414i
$214$		−	14.7159i		−	1.00595i
$215$	−1.04939	+	0.605865i	−0.0715677	+	0.0413196i
$216$	−4.10334	−	3.18788i	−0.279197	−	0.216908i
$217$	−3.27873	−	5.75474i	−0.222575	−	0.390657i
$218$	−15.5550	+	8.98070i	−1.05352	+	0.608250i
$219$	10.4642	−	11.3739i	0.707102	−	0.768576i
$220$	−0.540195	+	0.311882i	−0.0364199	+	0.0210271i
$221$	−0.391616	−	1.17273i	−0.0263429	−	0.0788866i
$222$	−7.18861	+	2.25077i	−0.482468	+	0.151062i
$223$	−4.67710	−	8.10097i	−0.313201	−	0.542481i	0.665852	−	0.746084i	$-0.268068\pi$
$223$	−4.67710	−	8.10097i	−0.313201	−	0.542481i	−0.979054	+	0.203603i	$0.934735\pi$
$224$	2.64571	+	0.0151415i	0.176774	+	0.00101169i
$225$	10.8278	+	5.10188i	0.721851	+	0.340125i
$226$	4.26195	+	2.46064i	0.283501	+	0.163679i
$227$			11.7911i			0.782600i	0.920263	+	0.391300i	$0.127974\pi$
$227$			11.7911i			0.782600i	−0.920263	+	0.391300i	$0.872026\pi$
$228$	−5.08741	+	5.52970i	−0.336922	+	0.366213i
$229$	−5.47329	+	9.48001i	−0.361685	+	0.626457i	−0.988238	−	0.152922i	$-0.951132\pi$
$229$	−5.47329	+	9.48001i	−0.361685	+	0.626457i	0.626553	+	0.779379i	$0.284465\pi$
$230$	1.41826	−	2.45650i	0.0935172	−	0.161977i
$231$	−2.77178	−	0.636985i	−0.182370	−	0.0419105i
$232$	−8.23191	+	4.75270i	−0.540451	+	0.312030i
$233$	5.40464	+	3.12037i	0.354070	+	0.204422i	0.666476	−	0.745526i	$-0.267802\pi$
$233$	5.40464	+	3.12037i	0.354070	+	0.204422i	−0.312406	+	0.949949i	$0.601135\pi$
$234$	8.66540	+	6.47386i	0.566475	+	0.423210i
$235$	0.0256723	+	0.0444658i	0.00167468	+	0.00290063i
$236$		−	3.08963i		−	0.201118i
$237$	1.54848	+	0.346539i	0.100585	+	0.0225101i
$238$	0.907250	+	0.00519224i	0.0588083	+	0.000336563i
$239$	−30.4624			−1.97045			−0.985225	−	0.171267i	$-0.945214\pi$
$239$	−30.4624			−1.97045			−0.985225	+	0.171267i	$0.945214\pi$
$240$	−0.380181	+	1.69880i	−0.0245405	+	0.109657i
$241$	5.69491			0.366842			0.183421	−	0.983034i	$-0.441283\pi$
$241$	5.69491			0.366842			0.183421	+	0.983034i	$0.441283\pi$
$242$	5.30742	+	9.19271i	0.341174	+	0.590930i
$243$	15.5660	+	0.835596i	0.998562	+	0.0536035i
$244$	5.78697	−	3.34111i	0.370473	−	0.213892i
$245$	6.05223	+	3.58724i	0.386663	+	0.229180i
$246$	11.0009	+	10.1210i	0.701393	+	0.645292i
$247$	10.3713	−	11.7086i	0.659913	−	0.745002i
$248$	−1.25167	−	2.16796i	−0.0794813	−	0.137666i
$249$	21.8618	−	6.84498i	1.38544	−	0.433783i
$250$		−	9.03538i		−	0.571448i
$251$	−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
$254$	−2.78854	−	4.82989i	−0.174969	−	0.303055i
$255$	−0.130369	+	0.582543i	−0.00816403	+	0.0364803i
$256$	1.00000			0.0625000
$257$	29.5356			1.84238			0.921189	−	0.389116i	$-0.127220\pi$
$257$	29.5356			1.84238			0.921189	+	0.389116i	$0.127220\pi$
$258$	−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
$261$	12.1547	−	25.7960i	0.752357	−	1.59673i
$262$	9.12794	−	15.8101i	0.563926	−	0.976748i
$263$	−19.0802	−	11.0160i	−1.17654	−	0.679274i	−0.221327	−	0.975200i	$-0.571039\pi$
$263$	−19.0802	−	11.0160i	−1.17654	−	0.679274i	−0.955211	+	0.295925i	$0.904372\pi$
$264$	−1.04900	−	0.234758i	−0.0645613	−	0.0144484i
$265$	−4.81839			−0.295991
$266$	5.68189	+	9.97269i	0.348379	+	0.611465i
$267$	−5.95077	+	1.86320i	−0.364181	+	0.114026i
$268$	−4.75367	−	2.74453i	−0.290377	−	0.167649i
$269$	6.41553			0.391162			0.195581	−	0.980688i	$-0.437341\pi$
$269$	6.41553			0.391162			0.195581	+	0.980688i	$0.437341\pi$
$270$	−1.96958	−	4.83684i	−0.119865	−	0.294361i
$271$	20.6367			1.25359			0.626794	−	0.779185i	$-0.284367\pi$
$271$	20.6367			1.25359			0.626794	+	0.779185i	$0.284367\pi$
$272$	0.342914			0.0207922
$273$	13.4475	−	9.60030i	0.813878	−	0.581036i
$274$	8.10612			0.489709
$275$	2.47617			0.149319
$276$	4.66492	−	1.46060i	0.280795	−	0.0879176i
$277$	12.0754			0.725543			0.362771	−	0.931878i	$-0.381831\pi$
$277$	12.0754			0.725543			0.362771	+	0.931878i	$0.381831\pi$
$278$	−16.5296	−	9.54339i	−0.991382	−	0.572375i
$279$	6.79366	+	3.20107i	0.406726	+	0.191643i
$280$	2.29525	+	1.34273i	0.137167	+	0.0802438i
$281$	−30.4581			−1.81698			−0.908488	−	0.417911i	$-0.862762\pi$
$281$	−30.4581			−1.81698			−0.908488	+	0.417911i	$0.862762\pi$
$282$	−0.0193240	+	0.0863474i	−0.00115072	+	0.00514192i
$283$	15.2403	+	8.79901i	0.905943	+	0.523047i	0.879124	−	0.476594i	$-0.158129\pi$
$283$	15.2403	+	8.79901i	0.905943	+	0.523047i	0.0268196	+	0.999640i	$0.491462\pi$
$284$	−0.621982	+	1.07730i	−0.0369079	+	0.0639263i
$285$	−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
$288$	−2.46432	+	1.71089i	−0.145211	+	0.100815i
$289$	−16.8824			−0.993083
$290$	−9.55354			−0.561003
$291$	−17.2539	−	3.86131i	−1.01144	−	0.226354i
$292$	−4.46154	−	7.72761i	−0.261092	−	0.452224i
$293$	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
$296$			4.34903i			0.252782i
$297$	2.98670	−	1.21620i	0.173306	−	0.0705710i
$298$	2.34608	+	4.06353i	0.135905	+	0.235394i
$299$	−9.65174	+	3.22304i	−0.558175	+	0.186393i
$300$	4.67892	−	5.08569i	0.270137	−	0.293623i
$301$	−1.61067	+	2.75325i	−0.0928375	+	0.158695i
$302$	6.80898	−	3.93117i	0.391813	−	0.226213i
$303$	16.7545	+	3.74954i	0.962519	+	0.215405i
$304$	2.16909	+	3.75697i	0.124406	+	0.215477i
$305$	6.71606			0.384561
$306$	−0.845048	+	0.586688i	−0.0483082	+	0.0335387i
$307$	−26.3002			−1.50103			−0.750514	−	0.660854i	$-0.770194\pi$
$307$	−26.3002			−1.50103			−0.750514	+	0.660854i	$0.770194\pi$
$308$	−0.829127	+	1.41730i	−0.0472439	+	0.0807579i
$309$	−3.90157	+	17.4338i	−0.221953	+	0.991776i
$310$		−	2.51603i		−	0.142901i
$311$	6.89170	+	11.9368i	0.390793	+	0.676873i	0.992554	−	0.121803i	$-0.0388676\pi$
$311$	6.89170	+	11.9368i	0.390793	+	0.676873i	−0.601762	+	0.798676i	$0.705534\pi$
$312$	5.06181	−	3.65760i	0.286569	−	0.207071i
$313$	7.93246	+	4.57981i	0.448369	+	0.258866i	0.707141	−	0.707072i	$-0.249985\pi$
$313$	7.93246	+	4.57981i	0.448369	+	0.258866i	−0.258772	+	0.965938i	$0.583318\pi$
$314$	−19.8931	+	11.4853i	−1.12263	+	0.648153i
$315$	−7.95349	+	0.617993i	−0.448128	+	0.0348200i
$316$	0.458065	−	0.793391i	0.0257681	−	0.0446317i
$317$	2.37076	−	4.10628i	0.133155	−	0.230631i	−0.791736	−	0.610863i	$-0.790822\pi$
$317$	2.37076	−	4.10628i	0.133155	−	0.230631i	0.924891	+	0.380232i	$0.124156\pi$
$318$	−6.11085	−	5.62208i	−0.342680	−	0.315271i
$319$		−	5.89923i		−	0.330293i
$320$	0.870413	+	0.502533i	0.0486575	+	0.0280924i
$321$	24.3242	−	7.61596i	1.35764	−	0.425081i
$322$	0.0427328	−	7.46677i	0.00238140	−	0.416107i
$323$	0.743810	+	1.28832i	0.0413867	+	0.0716838i
$324$	3.14571	−	8.43235i	0.174762	−	0.468464i
$325$	−9.53858	+	10.7685i	−0.529105	+	0.597328i
$326$	−7.66125	+	4.42322i	−0.424317	+	0.244980i
$327$	−22.8947	−	21.0635i	−1.26608	−	1.16481i
$328$	7.47421	−	4.31523i	0.412694	−	0.238269i
$329$	0.116664	+	0.0682490i	0.00643188	+	0.00376269i
$330$	−0.795086	−	0.731492i	−0.0437680	−	0.0402673i
$331$	21.1492	−	12.2105i	1.16246	−	0.671149i	0.210571	−	0.977579i	$-0.432468\pi$
$331$	21.1492	−	12.2105i	1.16246	−	0.671149i	0.951893	+	0.306430i	$0.0991345\pi$
$332$		−	13.2261i		−	0.725879i
$333$	−7.44070	−	10.7174i	−0.407748	−	0.587309i
$334$	−3.95886	+	2.28565i	−0.216619	+	0.125065i
$335$	−2.75844	−	4.77776i	−0.150710	−	0.261037i
$336$	1.34422	+	4.38099i	0.0733330	+	0.239003i
$337$	1.88882			0.102891			0.0514453	−	0.998676i	$-0.483617\pi$
$337$	1.88882			0.102891			0.0514453	+	0.998676i	$0.483617\pi$
$338$	−10.3916	+	7.81124i	−0.565226	+	0.424875i
$339$	−1.86154	+	8.31815i	−0.101105	+	0.451780i
$340$	0.298476	+	0.172325i	0.0161872	+	0.00934566i
$341$	1.55362			0.0841335
$342$	−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
$345$	4.79440	+	1.07295i	0.258122	+	0.0577659i
$346$	6.56172	+	11.3652i	0.352760	+	0.610999i
$347$			34.7424i			1.86507i	0.361079	+	0.932535i	$0.382408\pi$
$347$			34.7424i			1.86507i	−0.361079	+	0.932535i	$0.617592\pi$
$348$	−12.1161	−	11.1470i	−0.649493	−	0.597544i
$349$	4.20668	+	7.28618i	0.225178	+	0.390021i	0.956373	−	0.292148i	$-0.0943702\pi$
$349$	4.20668	+	7.28618i	0.225178	+	0.390021i	−0.731195	+	0.682169i	$0.761037\pi$
$350$	−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
$353$	17.1652	+	9.91033i	0.913611	+	0.527474i	0.881591	−	0.472014i	$-0.156473\pi$
$353$	17.1652	+	9.91033i	0.913611	+	0.527474i	0.0320198	+	0.999487i	$0.489806\pi$
$354$	5.10692	−	1.59899i	0.271430	−	0.0849852i
$355$	−1.08276	+	0.625133i	−0.0574671	+	0.0331786i
$356$			3.60015i			0.190807i
$357$	0.460950	+	1.50230i	0.0243961	+	0.0795102i
$358$	16.9504	+	9.78634i	0.895858	+	0.517224i
$359$	0.111157	−	0.192530i	0.00586667	−	0.0101614i	−0.863077	−	0.505072i	$-0.831466\pi$
$359$	0.111157	−	0.192530i	0.00586667	−	0.0101614i	0.868944	+	0.494911i	$0.164799\pi$
$360$	−3.00475	+	0.250780i	−0.158364	+	0.0132172i
$361$	0.0901205	−	0.156093i	0.00474318	−	0.00821544i
$362$			22.4310i			1.17895i
$363$	−12.4481	+	13.5303i	−0.653355	+	0.710157i
$364$	−2.96968	−	9.06537i	−0.155654	−	0.475155i
$365$		−	8.96828i		−	0.469421i
$366$	8.51755	+	7.83628i	0.445219	+	0.409609i
$367$	−11.6056	−	6.70049i	−0.605806	−	0.349763i	0.165516	−	0.986207i	$-0.447071\pi$
$367$	−11.6056	−	6.70049i	−0.605806	−	0.349763i	−0.771322	+	0.636445i	$0.780404\pi$
$368$		−	2.82222i		−	0.147118i
$369$	−11.0359	+	23.4216i	−0.574507	+	1.21928i
$370$	−2.18553	+	3.78545i	−0.113620	+	0.196796i
$371$	−11.0208	+	6.27904i	−0.572171	+	0.325991i
$372$	2.93569	−	3.19091i	0.152208	−	0.165441i
$373$	3.97778	+	6.88972i	0.205962	+	0.356736i	0.950439	−	0.310912i	$-0.100634\pi$
$373$	3.97778	+	6.88972i	0.205962	+	0.356736i	−0.744477	+	0.667648i	$0.767301\pi$
$374$	−0.106409	+	0.184307i	−0.00550230	+	0.00953026i
$375$	14.9348	−	4.67612i	0.771230	−	0.241474i
$376$	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	$0.373980\pi$
$380$			4.36015i			0.223671i
$381$	6.54028	−	7.10888i	0.335069	−	0.364199i
$382$	−11.3808	+	6.57071i	−0.582293	+	0.336187i
$383$	9.40956	−	5.43261i	0.480806	−	0.277594i	−0.239946	−	0.970786i	$-0.577130\pi$
$383$	9.40956	−	5.43261i	0.480806	−	0.277594i	0.720752	+	0.693193i	$0.243796\pi$
$384$	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
$387$	−0.300821	−	3.60433i	−0.0152916	−	0.183219i
$388$	−5.10398	+	8.84035i	−0.259115	+	0.448801i
$389$	−33.7632	+	19.4932i	−1.71186	+	0.988345i	−0.779815	+	0.626011i	$0.784687\pi$
$389$	−33.7632	+	19.4932i	−1.71186	+	0.988345i	−0.932048	+	0.362334i	$0.881980\pi$
$390$	6.24393	−	0.639892i	0.316174	−	0.0324022i
$391$		−	0.967778i		−	0.0489427i
$392$	6.99954	+	0.0801202i	0.353530	+	0.00404668i
$393$	30.8568	+	6.90555i	1.55652	+	0.348339i
$394$	−0.693687	−	1.20150i	−0.0349475	−	0.0605308i
$395$	0.797410	−	0.460385i	0.0401221	−	0.0231645i
$396$	−0.154854	−	1.85541i	−0.00778172	−	0.0932377i
$397$	−11.1038	−	19.2323i	−0.557282	−	0.965240i	−0.997722	−	0.0674585i	$-0.978511\pi$
$397$	−11.1038	−	19.2323i	−0.557282	−	0.965240i	0.440440	−	0.897782i	$-0.354822\pi$
$398$		−	8.75865i		−	0.439032i
$399$	−13.5435	+	14.5529i	−0.678024	+	0.728558i
$400$	−1.99492	−	3.45530i	−0.0997461	−	0.172765i
$401$	−29.6513			−1.48072			−0.740358	−	0.672213i	$-0.765344\pi$
$401$	−29.6513			−1.48072			−0.740358	+	0.672213i	$0.765344\pi$
$402$	2.07632	−	9.27785i	0.103557	−	0.462737i
$403$	−5.98479	+	6.75647i	−0.298124	+	0.336564i
$404$	4.95624	−	8.58446i	0.246582	−	0.427093i
$405$	6.97560	−	5.75880i	0.346620	−	0.286157i
$406$	−21.8512	+	12.4496i	−1.08446	+	0.617863i
$407$	−2.33748	−	1.34954i	−0.115865	−	0.0668944i
$408$	0.177470	+	0.566810i	0.00878605	+	0.0280613i
$409$	−1.06094			−0.0524602			−0.0262301	−	0.999656i	$-0.508350\pi$
$409$	−1.06094			−0.0524602			−0.0262301	+	0.999656i	$0.508350\pi$
$410$	8.67419			0.428388
$411$	4.19519	+	13.3988i	0.206934	+	0.660914i
$412$	8.93253	+	5.15720i	0.440074	+	0.254077i
$413$	0.0467817	−	8.17425i	0.00230198	−	0.402229i
$414$	4.82851	+	6.95485i	0.237308	+	0.341812i
$415$	6.64657	−	11.5122i	0.326268	−	0.565112i
$416$	−1.14202	−	3.41991i	−0.0559923	−	0.167675i
$417$	7.21985	−	32.2613i	0.353557	−	1.57984i
$418$	−2.69235			−0.131687
$419$	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	$0.800563\pi$
$420$	−1.03157	+	4.48878i	−0.0503354	+	0.219030i
$421$		−	12.1375i		−	0.591544i	−0.955259	−	0.295772i	$-0.904423\pi$
$421$		−	12.1375i		−	0.591544i	0.955259	−	0.295772i	$-0.0955768\pi$
$422$	12.8567	+	22.2684i	0.625853	+	1.08401i
$423$	−0.152727	+	0.0127467i	−0.00742582	+	0.000619767i
$424$	−4.15182	+	2.39705i	−0.201630	+	0.116411i
$425$	−0.684086	−	1.18487i	−0.0331830	−	0.0574747i
$426$	−2.10260	−	0.470547i	−0.101871	−	0.0227981i
$427$	15.3612	−	8.75197i	0.743381	−	0.423537i
$428$		−	14.7159i		−	0.711318i
$429$	0.395128	+	3.85557i	0.0190769	+	0.186149i
$430$	−1.04939	+	0.605865i	−0.0506060	+	0.0292174i
$431$	−3.37233	+	5.84104i	−0.162439	+	0.281353i	−0.935743	−	0.352683i	$-0.885269\pi$
$431$	−3.37233	+	5.84104i	−0.162439	+	0.281353i	0.773304	+	0.634036i	$0.218603\pi$
$432$	−4.10334	−	3.18788i	−0.197422	−	0.153377i
$433$	−25.4298	−	14.6819i	−1.22208	−	0.705566i	−0.256717	−	0.966487i	$-0.582641\pi$
$433$	−25.4298	−	14.6819i	−1.22208	−	0.705566i	−0.965360	+	0.260920i	$0.915974\pi$
$434$	−3.27873	−	5.75474i	−0.157384	−	0.276236i
$435$	−4.94429	−	15.7913i	−0.237060	−	0.757134i
$436$	−15.5550	+	8.98070i	−0.744951	+	0.430098i
$437$	10.6030	−	6.12164i	0.507210	−	0.292838i
$438$	10.4642	−	11.3739i	0.499996	−	0.543465i
$439$			3.82128i			0.182380i	0.995834	+	0.0911898i	$0.0290670\pi$
$439$			3.82128i			0.182380i	−0.995834	+	0.0911898i	$0.970933\pi$
$440$	−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	−0.0703604	−	0.997522i	$-0.522415\pi$
$443$	−20.4039	−	11.7802i	−0.969420	−	0.559695i	−0.899059	+	0.437827i	$0.855748\pi$
$444$	−7.18861	+	2.25077i	−0.341156	+	0.106817i
$445$	−1.80919	+	3.13361i	−0.0857640	+	0.148548i
$446$	−4.67710	−	8.10097i	−0.221467	−	0.383592i
$447$	−5.50253	+	5.98091i	−0.260261	+	0.282887i
$448$	2.64571	+	0.0151415i	0.124998	+	0.000715371i
$449$	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	$0.107526\pi$
$450$	10.8278	+	5.10188i	0.510426	+	0.240505i
$451$			5.35624i			0.252215i
$452$	4.26195	+	2.46064i	0.200465	+	0.115739i
$453$	10.0218	+	9.22021i	0.470865	+	0.433203i
$454$			11.7911i			0.553382i
$455$	1.97080	−	9.38298i	0.0923926	−	0.439881i
$456$	−5.08741	+	5.52970i	−0.238240	+	0.258952i
$457$			31.8029i			1.48768i	0.668360	+	0.743838i	$0.266997\pi$
$457$			31.8029i			1.48768i	−0.668360	+	0.743838i	$0.733003\pi$
$458$	−5.47329	+	9.48001i	−0.255750	+	0.442972i
$459$	−1.40709	−	1.09317i	−0.0656774	−	0.0510248i
$460$	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	$0.924059\pi$
$462$	−2.77178	−	0.636985i	−0.128955	−	0.0296352i
$463$		−	27.0578i		−	1.25748i	−0.777614	−	0.628742i	$-0.783570\pi$
$463$		−	27.0578i		−	1.25748i	0.777614	−	0.628742i	$-0.216430\pi$
$464$	−8.23191	+	4.75270i	−0.382157	+	0.220638i
$465$	4.15880	−	1.30213i	0.192860	−	0.0603848i
$466$	5.40464	+	3.12037i	0.250365	+	0.144548i
$467$	15.8112	−	27.3859i	0.731657	−	1.26727i	−0.224517	−	0.974470i	$-0.572081\pi$
$467$	15.8112	−	27.3859i	0.731657	−	1.26727i	0.956175	−	0.292797i	$-0.0945861\pi$
$468$	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
$471$	−29.2797	−	26.9378i	−1.34914	−	1.24123i
$472$		−	3.08963i		−	0.142212i
$473$	−0.374116	−	0.647988i	−0.0172019	−	0.0297945i
$474$	1.54848	+	0.346539i	0.0711240	+	0.0159171i
$475$	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
$478$	−30.4624			−1.39332
$479$	−9.21963	−	5.32296i	−0.421256	−	0.243212i	0.274359	−	0.961627i	$-0.411534\pi$
$479$	−9.21963	−	5.32296i	−0.421256	−	0.243212i	−0.695614	+	0.718415i	$0.744868\pi$
$480$	−0.380181	+	1.69880i	−0.0173528	+	0.0775394i
$481$	14.8733	−	4.96669i	0.678163	−	0.226462i
$482$	5.69491			0.259396
$483$	12.3641	−	3.79368i	0.562587	−	0.172618i
$484$	5.30742	+	9.19271i	0.241246	+	0.417851i
$485$	−8.88514	+	5.12984i	−0.403453	+	0.232934i
$486$	15.5660	+	0.835596i	0.706090	+	0.0379034i
$487$		−	39.5929i		−	1.79413i	−0.441903	−	0.897063i	$-0.645696\pi$
$487$		−	39.5929i		−	1.79413i	0.441903	−	0.897063i	$-0.354304\pi$
$488$	5.78697	−	3.34111i	0.261964	−	0.151245i
$489$	−11.2762	−	10.3743i	−0.509928	−	0.469142i
$490$	6.05223	+	3.58724i	0.273412	+	0.162055i
$491$	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	$0.0781181\pi$
$492$	11.0009	+	10.1210i	0.495959	+	0.456291i
$493$	−2.82283	+	1.62976i	−0.127134	+	0.0734009i
$494$	10.3713	−	11.7086i	0.466629	−	0.526796i
$495$	0.797616	−	1.69279i	0.0358502	−	0.0760852i
$496$	−1.25167	−	2.16796i	−0.0562018	−	0.0973443i
$497$	−1.66190	+	2.84082i	−0.0745462	+	0.127428i
$498$	21.8618	−	6.84498i	0.979651	−	0.306731i
$499$	7.30529	+	4.21771i	0.327030	+	0.188811i	0.654522	−	0.756043i	$-0.272870\pi$
$499$	7.30529	+	4.21771i	0.327030	+	0.188811i	−0.327492	+	0.944854i	$0.606203\pi$
$500$		−	9.03538i		−	0.404075i
$501$	−5.82684	−	5.36079i	−0.260324	−	0.239502i
$502$	−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	$0.226834\pi$
$504$	−6.54577	+	4.48920i	−0.291572	+	0.199965i
$505$	8.62794	−	4.98135i	0.383938	−	0.221667i
$506$	1.51687	+	0.875762i	0.0674329	+	0.0389324i
$507$	−18.2894	−	13.1339i	−0.812260	−	0.583296i
$508$	−2.78854	−	4.82989i	−0.123722	−	0.214292i
$509$			16.2934i			0.722191i	0.932529	+	0.361096i	$0.117597\pi$
$509$			16.2934i			0.722191i	−0.932529	+	0.361096i	$0.882403\pi$
$510$	−0.130369	+	0.582543i	−0.00577284	+	0.0257954i
$511$	−11.6869	−	20.5125i	−0.516999	−	0.907422i
$512$	1.00000			0.0441942
$513$	3.07628	−	22.3309i	0.135821	−	0.985934i
$514$	29.5356			1.30276
$515$	5.18333	+	8.97779i	0.228405	+	0.395609i
$516$	−2.03779	−	0.456044i	−0.0897088	−	0.0200762i
$517$	−0.0274572	+	0.0158524i	−0.00120757	+	0.000697189i
$518$	−0.0658509	+	11.5063i	−0.00289332	+	0.505556i
$519$	−15.3900	+	16.7279i	−0.675544	+	0.734275i
$520$	0.724585	−	3.55064i	0.0317752	−	0.155706i
$521$	9.43681	+	16.3450i	0.413434	+	0.716089i	0.995263	−	0.0972224i	$-0.0309958\pi$
$521$	9.43681	+	16.3450i	0.413434	+	0.716089i	−0.581828	+	0.813312i	$0.697662\pi$
$522$	12.1547	−	25.7960i	0.531997	−	1.12906i
$523$			18.3022i			0.800301i	0.916449	+	0.400151i	$0.131042\pi$
$523$			18.3022i			0.800301i	−0.916449	+	0.400151i	$0.868958\pi$
$524$	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
$527$	−0.429216	−	0.743423i	−0.0186969	−	0.0323840i
$528$	−1.04900	−	0.234758i	−0.0456517	−	0.0102165i
$529$	15.0351			0.653699
$530$	−4.81839			−0.209298
$531$	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
$534$	−5.95077	+	1.86320i	−0.257515	+	0.0806285i
$535$	7.39520	−	12.8089i	0.319722	−	0.553775i
$536$	−4.75367	−	2.74453i	−0.205327	−	0.118546i
$537$	−7.40364	+	33.0825i	−0.319491	+	1.42762i
$538$	6.41553			0.276593
$539$	−2.21509	+	3.73720i	−0.0954106	+	0.160972i
$540$	−1.96958	−	4.83684i	−0.0847573	−	0.208144i
$541$	1.05318	+	0.608052i	0.0452796	+	0.0261422i	0.522469	−	0.852658i	$-0.325011\pi$
$541$	1.05318	+	0.608052i	0.0452796	+	0.0261422i	−0.477189	+	0.878801i	$0.658344\pi$
$542$	20.6367			0.886420
$543$	−37.0768	+	11.6088i	−1.59112	+	0.498182i
$544$	0.342914			0.0147023
$545$	−18.0524			−0.773280
$546$	13.4475	−	9.60030i	0.575498	−	0.410855i
$547$	−11.3034			−0.483301			−0.241650	−	0.970363i	$-0.577689\pi$
$547$	−11.3034			−0.483301			−0.241650	+	0.970363i	$0.577689\pi$
$548$	8.10612			0.346276
$549$	−8.54465	+	18.1344i	−0.364677	+	0.773958i
$550$	2.47617			0.105584
$551$	−35.7115	−	20.6180i	−1.52136	−	0.878357i
$552$	4.66492	−	1.46060i	0.198552	−	0.0621671i
$553$	1.22392	−	2.09215i	0.0520463	−	0.0889671i
$554$	12.0754			0.513036
$555$	−7.38814	−	1.65341i	−0.313609	−	0.0701835i
$556$	−16.5296	−	9.54339i	−0.701013	−	0.404730i
$557$	−9.76868	+	16.9199i	−0.413912	+	0.716917i	−0.995314	−	0.0966996i	$-0.969171\pi$
$557$	−9.76868	+	16.9199i	−0.413912	+	0.716917i	0.581401	+	0.813617i	$0.302505\pi$
$558$	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
$561$	−0.359715	−	0.0805018i	−0.0151872	−	0.00339879i
$562$	−30.4581			−1.28480
$563$	31.1373			1.31228			0.656141	−	0.754638i	$-0.272188\pi$
$563$	31.1373			1.31228			0.656141	+	0.754638i	$0.272188\pi$
$564$	−0.0193240	+	0.0863474i	−0.000813685	+	0.00363588i
$565$	2.47311	+	4.28354i	0.104044	+	0.180210i
$566$	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
$569$		−	1.93823i		−	0.0812549i	−0.999174	−	0.0406275i	$-0.987064\pi$
$569$		−	1.93823i		−	0.0812549i	0.999174	−	0.0406275i	$-0.0129357\pi$
$570$	−7.20700	+	2.25653i	−0.301868	+	0.0945155i
$571$	5.29680	+	9.17432i	0.221664	+	0.383933i	0.955313	−	0.295595i	$-0.0955178\pi$
$571$	5.29680	+	9.17432i	0.221664	+	0.383933i	−0.733649	+	0.679528i	$0.762185\pi$
$572$	2.19249	+	0.447425i	0.0916725	+	0.0187078i
$573$	−16.7508	−	15.4110i	−0.699776	−	0.643805i
$574$	19.8399	−	11.3037i	0.828102	−	0.471806i
$575$	−9.75164	+	5.63011i	−0.406671	+	0.234792i
$576$	−2.46432	+	1.71089i	−0.102680	+	0.0712871i
$577$	−8.46005	−	14.6532i	−0.352197	−	0.610022i	0.634437	−	0.772974i	$-0.281232\pi$
$577$	−8.46005	−	14.6532i	−0.352197	−	0.610022i	−0.986634	+	0.162952i	$0.947898\pi$
$578$	−16.8824			−0.702216
$579$	−4.77340	+	21.3295i	−0.198376	+	0.886425i
$580$	−9.55354			−0.396689
$581$	0.200264	−	34.9925i	0.00830836	−	1.45173i
$582$	−17.2539	−	3.86131i	−0.715198	−	0.160056i
$583$		−	2.97531i		−	0.123225i
$584$	−4.46154	−	7.72761i	−0.184620	−	0.319771i
$585$	4.28914	+	9.98958i	0.177334	+	0.413018i
$586$	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	$0.466192\pi$
$588$	3.49007	+	11.6112i	0.143928	+	0.478837i
$589$	5.42997	−	9.40499i	0.223738	−	0.387526i
$590$	1.55264	−	2.68925i	0.0639212	−	0.110715i
$591$	1.62698	−	1.76843i	0.0669252	−	0.0727435i
$592$			4.34903i			0.178744i
$593$	−8.82193	−	5.09334i	−0.362273	−	0.209158i	0.307804	−	0.951450i	$-0.400406\pi$
$593$	−8.82193	−	5.09334i	−0.362273	−	0.209158i	−0.670077	+	0.742291i	$0.733739\pi$
$594$	2.98670	−	1.21620i	0.122546	−	0.0499012i
$595$	0.787072	+	0.460442i	0.0322668	+	0.0188763i
$596$	2.34608	+	4.06353i	0.0960992	+	0.166449i
$597$	14.4774	−	4.53290i	0.592520	−	0.185519i
$598$	−9.65174	+	3.22304i	−0.394689	+	0.131800i
$599$	1.11601	−	0.644326i	0.0455988	−	0.0263265i	−0.477027	−	0.878888i	$-0.658286\pi$
$599$	1.11601	−	0.644326i	0.0455988	−	0.0263265i	0.522626	+	0.852562i	$0.324952\pi$
$600$	4.67892	−	5.08569i	0.191016	−	0.207623i
$601$	11.6473	−	6.72456i	0.475103	−	0.274301i	−0.243271	−	0.969958i	$-0.578220\pi$
$601$	11.6473	−	6.72456i	0.475103	−	0.274301i	0.718373	+	0.695658i	$0.244887\pi$
$602$	−1.61067	+	2.75325i	−0.0656460	+	0.112214i
$603$	16.4102	−	1.36961i	0.668273	−	0.0557748i
$604$	6.80898	−	3.93117i	0.277053	−	0.159957i
$605$			10.6686i			0.433741i
$606$	16.7545	+	3.74954i	0.680604	+	0.152314i
$607$	26.8707	−	15.5138i	1.09065	−	0.629685i	0.156898	−	0.987615i	$-0.449851\pi$
$607$	26.8707	−	15.5138i	1.09065	−	0.629685i	0.933748	+	0.357930i	$0.116517\pi$
$608$	2.16909	+	3.75697i	0.0879681	+	0.152365i
$609$	−31.8870	−	29.6753i	−1.29213	−	1.20250i
$610$	6.71606			0.271926
$611$	0.0368295	−	0.180473i	0.00148996	−	0.00730116i
$612$	−0.845048	+	0.586688i	−0.0341590	+	0.0237154i
$613$	−16.9453	−	9.78339i	−0.684416	−	0.395148i	0.117101	−	0.993120i	$-0.462640\pi$
$613$	−16.9453	−	9.78339i	−0.684416	−	0.395148i	−0.801517	+	0.597972i	$0.795973\pi$
$614$	−26.3002			−1.06139
$615$	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	$-0.209287\pi$
$618$	−3.90157	+	17.4338i	−0.156944	+	0.701291i
$619$	8.61313	+	14.9184i	0.346191	+	0.599620i	0.985569	−	0.169272i	$-0.0541416\pi$
$619$	8.61313	+	14.9184i	0.346191	+	0.599620i	−0.639378	+	0.768892i	$0.720808\pi$
$620$		−	2.51603i		−	0.101046i
$621$	−8.99692	+	11.5805i	−0.361034	+	0.464711i
$622$	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
$626$	7.93246	+	4.57981i	0.317045	+	0.183046i
$627$	−1.39339	−	4.45026i	−0.0556465	−	0.177726i
$628$	−19.8931	+	11.4853i	−0.793822	+	0.458314i
$629$			1.49134i			0.0594636i
$630$	−7.95349	+	0.617993i	−0.316875	+	0.0246214i
$631$	−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
$633$	−30.1542	+	32.7757i	−1.19852	+	1.30272i
$634$	2.37076	−	4.10628i	0.0941549	−	0.163081i
$635$		−	5.60534i		−	0.222441i
$636$	−6.11085	−	5.62208i	−0.242311	−	0.222930i
$637$	−7.71964	−	24.0293i	−0.305863	−	0.952075i
$638$		−	5.89923i		−	0.233553i
$639$	−0.310389	−	3.71896i	−0.0122788	−	0.147120i
$640$	0.870413	+	0.502533i	0.0344061	+	0.0198644i
$641$		−	41.3412i		−	1.63288i	−0.577432	−	0.816439i	$-0.695945\pi$
$641$		−	41.3412i		−	1.63288i	0.577432	−	0.816439i	$-0.304055\pi$
$642$	24.3242	−	7.61596i	0.959999	−	0.300578i
$643$	16.2778	−	28.1940i	0.641934	−	1.11186i	−0.343067	−	0.939311i	$-0.611466\pi$
$643$	16.2778	−	28.1940i	0.641934	−	1.11186i	0.985001	−	0.172551i	$-0.0552009\pi$
$644$	0.0427328	−	7.46677i	0.00168391	−	0.294232i
$645$	−1.54454	−	1.42100i	−0.0608163	−	0.0559520i
$646$	0.743810	+	1.28832i	0.0292648	+	0.0506881i
$647$	2.13561	−	3.69899i	0.0839595	−	0.145422i	−0.820988	−	0.570946i	$-0.806577\pi$
$647$	2.13561	−	3.69899i	0.0839595	−	0.145422i	0.904947	+	0.425524i	$0.139910\pi$
$648$	3.14571	−	8.43235i	0.123575	−	0.331254i
$649$	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
$653$			12.9710i			0.507595i	0.967257	+	0.253798i	$0.0816797\pi$
$653$			12.9710i			0.507595i	−0.967257	+	0.253798i	$0.918320\pi$
$654$	−22.8947	−	21.0635i	−0.895253	−	0.823647i
$655$	15.8901	−	9.17418i	0.620879	−	0.358465i
$656$	7.47421	−	4.31523i	0.291819	−	0.168482i
$657$	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	$0.413271\pi$
$660$	−0.795086	−	0.731492i	−0.0309487	−	0.0284733i
$661$	−3.58999	+	6.21804i	−0.139634	+	0.241854i	−0.927358	−	0.374175i	$-0.877926\pi$
$661$	−3.58999	+	6.21804i	−0.139634	+	0.241854i	0.787724	+	0.616028i	$0.211259\pi$
$662$	21.1492	−	12.2105i	0.821986	−	0.474574i
$663$	1.73577	−	1.25424i	0.0674116	−	0.0487107i
$664$		−	13.2261i		−	0.513274i
$665$	−0.0660194	+	11.5357i	−0.00256012	+	0.447335i
$666$	−7.44070	−	10.7174i	−0.288321	−	0.415290i
$667$	13.4132	+	23.2323i	0.519360	+	0.899557i
$668$	−3.95886	+	2.28565i	−0.153173	+	0.0884343i
$669$	10.9697	−	11.9234i	0.424114	−	0.460986i
$670$	−2.75844	−	4.77776i	−0.106568	−	0.184581i
$671$			4.14711i			0.160097i
$672$	1.34422	+	4.38099i	0.0518543	+	0.169000i
$673$	−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	$0.858857\pi$
$674$	1.88882			0.0727546
$675$	−2.82927	+	20.5379i	−0.108899	+	0.790503i
$676$	−10.3916	+	7.81124i	−0.399675	+	0.300432i
$677$	−5.94798	+	10.3022i	−0.228599	+	0.395946i	−0.957393	−	0.288787i	$-0.906748\pi$
$677$	−5.94798	+	10.3022i	−0.228599	+	0.395946i	0.728794	+	0.684733i	$0.240081\pi$
$678$	−1.86154	+	8.31815i	−0.0714922	+	0.319457i
$679$	−13.6375	+	23.3117i	−0.523359	+	0.894621i
$680$	0.298476	+	0.172325i	0.0114460	+	0.00660838i
$681$	−19.4897	+	6.10227i	−0.746848	+	0.233840i
$682$	1.55362			0.0594913
$683$	−4.43181			−0.169578			−0.0847892	−	0.996399i	$-0.527022\pi$
$683$	−4.43181			−0.169578			−0.0847892	+	0.996399i	$0.527022\pi$
$684$	−11.7731	−	5.54729i	−0.450155	−	0.212106i
$685$	7.05567	+	4.07359i	0.269583	+	0.155644i
$686$	18.5175	+	0.317958i	0.707003	+	0.0121397i
$687$	−18.5024	−	4.14070i	−0.705909	−	0.157977i
$688$	−0.602811	+	1.04410i	−0.0229819	+	0.0398059i
$689$	12.9392	+	11.4613i	0.492943	+	0.436642i
$690$	4.79440	+	1.07295i	0.182520	+	0.0408466i
$691$	−33.6142			−1.27874			−0.639372	−	0.768897i	$-0.720806\pi$
$691$	−33.6142			−1.27874			−0.639372	+	0.768897i	$0.720806\pi$
$692$	6.56172	+	11.3652i	0.249439	+	0.432041i
$693$	−0.381605	−	4.91121i	−0.0144960	−	0.186561i
$694$			34.7424i			1.31880i
$695$	−9.59174	−	16.6134i	−0.363835	−	0.630181i
$696$	−12.1161	−	11.1470i	−0.459261	−	0.422527i
$697$	2.56301	−	1.47975i	0.0970808	−	0.0560496i
$698$	4.20668	+	7.28618i	0.159225	+	0.275786i
$699$	−2.36065	+	10.5484i	−0.0892880	+	0.398976i
$700$	−5.22566	−	9.17193i	−0.197511	−	0.346667i
$701$		−	37.0012i		−	1.39751i	−0.715359	−	0.698757i	$-0.753737\pi$
$701$		−	37.0012i		−	1.39751i	0.715359	−	0.698757i	$-0.246263\pi$
$702$	−6.21616	+	17.6737i	−0.234614	+	0.667050i
$703$	−16.3392	+	9.43342i	−0.616243	+	0.355788i
$704$	−0.310310	+	0.537472i	−0.0116952	+	0.0202567i
$705$	−0.0602123	+	0.0654470i	−0.00226772	+	0.00246488i
$706$	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
$709$	−38.2116	+	22.0615i	−1.43507	+	0.828537i	−0.997501	−	0.0706486i	$-0.977493\pi$
$709$	−38.2116	+	22.0615i	−1.43507	+	0.828537i	−0.437567	+	0.899186i	$0.644160\pi$
$710$	−1.08276	+	0.625133i	−0.0406354	+	0.0234608i
$711$	0.228589	+	2.73886i	0.00857274	+	0.102715i
$712$			3.60015i			0.134921i
$713$	−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
$717$	−15.7653	−	50.3520i	−0.588767	−	1.88043i
$718$	0.111157	−	0.192530i	0.00414836	−	0.00718517i
$719$	−9.72356	−	16.8417i	−0.362627	−	0.628089i	0.625765	−	0.780012i	$-0.284787\pi$
$719$	−9.72356	−	16.8417i	−0.362627	−	0.628089i	−0.988392	+	0.151923i	$0.951454\pi$
$720$	−3.00475	+	0.250780i	−0.111980	+	0.00934601i
$721$	23.5548	+	13.7797i	0.877226	+	0.513183i
$722$	0.0901205	−	0.156093i	0.00335394	−	0.00580919i
$723$	2.94731	+	9.41326i	0.109612	+	0.350083i
$724$			22.4310i			0.833642i
$725$	32.8440	+	18.9625i	1.21980	+	0.704250i
$726$	−12.4481	+	13.5303i	−0.461992	+	0.502157i
$727$		−	17.7877i		−	0.659708i	−0.944032	−	0.329854i	$-0.893000\pi$
$727$		−	17.7877i		−	0.659708i	0.944032	−	0.329854i	$-0.107000\pi$
$728$	−2.96968	−	9.06537i	−0.110064	−	0.335985i
$729$	6.67478	+	26.1619i	0.247214	+	0.968961i
$730$		−	8.96828i		−	0.331931i
$731$	−0.206712	+	0.358036i	−0.00764552	+	0.0132424i
$732$	8.51755	+	7.83628i	0.314818	+	0.289637i
$733$	−20.9177	+	36.2305i	−0.772613	+	1.33820i	0.163513	+	0.986541i	$0.447717\pi$
$733$	−20.9177	+	36.2305i	−0.772613	+	1.33820i	−0.936126	+	0.351664i	$0.885616\pi$
$734$	−11.6056	−	6.70049i	−0.428370	−	0.247319i
$735$	−2.79720	+	11.8604i	−0.103176	+	0.437477i
$736$		−	2.82222i		−	0.104028i
$737$	2.95022	−	1.70331i	0.108673	−	0.0627423i
$738$	−11.0359	+	23.4216i	−0.406238	+	0.862163i
$739$	15.7822	+	9.11186i	0.580558	+	0.335185i	0.761355	−	0.648335i	$-0.224534\pi$
$739$	15.7822	+	9.11186i	0.580558	+	0.335185i	−0.180797	+	0.983520i	$0.557868\pi$
$740$	−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	$0.633164\pi$
$744$	2.93569	−	3.19091i	0.107628	−	0.116985i
$745$			4.71593i			0.172778i
$746$	3.97778	+	6.88972i	0.145637	+	0.252251i
$747$	22.6285	+	32.5934i	0.827933	+	1.19253i
$748$	−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
$751$	26.9689			0.984110			0.492055	−	0.870564i	$-0.336246\pi$
$751$	26.9689			0.984110			0.492055	+	0.870564i	$0.336246\pi$
$752$	0.0442417	+	0.0255429i	0.00161333	+	0.000931455i
$753$	−40.6634	−	9.10018i	−1.48186	−	0.331629i
$754$	25.6548	+	22.7247i	0.934294	+	0.827585i
$755$	7.90216			0.287589
$756$	−10.8080	−	8.49634i	−0.393082	−	0.309009i
$757$	−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	$-0.356906\pi$
$758$	−4.29409	+	2.47919i	−0.155968	+	0.0900483i
$759$	−0.662539	+	2.96050i	−0.0240487	+	0.107459i
$760$			4.36015i			0.158159i
$761$	−2.09713	+	1.21078i	−0.0760207	+	0.0438906i	−0.537529	−	0.843246i	$-0.680642\pi$
$761$	−2.09713	+	1.21078i	−0.0760207	+	0.0438906i	0.461508	+	0.887136i	$0.347309\pi$
$762$	6.54028	−	7.10888i	0.236930	−	0.257528i
$763$	−41.2901	+	23.5248i	−1.49480	+	0.851654i
$764$	−11.3808	+	6.57071i	−0.411743	+	0.237720i
$765$	−1.03037	+	0.0859958i	−0.0372531	+	0.00310918i
$766$	9.40956	−	5.43261i	0.339981	−	0.196288i
$767$	−10.5662	+	3.52843i	−0.381525	+	0.127404i
$768$	0.517534	+	1.65292i	0.0186749	+	0.0596448i
$769$	4.75805	+	8.24119i	0.171580	+	0.297185i	0.938972	−	0.343993i	$-0.111780\pi$
$769$	4.75805	+	8.24119i	0.171580	+	0.297185i	−0.767393	+	0.641177i	$0.778446\pi$
$770$	−1.43392	+	0.816968i	−0.0516749	+	0.0294415i
$771$	15.2857	+	48.8200i	0.550500	+	1.75821i
$772$	10.9286	+	6.30961i	0.393328	+	0.227088i
$773$			34.8889i			1.25487i	0.778671	+	0.627433i	$0.215894\pi$
$773$			34.8889i			1.25487i	−0.778671	+	0.627433i	$0.784106\pi$
$774$	−0.300821	−	3.60433i	−0.0108128	−	0.129555i
$775$	−4.99398	+	8.64982i	−0.179389	+	0.310711i
$776$	−5.10398	+	8.84035i	−0.183222	+	0.317350i
$777$	−19.0530	+	5.84603i	−0.683524	+	0.209725i
$778$	−33.7632	+	19.4932i	−1.21047	+	0.698865i
$779$	32.4244	+	18.7202i	1.16172	+	0.670722i
$780$	6.24393	−	0.639892i	0.223569	−	0.0229118i
$781$	−0.386014	−	0.668596i	−0.0138127	−	0.0239243i
$782$		−	0.967778i		−	0.0346077i
$783$	48.9294	+	6.74046i	1.74859	+	0.240884i
$784$	6.99954	+	0.0801202i	0.249984	+	0.00286144i
$785$	−23.0870			−0.824010
$786$	30.8568	+	6.90555i	1.10063	+	0.246313i
$787$	38.4147			1.36933			0.684667	−	0.728856i	$-0.259948\pi$
$787$	38.4147			1.36933			0.684667	+	0.728856i	$0.259948\pi$
$788$	−0.693687	−	1.20150i	−0.0247116	−	0.0428017i
$789$	8.33390	−	37.2393i	0.296695	−	1.32576i
$790$	0.797410	−	0.460385i	0.0283706	−	0.0163798i
$791$	11.2386	+	6.57467i	0.399600	+	0.233768i
$792$	−0.154854	−	1.85541i	−0.00550250	−	0.0659290i
$793$	−18.0351	−	15.9753i	−0.640446	−	0.567299i
$794$	−11.1038	−	19.2323i	−0.394058	−	0.682528i
$795$	−2.49368	−	7.96443i	−0.0884418	−	0.282469i
$796$		−	8.75865i		−	0.310442i
$797$	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
$800$	−1.99492	−	3.45530i	−0.0705311	−	0.122163i
$801$	−6.15945	−	8.87190i	−0.217634	−	0.313473i
$802$	−29.6513			−1.04702
$803$	5.53783			0.195426
$804$	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
$807$	3.32026	+	10.6044i	0.116879	+	0.373292i
$808$	4.95624	−	8.58446i	0.174360	−	0.302000i
$809$	−19.6426	−	11.3406i	−0.690596	−	0.398716i	0.113239	−	0.993568i	$-0.463877\pi$
$809$	−19.6426	−	11.3406i	−0.690596	−	0.398716i	−0.803835	+	0.594852i	$0.797211\pi$
$810$	6.97560	−	5.75880i	0.245098	−	0.202344i
$811$	17.6451			0.619604			0.309802	−	0.950801i	$-0.399737\pi$
$811$	17.6451			0.619604			0.309802	+	0.950801i	$0.399737\pi$
$812$	−21.8512	+	12.4496i	−0.766827	+	0.436895i
$813$	10.6802	+	34.1108i	0.374570	+	1.19632i
$814$	−2.33748	−	1.34954i	−0.0819286	−	0.0473015i
$815$	−8.89127			−0.311447
$816$	0.177470	+	0.566810i	0.00621268	+	0.0198423i
$817$	−5.23020			−0.182981
$818$	−1.06094			−0.0370949
$819$	22.8281	+	17.2592i	0.797678	+	0.603084i
$820$	8.67419			0.302916
$821$	−6.27151			−0.218877			−0.109439	−	0.993994i	$-0.534905\pi$
$821$	−6.27151			−0.218877			−0.109439	+	0.993994i	$0.534905\pi$
$822$	4.19519	+	13.3988i	0.146324	+	0.467337i
$823$	−18.8732			−0.657880			−0.328940	−	0.944351i	$-0.606691\pi$
$823$	−18.8732			−0.657880			−0.328940	+	0.944351i	$0.606691\pi$
$824$	8.93253	+	5.15720i	0.311180	+	0.179660i
$825$	1.28150	+	4.09293i	0.0446163	+	0.142497i
$826$	0.0467817	−	8.17425i	0.00162774	−	0.284419i
$827$	37.5661			1.30630			0.653150	−	0.757229i	$-0.273447\pi$
$827$	37.5661			1.30630			0.653150	+	0.757229i	$0.273447\pi$
$828$	4.82851	+	6.95485i	0.167802	+	0.241698i
$829$	27.9539	+	16.1392i	0.970879	+	0.560537i	0.899504	−	0.436912i	$-0.143928\pi$
$829$	27.9539	+	16.1392i	0.970879	+	0.560537i	0.0713749	+	0.997450i	$0.477261\pi$
$830$	6.64657	−	11.5122i	0.230706	−	0.399594i
$831$	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
$834$	7.21985	−	32.2613i	0.250003	−	1.11712i
$835$	−4.59445			−0.158998
$836$	−2.69235			−0.0931170
$837$	−1.77517	+	12.8861i	−0.0613589	+	0.445408i
$838$	2.10360	+	3.64355i	0.0726678	+	0.125864i
$839$	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
$842$		−	12.1375i		−	0.418285i
$843$	−15.7631	−	50.3449i	−0.542910	−	1.73397i
$844$	12.8567	+	22.2684i	0.442545	+	0.766510i
$845$	−12.9704	+	1.57690i	−0.446194	+	0.0542470i
$846$	−0.152727	+	0.0127467i	−0.00525085	+	0.000438241i
$847$	13.9027	+	24.4016i	0.477702	+	0.838449i
$848$	−4.15182	+	2.39705i	−0.142574	+	0.0823151i
$849$	−6.65670	+	29.7449i	−0.228457	+	1.02084i
$850$	−0.684086	−	1.18487i	−0.0234640	−	0.0406408i
$851$	12.2739			0.420744
$852$	−2.10260	−	0.470547i	−0.0720339	−	0.0161207i
$853$	24.5020			0.838933			0.419467	−	0.907771i	$-0.362217\pi$
$853$	24.5020			0.838933			0.419467	+	0.907771i	$0.362217\pi$
$854$	15.3612	−	8.75197i	0.525650	−	0.299486i
$855$	−7.45974	−	10.7448i	−0.255118	−	0.367464i
$856$		−	14.7159i		−	0.502977i
$857$	4.35323	+	7.54001i	0.148703	+	0.257562i	0.930749	−	0.365660i	$-0.119157\pi$
$857$	4.35323	+	7.54001i	0.148703	+	0.257562i	−0.782045	+	0.623222i	$0.785823\pi$
$858$	0.395128	+	3.85557i	0.0134894	+	0.131627i
$859$	31.0506	+	17.9271i	1.05943	+	0.611664i	0.925275	−	0.379296i	$-0.123834\pi$
$859$	31.0506	+	17.9271i	1.05943	+	0.611664i	0.134158	+	0.990960i	$0.457167\pi$
$860$	−1.04939	+	0.605865i	−0.0357838	+	0.0206598i
$861$	28.9520	+	26.9438i	0.986680	+	0.918243i
$862$	−3.37233	+	5.84104i	−0.114862	+	0.198947i
$863$	5.26328	−	9.11626i	0.179164	−	0.310321i	−0.762430	−	0.647070i	$-0.775994\pi$
$863$	5.26328	−	9.11626i	0.179164	−	0.310321i	0.941594	+	0.336749i	$0.109327\pi$
$864$	−4.10334	−	3.18788i	−0.139598	−	0.108454i
$865$			13.1899i			0.448471i
$866$	−25.4298	−	14.6819i	−0.864139	−	0.498911i
$867$	−8.73723	−	27.9053i	−0.296732	−	0.947715i
$868$	−3.27873	−	5.75474i	−0.111287	−	0.195329i
$869$	0.284284	+	0.492394i	0.00964366	+	0.0167033i
$870$	−4.94429	−	15.7913i	−0.167627	−	0.535375i
$871$	−3.95725	+	19.3915i	−0.134086	+	0.657055i
$872$	−15.5550	+	8.98070i	−0.526760	+	0.304125i
$873$	−2.54705	−	30.5178i	−0.0862044	−	1.03287i
$874$	10.6030	−	6.12164i	0.358652	−	0.207068i
$875$	0.136810	−	23.9050i	0.00462501	−	0.808136i
$876$	10.4642	−	11.3739i	0.353551	−	0.384288i
$877$	45.3851	−	26.2031i	1.53255	−	0.884816i	0.533303	−	0.845924i	$-0.320950\pi$
$877$	45.3851	−	26.2031i	1.53255	−	0.884816i	0.999243	−	0.0388923i	$-0.0123829\pi$
$878$			3.82128i			0.128962i
$879$	−6.27786	+	28.0521i	−0.211747	+	0.946173i
$880$	−0.540195	+	0.311882i	−0.0182100	+	0.0105135i
$881$	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	$0.670252\pi$
$882$	−17.3862	+	11.7780i	−0.585423	+	0.396586i
$883$	0.360145			0.0121199			0.00605993	−	0.999982i	$-0.498071\pi$
$883$	0.360145			0.0121199			0.00605993	+	0.999982i	$0.498071\pi$
$884$	−0.391616	−	1.17273i	−0.0131715	−	0.0394433i
$885$	5.24867	+	1.17462i	0.176432	+	0.0394843i
$886$	−20.4039	−	11.7802i	−0.685483	−	0.395764i
$887$	14.3871			0.483072			0.241536	−	0.970392i	$-0.422349\pi$
$887$	14.3871			0.483072			0.241536	+	0.970392i	$0.422349\pi$
$888$	−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
$891$	3.55601	+	4.30737i	0.119131	+	0.144302i
$892$	−4.67710	−	8.10097i	−0.156601	−	0.271240i
$893$			0.221619i			0.00741621i
$894$	−5.50253	+	5.98091i	−0.184032	+	0.200032i
$895$	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
$899$	20.6073	+	11.8976i	0.687292	+	0.396808i
$900$	10.8278	+	5.10188i	0.360925	+	0.170063i
$901$	−1.42371	+	0.821982i	−0.0474308	+	0.0273842i
$902$			5.35624i			0.178343i
$903$	−5.38450	−	1.23741i	−0.179185	−	0.0411785i
$904$	4.26195	+	2.46064i	0.141750	+	0.0818397i
$905$	−11.2723	+	19.5242i	−0.374705	+	0.649008i
$906$	10.0218	+	9.22021i	0.332952	+	0.306321i
$907$	−1.38473	+	2.39843i	−0.0459793	+	0.0796385i	−0.888099	−	0.459652i	$-0.847974\pi$
$907$	−1.38473	+	2.39843i	−0.0459793	+	0.0796385i	0.842120	+	0.539290i	$0.181307\pi$
$908$			11.7911i			0.391300i
$909$	2.47332	+	29.6344i	0.0820348	+	0.982911i
$910$	1.97080	−	9.38298i	0.0653315	−	0.311043i
$911$			22.2089i			0.735813i	0.929863	+	0.367906i	$0.119925\pi$
$911$			22.2089i			0.735813i	−0.929863	+	0.367906i	$0.880075\pi$
$912$	−5.08741	+	5.52970i	−0.168461	+	0.183107i
$913$	7.10868	+	4.10420i	0.235263	+	0.135829i
$914$			31.8029i			1.05195i
$915$	3.47579	+	11.1011i	0.114906	+	0.366993i
$916$	−5.47329	+	9.48001i	−0.180842	+	0.313228i
$917$	24.3892	−	41.6906i	0.805404	−	1.37674i
$918$	−1.40709	−	1.09317i	−0.0464409	−	0.0360800i
$919$	15.5304	+	26.8995i	0.512302	+	0.887333i	0.999898	+	0.0142636i	$0.00454041\pi$
$919$	15.5304	+	26.8995i	0.512302	+	0.887333i	−0.487596	+	0.873069i	$0.662126\pi$
$920$	1.41826	−	2.45650i	0.0467586	−	0.0809883i
$921$	−13.6112	−	43.4722i	−0.448505	−	1.43246i
$922$	−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
$926$		−	27.0578i		−	0.889175i
$927$	−30.8360	+	2.57360i	−1.01279	+	0.0845283i
$928$	−8.23191	+	4.75270i	−0.270226	+	0.156015i
$929$	−45.6175	+	26.3373i	−1.49666	+	0.864097i	−0.999993	−	0.00384362i	$-0.998777\pi$
$929$	−45.6175	+	26.3373i	−1.49666	+	0.864097i	−0.496668	+	0.867941i	$0.665443\pi$
$930$	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
$933$	−16.1639	+	17.5692i	−0.529182	+	0.575188i
$934$	15.8112	−	27.3859i	0.517360	−	0.896093i
$935$	−0.185240	+	0.106948i	−0.00605800	+	0.00349759i
$936$	8.66540	+	6.47386i	0.283237	+	0.211605i
$937$			31.2959i			1.02239i	0.859464	+	0.511196i	$0.170797\pi$
$937$			31.2959i			1.02239i	−0.859464	+	0.511196i	$0.829203\pi$
$938$	−12.5353	−	7.33322i	−0.409291	−	0.239438i
$939$	−3.46476	+	15.4820i	−0.113068	+	0.505235i
$940$	0.0256723	+	0.0444658i	0.000837339	+	0.00145031i
$941$	−46.2726	+	26.7155i	−1.50844	+	0.870900i	−0.508492	+	0.861067i	$0.669797\pi$
$941$	−46.2726	+	26.7155i	−1.50844	+	0.870900i	−0.999952	+	0.00983388i	$0.996870\pi$
$942$	−29.2797	−	26.9378i	−0.953985	−	0.877681i
$943$	−12.1785	−	21.0939i	−0.396588	−	0.686911i
$944$		−	3.08963i		−	0.100559i
$945$	−5.13770	−	12.8267i	−0.167129	−	0.417252i
$946$	−0.374116	−	0.647988i	−0.0121636	−	0.0210679i
$947$	54.5826			1.77370			0.886849	−	0.462060i	$-0.152889\pi$
$947$	54.5826			1.77370			0.886849	+	0.462060i	$0.152889\pi$
$948$	1.54848	+	0.346539i	0.0502923	+	0.0112551i
$949$	−21.3325	+	24.0832i	−0.692483	+	0.781773i
$950$	8.65432	−	14.9897i	0.280783	−	0.486331i
$951$	8.01431	+	1.79355i	0.259882	+	0.0581598i
$952$	0.907250	+	0.00519224i	0.0294041	+	0.000168282i
$953$	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	$0.661413\pi$
$954$	6.13030	−	13.0104i	0.198476	−	0.421227i
$955$	−13.2080			−0.427401
$956$	−30.4624			−0.985225
$957$	9.75098	−	3.05305i	0.315204	−	0.0986912i
$958$	−9.21963	−	5.32296i	−0.297873	−	0.171977i
$959$	21.4464	+	0.122739i	0.692541	+	0.00396345i
$960$	−0.380181	+	1.69880i	−0.0122703	+	0.0548287i
$961$	12.3666	−	21.4196i	0.398924	−	0.690956i
$962$	14.8733	−	4.96669i	0.479534	−	0.160133i
$963$	25.1772	+	36.2645i	0.811324	+	1.16861i
$964$	5.69491			0.183421
$965$	6.34158	+	10.9839i	0.204143	+	0.353585i
$966$	12.3641	−	3.79368i	0.397809	−	0.122060i
$967$		−	31.5161i		−	1.01349i	−0.862096	−	0.506745i	$-0.830849\pi$
$967$		−	31.5161i		−	1.01349i	0.862096	−	0.506745i	$-0.169151\pi$
$968$	5.30742	+	9.19271i	0.170587	+	0.295465i
$969$	−1.74454	+	1.89621i	−0.0560428	+	0.0609150i
$970$	−8.88514	+	5.12984i	−0.285285	+	0.164709i
$971$	−9.45417	−	16.3751i	−0.303399	−	0.525502i	0.673505	−	0.739183i	$-0.264788\pi$
$971$	−9.45417	−	16.3751i	−0.303399	−	0.525502i	−0.976903	+	0.213681i	$0.931455\pi$
$972$	15.5660	+	0.835596i	0.499281	+	0.0268018i
$973$	−43.5881	−	25.4993i	−1.39737	−	0.817470i
$974$		−	39.5929i		−	1.26864i
$975$	−22.7360	−	10.1935i	−0.728136	−	0.326453i
$976$	5.78697	−	3.34111i	0.185236	−	0.106946i
$977$	−25.3197	+	43.8550i	−0.810049	+	1.40305i	0.102781	+	0.994704i	$0.467226\pi$
$977$	−25.3197	+	43.8550i	−0.810049	+	1.40305i	−0.912829	+	0.408341i	$0.866107\pi$
$978$	−11.2762	−	10.3743i	−0.360574	−	0.331733i
$979$	−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
$982$	27.5795	−	15.9230i	0.880098	−	0.508125i
$983$	21.4061	−	12.3588i	0.682750	−	0.394186i	−0.118140	−	0.992997i	$-0.537693\pi$
$983$	21.4061	−	12.3588i	0.682750	−	0.394186i	0.800890	+	0.598811i	$0.204360\pi$
$984$	11.0009	+	10.1210i	0.350696	+	0.322646i
$985$		−	1.39440i		−	0.0444294i
$986$	−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
$990$	0.797616	−	1.69279i	0.0253499	−	0.0538004i
$991$	8.33380	−	14.4346i	0.264732	−	0.458529i	−0.702761	−	0.711426i	$-0.748050\pi$
$991$	8.33380	−	14.4346i	0.264732	−	0.458529i	0.967493	+	0.252896i	$0.0813832\pi$
$992$	−1.25167	−	2.16796i	−0.0397406	−	0.0688328i
$993$	31.1284	+	28.6386i	0.987831	+	0.908820i
$994$	−1.66190	+	2.84082i	−0.0527121	+	0.0901052i
$995$	4.40151	−	7.62364i	0.139537	−	0.241686i
$996$	21.8618	−	6.84498i	0.692718	−	0.216892i
$997$		−	10.1184i		−	0.320452i	−0.987080	−	0.160226i	$-0.948778\pi$
$997$		−	10.1184i		−	0.320452i	0.987080	−	0.160226i	$-0.0512222\pi$
$998$	7.30529	+	4.21771i	0.231245	+	0.133509i
$999$	13.8642	−	17.8455i	0.438644	−	0.564607i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.16	✓	34	91.17	odd	6
546.2.bi.e.257.16	yes	34	3.2	odd	2
546.2.bi.f.17.10	yes	34	273.17	even	6	inner
546.2.bi.f.257.10	yes	34	1.1	even	1	trivial
546.2.bn.e.101.5	yes	34	7.3	odd	6
546.2.bn.e.173.5	yes	34	39.17	odd	6
546.2.bn.f.101.13	yes	34	21.17	even	6
546.2.bn.f.173.13	yes	34	13.4	even	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.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(0.517534 + 1.65292i) q^{3} +1.00000 q^{4} +(0.870413 + 0.502533i) q^{5} +(0.517534 + 1.65292i) q^{6} +(2.64571 + 0.0151415i) q^{7} +1.00000 q^{8} +(-2.46432 + 1.71089i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(0.517534 + 1.65292i) q^{3} +1.00000 q^{4} +(0.870413 + 0.502533i) q^{5} +(0.517534 + 1.65292i) q^{6} +(2.64571 + 0.0151415i) q^{7} +1.00000 q^{8} +(-2.46432 + 1.71089i) q^{9} +(0.870413 + 0.502533i) q^{10} +(-0.310310 + 0.537472i) q^{11} +(0.517534 + 1.65292i) q^{12} +(-1.14202 - 3.41991i) q^{13} +(2.64571 + 0.0151415i) q^{14} +(-0.380181 + 1.69880i) q^{15} +1.00000 q^{16} +0.342914 q^{17} +(-2.46432 + 1.71089i) q^{18} +(2.16909 + 3.75697i) q^{19} +(0.870413 + 0.502533i) q^{20} +(1.34422 + 4.38099i) q^{21} +(-0.310310 + 0.537472i) q^{22} -2.82222i q^{23} +(0.517534 + 1.65292i) q^{24} +(-1.99492 - 3.45530i) q^{25} +(-1.14202 - 3.41991i) q^{26} +(-4.10334 - 3.18788i) q^{27} +(2.64571 + 0.0151415i) q^{28} +(-8.23191 + 4.75270i) q^{29} +(-0.380181 + 1.69880i) q^{30} +(-1.25167 - 2.16796i) q^{31} +1.00000 q^{32} +(-1.04900 - 0.234758i) q^{33} +0.342914 q^{34} +(2.29525 + 1.34273i) q^{35} +(-2.46432 + 1.71089i) q^{36} +4.34903i q^{37} +(2.16909 + 3.75697i) q^{38} +(5.06181 - 3.65760i) q^{39} +(0.870413 + 0.502533i) q^{40} +(7.47421 - 4.31523i) q^{41} +(1.34422 + 4.38099i) q^{42} +(-0.602811 + 1.04410i) q^{43} +(-0.310310 + 0.537472i) q^{44} +(-3.00475 + 0.250780i) q^{45} -2.82222i q^{46} +(0.0442417 + 0.0255429i) q^{47} +(0.517534 + 1.65292i) q^{48} +(6.99954 + 0.0801202i) q^{49} +(-1.99492 - 3.45530i) q^{50} +(0.177470 + 0.566810i) q^{51} +(-1.14202 - 3.41991i) q^{52} +(-4.15182 + 2.39705i) q^{53} +(-4.10334 - 3.18788i) q^{54} +(-0.540195 + 0.311882i) q^{55} +(2.64571 + 0.0151415i) q^{56} +(-5.08741 + 5.52970i) q^{57} +(-8.23191 + 4.75270i) q^{58} -3.08963i q^{59} +(-0.380181 + 1.69880i) q^{60} +(5.78697 - 3.34111i) q^{61} +(-1.25167 - 2.16796i) q^{62} +(-6.54577 + 4.48920i) q^{63} +1.00000 q^{64} +(0.724585 - 3.55064i) q^{65} +(-1.04900 - 0.234758i) q^{66} +(-4.75367 - 2.74453i) q^{67} +0.342914 q^{68} +(4.66492 - 1.46060i) q^{69} +(2.29525 + 1.34273i) q^{70} +(-0.621982 + 1.07730i) q^{71} +(-2.46432 + 1.71089i) q^{72} +(-4.46154 - 7.72761i) q^{73} +4.34903i q^{74} +(4.67892 - 5.08569i) 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} +(0.870413 + 0.502533i) q^{80} +(3.14571 - 8.43235i) q^{81} +(7.47421 - 4.31523i) q^{82} -13.2261i q^{83} +(1.34422 + 4.38099i) q^{84} +(0.298476 + 0.172325i) q^{85} +(-0.602811 + 1.04410i) q^{86} +(-12.1161 - 11.1470i) q^{87} +(-0.310310 + 0.537472i) q^{88} +3.60015i q^{89} +(-3.00475 + 0.250780i) q^{90} +(-2.96968 - 9.06537i) q^{91} -2.82222i q^{92} +(2.93569 - 3.19091i) q^{93} +(0.0442417 + 0.0255429i) q^{94} +4.36015i q^{95} +(0.517534 + 1.65292i) q^{96} +(-5.10398 + 8.84035i) q^{97} +(6.99954 + 0.0801202i) q^{98} +(-0.154854 - 1.85541i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9}+O(q^{10}) \) 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9	\( 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9} + 9 q^{10} + 9 q^{11} + 6 q^{12} + 8 q^{13} + 4 q^{14} - 17 q^{15} + 34 q^{16} + 12 q^{17} + 4 q^{18} - 5 q^{19} + 9 q^{20} - 7 q^{21} + 9 q^{22} + 6 q^{24} + 16 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} + 27 q^{29} - 17 q^{30} - q^{31} + 34 q^{32} + 12 q^{34} - 3 q^{35} + 4 q^{36} - 5 q^{38} - 10 q^{39} + 9 q^{40} - 3 q^{41} - 7 q^{42} - 3 q^{43} + 9 q^{44} + 9 q^{45} - 27 q^{47} + 6 q^{48} - 2 q^{49} + 16 q^{50} - 36 q^{51} + 8 q^{52} - 21 q^{53} - 18 q^{54} - 57 q^{55} + 4 q^{56} - 17 q^{57} + 27 q^{58} - 17 q^{60} - 51 q^{61} - q^{62} - 24 q^{63} + 34 q^{64} - 21 q^{65} - 21 q^{67} + 12 q^{68} + 30 q^{69} - 3 q^{70} - 15 q^{71} + 4 q^{72} - 19 q^{73} - 54 q^{75} - 5 q^{76} + 9 q^{77} - 10 q^{78} - 9 q^{79} + 9 q^{80} + 28 q^{81} - 3 q^{82} - 7 q^{84} - 42 q^{85} - 3 q^{86} - 81 q^{87} + 9 q^{88} + 9 q^{90} - 72 q^{91} - 17 q^{93} - 27 q^{94} + 6 q^{96} + 19 q^{97} - 2 q^{98} - 27 q^{99}+O(q^{100}) \) 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9 + 9 * q^10 + 9 * q^11 + 6 * q^12 + 8 * q^13 + 4 * q^14 - 17 * q^15 + 34 * q^16 + 12 * q^17 + 4 * q^18 - 5 * q^19 + 9 * q^20 - 7 * q^21 + 9 * q^22 + 6 * q^24 + 16 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 + 27 * q^29 - 17 * q^30 - q^31 + 34 * q^32 + 12 * q^34 - 3 * q^35 + 4 * q^36 - 5 * q^38 - 10 * q^39 + 9 * q^40 - 3 * q^41 - 7 * q^42 - 3 * q^43 + 9 * q^44 + 9 * q^45 - 27 * q^47 + 6 * q^48 - 2 * q^49 + 16 * q^50 - 36 * q^51 + 8 * q^52 - 21 * q^53 - 18 * q^54 - 57 * q^55 + 4 * q^56 - 17 * q^57 + 27 * q^58 - 17 * q^60 - 51 * q^61 - q^62 - 24 * q^63 + 34 * q^64 - 21 * q^65 - 21 * q^67 + 12 * q^68 + 30 * q^69 - 3 * q^70 - 15 * q^71 + 4 * q^72 - 19 * q^73 - 54 * q^75 - 5 * q^76 + 9 * q^77 - 10 * q^78 - 9 * q^79 + 9 * q^80 + 28 * q^81 - 3 * q^82 - 7 * q^84 - 42 * q^85 - 3 * q^86 - 81 * q^87 + 9 * q^88 + 9 * q^90 - 72 * q^91 - 17 * q^93 - 27 * q^94 + 6 * q^96 + 19 * q^97 - 2 * q^98 - 27 * q^99

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