LMFDB - Embedded newform 546.2.bi.e.257.16

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			257.16
Character	$\chi$	$=$	546.257
Dual form			546.2.bi.e.17.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(1.69024 - 0.378264i) q^{3} +1.00000 q^{4} +(-0.870413 - 0.502533i) q^{5} +(-1.69024 + 0.378264i) q^{6} +(2.64571 + 0.0151415i) q^{7} -1.00000 q^{8} +(2.71383 - 1.27872i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(1.69024 - 0.378264i) q^{3} +1.00000 q^{4} +(-0.870413 - 0.502533i) q^{5} +(-1.69024 + 0.378264i) q^{6} +(2.64571 + 0.0151415i) q^{7} -1.00000 q^{8} +(2.71383 - 1.27872i) q^{9} +(0.870413 + 0.502533i) q^{10} +(0.310310 - 0.537472i) q^{11} +(1.69024 - 0.378264i) q^{12} +(-1.14202 - 3.41991i) q^{13} +(-2.64571 - 0.0151415i) q^{14} +(-1.66130 - 0.520156i) q^{15} +1.00000 q^{16} -0.342914 q^{17} +(-2.71383 + 1.27872i) q^{18} +(2.16909 + 3.75697i) q^{19} +(-0.870413 - 0.502533i) q^{20} +(4.47761 - 0.975184i) q^{21} +(-0.310310 + 0.537472i) q^{22} +2.82222i q^{23} +(-1.69024 + 0.378264i) 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} +(1.66130 + 0.520156i) q^{30} +(-1.25167 - 2.16796i) q^{31} -1.00000 q^{32} +(0.321192 - 1.02584i) q^{33} +0.342914 q^{34} +(-2.29525 - 1.34273i) q^{35} +(2.71383 - 1.27872i) q^{36} +4.34903i q^{37} +(-2.16909 - 3.75697i) q^{38} +(-3.22393 - 5.34849i) q^{39} +(0.870413 + 0.502533i) q^{40} +(-7.47421 + 4.31523i) q^{41} +(-4.47761 + 0.975184i) 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} +(1.69024 - 0.378264i) q^{48} +(6.99954 + 0.0801202i) q^{49} +(1.99492 + 3.45530i) q^{50} +(-0.579607 + 0.129712i) 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} +(-1.66130 - 0.520156i) q^{60} +(5.78697 - 3.34111i) q^{61} +(1.25167 + 2.16796i) q^{62} +(7.19937 - 3.34202i) q^{63} +1.00000 q^{64} +(-0.724585 + 3.55064i) q^{65} +(-0.321192 + 1.02584i) q^{66} +(-4.75367 - 2.74453i) q^{67} -0.342914 q^{68} +(1.06755 + 4.77024i) q^{69} +(2.29525 + 1.34273i) q^{70} +(0.621982 - 1.07730i) q^{71} +(-2.71383 + 1.27872i) 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} +(3.22393 + 5.34849i) q^{78} +(0.458065 - 0.793391i) q^{79} +(-0.870413 - 0.502533i) q^{80} +(5.72977 - 6.94044i) q^{81} +(7.47421 - 4.31523i) q^{82} +13.2261i q^{83} +(4.47761 - 0.975184i) 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} +(-1.69024 + 0.378264i) 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} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9} + 9 q^{10} - 9 q^{11} + 3 q^{12} + 8 q^{13} - 4 q^{14} - 4 q^{15} + 34 q^{16} - 12 q^{17} + 11 q^{18} - 5 q^{19} - 9 q^{20} + 4 q^{21} + 9 q^{22} - 3 q^{24} + 16 q^{25} - 8 q^{26} + 18 q^{27} + 4 q^{28} - 27 q^{29} + 4 q^{30} - q^{31} - 34 q^{32} + 21 q^{33} + 12 q^{34} + 3 q^{35} - 11 q^{36} + 5 q^{38} + 7 q^{39} + 9 q^{40} + 3 q^{41} - 4 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} + 27 q^{47} + 3 q^{48} - 2 q^{49} - 16 q^{50} + 24 q^{51} + 8 q^{52} + 21 q^{53} - 18 q^{54} - 57 q^{55} - 4 q^{56} + 17 q^{57} + 27 q^{58} - 4 q^{60} - 51 q^{61} + q^{62} + 3 q^{63} + 34 q^{64} + 21 q^{65} - 21 q^{66} - 21 q^{67} - 12 q^{68} + 42 q^{69} - 3 q^{70} + 15 q^{71} + 11 q^{72} - 19 q^{73} + 54 q^{75} - 5 q^{76} - 9 q^{77} - 7 q^{78} - 9 q^{79} - 9 q^{80} - 23 q^{81} - 3 q^{82} + 4 q^{84} - 42 q^{85} + 3 q^{86} + 81 q^{87} + 9 q^{88} - 9 q^{90} - 72 q^{91} + 17 q^{93} - 27 q^{94} - 3 q^{96} + 19 q^{97} + 2 q^{98} + 27 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9 + 9 * q^10 - 9 * q^11 + 3 * q^12 + 8 * q^13 - 4 * q^14 - 4 * q^15 + 34 * q^16 - 12 * q^17 + 11 * q^18 - 5 * q^19 - 9 * q^20 + 4 * q^21 + 9 * q^22 - 3 * q^24 + 16 * q^25 - 8 * q^26 + 18 * q^27 + 4 * q^28 - 27 * q^29 + 4 * q^30 - q^31 - 34 * q^32 + 21 * q^33 + 12 * q^34 + 3 * q^35 - 11 * q^36 + 5 * q^38 + 7 * q^39 + 9 * q^40 + 3 * q^41 - 4 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 + 27 * q^47 + 3 * q^48 - 2 * q^49 - 16 * q^50 + 24 * q^51 + 8 * q^52 + 21 * q^53 - 18 * q^54 - 57 * q^55 - 4 * q^56 + 17 * q^57 + 27 * q^58 - 4 * q^60 - 51 * q^61 + q^62 + 3 * q^63 + 34 * q^64 + 21 * q^65 - 21 * q^66 - 21 * q^67 - 12 * q^68 + 42 * q^69 - 3 * q^70 + 15 * q^71 + 11 * q^72 - 19 * q^73 + 54 * q^75 - 5 * q^76 - 9 * q^77 - 7 * q^78 - 9 * q^79 - 9 * q^80 - 23 * q^81 - 3 * q^82 + 4 * 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 - 3 * 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
$3$	1.69024	−	0.378264i	0.975861	−	0.218391i
$3$	1.69024	−	0.378264i	0.975861	−	0.218391i
$4$	1.00000			0.500000
$5$	−0.870413	−	0.502533i	−0.389260	−	0.224740i	0.292579	−	0.956241i	$-0.405486\pi$
$5$	−0.870413	−	0.502533i	−0.389260	−	0.224740i	−0.681840	+	0.731502i	$0.738820\pi$
$6$	−1.69024	+	0.378264i	−0.690038	+	0.154426i
$7$	2.64571	+	0.0151415i	0.999984	+	0.00572296i
$7$	2.64571	+	0.0151415i	0.999984	+	0.00572296i
$8$	−1.00000			−0.353553
$9$	2.71383	−	1.27872i	0.904611	−	0.426239i
$10$	0.870413	+	0.502533i	0.275249	+	0.158915i
$11$	0.310310	−	0.537472i	0.0935619	−	0.162054i	−0.815446	−	0.578834i	$-0.803508\pi$
$11$	0.310310	−	0.537472i	0.0935619	−	0.162054i	0.909007	+	0.416780i	$0.136841\pi$
$12$	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
$15$	−1.66130	−	0.520156i	−0.428945	−	0.134304i
$16$	1.00000			0.250000
$17$	−0.342914			−0.0831688			−0.0415844	−	0.999135i	$-0.513241\pi$
$17$	−0.342914			−0.0831688			−0.0415844	+	0.999135i	$0.513241\pi$
$18$	−2.71383	+	1.27872i	−0.639656	+	0.301396i
$19$	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
$21$	4.47761	−	0.975184i	0.977095	−	0.212803i
$22$	−0.310310	+	0.537472i	−0.0661582	+	0.114589i
$23$			2.82222i			0.588474i	0.955733	+	0.294237i	$0.0950655\pi$
$23$			2.82222i			0.588474i	−0.955733	+	0.294237i	$0.904935\pi$
$24$	−1.69024	+	0.378264i	−0.345019	+	0.0772129i
$25$	−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	$-0.322489\pi$
$29$	8.23191	−	4.75270i	1.52863	−	0.882553i	0.999420	−	0.0340609i	$-0.0108440\pi$
$30$	1.66130	+	0.520156i	0.303310	+	0.0949671i
$31$	−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
$33$	0.321192	−	1.02584i	0.0559123	−	0.178575i
$34$	0.342914			0.0588092
$35$	−2.29525	−	1.34273i	−0.387968	−	0.226964i
$36$	2.71383	−	1.27872i	0.452305	−	0.213119i
$37$			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
$39$	−3.22393	−	5.34849i	−0.516241	−	0.856443i
$40$	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	$0.568727\pi$
$42$	−4.47761	+	0.975184i	−0.690911	+	0.150474i
$43$	−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	0.496770	−	0.867882i	$-0.334519\pi$
$47$	−0.0442417	−	0.0255429i	−0.00645331	−	0.00372582i	−0.503223	+	0.864156i	$0.667853\pi$
$48$	1.69024	−	0.378264i	0.243965	−	0.0545977i
$49$	6.99954	+	0.0801202i	0.999934	+	0.0114457i
$50$	1.99492	+	3.45530i	0.282124	+	0.488654i
$51$	−0.579607	+	0.129712i	−0.0811612	+	0.0181633i
$52$	−1.14202	−	3.41991i	−0.158370	−	0.474256i
$53$	4.15182	−	2.39705i	0.570296	−	0.329260i	−0.186972	−	0.982365i	$-0.559867\pi$
$53$	4.15182	−	2.39705i	0.570296	−	0.329260i	0.757267	+	0.653105i	$0.226534\pi$
$54$	−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	$0.0644573\pi$
$59$			3.08963i			0.402235i	−0.979567	+	0.201118i	$0.935543\pi$
$60$	−1.66130	−	0.520156i	−0.214473	−	0.0671519i
$61$	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
$63$	7.19937	−	3.34202i	0.907035	−	0.421055i
$64$	1.00000			0.125000
$65$	−0.724585	+	3.55064i	−0.0898737	+	0.440402i
$66$	−0.321192	+	1.02584i	−0.0395360	+	0.126272i
$67$	−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
$69$	1.06755	+	4.77024i	0.128517	+	0.574269i
$70$	2.29525	+	1.34273i	0.274335	+	0.160488i
$71$	0.621982	−	1.07730i	0.0738157	−	0.127853i	−0.826755	−	0.562562i	$-0.809816\pi$
$71$	0.621982	−	1.07730i	0.0738157	−	0.127853i	0.900571	+	0.434710i	$0.143149\pi$
$72$	−2.71383	+	1.27872i	−0.319828	+	0.150698i
$73$	−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
$78$	3.22393	+	5.34849i	0.365038	+	0.605597i
$79$	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
$81$	5.72977	−	6.94044i	0.636641	−	0.771160i
$82$	7.47421	−	4.31523i	0.825388	−	0.476538i
$83$			13.2261i			1.45176i	0.687822	+	0.725879i	$0.258567\pi$
$83$			13.2261i			1.45176i	−0.687822	+	0.725879i	$0.741433\pi$
$84$	4.47761	−	0.975184i	0.488548	−	0.106401i
$85$	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	$-0.938889\pi$
$89$		−	3.60015i		−	0.381615i	0.981627	−	0.190807i	$-0.0611106\pi$
$90$	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
$96$	−1.69024	+	0.378264i	−0.172510	+	0.0386064i
$97$	−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	−0.999969	−	0.00787556i	$-0.997493\pi$
$101$	−4.95624	+	8.58446i	−0.493164	+	0.854185i	0.506805	+	0.862061i	$0.330826\pi$
$102$	0.579607	−	0.129712i	0.0573896	−	0.0128434i
$103$	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
$105$	−4.38743	−	1.40134i	−0.428170	−	0.136756i
$106$	−4.15182	+	2.39705i	−0.403260	+	0.232822i
$107$			14.7159i			1.42264i	0.702871	+	0.711318i	$0.251901\pi$
$107$			14.7159i			1.42264i	−0.702871	+	0.711318i	$0.748099\pi$
$108$	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
$111$	1.64508	+	7.35090i	0.156144	+	0.697717i
$112$	2.64571	+	0.0151415i	0.249996	+	0.00143074i
$113$	−4.26195	−	2.46064i	−0.400931	−	0.231478i	0.285955	−	0.958243i	$-0.407689\pi$
$113$	−4.26195	−	2.46064i	−0.400931	−	0.231478i	−0.686886	+	0.726766i	$0.741023\pi$
$114$	−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
$117$	−7.47235	−	7.82074i	−0.690819	−	0.723027i
$118$		−	3.08963i		−	0.284423i
$119$	−0.907250	−	0.00519224i	−0.0831674	−	0.000475972i
$120$	1.66130	+	0.520156i	0.151655	+	0.0474835i
$121$	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
$126$	−7.19937	+	3.34202i	−0.641371	+	0.297731i
$127$	−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
$129$	−0.623951	+	1.99280i	−0.0549358	+	0.175456i
$130$	0.724585	−	3.55064i	0.0635503	−	0.311411i
$131$	−9.12794	+	15.8101i	−0.797512	+	1.38133i	0.123720	+	0.992317i	$0.460517\pi$
$131$	−9.12794	+	15.8101i	−0.797512	+	1.38133i	−0.921232	+	0.389014i	$0.872816\pi$
$132$	0.321192	−	1.02584i	0.0279562	−	0.0892876i
$133$	5.68189	+	9.97269i	0.492682	+	0.864742i
$134$	4.75367	+	2.74453i	0.410655	+	0.237092i
$135$	−5.17362	+	0.712712i	−0.445274	+	0.0613405i
$136$	0.342914			0.0294046
$137$	−8.10612			−0.692553			−0.346276	−	0.938133i	$-0.612554\pi$
$137$	−8.10612			−0.692553			−0.346276	+	0.938133i	$0.612554\pi$
$138$	−1.06755	−	4.77024i	−0.0908755	−	0.406069i
$139$	−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
$141$	−0.0844411	−	0.0264387i	−0.00711122	−	0.00222654i
$142$	−0.621982	+	1.07730i	−0.0521956	+	0.0904054i
$143$	−2.19249	−	0.447425i	−0.183345	−	0.0374155i
$144$	2.71383	−	1.27872i	0.226153	−	0.106560i
$145$	−9.55354			−0.793379
$146$	4.46154	+	7.72761i	0.369239	+	0.639541i
$147$	11.8612	−	2.51225i	0.978297	−	0.207207i
$148$			4.34903i			0.357488i
$149$	−2.34608	−	4.06353i	−0.192198	−	0.332898i	0.753780	−	0.657127i	$-0.228228\pi$
$149$	−2.34608	−	4.06353i	−0.192198	−	0.332898i	−0.945979	+	0.324229i	$0.894895\pi$
$150$	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
$153$	−0.930610	+	0.438489i	−0.0752354	+	0.0354498i
$154$	−0.829127	+	1.41730i	−0.0668129	+	0.114209i
$155$			2.51603i			0.202092i
$156$	−3.22393	−	5.34849i	−0.258121	−	0.428222i
$157$	−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
$162$	−5.72977	+	6.94044i	−0.450173	+	0.545293i
$163$	−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	−0.338945	−	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
$171$	10.6906	+	7.42214i	0.817533	+	0.567585i
$172$	−0.602811	+	1.04410i	−0.0459639	+	0.0796118i
$173$	−6.56172	−	11.3652i	−0.498879	−	0.864083i	0.501121	−	0.865377i	$-0.332921\pi$
$173$	−6.56172	−	11.3652i	−0.498879	−	0.864083i	−0.999999	+	0.00129451i	$0.999588\pi$
$174$	−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
$177$	1.16870	+	5.22222i	0.0878445	+	0.392526i
$178$			3.60015i			0.269842i
$179$	−16.9504	−	9.78634i	−1.26693	−	0.731465i	−0.292528	−	0.956257i	$-0.594497\pi$
$179$	−16.9504	−	9.78634i	−1.26693	−	0.731465i	−0.974407	+	0.224792i	$0.927830\pi$
$180$	−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
$189$	10.9045	−	8.37208i	0.793186	−	0.608979i
$190$			4.36015i			0.316319i
$191$	11.3808	−	6.57071i	0.823486	−	0.475440i	−0.0281311	−	0.999604i	$-0.508956\pi$
$191$	11.3808	−	6.57071i	0.823486	−	0.475440i	0.851617	+	0.524164i	$0.175622\pi$
$192$	1.69024	−	0.378264i	0.121983	−	0.0272989i
$193$	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
$195$	0.118356	+	6.27552i	0.00847562	+	0.449399i
$196$	6.99954	+	0.0801202i	0.499967	+	0.00572287i
$197$	0.693687	+	1.20150i	0.0494232	+	0.0856034i	0.889679	−	0.456587i	$-0.150928\pi$
$197$	0.693687	+	1.20150i	0.0494232	+	0.0856034i	−0.840255	+	0.542191i	$0.817595\pi$
$198$	−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
$201$	−9.07302	−	2.84078i	−0.639961	−	0.200373i
$202$	4.95624	−	8.58446i	0.348720	−	0.604000i
$203$	21.8512	−	12.4496i	1.53365	−	0.873791i
$204$	−0.579607	+	0.129712i	−0.0405806	+	0.00908166i
$205$	8.67419			0.605832
$206$	−8.93253	−	5.15720i	−0.622359	−	0.359319i
$207$	3.60882	+	7.65904i	0.250830	+	0.532340i
$208$	−1.14202	−	3.41991i	−0.0791851	−	0.237128i
$209$	2.69235			0.186234
$210$	4.38743	+	1.40134i	0.302762	+	0.0967013i
$211$	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
$213$	0.643794	−	2.05618i	0.0441121	−	0.140887i
$214$		−	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
$222$	−1.64508	−	7.35090i	−0.110411	−	0.493360i
$223$	−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
$225$	−9.83224	−	6.82618i	−0.655482	−	0.455079i
$226$	4.26195	+	2.46064i	0.283501	+	0.163679i
$227$		−	11.7911i		−	0.782600i	−0.920263	−	0.391300i	$-0.872026\pi$
$227$		−	11.7911i		−	0.782600i	0.920263	−	0.391300i	$-0.127974\pi$
$228$	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
$231$	0.865312	−	2.70920i	0.0569334	−	0.178252i
$232$	−8.23191	+	4.75270i	−0.540451	+	0.312030i
$233$	−5.40464	−	3.12037i	−0.354070	−	0.204422i	0.312406	−	0.949949i	$-0.398865\pi$
$233$	−5.40464	−	3.12037i	−0.354070	−	0.204422i	−0.666476	+	0.745526i	$0.732198\pi$
$234$	7.47235	+	7.82074i	0.488483	+	0.511258i
$235$	0.0256723	+	0.0444658i	0.00167468	+	0.00290063i
$236$			3.08963i			0.201118i
$237$	0.474128	−	1.51429i	0.0307979	−	0.0983638i
$238$	0.907250	+	0.00519224i	0.0588083	+	0.000336563i
$239$	30.4624			1.97045			0.985225	−	0.171267i	$-0.0547862\pi$
$239$	30.4624			1.97045			0.985225	+	0.171267i	$0.0547862\pi$
$240$	−1.66130	−	0.520156i	−0.107236	−	0.0335759i
$241$	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
$243$	7.05938	−	13.8984i	0.452859	−	0.891582i
$244$	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
$249$	5.00298	+	22.3554i	0.317051	+	1.41671i
$250$		−	9.03538i		−	0.571448i
$251$	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
$254$	2.78854	+	4.82989i	0.174969	+	0.303055i
$255$	0.569682	+	0.178369i	0.0356749	+	0.0111699i
$256$	1.00000			0.0625000
$257$	−29.5356			−1.84238			−0.921189	−	0.389116i	$-0.872780\pi$
$257$	−29.5356			−1.84238			−0.921189	+	0.389116i	$0.872780\pi$
$258$	0.623951	−	1.99280i	0.0388455	−	0.124066i
$259$	−0.0658509	+	11.5063i	−0.00409178	+	0.714964i
$260$	−0.724585	+	3.55064i	−0.0449369	+	0.220201i
$261$	16.2627	−	23.4243i	1.00663	−	1.44993i
$262$	9.12794	−	15.8101i	0.563926	−	0.976748i
$263$	19.0802	+	11.0160i	1.17654	+	0.679274i	0.955211	−	0.295925i	$-0.0956280\pi$
$263$	19.0802	+	11.0160i	1.17654	+	0.679274i	0.221327	+	0.975200i	$0.428961\pi$
$264$	−0.321192	+	1.02584i	−0.0197680	+	0.0631359i
$265$	−4.81839			−0.295991
$266$	−5.68189	−	9.97269i	−0.348379	−	0.611465i
$267$	−1.36181	−	6.08512i	−0.0833412	−	0.372403i
$268$	−4.75367	−	2.74453i	−0.290377	−	0.167649i
$269$	−6.41553			−0.391162			−0.195581	−	0.980688i	$-0.562659\pi$
$269$	−6.41553			−0.391162			−0.195581	+	0.980688i	$0.562659\pi$
$270$	5.17362	−	0.712712i	0.314856	−	0.0433743i
$271$	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
$273$	−8.44858	−	14.1993i	−0.511331	−	0.859384i
$274$	8.10612			0.489709
$275$	−2.47617			−0.149319
$276$	1.06755	+	4.77024i	0.0642587	+	0.287134i
$277$	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
$279$	−6.16904	−	4.28295i	−0.369330	−	0.256413i
$280$	2.29525	+	1.34273i	0.137167	+	0.0802438i
$281$	30.4581			1.81698			0.908488	−	0.417911i	$-0.137238\pi$
$281$	30.4581			1.81698			0.908488	+	0.417911i	$0.137238\pi$
$282$	0.0844411	+	0.0264387i	0.00502839	+	0.00157440i
$283$	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
$285$	−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
$288$	−2.71383	+	1.27872i	−0.159914	+	0.0753491i
$289$	−16.8824			−0.993083
$290$	9.55354			0.561003
$291$	−5.28297	+	16.8730i	−0.309693	+	0.989112i
$292$	−4.46154	−	7.72761i	−0.261092	−	0.452224i
$293$	−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
$296$		−	4.34903i		−	0.252782i
$297$	−0.440093	−	3.19466i	−0.0255368	−	0.185373i
$298$	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
$303$	−5.13005	+	16.3846i	−0.294713	+	0.941269i
$304$	2.16909	+	3.75697i	0.124406	+	0.215477i
$305$	−6.71606			−0.384561
$306$	0.930610	−	0.438489i	0.0531995	−	0.0250668i
$307$	−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
$309$	17.0489	+	5.33806i	0.969879	+	0.303671i
$310$		−	2.51603i		−	0.142901i
$311$	−6.89170	−	11.9368i	−0.390793	−	0.676873i	0.601762	−	0.798676i	$-0.294466\pi$
$311$	−6.89170	−	11.9368i	−0.390793	−	0.676873i	−0.992554	+	0.121803i	$0.961132\pi$
$312$	3.22393	+	5.34849i	0.182519	+	0.302798i
$313$	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
$315$	−7.94590	−	0.708986i	−0.447701	−	0.0399469i
$316$	0.458065	−	0.793391i	0.0257681	−	0.0446317i
$317$	−2.37076	+	4.10628i	−0.133155	+	0.230631i	−0.924891	−	0.380232i	$-0.875844\pi$
$317$	−2.37076	+	4.10628i	−0.133155	+	0.230631i	0.791736	+	0.610863i	$0.209178\pi$
$318$	−6.11085	+	5.62208i	−0.342680	+	0.315271i
$319$		−	5.89923i		−	0.330293i
$320$	−0.870413	−	0.502533i	−0.0486575	−	0.0280924i
$321$	5.56648	+	24.8733i	0.310691	+	1.38829i
$322$	0.0427328	−	7.46677i	0.00238140	−	0.416107i
$323$	−0.743810	−	1.28832i	−0.0413867	−	0.0716838i
$324$	5.72977	−	6.94044i	0.318321	−	0.385580i
$325$	−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
$333$	5.56117	+	11.8025i	0.304750	+	0.646774i
$334$	−3.95886	+	2.28565i	−0.216619	+	0.125065i
$335$	2.75844	+	4.77776i	0.150710	+	0.261037i
$336$	4.47761	−	0.975184i	0.244274	−	0.0532006i
$337$	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
$339$	−8.13450	−	2.54693i	−0.441806	−	0.138330i
$340$	0.298476	+	0.172325i	0.0161872	+	0.00934566i
$341$	−1.55362			−0.0841335
$342$	−10.6906	−	7.42214i	−0.578083	−	0.401343i
$343$	18.5175	+	0.317958i	0.999853	+	0.0171681i
$344$	0.602811	−	1.04410i	0.0325014	−	0.0562940i
$345$	1.46800	−	4.68855i	0.0790342	−	0.252423i
$346$	6.56172	+	11.3652i	0.352760	+	0.610999i
$347$		−	34.7424i		−	1.86507i	−0.361079	−	0.932535i	$-0.617592\pi$
$347$		−	34.7424i		−	1.86507i	0.361079	−	0.932535i	$-0.382408\pi$
$348$	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
$351$	−15.5884	−	10.3924i	−0.832047	−	0.554706i
$352$	−0.310310	+	0.537472i	−0.0165396	+	0.0286474i
$353$	−17.1652	−	9.91033i	−0.913611	−	0.527474i	−0.0320198	−	0.999487i	$-0.510194\pi$
$353$	−17.1652	−	9.91033i	−0.913611	−	0.527474i	−0.881591	+	0.472014i	$0.843527\pi$
$354$	−1.16870	−	5.22222i	−0.0621155	−	0.277558i
$355$	−1.08276	+	0.625133i	−0.0574671	+	0.0331786i
$356$		−	3.60015i		−	0.190807i
$357$	−1.53543	+	0.334404i	−0.0812638	+	0.0176985i
$358$	16.9504	+	9.78634i	0.895858	+	0.517224i
$359$	−0.111157	+	0.192530i	−0.00586667	+	0.0101614i	−0.868944	−	0.494911i	$-0.835201\pi$
$359$	−0.111157	+	0.192530i	−0.00586667	+	0.0101614i	0.863077	+	0.505072i	$0.168534\pi$
$360$	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
$369$	−14.7658	+	21.2682i	−0.768676	+	1.10718i
$370$	−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
$375$	3.41776	+	15.2720i	0.176493	+	0.788642i
$376$	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	$0.373980\pi$
$380$		−	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	−0.720752	−	0.693193i	$-0.756204\pi$
$383$	−9.40956	+	5.43261i	−0.480806	+	0.277594i	0.239946	+	0.970786i	$0.422870\pi$
$384$	−1.69024	+	0.378264i	−0.0862548	+	0.0193032i
$385$	−1.43392	+	0.816968i	−0.0730793	+	0.0416366i
$386$	−10.9286	−	6.30961i	−0.556250	−	0.321151i
$387$	−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	$-0.215313\pi$
$389$	33.7632	−	19.4932i	1.71186	−	0.988345i	0.932048	−	0.362334i	$-0.118020\pi$
$390$	−0.118356	−	6.27552i	−0.00599317	−	0.317773i
$391$		−	0.967778i		−	0.0489427i
$392$	−6.99954	−	0.0801202i	−0.353530	−	0.00404668i
$393$	−9.44804	+	30.1756i	−0.476591	+	1.52216i
$394$	−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
$399$	13.3761	+	14.7070i	0.669641	+	0.736271i
$400$	−1.99492	−	3.45530i	−0.0997461	−	0.172765i
$401$	29.6513			1.48072			0.740358	−	0.672213i	$-0.234656\pi$
$401$	29.6513			1.48072			0.740358	+	0.672213i	$0.234656\pi$
$402$	9.07302	+	2.84078i	0.452521	+	0.141685i
$403$	−5.98479	+	6.75647i	−0.298124	+	0.336564i
$404$	−4.95624	+	8.58446i	−0.246582	+	0.427093i
$405$	−8.47507	+	3.16165i	−0.421129	+	0.157104i
$406$	−21.8512	+	12.4496i	−1.08446	+	0.617863i
$407$	2.33748	+	1.34954i	0.115865	+	0.0668944i
$408$	0.579607	−	0.129712i	0.0286948	−	0.00642170i
$409$	−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
$411$	−13.7013	+	3.06626i	−0.675835	+	0.151247i
$412$	8.93253	+	5.15720i	0.440074	+	0.254077i
$413$	−0.0467817	+	8.17425i	−0.00230198	+	0.402229i
$414$	−3.60882	−	7.65904i	−0.177364	−	0.376421i
$415$	6.64657	−	11.5122i	0.326268	−	0.565112i
$416$	1.14202	+	3.41991i	0.0559923	+	0.167675i
$417$	−31.5490	−	9.87806i	−1.54496	−	0.483731i
$418$	−2.69235			−0.131687
$419$	−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	$0.866103\pi$
$420$	−4.38743	−	1.40134i	−0.214085	−	0.0683782i
$421$		−	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
$426$	−0.643794	+	2.05618i	−0.0311919	+	0.0996222i
$427$	15.3612	−	8.75197i	0.743381	−	0.423537i
$428$			14.7159i			0.711318i
$429$	−3.87508	+	0.0730836i	−0.187090	+	0.00352851i
$430$	−1.04939	+	0.605865i	−0.0506060	+	0.0292174i
$431$	3.37233	−	5.84104i	0.162439	−	0.281353i	−0.773304	−	0.634036i	$-0.781397\pi$
$431$	3.37233	−	5.84104i	0.162439	−	0.281353i	0.935743	+	0.352683i	$0.114731\pi$
$432$	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
$435$	−16.1478	+	3.61376i	−0.774228	+	0.173267i
$436$	−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
$441$	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	0.899059	−	0.437827i	$-0.144252\pi$
$443$	20.4039	+	11.7802i	0.969420	+	0.559695i	0.0703604	+	0.997522i	$0.477585\pi$
$444$	1.64508	+	7.35090i	0.0780721	+	0.348858i
$445$	−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	−0.943485	−	0.331414i	$-0.892474\pi$
$449$	−3.91435	+	6.77986i	−0.184730	+	0.319961i	0.758756	+	0.651375i	$0.225808\pi$
$450$	9.83224	+	6.82618i	0.463496	+	0.321789i
$451$			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	0.971676	−	0.236318i	$-0.0759406\pi$
$461$	26.9000	+	15.5307i	1.25286	+	0.723337i	0.281181	+	0.959655i	$0.409274\pi$
$462$	−0.865312	+	2.70920i	−0.0402580	+	0.126043i
$463$		−	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
$465$	0.951723	+	4.25269i	0.0441351	+	0.197214i
$466$	5.40464	+	3.12037i	0.250365	+	0.144548i
$467$	−15.8112	+	27.3859i	−0.731657	+	1.26727i	0.224517	+	0.974470i	$0.427919\pi$
$467$	−15.8112	+	27.3859i	−0.731657	+	1.26727i	−0.956175	+	0.292797i	$0.905414\pi$
$468$	−7.47235	−	7.82074i	−0.345410	−	0.361514i
$469$	−12.5353	−	7.33322i	−0.578825	−	0.338616i
$470$	−0.0256723	−	0.0444658i	−0.00118418	−	0.00205105i
$471$	−29.2797	+	26.9378i	−1.34914	+	1.24123i
$472$		−	3.08963i		−	0.142212i
$473$	0.374116	+	0.647988i	0.0172019	+	0.0297945i
$474$	−0.474128	+	1.51429i	−0.0217774	+	0.0695537i
$475$	8.65432	−	14.9897i	0.397087	−	0.687775i
$476$	−0.907250	−	0.00519224i	−0.0415837	−	0.000237986i
$477$	8.20218	−	11.8142i	0.375552	−	0.540935i
$478$	−30.4624			−1.39332
$479$	9.21963	+	5.32296i	0.421256	+	0.243212i	0.695614	−	0.718415i	$-0.255132\pi$
$479$	9.21963	+	5.32296i	0.421256	+	0.243212i	−0.274359	+	0.961627i	$0.588466\pi$
$480$	1.66130	+	0.520156i	0.0758275	+	0.0237418i
$481$	14.8733	−	4.96669i	0.678163	−	0.226462i
$482$	−5.69491			−0.259396
$483$	2.75219	+	12.6368i	0.125229	+	0.574995i
$484$	5.30742	+	9.19271i	0.241246	+	0.417851i
$485$	8.88514	−	5.12984i	0.403453	−	0.232934i
$486$	−7.05938	+	13.8984i	−0.320220	+	0.630444i
$487$		−	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	−0.970037	−	0.242959i	$-0.921882\pi$
$491$	−27.5795	+	15.9230i	−1.24465	+	0.718597i	−0.274610	+	0.961556i	$0.588549\pi$
$492$	−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
$495$	−1.06719	+	1.53715i	−0.0479666	+	0.0690898i
$496$	−1.25167	−	2.16796i	−0.0562018	−	0.0973443i
$497$	1.66190	−	2.84082i	0.0745462	−	0.127428i
$498$	−5.00298	−	22.3554i	−0.224189	−	1.00177i
$499$	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	−0.756652	−	0.653818i	$-0.773166\pi$
$503$	4.21408	−	7.29900i	0.187896	−	0.325446i	0.944549	+	0.328371i	$0.106500\pi$
$504$	−7.19937	+	3.34202i	−0.320685	+	0.148865i
$505$	8.62794	−	4.98135i	0.383938	−	0.221667i
$506$	−1.51687	−	0.875762i	−0.0674329	−	0.0389324i
$507$	−14.6095	+	17.1336i	−0.648832	+	0.760931i
$508$	−2.78854	−	4.82989i	−0.123722	−	0.214292i
$509$		−	16.2934i		−	0.722191i	−0.932529	−	0.361096i	$-0.882403\pi$
$509$		−	16.2934i		−	0.722191i	0.932529	−	0.361096i	$-0.117597\pi$
$510$	−0.569682	−	0.178369i	−0.0252259	−	0.00789830i
$511$	−11.6869	−	20.5125i	−0.516999	−	0.907422i
$512$	−1.00000			−0.0441942
$513$	20.8773	+	8.50132i	0.921755	+	0.375342i
$514$	29.5356			1.30276
$515$	−5.18333	−	8.97779i	−0.228405	−	0.395609i
$516$	−0.623951	+	1.99280i	−0.0274679	+	0.0877282i
$517$	−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	0.581828	−	0.813312i	$-0.302338\pi$
$521$	−9.43681	−	16.3450i	−0.413434	−	0.716089i	−0.995263	+	0.0972224i	$0.969004\pi$
$522$	−16.2627	+	23.4243i	−0.711798	+	1.02525i
$523$			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
$525$	−12.3020	−	13.5261i	−0.536905	−	0.590327i
$526$	−19.0802	−	11.0160i	−0.831938	−	0.480319i
$527$	0.429216	+	0.743423i	0.0186969	+	0.0323840i
$528$	0.321192	−	1.02584i	0.0139781	−	0.0446438i
$529$	15.0351			0.653699
$530$	4.81839			0.209298
$531$	3.95076	+	8.38473i	0.171448	+	0.363866i
$532$	5.68189	+	9.97269i	0.246341	+	0.432371i
$533$	23.2934	+	20.6330i	1.00895	+	0.893715i
$534$	1.36181	+	6.08512i	0.0589312	+	0.263329i
$535$	7.39520	−	12.8089i	0.319722	−	0.553775i
$536$	4.75367	+	2.74453i	0.205327	+	0.118546i
$537$	−32.3521	−	10.1295i	−1.39610	−	0.437121i
$538$	6.41553			0.276593
$539$	2.21509	−	3.73720i	0.0954106	−	0.160972i
$540$	−5.17362	+	0.712712i	−0.222637	+	0.0306702i
$541$	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
$543$	8.48485	+	37.9138i	0.364120	+	1.62704i
$544$	0.342914			0.0147023
$545$	18.0524			0.773280
$546$	8.44858	+	14.1993i	0.361566	+	0.607676i
$547$	−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
$549$	11.4325	−	16.4671i	0.487928	−	0.702798i
$550$	2.47617			0.105584
$551$	35.7115	+	20.6180i	1.52136	+	0.878357i
$552$	−1.06755	−	4.77024i	−0.0454378	−	0.203035i
$553$	1.22392	−	2.09215i	0.0520463	−	0.0889671i
$554$	−12.0754			−0.513036
$555$	2.26217	−	7.22503i	0.0960238	−	0.306685i
$556$	−16.5296	−	9.54339i	−0.701013	−	0.404730i
$557$	9.76868	−	16.9199i	0.413912	−	0.716917i	−0.581401	−	0.813617i	$-0.697495\pi$
$557$	9.76868	−	16.9199i	0.413912	−	0.716917i	0.995314	+	0.0966996i	$0.0308286\pi$
$558$	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
$561$	−0.110141	+	0.351773i	−0.00465016	+	0.0148519i
$562$	−30.4581			−1.28480
$563$	−31.1373			−1.31228			−0.656141	−	0.754638i	$-0.727812\pi$
$563$	−31.1373			−1.31228			−0.656141	+	0.754638i	$0.727812\pi$
$564$	−0.0844411	−	0.0264387i	−0.00355561	−	0.00111327i
$565$	2.47311	+	4.28354i	0.104044	+	0.180210i
$566$	−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
$569$			1.93823i			0.0812549i	0.999174	+	0.0406275i	$0.0129357\pi$
$569$			1.93823i			0.0812549i	−0.999174	+	0.0406275i	$0.987064\pi$
$570$	1.64929	+	7.36971i	0.0690811	+	0.308683i
$571$	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
$576$	2.71383	−	1.27872i	0.113076	−	0.0532798i
$577$	−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
$579$	20.8586	+	6.53088i	0.866855	+	0.271414i
$580$	−9.55354			−0.396689
$581$	−0.200264	+	34.9925i	−0.00830836	+	1.45173i
$582$	5.28297	−	16.8730i	0.218986	−	0.699408i
$583$		−	2.97531i		−	0.123225i
$584$	4.46154	+	7.72761i	0.184620	+	0.319771i
$585$	2.57385	+	10.5624i	0.106416	+	0.436700i
$586$	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	$0.200475\pi$
$588$	11.8612	−	2.51225i	0.489149	−	0.103604i
$589$	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	0.670077	−	0.742291i	$-0.266261\pi$
$593$	8.82193	+	5.09334i	0.362273	+	0.209158i	−0.307804	+	0.951450i	$0.599594\pi$
$594$	0.440093	+	3.19466i	0.0180572	+	0.131079i
$595$	0.787072	+	0.460442i	0.0322668	+	0.0188763i
$596$	−2.34608	−	4.06353i	−0.0960992	−	0.166449i
$597$	−3.31309	−	14.8042i	−0.135596	−	0.605897i
$598$	−9.65174	+	3.22304i	−0.394689	+	0.131800i
$599$	−1.11601	+	0.644326i	−0.0455988	+	0.0263265i	−0.522626	−	0.852562i	$-0.675048\pi$
$599$	−1.11601	+	0.644326i	−0.0455988	+	0.0263265i	0.477027	+	0.878888i	$0.341714\pi$
$600$	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
$606$	5.13005	−	16.3846i	0.208394	−	0.665578i
$607$	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
$609$	32.2246	−	29.3084i	1.30580	−	1.18763i
$610$	6.71606			0.271926
$611$	−0.0368295	+	0.180473i	−0.00148996	+	0.00730116i
$612$	−0.930610	+	0.438489i	−0.0376177	+	0.0177249i
$613$	−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
$615$	14.6615	−	3.28114i	0.591208	−	0.132308i
$616$	−0.829127	+	1.41730i	−0.0334065	+	0.0571045i
$617$	−22.9771	+	39.7974i	−0.925022	+	1.60218i	−0.133495	+	0.991049i	$0.542620\pi$
$617$	−22.9771	+	39.7974i	−0.925022	+	1.60218i	−0.791526	+	0.611135i	$0.790713\pi$
$618$	−17.0489	−	5.33806i	−0.685808	−	0.214728i
$619$	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
$624$	−3.22393	−	5.34849i	−0.129060	−	0.214111i
$625$	−5.43403	+	9.41201i	−0.217361	+	0.376480i
$626$	−7.93246	−	4.57981i	−0.317045	−	0.183046i
$627$	4.55073	−	1.01842i	0.181739	−	0.0406718i
$628$	−19.8931	+	11.4853i	−0.793822	+	0.458314i
$629$		−	1.49134i		−	0.0594636i
$630$	7.94590	+	0.708986i	0.316572	+	0.0282467i
$631$	−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	$0.304055\pi$
$641$			41.3412i			1.63288i	−0.577432	+	0.816439i	$0.695945\pi$
$642$	−5.56648	−	24.8733i	−0.219691	−	0.981673i
$643$	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	−0.904947	−	0.425524i	$-0.860090\pi$
$647$	−2.13561	+	3.69899i	−0.0839595	+	0.145422i	0.820988	+	0.570946i	$0.193423\pi$
$648$	−5.72977	+	6.94044i	−0.225087	+	0.272646i
$649$	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
$653$		−	12.9710i		−	0.507595i	−0.967257	−	0.253798i	$-0.918320\pi$
$653$		−	12.9710i		−	0.507595i	0.967257	−	0.253798i	$-0.0816797\pi$
$654$	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
$657$	−21.9893	−	15.2664i	−0.857883	−	0.595599i
$658$	0.116664	+	0.0682490i	0.00454803	+	0.00266062i
$659$	−31.7740	−	18.3447i	−1.23774	−	0.714609i	−0.269107	−	0.963110i	$-0.586729\pi$
$659$	−31.7740	−	18.3447i	−1.23774	−	0.714609i	−0.968631	+	0.248502i	$0.920062\pi$
$660$	−0.795086	+	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
$663$	1.10553	+	1.83407i	0.0429352	+	0.0712293i
$664$		−	13.2261i		−	0.513274i
$665$	0.0660194	−	11.5357i	0.00256012	−	0.447335i
$666$	−5.56117	−	11.8025i	−0.215491	−	0.457339i
$667$	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
$672$	−4.47761	+	0.975184i	−0.172728	+	0.0376185i
$673$	−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
$675$	−19.2010	−	7.81871i	−0.739045	−	0.300942i
$676$	−10.3916	+	7.81124i	−0.399675	+	0.300432i
$677$	5.94798	−	10.3022i	0.228599	−	0.395946i	−0.728794	−	0.684733i	$-0.759919\pi$
$677$	5.94798	−	10.3022i	0.228599	−	0.395946i	0.957393	+	0.288787i	$0.0932521\pi$
$678$	8.13450	+	2.54693i	0.312404	+	0.0978143i
$679$	−13.6375	+	23.3117i	−0.523359	+	0.894621i
$680$	−0.298476	−	0.172325i	−0.0114460	−	0.00660838i
$681$	−4.46013	−	19.9297i	−0.170913	−	0.763709i
$682$	1.55362			0.0594913
$683$	4.43181			0.169578			0.0847892	−	0.996399i	$-0.472978\pi$
$683$	4.43181			0.169578			0.0847892	+	0.996399i	$0.472978\pi$
$684$	10.6906	+	7.42214i	0.408767	+	0.283793i
$685$	7.05567	+	4.07359i	0.269583	+	0.155644i
$686$	−18.5175	−	0.317958i	−0.707003	−	0.0121397i
$687$	−5.66523	+	18.0939i	−0.216142	+	0.690324i
$688$	−0.602811	+	1.04410i	−0.0229819	+	0.0398059i
$689$	−12.9392	−	11.4613i	−0.492943	−	0.436642i
$690$	−1.46800	+	4.68855i	−0.0558856	+	0.178490i
$691$	−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
$693$	0.437793	−	4.90652i	0.0166304	−	0.186383i
$694$			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
$699$	−10.3155	−	3.22980i	−0.390167	−	0.122162i
$700$	−5.22566	−	9.17193i	−0.197511	−	0.346667i
$701$			37.0012i			1.39751i	0.715359	+	0.698757i	$0.246263\pi$
$701$			37.0012i			1.39751i	−0.715359	+	0.698757i	$0.753737\pi$
$702$	15.5884	+	10.3924i	0.588346	+	0.392236i
$703$	−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
$708$	1.16870	+	5.22222i	0.0439223	+	0.196263i
$709$	−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
$714$	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
$717$	51.4888	−	11.5228i	1.92289	−	0.430328i
$718$	0.111157	−	0.192530i	0.00414836	−	0.00718517i
$719$	9.72356	+	16.8417i	0.362627	+	0.628089i	0.988392	−	0.151923i	$-0.0485464\pi$
$719$	9.72356	+	16.8417i	0.362627	+	0.628089i	−0.625765	+	0.780012i	$0.715213\pi$
$720$	−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
$723$	9.62578	−	2.15418i	0.357987	−	0.0801149i
$724$			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
$735$	−11.5866	−	3.77396i	−0.427380	−	0.139205i
$736$		−	2.82222i		−	0.104028i
$737$	−2.95022	+	1.70331i	−0.108673	+	0.0627423i
$738$	14.7658	−	21.2682i	0.543536	−	0.782894i
$739$	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
$741$	13.1011	−	23.7135i	0.481282	−	0.871138i
$742$	−11.0208	+	6.27904i	−0.404586	+	0.230511i
$743$	−16.0336	−	27.7710i	−0.588216	−	1.01882i	−0.994466	−	0.105058i	$-0.966497\pi$
$743$	−16.0336	−	27.7710i	−0.588216	−	1.01882i	0.406250	−	0.913762i	$-0.366836\pi$
$744$	2.93569	+	3.19091i	0.107628	+	0.116985i
$745$			4.71593i			0.172778i
$746$	−3.97778	−	6.88972i	−0.145637	−	0.252251i
$747$	16.9125	+	35.8935i	0.618795	+	1.31328i
$748$	−0.106409	+	0.184307i	−0.00389071	+	0.00673891i
$749$	−0.222821	+	38.9338i	−0.00814169	+	1.42261i
$750$	−3.41776	−	15.2720i	−0.124799	−	0.557654i
$751$	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
$753$	12.4507	−	39.7656i	0.453729	−	1.44914i
$754$	25.6548	+	22.7247i	0.934294	+	0.827585i
$755$	−7.90216			−0.287589
$756$	10.9045	−	8.37208i	0.396593	−	0.304490i
$757$	−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
$759$	2.89514	+	0.906474i	0.105087	+	0.0329029i
$760$			4.36015i			0.158159i
$761$	2.09713	−	1.21078i	0.0760207	−	0.0438906i	−0.461508	−	0.887136i	$-0.652691\pi$
$761$	2.09713	−	1.21078i	0.0760207	−	0.0438906i	0.537529	+	0.843246i	$0.319358\pi$
$762$	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
$768$	1.69024	−	0.378264i	0.0609913	−	0.0136494i
$769$	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
$771$	−49.9222	+	11.1722i	−1.79790	+	0.402359i
$772$	10.9286	+	6.30961i	0.393328	+	0.227088i
$773$		−	34.8889i		−	1.25487i	−0.778671	−	0.627433i	$-0.784106\pi$
$773$		−	34.8889i		−	1.25487i	0.778671	−	0.627433i	$-0.215894\pi$
$774$	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
$777$	4.24110	+	19.4733i	0.152149	+	0.698599i
$778$	−33.7632	+	19.4932i	−1.21047	+	0.698865i
$779$	−32.4244	−	18.7202i	−1.16172	−	0.670722i
$780$	0.118356	+	6.27552i	0.00423781	+	0.224700i
$781$	−0.386014	−	0.668596i	−0.0138127	−	0.0239243i
$782$			0.967778i			0.0346077i
$783$	18.6273	−	45.7443i	0.665684	−	1.63477i
$784$	6.99954	+	0.0801202i	0.249984	+	0.00286144i
$785$	23.0870			0.824010
$786$	9.44804	−	30.1756i	0.337000	−	1.07633i
$787$	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
$789$	36.4172	+	11.4023i	1.29648	+	0.405932i
$790$	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
$795$	−8.14424	+	1.82263i	−0.288847	+	0.0646419i
$796$		−	8.75865i		−	0.310442i
$797$	−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
$800$	1.99492	+	3.45530i	0.0705311	+	0.122163i
$801$	−4.60357	−	9.77020i	−0.162659	−	0.345213i
$802$	−29.6513			−1.04702
$803$	−5.53783			−0.195426
$804$	−9.07302	−	2.84078i	−0.319981	−	0.100187i
$805$	3.78950	−	6.47770i	0.133562	−	0.228309i
$806$	5.98479	−	6.75647i	0.210805	−	0.237987i
$807$	−10.8438	+	2.42677i	−0.381720	+	0.0854262i
$808$	4.95624	−	8.58446i	0.174360	−	0.302000i
$809$	19.6426	+	11.3406i	0.690596	+	0.398716i	0.803835	−	0.594852i	$-0.202789\pi$
$809$	19.6426	+	11.3406i	0.690596	+	0.398716i	−0.113239	+	0.993568i	$0.536123\pi$
$810$	8.47507	−	3.16165i	0.297783	−	0.111089i
$811$	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
$813$	34.8809	−	7.80611i	1.22333	−	0.273772i
$814$	−2.33748	−	1.34954i	−0.0819286	−	0.0473015i
$815$	8.89127			0.311447
$816$	−0.579607	+	0.129712i	−0.0202903	+	0.00454083i
$817$	−5.23020			−0.182981
$818$	1.06094			0.0370949
$819$	−19.6513	−	20.8045i	−0.686670	−	0.726969i
$820$	8.67419			0.302916
$821$	6.27151			0.218877			0.109439	−	0.993994i	$-0.465095\pi$
$821$	6.27151			0.218877			0.109439	+	0.993994i	$0.465095\pi$
$822$	13.7013	−	3.06626i	0.477888	−	0.106948i
$823$	−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
$825$	−4.18533	+	0.936648i	−0.145714	+	0.0326099i
$826$	0.0467817	−	8.17425i	0.00162774	−	0.284419i
$827$	−37.5661			−1.30630			−0.653150	−	0.757229i	$-0.726553\pi$
$827$	−37.5661			−1.30630			−0.653150	+	0.757229i	$0.726553\pi$
$828$	3.60882	+	7.65904i	0.125415	+	0.266170i
$829$	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
$831$	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
$834$	31.5490	+	9.87806i	1.09245	+	0.342049i
$835$	−4.59445			−0.158998
$836$	2.69235			0.0931170
$837$	−12.0472	−	4.90569i	−0.416414	−	0.169565i
$838$	2.10360	+	3.64355i	0.0726678	+	0.125864i
$839$	−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
$842$			12.1375i			0.418285i
$843$	51.4815	−	11.5212i	1.77312	−	0.396811i
$844$	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
$849$	29.0882	+	9.10757i	0.998304	+	0.312571i
$850$	−0.684086	−	1.18487i	−0.0234640	−	0.0406408i
$851$	−12.2739			−0.420744
$852$	0.643794	−	2.05618i	0.0220560	−	0.0704435i
$853$	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
$855$	−5.57540	−	11.8327i	−0.190675	−	0.404670i
$856$		−	14.7159i		−	0.502977i
$857$	−4.35323	−	7.54001i	−0.148703	−	0.257562i	0.782045	−	0.623222i	$-0.214177\pi$
$857$	−4.35323	−	7.54001i	−0.148703	−	0.257562i	−0.930749	+	0.365660i	$0.880843\pi$
$858$	3.87508	−	0.0730836i	0.132293	−	0.00249503i
$859$	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
$861$	−29.2584	+	26.6107i	−0.997125	+	0.906889i
$862$	−3.37233	+	5.84104i	−0.114862	+	0.198947i
$863$	−5.26328	+	9.11626i	−0.179164	+	0.310321i	−0.941594	−	0.336749i	$-0.890673\pi$
$863$	−5.26328	+	9.11626i	−0.179164	+	0.310321i	0.762430	+	0.647070i	$0.224006\pi$
$864$	−4.10334	+	3.18788i	−0.139598	+	0.108454i
$865$			13.1899i			0.448471i
$866$	25.4298	+	14.6819i	0.864139	+	0.498911i
$867$	−28.5353	+	6.38601i	−0.969111	+	0.216880i
$868$	−3.27873	−	5.75474i	−0.111287	−	0.195329i
$869$	−0.284284	−	0.492394i	−0.00964366	−	0.0167033i
$870$	16.1478	−	3.61376i	0.547462	−	0.122518i
$871$	−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
$879$	−27.4327	−	8.58925i	−0.925283	−	0.289708i
$880$	−0.540195	+	0.311882i	−0.0182100	+	0.0105135i
$881$	−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	$0.996415\pi$
$882$	−19.0980	+	8.73299i	−0.643064	+	0.294055i
$883$	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
$885$	1.60709	−	5.13279i	0.0540217	−	0.172537i
$886$	−20.4039	−	11.7802i	−0.685483	−	0.395764i
$887$	−14.3871			−0.483072			−0.241536	−	0.970392i	$-0.577651\pi$
$887$	−14.3871			−0.483072			−0.241536	+	0.970392i	$0.577651\pi$
$888$	−1.64508	−	7.35090i	−0.0552053	−	0.246680i
$889$	−7.30453	−	12.8207i	−0.244986	−	0.429993i
$890$	1.80919	−	3.13361i	0.0606443	−	0.105039i
$891$	−1.95229	−	5.23328i	−0.0654042	−	0.175321i
$892$	−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
$897$	15.0946	−	9.09863i	0.503994	−	0.303795i
$898$	3.91435	−	6.77986i	0.130624	−	0.226247i
$899$	−20.6073	−	11.8976i	−0.687292	−	0.396808i
$900$	−9.83224	−	6.82618i	−0.327741	−	0.227539i
$901$	−1.42371	+	0.821982i	−0.0474308	+	0.0273842i
$902$		−	5.35624i		−	0.178343i
$903$	−1.68096	+	5.26292i	−0.0559390	+	0.175139i
$904$	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	$-0.880075\pi$
$911$		−	22.2089i		−	0.735813i	0.929863	−	0.367906i	$-0.119925\pi$
$912$	5.08741	+	5.52970i	0.168461	+	0.183107i
$913$	7.10868	+	4.10420i	0.235263	+	0.135829i
$914$		−	31.8029i		−	1.05195i
$915$	−11.3518	+	2.54045i	−0.375278	+	0.0839846i
$916$	−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
$921$	−44.4536	+	9.94841i	−1.46480	+	0.327811i
$922$	−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
$926$			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	0.496668	−	0.867941i	$-0.334557\pi$
$929$	45.6175	−	26.3373i	1.49666	−	0.864097i	0.999993	+	0.00384362i	$0.00122347\pi$
$930$	−0.951723	−	4.25269i	−0.0312082	−	0.139451i
$931$	14.8816	+	26.4709i	0.487725	+	0.867547i
$932$	−5.40464	−	3.12037i	−0.177035	−	0.102211i
$933$	−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
$936$	7.47235	+	7.82074i	0.244242	+	0.255629i
$937$			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
$939$	15.1401	+	4.74041i	0.494080	+	0.154698i
$940$	0.0256723	+	0.0444658i	0.000837339	+	0.00145031i
$941$	46.2726	−	26.7155i	1.50844	−	0.870900i	0.508492	−	0.861067i	$-0.330203\pi$
$941$	46.2726	−	26.7155i	1.50844	−	0.870900i	0.999952	−	0.00983388i	$-0.00313027\pi$
$942$	29.2797	−	26.9378i	0.953985	−	0.877681i
$943$	−12.1785	−	21.0939i	−0.396588	−	0.686911i
$944$			3.08963i			0.100559i
$945$	−13.6987	+	1.80729i	−0.445618	+	0.0587912i
$946$	−0.374116	−	0.647988i	−0.0121636	−	0.0210679i
$947$	−54.5826			−1.77370			−0.886849	−	0.462060i	$-0.847111\pi$
$947$	−54.5826			−1.77370			−0.886849	+	0.462060i	$0.847111\pi$
$948$	0.474128	−	1.51429i	0.0153990	−	0.0491819i
$949$	−21.3325	+	24.0832i	−0.692483	+	0.781773i
$950$	−8.65432	+	14.9897i	−0.280783	+	0.486331i
$951$	−2.45390	+	7.83737i	−0.0795731	+	0.254144i
$952$	0.907250	+	0.00519224i	0.0294041	+	0.000168282i
$953$	−0.882484	−	0.509502i	−0.0285865	−	0.0165044i	0.485639	−	0.874160i	$-0.338587\pi$
$953$	−0.882484	−	0.509502i	−0.0285865	−	0.0165044i	−0.514225	+	0.857655i	$0.671920\pi$
$954$	−8.20218	+	11.8142i	−0.265556	+	0.382499i
$955$	−13.2080			−0.427401
$956$	30.4624			0.985225
$957$	−2.23147	−	9.97112i	−0.0721331	−	0.322321i
$958$	−9.21963	−	5.32296i	−0.297873	−	0.171977i
$959$	−21.4464	−	0.122739i	−0.692541	−	0.00396345i
$960$	−1.66130	−	0.520156i	−0.0536182	−	0.0167880i
$961$	12.3666	−	21.4196i	0.398924	−	0.690956i
$962$	−14.8733	+	4.96669i	−0.479534	+	0.160133i
$963$	18.8174	+	39.9364i	0.606382	+	1.28693i
$964$	5.69491			0.183421
$965$	−6.34158	−	10.9839i	−0.204143	−	0.353585i
$966$	−2.75219	−	12.6368i	−0.0885501	−	0.406583i
$967$		−	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	0.976903	−	0.213681i	$-0.0685453\pi$
$971$	9.45417	+	16.3751i	0.303399	+	0.525502i	−0.673505	+	0.739183i	$0.735212\pi$
$972$	7.05938	−	13.8984i	0.226430	−	0.445791i
$973$	−43.5881	−	25.4993i	−1.39737	−	0.817470i
$974$			39.5929i			1.26864i
$975$	−12.0492	+	21.8095i	−0.385882	+	0.698462i
$976$	5.78697	−	3.34111i	0.185236	−	0.106946i
$977$	25.3197	−	43.8550i	0.810049	−	1.40305i	−0.102781	−	0.994704i	$-0.532774\pi$
$977$	25.3197	−	43.8550i	0.810049	−	1.40305i	0.912829	−	0.408341i	$-0.133893\pi$
$978$	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
$981$	−30.7300	+	44.2626i	−0.981133	+	1.41320i
$982$	27.5795	−	15.9230i	0.880098	−	0.508125i
$983$	−21.4061	+	12.3588i	−0.682750	+	0.394186i	−0.800890	−	0.598811i	$-0.795640\pi$
$983$	−21.4061	+	12.3588i	−0.682750	+	0.394186i	0.118140	+	0.992997i	$0.462307\pi$
$984$	11.0009	−	10.1210i	0.350696	−	0.322646i
$985$		−	1.39440i		−	0.0444294i
$986$	2.82283	−	1.62976i	0.0898974	−	0.0519023i
$987$	−0.223006	−	0.0712276i	−0.00709836	−	0.00226720i
$988$	10.3713	−	11.7086i	0.329956	−	0.372501i
$989$	−2.94668	−	1.70127i	−0.0936989	−	0.0540971i
$990$	1.06719	−	1.53715i	0.0339175	−	0.0488538i
$991$	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
$996$	5.00298	+	22.3554i	0.158525	+	0.708357i
$997$		−	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.e.257.16	yes	34
3.2	odd	2		546.2.bi.f.257.10	yes	34
7.3	odd	6		546.2.bn.f.101.13	yes	34
13.4	even	6		546.2.bn.e.173.5	yes	34
21.17	even	6		546.2.bn.e.101.5	yes	34
39.17	odd	6		546.2.bn.f.173.13	yes	34
91.17	odd	6		546.2.bi.f.17.10	yes	34
273.17	even	6	inner	546.2.bi.e.17.16	✓	34

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(1.69024 - 0.378264i) q^{3} +1.00000 q^{4} +(-0.870413 - 0.502533i) q^{5} +(-1.69024 + 0.378264i) q^{6} +(2.64571 + 0.0151415i) q^{7} -1.00000 q^{8} +(2.71383 - 1.27872i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(1.69024 - 0.378264i) q^{3} +1.00000 q^{4} +(-0.870413 - 0.502533i) q^{5} +(-1.69024 + 0.378264i) q^{6} +(2.64571 + 0.0151415i) q^{7} -1.00000 q^{8} +(2.71383 - 1.27872i) q^{9} +(0.870413 + 0.502533i) q^{10} +(0.310310 - 0.537472i) q^{11} +(1.69024 - 0.378264i) q^{12} +(-1.14202 - 3.41991i) q^{13} +(-2.64571 - 0.0151415i) q^{14} +(-1.66130 - 0.520156i) q^{15} +1.00000 q^{16} -0.342914 q^{17} +(-2.71383 + 1.27872i) q^{18} +(2.16909 + 3.75697i) q^{19} +(-0.870413 - 0.502533i) q^{20} +(4.47761 - 0.975184i) q^{21} +(-0.310310 + 0.537472i) q^{22} +2.82222i q^{23} +(-1.69024 + 0.378264i) 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} +(1.66130 + 0.520156i) q^{30} +(-1.25167 - 2.16796i) q^{31} -1.00000 q^{32} +(0.321192 - 1.02584i) q^{33} +0.342914 q^{34} +(-2.29525 - 1.34273i) q^{35} +(2.71383 - 1.27872i) q^{36} +4.34903i q^{37} +(-2.16909 - 3.75697i) q^{38} +(-3.22393 - 5.34849i) q^{39} +(0.870413 + 0.502533i) q^{40} +(-7.47421 + 4.31523i) q^{41} +(-4.47761 + 0.975184i) 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} +(1.69024 - 0.378264i) q^{48} +(6.99954 + 0.0801202i) q^{49} +(1.99492 + 3.45530i) q^{50} +(-0.579607 + 0.129712i) 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} +(-1.66130 - 0.520156i) q^{60} +(5.78697 - 3.34111i) q^{61} +(1.25167 + 2.16796i) q^{62} +(7.19937 - 3.34202i) q^{63} +1.00000 q^{64} +(-0.724585 + 3.55064i) q^{65} +(-0.321192 + 1.02584i) q^{66} +(-4.75367 - 2.74453i) q^{67} -0.342914 q^{68} +(1.06755 + 4.77024i) q^{69} +(2.29525 + 1.34273i) q^{70} +(0.621982 - 1.07730i) q^{71} +(-2.71383 + 1.27872i) 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} +(3.22393 + 5.34849i) q^{78} +(0.458065 - 0.793391i) q^{79} +(-0.870413 - 0.502533i) q^{80} +(5.72977 - 6.94044i) q^{81} +(7.47421 - 4.31523i) q^{82} +13.2261i q^{83} +(4.47761 - 0.975184i) 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} +(-1.69024 + 0.378264i) q^{96} +(-5.10398 + 8.84035i) q^{97} +(-6.99954 - 0.0801202i) q^{98} +(0.154854 - 1.85541i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9} + 9 q^{10} - 9 q^{11} + 3 q^{12} + 8 q^{13} - 4 q^{14} - 4 q^{15} + 34 q^{16} - 12 q^{17} + 11 q^{18} - 5 q^{19} - 9 q^{20} + 4 q^{21} + 9 q^{22} - 3 q^{24} + 16 q^{25} - 8 q^{26} + 18 q^{27} + 4 q^{28} - 27 q^{29} + 4 q^{30} - q^{31} - 34 q^{32} + 21 q^{33} + 12 q^{34} + 3 q^{35} - 11 q^{36} + 5 q^{38} + 7 q^{39} + 9 q^{40} + 3 q^{41} - 4 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} + 27 q^{47} + 3 q^{48} - 2 q^{49} - 16 q^{50} + 24 q^{51} + 8 q^{52} + 21 q^{53} - 18 q^{54} - 57 q^{55} - 4 q^{56} + 17 q^{57} + 27 q^{58} - 4 q^{60} - 51 q^{61} + q^{62} + 3 q^{63} + 34 q^{64} + 21 q^{65} - 21 q^{66} - 21 q^{67} - 12 q^{68} + 42 q^{69} - 3 q^{70} + 15 q^{71} + 11 q^{72} - 19 q^{73} + 54 q^{75} - 5 q^{76} - 9 q^{77} - 7 q^{78} - 9 q^{79} - 9 q^{80} - 23 q^{81} - 3 q^{82} + 4 q^{84} - 42 q^{85} + 3 q^{86} + 81 q^{87} + 9 q^{88} - 9 q^{90} - 72 q^{91} + 17 q^{93} - 27 q^{94} - 3 q^{96} + 19 q^{97} + 2 q^{98} + 27 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9 + 9 * q^10 - 9 * q^11 + 3 * q^12 + 8 * q^13 - 4 * q^14 - 4 * q^15 + 34 * q^16 - 12 * q^17 + 11 * q^18 - 5 * q^19 - 9 * q^20 + 4 * q^21 + 9 * q^22 - 3 * q^24 + 16 * q^25 - 8 * q^26 + 18 * q^27 + 4 * q^28 - 27 * q^29 + 4 * q^30 - q^31 - 34 * q^32 + 21 * q^33 + 12 * q^34 + 3 * q^35 - 11 * q^36 + 5 * q^38 + 7 * q^39 + 9 * q^40 + 3 * q^41 - 4 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 + 27 * q^47 + 3 * q^48 - 2 * q^49 - 16 * q^50 + 24 * q^51 + 8 * q^52 + 21 * q^53 - 18 * q^54 - 57 * q^55 - 4 * q^56 + 17 * q^57 + 27 * q^58 - 4 * q^60 - 51 * q^61 + q^62 + 3 * q^63 + 34 * q^64 + 21 * q^65 - 21 * q^66 - 21 * q^67 - 12 * q^68 + 42 * q^69 - 3 * q^70 + 15 * q^71 + 11 * q^72 - 19 * q^73 + 54 * q^75 - 5 * q^76 - 9 * q^77 - 7 * q^78 - 9 * q^79 - 9 * q^80 - 23 * q^81 - 3 * q^82 + 4 * 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 - 3 * q^96 + 19 * q^97 + 2 * q^98 + 27 * q^99

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