LMFDB - Embedded newform 546.2.bi.e.257.12

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			257.12
Character	$\chi$	$=$	546.257
Dual form			546.2.bi.e.17.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(0.841952 - 1.51364i) q^{3} +1.00000 q^{4} +(2.84717 + 1.64381i) q^{5} +(-0.841952 + 1.51364i) q^{6} +(1.87202 - 1.86964i) q^{7} -1.00000 q^{8} +(-1.58223 - 2.54883i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(0.841952 - 1.51364i) q^{3} +1.00000 q^{4} +(2.84717 + 1.64381i) q^{5} +(-0.841952 + 1.51364i) q^{6} +(1.87202 - 1.86964i) q^{7} -1.00000 q^{8} +(-1.58223 - 2.54883i) q^{9} +(-2.84717 - 1.64381i) q^{10} +(-1.03510 + 1.79285i) q^{11} +(0.841952 - 1.51364i) q^{12} +(3.53365 - 0.716460i) q^{13} +(-1.87202 + 1.86964i) q^{14} +(4.88532 - 2.92558i) q^{15} +1.00000 q^{16} +1.12362 q^{17} +(1.58223 + 2.54883i) q^{18} +(-0.505430 - 0.875431i) q^{19} +(2.84717 + 1.64381i) q^{20} +(-1.25382 - 4.40771i) q^{21} +(1.03510 - 1.79285i) q^{22} +3.50085i q^{23} +(-0.841952 + 1.51364i) q^{24} +(2.90424 + 5.03029i) q^{25} +(-3.53365 + 0.716460i) q^{26} +(-5.19019 + 0.248945i) q^{27} +(1.87202 - 1.86964i) q^{28} +(-7.97573 + 4.60479i) q^{29} +(-4.88532 + 2.92558i) q^{30} +(-1.86666 - 3.23315i) q^{31} -1.00000 q^{32} +(1.84223 + 3.07626i) q^{33} -1.12362 q^{34} +(8.40328 - 2.24594i) q^{35} +(-1.58223 - 2.54883i) q^{36} +6.97226i q^{37} +(0.505430 + 0.875431i) q^{38} +(1.89070 - 5.95191i) q^{39} +(-2.84717 - 1.64381i) q^{40} +(8.52566 - 4.92229i) q^{41} +(1.25382 + 4.40771i) q^{42} +(3.35600 - 5.81276i) q^{43} +(-1.03510 + 1.79285i) q^{44} +(-0.315084 - 9.85784i) q^{45} -3.50085i q^{46} +(1.05515 + 0.609193i) q^{47} +(0.841952 - 1.51364i) q^{48} +(0.00888497 - 6.99999i) q^{49} +(-2.90424 - 5.03029i) q^{50} +(0.946035 - 1.70076i) q^{51} +(3.53365 - 0.716460i) q^{52} +(-5.05843 + 2.92049i) q^{53} +(5.19019 - 0.248945i) q^{54} +(-5.89421 + 3.40302i) q^{55} +(-1.87202 + 1.86964i) q^{56} +(-1.75064 + 0.0279705i) q^{57} +(7.97573 - 4.60479i) q^{58} -9.80909i q^{59} +(4.88532 - 2.92558i) q^{60} +(-0.209571 + 0.120996i) q^{61} +(1.86666 + 3.23315i) q^{62} +(-7.72736 - 1.81324i) q^{63} +1.00000 q^{64} +(11.2386 + 3.76878i) q^{65} +(-1.84223 - 3.07626i) q^{66} +(-10.2316 - 5.90721i) q^{67} +1.12362 q^{68} +(5.29905 + 2.94755i) q^{69} +(-8.40328 + 2.24594i) q^{70} +(3.94585 - 6.83441i) q^{71} +(1.58223 + 2.54883i) q^{72} +(0.878160 + 1.52102i) q^{73} -6.97226i q^{74} +(10.0593 - 0.160721i) q^{75} +(-0.505430 - 0.875431i) q^{76} +(1.41426 + 5.29150i) q^{77} +(-1.89070 + 5.95191i) q^{78} +(-2.48977 + 4.31240i) q^{79} +(2.84717 + 1.64381i) q^{80} +(-3.99307 + 8.06569i) q^{81} +(-8.52566 + 4.92229i) q^{82} -0.999900i q^{83} +(-1.25382 - 4.40771i) q^{84} +(3.19914 + 1.84702i) q^{85} +(-3.35600 + 5.81276i) q^{86} +(0.254829 + 15.9494i) q^{87} +(1.03510 - 1.79285i) q^{88} +7.61879i q^{89} +(0.315084 + 9.85784i) q^{90} +(5.27553 - 7.94788i) q^{91} +3.50085i q^{92} +(-6.46548 + 0.103301i) q^{93} +(-1.05515 - 0.609193i) q^{94} -3.32333i q^{95} +(-0.841952 + 1.51364i) q^{96} +(-3.21628 + 5.57077i) q^{97} +(-0.00888497 + 6.99999i) q^{98} +(6.20743 - 0.198407i) 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
$3$	0.841952	−	1.51364i	0.486101	−	0.873903i
$3$	0.841952	−	1.51364i	0.486101	−	0.873903i
$4$	1.00000			0.500000
$5$	2.84717	+	1.64381i	1.27329	+	0.735135i	0.975606	−	0.219529i	$-0.0704519\pi$
$5$	2.84717	+	1.64381i	1.27329	+	0.735135i	0.297686	+	0.954664i	$0.403785\pi$
$6$	−0.841952	+	1.51364i	−0.343725	+	0.617942i
$7$	1.87202	−	1.86964i	0.707555	−	0.706658i
$7$	1.87202	−	1.86964i	0.707555	−	0.706658i
$8$	−1.00000			−0.353553
$9$	−1.58223	−	2.54883i	−0.527411	−	0.849610i
$10$	−2.84717	−	1.64381i	−0.900353	−	0.519819i
$11$	−1.03510	+	1.79285i	−0.312095	+	0.540564i	−0.978816	−	0.204744i	$-0.934364\pi$
$11$	−1.03510	+	1.79285i	−0.312095	+	0.540564i	0.666721	+	0.745307i	$0.267697\pi$
$12$	0.841952	−	1.51364i	0.243051	−	0.436951i
$13$	3.53365	−	0.716460i	0.980058	−	0.198710i
$13$	3.53365	−	0.716460i	0.980058	−	0.198710i
$14$	−1.87202	+	1.86964i	−0.500317	+	0.499683i
$15$	4.88532	−	2.92558i	1.26139	−	0.755383i
$16$	1.00000			0.250000
$17$	1.12362			0.272518			0.136259	−	0.990673i	$-0.456492\pi$
$17$	1.12362			0.272518			0.136259	+	0.990673i	$0.456492\pi$
$18$	1.58223	+	2.54883i	0.372936	+	0.600765i
$19$	−0.505430	−	0.875431i	−0.115954	−	0.200838i	0.802207	−	0.597046i	$-0.203659\pi$
$19$	−0.505430	−	0.875431i	−0.115954	−	0.200838i	−0.918161	+	0.396209i	$0.870326\pi$
$20$	2.84717	+	1.64381i	0.636646	+	0.367568i
$21$	−1.25382	−	4.40771i	−0.273607	−	0.961842i
$22$	1.03510	−	1.79285i	0.220684	−	0.382236i
$23$			3.50085i			0.729979i	0.931012	+	0.364989i	$0.118927\pi$
$23$			3.50085i			0.729979i	−0.931012	+	0.364989i	$0.881073\pi$
$24$	−0.841952	+	1.51364i	−0.171863	+	0.308971i
$25$	2.90424	+	5.03029i	0.580848	+	1.00606i
$26$	−3.53365	+	0.716460i	−0.693006	+	0.140509i
$27$	−5.19019	+	0.248945i	−0.998852	+	0.0479096i
$28$	1.87202	−	1.86964i	0.353778	−	0.353329i
$29$	−7.97573	+	4.60479i	−1.48106	+	0.855088i	−0.999769	−	0.0214746i	$-0.993164\pi$
$29$	−7.97573	+	4.60479i	−1.48106	+	0.855088i	−0.481287	+	0.876563i	$0.659831\pi$
$30$	−4.88532	+	2.92558i	−0.891934	+	0.534136i
$31$	−1.86666	−	3.23315i	−0.335262	−	0.580691i	0.648273	−	0.761408i	$-0.275492\pi$
$31$	−1.86666	−	3.23315i	−0.335262	−	0.580691i	−0.983535	+	0.180717i	$0.942158\pi$
$32$	−1.00000			−0.176777
$33$	1.84223	+	3.07626i	0.320690	+	0.535509i
$34$	−1.12362			−0.192699
$35$	8.40328	−	2.24594i	1.42041	−	0.379633i
$36$	−1.58223	−	2.54883i	−0.263706	−	0.424805i
$37$			6.97226i			1.14623i	0.819474	+	0.573116i	$0.194266\pi$
$37$			6.97226i			1.14623i	−0.819474	+	0.573116i	$0.805734\pi$
$38$	0.505430	+	0.875431i	0.0819916	+	0.142014i
$39$	1.89070	−	5.95191i	0.302754	−	0.953069i
$40$	−2.84717	−	1.64381i	−0.450177	−	0.259910i
$41$	8.52566	−	4.92229i	1.33148	−	0.768733i	0.345957	−	0.938250i	$-0.387554\pi$
$41$	8.52566	−	4.92229i	1.33148	−	0.768733i	0.985527	+	0.169517i	$0.0542209\pi$
$42$	1.25382	+	4.40771i	0.193469	+	0.680125i
$43$	3.35600	−	5.81276i	0.511785	−	0.886438i	−0.488122	−	0.872776i	$-0.662318\pi$
$43$	3.35600	−	5.81276i	0.511785	−	0.886438i	0.999907	−	0.0136621i	$-0.00434890\pi$
$44$	−1.03510	+	1.79285i	−0.156047	+	0.270282i
$45$	−0.315084	−	9.85784i	−0.0469700	−	1.46952i
$46$		−	3.50085i		−	0.516173i
$47$	1.05515	+	0.609193i	0.153910	+	0.0888599i	0.574977	−	0.818170i	$-0.305011\pi$
$47$	1.05515	+	0.609193i	0.153910	+	0.0888599i	−0.421067	+	0.907029i	$0.638344\pi$
$48$	0.841952	−	1.51364i	0.121525	−	0.218476i
$49$	0.00888497	−	6.99999i	0.00126928	−	0.999999i
$50$	−2.90424	−	5.03029i	−0.410722	−	0.711391i
$51$	0.946035	−	1.70076i	0.132471	−	0.238154i
$52$	3.53365	−	0.716460i	0.490029	−	0.0993551i
$53$	−5.05843	+	2.92049i	−0.694829	+	0.401160i	−0.805419	−	0.592706i	$-0.798059\pi$
$53$	−5.05843	+	2.92049i	−0.694829	+	0.401160i	0.110589	+	0.993866i	$0.464726\pi$
$54$	5.19019	−	0.248945i	0.706295	−	0.0338772i
$55$	−5.89421	+	3.40302i	−0.794775	+	0.458863i
$56$	−1.87202	+	1.86964i	−0.250159	+	0.249841i
$57$	−1.75064	+	0.0279705i	−0.231878	+	0.00370479i
$58$	7.97573	−	4.60479i	1.04727	−	0.604639i
$59$		−	9.80909i		−	1.27703i	−0.769607	−	0.638517i	$-0.779548\pi$
$59$		−	9.80909i		−	1.27703i	0.769607	−	0.638517i	$-0.220452\pi$
$60$	4.88532	−	2.92558i	0.630693	−	0.377691i
$61$	−0.209571	+	0.120996i	−0.0268328	+	0.0154919i	−0.513356	−	0.858176i	$-0.671598\pi$
$61$	−0.209571	+	0.120996i	−0.0268328	+	0.0154919i	0.486524	+	0.873667i	$0.338265\pi$
$62$	1.86666	+	3.23315i	0.237066	+	0.410611i
$63$	−7.72736	−	1.81324i	−0.973556	−	0.228447i
$64$	1.00000			0.125000
$65$	11.2386	+	3.76878i	1.39398	+	0.467459i
$66$	−1.84223	−	3.07626i	−0.226762	−	0.378662i
$67$	−10.2316	−	5.90721i	−1.24999	−	0.721680i	−0.278880	−	0.960326i	$-0.589963\pi$
$67$	−10.2316	−	5.90721i	−1.24999	−	0.721680i	−0.971107	+	0.238645i	$0.923297\pi$
$68$	1.12362			0.136259
$69$	5.29905	+	2.94755i	0.637930	+	0.354843i
$70$	−8.40328	+	2.24594i	−1.00438	+	0.268441i
$71$	3.94585	−	6.83441i	0.468286	−	0.811096i	−0.531057	−	0.847336i	$-0.678205\pi$
$71$	3.94585	−	6.83441i	0.468286	−	0.811096i	0.999343	+	0.0362405i	$0.0115383\pi$
$72$	1.58223	+	2.54883i	0.186468	+	0.300383i
$73$	0.878160	+	1.52102i	0.102781	+	0.178022i	0.912829	−	0.408341i	$-0.133893\pi$
$73$	0.878160	+	1.52102i	0.102781	+	0.178022i	−0.810049	+	0.586363i	$0.800559\pi$
$74$		−	6.97226i		−	0.810509i
$75$	10.0593	−	0.160721i	1.16155	−	0.0185584i
$76$	−0.505430	−	0.875431i	−0.0579768	−	0.100419i
$77$	1.41426	+	5.29150i	0.161169	+	0.603023i
$78$	−1.89070	+	5.95191i	−0.214079	+	0.673921i
$79$	−2.48977	+	4.31240i	−0.280121	+	0.485183i	−0.971414	−	0.237391i	$-0.923708\pi$
$79$	−2.48977	+	4.31240i	−0.280121	+	0.485183i	0.691294	+	0.722574i	$0.257041\pi$
$80$	2.84717	+	1.64381i	0.318323	+	0.183784i
$81$	−3.99307	+	8.06569i	−0.443675	+	0.896188i
$82$	−8.52566	+	4.92229i	−0.941502	+	0.543576i
$83$		−	0.999900i		−	0.109753i	−0.998493	−	0.0548767i	$-0.982523\pi$
$83$		−	0.999900i		−	0.109753i	0.998493	−	0.0548767i	$-0.0174766\pi$
$84$	−1.25382	−	4.40771i	−0.136803	−	0.480921i
$85$	3.19914	+	1.84702i	0.346995	+	0.200338i
$86$	−3.35600	+	5.81276i	−0.361887	+	0.626806i
$87$	0.254829	+	15.9494i	0.0273206	+	1.70996i
$88$	1.03510	−	1.79285i	0.110342	−	0.191118i
$89$			7.61879i			0.807590i	0.914849	+	0.403795i	$0.132309\pi$
$89$			7.61879i			0.807590i	−0.914849	+	0.403795i	$0.867691\pi$
$90$	0.315084	+	9.85784i	0.0332128	+	1.03911i
$91$	5.27553	−	7.94788i	0.553025	−	0.833164i
$92$			3.50085i			0.364989i
$93$	−6.46548	+	0.103301i	−0.670439	+	0.0107118i
$94$	−1.05515	−	0.609193i	−0.108831	−	0.0628334i
$95$		−	3.32333i		−	0.340967i
$96$	−0.841952	+	1.51364i	−0.0859314	+	0.154486i
$97$	−3.21628	+	5.57077i	−0.326564	+	0.565626i	−0.981828	−	0.189775i	$-0.939224\pi$
$97$	−3.21628	+	5.57077i	−0.326564	+	0.565626i	0.655264	+	0.755400i	$0.272558\pi$
$98$	−0.00888497	+	6.99999i	−0.000897518	+	0.707106i
$99$	6.20743	−	0.198407i	0.623870	−	0.0199407i
$100$	2.90424	+	5.03029i	0.290424	+	0.503029i
$101$	−9.66204	+	16.7351i	−0.961409	+	1.66521i	−0.242441	+	0.970166i	$0.577948\pi$
$101$	−9.66204	+	16.7351i	−0.961409	+	1.66521i	−0.718968	+	0.695043i	$0.755385\pi$
$102$	−0.946035	+	1.70076i	−0.0936714	+	0.168400i
$103$	−7.86720	−	4.54213i	−0.775178	−	0.447549i	0.0595405	−	0.998226i	$-0.481036\pi$
$103$	−7.86720	−	4.54213i	−0.775178	−	0.447549i	−0.834719	+	0.550677i	$0.814370\pi$
$104$	−3.53365	+	0.716460i	−0.346503	+	0.0702547i
$105$	3.67561	−	14.6105i	0.358703	−	1.42584i
$106$	5.05843	−	2.92049i	0.491318	−	0.283663i
$107$		−	3.76351i		−	0.363832i	−0.983314	−	0.181916i	$-0.941770\pi$
$107$		−	3.76351i		−	0.363832i	0.983314	−	0.181916i	$-0.0582299\pi$
$108$	−5.19019	+	0.248945i	−0.499426	+	0.0239548i
$109$	−2.43945	+	1.40841i	−0.233657	+	0.134902i	−0.612258	−	0.790658i	$-0.709739\pi$
$109$	−2.43945	+	1.40841i	−0.233657	+	0.134902i	0.378601	+	0.925560i	$0.376405\pi$
$110$	5.89421	−	3.40302i	0.561991	−	0.324465i
$111$	10.5535	+	5.87031i	1.00170	+	0.557185i
$112$	1.87202	−	1.86964i	0.176889	−	0.176664i
$113$	4.57774	+	2.64296i	0.430637	+	0.248629i	0.699618	−	0.714517i	$-0.253354\pi$
$113$	4.57774	+	2.64296i	0.430637	+	0.248629i	−0.268981	+	0.963146i	$0.586687\pi$
$114$	1.75064	−	0.0279705i	0.163962	−	0.00261968i
$115$	−5.75475	+	9.96752i	−0.536633	+	0.929476i
$116$	−7.97573	+	4.60479i	−0.740528	+	0.427544i
$117$	−7.41720	−	7.87307i	−0.685720	−	0.727865i
$118$			9.80909i			0.903000i
$119$	2.10344	−	2.10077i	0.192822	−	0.192577i
$120$	−4.88532	+	2.92558i	−0.445967	+	0.267068i
$121$	3.35713	+	5.81473i	0.305194	+	0.528612i
$122$	0.209571	−	0.120996i	0.0189736	−	0.0109544i
$123$	−0.272400	−	17.0491i	−0.0245615	−	1.53727i
$124$	−1.86666	−	3.23315i	−0.167631	−	0.290346i
$125$			2.65798i			0.237737i
$126$	7.72736	+	1.81324i	0.688408	+	0.161536i
$127$	9.40084	+	16.2827i	0.834190	+	1.44486i	0.894688	+	0.446691i	$0.147398\pi$
$127$	9.40084	+	16.2827i	0.834190	+	1.44486i	−0.0604988	+	0.998168i	$0.519269\pi$
$128$	−1.00000			−0.0883883
$129$	−5.97286	−	9.97385i	−0.525881	−	0.878149i
$130$	−11.2386	−	3.76878i	−0.985692	−	0.330544i
$131$	−1.45204	+	2.51500i	−0.126865	+	0.219737i	−0.922460	−	0.386092i	$-0.873825\pi$
$131$	−1.45204	+	2.51500i	−0.126865	+	0.219737i	0.795595	+	0.605828i	$0.207158\pi$
$132$	1.84223	+	3.07626i	0.160345	+	0.267754i
$133$	−2.58291	−	0.693847i	−0.223967	−	0.0601642i
$134$	10.2316	+	5.90721i	0.883874	+	0.510305i
$135$	−15.1865	−	7.82290i	−1.30705	−	0.673288i
$136$	−1.12362			−0.0963497
$137$	−21.1790			−1.80945			−0.904724	−	0.425999i	$-0.859923\pi$
$137$	−21.1790			−1.80945			−0.904724	+	0.425999i	$0.859923\pi$
$138$	−5.29905	−	2.94755i	−0.451085	−	0.250912i
$139$	17.6205	+	10.1732i	1.49455	+	0.862878i	0.999980	−	0.00626156i	$-0.00199313\pi$
$139$	17.6205	+	10.1732i	1.49455	+	0.862878i	0.494568	+	0.869139i	$0.335326\pi$
$140$	8.40328	−	2.24594i	0.710207	−	0.189816i
$141$	1.81049	−	1.08421i	0.152471	−	0.0913073i
$142$	−3.94585	+	6.83441i	−0.331128	+	0.573531i
$143$	−2.37318	+	7.07690i	−0.198455	+	0.591800i
$144$	−1.58223	−	2.54883i	−0.131853	−	0.212403i
$145$	−30.2777			−2.51442
$146$	−0.878160	−	1.52102i	−0.0726770	−	0.125880i
$147$	−10.5880	−	5.90711i	−0.873285	−	0.487210i
$148$			6.97226i			0.573116i
$149$	−6.62502	−	11.4749i	−0.542743	−	0.940058i	−0.998745	−	0.0500793i	$-0.984053\pi$
$149$	−6.62502	−	11.4749i	−0.542743	−	0.940058i	0.456003	−	0.889978i	$-0.349281\pi$
$150$	−10.0593	+	0.160721i	−0.821338	+	0.0131228i
$151$	−15.0137	+	8.66818i	−1.22180	+	0.705407i	−0.965301	−	0.261138i	$-0.915902\pi$
$151$	−15.0137	+	8.66818i	−1.22180	+	0.705407i	−0.256499	+	0.966545i	$0.582569\pi$
$152$	0.505430	+	0.875431i	0.0409958	+	0.0710068i
$153$	−1.77783	−	2.86392i	−0.143729	−	0.231534i
$154$	−1.41426	−	5.29150i	−0.113964	−	0.426401i
$155$		−	12.2738i		−	0.985852i
$156$	1.89070	−	5.95191i	0.151377	−	0.476534i
$157$	12.2223	−	7.05652i	0.975442	−	0.563172i	0.0745511	−	0.997217i	$-0.476248\pi$
$157$	12.2223	−	7.05652i	0.975442	−	0.563172i	0.900891	+	0.434045i	$0.142914\pi$
$158$	2.48977	−	4.31240i	0.198075	−	0.343076i
$159$	0.161620	+	10.1156i	0.0128173	+	0.802217i
$160$	−2.84717	−	1.64381i	−0.225088	−	0.129955i
$161$	6.54534	+	6.55365i	0.515845	+	0.516500i
$162$	3.99307	−	8.06569i	0.313725	−	0.633701i
$163$	−8.93321	+	5.15759i	−0.699703	+	0.403974i	−0.807237	−	0.590228i	$-0.799038\pi$
$163$	−8.93321	+	5.15759i	−0.699703	+	0.403974i	0.107534	+	0.994201i	$0.465705\pi$
$164$	8.52566	−	4.92229i	0.665742	−	0.384366i
$165$	0.188323	+	11.7869i	0.0146610	+	0.917610i
$166$			0.999900i			0.0776073i
$167$	−12.1099	+	6.99167i	−0.937094	+	0.541032i	−0.889048	−	0.457813i	$-0.848633\pi$
$167$	−12.1099	+	6.99167i	−0.937094	+	0.541032i	−0.0480461	+	0.998845i	$0.515299\pi$
$168$	1.25382	+	4.40771i	0.0967345	+	0.340062i
$169$	11.9734	−	5.06344i	0.921028	−	0.389495i
$170$	−3.19914	−	1.84702i	−0.245363	−	0.141660i
$171$	−1.43162	+	2.67339i	−0.109478	+	0.204439i
$172$	3.35600	−	5.81276i	0.255893	−	0.443219i
$173$	−2.53897	−	4.39763i	−0.193035	−	0.334346i	0.753220	−	0.657769i	$-0.228500\pi$
$173$	−2.53897	−	4.39763i	−0.193035	−	0.334346i	−0.946254	+	0.323423i	$0.895166\pi$
$174$	−0.254829	−	15.9494i	−0.0193186	−	1.20912i
$175$	14.8416	+	3.98690i	1.12192	+	0.301381i
$176$	−1.03510	+	1.79285i	−0.0780236	+	0.135141i
$177$	−14.8475	−	8.25878i	−1.11600	−	0.620768i
$178$		−	7.61879i		−	0.571053i
$179$	−10.1439	−	5.85660i	−0.758193	−	0.437743i	0.0704536	−	0.997515i	$-0.477555\pi$
$179$	−10.1439	−	5.85660i	−0.758193	−	0.437743i	−0.828647	+	0.559772i	$0.810889\pi$
$180$	−0.315084	−	9.85784i	−0.0234850	−	0.734760i
$181$			22.6731i			1.68528i	0.538480	+	0.842638i	$0.318999\pi$
$181$			22.6731i			1.68528i	−0.538480	+	0.842638i	$0.681001\pi$
$182$	−5.27553	+	7.94788i	−0.391048	+	0.589136i
$183$	0.00669590	+	0.419088i	0.000494975	+	0.0309798i
$184$		−	3.50085i		−	0.258086i
$185$	−11.4611	+	19.8512i	−0.842636	+	1.45949i
$186$	6.46548	−	0.103301i	0.474072	−	0.00757440i
$187$	−1.16306	+	2.01448i	−0.0850514	+	0.147313i
$188$	1.05515	+	0.609193i	0.0769549	+	0.0444299i
$189$	−9.25067	+	10.1698i	−0.672887	+	0.739745i
$190$			3.32333i			0.241100i
$191$	22.3913	−	12.9276i	1.62017	−	0.935408i	0.633302	−	0.773905i	$-0.281699\pi$
$191$	22.3913	−	12.9276i	1.62017	−	0.935408i	0.986872	−	0.161503i	$-0.0516342\pi$
$192$	0.841952	−	1.51364i	0.0607626	−	0.109238i
$193$	18.8878	+	10.9049i	1.35957	+	0.784951i	0.989566	−	0.144078i	$-0.0460216\pi$
$193$	18.8878	+	10.9049i	1.35957	+	0.784951i	0.370008	+	0.929029i	$0.379355\pi$
$194$	3.21628	−	5.57077i	0.230916	−	0.399958i
$195$	15.1670	−	13.8381i	1.08613	−	0.990969i
$196$	0.00888497	−	6.99999i	0.000634641	−	0.500000i
$197$	−3.51025	−	6.07993i	−0.250095	−	0.433177i	0.713457	−	0.700699i	$-0.247128\pi$
$197$	−3.51025	−	6.07993i	−0.250095	−	0.433177i	−0.963552	+	0.267522i	$0.913795\pi$
$198$	−6.20743	+	0.198407i	−0.441143	+	0.0141002i
$199$			15.0791i			1.06893i	0.845191	+	0.534464i	$0.179487\pi$
$199$			15.0791i			1.06893i	−0.845191	+	0.534464i	$0.820513\pi$
$200$	−2.90424	−	5.03029i	−0.205361	−	0.355695i
$201$	−17.5559	+	10.5134i	−1.23830	+	0.741557i
$202$	9.66204	−	16.7351i	0.679819	−	1.17748i
$203$	−6.32139	+	23.5320i	−0.443675	+	1.65162i
$204$	0.946035	−	1.70076i	0.0662357	−	0.119077i
$205$	32.3653			2.26049
$206$	7.86720	+	4.54213i	0.548134	+	0.316465i
$207$	8.92308	−	5.53917i	0.620197	−	0.384999i
$208$	3.53365	−	0.716460i	0.245015	−	0.0496776i
$209$	2.09268			0.144754
$210$	−3.67561	+	14.6105i	−0.253641	+	1.00822i
$211$	−10.2101	−	17.6845i	−0.702895	−	1.21745i	−0.967446	−	0.253079i	$-0.918557\pi$
$211$	−10.2101	−	17.6845i	−0.702895	−	1.21745i	0.264550	−	0.964372i	$-0.414776\pi$
$212$	−5.05843	+	2.92049i	−0.347415	+	0.200580i
$213$	−7.02265	−	11.7269i	−0.481184	−	0.803511i
$214$			3.76351i			0.257268i
$215$	19.1102	−	11.0333i	1.30330	−	0.752463i
$216$	5.19019	−	0.248945i	0.353147	−	0.0169386i
$217$	−9.53925	−	2.56252i	−0.647567	−	0.173955i
$218$	2.43945	−	1.40841i	0.165220	−	0.0953899i
$219$	3.04165	−	0.0485974i	0.205535	−	0.00328391i
$220$	−5.89421	+	3.40302i	−0.397387	+	0.229432i
$221$	3.97048	−	0.805029i	0.267084	−	0.0541521i
$222$	−10.5535	−	5.87031i	−0.708306	−	0.393989i
$223$	1.37326	+	2.37855i	0.0919602	+	0.159280i	0.908336	−	0.418241i	$-0.137353\pi$
$223$	1.37326	+	2.37855i	0.0919602	+	0.159280i	−0.816376	+	0.577521i	$0.804020\pi$
$224$	−1.87202	+	1.86964i	−0.125079	+	0.124921i
$225$	8.22617	−	15.3615i	0.548411	−	1.02410i
$226$	−4.57774	−	2.64296i	−0.304507	−	0.175807i
$227$		−	8.98000i		−	0.596024i	−0.954562	−	0.298012i	$-0.903676\pi$
$227$		−	8.98000i		−	0.596024i	0.954562	−	0.298012i	$-0.0963235\pi$
$228$	−1.75064	+	0.0279705i	−0.115939	+	0.00185239i
$229$	8.23500	−	14.2634i	0.544184	−	0.942554i	−0.454474	−	0.890760i	$-0.650173\pi$
$229$	8.23500	−	14.2634i	0.544184	−	0.942554i	0.998658	−	0.0517940i	$-0.0164939\pi$
$230$	5.75475	−	9.96752i	0.379457	−	0.657239i
$231$	9.20018	+	2.31451i	0.605328	+	0.152284i
$232$	7.97573	−	4.60479i	0.523633	−	0.302319i
$233$	4.79194	+	2.76663i	0.313931	+	0.181248i	0.648684	−	0.761058i	$-0.275320\pi$
$233$	4.79194	+	2.76663i	0.313931	+	0.181248i	−0.334753	+	0.942306i	$0.608653\pi$
$234$	7.41720	+	7.87307i	0.484877	+	0.514679i
$235$	2.00280	+	3.46895i	0.130648	+	0.226289i
$236$		−	9.80909i		−	0.638517i
$237$	4.43118	+	7.39946i	0.287836	+	0.480646i
$238$	−2.10344	+	2.10077i	−0.136346	+	0.136173i
$239$	−4.33497			−0.280406			−0.140203	−	0.990123i	$-0.544776\pi$
$239$	−4.33497			−0.280406			−0.140203	+	0.990123i	$0.544776\pi$
$240$	4.88532	−	2.92558i	0.315346	−	0.188846i
$241$	4.20698			0.270995			0.135498	−	0.990778i	$-0.456737\pi$
$241$	4.20698			0.270995			0.135498	+	0.990778i	$0.456737\pi$
$242$	−3.35713	−	5.81473i	−0.215805	−	0.373785i
$243$	8.84661	+	12.8350i	0.567510	+	0.823366i
$244$	−0.209571	+	0.120996i	−0.0134164	+	0.00774595i
$245$	11.5320	−	19.9155i	0.736751	−	1.27236i
$246$	0.272400	+	17.0491i	0.0173676	+	1.08701i
$247$	−2.41322	−	2.73135i	−0.153550	−	0.173791i
$248$	1.86666	+	3.23315i	0.118533	+	0.205305i
$249$	−1.51349	−	0.841868i	−0.0959137	−	0.0533512i
$250$		−	2.65798i		−	0.168105i
$251$	−9.79168	+	16.9597i	−0.618045	+	1.07049i	0.371797	+	0.928314i	$0.378742\pi$
$251$	−9.79168	+	16.9597i	−0.618045	+	1.07049i	−0.989842	+	0.142172i	$0.954591\pi$
$252$	−7.72736	−	1.81324i	−0.486778	−	0.114223i
$253$	−6.27649	−	3.62374i	−0.394600	−	0.227822i
$254$	−9.40084	−	16.2827i	−0.589861	−	1.02167i
$255$	5.48925	−	3.28725i	0.343750	−	0.205855i
$256$	1.00000			0.0625000
$257$	−17.9497			−1.11967			−0.559837	−	0.828603i	$-0.689136\pi$
$257$	−17.9497			−1.11967			−0.559837	+	0.828603i	$0.689136\pi$
$258$	5.97286	+	9.97385i	0.371854	+	0.620945i
$259$	13.0356	+	13.0522i	0.809994	+	0.811023i
$260$	11.2386	+	3.76878i	0.696990	+	0.233730i
$261$	24.3563	+	13.0429i	1.50762	+	0.807337i
$262$	1.45204	−	2.51500i	0.0897072	−	0.155377i
$263$	24.1161	+	13.9235i	1.48707	+	0.858557i	0.999891	−	0.0147476i	$-0.00469446\pi$
$263$	24.1161	+	13.9235i	1.48707	+	0.858557i	0.487174	+	0.873305i	$0.338028\pi$
$264$	−1.84223	−	3.07626i	−0.113381	−	0.189331i
$265$	−19.2029			−1.17963
$266$	2.58291	+	0.693847i	0.158369	+	0.0425425i
$267$	11.5321	+	6.41466i	0.705755	+	0.392571i
$268$	−10.2316	−	5.90721i	−0.624994	−	0.360840i
$269$	−28.3069			−1.72590			−0.862951	−	0.505288i	$-0.831386\pi$
$269$	−28.3069			−1.72590			−0.862951	+	0.505288i	$0.831386\pi$
$270$	15.1865	+	7.82290i	0.924224	+	0.476087i
$271$	25.3037			1.53709			0.768546	−	0.639795i	$-0.220981\pi$
$271$	25.3037			1.53709			0.768546	+	0.639795i	$0.220981\pi$
$272$	1.12362			0.0681295
$273$	−7.58852	−	14.6770i	−0.459278	−	0.888292i
$274$	21.1790			1.27947
$275$	−12.0247			−0.725118
$276$	5.29905	+	2.94755i	0.318965	+	0.177422i
$277$	−13.0935			−0.786713			−0.393356	−	0.919386i	$-0.628686\pi$
$277$	−13.0935			−0.786713			−0.393356	+	0.919386i	$0.628686\pi$
$278$	−17.6205	−	10.1732i	−1.05680	−	0.610147i
$279$	−5.28726	+	9.87340i	−0.316540	+	0.591105i
$280$	−8.40328	+	2.24594i	−0.502192	+	0.134220i
$281$	16.5616			0.987980			0.493990	−	0.869468i	$-0.335538\pi$
$281$	16.5616			0.987980			0.493990	+	0.869468i	$0.335538\pi$
$282$	−1.81049	+	1.08421i	−0.107813	+	0.0645640i
$283$	−15.9278	−	9.19594i	−0.946811	−	0.546642i	−0.0547224	−	0.998502i	$-0.517427\pi$
$283$	−15.9278	−	9.19594i	−0.946811	−	0.546642i	−0.892089	+	0.451860i	$0.850761\pi$
$284$	3.94585	−	6.83441i	0.234143	−	0.405548i
$285$	−5.03034	−	2.79808i	−0.297971	−	0.165744i
$286$	2.37318	−	7.07690i	0.140329	−	0.418466i
$287$	6.75725	−	25.1545i	0.398868	−	1.48483i
$288$	1.58223	+	2.54883i	0.0932340	+	0.150191i
$289$	−15.7375			−0.925734
$290$	30.2777			1.77797
$291$	5.72420	+	9.55863i	0.335559	+	0.560337i
$292$	0.878160	+	1.52102i	0.0513904	+	0.0890108i
$293$	7.37759	+	4.25945i	0.431003	+	0.248840i	0.699774	−	0.714364i	$-0.253284\pi$
$293$	7.37759	+	4.25945i	0.431003	+	0.248840i	−0.268771	+	0.963204i	$0.586617\pi$
$294$	10.5880	+	5.90711i	0.617506	+	0.344510i
$295$	16.1243	−	27.9281i	0.938793	−	1.62604i
$296$		−	6.97226i		−	0.405254i
$297$	4.92604	−	9.56289i	0.285838	−	0.554895i
$298$	6.62502	+	11.4749i	0.383777	+	0.664721i
$299$	2.50822	+	12.3708i	0.145054	+	0.715422i
$300$	10.0593	−	0.160721i	0.580774	−	0.00927922i
$301$	−4.58529	−	17.1561i	−0.264292	−	0.988861i
$302$	15.0137	−	8.66818i	0.863943	−	0.498798i
$303$	17.1961	+	28.7151i	0.987889	+	1.64964i
$304$	−0.505430	−	0.875431i	−0.0289884	−	0.0502094i
$305$	−0.795576			−0.0455546
$306$	1.77783	+	2.86392i	0.101632	+	0.163719i
$307$	−21.3161			−1.21658			−0.608288	−	0.793716i	$-0.708143\pi$
$307$	−21.3161			−1.21658			−0.608288	+	0.793716i	$0.708143\pi$
$308$	1.41426	+	5.29150i	0.0805847	+	0.301511i
$309$	−13.4990	+	8.08388i	−0.767930	+	0.459876i
$310$			12.2738i			0.697103i
$311$	−7.40693	−	12.8292i	−0.420008	−	0.727476i	0.575931	−	0.817498i	$-0.304639\pi$
$311$	−7.40693	−	12.8292i	−0.420008	−	0.727476i	−0.995940	+	0.0900223i	$0.971306\pi$
$312$	−1.89070	+	5.95191i	−0.107040	+	0.336961i
$313$	−22.7031	−	13.1077i	−1.28326	−	0.740889i	−0.305814	−	0.952091i	$-0.598929\pi$
$313$	−22.7031	−	13.1077i	−1.28326	−	0.740889i	−0.977442	+	0.211203i	$0.932262\pi$
$314$	−12.2223	+	7.05652i	−0.689742	+	0.398223i
$315$	−19.0205	−	17.8649i	−1.07168	−	1.00658i
$316$	−2.48977	+	4.31240i	−0.140060	+	0.242592i
$317$	9.80532	−	16.9833i	0.550722	−	0.953878i	−0.447501	−	0.894283i	$-0.647686\pi$
$317$	9.80532	−	16.9833i	0.550722	−	0.953878i	0.998223	−	0.0595945i	$-0.0189808\pi$
$318$	−0.161620	−	10.1156i	−0.00906319	−	0.567253i
$319$		−	19.0657i		−	1.06747i
$320$	2.84717	+	1.64381i	0.159161	+	0.0918919i
$321$	−5.69661	−	3.16869i	−0.317954	−	0.176859i
$322$	−6.54534	−	6.55365i	−0.364758	−	0.365221i
$323$	−0.567912	−	0.983652i	−0.0315995	−	0.0547319i
$324$	−3.99307	+	8.06569i	−0.221837	+	0.448094i
$325$	13.8666	+	15.6945i	0.769179	+	0.870575i
$326$	8.93321	−	5.15759i	0.494765	−	0.285652i
$327$	0.0779417	+	4.87827i	0.00431019	+	0.269769i
$328$	−8.52566	+	4.92229i	−0.470751	+	0.271788i
$329$	3.11423	−	0.832338i	0.171693	−	0.0458883i
$330$	−0.188323	−	11.7869i	−0.0103669	−	0.648848i
$331$	22.5837	−	13.0387i	1.24131	−	0.716671i	0.271949	−	0.962312i	$-0.412332\pi$
$331$	22.5837	−	13.0387i	1.24131	−	0.716671i	0.969361	+	0.245641i	$0.0789985\pi$
$332$		−	0.999900i		−	0.0548767i
$333$	17.7711	−	11.0317i	0.973851	−	0.604536i
$334$	12.1099	−	6.99167i	0.662626	−	0.382567i
$335$	−19.4207	−	33.6376i	−1.06107	−	1.83782i
$336$	−1.25382	−	4.40771i	−0.0684016	−	0.240460i
$337$	−13.5184			−0.736394			−0.368197	−	0.929748i	$-0.620025\pi$
$337$	−13.5184			−0.736394			−0.368197	+	0.929748i	$0.620025\pi$
$338$	−11.9734	+	5.06344i	−0.651265	+	0.275415i
$339$	7.85473	−	4.70382i	0.426610	−	0.255476i
$340$	3.19914	+	1.84702i	0.173498	+	0.100169i
$341$	7.72873			0.418534
$342$	1.43162	−	2.67339i	0.0774129	−	0.144561i
$343$	−13.0708	−	13.1207i	−0.705759	−	0.708452i
$344$	−3.35600	+	5.81276i	−0.180943	+	0.313403i
$345$	10.2420	+	17.1028i	0.551413	+	0.920784i
$346$	2.53897	+	4.39763i	0.136496	+	0.236418i
$347$			33.5765i			1.80248i	0.433322	+	0.901239i	$0.357341\pi$
$347$			33.5765i			1.80248i	−0.433322	+	0.901239i	$0.642659\pi$
$348$	0.254829	+	15.9494i	0.0136603	+	0.854979i
$349$	11.8845	+	20.5845i	0.636161	+	1.10186i	0.986268	+	0.165153i	$0.0528118\pi$
$349$	11.8845	+	20.5845i	0.636161	+	1.10186i	−0.350107	+	0.936710i	$0.613855\pi$
$350$	−14.8416	−	3.98690i	−0.793318	−	0.213109i
$351$	−18.1619	+	4.59825i	−0.969413	+	0.245436i
$352$	1.03510	−	1.79285i	0.0551710	−	0.0955590i
$353$	9.28444	+	5.36037i	0.494161	+	0.285304i	0.726299	−	0.687379i	$-0.241239\pi$
$353$	9.28444	+	5.36037i	0.494161	+	0.285304i	−0.232138	+	0.972683i	$0.574572\pi$
$354$	14.8475	+	8.25878i	0.789134	+	0.438949i
$355$	22.4690	−	12.9725i	1.19253	−	0.688508i
$356$			7.61879i			0.403795i
$357$	−1.40882	−	4.95260i	−0.0745628	−	0.262119i
$358$	10.1439	+	5.85660i	0.536123	+	0.309531i
$359$	7.26878	−	12.5899i	0.383632	−	0.664469i	−0.607947	−	0.793978i	$-0.708007\pi$
$359$	7.26878	−	12.5899i	0.383632	−	0.664469i	0.991578	+	0.129508i	$0.0413399\pi$
$360$	0.315084	+	9.85784i	0.0166064	+	0.519554i
$361$	8.98908	−	15.5695i	0.473110	−	0.819450i
$362$		−	22.6731i		−	1.19167i
$363$	11.6280	−	0.185784i	0.610310	−	0.00975113i
$364$	5.27553	−	7.94788i	0.276513	−	0.416582i
$365$			5.77412i			0.302231i
$366$	−0.00669590	−	0.419088i	−0.000350000	−	0.0219061i
$367$	−15.1524	−	8.74823i	−0.790948	−	0.456654i	0.0493484	−	0.998782i	$-0.484286\pi$
$367$	−15.1524	−	8.74823i	−0.790948	−	0.456654i	−0.840296	+	0.542128i	$0.817619\pi$
$368$			3.50085i			0.182495i
$369$	−26.0357	−	13.9422i	−1.35536	−	0.725804i
$370$	11.4611	−	19.8512i	0.595834	−	1.03201i
$371$	−4.00920	+	14.9247i	−0.208147	+	0.774849i
$372$	−6.46548	+	0.103301i	−0.335219	+	0.00535591i
$373$	5.93324	+	10.2767i	0.307211	+	0.532106i	0.977751	−	0.209768i	$-0.0672708\pi$
$373$	5.93324	+	10.2767i	0.307211	+	0.532106i	−0.670540	+	0.741874i	$0.733937\pi$
$374$	1.16306	−	2.01448i	0.0601404	−	0.104166i
$375$	4.02323	+	2.23789i	0.207759	+	0.115564i
$376$	−1.05515	−	0.609193i	−0.0544153	−	0.0314167i
$377$	−24.8843	+	21.9860i	−1.28161	+	1.13234i
$378$	9.25067	−	10.1698i	0.475803	−	0.523079i
$379$	10.9141	−	6.30127i	0.560620	−	0.323674i	−0.192774	−	0.981243i	$-0.561748\pi$
$379$	10.9141	−	6.30127i	0.560620	−	0.323674i	0.753394	+	0.657569i	$0.228415\pi$
$380$		−	3.32333i		−	0.170483i
$381$	32.5613	−	0.520243i	1.66817	−	0.0266528i
$382$	−22.3913	+	12.9276i	−1.14564	+	0.661433i
$383$	−0.920885	+	0.531673i	−0.0470550	+	0.0271672i	−0.523343	−	0.852122i	$-0.675315\pi$
$383$	−0.920885	+	0.531673i	−0.0470550	+	0.0271672i	0.476288	+	0.879289i	$0.341982\pi$
$384$	−0.841952	+	1.51364i	−0.0429657	+	0.0772428i
$385$	−4.67162	+	17.3906i	−0.238088	+	0.886305i
$386$	−18.8878	−	10.9049i	−0.961364	−	0.555044i
$387$	−20.1257	+	0.643275i	−1.02305	+	0.0326995i
$388$	−3.21628	+	5.57077i	−0.163282	+	0.282813i
$389$	−2.28039	+	1.31658i	−0.115620	+	0.0667534i	−0.556695	−	0.830717i	$-0.687931\pi$
$389$	−2.28039	+	1.31658i	−0.115620	+	0.0667534i	0.441075	+	0.897470i	$0.354597\pi$
$390$	−15.1670	+	13.8381i	−0.768009	+	0.700721i
$391$			3.93363i			0.198932i
$392$	−0.00888497	+	6.99999i	−0.000448759	+	0.353553i
$393$	2.58427	+	4.31538i	0.130359	+	0.217682i
$394$	3.51025	+	6.07993i	0.176844	+	0.306302i
$395$	−14.1776	+	8.18542i	−0.713351	+	0.411853i
$396$	6.20743	−	0.198407i	0.311935	−	0.00997033i
$397$	−4.27357	−	7.40204i	−0.214484	−	0.371498i	0.738629	−	0.674113i	$-0.235474\pi$
$397$	−4.27357	−	7.40204i	−0.214484	−	0.371498i	−0.953113	+	0.302615i	$0.902140\pi$
$398$		−	15.0791i		−	0.755846i
$399$	−3.22493	+	3.32543i	−0.161448	+	0.166480i
$400$	2.90424	+	5.03029i	0.145212	+	0.251515i
$401$	−15.5754			−0.777797			−0.388898	−	0.921281i	$-0.627144\pi$
$401$	−15.5754			−0.777797			−0.388898	+	0.921281i	$0.627144\pi$
$402$	17.5559	−	10.5134i	0.875609	−	0.524360i
$403$	−8.91255	−	10.0874i	−0.443966	−	0.502491i
$404$	−9.66204	+	16.7351i	−0.480705	+	0.832605i
$405$	−24.6274	+	16.4005i	−1.22375	+	0.814948i
$406$	6.32139	−	23.5320i	0.313725	−	1.16787i
$407$	−12.5002	−	7.21699i	−0.619612	−	0.357733i
$408$	−0.946035	+	1.70076i	−0.0468357	+	0.0842002i
$409$	10.8097			0.534504			0.267252	−	0.963627i	$-0.413884\pi$
$409$	10.8097			0.534504			0.267252	+	0.963627i	$0.413884\pi$
$410$	−32.3653			−1.59841
$411$	−17.8317	+	32.0575i	−0.879575	+	1.58128i
$412$	−7.86720	−	4.54213i	−0.387589	−	0.223775i
$413$	−18.3395	−	18.3628i	−0.902427	−	0.903573i
$414$	−8.92308	+	5.53917i	−0.438546	+	0.272235i
$415$	1.64365	−	2.84688i	0.0806836	−	0.139748i
$416$	−3.53365	+	0.716460i	−0.173251	+	0.0351273i
$417$	30.2341	−	18.1058i	1.48057	−	0.886643i
$418$	−2.09268			−0.102357
$419$	−7.13932	−	12.3657i	−0.348779	−	0.604102i	0.637254	−	0.770654i	$-0.280070\pi$
$419$	−7.13932	−	12.3657i	−0.348779	−	0.604102i	−0.986033	+	0.166551i	$0.946737\pi$
$420$	3.67561	−	14.6105i	0.179351	−	0.712921i
$421$			31.1553i			1.51842i	0.650848	+	0.759208i	$0.274414\pi$
$421$			31.1553i			1.51842i	−0.650848	+	0.759208i	$0.725586\pi$
$422$	10.2101	+	17.6845i	0.497022	+	0.860867i
$423$	−0.116769	−	3.65329i	−0.00567753	−	0.177629i
$424$	5.05843	−	2.92049i	0.245659	−	0.141831i
$425$	3.26326	+	5.65214i	0.158292	+	0.274169i
$426$	7.02265	+	11.7269i	0.340249	+	0.568168i
$427$	−0.166101	+	0.618327i	−0.00803819	+	0.0299230i
$428$		−	3.76351i		−	0.181916i
$429$	8.71380	+	9.55056i	0.420706	+	0.461105i
$430$	−19.1102	+	11.0333i	−0.921575	+	0.532071i
$431$	10.7951	−	18.6976i	0.519981	−	0.900634i	−0.479749	−	0.877406i	$-0.659272\pi$
$431$	10.7951	−	18.6976i	0.519981	−	0.900634i	0.999730	−	0.0232279i	$-0.00739433\pi$
$432$	−5.19019	+	0.248945i	−0.249713	+	0.0119774i
$433$	16.2009	+	9.35358i	0.778565	+	0.449505i	0.835921	−	0.548849i	$-0.184934\pi$
$433$	16.2009	+	9.35358i	0.778565	+	0.449505i	−0.0573567	+	0.998354i	$0.518267\pi$
$434$	9.53925	+	2.56252i	0.457899	+	0.123005i
$435$	−25.4923	+	45.8296i	−1.22226	+	2.19736i
$436$	−2.43945	+	1.40841i	−0.116828	+	0.0674508i
$437$	3.06476	−	1.76944i	0.146607	−	0.0846437i
$438$	−3.04165	+	0.0485974i	−0.145336	+	0.00232207i
$439$		−	14.3709i		−	0.685885i	−0.939356	−	0.342943i	$-0.888576\pi$
$439$		−	14.3709i		−	0.685885i	0.939356	−	0.342943i	$-0.111424\pi$
$440$	5.89421	−	3.40302i	0.280995	−	0.162233i
$441$	−17.8559	+	11.0530i	−0.850279	+	0.526332i
$442$	−3.97048	+	0.805029i	−0.188857	+	0.0382913i
$443$	1.21594	+	0.702023i	0.0577711	+	0.0333541i	0.528607	−	0.848866i	$-0.322714\pi$
$443$	1.21594	+	0.702023i	0.0577711	+	0.0333541i	−0.470836	+	0.882221i	$0.656048\pi$
$444$	10.5535	+	5.87031i	0.500848	+	0.278593i
$445$	−12.5239	+	21.6920i	−0.593688	+	1.02830i
$446$	−1.37326	−	2.37855i	−0.0650257	−	0.112628i
$447$	−22.9468	+	0.366629i	−1.08535	+	0.0173409i
$448$	1.87202	−	1.86964i	0.0884444	−	0.0883322i
$449$	11.0266	−	19.0987i	0.520379	−	0.901323i	−0.479340	−	0.877629i	$-0.659124\pi$
$449$	11.0266	−	19.0987i	0.520379	−	0.901323i	0.999719	−	0.0236937i	$-0.00754264\pi$
$450$	−8.22617	+	15.3615i	−0.387785	+	0.724149i
$451$			20.3803i			0.959669i
$452$	4.57774	+	2.64296i	0.215319	+	0.124314i
$453$	0.479698	+	30.0236i	0.0225382	+	1.41063i
$454$			8.98000i			0.421453i
$455$	28.0851	−	13.9570i	1.31665	−	0.654313i
$456$	1.75064	−	0.0279705i	0.0819812	−	0.00130984i
$457$		−	42.3253i		−	1.97990i	−0.141432	−	0.989948i	$-0.545171\pi$
$457$		−	42.3253i		−	1.97990i	0.141432	−	0.989948i	$-0.454829\pi$
$458$	−8.23500	+	14.2634i	−0.384796	+	0.666486i
$459$	−5.83180	+	0.279720i	−0.272205	+	0.0130562i
$460$	−5.75475	+	9.96752i	−0.268317	+	0.464738i
$461$	10.2913	+	5.94166i	0.479312	+	0.276731i	0.720130	−	0.693839i	$-0.244082\pi$
$461$	10.2913	+	5.94166i	0.479312	+	0.276731i	−0.240818	+	0.970570i	$0.577416\pi$
$462$	−9.20018	−	2.31451i	−0.428031	−	0.107681i
$463$			3.56440i			0.165652i	0.996564	+	0.0828258i	$0.0263945\pi$
$463$			3.56440i			0.165652i	−0.996564	+	0.0828258i	$0.973605\pi$
$464$	−7.97573	+	4.60479i	−0.370264	+	0.213772i
$465$	−18.5781	−	10.3339i	−0.861539	−	0.479224i
$466$	−4.79194	−	2.76663i	−0.221983	−	0.128162i
$467$	−3.56143	+	6.16858i	−0.164803	+	0.285448i	−0.936585	−	0.350439i	$-0.886032\pi$
$467$	−3.56143	+	6.16858i	−0.164803	+	0.285448i	0.771782	+	0.635887i	$0.219366\pi$
$468$	−7.41720	−	7.87307i	−0.342860	−	0.363933i
$469$	−30.1981	+	8.07101i	−1.39442	+	0.372684i
$470$	−2.00280	−	3.46895i	−0.0923821	−	0.160011i
$471$	−0.390508	−	24.4414i	−0.0179937	−	1.12620i
$472$			9.80909i			0.451500i
$473$	6.94759	+	12.0336i	0.319451	+	0.553305i
$474$	−4.43118	−	7.39946i	−0.203531	−	0.339868i
$475$	2.93578	−	5.08492i	0.134703	−	0.233312i
$476$	2.10344	−	2.10077i	0.0964108	−	0.0962885i
$477$	15.4474	+	8.27219i	0.707290	+	0.378758i
$478$	4.33497			0.198277
$479$	26.4547	+	15.2736i	1.20875	+	0.697870i	0.962485	−	0.271334i	$-0.0874648\pi$
$479$	26.4547	+	15.2736i	1.20875	+	0.697870i	0.246260	+	0.969204i	$0.420798\pi$
$480$	−4.88532	+	2.92558i	−0.222984	+	0.133534i
$481$	4.99535	+	24.6375i	0.227768	+	1.12337i
$482$	−4.20698			−0.191623
$483$	15.4308	−	4.38945i	0.702124	−	0.199727i
$484$	3.35713	+	5.81473i	0.152597	+	0.264306i
$485$	−18.3146	+	10.5739i	−0.831623	+	0.480138i
$486$	−8.84661	−	12.8350i	−0.401290	−	0.582208i
$487$		−	32.0202i		−	1.45098i	−0.688235	−	0.725488i	$-0.741614\pi$
$487$		−	32.0202i		−	1.45098i	0.688235	−	0.725488i	$-0.258386\pi$
$488$	0.209571	−	0.120996i	0.00948681	−	0.00547721i
$489$	0.285421	+	17.8641i	0.0129072	+	0.807844i
$490$	−11.5320	+	19.9155i	−0.520962	+	0.899693i
$491$	13.0865	−	7.55549i	0.590585	−	0.340975i	−0.174744	−	0.984614i	$-0.555910\pi$
$491$	13.0865	−	7.55549i	0.590585	−	0.340975i	0.765329	+	0.643639i	$0.222576\pi$
$492$	−0.272400	−	17.0491i	−0.0122807	−	0.768635i
$493$	−8.96170	+	5.17404i	−0.403615	+	0.233027i
$494$	2.41322	+	2.73135i	0.108576	+	0.122889i
$495$	17.9997	+	9.63896i	0.809028	+	0.433239i
$496$	−1.86666	−	3.23315i	−0.0838156	−	0.145173i
$497$	−5.39121	−	20.1715i	−0.241829	−	0.904813i
$498$	1.51349	+	0.841868i	0.0678212	+	0.0377250i
$499$	−4.18606	−	2.41682i	−0.187394	−	0.108192i	0.403368	−	0.915038i	$-0.367839\pi$
$499$	−4.18606	−	2.41682i	−0.187394	−	0.108192i	−0.590762	+	0.806846i	$0.701173\pi$
$500$			2.65798i			0.118868i
$501$	0.386919	+	24.2168i	0.0172863	+	1.08193i
$502$	9.79168	−	16.9597i	0.437024	−	0.756948i
$503$	13.7946	−	23.8930i	0.615073	−	1.06534i	−0.375299	−	0.926904i	$-0.622460\pi$
$503$	13.7946	−	23.8930i	0.615073	−	1.06534i	0.990372	−	0.138433i	$-0.0442066\pi$
$504$	7.72736	+	1.81324i	0.344204	+	0.0807682i
$505$	−55.0189	+	31.7652i	−2.44831	+	1.41353i
$506$	6.27649	+	3.62374i	0.279024	+	0.161095i
$507$	2.41676	−	22.3866i	0.107332	−	0.994223i
$508$	9.40084	+	16.2827i	0.417095	+	0.722429i
$509$		−	31.3889i		−	1.39129i	−0.718386	−	0.695645i	$-0.755119\pi$
$509$		−	31.3889i		−	1.39129i	0.718386	−	0.695645i	$-0.244881\pi$
$510$	−5.48925	+	3.28725i	−0.243068	+	0.145562i
$511$	4.48769	+	1.20553i	0.198524	+	0.0533293i
$512$	−1.00000			−0.0441942
$513$	2.84121	+	4.41782i	0.125443	+	0.195052i
$514$	17.9497			0.791728
$515$	−14.9328	−	25.8644i	−0.658019	−	1.13972i
$516$	−5.97286	−	9.97385i	−0.262940	−	0.439074i
$517$	−2.18438	+	1.26115i	−0.0960688	+	0.0554654i
$518$	−13.0356	−	13.0522i	−0.572753	−	0.573480i
$519$	−8.79414	+	0.140507i	−0.386020	+	0.00616757i
$520$	−11.2386	−	3.76878i	−0.492846	−	0.165272i
$521$	0.178115	+	0.308505i	0.00780338	+	0.0135159i	0.869901	−	0.493227i	$-0.164183\pi$
$521$	0.178115	+	0.308505i	0.00780338	+	0.0135159i	−0.862097	+	0.506743i	$0.830849\pi$
$522$	−24.3563	−	13.0429i	−1.06605	−	0.570874i
$523$			24.9103i			1.08925i	0.838679	+	0.544626i	$0.183328\pi$
$523$			24.9103i			1.08925i	−0.838679	+	0.544626i	$0.816672\pi$
$524$	−1.45204	+	2.51500i	−0.0634326	+	0.109868i
$525$	18.5307	−	19.1081i	0.808745	−	0.833948i
$526$	−24.1161	−	13.9235i	−1.05151	−	0.607092i
$527$	−2.09742	−	3.63284i	−0.0913650	−	0.158249i
$528$	1.84223	+	3.07626i	0.0801726	+	0.133877i
$529$	10.7440			0.467131
$530$	19.2029			0.834122
$531$	−25.0017	+	15.5203i	−1.08498	+	0.673523i
$532$	−2.58291	−	0.693847i	−0.111984	−	0.0300821i
$533$	26.6001	−	23.5020i	1.15218	−	1.01798i
$534$	−11.5321	−	6.41466i	−0.499044	−	0.277589i
$535$	6.18650	−	10.7153i	0.267466	−	0.463264i
$536$	10.2316	+	5.90721i	0.441937	+	0.255153i
$537$	−17.4055	+	10.4233i	−0.751103	+	0.449799i
$538$	28.3069			1.22040
$539$	12.5407	+	7.26163i	0.540167	+	0.312780i
$540$	−15.1865	−	7.82290i	−0.653525	−	0.336644i
$541$	17.5713	+	10.1448i	0.755447	+	0.436158i	0.827659	−	0.561232i	$-0.189672\pi$
$541$	17.5713	+	10.1448i	0.755447	+	0.436158i	−0.0722115	+	0.997389i	$0.523006\pi$
$542$	−25.3037			−1.08689
$543$	34.3190	+	19.0896i	1.47277	+	0.819215i
$544$	−1.12362			−0.0481748
$545$	−9.26068			−0.396684
$546$	7.58852	+	14.6770i	0.324759	+	0.628118i
$547$	−18.3443			−0.784344			−0.392172	−	0.919892i	$-0.628276\pi$
$547$	−18.3443			−0.784344			−0.392172	+	0.919892i	$0.628276\pi$
$548$	−21.1790			−0.904724
$549$	0.639987	+	0.342716i	0.0273140	+	0.0146268i
$550$	12.0247			0.512736
$551$	8.06235	+	4.65480i	0.343468	+	0.198301i
$552$	−5.29905	−	2.94755i	−0.225542	−	0.125456i
$553$	3.40176	+	12.7279i	0.144658	+	0.541243i
$554$	13.0935			0.556290
$555$	20.3979	+	34.0618i	0.865844	+	1.44584i
$556$	17.6205	+	10.1732i	0.747274	+	0.431439i
$557$	−6.08906	+	10.5466i	−0.258002	+	0.446872i	−0.965707	−	0.259636i	$-0.916397\pi$
$557$	−6.08906	+	10.5466i	−0.258002	+	0.446872i	0.707705	+	0.706508i	$0.249731\pi$
$558$	5.28726	−	9.87340i	0.223828	−	0.417975i
$559$	7.69432	−	22.9447i	0.325435	−	0.970457i
$560$	8.40328	−	2.24594i	0.355103	−	0.0949082i
$561$	2.06996	+	3.45655i	0.0873939	+	0.145936i
$562$	−16.5616			−0.698608
$563$	11.3717			0.479262			0.239631	−	0.970864i	$-0.422974\pi$
$563$	11.3717			0.479262			0.239631	+	0.970864i	$0.422974\pi$
$564$	1.81049	−	1.08421i	0.0762353	−	0.0456536i
$565$	8.68905	+	15.0499i	0.365551	+	0.633153i
$566$	15.9278	+	9.19594i	0.669497	+	0.386534i
$567$	7.60485	+	22.5647i	0.319374	+	0.947629i
$568$	−3.94585	+	6.83441i	−0.165564	+	0.286766i
$569$		−	24.0497i		−	1.00822i	−0.863641	−	0.504108i	$-0.831821\pi$
$569$		−	24.0497i		−	1.00822i	0.863641	−	0.504108i	$-0.168179\pi$
$570$	5.03034	+	2.79808i	0.210698	+	0.117199i
$571$	3.64194	+	6.30802i	0.152410	+	0.263983i	0.932113	−	0.362167i	$-0.117963\pi$
$571$	3.64194	+	6.30802i	0.152410	+	0.263983i	−0.779703	+	0.626150i	$0.784630\pi$
$572$	−2.37318	+	7.07690i	−0.0992277	+	0.295900i
$573$	−0.715414	−	44.7768i	−0.0298868	−	1.87058i
$574$	−6.75725	+	25.1545i	−0.282042	+	1.04993i
$575$	−17.6103	+	10.1673i	−0.734401	+	0.424007i
$576$	−1.58223	−	2.54883i	−0.0659264	−	0.106201i
$577$	−2.11186	−	3.65785i	−0.0879179	−	0.152278i	0.818713	−	0.574203i	$-0.194688\pi$
$577$	−2.11186	−	3.65785i	−0.0879179	−	0.152278i	−0.906631	+	0.421925i	$0.861355\pi$
$578$	15.7375			0.654593
$579$	32.4087	−	19.4080i	1.34686	−	0.806570i
$580$	−30.2777			−1.25721
$581$	−1.86945	−	1.87183i	−0.0775581	−	0.0776566i
$582$	−5.72420	−	9.55863i	−0.237276	−	0.396218i
$583$		−	12.0920i		−	0.500799i
$584$	−0.878160	−	1.52102i	−0.0363385	−	0.0629402i
$585$	−8.17615	−	34.6084i	−0.338042	−	1.43088i
$586$	−7.37759	−	4.25945i	−0.304765	−	0.175956i
$587$	39.5103	−	22.8113i	1.63077	−	0.941523i	0.646908	−	0.762568i	$-0.276062\pi$
$587$	39.5103	−	22.8113i	1.63077	−	0.941523i	0.983857	−	0.178954i	$-0.0572714\pi$
$588$	−10.5880	−	5.90711i	−0.436642	−	0.243605i
$589$	−1.88693	+	3.26827i	−0.0777498	+	0.134667i
$590$	−16.1243	+	27.9281i	−0.663827	+	1.14978i
$591$	−12.1583	+	0.194257i	−0.500126	+	0.00799068i
$592$			6.97226i			0.286558i
$593$	21.1653	+	12.2198i	0.869154	+	0.501807i	0.867067	−	0.498191i	$-0.166002\pi$
$593$	21.1653	+	12.2198i	0.869154	+	0.501807i	0.00208732	+	0.999998i	$0.499336\pi$
$594$	−4.92604	+	9.56289i	−0.202118	+	0.392370i
$595$	9.44210	−	2.52358i	0.387088	−	0.103457i
$596$	−6.62502	−	11.4749i	−0.271371	−	0.470029i
$597$	22.8244	+	12.6959i	0.934139	+	0.519607i
$598$	−2.50822	−	12.3708i	−0.102569	−	0.505879i
$599$	−11.4214	+	6.59416i	−0.466667	+	0.269430i	−0.714843	−	0.699285i	$-0.753502\pi$
$599$	−11.4214	+	6.59416i	−0.466667	+	0.269430i	0.248177	+	0.968715i	$0.420169\pi$
$600$	−10.0593	+	0.160721i	−0.410669	+	0.00656140i
$601$	34.6176	−	19.9865i	1.41208	−	0.815266i	0.416497	−	0.909137i	$-0.363258\pi$
$601$	34.6176	−	19.9865i	1.41208	−	0.815266i	0.995584	+	0.0938714i	$0.0299242\pi$
$602$	4.58529	+	17.1561i	0.186883	+	0.699230i
$603$	1.13229	+	35.4252i	0.0461103	+	1.44262i
$604$	−15.0137	+	8.66818i	−0.610900	+	0.352703i
$605$			22.0740i			0.897436i
$606$	−17.1961	−	28.7151i	−0.698543	−	1.16647i
$607$	−17.4747	+	10.0890i	−0.709275	+	0.409500i	−0.810793	−	0.585334i	$-0.800964\pi$
$607$	−17.4747	+	10.0890i	−0.709275	+	0.409500i	0.101518	+	0.994834i	$0.467630\pi$
$608$	0.505430	+	0.875431i	0.0204979	+	0.0355034i
$609$	30.2968	+	29.3811i	1.22769	+	1.19058i
$610$	0.795576			0.0322119
$611$	4.16500	+	1.39670i	0.168498	+	0.0565044i
$612$	−1.77783	−	2.86392i	−0.0718646	−	0.115767i
$613$	21.6006	+	12.4711i	0.872440	+	0.503703i	0.868158	−	0.496288i	$-0.165304\pi$
$613$	21.6006	+	12.4711i	0.872440	+	0.503703i	0.00428146	+	0.999991i	$0.498637\pi$
$614$	21.3161			0.860249
$615$	27.2500	−	48.9895i	1.09883	−	1.97545i
$616$	−1.41426	−	5.29150i	−0.0569820	−	0.213201i
$617$	−1.22499	+	2.12175i	−0.0493164	+	0.0854185i	−0.889630	−	0.456682i	$-0.849038\pi$
$617$	−1.22499	+	2.12175i	−0.0493164	+	0.0854185i	0.840313	+	0.542101i	$0.182371\pi$
$618$	13.4990	−	8.08388i	0.543008	−	0.325181i
$619$	−11.9145	−	20.6365i	−0.478883	−	0.829449i	0.520824	−	0.853664i	$-0.325625\pi$
$619$	−11.9145	−	20.6365i	−0.478883	−	0.829449i	−0.999707	+	0.0242147i	$0.992291\pi$
$620$		−	12.2738i		−	0.492926i
$621$	−0.871522	−	18.1701i	−0.0349730	−	0.729140i
$622$	7.40693	+	12.8292i	0.296991	+	0.514403i
$623$	14.2444	+	14.2625i	0.570690	+	0.571415i
$624$	1.89070	−	5.95191i	0.0756885	−	0.238267i
$625$	10.1520	−	17.5837i	0.406079	−	0.703350i
$626$	22.7031	+	13.1077i	0.907399	+	0.523887i
$627$	1.76194	−	3.16758i	0.0703651	−	0.126501i
$628$	12.2223	−	7.05652i	0.487721	−	0.281586i
$629$			7.83418i			0.312369i
$630$	19.0205	+	17.8649i	0.757794	+	0.711756i
$631$	−17.5516	−	10.1334i	−0.698718	−	0.403405i	0.108152	−	0.994134i	$-0.465507\pi$
$631$	−17.5516	−	10.1334i	−0.698718	−	0.403405i	−0.806870	+	0.590729i	$0.798840\pi$
$632$	2.48977	−	4.31240i	0.0990376	−	0.171538i
$633$	−35.3645	+	0.565030i	−1.40561	+	0.0224579i
$634$	−9.80532	+	16.9833i	−0.389419	+	0.674494i
$635$			61.8129i			2.45297i
$636$	0.161620	+	10.1156i	0.00640865	+	0.401109i
$637$	−4.98382	−	24.7419i	−0.197466	−	0.980310i
$638$			19.0657i			0.754818i
$639$	−23.6630	+	0.756337i	−0.936095	+	0.0299202i
$640$	−2.84717	−	1.64381i	−0.112544	−	0.0649774i
$641$		−	33.2647i		−	1.31388i	−0.753945	−	0.656938i	$-0.771851\pi$
$641$		−	33.2647i		−	1.31388i	0.753945	−	0.656938i	$-0.228149\pi$
$642$	5.69661	+	3.16869i	0.224827	+	0.125058i
$643$	−3.65734	+	6.33469i	−0.144231	+	0.249816i	−0.929086	−	0.369864i	$-0.879404\pi$
$643$	−3.65734	+	6.33469i	−0.144231	+	0.249816i	0.784855	+	0.619680i	$0.212738\pi$
$644$	6.54534	+	6.55365i	0.257923	+	0.258250i
$645$	−0.610581	−	38.2155i	−0.0240416	−	1.50473i
$646$	0.567912	+	0.983652i	0.0223442	+	0.0387013i
$647$	−16.0186	+	27.7451i	−0.629757	+	1.09077i	0.357843	+	0.933782i	$0.383512\pi$
$647$	−16.0186	+	27.7451i	−0.629757	+	1.09077i	−0.987600	+	0.156990i	$0.949821\pi$
$648$	3.99307	−	8.06569i	0.156863	−	0.316850i
$649$	17.5862	+	10.1534i	0.690319	+	0.398556i
$650$	−13.8666	−	15.6945i	−0.543892	−	0.615590i
$651$	−11.9103	+	12.2815i	−0.466803	+	0.481350i
$652$	−8.93321	+	5.15759i	−0.349851	+	0.201987i
$653$		−	33.6453i		−	1.31664i	−0.752737	−	0.658321i	$-0.771267\pi$
$653$		−	33.6453i		−	1.31664i	0.752737	−	0.658321i	$-0.228733\pi$
$654$	−0.0779417	−	4.87827i	−0.00304776	−	0.190755i
$655$	−8.26839	+	4.77376i	−0.323073	+	0.186526i
$656$	8.52566	−	4.92229i	0.332871	−	0.192183i
$657$	2.48736	−	4.64489i	0.0970412	−	0.181214i
$658$	−3.11423	+	0.832338i	−0.121405	+	0.0324479i
$659$	−21.1966	−	12.2379i	−0.825704	−	0.476720i	0.0266755	−	0.999644i	$-0.491508\pi$
$659$	−21.1966	−	12.2379i	−0.825704	−	0.476720i	−0.852379	+	0.522924i	$0.824841\pi$
$660$	0.188323	+	11.7869i	0.00733048	+	0.458805i
$661$	2.77785	−	4.81137i	0.108046	−	0.187141i	−0.806933	−	0.590643i	$-0.798874\pi$
$661$	2.77785	−	4.81137i	0.108046	−	0.187141i	0.914979	+	0.403503i	$0.132207\pi$
$662$	−22.5837	+	13.0387i	−0.877739	+	0.506763i
$663$	2.12443	−	6.68769i	0.0825060	−	0.259728i
$664$			0.999900i			0.0388037i
$665$	−6.21343	−	6.22133i	−0.240947	−	0.241253i
$666$	−17.7711	+	11.0317i	−0.688617	+	0.427472i
$667$	−16.1207	−	27.9219i	−0.624196	−	1.08114i
$668$	−12.1099	+	6.99167i	−0.468547	+	0.270516i
$669$	4.75650	−	0.0759962i	0.183897	−	0.00293818i
$670$	19.4207	+	33.6376i	0.750287	+	1.29953i
$671$		−	0.500970i		−	0.0193397i
$672$	1.25382	+	4.40771i	0.0483673	+	0.170031i
$673$	9.31475	+	16.1336i	0.359057	+	0.621905i	0.987804	−	0.155705i	$-0.0497649\pi$
$673$	9.31475	+	16.1336i	0.359057	+	0.621905i	−0.628746	+	0.777610i	$0.716432\pi$
$674$	13.5184			0.520709
$675$	−16.3258	−	25.3851i	−0.628381	−	0.977075i
$676$	11.9734	−	5.06344i	0.460514	−	0.194748i
$677$	−13.4512	+	23.2982i	−0.516972	+	0.895422i	0.482833	+	0.875712i	$0.339608\pi$
$677$	−13.4512	+	23.2982i	−0.516972	+	0.895422i	−0.999806	+	0.0197102i	$0.993726\pi$
$678$	−7.85473	+	4.70382i	−0.301659	+	0.180649i
$679$	4.39440	+	16.4419i	0.168642	+	0.630981i
$680$	−3.19914	−	1.84702i	−0.122681	−	0.0708301i
$681$	−13.5925	−	7.56073i	−0.520867	−	0.289728i
$682$	−7.72873			−0.295948
$683$	−40.7673			−1.55992			−0.779958	−	0.625831i	$-0.784760\pi$
$683$	−40.7673			−1.55992			−0.779958	+	0.625831i	$0.784760\pi$
$684$	−1.43162	+	2.67339i	−0.0547392	+	0.102220i
$685$	−60.3003	−	34.8144i	−2.30395	−	1.33019i
$686$	13.0708	+	13.1207i	0.499047	+	0.500951i
$687$	−14.6563	−	24.4740i	−0.559172	−	0.933740i
$688$	3.35600	−	5.81276i	0.127946	−	0.221609i
$689$	−15.7823	+	13.9441i	−0.601258	+	0.531230i
$690$	−10.2420	−	17.1028i	−0.389908	−	0.651093i
$691$	13.7971			0.524865			0.262432	−	0.964950i	$-0.415475\pi$
$691$	13.7971			0.524865			0.262432	+	0.964950i	$0.415475\pi$
$692$	−2.53897	−	4.39763i	−0.0965173	−	0.167173i
$693$	11.2495	−	11.9771i	0.427332	−	0.454972i
$694$		−	33.5765i		−	1.27454i
$695$	33.4456	+	57.9295i	1.26866	+	2.19739i
$696$	−0.254829	−	15.9494i	−0.00965928	−	0.604562i
$697$	9.57961	−	5.53079i	0.362854	−	0.209494i
$698$	−11.8845	−	20.5845i	−0.449833	−	0.779134i
$699$	8.22228	−	4.92393i	0.310995	−	0.186240i
$700$	14.8416	+	3.98690i	0.560961	+	0.150691i
$701$		−	9.30649i		−	0.351501i	−0.984435	−	0.175751i	$-0.943765\pi$
$701$		−	9.30649i		−	0.351501i	0.984435	−	0.175751i	$-0.0562352\pi$
$702$	18.1619	−	4.59825i	0.685478	−	0.173550i
$703$	6.10373	−	3.52399i	0.230207	−	0.132910i
$704$	−1.03510	+	1.79285i	−0.0390118	+	0.0675704i
$705$	6.93701	−	0.110835i	0.261263	−	0.00417428i
$706$	−9.28444	−	5.36037i	−0.349425	−	0.201740i
$707$	13.2012	+	49.3930i	0.496483	+	1.85762i
$708$	−14.8475	−	8.25878i	−0.558002	−	0.310384i
$709$	−2.68396	+	1.54958i	−0.100798	+	0.0581958i	−0.549552	−	0.835460i	$-0.685201\pi$
$709$	−2.68396	+	1.54958i	−0.100798	+	0.0581958i	0.448754	+	0.893656i	$0.351868\pi$
$710$	−22.4690	+	12.9725i	−0.843246	+	0.486848i
$711$	14.9310	−	0.477236i	0.559955	−	0.0178978i
$712$		−	7.61879i		−	0.285526i
$713$	11.3188	−	6.53491i	0.423892	−	0.244734i
$714$	1.40882	+	4.95260i	0.0527238	+	0.185346i
$715$	−18.3899	+	16.2481i	−0.687745	+	0.607643i
$716$	−10.1439	−	5.85660i	−0.379097	−	0.218871i
$717$	−3.64984	+	6.56161i	−0.136306	+	0.245048i
$718$	−7.26878	+	12.5899i	−0.271268	+	0.469851i
$719$	−5.88702	−	10.1966i	−0.219549	−	0.380270i	0.735121	−	0.677936i	$-0.237125\pi$
$719$	−5.88702	−	10.1966i	−0.219549	−	0.380270i	−0.954670	+	0.297666i	$0.903792\pi$
$720$	−0.315084	−	9.85784i	−0.0117425	−	0.367380i
$721$	−23.2197	+	6.20590i	−0.864746	+	0.231120i
$722$	−8.98908	+	15.5695i	−0.334539	+	0.579438i
$723$	3.54207	−	6.36786i	0.131731	−	0.236823i
$724$			22.6731i			0.842638i
$725$	−46.3269	−	26.7468i	−1.72054	−	0.993353i
$726$	−11.6280	+	0.185784i	−0.431554	+	0.00689509i
$727$		−	13.8729i		−	0.514518i	−0.966342	−	0.257259i	$-0.917181\pi$
$727$		−	13.8729i		−	0.514518i	0.966342	−	0.257259i	$-0.0828194\pi$
$728$	−5.27553	+	7.94788i	−0.195524	+	0.294568i
$729$	26.8761	−	2.58415i	0.995409	−	0.0957091i
$730$		−	5.77412i		−	0.213710i
$731$	3.77087	−	6.53134i	0.139471	−	0.241570i
$732$	0.00669590	+	0.419088i	0.000247488	+	0.0154899i
$733$	21.6003	−	37.4129i	0.797827	−	1.38188i	−0.123202	−	0.992382i	$-0.539316\pi$
$733$	21.6003	−	37.4129i	0.797827	−	1.38188i	0.921029	−	0.389495i	$-0.127350\pi$
$734$	15.1524	+	8.74823i	0.559284	+	0.322903i
$735$	−20.4357	−	34.2232i	−0.753781	−	1.26234i
$736$		−	3.50085i		−	0.129043i
$737$	21.1814	−	12.2291i	0.780228	−	0.450465i
$738$	26.0357	+	13.9422i	0.958387	+	0.513221i
$739$	−29.5969	−	17.0878i	−1.08874	−	0.628585i	−0.155500	−	0.987836i	$-0.549699\pi$
$739$	−29.5969	−	17.0878i	−1.08874	−	0.628585i	−0.933241	+	0.359251i	$0.883032\pi$
$740$	−11.4611	+	19.8512i	−0.421318	+	0.729744i
$741$	−6.16610	+	1.35310i	−0.226517	+	0.0497074i
$742$	4.00920	−	14.9247i	0.147182	−	0.547901i
$743$	15.6321	+	27.0755i	0.573484	+	0.993304i	0.996204	+	0.0870439i	$0.0277420\pi$
$743$	15.6321	+	27.0755i	0.573484	+	0.993304i	−0.422720	+	0.906260i	$0.638925\pi$
$744$	6.46548	−	0.103301i	0.237036	−	0.00378720i
$745$		−	43.5611i		−	1.59596i
$746$	−5.93324	−	10.2767i	−0.217231	−	0.376256i
$747$	−2.54858	+	1.58208i	−0.0932475	+	0.0578851i
$748$	−1.16306	+	2.01448i	−0.0425257	+	0.0736567i
$749$	−7.03641	−	7.04534i	−0.257105	−	0.257431i
$750$	−4.02323	−	2.23789i	−0.146908	−	0.0817162i
$751$	2.10325			0.0767488			0.0383744	−	0.999263i	$-0.487782\pi$
$751$	2.10325			0.0767488			0.0383744	+	0.999263i	$0.487782\pi$
$752$	1.05515	+	0.609193i	0.0384775	+	0.0222150i
$753$	17.4268	+	29.1004i	0.635068	+	1.06048i
$754$	24.8843	−	21.9860i	0.906233	−	0.800684i
$755$	−56.9955			−2.07428
$756$	−9.25067	+	10.1698i	−0.336444	+	0.369873i
$757$	16.8638	+	29.2089i	0.612924	+	1.06162i	0.990745	+	0.135737i	$0.0433402\pi$
$757$	16.8638	+	29.2089i	0.612924	+	1.06162i	−0.377821	+	0.925879i	$0.623326\pi$
$758$	−10.9141	+	6.30127i	−0.396419	+	0.228872i
$759$	−10.7696	+	6.44936i	−0.390910	+	0.234097i
$760$			3.32333i			0.120550i
$761$	16.6410	−	9.60768i	0.603235	−	0.348278i	−0.167078	−	0.985944i	$-0.553433\pi$
$761$	16.6410	−	9.60768i	0.603235	−	0.348278i	0.770313	+	0.637666i	$0.220100\pi$
$762$	−32.5613	+	0.520243i	−1.17957	+	0.0188464i
$763$	−1.93345	+	7.19746i	−0.0699956	+	0.260566i
$764$	22.3913	−	12.9276i	0.810087	−	0.467704i
$765$	−0.354035	−	11.0765i	−0.0128002	−	0.400471i
$766$	0.920885	−	0.531673i	0.0332729	−	0.0192101i
$767$	−7.02782	−	34.6619i	−0.253760	−	1.25157i
$768$	0.841952	−	1.51364i	0.0303813	−	0.0546189i
$769$	19.1381	+	33.1482i	0.690139	+	1.19536i	0.971792	+	0.235840i	$0.0757840\pi$
$769$	19.1381	+	33.1482i	0.690139	+	1.19536i	−0.281653	+	0.959516i	$0.590883\pi$
$770$	4.67162	−	17.3906i	0.168353	−	0.626712i
$771$	−15.1128	+	27.1695i	−0.544274	+	0.978485i
$772$	18.8878	+	10.9049i	0.679787	+	0.392475i
$773$		−	2.52422i		−	0.0907898i	−0.998969	−	0.0453949i	$-0.985545\pi$
$773$		−	2.52422i		−	0.0907898i	0.998969	−	0.0453949i	$-0.0144546\pi$
$774$	20.1257	−	0.643275i	0.723404	−	0.0231220i
$775$	10.8425	−	18.7797i	0.389473	−	0.674587i
$776$	3.21628	−	5.57077i	0.115458	−	0.199979i
$777$	30.7317	−	8.74198i	1.10249	−	0.313617i
$778$	2.28039	−	1.31658i	0.0817558	−	0.0472018i
$779$	−8.61825	−	4.97575i	−0.308781	−	0.178275i
$780$	15.1670	−	13.8381i	0.543064	−	0.495485i
$781$	8.16870	+	14.1486i	0.292299	+	0.506277i
$782$		−	3.93363i		−	0.140666i
$783$	40.2492	−	25.8852i	1.43839	−	0.925063i
$784$	0.00888497	−	6.99999i	0.000317320	−	0.250000i
$785$	46.3984			1.65603
$786$	−2.58427	−	4.31538i	−0.0921780	−	0.153925i
$787$	−1.76492			−0.0629126			−0.0314563	−	0.999505i	$-0.510014\pi$
$787$	−1.76492			−0.0629126			−0.0314563	+	0.999505i	$0.510014\pi$
$788$	−3.51025	−	6.07993i	−0.125047	−	0.216588i
$789$	41.3798	−	24.7804i	1.47316	−	0.882204i
$790$	14.1776	−	8.18542i	0.504415	−	0.291224i
$791$	13.5110	−	3.61107i	0.480395	−	0.128395i
$792$	−6.20743	+	0.198407i	−0.220572	+	0.00705009i
$793$	−0.653860	+	0.577705i	−0.0232193	+	0.0205149i
$794$	4.27357	+	7.40204i	0.151663	+	0.262689i
$795$	−16.1679	+	29.0664i	−0.573418	+	1.03088i
$796$			15.0791i			0.534464i
$797$	−5.40206	+	9.35664i	−0.191351	+	0.331429i	−0.945698	−	0.325046i	$-0.894620\pi$
$797$	−5.40206	+	9.35664i	−0.191351	+	0.331429i	0.754347	+	0.656476i	$0.227953\pi$
$798$	3.22493	−	3.32543i	0.114161	−	0.117719i
$799$	1.18559	+	0.684502i	0.0419432	+	0.0242159i
$800$	−2.90424	−	5.03029i	−0.102680	−	0.177848i
$801$	19.4190	−	12.0547i	0.686137	−	0.425932i
$802$	15.5754			0.549985
$803$	−3.63594			−0.128309
$804$	−17.5559	+	10.5134i	−0.619149	+	0.370779i
$805$	7.86270	+	29.4187i	0.277124	+	1.03687i
$806$	8.91255	+	10.0874i	0.313931	+	0.355315i
$807$	−23.8330	+	42.8465i	−0.838963	+	1.50827i
$808$	9.66204	−	16.7351i	0.339909	−	0.588740i
$809$	14.3880	+	8.30689i	0.505854	+	0.292055i	0.731128	−	0.682241i	$-0.238994\pi$
$809$	14.3880	+	8.30689i	0.505854	+	0.292055i	−0.225274	+	0.974295i	$0.572328\pi$
$810$	24.6274	−	16.4005i	0.865320	−	0.576255i
$811$	−7.44633			−0.261476			−0.130738	−	0.991417i	$-0.541735\pi$
$811$	−7.44633			−0.261476			−0.130738	+	0.991417i	$0.541735\pi$
$812$	−6.32139	+	23.5320i	−0.221837	+	0.825811i
$813$	21.3045	−	38.3008i	0.747182	−	1.34327i
$814$	12.5002	+	7.21699i	0.438132	+	0.252955i
$815$	−33.9124			−1.18790
$816$	0.946035	−	1.70076i	0.0331178	−	0.0595386i
$817$	−6.78489			−0.237373
$818$	−10.8097			−0.377951
$819$	−28.6049	−	0.871013i	−0.999537	−	0.0304357i
$820$	32.3653			1.13025
$821$	3.42773			0.119629			0.0598143	−	0.998210i	$-0.480949\pi$
$821$	3.42773			0.119629			0.0598143	+	0.998210i	$0.480949\pi$
$822$	17.8317	−	32.0575i	0.621953	−	1.11813i
$823$	39.6380			1.38169			0.690847	−	0.723001i	$-0.257238\pi$
$823$	39.6380			1.38169			0.690847	+	0.723001i	$0.257238\pi$
$824$	7.86720	+	4.54213i	0.274067	+	0.158233i
$825$	−10.1242	+	18.2011i	−0.352481	+	0.633682i
$826$	18.3395	+	18.3628i	0.638112	+	0.638923i
$827$	−0.211856			−0.00736695			−0.00368347	−	0.999993i	$-0.501172\pi$
$827$	−0.211856			−0.00736695			−0.00368347	+	0.999993i	$0.501172\pi$
$828$	8.92308	−	5.53917i	0.310099	−	0.192499i
$829$	27.2898	+	15.7558i	0.947815	+	0.547221i	0.892401	−	0.451242i	$-0.149019\pi$
$829$	27.2898	+	15.7558i	0.947815	+	0.547221i	0.0554133	+	0.998464i	$0.482352\pi$
$830$	−1.64365	+	2.84688i	−0.0570519	+	0.0988168i
$831$	−11.0241	+	19.8189i	−0.382422	+	0.687510i
$832$	3.53365	−	0.716460i	0.122507	−	0.0248388i
$833$	0.00998334	−	7.86534i	0.000345902	−	0.272518i
$834$	−30.2341	+	18.1058i	−1.04692	+	0.626952i
$835$	−45.9720			−1.59093
$836$	2.09268			0.0723770
$837$	10.4932	+	16.3160i	0.362698	+	0.563962i
$838$	7.13932	+	12.3657i	0.246624	+	0.427165i
$839$	13.7645	+	7.94694i	0.475204	+	0.274359i	0.718416	−	0.695614i	$-0.244868\pi$
$839$	13.7645	+	7.94694i	0.475204	+	0.274359i	−0.243212	+	0.969973i	$0.578201\pi$
$840$	−3.67561	+	14.6105i	−0.126821	+	0.504112i
$841$	27.9082	−	48.3384i	0.962352	−	1.66684i
$842$		−	31.1553i		−	1.07368i
$843$	13.9440	−	25.0683i	0.480258	−	0.863398i
$844$	−10.2101	−	17.6845i	−0.351448	−	0.608725i
$845$	42.4135	+	5.26553i	1.45907	+	0.181140i
$846$	0.116769	+	3.65329i	0.00401462	+	0.125603i
$847$	17.1561	+	4.60862i	0.589489	+	0.158354i
$848$	−5.05843	+	2.92049i	−0.173707	+	0.100290i
$849$	−27.3298	+	16.3665i	−0.937958	+	0.561698i
$850$	−3.26326	−	5.65214i	−0.111929	−	0.193867i
$851$	−24.4089			−0.836725
$852$	−7.02265	−	11.7269i	−0.240592	−	0.401756i
$853$	−8.80214			−0.301379			−0.150690	−	0.988581i	$-0.548149\pi$
$853$	−8.80214			−0.301379			−0.150690	+	0.988581i	$0.548149\pi$
$854$	0.166101	−	0.618327i	0.00568386	−	0.0211587i
$855$	−8.47061	+	5.25829i	−0.289689	+	0.179830i
$856$			3.76351i			0.128634i
$857$	2.96296	+	5.13199i	0.101213	+	0.175305i	0.912185	−	0.409780i	$-0.134394\pi$
$857$	2.96296	+	5.13199i	0.101213	+	0.175305i	−0.810972	+	0.585085i	$0.801061\pi$
$858$	−8.71380	−	9.55056i	−0.297484	−	0.326051i
$859$	21.0079	+	12.1289i	0.716781	+	0.413834i	0.813567	−	0.581472i	$-0.197523\pi$
$859$	21.0079	+	12.1289i	0.716781	+	0.413834i	−0.0967860	+	0.995305i	$0.530856\pi$
$860$	19.1102	−	11.0333i	0.651652	−	0.376231i
$861$	−32.3857	−	31.4070i	−1.10370	−	1.07035i
$862$	−10.7951	+	18.6976i	−0.367682	+	0.636844i
$863$	−9.92236	+	17.1860i	−0.337761	+	0.585019i	−0.984011	−	0.178106i	$-0.943003\pi$
$863$	−9.92236	+	17.1860i	−0.337761	+	0.585019i	0.646250	+	0.763126i	$0.276336\pi$
$864$	5.19019	−	0.248945i	0.176574	−	0.00846930i
$865$		−	16.6944i		−	0.567626i
$866$	−16.2009	−	9.35358i	−0.550528	−	0.317848i
$867$	−13.2502	+	23.8209i	−0.450000	+	0.809001i
$868$	−9.53925	−	2.56252i	−0.323783	−	0.0869777i
$869$	−5.15432	−	8.92754i	−0.174848	−	0.302846i
$870$	25.4923	−	45.8296i	0.864271	−	1.55377i
$871$	−40.3871	−	13.5435i	−1.36847	−	0.458904i
$872$	2.43945	−	1.40841i	0.0826101	−	0.0476949i
$873$	19.2879	−	0.616494i	0.652795	−	0.0208652i
$874$	−3.06476	+	1.76944i	−0.103667	+	0.0598521i
$875$	4.96946	+	4.97578i	0.167999	+	0.168212i
$876$	3.04165	−	0.0485974i	0.102768	−	0.00164195i
$877$	−7.64550	+	4.41413i	−0.258170	+	0.149055i	−0.623500	−	0.781824i	$-0.714290\pi$
$877$	−7.64550	+	4.41413i	−0.258170	+	0.149055i	0.365329	+	0.930878i	$0.380956\pi$
$878$			14.3709i			0.484994i
$879$	12.6589	−	7.58078i	0.426973	−	0.255693i
$880$	−5.89421	+	3.40302i	−0.198694	+	0.114716i
$881$	9.51336	+	16.4776i	0.320513	+	0.555145i	0.980594	−	0.196049i	$-0.0628113\pi$
$881$	9.51336	+	16.4776i	0.320513	+	0.555145i	−0.660081	+	0.751195i	$0.729478\pi$
$882$	17.8559	−	11.0530i	0.601238	−	0.372173i
$883$	−30.8587			−1.03848			−0.519239	−	0.854629i	$-0.673785\pi$
$883$	−30.8587			−1.03848			−0.519239	+	0.854629i	$0.673785\pi$
$884$	3.97048	−	0.805029i	0.133542	−	0.0270761i
$885$	−28.6973	−	47.9206i	−0.964650	−	1.61083i
$886$	−1.21594	−	0.702023i	−0.0408503	−	0.0235849i
$887$	13.1419			0.441262			0.220631	−	0.975357i	$-0.429188\pi$
$887$	13.1419			0.441262			0.220631	+	0.975357i	$0.429188\pi$
$888$	−10.5535	−	5.87031i	−0.354153	−	0.196995i
$889$	48.0414	+	12.9053i	1.61126	+	0.432831i
$890$	12.5239	−	21.6920i	0.419801	−	0.727116i
$891$	−10.3273	−	15.5078i	−0.345978	−	0.519530i
$892$	1.37326	+	2.37855i	0.0459801	+	0.0796399i
$893$		−	1.23162i		−	0.0412145i
$894$	22.9468	−	0.366629i	0.767456	−	0.0122619i
$895$	−19.2543	−	33.3494i	−0.643601	−	1.11475i
$896$	−1.87202	+	1.86964i	−0.0625397	+	0.0624603i
$897$	20.8368	+	6.61906i	0.695720	+	0.221004i
$898$	−11.0266	+	19.0987i	−0.367963	+	0.637331i
$899$	29.7760	+	17.1912i	0.993085	+	0.573358i
$900$	8.22617	−	15.3615i	0.274206	−	0.512050i
$901$	−5.68376	+	3.28152i	−0.189354	+	0.109323i
$902$		−	20.3803i		−	0.678589i
$903$	−29.8288	−	7.50410i	−0.992640	−	0.249721i
$904$	−4.57774	−	2.64296i	−0.152253	−	0.0879035i
$905$	−37.2703	+	64.5540i	−1.23891	+	2.14585i
$906$	−0.479698	−	30.0236i	−0.0159369	−	0.997468i
$907$	−24.3534	+	42.1813i	−0.808640	+	1.40061i	0.105165	+	0.994455i	$0.466463\pi$
$907$	−24.3534	+	42.1813i	−0.808640	+	1.40061i	−0.913806	+	0.406151i	$0.866871\pi$
$908$		−	8.98000i		−	0.298012i
$909$	57.9427	−	1.85201i	1.92184	−	0.0614273i
$910$	−28.0851	+	13.9570i	−0.931013	+	0.462669i
$911$		−	7.94598i		−	0.263262i	−0.991299	−	0.131631i	$-0.957979\pi$
$911$		−	7.94598i		−	0.263262i	0.991299	−	0.131631i	$-0.0420214\pi$
$912$	−1.75064	+	0.0279705i	−0.0579694	+	0.000926197i
$913$	1.79267	+	1.03500i	0.0593287	+	0.0342534i
$914$			42.3253i			1.40000i
$915$	−0.669837	+	1.20422i	−0.0221441	+	0.0398103i
$916$	8.23500	−	14.2634i	0.272092	−	0.471277i
$917$	1.98392	+	7.42292i	0.0655147	+	0.245126i
$918$	5.83180	−	0.279720i	0.192478	−	0.00923215i
$919$	13.5830	+	23.5265i	0.448062	+	0.776067i	0.998260	−	0.0589679i	$-0.0187810\pi$
$919$	13.5830	+	23.5265i	0.448062	+	0.776067i	−0.550198	+	0.835034i	$0.685448\pi$
$920$	5.75475	−	9.96752i	0.189728	−	0.328619i
$921$	−17.9472	+	32.2650i	−0.591379	+	1.06317i
$922$	−10.2913	−	5.94166i	−0.338925	−	0.195678i
$923$	9.04667	−	26.9775i	0.297775	−	0.887974i
$924$	9.20018	+	2.31451i	0.302664	+	0.0761419i
$925$	−35.0725	+	20.2491i	−1.15318	+	0.665787i
$926$		−	3.56440i		−	0.117133i
$927$	0.870631	+	27.2389i	0.0285953	+	0.894642i
$928$	7.97573	−	4.60479i	0.261816	−	0.151160i
$929$	−20.5681	+	11.8750i	−0.674816	+	0.389605i	−0.797899	−	0.602791i	$-0.794055\pi$
$929$	−20.5681	+	11.8750i	−0.674816	+	0.389605i	0.123083	+	0.992396i	$0.460722\pi$
$930$	18.5781	+	10.3339i	0.609200	+	0.338863i
$931$	−6.13250	+	3.53023i	−0.200985	+	0.115699i
$932$	4.79194	+	2.76663i	0.156965	+	0.0906240i
$933$	−25.6551	+	0.409900i	−0.839909	+	0.0134195i
$934$	3.56143	−	6.16858i	0.116534	−	0.201842i
$935$	−6.62285	+	3.82371i	−0.216591	+	0.125049i
$936$	7.41720	+	7.87307i	0.242439	+	0.257339i
$937$		−	44.8244i		−	1.46435i	−0.681116	−	0.732175i	$-0.738505\pi$
$937$		−	44.8244i		−	1.46435i	0.681116	−	0.732175i	$-0.261495\pi$
$938$	30.1981	−	8.07101i	0.986001	−	0.263528i
$939$	−38.9553	+	23.3284i	−1.27126	+	0.761294i
$940$	2.00280	+	3.46895i	0.0653240	+	0.113145i
$941$	26.3318	−	15.2027i	0.858393	−	0.495593i	−0.00508113	−	0.999987i	$-0.501617\pi$
$941$	26.3318	−	15.2027i	0.858393	−	0.495593i	0.863474	+	0.504394i	$0.168284\pi$
$942$	0.390508	+	24.4414i	0.0127234	+	0.796343i
$943$	17.2322	+	29.8471i	0.561159	+	0.971955i
$944$		−	9.80909i		−	0.319259i
$945$	−43.0555	+	13.7488i	−1.40059	+	0.447248i
$946$	−6.94759	−	12.0336i	−0.225886	−	0.391245i
$947$	−8.01406			−0.260422			−0.130211	−	0.991486i	$-0.541565\pi$
$947$	−8.01406			−0.260422			−0.130211	+	0.991486i	$0.541565\pi$
$948$	4.43118	+	7.39946i	0.143918	+	0.240323i
$949$	4.19286	+	4.74558i	0.136106	+	0.154048i
$950$	−2.93578	+	5.08492i	−0.0952493	+	0.164977i
$951$	−17.4511	−	29.1409i	−0.565890	−	0.944958i
$952$	−2.10344	+	2.10077i	−0.0681728	+	0.0680863i
$953$	−4.48194	−	2.58765i	−0.145184	−	0.0838222i	0.425648	−	0.904889i	$-0.360046\pi$
$953$	−4.48194	−	2.58765i	−0.145184	−	0.0838222i	−0.570833	+	0.821067i	$0.693379\pi$
$954$	−15.4474	−	8.27219i	−0.500130	−	0.267822i
$955$	85.0022			2.75061
$956$	−4.33497			−0.140203
$957$	−28.8587	−	16.0524i	−0.932868	−	0.518900i
$958$	−26.4547	−	15.2736i	−0.854712	−	0.493468i
$959$	−39.6475	+	39.5972i	−1.28028	+	1.27866i
$960$	4.88532	−	2.92558i	0.157673	−	0.0944228i
$961$	8.53115	−	14.7764i	0.275199	−	0.476658i
$962$	−4.99535	−	24.6375i	−0.161056	−	0.794346i
$963$	−9.59254	+	5.95475i	−0.309115	+	0.191889i
$964$	4.20698			0.135498
$965$	35.8512	+	62.0960i	1.15409	+	1.99894i
$966$	−15.4308	+	4.38945i	−0.496477	+	0.141228i
$967$		−	14.4231i		−	0.463816i	−0.972738	−	0.231908i	$-0.925503\pi$
$967$		−	14.4231i		−	0.463816i	0.972738	−	0.231908i	$-0.0744968\pi$
$968$	−3.35713	−	5.81473i	−0.107902	−	0.186892i
$969$	−1.96705	+	0.0314283i	−0.0631909	+	0.00100962i
$970$	18.3146	−	10.5739i	0.588046	−	0.339509i
$971$	−0.714834	−	1.23813i	−0.0229401	−	0.0397335i	0.854327	−	0.519735i	$-0.173969\pi$
$971$	−0.714834	−	1.23813i	−0.0229401	−	0.0397335i	−0.877268	+	0.480002i	$0.840636\pi$
$972$	8.84661	+	12.8350i	0.283755	+	0.411683i
$973$	52.0060	−	13.8996i	1.66723	−	0.445600i
$974$			32.0202i			1.02599i
$975$	35.4309	−	7.77501i	1.13470	−	0.249000i
$976$	−0.209571	+	0.120996i	−0.00670819	+	0.00387297i
$977$	7.46343	−	12.9270i	0.238776	−	0.413573i	−0.721587	−	0.692324i	$-0.756587\pi$
$977$	7.46343	−	12.9270i	0.238776	−	0.413573i	0.960363	+	0.278751i	$0.0899204\pi$
$978$	−0.285421	−	17.8641i	−0.00912676	−	0.571232i
$979$	−13.6593	−	7.88621i	−0.436554	−	0.252044i
$980$	11.5320	−	19.9155i	0.368375	−	0.636179i
$981$	7.44958	+	3.98929i	0.237847	+	0.127368i
$982$	−13.0865	+	7.55549i	−0.417607	+	0.241106i
$983$	−2.34938	+	1.35641i	−0.0749334	+	0.0432628i	−0.536999	−	0.843583i	$-0.680442\pi$
$983$	−2.34938	+	1.35641i	−0.0749334	+	0.0432628i	0.462065	+	0.886846i	$0.347109\pi$
$984$	0.272400	+	17.0491i	0.00868379	+	0.543507i
$985$		−	23.0808i		−	0.735414i
$986$	8.96170	−	5.17404i	0.285399	−	0.164775i
$987$	1.36217	−	5.41463i	0.0433584	−	0.172350i
$988$	−2.41322	−	2.73135i	−0.0767749	−	0.0868957i
$989$	20.3496	+	11.7489i	0.647080	+	0.373592i
$990$	−17.9997	−	9.63896i	−0.572069	−	0.306346i
$991$	3.28838	−	5.69564i	0.104459	−	0.180928i	−0.809058	−	0.587729i	$-0.800022\pi$
$991$	3.28838	−	5.69564i	0.104459	−	0.180928i	0.913517	+	0.406801i	$0.133356\pi$
$992$	1.86666	+	3.23315i	0.0592665	+	0.102653i
$993$	−0.721561	−	45.1615i	−0.0228980	−	1.43316i
$994$	5.39121	+	20.1715i	0.170999	+	0.639800i
$995$	−24.7872	+	42.9327i	−0.785807	+	1.36106i
$996$	−1.51349	−	0.841868i	−0.0479569	−	0.0266756i
$997$		−	22.9904i		−	0.728114i	−0.931377	−	0.364057i	$-0.881391\pi$
$997$		−	22.9904i		−	0.728114i	0.931377	−	0.364057i	$-0.118609\pi$
$998$	4.18606	+	2.41682i	0.132508	+	0.0765033i
$999$	−1.73571	−	36.1873i	−0.0549155	−	1.14492i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bi.e.257.12	yes	34
3.2	odd	2		546.2.bi.f.257.6	yes	34
7.3	odd	6		546.2.bn.f.101.17	yes	34
13.4	even	6		546.2.bn.e.173.1	yes	34
21.17	even	6		546.2.bn.e.101.1	yes	34
39.17	odd	6		546.2.bn.f.173.17	yes	34
91.17	odd	6		546.2.bi.f.17.6	yes	34
273.17	even	6	inner	546.2.bi.e.17.12	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.12	✓	34	273.17	even	6	inner
546.2.bi.e.257.12	yes	34	1.1	even	1	trivial
546.2.bi.f.17.6	yes	34	91.17	odd	6
546.2.bi.f.257.6	yes	34	3.2	odd	2
546.2.bn.e.101.1	yes	34	21.17	even	6
546.2.bn.e.173.1	yes	34	13.4	even	6
546.2.bn.f.101.17	yes	34	7.3	odd	6
546.2.bn.f.173.17	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(0.841952 - 1.51364i) q^{3} +1.00000 q^{4} +(2.84717 + 1.64381i) q^{5} +(-0.841952 + 1.51364i) q^{6} +(1.87202 - 1.86964i) q^{7} -1.00000 q^{8} +(-1.58223 - 2.54883i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(0.841952 - 1.51364i) q^{3} +1.00000 q^{4} +(2.84717 + 1.64381i) q^{5} +(-0.841952 + 1.51364i) q^{6} +(1.87202 - 1.86964i) q^{7} -1.00000 q^{8} +(-1.58223 - 2.54883i) q^{9} +(-2.84717 - 1.64381i) q^{10} +(-1.03510 + 1.79285i) q^{11} +(0.841952 - 1.51364i) q^{12} +(3.53365 - 0.716460i) q^{13} +(-1.87202 + 1.86964i) q^{14} +(4.88532 - 2.92558i) q^{15} +1.00000 q^{16} +1.12362 q^{17} +(1.58223 + 2.54883i) q^{18} +(-0.505430 - 0.875431i) q^{19} +(2.84717 + 1.64381i) q^{20} +(-1.25382 - 4.40771i) q^{21} +(1.03510 - 1.79285i) q^{22} +3.50085i q^{23} +(-0.841952 + 1.51364i) q^{24} +(2.90424 + 5.03029i) q^{25} +(-3.53365 + 0.716460i) q^{26} +(-5.19019 + 0.248945i) q^{27} +(1.87202 - 1.86964i) q^{28} +(-7.97573 + 4.60479i) q^{29} +(-4.88532 + 2.92558i) q^{30} +(-1.86666 - 3.23315i) q^{31} -1.00000 q^{32} +(1.84223 + 3.07626i) q^{33} -1.12362 q^{34} +(8.40328 - 2.24594i) q^{35} +(-1.58223 - 2.54883i) q^{36} +6.97226i q^{37} +(0.505430 + 0.875431i) q^{38} +(1.89070 - 5.95191i) q^{39} +(-2.84717 - 1.64381i) q^{40} +(8.52566 - 4.92229i) q^{41} +(1.25382 + 4.40771i) q^{42} +(3.35600 - 5.81276i) q^{43} +(-1.03510 + 1.79285i) q^{44} +(-0.315084 - 9.85784i) q^{45} -3.50085i q^{46} +(1.05515 + 0.609193i) q^{47} +(0.841952 - 1.51364i) q^{48} +(0.00888497 - 6.99999i) q^{49} +(-2.90424 - 5.03029i) q^{50} +(0.946035 - 1.70076i) q^{51} +(3.53365 - 0.716460i) q^{52} +(-5.05843 + 2.92049i) q^{53} +(5.19019 - 0.248945i) q^{54} +(-5.89421 + 3.40302i) q^{55} +(-1.87202 + 1.86964i) q^{56} +(-1.75064 + 0.0279705i) q^{57} +(7.97573 - 4.60479i) q^{58} -9.80909i q^{59} +(4.88532 - 2.92558i) q^{60} +(-0.209571 + 0.120996i) q^{61} +(1.86666 + 3.23315i) q^{62} +(-7.72736 - 1.81324i) q^{63} +1.00000 q^{64} +(11.2386 + 3.76878i) q^{65} +(-1.84223 - 3.07626i) q^{66} +(-10.2316 - 5.90721i) q^{67} +1.12362 q^{68} +(5.29905 + 2.94755i) q^{69} +(-8.40328 + 2.24594i) q^{70} +(3.94585 - 6.83441i) q^{71} +(1.58223 + 2.54883i) q^{72} +(0.878160 + 1.52102i) q^{73} -6.97226i q^{74} +(10.0593 - 0.160721i) q^{75} +(-0.505430 - 0.875431i) q^{76} +(1.41426 + 5.29150i) q^{77} +(-1.89070 + 5.95191i) q^{78} +(-2.48977 + 4.31240i) q^{79} +(2.84717 + 1.64381i) q^{80} +(-3.99307 + 8.06569i) q^{81} +(-8.52566 + 4.92229i) q^{82} -0.999900i q^{83} +(-1.25382 - 4.40771i) q^{84} +(3.19914 + 1.84702i) q^{85} +(-3.35600 + 5.81276i) q^{86} +(0.254829 + 15.9494i) q^{87} +(1.03510 - 1.79285i) q^{88} +7.61879i q^{89} +(0.315084 + 9.85784i) q^{90} +(5.27553 - 7.94788i) q^{91} +3.50085i q^{92} +(-6.46548 + 0.103301i) q^{93} +(-1.05515 - 0.609193i) q^{94} -3.32333i q^{95} +(-0.841952 + 1.51364i) q^{96} +(-3.21628 + 5.57077i) q^{97} +(-0.00888497 + 6.99999i) q^{98} +(6.20743 - 0.198407i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more