LMFDB - Embedded newform 342.2.h.f.277.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(121,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 2]))

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

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

chi := DirichletCharacter("342.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.h (of order $3$, 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:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.50911458676875.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} + 12x^{8} - 28x^{7} + 58x^{6} - 111x^{5} + 174x^{4} - 252x^{3} + 324x^{2} - 324x + 243 $ x^10 - 4x^9 + 12x^8 - 28x^7 + 58x^6 - 111x^5 + 174x^4 - 252x^3 + 324x^2 - 324*x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.4
Root			$-0.378732 + 1.69014i$ of defining polynomial
Character	$\chi$	$=$	342.277
Dual form			342.2.h.f.121.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.378732 + 1.69014i) q^{3} +(-0.500000 + 0.866025i) q^{4} +2.54867 q^{5} +(1.27434 - 1.17306i) q^{6} +(2.28394 - 3.95589i) q^{7} +1.00000 q^{8} +(-2.71312 + 1.28022i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.378732 + 1.69014i) q^{3} +(-0.500000 + 0.866025i) q^{4} +2.54867 q^{5} +(1.27434 - 1.17306i) q^{6} +(2.28394 - 3.95589i) q^{7} +1.00000 q^{8} +(-2.71312 + 1.28022i) q^{9} +(-1.27434 - 2.20721i) q^{10} +(0.818674 - 1.41798i) q^{11} +(-1.65307 - 0.517077i) q^{12} +(-2.19741 + 3.80602i) q^{13} -4.56787 q^{14} +(0.965262 + 4.30760i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.60261 - 4.50785i) q^{17} +(2.46526 + 1.70953i) q^{18} +(1.58653 + 4.05992i) q^{19} +(-1.27434 + 2.20721i) q^{20} +(7.55100 + 2.36194i) q^{21} -1.63735 q^{22} +(0.796476 - 1.37954i) q^{23} +(0.378732 + 1.69014i) q^{24} +1.49573 q^{25} +4.39481 q^{26} +(-3.19129 - 4.10069i) q^{27} +(2.28394 + 3.95589i) q^{28} +6.30613 q^{29} +(3.24786 - 2.98974i) q^{30} +(3.29005 + 5.69854i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.70665 + 0.846635i) q^{33} -5.20522 q^{34} +(5.82100 - 10.0823i) q^{35} +(0.247863 - 2.98974i) q^{36} -8.93052 q^{37} +(2.72273 - 3.40393i) q^{38} +(-7.26492 - 2.27246i) q^{39} +2.54867 q^{40} -7.65424 q^{41} +(-1.73000 - 7.72033i) q^{42} +(4.76706 + 8.25680i) q^{43} +(0.818674 + 1.41798i) q^{44} +(-6.91486 + 3.26285i) q^{45} -1.59295 q^{46} -4.51493 q^{47} +(1.27434 - 1.17306i) q^{48} +(-6.93273 - 12.0078i) q^{49} +(-0.747863 - 1.29534i) q^{50} +(8.60458 + 2.69150i) q^{51} +(-2.19741 - 3.80602i) q^{52} +(-1.04434 - 1.80885i) q^{53} +(-1.95566 + 4.81408i) q^{54} +(2.08653 - 3.61398i) q^{55} +(2.28394 - 3.95589i) q^{56} +(-6.26094 + 4.21907i) q^{57} +(-3.15307 - 5.46127i) q^{58} +9.58083 q^{59} +(-4.21312 - 1.31786i) q^{60} -13.0256 q^{61} +(3.29005 - 5.69854i) q^{62} +(-1.13220 + 13.6568i) q^{63} +1.00000 q^{64} +(-5.60046 + 9.70029i) q^{65} +(-0.620115 - 2.76734i) q^{66} +(1.35011 - 2.33846i) q^{67} +(2.60261 + 4.50785i) q^{68} +(2.63326 + 0.823679i) q^{69} -11.6420 q^{70} +(-1.95133 + 3.37980i) q^{71} +(-2.71312 + 1.28022i) q^{72} +(0.127747 - 0.221265i) q^{73} +(4.46526 + 7.73406i) q^{74} +(0.566478 + 2.52798i) q^{75} +(-4.30926 - 0.655982i) q^{76} +(-3.73960 - 6.47717i) q^{77} +(1.66445 + 7.42783i) q^{78} +(-4.23000 - 7.32657i) q^{79} +(-1.27434 - 2.20721i) q^{80} +(5.72209 - 6.94677i) q^{81} +(3.82712 + 6.62877i) q^{82} +(-2.74920 + 4.76175i) q^{83} +(-5.82100 + 5.35839i) q^{84} +(6.63320 - 11.4890i) q^{85} +(4.76706 - 8.25680i) q^{86} +(2.38833 + 10.6582i) q^{87} +(0.818674 - 1.41798i) q^{88} +(-4.37758 - 7.58219i) q^{89} +(6.28314 + 4.35702i) q^{90} +(10.0375 + 17.3854i) q^{91} +(0.796476 + 1.37954i) q^{92} +(-8.38527 + 7.71886i) q^{93} +(2.25746 + 3.91004i) q^{94} +(4.04355 + 10.3474i) q^{95} +(-1.65307 - 0.517077i) q^{96} +(-1.68133 - 2.91214i) q^{97} +(-6.93273 + 12.0078i) q^{98} +(-0.405837 + 4.89525i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 5 q^{2} - 4 q^{3} - 5 q^{4} + 4 q^{5} + 2 q^{6} - 5 q^{7} + 10 q^{8} - 8 q^{9}+O(q^{10}) $ 10 * q - 5 * q^2 - 4 * q^3 - 5 * q^4 + 4 * q^5 + 2 * q^6 - 5 * q^7 + 10 * q^8 - 8 * q^9	\( 10 q - 5 q^{2} - 4 q^{3} - 5 q^{4} + 4 q^{5} + 2 q^{6} - 5 q^{7} + 10 q^{8} - 8 q^{9} - 2 q^{10} + q^{11} + 2 q^{12} - 7 q^{13} + 10 q^{14} - 11 q^{15} - 5 q^{16} - 9 q^{17} + 4 q^{18} + 3 q^{19} - 2 q^{20} + 15 q^{21} - 2 q^{22} + 10 q^{23} - 4 q^{24} + 18 q^{25} + 14 q^{26} - 4 q^{27} - 5 q^{28} + 26 q^{29} + 34 q^{30} + 18 q^{31} - 5 q^{32} + 13 q^{33} + 18 q^{34} + 12 q^{35} + 4 q^{36} - 48 q^{37} - 9 q^{38} - 20 q^{39} + 4 q^{40} - 10 q^{41} - 3 q^{42} + 15 q^{43} + q^{44} - 10 q^{45} - 20 q^{46} - 14 q^{47} + 2 q^{48} - 26 q^{49} - 9 q^{50} + 30 q^{51} - 7 q^{52} - 14 q^{53} - 16 q^{54} + 8 q^{55} - 5 q^{56} - 17 q^{57} - 13 q^{58} + 30 q^{59} - 23 q^{60} - 28 q^{61} + 18 q^{62} + 48 q^{63} + 10 q^{64} - q^{65} - 5 q^{66} - 2 q^{67} - 9 q^{68} - 44 q^{69} - 24 q^{70} - 41 q^{71} - 8 q^{72} + 4 q^{73} + 24 q^{74} + 22 q^{75} + 6 q^{76} - 6 q^{77} + 19 q^{78} - 28 q^{79} - 2 q^{80} - 8 q^{81} + 5 q^{82} + 21 q^{83} - 12 q^{84} + 18 q^{85} + 15 q^{86} - q^{87} + q^{88} - 27 q^{89} + 8 q^{90} - q^{91} + 10 q^{92} - 49 q^{93} + 7 q^{94} + 17 q^{95} + 2 q^{96} - 24 q^{97} - 26 q^{98} - 13 q^{99}+O(q^{100}) \) 10 * q - 5 * q^2 - 4 * q^3 - 5 * q^4 + 4 * q^5 + 2 * q^6 - 5 * q^7 + 10 * q^8 - 8 * q^9 - 2 * q^10 + q^11 + 2 * q^12 - 7 * q^13 + 10 * q^14 - 11 * q^15 - 5 * q^16 - 9 * q^17 + 4 * q^18 + 3 * q^19 - 2 * q^20 + 15 * q^21 - 2 * q^22 + 10 * q^23 - 4 * q^24 + 18 * q^25 + 14 * q^26 - 4 * q^27 - 5 * q^28 + 26 * q^29 + 34 * q^30 + 18 * q^31 - 5 * q^32 + 13 * q^33 + 18 * q^34 + 12 * q^35 + 4 * q^36 - 48 * q^37 - 9 * q^38 - 20 * q^39 + 4 * q^40 - 10 * q^41 - 3 * q^42 + 15 * q^43 + q^44 - 10 * q^45 - 20 * q^46 - 14 * q^47 + 2 * q^48 - 26 * q^49 - 9 * q^50 + 30 * q^51 - 7 * q^52 - 14 * q^53 - 16 * q^54 + 8 * q^55 - 5 * q^56 - 17 * q^57 - 13 * q^58 + 30 * q^59 - 23 * q^60 - 28 * q^61 + 18 * q^62 + 48 * q^63 + 10 * q^64 - q^65 - 5 * q^66 - 2 * q^67 - 9 * q^68 - 44 * q^69 - 24 * q^70 - 41 * q^71 - 8 * q^72 + 4 * q^73 + 24 * q^74 + 22 * q^75 + 6 * q^76 - 6 * q^77 + 19 * q^78 - 28 * q^79 - 2 * q^80 - 8 * q^81 + 5 * q^82 + 21 * q^83 - 12 * q^84 + 18 * q^85 + 15 * q^86 - q^87 + q^88 - 27 * q^89 + 8 * q^90 - q^91 + 10 * q^92 - 49 * q^93 + 7 * q^94 + 17 * q^95 + 2 * q^96 - 24 * q^97 - 26 * q^98 - 13 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	0.378732	+	1.69014i	0.218661	+	0.975801i
$3$	0.378732	+	1.69014i	0.218661	+	0.975801i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	2.54867			1.13980			0.569900	−	0.821714i	$-0.306982\pi$
$5$	2.54867			1.13980			0.569900	+	0.821714i	$0.306982\pi$
$6$	1.27434	−	1.17306i	0.520245	−	0.478900i
$7$	2.28394	−	3.95589i	0.863247	−	1.49519i	−0.00553088	−	0.999985i	$-0.501761\pi$
$7$	2.28394	−	3.95589i	0.863247	−	1.49519i	0.868778	−	0.495202i	$-0.164906\pi$
$8$	1.00000			0.353553
$9$	−2.71312	+	1.28022i	−0.904375	+	0.426739i
$10$	−1.27434	−	2.20721i	−0.402980	−	0.697982i
$11$	0.818674	−	1.41798i	0.246839	−	0.427539i	−0.715808	−	0.698297i	$-0.753941\pi$
$11$	0.818674	−	1.41798i	0.246839	−	0.427539i	0.962647	+	0.270759i	$0.0872746\pi$
$12$	−1.65307	−	0.517077i	−0.477199	−	0.149267i
$13$	−2.19741	+	3.80602i	−0.609451	+	1.05560i	0.381880	+	0.924212i	$0.375277\pi$
$13$	−2.19741	+	3.80602i	−0.609451	+	1.05560i	−0.991331	+	0.131388i	$0.958057\pi$
$14$	−4.56787			−1.22082
$15$	0.965262	+	4.30760i	0.249230	+	1.11222i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.60261	−	4.50785i	0.631226	−	1.09331i	−0.356076	−	0.934457i	$-0.615886\pi$
$17$	2.60261	−	4.50785i	0.631226	−	1.09331i	0.987301	−	0.158858i	$-0.0507812\pi$
$18$	2.46526	+	1.70953i	0.581068	+	0.402939i
$19$	1.58653	+	4.05992i	0.363975	+	0.931409i
$19$	1.58653	+	4.05992i	0.363975	+	0.931409i
$20$	−1.27434	+	2.20721i	−0.284950	+	0.493548i
$21$	7.55100	+	2.36194i	1.64776	+	0.515418i
$22$	−1.63735			−0.349084
$23$	0.796476	−	1.37954i	0.166077	−	0.287653i	−0.770960	−	0.636883i	$-0.780223\pi$
$23$	0.796476	−	1.37954i	0.166077	−	0.287653i	0.937037	+	0.349230i	$0.113557\pi$
$24$	0.378732	+	1.69014i	0.0773083	+	0.344998i
$25$	1.49573			0.299145
$26$	4.39481			0.861893
$27$	−3.19129	−	4.10069i	−0.614163	−	0.789179i
$28$	2.28394	+	3.95589i	0.431623	+	0.747594i
$29$	6.30613			1.17102			0.585510	−	0.810665i	$-0.300894\pi$
$29$	6.30613			1.17102			0.585510	+	0.810665i	$0.300894\pi$
$30$	3.24786	−	2.98974i	0.592976	−	0.545850i
$31$	3.29005	+	5.69854i	0.590911	+	1.02349i	0.994110	+	0.108376i	$0.0345650\pi$
$31$	3.29005	+	5.69854i	0.590911	+	1.02349i	−0.403199	+	0.915112i	$0.632102\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	2.70665	+	0.846635i	0.471167	+	0.147380i
$34$	−5.20522			−0.892688
$35$	5.82100	−	10.0823i	0.983929	−	1.70421i
$36$	0.247863	−	2.98974i	0.0413104	−	0.498291i
$37$	−8.93052			−1.46817			−0.734085	−	0.679058i	$-0.762388\pi$
$37$	−8.93052			−1.46817			−0.734085	+	0.679058i	$0.762388\pi$
$38$	2.72273	−	3.40393i	0.441684	−	0.552191i
$39$	−7.26492	−	2.27246i	−1.16332	−	0.363884i
$40$	2.54867			0.402980
$41$	−7.65424			−1.19539			−0.597696	−	0.801723i	$-0.703917\pi$
$41$	−7.65424			−1.19539			−0.597696	+	0.801723i	$0.703917\pi$
$42$	−1.73000	−	7.72033i	−0.266944	−	1.19127i
$43$	4.76706	+	8.25680i	0.726970	+	1.25915i	0.958158	+	0.286240i	$0.0924056\pi$
$43$	4.76706	+	8.25680i	0.726970	+	1.25915i	−0.231187	+	0.972909i	$0.574261\pi$
$44$	0.818674	+	1.41798i	0.123420	+	0.213769i
$45$	−6.91486	+	3.26285i	−1.03081	+	0.486397i
$46$	−1.59295			−0.234868
$47$	−4.51493			−0.658570			−0.329285	−	0.944231i	$-0.606808\pi$
$47$	−4.51493			−0.658570			−0.329285	+	0.944231i	$0.606808\pi$
$48$	1.27434	−	1.17306i	0.183935	−	0.169317i
$49$	−6.93273	−	12.0078i	−0.990390	−	1.71541i
$50$	−0.747863	−	1.29534i	−0.105764	−	0.183188i
$51$	8.60458	+	2.69150i	1.20488	+	0.376886i
$52$	−2.19741	−	3.80602i	−0.304725	−	0.527800i
$53$	−1.04434	−	1.80885i	−0.143451	−	0.248464i	0.785343	−	0.619061i	$-0.212487\pi$
$53$	−1.04434	−	1.80885i	−0.143451	−	0.248464i	−0.928794	+	0.370597i	$0.879153\pi$
$54$	−1.95566	+	4.81408i	−0.266132	+	0.655114i
$55$	2.08653	−	3.61398i	0.281348	−	0.487309i
$56$	2.28394	−	3.95589i	0.305204	−	0.528628i
$57$	−6.26094	+	4.21907i	−0.829282	+	0.558830i
$58$	−3.15307	−	5.46127i	−0.414018	−	0.717100i
$59$	9.58083			1.24732			0.623659	−	0.781697i	$-0.285645\pi$
$59$	9.58083			1.24732			0.623659	+	0.781697i	$0.285645\pi$
$60$	−4.21312	−	1.31786i	−0.543912	−	0.170135i
$61$	−13.0256			−1.66775			−0.833876	−	0.551952i	$-0.813883\pi$
$61$	−13.0256			−1.66775			−0.833876	+	0.551952i	$0.813883\pi$
$62$	3.29005	−	5.69854i	0.417837	−	0.723716i
$63$	−1.13220	+	13.6568i	−0.142644	+	1.72059i
$64$	1.00000			0.125000
$65$	−5.60046	+	9.70029i	−0.694652	+	1.20317i
$66$	−0.620115	−	2.76734i	−0.0763309	−	0.340636i
$67$	1.35011	−	2.33846i	0.164943	−	0.285689i	−0.771692	−	0.635996i	$-0.780589\pi$
$67$	1.35011	−	2.33846i	0.164943	−	0.285689i	0.936635	+	0.350307i	$0.113923\pi$
$68$	2.60261	+	4.50785i	0.315613	+	0.546657i
$69$	2.63326	+	0.823679i	0.317007	+	0.0991593i
$70$	−11.6420			−1.39149
$71$	−1.95133	+	3.37980i	−0.231580	+	0.401109i	−0.958273	−	0.285854i	$-0.907723\pi$
$71$	−1.95133	+	3.37980i	−0.231580	+	0.401109i	0.726693	+	0.686962i	$0.241056\pi$
$72$	−2.71312	+	1.28022i	−0.319745	+	0.150875i
$73$	0.127747	−	0.221265i	0.0149517	−	0.0258971i	−0.858453	−	0.512893i	$-0.828574\pi$
$73$	0.127747	−	0.221265i	0.0149517	−	0.0258971i	0.873404	+	0.486996i	$0.161907\pi$
$74$	4.46526	+	7.73406i	0.519076	+	0.899066i
$75$	0.566478	+	2.52798i	0.0654113	+	0.291906i
$76$	−4.30926	−	0.655982i	−0.494306	−	0.0752463i
$77$	−3.73960	−	6.47717i	−0.426167	−	0.738142i
$78$	1.66445	+	7.42783i	0.188462	+	0.841036i
$79$	−4.23000	−	7.32657i	−0.475912	−	0.824304i	0.523707	−	0.851898i	$-0.324549\pi$
$79$	−4.23000	−	7.32657i	−0.475912	−	0.824304i	−0.999619	+	0.0275947i	$0.991215\pi$
$80$	−1.27434	−	2.20721i	−0.142475	−	0.246774i
$81$	5.72209	−	6.94677i	0.635788	−	0.771864i
$82$	3.82712	+	6.62877i	0.422635	+	0.732025i
$83$	−2.74920	+	4.76175i	−0.301764	+	0.522670i	−0.976536	−	0.215356i	$-0.930909\pi$
$83$	−2.74920	+	4.76175i	−0.301764	+	0.522670i	0.674772	+	0.738026i	$0.264242\pi$
$84$	−5.82100	+	5.35839i	−0.635123	+	0.584648i
$85$	6.63320	−	11.4890i	0.719471	−	1.24616i
$86$	4.76706	−	8.25680i	0.514046	−	0.890353i
$87$	2.38833	+	10.6582i	0.256056	+	1.14268i
$88$	0.818674	−	1.41798i	0.0872709	−	0.151158i
$89$	−4.37758	−	7.58219i	−0.464022	−	0.803710i	0.535134	−	0.844767i	$-0.320261\pi$
$89$	−4.37758	−	7.58219i	−0.464022	−	0.803710i	−0.999157	+	0.0410566i	$0.986928\pi$
$90$	6.28314	+	4.35702i	0.662301	+	0.459270i
$91$	10.0375	+	17.3854i	1.05221	+	1.82249i
$92$	0.796476	+	1.37954i	0.0830383	+	0.143827i
$93$	−8.38527	+	7.71886i	−0.869512	+	0.800409i
$94$	2.25746	+	3.91004i	0.232840	+	0.403290i
$95$	4.04355	+	10.3474i	0.414859	+	1.06162i
$96$	−1.65307	−	0.517077i	−0.168715	−	0.0527740i
$97$	−1.68133	−	2.91214i	−0.170713	−	0.295683i	0.767956	−	0.640502i	$-0.221274\pi$
$97$	−1.68133	−	2.91214i	−0.170713	−	0.295683i	−0.938669	+	0.344819i	$0.887940\pi$
$98$	−6.93273	+	12.0078i	−0.700311	+	1.21297i
$99$	−0.405837	+	4.89525i	−0.0407882	+	0.491991i
$100$	−0.747863	+	1.29534i	−0.0747863	+	0.129534i
$101$	−3.38257			−0.336579			−0.168289	−	0.985738i	$-0.553824\pi$
$101$	−3.38257			−0.336579			−0.168289	+	0.985738i	$0.553824\pi$
$102$	−1.97138	−	8.79753i	−0.195196	−	0.871086i
$103$	−7.56708	−	13.1066i	−0.745606	−	1.29143i	−0.949911	−	0.312521i	$-0.898827\pi$
$103$	−7.56708	−	13.1066i	−0.745606	−	1.29143i	0.204304	−	0.978907i	$-0.434507\pi$
$104$	−2.19741	+	3.80602i	−0.215473	+	0.373211i
$105$	19.2450	+	6.01982i	1.87812	+	0.587474i
$106$	−1.04434	+	1.80885i	−0.101435	+	0.175691i
$107$	−0.920593			−0.0889971			−0.0444985	−	0.999009i	$-0.514169\pi$
$107$	−0.920593			−0.0889971			−0.0444985	+	0.999009i	$0.514169\pi$
$108$	5.14695	−	0.713388i	0.495265	−	0.0686458i
$109$	−8.16088	+	14.1351i	−0.781671	+	1.35389i	0.149297	+	0.988792i	$0.452299\pi$
$109$	−8.16088	+	14.1351i	−0.781671	+	1.35389i	−0.930968	+	0.365101i	$0.881034\pi$
$110$	−4.17306			−0.397886
$111$	−3.38227	−	15.0938i	−0.321031	−	1.43264i
$112$	−4.56787			−0.431623
$113$	−4.66694	−	8.08338i	−0.439029	−	0.760421i	0.558586	−	0.829447i	$-0.311344\pi$
$113$	−4.66694	−	8.08338i	−0.439029	−	0.760421i	−0.997615	+	0.0690262i	$0.978011\pi$
$114$	6.78430	+	3.31260i	0.635408	+	0.310254i
$115$	2.02995	−	3.51598i	0.189294	−	0.327867i
$116$	−3.15307	+	5.46127i	−0.292755	+	0.507066i
$117$	1.08931	−	13.1394i	0.100707	−	1.21473i
$118$	−4.79042	−	8.29724i	−0.440993	−	0.763823i
$119$	−11.8884	−	20.5913i	−1.08981	−	1.88760i
$120$	0.965262	+	4.30760i	0.0881160	+	0.393229i
$121$	4.15955	+	7.20455i	0.378141	+	0.654959i
$122$	6.51278	+	11.2805i	0.589639	+	1.02129i
$123$	−2.89890	−	12.9367i	−0.261385	−	1.16646i
$124$	−6.58011			−0.590911
$125$	−8.93124			−0.798835
$126$	12.3932	−	5.84786i	1.10407	−	0.520969i
$127$	0.709945	+	1.22966i	0.0629974	+	0.109115i	0.895804	−	0.444449i	$-0.146601\pi$
$127$	0.709945	+	1.22966i	0.0629974	+	0.109115i	−0.832806	+	0.553564i	$0.813267\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−12.1497	+	11.1841i	−1.06972	+	0.984705i
$130$	11.2009			0.982386
$131$	−11.2052			−0.979005			−0.489502	−	0.872002i	$-0.662822\pi$
$131$	−11.2052			−0.979005			−0.489502	+	0.872002i	$0.662822\pi$
$132$	−2.08653	+	1.92071i	−0.181609	+	0.167176i
$133$	19.6841	+	2.99644i	1.70683	+	0.259825i
$134$	−2.70023			−0.233264
$135$	−8.13354	−	10.4513i	−0.700024	−	0.899506i
$136$	2.60261	−	4.50785i	0.223172	−	0.386545i
$137$	2.09734			0.179188			0.0895940	−	0.995978i	$-0.471443\pi$
$137$	2.09734			0.179188			0.0895940	+	0.995978i	$0.471443\pi$
$138$	−0.603301	−	2.69231i	−0.0513564	−	0.229184i
$139$	−0.0442801	+	0.0766954i	−0.00375579	+	0.00650522i	−0.867897	−	0.496744i	$-0.834529\pi$
$139$	−0.0442801	+	0.0766954i	−0.00375579	+	0.00650522i	0.864141	+	0.503249i	$0.167862\pi$
$140$	5.82100	+	10.0823i	0.491964	+	0.852107i
$141$	−1.70995	−	7.63084i	−0.144003	−	0.642633i
$142$	3.90266			0.327504
$143$	3.59792	+	6.23178i	0.300873	+	0.521127i
$144$	2.46526	+	1.70953i	0.205439	+	0.142461i
$145$	16.0723			1.33473
$146$	−0.255495			−0.0211449
$147$	17.6692	−	16.2650i	1.45733	−	1.34152i
$148$	4.46526	−	7.73406i	0.367042	−	0.635736i
$149$	−4.23042			−0.346569			−0.173285	−	0.984872i	$-0.555438\pi$
$149$	−4.23042			−0.346569			−0.173285	+	0.984872i	$0.555438\pi$
$150$	1.90606	−	1.75457i	0.155629	−	0.143260i
$151$	−4.59418	+	7.95736i	−0.373869	+	0.647561i	−0.990157	−	0.139960i	$-0.955303\pi$
$151$	−4.59418	+	7.95736i	−0.373869	+	0.647561i	0.616288	+	0.787521i	$0.288636\pi$
$152$	1.58653	+	4.05992i	0.128685	+	0.329303i
$153$	−1.29018	+	15.5623i	−0.104305	+	1.25814i
$154$	−3.73960	+	6.47717i	−0.301345	+	0.521946i
$155$	8.38527	+	14.5237i	0.673521	+	1.16657i
$156$	5.60046	−	5.15537i	0.448396	−	0.412760i
$157$	12.3167			0.982977			0.491489	−	0.870884i	$-0.336453\pi$
$157$	12.3167			0.982977			0.491489	+	0.870884i	$0.336453\pi$
$158$	−4.23000	+	7.32657i	−0.336521	+	0.582871i
$159$	2.66167	−	2.45014i	0.211085	−	0.194309i
$160$	−1.27434	+	2.20721i	−0.100745	+	0.174496i
$161$	−3.63820	−	6.30155i	−0.286730	−	0.496631i
$162$	−8.87713	−	1.48209i	−0.697453	−	0.116444i
$163$	8.19194			0.641642			0.320821	−	0.947140i	$-0.396041\pi$
$163$	8.19194			0.641642			0.320821	+	0.947140i	$0.396041\pi$
$164$	3.82712	−	6.62877i	0.298848	−	0.517620i
$165$	6.89835	+	2.15780i	0.537036	+	0.167984i
$166$	5.49840			0.426758
$167$	12.3994	−	21.4764i	0.959493	−	1.66189i	0.235760	−	0.971811i	$-0.424242\pi$
$167$	12.3994	−	21.4764i	0.959493	−	1.66189i	0.723733	−	0.690080i	$-0.242424\pi$
$168$	7.55100	+	2.36194i	0.582572	+	0.182228i
$169$	−3.15718	−	5.46840i	−0.242860	−	0.420646i
$170$	−13.2664			−1.01749
$171$	−9.50203	−	8.98396i	−0.726638	−	0.687020i
$172$	−9.53413			−0.726970
$173$	3.68977	+	6.39088i	0.280528	+	0.485889i	0.971515	−	0.236978i	$-0.0761570\pi$
$173$	3.68977	+	6.39088i	0.280528	+	0.485889i	−0.690987	+	0.722867i	$0.742824\pi$
$174$	8.03613	−	7.39747i	0.609218	−	0.560801i
$175$	3.41614	−	5.91693i	0.258236	−	0.447278i
$176$	−1.63735			−0.123420
$177$	3.62856	+	16.1929i	0.272739	+	1.21713i
$178$	−4.37758	+	7.58219i	−0.328113	+	0.568309i
$179$	17.2644			1.29040			0.645201	−	0.764013i	$-0.276774\pi$
$179$	17.2644			1.29040			0.645201	+	0.764013i	$0.276774\pi$
$180$	0.631720	−	7.61987i	0.0470857	−	0.567952i
$181$	−8.78314	−	15.2128i	−0.652846	−	1.13076i	−0.982429	−	0.186636i	$-0.940242\pi$
$181$	−8.78314	−	15.2128i	−0.652846	−	1.13076i	0.329583	−	0.944126i	$-0.393092\pi$
$182$	10.0375	−	17.3854i	0.744027	−	1.28869i
$183$	−4.93319	−	22.0150i	−0.364672	−	1.62739i
$184$	0.796476	−	1.37954i	0.0587170	−	0.101701i
$185$	−22.7610			−1.67342
$186$	10.8774	+	3.40243i	0.797567	+	0.249478i
$187$	−4.26138	−	7.38092i	−0.311623	−	0.539747i
$188$	2.25746	−	3.91004i	0.164642	−	0.285169i
$189$	−23.5106	+	3.25867i	−1.71014	+	0.237033i
$190$	6.93933	−	8.67551i	0.503432	−	0.629388i
$191$	−7.63625	+	13.2264i	−0.552540	+	0.957027i	0.445551	+	0.895257i	$0.353008\pi$
$191$	−7.63625	+	13.2264i	−0.552540	+	0.957027i	−0.998090	+	0.0617703i	$0.980325\pi$
$192$	0.378732	+	1.69014i	0.0273326	+	0.121975i
$193$	9.67218			0.696219			0.348109	−	0.937454i	$-0.386824\pi$
$193$	9.67218			0.696219			0.348109	+	0.937454i	$0.386824\pi$
$194$	−1.68133	+	2.91214i	−0.120712	+	0.209080i
$195$	−18.5159	−	5.79175i	−1.32595	−	0.414755i
$196$	13.8655			0.990390
$197$	22.4098			1.59663			0.798317	−	0.602237i	$-0.205724\pi$
$197$	22.4098			1.59663			0.798317	+	0.602237i	$0.205724\pi$
$198$	4.44233	−	2.09616i	0.315703	−	0.148968i
$199$	2.11300	+	3.65983i	0.149787	+	0.259438i	0.931149	−	0.364640i	$-0.118808\pi$
$199$	2.11300	+	3.65983i	0.149787	+	0.259438i	−0.781362	+	0.624078i	$0.785475\pi$
$200$	1.49573			0.105764
$201$	4.46365	+	1.39623i	0.314842	+	0.0984821i
$202$	1.69129	+	2.92939i	0.118999	+	0.206111i
$203$	14.4028	−	24.9464i	1.01088	−	1.75089i
$204$	−6.63320	+	6.10603i	−0.464417	+	0.427508i
$205$	−19.5081			−1.36251
$206$	−7.56708	+	13.1066i	−0.527223	+	0.913178i
$207$	−0.394833	+	4.76252i	−0.0274428	+	0.331018i
$208$	4.39481			0.304725
$209$	7.05575	+	1.07407i	0.488056	+	0.0742951i
$210$	−4.40919	−	19.6766i	−0.304263	−	1.35781i
$211$	7.28535			0.501544			0.250772	−	0.968046i	$-0.419316\pi$
$211$	7.28535			0.501544			0.250772	+	0.968046i	$0.419316\pi$
$212$	2.08868			0.143451
$213$	−6.45135	−	2.01798i	−0.442040	−	0.138269i
$214$	0.460297	+	0.797257i	0.0314652	+	0.0544994i
$215$	12.1497	+	21.0439i	0.828601	+	1.43518i
$216$	−3.19129	−	4.10069i	−0.217140	−	0.279017i
$217$	30.0571			2.04041
$218$	16.3218			1.10545
$219$	0.422350	+	0.132110i	0.0285398	+	0.00892720i
$220$	2.08653	+	3.61398i	0.140674	+	0.243654i
$221$	11.4380	+	19.8112i	0.769402	+	1.33264i
$222$	−11.3805	+	10.4760i	−0.763808	+	0.703106i
$223$	2.96741	+	5.13970i	0.198712	+	0.344180i	0.948111	−	0.317939i	$-0.102991\pi$
$223$	2.96741	+	5.13970i	0.198712	+	0.344180i	−0.749399	+	0.662119i	$0.769657\pi$
$224$	2.28394	+	3.95589i	0.152602	+	0.264314i
$225$	−4.05809	+	1.91485i	−0.270539	+	0.127657i
$226$	−4.66694	+	8.08338i	−0.310440	+	0.537699i
$227$	−6.47904	+	11.2220i	−0.430029	+	0.744832i	−0.996875	−	0.0789919i	$-0.974830\pi$
$227$	−6.47904	+	11.2220i	−0.430029	+	0.744832i	0.566847	+	0.823823i	$0.308163\pi$
$228$	−0.523351	−	7.53167i	−0.0346598	−	0.498797i
$229$	5.51962	+	9.56026i	0.364747	+	0.631760i	0.988735	−	0.149673i	$-0.0478222\pi$
$229$	5.51962	+	9.56026i	0.364747	+	0.631760i	−0.623989	+	0.781433i	$0.714489\pi$
$230$	−4.05991			−0.267702
$231$	9.53101	−	8.77354i	0.627094	−	0.577257i
$232$	6.30613			0.414018
$233$	−1.92422	+	3.33285i	−0.126060	+	0.218342i	−0.922147	−	0.386840i	$-0.873567\pi$
$233$	−1.92422	+	3.33285i	−0.126060	+	0.218342i	0.796087	+	0.605183i	$0.206900\pi$
$234$	−11.9237	+	5.62631i	−0.779475	+	0.367803i
$235$	−11.5071			−0.750638
$236$	−4.79042	+	8.29724i	−0.311829	+	0.540104i
$237$	10.7809	−	9.92408i	0.700293	−	0.644638i
$238$	−11.8884	+	20.5913i	−0.770610	+	1.33474i
$239$	2.56242	+	4.43825i	0.165749	+	0.287086i	0.936921	−	0.349541i	$-0.113662\pi$
$239$	2.56242	+	4.43825i	0.165749	+	0.287086i	−0.771172	+	0.636627i	$0.780329\pi$
$240$	3.24786	−	2.98974i	0.209649	−	0.192987i
$241$	−8.52569			−0.549188			−0.274594	−	0.961560i	$-0.588543\pi$
$241$	−8.52569			−0.549188			−0.274594	+	0.961560i	$0.588543\pi$
$242$	4.15955	−	7.20455i	0.267386	−	0.463126i
$243$	13.9081	+	7.04016i	0.892207	+	0.451626i
$244$	6.51278	−	11.2805i	0.416938	−	0.722158i
$245$	−17.6692	−	30.6040i	−1.12885	−	1.95522i
$246$	−9.75407	+	8.97888i	−0.621897	+	0.572473i
$247$	−18.9384	−	2.88292i	−1.20502	−	0.183436i
$248$	3.29005	+	5.69854i	0.208919	+	0.361858i
$249$	−9.08922	−	2.84310i	−0.576006	−	0.180174i
$250$	4.46562	+	7.73468i	0.282431	+	0.489184i
$251$	−5.28491	−	9.15374i	−0.333581	−	0.577779i	0.649630	−	0.760250i	$-0.274924\pi$
$251$	−5.28491	−	9.15374i	−0.333581	−	0.577779i	−0.983211	+	0.182471i	$0.941590\pi$
$252$	−11.2610	−	7.80890i	−0.709377	−	0.491914i
$253$	−1.30411	−	2.25878i	−0.0819885	−	0.142008i
$254$	0.709945	−	1.22966i	0.0445459	−	0.0771558i
$255$	21.9302	+	6.85975i	1.37333	+	0.429574i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−12.6039	+	21.8307i	−0.786213	+	1.36176i	0.142059	+	0.989858i	$0.454628\pi$
$257$	−12.6039	+	21.8307i	−0.786213	+	1.36176i	−0.928272	+	0.371902i	$0.878706\pi$
$258$	15.7606	+	4.92988i	0.981209	+	0.306921i
$259$	−20.3967	+	35.3282i	−1.26739	+	2.19519i
$260$	−5.60046	−	9.70029i	−0.347326	−	0.601586i
$261$	−17.1093	+	8.07322i	−1.05904	+	0.499720i
$262$	5.60261	+	9.70401i	0.346130	+	0.599515i
$263$	6.46463	+	11.1971i	0.398626	+	0.690441i	0.993557	−	0.113336i	$-0.0361538\pi$
$263$	6.46463	+	11.1971i	0.398626	+	0.690441i	−0.594931	+	0.803777i	$0.702820\pi$
$264$	2.70665	+	0.846635i	0.166583	+	0.0521068i
$265$	−2.66167	−	4.61016i	−0.163505	−	0.283200i
$266$	−7.24707	−	18.5452i	−0.444346	−	1.13708i
$267$	11.1570	−	10.2703i	0.682798	−	0.628533i
$268$	1.35011	+	2.33846i	0.0824713	+	0.142844i
$269$	−13.7930	+	23.8901i	−0.840973	+	1.45661i	0.0480998	+	0.998843i	$0.484683\pi$
$269$	−13.7930	+	23.8901i	−0.840973	+	1.45661i	−0.889073	+	0.457766i	$0.848650\pi$
$270$	−4.98434	+	12.2695i	−0.303337	+	0.746699i
$271$	3.55748	−	6.16173i	0.216101	−	0.374299i	−0.737511	−	0.675335i	$-0.763999\pi$
$271$	3.55748	−	6.16173i	0.216101	−	0.374299i	0.953613	+	0.301036i	$0.0973325\pi$
$272$	−5.20522			−0.315613
$273$	−25.5822	+	23.5491i	−1.54831	+	1.42526i
$274$	−1.04867	−	1.81635i	−0.0633525	−	0.109730i
$275$	1.22451	−	2.12092i	0.0738408	−	0.127896i
$276$	−2.02995	+	1.86863i	−0.122189	+	0.112478i
$277$	5.86425	−	10.1572i	0.352348	−	0.610285i	−0.634312	−	0.773077i	$-0.718717\pi$
$277$	5.86425	−	10.1572i	0.352348	−	0.610285i	0.986660	+	0.162792i	$0.0520499\pi$
$278$	0.0885602			0.00531149
$279$	−16.2217	−	11.2489i	−0.971168	−	0.673453i
$280$	5.82100	−	10.0823i	0.347871	−	0.602531i
$281$	8.72607			0.520554			0.260277	−	0.965534i	$-0.416186\pi$
$281$	8.72607			0.520554			0.260277	+	0.965534i	$0.416186\pi$
$282$	−5.75353	+	5.29628i	−0.342618	+	0.315389i
$283$	−5.22544			−0.310620			−0.155310	−	0.987866i	$-0.549638\pi$
$283$	−5.22544			−0.310620			−0.155310	+	0.987866i	$0.549638\pi$
$284$	−1.95133	−	3.37980i	−0.115790	−	0.200554i
$285$	−15.9571	+	10.7530i	−0.945216	+	0.636954i
$286$	3.59792	−	6.23178i	0.212749	−	0.368493i
$287$	−17.4818	+	30.2794i	−1.03192	+	1.78733i
$288$	0.247863	−	2.98974i	0.0146054	−	0.176172i
$289$	−5.04716	−	8.74193i	−0.296892	−	0.514231i
$290$	−8.03613	−	13.9190i	−0.471898	−	0.817351i
$291$	4.28515	−	3.94459i	0.251200	−	0.231236i
$292$	0.127747	+	0.221265i	0.00747585	+	0.0129485i
$293$	−14.4930	−	25.1026i	−0.846688	−	1.46651i	−0.884147	−	0.467209i	$-0.845260\pi$
$293$	−14.4930	−	25.1026i	−0.846688	−	1.46651i	0.0374587	−	0.999298i	$-0.488074\pi$
$294$	−22.9205	−	7.16951i	−1.33675	−	0.418134i
$295$	24.4184			1.42169
$296$	−8.93052			−0.519076
$297$	−8.42734	+	1.16806i	−0.489004	+	0.0677780i
$298$	2.11521	+	3.66365i	0.122531	+	0.212229i
$299$	3.50036	+	6.06280i	0.202431	+	0.350621i
$300$	−2.47253	−	0.773405i	−0.142752	−	0.0446526i
$301$	43.5507			2.51022
$302$	9.18837			0.528731
$303$	−1.28109	−	5.71701i	−0.0735965	−	0.328434i
$304$	2.72273	−	3.40393i	0.156159	−	0.195229i
$305$	−33.1979			−1.90090
$306$	14.1224	−	6.66381i	0.807325	−	0.380945i
$307$	−0.233296	+	0.404081i	−0.0133149	+	0.0230621i	−0.872606	−	0.488425i	$-0.837572\pi$
$307$	−0.233296	+	0.404081i	−0.0133149	+	0.0230621i	0.859291	+	0.511487i	$0.170905\pi$
$308$	7.47920			0.426167
$309$	19.2860	−	17.7533i	1.09714	−	1.00995i
$310$	8.38527	−	14.5237i	0.476251	−	0.824891i
$311$	−10.9617	−	18.9862i	−0.621580	−	1.07661i	−0.989192	−	0.146629i	$-0.953158\pi$
$311$	−10.9617	−	18.9862i	−0.621580	−	1.07661i	0.367611	−	0.929980i	$-0.380176\pi$
$312$	−7.26492	−	2.27246i	−0.411295	−	0.128653i
$313$	−3.12676			−0.176735			−0.0883674	−	0.996088i	$-0.528165\pi$
$313$	−3.12676			−0.176735			−0.0883674	+	0.996088i	$0.528165\pi$
$314$	−6.15833	−	10.6665i	−0.347535	−	0.601948i
$315$	−2.88562	+	34.8066i	−0.162586	+	1.96113i
$316$	8.45999			0.475912
$317$	7.25477			0.407469			0.203734	−	0.979026i	$-0.434692\pi$
$317$	7.25477			0.407469			0.203734	+	0.979026i	$0.434692\pi$
$318$	−3.45272	−	1.08001i	−0.193619	−	0.0605638i
$319$	5.16267	−	8.94200i	0.289054	−	0.500656i
$320$	2.54867			0.142475
$321$	−0.348658	−	1.55593i	−0.0194602	−	0.0868434i
$322$	−3.63820	+	6.30155i	−0.202749	+	0.351171i
$323$	22.4306	+	3.41453i	1.24807	+	0.189990i
$324$	3.15504	+	8.42886i	0.175280	+	0.468270i
$325$	−3.28671	+	5.69276i	−0.182314	+	0.315777i
$326$	−4.09597	−	7.09443i	−0.226855	−	0.392924i
$327$	−26.9810	−	8.43961i	−1.49205	−	0.466712i
$328$	−7.65424			−0.422635
$329$	−10.3118	+	17.8606i	−0.568508	+	0.984685i
$330$	−1.58047	−	7.05304i	−0.0870020	−	0.388257i
$331$	2.30798	−	3.99754i	0.126858	−	0.219724i	−0.795600	−	0.605823i	$-0.792844\pi$
$331$	2.30798	−	3.99754i	0.126858	−	0.219724i	0.922458	+	0.386098i	$0.126177\pi$
$332$	−2.74920	−	4.76175i	−0.150882	−	0.261335i
$333$	24.2296	−	11.4330i	1.32778	−	0.626525i
$334$	−24.7988			−1.35693
$335$	3.44099	−	5.95998i	0.188002	−	0.325628i
$336$	−1.73000	−	7.72033i	−0.0943791	−	0.421178i
$337$	8.16313			0.444674			0.222337	−	0.974970i	$-0.428631\pi$
$337$	8.16313			0.444674			0.222337	+	0.974970i	$0.428631\pi$
$338$	−3.15718	+	5.46840i	−0.171728	+	0.297442i
$339$	11.8945	−	10.9492i	0.646021	−	0.594679i
$340$	6.63320	+	11.4890i	0.359736	+	0.623080i
$341$	10.7739			0.583441
$342$	−3.02932	+	12.7210i	−0.163807	+	0.687872i
$343$	−31.3605			−1.69331
$344$	4.76706	+	8.25680i	0.257023	+	0.445177i
$345$	6.71130	+	2.09929i	0.361324	+	0.113022i
$346$	3.68977	−	6.39088i	0.198363	−	0.343576i
$347$	13.6294			0.731663			0.365831	−	0.930681i	$-0.380785\pi$
$347$	13.6294			0.731663			0.365831	+	0.930681i	$0.380785\pi$
$348$	−10.4245	−	3.26076i	−0.558810	−	0.174795i
$349$	−8.36913	+	14.4958i	−0.447989	+	0.775940i	−0.998255	−	0.0590493i	$-0.981193\pi$
$349$	−8.36913	+	14.4958i	−0.447989	+	0.775940i	0.550266	+	0.834990i	$0.314526\pi$
$350$	−6.83228			−0.365201
$351$	22.6199	−	3.13521i	1.20736	−	0.167345i
$352$	0.818674	+	1.41798i	0.0436355	+	0.0755788i
$353$	−5.63816	+	9.76558i	−0.300089	+	0.519770i	−0.976156	−	0.217071i	$-0.930350\pi$
$353$	−5.63816	+	9.76558i	−0.300089	+	0.519770i	0.676067	+	0.736840i	$0.263683\pi$
$354$	12.2092	−	11.2389i	0.648911	−	0.597340i
$355$	−4.97330	+	8.61400i	−0.263955	+	0.457184i
$356$	8.75516			0.464022
$357$	30.2996	−	27.8916i	1.60362	−	1.47618i
$358$	−8.63220	−	14.9514i	−0.456226	−	0.790207i
$359$	17.8796	−	30.9683i	0.943648	−	1.63445i	0.185212	−	0.982699i	$-0.440703\pi$
$359$	17.8796	−	30.9683i	0.943648	−	1.63445i	0.758436	−	0.651747i	$-0.225964\pi$
$360$	−6.91486	+	3.26285i	−0.364445	+	0.171967i
$361$	−13.9658	+	12.8824i	−0.735044	+	0.678019i
$362$	−8.78314	+	15.2128i	−0.461632	+	0.799570i
$363$	−10.6013	+	9.75879i	−0.556425	+	0.512204i
$364$	−20.0749			−1.05221
$365$	0.325586	−	0.563931i	0.0170419	−	0.0295175i
$366$	−16.5989	+	15.2798i	−0.867640	+	0.798686i
$367$	26.3226			1.37403			0.687015	−	0.726643i	$-0.258920\pi$
$367$	26.3226			1.37403			0.687015	+	0.726643i	$0.258920\pi$
$368$	−1.59295			−0.0830383
$369$	20.7669	−	9.79909i	1.08108	−	0.510120i
$370$	11.3805	+	19.7116i	0.591643	+	1.02476i
$371$	−9.54081			−0.495334
$372$	−2.49210	−	11.1213i	−0.129209	−	0.576612i
$373$	7.55361	+	13.0832i	0.391111	+	0.677424i	0.992596	−	0.121460i	$-0.0387576\pi$
$373$	7.55361	+	13.0832i	0.391111	+	0.677424i	−0.601486	+	0.798884i	$0.705424\pi$
$374$	−4.26138	+	7.38092i	−0.220351	+	0.381658i
$375$	−3.38254	−	15.0950i	−0.174674	−	0.779504i
$376$	−4.51493			−0.232840
$377$	−13.8571	+	24.0013i	−0.713679	+	1.23613i
$378$	14.5774	+	18.7314i	0.749780	+	0.963442i
$379$	1.01932			0.0523588			0.0261794	−	0.999657i	$-0.491666\pi$
$379$	1.01932			0.0523588			0.0261794	+	0.999657i	$0.491666\pi$
$380$	−10.9829	−	1.67188i	−0.563410	−	0.0857658i
$381$	−1.80942	+	1.66562i	−0.0926992	+	0.0853321i
$382$	15.2725			0.781409
$383$	14.5949			0.745765			0.372882	−	0.927879i	$-0.378370\pi$
$383$	14.5949			0.745765			0.372882	+	0.927879i	$0.378370\pi$
$384$	1.27434	−	1.17306i	0.0650307	−	0.0598624i
$385$	−9.53101	−	16.5082i	−0.485745	−	0.841335i
$386$	−4.83609	−	8.37635i	−0.246150	−	0.426345i
$387$	−23.5041	−	16.2988i	−1.19478	−	0.828517i
$388$	3.36265			0.170713
$389$	−3.17882			−0.161173			−0.0805864	−	0.996748i	$-0.525679\pi$
$389$	−3.17882			−0.161173			−0.0805864	+	0.996748i	$0.525679\pi$
$390$	4.24214	+	18.9311i	0.214809	+	0.958614i
$391$	−4.14583	−	7.18079i	−0.209664	−	0.363148i
$392$	−6.93273	−	12.0078i	−0.350156	−	0.606487i
$393$	−4.24377	−	18.9384i	−0.214070	−	0.955314i
$394$	−11.2049	−	19.4075i	−0.564496	−	0.977735i
$395$	−10.7809	−	18.6730i	−0.542445	−	0.939542i
$396$	−4.03649	−	2.79909i	−0.202841	−	0.140660i
$397$	15.9934	−	27.7014i	0.802687	−	1.39030i	−0.115154	−	0.993348i	$-0.536736\pi$
$397$	15.9934	−	27.7014i	0.802687	−	1.39030i	0.917841	−	0.396948i	$-0.129931\pi$
$398$	2.11300	−	3.65983i	0.105915	−	0.183451i
$399$	2.39060	+	34.4037i	0.119680	+	1.72234i
$400$	−0.747863	−	1.29534i	−0.0373931	−	0.0647668i
$401$	−8.44744			−0.421845			−0.210922	−	0.977503i	$-0.567647\pi$
$401$	−8.44744			−0.421845			−0.210922	+	0.977503i	$0.567647\pi$
$402$	−1.02266	−	4.56375i	−0.0510057	−	0.227619i
$403$	−28.9183			−1.44053
$404$	1.69129	−	2.92939i	0.0841447	−	0.145743i
$405$	14.5837	−	17.7050i	0.724672	−	0.879771i
$406$	−28.8056			−1.42960
$407$	−7.31119	+	12.6633i	−0.362402	+	0.627699i
$408$	8.60458	+	2.69150i	0.425990	+	0.133249i
$409$	−14.7093	+	25.4773i	−0.727329	+	1.25977i	0.230679	+	0.973030i	$0.425905\pi$
$409$	−14.7093	+	25.4773i	−0.727329	+	1.25977i	−0.958008	+	0.286741i	$0.907428\pi$
$410$	9.75407	+	16.8946i	0.481719	+	0.834362i
$411$	0.794330	+	3.54480i	0.0391814	+	0.174852i
$412$	15.1342			0.745606
$413$	21.8820	−	37.9007i	1.07674	−	1.86497i
$414$	4.32188	−	2.03932i	0.212409	−	0.100227i
$415$	−7.00680	+	12.1361i	−0.343950	+	0.595740i
$416$	−2.19741	−	3.80602i	−0.107737	−	0.186605i
$417$	−0.146396	−	0.0457925i	−0.00716904	−	0.00224247i
$418$	−2.59770	−	6.64750i	−0.127058	−	0.325140i
$419$	−3.22036	−	5.57783i	−0.157325	−	0.272495i	0.776578	−	0.630021i	$-0.216954\pi$
$419$	−3.22036	−	5.57783i	−0.157325	−	0.272495i	−0.933903	+	0.357526i	$0.883620\pi$
$420$	−14.8358	+	13.6568i	−0.723914	+	0.666382i
$421$	−11.8500	−	20.5249i	−0.577536	−	1.00032i	−0.995761	−	0.0919777i	$-0.970681\pi$
$421$	−11.8500	−	20.5249i	−0.577536	−	1.00032i	0.418225	−	0.908343i	$-0.362652\pi$
$422$	−3.64267	−	6.30930i	−0.177323	−	0.307132i
$423$	12.2496	−	5.78008i	0.595594	−	0.281037i
$424$	−1.04434	−	1.80885i	−0.0507176	−	0.0878454i
$425$	3.89279	−	6.74251i	0.188828	−	0.327060i
$426$	1.47806	+	6.59603i	0.0716122	+	0.319578i
$427$	−29.7495	+	51.5277i	−1.43968	+	2.49360i
$428$	0.460297	−	0.797257i	0.0222493	−	0.0385369i
$429$	−9.16991	+	8.44114i	−0.442727	+	0.407542i
$430$	12.1497	−	21.0439i	0.585910	−	1.01483i
$431$	13.8562	+	23.9996i	0.667428	+	1.15602i	0.978621	+	0.205672i	$0.0659381\pi$
$431$	13.8562	+	23.9996i	0.667428	+	1.15602i	−0.311193	+	0.950347i	$0.600729\pi$
$432$	−1.95566	+	4.81408i	−0.0940918	+	0.231618i
$433$	14.7686	+	25.5800i	0.709734	+	1.22930i	0.964956	+	0.262413i	$0.0845184\pi$
$433$	14.7686	+	25.5800i	0.709734	+	1.22930i	−0.255221	+	0.966883i	$0.582148\pi$
$434$	−15.0286	−	26.0302i	−0.721394	−	1.24949i
$435$	6.08707	+	27.1643i	0.291853	+	1.30243i
$436$	−8.16088	−	14.1351i	−0.390835	−	0.676947i
$437$	6.86444	+	1.04495i	0.328370	+	0.0499866i
$438$	−0.0967639	−	0.431821i	−0.00462356	−	0.0206332i
$439$	6.15094	+	10.6537i	0.293569	+	0.508476i	0.974651	−	0.223731i	$-0.0718238\pi$
$439$	6.15094	+	10.6537i	0.293569	+	0.508476i	−0.681082	+	0.732207i	$0.738490\pi$
$440$	2.08653	−	3.61398i	0.0994714	−	0.172290i
$441$	34.1820	+	23.7034i	1.62771	+	1.12873i
$442$	11.4380	−	19.8112i	0.544049	−	0.942321i
$443$	32.4886			1.54358			0.771790	−	0.635878i	$-0.219362\pi$
$443$	32.4886			1.54358			0.771790	+	0.635878i	$0.219362\pi$
$444$	14.7628	+	4.61777i	0.700609	+	0.219150i
$445$	−11.1570	−	19.3245i	−0.528893	−	0.916069i
$446$	2.96741	−	5.13970i	0.140511	−	0.243372i
$447$	−1.60219	−	7.14998i	−0.0757811	−	0.338182i
$448$	2.28394	−	3.95589i	0.107906	−	0.186898i
$449$	3.25736			0.153724			0.0768622	−	0.997042i	$-0.475510\pi$
$449$	3.25736			0.153724			0.0768622	+	0.997042i	$0.475510\pi$
$450$	3.68735	+	2.55698i	0.173824	+	0.120537i
$451$	−6.26633	+	10.8536i	−0.295070	+	0.511076i
$452$	9.33388			0.439029
$453$	−15.1890	−	4.75110i	−0.713641	−	0.223226i
$454$	12.9581			0.608152
$455$	25.5822	+	44.3097i	1.19931	+	2.07727i
$456$	−6.26094	+	4.21907i	−0.293196	+	0.197576i
$457$	−2.30438	+	3.99130i	−0.107794	+	0.186705i	−0.914876	−	0.403734i	$-0.867712\pi$
$457$	−2.30438	+	3.99130i	−0.107794	+	0.186705i	0.807082	+	0.590439i	$0.201045\pi$
$458$	5.51962	−	9.56026i	0.257915	−	0.446722i
$459$	−26.7910	+	3.71334i	−1.25050	+	0.173324i
$460$	2.02995	+	3.51598i	0.0946471	+	0.163934i
$461$	2.51103	+	4.34923i	0.116950	+	0.202564i	0.918558	−	0.395287i	$-0.129355\pi$
$461$	2.51103	+	4.34923i	0.116950	+	0.202564i	−0.801607	+	0.597851i	$0.796022\pi$
$462$	−12.3636	−	3.86732i	−0.575207	−	0.179924i
$463$	−17.1424	−	29.6915i	−0.796675	−	1.37988i	−0.921770	−	0.387737i	$-0.873257\pi$
$463$	−17.1424	−	29.6915i	−0.796675	−	1.37988i	0.125095	−	0.992145i	$-0.460076\pi$
$464$	−3.15307	−	5.46127i	−0.146377	−	0.253533i
$465$	−21.3713	+	19.6728i	−0.991070	+	0.912306i
$466$	3.84845			0.178276
$467$	8.73692			0.404297			0.202148	−	0.979355i	$-0.435208\pi$
$467$	8.73692			0.404297			0.202148	+	0.979355i	$0.435208\pi$
$468$	10.8344	+	7.51305i	0.500819	+	0.347291i
$469$	−6.16714	−	10.6818i	−0.284772	−	0.493240i
$470$	5.75353	+	9.96541i	0.265391	+	0.459670i
$471$	4.66471	+	20.8169i	0.214939	+	0.959190i
$472$	9.58083			0.440993
$473$	15.6107			0.717780
$474$	−13.9849	−	4.37447i	−0.642350	−	0.200926i
$475$	2.37301	+	6.07252i	0.108881	+	0.278626i
$476$	23.7768			1.08981
$477$	5.14914	+	3.57065i	0.235763	+	0.163489i
$478$	2.56242	−	4.43825i	0.117202	−	0.203001i
$479$	−13.5669			−0.619890			−0.309945	−	0.950755i	$-0.600311\pi$
$479$	−13.5669			−0.619890			−0.309945	+	0.950755i	$0.600311\pi$
$480$	−4.21312	−	1.31786i	−0.192302	−	0.0601518i
$481$	19.6240	−	33.9897i	0.894777	−	1.54980i
$482$	4.26285	+	7.38347i	0.194167	+	0.336308i
$483$	9.27257	−	8.53565i	0.421917	−	0.388385i
$484$	−8.31909			−0.378141
$485$	−4.28515	−	7.42209i	−0.194579	−	0.337020i
$486$	−0.857112	−	15.5649i	−0.0388794	−	0.706037i
$487$	7.64991			0.346650			0.173325	−	0.984865i	$-0.444549\pi$
$487$	7.64991			0.346650			0.173325	+	0.984865i	$0.444549\pi$
$488$	−13.0256			−0.589639
$489$	3.10255	+	13.8455i	0.140302	+	0.626115i
$490$	−17.6692	+	30.6040i	−0.798215	+	1.38255i
$491$	−33.0249			−1.49039			−0.745197	−	0.666844i	$-0.767645\pi$
$491$	−33.0249			−1.49039			−0.745197	+	0.666844i	$0.767645\pi$
$492$	12.6530	+	3.95783i	0.570440	+	0.178433i
$493$	16.4124	−	28.4271i	0.739178	−	1.28029i
$494$	6.97250	+	17.8426i	0.313708	+	0.802775i
$495$	−1.03435	+	12.4764i	−0.0464904	+	0.560772i
$496$	3.29005	−	5.69854i	0.147728	−	0.255872i
$497$	8.91342	+	15.4385i	0.399822	+	0.692511i
$498$	2.08242	+	9.29304i	0.0933153	+	0.416431i
$499$	−28.2262			−1.26358			−0.631790	−	0.775140i	$-0.717679\pi$
$499$	−28.2262			−1.26358			−0.631790	+	0.775140i	$0.717679\pi$
$500$	4.46562	−	7.73468i	0.199709	−	0.345906i
$501$	40.9940	+	12.8229i	1.83148	+	0.572884i
$502$	−5.28491	+	9.15374i	−0.235877	+	0.408551i
$503$	12.5224	+	21.6894i	0.558345	+	0.967083i	0.997635	+	0.0687370i	$0.0218969\pi$
$503$	12.5224	+	21.6894i	0.558345	+	0.967083i	−0.439289	+	0.898346i	$0.644770\pi$
$504$	−1.13220	+	13.6568i	−0.0504324	+	0.608321i
$505$	−8.62107			−0.383632
$506$	−1.30411	+	2.25878i	−0.0579747	+	0.100415i
$507$	8.04662	−	7.40712i	0.357363	−	0.328962i
$508$	−1.41989			−0.0629974
$509$	4.83402	−	8.37277i	0.214264	−	0.371116i	−0.738781	−	0.673946i	$-0.764598\pi$
$509$	4.83402	−	8.37277i	0.214264	−	0.371116i	0.953045	+	0.302830i	$0.0979314\pi$
$510$	−5.02440	−	22.4220i	−0.222484	−	0.992864i
$511$	−0.583533	−	1.01071i	−0.0258140	−	0.0447112i
$512$	1.00000			0.0441942
$513$	11.5854	−	19.4622i	0.511508	−	0.859279i
$514$	25.2079			1.11187
$515$	−19.2860	−	33.4043i	−0.849843	−	1.47197i
$516$	−3.61087	−	16.1140i	−0.158960	−	0.709378i
$517$	−3.69625	+	6.40210i	−0.162561	+	0.281564i
$518$	40.7935			1.79236
$519$	−9.40402	+	8.65665i	−0.412791	+	0.379985i
$520$	−5.60046	+	9.70029i	−0.245597	+	0.425386i
$521$	21.7727			0.953879			0.476940	−	0.878936i	$-0.341746\pi$
$521$	21.7727			0.953879			0.476940	+	0.878936i	$0.341746\pi$
$522$	15.5463	+	10.7805i	0.680442	+	0.471850i
$523$	−0.165607	−	0.286839i	−0.00724148	−	0.0125426i	0.862382	−	0.506258i	$-0.168972\pi$
$523$	−0.165607	−	0.286839i	−0.00724148	−	0.0125426i	−0.869623	+	0.493716i	$0.835638\pi$
$524$	5.60261	−	9.70401i	0.244751	−	0.423921i
$525$	11.2942	+	3.53282i	0.492920	+	0.154185i
$526$	6.46463	−	11.1971i	0.281871	−	0.488215i
$527$	34.2509			1.49199
$528$	−0.620115	−	2.76734i	−0.0269871	−	0.120433i
$529$	10.2313	+	17.7210i	0.444837	+	0.770480i
$530$	−2.66167	+	4.61016i	−0.115616	+	0.200252i
$531$	−25.9940	+	12.2655i	−1.12804	+	0.532279i
$532$	−12.4371	+	15.5487i	−0.539215	+	0.674123i
$533$	16.8195	−	29.1322i	0.728532	−	1.26185i
$534$	−14.4729	−	4.52709i	−0.626302	−	0.195906i
$535$	−2.34629			−0.101439
$536$	1.35011	−	2.33846i	0.0583160	−	0.101006i
$537$	6.53858	+	29.1792i	0.282160	+	1.25918i
$538$	27.5860			1.18932
$539$	−22.7026			−0.977869
$540$	13.1179	−	1.81819i	0.564504	−	0.0782425i
$541$	−9.87743	−	17.1082i	−0.424664	−	0.735539i	0.571725	−	0.820445i	$-0.306274\pi$
$541$	−9.87743	−	17.1082i	−0.424664	−	0.735539i	−0.996389	+	0.0849058i	$0.972941\pi$
$542$	−7.11496			−0.305614
$543$	22.3853	−	20.6063i	0.960647	−	0.884301i
$544$	2.60261	+	4.50785i	0.111586	+	0.193273i
$545$	−20.7994	+	36.0256i	−0.890949	+	1.54317i
$546$	33.1852	+	10.3803i	1.42020	+	0.444235i
$547$	−16.1905			−0.692258			−0.346129	−	0.938187i	$-0.612504\pi$
$547$	−16.1905			−0.692258			−0.346129	+	0.938187i	$0.612504\pi$
$548$	−1.04867	+	1.81635i	−0.0447970	+	0.0775907i
$549$	35.3400	−	16.6755i	1.50827	−	0.711694i
$550$	−2.44902			−0.104427
$551$	10.0049	+	25.6024i	0.426222	+	1.09070i
$552$	2.63326	+	0.823679i	0.112079	+	0.0350581i
$553$	−38.6442			−1.64332
$554$	−11.7285			−0.498296
$555$	−8.62030	−	38.4692i	−0.365911	−	1.63292i
$556$	−0.0442801	−	0.0766954i	−0.00187789	−	0.00325261i
$557$	−10.5649	−	18.2989i	−0.447648	−	0.775349i	0.550584	−	0.834780i	$-0.314405\pi$
$557$	−10.5649	−	18.2989i	−0.447648	−	0.775349i	−0.998232	+	0.0594303i	$0.981072\pi$
$558$	−1.63096	+	19.6728i	−0.0690442	+	0.832818i
$559$	−41.9007			−1.77221
$560$	−11.6420			−0.491964
$561$	10.8609	−	9.99770i	0.458546	−	0.422103i
$562$	−4.36303	−	7.55700i	−0.184043	−	0.318773i
$563$	−9.26077	−	16.0401i	−0.390295	−	0.676010i	0.602193	−	0.798350i	$-0.294294\pi$
$563$	−9.26077	−	16.0401i	−0.390295	−	0.676010i	−0.992488	+	0.122340i	$0.960960\pi$
$564$	7.46348	+	2.33457i	0.314269	+	0.0983029i
$565$	−11.8945	−	20.6019i	−0.500405	−	0.866728i
$566$	2.61272	+	4.52536i	0.109821	+	0.190215i
$567$	−14.4118	−	38.5020i	−0.605239	−	1.61693i
$568$	−1.95133	+	3.37980i	−0.0818759	+	0.141813i
$569$	4.80474	−	8.32205i	0.201425	−	0.348879i	−0.747563	−	0.664191i	$-0.768776\pi$
$569$	4.80474	−	8.32205i	0.201425	−	0.348879i	0.948988	+	0.315313i	$0.102109\pi$
$570$	17.2909	+	8.44273i	0.724238	+	0.353627i
$571$	9.13737	+	15.8264i	0.382387	+	0.662314i	0.991403	−	0.130844i	$-0.0417688\pi$
$571$	9.13737	+	15.8264i	0.382387	+	0.662314i	−0.609016	+	0.793158i	$0.708435\pi$
$572$	−7.19583			−0.300873
$573$	−25.2465	−	7.89707i	−1.05469	−	0.329905i
$574$	34.9636			1.45935
$575$	1.19131	−	2.06341i	0.0496810	−	0.0860500i
$576$	−2.71312	+	1.28022i	−0.113047	+	0.0533423i
$577$	43.0716			1.79310			0.896548	−	0.442947i	$-0.146067\pi$
$577$	43.0716			1.79310			0.896548	+	0.442947i	$0.146067\pi$
$578$	−5.04716	+	8.74193i	−0.209934	+	0.363617i
$579$	3.66316	+	16.3473i	0.152236	+	0.679371i
$580$	−8.03613	+	13.9190i	−0.333682	+	0.577955i
$581$	12.5580	+	21.7511i	0.520993	+	0.902386i
$582$	−5.55869	−	1.73875i	−0.230415	−	0.0720735i
$583$	−3.41989			−0.141637
$584$	0.127747	−	0.221265i	0.00528622	−	0.00915600i
$585$	2.77629	−	33.4879i	0.114786	−	1.38455i
$586$	−14.4930	+	25.1026i	−0.598699	+	1.03698i
$587$	−22.8200	−	39.5255i	−0.941884	−	1.63139i	−0.761874	−	0.647726i	$-0.775720\pi$
$587$	−22.8200	−	39.5255i	−0.941884	−	1.63139i	−0.180010	−	0.983665i	$-0.557613\pi$
$588$	5.25129	+	23.4345i	0.216559	+	0.966423i
$589$	−17.9158	+	22.3983i	−0.738209	+	0.922904i
$590$	−12.2092	−	21.1469i	−0.502645	−	0.870606i
$591$	8.48731	+	37.8757i	0.349121	+	1.55800i
$592$	4.46526	+	7.73406i	0.183521	+	0.317868i
$593$	3.31673	+	5.74474i	0.136202	+	0.235908i	0.926056	−	0.377386i	$-0.123177\pi$
$593$	3.31673	+	5.74474i	0.136202	+	0.235908i	−0.789854	+	0.613295i	$0.789844\pi$
$594$	5.22525	+	6.71426i	0.214394	+	0.275490i
$595$	−30.2996	−	52.4804i	−1.24216	−	2.15149i
$596$	2.11521	−	3.66365i	0.0866423	−	0.150069i
$597$	−5.38535	+	4.95736i	−0.220408	+	0.202891i
$598$	3.50036	−	6.06280i	0.143140	−	0.247926i
$599$	14.7062	−	25.4718i	0.600877	−	1.04075i	−0.391811	−	0.920046i	$-0.628151\pi$
$599$	14.7062	−	25.4718i	0.600877	−	1.04075i	0.992689	−	0.120704i	$-0.0385152\pi$
$600$	0.566478	+	2.52798i	0.0231264	+	0.103204i
$601$	8.49664	−	14.7166i	0.346585	−	0.600303i	−0.639055	−	0.769161i	$-0.720674\pi$
$601$	8.49664	−	14.7166i	0.346585	−	0.600303i	0.985640	+	0.168858i	$0.0540078\pi$
$602$	−21.7753	−	37.7160i	−0.887497	−	1.53719i
$603$	−0.669285	+	8.07298i	−0.0272554	+	0.328757i
$604$	−4.59418	−	7.95736i	−0.186935	−	0.323780i
$605$	10.6013	+	18.3620i	0.431005	+	0.746522i
$606$	−4.31053	+	3.96796i	−0.175103	+	0.161187i
$607$	−1.02337	−	1.77253i	−0.0415375	−	0.0719450i	0.844509	−	0.535541i	$-0.179892\pi$
$607$	−1.02337	−	1.77253i	−0.0415375	−	0.0719450i	−0.886047	+	0.463596i	$0.846559\pi$
$608$	−4.30926	−	0.655982i	−0.174763	−	0.0266036i
$609$	47.6176	+	14.8947i	1.92956	+	0.603565i
$610$	16.5989	+	28.7502i	0.672071	+	1.16406i
$611$	9.92112	−	17.1839i	0.401366	−	0.695186i
$612$	−12.8322	−	8.89846i	−0.518712	−	0.359699i
$613$	20.9848	−	36.3468i	0.847569	−	1.46803i	−0.0358025	−	0.999359i	$-0.511399\pi$
$613$	20.9848	−	36.3468i	0.847569	−	1.46803i	0.883371	−	0.468674i	$-0.155268\pi$
$614$	0.466593			0.0188302
$615$	−7.38835	−	32.9714i	−0.297927	−	1.32954i
$616$	−3.73960	−	6.47717i	−0.150673	−	0.260973i
$617$	16.6620	−	28.8595i	0.670788	−	1.16184i	−0.306893	−	0.951744i	$-0.599289\pi$
$617$	16.6620	−	28.8595i	0.670788	−	1.16184i	0.977681	−	0.210095i	$-0.0673774\pi$
$618$	−25.0178	−	7.82553i	−1.00636	−	0.314789i
$619$	16.8021	−	29.1020i	0.675332	−	1.16971i	−0.301040	−	0.953612i	$-0.597334\pi$
$619$	16.8021	−	29.1020i	0.675332	−	1.16971i	0.976372	−	0.216098i	$-0.0693330\pi$
$620$	−16.7705			−0.673521
$621$	−8.19884	+	1.13639i	−0.329008	+	0.0456019i
$622$	−10.9617	+	18.9862i	−0.439524	+	0.761277i
$623$	−39.9924			−1.60226
$624$	1.66445	+	7.42783i	0.0666315	+	0.297351i
$625$	−30.2414			−1.20966
$626$	1.56338	+	2.70785i	0.0624852	+	0.108228i
$627$	0.856908	+	12.3320i	0.0342216	+	0.492491i
$628$	−6.15833	+	10.6665i	−0.245744	+	0.425642i
$629$	−23.2427	+	40.2575i	−0.926746	+	1.60517i
$630$	31.5862	−	14.9043i	1.25842	−	0.593801i
$631$	9.82619	+	17.0195i	0.391174	+	0.677534i	0.992605	−	0.121391i	$-0.0387356\pi$
$631$	9.82619	+	17.0195i	0.391174	+	0.677534i	−0.601430	+	0.798925i	$0.705402\pi$
$632$	−4.23000	−	7.32657i	−0.168260	−	0.291435i
$633$	2.75919	+	12.3132i	0.109668	+	0.489407i
$634$	−3.62739	−	6.28282i	−0.144062	−	0.249523i
$635$	1.80942	+	3.13400i	0.0718045	+	0.124369i
$636$	0.791048	+	3.53015i	0.0313671	+	0.139980i
$637$	60.9361			2.41437
$638$	−10.3253			−0.408784
$639$	0.967323	−	11.6679i	0.0382667	−	0.461577i
$640$	−1.27434	−	2.20721i	−0.0503725	−	0.0872478i
$641$	−23.1446	−	40.0876i	−0.914157	−	1.58337i	−0.808131	−	0.589003i	$-0.799520\pi$
$641$	−23.1446	−	40.0876i	−0.914157	−	1.58337i	−0.106027	−	0.994363i	$-0.533813\pi$
$642$	−1.17314	+	1.07991i	−0.0463003	+	0.0426207i
$643$	40.2091			1.58569			0.792847	−	0.609421i	$-0.208598\pi$
$643$	40.2091			1.58569			0.792847	+	0.609421i	$0.208598\pi$
$644$	7.27640			0.286730
$645$	−30.9655	+	28.5046i	−1.21927	+	1.12237i
$646$	−8.25824	−	21.1328i	−0.324916	−	0.831457i
$647$	−44.9646			−1.76774			−0.883870	−	0.467733i	$-0.845071\pi$
$647$	−44.9646			−1.76774			−0.883870	+	0.467733i	$0.845071\pi$
$648$	5.72209	−	6.94677i	0.224785	−	0.272895i
$649$	7.84358	−	13.5855i	0.307887	−	0.533276i
$650$	6.57343			0.257831
$651$	11.3836	+	50.8006i	0.446157	+	1.99103i
$652$	−4.09597	+	7.09443i	−0.160411	+	0.277839i
$653$	−18.2016	−	31.5261i	−0.712283	−	1.23371i	−0.963998	−	0.265909i	$-0.914328\pi$
$653$	−18.2016	−	31.5261i	−0.712283	−	1.23371i	0.251715	−	0.967801i	$-0.419005\pi$
$654$	6.18157	+	27.5860i	0.241718	+	1.07870i
$655$	−28.5584			−1.11587
$656$	3.82712	+	6.62877i	0.149424	+	0.258810i
$657$	−0.0633276	+	0.763863i	−0.00247064	+	0.0298011i
$658$	20.6236			0.803992
$659$	4.98350			0.194130			0.0970649	−	0.995278i	$-0.469055\pi$
$659$	4.98350			0.194130			0.0970649	+	0.995278i	$0.469055\pi$
$660$	−5.31788	+	4.89525i	−0.206998	+	0.190547i
$661$	−17.4759	+	30.2692i	−0.679735	+	1.17734i	0.295325	+	0.955397i	$0.404572\pi$
$661$	−17.4759	+	30.2692i	−0.679735	+	1.17734i	−0.975060	+	0.221939i	$0.928761\pi$
$662$	−4.61596			−0.179404
$663$	−29.1516	+	26.8349i	−1.13216	+	1.04218i
$664$	−2.74920	+	4.76175i	−0.106690	+	0.184792i
$665$	50.1684	+	7.63695i	1.94545	+	0.296148i
$666$	−22.0161	−	15.2670i	−0.853106	−	0.591583i
$667$	5.02268	−	8.69954i	0.194479	−	0.336848i
$668$	12.3994	+	21.4764i	0.479747	+	0.830945i
$669$	−7.56295	+	6.96189i	−0.292400	+	0.269162i
$670$	−6.88199			−0.265874
$671$	−10.6637	+	18.4700i	−0.411667	+	0.713028i
$672$	−5.82100	+	5.35839i	−0.224550	+	0.206704i
$673$	−7.11605	+	12.3254i	−0.274304	+	0.475108i	−0.969959	−	0.243268i	$-0.921781\pi$
$673$	−7.11605	+	12.3254i	−0.274304	+	0.475108i	0.695656	+	0.718375i	$0.255114\pi$
$674$	−4.08156	−	7.06948i	−0.157216	−	0.272306i
$675$	−4.77329	−	6.13351i	−0.183724	−	0.236079i
$676$	6.31436			0.242860
$677$	−17.4141	+	30.1621i	−0.669277	+	1.15922i	0.308830	+	0.951117i	$0.400063\pi$
$677$	−17.4141	+	30.1621i	−0.669277	+	1.15922i	−0.978107	+	0.208105i	$0.933271\pi$
$678$	−15.4295	−	4.82634i	−0.592568	−	0.185354i
$679$	−15.3602			−0.589469
$680$	6.63320	−	11.4890i	0.254372	−	0.440584i
$681$	−21.4206	−	6.70032i	−0.820838	−	0.256757i
$682$	−5.38696	−	9.33050i	−0.206278	−	0.357283i
$683$	43.2822			1.65615			0.828074	−	0.560619i	$-0.189437\pi$
$683$	43.2822			1.65615			0.828074	+	0.560619i	$0.189437\pi$
$684$	12.5313	−	3.73702i	0.479148	−	0.142888i
$685$	5.34544			0.204239
$686$	15.6803	+	27.1590i	0.598675	+	1.03694i
$687$	−14.0677	+	12.9497i	−0.536716	+	0.494061i
$688$	4.76706	−	8.25680i	0.181743	−	0.314787i
$689$	9.17934			0.349705
$690$	−1.53762	−	6.86180i	−0.0585360	−	0.261224i
$691$	13.1825	−	22.8328i	0.501487	−	0.868601i	−0.498512	−	0.866883i	$-0.666120\pi$
$691$	13.1825	−	22.8328i	0.501487	−	0.868601i	0.999999	−	0.00171788i	$-0.000546817\pi$
$692$	−7.37955			−0.280528
$693$	18.4382	+	12.7859i	0.700408	+	0.485696i
$694$	−6.81468	−	11.8034i	−0.258682	−	0.448050i
$695$	−0.112855	+	0.195471i	−0.00428085	+	0.00741465i
$696$	2.38833	+	10.6582i	0.0905295	+	0.403999i
$697$	−19.9210	+	34.5042i	−0.754562	+	1.30694i
$698$	16.7383			0.633553
$699$	−6.36174	−	1.98994i	−0.240623	−	0.0752666i
$700$	3.41614	+	5.91693i	0.129118	+	0.223639i
$701$	5.53649	−	9.58948i	0.209110	−	0.362190i	−0.742324	−	0.670041i	$-0.766277\pi$
$701$	5.53649	−	9.58948i	0.209110	−	0.362190i	0.951435	+	0.307851i	$0.0996099\pi$
$702$	−14.0251	−	18.0218i	−0.529343	−	0.680188i
$703$	−14.1686	−	36.2572i	−0.534377	−	1.36747i
$704$	0.818674	−	1.41798i	0.0308549	−	0.0534423i
$705$	−4.35809	−	19.4485i	−0.164135	−	0.732473i
$706$	11.2763			0.424390
$707$	−7.72558	+	13.3811i	−0.290550	+	0.503248i
$708$	−15.8378	−	4.95403i	−0.595219	−	0.186184i
$709$	3.85250			0.144684			0.0723418	−	0.997380i	$-0.476953\pi$
$709$	3.85250			0.144684			0.0723418	+	0.997380i	$0.476953\pi$
$710$	9.94659			0.373289
$711$	20.8561	+	14.4626i	0.782165	+	0.542389i
$712$	−4.37758	−	7.58219i	−0.164057	−	0.284155i
$713$	10.4818			0.392546
$714$	−39.3046	−	12.2944i	−1.47094	−	0.460108i
$715$	9.16991	+	15.8827i	0.342935	+	0.593981i
$716$	−8.63220	+	14.9514i	−0.322601	+	0.558761i
$717$	−6.53077	+	6.01175i	−0.243896	+	0.224513i
$718$	−35.7591			−1.33452
$719$	18.9191	−	32.7688i	0.705563	−	1.22207i	−0.260924	−	0.965359i	$-0.584027\pi$
$719$	18.9191	−	32.7688i	0.705563	−	1.22207i	0.966488	−	0.256712i	$-0.0826393\pi$
$720$	6.28314	+	4.35702i	0.234159	+	0.162377i
$721$	−69.1309			−2.57457
$722$	18.1394	+	5.65359i	0.675078	+	0.210405i
$723$	−3.22895	−	14.4096i	−0.120086	−	0.535898i
$724$	17.5663			0.652846
$725$	9.43224			0.350305
$726$	13.7520	+	4.30161i	0.510385	+	0.159648i
$727$	2.09111	+	3.62190i	0.0775549	+	0.134329i	0.902194	−	0.431330i	$-0.141955\pi$
$727$	2.09111	+	3.62190i	0.0775549	+	0.134329i	−0.824640	+	0.565659i	$0.808622\pi$
$728$	10.0375	+	17.3854i	0.372013	+	0.644346i
$729$	−6.63138	+	26.1730i	−0.245607	+	0.969370i
$730$	−0.651172			−0.0241010
$731$	49.6272			1.83553
$732$	21.5321	+	6.73522i	0.795850	+	0.248941i
$733$	−16.0155	−	27.7396i	−0.591546	−	1.02459i	−0.994024	−	0.109158i	$-0.965185\pi$
$733$	−16.0155	−	27.7396i	−0.591546	−	1.02459i	0.402479	−	0.915429i	$-0.368149\pi$
$734$	−13.1613	−	22.7961i	−0.485793	−	0.841419i
$735$	45.0331	−	41.4542i	1.66107	−	1.52906i
$736$	0.796476	+	1.37954i	0.0293585	+	0.0508504i
$737$	−2.21060	−	3.82888i	−0.0814286	−	0.141039i
$738$	−18.8697	−	13.0851i	−0.694604	−	0.481670i
$739$	−10.9889	+	19.0333i	−0.404233	+	0.700151i	−0.994232	−	0.107252i	$-0.965795\pi$
$739$	−10.9889	+	19.0333i	−0.404233	+	0.700151i	0.589999	+	0.807404i	$0.299128\pi$
$740$	11.3805	−	19.7116i	0.418355	−	0.724612i
$741$	−2.30003	−	33.1003i	−0.0844937	−	1.21597i
$742$	4.77040	+	8.26258i	0.175127	+	0.303329i
$743$	−18.9469			−0.695095			−0.347548	−	0.937662i	$-0.612985\pi$
$743$	−18.9469			−0.695095			−0.347548	+	0.937662i	$0.612985\pi$
$744$	−8.38527	+	7.71886i	−0.307419	+	0.282987i
$745$	−10.7819			−0.395020
$746$	7.55361	−	13.0832i	0.276557	−	0.479011i
$747$	1.36285	−	16.4388i	0.0498640	−	0.601464i
$748$	8.52276			0.311623
$749$	−2.10258	+	3.64177i	−0.0768264	+	0.133067i
$750$	−11.3814	+	10.4769i	−0.415590	+	0.382562i
$751$	−1.91302	+	3.31345i	−0.0698071	+	0.120909i	−0.898816	−	0.438326i	$-0.855572\pi$
$751$	−1.91302	+	3.31345i	−0.0698071	+	0.120909i	0.829009	+	0.559235i	$0.188905\pi$
$752$	2.25746	+	3.91004i	0.0823212	+	0.142585i
$753$	13.4695	−	12.3990i	0.490856	−	0.451846i
$754$	27.7143			1.00929
$755$	−11.7091	+	20.2807i	−0.426137	+	0.738090i
$756$	8.93321	−	21.9901i	0.324898	−	0.799773i
$757$	−9.39972	+	16.2808i	−0.341639	+	0.591735i	−0.984737	−	0.174048i	$-0.944315\pi$
$757$	−9.39972	+	16.2808i	−0.341639	+	0.591735i	0.643099	+	0.765783i	$0.277649\pi$
$758$	−0.509659	−	0.882755i	−0.0185116	−	0.0320631i
$759$	3.32374	−	3.05959i	0.120644	−	0.111056i
$760$	4.04355	+	10.3474i	0.146675	+	0.375339i
$761$	22.3480	+	38.7079i	0.810114	+	1.40316i	0.912783	+	0.408444i	$0.133928\pi$
$761$	22.3480	+	38.7079i	0.810114	+	1.40316i	−0.102669	+	0.994716i	$0.532738\pi$
$762$	2.34717	+	0.734193i	0.0850291	+	0.0265970i
$763$	37.2779	+	64.5672i	1.34955	+	2.33749i
$764$	−7.63625	−	13.2264i	−0.276270	−	0.478514i
$765$	−3.28824	+	39.6631i	−0.118887	+	1.43402i
$766$	−7.29745	−	12.6396i	−0.263668	−	0.456686i
$767$	−21.0530	+	36.4648i	−0.760179	+	1.31667i
$768$	−1.65307	−	0.517077i	−0.0596499	−	0.0186584i
$769$	0.743654	−	1.28805i	0.0268168	−	0.0464481i	−0.852306	−	0.523044i	$-0.824796\pi$
$769$	0.743654	−	1.28805i	0.0268168	−	0.0464481i	0.879122	+	0.476596i	$0.158130\pi$
$770$	−9.53101	+	16.5082i	−0.343474	+	0.594914i
$771$	−41.6703	−	13.0344i	−1.50072	−	0.469423i
$772$	−4.83609	+	8.37635i	−0.174055	+	0.301472i
$773$	−14.5206	−	25.1504i	−0.522269	−	0.904597i	−0.999664	−	0.0259084i	$-0.991752\pi$
$773$	−14.5206	−	25.1504i	−0.522269	−	0.904597i	0.477395	−	0.878689i	$-0.341581\pi$
$774$	−2.36315	+	28.5046i	−0.0849418	+	1.02458i
$775$	4.92102	+	8.52345i	0.176768	+	0.306171i
$776$	−1.68133	−	2.91214i	−0.0603561	−	0.104540i
$777$	−67.4344	−	21.0934i	−2.41920	−	0.756721i
$778$	1.58941	+	2.75294i	0.0569832	+	0.0986977i
$779$	−12.1437	−	31.0756i	−0.435093	−	1.11340i
$780$	14.2737	−	13.1394i	0.511082	−	0.470464i
$781$	3.19500	+	5.53391i	0.114326	+	0.198019i
$782$	−4.14583	+	7.18079i	−0.148255	+	0.256785i
$783$	−20.1247	−	25.8595i	−0.719197	−	0.924144i
$784$	−6.93273	+	12.0078i	−0.247597	+	0.428851i
$785$	31.3911			1.12040
$786$	−14.2792	+	13.1444i	−0.509323	+	0.468845i
$787$	20.7961	+	36.0200i	0.741302	+	1.28397i	0.951903	+	0.306401i	$0.0991248\pi$
$787$	20.7961	+	36.0200i	0.741302	+	1.28397i	−0.210600	+	0.977572i	$0.567542\pi$
$788$	−11.2049	+	19.4075i	−0.399159	+	0.691363i
$789$	−16.4762	+	15.1668i	−0.586569	+	0.539952i
$790$	−10.7809	+	18.6730i	−0.383566	+	0.664356i
$791$	−42.6360			−1.51596
$792$	−0.405837	+	4.89525i	−0.0144208	+	0.173945i
$793$	28.6224	−	49.5755i	1.01641	−	1.76048i
$794$	−31.9869			−1.13517
$795$	6.78373	−	6.24461i	0.240594	−	0.221473i
$796$	−4.22601			−0.149787
$797$	−15.7254	−	27.2373i	−0.557024	−	0.964794i	−0.997743	−	0.0671488i	$-0.978610\pi$
$797$	−15.7254	−	27.2373i	−0.557024	−	0.964794i	0.440719	−	0.897645i	$-0.354724\pi$
$798$	28.5992	−	19.2722i	1.01240	−	0.682228i
$799$	−11.7506	+	20.3526i	−0.415706	+	0.720024i
$800$	−0.747863	+	1.29534i	−0.0264409	+	0.0457970i
$801$	21.5838	+	14.9672i	0.762625	+	0.528839i
$802$	4.22372	+	7.31569i	0.149145	+	0.258326i
$803$	−0.209167	−	0.362288i	−0.00738134	−	0.0127848i
$804$	−3.44099	+	3.16753i	−0.121354	+	0.111710i
$805$	−9.27257	−	16.0606i	−0.326815	−	0.566061i
$806$	14.4592	+	25.0440i	0.509303	+	0.882138i
$807$	−45.6015	−	14.2641i	−1.60525	−	0.502119i
$808$	−3.38257			−0.118999
$809$	32.5597			1.14474			0.572370	−	0.819996i	$-0.306024\pi$
$809$	32.5597			1.14474			0.572370	+	0.819996i	$0.306024\pi$
$810$	−22.6249	−	3.77736i	−0.794957	−	0.132723i
$811$	13.6246	+	23.5984i	0.478423	+	0.828652i	0.999694	−	0.0247387i	$-0.00787536\pi$
$811$	13.6246	+	23.5984i	0.478423	+	0.828652i	−0.521271	+	0.853391i	$0.674542\pi$
$812$	14.4028	+	24.9464i	0.505439	+	0.875447i
$813$	11.7615	+	3.67898i	0.412494	+	0.129028i
$814$	14.6224			0.512514
$815$	20.8786			0.731344
$816$	−1.97138	−	8.79753i	−0.0690121	−	0.307975i
$817$	−25.9588	+	32.4535i	−0.908184	+	1.13541i
$818$	29.4186			1.02860
$819$	−49.4900	−	34.3186i	−1.72932	−	1.19919i
$820$	9.75407	−	16.8946i	0.340627	−	0.589983i
$821$	0.667463			0.0232946			0.0116473	−	0.999932i	$-0.496292\pi$
$821$	0.667463			0.0232946			0.0116473	+	0.999932i	$0.496292\pi$
$822$	2.67272	−	2.46031i	0.0932218	−	0.0858131i
$823$	−1.87004	+	3.23901i	−0.0651856	+	0.112905i	−0.896776	−	0.442484i	$-0.854097\pi$
$823$	−1.87004	+	3.23901i	−0.0651856	+	0.112905i	0.831591	+	0.555389i	$0.187431\pi$
$824$	−7.56708	−	13.1066i	−0.263612	−	0.456589i
$825$	4.04840	+	1.26633i	0.140947	+	0.0440881i
$826$	−43.7640			−1.52274
$827$	−15.4717	−	26.7977i	−0.538003	−	0.931849i	−0.999011	−	0.0444528i	$-0.985846\pi$
$827$	−15.4717	−	26.7977i	−0.538003	−	0.931849i	0.461008	−	0.887396i	$-0.347488\pi$
$828$	−3.92704	−	2.72319i	−0.136474	−	0.0946375i
$829$	−13.6618			−0.474494			−0.237247	−	0.971449i	$-0.576245\pi$
$829$	−13.6618			−0.474494			−0.237247	+	0.971449i	$0.576245\pi$
$830$	14.0136			0.486419
$831$	19.3880	+	6.06454i	0.672562	+	0.210376i
$832$	−2.19741	+	3.80602i	−0.0761813	+	0.131950i
$833$	−72.1728			−2.50064
$834$	0.0335405	+	0.149679i	0.00116141	+	0.00518295i
$835$	31.6020	−	54.7362i	1.09363	−	1.89422i
$836$	−4.45805	+	5.57342i	−0.154185	+	0.192761i
$837$	12.8685	−	31.6772i	0.444799	−	1.09492i
$838$	−3.22036	+	5.57783i	−0.111246	+	0.192683i
$839$	4.36846	+	7.56640i	0.150816	+	0.261221i	0.931528	−	0.363670i	$-0.118477\pi$
$839$	4.36846	+	7.56640i	0.150816	+	0.261221i	−0.780712	+	0.624891i	$0.785143\pi$
$840$	19.2450	+	6.01982i	0.664016	+	0.207703i
$841$	10.7673			0.371287
$842$	−11.8500	+	20.5249i	−0.408379	+	0.707334i
$843$	3.30484	+	14.7482i	0.113825	+	0.507957i
$844$	−3.64267	+	6.30930i	−0.125386	+	0.217175i
$845$	−8.04662	−	13.9372i	−0.276812	−	0.479453i
$846$	−11.1305	−	7.71839i	−0.382674	−	0.265364i
$847$	38.0006			1.30571
$848$	−1.04434	+	1.80885i	−0.0358627	+	0.0621161i
$849$	−1.97904	−	8.83170i	−0.0679204	−	0.303103i
$850$	−7.78558			−0.267043
$851$	−7.11295	+	12.3200i	−0.243829	+	0.422324i
$852$	4.97330	−	4.57805i	0.170382	−	0.156841i
$853$	22.6470	+	39.2257i	0.775418	+	1.34306i	0.934559	+	0.355807i	$0.115794\pi$
$853$	22.6470	+	39.2257i	0.775418	+	1.34306i	−0.159141	+	0.987256i	$0.550873\pi$
$854$	59.4991			2.03602
$855$	−24.2175	−	22.8972i	−0.828222	−	0.783066i
$856$	−0.920593			−0.0314652
$857$	−13.8812	−	24.0429i	−0.474172	−	0.821290i	0.525391	−	0.850861i	$-0.323919\pi$
$857$	−13.8812	−	24.0429i	−0.474172	−	0.821290i	−0.999563	+	0.0295712i	$0.990586\pi$
$858$	11.8952	+	3.72080i	0.406095	+	0.127026i
$859$	−7.50106	+	12.9922i	−0.255933	+	0.443288i	−0.965148	−	0.261703i	$-0.915716\pi$
$859$	−7.50106	+	12.9922i	−0.255933	+	0.443288i	0.709216	+	0.704992i	$0.249049\pi$
$860$	−24.2994			−0.828601
$861$	−57.7972	−	18.0789i	−1.96972	−	0.616127i
$862$	13.8562	−	23.9996i	0.471943	−	0.817429i
$863$	−47.8769			−1.62975			−0.814874	−	0.579638i	$-0.803194\pi$
$863$	−47.8769			−1.62975			−0.814874	+	0.579638i	$0.803194\pi$
$864$	5.14695	−	0.713388i	0.175103	−	0.0242700i
$865$	9.40402	+	16.2882i	0.319746	+	0.553817i
$866$	14.7686	−	25.5800i	0.501858	−	0.869244i
$867$	12.8635	−	11.8412i	0.436869	−	0.402149i
$868$	−15.0286	+	26.0302i	−0.510102	+	0.883523i
$869$	−13.8520			−0.469895
$870$	20.4815	−	18.8537i	0.694386	−	0.639201i
$871$	5.93349	+	10.2771i	0.201049	+	0.348226i
$872$	−8.16088	+	14.1351i	−0.276362	+	0.478674i
$873$	8.28982	+	5.74854i	0.280568	+	0.194559i
$874$	−2.52727	−	6.46725i	−0.0854861	−	0.218758i
$875$	−20.3984	+	35.3311i	−0.689592	+	1.19441i
$876$	−0.325586	+	0.299710i	−0.0110005	+	0.0101263i
$877$	33.1892			1.12072			0.560359	−	0.828250i	$-0.310663\pi$
$877$	33.1892			1.12072			0.560359	+	0.828250i	$0.310663\pi$
$878$	6.15094	−	10.6537i	0.207584	−	0.359547i
$879$	36.9378	−	34.0022i	1.24588	−	1.14687i
$880$	−4.17306			−0.140674
$881$	26.3261			0.886947			0.443474	−	0.896287i	$-0.353746\pi$
$881$	26.3261			0.886947			0.443474	+	0.896287i	$0.353746\pi$
$882$	3.43673	−	41.4542i	0.115721	−	1.39583i
$883$	8.91652	+	15.4439i	0.300065	+	0.519727i	0.976150	−	0.217096i	$-0.0696584\pi$
$883$	8.91652	+	15.4439i	0.300065	+	0.519727i	−0.676086	+	0.736823i	$0.736325\pi$
$884$	−22.8760			−0.769402
$885$	9.24801	+	41.2704i	0.310869	+	1.38729i
$886$	−16.2443	−	28.1359i	−0.545738	−	0.945245i
$887$	−6.83390	+	11.8367i	−0.229460	+	0.397436i	−0.957648	−	0.287941i	$-0.907029\pi$
$887$	−6.83390	+	11.8367i	−0.229460	+	0.397436i	0.728188	+	0.685377i	$0.240363\pi$
$888$	−3.38227	−	15.0938i	−0.113502	−	0.506515i
$889$	6.48588			0.217529
$890$	−11.1570	+	19.3245i	−0.373984	+	0.647759i
$891$	−5.16589	−	13.8010i	−0.173064	−	0.462350i
$892$	−5.93482			−0.198712
$893$	−7.16307	−	18.3302i	−0.239703	−	0.613398i
$894$	−5.39097	+	4.96253i	−0.180301	+	0.165972i
$895$	44.0013			1.47080
$896$	−4.56787			−0.152602
$897$	−8.92127	+	8.21226i	−0.297872	+	0.274199i
$898$	−1.62868	−	2.82096i	−0.0543498	−	0.0941366i
$899$	20.7475	+	35.9358i	0.691969	+	1.19853i
$900$	0.370734	−	4.47183i	0.0123578	−	0.149061i
$901$	−10.8720			−0.362200
$902$	12.5327			0.417292
$903$	16.4940	+	73.6066i	0.548886	+	2.44947i
$904$	−4.66694	−	8.08338i	−0.155220	−	0.268849i
$905$	−22.3853	−	38.7726i	−0.744114	−	1.28884i
$906$	3.47993	+	15.5296i	0.115613	+	0.515936i
$907$	14.0734	+	24.3759i	0.467300	+	0.809388i	0.999302	−	0.0373556i	$-0.0118934\pi$
$907$	14.0734	+	24.3759i	0.467300	+	0.809388i	−0.532002	+	0.846743i	$0.678560\pi$
$908$	−6.47904	−	11.2220i	−0.215014	−	0.372416i
$909$	9.17734	−	4.33043i	0.304393	−	0.143631i
$910$	25.5822	−	44.3097i	0.848042	−	1.46885i
$911$	11.8310	−	20.4918i	0.391977	−	0.678924i	−0.600733	−	0.799450i	$-0.705125\pi$
$911$	11.8310	−	20.4918i	0.391977	−	0.678924i	0.992710	+	0.120526i	$0.0384580\pi$
$912$	6.78430	+	3.31260i	0.224650	+	0.109691i
$913$	4.50139	+	7.79664i	0.148974	+	0.258031i
$914$	4.60876			0.152444
$915$	−12.5731	−	56.1089i	−0.415653	−	1.85490i
$916$	−11.0392			−0.364747
$917$	−25.5920	+	44.3267i	−0.845123	+	1.46380i
$918$	16.6113	+	21.3450i	0.548256	+	0.704490i
$919$	7.45588			0.245947			0.122973	−	0.992410i	$-0.460757\pi$
$919$	7.45588			0.245947			0.122973	+	0.992410i	$0.460757\pi$
$920$	2.02995	−	3.51598i	0.0669256	−	0.115919i
$921$	−0.771309	−	0.241265i	−0.0254155	−	0.00794994i
$922$	2.51103	−	4.34923i	0.0826962	−	0.143234i
$923$	−8.57572	−	14.8536i	−0.282273	−	0.488912i
$924$	2.83261	+	12.6409i	0.0931859	+	0.415854i
$925$	−13.3576			−0.439196
$926$	−17.1424	+	29.6915i	−0.563334	+	0.975724i
$927$	37.3097	+	25.8723i	1.22541	+	0.849756i
$928$	−3.15307	+	5.46127i	−0.103505	+	0.179275i
$929$	23.0218	+	39.8749i	0.755321	+	1.30825i	0.945215	+	0.326449i	$0.105852\pi$
$929$	23.0218	+	39.8749i	0.755321	+	1.30825i	−0.189894	+	0.981805i	$0.560815\pi$
$930$	27.7228	+	8.67166i	0.909067	+	0.284355i
$931$	37.7518	−	47.1971i	1.23727	−	1.54682i
$932$	−1.92422	−	3.33285i	−0.0630300	−	0.109171i
$933$	27.9377	−	25.7174i	0.914641	−	0.841951i
$934$	−4.36846	−	7.56640i	−0.142940	−	0.247580i
$935$	−10.8609	−	18.8115i	−0.355188	−	0.615203i
$936$	1.08931	−	13.1394i	0.0356052	−	0.429473i
$937$	6.28747	+	10.8902i	0.205403	+	0.355768i	0.950261	−	0.311455i	$-0.100816\pi$
$937$	6.28747	+	10.8902i	0.205403	+	0.355768i	−0.744858	+	0.667223i	$0.767483\pi$
$938$	−6.16714	+	10.6818i	−0.201364	+	0.348773i
$939$	−1.18420	−	5.28465i	−0.0386450	−	0.172458i
$940$	5.75353	−	9.96541i	0.187660	−	0.325036i
$941$	−2.85482	+	4.94469i	−0.0930645	+	0.161192i	−0.908799	−	0.417234i	$-0.863000\pi$
$941$	−2.85482	+	4.94469i	−0.0930645	+	0.161192i	0.815735	+	0.578426i	$0.196333\pi$
$942$	15.6956	−	14.4482i	0.511389	−	0.470747i
$943$	−6.09642	+	10.5593i	−0.198527	+	0.343858i
$944$	−4.79042	−	8.29724i	−0.155915	−	0.270052i
$945$	−59.9208	+	8.30527i	−1.94922	+	0.270170i
$946$	−7.80534	−	13.5192i	−0.253774	−	0.439549i
$947$	25.6061	+	44.3510i	0.832085	+	1.44121i	0.896382	+	0.443283i	$0.146186\pi$
$947$	25.6061	+	44.3510i	0.832085	+	1.44121i	−0.0642966	+	0.997931i	$0.520480\pi$
$948$	3.20407	+	14.2985i	0.104063	+	0.464395i
$949$	0.561425	+	0.972417i	0.0182246	+	0.0315660i
$950$	4.07245	−	5.09135i	0.132128	−	0.165185i
$951$	2.74761	+	12.2616i	0.0890974	+	0.397608i
$952$	−11.8884	−	20.5913i	−0.385305	−	0.667368i
$953$	17.5692	−	30.4308i	0.569123	−	0.985750i	−0.427530	−	0.904001i	$-0.640616\pi$
$953$	17.5692	−	30.4308i	0.569123	−	0.985750i	0.996653	−	0.0817490i	$-0.0260506\pi$
$954$	0.517705	−	6.24461i	0.0167613	−	0.202177i
$955$	−19.4623	+	33.7097i	−0.629785	+	1.09082i
$956$	−5.12484			−0.165749
$957$	17.0685	+	5.33900i	0.551745	+	0.172585i
$958$	6.78347	+	11.7493i	0.219164	+	0.379603i
$959$	4.79020	−	8.29686i	0.154684	−	0.267920i
$960$	0.965262	+	4.30760i	0.0311537	+	0.139027i
$961$	−6.14892	+	10.6502i	−0.198352	+	0.343556i
$962$	−39.2480			−1.26541
$963$	2.49768	−	1.17856i	0.0804867	−	0.0379785i
$964$	4.26285	−	7.38347i	0.137297	−	0.237805i
$965$	24.6512			0.793550
$966$	−12.0284	−	3.76246i	−0.387007	−	0.121055i
$967$	−15.5678			−0.500628			−0.250314	−	0.968165i	$-0.580534\pi$
$967$	−15.5678			−0.500628			−0.250314	+	0.968165i	$0.580534\pi$
$968$	4.15955	+	7.20455i	0.133693	+	0.231563i
$969$	2.72416	+	39.2040i	0.0875126	+	1.25941i
$970$	−4.28515	+	7.42209i	−0.137588	+	0.238309i
$971$	12.6423	−	21.8972i	0.405712	−	0.702714i	−0.588692	−	0.808357i	$-0.700357\pi$
$971$	12.6423	−	21.8972i	0.405712	−	0.702714i	0.994404	+	0.105643i	$0.0336902\pi$
$972$	−13.0510	+	8.52472i	−0.418612	+	0.273430i
$973$	0.202266	+	0.350335i	0.00648434	+	0.0112312i
$974$	−3.82495	−	6.62501i	−0.122559	−	0.212279i
$975$	−10.8663	−	3.39897i	−0.348001	−	0.108854i
$976$	6.51278	+	11.2805i	0.208469	+	0.361079i
$977$	−14.2668	−	24.7108i	−0.456435	−	0.790568i	0.542335	−	0.840162i	$-0.317540\pi$
$977$	−14.2668	−	24.7108i	−0.456435	−	0.790568i	−0.998769	+	0.0495946i	$0.984207\pi$
$978$	10.4393	−	9.60964i	0.333811	−	0.307282i
$979$	−14.3352			−0.458156
$980$	35.3385			1.12885
$981$	4.04555	−	48.7979i	0.129165	−	1.55800i
$982$	16.5125	+	28.6004i	0.526934	+	0.912676i
$983$	2.56492	+	4.44257i	0.0818083	+	0.141696i	0.904027	−	0.427476i	$-0.140597\pi$
$983$	2.56492	+	4.44257i	0.0818083	+	0.141696i	−0.822218	+	0.569172i	$0.807264\pi$
$984$	−2.89890	−	12.9367i	−0.0924137	−	0.412407i
$985$	57.1153			1.81984
$986$	−32.8248			−1.04536
$987$	−34.0922	−	10.6640i	−1.08517	−	0.339439i
$988$	11.9659	−	14.9596i	0.380685	−	0.475930i
$989$	15.1874			0.482931
$990$	11.3220	−	5.34242i	0.359838	−	0.169793i
$991$	0.424561	−	0.735361i	0.0134866	−	0.0233595i	−0.859203	−	0.511634i	$-0.829040\pi$
$991$	0.424561	−	0.735361i	0.0134866	−	0.0233595i	0.872690	+	0.488275i	$0.162374\pi$
$992$	−6.58011			−0.208919
$993$	7.63049	+	2.38681i	0.242146	+	0.0757430i
$994$	8.91342	−	15.4385i	0.282717	−	0.489679i
$995$	5.38535	+	9.32770i	0.170727	+	0.295708i
$996$	7.00680	−	6.44995i	0.222019	−	0.204374i
$997$	59.2647			1.87693			0.938467	−	0.345370i	$-0.112247\pi$
$997$	59.2647			1.87693			0.938467	+	0.345370i	$0.112247\pi$
$998$	14.1131	+	24.4446i	0.446743	+	0.773781i
$999$	28.4999	+	36.6213i	0.901696	+	1.15865i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.h.f.277.4	yes	10
3.2	odd	2		1026.2.h.f.505.2		10
9.4	even	3		342.2.f.f.49.1	yes	10
9.5	odd	6		1026.2.f.f.847.4		10
19.7	even	3		342.2.f.f.7.1	✓	10
57.26	odd	6		1026.2.f.f.235.4		10
171.121	even	3	inner	342.2.h.f.121.4	yes	10
171.140	odd	6		1026.2.h.f.577.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.f.f.7.1	✓	10	19.7	even	3
342.2.f.f.49.1	yes	10	9.4	even	3
342.2.h.f.121.4	yes	10	171.121	even	3	inner
342.2.h.f.277.4	yes	10	1.1	even	1	trivial
1026.2.f.f.235.4		10	57.26	odd	6
1026.2.f.f.847.4		10	9.5	odd	6
1026.2.h.f.505.2		10	3.2	odd	2
1026.2.h.f.577.2		10	171.140	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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.378732 + 1.69014i) q^{3} +(-0.500000 + 0.866025i) q^{4} +2.54867 q^{5} +(1.27434 - 1.17306i) q^{6} +(2.28394 - 3.95589i) q^{7} +1.00000 q^{8} +(-2.71312 + 1.28022i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.378732 + 1.69014i) q^{3} +(-0.500000 + 0.866025i) q^{4} +2.54867 q^{5} +(1.27434 - 1.17306i) q^{6} +(2.28394 - 3.95589i) q^{7} +1.00000 q^{8} +(-2.71312 + 1.28022i) q^{9} +(-1.27434 - 2.20721i) q^{10} +(0.818674 - 1.41798i) q^{11} +(-1.65307 - 0.517077i) q^{12} +(-2.19741 + 3.80602i) q^{13} -4.56787 q^{14} +(0.965262 + 4.30760i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.60261 - 4.50785i) q^{17} +(2.46526 + 1.70953i) q^{18} +(1.58653 + 4.05992i) q^{19} +(-1.27434 + 2.20721i) q^{20} +(7.55100 + 2.36194i) q^{21} -1.63735 q^{22} +(0.796476 - 1.37954i) q^{23} +(0.378732 + 1.69014i) q^{24} +1.49573 q^{25} +4.39481 q^{26} +(-3.19129 - 4.10069i) q^{27} +(2.28394 + 3.95589i) q^{28} +6.30613 q^{29} +(3.24786 - 2.98974i) q^{30} +(3.29005 + 5.69854i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.70665 + 0.846635i) q^{33} -5.20522 q^{34} +(5.82100 - 10.0823i) q^{35} +(0.247863 - 2.98974i) q^{36} -8.93052 q^{37} +(2.72273 - 3.40393i) q^{38} +(-7.26492 - 2.27246i) q^{39} +2.54867 q^{40} -7.65424 q^{41} +(-1.73000 - 7.72033i) q^{42} +(4.76706 + 8.25680i) q^{43} +(0.818674 + 1.41798i) q^{44} +(-6.91486 + 3.26285i) q^{45} -1.59295 q^{46} -4.51493 q^{47} +(1.27434 - 1.17306i) q^{48} +(-6.93273 - 12.0078i) q^{49} +(-0.747863 - 1.29534i) q^{50} +(8.60458 + 2.69150i) q^{51} +(-2.19741 - 3.80602i) q^{52} +(-1.04434 - 1.80885i) q^{53} +(-1.95566 + 4.81408i) q^{54} +(2.08653 - 3.61398i) q^{55} +(2.28394 - 3.95589i) q^{56} +(-6.26094 + 4.21907i) q^{57} +(-3.15307 - 5.46127i) q^{58} +9.58083 q^{59} +(-4.21312 - 1.31786i) q^{60} -13.0256 q^{61} +(3.29005 - 5.69854i) q^{62} +(-1.13220 + 13.6568i) q^{63} +1.00000 q^{64} +(-5.60046 + 9.70029i) q^{65} +(-0.620115 - 2.76734i) q^{66} +(1.35011 - 2.33846i) q^{67} +(2.60261 + 4.50785i) q^{68} +(2.63326 + 0.823679i) q^{69} -11.6420 q^{70} +(-1.95133 + 3.37980i) q^{71} +(-2.71312 + 1.28022i) q^{72} +(0.127747 - 0.221265i) q^{73} +(4.46526 + 7.73406i) q^{74} +(0.566478 + 2.52798i) q^{75} +(-4.30926 - 0.655982i) q^{76} +(-3.73960 - 6.47717i) q^{77} +(1.66445 + 7.42783i) q^{78} +(-4.23000 - 7.32657i) q^{79} +(-1.27434 - 2.20721i) q^{80} +(5.72209 - 6.94677i) q^{81} +(3.82712 + 6.62877i) q^{82} +(-2.74920 + 4.76175i) q^{83} +(-5.82100 + 5.35839i) q^{84} +(6.63320 - 11.4890i) q^{85} +(4.76706 - 8.25680i) q^{86} +(2.38833 + 10.6582i) q^{87} +(0.818674 - 1.41798i) q^{88} +(-4.37758 - 7.58219i) q^{89} +(6.28314 + 4.35702i) q^{90} +(10.0375 + 17.3854i) q^{91} +(0.796476 + 1.37954i) q^{92} +(-8.38527 + 7.71886i) q^{93} +(2.25746 + 3.91004i) q^{94} +(4.04355 + 10.3474i) q^{95} +(-1.65307 - 0.517077i) q^{96} +(-1.68133 - 2.91214i) q^{97} +(-6.93273 + 12.0078i) q^{98} +(-0.405837 + 4.89525i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 5 q^{2} - 4 q^{3} - 5 q^{4} + 4 q^{5} + 2 q^{6} - 5 q^{7} + 10 q^{8} - 8 q^{9}+O(q^{10}) \) 10 * q - 5 * q^2 - 4 * q^3 - 5 * q^4 + 4 * q^5 + 2 * q^6 - 5 * q^7 + 10 * q^8 - 8 * q^9	\( 10 q - 5 q^{2} - 4 q^{3} - 5 q^{4} + 4 q^{5} + 2 q^{6} - 5 q^{7} + 10 q^{8} - 8 q^{9} - 2 q^{10} + q^{11} + 2 q^{12} - 7 q^{13} + 10 q^{14} - 11 q^{15} - 5 q^{16} - 9 q^{17} + 4 q^{18} + 3 q^{19} - 2 q^{20} + 15 q^{21} - 2 q^{22} + 10 q^{23} - 4 q^{24} + 18 q^{25} + 14 q^{26} - 4 q^{27} - 5 q^{28} + 26 q^{29} + 34 q^{30} + 18 q^{31} - 5 q^{32} + 13 q^{33} + 18 q^{34} + 12 q^{35} + 4 q^{36} - 48 q^{37} - 9 q^{38} - 20 q^{39} + 4 q^{40} - 10 q^{41} - 3 q^{42} + 15 q^{43} + q^{44} - 10 q^{45} - 20 q^{46} - 14 q^{47} + 2 q^{48} - 26 q^{49} - 9 q^{50} + 30 q^{51} - 7 q^{52} - 14 q^{53} - 16 q^{54} + 8 q^{55} - 5 q^{56} - 17 q^{57} - 13 q^{58} + 30 q^{59} - 23 q^{60} - 28 q^{61} + 18 q^{62} + 48 q^{63} + 10 q^{64} - q^{65} - 5 q^{66} - 2 q^{67} - 9 q^{68} - 44 q^{69} - 24 q^{70} - 41 q^{71} - 8 q^{72} + 4 q^{73} + 24 q^{74} + 22 q^{75} + 6 q^{76} - 6 q^{77} + 19 q^{78} - 28 q^{79} - 2 q^{80} - 8 q^{81} + 5 q^{82} + 21 q^{83} - 12 q^{84} + 18 q^{85} + 15 q^{86} - q^{87} + q^{88} - 27 q^{89} + 8 q^{90} - q^{91} + 10 q^{92} - 49 q^{93} + 7 q^{94} + 17 q^{95} + 2 q^{96} - 24 q^{97} - 26 q^{98} - 13 q^{99}+O(q^{100}) \) 10 * q - 5 * q^2 - 4 * q^3 - 5 * q^4 + 4 * q^5 + 2 * q^6 - 5 * q^7 + 10 * q^8 - 8 * q^9 - 2 * q^10 + q^11 + 2 * q^12 - 7 * q^13 + 10 * q^14 - 11 * q^15 - 5 * q^16 - 9 * q^17 + 4 * q^18 + 3 * q^19 - 2 * q^20 + 15 * q^21 - 2 * q^22 + 10 * q^23 - 4 * q^24 + 18 * q^25 + 14 * q^26 - 4 * q^27 - 5 * q^28 + 26 * q^29 + 34 * q^30 + 18 * q^31 - 5 * q^32 + 13 * q^33 + 18 * q^34 + 12 * q^35 + 4 * q^36 - 48 * q^37 - 9 * q^38 - 20 * q^39 + 4 * q^40 - 10 * q^41 - 3 * q^42 + 15 * q^43 + q^44 - 10 * q^45 - 20 * q^46 - 14 * q^47 + 2 * q^48 - 26 * q^49 - 9 * q^50 + 30 * q^51 - 7 * q^52 - 14 * q^53 - 16 * q^54 + 8 * q^55 - 5 * q^56 - 17 * q^57 - 13 * q^58 + 30 * q^59 - 23 * q^60 - 28 * q^61 + 18 * q^62 + 48 * q^63 + 10 * q^64 - q^65 - 5 * q^66 - 2 * q^67 - 9 * q^68 - 44 * q^69 - 24 * q^70 - 41 * q^71 - 8 * q^72 + 4 * q^73 + 24 * q^74 + 22 * q^75 + 6 * q^76 - 6 * q^77 + 19 * q^78 - 28 * q^79 - 2 * q^80 - 8 * q^81 + 5 * q^82 + 21 * q^83 - 12 * q^84 + 18 * q^85 + 15 * q^86 - q^87 + q^88 - 27 * q^89 + 8 * q^90 - q^91 + 10 * q^92 - 49 * q^93 + 7 * q^94 + 17 * q^95 + 2 * q^96 - 24 * q^97 - 26 * q^98 - 13 * q^99

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