LMFDB - Embedded newform 126.2.t.a.59.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,2,Mod(47,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 5]))

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

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

chi := DirichletCharacter("126.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	126.t (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:	$1.00611506547$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			59.7
Root			$0.320287 + 1.70218i$ of defining polynomial
Character	$\chi$	$=$	126.59
Dual form			126.2.t.a.47.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(1.33318 - 1.10572i) q^{3} +(0.500000 + 0.866025i) q^{4} -0.0676069 q^{5} +(1.70743 - 0.290993i) q^{6} +(-2.64192 - 0.142361i) q^{7} +1.00000i q^{8} +(0.554753 - 2.94826i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(1.33318 - 1.10572i) q^{3} +(0.500000 + 0.866025i) q^{4} -0.0676069 q^{5} +(1.70743 - 0.290993i) q^{6} +(-2.64192 - 0.142361i) q^{7} +1.00000i q^{8} +(0.554753 - 2.94826i) q^{9} +(-0.0585493 - 0.0338034i) q^{10} +3.92924i q^{11} +(1.62418 + 0.601709i) q^{12} +(-3.32589 - 1.92020i) q^{13} +(-2.21679 - 1.44425i) q^{14} +(-0.0901323 + 0.0747545i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.775337 + 1.34292i) q^{17} +(1.95456 - 2.27589i) q^{18} +(5.06375 - 2.92356i) q^{19} +(-0.0338034 - 0.0585493i) q^{20} +(-3.67957 + 2.73144i) q^{21} +(-1.96462 + 3.40282i) q^{22} +5.52740i q^{23} +(1.10572 + 1.33318i) q^{24} -4.99543 q^{25} +(-1.92020 - 3.32589i) q^{26} +(-2.52037 - 4.54398i) q^{27} +(-1.19767 - 2.35915i) q^{28} +(1.20840 - 0.697671i) q^{29} +(-0.115434 + 0.0196731i) q^{30} +(1.09635 - 0.632976i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(4.34465 + 5.23840i) q^{33} +(-1.34292 + 0.775337i) q^{34} +(0.178612 + 0.00962461i) q^{35} +(2.83065 - 0.993700i) q^{36} +(-4.35534 - 7.54368i) q^{37} +5.84711 q^{38} +(-6.55723 + 1.11753i) q^{39} -0.0676069i q^{40} +(5.17415 - 8.96188i) q^{41} +(-4.55232 + 0.525707i) q^{42} +(0.735847 + 1.27452i) q^{43} +(-3.40282 + 1.96462i) q^{44} +(-0.0375051 + 0.199323i) q^{45} +(-2.76370 + 4.78687i) q^{46} +(-1.77132 + 3.06802i) q^{47} +(0.290993 + 1.70743i) q^{48} +(6.95947 + 0.752214i) q^{49} +(-4.32617 - 2.49771i) q^{50} +(0.451235 + 2.64767i) q^{51} -3.84040i q^{52} +(6.28910 + 3.63101i) q^{53} +(0.0892808 - 5.19539i) q^{54} -0.265644i q^{55} +(0.142361 - 2.64192i) q^{56} +(3.51826 - 9.49673i) q^{57} +1.39534 q^{58} +(4.70043 + 8.14138i) q^{59} +(-0.109805 - 0.0406796i) q^{60} +(0.0705919 + 0.0407562i) q^{61} +1.26595 q^{62} +(-1.88533 + 7.71009i) q^{63} -1.00000 q^{64} +(0.224853 + 0.129819i) q^{65} +(1.14338 + 6.70891i) q^{66} +(7.67257 + 13.2893i) q^{67} -1.55067 q^{68} +(6.11178 + 7.36904i) q^{69} +(0.149870 + 0.0976411i) q^{70} -4.30975i q^{71} +(2.94826 + 0.554753i) q^{72} +(6.12768 + 3.53782i) q^{73} -8.71069i q^{74} +(-6.65982 + 5.52356i) q^{75} +(5.06375 + 2.92356i) q^{76} +(0.559372 - 10.3807i) q^{77} +(-6.23749 - 2.31080i) q^{78} +(3.42320 - 5.92915i) q^{79} +(0.0338034 - 0.0585493i) q^{80} +(-8.38450 - 3.27112i) q^{81} +(8.96188 - 5.17415i) q^{82} +(-3.93194 - 6.81032i) q^{83} +(-4.20528 - 1.82089i) q^{84} +(0.0524181 - 0.0907908i) q^{85} +1.47169i q^{86} +(0.839589 - 2.26628i) q^{87} -3.92924 q^{88} +(-5.84745 - 10.1281i) q^{89} +(-0.132142 + 0.153866i) q^{90} +(8.51336 + 5.54650i) q^{91} +(-4.78687 + 2.76370i) q^{92} +(0.761734 - 2.05613i) q^{93} +(-3.06802 + 1.77132i) q^{94} +(-0.342344 + 0.197652i) q^{95} +(-0.601709 + 1.62418i) q^{96} +(0.363295 - 0.209749i) q^{97} +(5.65097 + 4.13117i) q^{98} +(11.5844 + 2.17976i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 2 q^{7} - 6 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 + 2 * q^7 - 6 * q^9	$ 16 q + 8 q^{4} + 2 q^{7} - 6 q^{9} - 6 q^{13} - 6 q^{14} - 18 q^{15} - 8 q^{16} + 18 q^{17} + 12 q^{18} - 18 q^{21} - 6 q^{24} + 16 q^{25} - 12 q^{26} - 36 q^{27} - 2 q^{28} + 6 q^{29} - 18 q^{30} + 6 q^{31} + 18 q^{33} - 30 q^{35} - 2 q^{37} - 30 q^{39} + 6 q^{41} + 30 q^{42} - 2 q^{43} + 12 q^{44} + 12 q^{45} + 6 q^{46} - 18 q^{47} + 10 q^{49} - 12 q^{50} + 36 q^{53} + 18 q^{54} + 6 q^{57} - 12 q^{58} + 30 q^{59} - 6 q^{60} - 60 q^{61} - 36 q^{62} + 42 q^{63} - 16 q^{64} + 42 q^{65} + 48 q^{66} + 14 q^{67} + 36 q^{68} + 42 q^{69} + 30 q^{75} - 18 q^{77} - 16 q^{79} + 54 q^{81} - 18 q^{84} - 12 q^{85} - 48 q^{87} + 24 q^{89} - 18 q^{90} - 12 q^{91} + 6 q^{92} + 30 q^{93} - 66 q^{95} - 6 q^{96} - 6 q^{97} + 24 q^{98} + 18 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 2 * q^7 - 6 * q^9 - 6 * q^13 - 6 * q^14 - 18 * q^15 - 8 * q^16 + 18 * q^17 + 12 * q^18 - 18 * q^21 - 6 * q^24 + 16 * q^25 - 12 * q^26 - 36 * q^27 - 2 * q^28 + 6 * q^29 - 18 * q^30 + 6 * q^31 + 18 * q^33 - 30 * q^35 - 2 * q^37 - 30 * q^39 + 6 * q^41 + 30 * q^42 - 2 * q^43 + 12 * q^44 + 12 * q^45 + 6 * q^46 - 18 * q^47 + 10 * q^49 - 12 * q^50 + 36 * q^53 + 18 * q^54 + 6 * q^57 - 12 * q^58 + 30 * q^59 - 6 * q^60 - 60 * q^61 - 36 * q^62 + 42 * q^63 - 16 * q^64 + 42 * q^65 + 48 * q^66 + 14 * q^67 + 36 * q^68 + 42 * q^69 + 30 * q^75 - 18 * q^77 - 16 * q^79 + 54 * q^81 - 18 * q^84 - 12 * q^85 - 48 * q^87 + 24 * q^89 - 18 * q^90 - 12 * q^91 + 6 * q^92 + 30 * q^93 - 66 * q^95 - 6 * q^96 - 6 * q^97 + 24 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	1.33318	−	1.10572i	0.769714	−	0.638389i
$3$	1.33318	−	1.10572i	0.769714	−	0.638389i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.0676069			−0.0302347			−0.0151174	−	0.999886i	$-0.504812\pi$
$5$	−0.0676069			−0.0302347			−0.0151174	+	0.999886i	$0.504812\pi$
$6$	1.70743	−	0.290993i	0.697056	−	0.118797i
$7$	−2.64192	−	0.142361i	−0.998551	−	0.0538075i
$7$	−2.64192	−	0.142361i	−0.998551	−	0.0538075i
$8$			1.00000i			0.353553i
$9$	0.554753	−	2.94826i	0.184918	−	0.982754i
$10$	−0.0585493	−	0.0338034i	−0.0185149	−	0.0106896i
$11$			3.92924i			1.18471i	0.805677	+	0.592356i	$0.201802\pi$
$11$			3.92924i			1.18471i	−0.805677	+	0.592356i	$0.798198\pi$
$12$	1.62418	+	0.601709i	0.468859	+	0.173698i
$13$	−3.32589	−	1.92020i	−0.922435	−	0.532568i	−0.0380241	−	0.999277i	$-0.512106\pi$
$13$	−3.32589	−	1.92020i	−0.922435	−	0.532568i	−0.884411	+	0.466709i	$0.845440\pi$
$14$	−2.21679	−	1.44425i	−0.592461	−	0.385991i
$15$	−0.0901323	+	0.0747545i	−0.0232721	+	0.0193015i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.775337	+	1.34292i	−0.188047	+	0.325707i	−0.944599	−	0.328227i	$-0.893549\pi$
$17$	−0.775337	+	1.34292i	−0.188047	+	0.325707i	0.756552	+	0.653933i	$0.226882\pi$
$18$	1.95456	−	2.27589i	0.460695	−	0.536433i
$19$	5.06375	−	2.92356i	1.16170	−	0.670710i	0.209991	−	0.977703i	$-0.432656\pi$
$19$	5.06375	−	2.92356i	1.16170	−	0.670710i	0.951712	+	0.306994i	$0.0993230\pi$
$20$	−0.0338034	−	0.0585493i	−0.00755868	−	0.0130920i
$21$	−3.67957	+	2.73144i	−0.802949	+	0.596048i
$22$	−1.96462	+	3.40282i	−0.418859	+	0.725484i
$23$			5.52740i			1.15254i	0.817258	+	0.576272i	$0.195493\pi$
$23$			5.52740i			1.15254i	−0.817258	+	0.576272i	$0.804507\pi$
$24$	1.10572	+	1.33318i	0.225705	+	0.272135i
$25$	−4.99543			−0.999086
$26$	−1.92020	−	3.32589i	−0.376583	−	0.652260i
$27$	−2.52037	−	4.54398i	−0.485046	−	0.874489i
$28$	−1.19767	−	2.35915i	−0.226338	−	0.445837i
$29$	1.20840	−	0.697671i	0.224394	−	0.129554i	−0.383589	−	0.923504i	$-0.625312\pi$
$29$	1.20840	−	0.697671i	0.224394	−	0.129554i	0.607983	+	0.793950i	$0.291979\pi$
$30$	−0.115434	+	0.0196731i	−0.0210753	+	0.00359180i
$31$	1.09635	−	0.632976i	0.196910	−	0.113686i	−0.398304	−	0.917254i	$-0.630401\pi$
$31$	1.09635	−	0.632976i	0.196910	−	0.113686i	0.595213	+	0.803568i	$0.297068\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	4.34465	+	5.23840i	0.756307	+	0.911888i
$34$	−1.34292	+	0.775337i	−0.230309	+	0.132969i
$35$	0.178612	+	0.00962461i	0.0301909	+	0.00162686i
$36$	2.83065	−	0.993700i	0.471774	−	0.165617i
$37$	−4.35534	−	7.54368i	−0.716014	−	1.24017i	−0.962567	−	0.271044i	$-0.912631\pi$
$37$	−4.35534	−	7.54368i	−0.716014	−	1.24017i	0.246553	−	0.969129i	$-0.420702\pi$
$38$	5.84711			0.948527
$39$	−6.55723	+	1.11753i	−1.05000	+	0.178948i
$40$		−	0.0676069i		−	0.0106896i
$41$	5.17415	−	8.96188i	0.808066	−	1.39961i	−0.106136	−	0.994352i	$-0.533848\pi$
$41$	5.17415	−	8.96188i	0.808066	−	1.39961i	0.914202	−	0.405260i	$-0.132819\pi$
$42$	−4.55232	+	0.525707i	−0.702438	+	0.0811183i
$43$	0.735847	+	1.27452i	0.112216	+	0.194363i	0.916663	−	0.399660i	$-0.130872\pi$
$43$	0.735847	+	1.27452i	0.112216	+	0.194363i	−0.804448	+	0.594023i	$0.797539\pi$
$44$	−3.40282	+	1.96462i	−0.512995	+	0.296178i
$45$	−0.0375051	+	0.199323i	−0.00559094	+	0.0297133i
$46$	−2.76370	+	4.78687i	−0.407486	+	0.705786i
$47$	−1.77132	+	3.06802i	−0.258374	+	0.447517i	−0.965806	−	0.259264i	$-0.916520\pi$
$47$	−1.77132	+	3.06802i	−0.258374	+	0.447517i	0.707432	+	0.706781i	$0.249853\pi$
$48$	0.290993	+	1.70743i	0.0420012	+	0.246447i
$49$	6.95947	+	0.752214i	0.994209	+	0.107459i
$50$	−4.32617	−	2.49771i	−0.611813	−	0.353230i
$51$	0.451235	+	2.64767i	0.0631855	+	0.370748i
$52$		−	3.84040i		−	0.532568i
$53$	6.28910	+	3.63101i	0.863874	+	0.498758i	0.865308	−	0.501241i	$-0.167123\pi$
$53$	6.28910	+	3.63101i	0.863874	+	0.498758i	−0.00143340	+	0.999999i	$0.500456\pi$
$54$	0.0892808	−	5.19539i	0.0121496	−	0.707002i
$55$		−	0.265644i		−	0.0358194i
$56$	0.142361	−	2.64192i	0.0190238	−	0.353041i
$57$	3.51826	−	9.49673i	0.466005	−	1.25787i
$58$	1.39534			0.183217
$59$	4.70043	+	8.14138i	0.611944	+	1.05992i	0.990912	+	0.134508i	$0.0429454\pi$
$59$	4.70043	+	8.14138i	0.611944	+	1.05992i	−0.378969	+	0.925409i	$0.623721\pi$
$60$	−0.109805	−	0.0406796i	−0.0141758	−	0.00525172i
$61$	0.0705919	+	0.0407562i	0.00903836	+	0.00521830i	0.504512	−	0.863404i	$-0.331672\pi$
$61$	0.0705919	+	0.0407562i	0.00903836	+	0.00521830i	−0.495474	+	0.868623i	$0.665006\pi$
$62$	1.26595			0.160776
$63$	−1.88533	+	7.71009i	−0.237529	+	0.971380i
$64$	−1.00000			−0.125000
$65$	0.224853	+	0.129819i	0.0278896	+	0.0161020i
$66$	1.14338	+	6.70891i	0.140740	+	0.825810i
$67$	7.67257	+	13.2893i	0.937354	+	1.62354i	0.770382	+	0.637583i	$0.220066\pi$
$67$	7.67257	+	13.2893i	0.937354	+	1.62354i	0.166972	+	0.985962i	$0.446601\pi$
$68$	−1.55067			−0.188047
$69$	6.11178	+	7.36904i	0.735772	+	0.887128i
$70$	0.149870	+	0.0976411i	0.0179129	+	0.0116703i
$71$		−	4.30975i		−	0.511474i	−0.966746	−	0.255737i	$-0.917682\pi$
$71$		−	4.30975i		−	0.511474i	0.966746	−	0.255737i	$-0.0823181\pi$
$72$	2.94826	+	0.554753i	0.347456	+	0.0653783i
$73$	6.12768	+	3.53782i	0.717191	+	0.414070i	0.813718	−	0.581260i	$-0.197440\pi$
$73$	6.12768	+	3.53782i	0.717191	+	0.414070i	−0.0965271	+	0.995330i	$0.530773\pi$
$74$		−	8.71069i		−	1.01260i
$75$	−6.65982	+	5.52356i	−0.769010	+	0.637806i
$76$	5.06375	+	2.92356i	0.580852	+	0.335355i
$77$	0.559372	−	10.3807i	0.0637464	−	1.18299i
$78$	−6.23749	−	2.31080i	−0.706257	−	0.261647i
$79$	3.42320	−	5.92915i	0.385140	−	0.667082i	−0.606649	−	0.794970i	$-0.707487\pi$
$79$	3.42320	−	5.92915i	0.385140	−	0.667082i	0.991789	+	0.127888i	$0.0408199\pi$
$80$	0.0338034	−	0.0585493i	0.00377934	−	0.00654601i
$81$	−8.38450	−	3.27112i	−0.931611	−	0.363457i
$82$	8.96188	−	5.17415i	0.989675	−	0.571389i
$83$	−3.93194	−	6.81032i	−0.431587	−	0.747530i	0.565423	−	0.824801i	$-0.308713\pi$
$83$	−3.93194	−	6.81032i	−0.431587	−	0.747530i	−0.997010	+	0.0772707i	$0.975379\pi$
$84$	−4.20528	−	1.82089i	−0.458834	−	0.198675i
$85$	0.0524181	−	0.0907908i	0.00568554	−	0.00984765i
$86$			1.47169i			0.158697i
$87$	0.839589	−	2.26628i	0.0900134	−	0.242971i
$88$	−3.92924			−0.418859
$89$	−5.84745	−	10.1281i	−0.619828	−	1.07357i	−0.989517	−	0.144418i	$-0.953869\pi$
$89$	−5.84745	−	10.1281i	−0.619828	−	1.07357i	0.369688	−	0.929156i	$-0.379464\pi$
$90$	−0.132142	+	0.153866i	−0.0139290	+	0.0162189i
$91$	8.51336	+	5.54650i	0.892443	+	0.581431i
$92$	−4.78687	+	2.76370i	−0.499066	+	0.288136i
$93$	0.761734	−	2.05613i	0.0789882	−	0.213211i
$94$	−3.06802	+	1.77132i	−0.316442	+	0.182698i
$95$	−0.342344	+	0.197652i	−0.0351238	+	0.0202787i
$96$	−0.601709	+	1.62418i	−0.0614116	+	0.165767i
$97$	0.363295	−	0.209749i	0.0368870	−	0.0212967i	−0.481443	−	0.876477i	$-0.659887\pi$
$97$	0.363295	−	0.209749i	0.0368870	−	0.0212967i	0.518330	+	0.855181i	$0.326554\pi$
$98$	5.65097	+	4.13117i	0.570834	+	0.417311i
$99$	11.5844	+	2.17976i	1.16428	+	0.219074i
$100$	−2.49771	−	4.32617i	−0.249771	−	0.432617i
$101$	−17.3924			−1.73061			−0.865305	−	0.501246i	$-0.832875\pi$
$101$	−17.3924			−1.73061			−0.865305	+	0.501246i	$0.832875\pi$
$102$	−0.933054	+	2.51857i	−0.0923861	+	0.249375i
$103$		−	1.00114i		−	0.0986449i	−0.998783	−	0.0493225i	$-0.984294\pi$
$103$		−	1.00114i		−	0.0986449i	0.998783	−	0.0493225i	$-0.0157062\pi$
$104$	1.92020	−	3.32589i	0.188291	−	0.326130i
$105$	0.248764	−	0.184664i	0.0242769	−	0.0180213i
$106$	3.63101	+	6.28910i	0.352675	+	0.610851i
$107$	−8.02352	+	4.63238i	−0.775663	+	0.447829i	−0.834891	−	0.550415i	$-0.814469\pi$
$107$	−8.02352	+	4.63238i	−0.775663	+	0.447829i	0.0592279	+	0.998244i	$0.481136\pi$
$108$	2.67501	−	4.45470i	0.257403	−	0.428653i
$109$	0.821501	−	1.42288i	0.0786855	−	0.136287i	−0.823998	−	0.566593i	$-0.808261\pi$
$109$	0.821501	−	1.42288i	0.0786855	−	0.136287i	0.902683	+	0.430306i	$0.141594\pi$
$110$	0.132822	−	0.230054i	0.0126641	−	0.0219348i
$111$	−14.1477	−	5.24130i	−1.34284	−	0.497482i
$112$	1.44425	−	2.21679i	0.136469	−	0.209467i
$113$	13.6537	+	7.88296i	1.28443	+	0.741567i	0.977655	−	0.210215i	$-0.0674164\pi$
$113$	13.6537	+	7.88296i	1.28443	+	0.741567i	0.306776	+	0.951782i	$0.400750\pi$
$114$	7.79527	−	6.46528i	0.730094	−	0.605529i
$115$		−	0.373691i		−	0.0348468i
$116$	1.20840	+	0.697671i	0.112197	+	0.0647771i
$117$	−7.50631	+	8.74035i	−0.693958	+	0.808046i
$118$			9.40086i			0.865419i
$119$	2.23956	−	3.43752i	0.205300	−	0.315117i
$120$	−0.0747545	−	0.0901323i	−0.00682412	−	0.00822792i
$121$	−4.43894			−0.403540
$122$	0.0407562	+	0.0705919i	0.00368990	+	0.00639109i
$123$	−3.01128	−	17.6690i	−0.271518	−	1.59316i
$124$	1.09635	+	0.632976i	0.0984548	+	0.0568429i
$125$	0.675760			0.0604418
$126$	−5.48779	+	5.73447i	−0.488891	+	0.510867i
$127$	−19.0776			−1.69286			−0.846430	−	0.532501i	$-0.821252\pi$
$127$	−19.0776			−1.69286			−0.846430	+	0.532501i	$0.821252\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	2.39029	+	0.885531i	0.210453	+	0.0779666i
$130$	0.129819	+	0.224853i	0.0113859	+	0.0197209i
$131$	−18.6681			−1.63104			−0.815519	−	0.578731i	$-0.803548\pi$
$131$	−18.6681			−1.63104			−0.815519	+	0.578731i	$0.803548\pi$
$132$	−2.36426	+	6.38178i	−0.205782	+	0.555463i
$133$	−13.7942	+	7.00291i	−1.19611	+	0.607230i
$134$			15.3451i			1.32562i
$135$	0.170395	+	0.307204i	0.0146652	+	0.0264399i
$136$	−1.34292	−	0.775337i	−0.115155	−	0.0664846i
$137$		−	6.28537i		−	0.536995i	−0.963280	−	0.268498i	$-0.913473\pi$
$137$		−	6.28537i		−	0.536995i	0.963280	−	0.268498i	$-0.0865272\pi$
$138$	1.60843	+	9.43767i	0.136919	+	0.803387i
$139$	−5.49596	−	3.17309i	−0.466161	−	0.269138i	0.248470	−	0.968640i	$-0.420072\pi$
$139$	−5.49596	−	3.17309i	−0.466161	−	0.269138i	−0.714631	+	0.699501i	$0.753406\pi$
$140$	0.0809708	+	0.159495i	0.00684328	+	0.0134798i
$141$	1.03088	+	6.04883i	0.0868161	+	0.509403i
$142$	2.15488	−	3.73236i	0.180833	−	0.313212i
$143$	7.54494	−	13.0682i	0.630939	−	1.09282i
$144$	2.27589	+	1.95456i	0.189658	+	0.162880i
$145$	−0.0816962	+	0.0471673i	−0.00678450	+	0.00391703i
$146$	3.53782	+	6.12768i	0.292792	+	0.507130i
$147$	10.1100	−	6.69240i	0.833857	−	0.551980i
$148$	4.35534	−	7.54368i	0.358007	−	0.620087i
$149$			8.33685i			0.682981i	0.939885	+	0.341491i	$0.110932\pi$
$149$			8.33685i			0.682981i	−0.939885	+	0.341491i	$0.889068\pi$
$150$	−8.52935	+	1.45363i	−0.696419	+	0.118689i
$151$	14.1544			1.15187			0.575935	−	0.817496i	$-0.304638\pi$
$151$	14.1544			1.15187			0.575935	+	0.817496i	$0.304638\pi$
$152$	2.92356	+	5.06375i	0.237132	+	0.410724i
$153$	3.52917	+	3.03089i	0.285316	+	0.245033i
$154$	5.67480	−	8.71030i	0.457288	−	0.701896i
$155$	−0.0741205	+	0.0427935i	−0.00595350	+	0.00343726i
$156$	−4.24642	−	5.11996i	−0.339986	−	0.409925i
$157$	−14.2542	+	8.22967i	−1.13761	+	0.656799i	−0.945838	−	0.324640i	$-0.894757\pi$
$157$	−14.2542	+	8.22967i	−1.13761	+	0.656799i	−0.191772	+	0.981439i	$0.561424\pi$
$158$	5.92915	−	3.42320i	0.471698	−	0.272335i
$159$	12.3994	−	2.11320i	0.983338	−	0.167587i
$160$	0.0585493	−	0.0338034i	0.00462873	−	0.00267240i
$161$	0.786889	−	14.6030i	0.0620155	−	1.15087i
$162$	−5.62563	−	7.02512i	−0.441991	−	0.551945i
$163$	−4.53345	−	7.85216i	−0.355087	−	0.615029i	0.632046	−	0.774931i	$-0.282215\pi$
$163$	−4.53345	−	7.85216i	−0.355087	−	0.615029i	−0.987133	+	0.159902i	$0.948882\pi$
$164$	10.3483			0.808066
$165$	−0.293728	−	0.354152i	−0.0228667	−	0.0275707i
$166$		−	7.86388i		−	0.610356i
$167$	−7.64922	+	13.2488i	−0.591914	+	1.02523i	0.402060	+	0.915613i	$0.368294\pi$
$167$	−7.64922	+	13.2488i	−0.591914	+	1.02523i	−0.993974	+	0.109612i	$0.965039\pi$
$168$	−2.73144	−	3.67957i	−0.210735	−	0.283885i
$169$	0.874352	+	1.51442i	0.0672579	+	0.116494i
$170$	0.0907908	−	0.0524181i	0.00696334	−	0.00402029i
$171$	−5.81028	−	16.5511i	−0.444323	−	1.26569i
$172$	−0.735847	+	1.27452i	−0.0561078	+	0.0971815i
$173$	−1.15062	+	1.99294i	−0.0874804	+	0.151520i	−0.906445	−	0.422323i	$-0.861215\pi$
$173$	−1.15062	+	1.99294i	−0.0874804	+	0.151520i	0.818965	+	0.573843i	$0.194548\pi$
$174$	1.86025	−	1.54286i	0.141025	−	0.116964i
$175$	13.1975	+	0.711156i	0.997639	+	0.0537583i
$176$	−3.40282	−	1.96462i	−0.256497	−	0.148089i
$177$	15.2686	+	5.65658i	1.14766	+	0.425174i
$178$		−	11.6949i		−	0.876570i
$179$	13.8077	+	7.97186i	1.03203	+	0.595845i	0.917567	−	0.397582i	$-0.130151\pi$
$179$	13.8077	+	7.97186i	1.03203	+	0.595845i	0.114467	+	0.993427i	$0.463484\pi$
$180$	−0.191371	+	0.0671810i	−0.0142640	+	0.00500737i
$181$			18.4526i			1.37157i	0.727804	+	0.685785i	$0.240541\pi$
$181$			18.4526i			1.37157i	−0.727804	+	0.685785i	$0.759459\pi$
$182$	4.59954	+	9.06009i	0.340941	+	0.671578i
$183$	0.139177	−	0.0237195i	0.0102883	−	0.00175340i
$184$	−5.52740			−0.407486
$185$	0.294451	+	0.510005i	0.0216485	+	0.0374963i
$186$	1.68774	−	1.39979i	0.123751	−	0.102638i
$187$	−5.27667	−	3.04649i	−0.385868	−	0.222781i
$188$	−3.54265			−0.258374
$189$	6.01173	+	12.3636i	0.437289	+	0.899321i
$190$	−0.395305			−0.0286784
$191$	20.2162	+	11.6719i	1.46280	+	0.844546i	0.999140	−	0.0414695i	$-0.0132040\pi$
$191$	20.2162	+	11.6719i	1.46280	+	0.844546i	0.463656	+	0.886015i	$0.346537\pi$
$192$	−1.33318	+	1.10572i	−0.0962142	+	0.0797987i
$193$	−10.6439	−	18.4357i	−0.766164	−	1.32703i	−0.939629	−	0.342194i	$-0.888830\pi$
$193$	−10.6439	−	18.4357i	−0.766164	−	1.32703i	0.173466	−	0.984840i	$-0.444503\pi$
$194$	0.419497			0.0301181
$195$	0.443314	−	0.0755527i	0.0317464	−	0.00541044i
$196$	2.82830	+	6.40318i	0.202021	+	0.457370i
$197$		−	12.8467i		−	0.915288i	−0.889136	−	0.457644i	$-0.848693\pi$
$197$		−	12.8467i		−	0.915288i	0.889136	−	0.457644i	$-0.151307\pi$
$198$	8.94253	+	7.67995i	0.635518	+	0.545790i
$199$	−3.24154	−	1.87150i	−0.229787	−	0.132667i	0.380687	−	0.924704i	$-0.375688\pi$
$199$	−3.24154	−	1.87150i	−0.229787	−	0.132667i	−0.610474	+	0.792037i	$0.709021\pi$
$200$		−	4.99543i		−	0.353230i
$201$	24.9232	+	9.23331i	1.75795	+	0.651267i
$202$	−15.0623	−	8.69621i	−1.05978	−	0.611863i
$203$	−3.29182	+	1.67116i	−0.231040	+	0.117292i
$204$	−2.06733	+	1.71462i	−0.144742	+	0.120047i
$205$	−0.349808	+	0.605885i	−0.0244316	+	0.0423168i
$206$	0.500568	−	0.867010i	0.0348762	−	0.0604074i
$207$	16.2962	+	3.06635i	1.13267	+	0.213126i
$208$	3.32589	−	1.92020i	0.230609	−	0.133142i
$209$	11.4874	+	19.8967i	0.794597	+	1.37628i
$210$	0.307768	−	0.0355414i	0.0212380	−	0.00245259i
$211$	4.69581	−	8.13339i	0.323273	−	0.559925i	−0.657888	−	0.753116i	$-0.728550\pi$
$211$	4.69581	−	8.13339i	0.323273	−	0.559925i	0.981161	+	0.193190i	$0.0618834\pi$
$212$			7.26203i			0.498758i
$213$	−4.76539	−	5.74569i	−0.326519	−	0.393688i
$214$	−9.26477			−0.633326
$215$	−0.0497483	−	0.0861666i	−0.00339281	−	0.00587651i
$216$	4.54398	−	2.52037i	0.309178	−	0.171490i
$217$	−2.98657	+	1.51619i	−0.202741	+	0.102926i
$218$	1.42288	−	0.821501i	0.0963697	−	0.0556391i
$219$	12.0812	−	2.05896i	0.816369	−	0.139132i
$220$	0.230054	−	0.132822i	0.0155103	−	0.00895485i
$221$	5.15737	−	2.97761i	0.346922	−	0.200296i
$222$	−9.63161	−	11.6129i	−0.646431	−	0.779410i
$223$	17.7695	−	10.2592i	1.18993	−	0.687008i	0.231642	−	0.972801i	$-0.425590\pi$
$223$	17.7695	−	10.2592i	1.18993	−	0.687008i	0.958291	+	0.285793i	$0.0922570\pi$
$224$	2.35915	−	1.19767i	0.157627	−	0.0800227i
$225$	−2.77123	+	14.7278i	−0.184749	+	0.981856i
$226$	7.88296	+	13.6537i	0.524367	+	0.908230i
$227$	−18.7766			−1.24624			−0.623122	−	0.782124i	$-0.714136\pi$
$227$	−18.7766			−1.24624			−0.623122	+	0.782124i	$0.714136\pi$
$228$	9.98354	−	1.70147i	0.661176	−	0.112682i
$229$			4.98531i			0.329438i	0.986341	+	0.164719i	$0.0526718\pi$
$229$			4.98531i			0.329438i	−0.986341	+	0.164719i	$0.947328\pi$
$230$	0.186845	−	0.323625i	0.0123202	−	0.0213392i
$231$	−10.7325	−	14.4579i	−0.706145	−	0.951262i
$232$	0.697671	+	1.20840i	0.0458043	+	0.0793354i
$233$	−12.7747	+	7.37548i	−0.836899	+	0.483184i	−0.856209	−	0.516630i	$-0.827186\pi$
$233$	−12.7747	+	7.37548i	−0.836899	+	0.483184i	0.0193101	+	0.999814i	$0.493853\pi$
$234$	−10.8708	+	3.81621i	−0.710648	+	0.249474i
$235$	0.119754	−	0.207419i	0.00781186	−	0.0135305i
$236$	−4.70043	+	8.14138i	−0.305972	+	0.529959i
$237$	−1.99225	−	11.6897i	−0.129411	−	0.759331i
$238$	3.65827	−	1.85720i	0.237131	−	0.120384i
$239$	−0.155388	−	0.0897132i	−0.0100512	−	0.00580307i	0.494966	−	0.868912i	$-0.335181\pi$
$239$	−0.155388	−	0.0897132i	−0.0100512	−	0.00580307i	−0.505017	+	0.863109i	$0.668514\pi$
$240$	−0.0196731	−	0.115434i	−0.00126989	−	0.00745124i
$241$			6.13358i			0.395098i	0.980293	+	0.197549i	$0.0632982\pi$
$241$			6.13358i			0.395098i	−0.980293	+	0.197549i	$0.936702\pi$
$242$	−3.84424	−	2.21947i	−0.247117	−	0.142673i
$243$	−14.7950	+	4.90993i	−0.949101	+	0.314972i
$244$			0.0815124i			0.00521830i
$245$	−0.470508	−	0.0508548i	−0.0300596	−	0.00324900i
$246$	6.22666	−	16.8074i	0.396997	−	1.07160i
$247$	−22.4553			−1.42879
$248$	0.632976	+	1.09635i	0.0401940	+	0.0696181i
$249$	−12.7723	−	4.73177i	−0.809413	−	0.299864i
$250$	0.585225	+	0.337880i	0.0370129	+	0.0213694i
$251$	1.11296			0.0702495			0.0351247	−	0.999383i	$-0.488817\pi$
$251$	1.11296			0.0702495			0.0351247	+	0.999383i	$0.488817\pi$
$252$	−7.61980	+	2.22230i	−0.480002	+	0.139992i
$253$	−21.7185			−1.36543
$254$	−16.5216	−	9.53878i	−1.03666	−	0.598516i
$255$	−0.0305066	−	0.179001i	−0.00191040	−	0.0112095i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	4.74732			0.296129			0.148065	−	0.988978i	$-0.452696\pi$
$257$	4.74732			0.296129			0.148065	+	0.988978i	$0.452696\pi$
$258$	1.62729	+	1.96204i	0.101310	+	0.122151i
$259$	10.4325	+	20.5498i	0.648246	+	1.27690i
$260$			0.259638i			0.0161020i
$261$	−1.38655	−	3.94972i	−0.0858254	−	0.244481i
$262$	−16.1670	−	9.33404i	−0.998803	−	0.576659i
$263$		−	4.21634i		−	0.259991i	−0.991515	−	0.129995i	$-0.958504\pi$
$263$		−	4.21634i		−	0.259991i	0.991515	−	0.129995i	$-0.0414962\pi$
$264$	−5.23840	+	4.34465i	−0.322401	+	0.267395i
$265$	−0.425186	−	0.245482i	−0.0261190	−	0.0150798i
$266$	−15.4476	−	0.832402i	−0.947152	−	0.0510379i
$267$	−18.9946	−	7.03692i	−1.16245	−	0.430653i
$268$	−7.67257	+	13.2893i	−0.468677	+	0.811772i
$269$	−7.97265	+	13.8090i	−0.486101	+	0.841952i	−0.999872	−	0.0159753i	$-0.994915\pi$
$269$	−7.97265	+	13.8090i	−0.486101	+	0.841952i	0.513771	+	0.857927i	$0.328248\pi$
$270$	−0.00603599	+	0.351244i	−0.000367339	+	0.0213760i
$271$	14.1913	−	8.19335i	0.862060	−	0.497710i	−0.00264173	−	0.999997i	$-0.500841\pi$
$271$	14.1913	−	8.19335i	0.862060	−	0.497710i	0.864702	+	0.502286i	$0.167508\pi$
$272$	−0.775337	−	1.34292i	−0.0470117	−	0.0814267i
$273$	17.4828	−	2.01893i	1.05810	−	0.122191i
$274$	3.14269	−	5.44329i	0.189857	−	0.328841i
$275$		−	19.6283i		−	1.18363i
$276$	−3.32589	+	8.97748i	−0.200195	+	0.540381i
$277$	−1.85601			−0.111517			−0.0557583	−	0.998444i	$-0.517758\pi$
$277$	−1.85601			−0.111517			−0.0557583	+	0.998444i	$0.517758\pi$
$278$	−3.17309	−	5.49596i	−0.190309	−	0.329626i
$279$	−1.25798	−	3.58346i	−0.0753131	−	0.214536i
$280$	−0.00962461	+	0.178612i	−0.000575180	+	0.0106741i
$281$	−0.628441	+	0.362830i	−0.0374896	+	0.0216446i	−0.518628	−	0.855000i	$-0.673557\pi$
$281$	−0.628441	+	0.362830i	−0.0374896	+	0.0216446i	0.481138	+	0.876645i	$0.340224\pi$
$282$	−2.13164	+	5.75388i	−0.126937	+	0.342639i
$283$	10.0698	−	5.81382i	0.598590	−	0.345596i	−0.169897	−	0.985462i	$-0.554343\pi$
$283$	10.0698	−	5.81382i	0.598590	−	0.345596i	0.768487	+	0.639866i	$0.221010\pi$
$284$	3.73236	−	2.15488i	0.221475	−	0.127868i
$285$	−0.237858	+	0.642045i	−0.0140895	+	0.0380314i
$286$	13.0682	−	7.54494i	0.772740	−	0.446142i
$287$	−14.9455	+	22.9400i	−0.882205	+	1.35410i
$288$	0.993700	+	2.83065i	0.0585544	+	0.166797i
$289$	7.29770	+	12.6400i	0.429277	+	0.743529i
$290$	−0.0943347			−0.00553952
$291$	0.252415	−	0.681337i	0.0147968	−	0.0399407i
$292$			7.07564i			0.414070i
$293$	6.45034	−	11.1723i	0.376833	−	0.652694i	−0.613766	−	0.789488i	$-0.710346\pi$
$293$	6.45034	−	11.1723i	0.376833	−	0.652694i	0.990600	+	0.136794i	$0.0436797\pi$
$294$	12.1017	−	0.740800i	0.705786	−	0.0432043i
$295$	−0.317781	−	0.550413i	−0.0185019	−	0.0320463i
$296$	7.54368	−	4.35534i	0.438467	−	0.253149i
$297$	17.8544	−	9.90316i	1.03602	−	0.574639i
$298$	−4.16842	+	7.21992i	−0.241470	+	0.418239i
$299$	10.6137	−	18.3835i	0.613808	−	1.06315i
$300$	−8.11345	−	3.00579i	−0.468431	−	0.173540i
$301$	−1.76260	−	3.47194i	−0.101595	−	0.200120i
$302$	12.2581	+	7.07721i	0.705373	+	0.407247i
$303$	−23.1873	+	19.2312i	−1.33207	+	1.10480i
$304$			5.84711i			0.335355i
$305$	−0.00477249	−	0.00275540i	−0.000273272	−	0.000157774i
$306$	1.54091	+	4.38941i	0.0880877	+	0.250926i
$307$			20.5111i			1.17063i	0.810806	+	0.585315i	$0.199029\pi$
$307$			20.5111i			1.17063i	−0.810806	+	0.585315i	$0.800971\pi$
$308$	9.26967	−	4.70594i	0.528188	−	0.268146i
$309$	−1.10698	−	1.33470i	−0.0629739	−	0.0759283i
$310$	−0.0855870			−0.00486102
$311$	−7.51441	−	13.0153i	−0.426103	−	0.738032i	0.570420	−	0.821353i	$-0.306781\pi$
$311$	−7.51441	−	13.0153i	−0.426103	−	0.738032i	−0.996523	+	0.0833212i	$0.973447\pi$
$312$	−1.11753	−	6.55723i	−0.0632677	−	0.371230i
$313$	−0.965929	−	0.557679i	−0.0545975	−	0.0315219i	0.472453	−	0.881356i	$-0.343369\pi$
$313$	−0.965929	−	0.557679i	−0.0545975	−	0.0315219i	−0.527050	+	0.849834i	$0.676702\pi$
$314$	−16.4593			−0.928855
$315$	0.127461	−	0.521255i	0.00718164	−	0.0293694i
$316$	6.84639			0.385140
$317$	−1.06819	−	0.616719i	−0.0599955	−	0.0346384i	0.469702	−	0.882825i	$-0.344361\pi$
$317$	−1.06819	−	0.616719i	−0.0599955	−	0.0346384i	−0.529698	+	0.848187i	$0.677695\pi$
$318$	11.7948	+	4.36963i	0.661420	+	0.245036i
$319$	2.74132	+	4.74810i	0.153484	+	0.265843i
$320$	0.0676069			0.00377934
$321$	−5.57469	+	15.0476i	−0.311149	+	0.839876i
$322$	7.98294	−	12.2531i	0.444872	−	0.682838i
$323$			9.06696i			0.504499i
$324$	−1.35938	−	8.89675i	−0.0755210	−	0.494264i
$325$	16.6142	+	9.59223i	0.921592	+	0.532081i
$326$		−	9.06690i		−	0.502169i
$327$	−0.478102	−	2.80531i	−0.0264391	−	0.155134i
$328$	8.96188	+	5.17415i	0.494837	+	0.285694i
$329$	5.11646	−	7.85329i	0.282079	−	0.432966i
$330$	−0.0773004	−	0.453569i	−0.00425525	−	0.0249681i
$331$	2.51231	−	4.35145i	0.138089	−	0.239177i	−0.788684	−	0.614799i	$-0.789237\pi$
$331$	2.51231	−	4.35145i	0.138089	−	0.239177i	0.926773	+	0.375621i	$0.122571\pi$
$332$	3.93194	−	6.81032i	0.215793	−	0.373765i
$333$	−24.6569	+	8.65582i	−1.35119	+	0.474336i
$334$	−13.2488	+	7.64922i	−0.724944	+	0.418546i
$335$	−0.518719	−	0.898447i	−0.0283406	−	0.0490874i
$336$	−0.525707	−	4.55232i	−0.0286797	−	0.248350i
$337$	10.6356	−	18.4213i	0.579356	−	1.00347i	−0.416198	−	0.909274i	$-0.636638\pi$
$337$	10.6356	−	18.4213i	0.579356	−	1.00347i	0.995553	−	0.0941995i	$-0.0300292\pi$
$338$			1.74870i			0.0951170i
$339$	26.9192	−	4.58777i	1.46205	−	0.249173i
$340$	0.104836			0.00568554
$341$	2.48712	+	4.30781i	0.134685	+	0.233281i
$342$	3.24370	−	17.2388i	0.175399	−	0.932168i
$343$	−18.2793	−	2.97805i	−0.986987	−	0.160799i
$344$	−1.27452	+	0.735847i	−0.0687177	+	0.0396742i
$345$	−0.413198	−	0.498198i	−0.0222458	−	0.0268221i
$346$	−1.99294	+	1.15062i	−0.107141	+	0.0618580i
$347$	−18.6832	+	10.7868i	−1.00297	+	0.579063i	−0.909125	−	0.416524i	$-0.863248\pi$
$347$	−18.6832	+	10.7868i	−1.00297	+	0.579063i	−0.0938425	+	0.995587i	$0.529915\pi$
$348$	2.38245	−	0.406034i	0.127713	−	0.0217657i
$349$	24.1105	−	13.9202i	1.29061	−	0.745132i	0.311845	−	0.950133i	$-0.399053\pi$
$349$	24.1105	−	13.9202i	1.29061	−	0.745132i	0.978762	+	0.205001i	$0.0657198\pi$
$350$	11.0738	+	7.21464i	0.591920	+	0.385639i
$351$	−0.342874	+	19.9524i	−0.0183013	+	1.06498i
$352$	−1.96462	−	3.40282i	−0.104715	−	0.181371i
$353$	5.70249			0.303513			0.151756	−	0.988418i	$-0.451507\pi$
$353$	5.70249			0.303513			0.151756	+	0.988418i	$0.451507\pi$
$354$	10.3947	+	12.5331i	0.552474	+	0.666125i
$355$			0.291369i			0.0154643i
$356$	5.84745	−	10.1281i	0.309914	−	0.536787i
$357$	−0.815200	−	7.05917i	−0.0431450	−	0.373611i
$358$	7.97186	+	13.8077i	0.421326	+	0.729758i
$359$	18.5815	−	10.7280i	0.980693	−	0.566203i	0.0782137	−	0.996937i	$-0.475078\pi$
$359$	18.5815	−	10.7280i	0.980693	−	0.566203i	0.902479	+	0.430733i	$0.141745\pi$
$360$	−0.199323	−	0.0375051i	−0.0105052	−	0.00197669i
$361$	7.59435	−	13.1538i	0.399703	−	0.692305i
$362$	−9.22629	+	15.9804i	−0.484923	+	0.839911i
$363$	−5.91792	+	4.90824i	−0.310610	+	0.257616i
$364$	−0.546725	+	10.1460i	−0.0286562	+	0.531797i
$365$	−0.414273	−	0.239181i	−0.0216841	−	0.0125193i
$366$	0.132391	+	0.0490468i	0.00692016	+	0.00256372i
$367$		−	9.20855i		−	0.480682i	−0.970688	−	0.240341i	$-0.922741\pi$
$367$		−	9.20855i		−	0.480682i	0.970688	−	0.240341i	$-0.0772593\pi$
$368$	−4.78687	−	2.76370i	−0.249533	−	0.144068i
$369$	−23.5516	−	20.2264i	−1.22605	−	1.05294i
$370$			0.588903i			0.0306156i
$371$	−16.0984	−	10.4882i	−0.835786	−	0.544519i
$372$	2.16153	−	0.368383i	0.112070	−	0.0190998i
$373$	28.2000			1.46014			0.730071	−	0.683371i	$-0.239487\pi$
$373$	28.2000			1.46014			0.730071	+	0.683371i	$0.239487\pi$
$374$	−3.04649	−	5.27667i	−0.157530	−	0.272850i
$375$	0.900911	−	0.747203i	0.0465229	−	0.0385854i
$376$	−3.06802	−	1.77132i	−0.158221	−	0.0913490i
$377$	−5.35867			−0.275986
$378$	−0.975495	+	13.7131i	−0.0501740	+	0.705324i
$379$	−4.72569			−0.242742			−0.121371	−	0.992607i	$-0.538729\pi$
$379$	−4.72569			−0.242742			−0.121371	+	0.992607i	$0.538729\pi$
$380$	−0.342344	−	0.197652i	−0.0175619	−	0.0101394i
$381$	−25.4339	+	21.0945i	−1.30302	+	1.08070i
$382$	11.6719	+	20.2162i	0.597184	+	1.03435i
$383$	34.2349			1.74932			0.874660	−	0.484737i	$-0.161085\pi$
$383$	34.2349			1.74932			0.874660	+	0.484737i	$0.161085\pi$
$384$	−1.70743	+	0.290993i	−0.0871320	+	0.0148497i
$385$	−0.0378174	+	0.701809i	−0.00192735	+	0.0357675i
$386$		−	21.2878i		−	1.08352i
$387$	4.16584	−	1.46242i	0.211762	−	0.0743391i
$388$	0.363295	+	0.209749i	0.0184435	+	0.0106484i
$389$			18.4945i			0.937710i	0.883275	+	0.468855i	$0.155333\pi$
$389$			18.4945i			0.937710i	−0.883275	+	0.468855i	$0.844667\pi$
$390$	0.421697	+	0.156226i	0.0213535	+	0.00791083i
$391$	−7.42288	−	4.28560i	−0.375391	−	0.216732i
$392$	−0.752214	+	6.95947i	−0.0379926	+	0.351506i
$393$	−24.8880	+	20.6417i	−1.25543	+	1.04124i
$394$	6.42334	−	11.1255i	0.323603	−	0.560497i
$395$	−0.231432	+	0.400851i	−0.0116446	+	0.0201690i
$396$	3.90449	+	11.1223i	0.196208	+	0.558916i
$397$	−1.76126	+	1.01687i	−0.0883952	+	0.0510350i	−0.543546	−	0.839379i	$-0.682919\pi$
$397$	−1.76126	+	1.01687i	−0.0883952	+	0.0510350i	0.455151	+	0.890414i	$0.349585\pi$
$398$	−1.87150	−	3.24154i	−0.0938100	−	0.162484i
$399$	−10.6469	+	24.5887i	−0.533013	+	1.23098i
$400$	2.49771	−	4.32617i	0.124886	−	0.216308i
$401$		−	31.4236i		−	1.56922i	−0.619989	−	0.784611i	$-0.712863\pi$
$401$		−	31.4236i		−	1.56922i	0.619989	−	0.784611i	$-0.287137\pi$
$402$	16.9675	+	20.4579i	0.846261	+	1.02035i
$403$	−4.86177			−0.242182
$404$	−8.69621	−	15.0623i	−0.432653	−	0.749376i
$405$	0.566850	+	0.221150i	0.0281670	+	0.0109890i
$406$	−3.68638	−	0.198643i	−0.182952	−	0.00985847i
$407$	29.6409	−	17.1132i	1.46925	−	0.848270i
$408$	−2.64767	+	0.451235i	−0.131079	+	0.0223395i
$409$	−0.476819	+	0.275292i	−0.0235772	+	0.0136123i	−0.511742	−	0.859139i	$-0.671000\pi$
$409$	−0.476819	+	0.275292i	−0.0235772	+	0.0136123i	0.488165	+	0.872751i	$0.337666\pi$
$410$	−0.605885	+	0.349808i	−0.0299225	+	0.0172758i
$411$	−6.94988	−	8.37955i	−0.342812	−	0.413333i
$412$	0.867010	−	0.500568i	0.0427145	−	0.0246612i
$413$	−11.2591	−	22.1780i	−0.554026	−	1.09131i
$414$	12.5798	+	10.8037i	0.618262	+	0.530970i
$415$	0.265826	+	0.460425i	0.0130489	+	0.0226014i
$416$	3.84040			0.188291
$417$	−10.8357	+	1.84669i	−0.530625	+	0.0904330i
$418$			22.9747i			1.12373i
$419$	−11.5649	+	20.0310i	−0.564984	+	0.978580i	0.432068	+	0.901841i	$0.357784\pi$
$419$	−11.5649	+	20.0310i	−0.564984	+	0.978580i	−0.997051	+	0.0767392i	$0.975549\pi$
$420$	0.284306	+	0.123104i	0.0138727	+	0.00600688i
$421$	5.49773	+	9.52235i	0.267943	+	0.464091i	0.968330	−	0.249672i	$-0.0803228\pi$
$421$	5.49773	+	9.52235i	0.267943	+	0.464091i	−0.700387	+	0.713763i	$0.746989\pi$
$422$	8.13339	−	4.69581i	0.395927	−	0.228589i
$423$	8.06268	+	6.92432i	0.392021	+	0.336672i
$424$	−3.63101	+	6.28910i	−0.176338	+	0.305426i
$425$	3.87314	−	6.70848i	0.187875	−	0.325409i
$426$	−1.25411	−	7.35861i	−0.0607617	−	0.356526i
$427$	−0.180696	−	0.117724i	−0.00874448	−	0.00569707i
$428$	−8.02352	−	4.63238i	−0.387832	−	0.223915i
$429$	−4.39104	−	25.7649i	−0.212002	−	1.24394i
$430$		−	0.0994966i		−	0.00479815i
$431$	7.19720	+	4.15530i	0.346677	+	0.200154i	0.663221	−	0.748424i	$-0.269189\pi$
$431$	7.19720	+	4.15530i	0.346677	+	0.200154i	−0.316544	+	0.948578i	$0.602522\pi$
$432$	5.19539	+	0.0892808i	0.249963	+	0.00429552i
$433$		−	26.1051i		−	1.25453i	−0.778806	−	0.627265i	$-0.784174\pi$
$433$		−	26.1051i		−	1.25453i	0.778806	−	0.627265i	$-0.215826\pi$
$434$	−3.34454	−	0.180223i	−0.160543	−	0.00865096i
$435$	−0.0567620	+	0.153216i	−0.00272153	+	0.00734615i
$436$	1.64300			0.0786855
$437$	16.1597	+	27.9894i	0.773022	+	1.33891i
$438$	11.4921	+	4.25747i	0.549113	+	0.203430i
$439$	−35.3605	−	20.4154i	−1.68766	−	0.974373i	−0.956301	−	0.292383i	$-0.905552\pi$
$439$	−35.3605	−	20.4154i	−1.68766	−	0.974373i	−0.731362	−	0.681990i	$-0.761115\pi$
$440$	0.265644			0.0126641
$441$	6.07851	−	20.1010i	0.289453	−	0.957192i
$442$	5.95522			0.283261
$443$	−15.8106	−	9.12824i	−0.751183	−	0.433696i	0.0749382	−	0.997188i	$-0.476124\pi$
$443$	−15.8106	−	9.12824i	−0.751183	−	0.433696i	−0.826121	+	0.563492i	$0.809457\pi$
$444$	−2.53475	−	14.8729i	−0.120294	−	0.705837i
$445$	0.395328	+	0.684728i	0.0187403	+	0.0324592i
$446$	20.5184			0.971576
$447$	9.21824	+	11.1145i	0.436008	+	0.525700i
$448$	2.64192	+	0.142361i	0.124819	+	0.00672594i
$449$			26.0881i			1.23117i	0.788070	+	0.615586i	$0.211081\pi$
$449$			26.0881i			1.23117i	−0.788070	+	0.615586i	$0.788919\pi$
$450$	−9.76387	+	11.3691i	−0.460273	+	0.535943i
$451$	35.2134	+	20.3305i	1.65813	+	0.957325i
$452$			15.7659i			0.741567i
$453$	18.8704	−	15.6509i	0.886610	−	0.735341i
$454$	−16.2610	−	9.38828i	−0.763166	−	0.440614i
$455$	−0.575562	−	0.374981i	−0.0269828	−	0.0175794i
$456$	9.49673	+	3.51826i	0.444725	+	0.164758i
$457$	3.19987	−	5.54233i	0.149683	−	0.259259i	−0.781427	−	0.623997i	$-0.785508\pi$
$457$	3.19987	−	5.54233i	0.149683	−	0.259259i	0.931110	+	0.364737i	$0.118841\pi$
$458$	−2.49265	+	4.31740i	−0.116474	+	0.201739i
$459$	8.05635	+	0.138445i	0.376038	+	0.00646208i
$460$	0.323625	−	0.186845i	0.0150891	−	0.00871170i
$461$	−1.04099	−	1.80304i	−0.0484836	−	0.0839761i	0.840765	−	0.541400i	$-0.182106\pi$
$461$	−1.04099	−	1.80304i	−0.0484836	−	0.0839761i	−0.889249	+	0.457424i	$0.848772\pi$
$462$	−2.06563	−	17.8872i	−0.0961018	−	0.832187i
$463$	−0.959084	+	1.66118i	−0.0445724	+	0.0772017i	−0.887451	−	0.460902i	$-0.847526\pi$
$463$	−0.959084	+	1.66118i	−0.0445724	+	0.0772017i	0.842879	+	0.538104i	$0.180859\pi$
$464$			1.39534i			0.0647771i
$465$	−0.0514985	+	0.139008i	−0.00238818	+	0.00644636i
$466$	−14.7510			−0.683325
$467$	17.1178	+	29.6488i	0.792116	+	1.37199i	0.924654	+	0.380807i	$0.124354\pi$
$467$	17.1178	+	29.6488i	0.792116	+	1.37199i	−0.132539	+	0.991178i	$0.542313\pi$
$468$	−11.3225	−	2.13048i	−0.523384	−	0.0984813i
$469$	−18.3784	−	36.2015i	−0.848637	−	1.67163i
$470$	0.207419	−	0.119754i	0.00956754	−	0.00552382i
$471$	−9.90373	+	26.7329i	−0.456340	+	1.23179i
$472$	−8.14138	+	4.70043i	−0.374737	+	0.216355i
$473$	−5.00791	+	2.89132i	−0.230264	+	0.132943i
$474$	4.11954	−	11.1197i	0.189217	−	0.510747i
$475$	−25.2956	+	14.6044i	−1.16064	+	0.670096i
$476$	4.09675	+	0.220756i	0.187774	+	0.0101183i
$477$	14.1941	−	16.5276i	0.649902	−	0.756747i
$478$	−0.0897132	−	0.155388i	−0.00410339	−	0.00710728i
$479$	10.5825			0.483525			0.241763	−	0.970335i	$-0.422274\pi$
$479$	10.5825			0.483525			0.241763	+	0.970335i	$0.422274\pi$
$480$	0.0406796	−	0.109805i	0.00185676	−	0.00501191i
$481$			33.4526i			1.52531i
$482$	−3.06679	+	5.31183i	−0.139688	+	0.241947i
$483$	−15.0978	−	20.3385i	−0.686972	−	0.925433i
$484$	−2.21947	−	3.84424i	−0.100885	−	0.174738i
$485$	−0.0245613	+	0.0141804i	−0.00111527	+	0.000643901i
$486$	−15.2678	−	3.14538i	−0.692563	−	0.142677i
$487$	5.95804	−	10.3196i	0.269985	−	0.467627i	−0.698873	−	0.715246i	$-0.746315\pi$
$487$	5.95804	−	10.3196i	0.269985	−	0.467627i	0.968858	+	0.247619i	$0.0796481\pi$
$488$	−0.0407562	+	0.0705919i	−0.00184495	+	0.00319554i
$489$	−14.7262	−	5.45563i	−0.665943	−	0.246712i
$490$	−0.382044	−	0.279295i	−0.0172590	−	0.0126173i
$491$	−14.9826	−	8.65023i	−0.676157	−	0.390379i	0.122248	−	0.992500i	$-0.460990\pi$
$491$	−14.9826	−	8.65023i	−0.676157	−	0.390379i	−0.798406	+	0.602120i	$0.794323\pi$
$492$	13.7962	−	11.4423i	0.621979	−	0.515861i
$493$			2.16372i			0.0974490i
$494$	−19.4468	−	11.2276i	−0.874954	−	0.505155i
$495$	−0.783187	−	0.147367i	−0.0352017	−	0.00662364i
$496$			1.26595i			0.0568429i
$497$	−0.613542	+	11.3860i	−0.0275211	+	0.510733i
$498$	−8.69528	−	10.4840i	−0.389645	−	0.469799i
$499$	−12.8297			−0.574335			−0.287168	−	0.957880i	$-0.592714\pi$
$499$	−12.8297			−0.574335			−0.287168	+	0.957880i	$0.592714\pi$
$500$	0.337880	+	0.585225i	0.0151104	+	0.0261721i
$501$	4.45173	+	26.1210i	0.198889	+	1.16700i
$502$	0.963852	+	0.556480i	0.0430188	+	0.0248369i
$503$	10.9868			0.489878			0.244939	−	0.969539i	$-0.421232\pi$
$503$	10.9868			0.489878			0.244939	+	0.969539i	$0.421232\pi$
$504$	−7.71009	−	1.88533i	−0.343435	−	0.0839794i
$505$	1.17585			0.0523245
$506$	−18.8088	−	10.8593i	−0.836152	−	0.482753i
$507$	2.84020	+	1.05221i	0.126138	+	0.0467303i
$508$	−9.53878	−	16.5216i	−0.423215	−	0.733030i
$509$	−28.9677			−1.28397			−0.641985	−	0.766717i	$-0.721889\pi$
$509$	−28.9677			−1.28397			−0.641985	+	0.766717i	$0.721889\pi$
$510$	0.0630809	−	0.170272i	0.00279327	−	0.00753979i
$511$	−15.6852	−	10.2190i	−0.693872	−	0.452061i
$512$		−	1.00000i		−	0.0441942i
$513$	−26.0471	−	15.6411i	−1.15001	−	0.690571i
$514$	4.11130	+	2.37366i	0.181342	+	0.104698i
$515$			0.0676837i			0.00298250i
$516$	0.428252	+	2.51282i	0.0188527	+	0.110621i
$517$	−12.0550	−	6.95996i	−0.530178	−	0.306099i
$518$	−1.24007	+	23.0129i	−0.0544854	+	1.01113i
$519$	0.669647	+	3.92923i	0.0293942	+	0.172474i
$520$	−0.129819	+	0.224853i	−0.00569293	+	0.00986045i
$521$	5.72133	−	9.90963i	0.250656	−	0.434149i	−0.713051	−	0.701113i	$-0.752687\pi$
$521$	5.72133	−	9.90963i	0.250656	−	0.434149i	0.963707	+	0.266964i	$0.0860204\pi$
$522$	0.774070	−	4.11383i	0.0338801	−	0.180058i
$523$	14.1536	−	8.17161i	0.618896	−	0.357320i	−0.157543	−	0.987512i	$-0.550357\pi$
$523$	14.1536	−	8.17161i	0.618896	−	0.357320i	0.776439	+	0.630192i	$0.217024\pi$
$524$	−9.33404	−	16.1670i	−0.407759	−	0.706260i
$525$	18.3810	−	13.6447i	0.802215	−	0.595503i
$526$	2.10817	−	3.65146i	0.0919206	−	0.159211i
$527$			1.96308i			0.0855130i
$528$	−6.70891	+	1.14338i	−0.291968	+	0.0497593i
$529$	−7.55220			−0.328356
$530$	−0.245482	−	0.425186i	−0.0106630	−	0.0184689i
$531$	26.6105	−	9.34164i	1.15480	−	0.405392i
$532$	−12.9618	−	8.44468i	−0.561965	−	0.366123i
$533$	−34.4173	+	19.8708i	−1.49078	+	0.860700i
$534$	−12.9313	−	15.5914i	−0.559593	−	0.674708i
$535$	0.542445	−	0.313181i	0.0234520	−	0.0135400i
$536$	−13.2893	+	7.67257i	−0.574010	+	0.331405i
$537$	27.2228	−	4.63951i	1.17475	−	0.200210i
$538$	−13.8090	+	7.97265i	−0.595350	+	0.343725i
$539$	−2.95563	+	27.3454i	−0.127308	+	1.17785i
$540$	−0.180849	+	0.301168i	−0.00778251	+	0.0129602i
$541$	15.9752	+	27.6699i	0.686830	+	1.18962i	0.972858	+	0.231403i	$0.0743314\pi$
$541$	15.9752	+	27.6699i	0.686830	+	1.18962i	−0.286029	+	0.958221i	$0.592335\pi$
$542$	16.3867			0.703869
$543$	20.4034	+	24.6007i	0.875595	+	1.05572i
$544$		−	1.55067i		−	0.0664846i
$545$	−0.0555391	+	0.0961966i	−0.00237903	+	0.00412061i
$546$	16.1500	+	6.99294i	0.691155	+	0.299270i
$547$	15.4351	+	26.7344i	0.659958	+	1.14308i	0.980626	+	0.195889i	$0.0627591\pi$
$547$	15.4351	+	26.7344i	0.659958	+	1.14308i	−0.320668	+	0.947192i	$0.603908\pi$
$548$	5.44329	−	3.14269i	0.232526	−	0.134249i
$549$	0.159321	−	0.185514i	0.00679966	−	0.00791753i
$550$	9.81413	−	16.9986i	0.418476	−	0.724821i
$551$	4.07936	−	7.06565i	0.173786	−	0.301007i
$552$	−7.36904	+	6.11178i	−0.313647	+	0.260135i
$553$	−9.88789	+	15.1770i	−0.420476	+	0.645392i
$554$	−1.60735	−	0.928004i	−0.0682897	−	0.0394271i
$555$	0.956481	+	0.354348i	0.0406004	+	0.0150412i
$556$		−	6.34619i		−	0.269138i
$557$	−12.2398	−	7.06667i	−0.518618	−	0.299424i	0.217751	−	0.976004i	$-0.430128\pi$
$557$	−12.2398	−	7.06667i	−0.518618	−	0.299424i	−0.736369	+	0.676580i	$0.763461\pi$
$558$	0.702291	−	3.73236i	0.0297303	−	0.158003i
$559$		−	5.65190i		−	0.239050i
$560$	−0.0976411	+	0.149870i	−0.00412609	+	0.00633317i
$561$	−10.4033	+	1.77301i	−0.439229	+	0.0748566i
$562$	−0.725661			−0.0306102
$563$	−2.55718	−	4.42916i	−0.107772	−	0.186667i	0.807095	−	0.590421i	$-0.201038\pi$
$563$	−2.55718	−	4.42916i	−0.107772	−	0.186667i	−0.914867	+	0.403754i	$0.867705\pi$
$564$	−4.72299	+	3.91718i	−0.198874	+	0.164943i
$565$	−0.923083	−	0.532942i	−0.0388344	−	0.0224211i
$566$	11.6276			0.488746
$567$	21.6855	+	9.83565i	0.910704	+	0.413059i
$568$	4.30975			0.180833
$569$	32.2337	+	18.6101i	1.35131	+	0.780177i	0.988433	−	0.151661i	$-0.0484623\pi$
$569$	32.2337	+	18.6101i	1.35131	+	0.780177i	0.362874	+	0.931838i	$0.381796\pi$
$570$	−0.527014	+	0.437098i	−0.0220742	+	0.0183080i
$571$	−2.63869	−	4.57035i	−0.110426	−	0.191263i	0.805516	−	0.592574i	$-0.201888\pi$
$571$	−2.63869	−	4.57035i	−0.110426	−	0.191263i	−0.915942	+	0.401311i	$0.868555\pi$
$572$	15.0899			0.630939
$573$	39.8578	−	6.79285i	1.66508	−	0.283775i
$574$	−24.4132	+	12.3938i	−1.01899	+	0.517309i
$575$		−	27.6118i		−	1.15149i
$576$	−0.554753	+	2.94826i	−0.0231147	+	0.122844i
$577$	−9.72172	−	5.61284i	−0.404721	−	0.233666i	0.283798	−	0.958884i	$-0.408405\pi$
$577$	−9.72172	−	5.61284i	−0.404721	−	0.233666i	−0.688519	+	0.725218i	$0.741739\pi$
$578$			14.5954i			0.607089i
$579$	−34.5751	−	12.8090i	−1.43689	−	0.532325i
$580$	−0.0816962	−	0.0471673i	−0.00339225	−	0.00195852i
$581$	9.41834	+	18.5521i	0.390739	+	0.769670i
$582$	0.559267	−	0.463848i	0.0231823	−	0.0192271i
$583$	−14.2671	+	24.7114i	−0.590884	+	1.02344i
$584$	−3.53782	+	6.12768i	−0.146396	+	0.253565i
$585$	0.507478	−	0.590908i	0.0209816	−	0.0244310i
$586$	11.1723	−	6.45034i	0.461524	−	0.266461i
$587$	−12.4037	−	21.4838i	−0.511955	−	0.886732i	−0.999904	−	0.0138602i	$-0.995588\pi$
$587$	−12.4037	−	21.4838i	−0.511955	−	0.886732i	0.487949	−	0.872872i	$-0.337745\pi$
$588$	10.8508	+	5.40930i	0.447479	+	0.223076i
$589$	3.70108	−	6.41046i	0.152500	−	0.264138i
$590$		−	0.635563i		−	0.0261657i
$591$	−14.2049	−	17.1270i	−0.584310	−	0.704509i
$592$	8.71069			0.358007
$593$	6.47382	+	11.2130i	0.265848	+	0.460462i	0.967785	−	0.251777i	$-0.0810148\pi$
$593$	6.47382	+	11.2130i	0.265848	+	0.460462i	−0.701938	+	0.712238i	$0.747681\pi$
$594$	20.4139	+	0.350806i	0.837594	+	0.0143937i
$595$	−0.151410	+	0.232400i	−0.00620718	+	0.00952746i
$596$	−7.21992	+	4.16842i	−0.295739	+	0.170745i
$597$	−6.39093	+	1.08919i	−0.261563	+	0.0445775i
$598$	18.3835	−	10.6137i	0.751758	−	0.434028i
$599$	−20.9209	+	12.0787i	−0.854804	+	0.493522i	−0.862269	−	0.506451i	$-0.830957\pi$
$599$	−20.9209	+	12.0787i	−0.854804	+	0.493522i	0.00746462	+	0.999972i	$0.497624\pi$
$600$	−5.52356	−	6.65982i	−0.225498	−	0.271886i
$601$	15.3377	−	8.85525i	0.625640	−	0.361213i	−0.153422	−	0.988161i	$-0.549029\pi$
$601$	15.3377	−	8.85525i	0.625640	−	0.361213i	0.779061	+	0.626948i	$0.215696\pi$
$602$	0.209512	−	3.88809i	0.00853908	−	0.158467i
$603$	43.4367	−	15.2485i	1.76888	−	0.620966i
$604$	7.07721	+	12.2581i	0.287967	+	0.498774i
$605$	0.300103			0.0122009
$606$	−29.6964	+	5.06107i	−1.20633	+	0.205592i
$607$			6.08758i			0.247087i	0.992339	+	0.123544i	$0.0394259\pi$
$607$			6.08758i			0.247087i	−0.992339	+	0.123544i	$0.960574\pi$
$608$	−2.92356	+	5.06375i	−0.118566	+	0.205362i
$609$	−2.54076	+	5.86780i	−0.102957	+	0.237775i
$610$	−0.00275540	−	0.00477249i	−0.000111563	−	0.000193233i
$611$	11.7824	−	6.80260i	0.476667	−	0.275204i
$612$	−0.860242	+	4.57179i	−0.0347732	+	0.184804i
$613$	16.5026	−	28.5834i	0.666535	−	1.15447i	−0.312332	−	0.949973i	$-0.601110\pi$
$613$	16.5026	−	28.5834i	0.666535	−	1.15447i	0.978867	−	0.204499i	$-0.0655566\pi$
$614$	−10.2555	+	17.7631i	−0.413880	+	0.716861i
$615$	0.203583	+	1.19455i	0.00820926	+	0.0481687i
$616$	10.3807	+	0.559372i	0.418252	+	0.0225377i
$617$	−8.36942	−	4.83209i	−0.336940	−	0.194533i	0.321978	−	0.946747i	$-0.395652\pi$
$617$	−8.36942	−	4.83209i	−0.336940	−	0.194533i	−0.658918	+	0.752215i	$0.728986\pi$
$618$	−0.291323	−	1.70937i	−0.0117187	−	0.0687610i
$619$			18.1007i			0.727528i	0.931491	+	0.363764i	$0.118508\pi$
$619$			18.1007i			0.727528i	−0.931491	+	0.363764i	$0.881492\pi$
$620$	−0.0741205	−	0.0427935i	−0.00297675	−	0.00171863i
$621$	25.1164	−	13.9311i	1.00789	−	0.559037i
$622$		−	15.0288i		−	0.602601i
$623$	14.0066	+	27.5900i	0.561164	+	1.10537i
$624$	2.31080	−	6.23749i	0.0925062	−	0.249699i
$625$	24.9315			0.997258
$626$	−0.557679	−	0.965929i	−0.0222893	−	0.0386063i
$627$	37.3150	+	13.8241i	1.49022	+	0.552081i
$628$	−14.2542	−	8.22967i	−0.568805	−	0.328400i
$629$	13.5074			0.538577
$630$	0.371012	−	0.387690i	0.0147815	−	0.0154459i
$631$	−5.07079			−0.201865			−0.100932	−	0.994893i	$-0.532183\pi$
$631$	−5.07079			−0.201865			−0.100932	+	0.994893i	$0.532183\pi$
$632$	5.92915	+	3.42320i	0.235849	+	0.136167i
$633$	−2.73289	−	16.0356i	−0.108623	−	0.637356i
$634$	−0.616719	−	1.06819i	−0.0244931	−	0.0424232i
$635$	1.28977			0.0511831
$636$	8.02979	+	9.68161i	0.318402	+	0.383901i
$637$	−21.7020	−	15.8654i	−0.859865	−	0.628609i
$638$			5.48263i			0.217060i
$639$	−12.7063	−	2.39085i	−0.502653	−	0.0945806i
$640$	0.0585493	+	0.0338034i	0.00231436	+	0.00133620i
$641$			8.80698i			0.347855i	0.984758	+	0.173927i	$0.0556458\pi$
$641$			8.80698i			0.347855i	−0.984758	+	0.173927i	$0.944354\pi$
$642$	−12.3516	+	10.2443i	−0.487480	+	0.404309i
$643$	2.52364	+	1.45702i	0.0995227	+	0.0574594i	0.548935	−	0.835865i	$-0.315033\pi$
$643$	2.52364	+	1.45702i	0.0995227	+	0.0574594i	−0.449413	+	0.893324i	$0.648367\pi$
$644$	13.0400	−	6.62001i	0.513847	−	0.260865i
$645$	−0.161600	−	0.0598680i	−0.00636299	−	0.00235730i
$646$	−4.53348	+	7.85222i	−0.178367	+	0.308941i
$647$	5.15173	−	8.92306i	0.202535	−	0.350802i	−0.746809	−	0.665038i	$-0.768415\pi$
$647$	5.15173	−	8.92306i	0.202535	−	0.350802i	0.949345	+	0.314237i	$0.101749\pi$
$648$	3.27112	−	8.38450i	0.128502	−	0.329374i
$649$	−31.9895	+	18.4691i	−1.25570	+	0.724976i
$650$	9.59223	+	16.6142i	0.376238	+	0.651664i
$651$	−2.30515	+	5.32368i	−0.0903461	+	0.208651i
$652$	4.53345	−	7.85216i	0.177544	−	0.307515i
$653$			17.7439i			0.694371i	0.937796	+	0.347186i	$0.112863\pi$
$653$			17.7439i			0.694371i	−0.937796	+	0.347186i	$0.887137\pi$
$654$	0.988609	−	2.66852i	0.0386577	−	0.104348i
$655$	1.26209			0.0493140
$656$	5.17415	+	8.96188i	0.202016	+	0.349903i
$657$	13.8298	−	16.1034i	0.539550	−	0.628253i
$658$	8.35763	−	4.24292i	0.325814	−	0.165406i
$659$	−4.08467	+	2.35828i	−0.159116	+	0.0918657i	−0.577444	−	0.816430i	$-0.695950\pi$
$659$	−4.08467	+	2.35828i	−0.159116	+	0.0918657i	0.418328	+	0.908296i	$0.362616\pi$
$660$	0.159840	−	0.431452i	0.00622177	−	0.0167943i
$661$	8.16557	−	4.71439i	0.317604	−	0.183369i	−0.332720	−	0.943026i	$-0.607966\pi$
$661$	8.16557	−	4.71439i	0.317604	−	0.183369i	0.650324	+	0.759657i	$0.274633\pi$
$662$	4.35145	−	2.51231i	0.169124	−	0.0976438i
$663$	3.58331	−	9.67232i	0.139164	−	0.375642i
$664$	6.81032	−	3.93194i	0.264292	−	0.152589i
$665$	0.932583	−	0.473445i	0.0361640	−	0.0183594i
$666$	−25.6814	−	4.83228i	−0.995134	−	0.187247i
$667$	3.85631	+	6.67932i	0.149317	+	0.258624i
$668$	−15.2984			−0.591914
$669$	12.3461	−	33.3255i	0.477329	−	1.28844i
$670$		−	1.03744i		−	0.0400797i
$671$	−0.160141	+	0.277372i	−0.00618218	+	0.0107078i
$672$	1.82089	−	4.20528i	0.0702422	−	0.162222i
$673$	−6.42728	−	11.1324i	−0.247753	−	0.429122i	0.715149	−	0.698972i	$-0.246359\pi$
$673$	−6.42728	−	11.1324i	−0.247753	−	0.429122i	−0.962902	+	0.269851i	$0.913026\pi$
$674$	18.4213	−	10.6356i	0.709563	−	0.409666i
$675$	12.5903	+	22.6991i	0.484603	+	0.873689i
$676$	−0.874352	+	1.51442i	−0.0336289	+	0.0582470i
$677$	24.5946	−	42.5991i	0.945248	−	1.63722i	0.189995	−	0.981785i	$-0.439153\pi$
$677$	24.5946	−	42.5991i	0.945248	−	1.63722i	0.755253	−	0.655433i	$-0.227514\pi$
$678$	25.6066	+	9.48649i	0.983417	+	0.364327i
$679$	−0.989657	+	0.502420i	−0.0379795	+	0.0192811i
$680$	0.0907908	+	0.0524181i	0.00348167	+	0.00201014i
$681$	−25.0326	+	20.7617i	−0.959251	+	0.795589i
$682$			4.97423i			0.190473i
$683$	−36.2732	−	20.9424i	−1.38796	−	0.801337i	−0.394872	−	0.918736i	$-0.629211\pi$
$683$	−36.2732	−	20.9424i	−1.38796	−	0.801337i	−0.993085	+	0.117399i	$0.962544\pi$
$684$	11.4285	−	13.3074i	0.436981	−	0.508821i
$685$			0.424934i			0.0162359i
$686$	−14.3413	−	11.7187i	−0.547553	−	0.447422i
$687$	5.51237	+	6.64633i	0.210310	+	0.253573i
$688$	−1.47169			−0.0561078
$689$	−13.9446	−	24.1527i	−0.531245	−	0.920144i
$690$	−0.108741	−	0.638051i	−0.00413971	−	0.0242902i
$691$	−5.56780	−	3.21457i	−0.211809	−	0.122288i	0.390343	−	0.920670i	$-0.372356\pi$
$691$	−5.56780	−	3.21457i	−0.211809	−	0.122288i	−0.602152	+	0.798382i	$0.705690\pi$
$692$	−2.30125			−0.0874804
$693$	−30.2948	−	7.40793i	−1.15081	−	0.281404i
$694$	−21.5735			−0.818919
$695$	0.371565	+	0.214523i	0.0140942	+	0.00813732i
$696$	2.26628	+	0.839589i	0.0859031	+	0.0318245i
$697$	8.02342	+	13.8970i	0.303909	+	0.526385i
$698$	27.8404			1.05378
$699$	−8.87578	+	23.9581i	−0.335713	+	0.906180i
$700$	5.98288	+	11.7850i	0.226132	+	0.445430i
$701$		−	33.7907i		−	1.27626i	−0.769930	−	0.638129i	$-0.779709\pi$
$701$		−	33.7907i		−	1.27626i	0.769930	−	0.638129i	$-0.220291\pi$
$702$	−10.2731	+	17.1078i	−0.387734	+	0.645693i
$703$	−44.1087	−	25.4662i	−1.66359	−	0.960475i
$704$		−	3.92924i		−	0.148089i
$705$	−0.0696949	−	0.408942i	−0.00262486	−	0.0154017i
$706$	4.93850	+	2.85124i	0.185863	+	0.107308i
$707$	45.9493	+	2.47601i	1.72810	+	0.0931199i
$708$	2.73558	+	16.0513i	0.102809	+	0.603246i
$709$	14.8416	−	25.7065i	0.557390	−	0.965427i	−0.440324	−	0.897839i	$-0.645136\pi$
$709$	14.8416	−	25.7065i	0.557390	−	0.965427i	0.997713	−	0.0675879i	$-0.0215303\pi$
$710$	−0.145685	+	0.252333i	−0.00546744	+	0.00946989i
$711$	−15.5817	−	13.3817i	−0.584358	−	0.501853i
$712$	10.1281	−	5.84745i	0.379566	−	0.219142i
$713$	3.49871	+	6.05995i	0.131028	+	0.226947i
$714$	2.82360	−	6.52102i	0.105671	−	0.244043i
$715$	−0.510090	+	0.883501i	−0.0190763	+	0.0330411i
$716$			15.9437i			0.595845i
$717$	−0.306358	+	0.0522118i	−0.0114412	+	0.00194989i
$718$	21.4560			0.800733
$719$	18.1588	+	31.4519i	0.677207	+	1.17296i	0.975818	+	0.218583i	$0.0701434\pi$
$719$	18.1588	+	31.4519i	0.677207	+	1.17296i	−0.298611	+	0.954375i	$0.596523\pi$
$720$	−0.153866	−	0.132142i	−0.00573425	−	0.00492463i
$721$	−0.142523	+	2.64492i	−0.00530784	+	0.0985020i
$722$	13.1538	−	7.59435i	0.489534	−	0.282632i
$723$	6.78204	+	8.17718i	0.252227	+	0.304113i
$724$	−15.9804	+	9.22629i	−0.593907	+	0.342892i
$725$	−6.03648	+	3.48516i	−0.224189	+	0.129436i
$726$	−7.57919	+	1.29170i	−0.281290	+	0.0479395i
$727$	−14.9225	+	8.61552i	−0.553446	+	0.319532i	−0.750511	−	0.660858i	$-0.770192\pi$
$727$	−14.9225	+	8.61552i	−0.553446	+	0.319532i	0.197065	+	0.980390i	$0.436859\pi$
$728$	−5.54650	+	8.51336i	−0.205567	+	0.315526i
$729$	−14.2954	+	22.9050i	−0.529461	+	0.848335i
$730$	−0.239181	−	0.414273i	−0.00885248	−	0.0153329i
$731$	−2.28212			−0.0844071
$732$	0.0901302	+	0.108671i	0.00333131	+	0.00401660i
$733$			43.0596i			1.59044i	0.606319	+	0.795222i	$0.292646\pi$
$733$			43.0596i			1.59044i	−0.606319	+	0.795222i	$0.707354\pi$
$734$	4.60428	−	7.97484i	0.169947	−	0.294357i
$735$	−0.683504	+	0.452452i	−0.0252114	+	0.0166890i
$736$	−2.76370	−	4.78687i	−0.101871	−	0.176446i
$737$	−52.2168	+	30.1474i	−1.92343	+	1.11049i
$738$	−10.2831	−	29.2924i	−0.378526	−	1.07827i
$739$	−1.87511	+	3.24778i	−0.0689770	+	0.119472i	−0.898451	−	0.439073i	$-0.855307\pi$
$739$	−1.87511	+	3.24778i	−0.0689770	+	0.119472i	0.829474	+	0.558545i	$0.188640\pi$
$740$	−0.294451	+	0.510005i	−0.0108242	+	0.0187481i
$741$	−29.9370	+	24.8293i	−1.09976	+	0.912127i
$742$	−8.69752	−	17.1322i	−0.319296	−	0.628943i
$743$	−23.9862	−	13.8484i	−0.879967	−	0.508049i	−0.00931965	−	0.999957i	$-0.502967\pi$
$743$	−23.9862	−	13.8484i	−0.879967	−	0.508049i	−0.870648	+	0.491907i	$0.836300\pi$
$744$	2.05613	+	0.761734i	0.0753813	+	0.0279265i
$745$		−	0.563628i		−	0.0206497i
$746$	24.4219	+	14.1000i	0.894151	+	0.516238i
$747$	−22.2599	+	7.81434i	−0.814446	+	0.285912i
$748$		−	6.09297i		−	0.222781i
$749$	21.8570	−	11.0961i	0.798636	−	0.405444i
$750$	1.15381	−	0.196641i	0.0421313	−	0.00718032i
$751$	−4.17712			−0.152425			−0.0762127	−	0.997092i	$-0.524283\pi$
$751$	−4.17712			−0.152425			−0.0762127	+	0.997092i	$0.524283\pi$
$752$	−1.77132	−	3.06802i	−0.0645935	−	0.111879i
$753$	1.48378	−	1.23063i	0.0540720	−	0.0448465i
$754$	−4.64075	−	2.67934i	−0.169006	−	0.0975757i
$755$	−0.956936			−0.0348264
$756$	−7.70134	+	11.3881i	−0.280095	+	0.414182i
$757$	35.9359			1.30611			0.653057	−	0.757309i	$-0.273486\pi$
$757$	35.9359			1.30611			0.653057	+	0.757309i	$0.273486\pi$
$758$	−4.09257	−	2.36284i	−0.148649	−	0.0858224i
$759$	−28.9547	+	24.0147i	−1.05099	+	0.871677i
$760$	−0.197652	−	0.342344i	−0.00716961	−	0.0124181i
$761$	−29.1430			−1.05643			−0.528216	−	0.849110i	$-0.677139\pi$
$761$	−29.1430			−1.05643			−0.528216	+	0.849110i	$0.677139\pi$
$762$	−32.5736	+	5.55143i	−1.18002	+	0.201107i
$763$	−2.37290	+	3.64219i	−0.0859048	+	0.131856i
$764$			23.3437i			0.844546i
$765$	−0.238596	−	0.204909i	−0.00862646	−	0.00740850i
$766$	29.6483	+	17.1174i	1.07124	+	0.618478i
$767$		−	36.1031i		−	1.30361i
$768$	−1.62418	−	0.601709i	−0.0586074	−	0.0217123i
$769$	−0.795911	−	0.459519i	−0.0287013	−	0.0165707i	0.485581	−	0.874192i	$-0.338608\pi$
$769$	−0.795911	−	0.459519i	−0.0287013	−	0.0165707i	−0.514282	+	0.857621i	$0.671942\pi$
$770$	−0.383655	+	0.588876i	−0.0138260	+	0.0212216i
$771$	6.32904	−	5.24922i	0.227935	−	0.189046i
$772$	10.6439	−	18.4357i	0.383082	−	0.663517i
$773$	4.69708	−	8.13558i	0.168942	−	0.292616i	−0.769106	−	0.639121i	$-0.779298\pi$
$773$	4.69708	−	8.13558i	0.168942	−	0.292616i	0.938048	+	0.346505i	$0.112632\pi$
$774$	4.33894	+	0.816427i	0.155960	+	0.0293459i
$775$	−5.47672	+	3.16199i	−0.196730	+	0.113582i
$776$	0.209749	+	0.363295i	0.00752954	+	0.0130415i
$777$	36.6309	+	15.8612i	1.31413	+	0.569016i
$778$	−9.24726	+	16.0167i	−0.331530	+	0.574228i
$779$		−	60.5076i		−	2.16791i
$780$	0.287087	+	0.346145i	0.0102794	+	0.0123940i
$781$	16.9341			0.605949
$782$	−4.28560	−	7.42288i	−0.153253	−	0.265442i
$783$	−6.21582	−	3.73256i	−0.222135	−	0.133391i
$784$	−4.13117	+	5.65097i	−0.147542	+	0.201820i
$785$	0.963683	−	0.556383i	0.0343953	−	0.0198581i
$786$	−31.8745	+	5.43228i	−1.13692	+	0.193763i
$787$	−26.4969	+	15.2980i	−0.944513	+	0.545315i	−0.891372	−	0.453272i	$-0.850257\pi$
$787$	−26.4969	+	15.2980i	−0.944513	+	0.545315i	−0.0531407	+	0.998587i	$0.516923\pi$
$788$	11.1255	−	6.42334i	0.396331	−	0.228822i
$789$	−4.66210	−	5.62115i	−0.165975	−	0.200118i
$790$	−0.400851	+	0.231432i	−0.0142617	+	0.00823397i
$791$	−34.9497	−	22.7699i	−1.24267	−	0.809604i
$792$	−2.17976	+	11.5844i	−0.0774544	+	0.411635i
$793$	−0.156520	−	0.271101i	−0.00555820	−	0.00962709i
$794$	−2.03373			−0.0721744
$795$	−0.838286	+	0.142867i	−0.0297309	+	0.00506696i
$796$		−	3.74301i		−	0.132667i
$797$	1.64717	−	2.85299i	0.0583459	−	0.101058i	−0.835377	−	0.549677i	$-0.814751\pi$
$797$	1.64717	−	2.85299i	0.0583459	−	0.101058i	0.893723	+	0.448619i	$0.148084\pi$
$798$	−21.5149	+	15.9710i	−0.761618	+	0.565368i
$799$	−2.74674	−	4.75750i	−0.0971728	−	0.168308i
$800$	4.32617	−	2.49771i	0.152953	−	0.0883075i
$801$	−33.1041	+	11.6212i	−1.16968	+	0.410616i
$802$	15.7118	−	27.2137i	0.554804	−	0.960948i
$803$	−13.9009	+	24.0771i	−0.490554	+	0.849664i
$804$	4.46532	+	26.2008i	0.157480	+	0.924030i
$805$	−0.0531991	+	0.987260i	−0.00187502	+	0.0347963i
$806$	−4.21041	−	2.43088i	−0.148305	−	0.0856242i
$807$	4.63997	+	27.2255i	0.163335	+	0.958384i
$808$		−	17.3924i		−	0.611863i
$809$	−19.7833	−	11.4219i	−0.695542	−	0.401572i	0.110143	−	0.993916i	$-0.464869\pi$
$809$	−19.7833	−	11.4219i	−0.695542	−	0.401572i	−0.805685	+	0.592344i	$0.798203\pi$
$810$	0.380331	+	0.474946i	0.0133635	+	0.0166879i
$811$			23.9412i			0.840691i	0.907364	+	0.420345i	$0.138091\pi$
$811$			23.9412i			0.840691i	−0.907364	+	0.420345i	$0.861909\pi$
$812$	−3.09318	−	2.01522i	−0.108549	−	0.0707203i
$813$	9.86002	−	26.6149i	0.345806	−	0.933424i
$814$	34.2264			1.19964
$815$	0.306492	+	0.530860i	0.0107360	+	0.0185952i
$816$	−2.51857	−	0.933054i	−0.0881675	−	0.0326634i
$817$	7.45228	+	4.30258i	0.260722	+	0.150528i
$818$	−0.550583			−0.0192507
$819$	21.0753	−	22.0227i	0.736432	−	0.769535i
$820$	−0.699616			−0.0244316
$821$	1.97936	+	1.14278i	0.0690802	+	0.0398834i	0.534142	−	0.845395i	$-0.320635\pi$
$821$	1.97936	+	1.14278i	0.0690802	+	0.0398834i	−0.465062	+	0.885278i	$0.653968\pi$
$822$	−1.82900	−	10.7318i	−0.0637936	−	0.374316i
$823$	11.4851	+	19.8928i	0.400347	+	0.693421i	0.993768	−	0.111471i	$-0.0355563\pi$
$823$	11.4851	+	19.8928i	0.400347	+	0.693421i	−0.593421	+	0.804892i	$0.702223\pi$
$824$	1.00114			0.0348762
$825$	−21.7034	−	26.1680i	−0.755616	−	0.911055i
$826$	1.33832	−	24.8363i	0.0465661	−	0.864165i
$827$			15.1679i			0.527438i	0.964600	+	0.263719i	$0.0849492\pi$
$827$			15.1679i			0.527438i	−0.964600	+	0.263719i	$0.915051\pi$
$828$	5.49258	+	15.6461i	0.190880	+	0.543740i
$829$	−5.73806	−	3.31287i	−0.199291	−	0.115061i	0.397034	−	0.917804i	$-0.370040\pi$
$829$	−5.73806	−	3.31287i	−0.199291	−	0.115061i	−0.596325	+	0.802743i	$0.703373\pi$
$830$			0.531653i			0.0184539i
$831$	−2.47440	+	2.05223i	−0.0858359	+	0.0711911i
$832$	3.32589	+	1.92020i	0.115304	+	0.0665710i
$833$	−6.40610	+	8.76281i	−0.221958	+	0.303613i
$834$	−10.3073	−	3.81856i	−0.356913	−	0.132226i
$835$	0.517140	−	0.895712i	0.0178964	−	0.0309974i
$836$	−11.4874	+	19.8967i	−0.397299	+	0.688141i
$837$	−5.63943	−	3.38644i	−0.194927	−	0.117052i
$838$	−20.0310	+	11.5649i	−0.691961	+	0.399504i
$839$	−23.8462	−	41.3029i	−0.823264	−	1.42593i	−0.903239	−	0.429138i	$-0.858818\pi$
$839$	−23.8462	−	41.3029i	−0.823264	−	1.42593i	0.0799756	−	0.996797i	$-0.474516\pi$
$840$	0.184664	+	0.248764i	0.00637151	+	0.00858319i
$841$	−13.5265	+	23.4286i	−0.466431	+	0.807883i
$842$			10.9955i			0.378929i
$843$	−0.436636	+	1.17860i	−0.0150386	+	0.0405932i
$844$	9.39162			0.323273
$845$	−0.0591122	−	0.102385i	−0.00203352	−	0.00352216i
$846$	3.52033	+	10.0280i	0.121031	+	0.344769i
$847$	11.7273	+	0.631934i	0.402956	+	0.0217135i
$848$	−6.28910	+	3.63101i	−0.215969	+	0.124690i
$849$	6.99646	−	18.8853i	0.240118	−	0.648143i
$850$	6.70848	−	3.87314i	0.230099	−	0.132848i
$851$	41.6970	−	24.0738i	1.42935	−	0.825238i
$852$	2.59322	−	6.99980i	0.0888422	−	0.239809i
$853$	−22.0983	+	12.7585i	−0.756632	+	0.436842i	−0.828085	−	0.560602i	$-0.810570\pi$
$853$	−22.0983	+	12.7585i	−0.756632	+	0.436842i	0.0714529	+	0.997444i	$0.477236\pi$
$854$	−0.0976251	−	0.192300i	−0.00334066	−	0.00658037i
$855$	0.392815	+	1.11897i	0.0134340	+	0.0382679i
$856$	−4.63238	−	8.02352i	−0.158332	−	0.274238i
$857$	−6.38085			−0.217966			−0.108983	−	0.994044i	$-0.534759\pi$
$857$	−6.38085			−0.217966			−0.108983	+	0.994044i	$0.534759\pi$
$858$	9.07971	−	24.5086i	0.309976	−	0.836710i
$859$		−	34.3486i		−	1.17196i	−0.810326	−	0.585980i	$-0.800710\pi$
$859$		−	34.3486i		−	1.17196i	0.810326	−	0.585980i	$-0.199290\pi$
$860$	0.0497483	−	0.0861666i	0.00169640	−	0.00293826i
$861$	5.44017	+	47.1088i	0.185400	+	1.60546i
$862$	4.15530	+	7.19720i	0.141530	+	0.245137i
$863$	31.3380	−	18.0930i	1.06676	−	0.615893i	0.139464	−	0.990227i	$-0.455462\pi$
$863$	31.3380	−	18.0930i	1.06676	−	0.615893i	0.927294	+	0.374334i	$0.122129\pi$
$864$	4.45470	+	2.67501i	0.151552	+	0.0910058i
$865$	0.0777901	−	0.134736i	0.00264494	−	0.00458118i
$866$	13.0525	−	22.6077i	0.443543	−	0.768240i
$867$	23.7055	+	8.78219i	0.805081	+	0.298259i
$868$	−2.80635	−	1.82835i	−0.0952536	−	0.0620582i
$869$	23.2971	+	13.4506i	0.790299	+	0.456279i
$870$	−0.125765	+	0.104308i	−0.00426385	+	0.00353637i
$871$		−	58.9315i		−	1.99682i
$872$	1.42288	+	0.821501i	0.0481849	+	0.0278195i
$873$	−0.416855	−	1.18745i	−0.0141084	−	0.0401890i
$874$			32.3193i			1.09322i
$875$	−1.78530	−	0.0962021i	−0.0603542	−	0.00325222i
$876$	7.82369	+	9.43312i	0.264338	+	0.318715i
$877$	34.0309			1.14914			0.574571	−	0.818455i	$-0.305169\pi$
$877$	34.0309			1.14914			0.574571	+	0.818455i	$0.305169\pi$
$878$	−20.4154	−	35.3605i	−0.688986	−	1.19336i
$879$	−3.75401	−	22.0270i	−0.126619	−	0.742954i
$880$	0.230054	+	0.132822i	0.00775513	+	0.00447742i
$881$	−26.6961			−0.899416			−0.449708	−	0.893176i	$-0.648472\pi$
$881$	−26.6961			−0.899416			−0.449708	+	0.893176i	$0.648472\pi$
$882$	15.3147	−	14.3688i	0.515672	−	0.483821i
$883$	11.2126			0.377333			0.188667	−	0.982041i	$-0.439583\pi$
$883$	11.2126			0.377333			0.188667	+	0.982041i	$0.439583\pi$
$884$	5.15737	+	2.97761i	0.173461	+	0.100148i
$885$	−1.03227	−	0.382424i	−0.0346992	−	0.0128550i
$886$	−9.12824	−	15.8106i	−0.306669	−	0.531167i
$887$	10.1871			0.342048			0.171024	−	0.985267i	$-0.445292\pi$
$887$	10.1871			0.342048			0.171024	+	0.985267i	$0.445292\pi$
$888$	5.24130	−	14.1477i	0.175886	−	0.474765i
$889$	50.4013	+	2.71591i	1.69041	+	0.0910886i
$890$			0.790656i			0.0265028i
$891$	12.8530	−	32.9447i	0.430592	−	1.10369i
$892$	17.7695	+	10.2592i	0.594966	+	0.343504i
$893$			20.7142i			0.693176i
$894$	2.42596	+	14.2346i	0.0811363	+	0.476076i
$895$	−0.933494	−	0.538953i	−0.0312033	−	0.0180152i
$896$	2.21679	+	1.44425i	0.0740577	+	0.0482489i
$897$	−6.17704	−	36.2445i	−0.206245	−	1.21017i
$898$	−13.0440	+	22.5929i	−0.435285	+	0.753936i
$899$	0.883217	−	1.52978i	0.0294569	−	0.0510209i
$900$	−14.1403	+	4.96396i	−0.471343	+	0.165465i
$901$	−9.75235	+	5.63052i	−0.324898	+	0.187580i
$902$	20.3305	+	35.2134i	0.676931	+	1.17248i
$903$	−6.18888	−	2.67978i	−0.205953	−	0.0891777i
$904$	−7.88296	+	13.6537i	−0.262183	+	0.454115i
$905$		−	1.24752i		−	0.0414690i
$906$	24.1677	−	4.11883i	0.802918	−	0.136839i
$907$	−15.1486			−0.503000			−0.251500	−	0.967857i	$-0.580924\pi$
$907$	−15.1486			−0.503000			−0.251500	+	0.967857i	$0.580924\pi$
$908$	−9.38828	−	16.2610i	−0.311561	−	0.539640i
$909$	−9.64850	+	51.2774i	−0.320021	+	1.70076i
$910$	−0.310960	−	0.612524i	−0.0103082	−	0.0203050i
$911$	−8.43020	+	4.86718i	−0.279305	+	0.161257i	−0.633109	−	0.774063i	$-0.718221\pi$
$911$	−8.43020	+	4.86718i	−0.279305	+	0.161257i	0.353804	+	0.935320i	$0.384888\pi$
$912$	6.46528	+	7.79527i	0.214087	+	0.258127i
$913$	26.7594	−	15.4496i	0.885607	−	0.511306i
$914$	5.54233	−	3.19987i	0.183324	−	0.105842i
$915$	−0.00940932	+	0.00160360i	−0.000311062	+	5.30135e-5i
$916$	−4.31740	+	2.49265i	−0.142651	+	0.0823596i
$917$	49.3195	+	2.65761i	1.62867	+	0.0877621i
$918$	6.90778	+	4.14807i	0.227991	+	0.136907i
$919$	−4.01638	−	6.95658i	−0.132488	−	0.229476i	0.792147	−	0.610330i	$-0.208963\pi$
$919$	−4.01638	−	6.95658i	−0.132488	−	0.229476i	−0.924635	+	0.380854i	$0.875630\pi$
$920$	0.373691			0.0123202
$921$	22.6796	+	27.3450i	0.747317	+	0.901049i
$922$		−	2.08197i		−	0.0685662i
$923$	−8.27560	+	14.3338i	−0.272395	+	0.471801i
$924$	7.15470	−	16.5236i	0.235372	−	0.543585i
$925$	21.7568	+	37.6839i	0.715360	+	1.23904i
$926$	−1.66118	+	0.959084i	−0.0545898	+	0.0315175i
$927$	−2.95161	−	0.555384i	−0.0969437	−	0.0182412i
$928$	−0.697671	+	1.20840i	−0.0229022	+	0.0396677i
$929$	−13.1064	+	22.7010i	−0.430007	+	0.744794i	−0.996873	−	0.0790158i	$-0.974822\pi$
$929$	−13.1064	+	22.7010i	−0.430007	+	0.744794i	0.566866	+	0.823810i	$0.308156\pi$
$930$	−0.114103	+	0.0946355i	−0.00374159	+	0.00310322i
$931$	37.4401	−	16.5374i	1.22705	−	0.541990i
$932$	−12.7747	−	7.37548i	−0.418449	−	0.241592i
$933$	−24.4094	−	9.04297i	−0.799129	−	0.296054i
$934$			34.2355i			1.12022i
$935$	0.356739	+	0.205963i	0.0116666	+	0.00673573i
$936$	−8.74035	−	7.50631i	−0.285687	−	0.245351i
$937$			37.5797i			1.22768i	0.789432	+	0.613838i	$0.210375\pi$
$937$			37.5797i			1.22768i	−0.789432	+	0.613838i	$0.789625\pi$
$938$	2.18456	−	40.5406i	0.0713283	−	1.32370i
$939$	−1.90440	+	0.324561i	−0.0621477	+	0.0105917i
$940$	0.239507			0.00781186
$941$	4.63655	+	8.03074i	0.151147	+	0.261794i	0.931649	−	0.363358i	$-0.118370\pi$
$941$	4.63655	+	8.03074i	0.151147	+	0.261794i	−0.780502	+	0.625153i	$0.785037\pi$
$942$	−21.9433	+	18.1995i	−0.714952	+	0.592971i
$943$	49.5360	+	28.5996i	1.61311	+	0.931331i
$944$	−9.40086			−0.305972
$945$	−0.406435	−	0.835866i	−0.0132213	−	0.0271907i
$946$	−5.78264			−0.188010
$947$	−12.0019	−	6.92928i	−0.390008	−	0.225171i	0.292155	−	0.956371i	$-0.405628\pi$
$947$	−12.0019	−	6.92928i	−0.390008	−	0.225171i	−0.682164	+	0.731199i	$0.738961\pi$
$948$	9.12749	−	7.57021i	0.296447	−	0.245869i
$949$	−13.5866	−	23.5328i	−0.441041	−	0.763906i
$950$	−29.2088			−0.947659
$951$	−2.10601	+	0.358922i	−0.0682921	+	0.0116388i
$952$	3.43752	+	2.23956i	0.111411	+	0.0725845i
$953$		−	2.65523i		−	0.0860115i	−0.999075	−	0.0430057i	$-0.986307\pi$
$953$		−	2.65523i		−	0.0860115i	0.999075	−	0.0430057i	$-0.0136934\pi$
$954$	20.5562	−	7.21628i	0.665533	−	0.233636i
$955$	−1.36676	−	0.789097i	−0.0442272	−	0.0255346i
$956$		−	0.179426i		−	0.00580307i
$957$	8.90476	+	3.29895i	0.287850	+	0.106640i
$958$	9.16468	+	5.29123i	0.296098	+	0.170952i
$959$	−0.894794	+	16.6054i	−0.0288944	+	0.536218i
$960$	0.0901323	−	0.0747545i	0.00290901	−	0.00241269i
$961$	−14.6987	+	25.4589i	−0.474151	+	0.821254i
$962$	−16.7263	+	28.9708i	−0.539277	+	0.934055i
$963$	9.20640	+	26.2253i	0.296672	+	0.845098i
$964$	−5.31183	+	3.06679i	−0.171083	+	0.0987746i
$965$	0.719600	+	1.24638i	0.0231647	+	0.0401225i
$966$	−2.90579	−	25.1625i	−0.0934924	−	0.809591i
$967$	7.14946	−	12.3832i	0.229911	−	0.398218i	−0.727870	−	0.685715i	$-0.759490\pi$
$967$	7.14946	−	12.3832i	0.229911	−	0.398218i	0.957782	+	0.287497i	$0.0928231\pi$
$968$		−	4.43894i		−	0.142673i
$969$	10.0255	+	12.0879i	0.322067	+	0.388320i
$970$	−0.0283609			−0.000910613
$971$	−0.130666	−	0.226320i	−0.00419326	−	0.00726295i	0.863921	−	0.503627i	$-0.168001\pi$
$971$	−0.130666	−	0.226320i	−0.00419326	−	0.00726295i	−0.868114	+	0.496364i	$0.834668\pi$
$972$	−11.6496	−	10.3579i	−0.373662	−	0.332230i
$973$	14.0681	+	9.16546i	0.451004	+	0.293831i
$974$	10.3196	−	5.95804i	0.330662	−	0.190908i
$975$	32.7562	−	5.58254i	1.04904	−	0.178784i
$976$	−0.0705919	+	0.0407562i	−0.00225959	+	0.00130457i
$977$	33.9113	−	19.5787i	1.08492	−	0.626378i	0.152700	−	0.988273i	$-0.451203\pi$
$977$	33.9113	−	19.5787i	1.08492	−	0.626378i	0.932219	+	0.361894i	$0.117870\pi$
$978$	−10.0255	−	12.0878i	−0.320579	−	0.386526i
$979$	39.7957	−	22.9760i	1.27188	−	0.734318i
$980$	−0.191212	−	0.432899i	−0.00610805	−	0.0138285i
$981$	−3.73930	−	3.21135i	−0.119387	−	0.102530i
$982$	−8.65023	−	14.9826i	−0.276040	−	0.478115i
$983$	26.3688			0.841035			0.420517	−	0.907285i	$-0.361849\pi$
$983$	26.3688			0.841035			0.420517	+	0.907285i	$0.361849\pi$
$984$	17.6690	−	3.01128i	0.563267	−	0.0959960i
$985$			0.868524i			0.0276735i
$986$	−1.08186	+	1.87384i	−0.0344534	+	0.0596751i
$987$	−1.86239	−	16.1273i	−0.0592806	−	0.513336i
$988$	−11.2276	−	19.4468i	−0.357199	−	0.618686i
$989$	−7.04481	+	4.06732i	−0.224012	+	0.129333i
$990$	−0.604577	−	0.519217i	−0.0192147	−	0.0165018i
$991$	−22.9516	+	39.7534i	−0.729082	+	1.26281i	0.228189	+	0.973617i	$0.426720\pi$
$991$	−22.9516	+	39.7534i	−0.729082	+	1.26281i	−0.957271	+	0.289191i	$0.906614\pi$
$992$	−0.632976	+	1.09635i	−0.0200970	+	0.0348090i
$993$	−1.46213	−	8.57920i	−0.0463993	−	0.272253i
$994$	−6.22435	+	9.55381i	−0.197424	+	0.303028i
$995$	0.219150	+	0.126526i	0.00694753	+	0.00401116i
$996$	−2.28833	−	13.4270i	−0.0725086	−	0.425452i
$997$		−	21.4693i		−	0.679939i	−0.940437	−	0.339969i	$-0.889583\pi$
$997$		−	21.4693i		−	0.679939i	0.940437	−	0.339969i	$-0.110417\pi$
$998$	−11.1108	−	6.41484i	−0.351707	−	0.203058i
$999$	−23.3012	+	38.8035i	−0.737217	+	1.22769i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.2.t.a.59.7	yes	16
3.2	odd	2		378.2.t.a.17.3		16
4.3	odd	2		1008.2.df.c.689.2		16
7.2	even	3		882.2.l.b.509.3		16
7.3	odd	6		882.2.m.b.293.4		16
7.4	even	3		882.2.m.a.293.1		16
7.5	odd	6		126.2.l.a.5.2	✓	16
7.6	odd	2		882.2.t.a.815.6		16
9.2	odd	6		126.2.l.a.101.6	yes	16
9.4	even	3		1134.2.k.b.647.3		16
9.5	odd	6		1134.2.k.a.647.6		16
9.7	even	3		378.2.l.a.143.3		16
12.11	even	2		3024.2.df.c.17.5		16
21.2	odd	6		2646.2.l.a.1097.6		16
21.5	even	6		378.2.l.a.341.7		16
21.11	odd	6		2646.2.m.a.881.6		16
21.17	even	6		2646.2.m.b.881.7		16
21.20	even	2		2646.2.t.b.2285.2		16
28.19	even	6		1008.2.ca.c.257.4		16
36.7	odd	6		3024.2.ca.c.2033.5		16
36.11	even	6		1008.2.ca.c.353.4		16
63.2	odd	6		882.2.t.a.803.6		16
63.5	even	6		1134.2.k.b.971.3		16
63.11	odd	6		882.2.m.b.587.4		16
63.16	even	3		2646.2.t.b.1979.2		16
63.20	even	6		882.2.l.b.227.7		16
63.25	even	3		2646.2.m.b.1763.7		16
63.34	odd	6		2646.2.l.a.521.2		16
63.38	even	6		882.2.m.a.587.1		16
63.40	odd	6		1134.2.k.a.971.6		16
63.47	even	6	inner	126.2.t.a.47.7	yes	16
63.52	odd	6		2646.2.m.a.1763.6		16
63.61	odd	6		378.2.t.a.89.3		16
84.47	odd	6		3024.2.ca.c.2609.5		16
252.47	odd	6		1008.2.df.c.929.2		16
252.187	even	6		3024.2.df.c.1601.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.2	✓	16	7.5	odd	6
126.2.l.a.101.6	yes	16	9.2	odd	6
126.2.t.a.47.7	yes	16	63.47	even	6	inner
126.2.t.a.59.7	yes	16	1.1	even	1	trivial
378.2.l.a.143.3		16	9.7	even	3
378.2.l.a.341.7		16	21.5	even	6
378.2.t.a.17.3		16	3.2	odd	2
378.2.t.a.89.3		16	63.61	odd	6
882.2.l.b.227.7		16	63.20	even	6
882.2.l.b.509.3		16	7.2	even	3
882.2.m.a.293.1		16	7.4	even	3
882.2.m.a.587.1		16	63.38	even	6
882.2.m.b.293.4		16	7.3	odd	6
882.2.m.b.587.4		16	63.11	odd	6
882.2.t.a.803.6		16	63.2	odd	6
882.2.t.a.815.6		16	7.6	odd	2
1008.2.ca.c.257.4		16	28.19	even	6
1008.2.ca.c.353.4		16	36.11	even	6
1008.2.df.c.689.2		16	4.3	odd	2
1008.2.df.c.929.2		16	252.47	odd	6
1134.2.k.a.647.6		16	9.5	odd	6
1134.2.k.a.971.6		16	63.40	odd	6
1134.2.k.b.647.3		16	9.4	even	3
1134.2.k.b.971.3		16	63.5	even	6
2646.2.l.a.521.2		16	63.34	odd	6
2646.2.l.a.1097.6		16	21.2	odd	6
2646.2.m.a.881.6		16	21.11	odd	6
2646.2.m.a.1763.6		16	63.52	odd	6
2646.2.m.b.881.7		16	21.17	even	6
2646.2.m.b.1763.7		16	63.25	even	3
2646.2.t.b.1979.2		16	63.16	even	3
2646.2.t.b.2285.2		16	21.20	even	2
3024.2.ca.c.2033.5		16	36.7	odd	6
3024.2.ca.c.2609.5		16	84.47	odd	6
3024.2.df.c.17.5		16	12.11	even	2
3024.2.df.c.1601.5		16	252.187	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	126.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(1.33318 - 1.10572i) q^{3} +(0.500000 + 0.866025i) q^{4} -0.0676069 q^{5} +(1.70743 - 0.290993i) q^{6} +(-2.64192 - 0.142361i) q^{7} +1.00000i q^{8} +(0.554753 - 2.94826i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(1.33318 - 1.10572i) q^{3} +(0.500000 + 0.866025i) q^{4} -0.0676069 q^{5} +(1.70743 - 0.290993i) q^{6} +(-2.64192 - 0.142361i) q^{7} +1.00000i q^{8} +(0.554753 - 2.94826i) q^{9} +(-0.0585493 - 0.0338034i) q^{10} +3.92924i q^{11} +(1.62418 + 0.601709i) q^{12} +(-3.32589 - 1.92020i) q^{13} +(-2.21679 - 1.44425i) q^{14} +(-0.0901323 + 0.0747545i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.775337 + 1.34292i) q^{17} +(1.95456 - 2.27589i) q^{18} +(5.06375 - 2.92356i) q^{19} +(-0.0338034 - 0.0585493i) q^{20} +(-3.67957 + 2.73144i) q^{21} +(-1.96462 + 3.40282i) q^{22} +5.52740i q^{23} +(1.10572 + 1.33318i) q^{24} -4.99543 q^{25} +(-1.92020 - 3.32589i) q^{26} +(-2.52037 - 4.54398i) q^{27} +(-1.19767 - 2.35915i) q^{28} +(1.20840 - 0.697671i) q^{29} +(-0.115434 + 0.0196731i) q^{30} +(1.09635 - 0.632976i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(4.34465 + 5.23840i) q^{33} +(-1.34292 + 0.775337i) q^{34} +(0.178612 + 0.00962461i) q^{35} +(2.83065 - 0.993700i) q^{36} +(-4.35534 - 7.54368i) q^{37} +5.84711 q^{38} +(-6.55723 + 1.11753i) q^{39} -0.0676069i q^{40} +(5.17415 - 8.96188i) q^{41} +(-4.55232 + 0.525707i) q^{42} +(0.735847 + 1.27452i) q^{43} +(-3.40282 + 1.96462i) q^{44} +(-0.0375051 + 0.199323i) q^{45} +(-2.76370 + 4.78687i) q^{46} +(-1.77132 + 3.06802i) q^{47} +(0.290993 + 1.70743i) q^{48} +(6.95947 + 0.752214i) q^{49} +(-4.32617 - 2.49771i) q^{50} +(0.451235 + 2.64767i) q^{51} -3.84040i q^{52} +(6.28910 + 3.63101i) q^{53} +(0.0892808 - 5.19539i) q^{54} -0.265644i q^{55} +(0.142361 - 2.64192i) q^{56} +(3.51826 - 9.49673i) q^{57} +1.39534 q^{58} +(4.70043 + 8.14138i) q^{59} +(-0.109805 - 0.0406796i) q^{60} +(0.0705919 + 0.0407562i) q^{61} +1.26595 q^{62} +(-1.88533 + 7.71009i) q^{63} -1.00000 q^{64} +(0.224853 + 0.129819i) q^{65} +(1.14338 + 6.70891i) q^{66} +(7.67257 + 13.2893i) q^{67} -1.55067 q^{68} +(6.11178 + 7.36904i) q^{69} +(0.149870 + 0.0976411i) q^{70} -4.30975i q^{71} +(2.94826 + 0.554753i) q^{72} +(6.12768 + 3.53782i) q^{73} -8.71069i q^{74} +(-6.65982 + 5.52356i) q^{75} +(5.06375 + 2.92356i) q^{76} +(0.559372 - 10.3807i) q^{77} +(-6.23749 - 2.31080i) q^{78} +(3.42320 - 5.92915i) q^{79} +(0.0338034 - 0.0585493i) q^{80} +(-8.38450 - 3.27112i) q^{81} +(8.96188 - 5.17415i) q^{82} +(-3.93194 - 6.81032i) q^{83} +(-4.20528 - 1.82089i) q^{84} +(0.0524181 - 0.0907908i) q^{85} +1.47169i q^{86} +(0.839589 - 2.26628i) q^{87} -3.92924 q^{88} +(-5.84745 - 10.1281i) q^{89} +(-0.132142 + 0.153866i) q^{90} +(8.51336 + 5.54650i) q^{91} +(-4.78687 + 2.76370i) q^{92} +(0.761734 - 2.05613i) q^{93} +(-3.06802 + 1.77132i) q^{94} +(-0.342344 + 0.197652i) q^{95} +(-0.601709 + 1.62418i) q^{96} +(0.363295 - 0.209749i) q^{97} +(5.65097 + 4.13117i) q^{98} +(11.5844 + 2.17976i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 2 q^{7} - 6 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 + 2 * q^7 - 6 * q^9	\( 16 q + 8 q^{4} + 2 q^{7} - 6 q^{9} - 6 q^{13} - 6 q^{14} - 18 q^{15} - 8 q^{16} + 18 q^{17} + 12 q^{18} - 18 q^{21} - 6 q^{24} + 16 q^{25} - 12 q^{26} - 36 q^{27} - 2 q^{28} + 6 q^{29} - 18 q^{30} + 6 q^{31} + 18 q^{33} - 30 q^{35} - 2 q^{37} - 30 q^{39} + 6 q^{41} + 30 q^{42} - 2 q^{43} + 12 q^{44} + 12 q^{45} + 6 q^{46} - 18 q^{47} + 10 q^{49} - 12 q^{50} + 36 q^{53} + 18 q^{54} + 6 q^{57} - 12 q^{58} + 30 q^{59} - 6 q^{60} - 60 q^{61} - 36 q^{62} + 42 q^{63} - 16 q^{64} + 42 q^{65} + 48 q^{66} + 14 q^{67} + 36 q^{68} + 42 q^{69} + 30 q^{75} - 18 q^{77} - 16 q^{79} + 54 q^{81} - 18 q^{84} - 12 q^{85} - 48 q^{87} + 24 q^{89} - 18 q^{90} - 12 q^{91} + 6 q^{92} + 30 q^{93} - 66 q^{95} - 6 q^{96} - 6 q^{97} + 24 q^{98} + 18 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 2 * q^7 - 6 * q^9 - 6 * q^13 - 6 * q^14 - 18 * q^15 - 8 * q^16 + 18 * q^17 + 12 * q^18 - 18 * q^21 - 6 * q^24 + 16 * q^25 - 12 * q^26 - 36 * q^27 - 2 * q^28 + 6 * q^29 - 18 * q^30 + 6 * q^31 + 18 * q^33 - 30 * q^35 - 2 * q^37 - 30 * q^39 + 6 * q^41 + 30 * q^42 - 2 * q^43 + 12 * q^44 + 12 * q^45 + 6 * q^46 - 18 * q^47 + 10 * q^49 - 12 * q^50 + 36 * q^53 + 18 * q^54 + 6 * q^57 - 12 * q^58 + 30 * q^59 - 6 * q^60 - 60 * q^61 - 36 * q^62 + 42 * q^63 - 16 * q^64 + 42 * q^65 + 48 * q^66 + 14 * q^67 + 36 * q^68 + 42 * q^69 + 30 * q^75 - 18 * q^77 - 16 * q^79 + 54 * q^81 - 18 * q^84 - 12 * q^85 - 48 * q^87 + 24 * q^89 - 18 * q^90 - 12 * q^91 + 6 * q^92 + 30 * q^93 - 66 * q^95 - 6 * q^96 - 6 * q^97 + 24 * q^98 + 18 * q^99

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