LMFDB - Embedded newform 546.2.cg.b.145.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(145,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 1]))

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

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

chi := DirichletCharacter("546.145");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.cg (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			145.8
Character	$\chi$	$=$	546.145
Dual form			546.2.cg.b.241.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000i q^{4} +(0.499350 - 0.133800i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(0.430450 + 2.61050i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000i q^{4} +(0.499350 - 0.133800i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(0.430450 + 2.61050i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(0.258483 - 0.447705i) q^{10} +(4.55131 - 1.21952i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(1.50046 - 3.27851i) q^{13} +(2.15028 + 1.54153i) q^{14} +(-0.499350 - 0.133800i) q^{15} -1.00000 q^{16} +1.33604 q^{17} +(0.965926 + 0.258819i) q^{18} +(2.16519 - 8.08058i) q^{19} +(-0.133800 - 0.499350i) q^{20} +(0.932469 - 2.47598i) q^{21} +(2.35593 - 4.08059i) q^{22} +4.09068i q^{23} +(0.258819 + 0.965926i) q^{24} +(-4.09868 + 2.36637i) q^{25} +(-1.25727 - 3.37924i) q^{26} -1.00000i q^{27} +(2.61050 - 0.430450i) q^{28} +(-1.91756 - 3.32131i) q^{29} +(-0.447705 + 0.258483i) q^{30} +(0.785461 - 2.93138i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-4.55131 - 1.21952i) q^{33} +(0.944725 - 0.944725i) q^{34} +(0.564231 + 1.24596i) q^{35} +(0.866025 - 0.500000i) q^{36} +(-1.49238 - 1.49238i) q^{37} +(-4.18282 - 7.24485i) q^{38} +(-2.93869 + 2.08904i) q^{39} +(-0.447705 - 0.258483i) q^{40} +(-1.92609 + 7.18828i) q^{41} +(-1.09143 - 2.41014i) q^{42} +(8.73281 + 5.04189i) q^{43} +(-1.21952 - 4.55131i) q^{44} +(0.365550 + 0.365550i) q^{45} +(2.89255 + 2.89255i) q^{46} +(-1.67580 - 6.25416i) q^{47} +(0.866025 + 0.500000i) q^{48} +(-6.62943 + 2.24738i) q^{49} +(-1.22493 + 4.57148i) q^{50} +(-1.15705 - 0.668021i) q^{51} +(-3.27851 - 1.50046i) q^{52} +(2.49408 + 4.31988i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(2.10952 - 1.21793i) q^{55} +(1.54153 - 2.15028i) q^{56} +(-5.91540 + 5.91540i) q^{57} +(-3.70444 - 0.992601i) q^{58} +(-0.738873 + 0.738873i) q^{59} +(-0.133800 + 0.499350i) q^{60} +(9.64567 - 5.56893i) q^{61} +(-1.51739 - 2.62820i) q^{62} +(-2.04553 + 1.67803i) q^{63} +1.00000i q^{64} +(0.310590 - 1.83789i) q^{65} +(-4.08059 + 2.35593i) q^{66} +(1.31257 + 4.89856i) q^{67} -1.33604i q^{68} +(2.04534 - 3.54263i) q^{69} +(1.28000 + 0.482054i) q^{70} +(1.85890 + 6.93749i) q^{71} +(0.258819 - 0.965926i) q^{72} +(3.00429 + 0.804997i) q^{73} -2.11055 q^{74} +4.73275 q^{75} +(-8.08058 - 2.16519i) q^{76} +(5.14267 + 11.3562i) q^{77} +(-0.600796 + 3.55514i) q^{78} +(5.35897 - 9.28201i) q^{79} +(-0.499350 + 0.133800i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.72093 + 6.44483i) q^{82} +(3.47927 + 3.47927i) q^{83} +(-2.47598 - 0.932469i) q^{84} +(0.667153 - 0.178763i) q^{85} +(9.74018 - 2.60987i) q^{86} +3.83512i q^{87} +(-4.08059 - 2.35593i) q^{88} +(-4.91933 + 4.91933i) q^{89} +0.516965 q^{90} +(9.20442 + 2.50572i) q^{91} +4.09068 q^{92} +(-2.14592 + 2.14592i) q^{93} +(-5.60732 - 3.23739i) q^{94} -4.32474i q^{95} +(0.965926 - 0.258819i) q^{96} +(-14.7177 + 3.94361i) q^{97} +(-3.09857 + 6.27685i) q^{98} +(3.33179 + 3.33179i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) $ 40 * q + 4 * q^7 + 20 * q^9	$ 40 q + 4 q^{7} + 20 q^{9} + 8 q^{11} - 20 q^{12} + 4 q^{14} - 40 q^{16} + 16 q^{17} + 4 q^{19} + 4 q^{21} - 4 q^{22} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 8 q^{33} - 8 q^{34} - 32 q^{35} + 40 q^{37} + 8 q^{38} + 20 q^{39} + 20 q^{41} + 12 q^{42} - 24 q^{43} - 4 q^{44} + 32 q^{46} + 4 q^{47} + 32 q^{49} - 16 q^{50} + 24 q^{51} + 16 q^{52} - 4 q^{53} + 24 q^{55} + 12 q^{56} + 8 q^{57} + 12 q^{58} + 24 q^{59} + 60 q^{61} + 32 q^{62} - 4 q^{63} + 44 q^{65} - 12 q^{67} - 8 q^{69} - 24 q^{70} - 28 q^{71} + 60 q^{73} - 40 q^{74} - 72 q^{75} + 4 q^{76} - 12 q^{77} + 4 q^{78} - 20 q^{81} - 24 q^{82} + 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{89} - 16 q^{92} - 24 q^{93} - 48 q^{97} - 88 q^{98} + 4 q^{99}+O(q^{100}) $ 40 * q + 4 * q^7 + 20 * q^9 + 8 * q^11 - 20 * q^12 + 4 * q^14 - 40 * q^16 + 16 * q^17 + 4 * q^19 + 4 * q^21 - 4 * q^22 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 8 * q^33 - 8 * q^34 - 32 * q^35 + 40 * q^37 + 8 * q^38 + 20 * q^39 + 20 * q^41 + 12 * q^42 - 24 * q^43 - 4 * q^44 + 32 * q^46 + 4 * q^47 + 32 * q^49 - 16 * q^50 + 24 * q^51 + 16 * q^52 - 4 * q^53 + 24 * q^55 + 12 * q^56 + 8 * q^57 + 12 * q^58 + 24 * q^59 + 60 * q^61 + 32 * q^62 - 4 * q^63 + 44 * q^65 - 12 * q^67 - 8 * q^69 - 24 * q^70 - 28 * q^71 + 60 * q^73 - 40 * q^74 - 72 * q^75 + 4 * q^76 - 12 * q^77 + 4 * q^78 - 20 * q^81 - 24 * q^82 + 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^89 - 16 * q^92 - 24 * q^93 - 48 * q^97 - 88 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{12}\right)$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$		−	1.00000i		−	0.500000i
$5$	0.499350	−	0.133800i	0.223316	−	0.0598374i	−0.145426	−	0.989369i	$-0.546455\pi$
$5$	0.499350	−	0.133800i	0.223316	−	0.0598374i	0.368742	+	0.929532i	$0.379789\pi$
$6$	−0.965926	+	0.258819i	−0.394338	+	0.105662i
$7$	0.430450	+	2.61050i	0.162695	+	0.986676i
$7$	0.430450	+	2.61050i	0.162695	+	0.986676i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	0.258483	−	0.447705i	0.0817394	−	0.141577i
$11$	4.55131	−	1.21952i	1.37227	−	0.367699i	0.503963	−	0.863725i	$-0.331875\pi$
$11$	4.55131	−	1.21952i	1.37227	−	0.367699i	0.868308	+	0.496026i	$0.165208\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	1.50046	−	3.27851i	0.416154	−	0.909294i
$13$	1.50046	−	3.27851i	0.416154	−	0.909294i
$14$	2.15028	+	1.54153i	0.574686	+	0.411991i
$15$	−0.499350	−	0.133800i	−0.128932	−	0.0345471i
$16$	−1.00000			−0.250000
$17$	1.33604			0.324038			0.162019	−	0.986788i	$-0.448199\pi$
$17$	1.33604			0.324038			0.162019	+	0.986788i	$0.448199\pi$
$18$	0.965926	+	0.258819i	0.227671	+	0.0610042i
$19$	2.16519	−	8.08058i	0.496728	−	1.85381i	−0.0234039	−	0.999726i	$-0.507450\pi$
$19$	2.16519	−	8.08058i	0.496728	−	1.85381i	0.520131	−	0.854086i	$-0.325883\pi$
$20$	−0.133800	−	0.499350i	−0.0299187	−	0.111658i
$21$	0.932469	−	2.47598i	0.203481	−	0.540304i
$22$	2.35593	−	4.08059i	0.502286	−	0.869985i
$23$			4.09068i			0.852966i	0.904496	+	0.426483i	$0.140248\pi$
$23$			4.09068i			0.852966i	−0.904496	+	0.426483i	$0.859752\pi$
$24$	0.258819	+	0.965926i	0.0528312	+	0.197169i
$25$	−4.09868	+	2.36637i	−0.819736	+	0.473275i
$26$	−1.25727	−	3.37924i	−0.246570	−	0.662724i
$27$		−	1.00000i		−	0.192450i
$28$	2.61050	−	0.430450i	0.493338	−	0.0813475i
$29$	−1.91756	−	3.32131i	−0.356082	−	0.616751i	0.631221	−	0.775603i	$-0.282554\pi$
$29$	−1.91756	−	3.32131i	−0.356082	−	0.616751i	−0.987302	+	0.158852i	$0.949221\pi$
$30$	−0.447705	+	0.258483i	−0.0817394	+	0.0471922i
$31$	0.785461	−	2.93138i	0.141073	−	0.526492i	−0.858826	−	0.512268i	$-0.828806\pi$
$31$	0.785461	−	2.93138i	0.141073	−	0.526492i	0.999899	−	0.0142239i	$-0.00452777\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−4.55131	−	1.21952i	−0.792281	−	0.212291i
$34$	0.944725	−	0.944725i	0.162019	−	0.162019i
$35$	0.564231	+	1.24596i	0.0953725	+	0.210605i
$36$	0.866025	−	0.500000i	0.144338	−	0.0833333i
$37$	−1.49238	−	1.49238i	−0.245346	−	0.245346i	0.573711	−	0.819058i	$-0.305503\pi$
$37$	−1.49238	−	1.49238i	−0.245346	−	0.245346i	−0.819058	+	0.573711i	$0.805503\pi$
$38$	−4.18282	−	7.24485i	−0.678542	−	1.17527i
$39$	−2.93869	+	2.08904i	−0.470567	+	0.334514i
$40$	−0.447705	−	0.258483i	−0.0707884	−	0.0408697i
$41$	−1.92609	+	7.18828i	−0.300805	+	1.12262i	0.635691	+	0.771943i	$0.280715\pi$
$41$	−1.92609	+	7.18828i	−0.300805	+	1.12262i	−0.936497	+	0.350677i	$0.885952\pi$
$42$	−1.09143	−	2.41014i	−0.168411	−	0.371893i
$43$	8.73281	+	5.04189i	1.33174	+	0.768881i	0.985566	−	0.169289i	$-0.0541472\pi$
$43$	8.73281	+	5.04189i	1.33174	+	0.768881i	0.346174	+	0.938170i	$0.387481\pi$
$44$	−1.21952	−	4.55131i	−0.183849	−	0.686135i
$45$	0.365550	+	0.365550i	0.0544929	+	0.0544929i
$46$	2.89255	+	2.89255i	0.426483	+	0.426483i
$47$	−1.67580	−	6.25416i	−0.244440	−	0.912262i	−0.973664	−	0.227987i	$-0.926785\pi$
$47$	−1.67580	−	6.25416i	−0.244440	−	0.912262i	0.729224	−	0.684275i	$-0.239881\pi$
$48$	0.866025	+	0.500000i	0.125000	+	0.0721688i
$49$	−6.62943	+	2.24738i	−0.947061	+	0.321054i
$50$	−1.22493	+	4.57148i	−0.173231	+	0.646505i
$51$	−1.15705	−	0.668021i	−0.162019	−	0.0935417i
$52$	−3.27851	−	1.50046i	−0.454647	−	0.208077i
$53$	2.49408	+	4.31988i	0.342589	+	0.593381i	0.984913	−	0.173052i	$-0.0553629\pi$
$53$	2.49408	+	4.31988i	0.342589	+	0.593381i	−0.642324	+	0.766433i	$0.722030\pi$
$54$	−0.707107	−	0.707107i	−0.0962250	−	0.0962250i
$55$	2.10952	−	1.21793i	0.284448	−	0.164226i
$56$	1.54153	−	2.15028i	0.205995	−	0.287343i
$57$	−5.91540	+	5.91540i	−0.783513	+	0.783513i
$58$	−3.70444	−	0.992601i	−0.486416	−	0.130335i
$59$	−0.738873	+	0.738873i	−0.0961930	+	0.0961930i	−0.753566	−	0.657373i	$-0.771668\pi$
$59$	−0.738873	+	0.738873i	−0.0961930	+	0.0961930i	0.657373	+	0.753566i	$0.271668\pi$
$60$	−0.133800	+	0.499350i	−0.0172736	+	0.0644658i
$61$	9.64567	−	5.56893i	1.23500	−	0.713028i	0.266933	−	0.963715i	$-0.413990\pi$
$61$	9.64567	−	5.56893i	1.23500	−	0.713028i	0.968068	+	0.250687i	$0.0806564\pi$
$62$	−1.51739	−	2.62820i	−0.192709	−	0.333782i
$63$	−2.04553	+	1.67803i	−0.257713	+	0.211412i
$64$			1.00000i			0.125000i
$65$	0.310590	−	1.83789i	0.0385240	−	0.227962i
$66$	−4.08059	+	2.35593i	−0.502286	+	0.289995i
$67$	1.31257	+	4.89856i	0.160355	+	0.598454i	0.998587	+	0.0531402i	$0.0169230\pi$
$67$	1.31257	+	4.89856i	0.160355	+	0.598454i	−0.838232	+	0.545314i	$0.816410\pi$
$68$		−	1.33604i		−	0.162019i
$69$	2.04534	−	3.54263i	0.246230	−	0.426483i
$70$	1.28000	+	0.482054i	0.152989	+	0.0576165i
$71$	1.85890	+	6.93749i	0.220610	+	0.823329i	0.984116	+	0.177528i	$0.0568099\pi$
$71$	1.85890	+	6.93749i	0.220610	+	0.823329i	−0.763505	+	0.645801i	$0.776523\pi$
$72$	0.258819	−	0.965926i	0.0305021	−	0.113835i
$73$	3.00429	+	0.804997i	0.351625	+	0.0942178i	0.430308	−	0.902682i	$-0.358405\pi$
$73$	3.00429	+	0.804997i	0.351625	+	0.0942178i	−0.0786830	+	0.996900i	$0.525071\pi$
$74$	−2.11055			−0.245346
$75$	4.73275			0.546491
$76$	−8.08058	−	2.16519i	−0.926906	−	0.248364i
$77$	5.14267	+	11.3562i	0.586061	+	1.29416i
$78$	−0.600796	+	3.55514i	−0.0680267	+	0.402541i
$79$	5.35897	−	9.28201i	0.602931	−	1.04431i	−0.389444	−	0.921050i	$-0.627333\pi$
$79$	5.35897	−	9.28201i	0.602931	−	1.04431i	0.992375	−	0.123257i	$-0.0393339\pi$
$80$	−0.499350	+	0.133800i	−0.0558290	+	0.0149593i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	3.72093	+	6.44483i	0.410907	+	0.711713i
$83$	3.47927	+	3.47927i	0.381899	+	0.381899i	0.871786	−	0.489887i	$-0.162962\pi$
$83$	3.47927	+	3.47927i	0.381899	+	0.381899i	−0.489887	+	0.871786i	$0.662962\pi$
$84$	−2.47598	−	0.932469i	−0.270152	−	0.101741i
$85$	0.667153	−	0.178763i	0.0723629	−	0.0193896i
$86$	9.74018	−	2.60987i	1.05031	−	0.281430i
$87$			3.83512i			0.411168i
$88$	−4.08059	−	2.35593i	−0.434992	−	0.251143i
$89$	−4.91933	+	4.91933i	−0.521448	+	0.521448i	−0.918009	−	0.396560i	$-0.870204\pi$
$89$	−4.91933	+	4.91933i	−0.521448	+	0.521448i	0.396560	+	0.918009i	$0.370204\pi$
$90$	0.516965			0.0544929
$91$	9.20442	+	2.50572i	0.964885	+	0.262671i
$92$	4.09068			0.426483
$93$	−2.14592	+	2.14592i	−0.222522	+	0.222522i
$94$	−5.60732	−	3.23739i	−0.578351	−	0.333911i
$95$		−	4.32474i		−	0.443709i
$96$	0.965926	−	0.258819i	0.0985844	−	0.0264156i
$97$	−14.7177	+	3.94361i	−1.49436	+	0.400413i	−0.911207	−	0.411950i	$-0.864848\pi$
$97$	−14.7177	+	3.94361i	−1.49436	+	0.400413i	−0.583153	+	0.812362i	$0.698181\pi$
$98$	−3.09857	+	6.27685i	−0.313003	+	0.634058i
$99$	3.33179	+	3.33179i	0.334857	+	0.334857i
$100$	2.36637	+	4.09868i	0.236637	+	0.409868i
$101$	−7.97917	+	13.8203i	−0.793957	+	1.37517i	0.129542	+	0.991574i	$0.458649\pi$
$101$	−7.97917	+	13.8203i	−0.793957	+	1.37517i	−0.923499	+	0.383600i	$0.874684\pi$
$102$	−1.29052	+	0.345793i	−0.127780	+	0.0342386i
$103$	2.64976	−	4.58953i	0.261089	−	0.452220i	−0.705443	−	0.708767i	$-0.749252\pi$
$103$	2.64976	−	4.58953i	0.261089	−	0.452220i	0.966532	+	0.256548i	$0.0825850\pi$
$104$	−3.37924	+	1.25727i	−0.331362	+	0.123285i
$105$	0.134341	−	1.36115i	0.0131103	−	0.132834i
$106$	4.81820	+	1.29103i	0.467985	+	0.125396i
$107$	−13.0348			−1.26012			−0.630059	−	0.776548i	$-0.716969\pi$
$107$	−13.0348			−1.26012			−0.630059	+	0.776548i	$0.716969\pi$
$108$	−1.00000			−0.0962250
$109$	−15.8583	−	4.24923i	−1.51895	−	0.407002i	−0.599557	−	0.800332i	$-0.704656\pi$
$109$	−15.8583	−	4.24923i	−1.51895	−	0.407002i	−0.919397	+	0.393330i	$0.871323\pi$
$110$	0.630449	−	2.35287i	0.0601109	−	0.224337i
$111$	0.546250	+	2.03863i	0.0518478	+	0.193499i
$112$	−0.430450	−	2.61050i	−0.0406737	−	0.246669i
$113$	−9.85871	+	17.0758i	−0.927430	+	1.60636i	−0.139824	+	0.990176i	$0.544654\pi$
$113$	−9.85871	+	17.0758i	−0.927430	+	1.60636i	−0.787606	+	0.616179i	$0.788680\pi$
$114$			8.36563i			0.783513i
$115$	0.547335	+	2.04268i	0.0510392	+	0.190481i
$116$	−3.32131	+	1.91756i	−0.308376	+	0.178041i
$117$	3.58950	−	0.339815i	0.331850	−	0.0314159i
$118$			1.04492i			0.0961930i
$119$	0.575100	+	3.48774i	0.0527193	+	0.319721i
$120$	0.258483	+	0.447705i	0.0235961	+	0.0408697i
$121$	9.70090	−	5.60081i	0.881900	−	0.509165i
$122$	2.88269	−	10.7583i	0.260986	−	0.974015i
$123$	5.26218	−	5.26218i	0.474475	−	0.474475i
$124$	−2.93138	−	0.785461i	−0.263246	−	0.0705365i
$125$	−3.55780	+	3.55780i	−0.318219	+	0.318219i
$126$	−0.259864	+	2.63296i	−0.0231505	+	0.234563i
$127$	3.47627	−	2.00703i	0.308469	−	0.178095i	−0.337772	−	0.941228i	$-0.609673\pi$
$127$	3.47627	−	2.00703i	0.308469	−	0.178095i	0.646241	+	0.763133i	$0.276340\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−5.04189	−	8.73281i	−0.443914	−	0.768881i
$130$	−1.07996	−	1.51920i	−0.0947188	−	0.133243i
$131$	−13.2614	−	7.65648i	−1.15866	−	0.668950i	−0.207674	−	0.978198i	$-0.566589\pi$
$131$	−13.2614	−	7.65648i	−1.15866	−	0.668950i	−0.950981	+	0.309248i	$0.899923\pi$
$132$	−1.21952	+	4.55131i	−0.106146	+	0.396140i
$133$	22.0264	+	2.17393i	1.90993	+	0.188503i
$134$	4.39193	+	2.53568i	0.379405	+	0.219050i
$135$	−0.133800	−	0.499350i	−0.0115157	−	0.0429772i
$136$	−0.944725	−	0.944725i	−0.0810095	−	0.0810095i
$137$	13.3624	+	13.3624i	1.14163	+	1.14163i	0.988152	+	0.153476i	$0.0490467\pi$
$137$	13.3624	+	13.3624i	1.14163	+	1.14163i	0.153476	+	0.988152i	$0.450953\pi$
$138$	−1.05875	−	3.95129i	−0.0901265	−	0.336356i
$139$	−2.82809	−	1.63280i	−0.239876	−	0.138492i	0.375244	−	0.926926i	$-0.377559\pi$
$139$	−2.82809	−	1.63280i	−0.239876	−	0.138492i	−0.615120	+	0.788434i	$0.710892\pi$
$140$	1.24596	−	0.564231i	0.105303	−	0.0476863i
$141$	−1.67580	+	6.25416i	−0.141127	+	0.526695i
$142$	6.21999	+	3.59111i	0.521970	+	0.301359i
$143$	2.83086	−	16.7513i	0.236729	−	1.40082i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−1.40192	−	1.40192i	−0.116424	−	0.116424i
$146$	2.69357	−	1.55513i	0.222922	−	0.128704i
$147$	6.86494	+	1.36842i	0.566211	+	0.112866i
$148$	−1.49238	+	1.49238i	−0.122673	+	0.122673i
$149$	−4.60358	−	1.23353i	−0.377140	−	0.101054i	0.0652692	−	0.997868i	$-0.479209\pi$
$149$	−4.60358	−	1.23353i	−0.377140	−	0.101054i	−0.442409	+	0.896813i	$0.645876\pi$
$150$	3.34656	−	3.34656i	0.273245	−	0.273245i
$151$	−1.82504	+	6.81115i	−0.148520	+	0.554283i	0.851054	+	0.525079i	$0.175964\pi$
$151$	−1.82504	+	6.81115i	−0.148520	+	0.554283i	−0.999573	+	0.0292047i	$0.990703\pi$
$152$	−7.24485	+	4.18282i	−0.587635	+	0.339271i
$153$	0.668021	+	1.15705i	0.0540063	+	0.0935417i
$154$	11.6665	+	4.39367i	0.940113	+	0.354052i
$155$		−	1.56888i		−	0.126015i
$156$	2.08904	+	2.93869i	0.167257	+	0.235284i
$157$	−6.74226	+	3.89265i	−0.538091	+	0.310667i	−0.744305	−	0.667840i	$-0.767219\pi$
$157$	−6.74226	+	3.89265i	−0.538091	+	0.310667i	0.206214	+	0.978507i	$0.433886\pi$
$158$	−2.77401	−	10.3527i	−0.220688	−	0.823619i
$159$		−	4.98817i		−	0.395587i
$160$	−0.258483	+	0.447705i	−0.0204348	+	0.0353942i
$161$	−10.6787	+	1.76083i	−0.841601	+	0.138773i
$162$	0.258819	+	0.965926i	0.0203347	+	0.0758903i
$163$	−1.78741	+	6.67072i	−0.140001	+	0.522491i	0.859926	+	0.510419i	$0.170510\pi$
$163$	−1.78741	+	6.67072i	−0.140001	+	0.522491i	−0.999927	+	0.0120724i	$0.996157\pi$
$164$	7.18828	+	1.92609i	0.561310	+	0.150403i
$165$	−2.43587			−0.189632
$166$	4.92043			0.381899
$167$	8.03262	+	2.15233i	0.621583	+	0.166553i	0.555847	−	0.831285i	$-0.312394\pi$
$167$	8.03262	+	2.15233i	0.621583	+	0.166553i	0.0657355	+	0.997837i	$0.479061\pi$
$168$	−2.41014	+	1.09143i	−0.185946	+	0.0842057i
$169$	−8.49722	−	9.83856i	−0.653633	−	0.756812i
$170$	0.345344	−	0.598153i	0.0264867	−	0.0458762i
$171$	8.08058	−	2.16519i	0.617937	−	0.165576i
$172$	5.04189	−	8.73281i	0.384440	−	0.665870i
$173$	−4.74061	−	8.21097i	−0.360422	−	0.624269i	0.627608	−	0.778529i	$-0.284034\pi$
$173$	−4.74061	−	8.21097i	−0.360422	−	0.624269i	−0.988030	+	0.154260i	$0.950701\pi$
$174$	2.71184	+	2.71184i	0.205584	+	0.205584i
$175$	−7.94170	−	9.68100i	−0.600336	−	0.731815i
$176$	−4.55131	+	1.21952i	−0.343068	+	0.0919247i
$177$	1.00932	−	0.270446i	0.0758650	−	0.0203280i
$178$			6.95699i			0.521448i
$179$	1.13620	+	0.655984i	0.0849234	+	0.0490306i	0.541860	−	0.840469i	$-0.317720\pi$
$179$	1.13620	+	0.655984i	0.0849234	+	0.0490306i	−0.456937	+	0.889499i	$0.651053\pi$
$180$	0.365550	−	0.365550i	0.0272465	−	0.0272465i
$181$	−21.6016			−1.60563			−0.802816	−	0.596227i	$-0.796666\pi$
$181$	−21.6016			−1.60563			−0.802816	+	0.596227i	$0.796666\pi$
$182$	8.28032	−	4.73669i	0.613778	−	0.351107i
$183$	−11.1379			−0.823334
$184$	2.89255	−	2.89255i	0.213241	−	0.213241i
$185$	−0.944903	−	0.545540i	−0.0694707	−	0.0401089i
$186$			3.03479i			0.222522i
$187$	6.08074	−	1.62933i	0.444668	−	0.119148i
$188$	−6.25416	+	1.67580i	−0.456131	+	0.122220i
$189$	2.61050	−	0.430450i	0.189886	−	0.0313107i
$190$	−3.05805	−	3.05805i	−0.221854	−	0.221854i
$191$	4.27639	+	7.40693i	0.309429	+	0.535946i	0.978238	−	0.207488i	$-0.0665288\pi$
$191$	4.27639	+	7.40693i	0.309429	+	0.535946i	−0.668809	+	0.743435i	$0.733195\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	21.4404	−	5.74494i	1.54331	−	0.413530i	0.615979	−	0.787763i	$-0.288761\pi$
$193$	21.4404	−	5.74494i	1.54331	−	0.413530i	0.927335	+	0.374233i	$0.122094\pi$
$194$	−7.61846	+	13.1956i	−0.546974	+	0.947386i
$195$	−1.18792	+	1.43636i	−0.0850688	+	0.102860i
$196$	2.24738	+	6.62943i	0.160527	+	0.473530i
$197$	11.3859	+	3.05084i	0.811211	+	0.217363i	0.640500	−	0.767958i	$-0.278727\pi$
$197$	11.3859	+	3.05084i	0.811211	+	0.217363i	0.170711	+	0.985321i	$0.445394\pi$
$198$	4.71186			0.334857
$199$	8.52764			0.604509			0.302254	−	0.953227i	$-0.402261\pi$
$199$	8.52764			0.604509			0.302254	+	0.953227i	$0.402261\pi$
$200$	4.57148	+	1.22493i	0.323253	+	0.0866153i
$201$	1.31257	−	4.89856i	0.0925812	−	0.345518i
$202$	4.13032	+	15.4146i	0.290608	+	1.08457i
$203$	7.84486	−	6.43544i	0.550601	−	0.451680i
$204$	−0.668021	+	1.15705i	−0.0467709	+	0.0810095i
$205$			3.84718i			0.268698i
$206$	−1.37162	−	5.11895i	−0.0955652	−	0.356654i
$207$	−3.54263	+	2.04534i	−0.246230	+	0.142161i
$208$	−1.50046	+	3.27851i	−0.104038	+	0.227324i
$209$		−	39.4177i		−	2.72658i
$210$	−0.867484	−	1.05747i	−0.0598621	−	0.0729724i
$211$	3.42891	+	5.93904i	0.236056	+	0.408861i	0.959579	−	0.281439i	$-0.0908119\pi$
$211$	3.42891	+	5.93904i	0.236056	+	0.408861i	−0.723523	+	0.690300i	$0.757479\pi$
$212$	4.31988	−	2.49408i	0.296691	−	0.171294i
$213$	1.85890	−	6.93749i	0.127369	−	0.475349i
$214$	−9.21696	+	9.21696i	−0.630059	+	0.630059i
$215$	5.03533	+	1.34921i	0.343407	+	0.0920156i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$	7.99047	+	0.788633i	0.542429	+	0.0535359i
$218$	−14.2182	+	8.20888i	−0.962978	+	0.555976i
$219$	−2.19929	−	2.19929i	−0.148614	−	0.148614i
$220$	−1.21793	−	2.10952i	−0.0821131	−	0.142224i
$221$	2.00468	−	4.38023i	0.134850	−	0.294646i
$222$	1.82779	+	1.05527i	0.122673	+	0.0708254i
$223$	0.744868	−	2.77988i	0.0498800	−	0.186155i	−0.936491	−	0.350692i	$-0.885946\pi$
$223$	0.744868	−	2.77988i	0.0498800	−	0.186155i	0.986371	+	0.164537i	$0.0526131\pi$
$224$	−2.15028	−	1.54153i	−0.143671	−	0.102998i
$225$	−4.09868	−	2.36637i	−0.273245	−	0.157758i
$226$	5.10325	+	19.0456i	0.339463	+	1.26689i
$227$	−11.5192	−	11.5192i	−0.764555	−	0.764555i	0.212587	−	0.977142i	$-0.431811\pi$
$227$	−11.5192	−	11.5192i	−0.764555	−	0.764555i	−0.977142	+	0.212587i	$0.931811\pi$
$228$	5.91540	+	5.91540i	0.391757	+	0.391757i
$229$	0.251684	+	0.939299i	0.0166318	+	0.0620706i	0.973743	−	0.227650i	$-0.0731042\pi$
$229$	0.251684	+	0.939299i	0.0166318	+	0.0620706i	−0.957111	+	0.289721i	$0.906438\pi$
$230$	1.83142	+	1.05737i	0.120760	+	0.0697209i
$231$	1.22444	−	12.4061i	0.0805625	−	0.816264i
$232$	−0.992601	+	3.70444i	−0.0651675	+	0.243208i
$233$	−22.4595	−	12.9670i	−1.47137	−	0.849498i	−0.471890	−	0.881657i	$-0.656428\pi$
$233$	−22.4595	−	12.9670i	−1.47137	−	0.849498i	−0.999483	+	0.0321599i	$0.989761\pi$
$234$	2.29788	−	2.77845i	0.150217	−	0.181633i
$235$	−1.67362	−	2.89879i	−0.109175	−	0.189096i
$236$	0.738873	+	0.738873i	0.0480965	+	0.0480965i
$237$	−9.28201	+	5.35897i	−0.602931	+	0.348102i
$238$	2.87286	+	2.05955i	0.186220	+	0.133501i
$239$	7.45111	−	7.45111i	0.481972	−	0.481972i	−0.423789	−	0.905761i	$-0.639300\pi$
$239$	7.45111	−	7.45111i	0.481972	−	0.481972i	0.905761	+	0.423789i	$0.139300\pi$
$240$	0.499350	+	0.133800i	0.0322329	+	0.00863678i
$241$	−15.4606	+	15.4606i	−0.995902	+	0.995902i	−0.999992	−	0.00408955i	$-0.998698\pi$
$241$	−15.4606	+	15.4606i	−0.995902	+	0.995902i	0.00408955	+	0.999992i	$0.498698\pi$
$242$	2.89919	−	10.8199i	0.186367	−	0.695532i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−5.56893	−	9.64567i	−0.356514	−	0.617501i
$245$	−3.00970	+	2.00925i	−0.192283	+	0.128366i
$246$		−	7.44185i		−	0.474475i
$247$	−23.2435	−	19.2232i	−1.47895	−	1.22314i
$248$	−2.62820	+	1.51739i	−0.166891	+	0.0963547i
$249$	−1.27350	−	4.75277i	−0.0807048	−	0.301194i
$250$			5.03149i			0.318219i
$251$	−12.3347	+	21.3643i	−0.778557	+	1.34850i	0.154216	+	0.988037i	$0.450715\pi$
$251$	−12.3347	+	21.3643i	−0.778557	+	1.34850i	−0.932773	+	0.360464i	$0.882619\pi$
$252$	1.67803	+	2.04553i	0.105706	+	0.128857i
$253$	4.98866	+	18.6179i	0.313635	+	1.17050i
$254$	1.03891	−	3.87728i	0.0651872	−	0.243282i
$255$	−0.667153	−	0.178763i	−0.0417787	−	0.0111946i
$256$	1.00000			0.0625000
$257$	30.1144			1.87849			0.939243	−	0.343252i	$-0.111529\pi$
$257$	30.1144			1.87849			0.939243	+	0.343252i	$0.111529\pi$
$258$	−9.74018	−	2.60987i	−0.606397	−	0.162484i
$259$	3.25347	−	4.53827i	0.202161	−	0.281994i
$260$	−1.83789	−	0.310590i	−0.113981	−	0.0192620i
$261$	1.91756	−	3.32131i	0.118694	−	0.205584i
$262$	−14.7912	+	3.96329i	−0.913803	+	0.244853i
$263$	−9.05557	+	15.6847i	−0.558390	+	0.967161i	0.439241	+	0.898369i	$0.355248\pi$
$263$	−9.05557	+	15.6847i	−0.558390	+	0.967161i	−0.997631	+	0.0687912i	$0.978086\pi$
$264$	2.35593	+	4.08059i	0.144997	+	0.251143i
$265$	1.82342	+	1.82342i	0.112012	+	0.112012i
$266$	17.1122	−	14.0378i	1.04922	−	0.860712i
$267$	6.71993	−	1.80060i	0.411253	−	0.110195i
$268$	4.89856	−	1.31257i	0.299227	−	0.0801777i
$269$		−	11.7544i		−	0.716678i	−0.933592	−	0.358339i	$-0.883343\pi$
$269$		−	11.7544i		−	0.716678i	0.933592	−	0.358339i	$-0.116657\pi$
$270$	−0.447705	−	0.258483i	−0.0272465	−	0.0157307i
$271$	18.5182	−	18.5182i	1.12490	−	1.12490i	0.133903	−	0.990994i	$-0.457249\pi$
$271$	18.5182	−	18.5182i	1.12490	−	1.12490i	0.990994	−	0.133903i	$-0.0427511\pi$
$272$	−1.33604			−0.0810095
$273$	−6.71840	−	6.77223i	−0.406616	−	0.409874i
$274$	18.8973			1.14163
$275$	−15.7685	+	15.7685i	−0.950877	+	0.950877i
$276$	−3.54263	−	2.04534i	−0.213241	−	0.123115i
$277$		−	25.9831i		−	1.56117i	−0.625048	−	0.780586i	$-0.714921\pi$
$277$		−	25.9831i		−	1.56117i	0.625048	−	0.780586i	$-0.285079\pi$
$278$	−3.15433	+	0.845200i	−0.189184	+	0.0506917i
$279$	2.93138	−	0.785461i	0.175497	−	0.0470243i
$280$	0.482054	−	1.28000i	0.0288082	−	0.0764945i
$281$	11.1800	+	11.1800i	0.666942	+	0.666942i	0.957007	−	0.290065i	$-0.0936770\pi$
$281$	11.1800	+	11.1800i	0.666942	+	0.666942i	−0.290065	+	0.957007i	$0.593677\pi$
$282$	3.23739	+	5.60732i	0.192784	+	0.333911i
$283$	−6.08447	+	10.5386i	−0.361684	+	0.626456i	−0.988238	−	0.152923i	$-0.951132\pi$
$283$	−6.08447	+	10.5386i	−0.361684	+	0.626456i	0.626554	+	0.779378i	$0.284465\pi$
$284$	6.93749	−	1.85890i	0.411665	−	0.110305i
$285$	−2.16237	+	3.74533i	−0.128088	+	0.221854i
$286$	−9.84326	−	13.8467i	−0.582044	−	0.818773i
$287$	−19.5941	−	1.93387i	−1.15660	−	0.114153i
$288$	−0.965926	−	0.258819i	−0.0569177	−	0.0152511i
$289$	−15.2150			−0.894999
$290$	−1.98262			−0.116424
$291$	14.7177	+	3.94361i	0.862769	+	0.231178i
$292$	0.804997	−	3.00429i	0.0471089	−	0.175813i
$293$	0.894661	+	3.33892i	0.0522666	+	0.195062i	0.987123	−	0.159965i	$-0.0511383\pi$
$293$	0.894661	+	3.33892i	0.0522666	+	0.195062i	−0.934856	+	0.355027i	$0.884472\pi$
$294$	5.82187	−	3.88663i	0.339538	−	0.226673i
$295$	−0.270095	+	0.467817i	−0.0157255	+	0.0272374i
$296$			2.11055i			0.122673i
$297$	−1.21952	−	4.55131i	−0.0707637	−	0.264094i
$298$	−4.12746	+	2.38299i	−0.239097	+	0.138043i
$299$	13.4113	+	6.13791i	0.775597	+	0.354965i
$300$		−	4.73275i		−	0.273245i
$301$	−9.40281	+	24.9673i	−0.541969	+	1.43909i
$302$	3.52571	+	6.10671i	0.202882	+	0.351402i
$303$	13.8203	−	7.97917i	0.793957	−	0.458391i
$304$	−2.16519	+	8.08058i	−0.124182	+	0.463453i
$305$	4.07144	−	4.07144i	0.233130	−	0.233130i
$306$	1.29052	+	0.345793i	0.0737740	+	0.0197677i
$307$	−0.304805	+	0.304805i	−0.0173961	+	0.0173961i	−0.715751	−	0.698355i	$-0.753916\pi$
$307$	−0.304805	+	0.304805i	−0.0173961	+	0.0173961i	0.698355	+	0.715751i	$0.253916\pi$
$308$	11.3562	−	5.14267i	0.647082	−	0.293031i
$309$	−4.58953	+	2.64976i	−0.261089	+	0.150740i
$310$	−1.10937	−	1.10937i	−0.0630077	−	0.0630077i
$311$	2.10107	+	3.63915i	0.119140	+	0.206357i	0.919427	−	0.393260i	$-0.128653\pi$
$311$	2.10107	+	3.63915i	0.119140	+	0.206357i	−0.800287	+	0.599617i	$0.795319\pi$
$312$	3.55514	+	0.600796i	0.201270	+	0.0340134i
$313$	−14.6700	−	8.46970i	−0.829195	−	0.478736i	0.0243821	−	0.999703i	$-0.492238\pi$
$313$	−14.6700	−	8.46970i	−0.829195	−	0.478736i	−0.853577	+	0.520967i	$0.825572\pi$
$314$	−2.01498	+	7.52002i	−0.113712	+	0.424379i
$315$	−0.796916	+	1.11162i	−0.0449011	+	0.0626326i
$316$	−9.28201	−	5.35897i	−0.522154	−	0.301466i
$317$	−3.52750	−	13.1648i	−0.198124	−	0.739410i	−0.991436	−	0.130594i	$-0.958312\pi$
$317$	−3.52750	−	13.1648i	−0.198124	−	0.739410i	0.793312	−	0.608816i	$-0.208355\pi$
$318$	−3.52717	−	3.52717i	−0.197794	−	0.197794i
$319$	−12.7778	−	12.7778i	−0.715419	−	0.715419i
$320$	0.133800	+	0.499350i	0.00747967	+	0.0279145i
$321$	11.2884	+	6.51738i	0.630059	+	0.363765i
$322$	−6.30590	+	8.79610i	−0.351414	+	0.490187i
$323$	2.89278	−	10.7960i	0.160959	−	0.600706i
$324$	0.866025	+	0.500000i	0.0481125	+	0.0277778i
$325$	1.60826	+	16.9882i	0.0892101	+	0.942336i
$326$	3.45302	+	5.98080i	0.191245	+	0.331246i
$327$	11.6091	+	11.6091i	0.641985	+	0.641985i
$328$	6.44483	−	3.72093i	0.355856	−	0.205454i
$329$	15.6051	−	7.06677i	0.860339	−	0.389604i
$330$	−1.72242	+	1.72242i	−0.0948160	+	0.0948160i
$331$	−10.1434	−	2.71791i	−0.557530	−	0.149390i	−0.0309588	−	0.999521i	$-0.509856\pi$
$331$	−10.1434	−	2.71791i	−0.557530	−	0.149390i	−0.526571	+	0.850131i	$0.676523\pi$
$332$	3.47927	−	3.47927i	0.190950	−	0.190950i
$333$	0.546250	−	2.03863i	0.0299343	−	0.111716i
$334$	7.20185	−	4.15799i	0.394068	−	0.227515i
$335$	1.31086	+	2.27047i	0.0716199	+	0.124049i
$336$	−0.932469	+	2.47598i	−0.0508704	+	0.135076i
$337$		−	17.2984i		−	0.942303i	−0.882052	−	0.471151i	$-0.843839\pi$
$337$		−	17.2984i		−	0.942303i	0.882052	−	0.471151i	$-0.156161\pi$
$338$	−12.9654	−	0.948467i	−0.705222	−	0.0515898i
$339$	17.0758	−	9.85871i	0.927430	−	0.535452i
$340$	−0.178763	−	0.667153i	−0.00969479	−	0.0361814i
$341$		−	14.2995i		−	0.774362i
$342$	4.18282	−	7.24485i	0.226181	−	0.391757i
$343$	−8.72043	−	16.3387i	−0.470859	−	0.882209i
$344$	−2.60987	−	9.74018i	−0.140715	−	0.525155i
$345$	0.547335	−	2.04268i	0.0294675	−	0.109974i
$346$	−9.15815	−	2.45392i	−0.492345	−	0.131924i
$347$	28.5418			1.53221			0.766103	−	0.642717i	$-0.222193\pi$
$347$	28.5418			1.53221			0.766103	+	0.642717i	$0.222193\pi$
$348$	3.83512			0.205584
$349$	18.0969	+	4.84905i	0.968704	+	0.259563i	0.708281	−	0.705931i	$-0.249471\pi$
$349$	18.0969	+	4.84905i	0.968704	+	0.259563i	0.260423	+	0.965495i	$0.416138\pi$
$350$	−12.4611	−	1.22987i	−0.666075	−	0.0657394i
$351$	−3.27851	−	1.50046i	−0.174994	−	0.0800888i
$352$	−2.35593	+	4.08059i	−0.125572	+	0.217496i
$353$	2.63247	−	0.705367i	0.140112	−	0.0375429i	−0.188081	−	0.982153i	$-0.560227\pi$
$353$	2.63247	−	0.705367i	0.140112	−	0.0375429i	0.328193	+	0.944611i	$0.393560\pi$
$354$	0.522462	−	0.904930i	0.0277685	−	0.0480965i
$355$	1.85648	+	3.21552i	0.0985317	+	0.170662i
$356$	4.91933	+	4.91933i	0.260724	+	0.260724i
$357$	1.24582	−	3.30802i	0.0659357	−	0.175079i
$358$	1.26726	−	0.339562i	0.0669770	−	0.0179464i
$359$	27.7541	−	7.43669i	1.46480	−	0.392493i	0.563658	−	0.826008i	$-0.309393\pi$
$359$	27.7541	−	7.43669i	1.46480	−	0.392493i	0.901146	+	0.433515i	$0.142727\pi$
$360$		−	0.516965i		−	0.0272465i
$361$	−44.1533	−	25.4919i	−2.32386	−	1.34168i
$362$	−15.2746	+	15.2746i	−0.802816	+	0.802816i
$363$	−11.2016			−0.587933
$364$	2.50572	−	9.20442i	0.131336	−	0.482443i
$365$	1.60790			0.0841614
$366$	−7.87566	+	7.87566i	−0.411667	+	0.411667i
$367$	22.8014	+	13.1644i	1.19022	+	0.687176i	0.958358	−	0.285571i	$-0.0921833\pi$
$367$	22.8014	+	13.1644i	1.19022	+	0.687176i	0.231867	+	0.972748i	$0.425517\pi$
$368$		−	4.09068i		−	0.213241i
$369$	−7.18828	+	1.92609i	−0.374207	+	0.100268i
$370$	−1.05390	+	0.282392i	−0.0547898	+	0.0146809i
$371$	−10.2035	+	8.37030i	−0.529738	+	0.434564i
$372$	2.14592	+	2.14592i	0.111261	+	0.111261i
$373$	4.10677	+	7.11313i	0.212640	+	0.368304i	0.952540	−	0.304413i	$-0.0984604\pi$
$373$	4.10677	+	7.11313i	0.212640	+	0.368304i	−0.739900	+	0.672717i	$0.765127\pi$
$374$	3.14762	−	5.45184i	0.162760	−	0.281908i
$375$	4.86005	−	1.30225i	0.250972	−	0.0672477i
$376$	−3.23739	+	5.60732i	−0.166956	+	0.289176i
$377$	−13.7662	+	1.30323i	−0.708993	+	0.0671197i
$378$	1.54153	−	2.15028i	0.0792877	−	0.110598i
$379$	−0.839171	−	0.224855i	−0.0431053	−	0.0115500i	0.237202	−	0.971460i	$-0.423770\pi$
$379$	−0.839171	−	0.224855i	−0.0431053	−	0.0115500i	−0.280307	+	0.959910i	$0.590436\pi$
$380$	−4.32474			−0.221854
$381$	−4.01405			−0.205646
$382$	8.26135	+	2.21362i	0.422688	+	0.113259i
$383$	1.09107	−	4.07191i	0.0557509	−	0.208065i	−0.932432	−	0.361346i	$-0.882317\pi$
$383$	1.09107	−	4.07191i	0.0557509	−	0.208065i	0.988183	+	0.153281i	$0.0489840\pi$
$384$	−0.258819	−	0.965926i	−0.0132078	−	0.0492922i
$385$	4.08746	+	4.98265i	0.208316	+	0.253939i
$386$	11.0984	−	19.2229i	0.564892	−	0.978422i
$387$			10.0838i			0.512587i
$388$	3.94361	+	14.7177i	0.200206	+	0.747180i
$389$	13.6483	−	7.87984i	0.691995	−	0.399524i	−0.112364	−	0.993667i	$-0.535842\pi$
$389$	13.6483	−	7.87984i	0.691995	−	0.399524i	0.804359	+	0.594144i	$0.202509\pi$
$390$	0.175672	+	1.85565i	0.00889552	+	0.0939644i
$391$			5.46532i			0.276393i
$392$	6.27685	+	3.09857i	0.317029	+	0.156502i
$393$	7.65648	+	13.2614i	0.386218	+	0.668950i
$394$	10.2083	−	5.89377i	0.514287	−	0.296924i
$395$	1.43406	−	5.35200i	0.0721556	−	0.269288i
$396$	3.33179	−	3.33179i	0.167429	−	0.167429i
$397$	27.5387	+	7.37897i	1.38213	+	0.370340i	0.871893	−	0.489696i	$-0.162892\pi$
$397$	27.5387	+	7.37897i	1.38213	+	0.370340i	0.510233	+	0.860036i	$0.329559\pi$
$398$	6.02995	−	6.02995i	0.302254	−	0.302254i
$399$	−17.9884	−	12.8959i	−0.900548	−	0.645600i
$400$	4.09868	−	2.36637i	0.204934	−	0.118319i
$401$	−1.54647	−	1.54647i	−0.0772268	−	0.0772268i	0.667438	−	0.744665i	$-0.267391\pi$
$401$	−1.54647	−	1.54647i	−0.0772268	−	0.0772268i	−0.744665	+	0.667438i	$0.767391\pi$
$402$	−2.53568	−	4.39193i	−0.126468	−	0.219050i
$403$	−8.43200	−	6.97357i	−0.420028	−	0.347378i
$404$	13.8203	+	7.97917i	0.687587	+	0.396978i
$405$	−0.133800	+	0.499350i	−0.00664860	+	0.0248129i
$406$	0.996609	−	10.0977i	0.0494609	−	0.501141i
$407$	−8.61229	−	4.97231i	−0.426895	−	0.246468i
$408$	0.345793	+	1.29052i	0.0171193	+	0.0638902i
$409$	−8.70860	−	8.70860i	−0.430613	−	0.430613i	0.458224	−	0.888837i	$-0.348486\pi$
$409$	−8.70860	−	8.70860i	−0.430613	−	0.430613i	−0.888837	+	0.458224i	$0.848486\pi$
$410$	2.72036	+	2.72036i	0.134349	+	0.134349i
$411$	−4.89098	−	18.2534i	−0.241254	−	0.900374i
$412$	−4.58953	−	2.64976i	−0.226110	−	0.130545i
$413$	−2.24688	−	1.61078i	−0.110561	−	0.0792613i
$414$	−1.05875	+	3.95129i	−0.0520345	+	0.194196i
$415$	2.20290	+	1.27184i	0.108136	+	0.0624324i
$416$	1.25727	+	3.37924i	0.0616426	+	0.165681i
$417$	1.63280	+	2.82809i	0.0799586	+	0.138492i
$418$	−27.8725	−	27.8725i	−1.36329	−	1.36329i
$419$	−0.142938	+	0.0825252i	−0.00698297	+	0.00403162i	−0.503487	−	0.864003i	$-0.667950\pi$
$419$	−0.142938	+	0.0825252i	−0.00698297	+	0.00403162i	0.496504	+	0.868034i	$0.334617\pi$
$420$	−1.36115	−	0.134341i	−0.0664172	−	0.00655516i
$421$	−16.5566	+	16.5566i	−0.806921	+	0.806921i	−0.984167	−	0.177246i	$-0.943281\pi$
$421$	−16.5566	+	16.5566i	−0.806921	+	0.806921i	0.177246	+	0.984167i	$0.443281\pi$
$422$	6.62414	+	1.77493i	0.322458	+	0.0864024i
$423$	4.57836	−	4.57836i	0.222607	−	0.222607i
$424$	1.29103	−	4.81820i	0.0626981	−	0.233992i
$425$	−5.47601	+	3.16158i	−0.265626	+	0.153359i
$426$	−3.59111	−	6.21999i	−0.173990	−	0.301359i
$427$	18.6897	+	22.7829i	0.904457	+	1.10254i
$428$			13.0348i			0.630059i
$429$	−10.8273	+	13.0917i	−0.522746	+	0.632071i
$430$	4.51456	−	2.60648i	0.217711	−	0.125696i
$431$	−2.66592	−	9.94935i	−0.128413	−	0.479243i	0.871525	−	0.490350i	$-0.163131\pi$
$431$	−2.66592	−	9.94935i	−0.128413	−	0.479243i	−0.999938	+	0.0111069i	$0.996464\pi$
$432$			1.00000i			0.0481125i
$433$	−4.50149	+	7.79682i	−0.216328	+	0.374691i	−0.953683	−	0.300815i	$-0.902741\pi$
$433$	−4.50149	+	7.79682i	−0.216328	+	0.374691i	0.737355	+	0.675506i	$0.236075\pi$
$434$	6.20777	−	5.09247i	0.297982	−	0.244446i
$435$	0.513140	+	1.91507i	0.0246032	+	0.0918203i
$436$	−4.24923	+	15.8583i	−0.203501	+	0.759477i
$437$	33.0551	+	8.85708i	1.58124	+	0.423692i
$438$	−3.11027			−0.148614
$439$	−12.9665			−0.618858			−0.309429	−	0.950923i	$-0.600138\pi$
$439$	−12.9665			−0.618858			−0.309429	+	0.950923i	$0.600138\pi$
$440$	−2.35287	−	0.630449i	−0.112169	−	0.0300555i
$441$	−5.26100	−	4.61756i	−0.250524	−	0.219884i
$442$	−1.67976	−	4.51481i	−0.0798982	−	0.214748i
$443$	3.41867	−	5.92130i	0.162426	−	0.281330i	−0.773312	−	0.634025i	$-0.781402\pi$
$443$	3.41867	−	5.92130i	0.162426	−	0.281330i	0.935738	+	0.352696i	$0.114735\pi$
$444$	2.03863	−	0.546250i	0.0967493	−	0.0259239i
$445$	−1.79826	+	3.11468i	−0.0852457	+	0.147650i
$446$	−1.43897	−	2.49238i	−0.0681374	−	0.118017i
$447$	3.37005	+	3.37005i	0.159398	+	0.159398i
$448$	−2.61050	+	0.430450i	−0.123335	+	0.0203369i
$449$	−30.0578	+	8.05396i	−1.41852	+	0.380090i	−0.884957	−	0.465673i	$-0.845812\pi$
$449$	−30.0578	+	8.05396i	−1.41852	+	0.380090i	−0.533558	+	0.845763i	$0.679146\pi$
$450$	−4.57148	+	1.22493i	−0.215502	+	0.0577435i
$451$			35.0650i			1.65114i
$452$	17.0758	+	9.85871i	0.803178	+	0.463715i
$453$	4.98611	−	4.98611i	0.234268	−	0.234268i
$454$	−16.2906			−0.764555
$455$	4.93149	+	0.0196780i	0.231192	+	0.000922521i
$456$	8.36563			0.391757
$457$	1.60045	−	1.60045i	0.0748657	−	0.0748657i	−0.668682	−	0.743548i	$-0.733141\pi$
$457$	1.60045	−	1.60045i	0.0748657	−	0.0748657i	0.743548	+	0.668682i	$0.233141\pi$
$458$	0.842152	+	0.486217i	0.0393512	+	0.0227194i
$459$		−	1.33604i		−	0.0623611i
$460$	2.04268	−	0.547335i	0.0952405	−	0.0255196i
$461$	28.4430	−	7.62128i	1.32472	−	0.354959i	0.473978	−	0.880537i	$-0.342818\pi$
$461$	28.4430	−	7.62128i	1.32472	−	0.354959i	0.850745	+	0.525578i	$0.176151\pi$
$462$	−7.90665	−	9.63827i	−0.367851	−	0.448413i
$463$	3.14619	+	3.14619i	0.146216	+	0.146216i	0.776425	−	0.630209i	$-0.217031\pi$
$463$	3.14619	+	3.14619i	0.146216	+	0.146216i	−0.630209	+	0.776425i	$0.717031\pi$
$464$	1.91756	+	3.32131i	0.0890204	+	0.154188i
$465$	−0.784440	+	1.35869i	−0.0363775	+	0.0630077i
$466$	−25.0504	+	6.71222i	−1.16044	+	0.310938i
$467$	−4.54212	+	7.86718i	−0.210184	+	0.364049i	−0.951772	−	0.306806i	$-0.900740\pi$
$467$	−4.54212	+	7.86718i	−0.210184	+	0.364049i	0.741588	+	0.670856i	$0.234073\pi$
$468$	−0.339815	−	3.58950i	−0.0157079	−	0.165925i
$469$	−12.2227	+	5.53504i	−0.564392	+	0.255584i
$470$	−3.23318	−	0.866328i	−0.149135	−	0.0399607i
$471$	7.78530			0.358728
$472$	1.04492			0.0480965
$473$	45.8944	+	12.2974i	2.11023	+	0.565433i
$474$	−2.77401	+	10.3527i	−0.127414	+	0.475517i
$475$	10.2473	+	38.2433i	0.470177	+	1.75473i
$476$	3.48774	−	0.575100i	0.159860	−	0.0263597i
$477$	−2.49408	+	4.31988i	−0.114196	+	0.197794i
$478$		−	10.5375i		−	0.481972i
$479$	8.55674	+	31.9342i	0.390967	+	1.45911i	0.828542	+	0.559928i	$0.189171\pi$
$479$	8.55674	+	31.9342i	0.390967	+	1.45911i	−0.437574	+	0.899182i	$0.644162\pi$
$480$	0.447705	−	0.258483i	0.0204348	−	0.0117981i
$481$	−7.13206	+	2.65353i	−0.325194	+	0.120990i
$482$			21.8645i			0.995902i
$483$	10.1285	+	3.81443i	0.460861	+	0.173563i
$484$	−5.60081	−	9.70090i	−0.254582	−	0.440950i
$485$	−6.82165	+	3.93848i	−0.309755	+	0.178837i
$486$	0.258819	−	0.965926i	0.0117403	−	0.0438153i
$487$	−21.7330	+	21.7330i	−0.984815	+	0.984815i	−0.999886	−	0.0150712i	$-0.995203\pi$
$487$	−21.7330	+	21.7330i	−0.984815	+	0.984815i	0.0150712	+	0.999886i	$0.495203\pi$
$488$	−10.7583	−	2.88269i	−0.487007	−	0.130493i
$489$	4.88330	−	4.88330i	0.220831	−	0.220831i
$490$	−0.707427	+	3.54894i	−0.0319583	+	0.160325i
$491$	21.6578	−	12.5041i	0.977402	−	0.564303i	0.0759169	−	0.997114i	$-0.475812\pi$
$491$	21.6578	−	12.5041i	0.977402	−	0.564303i	0.901485	+	0.432811i	$0.142478\pi$
$492$	−5.26218	−	5.26218i	−0.237238	−	0.237238i
$493$	−2.56194	−	4.43741i	−0.115384	−	0.199851i
$494$	−30.0285	+	2.84277i	−1.35104	+	0.127902i
$495$	2.10952	+	1.21793i	0.0948160	+	0.0547420i
$496$	−0.785461	+	2.93138i	−0.0352683	+	0.131623i
$497$	−17.3102	+	7.83890i	−0.776467	+	0.351623i
$498$	−4.26122	−	2.46021i	−0.190950	−	0.110245i
$499$	−1.46269	−	5.45883i	−0.0654789	−	0.244371i	0.925427	−	0.378925i	$-0.123706\pi$
$499$	−1.46269	−	5.45883i	−0.0654789	−	0.244371i	−0.990906	+	0.134555i	$0.957040\pi$
$500$	3.55780	+	3.55780i	0.159110	+	0.159110i
$501$	−5.88028	−	5.88028i	−0.262712	−	0.262712i
$502$	6.38489	+	23.8287i	0.284972	+	1.06353i
$503$	−34.3416	−	19.8272i	−1.53122	−	0.884049i	−0.999306	−	0.0372498i	$-0.988140\pi$
$503$	−34.3416	−	19.8272i	−1.53122	−	0.884049i	−0.531912	−	0.846799i	$-0.678526\pi$
$504$	2.63296	+	0.259864i	0.117281	+	0.0115753i
$505$	−2.13523	+	7.96880i	−0.0950166	+	0.354607i
$506$	16.6924	+	9.63736i	0.742067	+	0.428433i
$507$	2.43953	+	12.7691i	0.108343	+	0.567093i
$508$	−2.00703	−	3.47627i	−0.0890474	−	0.154235i
$509$	−11.9731	−	11.9731i	−0.530700	−	0.530700i	0.390081	−	0.920781i	$-0.372447\pi$
$509$	−11.9731	−	11.9731i	−0.530700	−	0.530700i	−0.920781	+	0.390081i	$0.872447\pi$
$510$	−0.598153	+	0.345344i	−0.0264867	+	0.0152921i
$511$	−0.808247	+	8.18921i	−0.0357548	+	0.362269i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−8.08058	−	2.16519i	−0.356766	−	0.0955953i
$514$	21.2941	−	21.2941i	0.939243	−	0.939243i
$515$	0.709079	−	2.64632i	0.0312458	−	0.116611i
$516$	−8.73281	+	5.04189i	−0.384440	+	0.221957i
$517$	−15.2541	−	26.4209i	−0.670876	−	1.16199i
$518$	−0.908487	−	5.50959i	−0.0399166	−	0.242078i
$519$			9.48122i			0.416179i
$520$	−1.51920	+	1.07996i	−0.0666214	+	0.0473594i
$521$	31.5750	−	18.2298i	1.38333	−	0.798663i	0.390773	−	0.920487i	$-0.372208\pi$
$521$	31.5750	−	18.2298i	1.38333	−	0.798663i	0.992552	+	0.121824i	$0.0388743\pi$
$522$	−0.992601	−	3.70444i	−0.0434450	−	0.162139i
$523$			6.97874i			0.305159i	0.988291	+	0.152580i	$0.0487580\pi$
$523$			6.97874i			0.305159i	−0.988291	+	0.152580i	$0.951242\pi$
$524$	−7.65648	+	13.2614i	−0.334475	+	0.579328i
$525$	2.03721	+	12.3548i	0.0889112	+	0.539209i
$526$	4.68751	+	17.4940i	0.204385	+	0.762776i
$527$	1.04941	−	3.91645i	0.0457130	−	0.170603i
$528$	4.55131	+	1.21952i	0.198070	+	0.0530728i
$529$	6.26633			0.272449
$530$	2.57871			0.112012
$531$	−1.00932	−	0.270446i	−0.0438007	−	0.0117364i
$532$	2.17393	−	22.0264i	0.0942517	−	0.954964i
$533$	20.6768	+	17.1004i	0.895611	+	0.740703i
$534$	3.47849	−	6.02493i	0.150529	−	0.260724i
$535$	−6.50890	+	1.74406i	−0.281404	+	0.0754021i
$536$	2.53568	−	4.39193i	0.109525	−	0.189702i
$537$	−0.655984	−	1.13620i	−0.0283078	−	0.0490306i
$538$	−8.31161	−	8.31161i	−0.358339	−	0.358339i
$539$	−27.4318	+	18.3132i	−1.18157	+	0.788807i
$540$	−0.499350	+	0.133800i	−0.0214886	+	0.00575785i
$541$	−38.1430	+	10.2204i	−1.63990	+	0.439409i	−0.956759	−	0.290881i	$-0.906052\pi$
$541$	−38.1430	+	10.2204i	−1.63990	+	0.439409i	−0.683137	+	0.730290i	$0.739385\pi$
$542$		−	26.1886i		−	1.12490i
$543$	18.7075	+	10.8008i	0.802816	+	0.463506i
$544$	−0.944725	+	0.944725i	−0.0405047	+	0.0405047i
$545$	−8.48741			−0.363561
$546$	−9.53932	−	0.0380645i	−0.408245	−	0.00162901i
$547$	27.6065			1.18037			0.590185	−	0.807268i	$-0.299055\pi$
$547$	27.6065			1.18037			0.590185	+	0.807268i	$0.299055\pi$
$548$	13.3624	−	13.3624i	0.570814	−	0.570814i
$549$	9.64567	+	5.56893i	0.411667	+	0.237676i
$550$			22.3000i			0.950877i
$551$	−30.9900	+	8.30374i	−1.32022	+	0.353751i
$552$	−3.95129	+	1.05875i	−0.168178	+	0.0450632i
$553$	26.5374	+	9.99415i	1.12849	+	0.424994i
$554$	−18.3728	−	18.3728i	−0.780586	−	0.780586i
$555$	0.545540	+	0.944903i	0.0231569	+	0.0401089i
$556$	−1.63280	+	2.82809i	−0.0692462	+	0.119938i
$557$	−6.39216	+	1.71277i	−0.270844	+	0.0725725i	−0.391685	−	0.920099i	$-0.628108\pi$
$557$	−6.39216	+	1.71277i	−0.270844	+	0.0725725i	0.120841	+	0.992672i	$0.461441\pi$
$558$	1.51739	−	2.62820i	0.0642364	−	0.111261i
$559$	29.6331	−	21.0654i	1.25335	−	0.890972i
$560$	−0.564231	−	1.24596i	−0.0238431	−	0.0526514i
$561$	−6.08074	−	1.62933i	−0.256729	−	0.0687904i
$562$	15.8109			0.666942
$563$	−25.3413			−1.06801			−0.534005	−	0.845481i	$-0.679314\pi$
$563$	−25.3413			−1.06801			−0.534005	+	0.845481i	$0.679314\pi$
$564$	6.25416	+	1.67580i	0.263347	+	0.0705637i
$565$	−2.63820	+	9.84590i	−0.110990	+	0.414220i
$566$	3.14955	+	11.7543i	0.132386	+	0.494070i
$567$	−2.47598	−	0.932469i	−0.103982	−	0.0391600i
$568$	3.59111	−	6.21999i	0.150680	−	0.260985i
$569$			4.07156i			0.170689i	0.996352	+	0.0853444i	$0.0271991\pi$
$569$			4.07156i			0.170689i	−0.996352	+	0.0853444i	$0.972801\pi$
$570$	1.11933	+	4.17738i	0.0468834	+	0.174971i
$571$	−1.45716	+	0.841291i	−0.0609802	+	0.0352069i	−0.530180	−	0.847885i	$-0.677876\pi$
$571$	−1.45716	+	0.841291i	−0.0609802	+	0.0352069i	0.469200	+	0.883092i	$0.344542\pi$
$572$	−16.7513	−	2.83086i	−0.700409	−	0.118364i
$573$		−	8.55278i		−	0.357298i
$574$	−15.2226	+	12.4877i	−0.635377	+	0.521225i
$575$	−9.68008	−	16.7664i	−0.403687	−	0.699207i
$576$	−0.866025	+	0.500000i	−0.0360844	+	0.0208333i
$577$	−8.75768	+	32.6841i	−0.364587	+	1.36066i	0.503393	+	0.864058i	$0.332085\pi$
$577$	−8.75768	+	32.6841i	−0.364587	+	1.36066i	−0.867980	+	0.496600i	$0.834582\pi$
$578$	−10.7586	+	10.7586i	−0.447500	+	0.447500i
$579$	−21.4404	−	5.74494i	−0.891033	−	0.238751i
$580$	−1.40192	+	1.40192i	−0.0582118	+	0.0582118i
$581$	−7.58498	+	10.5803i	−0.314678	+	0.438944i
$582$	13.1956	−	7.61846i	0.546974	−	0.315795i
$583$	16.6195	+	16.6195i	0.688310	+	0.688310i
$584$	−1.55513	−	2.69357i	−0.0643519	−	0.111461i
$585$	1.74695	−	0.649963i	0.0722275	−	0.0268727i
$586$	2.99359	+	1.72835i	0.123664	+	0.0713975i
$587$	−5.73741	+	21.4123i	−0.236808	+	0.883781i	0.740517	+	0.672038i	$0.234581\pi$
$587$	−5.73741	+	21.4123i	−0.236808	+	0.883781i	−0.977325	+	0.211743i	$0.932086\pi$
$588$	1.36842	−	6.86494i	0.0564328	−	0.283105i
$589$	−21.9866	−	12.6940i	−0.905942	−	0.523046i
$590$	0.139811	+	0.521783i	0.00575594	+	0.0214814i
$591$	−8.33505	−	8.33505i	−0.342858	−	0.342858i
$592$	1.49238	+	1.49238i	0.0613366	+	0.0613366i
$593$	9.61407	+	35.8802i	0.394803	+	1.47342i	0.822116	+	0.569320i	$0.192793\pi$
$593$	9.61407	+	35.8802i	0.394803	+	1.47342i	−0.427313	+	0.904104i	$0.640540\pi$
$594$	−4.08059	−	2.35593i	−0.167429	−	0.0966650i
$595$	0.753837	+	1.66465i	0.0309043	+	0.0682442i
$596$	−1.23353	+	4.60358i	−0.0505272	+	0.188570i
$597$	−7.38516	−	4.26382i	−0.302254	−	0.174507i
$598$	13.8234	−	5.14308i	0.565281	−	0.210316i
$599$	−22.8545	−	39.5852i	−0.933811	−	1.61741i	−0.776740	−	0.629822i	$-0.783128\pi$
$599$	−22.8545	−	39.5852i	−0.933811	−	1.61741i	−0.157071	−	0.987587i	$-0.550205\pi$
$600$	−3.34656	−	3.34656i	−0.136623	−	0.136623i
$601$	13.4905	−	7.78875i	0.550289	−	0.317710i	−0.198949	−	0.980010i	$-0.563753\pi$
$601$	13.4905	−	7.78875i	0.550289	−	0.317710i	0.749239	+	0.662300i	$0.230420\pi$
$602$	11.0057	+	24.3033i	0.448561	+	0.990530i
$603$	−3.58600	+	3.58600i	−0.146033	+	0.146033i
$604$	6.81115	+	1.82504i	0.277142	+	0.0742599i
$605$	4.09475	−	4.09475i	0.166475	−	0.166475i
$606$	4.13032	−	15.4146i	0.167783	−	0.626174i
$607$	−22.2787	+	12.8626i	−0.904263	+	0.522076i	−0.878581	−	0.477594i	$-0.841509\pi$
$607$	−22.2787	+	12.8626i	−0.904263	+	0.522076i	−0.0256821	+	0.999670i	$0.508176\pi$
$608$	4.18282	+	7.24485i	0.169636	+	0.293817i
$609$	−10.0116	+	1.65083i	−0.405689	+	0.0668949i
$610$		−	5.75788i		−	0.233130i
$611$	−23.0188	−	3.89002i	−0.931240	−	0.157373i
$612$	1.15705	−	0.668021i	0.0467709	−	0.0270032i
$613$	−1.37205	−	5.12055i	−0.0554164	−	0.206817i	0.932666	−	0.360740i	$-0.117476\pi$
$613$	−1.37205	−	5.12055i	−0.0554164	−	0.206817i	−0.988083	+	0.153923i	$0.950809\pi$
$614$			0.431059i			0.0173961i
$615$	1.92359	−	3.33175i	0.0775666	−	0.134349i
$616$	4.39367	−	11.6665i	0.177026	−	0.470056i
$617$	11.0875	+	41.3792i	0.446367	+	1.66586i	0.712302	+	0.701873i	$0.247652\pi$
$617$	11.0875	+	41.3792i	0.446367	+	1.66586i	−0.265936	+	0.963991i	$0.585681\pi$
$618$	−1.37162	+	5.11895i	−0.0551746	+	0.205914i
$619$	−4.18483	−	1.12132i	−0.168203	−	0.0450697i	0.173735	−	0.984792i	$-0.444416\pi$
$619$	−4.18483	−	1.12132i	−0.168203	−	0.0450697i	−0.341937	+	0.939723i	$0.611083\pi$
$620$	−1.56888			−0.0630077
$621$	4.09068			0.164153
$622$	4.05895	+	1.08759i	0.162749	+	0.0436084i
$623$	−14.9595	−	10.7244i	−0.599338	−	0.429664i
$624$	2.93869	−	2.08904i	0.117642	−	0.0836285i
$625$	10.5313	−	18.2408i	0.421253	−	0.729631i
$626$	−16.3622	+	4.38424i	−0.653965	+	0.175229i
$627$	−19.7088	+	34.1367i	−0.787096	+	1.36329i
$628$	3.89265	+	6.74226i	0.155334	+	0.269046i
$629$	−1.99389	−	1.99389i	−0.0795016	−	0.0795016i
$630$	0.222528	+	1.34954i	0.00886572	+	0.0537669i
$631$	0.711348	−	0.190605i	0.0283183	−	0.00758787i	−0.244632	−	0.969616i	$-0.578667\pi$
$631$	0.711348	−	0.190605i	0.0283183	−	0.00758787i	0.272950	+	0.962028i	$0.412001\pi$
$632$	−10.3527	+	2.77401i	−0.411810	+	0.110344i
$633$		−	6.85782i		−	0.272574i
$634$	−11.8033	−	6.81461i	−0.468767	−	0.270643i
$635$	1.46733	−	1.46733i	0.0582294	−	0.0582294i
$636$	−4.98817			−0.197794
$637$	−2.57915	+	25.1067i	−0.102190	+	0.994765i
$638$	−18.0705			−0.715419
$639$	−5.07860	+	5.07860i	−0.200906	+	0.200906i
$640$	0.447705	+	0.258483i	0.0176971	+	0.0102174i
$641$		−	3.90544i		−	0.154256i	−0.997021	−	0.0771278i	$-0.975425\pi$
$641$		−	3.90544i		−	0.154256i	0.997021	−	0.0771278i	$-0.0245749\pi$
$642$	12.5906	−	3.37364i	0.496912	−	0.133147i
$643$	24.5573	−	6.58011i	0.968446	−	0.259494i	0.260275	−	0.965535i	$-0.416187\pi$
$643$	24.5573	−	6.58011i	0.968446	−	0.259494i	0.708172	+	0.706040i	$0.249520\pi$
$644$	1.76083	+	10.6787i	0.0693866	+	0.420801i
$645$	−3.68612	−	3.68612i	−0.145141	−	0.145141i
$646$	−5.58842	−	9.67943i	−0.219874	−	0.380832i
$647$	−18.8076	+	32.5757i	−0.739402	+	1.28068i	0.213363	+	0.976973i	$0.431558\pi$
$647$	−18.8076	+	32.5757i	−0.739402	+	1.28068i	−0.952765	+	0.303709i	$0.901775\pi$
$648$	0.965926	−	0.258819i	0.0379452	−	0.0101674i
$649$	−2.46177	+	4.26391i	−0.0966328	+	0.167373i
$650$	13.1497	+	10.8753i	0.515773	+	0.426563i
$651$	−6.52564	−	4.67821i	−0.255760	−	0.183354i
$652$	6.67072	+	1.78741i	0.261245	+	0.0700005i
$653$	25.1888			0.985713			0.492856	−	0.870111i	$-0.335953\pi$
$653$	25.1888			0.985713			0.492856	+	0.870111i	$0.335953\pi$
$654$	16.4178			0.641985
$655$	−7.64653	−	2.04888i	−0.298775	−	0.0800564i
$656$	1.92609	−	7.18828i	0.0752013	−	0.280655i
$657$	0.804997	+	3.00429i	0.0314059	+	0.117208i
$658$	6.03753	−	16.0315i	0.235368	−	0.624971i
$659$	4.07472	−	7.05762i	0.158729	−	0.274926i	−0.775682	−	0.631124i	$-0.782594\pi$
$659$	4.07472	−	7.05762i	0.158729	−	0.274926i	0.934410	+	0.356198i	$0.115927\pi$
$660$			2.43587i			0.0948160i
$661$	−1.32521	−	4.94575i	−0.0515447	−	0.192367i	0.935353	−	0.353716i	$-0.115082\pi$
$661$	−1.32521	−	4.94575i	−0.0515447	−	0.192367i	−0.986897	+	0.161349i	$0.948416\pi$
$662$	−9.09430	+	5.25060i	−0.353460	+	0.204070i
$663$	−3.92622	+	2.79105i	−0.152482	+	0.108395i
$664$		−	4.92043i		−	0.190950i
$665$	11.2897	−	1.86159i	0.437797	−	0.0721892i
$666$	−1.05527	−	1.82779i	−0.0408911	−	0.0708254i
$667$	13.5864	−	7.84412i	0.526068	−	0.303725i
$668$	2.15233	−	8.03262i	0.0832763	−	0.310791i
$669$	−2.03502	+	2.03502i	−0.0786783	+	0.0786783i
$670$	2.53239	+	0.678551i	0.0978346	+	0.0262147i
$671$	37.1090	−	37.1090i	1.43258	−	1.43258i
$672$	1.09143	+	2.41014i	0.0421028	+	0.0929732i
$673$	38.4936	−	22.2243i	1.48382	−	0.856683i	0.483988	−	0.875075i	$-0.339188\pi$
$673$	38.4936	−	22.2243i	1.48382	−	0.856683i	0.999831	+	0.0183913i	$0.00585447\pi$
$674$	−12.2318	−	12.2318i	−0.471151	−	0.471151i
$675$	2.36637	+	4.09868i	0.0910818	+	0.157758i
$676$	−9.83856	+	8.49722i	−0.378406	+	0.326816i
$677$	7.89020	+	4.55541i	0.303245	+	0.175079i	0.643900	−	0.765110i	$-0.277315\pi$
$677$	7.89020	+	4.55541i	0.303245	+	0.175079i	−0.340655	+	0.940188i	$0.610649\pi$
$678$	5.10325	−	19.0456i	0.195989	−	0.731441i
$679$	−16.6300	−	36.7231i	−0.638202	−	1.40930i
$680$	−0.598153	−	0.345344i	−0.0229381	−	0.0132433i
$681$	4.21632	+	15.7355i	0.161570	+	0.602986i
$682$	−10.1113	−	10.1113i	−0.387181	−	0.387181i
$683$	16.9608	+	16.9608i	0.648986	+	0.648986i	0.952748	−	0.303762i	$-0.0982427\pi$
$683$	16.9608	+	16.9608i	0.648986	+	0.648986i	−0.303762	+	0.952748i	$0.598243\pi$
$684$	−2.16519	−	8.08058i	−0.0827879	−	0.308969i
$685$	8.46042	+	4.88463i	0.323256	+	0.186632i
$686$	−17.7195	−	5.38695i	−0.676534	−	0.205675i
$687$	0.251684	−	0.939299i	0.00960236	−	0.0358365i
$688$	−8.73281	−	5.04189i	−0.332935	−	0.192220i
$689$	17.9050	−	1.69505i	0.682128	−	0.0645764i
$690$	−1.05737	−	1.83142i	−0.0402534	−	0.0697209i
$691$	18.1778	+	18.1778i	0.691516	+	0.691516i	0.962565	−	0.271049i	$-0.0873707\pi$
$691$	18.1778	+	18.1778i	0.691516	+	0.691516i	−0.271049	+	0.962565i	$0.587371\pi$
$692$	−8.21097	+	4.74061i	−0.312134	+	0.180211i
$693$	−7.26347	+	10.1318i	−0.275916	+	0.384875i
$694$	20.1821	−	20.1821i	0.766103	−	0.766103i
$695$	−1.63068	−	0.436939i	−0.0618551	−	0.0165740i
$696$	2.71184	−	2.71184i	0.102792	−	0.102792i
$697$	−2.57334	+	9.60384i	−0.0974723	+	0.363772i
$698$	16.2252	−	9.36764i	0.614134	−	0.354570i
$699$	12.9670	+	22.4595i	0.490458	+	0.849498i
$700$	−9.68100	+	7.94170i	−0.365907	+	0.300168i
$701$		−	37.7415i		−	1.42548i	−0.701430	−	0.712738i	$-0.747455\pi$
$701$		−	37.7415i		−	1.42548i	0.701430	−	0.712738i	$-0.252545\pi$
$702$	−3.37924	+	1.25727i	−0.127541	+	0.0474525i
$703$	−15.2906	+	8.82804i	−0.576697	+	0.332956i
$704$	1.21952	+	4.55131i	0.0459624	+	0.171534i
$705$			3.34723i			0.126064i
$706$	1.36267	−	2.36021i	0.0512846	−	0.0888275i
$707$	−39.5126	−	14.8807i	−1.48602	−	0.559645i
$708$	−0.270446	−	1.00932i	−0.0101640	−	0.0379325i
$709$	4.24654	−	15.8483i	0.159482	−	0.595196i	−0.839198	−	0.543827i	$-0.816975\pi$
$709$	4.24654	−	15.8483i	0.159482	−	0.595196i	0.998680	−	0.0513690i	$-0.0163585\pi$
$710$	3.58644	+	0.960984i	0.134597	+	0.0360651i
$711$	10.7179			0.401954
$712$	6.95699			0.260724
$713$	11.9913	+	3.21307i	0.449079	+	0.120330i
$714$	−1.45820	−	3.22005i	−0.0545717	−	0.120507i
$715$	−0.827744	−	8.74355i	−0.0309559	−	0.326990i
$716$	0.655984	−	1.13620i	0.0245153	−	0.0424617i
$717$	−10.1784	+	2.72730i	−0.380119	+	0.101853i
$718$	14.3666	−	24.8836i	0.536156	−	0.928649i
$719$	−21.3926	−	37.0531i	−0.797810	−	1.38185i	−0.921040	−	0.389469i	$-0.872659\pi$
$719$	−21.3926	−	37.0531i	−0.797810	−	1.38185i	0.123230	−	0.992378i	$-0.460675\pi$
$720$	−0.365550	−	0.365550i	−0.0136232	−	0.0136232i
$721$	13.1216	+	4.94165i	0.488672	+	0.184037i
$722$	−49.2466	+	13.1956i	−1.83277	+	0.491089i
$723$	21.1195	−	5.65896i	0.785443	−	0.210459i
$724$			21.6016i			0.802816i
$725$	15.7189	+	9.07532i	0.583786	+	0.337049i
$726$	−7.92075	+	7.92075i	−0.293967	+	0.293967i
$727$	35.0382			1.29950			0.649748	−	0.760150i	$-0.274874\pi$
$727$	35.0382			1.29950			0.649748	+	0.760150i	$0.274874\pi$
$728$	−4.73669	−	8.28032i	−0.175554	−	0.306889i
$729$	−1.00000			−0.0370370
$730$	1.13696	−	1.13696i	0.0420807	−	0.0420807i
$731$	11.6674	+	6.73618i	0.431535	+	0.249147i
$732$			11.1379i			0.411667i
$733$	−0.544762	+	0.145969i	−0.0201213	+	0.00539147i	−0.268866	−	0.963178i	$-0.586649\pi$
$733$	−0.544762	+	0.145969i	−0.0201213	+	0.00539147i	0.248744	+	0.968569i	$0.419982\pi$
$734$	25.4317	−	6.81440i	0.938700	−	0.251524i
$735$	3.61110	−	0.235210i	0.133198	−	0.00867585i
$736$	−2.89255	−	2.89255i	−0.106621	−	0.106621i
$737$	11.9478	+	20.6942i	0.440102	+	0.762279i
$738$	−3.72093	+	6.44483i	−0.136969	+	0.237238i
$739$	5.87642	−	1.57458i	0.216168	−	0.0579220i	−0.149110	−	0.988821i	$-0.547641\pi$
$739$	5.87642	−	1.57458i	0.216168	−	0.0579220i	0.365277	+	0.930899i	$0.380974\pi$
$740$	−0.545540	+	0.944903i	−0.0200545	+	0.0347353i
$741$	10.5178	+	28.2695i	0.386382	+	1.03851i
$742$	−1.29625	+	13.1336i	−0.0475867	+	0.482151i
$743$	−16.3758	−	4.38787i	−0.600768	−	0.160975i	−0.0543983	−	0.998519i	$-0.517324\pi$
$743$	−16.3758	−	4.38787i	−0.600768	−	0.160975i	−0.546370	+	0.837544i	$0.683991\pi$
$744$	3.03479			0.111261
$745$	−2.46384			−0.0902682
$746$	7.93367	+	2.12582i	0.290472	+	0.0778318i
$747$	−1.27350	+	4.75277i	−0.0465949	+	0.173895i
$748$	−1.62933	−	6.08074i	−0.0595742	−	0.222334i
$749$	−5.61081	−	34.0272i	−0.205015	−	1.24333i
$750$	2.51575	−	4.35740i	0.0918620	−	0.159110i
$751$		−	49.4330i		−	1.80384i	−0.431906	−	0.901919i	$-0.642159\pi$
$751$		−	49.4330i		−	1.80384i	0.431906	−	0.901919i	$-0.357841\pi$
$752$	1.67580	+	6.25416i	0.0611100	+	0.228066i
$753$	21.3643	−	12.3347i	0.778557	−	0.449500i
$754$	−8.81262	+	10.6557i	−0.320937	+	0.388056i
$755$			3.64534i			0.132667i
$756$	−0.430450	−	2.61050i	−0.0156553	−	0.0949430i
$757$	−8.63889	−	14.9630i	−0.313986	−	0.543839i	0.665236	−	0.746633i	$-0.268331\pi$
$757$	−8.63889	−	14.9630i	−0.313986	−	0.543839i	−0.979221	+	0.202794i	$0.934998\pi$
$758$	−0.752381	+	0.434387i	−0.0273277	+	0.0157776i
$759$	4.98866	−	18.6179i	0.181077	−	0.675789i
$760$	−3.05805	+	3.05805i	−0.110927	+	0.110927i
$761$	5.55114	+	1.48742i	0.201229	+	0.0539190i	0.358025	−	0.933712i	$-0.383450\pi$
$761$	5.55114	+	1.48742i	0.201229	+	0.0539190i	−0.156797	+	0.987631i	$0.550117\pi$
$762$	−2.83836	+	2.83836i	−0.102823	+	0.102823i
$763$	4.26639	−	43.2273i	0.154454	−	1.56493i
$764$	7.40693	−	4.27639i	0.267973	−	0.154714i
$765$	0.488390	+	0.488390i	0.0176578	+	0.0176578i
$766$	−2.10778	−	3.65078i	−0.0761571	−	0.131908i
$767$	1.31375	+	3.53105i	0.0474367	+	0.127499i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	−3.92845	+	14.6612i	−0.141663	+	0.528695i	0.858218	+	0.513286i	$0.171572\pi$
$769$	−3.92845	+	14.6612i	−0.141663	+	0.528695i	−0.999881	+	0.0154095i	$0.995095\pi$
$770$	6.41354	+	0.632995i	0.231128	+	0.0228115i
$771$	−26.0799	−	15.0572i	−0.939243	−	0.542272i
$772$	−5.74494	−	21.4404i	−0.206765	−	0.771657i
$773$	−5.78121	−	5.78121i	−0.207936	−	0.207936i	0.595454	−	0.803390i	$-0.296972\pi$
$773$	−5.78121	−	5.78121i	−0.207936	−	0.207936i	−0.803390	+	0.595454i	$0.796972\pi$
$774$	7.13031	+	7.13031i	0.256294	+	0.256294i
$775$	3.71739	+	13.8735i	0.133533	+	0.498350i
$776$	13.1956	+	7.61846i	0.473693	+	0.273487i
$777$	−5.08672	+	2.30352i	−0.182485	+	0.0826382i
$778$	4.07890	−	15.2227i	0.146236	−	0.545759i
$779$	53.9151	+	31.1279i	1.93171	+	1.11527i
$780$	1.43636	+	1.18792i	0.0514299	+	0.0425344i
$781$	16.9208	+	29.3077i	0.605474	+	1.04871i
$782$	3.86457	+	3.86457i	0.138197	+	0.138197i
$783$	−3.32131	+	1.91756i	−0.118694	+	0.0685279i
$784$	6.62943	−	2.24738i	0.236765	−	0.0802636i
$785$	−2.84591	+	2.84591i	−0.101575	+	0.101575i
$786$	14.7912	+	3.96329i	0.527584	+	0.141366i
$787$	−8.25612	+	8.25612i	−0.294299	+	0.294299i	−0.838776	−	0.544477i	$-0.816728\pi$
$787$	−8.25612	+	8.25612i	−0.294299	+	0.294299i	0.544477	+	0.838776i	$0.316728\pi$
$788$	3.05084	−	11.3859i	0.108682	−	0.405605i
$789$	15.6847	−	9.05557i	0.558390	−	0.322387i
$790$	−2.77040	−	4.79847i	−0.0985664	−	0.170722i
$791$	−48.8201	−	18.3859i	−1.73584	−	0.653727i
$792$		−	4.71186i		−	0.167429i
$793$	−3.78481	−	39.9794i	−0.134403	−	1.41971i
$794$	24.6905	−	14.2551i	0.876233	−	0.505893i
$795$	−0.667419	−	2.49084i	−0.0236709	−	0.0883410i
$796$		−	8.52764i		−	0.302254i
$797$	3.38754	−	5.86739i	0.119993	−	0.207834i	−0.799772	−	0.600304i	$-0.795046\pi$
$797$	3.38754	−	5.86739i	0.119993	−	0.207834i	0.919765	+	0.392471i	$0.128380\pi$
$798$	−21.8385	+	3.60099i	−0.773074	+	0.127474i
$799$	−2.23894	−	8.35582i	−0.0792078	−	0.295608i
$800$	1.22493	−	4.57148i	0.0433076	−	0.161626i
$801$	−6.71993	−	1.80060i	−0.237437	−	0.0636211i
$802$	−2.18703			−0.0772268
$803$	14.6552			0.517169
$804$	−4.89856	−	1.31257i	−0.172759	−	0.0462906i
$805$	−5.09682	+	2.30809i	−0.179639	+	0.0813495i
$806$	−10.8934	+	1.03127i	−0.383703	+	0.0363248i
$807$	−5.87719	+	10.1796i	−0.206887	+	0.358339i
$808$	15.4146	−	4.13032i	0.542283	−	0.145304i
$809$	−20.0186	+	34.6732i	−0.703815	+	1.21904i	0.263302	+	0.964713i	$0.415188\pi$
$809$	−20.0186	+	34.6732i	−0.703815	+	1.21904i	−0.967117	+	0.254330i	$0.918145\pi$
$810$	0.258483	+	0.447705i	0.00908215	+	0.0157307i
$811$	−3.59793	−	3.59793i	−0.126340	−	0.126340i	0.641109	−	0.767450i	$-0.278475\pi$
$811$	−3.59793	−	3.59793i	−0.126340	−	0.126340i	−0.767450	+	0.641109i	$0.778475\pi$
$812$	−6.43544	−	7.84486i	−0.225840	−	0.275301i
$813$	−25.2963	+	6.77811i	−0.887179	+	0.237719i
$814$	−9.60576	+	2.57386i	−0.336682	+	0.0902136i
$815$			3.57018i			0.125058i
$816$	1.15705	+	0.668021i	0.0405047	+	0.0233854i
$817$	59.6495	−	59.6495i	2.08687	−	2.08687i
$818$	−12.3158			−0.430613
$819$	2.43219	+	9.22412i	0.0849876	+	0.322317i
$820$	3.84718			0.134349
$821$	4.05777	−	4.05777i	0.141617	−	0.141617i	−0.632744	−	0.774361i	$-0.718071\pi$
$821$	4.05777	−	4.05777i	0.141617	−	0.141617i	0.774361	+	0.632744i	$0.218071\pi$
$822$	−16.3656	−	9.44866i	−0.570814	−	0.329560i
$823$		−	18.1503i		−	0.632679i	−0.948646	−	0.316340i	$-0.897546\pi$
$823$		−	18.1503i		−	0.632679i	0.948646	−	0.316340i	$-0.102454\pi$
$824$	−5.11895	+	1.37162i	−0.178327	+	0.0477826i
$825$	21.5402	−	5.77168i	0.749933	−	0.200944i
$826$	−2.72777	+	0.449788i	−0.0949114	+	0.0156501i
$827$	−22.7159	−	22.7159i	−0.789911	−	0.789911i	0.191569	−	0.981479i	$-0.438643\pi$
$827$	−22.7159	−	22.7159i	−0.789911	−	0.789911i	−0.981479	+	0.191569i	$0.938643\pi$
$828$	2.04534	+	3.54263i	0.0710805	+	0.123115i
$829$	12.1196	−	20.9917i	0.420930	−	0.729072i	−0.575101	−	0.818082i	$-0.695037\pi$
$829$	12.1196	−	20.9917i	0.420930	−	0.729072i	0.996031	+	0.0890108i	$0.0283706\pi$
$830$	2.45702	−	0.658355i	0.0852842	−	0.0228518i
$831$	−12.9915	+	22.5020i	−0.450672	+	0.780586i
$832$	3.27851	+	1.50046i	0.113662	+	0.0520192i
$833$	−8.85720	+	3.00260i	−0.306884	+	0.104034i
$834$	3.15433	+	0.845200i	0.109225	+	0.0292669i
$835$	4.29907			0.148775
$836$	−39.4177			−1.36329
$837$	−2.93138	−	0.785461i	−0.101323	−	0.0271495i
$838$	−0.0427182	+	0.159426i	−0.00147568	+	0.00550730i
$839$	−5.61009	−	20.9371i	−0.193682	−	0.722830i	−0.992604	−	0.121396i	$-0.961263\pi$
$839$	−5.61009	−	20.9371i	−0.193682	−	0.722830i	0.798922	−	0.601434i	$-0.205404\pi$
$840$	−1.05747	+	0.867484i	−0.0364862	+	0.0299310i
$841$	7.14594	−	12.3771i	0.246412	−	0.426798i
$842$			23.4146i			0.806921i
$843$	−4.09216	−	15.2721i	−0.140941	−	0.526000i
$844$	5.93904	−	3.42891i	0.204430	−	0.118028i
$845$	−5.55949	−	3.77595i	−0.191252	−	0.129897i
$846$		−	6.47478i		−	0.222607i
$847$	18.7967	+	22.9133i	0.645862	+	0.787311i
$848$	−2.49408	−	4.31988i	−0.0856472	−	0.148345i
$849$	10.5386	−	6.08447i	0.361684	−	0.208819i
$850$	−1.63655	+	6.10770i	−0.0561333	+	0.209492i
$851$	6.10487	−	6.10487i	0.209272	−	0.209272i
$852$	−6.93749	−	1.85890i	−0.237675	−	0.0636847i
$853$	−17.6813	+	17.6813i	−0.605395	+	0.605395i	−0.941739	−	0.336344i	$-0.890810\pi$
$853$	−17.6813	+	17.6813i	−0.605395	+	0.605395i	0.336344	+	0.941739i	$0.390810\pi$
$854$	29.3255	+	2.89433i	1.00350	+	0.0990419i
$855$	3.74533	−	2.16237i	0.128088	−	0.0739515i
$856$	9.21696	+	9.21696i	0.315029	+	0.315029i
$857$	−15.1339	−	26.2128i	−0.516966	−	0.895411i	−0.999806	−	0.0197023i	$-0.993728\pi$
$857$	−15.1339	−	26.2128i	−0.516966	−	0.895411i	0.482840	−	0.875708i	$-0.339605\pi$
$858$	1.60116	+	16.9132i	0.0546627	+	0.577408i
$859$	2.73131	+	1.57692i	0.0931912	+	0.0538040i	0.545871	−	0.837869i	$-0.316199\pi$
$859$	2.73131	+	1.57692i	0.0931912	+	0.0538040i	−0.452680	+	0.891673i	$0.649532\pi$
$860$	1.34921	−	5.03533i	0.0460078	−	0.171703i
$861$	16.0020	+	11.4718i	0.545348	+	0.390959i
$862$	−8.92034	−	5.15016i	−0.303828	−	0.175415i
$863$	−1.86280	−	6.95207i	−0.0634105	−	0.236651i	0.926946	−	0.375195i	$-0.122424\pi$
$863$	−1.86280	−	6.95207i	−0.0634105	−	0.236651i	−0.990356	+	0.138544i	$0.955758\pi$
$864$	0.707107	+	0.707107i	0.0240563	+	0.0240563i
$865$	−3.46585	−	3.46585i	−0.117843	−	0.117843i
$866$	2.33014	+	8.69622i	0.0791815	+	0.295509i
$867$	13.1766	+	7.60749i	0.447500	+	0.258364i
$868$	0.788633	−	7.99047i	0.0267679	−	0.271214i
$869$	13.0707	−	48.7806i	0.443394	−	1.65477i
$870$	1.71700	+	0.991311i	0.0582118	+	0.0336086i
$871$	18.0294	+	3.04685i	0.610904	+	0.103239i
$872$	8.20888	+	14.2182i	0.277988	+	0.481489i
$873$	−10.7741	−	10.7741i	−0.364649	−	0.364649i
$874$	29.6364	−	17.1106i	1.00247	−	0.578774i
$875$	−10.8191	−	7.75618i	−0.365752	−	0.262207i
$876$	−2.19929	+	2.19929i	−0.0743072	+	0.0743072i
$877$	−15.3095	−	4.10218i	−0.516966	−	0.138521i	−0.00910335	−	0.999959i	$-0.502898\pi$
$877$	−15.3095	−	4.10218i	−0.516966	−	0.138521i	−0.507863	+	0.861438i	$0.669564\pi$
$878$	−9.16871	+	9.16871i	−0.309429	+	0.309429i
$879$	0.894661	−	3.33892i	0.0301762	−	0.112619i
$880$	−2.10952	+	1.21793i	−0.0711120	+	0.0410565i
$881$	−25.9386	−	44.9270i	−0.873894	−	1.51363i	−0.857936	−	0.513756i	$-0.828254\pi$
$881$	−25.9386	−	44.9270i	−0.873894	−	1.51363i	−0.0159575	−	0.999873i	$-0.505080\pi$
$882$	−6.98520	+	0.454982i	−0.235204	+	0.0153201i
$883$		−	24.2479i		−	0.816007i	−0.912980	−	0.408003i	$-0.866225\pi$
$883$		−	24.2479i		−	0.816007i	0.912980	−	0.408003i	$-0.133775\pi$
$884$	−4.38023	−	2.00468i	−0.147323	−	0.0674248i
$885$	0.467817	−	0.270095i	0.0157255	−	0.00907913i
$886$	−1.76963	−	6.60436i	−0.0594519	−	0.221878i
$887$			12.1738i			0.408755i	0.978892	+	0.204377i	$0.0655170\pi$
$887$			12.1738i			0.408755i	−0.978892	+	0.204377i	$0.934483\pi$
$888$	1.05527	−	1.82779i	0.0354127	−	0.0613366i
$889$	6.73570	+	8.21088i	0.225908	+	0.275384i
$890$	0.930848	+	3.47397i	0.0312021	+	0.116448i
$891$	−1.21952	+	4.55131i	−0.0408554	+	0.152475i
$892$	−2.77988	−	0.744868i	−0.0930774	−	0.0249400i
$893$	−54.1656			−1.81258
$894$	4.76598			0.159398
$895$	0.655131	+	0.175542i	0.0218986	+	0.00586772i
$896$	−1.54153	+	2.15028i	−0.0514988	+	0.0718357i
$897$	−8.54559	−	12.0213i	−0.285329	−	0.401378i
$898$	−15.5591	+	26.9491i	−0.519213	+	0.899303i
$899$	−11.2422	+	3.01234i	−0.374948	+	0.100467i
$900$	−2.36637	+	4.09868i	−0.0788791	+	0.136623i
$901$	3.33220	+	5.77155i	0.111012	+	0.192278i
$902$	24.7947	+	24.7947i	0.825572	+	0.825572i
$903$	20.6267	−	16.9209i	0.686414	−	0.563092i
$904$	19.0456	−	5.10325i	0.633446	−	0.169731i
$905$	−10.7867	+	2.89030i	−0.358563	+	0.0960768i
$906$		−	7.05142i		−	0.234268i
$907$	17.8243	+	10.2909i	0.591845	+	0.341702i	0.765827	−	0.643047i	$-0.222330\pi$
$907$	17.8243	+	10.2909i	0.591845	+	0.341702i	−0.173981	+	0.984749i	$0.555663\pi$
$908$	−11.5192	+	11.5192i	−0.382278	+	0.382278i
$909$	−15.9583			−0.529305
$910$	3.50101	−	3.47318i	0.116057	−	0.115135i
$911$	30.4748			1.00968			0.504838	−	0.863214i	$-0.331552\pi$
$911$	30.4748			1.00968			0.504838	+	0.863214i	$0.331552\pi$
$912$	5.91540	−	5.91540i	0.195878	−	0.195878i
$913$	20.0783	+	11.5922i	0.664493	+	0.383645i
$914$		−	2.26337i		−	0.0748657i
$915$	−5.56169	+	1.49025i	−0.183864	+	0.0492661i
$916$	0.939299	−	0.251684i	0.0310353	−	0.00831589i
$917$	14.2789	−	37.9147i	0.471530	−	1.25205i
$918$	−0.944725	−	0.944725i	−0.0311806	−	0.0311806i
$919$	11.0688	+	19.1717i	0.365126	+	0.632417i	0.988796	−	0.149271i	$-0.0476925\pi$
$919$	11.0688	+	19.1717i	0.365126	+	0.632417i	−0.623670	+	0.781688i	$0.714359\pi$
$920$	1.05737	−	1.83142i	0.0348604	−	0.0603801i
$921$	0.416371	−	0.111566i	0.0137199	−	0.00367624i
$922$	14.7232	−	25.5013i	0.484882	−	0.839841i
$923$	25.5338	+	4.31505i	0.840456	+	0.142032i
$924$	−12.4061	−	1.22444i	−0.408132	−	0.0402812i
$925$	9.64834	+	2.58527i	0.317235	+	0.0850030i
$926$	4.44938			0.146216
$927$	5.29953			0.174059
$928$	3.70444	+	0.992601i	0.121604	+	0.0325837i
$929$	−4.40723	+	16.4480i	−0.144596	+	0.539641i	0.855177	+	0.518337i	$0.173449\pi$
$929$	−4.40723	+	16.4480i	−0.144596	+	0.539641i	−0.999773	+	0.0213045i	$0.993218\pi$
$930$	0.406056	+	1.51542i	0.0133151	+	0.0496926i
$931$	3.80622	+	58.4356i	0.124744	+	1.91515i
$932$	−12.9670	+	22.4595i	−0.424749	+	0.735686i
$933$		−	4.20213i		−	0.137572i
$934$	2.35117	+	8.77469i	0.0769327	+	0.287117i
$935$	2.81841	−	1.62721i	0.0921720	−	0.0532155i
$936$	−2.77845	−	2.29788i	−0.0908164	−	0.0751084i
$937$		−	15.1174i		−	0.493865i	−0.969033	−	0.246932i	$-0.920577\pi$
$937$		−	15.1174i		−	0.493865i	0.969033	−	0.246932i	$-0.0794225\pi$
$938$	−4.72889	+	12.5566i	−0.154404	+	0.409988i
$939$	8.46970	+	14.6700i	0.276398	+	0.478736i
$940$	−2.89879	+	1.67362i	−0.0945481	+	0.0545874i
$941$	7.52302	−	28.0763i	0.245243	−	0.915260i	−0.728018	−	0.685558i	$-0.759558\pi$
$941$	7.52302	−	28.0763i	0.245243	−	0.915260i	0.973261	−	0.229702i	$-0.0737752\pi$
$942$	5.50504	−	5.50504i	0.179364	−	0.179364i
$943$	−29.4049	−	7.87903i	−0.957557	−	0.256577i
$944$	0.738873	−	0.738873i	0.0240483	−	0.0240483i
$945$	1.24596	−	0.564231i	0.0405310	−	0.0183544i
$946$	41.1478	−	23.7567i	1.33783	−	0.772396i
$947$	32.3347	+	32.3347i	1.05074	+	1.05074i	0.998642	+	0.0520931i	$0.0165893\pi$
$947$	32.3347	+	32.3347i	1.05074	+	1.05074i	0.0520931	+	0.998642i	$0.483411\pi$
$948$	5.35897	+	9.28201i	0.174051	+	0.301466i
$949$	7.14701	−	8.64172i	0.232002	−	0.280522i
$950$	34.2880	+	19.7962i	1.11245	+	0.642274i
$951$	−3.52750	+	13.1648i	−0.114387	+	0.426898i
$952$	2.05955	−	2.87286i	0.0667503	−	0.0931100i
$953$	−4.01742	−	2.31946i	−0.130137	−	0.0751346i	0.433518	−	0.901145i	$-0.357272\pi$
$953$	−4.01742	−	2.31946i	−0.130137	−	0.0751346i	−0.563655	+	0.826010i	$0.690605\pi$
$954$	1.29103	+	4.81820i	0.0417987	+	0.155995i
$955$	3.12647	+	3.12647i	0.101170	+	0.101170i
$956$	−7.45111	−	7.45111i	−0.240986	−	0.240986i
$957$	4.67700	+	17.4548i	0.151186	+	0.564233i
$958$	28.6314	+	16.5303i	0.925039	+	0.534071i
$959$	−29.1307	+	40.6345i	−0.940681	+	1.31215i
$960$	0.133800	−	0.499350i	0.00431839	−	0.0161165i
$961$	18.8707	+	10.8950i	0.608734	+	0.351452i
$962$	−3.16680	+	6.91945i	−0.102102	+	0.223092i
$963$	−6.51738	−	11.2884i	−0.210020	−	0.363765i
$964$	15.4606	+	15.4606i	0.497951	+	0.497951i
$965$	9.93759	−	5.73747i	0.319902	−	0.184696i
$966$	9.85912	−	4.46469i	0.317212	−	0.143649i
$967$	−4.25193	+	4.25193i	−0.136733	+	0.136733i	−0.772160	−	0.635428i	$-0.780824\pi$
$967$	−4.25193	+	4.25193i	−0.136733	+	0.136733i	0.635428	+	0.772160i	$0.280824\pi$
$968$	−10.8199	−	2.89919i	−0.347766	−	0.0931837i
$969$	−7.90322	+	7.90322i	−0.253888	+	0.253888i
$970$	−2.03871	+	7.60856i	−0.0654589	+	0.244296i
$971$	−11.6154	+	6.70616i	−0.372756	+	0.215211i	−0.674662	−	0.738127i	$-0.735711\pi$
$971$	−11.6154	+	6.70616i	−0.372756	+	0.215211i	0.301906	+	0.953338i	$0.402377\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	3.04507	−	8.08558i	0.0976206	−	0.259212i
$974$			30.7351i			0.984815i
$975$	7.10131	−	15.5163i	0.227424	−	0.496921i
$976$	−9.64567	+	5.56893i	−0.308750	+	0.178257i
$977$	8.26135	+	30.8318i	0.264304	+	0.986396i	0.962675	+	0.270660i	$0.0872420\pi$
$977$	8.26135	+	30.8318i	0.264304	+	0.986396i	−0.698371	+	0.715736i	$0.746091\pi$
$978$		−	6.90604i		−	0.220831i
$979$	−16.3902	+	28.3886i	−0.523832	+	0.907304i
$980$	2.00925	+	3.00970i	0.0641831	+	0.0961414i
$981$	−4.24923	−	15.8583i	−0.135667	−	0.506318i
$982$	6.47261	−	24.1561i	0.206549	−	0.770852i
$983$	−31.5204	−	8.44587i	−1.00535	−	0.269382i	−0.281662	−	0.959514i	$-0.590886\pi$
$983$	−31.5204	−	8.44587i	−1.00535	−	0.269382i	−0.723683	+	0.690132i	$0.757552\pi$
$984$	−7.44185			−0.237238
$985$	6.09375			0.194163
$986$	−4.94929	−	1.32616i	−0.157617	−	0.0422335i
$987$	−17.0478	−	1.68256i	−0.542638	−	0.0535566i
$988$	−19.2232	+	23.2435i	−0.611571	+	0.739473i
$989$	−20.6248	+	35.7231i	−0.655829	+	1.13593i
$990$	2.35287	−	0.630449i	0.0747790	−	0.0200370i
$991$	−25.1034	+	43.4804i	−0.797437	+	1.38120i	0.123843	+	0.992302i	$0.460478\pi$
$991$	−25.1034	+	43.4804i	−0.797437	+	1.38120i	−0.921280	+	0.388900i	$0.872855\pi$
$992$	1.51739	+	2.62820i	0.0481773	+	0.0834456i
$993$	7.42546	+	7.42546i	0.235640	+	0.235640i
$994$	−6.69720	+	17.7831i	−0.212422	+	0.564045i
$995$	4.25828	−	1.14100i	0.134996	−	0.0361722i
$996$	−4.75277	+	1.27350i	−0.150597	+	0.0403524i
$997$		−	27.7651i		−	0.879330i	−0.898162	−	0.439665i	$-0.855097\pi$
$997$		−	27.7651i		−	0.879330i	0.898162	−	0.439665i	$-0.144903\pi$
$998$	−4.89425	−	2.82570i	−0.154925	−	0.0894459i
$999$	−1.49238	+	1.49238i	−0.0472169	+	0.0472169i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.cg.b.145.8	yes	40
7.3	odd	6		546.2.by.b.535.8	yes	40
13.7	odd	12		546.2.by.b.397.8	✓	40
91.59	even	12	inner	546.2.cg.b.241.8	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.b.397.8	✓	40	13.7	odd	12
546.2.by.b.535.8	yes	40	7.3	odd	6
546.2.cg.b.145.8	yes	40	1.1	even	1	trivial
546.2.cg.b.241.8	yes	40	91.59	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000i q^{4} +(0.499350 - 0.133800i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(0.430450 + 2.61050i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000i q^{4} +(0.499350 - 0.133800i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(0.430450 + 2.61050i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(0.258483 - 0.447705i) q^{10} +(4.55131 - 1.21952i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(1.50046 - 3.27851i) q^{13} +(2.15028 + 1.54153i) q^{14} +(-0.499350 - 0.133800i) q^{15} -1.00000 q^{16} +1.33604 q^{17} +(0.965926 + 0.258819i) q^{18} +(2.16519 - 8.08058i) q^{19} +(-0.133800 - 0.499350i) q^{20} +(0.932469 - 2.47598i) q^{21} +(2.35593 - 4.08059i) q^{22} +4.09068i q^{23} +(0.258819 + 0.965926i) q^{24} +(-4.09868 + 2.36637i) q^{25} +(-1.25727 - 3.37924i) q^{26} -1.00000i q^{27} +(2.61050 - 0.430450i) q^{28} +(-1.91756 - 3.32131i) q^{29} +(-0.447705 + 0.258483i) q^{30} +(0.785461 - 2.93138i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-4.55131 - 1.21952i) q^{33} +(0.944725 - 0.944725i) q^{34} +(0.564231 + 1.24596i) q^{35} +(0.866025 - 0.500000i) q^{36} +(-1.49238 - 1.49238i) q^{37} +(-4.18282 - 7.24485i) q^{38} +(-2.93869 + 2.08904i) q^{39} +(-0.447705 - 0.258483i) q^{40} +(-1.92609 + 7.18828i) q^{41} +(-1.09143 - 2.41014i) q^{42} +(8.73281 + 5.04189i) q^{43} +(-1.21952 - 4.55131i) q^{44} +(0.365550 + 0.365550i) q^{45} +(2.89255 + 2.89255i) q^{46} +(-1.67580 - 6.25416i) q^{47} +(0.866025 + 0.500000i) q^{48} +(-6.62943 + 2.24738i) q^{49} +(-1.22493 + 4.57148i) q^{50} +(-1.15705 - 0.668021i) q^{51} +(-3.27851 - 1.50046i) q^{52} +(2.49408 + 4.31988i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(2.10952 - 1.21793i) q^{55} +(1.54153 - 2.15028i) q^{56} +(-5.91540 + 5.91540i) q^{57} +(-3.70444 - 0.992601i) q^{58} +(-0.738873 + 0.738873i) q^{59} +(-0.133800 + 0.499350i) q^{60} +(9.64567 - 5.56893i) q^{61} +(-1.51739 - 2.62820i) q^{62} +(-2.04553 + 1.67803i) q^{63} +1.00000i q^{64} +(0.310590 - 1.83789i) q^{65} +(-4.08059 + 2.35593i) q^{66} +(1.31257 + 4.89856i) q^{67} -1.33604i q^{68} +(2.04534 - 3.54263i) q^{69} +(1.28000 + 0.482054i) q^{70} +(1.85890 + 6.93749i) q^{71} +(0.258819 - 0.965926i) q^{72} +(3.00429 + 0.804997i) q^{73} -2.11055 q^{74} +4.73275 q^{75} +(-8.08058 - 2.16519i) q^{76} +(5.14267 + 11.3562i) q^{77} +(-0.600796 + 3.55514i) q^{78} +(5.35897 - 9.28201i) q^{79} +(-0.499350 + 0.133800i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.72093 + 6.44483i) q^{82} +(3.47927 + 3.47927i) q^{83} +(-2.47598 - 0.932469i) q^{84} +(0.667153 - 0.178763i) q^{85} +(9.74018 - 2.60987i) q^{86} +3.83512i q^{87} +(-4.08059 - 2.35593i) q^{88} +(-4.91933 + 4.91933i) q^{89} +0.516965 q^{90} +(9.20442 + 2.50572i) q^{91} +4.09068 q^{92} +(-2.14592 + 2.14592i) q^{93} +(-5.60732 - 3.23739i) q^{94} -4.32474i q^{95} +(0.965926 - 0.258819i) q^{96} +(-14.7177 + 3.94361i) q^{97} +(-3.09857 + 6.27685i) q^{98} +(3.33179 + 3.33179i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) \) 40 * q + 4 * q^7 + 20 * q^9	\( 40 q + 4 q^{7} + 20 q^{9} + 8 q^{11} - 20 q^{12} + 4 q^{14} - 40 q^{16} + 16 q^{17} + 4 q^{19} + 4 q^{21} - 4 q^{22} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 8 q^{33} - 8 q^{34} - 32 q^{35} + 40 q^{37} + 8 q^{38} + 20 q^{39} + 20 q^{41} + 12 q^{42} - 24 q^{43} - 4 q^{44} + 32 q^{46} + 4 q^{47} + 32 q^{49} - 16 q^{50} + 24 q^{51} + 16 q^{52} - 4 q^{53} + 24 q^{55} + 12 q^{56} + 8 q^{57} + 12 q^{58} + 24 q^{59} + 60 q^{61} + 32 q^{62} - 4 q^{63} + 44 q^{65} - 12 q^{67} - 8 q^{69} - 24 q^{70} - 28 q^{71} + 60 q^{73} - 40 q^{74} - 72 q^{75} + 4 q^{76} - 12 q^{77} + 4 q^{78} - 20 q^{81} - 24 q^{82} + 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{89} - 16 q^{92} - 24 q^{93} - 48 q^{97} - 88 q^{98} + 4 q^{99}+O(q^{100}) \) 40 * q + 4 * q^7 + 20 * q^9 + 8 * q^11 - 20 * q^12 + 4 * q^14 - 40 * q^16 + 16 * q^17 + 4 * q^19 + 4 * q^21 - 4 * q^22 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 8 * q^33 - 8 * q^34 - 32 * q^35 + 40 * q^37 + 8 * q^38 + 20 * q^39 + 20 * q^41 + 12 * q^42 - 24 * q^43 - 4 * q^44 + 32 * q^46 + 4 * q^47 + 32 * q^49 - 16 * q^50 + 24 * q^51 + 16 * q^52 - 4 * q^53 + 24 * q^55 + 12 * q^56 + 8 * q^57 + 12 * q^58 + 24 * q^59 + 60 * q^61 + 32 * q^62 - 4 * q^63 + 44 * q^65 - 12 * q^67 - 8 * q^69 - 24 * q^70 - 28 * q^71 + 60 * q^73 - 40 * q^74 - 72 * q^75 + 4 * q^76 - 12 * q^77 + 4 * q^78 - 20 * q^81 - 24 * q^82 + 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^89 - 16 * q^92 - 24 * q^93 - 48 * q^97 - 88 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more