LMFDB - Embedded newform 546.2.bn.f.101.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(101,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 5]))

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

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

chi := DirichletCharacter("546.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bn (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.12
Character	$\chi$	$=$	546.101
Dual form			546.2.bn.f.173.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.991815 - 1.41997i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-3.72094 + 2.14828i) q^{5} +(-0.733819 - 1.56892i) q^{6} +(-1.08595 + 2.41262i) q^{7} -1.00000 q^{8} +(-1.03261 - 2.81669i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.991815 - 1.41997i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-3.72094 + 2.14828i) q^{5} +(-0.733819 - 1.56892i) q^{6} +(-1.08595 + 2.41262i) q^{7} -1.00000 q^{8} +(-1.03261 - 2.81669i) q^{9} +4.29657i q^{10} -4.52020 q^{11} +(-1.72563 - 0.148954i) q^{12} +(2.01824 + 2.98776i) q^{13} +(1.54641 + 2.14677i) q^{14} +(-0.639991 + 7.41431i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.0962806 - 0.166763i) q^{17} +(-2.95563 - 0.514080i) q^{18} -1.69123 q^{19} +(3.72094 + 2.14828i) q^{20} +(2.34878 + 3.93488i) q^{21} +(-2.26010 + 3.91461i) q^{22} +(1.22075 + 0.704800i) q^{23} +(-0.991815 + 1.41997i) q^{24} +(6.73025 - 11.6571i) q^{25} +(3.59660 - 0.253971i) q^{26} +(-5.02375 - 1.32737i) q^{27} +(2.63236 - 0.265852i) q^{28} +(-8.66432 + 5.00235i) q^{29} +(6.10098 + 4.26140i) q^{30} +(-1.16127 + 2.01138i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-4.48320 + 6.41853i) q^{33} -0.192561 q^{34} +(-1.14225 - 11.3101i) q^{35} +(-1.92302 + 2.30261i) q^{36} +(-4.93806 - 2.85099i) q^{37} +(-0.845613 + 1.46464i) q^{38} +(6.24424 + 0.0974664i) q^{39} +(3.72094 - 2.14828i) q^{40} +(-1.24309 + 0.717699i) q^{41} +(4.58209 - 0.0666621i) q^{42} +(1.73181 - 2.99958i) q^{43} +(2.26010 + 3.91461i) q^{44} +(9.89331 + 8.26238i) q^{45} +(1.22075 - 0.704800i) q^{46} +(8.70281 - 5.02457i) q^{47} +(0.733819 + 1.56892i) q^{48} +(-4.64144 - 5.23994i) q^{49} +(-6.73025 - 11.6571i) q^{50} +(-0.332290 - 0.0286827i) q^{51} +(1.57835 - 3.24173i) q^{52} +(-5.59277 - 3.22899i) q^{53} +(-3.66141 + 3.68702i) q^{54} +(16.8194 - 9.71067i) q^{55} +(1.08595 - 2.41262i) q^{56} +(-1.67738 + 2.40148i) q^{57} +10.0047i q^{58} +(3.17719 - 1.83435i) q^{59} +(6.74097 - 3.15290i) q^{60} +8.11216i q^{61} +(1.16127 + 2.01138i) q^{62} +(7.91694 + 0.567486i) q^{63} +1.00000 q^{64} +(-13.9283 - 6.78150i) q^{65} +(3.31701 + 7.09183i) q^{66} +5.05773i q^{67} +(-0.0962806 + 0.166763i) q^{68} +(2.21155 - 1.03439i) q^{69} +(-10.3660 - 4.66584i) q^{70} +(-5.59208 + 9.68576i) q^{71} +(1.03261 + 2.81669i) q^{72} +(5.90130 - 10.2214i) q^{73} +(-4.93806 + 2.85099i) q^{74} +(-9.87758 - 21.1185i) q^{75} +(0.845613 + 1.46464i) q^{76} +(4.90869 - 10.9055i) q^{77} +(3.20653 - 5.35894i) q^{78} +(-1.93078 - 3.34421i) q^{79} -4.29657i q^{80} +(-6.86745 + 5.81706i) q^{81} +1.43540i q^{82} +4.15111i q^{83} +(2.23331 - 4.00154i) q^{84} +(0.716508 + 0.413676i) q^{85} +(-1.73181 - 2.99958i) q^{86} +(-1.49024 + 17.2644i) q^{87} +4.52020 q^{88} +(-1.87572 - 1.08295i) q^{89} +(12.1021 - 4.43667i) q^{90} +(-9.40002 + 1.62470i) q^{91} -1.40960i q^{92} +(1.70432 + 3.64388i) q^{93} -10.0491i q^{94} +(6.29295 - 3.63324i) q^{95} +(1.72563 + 0.148954i) q^{96} +(-6.86525 + 11.8910i) q^{97} +(-6.85865 + 1.39963i) q^{98} +(4.66759 + 12.7320i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 17 q^{2} - 3 q^{3} - 17 q^{4} - 9 q^{5} + 3 q^{6} + 5 q^{7} - 34 q^{8} + 7 q^{9}+O(q^{10}) $ 34 * q + 17 * q^2 - 3 * q^3 - 17 * q^4 - 9 * q^5 + 3 * q^6 + 5 * q^7 - 34 * q^8 + 7 * q^9	$ 34 q + 17 q^{2} - 3 q^{3} - 17 q^{4} - 9 q^{5} + 3 q^{6} + 5 q^{7} - 34 q^{8} + 7 q^{9} + 18 q^{11} + 6 q^{12} - 8 q^{13} + 4 q^{14} - 4 q^{15} - 17 q^{16} - 6 q^{17} - 4 q^{18} - 10 q^{19} + 9 q^{20} + 7 q^{21} + 9 q^{22} - 6 q^{23} + 3 q^{24} + 16 q^{25} - 13 q^{26} - 18 q^{27} - q^{28} - 27 q^{29} + 13 q^{30} + q^{31} + 17 q^{32} + 21 q^{33} - 12 q^{34} + 3 q^{35} - 11 q^{36} + 6 q^{37} - 5 q^{38} - 2 q^{39} + 9 q^{40} - 3 q^{41} + 8 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} - 6 q^{46} + 27 q^{47} - 3 q^{48} - 5 q^{49} - 16 q^{50} - 36 q^{51} - 5 q^{52} - 21 q^{53} + 57 q^{55} - 5 q^{56} + 17 q^{57} + 6 q^{59} + 17 q^{60} - q^{62} + 34 q^{64} - 33 q^{65} - 6 q^{68} - 42 q^{69} + 3 q^{70} + 15 q^{71} - 7 q^{72} + 19 q^{73} + 6 q^{74} - 9 q^{75} + 5 q^{76} + 9 q^{77} - 7 q^{78} - 9 q^{79} - 5 q^{81} + q^{84} - 42 q^{85} + 3 q^{86} + 6 q^{87} - 18 q^{88} + 18 q^{89} + 9 q^{90} - 27 q^{91} + 8 q^{93} + 3 q^{95} - 6 q^{96} - 19 q^{97} - 7 q^{98} + 27 q^{99}+O(q^{100}) $ 34 * q + 17 * q^2 - 3 * q^3 - 17 * q^4 - 9 * q^5 + 3 * q^6 + 5 * q^7 - 34 * q^8 + 7 * q^9 + 18 * q^11 + 6 * q^12 - 8 * q^13 + 4 * q^14 - 4 * q^15 - 17 * q^16 - 6 * q^17 - 4 * q^18 - 10 * q^19 + 9 * q^20 + 7 * q^21 + 9 * q^22 - 6 * q^23 + 3 * q^24 + 16 * q^25 - 13 * q^26 - 18 * q^27 - q^28 - 27 * q^29 + 13 * q^30 + q^31 + 17 * q^32 + 21 * q^33 - 12 * q^34 + 3 * q^35 - 11 * q^36 + 6 * q^37 - 5 * q^38 - 2 * q^39 + 9 * q^40 - 3 * q^41 + 8 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 - 6 * q^46 + 27 * q^47 - 3 * q^48 - 5 * q^49 - 16 * q^50 - 36 * q^51 - 5 * q^52 - 21 * q^53 + 57 * q^55 - 5 * q^56 + 17 * q^57 + 6 * q^59 + 17 * q^60 - q^62 + 34 * q^64 - 33 * q^65 - 6 * q^68 - 42 * q^69 + 3 * q^70 + 15 * q^71 - 7 * q^72 + 19 * q^73 + 6 * q^74 - 9 * q^75 + 5 * q^76 + 9 * q^77 - 7 * q^78 - 9 * q^79 - 5 * q^81 + q^84 - 42 * q^85 + 3 * q^86 + 6 * q^87 - 18 * q^88 + 18 * q^89 + 9 * q^90 - 27 * q^91 + 8 * q^93 + 3 * q^95 - 6 * q^96 - 19 * q^97 - 7 * q^98 + 27 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.991815	−	1.41997i	0.572625	−	0.819818i
$3$	0.991815	−	1.41997i	0.572625	−	0.819818i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−3.72094	+	2.14828i	−1.66405	+	0.960742i	−0.693306	+	0.720644i	$0.743846\pi$
$5$	−3.72094	+	2.14828i	−1.66405	+	0.960742i	−0.970749	+	0.240098i	$0.922820\pi$
$6$	−0.733819	−	1.56892i	−0.299580	−	0.640509i
$7$	−1.08595	+	2.41262i	−0.410449	+	0.911884i
$7$	−1.08595	+	2.41262i	−0.410449	+	0.911884i
$8$	−1.00000			−0.353553
$9$	−1.03261	−	2.81669i	−0.344202	−	0.938896i
$10$			4.29657i			1.35869i
$11$	−4.52020			−1.36289			−0.681446	−	0.731869i	$-0.738648\pi$
$11$	−4.52020			−1.36289			−0.681446	+	0.731869i	$0.738648\pi$
$12$	−1.72563	−	0.148954i	−0.498148	−	0.0429993i
$13$	2.01824	+	2.98776i	0.559760	+	0.828655i
$13$	2.01824	+	2.98776i	0.559760	+	0.828655i
$14$	1.54641	+	2.14677i	0.413297	+	0.573747i
$15$	−0.639991	+	7.41431i	−0.165245	+	1.91437i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.0962806	−	0.166763i	−0.0233515	−	0.0404459i	0.854114	−	0.520087i	$-0.174100\pi$
$17$	−0.0962806	−	0.166763i	−0.0233515	−	0.0404459i	−0.877465	+	0.479641i	$0.840767\pi$
$18$	−2.95563	−	0.514080i	−0.696648	−	0.121170i
$19$	−1.69123			−0.387994			−0.193997	−	0.981002i	$-0.562145\pi$
$19$	−1.69123			−0.387994			−0.193997	+	0.981002i	$0.562145\pi$
$20$	3.72094	+	2.14828i	0.832027	+	0.480371i
$21$	2.34878	+	3.93488i	0.512545	+	0.858660i
$22$	−2.26010	+	3.91461i	−0.481855	+	0.834597i
$23$	1.22075	+	0.704800i	0.254544	+	0.146961i	0.621843	−	0.783142i	$-0.286384\pi$
$23$	1.22075	+	0.704800i	0.254544	+	0.146961i	−0.367299	+	0.930103i	$0.619717\pi$
$24$	−0.991815	+	1.41997i	−0.202453	+	0.289849i
$25$	6.73025	−	11.6571i	1.34605	−	2.33143i
$26$	3.59660	−	0.253971i	0.705350	−	0.0498078i
$27$	−5.02375	−	1.32737i	−0.966822	−	0.255452i
$28$	2.63236	−	0.265852i	0.497469	−	0.0502412i
$29$	−8.66432	+	5.00235i	−1.60892	+	0.928913i	−0.619313	+	0.785144i	$0.712589\pi$
$29$	−8.66432	+	5.00235i	−1.60892	+	0.928913i	−0.989611	+	0.143769i	$0.954078\pi$
$30$	6.10098	+	4.26140i	1.11388	+	0.778022i
$31$	−1.16127	+	2.01138i	−0.208570	+	0.361254i	−0.951264	−	0.308377i	$-0.900214\pi$
$31$	−1.16127	+	2.01138i	−0.208570	+	0.361254i	0.742694	+	0.669631i	$0.233548\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−4.48320	+	6.41853i	−0.780425	+	1.11732i
$34$	−0.192561			−0.0330240
$35$	−1.14225	−	11.3101i	−0.193075	−	1.91176i
$36$	−1.92302	+	2.30261i	−0.320503	+	0.383768i
$37$	−4.93806	−	2.85099i	−0.811813	−	0.468700i	0.0357722	−	0.999360i	$-0.488611\pi$
$37$	−4.93806	−	2.85099i	−0.811813	−	0.468700i	−0.847585	+	0.530660i	$0.821944\pi$
$38$	−0.845613	+	1.46464i	−0.137177	+	0.237597i
$39$	6.24424	+	0.0974664i	0.999878	+	0.0156071i
$40$	3.72094	−	2.14828i	0.588332	−	0.339674i
$41$	−1.24309	+	0.717699i	−0.194138	+	0.112086i	−0.593918	−	0.804525i	$-0.702420\pi$
$41$	−1.24309	+	0.717699i	−0.194138	+	0.112086i	0.399780	+	0.916611i	$0.369086\pi$
$42$	4.58209	−	0.0666621i	0.707032	−	0.0102862i
$43$	1.73181	−	2.99958i	0.264099	−	0.457432i	−0.703229	−	0.710964i	$-0.748259\pi$
$43$	1.73181	−	2.99958i	0.264099	−	0.457432i	0.967327	+	0.253532i	$0.0815923\pi$
$44$	2.26010	+	3.91461i	0.340723	+	0.590149i
$45$	9.89331	+	8.26238i	1.47481	+	1.23168i
$46$	1.22075	−	0.704800i	0.179990	−	0.103917i
$47$	8.70281	−	5.02457i	1.26944	−	0.732909i	0.294554	−	0.955635i	$-0.404829\pi$
$47$	8.70281	−	5.02457i	1.26944	−	0.732909i	0.974881	+	0.222726i	$0.0714956\pi$
$48$	0.733819	+	1.56892i	0.105918	+	0.226454i
$49$	−4.64144	−	5.23994i	−0.663063	−	0.748564i
$50$	−6.73025	−	11.6571i	−0.951802	−	1.64857i
$51$	−0.332290	−	0.0286827i	−0.0465299	−	0.00401639i
$52$	1.57835	−	3.24173i	0.218878	−	0.449547i
$53$	−5.59277	−	3.22899i	−0.768226	−	0.443536i	0.0640153	−	0.997949i	$-0.479609\pi$
$53$	−5.59277	−	3.22899i	−0.768226	−	0.443536i	−0.832241	+	0.554413i	$0.812943\pi$
$54$	−3.66141	+	3.68702i	−0.498255	+	0.501739i
$55$	16.8194	−	9.71067i	2.26792	−	1.30939i
$56$	1.08595	−	2.41262i	0.145116	−	0.322400i
$57$	−1.67738	+	2.40148i	−0.222175	+	0.318084i
$58$			10.0047i			1.31368i
$59$	3.17719	−	1.83435i	0.413635	−	0.238813i	−0.278715	−	0.960374i	$-0.589909\pi$
$59$	3.17719	−	1.83435i	0.413635	−	0.238813i	0.692351	+	0.721561i	$0.256575\pi$
$60$	6.74097	−	3.15290i	0.870256	−	0.407038i
$61$			8.11216i			1.03866i	0.854575	+	0.519328i	$0.173818\pi$
$61$			8.11216i			1.03866i	−0.854575	+	0.519328i	$0.826182\pi$
$62$	1.16127	+	2.01138i	0.147481	+	0.255445i
$63$	7.91694	+	0.567486i	0.997441	+	0.0714965i
$64$	1.00000			0.125000
$65$	−13.9283	−	6.78150i	−1.72759	−	0.841142i
$66$	3.31701	+	7.09183i	0.408296	+	0.872944i
$67$			5.05773i			0.617900i	0.951078	+	0.308950i	$0.0999776\pi$
$67$			5.05773i			0.617900i	−0.951078	+	0.308950i	$0.900022\pi$
$68$	−0.0962806	+	0.166763i	−0.0116757	+	0.0202230i
$69$	2.21155	−	1.03439i	0.266239	−	0.124526i
$70$	−10.3660	−	4.66584i	−1.23897	−	0.557675i
$71$	−5.59208	+	9.68576i	−0.663658	+	1.14949i	0.315990	+	0.948763i	$0.397663\pi$
$71$	−5.59208	+	9.68576i	−0.663658	+	1.14949i	−0.979647	+	0.200726i	$0.935670\pi$
$72$	1.03261	+	2.81669i	0.121694	+	0.331950i
$73$	5.90130	−	10.2214i	0.690695	−	1.19632i	−0.280915	−	0.959733i	$-0.590638\pi$
$73$	5.90130	−	10.2214i	0.690695	−	1.19632i	0.971610	−	0.236586i	$-0.0760287\pi$
$74$	−4.93806	+	2.85099i	−0.574038	+	0.331421i
$75$	−9.87758	−	21.1185i	−1.14056	−	2.43855i
$76$	0.845613	+	1.46464i	0.0969985	+	0.168006i
$77$	4.90869	−	10.9055i	0.559397	−	1.24280i
$78$	3.20653	−	5.35894i	0.363068	−	0.606780i
$79$	−1.93078	−	3.34421i	−0.217230	−	0.376253i	0.736730	−	0.676187i	$-0.236369\pi$
$79$	−1.93078	−	3.34421i	−0.217230	−	0.376253i	−0.953960	+	0.299934i	$0.903035\pi$
$80$		−	4.29657i		−	0.480371i
$81$	−6.86745	+	5.81706i	−0.763050	+	0.646340i
$82$			1.43540i			0.158513i
$83$			4.15111i			0.455643i	0.973703	+	0.227822i	$0.0731603\pi$
$83$			4.15111i			0.455643i	−0.973703	+	0.227822i	$0.926840\pi$
$84$	2.23331	−	4.00154i	0.243675	−	0.436604i
$85$	0.716508	+	0.413676i	0.0777162	+	0.0448695i
$86$	−1.73181	−	2.99958i	−0.186746	−	0.323453i
$87$	−1.49024	+	17.2644i	−0.159770	+	1.85094i
$88$	4.52020			0.481855
$89$	−1.87572	−	1.08295i	−0.198826	−	0.114792i	0.397282	−	0.917697i	$-0.369954\pi$
$89$	−1.87572	−	1.08295i	−0.198826	−	0.114792i	−0.596108	+	0.802905i	$0.703287\pi$
$90$	12.1021	−	4.43667i	1.27567	−	0.467666i
$91$	−9.40002	+	1.62470i	−0.985390	+	0.170315i
$92$		−	1.40960i		−	0.146961i
$93$	1.70432	+	3.64388i	0.176730	+	0.377852i
$94$		−	10.0491i		−	1.03649i
$95$	6.29295	−	3.63324i	0.645643	−	0.372762i
$96$	1.72563	+	0.148954i	0.176122	+	0.0152025i
$97$	−6.86525	+	11.8910i	−0.697061	+	1.20735i	0.272420	+	0.962178i	$0.412176\pi$
$97$	−6.86525	+	11.8910i	−0.697061	+	1.20735i	−0.969481	+	0.245167i	$0.921157\pi$
$98$	−6.85865	+	1.39963i	−0.692828	+	0.141384i
$99$	4.66759	+	12.7320i	0.469110	+	1.27961i
$100$	−13.4605			−1.34605
$101$	0.0806167			0.00802166			0.00401083	−	0.999992i	$-0.498723\pi$
$101$	0.0806167			0.00802166			0.00401083	+	0.999992i	$0.498723\pi$
$102$	−0.190985	+	0.273430i	−0.0189103	+	0.0270736i
$103$	−9.05121	+	5.22572i	−0.891842	+	0.514905i	−0.874545	−	0.484945i	$-0.838840\pi$
$103$	−9.05121	+	5.22572i	−0.891842	+	0.514905i	−0.0172977	+	0.999850i	$0.505506\pi$
$104$	−2.01824	−	2.98776i	−0.197905	−	0.292974i
$105$	−17.1929	−	9.59559i	−1.67785	−	0.936434i
$106$	−5.59277	+	3.22899i	−0.543218	+	0.313627i
$107$	4.64534	+	2.68199i	0.449082	+	0.259277i	0.707442	−	0.706771i	$-0.249849\pi$
$107$	4.64534	+	2.68199i	0.449082	+	0.259277i	−0.258361	+	0.966049i	$0.583182\pi$
$108$	1.36234	+	5.01438i	0.131092	+	0.482509i
$109$	−6.11686	−	3.53157i	−0.585889	−	0.338263i	0.177581	−	0.984106i	$-0.443173\pi$
$109$	−6.11686	−	3.53157i	−0.585889	−	0.338263i	−0.763470	+	0.645843i	$0.776506\pi$
$110$		−	19.4213i		−	1.85175i
$111$	−8.94596	+	4.18423i	−0.849113	+	0.397149i
$112$	−1.54641	−	2.14677i	−0.146122	−	0.202850i
$113$	11.0639	+	6.38777i	1.04081	+	0.600911i	0.920062	−	0.391773i	$-0.128138\pi$
$113$	11.0639	+	6.38777i	1.04081	+	0.600911i	0.120746	+	0.992683i	$0.461471\pi$
$114$	1.24105	+	2.65340i	0.116235	+	0.248514i
$115$	−6.05645			−0.564767
$116$	8.66432	+	5.00235i	0.804462	+	0.464456i
$117$	6.33153	−	8.76994i	0.585350	−	0.810781i
$118$		−	3.66871i		−	0.337732i
$119$	0.506891	−	0.0511927i	0.0464666	−	0.00469283i
$120$	0.639991	−	7.41431i	0.0584229	−	0.676830i
$121$	9.43220			0.857473
$122$	7.02534	+	4.05608i	0.636044	+	0.367220i
$123$	−0.213808	+	2.47697i	−0.0192784	+	0.223341i
$124$	2.32254			0.208570
$125$			36.3512i			3.25135i
$126$	4.44993	−	6.57253i	0.396431	−	0.585527i
$127$	0.0510484	+	0.0884185i	0.00452982	+	0.00784587i	0.868281	−	0.496072i	$-0.165225\pi$
$127$	0.0510484	+	0.0884185i	0.00452982	+	0.00784587i	−0.863752	+	0.503918i	$0.831891\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−2.54167	−	5.43414i	−0.223782	−	0.478449i
$130$	−12.8371	+	8.67152i	−1.12589	+	0.760543i
$131$	0.746067	+	1.29223i	0.0651842	+	0.112902i	0.896776	−	0.442485i	$-0.145903\pi$
$131$	0.746067	+	1.29223i	0.0651842	+	0.112902i	−0.831591	+	0.555388i	$0.812570\pi$
$132$	7.80021	+	0.673301i	0.678921	+	0.0586033i
$133$	1.83658	−	4.08028i	0.159252	−	0.353805i
$134$	4.38012	+	2.52887i	0.378385	+	0.218461i
$135$	21.5446	−	5.85341i	1.85427	−	0.503781i
$136$	0.0962806	+	0.166763i	0.00825599	+	0.0142998i
$137$	−10.0544	−	17.4147i	−0.859005	−	1.48784i	−0.872879	−	0.487937i	$-0.837750\pi$
$137$	−10.0544	−	17.4147i	−0.859005	−	1.48784i	0.0138738	−	0.999904i	$-0.495584\pi$
$138$	0.209966	−	2.43246i	0.0178735	−	0.207064i
$139$	14.3239	+	8.26993i	1.21494	+	0.701446i	0.963831	−	0.266513i	$-0.0858714\pi$
$139$	14.3239	+	8.26993i	1.21494	+	0.701446i	0.251109	+	0.967959i	$0.419205\pi$
$140$	−9.22373	+	6.64428i	−0.779547	+	0.561544i
$141$	1.49686	−	17.3411i	0.126058	−	1.46039i
$142$	5.59208	+	9.68576i	0.469277	+	0.812811i
$143$	−9.12286	−	13.5053i	−0.762892	−	1.12937i
$144$	2.95563	+	0.514080i	0.246302	+	0.0428400i
$145$	21.4929	−	37.2269i	1.78489	−	3.09152i
$146$	−5.90130	−	10.2214i	−0.488395	−	0.845925i
$147$	−12.0440	+	1.39363i	−0.993372	+	0.114945i
$148$			5.70199i			0.468700i
$149$	4.09378			0.335375			0.167688	−	0.985840i	$-0.446370\pi$
$149$	4.09378			0.335375			0.167688	+	0.985840i	$0.446370\pi$
$150$	−23.2279	−	2.00499i	−1.89655	−	0.163707i
$151$	−6.54953	−	3.78138i	−0.532994	−	0.307724i	0.209241	−	0.977864i	$-0.432901\pi$
$151$	−6.54953	−	3.78138i	−0.532994	−	0.307724i	−0.742235	+	0.670140i	$0.766234\pi$
$152$	1.69123			0.137177
$153$	−0.370299	+	0.443393i	−0.0299369	+	0.0358462i
$154$	−6.99010	−	9.70381i	−0.563278	−	0.781955i
$155$		−	9.97895i		−	0.801528i
$156$	−3.03771	−	5.45640i	−0.243211	−	0.436862i
$157$	−4.42840	−	2.55674i	−0.353425	−	0.204050i	0.312768	−	0.949830i	$-0.398744\pi$
$157$	−4.42840	−	2.55674i	−0.353425	−	0.204050i	−0.666193	+	0.745780i	$0.732077\pi$
$158$	−3.86156			−0.307209
$159$	−10.1320	+	4.73899i	−0.803523	+	0.375826i
$160$	−3.72094	−	2.14828i	−0.294166	−	0.169837i
$161$	−3.02608	+	2.17983i	−0.238489	+	0.171794i
$162$	1.60400	+	8.85591i	0.126022	+	0.695786i
$163$			9.24295i			0.723964i	0.932185	+	0.361982i	$0.117900\pi$
$163$			9.24295i			0.723964i	−0.932185	+	0.361982i	$0.882100\pi$
$164$	1.24309	+	0.717699i	0.0970691	+	0.0560429i
$165$	2.89289	−	33.5141i	0.225211	−	2.60907i
$166$	3.59496	+	2.07555i	0.279023	+	0.161094i
$167$	13.7047	−	7.91242i	1.06050	−	0.612281i	0.134931	−	0.990855i	$-0.456919\pi$
$167$	13.7047	−	7.91242i	1.06050	−	0.612281i	0.925571	+	0.378574i	$0.123585\pi$
$168$	−2.34878	−	3.93488i	−0.181212	−	0.303582i
$169$	−4.85339	+	12.0600i	−0.373338	+	0.927695i
$170$	0.716508	−	0.413676i	0.0549537	−	0.0317275i
$171$	1.74637	+	4.76365i	0.133548	+	0.364286i
$172$	−3.46362			−0.264099
$173$	12.7234			0.967340			0.483670	−	0.875250i	$-0.339303\pi$
$173$	12.7234			0.967340			0.483670	+	0.875250i	$0.339303\pi$
$174$	14.2063	+	9.92281i	1.07698	+	0.752246i
$175$	20.8155	+	28.8966i	1.57351	+	2.18437i
$176$	2.26010	−	3.91461i	0.170361	−	0.295075i
$177$	0.546468	−	6.33085i	0.0410751	−	0.475856i
$178$	−1.87572	+	1.08295i	−0.140591	+	0.0811702i
$179$			5.51528i			0.412231i	0.978528	+	0.206116i	$0.0660823\pi$
$179$			5.51528i			0.412231i	−0.978528	+	0.206116i	$0.933918\pi$
$180$	2.20878	−	12.6990i	0.164633	−	0.946531i
$181$		−	3.95607i		−	0.294053i	−0.989133	−	0.147026i	$-0.953030\pi$
$181$		−	3.95607i		−	0.294053i	0.989133	−	0.147026i	$-0.0469702\pi$
$182$	−3.29298	+	8.95301i	−0.244092	+	0.663641i
$183$	11.5190	+	8.04576i	0.851509	+	0.594760i
$184$	−1.22075	−	0.704800i	−0.0899949	−	0.0519586i
$185$	24.4990			1.80120
$186$	4.00785	+	0.345951i	0.293870	+	0.0253664i
$187$	0.435207	+	0.753801i	0.0318255	+	0.0551234i
$188$	−8.70281	−	5.02457i	−0.634718	−	0.366454i
$189$	8.65795	−	10.6789i	0.629773	−	0.776779i
$190$		−	7.26647i		−	0.527165i
$191$		−	7.20142i		−	0.521077i	−0.965464	−	0.260538i	$-0.916100\pi$
$191$		−	7.20142i		−	0.521077i	0.965464	−	0.260538i	$-0.0839000\pi$
$192$	0.991815	−	1.41997i	0.0715781	−	0.102477i
$193$			20.5681i			1.48052i	0.672319	+	0.740262i	$0.265298\pi$
$193$			20.5681i			1.48052i	−0.672319	+	0.740262i	$0.734702\pi$
$194$	6.86525	+	11.8910i	0.492897	+	0.853722i
$195$	−23.4438	+	13.0517i	−1.67885	+	0.934654i
$196$	−2.21720	+	6.63958i	−0.158372	+	0.474256i
$197$	−12.5549	−	21.7458i	−0.894501	−	1.54932i	−0.834421	−	0.551128i	$-0.814198\pi$
$197$	−12.5549	−	21.7458i	−0.894501	−	1.54932i	−0.0600807	−	0.998194i	$-0.519136\pi$
$198$	13.3600	+	2.32374i	0.949455	+	0.165141i
$199$	−6.42858	+	3.71154i	−0.455710	+	0.263104i	−0.710239	−	0.703961i	$-0.751413\pi$
$199$	−6.42858	+	3.71154i	−0.455710	+	0.263104i	0.254529	+	0.967065i	$0.418080\pi$
$200$	−6.73025	+	11.6571i	−0.475901	+	0.824284i
$201$	7.18181	+	5.01633i	0.506566	+	0.353825i
$202$	0.0403083	−	0.0698161i	0.00283608	−	0.00491224i
$203$	−2.65976	−	26.3360i	−0.186679	−	1.84842i
$204$	0.141305	+	0.302113i	0.00989334	+	0.0211521i
$205$	3.08364	−	5.34103i	0.215371	−	0.373033i
$206$			10.4514i			0.728186i
$207$	0.724647	−	4.16625i	0.0503665	−	0.289575i
$208$	−3.59660	+	0.253971i	−0.249379	+	0.0176097i
$209$	7.64468			0.528794
$210$	−16.9065	+	10.0917i	−1.16666	+	0.696392i
$211$	2.60466	+	4.51140i	0.179312	+	0.310577i	0.941645	−	0.336607i	$-0.109280\pi$
$211$	2.60466	+	4.51140i	0.179312	+	0.310577i	−0.762333	+	0.647185i	$0.775946\pi$
$212$			6.45798i			0.443536i
$213$	8.20715	+	17.5470i	0.562345	+	1.20230i
$214$	4.64534	−	2.68199i	0.317549	−	0.183337i
$215$			14.8817i			1.01492i
$216$	5.02375	+	1.32737i	0.341823	+	0.0903158i
$217$	−3.59161	−	4.98594i	−0.243814	−	0.338468i
$218$	−6.11686	+	3.53157i	−0.414286	+	0.239188i
$219$	−8.66098	−	18.5173i	−0.585255	−	1.25129i
$220$	−16.8194	−	9.71067i	−1.13396	−	0.654694i
$221$	0.303929	−	0.624231i	0.0204445	−	0.0419903i
$222$	−0.849333	+	9.83954i	−0.0570035	+	0.660387i
$223$	3.67083	+	6.35806i	0.245817	+	0.425767i	0.962361	−	0.271775i	$-0.0876105\pi$
$223$	3.67083	+	6.35806i	0.245817	+	0.425767i	−0.716544	+	0.697542i	$0.754277\pi$
$224$	−2.63236	+	0.265852i	−0.175882	+	0.0177630i
$225$	−39.7842	−	6.91977i	−2.65228	−	0.461318i
$226$	11.0639	−	6.38777i	0.735963	−	0.424908i
$227$	−18.7060	+	10.7999i	−1.24156	+	0.716816i	−0.969412	−	0.245439i	$-0.921068\pi$
$227$	−18.7060	+	10.7999i	−1.24156	+	0.716816i	−0.272150	+	0.962255i	$0.587735\pi$
$228$	2.91844	+	0.251915i	0.193278	+	0.0166835i
$229$	5.53269	+	9.58290i	0.365610	+	0.633256i	0.988874	−	0.148756i	$-0.0475269\pi$
$229$	5.53269	+	9.58290i	0.365610	+	0.633256i	−0.623263	+	0.782012i	$0.714194\pi$
$230$	−3.02822	+	5.24504i	−0.199675	+	0.345848i
$231$	−10.6169	−	17.7864i	−0.698543	−	1.17026i
$232$	8.66432	−	5.00235i	0.568841	−	0.328420i
$233$	5.93673	−	3.42758i	0.388928	−	0.224548i	−0.292767	−	0.956184i	$-0.594576\pi$
$233$	5.93673	−	3.42758i	0.388928	−	0.224548i	0.681696	+	0.731636i	$0.261243\pi$
$234$	−4.42922	−	9.86823i	−0.289547	−	0.645106i
$235$	−21.5884	+	37.3922i	−1.40827	+	2.43920i
$236$	−3.17719	−	1.83435i	−0.206818	−	0.119406i
$237$	−6.66364	−	0.575194i	−0.432850	−	0.0373629i
$238$	0.209111	−	0.464576i	0.0135547	−	0.0301140i
$239$	7.06260			0.456841			0.228421	−	0.973563i	$-0.426644\pi$
$239$	7.06260			0.456841			0.228421	+	0.973563i	$0.426644\pi$
$240$	−6.10098	−	4.26140i	−0.393817	−	0.275072i
$241$	−9.86816	−	17.0922i	−0.635664	−	1.10100i	−0.986374	−	0.164518i	$-0.947393\pi$
$241$	−9.86816	−	17.0922i	−0.635664	−	1.10100i	0.350710	−	0.936484i	$-0.385940\pi$
$242$	4.71610	−	8.16852i	0.303162	−	0.525093i
$243$	1.44879	+	15.5210i	0.0929399	+	0.995672i
$244$	7.02534	−	4.05608i	0.449751	−	0.259664i
$245$	28.5274	+	9.52637i	1.82255	+	0.608618i
$246$	2.03822	+	1.42365i	0.129952	+	0.0907685i
$247$	−3.41331	−	5.05297i	−0.217183	−	0.321513i
$248$	1.16127	−	2.01138i	0.0737407	−	0.127723i
$249$	5.89443	+	4.11713i	0.373544	+	0.260912i
$250$	31.4810	+	18.1756i	1.99103	+	1.14952i
$251$	−2.00148	+	3.46666i	−0.126332	+	0.218814i	−0.922253	−	0.386587i	$-0.873654\pi$
$251$	−2.00148	+	3.46666i	−0.126332	+	0.218814i	0.795921	+	0.605401i	$0.206987\pi$
$252$	−3.46701	−	7.14002i	−0.218401	−	0.449779i
$253$	−5.51803	−	3.18584i	−0.346916	−	0.200292i
$254$	0.102097			0.00640613
$255$	1.29805	−	0.607127i	0.0812870	−	0.0380198i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.47752	+	7.75528i	−0.279300	+	0.483761i	−0.971211	−	0.238221i	$-0.923436\pi$
$257$	−4.47752	+	7.75528i	−0.279300	+	0.483761i	0.691911	+	0.721983i	$0.256769\pi$
$258$	−5.97694	−	0.515920i	−0.372108	−	0.0321197i
$259$	12.2408	−	8.81763i	0.760608	−	0.547901i
$260$	1.09120	+	15.4530i	0.0676735	+	0.958356i
$261$	23.0369	+	19.2392i	1.42595	+	1.19088i
$262$	1.49213			0.0921844
$263$			17.9782i			1.10858i	0.832323	+	0.554291i	$0.187011\pi$
$263$			17.9782i			1.10858i	−0.832323	+	0.554291i	$0.812989\pi$
$264$	4.48320	−	6.41853i	0.275922	−	0.395033i
$265$	27.7471			1.70449
$266$	−2.61534	−	3.63067i	−0.160357	−	0.222610i
$267$	−3.39811	+	1.58937i	−0.207961	+	0.0972681i
$268$	4.38012	−	2.52887i	0.267559	−	0.154475i
$269$	1.42759	+	2.47266i	0.0870417	+	0.150761i	0.906259	−	0.422722i	$-0.138925\pi$
$269$	1.42759	+	2.47266i	0.0870417	+	0.150761i	−0.819218	+	0.573483i	$0.805592\pi$
$270$	5.70312	−	21.5849i	0.347081	−	1.31362i
$271$	−2.23628	+	3.87335i	−0.135844	+	0.235289i	−0.925920	−	0.377720i	$-0.876708\pi$
$271$	−2.23628	+	3.87335i	−0.135844	+	0.235289i	0.790075	+	0.613010i	$0.210041\pi$
$272$	0.192561			0.0116757
$273$	−7.01605	+	14.9591i	−0.424631	+	0.905367i
$274$	−20.1088			−1.21482
$275$	−30.4221	+	52.6926i	−1.83452	+	3.17748i
$276$	−2.00159	−	1.39806i	−0.120481	−	0.0841535i
$277$	−7.40337	−	12.8230i	−0.444826	−	0.770461i	0.553214	−	0.833039i	$-0.313401\pi$
$277$	−7.40337	−	12.8230i	−0.444826	−	0.770461i	−0.998040	+	0.0625783i	$0.980068\pi$
$278$	14.3239	−	8.26993i	0.859093	−	0.495997i
$279$	6.86455	+	1.19397i	0.410970	+	0.0714811i
$280$	1.14225	+	11.3101i	0.0682625	+	0.675909i
$281$	−3.78960			−0.226069			−0.113034	−	0.993591i	$-0.536057\pi$
$281$	−3.78960			−0.226069			−0.113034	+	0.993591i	$0.536057\pi$
$282$	−14.2694	−	9.96688i	−0.849732	−	0.593519i
$283$			27.6901i			1.64600i	0.568038	+	0.823002i	$0.307703\pi$
$283$			27.6901i			1.64600i	−0.568038	+	0.823002i	$0.692297\pi$
$284$	11.1842			0.663658
$285$	1.08237	−	12.5393i	0.0641140	−	0.742762i
$286$	−16.2573	+	1.14800i	−0.961316	+	0.0678826i
$287$	−0.381603	−	3.77848i	−0.0225253	−	0.223037i
$288$	1.92302	−	2.30261i	0.113315	−	0.135682i
$289$	8.48146	−	14.6903i	0.498909	−	0.864136i
$290$	−21.4929	−	37.2269i	−1.26211	−	2.18604i
$291$	10.0757	+	21.5421i	0.590649	+	1.26282i
$292$	−11.8026			−0.690695
$293$	17.6685	+	10.2009i	1.03221	+	0.595944i	0.917616	−	0.397469i	$-0.130111\pi$
$293$	17.6685	+	10.2009i	1.03221	+	0.595944i	0.114590	+	0.993413i	$0.463445\pi$
$294$	−4.81507	+	11.1272i	−0.280821	+	0.648953i
$295$	−7.88143	+	13.6510i	−0.458875	+	0.794794i
$296$	4.93806	+	2.85099i	0.287019	+	0.165711i
$297$	22.7084	+	5.99996i	1.31767	+	0.348153i
$298$	2.04689	−	3.54532i	0.118573	−	0.205375i
$299$	0.357997	+	5.06976i	0.0207035	+	0.293192i
$300$	−13.3503	+	19.1135i	−0.770782	+	1.10352i
$301$	5.35619	+	7.43558i	0.308726	+	0.428580i
$302$	−6.54953	+	3.78138i	−0.376883	+	0.217594i
$303$	0.0799568	−	0.114473i	0.00459340	−	0.00657630i
$304$	0.845613	−	1.46464i	0.0484992	−	0.0840031i
$305$	−17.4272	−	30.1849i	−0.997881	−	1.72838i
$306$	0.198840	+	0.542385i	0.0113669	+	0.0310061i
$307$	−25.5018			−1.45546			−0.727731	−	0.685862i	$-0.759425\pi$
$307$	−25.5018			−1.45546			−0.727731	+	0.685862i	$0.759425\pi$
$308$	−11.8988	+	1.20170i	−0.677997	+	0.0684733i
$309$	−1.55678	+	18.0354i	−0.0885623	+	1.02600i
$310$	−8.64202	−	4.98947i	−0.490834	−	0.283383i
$311$	8.67002	−	15.0169i	0.491632	−	0.851531i	−0.508322	−	0.861167i	$-0.669734\pi$
$311$	8.67002	−	15.0169i	0.491632	−	0.851531i	0.999954	+	0.00963600i	$0.00306728\pi$
$312$	−6.24424	−	0.0974664i	−0.353510	−	0.00551795i
$313$	−7.84351	+	4.52845i	−0.443341	+	0.255963i	−0.705014	−	0.709194i	$-0.749059\pi$
$313$	−7.84351	+	4.52845i	−0.443341	+	0.255963i	0.261673	+	0.965157i	$0.415726\pi$
$314$	−4.42840	+	2.55674i	−0.249909	+	0.144285i
$315$	−30.6776	+	14.8963i	−1.72849	+	0.839309i
$316$	−1.93078	+	3.34421i	−0.108615	+	0.188126i
$317$	−4.97176	−	8.61134i	−0.279242	−	0.483661i	0.691955	−	0.721941i	$-0.256750\pi$
$317$	−4.97176	−	8.61134i	−0.279242	−	0.483661i	−0.971197	+	0.238280i	$0.923416\pi$
$318$	−0.961940	+	11.1441i	−0.0539429	+	0.624930i
$319$	39.1645	−	22.6116i	2.19279	−	1.26601i
$320$	−3.72094	+	2.14828i	−0.208007	+	0.120093i
$321$	8.41564	−	3.93619i	0.469715	−	0.219696i
$322$	0.374745	+	3.71058i	0.0208837	+	0.206782i
$323$	0.162832	+	0.282034i	0.00906023	+	0.0156928i
$324$	8.47144	+	3.03885i	0.470636	+	0.168825i
$325$	48.4120	−	3.41857i	2.68541	−	0.189628i
$326$	8.00463	+	4.62147i	0.443335	+	0.255960i
$327$	−11.0815	+	5.18307i	−0.612809	+	0.286624i
$328$	1.24309	−	0.717699i	0.0686382	−	0.0396283i
$329$	2.67158	+	26.4530i	0.147289	+	1.45840i
$330$	−27.5777	−	19.2624i	−1.51810	−	1.06036i
$331$		−	27.6837i		−	1.52163i	−0.648966	−	0.760817i	$-0.724798\pi$
$331$		−	27.6837i		−	1.52163i	0.648966	−	0.760817i	$-0.275202\pi$
$332$	3.59496	−	2.07555i	0.197299	−	0.113911i
$333$	−2.93128	+	16.8529i	−0.160633	+	0.923535i
$334$		−	15.8248i		−	0.865896i
$335$	−10.8654	−	18.8195i	−0.593643	−	1.02822i
$336$	−4.58209	+	0.0666621i	−0.249974	+	0.00363671i
$337$	−9.67002			−0.526760			−0.263380	−	0.964692i	$-0.584837\pi$
$337$	−9.67002			−0.526760			−0.263380	+	0.964692i	$0.584837\pi$
$338$	8.01761	+	10.2332i	0.436100	+	0.556612i
$339$	20.0438	−	9.37494i	1.08863	−	0.509177i
$340$		−	0.827353i		−	0.0448695i
$341$	5.24917	−	9.09182i	0.284258	−	0.492350i
$342$	4.99863	+	0.869425i	0.270295	+	0.0470131i
$343$	17.6823	−	5.50772i	0.954756	−	0.297389i
$344$	−1.73181	+	2.99958i	−0.0933729	+	0.161727i
$345$	−6.00688	+	8.59995i	−0.323399	+	0.463006i
$346$	6.36169	−	11.0188i	0.342006	−	0.592372i
$347$	−18.3909	+	10.6180i	−0.987278	+	0.570005i	−0.904460	−	0.426560i	$-0.859725\pi$
$347$	−18.3909	+	10.6180i	−0.987278	+	0.570005i	−0.0828184	+	0.996565i	$0.526392\pi$
$348$	15.6966	−	7.34164i	0.841424	−	0.393553i
$349$	−3.87087	−	6.70454i	−0.207203	−	0.358886i	0.743630	−	0.668592i	$-0.233103\pi$
$349$	−3.87087	−	6.70454i	−0.207203	−	0.358886i	−0.950832	+	0.309706i	$0.899769\pi$
$350$	35.4329	−	3.57850i	1.89397	−	0.191279i
$351$	−6.17331	−	17.6887i	−0.329507	−	0.944153i
$352$	−2.26010	−	3.91461i	−0.120464	−	0.208649i
$353$		−	4.76973i		−	0.253867i	−0.991911	−	0.126934i	$-0.959486\pi$
$353$		−	4.76973i		−	0.253867i	0.991911	−	0.126934i	$-0.0405135\pi$
$354$	−5.20944	−	3.63868i	−0.276879	−	0.193394i
$355$		−	48.0535i		−	2.55042i
$356$			2.16589i			0.114792i
$357$	0.430050	−	0.770541i	0.0227606	−	0.0407814i
$358$	4.77637	+	2.75764i	0.252439	+	0.145746i
$359$	14.0272	+	24.2958i	0.740328	+	1.28229i	0.952346	+	0.305020i	$0.0986630\pi$
$359$	14.0272	+	24.2958i	0.740328	+	1.28229i	−0.212018	+	0.977266i	$0.568004\pi$
$360$	−9.89331	−	8.26238i	−0.521423	−	0.435466i
$361$	−16.1398			−0.849461
$362$	−3.42606	−	1.97804i	−0.180070	−	0.103963i
$363$	9.35499	−	13.3934i	0.491010	−	0.702971i
$364$	6.10704	+	7.32830i	0.320096	+	0.384107i
$365$			50.7107i			2.65432i
$366$	12.7273	−	5.95286i	0.665268	−	0.311161i
$367$			10.6728i			0.557115i	0.960420	+	0.278558i	$0.0898563\pi$
$367$			10.6728i			0.557115i	−0.960420	+	0.278558i	$0.910144\pi$
$368$	−1.22075	+	0.704800i	−0.0636360	+	0.0367403i
$369$	3.30516	+	2.76030i	0.172060	+	0.143695i
$370$	12.2495	−	21.2167i	0.636821	−	1.10301i
$371$	13.8638	−	9.98671i	0.719770	−	0.518484i
$372$	2.30353	−	3.29793i	0.119432	−	0.170989i
$373$	−22.8957			−1.18549			−0.592746	−	0.805389i	$-0.701956\pi$
$373$	−22.8957			−1.18549			−0.592746	+	0.805389i	$0.701956\pi$
$374$	0.870415			0.0450081
$375$	51.6174	+	36.0536i	2.66551	+	1.86180i
$376$	−8.70281	+	5.02457i	−0.448813	+	0.259122i
$377$	−32.4325	−	15.7909i	−1.67036	−	0.813275i
$378$	−4.91926	−	12.8375i	−0.253020	−	0.660289i
$379$	2.11006	−	1.21824i	0.108387	−	0.0625770i	−0.444827	−	0.895617i	$-0.646735\pi$
$379$	2.11006	−	1.21824i	0.108387	−	0.0625770i	0.553213	+	0.833040i	$0.313401\pi$
$380$	−6.29295	−	3.63324i	−0.322821	−	0.186381i
$381$	0.176182	+	0.0152077i	0.00902607	+	0.000779115i
$382$	−6.23661	−	3.60071i	−0.319093	−	0.184228i
$383$			14.2737i			0.729351i	0.931135	+	0.364676i	$0.118820\pi$
$383$			14.2737i			0.729351i	−0.931135	+	0.364676i	$0.881180\pi$
$384$	−0.733819	−	1.56892i	−0.0374476	−	0.0800636i
$385$	5.16319	+	51.1240i	0.263141	+	2.60552i
$386$	17.8125	+	10.2840i	0.906632	+	0.523444i
$387$	−10.2372	−	1.78058i	−0.520384	−	0.0905118i
$388$	13.7305			0.697061
$389$	−7.37813	−	4.25977i	−0.374086	−	0.215979i	0.301156	−	0.953575i	$-0.402628\pi$
$389$	−7.37813	−	4.25977i	−0.374086	−	0.215979i	−0.675242	+	0.737596i	$0.735961\pi$
$390$	−0.418771	+	26.8288i	−0.0212053	+	1.35853i
$391$		−	0.271434i		−	0.0137270i
$392$	4.64144	+	5.23994i	0.234428	+	0.264657i
$393$	2.57488	+	0.222259i	0.129885	+	0.0112115i
$394$	−25.1098			−1.26502
$395$	14.3686	+	8.29573i	0.722964	+	0.417403i
$396$	8.69243	−	10.4082i	0.436811	−	0.523034i
$397$	−13.3952			−0.672288			−0.336144	−	0.941811i	$-0.609123\pi$
$397$	−13.3952			−0.672288			−0.336144	+	0.941811i	$0.609123\pi$
$398$			7.42309i			0.372086i
$399$	−3.97231	−	6.65477i	−0.198864	−	0.333155i
$400$	6.73025	+	11.6571i	0.336513	+	0.582857i
$401$	7.42476	−	12.8601i	0.370775	−	0.642201i	−0.618910	−	0.785462i	$-0.712425\pi$
$401$	7.42476	−	12.8601i	0.370775	−	0.642201i	0.989685	+	0.143261i	$0.0457588\pi$
$402$	7.93518	−	3.71146i	0.395771	−	0.185111i
$403$	−8.35323	+	0.589857i	−0.416104	+	0.0293829i
$404$	−0.0403083	−	0.0698161i	−0.00200541	−	0.00347348i
$405$	13.0566	−	36.3981i	0.648790	−	1.80864i
$406$	−24.1375	−	10.8646i	−1.19792	−	0.539199i
$407$	22.3210	+	12.8871i	1.10641	+	0.638788i
$408$	0.332290	+	0.0286827i	0.0164508	+	0.00142001i
$409$	9.24300	+	16.0093i	0.457037	+	0.791611i	0.998803	−	0.0489183i	$-0.0155774\pi$
$409$	9.24300	+	16.0093i	0.457037	+	0.791611i	−0.541766	+	0.840529i	$0.682244\pi$
$410$	−3.08364	−	5.34103i	−0.152290	−	0.263774i
$411$	−34.7004	−	2.99528i	−1.71165	−	0.147746i
$412$	9.05121	+	5.22572i	0.445921	+	0.257453i
$413$	0.975332	+	9.65736i	0.0479929	+	0.475208i
$414$	−3.24576	−	2.71069i	−0.159520	−	0.133223i
$415$	−8.91776	−	15.4460i	−0.437756	−	0.758215i
$416$	−1.57835	+	3.24173i	−0.0773851	+	0.158939i
$417$	25.9497	−	12.1373i	1.27076	−	0.594364i
$418$	3.82234	−	6.62049i	0.186957	−	0.323819i
$419$	11.7502	+	20.3519i	0.574035	+	0.994257i	0.996146	+	0.0877131i	$0.0279559\pi$
$419$	11.7502	+	20.3519i	0.574035	+	0.994257i	−0.422111	+	0.906544i	$0.638711\pi$
$420$	0.286418	+	19.6873i	0.0139758	+	0.960640i
$421$		−	7.74237i		−	0.377340i	−0.982041	−	0.188670i	$-0.939582\pi$
$421$		−	7.74237i		−	0.377340i	0.982041	−	0.188670i	$-0.0604176\pi$
$422$	5.20931			0.253585
$423$	−23.1392	−	19.3247i	−1.12507	−	0.939598i
$424$	5.59277	+	3.22899i	0.271609	+	0.156814i
$425$	−2.59197			−0.125729
$426$	19.2998	+	1.66592i	0.935076	+	0.0807143i
$427$	−19.5715	−	8.80937i	−0.947133	−	0.426315i
$428$		−	5.36397i		−	0.259277i
$429$	−28.2252	−	0.440567i	−1.36273	−	0.0212708i
$430$	12.8879	+	7.44084i	0.621510	+	0.358829i
$431$	−18.2786			−0.880451			−0.440225	−	0.897887i	$-0.645101\pi$
$431$	−18.2786			−0.880451			−0.440225	+	0.897887i	$0.645101\pi$
$432$	3.66141	−	3.68702i	0.176160	−	0.177392i
$433$	−28.5068	−	16.4584i	−1.36995	−	0.790940i	−0.379028	−	0.925385i	$-0.623741\pi$
$433$	−28.5068	−	16.4584i	−1.36995	−	0.790940i	−0.990921	+	0.134445i	$0.957075\pi$
$434$	−6.11376	+	0.617450i	−0.293470	+	0.0296386i
$435$	−31.5439	−	67.4414i	−1.51241	−	3.23357i
$436$			7.06314i			0.338263i
$437$	−2.06456	−	1.19198i	−0.0987615	−	0.0570200i
$438$	−20.3670	−	1.75804i	−0.973172	−	0.0840026i
$439$	7.49903	+	4.32957i	0.357909	+	0.206639i	0.668163	−	0.744015i	$-0.267081\pi$
$439$	7.49903	+	4.32957i	0.357909	+	0.206639i	−0.310254	+	0.950654i	$0.600414\pi$
$440$	−16.8194	+	9.71067i	−0.801833	+	0.462938i
$441$	−9.96650	+	18.4843i	−0.474595	+	0.880204i
$442$	−0.388635	−	0.575326i	−0.0184855	−	0.0273655i
$443$	−11.7488	+	6.78318i	−0.558203	+	0.322279i	−0.752424	−	0.658679i	$-0.771115\pi$
$443$	−11.7488	+	6.78318i	−0.558203	+	0.322279i	0.194221	+	0.980958i	$0.437782\pi$
$444$	8.09663	+	5.65531i	0.384249	+	0.268389i
$445$	9.30591			0.441142
$446$	7.34165			0.347637
$447$	4.06027	−	5.81303i	0.192044	−	0.274947i
$448$	−1.08595	+	2.41262i	−0.0513061	+	0.113985i
$449$	−1.47204	+	2.54965i	−0.0694699	+	0.120325i	−0.898668	−	0.438629i	$-0.855464\pi$
$449$	−1.47204	+	2.54965i	−0.0694699	+	0.120325i	0.829198	+	0.558955i	$0.188797\pi$
$450$	−25.8848	+	30.9943i	−1.22022	+	1.46108i
$451$	5.61902	−	3.24414i	0.264589	−	0.152761i
$452$		−	12.7755i		−	0.600911i
$453$	−11.8653	+	5.54969i	−0.557483	+	0.260747i
$454$			21.5999i			1.01373i
$455$	31.4866	−	26.2393i	1.47611	−	1.23012i
$456$	1.67738	−	2.40148i	0.0785507	−	0.112460i
$457$	14.5185	+	8.38227i	0.679147	+	0.392106i	0.799534	−	0.600621i	$-0.205080\pi$
$457$	14.5185	+	8.38227i	0.679147	+	0.392106i	−0.120386	+	0.992727i	$0.538413\pi$
$458$	11.0654			0.517051
$459$	0.262335	+	0.965575i	0.0122447	+	0.0450692i
$460$	3.02822	+	5.24504i	0.141192	+	0.244551i
$461$	−9.22401	−	5.32548i	−0.429605	−	0.248032i	0.269573	−	0.962980i	$-0.413117\pi$
$461$	−9.22401	−	5.32548i	−0.429605	−	0.248032i	−0.699178	+	0.714947i	$0.746451\pi$
$462$	−20.7120	+	0.301326i	−0.963608	+	0.0140189i
$463$		−	22.5835i		−	1.04954i	−0.851243	−	0.524772i	$-0.824151\pi$
$463$		−	22.5835i		−	1.04954i	0.851243	−	0.524772i	$-0.175849\pi$
$464$		−	10.0047i		−	0.464456i
$465$	−14.1698	−	9.89727i	−0.657107	−	0.458975i
$466$		−	6.85515i		−	0.317559i
$467$	14.0602	+	24.3530i	0.650629	+	1.12692i	0.982971	+	0.183763i	$0.0588279\pi$
$467$	14.0602	+	24.3530i	0.650629	+	1.12692i	−0.332342	+	0.943159i	$0.607839\pi$
$468$	−10.7608	−	1.09829i	−0.497416	−	0.0507687i
$469$	−12.2024	−	5.49243i	−0.563453	−	0.253617i
$470$	21.5884	+	37.3922i	0.995799	+	1.72477i
$471$	−8.02263	+	3.75237i	−0.369664	+	0.172900i
$472$	−3.17719	+	1.83435i	−0.146242	+	0.0844330i
$473$	−7.82812	+	13.5587i	−0.359938	+	0.623430i
$474$	−3.82995	+	5.48328i	−0.175915	+	0.251855i
$475$	−11.3824	+	19.7149i	−0.522260	+	0.904580i
$476$	−0.297779	−	0.413384i	−0.0136487	−	0.0189474i
$477$	−3.31991	+	19.0874i	−0.152008	+	0.873950i
$478$	3.53130	−	6.11639i	0.161518	−	0.279757i
$479$		−	19.8178i		−	0.905498i	−0.891638	−	0.452749i	$-0.850443\pi$
$479$		−	19.8178i		−	0.905498i	0.891638	−	0.452749i	$-0.149557\pi$
$480$	−6.74097	+	3.15290i	−0.307682	+	0.143910i
$481$	−1.44814	−	20.5077i	−0.0660294	−	0.935072i
$482$	−19.7363			−0.898965
$483$	0.0939669	+	6.45892i	0.00427564	+	0.293891i
$484$	−4.71610	−	8.16852i	−0.214368	−	0.371297i
$485$		−	58.9941i		−	2.67878i
$486$	14.1660	+	6.50581i	0.642581	+	0.295109i
$487$	−22.1300	+	12.7768i	−1.00281	+	0.578972i	−0.909078	−	0.416626i	$-0.863212\pi$
$487$	−22.1300	+	12.7768i	−1.00281	+	0.578972i	−0.0937303	+	0.995598i	$0.529879\pi$
$488$		−	8.11216i		−	0.367220i
$489$	13.1247	+	9.16729i	0.593518	+	0.414559i
$490$	22.5138	−	19.9423i	1.01707	−	0.900900i
$491$	4.29900	−	2.48203i	0.194011	−	0.112012i	−0.399848	−	0.916582i	$-0.630937\pi$
$491$	4.29900	−	2.48203i	0.194011	−	0.112012i	0.593859	+	0.804569i	$0.297604\pi$
$492$	2.25202	−	1.05332i	0.101529	−	0.0474874i
$493$	1.66841	+	0.963258i	0.0751415	+	0.0433830i
$494$	−6.08266	+	0.429522i	−0.273672	+	0.0193251i
$495$	−44.7197	−	37.3476i	−2.01000	−	1.67865i
$496$	−1.16127	−	2.01138i	−0.0521425	−	0.0903135i
$497$	−17.2953	−	24.0098i	−0.775802	−	1.07699i
$498$	6.51275	−	3.04616i	0.291843	−	0.136502i
$499$	7.88549	−	4.55269i	0.353003	−	0.203807i	−0.313004	−	0.949752i	$-0.601335\pi$
$499$	7.88549	−	4.55269i	0.353003	−	0.203807i	0.666007	+	0.745945i	$0.268002\pi$
$500$	31.4810	−	18.1756i	1.40787	−	0.812837i
$501$	2.35717	−	27.3079i	0.105311	−	1.22003i
$502$	2.00148	+	3.46666i	0.0893304	+	0.154725i
$503$	−5.79205	+	10.0321i	−0.258255	+	0.447310i	−0.965774	−	0.259383i	$-0.916481\pi$
$503$	−5.79205	+	10.0321i	−0.258255	+	0.447310i	0.707520	+	0.706693i	$0.249814\pi$
$504$	−7.91694	−	0.567486i	−0.352649	−	0.0252778i
$505$	−0.299970	+	0.173188i	−0.0133485	+	0.00770675i
$506$	−5.51803	+	3.18584i	−0.245307	+	0.141628i
$507$	12.3112	+	18.8530i	0.546759	+	0.837290i
$508$	0.0510484	−	0.0884185i	0.00226491	−	0.00392294i
$509$	−22.9331	−	13.2404i	−1.01649	−	0.586871i	−0.103405	−	0.994639i	$-0.532974\pi$
$509$	−22.9331	−	13.2404i	−1.01649	−	0.586871i	−0.913085	+	0.407769i	$0.866307\pi$
$510$	0.123237	−	1.42771i	0.00545704	−	0.0632200i
$511$	18.2517	+	25.3374i	0.807408	+	1.12086i
$512$	−1.00000			−0.0441942
$513$	8.49630	+	2.24488i	0.375121	+	0.0991137i
$514$	4.47752	+	7.75528i	0.197495	+	0.342071i
$515$	22.4527	−	38.8892i	0.989383	−	1.71366i
$516$	−3.43527	+	4.91822i	−0.151229	+	0.216513i
$517$	−39.3384	+	22.7121i	−1.73010	+	0.998875i
$518$	−1.51588	−	15.0097i	−0.0666040	−	0.659488i
$519$	12.6192	−	18.0668i	0.553923	−	0.793043i
$520$	13.9283	+	6.78150i	0.610797	+	0.297389i
$521$	4.04236	−	7.00158i	0.177099	−	0.306745i	−0.763787	−	0.645469i	$-0.776662\pi$
$521$	4.04236	−	7.00158i	0.177099	−	0.306745i	0.940886	+	0.338724i	$0.109995\pi$
$522$	28.1801	−	10.3309i	1.23341	−	0.452172i
$523$	−1.16369	−	0.671857i	−0.0508846	−	0.0293782i	0.474342	−	0.880341i	$-0.342686\pi$
$523$	−1.16369	−	0.671857i	−0.0508846	−	0.0293782i	−0.525226	+	0.850962i	$0.676019\pi$
$524$	0.746067	−	1.29223i	0.0325921	−	0.0564512i
$525$	61.6773	−	0.897305i	2.69182	−	0.0391616i
$526$	15.5696	+	8.98910i	0.678866	+	0.391943i
$527$	0.447231			0.0194817
$528$	−3.31701	−	7.09183i	−0.144354	−	0.308632i
$529$	−10.5065	−	18.1978i	−0.456805	−	0.791209i
$530$	13.8736	−	24.0297i	0.602629	−	1.04378i
$531$	−8.44759	−	7.05499i	−0.366594	−	0.306161i
$532$	−4.45192	+	0.449615i	−0.193015	+	0.0194933i
$533$	−4.65317	−	2.26556i	−0.201551	−	0.0981324i
$534$	−0.322618	+	3.73754i	−0.0139610	+	0.161739i
$535$	−23.0467			−0.996395
$536$		−	5.05773i		−	0.218461i
$537$	7.83151	+	5.47014i	0.337955	+	0.236054i
$538$	2.85518			0.123096
$539$	20.9802	+	23.6856i	0.903683	+	1.02021i
$540$	−15.8415	−	15.7315i	−0.681710	−	0.676976i
$541$	32.4126	−	18.7134i	1.39353	−	0.804553i	0.399823	−	0.916592i	$-0.369072\pi$
$541$	32.4126	−	18.7134i	1.39353	−	0.804553i	0.993704	+	0.112039i	$0.0357382\pi$
$542$	2.23628	+	3.87335i	0.0960565	+	0.166375i
$543$	−5.61749	−	3.92369i	−0.241070	−	0.168382i
$544$	0.0962806	−	0.166763i	0.00412800	−	0.00714990i
$545$	30.3473			1.29993
$546$	9.44694	+	13.5556i	0.404292	+	0.580128i
$547$	39.2814			1.67955			0.839775	−	0.542934i	$-0.182687\pi$
$547$	39.2814			1.67955			0.839775	+	0.542934i	$0.182687\pi$
$548$	−10.0544	+	17.4147i	−0.429503	+	0.743920i
$549$	22.8494	−	8.37667i	0.975190	−	0.357508i
$550$	30.4221	+	52.6926i	1.29720	+	2.24682i
$551$	14.6533	−	8.46010i	0.624253	−	0.360413i
$552$	−2.21155	+	1.03439i	−0.0941299	+	0.0440267i
$553$	10.1650	−	1.02660i	0.432260	−	0.0436555i
$554$	−14.8067			−0.629078
$555$	24.2984	−	34.7877i	1.03141	−	1.47666i
$556$		−	16.5399i		−	0.701446i
$557$	−3.79412			−0.160762			−0.0803811	−	0.996764i	$-0.525614\pi$
$557$	−3.79412			−0.160762			−0.0803811	+	0.996764i	$0.525614\pi$
$558$	4.46628	−	5.34789i	0.189073	−	0.226394i
$559$	12.4572	−	0.879658i	0.526885	−	0.0372056i
$560$	10.3660	+	4.66584i	0.438042	+	0.197168i
$561$	1.50202	+	0.129652i	0.0634152	+	0.00547390i
$562$	−1.89480	+	3.28189i	−0.0799273	+	0.138438i
$563$	−3.33637	−	5.77876i	−0.140611	−	0.243546i	0.787116	−	0.616805i	$-0.211573\pi$
$563$	−3.33637	−	5.77876i	−0.140611	−	0.243546i	−0.927727	+	0.373260i	$0.878240\pi$
$564$	−15.7663	+	7.37425i	−0.663881	+	0.310512i
$565$	−54.8910			−2.30928
$566$	23.9803	+	13.8450i	1.00797	+	0.581950i
$567$	−6.57666	−	22.8855i	−0.276194	−	0.961102i
$568$	5.59208	−	9.68576i	0.234638	−	0.406406i
$569$	15.7876	+	9.11496i	0.661850	+	0.382119i	0.792981	−	0.609246i	$-0.208528\pi$
$569$	15.7876	+	9.11496i	0.661850	+	0.382119i	−0.131132	+	0.991365i	$0.541861\pi$
$570$	−10.3181	−	7.20699i	−0.432179	−	0.301868i
$571$	22.5493	−	39.0565i	0.943657	−	1.63446i	0.185239	−	0.982693i	$-0.440694\pi$
$571$	22.5493	−	39.0565i	0.943657	−	1.63446i	0.758418	−	0.651769i	$-0.225973\pi$
$572$	−7.13447	+	14.6533i	−0.298307	+	0.612683i
$573$	−10.2258	−	7.14248i	−0.427188	−	0.298381i
$574$	−3.46306	−	1.55876i	−0.144546	−	0.0650616i
$575$	16.4319	−	9.48697i	0.685258	−	0.395634i
$576$	−1.03261	−	2.81669i	−0.0430253	−	0.117362i
$577$	−16.5263	+	28.6244i	−0.688000	+	1.19165i	0.284484	+	0.958681i	$0.408178\pi$
$577$	−16.5263	+	28.6244i	−0.688000	+	1.19165i	−0.972484	+	0.232970i	$0.925156\pi$
$578$	−8.48146	−	14.6903i	−0.352782	−	0.611037i
$579$	29.2060	+	20.3997i	1.21376	+	0.847784i
$580$	−42.9859			−1.78489
$581$	−10.0150	−	4.50788i	−0.415493	−	0.187018i
$582$	23.6938	+	2.04521i	0.982141	+	0.0847768i
$583$	25.2804	+	14.5957i	1.04701	+	0.604491i
$584$	−5.90130	+	10.2214i	−0.244198	+	0.422963i
$585$	−4.71890	+	46.2343i	−0.195102	+	1.91155i
$586$	17.6685	−	10.2009i	0.729879	−	0.421396i
$587$	−26.4828	+	15.2899i	−1.09306	+	0.631081i	−0.934390	−	0.356251i	$-0.884055\pi$
$587$	−26.4828	+	15.2899i	−1.09306	+	0.631081i	−0.158673	+	0.987331i	$0.550722\pi$
$588$	7.22892	+	9.73359i	0.298116	+	0.401406i
$589$	1.96397	−	3.40169i	0.0809239	−	0.140164i
$590$	7.88143	+	13.6510i	0.324473	+	0.562004i
$591$	−43.3304	−	3.74021i	−1.78237	−	0.153852i
$592$	4.93806	−	2.85099i	0.202953	−	0.117175i
$593$	14.5119	−	8.37847i	0.595934	−	0.344063i	−0.171506	−	0.985183i	$-0.554863\pi$
$593$	14.5119	−	8.37847i	0.595934	−	0.344063i	0.767440	+	0.641120i	$0.221530\pi$
$594$	16.5503	−	16.6660i	0.679067	−	0.683816i
$595$	−1.77613	+	1.27943i	−0.0728143	+	0.0524515i
$596$	−2.04689	−	3.54532i	−0.0838438	−	0.145222i
$597$	−1.10570	+	12.8095i	−0.0452532	+	0.524259i
$598$	4.56954	+	2.22485i	0.186863	+	0.0909808i
$599$	−19.4413	−	11.2245i	−0.794352	−	0.458619i	0.0471404	−	0.998888i	$-0.484989\pi$
$599$	−19.4413	−	11.2245i	−0.794352	−	0.458619i	−0.841492	+	0.540269i	$0.818323\pi$
$600$	9.87758	+	21.1185i	0.403250	+	0.862157i
$601$	−13.6726	+	7.89389i	−0.557718	+	0.321999i	−0.752229	−	0.658902i	$-0.771021\pi$
$601$	−13.6726	+	7.89389i	−0.557718	+	0.321999i	0.194511	+	0.980900i	$0.437688\pi$
$602$	9.11750	−	0.920808i	0.371601	−	0.0375294i
$603$	14.2460	−	5.22265i	0.580144	−	0.212683i
$604$			7.56275i			0.307724i
$605$	−35.0966	+	20.2630i	−1.42688	+	0.823810i
$606$	−0.0591581	−	0.126481i	−0.00240313	−	0.00513794i
$607$			7.65497i			0.310706i	0.987859	+	0.155353i	$0.0496515\pi$
$607$			7.65497i			0.310706i	−0.987859	+	0.155353i	$0.950349\pi$
$608$	−0.845613	−	1.46464i	−0.0342941	−	0.0593992i
$609$	−40.0342	−	22.3436i	−1.62227	−	0.905410i
$610$	−34.8545			−1.41122
$611$	32.5766	+	15.8611i	1.31791	+	0.641671i
$612$	0.569139	+	0.0989918i	0.0230061	+	0.00400151i
$613$			34.8130i			1.40608i	0.711149	+	0.703041i	$0.248175\pi$
$613$			34.8130i			1.40608i	−0.711149	+	0.703041i	$0.751825\pi$
$614$	−12.7509	+	22.0852i	−0.514584	+	0.891285i
$615$	−4.52567	−	9.67598i	−0.182493	−	0.390173i
$616$	−4.90869	+	10.9055i	−0.197777	+	0.439395i
$617$	12.4947	−	21.6415i	0.503019	−	0.871255i	−0.496975	−	0.867765i	$-0.665556\pi$
$617$	12.4947	−	21.6415i	0.503019	−	0.871255i	0.999994	−	0.00348999i	$-0.00111090\pi$
$618$	14.8407	+	10.3659i	0.596980	+	0.416977i
$619$	−1.25318	+	2.17058i	−0.0503697	+	0.0872429i	−0.890111	−	0.455744i	$-0.849373\pi$
$619$	−1.25318	+	2.17058i	−0.0503697	+	0.0872429i	0.839741	+	0.542987i	$0.182707\pi$
$620$	−8.64202	+	4.98947i	−0.347072	+	0.200382i
$621$	−5.19722	−	5.16113i	−0.208557	−	0.207109i
$622$	−8.67002	−	15.0169i	−0.347636	−	0.602123i
$623$	4.64966	−	3.34937i	0.186285	−	0.134190i
$624$	−3.20653	+	5.35894i	−0.128364	+	0.214529i
$625$	−44.4414	−	76.9747i	−1.77765	−	3.07899i
$626$			9.05690i			0.361987i
$627$	7.58211	−	10.8552i	0.302800	−	0.433514i
$628$			5.11348i			0.204050i
$629$			1.09798i			0.0437794i
$630$	−2.43824	+	34.0157i	−0.0971419	+	1.35522i
$631$	18.3250	+	10.5800i	0.729508	+	0.421182i	0.818242	−	0.574874i	$-0.194949\pi$
$631$	18.3250	+	10.5800i	0.729508	+	0.421182i	−0.0887343	+	0.996055i	$0.528282\pi$
$632$	1.93078	+	3.34421i	0.0768023	+	0.133025i
$633$	8.98937	+	0.775947i	0.357295	+	0.0308411i
$634$	−9.94352			−0.394908
$635$	−0.379896	−	0.219333i	−0.0150757	−	0.00870397i
$636$	9.17010	+	6.40512i	0.363618	+	0.253979i
$637$	6.28813	−	24.4430i	0.249145	−	0.968466i
$638$		−	45.2232i		−	1.79040i
$639$	33.0562	+	5.74955i	1.30768	+	0.227449i
$640$			4.29657i			0.169837i
$641$	29.0815	−	16.7902i	1.14865	−	0.663173i	0.200092	−	0.979777i	$-0.435876\pi$
$641$	29.0815	−	16.7902i	1.14865	−	0.663173i	0.948558	+	0.316604i	$0.102543\pi$
$642$	0.798984	−	9.25625i	0.0315334	−	0.365315i
$643$	12.7327	−	22.0537i	0.502129	−	0.869713i	−0.497868	−	0.867253i	$-0.665884\pi$
$643$	12.7327	−	22.0537i	0.502129	−	0.869713i	0.999997	−	0.00246038i	$-0.000783163\pi$
$644$	3.40083	+	1.53075i	0.134011	+	0.0603200i
$645$	21.1315	+	14.7599i	0.832051	+	0.581169i
$646$	0.325665			0.0128131
$647$	10.6192			0.417484			0.208742	−	0.977971i	$-0.433063\pi$
$647$	10.6192			0.417484			0.208742	+	0.977971i	$0.433063\pi$
$648$	6.86745	−	5.81706i	0.269779	−	0.228516i
$649$	−14.3616	+	8.29165i	−0.563740	+	0.325476i
$650$	21.2454	−	43.6353i	0.833314	−	1.71152i
$651$	−10.6421	+	0.154825i	−0.417096	+	0.00606808i
$652$	8.00463	−	4.62147i	0.313485	−	0.180991i
$653$	−7.62135	−	4.40019i	−0.298246	−	0.172193i	0.343408	−	0.939186i	$-0.388419\pi$
$653$	−7.62135	−	4.40019i	−0.298246	−	0.172193i	−0.641655	+	0.766993i	$0.721752\pi$
$654$	−1.05208	+	12.1884i	−0.0411397	+	0.476604i
$655$	−5.55214	−	3.20553i	−0.216940	−	0.125250i
$656$		−	1.43540i		−	0.0560429i
$657$	−34.8841	−	6.06748i	−1.36096	−	0.236715i
$658$	24.2447	+	10.9128i	0.945158	+	0.425426i
$659$	−5.79064	−	3.34323i	−0.225571	−	0.130234i	0.382956	−	0.923767i	$-0.374906\pi$
$659$	−5.79064	−	3.34323i	−0.225571	−	0.130234i	−0.608527	+	0.793533i	$0.708239\pi$
$660$	−30.4705	+	14.2518i	−1.18606	+	0.554749i
$661$	−49.7695			−1.93581			−0.967904	−	0.251319i	$-0.919136\pi$
$661$	−49.7695			−1.93581			−0.967904	+	0.251319i	$0.919136\pi$
$662$	−23.9748	−	13.8419i	−0.931807	−	0.537979i
$663$	−0.584945	−	1.05069i	−0.0227174	−	0.0408055i
$664$		−	4.15111i		−	0.161094i
$665$	1.93180	+	19.1280i	0.0749121	+	0.741751i
$666$	13.1294	+	10.9650i	0.508755	+	0.424886i
$667$	−14.1026			−0.546056
$668$	−13.7047	−	7.91242i	−0.530251	−	0.306141i
$669$	12.6690	+	1.09357i	0.489812	+	0.0422798i
$670$	−21.7309			−0.839538
$671$		−	36.6686i		−	1.41558i
$672$	−2.23331	+	4.00154i	−0.0861520	+	0.154363i
$673$	−22.5838	−	39.1163i	−0.870542	−	1.50782i	−0.861437	−	0.507864i	$-0.830435\pi$
$673$	−22.5838	−	39.1163i	−0.870542	−	1.50782i	−0.00910418	−	0.999959i	$-0.502898\pi$
$674$	−4.83501	+	8.37448i	−0.186238	+	0.322573i
$675$	−49.2844	+	49.6291i	−1.89696	+	1.91023i
$676$	12.8710	−	1.82686i	0.495038	−	0.0702638i
$677$	−10.7942	−	18.6960i	−0.414853	−	0.718546i	0.580560	−	0.814217i	$-0.302834\pi$
$677$	−10.7942	−	18.6960i	−0.414853	−	0.718546i	−0.995413	+	0.0956710i	$0.969500\pi$
$678$	1.90297	−	22.0459i	0.0730830	−	0.846668i
$679$	−21.2331	−	29.4762i	−0.814850	−	1.13119i
$680$	−0.716508	−	0.413676i	−0.0274768	−	0.0158638i
$681$	−3.21738	+	37.2734i	−0.123290	+	1.42832i
$682$	−5.24917	−	9.09182i	−0.201001	−	0.348144i
$683$	21.7930	+	37.7466i	0.833886	+	1.44433i	0.894934	+	0.446198i	$0.147222\pi$
$683$	21.7930	+	37.7466i	0.833886	+	1.44433i	−0.0610486	+	0.998135i	$0.519444\pi$
$684$	3.25226	−	3.89423i	0.124353	−	0.148900i
$685$	74.8236	+	43.1994i	2.85886	+	1.65056i
$686$	4.07134	−	18.0672i	0.155444	−	0.689809i
$687$	19.0948	+	1.64823i	0.728512	+	0.0628839i
$688$	1.73181	+	2.99958i	0.0660246	+	0.114358i
$689$	−1.64014	−	23.2267i	−0.0624842	−	0.884868i
$690$	4.44434	+	9.50208i	0.169193	+	0.361738i
$691$	−2.70189	+	4.67980i	−0.102785	+	0.178028i	−0.912831	−	0.408338i	$-0.866109\pi$
$691$	−2.70189	+	4.67980i	−0.102785	+	0.178028i	0.810046	+	0.586366i	$0.199442\pi$
$692$	−6.36169	−	11.0188i	−0.241835	−	0.418871i
$693$	−35.7861	−	2.56515i	−1.35940	−	0.0974420i
$694$			21.2360i			0.806109i
$695$	−71.0646			−2.69564
$696$	1.49024	−	17.2644i	0.0564874	−	0.654407i
$697$	0.239371	+	0.138201i	0.00906682	+	0.00523473i
$698$	−7.74174			−0.293029
$699$	1.02110	−	11.8295i	0.0386216	−	0.447432i
$700$	14.6174	−	32.4750i	0.552485	−	1.22744i
$701$			29.7087i			1.12208i	0.827787	+	0.561042i	$0.189599\pi$
$701$			29.7087i			1.12208i	−0.827787	+	0.561042i	$0.810401\pi$
$702$	−18.4055	−	3.49811i	−0.694672	−	0.132028i
$703$	8.35138	+	4.82167i	0.314978	+	0.181853i
$704$	−4.52020			−0.170361
$705$	31.6840	+	67.7410i	1.19329	+	2.55127i
$706$	−4.13071	−	2.38487i	−0.155461	−	0.0897556i
$707$	−0.0875454	+	0.194497i	−0.00329248	+	0.00731482i
$708$	−5.75591	+	2.69217i	−0.216320	+	0.101178i
$709$			34.0909i			1.28031i	0.768246	+	0.640155i	$0.221130\pi$
$709$			34.0909i			1.28031i	−0.768246	+	0.640155i	$0.778870\pi$
$710$	−41.6156	−	24.0268i	−1.56180	−	0.901708i
$711$	−7.42585	+	8.89165i	−0.278491	+	0.333463i
$712$	1.87572	+	1.08295i	0.0702955	+	0.0405851i
$713$	−2.83524	+	1.63693i	−0.106181	+	0.0613034i
$714$	−0.452283	−	0.757704i	−0.0169263	−	0.0283564i
$715$	62.9587	+	30.6537i	2.35452	+	1.14638i
$716$	4.77637	−	2.75764i	0.178501	−	0.103058i
$717$	7.00479	−	10.0286i	0.261599	−	0.374527i
$718$	28.0544			1.04698
$719$	−27.6178			−1.02997			−0.514985	−	0.857199i	$-0.672202\pi$
$719$	−27.6178			−1.02997			−0.514985	+	0.857199i	$0.672202\pi$
$720$	−12.1021	+	4.43667i	−0.451018	+	0.165345i
$721$	−2.77853	−	27.5120i	−0.103478	−	1.02460i
$722$	−8.06988	+	13.9774i	−0.300330	+	0.520186i
$723$	−34.0577	−	2.93980i	−1.26662	−	0.109332i
$724$	−3.42606	+	1.97804i	−0.127329	+	0.0735131i
$725$			134.668i			5.00146i
$726$	−6.92153	−	14.7984i	−0.256882	−	0.549219i
$727$		−	3.84648i		−	0.142658i	−0.997453	−	0.0713291i	$-0.977276\pi$
$727$		−	3.84648i		−	0.142658i	0.997453	−	0.0713291i	$-0.0227241\pi$
$728$	9.40002	−	1.62470i	0.348388	−	0.0602155i
$729$	23.4762	+	13.3367i	0.869489	+	0.493952i
$730$	43.9168	+	25.3554i	1.62543	+	0.938444i
$731$	−0.666959			−0.0246684
$732$	1.20834	−	13.9986i	0.0446615	−	0.517404i
$733$	−4.54533	−	7.87274i	−0.167886	−	0.290786i	0.769791	−	0.638296i	$-0.220361\pi$
$733$	−4.54533	−	7.87274i	−0.167886	−	0.290786i	−0.937676	+	0.347510i	$0.887027\pi$
$734$	9.24291	+	5.33639i	0.341162	+	0.196970i
$735$	41.8210	−	31.0596i	1.54259	−	1.14565i
$736$			1.40960i			0.0519586i
$737$		−	22.8620i		−	0.842131i
$738$	4.04306	−	1.48220i	0.148827	−	0.0545606i
$739$			17.3424i			0.637949i	0.947763	+	0.318974i	$0.103338\pi$
$739$			17.3424i			0.637949i	−0.947763	+	0.318974i	$0.896662\pi$
$740$	−12.2495	−	21.2167i	−0.450300	−	0.779943i
$741$	−10.5604	−	0.164838i	−0.387947	−	0.00605546i
$742$	−1.71686	−	16.9997i	−0.0630280	−	0.624079i
$743$	−12.2804	−	21.2704i	−0.450526	−	0.780334i	0.547893	−	0.836549i	$-0.315430\pi$
$743$	−12.2804	−	21.2704i	−0.450526	−	0.780334i	−0.998419	+	0.0562149i	$0.982097\pi$
$744$	−1.70432	−	3.64388i	−0.0624835	−	0.133591i
$745$	−15.2327	+	8.79460i	−0.558083	+	0.322209i
$746$	−11.4478	+	19.8282i	−0.419135	+	0.725963i
$747$	11.6924	−	4.28646i	0.427801	−	0.156833i
$748$	0.435207	−	0.753801i	0.0159128	−	0.0275617i
$749$	−11.5152	+	8.29492i	−0.420756	+	0.303090i
$750$	57.0321	−	26.6752i	2.08252	−	0.974040i
$751$	−18.2207	+	31.5593i	−0.664885	+	1.15161i	0.314432	+	0.949280i	$0.398186\pi$
$751$	−18.2207	+	31.5593i	−0.664885	+	1.15161i	−0.979317	+	0.202334i	$0.935147\pi$
$752$			10.0491i			0.366454i
$753$	2.93745	+	6.28032i	0.107047	+	0.228868i
$754$	−29.8916	+	20.1919i	−1.08859	+	0.735346i
$755$	32.4939			1.18257
$756$	−13.5772	−	2.15853i	−0.493798	−	0.0785051i
$757$	−10.7145	−	18.5581i	−0.389427	−	0.674507i	0.602946	−	0.797782i	$-0.293993\pi$
$757$	−10.7145	−	18.5581i	−0.389427	−	0.674507i	−0.992372	+	0.123275i	$0.960660\pi$
$758$		−	2.43649i		−	0.0884972i
$759$	−9.99665	+	4.67566i	−0.362855	+	0.169716i
$760$	−6.29295	+	3.63324i	−0.228269	+	0.131791i
$761$			34.6773i			1.25705i	0.777789	+	0.628525i	$0.216341\pi$
$761$			34.6773i			1.25705i	−0.777789	+	0.628525i	$0.783659\pi$
$762$	0.101261	−	0.144974i	0.00366831	−	0.00525186i
$763$	15.1629	−	10.9225i	0.548934	−	0.395423i
$764$	−6.23661	+	3.60071i	−0.225633	+	0.130269i
$765$	0.425325	−	2.44534i	0.0153777	−	0.0884116i
$766$	12.3614	+	7.13684i	0.446635	+	0.257865i
$767$	11.8930	+	5.79052i	0.429430	+	0.209083i
$768$	−1.72563	−	0.148954i	−0.0622685	−	0.00537491i
$769$	0.987858	+	1.71102i	0.0356231	+	0.0617010i	0.883287	−	0.468832i	$-0.155325\pi$
$769$	0.987858	+	1.71102i	0.0356231	+	0.0617010i	−0.847664	+	0.530533i	$0.821992\pi$
$770$	46.8563	+	21.0905i	1.68858	+	0.760050i
$771$	6.57137	+	14.0497i	0.236662	+	0.505989i
$772$	17.8125	−	10.2840i	0.641085	−	0.370131i
$773$	1.99789	−	1.15348i	0.0718591	−	0.0414879i	−0.463640	−	0.886024i	$-0.653457\pi$
$773$	1.99789	−	1.15348i	0.0718591	−	0.0414879i	0.535499	+	0.844536i	$0.320124\pi$
$774$	−6.66061	+	7.97535i	−0.239411	+	0.286668i
$775$	15.6313	+	27.0742i	0.561492	+	0.972532i
$776$	6.86525	−	11.8910i	0.246448	−	0.426861i
$777$	−0.380106	−	26.1270i	−0.0136362	−	0.937301i
$778$	−7.37813	+	4.25977i	−0.264519	+	0.152720i
$779$	2.10235	−	1.21379i	0.0753244	−	0.0434886i
$780$	23.0250	+	13.7771i	0.824429	+	0.493298i
$781$	25.2773	−	43.7816i	0.904493	−	1.56663i
$782$	−0.235069	−	0.135717i	−0.00840605	−	0.00485324i
$783$	50.1674	−	13.6298i	1.79284	−	0.487091i
$784$	6.85865	−	1.39963i	0.244952	−	0.0499869i
$785$	21.9704			0.784157
$786$	1.47992	−	2.11878i	0.0527870	−	0.0755744i
$787$	−22.5798	−	39.1094i	−0.804885	−	1.39410i	−0.916369	−	0.400335i	$-0.868894\pi$
$787$	−22.5798	−	39.1094i	−0.804885	−	1.39410i	0.111484	−	0.993766i	$-0.464439\pi$
$788$	−12.5549	+	21.7458i	−0.447251	+	0.774661i
$789$	25.5284	+	17.8310i	0.908836	+	0.634802i
$790$	14.3686	−	8.29573i	0.511213	−	0.295149i
$791$	−27.4261	+	19.7563i	−0.975160	+	0.702453i
$792$	−4.66759	−	12.7320i	−0.165855	−	0.452411i
$793$	−24.2372	+	16.3723i	−0.860687	+	0.581398i
$794$	−6.69762	+	11.6006i	−0.237690	+	0.411691i
$795$	27.5200	−	39.4000i	0.976035	−	1.39737i
$796$	6.42858	+	3.71154i	0.227855	+	0.131552i
$797$	−3.13411	+	5.42843i	−0.111016	+	0.192285i	−0.916180	−	0.400767i	$-0.868744\pi$
$797$	−3.13411	+	5.42843i	−0.111016	+	0.192285i	0.805164	+	0.593052i	$0.202077\pi$
$798$	−7.74935	+	0.112741i	−0.274324	+	0.00399098i
$799$	−1.67582	−	0.967537i	−0.0592864	−	0.0342290i
$800$	13.4605			0.475901
$801$	−1.11344	+	6.40157i	−0.0393415	+	0.226188i
$802$	−7.42476	−	12.8601i	−0.262177	−	0.454105i
$803$	−26.6751	+	46.2026i	−0.941342	+	1.63045i
$804$	0.753369	−	8.72779i	0.0265693	−	0.307806i
$805$	6.57698	−	14.6119i	0.231808	−	0.515001i
$806$	−3.66578	+	7.52904i	−0.129122	+	0.265199i
$807$	4.92699	+	0.425290i	0.173438	+	0.0149709i
$808$	−0.0806167			−0.00283608
$809$		−	19.6800i		−	0.691913i	−0.938251	−	0.345956i	$-0.887555\pi$
$809$		−	19.6800i		−	0.691913i	0.938251	−	0.345956i	$-0.112445\pi$
$810$	−24.9934	−	29.5065i	−0.878178	−	1.03675i
$811$	−55.9783			−1.96566			−0.982832	−	0.184501i	$-0.940933\pi$
$811$	−55.9783			−1.96566			−0.982832	+	0.184501i	$0.940933\pi$
$812$	−21.4777	+	15.4714i	−0.753721	+	0.542940i
$813$	3.28205	+	7.01709i	0.115107	+	0.246100i
$814$	22.3210	−	12.8871i	0.782352	−	0.451691i
$815$	−19.8565	−	34.3924i	−0.695542	−	1.20471i
$816$	0.190985	−	0.273430i	0.00668581	−	0.00957198i
$817$	−2.92888	+	5.07297i	−0.102469	+	0.177481i
$818$	18.4860			0.646348
$819$	14.2828	+	24.7992i	0.499081	+	0.866555i
$820$	−6.16728			−0.215371
$821$	5.76836	−	9.99109i	0.201317	−	0.348691i	−0.747636	−	0.664109i	$-0.768811\pi$
$821$	5.76836	−	9.99109i	0.201317	−	0.348691i	0.948953	+	0.315417i	$0.102144\pi$
$822$	−19.9442	+	28.5538i	−0.695634	+	0.995928i
$823$	8.26663	+	14.3182i	0.288157	+	0.499102i	0.973370	−	0.229241i	$-0.0736243\pi$
$823$	8.26663	+	14.3182i	0.288157	+	0.499102i	−0.685213	+	0.728343i	$0.740291\pi$
$824$	9.05121	−	5.22572i	0.315314	−	0.182047i
$825$	44.6486	+	95.4596i	1.55447	+	3.32348i
$826$	8.85119	+	3.98402i	0.307972	+	0.138622i
$827$	−1.49924			−0.0521335			−0.0260668	−	0.999660i	$-0.508298\pi$
$827$	−1.49924			−0.0521335			−0.0260668	+	0.999660i	$0.508298\pi$
$828$	−3.97040	+	1.45556i	−0.137981	+	0.0505843i
$829$			26.0800i			0.905796i	0.891562	+	0.452898i	$0.149610\pi$
$829$			26.0800i			0.905796i	−0.891562	+	0.452898i	$0.850390\pi$
$830$	−17.8355			−0.619080
$831$	−25.5510	−	2.20552i	−0.886355	−	0.0765087i
$832$	2.01824	+	2.98776i	0.0699700	+	0.103582i
$833$	−0.426948	+	1.27853i	−0.0147929	+	0.0442983i
$834$	2.46368	−	28.5417i	0.0853101	−	0.988320i
$835$	−33.9962	+	58.8832i	−1.17649	+	2.03774i
$836$	−3.82234	−	6.62049i	−0.132198	−	0.228974i
$837$	8.50376	−	8.56323i	0.293933	−	0.295989i
$838$	23.5004			0.811808
$839$	−37.0634	−	21.3986i	−1.27957	−	0.738761i	−0.302801	−	0.953054i	$-0.597922\pi$
$839$	−37.0634	−	21.3986i	−1.27957	−	0.738761i	−0.976769	+	0.214293i	$0.931255\pi$
$840$	17.1929	+	9.59559i	0.593211	+	0.331079i
$841$	35.5470	−	61.5692i	1.22576	−	2.12308i
$842$	−6.70509	−	3.87118i	−0.231073	−	0.133410i
$843$	−3.75858	+	5.38110i	−0.129452	+	0.185335i
$844$	2.60466	−	4.51140i	0.0896560	−	0.155289i
$845$	−7.84923	−	55.3011i	−0.270022	−	1.90242i
$846$	−28.3053	+	10.3768i	−0.973155	+	0.356762i
$847$	−10.2429	+	22.7563i	−0.351949	+	0.781915i
$848$	5.59277	−	3.22899i	0.192057	−	0.110884i
$849$	39.3190	+	27.4634i	1.34942	+	0.942542i
$850$	−1.29599	+	2.24471i	−0.0444519	+	0.0769930i
$851$	−4.01876	−	6.96070i	−0.137761	−	0.238610i
$852$	11.0926	−	15.8811i	0.380027	−	0.544078i
$853$	24.3552			0.833905			0.416952	−	0.908928i	$-0.363098\pi$
$853$	24.3552			0.833905			0.416952	+	0.908928i	$0.363098\pi$
$854$	−17.4149	+	12.5448i	−0.595926	+	0.429273i
$855$	−16.7318	−	13.9736i	−0.572216	−	0.477886i
$856$	−4.64534	−	2.68199i	−0.158774	−	0.0916684i
$857$	11.5857	−	20.0671i	0.395761	−	0.685479i	−0.597437	−	0.801916i	$-0.703814\pi$
$857$	11.5857	−	20.0671i	0.395761	−	0.685479i	0.993198	+	0.116437i	$0.0371474\pi$
$858$	−14.4941	+	24.2235i	−0.494822	+	0.826975i
$859$	6.79567	−	3.92348i	0.231865	−	0.133868i	−0.379567	−	0.925164i	$-0.623927\pi$
$859$	6.79567	−	3.92348i	0.231865	−	0.133868i	0.611432	+	0.791297i	$0.290594\pi$
$860$	12.8879	−	7.44084i	0.439474	−	0.253731i
$861$	−5.74380	−	3.20569i	−0.195748	−	0.109250i
$862$	−9.13932	+	15.8298i	−0.311286	+	0.539164i
$863$	−9.45505	−	16.3766i	−0.321854	−	0.557467i	0.659017	−	0.752128i	$-0.270973\pi$
$863$	−9.45505	−	16.3766i	−0.321854	−	0.557467i	−0.980870	+	0.194661i	$0.937639\pi$
$864$	−1.36234	−	5.01438i	−0.0463479	−	0.170593i
$865$	−47.3429	+	27.3334i	−1.60971	+	0.929364i
$866$	−28.5068	+	16.4584i	−0.968700	+	0.559279i
$867$	−12.4477	−	26.6135i	−0.422747	−	0.903841i
$868$	−2.52215	+	5.60339i	−0.0856074	+	0.190192i
$869$	8.72751	+	15.1165i	0.296060	+	0.512792i
$870$	−74.1779	−	6.40291i	−2.51487	−	0.217079i
$871$	−15.1113	+	10.2077i	−0.512026	+	0.345876i
$872$	6.11686	+	3.53157i	0.207143	+	0.119594i
$873$	40.5822	+	7.05858i	1.37350	+	0.238897i
$874$	−2.06456	+	1.19198i	−0.0698349	+	0.0403192i
$875$	−87.7014	−	39.4754i	−2.96485	−	1.33451i
$876$	−11.7060	+	16.7593i	−0.395509	+	0.566244i
$877$			31.1211i			1.05088i	0.850830	+	0.525442i	$0.176100\pi$
$877$			31.1211i			1.05088i	−0.850830	+	0.525442i	$0.823900\pi$
$878$	7.49903	−	4.32957i	0.253080	−	0.146116i
$879$	32.0088	−	14.9713i	1.07963	−	0.504968i
$880$			19.4213i			0.654694i
$881$	−11.3253	−	19.6159i	−0.381558	−	0.660877i	0.609727	−	0.792611i	$-0.291279\pi$
$881$	−11.3253	−	19.6159i	−0.381558	−	0.660877i	−0.991285	+	0.131734i	$0.957946\pi$
$882$	11.0246	+	17.8734i	0.371218	+	0.601828i
$883$	17.1794			0.578133			0.289067	−	0.957309i	$-0.406655\pi$
$883$	17.1794			0.578133			0.289067	+	0.957309i	$0.406655\pi$
$884$	−0.692565	+	0.0489049i	−0.0232935	+	0.00164485i
$885$	11.5671	+	24.7307i	0.388823	+	0.831312i
$886$			13.5664i			0.455771i
$887$	−2.20783	+	3.82407i	−0.0741316	+	0.128400i	−0.900708	−	0.434424i	$-0.856952\pi$
$887$	−2.20783	+	3.82407i	−0.0741316	+	0.128400i	0.826577	+	0.562824i	$0.190285\pi$
$888$	8.94596	−	4.18423i	0.300207	−	0.140413i
$889$	−0.268756	+	0.0271426i	−0.00901378	+	0.000910334i
$890$	4.65295	−	8.05915i	0.155967	−	0.270143i
$891$	31.0422	−	26.2943i	1.03995	−	0.880891i
$892$	3.67083	−	6.35806i	0.122908	−	0.212884i
$893$	−14.7184	+	8.49768i	−0.492533	+	0.284364i
$894$	−3.00409	−	6.42281i	−0.100472	−	0.214811i
$895$	−11.8484	−	20.5220i	−0.396048	−	0.685975i
$896$	1.54641	+	2.14677i	0.0516621	+	0.0717184i
$897$	7.55396	+	4.51992i	0.252219	+	0.150916i
$898$	1.47204	+	2.54965i	0.0491226	+	0.0850829i
$899$		−	23.2363i		−	0.774974i
$900$	13.8994	+	37.9140i	0.463314	+	1.26380i
$901$			1.24356i			0.0414288i
$902$		−	6.48828i		−	0.216036i
$903$	15.8706	−	0.230892i	0.528141	−	0.00768361i
$904$	−11.0639	−	6.38777i	−0.367981	−	0.212454i
$905$	8.49877	+	14.7203i	0.282509	+	0.489319i
$906$	−1.12650	+	13.0505i	−0.0374255	+	0.433575i
$907$	−42.5556			−1.41303			−0.706517	−	0.707696i	$-0.749735\pi$
$907$	−42.5556			−1.41303			−0.706517	+	0.707696i	$0.749735\pi$
$908$	18.7060	+	10.7999i	0.620781	+	0.358408i
$909$	−0.0832453	−	0.227072i	−0.00276107	−	0.00753150i
$910$	−6.98065	−	40.3878i	−0.231406	−	1.33884i
$911$			36.4179i			1.20658i	0.797522	+	0.603290i	$0.206144\pi$
$911$			36.4179i			1.20658i	−0.797522	+	0.603290i	$0.793856\pi$
$912$	−1.24105	−	2.65340i	−0.0410954	−	0.0878628i
$913$		−	18.7638i		−	0.620992i
$914$	14.5185	−	8.38227i	0.480230	−	0.277261i
$915$	−60.1461	−	5.19171i	−1.98837	−	0.171633i
$916$	5.53269	−	9.58290i	0.182805	−	0.316628i
$917$	−3.92784	+	0.396686i	−0.129709	+	0.0130997i
$918$	0.967380	+	0.255599i	0.0319283	+	0.00843603i
$919$	−22.9655			−0.757561			−0.378781	−	0.925487i	$-0.623656\pi$
$919$	−22.9655			−0.757561			−0.378781	+	0.925487i	$0.623656\pi$
$920$	6.05645			0.199675
$921$	−25.2930	+	36.2116i	−0.833434	+	1.19321i
$922$	−9.22401	+	5.32548i	−0.303776	+	0.175385i
$923$	−40.2249	+	2.84045i	−1.32402	+	0.0934945i
$924$	−10.0950	+	18.0877i	−0.332102	+	0.595043i
$925$	−66.4689	+	38.3758i	−2.18548	+	1.26179i
$926$	−19.5579	−	11.2917i	−0.642712	−	0.371070i
$927$	24.0656	+	20.0983i	0.790417	+	0.660115i
$928$	−8.66432	−	5.00235i	−0.284420	−	0.164210i
$929$			22.7177i			0.745343i	0.927963	+	0.372671i	$0.121558\pi$
$929$			22.7177i			0.745343i	−0.927963	+	0.372671i	$0.878442\pi$
$930$	−15.6562	+	7.32274i	−0.513386	+	0.240122i
$931$	7.84973	+	8.86193i	0.257264	+	0.290438i
$932$	−5.93673	−	3.42758i	−0.194464	−	0.112274i
$933$	−12.7245	−	27.2051i	−0.416580	−	0.890656i
$934$	28.1204			0.920128
$935$	−3.23876	−	1.86990i	−0.105919	−	0.0611522i
$936$	−6.33153	+	8.76994i	−0.206952	+	0.286654i
$937$		−	9.05679i		−	0.295872i	−0.988997	−	0.147936i	$-0.952737\pi$
$937$		−	9.05679i		−	0.295872i	0.988997	−	0.147936i	$-0.0472630\pi$
$938$	−10.8578	+	7.82135i	−0.354519	+	0.255376i
$939$	−1.34906	+	15.6289i	−0.0440249	+	0.510030i
$940$	43.1768			1.40827
$941$	−7.89775	−	4.55977i	−0.257459	−	0.148644i	0.365716	−	0.930727i	$-0.380824\pi$
$941$	−7.89775	−	4.55977i	−0.257459	−	0.148644i	−0.623175	+	0.782082i	$0.714158\pi$
$942$	−0.761672	+	8.82399i	−0.0248166	+	0.287501i
$943$	−2.02334			−0.0658889
$944$			3.66871i			0.119406i
$945$	−9.27428	+	58.3354i	−0.301692	+	1.89765i
$946$	7.82812	+	13.5587i	0.254514	+	0.440832i
$947$	−2.96612	+	5.13747i	−0.0963859	+	0.166945i	−0.910186	−	0.414199i	$-0.864062\pi$
$947$	−2.96612	+	5.13747i	−0.0963859	+	0.166945i	0.813800	+	0.581145i	$0.197395\pi$
$948$	2.83369	+	6.05848i	0.0920338	+	0.196770i
$949$	42.4492	−	2.99752i	1.37796	−	0.0973035i
$950$	11.3824	+	19.7149i	0.369293	+	0.639635i
$951$	−17.1589	−	1.48113i	−0.556415	−	0.0480288i
$952$	−0.506891	+	0.0511927i	−0.0164284	+	0.00165916i
$953$	26.0177	+	15.0213i	0.842795	+	0.486588i	0.858213	−	0.513293i	$-0.171575\pi$
$953$	26.0177	+	15.0213i	0.842795	+	0.486588i	−0.0154183	+	0.999881i	$0.504908\pi$
$954$	14.8702	+	12.4188i	0.481440	+	0.402074i
$955$	15.4707	+	26.7960i	0.500620	+	0.867100i
$956$	−3.53130	−	6.11639i	−0.114210	−	0.197818i
$957$	6.73618	−	78.0387i	0.217750	−	2.52263i
$958$	−17.1627	−	9.90890i	−0.554502	−	0.320142i
$959$	52.9336	−	5.34595i	1.70932	−	0.172630i
$960$	−0.639991	+	7.41431i	−0.0206556	+	0.239296i
$961$	12.8029	+	22.1753i	0.412997	+	0.715332i
$962$	−18.4843	−	8.99974i	−0.595957	−	0.290163i
$963$	2.75751	−	15.8539i	0.0888595	−	0.510885i
$964$	−9.86816	+	17.0922i	−0.317832	+	0.550501i
$965$	−44.1861	−	76.5326i	−1.42240	−	2.46367i
$966$	5.64057	+	3.14808i	0.181482	+	0.101288i
$967$			43.9319i			1.41275i	0.707836	+	0.706377i	$0.249671\pi$
$967$			43.9319i			1.41275i	−0.707836	+	0.706377i	$0.750329\pi$
$968$	−9.43220			−0.303162
$969$	0.561978	+	0.0485090i	0.0180533	+	0.00155833i
$970$	−51.0904	−	29.4970i	−1.64041	−	0.947093i
$971$	35.7791			1.14820			0.574102	−	0.818783i	$-0.305351\pi$
$971$	35.7791			1.14820			0.574102	+	0.818783i	$0.305351\pi$
$972$	12.7172	−	9.01518i	0.407904	−	0.289162i
$973$	−35.5072	+	25.5775i	−1.13831	+	0.819976i
$974$			25.5536i			0.818790i
$975$	43.1615	−	72.1340i	1.38227	−	2.31014i
$976$	−7.02534	−	4.05608i	−0.224876	−	0.129832i
$977$	−20.8729			−0.667784			−0.333892	−	0.942611i	$-0.608362\pi$
$977$	−20.8729			−0.667784			−0.333892	+	0.942611i	$0.608362\pi$
$978$	14.5014	−	6.78265i	0.463705	−	0.216885i
$979$	8.47862	+	4.89513i	0.270978	+	0.156449i
$980$	−6.01363	−	29.4686i	−0.192098	−	0.941341i
$981$	−3.63102	+	20.8760i	−0.115930	+	0.666520i
$982$		−	4.96406i		−	0.158410i
$983$	1.08229	+	0.624859i	0.0345196	+	0.0199299i	0.517161	−	0.855888i	$-0.326989\pi$
$983$	1.08229	+	0.624859i	0.0345196	+	0.0199299i	−0.482641	+	0.875818i	$0.660322\pi$
$984$	0.213808	−	2.47697i	0.00681595	−	0.0789629i
$985$	93.4322	+	53.9431i	2.97700	+	1.71877i
$986$	1.66841	−	0.963258i	0.0531331	−	0.0306764i
$987$	40.2120	+	22.4429i	1.27996	+	0.714365i
$988$	−2.66935	+	5.48250i	−0.0849234	+	0.174421i
$989$	4.22821	−	2.44116i	0.134449	−	0.0776244i
$990$	−54.7039	+	20.0546i	−1.73860	+	0.637377i
$991$	20.5965			0.654271			0.327135	−	0.944978i	$-0.393917\pi$
$991$	20.5965			0.654271			0.327135	+	0.944978i	$0.393917\pi$
$992$	−2.32254			−0.0737407
$993$	−39.3099	−	27.4571i	−1.24746	−	0.871325i
$994$	−29.4407	+	2.97332i	−0.933803	+	0.0943081i
$995$	15.9469	−	27.6208i	0.505551	−	0.875640i
$996$	0.618323	−	7.16329i	0.0195923	−	0.226978i
$997$	−25.2371	+	14.5707i	−0.799268	+	0.461457i	−0.843215	−	0.537576i	$-0.819340\pi$
$997$	−25.2371	+	14.5707i	−0.799268	+	0.461457i	0.0439473	+	0.999034i	$0.486007\pi$
$998$		−	9.10539i		−	0.288226i
$999$	21.0233	+	20.8773i	0.665148	+	0.660529i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bn.f.101.12	yes	34
3.2	odd	2		546.2.bn.e.101.6	yes	34
7.5	odd	6		546.2.bi.e.257.5	yes	34
13.4	even	6		546.2.bi.f.17.1	yes	34
21.5	even	6		546.2.bi.f.257.1	yes	34
39.17	odd	6		546.2.bi.e.17.5	✓	34
91.82	odd	6		546.2.bn.e.173.6	yes	34
273.173	even	6	inner	546.2.bn.f.173.12	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.5	✓	34	39.17	odd	6
546.2.bi.e.257.5	yes	34	7.5	odd	6
546.2.bi.f.17.1	yes	34	13.4	even	6
546.2.bi.f.257.1	yes	34	21.5	even	6
546.2.bn.e.101.6	yes	34	3.2	odd	2
546.2.bn.e.173.6	yes	34	91.82	odd	6
546.2.bn.f.101.12	yes	34	1.1	even	1	trivial
546.2.bn.f.173.12	yes	34	273.173	even	6	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.bn (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.991815 - 1.41997i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-3.72094 + 2.14828i) q^{5} +(-0.733819 - 1.56892i) q^{6} +(-1.08595 + 2.41262i) q^{7} -1.00000 q^{8} +(-1.03261 - 2.81669i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.991815 - 1.41997i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-3.72094 + 2.14828i) q^{5} +(-0.733819 - 1.56892i) q^{6} +(-1.08595 + 2.41262i) q^{7} -1.00000 q^{8} +(-1.03261 - 2.81669i) q^{9} +4.29657i q^{10} -4.52020 q^{11} +(-1.72563 - 0.148954i) q^{12} +(2.01824 + 2.98776i) q^{13} +(1.54641 + 2.14677i) q^{14} +(-0.639991 + 7.41431i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.0962806 - 0.166763i) q^{17} +(-2.95563 - 0.514080i) q^{18} -1.69123 q^{19} +(3.72094 + 2.14828i) q^{20} +(2.34878 + 3.93488i) q^{21} +(-2.26010 + 3.91461i) q^{22} +(1.22075 + 0.704800i) q^{23} +(-0.991815 + 1.41997i) q^{24} +(6.73025 - 11.6571i) q^{25} +(3.59660 - 0.253971i) q^{26} +(-5.02375 - 1.32737i) q^{27} +(2.63236 - 0.265852i) q^{28} +(-8.66432 + 5.00235i) q^{29} +(6.10098 + 4.26140i) q^{30} +(-1.16127 + 2.01138i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-4.48320 + 6.41853i) q^{33} -0.192561 q^{34} +(-1.14225 - 11.3101i) q^{35} +(-1.92302 + 2.30261i) q^{36} +(-4.93806 - 2.85099i) q^{37} +(-0.845613 + 1.46464i) q^{38} +(6.24424 + 0.0974664i) q^{39} +(3.72094 - 2.14828i) q^{40} +(-1.24309 + 0.717699i) q^{41} +(4.58209 - 0.0666621i) q^{42} +(1.73181 - 2.99958i) q^{43} +(2.26010 + 3.91461i) q^{44} +(9.89331 + 8.26238i) q^{45} +(1.22075 - 0.704800i) q^{46} +(8.70281 - 5.02457i) q^{47} +(0.733819 + 1.56892i) q^{48} +(-4.64144 - 5.23994i) q^{49} +(-6.73025 - 11.6571i) q^{50} +(-0.332290 - 0.0286827i) q^{51} +(1.57835 - 3.24173i) q^{52} +(-5.59277 - 3.22899i) q^{53} +(-3.66141 + 3.68702i) q^{54} +(16.8194 - 9.71067i) q^{55} +(1.08595 - 2.41262i) q^{56} +(-1.67738 + 2.40148i) q^{57} +10.0047i q^{58} +(3.17719 - 1.83435i) q^{59} +(6.74097 - 3.15290i) q^{60} +8.11216i q^{61} +(1.16127 + 2.01138i) q^{62} +(7.91694 + 0.567486i) q^{63} +1.00000 q^{64} +(-13.9283 - 6.78150i) q^{65} +(3.31701 + 7.09183i) q^{66} +5.05773i q^{67} +(-0.0962806 + 0.166763i) q^{68} +(2.21155 - 1.03439i) q^{69} +(-10.3660 - 4.66584i) q^{70} +(-5.59208 + 9.68576i) q^{71} +(1.03261 + 2.81669i) q^{72} +(5.90130 - 10.2214i) q^{73} +(-4.93806 + 2.85099i) q^{74} +(-9.87758 - 21.1185i) q^{75} +(0.845613 + 1.46464i) q^{76} +(4.90869 - 10.9055i) q^{77} +(3.20653 - 5.35894i) q^{78} +(-1.93078 - 3.34421i) q^{79} -4.29657i q^{80} +(-6.86745 + 5.81706i) q^{81} +1.43540i q^{82} +4.15111i q^{83} +(2.23331 - 4.00154i) q^{84} +(0.716508 + 0.413676i) q^{85} +(-1.73181 - 2.99958i) q^{86} +(-1.49024 + 17.2644i) q^{87} +4.52020 q^{88} +(-1.87572 - 1.08295i) q^{89} +(12.1021 - 4.43667i) q^{90} +(-9.40002 + 1.62470i) q^{91} -1.40960i q^{92} +(1.70432 + 3.64388i) q^{93} -10.0491i q^{94} +(6.29295 - 3.63324i) q^{95} +(1.72563 + 0.148954i) q^{96} +(-6.86525 + 11.8910i) q^{97} +(-6.85865 + 1.39963i) q^{98} +(4.66759 + 12.7320i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 17 q^{2} - 3 q^{3} - 17 q^{4} - 9 q^{5} + 3 q^{6} + 5 q^{7} - 34 q^{8} + 7 q^{9}+O(q^{10}) \) 34 * q + 17 * q^2 - 3 * q^3 - 17 * q^4 - 9 * q^5 + 3 * q^6 + 5 * q^7 - 34 * q^8 + 7 * q^9	\( 34 q + 17 q^{2} - 3 q^{3} - 17 q^{4} - 9 q^{5} + 3 q^{6} + 5 q^{7} - 34 q^{8} + 7 q^{9} + 18 q^{11} + 6 q^{12} - 8 q^{13} + 4 q^{14} - 4 q^{15} - 17 q^{16} - 6 q^{17} - 4 q^{18} - 10 q^{19} + 9 q^{20} + 7 q^{21} + 9 q^{22} - 6 q^{23} + 3 q^{24} + 16 q^{25} - 13 q^{26} - 18 q^{27} - q^{28} - 27 q^{29} + 13 q^{30} + q^{31} + 17 q^{32} + 21 q^{33} - 12 q^{34} + 3 q^{35} - 11 q^{36} + 6 q^{37} - 5 q^{38} - 2 q^{39} + 9 q^{40} - 3 q^{41} + 8 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} - 6 q^{46} + 27 q^{47} - 3 q^{48} - 5 q^{49} - 16 q^{50} - 36 q^{51} - 5 q^{52} - 21 q^{53} + 57 q^{55} - 5 q^{56} + 17 q^{57} + 6 q^{59} + 17 q^{60} - q^{62} + 34 q^{64} - 33 q^{65} - 6 q^{68} - 42 q^{69} + 3 q^{70} + 15 q^{71} - 7 q^{72} + 19 q^{73} + 6 q^{74} - 9 q^{75} + 5 q^{76} + 9 q^{77} - 7 q^{78} - 9 q^{79} - 5 q^{81} + q^{84} - 42 q^{85} + 3 q^{86} + 6 q^{87} - 18 q^{88} + 18 q^{89} + 9 q^{90} - 27 q^{91} + 8 q^{93} + 3 q^{95} - 6 q^{96} - 19 q^{97} - 7 q^{98} + 27 q^{99}+O(q^{100}) \) 34 * q + 17 * q^2 - 3 * q^3 - 17 * q^4 - 9 * q^5 + 3 * q^6 + 5 * q^7 - 34 * q^8 + 7 * q^9 + 18 * q^11 + 6 * q^12 - 8 * q^13 + 4 * q^14 - 4 * q^15 - 17 * q^16 - 6 * q^17 - 4 * q^18 - 10 * q^19 + 9 * q^20 + 7 * q^21 + 9 * q^22 - 6 * q^23 + 3 * q^24 + 16 * q^25 - 13 * q^26 - 18 * q^27 - q^28 - 27 * q^29 + 13 * q^30 + q^31 + 17 * q^32 + 21 * q^33 - 12 * q^34 + 3 * q^35 - 11 * q^36 + 6 * q^37 - 5 * q^38 - 2 * q^39 + 9 * q^40 - 3 * q^41 + 8 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 - 6 * q^46 + 27 * q^47 - 3 * q^48 - 5 * q^49 - 16 * q^50 - 36 * q^51 - 5 * q^52 - 21 * q^53 + 57 * q^55 - 5 * q^56 + 17 * q^57 + 6 * q^59 + 17 * q^60 - q^62 + 34 * q^64 - 33 * q^65 - 6 * q^68 - 42 * q^69 + 3 * q^70 + 15 * q^71 - 7 * q^72 + 19 * q^73 + 6 * q^74 - 9 * q^75 + 5 * q^76 + 9 * q^77 - 7 * q^78 - 9 * q^79 - 5 * q^81 + q^84 - 42 * q^85 + 3 * q^86 + 6 * q^87 - 18 * q^88 + 18 * q^89 + 9 * q^90 - 27 * q^91 + 8 * q^93 + 3 * q^95 - 6 * q^96 - 19 * q^97 - 7 * q^98 + 27 * q^99

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