LMFDB - Embedded newform 546.2.bi.f.257.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(17,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("546.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			257.1
Character	$\chi$	$=$	546.257
Dual form			546.2.bi.f.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-1.72563 + 0.148954i) q^{3} +1.00000 q^{4} +(3.72094 + 2.14828i) q^{5} +(-1.72563 + 0.148954i) q^{6} +(1.54641 - 2.14677i) q^{7} +1.00000 q^{8} +(2.95563 - 0.514080i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-1.72563 + 0.148954i) q^{3} +1.00000 q^{4} +(3.72094 + 2.14828i) q^{5} +(-1.72563 + 0.148954i) q^{6} +(1.54641 - 2.14677i) q^{7} +1.00000 q^{8} +(2.95563 - 0.514080i) q^{9} +(3.72094 + 2.14828i) q^{10} +(-2.26010 + 3.91461i) q^{11} +(-1.72563 + 0.148954i) q^{12} +(-2.01824 - 2.98776i) q^{13} +(1.54641 - 2.14677i) q^{14} +(-6.74097 - 3.15290i) q^{15} +1.00000 q^{16} +0.192561 q^{17} +(2.95563 - 0.514080i) q^{18} +(-0.845613 - 1.46464i) q^{19} +(3.72094 + 2.14828i) q^{20} +(-2.34878 + 3.93488i) q^{21} +(-2.26010 + 3.91461i) q^{22} +1.40960i q^{23} +(-1.72563 + 0.148954i) q^{24} +(6.73025 + 11.6571i) q^{25} +(-2.01824 - 2.98776i) q^{26} +(-5.02375 + 1.32737i) q^{27} +(1.54641 - 2.14677i) q^{28} +(8.66432 - 5.00235i) q^{29} +(-6.74097 - 3.15290i) q^{30} +(1.16127 + 2.01138i) q^{31} +1.00000 q^{32} +(3.31701 - 7.09183i) q^{33} +0.192561 q^{34} +(10.3660 - 4.66584i) q^{35} +(2.95563 - 0.514080i) q^{36} +5.70199i q^{37} +(-0.845613 - 1.46464i) q^{38} +(3.92779 + 4.85515i) q^{39} +(3.72094 + 2.14828i) q^{40} +(-1.24309 + 0.717699i) q^{41} +(-2.34878 + 3.93488i) q^{42} +(1.73181 - 2.99958i) q^{43} +(-2.26010 + 3.91461i) q^{44} +(12.1021 + 4.43667i) q^{45} +1.40960i q^{46} +(-8.70281 - 5.02457i) q^{47} +(-1.72563 + 0.148954i) q^{48} +(-2.21720 - 6.63958i) q^{49} +(6.73025 + 11.6571i) q^{50} +(-0.332290 + 0.0286827i) q^{51} +(-2.01824 - 2.98776i) q^{52} +(-5.59277 + 3.22899i) q^{53} +(-5.02375 + 1.32737i) q^{54} +(-16.8194 + 9.71067i) q^{55} +(1.54641 - 2.14677i) q^{56} +(1.67738 + 2.40148i) q^{57} +(8.66432 - 5.00235i) q^{58} +3.66871i q^{59} +(-6.74097 - 3.15290i) q^{60} +(-7.02534 + 4.05608i) q^{61} +(1.16127 + 2.01138i) q^{62} +(3.46701 - 7.14002i) q^{63} +1.00000 q^{64} +(-1.09120 - 15.4530i) q^{65} +(3.31701 - 7.09183i) q^{66} +(-4.38012 - 2.52887i) q^{67} +0.192561 q^{68} +(-0.209966 - 2.43246i) q^{69} +(10.3660 - 4.66584i) q^{70} +(5.59208 - 9.68576i) q^{71} +(2.95563 - 0.514080i) q^{72} +(-5.90130 - 10.2214i) q^{73} +5.70199i q^{74} +(-13.3503 - 19.1135i) q^{75} +(-0.845613 - 1.46464i) q^{76} +(4.90869 + 10.9055i) q^{77} +(3.92779 + 4.85515i) q^{78} +(-1.93078 + 3.34421i) q^{79} +(3.72094 + 2.14828i) q^{80} +(8.47144 - 3.03885i) q^{81} +(-1.24309 + 0.717699i) q^{82} +4.15111i q^{83} +(-2.34878 + 3.93488i) q^{84} +(0.716508 + 0.413676i) q^{85} +(1.73181 - 2.99958i) q^{86} +(-14.2063 + 9.92281i) q^{87} +(-2.26010 + 3.91461i) q^{88} +2.16589i q^{89} +(12.1021 + 4.43667i) q^{90} +(-9.53506 - 0.287618i) q^{91} +1.40960i q^{92} +(-2.30353 - 3.29793i) q^{93} +(-8.70281 - 5.02457i) q^{94} -7.26647i q^{95} +(-1.72563 + 0.148954i) q^{96} +(6.86525 - 11.8910i) q^{97} +(-2.21720 - 6.63958i) q^{98} +(-4.66759 + 12.7320i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9}+O(q^{10}) $ 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9	$ 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9} + 9 q^{10} + 9 q^{11} + 6 q^{12} + 8 q^{13} + 4 q^{14} - 17 q^{15} + 34 q^{16} + 12 q^{17} + 4 q^{18} - 5 q^{19} + 9 q^{20} - 7 q^{21} + 9 q^{22} + 6 q^{24} + 16 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} + 27 q^{29} - 17 q^{30} - q^{31} + 34 q^{32} + 12 q^{34} - 3 q^{35} + 4 q^{36} - 5 q^{38} - 10 q^{39} + 9 q^{40} - 3 q^{41} - 7 q^{42} - 3 q^{43} + 9 q^{44} + 9 q^{45} - 27 q^{47} + 6 q^{48} - 2 q^{49} + 16 q^{50} - 36 q^{51} + 8 q^{52} - 21 q^{53} - 18 q^{54} - 57 q^{55} + 4 q^{56} - 17 q^{57} + 27 q^{58} - 17 q^{60} - 51 q^{61} - q^{62} - 24 q^{63} + 34 q^{64} - 21 q^{65} - 21 q^{67} + 12 q^{68} + 30 q^{69} - 3 q^{70} - 15 q^{71} + 4 q^{72} - 19 q^{73} - 54 q^{75} - 5 q^{76} + 9 q^{77} - 10 q^{78} - 9 q^{79} + 9 q^{80} + 28 q^{81} - 3 q^{82} - 7 q^{84} - 42 q^{85} - 3 q^{86} - 81 q^{87} + 9 q^{88} + 9 q^{90} - 72 q^{91} - 17 q^{93} - 27 q^{94} + 6 q^{96} + 19 q^{97} - 2 q^{98} - 27 q^{99}+O(q^{100}) $ 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9 + 9 * q^10 + 9 * q^11 + 6 * q^12 + 8 * q^13 + 4 * q^14 - 17 * q^15 + 34 * q^16 + 12 * q^17 + 4 * q^18 - 5 * q^19 + 9 * q^20 - 7 * q^21 + 9 * q^22 + 6 * q^24 + 16 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 + 27 * q^29 - 17 * q^30 - q^31 + 34 * q^32 + 12 * q^34 - 3 * q^35 + 4 * q^36 - 5 * q^38 - 10 * q^39 + 9 * q^40 - 3 * q^41 - 7 * q^42 - 3 * q^43 + 9 * q^44 + 9 * q^45 - 27 * q^47 + 6 * q^48 - 2 * q^49 + 16 * q^50 - 36 * q^51 + 8 * q^52 - 21 * q^53 - 18 * q^54 - 57 * q^55 + 4 * q^56 - 17 * q^57 + 27 * q^58 - 17 * q^60 - 51 * q^61 - q^62 - 24 * q^63 + 34 * q^64 - 21 * q^65 - 21 * q^67 + 12 * q^68 + 30 * q^69 - 3 * q^70 - 15 * q^71 + 4 * q^72 - 19 * q^73 - 54 * q^75 - 5 * q^76 + 9 * q^77 - 10 * q^78 - 9 * q^79 + 9 * q^80 + 28 * q^81 - 3 * q^82 - 7 * q^84 - 42 * q^85 - 3 * q^86 - 81 * q^87 + 9 * q^88 + 9 * q^90 - 72 * q^91 - 17 * q^93 - 27 * q^94 + 6 * q^96 + 19 * q^97 - 2 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−1.72563	+	0.148954i	−0.996295	+	0.0859986i
$3$	−1.72563	+	0.148954i	−0.996295	+	0.0859986i
$4$	1.00000			0.500000
$5$	3.72094	+	2.14828i	1.66405	+	0.960742i	0.970749	+	0.240098i	$0.0771797\pi$
$5$	3.72094	+	2.14828i	1.66405	+	0.960742i	0.693306	+	0.720644i	$0.256154\pi$
$6$	−1.72563	+	0.148954i	−0.704487	+	0.0608102i
$7$	1.54641	−	2.14677i	0.584490	−	0.811401i
$7$	1.54641	−	2.14677i	0.584490	−	0.811401i
$8$	1.00000			0.353553
$9$	2.95563	−	0.514080i	0.985208	−	0.171360i
$10$	3.72094	+	2.14828i	1.17666	+	0.679347i
$11$	−2.26010	+	3.91461i	−0.681446	+	1.18030i	0.293094	+	0.956084i	$0.405315\pi$
$11$	−2.26010	+	3.91461i	−0.681446	+	1.18030i	−0.974540	+	0.224215i	$0.928018\pi$
$12$	−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
$15$	−6.74097	−	3.15290i	−1.74051	−	0.814077i
$16$	1.00000			0.250000
$17$	0.192561			0.0467030			0.0233515	−	0.999727i	$-0.492566\pi$
$17$	0.192561			0.0467030			0.0233515	+	0.999727i	$0.492566\pi$
$18$	2.95563	−	0.514080i	0.696648	−	0.121170i
$19$	−0.845613	−	1.46464i	−0.193997	−	0.336013i	0.752574	−	0.658507i	$-0.228812\pi$
$19$	−0.845613	−	1.46464i	−0.193997	−	0.336013i	−0.946571	+	0.322495i	$0.895479\pi$
$20$	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
$23$			1.40960i			0.293922i	0.989142	+	0.146961i	$0.0469492\pi$
$23$			1.40960i			0.293922i	−0.989142	+	0.146961i	$0.953051\pi$
$24$	−1.72563	+	0.148954i	−0.352244	+	0.0304051i
$25$	6.73025	+	11.6571i	1.34605	+	2.33143i
$26$	−2.01824	−	2.98776i	−0.395810	−	0.585947i
$27$	−5.02375	+	1.32737i	−0.966822	+	0.255452i
$28$	1.54641	−	2.14677i	0.292245	−	0.405701i
$29$	8.66432	−	5.00235i	1.60892	−	0.928913i	0.619313	−	0.785144i	$-0.287411\pi$
$29$	8.66432	−	5.00235i	1.60892	−	0.928913i	0.989611	−	0.143769i	$-0.0459222\pi$
$30$	−6.74097	−	3.15290i	−1.23073	−	0.575639i
$31$	1.16127	+	2.01138i	0.208570	+	0.361254i	0.951264	−	0.308377i	$-0.0997857\pi$
$31$	1.16127	+	2.01138i	0.208570	+	0.361254i	−0.742694	+	0.669631i	$0.766452\pi$
$32$	1.00000			0.176777
$33$	3.31701	−	7.09183i	0.577417	−	1.23453i
$34$	0.192561			0.0330240
$35$	10.3660	−	4.66584i	1.75217	−	0.788671i
$36$	2.95563	−	0.514080i	0.492604	−	0.0856800i
$37$			5.70199i			0.937401i	0.883357	+	0.468700i	$0.155278\pi$
$37$			5.70199i			0.937401i	−0.883357	+	0.468700i	$0.844722\pi$
$38$	−0.845613	−	1.46464i	−0.137177	−	0.237597i
$39$	3.92779	+	4.85515i	0.628949	+	0.777446i
$40$	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	$0.369086\pi$
$42$	−2.34878	+	3.93488i	−0.362424	+	0.607165i
$43$	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
$45$	12.1021	+	4.43667i	1.80407	+	0.661379i
$46$			1.40960i			0.207834i
$47$	−8.70281	−	5.02457i	−1.26944	−	0.732909i	−0.294554	−	0.955635i	$-0.595171\pi$
$47$	−8.70281	−	5.02457i	−1.26944	−	0.732909i	−0.974881	+	0.222726i	$0.928504\pi$
$48$	−1.72563	+	0.148954i	−0.249074	+	0.0214996i
$49$	−2.21720	−	6.63958i	−0.316743	−	0.948511i
$50$	6.73025	+	11.6571i	0.951802	+	1.64857i
$51$	−0.332290	+	0.0286827i	−0.0465299	+	0.00401639i
$52$	−2.01824	−	2.98776i	−0.279880	−	0.414327i
$53$	−5.59277	+	3.22899i	−0.768226	+	0.443536i	−0.832241	−	0.554413i	$-0.812943\pi$
$53$	−5.59277	+	3.22899i	−0.768226	+	0.443536i	0.0640153	+	0.997949i	$0.479609\pi$
$54$	−5.02375	+	1.32737i	−0.683646	+	0.180632i
$55$	−16.8194	+	9.71067i	−2.26792	+	1.30939i
$56$	1.54641	−	2.14677i	0.206648	−	0.286874i
$57$	1.67738	+	2.40148i	0.222175	+	0.318084i
$58$	8.66432	−	5.00235i	1.13768	−	0.656841i
$59$			3.66871i			0.477625i	0.971066	+	0.238813i	$0.0767582\pi$
$59$			3.66871i			0.477625i	−0.971066	+	0.238813i	$0.923242\pi$
$60$	−6.74097	−	3.15290i	−0.870256	−	0.407038i
$61$	−7.02534	+	4.05608i	−0.899503	+	0.519328i	−0.877039	−	0.480420i	$-0.840484\pi$
$61$	−7.02534	+	4.05608i	−0.899503	+	0.519328i	−0.0224638	+	0.999748i	$0.507151\pi$
$62$	1.16127	+	2.01138i	0.147481	+	0.255445i
$63$	3.46701	−	7.14002i	0.436803	−	0.899557i
$64$	1.00000			0.125000
$65$	−1.09120	−	15.4530i	−0.135347	−	1.91671i
$66$	3.31701	−	7.09183i	0.408296	−	0.872944i
$67$	−4.38012	−	2.52887i	−0.535117	−	0.308950i	0.207980	−	0.978133i	$-0.433311\pi$
$67$	−4.38012	−	2.52887i	−0.535117	−	0.308950i	−0.743098	+	0.669183i	$0.766644\pi$
$68$	0.192561			0.0233515
$69$	−0.209966	−	2.43246i	−0.0252769	−	0.292833i
$70$	10.3660	−	4.66584i	1.23897	−	0.557675i
$71$	5.59208	−	9.68576i	0.663658	−	1.14949i	−0.315990	−	0.948763i	$-0.602337\pi$
$71$	5.59208	−	9.68576i	0.663658	−	1.14949i	0.979647	−	0.200726i	$-0.0643301\pi$
$72$	2.95563	−	0.514080i	0.348324	−	0.0605849i
$73$	−5.90130	−	10.2214i	−0.690695	−	1.19632i	−0.971610	−	0.236586i	$-0.923971\pi$
$73$	−5.90130	−	10.2214i	−0.690695	−	1.19632i	0.280915	−	0.959733i	$-0.409362\pi$
$74$			5.70199i			0.662842i
$75$	−13.3503	−	19.1135i	−1.54156	−	2.20703i
$76$	−0.845613	−	1.46464i	−0.0969985	−	0.168006i
$77$	4.90869	+	10.9055i	0.559397	+	1.24280i
$78$	3.92779	+	4.85515i	0.444734	+	0.549738i
$79$	−1.93078	+	3.34421i	−0.217230	+	0.376253i	−0.953960	−	0.299934i	$-0.903035\pi$
$79$	−1.93078	+	3.34421i	−0.217230	+	0.376253i	0.736730	+	0.676187i	$0.236369\pi$
$80$	3.72094	+	2.14828i	0.416014	+	0.240186i
$81$	8.47144	−	3.03885i	0.941272	−	0.337650i
$82$	−1.24309	+	0.717699i	−0.137276	+	0.0792566i
$83$			4.15111i			0.455643i	0.973703	+	0.227822i	$0.0731603\pi$
$83$			4.15111i			0.455643i	−0.973703	+	0.227822i	$0.926840\pi$
$84$	−2.34878	+	3.93488i	−0.256273	+	0.429330i
$85$	0.716508	+	0.413676i	0.0777162	+	0.0448695i
$86$	1.73181	−	2.99958i	0.186746	−	0.323453i
$87$	−14.2063	+	9.92281i	−1.52308	+	1.06384i
$88$	−2.26010	+	3.91461i	−0.240927	+	0.417299i
$89$			2.16589i			0.229584i	0.993390	+	0.114792i	$0.0366202\pi$
$89$			2.16589i			0.229584i	−0.993390	+	0.114792i	$0.963380\pi$
$90$	12.1021	+	4.43667i	1.27567	+	0.467666i
$91$	−9.53506	−	0.287618i	−0.999545	−	0.0301505i
$92$			1.40960i			0.146961i
$93$	−2.30353	−	3.29793i	−0.238865	−	0.341979i
$94$	−8.70281	−	5.02457i	−0.897626	−	0.518245i
$95$		−	7.26647i		−	0.745524i
$96$	−1.72563	+	0.148954i	−0.176122	+	0.0152025i
$97$	6.86525	−	11.8910i	0.697061	−	1.20735i	−0.272420	−	0.962178i	$-0.587824\pi$
$97$	6.86525	−	11.8910i	0.697061	−	1.20735i	0.969481	−	0.245167i	$-0.0788427\pi$
$98$	−2.21720	−	6.63958i	−0.223971	−	0.670699i
$99$	−4.66759	+	12.7320i	−0.469110	+	1.27961i
$100$	6.73025	+	11.6571i	0.673025	+	1.16571i
$101$	−0.0403083	+	0.0698161i	−0.00401083	+	0.00694696i	−0.868024	−	0.496522i	$-0.834610\pi$
$101$	−0.0403083	+	0.0698161i	−0.00401083	+	0.00694696i	0.864013	+	0.503469i	$0.167943\pi$
$102$	−0.332290	+	0.0286827i	−0.0329016	+	0.00284001i
$103$	−9.05121	−	5.22572i	−0.891842	−	0.514905i	−0.0172977	−	0.999850i	$-0.505506\pi$
$103$	−9.05121	−	5.22572i	−0.891842	−	0.514905i	−0.874545	+	0.484945i	$0.838840\pi$
$104$	−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
$107$			5.36397i			0.518555i	0.965803	+	0.259277i	$0.0834844\pi$
$107$			5.36397i			0.518555i	−0.965803	+	0.259277i	$0.916516\pi$
$108$	−5.02375	+	1.32737i	−0.483411	+	0.127726i
$109$	6.11686	−	3.53157i	0.585889	−	0.338263i	−0.177581	−	0.984106i	$-0.556827\pi$
$109$	6.11686	−	3.53157i	0.585889	−	0.338263i	0.763470	+	0.645843i	$0.223494\pi$
$110$	−16.8194	+	9.71067i	−1.60367	+	0.925876i
$111$	−0.849333	−	9.83954i	−0.0806151	−	0.933928i
$112$	1.54641	−	2.14677i	0.146122	−	0.202850i
$113$	−11.0639	−	6.38777i	−1.04081	−	0.600911i	−0.120746	−	0.992683i	$-0.538529\pi$
$113$	−11.0639	−	6.38777i	−1.04081	−	0.600911i	−0.920062	+	0.391773i	$0.871862\pi$
$114$	1.67738	+	2.40148i	0.157101	+	0.224920i
$115$	−3.02822	+	5.24504i	−0.282383	+	0.489102i
$116$	8.66432	−	5.00235i	0.804462	−	0.464456i
$117$	−7.50112	−	7.79315i	−0.693478	−	0.720477i
$118$			3.66871i			0.337732i
$119$	0.297779	−	0.413384i	0.0272974	−	0.0378948i
$120$	−6.74097	−	3.15290i	−0.615364	−	0.287820i
$121$	−4.71610	−	8.16852i	−0.428736	−	0.742593i
$122$	−7.02534	+	4.05608i	−0.636044	+	0.367220i
$123$	2.03822	−	1.42365i	0.183780	−	0.128366i
$124$	1.16127	+	2.01138i	0.104285	+	0.180627i
$125$			36.3512i			3.25135i
$126$	3.46701	−	7.14002i	0.308866	−	0.636083i
$127$	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	$0.831891\pi$
$128$	1.00000			0.0883883
$129$	−2.54167	+	5.43414i	−0.223782	+	0.478449i
$130$	−1.09120	−	15.4530i	−0.0957048	−	1.35532i
$131$	0.746067	−	1.29223i	0.0651842	−	0.112902i	−0.831591	−	0.555388i	$-0.812570\pi$
$131$	0.746067	−	1.29223i	0.0651842	−	0.112902i	0.896776	+	0.442485i	$0.145903\pi$
$132$	3.31701	−	7.09183i	0.288709	−	0.617265i
$133$	−4.45192	−	0.449615i	−0.386030	−	0.0389866i
$134$	−4.38012	−	2.52887i	−0.378385	−	0.218461i
$135$	−21.5446	−	5.85341i	−1.85427	−	0.503781i
$136$	0.192561			0.0165120
$137$	−20.1088			−1.71801			−0.859005	−	0.511967i	$-0.828917\pi$
$137$	−20.1088			−1.71801			−0.859005	+	0.511967i	$0.828917\pi$
$138$	−0.209966	−	2.43246i	−0.0178735	−	0.207064i
$139$	−14.3239	−	8.26993i	−1.21494	−	0.701446i	−0.251109	−	0.967959i	$-0.580795\pi$
$139$	−14.3239	−	8.26993i	−1.21494	−	0.701446i	−0.963831	+	0.266513i	$0.914129\pi$
$140$	10.3660	−	4.66584i	0.876085	−	0.394336i
$141$	15.7663	+	7.37425i	1.32776	+	0.621024i
$142$	5.59208	−	9.68576i	0.469277	−	0.812811i
$143$	16.2573	−	1.14800i	1.35951	−	0.0960004i
$144$	2.95563	−	0.514080i	0.246302	−	0.0428400i
$145$	42.9859			3.56978
$146$	−5.90130	−	10.2214i	−0.488395	−	0.845925i
$147$	4.81507	+	11.1272i	0.397141	+	0.917758i
$148$			5.70199i			0.468700i
$149$	2.04689	+	3.54532i	0.167688	+	0.290444i	0.937606	−	0.347698i	$-0.113037\pi$
$149$	2.04689	+	3.54532i	0.167688	+	0.290444i	−0.769919	+	0.638142i	$0.779703\pi$
$150$	−13.3503	−	19.1135i	−1.09005	−	1.56061i
$151$	6.54953	−	3.78138i	0.532994	−	0.307724i	−0.209241	−	0.977864i	$-0.567099\pi$
$151$	6.54953	−	3.78138i	0.532994	−	0.307724i	0.742235	+	0.670140i	$0.233766\pi$
$152$	−0.845613	−	1.46464i	−0.0685883	−	0.118798i
$153$	0.569139	−	0.0989918i	0.0460121	−	0.00800301i
$154$	4.90869	+	10.9055i	0.395554	+	0.878791i
$155$			9.97895i			0.801528i
$156$	3.92779	+	4.85515i	0.314475	+	0.388723i
$157$	−4.42840	+	2.55674i	−0.353425	+	0.204050i	−0.666193	−	0.745780i	$-0.732077\pi$
$157$	−4.42840	+	2.55674i	−0.353425	+	0.204050i	0.312768	+	0.949830i	$0.398744\pi$
$158$	−1.93078	+	3.34421i	−0.153605	+	0.266051i
$159$	9.17010	−	6.40512i	0.727237	−	0.507959i
$160$	3.72094	+	2.14828i	0.294166	+	0.169837i
$161$	3.02608	+	2.17983i	0.238489	+	0.171794i
$162$	8.47144	−	3.03885i	0.665580	−	0.238755i
$163$	8.00463	−	4.62147i	0.626971	−	0.361982i	−0.152607	−	0.988287i	$-0.548767\pi$
$163$	8.00463	−	4.62147i	0.626971	−	0.361982i	0.779578	+	0.626305i	$0.215434\pi$
$164$	−1.24309	+	0.717699i	−0.0970691	+	0.0560429i
$165$	27.5777	−	19.2624i	2.14692	−	1.49957i
$166$			4.15111i			0.322188i
$167$	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
$171$	−3.25226	−	3.89423i	−0.248707	−	0.297799i
$172$	1.73181	−	2.99958i	0.132049	−	0.228716i
$173$	−6.36169	−	11.0188i	−0.483670	−	0.837741i	0.516154	−	0.856496i	$-0.327363\pi$
$173$	−6.36169	−	11.0188i	−0.483670	−	0.837741i	−0.999824	+	0.0187546i	$0.994030\pi$
$174$	−14.2063	+	9.92281i	−1.07698	+	0.752246i
$175$	35.4329	+	3.57850i	2.67848	+	0.270509i
$176$	−2.26010	+	3.91461i	−0.170361	+	0.295075i
$177$	−0.546468	−	6.33085i	−0.0410751	−	0.475856i
$178$			2.16589i			0.162340i
$179$	4.77637	+	2.75764i	0.357003	+	0.206116i	0.667765	−	0.744372i	$-0.267251\pi$
$179$	4.77637	+	2.75764i	0.357003	+	0.206116i	−0.310762	+	0.950488i	$0.600584\pi$
$180$	12.1021	+	4.43667i	0.902036	+	0.330690i
$181$			3.95607i			0.294053i	0.989133	+	0.147026i	$0.0469702\pi$
$181$			3.95607i			0.294053i	−0.989133	+	0.147026i	$0.953030\pi$
$182$	−9.53506	−	0.287618i	−0.706785	−	0.0213197i
$183$	11.5190	−	8.04576i	0.851509	−	0.594760i
$184$			1.40960i			0.103917i
$185$	−12.2495	+	21.2167i	−0.900600	+	1.55989i
$186$	−2.30353	−	3.29793i	−0.168903	−	0.241816i
$187$	−0.435207	+	0.753801i	−0.0318255	+	0.0551234i
$188$	−8.70281	−	5.02457i	−0.634718	−	0.366454i
$189$	−4.91926	+	12.8375i	−0.357824	+	0.933789i
$190$		−	7.26647i		−	0.527165i
$191$	6.23661	−	3.60071i	0.451266	−	0.260538i	−0.257099	−	0.966385i	$-0.582767\pi$
$191$	6.23661	−	3.60071i	0.451266	−	0.260538i	0.708365	+	0.705847i	$0.249433\pi$
$192$	−1.72563	+	0.148954i	−0.124537	+	0.0107498i
$193$	−17.8125	−	10.2840i	−1.28217	−	0.740262i	−0.304926	−	0.952376i	$-0.598632\pi$
$193$	−17.8125	−	10.2840i	−1.28217	−	0.740262i	−0.977245	+	0.212114i	$0.931965\pi$
$194$	6.86525	−	11.8910i	0.492897	−	0.853722i
$195$	4.18480	+	26.5037i	0.299680	+	1.89797i
$196$	−2.21720	−	6.63958i	−0.158372	−	0.474256i
$197$	12.5549	+	21.7458i	0.894501	+	1.54932i	0.834421	+	0.551128i	$0.185802\pi$
$197$	12.5549	+	21.7458i	0.894501	+	1.54932i	0.0600807	+	0.998194i	$0.480864\pi$
$198$	−4.66759	+	12.7320i	−0.331711	+	0.904823i
$199$			7.42309i			0.526209i	0.964767	+	0.263104i	$0.0847463\pi$
$199$			7.42309i			0.526209i	−0.964767	+	0.263104i	$0.915254\pi$
$200$	6.73025	+	11.6571i	0.475901	+	0.824284i
$201$	7.93518	+	3.71146i	0.559704	+	0.261786i
$202$	−0.0403083	+	0.0698161i	−0.00283608	+	0.00491224i
$203$	2.65976	−	26.3360i	0.186679	−	1.84842i
$204$	−0.332290	+	0.0286827i	−0.0232650	+	0.00200819i
$205$	−6.16728			−0.430742
$206$	−9.05121	−	5.22572i	−0.630628	−	0.364093i
$207$	0.724647	+	4.16625i	0.0503665	+	0.289575i
$208$	−2.01824	−	2.98776i	−0.139940	−	0.207164i
$209$	7.64468			0.528794
$210$	−17.1929	+	9.59559i	−1.18642	+	0.662159i
$211$	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	$0.775946\pi$
$212$	−5.59277	+	3.22899i	−0.384113	+	0.221768i
$213$	−8.20715	+	17.5470i	−0.562345	+	1.20230i
$214$			5.36397i			0.366674i
$215$	12.8879	−	7.44084i	0.878948	−	0.507461i
$216$	−5.02375	+	1.32737i	−0.341823	+	0.0903158i
$217$	6.11376	+	0.617450i	0.415029	+	0.0419153i
$218$	6.11686	−	3.53157i	0.414286	−	0.239188i
$219$	11.7060	+	16.7593i	0.791018	+	1.13249i
$220$	−16.8194	+	9.71067i	−1.13396	+	0.654694i
$221$	−0.388635	−	0.575326i	−0.0261424	−	0.0387006i
$222$	−0.849333	−	9.83954i	−0.0570035	−	0.660387i
$223$	−3.67083	−	6.35806i	−0.245817	−	0.425767i	0.716544	−	0.697542i	$-0.245723\pi$
$223$	−3.67083	−	6.35806i	−0.245817	−	0.425767i	−0.962361	+	0.271775i	$0.912389\pi$
$224$	1.54641	−	2.14677i	0.103324	−	0.143437i
$225$	25.8848	+	30.9943i	1.72565	+	2.06628i
$226$	−11.0639	−	6.38777i	−0.735963	−	0.424908i
$227$		−	21.5999i		−	1.43363i	−0.697262	−	0.716816i	$-0.745599\pi$
$227$		−	21.5999i		−	1.43363i	0.697262	−	0.716816i	$-0.254401\pi$
$228$	1.67738	+	2.40148i	0.111087	+	0.159042i
$229$	−5.53269	+	9.58290i	−0.365610	+	0.633256i	−0.988874	−	0.148756i	$-0.952473\pi$
$229$	−5.53269	+	9.58290i	−0.365610	+	0.633256i	0.623263	+	0.782012i	$0.285806\pi$
$230$	−3.02822	+	5.24504i	−0.199675	+	0.345848i
$231$	−10.0950	−	18.0877i	−0.664204	−	1.19009i
$232$	8.66432	−	5.00235i	0.568841	−	0.328420i
$233$	5.93673	+	3.42758i	0.388928	+	0.224548i	0.681696	−	0.731636i	$-0.261243\pi$
$233$	5.93673	+	3.42758i	0.388928	+	0.224548i	−0.292767	+	0.956184i	$0.594576\pi$
$234$	−7.50112	−	7.79315i	−0.490363	−	0.509454i
$235$	−21.5884	−	37.3922i	−1.40827	−	2.43920i
$236$			3.66871i			0.238813i
$237$	2.83369	−	6.05848i	0.184068	−	0.393540i
$238$	0.297779	−	0.413384i	0.0193022	−	0.0267957i
$239$	−7.06260			−0.456841			−0.228421	−	0.973563i	$-0.573356\pi$
$239$	−7.06260			−0.456841			−0.228421	+	0.973563i	$0.573356\pi$
$240$	−6.74097	−	3.15290i	−0.435128	−	0.203519i
$241$	−19.7363			−1.27133			−0.635664	−	0.771966i	$-0.719274\pi$
$241$	−19.7363			−1.27133			−0.635664	+	0.771966i	$0.719274\pi$
$242$	−4.71610	−	8.16852i	−0.303162	−	0.525093i
$243$	−14.1660	+	6.50581i	−0.908747	+	0.417348i
$244$	−7.02534	+	4.05608i	−0.449751	+	0.259664i
$245$	6.01363	−	29.4686i	0.384196	−	1.88268i
$246$	2.03822	−	1.42365i	0.129952	−	0.0907685i
$247$	−2.66935	+	5.48250i	−0.169847	+	0.348843i
$248$	1.16127	+	2.01138i	0.0737407	+	0.127723i
$249$	−0.618323	−	7.16329i	−0.0391847	−	0.453955i
$250$			36.3512i			2.29905i
$251$	−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
$254$	0.0510484	+	0.0884185i	0.00320306	+	0.00554787i
$255$	−1.29805	−	0.607127i	−0.0812870	−	0.0380198i
$256$	1.00000			0.0625000
$257$	8.95503			0.558599			0.279300	−	0.960204i	$-0.409898\pi$
$257$	8.95503			0.558599			0.279300	+	0.960204i	$0.409898\pi$
$258$	−2.54167	+	5.43414i	−0.158237	+	0.338315i
$259$	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
$262$	0.746067	−	1.29223i	0.0460922	−	0.0798340i
$263$	15.5696	+	8.98910i	0.960061	+	0.554291i	0.896192	−	0.443667i	$-0.146323\pi$
$263$	15.5696	+	8.98910i	0.960061	+	0.554291i	0.0638691	+	0.997958i	$0.479656\pi$
$264$	3.31701	−	7.09183i	0.204148	−	0.436472i
$265$	−27.7471			−1.70449
$266$	−4.45192	−	0.449615i	−0.272965	−	0.0275677i
$267$	−0.322618	−	3.73754i	−0.0197439	−	0.228734i
$268$	−4.38012	−	2.52887i	−0.267559	−	0.154475i
$269$	−2.85518			−0.174083			−0.0870417	−	0.996205i	$-0.527741\pi$
$269$	−2.85518			−0.174083			−0.0870417	+	0.996205i	$0.527741\pi$
$270$	−21.5446	−	5.85341i	−1.31116	−	0.356227i
$271$	−4.47256			−0.271689			−0.135844	−	0.990730i	$-0.543375\pi$
$271$	−4.47256			−0.271689			−0.135844	+	0.990730i	$0.543375\pi$
$272$	0.192561			0.0116757
$273$	16.4969	−	0.923960i	0.998435	−	0.0559206i
$274$	−20.1088			−1.21482
$275$	−60.8442			−3.66904
$276$	−0.209966	−	2.43246i	−0.0126384	−	0.146417i
$277$	14.8067			0.889651			0.444826	−	0.895617i	$-0.353266\pi$
$277$	14.8067			0.889651			0.444826	+	0.895617i	$0.353266\pi$
$278$	−14.3239	−	8.26993i	−0.859093	−	0.495997i
$279$	4.46628	+	5.34789i	0.267389	+	0.320170i
$280$	10.3660	−	4.66584i	0.619486	−	0.278837i
$281$	3.78960			0.226069			0.113034	−	0.993591i	$-0.463943\pi$
$281$	3.78960			0.226069			0.113034	+	0.993591i	$0.463943\pi$
$282$	15.7663	+	7.37425i	0.938869	+	0.439130i
$283$	23.9803	+	13.8450i	1.42548	+	0.823002i	0.996760	−	0.0804346i	$-0.0256308\pi$
$283$	23.9803	+	13.8450i	1.42548	+	0.823002i	0.428722	+	0.903437i	$0.358964\pi$
$284$	5.59208	−	9.68576i	0.331829	−	0.574744i
$285$	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
$288$	2.95563	−	0.514080i	0.174162	−	0.0302924i
$289$	−16.9629			−0.997819
$290$	42.9859			2.52422
$291$	−10.0757	+	21.5421i	−0.590649	+	1.26282i
$292$	−5.90130	−	10.2214i	−0.345348	−	0.598160i
$293$	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
$296$			5.70199i			0.331421i
$297$	6.15807	−	22.6660i	0.357327	−	1.31521i
$298$	2.04689	+	3.54532i	0.118573	+	0.205375i
$299$	4.21155	−	2.84492i	0.243560	−	0.164526i
$300$	−13.3503	−	19.1135i	−0.770782	−	1.10352i
$301$	−3.76130	−	8.35639i	−0.216798	−	0.481654i
$302$	6.54953	−	3.78138i	0.376883	−	0.217594i
$303$	0.0591581	−	0.126481i	0.00339854	−	0.00726615i
$304$	−0.845613	−	1.46464i	−0.0484992	−	0.0840031i
$305$	−34.8545			−1.99576
$306$	0.569139	−	0.0989918i	0.0325355	−	0.00565899i
$307$	25.5018			1.45546			0.727731	−	0.685862i	$-0.240575\pi$
$307$	25.5018			1.45546			0.727731	+	0.685862i	$0.240575\pi$
$308$	4.90869	+	10.9055i	0.279699	+	0.621399i
$309$	16.3975	+	7.66947i	0.932819	+	0.436301i
$310$			9.97895i			0.566766i
$311$	8.67002	+	15.0169i	0.491632	+	0.851531i	0.999954	−	0.00963600i	$-0.00306728\pi$
$311$	8.67002	+	15.0169i	0.491632	+	0.851531i	−0.508322	+	0.861167i	$0.669734\pi$
$312$	3.92779	+	4.85515i	0.222367	+	0.274869i
$313$	−7.84351	−	4.52845i	−0.443341	−	0.255963i	0.261673	−	0.965157i	$-0.415726\pi$
$313$	−7.84351	−	4.52845i	−0.443341	−	0.255963i	−0.705014	+	0.709194i	$0.749059\pi$
$314$	−4.42840	+	2.55674i	−0.249909	+	0.144285i
$315$	28.2393	−	19.1194i	1.59111	−	1.07726i
$316$	−1.93078	+	3.34421i	−0.108615	+	0.188126i
$317$	4.97176	−	8.61134i	0.279242	−	0.483661i	−0.691955	−	0.721941i	$-0.743250\pi$
$317$	4.97176	−	8.61134i	0.279242	−	0.483661i	0.971197	+	0.238280i	$0.0765836\pi$
$318$	9.17010	−	6.40512i	0.514234	−	0.359181i
$319$			45.2232i			2.53201i
$320$	3.72094	+	2.14828i	0.208007	+	0.120093i
$321$	−0.798984	−	9.25625i	−0.0445950	−	0.516634i
$322$	3.02608	+	2.17983i	0.168637	+	0.121477i
$323$	−0.162832	−	0.282034i	−0.00906023	−	0.0156928i
$324$	8.47144	−	3.03885i	0.470636	−	0.168825i
$325$	21.2454	−	43.6353i	1.17848	−	2.42045i
$326$	8.00463	−	4.62147i	0.443335	−	0.255960i
$327$	−10.0294	+	7.00533i	−0.554628	+	0.387396i
$328$	−1.24309	+	0.717699i	−0.0686382	+	0.0396283i
$329$	−24.2447	+	10.9128i	−1.33665	+	0.601643i
$330$	27.5777	−	19.2624i	1.51810	−	1.06036i
$331$	−23.9748	+	13.8419i	−1.31777	+	0.760817i	−0.983370	−	0.181613i	$-0.941868\pi$
$331$	−23.9748	+	13.8419i	−1.31777	+	0.760817i	−0.334404	+	0.942430i	$0.608535\pi$
$332$			4.15111i			0.227822i
$333$	2.93128	+	16.8529i	0.160633	+	0.923535i
$334$	13.7047	−	7.91242i	0.749888	−	0.432948i
$335$	−10.8654	−	18.8195i	−0.593643	−	1.02822i
$336$	−2.34878	+	3.93488i	−0.128136	+	0.214665i
$337$	−9.67002			−0.526760			−0.263380	−	0.964692i	$-0.584837\pi$
$337$	−9.67002			−0.526760			−0.263380	+	0.964692i	$0.584837\pi$
$338$	−4.85339	+	12.0600i	−0.263990	+	0.655980i
$339$	20.0438	+	9.37494i	1.08863	+	0.509177i
$340$	0.716508	+	0.413676i	0.0388581	+	0.0224347i
$341$	−10.4983			−0.568517
$342$	−3.25226	−	3.89423i	−0.175862	−	0.210576i
$343$	−17.6823	−	5.50772i	−0.954756	−	0.297389i
$344$	1.73181	−	2.99958i	0.0933729	−	0.161727i
$345$	4.44434	−	9.50208i	0.239275	−	0.511575i
$346$	−6.36169	−	11.0188i	−0.342006	−	0.592372i
$347$			21.2360i			1.14001i	0.821641	+	0.570005i	$0.193059\pi$
$347$			21.2360i			1.14001i	−0.821641	+	0.570005i	$0.806941\pi$
$348$	−14.2063	+	9.92281i	−0.761539	+	0.531918i
$349$	3.87087	+	6.70454i	0.207203	+	0.358886i	0.950832	−	0.309706i	$-0.100231\pi$
$349$	3.87087	+	6.70454i	0.207203	+	0.358886i	−0.743630	+	0.668592i	$0.766897\pi$
$350$	35.4329	+	3.57850i	1.89397	+	0.191279i
$351$	14.1050	+	12.3308i	0.752869	+	0.658170i
$352$	−2.26010	+	3.91461i	−0.120464	+	0.208649i
$353$	4.13071	+	2.38487i	0.219855	+	0.126934i	0.605883	−	0.795554i	$-0.292820\pi$
$353$	4.13071	+	2.38487i	0.219855	+	0.126934i	−0.386028	+	0.922487i	$0.626153\pi$
$354$	−0.546468	−	6.33085i	−0.0290445	−	0.336481i
$355$	41.6156	−	24.0268i	2.20872	−	1.27521i
$356$			2.16589i			0.114792i
$357$	−0.452283	+	0.757704i	−0.0239374	+	0.0401020i
$358$	4.77637	+	2.75764i	0.252439	+	0.145746i
$359$	−14.0272	+	24.2958i	−0.740328	+	1.28229i	0.212018	+	0.977266i	$0.431996\pi$
$359$	−14.0272	+	24.2958i	−0.740328	+	1.28229i	−0.952346	+	0.305020i	$0.901337\pi$
$360$	12.1021	+	4.43667i	0.637836	+	0.233833i
$361$	8.06988	−	13.9774i	0.424730	−	0.735655i
$362$			3.95607i			0.207927i
$363$	9.35499	+	13.3934i	0.491010	+	0.702971i
$364$	−9.53506	−	0.287618i	−0.499773	−	0.0150753i
$365$		−	50.7107i		−	2.65432i
$366$	11.5190	−	8.04576i	0.602108	−	0.420559i
$367$	9.24291	+	5.33639i	0.482476	+	0.278558i	0.721448	−	0.692469i	$-0.243477\pi$
$367$	9.24291	+	5.33639i	0.482476	+	0.278558i	−0.238972	+	0.971026i	$0.576810\pi$
$368$			1.40960i			0.0734805i
$369$	−3.30516	+	2.76030i	−0.172060	+	0.143695i
$370$	−12.2495	+	21.2167i	−0.636821	+	1.10301i
$371$	−1.71686	+	16.9997i	−0.0891351	+	0.882582i
$372$	−2.30353	−	3.29793i	−0.119432	−	0.170989i
$373$	11.4478	+	19.8282i	0.592746	+	1.02667i	0.993861	+	0.110638i	$0.0352895\pi$
$373$	11.4478	+	19.8282i	0.592746	+	1.02667i	−0.401115	+	0.916028i	$0.631377\pi$
$374$	−0.435207	+	0.753801i	−0.0225040	+	0.0389781i
$375$	−5.41465	−	62.7288i	−0.279611	−	3.23930i
$376$	−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	$0.313401\pi$
$380$		−	7.26647i		−	0.372762i
$381$	−0.101261	−	0.144974i	−0.00518777	−	0.00742725i
$382$	6.23661	−	3.60071i	0.319093	−	0.184228i
$383$	12.3614	−	7.13684i	0.631637	−	0.364676i	−0.149749	−	0.988724i	$-0.547847\pi$
$383$	12.3614	−	7.13684i	0.631637	−	0.364676i	0.781386	+	0.624048i	$0.214513\pi$
$384$	−1.72563	+	0.148954i	−0.0880609	+	0.00760127i
$385$	−5.16319	+	51.1240i	−0.263141	+	2.60552i
$386$	−17.8125	−	10.2840i	−0.906632	−	0.523444i
$387$	3.57656	−	9.75593i	0.181807	−	0.495922i
$388$	6.86525	−	11.8910i	0.348531	−	0.603673i
$389$	−7.37813	+	4.25977i	−0.374086	+	0.215979i	−0.675242	−	0.737596i	$-0.735961\pi$
$389$	−7.37813	+	4.25977i	−0.374086	+	0.215979i	0.301156	+	0.953575i	$0.402628\pi$
$390$	4.18480	+	26.5037i	0.211906	+	1.34207i
$391$			0.271434i			0.0137270i
$392$	−2.21720	−	6.63958i	−0.111986	−	0.335349i
$393$	−1.09496	+	2.34104i	−0.0552333	+	0.118090i
$394$	12.5549	+	21.7458i	0.632508	+	1.09554i
$395$	−14.3686	+	8.29573i	−0.722964	+	0.417403i
$396$	−4.66759	+	12.7320i	−0.234555	+	0.639806i
$397$	−6.69762	−	11.6006i	−0.336144	−	0.582218i	0.647560	−	0.762015i	$-0.275790\pi$
$397$	−6.69762	−	11.6006i	−0.336144	−	0.582218i	−0.983704	+	0.179796i	$0.942456\pi$
$398$			7.42309i			0.372086i
$399$	7.74935	+	0.112741i	0.387953	+	0.00564409i
$400$	6.73025	+	11.6571i	0.336513	+	0.582857i
$401$	14.8495			0.741550			0.370775	−	0.928723i	$-0.379092\pi$
$401$	14.8495			0.741550			0.370775	+	0.928723i	$0.379092\pi$
$402$	7.93518	+	3.71146i	0.395771	+	0.185111i
$403$	3.66578	−	7.52904i	0.182606	−	0.375048i
$404$	−0.0403083	+	0.0698161i	−0.00200541	+	0.00347348i
$405$	38.0500	+	6.89168i	1.89072	+	0.342451i
$406$	2.65976	−	26.3360i	0.132002	−	1.30703i
$407$	−22.3210	−	12.8871i	−1.10641	−	0.638788i
$408$	−0.332290	+	0.0286827i	−0.0164508	+	0.00142001i
$409$	18.4860			0.914074			0.457037	−	0.889448i	$-0.348911\pi$
$409$	18.4860			0.914074			0.457037	+	0.889448i	$0.348911\pi$
$410$	−6.16728			−0.304580
$411$	34.7004	−	2.99528i	1.71165	−	0.147746i
$412$	−9.05121	−	5.22572i	−0.445921	−	0.257453i
$413$	7.87586	+	5.67334i	0.387546	+	0.279167i
$414$	0.724647	+	4.16625i	0.0356145	+	0.204760i
$415$	−8.91776	+	15.4460i	−0.437756	+	0.758215i
$416$	−2.01824	−	2.98776i	−0.0989525	−	0.146487i
$417$	25.9497	+	12.1373i	1.27076	+	0.594364i
$418$	7.64468			0.373913
$419$	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	$0.638711\pi$
$420$	−17.1929	+	9.59559i	−0.838927	+	0.468217i
$421$		−	7.74237i		−	0.377340i	−0.982041	−	0.188670i	$-0.939582\pi$
$421$		−	7.74237i		−	0.377340i	0.982041	−	0.188670i	$-0.0604176\pi$
$422$	2.60466	+	4.51140i	0.126793	+	0.219611i
$423$	−28.3053	−	10.3768i	−1.37625	−	0.504538i
$424$	−5.59277	+	3.22899i	−0.271609	+	0.156814i
$425$	1.29599	+	2.24471i	0.0628645	+	0.108885i
$426$	−8.20715	+	17.5470i	−0.397638	+	0.850157i
$427$	−2.15663	+	21.3541i	−0.104367	+	1.03340i
$428$			5.36397i			0.259277i
$429$	−27.8832	+	4.40262i	−1.34621	+	0.212560i
$430$	12.8879	−	7.44084i	0.621510	−	0.358829i
$431$	−9.13932	+	15.8298i	−0.440225	+	0.762493i	−0.997706	−	0.0676972i	$-0.978435\pi$
$431$	−9.13932	+	15.8298i	−0.440225	+	0.762493i	0.557480	+	0.830190i	$0.311768\pi$
$432$	−5.02375	+	1.32737i	−0.241705	+	0.0638629i
$433$	28.5068	+	16.4584i	1.36995	+	0.790940i	0.990921	−	0.134445i	$-0.0429252\pi$
$433$	28.5068	+	16.4584i	1.36995	+	0.790940i	0.379028	+	0.925385i	$0.376259\pi$
$434$	6.11376	+	0.617450i	0.293470	+	0.0296386i
$435$	−74.1779	+	6.40291i	−3.55656	+	0.306996i
$436$	6.11686	−	3.53157i	0.292945	−	0.169132i
$437$	2.06456	−	1.19198i	0.0987615	−	0.0570200i
$438$	11.7060	+	16.7593i	0.559334	+	0.800790i
$439$			8.65914i			0.413278i	0.978417	+	0.206639i	$0.0662526\pi$
$439$			8.65914i			0.413278i	−0.978417	+	0.206639i	$0.933747\pi$
$440$	−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	0.194221	−	0.980958i	$-0.437782\pi$
$443$	−11.7488	−	6.78318i	−0.558203	−	0.322279i	−0.752424	+	0.658679i	$0.771115\pi$
$444$	−0.849333	−	9.83954i	−0.0403076	−	0.466964i
$445$	−4.65295	+	8.05915i	−0.220571	+	0.382040i
$446$	−3.67083	−	6.35806i	−0.173819	−	0.301063i
$447$	−4.06027	−	5.81303i	−0.192044	−	0.274947i
$448$	1.54641	−	2.14677i	0.0730612	−	0.101425i
$449$	1.47204	−	2.54965i	0.0694699	−	0.120325i	−0.829198	−	0.558955i	$-0.811203\pi$
$449$	1.47204	−	2.54965i	0.0694699	−	0.120325i	0.898668	+	0.438629i	$0.144536\pi$
$450$	25.8848	+	30.9943i	1.22022	+	1.46108i
$451$		−	6.48828i		−	0.305521i
$452$	−11.0639	−	6.38777i	−0.520404	−	0.300455i
$453$	−10.7388	+	7.50085i	−0.504555	+	0.352421i
$454$		−	21.5999i		−	1.01373i
$455$	−34.8615	−	21.5542i	−1.63433	−	1.01048i
$456$	1.67738	+	2.40148i	0.0785507	+	0.112460i
$457$		−	16.7645i		−	0.784212i	−0.919920	−	0.392106i	$-0.871747\pi$
$457$		−	16.7645i		−	0.784212i	0.919920	−	0.392106i	$-0.128253\pi$
$458$	−5.53269	+	9.58290i	−0.258526	+	0.447780i
$459$	−0.967380	+	0.255599i	−0.0451534	+	0.0119303i
$460$	−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	$0.746451\pi$
$462$	−10.0950	−	18.0877i	−0.469663	−	0.841518i
$463$		−	22.5835i		−	1.04954i	−0.851243	−	0.524772i	$-0.824151\pi$
$463$		−	22.5835i		−	1.04954i	0.851243	−	0.524772i	$-0.175849\pi$
$464$	8.66432	−	5.00235i	0.402231	−	0.232228i
$465$	−1.48640	−	17.2200i	−0.0689303	−	0.798559i
$466$	5.93673	+	3.42758i	0.275014	+	0.158779i
$467$	14.0602	−	24.3530i	0.650629	−	1.12692i	−0.332342	−	0.943159i	$-0.607839\pi$
$467$	14.0602	−	24.3530i	0.650629	−	1.12692i	0.982971	−	0.183763i	$-0.0588279\pi$
$468$	−7.50112	−	7.79315i	−0.346739	−	0.360239i
$469$	−12.2024	+	5.49243i	−0.563453	+	0.253617i
$470$	−21.5884	−	37.3922i	−0.995799	−	1.72477i
$471$	7.26096	−	5.07162i	0.334568	−	0.233688i
$472$			3.66871i			0.168866i
$473$	7.82812	+	13.5587i	0.359938	+	0.623430i
$474$	2.83369	−	6.05848i	0.130155	−	0.278275i
$475$	11.3824	−	19.7149i	0.522260	−	0.904580i
$476$	0.297779	−	0.413384i	0.0136487	−	0.0189474i
$477$	−14.8702	+	12.4188i	−0.680859	+	0.568618i
$478$	−7.06260			−0.323036
$479$	17.1627	+	9.90890i	0.784184	+	0.452749i	0.837911	−	0.545807i	$-0.183777\pi$
$479$	17.1627	+	9.90890i	0.784184	+	0.452749i	−0.0537268	+	0.998556i	$0.517110\pi$
$480$	−6.74097	−	3.15290i	−0.307682	−	0.143910i
$481$	17.0362	−	11.5080i	0.776782	−	0.524719i
$482$	−19.7363			−0.898965
$483$	−5.54660	−	3.31084i	−0.252379	−	0.150648i
$484$	−4.71610	−	8.16852i	−0.214368	−	0.371297i
$485$	51.0904	−	29.4970i	2.31989	−	1.33939i
$486$	−14.1660	+	6.50581i	−0.642581	+	0.295109i
$487$		−	25.5536i		−	1.15794i	−0.815348	−	0.578972i	$-0.803454\pi$
$487$		−	25.5536i		−	1.15794i	0.815348	−	0.578972i	$-0.196546\pi$
$488$	−7.02534	+	4.05608i	−0.318022	+	0.183610i
$489$	−13.1247	+	9.16729i	−0.593518	+	0.414559i
$490$	6.01363	−	29.4686i	0.271668	−	1.33126i
$491$	−4.29900	+	2.48203i	−0.194011	+	0.112012i	−0.593859	−	0.804569i	$-0.702396\pi$
$491$	−4.29900	+	2.48203i	−0.194011	+	0.112012i	0.399848	+	0.916582i	$0.369063\pi$
$492$	2.03822	−	1.42365i	0.0918899	−	0.0641830i
$493$	1.66841	−	0.963258i	0.0751415	−	0.0433830i
$494$	−2.66935	+	5.48250i	−0.120100	+	0.246669i
$495$	−44.7197	+	37.3476i	−2.01000	+	1.67865i
$496$	1.16127	+	2.01138i	0.0521425	+	0.0903135i
$497$	−12.1454	−	26.9831i	−0.544795	−	1.21036i
$498$	−0.618323	−	7.16329i	−0.0277077	−	0.320995i
$499$	−7.88549	−	4.55269i	−0.353003	−	0.203807i	0.313004	−	0.949752i	$-0.398665\pi$
$499$	−7.88549	−	4.55269i	−0.353003	−	0.203807i	−0.666007	+	0.745945i	$0.731998\pi$
$500$			36.3512i			1.62567i
$501$	−22.4707	+	15.6953i	−1.00392	+	0.701215i
$502$	−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	$0.249814\pi$
$504$	3.46701	−	7.14002i	0.154433	−	0.318042i
$505$	−0.299970	+	0.173188i	−0.0133485	+	0.00770675i
$506$	−5.51803	−	3.18584i	−0.245307	−	0.141628i
$507$	6.57879	−	21.5341i	0.292174	−	0.956365i
$508$	0.0510484	+	0.0884185i	0.00226491	+	0.00392294i
$509$			26.4808i			1.17374i	0.809681	+	0.586871i	$0.199640\pi$
$509$			26.4808i			1.17374i	−0.809681	+	0.586871i	$0.800360\pi$
$510$	−1.29805	−	0.607127i	−0.0574786	−	0.0268840i
$511$	−31.0687	−	3.13774i	−1.37440	−	0.138805i
$512$	1.00000			0.0441942
$513$	6.19227	+	6.23558i	0.273395	+	0.275307i
$514$	8.95503			0.394989
$515$	−22.4527	−	38.8892i	−0.989383	−	1.71366i
$516$	−2.54167	+	5.43414i	−0.111891	+	0.239225i
$517$	39.3384	−	22.7121i	1.73010	−	0.998875i
$518$	12.2408	+	8.81763i	0.537831	+	0.387425i
$519$	12.6192	+	18.0668i	0.553923	+	0.793043i
$520$	−1.09120	−	15.4530i	−0.0478524	−	0.677660i
$521$	4.04236	+	7.00158i	0.177099	+	0.306745i	0.940886	−	0.338724i	$-0.109995\pi$
$521$	4.04236	+	7.00158i	0.177099	+	0.306745i	−0.763787	+	0.645469i	$0.776662\pi$
$522$	23.0369	−	19.2392i	1.00830	−	0.842078i
$523$		−	1.34371i		−	0.0587565i	−0.999568	−	0.0293782i	$-0.990647\pi$
$523$		−	1.34371i		−	0.0587565i	0.999568	−	0.0293782i	$-0.00935273\pi$
$524$	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
$527$	0.223615	+	0.387313i	0.00974084	+	0.0168716i
$528$	3.31701	−	7.09183i	0.144354	−	0.308632i
$529$	21.0130			0.913610
$530$	−27.7471			−1.20526
$531$	1.88601	+	10.8433i	0.0818458	+	0.470560i
$532$	−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
$535$	−11.5233	+	19.9590i	−0.498197	+	0.862903i
$536$	−4.38012	−	2.52887i	−0.189193	−	0.109230i
$537$	−8.65303	−	4.04722i	−0.373406	−	0.174650i
$538$	−2.85518			−0.123096
$539$	31.0024	+	6.32662i	1.33537	+	0.272507i
$540$	−21.5446	−	5.85341i	−0.927133	−	0.251891i
$541$	−32.4126	−	18.7134i	−1.39353	−	0.804553i	−0.399823	−	0.916592i	$-0.630928\pi$
$541$	−32.4126	−	18.7134i	−1.39353	−	0.804553i	−0.993704	+	0.112039i	$0.964262\pi$
$542$	−4.47256			−0.192113
$543$	−0.589272	−	6.82673i	−0.0252881	−	0.292963i
$544$	0.192561			0.00825599
$545$	30.3473			1.29993
$546$	16.4969	−	0.923960i	0.706000	−	0.0395419i
$547$	39.2814			1.67955			0.839775	−	0.542934i	$-0.182687\pi$
$547$	39.2814			1.67955			0.839775	+	0.542934i	$0.182687\pi$
$548$	−20.1088			−0.859005
$549$	−18.6791	+	15.5998i	−0.797206	+	0.665785i
$550$	−60.8442			−2.59440
$551$	−14.6533	−	8.46010i	−0.624253	−	0.360413i
$552$	−0.209966	−	2.43246i	−0.00893673	−	0.103532i
$553$	4.19344	+	9.31646i	0.178323	+	0.396176i
$554$	14.8067			0.629078
$555$	17.9778	−	38.4369i	0.763116	−	1.63156i
$556$	−14.3239	−	8.26993i	−0.607470	−	0.350723i
$557$	−1.89706	+	3.28581i	−0.0803811	+	0.139224i	−0.903414	−	0.428770i	$-0.858947\pi$
$557$	−1.89706	+	3.28581i	−0.0803811	+	0.139224i	0.823033	+	0.567994i	$0.192280\pi$
$558$	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
$561$	0.638727	−	1.36561i	0.0269671	−	0.0576562i
$562$	3.78960			0.159855
$563$	6.67273			0.281222			0.140611	−	0.990065i	$-0.455093\pi$
$563$	6.67273			0.281222			0.140611	+	0.990065i	$0.455093\pi$
$564$	15.7663	+	7.37425i	0.663881	+	0.310512i
$565$	−27.4455	−	47.5370i	−1.15464	−	1.99990i
$566$	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
$569$			18.2299i			0.764238i	0.924113	+	0.382119i	$0.124806\pi$
$569$			18.2299i			0.764238i	−0.924113	+	0.382119i	$0.875194\pi$
$570$	1.08237	+	12.5393i	0.0453354	+	0.525212i
$571$	22.5493	+	39.0565i	0.943657	+	1.63446i	0.758418	+	0.651769i	$0.225973\pi$
$571$	22.5493	+	39.0565i	0.943657	+	1.63446i	0.185239	+	0.982693i	$0.440694\pi$
$572$	16.2573	−	1.14800i	0.679753	−	0.0480002i
$573$	−10.2258	+	7.14248i	−0.427188	+	0.298381i
$574$	−0.381603	+	3.77848i	−0.0159278	+	0.157711i
$575$	−16.4319	+	9.48697i	−0.685258	+	0.395634i
$576$	2.95563	−	0.514080i	0.123151	−	0.0214200i
$577$	16.5263	+	28.6244i	0.688000	+	1.19165i	0.972484	+	0.232970i	$0.0748444\pi$
$577$	16.5263	+	28.6244i	0.688000	+	1.19165i	−0.284484	+	0.958681i	$0.591822\pi$
$578$	−16.9629			−0.705564
$579$	32.2697	+	15.0933i	1.34108	+	0.627254i
$580$	42.9859			1.78489
$581$	8.91145	+	6.41933i	0.369709	+	0.266319i
$582$	−10.0757	+	21.5421i	−0.417652	+	0.892947i
$583$		−	29.1913i		−	1.20898i
$584$	−5.90130	−	10.2214i	−0.244198	−	0.422963i
$585$	−11.1693	−	45.1124i	−0.461793	−	1.86517i
$586$	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	$0.550722\pi$
$588$	4.81507	+	11.1272i	0.198570	+	0.458879i
$589$	1.96397	−	3.40169i	0.0809239	−	0.140164i
$590$	−7.88143	+	13.6510i	−0.324473	+	0.562004i
$591$	−24.9043	−	35.6551i	−1.02443	−	1.46666i
$592$			5.70199i			0.234350i
$593$	−14.5119	−	8.37847i	−0.595934	−	0.344063i	0.171506	−	0.985183i	$-0.445137\pi$
$593$	−14.5119	−	8.37847i	−0.595934	−	0.344063i	−0.767440	+	0.641120i	$0.778470\pi$
$594$	6.15807	−	22.6660i	0.252669	−	0.929997i
$595$	1.99608	−	0.898460i	0.0818315	−	0.0368333i
$596$	2.04689	+	3.54532i	0.0838438	+	0.145222i
$597$	−1.10570	−	12.8095i	−0.0452532	−	0.524259i
$598$	4.21155	−	2.84492i	0.172223	−	0.116337i
$599$	−19.4413	+	11.2245i	−0.794352	+	0.458619i	−0.841492	−	0.540269i	$-0.818323\pi$
$599$	−19.4413	+	11.2245i	−0.794352	+	0.458619i	0.0471404	+	0.998888i	$0.484989\pi$
$600$	−13.3503	−	19.1135i	−0.545025	−	0.780304i
$601$	13.6726	−	7.89389i	0.557718	−	0.321999i	−0.194511	−	0.980900i	$-0.562312\pi$
$601$	13.6726	−	7.89389i	0.557718	−	0.321999i	0.752229	+	0.658902i	$0.228979\pi$
$602$	−3.76130	−	8.35639i	−0.153299	−	0.340581i
$603$	−14.2460	−	5.22265i	−0.580144	−	0.212683i
$604$	6.54953	−	3.78138i	0.266497	−	0.153862i
$605$		−	40.5261i		−	1.64762i
$606$	0.0591581	−	0.126481i	0.00240313	−	0.00513794i
$607$	−6.62940	+	3.82749i	−0.269079	+	0.155353i	−0.628469	−	0.777835i	$-0.716318\pi$
$607$	−6.62940	+	3.82749i	−0.269079	+	0.155353i	0.359390	+	0.933187i	$0.382985\pi$
$608$	−0.845613	−	1.46464i	−0.0342941	−	0.0593992i
$609$	−0.666934	+	45.8424i	−0.0270255	+	1.85763i
$610$	−34.8545			−1.41122
$611$	2.55219	+	36.1427i	0.103250	+	1.46218i
$612$	0.569139	−	0.0989918i	0.0230061	−	0.00400151i
$613$	−30.1489	−	17.4065i	−1.21770	−	0.703041i	−0.253277	−	0.967394i	$-0.581508\pi$
$613$	−30.1489	−	17.4065i	−1.21770	−	0.703041i	−0.964426	+	0.264353i	$0.914842\pi$
$614$	25.5018			1.02917
$615$	10.6425	−	0.918641i	0.429146	−	0.0370432i
$616$	4.90869	+	10.9055i	0.197777	+	0.439395i
$617$	−12.4947	+	21.6415i	−0.503019	+	0.871255i	0.496975	+	0.867765i	$0.334444\pi$
$617$	−12.4947	+	21.6415i	−0.503019	+	0.871255i	−0.999994	+	0.00348999i	$0.998889\pi$
$618$	16.3975	+	7.66947i	0.659603	+	0.308511i
$619$	1.25318	+	2.17058i	0.0503697	+	0.0872429i	0.890111	−	0.455744i	$-0.150627\pi$
$619$	1.25318	+	2.17058i	0.0503697	+	0.0872429i	−0.839741	+	0.542987i	$0.817293\pi$
$620$			9.97895i			0.400764i
$621$	−1.87106	−	7.08149i	−0.0750829	−	0.284170i
$622$	8.67002	+	15.0169i	0.347636	+	0.602123i
$623$	4.64966	+	3.34937i	0.186285	+	0.134190i
$624$	3.92779	+	4.85515i	0.157237	+	0.194362i
$625$	−44.4414	+	76.9747i	−1.77765	+	3.07899i
$626$	−7.84351	−	4.52845i	−0.313490	−	0.180993i
$627$	−13.1919	+	1.13870i	−0.526834	+	0.0454755i
$628$	−4.42840	+	2.55674i	−0.176712	+	0.102025i
$629$			1.09798i			0.0437794i
$630$	28.2393	−	19.1194i	1.12508	−	0.761736i
$631$	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
$633$	−5.16667	−	7.39705i	−0.205357	−	0.294006i
$634$	4.97176	−	8.61134i	0.197454	−	0.342000i
$635$			0.438666i			0.0174079i
$636$	9.17010	−	6.40512i	0.363618	−	0.253979i
$637$	−15.3626	+	20.0248i	−0.608688	+	0.793410i
$638$			45.2232i			1.79040i
$639$	11.5488	−	31.5023i	0.456865	−	1.24621i
$640$	3.72094	+	2.14828i	0.147083	+	0.0849184i
$641$		−	33.5804i		−	1.32635i	−0.748466	−	0.663173i	$-0.769209\pi$
$641$		−	33.5804i		−	1.32635i	0.748466	−	0.663173i	$-0.230791\pi$
$642$	−0.798984	−	9.25625i	−0.0315334	−	0.365315i
$643$	−12.7327	+	22.0537i	−0.502129	+	0.869713i	0.497868	+	0.867253i	$0.334116\pi$
$643$	−12.7327	+	22.0537i	−0.502129	+	0.869713i	−0.999997	+	0.00246038i	$0.999217\pi$
$644$	3.02608	+	2.17983i	0.119244	+	0.0858972i
$645$	−21.1315	+	14.7599i	−0.832051	+	0.581169i
$646$	−0.162832	−	0.282034i	−0.00640655	−	0.0110965i
$647$	−5.30960	+	9.19649i	−0.208742	+	0.361552i	−0.951318	−	0.308210i	$-0.900270\pi$
$647$	−5.30960	+	9.19649i	−0.208742	+	0.361552i	0.742577	+	0.669761i	$0.233604\pi$
$648$	8.47144	−	3.03885i	0.332790	−	0.119377i
$649$	−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
$653$		−	8.80038i		−	0.344385i	−0.985063	−	0.172193i	$-0.944915\pi$
$653$		−	8.80038i		−	0.344385i	0.985063	−	0.172193i	$-0.0550852\pi$
$654$	−10.0294	+	7.00533i	−0.392181	+	0.273930i
$655$	5.55214	−	3.20553i	0.216940	−	0.125250i
$656$	−1.24309	+	0.717699i	−0.0485345	+	0.0280214i
$657$	−22.6966	−	27.1768i	−0.885480	−	1.06027i
$658$	−24.2447	+	10.9128i	−0.945158	+	0.425426i
$659$	5.79064	+	3.34323i	0.225571	+	0.130234i	0.608527	−	0.793533i	$-0.291761\pi$
$659$	5.79064	+	3.34323i	0.225571	+	0.130234i	−0.382956	+	0.923767i	$0.625094\pi$
$660$	27.5777	−	19.2624i	1.07346	−	0.749787i
$661$	−24.8847	+	43.1016i	−0.967904	+	1.67646i	−0.266303	+	0.963889i	$0.585802\pi$
$661$	−24.8847	+	43.1016i	−0.967904	+	1.67646i	−0.701601	+	0.712570i	$0.747531\pi$
$662$	−23.9748	+	13.8419i	−0.931807	+	0.537979i
$663$	0.756339	+	0.934914i	0.0293738	+	0.0363090i
$664$			4.15111i			0.161094i
$665$	−15.5994	−	11.2370i	−0.604919	−	0.435751i
$666$	2.93128	+	16.8529i	0.113585	+	0.653038i
$667$	7.05132	+	12.2132i	0.273028	+	0.472898i
$668$	13.7047	−	7.91242i	0.530251	−	0.306141i
$669$	7.28156	+	10.4249i	0.281521	+	0.403050i
$670$	−10.8654	−	18.8195i	−0.419769	−	0.727061i
$671$		−	36.6686i		−	1.41558i
$672$	−2.34878	+	3.93488i	−0.0906060	+	0.151791i
$673$	−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	$-0.502898\pi$
$674$	−9.67002			−0.372475
$675$	−49.2844	−	49.6291i	−1.89696	−	1.91023i
$676$	−4.85339	+	12.0600i	−0.186669	+	0.463848i
$677$	−10.7942	+	18.6960i	−0.414853	+	0.718546i	−0.995413	−	0.0956710i	$-0.969500\pi$
$677$	−10.7942	+	18.6960i	−0.414853	+	0.718546i	0.580560	+	0.814217i	$0.302834\pi$
$678$	20.0438	+	9.37494i	0.769777	+	0.360042i
$679$	−14.9106	−	33.1265i	−0.572216	−	1.27128i
$680$	0.716508	+	0.413676i	0.0274768	+	0.0158638i
$681$	3.21738	+	37.2734i	0.123290	+	1.42832i
$682$	−10.4983			−0.402002
$683$	43.5860			1.66777			0.833886	−	0.551937i	$-0.186111\pi$
$683$	43.5860			1.66777			0.833886	+	0.551937i	$0.186111\pi$
$684$	−3.25226	−	3.89423i	−0.124353	−	0.148900i
$685$	−74.8236	−	43.1994i	−2.85886	−	1.65056i
$686$	−17.6823	−	5.50772i	−0.675115	−	0.210286i
$687$	8.11999	−	17.3607i	0.309797	−	0.662352i
$688$	1.73181	−	2.99958i	0.0660246	−	0.114358i
$689$	20.9350	+	10.1930i	0.797560	+	0.388321i
$690$	4.44434	−	9.50208i	0.169193	−	0.361738i
$691$	−5.40377			−0.205569			−0.102785	−	0.994704i	$-0.532775\pi$
$691$	−5.40377			−0.205569			−0.102785	+	0.994704i	$0.532775\pi$
$692$	−6.36169	−	11.0188i	−0.241835	−	0.418871i
$693$	20.1146	+	29.7091i	0.764089	+	1.12856i
$694$			21.2360i			0.806109i
$695$	−35.5323	−	61.5438i	−1.34782	−	2.33449i
$696$	−14.2063	+	9.92281i	−0.538490	+	0.376123i
$697$	−0.239371	+	0.138201i	−0.00906682	+	0.00523473i
$698$	3.87087	+	6.70454i	0.146515	+	0.253771i
$699$	−10.7552	−	5.03044i	−0.406798	−	0.190269i
$700$	35.4329	+	3.57850i	1.33924	+	0.135254i
$701$		−	29.7087i		−	1.12208i	−0.827787	−	0.561042i	$-0.810401\pi$
$701$		−	29.7087i		−	1.12208i	0.827787	−	0.561042i	$-0.189599\pi$
$702$	14.1050	+	12.3308i	0.532359	+	0.465397i
$703$	8.35138	−	4.82167i	0.314978	−	0.181853i
$704$	−2.26010	+	3.91461i	−0.0851807	+	0.147537i
$705$	42.8234	+	61.3096i	1.61282	+	2.30905i
$706$	4.13071	+	2.38487i	0.155461	+	0.0897556i
$707$	0.0875454	+	0.194497i	0.00329248	+	0.00731482i
$708$	−0.546468	−	6.33085i	−0.0205375	−	0.237928i
$709$	29.5236	−	17.0454i	1.10878	−	0.640155i	0.170268	−	0.985398i	$-0.445537\pi$
$709$	29.5236	−	17.0454i	1.10878	−	0.640155i	0.938513	+	0.345243i	$0.112203\pi$
$710$	41.6156	−	24.0268i	1.56180	−	0.901708i
$711$	−3.98747	+	10.8768i	−0.149542	+	0.407912i
$712$			2.16589i			0.0811702i
$713$	−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
$717$	12.1875	−	1.05200i	0.455149	−	0.0392877i
$718$	−14.0272	+	24.2958i	−0.523491	+	0.906713i
$719$	13.8089	+	23.9177i	0.514985	+	0.891979i	0.999849	+	0.0173900i	$0.00553570\pi$
$719$	13.8089	+	23.9177i	0.514985	+	0.891979i	−0.484864	+	0.874589i	$0.661131\pi$
$720$	12.1021	+	4.43667i	0.451018	+	0.165345i
$721$	−25.2153	+	11.3497i	−0.939068	+	0.422685i
$722$	8.06988	−	13.9774i	0.300330	−	0.520186i
$723$	34.0577	−	2.93980i	1.26662	−	0.109332i
$724$			3.95607i			0.147026i
$725$	116.626	+	67.3342i	4.33139	+	2.50073i
$726$	9.35499	+	13.3934i	0.347196	+	0.497076i
$727$			3.84648i			0.142658i	0.997453	+	0.0713291i	$0.0227241\pi$
$727$			3.84648i			0.142658i	−0.997453	+	0.0713291i	$0.977276\pi$
$728$	−9.53506	−	0.287618i	−0.353393	−	0.0106598i
$729$	23.4762	−	13.3367i	0.869489	−	0.493952i
$730$		−	50.7107i		−	1.87689i
$731$	0.333479	−	0.577603i	0.0123342	−	0.0213634i
$732$	11.5190	−	8.04576i	0.425754	−	0.297380i
$733$	4.54533	−	7.87274i	0.167886	−	0.290786i	−0.769791	−	0.638296i	$-0.779639\pi$
$733$	4.54533	−	7.87274i	0.167886	−	0.290786i	0.937676	+	0.347510i	$0.112973\pi$
$734$	9.24291	+	5.33639i	0.341162	+	0.196970i
$735$	−5.98785	+	51.7479i	−0.220865	+	1.90875i
$736$			1.40960i			0.0519586i
$737$	19.7990	−	11.4310i	0.729307	−	0.421065i
$738$	−3.30516	+	2.76030i	−0.121664	+	0.101608i
$739$	−15.0189	−	8.67118i	−0.552480	−	0.318974i	0.197642	−	0.980274i	$-0.436672\pi$
$739$	−15.0189	−	8.67118i	−0.552480	−	0.318974i	−0.750122	+	0.661300i	$0.770005\pi$
$740$	−12.2495	+	21.2167i	−0.450300	+	0.779943i
$741$	3.78968	−	9.85839i	0.139218	−	0.362157i
$742$	−1.71686	+	16.9997i	−0.0630280	+	0.624079i
$743$	12.2804	+	21.2704i	0.450526	+	0.780334i	0.998419	−	0.0562149i	$-0.0179032\pi$
$743$	12.2804	+	21.2704i	0.450526	+	0.780334i	−0.547893	+	0.836549i	$0.684570\pi$
$744$	−2.30353	−	3.29793i	−0.0844514	−	0.120908i
$745$			17.5892i			0.644418i
$746$	11.4478	+	19.8282i	0.419135	+	0.725963i
$747$	2.13400	+	12.2691i	0.0780790	+	0.448903i
$748$	−0.435207	+	0.753801i	−0.0159128	+	0.0275617i
$749$	11.5152	+	8.29492i	0.420756	+	0.303090i
$750$	−5.41465	−	62.7288i	−0.197715	−	2.29053i
$751$	36.4415			1.32977			0.664885	−	0.746946i	$-0.268481\pi$
$751$	36.4415			1.32977			0.664885	+	0.746946i	$0.268481\pi$
$752$	−8.70281	−	5.02457i	−0.317359	−	0.183227i
$753$	2.93745	−	6.28032i	0.107047	−	0.228868i
$754$	−32.4325	−	15.7909i	−1.18112	−	0.575072i
$755$	32.4939			1.18257
$756$	−4.91926	+	12.8375i	−0.178912	+	0.466895i
$757$	−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	$0.960660\pi$
$758$	2.11006	−	1.21824i	0.0766408	−	0.0442486i
$759$	9.99665	+	4.67566i	0.362855	+	0.169716i
$760$		−	7.26647i		−	0.263583i
$761$	30.0314	−	17.3386i	1.08864	−	0.628525i	0.155424	−	0.987848i	$-0.450326\pi$
$761$	30.0314	−	17.3386i	1.08864	−	0.628525i	0.933213	+	0.359323i	$0.116992\pi$
$762$	−0.101261	−	0.144974i	−0.00366831	−	0.00525186i
$763$	1.87775	−	18.5927i	0.0679790	−	0.673102i
$764$	6.23661	−	3.60071i	0.225633	−	0.130269i
$765$	2.33039	+	0.854330i	0.0842555	+	0.0308884i
$766$	12.3614	−	7.13684i	0.446635	−	0.257865i
$767$	10.9612	−	7.40434i	0.395786	−	0.267355i
$768$	−1.72563	+	0.148954i	−0.0622685	+	0.00537491i
$769$	−0.987858	−	1.71102i	−0.0356231	−	0.0617010i	0.847664	−	0.530533i	$-0.178008\pi$
$769$	−0.987858	−	1.71102i	−0.0356231	−	0.0617010i	−0.883287	+	0.468832i	$0.844675\pi$
$770$	−5.16319	+	51.1240i	−0.186069	+	1.84238i
$771$	−15.4531	+	1.33389i	−0.556530	+	0.0480388i
$772$	−17.8125	−	10.2840i	−0.641085	−	0.370131i
$773$			2.30696i			0.0829757i	0.999139	+	0.0414879i	$0.0132098\pi$
$773$			2.30696i			0.0829757i	−0.999139	+	0.0414879i	$0.986790\pi$
$774$	3.57656	−	9.75593i	0.128557	−	0.350670i
$775$	−15.6313	+	27.0742i	−0.561492	+	0.972532i
$776$	6.86525	−	11.8910i	0.246448	−	0.426861i
$777$	−22.4366	−	13.3927i	−0.804909	−	0.480460i
$778$	−7.37813	+	4.25977i	−0.264519	+	0.152720i
$779$	2.10235	+	1.21379i	0.0753244	+	0.0434886i
$780$	4.18480	+	26.5037i	0.149840	+	0.948985i
$781$	25.2773	+	43.7816i	0.904493	+	1.56663i
$782$			0.271434i			0.00970648i
$783$	−36.8875	+	36.6313i	−1.31825	+	1.30910i
$784$	−2.21720	−	6.63958i	−0.0791859	−	0.237128i
$785$	−21.9704			−0.784157
$786$	−1.09496	+	2.34104i	−0.0390558	+	0.0835021i
$787$	−45.1597			−1.60977			−0.804885	−	0.593431i	$-0.797773\pi$
$787$	−45.1597			−1.60977			−0.804885	+	0.593431i	$0.797773\pi$
$788$	12.5549	+	21.7458i	0.447251	+	0.774661i
$789$	−28.2063	−	13.1927i	−1.00417	−	0.469674i
$790$	−14.3686	+	8.29573i	−0.511213	+	0.295149i
$791$	−30.8225	+	13.8736i	−1.09592	+	0.493287i
$792$	−4.66759	+	12.7320i	−0.165855	+	0.452411i
$793$	26.2974	+	12.8039i	0.933849	+	0.454678i
$794$	−6.69762	−	11.6006i	−0.237690	−	0.411691i
$795$	47.8814	−	4.13304i	1.69818	−	0.146584i
$796$			7.42309i			0.263104i
$797$	−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
$800$	6.73025	+	11.6571i	0.237950	+	0.412142i
$801$	1.11344	+	6.40157i	0.0393415	+	0.226188i
$802$	14.8495			0.524355
$803$	53.3501			1.88268
$804$	7.93518	+	3.71146i	0.279852	+	0.130893i
$805$	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
$808$	−0.0403083	+	0.0698161i	−0.00141804	+	0.00245612i
$809$	−17.0434	−	9.84001i	−0.599214	−	0.345956i	0.169518	−	0.985527i	$-0.445779\pi$
$809$	−17.0434	−	9.84001i	−0.599214	−	0.345956i	−0.768732	+	0.639571i	$0.779112\pi$
$810$	38.0500	+	6.89168i	1.33694	+	0.242149i
$811$	55.9783			1.96566			0.982832	−	0.184501i	$-0.0590669\pi$
$811$	55.9783			1.96566			0.982832	+	0.184501i	$0.0590669\pi$
$812$	2.65976	−	26.3360i	0.0933394	−	0.924212i
$813$	7.71800	−	0.666205i	0.270682	−	0.0233648i
$814$	−22.3210	−	12.8871i	−0.782352	−	0.451691i
$815$	39.7130			1.39108
$816$	−0.332290	+	0.0286827i	−0.0116325	+	0.00100410i
$817$	−5.85776			−0.204937
$818$	18.4860			0.646348
$819$	−28.3299	+	4.05169i	−0.989927	+	0.141577i
$820$	−6.16728			−0.215371
$821$	11.5367			0.402634			0.201317	−	0.979526i	$-0.435478\pi$
$821$	11.5367			0.402634			0.201317	+	0.979526i	$0.435478\pi$
$822$	34.7004	−	2.99528i	1.21032	−	0.104472i
$823$	−16.5333			−0.576313			−0.288157	−	0.957583i	$-0.593042\pi$
$823$	−16.5333			−0.576313			−0.288157	+	0.957583i	$0.593042\pi$
$824$	−9.05121	−	5.22572i	−0.315314	−	0.182047i
$825$	104.995	−	9.06298i	3.65545	−	0.315532i
$826$	7.87586	+	5.67334i	0.274036	+	0.197401i
$827$	1.49924			0.0521335			0.0260668	−	0.999660i	$-0.491702\pi$
$827$	1.49924			0.0521335			0.0260668	+	0.999660i	$0.491702\pi$
$828$	0.724647	+	4.16625i	0.0251832	+	0.144787i
$829$	22.5860	+	13.0400i	0.784443	+	0.452898i	0.838002	−	0.545666i	$-0.183723\pi$
$829$	22.5860	+	13.0400i	0.784443	+	0.452898i	−0.0535597	+	0.998565i	$0.517057\pi$
$830$	−8.91776	+	15.4460i	−0.309540	+	0.536139i
$831$	−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
$834$	25.9497	+	12.1373i	0.898565	+	0.420279i
$835$	67.9925			2.35298
$836$	7.64468			0.264397
$837$	−8.50376	−	8.56323i	−0.293933	−	0.295989i
$838$	11.7502	+	20.3519i	0.405904	+	0.703046i
$839$	−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
$842$		−	7.74237i		−	0.266820i
$843$	−6.53946	+	0.564475i	−0.225231	+	0.0194416i
$844$	2.60466	+	4.51140i	0.0896560	+	0.155289i
$845$	−43.9676	+	34.4482i	−1.51253	+	1.18505i
$846$	−28.3053	−	10.3768i	−0.973155	−	0.356762i
$847$	−24.8289	−	2.50756i	−0.853133	−	0.0861609i
$848$	−5.59277	+	3.22899i	−0.192057	+	0.110884i
$849$	−43.4435	−	20.3195i	−1.49098	−	0.697364i
$850$	1.29599	+	2.24471i	0.0444519	+	0.0769930i
$851$	−8.03752			−0.275523
$852$	−8.20715	+	17.5470i	−0.281172	+	0.601152i
$853$	−24.3552			−0.833905			−0.416952	−	0.908928i	$-0.636902\pi$
$853$	−24.3552			−0.833905			−0.416952	+	0.908928i	$0.636902\pi$
$854$	−2.15663	+	21.3541i	−0.0737984	+	0.730724i
$855$	−3.73555	−	21.4770i	−0.127753	−	0.734497i
$856$			5.36397i			0.183337i
$857$	11.5857	+	20.0671i	0.395761	+	0.685479i	0.993198	−	0.116437i	$-0.0371474\pi$
$857$	11.5857	+	20.0671i	0.395761	+	0.685479i	−0.597437	+	0.801916i	$0.703814\pi$
$858$	−27.8832	+	4.40262i	−0.951917	+	0.150303i
$859$	6.79567	+	3.92348i	0.231865	+	0.133868i	0.611432	−	0.791297i	$-0.290594\pi$
$859$	6.79567	+	3.92348i	0.231865	+	0.133868i	−0.379567	+	0.925164i	$0.623927\pi$
$860$	12.8879	−	7.44084i	0.439474	−	0.253731i
$861$	0.0956866	−	6.57712i	0.00326099	−	0.224148i
$862$	−9.13932	+	15.8298i	−0.311286	+	0.539164i
$863$	9.45505	−	16.3766i	0.321854	−	0.557467i	−0.659017	−	0.752128i	$-0.729027\pi$
$863$	9.45505	−	16.3766i	0.321854	−	0.557467i	0.980870	+	0.194661i	$0.0623608\pi$
$864$	−5.02375	+	1.32737i	−0.170912	+	0.0451579i
$865$		−	54.6669i		−	1.85873i
$866$	28.5068	+	16.4584i	0.968700	+	0.559279i
$867$	29.2718	−	2.52669i	0.994122	−	0.0858110i
$868$	6.11376	+	0.617450i	0.207514	+	0.0209576i
$869$	−8.72751	−	15.1165i	−0.296060	−	0.512792i
$870$	−74.1779	+	6.40291i	−2.51487	+	0.217079i
$871$	1.28452	+	18.1906i	0.0435242	+	0.616366i
$872$	6.11686	−	3.53157i	0.207143	−	0.119594i
$873$	14.1782	−	38.6745i	0.479860	−	1.30893i
$874$	2.06456	−	1.19198i	0.0698349	−	0.0403192i
$875$	78.0374	+	56.2140i	2.63815	+	1.90038i
$876$	11.7060	+	16.7593i	0.395509	+	0.566244i
$877$	26.9516	−	15.5605i	0.910092	−	0.525442i	0.0296310	−	0.999561i	$-0.490567\pi$
$877$	26.9516	−	15.5605i	0.910092	−	0.525442i	0.880461	+	0.474119i	$0.157233\pi$
$878$			8.65914i			0.292232i
$879$	−32.0088	−	14.9713i	−1.07963	−	0.504968i
$880$	−16.8194	+	9.71067i	−0.566981	+	0.327347i
$881$	−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	$0.957946\pi$
$882$	−9.96650	−	18.4843i	−0.335589	−	0.622398i
$883$	17.1794			0.578133			0.289067	−	0.957309i	$-0.406655\pi$
$883$	17.1794			0.578133			0.289067	+	0.957309i	$0.406655\pi$
$884$	−0.388635	−	0.575326i	−0.0130712	−	0.0193503i
$885$	11.5671	−	24.7307i	0.388823	−	0.831312i
$886$	−11.7488	−	6.78318i	−0.394709	−	0.227885i
$887$	4.41565			0.148263			0.0741316	−	0.997248i	$-0.476382\pi$
$887$	4.41565			0.148263			0.0741316	+	0.997248i	$0.476382\pi$
$888$	−0.849333	−	9.83954i	−0.0285017	−	0.330193i
$889$	0.268756	+	0.0271426i	0.00901378	+	0.000910334i
$890$	−4.65295	+	8.05915i	−0.155967	+	0.270143i
$891$	−7.25038	+	40.0305i	−0.242897	+	1.34107i
$892$	−3.67083	−	6.35806i	−0.122908	−	0.212884i
$893$			16.9954i			0.568728i
$894$	−4.06027	−	5.81303i	−0.135796	−	0.194417i
$895$	11.8484	+	20.5220i	0.396048	+	0.685975i
$896$	1.54641	−	2.14677i	0.0516621	−	0.0717184i
$897$	−6.84383	+	5.53661i	−0.228509	+	0.184862i
$898$	1.47204	−	2.54965i	0.0491226	−	0.0850829i
$899$	20.1232	+	11.6181i	0.671147	+	0.387487i
$900$	25.8848	+	30.9943i	0.862827	+	1.03314i
$901$	−1.07695	+	0.621778i	−0.0358784	+	0.0207144i
$902$		−	6.48828i		−	0.216036i
$903$	7.73535	+	13.8598i	0.257416	+	0.461225i
$904$	−11.0639	−	6.38777i	−0.367981	−	0.212454i
$905$	−8.49877	+	14.7203i	−0.282509	+	0.489319i
$906$	−10.7388	+	7.50085i	−0.356774	+	0.249199i
$907$	21.2778	−	36.8542i	0.706517	−	1.22372i	−0.259624	−	0.965710i	$-0.583599\pi$
$907$	21.2778	−	36.8542i	0.706517	−	1.22372i	0.966141	−	0.258014i	$-0.0830679\pi$
$908$		−	21.5999i		−	0.716816i
$909$	−0.0832453	+	0.227072i	−0.00276107	+	0.00753150i
$910$	−34.8615	−	21.5542i	−1.15565	−	0.714515i
$911$		−	36.4179i		−	1.20658i	−0.797522	−	0.603290i	$-0.793856\pi$
$911$		−	36.4179i		−	1.20658i	0.797522	−	0.603290i	$-0.206144\pi$
$912$	1.67738	+	2.40148i	0.0555437	+	0.0795211i
$913$	−16.2500	−	9.38191i	−0.537795	−	0.310496i
$914$		−	16.7645i		−	0.554522i
$915$	60.1461	−	5.19171i	1.98837	−	0.171633i
$916$	−5.53269	+	9.58290i	−0.182805	+	0.316628i
$917$	−1.62038	−	3.59995i	−0.0535096	−	0.118881i
$918$	−0.967380	+	0.255599i	−0.0319283	+	0.00843603i
$919$	11.4827	+	19.8887i	0.378781	+	0.656067i	0.990885	−	0.134710i	$-0.0430102\pi$
$919$	11.4827	+	19.8887i	0.378781	+	0.656067i	−0.612105	+	0.790777i	$0.709677\pi$
$920$	−3.02822	+	5.24504i	−0.0998376	+	0.172924i
$921$	−44.0067	+	3.79859i	−1.45007	+	0.125168i
$922$	−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
$926$		−	22.5835i		−	0.742140i
$927$	−29.4384	−	10.7922i	−0.966885	−	0.354463i
$928$	8.66432	−	5.00235i	0.284420	−	0.164210i
$929$	19.6741	−	11.3588i	0.645486	−	0.372671i	−0.141239	−	0.989976i	$-0.545109\pi$
$929$	19.6741	−	11.3588i	0.645486	−	0.372671i	0.786725	+	0.617304i	$0.211775\pi$
$930$	−1.48640	−	17.2200i	−0.0487411	−	0.564666i
$931$	−7.84973	+	8.86193i	−0.257264	+	0.290438i
$932$	5.93673	+	3.42758i	0.194464	+	0.112274i
$933$	−17.1981	−	24.6223i	−0.563041	−	0.806097i
$934$	14.0602	−	24.3530i	0.460064	−	0.796854i
$935$	−3.23876	+	1.86990i	−0.105919	+	0.0611522i
$936$	−7.50112	−	7.79315i	−0.245182	−	0.254727i
$937$			9.05679i			0.295872i	0.988997	+	0.147936i	$0.0472630\pi$
$937$			9.05679i			0.295872i	−0.988997	+	0.147936i	$0.952737\pi$
$938$	−12.2024	+	5.49243i	−0.398422	+	0.179334i
$939$	14.2095	+	6.64613i	0.463711	+	0.216888i
$940$	−21.5884	−	37.3922i	−0.704136	−	1.21960i
$941$	7.89775	−	4.55977i	0.257459	−	0.148644i	−0.365716	−	0.930727i	$-0.619176\pi$
$941$	7.89775	−	4.55977i	0.257459	−	0.148644i	0.623175	+	0.782082i	$0.285842\pi$
$942$	7.26096	−	5.07162i	0.236575	−	0.165242i
$943$	−1.01167	−	1.75226i	−0.0329445	−	0.0570615i
$944$			3.66871i			0.119406i
$945$	−45.8828	+	37.1995i	−1.49257	+	1.21010i
$946$	7.82812	+	13.5587i	0.254514	+	0.440832i
$947$	−5.93223			−0.192772			−0.0963859	−	0.995344i	$-0.530728\pi$
$947$	−5.93223			−0.192772			−0.0963859	+	0.995344i	$0.530728\pi$
$948$	2.83369	−	6.05848i	0.0920338	−	0.196770i
$949$	−18.6287	+	38.2608i	−0.604712	+	1.24200i
$950$	11.3824	−	19.7149i	0.369293	−	0.639635i
$951$	−7.29674	+	15.6006i	−0.236613	+	0.505884i
$952$	0.297779	−	0.413384i	0.00965109	−	0.0133978i
$953$	−26.0177	−	15.0213i	−0.842795	−	0.486588i	0.0154183	−	0.999881i	$-0.495092\pi$
$953$	−26.0177	−	15.0213i	−0.842795	−	0.486588i	−0.858213	+	0.513293i	$0.828425\pi$
$954$	−14.8702	+	12.4188i	−0.481440	+	0.402074i
$955$	30.9414			1.00124
$956$	−7.06260			−0.228421
$957$	−6.73618	−	78.0387i	−0.217750	−	2.52263i
$958$	17.1627	+	9.90890i	0.554502	+	0.320142i
$959$	−31.0965	+	43.1689i	−1.00416	+	1.39400i
$960$	−6.74097	−	3.15290i	−0.217564	−	0.101760i
$961$	12.8029	−	22.1753i	0.412997	−	0.715332i
$962$	17.0362	−	11.5080i	0.549268	−	0.371033i
$963$	2.75751	+	15.8539i	0.0888595	+	0.510885i
$964$	−19.7363			−0.635664
$965$	−44.1861	−	76.5326i	−1.42240	−	2.46367i
$966$	−5.54660	−	3.31084i	−0.178459	−	0.106524i
$967$			43.9319i			1.41275i	0.707836	+	0.706377i	$0.249671\pi$
$967$			43.9319i			1.41275i	−0.707836	+	0.706377i	$0.750329\pi$
$968$	−4.71610	−	8.16852i	−0.151581	−	0.262546i
$969$	0.322999	+	0.462433i	0.0103762	+	0.0148555i
$970$	51.0904	−	29.4970i	1.64041	−	0.947093i
$971$	−17.8895	−	30.9856i	−0.574102	−	0.994375i	−0.996139	−	0.0877955i	$-0.972018\pi$
$971$	−17.8895	−	30.9856i	−0.574102	−	0.994375i	0.422036	−	0.906579i	$-0.361316\pi$
$972$	−14.1660	+	6.50581i	−0.454373	+	0.208674i
$973$	−39.9043	+	17.9614i	−1.27927	+	0.575816i
$974$		−	25.5536i		−	0.818790i
$975$	−30.1622	+	78.4632i	−0.965963	+	2.51283i
$976$	−7.02534	+	4.05608i	−0.224876	+	0.129832i
$977$	−10.4365	+	18.0765i	−0.333892	+	0.578318i	−0.983271	−	0.182147i	$-0.941695\pi$
$977$	−10.4365	+	18.0765i	−0.333892	+	0.578318i	0.649379	+	0.760465i	$0.275029\pi$
$978$	−13.1247	+	9.16729i	−0.419681	+	0.293138i
$979$	−8.47862	−	4.89513i	−0.270978	−	0.156449i
$980$	6.01363	−	29.4686i	0.192098	−	0.941341i
$981$	16.2636	−	13.5826i	0.519258	−	0.433658i
$982$	−4.29900	+	2.48203i	−0.137187	+	0.0792048i
$983$	−1.08229	+	0.624859i	−0.0345196	+	0.0199299i	−0.517161	−	0.855888i	$-0.673011\pi$
$983$	−1.08229	+	0.624859i	−0.0345196	+	0.0199299i	0.482641	+	0.875818i	$0.339678\pi$
$984$	2.03822	−	1.42365i	0.0649759	−	0.0453843i
$985$			107.886i			3.43754i
$986$	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
$990$	−44.7197	+	37.3476i	−1.42129	+	1.18699i
$991$	−10.2983	+	17.8371i	−0.327135	+	0.566615i	−0.981942	−	0.189181i	$-0.939417\pi$
$991$	−10.2983	+	17.8371i	−0.327135	+	0.566615i	0.654807	+	0.755796i	$0.272750\pi$
$992$	1.16127	+	2.01138i	0.0368703	+	0.0638613i
$993$	39.3099	−	27.4571i	1.24746	−	0.871325i
$994$	−12.1454	−	26.9831i	−0.385228	−	0.855852i
$995$	−15.9469	+	27.6208i	−0.505551	+	0.875640i
$996$	−0.618323	−	7.16329i	−0.0195923	−	0.226978i
$997$			29.1413i			0.922915i	0.887162	+	0.461457i	$0.152673\pi$
$997$			29.1413i			0.922915i	−0.887162	+	0.461457i	$0.847327\pi$
$998$	−7.88549	−	4.55269i	−0.249611	−	0.144113i
$999$	−7.56862	−	28.6454i	−0.239460	−	0.906299i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.5	✓	34	91.17	odd	6
546.2.bi.e.257.5	yes	34	3.2	odd	2
546.2.bi.f.17.1	yes	34	273.17	even	6	inner
546.2.bi.f.257.1	yes	34	1.1	even	1	trivial
546.2.bn.e.101.6	yes	34	7.3	odd	6
546.2.bn.e.173.6	yes	34	39.17	odd	6
546.2.bn.f.101.12	yes	34	21.17	even	6
546.2.bn.f.173.12	yes	34	13.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-1.72563 + 0.148954i) q^{3} +1.00000 q^{4} +(3.72094 + 2.14828i) q^{5} +(-1.72563 + 0.148954i) q^{6} +(1.54641 - 2.14677i) q^{7} +1.00000 q^{8} +(2.95563 - 0.514080i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-1.72563 + 0.148954i) q^{3} +1.00000 q^{4} +(3.72094 + 2.14828i) q^{5} +(-1.72563 + 0.148954i) q^{6} +(1.54641 - 2.14677i) q^{7} +1.00000 q^{8} +(2.95563 - 0.514080i) q^{9} +(3.72094 + 2.14828i) q^{10} +(-2.26010 + 3.91461i) q^{11} +(-1.72563 + 0.148954i) q^{12} +(-2.01824 - 2.98776i) q^{13} +(1.54641 - 2.14677i) q^{14} +(-6.74097 - 3.15290i) q^{15} +1.00000 q^{16} +0.192561 q^{17} +(2.95563 - 0.514080i) q^{18} +(-0.845613 - 1.46464i) q^{19} +(3.72094 + 2.14828i) q^{20} +(-2.34878 + 3.93488i) q^{21} +(-2.26010 + 3.91461i) q^{22} +1.40960i q^{23} +(-1.72563 + 0.148954i) q^{24} +(6.73025 + 11.6571i) q^{25} +(-2.01824 - 2.98776i) q^{26} +(-5.02375 + 1.32737i) q^{27} +(1.54641 - 2.14677i) q^{28} +(8.66432 - 5.00235i) q^{29} +(-6.74097 - 3.15290i) q^{30} +(1.16127 + 2.01138i) q^{31} +1.00000 q^{32} +(3.31701 - 7.09183i) q^{33} +0.192561 q^{34} +(10.3660 - 4.66584i) q^{35} +(2.95563 - 0.514080i) q^{36} +5.70199i q^{37} +(-0.845613 - 1.46464i) q^{38} +(3.92779 + 4.85515i) q^{39} +(3.72094 + 2.14828i) q^{40} +(-1.24309 + 0.717699i) q^{41} +(-2.34878 + 3.93488i) q^{42} +(1.73181 - 2.99958i) q^{43} +(-2.26010 + 3.91461i) q^{44} +(12.1021 + 4.43667i) q^{45} +1.40960i q^{46} +(-8.70281 - 5.02457i) q^{47} +(-1.72563 + 0.148954i) q^{48} +(-2.21720 - 6.63958i) q^{49} +(6.73025 + 11.6571i) q^{50} +(-0.332290 + 0.0286827i) q^{51} +(-2.01824 - 2.98776i) q^{52} +(-5.59277 + 3.22899i) q^{53} +(-5.02375 + 1.32737i) q^{54} +(-16.8194 + 9.71067i) q^{55} +(1.54641 - 2.14677i) q^{56} +(1.67738 + 2.40148i) q^{57} +(8.66432 - 5.00235i) q^{58} +3.66871i q^{59} +(-6.74097 - 3.15290i) q^{60} +(-7.02534 + 4.05608i) q^{61} +(1.16127 + 2.01138i) q^{62} +(3.46701 - 7.14002i) q^{63} +1.00000 q^{64} +(-1.09120 - 15.4530i) q^{65} +(3.31701 - 7.09183i) q^{66} +(-4.38012 - 2.52887i) q^{67} +0.192561 q^{68} +(-0.209966 - 2.43246i) q^{69} +(10.3660 - 4.66584i) q^{70} +(5.59208 - 9.68576i) q^{71} +(2.95563 - 0.514080i) q^{72} +(-5.90130 - 10.2214i) q^{73} +5.70199i q^{74} +(-13.3503 - 19.1135i) q^{75} +(-0.845613 - 1.46464i) q^{76} +(4.90869 + 10.9055i) q^{77} +(3.92779 + 4.85515i) q^{78} +(-1.93078 + 3.34421i) q^{79} +(3.72094 + 2.14828i) q^{80} +(8.47144 - 3.03885i) q^{81} +(-1.24309 + 0.717699i) q^{82} +4.15111i q^{83} +(-2.34878 + 3.93488i) q^{84} +(0.716508 + 0.413676i) q^{85} +(1.73181 - 2.99958i) q^{86} +(-14.2063 + 9.92281i) q^{87} +(-2.26010 + 3.91461i) q^{88} +2.16589i q^{89} +(12.1021 + 4.43667i) q^{90} +(-9.53506 - 0.287618i) q^{91} +1.40960i q^{92} +(-2.30353 - 3.29793i) q^{93} +(-8.70281 - 5.02457i) q^{94} -7.26647i q^{95} +(-1.72563 + 0.148954i) q^{96} +(6.86525 - 11.8910i) q^{97} +(-2.21720 - 6.63958i) q^{98} +(-4.66759 + 12.7320i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9}+O(q^{10}) \) 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9	\( 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9} + 9 q^{10} + 9 q^{11} + 6 q^{12} + 8 q^{13} + 4 q^{14} - 17 q^{15} + 34 q^{16} + 12 q^{17} + 4 q^{18} - 5 q^{19} + 9 q^{20} - 7 q^{21} + 9 q^{22} + 6 q^{24} + 16 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} + 27 q^{29} - 17 q^{30} - q^{31} + 34 q^{32} + 12 q^{34} - 3 q^{35} + 4 q^{36} - 5 q^{38} - 10 q^{39} + 9 q^{40} - 3 q^{41} - 7 q^{42} - 3 q^{43} + 9 q^{44} + 9 q^{45} - 27 q^{47} + 6 q^{48} - 2 q^{49} + 16 q^{50} - 36 q^{51} + 8 q^{52} - 21 q^{53} - 18 q^{54} - 57 q^{55} + 4 q^{56} - 17 q^{57} + 27 q^{58} - 17 q^{60} - 51 q^{61} - q^{62} - 24 q^{63} + 34 q^{64} - 21 q^{65} - 21 q^{67} + 12 q^{68} + 30 q^{69} - 3 q^{70} - 15 q^{71} + 4 q^{72} - 19 q^{73} - 54 q^{75} - 5 q^{76} + 9 q^{77} - 10 q^{78} - 9 q^{79} + 9 q^{80} + 28 q^{81} - 3 q^{82} - 7 q^{84} - 42 q^{85} - 3 q^{86} - 81 q^{87} + 9 q^{88} + 9 q^{90} - 72 q^{91} - 17 q^{93} - 27 q^{94} + 6 q^{96} + 19 q^{97} - 2 q^{98} - 27 q^{99}+O(q^{100}) \) 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9 + 9 * q^10 + 9 * q^11 + 6 * q^12 + 8 * q^13 + 4 * q^14 - 17 * q^15 + 34 * q^16 + 12 * q^17 + 4 * q^18 - 5 * q^19 + 9 * q^20 - 7 * q^21 + 9 * q^22 + 6 * q^24 + 16 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 + 27 * q^29 - 17 * q^30 - q^31 + 34 * q^32 + 12 * q^34 - 3 * q^35 + 4 * q^36 - 5 * q^38 - 10 * q^39 + 9 * q^40 - 3 * q^41 - 7 * q^42 - 3 * q^43 + 9 * q^44 + 9 * q^45 - 27 * q^47 + 6 * q^48 - 2 * q^49 + 16 * q^50 - 36 * q^51 + 8 * q^52 - 21 * q^53 - 18 * q^54 - 57 * q^55 + 4 * q^56 - 17 * q^57 + 27 * q^58 - 17 * q^60 - 51 * q^61 - q^62 - 24 * q^63 + 34 * q^64 - 21 * q^65 - 21 * q^67 + 12 * q^68 + 30 * q^69 - 3 * q^70 - 15 * q^71 + 4 * q^72 - 19 * q^73 - 54 * q^75 - 5 * q^76 + 9 * q^77 - 10 * q^78 - 9 * q^79 + 9 * q^80 + 28 * q^81 - 3 * q^82 - 7 * q^84 - 42 * q^85 - 3 * q^86 - 81 * q^87 + 9 * q^88 + 9 * q^90 - 72 * q^91 - 17 * q^93 - 27 * q^94 + 6 * q^96 + 19 * q^97 - 2 * q^98 - 27 * q^99

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