LMFDB - Embedded newform 546.2.bi.e.257.5

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			257.5
Character	$\chi$	$=$	546.257
Dual form			546.2.bi.e.17.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-0.733819 - 1.56892i) q^{3} +1.00000 q^{4} +(-3.72094 - 2.14828i) q^{5} +(0.733819 + 1.56892i) q^{6} +(1.54641 - 2.14677i) q^{7} -1.00000 q^{8} +(-1.92302 + 2.30261i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-0.733819 - 1.56892i) q^{3} +1.00000 q^{4} +(-3.72094 - 2.14828i) q^{5} +(0.733819 + 1.56892i) q^{6} +(1.54641 - 2.14677i) q^{7} -1.00000 q^{8} +(-1.92302 + 2.30261i) q^{9} +(3.72094 + 2.14828i) q^{10} +(2.26010 - 3.91461i) q^{11} +(-0.733819 - 1.56892i) q^{12} +(-2.01824 - 2.98776i) q^{13} +(-1.54641 + 2.14677i) q^{14} +(-0.639991 + 7.41431i) q^{15} +1.00000 q^{16} -0.192561 q^{17} +(1.92302 - 2.30261i) q^{18} +(-0.845613 - 1.46464i) q^{19} +(-3.72094 - 2.14828i) q^{20} +(-4.50289 - 0.850863i) q^{21} +(-2.26010 + 3.91461i) q^{22} -1.40960i q^{23} +(0.733819 + 1.56892i) 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} +(0.639991 - 7.41431i) q^{30} +(1.16127 + 2.01138i) q^{31} -1.00000 q^{32} +(-7.80021 - 0.673301i) q^{33} +0.192561 q^{34} +(-10.3660 + 4.66584i) q^{35} +(-1.92302 + 2.30261i) q^{36} +5.70199i q^{37} +(0.845613 + 1.46464i) q^{38} +(-3.20653 + 5.35894i) q^{39} +(3.72094 + 2.14828i) q^{40} +(1.24309 - 0.717699i) q^{41} +(4.50289 + 0.850863i) 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} +(-0.733819 - 1.56892i) q^{48} +(-2.21720 - 6.63958i) q^{49} +(-6.73025 - 11.6571i) q^{50} +(0.141305 + 0.302113i) 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} +(-0.639991 + 7.41431i) q^{60} +(-7.02534 + 4.05608i) q^{61} +(-1.16127 - 2.01138i) q^{62} +(1.96937 + 7.68906i) q^{63} +1.00000 q^{64} +(1.09120 + 15.4530i) q^{65} +(7.80021 + 0.673301i) q^{66} +(-4.38012 - 2.52887i) q^{67} -0.192561 q^{68} +(-2.21155 + 1.03439i) q^{69} +(10.3660 - 4.66584i) q^{70} +(-5.59208 + 9.68576i) q^{71} +(1.92302 - 2.30261i) 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} +(3.20653 - 5.35894i) q^{78} +(-1.93078 + 3.34421i) q^{79} +(-3.72094 - 2.14828i) q^{80} +(-1.60400 - 8.85591i) q^{81} +(-1.24309 + 0.717699i) q^{82} -4.15111i q^{83} +(-4.50289 - 0.850863i) 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} +(0.733819 + 1.56892i) 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} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9} + 9 q^{10} - 9 q^{11} + 3 q^{12} + 8 q^{13} - 4 q^{14} - 4 q^{15} + 34 q^{16} - 12 q^{17} + 11 q^{18} - 5 q^{19} - 9 q^{20} + 4 q^{21} + 9 q^{22} - 3 q^{24} + 16 q^{25} - 8 q^{26} + 18 q^{27} + 4 q^{28} - 27 q^{29} + 4 q^{30} - q^{31} - 34 q^{32} + 21 q^{33} + 12 q^{34} + 3 q^{35} - 11 q^{36} + 5 q^{38} + 7 q^{39} + 9 q^{40} + 3 q^{41} - 4 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} + 27 q^{47} + 3 q^{48} - 2 q^{49} - 16 q^{50} + 24 q^{51} + 8 q^{52} + 21 q^{53} - 18 q^{54} - 57 q^{55} - 4 q^{56} + 17 q^{57} + 27 q^{58} - 4 q^{60} - 51 q^{61} + q^{62} + 3 q^{63} + 34 q^{64} + 21 q^{65} - 21 q^{66} - 21 q^{67} - 12 q^{68} + 42 q^{69} - 3 q^{70} + 15 q^{71} + 11 q^{72} - 19 q^{73} + 54 q^{75} - 5 q^{76} - 9 q^{77} - 7 q^{78} - 9 q^{79} - 9 q^{80} - 23 q^{81} - 3 q^{82} + 4 q^{84} - 42 q^{85} + 3 q^{86} + 81 q^{87} + 9 q^{88} - 9 q^{90} - 72 q^{91} + 17 q^{93} - 27 q^{94} - 3 q^{96} + 19 q^{97} + 2 q^{98} + 27 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9 + 9 * q^10 - 9 * q^11 + 3 * q^12 + 8 * q^13 - 4 * q^14 - 4 * q^15 + 34 * q^16 - 12 * q^17 + 11 * q^18 - 5 * q^19 - 9 * q^20 + 4 * q^21 + 9 * q^22 - 3 * q^24 + 16 * q^25 - 8 * q^26 + 18 * q^27 + 4 * q^28 - 27 * q^29 + 4 * q^30 - q^31 - 34 * q^32 + 21 * q^33 + 12 * q^34 + 3 * q^35 - 11 * q^36 + 5 * q^38 + 7 * q^39 + 9 * q^40 + 3 * q^41 - 4 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 + 27 * q^47 + 3 * q^48 - 2 * q^49 - 16 * q^50 + 24 * q^51 + 8 * q^52 + 21 * q^53 - 18 * q^54 - 57 * q^55 - 4 * q^56 + 17 * q^57 + 27 * q^58 - 4 * q^60 - 51 * q^61 + q^62 + 3 * q^63 + 34 * q^64 + 21 * q^65 - 21 * q^66 - 21 * q^67 - 12 * q^68 + 42 * q^69 - 3 * q^70 + 15 * q^71 + 11 * q^72 - 19 * q^73 + 54 * q^75 - 5 * q^76 - 9 * q^77 - 7 * q^78 - 9 * q^79 - 9 * q^80 - 23 * q^81 - 3 * q^82 + 4 * 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 - 3 * 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
$3$	−0.733819	−	1.56892i	−0.423671	−	0.905816i
$3$	−0.733819	−	1.56892i	−0.423671	−	0.905816i
$4$	1.00000			0.500000
$5$	−3.72094	−	2.14828i	−1.66405	−	0.960742i	−0.970749	−	0.240098i	$-0.922820\pi$
$5$	−3.72094	−	2.14828i	−1.66405	−	0.960742i	−0.693306	−	0.720644i	$-0.743846\pi$
$6$	0.733819	+	1.56892i	0.299580	+	0.640509i
$7$	1.54641	−	2.14677i	0.584490	−	0.811401i
$7$	1.54641	−	2.14677i	0.584490	−	0.811401i
$8$	−1.00000			−0.353553
$9$	−1.92302	+	2.30261i	−0.641006	+	0.767536i
$10$	3.72094	+	2.14828i	1.17666	+	0.679347i
$11$	2.26010	−	3.91461i	0.681446	−	1.18030i	−0.293094	−	0.956084i	$-0.594685\pi$
$11$	2.26010	−	3.91461i	0.681446	−	1.18030i	0.974540	−	0.224215i	$-0.0719817\pi$
$12$	−0.733819	−	1.56892i	−0.211835	−	0.452908i
$13$	−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
$16$	1.00000			0.250000
$17$	−0.192561			−0.0467030			−0.0233515	−	0.999727i	$-0.507434\pi$
$17$	−0.192561			−0.0467030			−0.0233515	+	0.999727i	$0.507434\pi$
$18$	1.92302	−	2.30261i	0.453260	−	0.542730i
$19$	−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
$21$	−4.50289	−	0.850863i	−0.982612	−	0.185673i
$22$	−2.26010	+	3.91461i	−0.481855	+	0.834597i
$23$		−	1.40960i		−	0.293922i	−0.989142	−	0.146961i	$-0.953051\pi$
$23$		−	1.40960i		−	0.293922i	0.989142	−	0.146961i	$-0.0469492\pi$
$24$	0.733819	+	1.56892i	0.149790	+	0.320254i
$25$	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	$0.712589\pi$
$29$	−8.66432	+	5.00235i	−1.60892	+	0.928913i	−0.989611	+	0.143769i	$0.954078\pi$
$30$	0.639991	−	7.41431i	0.116846	−	1.35366i
$31$	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
$33$	−7.80021	−	0.673301i	−1.35784	−	0.117207i
$34$	0.192561			0.0330240
$35$	−10.3660	+	4.66584i	−1.75217	+	0.788671i
$36$	−1.92302	+	2.30261i	−0.320503	+	0.383768i
$37$			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
$39$	−3.20653	+	5.35894i	−0.513455	+	0.858116i
$40$	3.72094	+	2.14828i	0.588332	+	0.339674i
$41$	1.24309	−	0.717699i	0.194138	−	0.112086i	−0.399780	−	0.916611i	$-0.630914\pi$
$41$	1.24309	−	0.717699i	0.194138	−	0.112086i	0.593918	+	0.804525i	$0.297580\pi$
$42$	4.50289	+	0.850863i	0.694811	+	0.131291i
$43$	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	0.974881	−	0.222726i	$-0.0714956\pi$
$47$	8.70281	+	5.02457i	1.26944	+	0.732909i	0.294554	+	0.955635i	$0.404829\pi$
$48$	−0.733819	−	1.56892i	−0.105918	−	0.226454i
$49$	−2.21720	−	6.63958i	−0.316743	−	0.948511i
$50$	−6.73025	−	11.6571i	−0.951802	−	1.64857i
$51$	0.141305	+	0.302113i	0.0197867	+	0.0423043i
$52$	−2.01824	−	2.98776i	−0.279880	−	0.414327i
$53$	5.59277	−	3.22899i	0.768226	−	0.443536i	−0.0640153	−	0.997949i	$-0.520391\pi$
$53$	5.59277	−	3.22899i	0.768226	−	0.443536i	0.832241	+	0.554413i	$0.187057\pi$
$54$	−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	$-0.923242\pi$
$59$		−	3.66871i		−	0.477625i	0.971066	−	0.238813i	$-0.0767582\pi$
$60$	−0.639991	+	7.41431i	−0.0826224	+	0.957183i
$61$	−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
$63$	1.96937	+	7.68906i	0.248118	+	0.968730i
$64$	1.00000			0.125000
$65$	1.09120	+	15.4530i	0.135347	+	1.91671i
$66$	7.80021	+	0.673301i	0.960139	+	0.0828776i
$67$	−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
$69$	−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	$0.935670\pi$
$72$	1.92302	−	2.30261i	0.226630	−	0.271365i
$73$	−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
$78$	3.20653	−	5.35894i	0.363068	−	0.606780i
$79$	−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
$81$	−1.60400	−	8.85591i	−0.178222	−	0.983990i
$82$	−1.24309	+	0.717699i	−0.137276	+	0.0792566i
$83$		−	4.15111i		−	0.455643i	−0.973703	−	0.227822i	$-0.926840\pi$
$83$		−	4.15111i		−	0.455643i	0.973703	−	0.227822i	$-0.0731603\pi$
$84$	−4.50289	−	0.850863i	−0.491306	−	0.0928367i
$85$	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	$-0.963380\pi$
$89$		−	2.16589i		−	0.229584i	0.993390	−	0.114792i	$-0.0366202\pi$
$90$	−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
$96$	0.733819	+	1.56892i	0.0748951	+	0.160127i
$97$	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	−0.864013	−	0.503469i	$-0.832057\pi$
$101$	0.0403083	−	0.0698161i	0.00401083	−	0.00694696i	0.868024	+	0.496522i	$0.165390\pi$
$102$	−0.141305	−	0.302113i	−0.0139913	−	0.0299137i
$103$	−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
$105$	14.9271	+	12.8395i	1.45673	+	1.25301i
$106$	−5.59277	+	3.22899i	−0.543218	+	0.313627i
$107$		−	5.36397i		−	0.518555i	−0.965803	−	0.259277i	$-0.916516\pi$
$107$		−	5.36397i		−	0.518555i	0.965803	−	0.259277i	$-0.0834844\pi$
$108$	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
$111$	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	$0.461471\pi$
$114$	1.67738	−	2.40148i	0.157101	−	0.224920i
$115$	−3.02822	+	5.24504i	−0.282383	+	0.489102i
$116$	−8.66432	+	5.00235i	−0.804462	+	0.464456i
$117$	10.7608	+	1.09829i	0.994832	+	0.101537i
$118$			3.66871i			0.337732i
$119$	−0.297779	+	0.413384i	−0.0272974	+	0.0378948i
$120$	0.639991	−	7.41431i	0.0584229	−	0.676830i
$121$	−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
$126$	−1.96937	−	7.68906i	−0.175446	−	0.684995i
$127$	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
$129$	−5.97694	−	0.515920i	−0.526240	−	0.0454242i
$130$	−1.09120	−	15.4530i	−0.0957048	−	1.35532i
$131$	−0.746067	+	1.29223i	−0.0651842	+	0.112902i	−0.896776	−	0.442485i	$-0.854097\pi$
$131$	−0.746067	+	1.29223i	−0.0651842	+	0.112902i	0.831591	+	0.555388i	$0.187430\pi$
$132$	−7.80021	−	0.673301i	−0.678921	−	0.0586033i
$133$	−4.45192	−	0.449615i	−0.386030	−	0.0389866i
$134$	4.38012	+	2.52887i	0.378385	+	0.218461i
$135$	−15.8415	−	15.7315i	−1.36342	−	1.35395i
$136$	0.192561			0.0165120
$137$	20.1088			1.71801			0.859005	−	0.511967i	$-0.171083\pi$
$137$	20.1088			1.71801			0.859005	+	0.511967i	$0.171083\pi$
$138$	2.21155	−	1.03439i	0.188260	−	0.0880533i
$139$	−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
$141$	1.49686	−	17.3411i	0.126058	−	1.46039i
$142$	5.59208	−	9.68576i	0.469277	−	0.812811i
$143$	−16.2573	+	1.14800i	−1.35951	+	0.0960004i
$144$	−1.92302	+	2.30261i	−0.160252	+	0.191884i
$145$	42.9859			3.56978
$146$	5.90130	+	10.2214i	0.488395	+	0.845925i
$147$	−8.78994	+	8.35087i	−0.724982	+	0.688768i
$148$			5.70199i			0.468700i
$149$	−2.04689	−	3.54532i	−0.167688	−	0.290444i	0.769919	−	0.638142i	$-0.220297\pi$
$149$	−2.04689	−	3.54532i	−0.167688	−	0.290444i	−0.937606	+	0.347698i	$0.886963\pi$
$150$	−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
$153$	0.370299	−	0.443393i	0.0299369	−	0.0358462i
$154$	4.90869	+	10.9055i	0.395554	+	0.878791i
$155$		−	9.97895i		−	0.801528i
$156$	−3.20653	+	5.35894i	−0.256728	+	0.429058i
$157$	−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
$162$	1.60400	+	8.85591i	0.126022	+	0.695786i
$163$	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	−0.925571	−	0.378574i	$-0.876415\pi$
$167$	−13.7047	+	7.91242i	−1.06050	+	0.612281i	−0.134931	+	0.990855i	$0.543081\pi$
$168$	4.50289	+	0.850863i	0.347406	+	0.0656455i
$169$	−4.85339	+	12.0600i	−0.373338	+	0.927695i
$170$	−0.716508	−	0.413676i	−0.0549537	−	0.0317275i
$171$	4.99863	+	0.869425i	0.382255	+	0.0664866i
$172$	1.73181	−	2.99958i	0.132049	−	0.228716i
$173$	6.36169	+	11.0188i	0.483670	+	0.837741i	0.999824	−	0.0187546i	$-0.00597013\pi$
$173$	6.36169	+	11.0188i	0.483670	+	0.837741i	−0.516154	+	0.856496i	$0.672637\pi$
$174$	−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
$177$	−5.75591	+	2.69217i	−0.432641	+	0.202356i
$178$			2.16589i			0.162340i
$179$	−4.77637	−	2.75764i	−0.357003	−	0.206116i	0.310762	−	0.950488i	$-0.399416\pi$
$179$	−4.77637	−	2.75764i	−0.357003	−	0.206116i	−0.667765	+	0.744372i	$0.732749\pi$
$180$	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
$189$	10.6183	−	8.73216i	0.772371	−	0.635171i
$190$		−	7.26647i		−	0.527165i
$191$	−6.23661	+	3.60071i	−0.451266	+	0.260538i	−0.708365	−	0.705847i	$-0.750567\pi$
$191$	−6.23661	+	3.60071i	−0.451266	+	0.260538i	0.257099	+	0.966385i	$0.417233\pi$
$192$	−0.733819	−	1.56892i	−0.0529588	−	0.113227i
$193$	−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
$195$	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	$-0.519136\pi$
$198$	−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
$201$	−0.753369	+	8.72779i	−0.0531385	+	0.615611i
$202$	−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
$205$	−6.16728			−0.430742
$206$	9.05121	+	5.22572i	0.630628	+	0.364093i
$207$	3.24576	+	2.71069i	0.225596	+	0.188406i
$208$	−2.01824	−	2.98776i	−0.139940	−	0.207164i
$209$	−7.64468			−0.528794
$210$	−14.9271	−	12.8395i	−1.03007	−	0.886010i
$211$	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
$213$	19.2998	+	1.66592i	1.32240	+	0.114147i
$214$			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
$222$	−8.94596	+	4.18423i	−0.600413	+	0.280827i
$223$	−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
$225$	−39.7842	−	6.91977i	−2.65228	−	0.461318i
$226$	−11.0639	−	6.38777i	−0.735963	−	0.424908i
$227$			21.5999i			1.43363i	0.697262	+	0.716816i	$0.254401\pi$
$227$			21.5999i			1.43363i	−0.697262	+	0.716816i	$0.745599\pi$
$228$	−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
$231$	−13.5078	+	15.7040i	−0.888746	+	1.03325i
$232$	8.66432	−	5.00235i	0.568841	−	0.328420i
$233$	−5.93673	−	3.42758i	−0.388928	−	0.224548i	0.292767	−	0.956184i	$-0.405424\pi$
$233$	−5.93673	−	3.42758i	−0.388928	−	0.224548i	−0.681696	+	0.731636i	$0.738757\pi$
$234$	−10.7608	−	1.09829i	−0.703452	−	0.0717978i
$235$	−21.5884	−	37.3922i	−1.40827	−	2.43920i
$236$		−	3.66871i		−	0.238813i
$237$	6.66364	+	0.575194i	0.432850	+	0.0373629i
$238$	0.297779	−	0.413384i	0.0193022	−	0.0267957i
$239$	7.06260			0.456841			0.228421	−	0.973563i	$-0.426644\pi$
$239$	7.06260			0.456841			0.228421	+	0.973563i	$0.426644\pi$
$240$	−0.639991	+	7.41431i	−0.0413112	+	0.478591i
$241$	−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
$243$	−12.7172	+	9.01518i	−0.815807	+	0.578324i
$244$	−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
$249$	−6.51275	+	3.04616i	−0.412729	+	0.193043i
$250$			36.3512i			2.29905i
$251$	2.00148	−	3.46666i	0.126332	−	0.218814i	−0.795921	−	0.605401i	$-0.793013\pi$
$251$	2.00148	−	3.46666i	0.126332	−	0.218814i	0.922253	+	0.386587i	$0.126346\pi$
$252$	1.96937	+	7.68906i	0.124059	+	0.484365i
$253$	−5.51803	−	3.18584i	−0.346916	−	0.200292i
$254$	−0.0510484	−	0.0884185i	−0.00320306	−	0.00554787i
$255$	0.123237	−	1.42771i	0.00771742	−	0.0894065i
$256$	1.00000			0.0625000
$257$	−8.95503			−0.558599			−0.279300	−	0.960204i	$-0.590102\pi$
$257$	−8.95503			−0.558599			−0.279300	+	0.960204i	$0.590102\pi$
$258$	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
$261$	5.14321	−	29.5701i	0.318357	−	1.83035i
$262$	0.746067	−	1.29223i	0.0460922	−	0.0798340i
$263$	−15.5696	−	8.98910i	−0.960061	−	0.554291i	−0.0638691	−	0.997958i	$-0.520344\pi$
$263$	−15.5696	−	8.98910i	−0.960061	−	0.554291i	−0.896192	+	0.443667i	$0.853677\pi$
$264$	7.80021	+	0.673301i	0.480070	+	0.0414388i
$265$	−27.7471			−1.70449
$266$	4.45192	+	0.449615i	0.272965	+	0.0275677i
$267$	−3.39811	+	1.58937i	−0.207961	+	0.0972681i
$268$	−4.38012	−	2.52887i	−0.267559	−	0.154475i
$269$	2.85518			0.174083			0.0870417	−	0.996205i	$-0.472259\pi$
$269$	2.85518			0.174083			0.0870417	+	0.996205i	$0.472259\pi$
$270$	15.8415	+	15.7315i	0.964084	+	0.957388i
$271$	−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
$273$	6.54576	+	15.1708i	0.396167	+	0.918178i
$274$	−20.1088			−1.21482
$275$	60.8442			3.66904
$276$	−2.21155	+	1.03439i	−0.133120	+	0.0622631i
$277$	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
$279$	−6.86455	−	1.19397i	−0.410970	−	0.0714811i
$280$	10.3660	−	4.66584i	0.619486	−	0.278837i
$281$	−3.78960			−0.226069			−0.113034	−	0.993591i	$-0.536057\pi$
$281$	−3.78960			−0.226069			−0.113034	+	0.993591i	$0.536057\pi$
$282$	−1.49686	+	17.3411i	−0.0891366	+	1.03265i
$283$	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
$285$	11.4005	−	5.33228i	0.675308	−	0.315857i
$286$	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
$289$	−16.9629			−0.997819
$290$	−42.9859			−2.52422
$291$	−23.6938	−	2.04521i	−1.38896	−	0.119892i
$292$	−5.90130	−	10.2214i	−0.345348	−	0.598160i
$293$	−17.6685	−	10.2009i	−1.03221	−	0.595944i	−0.114590	−	0.993413i	$-0.536555\pi$
$293$	−17.6685	−	10.2009i	−1.03221	−	0.595944i	−0.917616	+	0.397469i	$0.869889\pi$
$294$	8.78994	−	8.35087i	0.512640	−	0.487032i
$295$	−7.88143	+	13.6510i	−0.458875	+	0.794794i
$296$		−	5.70199i		−	0.331421i
$297$	16.5503	−	16.6660i	0.960346	−	0.967062i
$298$	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
$303$	−0.139115	−	0.0120082i	−0.00799194	−	0.000689851i
$304$	−0.845613	−	1.46464i	−0.0484992	−	0.0840031i
$305$	34.8545			1.99576
$306$	−0.370299	+	0.443393i	−0.0211686	+	0.0253471i
$307$	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
$309$	−1.55678	+	18.0354i	−0.0885623	+	1.02600i
$310$			9.97895i			0.566766i
$311$	−8.67002	−	15.0169i	−0.491632	−	0.851531i	0.508322	−	0.861167i	$-0.330266\pi$
$311$	−8.67002	−	15.0169i	−0.491632	−	0.851531i	−0.999954	+	0.00963600i	$0.996933\pi$
$312$	3.20653	−	5.35894i	0.181534	−	0.303390i
$313$	−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
$315$	9.19037	−	32.8413i	0.517818	−	1.85040i
$316$	−1.93078	+	3.34421i	−0.108615	+	0.188126i
$317$	−4.97176	+	8.61134i	−0.279242	+	0.483661i	−0.971197	−	0.238280i	$-0.923416\pi$
$317$	−4.97176	+	8.61134i	−0.279242	+	0.483661i	0.691955	+	0.721941i	$0.256750\pi$
$318$	9.17010	+	6.40512i	0.514234	+	0.359181i
$319$			45.2232i			2.53201i
$320$	−3.72094	−	2.14828i	−0.208007	−	0.120093i
$321$	−8.41564	+	3.93619i	−0.469715	+	0.219696i
$322$	3.02608	+	2.17983i	0.168637	+	0.121477i
$323$	0.162832	+	0.282034i	0.00906023	+	0.0156928i
$324$	−1.60400	−	8.85591i	−0.0891109	−	0.491995i
$325$	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
$333$	−13.1294	−	10.9650i	−0.719488	−	0.600880i
$334$	13.7047	−	7.91242i	0.749888	−	0.432948i
$335$	10.8654	+	18.8195i	0.593643	+	1.02822i
$336$	−4.50289	−	0.850863i	−0.245653	−	0.0464184i
$337$	−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
$339$	1.90297	−	22.0459i	0.103355	−	1.19737i
$340$	0.716508	+	0.413676i	0.0388581	+	0.0224347i
$341$	10.4983			0.568517
$342$	−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
$345$	10.4512	+	0.902131i	0.562674	+	0.0485691i
$346$	−6.36169	−	11.0188i	−0.342006	−	0.592372i
$347$		−	21.2360i		−	1.14001i	−0.821641	−	0.570005i	$-0.806941\pi$
$347$		−	21.2360i		−	1.14001i	0.821641	−	0.570005i	$-0.193059\pi$
$348$	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
$351$	−6.17331	−	17.6887i	−0.329507	−	0.944153i
$352$	−2.26010	+	3.91461i	−0.120464	+	0.208649i
$353$	−4.13071	−	2.38487i	−0.219855	−	0.126934i	0.386028	−	0.922487i	$-0.373847\pi$
$353$	−4.13071	−	2.38487i	−0.219855	−	0.126934i	−0.605883	+	0.795554i	$0.707180\pi$
$354$	5.75591	−	2.69217i	0.305923	−	0.143087i
$355$	41.6156	−	24.0268i	2.20872	−	1.27521i
$356$		−	2.16589i		−	0.114792i
$357$	0.867082	+	0.163843i	0.0458909	+	0.00867150i
$358$	4.77637	+	2.75764i	0.252439	+	0.145746i
$359$	14.0272	−	24.2958i	0.740328	−	1.28229i	−0.212018	−	0.977266i	$-0.568004\pi$
$359$	14.0272	−	24.2958i	0.740328	−	1.28229i	0.952346	−	0.305020i	$-0.0986630\pi$
$360$	−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
$369$	−0.737909	+	4.24250i	−0.0384140	+	0.220856i
$370$	−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
$375$	−57.0321	+	26.6752i	−2.94512	+	1.37750i
$376$	−8.70281	−	5.02457i	−0.448813	−	0.259122i
$377$	32.4325	+	15.7909i	1.67036	+	0.813275i
$378$	−10.6183	+	8.73216i	−0.546149	+	0.449134i
$379$	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	−0.781386	−	0.624048i	$-0.785487\pi$
$383$	−12.3614	+	7.13684i	−0.631637	+	0.364676i	0.149749	+	0.988724i	$0.452153\pi$
$384$	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
$387$	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	−0.301156	−	0.953575i	$-0.597372\pi$
$389$	7.37813	−	4.25977i	0.374086	−	0.215979i	0.675242	+	0.737596i	$0.264039\pi$
$390$	−23.4438	+	13.0517i	−1.18712	+	0.660900i
$391$			0.271434i			0.0137270i
$392$	2.21720	+	6.63958i	0.111986	+	0.335349i
$393$	2.57488	+	0.222259i	0.129885	+	0.0112115i
$394$	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
$399$	2.56149	+	7.31464i	0.128235	+	0.366190i
$400$	6.73025	+	11.6571i	0.336513	+	0.582857i
$401$	−14.8495			−0.741550			−0.370775	−	0.928723i	$-0.620908\pi$
$401$	−14.8495			−0.741550			−0.370775	+	0.928723i	$0.620908\pi$
$402$	0.753369	−	8.72779i	0.0375746	−	0.435303i
$403$	3.66578	−	7.52904i	0.182606	−	0.375048i
$404$	0.0403083	−	0.0698161i	0.00200541	−	0.00347348i
$405$	−13.0566	+	36.3981i	−0.648790	+	1.80864i
$406$	2.65976	−	26.3360i	0.132002	−	1.30703i
$407$	22.3210	+	12.8871i	1.10641	+	0.638788i
$408$	−0.141305	−	0.302113i	−0.00699564	−	0.0149568i
$409$	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
$411$	−14.7562	−	31.5491i	−0.727871	−	1.55620i
$412$	−9.05121	−	5.22572i	−0.445921	−	0.257453i
$413$	−7.87586	−	5.67334i	−0.387546	−	0.279167i
$414$	−3.24576	−	2.71069i	−0.159520	−	0.133223i
$415$	−8.91776	+	15.4460i	−0.437756	+	0.758215i
$416$	2.01824	+	2.98776i	0.0989525	+	0.146487i
$417$	−2.46368	+	28.5417i	−0.120647	+	1.39770i
$418$	7.64468			0.373913
$419$	−11.7502	−	20.3519i	−0.574035	−	0.994257i	−0.996146	−	0.0877131i	$-0.972044\pi$
$419$	−11.7502	−	20.3519i	−0.574035	−	0.994257i	0.422111	−	0.906544i	$-0.361289\pi$
$420$	14.9271	+	12.8395i	0.728367	+	0.626503i
$421$		−	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
$426$	−19.2998	−	1.66592i	−0.935076	−	0.0807143i
$427$	−2.15663	+	21.3541i	−0.104367	+	1.03340i
$428$		−	5.36397i		−	0.259277i
$429$	13.7311	+	24.6640i	0.662942	+	1.19079i
$430$	12.8879	−	7.44084i	0.621510	−	0.358829i
$431$	9.13932	−	15.8298i	0.440225	−	0.762493i	−0.557480	−	0.830190i	$-0.688232\pi$
$431$	9.13932	−	15.8298i	0.440225	−	0.762493i	0.997706	+	0.0676972i	$0.0215652\pi$
$432$	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
$435$	−31.5439	−	67.4414i	−1.51241	−	3.23357i
$436$	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
$441$	19.5521	+	7.66269i	0.931051	+	0.364890i
$442$	−0.388635	−	0.575326i	−0.0184855	−	0.0273655i
$443$	11.7488	+	6.78318i	0.558203	+	0.322279i	0.752424	−	0.658679i	$-0.228885\pi$
$443$	11.7488	+	6.78318i	0.558203	+	0.322279i	−0.194221	+	0.980958i	$0.562218\pi$
$444$	8.94596	−	4.18423i	0.424556	−	0.198575i
$445$	−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	−0.898668	−	0.438629i	$-0.855464\pi$
$449$	−1.47204	+	2.54965i	−0.0694699	+	0.120325i	0.829198	+	0.558955i	$0.188797\pi$
$450$	39.7842	+	6.91977i	1.87545	+	0.326201i
$451$		−	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	0.699178	−	0.714947i	$-0.253549\pi$
$461$	9.22401	+	5.32548i	0.429605	+	0.248032i	−0.269573	+	0.962980i	$0.586883\pi$
$462$	13.5078	−	15.7040i	0.628439	−	0.730617i
$463$		−	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
$465$	−15.6562	+	7.32274i	−0.726037	+	0.339584i
$466$	5.93673	+	3.42758i	0.275014	+	0.158779i
$467$	−14.0602	+	24.3530i	−0.650629	+	1.12692i	0.332342	+	0.943159i	$0.392161\pi$
$467$	−14.0602	+	24.3530i	−0.650629	+	1.12692i	−0.982971	+	0.183763i	$0.941172\pi$
$468$	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
$471$	7.26096	+	5.07162i	0.334568	+	0.233688i
$472$			3.66871i			0.168866i
$473$	−7.82812	−	13.5587i	−0.359938	−	0.623430i
$474$	−6.66364	−	0.575194i	−0.306071	−	0.0264195i
$475$	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
$478$	−7.06260			−0.323036
$479$	−17.1627	−	9.90890i	−0.784184	−	0.452749i	0.0537268	−	0.998556i	$-0.482890\pi$
$479$	−17.1627	−	9.90890i	−0.784184	−	0.452749i	−0.837911	+	0.545807i	$0.816223\pi$
$480$	0.639991	−	7.41431i	0.0292114	−	0.338415i
$481$	17.0362	−	11.5080i	0.776782	−	0.524719i
$482$	19.7363			0.898965
$483$	−1.19938	+	6.34728i	−0.0545735	+	0.288811i
$484$	−4.71610	−	8.16852i	−0.214368	−	0.371297i
$485$	−51.0904	+	29.4970i	−2.31989	+	1.33939i
$486$	12.7172	−	9.01518i	0.576863	−	0.408937i
$487$		−	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	−0.399848	−	0.916582i	$-0.630937\pi$
$491$	4.29900	−	2.48203i	0.194011	−	0.112012i	0.593859	+	0.804569i	$0.297604\pi$
$492$	−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
$495$	9.98412	−	57.4022i	0.448753	−	2.58004i
$496$	1.16127	+	2.01138i	0.0521425	+	0.0903135i
$497$	12.1454	+	26.9831i	0.544795	+	1.21036i
$498$	6.51275	−	3.04616i	0.291843	−	0.136502i
$499$	−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	−0.707520	−	0.706693i	$-0.750186\pi$
$503$	5.79205	−	10.0321i	0.258255	−	0.447310i	0.965774	+	0.259383i	$0.0835193\pi$
$504$	−1.96937	−	7.68906i	−0.0877228	−	0.342498i
$505$	−0.299970	+	0.173188i	−0.0133485	+	0.00770675i
$506$	5.51803	+	3.18584i	0.245307	+	0.141628i
$507$	22.4827	−	1.23531i	0.998494	−	0.0548619i
$508$	0.0510484	+	0.0884185i	0.00226491	+	0.00392294i
$509$		−	26.4808i		−	1.17374i	−0.809681	−	0.586871i	$-0.800360\pi$
$509$		−	26.4808i		−	1.17374i	0.809681	−	0.586871i	$-0.199640\pi$
$510$	−0.123237	+	1.42771i	−0.00545704	+	0.0632200i
$511$	−31.0687	−	3.13774i	−1.37440	−	0.138805i
$512$	−1.00000			−0.0441942
$513$	−2.30403	−	8.48045i	−0.101726	−	0.374421i
$514$	8.95503			0.394989
$515$	22.4527	+	38.8892i	0.989383	+	1.71366i
$516$	−5.97694	−	0.515920i	−0.263120	−	0.0227121i
$517$	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	0.763787	−	0.645469i	$-0.223338\pi$
$521$	−4.04236	−	7.00158i	−0.177099	−	0.306745i	−0.940886	+	0.338724i	$0.890005\pi$
$522$	−5.14321	+	29.5701i	−0.225112	+	1.29425i
$523$		−	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
$525$	−20.3870	−	58.2174i	−0.889761	−	2.54081i
$526$	15.5696	+	8.98910i	0.678866	+	0.391943i
$527$	−0.223615	−	0.387313i	−0.00974084	−	0.0168716i
$528$	−7.80021	−	0.673301i	−0.339461	−	0.0293017i
$529$	21.0130			0.913610
$530$	27.7471			1.20526
$531$	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
$534$	3.39811	−	1.58937i	0.147051	−	0.0687789i
$535$	−11.5233	+	19.9590i	−0.498197	+	0.862903i
$536$	4.38012	+	2.52887i	0.189193	+	0.109230i
$537$	−0.821522	+	9.51735i	−0.0354513	+	0.410704i
$538$	−2.85518			−0.123096
$539$	−31.0024	−	6.32662i	−1.33537	−	0.272507i
$540$	−15.8415	−	15.7315i	−0.681710	−	0.676976i
$541$	−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
$543$	6.20676	−	2.90304i	0.266358	−	0.124581i
$544$	0.192561			0.00825599
$545$	−30.3473			−1.29993
$546$	−6.54576	−	15.1708i	−0.280133	−	0.649250i
$547$	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
$549$	4.17030	−	23.9765i	0.177984	−	1.02329i
$550$	−60.8442			−2.59440
$551$	14.6533	+	8.46010i	0.624253	+	0.360413i
$552$	2.21155	−	1.03439i	0.0941299	−	0.0440267i
$553$	4.19344	+	9.31646i	0.178323	+	0.396176i
$554$	−14.8067			−0.629078
$555$	−42.2763	−	3.64922i	−1.79453	−	0.154901i
$556$	−14.3239	−	8.26993i	−0.607470	−	0.350723i
$557$	1.89706	−	3.28581i	0.0803811	−	0.139224i	−0.823033	−	0.567994i	$-0.807720\pi$
$557$	1.89706	−	3.28581i	0.0803811	−	0.139224i	0.903414	+	0.428770i	$0.141053\pi$
$558$	6.86455	+	1.19397i	0.290600	+	0.0505448i
$559$	−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
$562$	3.78960			0.159855
$563$	−6.67273			−0.281222			−0.140611	−	0.990065i	$-0.544907\pi$
$563$	−6.67273			−0.281222			−0.140611	+	0.990065i	$0.544907\pi$
$564$	1.49686	−	17.3411i	0.0630291	−	0.730193i
$565$	−27.4455	−	47.5370i	−1.15464	−	1.99990i
$566$	−23.9803	−	13.8450i	−1.00797	−	0.581950i
$567$	−21.4920	−	10.2515i	−0.902580	−	0.430523i
$568$	5.59208	−	9.68576i	0.234638	−	0.406406i
$569$		−	18.2299i		−	0.764238i	−0.924113	−	0.382119i	$-0.875194\pi$
$569$		−	18.2299i		−	0.764238i	0.924113	−	0.382119i	$-0.124806\pi$
$570$	−11.4005	+	5.33228i	−0.477515	+	0.223344i
$571$	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
$576$	−1.92302	+	2.30261i	−0.0801258	+	0.0959420i
$577$	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
$579$	−3.06370	+	35.4930i	−0.127323	+	1.47504i
$580$	42.9859			1.78489
$581$	−8.91145	−	6.41933i	−0.369709	−	0.266319i
$582$	23.6938	+	2.04521i	0.982141	+	0.0847768i
$583$		−	29.1913i		−	1.20898i
$584$	5.90130	+	10.2214i	0.244198	+	0.422963i
$585$	−37.6806	−	27.2038i	−1.55790	−	1.12474i
$586$	17.6685	+	10.2009i	0.729879	+	0.421396i
$587$	26.4828	−	15.2899i	1.09306	−	0.631081i	0.158673	−	0.987331i	$-0.449278\pi$
$587$	26.4828	−	15.2899i	1.09306	−	0.631081i	0.934390	+	0.356251i	$0.115945\pi$
$588$	−8.78994	+	8.35087i	−0.362491	+	0.344384i
$589$	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	0.767440	−	0.641120i	$-0.221530\pi$
$593$	14.5119	+	8.37847i	0.595934	+	0.344063i	−0.171506	+	0.985183i	$0.554863\pi$
$594$	−16.5503	+	16.6660i	−0.679067	+	0.683816i
$595$	1.99608	−	0.898460i	0.0818315	−	0.0368333i
$596$	−2.04689	−	3.54532i	−0.0838438	−	0.145222i
$597$	11.6462	−	5.44720i	0.476648	−	0.222939i
$598$	4.21155	−	2.84492i	0.172223	−	0.116337i
$599$	19.4413	−	11.2245i	0.794352	−	0.458619i	−0.0471404	−	0.998888i	$-0.515011\pi$
$599$	19.4413	−	11.2245i	0.794352	−	0.458619i	0.841492	+	0.540269i	$0.181677\pi$
$600$	−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
$606$	0.139115	+	0.0120082i	0.00565116	+	0.000487798i
$607$	−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
$609$	43.2708	−	15.1529i	1.75342	−	0.614026i
$610$	−34.8545			−1.41122
$611$	−2.55219	−	36.1427i	−0.103250	−	1.46218i
$612$	0.370299	−	0.443393i	0.0149684	−	0.0179231i
$613$	−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
$615$	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	$-0.00111090\pi$
$618$	1.55678	−	18.0354i	0.0626230	−	0.725489i
$619$	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
$624$	−3.20653	+	5.35894i	−0.128364	+	0.214529i
$625$	−44.4414	+	76.9747i	−1.77765	+	3.07899i
$626$	7.84351	+	4.52845i	0.313490	+	0.180993i
$627$	5.60981	+	11.9939i	0.224034	+	0.478990i
$628$	−4.42840	+	2.55674i	−0.176712	+	0.102025i
$629$		−	1.09798i		−	0.0437794i
$630$	−9.19037	+	32.8413i	−0.366153	+	1.30843i
$631$	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	$0.230791\pi$
$641$			33.5804i			1.32635i	−0.748466	+	0.663173i	$0.769209\pi$
$642$	8.41564	−	3.93619i	0.332139	−	0.155349i
$643$	−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	−0.742577	−	0.669761i	$-0.766396\pi$
$647$	5.30960	−	9.19649i	0.208742	−	0.361552i	0.951318	+	0.308210i	$0.0997298\pi$
$648$	1.60400	+	8.85591i	0.0630109	+	0.347893i
$649$	−14.3616	−	8.29165i	−0.563740	−	0.325476i
$650$	−21.2454	+	43.6353i	−0.833314	+	1.71152i
$651$	−3.51766	−	10.0451i	−0.137868	−	0.393698i
$652$	8.00463	−	4.62147i	0.313485	−	0.180991i
$653$			8.80038i			0.344385i	0.985063	+	0.172193i	$0.0550852\pi$
$653$			8.80038i			0.344385i	−0.985063	+	0.172193i	$0.944915\pi$
$654$	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
$657$	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	$0.708239\pi$
$660$	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
$663$	0.617453	−	1.03192i	0.0239799	−	0.0400766i
$664$			4.15111i			0.161094i
$665$	15.5994	+	11.2370i	0.604919	+	0.435751i
$666$	13.1294	+	10.9650i	0.508755	+	0.424886i
$667$	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
$672$	4.50289	+	0.850863i	0.173703	+	0.0328227i
$673$	−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
$675$	18.3379	+	67.4961i	0.705824	+	2.59793i
$676$	−4.85339	+	12.0600i	−0.186669	+	0.463848i
$677$	10.7942	−	18.6960i	0.414853	−	0.718546i	−0.580560	−	0.814217i	$-0.697166\pi$
$677$	10.7942	−	18.6960i	0.414853	−	0.718546i	0.995413	+	0.0956710i	$0.0304997\pi$
$678$	−1.90297	+	22.0459i	−0.0730830	+	0.846668i
$679$	−14.9106	−	33.1265i	−0.572216	−	1.27128i
$680$	−0.716508	−	0.413676i	−0.0274768	−	0.0158638i
$681$	33.8884	−	15.8504i	1.29861	−	0.607388i
$682$	−10.4983			−0.402002
$683$	−43.5860			−1.66777			−0.833886	−	0.551937i	$-0.813889\pi$
$683$	−43.5860			−1.66777			−0.833886	+	0.551937i	$0.813889\pi$
$684$	4.99863	+	0.869425i	0.191127	+	0.0332433i
$685$	−74.8236	−	43.1994i	−2.85886	−	1.65056i
$686$	17.6823	+	5.50772i	0.675115	+	0.210286i
$687$	19.0948	+	1.64823i	0.728512	+	0.0628839i
$688$	1.73181	−	2.99958i	0.0660246	−	0.114358i
$689$	−20.9350	−	10.1930i	−0.797560	−	0.388321i
$690$	−10.4512	−	0.902131i	−0.397871	−	0.0343436i
$691$	−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
$693$	34.5506	+	9.66871i	1.31247	+	0.367284i
$694$			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
$699$	−1.02110	+	11.8295i	−0.0386216	+	0.447432i
$700$	35.4329	+	3.57850i	1.33924	+	0.135254i
$701$			29.7087i			1.12208i	0.827787	+	0.561042i	$0.189599\pi$
$701$			29.7087i			1.12208i	−0.827787	+	0.561042i	$0.810401\pi$
$702$	6.17331	+	17.6887i	0.232997	+	0.667617i
$703$	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
$708$	−5.75591	+	2.69217i	−0.216320	+	0.101178i
$709$	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
$714$	−0.867082	−	0.163843i	−0.0324497	−	0.00613168i
$715$	62.9587	+	30.6537i	2.35452	+	1.14638i
$716$	−4.77637	−	2.75764i	−0.178501	−	0.103058i
$717$	−5.18267	−	11.0807i	−0.193550	−	0.413814i
$718$	−14.0272	+	24.2958i	−0.523491	+	0.906713i
$719$	−13.8089	−	23.9177i	−0.514985	−	0.891979i	−0.999849	−	0.0173900i	$-0.994464\pi$
$719$	−13.8089	−	23.9177i	−0.514985	−	0.891979i	0.484864	−	0.874589i	$-0.338869\pi$
$720$	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
$723$	14.4829	+	30.9647i	0.538625	+	1.15159i
$724$			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
$735$	50.6469	−	12.1898i	1.86814	−	0.449626i
$736$			1.40960i			0.0519586i
$737$	−19.7990	+	11.4310i	−0.729307	+	0.421065i
$738$	0.737909	−	4.24250i	0.0271628	−	0.156168i
$739$	−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
$741$	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	$0.982097\pi$
$744$	−2.30353	+	3.29793i	−0.0844514	+	0.120908i
$745$			17.5892i			0.644418i
$746$	−11.4478	−	19.8282i	−0.419135	−	0.725963i
$747$	9.55837	+	7.98266i	0.349722	+	0.292070i
$748$	−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
$751$	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
$753$	−6.90764	−	0.596256i	−0.251728	−	0.0217288i
$754$	−32.4325	−	15.7909i	−1.18112	−	0.575072i
$755$	−32.4939			−1.18257
$756$	10.6183	−	8.73216i	0.386186	−	0.317586i
$757$	−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
$759$	−0.949086	+	10.9952i	−0.0344496	+	0.399100i
$760$		−	7.26647i		−	0.263583i
$761$	−30.0314	+	17.3386i	−1.08864	+	0.628525i	−0.933213	−	0.359323i	$-0.883008\pi$
$761$	−30.0314	+	17.3386i	−1.08864	+	0.628525i	−0.155424	+	0.987848i	$0.549674\pi$
$762$	−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
$768$	−0.733819	−	1.56892i	−0.0264794	−	0.0566135i
$769$	−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
$771$	6.57137	+	14.0497i	0.236662	+	0.505989i
$772$	−17.8125	−	10.2840i	−0.641085	−	0.370131i
$773$		−	2.30696i		−	0.0829757i	−0.999139	−	0.0414879i	$-0.986790\pi$
$773$		−	2.30696i		−	0.0829757i	0.999139	−	0.0414879i	$-0.0132098\pi$
$774$	−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
$777$	4.85161	−	25.6754i	0.174050	−	0.921101i
$778$	−7.37813	+	4.25977i	−0.264519	+	0.152720i
$779$	−2.10235	−	1.21379i	−0.0753244	−	0.0434886i
$780$	23.4438	−	13.0517i	0.839423	−	0.467327i
$781$	25.2773	+	43.7816i	0.904493	+	1.56663i
$782$		−	0.271434i		−	0.00970648i
$783$	−50.1674	+	13.6298i	−1.79284	+	0.487091i
$784$	−2.21720	−	6.63958i	−0.0791859	−	0.237128i
$785$	21.9704			0.784157
$786$	−2.57488	−	0.222259i	−0.0918429	−	0.00792772i
$787$	−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
$789$	−2.67792	+	31.0238i	−0.0953365	+	1.10448i
$790$	−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
$795$	20.3614	+	43.5330i	0.722144	+	1.54396i
$796$			7.42309i			0.263104i
$797$	3.13411	−	5.42843i	0.111016	−	0.192285i	−0.805164	−	0.593052i	$-0.797923\pi$
$797$	3.13411	−	5.42843i	0.111016	−	0.192285i	0.916180	+	0.400767i	$0.131256\pi$
$798$	−2.56149	−	7.31464i	−0.0906758	−	0.258935i
$799$	−1.67582	−	0.967537i	−0.0592864	−	0.0342290i
$800$	−6.73025	−	11.6571i	−0.237950	−	0.412142i
$801$	4.98720	+	4.16505i	0.176214	+	0.147165i
$802$	14.8495			0.524355
$803$	−53.3501			−1.88268
$804$	−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
$807$	−2.09518	−	4.47955i	−0.0737540	−	0.157688i
$808$	−0.0403083	+	0.0698161i	−0.00141804	+	0.00245612i
$809$	17.0434	+	9.84001i	0.599214	+	0.345956i	0.768732	−	0.639571i	$-0.220888\pi$
$809$	17.0434	+	9.84001i	0.599214	+	0.345956i	−0.169518	+	0.985527i	$0.554221\pi$
$810$	13.0566	−	36.3981i	0.458764	−	1.27890i
$811$	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
$813$	3.28205	+	7.01709i	0.115107	+	0.246100i
$814$	−22.3210	−	12.8871i	−0.782352	−	0.451691i
$815$	−39.7130			−1.39108
$816$	0.141305	+	0.302113i	0.00494667	+	0.0105761i
$817$	−5.85776			−0.204937
$818$	−18.4860			−0.646348
$819$	18.9984	−	21.4024i	0.663856	−	0.747860i
$820$	−6.16728			−0.215371
$821$	−11.5367			−0.402634			−0.201317	−	0.979526i	$-0.564522\pi$
$821$	−11.5367			−0.402634			−0.201317	+	0.979526i	$0.564522\pi$
$822$	14.7562	+	31.5491i	0.514682	+	1.10040i
$823$	−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
$825$	−44.6486	−	95.4596i	−1.55447	−	3.32348i
$826$	7.87586	+	5.67334i	0.274036	+	0.197401i
$827$	−1.49924			−0.0521335			−0.0260668	−	0.999660i	$-0.508298\pi$
$827$	−1.49924			−0.0521335			−0.0260668	+	0.999660i	$0.508298\pi$
$828$	3.24576	+	2.71069i	0.112798	+	0.0942030i
$829$	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
$831$	−10.8655	−	23.2306i	−0.376919	−	0.805861i
$832$	−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
$835$	67.9925			2.35298
$836$	−7.64468			−0.264397
$837$	3.16410	+	11.6461i	0.109367	+	0.402548i
$838$	11.7502	+	20.3519i	0.405904	+	0.703046i
$839$	37.0634	+	21.3986i	1.27957	+	0.738761i	0.976769	−	0.214293i	$-0.0687448\pi$
$839$	37.0634	+	21.3986i	1.27957	+	0.738761i	0.302801	+	0.953054i	$0.402078\pi$
$840$	−14.9271	−	12.8395i	−0.515033	−	0.443005i
$841$	35.5470	−	61.5692i	1.22576	−	2.12308i
$842$			7.74237i			0.266820i
$843$	2.78088	+	5.94558i	0.0957786	+	0.204777i
$844$	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
$849$	4.12454	−	47.7829i	0.141554	−	1.63991i
$850$	1.29599	+	2.24471i	0.0444519	+	0.0769930i
$851$	8.03752			0.275523
$852$	19.2998	+	1.66592i	0.661199	+	0.0570736i
$853$	−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
$855$	−16.7318	−	13.9736i	−0.572216	−	0.477886i
$856$			5.36397i			0.183337i
$857$	−11.5857	−	20.0671i	−0.395761	−	0.685479i	0.597437	−	0.801916i	$-0.296186\pi$
$857$	−11.5857	−	20.0671i	−0.395761	−	0.685479i	−0.993198	+	0.116437i	$0.962853\pi$
$858$	−13.7311	−	24.6640i	−0.468770	−	0.842016i
$859$	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
$861$	−6.20817	+	2.17402i	−0.211574	+	0.0740904i
$862$	−9.13932	+	15.8298i	−0.311286	+	0.539164i
$863$	−9.45505	+	16.3766i	−0.321854	+	0.557467i	−0.980870	−	0.194661i	$-0.937639\pi$
$863$	−9.45505	+	16.3766i	−0.321854	+	0.557467i	0.659017	+	0.752128i	$0.270973\pi$
$864$	−5.02375	−	1.32737i	−0.170912	−	0.0451579i
$865$		−	54.6669i		−	1.85873i
$866$	−28.5068	−	16.4584i	−0.968700	−	0.559279i
$867$	12.4477	+	26.6135i	0.422747	+	0.903841i
$868$	6.11376	+	0.617450i	0.207514	+	0.0209576i
$869$	8.72751	+	15.1165i	0.296060	+	0.512792i
$870$	31.5439	+	67.4414i	1.06944	+	2.28648i
$871$	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
$879$	−3.03893	+	35.2061i	−0.102501	+	1.18747i
$880$	−16.8194	+	9.71067i	−0.566981	+	0.327347i
$881$	11.3253	+	19.6159i	0.381558	+	0.660877i	0.991285	−	0.131734i	$-0.0420544\pi$
$881$	11.3253	+	19.6159i	0.381558	+	0.660877i	−0.609727	+	0.792611i	$0.708721\pi$
$882$	−19.5521	−	7.66269i	−0.658352	−	0.258016i
$883$	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
$885$	27.2009	+	2.34794i	0.914349	+	0.0789251i
$886$	−11.7488	−	6.78318i	−0.394709	−	0.227885i
$887$	−4.41565			−0.148263			−0.0741316	−	0.997248i	$-0.523618\pi$
$887$	−4.41565			−0.148263			−0.0741316	+	0.997248i	$0.523618\pi$
$888$	−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
$891$	−38.2926	−	13.7362i	−1.28285	−	0.460181i
$892$	−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
$897$	7.55396	+	4.51992i	0.252219	+	0.150916i
$898$	1.47204	−	2.54965i	0.0491226	−	0.0850829i
$899$	−20.1232	−	11.6181i	−0.671147	−	0.387487i
$900$	−39.7842	−	6.91977i	−1.32614	−	0.230659i
$901$	−1.07695	+	0.621778i	−0.0358784	+	0.0207144i
$902$			6.48828i			0.216036i
$903$	−10.3504	+	12.0333i	−0.344439	+	0.400442i
$904$	−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	$0.206144\pi$
$911$			36.4179i			1.20658i	−0.797522	+	0.603290i	$0.793856\pi$
$912$	−1.67738	+	2.40148i	−0.0555437	+	0.0795211i
$913$	−16.2500	−	9.38191i	−0.537795	−	0.310496i
$914$			16.7645i			0.554522i
$915$	−25.5769	−	54.6839i	−0.845546	−	1.80779i
$916$	−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
$921$	−18.7137	−	40.0102i	−0.616637	−	1.31838i
$922$	−9.22401	−	5.32548i	−0.303776	−	0.175385i
$923$	40.2249	−	2.84045i	1.32402	−	0.0934945i
$924$	−13.5078	+	15.7040i	−0.444373	+	0.516624i
$925$	−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	−0.786725	−	0.617304i	$-0.788225\pi$
$929$	−19.6741	+	11.3588i	−0.645486	+	0.372671i	0.141239	+	0.989976i	$0.454891\pi$
$930$	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
$933$	−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
$936$	−10.7608	−	1.09829i	−0.351726	−	0.0358989i
$937$			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
$939$	−1.34906	+	15.6289i	−0.0440249	+	0.510030i
$940$	−21.5884	−	37.3922i	−0.704136	−	1.21960i
$941$	−7.89775	+	4.55977i	−0.257459	+	0.148644i	−0.623175	−	0.782082i	$-0.714158\pi$
$941$	−7.89775	+	4.55977i	−0.257459	+	0.148644i	0.365716	+	0.930727i	$0.380824\pi$
$942$	−7.26096	−	5.07162i	−0.236575	−	0.165242i
$943$	−1.01167	−	1.75226i	−0.0329445	−	0.0570615i
$944$		−	3.66871i		−	0.119406i
$945$	−58.2694	+	9.68061i	−1.89550	+	0.314910i
$946$	7.82812	+	13.5587i	0.254514	+	0.440832i
$947$	5.93223			0.192772			0.0963859	−	0.995344i	$-0.469272\pi$
$947$	5.93223			0.192772			0.0963859	+	0.995344i	$0.469272\pi$
$948$	6.66364	+	0.575194i	0.216425	+	0.0186814i
$949$	−18.6287	+	38.2608i	−0.604712	+	1.24200i
$950$	−11.3824	+	19.7149i	−0.369293	+	0.639635i
$951$	17.1589	+	1.48113i	0.556415	+	0.0480288i
$952$	0.297779	−	0.413384i	0.00965109	−	0.0133978i
$953$	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	$0.504908\pi$
$954$	3.31991	−	19.0874i	0.107486	−	0.617976i
$955$	30.9414			1.00124
$956$	7.06260			0.228421
$957$	70.9516	−	33.1857i	2.29354	−	1.07274i
$958$	17.1627	+	9.90890i	0.554502	+	0.320142i
$959$	31.0965	−	43.1689i	1.00416	−	1.39400i
$960$	−0.639991	+	7.41431i	−0.0206556	+	0.239296i
$961$	12.8029	−	22.1753i	0.412997	−	0.715332i
$962$	−17.0362	+	11.5080i	−0.549268	+	0.371033i
$963$	12.3511	+	10.3150i	0.398009	+	0.332397i
$964$	−19.7363			−0.635664
$965$	44.1861	+	76.5326i	1.42240	+	2.46367i
$966$	1.19938	−	6.34728i	0.0385893	−	0.204220i
$967$			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	$0.0279822\pi$
$971$	17.8895	+	30.9856i	0.574102	+	0.994375i	−0.422036	+	0.906579i	$0.638684\pi$
$972$	−12.7172	+	9.01518i	−0.407904	+	0.289162i
$973$	−39.9043	+	17.9614i	−1.27927	+	0.575816i
$974$			25.5536i			0.818790i
$975$	−84.0506	−	1.31195i	−2.69177	−	0.0420159i
$976$	−7.02534	+	4.05608i	−0.224876	+	0.129832i
$977$	10.4365	−	18.0765i	0.333892	−	0.578318i	−0.649379	−	0.760465i	$-0.724971\pi$
$977$	10.4365	−	18.0765i	0.333892	−	0.578318i	0.983271	+	0.182147i	$0.0583046\pi$
$978$	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
$981$	−3.63102	+	20.8760i	−0.115930	+	0.666520i
$982$	−4.29900	+	2.48203i	−0.137187	+	0.0792048i
$983$	1.08229	−	0.624859i	0.0345196	−	0.0199299i	−0.482641	−	0.875818i	$-0.660322\pi$
$983$	1.08229	−	0.624859i	0.0345196	−	0.0199299i	0.517161	+	0.855888i	$0.326989\pi$
$984$	2.03822	+	1.42365i	0.0649759	+	0.0453843i
$985$			107.886i			3.43754i
$986$	−1.66841	+	0.963258i	−0.0531331	+	0.0306764i
$987$	−34.9126	−	30.0300i	−1.11128	−	0.955865i
$988$	−2.66935	+	5.48250i	−0.0849234	+	0.174421i
$989$	−4.22821	−	2.44116i	−0.134449	−	0.0776244i
$990$	−9.98412	+	57.4022i	−0.317316	+	1.82436i
$991$	−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
$996$	−6.51275	+	3.04616i	−0.206364	+	0.0965213i
$997$			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.e.257.5	yes	34
3.2	odd	2		546.2.bi.f.257.1	yes	34
7.3	odd	6		546.2.bn.f.101.12	yes	34
13.4	even	6		546.2.bn.e.173.6	yes	34
21.17	even	6		546.2.bn.e.101.6	yes	34
39.17	odd	6		546.2.bn.f.173.12	yes	34
91.17	odd	6		546.2.bi.f.17.1	yes	34
273.17	even	6	inner	546.2.bi.e.17.5	✓	34

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-0.733819 - 1.56892i) q^{3} +1.00000 q^{4} +(-3.72094 - 2.14828i) q^{5} +(0.733819 + 1.56892i) q^{6} +(1.54641 - 2.14677i) q^{7} -1.00000 q^{8} +(-1.92302 + 2.30261i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-0.733819 - 1.56892i) q^{3} +1.00000 q^{4} +(-3.72094 - 2.14828i) q^{5} +(0.733819 + 1.56892i) q^{6} +(1.54641 - 2.14677i) q^{7} -1.00000 q^{8} +(-1.92302 + 2.30261i) q^{9} +(3.72094 + 2.14828i) q^{10} +(2.26010 - 3.91461i) q^{11} +(-0.733819 - 1.56892i) q^{12} +(-2.01824 - 2.98776i) q^{13} +(-1.54641 + 2.14677i) q^{14} +(-0.639991 + 7.41431i) q^{15} +1.00000 q^{16} -0.192561 q^{17} +(1.92302 - 2.30261i) q^{18} +(-0.845613 - 1.46464i) q^{19} +(-3.72094 - 2.14828i) q^{20} +(-4.50289 - 0.850863i) q^{21} +(-2.26010 + 3.91461i) q^{22} -1.40960i q^{23} +(0.733819 + 1.56892i) 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} +(0.639991 - 7.41431i) q^{30} +(1.16127 + 2.01138i) q^{31} -1.00000 q^{32} +(-7.80021 - 0.673301i) q^{33} +0.192561 q^{34} +(-10.3660 + 4.66584i) q^{35} +(-1.92302 + 2.30261i) q^{36} +5.70199i q^{37} +(0.845613 + 1.46464i) q^{38} +(-3.20653 + 5.35894i) q^{39} +(3.72094 + 2.14828i) q^{40} +(1.24309 - 0.717699i) q^{41} +(4.50289 + 0.850863i) 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} +(-0.733819 - 1.56892i) q^{48} +(-2.21720 - 6.63958i) q^{49} +(-6.73025 - 11.6571i) q^{50} +(0.141305 + 0.302113i) 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} +(-0.639991 + 7.41431i) q^{60} +(-7.02534 + 4.05608i) q^{61} +(-1.16127 - 2.01138i) q^{62} +(1.96937 + 7.68906i) q^{63} +1.00000 q^{64} +(1.09120 + 15.4530i) q^{65} +(7.80021 + 0.673301i) q^{66} +(-4.38012 - 2.52887i) q^{67} -0.192561 q^{68} +(-2.21155 + 1.03439i) q^{69} +(10.3660 - 4.66584i) q^{70} +(-5.59208 + 9.68576i) q^{71} +(1.92302 - 2.30261i) 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} +(3.20653 - 5.35894i) q^{78} +(-1.93078 + 3.34421i) q^{79} +(-3.72094 - 2.14828i) q^{80} +(-1.60400 - 8.85591i) q^{81} +(-1.24309 + 0.717699i) q^{82} -4.15111i q^{83} +(-4.50289 - 0.850863i) 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} +(0.733819 + 1.56892i) q^{96} +(6.86525 - 11.8910i) q^{97} +(2.21720 + 6.63958i) q^{98} +(4.66759 + 12.7320i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9} + 9 q^{10} - 9 q^{11} + 3 q^{12} + 8 q^{13} - 4 q^{14} - 4 q^{15} + 34 q^{16} - 12 q^{17} + 11 q^{18} - 5 q^{19} - 9 q^{20} + 4 q^{21} + 9 q^{22} - 3 q^{24} + 16 q^{25} - 8 q^{26} + 18 q^{27} + 4 q^{28} - 27 q^{29} + 4 q^{30} - q^{31} - 34 q^{32} + 21 q^{33} + 12 q^{34} + 3 q^{35} - 11 q^{36} + 5 q^{38} + 7 q^{39} + 9 q^{40} + 3 q^{41} - 4 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} + 27 q^{47} + 3 q^{48} - 2 q^{49} - 16 q^{50} + 24 q^{51} + 8 q^{52} + 21 q^{53} - 18 q^{54} - 57 q^{55} - 4 q^{56} + 17 q^{57} + 27 q^{58} - 4 q^{60} - 51 q^{61} + q^{62} + 3 q^{63} + 34 q^{64} + 21 q^{65} - 21 q^{66} - 21 q^{67} - 12 q^{68} + 42 q^{69} - 3 q^{70} + 15 q^{71} + 11 q^{72} - 19 q^{73} + 54 q^{75} - 5 q^{76} - 9 q^{77} - 7 q^{78} - 9 q^{79} - 9 q^{80} - 23 q^{81} - 3 q^{82} + 4 q^{84} - 42 q^{85} + 3 q^{86} + 81 q^{87} + 9 q^{88} - 9 q^{90} - 72 q^{91} + 17 q^{93} - 27 q^{94} - 3 q^{96} + 19 q^{97} + 2 q^{98} + 27 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9 + 9 * q^10 - 9 * q^11 + 3 * q^12 + 8 * q^13 - 4 * q^14 - 4 * q^15 + 34 * q^16 - 12 * q^17 + 11 * q^18 - 5 * q^19 - 9 * q^20 + 4 * q^21 + 9 * q^22 - 3 * q^24 + 16 * q^25 - 8 * q^26 + 18 * q^27 + 4 * q^28 - 27 * q^29 + 4 * q^30 - q^31 - 34 * q^32 + 21 * q^33 + 12 * q^34 + 3 * q^35 - 11 * q^36 + 5 * q^38 + 7 * q^39 + 9 * q^40 + 3 * q^41 - 4 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 + 27 * q^47 + 3 * q^48 - 2 * q^49 - 16 * q^50 + 24 * q^51 + 8 * q^52 + 21 * q^53 - 18 * q^54 - 57 * q^55 - 4 * q^56 + 17 * q^57 + 27 * q^58 - 4 * q^60 - 51 * q^61 + q^62 + 3 * q^63 + 34 * q^64 + 21 * q^65 - 21 * q^66 - 21 * q^67 - 12 * q^68 + 42 * q^69 - 3 * q^70 + 15 * q^71 + 11 * q^72 - 19 * q^73 + 54 * q^75 - 5 * q^76 - 9 * q^77 - 7 * q^78 - 9 * q^79 - 9 * q^80 - 23 * q^81 - 3 * q^82 + 4 * 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 - 3 * q^96 + 19 * q^97 + 2 * q^98 + 27 * q^99

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