LMFDB - Embedded newform 546.2.bi.e.17.3

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			17.3
Character	$\chi$	$=$	546.17
Dual form			546.2.bi.e.257.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-1.36360 - 1.06799i) q^{3} +1.00000 q^{4} +(2.60318 - 1.50295i) q^{5} +(1.36360 + 1.06799i) q^{6} +(-2.60776 - 0.446759i) q^{7} -1.00000 q^{8} +(0.718787 + 2.91262i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-1.36360 - 1.06799i) q^{3} +1.00000 q^{4} +(2.60318 - 1.50295i) q^{5} +(1.36360 + 1.06799i) q^{6} +(-2.60776 - 0.446759i) q^{7} -1.00000 q^{8} +(0.718787 + 2.91262i) q^{9} +(-2.60318 + 1.50295i) q^{10} +(-2.01609 - 3.49197i) q^{11} +(-1.36360 - 1.06799i) q^{12} +(0.138085 - 3.60291i) q^{13} +(2.60776 + 0.446759i) q^{14} +(-5.15482 - 0.730764i) q^{15} +1.00000 q^{16} +3.34332 q^{17} +(-0.718787 - 2.91262i) q^{18} +(-2.56879 + 4.44927i) q^{19} +(2.60318 - 1.50295i) q^{20} +(3.07879 + 3.39426i) q^{21} +(2.01609 + 3.49197i) q^{22} -2.48119i q^{23} +(1.36360 + 1.06799i) q^{24} +(2.01770 - 3.49476i) q^{25} +(-0.138085 + 3.60291i) q^{26} +(2.13052 - 4.73929i) q^{27} +(-2.60776 - 0.446759i) q^{28} +(-3.74921 - 2.16461i) q^{29} +(5.15482 + 0.730764i) q^{30} +(-2.95768 + 5.12285i) q^{31} -1.00000 q^{32} +(-0.980263 + 6.91480i) q^{33} -3.34332 q^{34} +(-7.45993 + 2.75633i) q^{35} +(0.718787 + 2.91262i) q^{36} -2.57002i q^{37} +(2.56879 - 4.44927i) q^{38} +(-4.03617 + 4.76543i) q^{39} +(-2.60318 + 1.50295i) q^{40} +(-6.29653 - 3.63530i) q^{41} +(-3.07879 - 3.39426i) q^{42} +(-2.23692 - 3.87445i) q^{43} +(-2.01609 - 3.49197i) q^{44} +(6.24865 + 6.50178i) q^{45} +2.48119i q^{46} +(-5.77285 + 3.33296i) q^{47} +(-1.36360 - 1.06799i) q^{48} +(6.60081 + 2.33008i) q^{49} +(-2.01770 + 3.49476i) q^{50} +(-4.55894 - 3.57064i) q^{51} +(0.138085 - 3.60291i) q^{52} +(-8.50304 - 4.90923i) q^{53} +(-2.13052 + 4.73929i) q^{54} +(-10.4965 - 6.06015i) q^{55} +(2.60776 + 0.446759i) q^{56} +(8.25457 - 3.32356i) q^{57} +(3.74921 + 2.16461i) q^{58} -3.18073i q^{59} +(-5.15482 - 0.730764i) q^{60} +(-5.77255 - 3.33278i) q^{61} +(2.95768 - 5.12285i) q^{62} +(-0.573184 - 7.91653i) q^{63} +1.00000 q^{64} +(-5.05552 - 9.58655i) q^{65} +(0.980263 - 6.91480i) q^{66} +(7.04993 - 4.07028i) q^{67} +3.34332 q^{68} +(-2.64989 + 3.38334i) q^{69} +(7.45993 - 2.75633i) q^{70} +(-0.436496 - 0.756034i) q^{71} +(-0.718787 - 2.91262i) q^{72} +(-6.78690 + 11.7553i) q^{73} +2.57002i q^{74} +(-6.48371 + 2.61056i) q^{75} +(-2.56879 + 4.44927i) q^{76} +(3.69740 + 10.0069i) q^{77} +(4.03617 - 4.76543i) q^{78} +(8.50477 + 14.7307i) q^{79} +(2.60318 - 1.50295i) q^{80} +(-7.96669 + 4.18710i) q^{81} +(6.29653 + 3.63530i) q^{82} -12.6597i q^{83} +(3.07879 + 3.39426i) q^{84} +(8.70327 - 5.02484i) q^{85} +(2.23692 + 3.87445i) q^{86} +(2.80062 + 6.95578i) q^{87} +(2.01609 + 3.49197i) q^{88} -3.63877i q^{89} +(-6.24865 - 6.50178i) q^{90} +(-1.96972 + 9.33382i) q^{91} -2.48119i q^{92} +(9.50424 - 3.82672i) q^{93} +(5.77285 - 3.33296i) q^{94} +15.4430i q^{95} +(1.36360 + 1.06799i) q^{96} +(1.10676 + 1.91696i) q^{97} +(-6.60081 - 2.33008i) q^{98} +(8.72163 - 8.38208i) 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−1.36360	−	1.06799i	−0.787272	−	0.616605i
$3$	−1.36360	−	1.06799i	−0.787272	−	0.616605i
$4$	1.00000			0.500000
$5$	2.60318	−	1.50295i	1.16418	−	0.672139i	0.211876	−	0.977296i	$-0.432043\pi$
$5$	2.60318	−	1.50295i	1.16418	−	0.672139i	0.952302	+	0.305158i	$0.0987092\pi$
$6$	1.36360	+	1.06799i	0.556686	+	0.436006i
$7$	−2.60776	−	0.446759i	−0.985640	−	0.168859i
$7$	−2.60776	−	0.446759i	−0.985640	−	0.168859i
$8$	−1.00000			−0.353553
$9$	0.718787	+	2.91262i	0.239596	+	0.970873i
$10$	−2.60318	+	1.50295i	−0.823198	+	0.475274i
$11$	−2.01609	−	3.49197i	−0.607873	−	1.05287i	−0.991590	−	0.129417i	$-0.958689\pi$
$11$	−2.01609	−	3.49197i	−0.607873	−	1.05287i	0.383717	−	0.923451i	$-0.374644\pi$
$12$	−1.36360	−	1.06799i	−0.393636	−	0.308303i
$13$	0.138085	−	3.60291i	0.0382978	−	0.999266i
$13$	0.138085	−	3.60291i	0.0382978	−	0.999266i
$14$	2.60776	+	0.446759i	0.696953	+	0.119401i
$15$	−5.15482	−	0.730764i	−1.33097	−	0.188682i
$16$	1.00000			0.250000
$17$	3.34332			0.810874			0.405437	−	0.914123i	$-0.367119\pi$
$17$	3.34332			0.810874			0.405437	+	0.914123i	$0.367119\pi$
$18$	−0.718787	−	2.91262i	−0.169420	−	0.686511i
$19$	−2.56879	+	4.44927i	−0.589320	+	1.02073i	0.405001	+	0.914316i	$0.367271\pi$
$19$	−2.56879	+	4.44927i	−0.589320	+	1.02073i	−0.994322	+	0.106417i	$0.966062\pi$
$20$	2.60318	−	1.50295i	0.582089	−	0.336069i
$21$	3.07879	+	3.39426i	0.671848	+	0.740689i
$22$	2.01609	+	3.49197i	0.429831	+	0.744490i
$23$		−	2.48119i		−	0.517363i	−0.965963	−	0.258682i	$-0.916712\pi$
$23$		−	2.48119i		−	0.517363i	0.965963	−	0.258682i	$-0.0832881\pi$
$24$	1.36360	+	1.06799i	0.278343	+	0.218003i
$25$	2.01770	−	3.49476i	0.403541	−	0.698953i
$26$	−0.138085	+	3.60291i	−0.0270806	+	0.706588i
$27$	2.13052	−	4.73929i	0.410018	−	0.912077i
$28$	−2.60776	−	0.446759i	−0.492820	−	0.0844295i
$29$	−3.74921	−	2.16461i	−0.696211	−	0.401958i	0.109724	−	0.993962i	$-0.465003\pi$
$29$	−3.74921	−	2.16461i	−0.696211	−	0.401958i	−0.805935	+	0.592005i	$0.798337\pi$
$30$	5.15482	+	0.730764i	0.941138	+	0.133419i
$31$	−2.95768	+	5.12285i	−0.531215	+	0.920091i	0.468121	+	0.883664i	$0.344931\pi$
$31$	−2.95768	+	5.12285i	−0.531215	+	0.920091i	−0.999336	+	0.0364270i	$0.988402\pi$
$32$	−1.00000			−0.176777
$33$	−0.980263	+	6.91480i	−0.170642	+	1.20371i
$34$	−3.34332			−0.573375
$35$	−7.45993	+	2.75633i	−1.26096	+	0.465905i
$36$	0.718787	+	2.91262i	0.119798	+	0.485436i
$37$		−	2.57002i		−	0.422509i	−0.977431	−	0.211255i	$-0.932245\pi$
$37$		−	2.57002i		−	0.422509i	0.977431	−	0.211255i	$-0.0677549\pi$
$38$	2.56879	−	4.44927i	0.416712	−	0.721767i
$39$	−4.03617	+	4.76543i	−0.646304	+	0.763080i
$40$	−2.60318	+	1.50295i	−0.411599	+	0.237637i
$41$	−6.29653	−	3.63530i	−0.983352	−	0.567739i	−0.0800717	−	0.996789i	$-0.525515\pi$
$41$	−6.29653	−	3.63530i	−0.983352	−	0.567739i	−0.903281	+	0.429050i	$0.858848\pi$
$42$	−3.07879	−	3.39426i	−0.475068	−	0.523746i
$43$	−2.23692	−	3.87445i	−0.341127	−	0.590849i	0.643516	−	0.765433i	$-0.277475\pi$
$43$	−2.23692	−	3.87445i	−0.341127	−	0.590849i	−0.984642	+	0.174584i	$0.944142\pi$
$44$	−2.01609	−	3.49197i	−0.303937	−	0.526434i
$45$	6.24865	+	6.50178i	0.931493	+	0.969227i
$46$			2.48119i			0.365831i
$47$	−5.77285	+	3.33296i	−0.842057	+	0.486162i	−0.857963	−	0.513712i	$-0.828270\pi$
$47$	−5.77285	+	3.33296i	−0.842057	+	0.486162i	0.0159060	+	0.999873i	$0.494937\pi$
$48$	−1.36360	−	1.06799i	−0.196818	−	0.154151i
$49$	6.60081	+	2.33008i	0.942973	+	0.332869i
$50$	−2.01770	+	3.49476i	−0.285346	+	0.494234i
$51$	−4.55894	−	3.57064i	−0.638379	−	0.499990i
$52$	0.138085	−	3.60291i	0.0191489	−	0.499633i
$53$	−8.50304	−	4.90923i	−1.16798	−	0.674335i	−0.214779	−	0.976663i	$-0.568903\pi$
$53$	−8.50304	−	4.90923i	−1.16798	−	0.674335i	−0.953204	+	0.302327i	$0.902236\pi$
$54$	−2.13052	+	4.73929i	−0.289927	+	0.644936i
$55$	−10.4965	−	6.06015i	−1.41535	−	0.817150i
$56$	2.60776	+	0.446759i	0.348476	+	0.0597007i
$57$	8.25457	−	3.32356i	1.09335	−	0.440217i
$58$	3.74921	+	2.16461i	0.492295	+	0.284227i
$59$		−	3.18073i		−	0.414096i	−0.978331	−	0.207048i	$-0.933614\pi$
$59$		−	3.18073i		−	0.414096i	0.978331	−	0.207048i	$-0.0663856\pi$
$60$	−5.15482	−	0.730764i	−0.665485	−	0.0943412i
$61$	−5.77255	−	3.33278i	−0.739099	−	0.426719i	0.0826424	−	0.996579i	$-0.473664\pi$
$61$	−5.77255	−	3.33278i	−0.739099	−	0.426719i	−0.821742	+	0.569860i	$0.806997\pi$
$62$	2.95768	−	5.12285i	0.375626	−	0.650603i
$63$	−0.573184	−	7.91653i	−0.0722144	−	0.997389i
$64$	1.00000			0.125000
$65$	−5.05552	−	9.58655i	−0.627060	−	1.18907i
$66$	0.980263	−	6.91480i	0.120662	−	0.851153i
$67$	7.04993	−	4.07028i	0.861286	−	0.497264i	−0.00315695	−	0.999995i	$-0.501005\pi$
$67$	7.04993	−	4.07028i	0.861286	−	0.497264i	0.864443	+	0.502732i	$0.167672\pi$
$68$	3.34332			0.405437
$69$	−2.64989	+	3.38334i	−0.319009	+	0.407306i
$70$	7.45993	−	2.75633i	0.891632	−	0.329444i
$71$	−0.436496	−	0.756034i	−0.0518026	−	0.0897247i	0.838961	−	0.544191i	$-0.183163\pi$
$71$	−0.436496	−	0.756034i	−0.0518026	−	0.0897247i	−0.890764	+	0.454466i	$0.849830\pi$
$72$	−0.718787	−	2.91262i	−0.0847098	−	0.343255i
$73$	−6.78690	+	11.7553i	−0.794347	+	1.37585i	0.128906	+	0.991657i	$0.458853\pi$
$73$	−6.78690	+	11.7553i	−0.794347	+	1.37585i	−0.923253	+	0.384192i	$0.874480\pi$
$74$			2.57002i			0.298759i
$75$	−6.48371	+	2.61056i	−0.748674	+	0.301441i
$76$	−2.56879	+	4.44927i	−0.294660	+	0.510366i
$77$	3.69740	+	10.0069i	0.421358	+	1.14039i
$78$	4.03617	−	4.76543i	0.457006	−	0.539579i
$79$	8.50477	+	14.7307i	0.956862	+	1.65733i	0.730049	+	0.683395i	$0.239497\pi$
$79$	8.50477	+	14.7307i	0.956862	+	1.65733i	0.226813	+	0.973938i	$0.427169\pi$
$80$	2.60318	−	1.50295i	0.291045	−	0.168035i
$81$	−7.96669	+	4.18710i	−0.885188	+	0.465234i
$82$	6.29653	+	3.63530i	0.695335	+	0.401452i
$83$		−	12.6597i		−	1.38958i	−0.719211	−	0.694792i	$-0.755496\pi$
$83$		−	12.6597i		−	1.38958i	0.719211	−	0.694792i	$-0.244504\pi$
$84$	3.07879	+	3.39426i	0.335924	+	0.370345i
$85$	8.70327	−	5.02484i	0.944002	−	0.545020i
$86$	2.23692	+	3.87445i	0.241213	+	0.417793i
$87$	2.80062	+	6.95578i	0.300258	+	0.745738i
$88$	2.01609	+	3.49197i	0.214916	+	0.372245i
$89$		−	3.63877i		−	0.385709i	−0.981227	−	0.192855i	$-0.938225\pi$
$89$		−	3.63877i		−	0.385709i	0.981227	−	0.192855i	$-0.0617746\pi$
$90$	−6.24865	−	6.50178i	−0.658665	−	0.685347i
$91$	−1.96972	+	9.33382i	−0.206483	+	0.978450i
$92$		−	2.48119i		−	0.258682i
$93$	9.50424	−	3.82672i	0.985544	−	0.396812i
$94$	5.77285	−	3.33296i	0.595424	−	0.343768i
$95$			15.4430i			1.58442i
$96$	1.36360	+	1.06799i	0.139171	+	0.109001i
$97$	1.10676	+	1.91696i	0.112374	+	0.194638i	0.916727	−	0.399514i	$-0.130821\pi$
$97$	1.10676	+	1.91696i	0.112374	+	0.194638i	−0.804353	+	0.594152i	$0.797488\pi$
$98$	−6.60081	−	2.33008i	−0.666783	−	0.235374i
$99$	8.72163	−	8.38208i	0.876557	−	0.842430i
$100$	2.01770	−	3.49476i	0.201770	−	0.349476i
$101$	6.53158	+	11.3130i	0.649917	+	1.12569i	0.983142	+	0.182842i	$0.0585296\pi$
$101$	6.53158	+	11.3130i	0.649917	+	1.12569i	−0.333226	+	0.942847i	$0.608137\pi$
$102$	4.55894	+	3.57064i	0.451402	+	0.353546i
$103$	14.8587	−	8.57869i	1.46407	−	0.845283i	0.464878	−	0.885375i	$-0.346098\pi$
$103$	14.8587	−	8.57869i	1.46407	−	0.845283i	0.999196	+	0.0400914i	$0.0127649\pi$
$104$	−0.138085	+	3.60291i	−0.0135403	+	0.353294i
$105$	13.1161	+	4.20862i	1.28000	+	0.410719i
$106$	8.50304	+	4.90923i	0.825889	+	0.476827i
$107$			2.02353i			0.195622i	0.995205	+	0.0978109i	$0.0311840\pi$
$107$			2.02353i			0.195622i	−0.995205	+	0.0978109i	$0.968816\pi$
$108$	2.13052	−	4.73929i	0.205009	−	0.456039i
$109$	−11.9872	−	6.92083i	−1.14817	−	0.662895i	−0.199728	−	0.979851i	$-0.564006\pi$
$109$	−11.9872	−	6.92083i	−1.14817	−	0.662895i	−0.948440	+	0.316956i	$0.897339\pi$
$110$	10.4965	+	6.06015i	1.00080	+	0.577813i
$111$	−2.74476	+	3.50447i	−0.260521	+	0.332630i
$112$	−2.60776	−	0.446759i	−0.246410	−	0.0422148i
$113$	12.1559	−	7.01820i	1.14353	−	0.660217i	0.196227	−	0.980559i	$-0.437131\pi$
$113$	12.1559	−	7.01820i	1.14353	−	0.660217i	0.947302	+	0.320342i	$0.103798\pi$
$114$	−8.25457	+	3.32356i	−0.773112	+	0.311280i
$115$	−3.72910	−	6.45898i	−0.347740	−	0.602303i
$116$	−3.74921	−	2.16461i	−0.348105	−	0.200979i
$117$	10.5931	−	2.18753i	0.979336	−	0.202238i
$118$			3.18073i			0.292810i
$119$	−8.71857	−	1.49366i	−0.799230	−	0.136924i
$120$	5.15482	+	0.730764i	0.470569	+	0.0667093i
$121$	−2.62922	+	4.55395i	−0.239020	+	0.413995i
$122$	5.77255	+	3.33278i	0.522622	+	0.301736i
$123$	4.70344	+	11.6817i	0.424095	+	1.05331i
$124$	−2.95768	+	5.12285i	−0.265607	+	0.460046i
$125$			2.89947i			0.259336i
$126$	0.573184	+	7.91653i	0.0510633	+	0.705261i
$127$	8.26677	−	14.3185i	0.733558	−	1.27056i	−0.221796	−	0.975093i	$-0.571192\pi$
$127$	8.26677	−	14.3185i	0.733558	−	1.27056i	0.955353	−	0.295466i	$-0.0954748\pi$
$128$	−1.00000			−0.0883883
$129$	−1.08763	+	7.67220i	−0.0957609	+	0.675499i
$130$	5.05552	+	9.58655i	0.443398	+	0.840796i
$131$	−4.18649	−	7.25122i	−0.365776	−	0.633542i	0.623125	−	0.782122i	$-0.285863\pi$
$131$	−4.18649	−	7.25122i	−0.365776	−	0.633542i	−0.988900	+	0.148581i	$0.952530\pi$
$132$	−0.980263	+	6.91480i	−0.0853210	+	0.601856i
$133$	8.68653	−	10.4550i	0.753218	−	0.906563i
$134$	−7.04993	+	4.07028i	−0.609021	+	0.351618i
$135$	−1.57678	−	15.5393i	−0.135708	−	1.33741i
$136$	−3.34332			−0.286687
$137$	20.8869			1.78449			0.892244	−	0.451553i	$-0.149130\pi$
$137$	20.8869			1.78449			0.892244	+	0.451553i	$0.149130\pi$
$138$	2.64989	−	3.38334i	0.225573	−	0.288009i
$139$	12.4500	−	7.18799i	1.05599	−	0.609677i	0.131671	−	0.991293i	$-0.457966\pi$
$139$	12.4500	−	7.18799i	1.05599	−	0.609677i	0.924321	+	0.381616i	$0.124632\pi$
$140$	−7.45993	+	2.75633i	−0.630479	+	0.232952i
$141$	11.4314	+	1.62055i	0.962698	+	0.136475i
$142$	0.436496	+	0.756034i	0.0366300	+	0.0634450i
$143$	−12.8596	+	6.78159i	−1.07538	+	0.567105i
$144$	0.718787	+	2.91262i	0.0598989	+	0.242718i
$145$	−13.0132			−1.08068
$146$	6.78690	−	11.7553i	0.561688	−	0.972872i
$147$	−6.51233	−	10.2269i	−0.537128	−	0.843501i
$148$		−	2.57002i		−	0.211255i
$149$	4.93899	−	8.55458i	0.404618	−	0.700818i	−0.589659	−	0.807652i	$-0.700738\pi$
$149$	4.93899	−	8.55458i	0.404618	−	0.700818i	0.994277	+	0.106834i	$0.0340713\pi$
$150$	6.48371	−	2.61056i	0.529393	−	0.213151i
$151$	−4.74145	−	2.73748i	−0.385854	−	0.222773i	0.294508	−	0.955649i	$-0.404844\pi$
$151$	−4.74145	−	2.73748i	−0.385854	−	0.222773i	−0.680362	+	0.732876i	$0.738178\pi$
$152$	2.56879	−	4.44927i	0.208356	−	0.360884i
$153$	2.40313	+	9.73782i	0.194282	+	0.787256i
$154$	−3.69740	−	10.0069i	−0.297945	−	0.806380i
$155$			17.7809i			1.42820i
$156$	−4.03617	+	4.76543i	−0.323152	+	0.381540i
$157$	−7.68837	−	4.43888i	−0.613598	−	0.354261i	0.160774	−	0.986991i	$-0.448601\pi$
$157$	−7.68837	−	4.43888i	−0.613598	−	0.354261i	−0.774372	+	0.632730i	$0.781934\pi$
$158$	−8.50477	−	14.7307i	−0.676603	−	1.17191i
$159$	6.35169	+	15.7754i	0.503722	+	1.25107i
$160$	−2.60318	+	1.50295i	−0.205800	+	0.118818i
$161$	−1.10849	+	6.47034i	−0.0873615	+	0.509934i
$162$	7.96669	−	4.18710i	0.625922	−	0.328970i
$163$	4.75335	+	2.74435i	0.372311	+	0.214954i	0.674468	−	0.738304i	$-0.264373\pi$
$163$	4.75335	+	2.74435i	0.372311	+	0.214954i	−0.302157	+	0.953258i	$0.597707\pi$
$164$	−6.29653	−	3.63530i	−0.491676	−	0.283869i
$165$	7.84078	+	19.4738i	0.610404	+	1.51603i
$166$			12.6597i			0.982584i
$167$	−3.01387	−	1.74006i	−0.233221	−	0.134650i	0.378836	−	0.925464i	$-0.376324\pi$
$167$	−3.01387	−	1.74006i	−0.233221	−	0.134650i	−0.612057	+	0.790814i	$0.709658\pi$
$168$	−3.07879	−	3.39426i	−0.237534	−	0.261873i
$169$	−12.9619	−	0.995011i	−0.997067	−	0.0765393i
$170$	−8.70327	+	5.02484i	−0.667510	+	0.385387i
$171$	−14.8054	−	4.28382i	−1.13220	−	0.327592i
$172$	−2.23692	−	3.87445i	−0.170563	−	0.295424i
$173$	−5.87790	+	10.1808i	−0.446888	+	0.774033i	−0.998182	−	0.0602784i	$-0.980801\pi$
$173$	−5.87790	+	10.1808i	−0.446888	+	0.774033i	0.551293	+	0.834311i	$0.314134\pi$
$174$	−2.80062	−	6.95578i	−0.212315	−	0.527316i
$175$	−6.82300	+	8.21208i	−0.515770	+	0.620775i
$176$	−2.01609	−	3.49197i	−0.151968	−	0.263217i
$177$	−3.39700	+	4.33723i	−0.255334	+	0.326006i
$178$			3.63877i			0.272738i
$179$	9.26309	−	5.34805i	0.692356	−	0.399732i	−0.112138	−	0.993693i	$-0.535770\pi$
$179$	9.26309	−	5.34805i	0.692356	−	0.399732i	0.804494	+	0.593961i	$0.202437\pi$
$180$	6.24865	+	6.50178i	0.465747	+	0.484614i
$181$		−	15.8900i		−	1.18110i	−0.807002	−	0.590549i	$-0.798911\pi$
$181$		−	15.8900i		−	1.18110i	0.807002	−	0.590549i	$-0.201089\pi$
$182$	1.96972	−	9.33382i	0.146006	−	0.691869i
$183$	4.31204	+	10.7096i	0.318755	+	0.791677i
$184$			2.48119i			0.182916i
$185$	−3.86261	−	6.69024i	−0.283985	−	0.491876i
$186$	−9.50424	+	3.82672i	−0.696885	+	0.280589i
$187$	−6.74043	−	11.6748i	−0.492909	−	0.853743i
$188$	−5.77285	+	3.33296i	−0.421028	+	0.243081i
$189$	−7.67320	+	11.4071i	−0.558143	+	0.829745i
$190$		−	15.4430i		−	1.12035i
$191$	14.9297	+	8.61966i	1.08027	+	0.623697i	0.930970	−	0.365095i	$-0.118963\pi$
$191$	14.9297	+	8.61966i	1.08027	+	0.623697i	0.149304	+	0.988791i	$0.452297\pi$
$192$	−1.36360	−	1.06799i	−0.0984090	−	0.0770757i
$193$	10.8338	−	6.25490i	0.779834	−	0.450237i	−0.0565375	−	0.998400i	$-0.518006\pi$
$193$	10.8338	−	6.25490i	0.779834	−	0.450237i	0.836371	+	0.548163i	$0.184673\pi$
$194$	−1.10676	−	1.91696i	−0.0794606	−	0.137630i
$195$	−3.34467	+	18.4714i	−0.239517	+	1.32277i
$196$	6.60081	+	2.33008i	0.471487	+	0.166434i
$197$	5.30659	−	9.19128i	0.378079	−	0.654852i	−0.612704	−	0.790313i	$-0.709918\pi$
$197$	5.30659	−	9.19128i	0.378079	−	0.654852i	0.990783	+	0.135461i	$0.0432515\pi$
$198$	−8.72163	+	8.38208i	−0.619819	+	0.595688i
$199$			7.58421i			0.537630i	0.963192	+	0.268815i	$0.0866320\pi$
$199$			7.58421i			0.537630i	−0.963192	+	0.268815i	$0.913368\pi$
$200$	−2.01770	+	3.49476i	−0.142673	+	0.247117i
$201$	−13.9603	−	1.97905i	−0.984682	−	0.139592i
$202$	−6.53158	−	11.3130i	−0.459560	−	0.795982i
$203$	8.80998	+	7.31977i	0.618339	+	0.513747i
$204$	−4.55894	−	3.57064i	−0.319190	−	0.249995i
$205$	−21.8547			−1.52640
$206$	−14.8587	+	8.57869i	−1.03526	+	0.597706i
$207$	7.22675	−	1.78345i	0.502294	−	0.123958i
$208$	0.138085	−	3.60291i	0.00957444	−	0.249817i
$209$	20.7156			1.43293
$210$	−13.1161	−	4.20862i	−0.905094	−	0.290422i
$211$	5.81722	−	10.0757i	0.400474	−	0.693641i	−0.593309	−	0.804975i	$-0.702179\pi$
$211$	5.81722	−	10.0757i	0.400474	−	0.693641i	0.993783	+	0.111334i	$0.0355123\pi$
$212$	−8.50304	−	4.90923i	−0.583991	−	0.337168i
$213$	−0.212233	+	1.49710i	−0.0145420	+	0.102580i
$214$		−	2.02353i		−	0.138325i
$215$	−11.6462	−	6.72394i	−0.794264	−	0.458569i
$216$	−2.13052	+	4.73929i	−0.144963	+	0.322468i
$217$	10.0016	−	12.0378i	0.678953	−	0.817178i
$218$	11.9872	+	6.92083i	0.811877	+	0.468738i
$219$	21.8091	−	8.78107i	1.47372	−	0.593369i
$220$	−10.4965	−	6.06015i	−0.707673	−	0.408575i
$221$	0.461661	−	12.0457i	0.0310547	−	0.810280i
$222$	2.74476	−	3.50447i	0.184216	−	0.235205i
$223$	−0.696107	+	1.20569i	−0.0466148	+	0.0807391i	−0.888391	−	0.459087i	$-0.848177\pi$
$223$	−0.696107	+	1.20569i	−0.0466148	+	0.0807391i	0.841777	+	0.539826i	$0.181510\pi$
$224$	2.60776	+	0.446759i	0.174238	+	0.0298504i
$225$	11.6292	+	3.36481i	0.775281	+	0.224321i
$226$	−12.1559	+	7.01820i	−0.808597	+	0.466844i
$227$		−	7.24063i		−	0.480577i	−0.970701	−	0.240289i	$-0.922758\pi$
$227$		−	7.24063i		−	0.480577i	0.970701	−	0.240289i	$-0.0772421\pi$
$228$	8.25457	−	3.32356i	0.546673	−	0.220108i
$229$	12.0113	+	20.8043i	0.793732	+	1.37478i	0.923641	+	0.383258i	$0.125198\pi$
$229$	12.0113	+	20.8043i	0.793732	+	1.37478i	−0.129909	+	0.991526i	$0.541469\pi$
$230$	3.72910	+	6.45898i	0.245889	+	0.425893i
$231$	5.64554	−	17.5942i	0.371449	−	1.15761i
$232$	3.74921	+	2.16461i	0.246148	+	0.142113i
$233$	−3.29311	+	1.90128i	−0.215739	+	0.124557i	−0.603976	−	0.797003i	$-0.706418\pi$
$233$	−3.29311	+	1.90128i	−0.215739	+	0.124557i	0.388237	+	0.921560i	$0.373084\pi$
$234$	−10.5931	+	2.18753i	−0.692495	+	0.143004i
$235$	−10.0185	+	17.3526i	−0.653536	+	1.13196i
$236$		−	3.18073i		−	0.207048i
$237$	4.13519	−	29.1697i	0.268610	−	1.89478i
$238$	8.71857	+	1.49366i	0.565141	+	0.0968195i
$239$	−8.77151			−0.567382			−0.283691	−	0.958916i	$-0.591559\pi$
$239$	−8.77151			−0.567382			−0.283691	+	0.958916i	$0.591559\pi$
$240$	−5.15482	−	0.730764i	−0.332742	−	0.0471706i
$241$	5.66694			0.365040			0.182520	−	0.983202i	$-0.441575\pi$
$241$	5.66694			0.365040			0.182520	+	0.983202i	$0.441575\pi$
$242$	2.62922	−	4.55395i	0.169013	−	0.292739i
$243$	15.3351	+	2.79884i	0.983750	+	0.179546i
$244$	−5.77255	−	3.33278i	−0.369550	−	0.213360i
$245$	20.6851	−	3.85505i	1.32152	−	0.246290i
$246$	−4.70344	−	11.6817i	−0.299881	−	0.744799i
$247$	15.6756	+	9.86948i	0.997414	+	0.627980i
$248$	2.95768	−	5.12285i	0.187813	−	0.325301i
$249$	−13.5205	+	17.2627i	−0.856825	+	1.09398i
$250$		−	2.89947i		−	0.183378i
$251$	4.10301	+	7.10662i	0.258980	+	0.448566i	0.965969	−	0.258658i	$-0.0832804\pi$
$251$	4.10301	+	7.10662i	0.258980	+	0.448566i	−0.706989	+	0.707224i	$0.749947\pi$
$252$	−0.573184	−	7.91653i	−0.0361072	−	0.498695i
$253$	−8.66423	+	5.00229i	−0.544715	+	0.314491i
$254$	−8.26677	+	14.3185i	−0.518703	+	0.898421i
$255$	−17.2342	−	2.44318i	−1.07925	−	0.152998i
$256$	1.00000			0.0625000
$257$	−27.0624			−1.68810			−0.844052	−	0.536261i	$-0.819836\pi$
$257$	−27.0624			−1.68810			−0.844052	+	0.536261i	$0.819836\pi$
$258$	1.08763	−	7.67220i	0.0677132	−	0.477650i
$259$	−1.14818	+	6.70200i	−0.0713445	+	0.416442i
$260$	−5.05552	−	9.58655i	−0.313530	−	0.594533i
$261$	3.60979	−	12.4759i	0.223441	−	0.772240i
$262$	4.18649	+	7.25122i	0.258642	+	0.447982i
$263$	−12.6627	+	7.31080i	−0.780814	+	0.450803i	−0.836719	−	0.547633i	$-0.815529\pi$
$263$	−12.6627	+	7.31080i	−0.780814	+	0.450803i	0.0559046	+	0.998436i	$0.482196\pi$
$264$	0.980263	−	6.91480i	0.0603310	−	0.425576i
$265$	−29.5133			−1.81299
$266$	−8.68653	+	10.4550i	−0.532606	+	0.641037i
$267$	−3.88618	+	4.96182i	−0.237830	+	0.303658i
$268$	7.04993	−	4.07028i	0.430643	−	0.248632i
$269$	28.7012			1.74994			0.874970	−	0.484177i	$-0.160881\pi$
$269$	28.7012			1.74994			0.874970	+	0.484177i	$0.160881\pi$
$270$	1.57678	+	15.5393i	0.0959600	+	0.945691i
$271$	7.22007			0.438588			0.219294	−	0.975659i	$-0.429625\pi$
$271$	7.22007			0.438588			0.219294	+	0.975659i	$0.429625\pi$
$272$	3.34332			0.202719
$273$	12.6543	−	10.6239i	0.765876	−	0.642988i
$274$	−20.8869			−1.26182
$275$	−16.2715			−0.981207
$276$	−2.64989	+	3.38334i	−0.159505	+	0.203653i
$277$	20.2042			1.21395			0.606976	−	0.794720i	$-0.292382\pi$
$277$	20.2042			1.21395			0.606976	+	0.794720i	$0.292382\pi$
$278$	−12.4500	+	7.18799i	−0.746699	+	0.431107i
$279$	−17.0469	−	4.93235i	−1.02057	−	0.295292i
$280$	7.45993	−	2.75633i	0.445816	−	0.164722i
$281$	5.71978			0.341214			0.170607	−	0.985339i	$-0.445427\pi$
$281$	5.71978			0.341214			0.170607	+	0.985339i	$0.445427\pi$
$282$	−11.4314	−	1.62055i	−0.680730	−	0.0965024i
$283$	−2.40181	+	1.38668i	−0.142773	+	0.0824298i	−0.569685	−	0.821863i	$-0.692935\pi$
$283$	−2.40181	+	1.38668i	−0.142773	+	0.0824298i	0.426912	+	0.904293i	$0.359601\pi$
$284$	−0.436496	−	0.756034i	−0.0259013	−	0.0448624i
$285$	16.4930	−	21.0580i	0.976962	−	1.24737i
$286$	12.8596	−	6.78159i	0.760405	−	0.401004i
$287$	14.7957	+	12.2930i	0.873364	+	0.725634i
$288$	−0.718787	−	2.91262i	−0.0423549	−	0.171628i
$289$	−5.82221			−0.342483
$290$	13.0132			0.764160
$291$	0.538129	−	3.79597i	0.0315457	−	0.222524i
$292$	−6.78690	+	11.7553i	−0.397173	+	0.687925i
$293$	−11.4769	+	6.62619i	−0.670488	+	0.387106i	−0.796261	−	0.604953i	$-0.793192\pi$
$293$	−11.4769	+	6.62619i	−0.670488	+	0.387106i	0.125774	+	0.992059i	$0.459859\pi$
$294$	6.51233	+	10.2269i	0.379807	+	0.596445i
$295$	−4.78047	−	8.28002i	−0.278330	−	0.482082i
$296$			2.57002i			0.149380i
$297$	−20.8448	+	2.11513i	−1.20954	+	0.122732i
$298$	−4.93899	+	8.55458i	−0.286108	+	0.495553i
$299$	−8.93949	−	0.342614i	−0.516984	−	0.0198139i
$300$	−6.48371	+	2.61056i	−0.374337	+	0.150720i
$301$	4.10239	+	11.1030i	0.236458	+	0.639966i
$302$	4.74145	+	2.73748i	0.272840	+	0.157524i
$303$	3.17579	−	22.4021i	0.182444	−	1.28697i
$304$	−2.56879	+	4.44927i	−0.147330	+	0.255183i
$305$	−20.0360			−1.14726
$306$	−2.40313	−	9.73782i	−0.137378	−	0.556674i
$307$	−20.2861			−1.15779			−0.578894	−	0.815403i	$-0.696516\pi$
$307$	−20.2861			−1.15779			−0.578894	+	0.815403i	$0.696516\pi$
$308$	3.69740	+	10.0069i	0.210679	+	0.570197i
$309$	−29.4233	−	4.17113i	−1.67383	−	0.237288i
$310$		−	17.7809i		−	1.00989i
$311$	8.05505	−	13.9518i	0.456760	−	0.791131i	−0.542028	−	0.840361i	$-0.682343\pi$
$311$	8.05505	−	13.9518i	0.456760	−	0.791131i	0.998788	+	0.0492293i	$0.0156765\pi$
$312$	4.03617	−	4.76543i	0.228503	−	0.269790i
$313$	−23.6806	+	13.6720i	−1.33851	+	0.772789i	−0.986586	−	0.163240i	$-0.947805\pi$
$313$	−23.6806	+	13.6720i	−1.33851	+	0.772789i	−0.351923	+	0.936029i	$0.614472\pi$
$314$	7.68837	+	4.43888i	0.433880	+	0.250501i
$315$	−13.3902	−	19.7467i	−0.754454	−	1.11260i
$316$	8.50477	+	14.7307i	0.478431	+	0.828667i
$317$	−13.0955	−	22.6820i	−0.735514	−	1.27395i	−0.954497	−	0.298219i	$-0.903607\pi$
$317$	−13.0955	−	22.6820i	−0.735514	−	1.27395i	0.218983	−	0.975729i	$-0.429726\pi$
$318$	−6.35169	−	15.7754i	−0.356185	−	0.884640i
$319$			17.4562i			0.977357i
$320$	2.60318	−	1.50295i	0.145522	−	0.0840173i
$321$	2.16111	−	2.75927i	0.120621	−	0.154008i
$322$	1.10849	−	6.47034i	0.0617739	−	0.360578i
$323$	−8.58828	+	14.8753i	−0.477865	+	0.827686i
$324$	−7.96669	+	4.18710i	−0.442594	+	0.232617i
$325$	−12.3127	−	7.75217i	−0.682985	−	0.430013i
$326$	−4.75335	−	2.74435i	−0.263264	−	0.151995i
$327$	8.95434	+	22.2395i	0.495176	+	1.22985i
$328$	6.29653	+	3.63530i	0.347668	+	0.200726i
$329$	16.5432	−	6.11247i	0.912058	−	0.336992i
$330$	−7.84078	−	19.4738i	−0.431620	−	1.07200i
$331$	−11.7438	−	6.78028i	−0.645497	−	0.372678i	0.141232	−	0.989977i	$-0.454894\pi$
$331$	−11.7438	−	6.78028i	−0.645497	−	0.372678i	−0.786729	+	0.617299i	$0.788227\pi$
$332$		−	12.6597i		−	0.694792i
$333$	7.48550	−	1.84730i	0.410203	−	0.101231i
$334$	3.01387	+	1.74006i	0.164912	+	0.0952119i
$335$	12.2348	−	21.1913i	0.668460	−	1.15781i
$336$	3.07879	+	3.39426i	0.167962	+	0.185172i
$337$	9.84727			0.536415			0.268208	−	0.963361i	$-0.413569\pi$
$337$	9.84727			0.536415			0.268208	+	0.963361i	$0.413569\pi$
$338$	12.9619	+	0.995011i	0.705033	+	0.0541215i
$339$	−24.0711	−	3.41239i	−1.30736	−	0.185336i
$340$	8.70327	−	5.02484i	0.472001	−	0.272510i
$341$	23.8518			1.29165
$342$	14.8054	+	4.28382i	0.800587	+	0.231643i
$343$	−16.1723	−	9.02526i	−0.873224	−	0.487318i
$344$	2.23692	+	3.87445i	0.120606	+	0.208897i
$345$	−1.81316	+	12.7901i	−0.0976174	+	0.688595i
$346$	5.87790	−	10.1808i	0.315998	−	0.547324i
$347$		−	27.2395i		−	1.46229i	−0.682221	−	0.731146i	$-0.738986\pi$
$347$		−	27.2395i		−	1.46229i	0.682221	−	0.731146i	$-0.261014\pi$
$348$	2.80062	+	6.95578i	0.150129	+	0.372869i
$349$	−6.39541	+	11.0772i	−0.342339	+	0.592948i	−0.984867	−	0.173314i	$-0.944552\pi$
$349$	−6.39541	+	11.0772i	−0.342339	+	0.592948i	0.642528	+	0.766262i	$0.277886\pi$
$350$	6.82300	−	8.21208i	0.364705	−	0.438954i
$351$	−16.7810	−	8.33048i	−0.895705	−	0.444648i
$352$	2.01609	+	3.49197i	0.107458	+	0.186122i
$353$	6.71764	−	3.87843i	0.357544	−	0.206428i	−0.310459	−	0.950587i	$-0.600483\pi$
$353$	6.71764	−	3.87843i	0.357544	−	0.206428i	0.668003	+	0.744159i	$0.267149\pi$
$354$	3.39700	−	4.33723i	0.180548	−	0.230521i
$355$	−2.27256	−	1.31206i	−0.120615	−	0.0696370i
$356$		−	3.63877i		−	0.192855i
$357$	10.2934	+	11.3481i	0.544784	+	0.600606i
$358$	−9.26309	+	5.34805i	−0.489570	+	0.282653i
$359$	−0.650209	−	1.12619i	−0.0343167	−	0.0594383i	0.848357	−	0.529425i	$-0.177592\pi$
$359$	−0.650209	−	1.12619i	−0.0343167	−	0.0594383i	−0.882674	+	0.469986i	$0.844259\pi$
$360$	−6.24865	−	6.50178i	−0.329333	−	0.342674i
$361$	−3.69734	−	6.40399i	−0.194597	−	0.337052i
$362$			15.8900i			0.835162i
$363$	8.44878	−	3.40176i	0.443446	−	0.178546i
$364$	−1.96972	+	9.33382i	−0.103242	+	0.489225i
$365$			40.8014i			2.13564i
$366$	−4.31204	−	10.7096i	−0.225394	−	0.559800i
$367$	18.2652	−	10.5454i	0.953437	−	0.550467i	0.0592901	−	0.998241i	$-0.481116\pi$
$367$	18.2652	−	10.5454i	0.953437	−	0.550467i	0.894147	+	0.447774i	$0.147783\pi$
$368$		−	2.48119i		−	0.129341i
$369$	6.06238	−	20.9524i	0.315595	−	1.09074i
$370$	3.86261	+	6.69024i	0.200808	+	0.347809i
$371$	19.9806	+	16.6009i	1.03734	+	0.861877i
$372$	9.50424	−	3.82672i	0.492772	−	0.198406i
$373$	−11.0125	+	19.0742i	−0.570206	+	0.987625i	0.426339	+	0.904564i	$0.359803\pi$
$373$	−11.0125	+	19.0742i	−0.570206	+	0.987625i	−0.996544	+	0.0830618i	$0.973530\pi$
$374$	6.74043	+	11.6748i	0.348539	+	0.603688i
$375$	3.09661	−	3.95370i	0.159908	−	0.204168i
$376$	5.77285	−	3.33296i	0.297712	−	0.171884i
$377$	−8.31659	+	13.2092i	−0.428326	+	0.680306i
$378$	7.67320	−	11.4071i	0.394667	−	0.586718i
$379$	6.24288	+	3.60433i	0.320675	+	0.185142i	0.651694	−	0.758482i	$-0.274059\pi$
$379$	6.24288	+	3.60433i	0.320675	+	0.185142i	−0.331018	+	0.943624i	$0.607392\pi$
$380$			15.4430i			0.792210i
$381$	−26.5645	+	10.6958i	−1.36094	+	0.547960i
$382$	−14.9297	−	8.61966i	−0.763869	−	0.441020i
$383$	−28.3175	−	16.3491i	−1.44696	−	0.835402i	−0.448660	−	0.893703i	$-0.648099\pi$
$383$	−28.3175	−	16.3491i	−1.44696	−	0.835402i	−0.998299	+	0.0583003i	$0.981432\pi$
$384$	1.36360	+	1.06799i	0.0695857	+	0.0545007i
$385$	24.6649	+	20.4928i	1.25704	+	1.04441i
$386$	−10.8338	+	6.25490i	−0.551426	+	0.318366i
$387$	9.67694	−	9.30019i	0.491906	−	0.472755i
$388$	1.10676	+	1.91696i	0.0561872	+	0.0973190i
$389$	24.6307	+	14.2206i	1.24883	+	0.721012i	0.970876	−	0.239583i	$-0.0770108\pi$
$389$	24.6307	+	14.2206i	1.24883	+	0.721012i	0.277953	+	0.960595i	$0.410344\pi$
$390$	3.34467	−	18.4714i	0.169364	−	0.935338i
$391$		−	8.29541i		−	0.419517i
$392$	−6.60081	−	2.33008i	−0.333391	−	0.117687i
$393$	−2.03556	+	14.3589i	−0.102680	+	0.724309i
$394$	−5.30659	+	9.19128i	−0.267342	+	0.463050i
$395$	44.2789	+	25.5645i	2.22792	+	1.28629i
$396$	8.72163	−	8.38208i	0.438278	−	0.421215i
$397$	10.0412	−	17.3918i	0.503952	−	0.872871i	−0.496037	−	0.868301i	$-0.665212\pi$
$397$	10.0412	−	17.3918i	0.503952	−	0.872871i	0.999990	−	0.00456967i	$-0.00145458\pi$
$398$		−	7.58421i		−	0.380162i
$399$	−23.0108	+	4.97924i	−1.15198	+	0.249274i
$400$	2.01770	−	3.49476i	0.100885	−	0.174738i
$401$	5.32156			0.265746			0.132873	−	0.991133i	$-0.457580\pi$
$401$	5.32156			0.265746			0.132873	+	0.991133i	$0.457580\pi$
$402$	13.9603	+	1.97905i	0.696275	+	0.0987061i
$403$	18.0487	+	11.3636i	0.899072	+	0.566063i
$404$	6.53158	+	11.3130i	0.324958	+	0.562844i
$405$	−14.4457	+	22.8733i	−0.717815	+	1.13658i
$406$	−8.80998	−	7.31977i	−0.437232	−	0.363274i
$407$	−8.97444	+	5.18139i	−0.444846	+	0.256832i
$408$	4.55894	+	3.57064i	0.225701	+	0.176773i
$409$	17.5007			0.865356			0.432678	−	0.901548i	$-0.357569\pi$
$409$	17.5007			0.865356			0.432678	+	0.901548i	$0.357569\pi$
$410$	21.8547			1.07933
$411$	−28.4813	−	22.3070i	−1.40488	−	1.10033i
$412$	14.8587	−	8.57869i	0.732037	−	0.422642i
$413$	−1.42102	+	8.29458i	−0.0699239	+	0.408150i
$414$	−7.22675	+	1.78345i	−0.355176	+	0.0876515i
$415$	−19.0269	−	32.9555i	−0.933993	−	1.61772i
$416$	−0.138085	+	3.60291i	−0.00677015	+	0.176647i
$417$	−24.6534	−	3.49495i	−1.20728	−	0.171148i
$418$	−20.7156			−1.01323
$419$	−11.9702	+	20.7329i	−0.584780	+	1.01287i	0.410122	+	0.912030i	$0.365486\pi$
$419$	−11.9702	+	20.7329i	−0.584780	+	1.01287i	−0.994903	+	0.100839i	$0.967847\pi$
$420$	13.1161	+	4.20862i	0.639998	+	0.205360i
$421$			18.4384i			0.898634i	0.893372	+	0.449317i	$0.148333\pi$
$421$			18.4384i			0.898634i	−0.893372	+	0.449317i	$0.851667\pi$
$422$	−5.81722	+	10.0757i	−0.283178	+	0.490478i
$423$	−13.8571	−	14.4184i	−0.673754	−	0.701048i
$424$	8.50304	+	4.90923i	0.412944	+	0.238414i
$425$	6.74583	−	11.6841i	0.327221	−	0.566763i
$426$	0.212233	−	1.49710i	0.0102827	−	0.0725347i
$427$	13.5645	+	11.2700i	0.656431	+	0.545395i
$428$			2.02353i			0.0978109i
$429$	24.7780	+	4.48662i	1.19629	+	0.216616i
$430$	11.6462	+	6.72394i	0.561630	+	0.324257i
$431$	−7.38913	−	12.7984i	−0.355922	−	0.616475i	0.631353	−	0.775495i	$-0.282500\pi$
$431$	−7.38913	−	12.7984i	−0.355922	−	0.616475i	−0.987275	+	0.159020i	$0.949166\pi$
$432$	2.13052	−	4.73929i	0.102505	−	0.228019i
$433$	24.1602	−	13.9489i	1.16107	−	0.670342i	0.209507	−	0.977807i	$-0.432814\pi$
$433$	24.1602	−	13.9489i	1.16107	−	0.670342i	0.951559	+	0.307465i	$0.0994807\pi$
$434$	−10.0016	+	12.0378i	−0.480092	+	0.577832i
$435$	17.7447	+	13.8980i	0.850793	+	0.666356i
$436$	−11.9872	−	6.92083i	−0.574084	−	0.331447i
$437$	11.0395	+	6.37365i	0.528090	+	0.304893i
$438$	−21.8091	+	8.78107i	−1.04208	+	0.419576i
$439$			6.20525i			0.296160i	0.988975	+	0.148080i	$0.0473094\pi$
$439$			6.20525i			0.296160i	−0.988975	+	0.148080i	$0.952691\pi$
$440$	10.4965	+	6.06015i	0.500400	+	0.288906i
$441$	−2.04206	+	20.9005i	−0.0972409	+	0.995261i
$442$	−0.461661	+	12.0457i	−0.0219590	+	0.572954i
$443$	5.47785	−	3.16264i	0.260261	−	0.150261i	−0.364193	−	0.931324i	$-0.618655\pi$
$443$	5.47785	−	3.16264i	0.260261	−	0.150261i	0.624453	+	0.781062i	$0.285322\pi$
$444$	−2.74476	+	3.50447i	−0.130261	+	0.166315i
$445$	−5.46888	−	9.47239i	−0.259250	−	0.449034i
$446$	0.696107	−	1.20569i	0.0329616	−	0.0570912i
$447$	−15.8710	+	6.39019i	−0.750672	+	0.302245i
$448$	−2.60776	−	0.446759i	−0.123205	−	0.0211074i
$449$	−17.8544	−	30.9247i	−0.842600	−	1.45943i	−0.887689	−	0.460444i	$-0.847690\pi$
$449$	−17.8544	−	30.9247i	−0.842600	−	1.45943i	0.0450883	−	0.998983i	$-0.485643\pi$
$450$	−11.6292	−	3.36481i	−0.548206	−	0.158619i
$451$			29.3164i			1.38045i
$452$	12.1559	−	7.01820i	0.571764	−	0.330108i
$453$	3.54182	+	8.79665i	0.166409	+	0.413303i
$454$			7.24063i			0.339819i
$455$	8.90070	+	27.2580i	0.417271	+	1.27788i
$456$	−8.25457	+	3.32356i	−0.386556	+	0.155640i
$457$		−	2.30897i		−	0.108009i	−0.998541	−	0.0540045i	$-0.982801\pi$
$457$		−	2.30897i		−	0.108009i	0.998541	−	0.0540045i	$-0.0171985\pi$
$458$	−12.0113	−	20.8043i	−0.561253	−	0.972119i
$459$	7.12301	−	15.8450i	0.332473	−	0.739580i
$460$	−3.72910	−	6.45898i	−0.173870	−	0.301152i
$461$	−30.3853	+	17.5430i	−1.41519	+	0.817058i	−0.995871	−	0.0907832i	$-0.971063\pi$
$461$	−30.3853	+	17.5430i	−1.41519	+	0.817058i	−0.419315	+	0.907841i	$0.637730\pi$
$462$	−5.64554	+	17.5942i	−0.262654	+	0.818555i
$463$		−	34.0752i		−	1.58361i	−0.610776	−	0.791804i	$-0.709142\pi$
$463$		−	34.0752i		−	1.58361i	0.610776	−	0.791804i	$-0.290858\pi$
$464$	−3.74921	−	2.16461i	−0.174053	−	0.100489i
$465$	18.9899	−	24.2460i	0.880636	−	1.12438i
$466$	3.29311	−	1.90128i	0.152550	−	0.0880751i
$467$	17.7900	+	30.8133i	0.823225	+	1.42587i	0.903268	+	0.429076i	$0.141161\pi$
$467$	17.7900	+	30.8133i	0.823225	+	1.42587i	−0.0800430	+	0.996791i	$0.525506\pi$
$468$	10.5931	−	2.18753i	0.489668	−	0.101119i
$469$	−20.2029	+	7.46468i	−0.932885	+	0.344687i
$470$	10.0185	−	17.3526i	0.462120	−	0.800415i
$471$	5.74314	+	14.2640i	0.264630	+	0.657248i
$472$			3.18073i			0.146405i
$473$	−9.01964	+	15.6225i	−0.414724	+	0.718322i
$474$	−4.13519	+	29.1697i	−0.189936	+	1.33981i
$475$	10.3661	+	17.9546i	0.475629	+	0.823814i
$476$	−8.71857	−	1.49366i	−0.399615	−	0.0684618i
$477$	8.18685	−	28.2948i	0.374850	−	1.29553i
$478$	8.77151			0.401199
$479$	6.44067	−	3.71852i	0.294282	−	0.169904i	−0.345590	−	0.938386i	$-0.612321\pi$
$479$	6.44067	−	3.71852i	0.294282	−	0.169904i	0.639871	+	0.768482i	$0.278988\pi$
$480$	5.15482	+	0.730764i	0.235284	+	0.0333547i
$481$	−9.25955	−	0.354881i	−0.422199	−	0.0161812i
$482$	−5.66694			−0.258122
$483$	8.42181	−	7.63907i	0.383205	−	0.347590i
$484$	−2.62922	+	4.55395i	−0.119510	+	0.206998i
$485$	5.76219	+	3.32680i	0.261647	+	0.151062i
$486$	−15.3351	−	2.79884i	−0.695616	−	0.126958i
$487$		−	17.9702i		−	0.814309i	−0.913359	−	0.407154i	$-0.866521\pi$
$487$		−	17.9702i		−	0.814309i	0.913359	−	0.407154i	$-0.133479\pi$
$488$	5.77255	+	3.33278i	0.261311	+	0.150868i
$489$	−3.55071	−	8.81872i	−0.160569	−	0.398796i
$490$	−20.6851	+	3.85505i	−0.934458	+	0.174154i
$491$	2.56980	+	1.48368i	0.115974	+	0.0669573i	0.556865	−	0.830603i	$-0.312004\pi$
$491$	2.56980	+	1.48368i	0.115974	+	0.0669573i	−0.440891	+	0.897561i	$0.645338\pi$
$492$	4.70344	+	11.6817i	0.212048	+	0.526653i
$493$	−12.5348	−	7.23698i	−0.564540	−	0.325937i
$494$	−15.6756	−	9.86948i	−0.705278	−	0.444049i
$495$	10.1062	−	34.9282i	0.454238	−	1.56991i
$496$	−2.95768	+	5.12285i	−0.132804	+	0.230023i
$497$	0.800512	+	2.16656i	0.0359079	+	0.0971836i
$498$	13.5205	−	17.2627i	0.605867	−	0.773562i
$499$	14.4827	−	8.36158i	0.648334	−	0.374316i	−0.139484	−	0.990224i	$-0.544544\pi$
$499$	14.4827	−	8.36158i	0.648334	−	0.374316i	0.787818	+	0.615909i	$0.211211\pi$
$500$			2.89947i			0.129668i
$501$	2.25133	+	5.59153i	0.100582	+	0.249811i
$502$	−4.10301	−	7.10662i	−0.183126	−	0.317184i
$503$	−13.2712	−	22.9863i	−0.591732	−	1.02491i	−0.993999	−	0.109387i	$-0.965111\pi$
$503$	−13.2712	−	22.9863i	−0.591732	−	1.02491i	0.402268	−	0.915522i	$-0.368222\pi$
$504$	0.573184	+	7.91653i	0.0255316	+	0.352630i
$505$	34.0058	+	19.6333i	1.51324	+	0.873668i
$506$	8.66423	−	5.00229i	0.385172	−	0.222379i
$507$	16.6121	+	15.2000i	0.737768	+	0.675054i
$508$	8.26677	−	14.3185i	0.366779	−	0.635279i
$509$			4.93479i			0.218731i	0.994002	+	0.109365i	$0.0348818\pi$
$509$			4.93479i			0.218731i	−0.994002	+	0.109365i	$0.965118\pi$
$510$	17.2342	+	2.44318i	0.763144	+	0.108186i
$511$	22.9504	−	27.6228i	1.01526	−	1.22196i
$512$	−1.00000			−0.0441942
$513$	15.6135	+	21.6535i	0.689355	+	0.956025i
$514$	27.0624			1.19367
$515$	25.7866	−	44.6638i	1.13630	−	1.96812i
$516$	−1.08763	+	7.67220i	−0.0478804	+	0.337750i
$517$	23.2772	+	13.4391i	1.02373	+	0.591050i
$518$	1.14818	−	6.70200i	0.0504482	−	0.294469i
$519$	18.8881	−	7.60497i	0.829096	−	0.333821i
$520$	5.05552	+	9.58655i	0.221699	+	0.420398i
$521$	3.36581	−	5.82976i	0.147459	−	0.255407i	−0.782829	−	0.622237i	$-0.786224\pi$
$521$	3.36581	−	5.82976i	0.147459	−	0.255407i	0.930288	+	0.366831i	$0.119557\pi$
$522$	−3.60979	+	12.4759i	−0.157996	+	0.546056i
$523$			39.2355i			1.71565i	0.513942	+	0.857825i	$0.328185\pi$
$523$			39.2355i			1.71565i	−0.513942	+	0.857825i	$0.671815\pi$
$524$	−4.18649	−	7.25122i	−0.182888	−	0.316771i
$525$	18.0742	−	3.91104i	0.788825	−	0.170692i
$526$	12.6627	−	7.31080i	0.552119	−	0.318766i
$527$	−9.88847	+	17.1273i	−0.430749	+	0.746078i
$528$	−0.980263	+	6.91480i	−0.0426605	+	0.300928i
$529$	16.8437			0.732335
$530$	29.5133			1.28198
$531$	9.26426	−	2.28627i	0.402035	−	0.0992156i
$532$	8.68653	−	10.4550i	0.376609	−	0.453282i
$533$	−13.9671	+	22.1838i	−0.604982	+	0.960888i
$534$	3.88618	−	4.96182i	0.168171	−	0.214719i
$535$	3.04126	+	5.26761i	0.131485	+	0.227739i
$536$	−7.04993	+	4.07028i	−0.304510	+	0.175809i
$537$	−18.3428	−	2.60033i	−0.791549	−	0.112213i
$538$	−28.7012			−1.23739
$539$	−5.17126	−	27.7475i	−0.222742	−	1.19517i
$540$	−1.57678	−	15.5393i	−0.0678539	−	0.668705i
$541$	23.6391	−	13.6481i	1.01633	−	0.586776i	0.103288	−	0.994652i	$-0.467064\pi$
$541$	23.6391	−	13.6481i	1.01633	−	0.586776i	0.913037	+	0.407876i	$0.133730\pi$
$542$	−7.22007			−0.310129
$543$	−16.9704	+	21.6676i	−0.728271	+	0.929846i
$544$	−3.34332			−0.143344
$545$	−41.6066			−1.78223
$546$	−12.6543	+	10.6239i	−0.541556	+	0.454661i
$547$	31.5392			1.34852			0.674259	−	0.738495i	$-0.264463\pi$
$547$	31.5392			1.34852			0.674259	+	0.738495i	$0.264463\pi$
$548$	20.8869			0.892244
$549$	5.55789	−	19.2088i	0.237205	−	0.819811i
$550$	16.2715			0.693818
$551$	19.2619	−	11.1208i	0.820583	−	0.473764i
$552$	2.64989	−	3.38334i	0.112787	−	0.144004i
$553$	−15.5973	−	42.2137i	−0.663266	−	1.79511i
$554$	−20.2042			−0.858394
$555$	−1.87808	+	13.2480i	−0.0797200	+	0.562347i
$556$	12.4500	−	7.18799i	0.527996	−	0.304839i
$557$	−2.63266	−	4.55989i	−0.111549	−	0.193209i	0.804846	−	0.593484i	$-0.202248\pi$
$557$	−2.63266	−	4.55989i	−0.111549	−	0.193209i	−0.916395	+	0.400275i	$0.868915\pi$
$558$	17.0469	+	4.93235i	0.721651	+	0.208803i
$559$	−14.2682	+	7.52440i	−0.603480	+	0.318248i
$560$	−7.45993	+	2.75633i	−0.315239	+	0.116476i
$561$	−3.27733	+	23.1184i	−0.138369	+	0.976059i
$562$	−5.71978			−0.241275
$563$	−42.1634			−1.77698			−0.888489	−	0.458898i	$-0.848244\pi$
$563$	−42.1634			−1.77698			−0.888489	+	0.458898i	$0.848244\pi$
$564$	11.4314	+	1.62055i	0.481349	+	0.0682375i
$565$	21.0960	−	36.5393i	0.887514	−	1.53722i
$566$	2.40181	−	1.38668i	0.100955	−	0.0582866i
$567$	22.6458	−	7.35976i	0.951036	−	0.309081i
$568$	0.436496	+	0.756034i	0.0183150	+	0.0317225i
$569$		−	4.97346i		−	0.208498i	−0.994551	−	0.104249i	$-0.966756\pi$
$569$		−	4.97346i		−	0.208498i	0.994551	−	0.104249i	$-0.0332439\pi$
$570$	−16.4930	+	21.0580i	−0.690816	+	0.882024i
$571$	8.28254	−	14.3458i	0.346613	−	0.600352i	−0.639032	−	0.769180i	$-0.720665\pi$
$571$	8.28254	−	14.3458i	0.346613	−	0.600352i	0.985646	+	0.168828i	$0.0539983\pi$
$572$	−12.8596	+	6.78159i	−0.537688	+	0.283553i
$573$	−11.1523	−	27.6985i	−0.465895	−	1.15712i
$574$	−14.7957	−	12.2930i	−0.617561	−	0.513101i
$575$	−8.67117	−	5.00630i	−0.361613	−	0.208777i
$576$	0.718787	+	2.91262i	0.0299495	+	0.121359i
$577$	0.888204	−	1.53841i	0.0369764	−	0.0640450i	−0.846945	−	0.531681i	$-0.821561\pi$
$577$	0.888204	−	1.53841i	0.0369764	−	0.0640450i	0.883921	+	0.467636i	$0.154894\pi$
$578$	5.82221			0.242172
$579$	−21.4531	−	3.04126i	−0.891560	−	0.126390i
$580$	−13.0132			−0.540342
$581$	−5.65584	+	33.0135i	−0.234644	+	1.36963i
$582$	−0.538129	+	3.79597i	−0.0223062	+	0.157348i
$583$			39.5898i			1.63964i
$584$	6.78690	−	11.7553i	0.280844	−	0.486436i
$585$	24.2881	−	21.6155i	1.00419	−	0.893690i
$586$	11.4769	−	6.62619i	0.474106	−	0.273725i
$587$	25.1460	+	14.5180i	1.03789	+	0.599224i	0.919234	−	0.393712i	$-0.128809\pi$
$587$	25.1460	+	14.5180i	1.03789	+	0.599224i	0.118652	+	0.992936i	$0.462143\pi$
$588$	−6.51233	−	10.2269i	−0.268564	−	0.421750i
$589$	−15.1953	−	26.3190i	−0.626112	−	1.08446i
$590$	4.78047	+	8.28002i	0.196809	+	0.340883i
$591$	−17.0523	+	6.86580i	−0.701436	+	0.282421i
$592$		−	2.57002i		−	0.105627i
$593$	−32.7140	+	18.8874i	−1.34340	+	0.775614i	−0.987305	−	0.158835i	$-0.949226\pi$
$593$	−32.7140	+	18.8874i	−1.34340	+	0.775614i	−0.356097	+	0.934449i	$0.615893\pi$
$594$	20.8448	−	2.11513i	0.855271	−	0.0867849i
$595$	−24.9409	+	9.21529i	−1.02248	+	0.377790i
$596$	4.93899	−	8.55458i	0.202309	−	0.350409i
$597$	8.09987	−	10.3418i	0.331506	−	0.423261i
$598$	8.93949	+	0.342614i	0.365563	+	0.0140105i
$599$	−37.6285	−	21.7248i	−1.53746	−	0.887653i	−0.998987	−	0.0450101i	$-0.985668\pi$
$599$	−37.6285	−	21.7248i	−1.53746	−	0.887653i	−0.538473	−	0.842643i	$-0.680999\pi$
$600$	6.48371	−	2.61056i	0.264696	−	0.106575i
$601$	13.6314	+	7.87007i	0.556035	+	0.321027i	0.751553	−	0.659673i	$-0.229305\pi$
$601$	13.6314	+	7.87007i	0.556035	+	0.321027i	−0.195518	+	0.980700i	$0.562639\pi$
$602$	−4.10239	−	11.1030i	−0.167201	−	0.452525i
$603$	16.9226	+	17.6081i	0.689140	+	0.717057i
$604$	−4.74145	−	2.73748i	−0.192927	−	0.111386i
$605$			15.8063i			0.642619i
$606$	−3.17579	+	22.4021i	−0.129008	+	0.910022i
$607$	−8.61491	−	4.97382i	−0.349669	−	0.201881i	0.314871	−	0.949135i	$-0.398039\pi$
$607$	−8.61491	−	4.97382i	−0.349669	−	0.201881i	−0.664539	+	0.747253i	$0.731372\pi$
$608$	2.56879	−	4.44927i	0.104178	−	0.180442i
$609$	−4.19580	−	19.3902i	−0.170022	−	0.785730i
$610$	20.0360			0.811234
$611$	11.2112	+	21.2593i	0.453556	+	0.860058i
$612$	2.40313	+	9.73782i	0.0971410	+	0.393628i
$613$	−34.4802	+	19.9071i	−1.39264	+	0.804041i	−0.993607	−	0.112895i	$-0.963988\pi$
$613$	−34.4802	+	19.9071i	−1.39264	+	0.804041i	−0.399034	+	0.916936i	$0.630654\pi$
$614$	20.2861			0.818680
$615$	29.8009	+	23.3406i	1.20169	+	0.941184i
$616$	−3.69740	−	10.0069i	−0.148973	−	0.403190i
$617$	3.33450	+	5.77553i	0.134242	+	0.232514i	0.925308	−	0.379217i	$-0.123807\pi$
$617$	3.33450	+	5.77553i	0.134242	+	0.232514i	−0.791066	+	0.611731i	$0.790473\pi$
$618$	29.4233	+	4.17113i	1.18358	+	0.167788i
$619$	1.64337	−	2.84640i	0.0660526	−	0.114406i	−0.831108	−	0.556111i	$-0.812293\pi$
$619$	1.64337	−	2.84640i	0.0660526	−	0.114406i	0.897160	+	0.441705i	$0.145626\pi$
$620$			17.7809i			0.714100i
$621$	−11.7591	−	5.28622i	−0.471875	−	0.212129i
$622$	−8.05505	+	13.9518i	−0.322978	+	0.559414i
$623$	−1.62566	+	9.48904i	−0.0651305	+	0.380170i
$624$	−4.03617	+	4.76543i	−0.161576	+	0.190770i
$625$	14.4463	+	25.0217i	0.577851	+	1.00087i
$626$	23.6806	−	13.6720i	0.946469	−	0.546444i
$627$	−28.2477	−	22.1241i	−1.12811	−	0.883552i
$628$	−7.68837	−	4.43888i	−0.306799	−	0.177131i
$629$		−	8.59241i		−	0.342602i
$630$	13.3902	+	19.7467i	0.533480	+	0.786727i
$631$	−25.0289	+	14.4504i	−0.996383	+	0.575262i	−0.907176	−	0.420751i	$-0.861767\pi$
$631$	−25.0289	+	14.4504i	−0.996383	+	0.575262i	−0.0892070	+	0.996013i	$0.528433\pi$
$632$	−8.50477	−	14.7307i	−0.338302	−	0.585956i
$633$	−18.6931	+	7.52646i	−0.742985	+	0.299150i
$634$	13.0955	+	22.6820i	0.520087	+	0.900817i
$635$		−	49.6981i		−	1.97221i
$636$	6.35169	+	15.7754i	0.251861	+	0.625535i
$637$	9.30653	−	23.4604i	0.368738	−	0.929533i
$638$		−	17.4562i		−	0.691096i
$639$	1.88829	−	1.81477i	0.0746996	−	0.0717914i
$640$	−2.60318	+	1.50295i	−0.102900	+	0.0594092i
$641$		−	17.0406i		−	0.673065i	−0.941672	−	0.336533i	$-0.890746\pi$
$641$		−	17.0406i		−	0.673065i	0.941672	−	0.336533i	$-0.109254\pi$
$642$	−2.16111	+	2.75927i	−0.0852922	+	0.108900i
$643$	21.5514	+	37.3282i	0.849906	+	1.47208i	0.881291	+	0.472573i	$0.156675\pi$
$643$	21.5514	+	37.3282i	0.849906	+	1.47208i	−0.0313853	+	0.999507i	$0.509992\pi$
$644$	−1.10849	+	6.47034i	−0.0436808	+	0.254967i
$645$	8.69960	+	21.6068i	0.342546	+	0.850766i
$646$	8.58828	−	14.8753i	0.337901	−	0.585263i
$647$	4.56938	+	7.91441i	0.179641	+	0.311147i	0.941758	−	0.336292i	$-0.109173\pi$
$647$	4.56938	+	7.91441i	0.179641	+	0.311147i	−0.762117	+	0.647440i	$0.775840\pi$
$648$	7.96669	−	4.18710i	0.312961	−	0.164485i
$649$	−11.1070	+	6.41264i	−0.435988	+	0.251718i
$650$	12.3127	+	7.75217i	0.482944	+	0.304065i
$651$	−26.4944	+	5.73306i	−1.03840	+	0.224696i
$652$	4.75335	+	2.74435i	0.186156	+	0.107477i
$653$		−	14.5764i		−	0.570420i	−0.958465	−	0.285210i	$-0.907937\pi$
$653$		−	14.5764i		−	0.570420i	0.958465	−	0.285210i	$-0.0920633\pi$
$654$	−8.95434	−	22.2395i	−0.350142	−	0.869632i
$655$	−21.7964	−	12.5842i	−0.851656	−	0.491704i
$656$	−6.29653	−	3.63530i	−0.245838	−	0.141935i
$657$	−39.1169	−	11.3181i	−1.52610	−	0.441562i
$658$	−16.5432	+	6.11247i	−0.644922	+	0.238289i
$659$	−23.2554	+	13.4265i	−0.905901	+	0.523022i	−0.879110	−	0.476619i	$-0.841862\pi$
$659$	−23.2554	+	13.4265i	−0.905901	+	0.523022i	−0.0267913	+	0.999641i	$0.508529\pi$
$660$	7.84078	+	19.4738i	0.305202	+	0.758015i
$661$	−12.5892	−	21.8051i	−0.489663	−	0.848122i	0.510266	−	0.860017i	$-0.329547\pi$
$661$	−12.5892	−	21.8051i	−0.489663	−	0.848122i	−0.999929	+	0.0118949i	$0.996214\pi$
$662$	11.7438	+	6.78028i	0.456435	+	0.263523i
$663$	−13.4942	+	15.9324i	−0.524071	+	0.618762i
$664$			12.6597i			0.491292i
$665$	6.89931	−	40.2717i	0.267544	−	1.56167i
$666$	−7.48550	+	1.84730i	−0.290057	+	0.0715814i
$667$	−5.37080	+	9.30250i	−0.207958	+	0.360194i
$668$	−3.01387	−	1.74006i	−0.116610	−	0.0673250i
$669$	2.23688	−	0.900641i	0.0864827	−	0.0348208i
$670$	−12.2348	+	21.1913i	−0.472673	+	0.818693i
$671$			26.8767i			1.03757i
$672$	−3.07879	−	3.39426i	−0.118767	−	0.130937i
$673$	−9.27973	+	16.0730i	−0.357707	+	0.619567i	−0.987577	−	0.157133i	$-0.949775\pi$
$673$	−9.27973	+	16.0730i	−0.357707	+	0.619567i	0.629870	+	0.776700i	$0.283108\pi$
$674$	−9.84727			−0.379303
$675$	−12.2640	−	17.0081i	−0.472040	−	0.654644i
$676$	−12.9619	−	0.995011i	−0.498533	−	0.0382697i
$677$	9.29724	+	16.1033i	0.357322	+	0.618900i	0.987512	−	0.157541i	$-0.0503566\pi$
$677$	9.29724	+	16.1033i	0.357322	+	0.618900i	−0.630191	+	0.776441i	$0.717023\pi$
$678$	24.0711	+	3.41239i	0.924445	+	0.131052i
$679$	−2.02974	−	5.49343i	−0.0778942	−	0.210818i
$680$	−8.70327	+	5.02484i	−0.333755	+	0.192694i
$681$	−7.73293	+	9.87329i	−0.296326	+	0.378345i
$682$	−23.8518			−0.913331
$683$	33.1927			1.27008			0.635041	−	0.772478i	$-0.280983\pi$
$683$	33.1927			1.27008			0.635041	+	0.772478i	$0.280983\pi$
$684$	−14.8054	−	4.28382i	−0.566100	−	0.163796i
$685$	54.3724	−	31.3919i	2.07746	−	1.19942i
$686$	16.1723	+	9.02526i	0.617463	+	0.344586i
$687$	5.84016	−	41.1966i	0.222816	−	1.57175i
$688$	−2.23692	−	3.87445i	−0.0852816	−	0.147712i
$689$	−18.8617	+	29.9578i	−0.718572	+	1.14130i
$690$	1.81316	−	12.7901i	0.0690259	−	0.486910i
$691$	−20.6733			−0.786449			−0.393224	−	0.919443i	$-0.628640\pi$
$691$	−20.6733			−0.786449			−0.393224	+	0.919443i	$0.628640\pi$
$692$	−5.87790	+	10.1808i	−0.223444	+	0.387016i
$693$	−26.4887	+	17.9620i	−1.00622	+	0.682319i
$694$			27.2395i			1.03400i
$695$	21.6063	−	37.4233i	0.819575	−	1.41955i
$696$	−2.80062	−	6.95578i	−0.106157	−	0.263658i
$697$	−21.0513	−	12.1540i	−0.797375	−	0.460365i
$698$	6.39541	−	11.0772i	0.242070	−	0.419277i
$699$	6.52103	+	0.924441i	0.246648	+	0.0349656i
$700$	−6.82300	+	8.21208i	−0.257885	+	0.310387i
$701$		−	5.92119i		−	0.223640i	−0.993728	−	0.111820i	$-0.964332\pi$
$701$		−	5.92119i		−	0.223640i	0.993728	−	0.111820i	$-0.0356681\pi$
$702$	16.7810	+	8.33048i	0.633359	+	0.314414i
$703$	11.4347	+	6.60184i	0.431269	+	0.248993i
$704$	−2.01609	−	3.49197i	−0.0759842	−	0.131608i
$705$	32.1936	−	12.9622i	1.21248	−	0.488185i
$706$	−6.71764	+	3.87843i	−0.252822	+	0.145967i
$707$	−11.9786	−	32.4197i	−0.450501	−	1.21927i
$708$	−3.39700	+	4.33723i	−0.127667	+	0.163003i
$709$	−33.7421	−	19.4810i	−1.26721	−	0.731624i	−0.292750	−	0.956189i	$-0.594570\pi$
$709$	−33.7421	−	19.4810i	−1.26721	−	0.731624i	−0.974459	+	0.224565i	$0.927904\pi$
$710$	2.27256	+	1.31206i	0.0852876	+	0.0492408i
$711$	−36.7918	+	35.3594i	−1.37980	+	1.32608i
$712$			3.63877i			0.136369i
$713$	12.7108	+	7.33856i	0.476022	+	0.274831i
$714$	−10.2934	−	11.3481i	−0.385221	−	0.424692i
$715$	−23.2836	+	36.9810i	−0.870756	+	1.38301i
$716$	9.26309	−	5.34805i	0.346178	−	0.199866i
$717$	11.9608	+	9.36790i	0.446684	+	0.349851i
$718$	0.650209	+	1.12619i	0.0242656	+	0.0420292i
$719$	−12.2366	+	21.1944i	−0.456347	+	0.790416i	−0.998765	−	0.0496928i	$-0.984176\pi$
$719$	−12.2366	+	21.1944i	−0.456347	+	0.790416i	0.542418	+	0.840109i	$0.317509\pi$
$720$	6.24865	+	6.50178i	0.232873	+	0.242307i
$721$	−42.5806	+	15.7329i	−1.58578	+	0.585923i
$722$	3.69734	+	6.40399i	0.137601	+	0.238332i
$723$	−7.72741	−	6.05224i	−0.287386	−	0.225085i
$724$		−	15.8900i		−	0.590549i
$725$	−15.1296	+	8.73507i	−0.561899	+	0.324412i
$726$	−8.44878	+	3.40176i	−0.313564	+	0.126251i
$727$			49.5341i			1.83712i	0.395283	+	0.918560i	$0.370647\pi$
$727$			49.5341i			1.83712i	−0.395283	+	0.918560i	$0.629353\pi$
$728$	1.96972	−	9.33382i	0.0730028	−	0.345934i
$729$	−17.9218	−	20.1943i	−0.663770	−	0.747937i
$730$		−	40.8014i		−	1.51013i
$731$	−7.47873	−	12.9535i	−0.276611	−	0.479104i
$732$	4.31204	+	10.7096i	0.159378	+	0.395838i
$733$	−17.0909	−	29.6023i	−0.631266	−	1.09338i	−0.987293	−	0.158909i	$-0.949202\pi$
$733$	−17.0909	−	29.6023i	−0.631266	−	1.09338i	0.356027	−	0.934476i	$-0.384131\pi$
$734$	−18.2652	+	10.5454i	−0.674182	+	0.389239i
$735$	−32.3233	−	16.8348i	−1.19226	−	0.620960i
$736$			2.48119i			0.0914578i
$737$	−28.4265	−	16.4121i	−1.04711	−	0.604547i
$738$	−6.06238	+	20.9524i	−0.223159	+	0.771268i
$739$	5.40583	−	3.12105i	0.198857	−	0.114810i	−0.397265	−	0.917704i	$-0.630041\pi$
$739$	5.40583	−	3.12105i	0.198857	−	0.114810i	0.596122	+	0.802894i	$0.296707\pi$
$740$	−3.86261	−	6.69024i	−0.141992	−	0.245938i
$741$	−10.8347	−	30.1994i	−0.398021	−	1.10940i
$742$	−19.9806	−	16.6009i	−0.733512	−	0.609439i
$743$	−3.45608	+	5.98611i	−0.126791	+	0.219609i	−0.922432	−	0.386160i	$-0.873801\pi$
$743$	−3.45608	+	5.98611i	−0.126791	+	0.219609i	0.795640	+	0.605769i	$0.207135\pi$
$744$	−9.50424	+	3.82672i	−0.348442	+	0.140294i
$745$		−	29.6922i		−	1.08784i
$746$	11.0125	−	19.0742i	0.403196	−	0.698357i
$747$	36.8729	−	9.09964i	1.34911	−	0.332938i
$748$	−6.74043	−	11.6748i	−0.246455	−	0.426872i
$749$	0.904029	−	5.27687i	0.0330325	−	0.192813i
$750$	−3.09661	+	3.95370i	−0.113072	+	0.144369i
$751$	41.1695			1.50229			0.751147	−	0.660135i	$-0.229501\pi$
$751$	41.1695			1.50229			0.751147	+	0.660135i	$0.229501\pi$
$752$	−5.77285	+	3.33296i	−0.210514	+	0.121540i
$753$	1.99497	−	14.0725i	0.0727006	−	0.512832i
$754$	8.31659	−	13.2092i	0.302872	−	0.481049i
$755$	−16.4572			−0.598937
$756$	−7.67320	+	11.4071i	−0.279072	+	0.414872i
$757$	2.12231	−	3.67595i	0.0771367	−	0.133605i	−0.824877	−	0.565313i	$-0.808756\pi$
$757$	2.12231	−	3.67595i	0.0771367	−	0.133605i	0.902013	+	0.431708i	$0.142089\pi$
$758$	−6.24288	−	3.60433i	−0.226752	−	0.130915i
$759$	17.1569	+	2.43222i	0.622756	+	0.0882839i
$760$		−	15.4430i		−	0.560177i
$761$	38.7363	+	22.3644i	1.40419	+	0.810710i	0.994819	−	0.101658i	$-0.0324148\pi$
$761$	38.7363	+	22.3644i	1.40419	+	0.810710i	0.409371	+	0.912368i	$0.365748\pi$
$762$	26.5645	−	10.6958i	0.962332	−	0.387467i
$763$	28.1678	+	23.4032i	1.01974	+	0.847254i
$764$	14.9297	+	8.61966i	0.540137	+	0.311848i
$765$	20.8912	+	21.7375i	0.755324	+	0.785922i
$766$	28.3175	+	16.3491i	1.02315	+	0.590719i
$767$	−11.4599	−	0.439210i	−0.413792	−	0.0158590i
$768$	−1.36360	−	1.06799i	−0.0492045	−	0.0385378i
$769$	6.20113	−	10.7407i	0.223618	−	0.387318i	−0.732286	−	0.680998i	$-0.761546\pi$
$769$	6.20113	−	10.7407i	0.223618	−	0.387318i	0.955904	+	0.293679i	$0.0948798\pi$
$770$	−24.6649	−	20.4928i	−0.888861	−	0.738510i
$771$	36.9021	+	28.9024i	1.32900	+	1.04089i
$772$	10.8338	−	6.25490i	0.389917	−	0.225119i
$773$		−	11.9051i		−	0.428197i	−0.976812	−	0.214099i	$-0.931319\pi$
$773$		−	11.9051i		−	0.428197i	0.976812	−	0.214099i	$-0.0686814\pi$
$774$	−9.67694	+	9.30019i	−0.347830	+	0.334288i
$775$	11.9354	+	20.6728i	0.428734	+	0.742588i
$776$	−1.10676	−	1.91696i	−0.0397303	−	0.0688149i
$777$	8.72334	−	7.91257i	0.312948	−	0.283862i
$778$	−24.6307	−	14.2206i	−0.883055	−	0.509832i
$779$	32.3489	−	18.6766i	1.15902	−	0.669160i
$780$	−3.34467	+	18.4714i	−0.119759	+	0.661384i
$781$	−1.76003	+	3.04846i	−0.0629788	+	0.109083i
$782$			8.29541i			0.296643i
$783$	−18.2465	+	13.1569i	−0.652076	+	0.470188i
$784$	6.60081	+	2.33008i	0.235743	+	0.0832172i
$785$	−26.6856			−0.952451
$786$	2.03556	−	14.3589i	0.0726059	−	0.512164i
$787$	22.2051			0.791526			0.395763	−	0.918353i	$-0.370480\pi$
$787$	22.2051			0.791526			0.395763	+	0.918353i	$0.370480\pi$
$788$	5.30659	−	9.19128i	0.189039	−	0.327426i
$789$	25.0746	+	3.55466i	0.892681	+	0.126549i
$790$	−44.2789	−	25.5645i	−1.57537	−	0.909543i
$791$	−34.8350	+	12.8710i	−1.23859	+	0.457641i
$792$	−8.72163	+	8.38208i	−0.309910	+	0.297844i
$793$	−12.8048	+	20.3378i	−0.454712	+	0.722215i
$794$	−10.0412	+	17.3918i	−0.356348	+	0.617213i
$795$	40.2442	+	31.5200i	1.42731	+	1.11790i
$796$			7.58421i			0.268815i
$797$	−2.52557	−	4.37441i	−0.0894601	−	0.154949i	0.817823	−	0.575470i	$-0.195181\pi$
$797$	−2.52557	−	4.37441i	−0.0894601	−	0.154949i	−0.907283	+	0.420520i	$0.861847\pi$
$798$	23.0108	−	4.97924i	0.814572	−	0.176263i
$799$	−19.3005	+	11.1431i	−0.682802	+	0.394216i
$800$	−2.01770	+	3.49476i	−0.0713366	+	0.123559i
$801$	10.5984	−	2.61550i	0.374474	−	0.0924142i
$802$	−5.32156			−0.187911
$803$	54.7320			1.93145
$804$	−13.9603	−	1.97905i	−0.492341	−	0.0697958i
$805$	6.83897	+	18.5095i	0.241042	+	0.652373i
$806$	−18.0487	−	11.3636i	−0.635740	−	0.400267i
$807$	−39.1368	−	30.6526i	−1.37768	−	1.07902i
$808$	−6.53158	−	11.3130i	−0.229780	−	0.397991i
$809$	5.94536	−	3.43256i	0.209028	−	0.120682i	−0.391832	−	0.920037i	$-0.628158\pi$
$809$	5.94536	−	3.43256i	0.209028	−	0.120682i	0.600860	+	0.799355i	$0.294825\pi$
$810$	14.4457	−	22.8733i	0.507572	−	0.803686i
$811$	54.3239			1.90757			0.953785	−	0.300491i	$-0.0971504\pi$
$811$	54.3239			1.90757			0.953785	+	0.300491i	$0.0971504\pi$
$812$	8.80998	+	7.31977i	0.309170	+	0.256874i
$813$	−9.84526	−	7.71098i	−0.345288	−	0.270436i
$814$	8.97444	−	5.18139i	0.314554	−	0.181608i
$815$	16.4984			0.577915
$816$	−4.55894	−	3.57064i	−0.159595	−	0.124997i
$817$	22.9847			0.804131
$818$	−17.5007			−0.611899
$819$	−28.6017	+	0.971976i	−0.999423	+	0.0339636i
$820$	−21.8547			−0.763198
$821$	−42.3893			−1.47940			−0.739698	−	0.672939i	$-0.765032\pi$
$821$	−42.3893			−1.47940			−0.739698	+	0.672939i	$0.765032\pi$
$822$	28.4813	+	22.3070i	0.993399	+	0.778048i
$823$	−36.7062			−1.27950			−0.639749	−	0.768584i	$-0.720962\pi$
$823$	−36.7062			−1.27950			−0.639749	+	0.768584i	$0.720962\pi$
$824$	−14.8587	+	8.57869i	−0.517628	+	0.298853i
$825$	22.1877	+	17.3778i	0.772477	+	0.605017i
$826$	1.42102	−	8.29458i	0.0494436	−	0.288605i
$827$	−3.97539			−0.138238			−0.0691189	−	0.997608i	$-0.522019\pi$
$827$	−3.97539			−0.138238			−0.0691189	+	0.997608i	$0.522019\pi$
$828$	7.22675	−	1.78345i	0.251147	−	0.0619790i
$829$	−32.5527	+	18.7943i	−1.13060	+	0.652754i	−0.944087	−	0.329698i	$-0.893053\pi$
$829$	−32.5527	+	18.7943i	−1.13060	+	0.652754i	−0.186517	+	0.982452i	$0.559720\pi$
$830$	19.0269	+	32.9555i	0.660433	+	1.14390i
$831$	−27.5503	−	21.5779i	−0.955711	−	0.748529i
$832$	0.138085	−	3.60291i	0.00478722	−	0.124908i
$833$	22.0686	+	7.79021i	0.764633	+	0.269915i
$834$	24.6534	+	3.49495i	0.853679	+	0.121020i
$835$	−10.4609			−0.362014
$836$	20.7156			0.716464
$837$	17.9773	+	24.9316i	0.621386	+	0.861763i
$838$	11.9702	−	20.7329i	0.413502	−	0.716207i
$839$	32.8698	−	18.9774i	1.13479	−	0.655172i	0.189656	−	0.981851i	$-0.439263\pi$
$839$	32.8698	−	18.9774i	1.13479	−	0.655172i	0.945135	+	0.326679i	$0.105929\pi$
$840$	−13.1161	−	4.20862i	−0.452547	−	0.145211i
$841$	−5.12895	−	8.88359i	−0.176860	−	0.306331i
$842$		−	18.4384i		−	0.635430i
$843$	−7.79947	−	6.10868i	−0.268628	−	0.210394i
$844$	5.81722	−	10.0757i	0.200237	−	0.346820i
$845$	−35.2375	+	16.8908i	−1.21221	+	0.581061i
$846$	13.8571	+	14.4184i	0.476416	+	0.495716i
$847$	8.89090	−	10.7010i	0.305495	−	0.367690i
$848$	−8.50304	−	4.90923i	−0.291996	−	0.168584i
$849$	4.75606	+	0.674234i	0.163228	+	0.0231396i
$850$	−6.74583	+	11.6841i	−0.231380	+	0.400762i
$851$	−6.37671			−0.218591
$852$	−0.212233	+	1.49710i	−0.00727100	+	0.0512898i
$853$	33.6251			1.15130			0.575651	−	0.817695i	$-0.304749\pi$
$853$	33.6251			1.15130			0.575651	+	0.817695i	$0.304749\pi$
$854$	−13.5645	−	11.2700i	−0.464167	−	0.385653i
$855$	−44.9796	+	11.1002i	−1.53827	+	0.379620i
$856$		−	2.02353i		−	0.0691627i
$857$	11.5390	−	19.9861i	0.394164	−	0.682712i	−0.598830	−	0.800876i	$-0.704368\pi$
$857$	11.5390	−	19.9861i	0.394164	−	0.682712i	0.992994	+	0.118164i	$0.0377009\pi$
$858$	−24.7780	−	4.48662i	−0.845907	−	0.153171i
$859$	12.1144	−	6.99427i	0.413339	−	0.238642i	−0.278884	−	0.960325i	$-0.589965\pi$
$859$	12.1144	−	6.99427i	0.413339	−	0.238642i	0.692223	+	0.721683i	$0.256631\pi$
$860$	−11.6462	−	6.72394i	−0.397132	−	0.229284i
$861$	−7.04653	−	32.5644i	−0.240145	−	1.10979i
$862$	7.38913	+	12.7984i	0.251675	+	0.435914i
$863$	8.37357	+	14.5034i	0.285040	+	0.493703i	0.972619	−	0.232406i	$-0.0746599\pi$
$863$	8.37357	+	14.5034i	0.285040	+	0.493703i	−0.687579	+	0.726109i	$0.741327\pi$
$864$	−2.13052	+	4.73929i	−0.0724817	+	0.161234i
$865$			35.3367i			1.20148i
$866$	−24.1602	+	13.9489i	−0.820998	+	0.474003i
$867$	7.93914	+	6.21807i	0.269627	+	0.211177i
$868$	10.0016	−	12.0378i	0.339476	−	0.408589i
$869$	34.2927	−	59.3968i	1.16330	−	2.01490i
$870$	−17.7447	−	13.8980i	−0.601602	−	0.471185i
$871$	−13.6913	−	25.9623i	−0.463913	−	0.879698i
$872$	11.9872	+	6.92083i	0.405939	+	0.234369i
$873$	−4.78786	+	4.60145i	−0.162044	+	0.155736i
$874$	−11.0395	−	6.37365i	−0.373416	−	0.215592i
$875$	1.29536	−	7.56111i	0.0437913	−	0.255612i
$876$	21.8091	−	8.78107i	0.736862	−	0.296685i
$877$	−22.1625	−	12.7955i	−0.748374	−	0.432074i	0.0767319	−	0.997052i	$-0.475551\pi$
$877$	−22.1625	−	12.7955i	−0.748374	−	0.432074i	−0.825106	+	0.564978i	$0.808885\pi$
$878$		−	6.20525i		−	0.209417i
$879$	22.7266	+	3.22179i	0.766548	+	0.108668i
$880$	−10.4965	−	6.06015i	−0.353837	−	0.204288i
$881$	9.90378	−	17.1539i	0.333667	−	0.577928i	−0.649561	−	0.760310i	$-0.725047\pi$
$881$	9.90378	−	17.1539i	0.333667	−	0.577928i	0.983228	+	0.182381i	$0.0583806\pi$
$882$	2.04206	−	20.9005i	0.0687597	−	0.703756i
$883$	−25.8694			−0.870576			−0.435288	−	0.900291i	$-0.643353\pi$
$883$	−25.8694			−0.870576			−0.435288	+	0.900291i	$0.643353\pi$
$884$	0.461661	−	12.0457i	0.0155273	−	0.405140i
$885$	−2.32436	+	16.3961i	−0.0781326	+	0.551149i
$886$	−5.47785	+	3.16264i	−0.184032	+	0.106251i
$887$	−47.5894			−1.59789			−0.798947	−	0.601401i	$-0.794609\pi$
$887$	−47.5894			−1.59789			−0.798947	+	0.601401i	$0.794609\pi$
$888$	2.74476	−	3.50447i	0.0921082	−	0.117602i
$889$	−27.9547	+	33.6459i	−0.937569	+	1.12845i
$890$	5.46888	+	9.47239i	0.183317	+	0.317515i
$891$	30.6828	+	19.3779i	1.02791	+	0.649183i
$892$	−0.696107	+	1.20569i	−0.0233074	+	0.0403696i
$893$		−	34.2466i		−	1.14602i
$894$	15.8710	−	6.39019i	0.530806	−	0.213720i
$895$	16.0757	−	27.8439i	0.537350	−	0.930718i
$896$	2.60776	+	0.446759i	0.0871191	+	0.0149252i
$897$	11.8239	+	10.0145i	0.394790	+	0.334374i
$898$	17.8544	+	30.9247i	0.595809	+	1.03197i
$899$	22.1779	−	12.8044i	0.739675	−	0.427052i
$900$	11.6292	+	3.36481i	0.387640	+	0.112160i
$901$	−28.4284	−	16.4131i	−0.947087	−	0.546801i
$902$		−	29.3164i		−	0.976128i
$903$	6.26391	−	19.5213i	0.208450	−	0.649629i
$904$	−12.1559	+	7.01820i	−0.404299	+	0.233422i
$905$	−23.8819	−	41.3647i	−0.793861	−	1.37501i
$906$	−3.54182	−	8.79665i	−0.117669	−	0.292249i
$907$	−13.6389	−	23.6233i	−0.452872	−	0.784398i	0.545691	−	0.837987i	$-0.316267\pi$
$907$	−13.6389	−	23.6233i	−0.452872	−	0.784398i	−0.998563	+	0.0535890i	$0.982934\pi$
$908$		−	7.24063i		−	0.240289i
$909$	−28.2557	+	27.1557i	−0.937183	+	0.900696i
$910$	−8.90070	−	27.2580i	−0.295055	−	0.903595i
$911$		−	6.68687i		−	0.221546i	−0.993846	−	0.110773i	$-0.964667\pi$
$911$		−	6.68687i		−	0.221546i	0.993846	−	0.110773i	$-0.0353326\pi$
$912$	8.25457	−	3.32356i	0.273336	−	0.110054i
$913$	−44.2073	+	25.5231i	−1.46305	+	0.844691i
$914$			2.30897i			0.0763739i
$915$	27.3210	+	21.3983i	0.903204	+	0.707405i
$916$	12.0113	+	20.8043i	0.396866	+	0.687392i
$917$	7.67781	+	20.7798i	0.253544	+	0.686209i
$918$	−7.12301	+	15.8450i	−0.235094	+	0.522962i
$919$	−19.9827	+	34.6110i	−0.659168	+	1.14171i	0.321663	+	0.946854i	$0.395758\pi$
$919$	−19.9827	+	34.6110i	−0.659168	+	1.14171i	−0.980831	+	0.194859i	$0.937575\pi$
$920$	3.72910	+	6.45898i	0.122945	+	0.212946i
$921$	27.6620	+	21.6654i	0.911495	+	0.713899i
$922$	30.3853	−	17.5430i	1.00069	−	0.577747i
$923$	−2.78419	+	1.46826i	−0.0916428	+	0.0483283i
$924$	5.64554	−	17.5942i	0.185725	−	0.578806i
$925$	−8.98162	−	5.18554i	−0.295314	−	0.170500i
$926$			34.0752i			1.11978i
$927$	35.6667	+	37.1116i	1.17145	+	1.21890i
$928$	3.74921	+	2.16461i	0.123074	+	0.0710567i
$929$	13.7638	+	7.94652i	0.451575	+	0.260717i	0.708495	−	0.705716i	$-0.249374\pi$
$929$	13.7638	+	7.94652i	0.451575	+	0.260717i	−0.256920	+	0.966433i	$0.582708\pi$
$930$	−18.9899	+	24.2460i	−0.622704	+	0.795059i
$931$	−27.3232	+	23.3833i	−0.895483	+	0.766358i
$932$	−3.29311	+	1.90128i	−0.107869	+	0.0622785i
$933$	−25.8842	+	10.4218i	−0.847410	+	0.341195i
$934$	−17.7900	−	30.8133i	−0.582108	−	1.00824i
$935$	−35.0931	−	20.2610i	−1.14767	−	0.662606i
$936$	−10.5931	+	2.18753i	−0.346248	+	0.0715018i
$937$		−	43.8201i		−	1.43154i	−0.698336	−	0.715770i	$-0.746076\pi$
$937$		−	43.8201i		−	1.43154i	0.698336	−	0.715770i	$-0.253924\pi$
$938$	20.2029	−	7.46468i	0.659649	−	0.243731i
$939$	46.8924	+	6.64762i	1.53028	+	0.216937i
$940$	−10.0185	+	17.3526i	−0.326768	+	0.565979i
$941$	8.41134	+	4.85629i	0.274202	+	0.158311i	0.630796	−	0.775949i	$-0.282729\pi$
$941$	8.41134	+	4.85629i	0.274202	+	0.158311i	−0.356594	+	0.934260i	$0.616062\pi$
$942$	−5.74314	−	14.2640i	−0.187121	−	0.464745i
$943$	−9.01986	+	15.6229i	−0.293727	+	0.508750i
$944$		−	3.18073i		−	0.103524i
$945$	−2.83045	+	41.2272i	−0.0920746	+	1.34112i
$946$	9.01964	−	15.6225i	0.293254	−	0.507931i
$947$	31.8619			1.03537			0.517686	−	0.855571i	$-0.326794\pi$
$947$	31.8619			1.03537			0.517686	+	0.855571i	$0.326794\pi$
$948$	4.13519	−	29.1697i	0.134305	−	0.947389i
$949$	41.4159	+	26.0758i	1.34442	+	0.846456i
$950$	−10.3661	−	17.9546i	−0.336321	−	0.582525i
$951$	−6.36728	+	44.9149i	−0.206473	+	1.45647i
$952$	8.71857	+	1.49366i	0.282571	+	0.0484098i
$953$	−6.47475	+	3.73820i	−0.209738	+	0.121092i	−0.601190	−	0.799106i	$-0.705306\pi$
$953$	−6.47475	+	3.73820i	−0.209738	+	0.121092i	0.391452	+	0.920199i	$0.371973\pi$
$954$	−8.18685	+	28.2948i	−0.265059	+	0.916078i
$955$	51.8196			1.67684
$956$	−8.77151			−0.283691
$957$	18.6430	−	23.8031i	0.602644	−	0.769446i
$958$	−6.44067	+	3.71852i	−0.208089	+	0.120140i
$959$	−54.4680	−	9.33142i	−1.75886	−	0.301327i
$960$	−5.15482	−	0.730764i	−0.166371	−	0.0235853i
$961$	−1.99573	−	3.45671i	−0.0643785	−	0.111507i
$962$	9.25955	+	0.354881i	0.298540	+	0.0114418i
$963$	−5.89376	+	1.45448i	−0.189924	+	0.0468701i
$964$	5.66694			0.182520
$965$	18.8016	−	32.5653i	0.605244	−	1.04831i
$966$	−8.42181	+	7.63907i	−0.270967	+	0.245783i
$967$			8.01618i			0.257783i	0.991659	+	0.128891i	$0.0411419\pi$
$967$			8.01618i			0.257783i	−0.991659	+	0.128891i	$0.958858\pi$
$968$	2.62922	−	4.55395i	0.0845064	−	0.146369i
$969$	27.5977	−	11.1117i	0.886566	−	0.356960i
$970$	−5.76219	−	3.32680i	−0.185013	−	0.106817i
$971$	18.1376	−	31.4152i	0.582063	−	1.00816i	−0.413172	−	0.910653i	$-0.635579\pi$
$971$	18.1376	−	31.4152i	0.582063	−	1.00816i	0.995235	−	0.0975092i	$-0.0310875\pi$
$972$	15.3351	+	2.79884i	0.491875	+	0.0897730i
$973$	−35.6778	+	13.1824i	−1.14378	+	0.422609i
$974$			17.9702i			0.575803i
$975$	8.51029	+	23.7207i	0.272547	+	0.759670i
$976$	−5.77255	−	3.33278i	−0.184775	−	0.106680i
$977$	3.50153	+	6.06482i	0.112024	+	0.194031i	0.916586	−	0.399837i	$-0.130933\pi$
$977$	3.50153	+	6.06482i	0.112024	+	0.194031i	−0.804562	+	0.593868i	$0.797600\pi$
$978$	3.55071	+	8.81872i	0.113539	+	0.281992i
$979$	−12.7065	+	7.33609i	−0.406101	+	0.234462i
$980$	20.6851	−	3.85505i	0.660761	−	0.123145i
$981$	11.5415	−	39.8888i	0.368491	−	1.27355i
$982$	−2.56980	−	1.48368i	−0.0820057	−	0.0473460i
$983$	27.4636	+	15.8561i	0.875954	+	0.505732i	0.869322	−	0.494246i	$-0.164556\pi$
$983$	27.4636	+	15.8561i	0.875954	+	0.505732i	0.00663162	+	0.999978i	$0.497889\pi$
$984$	−4.70344	−	11.6817i	−0.149940	−	0.372400i
$985$		−	31.9021i		−	1.01649i
$986$	12.5348	+	7.23698i	0.399190	+	0.230472i
$987$	−29.0864	−	9.33309i	−0.925829	−	0.297076i
$988$	15.6756	+	9.86948i	0.498707	+	0.313990i
$989$	−9.61325	+	5.55021i	−0.305683	+	0.176486i
$990$	−10.1062	+	34.9282i	−0.321195	+	1.11009i
$991$	2.53877	+	4.39727i	0.0806465	+	0.139684i	0.903528	−	0.428529i	$-0.140968\pi$
$991$	2.53877	+	4.39727i	0.0806465	+	0.139684i	−0.822881	+	0.568213i	$0.807635\pi$
$992$	2.95768	−	5.12285i	0.0939064	−	0.162651i
$993$	8.77250	+	21.7878i	0.278387	+	0.691416i
$994$	−0.800512	−	2.16656i	−0.0253907	−	0.0687192i
$995$	11.3987	+	19.7431i	0.361362	+	0.625897i
$996$	−13.5205	+	17.2627i	−0.428413	+	0.546991i
$997$		−	36.1320i		−	1.14431i	−0.820145	−	0.572156i	$-0.806107\pi$
$997$		−	36.1320i		−	1.14431i	0.820145	−	0.572156i	$-0.193893\pi$
$998$	−14.4827	+	8.36158i	−0.458441	+	0.264681i
$999$	−12.1801	−	5.47548i	−0.385361	−	0.173237i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bi.e.17.3	✓	34
3.2	odd	2		546.2.bi.f.17.8	yes	34
7.5	odd	6		546.2.bn.f.173.3	yes	34
13.10	even	6		546.2.bn.e.101.15	yes	34
21.5	even	6		546.2.bn.e.173.15	yes	34
39.23	odd	6		546.2.bn.f.101.3	yes	34
91.75	odd	6		546.2.bi.f.257.8	yes	34
273.257	even	6	inner	546.2.bi.e.257.3	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.3	✓	34	1.1	even	1	trivial
546.2.bi.e.257.3	yes	34	273.257	even	6	inner
546.2.bi.f.17.8	yes	34	3.2	odd	2
546.2.bi.f.257.8	yes	34	91.75	odd	6
546.2.bn.e.101.15	yes	34	13.10	even	6
546.2.bn.e.173.15	yes	34	21.5	even	6
546.2.bn.f.101.3	yes	34	39.23	odd	6
546.2.bn.f.173.3	yes	34	7.5	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-1.36360 - 1.06799i) q^{3} +1.00000 q^{4} +(2.60318 - 1.50295i) q^{5} +(1.36360 + 1.06799i) q^{6} +(-2.60776 - 0.446759i) q^{7} -1.00000 q^{8} +(0.718787 + 2.91262i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-1.36360 - 1.06799i) q^{3} +1.00000 q^{4} +(2.60318 - 1.50295i) q^{5} +(1.36360 + 1.06799i) q^{6} +(-2.60776 - 0.446759i) q^{7} -1.00000 q^{8} +(0.718787 + 2.91262i) q^{9} +(-2.60318 + 1.50295i) q^{10} +(-2.01609 - 3.49197i) q^{11} +(-1.36360 - 1.06799i) q^{12} +(0.138085 - 3.60291i) q^{13} +(2.60776 + 0.446759i) q^{14} +(-5.15482 - 0.730764i) q^{15} +1.00000 q^{16} +3.34332 q^{17} +(-0.718787 - 2.91262i) q^{18} +(-2.56879 + 4.44927i) q^{19} +(2.60318 - 1.50295i) q^{20} +(3.07879 + 3.39426i) q^{21} +(2.01609 + 3.49197i) q^{22} -2.48119i q^{23} +(1.36360 + 1.06799i) q^{24} +(2.01770 - 3.49476i) q^{25} +(-0.138085 + 3.60291i) q^{26} +(2.13052 - 4.73929i) q^{27} +(-2.60776 - 0.446759i) q^{28} +(-3.74921 - 2.16461i) q^{29} +(5.15482 + 0.730764i) q^{30} +(-2.95768 + 5.12285i) q^{31} -1.00000 q^{32} +(-0.980263 + 6.91480i) q^{33} -3.34332 q^{34} +(-7.45993 + 2.75633i) q^{35} +(0.718787 + 2.91262i) q^{36} -2.57002i q^{37} +(2.56879 - 4.44927i) q^{38} +(-4.03617 + 4.76543i) q^{39} +(-2.60318 + 1.50295i) q^{40} +(-6.29653 - 3.63530i) q^{41} +(-3.07879 - 3.39426i) q^{42} +(-2.23692 - 3.87445i) q^{43} +(-2.01609 - 3.49197i) q^{44} +(6.24865 + 6.50178i) q^{45} +2.48119i q^{46} +(-5.77285 + 3.33296i) q^{47} +(-1.36360 - 1.06799i) q^{48} +(6.60081 + 2.33008i) q^{49} +(-2.01770 + 3.49476i) q^{50} +(-4.55894 - 3.57064i) q^{51} +(0.138085 - 3.60291i) q^{52} +(-8.50304 - 4.90923i) q^{53} +(-2.13052 + 4.73929i) q^{54} +(-10.4965 - 6.06015i) q^{55} +(2.60776 + 0.446759i) q^{56} +(8.25457 - 3.32356i) q^{57} +(3.74921 + 2.16461i) q^{58} -3.18073i q^{59} +(-5.15482 - 0.730764i) q^{60} +(-5.77255 - 3.33278i) q^{61} +(2.95768 - 5.12285i) q^{62} +(-0.573184 - 7.91653i) q^{63} +1.00000 q^{64} +(-5.05552 - 9.58655i) q^{65} +(0.980263 - 6.91480i) q^{66} +(7.04993 - 4.07028i) q^{67} +3.34332 q^{68} +(-2.64989 + 3.38334i) q^{69} +(7.45993 - 2.75633i) q^{70} +(-0.436496 - 0.756034i) q^{71} +(-0.718787 - 2.91262i) q^{72} +(-6.78690 + 11.7553i) q^{73} +2.57002i q^{74} +(-6.48371 + 2.61056i) q^{75} +(-2.56879 + 4.44927i) q^{76} +(3.69740 + 10.0069i) q^{77} +(4.03617 - 4.76543i) q^{78} +(8.50477 + 14.7307i) q^{79} +(2.60318 - 1.50295i) q^{80} +(-7.96669 + 4.18710i) q^{81} +(6.29653 + 3.63530i) q^{82} -12.6597i q^{83} +(3.07879 + 3.39426i) q^{84} +(8.70327 - 5.02484i) q^{85} +(2.23692 + 3.87445i) q^{86} +(2.80062 + 6.95578i) q^{87} +(2.01609 + 3.49197i) q^{88} -3.63877i q^{89} +(-6.24865 - 6.50178i) q^{90} +(-1.96972 + 9.33382i) q^{91} -2.48119i q^{92} +(9.50424 - 3.82672i) q^{93} +(5.77285 - 3.33296i) q^{94} +15.4430i q^{95} +(1.36360 + 1.06799i) q^{96} +(1.10676 + 1.91696i) q^{97} +(-6.60081 - 2.33008i) q^{98} +(8.72163 - 8.38208i) 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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