LMFDB - Embedded newform 560.2.bb.d.29.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(29,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2, 0]))

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

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

chi := DirichletCharacter("560.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.bb (of order $4$, 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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$70$
Relative dimension:	$35$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			29.9
Character	$\chi$	$=$	560.29
Dual form			560.2.bb.d.309.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.868292 - 1.11627i) q^{2} +(2.38527 - 2.38527i) q^{3} +(-0.492138 + 1.93850i) q^{4} +(-0.763308 - 2.10175i) q^{5} +(-4.73373 - 0.591506i) q^{6} +1.00000 q^{7} +(2.59122 - 1.13383i) q^{8} -8.37902i q^{9} +O(q^{10})$	\(q+(-0.868292 - 1.11627i) q^{2} +(2.38527 - 2.38527i) q^{3} +(-0.492138 + 1.93850i) q^{4} +(-0.763308 - 2.10175i) q^{5} +(-4.73373 - 0.591506i) q^{6} +1.00000 q^{7} +(2.59122 - 1.13383i) q^{8} -8.37902i q^{9} +(-1.68336 + 2.67700i) q^{10} +(-1.71868 + 1.71868i) q^{11} +(3.44997 + 5.79774i) q^{12} +(3.59592 - 3.59592i) q^{13} +(-0.868292 - 1.11627i) q^{14} +(-6.83394 - 3.19255i) q^{15} +(-3.51560 - 1.90803i) q^{16} +4.59341i q^{17} +(-9.35328 + 7.27543i) q^{18} +(3.42383 + 3.42383i) q^{19} +(4.44991 - 0.445324i) q^{20} +(2.38527 - 2.38527i) q^{21} +(3.41083 + 0.426203i) q^{22} -1.76828 q^{23} +(3.47628 - 8.88524i) q^{24} +(-3.83472 + 3.20857i) q^{25} +(-7.13634 - 0.891726i) q^{26} +(-12.8304 - 12.8304i) q^{27} +(-0.492138 + 1.93850i) q^{28} +(-2.84560 - 2.84560i) q^{29} +(2.37009 + 10.4006i) q^{30} +0.809210 q^{31} +(0.922686 + 5.58110i) q^{32} +8.19902i q^{33} +(5.12751 - 3.98842i) q^{34} +(-0.763308 - 2.10175i) q^{35} +(16.2428 + 4.12364i) q^{36} +(-0.331345 - 0.331345i) q^{37} +(0.849050 - 6.79481i) q^{38} -17.1545i q^{39} +(-4.36092 - 4.58065i) q^{40} +5.92254i q^{41} +(-4.73373 - 0.591506i) q^{42} +(7.77881 + 7.77881i) q^{43} +(-2.48584 - 4.17749i) q^{44} +(-17.6106 + 6.39577i) q^{45} +(1.53539 + 1.97389i) q^{46} -5.21145i q^{47} +(-12.9368 + 3.83450i) q^{48} +1.00000 q^{49} +(6.91130 + 1.49463i) q^{50} +(10.9565 + 10.9565i) q^{51} +(5.20102 + 8.74040i) q^{52} +(-2.65166 - 2.65166i) q^{53} +(-3.18172 + 25.4628i) q^{54} +(4.92411 + 2.30035i) q^{55} +(2.59122 - 1.13383i) q^{56} +16.3335 q^{57} +(-0.705661 + 5.64729i) q^{58} +(-3.31292 + 3.31292i) q^{59} +(9.55201 - 11.6764i) q^{60} +(6.99798 + 6.99798i) q^{61} +(-0.702631 - 0.903301i) q^{62} -8.37902i q^{63} +(5.42888 - 5.87599i) q^{64} +(-10.3025 - 4.81294i) q^{65} +(9.15235 - 7.11914i) q^{66} +(7.00535 - 7.00535i) q^{67} +(-8.90435 - 2.26060i) q^{68} +(-4.21784 + 4.21784i) q^{69} +(-1.68336 + 2.67700i) q^{70} +1.44994i q^{71} +(-9.50035 - 21.7119i) q^{72} -5.27531 q^{73} +(-0.0821678 + 0.657576i) q^{74} +(-1.49354 + 16.8001i) q^{75} +(-8.32210 + 4.95210i) q^{76} +(-1.71868 + 1.71868i) q^{77} +(-19.1491 + 14.8951i) q^{78} -7.40856 q^{79} +(-1.32671 + 8.84533i) q^{80} -36.0709 q^{81} +(6.61118 - 5.14250i) q^{82} +(1.21677 - 1.21677i) q^{83} +(3.44997 + 5.79774i) q^{84} +(9.65421 - 3.50619i) q^{85} +(1.92901 - 15.4376i) q^{86} -13.5751 q^{87} +(-2.50480 + 6.40216i) q^{88} -2.76507i q^{89} +(22.4306 + 14.1049i) q^{90} +(3.59592 - 3.59592i) q^{91} +(0.870241 - 3.42783i) q^{92} +(1.93018 - 1.93018i) q^{93} +(-5.81741 + 4.52506i) q^{94} +(4.58260 - 9.80946i) q^{95} +(15.5133 + 11.1116i) q^{96} -5.15345i q^{97} +(-0.868292 - 1.11627i) q^{98} +(14.4008 + 14.4008i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 70 q + 2 q^{2} + 2 q^{3} + 2 q^{5} + 70 q^{7} + 8 q^{8}+O(q^{10}) $ 70 * q + 2 * q^2 + 2 * q^3 + 2 * q^5 + 70 * q^7 + 8 * q^8	$ 70 q + 2 q^{2} + 2 q^{3} + 2 q^{5} + 70 q^{7} + 8 q^{8} - 18 q^{10} - 2 q^{11} - 4 q^{12} + 6 q^{13} + 2 q^{14} - 6 q^{15} + 4 q^{16} - 18 q^{18} + 14 q^{19} + 12 q^{20} + 2 q^{21} - 12 q^{22} + 20 q^{24} + 6 q^{25} - 36 q^{26} + 8 q^{27} + 2 q^{29} + 8 q^{30} + 16 q^{31} - 8 q^{32} + 4 q^{34} + 2 q^{35} - 40 q^{36} + 10 q^{37} - 12 q^{38} - 24 q^{40} + 2 q^{43} - 24 q^{44} - 24 q^{45} - 16 q^{46} - 44 q^{48} + 70 q^{49} - 10 q^{50} + 8 q^{51} + 28 q^{52} - 30 q^{53} - 32 q^{54} + 6 q^{55} + 8 q^{56} - 76 q^{57} + 56 q^{58} + 2 q^{59} - 8 q^{60} + 30 q^{61} + 48 q^{62} + 12 q^{64} - 10 q^{65} + 80 q^{66} + 6 q^{67} - 36 q^{68} - 16 q^{69} - 18 q^{70} + 4 q^{72} - 36 q^{73} - 32 q^{74} - 2 q^{75} + 44 q^{76} - 2 q^{77} - 84 q^{78} - 40 q^{79} + 12 q^{80} - 82 q^{81} + 24 q^{82} + 10 q^{83} - 4 q^{84} + 32 q^{85} + 32 q^{86} - 4 q^{87} + 32 q^{88} + 18 q^{90} + 6 q^{91} - 92 q^{92} - 56 q^{93} - 20 q^{94} + 6 q^{95} + 16 q^{96} + 2 q^{98} - 34 q^{99}+O(q^{100}) $ 70 * q + 2 * q^2 + 2 * q^3 + 2 * q^5 + 70 * q^7 + 8 * q^8 - 18 * q^10 - 2 * q^11 - 4 * q^12 + 6 * q^13 + 2 * q^14 - 6 * q^15 + 4 * q^16 - 18 * q^18 + 14 * q^19 + 12 * q^20 + 2 * q^21 - 12 * q^22 + 20 * q^24 + 6 * q^25 - 36 * q^26 + 8 * q^27 + 2 * q^29 + 8 * q^30 + 16 * q^31 - 8 * q^32 + 4 * q^34 + 2 * q^35 - 40 * q^36 + 10 * q^37 - 12 * q^38 - 24 * q^40 + 2 * q^43 - 24 * q^44 - 24 * q^45 - 16 * q^46 - 44 * q^48 + 70 * q^49 - 10 * q^50 + 8 * q^51 + 28 * q^52 - 30 * q^53 - 32 * q^54 + 6 * q^55 + 8 * q^56 - 76 * q^57 + 56 * q^58 + 2 * q^59 - 8 * q^60 + 30 * q^61 + 48 * q^62 + 12 * q^64 - 10 * q^65 + 80 * q^66 + 6 * q^67 - 36 * q^68 - 16 * q^69 - 18 * q^70 + 4 * q^72 - 36 * q^73 - 32 * q^74 - 2 * q^75 + 44 * q^76 - 2 * q^77 - 84 * q^78 - 40 * q^79 + 12 * q^80 - 82 * q^81 + 24 * q^82 + 10 * q^83 - 4 * q^84 + 32 * q^85 + 32 * q^86 - 4 * q^87 + 32 * q^88 + 18 * q^90 + 6 * q^91 - 92 * q^92 - 56 * q^93 - 20 * q^94 + 6 * q^95 + 16 * q^96 + 2 * q^98 - 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.868292	−	1.11627i	−0.613975	−	0.789325i
$2$	−0.868292	−	1.11627i	−0.613975	−	0.789325i
$3$	2.38527	−	2.38527i	1.37714	−	1.37714i	0.527713	−	0.849423i	$-0.323050\pi$
$3$	2.38527	−	2.38527i	1.37714	−	1.37714i	0.849423	−	0.527713i	$-0.176950\pi$
$4$	−0.492138	+	1.93850i	−0.246069	+	0.969252i
$5$	−0.763308	−	2.10175i	−0.341362	−	0.939932i
$5$	−0.763308	−	2.10175i	−0.341362	−	0.939932i
$6$	−4.73373	−	0.591506i	−1.93254	−	0.241481i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	2.59122	−	1.13383i	0.916136	−	0.400868i
$9$		−	8.37902i		−	2.79301i
$10$	−1.68336	+	2.67700i	−0.532325	+	0.846540i
$11$	−1.71868	+	1.71868i	−0.518201	+	0.518201i	−0.917027	−	0.398826i	$-0.869418\pi$
$11$	−1.71868	+	1.71868i	−0.518201	+	0.518201i	0.398826	+	0.917027i	$0.369418\pi$
$12$	3.44997	+	5.79774i	0.995921	+	1.67366i
$13$	3.59592	−	3.59592i	0.997329	−	0.997329i	−0.00266780	−	0.999996i	$-0.500849\pi$
$13$	3.59592	−	3.59592i	0.997329	−	0.997329i	0.999996	+	0.00266780i	$0.000849188\pi$
$14$	−0.868292	−	1.11627i	−0.232061	−	0.298337i
$15$	−6.83394	−	3.19255i	−1.76452	−	0.824312i
$16$	−3.51560	−	1.90803i	−0.878900	−	0.477006i
$17$			4.59341i			1.11407i	0.830490	+	0.557033i	$0.188060\pi$
$17$			4.59341i			1.11407i	−0.830490	+	0.557033i	$0.811940\pi$
$18$	−9.35328	+	7.27543i	−2.20459	+	1.71484i
$19$	3.42383	+	3.42383i	0.785479	+	0.785479i	0.980749	−	0.195270i	$-0.0625584\pi$
$19$	3.42383	+	3.42383i	0.785479	+	0.785479i	−0.195270	+	0.980749i	$0.562558\pi$
$20$	4.44991	−	0.445324i	0.995030	−	0.0995774i
$21$	2.38527	−	2.38527i	0.520508	−	0.520508i
$22$	3.41083	+	0.426203i	0.727191	+	0.0908667i
$23$	−1.76828			−0.368713			−0.184356	−	0.982859i	$-0.559020\pi$
$23$	−1.76828			−0.368713			−0.184356	+	0.982859i	$0.559020\pi$
$24$	3.47628	−	8.88524i	0.709594	−	1.81369i
$25$	−3.83472	+	3.20857i	−0.766944	+	0.641714i
$26$	−7.13634	−	0.891726i	−1.39955	−	0.174882i
$27$	−12.8304	−	12.8304i	−2.46921	−	2.46921i
$28$	−0.492138	+	1.93850i	−0.0930054	+	0.366343i
$29$	−2.84560	−	2.84560i	−0.528415	−	0.528415i	0.391684	−	0.920100i	$-0.371892\pi$
$29$	−2.84560	−	2.84560i	−0.528415	−	0.528415i	−0.920100	+	0.391684i	$0.871892\pi$
$30$	2.37009	+	10.4006i	0.432718	+	1.89888i
$31$	0.809210			0.145338			0.0726692	−	0.997356i	$-0.476848\pi$
$31$	0.809210			0.145338			0.0726692	+	0.997356i	$0.476848\pi$
$32$	0.922686	+	5.58110i	0.163109	+	0.986608i
$33$			8.19902i			1.42727i
$34$	5.12751	−	3.98842i	0.879361	−	0.684009i
$35$	−0.763308	−	2.10175i	−0.129023	−	0.355261i
$36$	16.2428	+	4.12364i	2.70713	+	0.687273i
$37$	−0.331345	−	0.331345i	−0.0544727	−	0.0544727i	0.679346	−	0.733818i	$-0.262264\pi$
$37$	−0.331345	−	0.331345i	−0.0544727	−	0.0544727i	−0.733818	+	0.679346i	$0.762264\pi$
$38$	0.849050	−	6.79481i	0.137734	−	1.10226i
$39$		−	17.1545i		−	2.74691i
$40$	−4.36092	−	4.58065i	−0.689522	−	0.724264i
$41$			5.92254i			0.924946i	0.886633	+	0.462473i	$0.153038\pi$
$41$			5.92254i			0.924946i	−0.886633	+	0.462473i	$0.846962\pi$
$42$	−4.73373	−	0.591506i	−0.730430	−	0.0912713i
$43$	7.77881	+	7.77881i	1.18626	+	1.18626i	0.978094	+	0.208164i	$0.0667488\pi$
$43$	7.77881	+	7.77881i	1.18626	+	1.18626i	0.208164	+	0.978094i	$0.433251\pi$
$44$	−2.48584	−	4.17749i	−0.374754	−	0.629781i
$45$	−17.6106	+	6.39577i	−2.62524	+	0.953425i
$46$	1.53539	+	1.97389i	0.226381	+	0.291034i
$47$		−	5.21145i		−	0.760169i	−0.924952	−	0.380084i	$-0.875895\pi$
$47$		−	5.21145i		−	0.760169i	0.924952	−	0.380084i	$-0.124105\pi$
$48$	−12.9368	+	3.83450i	−1.86727	+	0.553462i
$49$	1.00000			0.142857
$50$	6.91130	+	1.49463i	0.977406	+	0.211372i
$51$	10.9565	+	10.9565i	1.53422	+	1.53422i
$52$	5.20102	+	8.74040i	0.721251	+	1.21207i
$53$	−2.65166	−	2.65166i	−0.364233	−	0.364233i	0.501135	−	0.865369i	$-0.332916\pi$
$53$	−2.65166	−	2.65166i	−0.364233	−	0.364233i	−0.865369	+	0.501135i	$0.832916\pi$
$54$	−3.18172	+	25.4628i	−0.432977	+	3.46505i
$55$	4.92411	+	2.30035i	0.663967	+	0.310180i
$56$	2.59122	−	1.13383i	0.346267	−	0.151514i
$57$	16.3335			2.16342
$58$	−0.705661	+	5.64729i	−0.0926578	+	0.741525i
$59$	−3.31292	+	3.31292i	−0.431306	+	0.431306i	−0.889072	−	0.457767i	$-0.848650\pi$
$59$	−3.31292	+	3.31292i	−0.431306	+	0.431306i	0.457767	+	0.889072i	$0.348650\pi$
$60$	9.55201	−	11.6764i	1.23316	−	1.50742i
$61$	6.99798	+	6.99798i	0.896000	+	0.896000i	0.995080	−	0.0990796i	$-0.0315899\pi$
$61$	6.99798	+	6.99798i	0.896000	+	0.896000i	−0.0990796	+	0.995080i	$0.531590\pi$
$62$	−0.702631	−	0.903301i	−0.0892342	−	0.114719i
$63$		−	8.37902i		−	1.05566i
$64$	5.42888	−	5.87599i	0.678610	−	0.734499i
$65$	−10.3025	−	4.81294i	−1.27787	−	0.596971i
$66$	9.15235	−	7.11914i	1.12658	−	0.876306i
$67$	7.00535	−	7.00535i	0.855840	−	0.855840i	−0.135005	−	0.990845i	$-0.543105\pi$
$67$	7.00535	−	7.00535i	0.855840	−	0.855840i	0.990845	+	0.135005i	$0.0431050\pi$
$68$	−8.90435	−	2.26060i	−1.07981	−	0.274137i
$69$	−4.21784	+	4.21784i	−0.507768	+	0.507768i
$70$	−1.68336	+	2.67700i	−0.201200	+	0.319962i
$71$			1.44994i			0.172077i	0.996292	+	0.0860383i	$0.0274207\pi$
$71$			1.44994i			0.172077i	−0.996292	+	0.0860383i	$0.972579\pi$
$72$	−9.50035	−	21.7119i	−1.11963	−	2.55877i
$73$	−5.27531			−0.617429			−0.308714	−	0.951155i	$-0.599899\pi$
$73$	−5.27531			−0.617429			−0.308714	+	0.951155i	$0.599899\pi$
$74$	−0.0821678	+	0.657576i	−0.00955181	+	0.0764416i
$75$	−1.49354	+	16.8001i	−0.172459	+	1.93991i
$76$	−8.32210	+	4.95210i	−0.954610	+	0.568045i
$77$	−1.71868	+	1.71868i	−0.195861	+	0.195861i
$78$	−19.1491	+	14.8951i	−2.16821	+	1.68654i
$79$	−7.40856			−0.833529			−0.416764	−	0.909015i	$-0.636836\pi$
$79$	−7.40856			−0.833529			−0.416764	+	0.909015i	$0.636836\pi$
$80$	−1.32671	+	8.84533i	−0.148331	+	0.988938i
$81$	−36.0709			−4.00787
$82$	6.61118	−	5.14250i	0.730083	−	0.567894i
$83$	1.21677	−	1.21677i	0.133557	−	0.133557i	−0.637168	−	0.770725i	$-0.719894\pi$
$83$	1.21677	−	1.21677i	0.133557	−	0.133557i	0.770725	+	0.637168i	$0.219894\pi$
$84$	3.44997	+	5.79774i	0.376423	+	0.632585i
$85$	9.65421	−	3.50619i	1.04715	−	0.380300i
$86$	1.92901	−	15.4376i	0.208011	−	1.66468i
$87$	−13.5751			−1.45540
$88$	−2.50480	+	6.40216i	−0.267012	+	0.682472i
$89$		−	2.76507i		−	0.293097i	−0.989204	−	0.146548i	$-0.953184\pi$
$89$		−	2.76507i		−	0.293097i	0.989204	−	0.146548i	$-0.0468164\pi$
$90$	22.4306	+	14.1049i	2.36439	+	1.48679i
$91$	3.59592	−	3.59592i	0.376955	−	0.376955i
$92$	0.870241	−	3.42783i	0.0907289	−	0.357376i
$93$	1.93018	−	1.93018i	0.200151	−	0.200151i
$94$	−5.81741	+	4.52506i	−0.600020	+	0.466725i
$95$	4.58260	−	9.80946i	0.470164	−	1.00643i
$96$	15.5133	+	11.1116i	1.58332	+	1.13407i
$97$		−	5.15345i		−	0.523254i	−0.965169	−	0.261627i	$-0.915741\pi$
$97$		−	5.15345i		−	0.523254i	0.965169	−	0.261627i	$-0.0842590\pi$
$98$	−0.868292	−	1.11627i	−0.0877107	−	0.112761i
$99$	14.4008	+	14.4008i	1.44734	+	1.44734i
$100$	−4.33261	−	9.01268i	−0.433261	−	0.901268i
$101$	−1.30263	+	1.30263i	−0.129616	+	0.129616i	−0.768939	−	0.639323i	$-0.779215\pi$
$101$	−1.30263	+	1.30263i	−0.129616	+	0.129616i	0.639323	+	0.768939i	$0.279215\pi$
$102$	2.71703	−	21.7440i	0.269026	−	2.15297i
$103$	7.91577			0.779964			0.389982	−	0.920822i	$-0.372481\pi$
$103$	7.91577			0.779964			0.389982	+	0.920822i	$0.372481\pi$
$104$	5.24068	−	13.3950i	0.513891	−	1.31349i
$105$	−6.83394	−	3.19255i	−0.666924	−	0.311561i
$106$	−0.657566	+	5.26239i	−0.0638685	+	0.511129i
$107$	9.75809	+	9.75809i	0.943351	+	0.943351i	0.998479	−	0.0551287i	$-0.0175569\pi$
$107$	9.75809	+	9.75809i	0.943351	+	0.943351i	−0.0551287	+	0.998479i	$0.517557\pi$
$108$	31.1861	−	18.5575i	3.00089	−	1.78569i
$109$	2.14870	+	2.14870i	0.205808	+	0.205808i	0.802483	−	0.596675i	$-0.203512\pi$
$109$	2.14870	+	2.14870i	0.205808	+	0.205808i	−0.596675	+	0.802483i	$0.703512\pi$
$110$	−1.70774	−	7.49404i	−0.162827	−	0.714529i
$111$	−1.58069			−0.150033
$112$	−3.51560	−	1.90803i	−0.332193	−	0.180291i
$113$		−	17.5986i		−	1.65553i	−0.561073	−	0.827767i	$-0.689611\pi$
$113$		−	17.5986i		−	1.65553i	0.561073	−	0.827767i	$-0.310389\pi$
$114$	−14.1822	−	18.2327i	−1.32829	−	1.70765i
$115$	1.34975	+	3.71650i	0.125865	+	0.346565i
$116$	6.91664	−	4.11578i	0.642194	−	0.382141i
$117$	−30.1303	−	30.1303i	−2.78554	−	2.78554i
$118$	6.57472	+	0.821548i	0.605252	+	0.0756296i
$119$			4.59341i			0.421078i
$120$	−21.3281	−	0.524107i	−1.94698	−	0.0478442i
$121$			5.09229i			0.462936i
$122$	1.73538	−	13.8880i	0.157114	−	1.25736i
$123$	14.1269	+	14.1269i	1.27378	+	1.27378i
$124$	−0.398243	+	1.56866i	−0.0357633	+	0.140870i
$125$	9.67069	+	5.61050i	0.864973	+	0.501819i
$126$	−9.35328	+	7.27543i	−0.833257	+	0.648147i
$127$		−	1.90985i		−	0.169472i	−0.996403	−	0.0847360i	$-0.972995\pi$
$127$		−	1.90985i		−	0.169472i	0.996403	−	0.0847360i	$-0.0270047\pi$
$128$	−11.2731	−	0.958041i	−0.996408	−	0.0846797i
$129$	37.1091			3.26728
$130$	3.57304	+	15.6795i	0.313376	+	1.37518i
$131$	−0.438064	−	0.438064i	−0.0382739	−	0.0382739i	0.687711	−	0.725985i	$-0.258616\pi$
$131$	−0.438064	−	0.438064i	−0.0382739	−	0.0382739i	−0.725985	+	0.687711i	$0.758616\pi$
$132$	−15.8938	−	4.03505i	−1.38338	−	0.351206i
$133$	3.42383	+	3.42383i	0.296883	+	0.296883i
$134$	−13.9026	−	1.73721i	−1.20100	−	0.150072i
$135$	−17.1728	+	36.7599i	−1.47800	+	3.16379i
$136$	5.20813	+	11.9026i	0.446594	+	1.02064i
$137$	6.28646			0.537089			0.268544	−	0.963267i	$-0.413457\pi$
$137$	6.28646			0.537089			0.268544	+	0.963267i	$0.413457\pi$
$138$	8.37057	+	1.04595i	0.712551	+	0.0890372i
$139$	9.76084	−	9.76084i	0.827904	−	0.827904i	−0.159323	−	0.987227i	$-0.550931\pi$
$139$	9.76084	−	9.76084i	0.827904	−	0.827904i	0.987227	+	0.159323i	$0.0509310\pi$
$140$	4.44991	−	0.445324i	0.376086	−	0.0376367i
$141$	−12.4307	−	12.4307i	−1.04686	−	1.04686i
$142$	1.61853	−	1.25897i	0.135824	−	0.105651i
$143$			12.3605i			1.03363i
$144$	−15.9874	+	29.4573i	−1.33228	+	2.45477i
$145$	−3.80868	+	8.15282i	−0.316294	+	0.677055i
$146$	4.58051	+	5.88870i	0.379086	+	0.487352i
$147$	2.38527	−	2.38527i	0.196734	−	0.196734i
$148$	0.805381	−	0.479246i	0.0662019	−	0.0393938i
$149$	9.29670	−	9.29670i	0.761616	−	0.761616i	−0.214999	−	0.976614i	$-0.568975\pi$
$149$	9.29670	−	9.29670i	0.761616	−	0.761616i	0.976614	+	0.214999i	$0.0689747\pi$
$150$	20.0504	−	12.9202i	1.63711	−	1.05493i
$151$		−	12.7992i		−	1.04158i	−0.853684	−	0.520792i	$-0.825637\pi$
$151$		−	12.7992i		−	1.04158i	0.853684	−	0.520792i	$-0.174363\pi$
$152$	12.7539	+	4.98987i	1.03448	+	0.404732i
$153$	38.4883			3.11159
$154$	3.41083	+	0.426203i	0.274853	+	0.0343444i
$155$	−0.617677	−	1.70076i	−0.0496130	−	0.136608i
$156$	33.2540	+	8.44237i	2.66245	+	0.675931i
$157$	−2.78668	+	2.78668i	−0.222401	+	0.222401i	−0.809509	−	0.587108i	$-0.800267\pi$
$157$	−2.78668	+	2.78668i	−0.222401	+	0.222401i	0.587108	+	0.809509i	$0.300267\pi$
$158$	6.43280	+	8.26999i	0.511766	+	0.657925i
$159$	−12.6498			−1.00320
$160$	11.0258	−	6.19936i	0.871665	−	0.490102i
$161$	−1.76828			−0.139360
$162$	31.3200	+	40.2650i	2.46073	+	3.16352i
$163$	−7.41705	+	7.41705i	−0.580948	+	0.580948i	−0.935164	−	0.354216i	$-0.884748\pi$
$163$	−7.41705	+	7.41705i	−0.580948	+	0.580948i	0.354216	+	0.935164i	$0.384748\pi$
$164$	−11.4809	−	2.91471i	−0.896506	−	0.227601i
$165$	17.2323	−	6.25838i	1.34153	−	0.487214i
$166$	−2.41475	−	0.301737i	−0.187421	−	0.0234193i
$167$	2.55872			0.198000			0.0989998	−	0.995087i	$-0.468436\pi$
$167$	2.55872			0.198000			0.0989998	+	0.995087i	$0.468436\pi$
$168$	3.47628	−	8.88524i	0.268201	−	0.685512i
$169$		−	12.8613i		−	0.989329i
$170$	−12.2965	−	7.73236i	−0.943102	−	0.593045i
$171$	28.6883	−	28.6883i	2.19385	−	2.19385i
$172$	−18.9075	+	11.2510i	−1.44168	+	0.857882i
$173$	−0.531721	+	0.531721i	−0.0404260	+	0.0404260i	−0.727031	−	0.686605i	$-0.759100\pi$
$173$	−0.531721	+	0.531721i	−0.0404260	+	0.0404260i	0.686605	+	0.727031i	$0.259100\pi$
$174$	11.7871	+	15.1535i	0.893579	+	1.14878i
$175$	−3.83472	+	3.20857i	−0.289878	+	0.242545i
$176$	9.32146	−	2.76290i	0.702632	−	0.208262i
$177$			15.8044i			1.18793i
$178$	−3.08658	+	2.40089i	−0.231349	+	0.179954i
$179$	12.8188	+	12.8188i	0.958124	+	0.958124i	0.999158	−	0.0410335i	$-0.0130650\pi$
$179$	12.8188	+	12.8188i	0.958124	+	0.958124i	−0.0410335	+	0.999158i	$0.513065\pi$
$180$	−3.73137	−	37.2859i	−0.278120	−	2.77912i
$181$	−17.2019	+	17.2019i	−1.27860	+	1.27860i	−0.337154	+	0.941449i	$0.609464\pi$
$181$	−17.2019	+	17.2019i	−1.27860	+	1.27860i	−0.941449	+	0.337154i	$0.890536\pi$
$182$	−7.13634	−	0.891726i	−0.528981	−	0.0660992i
$183$	33.3841			2.46783
$184$	−4.58202	+	2.00493i	−0.337791	+	0.147805i
$185$	−0.443486	+	0.949323i	−0.0326058	+	0.0697956i
$186$	−3.83058	−	0.478652i	−0.280872	−	0.0350965i
$187$	−7.89460	−	7.89460i	−0.577310	−	0.577310i
$188$	10.1024	+	2.56476i	0.736795	+	0.187054i
$189$	−12.8304	−	12.8304i	−0.933274	−	0.933274i
$190$	−14.9291	+	3.40204i	−1.08307	+	0.246810i
$191$	22.4272			1.62278			0.811389	−	0.584507i	$-0.198712\pi$
$191$	22.4272			1.62278			0.811389	+	0.584507i	$0.198712\pi$
$192$	−1.06649	−	26.9652i	−0.0769674	−	1.94604i
$193$		−	1.27540i		−	0.0918055i	−0.998946	−	0.0459028i	$-0.985384\pi$
$193$		−	1.27540i		−	0.0918055i	0.998946	−	0.0459028i	$-0.0146164\pi$
$194$	−5.75267	+	4.47470i	−0.413018	+	0.321265i
$195$	−36.0544	+	13.0941i	−2.58191	+	0.937692i
$196$	−0.492138	+	1.93850i	−0.0351527	+	0.138465i
$197$	−11.2903	−	11.2903i	−0.804402	−	0.804402i	0.179378	−	0.983780i	$-0.442592\pi$
$197$	−11.2903	−	11.2903i	−0.804402	−	0.804402i	−0.983780	+	0.179378i	$0.942592\pi$
$198$	3.57116	−	28.5794i	0.253791	−	2.03105i
$199$			0.254961i			0.0180737i	0.999959	+	0.00903686i	$0.00287656\pi$
$199$			0.254961i			0.0180737i	−0.999959	+	0.00903686i	$0.997123\pi$
$200$	−6.29866	+	12.6620i	−0.445382	+	0.895340i
$201$		−	33.4193i		−	2.35722i
$202$	2.58515	+	0.323029i	0.181890	+	0.0227282i
$203$	−2.84560	−	2.84560i	−0.199722	−	0.199722i
$204$	−26.6314	+	15.8471i	−1.86457	+	1.10952i
$205$	12.4477	−	4.52073i	0.869386	−	0.315741i
$206$	−6.87320	−	8.83618i	−0.478879	−	0.615646i
$207$			14.8165i			1.02982i
$208$	−19.5029	+	5.78071i	−1.35228	+	0.400820i
$209$	−11.7689			−0.814072
$210$	2.37009	+	10.4006i	0.163552	+	0.717711i
$211$	0.777775	+	0.777775i	0.0535443	+	0.0535443i	0.733372	−	0.679828i	$-0.237945\pi$
$211$	0.777775	+	0.777775i	0.0535443	+	0.0535443i	−0.679828	+	0.733372i	$0.737945\pi$
$212$	6.44524	−	3.83527i	0.442661	−	0.263407i
$213$	3.45850	+	3.45850i	0.236973	+	0.236973i
$214$	2.41984	−	19.3656i	0.165417	−	1.32380i
$215$	10.4115	−	22.2868i	0.710059	−	1.51994i
$216$	−47.7939	−	18.6990i	−3.25196	−	1.27231i
$217$	0.809210			0.0549328
$218$	0.532841	−	4.26424i	0.0360885	−	0.288811i
$219$	−12.5830	+	12.5830i	−0.850283	+	0.850283i
$220$	−6.88259	+	8.41333i	−0.464024	+	0.567226i
$221$	16.5175	+	16.5175i	1.11109	+	1.11109i
$222$	1.37250	+	1.76449i	0.0921163	+	0.118425i
$223$		−	17.5805i		−	1.17728i	−0.808396	−	0.588638i	$-0.799664\pi$
$223$		−	17.5805i		−	1.17728i	0.808396	−	0.588638i	$-0.200336\pi$
$224$	0.922686	+	5.58110i	0.0616496	+	0.372903i
$225$	26.8847	+	32.1312i	1.79231	+	2.14208i
$226$	−19.6448	+	15.2807i	−1.30675	+	1.01646i
$227$	−2.49527	+	2.49527i	−0.165617	+	0.165617i	−0.785050	−	0.619433i	$-0.787363\pi$
$227$	−2.49527	+	2.49527i	−0.165617	+	0.165617i	0.619433	+	0.785050i	$0.287363\pi$
$228$	−8.03834	+	31.6625i	−0.532352	+	2.09690i
$229$	−10.0931	+	10.0931i	−0.666972	+	0.666972i	−0.957014	−	0.290042i	$-0.906331\pi$
$229$	−10.0931	+	10.0931i	−0.666972	+	0.666972i	0.290042	+	0.957014i	$0.406331\pi$
$230$	2.97666	−	4.73369i	0.196275	−	0.312130i
$231$			8.19902i			0.539456i
$232$	−10.6000	−	4.14717i	−0.695925	−	0.272275i
$233$	−29.5446			−1.93553			−0.967764	−	0.251857i	$-0.918959\pi$
$233$	−29.5446			−1.93553			−0.967764	+	0.251857i	$0.918959\pi$
$234$	−7.47179	+	59.7955i	−0.488446	+	3.90896i
$235$	−10.9532	+	3.97795i	−0.714507	+	0.259493i
$236$	−4.79170	−	8.05253i	−0.311913	−	0.524175i
$237$	−17.6714	+	17.6714i	−1.14788	+	1.14788i
$238$	5.12751	−	3.98842i	0.332367	−	0.258531i
$239$	21.3312			1.37980			0.689902	−	0.723903i	$-0.257654\pi$
$239$	21.3312			1.37980			0.689902	+	0.723903i	$0.257654\pi$
$240$	17.9339	+	24.2630i	1.15763	+	1.56617i
$241$	−26.6451			−1.71636			−0.858181	−	0.513347i	$-0.828406\pi$
$241$	−26.6451			−1.71636			−0.858181	+	0.513347i	$0.828406\pi$
$242$	5.68440	−	4.42160i	0.365407	−	0.284231i
$243$	−47.5475	+	47.5475i	−3.05017	+	3.05017i
$244$	−17.0096	+	10.1216i	−1.08893	+	0.647972i
$245$	−0.763308	−	2.10175i	−0.0487660	−	0.134276i
$246$	3.50322	−	28.0357i	0.223357	−	1.78749i
$247$	24.6236			1.56676
$248$	2.09684	−	0.917504i	0.133150	−	0.0582615i
$249$		−	5.80462i		−	0.367853i
$250$	−2.13412	−	15.6667i	−0.134973	−	0.990849i
$251$	7.20385	−	7.20385i	0.454703	−	0.454703i	−0.442209	−	0.896912i	$-0.645805\pi$
$251$	7.20385	−	7.20385i	0.454703	−	0.454703i	0.896912	+	0.442209i	$0.145805\pi$
$252$	16.2428	+	4.12364i	1.02320	+	0.259765i
$253$	3.03911	−	3.03911i	0.191067	−	0.191067i
$254$	−2.13192	+	1.65831i	−0.133769	+	0.104052i
$255$	14.6647	−	31.3911i	0.918339	−	1.96579i
$256$	8.71888	+	13.4157i	0.544930	+	0.838482i
$257$			6.46889i			0.403518i	0.979435	+	0.201759i	$0.0646658\pi$
$257$			6.46889i			0.403518i	−0.979435	+	0.201759i	$0.935334\pi$
$258$	−32.2216	−	41.4240i	−2.00603	−	2.57894i
$259$	−0.331345	−	0.331345i	−0.0205888	−	0.0205888i
$260$	14.4002	−	17.6029i	0.893060	−	1.09168i
$261$	−23.8434	+	23.8434i	−1.47587	+	1.47587i
$262$	−0.108632	+	0.869368i	−0.00671133	+	0.0537097i
$263$	−31.0166			−1.91256			−0.956281	−	0.292449i	$-0.905530\pi$
$263$	−31.0166			−1.91256			−0.956281	+	0.292449i	$0.905530\pi$
$264$	9.29626	+	21.2455i	0.572145	+	1.30757i
$265$	−3.54910	+	7.59716i	−0.218019	+	0.466690i
$266$	0.849050	−	6.79481i	0.0520586	−	0.416616i
$267$	−6.59543	−	6.59543i	−0.403634	−	0.403634i
$268$	10.1323	+	17.0275i	0.618929	+	1.04012i
$269$	−2.47842	−	2.47842i	−0.151112	−	0.151112i	0.627503	−	0.778614i	$-0.284077\pi$
$269$	−2.47842	−	2.47842i	−0.151112	−	0.151112i	−0.778614	+	0.627503i	$0.784077\pi$
$270$	55.9451	−	12.7488i	3.40471	−	0.775865i
$271$	15.9465			0.968680			0.484340	−	0.874880i	$-0.339060\pi$
$271$	15.9465			0.968680			0.484340	+	0.874880i	$0.339060\pi$
$272$	8.76435	−	16.1486i	0.531417	−	0.979153i
$273$		−	17.1545i		−	1.03824i
$274$	−5.45849	−	7.01742i	−0.329759	−	0.423938i
$275$	1.07615	−	12.1051i	0.0648945	−	0.729968i
$276$	−6.10053	−	10.2521i	−0.367209	−	0.617101i
$277$	2.59371	+	2.59371i	0.155841	+	0.155841i	0.780721	−	0.624880i	$-0.214852\pi$
$277$	2.59371	+	2.59371i	0.155841	+	0.155841i	−0.624880	+	0.780721i	$0.714852\pi$
$278$	−19.3710	−	2.42052i	−1.16180	−	0.145173i
$279$		−	6.78038i		−	0.405931i
$280$	−4.36092	−	4.58065i	−0.260615	−	0.273746i
$281$			11.1192i			0.663314i	0.943400	+	0.331657i	$0.107608\pi$
$281$			11.1192i			0.663314i	−0.943400	+	0.331657i	$0.892392\pi$
$282$	−3.08260	+	24.6696i	−0.183566	+	1.46905i
$283$	−7.12540	−	7.12540i	−0.423561	−	0.423561i	0.462867	−	0.886428i	$-0.346821\pi$
$283$	−7.12540	−	7.12540i	−0.423561	−	0.423561i	−0.886428	+	0.462867i	$0.846821\pi$
$284$	−2.81072	−	0.713573i	−0.166786	−	0.0423427i
$285$	−12.4675	−	34.3289i	−0.738510	−	2.03347i
$286$	13.7977	−	10.7325i	0.815873	−	0.634625i
$287$			5.92254i			0.349597i
$288$	46.7641	−	7.73120i	2.75560	−	0.455565i
$289$	−4.09945			−0.241144
$290$	12.4078	−	2.82750i	0.728613	−	0.166036i
$291$	−12.2924	−	12.2924i	−0.720591	−	0.720591i
$292$	2.59618	−	10.2262i	0.151930	−	0.598444i
$293$	−16.0094	−	16.0094i	−0.935278	−	0.935278i	0.0627512	−	0.998029i	$-0.480013\pi$
$293$	−16.0094	−	16.0094i	−0.935278	−	0.935278i	−0.998029	+	0.0627512i	$0.980013\pi$
$294$	−4.73373	−	0.591506i	−0.276076	−	0.0344973i
$295$	9.49172	+	4.43416i	0.552629	+	0.258167i
$296$	−1.23428	−	0.482901i	−0.0717408	−	0.0280680i
$297$	44.1026			2.55909
$298$	−18.4499	−	2.30542i	−1.06878	−	0.133550i
$299$	−6.35861	+	6.35861i	−0.367728	+	0.367728i
$300$	−31.8321	−	11.1632i	−1.83783	−	0.644509i
$301$	7.77881	+	7.77881i	0.448363	+	0.448363i
$302$	−14.2874	+	11.1134i	−0.822148	+	0.639506i
$303$			6.21423i			0.356998i
$304$	−5.50405	−	18.5695i	−0.315679	−	1.06504i
$305$	9.36640	−	20.0496i	0.536319	−	1.14804i
$306$	−33.4191	−	42.9635i	−1.91044	−	2.45606i
$307$	−0.0673141	+	0.0673141i	−0.00384182	+	0.00384182i	−0.709025	−	0.705183i	$-0.750865\pi$
$307$	−0.0673141	+	0.0673141i	−0.00384182	+	0.00384182i	0.705183	+	0.709025i	$0.250865\pi$
$308$	−2.48584	−	4.17749i	−0.141644	−	0.238035i
$309$	18.8812	−	18.8812i	1.07412	−	1.07412i
$310$	−1.36219	+	2.16625i	−0.0773672	+	0.123035i
$311$			29.5091i			1.67331i	0.547732	+	0.836654i	$0.315491\pi$
$311$			29.5091i			1.67331i	−0.547732	+	0.836654i	$0.684509\pi$
$312$	−19.4502	−	44.4511i	−1.10115	−	2.51655i
$313$	−5.95189			−0.336421			−0.168210	−	0.985751i	$-0.553799\pi$
$313$	−5.95189			−0.336421			−0.168210	+	0.985751i	$0.553799\pi$
$314$	5.53036	+	0.691049i	0.312096	+	0.0389982i
$315$	−17.6106	+	6.39577i	−0.992246	+	0.360361i
$316$	3.64604	−	14.3615i	0.205106	−	0.807899i
$317$	−23.7365	+	23.7365i	−1.33317	+	1.33317i	−0.430661	+	0.902514i	$0.641720\pi$
$317$	−23.7365	+	23.7365i	−1.33317	+	1.33317i	−0.902514	+	0.430661i	$0.858280\pi$
$318$	10.9838	+	14.1207i	0.615938	+	0.791849i
$319$	9.78135			0.547650
$320$	−16.4938	−	6.92496i	−0.922031	−	0.387117i
$321$	46.5514			2.59824
$322$	1.53539	+	1.97389i	0.0855638	+	0.110001i
$323$	−15.7270	+	15.7270i	−0.875076	+	0.875076i
$324$	17.7519	−	69.9235i	0.986214	−	3.88464i
$325$	−2.25159	+	25.3271i	−0.124896	+	1.40489i
$326$	14.7196	+	1.83930i	0.815245	+	0.101869i
$327$	10.2505			0.566851
$328$	6.71513	+	15.3466i	0.370781	+	0.847376i
$329$		−	5.21145i		−	0.287317i
$330$	−21.9487	−	13.8019i	−1.20824	−	0.759768i
$331$	−9.90992	+	9.90992i	−0.544698	+	0.544698i	−0.924903	−	0.380204i	$-0.875854\pi$
$331$	−9.90992	+	9.90992i	−0.544698	+	0.544698i	0.380204	+	0.924903i	$0.375854\pi$
$332$	1.75989	+	2.95752i	0.0965864	+	0.162315i
$333$	−2.77634	+	2.77634i	−0.152143	+	0.152143i
$334$	−2.22171	−	2.85623i	−0.121567	−	0.156286i
$335$	−20.0708	−	9.37627i	−1.09658	−	0.512280i
$336$	−12.9368	+	3.83450i	−0.705761	+	0.209189i
$337$			26.0747i			1.42038i	0.704010	+	0.710190i	$0.251391\pi$
$337$			26.0747i			1.42038i	−0.704010	+	0.710190i	$0.748609\pi$
$338$	−14.3567	+	11.1673i	−0.780902	+	0.607423i
$339$	−41.9773	−	41.9773i	−2.27989	−	2.27989i
$340$	2.04556	+	20.4403i	0.110936	+	1.10853i
$341$	−1.39077	+	1.39077i	−0.0753145	+	0.0753145i
$342$	−56.9338	−	7.11420i	−3.07863	−	0.384692i
$343$	1.00000			0.0539949
$344$	28.9765	+	11.3368i	1.56231	+	0.611240i
$345$	12.0844	+	5.64533i	0.650600	+	0.303935i
$346$	1.05524	+	0.131858i	0.0567298	+	0.00708871i
$347$	13.3217	+	13.3217i	0.715144	+	0.715144i	0.967607	−	0.252463i	$-0.0812405\pi$
$347$	13.3217	+	13.3217i	0.715144	+	0.715144i	−0.252463	+	0.967607i	$0.581241\pi$
$348$	6.68081	−	26.3153i	0.358129	−	1.41065i
$349$	4.95741	+	4.95741i	0.265364	+	0.265364i	0.827229	−	0.561865i	$-0.189916\pi$
$349$	4.95741	+	4.95741i	0.265364	+	0.265364i	−0.561865	+	0.827229i	$0.689916\pi$
$350$	6.91130	+	1.49463i	0.369425	+	0.0798912i
$351$	−92.2742			−4.92523
$352$	−11.1779	−	8.00631i	−0.595784	−	0.426738i
$353$			13.0813i			0.696247i	0.937449	+	0.348123i	$0.113181\pi$
$353$			13.0813i			0.696247i	−0.937449	+	0.348123i	$0.886819\pi$
$354$	17.6421	−	13.7229i	0.937666	−	0.729361i
$355$	3.04742	−	1.10675i	0.161740	−	0.0587404i
$356$	5.36010	+	1.36080i	0.284085	+	0.0721221i
$357$	10.9565	+	10.9565i	0.579881	+	0.579881i
$358$	3.17885	−	25.4398i	0.168007	−	1.34454i
$359$			7.74267i			0.408643i	0.978904	+	0.204321i	$0.0654987\pi$
$359$			7.74267i			0.408643i	−0.978904	+	0.204321i	$0.934501\pi$
$360$	−38.3813	+	36.5402i	−2.02287	+	1.92584i
$361$			4.44516i			0.233956i
$362$	34.1382	+	4.26576i	1.79427	+	0.224204i
$363$	12.1465	+	12.1465i	0.637526	+	0.637526i
$364$	5.20102	+	8.74040i	0.272607	+	0.458121i
$365$	4.02669	+	11.0874i	0.210767	+	0.580341i
$366$	−28.9872	−	37.2659i	−1.51518	−	1.94792i
$367$			33.1187i			1.72878i	0.502819	+	0.864392i	$0.332296\pi$
$367$			33.1187i			1.72878i	−0.502819	+	0.864392i	$0.667704\pi$
$368$	6.21658	+	3.37393i	0.324062	+	0.175878i
$369$	49.6251			2.58338
$370$	1.44478	−	0.329237i	0.0751105	−	0.0171162i
$371$	−2.65166	−	2.65166i	−0.137667	−	0.137667i
$372$	2.79175	+	4.69159i	0.144746	+	0.243247i
$373$	8.95484	+	8.95484i	0.463664	+	0.463664i	0.899854	−	0.436190i	$-0.143673\pi$
$373$	8.95484	+	8.95484i	0.463664	+	0.463664i	−0.436190	+	0.899854i	$0.643673\pi$
$374$	−1.95772	+	15.6674i	−0.101232	+	0.810139i
$375$	36.4498	−	9.68464i	1.88226	−	0.500112i
$376$	−5.90888	−	13.5040i	−0.304727	−	0.696418i
$377$	−20.4651			−1.05401
$378$	−3.18172	+	25.4628i	−0.163650	+	1.30966i
$379$	0.100978	−	0.100978i	0.00518689	−	0.00518689i	−0.704509	−	0.709695i	$-0.748833\pi$
$379$	0.100978	−	0.100978i	0.00518689	−	0.00518689i	0.709695	+	0.704509i	$0.248833\pi$
$380$	16.7604	+	13.7110i	0.859791	+	0.703359i
$381$	−4.55551	−	4.55551i	−0.233386	−	0.233386i
$382$	−19.4734	−	25.0350i	−0.996345	−	1.28090i
$383$		−	22.3997i		−	1.14457i	−0.820054	−	0.572287i	$-0.806056\pi$
$383$		−	22.3997i		−	1.14457i	0.820054	−	0.572287i	$-0.193944\pi$
$384$	−29.1745	+	24.6041i	−1.48880	+	1.25557i
$385$	4.92411	+	2.30035i	0.250956	+	0.117237i
$386$	−1.42370	+	1.10742i	−0.0724644	+	0.0563663i
$387$	65.1788	−	65.1788i	3.31322	−	3.31322i
$388$	9.98999	+	2.53621i	0.507165	+	0.128757i
$389$	−12.5317	+	12.5317i	−0.635381	+	0.635381i	−0.949413	−	0.314032i	$-0.898320\pi$
$389$	−12.5317	+	12.5317i	−0.635381	+	0.635381i	0.314032	+	0.949413i	$0.398320\pi$
$390$	45.9224	+	28.8771i	2.32537	+	1.46225i
$391$		−	8.12246i		−	0.410771i
$392$	2.59122	−	1.13383i	0.130877	−	0.0572669i
$393$	−2.08980			−0.105417
$394$	−2.79981	+	22.4064i	−0.141052	+	1.12882i
$395$	5.65502	+	15.5710i	0.284535	+	0.783460i
$396$	−35.0033	+	20.8289i	−1.75898	+	1.04669i
$397$	7.25678	−	7.25678i	0.364207	−	0.364207i	−0.501152	−	0.865359i	$-0.667090\pi$
$397$	7.25678	−	7.25678i	0.364207	−	0.364207i	0.865359	+	0.501152i	$0.167090\pi$
$398$	0.284607	−	0.221381i	0.0142660	−	0.0110968i
$399$	16.3335			0.817697
$400$	19.6034	−	3.96330i	0.980169	−	0.198165i
$401$	27.0791			1.35227			0.676134	−	0.736779i	$-0.263654\pi$
$401$	27.0791			1.35227			0.676134	+	0.736779i	$0.263654\pi$
$402$	−37.3051	+	29.0177i	−1.86061	+	1.44727i
$403$	2.90985	−	2.90985i	0.144950	−	0.144950i
$404$	−1.88407	−	3.16622i	−0.0937362	−	0.157525i
$405$	27.5332	+	75.8120i	1.36814	+	3.76713i
$406$	−0.705661	+	5.64729i	−0.0350214	+	0.280270i
$407$	1.13895			0.0564556
$408$	40.8136	+	15.9680i	2.02057	+	0.790534i
$409$			5.15928i			0.255110i	0.991831	+	0.127555i	$0.0407129\pi$
$409$			5.15928i			0.255110i	−0.991831	+	0.127555i	$0.959287\pi$
$410$	−15.8546	−	9.96976i	−0.783004	−	0.492371i
$411$	14.9949	−	14.9949i	0.739644	−	0.739644i
$412$	−3.89566	+	15.3448i	−0.191925	+	0.755982i
$413$	−3.31292	+	3.31292i	−0.163018	+	0.163018i
$414$	16.5393	−	12.8650i	0.812861	−	0.632282i
$415$	−3.48610	−	1.62857i	−0.171126	−	0.0799434i
$416$	23.3871	+	16.7513i	1.14665	+	0.821299i
$417$		−	46.5645i		−	2.28027i
$418$	10.2188	+	13.1373i	0.499820	+	0.642568i
$419$	−12.0629	−	12.0629i	−0.589311	−	0.589311i	0.348134	−	0.937445i	$-0.386816\pi$
$419$	−12.0629	−	12.0629i	−0.589311	−	0.589311i	−0.937445	+	0.348134i	$0.886816\pi$
$420$	9.55201	−	11.6764i	0.466090	−	0.569752i
$421$	−13.7925	+	13.7925i	−0.672207	+	0.672207i	−0.958224	−	0.286017i	$-0.907668\pi$
$421$	−13.7925	+	13.7925i	−0.672207	+	0.672207i	0.286017	+	0.958224i	$0.407668\pi$
$422$	0.192875	−	1.54355i	0.00938900	−	0.0751387i
$423$	−43.6668			−2.12315
$424$	−9.87756	−	3.86452i	−0.479697	−	0.187678i
$425$	−14.7383	−	17.6145i	−0.714912	−	0.854427i
$426$	0.857649	−	6.86363i	0.0415533	−	0.332544i
$427$	6.99798	+	6.99798i	0.338656	+	0.338656i
$428$	−23.7184	+	14.1138i	−1.14647	+	0.682215i
$429$	29.4830	+	29.4830i	1.42345	+	1.42345i
$430$	−33.9184	+	7.72932i	−1.63569	+	0.372741i
$431$	9.07113			0.436941			0.218470	−	0.975844i	$-0.429893\pi$
$431$	9.07113			0.436941			0.218470	+	0.975844i	$0.429893\pi$
$432$	20.6258	+	69.5873i	0.992360	+	3.34802i
$433$			34.6195i			1.66371i	0.554996	+	0.831853i	$0.312720\pi$
$433$			34.6195i			1.66371i	−0.554996	+	0.831853i	$0.687280\pi$
$434$	−0.702631	−	0.903301i	−0.0337273	−	0.0433598i
$435$	10.3620	+	28.5314i	0.496818	+	1.36798i
$436$	−5.22272	+	3.10781i	−0.250123	+	0.148837i
$437$	−6.05430	−	6.05430i	−0.289616	−	0.289616i
$438$	24.9719	+	3.12038i	1.19320	+	0.149097i
$439$			5.49191i			0.262115i	0.991375	+	0.131057i	$0.0418372\pi$
$439$			5.49191i			0.262115i	−0.991375	+	0.131057i	$0.958163\pi$
$440$	15.3677	+	0.377639i	0.732625	+	0.0180032i
$441$		−	8.37902i		−	0.399001i
$442$	4.09607	−	32.7802i	0.194830	−	1.55919i
$443$	18.8600	+	18.8600i	0.896068	+	0.896068i	0.995086	−	0.0990180i	$-0.0315701\pi$
$443$	18.8600	+	18.8600i	0.896068	+	0.896068i	−0.0990180	+	0.995086i	$0.531570\pi$
$444$	0.777920	−	3.06418i	0.0369184	−	0.145420i
$445$	−5.81149	+	2.11060i	−0.275491	+	0.100052i
$446$	−19.6247	+	15.2650i	−0.929254	+	0.722819i
$447$		−	44.3503i		−	2.09770i
$448$	5.42888	−	5.87599i	0.256490	−	0.277615i
$449$	−21.9379			−1.03532			−0.517658	−	0.855588i	$-0.673196\pi$
$449$	−21.9379			−1.03532			−0.517658	+	0.855588i	$0.673196\pi$
$450$	12.5235	−	57.9099i	0.590364	−	2.72990i
$451$	−10.1789	−	10.1789i	−0.479308	−	0.479308i
$452$	34.1149	+	8.66093i	1.60463	+	0.407376i
$453$	−30.5295	−	30.5295i	−1.43440	−	1.43440i
$454$	4.95204	+	0.618785i	0.232411	+	0.0290410i
$455$	−10.3025	−	4.81294i	−0.482990	−	0.225634i
$456$	42.3237	−	18.5193i	1.98199	−	0.867247i
$457$	4.60165			0.215256			0.107628	−	0.994191i	$-0.465674\pi$
$457$	4.60165			0.215256			0.107628	+	0.994191i	$0.465674\pi$
$458$	20.0305	+	2.50292i	0.935963	+	0.116954i
$459$	58.9353	−	58.9353i	2.75087	−	2.75087i
$460$	−7.86871	+	0.787459i	−0.366880	+	0.0367155i
$461$	15.0173	+	15.0173i	0.699427	+	0.699427i	0.964287	−	0.264860i	$-0.0853257\pi$
$461$	15.0173	+	15.0173i	0.699427	+	0.699427i	−0.264860	+	0.964287i	$0.585326\pi$
$462$	9.15235	−	7.11914i	0.425806	−	0.331212i
$463$		−	23.4758i		−	1.09101i	−0.838107	−	0.545507i	$-0.816337\pi$
$463$		−	23.4758i		−	1.09101i	0.838107	−	0.545507i	$-0.183663\pi$
$464$	4.57452	+	15.4335i	0.212367	+	0.716481i
$465$	−5.53009	−	2.58344i	−0.256452	−	0.119804i
$466$	25.6533	+	32.9799i	1.18837	+	1.52776i
$467$	−13.4848	+	13.4848i	−0.624004	+	0.624004i	−0.946553	−	0.322549i	$-0.895460\pi$
$467$	−13.4848	+	13.4848i	−0.624004	+	0.624004i	0.322549	+	0.946553i	$0.395460\pi$
$468$	73.2359	−	43.5794i	3.38533	−	2.01446i
$469$	7.00535	−	7.00535i	0.323477	−	0.323477i
$470$	13.9510	+	8.77274i	0.643513	+	0.404656i
$471$			13.2940i			0.612554i
$472$	−4.82824	+	12.3408i	−0.222238	+	0.568031i
$473$	−26.7385			−1.22944
$474$	35.0701	+	4.38221i	1.61082	+	0.201281i
$475$	−24.1150	−	2.14383i	−1.10647	−	0.0983659i
$476$	−8.90435	−	2.26060i	−0.408130	−	0.103614i
$477$	−22.2183	+	22.2183i	−1.01731	+	1.01731i
$478$	−18.5217	−	23.8115i	−0.847165	−	1.08911i
$479$	−23.1995			−1.06001			−0.530007	−	0.847993i	$-0.677811\pi$
$479$	−23.1995			−1.06001			−0.530007	+	0.847993i	$0.677811\pi$
$480$	11.5123	−	41.0866i	0.525464	−	1.87534i
$481$	−2.38298			−0.108654
$482$	23.1357	+	29.7433i	1.05380	+	1.35477i
$483$	−4.21784	+	4.21784i	−0.191918	+	0.191918i
$484$	−9.87144	−	2.50611i	−0.448702	−	0.113914i
$485$	−10.8313	+	3.93367i	−0.491823	+	0.178619i
$486$	94.3612	+	11.7910i	4.28031	+	0.534849i
$487$	−36.9509			−1.67441			−0.837203	−	0.546892i	$-0.815811\pi$
$487$	−36.9509			−1.67441			−0.837203	+	0.546892i	$0.815811\pi$
$488$	26.0678	+	10.1988i	1.18004	+	0.461680i
$489$			35.3833i			1.60009i
$490$	−1.68336	+	2.67700i	−0.0760464	+	0.120934i
$491$	−13.0153	+	13.0153i	−0.587372	+	0.587372i	−0.936919	−	0.349547i	$-0.886336\pi$
$491$	−13.0153	+	13.0153i	−0.587372	+	0.587372i	0.349547	+	0.936919i	$0.386336\pi$
$492$	−34.3373	+	20.4326i	−1.54805	+	0.921173i
$493$	13.0710	−	13.0710i	0.588690	−	0.588690i
$494$	−21.3805	−	27.4867i	−0.961953	−	1.23669i
$495$	19.2747	−	41.2592i	0.866333	−	1.85446i
$496$	−2.84486	−	1.54399i	−0.127738	−	0.0693273i
$497$			1.44994i			0.0650388i
$498$	−6.47955	+	5.04011i	−0.290356	+	0.225853i
$499$	−18.6909	−	18.6909i	−0.836721	−	0.836721i	0.151705	−	0.988426i	$-0.451524\pi$
$499$	−18.6909	−	18.6909i	−0.836721	−	0.836721i	−0.988426	+	0.151705i	$0.951524\pi$
$500$	−15.6353	+	15.9855i	−0.699232	+	0.714895i
$501$	6.10323	−	6.10323i	0.272672	−	0.272672i
$502$	−14.2965	−	1.78643i	−0.638085	−	0.0797323i
$503$	−36.0463			−1.60723			−0.803613	−	0.595152i	$-0.797092\pi$
$503$	−36.0463			−1.60723			−0.803613	+	0.595152i	$0.797092\pi$
$504$	−9.50035	−	21.7119i	−0.423179	−	0.967125i
$505$	3.73210	+	1.74349i	0.166076	+	0.0775844i
$506$	−6.03132	−	0.753648i	−0.268125	−	0.0335037i
$507$	−30.6776	−	30.6776i	−1.36244	−	1.36244i
$508$	3.70226	+	0.939912i	0.164261	+	0.0417018i
$509$	−2.17289	−	2.17289i	−0.0963118	−	0.0963118i	0.657309	−	0.753621i	$-0.271695\pi$
$509$	−2.17289	−	2.17289i	−0.0963118	−	0.0963118i	−0.753621	+	0.657309i	$0.771695\pi$
$510$	−47.7743	+	10.8868i	−2.11548	+	0.482076i
$511$	−5.27531			−0.233366
$512$	7.40508	−	21.3814i	0.327261	−	0.944934i
$513$		−	87.8581i		−	3.87903i
$514$	7.22106	−	5.61689i	0.318507	−	0.247750i
$515$	−6.04217	−	16.6370i	−0.266250	−	0.733113i
$516$	−18.2628	+	71.9362i	−0.803976	+	3.16681i
$517$	8.95681	+	8.95681i	0.393920	+	0.393920i
$518$	−0.0821678	+	0.657576i	−0.00361025	+	0.0288922i
$519$			2.53659i			0.111344i
$520$	−32.1532	−	0.790118i	−1.41001	−	0.0346490i
$521$		−	26.1029i		−	1.14359i	−0.820396	−	0.571795i	$-0.806247\pi$
$521$		−	26.1029i		−	1.14359i	0.820396	−	0.571795i	$-0.193753\pi$
$522$	47.3187	+	5.91274i	2.07108	+	0.258794i
$523$	12.2265	+	12.2265i	0.534627	+	0.534627i	0.921946	−	0.387319i	$-0.126599\pi$
$523$	12.2265	+	12.2265i	0.534627	+	0.534627i	−0.387319	+	0.921946i	$0.626599\pi$
$524$	1.06478	−	0.633601i	0.0465150	−	0.0276790i
$525$	−1.49354	+	16.8001i	−0.0651835	+	0.733218i
$526$	26.9314	+	34.6230i	1.17427	+	1.50963i
$527$			3.71704i			0.161917i
$528$	15.6439	−	28.8245i	0.680815	−	1.25442i
$529$	−19.8732			−0.864051
$530$	11.5622	−	2.63479i	0.502229	−	0.114448i
$531$	27.7590	+	27.7590i	1.20464	+	1.20464i
$532$	−8.32210	+	4.95210i	−0.360809	+	0.214701i
$533$	21.2970	+	21.2970i	0.922475	+	0.922475i
$534$	−1.63555	+	13.0891i	−0.0707774	+	0.566420i
$535$	13.0607	−	27.9575i	0.564661	−	1.20871i
$536$	10.2096	−	26.0953i	0.440987	−	1.12714i
$537$	61.1527			2.63893
$538$	−0.614605	+	4.91859i	−0.0264975	+	0.212055i
$539$	−1.71868	+	1.71868i	−0.0740287	+	0.0740287i
$540$	−62.8078	−	51.3804i	−2.70282	−	2.21106i
$541$	−0.367830	−	0.367830i	−0.0158143	−	0.0158143i	0.699155	−	0.714970i	$-0.253560\pi$
$541$	−0.367830	−	0.367830i	−0.0158143	−	0.0158143i	−0.714970	+	0.699155i	$0.753560\pi$
$542$	−13.8462	−	17.8007i	−0.594745	−	0.764603i
$543$			82.0621i			3.52162i
$544$	−25.6363	+	4.23828i	−1.09915	+	0.181715i
$545$	2.87591	−	6.15615i	0.123191	−	0.263701i
$546$	−19.1491	+	14.8951i	−0.819506	+	0.637451i
$547$	3.43264	−	3.43264i	0.146769	−	0.146769i	−0.629904	−	0.776673i	$-0.716906\pi$
$547$	3.43264	−	3.43264i	0.146769	−	0.146769i	0.776673	+	0.629904i	$0.216906\pi$
$548$	−3.09381	+	12.1863i	−0.132161	+	0.520575i
$549$	58.6362	−	58.6362i	2.50253	−	2.50253i
$550$	−14.4471	+	9.30952i	−0.616026	+	0.396959i
$551$		−	19.4857i		−	0.830118i
$552$	−6.14706	+	15.7116i	−0.261636	+	0.668732i
$553$	−7.40856			−0.315044
$554$	0.643196	−	5.14739i	0.0273268	−	0.218692i
$555$	1.20656	+	3.32222i	0.0512154	+	0.141021i
$556$	14.1178	+	23.7251i	0.598726	+	1.00617i
$557$	5.78902	−	5.78902i	0.245288	−	0.245288i	−0.573745	−	0.819034i	$-0.694510\pi$
$557$	5.78902	−	5.78902i	0.245288	−	0.245288i	0.819034	+	0.573745i	$0.194510\pi$
$558$	−7.56877	+	5.88735i	−0.320412	+	0.249232i
$559$	55.9440			2.36618
$560$	−1.32671	+	8.84533i	−0.0560637	+	0.373783i
$561$	−37.6615			−1.59007
$562$	12.4120	−	9.65468i	0.523571	−	0.407258i
$563$	26.0736	−	26.0736i	1.09887	−	1.09887i	0.104330	−	0.994543i	$-0.466730\pi$
$563$	26.0736	−	26.0736i	1.09887	−	1.09887i	0.994543	−	0.104330i	$-0.0332697\pi$
$564$	30.2146	−	17.9794i	1.27227	−	0.757068i
$565$	−36.9878	+	13.4331i	−1.55609	+	0.565136i
$566$	−1.76698	+	14.1408i	−0.0742715	+	0.594383i
$567$	−36.0709			−1.51483
$568$	1.64398	+	3.75713i	0.0689800	+	0.157645i
$569$			0.651442i			0.0273099i	0.999907	+	0.0136549i	$0.00434664\pi$
$569$			0.651442i			0.0273099i	−0.999907	+	0.0136549i	$0.995653\pi$
$570$	−27.4951	+	43.7247i	−1.15164	+	1.83143i
$571$	14.8268	−	14.8268i	0.620481	−	0.620481i	−0.325173	−	0.945655i	$-0.605423\pi$
$571$	14.8268	−	14.8268i	0.620481	−	0.620481i	0.945655	+	0.325173i	$0.105423\pi$
$572$	−23.9608	−	6.08305i	−1.00185	−	0.254345i
$573$	53.4950	−	53.4950i	2.23479	−	2.23479i
$574$	6.61118	−	5.14250i	0.275945	−	0.214644i
$575$	6.78088	−	5.67366i	0.282782	−	0.236608i
$576$	−49.2350	−	45.4886i	−2.05146	−	1.89536i
$577$		−	11.5626i		−	0.481356i	−0.970605	−	0.240678i	$-0.922630\pi$
$577$		−	11.5626i		−	0.481356i	0.970605	−	0.240678i	$-0.0773699\pi$
$578$	3.55952	+	4.57611i	0.148056	+	0.190341i
$579$	−3.04218	−	3.04218i	−0.126429	−	0.126429i
$580$	−13.9299	−	11.3955i	−0.578407	−	0.473171i
$581$	1.21677	−	1.21677i	0.0504799	−	0.0504799i
$582$	−3.04830	+	24.3950i	−0.126356	+	1.01121i
$583$	9.11469			0.377492
$584$	−13.6695	+	5.98129i	−0.565648	+	0.247507i
$585$	−40.3277	+	86.3250i	−1.66734	+	3.56910i
$586$	−3.97005	+	31.7717i	−0.164001	+	1.31248i
$587$	−1.78630	−	1.78630i	−0.0737285	−	0.0737285i	0.669281	−	0.743009i	$-0.266602\pi$
$587$	−1.78630	−	1.78630i	−0.0737285	−	0.0737285i	−0.743009	+	0.669281i	$0.766602\pi$
$588$	3.44997	+	5.79774i	0.142274	+	0.239095i
$589$	2.77059	+	2.77059i	0.114160	+	0.114160i
$590$	−3.29185	−	14.4455i	−0.135523	−	0.594712i
$591$	−53.8609			−2.21554
$592$	0.532661	+	1.79709i	0.0218922	+	0.0738599i
$593$		−	32.7537i		−	1.34503i	−0.740082	−	0.672517i	$-0.765213\pi$
$593$		−	32.7537i		−	1.34503i	0.740082	−	0.672517i	$-0.234787\pi$
$594$	−38.2940	−	49.2307i	−1.57122	−	2.01996i
$595$	9.65421	−	3.50619i	0.395784	−	0.143740i
$596$	13.4464	+	22.5970i	0.550788	+	0.925608i
$597$	0.608151	+	0.608151i	0.0248900	+	0.0248900i
$598$	12.6191	+	1.57683i	0.516033	+	0.0644812i
$599$		−	0.336001i		−	0.0137286i	−0.999976	−	0.00686432i	$-0.997815\pi$
$599$		−	0.336001i		−	0.0137286i	0.999976	−	0.00686432i	$-0.00218500\pi$
$600$	15.1783	+	45.2263i	0.619653	+	1.84636i
$601$		−	32.4976i		−	1.32561i	−0.748794	−	0.662803i	$-0.769367\pi$
$601$		−	32.4976i		−	1.32561i	0.748794	−	0.662803i	$-0.230633\pi$
$602$	1.92901	−	15.4376i	0.0786207	−	0.629189i
$603$	−58.6980	−	58.6980i	−2.39037	−	2.39037i
$604$	24.8113	+	6.29897i	1.00956	+	0.256302i
$605$	10.7027	−	3.88699i	0.435128	−	0.158029i
$606$	6.93678	−	5.39576i	0.281788	−	0.219188i
$607$			35.7708i			1.45189i	0.687752	+	0.725946i	$0.258598\pi$
$607$			35.7708i			1.45189i	−0.687752	+	0.725946i	$0.741402\pi$
$608$	−15.9496	+	22.2678i	−0.646841	+	0.903079i
$609$	−13.5751			−0.550089
$610$	−30.5137	+	6.95346i	−1.23546	+	0.281537i
$611$	−18.7400	−	18.7400i	−0.758138	−	0.758138i
$612$	−18.9416	+	74.6097i	−0.765667	+	3.01592i
$613$	−21.7494	−	21.7494i	−0.878449	−	0.878449i	0.114925	−	0.993374i	$-0.463337\pi$
$613$	−21.7494	−	21.7494i	−0.878449	−	0.878449i	−0.993374	+	0.114925i	$0.963337\pi$
$614$	0.133589	+	0.0166927i	0.00539122	+	0.000673664i
$615$	18.9080	−	40.4743i	0.762444	−	1.63208i
$616$	−2.50480	+	6.40216i	−0.100921	+	0.257950i
$617$	37.5170			1.51038			0.755188	−	0.655508i	$-0.227546\pi$
$617$	37.5170			1.51038			0.755188	+	0.655508i	$0.227546\pi$
$618$	−37.4711	−	4.68223i	−1.50731	−	0.188347i
$619$	1.50790	−	1.50790i	0.0606078	−	0.0606078i	−0.676153	−	0.736761i	$-0.736354\pi$
$619$	1.50790	−	1.50790i	0.0606078	−	0.0606078i	0.736761	+	0.676153i	$0.236354\pi$
$620$	3.60091	−	0.360360i	0.144616	−	0.0144724i
$621$	22.6878	+	22.6878i	0.910430	+	0.910430i
$622$	32.9403	−	25.6225i	1.32078	−	1.02737i
$623$		−	2.76507i		−	0.110780i
$624$	−32.7312	+	60.3082i	−1.31030	+	2.41426i
$625$	4.41017	−	24.6079i	0.176407	−	0.984317i
$626$	5.16798	+	6.64394i	0.206554	+	0.265545i
$627$	−28.0720	+	28.0720i	−1.12109	+	1.12109i
$628$	−4.03056	−	6.77343i	−0.160837	−	0.270289i
$629$	1.52200	−	1.52200i	0.0606862	−	0.0606862i
$630$	22.4306	+	14.1049i	0.893656	+	0.561952i
$631$		−	20.6742i		−	0.823026i	−0.911404	−	0.411513i	$-0.865000\pi$
$631$		−	20.6742i		−	0.823026i	0.911404	−	0.411513i	$-0.135000\pi$
$632$	−19.1972	+	8.40002i	−0.763625	+	0.334135i
$633$	3.71041			0.147475
$634$	47.1067	+	5.88624i	1.87084	+	0.233773i
$635$	−4.01403	+	1.45781i	−0.159292	+	0.0578513i
$636$	6.22547	−	24.5218i	0.246856	−	0.972352i
$637$	3.59592	−	3.59592i	0.142476	−	0.142476i
$638$	−8.49306	−	10.9187i	−0.336244	−	0.432274i
$639$	12.1491			0.480611
$640$	6.59126	+	24.4245i	0.260543	+	0.965462i
$641$	32.1794			1.27101			0.635504	−	0.772097i	$-0.280792\pi$
$641$	32.1794			1.27101			0.635504	+	0.772097i	$0.280792\pi$
$642$	−40.4202	−	51.9641i	−1.59526	−	2.05086i
$643$	21.4928	−	21.4928i	0.847595	−	0.847595i	−0.142238	−	0.989833i	$-0.545430\pi$
$643$	21.4928	−	21.4928i	0.847595	−	0.847595i	0.989833	+	0.142238i	$0.0454297\pi$
$644$	0.870241	−	3.42783i	0.0342923	−	0.135075i
$645$	−28.3257	−	77.9942i	−1.11532	−	3.07102i
$646$	31.2114	+	3.90004i	1.22799	+	0.153445i
$647$	−14.0738			−0.553299			−0.276650	−	0.960971i	$-0.589224\pi$
$647$	−14.0738			−0.553299			−0.276650	+	0.960971i	$0.589224\pi$
$648$	−93.4677	+	40.8981i	−3.67176	+	1.60663i
$649$		−	11.3877i		−	0.447006i
$650$	30.2270	−	19.4779i	1.18560	−	0.763987i
$651$	1.93018	−	1.93018i	0.0756499	−	0.0756499i
$652$	−10.7278	−	18.0282i	−0.420132	−	0.706039i
$653$	−14.6061	+	14.6061i	−0.571579	+	0.571579i	−0.932570	−	0.360990i	$-0.882439\pi$
$653$	−14.6061	+	14.6061i	−0.571579	+	0.571579i	0.360990	+	0.932570i	$0.382439\pi$
$654$	−8.90039	−	11.4423i	−0.348033	−	0.447430i
$655$	−0.586324	+	1.25508i	−0.0229096	+	0.0490400i
$656$	11.3004	−	20.8213i	0.441205	−	0.812935i
$657$			44.2019i			1.72448i
$658$	−5.81741	+	4.52506i	−0.226786	+	0.176405i
$659$	29.5131	+	29.5131i	1.14967	+	1.14967i	0.986618	+	0.163047i	$0.0521322\pi$
$659$	29.5131	+	29.5131i	1.14967	+	1.14967i	0.163047	+	0.986618i	$0.447868\pi$
$660$	3.65122	+	36.4849i	0.142123	+	1.42017i
$661$	0.980890	−	0.980890i	0.0381522	−	0.0381522i	−0.687773	−	0.725926i	$-0.741412\pi$
$661$	0.980890	−	0.980890i	0.0381522	−	0.0381522i	0.725926	+	0.687773i	$0.241412\pi$
$662$	19.6669	+	2.45749i	0.764375	+	0.0955130i
$663$	78.7976			3.06024
$664$	1.77331	−	4.53251i	0.0688178	−	0.175895i
$665$	4.58260	−	9.80946i	0.177705	−	0.380395i
$666$	5.50984	+	0.688485i	0.213502	+	0.0266783i
$667$	5.03184	+	5.03184i	0.194833	+	0.194833i
$668$	−1.25924	+	4.96009i	−0.0487216	+	0.191912i
$669$	−41.9342	−	41.9342i	−1.62127	−	1.62127i
$670$	6.96078	+	30.5458i	0.268918	+	1.18009i
$671$	−24.0546			−0.928616
$672$	15.5133	+	11.1116i	0.598438	+	0.428638i
$673$			8.18720i			0.315593i	0.987472	+	0.157797i	$0.0504390\pi$
$673$			8.18720i			0.315593i	−0.987472	+	0.157797i	$0.949561\pi$
$674$	29.1066	−	22.6405i	1.12114	−	0.872078i
$675$	90.3682	+	8.03378i	3.47827	+	0.309220i
$676$	24.9316	+	6.32953i	0.958909	+	0.243443i
$677$	15.8960	+	15.8960i	0.610934	+	0.610934i	0.943189	−	0.332255i	$-0.107810\pi$
$677$	15.8960	+	15.8960i	0.610934	+	0.610934i	−0.332255	+	0.943189i	$0.607810\pi$
$678$	−10.4096	+	83.3067i	−0.399780	+	3.19938i
$679$		−	5.15345i		−	0.197771i
$680$	21.0408	−	20.0315i	0.806878	−	0.768174i
$681$			11.9038i			0.456155i
$682$	2.76008	+	0.344887i	0.105689	+	0.0132064i
$683$	1.55620	+	1.55620i	0.0595464	+	0.0595464i	0.736253	−	0.676706i	$-0.236593\pi$
$683$	1.55620	+	1.55620i	0.0595464	+	0.0595464i	−0.676706	+	0.736253i	$0.736593\pi$
$684$	41.4938	+	69.7310i	1.58655	+	2.66623i
$685$	−4.79851	−	13.2126i	−0.183342	−	0.504827i
$686$	−0.868292	−	1.11627i	−0.0331515	−	0.0426196i
$687$			48.1496i			1.83702i
$688$	−12.5050	−	42.1894i	−0.476749	−	1.60845i
$689$	−19.0703			−0.726521
$690$	−4.19100	−	18.3913i	−0.159549	−	0.700143i
$691$	18.2610	+	18.2610i	0.694681	+	0.694681i	0.963258	−	0.268577i	$-0.0865534\pi$
$691$	18.2610	+	18.2610i	0.694681	+	0.694681i	−0.268577	+	0.963258i	$0.586553\pi$
$692$	−0.769063	−	1.29242i	−0.0292354	−	0.0491306i
$693$	14.4008	+	14.4008i	0.547042	+	0.547042i
$694$	3.30354	−	26.4377i	0.125401	−	1.00356i
$695$	−27.9654	−	13.0643i	−1.06079	−	0.495559i
$696$	−35.1760	+	15.3918i	−1.33334	+	0.583423i
$697$	−27.2047			−1.03045
$698$	1.22935	−	9.83831i	0.0465317	−	0.372385i
$699$	−70.4717	+	70.4717i	−2.66549	+	2.66549i
$700$	−4.33261	−	9.01268i	−0.163757	−	0.340647i
$701$	9.37361	+	9.37361i	0.354036	+	0.354036i	0.861609	−	0.507573i	$-0.169457\pi$
$701$	9.37361	+	9.37361i	0.354036	+	0.354036i	−0.507573	+	0.861609i	$0.669457\pi$
$702$	80.1209	+	103.003i	3.02397	+	3.88761i
$703$		−	2.26893i		−	0.0855744i
$704$	0.768448	+	19.4294i	0.0289620	+	0.732274i
$705$	−16.6378	+	35.6147i	−0.626616	+	1.34133i
$706$	14.6023	−	11.3584i	0.549565	−	0.427478i
$707$	−1.30263	+	1.30263i	−0.0489903	+	0.0489903i
$708$	−30.6369	−	7.77796i	−1.15141	−	0.292314i
$709$	10.7060	−	10.7060i	0.402071	−	0.402071i	−0.476891	−	0.878962i	$-0.658237\pi$
$709$	10.7060	−	10.7060i	0.402071	−	0.402071i	0.878962	+	0.476891i	$0.158237\pi$
$710$	−3.88149	−	2.44077i	−0.145670	−	0.0916006i
$711$			62.0765i			2.32805i
$712$	−3.13511	−	7.16491i	−0.117493	−	0.268516i
$713$	−1.43091			−0.0535882
$714$	2.71703	−	21.7440i	0.101682	−	0.813747i
$715$	25.9786	−	9.43484i	0.971545	−	0.352843i
$716$	−31.1580	+	18.5407i	−1.16443	+	0.692899i
$717$	50.8807	−	50.8807i	1.90018	−	1.90018i
$718$	8.64295	−	6.72290i	0.322552	−	0.250896i
$719$	−3.83794			−0.143131			−0.0715655	−	0.997436i	$-0.522799\pi$
$719$	−3.83794			−0.143131			−0.0715655	+	0.997436i	$0.522799\pi$
$720$	74.1152	+	11.1165i	2.76211	+	0.414288i
$721$	7.91577			0.294799
$722$	4.96202	−	3.85969i	0.184667	−	0.143643i
$723$	−63.5558	+	63.5558i	−2.36366	+	2.36366i
$724$	−24.8802	−	41.8116i	−0.924665	−	1.55391i
$725$	20.0424	+	1.78178i	0.744356	+	0.0661736i
$726$	3.01212	−	24.1055i	0.111790	−	0.894640i
$727$	6.34731			0.235409			0.117704	−	0.993049i	$-0.462446\pi$
$727$	6.34731			0.235409			0.117704	+	0.993049i	$0.462446\pi$
$728$	5.24068	−	13.3950i	0.194233	−	0.496451i
$729$			118.615i			4.39313i
$730$	8.88024	−	14.1220i	0.328672	−	0.522678i
$731$	−35.7313	+	35.7313i	−1.32157	+	1.32157i
$732$	−16.4296	+	64.7153i	−0.607256	+	2.39195i
$733$	−8.48596	+	8.48596i	−0.313436	+	0.313436i	−0.846239	−	0.532803i	$-0.821139\pi$
$733$	−8.48596	+	8.48596i	−0.313436	+	0.313436i	0.532803	+	0.846239i	$0.321139\pi$
$734$	36.9696	−	28.7567i	1.36457	−	1.06143i
$735$	−6.83394	−	3.19255i	−0.252074	−	0.117759i
$736$	−1.63157	−	9.86897i	−0.0601405	−	0.363775i
$737$			24.0799i			0.886994i
$738$	−43.0891	−	55.3952i	−1.58613	−	2.03913i
$739$	−9.52630	−	9.52630i	−0.350431	−	0.350431i	0.509839	−	0.860270i	$-0.329705\pi$
$739$	−9.52630	−	9.52630i	−0.350431	−	0.350431i	−0.860270	+	0.509839i	$0.829705\pi$
$740$	−1.62201	−	1.32690i	−0.0596263	−	0.0487777i
$741$	58.7339	−	58.7339i	2.15764	−	2.15764i
$742$	−0.657566	+	5.26239i	−0.0241400	+	0.193189i
$743$	−6.94813			−0.254902			−0.127451	−	0.991845i	$-0.540680\pi$
$743$	−6.94813			−0.254902			−0.127451	+	0.991845i	$0.540680\pi$
$744$	2.81304	−	7.19003i	0.103131	−	0.263599i
$745$	−26.6356	−	12.4431i	−0.975853	−	0.455880i
$746$	2.22065	−	17.7715i	0.0813036	−	0.650660i
$747$	−10.1953	−	10.1953i	−0.373026	−	0.373026i
$748$	19.1889	−	11.4185i	0.701617	−	0.417501i
$749$	9.75809	+	9.75809i	0.356553	+	0.356553i
$750$	−42.4597	−	32.2789i	−1.55041	−	1.17866i
$751$	7.11844			0.259756			0.129878	−	0.991530i	$-0.458542\pi$
$751$	7.11844			0.259756			0.129878	+	0.991530i	$0.458542\pi$
$752$	−9.94358	+	18.3214i	−0.362605	+	0.668112i
$753$		−	34.3662i		−	1.25237i
$754$	17.7697	+	22.8447i	0.647134	+	0.831955i
$755$	−26.9007	+	9.76973i	−0.979017	+	0.355557i
$756$	31.1861	−	18.5575i	1.13423	−	0.674928i
$757$	−14.4520	−	14.4520i	−0.525266	−	0.525266i	0.393891	−	0.919157i	$-0.371129\pi$
$757$	−14.4520	−	14.4520i	−0.525266	−	0.525266i	−0.919157	+	0.393891i	$0.871129\pi$
$758$	−0.200398	−	0.0250408i	−0.00727877	−	0.000909523i
$759$		−	14.4982i		−	0.526251i
$760$	0.752305	−	30.6144i	0.0272890	−	1.11050i
$761$		−	6.22415i		−	0.225625i	−0.993616	−	0.112813i	$-0.964014\pi$
$761$		−	6.22415i		−	0.225625i	0.993616	−	0.112813i	$-0.0359860\pi$
$762$	−1.12969	+	9.04071i	−0.0409243	+	0.327511i
$763$	2.14870	+	2.14870i	0.0777881	+	0.0777881i
$764$	−11.0373	+	43.4753i	−0.399316	+	1.57288i
$765$	−29.3784	−	80.8928i	−1.06218	−	2.92469i
$766$	−25.0043	+	19.4495i	−0.903441	+	0.702739i
$767$			23.8260i			0.860307i
$768$	52.7969	+	11.2032i	1.90515	+	0.404260i
$769$	−45.0517			−1.62461			−0.812303	−	0.583236i	$-0.801786\pi$
$769$	−45.0517			−1.62461			−0.812303	+	0.583236i	$0.801786\pi$
$770$	−1.70774	−	7.49404i	−0.0615428	−	0.270067i
$771$	15.4300	+	15.4300i	0.555700	+	0.555700i
$772$	2.47237	+	0.627675i	0.0889827	+	0.0225905i
$773$	−10.7382	−	10.7382i	−0.386225	−	0.386225i	0.487113	−	0.873339i	$-0.338050\pi$
$773$	−10.7382	−	10.7382i	−0.386225	−	0.386225i	−0.873339	+	0.487113i	$0.838050\pi$
$774$	−129.352	−	16.1632i	−4.64945	−	0.580975i
$775$	−3.10310	+	2.59641i	−0.111466	+	0.0932657i
$776$	−5.84312	−	13.3537i	−0.209756	−	0.479372i
$777$	−1.58069			−0.0567070
$778$	24.8699	+	3.10764i	0.891630	+	0.111414i
$779$	−20.2777	+	20.2777i	−0.726526	+	0.726526i
$780$	−7.63929	−	76.3358i	−0.273531	−	2.73326i
$781$	−2.49198	−	2.49198i	−0.0891702	−	0.0891702i
$782$	−9.06690	+	7.05267i	−0.324232	+	0.252203i
$783$			73.0205i			2.60954i
$784$	−3.51560	−	1.90803i	−0.125557	−	0.0681438i
$785$	7.98401	+	3.72982i	0.284962	+	0.133123i
$786$	1.81456	+	2.33279i	0.0647231	+	0.0832080i
$787$	5.56379	−	5.56379i	0.198328	−	0.198328i	−0.600955	−	0.799283i	$-0.705213\pi$
$787$	5.56379	−	5.56379i	0.198328	−	0.198328i	0.799283	+	0.600955i	$0.205213\pi$
$788$	27.4427	−	16.3299i	0.977607	−	0.581730i
$789$	−73.9828	+	73.9828i	−2.63386	+	2.63386i
$790$	12.4713	−	19.8327i	0.443708	−	0.705616i
$791$		−	17.5986i		−	0.625733i
$792$	53.6438	+	20.9877i	1.90615	+	0.745766i
$793$	50.3284			1.78721
$794$	−14.4016	−	1.79956i	−0.511092	−	0.0638639i
$795$	9.65573	+	26.5868i	0.342453	+	0.942938i
$796$	−0.494243	−	0.125476i	−0.0175180	−	0.00444739i
$797$	−29.0968	+	29.0968i	−1.03066	+	1.03066i	−0.0311458	+	0.999515i	$0.509916\pi$
$797$	−29.0968	+	29.0968i	−1.03066	+	1.03066i	−0.999515	+	0.0311458i	$0.990084\pi$
$798$	−14.1822	−	18.2327i	−0.502046	−	0.645429i
$799$	23.9384			0.846878
$800$	−21.4456	−	18.4414i	−0.758216	−	0.652004i
$801$	−23.1686			−0.818621
$802$	−23.5126	−	30.2277i	−0.830258	−	1.06738i
$803$	9.06656	−	9.06656i	0.319952	−	0.319952i
$804$	64.7835	+	16.4469i	2.28474	+	0.580038i
$805$	1.34975	+	3.71650i	0.0475723	+	0.130989i
$806$	−5.77480	−	0.721594i	−0.203409	−	0.0254171i
$807$	−11.8234			−0.416203
$808$	−1.89844	+	4.85235i	−0.0667870	+	0.170705i
$809$		−	40.5547i		−	1.42583i	−0.701252	−	0.712914i	$-0.747375\pi$
$809$		−	40.5547i		−	1.42583i	0.701252	−	0.712914i	$-0.252625\pi$
$810$	60.7202	−	96.5615i	2.13349	−	3.39283i
$811$	−20.5780	+	20.5780i	−0.722593	+	0.722593i	−0.969133	−	0.246540i	$-0.920706\pi$
$811$	−20.5780	+	20.5780i	−0.722593	+	0.722593i	0.246540	+	0.969133i	$0.420706\pi$
$812$	6.91664	−	4.11578i	0.242727	−	0.144436i
$813$	38.0366	−	38.0366i	1.33400	−	1.33400i
$814$	−0.988941	−	1.27138i	−0.0346624	−	0.0445619i
$815$	21.2503	+	9.92730i	0.744365	+	0.347738i
$816$	−17.6134	−	59.4241i	−0.616593	−	2.08026i
$817$			53.2666i			1.86356i
$818$	5.75918	−	4.47976i	0.201365	−	0.156631i
$819$	−30.1303	−	30.1303i	−1.05284	−	1.05284i
$820$	2.63745	+	26.3548i	0.0921037	+	0.920349i
$821$	13.9654	−	13.9654i	0.487395	−	0.487395i	−0.420089	−	0.907483i	$-0.638001\pi$
$821$	13.9654	−	13.9654i	0.487395	−	0.487395i	0.907483	+	0.420089i	$0.138001\pi$
$822$	−29.7584	−	3.71848i	−1.03794	−	0.129697i
$823$	38.1318			1.32919			0.664596	−	0.747203i	$-0.268604\pi$
$823$	38.1318			1.32919			0.664596	+	0.747203i	$0.268604\pi$
$824$	20.5115	−	8.97511i	0.714553	−	0.312663i
$825$	−26.3071	−	31.4409i	−0.915896	−	1.09463i
$826$	6.57472	+	0.821548i	0.228764	+	0.0285853i
$827$	5.10401	+	5.10401i	0.177484	+	0.177484i	0.790258	−	0.612774i	$-0.209947\pi$
$827$	5.10401	+	5.10401i	0.177484	+	0.177484i	−0.612774	+	0.790258i	$0.709947\pi$
$828$	−28.7218	−	7.29176i	−0.998153	−	0.253406i
$829$	−1.48998	−	1.48998i	−0.0517490	−	0.0517490i	0.680759	−	0.732508i	$-0.261650\pi$
$829$	−1.48998	−	1.48998i	−0.0517490	−	0.0517490i	−0.732508	+	0.680759i	$0.761650\pi$
$830$	1.20902	+	5.30553i	0.0419658	+	0.184157i
$831$	12.3734			0.429228
$832$	−1.60779	−	40.6514i	−0.0557402	−	1.40933i
$833$			4.59341i			0.159152i
$834$	−51.9788	+	40.4316i	−1.79988	+	1.40003i
$835$	−1.95309	−	5.37779i	−0.0675895	−	0.186106i
$836$	5.79193	−	22.8141i	0.200318	−	0.789041i
$837$	−10.3825	−	10.3825i	−0.358871	−	0.358871i
$838$	−2.99139	+	23.9396i	−0.103336	+	0.826981i
$839$			12.7564i			0.440399i	0.975455	+	0.220199i	$0.0706708\pi$
$839$			12.7564i			0.440399i	−0.975455	+	0.220199i	$0.929329\pi$
$840$	−21.3281	−	0.524107i	−0.735888	−	0.0180834i
$841$		−	12.8051i		−	0.441555i
$842$	27.3722	+	3.42031i	0.943308	+	0.117872i
$843$	26.5222	+	26.5222i	0.913473	+	0.913473i
$844$	−1.89049	+	1.12495i	−0.0650735	+	0.0387223i
$845$	−27.0312	+	9.81712i	−0.929902	+	0.337719i
$846$	37.9156	+	48.7442i	1.30356	+	1.67586i
$847$			5.09229i			0.174973i
$848$	4.26274	+	14.3816i	0.146383	+	0.493866i
$849$	−33.9920			−1.16660
$850$	−6.86544	+	31.7465i	−0.235483	+	1.08889i
$851$	0.585912	+	0.585912i	0.0200848	+	0.0200848i
$852$	−8.40639	+	5.00226i	−0.287998	+	0.171375i
$853$	−39.7475	−	39.7475i	−1.36093	−	1.36093i	−0.872737	−	0.488191i	$-0.837657\pi$
$853$	−39.7475	−	39.7475i	−1.36093	−	1.36093i	−0.488191	−	0.872737i	$-0.662343\pi$
$854$	1.73538	−	13.8880i	0.0593835	−	0.475236i
$855$	−82.1937	−	38.3977i	−2.81096	−	1.31317i
$856$	36.3494	+	14.2214i	1.24240	+	0.486078i
$857$	−52.5148			−1.79387			−0.896936	−	0.442161i	$-0.854212\pi$
$857$	−52.5148			−1.79387			−0.896936	+	0.442161i	$0.854212\pi$
$858$	7.31128	−	58.5110i	0.249603	−	1.99753i
$859$	13.0865	−	13.0865i	0.446505	−	0.446505i	−0.447686	−	0.894191i	$-0.647752\pi$
$859$	13.0865	−	13.0865i	0.446505	−	0.446505i	0.894191	+	0.447686i	$0.147752\pi$
$860$	38.0791	+	31.1509i	1.29849	+	1.06224i
$861$	14.1269	+	14.1269i	0.481442	+	0.481442i
$862$	−7.87639	−	10.1259i	−0.268271	−	0.344889i
$863$			25.9832i			0.884480i	0.896897	+	0.442240i	$0.145816\pi$
$863$			25.9832i			0.884480i	−0.896897	+	0.442240i	$0.854184\pi$
$864$	59.7693	−	83.4462i	2.03339	−	2.83890i
$865$	1.52341	+	0.711678i	0.0517976	+	0.0241978i
$866$	38.6448	−	30.0598i	1.31321	−	1.02147i
$867$	−9.77828	+	9.77828i	−0.332088	+	0.332088i
$868$	−0.398243	+	1.56866i	−0.0135173	+	0.0532437i
$869$	12.7329	−	12.7329i	0.431935	−	0.431935i
$870$	22.8517	−	36.3404i	0.774744	−	1.23205i
$871$		−	50.3814i		−	1.70711i
$872$	8.00401	+	3.13151i	0.271050	+	0.106046i
$873$	−43.1809			−1.46145
$874$	−1.50136	+	12.0152i	−0.0507843	+	0.406419i
$875$	9.67069	+	5.61050i	0.326929	+	0.189670i
$876$	−18.1997	−	30.5849i	−0.614910	−	1.03337i
$877$	27.8810	−	27.8810i	0.941473	−	0.941473i	−0.0569061	−	0.998380i	$-0.518124\pi$
$877$	27.8810	−	27.8810i	0.941473	−	0.941473i	0.998380	+	0.0569061i	$0.0181236\pi$
$878$	6.13048	−	4.76858i	0.206894	−	0.160932i
$879$	−76.3734			−2.57601
$880$	−12.9221	−	17.4825i	−0.435603	−	0.589333i
$881$	−27.2097			−0.916716			−0.458358	−	0.888768i	$-0.651562\pi$
$881$	−27.2097			−0.916716			−0.458358	+	0.888768i	$0.651562\pi$
$882$	−9.35328	+	7.27543i	−0.314941	+	0.244977i
$883$	5.76863	−	5.76863i	0.194130	−	0.194130i	−0.603348	−	0.797478i	$-0.706167\pi$
$883$	5.76863	−	5.76863i	0.194130	−	0.194130i	0.797478	+	0.603348i	$0.206167\pi$
$884$	−40.1483	+	23.8904i	−1.35033	+	0.803522i
$885$	33.2170	−	12.0636i	1.11658	−	0.405515i
$886$	4.67697	−	37.4290i	0.157126	−	1.25745i
$887$	43.6530			1.46573			0.732863	−	0.680377i	$-0.238184\pi$
$887$	43.6530			1.46573			0.732863	+	0.680377i	$0.238184\pi$
$888$	−4.09593	+	1.79223i	−0.137450	+	0.0601433i
$889$		−	1.90985i		−	0.0640544i
$890$	7.40208	+	4.65460i	0.248118	+	0.156023i
$891$	61.9942	−	61.9942i	2.07688	−	2.07688i
$892$	34.0799	+	8.65204i	1.14108	+	0.289692i
$893$	17.8431	−	17.8431i	0.597097	−	0.597097i
$894$	−49.5071	+	38.5090i	−1.65576	+	1.28793i
$895$	17.1573	−	36.7267i	0.573505	−	1.22764i
$896$	−11.2731	−	0.958041i	−0.376607	−	0.0320059i
$897$			30.3340i			1.01282i
$898$	19.0485	+	24.4888i	0.635658	+	0.817201i
$899$	−2.30269	−	2.30269i	−0.0767990	−	0.0767990i
$900$	−75.5174	+	36.3030i	−2.51725	+	1.21010i
$901$	12.1802	−	12.1802i	0.405780	−	0.405780i
$902$	−2.52420	+	20.2008i	−0.0840468	+	0.672613i
$903$	37.1091			1.23491
$904$	−19.9537	−	45.6018i	−0.663650	−	1.51669i
$905$	49.2843	+	23.0237i	1.63827	+	0.765334i
$906$	−7.57079	+	60.5878i	−0.251523	+	2.01290i
$907$	−11.4092	−	11.4092i	−0.378836	−	0.378836i	0.491846	−	0.870682i	$-0.336322\pi$
$907$	−11.4092	−	11.4092i	−0.378836	−	0.378836i	−0.870682	+	0.491846i	$0.836322\pi$
$908$	−3.60908	−	6.06512i	−0.119772	−	0.201278i
$909$	10.9147	+	10.9147i	0.362019	+	0.362019i
$910$	3.57304	+	15.6795i	0.118445	+	0.519770i
$911$	−13.2823			−0.440061			−0.220031	−	0.975493i	$-0.570616\pi$
$911$	−13.2823			−0.440061			−0.220031	+	0.975493i	$0.570616\pi$
$912$	−57.4220	−	31.1647i	−1.90143	−	1.03197i
$913$			4.18245i			0.138419i
$914$	−3.99557	−	5.13670i	−0.132162	−	0.169907i
$915$	−25.4824	−	70.1652i	−0.842422	−	2.31959i
$916$	−14.5983	−	24.5328i	−0.482343	−	0.810586i
$917$	−0.438064	−	0.438064i	−0.0144662	−	0.0144662i
$918$	−116.961	−	14.6150i	−3.86029	−	0.482365i
$919$		−	44.4244i		−	1.46543i	−0.680538	−	0.732713i	$-0.738254\pi$
$919$		−	44.4244i		−	1.46543i	0.680538	−	0.732713i	$-0.261746\pi$
$920$	7.71135	+	8.09989i	0.254236	+	0.267046i
$921$			0.321124i			0.0105814i
$922$	3.72404	−	29.8029i	0.122645	−	0.981506i
$923$	5.21388	+	5.21388i	0.171617	+	0.171617i
$924$	−15.8938	−	4.03505i	−0.522869	−	0.132743i
$925$	2.33376	+	0.207472i	0.0767335	+	0.00682164i
$926$	−26.2054	+	20.3838i	−0.861164	+	0.669855i
$927$		−	66.3264i		−	2.17844i
$928$	13.2560	−	18.5072i	0.435149	−	0.607528i
$929$	−22.6116			−0.741861			−0.370931	−	0.928661i	$-0.620961\pi$
$929$	−22.6116			−0.741861			−0.370931	+	0.928661i	$0.620961\pi$
$930$	1.91790	+	8.41628i	0.0628905	+	0.275981i
$931$	3.42383	+	3.42383i	0.112211	+	0.112211i
$932$	14.5400	−	57.2723i	0.476274	−	1.87602i
$933$	70.3871	+	70.3871i	2.30437	+	2.30437i
$934$	26.7616	+	3.34401i	0.875666	+	0.109419i
$935$	−10.5665	+	22.6185i	−0.345561	+	0.739704i
$936$	−112.237	−	43.9118i	−3.66857	−	1.43530i
$937$	10.3768			0.338996			0.169498	−	0.985531i	$-0.445785\pi$
$937$	10.3768			0.338996			0.169498	+	0.985531i	$0.445785\pi$
$938$	−13.9026	−	1.73721i	−0.453936	−	0.0567218i
$939$	−14.1969	+	14.1969i	−0.463297	+	0.463297i
$940$	−2.32078	−	23.1905i	−0.0756956	−	0.756390i
$941$	6.64571	+	6.64571i	0.216644	+	0.216644i	0.807083	−	0.590439i	$-0.201045\pi$
$941$	6.64571	+	6.64571i	0.216644	+	0.216644i	−0.590439	+	0.807083i	$0.701045\pi$
$942$	14.8397	−	11.5430i	0.483504	−	0.376093i
$943$		−	10.4727i		−	0.341039i
$944$	17.9681	−	5.32577i	0.584810	−	0.173339i
$945$	−17.1728	+	36.7599i	−0.558630	+	1.19580i
$946$	23.2169	+	29.8476i	0.754845	+	0.970428i
$947$	6.49840	−	6.49840i	0.211169	−	0.211169i	−0.593595	−	0.804764i	$-0.702292\pi$
$947$	6.49840	−	6.49840i	0.211169	−	0.211169i	0.804764	+	0.593595i	$0.202292\pi$
$948$	−25.5593	−	42.9529i	−0.830129	−	1.39505i
$949$	−18.9696	+	18.9696i	−0.615779	+	0.615779i
$950$	18.5457	+	28.7804i	0.601703	+	0.933761i
$951$			113.236i			3.67193i
$952$	5.20813	+	11.9026i	0.168797	+	0.385764i
$953$	20.6782			0.669833			0.334917	−	0.942248i	$-0.391292\pi$
$953$	20.6782			0.669833			0.334917	+	0.942248i	$0.391292\pi$
$954$	44.0937	+	5.50976i	1.42759	+	0.178385i
$955$	−17.1189	−	47.1365i	−0.553954	−	1.52530i
$956$	−10.4979	+	41.3507i	−0.339527	+	1.33738i
$957$	23.3311	−	23.3311i	0.754189	−	0.754189i
$958$	20.1440	+	25.8971i	0.650822	+	0.836696i
$959$	6.28646			0.203001
$960$	−55.8600	+	22.8242i	−1.80287	+	0.736649i
$961$	−30.3452			−0.978877
$962$	2.06912	+	2.66006i	0.0667111	+	0.0857637i
$963$	81.7632	−	81.7632i	2.63478	−	2.63478i
$964$	13.1131	−	51.6517i	0.422344	−	1.66359i
$965$	−2.68058	+	0.973526i	−0.0862910	+	0.0313389i
$966$	8.37057	+	1.04595i	0.269319	+	0.0336529i
$967$	−12.1566			−0.390931			−0.195465	−	0.980711i	$-0.562622\pi$
$967$	−12.1566			−0.390931			−0.195465	+	0.980711i	$0.562622\pi$
$968$	5.77378	+	13.1953i	0.185576	+	0.424112i
$969$			75.0265i			2.41020i
$970$	13.7958	+	8.67510i	0.442955	+	0.278541i
$971$	11.3475	−	11.3475i	0.364158	−	0.364158i	−0.501183	−	0.865341i	$-0.667102\pi$
$971$	11.3475	−	11.3475i	0.364158	−	0.364158i	0.865341	+	0.501183i	$0.167102\pi$
$972$	−68.7711	−	115.571i	−2.20583	−	3.70694i
$973$	9.76084	−	9.76084i	0.312918	−	0.312918i
$974$	32.0842	+	41.2474i	1.02804	+	1.32165i
$975$	55.0413	+	65.7826i	1.76273	+	2.10673i
$976$	−11.2498	−	37.9544i	−0.360097	−	1.21489i
$977$		−	42.4908i		−	1.35940i	−0.733490	−	0.679701i	$-0.762110\pi$
$977$		−	42.4908i		−	1.35940i	0.733490	−	0.679701i	$-0.237890\pi$
$978$	39.4975	−	30.7230i	1.26299	−	0.982415i
$979$	4.75226	+	4.75226i	0.151883	+	0.151883i
$980$	4.44991	−	0.445324i	0.142147	−	0.0142253i
$981$	18.0040	−	18.0040i	0.574823	−	0.574823i
$982$	25.8297	+	3.22757i	0.824259	+	0.102996i
$983$	−37.2894			−1.18935			−0.594673	−	0.803968i	$-0.702718\pi$
$983$	−37.2894			−1.18935			−0.594673	+	0.803968i	$0.702718\pi$
$984$	52.6232	+	20.5884i	1.67757	+	0.656336i
$985$	−15.1115	+	32.3475i	−0.481491	+	1.03068i
$986$	−25.9403	−	3.24139i	−0.826108	−	0.103227i
$987$	−12.4307	−	12.4307i	−0.395674	−	0.395674i
$988$	−12.1182	+	47.7330i	−0.385532	+	1.51859i
$989$	−13.7552	−	13.7552i	−0.437389	−	0.437389i
$990$	−62.7927	+	14.3092i	−1.99568	+	0.454776i
$991$	−21.4120			−0.680176			−0.340088	−	0.940394i	$-0.610457\pi$
$991$	−21.4120			−0.680176			−0.340088	+	0.940394i	$0.610457\pi$
$992$	0.746647	+	4.51628i	0.0237061	+	0.143392i
$993$			47.2756i			1.50025i
$994$	1.61853	−	1.25897i	0.0513368	−	0.0399322i
$995$	0.535865	−	0.194614i	0.0169881	−	0.00616968i
$996$	11.2523	+	2.85668i	0.356542	+	0.0905173i
$997$	33.8659	+	33.8659i	1.07254	+	1.07254i	0.997154	+	0.0753904i	$0.0240203\pi$
$997$	33.8659	+	33.8659i	1.07254	+	1.07254i	0.0753904	+	0.997154i	$0.475980\pi$
$998$	−4.63503	+	37.0934i	−0.146719	+	1.17417i
$999$			8.50257i			0.269009i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bb.d.29.9	yes	70
5.4	even	2		560.2.bb.c.29.27	✓	70
16.5	even	4		560.2.bb.c.309.27	yes	70
80.69	even	4	inner	560.2.bb.d.309.9	yes	70

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bb.c.29.27	✓	70	5.4	even	2
560.2.bb.c.309.27	yes	70	16.5	even	4
560.2.bb.d.29.9	yes	70	1.1	even	1	trivial
560.2.bb.d.309.9	yes	70	80.69	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.bb (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.868292 - 1.11627i) q^{2} +(2.38527 - 2.38527i) q^{3} +(-0.492138 + 1.93850i) q^{4} +(-0.763308 - 2.10175i) q^{5} +(-4.73373 - 0.591506i) q^{6} +1.00000 q^{7} +(2.59122 - 1.13383i) q^{8} -8.37902i q^{9} +O(q^{10})\)	\(q+(-0.868292 - 1.11627i) q^{2} +(2.38527 - 2.38527i) q^{3} +(-0.492138 + 1.93850i) q^{4} +(-0.763308 - 2.10175i) q^{5} +(-4.73373 - 0.591506i) q^{6} +1.00000 q^{7} +(2.59122 - 1.13383i) q^{8} -8.37902i q^{9} +(-1.68336 + 2.67700i) q^{10} +(-1.71868 + 1.71868i) q^{11} +(3.44997 + 5.79774i) q^{12} +(3.59592 - 3.59592i) q^{13} +(-0.868292 - 1.11627i) q^{14} +(-6.83394 - 3.19255i) q^{15} +(-3.51560 - 1.90803i) q^{16} +4.59341i q^{17} +(-9.35328 + 7.27543i) q^{18} +(3.42383 + 3.42383i) q^{19} +(4.44991 - 0.445324i) q^{20} +(2.38527 - 2.38527i) q^{21} +(3.41083 + 0.426203i) q^{22} -1.76828 q^{23} +(3.47628 - 8.88524i) q^{24} +(-3.83472 + 3.20857i) q^{25} +(-7.13634 - 0.891726i) q^{26} +(-12.8304 - 12.8304i) q^{27} +(-0.492138 + 1.93850i) q^{28} +(-2.84560 - 2.84560i) q^{29} +(2.37009 + 10.4006i) q^{30} +0.809210 q^{31} +(0.922686 + 5.58110i) q^{32} +8.19902i q^{33} +(5.12751 - 3.98842i) q^{34} +(-0.763308 - 2.10175i) q^{35} +(16.2428 + 4.12364i) q^{36} +(-0.331345 - 0.331345i) q^{37} +(0.849050 - 6.79481i) q^{38} -17.1545i q^{39} +(-4.36092 - 4.58065i) q^{40} +5.92254i q^{41} +(-4.73373 - 0.591506i) q^{42} +(7.77881 + 7.77881i) q^{43} +(-2.48584 - 4.17749i) q^{44} +(-17.6106 + 6.39577i) q^{45} +(1.53539 + 1.97389i) q^{46} -5.21145i q^{47} +(-12.9368 + 3.83450i) q^{48} +1.00000 q^{49} +(6.91130 + 1.49463i) q^{50} +(10.9565 + 10.9565i) q^{51} +(5.20102 + 8.74040i) q^{52} +(-2.65166 - 2.65166i) q^{53} +(-3.18172 + 25.4628i) q^{54} +(4.92411 + 2.30035i) q^{55} +(2.59122 - 1.13383i) q^{56} +16.3335 q^{57} +(-0.705661 + 5.64729i) q^{58} +(-3.31292 + 3.31292i) q^{59} +(9.55201 - 11.6764i) q^{60} +(6.99798 + 6.99798i) q^{61} +(-0.702631 - 0.903301i) q^{62} -8.37902i q^{63} +(5.42888 - 5.87599i) q^{64} +(-10.3025 - 4.81294i) q^{65} +(9.15235 - 7.11914i) q^{66} +(7.00535 - 7.00535i) q^{67} +(-8.90435 - 2.26060i) q^{68} +(-4.21784 + 4.21784i) q^{69} +(-1.68336 + 2.67700i) q^{70} +1.44994i q^{71} +(-9.50035 - 21.7119i) q^{72} -5.27531 q^{73} +(-0.0821678 + 0.657576i) q^{74} +(-1.49354 + 16.8001i) q^{75} +(-8.32210 + 4.95210i) q^{76} +(-1.71868 + 1.71868i) q^{77} +(-19.1491 + 14.8951i) q^{78} -7.40856 q^{79} +(-1.32671 + 8.84533i) q^{80} -36.0709 q^{81} +(6.61118 - 5.14250i) q^{82} +(1.21677 - 1.21677i) q^{83} +(3.44997 + 5.79774i) q^{84} +(9.65421 - 3.50619i) q^{85} +(1.92901 - 15.4376i) q^{86} -13.5751 q^{87} +(-2.50480 + 6.40216i) q^{88} -2.76507i q^{89} +(22.4306 + 14.1049i) q^{90} +(3.59592 - 3.59592i) q^{91} +(0.870241 - 3.42783i) q^{92} +(1.93018 - 1.93018i) q^{93} +(-5.81741 + 4.52506i) q^{94} +(4.58260 - 9.80946i) q^{95} +(15.5133 + 11.1116i) q^{96} -5.15345i q^{97} +(-0.868292 - 1.11627i) q^{98} +(14.4008 + 14.4008i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q + 2 q^{2} + 2 q^{3} + 2 q^{5} + 70 q^{7} + 8 q^{8}+O(q^{10}) \) 70 * q + 2 * q^2 + 2 * q^3 + 2 * q^5 + 70 * q^7 + 8 * q^8	\( 70 q + 2 q^{2} + 2 q^{3} + 2 q^{5} + 70 q^{7} + 8 q^{8} - 18 q^{10} - 2 q^{11} - 4 q^{12} + 6 q^{13} + 2 q^{14} - 6 q^{15} + 4 q^{16} - 18 q^{18} + 14 q^{19} + 12 q^{20} + 2 q^{21} - 12 q^{22} + 20 q^{24} + 6 q^{25} - 36 q^{26} + 8 q^{27} + 2 q^{29} + 8 q^{30} + 16 q^{31} - 8 q^{32} + 4 q^{34} + 2 q^{35} - 40 q^{36} + 10 q^{37} - 12 q^{38} - 24 q^{40} + 2 q^{43} - 24 q^{44} - 24 q^{45} - 16 q^{46} - 44 q^{48} + 70 q^{49} - 10 q^{50} + 8 q^{51} + 28 q^{52} - 30 q^{53} - 32 q^{54} + 6 q^{55} + 8 q^{56} - 76 q^{57} + 56 q^{58} + 2 q^{59} - 8 q^{60} + 30 q^{61} + 48 q^{62} + 12 q^{64} - 10 q^{65} + 80 q^{66} + 6 q^{67} - 36 q^{68} - 16 q^{69} - 18 q^{70} + 4 q^{72} - 36 q^{73} - 32 q^{74} - 2 q^{75} + 44 q^{76} - 2 q^{77} - 84 q^{78} - 40 q^{79} + 12 q^{80} - 82 q^{81} + 24 q^{82} + 10 q^{83} - 4 q^{84} + 32 q^{85} + 32 q^{86} - 4 q^{87} + 32 q^{88} + 18 q^{90} + 6 q^{91} - 92 q^{92} - 56 q^{93} - 20 q^{94} + 6 q^{95} + 16 q^{96} + 2 q^{98} - 34 q^{99}+O(q^{100}) \) 70 * q + 2 * q^2 + 2 * q^3 + 2 * q^5 + 70 * q^7 + 8 * q^8 - 18 * q^10 - 2 * q^11 - 4 * q^12 + 6 * q^13 + 2 * q^14 - 6 * q^15 + 4 * q^16 - 18 * q^18 + 14 * q^19 + 12 * q^20 + 2 * q^21 - 12 * q^22 + 20 * q^24 + 6 * q^25 - 36 * q^26 + 8 * q^27 + 2 * q^29 + 8 * q^30 + 16 * q^31 - 8 * q^32 + 4 * q^34 + 2 * q^35 - 40 * q^36 + 10 * q^37 - 12 * q^38 - 24 * q^40 + 2 * q^43 - 24 * q^44 - 24 * q^45 - 16 * q^46 - 44 * q^48 + 70 * q^49 - 10 * q^50 + 8 * q^51 + 28 * q^52 - 30 * q^53 - 32 * q^54 + 6 * q^55 + 8 * q^56 - 76 * q^57 + 56 * q^58 + 2 * q^59 - 8 * q^60 + 30 * q^61 + 48 * q^62 + 12 * q^64 - 10 * q^65 + 80 * q^66 + 6 * q^67 - 36 * q^68 - 16 * q^69 - 18 * q^70 + 4 * q^72 - 36 * q^73 - 32 * q^74 - 2 * q^75 + 44 * q^76 - 2 * q^77 - 84 * q^78 - 40 * q^79 + 12 * q^80 - 82 * q^81 + 24 * q^82 + 10 * q^83 - 4 * q^84 + 32 * q^85 + 32 * q^86 - 4 * q^87 + 32 * q^88 + 18 * q^90 + 6 * q^91 - 92 * q^92 - 56 * q^93 - 20 * q^94 + 6 * q^95 + 16 * q^96 + 2 * q^98 - 34 * q^99

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