LMFDB - Embedded newform 546.2.bu.b.449.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(71,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 5]))

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

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

chi := DirichletCharacter("546.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bu (of order $12$, degree $4$, 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:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			449.1
Character	$\chi$	$=$	546.449
Dual form			546.2.bu.b.197.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(-1.64483 - 0.542708i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.01262 - 1.01262i) q^{5} +(-0.0985019 + 1.72925i) q^{6} +(-0.965926 - 0.258819i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.41094 + 1.78532i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(-1.64483 - 0.542708i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.01262 - 1.01262i) q^{5} +(-0.0985019 + 1.72925i) q^{6} +(-0.965926 - 0.258819i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.41094 + 1.78532i) q^{9} +(-1.24020 - 0.716030i) q^{10} +(5.93999 - 1.59162i) q^{11} +(1.69582 - 0.352417i) q^{12} +(-2.27066 - 2.80073i) q^{13} +1.00000i q^{14} +(-2.21514 + 1.11603i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-3.35614 - 5.81300i) q^{17} +(1.10050 - 2.79086i) q^{18} +(0.0419710 - 0.156638i) q^{19} +(-0.370644 + 1.38326i) q^{20} +(1.44832 + 0.949929i) q^{21} +(-3.07476 - 5.32565i) q^{22} +(-1.55923 + 2.70067i) q^{23} +(-0.779319 - 1.54682i) q^{24} +2.94920i q^{25} +(-2.11761 + 2.91818i) q^{26} +(-2.99667 - 4.24499i) q^{27} +(0.965926 - 0.258819i) q^{28} +(-6.86770 - 3.96507i) q^{29} +(1.65132 + 1.85081i) q^{30} +(2.28135 + 2.28135i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(-10.6341 - 0.605740i) q^{33} +(-4.74629 + 4.74629i) q^{34} +(-1.24020 + 0.716030i) q^{35} +(-2.98059 - 0.340668i) q^{36} +(-1.39698 - 5.21359i) q^{37} -0.162163 q^{38} +(2.21488 + 5.83903i) q^{39} +1.43206 q^{40} +(-0.728231 - 2.71779i) q^{41} +(0.542708 - 1.64483i) q^{42} +(-1.39389 + 0.804764i) q^{43} +(-4.34837 + 4.34837i) q^{44} +(4.24921 - 0.633506i) q^{45} +(3.01221 + 0.807119i) q^{46} +(-1.71389 - 1.71389i) q^{47} +(-1.29241 + 1.15311i) q^{48} +(0.866025 + 0.500000i) q^{49} +(2.84871 - 0.763310i) q^{50} +(2.36552 + 11.3828i) q^{51} +(3.36682 + 1.29017i) q^{52} -8.12791i q^{53} +(-3.32475 + 3.99325i) q^{54} +(4.40325 - 7.62665i) q^{55} +(-0.500000 - 0.866025i) q^{56} +(-0.154044 + 0.234865i) q^{57} +(-2.05247 + 7.65992i) q^{58} +(-1.78883 + 6.67601i) q^{59} +(1.36036 - 2.07408i) q^{60} +(-4.36155 - 7.55443i) q^{61} +(1.61316 - 2.79408i) q^{62} +(-1.86671 - 2.34849i) q^{63} +1.00000i q^{64} +(-5.13539 - 0.536755i) q^{65} +(2.16720 + 10.4285i) q^{66} +(5.05737 - 1.35512i) q^{67} +(5.81300 + 3.35614i) q^{68} +(4.03035 - 3.59594i) q^{69} +(1.01262 + 1.01262i) q^{70} +(-9.93919 - 2.66320i) q^{71} +(0.442374 + 2.96720i) q^{72} +(2.46804 - 2.46804i) q^{73} +(-4.67438 + 2.69875i) q^{74} +(1.60056 - 4.85094i) q^{75} +(0.0419710 + 0.156638i) q^{76} -6.14953 q^{77} +(5.06682 - 3.65066i) q^{78} +5.05115 q^{79} +(-0.370644 - 1.38326i) q^{80} +(2.62523 + 8.60861i) q^{81} +(-2.43671 + 1.40683i) q^{82} +(3.93809 - 3.93809i) q^{83} +(-1.72925 - 0.0985019i) q^{84} +(-9.28484 - 2.48787i) q^{85} +(1.13811 + 1.13811i) q^{86} +(9.14433 + 10.2490i) q^{87} +(5.32565 + 3.07476i) q^{88} +(10.2688 - 2.75151i) q^{89} +(-1.71170 - 3.94046i) q^{90} +(1.46841 + 3.29299i) q^{91} -3.11847i q^{92} +(-2.51433 - 4.99055i) q^{93} +(-1.21190 + 2.09907i) q^{94} +(-0.116114 - 0.201115i) q^{95} +(1.44832 + 0.949929i) q^{96} +(-1.05510 + 3.93768i) q^{97} +(0.258819 - 0.965926i) q^{98} +(17.1625 + 6.76753i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 8 q^{6} - 24 q^{9}+O(q^{10}) $ 56 * q + 8 * q^6 - 24 * q^9	$ 56 q + 8 q^{6} - 24 q^{9} + 24 q^{10} + 8 q^{11} + 24 q^{13} + 4 q^{15} + 28 q^{16} - 4 q^{17} - 8 q^{18} + 8 q^{19} + 4 q^{21} - 8 q^{23} - 8 q^{24} - 4 q^{26} - 24 q^{27} - 8 q^{30} - 8 q^{31} + 8 q^{33} - 24 q^{34} + 24 q^{35} - 12 q^{36} - 8 q^{37} - 20 q^{39} - 28 q^{41} + 8 q^{44} + 72 q^{45} - 20 q^{46} + 64 q^{50} + 16 q^{54} + 8 q^{55} - 28 q^{56} + 4 q^{58} - 8 q^{59} + 20 q^{60} + 8 q^{61} - 32 q^{62} - 16 q^{63} - 24 q^{65} + 32 q^{66} - 16 q^{69} - 112 q^{71} + 8 q^{73} + 48 q^{74} + 40 q^{75} + 8 q^{76} + 16 q^{79} + 12 q^{81} - 4 q^{83} - 4 q^{84} + 32 q^{85} - 16 q^{86} - 144 q^{87} + 88 q^{89} - 8 q^{90} - 8 q^{91} + 52 q^{93} - 8 q^{94} - 48 q^{95} + 4 q^{96} - 64 q^{97} + 56 q^{99}+O(q^{100}) $ 56 * q + 8 * q^6 - 24 * q^9 + 24 * q^10 + 8 * q^11 + 24 * q^13 + 4 * q^15 + 28 * q^16 - 4 * q^17 - 8 * q^18 + 8 * q^19 + 4 * q^21 - 8 * q^23 - 8 * q^24 - 4 * q^26 - 24 * q^27 - 8 * q^30 - 8 * q^31 + 8 * q^33 - 24 * q^34 + 24 * q^35 - 12 * q^36 - 8 * q^37 - 20 * q^39 - 28 * q^41 + 8 * q^44 + 72 * q^45 - 20 * q^46 + 64 * q^50 + 16 * q^54 + 8 * q^55 - 28 * q^56 + 4 * q^58 - 8 * q^59 + 20 * q^60 + 8 * q^61 - 32 * q^62 - 16 * q^63 - 24 * q^65 + 32 * q^66 - 16 * q^69 - 112 * q^71 + 8 * q^73 + 48 * q^74 + 40 * q^75 + 8 * q^76 + 16 * q^79 + 12 * q^81 - 4 * q^83 - 4 * q^84 + 32 * q^85 - 16 * q^86 - 144 * q^87 + 88 * q^89 - 8 * q^90 - 8 * q^91 + 52 * q^93 - 8 * q^94 - 48 * q^95 + 4 * q^96 - 64 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{12}\right)$

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 $

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$	−1.64483	−	0.542708i	−0.949643	−	0.313332i
$3$	−1.64483	−	0.542708i	−0.949643	−	0.313332i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	1.01262	−	1.01262i	0.452857	−	0.452857i	−0.443445	−	0.896302i	$-0.646244\pi$
$5$	1.01262	−	1.01262i	0.452857	−	0.452857i	0.896302	+	0.443445i	$0.146244\pi$
$6$	−0.0985019	+	1.72925i	−0.0402132	+	0.705962i
$7$	−0.965926	−	0.258819i	−0.365086	−	0.0978244i
$7$	−0.965926	−	0.258819i	−0.365086	−	0.0978244i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	2.41094	+	1.78532i	0.803646	+	0.595108i
$10$	−1.24020	−	0.716030i	−0.392186	−	0.226429i
$11$	5.93999	−	1.59162i	1.79097	−	0.479890i	0.798463	−	0.602044i	$-0.205647\pi$
$11$	5.93999	−	1.59162i	1.79097	−	0.479890i	0.992511	+	0.122154i	$0.0389801\pi$
$12$	1.69582	−	0.352417i	0.489541	−	0.101734i
$13$	−2.27066	−	2.80073i	−0.629769	−	0.776783i
$13$	−2.27066	−	2.80073i	−0.629769	−	0.776783i
$14$			1.00000i			0.267261i
$15$	−2.21514	+	1.11603i	−0.571948	+	0.288158i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−3.35614	−	5.81300i	−0.813983	−	1.40986i	−0.910056	−	0.414485i	$-0.863962\pi$
$17$	−3.35614	−	5.81300i	−0.813983	−	1.40986i	0.0960735	−	0.995374i	$-0.469372\pi$
$18$	1.10050	−	2.79086i	0.259389	−	0.657812i
$19$	0.0419710	−	0.156638i	0.00962880	−	0.0359352i	−0.960944	−	0.276742i	$-0.910745\pi$
$19$	0.0419710	−	0.156638i	0.00962880	−	0.0359352i	0.970573	+	0.240807i	$0.0774120\pi$
$20$	−0.370644	+	1.38326i	−0.0828786	+	0.309307i
$21$	1.44832	+	0.949929i	0.316050	+	0.207291i
$22$	−3.07476	−	5.32565i	−0.655542	−	1.13543i
$23$	−1.55923	+	2.70067i	−0.325123	+	0.563129i	−0.981537	−	0.191271i	$-0.938739\pi$
$23$	−1.55923	+	2.70067i	−0.325123	+	0.563129i	0.656414	+	0.754401i	$0.272072\pi$
$24$	−0.779319	−	1.54682i	−0.159078	−	0.315744i
$25$			2.94920i			0.589841i
$26$	−2.11761	+	2.91818i	−0.415297	+	0.572301i
$27$	−2.99667	−	4.24499i	−0.576710	−	0.816949i
$28$	0.965926	−	0.258819i	0.182543	−	0.0489122i
$29$	−6.86770	−	3.96507i	−1.27530	−	0.736295i	−0.299319	−	0.954153i	$-0.596760\pi$
$29$	−6.86770	−	3.96507i	−1.27530	−	0.736295i	−0.975980	+	0.217858i	$0.930093\pi$
$30$	1.65132	+	1.85081i	0.301489	+	0.337911i
$31$	2.28135	+	2.28135i	0.409743	+	0.409743i	0.881649	−	0.471906i	$-0.156434\pi$
$31$	2.28135	+	2.28135i	0.409743	+	0.409743i	−0.471906	+	0.881649i	$0.656434\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	−10.6341	−	0.605740i	−1.85115	−	0.105446i
$34$	−4.74629	+	4.74629i	−0.813983	+	0.813983i
$35$	−1.24020	+	0.716030i	−0.209632	+	0.121031i
$36$	−2.98059	−	0.340668i	−0.496766	−	0.0567781i
$37$	−1.39698	−	5.21359i	−0.229662	−	0.857109i	−0.980483	−	0.196604i	$-0.937009\pi$
$37$	−1.39698	−	5.21359i	−0.229662	−	0.857109i	0.750821	−	0.660506i	$-0.229658\pi$
$38$	−0.162163			−0.0263064
$39$	2.21488	+	5.83903i	0.354665	+	0.934994i
$40$	1.43206			0.226429
$41$	−0.728231	−	2.71779i	−0.113731	−	0.424448i	0.885458	−	0.464719i	$-0.153845\pi$
$41$	−0.728231	−	2.71779i	−0.113731	−	0.424448i	−0.999189	+	0.0402708i	$0.987178\pi$
$42$	0.542708	−	1.64483i	0.0837416	−	0.253803i
$43$	−1.39389	+	0.804764i	−0.212566	+	0.122725i	−0.602504	−	0.798116i	$-0.705830\pi$
$43$	−1.39389	+	0.804764i	−0.212566	+	0.122725i	0.389937	+	0.920841i	$0.372497\pi$
$44$	−4.34837	+	4.34837i	−0.655542	+	0.655542i
$45$	4.24921	−	0.633506i	0.633436	−	0.0944376i
$46$	3.01221	+	0.807119i	0.444126	+	0.119003i
$47$	−1.71389	−	1.71389i	−0.249996	−	0.249996i	0.570973	−	0.820969i	$-0.306566\pi$
$47$	−1.71389	−	1.71389i	−0.249996	−	0.249996i	−0.820969	+	0.570973i	$0.806566\pi$
$48$	−1.29241	+	1.15311i	−0.186544	+	0.166437i
$49$	0.866025	+	0.500000i	0.123718	+	0.0714286i
$50$	2.84871	−	0.763310i	0.402869	−	0.107948i
$51$	2.36552	+	11.3828i	0.331239	+	1.59391i
$52$	3.36682	+	1.29017i	0.466894	+	0.178915i
$53$		−	8.12791i		−	1.11645i	−0.829688	−	0.558227i	$-0.811482\pi$
$53$		−	8.12791i		−	1.11645i	0.829688	−	0.558227i	$-0.188518\pi$
$54$	−3.32475	+	3.99325i	−0.452441	+	0.543412i
$55$	4.40325	−	7.62665i	0.593734	−	1.02838i
$56$	−0.500000	−	0.866025i	−0.0668153	−	0.115728i
$57$	−0.154044	+	0.234865i	−0.0204036	+	0.0311086i
$58$	−2.05247	+	7.65992i	−0.269503	+	1.00580i
$59$	−1.78883	+	6.67601i	−0.232886	+	0.869142i	0.746205	+	0.665717i	$0.231874\pi$
$59$	−1.78883	+	6.67601i	−0.232886	+	0.869142i	−0.979090	+	0.203425i	$0.934793\pi$
$60$	1.36036	−	2.07408i	0.175621	−	0.267763i
$61$	−4.36155	−	7.55443i	−0.558440	−	0.967246i	−0.997627	−	0.0688502i	$-0.978067\pi$
$61$	−4.36155	−	7.55443i	−0.558440	−	0.967246i	0.439187	−	0.898395i	$-0.355266\pi$
$62$	1.61316	−	2.79408i	0.204872	−	0.354848i
$63$	−1.86671	−	2.34849i	−0.235183	−	0.295882i
$64$			1.00000i			0.125000i
$65$	−5.13539	−	0.536755i	−0.636967	−	0.0665762i
$66$	2.16720	+	10.4285i	0.266763	+	1.28366i
$67$	5.05737	−	1.35512i	0.617857	−	0.165554i	0.0637034	−	0.997969i	$-0.479709\pi$
$67$	5.05737	−	1.35512i	0.617857	−	0.165554i	0.554153	+	0.832415i	$0.313042\pi$
$68$	5.81300	+	3.35614i	0.704930	+	0.406991i
$69$	4.03035	−	3.59594i	0.485197	−	0.432900i
$70$	1.01262	+	1.01262i	0.121031	+	0.121031i
$71$	−9.93919	−	2.66320i	−1.17956	−	0.316063i	−0.384811	−	0.922995i	$-0.625733\pi$
$71$	−9.93919	−	2.66320i	−1.17956	−	0.316063i	−0.794754	+	0.606932i	$0.792400\pi$
$72$	0.442374	+	2.96720i	0.0521343	+	0.349688i
$73$	2.46804	−	2.46804i	0.288862	−	0.288862i	−0.547768	−	0.836630i	$-0.684522\pi$
$73$	2.46804	−	2.46804i	0.288862	−	0.288862i	0.836630	+	0.547768i	$0.184522\pi$
$74$	−4.67438	+	2.69875i	−0.543386	+	0.313724i
$75$	1.60056	−	4.85094i	0.184816	−	0.560139i
$76$	0.0419710	+	0.156638i	0.00481440	+	0.0179676i
$77$	−6.14953			−0.700804
$78$	5.06682	−	3.65066i	0.573704	−	0.413356i
$79$	5.05115			0.568298			0.284149	−	0.958780i	$-0.408289\pi$
$79$	5.05115			0.568298			0.284149	+	0.958780i	$0.408289\pi$
$80$	−0.370644	−	1.38326i	−0.0414393	−	0.154654i
$81$	2.62523	+	8.60861i	0.291692	+	0.956512i
$82$	−2.43671	+	1.40683i	−0.269089	+	0.155359i
$83$	3.93809	−	3.93809i	0.432261	−	0.432261i	−0.457136	−	0.889397i	$-0.651125\pi$
$83$	3.93809	−	3.93809i	0.432261	−	0.432261i	0.889397	+	0.457136i	$0.151125\pi$
$84$	−1.72925	−	0.0985019i	−0.188676	−	0.0107474i
$85$	−9.28484	−	2.48787i	−1.00708	−	0.269847i
$86$	1.13811	+	1.13811i	0.122725	+	0.122725i
$87$	9.14433	+	10.2490i	0.980375	+	1.09881i
$88$	5.32565	+	3.07476i	0.567716	+	0.327771i
$89$	10.2688	−	2.75151i	1.08849	−	0.291659i	0.330419	−	0.943834i	$-0.392810\pi$
$89$	10.2688	−	2.75151i	1.08849	−	0.291659i	0.758068	+	0.652175i	$0.226143\pi$
$90$	−1.71170	−	3.94046i	−0.180429	−	0.415361i
$91$	1.46841	+	3.29299i	0.153931	+	0.345199i
$92$		−	3.11847i		−	0.325123i
$93$	−2.51433	−	4.99055i	−0.260724	−	0.517496i
$94$	−1.21190	+	2.09907i	−0.124998	+	0.216503i
$95$	−0.116114	−	0.201115i	−0.0119130	−	0.0206340i
$96$	1.44832	+	0.949929i	0.147819	+	0.0969517i
$97$	−1.05510	+	3.93768i	−0.107129	+	0.399811i	−0.998578	−	0.0533101i	$-0.983023\pi$
$97$	−1.05510	+	3.93768i	−0.107129	+	0.399811i	0.891449	+	0.453121i	$0.149689\pi$
$98$	0.258819	−	0.965926i	0.0261447	−	0.0975732i
$99$	17.1625	+	6.76753i	1.72489	+	0.680162i
$100$	−1.47460	−	2.55409i	−0.147460	−	0.255409i
$101$	5.63686	−	9.76334i	0.560889	−	0.971488i	−0.436530	−	0.899690i	$-0.643793\pi$
$101$	5.63686	−	9.76334i	0.560889	−	0.971488i	0.997419	−	0.0717986i	$-0.0228739\pi$
$102$	10.3827	−	5.23100i	1.02804	−	0.517946i
$103$			6.36367i			0.627031i	0.949583	+	0.313516i	$0.101507\pi$
$103$			6.36367i			0.627031i	−0.949583	+	0.313516i	$0.898493\pi$
$104$	0.374813	−	3.58602i	0.0367534	−	0.351638i
$105$	2.42851	−	0.504682i	0.236999	−	0.0492519i
$106$	−7.85096	+	2.10366i	−0.762553	+	0.204325i
$107$	13.3862	+	7.72854i	1.29410	+	0.747147i	0.979378	−	0.202039i	$-0.0647566\pi$
$107$	13.3862	+	7.72854i	1.29410	+	0.747147i	0.314718	+	0.949185i	$0.398090\pi$
$108$	4.71769	+	2.17793i	0.453960	+	0.209572i
$109$	10.9344	+	10.9344i	1.04732	+	1.04732i	0.998823	+	0.0485013i	$0.0154445\pi$
$109$	10.9344	+	10.9344i	1.04732	+	1.04732i	0.0485013	+	0.998823i	$0.484555\pi$
$110$	−8.50642	−	2.27929i	−0.811055	−	0.217322i
$111$	−0.531665	+	9.33363i	−0.0504634	+	0.885909i
$112$	−0.707107	+	0.707107i	−0.0668153	+	0.0668153i
$113$	−10.5422	+	6.08657i	−0.991731	+	0.572576i	−0.905791	−	0.423724i	$-0.860723\pi$
$113$	−10.5422	+	6.08657i	−0.991731	+	0.572576i	−0.0859400	+	0.996300i	$0.527389\pi$
$114$	0.266731	+	0.0880073i	0.0249817	+	0.00824264i
$115$	1.15584	+	4.31366i	0.107783	+	0.402251i
$116$	7.93014			0.736295
$117$	−0.474215	−	10.8063i	−0.0438412	−	0.999039i
$118$	6.91151			0.636256
$119$	1.73726	+	6.48356i	0.159255	+	0.594347i
$120$	−2.35550	−	0.777190i	−0.215026	−	0.0709474i
$121$	23.2240	−	13.4084i	2.11127	−	1.21894i
$122$	−6.16817	+	6.16817i	−0.558440	+	0.558440i
$123$	−0.277152	+	4.86553i	−0.0249899	+	0.438710i
$124$	−3.11639	−	0.835033i	−0.279860	−	0.0749882i
$125$	8.04952	+	8.04952i	0.719971	+	0.719971i
$126$	−1.78532	+	2.41094i	−0.159049	+	0.214783i
$127$	−5.34018	−	3.08315i	−0.473864	−	0.273586i	0.243992	−	0.969777i	$-0.421543\pi$
$127$	−5.34018	−	3.08315i	−0.473864	−	0.273586i	−0.717856	+	0.696192i	$0.754876\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	2.72947	−	0.567224i	0.240316	−	0.0499413i
$130$	0.810672	+	5.09933i	0.0711006	+	0.447241i
$131$		−	4.60034i		−	0.401934i	−0.979598	−	0.200967i	$-0.935592\pi$
$131$		−	4.60034i		−	0.401934i	0.979598	−	0.200967i	$-0.0644083\pi$
$132$	9.51224	−	4.79244i	0.827934	−	0.417129i
$133$	−0.0810817	+	0.140438i	−0.00703067	+	0.0121775i
$134$	−2.61789	−	4.53432i	−0.226151	−	0.391705i
$135$	−7.33305	−	1.26407i	−0.631128	−	0.108794i
$136$	1.73726	−	6.48356i	0.148969	−	0.555960i
$137$	3.12108	−	11.6480i	0.266652	−	0.995158i	−0.694580	−	0.719416i	$-0.744410\pi$
$137$	3.12108	−	11.6480i	0.266652	−	0.995158i	0.961232	−	0.275742i	$-0.0889236\pi$
$138$	−4.51654	−	2.96232i	−0.384474	−	0.252170i
$139$	−3.90855	−	6.76981i	−0.331519	−	0.574208i	0.651291	−	0.758828i	$-0.274228\pi$
$139$	−3.90855	−	6.76981i	−0.331519	−	0.574208i	−0.982810	+	0.184620i	$0.940894\pi$
$140$	0.716030	−	1.24020i	0.0605156	−	0.104816i
$141$	1.88891	+	3.74919i	0.159075	+	0.315739i
$142$			10.2898i			0.863501i
$143$	−17.9454	−	13.0223i	−1.50067	−	1.08898i
$144$	2.75160	−	1.19527i	0.229300	−	0.0996058i
$145$	−10.9695	+	2.93926i	−0.910965	+	0.244092i
$146$	−3.02272	−	1.74517i	−0.250162	−	0.144431i
$147$	−1.15311	−	1.29241i	−0.0951070	−	0.106597i
$148$	3.81662	+	3.81662i	0.313724	+	0.313724i
$149$	−14.6256	−	3.91893i	−1.19818	−	0.321051i	−0.396065	−	0.918223i	$-0.629624\pi$
$149$	−14.6256	−	3.91893i	−1.19818	−	0.321051i	−0.802114	+	0.597172i	$0.796291\pi$
$150$	−5.09991	−	0.290502i	−0.416406	−	0.0237194i
$151$	14.0334	−	14.0334i	1.14202	−	1.14202i	0.153940	−	0.988080i	$-0.450804\pi$
$151$	14.0334	−	14.0334i	1.14202	−	1.14202i	0.988080	−	0.153940i	$-0.0491963\pi$
$152$	0.140438	−	0.0810817i	0.0113910	−	0.00657659i
$153$	2.28666	−	20.0066i	0.184865	−	1.61743i
$154$	1.59162	+	5.93999i	0.128256	+	0.478658i
$155$	4.62028			0.371110
$156$	−4.83766	−	3.94931i	−0.387323	−	0.316198i
$157$	11.1221			0.887637			0.443819	−	0.896117i	$-0.353623\pi$
$157$	11.1221			0.887637			0.443819	+	0.896117i	$0.353623\pi$
$158$	−1.30733	−	4.87903i	−0.104006	−	0.388155i
$159$	−4.41108	+	13.3690i	−0.349822	+	1.06023i
$160$	−1.24020	+	0.716030i	−0.0980464	+	0.0566071i
$161$	2.20509	−	2.20509i	0.173785	−	0.173785i
$162$	7.63582	−	4.76385i	0.599927	−	0.374283i
$163$	12.2065	+	3.27073i	0.956089	+	0.256183i	0.702944	−	0.711245i	$-0.251868\pi$
$163$	12.2065	+	3.27073i	0.956089	+	0.256183i	0.253145	+	0.967428i	$0.418535\pi$
$164$	1.98956	+	1.98956i	0.155359	+	0.155359i
$165$	−11.3816	+	10.1549i	−0.886059	+	0.790555i
$166$	−4.82315	−	2.78465i	−0.374349	−	0.216131i
$167$	−6.09250	+	1.63248i	−0.471452	+	0.126325i	−0.486720	−	0.873558i	$-0.661807\pi$
$167$	−6.09250	+	1.63248i	−0.471452	+	0.126325i	0.0152676	+	0.999883i	$0.495140\pi$
$168$	0.352417	+	1.69582i	0.0271895	+	0.130835i
$169$	−2.68817	+	12.7190i	−0.206782	+	0.978387i
$170$			9.61238i			0.737236i
$171$	0.380839	−	0.302712i	0.0291235	−	0.0231490i
$172$	0.804764	−	1.39389i	0.0613627	−	0.106283i
$173$	−1.05378	−	1.82519i	−0.0801171	−	0.138767i	0.823183	−	0.567776i	$-0.192196\pi$
$173$	−1.05378	−	1.82519i	−0.0801171	−	0.138767i	−0.903300	+	0.429009i	$0.858863\pi$
$174$	7.53307	−	11.4854i	0.571080	−	0.870705i
$175$	0.763310	−	2.84871i	0.0577008	−	0.215342i
$176$	1.59162	−	5.93999i	0.119973	−	0.447744i
$177$	6.56544	−	10.0101i	0.493489	−	0.752404i
$178$	−5.31551	−	9.20673i	−0.398414	−	0.690073i
$179$	−11.4325	+	19.8016i	−0.854503	+	1.48004i	0.0226027	+	0.999745i	$0.492805\pi$
$179$	−11.4325	+	19.8016i	−0.854503	+	1.48004i	−0.877105	+	0.480298i	$0.840529\pi$
$180$	−3.36317	+	2.67324i	−0.250676	+	0.199252i
$181$			17.3739i			1.29139i	0.763594	+	0.645697i	$0.223433\pi$
$181$			17.3739i			1.29139i	−0.763594	+	0.645697i	$0.776567\pi$
$182$	2.80073	−	2.27066i	0.207604	−	0.168313i
$183$	3.07417	+	14.7928i	0.227249	+	1.09352i
$184$	−3.01221	+	0.807119i	−0.222063	+	0.0595016i
$185$	−6.69399	−	3.86478i	−0.492152	−	0.284144i
$186$	−4.16974	+	3.72031i	−0.305740	+	0.272786i
$187$	−29.1875	−	29.1875i	−2.13440	−	2.13440i
$188$	2.34121	+	0.627326i	0.170750	+	0.0457524i
$189$	1.79588	+	4.87594i	0.130631	+	0.354673i
$190$	−0.164210	+	0.164210i	−0.0119130	+	0.0119130i
$191$	12.2932	−	7.09748i	0.889505	−	0.513556i	0.0157241	−	0.999876i	$-0.494995\pi$
$191$	12.2932	−	7.09748i	0.889505	−	0.513556i	0.873780	+	0.486321i	$0.161661\pi$
$192$	0.542708	−	1.64483i	0.0391666	−	0.118705i
$193$	4.95428	+	18.4896i	0.356617	+	1.33091i	0.878437	+	0.477858i	$0.158586\pi$
$193$	4.95428	+	18.4896i	0.356617	+	1.33091i	−0.521820	+	0.853055i	$0.674747\pi$
$194$	4.07659			0.292682
$195$	8.15555	+	3.66989i	0.584031	+	0.262806i
$196$	−1.00000			−0.0714286
$197$	6.06475	+	22.6340i	0.432096	+	1.61260i	0.747923	+	0.663786i	$0.231051\pi$
$197$	6.06475	+	22.6340i	0.432096	+	1.61260i	−0.315827	+	0.948817i	$0.602282\pi$
$198$	2.09495	−	18.3293i	0.148882	−	1.30260i
$199$	−6.10110	+	3.52247i	−0.432495	+	0.249701i	−0.700409	−	0.713742i	$-0.746999\pi$
$199$	−6.10110	+	3.52247i	−0.432495	+	0.249701i	0.267914	+	0.963443i	$0.413666\pi$
$200$	−2.08540	+	2.08540i	−0.147460	+	0.147460i
$201$	−9.05396	−	0.515734i	−0.638617	−	0.0363771i
$202$	−10.8896	−	2.91786i	−0.766189	−	0.205300i
$203$	5.60745	+	5.60745i	0.393566	+	0.393566i
$204$	−7.74000	−	8.67504i	−0.541908	−	0.607374i
$205$	−3.48951	−	2.01467i	−0.243718	−	0.140711i
$206$	6.14683	−	1.64704i	0.428270	−	0.114755i
$207$	−8.58079	+	3.72741i	−0.596406	+	0.259073i
$208$	−3.56083	+	0.566088i	−0.246899	+	0.0392511i
$209$		−	0.997228i		−	0.0689797i
$210$	−1.11603	−	2.21514i	−0.0770134	−	0.152859i
$211$	7.00393	−	12.1312i	0.482171	−	0.835144i	−0.517620	−	0.855611i	$-0.673182\pi$
$211$	7.00393	−	12.1312i	0.482171	−	0.835144i	0.999791	+	0.0204668i	$0.00651522\pi$
$212$	4.06396	+	7.03898i	0.279114	+	0.483439i
$213$	14.9029	+	9.77458i	1.02113	+	0.669743i
$214$	4.00059	−	14.9304i	0.273475	−	1.02062i
$215$	−0.596562	+	2.22640i	−0.0406852	+	0.151839i
$216$	0.882694	−	5.12063i	0.0600597	−	0.348415i
$217$	−1.61316	−	2.79408i	−0.109508	−	0.189674i
$218$	7.73178	−	13.3918i	0.523662	−	0.907010i
$219$	−5.39894	+	2.72009i	−0.364826	+	0.183806i
$220$			8.80649i			0.593734i
$221$	−8.65998	+	22.5990i	−0.582533	+	1.52017i
$222$	9.15320	−	1.90217i	0.614322	−	0.127665i
$223$	−28.3377	+	7.59306i	−1.89763	+	0.508469i	−0.900317	+	0.435234i	$0.856666\pi$
$223$	−28.3377	+	7.59306i	−1.89763	+	0.508469i	−0.997315	+	0.0732348i	$0.976668\pi$
$224$	0.866025	+	0.500000i	0.0578638	+	0.0334077i
$225$	−5.26529	+	7.11035i	−0.351019	+	0.474023i
$226$	8.60771	+	8.60771i	0.572576	+	0.572576i
$227$	10.9930	+	2.94557i	0.729631	+	0.195504i	0.604465	−	0.796632i	$-0.293387\pi$
$227$	10.9930	+	2.94557i	0.729631	+	0.195504i	0.125166	+	0.992136i	$0.460054\pi$
$228$	0.0159734	−	0.280421i	0.00105786	−	0.0185713i
$229$	6.80059	−	6.80059i	0.449395	−	0.449395i	−0.445758	−	0.895153i	$-0.647066\pi$
$229$	6.80059	−	6.80059i	0.449395	−	0.449395i	0.895153	+	0.445758i	$0.147066\pi$
$230$	3.86752	−	2.23292i	0.255017	−	0.147234i
$231$	10.1149	+	3.33740i	0.665514	+	0.219585i
$232$	−2.05247	−	7.65992i	−0.134751	−	0.502899i
$233$	−3.30963			−0.216821			−0.108411	−	0.994106i	$-0.534576\pi$
$233$	−3.30963			−0.216821			−0.108411	+	0.994106i	$0.534576\pi$
$234$	−10.3153	+	3.25492i	−0.674333	+	0.212781i
$235$	−3.47103			−0.226425
$236$	−1.78883	−	6.67601i	−0.116443	−	0.434571i
$237$	−8.30828	−	2.74130i	−0.539681	−	0.178066i
$238$	5.81300	−	3.35614i	0.376801	−	0.217546i
$239$	11.9734	−	11.9734i	0.774492	−	0.774492i	−0.204396	−	0.978888i	$-0.565523\pi$
$239$	11.9734	−	11.9734i	0.774492	−	0.774492i	0.978888	+	0.204396i	$0.0655230\pi$
$240$	−0.141061	+	2.47639i	−0.00910542	+	0.159850i
$241$	−26.9210	−	7.21346i	−1.73413	−	0.464660i	−0.753006	−	0.658014i	$-0.771397\pi$
$241$	−26.9210	−	7.21346i	−1.73413	−	0.464660i	−0.981129	+	0.193354i	$0.938063\pi$
$242$	−18.9623	−	18.9623i	−1.21894	−	1.21894i
$243$	0.353900	−	15.5844i	0.0227027	−	0.999742i
$244$	7.55443	+	4.36155i	0.483623	+	0.279220i
$245$	1.38326	−	0.370644i	0.0883735	−	0.0236796i
$246$	4.77147	−	0.991583i	0.304218	−	0.0632210i
$247$	−0.534002	+	0.238122i	−0.0339777	+	0.0151514i
$248$			3.22632i			0.204872i
$249$	−8.61471	+	4.34025i	−0.545935	+	0.275052i
$250$	5.69187	−	9.85860i	0.359985	−	0.623513i
$251$	11.6110	+	20.1109i	0.732881	+	1.26939i	0.955647	+	0.294516i	$0.0951583\pi$
$251$	11.6110	+	20.1109i	0.732881	+	1.26939i	−0.222765	+	0.974872i	$0.571508\pi$
$252$	2.79086	+	1.10050i	0.175808	+	0.0693247i
$253$	−4.96340	+	18.5237i	−0.312046	+	1.16457i
$254$	−1.59596	+	5.95620i	−0.100139	+	0.373725i
$255$	13.9218	+	9.13107i	0.871817	+	0.571810i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−10.8682	+	18.8242i	−0.677937	+	1.17422i	0.297664	+	0.954671i	$0.403792\pi$
$257$	−10.8682	+	18.8242i	−0.677937	+	1.17422i	−0.975601	+	0.219550i	$0.929541\pi$
$258$	−1.25433	−	2.48965i	−0.0780915	−	0.154999i
$259$			5.39751i			0.335385i
$260$	4.71576	−	2.10285i	0.292459	−	0.130413i
$261$	−9.47865	−	21.8206i	−0.586714	−	1.35066i
$262$	−4.44359	+	1.19066i	−0.274526	+	0.0735590i
$263$	6.30441	+	3.63985i	0.388747	+	0.224443i	0.681617	−	0.731709i	$-0.261277\pi$
$263$	6.30441	+	3.63985i	0.388747	+	0.224443i	−0.292870	+	0.956152i	$0.594610\pi$
$264$	−7.09109	−	7.94774i	−0.436427	−	0.489149i
$265$	−8.23048	−	8.23048i	−0.505594	−	0.505594i
$266$	0.156638	+	0.0419710i	0.00960408	+	0.00257340i
$267$	−18.3837	−	1.04718i	−1.12506	−	0.0640861i
$268$	−3.70225	+	3.70225i	−0.226151	+	0.226151i
$269$	16.1674	−	9.33424i	0.985743	−	0.569119i	0.0817439	−	0.996653i	$-0.473951\pi$
$269$	16.1674	−	9.33424i	0.985743	−	0.569119i	0.903999	+	0.427534i	$0.140618\pi$
$270$	0.676934	+	7.41035i	0.0411969	+	0.450979i
$271$	−3.19612	−	11.9281i	−0.194151	−	0.724580i	−0.992485	−	0.122366i	$-0.960952\pi$
$271$	−3.19612	−	11.9281i	−0.194151	−	0.724580i	0.798334	−	0.602214i	$-0.205715\pi$
$272$	−6.71227			−0.406991
$273$	−0.628157	−	6.21333i	−0.0380178	−	0.376048i
$274$	−12.0589			−0.728506
$275$	4.69400	+	17.5182i	0.283059	+	1.05639i
$276$	−1.69242	+	5.12935i	−0.101872	+	0.308751i
$277$	27.0494	−	15.6170i	1.62524	−	0.938333i	0.639755	−	0.768579i	$-0.279036\pi$
$277$	27.0494	−	15.6170i	1.62524	−	0.938333i	0.985486	−	0.169754i	$-0.0542974\pi$
$278$	−5.52753	+	5.52753i	−0.331519	+	0.331519i
$279$	1.42724	+	9.57315i	0.0854467	+	0.573130i
$280$	−1.38326	−	0.370644i	−0.0826658	−	0.0221502i
$281$	−9.52174	−	9.52174i	−0.568019	−	0.568019i	0.363554	−	0.931573i	$-0.381563\pi$
$281$	−9.52174	−	9.52174i	−0.568019	−	0.568019i	−0.931573	+	0.363554i	$0.881563\pi$
$282$	3.13255	−	2.79491i	0.186541	−	0.166435i
$283$	13.2517	+	7.65087i	0.787732	+	0.454797i	0.839163	−	0.543879i	$-0.183045\pi$
$283$	13.2517	+	7.65087i	0.787732	+	0.454797i	−0.0514315	+	0.998677i	$0.516378\pi$
$284$	9.93919	−	2.66320i	0.589782	−	0.158032i
$285$	0.0818409	+	0.393816i	0.00484783	+	0.0233276i
$286$	−7.93394	+	20.7043i	−0.469144	+	1.22427i
$287$			2.81367i			0.166086i
$288$	−1.86671	−	2.34849i	−0.109997	−	0.138386i
$289$	−14.0273	+	24.2960i	−0.825135	+	1.42918i
$290$	5.67821	+	9.83496i	0.333436	+	0.577529i
$291$	3.87247	−	5.90421i	0.227008	−	0.346111i
$292$	−0.903366	+	3.37141i	−0.0528655	+	0.197297i
$293$	−2.15518	+	8.04324i	−0.125907	+	0.469891i	−0.999870	−	0.0161006i	$-0.994875\pi$
$293$	−2.15518	+	8.04324i	−0.125907	+	0.469891i	0.873963	+	0.485992i	$0.161541\pi$
$294$	−0.949929	+	1.44832i	−0.0554010	+	0.0844678i
$295$	4.94885	+	8.57166i	0.288133	+	0.499061i
$296$	2.69875	−	4.67438i	0.156862	−	0.271693i
$297$	−24.5566	−	20.4457i	−1.42492	−	1.18638i
$298$			15.1416i			0.877127i
$299$	11.1044	−	1.76533i	0.642181	−	0.102091i
$300$	1.03935	+	5.00132i	0.0600068	+	0.288751i
$301$	1.55468	−	0.416576i	0.0896105	−	0.0240111i
$302$	−17.1873	−	9.92310i	−0.989019	−	0.571010i
$303$	−14.5703	+	12.9999i	−0.837043	+	0.746823i
$304$	−0.114667	−	0.114667i	−0.00657659	−	0.00657659i
$305$	−12.0664	−	3.23317i	−0.690917	−	0.185131i
$306$	−19.9167	+	2.96934i	−1.13856	+	0.169746i
$307$	8.34685	−	8.34685i	0.476380	−	0.476380i	−0.427592	−	0.903972i	$-0.640638\pi$
$307$	8.34685	−	8.34685i	0.476380	−	0.476380i	0.903972	+	0.427592i	$0.140638\pi$
$308$	5.32565	−	3.07476i	0.303457	−	0.175201i
$309$	3.45361	−	10.4672i	0.196469	−	0.595456i
$310$	−1.19582	−	4.46285i	−0.0679179	−	0.253473i
$311$	26.0701			1.47830			0.739149	−	0.673542i	$-0.235228\pi$
$311$	26.0701			1.47830			0.739149	+	0.673542i	$0.235228\pi$
$312$	−2.56266	+	5.69498i	−0.145082	+	0.322415i
$313$	3.52605			0.199304			0.0996520	−	0.995022i	$-0.468227\pi$
$313$	3.52605			0.199304			0.0996520	+	0.995022i	$0.468227\pi$
$314$	−2.87860	−	10.7431i	−0.162449	−	0.606268i
$315$	−4.26839	−	0.487857i	−0.240497	−	0.0274877i
$316$	−4.37442	+	2.52557i	−0.246080	+	0.142075i
$317$	−4.13339	+	4.13339i	−0.232154	+	0.232154i	−0.813591	−	0.581437i	$-0.802491\pi$
$317$	−4.13339	+	4.13339i	−0.232154	+	0.232154i	0.581437	+	0.813591i	$0.302491\pi$
$318$	14.0552	+	0.800615i	0.788175	+	0.0448963i
$319$	−47.1049	−	12.6217i	−2.63737	−	0.706681i
$320$	1.01262	+	1.01262i	0.0566071	+	0.0566071i
$321$	−17.8237	−	19.9770i	−0.994824	−	1.11501i
$322$	−2.70067	−	1.55923i	−0.150503	−	0.0868927i
$323$	−1.05140	+	0.281721i	−0.0585012	+	0.0156753i
$324$	−6.57782	−	6.14266i	−0.365435	−	0.341259i
$325$	8.25993	−	6.69665i	0.458178	−	0.371463i
$326$		−	12.6371i		−	0.699906i
$327$	−12.0510	−	23.9194i	−0.666424	−	1.32275i
$328$	1.40683	−	2.43671i	0.0776794	−	0.134545i
$329$	1.21190	+	2.09907i	0.0668142	+	0.115726i
$330$	12.7546	+	8.36554i	0.702119	+	0.460508i
$331$	−1.12226	+	4.18832i	−0.0616848	+	0.230211i	−0.989885	−	0.141869i	$-0.954689\pi$
$331$	−1.12226	+	4.18832i	−0.0616848	+	0.230211i	0.928201	+	0.372080i	$0.121355\pi$
$332$	−1.44144	+	5.37952i	−0.0791093	+	0.295240i
$333$	5.93993	−	15.0637i	0.325506	−	0.825486i
$334$	3.15371	+	5.46239i	0.172563	+	0.298889i
$335$	3.74897	−	6.49341i	0.204828	−	0.354773i
$336$	1.54682	−	0.779319i	0.0843861	−	0.0425153i
$337$		−	28.1885i		−	1.53552i	−0.640735	−	0.767762i	$-0.721370\pi$
$337$		−	28.1885i		−	1.53552i	0.640735	−	0.767762i	$-0.278630\pi$
$338$	12.9814	−	0.695353i	0.706095	−	0.0378222i
$339$	20.6434	−	4.29002i	1.12120	−	0.233002i
$340$	9.28484	−	2.48787i	0.503541	−	0.134923i
$341$	17.1822	+	9.92018i	0.930471	+	0.537208i
$342$	−0.390966	−	0.289514i	−0.0211410	−	0.0156551i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	−1.55468	−	0.416576i	−0.0838229	−	0.0224603i
$345$	0.439893	−	7.72253i	0.0236830	−	0.415767i
$346$	−1.49026	+	1.49026i	−0.0801171	+	0.0801171i
$347$	4.48337	−	2.58848i	0.240680	−	0.138957i	−0.374809	−	0.927102i	$-0.622292\pi$
$347$	4.48337	−	2.58848i	0.240680	−	0.138957i	0.615489	+	0.788145i	$0.288958\pi$
$348$	−13.0437	−	4.30375i	−0.699217	−	0.230705i
$349$	−2.58678	−	9.65399i	−0.138467	−	0.516766i	−0.999960	−	0.00899587i	$-0.997136\pi$
$349$	−2.58678	−	9.65399i	−0.138467	−	0.516766i	0.861492	−	0.507770i	$-0.169530\pi$
$350$	−2.94920			−0.157642
$351$	−5.08464	+	18.0318i	−0.271398	+	0.962467i
$352$	−6.14953			−0.327771
$353$	−7.77840	−	29.0294i	−0.414003	−	1.54508i	−0.786825	−	0.617176i	$-0.788277\pi$
$353$	−7.77840	−	29.0294i	−0.414003	−	1.54508i	0.372822	−	0.927903i	$-0.378390\pi$
$354$	−11.3683	−	3.75093i	−0.604217	−	0.199360i
$355$	−12.7614	+	7.36781i	−0.677306	+	0.391043i
$356$	−7.51726	+	7.51726i	−0.398414	+	0.398414i
$357$	0.661172	−	11.6072i	0.0349929	−	0.614317i
$358$	22.0858	+	5.91788i	1.16727	+	0.312770i
$359$	−4.39884	−	4.39884i	−0.232162	−	0.232162i	0.581433	−	0.813594i	$-0.302492\pi$
$359$	−4.39884	−	4.39884i	−0.232162	−	0.232162i	−0.813594	+	0.581433i	$0.802492\pi$
$360$	3.45261	+	2.55669i	0.181968	+	0.134749i
$361$	16.4317	+	9.48685i	0.864827	+	0.499308i
$362$	16.7819	−	4.49670i	0.882039	−	0.236342i
$363$	−45.4763	+	9.45066i	−2.38689	+	0.496031i
$364$	−2.91818	−	2.11761i	−0.152954	−	0.110993i
$365$		−	4.99837i		−	0.261627i
$366$	13.4931	−	6.79808i	0.705296	−	0.355341i
$367$	2.35165	−	4.07318i	0.122755	−	0.212618i	−0.798098	−	0.602528i	$-0.794160\pi$
$367$	2.35165	−	4.07318i	0.122755	−	0.212618i	0.920853	+	0.389909i	$0.127494\pi$
$368$	1.55923	+	2.70067i	0.0812807	+	0.140782i
$369$	3.09643	−	7.85256i	0.161194	−	0.408788i
$370$	−2.00056	+	7.46618i	−0.104004	+	0.388148i
$371$	−2.10366	+	7.85096i	−0.109217	+	0.407602i
$372$	4.67275	+	3.06478i	0.242271	+	0.158901i
$373$	5.29582	+	9.17262i	0.274207	+	0.474940i	0.969935	−	0.243365i	$-0.0782514\pi$
$373$	5.29582	+	9.17262i	0.274207	+	0.474940i	−0.695728	+	0.718306i	$0.744918\pi$
$374$	−20.6387	+	35.7472i	−1.06720	+	1.84844i
$375$	−8.87156	−	17.6086i	−0.458125	−	0.909306i
$376$		−	2.42380i		−	0.124998i
$377$	4.48915	+	28.2379i	0.231203	+	1.45433i
$378$	4.24499	−	2.99667i	0.218339	−	0.154132i
$379$	−21.5507	+	5.77450i	−1.10699	+	0.296616i	−0.765607	−	0.643309i	$-0.777561\pi$
$379$	−21.5507	+	5.77450i	−1.10699	+	0.296616i	−0.341380	+	0.939925i	$0.610894\pi$
$380$	0.201115	+	0.116114i	0.0103170	+	0.00595651i
$381$	7.11044	+	7.96942i	0.364279	+	0.408286i
$382$	−10.0374	−	10.0374i	−0.513556	−	0.513556i
$383$	−14.4047	−	3.85972i	−0.736044	−	0.197222i	−0.128725	−	0.991680i	$-0.541088\pi$
$383$	−14.4047	−	3.85972i	−0.736044	−	0.197222i	−0.607319	+	0.794458i	$0.707755\pi$
$384$	−1.72925	−	0.0985019i	−0.0882453	−	0.00502665i
$385$	−6.22713	+	6.22713i	−0.317364	+	0.317364i
$386$	16.5774	−	9.57094i	0.843765	−	0.487148i
$387$	−4.79735	−	0.548315i	−0.243863	−	0.0278724i
$388$	−1.05510	−	3.93768i	−0.0535645	−	0.199906i
$389$	−14.6386			−0.742205			−0.371103	−	0.928592i	$-0.621020\pi$
$389$	−14.6386			−0.742205			−0.371103	+	0.928592i	$0.621020\pi$
$390$	1.43403	−	8.82749i	0.0726148	−	0.446997i
$391$	20.9320			1.05858
$392$	0.258819	+	0.965926i	0.0130723	+	0.0487866i
$393$	−2.49664	+	7.56678i	−0.125939	+	0.381694i
$394$	20.2930	−	11.7162i	1.02235	−	0.590253i
$395$	5.11489	−	5.11489i	0.257358	−	0.257358i
$396$	−18.2469	+	2.72039i	−0.916942	+	0.136705i
$397$	22.0441	+	5.90671i	1.10636	+	0.296449i	0.765353	−	0.643611i	$-0.222564\pi$
$397$	22.0441	+	5.90671i	1.10636	+	0.296449i	0.341010	+	0.940060i	$0.389231\pi$
$398$	4.98153	+	4.98153i	0.249701	+	0.249701i
$399$	0.209582	−	0.186992i	0.0104922	−	0.00936133i
$400$	2.55409	+	1.47460i	0.127704	+	0.0737301i
$401$	19.3124	−	5.17474i	0.964414	−	0.258414i	0.257946	−	0.966159i	$-0.416954\pi$
$401$	19.3124	−	5.17474i	0.964414	−	0.258414i	0.706468	+	0.707745i	$0.250288\pi$
$402$	1.84518	+	8.87893i	0.0920290	+	0.442841i
$403$	1.20927	−	11.5696i	0.0602379	−	0.576325i
$404$			11.2737i			0.560889i
$405$	11.3756	+	6.05888i	0.565258	+	0.301068i
$406$	3.96507	−	6.86770i	0.196783	−	0.340838i
$407$	−16.5961	−	28.7452i	−0.822637	−	1.42485i
$408$	−6.37618	+	9.72153i	−0.315668	+	0.481287i
$409$	−4.36347	+	16.2847i	−0.215760	+	0.805226i	0.770138	+	0.637877i	$0.220187\pi$
$409$	−4.36347	+	16.2847i	−0.215760	+	0.805226i	−0.985898	+	0.167349i	$0.946479\pi$
$410$	−1.04287	+	3.89204i	−0.0515037	+	0.192214i
$411$	−11.4551	+	17.4652i	−0.565039	+	0.861495i
$412$	−3.18184	−	5.51110i	−0.156758	−	0.271512i
$413$	3.45576	−	5.98554i	0.170047	−	0.294529i
$414$	5.82128	+	7.32368i	0.286100	+	0.359939i
$415$		−	7.97556i		−	0.391505i
$416$	1.46841	+	3.29299i	0.0719948	+	0.161452i
$417$	2.75488	+	13.2564i	0.134907	+	0.649168i
$418$	−0.963248	+	0.258102i	−0.0471140	+	0.0126242i
$419$	27.4158	+	15.8285i	1.33935	+	0.773275i	0.986711	−	0.162484i	$-0.0519506\pi$
$419$	27.4158	+	15.8285i	1.33935	+	0.773275i	0.352640	+	0.935759i	$0.385284\pi$
$420$	−1.85081	+	1.65132i	−0.0903105	+	0.0805764i
$421$	−10.9210	−	10.9210i	−0.532256	−	0.532256i	0.388987	−	0.921243i	$-0.372825\pi$
$421$	−10.9210	−	10.9210i	−0.532256	−	0.532256i	−0.921243	+	0.388987i	$0.872825\pi$
$422$	−13.5306	−	3.62550i	−0.658657	−	0.176487i
$423$	−1.07223	−	7.19191i	−0.0521334	−	0.349683i
$424$	5.74730	−	5.74730i	0.279114	−	0.279114i
$425$	17.1437	−	9.89793i	0.831593	−	0.480120i
$426$	5.58436	−	16.9250i	0.270563	−	0.820018i
$427$	2.25771	+	8.42587i	0.109258	+	0.407756i
$428$	−15.4571			−0.747147
$429$	22.4499	+	31.1586i	1.08389	+	1.50435i
$430$	2.30494			0.111154
$431$	4.82835	+	18.0196i	0.232573	+	0.867976i	0.979228	+	0.202763i	$0.0649922\pi$
$431$	4.82835	+	18.0196i	0.232573	+	0.867976i	−0.746654	+	0.665212i	$0.768341\pi$
$432$	−5.17461	+	0.472699i	−0.248963	+	0.0227428i
$433$	18.0627	−	10.4285i	0.868037	−	0.501161i	0.00134144	−	0.999999i	$-0.499573\pi$
$433$	18.0627	−	10.4285i	0.868037	−	0.501161i	0.866695	+	0.498838i	$0.166240\pi$
$434$	−2.28135	+	2.28135i	−0.109508	+	0.109508i
$435$	19.6381	+	1.11863i	0.941574	+	0.0536342i
$436$	−14.9367	−	4.00226i	−0.715336	−	0.191674i
$437$	0.357585	+	0.357585i	0.0171056	+	0.0171056i
$438$	4.02475	+	4.51096i	0.192310	+	0.215542i
$439$	34.7872	+	20.0844i	1.66030	+	0.958577i	0.972568	+	0.232617i	$0.0747288\pi$
$439$	34.7872	+	20.0844i	1.66030	+	0.958577i	0.687736	+	0.725961i	$0.258605\pi$
$440$	8.50642	−	2.27929i	0.405528	−	0.108661i
$441$	1.19527	+	2.75160i	0.0569176	+	0.131029i
$442$	24.0703	+	2.51585i	1.14491	+	0.119667i
$443$		−	22.0050i		−	1.04549i	−0.852490	−	0.522744i	$-0.824908\pi$
$443$		−	22.0050i		−	1.04549i	0.852490	−	0.522744i	$-0.175092\pi$
$444$	−4.20638	−	8.34899i	−0.199626	−	0.396226i
$445$	7.61212	−	13.1846i	0.360849	−	0.625009i
$446$	14.6687	+	25.4069i	0.694582	+	1.20305i
$447$	21.9299	+	14.3834i	1.03725	+	0.680312i
$448$	0.258819	−	0.965926i	0.0122281	−	0.0456357i
$449$	8.30965	−	31.0120i	0.392157	−	1.46355i	−0.434413	−	0.900714i	$-0.643044\pi$
$449$	8.30965	−	31.0120i	0.392157	−	1.46355i	0.826569	−	0.562835i	$-0.190289\pi$
$450$	8.23082	+	3.24559i	0.388005	+	0.152998i
$451$	−8.65137	−	14.9846i	−0.407377	−	0.705598i
$452$	6.08657	−	10.5422i	0.286288	−	0.495866i
$453$	−30.6986	+	15.4665i	−1.44234	+	0.726680i
$454$		−	11.3808i		−	0.534127i
$455$	4.82148	+	1.84760i	0.226035	+	0.0866169i
$456$	−0.275000	+	0.0571491i	−0.0128780	+	0.00267625i
$457$	18.3393	−	4.91399i	0.857875	−	0.229867i	0.197037	−	0.980396i	$-0.436868\pi$
$457$	18.3393	−	4.91399i	0.857875	−	0.229867i	0.660837	+	0.750529i	$0.270201\pi$
$458$	−8.32898	−	4.80874i	−0.389188	−	0.224698i
$459$	−14.6189	+	31.6664i	−0.682351	+	1.47806i
$460$	−3.15782	−	3.15782i	−0.147234	−	0.147234i
$461$	5.62076	+	1.50608i	0.261785	+	0.0701450i	0.387324	−	0.921944i	$-0.373399\pi$
$461$	5.62076	+	1.50608i	0.261785	+	0.0701450i	−0.125539	+	0.992089i	$0.540066\pi$
$462$	0.605740	−	10.6341i	0.0281816	−	0.494741i
$463$	14.7365	−	14.7365i	0.684863	−	0.684863i	−0.276229	−	0.961092i	$-0.589085\pi$
$463$	14.7365	−	14.7365i	0.684863	−	0.684863i	0.961092	+	0.276229i	$0.0890849\pi$
$464$	−6.86770	+	3.96507i	−0.318825	+	0.184074i
$465$	−7.59958	−	2.50746i	−0.352422	−	0.116281i
$466$	0.856596	+	3.19686i	0.0396811	+	0.148092i
$467$	−7.39814			−0.342345			−0.171173	−	0.985241i	$-0.554756\pi$
$467$	−7.39814			−0.342345			−0.171173	+	0.985241i	$0.554756\pi$
$468$	5.81381	+	9.12138i	0.268743	+	0.421636i
$469$	−5.23578			−0.241766
$470$	0.898368	+	3.35275i	0.0414386	+	0.154651i
$471$	−18.2939	−	6.03603i	−0.842939	−	0.278126i
$472$	−5.98554	+	3.45576i	−0.275507	+	0.159064i
$473$	−6.99883	+	6.99883i	−0.321806	+	0.321806i
$474$	−0.497548	+	8.73468i	−0.0228531	+	0.401197i
$475$	0.461957	+	0.123781i	0.0211960	+	0.00567946i
$476$	−4.74629	−	4.74629i	−0.217546	−	0.217546i
$477$	14.5110	−	19.5959i	0.664412	−	0.897234i
$478$	−14.6643	−	8.46645i	−0.670730	−	0.387246i
$479$	−37.4614	+	10.0378i	−1.71166	+	0.458637i	−0.975829	−	0.218534i	$-0.929873\pi$
$479$	−37.4614	+	10.0378i	−1.71166	+	0.458637i	−0.735826	+	0.677171i	$0.763206\pi$
$480$	2.42851	−	0.504682i	0.110846	−	0.0230355i
$481$	−11.4298	+	15.7509i	−0.521154	+	0.718178i
$482$			27.8707i			1.26947i
$483$	−4.82372	+	2.43028i	−0.219487	+	0.110582i
$484$	−13.4084	+	23.2240i	−0.609471	+	1.05563i
$485$	2.91896	+	5.05579i	0.132543	+	0.229571i
$486$	−15.1450	+	3.69171i	−0.686992	+	0.167459i
$487$	0.671688	−	2.50677i	0.0304371	−	0.113593i	−0.949036	−	0.315168i	$-0.897939\pi$
$487$	0.671688	−	2.50677i	0.0304371	−	0.113593i	0.979473	+	0.201575i	$0.0646059\pi$
$488$	2.25771	−	8.42587i	0.102202	−	0.381421i
$489$	−18.3026	−	12.0044i	−0.827674	−	0.542857i
$490$	−0.716030	−	1.24020i	−0.0323469	−	0.0560265i
$491$	−6.49780	+	11.2545i	−0.293241	+	0.507909i	−0.974574	−	0.224065i	$-0.928067\pi$
$491$	−6.49780	+	11.2545i	−0.293241	+	0.507909i	0.681333	+	0.731974i	$0.261401\pi$
$492$	−2.19274	−	4.35225i	−0.0988565	−	0.196214i
$493$			53.2292i			2.39732i
$494$	0.368218	+	0.454176i	0.0165669	+	0.0204343i
$495$	24.2320	−	10.5261i	1.08915	−	0.473115i
$496$	3.11639	−	0.835033i	0.139930	−	0.0374941i
$497$	8.91123	+	5.14490i	0.399723	+	0.230780i
$498$	6.42202	+	7.19783i	0.287777	+	0.322543i
$499$	3.36337	+	3.36337i	0.150565	+	0.150565i	0.778370	−	0.627805i	$-0.216047\pi$
$499$	3.36337	+	3.36337i	0.150565	+	0.150565i	−0.627805	+	0.778370i	$0.716047\pi$
$500$	−10.9958	−	2.94633i	−0.491749	−	0.131764i
$501$	10.9071	+	0.621293i	0.487293	+	0.0277573i
$502$	16.4205	−	16.4205i	0.732881	−	0.732881i
$503$	−20.9751	+	12.1100i	−0.935233	+	0.539957i	−0.888463	−	0.458949i	$-0.848226\pi$
$503$	−20.9751	+	12.1100i	−0.935233	+	0.539957i	−0.0467700	+	0.998906i	$0.514893\pi$
$504$	0.340668	−	2.98059i	0.0151746	−	0.132766i
$505$	−4.17854	−	15.5945i	−0.185943	−	0.693948i
$506$	19.1771			0.852527
$507$	11.3243	−	19.4618i	0.502930	−	0.864327i
$508$	6.16631			0.273586
$509$	0.997603	+	3.72310i	0.0442180	+	0.165024i	0.984504	−	0.175361i	$-0.0561093\pi$
$509$	0.997603	+	3.72310i	0.0442180	+	0.165024i	−0.940286	+	0.340385i	$0.889443\pi$
$510$	5.21671	−	15.8107i	0.231000	−	0.700111i
$511$	−3.02272	+	1.74517i	−0.133717	+	0.0772017i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−0.790699	+	0.291226i	−0.0349102	+	0.0128579i
$514$	20.9957	+	5.62577i	0.926079	+	0.248142i
$515$	6.44397	+	6.44397i	0.283955	+	0.283955i
$516$	−2.08018	+	1.85596i	−0.0915746	+	0.0817043i
$517$	−12.9083	−	7.45261i	−0.567707	−	0.327766i
$518$	5.21359	−	1.39698i	0.229072	−	0.0613797i
$519$	0.742736	+	3.57403i	0.0326025	+	0.156882i
$520$	−3.25173	−	4.01081i	−0.142598	−	0.175886i
$521$		−	39.7240i		−	1.74034i	−0.492750	−	0.870171i	$-0.664008\pi$
$521$		−	39.7240i		−	1.74034i	0.492750	−	0.870171i	$-0.335992\pi$
$522$	−18.6238	+	14.8033i	−0.815143	+	0.647921i
$523$	10.6683	−	18.4781i	0.466493	−	0.807989i	−0.532775	−	0.846257i	$-0.678851\pi$
$523$	10.6683	−	18.4781i	0.466493	−	0.807989i	0.999268	+	0.0382680i	$0.0121841\pi$
$524$	2.30017	+	3.98401i	0.100483	+	0.174042i
$525$	−2.80154	+	4.27140i	−0.122269	+	0.186419i
$526$	1.88413	−	7.03166i	0.0821518	−	0.306595i
$527$	5.60497	−	20.9180i	0.244156	−	0.911204i
$528$	−5.84162	+	8.90650i	−0.254224	+	0.387605i
$529$	6.63758	+	11.4966i	0.288590	+	0.499853i
$530$	−5.81983	+	10.0802i	−0.252797	+	0.437858i
$531$	−16.2316	+	12.9018i	−0.704391	+	0.559890i
$532$		−	0.162163i		−	0.00703067i
$533$	−5.95824	+	8.21077i	−0.258080	+	0.355648i
$534$	3.74655	+	18.0283i	0.162129	+	0.780160i
$535$	21.3812	−	5.72908i	0.924391	−	0.247690i
$536$	4.53432	+	2.61789i	0.195853	+	0.113076i
$537$	29.5510	−	26.3658i	1.27522	−	1.13777i
$538$	−13.2006	−	13.2006i	−0.569119	−	0.569119i
$539$	5.93999	+	1.59162i	0.255853	+	0.0685557i
$540$	6.98264	−	2.57181i	0.300485	−	0.110673i
$541$	12.5794	−	12.5794i	0.540830	−	0.540830i	−0.382942	−	0.923772i	$-0.625089\pi$
$541$	12.5794	−	12.5794i	0.540830	−	0.540830i	0.923772	+	0.382942i	$0.125089\pi$
$542$	−10.6944	+	6.17444i	−0.459365	+	0.265215i
$543$	9.42897	−	28.5772i	0.404636	−	1.22636i
$544$	1.73726	+	6.48356i	0.0744846	+	0.277980i
$545$	22.1447			0.948576
$546$	−5.83903	+	2.21488i	−0.249888	+	0.0947881i
$547$	34.7955			1.48775			0.743874	−	0.668320i	$-0.232986\pi$
$547$	34.7955			1.48775			0.743874	+	0.668320i	$0.232986\pi$
$548$	3.12108	+	11.6480i	0.133326	+	0.497579i
$549$	2.97169	−	26.0000i	0.126828	−	1.10965i
$550$	15.7064	−	9.06811i	0.669724	−	0.386666i
$551$	−0.909323	+	0.909323i	−0.0387385	+	0.0387385i
$552$	5.39260	+	0.307175i	0.229524	+	0.0130742i
$553$	−4.87903	−	1.30733i	−0.207478	−	0.0555934i
$554$	−22.0857	−	22.0857i	−0.938333	−	0.938333i
$555$	8.91304	+	9.98979i	0.378337	+	0.424043i
$556$	6.76981	+	3.90855i	0.287104	+	0.165760i
$557$	4.18738	−	1.12200i	0.177425	−	0.0475408i	−0.169013	−	0.985614i	$-0.554058\pi$
$557$	4.18738	−	1.12200i	0.177425	−	0.0475408i	0.346438	+	0.938073i	$0.387391\pi$
$558$	8.87756	−	3.85632i	0.375817	−	0.163251i
$559$	5.41898	+	2.07657i	0.229199	+	0.0878294i
$560$			1.43206i			0.0605156i
$561$	32.1682	+	63.8487i	1.35814	+	2.69570i
$562$	−6.73289	+	11.6617i	−0.284010	+	0.491919i
$563$	3.27325	+	5.66944i	0.137951	+	0.238939i	0.926721	−	0.375750i	$-0.122615\pi$
$563$	3.27325	+	5.66944i	0.137951	+	0.238939i	−0.788770	+	0.614689i	$0.789282\pi$
$564$	−3.51044	−	2.30244i	−0.147816	−	0.0969501i
$565$	−4.51191	+	16.8387i	−0.189817	+	0.708408i
$566$	3.96038	−	14.7804i	0.166467	−	0.621265i
$567$	−0.307705	−	8.99474i	−0.0129224	−	0.377744i
$568$	−5.14490	−	8.91123i	−0.215875	−	0.373907i
$569$	−6.25227	+	10.8293i	−0.262109	+	0.453986i	−0.966802	−	0.255526i	$-0.917751\pi$
$569$	−6.25227	+	10.8293i	−0.262109	+	0.453986i	0.704693	+	0.709512i	$0.251085\pi$
$570$	0.359215	−	0.180979i	0.0150459	−	0.00758039i
$571$			26.7641i			1.12004i	0.828478	+	0.560022i	$0.189207\pi$
$571$			26.7641i			1.12004i	−0.828478	+	0.560022i	$0.810793\pi$
$572$	22.0523	+	2.30492i	0.922054	+	0.0963737i
$573$	−24.0721	+	5.00254i	−1.00563	+	0.208984i
$574$	2.71779	−	0.728231i	0.113439	−	0.0303958i
$575$	−7.96484	−	4.59850i	−0.332157	−	0.191771i
$576$	−1.78532	+	2.41094i	−0.0743885	+	0.100456i
$577$	4.03263	+	4.03263i	0.167881	+	0.167881i	0.786047	−	0.618166i	$-0.212124\pi$
$577$	4.03263	+	4.03263i	0.167881	+	0.167881i	−0.618166	+	0.786047i	$0.712124\pi$
$578$	27.0987	+	7.26107i	1.12716	+	0.302021i
$579$	1.88551	−	33.1010i	0.0783592	−	1.37563i
$580$	8.03021	−	8.03021i	0.333436	−	0.333436i
$581$	−4.82315	+	2.78465i	−0.200098	+	0.115527i
$582$	−6.70530	−	2.21240i	−0.277944	−	0.0917068i
$583$	−12.9365	−	48.2797i	−0.535776	−	1.99954i
$584$	3.49034			0.144431
$585$	−11.4228	−	10.4624i	−0.472275	−	0.432568i
$586$	8.32698			0.343984
$587$	−2.24740	−	8.38743i	−0.0927603	−	0.346186i	0.903910	−	0.427723i	$-0.140684\pi$
$587$	−2.24740	−	8.38743i	−0.0927603	−	0.346186i	−0.996670	+	0.0815364i	$0.974017\pi$
$588$	1.64483	+	0.542708i	0.0678317	+	0.0223809i
$589$	0.453097	−	0.261595i	0.0186695	−	0.0107789i
$590$	6.99873	−	6.99873i	0.288133	−	0.288133i
$591$	2.30814	−	40.5204i	0.0949440	−	1.66679i
$592$	−5.21359	−	1.39698i	−0.214277	−	0.0574154i
$593$	24.5123	+	24.5123i	1.00660	+	1.00660i	0.999978	+	0.00662184i	$0.00210781\pi$
$593$	24.5123	+	24.5123i	1.00660	+	1.00660i	0.00662184	+	0.999978i	$0.497892\pi$
$594$	−13.3933	+	29.0116i	−0.549532	+	1.19036i
$595$	8.32456	+	4.80619i	0.341274	+	0.197034i
$596$	14.6256	−	3.91893i	0.599089	−	0.160525i
$597$	11.9469	−	2.48275i	0.488956	−	0.101612i
$598$	−4.57919	−	10.2691i	−0.187257	−	0.419934i
$599$			18.6052i			0.760188i	0.924948	+	0.380094i	$0.124108\pi$
$599$			18.6052i			0.760188i	−0.924948	+	0.380094i	$0.875892\pi$
$600$	4.56190	−	2.29837i	0.186239	−	0.0938306i
$601$	−17.0251	+	29.4883i	−0.694467	+	1.20285i	0.275893	+	0.961188i	$0.411026\pi$
$601$	−17.0251	+	29.4883i	−0.694467	+	1.20285i	−0.970360	+	0.241664i	$0.922307\pi$
$602$	−0.804764	−	1.39389i	−0.0327997	−	0.0568108i
$603$	14.6123	+	5.76195i	0.595060	+	0.234645i
$604$	−5.13657	+	19.1700i	−0.209004	+	0.780014i
$605$	9.93946	−	37.0946i	0.404097	−	1.50811i
$606$	16.3280	+	10.7092i	0.663279	+	0.435033i
$607$	17.2735	+	29.9185i	0.701108	+	1.21435i	0.968078	+	0.250650i	$0.0806442\pi$
$607$	17.2735	+	29.9185i	0.701108	+	1.21435i	−0.266970	+	0.963705i	$0.586022\pi$
$608$	−0.0810817	+	0.140438i	−0.00328830	+	0.00569550i
$609$	−6.18010	−	12.2665i	−0.250430	−	0.497064i
$610$			12.4920i			0.505787i
$611$	−0.908472	+	8.69179i	−0.0367528	+	0.351632i
$612$	8.02298	+	18.4695i	0.324310	+	0.746586i
$613$	−25.0018	+	6.69922i	−1.00981	+	0.270579i	−0.725552	−	0.688167i	$-0.758415\pi$
$613$	−25.0018	+	6.69922i	−1.00981	+	0.270579i	−0.284263	+	0.958746i	$0.591749\pi$
$614$	−10.2228	−	5.90212i	−0.412557	−	0.238190i
$615$	4.64628	+	5.20758i	0.187356	+	0.209990i
$616$	−4.34837	−	4.34837i	−0.175201	−	0.175201i
$617$	4.60799	+	1.23471i	0.185511	+	0.0497074i	0.350378	−	0.936608i	$-0.386053\pi$
$617$	4.60799	+	1.23471i	0.185511	+	0.0497074i	−0.164868	+	0.986316i	$0.552720\pi$
$618$	−11.0044	−	0.626834i	−0.442660	−	0.0252149i
$619$	−26.5606	+	26.5606i	−1.06756	+	1.06756i	−0.0700151	+	0.997546i	$0.522305\pi$
$619$	−26.5606	+	26.5606i	−1.06756	+	1.06756i	−0.997546	+	0.0700151i	$0.977695\pi$
$620$	−4.00128	+	2.31014i	−0.160695	+	0.0927775i
$621$	16.1368	−	1.47410i	0.647549	−	0.0591535i
$622$	−6.74743	−	25.1817i	−0.270547	−	1.00970i
$623$	−10.6310			−0.425923
$624$	6.16419	+	1.00137i	0.246765	+	0.0400870i
$625$	1.55617			0.0622466
$626$	−0.912608	−	3.40590i	−0.0364751	−	0.136127i
$627$	−0.541203	+	1.64027i	−0.0216136	+	0.0655061i
$628$	−9.63199	+	5.56103i	−0.384358	+	0.221909i
$629$	−25.6182	+	25.6182i	−1.02146	+	1.02146i
$630$	0.633506	+	4.24921i	0.0252395	+	0.169293i
$631$	13.2623	+	3.55363i	0.527964	+	0.141468i	0.512948	−	0.858420i	$-0.328553\pi$
$631$	13.2623	+	3.55363i	0.527964	+	0.141468i	0.0150163	+	0.999887i	$0.495220\pi$
$632$	3.57170	+	3.57170i	0.142075	+	0.142075i
$633$	−18.1040	+	16.1526i	−0.719568	+	0.642009i
$634$	5.06235	+	2.92275i	0.201052	+	0.116077i
$635$	−8.52963	+	2.28551i	−0.338488	+	0.0906976i
$636$	−2.86441	−	13.7835i	−0.113581	−	0.546550i
$637$	−0.566088	−	3.56083i	−0.0224292	−	0.141085i
$638$			48.7666i			1.93069i
$639$	−19.2081	−	24.1655i	−0.759860	−	0.955972i
$640$	0.716030	−	1.24020i	0.0283036	−	0.0490232i
$641$	−18.4787	−	32.0060i	−0.729863	−	1.26416i	−0.956941	−	0.290284i	$-0.906250\pi$
$641$	−18.4787	−	32.0060i	−0.729863	−	1.26416i	0.227077	−	0.973877i	$-0.427083\pi$
$642$	−14.6831	+	22.3868i	−0.579497	+	0.883538i
$643$	−6.19110	+	23.1055i	−0.244153	+	0.911192i	0.729654	+	0.683817i	$0.239681\pi$
$643$	−6.19110	+	23.1055i	−0.244153	+	0.911192i	−0.973807	+	0.227376i	$0.926986\pi$
$644$	−0.807119	+	3.01221i	−0.0318049	+	0.118698i
$645$	2.18953	−	3.33829i	0.0862126	−	0.131445i
$646$	0.544242	+	0.942655i	0.0214129	+	0.0370883i
$647$	−23.0389	+	39.9046i	−0.905753	+	1.56881i	−0.0858500	+	0.996308i	$0.527361\pi$
$647$	−23.0389	+	39.9046i	−0.905753	+	1.56881i	−0.819903	+	0.572502i	$0.805973\pi$
$648$	−4.23089	+	7.94352i	−0.166205	+	0.312051i
$649$			42.5025i			1.66837i
$650$	−8.60630	−	6.24525i	−0.337567	−	0.244959i
$651$	1.13701	+	5.47126i	0.0445629	+	0.214435i
$652$	−12.2065	+	3.27073i	−0.478045	+	0.128092i
$653$	10.9970	+	6.34912i	0.430346	+	0.248460i	0.699494	−	0.714638i	$-0.253409\pi$
$653$	10.9970	+	6.34912i	0.430346	+	0.248460i	−0.269148	+	0.963099i	$0.586742\pi$
$654$	−19.9853	+	17.8312i	−0.781488	+	0.697255i
$655$	−4.65839	−	4.65839i	−0.182018	−	0.182018i
$656$	−2.71779	−	0.728231i	−0.106112	−	0.0284326i
$657$	10.3565	−	1.54404i	0.404047	−	0.0602386i
$658$	1.71389	−	1.71389i	0.0668142	−	0.0668142i
$659$	0.264972	−	0.152982i	0.0103219	−	0.00595932i	−0.494830	−	0.868990i	$-0.664770\pi$
$659$	0.264972	−	0.152982i	0.0103219	−	0.00595932i	0.505152	+	0.863030i	$0.331436\pi$
$660$	4.77935	−	14.4852i	0.186036	−	0.563835i
$661$	−1.17446	−	4.38314i	−0.0456812	−	0.170484i	0.939317	−	0.343051i	$-0.111461\pi$
$661$	−1.17446	−	4.38314i	−0.0456812	−	0.170484i	−0.984998	+	0.172567i	$0.944794\pi$
$662$	4.33607			0.168526
$663$	26.5089	−	32.4717i	1.02952	−	1.26110i
$664$	5.56929			0.216131
$665$	0.0601049	+	0.224315i	0.00233077	+	0.00869855i
$666$	−16.0878	−	1.83876i	−0.623389	−	0.0712505i
$667$	21.4167	−	12.3649i	0.829258	−	0.478772i
$668$	4.46002	−	4.46002i	0.172563	−	0.172563i
$669$	50.7315	+	2.88978i	1.96139	+	0.111725i
$670$	−7.24246	−	1.94061i	−0.279801	−	0.0749724i
$671$	−37.9313	−	37.9313i	−1.46432	−	1.46432i
$672$	−1.15311	−	1.29241i	−0.0444822	−	0.0498560i
$673$	−12.7661	−	7.37053i	−0.492098	−	0.284113i	0.233346	−	0.972394i	$-0.425032\pi$
$673$	−12.7661	−	7.37053i	−0.492098	−	0.284113i	−0.725444	+	0.688281i	$0.758366\pi$
$674$	−27.2280	+	7.29571i	−1.04878	+	0.281020i
$675$	12.5193	−	8.83780i	0.481870	−	0.340167i
$676$	−4.03149	−	12.3591i	−0.155057	−	0.475350i
$677$			11.4682i			0.440758i	0.975414	+	0.220379i	$0.0707295\pi$
$677$			11.4682i			0.440758i	−0.975414	+	0.220379i	$0.929271\pi$
$678$	−9.48676	−	18.8297i	−0.364337	−	0.723150i
$679$	2.03829	−	3.53043i	0.0782226	−	0.135485i
$680$	−4.80619	−	8.32456i	−0.184309	−	0.319232i
$681$	−16.4830	−	10.8109i	−0.631632	−	0.414276i
$682$	5.13506	−	19.1643i	0.196632	−	0.733839i
$683$	6.90186	−	25.7581i	0.264093	−	0.985607i	−0.698711	−	0.715404i	$-0.746243\pi$
$683$	6.90186	−	25.7581i	0.264093	−	0.985607i	0.962803	−	0.270203i	$-0.0870907\pi$
$684$	−0.178460	+	0.452575i	−0.00682359	+	0.0173047i
$685$	−8.63455	−	14.9555i	−0.329909	−	0.571419i
$686$	−0.500000	+	0.866025i	−0.0190901	+	0.0330650i
$687$	−14.8765	+	7.49508i	−0.567576	+	0.285955i
$688$			1.60953i			0.0613627i
$689$	−22.7641	+	18.4558i	−0.867243	+	0.703109i
$690$	−7.57324	+	1.57383i	−0.288308	+	0.0599148i
$691$	−5.77582	+	1.54763i	−0.219723	+	0.0588745i	−0.367001	−	0.930221i	$-0.619615\pi$
$691$	−5.77582	+	1.54763i	−0.219723	+	0.0588745i	0.147278	+	0.989095i	$0.452949\pi$
$692$	1.82519	+	1.05378i	0.0693834	+	0.0400585i
$693$	−14.8261	−	10.9789i	−0.563198	−	0.417054i
$694$	−3.66066	−	3.66066i	−0.138957	−	0.138957i
$695$	−10.8131	−	2.89737i	−0.410165	−	0.109903i
$696$	−0.781134	+	13.7132i	−0.0296088	+	0.519796i
$697$	−13.3545	+	13.3545i	−0.505837	+	0.505837i
$698$	−8.65553	+	4.99727i	−0.327617	+	0.189150i
$699$	5.44379	+	1.79616i	0.205903	+	0.0679372i
$700$	0.763310	+	2.84871i	0.0288504	+	0.107671i
$701$	−23.1781			−0.875426			−0.437713	−	0.899115i	$-0.644211\pi$
$701$	−23.1781			−0.875426			−0.437713	+	0.899115i	$0.644211\pi$
$702$	18.7334	+	0.244402i	0.707047	+	0.00922437i
$703$	−0.875278			−0.0330117
$704$	1.59162	+	5.93999i	0.0599863	+	0.223872i
$705$	5.70925	+	1.88375i	0.215023	+	0.0709462i
$706$	−26.0270	+	15.0267i	−0.979541	+	0.565538i
$707$	−7.97173	+	7.97173i	−0.299808	+	0.299808i
$708$	−0.680797	+	11.9517i	−0.0255859	+	0.449173i
$709$	−1.41382	−	0.378832i	−0.0530972	−	0.0142273i	0.232173	−	0.972675i	$-0.425417\pi$
$709$	−1.41382	−	0.378832i	−0.0530972	−	0.0142273i	−0.285270	+	0.958447i	$0.592083\pi$
$710$	10.4197	+	10.4197i	0.391043	+	0.391043i
$711$	12.1780	+	9.01794i	0.456710	+	0.338199i
$712$	9.20673	+	5.31551i	0.345037	+	0.199207i
$713$	−9.71835	+	2.60402i	−0.363955	+	0.0975215i
$714$	−11.3828	+	2.36552i	−0.425991	+	0.0885272i
$715$	−31.3585	+	4.98525i	−1.17274	+	0.186438i
$716$		−	22.8649i		−	0.854503i
$717$	−26.1922	+	13.1961i	−0.978165	+	0.492818i
$718$	−3.11045	+	5.38745i	−0.116081	+	0.201058i
$719$	−6.54962	−	11.3443i	−0.244260	−	0.423070i	0.717664	−	0.696390i	$-0.245212\pi$
$719$	−6.54962	−	11.3443i	−0.244260	−	0.423070i	−0.961923	+	0.273320i	$0.911878\pi$
$720$	1.57597	−	3.99668i	0.0587331	−	0.148948i
$721$	1.64704	−	6.14683i	0.0613389	−	0.228920i
$722$	4.91076	−	18.3272i	0.182759	−	0.682067i
$723$	40.3657	+	26.4752i	1.50122	+	0.984622i
$724$	−8.68697	−	15.0463i	−0.322849	−	0.559190i
$725$	11.6938	−	20.2543i	0.434297	−	0.752224i
$726$	20.8988	+	41.4807i	0.775626	+	1.53949i
$727$		−	38.1313i		−	1.41421i	−0.707108	−	0.707105i	$-0.750001\pi$
$727$		−	38.1313i		−	1.41421i	0.707108	−	0.707105i	$-0.249999\pi$
$728$	−1.29017	+	3.36682i	−0.0478169	+	0.124783i
$729$	−9.03990	+	25.4417i	−0.334811	+	0.942285i
$730$	−4.82806	+	1.29367i	−0.178694	+	0.0478810i
$731$	9.35618	+	5.40179i	0.346051	+	0.199793i
$732$	−10.0587	−	11.2739i	−0.371781	−	0.416694i
$733$	9.76791	+	9.76791i	0.360786	+	0.360786i	0.864102	−	0.503316i	$-0.167887\pi$
$733$	9.76791	+	9.76791i	0.360786	+	0.360786i	−0.503316	+	0.864102i	$0.667887\pi$
$734$	−4.54304	−	1.21730i	−0.167687	−	0.0449315i
$735$	−2.47639	−	0.141061i	−0.0913429	−	0.00520310i
$736$	2.20509	−	2.20509i	0.0812807	−	0.0812807i
$737$	27.8839	−	16.0988i	1.02712	−	0.593006i
$738$	−8.38640	−	0.958528i	−0.308708	−	0.0352839i
$739$	−1.19404	−	4.45623i	−0.0439236	−	0.163925i	0.940480	−	0.339848i	$-0.110376\pi$
$739$	−1.19404	−	4.45623i	−0.0439236	−	0.163925i	−0.984404	+	0.175923i	$0.943709\pi$
$740$	7.72956			0.284144
$741$	1.00757	−	0.101864i	0.0370141	−	0.00374207i
$742$	8.12791			0.298385
$743$	1.49496	+	5.57927i	0.0548448	+	0.204683i	0.987911	−	0.155021i	$-0.0495444\pi$
$743$	1.49496	+	5.57927i	0.0548448	+	0.204683i	−0.933066	+	0.359704i	$0.882878\pi$
$744$	1.75095	−	5.30675i	0.0641929	−	0.194555i
$745$	−18.7786	+	10.8418i	−0.687994	+	0.397213i
$746$	7.48941	−	7.48941i	0.274207	−	0.274207i
$747$	16.5252	−	2.46371i	0.604627	−	0.0901425i
$748$	39.8708	+	10.6834i	1.45782	+	0.390622i
$749$	−10.9298	−	10.9298i	−0.399367	−	0.399367i
$750$	−14.7125	+	13.1267i	−0.537225	+	0.479320i
$751$	−38.9228	−	22.4721i	−1.42031	−	0.820018i	−0.423988	−	0.905668i	$-0.639370\pi$
$751$	−38.9228	−	22.4721i	−1.42031	−	0.820018i	−0.996325	+	0.0856499i	$0.972703\pi$
$752$	−2.34121	+	0.627326i	−0.0853752	+	0.0228762i
$753$	−8.18384	−	39.3804i	−0.298236	−	1.43510i
$754$	26.1138	−	11.6447i	0.951010	−	0.424075i
$755$		−	28.4209i		−	1.03434i
$756$	−3.99325	−	3.32475i	−0.145233	−	0.120920i
$757$	21.2721	−	36.8443i	0.773147	−	1.33913i	−0.162683	−	0.986678i	$-0.552015\pi$
$757$	21.2721	−	36.8443i	0.773147	−	1.33913i	0.935830	−	0.352451i	$-0.114652\pi$
$758$	11.1555	+	19.3219i	0.405185	+	0.701802i
$759$	18.2169	−	27.7746i	0.661231	−	1.00815i
$760$	0.0601049	−	0.224315i	0.00218023	−	0.00813675i
$761$	−10.7212	+	40.0122i	−0.388644	+	1.45044i	0.443697	+	0.896177i	$0.353667\pi$
$761$	−10.7212	+	40.0122i	−0.388644	+	1.45044i	−0.832341	+	0.554264i	$0.813000\pi$
$762$	5.85755	−	8.93080i	0.212197	−	0.323529i
$763$	−7.73178	−	13.3918i	−0.279909	−	0.484817i
$764$	−7.09748	+	12.2932i	−0.256778	+	0.444752i
$765$	−17.9435	−	22.5745i	−0.648749	−	0.816184i
$766$			14.9128i			0.538822i
$767$	22.7595	−	10.1489i	0.821799	−	0.366457i
$768$	0.352417	+	1.69582i	0.0127167	+	0.0611926i
$769$	47.3522	−	12.6880i	1.70756	−	0.457540i	0.732738	−	0.680511i	$-0.238242\pi$
$769$	47.3522	−	12.6880i	1.70756	−	0.457540i	0.974825	+	0.222971i	$0.0715755\pi$
$770$	7.62665	+	4.40325i	0.274845	+	0.158682i
$771$	28.0923	−	25.0644i	1.01172	−	0.902672i
$772$	−13.5354	−	13.5354i	−0.487148	−	0.487148i
$773$	11.6101	+	3.11093i	0.417588	+	0.111892i	0.461494	−	0.887143i	$-0.347314\pi$
$773$	11.6101	+	3.11093i	0.417588	+	0.111892i	−0.0439062	+	0.999036i	$0.513980\pi$
$774$	0.712014	+	4.77580i	0.0255928	+	0.171663i
$775$	−6.72818	+	6.72818i	−0.241683	+	0.241683i
$776$	−3.53043	+	2.03829i	−0.126735	+	0.0731705i
$777$	2.92927	−	8.87799i	0.105087	−	0.318496i
$778$	3.78874	+	14.1398i	0.135833	+	0.506936i
$779$	−0.456274			−0.0163477
$780$	−8.89785	+	0.899558i	−0.318594	+	0.0322094i
$781$	−63.2775			−2.26425
$782$	−5.41760	−	20.2188i	−0.193733	−	0.723022i
$783$	3.74857	+	41.0353i	0.133963	+	1.46648i
$784$	0.866025	−	0.500000i	0.0309295	−	0.0178571i
$785$	11.2624	−	11.2624i	0.401973	−	0.401973i
$786$	7.95513	+	0.453142i	0.283750	+	0.0161631i
$787$	−32.8961	−	8.81448i	−1.17262	−	0.314202i	−0.380624	−	0.924730i	$-0.624291\pi$
$787$	−32.8961	−	8.81448i	−1.17262	−	0.314202i	−0.791995	+	0.610528i	$0.790957\pi$
$788$	−16.5692	−	16.5692i	−0.590253	−	0.590253i
$789$	−8.39431	−	9.40839i	−0.298845	−	0.334948i
$790$	−6.26443	−	3.61677i	−0.222878	−	0.128679i
$791$	11.7584	−	3.15064i	0.418079	−	0.112024i
$792$	7.35035	+	16.9211i	0.261183	+	0.601264i
$793$	−11.2543	+	29.3691i	−0.399652	+	1.04293i
$794$		−	22.8218i		−	0.809914i
$795$	9.07100	+	18.0045i	0.321715	+	0.638554i
$796$	3.52247	−	6.10110i	0.124851	−	0.216248i
$797$	−18.1684	−	31.4686i	−0.643557	−	1.11467i	−0.984633	−	0.174638i	$-0.944125\pi$
$797$	−18.1684	−	31.4686i	−0.643557	−	1.11467i	0.341076	−	0.940036i	$-0.389209\pi$
$798$	−0.234865	−	0.154044i	−0.00831412	−	0.00545309i
$799$	−4.21078	+	15.7148i	−0.148967	+	0.555951i
$800$	0.763310	−	2.84871i	0.0269871	−	0.100717i
$801$	29.6697	+	11.6994i	1.04833	+	0.413377i
$802$	−9.99682	−	17.3150i	−0.353000	−	0.611414i
$803$	10.7320	−	18.5883i	0.378723	−	0.655967i
$804$	8.09883	−	4.08034i	0.285624	−	0.143903i
$805$		−	4.46583i		−	0.157400i
$806$	−11.4884	+	1.82638i	−0.404661	+	0.0643315i
$807$	−31.6584	+	6.57909i	−1.11443	+	0.231595i
$808$	10.8896	−	2.91786i	0.383094	−	0.102650i
$809$	−11.1337	−	6.42803i	−0.391439	−	0.225998i	0.291344	−	0.956618i	$-0.405897\pi$
$809$	−11.1337	−	6.42803i	−0.391439	−	0.225998i	−0.682784	+	0.730621i	$0.739231\pi$
$810$	2.90821	−	12.5561i	0.102184	−	0.441178i
$811$	17.4981	+	17.4981i	0.614440	+	0.614440i	0.944100	−	0.329660i	$-0.106934\pi$
$811$	17.4981	+	17.4981i	0.614440	+	0.614440i	−0.329660	+	0.944100i	$0.606934\pi$
$812$	−7.65992	−	2.05247i	−0.268811	−	0.0720276i
$813$	−1.21639	+	21.3543i	−0.0426606	+	0.748926i
$814$	−23.4704	+	23.4704i	−0.822637	+	0.822637i
$815$	15.6726	−	9.04856i	0.548986	−	0.316957i
$816$	11.0406	+	3.64280i	0.386497	+	0.127524i
$817$	0.0675534	+	0.252113i	0.00236339	+	0.00882031i
$818$	16.8591			0.589466
$819$	−2.33881	+	10.5608i	−0.0817246	+	0.369023i
$820$	4.02934			0.140711
$821$	−10.5371	−	39.3250i	−0.367747	−	1.37245i	−0.863658	−	0.504078i	$-0.831832\pi$
$821$	−10.5371	−	39.3250i	−0.367747	−	1.37245i	0.495911	−	0.868374i	$-0.334834\pi$
$822$	19.8349	+	6.54447i	0.691821	+	0.228265i
$823$	−13.8783	+	8.01263i	−0.483766	+	0.279303i	−0.721985	−	0.691909i	$-0.756770\pi$
$823$	−13.8783	+	8.01263i	−0.483766	+	0.279303i	0.238218	+	0.971212i	$0.423437\pi$
$824$	−4.49979	+	4.49979i	−0.156758	+	0.156758i
$825$	1.78645	−	31.3620i	0.0621963	−	1.09189i
$826$	−6.67601	−	1.78883i	−0.232288	−	0.0622414i
$827$	−36.5847	−	36.5847i	−1.27217	−	1.27217i	−0.944945	−	0.327230i	$-0.893885\pi$
$827$	−36.5847	−	36.5847i	−1.27217	−	1.27217i	−0.327230	−	0.944945i	$-0.606115\pi$
$828$	5.56748	−	7.51843i	0.193483	−	0.261283i
$829$	−40.7093	−	23.5035i	−1.41389	−	0.816311i	−0.418140	−	0.908382i	$-0.637318\pi$
$829$	−40.7093	−	23.5035i	−1.41389	−	0.816311i	−0.995752	+	0.0920709i	$0.970651\pi$
$830$	−7.70380	+	2.06423i	−0.267403	+	0.0716504i
$831$	−52.9671	+	11.0074i	−1.83741	+	0.381841i
$832$	2.80073	−	2.27066i	0.0970978	−	0.0787211i
$833$		−	6.71227i		−	0.232566i
$834$	12.0917	−	6.09202i	0.418701	−	0.210949i
$835$	−4.51630	+	7.82246i	−0.156293	+	0.270708i
$836$	0.498614	+	0.863625i	0.0172449	+	0.0298691i
$837$	2.84785	−	16.5208i	0.0984363	−	0.571042i
$838$	8.19346	−	30.5784i	0.283038	−	1.05631i
$839$	−0.387495	+	1.44615i	−0.0133778	+	0.0499267i	−0.972292	−	0.233769i	$-0.924894\pi$
$839$	−0.387495	+	1.44615i	−0.0133778	+	0.0499267i	0.958914	+	0.283696i	$0.0915606\pi$
$840$	2.07408	+	1.36036i	0.0715627	+	0.0469367i
$841$	16.9435	+	29.3471i	0.584260	+	1.01197i
$842$	−7.72230	+	13.3754i	−0.266128	+	0.460947i
$843$	10.4941	+	20.8292i	0.361437	+	0.717395i
$844$			14.0079i			0.482171i
$845$	10.1574	+	15.6016i	0.349427	+	0.536712i
$846$	−6.66934	+	2.89709i	−0.229297	+	0.0996042i
$847$	−25.9030	+	6.94068i	−0.890036	+	0.238484i
$848$	−7.03898	−	4.06396i	−0.241720	−	0.139557i
$849$	−17.6446	−	19.7762i	−0.605562	−	0.678717i
$850$	−13.9978	−	13.9978i	−0.480120	−	0.480120i
$851$	16.2584	+	4.35643i	0.557332	+	0.149337i
$852$	−17.7936	−	1.01357i	−0.609599	−	0.0347242i
$853$	−23.8323	+	23.8323i	−0.816004	+	0.816004i	−0.985526	−	0.169522i	$-0.945777\pi$
$853$	−23.8323	+	23.8323i	−0.816004	+	0.816004i	0.169522	+	0.985526i	$0.445777\pi$
$854$	7.55443	−	4.36155i	0.258507	−	0.149249i
$855$	0.0791126	−	0.692176i	0.00270559	−	0.0236719i
$856$	4.00059	+	14.9304i	0.136737	+	0.510311i
$857$	18.8568			0.644134			0.322067	−	0.946717i	$-0.395622\pi$
$857$	18.8568			0.644134			0.322067	+	0.946717i	$0.395622\pi$
$858$	24.2864	−	29.7493i	0.829124	−	1.01563i
$859$	31.6606			1.08025			0.540123	−	0.841586i	$-0.318378\pi$
$859$	31.6606			1.08025			0.540123	+	0.841586i	$0.318378\pi$
$860$	−0.596562	−	2.22640i	−0.0203426	−	0.0759196i
$861$	1.52700	−	4.62801i	0.0520400	−	0.157722i
$862$	16.1560	−	9.32765i	0.550274	−	0.317701i
$863$	−17.6792	+	17.6792i	−0.601806	+	0.601806i	−0.940791	−	0.338986i	$-0.889916\pi$
$863$	−17.6792	+	17.6792i	−0.601806	+	0.601806i	0.338986	+	0.940791i	$0.389916\pi$
$864$	1.79588	+	4.87594i	0.0610971	+	0.165883i
$865$	−2.91530	−	0.781152i	−0.0991232	−	0.0265600i
$866$	−14.7481	−	14.7481i	−0.501161	−	0.501161i
$867$	36.2582	−	32.3501i	1.23139	−	1.09867i
$868$	2.79408	+	1.61316i	0.0948371	+	0.0547542i
$869$	30.0038	−	8.03948i	1.01781	−	0.272721i
$870$	−4.00219	−	19.2584i	−0.135687	−	0.652923i
$871$	−15.2789	−	11.0873i	−0.517706	−	0.375679i
$872$			15.4636i			0.523662i
$873$	−9.57382	+	7.60981i	−0.324025	+	0.257553i
$874$	0.252851	−	0.437950i	0.00855280	−	0.0148139i
$875$	−5.69187	−	9.85860i	−0.192420	−	0.333282i
$876$	3.31557	−	5.05513i	0.112023	−	0.170797i
$877$	−8.52826	+	31.8279i	−0.287979	+	1.07475i	0.658656	+	0.752444i	$0.271125\pi$
$877$	−8.52826	+	31.8279i	−0.287979	+	1.07475i	−0.946635	+	0.322308i	$0.895541\pi$
$878$	10.3965	−	38.8001i	0.350864	−	1.30944i
$879$	7.91004	−	12.0601i	0.266799	−	0.406778i
$880$	−4.40325	−	7.62665i	−0.148433	−	0.257094i
$881$	7.26029	−	12.5752i	0.244605	−	0.423669i	−0.717415	−	0.696646i	$-0.754675\pi$
$881$	7.26029	−	12.5752i	0.244605	−	0.423669i	0.962021	+	0.272977i	$0.0880082\pi$
$882$	2.34849	−	1.86671i	0.0790777	−	0.0628554i
$883$			20.5426i			0.691314i	0.938361	+	0.345657i	$0.112344\pi$
$883$			20.5426i			0.691314i	−0.938361	+	0.345657i	$0.887656\pi$
$884$	−3.79974	−	23.9013i	−0.127799	−	0.803888i
$885$	−3.48811	−	16.7847i	−0.117252	−	0.564212i
$886$	−21.2552	+	5.69530i	−0.714081	+	0.191337i
$887$	5.19173	+	2.99745i	0.174321	+	0.100644i	0.584622	−	0.811306i	$-0.301243\pi$
$887$	5.19173	+	2.99745i	0.174321	+	0.100644i	−0.410301	+	0.911950i	$0.634576\pi$
$888$	−6.97582	+	6.22393i	−0.234093	+	0.208861i
$889$	4.36024	+	4.36024i	0.146238	+	0.146238i
$890$	−14.7055	−	3.94032i	−0.492929	−	0.132080i
$891$	29.2954	+	46.9567i	0.981434	+	1.57311i
$892$	20.7446	−	20.7446i	0.694582	−	0.694582i
$893$	−0.340393	+	0.196526i	−0.0113908	+	0.00657648i
$894$	8.21745	−	24.9053i	0.274833	−	0.832958i
$895$	8.47476	+	31.6282i	0.283280	+	1.05722i
$896$	−1.00000			−0.0334077
$897$	−19.2228	−	3.12275i	−0.641832	−	0.104266i
$898$	−32.1060			−1.07139
$899$	−6.62193	−	24.7134i	−0.220854	−	0.824237i
$900$	1.00470	−	8.79038i	0.0334900	−	0.293013i
$901$	−47.2476	+	27.2784i	−1.57404	+	0.908775i
$902$	−12.2349	+	12.2349i	−0.407377	+	0.407377i
$903$	−2.78327	−	0.158542i	−0.0926215	−	0.00527593i
$904$	−11.7584	−	3.15064i	−0.391077	−	0.104789i
$905$	17.5932	+	17.5932i	0.584817	+	0.584817i
$906$	22.8849	+	25.6495i	0.760299	+	0.852148i
$907$	−15.4295	−	8.90824i	−0.512329	−	0.295793i	0.221462	−	0.975169i	$-0.428917\pi$
$907$	−15.4295	−	8.90824i	−0.512329	−	0.295793i	−0.733790	+	0.679376i	$0.762251\pi$
$908$	−10.9930	+	2.94557i	−0.364816	+	0.0977520i
$909$	31.0209	−	13.4751i	1.02890	−	0.446943i
$910$	0.536755	−	5.13539i	0.0177932	−	0.170237i
$911$		−	23.9497i		−	0.793490i	−0.917929	−	0.396745i	$-0.870140\pi$
$911$		−	23.9497i		−	0.793490i	0.917929	−	0.396745i	$-0.129860\pi$
$912$	0.126377	+	0.250838i	0.00418476	+	0.00830608i
$913$	17.1243	−	29.6601i	0.566731	−	0.981606i
$914$	−9.49310	−	16.4425i	−0.314004	−	0.543871i
$915$	18.0924	+	11.8665i	0.598118	+	0.392295i
$916$	−2.48919	+	9.28977i	−0.0822451	+	0.306943i
$917$	−1.19066	+	4.44359i	−0.0393189	+	0.146740i
$918$	34.3711	+	5.92488i	1.13441	+	0.195550i
$919$	−12.9296	−	22.3947i	−0.426508	−	0.738734i	0.570052	−	0.821609i	$-0.306923\pi$
$919$	−12.9296	−	22.3947i	−0.426508	−	0.738734i	−0.996560	+	0.0828750i	$0.973590\pi$
$920$	−2.23292	+	3.86752i	−0.0736171	+	0.127509i
$921$	−18.2591	+	9.19926i	−0.601657	+	0.303126i
$922$		−	5.81903i		−	0.191640i
$923$	15.1097	+	33.8842i	0.497340	+	1.11531i
$924$	−10.4285	+	2.16720i	−0.343072	+	0.0712955i
$925$	15.3760	−	4.11997i	0.505558	−	0.135464i
$926$	−18.0484	−	10.4203i	−0.593109	−	0.342431i
$927$	−11.3612	+	15.3424i	−0.373151	+	0.503911i
$928$	5.60745	+	5.60745i	0.184074	+	0.184074i
$929$	15.5339	+	4.16230i	0.509651	+	0.136561i	0.504476	−	0.863426i	$-0.331686\pi$
$929$	15.5339	+	4.16230i	0.509651	+	0.136561i	0.00517576	+	0.999987i	$0.498352\pi$
$930$	−0.455107	+	7.98961i	−0.0149235	+	0.261990i
$931$	0.114667	−	0.114667i	0.00375805	−	0.00375805i
$932$	2.86623	−	1.65482i	0.0938864	−	0.0542053i
$933$	−42.8808	−	14.1484i	−1.40386	−	0.463199i
$934$	1.91478	+	7.14606i	0.0626535	+	0.233826i
$935$	−59.1116			−1.93316
$936$	7.30585	−	7.97650i	0.238799	−	0.260720i
$937$	10.6690			0.348541			0.174271	−	0.984698i	$-0.444243\pi$
$937$	10.6690			0.348541			0.174271	+	0.984698i	$0.444243\pi$
$938$	1.35512	+	5.05737i	0.0442462	+	0.165129i
$939$	−5.79975	−	1.91361i	−0.189268	−	0.0624484i
$940$	3.00600	−	1.73551i	0.0980448	−	0.0566062i
$941$	−22.8371	+	22.8371i	−0.744469	+	0.744469i	−0.973435	−	0.228966i	$-0.926466\pi$
$941$	−22.8371	+	22.8371i	−0.744469	+	0.744469i	0.228966	+	0.973435i	$0.426466\pi$
$942$	−1.09554	+	19.2328i	−0.0356948	+	0.626639i
$943$	8.47536	+	2.27096i	0.275996	+	0.0739528i
$944$	4.88718	+	4.88718i	0.159064	+	0.159064i
$945$	6.75601	+	3.11893i	0.219773	+	0.101459i
$946$	8.57178	+	4.94892i	0.278693	+	0.160903i
$947$	−6.01194	+	1.61090i	−0.195362	+	0.0523471i	−0.355173	−	0.934801i	$-0.615578\pi$
$947$	−6.01194	+	1.61090i	−0.195362	+	0.0523471i	0.159811	+	0.987148i	$0.448911\pi$
$948$	8.56583	−	1.78011i	0.278205	−	0.0578152i
$949$	−12.5164	−	1.30822i	−0.406300	−	0.0424668i
$950$		−	0.478253i		−	0.0155166i
$951$	9.04195	−	4.55550i	0.293205	−	0.147722i
$952$	−3.35614	+	5.81300i	−0.108773	+	0.188400i
$953$	13.2498	+	22.9493i	0.429203	+	0.743401i	0.996803	−	0.0799036i	$-0.0254612\pi$
$953$	13.2498	+	22.9493i	0.429203	+	0.743401i	−0.567600	+	0.823305i	$0.692128\pi$
$954$	−22.6839	−	8.94473i	−0.734418	−	0.289596i
$955$	5.26128	−	19.6354i	0.170251	−	0.635386i
$956$	−4.38255	+	16.3559i	−0.141742	+	0.528988i
$957$	70.6297	+	46.3248i	2.28313	+	1.49747i
$958$	19.3915	+	33.5870i	0.626509	+	1.08515i
$959$	−6.02946	+	10.4433i	−0.194701	+	0.337233i
$960$	−1.11603	−	2.21514i	−0.0360197	−	0.0714934i
$961$		−	20.5909i		−	0.664221i
$962$	18.1724	+	6.96371i	0.585903	+	0.224519i
$963$	18.4754	+	42.5318i	0.595361	+	1.37057i
$964$	26.9210	−	7.21346i	0.867067	−	0.232330i
$965$	23.7398	+	13.7062i	0.764210	+	0.441217i
$966$	3.59594	+	4.03035i	0.115698	+	0.129674i
$967$	6.87652	+	6.87652i	0.221134	+	0.221134i	0.808976	−	0.587842i	$-0.200022\pi$
$967$	6.87652	+	6.87652i	0.221134	+	0.221134i	−0.587842	+	0.808976i	$0.700022\pi$
$968$	25.9030	+	6.94068i	0.832553	+	0.223082i
$969$	1.88226	+	0.107218i	0.0604669	+	0.00344433i
$970$	4.12803	−	4.12803i	0.132543	−	0.132543i
$971$	9.08309	−	5.24412i	0.291490	−	0.168292i	−0.347124	−	0.937819i	$-0.612842\pi$
$971$	9.08309	−	5.24412i	0.291490	−	0.168292i	0.638614	+	0.769527i	$0.279508\pi$
$972$	7.48573	+	13.6735i	0.240105	+	0.438577i
$973$	2.02322	+	7.55074i	0.0648613	+	0.242066i
$974$	−2.59520			−0.0831557
$975$	−17.2205	+	6.53214i	−0.551498	+	0.209196i
$976$	−8.72310			−0.279220
$977$	0.208291	+	0.777353i	0.00666383	+	0.0248697i	0.969178	−	0.246363i	$-0.0792354\pi$
$977$	0.208291	+	0.777353i	0.00666383	+	0.0248697i	−0.962514	+	0.271232i	$0.912569\pi$
$978$	−6.85827	+	20.7859i	−0.219303	+	0.664661i
$979$	56.6170	−	32.6879i	1.80949	−	1.04471i
$980$	−1.01262	+	1.01262i	−0.0323469	+	0.0323469i
$981$	6.84068	+	45.8836i	0.218406	+	1.46495i
$982$	12.5528	+	3.36351i	0.400575	+	0.107334i
$983$	−40.7061	−	40.7061i	−1.29832	−	1.29832i	−0.929500	−	0.368821i	$-0.879762\pi$
$983$	−40.7061	−	40.7061i	−1.29832	−	1.29832i	−0.368821	−	0.929500i	$-0.620238\pi$
$984$	−3.63642	+	3.24447i	−0.115925	+	0.103430i
$985$	29.0609	+	16.7783i	0.925956	+	0.534601i
$986$	51.4155	−	13.7767i	1.63740	−	0.438741i
$987$	−0.854187	−	4.11033i	−0.0271891	−	0.130833i
$988$	0.343398	−	0.473221i	0.0109249	−	0.0150552i
$989$		−	5.01926i		−	0.159603i
$990$	−16.4392	−	20.6819i	−0.522471	−	0.657315i
$991$	−2.48775	+	4.30891i	−0.0790261	+	0.136877i	−0.902830	−	0.429998i	$-0.858514\pi$
$991$	−2.48775	+	4.30891i	−0.0790261	+	0.136877i	0.823804	+	0.566875i	$0.191848\pi$
$992$	−1.61316	−	2.79408i	−0.0512179	−	0.0887120i
$993$	4.11896	−	6.28002i	0.130711	−	0.199290i
$994$	2.66320	−	9.93919i	0.0844715	−	0.315252i
$995$	−2.61117	+	9.74501i	−0.0827796	+	0.308938i
$996$	5.29043	−	8.06613i	0.167634	−	0.255585i
$997$	−7.11658	−	12.3263i	−0.225384	−	0.390377i	0.731050	−	0.682324i	$-0.239030\pi$
$997$	−7.11658	−	12.3263i	−0.225384	−	0.390377i	−0.956435	+	0.291946i	$0.905697\pi$
$998$	2.37826	−	4.11927i	0.0752825	−	0.130393i
$999$	−17.9454	+	21.5536i	−0.567766	+	0.681926i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bu.b.449.1	yes	56
3.2	odd	2		546.2.bu.a.449.13	yes	56
13.2	odd	12		546.2.bu.a.197.13	✓	56
39.2	even	12	inner	546.2.bu.b.197.1	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bu.a.197.13	✓	56	13.2	odd	12
546.2.bu.a.449.13	yes	56	3.2	odd	2
546.2.bu.b.197.1	yes	56	39.2	even	12	inner
546.2.bu.b.449.1	yes	56	1.1	even	1	trivial

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.bu (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-1.64483 - 0.542708i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.01262 - 1.01262i) q^{5} +(-0.0985019 + 1.72925i) q^{6} +(-0.965926 - 0.258819i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.41094 + 1.78532i) q^{9} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-1.64483 - 0.542708i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.01262 - 1.01262i) q^{5} +(-0.0985019 + 1.72925i) q^{6} +(-0.965926 - 0.258819i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.41094 + 1.78532i) q^{9} +(-1.24020 - 0.716030i) q^{10} +(5.93999 - 1.59162i) q^{11} +(1.69582 - 0.352417i) q^{12} +(-2.27066 - 2.80073i) q^{13} +1.00000i q^{14} +(-2.21514 + 1.11603i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-3.35614 - 5.81300i) q^{17} +(1.10050 - 2.79086i) q^{18} +(0.0419710 - 0.156638i) q^{19} +(-0.370644 + 1.38326i) q^{20} +(1.44832 + 0.949929i) q^{21} +(-3.07476 - 5.32565i) q^{22} +(-1.55923 + 2.70067i) q^{23} +(-0.779319 - 1.54682i) q^{24} +2.94920i q^{25} +(-2.11761 + 2.91818i) q^{26} +(-2.99667 - 4.24499i) q^{27} +(0.965926 - 0.258819i) q^{28} +(-6.86770 - 3.96507i) q^{29} +(1.65132 + 1.85081i) q^{30} +(2.28135 + 2.28135i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(-10.6341 - 0.605740i) q^{33} +(-4.74629 + 4.74629i) q^{34} +(-1.24020 + 0.716030i) q^{35} +(-2.98059 - 0.340668i) q^{36} +(-1.39698 - 5.21359i) q^{37} -0.162163 q^{38} +(2.21488 + 5.83903i) q^{39} +1.43206 q^{40} +(-0.728231 - 2.71779i) q^{41} +(0.542708 - 1.64483i) q^{42} +(-1.39389 + 0.804764i) q^{43} +(-4.34837 + 4.34837i) q^{44} +(4.24921 - 0.633506i) q^{45} +(3.01221 + 0.807119i) q^{46} +(-1.71389 - 1.71389i) q^{47} +(-1.29241 + 1.15311i) q^{48} +(0.866025 + 0.500000i) q^{49} +(2.84871 - 0.763310i) q^{50} +(2.36552 + 11.3828i) q^{51} +(3.36682 + 1.29017i) q^{52} -8.12791i q^{53} +(-3.32475 + 3.99325i) q^{54} +(4.40325 - 7.62665i) q^{55} +(-0.500000 - 0.866025i) q^{56} +(-0.154044 + 0.234865i) q^{57} +(-2.05247 + 7.65992i) q^{58} +(-1.78883 + 6.67601i) q^{59} +(1.36036 - 2.07408i) q^{60} +(-4.36155 - 7.55443i) q^{61} +(1.61316 - 2.79408i) q^{62} +(-1.86671 - 2.34849i) q^{63} +1.00000i q^{64} +(-5.13539 - 0.536755i) q^{65} +(2.16720 + 10.4285i) q^{66} +(5.05737 - 1.35512i) q^{67} +(5.81300 + 3.35614i) q^{68} +(4.03035 - 3.59594i) q^{69} +(1.01262 + 1.01262i) q^{70} +(-9.93919 - 2.66320i) q^{71} +(0.442374 + 2.96720i) q^{72} +(2.46804 - 2.46804i) q^{73} +(-4.67438 + 2.69875i) q^{74} +(1.60056 - 4.85094i) q^{75} +(0.0419710 + 0.156638i) q^{76} -6.14953 q^{77} +(5.06682 - 3.65066i) q^{78} +5.05115 q^{79} +(-0.370644 - 1.38326i) q^{80} +(2.62523 + 8.60861i) q^{81} +(-2.43671 + 1.40683i) q^{82} +(3.93809 - 3.93809i) q^{83} +(-1.72925 - 0.0985019i) q^{84} +(-9.28484 - 2.48787i) q^{85} +(1.13811 + 1.13811i) q^{86} +(9.14433 + 10.2490i) q^{87} +(5.32565 + 3.07476i) q^{88} +(10.2688 - 2.75151i) q^{89} +(-1.71170 - 3.94046i) q^{90} +(1.46841 + 3.29299i) q^{91} -3.11847i q^{92} +(-2.51433 - 4.99055i) q^{93} +(-1.21190 + 2.09907i) q^{94} +(-0.116114 - 0.201115i) q^{95} +(1.44832 + 0.949929i) q^{96} +(-1.05510 + 3.93768i) q^{97} +(0.258819 - 0.965926i) q^{98} +(17.1625 + 6.76753i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 8 q^{6} - 24 q^{9}+O(q^{10}) \) 56 * q + 8 * q^6 - 24 * q^9	\( 56 q + 8 q^{6} - 24 q^{9} + 24 q^{10} + 8 q^{11} + 24 q^{13} + 4 q^{15} + 28 q^{16} - 4 q^{17} - 8 q^{18} + 8 q^{19} + 4 q^{21} - 8 q^{23} - 8 q^{24} - 4 q^{26} - 24 q^{27} - 8 q^{30} - 8 q^{31} + 8 q^{33} - 24 q^{34} + 24 q^{35} - 12 q^{36} - 8 q^{37} - 20 q^{39} - 28 q^{41} + 8 q^{44} + 72 q^{45} - 20 q^{46} + 64 q^{50} + 16 q^{54} + 8 q^{55} - 28 q^{56} + 4 q^{58} - 8 q^{59} + 20 q^{60} + 8 q^{61} - 32 q^{62} - 16 q^{63} - 24 q^{65} + 32 q^{66} - 16 q^{69} - 112 q^{71} + 8 q^{73} + 48 q^{74} + 40 q^{75} + 8 q^{76} + 16 q^{79} + 12 q^{81} - 4 q^{83} - 4 q^{84} + 32 q^{85} - 16 q^{86} - 144 q^{87} + 88 q^{89} - 8 q^{90} - 8 q^{91} + 52 q^{93} - 8 q^{94} - 48 q^{95} + 4 q^{96} - 64 q^{97} + 56 q^{99}+O(q^{100}) \) 56 * q + 8 * q^6 - 24 * q^9 + 24 * q^10 + 8 * q^11 + 24 * q^13 + 4 * q^15 + 28 * q^16 - 4 * q^17 - 8 * q^18 + 8 * q^19 + 4 * q^21 - 8 * q^23 - 8 * q^24 - 4 * q^26 - 24 * q^27 - 8 * q^30 - 8 * q^31 + 8 * q^33 - 24 * q^34 + 24 * q^35 - 12 * q^36 - 8 * q^37 - 20 * q^39 - 28 * q^41 + 8 * q^44 + 72 * q^45 - 20 * q^46 + 64 * q^50 + 16 * q^54 + 8 * q^55 - 28 * q^56 + 4 * q^58 - 8 * q^59 + 20 * q^60 + 8 * q^61 - 32 * q^62 - 16 * q^63 - 24 * q^65 + 32 * q^66 - 16 * q^69 - 112 * q^71 + 8 * q^73 + 48 * q^74 + 40 * q^75 + 8 * q^76 + 16 * q^79 + 12 * q^81 - 4 * q^83 - 4 * q^84 + 32 * q^85 - 16 * q^86 - 144 * q^87 + 88 * q^89 - 8 * q^90 - 8 * q^91 + 52 * q^93 - 8 * q^94 - 48 * q^95 + 4 * q^96 - 64 * q^97 + 56 * q^99

Introduction

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