LMFDB - Embedded newform 546.2.bu.a.197.13

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			197.13
Character	$\chi$	$=$	546.197
Dual form			546.2.bu.a.449.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(1.29241 - 1.15311i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.01262 - 1.01262i) q^{5} +(-0.779319 - 1.54682i) q^{6} +(-0.965926 + 0.258819i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.340668 - 2.98059i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(1.29241 - 1.15311i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.01262 - 1.01262i) q^{5} +(-0.779319 - 1.54682i) q^{6} +(-0.965926 + 0.258819i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.340668 - 2.98059i) 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} +(-2.47639 - 0.141061i) q^{15} +(0.500000 + 0.866025i) q^{16} +(3.35614 - 5.81300i) q^{17} +(-2.79086 - 1.10050i) q^{18} +(0.0419710 + 0.156638i) q^{19} +(0.370644 + 1.38326i) q^{20} +(-0.949929 + 1.44832i) q^{21} +(-3.07476 + 5.32565i) q^{22} +(1.55923 + 2.70067i) q^{23} +(-0.0985019 + 1.72925i) 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} +(-0.777190 + 2.35550i) q^{30} +(2.28135 - 2.28135i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-9.51224 + 4.79244i) q^{33} +(-4.74629 - 4.74629i) q^{34} +(1.24020 + 0.716030i) q^{35} +(-1.78532 + 2.41094i) q^{36} +(-1.39698 + 5.21359i) q^{37} +0.162163 q^{38} +(0.294915 + 6.23803i) q^{39} +1.43206 q^{40} +(0.728231 - 2.71779i) q^{41} +(1.15311 + 1.29241i) q^{42} +(-1.39389 - 0.804764i) q^{43} +(4.34837 + 4.34837i) q^{44} +(-3.36317 + 2.67324i) q^{45} +(3.01221 - 0.807119i) q^{46} +(1.71389 - 1.71389i) q^{47} +(1.64483 + 0.542708i) 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} +(-4.87594 + 1.79588i) q^{54} +(4.40325 + 7.62665i) q^{55} +(0.500000 - 0.866025i) q^{56} +(0.234865 + 0.154044i) q^{57} +(-2.05247 - 7.65992i) q^{58} +(1.78883 + 6.67601i) q^{59} +(2.07408 + 1.36036i) q^{60} +(-4.36155 + 7.55443i) q^{61} +(-1.61316 - 2.79408i) q^{62} +(0.442374 + 2.96720i) 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} +(5.12935 + 1.69242i) q^{69} +(1.01262 - 1.01262i) q^{70} +(9.93919 - 2.66320i) q^{71} +(1.86671 + 2.34849i) q^{72} +(2.46804 + 2.46804i) q^{73} +(4.67438 + 2.69875i) q^{74} +(-3.40076 - 3.81159i) q^{75} +(0.0419710 - 0.156638i) q^{76} +6.14953 q^{77} +(6.10180 + 1.32966i) q^{78} +5.05115 q^{79} +(0.370644 - 1.38326i) q^{80} +(-8.76789 - 2.03079i) q^{81} +(-2.43671 - 1.40683i) q^{82} +(-3.93809 - 3.93809i) q^{83} +(1.54682 - 0.779319i) q^{84} +(-9.28484 + 2.48787i) q^{85} +(-1.13811 + 1.13811i) q^{86} +(4.30375 - 13.0437i) 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} +(0.317799 - 5.57911i) q^{93} +(-1.21190 - 2.09907i) q^{94} +(0.116114 - 0.201115i) q^{95} +(0.949929 - 1.44832i) q^{96} +(-1.05510 - 3.93768i) q^{97} +(-0.258819 - 0.965926i) q^{98} +(-6.76753 + 17.1625i) 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^{19} + 4 q^{21} + 8 q^{23} + 8 q^{24} + 4 q^{26} - 24 q^{27} - 16 q^{30} - 8 q^{31} - 32 q^{33} - 24 q^{34} - 24 q^{35} - 12 q^{36} - 8 q^{37} - 60 q^{39} + 28 q^{41} - 8 q^{44} - 40 q^{45} - 20 q^{46} - 64 q^{50} + 8 q^{54} + 8 q^{55} + 28 q^{56} + 40 q^{57} + 4 q^{58} + 8 q^{59} + 4 q^{60} + 8 q^{61} + 32 q^{62} + 24 q^{65} + 32 q^{66} - 56 q^{69} + 112 q^{71} + 16 q^{72} + 8 q^{73} - 48 q^{74} - 40 q^{75} + 8 q^{76} - 8 q^{78} + 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} - 76 q^{93} - 8 q^{94} + 48 q^{95} - 4 q^{96} - 64 q^{97} - 40 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^19 + 4 * q^21 + 8 * q^23 + 8 * q^24 + 4 * q^26 - 24 * q^27 - 16 * q^30 - 8 * q^31 - 32 * q^33 - 24 * q^34 - 24 * q^35 - 12 * q^36 - 8 * q^37 - 60 * q^39 + 28 * q^41 - 8 * q^44 - 40 * q^45 - 20 * q^46 - 64 * q^50 + 8 * q^54 + 8 * q^55 + 28 * q^56 + 40 * q^57 + 4 * q^58 + 8 * q^59 + 4 * q^60 + 8 * q^61 + 32 * q^62 + 24 * q^65 + 32 * q^66 - 56 * q^69 + 112 * q^71 + 16 * q^72 + 8 * q^73 - 48 * q^74 - 40 * q^75 + 8 * q^76 - 8 * q^78 + 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 - 76 * q^93 - 8 * q^94 + 48 * q^95 - 4 * q^96 - 64 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	1.29241	−	1.15311i	0.746176	−	0.665749i
$3$	1.29241	−	1.15311i	0.746176	−	0.665749i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−1.01262	−	1.01262i	−0.452857	−	0.452857i	0.443445	−	0.896302i	$-0.353756\pi$
$5$	−1.01262	−	1.01262i	−0.452857	−	0.452857i	−0.896302	+	0.443445i	$0.853756\pi$
$6$	−0.779319	−	1.54682i	−0.318156	−	0.631488i
$7$	−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
$9$	0.340668	−	2.98059i	0.113556	−	0.993532i
$10$	−1.24020	+	0.716030i	−0.392186	+	0.226429i
$11$	−5.93999	−	1.59162i	−1.79097	−	0.479890i	−0.798463	−	0.602044i	$-0.794353\pi$
$11$	−5.93999	−	1.59162i	−1.79097	−	0.479890i	−0.992511	+	0.122154i	$0.961020\pi$
$12$	−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
$15$	−2.47639	−	0.141061i	−0.639400	−	0.0364217i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	3.35614	−	5.81300i	0.813983	−	1.40986i	−0.0960735	−	0.995374i	$-0.530628\pi$
$17$	3.35614	−	5.81300i	0.813983	−	1.40986i	0.910056	−	0.414485i	$-0.136038\pi$
$18$	−2.79086	−	1.10050i	−0.657812	−	0.259389i
$19$	0.0419710	+	0.156638i	0.00962880	+	0.0359352i	0.970573	−	0.240807i	$-0.0774120\pi$
$19$	0.0419710	+	0.156638i	0.00962880	+	0.0359352i	−0.960944	+	0.276742i	$0.910745\pi$
$20$	0.370644	+	1.38326i	0.0828786	+	0.309307i
$21$	−0.949929	+	1.44832i	−0.207291	+	0.316050i
$22$	−3.07476	+	5.32565i	−0.655542	+	1.13543i
$23$	1.55923	+	2.70067i	0.325123	+	0.563129i	0.981537	−	0.191271i	$-0.0612610\pi$
$23$	1.55923	+	2.70067i	0.325123	+	0.563129i	−0.656414	+	0.754401i	$0.727928\pi$
$24$	−0.0985019	+	1.72925i	−0.0201066	+	0.352981i
$25$		−	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	$-0.403240\pi$
$29$	6.86770	−	3.96507i	1.27530	−	0.736295i	0.975980	+	0.217858i	$0.0699071\pi$
$30$	−0.777190	+	2.35550i	−0.141895	+	0.430053i
$31$	2.28135	−	2.28135i	0.409743	−	0.409743i	−0.471906	−	0.881649i	$-0.656434\pi$
$31$	2.28135	−	2.28135i	0.409743	−	0.409743i	0.881649	+	0.471906i	$0.156434\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	−9.51224	+	4.79244i	−1.65587	+	0.834257i
$34$	−4.74629	−	4.74629i	−0.813983	−	0.813983i
$35$	1.24020	+	0.716030i	0.209632	+	0.121031i
$36$	−1.78532	+	2.41094i	−0.297554	+	0.401823i
$37$	−1.39698	+	5.21359i	−0.229662	+	0.857109i	0.750821	+	0.660506i	$0.229658\pi$
$37$	−1.39698	+	5.21359i	−0.229662	+	0.857109i	−0.980483	+	0.196604i	$0.937009\pi$
$38$	0.162163			0.0263064
$39$	0.294915	+	6.23803i	0.0472242	+	0.998884i
$40$	1.43206			0.226429
$41$	0.728231	−	2.71779i	0.113731	−	0.424448i	−0.885458	−	0.464719i	$-0.846155\pi$
$41$	0.728231	−	2.71779i	0.113731	−	0.424448i	0.999189	+	0.0402708i	$0.0128220\pi$
$42$	1.15311	+	1.29241i	0.177929	+	0.199424i
$43$	−1.39389	−	0.804764i	−0.212566	−	0.122725i	0.389937	−	0.920841i	$-0.372497\pi$
$43$	−1.39389	−	0.804764i	−0.212566	−	0.122725i	−0.602504	+	0.798116i	$0.705830\pi$
$44$	4.34837	+	4.34837i	0.655542	+	0.655542i
$45$	−3.36317	+	2.67324i	−0.501352	+	0.398503i
$46$	3.01221	−	0.807119i	0.444126	−	0.119003i
$47$	1.71389	−	1.71389i	0.249996	−	0.249996i	−0.570973	−	0.820969i	$-0.693434\pi$
$47$	1.71389	−	1.71389i	0.249996	−	0.249996i	0.820969	+	0.570973i	$0.193434\pi$
$48$	1.64483	+	0.542708i	0.237411	+	0.0783331i
$49$	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	$-0.188518\pi$
$54$	−4.87594	+	1.79588i	−0.663532	+	0.244388i
$55$	4.40325	+	7.62665i	0.593734	+	1.02838i
$56$	0.500000	−	0.866025i	0.0668153	−	0.115728i
$57$	0.234865	+	0.154044i	0.0311086	+	0.0204036i
$58$	−2.05247	−	7.65992i	−0.269503	−	1.00580i
$59$	1.78883	+	6.67601i	0.232886	+	0.869142i	0.979090	+	0.203425i	$0.0652074\pi$
$59$	1.78883	+	6.67601i	0.232886	+	0.869142i	−0.746205	+	0.665717i	$0.768126\pi$
$60$	2.07408	+	1.36036i	0.267763	+	0.175621i
$61$	−4.36155	+	7.55443i	−0.558440	+	0.967246i	0.439187	+	0.898395i	$0.355266\pi$
$61$	−4.36155	+	7.55443i	−0.558440	+	0.967246i	−0.997627	+	0.0688502i	$0.978067\pi$
$62$	−1.61316	−	2.79408i	−0.204872	−	0.354848i
$63$	0.442374	+	2.96720i	0.0557339	+	0.373833i
$64$		−	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	0.554153	−	0.832415i	$-0.313042\pi$
$67$	5.05737	+	1.35512i	0.617857	+	0.165554i	0.0637034	+	0.997969i	$0.479709\pi$
$68$	−5.81300	+	3.35614i	−0.704930	+	0.406991i
$69$	5.12935	+	1.69242i	0.617501	+	0.203743i
$70$	1.01262	−	1.01262i	0.121031	−	0.121031i
$71$	9.93919	−	2.66320i	1.17956	−	0.316063i	0.384811	−	0.922995i	$-0.374267\pi$
$71$	9.93919	−	2.66320i	1.17956	−	0.316063i	0.794754	+	0.606932i	$0.207600\pi$
$72$	1.86671	+	2.34849i	0.219994	+	0.276772i
$73$	2.46804	+	2.46804i	0.288862	+	0.288862i	0.836630	−	0.547768i	$-0.184522\pi$
$73$	2.46804	+	2.46804i	0.288862	+	0.288862i	−0.547768	+	0.836630i	$0.684522\pi$
$74$	4.67438	+	2.69875i	0.543386	+	0.313724i
$75$	−3.40076	−	3.81159i	−0.392686	−	0.440125i
$76$	0.0419710	−	0.156638i	0.00481440	−	0.0179676i
$77$	6.14953			0.700804
$78$	6.10180	+	1.32966i	0.690893	+	0.150554i
$79$	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
$81$	−8.76789	−	2.03079i	−0.974210	−	0.225643i
$82$	−2.43671	−	1.40683i	−0.269089	−	0.155359i
$83$	−3.93809	−	3.93809i	−0.432261	−	0.432261i	0.457136	−	0.889397i	$-0.348875\pi$
$83$	−3.93809	−	3.93809i	−0.432261	−	0.432261i	−0.889397	+	0.457136i	$0.848875\pi$
$84$	1.54682	−	0.779319i	0.168772	−	0.0850306i
$85$	−9.28484	+	2.48787i	−1.00708	+	0.269847i
$86$	−1.13811	+	1.13811i	−0.122725	+	0.122725i
$87$	4.30375	−	13.0437i	0.461410	−	1.39843i
$88$	5.32565	−	3.07476i	0.567716	−	0.327771i
$89$	−10.2688	−	2.75151i	−1.08849	−	0.291659i	−0.330419	−	0.943834i	$-0.607190\pi$
$89$	−10.2688	−	2.75151i	−1.08849	−	0.291659i	−0.758068	+	0.652175i	$0.773857\pi$
$90$	1.71170	+	3.94046i	0.180429	+	0.415361i
$91$	1.46841	−	3.29299i	0.153931	−	0.345199i
$92$		−	3.11847i		−	0.325123i
$93$	0.317799	−	5.57911i	0.0329542	−	0.578526i
$94$	−1.21190	−	2.09907i	−0.124998	−	0.216503i
$95$	0.116114	−	0.201115i	0.0119130	−	0.0206340i
$96$	0.949929	−	1.44832i	0.0969517	−	0.147819i
$97$	−1.05510	−	3.93768i	−0.107129	−	0.399811i	0.891449	−	0.453121i	$-0.149689\pi$
$97$	−1.05510	−	3.93768i	−0.107129	−	0.399811i	−0.998578	+	0.0533101i	$0.983023\pi$
$98$	−0.258819	−	0.965926i	−0.0261447	−	0.0975732i
$99$	−6.76753	+	17.1625i	−0.680162	+	1.72489i
$100$	−1.47460	+	2.55409i	−0.147460	+	0.255409i
$101$	−5.63686	−	9.76334i	−0.560889	−	0.971488i	−0.997419	−	0.0717986i	$-0.977126\pi$
$101$	−5.63686	−	9.76334i	−0.560889	−	0.971488i	0.436530	−	0.899690i	$-0.356207\pi$
$102$	−11.6072	−	0.661172i	−1.14928	−	0.0654658i
$103$		−	6.36367i		−	0.627031i	−0.949583	−	0.313516i	$-0.898493\pi$
$103$		−	6.36367i		−	0.627031i	0.949583	−	0.313516i	$-0.101507\pi$
$104$	−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	$-0.935243\pi$
$107$	−13.3862	+	7.72854i	−1.29410	+	0.747147i	−0.314718	+	0.949185i	$0.601910\pi$
$108$	0.472699	+	5.17461i	0.0454855	+	0.497927i
$109$	10.9344	−	10.9344i	1.04732	−	1.04732i	0.0485013	−	0.998823i	$-0.484555\pi$
$109$	10.9344	−	10.9344i	1.04732	−	1.04732i	0.998823	−	0.0485013i	$-0.0154445\pi$
$110$	8.50642	−	2.27929i	0.811055	−	0.217322i
$111$	4.20638	+	8.34899i	0.399252	+	0.792451i
$112$	−0.707107	−	0.707107i	−0.0668153	−	0.0668153i
$113$	10.5422	+	6.08657i	0.991731	+	0.572576i	0.905791	−	0.423724i	$-0.139277\pi$
$113$	10.5422	+	6.08657i	0.991731	+	0.572576i	0.0859400	+	0.996300i	$0.472611\pi$
$114$	0.209582	−	0.186992i	0.0196292	−	0.0175134i
$115$	1.15584	−	4.31366i	0.107783	−	0.402251i
$116$	−7.93014			−0.736295
$117$	7.57430	+	7.72205i	0.700244	+	0.713904i
$118$	6.91151			0.636256
$119$	−1.73726	+	6.48356i	−0.159255	+	0.594347i
$120$	1.85081	−	1.65132i	0.168955	−	0.150745i
$121$	23.2240	+	13.4084i	2.11127	+	1.21894i
$122$	6.16817	+	6.16817i	0.558440	+	0.558440i
$123$	−2.19274	−	4.35225i	−0.197713	−	0.392429i
$124$	−3.11639	+	0.835033i	−0.279860	+	0.0749882i
$125$	−8.04952	+	8.04952i	−0.719971	+	0.719971i
$126$	2.98059	+	0.340668i	0.265532	+	0.0303492i
$127$	−5.34018	+	3.08315i	−0.473864	+	0.273586i	−0.717856	−	0.696192i	$-0.754876\pi$
$127$	−5.34018	+	3.08315i	−0.473864	+	0.273586i	0.243992	+	0.969777i	$0.421543\pi$
$128$	−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	$-0.0644083\pi$
$132$	10.6341	+	0.605740i	0.925576	+	0.0527229i
$133$	−0.0810817	−	0.140438i	−0.00703067	−	0.0121775i
$134$	2.61789	−	4.53432i	0.226151	−	0.391705i
$135$	−1.26407	+	7.33305i	−0.108794	+	0.631128i
$136$	1.73726	+	6.48356i	0.148969	+	0.555960i
$137$	−3.12108	−	11.6480i	−0.266652	−	0.995158i	−0.961232	−	0.275742i	$-0.911076\pi$
$137$	−3.12108	−	11.6480i	−0.266652	−	0.995158i	0.694580	−	0.719416i	$-0.255590\pi$
$138$	2.96232	−	4.51654i	0.252170	−	0.384474i
$139$	−3.90855	+	6.76981i	−0.331519	+	0.574208i	−0.982810	−	0.184620i	$-0.940894\pi$
$139$	−3.90855	+	6.76981i	−0.331519	+	0.574208i	0.651291	+	0.758828i	$0.274228\pi$
$140$	−0.716030	−	1.24020i	−0.0605156	−	0.104816i
$141$	0.238749	−	4.19135i	0.0201063	−	0.352975i
$142$		−	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
$147$	0.542708	−	1.64483i	0.0447618	−	0.135663i
$148$	3.81662	−	3.81662i	0.313724	−	0.313724i
$149$	14.6256	−	3.91893i	1.19818	−	0.321051i	0.396065	−	0.918223i	$-0.370376\pi$
$149$	14.6256	−	3.91893i	1.19818	−	0.321051i	0.802114	+	0.597172i	$0.203709\pi$
$150$	−4.56190	+	2.29837i	−0.372477	+	0.187661i
$151$	14.0334	+	14.0334i	1.14202	+	1.14202i	0.988080	+	0.153940i	$0.0491963\pi$
$151$	14.0334	+	14.0334i	1.14202	+	1.14202i	0.153940	+	0.988080i	$0.450804\pi$
$152$	−0.140438	−	0.0810817i	−0.0113910	−	0.00657659i
$153$	−16.1829	−	11.9836i	−1.30831	−	0.968816i
$154$	1.59162	−	5.93999i	0.128256	−	0.478658i
$155$	−4.62028			−0.371110
$156$	2.86361	−	5.54975i	0.229272	−	0.444336i
$157$	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
$159$	−9.37239	−	10.5046i	−0.743279	−	0.833071i
$160$	−1.24020	−	0.716030i	−0.0980464	−	0.0566071i
$161$	−2.20509	−	2.20509i	−0.173785	−	0.173785i
$162$	−4.23089	+	7.94352i	−0.332410	+	0.624102i
$163$	12.2065	−	3.27073i	0.956089	−	0.256183i	0.253145	−	0.967428i	$-0.418535\pi$
$163$	12.2065	−	3.27073i	0.956089	−	0.256183i	0.702944	+	0.711245i	$0.251868\pi$
$164$	−1.98956	+	1.98956i	−0.155359	+	0.155359i
$165$	14.4852	+	4.77935i	1.12767	+	0.372072i
$166$	−4.82315	+	2.78465i	−0.374349	+	0.216131i
$167$	6.09250	+	1.63248i	0.471452	+	0.126325i	0.486720	−	0.873558i	$-0.338193\pi$
$167$	6.09250	+	1.63248i	0.471452	+	0.126325i	−0.0152676	+	0.999883i	$0.504860\pi$
$168$	−0.352417	−	1.69582i	−0.0271895	−	0.130835i
$169$	−2.68817	−	12.7190i	−0.206782	−	0.978387i
$170$			9.61238i			0.737236i
$171$	0.481172	−	0.0717369i	0.0367961	−	0.00548586i
$172$	0.804764	+	1.39389i	0.0613627	+	0.106283i
$173$	1.05378	−	1.82519i	0.0801171	−	0.138767i	−0.823183	−	0.567776i	$-0.807804\pi$
$173$	1.05378	−	1.82519i	0.0801171	−	0.138767i	0.903300	+	0.429009i	$0.141137\pi$
$174$	−11.4854	−	7.53307i	−0.870705	−	0.571080i
$175$	0.763310	+	2.84871i	0.0577008	+	0.215342i
$176$	−1.59162	−	5.93999i	−0.119973	−	0.447744i
$177$	10.0101	+	6.56544i	0.752404	+	0.493489i
$178$	−5.31551	+	9.20673i	−0.398414	+	0.690073i
$179$	11.4325	+	19.8016i	0.854503	+	1.48004i	0.877105	+	0.480298i	$0.159471\pi$
$179$	11.4325	+	19.8016i	0.854503	+	1.48004i	−0.0226027	+	0.999745i	$0.507195\pi$
$180$	4.24921	−	0.633506i	0.316718	−	0.0472188i
$181$		−	17.3739i		−	1.29139i	−0.763594	−	0.645697i	$-0.776567\pi$
$181$		−	17.3739i		−	1.29139i	0.763594	−	0.645697i	$-0.223433\pi$
$182$	−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
$186$	−5.30675	−	1.75095i	−0.389110	−	0.128386i
$187$	−29.1875	+	29.1875i	−2.13440	+	2.13440i
$188$	−2.34121	+	0.627326i	−0.170750	+	0.0457524i
$189$	3.99325	+	3.32475i	0.290466	+	0.241840i
$190$	−0.164210	−	0.164210i	−0.0119130	−	0.0119130i
$191$	−12.2932	−	7.09748i	−0.889505	−	0.513556i	−0.0157241	−	0.999876i	$-0.505005\pi$
$191$	−12.2932	−	7.09748i	−0.889505	−	0.513556i	−0.873780	+	0.486321i	$0.838339\pi$
$192$	−1.15311	−	1.29241i	−0.0832186	−	0.0932720i
$193$	4.95428	−	18.4896i	0.356617	−	1.33091i	−0.521820	−	0.853055i	$-0.674747\pi$
$193$	4.95428	−	18.4896i	0.356617	−	1.33091i	0.878437	−	0.477858i	$-0.158586\pi$
$194$	−4.07659			−0.292682
$195$	6.01811	−	6.61539i	0.430966	−	0.473738i
$196$	−1.00000			−0.0714286
$197$	−6.06475	+	22.6340i	−0.432096	+	1.61260i	0.315827	+	0.948817i	$0.397718\pi$
$197$	−6.06475	+	22.6340i	−0.432096	+	1.61260i	−0.747923	+	0.663786i	$0.768949\pi$
$198$	14.8261	+	10.9789i	1.05365	+	0.780237i
$199$	−6.10110	−	3.52247i	−0.432495	−	0.249701i	0.267914	−	0.963443i	$-0.413666\pi$
$199$	−6.10110	−	3.52247i	−0.432495	−	0.249701i	−0.700409	+	0.713742i	$0.746999\pi$
$200$	2.08540	+	2.08540i	0.147460	+	0.147460i
$201$	8.09883	−	4.08034i	0.571247	−	0.287805i
$202$	−10.8896	+	2.91786i	−0.766189	+	0.205300i
$203$	−5.60745	+	5.60745i	−0.393566	+	0.393566i
$204$	−3.64280	+	11.0406i	−0.255047	+	0.772993i
$205$	−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
$210$	0.141061	−	2.47639i	0.00973411	−	0.170887i
$211$	7.00393	+	12.1312i	0.482171	+	0.835144i	0.999791	−	0.0204668i	$-0.00651522\pi$
$211$	7.00393	+	12.1312i	0.482171	+	0.835144i	−0.517620	+	0.855611i	$0.673182\pi$
$212$	−4.06396	+	7.03898i	−0.279114	+	0.483439i
$213$	9.77458	−	14.9029i	0.669743	−	1.02113i
$214$	4.00059	+	14.9304i	0.273475	+	1.02062i
$215$	0.596562	+	2.22640i	0.0406852	+	0.151839i
$216$	5.12063	+	0.882694i	0.348415	+	0.0600597i
$217$	−1.61316	+	2.79408i	−0.109508	+	0.189674i
$218$	−7.73178	−	13.3918i	−0.523662	−	0.907010i
$219$	6.03566	+	0.343805i	0.407852	+	0.0232322i
$220$		−	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	−0.997315	−	0.0732348i	$-0.976668\pi$
$223$	−28.3377	−	7.59306i	−1.89763	−	0.508469i	−0.900317	−	0.435234i	$-0.856666\pi$
$224$	−0.866025	+	0.500000i	−0.0578638	+	0.0334077i
$225$	−8.79038	−	1.00470i	−0.586026	−	0.0669801i
$226$	8.60771	−	8.60771i	0.572576	−	0.572576i
$227$	−10.9930	+	2.94557i	−0.729631	+	0.195504i	−0.604465	−	0.796632i	$-0.706613\pi$
$227$	−10.9930	+	2.94557i	−0.729631	+	0.195504i	−0.125166	+	0.992136i	$0.539946\pi$
$228$	−0.126377	−	0.250838i	−0.00836952	−	0.0166122i
$229$	6.80059	+	6.80059i	0.449395	+	0.449395i	0.895153	−	0.445758i	$-0.147066\pi$
$229$	6.80059	+	6.80059i	0.449395	+	0.449395i	−0.445758	+	0.895153i	$0.647066\pi$
$230$	−3.86752	−	2.23292i	−0.255017	−	0.147234i
$231$	7.94774	−	7.09109i	0.522923	−	0.466560i
$232$	−2.05247	+	7.65992i	−0.134751	+	0.502899i
$233$	3.30963			0.216821			0.108411	−	0.994106i	$-0.465424\pi$
$233$	3.30963			0.216821			0.108411	+	0.994106i	$0.465424\pi$
$234$	9.41930	−	5.31759i	0.615759	−	0.347622i
$235$	−3.47103			−0.226425
$236$	1.78883	−	6.67601i	0.116443	−	0.434571i
$237$	6.52817	−	5.82453i	0.424050	−	0.378344i
$238$	5.81300	+	3.35614i	0.376801	+	0.217546i
$239$	−11.9734	−	11.9734i	−0.774492	−	0.774492i	0.204396	−	0.978888i	$-0.434477\pi$
$239$	−11.9734	−	11.9734i	−0.774492	−	0.774492i	−0.978888	+	0.204396i	$0.934477\pi$
$240$	−1.11603	−	2.21514i	−0.0720395	−	0.142987i
$241$	−26.9210	+	7.21346i	−1.73413	+	0.464660i	−0.981129	−	0.193354i	$-0.938063\pi$
$241$	−26.9210	+	7.21346i	−1.73413	+	0.464660i	−0.753006	+	0.658014i	$0.771397\pi$
$242$	18.9623	−	18.9623i	1.21894	−	1.21894i
$243$	−13.6735	+	7.48573i	−0.877154	+	0.480210i
$244$	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
$249$	−9.63069	−	0.548586i	−0.610320	−	0.0347652i
$250$	5.69187	+	9.85860i	0.359985	+	0.623513i
$251$	−11.6110	+	20.1109i	−0.732881	+	1.26939i	0.222765	+	0.974872i	$0.428492\pi$
$251$	−11.6110	+	20.1109i	−0.732881	+	1.26939i	−0.955647	+	0.294516i	$0.904842\pi$
$252$	1.10050	−	2.79086i	0.0693247	−	0.175808i
$253$	−4.96340	−	18.5237i	−0.312046	−	1.16457i
$254$	1.59596	+	5.95620i	0.100139	+	0.373725i
$255$	−9.13107	+	13.9218i	−0.571810	+	0.871817i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	10.8682	+	18.8242i	0.677937	+	1.17422i	0.975601	+	0.219550i	$0.0704591\pi$
$257$	10.8682	+	18.8242i	0.677937	+	1.17422i	−0.297664	+	0.954671i	$0.596208\pi$
$258$	−0.158542	+	2.78327i	−0.00987036	+	0.173279i
$259$		−	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	$-0.738723\pi$
$263$	−6.30441	+	3.63985i	−0.388747	+	0.224443i	0.292870	+	0.956152i	$0.405390\pi$
$264$	3.33740	−	10.1149i	0.205403	−	0.622531i
$265$	−8.23048	+	8.23048i	−0.505594	+	0.505594i
$266$	−0.156638	+	0.0419710i	−0.00960408	+	0.00257340i
$267$	−16.4443	+	8.28495i	−1.00637	+	0.507031i
$268$	−3.70225	−	3.70225i	−0.226151	−	0.226151i
$269$	−16.1674	−	9.33424i	−0.985743	−	0.569119i	−0.0817439	−	0.996653i	$-0.526049\pi$
$269$	−16.1674	−	9.33424i	−0.985743	−	0.569119i	−0.903999	+	0.427534i	$0.859382\pi$
$270$	6.75601	+	3.11893i	0.411158	+	0.189812i
$271$	−3.19612	+	11.9281i	−0.194151	+	0.724580i	0.798334	+	0.602214i	$0.205715\pi$
$271$	−3.19612	+	11.9281i	−0.194151	+	0.724580i	−0.992485	+	0.122366i	$0.960952\pi$
$272$	6.71227			0.406991
$273$	−1.89939	−	5.94915i	−0.114956	−	0.360059i
$274$	−12.0589			−0.728506
$275$	−4.69400	+	17.5182i	−0.283059	+	1.05639i
$276$	−3.59594	−	4.03035i	−0.216450	−	0.242599i
$277$	27.0494	+	15.6170i	1.62524	+	0.938333i	0.985486	+	0.169754i	$0.0542974\pi$
$277$	27.0494	+	15.6170i	1.62524	+	0.938333i	0.639755	+	0.768579i	$0.279036\pi$
$278$	5.52753	+	5.52753i	0.331519	+	0.331519i
$279$	−6.02260	−	7.57697i	−0.360564	−	0.453622i
$280$	−1.38326	+	0.370644i	−0.0826658	+	0.0221502i
$281$	9.52174	−	9.52174i	0.568019	−	0.568019i	−0.363554	−	0.931573i	$-0.618437\pi$
$281$	9.52174	−	9.52174i	0.568019	−	0.568019i	0.931573	+	0.363554i	$0.118437\pi$
$282$	−3.98674	−	1.31541i	−0.237407	−	0.0783318i
$283$	13.2517	−	7.65087i	0.787732	−	0.454797i	−0.0514315	−	0.998677i	$-0.516378\pi$
$283$	13.2517	−	7.65087i	0.787732	−	0.454797i	0.839163	+	0.543879i	$0.183045\pi$
$284$	−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
$288$	−0.442374	−	2.96720i	−0.0260672	−	0.174844i
$289$	−14.0273	−	24.2960i	−0.825135	−	1.42918i
$290$	−5.67821	+	9.83496i	−0.333436	+	0.577529i
$291$	−5.90421	−	3.87247i	−0.346111	−	0.227008i
$292$	−0.903366	−	3.37141i	−0.0528655	−	0.197297i
$293$	2.15518	+	8.04324i	0.125907	+	0.469891i	0.999870	−	0.0161006i	$-0.00512519\pi$
$293$	2.15518	+	8.04324i	0.125907	+	0.469891i	−0.873963	+	0.485992i	$0.838459\pi$
$294$	−1.44832	−	0.949929i	−0.0844678	−	0.0554010i
$295$	4.94885	−	8.57166i	0.288133	−	0.499061i
$296$	−2.69875	−	4.67438i	−0.156862	−	0.271693i
$297$	11.0438	+	29.9848i	0.640827	+	1.73989i
$298$		−	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
$303$	−18.5434	−	6.11834i	−1.06529	−	0.351489i
$304$	−0.114667	+	0.114667i	−0.00657659	+	0.00657659i
$305$	12.0664	−	3.23317i	0.690917	−	0.185131i
$306$	−15.7637	+	12.5299i	−0.901150	+	0.716285i
$307$	8.34685	+	8.34685i	0.476380	+	0.476380i	0.903972	−	0.427592i	$-0.140638\pi$
$307$	8.34685	+	8.34685i	0.476380	+	0.476380i	−0.427592	+	0.903972i	$0.640638\pi$
$308$	−5.32565	−	3.07476i	−0.303457	−	0.175201i
$309$	−7.33802	−	8.22450i	−0.417445	−	0.467875i
$310$	−1.19582	+	4.46285i	−0.0679179	+	0.253473i
$311$	−26.0701			−1.47830			−0.739149	−	0.673542i	$-0.764772\pi$
$311$	−26.0701			−1.47830			−0.739149	+	0.673542i	$0.764772\pi$
$312$	−4.61949	−	4.20242i	−0.261527	−	0.237915i
$313$	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
$315$	2.55669	−	3.45261i	0.144053	−	0.194532i
$316$	−4.37442	−	2.52557i	−0.246080	−	0.142075i
$317$	4.13339	+	4.13339i	0.232154	+	0.232154i	0.813591	−	0.581437i	$-0.197509\pi$
$317$	4.13339	+	4.13339i	0.232154	+	0.232154i	−0.581437	+	0.813591i	$0.697509\pi$
$318$	−12.5724	+	6.33424i	−0.705028	+	0.355206i
$319$	−47.1049	+	12.6217i	−2.63737	+	0.706681i
$320$	−1.01262	+	1.01262i	−0.0566071	+	0.0566071i
$321$	−8.38868	+	25.4243i	−0.468211	+	1.41905i
$322$	−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
$327$	1.52319	−	26.7403i	0.0842326	−	1.47874i
$328$	1.40683	+	2.43671i	0.0776794	+	0.134545i
$329$	−1.21190	+	2.09907i	−0.0668142	+	0.115726i
$330$	8.36554	−	12.7546i	0.460508	−	0.702119i
$331$	−1.12226	−	4.18832i	−0.0616848	−	0.230211i	0.928201	−	0.372080i	$-0.121355\pi$
$331$	−1.12226	−	4.18832i	−0.0616848	−	0.230211i	−0.989885	+	0.141869i	$0.954689\pi$
$332$	1.44144	+	5.37952i	0.0791093	+	0.295240i
$333$	15.0637	+	5.93993i	0.825486	+	0.325506i
$334$	3.15371	−	5.46239i	0.172563	−	0.298889i
$335$	−3.74897	−	6.49341i	−0.204828	−	0.354773i
$336$	−1.72925	−	0.0985019i	−0.0943382	−	0.00537372i
$337$			28.1885i			1.53552i	0.640735	+	0.767762i	$0.278630\pi$
$337$			28.1885i			1.53552i	−0.640735	+	0.767762i	$0.721370\pi$
$338$	−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
$342$	0.0552439	−	0.483343i	0.00298725	−	0.0261362i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	1.55468	−	0.416576i	0.0838229	−	0.0224603i
$345$	−3.48031	−	6.90785i	−0.187373	−	0.371906i
$346$	−1.49026	−	1.49026i	−0.0801171	−	0.0801171i
$347$	−4.48337	−	2.58848i	−0.240680	−	0.138957i	0.374809	−	0.927102i	$-0.377708\pi$
$347$	−4.48337	−	2.58848i	−0.240680	−	0.138957i	−0.615489	+	0.788145i	$0.711042\pi$
$348$	−10.2490	+	9.14433i	−0.549405	+	0.490188i
$349$	−2.58678	+	9.65399i	−0.138467	+	0.516766i	0.861492	+	0.507770i	$0.169530\pi$
$349$	−2.58678	+	9.65399i	−0.138467	+	0.516766i	−0.999960	+	0.00899587i	$0.997136\pi$
$350$	2.94920			0.157642
$351$	18.6935	+	1.24608i	0.997786	+	0.0665107i
$352$	−6.14953			−0.327771
$353$	7.77840	−	29.0294i	0.414003	−	1.54508i	−0.372822	−	0.927903i	$-0.621610\pi$
$353$	7.77840	−	29.0294i	0.414003	−	1.54508i	0.786825	−	0.617176i	$-0.211723\pi$
$354$	8.93253	−	7.96974i	0.474759	−	0.423587i
$355$	−12.7614	−	7.36781i	−0.677306	−	0.391043i
$356$	7.51726	+	7.51726i	0.398414	+	0.398414i
$357$	5.23100	+	10.3827i	0.276854	+	0.549511i
$358$	22.0858	−	5.91788i	1.16727	−	0.312770i
$359$	4.39884	−	4.39884i	0.232162	−	0.232162i	−0.581433	−	0.813594i	$-0.697508\pi$
$359$	4.39884	−	4.39884i	0.232162	−	0.232162i	0.813594	+	0.581433i	$0.197508\pi$
$360$	0.487857	−	4.26839i	0.0257123	−	0.224964i
$361$	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
$366$	15.0844	+	0.859242i	0.788475	+	0.0449133i
$367$	2.35165	+	4.07318i	0.122755	+	0.212618i	0.920853	−	0.389909i	$-0.127494\pi$
$367$	2.35165	+	4.07318i	0.122755	+	0.212618i	−0.798098	+	0.602528i	$0.794160\pi$
$368$	−1.55923	+	2.70067i	−0.0812807	+	0.140782i
$369$	−7.85256	−	3.09643i	−0.408788	−	0.161194i
$370$	−2.00056	−	7.46618i	−0.104004	−	0.388148i
$371$	2.10366	+	7.85096i	0.109217	+	0.407602i
$372$	−3.06478	+	4.67275i	−0.158901	+	0.242271i
$373$	5.29582	−	9.17262i	0.274207	−	0.474940i	−0.695728	−	0.718306i	$-0.744918\pi$
$373$	5.29582	−	9.17262i	0.274207	−	0.474940i	0.969935	+	0.243365i	$0.0782514\pi$
$374$	20.6387	+	35.7472i	1.06720	+	1.84844i
$375$	−1.12132	+	19.6853i	−0.0579047	+	1.01654i
$376$			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	−0.341380	−	0.939925i	$-0.610894\pi$
$379$	−21.5507	−	5.77450i	−1.10699	−	0.296616i	−0.765607	+	0.643309i	$0.777561\pi$
$380$	−0.201115	+	0.116114i	−0.0103170	+	0.00595651i
$381$	−3.34650	+	10.1425i	−0.171447	+	0.519618i
$382$	−10.0374	+	10.0374i	−0.513556	+	0.513556i
$383$	14.4047	−	3.85972i	0.736044	−	0.197222i	0.128725	−	0.991680i	$-0.458912\pi$
$383$	14.4047	−	3.85972i	0.736044	−	0.197222i	0.607319	+	0.794458i	$0.292245\pi$
$384$	−1.54682	+	0.779319i	−0.0789360	+	0.0397694i
$385$	−6.22713	−	6.22713i	−0.317364	−	0.317364i
$386$	−16.5774	−	9.57094i	−0.843765	−	0.487148i
$387$	−2.87353	+	3.88047i	−0.146070	+	0.197255i
$388$	−1.05510	+	3.93768i	−0.0535645	+	0.199906i
$389$	14.6386			0.742205			0.371103	−	0.928592i	$-0.378980\pi$
$389$	14.6386			0.742205			0.371103	+	0.928592i	$0.378980\pi$
$390$	−4.83237	−	7.52524i	−0.244697	−	0.381055i
$391$	20.9320			1.05858
$392$	−0.258819	+	0.965926i	−0.0130723	+	0.0487866i
$393$	−5.30470	−	5.94554i	−0.267587	−	0.299913i
$394$	20.2930	+	11.7162i	1.02235	+	0.590253i
$395$	−5.11489	−	5.11489i	−0.257358	−	0.257358i
$396$	14.4421	−	11.4794i	0.725743	−	0.576861i
$397$	22.0441	−	5.90671i	1.10636	−	0.296449i	0.341010	−	0.940060i	$-0.389231\pi$
$397$	22.0441	−	5.90671i	1.10636	−	0.296449i	0.765353	+	0.643611i	$0.222564\pi$
$398$	−4.98153	+	4.98153i	−0.249701	+	0.249701i
$399$	−0.266731	−	0.0880073i	−0.0133533	−	0.00440588i
$400$	2.55409	−	1.47460i	0.127704	−	0.0737301i
$401$	−19.3124	−	5.17474i	−0.964414	−	0.258414i	−0.257946	−	0.966159i	$-0.583046\pi$
$401$	−19.3124	−	5.17474i	−0.964414	−	0.258414i	−0.706468	+	0.707745i	$0.749712\pi$
$402$	−1.84518	−	8.87893i	−0.0920290	−	0.442841i
$403$	1.20927	+	11.5696i	0.0602379	+	0.576325i
$404$			11.2737i			0.560889i
$405$	6.82212	+	10.9349i	0.338994	+	0.543362i
$406$	3.96507	+	6.86770i	0.196783	+	0.340838i
$407$	16.5961	−	28.7452i	0.822637	−	1.42485i
$408$	9.72153	+	6.37618i	0.481287	+	0.315668i
$409$	−4.36347	−	16.2847i	−0.215760	−	0.805226i	−0.985898	−	0.167349i	$-0.946479\pi$
$409$	−4.36347	−	16.2847i	−0.215760	−	0.805226i	0.770138	−	0.637877i	$-0.220187\pi$
$410$	1.04287	+	3.89204i	0.0515037	+	0.192214i
$411$	−17.4652	−	11.4551i	−0.861495	−	0.565039i
$412$	−3.18184	+	5.51110i	−0.156758	+	0.271512i
$413$	−3.45576	−	5.98554i	−0.170047	−	0.294529i
$414$	−1.37953	−	9.25313i	−0.0678002	−	0.454767i
$415$			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	$-0.948049\pi$
$419$	−27.4158	+	15.8285i	−1.33935	+	0.773275i	−0.352640	+	0.935759i	$0.614716\pi$
$420$	−2.35550	−	0.777190i	−0.114936	−	0.0379230i
$421$	−10.9210	+	10.9210i	−0.532256	+	0.532256i	−0.921243	−	0.388987i	$-0.872825\pi$
$421$	−10.9210	+	10.9210i	−0.532256	+	0.532256i	0.388987	+	0.921243i	$0.372825\pi$
$422$	13.5306	−	3.62550i	0.658657	−	0.176487i
$423$	−4.52453	−	5.69226i	−0.219990	−	0.276767i
$424$	5.74730	+	5.74730i	0.279114	+	0.279114i
$425$	−17.1437	−	9.89793i	−0.831593	−	0.480120i
$426$	−11.8653	−	13.2987i	−0.574875	−	0.644324i
$427$	2.25771	−	8.42587i	0.109258	−	0.407756i
$428$	15.4571			0.747147
$429$	8.17675	−	37.5232i	0.394777	−	1.81164i
$430$	2.30494			0.111154
$431$	−4.82835	+	18.0196i	−0.232573	+	0.867976i	0.746654	+	0.665212i	$0.231659\pi$
$431$	−4.82835	+	18.0196i	−0.232573	+	0.867976i	−0.979228	+	0.202763i	$0.935008\pi$
$432$	2.17793	−	4.71769i	0.104786	−	0.226980i
$433$	18.0627	+	10.4285i	0.868037	+	0.501161i	0.866695	−	0.498838i	$-0.166240\pi$
$433$	18.0627	+	10.4285i	0.868037	+	0.501161i	0.00134144	+	0.999999i	$0.499573\pi$
$434$	2.28135	+	2.28135i	0.109508	+	0.109508i
$435$	−17.5664	+	8.85028i	−0.842244	+	0.424338i
$436$	−14.9367	+	4.00226i	−0.715336	+	0.191674i
$437$	−0.357585	+	0.357585i	−0.0171056	+	0.0171056i
$438$	1.89423	−	5.74102i	0.0905100	−	0.274316i
$439$	34.7872	−	20.0844i	1.66030	−	0.958577i	0.687736	−	0.725961i	$-0.258605\pi$
$439$	34.7872	−	20.0844i	1.66030	−	0.958577i	0.972568	−	0.232617i	$-0.0747288\pi$
$440$	−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	$-0.175092\pi$
$444$	0.531665	−	9.33363i	0.0252317	−	0.442954i
$445$	7.61212	+	13.1846i	0.360849	+	0.625009i
$446$	−14.6687	+	25.4069i	−0.694582	+	1.20305i
$447$	14.3834	−	21.9299i	0.680312	−	1.03725i
$448$	0.258819	+	0.965926i	0.0122281	+	0.0456357i
$449$	−8.30965	−	31.0120i	−0.392157	−	1.46355i	−0.826569	−	0.562835i	$-0.809711\pi$
$449$	−8.30965	−	31.0120i	−0.392157	−	1.46355i	0.434413	−	0.900714i	$-0.356956\pi$
$450$	−3.24559	+	8.23082i	−0.152998	+	0.388005i
$451$	−8.65137	+	14.9846i	−0.407377	+	0.705598i
$452$	−6.08657	−	10.5422i	−0.286288	−	0.495866i
$453$	34.3190	+	1.95489i	1.61245	+	0.0918487i
$454$			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	0.660837	−	0.750529i	$-0.270201\pi$
$457$	18.3393	+	4.91399i	0.857875	+	0.229867i	0.197037	+	0.980396i	$0.436868\pi$
$458$	8.32898	−	4.80874i	0.389188	−	0.224698i
$459$	−34.7334	+	3.17289i	−1.62121	+	0.148098i
$460$	−3.15782	+	3.15782i	−0.147234	+	0.147234i
$461$	−5.62076	+	1.50608i	−0.261785	+	0.0701450i	−0.387324	−	0.921944i	$-0.626601\pi$
$461$	−5.62076	+	1.50608i	−0.261785	+	0.0701450i	0.125539	+	0.992089i	$0.459934\pi$
$462$	−4.79244	−	9.51224i	−0.222965	−	0.442549i
$463$	14.7365	+	14.7365i	0.684863	+	0.684863i	0.961092	−	0.276229i	$-0.0890849\pi$
$463$	14.7365	+	14.7365i	0.684863	+	0.684863i	−0.276229	+	0.961092i	$0.589085\pi$
$464$	6.86770	+	3.96507i	0.318825	+	0.184074i
$465$	−5.97132	+	5.32770i	−0.276913	+	0.247066i
$466$	0.856596	−	3.19686i	0.0396811	−	0.148092i
$467$	7.39814			0.342345			0.171173	−	0.985241i	$-0.445244\pi$
$467$	7.39814			0.342345			0.171173	+	0.985241i	$0.445244\pi$
$468$	−2.69851	−	10.4746i	−0.124739	−	0.484190i
$469$	−5.23578			−0.241766
$470$	−0.898368	+	3.35275i	−0.0414386	+	0.154651i
$471$	14.3743	−	12.8250i	0.662333	−	0.590944i
$472$	−5.98554	−	3.45576i	−0.275507	−	0.159064i
$473$	6.99883	+	6.99883i	0.321806	+	0.321806i
$474$	−3.93645	−	7.81323i	−0.180807	−	0.358874i
$475$	0.461957	−	0.123781i	0.0211960	−	0.00567946i
$476$	4.74629	−	4.74629i	0.217546	−	0.217546i
$477$	−24.2260	−	2.76892i	−1.10923	−	0.126780i
$478$	−14.6643	+	8.46645i	−0.670730	+	0.387246i
$479$	37.4614	+	10.0378i	1.71166	+	0.458637i	0.975829	−	0.218534i	$-0.0701274\pi$
$479$	37.4614	+	10.0378i	1.71166	+	0.458637i	0.735826	+	0.677171i	$0.236794\pi$
$480$	−2.42851	+	0.504682i	−0.110846	+	0.0230355i
$481$	−11.4298	−	15.7509i	−0.521154	−	0.718178i
$482$			27.8707i			1.26947i
$483$	−5.39260	−	0.307175i	−0.245372	−	0.0139770i
$484$	−13.4084	−	23.2240i	−0.609471	−	1.05563i
$485$	−2.91896	+	5.05579i	−0.132543	+	0.229571i
$486$	3.69171	+	15.1450i	0.167459	+	0.686992i
$487$	0.671688	+	2.50677i	0.0304371	+	0.113593i	0.979473	−	0.201575i	$-0.0646059\pi$
$487$	0.671688	+	2.50677i	0.0304371	+	0.113593i	−0.949036	+	0.315168i	$0.897939\pi$
$488$	−2.25771	−	8.42587i	−0.102202	−	0.381421i
$489$	12.0044	−	18.3026i	0.542857	−	0.827674i
$490$	−0.716030	+	1.24020i	−0.0323469	+	0.0560265i
$491$	6.49780	+	11.2545i	0.293241	+	0.507909i	0.974574	−	0.224065i	$-0.0719327\pi$
$491$	6.49780	+	11.2545i	0.293241	+	0.507909i	−0.681333	+	0.731974i	$0.738599\pi$
$492$	−0.277152	+	4.86553i	−0.0124950	+	0.219355i
$493$		−	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
$498$	−3.02250	+	9.16055i	−0.135441	+	0.410494i
$499$	3.36337	−	3.36337i	0.150565	−	0.150565i	−0.627805	−	0.778370i	$-0.716047\pi$
$499$	3.36337	−	3.36337i	0.150565	−	0.150565i	0.778370	+	0.627805i	$0.216047\pi$
$500$	10.9958	−	2.94633i	0.491749	−	0.131764i
$501$	9.75647	−	4.91549i	0.435887	−	0.219608i
$502$	16.4205	+	16.4205i	0.732881	+	0.732881i
$503$	20.9751	+	12.1100i	0.935233	+	0.539957i	0.888463	−	0.458949i	$-0.151774\pi$
$503$	20.9751	+	12.1100i	0.935233	+	0.539957i	0.0467700	+	0.998906i	$0.485107\pi$
$504$	−2.41094	−	1.78532i	−0.107392	−	0.0795247i
$505$	−4.17854	+	15.5945i	−0.185943	+	0.693948i
$506$	−19.1771			−0.852527
$507$	−18.1407	−	13.3385i	−0.805656	−	0.592383i
$508$	6.16631			0.273586
$509$	−0.997603	+	3.72310i	−0.0442180	+	0.165024i	−0.984504	−	0.175361i	$-0.943891\pi$
$509$	−0.997603	+	3.72310i	−0.0442180	+	0.165024i	0.940286	+	0.340385i	$0.110557\pi$
$510$	11.0841	+	12.4232i	0.490814	+	0.550107i
$511$	−3.02272	−	1.74517i	−0.133717	−	0.0772017i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	0.539153	−	0.647558i	0.0238042	−	0.0285904i
$514$	20.9957	−	5.62577i	0.926079	−	0.248142i
$515$	−6.44397	+	6.44397i	−0.283955	+	0.283955i
$516$	2.64740	+	0.873503i	0.116545	+	0.0384538i
$517$	−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	$-0.335992\pi$
$522$	−23.5303	+	3.50809i	−1.02989	+	0.153545i
$523$	10.6683	+	18.4781i	0.466493	+	0.807989i	0.999268	−	0.0382680i	$-0.0121841\pi$
$523$	10.6683	+	18.4781i	0.466493	+	0.807989i	−0.532775	+	0.846257i	$0.678851\pi$
$524$	−2.30017	+	3.98401i	−0.100483	+	0.174042i
$525$	4.27140	+	2.80154i	0.186419	+	0.122269i
$526$	1.88413	+	7.03166i	0.0821518	+	0.306595i
$527$	−5.60497	−	20.9180i	−0.244156	−	0.911204i
$528$	−8.90650	−	5.84162i	−0.387605	−	0.254224i
$529$	6.63758	−	11.4966i	0.288590	−	0.499853i
$530$	5.81983	+	10.0802i	0.252797	+	0.437858i
$531$	20.5079	−	3.05747i	0.889966	−	0.132683i
$532$			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
$537$	37.6090	+	12.4090i	1.62295	+	0.535487i
$538$	−13.2006	+	13.2006i	−0.569119	+	0.569119i
$539$	−5.93999	+	1.59162i	−0.255853	+	0.0685557i
$540$	4.76124	−	5.71857i	0.204891	−	0.246088i
$541$	12.5794	+	12.5794i	0.540830	+	0.540830i	0.923772	−	0.382942i	$-0.125089\pi$
$541$	12.5794	+	12.5794i	0.540830	+	0.540830i	−0.382942	+	0.923772i	$0.625089\pi$
$542$	10.6944	+	6.17444i	0.459365	+	0.265215i
$543$	−20.0341	−	22.4543i	−0.859745	−	0.963607i
$544$	1.73726	−	6.48356i	0.0744846	−	0.277980i
$545$	−22.1447			−0.948576
$546$	−6.23803	+	0.294915i	−0.266963	+	0.0126212i
$547$	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
$549$	21.0309	+	15.5736i	0.897575	+	0.664664i
$550$	15.7064	+	9.06811i	0.669724	+	0.386666i
$551$	0.909323	+	0.909323i	0.0387385	+	0.0387385i
$552$	−4.82372	+	2.43028i	−0.205311	+	0.103440i
$553$	−4.87903	+	1.30733i	−0.207478	+	0.0555934i
$554$	22.0857	−	22.0857i	0.938333	−	0.938333i
$555$	4.19489	−	12.7138i	0.178063	−	0.539671i
$556$	6.76981	−	3.90855i	0.287104	−	0.165760i
$557$	−4.18738	−	1.12200i	−0.177425	−	0.0475408i	0.169013	−	0.985614i	$-0.445942\pi$
$557$	−4.18738	−	1.12200i	−0.177425	−	0.0475408i	−0.346438	+	0.938073i	$0.612609\pi$
$558$	−8.87756	+	3.85632i	−0.375817	+	0.163251i
$559$	5.41898	−	2.07657i	0.229199	−	0.0878294i
$560$			1.43206i			0.0605156i
$561$	−4.06589	+	71.3787i	−0.171662	+	3.01361i
$562$	−6.73289	−	11.6617i	−0.284010	−	0.491919i
$563$	−3.27325	+	5.66944i	−0.137951	+	0.238939i	−0.926721	−	0.375750i	$-0.877385\pi$
$563$	−3.27325	+	5.66944i	−0.137951	+	0.238939i	0.788770	+	0.614689i	$0.210718\pi$
$564$	−2.30244	+	3.51044i	−0.0969501	+	0.147816i
$565$	−4.51191	−	16.8387i	−0.189817	−	0.708408i
$566$	−3.96038	−	14.7804i	−0.166467	−	0.621265i
$567$	8.99474	−	0.307705i	0.377744	−	0.0129224i
$568$	−5.14490	+	8.91123i	−0.215875	+	0.373907i
$569$	6.25227	+	10.8293i	0.262109	+	0.453986i	0.966802	−	0.255526i	$-0.0822487\pi$
$569$	6.25227	+	10.8293i	0.262109	+	0.453986i	−0.704693	+	0.709512i	$0.748915\pi$
$570$	−0.401579	−	0.0228749i	−0.0168203	−	0.000958122i
$571$		−	26.7641i		−	1.12004i	−0.828478	−	0.560022i	$-0.810793\pi$
$571$		−	26.7641i		−	1.12004i	0.828478	−	0.560022i	$-0.189207\pi$
$572$	−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
$576$	−2.98059	−	0.340668i	−0.124191	−	0.0141945i
$577$	4.03263	−	4.03263i	0.167881	−	0.167881i	−0.618166	−	0.786047i	$-0.712124\pi$
$577$	4.03263	−	4.03263i	0.167881	−	0.167881i	0.786047	+	0.618166i	$0.212124\pi$
$578$	−27.0987	+	7.26107i	−1.12716	+	0.302021i
$579$	−14.9176	−	29.6091i	−0.619955	−	1.23051i
$580$	8.03021	+	8.03021i	0.333436	+	0.333436i
$581$	4.82315	+	2.78465i	0.200098	+	0.115527i
$582$	−5.26864	+	4.70076i	−0.218392	+	0.194853i
$583$	−12.9365	+	48.2797i	−0.535776	+	1.99954i
$584$	−3.49034			−0.144431
$585$	0.149617	−	15.4894i	0.00618591	−	0.640407i
$586$	8.32698			0.343984
$587$	2.24740	−	8.38743i	0.0927603	−	0.346186i	−0.903910	−	0.427723i	$-0.859316\pi$
$587$	2.24740	−	8.38743i	0.0927603	−	0.346186i	0.996670	+	0.0815364i	$0.0259827\pi$
$588$	−1.29241	+	1.15311i	−0.0532983	+	0.0475535i
$589$	0.453097	+	0.261595i	0.0186695	+	0.0107789i
$590$	−6.99873	−	6.99873i	−0.288133	−	0.288133i
$591$	18.2613	+	36.2458i	0.751170	+	1.49095i
$592$	−5.21359	+	1.39698i	−0.214277	+	0.0574154i
$593$	−24.5123	+	24.5123i	−1.00660	+	1.00660i	−0.00662184	+	0.999978i	$0.502108\pi$
$593$	−24.5123	+	24.5123i	−1.00660	+	1.00660i	−0.999978	+	0.00662184i	$0.997892\pi$
$594$	31.8214	−	2.90688i	1.30565	−	0.119271i
$595$	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	$0.875892\pi$
$600$	5.09991	+	0.290502i	0.208203	+	0.0118597i
$601$	−17.0251	−	29.4883i	−0.694467	−	1.20285i	−0.970360	−	0.241664i	$-0.922307\pi$
$601$	−17.0251	−	29.4883i	−0.694467	−	1.20285i	0.275893	−	0.961188i	$-0.411026\pi$
$602$	0.804764	−	1.39389i	0.0327997	−	0.0568108i
$603$	5.76195	−	14.6123i	0.234645	−	0.595060i
$604$	−5.13657	−	19.1700i	−0.209004	−	0.780014i
$605$	−9.93946	−	37.0946i	−0.404097	−	1.50811i
$606$	−10.7092	+	16.3280i	−0.435033	+	0.663279i
$607$	17.2735	−	29.9185i	0.701108	−	1.21435i	−0.266970	−	0.963705i	$-0.586022\pi$
$607$	17.2735	−	29.9185i	0.701108	−	1.21435i	0.968078	−	0.250650i	$-0.0806442\pi$
$608$	0.0810817	+	0.140438i	0.00328830	+	0.00569550i
$609$	−0.781134	+	13.7132i	−0.0316531	+	0.555686i
$610$		−	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	−0.284263	−	0.958746i	$-0.591749\pi$
$613$	−25.0018	−	6.69922i	−1.00981	−	0.270579i	−0.725552	+	0.688167i	$0.758415\pi$
$614$	10.2228	−	5.90212i	0.412557	−	0.238190i
$615$	−2.18675	+	6.62758i	−0.0881784	+	0.267250i
$616$	−4.34837	+	4.34837i	−0.175201	+	0.175201i
$617$	−4.60799	+	1.23471i	−0.185511	+	0.0497074i	−0.350378	−	0.936608i	$-0.613947\pi$
$617$	−4.60799	+	1.23471i	−0.185511	+	0.0497074i	0.164868	+	0.986316i	$0.447280\pi$
$618$	−9.84347	+	4.95933i	−0.395963	+	0.199493i
$619$	−26.5606	−	26.5606i	−1.06756	−	1.06756i	−0.997546	−	0.0700151i	$-0.977695\pi$
$619$	−26.5606	−	26.5606i	−1.06756	−	1.06756i	−0.0700151	−	0.997546i	$-0.522305\pi$
$620$	4.00128	+	2.31014i	0.160695	+	0.0927775i
$621$	6.79182	−	14.7120i	0.272546	−	0.590371i
$622$	−6.74743	+	25.1817i	−0.270547	+	1.00970i
$623$	10.6310			0.425923
$624$	−5.25484	+	3.37442i	−0.210362	+	0.135085i
$625$	1.55617			0.0622466
$626$	0.912608	−	3.40590i	0.0364751	−	0.136127i
$627$	−1.14992	−	1.28883i	−0.0459232	−	0.0514710i
$628$	−9.63199	−	5.56103i	−0.384358	−	0.221909i
$629$	25.6182	+	25.6182i	1.02146	+	1.02146i
$630$	−2.67324	−	3.36317i	−0.106504	−	0.133992i
$631$	13.2623	−	3.55363i	0.527964	−	0.141468i	0.0150163	−	0.999887i	$-0.495220\pi$
$631$	13.2623	−	3.55363i	0.527964	−	0.141468i	0.512948	+	0.858420i	$0.328553\pi$
$632$	−3.57170	+	3.57170i	−0.142075	+	0.142075i
$633$	23.0406	+	7.60218i	0.915780	+	0.302159i
$634$	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
$639$	−4.55194	−	30.5320i	−0.180072	−	1.20783i
$640$	0.716030	+	1.24020i	0.0283036	+	0.0490232i
$641$	18.4787	−	32.0060i	0.729863	−	1.26416i	−0.227077	−	0.973877i	$-0.572917\pi$
$641$	18.4787	−	32.0060i	0.729863	−	1.26416i	0.956941	−	0.290284i	$-0.0937497\pi$
$642$	22.3868	+	14.6831i	0.883538	+	0.579497i
$643$	−6.19110	−	23.1055i	−0.244153	−	0.911192i	−0.973807	−	0.227376i	$-0.926986\pi$
$643$	−6.19110	−	23.1055i	−0.244153	−	0.911192i	0.729654	−	0.683817i	$-0.239681\pi$
$644$	0.807119	+	3.01221i	0.0318049	+	0.118698i
$645$	3.33829	+	2.18953i	0.131445	+	0.0862126i
$646$	0.544242	−	0.942655i	0.0214129	−	0.0370883i
$647$	23.0389	+	39.9046i	0.905753	+	1.56881i	0.819903	+	0.572502i	$0.194027\pi$
$647$	23.0389	+	39.9046i	0.905753	+	1.56881i	0.0858500	+	0.996308i	$0.472639\pi$
$648$	7.63582	−	4.76385i	0.299963	−	0.187142i
$649$		−	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	$-0.746591\pi$
$653$	−10.9970	+	6.34912i	−0.430346	+	0.248460i	0.269148	+	0.963099i	$0.413258\pi$
$654$	−25.4349	−	8.39219i	−0.994585	−	0.328161i
$655$	−4.65839	+	4.65839i	−0.182018	+	0.182018i
$656$	2.71779	−	0.728231i	0.106112	−	0.0284326i
$657$	8.19702	−	6.51545i	0.319796	−	0.254192i
$658$	1.71389	+	1.71389i	0.0668142	+	0.0668142i
$659$	−0.264972	−	0.152982i	−0.0103219	−	0.00595932i	0.494830	−	0.868990i	$-0.335230\pi$
$659$	−0.264972	−	0.152982i	−0.0103219	−	0.00595932i	−0.505152	+	0.863030i	$0.668564\pi$
$660$	−10.1549	−	11.3816i	−0.395278	−	0.443030i
$661$	−1.17446	+	4.38314i	−0.0456812	+	0.170484i	−0.984998	−	0.172567i	$-0.944794\pi$
$661$	−1.17446	+	4.38314i	−0.0456812	+	0.170484i	0.939317	+	0.343051i	$0.111461\pi$
$662$	−4.33607			−0.168526
$663$	37.2514	+	19.2213i	1.44673	+	0.746495i
$664$	5.56929			0.216131
$665$	−0.0601049	+	0.224315i	−0.00233077	+	0.00869855i
$666$	9.63631	−	13.0131i	0.373399	−	0.504246i
$667$	21.4167	+	12.3649i	0.829258	+	0.478772i
$668$	−4.46002	−	4.46002i	−0.172563	−	0.172563i
$669$	−45.3797	+	22.8631i	−1.75448	+	0.883940i
$670$	−7.24246	+	1.94061i	−0.279801	+	0.0749724i
$671$	37.9313	−	37.9313i	1.46432	−	1.46432i
$672$	−0.542708	+	1.64483i	−0.0209354	+	0.0634507i
$673$	−12.7661	+	7.37053i	−0.492098	+	0.284113i	−0.725444	−	0.688281i	$-0.758366\pi$
$673$	−12.7661	+	7.37053i	−0.492098	+	0.284113i	0.233346	+	0.972394i	$0.425032\pi$
$674$	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	$0.929271\pi$
$678$	1.19908	−	21.0504i	0.0460503	−	0.808435i
$679$	2.03829	+	3.53043i	0.0782226	+	0.135485i
$680$	4.80619	−	8.32456i	0.184309	−	0.319232i
$681$	−10.8109	+	16.4830i	−0.414276	+	0.631632i
$682$	5.13506	+	19.1643i	0.196632	+	0.733839i
$683$	−6.90186	−	25.7581i	−0.264093	−	0.985607i	−0.962803	−	0.270203i	$-0.912909\pi$
$683$	−6.90186	−	25.7581i	−0.264093	−	0.985607i	0.698711	−	0.715404i	$-0.253757\pi$
$684$	−0.452575	−	0.178460i	−0.0173047	−	0.00682359i
$685$	−8.63455	+	14.9555i	−0.329909	+	0.571419i
$686$	0.500000	+	0.866025i	0.0190901	+	0.0330650i
$687$	16.6310	+	0.947340i	0.634512	+	0.0361433i
$688$		−	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	0.147278	−	0.989095i	$-0.452949\pi$
$691$	−5.77582	−	1.54763i	−0.219723	−	0.0588745i	−0.367001	+	0.930221i	$0.619615\pi$
$692$	−1.82519	+	1.05378i	−0.0693834	+	0.0400585i
$693$	2.09495	−	18.3293i	0.0795806	−	0.696271i
$694$	−3.66066	+	3.66066i	−0.138957	+	0.138957i
$695$	10.8131	−	2.89737i	0.410165	−	0.109903i
$696$	6.18010	+	12.2665i	0.234256	+	0.464961i
$697$	−13.3545	−	13.3545i	−0.505837	−	0.505837i
$698$	8.65553	+	4.99727i	0.327617	+	0.189150i
$699$	4.27742	−	3.81638i	0.161787	−	0.144349i
$700$	0.763310	−	2.84871i	0.0288504	−	0.107671i
$701$	23.1781			0.875426			0.437713	−	0.899115i	$-0.355789\pi$
$701$	23.1781			0.875426			0.437713	+	0.899115i	$0.355789\pi$
$702$	6.04186	−	17.7340i	0.228035	−	0.669328i
$703$	−0.875278			−0.0330117
$704$	−1.59162	+	5.93999i	−0.0599863	+	0.223872i
$705$	−4.48600	+	4.00248i	−0.168953	+	0.150742i
$706$	−26.0270	−	15.0267i	−0.979541	−	0.565538i
$707$	7.97173	+	7.97173i	0.299808	+	0.299808i
$708$	−5.38627	−	10.6909i	−0.202428	−	0.401788i
$709$	−1.41382	+	0.378832i	−0.0530972	+	0.0142273i	−0.285270	−	0.958447i	$-0.592083\pi$
$709$	−1.41382	+	0.378832i	−0.0530972	+	0.0142273i	0.232173	+	0.972675i	$0.425417\pi$
$710$	−10.4197	+	10.4197i	−0.391043	+	0.391043i
$711$	1.72077	−	15.0554i	0.0645338	−	0.564622i
$712$	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
$717$	−29.2812	−	1.66792i	−1.09353	−	0.0622897i
$718$	−3.11045	−	5.38745i	−0.116081	−	0.201058i
$719$	6.54962	−	11.3443i	0.244260	−	0.423070i	−0.717664	−	0.696390i	$-0.754788\pi$
$719$	6.54962	−	11.3443i	0.244260	−	0.423070i	0.961923	+	0.273320i	$0.0881218\pi$
$720$	−3.99668	−	1.57597i	−0.148948	−	0.0587331i
$721$	1.64704	+	6.14683i	0.0613389	+	0.228920i
$722$	−4.91076	−	18.3272i	−0.182759	−	0.682067i
$723$	−26.4752	+	40.3657i	−0.984622	+	1.50122i
$724$	−8.68697	+	15.0463i	−0.322849	+	0.559190i
$725$	−11.6938	−	20.2543i	−0.434297	−	0.752224i
$726$	2.64150	−	46.3727i	0.0980352	−	1.72105i
$727$			38.1313i			1.41421i	0.707108	+	0.707105i	$0.249999\pi$
$727$			38.1313i			1.41421i	−0.707108	+	0.707105i	$0.750001\pi$
$728$	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
$732$	4.73410	−	14.3480i	0.174977	−	0.530318i
$733$	9.76791	−	9.76791i	0.360786	−	0.360786i	−0.503316	−	0.864102i	$-0.667887\pi$
$733$	9.76791	−	9.76791i	0.360786	−	0.360786i	0.864102	+	0.503316i	$0.167887\pi$
$734$	4.54304	−	1.21730i	0.167687	−	0.0449315i
$735$	−2.21514	+	1.11603i	−0.0817068	+	0.0411654i
$736$	2.20509	+	2.20509i	0.0812807	+	0.0812807i
$737$	−27.8839	−	16.0988i	−1.02712	−	0.593006i
$738$	−5.02331	+	6.78357i	−0.184911	+	0.249707i
$739$	−1.19404	+	4.45623i	−0.0439236	+	0.163925i	−0.984404	−	0.175923i	$-0.943709\pi$
$739$	−1.19404	+	4.45623i	−0.0439236	+	0.163925i	0.940480	+	0.339848i	$0.110376\pi$
$740$	−7.72956			−0.284144
$741$	−0.964733	+	0.308011i	−0.0354404	+	0.0113151i
$742$	8.12791			0.298385
$743$	−1.49496	+	5.57927i	−0.0548448	+	0.204683i	−0.987911	−	0.155021i	$-0.950456\pi$
$743$	−1.49496	+	5.57927i	−0.0548448	+	0.204683i	0.933066	+	0.359704i	$0.117122\pi$
$744$	3.72031	+	4.16974i	0.136393	+	0.152870i
$745$	−18.7786	−	10.8418i	−0.687994	−	0.397213i
$746$	−7.48941	−	7.48941i	−0.274207	−	0.274207i
$747$	−13.0794	+	10.3963i	−0.478551	+	0.380379i
$748$	39.8708	−	10.6834i	1.45782	−	0.390622i
$749$	10.9298	−	10.9298i	0.399367	−	0.399367i
$750$	18.7243	+	6.17804i	0.683715	+	0.225590i
$751$	−38.9228	+	22.4721i	−1.42031	+	0.820018i	−0.996325	−	0.0856499i	$-0.972703\pi$
$751$	−38.9228	+	22.4721i	−1.42031	+	0.820018i	−0.423988	+	0.905668i	$0.639370\pi$
$752$	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
$756$	−1.79588	−	4.87594i	−0.0653155	−	0.177336i
$757$	21.2721	+	36.8443i	0.773147	+	1.33913i	0.935830	+	0.352451i	$0.114652\pi$
$757$	21.2721	+	36.8443i	0.773147	+	1.33913i	−0.162683	+	0.986678i	$0.552015\pi$
$758$	−11.1555	+	19.3219i	−0.405185	+	0.701802i
$759$	−27.7746	−	18.2169i	−1.00815	−	0.661231i
$760$	0.0601049	+	0.224315i	0.00218023	+	0.00813675i
$761$	10.7212	+	40.0122i	0.388644	+	1.45044i	0.832341	+	0.554264i	$0.187000\pi$
$761$	10.7212	+	40.0122i	0.388644	+	1.45044i	−0.443697	+	0.896177i	$0.646333\pi$
$762$	8.93080	+	5.85755i	0.323529	+	0.212197i
$763$	−7.73178	+	13.3918i	−0.279909	+	0.484817i
$764$	7.09748	+	12.2932i	0.256778	+	0.444752i
$765$	4.25227	+	28.5219i	0.153741	+	1.03121i
$766$		−	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	0.974825	−	0.222971i	$-0.0715755\pi$
$769$	47.3522	+	12.6880i	1.70756	+	0.457540i	0.732738	+	0.680511i	$0.238242\pi$
$770$	−7.62665	+	4.40325i	−0.274845	+	0.158682i
$771$	35.7526	+	11.7965i	1.28760	+	0.424839i
$772$	−13.5354	+	13.5354i	−0.487148	+	0.487148i
$773$	−11.6101	+	3.11093i	−0.417588	+	0.111892i	−0.461494	−	0.887143i	$-0.652686\pi$
$773$	−11.6101	+	3.11093i	−0.417588	+	0.111892i	0.0439062	+	0.999036i	$0.486020\pi$
$774$	3.00452	+	3.77996i	0.107995	+	0.135868i
$775$	−6.72818	−	6.72818i	−0.241683	−	0.241683i
$776$	3.53043	+	2.03829i	0.126735	+	0.0731705i
$777$	−6.22393	−	6.97582i	−0.223282	−	0.250256i
$778$	3.78874	−	14.1398i	0.135833	−	0.506936i
$779$	0.456274			0.0163477
$780$	−8.51953	+	2.72004i	−0.305048	+	0.0973929i
$781$	−63.2775			−2.26425
$782$	5.41760	−	20.2188i	0.193733	−	0.723022i
$783$	−37.4119	−	17.2713i	−1.33699	−	0.617226i
$784$	0.866025	+	0.500000i	0.0309295	+	0.0178571i
$785$	−11.2624	−	11.2624i	−0.401973	−	0.401973i
$786$	−7.11591	+	3.58513i	−0.253816	+	0.127877i
$787$	−32.8961	+	8.81448i	−1.17262	+	0.314202i	−0.791995	−	0.610528i	$-0.790957\pi$
$787$	−32.8961	+	8.81448i	−1.17262	+	0.314202i	−0.380624	+	0.924730i	$0.624291\pi$
$788$	16.5692	−	16.5692i	0.590253	−	0.590253i
$789$	−3.95075	+	11.9739i	−0.140651	+	0.426282i
$790$	−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
$795$	−1.14653	+	20.1279i	−0.0406632	+	0.713861i
$796$	3.52247	+	6.10110i	0.124851	+	0.216248i
$797$	18.1684	−	31.4686i	0.643557	−	1.11467i	−0.341076	−	0.940036i	$-0.610791\pi$
$797$	18.1684	−	31.4686i	0.643557	−	1.11467i	0.984633	−	0.174638i	$-0.0558755\pi$
$798$	−0.154044	+	0.234865i	−0.00545309	+	0.00831412i
$799$	−4.21078	−	15.7148i	−0.148967	−	0.555951i
$800$	−0.763310	−	2.84871i	−0.0269871	−	0.100717i
$801$	−11.6994	+	29.6697i	−0.413377	+	1.04833i
$802$	−9.99682	+	17.3150i	−0.353000	+	0.611414i
$803$	−10.7320	−	18.5883i	−0.378723	−	0.655967i
$804$	−9.05396	−	0.515734i	−0.319308	−	0.0181885i
$805$			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	$-0.594103\pi$
$809$	11.1337	−	6.42803i	0.391439	−	0.225998i	0.682784	+	0.730621i	$0.260769\pi$
$810$	12.3280	−	3.75949i	0.433163	−	0.132095i
$811$	17.4981	−	17.4981i	0.614440	−	0.614440i	−0.329660	−	0.944100i	$-0.606934\pi$
$811$	17.4981	−	17.4981i	0.614440	−	0.614440i	0.944100	+	0.329660i	$0.106934\pi$
$812$	7.65992	−	2.05247i	0.268811	−	0.0720276i
$813$	9.62371	+	19.1015i	0.337518	+	0.669920i
$814$	−23.4704	−	23.4704i	−0.822637	−	0.822637i
$815$	−15.6726	−	9.04856i	−0.548986	−	0.316957i
$816$	8.67504	−	7.74000i	0.303687	−	0.270954i
$817$	0.0675534	−	0.252113i	0.00236339	−	0.00882031i
$818$	−16.8591			−0.589466
$819$	−9.31482	−	5.49855i	−0.325486	−	0.192135i
$820$	4.02934			0.140711
$821$	10.5371	−	39.3250i	0.367747	−	1.37245i	−0.495911	−	0.868374i	$-0.665166\pi$
$821$	10.5371	−	39.3250i	0.367747	−	1.37245i	0.863658	−	0.504078i	$-0.168168\pi$
$822$	−15.5851	+	13.9053i	−0.543594	+	0.485002i
$823$	−13.8783	−	8.01263i	−0.483766	−	0.279303i	0.238218	−	0.971212i	$-0.423437\pi$
$823$	−13.8783	−	8.01263i	−0.483766	−	0.279303i	−0.721985	+	0.691909i	$0.756770\pi$
$824$	4.49979	+	4.49979i	0.156758	+	0.156758i
$825$	14.1339	+	28.0535i	0.492079	+	0.976699i
$826$	−6.67601	+	1.78883i	−0.232288	+	0.0622414i
$827$	36.5847	−	36.5847i	1.27217	−	1.27217i	0.327230	−	0.944945i	$-0.393885\pi$
$827$	36.5847	−	36.5847i	1.27217	−	1.27217i	0.944945	−	0.327230i	$-0.106115\pi$
$828$	−9.29489	−	1.06236i	−0.323020	−	0.0369197i
$829$	−40.7093	+	23.5035i	−1.41389	+	0.816311i	−0.995752	−	0.0920709i	$-0.970651\pi$
$829$	−40.7093	+	23.5035i	−1.41389	+	0.816311i	−0.418140	+	0.908382i	$0.637318\pi$
$830$	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
$834$	13.5177	+	0.770000i	0.468080	+	0.0266629i
$835$	−4.51630	−	7.82246i	−0.156293	−	0.270708i
$836$	−0.498614	+	0.863625i	−0.0172449	+	0.0298691i
$837$	−16.5208	−	2.84785i	−0.571042	−	0.0984363i
$838$	8.19346	+	30.5784i	0.283038	+	1.05631i
$839$	0.387495	+	1.44615i	0.0133778	+	0.0499267i	0.972292	−	0.233769i	$-0.0751060\pi$
$839$	0.387495	+	1.44615i	0.0133778	+	0.0499267i	−0.958914	+	0.283696i	$0.908439\pi$
$840$	−1.36036	+	2.07408i	−0.0469367	+	0.0715627i
$841$	16.9435	−	29.3471i	0.584260	−	1.01197i
$842$	7.72230	+	13.3754i	0.266128	+	0.460947i
$843$	1.32640	−	23.2857i	0.0456838	−	0.802001i
$844$		−	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
$849$	8.30438	−	25.1688i	0.285005	−	0.863790i
$850$	−13.9978	+	13.9978i	−0.480120	+	0.480120i
$851$	−16.2584	+	4.35643i	−0.557332	+	0.149337i
$852$	−15.9165	+	8.01904i	−0.545291	+	0.274728i
$853$	−23.8323	−	23.8323i	−0.816004	−	0.816004i	0.169522	−	0.985526i	$-0.445777\pi$
$853$	−23.8323	−	23.8323i	−0.816004	−	0.816004i	−0.985526	+	0.169522i	$0.945777\pi$
$854$	−7.55443	−	4.36155i	−0.258507	−	0.149249i
$855$	−0.559886	−	0.414602i	−0.0191477	−	0.0141791i
$856$	4.00059	−	14.9304i	0.136737	−	0.510311i
$857$	−18.8568			−0.644134			−0.322067	−	0.946717i	$-0.604378\pi$
$857$	−18.8568			−0.644134			−0.322067	+	0.946717i	$0.604378\pi$
$858$	−34.1284	−	17.6099i	−1.16512	−	0.601191i
$859$	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
$861$	3.24447	+	3.63642i	0.110571	+	0.123929i
$862$	16.1560	+	9.32765i	0.550274	+	0.317701i
$863$	17.6792	+	17.6792i	0.601806	+	0.601806i	0.940791	−	0.338986i	$-0.110084\pi$
$863$	17.6792	+	17.6792i	0.601806	+	0.601806i	−0.338986	+	0.940791i	$0.610084\pi$
$864$	−3.99325	−	3.32475i	−0.135853	−	0.113110i
$865$	−2.91530	+	0.781152i	−0.0991232	+	0.0265600i
$866$	14.7481	−	14.7481i	0.501161	−	0.501161i
$867$	−46.1451	−	15.2255i	−1.56717	−	0.517083i
$868$	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
$873$	−12.0961	+	1.80338i	−0.409390	+	0.0610351i
$874$	0.252851	+	0.437950i	0.00855280	+	0.0148139i
$875$	5.69187	−	9.85860i	0.192420	−	0.333282i
$876$	−5.05513	−	3.31557i	−0.170797	−	0.112023i
$877$	−8.52826	−	31.8279i	−0.287979	−	1.07475i	−0.946635	−	0.322308i	$-0.895541\pi$
$877$	−8.52826	−	31.8279i	−0.287979	−	1.07475i	0.658656	−	0.752444i	$-0.271125\pi$
$878$	−10.3965	−	38.8001i	−0.350864	−	1.30944i
$879$	12.0601	+	7.91004i	0.406778	+	0.266799i
$880$	−4.40325	+	7.62665i	−0.148433	+	0.257094i
$881$	−7.26029	−	12.5752i	−0.244605	−	0.423669i	0.717415	−	0.696646i	$-0.245325\pi$
$881$	−7.26029	−	12.5752i	−0.244605	−	0.423669i	−0.962021	+	0.272977i	$0.911992\pi$
$882$	−2.96720	+	0.442374i	−0.0999110	+	0.0148955i
$883$		−	20.5426i		−	0.691314i	−0.938361	−	0.345657i	$-0.887656\pi$
$883$		−	20.5426i		−	0.691314i	0.938361	−	0.345657i	$-0.112344\pi$
$884$	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	$-0.698757\pi$
$887$	−5.19173	+	2.99745i	−0.174321	+	0.100644i	0.410301	+	0.911950i	$0.365424\pi$
$888$	−8.87799	−	2.92927i	−0.297926	−	0.0982999i
$889$	4.36024	−	4.36024i	0.146238	−	0.146238i
$890$	14.7055	−	3.94032i	0.492929	−	0.132080i
$891$	48.8489	+	26.0180i	1.63650	+	0.871635i
$892$	20.7446	+	20.7446i	0.694582	+	0.694582i
$893$	0.340393	+	0.196526i	0.0113908	+	0.00657648i
$894$	−17.4599	−	19.5692i	−0.583947	−	0.654491i
$895$	8.47476	−	31.6282i	0.283280	−	1.05722i
$896$	1.00000			0.0334077
$897$	−16.3870	+	10.5230i	−0.547147	+	0.351353i
$898$	−32.1060			−1.07139
$899$	6.62193	−	24.7134i	0.220854	−	0.824237i
$900$	7.11035	+	5.26529i	0.237012	+	0.175510i
$901$	−47.2476	−	27.2784i	−1.57404	−	0.908775i
$902$	12.2349	+	12.2349i	0.407377	+	0.407377i
$903$	2.48965	−	1.25433i	0.0828505	−	0.0417416i
$904$	−11.7584	+	3.15064i	−0.391077	+	0.104789i
$905$	−17.5932	+	17.5932i	−0.584817	+	0.584817i
$906$	10.7707	−	32.6436i	0.357832	−	1.08451i
$907$	−15.4295	+	8.90824i	−0.512329	+	0.295793i	−0.733790	−	0.679376i	$-0.762251\pi$
$907$	−15.4295	+	8.90824i	−0.512329	+	0.295793i	0.221462	+	0.975169i	$0.428917\pi$
$908$	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	$-0.129860\pi$
$912$	−0.0159734	+	0.280421i	−0.000528932	+	0.00928565i
$913$	17.1243	+	29.6601i	0.566731	+	0.981606i
$914$	9.49310	−	16.4425i	0.314004	−	0.543871i
$915$	11.8665	−	18.0924i	0.392295	−	0.598118i
$916$	−2.48919	−	9.28977i	−0.0822451	−	0.306943i
$917$	1.19066	+	4.44359i	0.0393189	+	0.146740i
$918$	−5.92488	+	34.3711i	−0.195550	+	1.13441i
$919$	−12.9296	+	22.3947i	−0.426508	+	0.738734i	−0.996560	−	0.0828750i	$-0.973590\pi$
$919$	−12.9296	+	22.3947i	−0.426508	+	0.738734i	0.570052	+	0.821609i	$0.306923\pi$
$920$	2.23292	+	3.86752i	0.0736171	+	0.127509i
$921$	20.4124	+	1.16274i	0.672613	+	0.0383136i
$922$			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
$927$	−18.9675	−	2.16790i	−0.622975	−	0.0712032i
$928$	5.60745	−	5.60745i	0.184074	−	0.184074i
$929$	−15.5339	+	4.16230i	−0.509651	+	0.136561i	−0.504476	−	0.863426i	$-0.668314\pi$
$929$	−15.5339	+	4.16230i	−0.509651	+	0.136561i	−0.00517576	+	0.999987i	$0.501648\pi$
$930$	3.60067	+	7.14676i	0.118071	+	0.234352i
$931$	0.114667	+	0.114667i	0.00375805	+	0.00375805i
$932$	−2.86623	−	1.65482i	−0.0938864	−	0.0542053i
$933$	−33.6933	+	30.0617i	−1.10307	+	0.984175i
$934$	1.91478	−	7.14606i	0.0626535	−	0.233826i
$935$	59.1116			1.93316
$936$	−10.8161	−	0.104477i	−0.353537	−	0.00341494i
$937$	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
$939$	4.55711	−	4.06592i	0.148716	−	0.132686i
$940$	3.00600	+	1.73551i	0.0980448	+	0.0566062i
$941$	22.8371	+	22.8371i	0.744469	+	0.744469i	0.973435	−	0.228966i	$-0.0735343\pi$
$941$	22.8371	+	22.8371i	0.744469	+	0.744469i	−0.228966	+	0.973435i	$0.573534\pi$
$942$	−8.66763	−	17.2039i	−0.282407	−	0.560532i
$943$	8.47536	−	2.27096i	0.275996	−	0.0739528i
$944$	−4.88718	+	4.88718i	−0.159064	+	0.159064i
$945$	−0.676934	−	7.41035i	−0.0220207	−	0.241059i
$946$	8.57178	−	4.94892i	0.278693	−	0.160903i
$947$	6.01194	+	1.61090i	0.195362	+	0.0523471i	0.355173	−	0.934801i	$-0.384422\pi$
$947$	6.01194	+	1.61090i	0.195362	+	0.0523471i	−0.159811	+	0.987148i	$0.551089\pi$
$948$	−8.56583	+	1.78011i	−0.278205	+	0.0578152i
$949$	−12.5164	+	1.30822i	−0.406300	+	0.0424668i
$950$		−	0.478253i		−	0.0155166i
$951$	10.1083	+	0.575793i	0.327784	+	0.0186714i
$952$	−3.35614	−	5.81300i	−0.108773	−	0.188400i
$953$	−13.2498	+	22.9493i	−0.429203	+	0.743401i	−0.996803	−	0.0799036i	$-0.974539\pi$
$953$	−13.2498	+	22.9493i	−0.429203	+	0.743401i	0.567600	+	0.823305i	$0.307872\pi$
$954$	−8.94473	+	22.6839i	−0.289596	+	0.734418i
$955$	5.26128	+	19.6354i	0.170251	+	0.635386i
$956$	4.38255	+	16.3559i	0.141742	+	0.528988i
$957$	−46.3248	+	70.6297i	−1.49747	+	2.28313i
$958$	19.3915	−	33.5870i	0.626509	−	1.08515i
$959$	6.02946	+	10.4433i	0.194701	+	0.337233i
$960$	−0.141061	+	2.47639i	−0.00455271	+	0.0799250i
$961$			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
$966$	−1.69242	+	5.12935i	−0.0544526	+	0.165034i
$967$	6.87652	−	6.87652i	0.221134	−	0.221134i	−0.587842	−	0.808976i	$-0.700022\pi$
$967$	6.87652	−	6.87652i	0.221134	−	0.221134i	0.808976	+	0.587842i	$0.200022\pi$
$968$	−25.9030	+	6.94068i	−0.832553	+	0.223082i
$969$	1.68369	−	0.848276i	0.0540880	−	0.0272506i
$970$	4.12803	+	4.12803i	0.132543	+	0.132543i
$971$	−9.08309	−	5.24412i	−0.291490	−	0.168292i	0.347124	−	0.937819i	$-0.387158\pi$
$971$	−9.08309	−	5.24412i	−0.291490	−	0.168292i	−0.638614	+	0.769527i	$0.720492\pi$
$972$	15.5844	+	0.353900i	0.499871	+	0.0113513i
$973$	2.02322	−	7.55074i	0.0648613	−	0.242066i
$974$	2.59520			0.0831557
$975$	18.3972	−	0.869765i	0.589183	−	0.0278548i
$976$	−8.72310			−0.279220
$977$	−0.208291	+	0.777353i	−0.00666383	+	0.0248697i	−0.969178	−	0.246363i	$-0.920765\pi$
$977$	−0.208291	+	0.777353i	−0.00666383	+	0.0248697i	0.962514	+	0.271232i	$0.0874312\pi$
$978$	−14.5720	−	16.3324i	−0.465962	−	0.522253i
$979$	56.6170	+	32.6879i	1.80949	+	1.04471i
$980$	1.01262	+	1.01262i	0.0323469	+	0.0323469i
$981$	−28.8660	−	36.3160i	−0.921620	−	1.15948i
$982$	12.5528	−	3.36351i	0.400575	−	0.107334i
$983$	40.7061	−	40.7061i	1.29832	−	1.29832i	0.368821	−	0.929500i	$-0.379762\pi$
$983$	40.7061	−	40.7061i	1.29832	−	1.29832i	0.929500	−	0.368821i	$-0.120238\pi$
$984$	4.62801	+	1.52700i	0.147535	+	0.0486790i
$985$	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
$990$	−3.89577	−	26.1307i	−0.123816	−	0.830487i
$991$	−2.48775	−	4.30891i	−0.0790261	−	0.136877i	0.823804	−	0.566875i	$-0.191848\pi$
$991$	−2.48775	−	4.30891i	−0.0790261	−	0.136877i	−0.902830	+	0.429998i	$0.858514\pi$
$992$	1.61316	−	2.79408i	0.0512179	−	0.0887120i
$993$	−6.28002	−	4.11896i	−0.199290	−	0.130711i
$994$	2.66320	+	9.93919i	0.0844715	+	0.315252i
$995$	2.61117	+	9.74501i	0.0827796	+	0.308938i
$996$	8.06613	+	5.29043i	0.255585	+	0.167634i
$997$	−7.11658	+	12.3263i	−0.225384	+	0.390377i	−0.956435	−	0.291946i	$-0.905697\pi$
$997$	−7.11658	+	12.3263i	−0.225384	+	0.390377i	0.731050	+	0.682324i	$0.239030\pi$
$998$	−2.37826	−	4.11927i	−0.0752825	−	0.130393i
$999$	26.3179	−	9.69327i	0.832663	−	0.306682i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bu.a.197.13	✓	56	1.1	even	1	trivial
546.2.bu.a.449.13	yes	56	39.20	even	12	inner
546.2.bu.b.197.1	yes	56	3.2	odd	2
546.2.bu.b.449.1	yes	56	13.7	odd	12

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)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(1.29241 - 1.15311i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.01262 - 1.01262i) q^{5} +(-0.779319 - 1.54682i) q^{6} +(-0.965926 + 0.258819i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.340668 - 2.98059i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(1.29241 - 1.15311i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.01262 - 1.01262i) q^{5} +(-0.779319 - 1.54682i) q^{6} +(-0.965926 + 0.258819i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.340668 - 2.98059i) 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} +(-2.47639 - 0.141061i) q^{15} +(0.500000 + 0.866025i) q^{16} +(3.35614 - 5.81300i) q^{17} +(-2.79086 - 1.10050i) q^{18} +(0.0419710 + 0.156638i) q^{19} +(0.370644 + 1.38326i) q^{20} +(-0.949929 + 1.44832i) q^{21} +(-3.07476 + 5.32565i) q^{22} +(1.55923 + 2.70067i) q^{23} +(-0.0985019 + 1.72925i) 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} +(-0.777190 + 2.35550i) q^{30} +(2.28135 - 2.28135i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-9.51224 + 4.79244i) q^{33} +(-4.74629 - 4.74629i) q^{34} +(1.24020 + 0.716030i) q^{35} +(-1.78532 + 2.41094i) q^{36} +(-1.39698 + 5.21359i) q^{37} +0.162163 q^{38} +(0.294915 + 6.23803i) q^{39} +1.43206 q^{40} +(0.728231 - 2.71779i) q^{41} +(1.15311 + 1.29241i) q^{42} +(-1.39389 - 0.804764i) q^{43} +(4.34837 + 4.34837i) q^{44} +(-3.36317 + 2.67324i) q^{45} +(3.01221 - 0.807119i) q^{46} +(1.71389 - 1.71389i) q^{47} +(1.64483 + 0.542708i) 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} +(-4.87594 + 1.79588i) q^{54} +(4.40325 + 7.62665i) q^{55} +(0.500000 - 0.866025i) q^{56} +(0.234865 + 0.154044i) q^{57} +(-2.05247 - 7.65992i) q^{58} +(1.78883 + 6.67601i) q^{59} +(2.07408 + 1.36036i) q^{60} +(-4.36155 + 7.55443i) q^{61} +(-1.61316 - 2.79408i) q^{62} +(0.442374 + 2.96720i) 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} +(5.12935 + 1.69242i) q^{69} +(1.01262 - 1.01262i) q^{70} +(9.93919 - 2.66320i) q^{71} +(1.86671 + 2.34849i) q^{72} +(2.46804 + 2.46804i) q^{73} +(4.67438 + 2.69875i) q^{74} +(-3.40076 - 3.81159i) q^{75} +(0.0419710 - 0.156638i) q^{76} +6.14953 q^{77} +(6.10180 + 1.32966i) q^{78} +5.05115 q^{79} +(0.370644 - 1.38326i) q^{80} +(-8.76789 - 2.03079i) q^{81} +(-2.43671 - 1.40683i) q^{82} +(-3.93809 - 3.93809i) q^{83} +(1.54682 - 0.779319i) q^{84} +(-9.28484 + 2.48787i) q^{85} +(-1.13811 + 1.13811i) q^{86} +(4.30375 - 13.0437i) 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} +(0.317799 - 5.57911i) q^{93} +(-1.21190 - 2.09907i) q^{94} +(0.116114 - 0.201115i) q^{95} +(0.949929 - 1.44832i) q^{96} +(-1.05510 - 3.93768i) q^{97} +(-0.258819 - 0.965926i) q^{98} +(-6.76753 + 17.1625i) 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	\( 56 q - 8 q^{6} + 24 q^{9} + 24 q^{10} - 8 q^{11} + 24 q^{13} - 4 q^{15} + 28 q^{16} + 4 q^{17} + 8 q^{19} + 4 q^{21} + 8 q^{23} + 8 q^{24} + 4 q^{26} - 24 q^{27} - 16 q^{30} - 8 q^{31} - 32 q^{33} - 24 q^{34} - 24 q^{35} - 12 q^{36} - 8 q^{37} - 60 q^{39} + 28 q^{41} - 8 q^{44} - 40 q^{45} - 20 q^{46} - 64 q^{50} + 8 q^{54} + 8 q^{55} + 28 q^{56} + 40 q^{57} + 4 q^{58} + 8 q^{59} + 4 q^{60} + 8 q^{61} + 32 q^{62} + 24 q^{65} + 32 q^{66} - 56 q^{69} + 112 q^{71} + 16 q^{72} + 8 q^{73} - 48 q^{74} - 40 q^{75} + 8 q^{76} - 8 q^{78} + 16 q^{79} + 12 q^{81} + 4 q^{83} - 4 q^{84} + 32 q^{85} + 16 q^{86} + 144 q^{87} - 88 q^{89} + 8 q^{90} - 8 q^{91} - 76 q^{93} - 8 q^{94} + 48 q^{95} - 4 q^{96} - 64 q^{97} - 40 q^{99}+O(q^{100}) \) 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^19 + 4 * q^21 + 8 * q^23 + 8 * q^24 + 4 * q^26 - 24 * q^27 - 16 * q^30 - 8 * q^31 - 32 * q^33 - 24 * q^34 - 24 * q^35 - 12 * q^36 - 8 * q^37 - 60 * q^39 + 28 * q^41 - 8 * q^44 - 40 * q^45 - 20 * q^46 - 64 * q^50 + 8 * q^54 + 8 * q^55 + 28 * q^56 + 40 * q^57 + 4 * q^58 + 8 * q^59 + 4 * q^60 + 8 * q^61 + 32 * q^62 + 24 * q^65 + 32 * q^66 - 56 * q^69 + 112 * q^71 + 16 * q^72 + 8 * q^73 - 48 * q^74 - 40 * q^75 + 8 * q^76 - 8 * q^78 + 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 - 76 * q^93 - 8 * q^94 + 48 * q^95 - 4 * q^96 - 64 * q^97 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more