LMFDB - Embedded newform 429.2.n.d.157.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(157,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8, 0]))

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

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

chi := DirichletCharacter("429.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.n (of order $5$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			157.7
Character	$\chi$	$=$	429.157
Dual form			429.2.n.d.235.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30744 - 0.949910i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.189034 - 0.581786i) q^{4} +(1.69854 + 1.23406i) q^{5} +(1.30744 + 0.949910i) q^{6} +(1.36281 - 4.19429i) q^{7} +(0.693300 + 2.13376i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(1.30744 - 0.949910i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.189034 - 0.581786i) q^{4} +(1.69854 + 1.23406i) q^{5} +(1.30744 + 0.949910i) q^{6} +(1.36281 - 4.19429i) q^{7} +(0.693300 + 2.13376i) q^{8} +(-0.809017 + 0.587785i) q^{9} +3.39298 q^{10} +(-3.28357 - 0.467064i) q^{11} +0.611726 q^{12} +(0.809017 - 0.587785i) q^{13} +(-2.20241 - 6.77832i) q^{14} +(-0.648783 + 1.99675i) q^{15} +(3.92312 + 2.85031i) q^{16} +(5.73404 + 4.16602i) q^{17} +(-0.499397 + 1.53699i) q^{18} +(0.292494 + 0.900203i) q^{19} +(1.03904 - 0.754906i) q^{20} +4.41014 q^{21} +(-4.73674 + 2.50844i) q^{22} -4.97977 q^{23} +(-1.81508 + 1.31874i) q^{24} +(-0.182961 - 0.563098i) q^{25} +(0.499397 - 1.53699i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-2.18256 - 1.58572i) q^{28} +(1.54168 - 4.74480i) q^{29} +(1.04849 + 3.22691i) q^{30} +(-6.38023 + 4.63551i) q^{31} +3.34965 q^{32} +(-0.570475 - 3.26719i) q^{33} +11.4543 q^{34} +(7.49077 - 5.44237i) q^{35} +(0.189034 + 0.581786i) q^{36} +(2.40088 - 7.38914i) q^{37} +(1.23753 + 0.899118i) q^{38} +(0.809017 + 0.587785i) q^{39} +(-1.45559 + 4.47984i) q^{40} +(-0.153644 - 0.472869i) q^{41} +(5.76598 - 4.18923i) q^{42} -11.1839 q^{43} +(-0.892438 + 1.82205i) q^{44} -2.09951 q^{45} +(-6.51075 + 4.73034i) q^{46} +(0.374620 + 1.15296i) q^{47} +(-1.49850 + 4.61190i) q^{48} +(-10.0717 - 7.31752i) q^{49} +(-0.774103 - 0.562419i) q^{50} +(-2.19021 + 6.74077i) q^{51} +(-0.189034 - 0.581786i) q^{52} +(-0.886832 + 0.644321i) q^{53} -1.61608 q^{54} +(-5.00088 - 4.84545i) q^{55} +9.89444 q^{56} +(-0.765759 + 0.556356i) q^{57} +(-2.49148 - 7.66799i) q^{58} +(-0.0285215 + 0.0877803i) q^{59} +(1.03904 + 0.754906i) q^{60} +(-7.82276 - 5.68357i) q^{61} +(-3.93845 + 12.1213i) q^{62} +(1.36281 + 4.19429i) q^{63} +(-3.46678 + 2.51876i) q^{64} +2.09951 q^{65} +(-3.84940 - 3.72976i) q^{66} +8.50741 q^{67} +(3.50766 - 2.54847i) q^{68} +(-1.53883 - 4.73604i) q^{69} +(4.62397 - 14.2311i) q^{70} +(-13.0623 - 9.49035i) q^{71} +(-1.81508 - 1.31874i) q^{72} +(-0.962901 + 2.96350i) q^{73} +(-3.88002 - 11.9415i) q^{74} +(0.478999 - 0.348013i) q^{75} +0.579017 q^{76} +(-6.43388 + 13.1357i) q^{77} +1.61608 q^{78} +(-1.97455 + 1.43459i) q^{79} +(3.14611 + 9.68272i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-0.650064 - 0.472299i) q^{82} +(11.1230 + 8.08132i) q^{83} +(0.833665 - 2.56576i) q^{84} +(4.59835 + 14.1523i) q^{85} +(-14.6222 + 10.6237i) q^{86} +4.98898 q^{87} +(-1.27990 - 7.33017i) q^{88} +7.34531 q^{89} +(-2.74498 + 1.99434i) q^{90} +(-1.36281 - 4.19429i) q^{91} +(-0.941345 + 2.89716i) q^{92} +(-6.38023 - 4.63551i) q^{93} +(1.58500 + 1.15157i) q^{94} +(-0.614092 + 1.88998i) q^{95} +(1.03510 + 3.18571i) q^{96} +(6.01556 - 4.37056i) q^{97} -20.1191 q^{98} +(2.93100 - 1.55217i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 3 q^{2} - 9 q^{3} - 11 q^{4} + 3 q^{6} + q^{7} - q^{8} - 9 q^{9}+O(q^{10}) $ 36 * q + 3 * q^2 - 9 * q^3 - 11 * q^4 + 3 * q^6 + q^7 - q^8 - 9 * q^9	\( 36 q + 3 q^{2} - 9 q^{3} - 11 q^{4} + 3 q^{6} + q^{7} - q^{8} - 9 q^{9} + 6 q^{10} - 10 q^{11} + 54 q^{12} + 9 q^{13} - 5 q^{14} - 10 q^{15} - 13 q^{16} - 2 q^{18} + 10 q^{19} + 37 q^{20} - 14 q^{21} - 9 q^{22} + 18 q^{23} + 4 q^{24} - 31 q^{25} + 2 q^{26} - 9 q^{27} + 12 q^{28} + 10 q^{29} + q^{30} - 28 q^{31} - 74 q^{32} + 5 q^{33} + 40 q^{34} - 14 q^{35} - 11 q^{36} - 26 q^{37} + 7 q^{38} + 9 q^{39} - 72 q^{40} + 26 q^{41} - 5 q^{42} + 4 q^{43} - 68 q^{44} + 20 q^{45} - 57 q^{46} - 28 q^{48} - 18 q^{49} + 11 q^{50} - 5 q^{51} + 11 q^{52} + 11 q^{53} - 2 q^{54} - 32 q^{55} + 72 q^{56} + 50 q^{58} + 55 q^{59} + 37 q^{60} + 14 q^{61} - 50 q^{62} + q^{63} - q^{64} - 20 q^{65} - 14 q^{66} + 104 q^{67} - 9 q^{68} + 8 q^{69} + 44 q^{70} - 8 q^{71} + 4 q^{72} - 3 q^{73} + 69 q^{74} - 21 q^{75} - 52 q^{76} + 2 q^{77} + 2 q^{78} - 19 q^{79} - 159 q^{80} - 9 q^{81} + 58 q^{82} + 12 q^{83} - 8 q^{84} + 63 q^{86} - 97 q^{88} + 118 q^{89} - 4 q^{90} - q^{91} + 98 q^{92} - 28 q^{93} - 99 q^{94} - 45 q^{95} + q^{96} + 50 q^{97} - 186 q^{98}+O(q^{100}) \) 36 * q + 3 * q^2 - 9 * q^3 - 11 * q^4 + 3 * q^6 + q^7 - q^8 - 9 * q^9 + 6 * q^10 - 10 * q^11 + 54 * q^12 + 9 * q^13 - 5 * q^14 - 10 * q^15 - 13 * q^16 - 2 * q^18 + 10 * q^19 + 37 * q^20 - 14 * q^21 - 9 * q^22 + 18 * q^23 + 4 * q^24 - 31 * q^25 + 2 * q^26 - 9 * q^27 + 12 * q^28 + 10 * q^29 + q^30 - 28 * q^31 - 74 * q^32 + 5 * q^33 + 40 * q^34 - 14 * q^35 - 11 * q^36 - 26 * q^37 + 7 * q^38 + 9 * q^39 - 72 * q^40 + 26 * q^41 - 5 * q^42 + 4 * q^43 - 68 * q^44 + 20 * q^45 - 57 * q^46 - 28 * q^48 - 18 * q^49 + 11 * q^50 - 5 * q^51 + 11 * q^52 + 11 * q^53 - 2 * q^54 - 32 * q^55 + 72 * q^56 + 50 * q^58 + 55 * q^59 + 37 * q^60 + 14 * q^61 - 50 * q^62 + q^63 - q^64 - 20 * q^65 - 14 * q^66 + 104 * q^67 - 9 * q^68 + 8 * q^69 + 44 * q^70 - 8 * q^71 + 4 * q^72 - 3 * q^73 + 69 * q^74 - 21 * q^75 - 52 * q^76 + 2 * q^77 + 2 * q^78 - 19 * q^79 - 159 * q^80 - 9 * q^81 + 58 * q^82 + 12 * q^83 - 8 * q^84 + 63 * q^86 - 97 * q^88 + 118 * q^89 - 4 * q^90 - q^91 + 98 * q^92 - 28 * q^93 - 99 * q^94 - 45 * q^95 + q^96 + 50 * q^97 - 186 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	1.30744	−	0.949910i	0.924499	−	0.671688i	−0.0201407	−	0.999797i	$-0.506411\pi$
$2$	1.30744	−	0.949910i	0.924499	−	0.671688i	0.944640	+	0.328109i	$0.106411\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	0.189034	−	0.581786i	0.0945169	−	0.290893i
$5$	1.69854	+	1.23406i	0.759608	+	0.551888i	0.898790	−	0.438379i	$-0.144447\pi$
$5$	1.69854	+	1.23406i	0.759608	+	0.551888i	−0.139182	+	0.990267i	$0.544447\pi$
$6$	1.30744	+	0.949910i	0.533760	+	0.387799i
$7$	1.36281	−	4.19429i	0.515093	−	1.58529i	−0.268021	−	0.963413i	$-0.586370\pi$
$7$	1.36281	−	4.19429i	0.515093	−	1.58529i	0.783113	−	0.621879i	$-0.213630\pi$
$8$	0.693300	+	2.13376i	0.245119	+	0.754398i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	3.39298			1.07295
$11$	−3.28357	−	0.467064i	−0.990034	−	0.140825i
$11$	−3.28357	−	0.467064i	−0.990034	−	0.140825i
$12$	0.611726			0.176590
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i
$14$	−2.20241	−	6.77832i	−0.588619	−	1.81158i
$15$	−0.648783	+	1.99675i	−0.167515	+	0.515558i
$16$	3.92312	+	2.85031i	0.980780	+	0.712578i
$17$	5.73404	+	4.16602i	1.39071	+	1.01041i	0.995787	+	0.0916944i	$0.0292283\pi$
$17$	5.73404	+	4.16602i	1.39071	+	1.01041i	0.394922	+	0.918715i	$0.370772\pi$
$18$	−0.499397	+	1.53699i	−0.117709	+	0.362271i
$19$	0.292494	+	0.900203i	0.0671027	+	0.206521i	0.978986	−	0.203930i	$-0.0653714\pi$
$19$	0.292494	+	0.900203i	0.0671027	+	0.206521i	−0.911883	+	0.410451i	$0.865371\pi$
$20$	1.03904	−	0.754906i	0.232336	−	0.168802i
$21$	4.41014			0.962371
$22$	−4.73674	+	2.50844i	−1.00988	+	0.534801i
$23$	−4.97977			−1.03835			−0.519177	−	0.854667i	$-0.673762\pi$
$23$	−4.97977			−1.03835			−0.519177	+	0.854667i	$0.673762\pi$
$24$	−1.81508	+	1.31874i	−0.370502	+	0.269186i
$25$	−0.182961	−	0.563098i	−0.0365923	−	0.112620i
$26$	0.499397	−	1.53699i	0.0979399	−	0.301428i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	−2.18256	−	1.58572i	−0.412466	−	0.299674i
$29$	1.54168	−	4.74480i	0.286282	−	0.881087i	−0.699729	−	0.714409i	$-0.746696\pi$
$29$	1.54168	−	4.74480i	0.286282	−	0.881087i	0.986011	−	0.166678i	$-0.0533041\pi$
$30$	1.04849	+	3.22691i	0.191427	+	0.589151i
$31$	−6.38023	+	4.63551i	−1.14592	+	0.832562i	−0.987934	−	0.154878i	$-0.950501\pi$
$31$	−6.38023	+	4.63551i	−1.14592	+	0.832562i	−0.157990	+	0.987441i	$0.550501\pi$
$32$	3.34965			0.592140
$33$	−0.570475	−	3.26719i	−0.0993070	−	0.568746i
$34$	11.4543			1.96439
$35$	7.49077	−	5.44237i	1.26617	−	0.919928i
$36$	0.189034	+	0.581786i	0.0315056	+	0.0969644i
$37$	2.40088	−	7.38914i	0.394702	−	1.21477i	−0.534492	−	0.845174i	$-0.679497\pi$
$37$	2.40088	−	7.38914i	0.394702	−	1.21477i	0.929193	−	0.369594i	$-0.120503\pi$
$38$	1.23753	+	0.899118i	0.200754	+	0.145856i
$39$	0.809017	+	0.587785i	0.129546	+	0.0941210i
$40$	−1.45559	+	4.47984i	−0.230149	+	0.708325i
$41$	−0.153644	−	0.472869i	−0.0239952	−	0.0738497i	0.938342	−	0.345709i	$-0.112362\pi$
$41$	−0.153644	−	0.472869i	−0.0239952	−	0.0738497i	−0.962337	+	0.271859i	$0.912362\pi$
$42$	5.76598	−	4.18923i	0.889711	−	0.646413i
$43$	−11.1839			−1.70553			−0.852763	−	0.522298i	$-0.825075\pi$
$43$	−11.1839			−1.70553			−0.852763	+	0.522298i	$0.825075\pi$
$44$	−0.892438	+	1.82205i	−0.134540	+	0.274684i
$45$	−2.09951			−0.312976
$46$	−6.51075	+	4.73034i	−0.959958	+	0.697450i
$47$	0.374620	+	1.15296i	0.0546439	+	0.168177i	0.974654	−	0.223718i	$-0.0718196\pi$
$47$	0.374620	+	1.15296i	0.0546439	+	0.168177i	−0.920010	+	0.391895i	$0.871820\pi$
$48$	−1.49850	+	4.61190i	−0.216290	+	0.665671i
$49$	−10.0717	−	7.31752i	−1.43881	−	1.04536i
$50$	−0.774103	−	0.562419i	−0.109475	−	0.0795380i
$51$	−2.19021	+	6.74077i	−0.306691	+	0.943896i
$52$	−0.189034	−	0.581786i	−0.0262143	−	0.0806792i
$53$	−0.886832	+	0.644321i	−0.121816	+	0.0885043i	−0.647025	−	0.762469i	$-0.723987\pi$
$53$	−0.886832	+	0.644321i	−0.121816	+	0.0885043i	0.525209	+	0.850973i	$0.323987\pi$
$54$	−1.61608			−0.219921
$55$	−5.00088	−	4.84545i	−0.674319	−	0.653360i
$56$	9.89444			1.32220
$57$	−0.765759	+	0.556356i	−0.101427	+	0.0736912i
$58$	−2.49148	−	7.66799i	−0.327147	−	1.00686i
$59$	−0.0285215	+	0.0877803i	−0.00371319	+	0.0114280i	−0.952896	−	0.303297i	$-0.901912\pi$
$59$	−0.0285215	+	0.0877803i	−0.00371319	+	0.0114280i	0.949183	+	0.314725i	$0.101912\pi$
$60$	1.03904	+	0.754906i	0.134139	+	0.0974579i
$61$	−7.82276	−	5.68357i	−1.00160	−	0.727706i	−0.0391708	−	0.999233i	$-0.512472\pi$
$61$	−7.82276	−	5.68357i	−1.00160	−	0.727706i	−0.962431	+	0.271526i	$0.912472\pi$
$62$	−3.93845	+	12.1213i	−0.500183	+	1.53941i
$63$	1.36281	+	4.19429i	0.171698	+	0.528431i
$64$	−3.46678	+	2.51876i	−0.433347	+	0.314845i
$65$	2.09951			0.260412
$66$	−3.84940	−	3.72976i	−0.473829	−	0.459101i
$67$	8.50741			1.03935			0.519673	−	0.854365i	$-0.326054\pi$
$67$	8.50741			1.03935			0.519673	+	0.854365i	$0.326054\pi$
$68$	3.50766	−	2.54847i	0.425366	−	0.309047i
$69$	−1.53883	−	4.73604i	−0.185254	−	0.570153i
$70$	4.62397	−	14.2311i	0.552670	−	1.70094i
$71$	−13.0623	−	9.49035i	−1.55022	−	1.12630i	−0.943497	−	0.331380i	$-0.892486\pi$
$71$	−13.0623	−	9.49035i	−1.55022	−	1.12630i	−0.606718	−	0.794917i	$-0.707514\pi$
$72$	−1.81508	−	1.31874i	−0.213910	−	0.155414i
$73$	−0.962901	+	2.96350i	−0.112699	+	0.346852i	−0.991460	−	0.130410i	$-0.958371\pi$
$73$	−0.962901	+	2.96350i	−0.112699	+	0.346852i	0.878761	+	0.477262i	$0.158371\pi$
$74$	−3.88002	−	11.9415i	−0.451043	−	1.38817i
$75$	0.478999	−	0.348013i	0.0553101	−	0.0401851i
$76$	0.579017			0.0664178
$77$	−6.43388	+	13.1357i	−0.733209	+	1.49696i
$78$	1.61608			0.182985
$79$	−1.97455	+	1.43459i	−0.222154	+	0.161404i	−0.693296	−	0.720653i	$-0.743842\pi$
$79$	−1.97455	+	1.43459i	−0.222154	+	0.161404i	0.471142	+	0.882057i	$0.343842\pi$
$80$	3.14611	+	9.68272i	0.351745	+	1.08256i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−0.650064	−	0.472299i	−0.0717875	−	0.0521567i
$83$	11.1230	+	8.08132i	1.22091	+	0.887040i	0.996175	−	0.0873803i	$-0.0278495\pi$
$83$	11.1230	+	8.08132i	1.22091	+	0.887040i	0.224731	+	0.974421i	$0.427850\pi$
$84$	0.833665	−	2.56576i	0.0909603	−	0.279947i
$85$	4.59835	+	14.1523i	0.498762	+	1.53503i
$86$	−14.6222	+	10.6237i	−1.57676	+	1.14558i
$87$	4.98898			0.534874
$88$	−1.27990	−	7.33017i	−0.136438	−	0.781399i
$89$	7.34531			0.778601			0.389301	−	0.921111i	$-0.372717\pi$
$89$	7.34531			0.778601			0.389301	+	0.921111i	$0.372717\pi$
$90$	−2.74498	+	1.99434i	−0.289346	+	0.210222i
$91$	−1.36281	−	4.19429i	−0.142861	−	0.439681i
$92$	−0.941345	+	2.89716i	−0.0981420	+	0.302050i
$93$	−6.38023	−	4.63551i	−0.661599	−	0.480680i
$94$	1.58500	+	1.15157i	0.163480	+	0.118776i
$95$	−0.614092	+	1.88998i	−0.0630045	+	0.193908i
$96$	1.03510	+	3.18571i	0.105644	+	0.325140i
$97$	6.01556	−	4.37056i	0.610787	−	0.443763i	−0.238904	−	0.971043i	$-0.576788\pi$
$97$	6.01556	−	4.37056i	0.610787	−	0.443763i	0.849691	+	0.527280i	$0.176788\pi$
$98$	−20.1191			−2.03234
$99$	2.93100	−	1.55217i	0.294577	−	0.155999i
$100$	−0.362188			−0.0362188
$101$	−6.34482	+	4.60978i	−0.631333	+	0.458690i	−0.856862	−	0.515546i	$-0.827589\pi$
$101$	−6.34482	+	4.60978i	−0.631333	+	0.458690i	0.225529	+	0.974237i	$0.427589\pi$
$102$	3.53956	+	10.8936i	0.350469	+	1.07863i
$103$	−3.60560	+	11.0969i	−0.355270	+	1.09341i	0.600582	+	0.799563i	$0.294936\pi$
$103$	−3.60560	+	11.0969i	−0.355270	+	1.09341i	−0.955852	+	0.293847i	$0.905064\pi$
$104$	1.81508	+	1.31874i	0.177984	+	0.129313i
$105$	7.49077	+	5.44237i	0.731025	+	0.531121i
$106$	−0.547432	+	1.68482i	−0.0531712	+	0.163644i
$107$	0.413186	+	1.27166i	0.0399442	+	0.122936i	0.969040	−	0.246903i	$-0.0794129\pi$
$107$	0.413186	+	1.27166i	0.0399442	+	0.122936i	−0.929096	+	0.369839i	$0.879413\pi$
$108$	−0.494897	+	0.359564i	−0.0476215	+	0.0345990i
$109$	3.08747			0.295726			0.147863	−	0.989008i	$-0.452761\pi$
$109$	3.08747			0.295726			0.147863	+	0.989008i	$0.452761\pi$
$110$	−11.1411	−	1.58474i	−1.06226	−	0.151099i
$111$	7.76940			0.737439
$112$	17.3015	−	12.5703i	1.63484	−	1.18778i
$113$	1.30386	+	4.01288i	0.122657	+	0.377500i	0.993467	−	0.114120i	$-0.0364048\pi$
$113$	1.30386	+	4.01288i	0.122657	+	0.377500i	−0.870810	+	0.491620i	$0.836405\pi$
$114$	−0.472694	+	1.45480i	−0.0442719	+	0.136255i
$115$	−8.45832	−	6.14533i	−0.788743	−	0.573055i
$116$	−2.46903	−	1.79385i	−0.229244	−	0.166555i
$117$	−0.309017	+	0.951057i	−0.0285686	+	0.0879252i
$118$	0.0460932	+	0.141860i	0.00424322	+	0.0130593i
$119$	25.2879	−	18.3727i	2.31814	−	1.68423i
$120$	−4.71038			−0.429997
$121$	10.5637	+	3.06728i	0.960337	+	0.278844i
$122$	−15.6267			−1.41477
$123$	0.402246	−	0.292249i	0.0362693	−	0.0263512i
$124$	1.49080	+	4.58820i	0.133877	+	0.412033i
$125$	3.62804	−	11.1660i	0.324502	−	0.998715i
$126$	5.76598	+	4.18923i	0.513675	+	0.373207i
$127$	−8.47569	−	6.15795i	−0.752095	−	0.546429i	0.144380	−	0.989522i	$-0.453881\pi$
$127$	−8.47569	−	6.15795i	−0.752095	−	0.546429i	−0.896476	+	0.443093i	$0.853881\pi$
$128$	−4.21020	+	12.9577i	−0.372133	+	1.14531i
$129$	−3.45601	−	10.6365i	−0.304285	−	0.936492i
$130$	2.74498	−	1.99434i	0.240750	−	0.174915i
$131$	1.45244			0.126901			0.0634503	−	0.997985i	$-0.479790\pi$
$131$	1.45244			0.126901			0.0634503	+	0.997985i	$0.479790\pi$
$132$	−2.00865	−	0.285715i	−0.174830	−	0.0248683i
$133$	4.17433			0.361960
$134$	11.1229	−	8.08127i	0.960874	−	0.698116i
$135$	−0.648783	−	1.99675i	−0.0558383	−	0.171853i
$136$	−4.91388	+	15.1234i	−0.421362	+	1.29682i
$137$	15.7711	+	11.4584i	1.34742	+	0.978958i	0.999136	+	0.0415692i	$0.0132357\pi$
$137$	15.7711	+	11.4584i	1.34742	+	0.978958i	0.348285	+	0.937389i	$0.386764\pi$
$138$	−6.51075	−	4.73034i	−0.554232	−	0.402673i
$139$	2.99391	−	9.21432i	0.253940	−	0.781548i	−0.740096	−	0.672501i	$-0.765220\pi$
$139$	2.99391	−	9.21432i	0.253940	−	0.781548i	0.994037	−	0.109047i	$-0.0347799\pi$
$140$	−1.75028	−	5.38682i	−0.147926	−	0.455269i
$141$	−0.980767	+	0.712569i	−0.0825955	+	0.0600092i
$142$	−26.0932			−2.18969
$143$	−2.93100	+	1.55217i	−0.245103	+	0.129799i
$144$	−4.84924			−0.404104
$145$	8.47395	−	6.15669i	0.703724	−	0.511285i
$146$	1.55613	+	4.78927i	0.128786	+	0.396363i
$147$	3.84705	−	11.8400i	0.317299	−	0.976546i
$148$	−3.84505	−	2.79360i	−0.316061	−	0.229632i
$149$	4.53248	+	3.29304i	0.371315	+	0.269776i	0.757756	−	0.652538i	$-0.226296\pi$
$149$	4.53248	+	3.29304i	0.371315	+	0.269776i	−0.386441	+	0.922314i	$0.626296\pi$
$150$	0.295681	−	0.910013i	0.0241423	−	0.0743022i
$151$	1.18800	+	3.65628i	0.0966779	+	0.297544i	0.987687	−	0.156441i	$-0.0500021\pi$
$151$	1.18800	+	3.65628i	0.0966779	+	0.297544i	−0.891009	+	0.453985i	$0.850002\pi$
$152$	−1.71803	+	1.24822i	−0.139351	+	0.101244i
$153$	−7.08766			−0.573004
$154$	4.06586	+	23.2858i	0.327637	+	1.87642i
$155$	−16.5575			−1.32993
$156$	0.494897	−	0.359564i	0.0396235	−	0.0287881i
$157$	−2.59264	−	7.97932i	−0.206915	−	0.636819i	−0.999629	−	0.0272259i	$-0.991333\pi$
$157$	−2.59264	−	7.97932i	−0.206915	−	0.636819i	0.792714	−	0.609594i	$-0.208667\pi$
$158$	−1.21887	+	3.75128i	−0.0969678	+	0.298436i
$159$	−0.886832	−	0.644321i	−0.0703303	−	0.0510980i
$160$	5.68950	+	4.13366i	0.449794	+	0.326795i
$161$	−6.78647	+	20.8866i	−0.534849	+	1.64609i
$162$	−0.499397	−	1.53699i	−0.0392364	−	0.120757i
$163$	−14.1203	+	10.2590i	−1.10598	+	0.803545i	−0.982027	−	0.188743i	$-0.939559\pi$
$163$	−14.1203	+	10.2590i	−1.10598	+	0.803545i	−0.123958	+	0.992287i	$0.539559\pi$
$164$	−0.304152			−0.0237503
$165$	3.06294	−	6.25345i	0.238449	−	0.486830i
$166$	22.2192			1.72454
$167$	9.69746	−	7.04562i	0.750412	−	0.545206i	−0.145543	−	0.989352i	$-0.546493\pi$
$167$	9.69746	−	7.04562i	0.750412	−	0.545206i	0.895954	+	0.444146i	$0.146493\pi$
$168$	3.05755	+	9.41017i	0.235895	+	0.726010i
$169$	0.309017	−	0.951057i	0.0237705	−	0.0731582i
$170$	19.4555	+	14.1352i	1.49217	+	1.08412i
$171$	−0.765759	−	0.556356i	−0.0585590	−	0.0425456i
$172$	−2.11413	+	6.50663i	−0.161201	+	0.496126i
$173$	4.64048	+	14.2819i	0.352809	+	1.08584i	0.957269	+	0.289200i	$0.0933891\pi$
$173$	4.64048	+	14.2819i	0.352809	+	1.08584i	−0.604459	+	0.796636i	$0.706611\pi$
$174$	6.52278	−	4.73908i	0.494491	−	0.359269i
$175$	−2.61114			−0.197383
$176$	−11.5506	−	11.1916i	−0.870657	−	0.843596i
$177$	−0.0922977			−0.00693752
$178$	9.60355	−	6.97738i	0.719816	−	0.522977i
$179$	2.94088	+	9.05110i	0.219812	+	0.676511i	0.998777	+	0.0494439i	$0.0157449\pi$
$179$	2.94088	+	9.05110i	0.219812	+	0.676511i	−0.778965	+	0.627067i	$0.784255\pi$
$180$	−0.396877	+	1.22146i	−0.0295815	+	0.0910425i
$181$	−11.4975	−	8.35344i	−0.854604	−	0.620906i	0.0718074	−	0.997419i	$-0.477123\pi$
$181$	−11.4975	−	8.35344i	−0.854604	−	0.620906i	−0.926412	+	0.376512i	$0.877123\pi$
$182$	−5.76598	−	4.18923i	−0.427403	−	0.310527i
$183$	2.98803	−	9.19621i	0.220881	−	0.679803i
$184$	−3.45248	−	10.6256i	−0.254520	−	0.783332i
$185$	13.1966	−	9.58790i	0.970234	−	0.704916i
$186$	−12.7451			−0.934515
$187$	−16.8823	−	16.3576i	−1.23456	−	1.19619i
$188$	0.741593			0.0540862
$189$	−3.56788	+	2.59221i	−0.259525	+	0.188556i
$190$	0.992425	+	3.05437i	0.0719980	+	0.221587i
$191$	3.11863	−	9.59816i	0.225656	−	0.694498i	−0.772568	−	0.634932i	$-0.781028\pi$
$191$	3.11863	−	9.59816i	0.225656	−	0.694498i	0.998224	−	0.0595665i	$-0.0189719\pi$
$192$	−3.46678	−	2.51876i	−0.250193	−	0.181776i
$193$	7.65399	+	5.56095i	0.550946	+	0.400286i	0.828134	−	0.560530i	$-0.189402\pi$
$193$	7.65399	+	5.56095i	0.550946	+	0.400286i	−0.277188	+	0.960816i	$0.589402\pi$
$194$	3.71334	−	11.4285i	0.266602	−	0.820517i
$195$	0.648783	+	1.99675i	0.0464603	+	0.142990i
$196$	−6.16112	+	4.47632i	−0.440080	+	0.319737i
$197$	−15.5981			−1.11132			−0.555661	−	0.831409i	$-0.687535\pi$
$197$	−15.5981			−1.11132			−0.555661	+	0.831409i	$0.687535\pi$
$198$	2.35768	−	4.81356i	0.167553	−	0.342085i
$199$	7.17405			0.508555			0.254277	−	0.967131i	$-0.418162\pi$
$199$	7.17405			0.508555			0.254277	+	0.967131i	$0.418162\pi$
$200$	1.07467	−	0.780791i	0.0759904	−	0.0552103i
$201$	2.62893	+	8.09103i	0.185431	+	0.570697i
$202$	−3.91659	+	12.0540i	−0.275570	+	0.848118i
$203$	−17.8000	−	12.9325i	−1.24932	−	0.907683i
$204$	3.50766	+	2.54847i	0.245585	+	0.178428i
$205$	0.322577	−	0.992791i	0.0225298	−	0.0693395i
$206$	5.82695	+	17.9335i	0.405983	+	1.24949i
$207$	4.02872	−	2.92704i	0.280015	−	0.203443i
$208$	4.84924			0.336235
$209$	−0.539972	−	3.09250i	−0.0373506	−	0.213912i
$210$	14.9635			1.03258
$211$	23.1195	−	16.7973i	1.59161	−	1.15637i	0.690016	−	0.723794i	$-0.257603\pi$
$211$	23.1195	−	16.7973i	1.59161	−	1.15637i	0.901596	−	0.432580i	$-0.142397\pi$
$212$	0.207216	+	0.637745i	0.0142316	+	0.0438005i
$213$	4.98937	−	15.3557i	0.341866	−	1.05216i
$214$	1.74817	+	1.27012i	0.119503	+	0.0868238i
$215$	−18.9962	−	13.8016i	−1.29553	−	0.941259i
$216$	0.693300	−	2.13376i	0.0471731	−	0.145184i
$217$	10.7476	+	33.0779i	0.729598	+	2.24547i
$218$	4.03668	−	2.93282i	0.273398	−	0.198636i
$219$	−3.11601			−0.210561
$220$	−3.76435	+	1.99349i	−0.253792	+	0.134401i
$221$	7.08766			0.476768
$222$	10.1580	−	7.38024i	0.681762	−	0.495329i
$223$	0.0619908	+	0.190788i	0.00415121	+	0.0127761i	0.953111	−	0.302622i	$-0.0978620\pi$
$223$	0.0619908	+	0.190788i	0.00415121	+	0.0127761i	−0.948959	+	0.315398i	$0.897862\pi$
$224$	4.56493	−	14.0494i	0.305007	−	0.938715i
$225$	0.478999	+	0.348013i	0.0319333	+	0.0232009i
$226$	5.51660	+	4.00805i	0.366959	+	0.266611i
$227$	0.471657	−	1.45161i	0.0313050	−	0.0963468i	−0.934183	−	0.356794i	$-0.883870\pi$
$227$	0.471657	−	1.45161i	0.0313050	−	0.0963468i	0.965488	+	0.260447i	$0.0838699\pi$
$228$	0.178926	+	0.550678i	0.0118497	+	0.0364695i
$229$	−22.3704	+	16.2531i	−1.47828	+	1.07403i	−0.500173	+	0.865925i	$0.666730\pi$
$229$	−22.3704	+	16.2531i	−1.47828	+	1.07403i	−0.978106	+	0.208107i	$0.933270\pi$
$230$	−16.8963			−1.11411
$231$	−14.4810	−	2.05982i	−0.952780	−	0.135526i
$232$	11.1931			0.734863
$233$	6.66133	−	4.83974i	0.436399	−	0.317062i	−0.347804	−	0.937567i	$-0.613072\pi$
$233$	6.66133	−	4.83974i	0.436399	−	0.317062i	0.784202	+	0.620505i	$0.213072\pi$
$234$	0.499397	+	1.53699i	0.0326466	+	0.100476i
$235$	−0.786516	+	2.42065i	−0.0513067	+	0.157906i
$236$	0.0456778	+	0.0331869i	0.00297337	+	0.00216028i
$237$	−1.97455	−	1.43459i	−0.128261	−	0.0931868i
$238$	15.6099	−	48.0425i	1.01184	−	3.11413i
$239$	9.18787	+	28.2774i	0.594314	+	1.82911i	0.558111	+	0.829766i	$0.311526\pi$
$239$	9.18787	+	28.2774i	0.594314	+	1.82911i	0.0362025	+	0.999344i	$0.488474\pi$
$240$	−8.23661	+	5.98425i	−0.531671	+	0.386282i
$241$	12.8808			0.829728			0.414864	−	0.909884i	$-0.363829\pi$
$241$	12.8808			0.829728			0.414864	+	0.909884i	$0.363829\pi$
$242$	16.7250	−	6.02429i	1.07513	−	0.387256i
$243$	1.00000			0.0641500
$244$	−4.78539	+	3.47679i	−0.306353	+	0.222578i
$245$	−8.07690	−	24.8581i	−0.516014	−	1.58813i
$246$	0.248302	−	0.764195i	0.0158312	−	0.0487233i
$247$	0.765759	+	0.556356i	0.0487241	+	0.0354001i
$248$	−14.3145	−	10.4001i	−0.908970	−	0.660406i
$249$	−4.24860	+	13.0759i	−0.269244	+	0.828649i
$250$	−5.86322	−	18.0451i	−0.370823	−	1.14127i
$251$	10.6204	−	7.71616i	0.670353	−	0.487040i	−0.199790	−	0.979839i	$-0.564026\pi$
$251$	10.6204	−	7.71616i	0.670353	−	0.487040i	0.870143	+	0.492799i	$0.164026\pi$
$252$	2.69780			0.169945
$253$	16.3514	+	2.32587i	1.02801	+	0.146226i
$254$	−16.9309			−1.06234
$255$	−12.0386	+	8.74659i	−0.753889	+	0.547733i
$256$	4.15565	+	12.7898i	0.259728	+	0.799362i
$257$	8.32381	−	25.6181i	0.519225	−	1.59801i	−0.256235	−	0.966614i	$-0.582482\pi$
$257$	8.32381	−	25.6181i	0.519225	−	1.59801i	0.775460	−	0.631396i	$-0.217518\pi$
$258$	−14.6222	−	10.6237i	−0.910341	−	0.661401i
$259$	−27.7203	−	20.1400i	−1.72245	−	1.25144i
$260$	0.396877	−	1.22146i	0.0246133	−	0.0757519i
$261$	1.54168	+	4.74480i	0.0954275	+	0.293696i
$262$	1.89898	−	1.37969i	0.117320	−	0.0852376i
$263$	17.2319			1.06256			0.531282	−	0.847195i	$-0.321711\pi$
$263$	17.2319			1.06256			0.531282	+	0.847195i	$0.321711\pi$
$264$	6.57589	−	3.48240i	0.404718	−	0.214327i
$265$	−2.30145			−0.141377
$266$	5.45768	−	3.96523i	0.334632	−	0.243124i
$267$	2.26983	+	6.98580i	0.138911	+	0.427524i
$268$	1.60819	−	4.94949i	0.0982357	−	0.302338i
$269$	−1.33811	−	0.972196i	−0.0815862	−	0.0592759i	0.546244	−	0.837626i	$-0.316057\pi$
$269$	−1.33811	−	0.972196i	−0.0815862	−	0.0592759i	−0.627831	+	0.778350i	$0.716057\pi$
$270$	−2.74498	−	1.99434i	−0.167054	−	0.121372i
$271$	0.415173	−	1.27777i	0.0252199	−	0.0776190i	−0.937654	−	0.347569i	$-0.887007\pi$
$271$	0.415173	−	1.27777i	0.0252199	−	0.0776190i	0.962874	+	0.269950i	$0.0870072\pi$
$272$	10.6209	+	32.6876i	0.643984	+	1.98198i
$273$	3.56788	−	2.59221i	0.215938	−	0.156888i
$274$	31.5043			1.90324
$275$	0.337765	+	1.93443i	0.0203680	+	0.116650i
$276$	−3.04626			−0.183363
$277$	−10.5510	+	7.66576i	−0.633949	+	0.460591i	−0.857766	−	0.514040i	$-0.828148\pi$
$277$	−10.5510	+	7.66576i	−0.633949	+	0.460591i	0.223817	+	0.974631i	$0.428148\pi$
$278$	−4.83841	−	14.8911i	−0.290189	−	0.893109i
$279$	2.43703	−	7.50042i	0.145901	−	0.449038i
$280$	16.8061	+	12.2103i	1.00435	+	0.729706i
$281$	18.8714	+	13.7109i	1.12578	+	0.817924i	0.985075	−	0.172128i	$-0.0550643\pi$
$281$	18.8714	+	13.7109i	1.12578	+	0.817924i	0.140701	+	0.990052i	$0.455064\pi$
$282$	−0.605417	+	1.86328i	−0.0360521	+	0.110957i
$283$	3.18956	+	9.81645i	0.189600	+	0.583527i	0.999997	−	0.00235273i	$-0.000748899\pi$
$283$	3.18956	+	9.81645i	0.189600	+	0.583527i	−0.810398	+	0.585880i	$0.800749\pi$
$284$	−7.99058	+	5.80549i	−0.474154	+	0.344493i
$285$	−1.98724			−0.117714
$286$	−2.35768	+	4.81356i	−0.139412	+	0.284632i
$287$	−2.19274			−0.129433
$288$	−2.70992	+	1.96887i	−0.159684	+	0.116017i
$289$	10.2702	+	31.6083i	0.604128	+	1.85931i
$290$	5.23088	−	16.0990i	0.307168	−	0.945365i
$291$	6.01556	+	4.37056i	0.352638	+	0.256207i
$292$	1.54210	+	1.12040i	0.0902448	+	0.0655667i
$293$	−0.629549	+	1.93755i	−0.0367787	+	0.113193i	−0.967760	−	0.251873i	$-0.918954\pi$
$293$	−0.629549	+	1.93755i	−0.0367787	+	0.113193i	0.930982	+	0.365066i	$0.118954\pi$
$294$	−6.21715	−	19.1344i	−0.362592	−	1.11594i
$295$	−0.156771	+	0.113901i	−0.00912755	+	0.00663156i
$296$	17.4312			1.01317
$297$	2.38193	+	2.30790i	0.138214	+	0.133918i
$298$	9.05403			0.524486
$299$	−4.02872	+	2.92704i	−0.232987	+	0.169275i
$300$	−0.111922	−	0.344461i	−0.00646184	−	0.0198875i
$301$	−15.2415	+	46.9084i	−0.878504	+	2.70376i
$302$	5.02637	+	3.65187i	0.289235	+	0.210142i
$303$	−6.34482	−	4.60978i	−0.364500	−	0.264825i
$304$	−1.41837	+	4.36530i	−0.0813493	+	0.250367i
$305$	−6.27338	−	19.3075i	−0.359213	−	1.10554i
$306$	−9.26669	+	6.73264i	−0.529741	+	0.384880i
$307$	26.8345			1.53153			0.765763	−	0.643123i	$-0.222362\pi$
$307$	26.8345			1.53153			0.765763	+	0.643123i	$0.222362\pi$
$308$	6.42597	+	6.22624i	0.366154	+	0.354773i
$309$	−11.6680			−0.663768
$310$	−21.6480	+	15.7282i	−1.22952	+	0.893301i
$311$	4.93791	+	15.1973i	0.280003	+	0.861761i	0.987852	+	0.155397i	$0.0496657\pi$
$311$	4.93791	+	15.1973i	0.280003	+	0.861761i	−0.707849	+	0.706364i	$0.750334\pi$
$312$	−0.693300	+	2.13376i	−0.0392504	+	0.120800i
$313$	−5.37012	−	3.90162i	−0.303537	−	0.220533i	0.425581	−	0.904920i	$-0.360070\pi$
$313$	−5.37012	−	3.90162i	−0.303537	−	0.220533i	−0.729118	+	0.684387i	$0.760070\pi$
$314$	−10.9694	−	7.96971i	−0.619037	−	0.449757i
$315$	−2.86122	+	8.80593i	−0.161212	+	0.496158i
$316$	0.461370	+	1.41995i	0.0259541	+	0.0798785i
$317$	−3.78387	+	2.74914i	−0.212523	+	0.154407i	−0.688955	−	0.724805i	$-0.741930\pi$
$317$	−3.78387	+	2.74914i	−0.212523	+	0.154407i	0.476431	+	0.879212i	$0.341930\pi$
$318$	−1.77153			−0.0993422
$319$	−7.27834	+	14.8598i	−0.407509	+	0.831991i
$320$	−8.99675			−0.502933
$321$	−1.08173	+	0.785926i	−0.0603766	+	0.0438661i
$322$	10.9675	+	33.7545i	0.611195	+	1.88106i
$323$	−2.07310	+	6.38034i	−0.115350	+	0.355011i
$324$	−0.494897	−	0.359564i	−0.0274943	−	0.0199758i
$325$	−0.478999	−	0.348013i	−0.0265701	−	0.0193043i
$326$	−8.71628	+	26.8260i	−0.482750	+	1.48575i
$327$	0.954081	+	2.93636i	0.0527608	+	0.162381i
$328$	0.902466	−	0.655680i	0.0498304	−	0.0362039i
$329$	5.34639			0.294756
$330$	−1.93561	−	11.0855i	−0.106552	−	0.610237i
$331$	7.33259			0.403036			0.201518	−	0.979485i	$-0.435413\pi$
$331$	7.33259			0.403036			0.201518	+	0.979485i	$0.435413\pi$
$332$	6.80422	−	4.94356i	0.373430	−	0.271313i
$333$	2.40088	+	7.38914i	0.131567	+	0.404923i
$334$	5.98613	−	18.4234i	0.327547	−	1.00808i
$335$	14.4501	+	10.4986i	0.789495	+	0.573602i
$336$	17.3015	+	12.5703i	0.943874	+	0.685765i
$337$	−9.70689	+	29.8747i	−0.528768	+	1.62738i	0.227975	+	0.973667i	$0.426790\pi$
$337$	−9.70689	+	29.8747i	−0.528768	+	1.62738i	−0.756743	+	0.653713i	$0.773210\pi$
$338$	−0.499397	−	1.53699i	−0.0271636	−	0.0836011i
$339$	−3.41356	+	2.48010i	−0.185399	+	0.134700i
$340$	9.10284			0.493671
$341$	23.1150	−	12.2411i	1.25175	−	0.662891i
$342$	−1.52967			−0.0827151
$343$	−19.4424	+	14.1258i	−1.04979	+	0.762719i
$344$	−7.75379	−	23.8637i	−0.418056	−	1.28664i
$345$	3.23079	−	9.94335i	0.173940	−	0.535332i
$346$	19.6337	+	14.2647i	1.05551	+	0.766876i
$347$	−21.9137	−	15.9212i	−1.17639	−	0.854695i	−0.184627	−	0.982809i	$-0.559108\pi$
$347$	−21.9137	−	15.9212i	−1.17639	−	0.854695i	−0.991759	+	0.128114i	$0.959108\pi$
$348$	0.943085	−	2.90252i	0.0505547	−	0.155591i
$349$	−5.89468	−	18.1420i	−0.315535	−	0.971117i	−0.975534	−	0.219850i	$-0.929443\pi$
$349$	−5.89468	−	18.1420i	−0.315535	−	0.971117i	0.659998	−	0.751267i	$-0.270557\pi$
$350$	−3.41390	+	2.48034i	−0.182481	+	0.132580i
$351$	−1.00000			−0.0533761
$352$	−10.9988	−	1.56450i	−0.586239	−	0.0833882i
$353$	0.825609			0.0439427			0.0219714	−	0.999759i	$-0.493006\pi$
$353$	0.825609			0.0439427			0.0219714	+	0.999759i	$0.493006\pi$
$354$	−0.120674	+	0.0876745i	−0.00641373	+	0.00465985i
$355$	−10.4752	−	32.2394i	−0.555967	−	1.71109i
$356$	1.38851	−	4.27340i	0.0735910	−	0.226490i
$357$	25.2879	+	18.3727i	1.33838	+	0.972388i
$358$	12.4428	+	9.04019i	0.657620	+	0.477789i
$359$	6.20649	−	19.1016i	0.327566	−	1.00814i	−0.642703	−	0.766116i	$-0.722187\pi$
$359$	6.20649	−	19.1016i	0.327566	−	1.00814i	0.970269	−	0.242029i	$-0.0778130\pi$
$360$	−1.45559	−	4.47984i	−0.0767162	−	0.236108i
$361$	14.6465	−	10.6413i	0.770869	−	0.560069i
$362$	−22.9673			−1.20714
$363$	0.347208	+	10.9945i	0.0182237	+	0.577063i
$364$	−2.69780			−0.141403
$365$	−5.29266	+	3.84534i	−0.277030	+	0.201274i
$366$	−4.82890	−	14.8618i	−0.252411	−	0.776841i
$367$	7.70602	−	23.7167i	0.402251	−	1.23800i	−0.520918	−	0.853607i	$-0.674410\pi$
$367$	7.70602	−	23.7167i	0.402251	−	1.23800i	0.923169	−	0.384395i	$-0.125590\pi$
$368$	−19.5362	−	14.1939i	−1.01840	−	0.739909i
$369$	0.402246	+	0.292249i	0.0209401	+	0.0152139i
$370$	8.14612	−	25.0712i	0.423497	−	1.30339i
$371$	1.49389	+	4.59771i	0.0775588	+	0.238701i
$372$	−3.90296	+	2.83566i	−0.202359	+	0.147022i
$373$	−23.7393			−1.22917			−0.614587	−	0.788849i	$-0.710677\pi$
$373$	−23.7393			−1.22917			−0.614587	+	0.788849i	$0.710677\pi$
$374$	−37.6109	−	5.34987i	−1.94481	−	0.276635i
$375$	11.7406			0.606282
$376$	−2.20042	+	1.59870i	−0.113478	+	0.0824465i
$377$	−1.54168	−	4.74480i	−0.0794005	−	0.244370i
$378$	−2.20241	+	6.77832i	−0.113280	+	0.348639i
$379$	18.4708	+	13.4198i	0.948782	+	0.689330i	0.950518	−	0.310668i	$-0.100553\pi$
$379$	18.4708	+	13.4198i	0.948782	+	0.689330i	−0.00173686	+	0.999998i	$0.500553\pi$
$380$	0.983481	+	0.714541i	0.0504515	+	0.0366552i
$381$	3.23742	−	9.96377i	0.165858	−	0.510459i
$382$	−5.03997	−	15.5114i	−0.257867	−	0.793634i
$383$	5.59079	−	4.06195i	0.285676	−	0.207556i	−0.435713	−	0.900085i	$-0.643504\pi$
$383$	5.59079	−	4.06195i	0.285676	−	0.207556i	0.721389	+	0.692530i	$0.243504\pi$
$384$	−13.6245			−0.695272
$385$	−27.1384	+	14.3717i	−1.38310	+	0.732451i
$386$	15.2895			0.778217
$387$	9.04795	−	6.57372i	0.459933	−	0.334161i
$388$	−1.40559	−	4.32595i	−0.0713578	−	0.219617i
$389$	−3.86991	+	11.9104i	−0.196212	+	0.603880i	0.803748	+	0.594970i	$0.202836\pi$
$389$	−3.86991	+	11.9104i	−0.196212	+	0.603880i	−0.999960	+	0.00890978i	$0.997164\pi$
$390$	2.74498	+	1.99434i	0.138997	+	0.100987i
$391$	−28.5542	−	20.7458i	−1.44405	−	1.04916i
$392$	8.63111	−	26.5638i	0.435937	−	1.34168i
$393$	0.448830	+	1.38136i	0.0226405	+	0.0696802i
$394$	−20.3936	+	14.8168i	−1.02742	+	0.746461i
$395$	−5.12421			−0.257827
$396$	−0.348975	−	1.99863i	−0.0175366	−	0.100435i
$397$	14.6729			0.736409			0.368205	−	0.929745i	$-0.379973\pi$
$397$	14.6729			0.736409			0.368205	+	0.929745i	$0.379973\pi$
$398$	9.37963	−	6.81470i	0.470158	−	0.341590i
$399$	1.28994	+	3.97002i	0.0645776	+	0.198750i
$400$	0.887225	−	2.73060i	0.0443612	−	0.136530i
$401$	−24.3143	−	17.6653i	−1.21420	−	0.882165i	−0.218591	−	0.975817i	$-0.570146\pi$
$401$	−24.3143	−	17.6653i	−1.21420	−	0.882165i	−0.995605	+	0.0936512i	$0.970146\pi$
$402$	11.1229	+	8.08127i	0.554761	+	0.403057i
$403$	−2.43703	+	7.50042i	−0.121397	+	0.373622i
$404$	1.48252	+	4.56273i	0.0737582	+	0.227004i
$405$	1.69854	−	1.23406i	0.0844009	−	0.0613209i
$406$	−35.5572			−1.76467
$407$	−11.3347	+	23.1414i	−0.561838	+	1.14708i
$408$	−15.9016			−0.787249
$409$	−6.65695	+	4.83656i	−0.329165	+	0.239153i	−0.740076	−	0.672523i	$-0.765211\pi$
$409$	−6.65695	+	4.83656i	−0.329165	+	0.239153i	0.410911	+	0.911675i	$0.365211\pi$
$410$	−0.521312	−	1.60443i	−0.0257458	−	0.0792373i
$411$	−6.02404	+	18.5401i	−0.297144	+	0.914516i
$412$	5.77444	+	4.19538i	0.284486	+	0.206691i
$413$	0.329307	+	0.239255i	0.0162041	+	0.0117730i
$414$	2.48688	−	7.65384i	0.122224	−	0.376166i
$415$	8.91997	+	27.4528i	0.437864	+	1.34761i
$416$	2.70992	−	1.96887i	0.132865	−	0.0965320i
$417$	9.68851			0.474448
$418$	−3.64357	−	3.53033i	−0.178213	−	0.172674i
$419$	−31.4008			−1.53403			−0.767015	−	0.641630i	$-0.778259\pi$
$419$	−31.4008			−1.53403			−0.767015	+	0.641630i	$0.778259\pi$
$420$	4.58230	−	3.32924i	0.223593	−	0.162450i
$421$	−2.30727	−	7.10106i	−0.112450	−	0.346084i	0.878957	−	0.476901i	$-0.158240\pi$
$421$	−2.30727	−	7.10106i	−0.112450	−	0.346084i	−0.991407	+	0.130817i	$0.958240\pi$
$422$	14.2714	−	43.9229i	0.694721	−	2.13813i
$423$	−0.980767	−	0.712569i	−0.0476865	−	0.0346463i
$424$	−1.98967	−	1.44558i	−0.0966267	−	0.0702034i
$425$	1.29677	−	3.99105i	0.0629026	−	0.193594i
$426$	−8.06324	−	24.8161i	−0.390665	−	1.20234i
$427$	−34.4994	+	25.0653i	−1.66955	+	1.21300i
$428$	0.817938			0.0395365
$429$	−2.38193	−	2.30790i	−0.115001	−	0.111426i
$430$	−37.9466			−1.82995
$431$	−26.1632	+	19.0087i	−1.26024	+	0.915615i	−0.998769	−	0.0495977i	$-0.984206\pi$
$431$	−26.1632	+	19.0087i	−1.26024	+	0.915615i	−0.261466	+	0.965213i	$0.584206\pi$
$432$	−1.49850	−	4.61190i	−0.0720965	−	0.221890i
$433$	5.68893	−	17.5087i	0.273393	−	0.841416i	−0.716248	−	0.697846i	$-0.754142\pi$
$433$	5.68893	−	17.5087i	0.273393	−	0.841416i	0.989640	−	0.143570i	$-0.0458581\pi$
$434$	45.4729	+	33.0380i	2.18277	+	1.58587i
$435$	8.47395	+	6.15669i	0.406295	+	0.295191i
$436$	0.583636	−	1.79625i	0.0279511	−	0.0860246i
$437$	−1.45655	−	4.48281i	−0.0696763	−	0.214442i
$438$	−4.07400	+	2.95993i	−0.194663	+	0.141431i
$439$	4.35766			0.207980			0.103990	−	0.994578i	$-0.466839\pi$
$439$	4.35766			0.207980			0.103990	+	0.994578i	$0.466839\pi$
$440$	6.87190	−	14.0300i	0.327605	−	0.668855i
$441$	12.4493			0.592824
$442$	9.26669	−	6.73264i	0.440771	−	0.320239i
$443$	−3.68705	−	11.3476i	−0.175177	−	0.539139i	0.824465	−	0.565913i	$-0.191476\pi$
$443$	−3.68705	−	11.3476i	−0.175177	−	0.539139i	−0.999641	+	0.0267746i	$0.991476\pi$
$444$	1.46868	−	4.52013i	0.0697005	−	0.214516i
$445$	12.4763	+	9.06454i	0.591432	+	0.429701i
$446$	0.262281	+	0.190558i	0.0124193	+	0.00902318i
$447$	−1.73125	+	5.32825i	−0.0818854	+	0.252017i
$448$	5.83987	+	17.9733i	0.275908	+	0.849157i
$449$	−17.9031	+	13.0074i	−0.844899	+	0.613855i	−0.923735	−	0.383032i	$-0.874880\pi$
$449$	−17.9031	+	13.0074i	−0.844899	+	0.613855i	0.0788355	+	0.996888i	$0.474880\pi$
$450$	0.956844			0.0451061
$451$	0.283642	+	1.62446i	0.0133562	+	0.0764929i
$452$	2.58111			0.121405
$453$	−3.11022	+	2.25971i	−0.146131	+	0.106170i
$454$	−0.762237	−	2.34592i	−0.0357735	−	0.110100i
$455$	2.86122	−	8.80593i	0.134136	−	0.412829i
$456$	−1.71803	−	1.24822i	−0.0804541	−	0.0584534i
$457$	16.6608	+	12.1048i	0.779359	+	0.566237i	0.904786	−	0.425866i	$-0.140030\pi$
$457$	16.6608	+	12.1048i	0.779359	+	0.566237i	−0.125428	+	0.992103i	$0.540030\pi$
$458$	−13.8090	+	42.4998i	−0.645253	+	1.98588i
$459$	−2.19021	−	6.74077i	−0.102230	−	0.314632i
$460$	−5.17418	+	3.75926i	−0.241247	+	0.175276i
$461$	−4.11740			−0.191766			−0.0958831	−	0.995393i	$-0.530568\pi$
$461$	−4.11740			−0.191766			−0.0958831	+	0.995393i	$0.530568\pi$
$462$	−20.8897	+	11.0626i	−0.971876	+	0.514677i
$463$	13.5247			0.628546			0.314273	−	0.949333i	$-0.398239\pi$
$463$	13.5247			0.628546			0.314273	+	0.949333i	$0.398239\pi$
$464$	19.5724	−	14.2201i	0.908624	−	0.660154i
$465$	−5.11656	−	15.7472i	−0.237275	−	0.730257i
$466$	4.11197	−	12.6553i	0.190483	−	0.586247i
$467$	−12.2634	−	8.90988i	−0.567482	−	0.412300i	0.266708	−	0.963778i	$-0.414064\pi$
$467$	−12.2634	−	8.90988i	−0.567482	−	0.412300i	−0.834190	+	0.551478i	$0.814064\pi$
$468$	0.494897	+	0.359564i	0.0228766	+	0.0166208i
$469$	11.5940	−	35.6825i	0.535359	−	1.64767i
$470$	1.27108	+	3.91197i	0.0586304	+	0.180446i
$471$	6.78762	−	4.93149i	0.312757	−	0.227231i
$472$	−0.207076			−0.00953144
$473$	36.7231	+	5.22359i	1.68853	+	0.240181i
$474$	−3.94433			−0.181169
$475$	0.453387	−	0.329405i	0.0208028	−	0.0151141i
$476$	−5.90873	−	18.1852i	−0.270826	−	0.833518i
$477$	0.338740	−	1.04253i	0.0155098	−	0.0477343i
$478$	38.8735	+	28.2433i	1.77803	+	1.29182i
$479$	−0.383924	−	0.278937i	−0.0175419	−	0.0127450i	0.578980	−	0.815342i	$-0.303451\pi$
$479$	−0.383924	−	0.278937i	−0.0175419	−	0.0127450i	−0.596522	+	0.802597i	$0.703451\pi$
$480$	−2.17320	+	6.68841i	−0.0991923	+	0.305283i
$481$	−2.40088	−	7.38914i	−0.109471	−	0.336916i
$482$	16.8409	−	12.2356i	0.767082	−	0.557318i
$483$	−21.9615			−0.999282
$484$	3.78140	−	5.56600i	0.171882	−	0.253000i
$485$	15.6112			0.708866
$486$	1.30744	−	0.949910i	0.0593066	−	0.0430888i
$487$	4.46306	+	13.7359i	0.202240	+	0.622432i	0.999815	+	0.0192121i	$0.00611578\pi$
$487$	4.46306	+	13.7359i	0.202240	+	0.622432i	−0.797575	+	0.603220i	$0.793884\pi$
$488$	6.70384	−	20.6323i	0.303469	−	0.933980i
$489$	−14.1203	−	10.2590i	−0.638540	−	0.463927i
$490$	−34.1730	−	24.8282i	−1.54378	−	1.12162i
$491$	−8.31046	+	25.5770i	−0.375046	+	1.15427i	0.568402	+	0.822751i	$0.307562\pi$
$491$	−8.31046	+	25.5770i	−0.375046	+	1.15427i	−0.943448	+	0.331521i	$0.892438\pi$
$492$	−0.0939883	−	0.289266i	−0.00423732	−	0.0130411i
$493$	28.6070	−	20.7842i	1.28839	−	0.936073i
$494$	1.52967			0.0688232
$495$	6.89388	+	0.980604i	0.309857	+	0.0440749i
$496$	−38.2431			−1.71717
$497$	−57.6067	+	41.8537i	−2.58401	+	1.87740i
$498$	6.86610	+	21.1317i	0.307677	+	0.946933i
$499$	−4.35334	+	13.3982i	−0.194882	+	0.599786i	0.805096	+	0.593145i	$0.202114\pi$
$499$	−4.35334	+	13.3982i	−0.194882	+	0.599786i	−0.999978	+	0.00664097i	$0.997886\pi$
$500$	−5.81038	−	4.22149i	−0.259848	−	0.188791i
$501$	9.69746	+	7.04562i	0.433250	+	0.314775i
$502$	6.55585	−	20.1768i	0.292602	−	0.900536i
$503$	3.59302	+	11.0582i	0.160205	+	0.493060i	0.998651	−	0.0519248i	$-0.0165356\pi$
$503$	3.59302	+	11.0582i	0.160205	+	0.493060i	−0.838446	+	0.544984i	$0.816536\pi$
$504$	−8.00477	+	5.81580i	−0.356561	+	0.259056i
$505$	−16.4656			−0.732712
$506$	23.5879	−	12.4915i	1.04861	−	0.555313i
$507$	1.00000			0.0444116
$508$	−5.18480	+	3.76698i	−0.230038	+	0.167133i
$509$	−3.40327	−	10.4742i	−0.150847	−	0.464261i	0.846869	−	0.531802i	$-0.178485\pi$
$509$	−3.40327	−	10.4742i	−0.150847	−	0.464261i	−0.997717	+	0.0675407i	$0.978485\pi$
$510$	−7.43133	+	22.8713i	−0.329065	+	1.01276i
$511$	11.1175	+	8.07737i	0.491811	+	0.357322i
$512$	−4.46249	−	3.24219i	−0.197216	−	0.143286i
$513$	0.292494	−	0.900203i	0.0129139	−	0.0397449i
$514$	−13.4520	−	41.4009i	−0.593341	−	1.82612i
$515$	−19.8185	+	14.3990i	−0.873306	+	0.634494i
$516$	−6.84147			−0.301179
$517$	−0.691585	−	3.96080i	−0.0304159	−	0.174196i
$518$	−55.3737			−2.43298
$519$	−12.1489	+	8.82672i	−0.533279	+	0.387450i
$520$	1.45559	+	4.47984i	0.0638317	+	0.196454i
$521$	−10.7307	+	33.0257i	−0.470120	+	1.44688i	0.382307	+	0.924035i	$0.375130\pi$
$521$	−10.7307	+	33.0257i	−0.470120	+	1.44688i	−0.852427	+	0.522846i	$0.824870\pi$
$522$	6.52278	+	4.73908i	0.285494	+	0.207424i
$523$	−32.6239	−	23.7027i	−1.42654	−	1.03645i	−0.990647	−	0.136449i	$-0.956431\pi$
$523$	−32.6239	−	23.7027i	−1.42654	−	1.03645i	−0.435898	−	0.899996i	$-0.643569\pi$
$524$	0.274561	−	0.845012i	0.0119943	−	0.0369145i
$525$	−0.806885	−	2.48334i	−0.0352154	−	0.108382i
$526$	22.5296	−	16.3687i	0.982339	−	0.713711i
$527$	−55.8962			−2.43488
$528$	7.07449	−	14.4436i	0.307877	−	0.628578i
$529$	1.79813			0.0781795
$530$	−3.00900	+	2.18617i	−0.130703	+	0.0949610i
$531$	−0.0285215	−	0.0877803i	−0.00123773	−	0.00380934i
$532$	0.789088	−	2.42856i	0.0342113	−	0.105292i
$533$	−0.402246	−	0.292249i	−0.0174232	−	0.0126587i
$534$	9.60355	+	6.97738i	0.415586	+	0.301941i
$535$	−0.867486	+	2.66985i	−0.0375047	+	0.115428i
$536$	5.89819	+	18.1528i	0.254763	+	0.784080i
$537$	−7.69933	+	5.59389i	−0.332251	+	0.241394i
$538$	−2.67300			−0.115241
$539$	29.6534	+	28.7317i	1.27726	+	1.23756i
$540$	−1.28432			−0.0552684
$541$	−3.06411	+	2.22621i	−0.131736	+	0.0957120i	−0.651702	−	0.758475i	$-0.725945\pi$
$541$	−3.06411	+	2.22621i	−0.131736	+	0.0957120i	0.519966	+	0.854187i	$0.325945\pi$
$542$	−0.670954	−	2.06498i	−0.0288199	−	0.0886986i
$543$	4.39166	−	13.5162i	0.188464	−	0.580034i
$544$	19.2070	+	13.9547i	0.823494	+	0.598304i
$545$	5.24418	+	3.81012i	0.224636	+	0.163208i
$546$	2.20241	−	6.77832i	0.0942545	−	0.290085i
$547$	−11.9571	−	36.8000i	−0.511247	−	1.57346i	−0.790009	−	0.613096i	$-0.789924\pi$
$547$	−11.9571	−	36.8000i	−0.511247	−	1.57346i	0.278762	−	0.960360i	$-0.410076\pi$
$548$	9.64762	−	7.00941i	0.412126	−	0.299427i
$549$	9.66946			0.412683
$550$	2.27914	+	2.20830i	0.0971828	+	0.0941622i
$551$	4.72221			0.201173
$552$	9.03870	−	6.56700i	0.384713	−	0.279510i
$553$	3.32617	+	10.2369i	0.141443	+	0.435317i
$554$	−6.51302	+	20.0450i	−0.276712	+	0.851632i
$555$	13.1966	+	9.58790i	0.560165	+	0.406984i
$556$	−4.79481	−	3.48363i	−0.203345	−	0.147739i
$557$	4.36248	−	13.4263i	0.184844	−	0.568892i	−0.815102	−	0.579318i	$-0.803319\pi$
$557$	4.36248	−	13.4263i	0.184844	−	0.568892i	0.999946	+	0.0104264i	$0.00331889\pi$
$558$	−3.93845	−	12.1213i	−0.166728	−	0.513135i
$559$	−9.04795	+	6.57372i	−0.382687	+	0.278039i
$560$	44.8997			1.89736
$561$	10.3401	−	21.1108i	0.436559	−	0.891300i
$562$	37.6974			1.59017
$563$	−16.1663	+	11.7455i	−0.681329	+	0.495014i	−0.873798	−	0.486289i	$-0.838350\pi$
$563$	−16.1663	+	11.7455i	−0.681329	+	0.495014i	0.192469	+	0.981303i	$0.438350\pi$
$564$	0.229165	+	0.705297i	0.00964958	+	0.0296983i
$565$	−2.73747	+	8.42507i	−0.115166	+	0.354445i
$566$	13.4949	+	9.80462i	0.567233	+	0.412119i
$567$	−3.56788	−	2.59221i	−0.149837	−	0.108863i
$568$	11.1940	−	34.4516i	0.469689	−	1.44556i
$569$	0.624122	+	1.92085i	0.0261646	+	0.0805263i	0.963286	−	0.268477i	$-0.0865203\pi$
$569$	0.624122	+	1.92085i	0.0261646	+	0.0805263i	−0.937122	+	0.349003i	$0.886520\pi$
$570$	−2.59820	+	1.88770i	−0.108827	+	0.0790672i
$571$	25.0318			1.04755			0.523774	−	0.851857i	$-0.324524\pi$
$571$	25.0318			1.04755			0.523774	+	0.851857i	$0.324524\pi$
$572$	0.348975	+	1.99863i	0.0145914	+	0.0835668i
$573$	10.0921			0.421604
$574$	−2.86687	+	2.08290i	−0.119661	+	0.0869387i
$575$	0.911106	+	2.80410i	0.0379958	+	0.116939i
$576$	1.32419	−	4.07544i	0.0551746	−	0.169810i
$577$	−20.0401	−	14.5600i	−0.834279	−	0.606139i	0.0864876	−	0.996253i	$-0.472436\pi$
$577$	−20.0401	−	14.5600i	−0.834279	−	0.606139i	−0.920767	+	0.390114i	$0.872436\pi$
$578$	43.4527	+	31.5702i	1.80739	+	1.31315i
$579$	−2.92357	+	8.99781i	−0.121499	+	0.373936i
$580$	−1.98001	−	6.09385i	−0.0822155	−	0.253033i
$581$	49.0539	−	35.6397i	2.03510	−	1.47859i
$582$	12.0166			0.498105
$583$	3.21292	−	1.70147i	0.133065	−	0.0704676i
$584$	−6.99098			−0.289289
$585$	−1.69854	+	1.23406i	−0.0702258	+	0.0510220i
$586$	1.01740	+	3.13125i	0.0420286	+	0.129351i
$587$	−13.1771	+	40.5550i	−0.543878	+	1.67389i	0.179763	+	0.983710i	$0.442467\pi$
$587$	−13.1771	+	40.5550i	−0.543878	+	1.67389i	−0.723642	+	0.690176i	$0.757533\pi$
$588$	−6.16112	−	4.47632i	−0.254080	−	0.184600i
$589$	−6.03908	−	4.38765i	−0.248836	−	0.180790i
$590$	−0.0967729	+	0.297837i	−0.00398408	+	0.0122617i
$591$	−4.82009	−	14.8347i	−0.198272	−	0.610219i
$592$	30.4803	−	22.1452i	1.25273	−	0.910164i
$593$	−22.8548			−0.938534			−0.469267	−	0.883056i	$-0.655482\pi$
$593$	−22.8548			−0.938534			−0.469267	+	0.883056i	$0.655482\pi$
$594$	5.30653	+	0.754815i	0.217729	+	0.0309704i
$595$	65.6254			2.69038
$596$	2.77264	−	2.01444i	0.113572	−	0.0825146i
$597$	2.21690	+	6.82292i	0.0907318	+	0.279244i
$598$	−2.48688	+	7.65384i	−0.101696	+	0.312989i
$599$	18.6876	+	13.5774i	0.763556	+	0.554756i	0.899999	−	0.435892i	$-0.143567\pi$
$599$	18.6876	+	13.5774i	0.763556	+	0.554756i	−0.136443	+	0.990648i	$0.543567\pi$
$600$	1.07467	+	0.780791i	0.0438731	+	0.0318757i
$601$	−4.12736	+	12.7027i	−0.168359	+	0.518154i	−0.999268	−	0.0382532i	$-0.987821\pi$
$601$	−4.12736	+	12.7027i	−0.168359	+	0.518154i	0.830910	+	0.556408i	$0.187821\pi$
$602$	24.6315	+	75.8079i	1.00390	+	3.08970i
$603$	−6.88264	+	5.00053i	−0.280283	+	0.203637i
$604$	2.35175			0.0956912
$605$	14.1576	+	18.2461i	0.575589	+	0.741810i
$606$	−12.6743			−0.514860
$607$	6.14272	−	4.46294i	0.249325	−	0.181145i	−0.456103	−	0.889927i	$-0.650755\pi$
$607$	6.14272	−	4.46294i	0.249325	−	0.181145i	0.705428	+	0.708782i	$0.250755\pi$
$608$	0.979752	+	3.01537i	0.0397342	+	0.122289i
$609$	6.79901	−	20.9252i	0.275510	−	0.847932i
$610$	−26.5424	−	19.2842i	−1.07467	−	0.780795i
$611$	0.980767	+	0.712569i	0.0396776	+	0.0288275i
$612$	−1.33981	+	4.12350i	−0.0541585	+	0.166683i
$613$	−8.22487	−	25.3135i	−0.332199	−	1.02240i	−0.968085	−	0.250621i	$-0.919365\pi$
$613$	−8.22487	−	25.3135i	−0.332199	−	1.02240i	0.635886	−	0.771783i	$-0.280635\pi$
$614$	35.0845	−	25.4904i	1.41589	−	1.02871i
$615$	1.04388			0.0420934
$616$	−32.4891	−	4.62134i	−1.30902	−	0.186199i
$617$	−21.5936			−0.869326			−0.434663	−	0.900593i	$-0.643133\pi$
$617$	−21.5936			−0.869326			−0.434663	+	0.900593i	$0.643133\pi$
$618$	−15.2552	+	11.0835i	−0.613653	+	0.445845i
$619$	4.13104	+	12.7140i	0.166041	+	0.511020i	0.999111	−	0.0421460i	$-0.0134195\pi$
$619$	4.13104	+	12.7140i	0.166041	+	0.511020i	−0.833071	+	0.553166i	$0.813419\pi$
$620$	−3.12994	+	9.63295i	−0.125701	+	0.386869i
$621$	4.02872	+	2.92704i	0.161667	+	0.117458i
$622$	20.8921	+	15.1790i	0.837697	+	0.608622i
$623$	10.0102	−	30.8084i	0.401052	−	1.23431i
$624$	1.49850	+	4.61190i	0.0599880	+	0.184624i
$625$	17.5468	−	12.7485i	0.701873	−	0.509941i
$626$	−10.7273			−0.428749
$627$	2.77428	−	1.46918i	0.110794	−	0.0586733i
$628$	−5.13236			−0.204803
$629$	44.5501	−	32.3675i	1.77633	−	1.29058i
$630$	4.62397	+	14.2311i	0.184223	+	0.566982i
$631$	11.5516	−	35.5522i	0.459862	−	1.41531i	−0.405468	−	0.914109i	$-0.632891\pi$
$631$	11.5516	−	35.5522i	0.459862	−	1.41531i	0.865330	−	0.501202i	$-0.167109\pi$
$632$	−4.43003	−	3.21860i	−0.176217	−	0.128029i
$633$	23.1195	+	16.7973i	0.918918	+	0.667633i
$634$	−2.33574	+	7.18867i	−0.0927641	+	0.285498i
$635$	−6.79699	−	20.9190i	−0.269730	−	0.830145i
$636$	−0.542498	+	0.394148i	−0.0215115	+	0.0156290i
$637$	−12.4493			−0.493259
$638$	4.59952	+	26.3421i	0.182097	+	1.04289i
$639$	16.1459			0.638724
$640$	−23.1417	+	16.8134i	−0.914756	+	0.664609i
$641$	7.27351	+	22.3856i	0.287286	+	0.884177i	0.985704	+	0.168486i	$0.0538879\pi$
$641$	7.27351	+	22.3856i	0.287286	+	0.884177i	−0.698418	+	0.715691i	$0.746112\pi$
$642$	−0.667743	+	2.05510i	−0.0263537	+	0.0811084i
$643$	−32.1590	−	23.3649i	−1.26823	−	0.921421i	−0.269097	−	0.963113i	$-0.586725\pi$
$643$	−32.1590	−	23.3649i	−1.26823	−	0.921421i	−0.999131	+	0.0416919i	$0.986725\pi$
$644$	10.8687	+	7.89655i	0.428285	+	0.311168i
$645$	7.25591	−	22.3314i	0.285701	−	0.879298i
$646$	3.35030	+	10.3112i	0.131816	+	0.405687i
$647$	10.4115	−	7.56442i	0.409320	−	0.297388i	−0.364007	−	0.931396i	$-0.618591\pi$
$647$	10.4115	−	7.56442i	0.409320	−	0.297388i	0.773326	+	0.634008i	$0.218591\pi$
$648$	2.24357			0.0881356
$649$	0.134652	−	0.274912i	0.00528554	−	0.0107912i
$650$	−0.956844			−0.0375305
$651$	−28.1377	+	20.4432i	−1.10280	+	0.801234i
$652$	3.29932	+	10.1543i	0.129211	+	0.397672i
$653$	11.0056	−	33.8718i	0.430683	−	1.32551i	−0.466764	−	0.884382i	$-0.654580\pi$
$653$	11.0056	−	33.8718i	0.430683	−	1.32551i	0.897446	−	0.441123i	$-0.145420\pi$
$654$	4.03668	+	2.93282i	0.157847	+	0.114682i
$655$	2.46703	+	1.79240i	0.0963948	+	0.0700349i
$656$	0.745059	−	2.29306i	0.0290897	−	0.0895288i
$657$	−0.962901	−	2.96350i	−0.0375663	−	0.115617i
$658$	6.99008	−	5.07859i	0.272502	−	0.197984i
$659$	27.4165			1.06800			0.533998	−	0.845486i	$-0.320689\pi$
$659$	27.4165			1.06800			0.533998	+	0.845486i	$0.320689\pi$
$660$	−3.05917	−	2.96409i	−0.119078	−	0.115377i
$661$	2.93350			0.114100			0.0570499	−	0.998371i	$-0.481831\pi$
$661$	2.93350			0.114100			0.0570499	+	0.998371i	$0.481831\pi$
$662$	9.58692	−	6.96530i	0.372606	−	0.270714i
$663$	2.19021	+	6.74077i	0.0850606	+	0.261790i
$664$	−9.53202	+	29.3366i	−0.369914	+	1.13848i
$665$	7.09024	+	5.15136i	0.274948	+	0.199761i
$666$	10.1580	+	7.38024i	0.393615	+	0.285978i
$667$	−7.67721	+	23.6280i	−0.297263	+	0.914880i
$668$	−2.26589	−	6.97371i	−0.0876701	−	0.269821i
$669$	−0.162294	+	0.117913i	−0.00627465	+	0.00455880i
$670$	28.8654			1.11517
$671$	23.0320	+	22.3161i	0.889141	+	0.861505i
$672$	14.7724			0.569858
$673$	2.21758	−	1.61116i	0.0854813	−	0.0621058i	−0.544224	−	0.838940i	$-0.683176\pi$
$673$	2.21758	−	1.61116i	0.0854813	−	0.0621058i	0.629705	+	0.776834i	$0.283176\pi$
$674$	15.6871	+	48.2801i	0.604246	+	1.85968i
$675$	−0.182961	+	0.563098i	−0.00704219	+	0.0216736i
$676$	−0.494897	−	0.359564i	−0.0190345	−	0.0138294i
$677$	18.7138	+	13.5964i	0.719230	+	0.522551i	0.886138	−	0.463421i	$-0.153378\pi$
$677$	18.7138	+	13.5964i	0.719230	+	0.522551i	−0.166908	+	0.985972i	$0.553378\pi$
$678$	−2.10715	+	6.48515i	−0.0809248	+	0.249061i
$679$	−10.1333	−	31.1872i	−0.388882	−	1.19686i
$680$	−27.0095	+	19.6236i	−1.03577	+	0.752529i
$681$	1.52631			0.0584885
$682$	18.5936	−	37.9617i	0.711986	−	1.45363i
$683$	10.6098			0.405971			0.202986	−	0.979182i	$-0.434936\pi$
$683$	10.6098			0.405971			0.202986	+	0.979182i	$0.434936\pi$
$684$	−0.468435	+	0.340338i	−0.0179110	+	0.0130131i
$685$	12.6475	+	38.9250i	0.483237	+	1.48725i
$686$	−12.0016	+	36.9371i	−0.458223	+	1.41027i
$687$	−22.3704	−	16.2531i	−0.853485	−	0.620093i
$688$	−43.8757	−	31.8776i	−1.67275	−	1.21532i
$689$	−0.338740	+	1.04253i	−0.0129050	+	0.0397174i
$690$	−5.22123	−	16.0693i	−0.198769	−	0.611747i
$691$	0.460311	−	0.334435i	0.0175110	−	0.0127225i	−0.578995	−	0.815331i	$-0.696555\pi$
$691$	0.460311	−	0.334435i	0.0175110	−	0.0127225i	0.596506	+	0.802608i	$0.296555\pi$
$692$	9.18624			0.349208
$693$	−2.51587	−	14.4088i	−0.0955702	−	0.547344i
$694$	−43.7745			−1.66166
$695$	16.4563	−	11.9562i	0.624222	−	0.453524i
$696$	3.45886	+	10.6453i	0.131108	+	0.403508i
$697$	1.08898	−	3.35153i	0.0412480	−	0.126948i
$698$	−24.9402	−	18.1201i	−0.944000	−	0.685856i
$699$	6.66133	+	4.83974i	0.251955	+	0.183056i
$700$	−0.493593	+	1.51912i	−0.0186561	+	0.0574174i
$701$	3.33374	+	10.2602i	0.125914	+	0.387523i	0.994066	−	0.108774i	$-0.0346926\pi$
$701$	3.33374	+	10.2602i	0.125914	+	0.387523i	−0.868153	+	0.496297i	$0.834693\pi$
$702$	−1.30744	+	0.949910i	−0.0493461	+	0.0358520i
$703$	7.35397			0.277360
$704$	12.5598	−	6.65133i	0.473367	−	0.250681i
$705$	−2.54522			−0.0958586
$706$	1.07943	−	0.784255i	0.0406250	−	0.0295158i
$707$	10.6880	+	32.8943i	0.401963	+	1.23712i
$708$	−0.0174474	+	0.0536975i	−0.000655713	+	0.00201808i
$709$	−25.6535	−	18.6384i	−0.963439	−	0.699979i	−0.00949199	−	0.999955i	$-0.503021\pi$
$709$	−25.6535	−	18.6384i	−0.963439	−	0.699979i	−0.953947	+	0.299976i	$0.903021\pi$
$710$	−44.3202	−	32.2005i	−1.66331	−	1.20846i
$711$	0.754210	−	2.32122i	0.0282851	−	0.0870525i
$712$	5.09250	+	15.6731i	0.190850	+	0.587375i
$713$	31.7721	−	23.0838i	1.18987	−	0.864495i
$714$	50.5148			1.89047
$715$	−6.89388	−	0.980604i	−0.257816	−	0.0366725i
$716$	5.82173			0.217568
$717$	−24.0542	+	17.4764i	−0.898319	+	0.652667i
$718$	−10.0302	−	30.8698i	−0.374324	−	1.15205i
$719$	12.4350	−	38.2709i	0.463746	−	1.42726i	−0.396807	−	0.917902i	$-0.629882\pi$
$719$	12.4350	−	38.2709i	0.463746	−	1.42726i	0.860553	−	0.509361i	$-0.170118\pi$
$720$	−8.23661	−	5.98425i	−0.306960	−	0.223020i
$721$	41.6299	+	30.2459i	1.55038	+	1.12642i
$722$	9.04113	−	27.8257i	0.336476	−	1.03557i
$723$	3.98040	+	12.2504i	0.148033	+	0.455597i
$724$	−7.03334	+	5.11002i	−0.261392	+	0.189912i
$725$	−2.95385			−0.109703
$726$	10.8978	+	14.0448i	0.404454	+	0.521253i
$727$	28.7502			1.06628			0.533142	−	0.846026i	$-0.321011\pi$
$727$	28.7502			1.06628			0.533142	+	0.846026i	$0.321011\pi$
$728$	8.00477	−	5.81580i	0.296676	−	0.215548i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−3.26710	+	10.0551i	−0.120921	+	0.372156i
$731$	−64.1288	−	46.5923i	−2.37189	−	1.72328i
$732$	−4.78539	−	3.47679i	−0.176873	−	0.128506i
$733$	3.74810	−	11.5355i	0.138439	−	0.426072i	−0.857670	−	0.514201i	$-0.828089\pi$
$733$	3.74810	−	11.5355i	0.138439	−	0.426072i	0.996109	+	0.0881288i	$0.0280887\pi$
$734$	−12.4536	−	38.3282i	−0.459670	−	1.41472i
$735$	21.1456	−	15.3632i	0.779967	−	0.566679i
$736$	−16.6805			−0.614851
$737$	−27.9347	−	3.97351i	−1.02899	−	0.146366i
$738$	0.803523			0.0295781
$739$	21.1216	−	15.3457i	0.776969	−	0.564501i	−0.127099	−	0.991890i	$-0.540567\pi$
$739$	21.1216	−	15.3457i	0.776969	−	0.564501i	0.904068	+	0.427389i	$0.140567\pi$
$740$	−3.08350	−	9.49004i	−0.113352	−	0.348861i
$741$	−0.292494	+	0.900203i	−0.0107450	+	0.0330698i
$742$	6.32058	+	4.59217i	0.232036	+	0.168584i
$743$	−30.4945	−	22.1556i	−1.11874	−	0.812810i	−0.134719	−	0.990884i	$-0.543013\pi$
$743$	−30.4945	−	22.1556i	−1.11874	−	0.812810i	−0.984017	+	0.178074i	$0.943013\pi$
$744$	5.46765	−	16.8277i	0.200454	−	0.616933i
$745$	3.63478	+	11.1867i	0.133168	+	0.409849i
$746$	−31.0377	+	22.5502i	−1.13637	+	0.825621i
$747$	−13.7488			−0.503041
$748$	−12.7080	+	6.72977i	−0.464649	+	0.246065i
$749$	5.89678			0.215464
$750$	15.3501	−	11.1525i	0.560507	−	0.407232i
$751$	−7.21031	−	22.1910i	−0.263108	−	0.809763i	−0.992123	−	0.125265i	$-0.960022\pi$
$751$	−7.21031	−	22.1910i	−0.263108	−	0.809763i	0.729015	−	0.684497i	$-0.239978\pi$
$752$	−1.81662	+	5.59099i	−0.0662454	+	0.203882i
$753$	10.6204	+	7.71616i	0.387028	+	0.281193i
$754$	−6.52278	−	4.73908i	−0.237546	−	0.172587i
$755$	−2.49421	+	7.67638i	−0.0907735	+	0.279372i
$756$	0.833665	+	2.56576i	0.0303201	+	0.0933157i
$757$	−31.4875	+	22.8770i	−1.14443	+	0.831480i	−0.987731	−	0.156166i	$-0.950087\pi$
$757$	−31.4875	+	22.8770i	−1.14443	+	0.831480i	−0.156703	+	0.987646i	$0.550087\pi$
$758$	36.8971			1.34016
$759$	2.84084	+	16.2699i	0.103116	+	0.590559i
$760$	−4.45852			−0.161727
$761$	3.01413	−	2.18989i	0.109262	−	0.0793835i	−0.531813	−	0.846862i	$-0.678489\pi$
$761$	3.01413	−	2.18989i	0.109262	−	0.0793835i	0.641075	+	0.767479i	$0.278489\pi$
$762$	−5.23195	−	16.1023i	−0.189533	−	0.583324i
$763$	4.20763	−	12.9497i	0.152326	−	0.468812i
$764$	−4.99455	−	3.62875i	−0.180696	−	0.131284i
$765$	−12.0386	−	8.74659i	−0.435258	−	0.316234i
$766$	3.45113	−	10.6215i	0.124694	−	0.383770i
$767$	0.0285215	+	0.0877803i	0.00102985	+	0.00316956i
$768$	−10.8796	+	7.90452i	−0.392585	+	0.285230i
$769$	52.0029			1.87527			0.937636	−	0.347618i	$-0.113009\pi$
$769$	52.0029			1.87527			0.937636	+	0.347618i	$0.113009\pi$
$770$	−21.8300	+	44.5692i	−0.786699	+	1.60616i
$771$	26.9364			0.970092
$772$	4.68215	−	3.40178i	0.168514	−	0.122433i
$773$	−3.93228	−	12.1023i	−0.141434	−	0.435290i	0.855101	−	0.518461i	$-0.173495\pi$
$773$	−3.93228	−	12.1023i	−0.141434	−	0.435290i	−0.996535	+	0.0831717i	$0.973495\pi$
$774$	5.58520	−	17.1895i	0.200756	−	0.617863i
$775$	3.77758	+	2.74457i	0.135695	+	0.0985880i
$776$	13.4963	+	9.80564i	0.484489	+	0.352002i
$777$	10.5882	−	32.5871i	0.379850	−	1.16906i
$778$	6.25411	+	19.2482i	0.224221	+	0.690080i
$779$	0.380738	−	0.276622i	0.0136414	−	0.00991102i
$780$	1.28432			0.0459861
$781$	38.4586	+	37.2632i	1.37616	+	1.33338i
$782$	−57.0396			−2.03973
$783$	−4.03617	+	2.93245i	−0.144241	+	0.104797i
$784$	−18.6553	−	57.4150i	−0.666260	−	2.05054i
$785$	5.44326	−	16.7526i	0.194278	−	0.597927i
$786$	1.89898	+	1.37969i	0.0677345	+	0.0492120i
$787$	24.3861	+	17.7176i	0.869272	+	0.631563i	0.930392	−	0.366567i	$-0.119467\pi$
$787$	24.3861	+	17.7176i	0.869272	+	0.631563i	−0.0611194	+	0.998130i	$0.519467\pi$
$788$	−2.94858	+	9.07478i	−0.105039	+	0.323276i
$789$	5.32495	+	16.3885i	0.189573	+	0.583446i
$790$	−6.69959	+	4.86754i	−0.238361	+	0.173179i
$791$	18.6081			0.661628
$792$	5.34402	+	5.17792i	0.189892	+	0.183990i
$793$	−9.66946			−0.343373
$794$	19.1839	−	13.9379i	0.680810	−	0.494637i
$795$	−0.711186	−	2.18880i	−0.0252232	−	0.0776289i
$796$	1.35614	−	4.17376i	0.0480670	−	0.147935i
$797$	−15.1658	−	11.0186i	−0.537202	−	0.390300i	0.285843	−	0.958276i	$-0.407726\pi$
$797$	−15.1658	−	11.0186i	−0.537202	−	0.390300i	−0.823045	+	0.567977i	$0.807726\pi$
$798$	5.45768	+	3.96523i	0.193200	+	0.140368i
$799$	−2.65518	+	8.17180i	−0.0939335	+	0.289098i
$800$	−0.612857	−	1.88618i	−0.0216678	−	0.0666865i
$801$	−5.94248	+	4.31746i	−0.209967	+	0.152550i
$802$	−48.5699			−1.71506
$803$	4.54590	−	9.28114i	0.160421	−	0.327524i
$804$	5.20420			0.183538
$805$	−37.3024	+	27.1017i	−1.31474	+	0.955211i
$806$	3.93845	+	12.1213i	0.138726	+	0.426955i
$807$	0.511114	−	1.57305i	0.0179921	−	0.0553739i
$808$	−14.2350	−	10.3424i	−0.500787	−	0.363843i
$809$	−10.0588	−	7.30814i	−0.353648	−	0.256940i	0.396750	−	0.917927i	$-0.370138\pi$
$809$	−10.0588	−	7.30814i	−0.353648	−	0.256940i	−0.750398	+	0.660986i	$0.770138\pi$
$810$	1.04849	−	3.22691i	0.0368401	−	0.113382i
$811$	−8.36700	−	25.7510i	−0.293805	−	0.904239i	−0.983620	−	0.180253i	$-0.942308\pi$
$811$	−8.36700	−	25.7510i	−0.293805	−	0.904239i	0.689815	−	0.723985i	$-0.257692\pi$
$812$	−10.8888	+	7.91114i	−0.382120	+	0.277627i
$813$	1.34353			0.0471195
$814$	7.16289	+	41.0229i	0.251059	+	1.43785i
$815$	−36.6439			−1.28358
$816$	−27.8058	+	20.2021i	−0.973396	+	0.707214i
$817$	−3.27121	−	10.0678i	−0.114445	−	0.352226i
$818$	−4.10926	+	12.6470i	−0.143677	+	0.442193i
$819$	3.56788	+	2.59221i	0.124672	+	0.0905793i
$820$	−0.516614	−	0.375342i	−0.0180409	−	0.0131075i
$821$	−9.34055	+	28.7473i	−0.325987	+	1.00329i	0.645006	+	0.764178i	$0.276855\pi$
$821$	−9.34055	+	28.7473i	−0.325987	+	1.00329i	−0.970993	+	0.239108i	$0.923145\pi$
$822$	9.73536	+	29.9623i	0.339560	+	1.04506i
$823$	23.8304	−	17.3138i	0.830674	−	0.603520i	−0.0890759	−	0.996025i	$-0.528391\pi$
$823$	23.8304	−	17.3138i	0.830674	−	0.603520i	0.919750	+	0.392505i	$0.128391\pi$
$824$	−26.1779			−0.911949
$825$	−1.73537	+	0.919004i	−0.0604180	+	0.0319956i
$826$	0.657819			0.0228885
$827$	−35.6492	+	25.9007i	−1.23964	+	0.900654i	−0.997575	−	0.0696051i	$-0.977826\pi$
$827$	−35.6492	+	25.9007i	−1.23964	+	0.900654i	−0.242069	+	0.970259i	$0.577826\pi$
$828$	−0.941345	−	2.89716i	−0.0327140	−	0.100683i
$829$	−10.5238	+	32.3888i	−0.365505	+	1.12491i	0.584159	+	0.811639i	$0.301424\pi$
$829$	−10.5238	+	32.3888i	−0.365505	+	1.12491i	−0.949664	+	0.313270i	$0.898576\pi$
$830$	37.7400	+	27.4197i	1.30998	+	0.951753i
$831$	−10.5510	−	7.66576i	−0.366011	−	0.265922i
$832$	−1.32419	+	4.07544i	−0.0459081	+	0.141291i
$833$	−27.2666	−	83.9179i	−0.944731	−	2.90758i
$834$	12.6671	−	9.20321i	0.438627	−	0.318681i
$835$	25.1662			0.870912
$836$	−1.90124	−	0.270438i	−0.0657559	−	0.00935330i
$837$	7.88640			0.272594
$838$	−41.0546	+	29.8279i	−1.41821	+	1.03039i
$839$	0.667628	+	2.05475i	0.0230491	+	0.0709378i	0.961919	−	0.273333i	$-0.0881261\pi$
$839$	0.667628	+	2.05475i	0.0230491	+	0.0709378i	−0.938870	+	0.344271i	$0.888126\pi$
$840$	−6.41934	+	19.7567i	−0.221488	+	0.681671i
$841$	3.32516	+	2.41587i	0.114661	+	0.0833058i
$842$	−9.76198	−	7.09250i	−0.336420	−	0.244424i
$843$	−7.20825	+	22.1847i	−0.248265	+	0.764082i
$844$	−5.40207	−	16.6259i	−0.185947	−	0.572286i
$845$	1.69854	−	1.23406i	0.0584314	−	0.0424529i
$846$	−1.95917			−0.0673577
$847$	27.2613	−	40.1271i	0.936711	−	1.37878i
$848$	−5.31566			−0.182541
$849$	−8.35037	+	6.06690i	−0.286584	+	0.208215i
$850$	−2.09569	−	6.44986i	−0.0718815	−	0.221228i
$851$	−11.9558	+	36.7962i	−0.409840	+	1.26136i
$852$	−7.99058	−	5.80549i	−0.273753	−	0.198893i
$853$	32.8705	+	23.8818i	1.12547	+	0.817699i	0.985029	−	0.172391i	$-0.0551492\pi$
$853$	32.8705	+	23.8818i	1.12547	+	0.817699i	0.140437	+	0.990090i	$0.455149\pi$
$854$	−21.2961	+	65.5427i	−0.728738	+	2.24283i
$855$	−0.614092	−	1.88998i	−0.0210015	−	0.0646360i
$856$	−2.42694	+	1.76328i	−0.0829512	+	0.0602676i
$857$	6.55009			0.223747			0.111873	−	0.993722i	$-0.464315\pi$
$857$	6.55009			0.223747			0.111873	+	0.993722i	$0.464315\pi$
$858$	−5.30653	−	0.754815i	−0.181162	−	0.0257690i
$859$	−17.9430			−0.612207			−0.306103	−	0.951998i	$-0.599025\pi$
$859$	−17.9430			−0.612207			−0.306103	+	0.951998i	$0.599025\pi$
$860$	−11.6205	+	8.44278i	−0.396255	+	0.287896i
$861$	−0.677593	−	2.08542i	−0.0230923	−	0.0710708i
$862$	−16.1502	+	49.7053i	−0.550079	+	1.69297i
$863$	11.0397	+	8.02079i	0.375795	+	0.273031i	0.759610	−	0.650379i	$-0.225390\pi$
$863$	11.0397	+	8.02079i	0.375795	+	0.273031i	−0.383815	+	0.923410i	$0.625390\pi$
$864$	−2.70992	−	1.96887i	−0.0921935	−	0.0669825i
$865$	−9.74272	+	29.9850i	−0.331262	+	1.01952i
$866$	−9.19379	−	28.2956i	−0.312418	−	0.961523i
$867$	−26.8877	+	19.5350i	−0.913153	+	0.663444i
$868$	21.2759			0.722151
$869$	7.15362	−	3.78835i	0.242670	−	0.128511i
$870$	16.9275			0.573895
$871$	6.88264	−	5.00053i	0.233209	−	0.169436i
$872$	2.14054	+	6.58791i	0.0724879	+	0.223095i
$873$	−2.29774	+	7.07171i	−0.0777667	+	0.239341i
$874$	−6.16262	−	4.47740i	−0.208454	−	0.151450i
$875$	−41.8890	−	30.4341i	−1.41611	−	1.02886i
$876$	−0.589031	+	1.81285i	−0.0199015	+	0.0612506i
$877$	−14.0168	−	43.1392i	−0.473313	−	1.45671i	−0.848219	−	0.529645i	$-0.822325\pi$
$877$	−14.0168	−	43.1392i	−0.473313	−	1.45671i	0.374906	−	0.927063i	$-0.377675\pi$
$878$	5.69738	−	4.13939i	0.192277	−	0.139698i
$879$	−2.03726			−0.0687152
$880$	−5.80802	−	33.2634i	−0.195788	−	1.12131i
$881$	−0.648468			−0.0218474			−0.0109237	−	0.999940i	$-0.503477\pi$
$881$	−0.648468			−0.0218474			−0.0109237	+	0.999940i	$0.503477\pi$
$882$	16.2767	−	11.8257i	0.548065	−	0.398193i
$883$	−16.6313	−	51.1859i	−0.559688	−	1.72254i	−0.683229	−	0.730204i	$-0.739425\pi$
$883$	−16.6313	−	51.1859i	−0.559688	−	1.72254i	0.123541	−	0.992340i	$-0.460575\pi$
$884$	1.33981	−	4.12350i	0.0450626	−	0.138688i
$885$	−0.156771	−	0.113901i	−0.00526980	−	0.00382873i
$886$	−15.5997	−	11.3339i	−0.524084	−	0.380769i
$887$	0.227875	−	0.701327i	0.00765129	−	0.0235483i	−0.947158	−	0.320767i	$-0.896059\pi$
$887$	0.227875	−	0.701327i	0.00765129	−	0.0235483i	0.954809	+	0.297219i	$0.0960592\pi$
$888$	5.38653	+	16.5780i	0.180760	+	0.556322i
$889$	−37.3789	+	27.1574i	−1.25365	+	0.910829i
$890$	24.9225			0.835403
$891$	−1.45888	+	2.97853i	−0.0488745	+	0.0997846i
$892$	0.122716			0.00410884
$893$	−0.928326	+	0.674468i	−0.0310652	+	0.0225702i
$894$	2.79785	+	8.61089i	0.0935741	+	0.287991i
$895$	−6.17440	+	19.0028i	−0.206387	+	0.635195i
$896$	48.6105	+	35.3176i	1.62396	+	1.17988i
$897$	−4.02872	−	2.92704i	−0.134515	−	0.0977309i
$898$	−11.0514	+	34.0127i	−0.368790	+	1.13502i
$899$	12.1583	+	37.4194i	0.405502	+	1.24801i
$900$	0.293016	−	0.212889i	0.00976721	−	0.00709630i
$901$	−7.76939			−0.258836
$902$	1.91394	+	1.85445i	0.0637271	+	0.0617464i
$903$	−49.3224			−1.64135
$904$	−7.65855	+	5.56426i	−0.254720	+	0.185065i
$905$	−9.22032	−	28.3772i	−0.306494	−	0.943291i
$906$	−1.91990	+	5.90886i	−0.0637845	+	0.196309i
$907$	−17.5533	−	12.7532i	−0.582848	−	0.423464i	0.256902	−	0.966438i	$-0.417298\pi$
$907$	−17.5533	−	12.7532i	−0.582848	−	0.423464i	−0.839750	+	0.542974i	$0.817298\pi$
$908$	−0.755368	−	0.548807i	−0.0250678	−	0.0182128i
$909$	2.42351	−	7.45878i	0.0803826	−	0.247392i
$910$	−4.62397	−	14.2311i	−0.153283	−	0.471757i
$911$	−6.16070	+	4.47601i	−0.204113	+	0.148297i	−0.685146	−	0.728406i	$-0.740262\pi$
$911$	−6.16070	+	4.47601i	−0.204113	+	0.148297i	0.481033	+	0.876702i	$0.340262\pi$
$912$	−4.58995			−0.151989
$913$	−32.7486	−	31.7308i	−1.08382	−	1.05014i
$914$	33.2814			1.10085
$915$	16.4239	−	11.9327i	0.542958	−	0.394482i
$916$	5.22704	+	16.0872i	0.172706	+	0.531535i
$917$	1.97940	−	6.09197i	0.0653656	−	0.201175i
$918$	−9.26669	−	6.73264i	−0.305846	−	0.222210i
$919$	12.3268	+	8.95593i	0.406623	+	0.295429i	0.772233	−	0.635339i	$-0.219140\pi$
$919$	12.3268	+	8.95593i	0.406623	+	0.295429i	−0.365610	+	0.930768i	$0.619140\pi$
$920$	7.24850	−	22.3086i	0.238976	−	0.735492i
$921$	8.29232	+	25.5211i	0.273241	+	0.840950i
$922$	−5.38325	+	3.91116i	−0.177288	+	0.128807i
$923$	−16.1459			−0.531450
$924$	−3.93577	+	8.03547i	−0.129477	+	0.264348i
$925$	−4.60008			−0.151250
$926$	17.6827	−	12.8472i	0.581090	−	0.422187i
$927$	−3.60560	−	11.0969i	−0.118423	−	0.364470i
$928$	5.16408	−	15.8934i	0.169519	−	0.521727i
$929$	−34.1610	−	24.8194i	−1.12079	−	0.814298i	−0.136457	−	0.990646i	$-0.543572\pi$
$929$	−34.1610	−	24.8194i	−1.12079	−	0.814298i	−0.984328	+	0.176348i	$0.943572\pi$
$930$	−21.6480	−	15.7282i	−0.709865	−	0.515747i
$931$	3.64134	−	11.2069i	0.119340	−	0.367291i
$932$	−1.55648	−	4.79035i	−0.0509841	−	0.156913i
$933$	−12.9276	+	9.39246i	−0.423231	+	0.307495i
$934$	−24.4972			−0.801574
$935$	−8.48901	−	48.6178i	−0.277620	−	1.58997i
$936$	−2.24357			−0.0733333
$937$	10.3811	−	7.54231i	0.339136	−	0.246396i	−0.405161	−	0.914245i	$-0.632785\pi$
$937$	10.3811	−	7.54231i	0.339136	−	0.246396i	0.744297	+	0.667849i	$0.232785\pi$
$938$	−18.7368	−	57.6660i	−0.611778	−	1.88286i
$939$	2.05120	−	6.31296i	0.0669385	−	0.206016i
$940$	1.25962	+	0.915169i	0.0410843	+	0.0298495i
$941$	23.6940	+	17.2147i	0.772402	+	0.561183i	0.902689	−	0.430293i	$-0.141590\pi$
$941$	23.6940	+	17.2147i	0.772402	+	0.561183i	−0.130287	+	0.991476i	$0.541590\pi$
$942$	4.18992	−	12.8953i	0.136515	−	0.420150i
$943$	0.765114	+	2.35478i	0.0249155	+	0.0766821i
$944$	−0.362095	+	0.263077i	−0.0117852	+	0.00856244i
$945$	−9.25911			−0.301199
$946$	52.9751	−	28.0541i	1.72237	−	0.912118i
$947$	−5.04354			−0.163893			−0.0819466	−	0.996637i	$-0.526114\pi$
$947$	−5.04354			−0.163893			−0.0819466	+	0.996637i	$0.526114\pi$
$948$	−1.20788	+	0.877578i	−0.0392302	+	0.0285024i
$949$	0.962901	+	2.96350i	0.0312571	+	0.0961994i
$950$	0.279871	−	0.861354i	0.00908021	−	0.0279460i
$951$	−3.78387	−	2.74914i	−0.122700	−	0.0891470i
$952$	56.7351	+	41.2205i	1.83879	+	1.33596i
$953$	−4.58297	+	14.1049i	−0.148457	+	0.456904i	−0.997439	−	0.0715175i	$-0.977216\pi$
$953$	−4.58297	+	14.1049i	−0.148457	+	0.456904i	0.848982	+	0.528421i	$0.177216\pi$
$954$	−0.547432	−	1.68482i	−0.0177237	−	0.0545481i
$955$	17.1418	−	12.4542i	0.554696	−	0.403010i
$956$	18.1882			0.588248
$957$	−16.3817	−	2.33017i	−0.529544	−	0.0753238i
$958$	−0.766922			−0.0247781
$959$	69.5529	−	50.5332i	2.24598	−	1.63180i
$960$	−2.78015	−	8.55641i	−0.0897289	−	0.276157i
$961$	9.63990	−	29.6686i	0.310964	−	0.957050i
$962$	−10.1580	−	7.38024i	−0.327508	−	0.237948i
$963$	−1.08173	−	0.785926i	−0.0348584	−	0.0253261i
$964$	2.43491	−	7.49389i	0.0784233	−	0.241362i
$965$	6.13804	+	18.8909i	0.197591	+	0.608121i
$966$	−28.7133	+	20.8614i	−0.923835	+	0.671205i
$967$	27.0278			0.869156			0.434578	−	0.900634i	$-0.356898\pi$
$967$	27.0278			0.869156			0.434578	+	0.900634i	$0.356898\pi$
$968$	0.778984	+	24.6669i	0.0250375	+	0.792825i
$969$	−6.70868			−0.215514
$970$	20.4106	−	14.8292i	0.655346	−	0.476137i
$971$	4.08660	+	12.5773i	0.131145	+	0.403624i	0.994971	−	0.100168i	$-0.0319379\pi$
$971$	4.08660	+	12.5773i	0.131145	+	0.403624i	−0.863825	+	0.503792i	$0.831938\pi$
$972$	0.189034	−	0.581786i	0.00606326	−	0.0186608i
$973$	−34.5674	−	25.1147i	−1.10818	−	0.805139i
$974$	18.8830	+	13.7193i	0.605051	+	0.439595i
$975$	0.182961	−	0.563098i	0.00585946	−	0.0180336i
$976$	−14.4897	−	44.5946i	−0.463803	−	1.42744i
$977$	−20.3209	+	14.7640i	−0.650124	+	0.472343i	−0.863313	−	0.504668i	$-0.831615\pi$
$977$	−20.3209	+	14.7640i	−0.650124	+	0.472343i	0.213190	+	0.977011i	$0.431615\pi$
$978$	−28.2065			−0.901944
$979$	−24.1189	−	3.43073i	−0.770842	−	0.109647i
$980$	−15.9889			−0.510747
$981$	−2.49782	+	1.81477i	−0.0797491	+	0.0579411i
$982$	13.4304	+	41.3345i	0.428581	+	1.31904i
$983$	−1.52431	+	4.69134i	−0.0486179	+	0.149630i	−0.972418	−	0.233244i	$-0.925066\pi$
$983$	−1.52431	+	4.69134i	−0.0486179	+	0.149630i	0.923800	+	0.382875i	$0.125066\pi$
$984$	0.902466	+	0.655680i	0.0287696	+	0.0209023i
$985$	−26.4940	−	19.2490i	−0.844169	−	0.613325i
$986$	17.6588	−	54.3481i	0.562370	−	1.73080i
$987$	1.65212	+	5.08472i	0.0525877	+	0.161848i
$988$	0.468435	−	0.340338i	0.0149029	−	0.0108276i
$989$	55.6932			1.77094
$990$	9.94481	−	5.26649i	0.316067	−	0.167380i
$991$	9.74941			0.309700			0.154850	−	0.987938i	$-0.450511\pi$
$991$	9.74941			0.309700			0.154850	+	0.987938i	$0.450511\pi$
$992$	−21.3715	+	15.5273i	−0.678547	+	0.492994i
$993$	2.26590	+	6.97371i	0.0719060	+	0.221304i
$994$	−35.5600	+	109.442i	−1.12789	+	3.47130i
$995$	12.1854	+	8.85319i	0.386302	+	0.280665i
$996$	6.80422	+	4.94356i	0.215600	+	0.156643i
$997$	1.45918	−	4.49089i	0.0462126	−	0.142228i	−0.925288	−	0.379266i	$-0.876177\pi$
$997$	1.45918	−	4.49089i	0.0462126	−	0.142228i	0.971500	+	0.237038i	$0.0761766\pi$
$998$	7.03536	+	21.6526i	0.222700	+	0.685402i
$999$	−6.28558	+	4.56674i	−0.198867	+	0.144485i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.n.d.157.7	✓	36
11.2	odd	10		4719.2.a.br.1.14		18
11.4	even	5	inner	429.2.n.d.235.7	yes	36
11.9	even	5		4719.2.a.bq.1.5		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.n.d.157.7	✓	36	1.1	even	1	trivial
429.2.n.d.235.7	yes	36	11.4	even	5	inner
4719.2.a.bq.1.5		18	11.9	even	5
4719.2.a.br.1.14		18	11.2	odd	10

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.30744 - 0.949910i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.189034 - 0.581786i) q^{4} +(1.69854 + 1.23406i) q^{5} +(1.30744 + 0.949910i) q^{6} +(1.36281 - 4.19429i) q^{7} +(0.693300 + 2.13376i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(1.30744 - 0.949910i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.189034 - 0.581786i) q^{4} +(1.69854 + 1.23406i) q^{5} +(1.30744 + 0.949910i) q^{6} +(1.36281 - 4.19429i) q^{7} +(0.693300 + 2.13376i) q^{8} +(-0.809017 + 0.587785i) q^{9} +3.39298 q^{10} +(-3.28357 - 0.467064i) q^{11} +0.611726 q^{12} +(0.809017 - 0.587785i) q^{13} +(-2.20241 - 6.77832i) q^{14} +(-0.648783 + 1.99675i) q^{15} +(3.92312 + 2.85031i) q^{16} +(5.73404 + 4.16602i) q^{17} +(-0.499397 + 1.53699i) q^{18} +(0.292494 + 0.900203i) q^{19} +(1.03904 - 0.754906i) q^{20} +4.41014 q^{21} +(-4.73674 + 2.50844i) q^{22} -4.97977 q^{23} +(-1.81508 + 1.31874i) q^{24} +(-0.182961 - 0.563098i) q^{25} +(0.499397 - 1.53699i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-2.18256 - 1.58572i) q^{28} +(1.54168 - 4.74480i) q^{29} +(1.04849 + 3.22691i) q^{30} +(-6.38023 + 4.63551i) q^{31} +3.34965 q^{32} +(-0.570475 - 3.26719i) q^{33} +11.4543 q^{34} +(7.49077 - 5.44237i) q^{35} +(0.189034 + 0.581786i) q^{36} +(2.40088 - 7.38914i) q^{37} +(1.23753 + 0.899118i) q^{38} +(0.809017 + 0.587785i) q^{39} +(-1.45559 + 4.47984i) q^{40} +(-0.153644 - 0.472869i) q^{41} +(5.76598 - 4.18923i) q^{42} -11.1839 q^{43} +(-0.892438 + 1.82205i) q^{44} -2.09951 q^{45} +(-6.51075 + 4.73034i) q^{46} +(0.374620 + 1.15296i) q^{47} +(-1.49850 + 4.61190i) q^{48} +(-10.0717 - 7.31752i) q^{49} +(-0.774103 - 0.562419i) q^{50} +(-2.19021 + 6.74077i) q^{51} +(-0.189034 - 0.581786i) q^{52} +(-0.886832 + 0.644321i) q^{53} -1.61608 q^{54} +(-5.00088 - 4.84545i) q^{55} +9.89444 q^{56} +(-0.765759 + 0.556356i) q^{57} +(-2.49148 - 7.66799i) q^{58} +(-0.0285215 + 0.0877803i) q^{59} +(1.03904 + 0.754906i) q^{60} +(-7.82276 - 5.68357i) q^{61} +(-3.93845 + 12.1213i) q^{62} +(1.36281 + 4.19429i) q^{63} +(-3.46678 + 2.51876i) q^{64} +2.09951 q^{65} +(-3.84940 - 3.72976i) q^{66} +8.50741 q^{67} +(3.50766 - 2.54847i) q^{68} +(-1.53883 - 4.73604i) q^{69} +(4.62397 - 14.2311i) q^{70} +(-13.0623 - 9.49035i) q^{71} +(-1.81508 - 1.31874i) q^{72} +(-0.962901 + 2.96350i) q^{73} +(-3.88002 - 11.9415i) q^{74} +(0.478999 - 0.348013i) q^{75} +0.579017 q^{76} +(-6.43388 + 13.1357i) q^{77} +1.61608 q^{78} +(-1.97455 + 1.43459i) q^{79} +(3.14611 + 9.68272i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-0.650064 - 0.472299i) q^{82} +(11.1230 + 8.08132i) q^{83} +(0.833665 - 2.56576i) q^{84} +(4.59835 + 14.1523i) q^{85} +(-14.6222 + 10.6237i) q^{86} +4.98898 q^{87} +(-1.27990 - 7.33017i) q^{88} +7.34531 q^{89} +(-2.74498 + 1.99434i) q^{90} +(-1.36281 - 4.19429i) q^{91} +(-0.941345 + 2.89716i) q^{92} +(-6.38023 - 4.63551i) q^{93} +(1.58500 + 1.15157i) q^{94} +(-0.614092 + 1.88998i) q^{95} +(1.03510 + 3.18571i) q^{96} +(6.01556 - 4.37056i) q^{97} -20.1191 q^{98} +(2.93100 - 1.55217i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{2} - 9 q^{3} - 11 q^{4} + 3 q^{6} + q^{7} - q^{8} - 9 q^{9}+O(q^{10}) \) 36 * q + 3 * q^2 - 9 * q^3 - 11 * q^4 + 3 * q^6 + q^7 - q^8 - 9 * q^9	\( 36 q + 3 q^{2} - 9 q^{3} - 11 q^{4} + 3 q^{6} + q^{7} - q^{8} - 9 q^{9} + 6 q^{10} - 10 q^{11} + 54 q^{12} + 9 q^{13} - 5 q^{14} - 10 q^{15} - 13 q^{16} - 2 q^{18} + 10 q^{19} + 37 q^{20} - 14 q^{21} - 9 q^{22} + 18 q^{23} + 4 q^{24} - 31 q^{25} + 2 q^{26} - 9 q^{27} + 12 q^{28} + 10 q^{29} + q^{30} - 28 q^{31} - 74 q^{32} + 5 q^{33} + 40 q^{34} - 14 q^{35} - 11 q^{36} - 26 q^{37} + 7 q^{38} + 9 q^{39} - 72 q^{40} + 26 q^{41} - 5 q^{42} + 4 q^{43} - 68 q^{44} + 20 q^{45} - 57 q^{46} - 28 q^{48} - 18 q^{49} + 11 q^{50} - 5 q^{51} + 11 q^{52} + 11 q^{53} - 2 q^{54} - 32 q^{55} + 72 q^{56} + 50 q^{58} + 55 q^{59} + 37 q^{60} + 14 q^{61} - 50 q^{62} + q^{63} - q^{64} - 20 q^{65} - 14 q^{66} + 104 q^{67} - 9 q^{68} + 8 q^{69} + 44 q^{70} - 8 q^{71} + 4 q^{72} - 3 q^{73} + 69 q^{74} - 21 q^{75} - 52 q^{76} + 2 q^{77} + 2 q^{78} - 19 q^{79} - 159 q^{80} - 9 q^{81} + 58 q^{82} + 12 q^{83} - 8 q^{84} + 63 q^{86} - 97 q^{88} + 118 q^{89} - 4 q^{90} - q^{91} + 98 q^{92} - 28 q^{93} - 99 q^{94} - 45 q^{95} + q^{96} + 50 q^{97} - 186 q^{98}+O(q^{100}) \) 36 * q + 3 * q^2 - 9 * q^3 - 11 * q^4 + 3 * q^6 + q^7 - q^8 - 9 * q^9 + 6 * q^10 - 10 * q^11 + 54 * q^12 + 9 * q^13 - 5 * q^14 - 10 * q^15 - 13 * q^16 - 2 * q^18 + 10 * q^19 + 37 * q^20 - 14 * q^21 - 9 * q^22 + 18 * q^23 + 4 * q^24 - 31 * q^25 + 2 * q^26 - 9 * q^27 + 12 * q^28 + 10 * q^29 + q^30 - 28 * q^31 - 74 * q^32 + 5 * q^33 + 40 * q^34 - 14 * q^35 - 11 * q^36 - 26 * q^37 + 7 * q^38 + 9 * q^39 - 72 * q^40 + 26 * q^41 - 5 * q^42 + 4 * q^43 - 68 * q^44 + 20 * q^45 - 57 * q^46 - 28 * q^48 - 18 * q^49 + 11 * q^50 - 5 * q^51 + 11 * q^52 + 11 * q^53 - 2 * q^54 - 32 * q^55 + 72 * q^56 + 50 * q^58 + 55 * q^59 + 37 * q^60 + 14 * q^61 - 50 * q^62 + q^63 - q^64 - 20 * q^65 - 14 * q^66 + 104 * q^67 - 9 * q^68 + 8 * q^69 + 44 * q^70 - 8 * q^71 + 4 * q^72 - 3 * q^73 + 69 * q^74 - 21 * q^75 - 52 * q^76 + 2 * q^77 + 2 * q^78 - 19 * q^79 - 159 * q^80 - 9 * q^81 + 58 * q^82 + 12 * q^83 - 8 * q^84 + 63 * q^86 - 97 * q^88 + 118 * q^89 - 4 * q^90 - q^91 + 98 * q^92 - 28 * q^93 - 99 * q^94 - 45 * q^95 + q^96 + 50 * q^97 - 186 * q^98

Introduction

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