LMFDB - Embedded newform 462.2.j.g.169.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(169,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("462.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.j (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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.324000000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 9x^{4} + 27x^{2} + 81 $ x^8 + 3x^6 + 9x^4 + 27*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			169.1
Root			$0.535233 - 1.64728i$ of defining polynomial
Character	$\chi$	$=$	462.169
Dual form			462.2.j.g.421.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.26728 + 1.64728i) q^{5} +(0.809017 - 0.587785i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.26728 + 1.64728i) q^{5} +(0.809017 - 0.587785i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.809017 - 0.587785i) q^{9} -2.80252 q^{10} +(3.31485 - 0.108436i) q^{11} +1.00000 q^{12} +(5.56036 + 4.03984i) q^{13} +(-0.309017 + 0.951057i) q^{14} +(0.866025 + 2.66535i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.68448 + 1.22385i) q^{17} +(-0.309017 - 0.951057i) q^{18} +(-2.10570 + 6.48068i) q^{19} +(-2.26728 - 1.64728i) q^{20} +1.00000 q^{21} +(2.74551 + 1.86069i) q^{22} -1.57448 q^{23} +(0.809017 + 0.587785i) q^{24} +(0.881966 - 2.71441i) q^{25} +(2.12387 + 6.53660i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(-0.809017 + 0.587785i) q^{28} +(-2.16672 - 6.66849i) q^{29} +(-0.866025 + 2.66535i) q^{30} +(3.70378 + 2.69095i) q^{31} -1.00000 q^{32} +(0.921216 - 3.18612i) q^{33} -2.08214 q^{34} +(-2.26728 - 1.64728i) q^{35} +(0.309017 - 0.951057i) q^{36} +(-3.36201 - 10.3472i) q^{37} +(-5.51279 + 4.00528i) q^{38} +(5.56036 - 4.03984i) q^{39} +(-0.866025 - 2.66535i) q^{40} +(-0.0475677 + 0.146398i) q^{41} +(0.809017 + 0.587785i) q^{42} +7.20419 q^{43} +(1.12747 + 3.11910i) q^{44} +2.80252 q^{45} +(-1.27378 - 0.925458i) q^{46} +(1.91541 - 5.89503i) q^{47} +(0.309017 + 0.951057i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(2.30902 - 1.67760i) q^{50} +(0.643415 + 1.98023i) q^{51} +(-2.12387 + 6.53660i) q^{52} +(3.49283 + 2.53769i) q^{53} -1.00000 q^{54} +(-7.33708 + 5.70634i) q^{55} -1.00000 q^{56} +(5.51279 + 4.00528i) q^{57} +(2.16672 - 6.66849i) q^{58} +(-2.89878 - 8.92151i) q^{59} +(-2.26728 + 1.64728i) q^{60} +(5.96630 - 4.33477i) q^{61} +(1.41472 + 4.35405i) q^{62} +(0.309017 - 0.951057i) q^{63} +(-0.809017 - 0.587785i) q^{64} -19.2617 q^{65} +(2.61803 - 2.03615i) q^{66} -6.66465 q^{67} +(-1.68448 - 1.22385i) q^{68} +(-0.486542 + 1.49742i) q^{69} +(-0.866025 - 2.66535i) q^{70} +(4.26662 - 3.09988i) q^{71} +(0.809017 - 0.587785i) q^{72} +(-1.23494 - 3.80077i) q^{73} +(3.36201 - 10.3472i) q^{74} +(-2.30902 - 1.67760i) q^{75} -6.81419 q^{76} +(1.12747 + 3.11910i) q^{77} +6.87298 q^{78} +(-7.97106 - 5.79131i) q^{79} +(0.866025 - 2.66535i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-0.124534 + 0.0904792i) q^{82} +(-7.00985 + 5.09296i) q^{83} +(0.309017 + 0.951057i) q^{84} +(1.80318 - 5.54962i) q^{85} +(5.82831 + 4.23451i) q^{86} -7.01167 q^{87} +(-0.921216 + 3.18612i) q^{88} -1.48514 q^{89} +(2.26728 + 1.64728i) q^{90} +(-2.12387 + 6.53660i) q^{91} +(-0.486542 - 1.49742i) q^{92} +(3.70378 - 2.69095i) q^{93} +(5.01461 - 3.64333i) q^{94} +(-5.90126 - 18.1622i) q^{95} +(-0.309017 + 0.951057i) q^{96} +(4.74190 + 3.44519i) q^{97} -1.00000 q^{98} +(-2.74551 - 1.86069i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9	$ 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} + 8 q^{11} + 8 q^{12} + 6 q^{13} + 2 q^{14} - 2 q^{16} + 2 q^{18} - 4 q^{19} + 8 q^{21} + 2 q^{22} + 2 q^{24} + 16 q^{25} - 6 q^{26} - 2 q^{27} - 2 q^{28} + 2 q^{29} - 4 q^{31} - 8 q^{32} + 8 q^{33} + 20 q^{34} - 2 q^{36} - 24 q^{37} - 6 q^{38} + 6 q^{39} + 2 q^{42} + 8 q^{43} - 2 q^{44} - 10 q^{46} - 2 q^{47} - 2 q^{48} - 2 q^{49} + 14 q^{50} + 10 q^{51} + 6 q^{52} - 22 q^{53} - 8 q^{54} - 8 q^{56} + 6 q^{57} - 2 q^{58} + 10 q^{59} + 26 q^{61} - 6 q^{62} - 2 q^{63} - 2 q^{64} - 60 q^{65} + 12 q^{66} + 4 q^{67} - 10 q^{69} - 16 q^{71} + 2 q^{72} - 2 q^{73} + 24 q^{74} - 14 q^{75} - 4 q^{76} - 2 q^{77} + 24 q^{78} - 12 q^{79} - 2 q^{81} - 10 q^{82} - 38 q^{83} - 2 q^{84} + 24 q^{85} + 22 q^{86} - 28 q^{87} - 8 q^{88} - 12 q^{89} + 6 q^{91} - 10 q^{92} - 4 q^{93} - 8 q^{94} - 36 q^{95} + 2 q^{96} + 6 q^{97} - 8 q^{98} - 2 q^{99}+O(q^{100}) $ 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9 + 8 * q^11 + 8 * q^12 + 6 * q^13 + 2 * q^14 - 2 * q^16 + 2 * q^18 - 4 * q^19 + 8 * q^21 + 2 * q^22 + 2 * q^24 + 16 * q^25 - 6 * q^26 - 2 * q^27 - 2 * q^28 + 2 * q^29 - 4 * q^31 - 8 * q^32 + 8 * q^33 + 20 * q^34 - 2 * q^36 - 24 * q^37 - 6 * q^38 + 6 * q^39 + 2 * q^42 + 8 * q^43 - 2 * q^44 - 10 * q^46 - 2 * q^47 - 2 * q^48 - 2 * q^49 + 14 * q^50 + 10 * q^51 + 6 * q^52 - 22 * q^53 - 8 * q^54 - 8 * q^56 + 6 * q^57 - 2 * q^58 + 10 * q^59 + 26 * q^61 - 6 * q^62 - 2 * q^63 - 2 * q^64 - 60 * q^65 + 12 * q^66 + 4 * q^67 - 10 * q^69 - 16 * q^71 + 2 * q^72 - 2 * q^73 + 24 * q^74 - 14 * q^75 - 4 * q^76 - 2 * q^77 + 24 * q^78 - 12 * q^79 - 2 * q^81 - 10 * q^82 - 38 * q^83 - 2 * q^84 + 24 * q^85 + 22 * q^86 - 28 * q^87 - 8 * q^88 - 12 * q^89 + 6 * q^91 - 10 * q^92 - 4 * q^93 - 8 * q^94 - 36 * q^95 + 2 * q^96 + 6 * q^97 - 8 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−2.26728	+	1.64728i	−1.01396	+	0.736685i	−0.965036	−	0.262117i	$-0.915579\pi$
$5$	−2.26728	+	1.64728i	−1.01396	+	0.736685i	−0.0489242	+	0.998802i	$0.515579\pi$
$6$	0.809017	−	0.587785i	0.330280	−	0.239962i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	−2.80252			−0.886234
$11$	3.31485	−	0.108436i	0.999465	−	0.0326948i
$11$	3.31485	−	0.108436i	0.999465	−	0.0326948i
$12$	1.00000			0.288675
$13$	5.56036	+	4.03984i	1.54217	+	1.12045i	0.948959	+	0.315400i	$0.102139\pi$
$13$	5.56036	+	4.03984i	1.54217	+	1.12045i	0.593208	+	0.805049i	$0.297861\pi$
$14$	−0.309017	+	0.951057i	−0.0825883	+	0.254181i
$15$	0.866025	+	2.66535i	0.223607	+	0.688191i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−1.68448	+	1.22385i	−0.408547	+	0.296827i	−0.773013	−	0.634390i	$-0.781251\pi$
$17$	−1.68448	+	1.22385i	−0.408547	+	0.296827i	0.364466	+	0.931217i	$0.381251\pi$
$18$	−0.309017	−	0.951057i	−0.0728360	−	0.224166i
$19$	−2.10570	+	6.48068i	−0.483081	+	1.48677i	0.351661	+	0.936127i	$0.385617\pi$
$19$	−2.10570	+	6.48068i	−0.483081	+	1.48677i	−0.834742	+	0.550642i	$0.814383\pi$
$20$	−2.26728	−	1.64728i	−0.506980	−	0.368343i
$21$	1.00000			0.218218
$22$	2.74551	+	1.86069i	0.585344	+	0.396701i
$23$	−1.57448			−0.328302			−0.164151	−	0.986435i	$-0.552489\pi$
$23$	−1.57448			−0.328302			−0.164151	+	0.986435i	$0.552489\pi$
$24$	0.809017	+	0.587785i	0.165140	+	0.119981i
$25$	0.881966	−	2.71441i	0.176393	−	0.542882i
$26$	2.12387	+	6.53660i	0.416525	+	1.28193i
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	−0.809017	+	0.587785i	−0.152890	+	0.111081i
$29$	−2.16672	−	6.66849i	−0.402351	−	1.23831i	−0.923087	−	0.384591i	$-0.874343\pi$
$29$	−2.16672	−	6.66849i	−0.402351	−	1.23831i	0.520736	−	0.853717i	$-0.325657\pi$
$30$	−0.866025	+	2.66535i	−0.158114	+	0.486624i
$31$	3.70378	+	2.69095i	0.665218	+	0.483309i	0.868421	−	0.495828i	$-0.165135\pi$
$31$	3.70378	+	2.69095i	0.665218	+	0.483309i	−0.203203	+	0.979137i	$0.565135\pi$
$32$	−1.00000			−0.176777
$33$	0.921216	−	3.18612i	0.160363	−	0.554632i
$34$	−2.08214			−0.357083
$35$	−2.26728	−	1.64728i	−0.383241	−	0.278441i
$36$	0.309017	−	0.951057i	0.0515028	−	0.158509i
$37$	−3.36201	−	10.3472i	−0.552711	−	1.70107i	−0.701914	−	0.712262i	$-0.747671\pi$
$37$	−3.36201	−	10.3472i	−0.552711	−	1.70107i	0.149203	−	0.988807i	$-0.452329\pi$
$38$	−5.51279	+	4.00528i	−0.894293	+	0.649742i
$39$	5.56036	−	4.03984i	0.890370	−	0.646892i
$40$	−0.866025	−	2.66535i	−0.136931	−	0.421429i
$41$	−0.0475677	+	0.146398i	−0.00742883	+	0.0228636i	−0.954702	−	0.297563i	$-0.903826\pi$
$41$	−0.0475677	+	0.146398i	−0.00742883	+	0.0228636i	0.947273	+	0.320426i	$0.103826\pi$
$42$	0.809017	+	0.587785i	0.124834	+	0.0906972i
$43$	7.20419			1.09863			0.549314	−	0.835616i	$-0.314889\pi$
$43$	7.20419			1.09863			0.549314	+	0.835616i	$0.314889\pi$
$44$	1.12747	+	3.11910i	0.169973	+	0.470222i
$45$	2.80252			0.417775
$46$	−1.27378	−	0.925458i	−0.187809	−	0.136451i
$47$	1.91541	−	5.89503i	0.279391	−	0.859878i	−0.708633	−	0.705578i	$-0.750688\pi$
$47$	1.91541	−	5.89503i	0.279391	−	0.859878i	0.988024	−	0.154301i	$-0.0493124\pi$
$48$	0.309017	+	0.951057i	0.0446028	+	0.137273i
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	2.30902	−	1.67760i	0.326544	−	0.237248i
$51$	0.643415	+	1.98023i	0.0900962	+	0.277287i
$52$	−2.12387	+	6.53660i	−0.294528	+	0.906463i
$53$	3.49283	+	2.53769i	0.479778	+	0.348579i	0.801240	−	0.598344i	$-0.204174\pi$
$53$	3.49283	+	2.53769i	0.479778	+	0.348579i	−0.321462	+	0.946923i	$0.604174\pi$
$54$	−1.00000			−0.136083
$55$	−7.33708	+	5.70634i	−0.989332	+	0.769443i
$56$	−1.00000			−0.133631
$57$	5.51279	+	4.00528i	0.730187	+	0.530512i
$58$	2.16672	−	6.66849i	0.284505	−	0.875616i
$59$	−2.89878	−	8.92151i	−0.377388	−	1.16148i	−0.941853	−	0.336025i	$-0.890917\pi$
$59$	−2.89878	−	8.92151i	−0.377388	−	1.16148i	0.564465	−	0.825457i	$-0.309083\pi$
$60$	−2.26728	+	1.64728i	−0.292705	+	0.212663i
$61$	5.96630	−	4.33477i	0.763907	−	0.555011i	−0.136199	−	0.990681i	$-0.543489\pi$
$61$	5.96630	−	4.33477i	0.763907	−	0.555011i	0.900106	+	0.435671i	$0.143489\pi$
$62$	1.41472	+	4.35405i	0.179669	+	0.552965i
$63$	0.309017	−	0.951057i	0.0389325	−	0.119822i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−19.2617			−2.38911
$66$	2.61803	−	2.03615i	0.322258	−	0.250632i
$67$	−6.66465			−0.814217			−0.407109	−	0.913380i	$-0.633463\pi$
$67$	−6.66465			−0.814217			−0.407109	+	0.913380i	$0.633463\pi$
$68$	−1.68448	−	1.22385i	−0.204274	−	0.148413i
$69$	−0.486542	+	1.49742i	−0.0585728	+	0.180269i
$70$	−0.866025	−	2.66535i	−0.103510	−	0.318571i
$71$	4.26662	−	3.09988i	0.506354	−	0.367888i	−0.305084	−	0.952325i	$-0.598685\pi$
$71$	4.26662	−	3.09988i	0.506354	−	0.367888i	0.811439	+	0.584437i	$0.198685\pi$
$72$	0.809017	−	0.587785i	0.0953436	−	0.0692712i
$73$	−1.23494	−	3.80077i	−0.144539	−	0.444846i	0.852412	−	0.522871i	$-0.175139\pi$
$73$	−1.23494	−	3.80077i	−0.144539	−	0.444846i	−0.996951	+	0.0780241i	$0.975139\pi$
$74$	3.36201	−	10.3472i	0.390826	−	1.20284i
$75$	−2.30902	−	1.67760i	−0.266622	−	0.193712i
$76$	−6.81419			−0.781641
$77$	1.12747	+	3.11910i	0.128488	+	0.355455i
$78$	6.87298			0.778212
$79$	−7.97106	−	5.79131i	−0.896814	−	0.651574i	0.0408315	−	0.999166i	$-0.486999\pi$
$79$	−7.97106	−	5.79131i	−0.896814	−	0.651574i	−0.937646	+	0.347592i	$0.886999\pi$
$80$	0.866025	−	2.66535i	0.0968246	−	0.297995i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	−0.124534	+	0.0904792i	−0.0137525	+	0.00999175i
$83$	−7.00985	+	5.09296i	−0.769431	+	0.559024i	−0.901789	−	0.432178i	$-0.857745\pi$
$83$	−7.00985	+	5.09296i	−0.769431	+	0.559024i	0.132357	+	0.991202i	$0.457745\pi$
$84$	0.309017	+	0.951057i	0.0337165	+	0.103769i
$85$	1.80318	−	5.54962i	0.195583	−	0.601941i
$86$	5.82831	+	4.23451i	0.628483	+	0.456619i
$87$	−7.01167			−0.751730
$88$	−0.921216	+	3.18612i	−0.0982020	+	0.339642i
$89$	−1.48514			−0.157424			−0.0787120	−	0.996897i	$-0.525081\pi$
$89$	−1.48514			−0.157424			−0.0787120	+	0.996897i	$0.525081\pi$
$90$	2.26728	+	1.64728i	0.238993	+	0.173638i
$91$	−2.12387	+	6.53660i	−0.222642	+	0.685221i
$92$	−0.486542	−	1.49742i	−0.0507255	−	0.156117i
$93$	3.70378	−	2.69095i	0.384064	−	0.279039i
$94$	5.01461	−	3.64333i	0.517218	−	0.375781i
$95$	−5.90126	−	18.1622i	−0.605456	−	1.86340i
$96$	−0.309017	+	0.951057i	−0.0315389	+	0.0970668i
$97$	4.74190	+	3.44519i	0.481467	+	0.349806i	0.801893	−	0.597467i	$-0.203826\pi$
$97$	4.74190	+	3.44519i	0.481467	+	0.349806i	−0.320426	+	0.947273i	$0.603826\pi$
$98$	−1.00000			−0.101015
$99$	−2.74551	−	1.86069i	−0.275934	−	0.187007i
$100$	2.85410			0.285410
$101$	9.35745	+	6.79859i	0.931101	+	0.676485i	0.946262	−	0.323400i	$-0.104826\pi$
$101$	9.35745	+	6.79859i	0.931101	+	0.676485i	−0.0151608	+	0.999885i	$0.504826\pi$
$102$	−0.643415	+	1.98023i	−0.0637076	+	0.196072i
$103$	3.89046	+	11.9736i	0.383338	+	1.17979i	0.937679	+	0.347504i	$0.112971\pi$
$103$	3.89046	+	11.9736i	0.383338	+	1.17979i	−0.554340	+	0.832290i	$0.687029\pi$
$104$	−5.56036	+	4.03984i	−0.545238	+	0.396139i
$105$	−2.26728	+	1.64728i	−0.221264	+	0.160758i
$106$	1.33414	+	4.10607i	0.129584	+	0.398817i
$107$	−4.29822	+	13.2286i	−0.415524	+	1.27885i	0.496257	+	0.868176i	$0.334707\pi$
$107$	−4.29822	+	13.2286i	−0.415524	+	1.27885i	−0.911781	+	0.410677i	$0.865293\pi$
$108$	−0.809017	−	0.587785i	−0.0778477	−	0.0565597i
$109$	19.0440			1.82408			0.912040	−	0.410101i	$-0.134506\pi$
$109$	19.0440			1.82408			0.912040	+	0.410101i	$0.134506\pi$
$110$	−9.28993	+	0.303895i	−0.885760	+	0.0289752i
$111$	−10.8797			−1.03265
$112$	−0.809017	−	0.587785i	−0.0764449	−	0.0555405i
$113$	1.35436	−	4.16828i	0.127407	−	0.392119i	−0.866925	−	0.498439i	$-0.833907\pi$
$113$	1.35436	−	4.16828i	0.127407	−	0.392119i	0.994332	+	0.106320i	$0.0339068\pi$
$114$	2.10570	+	6.48068i	0.197217	+	0.606971i
$115$	3.56980	−	2.59361i	0.332886	−	0.241856i
$116$	5.67256	−	4.12136i	0.526684	−	0.382658i
$117$	−2.12387	−	6.53660i	−0.196352	−	0.604308i
$118$	2.89878	−	8.92151i	0.266854	−	0.821292i
$119$	−1.68448	−	1.22385i	−0.154416	−	0.112190i
$120$	−2.80252			−0.255834
$121$	10.9765	−	0.718901i	0.997862	−	0.0653547i
$122$	7.37475			0.667679
$123$	0.124534	+	0.0904792i	0.0112288	+	0.00815823i
$124$	−1.41472	+	4.35405i	−0.127045	+	0.391005i
$125$	−1.85840	−	5.71957i	−0.166221	−	0.511574i
$126$	0.809017	−	0.587785i	0.0720730	−	0.0523641i
$127$	8.64383	−	6.28011i	0.767016	−	0.557269i	−0.134039	−	0.990976i	$-0.542795\pi$
$127$	8.64383	−	6.28011i	0.767016	−	0.557269i	0.901054	+	0.433707i	$0.142795\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	2.22622	−	6.85159i	0.196007	−	0.603249i
$130$	−15.5830	−	11.3217i	−1.36672	−	0.992980i
$131$	−16.0292			−1.40048			−0.700240	−	0.713908i	$-0.746924\pi$
$131$	−16.0292			−1.40048			−0.700240	+	0.713908i	$0.746924\pi$
$132$	3.31485	−	0.108436i	0.288521	−	0.00943818i
$133$	−6.81419			−0.590865
$134$	−5.39182	−	3.91738i	−0.465782	−	0.338411i
$135$	0.866025	−	2.66535i	0.0745356	−	0.229397i
$136$	−0.643415	−	1.98023i	−0.0551724	−	0.169803i
$137$	−7.51863	+	5.46260i	−0.642360	+	0.466702i	−0.860660	−	0.509180i	$-0.829949\pi$
$137$	−7.51863	+	5.46260i	−0.642360	+	0.466702i	0.218300	+	0.975882i	$0.429949\pi$
$138$	−1.27378	+	0.925458i	−0.108432	+	0.0787802i
$139$	−4.01056	−	12.3432i	−0.340172	−	1.04694i	−0.964118	−	0.265474i	$-0.914472\pi$
$139$	−4.01056	−	12.3432i	−0.340172	−	1.04694i	0.623947	−	0.781467i	$-0.285528\pi$
$140$	0.866025	−	2.66535i	0.0731925	−	0.225263i
$141$	−5.01461	−	3.64333i	−0.422306	−	0.306824i
$142$	5.27383			0.442570
$143$	18.8698	+	12.7885i	1.57797	+	1.06943i
$144$	1.00000			0.0833333
$145$	15.8974	+	11.5502i	1.32021	+	0.959189i
$146$	1.23494	−	3.80077i	0.102205	−	0.314554i
$147$	0.309017	+	0.951057i	0.0254873	+	0.0784418i
$148$	8.80185	−	6.39492i	0.723508	−	0.525659i
$149$	1.23607	−	0.898056i	0.101263	−	0.0735716i	−0.536002	−	0.844217i	$-0.680066\pi$
$149$	1.23607	−	0.898056i	0.101263	−	0.0735716i	0.637264	+	0.770645i	$0.280066\pi$
$150$	−0.881966	−	2.71441i	−0.0720122	−	0.221631i
$151$	1.58434	−	4.87608i	0.128931	−	0.396810i	−0.865665	−	0.500623i	$-0.833104\pi$
$151$	1.58434	−	4.87608i	0.128931	−	0.396810i	0.994597	+	0.103813i	$0.0331043\pi$
$152$	−5.51279	−	4.00528i	−0.447147	−	0.324871i
$153$	2.08214			0.168331
$154$	−0.921216	+	3.18612i	−0.0742337	+	0.256745i
$155$	−12.8303			−1.03055
$156$	5.56036	+	4.03984i	0.445185	+	0.323446i
$157$	5.14093	−	15.8222i	0.410291	−	1.26275i	−0.506104	−	0.862472i	$-0.668915\pi$
$157$	5.14093	−	15.8222i	0.410291	−	1.26275i	0.916396	−	0.400274i	$-0.131085\pi$
$158$	−3.04467	−	9.37054i	−0.242221	−	0.745480i
$159$	3.49283	−	2.53769i	0.277000	−	0.201252i
$160$	2.26728	−	1.64728i	0.179245	−	0.130229i
$161$	−0.486542	−	1.49742i	−0.0383449	−	0.118013i
$162$	−0.309017	+	0.951057i	−0.0242787	+	0.0747221i
$163$	6.85410	+	4.97980i	0.536855	+	0.390048i	0.822916	−	0.568164i	$-0.192346\pi$
$163$	6.85410	+	4.97980i	0.536855	+	0.390048i	−0.286061	+	0.958211i	$0.592346\pi$
$164$	−0.153932			−0.0120201
$165$	3.15977	+	8.74134i	0.245988	+	0.680512i
$166$	−8.66465			−0.672508
$167$	−3.31444	−	2.40808i	−0.256479	−	0.186343i	0.452114	−	0.891960i	$-0.350670\pi$
$167$	−3.31444	−	2.40808i	−0.256479	−	0.186343i	−0.708593	+	0.705617i	$0.750670\pi$
$168$	−0.309017	+	0.951057i	−0.0238412	+	0.0733756i
$169$	10.5801	+	32.5622i	0.813853	+	2.50478i
$170$	4.72079	−	3.42986i	0.362068	−	0.263058i
$171$	5.51279	−	4.00528i	0.421574	−	0.306291i
$172$	2.22622	+	6.85159i	0.169747	+	0.522429i
$173$	4.95107	−	15.2378i	0.376423	−	1.15851i	−0.566090	−	0.824343i	$-0.691545\pi$
$173$	4.95107	−	15.2378i	0.376423	−	1.15851i	0.942514	−	0.334168i	$-0.108455\pi$
$174$	−5.67256	−	4.12136i	−0.430036	−	0.312439i
$175$	2.85410			0.215750
$176$	−2.61803	+	2.03615i	−0.197342	+	0.153480i
$177$	−9.38064			−0.705092
$178$	−1.20150	−	0.872941i	−0.0900562	−	0.0654297i
$179$	−2.03344	+	6.25830i	−0.151987	+	0.467767i	−0.997843	−	0.0656435i	$-0.979090\pi$
$179$	−2.03344	+	6.25830i	−0.151987	+	0.467767i	0.845856	+	0.533411i	$0.179090\pi$
$180$	0.866025	+	2.66535i	0.0645497	+	0.198664i
$181$	−12.0949	+	8.78748i	−0.899009	+	0.653168i	−0.938211	−	0.346063i	$-0.887518\pi$
$181$	−12.0949	+	8.78748i	−0.899009	+	0.653168i	0.0392023	+	0.999231i	$0.487518\pi$
$182$	−5.56036	+	4.03984i	−0.412161	+	0.299453i
$183$	−2.27892	−	7.01381i	−0.168463	−	0.518476i
$184$	0.486542	−	1.49742i	0.0358684	−	0.110391i
$185$	24.6673	+	17.9219i	1.81358	+	1.31764i
$186$	4.57812			0.335684
$187$	−5.45110	+	4.23954i	−0.398624	+	0.310026i
$188$	6.19840			0.452065
$189$	−0.809017	−	0.587785i	−0.0588473	−	0.0427551i
$190$	5.90126	−	18.1622i	0.428122	−	1.31762i
$191$	3.97892	+	12.2459i	0.287904	+	0.886079i	0.985513	+	0.169600i	$0.0542475\pi$
$191$	3.97892	+	12.2459i	0.287904	+	0.886079i	−0.697609	+	0.716479i	$0.745753\pi$
$192$	−0.809017	+	0.587785i	−0.0583858	+	0.0424197i
$193$	5.90817	−	4.29254i	0.425279	−	0.308984i	−0.354479	−	0.935064i	$-0.615342\pi$
$193$	5.90817	−	4.29254i	0.425279	−	0.308984i	0.779759	+	0.626080i	$0.215342\pi$
$194$	1.81125	+	5.57444i	0.130040	+	0.400222i
$195$	−5.95218	+	18.3189i	−0.426244	+	1.31185i
$196$	−0.809017	−	0.587785i	−0.0577869	−	0.0419847i
$197$	17.3388			1.23534			0.617670	−	0.786437i	$-0.288077\pi$
$197$	17.3388			1.23534			0.617670	+	0.786437i	$0.288077\pi$
$198$	−1.12747	−	3.11910i	−0.0801261	−	0.221665i
$199$	−20.7862			−1.47349			−0.736747	−	0.676168i	$-0.763639\pi$
$199$	−20.7862			−1.47349			−0.736747	+	0.676168i	$0.763639\pi$
$200$	2.30902	+	1.67760i	0.163272	+	0.118624i
$201$	−2.05949	+	6.33846i	−0.145265	+	0.447081i
$202$	3.57423	+	11.0003i	0.251482	+	0.773982i
$203$	5.67256	−	4.12136i	0.398136	−	0.289262i
$204$	−1.68448	+	1.22385i	−0.117937	+	0.0856865i
$205$	−0.133309	−	0.410284i	−0.00931073	−	0.0286555i
$206$	−3.89046	+	11.9736i	−0.271061	+	0.834240i
$207$	1.27378	+	0.925458i	0.0885341	+	0.0643238i
$208$	−6.87298			−0.476556
$209$	−6.27734	+	21.7108i	−0.434213	+	1.50177i
$210$	−2.80252			−0.193392
$211$	−18.0471	−	13.1120i	−1.24241	−	0.902667i	−0.244657	−	0.969610i	$-0.578675\pi$
$211$	−18.0471	−	13.1120i	−1.24241	−	0.902667i	−0.997757	+	0.0669430i	$0.978675\pi$
$212$	−1.33414	+	4.10607i	−0.0916294	+	0.282006i
$213$	−1.62970	−	5.01571i	−0.111665	−	0.343671i
$214$	−11.2529	+	8.17569i	−0.769231	+	0.558879i
$215$	−16.3339	+	11.8673i	−1.11397	+	0.809343i
$216$	−0.309017	−	0.951057i	−0.0210259	−	0.0647112i
$217$	−1.41472	+	4.35405i	−0.0960372	+	0.295572i
$218$	15.4069	+	11.1938i	1.04349	+	0.758137i
$219$	−3.99637			−0.270049
$220$	−7.69433	−	5.21463i	−0.518752	−	0.351570i
$221$	−14.3105			−0.962627
$222$	−8.80185	−	6.39492i	−0.590742	−	0.429199i
$223$	1.94394	−	5.98283i	0.130176	−	0.400640i	−0.864633	−	0.502405i	$-0.832449\pi$
$223$	1.94394	−	5.98283i	0.130176	−	0.400640i	0.994809	+	0.101765i	$0.0324488\pi$
$224$	−0.309017	−	0.951057i	−0.0206471	−	0.0635451i
$225$	−2.30902	+	1.67760i	−0.153934	+	0.111840i
$226$	3.54575	−	2.57614i	0.235860	−	0.171362i
$227$	−4.21455	−	12.9710i	−0.279729	−	0.860918i	−0.987929	−	0.154906i	$-0.950492\pi$
$227$	−4.21455	−	12.9710i	−0.279729	−	0.860918i	0.708200	−	0.706012i	$-0.249508\pi$
$228$	−2.10570	+	6.48068i	−0.139453	+	0.429193i
$229$	−18.2635	−	13.2692i	−1.20688	−	0.876853i	−0.211940	−	0.977283i	$-0.567978\pi$
$229$	−18.2635	−	13.2692i	−1.20688	−	0.876853i	−0.994944	+	0.100430i	$0.967978\pi$
$230$	4.41252			0.290953
$231$	3.31485	−	0.108436i	0.218101	−	0.00713459i
$232$	7.01167			0.460339
$233$	1.43864	+	1.04524i	0.0942487	+	0.0684757i	0.633912	−	0.773406i	$-0.281448\pi$
$233$	1.43864	+	1.04524i	0.0942487	+	0.0684757i	−0.539663	+	0.841881i	$0.681448\pi$
$234$	2.12387	−	6.53660i	0.138842	−	0.427311i
$235$	5.36797	+	16.5209i	0.350168	+	1.07771i
$236$	7.58909	−	5.51380i	0.494008	−	0.358918i
$237$	−7.97106	+	5.79131i	−0.517776	+	0.376186i
$238$	−0.643415	−	1.98023i	−0.0417064	−	0.128359i
$239$	7.98426	−	24.5730i	0.516459	−	1.58950i	−0.264152	−	0.964481i	$-0.585092\pi$
$239$	7.98426	−	24.5730i	0.516459	−	1.58950i	0.780611	−	0.625017i	$-0.214908\pi$
$240$	−2.26728	−	1.64728i	−0.146353	−	0.106331i
$241$	14.9321			0.961861			0.480930	−	0.876759i	$-0.340299\pi$
$241$	14.9321			0.961861			0.480930	+	0.876759i	$0.340299\pi$
$242$	9.30272	+	5.87021i	0.598002	+	0.377351i
$243$	1.00000			0.0641500
$244$	5.96630	+	4.33477i	0.381953	+	0.277505i
$245$	0.866025	−	2.66535i	0.0553283	−	0.170283i
$246$	0.0475677	+	0.146398i	0.00303281	+	0.00933402i
$247$	−37.8893	+	27.5282i	−2.41084	+	1.75158i
$248$	−3.70378	+	2.69095i	−0.235190	+	0.170876i
$249$	2.67753	+	8.24058i	0.169681	+	0.522225i
$250$	1.85840	−	5.71957i	0.117536	−	0.361738i
$251$	4.59734	+	3.34016i	0.290181	+	0.210829i	0.723346	−	0.690486i	$-0.242603\pi$
$251$	4.59734	+	3.34016i	0.290181	+	0.210829i	−0.433165	+	0.901315i	$0.642603\pi$
$252$	1.00000			0.0629941
$253$	−5.21918	+	0.170731i	−0.328127	+	0.0107338i
$254$	10.6844			0.670396
$255$	−4.72079	−	3.42986i	−0.295628	−	0.214786i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	7.87145	+	24.2258i	0.491007	+	1.51117i	0.823088	+	0.567914i	$0.192250\pi$
$257$	7.87145	+	24.2258i	0.491007	+	1.51117i	−0.332080	+	0.943251i	$0.607750\pi$
$258$	5.82831	−	4.23451i	0.362855	−	0.263629i
$259$	8.80185	−	6.39492i	0.546920	−	0.397361i
$260$	−5.95218	−	18.3189i	−0.369138	−	1.13609i
$261$	−2.16672	+	6.66849i	−0.134117	+	0.412769i
$262$	−12.9679	−	9.42174i	−0.801160	−	0.582077i
$263$	20.3518			1.25495			0.627474	−	0.778638i	$-0.284089\pi$
$263$	20.3518			1.25495			0.627474	+	0.778638i	$0.284089\pi$
$264$	2.74551	+	1.86069i	0.168974	+	0.114518i
$265$	−12.0995			−0.743269
$266$	−5.51279	−	4.00528i	−0.338011	−	0.245579i
$267$	−0.458932	+	1.41245i	−0.0280862	+	0.0864404i
$268$	−2.05949	−	6.33846i	−0.125803	−	0.387183i
$269$	2.23019	−	1.62033i	0.135977	−	0.0987930i	−0.517718	−	0.855552i	$-0.673218\pi$
$269$	2.23019	−	1.62033i	0.135977	−	0.0987930i	0.653694	+	0.756759i	$0.273218\pi$
$270$	2.26728	−	1.64728i	0.137983	−	0.100250i
$271$	5.79668	+	17.8404i	0.352123	+	1.08372i	0.957659	+	0.287906i	$0.0929590\pi$
$271$	5.79668	+	17.8404i	0.352123	+	1.08372i	−0.605535	+	0.795818i	$0.707041\pi$
$272$	0.643415	−	1.98023i	0.0390128	−	0.120069i
$273$	5.56036	+	4.03984i	0.336528	+	0.244502i
$274$	−9.29353			−0.561443
$275$	2.62925	−	9.09351i	0.158549	−	0.548359i
$276$	−1.57448			−0.0947728
$277$	2.51594	+	1.82794i	0.151168	+	0.109830i	0.660798	−	0.750563i	$-0.270218\pi$
$277$	2.51594	+	1.82794i	0.151168	+	0.109830i	−0.509630	+	0.860394i	$0.670218\pi$
$278$	4.01056	−	12.3432i	0.240538	−	0.740299i
$279$	−1.41472	−	4.35405i	−0.0846969	−	0.260670i
$280$	2.26728	−	1.64728i	0.135496	−	0.0984437i
$281$	2.32135	−	1.68656i	0.138480	−	0.100612i	−0.516388	−	0.856354i	$-0.672724\pi$
$281$	2.32135	−	1.68656i	0.138480	−	0.100612i	0.654869	+	0.755743i	$0.272724\pi$
$282$	−1.91541	−	5.89503i	−0.114061	−	0.351044i
$283$	0.686429	−	2.11261i	0.0408039	−	0.125582i	−0.928579	−	0.371134i	$-0.878969\pi$
$283$	0.686429	−	2.11261i	0.0408039	−	0.125582i	0.969383	+	0.245552i	$0.0789692\pi$
$284$	4.26662	+	3.09988i	0.253177	+	0.183944i
$285$	−19.0969			−1.13120
$286$	7.74911	+	21.4375i	0.458215	+	1.26763i
$287$	−0.153932			−0.00908634
$288$	0.809017	+	0.587785i	0.0476718	+	0.0346356i
$289$	−3.91361	+	12.0449i	−0.230212	+	0.708521i
$290$	6.07228	+	18.6886i	0.356577	+	1.09743i
$291$	4.74190	−	3.44519i	0.277975	−	0.201961i
$292$	3.23313	−	2.34900i	0.189204	−	0.137465i
$293$	−8.26463	−	25.4359i	−0.482825	−	1.48598i	−0.835107	−	0.550088i	$-0.814594\pi$
$293$	−8.26463	−	25.4359i	−0.482825	−	1.48598i	0.352282	−	0.935894i	$-0.385406\pi$
$294$	−0.309017	+	0.951057i	−0.0180222	+	0.0554667i
$295$	21.2686	+	15.4525i	1.23830	+	0.899680i
$296$	10.8797			0.632369
$297$	−2.61803	+	2.03615i	−0.151914	+	0.118149i
$298$	1.52786			0.0885068
$299$	−8.75470	−	6.36066i	−0.506297	−	0.367846i
$300$	0.881966	−	2.71441i	0.0509203	−	0.156717i
$301$	2.22622	+	6.85159i	0.128317	+	0.394919i
$302$	4.14784	−	3.01358i	0.238682	−	0.173412i
$303$	9.35745	−	6.79859i	0.537572	−	0.390569i
$304$	−2.10570	−	6.48068i	−0.120770	−	0.371692i
$305$	−6.38672	+	19.6563i	−0.365703	+	1.12552i
$306$	1.68448	+	1.22385i	0.0962955	+	0.0699628i
$307$	−5.34430			−0.305015			−0.152508	−	0.988302i	$-0.548735\pi$
$307$	−5.34430			−0.305015			−0.152508	+	0.988302i	$0.548735\pi$
$308$	−2.61803	+	2.03615i	−0.149176	+	0.116020i
$309$	12.5898			0.716208
$310$	−10.3799	−	7.54143i	−0.589538	−	0.428325i
$311$	−10.6981	+	32.9255i	−0.606636	+	1.86703i	−0.121509	+	0.992590i	$0.538773\pi$
$311$	−10.6981	+	32.9255i	−0.606636	+	1.86703i	−0.485127	+	0.874444i	$0.661227\pi$
$312$	2.12387	+	6.53660i	0.120240	+	0.370062i
$313$	16.9007	−	12.2791i	0.955285	−	0.694055i	0.00323427	−	0.999995i	$-0.498970\pi$
$313$	16.9007	−	12.2791i	0.955285	−	0.694055i	0.952051	+	0.305939i	$0.0989705\pi$
$314$	13.4591	−	9.77863i	0.759543	−	0.551840i
$315$	0.866025	+	2.66535i	0.0487950	+	0.150176i
$316$	3.04467	−	9.37054i	0.171276	−	0.527134i
$317$	1.15575	+	0.839701i	0.0649134	+	0.0471623i	0.619769	−	0.784785i	$-0.287226\pi$
$317$	1.15575	+	0.839701i	0.0649134	+	0.0471623i	−0.554855	+	0.831947i	$0.687226\pi$
$318$	4.31738			0.242107
$319$	−7.90548	−	21.8701i	−0.442622	−	1.22449i
$320$	2.80252			0.156665
$321$	11.2529	+	8.17569i	0.628074	+	0.456323i
$322$	0.486542	−	1.49742i	0.0271139	−	0.0834481i
$323$	−4.38435	−	13.4936i	−0.243952	−	0.750807i
$324$	−0.809017	+	0.587785i	−0.0449454	+	0.0326547i
$325$	15.8698	−	11.5301i	0.880300	−	0.639575i
$326$	2.61803	+	8.05748i	0.144999	+	0.446263i
$327$	5.88491	−	18.1119i	0.325436	−	1.00159i
$328$	−0.124534	−	0.0904792i	−0.00687623	−	0.00499588i
$329$	6.19840			0.341729
$330$	−2.58172	+	8.92916i	−0.142119	+	0.491534i
$331$	−22.6880			−1.24704			−0.623522	−	0.781805i	$-0.714299\pi$
$331$	−22.6880			−1.24704			−0.623522	+	0.781805i	$0.714299\pi$
$332$	−7.00985	−	5.09296i	−0.384716	−	0.279512i
$333$	−3.36201	+	10.3472i	−0.184237	+	0.567023i
$334$	−1.26600	−	3.89636i	−0.0692726	−	0.213199i
$335$	15.1107	−	10.9785i	0.825584	−	0.599822i
$336$	−0.809017	+	0.587785i	−0.0441355	+	0.0320663i
$337$	8.01569	+	24.6697i	0.436642	+	1.34385i	0.891394	+	0.453229i	$0.149728\pi$
$337$	8.01569	+	24.6697i	0.436642	+	1.34385i	−0.454752	+	0.890618i	$0.650272\pi$
$338$	−10.5801	+	32.5622i	−0.575481	+	1.77115i
$339$	−3.54575	−	2.57614i	−0.192579	−	0.139917i
$340$	5.83522			0.316459
$341$	12.5693	+	8.51848i	0.680664	+	0.461301i
$342$	6.81419			0.368469
$343$	−0.809017	−	0.587785i	−0.0436828	−	0.0317374i
$344$	−2.22622	+	6.85159i	−0.120030	+	0.369413i
$345$	−1.36354	−	4.19655i	−0.0734107	−	0.225935i
$346$	12.9621	−	9.41750i	0.696846	−	0.506288i
$347$	24.1786	−	17.5668i	1.29798	−	0.943036i	0.298044	−	0.954552i	$-0.403666\pi$
$347$	24.1786	−	17.5668i	1.29798	−	0.943036i	0.999934	+	0.0115162i	$0.00366579\pi$
$348$	−2.16672	−	6.66849i	−0.116149	−	0.357469i
$349$	6.14427	−	18.9101i	0.328895	−	1.01223i	−0.640757	−	0.767744i	$-0.721379\pi$
$349$	6.14427	−	18.9101i	0.328895	−	1.01223i	0.969652	−	0.244491i	$-0.0786208\pi$
$350$	2.30902	+	1.67760i	0.123422	+	0.0896714i
$351$	−6.87298			−0.366853
$352$	−3.31485	+	0.108436i	−0.176682	+	0.00577968i
$353$	−2.87886			−0.153227			−0.0766133	−	0.997061i	$-0.524411\pi$
$353$	−2.87886			−0.153227			−0.0766133	+	0.997061i	$0.524411\pi$
$354$	−7.58909	−	5.51380i	−0.403356	−	0.293055i
$355$	−4.56727	+	14.0566i	−0.242406	+	0.746048i
$356$	−0.458932	−	1.41245i	−0.0243234	−	0.0748596i
$357$	−1.68448	+	1.22385i	−0.0891523	+	0.0647729i
$358$	−5.32363	+	3.86784i	−0.281362	+	0.204422i
$359$	5.21416	+	16.0475i	0.275193	+	0.846957i	0.989168	+	0.146786i	$0.0468929\pi$
$359$	5.21416	+	16.0475i	0.275193	+	0.846957i	−0.713975	+	0.700171i	$0.753107\pi$
$360$	−0.866025	+	2.66535i	−0.0456435	+	0.140476i
$361$	−22.1939	−	16.1248i	−1.16810	−	0.848673i
$362$	−14.9502			−0.785763
$363$	2.70820	−	10.6614i	0.142144	−	0.559579i
$364$	−6.87298			−0.360242
$365$	9.06089	+	6.58312i	0.474269	+	0.344577i
$366$	2.27892	−	7.01381i	0.119121	−	0.366618i
$367$	1.48518	+	4.57092i	0.0775259	+	0.238600i	0.982307	−	0.187276i	$-0.0599659\pi$
$367$	1.48518	+	4.57092i	0.0775259	+	0.238600i	−0.904781	+	0.425876i	$0.859966\pi$
$368$	1.27378	−	0.925458i	0.0664006	−	0.0482428i
$369$	0.124534	−	0.0904792i	0.00648298	−	0.00471016i
$370$	9.42209	+	28.9982i	0.489831	+	1.50754i
$371$	−1.33414	+	4.10607i	−0.0692653	+	0.213177i
$372$	3.70378	+	2.69095i	0.192032	+	0.139519i
$373$	−30.8275			−1.59619			−0.798094	−	0.602533i	$-0.794158\pi$
$373$	−30.8275			−1.59619			−0.798094	+	0.602533i	$0.794158\pi$
$374$	−6.90197	+	0.225779i	−0.356892	+	0.0116748i
$375$	−6.01392			−0.310557
$376$	5.01461	+	3.64333i	0.258609	+	0.187890i
$377$	14.8919	−	45.8324i	0.766970	−	2.36049i
$378$	−0.309017	−	0.951057i	−0.0158941	−	0.0489171i
$379$	−9.34714	+	6.79110i	−0.480131	+	0.348835i	−0.801376	−	0.598161i	$-0.795898\pi$
$379$	−9.34714	+	6.79110i	−0.480131	+	0.348835i	0.321246	+	0.946996i	$0.395898\pi$
$380$	15.4497	−	11.2249i	0.792553	−	0.575823i
$381$	−3.30165	−	10.1614i	−0.169149	−	0.520586i
$382$	−3.97892	+	12.2459i	−0.203579	+	0.626552i
$383$	16.7962	+	12.2032i	0.858247	+	0.623553i	0.927407	−	0.374053i	$-0.122032\pi$
$383$	16.7962	+	12.2032i	0.858247	+	0.623553i	−0.0691606	+	0.997606i	$0.522032\pi$
$384$	−1.00000			−0.0510310
$385$	−7.69433	−	5.21463i	−0.392140	−	0.265762i
$386$	7.30290			0.371708
$387$	−5.82831	−	4.23451i	−0.296270	−	0.215252i
$388$	−1.81125	+	5.57444i	−0.0919521	+	0.282999i
$389$	1.04480	+	3.21557i	0.0529736	+	0.163036i	0.974043	−	0.226362i	$-0.0726832\pi$
$389$	1.04480	+	3.21557i	0.0529736	+	0.163036i	−0.921070	+	0.389398i	$0.872683\pi$
$390$	−15.5830	+	11.3217i	−0.789076	+	0.573297i
$391$	2.65219	−	1.92693i	0.134127	−	0.0974490i
$392$	−0.309017	−	0.951057i	−0.0156077	−	0.0480356i
$393$	−4.95330	+	15.2447i	−0.249861	+	0.768993i
$394$	14.0274	+	10.1915i	0.706690	+	0.513441i
$395$	27.6126			1.38934
$396$	0.921216	−	3.18612i	0.0462929	−	0.160109i
$397$	−2.73835			−0.137434			−0.0687168	−	0.997636i	$-0.521891\pi$
$397$	−2.73835			−0.137434			−0.0687168	+	0.997636i	$0.521891\pi$
$398$	−16.8164	−	12.2178i	−0.842929	−	0.612424i
$399$	−2.10570	+	6.48068i	−0.105417	+	0.324440i
$400$	0.881966	+	2.71441i	0.0440983	+	0.135721i
$401$	21.1692	−	15.3803i	1.05714	−	0.768055i	0.0835807	−	0.996501i	$-0.473364\pi$
$401$	21.1692	−	15.3803i	1.05714	−	0.768055i	0.973557	+	0.228446i	$0.0733644\pi$
$402$	−5.39182	+	3.91738i	−0.268919	+	0.195381i
$403$	9.72332	+	29.9253i	0.484353	+	1.49069i
$404$	−3.57423	+	11.0003i	−0.177825	+	0.547288i
$405$	−2.26728	−	1.64728i	−0.112662	−	0.0818539i
$406$	7.01167			0.347983
$407$	−12.2666	−	33.9349i	−0.608031	−	1.68209i
$408$	−2.08214			−0.103081
$409$	−30.9685	−	22.5000i	−1.53130	−	1.11255i	−0.955513	−	0.294947i	$-0.904698\pi$
$409$	−30.9685	−	22.5000i	−1.53130	−	1.11255i	−0.575782	−	0.817604i	$-0.695302\pi$
$410$	0.133309	−	0.410284i	0.00658368	−	0.0202625i
$411$	2.87186	+	8.83868i	0.141658	+	0.435980i
$412$	−10.1854	+	7.40009i	−0.501796	+	0.364576i
$413$	7.58909	−	5.51380i	0.373435	−	0.271316i
$414$	0.486542	+	1.49742i	0.0239122	+	0.0735943i
$415$	7.50381	−	23.0944i	0.368348	−	1.13366i
$416$	−5.56036	−	4.03984i	−0.272619	−	0.198069i
$417$	−12.9785			−0.635558
$418$	−17.8398	+	13.8747i	−0.872572	+	0.678633i
$419$	1.43586			0.0701461			0.0350731	−	0.999385i	$-0.488834\pi$
$419$	1.43586			0.0701461			0.0350731	+	0.999385i	$0.488834\pi$
$420$	−2.26728	−	1.64728i	−0.110632	−	0.0803789i
$421$	6.18853	−	19.0463i	0.301610	−	0.928262i	−0.679310	−	0.733852i	$-0.737721\pi$
$421$	6.18853	−	19.0463i	0.301610	−	0.928262i	0.980920	−	0.194410i	$-0.0622792\pi$
$422$	−6.89338	−	21.2156i	−0.335565	−	1.03276i
$423$	−5.01461	+	3.64333i	−0.243819	+	0.177145i
$424$	−3.49283	+	2.53769i	−0.169627	+	0.123241i
$425$	1.83637	+	5.65177i	0.0890772	+	0.274151i
$426$	1.62970	−	5.01571i	0.0789594	−	0.243012i
$427$	5.96630	+	4.33477i	0.288730	+	0.209774i
$428$	−13.9093			−0.672332
$429$	17.9937	−	13.9944i	0.868744	−	0.675656i
$430$	−20.1899			−0.973641
$431$	−6.08789	−	4.42311i	−0.293244	−	0.213054i	0.431430	−	0.902147i	$-0.358009\pi$
$431$	−6.08789	−	4.42311i	−0.293244	−	0.213054i	−0.724673	+	0.689093i	$0.758009\pi$
$432$	0.309017	−	0.951057i	0.0148676	−	0.0457577i
$433$	−4.20237	−	12.9336i	−0.201953	−	0.621547i	−0.999825	−	0.0187202i	$-0.994041\pi$
$433$	−4.20237	−	12.9336i	−0.201953	−	0.621547i	0.797872	−	0.602827i	$-0.205959\pi$
$434$	−3.70378	+	2.69095i	−0.177787	+	0.129170i
$435$	15.8974	−	11.5502i	0.762224	−	0.553788i
$436$	5.88491	+	18.1119i	0.281836	+	0.867402i
$437$	3.31539	−	10.2037i	0.158597	−	0.488110i
$438$	−3.23313	−	2.34900i	−0.154485	−	0.112240i
$439$	−3.22895			−0.154109			−0.0770547	−	0.997027i	$-0.524552\pi$
$439$	−3.22895			−0.154109			−0.0770547	+	0.997027i	$0.524552\pi$
$440$	−3.15977	−	8.74134i	−0.150636	−	0.416727i
$441$	1.00000			0.0476190
$442$	−11.5774	−	8.41149i	−0.550682	−	0.400094i
$443$	−0.0401986	+	0.123719i	−0.00190989	+	0.00587805i	−0.952007	−	0.306076i	$-0.900984\pi$
$443$	−0.0401986	+	0.123719i	−0.00190989	+	0.00587805i	0.950097	+	0.311955i	$0.100984\pi$
$444$	−3.36201	−	10.3472i	−0.159554	−	0.491056i
$445$	3.36722	−	2.44643i	0.159622	−	0.115972i
$446$	5.08930	−	3.69759i	0.240985	−	0.175086i
$447$	−0.472136	−	1.45309i	−0.0223313	−	0.0687286i
$448$	0.309017	−	0.951057i	0.0145997	−	0.0449332i
$449$	−2.52451	−	1.83416i	−0.119139	−	0.0865595i	0.526620	−	0.850101i	$-0.323459\pi$
$449$	−2.52451	−	1.83416i	−0.119139	−	0.0865595i	−0.645759	+	0.763541i	$0.723459\pi$
$450$	−2.85410			−0.134544
$451$	−0.141805	+	0.490447i	−0.00667734	+	0.0230942i
$452$	4.38279			0.206149
$453$	−4.14784	−	3.01358i	−0.194883	−	0.141591i
$454$	4.21455	−	12.9710i	0.197798	−	0.608761i
$455$	−5.95218	−	18.3189i	−0.279042	−	0.858804i
$456$	−5.51279	+	4.00528i	−0.258160	+	0.187564i
$457$	6.18448	−	4.49329i	0.289298	−	0.210187i	−0.433665	−	0.901074i	$-0.642780\pi$
$457$	6.18448	−	4.49329i	0.289298	−	0.210187i	0.722963	+	0.690887i	$0.242780\pi$
$458$	−6.97603	−	21.4700i	−0.325968	−	1.00323i
$459$	0.643415	−	1.98023i	0.0300321	−	0.0924292i
$460$	3.56980	+	2.59361i	0.166443	+	0.120928i
$461$	−34.7136			−1.61677			−0.808386	−	0.588652i	$-0.799659\pi$
$461$	−34.7136			−1.61677			−0.808386	+	0.588652i	$0.799659\pi$
$462$	2.74551	+	1.86069i	0.127733	+	0.0865673i
$463$	3.56322			0.165597			0.0827985	−	0.996566i	$-0.473614\pi$
$463$	3.56322			0.165597			0.0827985	+	0.996566i	$0.473614\pi$
$464$	5.67256	+	4.12136i	0.263342	+	0.191329i
$465$	−3.96477	+	12.2023i	−0.183862	+	0.565868i
$466$	0.549513	+	1.69123i	0.0254557	+	0.0783446i
$467$	−0.0512496	+	0.0372350i	−0.00237155	+	0.00172303i	−0.588970	−	0.808155i	$-0.700467\pi$
$467$	−0.0512496	+	0.0372350i	−0.00237155	+	0.00172303i	0.586599	+	0.809878i	$0.300467\pi$
$468$	5.56036	−	4.03984i	0.257028	−	0.186742i
$469$	−2.05949	−	6.33846i	−0.0950985	−	0.292683i
$470$	−5.36797	+	16.5209i	−0.247606	+	0.762053i
$471$	−13.4591	−	9.77863i	−0.620164	−	0.450576i
$472$	9.38064			0.431779
$473$	23.8808	−	0.781196i	1.09804	−	0.0359194i
$474$	−9.85277			−0.452553
$475$	15.7341	+	11.4315i	0.721929	+	0.524512i
$476$	0.643415	−	1.98023i	0.0294909	−	0.0907636i
$477$	−1.33414	−	4.10607i	−0.0610863	−	0.188004i
$478$	20.9031	−	15.1870i	0.956084	−	0.694636i
$479$	−26.8864	+	19.5341i	−1.22847	+	0.892536i	−0.996775	−	0.0802521i	$-0.974427\pi$
$479$	−26.8864	+	19.5341i	−1.22847	+	0.892536i	−0.231696	+	0.972788i	$0.574427\pi$
$480$	−0.866025	−	2.66535i	−0.0395285	−	0.121656i
$481$	23.1070	−	71.1161i	1.05359	−	3.24262i
$482$	12.0803	+	8.77686i	0.550243	+	0.399775i
$483$	−1.57448			−0.0716415
$484$	4.07564	+	10.2171i	0.185256	+	0.464414i
$485$	−16.4264			−0.745886
$486$	0.809017	+	0.587785i	0.0366978	+	0.0266625i
$487$	−2.82706	+	8.70079i	−0.128106	+	0.394270i	−0.994454	−	0.105170i	$-0.966461\pi$
$487$	−2.82706	+	8.70079i	−0.128106	+	0.394270i	0.866348	+	0.499441i	$0.166461\pi$
$488$	2.27892	+	7.01381i	0.103162	+	0.317500i
$489$	6.85410	−	4.97980i	0.309953	−	0.225194i
$490$	2.26728	−	1.64728i	0.102425	−	0.0744164i
$491$	−5.91539	−	18.2057i	−0.266958	−	0.821612i	−0.991236	−	0.132104i	$-0.957827\pi$
$491$	−5.91539	−	18.2057i	−0.266958	−	0.821612i	0.724278	−	0.689508i	$-0.242173\pi$
$492$	−0.0475677	+	0.146398i	−0.00214452	+	0.00660015i
$493$	11.8110	+	8.58122i	0.531942	+	0.386479i
$494$	−46.8338			−2.10715
$495$	9.28993	−	0.303895i	0.417551	−	0.0136591i
$496$	−4.57812			−0.205564
$497$	4.26662	+	3.09988i	0.191384	+	0.139049i
$498$	−2.67753	+	8.24058i	−0.119983	+	0.369269i
$499$	−7.20825	−	22.1847i	−0.322686	−	0.993124i	−0.972474	−	0.233009i	$-0.925143\pi$
$499$	−7.20825	−	22.1847i	−0.322686	−	0.993124i	0.649789	−	0.760115i	$-0.274857\pi$
$500$	4.86536	−	3.53489i	0.217586	−	0.158085i
$501$	−3.31444	+	2.40808i	−0.148078	+	0.107585i
$502$	1.75603	+	5.40449i	0.0783753	+	0.241214i
$503$	−7.46034	+	22.9606i	−0.332640	+	1.02376i	0.635233	+	0.772321i	$0.280904\pi$
$503$	−7.46034	+	22.9606i	−0.332640	+	1.02376i	−0.967873	+	0.251440i	$0.919096\pi$
$504$	0.809017	+	0.587785i	0.0360365	+	0.0261820i
$505$	−32.4152			−1.44246
$506$	−4.32276	−	2.92963i	−0.192170	−	0.130238i
$507$	34.2379			1.52056
$508$	8.64383	+	6.28011i	0.383508	+	0.278635i
$509$	−0.355304	+	1.09351i	−0.0157486	+	0.0484692i	−0.958622	−	0.284682i	$-0.908112\pi$
$509$	−0.355304	+	1.09351i	−0.0157486	+	0.0484692i	0.942873	+	0.333151i	$0.108112\pi$
$510$	−1.80318	−	5.54962i	−0.0798463	−	0.245742i
$511$	3.23313	−	2.34900i	0.143025	−	0.103914i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−2.10570	−	6.48068i	−0.0929689	−	0.286129i
$514$	−7.87145	+	24.2258i	−0.347195	+	1.06856i
$515$	−28.5446	−	20.7389i	−1.25783	−	0.913864i
$516$	7.20419			0.317147
$517$	5.71007	−	19.7488i	0.251128	−	0.868553i
$518$	10.8797			0.478026
$519$	−12.9621	−	9.41750i	−0.568972	−	0.413382i
$520$	5.95218	−	18.3189i	0.261020	−	0.803338i
$521$	8.06420	+	24.8191i	0.353299	+	1.08734i	0.956989	+	0.290124i	$0.0936965\pi$
$521$	8.06420	+	24.8191i	0.353299	+	1.08734i	−0.603690	+	0.797219i	$0.706304\pi$
$522$	−5.67256	+	4.12136i	−0.248281	+	0.180387i
$523$	−7.63269	+	5.54547i	−0.333754	+	0.242487i	−0.742022	−	0.670376i	$-0.766133\pi$
$523$	−7.63269	+	5.54547i	−0.333754	+	0.242487i	0.408268	+	0.912862i	$0.366133\pi$
$524$	−4.95330	−	15.2447i	−0.216386	−	0.665968i
$525$	0.881966	−	2.71441i	0.0384922	−	0.118467i
$526$	16.4650	+	11.9625i	0.717907	+	0.521590i
$527$	−9.53226			−0.415232
$528$	1.12747	+	3.11910i	0.0490670	+	0.135742i
$529$	−20.5210			−0.892217
$530$	−9.78873	−	7.11193i	−0.425195	−	0.308922i
$531$	−2.89878	+	8.92151i	−0.125796	+	0.387161i
$532$	−2.10570	−	6.48068i	−0.0912936	−	0.280973i
$533$	−0.855919	+	0.621862i	−0.0370740	+	0.0269358i
$534$	−1.20150	+	0.872941i	−0.0519940	+	0.0377758i
$535$	−12.0458	−	37.0732i	−0.520786	−	1.60282i
$536$	2.05949	−	6.33846i	0.0889565	−	0.273780i
$537$	5.32363	+	3.86784i	0.229731	+	0.166910i
$538$	2.75666			0.118848
$539$	−2.61803	+	2.03615i	−0.112767	+	0.0877031i
$540$	2.80252			0.120601
$541$	−5.70299	−	4.14346i	−0.245191	−	0.178141i	0.458402	−	0.888745i	$-0.348422\pi$
$541$	−5.70299	−	4.14346i	−0.245191	−	0.178141i	−0.703593	+	0.710604i	$0.748422\pi$
$542$	−5.79668	+	17.8404i	−0.248989	+	0.766309i
$543$	4.61985	+	14.2184i	0.198257	+	0.610172i
$544$	1.68448	−	1.22385i	0.0722216	−	0.0524721i
$545$	−43.1781	+	31.3707i	−1.84954	+	1.34377i
$546$	2.12387	+	6.53660i	0.0908932	+	0.279740i
$547$	−10.6940	+	32.9126i	−0.457240	+	1.40724i	0.411244	+	0.911525i	$0.365094\pi$
$547$	−10.6940	+	32.9126i	−0.457240	+	1.40724i	−0.868485	+	0.495716i	$0.834906\pi$
$548$	−7.51863	−	5.46260i	−0.321180	−	0.233351i
$549$	−7.37475			−0.314747
$550$	7.47214	−	5.81137i	0.318613	−	0.247798i
$551$	47.7788			2.03545
$552$	−1.27378	−	0.925458i	−0.0542158	−	0.0393901i
$553$	3.04467	−	9.37054i	0.129473	−	0.398476i
$554$	0.961004	+	2.95767i	0.0408291	+	0.125659i
$555$	24.6673	−	17.9219i	1.04707	−	0.760741i
$556$	10.4998	−	7.62855i	0.445290	−	0.323522i
$557$	−2.67325	−	8.22743i	−0.113269	−	0.348607i	0.878313	−	0.478087i	$-0.158669\pi$
$557$	−2.67325	−	8.22743i	−0.113269	−	0.348607i	−0.991582	+	0.129479i	$0.958669\pi$
$558$	1.41472	−	4.35405i	0.0598897	−	0.184322i
$559$	40.0579	+	29.1037i	1.69427	+	1.23096i
$560$	2.80252			0.118428
$561$	2.34756	+	6.49439i	0.0991139	+	0.274194i
$562$	2.86935			0.121036
$563$	16.9889	+	12.3432i	0.715999	+	0.520204i	0.885103	−	0.465395i	$-0.154088\pi$
$563$	16.9889	+	12.3432i	0.715999	+	0.520204i	−0.169105	+	0.985598i	$0.554088\pi$
$564$	1.91541	−	5.89503i	0.0806533	−	0.248225i
$565$	3.79561	+	11.6817i	0.159682	+	0.491452i
$566$	1.79709	−	1.30566i	0.0755375	−	0.0548812i
$567$	−0.809017	+	0.587785i	−0.0339755	+	0.0246847i
$568$	1.62970	+	5.01571i	0.0683808	+	0.210455i
$569$	−6.73197	+	20.7189i	−0.282219	+	0.868581i	0.705000	+	0.709208i	$0.250947\pi$
$569$	−6.73197	+	20.7189i	−0.282219	+	0.868581i	−0.987218	+	0.159373i	$0.949053\pi$
$570$	−15.4497	−	11.2249i	−0.647117	−	0.470158i
$571$	−9.04130			−0.378367			−0.189183	−	0.981942i	$-0.560584\pi$
$571$	−9.04130			−0.378367			−0.189183	+	0.981942i	$0.560584\pi$
$572$	−6.33150	+	21.8981i	−0.264733	+	0.915608i
$573$	12.8761			0.537905
$574$	−0.124534	−	0.0904792i	−0.00519794	−	0.00377653i
$575$	−1.38864	+	4.27380i	−0.0579103	+	0.178230i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	−1.83125	+	1.33048i	−0.0762359	+	0.0553887i	−0.625250	−	0.780424i	$-0.715003\pi$
$577$	−1.83125	+	1.33048i	−0.0762359	+	0.0553887i	0.549014	+	0.835813i	$0.315003\pi$
$578$	−10.2460	+	7.44413i	−0.426176	+	0.309635i
$579$	−2.25672	−	6.94547i	−0.0937861	−	0.288644i
$580$	−6.07228	+	18.6886i	−0.252138	+	0.776001i
$581$	−7.00985	−	5.09296i	−0.290818	−	0.211291i
$582$	5.86131			0.242959
$583$	11.8534	+	8.03333i	0.490918	+	0.332706i
$584$	3.99637			0.165371
$585$	15.5830	+	11.3217i	0.644278	+	0.468095i
$586$	8.26463	−	25.4359i	0.341409	−	1.05075i
$587$	−1.45187	−	4.46838i	−0.0599249	−	0.184430i	0.916613	−	0.399776i	$-0.130912\pi$
$587$	−1.45187	−	4.46838i	−0.0599249	−	0.184430i	−0.976538	+	0.215346i	$0.930912\pi$
$588$	−0.809017	+	0.587785i	−0.0333633	+	0.0242399i
$589$	−25.2382	+	18.3366i	−1.03992	+	0.755548i
$590$	8.12387	+	25.0027i	0.334454	+	1.02934i
$591$	5.35799	−	16.4902i	0.220398	−	0.678316i
$592$	8.80185	+	6.39492i	0.361754	+	0.262830i
$593$	22.3415			0.917457			0.458729	−	0.888576i	$-0.348305\pi$
$593$	22.3415			0.917457			0.458729	+	0.888576i	$0.348305\pi$
$594$	−3.31485	+	0.108436i	−0.136010	+	0.00444920i
$595$	5.83522			0.239221
$596$	1.23607	+	0.898056i	0.0506313	+	0.0367858i
$597$	−6.42329	+	19.7688i	−0.262888	+	0.809085i
$598$	−3.34400	−	10.2918i	−0.136746	−	0.420861i
$599$	−25.9900	+	18.8829i	−1.06192	+	0.771533i	−0.974443	−	0.224634i	$-0.927881\pi$
$599$	−25.9900	+	18.8829i	−1.06192	+	0.771533i	−0.0874802	+	0.996166i	$0.527881\pi$
$600$	2.30902	−	1.67760i	0.0942652	−	0.0684877i
$601$	−4.51123	−	13.8841i	−0.184017	−	0.566346i	0.815913	−	0.578174i	$-0.196235\pi$
$601$	−4.51123	−	13.8841i	−0.184017	−	0.566346i	−0.999930	+	0.0118288i	$0.996235\pi$
$602$	−2.22622	+	6.85159i	−0.0907338	+	0.279250i
$603$	5.39182	+	3.91738i	0.219572	+	0.159528i
$604$	5.12702			0.208615
$605$	−23.7026	+	19.7113i	−0.963647	+	0.801377i
$606$	11.5664			0.469855
$607$	9.37117	+	6.80855i	0.380364	+	0.276351i	0.761495	−	0.648170i	$-0.224466\pi$
$607$	9.37117	+	6.80855i	0.380364	+	0.276351i	−0.381132	+	0.924521i	$0.624466\pi$
$608$	2.10570	−	6.48068i	0.0853974	−	0.262826i
$609$	−2.16672	−	6.66849i	−0.0878001	−	0.270221i
$610$	−16.7207	+	12.1483i	−0.677000	+	0.491869i
$611$	34.4653	−	25.0405i	1.39432	−	1.01303i
$612$	0.643415	+	1.98023i	0.0260085	+	0.0800460i
$613$	−0.0992174	+	0.305360i	−0.00400735	+	0.0123334i	−0.953040	−	0.302844i	$-0.902064\pi$
$613$	−0.0992174	+	0.305360i	−0.00400735	+	0.0123334i	0.949033	+	0.315177i	$0.102064\pi$
$614$	−4.32363	−	3.14130i	−0.174487	−	0.126773i
$615$	−0.431398			−0.0173957
$616$	−3.31485	+	0.108436i	−0.133559	+	0.00436903i
$617$	−34.5805			−1.39216			−0.696080	−	0.717965i	$-0.745074\pi$
$617$	−34.5805			−1.39216			−0.696080	+	0.717965i	$0.745074\pi$
$618$	10.1854	+	7.40009i	0.409715	+	0.297675i
$619$	2.85228	−	8.77842i	0.114643	−	0.352835i	−0.877229	−	0.480071i	$-0.840611\pi$
$619$	2.85228	−	8.77842i	0.114643	−	0.352835i	0.991872	+	0.127237i	$0.0406108\pi$
$620$	−3.96477	−	12.2023i	−0.159229	−	0.490056i
$621$	1.27378	−	0.925458i	0.0511152	−	0.0371374i
$622$	−28.0081	+	20.3491i	−1.12302	+	0.815924i
$623$	−0.458932	−	1.41245i	−0.0183867	−	0.0565885i
$624$	−2.12387	+	6.53660i	−0.0850228	+	0.261673i
$625$	25.1803	+	18.2946i	1.00721	+	0.731784i
$626$	20.8904			0.834950
$627$	18.7084	+	12.6791i	0.747142	+	0.506355i
$628$	16.6364			0.663865
$629$	18.3266	+	13.3151i	0.730731	+	0.530907i
$630$	−0.866025	+	2.66535i	−0.0345033	+	0.106190i
$631$	−12.0626	−	37.1249i	−0.480205	−	1.47792i	−0.838807	−	0.544429i	$-0.816746\pi$
$631$	−12.0626	−	37.1249i	−0.480205	−	1.47792i	0.358602	−	0.933491i	$-0.383254\pi$
$632$	7.97106	−	5.79131i	0.317072	−	0.230366i
$633$	−18.0471	+	13.1120i	−0.717308	+	0.521155i
$634$	0.441457	+	1.35867i	0.0175325	+	0.0539595i
$635$	−9.25292	+	28.4776i	−0.367191	+	1.13010i
$636$	3.49283	+	2.53769i	0.138500	+	0.100626i
$637$	−6.87298			−0.272318
$638$	6.45926	−	22.3400i	0.255725	−	0.884450i
$639$	−5.27383			−0.208630
$640$	2.26728	+	1.64728i	0.0896223	+	0.0651144i
$641$	6.71245	−	20.6588i	0.265126	−	0.815974i	−0.726538	−	0.687126i	$-0.758872\pi$
$641$	6.71245	−	20.6588i	0.265126	−	0.815974i	0.991664	−	0.128848i	$-0.0411279\pi$
$642$	4.29822	+	13.2286i	0.169637	+	0.522089i
$643$	22.5572	−	16.3887i	0.889568	−	0.646309i	−0.0461975	−	0.998932i	$-0.514710\pi$
$643$	22.5572	−	16.3887i	0.889568	−	0.646309i	0.935765	+	0.352624i	$0.114710\pi$
$644$	1.27378	−	0.925458i	0.0501941	−	0.0364682i
$645$	6.23901	+	19.2017i	0.245661	+	0.756066i
$646$	4.38435	−	13.4936i	0.172500	−	0.530900i
$647$	2.78069	+	2.02029i	0.109320	+	0.0794259i	0.641102	−	0.767455i	$-0.278477\pi$
$647$	2.78069	+	2.02029i	0.109320	+	0.0794259i	−0.531782	+	0.846881i	$0.678477\pi$
$648$	−1.00000			−0.0392837
$649$	−10.5764	−	29.2592i	−0.415161	−	1.14852i
$650$	19.6162			0.769410
$651$	3.70378	+	2.69095i	0.145162	+	0.105467i
$652$	−2.61803	+	8.05748i	−0.102530	+	0.315555i
$653$	−0.158819	−	0.488794i	−0.00621506	−	0.0191280i	0.947901	−	0.318565i	$-0.103201\pi$
$653$	−0.158819	−	0.488794i	−0.00621506	−	0.0191280i	−0.954116	+	0.299437i	$0.903201\pi$
$654$	15.4069	−	11.1938i	0.602457	−	0.437711i
$655$	36.3428	−	26.4046i	1.42003	−	1.03171i
$656$	−0.0475677	−	0.146398i	−0.00185721	−	0.00571590i
$657$	−1.23494	+	3.80077i	−0.0481798	+	0.148282i
$658$	5.01461	+	3.64333i	0.195490	+	0.142032i
$659$	−31.2923			−1.21897			−0.609487	−	0.792796i	$-0.708625\pi$
$659$	−31.2923			−1.21897			−0.609487	+	0.792796i	$0.708625\pi$
$660$	−7.33708	+	5.70634i	−0.285596	+	0.222119i
$661$	2.53548			0.0986189			0.0493094	−	0.998784i	$-0.484298\pi$
$661$	2.53548			0.0986189			0.0493094	+	0.998784i	$0.484298\pi$
$662$	−18.3550	−	13.3357i	−0.713386	−	0.518305i
$663$	−4.42218	+	13.6101i	−0.171743	+	0.528572i
$664$	−2.67753	−	8.24058i	−0.103908	−	0.319796i
$665$	15.4497	−	11.2249i	0.599113	−	0.435281i
$666$	−8.80185	+	6.39492i	−0.341065	+	0.247798i
$667$	3.41147	+	10.4994i	0.132093	+	0.406540i
$668$	1.26600	−	3.89636i	0.0489832	−	0.150755i
$669$	−5.08930	−	3.69759i	−0.196764	−	0.142957i
$670$	18.6778			0.721587
$671$	19.3074	−	15.0161i	0.745352	−	0.579690i
$672$	−1.00000			−0.0385758
$673$	17.0843	+	12.4125i	0.658551	+	0.478465i	0.866173	−	0.499744i	$-0.166573\pi$
$673$	17.0843	+	12.4125i	0.658551	+	0.478465i	−0.207622	+	0.978209i	$0.566573\pi$
$674$	−8.01569	+	24.6697i	−0.308753	+	0.950243i
$675$	0.881966	+	2.71441i	0.0339469	+	0.104478i
$676$	−27.6990	+	20.1245i	−1.06535	+	0.774020i
$677$	32.9614	−	23.9479i	1.26681	−	0.920391i	0.267739	−	0.963491i	$-0.413723\pi$
$677$	32.9614	−	23.9479i	1.26681	−	0.920391i	0.999071	+	0.0431002i	$0.0137235\pi$
$678$	−1.35436	−	4.16828i	−0.0520137	−	0.160082i
$679$	−1.81125	+	5.57444i	−0.0695092	+	0.213927i
$680$	4.72079	+	3.42986i	0.181034	+	0.131529i
$681$	−13.6386			−0.522631
$682$	5.16171	+	14.2796i	0.197652	+	0.546795i
$683$	−23.0021			−0.880153			−0.440076	−	0.897960i	$-0.645049\pi$
$683$	−23.0021			−0.880153			−0.440076	+	0.897960i	$0.645049\pi$
$684$	5.51279	+	4.00528i	0.210787	+	0.153146i
$685$	8.04844	−	24.7705i	0.307515	−	0.946434i
$686$	−0.309017	−	0.951057i	−0.0117983	−	0.0363115i
$687$	−18.2635	+	13.2692i	−0.696795	+	0.506251i
$688$	−5.82831	+	4.23451i	−0.222202	+	0.161439i
$689$	9.16955	+	28.2210i	0.349332	+	1.07513i
$690$	1.36354	−	4.19655i	0.0519092	−	0.159760i
$691$	4.88043	+	3.54584i	0.185660	+	0.134890i	0.676733	−	0.736228i	$-0.263395\pi$
$691$	4.88043	+	3.54584i	0.185660	+	0.134890i	−0.491073	+	0.871119i	$0.663395\pi$
$692$	16.0220			0.609065
$693$	0.921216	−	3.18612i	0.0349941	−	0.121031i
$694$	29.8864			1.13447
$695$	29.4258	+	21.3791i	1.11619	+	0.810957i
$696$	2.16672	−	6.66849i	0.0821295	−	0.252769i
$697$	−0.0990424	−	0.304821i	−0.00375150	−	0.0115459i
$698$	16.0859	−	11.6871i	0.608860	−	0.442363i
$699$	1.43864	−	1.04524i	0.0544145	−	0.0395345i
$700$	0.881966	+	2.71441i	0.0333352	+	0.102595i
$701$	−7.63704	+	23.5044i	−0.288447	+	0.887749i	0.696897	+	0.717171i	$0.254563\pi$
$701$	−7.63704	+	23.5044i	−0.288447	+	0.887749i	−0.985344	+	0.170578i	$0.945437\pi$
$702$	−5.56036	−	4.03984i	−0.209862	−	0.152474i
$703$	74.1362			2.79610
$704$	−2.74551	−	1.86069i	−0.103475	−	0.0701275i
$705$	17.3711			0.654234
$706$	−2.32905	−	1.69215i	−0.0876550	−	0.0636851i
$707$	−3.57423	+	11.0003i	−0.134423	+	0.413711i
$708$	−2.89878	−	8.92151i	−0.108943	−	0.335291i
$709$	−31.6416	+	22.9890i	−1.18833	+	0.863369i	−0.993086	−	0.117386i	$-0.962548\pi$
$709$	−31.6416	+	22.9890i	−1.18833	+	0.863369i	−0.195240	+	0.980756i	$0.562548\pi$
$710$	−11.9573	+	8.68747i	−0.448748	+	0.326035i
$711$	3.04467	+	9.37054i	0.114184	+	0.351423i
$712$	0.458932	−	1.41245i	0.0171992	−	0.0529337i
$713$	−5.83153	−	4.23686i	−0.218393	−	0.158672i
$714$	−2.08214			−0.0779220
$715$	−63.8495	+	2.08867i	−2.38784	+	0.0781116i
$716$	−6.58036			−0.245920
$717$	−20.9031	−	15.1870i	−0.780640	−	0.567168i
$718$	−5.21416	+	16.0475i	−0.194591	+	0.598889i
$719$	0.341829	+	1.05204i	0.0127481	+	0.0392345i	0.957228	−	0.289334i	$-0.0934338\pi$
$719$	0.341829	+	1.05204i	0.0127481	+	0.0392345i	−0.944480	+	0.328568i	$0.893434\pi$
$720$	−2.26728	+	1.64728i	−0.0844967	+	0.0613904i
$721$	−10.1854	+	7.40009i	−0.379322	+	0.275594i
$722$	−8.47731	−	26.0905i	−0.315493	−	0.970986i
$723$	4.61427	−	14.2013i	0.171607	−	0.528151i
$724$	−12.0949	−	8.78748i	−0.449504	−	0.326584i
$725$	−20.0120			−0.743228
$726$	8.45760	−	7.03342i	0.313891	−	0.261035i
$727$	−25.1214			−0.931700			−0.465850	−	0.884864i	$-0.654251\pi$
$727$	−25.1214			−0.931700			−0.465850	+	0.884864i	$0.654251\pi$
$728$	−5.56036	−	4.03984i	−0.206081	−	0.149726i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	3.46095	+	10.6517i	0.128096	+	0.394238i
$731$	−12.1353	+	8.81683i	−0.448841	+	0.326102i
$732$	5.96630	−	4.33477i	0.220521	−	0.160218i
$733$	9.38033	+	28.8697i	0.346471	+	1.06633i	0.960792	+	0.277271i	$0.0894299\pi$
$733$	9.38033	+	28.8697i	0.346471	+	1.06633i	−0.614321	+	0.789056i	$0.710570\pi$
$734$	−1.48518	+	4.57092i	−0.0548191	+	0.168716i
$735$	−2.26728	−	1.64728i	−0.0836300	−	0.0607608i
$736$	1.57448			0.0580362
$737$	−22.0923	+	0.722691i	−0.813782	+	0.0266207i
$738$	0.153932			0.00566633
$739$	−7.58119	−	5.50805i	−0.278878	−	0.202617i	0.439550	−	0.898218i	$-0.355138\pi$
$739$	−7.58119	−	5.50805i	−0.278878	−	0.202617i	−0.718428	+	0.695601i	$0.755138\pi$
$740$	−9.42209	+	28.9982i	−0.346363	+	1.06599i
$741$	14.4724	+	44.5416i	0.531658	+	1.63628i
$742$	−3.49283	+	2.53769i	−0.128226	+	0.0931616i
$743$	−27.8194	+	20.2120i	−1.02060	+	0.741507i	−0.966405	−	0.257024i	$-0.917258\pi$
$743$	−27.8194	+	20.2120i	−1.02060	+	0.741507i	−0.0541912	+	0.998531i	$0.517258\pi$
$744$	1.41472	+	4.35405i	0.0518660	+	0.159627i
$745$	−1.32317	+	4.07230i	−0.0484772	+	0.149197i
$746$	−24.9400	−	18.1200i	−0.913117	−	0.663419i
$747$	8.66465			0.317023
$748$	−5.71652	−	3.87422i	−0.209017	−	0.141655i
$749$	−13.9093			−0.508236
$750$	−4.86536	−	3.53489i	−0.177658	−	0.129076i
$751$	−8.18769	+	25.1991i	−0.298773	+	0.919529i	0.683155	+	0.730273i	$0.260607\pi$
$751$	−8.18769	+	25.1991i	−0.298773	+	0.919529i	−0.981928	+	0.189255i	$0.939393\pi$
$752$	1.91541	+	5.89503i	0.0698478	+	0.214970i
$753$	4.59734	−	3.34016i	0.167536	−	0.121722i
$754$	38.9874	−	28.3260i	1.41984	−	1.03157i
$755$	4.44013	+	13.6653i	0.161593	+	0.497331i
$756$	0.309017	−	0.951057i	0.0112388	−	0.0345896i
$757$	14.7811	+	10.7391i	0.537227	+	0.390319i	0.823054	−	0.567963i	$-0.192268\pi$
$757$	14.7811	+	10.7391i	0.537227	+	0.390319i	−0.285827	+	0.958281i	$0.592268\pi$
$758$	−11.5537			−0.419649
$759$	−1.45044	+	5.01649i	−0.0526476	+	0.182087i
$760$	19.0969			0.692716
$761$	−20.1463	−	14.6371i	−0.730303	−	0.530596i	0.159356	−	0.987221i	$-0.449058\pi$
$761$	−20.1463	−	14.6371i	−0.730303	−	0.530596i	−0.889659	+	0.456625i	$0.849058\pi$
$762$	3.30165	−	10.1614i	0.119606	−	0.368110i
$763$	5.88491	+	18.1119i	0.213048	+	0.655694i
$764$	−10.4169	+	7.56835i	−0.376872	+	0.273813i
$765$	−4.72079	+	3.42986i	−0.170681	+	0.124007i
$766$	6.41559	+	19.7451i	0.231805	+	0.713421i
$767$	19.9232	−	61.3174i	0.719386	−	2.21404i
$768$	−0.809017	−	0.587785i	−0.0291929	−	0.0212099i
$769$	23.7581			0.856739			0.428370	−	0.903604i	$-0.359088\pi$
$769$	23.7581			0.856739			0.428370	+	0.903604i	$0.359088\pi$
$770$	−3.15977	−	8.74134i	−0.113870	−	0.315016i
$771$	25.4725			0.917371
$772$	5.90817	+	4.29254i	0.212640	+	0.154492i
$773$	−10.7657	+	33.1333i	−0.387214	+	1.19172i	0.547647	+	0.836710i	$0.315524\pi$
$773$	−10.7657	+	33.1333i	−0.387214	+	1.19172i	−0.934861	+	0.355013i	$0.884476\pi$
$774$	−2.22622	−	6.85159i	−0.0800197	−	0.246275i
$775$	10.5710	−	7.68025i	0.379720	−	0.275883i
$776$	−4.74190	+	3.44519i	−0.170224	+	0.123675i
$777$	−3.36201	−	10.3472i	−0.120611	−	0.371204i
$778$	−1.04480	+	3.21557i	−0.0374580	+	0.115284i
$779$	−0.848597	−	0.616542i	−0.0304042	−	0.0220899i
$780$	−19.2617			−0.689678
$781$	13.8071	−	10.7383i	0.494056	−	0.384247i
$782$	3.27829			0.117231
$783$	5.67256	+	4.12136i	0.202721	+	0.147285i
$784$	0.309017	−	0.951057i	0.0110363	−	0.0339663i
$785$	14.4076	+	44.3419i	0.514228	+	1.58263i
$786$	−12.9679	+	9.42174i	−0.462550	+	0.336062i
$787$	−24.2935	+	17.6502i	−0.865969	+	0.629163i	−0.929502	−	0.368816i	$-0.879763\pi$
$787$	−24.2935	+	17.6502i	−0.865969	+	0.629163i	0.0635331	+	0.997980i	$0.479763\pi$
$788$	5.35799	+	16.4902i	0.190871	+	0.587439i
$789$	6.28906	−	19.3557i	0.223896	−	0.689082i
$790$	22.3390	+	16.2303i	0.794787	+	0.577447i
$791$	4.38279			0.155834
$792$	2.61803	−	2.03615i	0.0930278	−	0.0723514i
$793$	50.6866			1.79993
$794$	−2.21537	−	1.60956i	−0.0786205	−	0.0571211i
$795$	−3.73896	+	11.5073i	−0.132607	+	0.408123i
$796$	−6.42329	−	19.7688i	−0.227667	−	0.700688i
$797$	17.7889	−	12.9244i	0.630113	−	0.457804i	−0.226326	−	0.974052i	$-0.572671\pi$
$797$	17.7889	−	12.9244i	0.630113	−	0.457804i	0.856440	+	0.516247i	$0.172671\pi$
$798$	−5.51279	+	4.00528i	−0.195151	+	0.141785i
$799$	3.98814	+	12.2742i	0.141090	+	0.434232i
$800$	−0.881966	+	2.71441i	−0.0311822	+	0.0959690i
$801$	1.20150	+	0.872941i	0.0424529	+	0.0308439i
$802$	26.1665			0.923972
$803$	−4.50580	−	12.4651i	−0.159006	−	0.439883i
$804$	−6.66465			−0.235044
$805$	3.56980	+	2.59361i	0.125819	+	0.0914128i
$806$	−9.72332	+	29.9253i	−0.342489	+	1.05407i
$807$	−0.851855	−	2.62174i	−0.0299867	−	0.0922897i
$808$	−9.35745	+	6.79859i	−0.329194	+	0.239173i
$809$	−6.84719	+	4.97478i	−0.240734	+	0.174904i	−0.701610	−	0.712561i	$-0.747535\pi$
$809$	−6.84719	+	4.97478i	−0.240734	+	0.174904i	0.460876	+	0.887465i	$0.347535\pi$
$810$	−0.866025	−	2.66535i	−0.0304290	−	0.0936509i
$811$	−7.45464	+	22.9430i	−0.261768	+	0.805639i	0.730652	+	0.682750i	$0.239216\pi$
$811$	−7.45464	+	22.9430i	−0.261768	+	0.805639i	−0.992420	+	0.122889i	$0.960784\pi$
$812$	5.67256	+	4.12136i	0.199068	+	0.144631i
$813$	18.7585			0.657888
$814$	10.0225	−	34.6640i	0.351290	−	1.21497i
$815$	−23.7433			−0.831692
$816$	−1.68448	−	1.22385i	−0.0589687	−	0.0428433i
$817$	−15.1699	+	46.6880i	−0.530726	+	1.63341i
$818$	−11.8289	−	36.4057i	−0.413589	−	1.27289i
$819$	5.56036	−	4.03984i	0.194295	−	0.141163i
$820$	0.349008	−	0.253569i	0.0121879	−	0.00885503i
$821$	−14.7713	−	45.4612i	−0.515520	−	1.58661i	−0.782333	−	0.622860i	$-0.785971\pi$
$821$	−14.7713	−	45.4612i	−0.515520	−	1.58661i	0.266813	−	0.963748i	$-0.414029\pi$
$822$	−2.87186	+	8.83868i	−0.100168	+	0.308284i
$823$	−4.87038	−	3.53854i	−0.169771	−	0.123346i	0.499655	−	0.866224i	$-0.333460\pi$
$823$	−4.87038	−	3.53854i	−0.169771	−	0.123346i	−0.669426	+	0.742879i	$0.733460\pi$
$824$	−12.5898			−0.438586
$825$	−7.83596	−	5.31061i	−0.272813	−	0.184892i
$826$	9.38064			0.326394
$827$	33.9387	+	24.6579i	1.18016	+	0.857440i	0.992190	−	0.124734i	$-0.0398077\pi$
$827$	33.9387	+	24.6579i	1.18016	+	0.857440i	0.187975	+	0.982174i	$0.439808\pi$
$828$	−0.486542	+	1.49742i	−0.0169085	+	0.0520390i
$829$	0.816640	+	2.51336i	0.0283631	+	0.0872926i	0.964236	−	0.265045i	$-0.0853869\pi$
$829$	0.816640	+	2.51336i	0.0283631	+	0.0872926i	−0.935873	+	0.352338i	$0.885387\pi$
$830$	19.6452	−	14.2731i	0.681896	−	0.495426i
$831$	2.51594	−	1.82794i	0.0872770	−	0.0634105i
$832$	−2.12387	−	6.53660i	−0.0736319	−	0.226616i
$833$	0.643415	−	1.98023i	0.0222930	−	0.0686109i
$834$	−10.4998	−	7.62855i	−0.363578	−	0.264155i
$835$	11.4816			0.397336
$836$	−22.5880	+	0.738906i	−0.781223	+	0.0255556i
$837$	−4.57812			−0.158243
$838$	1.16163	+	0.843975i	0.0401279	+	0.0291546i
$839$	−14.1275	+	43.4800i	−0.487736	+	1.50110i	0.340244	+	0.940337i	$0.389490\pi$
$839$	−14.1275	+	43.4800i	−0.487736	+	1.50110i	−0.827979	+	0.560759i	$0.810510\pi$
$840$	−0.866025	−	2.66535i	−0.0298807	−	0.0919634i
$841$	−16.3126	+	11.8518i	−0.562504	+	0.408683i
$842$	16.2018	−	11.7713i	0.558350	−	0.405665i
$843$	−0.886677	−	2.72891i	−0.0305388	−	0.0939887i
$844$	6.89338	−	21.2156i	0.237280	−	0.730273i
$845$	−77.6270	−	56.3993i	−2.67045	−	1.94020i
$846$	−6.19840			−0.213105
$847$	4.07564	+	10.2171i	0.140040	+	0.351064i
$848$	−4.31738			−0.148259
$849$	−1.79709	−	1.30566i	−0.0616761	−	0.0448103i
$850$	−1.83637	+	5.65177i	−0.0629871	+	0.193854i
$851$	5.29343	+	16.2915i	0.181456	+	0.558465i
$852$	4.26662	−	3.09988i	0.146172	−	0.106200i
$853$	19.0804	−	13.8627i	0.653300	−	0.474650i	−0.211094	−	0.977466i	$-0.567702\pi$
$853$	19.0804	−	13.8627i	0.653300	−	0.474650i	0.864394	+	0.502816i	$0.167702\pi$
$854$	2.27892	+	7.01381i	0.0779832	+	0.240008i
$855$	−5.90126	+	18.1622i	−0.201819	+	0.621134i
$856$	−11.2529	−	8.17569i	−0.384615	−	0.279439i
$857$	−27.7693			−0.948581			−0.474291	−	0.880368i	$-0.657295\pi$
$857$	−27.7693			−0.948581			−0.474291	+	0.880368i	$0.657295\pi$
$858$	22.7829	−	0.745282i	0.777796	−	0.0254435i
$859$	−31.8564			−1.08693			−0.543463	−	0.839433i	$-0.682887\pi$
$859$	−31.8564			−1.08693			−0.543463	+	0.839433i	$0.682887\pi$
$860$	−16.3339	−	11.8673i	−0.556983	−	0.404672i
$861$	−0.0475677	+	0.146398i	−0.00162110	+	0.00498924i
$862$	−2.32537	−	7.15675i	−0.0792024	−	0.243760i
$863$	−22.9205	+	16.6528i	−0.780225	+	0.566866i	−0.905046	−	0.425313i	$-0.860164\pi$
$863$	−22.9205	+	16.6528i	−0.780225	+	0.566866i	0.124822	+	0.992179i	$0.460164\pi$
$864$	0.809017	−	0.587785i	0.0275233	−	0.0199969i
$865$	13.8755	+	42.7043i	0.471780	+	1.45199i
$866$	4.20237	−	12.9336i	0.142802	−	0.439500i
$867$	10.2460	+	7.44413i	0.347971	+	0.252816i
$868$	−4.57812			−0.155391
$869$	−27.0509	−	18.3330i	−0.917638	−	0.621904i
$870$	19.6503			0.666208
$871$	−37.0579	−	26.9241i	−1.25566	−	0.912289i
$872$	−5.88491	+	18.1119i	−0.199288	+	0.613346i
$873$	−1.81125	−	5.57444i	−0.0613014	−	0.188666i
$874$	8.67980	−	6.30624i	0.293599	−	0.213312i
$875$	4.86536	−	3.53489i	0.164479	−	0.119501i
$876$	−1.23494	−	3.80077i	−0.0417249	−	0.128416i
$877$	12.5399	−	38.5938i	0.423442	−	1.30322i	−0.481037	−	0.876700i	$-0.659740\pi$
$877$	12.5399	−	38.5938i	0.423442	−	1.30322i	0.904478	−	0.426519i	$-0.140260\pi$
$878$	−2.61228	−	1.89793i	−0.0881600	−	0.0640520i
$879$	−26.7449			−0.902083
$880$	2.58172	−	8.92916i	0.0870299	−	0.301002i
$881$	22.8128			0.768583			0.384291	−	0.923212i	$-0.374446\pi$
$881$	22.8128			0.768583			0.384291	+	0.923212i	$0.374446\pi$
$882$	0.809017	+	0.587785i	0.0272410	+	0.0197918i
$883$	−1.75245	+	5.39348i	−0.0589746	+	0.181505i	−0.976204	−	0.216854i	$-0.930420\pi$
$883$	−1.75245	+	5.39348i	−0.0589746	+	0.181505i	0.917229	+	0.398359i	$0.130420\pi$
$884$	−4.42218	−	13.6101i	−0.148734	−	0.457756i
$885$	21.2686	−	15.4525i	0.714935	−	0.519431i
$886$	−0.105241	+	0.0764623i	−0.00353565	+	0.00256880i
$887$	−17.6891	−	54.4415i	−0.593942	−	1.82797i	−0.559922	−	0.828546i	$-0.689169\pi$
$887$	−17.6891	−	54.4415i	−0.593942	−	1.82797i	−0.0340206	−	0.999421i	$-0.510831\pi$
$888$	3.36201	−	10.3472i	0.112822	−	0.347229i
$889$	8.64383	+	6.28011i	0.289905	+	0.210628i
$890$	4.16212			0.139515
$891$	1.12747	+	3.11910i	0.0377718	+	0.104494i
$892$	6.29072			0.210629
$893$	34.1705	+	24.8263i	1.14347	+	0.830781i
$894$	0.472136	−	1.45309i	0.0157906	−	0.0485984i
$895$	−5.69876	−	17.5390i	−0.190489	−	0.586264i
$896$	0.809017	−	0.587785i	0.0270274	−	0.0196365i
$897$	−8.75470	+	6.36066i	−0.292311	+	0.212376i
$898$	−0.964277	−	2.96774i	−0.0321783	−	0.0990347i
$899$	9.91952	−	30.5292i	0.330835	−	1.01820i
$900$	−2.30902	−	1.67760i	−0.0769672	−	0.0559200i
$901$	−8.98937			−0.299479
$902$	−0.403000	+	0.313429i	−0.0134184	+	0.0104360i
$903$	7.20419			0.239740
$904$	3.54575	+	2.57614i	0.117930	+	0.0856811i
$905$	12.9472	−	39.8474i	0.430380	−	1.32457i
$906$	−1.58434	−	4.87608i	−0.0526360	−	0.161997i
$907$	−6.01515	+	4.37026i	−0.199730	+	0.145112i	−0.683155	−	0.730274i	$-0.739393\pi$
$907$	−6.01515	+	4.37026i	−0.199730	+	0.145112i	0.483425	+	0.875386i	$0.339393\pi$
$908$	11.0338	−	8.01654i	0.366170	−	0.266038i
$909$	−3.57423	−	11.0003i	−0.118550	−	0.364858i
$910$	5.95218	−	18.3189i	0.197313	−	0.607266i
$911$	19.1558	+	13.9175i	0.634661	+	0.461108i	0.858012	−	0.513630i	$-0.171700\pi$
$911$	19.1558	+	13.9175i	0.634661	+	0.461108i	−0.223351	+	0.974738i	$0.571700\pi$
$912$	−6.81419			−0.225640
$913$	−22.6844	+	17.6425i	−0.750743	+	0.583882i
$914$	7.64444			0.252856
$915$	16.7207	+	12.1483i	0.552768	+	0.401609i
$916$	6.97603	−	21.4700i	0.230494	−	0.709389i
$917$	−4.95330	−	15.2447i	−0.163572	−	0.503424i
$918$	1.68448	−	1.22385i	0.0555962	−	0.0403930i
$919$	5.44110	−	3.95319i	0.179485	−	0.130404i	−0.494415	−	0.869226i	$-0.664618\pi$
$919$	5.44110	−	3.95319i	0.179485	−	0.130404i	0.673900	+	0.738822i	$0.264618\pi$
$920$	1.36354	+	4.19655i	0.0449547	+	0.138356i
$921$	−1.65148	+	5.08273i	−0.0544181	+	0.167482i
$922$	−28.0839	−	20.4041i	−0.924893	−	0.671974i
$923$	36.2470			1.19308
$924$	1.12747	+	3.11910i	0.0370912	+	0.102611i
$925$	−31.0517			−1.02097
$926$	2.88271	+	2.09441i	0.0947316	+	0.0688266i
$927$	3.89046	−	11.9736i	0.127779	−	0.393265i
$928$	2.16672	+	6.66849i	0.0711262	+	0.218904i
$929$	11.3745	−	8.26403i	0.373184	−	0.271134i	−0.385346	−	0.922772i	$-0.625918\pi$
$929$	11.3745	−	8.26403i	0.373184	−	0.271134i	0.758530	+	0.651638i	$0.225918\pi$
$930$	−10.3799	+	7.54143i	−0.340370	+	0.247293i
$931$	−2.10570	−	6.48068i	−0.0690115	−	0.212396i
$932$	−0.549513	+	1.69123i	−0.0179999	+	0.0553980i
$933$	28.0081	+	20.3491i	0.916944	+	0.666199i
$934$	−0.0633480			−0.00207281
$935$	5.37550	−	18.5917i	0.175798	−	0.608014i
$936$	6.87298			0.224650
$937$	5.55706	+	4.03744i	0.181541	+	0.131897i	0.674844	−	0.737960i	$-0.264211\pi$
$937$	5.55706	+	4.03744i	0.181541	+	0.131897i	−0.493303	+	0.869857i	$0.664211\pi$
$938$	2.05949	−	6.33846i	0.0672448	−	0.206958i
$939$	−6.45550	−	19.8680i	−0.210667	−	0.648367i
$940$	−14.0535	+	10.2105i	−0.458376	+	0.333029i
$941$	−40.4795	+	29.4101i	−1.31959	+	0.958741i	−0.319657	+	0.947533i	$0.603568\pi$
$941$	−40.4795	+	29.4101i	−1.31959	+	0.958741i	−0.999937	+	0.0112078i	$0.996432\pi$
$942$	−5.14093	−	15.8222i	−0.167501	−	0.515514i
$943$	0.0748946	−	0.230502i	0.00243890	−	0.00750617i
$944$	7.58909	+	5.51380i	0.247004	+	0.179459i
$945$	2.80252			0.0911659
$946$	19.7792	+	13.4048i	0.643076	+	0.435827i
$947$	54.9241			1.78479			0.892397	−	0.451250i	$-0.149022\pi$
$947$	54.9241			1.78479			0.892397	+	0.451250i	$0.149022\pi$
$948$	−7.97106	−	5.79131i	−0.258888	−	0.188093i
$949$	8.48775	−	26.1226i	0.275524	−	0.847976i
$950$	6.00988	+	18.4965i	0.194986	+	0.600106i
$951$	1.15575	−	0.839701i	0.0374778	−	0.0272292i
$952$	1.68448	−	1.22385i	0.0545944	−	0.0396652i
$953$	−7.66413	−	23.5878i	−0.248266	−	0.764083i	−0.995082	−	0.0990529i	$-0.968419\pi$
$953$	−7.66413	−	23.5878i	−0.248266	−	0.764083i	0.746817	−	0.665030i	$-0.231581\pi$
$954$	1.33414	−	4.10607i	0.0431945	−	0.132939i
$955$	−29.1937	−	21.2104i	−0.944685	−	0.686354i
$956$	25.8376			0.835648
$957$	−23.2426	+	0.760320i	−0.751328	+	0.0245777i
$958$	−33.2334			−1.07372
$959$	−7.51863	−	5.46260i	−0.242789	−	0.176397i
$960$	0.866025	−	2.66535i	0.0279508	−	0.0860239i
$961$	−3.10279	−	9.54940i	−0.100090	−	0.308045i
$962$	60.4950	−	43.9522i	1.95044	−	1.41708i
$963$	11.2529	−	8.17569i	0.362619	−	0.263458i
$964$	4.61427	+	14.2013i	0.148616	+	0.457392i
$965$	−6.32450	+	19.4648i	−0.203593	+	0.626594i
$966$	−1.27378	−	0.925458i	−0.0409833	−	0.0297761i
$967$	19.1238			0.614981			0.307490	−	0.951551i	$-0.400511\pi$
$967$	19.1238			0.614981			0.307490	+	0.951551i	$0.400511\pi$
$968$	−2.70820	+	10.6614i	−0.0870450	+	0.342671i
$969$	−14.1881			−0.455786
$970$	−13.2893	−	9.65521i	−0.426693	−	0.310010i
$971$	−4.46349	+	13.7372i	−0.143240	+	0.440848i	−0.996780	−	0.0801790i	$-0.974451\pi$
$971$	−4.46349	+	13.7372i	−0.143240	+	0.440848i	0.853540	+	0.521027i	$0.174451\pi$
$972$	0.309017	+	0.951057i	0.00991172	+	0.0305052i
$973$	10.4998	−	7.62855i	0.336608	−	0.244560i
$974$	−7.40133	+	5.37738i	−0.237154	+	0.172303i
$975$	−6.06174	−	18.6561i	−0.194131	−	0.597474i
$976$	−2.27892	+	7.01381i	−0.0729466	+	0.224507i
$977$	−21.7263	−	15.7851i	−0.695086	−	0.505009i	0.183242	−	0.983068i	$-0.441341\pi$
$977$	−21.7263	−	15.7851i	−0.695086	−	0.505009i	−0.878328	+	0.478058i	$0.841341\pi$
$978$	8.47214			0.270909
$979$	−4.92300	+	0.161043i	−0.157340	+	0.00514695i
$980$	2.80252			0.0895231
$981$	−15.4069	−	11.1938i	−0.491904	−	0.357389i
$982$	5.91539	−	18.2057i	0.188768	−	0.580967i
$983$	−10.6710	−	32.8420i	−0.340352	−	1.04750i	−0.964025	−	0.265811i	$-0.914360\pi$
$983$	−10.6710	−	32.8420i	−0.340352	−	1.04750i	0.623673	−	0.781685i	$-0.285640\pi$
$984$	−0.124534	+	0.0904792i	−0.00397000	+	0.00288437i
$985$	−39.3120	+	28.5619i	−1.25259	+	0.910057i
$986$	4.51142	+	13.8847i	0.143673	+	0.442179i
$987$	1.91541	−	5.89503i	0.0609682	−	0.187641i
$988$	−37.8893	−	27.5282i	−1.20542	−	0.875789i
$989$	−11.3429			−0.360682
$990$	7.69433	+	5.21463i	0.244542	+	0.165732i
$991$	29.8475			0.948137			0.474068	−	0.880488i	$-0.342785\pi$
$991$	29.8475			0.948137			0.474068	+	0.880488i	$0.342785\pi$
$992$	−3.70378	−	2.69095i	−0.117595	−	0.0854378i
$993$	−7.01098	+	21.5776i	−0.222487	+	0.684743i
$994$	1.62970	+	5.01571i	0.0516911	+	0.159089i
$995$	47.1282	−	34.2406i	1.49406	−	1.08550i
$996$	−7.00985	+	5.09296i	−0.222116	+	0.161376i
$997$	10.2947	+	31.6837i	0.326035	+	1.00343i	0.970971	+	0.239196i	$0.0768840\pi$
$997$	10.2947	+	31.6837i	0.326035	+	1.00343i	−0.644936	+	0.764236i	$0.723116\pi$
$998$	7.20825	−	22.1847i	0.228173	−	0.702245i
$999$	8.80185	+	6.39492i	0.278478	+	0.202326i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.j.g.169.1	✓	8
11.3	even	5	inner	462.2.j.g.421.1	yes	8
11.5	even	5		5082.2.a.bz.1.4		4
11.6	odd	10		5082.2.a.ce.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.j.g.169.1	✓	8	1.1	even	1	trivial
462.2.j.g.421.1	yes	8	11.3	even	5	inner
5082.2.a.bz.1.4		4	11.5	even	5
5082.2.a.ce.1.4		4	11.6	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.26728 + 1.64728i) q^{5} +(0.809017 - 0.587785i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.26728 + 1.64728i) q^{5} +(0.809017 - 0.587785i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.809017 - 0.587785i) q^{9} -2.80252 q^{10} +(3.31485 - 0.108436i) q^{11} +1.00000 q^{12} +(5.56036 + 4.03984i) q^{13} +(-0.309017 + 0.951057i) q^{14} +(0.866025 + 2.66535i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.68448 + 1.22385i) q^{17} +(-0.309017 - 0.951057i) q^{18} +(-2.10570 + 6.48068i) q^{19} +(-2.26728 - 1.64728i) q^{20} +1.00000 q^{21} +(2.74551 + 1.86069i) q^{22} -1.57448 q^{23} +(0.809017 + 0.587785i) q^{24} +(0.881966 - 2.71441i) q^{25} +(2.12387 + 6.53660i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(-0.809017 + 0.587785i) q^{28} +(-2.16672 - 6.66849i) q^{29} +(-0.866025 + 2.66535i) q^{30} +(3.70378 + 2.69095i) q^{31} -1.00000 q^{32} +(0.921216 - 3.18612i) q^{33} -2.08214 q^{34} +(-2.26728 - 1.64728i) q^{35} +(0.309017 - 0.951057i) q^{36} +(-3.36201 - 10.3472i) q^{37} +(-5.51279 + 4.00528i) q^{38} +(5.56036 - 4.03984i) q^{39} +(-0.866025 - 2.66535i) q^{40} +(-0.0475677 + 0.146398i) q^{41} +(0.809017 + 0.587785i) q^{42} +7.20419 q^{43} +(1.12747 + 3.11910i) q^{44} +2.80252 q^{45} +(-1.27378 - 0.925458i) q^{46} +(1.91541 - 5.89503i) q^{47} +(0.309017 + 0.951057i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(2.30902 - 1.67760i) q^{50} +(0.643415 + 1.98023i) q^{51} +(-2.12387 + 6.53660i) q^{52} +(3.49283 + 2.53769i) q^{53} -1.00000 q^{54} +(-7.33708 + 5.70634i) q^{55} -1.00000 q^{56} +(5.51279 + 4.00528i) q^{57} +(2.16672 - 6.66849i) q^{58} +(-2.89878 - 8.92151i) q^{59} +(-2.26728 + 1.64728i) q^{60} +(5.96630 - 4.33477i) q^{61} +(1.41472 + 4.35405i) q^{62} +(0.309017 - 0.951057i) q^{63} +(-0.809017 - 0.587785i) q^{64} -19.2617 q^{65} +(2.61803 - 2.03615i) q^{66} -6.66465 q^{67} +(-1.68448 - 1.22385i) q^{68} +(-0.486542 + 1.49742i) q^{69} +(-0.866025 - 2.66535i) q^{70} +(4.26662 - 3.09988i) q^{71} +(0.809017 - 0.587785i) q^{72} +(-1.23494 - 3.80077i) q^{73} +(3.36201 - 10.3472i) q^{74} +(-2.30902 - 1.67760i) q^{75} -6.81419 q^{76} +(1.12747 + 3.11910i) q^{77} +6.87298 q^{78} +(-7.97106 - 5.79131i) q^{79} +(0.866025 - 2.66535i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-0.124534 + 0.0904792i) q^{82} +(-7.00985 + 5.09296i) q^{83} +(0.309017 + 0.951057i) q^{84} +(1.80318 - 5.54962i) q^{85} +(5.82831 + 4.23451i) q^{86} -7.01167 q^{87} +(-0.921216 + 3.18612i) q^{88} -1.48514 q^{89} +(2.26728 + 1.64728i) q^{90} +(-2.12387 + 6.53660i) q^{91} +(-0.486542 - 1.49742i) q^{92} +(3.70378 - 2.69095i) q^{93} +(5.01461 - 3.64333i) q^{94} +(-5.90126 - 18.1622i) q^{95} +(-0.309017 + 0.951057i) q^{96} +(4.74190 + 3.44519i) q^{97} -1.00000 q^{98} +(-2.74551 - 1.86069i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9	\( 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} + 8 q^{11} + 8 q^{12} + 6 q^{13} + 2 q^{14} - 2 q^{16} + 2 q^{18} - 4 q^{19} + 8 q^{21} + 2 q^{22} + 2 q^{24} + 16 q^{25} - 6 q^{26} - 2 q^{27} - 2 q^{28} + 2 q^{29} - 4 q^{31} - 8 q^{32} + 8 q^{33} + 20 q^{34} - 2 q^{36} - 24 q^{37} - 6 q^{38} + 6 q^{39} + 2 q^{42} + 8 q^{43} - 2 q^{44} - 10 q^{46} - 2 q^{47} - 2 q^{48} - 2 q^{49} + 14 q^{50} + 10 q^{51} + 6 q^{52} - 22 q^{53} - 8 q^{54} - 8 q^{56} + 6 q^{57} - 2 q^{58} + 10 q^{59} + 26 q^{61} - 6 q^{62} - 2 q^{63} - 2 q^{64} - 60 q^{65} + 12 q^{66} + 4 q^{67} - 10 q^{69} - 16 q^{71} + 2 q^{72} - 2 q^{73} + 24 q^{74} - 14 q^{75} - 4 q^{76} - 2 q^{77} + 24 q^{78} - 12 q^{79} - 2 q^{81} - 10 q^{82} - 38 q^{83} - 2 q^{84} + 24 q^{85} + 22 q^{86} - 28 q^{87} - 8 q^{88} - 12 q^{89} + 6 q^{91} - 10 q^{92} - 4 q^{93} - 8 q^{94} - 36 q^{95} + 2 q^{96} + 6 q^{97} - 8 q^{98} - 2 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9 + 8 * q^11 + 8 * q^12 + 6 * q^13 + 2 * q^14 - 2 * q^16 + 2 * q^18 - 4 * q^19 + 8 * q^21 + 2 * q^22 + 2 * q^24 + 16 * q^25 - 6 * q^26 - 2 * q^27 - 2 * q^28 + 2 * q^29 - 4 * q^31 - 8 * q^32 + 8 * q^33 + 20 * q^34 - 2 * q^36 - 24 * q^37 - 6 * q^38 + 6 * q^39 + 2 * q^42 + 8 * q^43 - 2 * q^44 - 10 * q^46 - 2 * q^47 - 2 * q^48 - 2 * q^49 + 14 * q^50 + 10 * q^51 + 6 * q^52 - 22 * q^53 - 8 * q^54 - 8 * q^56 + 6 * q^57 - 2 * q^58 + 10 * q^59 + 26 * q^61 - 6 * q^62 - 2 * q^63 - 2 * q^64 - 60 * q^65 + 12 * q^66 + 4 * q^67 - 10 * q^69 - 16 * q^71 + 2 * q^72 - 2 * q^73 + 24 * q^74 - 14 * q^75 - 4 * q^76 - 2 * q^77 + 24 * q^78 - 12 * q^79 - 2 * q^81 - 10 * q^82 - 38 * q^83 - 2 * q^84 + 24 * q^85 + 22 * q^86 - 28 * q^87 - 8 * q^88 - 12 * q^89 + 6 * q^91 - 10 * q^92 - 4 * q^93 - 8 * q^94 - 36 * q^95 + 2 * q^96 + 6 * q^97 - 8 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more