LMFDB - Embedded newform 60.2.j.a.43.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,2,Mod(7,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

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

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

chi := DirichletCharacter("60.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	60.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.479102412128$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.426337261060096.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{9} - 3x^{8} + 4x^{7} + 8x^{6} + 8x^{5} - 12x^{4} - 32x^{3} + 64 $ x^12 - 4x^9 - 3x^8 + 4x^7 + 8x^6 + 8x^5 - 12x^4 - 32*x^3 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.2
Root			$1.19252 - 0.760198i$ of defining polynomial
Character	$\chi$	$=$	60.43
Dual form			60.2.j.a.7.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.19252 - 0.760198i) q^{2} +(0.707107 - 0.707107i) q^{3} +(0.844199 + 1.81310i) q^{4} +(0.432320 - 2.19388i) q^{5} +(-1.38078 + 0.305697i) q^{6} +(-0.611393 - 0.611393i) q^{7} +(0.371591 - 2.80391i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-1.19252 - 0.760198i) q^{2} +(0.707107 - 0.707107i) q^{3} +(0.844199 + 1.81310i) q^{4} +(0.432320 - 2.19388i) q^{5} +(-1.38078 + 0.305697i) q^{6} +(-0.611393 - 0.611393i) q^{7} +(0.371591 - 2.80391i) q^{8} -1.00000i q^{9} +(-2.18333 + 2.28759i) q^{10} +5.12822i q^{11} +(1.87899 + 0.685116i) q^{12} +(1.76156 + 1.76156i) q^{13} +(0.264318 + 1.19388i) q^{14} +(-1.24561 - 1.85700i) q^{15} +(-2.57466 + 3.06123i) q^{16} +(-3.76156 + 3.76156i) q^{17} +(-0.760198 + 1.19252i) q^{18} +1.22279 q^{19} +(4.34268 - 1.06823i) q^{20} -0.864641 q^{21} +(3.89846 - 6.11549i) q^{22} +(1.07700 - 1.07700i) q^{23} +(-1.71991 - 2.24542i) q^{24} +(-4.62620 - 1.89692i) q^{25} +(-0.761557 - 3.43982i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(0.592379 - 1.62465i) q^{28} +0.864641i q^{29} +(0.0737224 + 3.16142i) q^{30} -7.81086i q^{31} +(5.39747 - 1.69333i) q^{32} +(3.62620 + 3.62620i) q^{33} +(7.34525 - 1.62620i) q^{34} +(-1.60564 + 1.07700i) q^{35} +(1.81310 - 0.844199i) q^{36} +(-1.76156 + 1.76156i) q^{37} +(-1.45820 - 0.929560i) q^{38} +2.49122 q^{39} +(-5.99079 - 2.02741i) q^{40} +5.52311 q^{41} +(1.03110 + 0.657298i) q^{42} +(-6.20522 + 6.20522i) q^{43} +(-9.29797 + 4.32924i) q^{44} +(-2.19388 - 0.432320i) q^{45} +(-2.10308 + 0.465611i) q^{46} +(-2.29979 - 2.29979i) q^{47} +(0.344061 + 3.98518i) q^{48} -6.25240i q^{49} +(4.07479 + 5.77893i) q^{50} +5.31965i q^{51} +(-1.70677 + 4.68098i) q^{52} +(-2.62620 - 2.62620i) q^{53} +(0.305697 + 1.38078i) q^{54} +(11.2507 + 2.21703i) q^{55} +(-1.94148 + 1.48710i) q^{56} +(0.864641 - 0.864641i) q^{57} +(0.657298 - 1.03110i) q^{58} +0.528636 q^{59} +(2.31539 - 3.82609i) q^{60} +4.98168 q^{61} +(-5.93780 + 9.31460i) q^{62} +(-0.611393 + 0.611393i) q^{63} +(-7.72384 - 2.08382i) q^{64} +(4.62620 - 3.10308i) q^{65} +(-1.56768 - 7.08093i) q^{66} +(6.20522 + 6.20522i) q^{67} +(-9.99558 - 3.64457i) q^{68} -1.52311i q^{69} +(2.73349 - 0.0637434i) q^{70} -8.10243i q^{71} +(-2.80391 - 0.371591i) q^{72} +(-2.25240 - 2.25240i) q^{73} +(3.43982 - 0.761557i) q^{74} +(-4.61254 + 1.92989i) q^{75} +(1.03228 + 2.21703i) q^{76} +(3.13536 - 3.13536i) q^{77} +(-2.97082 - 1.89382i) q^{78} -15.9133 q^{79} +(5.60289 + 6.97191i) q^{80} -1.00000 q^{81} +(-6.58641 - 4.19866i) q^{82} +(7.95665 - 7.95665i) q^{83} +(-0.729929 - 1.56768i) q^{84} +(6.62620 + 9.87859i) q^{85} +(12.1170 - 2.68264i) q^{86} +(0.611393 + 0.611393i) q^{87} +(14.3791 + 1.90560i) q^{88} +7.25240i q^{89} +(2.28759 + 2.18333i) q^{90} -2.15401i q^{91} +(2.86192 + 1.04351i) q^{92} +(-5.52311 - 5.52311i) q^{93} +(0.994247 + 4.49084i) q^{94} +(0.528636 - 2.68264i) q^{95} +(2.61922 - 5.01395i) q^{96} +(0.793833 - 0.793833i) q^{97} +(-4.75306 + 7.45610i) q^{98} +5.12822 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{6} - 12 q^{8}+O(q^{10}) $ 12 * q - 4 * q^6 - 12 * q^8	$ 12 q - 4 q^{6} - 12 q^{8} - 8 q^{10} - 8 q^{12} - 4 q^{13} + 12 q^{16} - 20 q^{17} + 20 q^{20} + 12 q^{22} - 20 q^{25} + 16 q^{26} - 4 q^{28} + 8 q^{30} + 20 q^{32} + 8 q^{33} + 4 q^{36} + 4 q^{37} + 16 q^{38} - 8 q^{40} + 16 q^{41} + 20 q^{42} + 4 q^{45} - 40 q^{46} + 16 q^{48} - 16 q^{50} - 8 q^{52} + 4 q^{53} - 64 q^{56} - 20 q^{58} - 20 q^{60} - 32 q^{61} - 56 q^{62} + 20 q^{65} - 24 q^{66} - 16 q^{68} + 44 q^{70} - 12 q^{72} + 44 q^{73} + 8 q^{76} + 48 q^{77} - 24 q^{78} + 4 q^{80} - 12 q^{81} + 16 q^{82} + 44 q^{85} + 64 q^{86} + 60 q^{88} + 12 q^{90} + 56 q^{92} - 16 q^{93} + 44 q^{96} - 20 q^{97} + 24 q^{98}+O(q^{100}) $ 12 * q - 4 * q^6 - 12 * q^8 - 8 * q^10 - 8 * q^12 - 4 * q^13 + 12 * q^16 - 20 * q^17 + 20 * q^20 + 12 * q^22 - 20 * q^25 + 16 * q^26 - 4 * q^28 + 8 * q^30 + 20 * q^32 + 8 * q^33 + 4 * q^36 + 4 * q^37 + 16 * q^38 - 8 * q^40 + 16 * q^41 + 20 * q^42 + 4 * q^45 - 40 * q^46 + 16 * q^48 - 16 * q^50 - 8 * q^52 + 4 * q^53 - 64 * q^56 - 20 * q^58 - 20 * q^60 - 32 * q^61 - 56 * q^62 + 20 * q^65 - 24 * q^66 - 16 * q^68 + 44 * q^70 - 12 * q^72 + 44 * q^73 + 8 * q^76 + 48 * q^77 - 24 * q^78 + 4 * q^80 - 12 * q^81 + 16 * q^82 + 44 * q^85 + 64 * q^86 + 60 * q^88 + 12 * q^90 + 56 * q^92 - 16 * q^93 + 44 * q^96 - 20 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−1.19252	−	0.760198i	−0.843238	−	0.537541i
$2$	−1.19252	−	0.760198i	−0.843238	−	0.537541i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	0.844199	+	1.81310i	0.422099	+	0.906550i
$5$	0.432320	−	2.19388i	0.193340	−	0.981132i
$5$	0.432320	−	2.19388i	0.193340	−	0.981132i
$6$	−1.38078	+	0.305697i	−0.563700	+	0.124800i
$7$	−0.611393	−	0.611393i	−0.231085	−	0.231085i	0.582060	−	0.813145i	$-0.302247\pi$
$7$	−0.611393	−	0.611393i	−0.231085	−	0.231085i	−0.813145	+	0.582060i	$0.802247\pi$
$8$	0.371591	−	2.80391i	0.131377	−	0.991332i
$9$		−	1.00000i		−	0.333333i
$10$	−2.18333	+	2.28759i	−0.690430	+	0.723399i
$11$			5.12822i			1.54622i	0.634274	+	0.773108i	$0.281299\pi$
$11$			5.12822i			1.54622i	−0.634274	+	0.773108i	$0.718701\pi$
$12$	1.87899	+	0.685116i	0.542419	+	0.197776i
$13$	1.76156	+	1.76156i	0.488568	+	0.488568i	0.907854	−	0.419286i	$-0.137720\pi$
$13$	1.76156	+	1.76156i	0.488568	+	0.488568i	−0.419286	+	0.907854i	$0.637720\pi$
$14$	0.264318	+	1.19388i	0.0706419	+	0.319077i
$15$	−1.24561	−	1.85700i	−0.321615	−	0.479476i
$16$	−2.57466	+	3.06123i	−0.643664	+	0.765308i
$17$	−3.76156	+	3.76156i	−0.912312	+	0.912312i	−0.996454	−	0.0841421i	$-0.973185\pi$
$17$	−3.76156	+	3.76156i	−0.912312	+	0.912312i	0.0841421	+	0.996454i	$0.473185\pi$
$18$	−0.760198	+	1.19252i	−0.179180	+	0.281079i
$19$	1.22279			0.280527			0.140263	−	0.990114i	$-0.455205\pi$
$19$	1.22279			0.280527			0.140263	+	0.990114i	$0.455205\pi$
$20$	4.34268	−	1.06823i	0.971053	−	0.238863i
$21$	−0.864641			−0.188680
$22$	3.89846	−	6.11549i	0.831154	−	1.30383i
$23$	1.07700	−	1.07700i	0.224571	−	0.224571i	−0.585849	−	0.810420i	$-0.699239\pi$
$23$	1.07700	−	1.07700i	0.224571	−	0.224571i	0.810420	+	0.585849i	$0.199239\pi$
$24$	−1.71991	−	2.24542i	−0.351075	−	0.458344i
$25$	−4.62620	−	1.89692i	−0.925240	−	0.379383i
$26$	−0.761557	−	3.43982i	−0.149354	−	0.674604i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	0.592379	−	1.62465i	0.111949	−	0.307031i
$29$			0.864641i			0.160560i	0.996772	+	0.0802799i	$0.0255814\pi$
$29$			0.864641i			0.160560i	−0.996772	+	0.0802799i	$0.974419\pi$
$30$	0.0737224	+	3.16142i	0.0134598	+	0.577193i
$31$		−	7.81086i		−	1.40287i	−0.712732	−	0.701436i	$-0.752543\pi$
$31$		−	7.81086i		−	1.40287i	0.712732	−	0.701436i	$-0.247457\pi$
$32$	5.39747	−	1.69333i	0.954146	−	0.299341i
$33$	3.62620	+	3.62620i	0.631240	+	0.631240i
$34$	7.34525	−	1.62620i	1.25970	−	0.278891i
$35$	−1.60564	+	1.07700i	−0.271403	+	0.182047i
$36$	1.81310	−	0.844199i	0.302183	−	0.140700i
$37$	−1.76156	+	1.76156i	−0.289598	+	0.289598i	−0.836921	−	0.547323i	$-0.815647\pi$
$37$	−1.76156	+	1.76156i	−0.289598	+	0.289598i	0.547323	+	0.836921i	$0.315647\pi$
$38$	−1.45820	−	0.929560i	−0.236551	−	0.150795i
$39$	2.49122			0.398914
$40$	−5.99079	−	2.02741i	−0.947227	−	0.320562i
$41$	5.52311			0.862566			0.431283	−	0.902217i	$-0.358061\pi$
$41$	5.52311			0.862566			0.431283	+	0.902217i	$0.358061\pi$
$42$	1.03110	+	0.657298i	0.159102	+	0.101423i
$43$	−6.20522	+	6.20522i	−0.946288	+	0.946288i	−0.998629	−	0.0523416i	$-0.983332\pi$
$43$	−6.20522	+	6.20522i	−0.946288	+	0.946288i	0.0523416	+	0.998629i	$0.483332\pi$
$44$	−9.29797	+	4.32924i	−1.40172	+	0.652657i
$45$	−2.19388	−	0.432320i	−0.327044	−	0.0644465i
$46$	−2.10308	+	0.465611i	−0.310083	+	0.0686506i
$47$	−2.29979	−	2.29979i	−0.335459	−	0.335459i	0.519196	−	0.854655i	$-0.326231\pi$
$47$	−2.29979	−	2.29979i	−0.335459	−	0.335459i	−0.854655	+	0.519196i	$0.826231\pi$
$48$	0.344061	+	3.98518i	0.0496610	+	0.575210i
$49$		−	6.25240i		−	0.893199i
$50$	4.07479	+	5.77893i	0.576263	+	0.817264i
$51$			5.31965i			0.744899i
$52$	−1.70677	+	4.68098i	−0.236687	+	0.649135i
$53$	−2.62620	−	2.62620i	−0.360736	−	0.360736i	0.503348	−	0.864084i	$-0.332101\pi$
$53$	−2.62620	−	2.62620i	−0.360736	−	0.360736i	−0.864084	+	0.503348i	$0.832101\pi$
$54$	0.305697	+	1.38078i	0.0416001	+	0.187900i
$55$	11.2507	+	2.21703i	1.51704	+	0.298945i
$56$	−1.94148	+	1.48710i	−0.259441	+	0.198723i
$57$	0.864641	−	0.864641i	0.114524	−	0.114524i
$58$	0.657298	−	1.03110i	0.0863075	−	0.135390i
$59$	0.528636			0.0688225			0.0344113	−	0.999408i	$-0.489044\pi$
$59$	0.528636			0.0688225			0.0344113	+	0.999408i	$0.489044\pi$
$60$	2.31539	−	3.82609i	0.298915	−	0.493946i
$61$	4.98168			0.637838			0.318919	−	0.947782i	$-0.396680\pi$
$61$	4.98168			0.637838			0.318919	+	0.947782i	$0.396680\pi$
$62$	−5.93780	+	9.31460i	−0.754101	+	1.18295i
$63$	−0.611393	+	0.611393i	−0.0770283	+	0.0770283i
$64$	−7.72384	−	2.08382i	−0.965480	−	0.260477i
$65$	4.62620	−	3.10308i	0.573809	−	0.384890i
$66$	−1.56768	−	7.08093i	−0.192968	−	0.871603i
$67$	6.20522	+	6.20522i	0.758089	+	0.758089i	0.975974	−	0.217886i	$-0.0699160\pi$
$67$	6.20522	+	6.20522i	0.758089	+	0.758089i	−0.217886	+	0.975974i	$0.569916\pi$
$68$	−9.99558	−	3.64457i	−1.21214	−	0.441969i
$69$		−	1.52311i		−	0.183361i
$70$	2.73349	−	0.0637434i	0.326715	−	0.00761879i
$71$		−	8.10243i		−	0.961581i	−0.876835	−	0.480791i	$-0.840350\pi$
$71$		−	8.10243i		−	0.961581i	0.876835	−	0.480791i	$-0.159650\pi$
$72$	−2.80391	−	0.371591i	−0.330444	−	0.0437924i
$73$	−2.25240	−	2.25240i	−0.263623	−	0.263623i	0.562901	−	0.826524i	$-0.309685\pi$
$73$	−2.25240	−	2.25240i	−0.263623	−	0.263623i	−0.826524	+	0.562901i	$0.809685\pi$
$74$	3.43982	−	0.761557i	0.399871	−	0.0885292i
$75$	−4.61254	+	1.92989i	−0.532610	+	0.222845i
$76$	1.03228	+	2.21703i	0.118410	+	0.254311i
$77$	3.13536	−	3.13536i	0.357307	−	0.357307i
$78$	−2.97082	−	1.89382i	−0.336379	−	0.214433i
$79$	−15.9133			−1.79039			−0.895193	−	0.445680i	$-0.852962\pi$
$79$	−15.9133			−1.79039			−0.895193	+	0.445680i	$0.852962\pi$
$80$	5.60289	+	6.97191i	0.626423	+	0.779484i
$81$	−1.00000			−0.111111
$82$	−6.58641	−	4.19866i	−0.727348	−	0.463664i
$83$	7.95665	−	7.95665i	0.873355	−	0.873355i	−0.119481	−	0.992836i	$-0.538123\pi$
$83$	7.95665	−	7.95665i	0.873355	−	0.873355i	0.992836	+	0.119481i	$0.0381231\pi$
$84$	−0.729929	−	1.56768i	−0.0796418	−	0.171048i
$85$	6.62620	+	9.87859i	0.718712	+	1.07148i
$86$	12.1170	−	2.68264i	1.30661	−	0.289277i
$87$	0.611393	+	0.611393i	0.0655483	+	0.0655483i
$88$	14.3791	+	1.90560i	1.53281	+	0.203138i
$89$			7.25240i			0.768752i	0.923177	+	0.384376i	$0.125583\pi$
$89$			7.25240i			0.768752i	−0.923177	+	0.384376i	$0.874417\pi$
$90$	2.28759	+	2.18333i	0.241133	+	0.230143i
$91$		−	2.15401i		−	0.225801i
$92$	2.86192	+	1.04351i	0.298376	+	0.108793i
$93$	−5.52311	−	5.52311i	−0.572720	−	0.572720i
$94$	0.994247	+	4.49084i	0.102549	+	0.463195i
$95$	0.528636	−	2.68264i	0.0542369	−	0.275234i
$96$	2.61922	−	5.01395i	0.267323	−	0.511734i
$97$	0.793833	−	0.793833i	0.0806015	−	0.0806015i	−0.665657	−	0.746258i	$-0.731848\pi$
$97$	0.793833	−	0.793833i	0.0806015	−	0.0806015i	0.746258	+	0.665657i	$0.231848\pi$
$98$	−4.75306	+	7.45610i	−0.480131	+	0.753179i
$99$	5.12822			0.515405
$100$	−0.466135	−	9.98913i	−0.0466135	−	0.998913i
$101$	−10.1170			−1.00668			−0.503341	−	0.864088i	$-0.667896\pi$
$101$	−10.1170			−1.00668			−0.503341	+	0.864088i	$0.667896\pi$
$102$	4.04398	−	6.34377i	0.400414	−	0.628127i
$103$	−3.82267	+	3.82267i	−0.376659	+	0.376659i	−0.869895	−	0.493236i	$-0.835814\pi$
$103$	−3.82267	+	3.82267i	−0.376659	+	0.376659i	0.493236	+	0.869895i	$0.335814\pi$
$104$	5.59383	−	4.28467i	0.548520	−	0.420147i
$105$	−0.373802	+	1.89692i	−0.0364793	+	0.185120i
$106$	1.13536	+	5.12822i	0.110276	+	0.498097i
$107$	−5.51107	−	5.51107i	−0.532775	−	0.532775i	0.388622	−	0.921397i	$-0.372951\pi$
$107$	−5.51107	−	5.51107i	−0.532775	−	0.532775i	−0.921397	+	0.388622i	$0.872951\pi$
$108$	0.685116	−	1.87899i	0.0659253	−	0.180806i
$109$			7.31695i			0.700836i	0.936593	+	0.350418i	$0.113961\pi$
$109$			7.31695i			0.700836i	−0.936593	+	0.350418i	$0.886039\pi$
$110$	−11.7313	−	11.1966i	−1.11853	−	1.06755i
$111$			2.49122i			0.236456i
$112$	3.44575	−	0.297490i	0.325592	−	0.0281101i
$113$	−0.509161	−	0.509161i	−0.0478978	−	0.0478978i	0.682752	−	0.730650i	$-0.260783\pi$
$113$	−0.509161	−	0.509161i	−0.0478978	−	0.0478978i	−0.730650	+	0.682752i	$0.760783\pi$
$114$	−1.68840	+	0.373802i	−0.158133	+	0.0350098i
$115$	−1.89721	−	2.82843i	−0.176915	−	0.263752i
$116$	−1.56768	+	0.729929i	−0.145555	+	0.0677722i
$117$	1.76156	−	1.76156i	0.162856	−	0.162856i
$118$	−0.630408	−	0.401868i	−0.0580337	−	0.0369949i
$119$	4.59958			0.421643
$120$	−5.66973	+	2.80253i	−0.517573	+	0.255835i
$121$	−15.2986			−1.39078
$122$	−5.94074	−	3.78706i	−0.537849	−	0.342864i
$123$	3.90543	−	3.90543i	0.352141	−	0.352141i
$124$	14.1619	−	6.59392i	1.27177	−	0.592152i
$125$	−6.16160	+	9.32924i	−0.551110	+	0.834432i
$126$	1.19388	−	0.264318i	0.106359	−	0.0235473i
$127$	7.49103	+	7.49103i	0.664722	+	0.664722i	0.956489	−	0.291767i	$-0.0942433\pi$
$127$	7.49103	+	7.49103i	0.664722	+	0.664722i	−0.291767	+	0.956489i	$0.594243\pi$
$128$	7.62671	+	8.35664i	0.674112	+	0.738629i
$129$			8.77551i			0.772641i
$130$	−7.87578	+	0.183659i	−0.690752	+	0.0161079i
$131$			13.9964i			1.22287i	0.791296	+	0.611434i	$0.209407\pi$
$131$			13.9964i			1.22287i	−0.791296	+	0.611434i	$0.790593\pi$
$132$	−3.51342	+	9.63589i	−0.305804	+	0.838696i
$133$	−0.747604	−	0.747604i	−0.0648255	−	0.0648255i
$134$	−2.68264	−	12.1170i	−0.231745	−	1.04675i
$135$	−1.85700	+	1.24561i	−0.159825	+	0.107205i
$136$	9.14931	+	11.9448i	0.784547	+	1.02426i
$137$	7.01395	−	7.01395i	0.599242	−	0.599242i	−0.340869	−	0.940111i	$-0.610721\pi$
$137$	7.01395	−	7.01395i	0.599242	−	0.599242i	0.940111	+	0.340869i	$0.110721\pi$
$138$	−1.15787	+	1.81634i	−0.0985643	+	0.154617i
$139$	2.28006			0.193392			0.0966960	−	0.995314i	$-0.469173\pi$
$139$	2.28006			0.193392			0.0966960	+	0.995314i	$0.469173\pi$
$140$	−3.30820	−	2.00198i	−0.279594	−	0.169198i
$141$	−3.25240			−0.273901
$142$	−6.15945	+	9.66229i	−0.516889	+	0.810842i
$143$	−9.03365	+	9.03365i	−0.755432	+	0.755432i
$144$	3.06123	+	2.57466i	0.255103	+	0.214555i
$145$	1.89692	+	0.373802i	0.157530	+	0.0310426i
$146$	0.973757	+	4.39829i	0.0805887	+	0.364005i
$147$	−4.42111	−	4.42111i	−0.364647	−	0.364647i
$148$	−4.68098	−	1.70677i	−0.384774	−	0.140296i
$149$		−	10.1170i		−	0.828820i	−0.910090	−	0.414410i	$-0.863988\pi$
$149$		−	10.1170i		−	0.828820i	0.910090	−	0.414410i	$-0.136012\pi$
$150$	6.96764	+	1.20501i	0.568905	+	0.0983885i
$151$		−	7.93691i		−	0.645897i	−0.946417	−	0.322948i	$-0.895326\pi$
$151$		−	7.93691i		−	0.645897i	0.946417	−	0.322948i	$-0.104674\pi$
$152$	0.454377	−	3.42859i	0.0368548	−	0.278095i
$153$	3.76156	+	3.76156i	0.304104	+	0.304104i
$154$	−6.12247	+	1.35548i	−0.493362	+	0.109228i
$155$	−17.1361	−	3.37680i	−1.37640	−	0.271231i
$156$	2.10308	+	4.51683i	0.168381	+	0.361635i
$157$	9.01395	−	9.01395i	0.719392	−	0.719392i	−0.249089	−	0.968481i	$-0.580131\pi$
$157$	9.01395	−	9.01395i	0.719392	−	0.719392i	0.968481	+	0.249089i	$0.0801311\pi$
$158$	18.9769	+	12.0972i	1.50972	+	0.962405i
$159$	−3.71400			−0.294540
$160$	−1.38152	−	12.5734i	−0.109219	−	0.994018i
$161$	−1.31695			−0.103790
$162$	1.19252	+	0.760198i	0.0936931	+	0.0597268i
$163$	13.0849	−	13.0849i	1.02489	−	1.02489i	0.0252033	−	0.999682i	$-0.491977\pi$
$163$	13.0849	−	13.0849i	1.02489	−	1.02489i	0.999682	−	0.0252033i	$-0.00802331\pi$
$164$	4.66261	+	10.0140i	0.364088	+	0.781958i
$165$	9.52311	−	6.38776i	0.741373	−	0.497286i
$166$	−15.5371	+	3.43982i	−1.20591	+	0.266982i
$167$	11.3334	+	11.3334i	0.877008	+	0.877008i	0.993224	−	0.116216i	$-0.0370765\pi$
$167$	11.3334	+	11.3334i	0.877008	+	0.877008i	−0.116216	+	0.993224i	$0.537076\pi$
$168$	−0.321293	+	2.42438i	−0.0247883	+	0.187045i
$169$		−	6.79383i		−	0.522603i
$170$	−0.392177	−	16.8176i	−0.0300786	−	1.28985i
$171$		−	1.22279i		−	0.0935088i
$172$	−16.4891	−	6.01224i	−1.25728	−	0.458429i
$173$	7.96772	+	7.96772i	0.605775	+	0.605775i	0.941839	−	0.336064i	$-0.109096\pi$
$173$	7.96772	+	7.96772i	0.605775	+	0.605775i	−0.336064	+	0.941839i	$0.609096\pi$
$174$	−0.264318	−	1.19388i	−0.0200379	−	0.0905076i
$175$	1.66866	+	3.98819i	0.126139	+	0.301479i
$176$	−15.6987	−	13.2034i	−1.18333	−	0.995244i
$177$	0.373802	−	0.373802i	0.0280967	−	0.0280967i
$178$	5.51325	−	8.64861i	0.413236	−	0.648241i
$179$	12.6475			0.945320			0.472660	−	0.881245i	$-0.343294\pi$
$179$	12.6475			0.945320			0.472660	+	0.881245i	$0.343294\pi$
$180$	−1.06823	−	4.34268i	−0.0796211	−	0.323684i
$181$	7.72928			0.574513			0.287256	−	0.957854i	$-0.407257\pi$
$181$	7.72928			0.574513			0.287256	+	0.957854i	$0.407257\pi$
$182$	−1.63747	+	2.56869i	−0.121378	+	0.190404i
$183$	3.52258	−	3.52258i	0.260396	−	0.260396i
$184$	−2.61962	−	3.42003i	−0.193121	−	0.252128i
$185$	3.10308	+	4.62620i	0.228143	+	0.340125i
$186$	2.38776	+	10.7851i	0.175079	+	0.790800i
$187$	−19.2901	−	19.2901i	−1.41063	−	1.41063i
$188$	2.22827	−	6.11123i	0.162513	−	0.445707i
$189$			0.864641i			0.0628934i
$190$	−2.66975	+	2.79723i	−0.193684	+	0.202933i
$191$			7.04516i			0.509770i	0.966971	+	0.254885i	$0.0820376\pi$
$191$			7.04516i			0.509770i	−0.966971	+	0.254885i	$0.917962\pi$
$192$	−6.93506	+	3.98810i	−0.500495	+	0.287816i
$193$	−11.5048	−	11.5048i	−0.828133	−	0.828133i	0.159125	−	0.987258i	$-0.449133\pi$
$193$	−11.5048	−	11.5048i	−0.828133	−	0.828133i	−0.987258	+	0.159125i	$0.949133\pi$
$194$	−1.55013	+	0.343190i	−0.111293	+	0.0246396i
$195$	1.07700	−	5.46543i	0.0771259	−	0.391387i
$196$	11.3362	−	5.27827i	0.809730	−	0.377019i
$197$	7.87859	−	7.87859i	0.561327	−	0.561327i	−0.368358	−	0.929684i	$-0.620080\pi$
$197$	7.87859	−	7.87859i	0.561327	−	0.561327i	0.929684	+	0.368358i	$0.120080\pi$
$198$	−6.11549	−	3.89846i	−0.434609	−	0.277051i
$199$	11.4792			0.813741			0.406870	−	0.913486i	$-0.366620\pi$
$199$	11.4792			0.813741			0.406870	+	0.913486i	$0.366620\pi$
$200$	−7.03784	+	12.2666i	−0.497650	+	0.867378i
$201$	8.77551			0.618977
$202$	12.0648	+	7.69095i	0.848873	+	0.541133i
$203$	0.528636	−	0.528636i	0.0371030	−	0.0371030i
$204$	−9.64504	+	4.49084i	−0.675288	+	0.314422i
$205$	2.38776	−	12.1170i	0.166768	−	0.846291i
$206$	7.46460	−	1.65262i	0.520083	−	0.115143i
$207$	−1.07700	−	1.07700i	−0.0748570	−	0.0748570i
$208$	−9.92794	+	0.857132i	−0.688379	+	0.0594314i
$209$			6.27072i			0.433755i
$210$	1.88780	−	1.97794i	0.130270	−	0.136491i
$211$			5.49134i			0.378039i	0.981973	+	0.189020i	$0.0605310\pi$
$211$			5.49134i			0.378039i	−0.981973	+	0.189020i	$0.939469\pi$
$212$	2.54452	−	6.97859i	0.174759	−	0.479292i
$213$	−5.72928	−	5.72928i	−0.392564	−	0.392564i
$214$	2.38255	+	10.7616i	0.162868	+	0.735645i
$215$	10.9309	+	16.2961i	0.745478	+	1.11139i
$216$	−2.24542	+	1.71991i	−0.152781	+	0.117025i
$217$	−4.77551	+	4.77551i	−0.324183	+	0.324183i
$218$	5.56233	−	8.72559i	0.376728	−	0.590972i
$219$	−3.18537			−0.215247
$220$	5.47811	+	22.2702i	0.369334	+	1.50146i
$221$	−13.2524			−0.891453
$222$	1.89382	−	2.97082i	0.127105	−	0.199389i
$223$	−10.8678	+	10.8678i	−0.727764	+	0.727764i	−0.970174	−	0.242410i	$-0.922062\pi$
$223$	−10.8678	+	10.8678i	−0.727764	+	0.727764i	0.242410	+	0.970174i	$0.422062\pi$
$224$	−4.33526	−	2.26469i	−0.289662	−	0.151316i
$225$	−1.89692	+	4.62620i	−0.126461	+	0.308413i
$226$	0.220121	+	0.994247i	0.0146422	+	0.0661363i
$227$	4.98244	+	4.98244i	0.330696	+	0.330696i	0.852851	−	0.522155i	$-0.174872\pi$
$227$	4.98244	+	4.98244i	0.330696	+	0.330696i	−0.522155	+	0.852851i	$0.674872\pi$
$228$	2.29761	+	0.837751i	0.152163	+	0.0554814i
$229$			25.7572i			1.70208i	0.525098	+	0.851041i	$0.324028\pi$
$229$			25.7572i			1.70208i	−0.525098	+	0.851041i	$0.675972\pi$
$230$	0.112288	+	4.81520i	0.00740403	+	0.317505i
$231$		−	4.43407i		−	0.291740i
$232$	2.42438	+	0.321293i	0.159168	+	0.0210939i
$233$	−0.715328	−	0.715328i	−0.0468627	−	0.0468627i	0.683287	−	0.730150i	$-0.260550\pi$
$233$	−0.715328	−	0.715328i	−0.0468627	−	0.0468627i	−0.730150	+	0.683287i	$0.760550\pi$
$234$	−3.43982	+	0.761557i	−0.224868	+	0.0497846i
$235$	−6.03971	+	4.05121i	−0.393987	+	0.264272i
$236$	0.446274	+	0.958469i	0.0290499	+	0.0623910i
$237$	−11.2524	+	11.2524i	−0.730922	+	0.730922i
$238$	−5.48509	−	3.49659i	−0.355545	−	0.226650i
$239$	−26.9354			−1.74231			−0.871154	−	0.491009i	$-0.836628\pi$
$239$	−26.9354			−1.74231			−0.871154	+	0.491009i	$0.836628\pi$
$240$	8.89173	+	0.968044i	0.573959	+	0.0624870i
$241$	14.0925			0.907775			0.453887	−	0.891059i	$-0.350037\pi$
$241$	14.0925			0.907775			0.453887	+	0.891059i	$0.350037\pi$
$242$	18.2439	+	11.6300i	1.17276	+	0.747603i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	4.20553	+	9.03228i	0.269231	+	0.578232i
$245$	−13.7170	−	2.70304i	−0.876346	−	0.172691i
$246$	−7.62620	+	1.68840i	−0.486229	+	0.107648i
$247$	2.15401	+	2.15401i	0.137056	+	0.137056i
$248$	−21.9010	−	2.90245i	−1.39071	−	0.184306i
$249$		−	11.2524i		−	0.713092i
$250$	14.4399	−	6.44125i	0.913259	−	0.407380i
$251$		−	17.2471i		−	1.08863i	−0.838882	−	0.544314i	$-0.816790\pi$
$251$		−	17.2471i		−	1.08863i	0.838882	−	0.544314i	$-0.183210\pi$
$252$	−1.62465	−	0.592379i	−0.102344	−	0.0373164i
$253$	5.52311	+	5.52311i	0.347235	+	0.347235i
$254$	−3.23853	−	14.6279i	−0.203203	−	0.917834i
$255$	11.6707	+	2.29979i	0.730844	+	0.144019i
$256$	−2.74229	−	15.7632i	−0.171393	−	0.985203i
$257$	−15.0140	+	15.0140i	−0.936545	+	0.936545i	−0.998103	−	0.0615588i	$-0.980393\pi$
$257$	−15.0140	+	15.0140i	−0.936545	+	0.936545i	0.0615588	+	0.998103i	$0.480393\pi$
$258$	6.67112	−	10.4650i	0.415326	−	0.651520i
$259$	2.15401			0.133844
$260$	9.53163	+	5.76814i	0.591127	+	0.357725i
$261$	0.864641			0.0535199
$262$	10.6400	−	16.6909i	0.657341	−	1.03117i
$263$	−6.73386	+	6.73386i	−0.415228	+	0.415228i	−0.883555	−	0.468327i	$-0.844857\pi$
$263$	−6.73386	+	6.73386i	−0.415228	+	0.415228i	0.468327	+	0.883555i	$0.344857\pi$
$264$	11.5150	−	8.82008i	0.708699	−	0.542838i
$265$	−6.89692	+	4.62620i	−0.423674	+	0.284185i
$266$	0.323204	+	1.45986i	0.0198169	+	0.0895096i
$267$	5.12822	+	5.12822i	0.313842	+	0.313842i
$268$	−6.01224	+	16.4891i	−0.367256	+	1.00723i
$269$		−	25.7047i		−	1.56724i	−0.621238	−	0.783622i	$-0.713370\pi$
$269$		−	25.7047i		−	1.56724i	0.621238	−	0.783622i	$-0.286630\pi$
$270$	3.16142	−	0.0737224i	0.192398	−	0.00448660i
$271$			0.931222i			0.0565677i	0.999600	+	0.0282839i	$0.00900423\pi$
$271$			0.931222i			0.0565677i	−0.999600	+	0.0282839i	$0.990996\pi$
$272$	−1.83029	−	21.1997i	−0.110977	−	1.28542i
$273$	−1.52311	−	1.52311i	−0.0921831	−	0.0921831i
$274$	−13.6963	+	3.03228i	−0.827421	+	0.183186i
$275$	9.72780	−	23.7242i	0.586608	−	1.43062i
$276$	2.76156	−	1.28581i	0.166226	−	0.0773968i
$277$	−22.0602	+	22.0602i	−1.32547	+	1.32547i	−0.416190	+	0.909277i	$0.636635\pi$
$277$	−22.0602	+	22.0602i	−1.32547	+	1.32547i	−0.909277	+	0.416190i	$0.863365\pi$
$278$	−2.71901	−	1.73330i	−0.163075	−	0.103956i
$279$	−7.81086			−0.467624
$280$	2.42318	+	4.90228i	0.144813	+	0.292967i
$281$	8.56934			0.511204			0.255602	−	0.966782i	$-0.417726\pi$
$281$	8.56934			0.511204			0.255602	+	0.966782i	$0.417726\pi$
$282$	3.87854	+	2.47246i	0.230964	+	0.147233i
$283$	11.5705	−	11.5705i	0.687796	−	0.687796i	−0.273949	−	0.961744i	$-0.588330\pi$
$283$	11.5705	−	11.5705i	0.687796	−	0.687796i	0.961744	+	0.273949i	$0.0883299\pi$
$284$	14.6905	−	6.84006i	0.871721	−	0.405883i
$285$	−1.52311	−	2.27072i	−0.0902215	−	0.134506i
$286$	17.6402	−	3.90543i	1.04308	−	0.230933i
$287$	−3.37680	−	3.37680i	−0.199326	−	0.199326i
$288$	−1.69333	−	5.39747i	−0.0997803	−	0.318049i
$289$		−	11.2986i		−	0.664625i
$290$	−1.97794	−	1.88780i	−0.116149	−	0.110855i
$291$		−	1.12265i		−	0.0658108i
$292$	2.18235	−	5.98529i	0.127712	−	0.350262i
$293$	12.8969	+	12.8969i	0.753446	+	0.753446i	0.975121	−	0.221675i	$-0.0711523\pi$
$293$	12.8969	+	12.8969i	0.753446	+	0.753446i	−0.221675	+	0.975121i	$0.571152\pi$
$294$	1.91134	+	8.63317i	0.111471	+	0.503497i
$295$	0.228540	−	1.15976i	0.0133061	−	0.0675240i
$296$	4.28467	+	5.59383i	0.249041	+	0.325135i
$297$	3.62620	−	3.62620i	0.210413	−	0.210413i
$298$	−7.69095	+	12.0648i	−0.445525	+	0.698892i
$299$	3.79441			0.219436
$300$	−7.39299	−	6.73377i	−0.426834	−	0.388775i
$301$	7.58767			0.437346
$302$	−6.03362	+	9.46491i	−0.347196	+	0.544644i
$303$	−7.15383	+	7.15383i	−0.410977	+	0.410977i
$304$	−3.14826	+	3.74324i	−0.180565	+	0.214689i
$305$	2.15368	−	10.9292i	0.123319	−	0.625804i
$306$	−1.62620	−	7.34525i	−0.0929636	−	0.419900i
$307$	1.60564	+	1.60564i	0.0916387	+	0.0916387i	0.751440	−	0.659801i	$-0.229360\pi$
$307$	1.60564	+	1.60564i	0.0916387	+	0.0916387i	−0.659801	+	0.751440i	$0.729360\pi$
$308$	8.33158	+	3.03785i	0.474736	+	0.173098i
$309$			5.40608i			0.307541i
$310$	17.8681	+	17.0537i	1.01484	+	0.968585i
$311$		−	19.4161i		−	1.10099i	−0.834839	−	0.550494i	$-0.814439\pi$
$311$		−	19.4161i		−	1.10099i	0.834839	−	0.550494i	$-0.185561\pi$
$312$	0.925715	−	6.98516i	0.0524083	−	0.395457i
$313$	17.7110	+	17.7110i	1.00108	+	1.00108i	0.999999	+	0.00108322i	$0.000344798\pi$
$313$	17.7110	+	17.7110i	1.00108	+	1.00108i	0.00108322	+	0.999999i	$0.499655\pi$
$314$	−17.6017	+	3.89692i	−0.993321	+	0.219916i
$315$	1.07700	+	1.60564i	0.0606823	+	0.0904676i
$316$	−13.4340	−	28.8524i	−0.755721	−	1.62307i
$317$	−7.78946	+	7.78946i	−0.437500	+	0.437500i	−0.891170	−	0.453670i	$-0.850115\pi$
$317$	−7.78946	+	7.78946i	−0.437500	+	0.437500i	0.453670	+	0.891170i	$0.350115\pi$
$318$	4.42902	+	2.82338i	0.248367	+	0.158327i
$319$	−4.43407			−0.248260
$320$	−7.91081	+	16.0443i	−0.442228	+	0.896903i
$321$	−7.79383			−0.435009
$322$	1.57048	+	1.00114i	0.0875196	+	0.0557914i
$323$	−4.59958	+	4.59958i	−0.255928	+	0.255928i
$324$	−0.844199	−	1.81310i	−0.0468999	−	0.100728i
$325$	−4.80779	−	11.4908i	−0.266688	−	0.637397i
$326$	−25.5510	+	5.65685i	−1.41514	+	0.313304i
$327$	5.17386	+	5.17386i	0.286115	+	0.286115i
$328$	2.05234	−	15.4863i	0.113322	−	0.855089i
$329$			2.81215i			0.155039i
$330$	−16.2124	+	0.378064i	−0.892466	+	0.0208118i
$331$			31.7005i			1.74242i	0.490912	+	0.871209i	$0.336664\pi$
$331$			31.7005i			1.74242i	−0.490912	+	0.871209i	$0.663336\pi$
$332$	21.1432	+	7.70919i	1.16038	+	0.423097i
$333$	1.76156	+	1.76156i	0.0965327	+	0.0965327i
$334$	−4.89968	−	22.1310i	−0.268098	−	1.21095i
$335$	16.2961	−	10.9309i	0.890353	−	0.597216i
$336$	2.22615	−	2.64687i	0.121447	−	0.144398i
$337$	18.9634	−	18.9634i	1.03300	−	1.03300i	0.0335632	−	0.999437i	$-0.489314\pi$
$337$	18.9634	−	18.9634i	1.03300	−	1.03300i	0.999437	−	0.0335632i	$-0.0106855\pi$
$338$	−5.16466	+	8.10177i	−0.280920	+	0.440678i
$339$	−0.720062			−0.0391084
$340$	−12.3170	+	20.3535i	−0.667985	+	1.10382i
$341$	40.0558			2.16914
$342$	−0.929560	+	1.45820i	−0.0502648	+	0.0788502i
$343$	−8.10243	+	8.10243i	−0.437490	+	0.437490i
$344$	15.0931	+	19.7047i	0.813765	+	1.06241i
$345$	−3.34153	−	0.658473i	−0.179902	−	0.0354510i
$346$	−3.44461	−	15.5587i	−0.185183	−	0.836441i
$347$	−7.71957	−	7.71957i	−0.414408	−	0.414408i	0.468863	−	0.883271i	$-0.344664\pi$
$347$	−7.71957	−	7.71957i	−0.414408	−	0.414408i	−0.883271	+	0.468863i	$0.844664\pi$
$348$	−0.592379	+	1.62465i	−0.0317549	+	0.0870906i
$349$		−	27.0741i		−	1.44925i	−0.689146	−	0.724623i	$-0.742014\pi$
$349$		−	27.0741i		−	1.44925i	0.689146	−	0.724623i	$-0.257986\pi$
$350$	1.04190	−	6.02450i	0.0556918	−	0.322023i
$351$		−	2.49122i		−	0.132971i
$352$	8.68375	+	27.6794i	0.462846	+	1.47532i
$353$	−9.96772	−	9.96772i	−0.530528	−	0.530528i	0.390201	−	0.920730i	$-0.372405\pi$
$353$	−9.96772	−	9.96772i	−0.530528	−	0.530528i	−0.920730	+	0.390201i	$0.872405\pi$
$354$	−0.729929	+	0.161602i	−0.0387953	+	0.00858906i
$355$	−17.7757	−	3.50285i	−0.943438	−	0.185912i
$356$	−13.1493	+	6.12247i	−0.696912	+	0.324490i
$357$	3.25240	−	3.25240i	0.172135	−	0.172135i
$358$	−15.0824	−	9.61461i	−0.797129	−	0.508148i
$359$	14.2334			0.751211			0.375606	−	0.926780i	$-0.377435\pi$
$359$	14.2334			0.751211			0.375606	+	0.926780i	$0.377435\pi$
$360$	−2.02741	+	5.99079i	−0.106854	+	0.315742i
$361$	−17.5048			−0.921305
$362$	−9.21731	−	5.87578i	−0.484451	−	0.308824i
$363$	−10.8178	+	10.8178i	−0.567785	+	0.567785i
$364$	3.90543	−	1.81841i	0.204700	−	0.0953107i
$365$	−5.91524	+	3.96772i	−0.309618	+	0.207680i
$366$	−6.87859	+	1.52288i	−0.359550	+	0.0796023i
$367$	2.89145	+	2.89145i	0.150933	+	0.150933i	0.778534	−	0.627602i	$-0.215963\pi$
$367$	2.89145	+	2.89145i	0.150933	+	0.150933i	−0.627602	+	0.778534i	$0.715963\pi$
$368$	0.524045	+	6.06988i	0.0273177	+	0.316414i
$369$		−	5.52311i		−	0.287522i
$370$	−0.183659	−	7.87578i	−0.00954795	−	0.409442i
$371$			3.21128i			0.166721i
$372$	5.35135	−	14.6766i	0.277454	−	0.760944i
$373$	−11.2847	−	11.2847i	−0.584298	−	0.584298i	0.351783	−	0.936081i	$-0.385575\pi$
$373$	−11.2847	−	11.2847i	−0.584298	−	0.584298i	−0.936081	+	0.351783i	$0.885575\pi$
$374$	8.33950	+	37.6681i	0.431225	+	1.94777i
$375$	2.23986	+	10.9537i	0.115666	+	0.565645i
$376$	−7.30299	+	5.59383i	−0.376623	+	0.288480i
$377$	−1.52311	+	1.52311i	−0.0784444	+	0.0784444i
$378$	0.657298	−	1.03110i	0.0338078	−	0.0530341i
$379$	15.4562			0.793932			0.396966	−	0.917833i	$-0.370063\pi$
$379$	15.4562			0.793932			0.396966	+	0.917833i	$0.370063\pi$
$380$	5.31017	−	1.30622i	0.272406	−	0.0670075i
$381$	10.5939			0.542743
$382$	5.35571	−	8.40148i	0.274022	−	0.429857i
$383$	12.5562	−	12.5562i	0.641593	−	0.641593i	−0.309354	−	0.950947i	$-0.600113\pi$
$383$	12.5562	−	12.5562i	0.641593	−	0.641593i	0.950947	+	0.309354i	$0.100113\pi$
$384$	11.3019	+	0.516138i	0.576749	+	0.0263390i
$385$	−5.52311	−	8.23407i	−0.281484	−	0.419647i
$386$	4.97376	+	22.4656i	0.253158	+	1.14347i
$387$	6.20522	+	6.20522i	0.315429	+	0.315429i
$388$	2.10945	+	0.769144i	0.107091	+	0.0390474i
$389$			5.16327i			0.261788i	0.991396	+	0.130894i	$0.0417848\pi$
$389$			5.16327i			0.261788i	−0.991396	+	0.130894i	$0.958215\pi$
$390$	−5.43915	+	5.69889i	−0.275422	+	0.288574i
$391$			8.10243i			0.409757i
$392$	−17.5312	−	2.32333i	−0.885458	−	0.117346i
$393$	9.89692	+	9.89692i	0.499233	+	0.499233i
$394$	−15.3847	+	3.40608i	−0.775068	+	0.171596i
$395$	−6.87964	+	34.9118i	−0.346152	+	1.75660i
$396$	4.32924	+	9.29797i	0.217552	+	0.467240i
$397$	−3.46293	+	3.46293i	−0.173800	+	0.173800i	−0.788646	−	0.614847i	$-0.789218\pi$
$397$	−3.46293	+	3.46293i	−0.173800	+	0.173800i	0.614847	+	0.788646i	$0.289218\pi$
$398$	−13.6892	−	8.72648i	−0.686177	−	0.437419i
$399$	−1.05727			−0.0529298
$400$	17.7178	−	9.27796i	0.885889	−	0.463898i
$401$	3.49521			0.174542			0.0872712	−	0.996185i	$-0.472185\pi$
$401$	3.49521			0.174542			0.0872712	+	0.996185i	$0.472185\pi$
$402$	−10.4650	−	6.67112i	−0.521945	−	0.332725i
$403$	13.7593	−	13.7593i	0.685399	−	0.685399i
$404$	−8.54079	−	18.3432i	−0.424920	−	0.912608i
$405$	−0.432320	+	2.19388i	−0.0214822	+	0.109015i
$406$	−1.03228	+	0.228540i	−0.0512310	+	0.0113423i
$407$	−9.03365	−	9.03365i	−0.447781	−	0.447781i
$408$	14.9158	+	1.97673i	0.738443	+	0.0978629i
$409$			14.8034i			0.731982i	0.930618	+	0.365991i	$0.119270\pi$
$409$			14.8034i			0.731982i	−0.930618	+	0.365991i	$0.880730\pi$
$410$	−12.0588	+	12.6346i	−0.595541	+	0.623979i
$411$		−	9.91923i		−	0.489279i
$412$	−10.1580	−	3.70379i	−0.500448	−	0.182473i
$413$	−0.323204	−	0.323204i	−0.0159039	−	0.0159039i
$414$	0.465611	+	2.10308i	0.0228835	+	0.103361i
$415$	−14.0161	−	20.8957i	−0.688023	−	1.02573i
$416$	12.4908	+	6.52505i	0.612414	+	0.319917i
$417$	1.61224	−	1.61224i	0.0789520	−	0.0789520i
$418$	4.76699	−	7.47795i	0.233161	−	0.365758i
$419$	−19.0701			−0.931634			−0.465817	−	0.884881i	$-0.654240\pi$
$419$	−19.0701			−0.931634			−0.465817	+	0.884881i	$0.654240\pi$
$420$	−3.75486	+	0.923635i	−0.183218	+	0.0450688i
$421$	−20.8034			−1.01390			−0.506948	−	0.861976i	$-0.669226\pi$
$421$	−20.8034			−1.01390			−0.506948	+	0.861976i	$0.669226\pi$
$422$	4.17450	−	6.54852i	0.203212	−	0.318777i
$423$	−2.29979	+	2.29979i	−0.111820	+	0.111820i
$424$	−8.33950	+	6.38776i	−0.405002	+	0.310217i
$425$	24.5371	−	10.2663i	1.19022	−	0.497991i
$426$	2.47689	+	11.1877i	0.120006	+	0.542044i
$427$	−3.04577	−	3.04577i	−0.147395	−	0.147395i
$428$	5.33968	−	14.6446i	0.258103	−	0.707872i
$429$			12.7755i			0.616807i
$430$	−0.646951	−	27.7431i	−0.0311988	−	1.33789i
$431$		−	15.3302i		−	0.738428i	−0.929344	−	0.369214i	$-0.879627\pi$
$431$		−	15.3302i		−	0.738428i	0.929344	−	0.369214i	$-0.120373\pi$
$432$	3.98518	−	0.344061i	0.191737	−	0.0165537i
$433$	16.2803	+	16.2803i	0.782381	+	0.782381i	0.980232	−	0.197851i	$-0.0633961\pi$
$433$	16.2803	+	16.2803i	0.782381	+	0.782381i	−0.197851	+	0.980232i	$0.563396\pi$
$434$	9.32521	−	2.06455i	0.447625	−	0.0991016i
$435$	1.60564	−	1.07700i	0.0769846	−	0.0516384i
$436$	−13.2663	+	6.17696i	−0.635343	+	0.295823i
$437$	1.31695	−	1.31695i	0.0629981	−	0.0629981i
$438$	3.79861	+	2.42151i	0.181505	+	0.115704i
$439$	24.6554			1.17674			0.588368	−	0.808593i	$-0.299770\pi$
$439$	24.6554			1.17674			0.588368	+	0.808593i	$0.299770\pi$
$440$	10.3970	−	30.7221i	0.495659	−	1.46462i
$441$	−6.25240			−0.297733
$442$	15.8037	+	10.0744i	0.751706	+	0.479192i
$443$	1.77116	−	1.77116i	0.0841501	−	0.0841501i	−0.663779	−	0.747929i	$-0.731048\pi$
$443$	1.77116	−	1.77116i	0.0841501	−	0.0841501i	0.747929	+	0.663779i	$0.231048\pi$
$444$	−4.51683	+	2.10308i	−0.214359	+	0.0998079i
$445$	15.9109	+	3.13536i	0.754248	+	0.148630i
$446$	21.2218	−	4.69839i	1.00488	−	0.222475i
$447$	−7.15383	−	7.15383i	−0.338364	−	0.338364i
$448$	3.44827	+	5.99634i	0.162916	+	0.283300i
$449$			33.1512i			1.56450i	0.622963	+	0.782251i	$0.285929\pi$
$449$			33.1512i			1.56450i	−0.622963	+	0.782251i	$0.714071\pi$
$450$	5.77893	−	4.07479i	0.272421	−	0.192088i
$451$			28.3237i			1.33371i
$452$	0.493326	−	1.35299i	0.0232041	−	0.0636394i
$453$	−5.61224	−	5.61224i	−0.263686	−	0.263686i
$454$	−2.15401	−	9.72928i	−0.101093	−	0.456618i
$455$	−4.72563	−	0.931222i	−0.221541	−	0.0436564i
$456$	−2.10308	−	2.74567i	−0.0984859	−	0.128578i
$457$	−7.50479	+	7.50479i	−0.351059	+	0.351059i	−0.860504	−	0.509444i	$-0.829851\pi$
$457$	−7.50479	+	7.50479i	−0.351059	+	0.351059i	0.509444	+	0.860504i	$0.329851\pi$
$458$	19.5806	−	30.7159i	0.914939	−	1.43526i
$459$	5.31965			0.248300
$460$	3.52660	−	5.82758i	0.164429	−	0.271712i
$461$	−27.0216			−1.25852			−0.629262	−	0.777193i	$-0.716643\pi$
$461$	−27.0216			−1.25852			−0.629262	+	0.777193i	$0.716643\pi$
$462$	−3.37077	+	5.28771i	−0.156822	+	0.246006i
$463$	27.7123	−	27.7123i	1.28790	−	1.28790i	0.351843	−	0.936059i	$-0.385555\pi$
$463$	27.7123	−	27.7123i	1.28790	−	1.28790i	0.936059	−	0.351843i	$-0.114445\pi$
$464$	−2.64687	−	2.22615i	−0.122878	−	0.103347i
$465$	−14.5048	+	9.72928i	−0.672644	+	0.451185i
$466$	0.309251	+	1.39683i	0.0143258	+	0.0647070i
$467$	−2.00823	−	2.00823i	−0.0929296	−	0.0929296i	0.659114	−	0.752043i	$-0.270932\pi$
$467$	−2.00823	−	2.00823i	−0.0929296	−	0.0929296i	−0.752043	+	0.659114i	$0.770932\pi$
$468$	4.68098	+	1.70677i	0.216378	+	0.0788956i
$469$		−	7.58767i		−	0.350366i
$470$	10.2822	−	0.239774i	0.474282	−	0.0110600i
$471$		−	12.7477i		−	0.587381i
$472$	0.196436	−	1.48225i	0.00904172	−	0.0682260i
$473$	−31.8217	−	31.8217i	−1.46317	−	1.46317i
$474$	21.9727	−	4.86464i	1.00924	−	0.223440i
$475$	−5.65685	−	2.31952i	−0.259554	−	0.106427i
$476$	3.88296	+	8.33950i	0.177975	+	0.382240i
$477$	−2.62620	+	2.62620i	−0.120245	+	0.120245i
$478$	32.1210	+	20.4763i	1.46918	+	0.936562i
$479$	−13.7593			−0.628678			−0.314339	−	0.949311i	$-0.601783\pi$
$479$	−13.7593			−0.628678			−0.314339	+	0.949311i	$0.601783\pi$
$480$	−9.86765	−	7.91388i	−0.450394	−	0.361218i
$481$	−6.20617			−0.282977
$482$	−16.8055	−	10.7131i	−0.765470	−	0.487966i
$483$	−0.931222	+	0.931222i	−0.0423721	+	0.0423721i
$484$	−12.9151	−	27.7379i	−0.587049	−	1.26081i
$485$	−1.39838	−	2.08476i	−0.0634972	−	0.0946641i
$486$	1.38078	−	0.305697i	0.0626334	−	0.0138667i
$487$	−24.3355	−	24.3355i	−1.10275	−	1.10275i	−0.994078	−	0.108671i	$-0.965340\pi$
$487$	−24.3355	−	24.3355i	−1.10275	−	1.10275i	−0.108671	−	0.994078i	$-0.534660\pi$
$488$	1.85115	−	13.9682i	0.0837975	−	0.632310i
$489$		−	18.5048i		−	0.836816i
$490$	14.3029	+	13.6510i	0.646140	+	0.616691i
$491$			28.8918i			1.30387i	0.758275	+	0.651935i	$0.226043\pi$
$491$			28.8918i			1.30387i	−0.758275	+	0.651935i	$0.773957\pi$
$492$	10.3779	+	3.78397i	0.467872	+	0.170595i
$493$	−3.25240	−	3.25240i	−0.146481	−	0.146481i
$494$	−0.931222	−	4.20617i	−0.0418977	−	0.189244i
$495$	2.21703	−	11.2507i	0.0996483	−	0.505681i
$496$	23.9109	+	20.1103i	1.07363	+	0.902979i
$497$	−4.95377	+	4.95377i	−0.222207	+	0.222207i
$498$	−8.55405	+	13.4187i	−0.383316	+	0.601306i
$499$	−12.5365			−0.561211			−0.280605	−	0.959823i	$-0.590535\pi$
$499$	−12.5365			−0.561211			−0.280605	+	0.959823i	$0.590535\pi$
$500$	−22.1164	−	3.29586i	−0.989078	−	0.147395i
$501$	16.0279			0.716074
$502$	−13.1112	+	20.5675i	−0.585182	+	0.917972i
$503$	−9.01392	+	9.01392i	−0.401911	+	0.401911i	−0.878906	−	0.476995i	$-0.841726\pi$
$503$	−9.01392	+	9.01392i	−0.401911	+	0.401911i	0.476995	+	0.878906i	$0.341726\pi$
$504$	1.48710	+	1.94148i	0.0662409	+	0.0864805i
$505$	−4.37380	+	22.1955i	−0.194632	+	0.987689i
$506$	−2.38776	−	10.7851i	−0.106149	−	0.479455i
$507$	−4.80397	−	4.80397i	−0.213352	−	0.213352i
$508$	−7.25806	+	19.9059i	−0.322025	+	0.883182i
$509$			22.5448i			0.999279i	0.866233	+	0.499640i	$0.166534\pi$
$509$			22.5448i			0.999279i	−0.866233	+	0.499640i	$0.833466\pi$
$510$	−12.1692	−	11.6145i	−0.538860	−	0.514301i
$511$			2.75420i			0.121839i
$512$	−8.71295	+	20.8826i	−0.385062	+	0.922891i
$513$	−0.864641	−	0.864641i	−0.0381748	−	0.0381748i
$514$	29.3180	−	6.49084i	1.29316	−	0.286299i
$515$	6.73386	+	10.0391i	0.296729	+	0.442376i
$516$	−15.9109	+	7.40828i	−0.700437	+	0.326131i
$517$	11.7938	−	11.7938i	0.518692	−	0.518692i
$518$	−2.56869	−	1.63747i	−0.112862	−	0.0719464i
$519$	11.2681			0.494613
$520$	−6.98172	−	14.1245i	−0.306169	−	0.619402i
$521$	−18.9046			−0.828226			−0.414113	−	0.910225i	$-0.635908\pi$
$521$	−18.9046			−0.828226			−0.414113	+	0.910225i	$0.635908\pi$
$522$	−1.03110	−	0.657298i	−0.0451300	−	0.0287692i
$523$	−21.8269	+	21.8269i	−0.954426	+	0.954426i	−0.999006	−	0.0445800i	$-0.985805\pi$
$523$	−21.8269	+	21.8269i	−0.954426	+	0.954426i	0.0445800	+	0.999006i	$0.485805\pi$
$524$	−25.3768	+	11.8157i	−1.10859	+	0.516172i
$525$	4.00000	+	1.64015i	0.174574	+	0.0715821i
$526$	13.1493	−	2.91118i	0.573337	−	0.126934i
$527$	29.3810	+	29.3810i	1.27986	+	1.27986i
$528$	−20.4368	+	1.76442i	−0.889400	+	0.0767866i
$529$			20.6801i			0.899136i
$530$	11.7415	−	0.273805i	0.510019	−	0.0118933i
$531$		−	0.528636i		−	0.0229408i
$532$	0.724353	−	1.98661i	0.0314047	−	0.0861303i
$533$	9.72928	+	9.72928i	0.421422	+	0.421422i
$534$	−2.21703	−	10.0140i	−0.0959404	−	0.433346i
$535$	−14.4732	+	9.70807i	−0.625730	+	0.419716i
$536$	19.7047	−	15.0931i	0.851114	−	0.651922i
$537$	8.94315	−	8.94315i	0.385925	−	0.385925i
$538$	−19.5407	+	30.6533i	−0.842457	+	1.32156i
$539$	32.0637			1.38108
$540$	−3.82609	−	2.31539i	−0.164649	−	0.0996384i
$541$	7.85838			0.337858			0.168929	−	0.985628i	$-0.445969\pi$
$541$	7.85838			0.337858			0.168929	+	0.985628i	$0.445969\pi$
$542$	0.707913	−	1.11050i	0.0304075	−	0.0477000i
$543$	5.46543	−	5.46543i	0.234544	−	0.234544i
$544$	−13.9333	+	26.6724i	−0.597387	+	1.14357i
$545$	16.0525	+	3.16327i	0.687613	+	0.135499i
$546$	0.658473	+	2.97421i	0.0281801	+	0.127284i
$547$	17.8105	+	17.8105i	0.761522	+	0.761522i	0.976597	−	0.215076i	$-0.0689998\pi$
$547$	17.8105	+	17.8105i	0.761522	+	0.761522i	−0.215076	+	0.976597i	$0.569000\pi$
$548$	18.6382	+	6.79582i	0.796183	+	0.290303i
$549$		−	4.98168i		−	0.212613i
$550$	−29.6356	+	20.8964i	−1.26367	+	0.891027i
$551$			1.05727i			0.0450413i
$552$	−4.27068	−	0.565976i	−0.181772	−	0.0240895i
$553$	9.72928	+	9.72928i	0.413731	+	0.413731i
$554$	43.0773	−	9.53707i	1.83018	−	0.405191i
$555$	5.46543	+	1.07700i	0.231994	+	0.0457163i
$556$	1.92482	+	4.13397i	0.0816307	+	0.175319i
$557$	23.3372	−	23.3372i	0.988827	−	0.988827i	−0.0111112	−	0.999938i	$-0.503537\pi$
$557$	23.3372	−	23.3372i	0.988827	−	0.988827i	0.999938	+	0.0111112i	$0.00353686\pi$
$558$	9.31460	+	5.93780i	0.394318	+	0.251367i
$559$	−21.8617			−0.924652
$560$	0.837010	−	7.68815i	0.0353701	−	0.324884i
$561$	−27.2803			−1.15178
$562$	−10.2191	−	6.51439i	−0.431067	−	0.274793i
$563$	−5.27400	+	5.27400i	−0.222273	+	0.222273i	−0.809455	−	0.587182i	$-0.800237\pi$
$563$	−5.27400	+	5.27400i	−0.222273	+	0.222273i	0.587182	+	0.809455i	$0.300237\pi$
$564$	−2.74567	−	5.89692i	−0.115614	−	0.248305i
$565$	−1.33716	+	0.896916i	−0.0562546	+	0.0377336i
$566$	−22.5939	+	5.00217i	−0.949693	+	0.210257i
$567$	0.611393	+	0.611393i	0.0256761	+	0.0256761i
$568$	−22.7185	−	3.01079i	−0.953247	−	0.126330i
$569$		−	28.5606i		−	1.19732i	−0.801002	−	0.598661i	$-0.795699\pi$
$569$		−	28.5606i		−	1.19732i	0.801002	−	0.598661i	$-0.204301\pi$
$570$	0.0901468	+	3.86574i	0.00377583	+	0.161918i
$571$		−	32.2837i		−	1.35103i	−0.737347	−	0.675515i	$-0.763922\pi$
$571$		−	32.2837i		−	1.35103i	0.737347	−	0.675515i	$-0.236078\pi$
$572$	−24.0051	−	8.75270i	−1.00370	−	0.365969i
$573$	4.98168	+	4.98168i	0.208113	+	0.208113i
$574$	1.45986	+	6.59392i	0.0609333	+	0.275225i
$575$	−7.02542	+	2.93945i	−0.292980	+	0.122583i
$576$	−2.08382	+	7.72384i	−0.0868257	+	0.321827i
$577$	27.0279	−	27.0279i	1.12519	−	1.12519i	0.134237	−	0.990949i	$-0.457142\pi$
$577$	27.0279	−	27.0279i	1.12519	−	1.12519i	0.990949	−	0.134237i	$-0.0428584\pi$
$578$	−8.58919	+	13.4738i	−0.357263	+	0.560437i
$579$	−16.2702			−0.676168
$580$	0.923635	+	3.75486i	0.0383518	+	0.155912i
$581$	−9.72928			−0.403639
$582$	−0.853435	+	1.33878i	−0.0353760	+	0.0554942i
$583$	13.4677	−	13.4677i	0.557776	−	0.557776i
$584$	−7.15249	+	5.47855i	−0.295972	+	0.226704i
$585$	−3.10308	−	4.62620i	−0.128297	−	0.191270i
$586$	−5.57560	−	25.1840i	−0.230326	−	1.04034i
$587$	17.1558	+	17.1558i	0.708096	+	0.708096i	0.966135	−	0.258039i	$-0.0830761\pi$
$587$	17.1558	+	17.1558i	0.708096	+	0.708096i	−0.258039	+	0.966135i	$0.583076\pi$
$588$	4.28362	−	11.7482i	0.176653	−	0.484488i
$589$		−	9.55102i		−	0.393543i
$590$	−1.15419	+	1.20930i	−0.0475171	+	0.0497862i
$591$		−	11.1420i		−	0.458321i
$592$	−0.857132	−	9.92794i	−0.0352279	−	0.408036i
$593$	−21.5833	−	21.5833i	−0.886320	−	0.886320i	0.107848	−	0.994167i	$-0.465604\pi$
$593$	−21.5833	−	21.5833i	−0.886320	−	0.886320i	−0.994167	+	0.107848i	$0.965604\pi$
$594$	−7.08093	+	1.56768i	−0.290534	+	0.0643227i
$595$	1.98849	−	10.0909i	0.0815203	−	0.413687i
$596$	18.3432	−	8.54079i	0.751366	−	0.349844i
$597$	8.11704	−	8.11704i	0.332208	−	0.332208i
$598$	−4.52490	−	2.88450i	−0.185037	−	0.117956i
$599$	−23.7636			−0.970955			−0.485478	−	0.874249i	$-0.661354\pi$
$599$	−23.7636			−0.970955			−0.485478	+	0.874249i	$0.661354\pi$
$600$	3.69727	+	13.6503i	0.150941	+	0.557270i
$601$	22.1695			0.904314			0.452157	−	0.891938i	$-0.350655\pi$
$601$	22.1695			0.904314			0.452157	+	0.891938i	$0.350655\pi$
$602$	−9.04843	−	5.76813i	−0.368786	−	0.235091i
$603$	6.20522	−	6.20522i	0.252696	−	0.252696i
$604$	14.3904	−	6.70033i	0.585537	−	0.272633i
$605$	−6.61391	+	33.5633i	−0.268894	+	1.36454i
$606$	13.9694	−	3.09275i	0.567468	−	0.125634i
$607$	9.35348	+	9.35348i	0.379646	+	0.379646i	0.870974	−	0.491328i	$-0.163489\pi$
$607$	9.35348	+	9.35348i	0.379646	+	0.379646i	−0.491328	+	0.870974i	$0.663489\pi$
$608$	6.59995	−	2.07058i	0.267663	−	0.0839731i
$609$		−	0.747604i		−	0.0302944i
$610$	−10.8767	+	11.3960i	−0.440383	+	0.461412i
$611$		−	8.10243i		−	0.327789i
$612$	−3.64457	+	9.99558i	−0.147323	+	0.404047i
$613$	−24.1247	−	24.1247i	−0.974389	−	0.974389i	0.0252913	−	0.999680i	$-0.491949\pi$
$613$	−24.1247	−	24.1247i	−0.974389	−	0.974389i	−0.999680	+	0.0252913i	$0.991949\pi$
$614$	−0.694151	−	3.13536i	−0.0280137	−	0.126533i
$615$	−6.87964	−	10.2564i	−0.277414	−	0.413579i
$616$	−7.62620	−	9.95634i	−0.307268	−	0.401152i
$617$	3.82611	−	3.82611i	0.154033	−	0.154033i	−0.625883	−	0.779917i	$-0.715261\pi$
$617$	3.82611	−	3.82611i	0.154033	−	0.154033i	0.779917	+	0.625883i	$0.215261\pi$
$618$	4.10969	−	6.44685i	0.165316	−	0.259330i
$619$	30.1297			1.21101			0.605507	−	0.795840i	$-0.292971\pi$
$619$	30.1297			1.21101			0.605507	+	0.795840i	$0.292971\pi$
$620$	−8.34379	−	33.9201i	−0.335095	−	1.36226i
$621$	−1.52311			−0.0611205
$622$	−14.7601	+	23.1541i	−0.591826	+	0.928395i
$623$	4.43407	−	4.43407i	0.177647	−	0.177647i
$624$	−6.41403	+	7.62620i	−0.256767	+	0.305292i
$625$	17.8034	+	17.5510i	0.712137	+	0.702041i
$626$	−7.65681	−	34.5845i	−0.306028	−	1.38227i
$627$	4.43407	+	4.43407i	0.177080	+	0.177080i
$628$	23.9528	+	8.73362i	0.955819	+	0.348509i
$629$		−	13.2524i		−	0.528408i
$630$	−0.0637434	−	2.73349i	−0.00253960	−	0.108905i
$631$		−	21.5701i		−	0.858694i	−0.903140	−	0.429347i	$-0.858744\pi$
$631$		−	21.5701i		−	0.858694i	0.903140	−	0.429347i	$-0.141256\pi$
$632$	−5.91324	+	44.6195i	−0.235216	+	1.77487i
$633$	3.88296	+	3.88296i	0.154334	+	0.154334i
$634$	15.2106	−	3.36754i	0.604090	−	0.133742i
$635$	19.6729	−	13.1959i	0.780697	−	0.523663i
$636$	−3.13536	−	6.73386i	−0.124325	−	0.267015i
$637$	11.0140	−	11.0140i	0.436389	−	0.436389i
$638$	5.28771	+	3.37077i	0.209342	+	0.133450i
$639$	−8.10243			−0.320527
$640$	21.6306	−	13.1193i	0.855025	−	0.518586i
$641$	48.3911			1.91133			0.955666	−	0.294452i	$-0.0951370\pi$
$641$	48.3911			1.91133			0.955666	+	0.294452i	$0.0951370\pi$
$642$	9.29429	+	5.92485i	0.366816	+	0.233835i
$643$	−23.3413	+	23.3413i	−0.920491	+	0.920491i	−0.997064	−	0.0765729i	$-0.975602\pi$
$643$	−23.3413	+	23.3413i	−0.920491	+	0.920491i	0.0765729	+	0.997064i	$0.475602\pi$
$644$	−1.11177	−	2.38776i	−0.0438097	−	0.0940907i
$645$	19.2524	+	3.79383i	0.758062	+	0.149382i
$646$	8.98168	−	1.98849i	0.353379	−	0.0782362i
$647$	−32.4465	−	32.4465i	−1.27560	−	1.27560i	−0.943103	−	0.332501i	$-0.892108\pi$
$647$	−32.4465	−	32.4465i	−1.27560	−	1.27560i	−0.332501	−	0.943103i	$-0.607892\pi$
$648$	−0.371591	+	2.80391i	−0.0145975	+	0.110148i
$649$			2.71096i			0.106414i
$650$	−3.00194	+	17.3579i	−0.117746	+	0.680833i
$651$			6.75359i			0.264694i
$652$	34.7704	+	12.6779i	1.36171	+	0.496506i
$653$	18.4725	+	18.4725i	0.722885	+	0.722885i	0.969192	−	0.246307i	$-0.0792170\pi$
$653$	18.4725	+	18.4725i	0.722885	+	0.722885i	−0.246307	+	0.969192i	$0.579217\pi$
$654$	−2.23677	−	10.1031i	−0.0874645	−	0.395062i
$655$	30.7063	+	6.05091i	1.19979	+	0.236429i
$656$	−14.2201	+	16.9075i	−0.555202	+	0.660128i
$657$	−2.25240	+	2.25240i	−0.0878743	+	0.0878743i
$658$	2.13779	−	3.35355i	0.0833399	−	0.130735i
$659$	−47.5028			−1.85045			−0.925223	−	0.379423i	$-0.876122\pi$
$659$	−47.5028			−1.85045			−0.925223	+	0.379423i	$0.876122\pi$
$660$	19.6210	+	11.8738i	0.763748	+	0.462188i
$661$	−46.1204			−1.79387			−0.896937	−	0.442158i	$-0.854213\pi$
$661$	−46.1204			−1.79387			−0.896937	+	0.442158i	$0.854213\pi$
$662$	24.0987	−	37.8035i	0.936621	−	1.46927i
$663$	−9.37086	+	9.37086i	−0.363934	+	0.363934i
$664$	−19.3531	−	25.2663i	−0.751046	−	0.980525i
$665$	−1.96336	+	1.31695i	−0.0761357	+	0.0510690i
$666$	−0.761557	−	3.43982i	−0.0295097	−	0.133290i
$667$	0.931222	+	0.931222i	0.0360571	+	0.0360571i
$668$	−10.9810	+	30.1163i	−0.424867	+	1.16524i
$669$			15.3694i			0.594217i
$670$	−27.7431	+	0.646951i	−1.07181	+	0.0249939i
$671$			25.5471i			0.986236i
$672$	−4.66687	+	1.46412i	−0.180028	+	0.0564797i
$673$	3.60599	+	3.60599i	0.139001	+	0.139001i	0.773183	−	0.634183i	$-0.218663\pi$
$673$	3.60599	+	3.60599i	0.139001	+	0.139001i	−0.634183	+	0.773183i	$0.718663\pi$
$674$	−37.0300	+	8.19825i	−1.42634	+	0.315785i
$675$	1.92989	+	4.61254i	0.0742816	+	0.177537i
$676$	12.3179	−	5.73535i	0.473765	−	0.220590i
$677$	−8.26635	+	8.26635i	−0.317702	+	0.317702i	−0.847884	−	0.530182i	$-0.822124\pi$
$677$	−8.26635	+	8.26635i	−0.317702	+	0.317702i	0.530182	+	0.847884i	$0.322124\pi$
$678$	0.858688	+	0.547390i	0.0329777	+	0.0210224i
$679$	−0.970688			−0.0372516
$680$	30.1609	−	14.9085i	1.15662	−	0.571714i
$681$	7.04623			0.270012
$682$	−47.7673	−	30.4503i	−1.82910	−	1.16600i
$683$	−8.43079	+	8.43079i	−0.322595	+	0.322595i	−0.849762	−	0.527167i	$-0.823254\pi$
$683$	−8.43079	+	8.43079i	−0.322595	+	0.322595i	0.527167	+	0.849762i	$0.323254\pi$
$684$	2.21703	−	1.03228i	0.0847704	−	0.0394700i
$685$	−12.3555	−	18.4200i	−0.472079	−	0.703793i
$686$	15.8217	−	3.50285i	0.604077	−	0.133739i
$687$	18.2131	+	18.2131i	0.694872	+	0.694872i
$688$	−3.01932	−	34.9719i	−0.115110	−	1.33329i
$689$		−	9.25240i		−	0.352488i
$690$	3.48426	+	3.32546i	0.132644	+	0.126598i
$691$		−	21.9182i		−	0.833809i	−0.908950	−	0.416905i	$-0.863115\pi$
$691$		−	21.9182i		−	0.833809i	0.908950	−	0.416905i	$-0.136885\pi$
$692$	−7.71993	+	21.1726i	−0.293468	+	0.804862i
$693$	−3.13536	−	3.13536i	−0.119102	−	0.119102i
$694$	3.33733	+	15.0741i	0.126683	+	0.572206i
$695$	0.985716	−	5.00217i	0.0373903	−	0.189743i
$696$	1.94148	−	1.48710i	0.0735917	−	0.0563686i
$697$	−20.7755	+	20.7755i	−0.786929	+	0.786929i
$698$	−20.5817	+	32.2864i	−0.779029	+	1.22206i
$699$	−1.01163			−0.0382633
$700$	−5.82230	+	6.39228i	−0.220062	+	0.241605i
$701$	−21.8184			−0.824070			−0.412035	−	0.911168i	$-0.635182\pi$
$701$	−21.8184			−0.824070			−0.412035	+	0.911168i	$0.635182\pi$
$702$	−1.89382	+	2.97082i	−0.0714776	+	0.112126i
$703$	−2.15401	+	2.15401i	−0.0812400	+	0.0812400i
$704$	10.6863	−	39.6095i	0.402754	−	1.49284i
$705$	−1.40608	+	7.13536i	−0.0529559	+	0.268733i
$706$	4.30925	+	19.4641i	0.162181	+	0.732542i
$707$	6.18549	+	6.18549i	0.232629	+	0.232629i
$708$	0.993303	+	0.362177i	0.0373306	+	0.0136114i
$709$			31.7938i			1.19404i	0.802225	+	0.597021i	$0.203649\pi$
$709$			31.7938i			1.19404i	−0.802225	+	0.597021i	$0.796351\pi$
$710$	18.5350	+	17.6903i	0.695607	+	0.663904i
$711$			15.9133i			0.596795i
$712$	20.3351	+	2.69493i	0.762089	+	0.100997i
$713$	−8.41233	−	8.41233i	−0.315044	−	0.315044i
$714$	−6.35101	+	1.40608i	−0.237680	+	0.0526211i
$715$	15.9133	+	23.7242i	0.595123	+	0.887233i
$716$	10.6770	+	22.9312i	0.399019	+	0.856979i
$717$	−19.0462	+	19.0462i	−0.711294	+	0.711294i
$718$	−16.9736	−	10.8202i	−0.633450	−	0.403807i
$719$	52.0874			1.94253			0.971265	−	0.237999i	$-0.0764916\pi$
$719$	52.0874			1.94253			0.971265	+	0.237999i	$0.0764916\pi$
$720$	6.97191	−	5.60289i	0.259828	−	0.208808i
$721$	4.67432			0.174081
$722$	20.8748	+	13.3071i	0.776879	+	0.495239i
$723$	9.96487	−	9.96487i	0.370598	−	0.370598i
$724$	6.52505	+	14.0140i	0.242502	+	0.520824i
$725$	1.64015	−	4.00000i	0.0609137	−	0.148556i
$726$	21.1240	−	4.67674i	0.783986	−	0.173570i
$727$	−8.13069	−	8.13069i	−0.301551	−	0.301551i	0.540070	−	0.841620i	$-0.318398\pi$
$727$	−8.13069	−	8.13069i	−0.301551	−	0.301551i	−0.841620	+	0.540070i	$0.818398\pi$
$728$	−6.03965	−	0.800411i	−0.223844	−	0.0296652i
$729$			1.00000i			0.0370370i
$730$	10.0703	−	0.234833i	0.372718	−	0.00869156i
$731$		−	46.6826i		−	1.72662i
$732$	9.36054	+	3.41303i	0.345976	+	0.126149i
$733$	−29.9956	−	29.9956i	−1.10791	−	1.10791i	−0.993424	−	0.114489i	$-0.963477\pi$
$733$	−29.9956	−	29.9956i	−1.10791	−	1.10791i	−0.114489	−	0.993424i	$-0.536523\pi$
$734$	−1.25003	−	5.64618i	−0.0461396	−	0.208404i
$735$	−11.6107	+	7.78804i	−0.428268	+	0.287266i
$736$	3.98937	−	7.63682i	0.147050	−	0.281497i
$737$	−31.8217	+	31.8217i	−1.17217	+	1.17217i
$738$	−4.19866	+	6.58641i	−0.154555	+	0.242449i
$739$	−39.4719			−1.45200			−0.725999	−	0.687696i	$-0.758622\pi$
$739$	−39.4719			−1.45200			−0.725999	+	0.687696i	$0.758622\pi$
$740$	−5.76814	+	9.53163i	−0.212041	+	0.350390i
$741$	3.04623			0.111906
$742$	2.44121	−	3.82951i	0.0896196	−	0.140586i
$743$	12.2252	−	12.2252i	0.448499	−	0.448499i	−0.446356	−	0.894855i	$-0.647279\pi$
$743$	12.2252	−	12.2252i	0.448499	−	0.448499i	0.894855	+	0.446356i	$0.147279\pi$
$744$	−17.5387	+	13.4340i	−0.642999	+	0.492514i
$745$	−22.1955	−	4.37380i	−0.813182	−	0.160244i
$746$	4.87859	+	22.0358i	0.178618	+	0.806786i
$747$	−7.95665	−	7.95665i	−0.291118	−	0.291118i
$748$	18.6902	−	51.2595i	0.683380	−	1.87423i
$749$			6.73887i			0.246233i
$750$	5.65589	−	14.7652i	0.206524	−	0.539149i
$751$			28.9069i			1.05483i	0.849609	+	0.527413i	$0.176838\pi$
$751$			28.9069i			1.05483i	−0.849609	+	0.527413i	$0.823162\pi$
$752$	12.9614	−	1.11902i	0.472652	−	0.0408066i
$753$	−12.1955	−	12.1955i	−0.444430	−	0.444430i
$754$	2.97421	−	0.658473i	0.108314	−	0.0239802i
$755$	−17.4126	−	3.43129i	−0.633710	−	0.124877i
$756$	−1.56768	+	0.729929i	−0.0570160	+	0.0265473i
$757$	−16.2018	+	16.2018i	−0.588864	+	0.588864i	−0.937324	−	0.348459i	$-0.886705\pi$
$757$	−16.2018	+	16.2018i	−0.588864	+	0.588864i	0.348459	+	0.937324i	$0.386705\pi$
$758$	−18.4318	−	11.7498i	−0.669474	−	0.426771i
$759$	7.81086			0.283516
$760$	−7.32546	−	2.47909i	−0.265722	−	0.0899262i
$761$	−6.64641			−0.240932			−0.120466	−	0.992717i	$-0.538439\pi$
$761$	−6.64641			−0.240932			−0.120466	+	0.992717i	$0.538439\pi$
$762$	−12.6334	−	8.05348i	−0.457661	−	0.291747i
$763$	4.47353	−	4.47353i	0.161953	−	0.161953i
$764$	−12.7736	+	5.94751i	−0.462131	+	0.215173i
$765$	9.87859	−	6.62620i	0.357161	−	0.239571i
$766$	−24.5187	+	5.42831i	−0.885898	+	0.196133i
$767$	0.931222	+	0.931222i	0.0336245	+	0.0336245i
$768$	−13.0854	−	9.20720i	−0.472178	−	0.332236i
$769$		−	29.3449i		−	1.05820i	−0.848559	−	0.529101i	$-0.822529\pi$
$769$		−	29.3449i		−	1.05820i	0.848559	−	0.529101i	$-0.177471\pi$
$770$	0.326890	+	14.0179i	0.0117803	+	0.505172i
$771$			21.2329i			0.764686i
$772$	11.1470	−	30.5717i	0.401189	−	1.10030i
$773$	37.5833	+	37.5833i	1.35178	+	1.35178i	0.883674	+	0.468104i	$0.155063\pi$
$773$	37.5833	+	37.5833i	1.35178	+	1.35178i	0.468104	+	0.883674i	$0.344937\pi$
$774$	−2.68264	−	12.1170i	−0.0964257	−	0.435538i
$775$	−14.8166	+	36.1346i	−0.532226	+	1.29799i
$776$	−1.93086	−	2.52082i	−0.0693137	−	0.0904921i
$777$	1.52311	−	1.52311i	0.0546414	−	0.0546414i
$778$	3.92510	−	6.15729i	0.140722	−	0.220749i
$779$	6.75359			0.241973
$780$	10.8186	−	2.66119i	0.387367	−	0.0952860i
$781$	41.5510			1.48681
$782$	6.15945	−	9.66229i	0.220261	−	0.345523i
$783$	0.611393	−	0.611393i	0.0218494	−	0.0218494i
$784$	19.1400	+	16.0978i	0.683573	+	0.574920i
$785$	−15.8786	−	23.6724i	−0.566731	−	0.844905i
$786$	−4.27864	−	19.3259i	−0.152614	−	0.689331i
$787$	−7.59353	−	7.59353i	−0.270680	−	0.270680i	0.558694	−	0.829374i	$-0.311303\pi$
$787$	−7.59353	−	7.59353i	−0.270680	−	0.270680i	−0.829374	+	0.558694i	$0.811303\pi$
$788$	20.9358	+	7.63357i	0.745806	+	0.271935i
$789$			9.52311i			0.339032i
$790$	34.7440	−	36.4031i	1.23614	−	1.29516i
$791$			0.622595i			0.0221369i
$792$	1.90560	−	14.3791i	0.0677126	−	0.510938i
$793$	8.77551	+	8.77551i	0.311628	+	0.311628i
$794$	6.76212	−	1.49710i	0.239979	−	0.0531300i
$795$	−1.60564	+	8.14807i	−0.0569462	+	0.288982i
$796$	9.69075	+	20.8130i	0.343479	+	0.737696i
$797$	27.4908	−	27.4908i	0.973775	−	0.973775i	−0.0258893	−	0.999665i	$-0.508242\pi$
$797$	27.4908	−	27.4908i	0.973775	−	0.973775i	0.999665	+	0.0258893i	$0.00824175\pi$
$798$	1.26082	+	0.803735i	0.0446324	+	0.0284519i
$799$	17.3016			0.612086
$800$	−28.1818	−	2.40487i	−0.996379	−	0.0850251i
$801$	7.25240			0.256251
$802$	−4.16810	−	2.65705i	−0.147181	−	0.0938237i
$803$	11.5508	−	11.5508i	0.407618	−	0.407618i
$804$	7.40828	+	15.9109i	0.261270	+	0.561133i
$805$	−0.569343	+	2.88922i	−0.0200667	+	0.101832i
$806$	−26.8680	+	5.94842i	−0.946384	+	0.209524i
$807$	−18.1760	−	18.1760i	−0.639824	−	0.639824i
$808$	−3.75940	+	28.3673i	−0.132255	+	0.997957i
$809$			47.7205i			1.67776i	0.544313	+	0.838882i	$0.316791\pi$
$809$			47.7205i			1.67776i	−0.544313	+	0.838882i	$0.683209\pi$
$810$	2.18333	−	2.28759i	0.0767144	−	0.0803777i
$811$		−	37.3179i		−	1.31041i	−0.755451	−	0.655205i	$-0.772582\pi$
$811$		−	37.3179i		−	1.31041i	0.755451	−	0.655205i	$-0.227418\pi$
$812$	1.40474	+	0.512195i	0.0492968	+	0.0179745i
$813$	0.658473	+	0.658473i	0.0230937	+	0.0230937i
$814$	3.90543	+	17.6402i	0.136885	+	0.618287i
$815$	−23.0497	−	34.3634i	−0.807397	−	1.20370i
$816$	−16.2847	−	13.6963i	−0.570078	−	0.479465i
$817$	−7.58767	+	7.58767i	−0.265459	+	0.265459i
$818$	11.2535	−	17.6533i	0.393470	−	0.617235i
$819$	−2.15401			−0.0752672
$820$	23.9851	−	5.89995i	0.837597	−	0.206035i
$821$	−0.686380			−0.0239548			−0.0119774	−	0.999928i	$-0.503813\pi$
$821$	−0.686380			−0.0239548			−0.0119774	+	0.999928i	$0.503813\pi$
$822$	−7.54057	+	11.8289i	−0.263008	+	0.412579i
$823$	−27.2553	+	27.2553i	−0.950059	+	0.950059i	−0.998811	−	0.0487521i	$-0.984476\pi$
$823$	−27.2553	+	27.2553i	−0.950059	+	0.950059i	0.0487521	+	0.998811i	$0.484476\pi$
$824$	9.29797	+	12.1389i	0.323910	+	0.422879i
$825$	−9.89692	−	23.6541i	−0.344566	−	0.823530i
$826$	0.139728	+	0.631126i	0.00486175	+	0.0219597i
$827$	−31.4437	−	31.4437i	−1.09341	−	1.09341i	−0.995162	−	0.0982432i	$-0.968678\pi$
$827$	−31.4437	−	31.4437i	−1.09341	−	1.09341i	−0.0982432	−	0.995162i	$-0.531322\pi$
$828$	1.04351	−	2.86192i	0.0362645	−	0.0994587i
$829$			0.270718i			0.00940243i	0.999989	+	0.00470122i	$0.00149645\pi$
$829$			0.270718i			0.00940243i	−0.999989	+	0.00470122i	$0.998504\pi$
$830$	0.829553	+	35.5735i	0.0287942	+	1.23478i
$831$			31.1978i			1.08224i
$832$	−9.93522	−	17.2767i	−0.344442	−	0.598964i
$833$	23.5187	+	23.5187i	0.814876	+	0.814876i
$834$	−3.14826	+	0.697006i	−0.109015	+	0.0241354i
$835$	29.7639	−	19.9645i	1.03002	−	0.690900i
$836$	−11.3694	+	5.29373i	−0.393220	+	0.183088i
$837$	−5.52311	+	5.52311i	−0.190907	+	0.190907i
$838$	22.7414	+	14.4970i	0.785589	+	0.500792i
$839$	31.0214			1.07098			0.535489	−	0.844542i	$-0.320127\pi$
$839$	31.0214			1.07098			0.535489	+	0.844542i	$0.320127\pi$
$840$	5.17988	+	1.75298i	0.178723	+	0.0604837i
$841$	28.2524			0.974221
$842$	24.8085	+	15.8147i	0.854956	+	0.545011i
$843$	6.05944	−	6.05944i	0.208698	−	0.208698i
$844$	−9.95634	+	4.63578i	−0.342711	+	0.159570i
$845$	−14.9048	−	2.93711i	−0.512742	−	0.101040i
$846$	4.49084	−	0.994247i	0.154398	−	0.0341829i
$847$	9.35348	+	9.35348i	0.321389	+	0.321389i
$848$	14.8010	−	1.27785i	0.508267	−	0.0438814i
$849$		−	16.3632i		−	0.561583i
$850$	−37.0654	−	6.41021i	−1.27133	−	0.219869i
$851$			3.79441i			0.130071i
$852$	5.55110	−	15.2244i	0.190178	−	0.521580i
$853$	3.82611	+	3.82611i	0.131003	+	0.131003i	0.769568	−	0.638565i	$-0.220472\pi$
$853$	3.82611	+	3.82611i	0.131003	+	0.131003i	−0.638565	+	0.769568i	$0.720472\pi$
$854$	1.31675	+	5.94751i	0.0450581	+	0.203520i
$855$	−2.68264	−	0.528636i	−0.0917445	−	0.0180790i
$856$	−17.5004	+	13.4047i	−0.598152	+	0.458163i
$857$	20.7711	−	20.7711i	0.709529	−	0.709529i	−0.256907	−	0.966436i	$-0.582704\pi$
$857$	20.7711	−	20.7711i	0.709529	−	0.709529i	0.966436	+	0.256907i	$0.0827035\pi$
$858$	9.71191	−	15.2350i	0.331559	−	0.520115i
$859$	1.69693			0.0578985			0.0289492	−	0.999581i	$-0.490784\pi$
$859$	1.69693			0.0578985			0.0289492	+	0.999581i	$0.490784\pi$
$860$	−20.3187	+	33.5759i	−0.692862	+	1.14493i
$861$	−4.77551			−0.162749
$862$	−11.6540	+	18.2815i	−0.396935	+	0.622670i
$863$	5.92869	−	5.92869i	0.201815	−	0.201815i	−0.598962	−	0.800777i	$-0.704420\pi$
$863$	5.92869	−	5.92869i	0.201815	−	0.201815i	0.800777	+	0.598962i	$0.204420\pi$
$864$	−5.01395	−	2.61922i	−0.170578	−	0.0891077i
$865$	20.9248	−	14.0356i	0.711465	−	0.477225i
$866$	−7.03831	−	31.7908i	−0.239171	−	1.08030i
$867$	−7.98933	−	7.98933i	−0.271332	−	0.271332i
$868$	−12.6900	−	4.62699i	−0.430725	−	0.157050i
$869$		−	81.6068i		−	2.76832i
$870$	−2.73349	+	0.0637434i	−0.0926740	+	0.00216110i
$871$			21.8617i			0.740756i
$872$	20.5161	+	2.71891i	0.694762	+	0.0920740i
$873$	−0.793833	−	0.793833i	−0.0268672	−	0.0268672i
$874$	−2.57162	+	0.569343i	−0.0869865	+	0.0192583i
$875$	9.47100	−	1.93667i	0.320178	−	0.0654714i
$876$	−2.68909	−	5.77539i	−0.0908558	−	0.195132i
$877$	−10.0323	+	10.0323i	−0.338766	+	0.338766i	−0.855903	−	0.517137i	$-0.826998\pi$
$877$	−10.0323	+	10.0323i	−0.338766	+	0.338766i	0.517137	+	0.855903i	$0.326998\pi$
$878$	−29.4020	−	18.7430i	−0.992269	−	0.632544i
$879$	18.2390			0.615186
$880$	−35.7535	+	28.7329i	−1.20525	+	0.968585i
$881$	−29.8130			−1.00443			−0.502213	−	0.864744i	$-0.667481\pi$
$881$	−29.8130			−1.00443			−0.502213	+	0.864744i	$0.667481\pi$
$882$	7.45610	+	4.75306i	0.251060	+	0.160044i
$883$	−5.56557	+	5.56557i	−0.187296	+	0.187296i	−0.794526	−	0.607230i	$-0.792281\pi$
$883$	−5.56557	+	5.56557i	−0.187296	+	0.187296i	0.607230	+	0.794526i	$0.292281\pi$
$884$	−11.1877	−	24.0279i	−0.376282	−	0.808146i
$885$	−0.658473	−	0.981678i	−0.0221343	−	0.0329987i
$886$	−3.45856	+	0.765707i	−0.116193	+	0.0257244i
$887$	8.59630	+	8.59630i	0.288636	+	0.288636i	0.836541	−	0.547905i	$-0.184574\pi$
$887$	8.59630	+	8.59630i	0.288636	+	0.288636i	−0.547905	+	0.836541i	$0.684574\pi$
$888$	6.98516	+	0.925715i	0.234406	+	0.0310649i
$889$		−	9.15994i		−	0.307214i
$890$	−16.5905	−	15.8344i	−0.556115	−	0.530770i
$891$		−	5.12822i		−	0.171802i
$892$	−28.8791	−	10.5298i	−0.966943	−	0.352565i
$893$	−2.81215	−	2.81215i	−0.0941052	−	0.0941052i
$894$	3.09275	+	13.9694i	0.103437	+	0.467206i
$895$	5.46778	−	27.7471i	0.182768	−	0.927483i
$896$	0.446274	−	9.77211i	0.0149090	−	0.326463i
$897$	2.68305	−	2.68305i	0.0895845	−	0.0895845i
$898$	25.2015	−	39.5334i	0.840984	−	1.31925i
$899$	6.75359			0.225245
$900$	−9.98913	+	0.466135i	−0.332971	+	0.0155378i
$901$	19.7572			0.658207
$902$	21.5316	−	33.7766i	0.716925	−	1.12464i
$903$	5.36529	−	5.36529i	0.178546	−	0.178546i
$904$	−1.61684	+	1.23844i	−0.0537754	+	0.0411900i
$905$	3.34153	−	16.9571i	0.111076	−	0.563673i
$906$	2.42629	+	10.9591i	0.0806080	+	0.364092i
$907$	31.6263	+	31.6263i	1.05013	+	1.05013i	0.998675	+	0.0514592i	$0.0163872\pi$
$907$	31.6263	+	31.6263i	1.05013	+	1.05013i	0.0514592	+	0.998675i	$0.483613\pi$
$908$	−4.82748	+	13.2398i	−0.160206	+	0.439379i
$909$			10.1170i			0.335561i
$910$	4.92749	+	4.70291i	0.163345	+	0.155900i
$911$			42.2656i			1.40032i	0.713985	+	0.700161i	$0.246888\pi$
$911$			42.2656i			1.40032i	−0.713985	+	0.700161i	$0.753112\pi$
$912$	0.420714	+	4.87302i	0.0139312	+	0.161362i
$913$	40.8034	+	40.8034i	1.35040	+	1.35040i
$914$	14.6547	−	3.24448i	0.484735	−	0.107318i
$915$	−6.20522	−	9.25099i	−0.205138	−	0.305828i
$916$	−46.7003	+	21.7442i	−1.54302	+	0.718448i
$917$	8.55728	−	8.55728i	0.282586	−	0.282586i
$918$	−6.34377	−	4.04398i	−0.209376	−	0.133471i
$919$	−31.2829			−1.03193			−0.515964	−	0.856610i	$-0.672566\pi$
$919$	−31.2829			−1.03193			−0.515964	+	0.856610i	$0.672566\pi$
$920$	−8.63564	+	4.26858i	−0.284709	+	0.140731i
$921$	2.27072			0.0748227
$922$	32.2238	+	20.5418i	1.06123	+	0.676508i
$923$	14.2729	−	14.2729i	0.469798	−	0.469798i
$924$	8.03940	−	3.74324i	0.264477	−	0.123143i
$925$	11.4908	−	4.80779i	0.377816	−	0.158079i
$926$	−54.1143	+	11.9806i	−1.77831	+	0.393707i
$927$	3.82267	+	3.82267i	0.125553	+	0.125553i
$928$	1.46412	+	4.66687i	0.0480621	+	0.153198i
$929$		−	22.1050i		−	0.725241i	−0.931937	−	0.362620i	$-0.881882\pi$
$929$		−	22.1050i		−	0.725241i	0.931937	−	0.362620i	$-0.118118\pi$
$930$	24.6934	−	0.575835i	0.809729	−	0.0188824i
$931$		−	7.64535i		−	0.250566i
$932$	0.693082	−	1.90084i	0.0227026	−	0.0622641i
$933$	−13.7293	−	13.7293i	−0.449477	−	0.449477i
$934$	0.868197	+	3.92150i	0.0284083	+	0.128315i
$935$	−50.6596	+	33.9806i	−1.65675	+	1.11128i
$936$	−4.28467	−	5.59383i	−0.140049	−	0.182840i
$937$	−15.2986	+	15.2986i	−0.499784	+	0.499784i	−0.911371	−	0.411586i	$-0.864975\pi$
$937$	−15.2986	+	15.2986i	−0.499784	+	0.499784i	0.411586	+	0.911371i	$0.364975\pi$
$938$	−5.76813	+	9.04843i	−0.188336	+	0.295442i
$939$	25.0471			0.817381
$940$	−12.4440	−	7.53056i	−0.405877	−	0.245620i
$941$	25.5264			0.832138			0.416069	−	0.909333i	$-0.363407\pi$
$941$	25.5264			0.832138			0.416069	+	0.909333i	$0.363407\pi$
$942$	−9.69074	+	15.2018i	−0.315741	+	0.495302i
$943$	5.94842	−	5.94842i	0.193707	−	0.193707i
$944$	−1.36106	+	1.61828i	−0.0442986	+	0.0526704i
$945$	1.89692	+	0.373802i	0.0617067	+	0.0121598i
$946$	13.7572	+	62.1388i	0.447285	+	2.02031i
$947$	11.9881	+	11.9881i	0.389562	+	0.389562i	0.874531	−	0.484969i	$-0.161169\pi$
$947$	11.9881	+	11.9881i	0.389562	+	0.389562i	−0.484969	+	0.874531i	$0.661169\pi$
$948$	−29.9010	−	10.9024i	−0.971138	−	0.354095i
$949$		−	7.93545i		−	0.257596i
$950$	4.98260	+	7.06640i	0.161657	+	0.229264i
$951$			11.0160i			0.357217i
$952$	1.70916	−	12.8968i	0.0553943	−	0.417988i
$953$	5.99563	+	5.99563i	0.194218	+	0.194218i	0.797516	−	0.603298i	$-0.206147\pi$
$953$	5.99563	+	5.99563i	0.194218	+	0.194218i	−0.603298	+	0.797516i	$0.706147\pi$
$954$	5.12822	−	1.13536i	0.166032	−	0.0367586i
$955$	15.4562	+	3.04577i	0.500151	+	0.0985586i
$956$	−22.7389	−	48.8366i	−0.735427	−	1.57949i
$957$	−3.13536	+	3.13536i	−0.101352	+	0.101352i
$958$	16.4082	+	10.4598i	0.530125	+	0.337940i
$959$	−8.57657			−0.276952
$960$	5.75123	+	16.9388i	0.185620	+	0.546698i
$961$	−30.0096			−0.968051
$962$	7.40097	+	4.71791i	0.238617	+	0.152112i
$963$	−5.51107	+	5.51107i	−0.177592	+	0.177592i
$964$	11.8968	+	25.5510i	0.383171	+	0.822943i
$965$	−30.2139	+	20.2663i	−0.972619	+	0.652397i
$966$	1.81841	−	0.402586i	0.0585065	−	0.0129530i
$967$	−1.66866	−	1.66866i	−0.0536606	−	0.0536606i	0.679767	−	0.733428i	$-0.262081\pi$
$967$	−1.66866	−	1.66866i	−0.0536606	−	0.0536606i	−0.733428	+	0.679767i	$0.762081\pi$
$968$	−5.68483	+	42.8960i	−0.182717	+	1.37873i
$969$			6.50479i			0.208964i
$970$	0.0827643	+	3.54916i	0.00265740	+	0.113957i
$971$		−	4.79719i		−	0.153949i	−0.997033	−	0.0769745i	$-0.975474\pi$
$971$		−	4.79719i		−	0.153949i	0.997033	−	0.0769745i	$-0.0245260\pi$
$972$	−1.87899	−	0.685116i	−0.0602687	−	0.0219751i
$973$	−1.39401	−	1.39401i	−0.0446900	−	0.0446900i
$974$	10.5208	+	47.5204i	0.337107	+	1.52265i
$975$	−11.5249	−	4.72563i	−0.369091	−	0.151341i
$976$	−12.8261	+	15.2501i	−0.410554	+	0.488143i
$977$	−25.0140	+	25.0140i	−0.800267	+	0.800267i	−0.983137	−	0.182870i	$-0.941461\pi$
$977$	−25.0140	+	25.0140i	−0.800267	+	0.800267i	0.182870	+	0.983137i	$0.441461\pi$
$978$	−14.0673	+	22.0673i	−0.449823	+	0.705634i
$979$	−37.1919			−1.18866
$980$	−6.67899	−	27.1522i	−0.213353	−	0.867344i
$981$	7.31695			0.233612
$982$	21.9635	−	34.4540i	0.700884	−	1.09947i
$983$	−30.9151	+	30.9151i	−0.986038	+	0.986038i	−0.999904	−	0.0138655i	$-0.995586\pi$
$983$	−30.9151	+	30.9151i	−0.986038	+	0.986038i	0.0138655	+	0.999904i	$0.495586\pi$
$984$	−9.49926	−	12.4017i	−0.302825	−	0.395352i
$985$	−13.8786	−	20.6907i	−0.442209	−	0.659262i
$986$	1.40608	+	6.35101i	0.0447786	+	0.202257i
$987$	1.98849	+	1.98849i	0.0632945	+	0.0632945i
$988$	−2.08702	+	5.72384i	−0.0663969	+	0.182100i
$989$			13.3661i			0.425017i
$990$	−11.1966	+	11.7313i	−0.355851	+	0.372844i
$991$			26.5873i			0.844575i	0.906462	+	0.422287i	$0.138773\pi$
$991$			26.5873i			0.844575i	−0.906462	+	0.422287i	$0.861227\pi$
$992$	−13.2264	−	42.1589i	−0.419937	−	1.33855i
$993$	22.4157	+	22.4157i	0.711340	+	0.711340i
$994$	9.67331	−	2.14162i	0.306819	−	0.0679280i
$995$	4.96270	−	25.1840i	0.157328	−	0.798387i
$996$	20.4017	−	9.49926i	0.646453	−	0.300996i
$997$	−2.47252	+	2.47252i	−0.0783054	+	0.0783054i	−0.745175	−	0.666869i	$-0.767634\pi$
$997$	−2.47252	+	2.47252i	−0.0783054	+	0.0783054i	0.666869	+	0.745175i	$0.267634\pi$
$998$	14.9500	+	9.53021i	0.473234	+	0.301674i
$999$	2.49122			0.0788187

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.2.j.a.43.2	yes	12
3.2	odd	2		180.2.k.e.163.5		12
4.3	odd	2	inner	60.2.j.a.43.5	yes	12
5.2	odd	4	inner	60.2.j.a.7.5	yes	12
5.3	odd	4		300.2.j.d.7.2		12
5.4	even	2		300.2.j.d.43.5		12
8.3	odd	2		960.2.w.g.703.5		12
8.5	even	2		960.2.w.g.703.2		12
12.11	even	2		180.2.k.e.163.2		12
15.2	even	4		180.2.k.e.127.2		12
15.8	even	4		900.2.k.n.307.5		12
15.14	odd	2		900.2.k.n.343.2		12
20.3	even	4		300.2.j.d.7.5		12
20.7	even	4	inner	60.2.j.a.7.2	✓	12
20.19	odd	2		300.2.j.d.43.2		12
40.27	even	4		960.2.w.g.127.2		12
40.37	odd	4		960.2.w.g.127.5		12
60.23	odd	4		900.2.k.n.307.2		12
60.47	odd	4		180.2.k.e.127.5		12
60.59	even	2		900.2.k.n.343.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.2.j.a.7.2	✓	12	20.7	even	4	inner
60.2.j.a.7.5	yes	12	5.2	odd	4	inner
60.2.j.a.43.2	yes	12	1.1	even	1	trivial
60.2.j.a.43.5	yes	12	4.3	odd	2	inner
180.2.k.e.127.2		12	15.2	even	4
180.2.k.e.127.5		12	60.47	odd	4
180.2.k.e.163.2		12	12.11	even	2
180.2.k.e.163.5		12	3.2	odd	2
300.2.j.d.7.2		12	5.3	odd	4
300.2.j.d.7.5		12	20.3	even	4
300.2.j.d.43.2		12	20.19	odd	2
300.2.j.d.43.5		12	5.4	even	2
900.2.k.n.307.2		12	60.23	odd	4
900.2.k.n.307.5		12	15.8	even	4
900.2.k.n.343.2		12	15.14	odd	2
900.2.k.n.343.5		12	60.59	even	2
960.2.w.g.127.2		12	40.27	even	4
960.2.w.g.127.5		12	40.37	odd	4
960.2.w.g.703.2		12	8.5	even	2
960.2.w.g.703.5		12	8.3	odd	2

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:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	60.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.19252 - 0.760198i) q^{2} +(0.707107 - 0.707107i) q^{3} +(0.844199 + 1.81310i) q^{4} +(0.432320 - 2.19388i) q^{5} +(-1.38078 + 0.305697i) q^{6} +(-0.611393 - 0.611393i) q^{7} +(0.371591 - 2.80391i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-1.19252 - 0.760198i) q^{2} +(0.707107 - 0.707107i) q^{3} +(0.844199 + 1.81310i) q^{4} +(0.432320 - 2.19388i) q^{5} +(-1.38078 + 0.305697i) q^{6} +(-0.611393 - 0.611393i) q^{7} +(0.371591 - 2.80391i) q^{8} -1.00000i q^{9} +(-2.18333 + 2.28759i) q^{10} +5.12822i q^{11} +(1.87899 + 0.685116i) q^{12} +(1.76156 + 1.76156i) q^{13} +(0.264318 + 1.19388i) q^{14} +(-1.24561 - 1.85700i) q^{15} +(-2.57466 + 3.06123i) q^{16} +(-3.76156 + 3.76156i) q^{17} +(-0.760198 + 1.19252i) q^{18} +1.22279 q^{19} +(4.34268 - 1.06823i) q^{20} -0.864641 q^{21} +(3.89846 - 6.11549i) q^{22} +(1.07700 - 1.07700i) q^{23} +(-1.71991 - 2.24542i) q^{24} +(-4.62620 - 1.89692i) q^{25} +(-0.761557 - 3.43982i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(0.592379 - 1.62465i) q^{28} +0.864641i q^{29} +(0.0737224 + 3.16142i) q^{30} -7.81086i q^{31} +(5.39747 - 1.69333i) q^{32} +(3.62620 + 3.62620i) q^{33} +(7.34525 - 1.62620i) q^{34} +(-1.60564 + 1.07700i) q^{35} +(1.81310 - 0.844199i) q^{36} +(-1.76156 + 1.76156i) q^{37} +(-1.45820 - 0.929560i) q^{38} +2.49122 q^{39} +(-5.99079 - 2.02741i) q^{40} +5.52311 q^{41} +(1.03110 + 0.657298i) q^{42} +(-6.20522 + 6.20522i) q^{43} +(-9.29797 + 4.32924i) q^{44} +(-2.19388 - 0.432320i) q^{45} +(-2.10308 + 0.465611i) q^{46} +(-2.29979 - 2.29979i) q^{47} +(0.344061 + 3.98518i) q^{48} -6.25240i q^{49} +(4.07479 + 5.77893i) q^{50} +5.31965i q^{51} +(-1.70677 + 4.68098i) q^{52} +(-2.62620 - 2.62620i) q^{53} +(0.305697 + 1.38078i) q^{54} +(11.2507 + 2.21703i) q^{55} +(-1.94148 + 1.48710i) q^{56} +(0.864641 - 0.864641i) q^{57} +(0.657298 - 1.03110i) q^{58} +0.528636 q^{59} +(2.31539 - 3.82609i) q^{60} +4.98168 q^{61} +(-5.93780 + 9.31460i) q^{62} +(-0.611393 + 0.611393i) q^{63} +(-7.72384 - 2.08382i) q^{64} +(4.62620 - 3.10308i) q^{65} +(-1.56768 - 7.08093i) q^{66} +(6.20522 + 6.20522i) q^{67} +(-9.99558 - 3.64457i) q^{68} -1.52311i q^{69} +(2.73349 - 0.0637434i) q^{70} -8.10243i q^{71} +(-2.80391 - 0.371591i) q^{72} +(-2.25240 - 2.25240i) q^{73} +(3.43982 - 0.761557i) q^{74} +(-4.61254 + 1.92989i) q^{75} +(1.03228 + 2.21703i) q^{76} +(3.13536 - 3.13536i) q^{77} +(-2.97082 - 1.89382i) q^{78} -15.9133 q^{79} +(5.60289 + 6.97191i) q^{80} -1.00000 q^{81} +(-6.58641 - 4.19866i) q^{82} +(7.95665 - 7.95665i) q^{83} +(-0.729929 - 1.56768i) q^{84} +(6.62620 + 9.87859i) q^{85} +(12.1170 - 2.68264i) q^{86} +(0.611393 + 0.611393i) q^{87} +(14.3791 + 1.90560i) q^{88} +7.25240i q^{89} +(2.28759 + 2.18333i) q^{90} -2.15401i q^{91} +(2.86192 + 1.04351i) q^{92} +(-5.52311 - 5.52311i) q^{93} +(0.994247 + 4.49084i) q^{94} +(0.528636 - 2.68264i) q^{95} +(2.61922 - 5.01395i) q^{96} +(0.793833 - 0.793833i) q^{97} +(-4.75306 + 7.45610i) q^{98} +5.12822 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{6} - 12 q^{8}+O(q^{10}) \) 12 * q - 4 * q^6 - 12 * q^8	\( 12 q - 4 q^{6} - 12 q^{8} - 8 q^{10} - 8 q^{12} - 4 q^{13} + 12 q^{16} - 20 q^{17} + 20 q^{20} + 12 q^{22} - 20 q^{25} + 16 q^{26} - 4 q^{28} + 8 q^{30} + 20 q^{32} + 8 q^{33} + 4 q^{36} + 4 q^{37} + 16 q^{38} - 8 q^{40} + 16 q^{41} + 20 q^{42} + 4 q^{45} - 40 q^{46} + 16 q^{48} - 16 q^{50} - 8 q^{52} + 4 q^{53} - 64 q^{56} - 20 q^{58} - 20 q^{60} - 32 q^{61} - 56 q^{62} + 20 q^{65} - 24 q^{66} - 16 q^{68} + 44 q^{70} - 12 q^{72} + 44 q^{73} + 8 q^{76} + 48 q^{77} - 24 q^{78} + 4 q^{80} - 12 q^{81} + 16 q^{82} + 44 q^{85} + 64 q^{86} + 60 q^{88} + 12 q^{90} + 56 q^{92} - 16 q^{93} + 44 q^{96} - 20 q^{97} + 24 q^{98}+O(q^{100}) \) 12 * q - 4 * q^6 - 12 * q^8 - 8 * q^10 - 8 * q^12 - 4 * q^13 + 12 * q^16 - 20 * q^17 + 20 * q^20 + 12 * q^22 - 20 * q^25 + 16 * q^26 - 4 * q^28 + 8 * q^30 + 20 * q^32 + 8 * q^33 + 4 * q^36 + 4 * q^37 + 16 * q^38 - 8 * q^40 + 16 * q^41 + 20 * q^42 + 4 * q^45 - 40 * q^46 + 16 * q^48 - 16 * q^50 - 8 * q^52 + 4 * q^53 - 64 * q^56 - 20 * q^58 - 20 * q^60 - 32 * q^61 - 56 * q^62 + 20 * q^65 - 24 * q^66 - 16 * q^68 + 44 * q^70 - 12 * q^72 + 44 * q^73 + 8 * q^76 + 48 * q^77 - 24 * q^78 + 4 * q^80 - 12 * q^81 + 16 * q^82 + 44 * q^85 + 64 * q^86 + 60 * q^88 + 12 * q^90 + 56 * q^92 - 16 * q^93 + 44 * q^96 - 20 * q^97 + 24 * q^98

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