LMFDB - Embedded newform 60.2.j.a.43.5

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			43.5
Root			$-0.760198 + 1.19252i$ of defining polynomial
Character	$\chi$	$=$	60.43
Dual form			60.2.j.a.7.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.760198 + 1.19252i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-0.844199 + 1.81310i) q^{4} +(0.432320 - 2.19388i) q^{5} +(-1.38078 - 0.305697i) q^{6} +(0.611393 + 0.611393i) q^{7} +(-2.80391 + 0.371591i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(0.760198 + 1.19252i) 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} +(-2.80391 + 0.371591i) q^{8} -1.00000i q^{9} +(2.94489 - 1.15223i) q^{10} -5.12822i q^{11} +(-0.685116 - 1.87899i) 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} +(1.19252 - 0.760198i) q^{18} -1.22279 q^{19} +(3.61275 + 2.63591i) q^{20} -0.864641 q^{21} +(6.11549 - 3.89846i) 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} +(-1.62465 + 0.592379i) q^{28} +0.864641i q^{29} +(-1.26760 + 2.89710i) q^{30} +7.81086i q^{31} +(1.69333 - 5.39747i) 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} +(-0.929560 - 1.45820i) q^{38} -2.49122 q^{39} +(-0.396963 + 6.31209i) q^{40} +5.52311 q^{41} +(-0.657298 - 1.03110i) 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} +(3.98518 + 0.344061i) q^{48} -6.25240i q^{49} +(-1.25472 - 6.95886i) q^{50} -5.31965i q^{51} +(-4.68098 + 1.70677i) 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} +(-1.03110 + 0.657298i) q^{58} -0.528636 q^{59} +(-4.41847 + 0.690733i) q^{60} +4.98168 q^{61} +(-9.31460 + 5.93780i) 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} +(-3.64457 - 9.99558i) q^{68} -1.52311i q^{69} +(2.50495 + 1.09602i) q^{70} +8.10243i q^{71} +(0.371591 + 2.80391i) 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} +(-1.89382 - 2.97082i) q^{78} +15.9133 q^{79} +(-7.82905 + 4.32505i) q^{80} -1.00000 q^{81} +(4.19866 + 6.58641i) 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} +(1.90560 + 14.3791i) q^{88} +7.25240i q^{89} +(-1.15223 - 2.94489i) q^{90} +2.15401i q^{91} +(-1.04351 - 2.86192i) 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} +(7.45610 - 4.75306i) 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 $

$2$	0.760198	+	1.19252i	0.537541	+	0.843238i
$2$	0.760198	+	1.19252i	0.537541	+	0.843238i
$3$	−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	0.813145	−	0.582060i	$-0.197753\pi$
$7$	0.611393	+	0.611393i	0.231085	+	0.231085i	−0.582060	+	0.813145i	$0.697753\pi$
$8$	−2.80391	+	0.371591i	−0.991332	+	0.131377i
$9$		−	1.00000i		−	0.333333i
$10$	2.94489	−	1.15223i	0.931255	−	0.364367i
$11$		−	5.12822i		−	1.54622i	−0.634274	−	0.773108i	$-0.718701\pi$
$11$		−	5.12822i		−	1.54622i	0.634274	−	0.773108i	$-0.281299\pi$
$12$	−0.685116	−	1.87899i	−0.197776	−	0.542419i
$13$	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	$0.473185\pi$
$18$	1.19252	−	0.760198i	0.281079	−	0.179180i
$19$	−1.22279			−0.280527			−0.140263	−	0.990114i	$-0.544795\pi$
$19$	−1.22279			−0.280527			−0.140263	+	0.990114i	$0.544795\pi$
$20$	3.61275	+	2.63591i	0.807836	+	0.589407i
$21$	−0.864641			−0.188680
$22$	6.11549	−	3.89846i	1.30383	−	0.831154i
$23$	−1.07700	+	1.07700i	−0.224571	+	0.224571i	−0.810420	−	0.585849i	$-0.800761\pi$
$23$	−1.07700	+	1.07700i	−0.224571	+	0.224571i	0.585849	+	0.810420i	$0.300761\pi$
$24$	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
$28$	−1.62465	+	0.592379i	−0.307031	+	0.111949i
$29$			0.864641i			0.160560i	0.996772	+	0.0802799i	$0.0255814\pi$
$29$			0.864641i			0.160560i	−0.996772	+	0.0802799i	$0.974419\pi$
$30$	−1.26760	+	2.89710i	−0.231431	+	0.528936i
$31$			7.81086i			1.40287i	0.712732	+	0.701436i	$0.247457\pi$
$31$			7.81086i			1.40287i	−0.712732	+	0.701436i	$0.752543\pi$
$32$	1.69333	−	5.39747i	0.299341	−	0.954146i
$33$	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	$0.315647\pi$
$38$	−0.929560	−	1.45820i	−0.150795	−	0.236551i
$39$	−2.49122			−0.398914
$40$	−0.396963	+	6.31209i	−0.0627653	+	0.998028i
$41$	5.52311			0.862566			0.431283	−	0.902217i	$-0.358061\pi$
$41$	5.52311			0.862566			0.431283	+	0.902217i	$0.358061\pi$
$42$	−0.657298	−	1.03110i	−0.101423	−	0.159102i
$43$	6.20522	−	6.20522i	0.946288	−	0.946288i	−0.0523416	−	0.998629i	$-0.516668\pi$
$43$	6.20522	−	6.20522i	0.946288	−	0.946288i	0.998629	+	0.0523416i	$0.0166685\pi$
$44$	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	0.854655	−	0.519196i	$-0.173769\pi$
$47$	2.29979	+	2.29979i	0.335459	+	0.335459i	−0.519196	+	0.854655i	$0.673769\pi$
$48$	3.98518	+	0.344061i	0.575210	+	0.0496610i
$49$		−	6.25240i		−	0.893199i
$50$	−1.25472	−	6.95886i	−0.177444	−	0.984131i
$51$		−	5.31965i		−	0.744899i
$52$	−4.68098	+	1.70677i	−0.649135	+	0.236687i
$53$	−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
$58$	−1.03110	+	0.657298i	−0.135390	+	0.0863075i
$59$	−0.528636			−0.0688225			−0.0344113	−	0.999408i	$-0.510956\pi$
$59$	−0.528636			−0.0688225			−0.0344113	+	0.999408i	$0.510956\pi$
$60$	−4.41847	+	0.690733i	−0.570422	+	0.0891732i
$61$	4.98168			0.637838			0.318919	−	0.947782i	$-0.396680\pi$
$61$	4.98168			0.637838			0.318919	+	0.947782i	$0.396680\pi$
$62$	−9.31460	+	5.93780i	−1.18295	+	0.754101i
$63$	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	0.217886	−	0.975974i	$-0.430084\pi$
$67$	−6.20522	−	6.20522i	−0.758089	−	0.758089i	−0.975974	+	0.217886i	$0.930084\pi$
$68$	−3.64457	−	9.99558i	−0.441969	−	1.21214i
$69$		−	1.52311i		−	0.183361i
$70$	2.50495	+	1.09602i	0.299399	+	0.130999i
$71$			8.10243i			0.961581i	0.876835	+	0.480791i	$0.159650\pi$
$71$			8.10243i			0.961581i	−0.876835	+	0.480791i	$0.840350\pi$
$72$	0.371591	+	2.80391i	0.0437924	+	0.330444i
$73$	−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
$78$	−1.89382	−	2.97082i	−0.214433	−	0.336379i
$79$	15.9133			1.79039			0.895193	−	0.445680i	$-0.147038\pi$
$79$	15.9133			1.79039			0.895193	+	0.445680i	$0.147038\pi$
$80$	−7.82905	+	4.32505i	−0.875314	+	0.483555i
$81$	−1.00000			−0.111111
$82$	4.19866	+	6.58641i	0.463664	+	0.727348i
$83$	−7.95665	+	7.95665i	−0.873355	+	0.873355i	−0.992836	−	0.119481i	$-0.961877\pi$
$83$	−7.95665	+	7.95665i	−0.873355	+	0.873355i	0.119481	+	0.992836i	$0.461877\pi$
$84$	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
$88$	1.90560	+	14.3791i	0.203138	+	1.53281i
$89$			7.25240i			0.768752i	0.923177	+	0.384376i	$0.125583\pi$
$89$			7.25240i			0.768752i	−0.923177	+	0.384376i	$0.874417\pi$
$90$	−1.15223	−	2.94489i	−0.121456	−	0.310418i
$91$			2.15401i			0.225801i
$92$	−1.04351	−	2.86192i	−0.108793	−	0.298376i
$93$	−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	$0.231848\pi$
$98$	7.45610	−	4.75306i	0.753179	−	0.480131i
$99$	−5.12822			−0.515405
$100$	7.34473	−	6.78638i	0.734473	−	0.678638i
$101$	−10.1170			−1.00668			−0.503341	−	0.864088i	$-0.667896\pi$
$101$	−10.1170			−1.00668			−0.503341	+	0.864088i	$0.667896\pi$
$102$	6.34377	−	4.04398i	0.628127	−	0.400414i
$103$	3.82267	−	3.82267i	0.376659	−	0.376659i	−0.493236	−	0.869895i	$-0.664186\pi$
$103$	3.82267	−	3.82267i	0.376659	−	0.376659i	0.869895	+	0.493236i	$0.164186\pi$
$104$	−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	0.921397	−	0.388622i	$-0.127049\pi$
$107$	5.51107	+	5.51107i	0.532775	+	0.532775i	−0.388622	+	0.921397i	$0.627049\pi$
$108$	−1.87899	+	0.685116i	−0.180806	+	0.0659253i
$109$			7.31695i			0.700836i	0.936593	+	0.350418i	$0.113961\pi$
$109$			7.31695i			0.700836i	−0.936593	+	0.350418i	$0.886039\pi$
$110$	−5.90889	−	15.1020i	−0.563391	−	1.43992i
$111$		−	2.49122i		−	0.236456i
$112$	0.297490	−	3.44575i	0.0281101	−	0.325592i
$113$	−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
$118$	−0.401868	−	0.630408i	−0.0369949	−	0.0580337i
$119$	−4.59958			−0.421643
$120$	−4.18262	−	4.74401i	−0.381820	−	0.433067i
$121$	−15.2986			−1.39078
$122$	3.78706	+	5.94074i	0.342864	+	0.537849i
$123$	−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	0.291767	−	0.956489i	$-0.405757\pi$
$127$	−7.49103	−	7.49103i	−0.664722	−	0.664722i	−0.956489	+	0.291767i	$0.905757\pi$
$128$	8.35664	+	7.62671i	0.738629	+	0.674112i
$129$			8.77551i			0.772641i
$130$	7.21731	+	3.15787i	0.633000	+	0.276963i
$131$		−	13.9964i		−	1.22287i	−0.791296	−	0.611434i	$-0.790593\pi$
$131$		−	13.9964i		−	1.22287i	0.791296	−	0.611434i	$-0.209407\pi$
$132$	−9.63589	+	3.51342i	−0.838696	+	0.305804i
$133$	−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	$0.110721\pi$
$138$	1.81634	−	1.15787i	0.154617	−	0.0985643i
$139$	−2.28006			−0.193392			−0.0966960	−	0.995314i	$-0.530827\pi$
$139$	−2.28006			−0.193392			−0.0966960	+	0.995314i	$0.530827\pi$
$140$	0.597236	+	3.82039i	0.0504757	+	0.322882i
$141$	−3.25240			−0.273901
$142$	−9.66229	+	6.15945i	−0.810842	+	0.516889i
$143$	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
$148$	−1.70677	−	4.68098i	−0.140296	−	0.384774i
$149$		−	10.1170i		−	0.828820i	−0.910090	−	0.414410i	$-0.863988\pi$
$149$		−	10.1170i		−	0.828820i	0.910090	−	0.414410i	$-0.136012\pi$
$150$	5.80787	+	4.03343i	0.474211	+	0.329329i
$151$			7.93691i			0.645897i	0.946417	+	0.322948i	$0.104674\pi$
$151$			7.93691i			0.645897i	−0.946417	+	0.322948i	$0.895326\pi$
$152$	3.42859	−	0.454377i	0.278095	−	0.0368548i
$153$	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	$0.0801311\pi$
$158$	12.0972	+	18.9769i	0.962405	+	1.50972i
$159$	3.71400			0.294540
$160$	−11.1093	−	6.04839i	−0.878269	−	0.478167i
$161$	−1.31695			−0.103790
$162$	−0.760198	−	1.19252i	−0.0597268	−	0.0936931i
$163$	−13.0849	+	13.0849i	−1.02489	+	1.02489i	−0.0252033	+	0.999682i	$0.508023\pi$
$163$	−13.0849	+	13.0849i	−1.02489	+	1.02489i	−0.999682	+	0.0252033i	$0.991977\pi$
$164$	−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	0.116216	−	0.993224i	$-0.462924\pi$
$167$	−11.3334	−	11.3334i	−0.877008	−	0.877008i	−0.993224	+	0.116216i	$0.962924\pi$
$168$	2.42438	−	0.321293i	0.187045	−	0.0247883i
$169$		−	6.79383i		−	0.522603i
$170$	−6.74318	+	15.4115i	−0.517178	+	1.18201i
$171$			1.22279i			0.0935088i
$172$	6.01224	+	16.4891i	0.458429	+	1.25728i
$173$	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
$178$	−8.64861	+	5.51325i	−0.648241	+	0.413236i
$179$	−12.6475			−0.945320			−0.472660	−	0.881245i	$-0.656706\pi$
$179$	−12.6475			−0.945320			−0.472660	+	0.881245i	$0.656706\pi$
$180$	2.63591	−	3.61275i	0.196469	−	0.269279i
$181$	7.72928			0.574513			0.287256	−	0.957854i	$-0.407257\pi$
$181$	7.72928			0.574513			0.287256	+	0.957854i	$0.407257\pi$
$182$	−2.56869	+	1.63747i	−0.190404	+	0.121378i
$183$	−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
$188$	−6.11123	+	2.22827i	−0.445707	+	0.162513i
$189$			0.864641i			0.0628934i
$190$	−3.60097	+	1.40893i	−0.261242	+	0.102215i
$191$		−	7.04516i		−	0.509770i	−0.966971	−	0.254885i	$-0.917962\pi$
$191$		−	7.04516i		−	0.509770i	0.966971	−	0.254885i	$-0.0820376\pi$
$192$	−3.98810	+	6.93506i	−0.287816	+	0.500495i
$193$	−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	$0.120080\pi$
$198$	−3.89846	−	6.11549i	−0.277051	−	0.434609i
$199$	−11.4792			−0.813741			−0.406870	−	0.913486i	$-0.633380\pi$
$199$	−11.4792			−0.813741			−0.406870	+	0.913486i	$0.633380\pi$
$200$	13.6763	+	3.59973i	0.967062	+	0.254539i
$201$	8.77551			0.618977
$202$	−7.69095	−	12.0648i	−0.541133	−	0.848873i
$203$	−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
$208$	0.857132	−	9.92794i	0.0594314	−	0.688379i
$209$			6.27072i			0.433755i
$210$	−2.54627	+	0.996266i	−0.175709	+	0.0687489i
$211$		−	5.49134i		−	0.378039i	−0.981973	−	0.189020i	$-0.939469\pi$
$211$		−	5.49134i		−	0.378039i	0.981973	−	0.189020i	$-0.0605310\pi$
$212$	6.97859	−	2.54452i	0.479292	−	0.174759i
$213$	−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
$218$	−8.72559	+	5.56233i	−0.590972	+	0.376728i
$219$	3.18537			0.215247
$220$	13.5175	−	18.5270i	0.911351	−	1.24909i
$221$	−13.2524			−0.891453
$222$	2.97082	−	1.89382i	0.199389	−	0.127105i
$223$	10.8678	−	10.8678i	0.727764	−	0.727764i	−0.242410	−	0.970174i	$-0.577938\pi$
$223$	10.8678	−	10.8678i	0.727764	−	0.727764i	0.970174	+	0.242410i	$0.0779380\pi$
$224$	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	0.522155	−	0.852851i	$-0.325128\pi$
$227$	−4.98244	−	4.98244i	−0.330696	−	0.330696i	−0.852851	+	0.522155i	$0.825128\pi$
$228$	0.837751	+	2.29761i	0.0554814	+	0.152163i
$229$			25.7572i			1.70208i	0.525098	+	0.851041i	$0.324028\pi$
$229$			25.7572i			1.70208i	−0.525098	+	0.851041i	$0.675972\pi$
$230$	−1.93070	+	4.41262i	−0.127307	+	0.290959i
$231$			4.43407i			0.291740i
$232$	−0.321293	−	2.42438i	−0.0210939	−	0.159168i
$233$	−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
$238$	−3.49659	−	5.48509i	−0.226650	−	0.355545i
$239$	26.9354			1.74231			0.871154	−	0.491009i	$-0.163372\pi$
$239$	26.9354			1.74231			0.871154	+	0.491009i	$0.163372\pi$
$240$	2.47770	−	8.59424i	0.159935	−	0.554756i
$241$	14.0925			0.907775			0.453887	−	0.891059i	$-0.350037\pi$
$241$	14.0925			0.907775			0.453887	+	0.891059i	$0.350037\pi$
$242$	−11.6300	−	18.2439i	−0.747603	−	1.17276i
$243$	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
$248$	−2.90245	−	21.9010i	−0.184306	−	1.39071i
$249$		−	11.2524i		−	0.713092i
$250$	−15.8093	−	0.255758i	−0.999869	−	0.0161756i
$251$			17.2471i			1.08863i	0.838882	+	0.544314i	$0.183210\pi$
$251$			17.2471i			1.08863i	−0.838882	+	0.544314i	$0.816790\pi$
$252$	0.592379	+	1.62465i	0.0373164	+	0.102344i
$253$	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	$0.480393\pi$
$258$	−10.4650	+	6.67112i	−0.651520	+	0.415326i
$259$	−2.15401			−0.133844
$260$	1.72077	+	11.0074i	0.106717	+	0.682648i
$261$	0.864641			0.0535199
$262$	16.6909	−	10.6400i	1.03117	−	0.657341i
$263$	6.73386	−	6.73386i	0.415228	−	0.415228i	−0.468327	−	0.883555i	$-0.655143\pi$
$263$	6.73386	−	6.73386i	0.415228	−	0.415228i	0.883555	+	0.468327i	$0.155143\pi$
$264$	−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
$268$	16.4891	−	6.01224i	1.00723	−	0.367256i
$269$		−	25.7047i		−	1.56724i	−0.621238	−	0.783622i	$-0.713370\pi$
$269$		−	25.7047i		−	1.56724i	0.621238	−	0.783622i	$-0.286630\pi$
$270$	2.89710	+	1.26760i	0.176312	+	0.0771437i
$271$		−	0.931222i		−	0.0565677i	−0.999600	−	0.0282839i	$-0.990996\pi$
$271$		−	0.931222i		−	0.0565677i	0.999600	−	0.0282839i	$-0.00900423\pi$
$272$	21.1997	+	1.83029i	1.28542	+	0.110977i
$273$	−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	$0.863365\pi$
$278$	−1.73330	−	2.71901i	−0.103956	−	0.163075i
$279$	7.81086			0.467624
$280$	−4.10187	+	3.61647i	−0.245133	+	0.216125i
$281$	8.56934			0.511204			0.255602	−	0.966782i	$-0.417726\pi$
$281$	8.56934			0.511204			0.255602	+	0.966782i	$0.417726\pi$
$282$	−2.47246	−	3.87854i	−0.147233	−	0.230964i
$283$	−11.5705	+	11.5705i	−0.687796	+	0.687796i	−0.961744	−	0.273949i	$-0.911670\pi$
$283$	−11.5705	+	11.5705i	−0.687796	+	0.687796i	0.273949	+	0.961744i	$0.411670\pi$
$284$	−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
$288$	−5.39747	−	1.69333i	−0.318049	−	0.0997803i
$289$		−	11.2986i		−	0.664625i
$290$	0.996266	+	2.54627i	0.0585027	+	0.149522i
$291$			1.12265i			0.0658108i
$292$	5.98529	−	2.18235i	0.350262	−	0.127712i
$293$	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
$298$	12.0648	−	7.69095i	0.698892	−	0.445525i
$299$	−3.79441			−0.219436
$300$	−0.394812	+	9.99220i	−0.0227945	+	0.576900i
$301$	7.58767			0.437346
$302$	−9.46491	+	6.03362i	−0.544644	+	0.347196i
$303$	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	0.659801	−	0.751440i	$-0.270640\pi$
$307$	−1.60564	−	1.60564i	−0.0916387	−	0.0916387i	−0.751440	+	0.659801i	$0.770640\pi$
$308$	3.03785	+	8.33158i	0.173098	+	0.474736i
$309$			5.40608i			0.307541i
$310$	8.99992	+	23.0021i	0.511161	+	1.30643i
$311$			19.4161i			1.10099i	0.834839	+	0.550494i	$0.185561\pi$
$311$			19.4161i			1.10099i	−0.834839	+	0.550494i	$0.814439\pi$
$312$	6.98516	−	0.925715i	0.395457	−	0.0524083i
$313$	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	$0.350115\pi$
$318$	2.82338	+	4.42902i	0.158327	+	0.248367i
$319$	4.43407			0.248260
$320$	−1.23247	−	17.8460i	−0.0688969	−	0.997624i
$321$	−7.79383			−0.435009
$322$	−1.00114	−	1.57048i	−0.0557914	−	0.0875196i
$323$	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
$328$	−15.4863	+	2.05234i	−0.855089	+	0.113322i
$329$			2.81215i			0.155039i
$330$	14.8570	+	6.50053i	0.817849	+	0.357842i
$331$		−	31.7005i		−	1.74242i	−0.490912	−	0.871209i	$-0.663336\pi$
$331$		−	31.7005i		−	1.74242i	0.490912	−	0.871209i	$-0.336664\pi$
$332$	−7.70919	−	21.1432i	−0.423097	−	1.16038i
$333$	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	$-0.0106855\pi$
$338$	8.10177	−	5.16466i	0.440678	−	0.280920i
$339$	0.720062			0.0391084
$340$	−23.5047	+	3.67445i	−1.27472	+	0.199275i
$341$	40.0558			2.16914
$342$	−1.45820	+	0.929560i	−0.0788502	+	0.0502648i
$343$	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	0.883271	−	0.468863i	$-0.155336\pi$
$347$	7.71957	+	7.71957i	0.414408	+	0.414408i	−0.468863	+	0.883271i	$0.655336\pi$
$348$	1.62465	−	0.592379i	0.0870906	−	0.0317549i
$349$		−	27.0741i		−	1.44925i	−0.689146	−	0.724623i	$-0.742014\pi$
$349$		−	27.0741i		−	1.44925i	0.689146	−	0.724623i	$-0.257986\pi$
$350$	3.48747	−	5.02173i	0.186413	−	0.268423i
$351$			2.49122i			0.132971i
$352$	−27.6794	−	8.68375i	−1.47532	−	0.462846i
$353$	−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
$358$	−9.61461	−	15.0824i	−0.508148	−	0.797129i
$359$	−14.2334			−0.751211			−0.375606	−	0.926780i	$-0.622565\pi$
$359$	−14.2334			−0.751211			−0.375606	+	0.926780i	$0.622565\pi$
$360$	6.31209	+	0.396963i	0.332676	+	0.0209218i
$361$	−17.5048			−0.921305
$362$	5.87578	+	9.21731i	0.308824	+	0.484451i
$363$	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	0.627602	−	0.778534i	$-0.284037\pi$
$367$	−2.89145	−	2.89145i	−0.150933	−	0.150933i	−0.778534	+	0.627602i	$0.784037\pi$
$368$	6.06988	+	0.524045i	0.316414	+	0.0273177i
$369$		−	5.52311i		−	0.287522i
$370$	−3.15787	+	7.21731i	−0.164170	+	0.375210i
$371$		−	3.21128i		−	0.166721i
$372$	14.6766	−	5.35135i	0.760944	−	0.277454i
$373$	−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
$378$	−1.03110	+	0.657298i	−0.0530341	+	0.0338078i
$379$	−15.4562			−0.793932			−0.396966	−	0.917833i	$-0.629937\pi$
$379$	−15.4562			−0.793932			−0.396966	+	0.917833i	$0.629937\pi$
$380$	−4.41763	−	3.22315i	−0.226619	−	0.165344i
$381$	10.5939			0.542743
$382$	8.40148	−	5.35571i	0.429857	−	0.274022i
$383$	−12.5562	+	12.5562i	−0.641593	+	0.641593i	−0.950947	−	0.309354i	$-0.899887\pi$
$383$	−12.5562	+	12.5562i	−0.641593	+	0.641593i	0.309354	+	0.950947i	$0.399887\pi$
$384$	−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
$388$	0.769144	+	2.10945i	0.0390474	+	0.107091i
$389$			5.16327i			0.261788i	0.991396	+	0.130894i	$0.0417848\pi$
$389$			5.16327i			0.261788i	−0.991396	+	0.130894i	$0.958215\pi$
$390$	−7.33636	+	2.87046i	−0.371491	+	0.145351i
$391$		−	8.10243i		−	0.409757i
$392$	2.32333	+	17.5312i	0.117346	+	0.885458i
$393$	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	$0.289218\pi$
$398$	−8.72648	−	13.6892i	−0.437419	−	0.686177i
$399$	1.05727			0.0529298
$400$	6.10397	+	19.0458i	0.305198	+	0.952289i
$401$	3.49521			0.174542			0.0872712	−	0.996185i	$-0.472185\pi$
$401$	3.49521			0.174542			0.0872712	+	0.996185i	$0.472185\pi$
$402$	6.67112	+	10.4650i	0.332725	+	0.521945i
$403$	−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
$408$	1.97673	+	14.9158i	0.0978629	+	0.738443i
$409$			14.8034i			0.731982i	0.930618	+	0.365991i	$0.119270\pi$
$409$			14.8034i			0.731982i	−0.930618	+	0.365991i	$0.880730\pi$
$410$	16.2650	−	6.36390i	0.803269	−	0.314291i
$411$			9.91923i			0.489279i
$412$	3.70379	+	10.1580i	0.182473	+	0.500448i
$413$	−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
$418$	−7.47795	+	4.76699i	−0.365758	+	0.233161i
$419$	19.0701			0.931634			0.465817	−	0.884881i	$-0.345760\pi$
$419$	19.0701			0.931634			0.465817	+	0.884881i	$0.345760\pi$
$420$	−3.12373	−	2.27911i	−0.152423	−	0.111209i
$421$	−20.8034			−1.01390			−0.506948	−	0.861976i	$-0.669226\pi$
$421$	−20.8034			−1.01390			−0.506948	+	0.861976i	$0.669226\pi$
$422$	6.54852	−	4.17450i	0.318777	−	0.203212i
$423$	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
$428$	−14.6446	+	5.33968i	−0.707872	+	0.258103i
$429$			12.7755i			0.616807i
$430$	11.1238	−	25.4235i	0.536439	−	1.22603i
$431$			15.3302i			0.738428i	0.929344	+	0.369214i	$0.120373\pi$
$431$			15.3302i			0.738428i	−0.929344	+	0.369214i	$0.879627\pi$
$432$	0.344061	−	3.98518i	0.0165537	−	0.191737i
$433$	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
$438$	2.42151	+	3.79861i	0.115704	+	0.181505i
$439$	−24.6554			−1.17674			−0.588368	−	0.808593i	$-0.700230\pi$
$439$	−24.6554			−1.17674			−0.588368	+	0.808593i	$0.700230\pi$
$440$	32.3698	+	2.03571i	1.54317	+	0.0970488i
$441$	−6.25240			−0.297733
$442$	−10.0744	−	15.8037i	−0.479192	−	0.751706i
$443$	−1.77116	+	1.77116i	−0.0841501	+	0.0841501i	−0.747929	−	0.663779i	$-0.768952\pi$
$443$	−1.77116	+	1.77116i	−0.0841501	+	0.0841501i	0.663779	+	0.747929i	$0.268952\pi$
$444$	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
$448$	5.99634	+	3.44827i	0.283300	+	0.162916i
$449$			33.1512i			1.56450i	0.622963	+	0.782251i	$0.285929\pi$
$449$			33.1512i			1.56450i	−0.622963	+	0.782251i	$0.714071\pi$
$450$	−6.95886	+	1.25472i	−0.328044	+	0.0591480i
$451$		−	28.3237i		−	1.33371i
$452$	1.35299	−	0.493326i	0.0636394	−	0.0232041i
$453$	−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	$0.329851\pi$
$458$	−30.7159	+	19.5806i	−1.43526	+	0.914939i
$459$	−5.31965			−0.248300
$460$	−6.72984	+	1.05207i	−0.313780	+	0.0490528i
$461$	−27.0216			−1.25852			−0.629262	−	0.777193i	$-0.716643\pi$
$461$	−27.0216			−1.25852			−0.629262	+	0.777193i	$0.716643\pi$
$462$	−5.28771	+	3.37077i	−0.246006	+	0.156822i
$463$	−27.7123	+	27.7123i	−1.28790	+	1.28790i	−0.351843	+	0.936059i	$0.614445\pi$
$463$	−27.7123	+	27.7123i	−1.28790	+	1.28790i	−0.936059	+	0.351843i	$0.885555\pi$
$464$	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	0.752043	−	0.659114i	$-0.229068\pi$
$467$	2.00823	+	2.00823i	0.0929296	+	0.0929296i	−0.659114	+	0.752043i	$0.729068\pi$
$468$	1.70677	+	4.68098i	0.0788956	+	0.216378i
$469$		−	7.58767i		−	0.350366i
$470$	9.42252	+	4.12274i	0.434628	+	0.190168i
$471$			12.7477i			0.587381i
$472$	1.48225	−	0.196436i	0.0682260	−	0.00904172i
$473$	−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
$478$	20.4763	+	32.1210i	0.936562	+	1.46918i
$479$	13.7593			0.628678			0.314339	−	0.949311i	$-0.398217\pi$
$479$	13.7593			0.628678			0.314339	+	0.949311i	$0.398217\pi$
$480$	12.1323	−	3.57862i	0.553763	−	0.163341i
$481$	−6.20617			−0.282977
$482$	10.7131	+	16.8055i	0.487966	+	0.765470i
$483$	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	$0.0346596\pi$
$487$	24.3355	+	24.3355i	1.10275	+	1.10275i	0.108671	+	0.994078i	$0.465340\pi$
$488$	−13.9682	+	1.85115i	−0.632310	+	0.0837975i
$489$		−	18.5048i		−	0.836816i
$490$	−7.20420	−	18.4126i	−0.325453	−	0.831797i
$491$		−	28.8918i		−	1.30387i	−0.758275	−	0.651935i	$-0.773957\pi$
$491$		−	28.8918i		−	1.30387i	0.758275	−	0.651935i	$-0.226043\pi$
$492$	−3.78397	−	10.3779i	−0.170595	−	0.467872i
$493$	−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
$498$	13.4187	−	8.55405i	0.601306	−	0.383316i
$499$	12.5365			0.561211			0.280605	−	0.959823i	$-0.409465\pi$
$499$	12.5365			0.561211			0.280605	+	0.959823i	$0.409465\pi$
$500$	−11.7132	−	19.0473i	−0.523831	−	0.851822i
$501$	16.0279			0.716074
$502$	−20.5675	+	13.1112i	−0.917972	+	0.585182i
$503$	9.01392	−	9.01392i	0.401911	−	0.401911i	−0.476995	−	0.878906i	$-0.658274\pi$
$503$	9.01392	−	9.01392i	0.401911	−	0.401911i	0.878906	+	0.476995i	$0.158274\pi$
$504$	−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
$508$	19.9059	−	7.25806i	0.883182	−	0.322025i
$509$			22.5448i			0.999279i	0.866233	+	0.499640i	$0.166534\pi$
$509$			22.5448i			0.999279i	−0.866233	+	0.499640i	$0.833466\pi$
$510$	−6.12946	−	15.6658i	−0.271417	−	0.693691i
$511$		−	2.75420i		−	0.121839i
$512$	−20.8826	+	8.71295i	−0.922891	+	0.385062i
$513$	−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
$518$	−1.63747	−	2.56869i	−0.0719464	−	0.112862i
$519$	−11.2681			−0.494613
$520$	−11.8184	+	10.4198i	−0.518270	+	0.456940i
$521$	−18.9046			−0.828226			−0.414113	−	0.910225i	$-0.635908\pi$
$521$	−18.9046			−0.828226			−0.414113	+	0.910225i	$0.635908\pi$
$522$	0.657298	+	1.03110i	0.0287692	+	0.0451300i
$523$	21.8269	−	21.8269i	0.954426	−	0.954426i	−0.0445800	−	0.999006i	$-0.514195\pi$
$523$	21.8269	−	21.8269i	0.954426	−	0.954426i	0.999006	+	0.0445800i	$0.0141949\pi$
$524$	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
$528$	1.76442	−	20.4368i	0.0767866	−	0.889400i
$529$			20.6801i			0.899136i
$530$	−10.7598	−	4.70787i	−0.467378	−	0.204497i
$531$			0.528636i			0.0229408i
$532$	1.98661	−	0.724353i	0.0861303	−	0.0314047i
$533$	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
$538$	30.6533	−	19.5407i	1.32156	−	0.842457i
$539$	−32.0637			−1.38108
$540$	0.690733	+	4.41847i	0.0297244	+	0.190141i
$541$	7.85838			0.337858			0.168929	−	0.985628i	$-0.445969\pi$
$541$	7.85838			0.337858			0.168929	+	0.985628i	$0.445969\pi$
$542$	1.11050	−	0.707913i	0.0477000	−	0.0304075i
$543$	−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	0.215076	−	0.976597i	$-0.431000\pi$
$547$	−17.8105	−	17.8105i	−0.761522	−	0.761522i	−0.976597	+	0.215076i	$0.931000\pi$
$548$	6.79582	+	18.6382i	0.290303	+	0.796183i
$549$		−	4.98168i		−	0.212613i
$550$	−35.6865	+	6.43447i	−1.52168	+	0.274367i
$551$		−	1.05727i		−	0.0450413i
$552$	0.565976	+	4.27068i	0.0240895	+	0.181772i
$553$	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	$0.00353686\pi$
$558$	5.93780	+	9.31460i	0.251367	+	0.394318i
$559$	21.8617			0.924652
$560$	−7.43093	−	2.14232i	−0.314014	−	0.0905296i
$561$	−27.2803			−1.15178
$562$	6.51439	+	10.2191i	0.274793	+	0.431067i
$563$	5.27400	−	5.27400i	0.222273	−	0.222273i	−0.587182	−	0.809455i	$-0.699763\pi$
$563$	5.27400	−	5.27400i	0.222273	−	0.222273i	0.809455	+	0.587182i	$0.199763\pi$
$564$	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
$568$	−3.01079	−	22.7185i	−0.126330	−	0.953247i
$569$		−	28.5606i		−	1.19732i	−0.801002	−	0.598661i	$-0.795699\pi$
$569$		−	28.5606i		−	1.19732i	0.801002	−	0.598661i	$-0.204301\pi$
$570$	1.55000	−	3.54254i	0.0649225	−	0.148381i
$571$			32.2837i			1.35103i	0.737347	+	0.675515i	$0.236078\pi$
$571$			32.2837i			1.35103i	−0.737347	+	0.675515i	$0.763922\pi$
$572$	8.75270	+	24.0051i	0.365969	+	1.00370i
$573$	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	$-0.0428584\pi$
$578$	13.4738	−	8.58919i	0.560437	−	0.357263i
$579$	16.2702			0.676168
$580$	−2.27911	+	3.12373i	−0.0946351	+	0.129706i
$581$	−9.72928			−0.403639
$582$	−1.33878	+	0.853435i	−0.0554942	+	0.0353760i
$583$	−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	0.258039	−	0.966135i	$-0.416924\pi$
$587$	−17.1558	−	17.1558i	−0.708096	−	0.708096i	−0.966135	+	0.258039i	$0.916924\pi$
$588$	−11.7482	+	4.28362i	−0.484488	+	0.176653i
$589$		−	9.55102i		−	0.393543i
$590$	−1.55677	+	0.609110i	−0.0640913	+	0.0250767i
$591$			11.1420i			0.458321i
$592$	9.92794	+	0.857132i	0.408036	+	0.0352279i
$593$	−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
$598$	−2.88450	−	4.52490i	−0.117956	−	0.185037i
$599$	23.7636			0.970955			0.485478	−	0.874249i	$-0.338646\pi$
$599$	23.7636			0.970955			0.485478	+	0.874249i	$0.338646\pi$
$600$	−12.2160	+	7.12523i	−0.498717	+	0.290886i
$601$	22.1695			0.904314			0.452157	−	0.891938i	$-0.350655\pi$
$601$	22.1695			0.904314			0.452157	+	0.891938i	$0.350655\pi$
$602$	5.76813	+	9.04843i	0.235091	+	0.368786i
$603$	−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	0.491328	−	0.870974i	$-0.336511\pi$
$607$	−9.35348	−	9.35348i	−0.379646	−	0.379646i	−0.870974	+	0.491328i	$0.836511\pi$
$608$	−2.07058	+	6.59995i	−0.0839731	+	0.267663i
$609$		−	0.747604i		−	0.0302944i
$610$	14.6705	−	5.74004i	0.593990	−	0.232408i
$611$			8.10243i			0.327789i
$612$	−9.99558	+	3.64457i	−0.404047	+	0.147323i
$613$	−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	$0.215261\pi$
$618$	−6.44685	+	4.10969i	−0.259330	+	0.165316i
$619$	−30.1297			−1.21101			−0.605507	−	0.795840i	$-0.707029\pi$
$619$	−30.1297			−1.21101			−0.605507	+	0.795840i	$0.707029\pi$
$620$	−20.5887	+	28.2187i	−0.826863	+	1.13329i
$621$	−1.52311			−0.0611205
$622$	−23.1541	+	14.7601i	−0.928395	+	0.591826i
$623$	−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
$628$	8.73362	+	23.9528i	0.348509	+	0.955819i
$629$		−	13.2524i		−	0.528408i
$630$	1.09602	−	2.50495i	0.0436664	−	0.0997997i
$631$			21.5701i			0.858694i	0.903140	+	0.429347i	$0.141256\pi$
$631$			21.5701i			0.858694i	−0.903140	+	0.429347i	$0.858744\pi$
$632$	−44.6195	+	5.91324i	−1.77487	+	0.235216i
$633$	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
$638$	3.37077	+	5.28771i	0.133450	+	0.209342i
$639$	8.10243			0.320527
$640$	20.3448	−	15.0363i	0.804199	−	0.594360i
$641$	48.3911			1.91133			0.955666	−	0.294452i	$-0.0951370\pi$
$641$	48.3911			1.91133			0.955666	+	0.294452i	$0.0951370\pi$
$642$	−5.92485	−	9.29429i	−0.233835	−	0.366816i
$643$	23.3413	−	23.3413i	0.920491	−	0.920491i	−0.0765729	−	0.997064i	$-0.524398\pi$
$643$	23.3413	−	23.3413i	0.920491	−	0.920491i	0.997064	+	0.0765729i	$0.0243978\pi$
$644$	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	$0.107892\pi$
$647$	32.4465	+	32.4465i	1.27560	+	1.27560i	0.332501	+	0.943103i	$0.392108\pi$
$648$	2.80391	−	0.371591i	0.110148	−	0.0145975i
$649$			2.71096i			0.106414i
$650$	10.0482	−	14.4687i	0.394121	−	0.567508i
$651$		−	6.75359i		−	0.264694i
$652$	−12.6779	−	34.7704i	−0.496506	−	1.36171i
$653$	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
$658$	−3.35355	+	2.13779i	−0.130735	+	0.0833399i
$659$	47.5028			1.85045			0.925223	−	0.379423i	$-0.123878\pi$
$659$	47.5028			1.85045			0.925223	+	0.379423i	$0.123878\pi$
$660$	3.54223	+	22.6589i	0.137881	+	0.881996i
$661$	−46.1204			−1.79387			−0.896937	−	0.442158i	$-0.854213\pi$
$661$	−46.1204			−1.79387			−0.896937	+	0.442158i	$0.854213\pi$
$662$	37.8035	−	24.0987i	1.46927	−	0.936621i
$663$	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
$668$	30.1163	−	10.9810i	1.16524	−	0.424867i
$669$			15.3694i			0.594217i
$670$	−25.4235	−	11.1238i	−0.982197	−	0.429751i
$671$		−	25.5471i		−	0.986236i
$672$	−1.46412	+	4.66687i	−0.0564797	+	0.180028i
$673$	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	$0.322124\pi$
$678$	0.547390	+	0.858688i	0.0210224	+	0.0329777i
$679$	0.970688			0.0372516
$680$	−22.2501	−	25.2365i	−0.853251	−	0.967774i
$681$	7.04623			0.270012
$682$	30.4503	+	47.7673i	1.16600	+	1.82910i
$683$	8.43079	−	8.43079i	0.322595	−	0.322595i	−0.527167	−	0.849762i	$-0.676746\pi$
$683$	8.43079	−	8.43079i	0.322595	−	0.322595i	0.849762	+	0.527167i	$0.176746\pi$
$684$	−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
$688$	−34.9719	−	3.01932i	−1.33329	−	0.115110i
$689$		−	9.25240i		−	0.352488i
$690$	−1.75498	−	4.48540i	−0.0668109	−	0.170756i
$691$			21.9182i			0.833809i	0.908950	+	0.416905i	$0.136885\pi$
$691$			21.9182i			0.833809i	−0.908950	+	0.416905i	$0.863115\pi$
$692$	−21.1726	+	7.71993i	−0.804862	+	0.293468i
$693$	−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
$698$	32.2864	−	20.5817i	1.22206	−	0.779029i
$699$	1.01163			0.0382633
$700$	8.63967	+	0.341370i	0.326549	+	0.0129026i
$701$	−21.8184			−0.824070			−0.412035	−	0.911168i	$-0.635182\pi$
$701$	−21.8184			−0.824070			−0.412035	+	0.911168i	$0.635182\pi$
$702$	−2.97082	+	1.89382i	−0.112126	+	0.0714776i
$703$	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
$708$	0.362177	+	0.993303i	0.0136114	+	0.0373306i
$709$			31.7938i			1.19404i	0.802225	+	0.597021i	$0.203649\pi$
$709$			31.7938i			1.19404i	−0.802225	+	0.597021i	$0.796351\pi$
$710$	9.33587	+	23.8607i	0.350369	+	0.895478i
$711$		−	15.9133i		−	0.596795i
$712$	−2.69493	−	20.3351i	−0.100997	−	0.762089i
$713$	−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
$718$	−10.8202	−	16.9736i	−0.403807	−	0.633450i
$719$	−52.0874			−1.94253			−0.971265	−	0.237999i	$-0.923508\pi$
$719$	−52.0874			−1.94253			−0.971265	+	0.237999i	$0.923508\pi$
$720$	4.32505	+	7.82905i	0.161185	+	0.291771i
$721$	4.67432			0.174081
$722$	−13.3071	−	20.8748i	−0.495239	−	0.776879i
$723$	−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	0.841620	−	0.540070i	$-0.181602\pi$
$727$	8.13069	+	8.13069i	0.301551	+	0.301551i	−0.540070	+	0.841620i	$0.681602\pi$
$728$	−0.800411	−	6.03965i	−0.0296652	−	0.223844i
$729$			1.00000i			0.0370370i
$730$	−9.22833	−	4.03777i	−0.341556	−	0.149445i
$731$			46.6826i			1.72662i
$732$	−3.41303	−	9.36054i	−0.126149	−	0.345976i
$733$	−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
$738$	6.58641	−	4.19866i	0.242449	−	0.154555i
$739$	39.4719			1.45200			0.725999	−	0.687696i	$-0.241378\pi$
$739$	39.4719			1.45200			0.725999	+	0.687696i	$0.241378\pi$
$740$	−11.0074	+	1.72077i	−0.404639	+	0.0632566i
$741$	3.04623			0.111906
$742$	3.82951	−	2.44121i	0.140586	−	0.0896196i
$743$	−12.2252	+	12.2252i	−0.448499	+	0.448499i	−0.894855	−	0.446356i	$-0.852721\pi$
$743$	−12.2252	+	12.2252i	−0.448499	+	0.448499i	0.446356	+	0.894855i	$0.352721\pi$
$744$	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
$748$	−51.2595	+	18.6902i	−1.87423	+	0.683380i
$749$			6.73887i			0.246233i
$750$	11.3597	−	10.9980i	0.414799	−	0.401591i
$751$		−	28.9069i		−	1.05483i	−0.849609	−	0.527413i	$-0.823162\pi$
$751$		−	28.9069i		−	1.05483i	0.849609	−	0.527413i	$-0.176838\pi$
$752$	1.11902	−	12.9614i	0.0408066	−	0.472652i
$753$	−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	$0.386705\pi$
$758$	−11.7498	−	18.4318i	−0.426771	−	0.669474i
$759$	−7.81086			−0.283516
$760$	0.485401	−	7.71833i	0.0176073	−	0.279973i
$761$	−6.64641			−0.240932			−0.120466	−	0.992717i	$-0.538439\pi$
$761$	−6.64641			−0.240932			−0.120466	+	0.992717i	$0.538439\pi$
$762$	8.05348	+	12.6334i	0.291747	+	0.457661i
$763$	−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
$768$	−9.20720	−	13.0854i	−0.332236	−	0.472178i
$769$		−	29.3449i		−	1.05820i	−0.848559	−	0.529101i	$-0.822529\pi$
$769$		−	29.3449i		−	1.05820i	0.848559	−	0.529101i	$-0.177471\pi$
$770$	5.62062	−	12.8459i	0.202553	−	0.462935i
$771$		−	21.2329i		−	0.764686i
$772$	30.5717	−	11.1470i	1.10030	−	0.401189i
$773$	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
$778$	−6.15729	+	3.92510i	−0.220749	+	0.140722i
$779$	−6.75359			−0.241973
$780$	−9.00016	−	6.56662i	−0.322257	−	0.235123i
$781$	41.5510			1.48681
$782$	9.66229	−	6.15945i	0.345523	−	0.220261i
$783$	−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	0.829374	−	0.558694i	$-0.188697\pi$
$787$	7.59353	+	7.59353i	0.270680	+	0.270680i	−0.558694	+	0.829374i	$0.688697\pi$
$788$	7.63357	+	20.9358i	0.271935	+	0.745806i
$789$			9.52311i			0.339032i
$790$	46.8629	−	18.3358i	1.66731	−	0.652358i
$791$		−	0.622595i		−	0.0221369i
$792$	14.3791	−	1.90560i	0.510938	−	0.0677126i
$793$	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	$0.00824175\pi$
$798$	0.803735	+	1.26082i	0.0284519	+	0.0446324i
$799$	−17.3016			−0.612086
$800$	−18.0722	+	21.7576i	−0.638949	+	0.769249i
$801$	7.25240			0.256251
$802$	2.65705	+	4.16810i	0.0938237	+	0.147181i
$803$	−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
$808$	28.3673	−	3.75940i	0.997957	−	0.132255i
$809$			47.7205i			1.67776i	0.544313	+	0.838882i	$0.316791\pi$
$809$			47.7205i			1.67776i	−0.544313	+	0.838882i	$0.683209\pi$
$810$	−2.94489	+	1.15223i	−0.103473	+	0.0404853i
$811$			37.3179i			1.31041i	0.755451	+	0.655205i	$0.227418\pi$
$811$			37.3179i			1.31041i	−0.755451	+	0.655205i	$0.772582\pi$
$812$	−0.512195	−	1.40474i	−0.0179745	−	0.0492968i
$813$	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
$818$	−17.6533	+	11.2535i	−0.617235	+	0.393470i
$819$	2.15401			0.0752672
$820$	19.9536	+	14.5584i	0.696812	+	0.508402i
$821$	−0.686380			−0.0239548			−0.0119774	−	0.999928i	$-0.503813\pi$
$821$	−0.686380			−0.0239548			−0.0119774	+	0.999928i	$0.503813\pi$
$822$	−11.8289	+	7.54057i	−0.412579	+	0.263008i
$823$	27.2553	−	27.2553i	0.950059	−	0.950059i	−0.0487521	−	0.998811i	$-0.515524\pi$
$823$	27.2553	−	27.2553i	0.950059	−	0.950059i	0.998811	+	0.0487521i	$0.0155244\pi$
$824$	−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	$0.0313223\pi$
$827$	31.4437	+	31.4437i	1.09341	+	1.09341i	0.0982432	+	0.995162i	$0.468678\pi$
$828$	−2.86192	+	1.04351i	−0.0994587	+	0.0362645i
$829$			0.270718i			0.00940243i	0.999989	+	0.00470122i	$0.00149645\pi$
$829$			0.270718i			0.00940243i	−0.999989	+	0.00470122i	$0.998504\pi$
$830$	−14.2635	+	32.5993i	−0.495095	+	1.13154i
$831$		−	31.1978i		−	1.08224i
$832$	17.2767	+	9.93522i	0.598964	+	0.344442i
$833$	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
$838$	14.4970	+	22.7414i	0.500792	+	0.785589i
$839$	−31.0214			−1.07098			−0.535489	−	0.844542i	$-0.679873\pi$
$839$	−31.0214			−1.07098			−0.535489	+	0.844542i	$0.679873\pi$
$840$	0.343230	−	5.45769i	0.0118426	−	0.188308i
$841$	28.2524			0.974221
$842$	−15.8147	−	24.8085i	−0.545011	−	0.854956i
$843$	−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
$848$	−1.27785	+	14.8010i	−0.0438814	+	0.508267i
$849$		−	16.3632i		−	0.561583i
$850$	30.8958	+	21.4564i	1.05972	+	0.735950i
$851$		−	3.79441i		−	0.130071i
$852$	15.2244	−	5.55110i	0.521580	−	0.190178i
$853$	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	$0.0827035\pi$
$858$	−15.2350	+	9.71191i	−0.520115	+	0.331559i
$859$	−1.69693			−0.0578985			−0.0289492	−	0.999581i	$-0.509216\pi$
$859$	−1.69693			−0.0578985			−0.0289492	+	0.999581i	$0.509216\pi$
$860$	38.7743	−	6.06153i	1.32219	−	0.206697i
$861$	−4.77551			−0.162749
$862$	−18.2815	+	11.6540i	−0.622670	+	0.396935i
$863$	−5.92869	+	5.92869i	−0.201815	+	0.201815i	−0.800777	−	0.598962i	$-0.795580\pi$
$863$	−5.92869	+	5.92869i	−0.201815	+	0.201815i	0.598962	+	0.800777i	$0.295580\pi$
$864$	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
$868$	−4.62699	−	12.6900i	−0.157050	−	0.430725i
$869$		−	81.6068i		−	2.76832i
$870$	−2.50495	−	1.09602i	−0.0849258	−	0.0371585i
$871$		−	21.8617i		−	0.740756i
$872$	−2.71891	−	20.5161i	−0.0920740	−	0.694762i
$873$	−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	$0.326998\pi$
$878$	−18.7430	−	29.4020i	−0.632544	−	0.992269i
$879$	−18.2390			−0.615186
$880$	22.1798	+	40.1491i	0.747680	+	1.35342i
$881$	−29.8130			−1.00443			−0.502213	−	0.864744i	$-0.667481\pi$
$881$	−29.8130			−1.00443			−0.502213	+	0.864744i	$0.667481\pi$
$882$	−4.75306	−	7.45610i	−0.160044	−	0.251060i
$883$	5.56557	−	5.56557i	0.187296	−	0.187296i	−0.607230	−	0.794526i	$-0.707719\pi$
$883$	5.56557	−	5.56557i	0.187296	−	0.187296i	0.794526	+	0.607230i	$0.207719\pi$
$884$	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	0.547905	−	0.836541i	$-0.315426\pi$
$887$	−8.59630	−	8.59630i	−0.288636	−	0.288636i	−0.836541	+	0.547905i	$0.815426\pi$
$888$	0.925715	+	6.98516i	0.0310649	+	0.234406i
$889$		−	9.15994i		−	0.307214i
$890$	8.35643	+	21.3575i	0.280108	+	0.715905i
$891$			5.12822i			0.171802i
$892$	10.5298	+	28.8791i	0.352565	+	0.966943i
$893$	−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
$898$	−39.5334	+	25.2015i	−1.31925	+	0.840984i
$899$	−6.75359			−0.225245
$900$	−6.78638	−	7.34473i	−0.226213	−	0.244824i
$901$	19.7572			0.658207
$902$	33.7766	−	21.5316i	1.12464	−	0.716925i
$903$	−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	$-0.983613\pi$
$907$	−31.6263	−	31.6263i	−1.05013	−	1.05013i	−0.0514592	−	0.998675i	$-0.516387\pi$
$908$	13.2398	−	4.82748i	0.439379	−	0.160206i
$909$			10.1170i			0.335561i
$910$	2.48192	+	6.34331i	0.0822747	+	0.210279i
$911$		−	42.2656i		−	1.40032i	−0.713985	−	0.700161i	$-0.753112\pi$
$911$		−	42.2656i		−	1.40032i	0.713985	−	0.700161i	$-0.246888\pi$
$912$	−4.87302	−	0.420714i	−0.161362	−	0.0139312i
$913$	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
$918$	−4.04398	−	6.34377i	−0.133471	−	0.209376i
$919$	31.2829			1.03193			0.515964	−	0.856610i	$-0.327434\pi$
$919$	31.2829			1.03193			0.515964	+	0.856610i	$0.327434\pi$
$920$	−6.37061	−	7.22567i	−0.210033	−	0.238223i
$921$	2.27072			0.0748227
$922$	−20.5418	−	32.2238i	−0.676508	−	1.06123i
$923$	−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
$928$	4.66687	+	1.46412i	0.153198	+	0.0480621i
$929$		−	22.1050i		−	0.725241i	−0.931937	−	0.362620i	$-0.881882\pi$
$929$		−	22.1050i		−	0.725241i	0.931937	−	0.362620i	$-0.118118\pi$
$930$	−22.6289	−	9.90105i	−0.742029	−	0.324668i
$931$			7.64535i			0.250566i
$932$	1.90084	−	0.693082i	0.0622641	−	0.0227026i
$933$	−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	$0.364975\pi$
$938$	9.04843	−	5.76813i	0.295442	−	0.188336i
$939$	−25.0471			−0.817381
$940$	2.24654	+	14.3706i	0.0732740	+	0.468718i
$941$	25.5264			0.832138			0.416069	−	0.909333i	$-0.363407\pi$
$941$	25.5264			0.832138			0.416069	+	0.909333i	$0.363407\pi$
$942$	−15.2018	+	9.69074i	−0.495302	+	0.315741i
$943$	−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	0.484969	−	0.874531i	$-0.338831\pi$
$947$	−11.9881	−	11.9881i	−0.389562	−	0.389562i	−0.874531	+	0.484969i	$0.838831\pi$
$948$	−10.9024	−	29.9010i	−0.354095	−	0.971138i
$949$		−	7.93545i		−	0.257596i
$950$	1.53425	+	8.50920i	0.0497777	+	0.276075i
$951$		−	11.0160i		−	0.357217i
$952$	12.8968	−	1.70916i	0.417988	−	0.0553943i
$953$	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
$958$	10.4598	+	16.4082i	0.337940	+	0.530125i
$959$	8.57657			0.276952
$960$	13.4905	+	11.7476i	0.435405	+	0.379151i
$961$	−30.0096			−0.968051
$962$	−4.71791	−	7.40097i	−0.152112	−	0.238617i
$963$	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	0.733428	−	0.679767i	$-0.237919\pi$
$967$	1.66866	+	1.66866i	0.0536606	+	0.0536606i	−0.679767	+	0.733428i	$0.737919\pi$
$968$	42.8960	−	5.68483i	1.37873	−	0.182717i
$969$			6.50479i			0.208964i
$970$	1.42307	−	3.25243i	0.0456920	−	0.104429i
$971$			4.79719i			0.153949i	0.997033	+	0.0769745i	$0.0245260\pi$
$971$			4.79719i			0.153949i	−0.997033	+	0.0769745i	$0.975474\pi$
$972$	0.685116	+	1.87899i	0.0219751	+	0.0602687i
$973$	−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	$0.441461\pi$
$978$	22.0673	−	14.0673i	0.705634	−	0.449823i
$979$	37.1919			1.18866
$980$	16.4807	−	22.5884i	0.526458	−	0.721559i
$981$	7.31695			0.233612
$982$	34.4540	−	21.9635i	1.09947	−	0.700884i
$983$	30.9151	−	30.9151i	0.986038	−	0.986038i	−0.0138655	−	0.999904i	$-0.504414\pi$
$983$	30.9151	−	30.9151i	0.986038	−	0.986038i	0.999904	+	0.0138655i	$0.00441368\pi$
$984$	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
$988$	5.72384	−	2.08702i	0.182100	−	0.0663969i
$989$			13.3661i			0.425017i
$990$	−15.1020	+	5.90889i	−0.479974	+	0.187797i
$991$		−	26.5873i		−	0.844575i	−0.906462	−	0.422287i	$-0.861227\pi$
$991$		−	26.5873i		−	0.844575i	0.906462	−	0.422287i	$-0.138773\pi$
$992$	42.1589	+	13.2264i	1.33855	+	0.419937i
$993$	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	$0.267634\pi$
$998$	9.53021	+	14.9500i	0.301674	+	0.473234i
$999$	−2.49122			−0.0788187

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.760198 + 1.19252i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-0.844199 + 1.81310i) q^{4} +(0.432320 - 2.19388i) q^{5} +(-1.38078 - 0.305697i) q^{6} +(0.611393 + 0.611393i) q^{7} +(-2.80391 + 0.371591i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.760198 + 1.19252i) 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} +(-2.80391 + 0.371591i) q^{8} -1.00000i q^{9} +(2.94489 - 1.15223i) q^{10} -5.12822i q^{11} +(-0.685116 - 1.87899i) 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} +(1.19252 - 0.760198i) q^{18} -1.22279 q^{19} +(3.61275 + 2.63591i) q^{20} -0.864641 q^{21} +(6.11549 - 3.89846i) 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} +(-1.62465 + 0.592379i) q^{28} +0.864641i q^{29} +(-1.26760 + 2.89710i) q^{30} +7.81086i q^{31} +(1.69333 - 5.39747i) 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} +(-0.929560 - 1.45820i) q^{38} -2.49122 q^{39} +(-0.396963 + 6.31209i) q^{40} +5.52311 q^{41} +(-0.657298 - 1.03110i) 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} +(3.98518 + 0.344061i) q^{48} -6.25240i q^{49} +(-1.25472 - 6.95886i) q^{50} -5.31965i q^{51} +(-4.68098 + 1.70677i) 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} +(-1.03110 + 0.657298i) q^{58} -0.528636 q^{59} +(-4.41847 + 0.690733i) q^{60} +4.98168 q^{61} +(-9.31460 + 5.93780i) 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} +(-3.64457 - 9.99558i) q^{68} -1.52311i q^{69} +(2.50495 + 1.09602i) q^{70} +8.10243i q^{71} +(0.371591 + 2.80391i) 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} +(-1.89382 - 2.97082i) q^{78} +15.9133 q^{79} +(-7.82905 + 4.32505i) q^{80} -1.00000 q^{81} +(4.19866 + 6.58641i) 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} +(1.90560 + 14.3791i) q^{88} +7.25240i q^{89} +(-1.15223 - 2.94489i) q^{90} +2.15401i q^{91} +(-1.04351 - 2.86192i) 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} +(7.45610 - 4.75306i) 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

Introduction

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