LMFDB - Embedded newform 429.2.bd.b.175.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(76,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 7]))

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

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

chi := DirichletCharacter("429.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bd (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			175.2
Character	$\chi$	$=$	429.175
Dual form			429.2.bd.b.76.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.02512 + 0.542629i) q^{2} +(0.500000 - 0.866025i) q^{3} +(2.07462 - 1.19778i) q^{4} +(1.41467 - 1.41467i) q^{5} +(-0.542629 + 2.02512i) q^{6} +(-0.256787 - 0.0688060i) q^{7} +(-0.586415 + 0.586415i) q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-2.02512 + 0.542629i) q^{2} +(0.500000 - 0.866025i) q^{3} +(2.07462 - 1.19778i) q^{4} +(1.41467 - 1.41467i) q^{5} +(-0.542629 + 2.02512i) q^{6} +(-0.256787 - 0.0688060i) q^{7} +(-0.586415 + 0.586415i) q^{8} +(-0.500000 - 0.866025i) q^{9} +(-2.09724 + 3.63252i) q^{10} +(-0.380826 - 3.29469i) q^{11} -2.39556i q^{12} +(3.57394 - 0.476385i) q^{13} +0.557361 q^{14} +(-0.517806 - 1.93248i) q^{15} +(-1.52621 + 2.64347i) q^{16} +(-0.0704496 - 0.122022i) q^{17} +(1.48249 + 1.48249i) q^{18} +(-0.589954 + 2.20174i) q^{19} +(1.24043 - 4.62937i) q^{20} +(-0.187981 + 0.187981i) q^{21} +(2.55901 + 6.46549i) q^{22} +(-6.13195 - 3.54029i) q^{23} +(0.214643 + 0.801057i) q^{24} +0.997410i q^{25} +(-6.97916 + 2.90406i) q^{26} -1.00000 q^{27} +(-0.615150 + 0.164829i) q^{28} +(-4.96680 - 2.86759i) q^{29} +(2.09724 + 3.63252i) q^{30} +(3.11989 - 3.11989i) q^{31} +(2.08561 - 7.78362i) q^{32} +(-3.04370 - 1.31754i) q^{33} +(0.208882 + 0.208882i) q^{34} +(-0.460608 + 0.265932i) q^{35} +(-2.07462 - 1.19778i) q^{36} +(4.30965 - 1.15477i) q^{37} -4.77891i q^{38} +(1.37441 - 3.33332i) q^{39} +1.65917i q^{40} +(8.30041 - 2.22409i) q^{41} +(0.278681 - 0.482689i) q^{42} +(-3.30981 - 5.73276i) q^{43} +(-4.73638 - 6.37907i) q^{44} +(-1.93248 - 0.517806i) q^{45} +(14.3390 + 3.84213i) q^{46} +(3.24615 + 3.24615i) q^{47} +(1.52621 + 2.64347i) q^{48} +(-6.00097 - 3.46466i) q^{49} +(-0.541224 - 2.01987i) q^{50} -0.140899 q^{51} +(6.84395 - 5.26911i) q^{52} +5.81491 q^{53} +(2.02512 - 0.542629i) q^{54} +(-5.19965 - 4.12216i) q^{55} +(0.190933 - 0.110235i) q^{56} +(1.61178 + 1.61178i) q^{57} +(11.6144 + 3.11207i) q^{58} +(2.01541 - 7.52163i) q^{59} +(-3.38893 - 3.38893i) q^{60} +(2.54936 - 1.47187i) q^{61} +(-4.62521 + 8.01109i) q^{62} +(0.0688060 + 0.256787i) q^{63} +10.7897i q^{64} +(4.38202 - 5.72988i) q^{65} +(6.87879 + 1.01658i) q^{66} +(-0.0863596 - 0.322298i) q^{67} +(-0.292312 - 0.168766i) q^{68} +(-6.13195 + 3.54029i) q^{69} +(0.788483 - 0.788483i) q^{70} +(-8.46578 - 2.26840i) q^{71} +(0.801057 + 0.214643i) q^{72} +(-1.72404 + 1.72404i) q^{73} +(-8.10095 + 4.67708i) q^{74} +(0.863782 + 0.498705i) q^{75} +(1.41327 + 5.27439i) q^{76} +(-0.128903 + 0.872237i) q^{77} +(-0.974588 + 7.49616i) q^{78} -5.78756i q^{79} +(1.58056 + 5.89871i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-15.6025 + 9.00809i) q^{82} +(6.11997 + 6.11997i) q^{83} +(-0.164829 + 0.615150i) q^{84} +(-0.272285 - 0.0729584i) q^{85} +(9.81353 + 9.81353i) q^{86} +(-4.96680 + 2.86759i) q^{87} +(2.15538 + 1.70873i) q^{88} +(-16.7450 + 4.48680i) q^{89} +4.19448 q^{90} +(-0.950521 - 0.123579i) q^{91} -16.9619 q^{92} +(-1.14196 - 4.26185i) q^{93} +(-8.33531 - 4.81239i) q^{94} +(2.28014 + 3.94933i) q^{95} +(-5.69800 - 5.69800i) q^{96} +(18.6214 + 4.98959i) q^{97} +(14.0327 + 3.76006i) q^{98} +(-2.66287 + 1.97715i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 28 q^{3} - 4 q^{5} - 28 q^{9}+O(q^{10}) $ 56 * q + 28 * q^3 - 4 * q^5 - 28 * q^9	$ 56 q + 28 q^{3} - 4 q^{5} - 28 q^{9} - 4 q^{11} - 24 q^{14} - 8 q^{15} + 4 q^{16} + 80 q^{20} - 10 q^{22} - 12 q^{23} + 40 q^{26} - 56 q^{27} - 12 q^{31} - 8 q^{33} - 16 q^{34} - 12 q^{37} - 12 q^{42} + 24 q^{44} - 4 q^{45} - 40 q^{47} - 4 q^{48} + 24 q^{49} - 88 q^{53} - 18 q^{55} + 72 q^{56} + 40 q^{58} + 8 q^{59} + 52 q^{60} - 20 q^{66} - 4 q^{67} - 12 q^{69} + 40 q^{70} - 24 q^{71} + 12 q^{75} - 4 q^{78} - 188 q^{80} - 28 q^{81} - 12 q^{82} + 32 q^{86} + 18 q^{88} - 16 q^{89} + 28 q^{91} - 96 q^{92} - 12 q^{93} - 28 q^{97} - 4 q^{99}+O(q^{100}) $ 56 * q + 28 * q^3 - 4 * q^5 - 28 * q^9 - 4 * q^11 - 24 * q^14 - 8 * q^15 + 4 * q^16 + 80 * q^20 - 10 * q^22 - 12 * q^23 + 40 * q^26 - 56 * q^27 - 12 * q^31 - 8 * q^33 - 16 * q^34 - 12 * q^37 - 12 * q^42 + 24 * q^44 - 4 * q^45 - 40 * q^47 - 4 * q^48 + 24 * q^49 - 88 * q^53 - 18 * q^55 + 72 * q^56 + 40 * q^58 + 8 * q^59 + 52 * q^60 - 20 * q^66 - 4 * q^67 - 12 * q^69 + 40 * q^70 - 24 * q^71 + 12 * q^75 - 4 * q^78 - 188 * q^80 - 28 * q^81 - 12 * q^82 + 32 * q^86 + 18 * q^88 - 16 * q^89 + 28 * q^91 - 96 * q^92 - 12 * q^93 - 28 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$-1$	$1$

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 $

$2$	−2.02512	+	0.542629i	−1.43198	+	0.383697i	−0.889716	−	0.456514i	$-0.849098\pi$
$2$	−2.02512	+	0.542629i	−1.43198	+	0.383697i	−0.542260	+	0.840211i	$0.682431\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	2.07462	−	1.19778i	1.03731	−	0.598890i
$5$	1.41467	−	1.41467i	0.632660	−	0.632660i	−0.316074	−	0.948734i	$-0.602365\pi$
$5$	1.41467	−	1.41467i	0.632660	−	0.632660i	0.948734	+	0.316074i	$0.102365\pi$
$6$	−0.542629	+	2.02512i	−0.221528	+	0.826752i
$7$	−0.256787	−	0.0688060i	−0.0970565	−	0.0260062i	0.209964	−	0.977709i	$-0.432665\pi$
$7$	−0.256787	−	0.0688060i	−0.0970565	−	0.0260062i	−0.307020	+	0.951703i	$0.599332\pi$
$8$	−0.586415	+	0.586415i	−0.207329	+	0.207329i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−2.09724	+	3.63252i	−0.663205	+	1.14870i
$11$	−0.380826	−	3.29469i	−0.114823	−	0.993386i
$11$	−0.380826	−	3.29469i	−0.114823	−	0.993386i
$12$		−	2.39556i		−	0.691539i
$13$	3.57394	−	0.476385i	0.991233	−	0.132126i
$13$	3.57394	−	0.476385i	0.991233	−	0.132126i
$14$	0.557361			0.148961
$15$	−0.517806	−	1.93248i	−0.133697	−	0.498963i
$16$	−1.52621	+	2.64347i	−0.381551	+	0.660866i
$17$	−0.0704496	−	0.122022i	−0.0170865	−	0.0295948i	0.857356	−	0.514724i	$-0.172106\pi$
$17$	−0.0704496	−	0.122022i	−0.0170865	−	0.0295948i	−0.874442	+	0.485130i	$0.838772\pi$
$18$	1.48249	+	1.48249i	0.349427	+	0.349427i
$19$	−0.589954	+	2.20174i	−0.135345	+	0.505113i	0.864652	+	0.502372i	$0.167539\pi$
$19$	−0.589954	+	2.20174i	−0.135345	+	0.505113i	−0.999996	+	0.00274114i	$0.999127\pi$
$20$	1.24043	−	4.62937i	0.277370	−	1.03516i
$21$	−0.187981	+	0.187981i	−0.0410209	+	0.0410209i
$22$	2.55901	+	6.46549i	0.545584	+	1.37845i
$23$	−6.13195	−	3.54029i	−1.27860	−	0.738201i	−0.302010	−	0.953305i	$-0.597658\pi$
$23$	−6.13195	−	3.54029i	−1.27860	−	0.738201i	−0.976591	+	0.215104i	$0.930991\pi$
$24$	0.214643	+	0.801057i	0.0438138	+	0.163515i
$25$			0.997410i			0.199482i
$26$	−6.97916	+	2.90406i	−1.36873	+	0.569534i
$27$	−1.00000			−0.192450
$28$	−0.615150	+	0.164829i	−0.116252	+	0.0311497i
$29$	−4.96680	−	2.86759i	−0.922313	−	0.532497i	−0.0379404	−	0.999280i	$-0.512080\pi$
$29$	−4.96680	−	2.86759i	−0.922313	−	0.532497i	−0.884372	+	0.466783i	$0.845413\pi$
$30$	2.09724	+	3.63252i	0.382902	+	0.663205i
$31$	3.11989	−	3.11989i	0.560348	−	0.560348i	−0.369058	−	0.929406i	$-0.620320\pi$
$31$	3.11989	−	3.11989i	0.560348	−	0.560348i	0.929406	+	0.369058i	$0.120320\pi$
$32$	2.08561	−	7.78362i	0.368688	−	1.37596i
$33$	−3.04370	−	1.31754i	−0.529840	−	0.229354i
$34$	0.208882	+	0.208882i	0.0358230	+	0.0358230i
$35$	−0.460608	+	0.265932i	−0.0778569	+	0.0449507i
$36$	−2.07462	−	1.19778i	−0.345769	−	0.199630i
$37$	4.30965	−	1.15477i	0.708502	−	0.189842i	0.113466	−	0.993542i	$-0.463805\pi$
$37$	4.30965	−	1.15477i	0.708502	−	0.189842i	0.595036	+	0.803699i	$0.297138\pi$
$38$		−	4.77891i		−	0.775242i
$39$	1.37441	−	3.33332i	0.220082	−	0.533758i
$40$			1.65917i			0.262338i
$41$	8.30041	−	2.22409i	1.29631	−	0.347344i	0.456254	−	0.889850i	$-0.349191\pi$
$41$	8.30041	−	2.22409i	1.29631	−	0.347344i	0.840052	+	0.542506i	$0.182524\pi$
$42$	0.278681	−	0.482689i	0.0430014	−	0.0744806i
$43$	−3.30981	−	5.73276i	−0.504741	−	0.874238i	−0.999985	−	0.00548351i	$-0.998255\pi$
$43$	−3.30981	−	5.73276i	−0.504741	−	0.874238i	0.495244	−	0.868754i	$-0.335079\pi$
$44$	−4.73638	−	6.37907i	−0.714036	−	0.961681i
$45$	−1.93248	−	0.517806i	−0.288077	−	0.0771899i
$46$	14.3390	+	3.84213i	2.11417	+	0.566491i
$47$	3.24615	+	3.24615i	0.473500	+	0.473500i	0.903045	−	0.429545i	$-0.141326\pi$
$47$	3.24615	+	3.24615i	0.473500	+	0.473500i	−0.429545	+	0.903045i	$0.641326\pi$
$48$	1.52621	+	2.64347i	0.220289	+	0.381551i
$49$	−6.00097	−	3.46466i	−0.857282	−	0.494952i
$50$	−0.541224	−	2.01987i	−0.0765406	−	0.285653i
$51$	−0.140899			−0.0197298
$52$	6.84395	−	5.26911i	0.949085	−	0.730695i
$53$	5.81491			0.798739			0.399370	−	0.916790i	$-0.369229\pi$
$53$	5.81491			0.798739			0.399370	+	0.916790i	$0.369229\pi$
$54$	2.02512	−	0.542629i	0.275584	−	0.0738425i
$55$	−5.19965	−	4.12216i	−0.701120	−	0.555832i
$56$	0.190933	−	0.110235i	0.0255145	−	0.0147308i
$57$	1.61178	+	1.61178i	0.213486	+	0.213486i
$58$	11.6144	+	3.11207i	1.52505	+	0.408635i
$59$	2.01541	−	7.52163i	0.262384	−	0.979232i	−0.701447	−	0.712721i	$-0.747462\pi$
$59$	2.01541	−	7.52163i	0.262384	−	0.979232i	0.963832	−	0.266511i	$-0.0858709\pi$
$60$	−3.38893	−	3.38893i	−0.437509	−	0.437509i
$61$	2.54936	−	1.47187i	0.326412	−	0.188454i	−0.327835	−	0.944735i	$-0.606319\pi$
$61$	2.54936	−	1.47187i	0.326412	−	0.188454i	0.654247	+	0.756281i	$0.272986\pi$
$62$	−4.62521	+	8.01109i	−0.587402	+	1.01741i
$63$	0.0688060	+	0.256787i	0.00866874	+	0.0323522i
$64$			10.7897i			1.34871i
$65$	4.38202	−	5.72988i	0.543523	−	0.710704i
$66$	6.87879	+	1.01658i	0.846720	+	0.125132i
$67$	−0.0863596	−	0.322298i	−0.0105505	−	0.0393750i	0.960450	−	0.278453i	$-0.0898216\pi$
$67$	−0.0863596	−	0.322298i	−0.0105505	−	0.0393750i	−0.971000	+	0.239078i	$0.923155\pi$
$68$	−0.292312	−	0.168766i	−0.0354480	−	0.0204659i
$69$	−6.13195	+	3.54029i	−0.738201	+	0.426200i
$70$	0.788483	−	0.788483i	0.0942418	−	0.0942418i
$71$	−8.46578	−	2.26840i	−1.00470	−	0.269209i	−0.281289	−	0.959623i	$-0.590762\pi$
$71$	−8.46578	−	2.26840i	−1.00470	−	0.269209i	−0.723415	+	0.690414i	$0.757428\pi$
$72$	0.801057	+	0.214643i	0.0944055	+	0.0252959i
$73$	−1.72404	+	1.72404i	−0.201784	+	0.201784i	−0.800764	−	0.598980i	$-0.795573\pi$
$73$	−1.72404	+	1.72404i	−0.201784	+	0.201784i	0.598980	+	0.800764i	$0.295573\pi$
$74$	−8.10095	+	4.67708i	−0.941716	+	0.543700i
$75$	0.863782	+	0.498705i	0.0997410	+	0.0575855i
$76$	1.41327	+	5.27439i	0.162113	+	0.605015i
$77$	−0.128903	+	0.872237i	−0.0146898	+	0.0994007i
$78$	−0.974588	+	7.49616i	−0.110350	+	0.848773i
$79$		−	5.78756i		−	0.651151i	−0.945516	−	0.325576i	$-0.894442\pi$
$79$		−	5.78756i		−	0.651151i	0.945516	−	0.325576i	$-0.105558\pi$
$80$	1.58056	+	5.89871i	0.176712	+	0.659496i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−15.6025	+	9.00809i	−1.72300	+	0.994777i
$83$	6.11997	+	6.11997i	0.671754	+	0.671754i	0.958120	−	0.286366i	$-0.0924473\pi$
$83$	6.11997	+	6.11997i	0.671754	+	0.671754i	−0.286366	+	0.958120i	$0.592447\pi$
$84$	−0.164829	+	0.615150i	−0.0179843	+	0.0671183i
$85$	−0.272285	−	0.0729584i	−0.0295334	−	0.00791345i
$86$	9.81353	+	9.81353i	1.05822	+	1.05822i
$87$	−4.96680	+	2.86759i	−0.532497	+	0.307438i
$88$	2.15538	+	1.70873i	0.229764	+	0.182151i
$89$	−16.7450	+	4.48680i	−1.77496	+	0.475600i	−0.989651	−	0.143498i	$-0.954165\pi$
$89$	−16.7450	+	4.48680i	−1.77496	+	0.475600i	−0.785314	+	0.619098i	$0.787498\pi$
$90$	4.19448			0.442137
$91$	−0.950521	−	0.123579i	−0.0996417	−	0.0129546i
$92$	−16.9619			−1.76840
$93$	−1.14196	−	4.26185i	−0.118416	−	0.441933i
$94$	−8.33531	−	4.81239i	−0.859722	−	0.496361i
$95$	2.28014	+	3.94933i	0.233938	+	0.405192i
$96$	−5.69800	−	5.69800i	−0.581550	−	0.581550i
$97$	18.6214	+	4.98959i	1.89072	+	0.506616i	0.998484	+	0.0550396i	$0.0175285\pi$
$97$	18.6214	+	4.98959i	1.89072	+	0.506616i	0.892232	+	0.451576i	$0.149138\pi$
$98$	14.0327	+	3.76006i	1.41752	+	0.379823i
$99$	−2.66287	+	1.97715i	−0.267629	+	0.198711i
$100$	1.19468	+	2.06924i	0.119468	+	0.206924i
$101$	−5.86539	+	10.1592i	−0.583628	+	1.01087i	0.411417	+	0.911447i	$0.365034\pi$
$101$	−5.86539	+	10.1592i	−0.583628	+	1.01087i	−0.995045	+	0.0994266i	$0.968299\pi$
$102$	0.285338	−	0.0764561i	0.0282527	−	0.00757028i
$103$		−	1.23863i		−	0.122046i	−0.998136	−	0.0610230i	$-0.980564\pi$
$103$		−	1.23863i		−	0.122046i	0.998136	−	0.0610230i	$-0.0194363\pi$
$104$	−1.81645	+	2.37517i	−0.178118	+	0.232905i
$105$			0.531864i			0.0519046i
$106$	−11.7759	+	3.15534i	−1.14378	+	0.306474i
$107$	11.7464	+	6.78180i	1.13557	+	0.655621i	0.945329	−	0.326117i	$-0.105740\pi$
$107$	11.7464	+	6.78180i	1.13557	+	0.655621i	0.190239	+	0.981738i	$0.439074\pi$
$108$	−2.07462	+	1.19778i	−0.199630	+	0.115256i
$109$	−3.88405	−	3.88405i	−0.372025	−	0.372025i	0.496189	−	0.868214i	$-0.334732\pi$
$109$	−3.88405	−	3.88405i	−0.372025	−	0.372025i	−0.868214	+	0.496189i	$0.834732\pi$
$110$	12.7667	+	5.52638i	1.21726	+	0.526920i
$111$	1.15477	−	4.30965i	0.109606	−	0.409054i
$112$	0.573796	−	0.573796i	0.0542187	−	0.0542187i
$113$	4.06660	+	7.04356i	0.382554	+	0.662603i	0.991427	−	0.130665i	$-0.0417113\pi$
$113$	4.06660	+	7.04356i	0.382554	+	0.662603i	−0.608873	+	0.793268i	$0.708378\pi$
$114$	−4.13866	−	2.38945i	−0.387621	−	0.223793i
$115$	−13.6830	+	3.66636i	−1.27595	+	0.341890i
$116$	−13.7390			−1.27563
$117$	−2.19953	−	2.85693i	−0.203347	−	0.264123i
$118$			16.3258i			1.50291i
$119$	0.00969471	+	0.0361811i	0.000888713	+	0.00331672i
$120$	1.43688	+	0.829584i	0.131169	+	0.0757303i
$121$	−10.7099	+	2.50941i	−0.973631	+	0.228128i
$122$	−4.36408	+	4.36408i	−0.395105	+	0.395105i
$123$	2.22409	−	8.30041i	0.200539	−	0.748423i
$124$	2.73563	−	10.2095i	0.245667	−	0.916841i
$125$	8.48436	+	8.48436i	0.758865	+	0.758865i
$126$	−0.278681	−	0.482689i	−0.0248269	−	0.0430014i
$127$	−7.88260	+	13.6531i	−0.699468	+	1.21151i	0.269183	+	0.963089i	$0.413246\pi$
$127$	−7.88260	+	13.6531i	−0.699468	+	1.21151i	−0.968651	+	0.248425i	$0.920087\pi$
$128$	−1.68356	−	6.28312i	−0.148807	−	0.555355i
$129$	−6.61962			−0.582825
$130$	−5.76492	+	13.9815i	−0.505617	+	1.22626i
$131$			18.0714i			1.57891i	0.613809	+	0.789454i	$0.289636\pi$
$131$			18.0714i			1.57891i	−0.613809	+	0.789454i	$0.710364\pi$
$132$	−7.89262	+	0.912293i	−0.686965	+	0.0794049i
$133$	0.302985	−	0.524786i	0.0262722	−	0.0455047i
$134$	0.349777	+	0.605832i	0.0302161	+	0.0523359i
$135$	−1.41467	+	1.41467i	−0.121756	+	0.121756i
$136$	0.112868	+	0.0302430i	0.00967839	+	0.00259332i
$137$	3.70530	−	13.8284i	0.316565	−	1.18144i	−0.605959	−	0.795496i	$-0.707210\pi$
$137$	3.70530	−	13.8284i	0.316565	−	1.18144i	0.922524	−	0.385940i	$-0.126123\pi$
$138$	10.4969	−	10.4969i	0.893554	−	0.893554i
$139$	2.79096	−	1.61136i	0.236726	−	0.136674i	−0.376945	−	0.926236i	$-0.623025\pi$
$139$	2.79096	−	1.61136i	0.236726	−	0.136674i	0.613671	+	0.789562i	$0.289692\pi$
$140$	−0.637056	+	1.10341i	−0.0538410	+	0.0932554i
$141$	4.43433	−	1.18817i	0.373438	−	0.100062i
$142$	18.3751			1.54201
$143$	−2.93059	−	11.5936i	−0.245068	−	0.969506i
$144$	3.05241			0.254368
$145$	−11.0831	+	2.96970i	−0.920400	+	0.246621i
$146$	2.55587	−	4.42690i	0.211526	−	0.366373i
$147$	−6.00097	+	3.46466i	−0.494952	+	0.285761i
$148$	7.55771	−	7.55771i	0.621240	−	0.621240i
$149$	−1.63076	+	6.08609i	−0.133597	+	0.498592i	−1.00000		0.000754621i	$-0.999760\pi$
$149$	−1.63076	+	6.08609i	−0.133597	+	0.498592i	0.866402	+	0.499346i	$0.166426\pi$
$150$	−2.01987	−	0.541224i	−0.164922	−	0.0441907i
$151$	8.31269	−	8.31269i	0.676477	−	0.676477i	−0.282724	−	0.959201i	$-0.591238\pi$
$151$	8.31269	−	8.31269i	0.676477	−	0.676477i	0.959201	+	0.282724i	$0.0912381\pi$
$152$	−0.945174	−	1.63709i	−0.0766637	−	0.132785i
$153$	−0.0704496	+	0.122022i	−0.00569552	+	0.00986492i
$154$	−0.212258	−	1.83633i	−0.0171042	−	0.147976i
$155$		−	8.82723i		−	0.709020i
$156$	−1.14121	−	8.56159i	−0.0913699	−	0.685476i
$157$	20.2360			1.61500			0.807502	−	0.589864i	$-0.200819\pi$
$157$	20.2360			1.61500			0.807502	+	0.589864i	$0.200819\pi$
$158$	3.14050	+	11.7205i	0.249845	+	0.932433i
$159$	2.90746	−	5.03586i	0.230576	−	0.399370i
$160$	−8.06080	−	13.9617i	−0.637262	−	1.10377i
$161$	1.33102	+	1.33102i	0.104899	+	0.104899i
$162$	0.542629	−	2.02512i	0.0426330	−	0.159109i
$163$	−0.415061	+	1.54903i	−0.0325101	+	0.121329i	−0.980274	−	0.197643i	$-0.936671\pi$
$163$	−0.415061	+	1.54903i	−0.0325101	+	0.121329i	0.947764	+	0.318973i	$0.103338\pi$
$164$	14.5562	−	14.5562i	1.13665	−	1.13665i
$165$	−6.16972	+	2.44195i	−0.480312	+	0.190105i
$166$	−15.7146	−	9.07281i	−1.21969	−	0.704186i
$167$	1.42829	+	5.33046i	0.110525	+	0.412483i	0.998913	−	0.0466088i	$-0.0148414\pi$
$167$	1.42829	+	5.33046i	0.110525	+	0.412483i	−0.888389	+	0.459092i	$0.848175\pi$
$168$		−	0.220470i		−	0.0170096i
$169$	12.5461	−	3.40515i	0.965086	−	0.261934i
$170$	0.590999			0.0453275
$171$	2.20174	−	0.589954i	0.168371	−	0.0451149i
$172$	−13.7332	−	7.92885i	−1.04714	−	0.604569i
$173$	7.05523	+	12.2200i	0.536399	+	0.929071i	0.999094	+	0.0425534i	$0.0135493\pi$
$173$	7.05523	+	12.2200i	0.536399	+	0.929071i	−0.462695	+	0.886518i	$0.653117\pi$
$174$	8.50234	−	8.50234i	0.644561	−	0.644561i
$175$	0.0686277	−	0.256122i	0.00518777	−	0.0193610i
$176$	9.29062	+	4.02167i	0.700306	+	0.303145i
$177$	−5.50621	−	5.50621i	−0.413872	−	0.413872i
$178$	31.4759	−	18.1726i	2.35922	−	1.36210i
$179$	−16.7426	−	9.66636i	−1.25140	−	0.722497i	−0.280014	−	0.959996i	$-0.590339\pi$
$179$	−16.7426	−	9.66636i	−1.25140	−	0.722497i	−0.971388	+	0.237498i	$0.923673\pi$
$180$	−4.62937	+	1.24043i	−0.345053	+	0.0924565i
$181$			11.6791i			0.868102i	0.900888	+	0.434051i	$0.142916\pi$
$181$			11.6791i			0.868102i	−0.900888	+	0.434051i	$0.857084\pi$
$182$	1.99198	−	0.265519i	0.147655	−	0.0196816i
$183$		−	2.94375i		−	0.217608i
$184$	5.67194	−	1.51979i	0.418141	−	0.112041i
$185$	4.46312	−	7.73035i	0.328135	−	0.568347i
$186$	4.62521	+	8.01109i	0.339137	+	0.587402i
$187$	−0.375197	+	0.278579i	−0.0274371	+	0.0203717i
$188$	10.6227	+	2.84634i	0.774740	+	0.207591i
$189$	0.256787	+	0.0688060i	0.0186785	+	0.00500490i
$190$	−6.76059	−	6.76059i	−0.490465	−	0.490465i
$191$	0.111768	+	0.193588i	0.00808724	+	0.0140075i	0.870041	−	0.492980i	$-0.164092\pi$
$191$	0.111768	+	0.193588i	0.00808724	+	0.0140075i	−0.861953	+	0.506987i	$0.830759\pi$
$192$	9.34411	+	5.39483i	0.674353	+	0.389338i
$193$	−0.995595	−	3.71561i	−0.0716645	−	0.267456i	0.920792	−	0.390054i	$-0.127544\pi$
$193$	−0.995595	−	3.71561i	−0.0716645	−	0.267456i	−0.992456	+	0.122599i	$0.960877\pi$
$194$	−40.4181			−2.90185
$195$	−2.77121	−	6.65988i	−0.198451	−	0.476924i
$196$	−16.5996			−1.18569
$197$	15.4513	−	4.14017i	1.10086	−	0.294975i	0.337746	−	0.941237i	$-0.390335\pi$
$197$	15.4513	−	4.14017i	1.10086	−	0.294975i	0.763115	+	0.646262i	$0.223669\pi$
$198$	4.31977	−	5.44892i	0.306993	−	0.387238i
$199$	0.578892	−	0.334224i	0.0410366	−	0.0236925i	−0.479341	−	0.877629i	$-0.659124\pi$
$199$	0.578892	−	0.334224i	0.0410366	−	0.0236925i	0.520378	+	0.853936i	$0.325791\pi$
$200$	−0.584896	−	0.584896i	−0.0413584	−	0.0413584i
$201$	−0.322298	−	0.0863596i	−0.0227332	−	0.00609134i
$202$	6.36547	−	23.7563i	0.447873	−	1.67148i
$203$	1.07811	+	1.07811i	0.0756682	+	0.0756682i
$204$	−0.292312	+	0.168766i	−0.0204659	+	0.0118160i
$205$	8.59600	−	14.8887i	0.600370	−	1.03987i
$206$	0.672118	+	2.50838i	0.0468287	+	0.174767i
$207$			7.08057i			0.492134i
$208$	−4.19526	+	10.1747i	−0.290889	+	0.705485i
$209$	7.47871	+	1.10523i	0.517313	+	0.0764506i
$210$	−0.288605	−	1.07709i	−0.0199156	−	0.0743262i
$211$	2.98094	+	1.72105i	0.205216	+	0.118482i	0.599086	−	0.800684i	$-0.295531\pi$
$211$	2.98094	+	1.72105i	0.205216	+	0.118482i	−0.393870	+	0.919166i	$0.628864\pi$
$212$	12.0637	−	6.96498i	0.828539	−	0.478357i
$213$	−6.19738	+	6.19738i	−0.424638	+	0.424638i
$214$	−27.4679	−	7.36000i	−1.87767	−	0.503120i
$215$	−12.7923	−	3.42768i	−0.872425	−	0.233766i
$216$	0.586415	−	0.586415i	0.0399005	−	0.0399005i
$217$	−1.01581	+	0.586481i	−0.0689580	+	0.0398129i
$218$	9.97328	+	5.75808i	0.675476	+	0.389986i
$219$	0.631042	+	2.35508i	0.0426419	+	0.159142i
$220$	−15.7247	−	2.32386i	−1.06016	−	0.156675i
$221$	−0.309913	−	0.402540i	−0.0208470	−	0.0270777i
$222$			9.35417i			0.627811i
$223$	−1.31722	−	4.91594i	−0.0882076	−	0.329195i	0.907695	−	0.419631i	$-0.137841\pi$
$223$	−1.31722	−	4.91594i	−0.0882076	−	0.329195i	−0.995902	+	0.0904359i	$0.971174\pi$
$224$	−1.07112	+	1.85523i	−0.0715671	+	0.123958i
$225$	0.863782	−	0.498705i	0.0575855	−	0.0332470i
$226$	−12.0574	−	12.0574i	−0.802047	−	0.802047i
$227$	0.293007	−	1.09352i	0.0194476	−	0.0725794i	−0.955520	−	0.294926i	$-0.904705\pi$
$227$	0.293007	−	1.09352i	0.0194476	−	0.0725794i	0.974968	+	0.222347i	$0.0713717\pi$
$228$	5.27439	+	1.41327i	0.349305	+	0.0935961i
$229$	4.07220	+	4.07220i	0.269098	+	0.269098i	0.828737	−	0.559638i	$-0.189060\pi$
$229$	4.07220	+	4.07220i	0.269098	+	0.269098i	−0.559638	+	0.828737i	$0.689060\pi$
$230$	25.7203	−	14.8496i	1.69595	−	0.979156i
$231$	0.690928	+	0.547752i	0.0454597	+	0.0360394i
$232$	4.59420	−	1.23101i	0.301624	−	0.0808200i
$233$	−1.62821			−0.106667			−0.0533337	−	0.998577i	$-0.516985\pi$
$233$	−1.62821			−0.106667			−0.0533337	+	0.998577i	$0.516985\pi$
$234$	6.00457	+	4.59210i	0.392531	+	0.300195i
$235$	9.18448			0.599130
$236$	−4.82804	−	18.0185i	−0.314279	−	1.17290i
$237$	−5.01217	−	2.89378i	−0.325576	−	0.187971i
$238$	−0.0392659	−	0.0680106i	−0.00254523	−	0.00440847i
$239$	−18.7321	−	18.7321i	−1.21168	−	1.21168i	−0.970475	−	0.241202i	$-0.922458\pi$
$239$	−18.7321	−	18.7321i	−1.21168	−	1.21168i	−0.241202	−	0.970475i	$-0.577542\pi$
$240$	5.89871	+	1.58056i	0.380760	+	0.102024i
$241$	17.0050	+	4.55648i	1.09539	+	0.293508i	0.760885	−	0.648886i	$-0.224765\pi$
$241$	17.0050	+	4.55648i	1.09539	+	0.293508i	0.334503	+	0.942395i	$0.391432\pi$
$242$	20.3272	−	10.8934i	1.30668	−	0.700253i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	3.52596	−	6.10714i	0.225726	−	0.390970i
$245$	−13.3908	+	3.58804i	−0.855505	+	0.229232i
$246$			18.0162i			1.14867i
$247$	−1.05958	+	8.14993i	−0.0674197	+	0.518567i
$248$			3.65910i			0.232353i
$249$	8.36004	−	2.24007i	0.529796	−	0.141958i
$250$	−21.7857	−	12.5780i	−1.37785	−	0.795502i
$251$	5.04161	−	2.91077i	0.318223	−	0.183726i	−0.332377	−	0.943147i	$-0.607851\pi$
$251$	5.04161	−	2.91077i	0.318223	−	0.183726i	0.650600	+	0.759420i	$0.274517\pi$
$252$	0.450321	+	0.450321i	0.0283675	+	0.0283675i
$253$	−9.32893	+	21.5511i	−0.586505	+	1.35491i
$254$	8.55466	−	31.9264i	0.536767	−	2.00324i
$255$	−0.199326	+	0.199326i	−0.0124823	+	0.0124823i
$256$	−3.97084	−	6.87770i	−0.248178	−	0.429856i
$257$	−4.30745	−	2.48691i	−0.268691	−	0.155129i	0.359602	−	0.933106i	$-0.382913\pi$
$257$	−4.30745	−	2.48691i	−0.268691	−	0.155129i	−0.628293	+	0.777977i	$0.716246\pi$
$258$	13.4055	−	3.59200i	0.834592	−	0.223628i
$259$	−1.18612			−0.0737018
$260$	2.22788	−	17.1360i	0.138167	−	1.06273i
$261$			5.73517i			0.354998i
$262$	−9.80609	−	36.5968i	−0.605822	−	2.26096i
$263$	10.9912	+	6.34575i	0.677744	+	0.391296i	0.799005	−	0.601325i	$-0.205360\pi$
$263$	10.9912	+	6.34575i	0.677744	+	0.391296i	−0.121260	+	0.992621i	$0.538694\pi$
$264$	2.55749	−	1.01224i	0.157403	−	0.0622994i
$265$	8.22619	−	8.22619i	0.505331	−	0.505331i
$266$	−0.328817	+	1.22716i	−0.0201611	+	0.0752422i
$267$	−4.48680	+	16.7450i	−0.274588	+	1.02478i
$268$	−0.565206	−	0.565206i	−0.0345254	−	0.0345254i
$269$	14.3929	+	24.9292i	0.877549	+	1.51996i	0.854022	+	0.520237i	$0.174156\pi$
$269$	14.3929	+	24.9292i	0.877549	+	1.51996i	0.0235274	+	0.999723i	$0.492510\pi$
$270$	2.09724	−	3.63252i	0.127634	−	0.221068i
$271$	6.77684	+	25.2915i	0.411663	+	1.53635i	0.791426	+	0.611265i	$0.209339\pi$
$271$	6.77684	+	25.2915i	0.411663	+	1.53635i	−0.379763	+	0.925084i	$0.623994\pi$
$272$	0.430083			0.0260776
$273$	−0.582283	+	0.761386i	−0.0352414	+	0.0460812i
$274$			30.0147i			1.81325i
$275$	3.28615	−	0.379840i	0.198163	−	0.0229052i
$276$	−8.48097	+	14.6895i	−0.510494	+	0.884202i
$277$	1.63058	+	2.82425i	0.0979722	+	0.169693i	0.910845	−	0.412748i	$-0.135431\pi$
$277$	1.63058	+	2.82425i	0.0979722	+	0.169693i	−0.812873	+	0.582441i	$0.802098\pi$
$278$	−4.77765	+	4.77765i	−0.286545	+	0.286545i
$279$	−4.26185	−	1.14196i	−0.255150	−	0.0683673i
$280$	0.114161	−	0.426053i	0.00682240	−	0.0254616i
$281$	−2.28279	+	2.28279i	−0.136180	+	0.136180i	−0.771911	−	0.635731i	$-0.780699\pi$
$281$	−2.28279	+	2.28279i	−0.136180	+	0.136180i	0.635731	+	0.771911i	$0.280699\pi$
$282$	−8.33531	+	4.81239i	−0.496361	+	0.286574i
$283$	0.687244	−	1.19034i	0.0408524	−	0.0707585i	−0.844876	−	0.534962i	$-0.820326\pi$
$283$	0.687244	−	1.19034i	0.0408524	−	0.0707585i	0.885729	+	0.464203i	$0.153659\pi$
$284$	−20.2803	+	5.43409i	−1.20341	+	0.322454i
$285$	4.56029			0.270128
$286$	12.2258	+	21.8882i	0.722929	+	1.29428i
$287$	−2.28447			−0.134848
$288$	−7.78362	+	2.08561i	−0.458654	+	0.122896i
$289$	8.49007	−	14.7052i	0.499416	−	0.865014i
$290$	20.8331	−	12.0280i	1.22336	−	0.706310i
$291$	13.6318	−	13.6318i	0.799111	−	0.799111i
$292$	−1.51170	+	5.64174i	−0.0884655	+	0.330158i
$293$	−3.24997	−	0.870826i	−0.189865	−	0.0508742i	0.162634	−	0.986687i	$-0.448001\pi$
$293$	−3.24997	−	0.870826i	−0.189865	−	0.0508742i	−0.352499	+	0.935812i	$0.614668\pi$
$294$	10.2727	−	10.2727i	0.599114	−	0.599114i
$295$	−7.78948	−	13.4918i	−0.453521	−	0.785522i
$296$	−1.85007	+	3.20441i	−0.107533	+	0.186253i
$297$	0.380826	+	3.29469i	0.0220978	+	0.191177i
$298$		−	13.2100i		−	0.765233i
$299$	−23.6018	−	9.73160i	−1.36493	−	0.562793i
$300$	2.38935			0.137949
$301$	0.455469	+	1.69983i	0.0262528	+	0.0979768i
$302$	−12.3235	+	21.3449i	−0.709137	+	1.22826i
$303$	5.86539	+	10.1592i	0.336958	+	0.583628i
$304$	−4.91983	−	4.91983i	−0.282171	−	0.282171i
$305$	1.52429	−	5.68872i	0.0872805	−	0.325735i
$306$	0.0764561	−	0.285338i	0.00437070	−	0.0163117i
$307$	−10.1864	+	10.1864i	−0.581368	+	0.581368i	−0.935279	−	0.353911i	$-0.884852\pi$
$307$	−10.1864	+	10.1864i	−0.581368	+	0.581368i	0.353911	+	0.935279i	$0.384852\pi$
$308$	0.777325	+	1.96395i	0.0442922	+	0.111907i
$309$	−1.07269	−	0.619316i	−0.0610230	−	0.0352316i
$310$	4.78992	+	17.8762i	0.272049	+	1.01530i
$311$			8.24874i			0.467743i	0.972267	+	0.233872i	$0.0751396\pi$
$311$			8.24874i			0.467743i	−0.972267	+	0.233872i	$0.924860\pi$
$312$	1.14873	+	2.76068i	0.0650342	+	0.156293i
$313$	18.7832			1.06169			0.530845	−	0.847469i	$-0.321875\pi$
$313$	18.7832			1.06169			0.530845	+	0.847469i	$0.321875\pi$
$314$	−40.9802	+	10.9806i	−2.31265	+	0.619672i
$315$	0.460608	+	0.265932i	0.0259523	+	0.0149836i
$316$	−6.93222	−	12.0070i	−0.389968	−	0.675444i
$317$	−5.62036	+	5.62036i	−0.315671	+	0.315671i	−0.847102	−	0.531431i	$-0.821655\pi$
$317$	−5.62036	+	5.62036i	−0.315671	+	0.315671i	0.531431	+	0.847102i	$0.321655\pi$
$318$	−3.15534	+	11.7759i	−0.176943	+	0.660359i
$319$	−7.55631	+	17.4561i	−0.423072	+	0.977355i
$320$	15.2638	+	15.2638i	0.853273	+	0.853273i
$321$	11.7464	−	6.78180i	0.655621	−	0.378523i
$322$	−3.41772	−	1.97322i	−0.190462	−	0.109963i
$323$	0.310223	−	0.0831241i	0.0172613	−	0.00462515i
$324$			2.39556i			0.133087i
$325$	0.475151	+	3.56468i	0.0263567	+	0.197733i
$326$		−	3.36219i		−	0.186215i
$327$	−5.30572	+	1.42166i	−0.293407	+	0.0786181i
$328$	−3.56324	+	6.17172i	−0.196747	+	0.340776i
$329$	−0.610216	−	1.05693i	−0.0336423	−	0.0582702i
$330$	11.1693	−	8.29311i	0.614852	−	0.456520i
$331$	−21.4754	−	5.75432i	−1.18040	−	0.316286i	−0.385313	−	0.922786i	$-0.625906\pi$
$331$	−21.4754	−	5.75432i	−1.18040	−	0.316286i	−0.795084	+	0.606500i	$0.792573\pi$
$332$	20.0270	+	5.36621i	1.09912	+	0.294509i
$333$	−3.15488	−	3.15488i	−0.172886	−	0.172886i
$334$	−5.78493	−	10.0198i	−0.316537	−	0.548259i
$335$	−0.578117	−	0.333776i	−0.0315859	−	0.0182361i
$336$	−0.210024	−	0.783821i	−0.0114578	−	0.0427609i
$337$	−35.0897			−1.91146			−0.955728	−	0.294252i	$-0.904929\pi$
$337$	−35.0897			−1.91146			−0.955728	+	0.294252i	$0.904929\pi$
$338$	−23.5597	+	13.7037i	−1.28148	+	0.745384i
$339$	8.13321			0.441735
$340$	−0.652274	+	0.174776i	−0.0353745	+	0.00947858i
$341$	−11.4672	−	9.09092i	−0.620983	−	0.492301i
$342$	−4.13866	+	2.38945i	−0.223793	+	0.129207i
$343$	2.61845	+	2.61845i	0.141383	+	0.141383i
$344$	5.30270	+	1.42085i	0.285902	+	0.0766073i
$345$	−3.66636	+	13.6830i	−0.197390	+	0.736670i
$346$	−20.9186	−	20.9186i	−1.12459	−	1.12459i
$347$	−1.24203	+	0.717087i	−0.0666757	+	0.0384952i	−0.532967	−	0.846136i	$-0.678923\pi$
$347$	−1.24203	+	0.717087i	−0.0666757	+	0.0384952i	0.466292	+	0.884631i	$0.345590\pi$
$348$	−6.86948	+	11.8983i	−0.368243	+	0.637815i
$349$	−4.68016	−	17.4666i	−0.250523	−	0.934966i	−0.970526	−	0.240995i	$-0.922526\pi$
$349$	−4.68016	−	17.4666i	−0.250523	−	0.934966i	0.720003	−	0.693971i	$-0.244140\pi$
$350$			0.555918i			0.0297150i
$351$	−3.57394	+	0.476385i	−0.190763	+	0.0254276i
$352$	−26.4388	−	3.90724i	−1.40920	−	0.208257i
$353$	9.32159	+	34.7886i	0.496138	+	1.85161i	0.523560	+	0.851989i	$0.324604\pi$
$353$	9.32159	+	34.7886i	0.496138	+	1.85161i	−0.0274217	+	0.999624i	$0.508730\pi$
$354$	14.1386	+	8.16291i	0.751457	+	0.433854i
$355$	−15.1853	+	8.76726i	−0.805954	+	0.465318i
$356$	−29.3652	+	29.3652i	−1.55635	+	1.55635i
$357$	0.0361811	+	0.00969471i	0.00191491	+	0.000513098i
$358$	39.1511	+	10.4905i	2.06920	+	0.554440i
$359$	11.2626	−	11.2626i	0.594417	−	0.594417i	−0.344404	−	0.938821i	$-0.611919\pi$
$359$	11.2626	−	11.2626i	0.594417	−	0.594417i	0.938821	+	0.344404i	$0.111919\pi$
$360$	1.43688	−	0.829584i	0.0757303	−	0.0437229i
$361$	11.9549	+	6.90215i	0.629204	+	0.363271i
$362$	−6.33743	−	23.6516i	−0.333088	−	1.24310i
$363$	−3.18176	+	10.5298i	−0.166999	+	0.552670i
$364$	−2.11999	+	0.882137i	−0.111117	+	0.0462365i
$365$			4.87790i			0.255321i
$366$	1.59736	+	5.96144i	0.0834955	+	0.311609i
$367$	14.0376	−	24.3139i	0.732759	−	1.26918i	−0.222941	−	0.974832i	$-0.571566\pi$
$367$	14.0376	−	24.3139i	0.732759	−	1.26918i	0.955700	−	0.294343i	$-0.0951009\pi$
$368$	18.7172	−	10.8064i	0.975704	−	0.563323i
$369$	−6.07632	−	6.07632i	−0.316321	−	0.316321i
$370$	−4.84364	+	18.0767i	−0.251809	+	0.939764i
$371$	−1.49320	−	0.400100i	−0.0775228	−	0.0207722i
$372$	−7.47388	−	7.47388i	−0.387503	−	0.387503i
$373$	18.3789	−	10.6111i	0.951625	−	0.549421i	0.0580394	−	0.998314i	$-0.481515\pi$
$373$	18.3789	−	10.6111i	0.951625	−	0.549421i	0.893585	+	0.448894i	$0.148182\pi$
$374$	0.608653	−	0.767749i	0.0314727	−	0.0396993i
$375$	11.5899	−	3.10549i	0.598498	−	0.160367i
$376$	−3.80718			−0.196341
$377$	−19.1171	−	7.88247i	−0.984583	−	0.405968i
$378$	−0.557361			−0.0286676
$379$	9.33334	+	34.8325i	0.479421	+	1.78922i	0.603965	+	0.797011i	$0.293587\pi$
$379$	9.33334	+	34.8325i	0.479421	+	1.78922i	−0.124544	+	0.992214i	$0.539747\pi$
$380$	9.46085	+	5.46222i	0.485331	+	0.280206i
$381$	7.88260	+	13.6531i	0.403838	+	0.699468i
$382$	−0.331390	−	0.331390i	−0.0169554	−	0.0169554i
$383$	7.60042	+	2.03653i	0.388363	+	0.104062i	0.447717	−	0.894175i	$-0.352237\pi$
$383$	7.60042	+	2.03653i	0.388363	+	0.104062i	−0.0593536	+	0.998237i	$0.518904\pi$
$384$	−6.28312	−	1.68356i	−0.320634	−	0.0859137i
$385$	1.05157	+	1.41628i	0.0535932	+	0.0721805i
$386$	4.03240	+	6.98432i	0.205244	+	0.355493i
$387$	−3.30981	+	5.73276i	−0.168247	+	0.291413i
$388$	44.6087	−	11.9529i	2.26466	−	0.606815i
$389$		−	2.56429i		−	0.130015i	−0.997885	−	0.0650074i	$-0.979293\pi$
$389$		−	2.56429i		−	0.130015i	0.997885	−	0.0650074i	$-0.0207071\pi$
$390$	9.22589	+	11.9833i	0.467171	+	0.606799i
$391$			0.997647i			0.0504532i
$392$	5.55079	−	1.48733i	0.280357	−	0.0751215i
$393$	15.6503	+	9.03572i	0.789454	+	0.455792i
$394$	−29.0442	+	16.7687i	−1.46323	+	0.844795i
$395$	−8.18749	−	8.18749i	−0.411958	−	0.411958i
$396$	−3.15624	+	7.29136i	−0.158607	+	0.366405i
$397$	−7.38686	+	27.5682i	−0.370736	+	1.38361i	0.488740	+	0.872430i	$0.337457\pi$
$397$	−7.38686	+	27.5682i	−0.370736	+	1.38361i	−0.859476	+	0.511176i	$0.829210\pi$
$398$	−0.990967	+	0.990967i	−0.0496727	+	0.0496727i
$399$	−0.302985	−	0.524786i	−0.0151682	−	0.0262722i
$400$	−2.63662	−	1.52225i	−0.131831	−	0.0761126i
$401$	0.723511	−	0.193864i	0.0361304	−	0.00968111i	−0.240709	−	0.970597i	$-0.577380\pi$
$401$	0.723511	−	0.193864i	0.0361304	−	0.00968111i	0.276839	+	0.960916i	$0.410713\pi$
$402$	0.699554			0.0348906
$403$	9.66403	−	12.6366i	0.481400	−	0.629472i
$404$			28.1018i			1.39812i
$405$	0.517806	+	1.93248i	0.0257300	+	0.0960256i
$406$	−2.76831	−	1.59828i	−0.137389	−	0.0793214i
$407$	−5.44582	−	13.7592i	−0.269939	−	0.682017i
$408$	0.0826254	−	0.0826254i	0.00409057	−	0.00409057i
$409$	5.86372	−	21.8837i	0.289942	−	1.08208i	−0.655210	−	0.755447i	$-0.727420\pi$
$409$	5.86372	−	21.8837i	0.289942	−	1.08208i	0.945152	−	0.326632i	$-0.105914\pi$
$410$	−9.32888	+	34.8159i	−0.460721	+	1.71943i
$411$	−10.1231	−	10.1231i	−0.499334	−	0.499334i
$412$	−1.48361	−	2.56968i	−0.0730921	−	0.126599i
$413$	−1.03507	+	1.79279i	−0.0509322	+	0.0882172i
$414$	−3.84213	−	14.3390i	−0.188830	−	0.704724i
$415$	17.3155			0.849985
$416$	3.74586	−	28.8117i	0.183656	−	1.41261i
$417$		−	3.22272i		−	0.157817i
$418$	−15.7450	+	1.81994i	−0.770114	+	0.0890159i
$419$	−12.3625	+	21.4125i	−0.603949	+	1.04607i	0.388268	+	0.921547i	$0.373074\pi$
$419$	−12.3625	+	21.4125i	−0.603949	+	1.04607i	−0.992217	+	0.124524i	$0.960260\pi$
$420$	0.637056	+	1.10341i	0.0310851	+	0.0538410i
$421$	−5.21060	+	5.21060i	−0.253949	+	0.253949i	−0.822588	−	0.568638i	$-0.807470\pi$
$421$	−5.21060	+	5.21060i	−0.253949	+	0.253949i	0.568638	+	0.822588i	$0.307470\pi$
$422$	−6.97065	−	1.86778i	−0.339326	−	0.0909221i
$423$	1.18817	−	4.43433i	0.0577710	−	0.215604i
$424$	−3.40995	+	3.40995i	−0.165602	+	0.165602i
$425$	0.121706	−	0.0702671i	0.00590362	−	0.00340846i
$426$	9.18756	−	15.9133i	0.445139	−	0.771003i
$427$	−0.755917	+	0.202547i	−0.0365814	+	0.00980195i
$428$	32.4924			1.57058
$429$	−11.5057	−	3.25883i	−0.555498	−	0.157338i
$430$	27.7658			1.33899
$431$	18.3017	−	4.90394i	0.881564	−	0.236214i	0.210482	−	0.977598i	$-0.432497\pi$
$431$	18.3017	−	4.90394i	0.881564	−	0.236214i	0.671082	+	0.741383i	$0.265830\pi$
$432$	1.52621	−	2.64347i	0.0734296	−	0.127184i
$433$	19.2519	−	11.1151i	0.925188	−	0.534157i	0.0399014	−	0.999204i	$-0.487296\pi$
$433$	19.2519	−	11.1151i	0.925188	−	0.534157i	0.885286	+	0.465046i	$0.153962\pi$
$434$	1.73891	−	1.73891i	0.0834701	−	0.0834701i
$435$	−2.96970	+	11.0831i	−0.142386	+	0.531393i
$436$	−12.7102	−	3.40568i	−0.608707	−	0.163102i
$437$	11.4123	−	11.4123i	0.545927	−	0.545927i
$438$	−2.55587	−	4.42690i	−0.122124	−	0.211526i
$439$	3.64356	−	6.31083i	0.173898	−	0.301199i	−0.765882	−	0.642982i	$-0.777697\pi$
$439$	3.64356	−	6.31083i	0.173898	−	0.301199i	0.939779	+	0.341782i	$0.111030\pi$
$440$	5.46644	−	0.631855i	0.260602	−	0.0301225i
$441$			6.92933i			0.329968i
$442$	0.846040	+	0.647024i	0.0402420	+	0.0307758i
$443$	−27.4759			−1.30542			−0.652710	−	0.757608i	$-0.726368\pi$
$443$	−27.4759			−1.30542			−0.652710	+	0.757608i	$0.726368\pi$
$444$	−2.76631	−	10.3240i	−0.131283	−	0.489956i
$445$	−17.3413	+	30.0360i	−0.822056	+	1.42384i
$446$	5.33506	+	9.24060i	0.252623	+	0.437555i
$447$	4.45533	+	4.45533i	0.210730	+	0.210730i
$448$	0.742392	−	2.77065i	0.0350747	−	0.130901i
$449$	−1.14327	+	4.26674i	−0.0539542	+	0.201360i	−0.987642	−	0.156729i	$-0.949905\pi$
$449$	−1.14327	+	4.26674i	−0.0539542	+	0.201360i	0.933687	+	0.358089i	$0.116572\pi$
$450$	−1.47865	+	1.47865i	−0.0697043	+	0.0697043i
$451$	−10.4887	−	26.5003i	−0.493893	−	1.24785i
$452$	16.8733	+	9.74179i	0.793652	+	0.458215i
$453$	−3.04266	−	11.3553i	−0.142956	−	0.533521i
$454$			2.37350i			0.111394i
$455$	−1.51950	+	1.16985i	−0.0712352	+	0.0548435i
$456$	−1.89035			−0.0885236
$457$	13.2795	−	3.55823i	0.621188	−	0.166447i	0.0655203	−	0.997851i	$-0.479129\pi$
$457$	13.2795	−	3.55823i	0.621188	−	0.166447i	0.555668	+	0.831404i	$0.312463\pi$
$458$	−10.4564	−	6.03700i	−0.488595	−	0.282090i
$459$	0.0704496	+	0.122022i	0.00328831	+	0.00569552i
$460$	−23.9956	+	23.9956i	−1.11880	+	1.11880i
$461$	8.45031	−	31.5370i	0.393570	−	1.46882i	−0.430632	−	0.902528i	$-0.641709\pi$
$461$	8.45031	−	31.5370i	0.393570	−	1.46882i	0.824202	−	0.566296i	$-0.191624\pi$
$462$	−1.69644	−	0.734345i	−0.0789255	−	0.0341648i
$463$	4.07962	+	4.07962i	0.189596	+	0.189596i	0.795522	−	0.605925i	$-0.207197\pi$
$463$	4.07962	+	4.07962i	0.189596	+	0.189596i	−0.605925	+	0.795522i	$0.707197\pi$
$464$	15.1607	−	8.75305i	0.703819	−	0.406350i
$465$	−7.64461	−	4.41362i	−0.354510	−	0.204677i
$466$	3.29732	−	0.883514i	0.152745	−	0.0409280i
$467$		−	33.7189i		−	1.56032i	−0.625577	−	0.780162i	$-0.715136\pi$
$467$		−	33.7189i		−	1.56032i	0.625577	−	0.780162i	$-0.284864\pi$
$468$	−7.98516	−	3.29248i	−0.369114	−	0.152195i
$469$			0.0887042i			0.00409598i
$470$	−18.5997	+	4.98377i	−0.857939	+	0.229884i
$471$	10.1180	−	17.5248i	0.466212	−	0.807502i
$472$	3.22892	+	5.59266i	0.148623	+	0.257423i
$473$	−17.6272	+	13.0880i	−0.810499	+	0.601786i
$474$	11.7205	+	3.14050i	0.538341	+	0.144248i
$475$	−2.19603	−	0.588425i	−0.100761	−	0.0269988i
$476$	0.0634499	+	0.0634499i	0.00290822	+	0.00290822i
$477$	−2.90746	−	5.03586i	−0.133123	−	0.230576i
$478$	48.0993	+	27.7701i	2.20001	+	1.27018i
$479$	−3.26869	−	12.1989i	−0.149350	−	0.557383i	−0.999523	−	0.0308792i	$-0.990169\pi$
$479$	−3.26869	−	12.1989i	−0.149350	−	0.557383i	0.850173	−	0.526504i	$-0.176497\pi$
$480$	−16.1216			−0.735847
$481$	14.8523	−	6.18012i	0.677207	−	0.281789i
$482$	−36.9097			−1.68119
$483$	1.81820	−	0.487185i	0.0827310	−	0.0221677i
$484$	−19.2133	+	18.0342i	−0.873332	+	0.819737i
$485$	33.4018	−	19.2845i	1.51670	−	0.875666i
$486$	−1.48249	−	1.48249i	−0.0672472	−	0.0672472i
$487$	4.85680	+	1.30138i	0.220083	+	0.0589710i	0.367175	−	0.930152i	$-0.380325\pi$
$487$	4.85680	+	1.30138i	0.220083	+	0.0589710i	−0.147093	+	0.989123i	$0.546992\pi$
$488$	−0.631853	+	2.35811i	−0.0286027	+	0.106747i
$489$	1.13397	+	1.13397i	0.0512798	+	0.0512798i
$490$	25.1709	−	14.5324i	1.13711	−	0.656509i
$491$	21.0976	−	36.5421i	0.952122	−	1.64912i	0.211302	−	0.977421i	$-0.432230\pi$
$491$	21.0976	−	36.5421i	0.952122	−	1.64912i	0.740821	−	0.671703i	$-0.234437\pi$
$492$	−5.32794	−	19.8841i	−0.240202	−	0.896446i
$493$			0.808082i			0.0363942i
$494$	−2.27660	−	17.0795i	−0.102429	−	0.768445i
$495$	−0.970070	+	6.56410i	−0.0436014	+	0.295035i
$496$	3.48573	+	13.0089i	0.156514	+	0.584117i
$497$	2.01783	+	1.16499i	0.0905119	+	0.0522570i
$498$	−15.7146	+	9.07281i	−0.704186	+	0.406562i
$499$	2.57602	−	2.57602i	0.115319	−	0.115319i	−0.647093	−	0.762411i	$-0.724015\pi$
$499$	2.57602	−	2.57602i	0.115319	−	0.115319i	0.762411	+	0.647093i	$0.224015\pi$
$500$	27.7642	+	7.43940i	1.24165	+	0.332700i
$501$	5.33046	+	1.42829i	0.238147	+	0.0638114i
$502$	−8.63039	+	8.63039i	−0.385193	+	0.385193i
$503$	−20.1943	+	11.6592i	−0.900419	+	0.519857i	−0.877336	−	0.479877i	$-0.840681\pi$
$503$	−20.1943	+	11.6592i	−0.900419	+	0.519857i	−0.0230826	+	0.999734i	$0.507348\pi$
$504$	−0.190933	−	0.110235i	−0.00850482	−	0.00491026i
$505$	6.07427	+	22.6695i	0.270301	+	1.00878i
$506$	7.19793	−	48.7058i	0.319987	−	2.16524i
$507$	3.32411	−	12.5678i	0.147629	−	0.558157i
$508$			37.7665i			1.67562i
$509$	5.77553	+	21.5546i	0.255996	+	0.955390i	0.967534	+	0.252742i	$0.0813324\pi$
$509$	5.77553	+	21.5546i	0.255996	+	0.955390i	−0.711538	+	0.702648i	$0.752001\pi$
$510$	0.295499	−	0.511820i	0.0130849	−	0.0226638i
$511$	0.561336	−	0.324087i	0.0248320	−	0.0143368i
$512$	20.9726	+	20.9726i	0.926867	+	0.926867i
$513$	0.589954	−	2.20174i	0.0260471	−	0.0972091i
$514$	10.0726	+	2.69894i	0.444282	+	0.119045i
$515$	−1.75226	−	1.75226i	−0.0772136	−	0.0772136i
$516$	−13.7332	+	7.92885i	−0.604569	+	0.349048i
$517$	9.45884	−	11.9313i	0.415999	−	0.524737i
$518$	2.40203	−	0.643622i	0.105539	−	0.0282791i
$519$	14.1105			0.619381
$520$	0.790404	+	5.92977i	0.0346615	+	0.260038i
$521$	−9.31060			−0.407905			−0.203952	−	0.978981i	$-0.565379\pi$
$521$	−9.31060			−0.407905			−0.203952	+	0.978981i	$0.565379\pi$
$522$	−3.11207	−	11.6144i	−0.136212	−	0.508349i
$523$	−29.3077	−	16.9208i	−1.28153	−	0.739894i	−0.304405	−	0.952543i	$-0.598458\pi$
$523$	−29.3077	−	16.9208i	−1.28153	−	0.739894i	−0.977129	+	0.212649i	$0.931791\pi$
$524$	21.6456	+	37.4913i	0.945593	+	1.63781i
$525$	−0.187494	−	0.187494i	−0.00818293	−	0.00818293i
$526$	−25.7018	−	6.88678i	−1.12065	−	0.300278i
$527$	−0.600491	−	0.160901i	−0.0261578	−	0.00700896i
$528$	8.12818	−	6.03507i	0.353733	−	0.262643i
$529$	13.5672	+	23.4992i	0.589880	+	1.02170i
$530$	−12.1953	+	21.1228i	−0.529728	+	0.917516i
$531$	−7.52163	+	2.01541i	−0.326411	+	0.0874615i
$532$		−	1.45164i		−	0.0629365i
$533$	28.6056	−	11.9030i	1.23905	−	0.515574i
$534$		−	36.3453i		−	1.57281i
$535$	26.2113	−	7.02330i	1.13321	−	0.303644i
$536$	0.239643	+	0.138358i	0.0103510	+	0.00597616i
$537$	−16.7426	+	9.66636i	−0.722497	+	0.417134i
$538$	−42.6746	−	42.6746i	−1.83983	−	1.83983i
$539$	−9.12966	+	21.0908i	−0.393242	+	0.908444i
$540$	−1.24043	+	4.62937i	−0.0533798	+	0.199216i
$541$	−19.1655	+	19.1655i	−0.823988	+	0.823988i	−0.986677	−	0.162689i	$-0.947983\pi$
$541$	−19.1655	+	19.1655i	−0.823988	+	0.823988i	0.162689	+	0.986677i	$0.447983\pi$
$542$	−27.4478	−	47.5410i	−1.17898	−	2.04206i
$543$	10.1144	+	5.83956i	0.434051	+	0.250600i
$544$	−1.09671	+	0.293861i	−0.0470209	+	0.0125992i
$545$	−10.9893			−0.470731
$546$	0.766042	−	1.85786i	0.0327836	−	0.0795092i
$547$		−	5.51777i		−	0.235923i	−0.993018	−	0.117961i	$-0.962364\pi$
$547$		−	5.51777i		−	0.235923i	0.993018	−	0.117961i	$-0.0376359\pi$
$548$	−8.87626	−	33.1267i	−0.379175	−	1.41510i
$549$	−2.54936	−	1.47187i	−0.108804	−	0.0628180i
$550$	−6.44875	+	2.55239i	−0.274975	+	0.108834i
$551$	9.24386	−	9.24386i	0.393802	−	0.393802i
$552$	1.51979	−	5.67194i	0.0646867	−	0.241414i
$553$	−0.398219	+	1.48617i	−0.0169340	+	0.0631985i
$554$	−4.83465	−	4.83465i	−0.205405	−	0.205405i
$555$	−4.46312	−	7.73035i	−0.189449	−	0.328135i
$556$	3.86011	−	6.68591i	0.163705	−	0.283546i
$557$	−5.08832	−	18.9899i	−0.215599	−	0.804627i	−0.985955	−	0.167012i	$-0.946588\pi$
$557$	−5.08832	−	18.9899i	−0.215599	−	0.804627i	0.770356	−	0.637614i	$-0.220079\pi$
$558$	9.25041			0.391601
$559$	−14.5601	−	18.9118i	−0.615825	−	0.799884i
$560$		−	1.62347i		−	0.0686040i
$561$	0.0536582	+	0.464219i	0.00226545	+	0.0195994i
$562$	3.38422	−	5.86164i	0.142755	−	0.247258i
$563$	1.98757	+	3.44256i	0.0837659	+	0.145087i	0.904865	−	0.425699i	$-0.139972\pi$
$563$	1.98757	+	3.44256i	0.0837659	+	0.145087i	−0.821099	+	0.570786i	$0.806639\pi$
$564$	7.77636	−	7.77636i	0.327444	−	0.327444i
$565$	15.7172	+	4.21142i	0.661229	+	0.177176i
$566$	−0.745838	+	2.78351i	−0.0313499	+	0.116999i
$567$	0.187981	−	0.187981i	0.00789448	−	0.00789448i
$568$	6.29468	−	3.63424i	0.264119	−	0.152489i
$569$	−21.8186	+	37.7908i	−0.914681	+	1.58427i	−0.107314	+	0.994225i	$0.534225\pi$
$569$	−21.8186	+	37.7908i	−0.914681	+	1.58427i	−0.807367	+	0.590049i	$0.799108\pi$
$570$	−9.23513	+	2.47455i	−0.386817	+	0.103647i
$571$	3.41122			0.142755			0.0713775	−	0.997449i	$-0.477260\pi$
$571$	3.41122			0.142755			0.0713775	+	0.997449i	$0.477260\pi$
$572$	−19.9664	−	20.5421i	−0.834839	−	0.858907i
$573$	0.223536			0.00933834
$574$	4.62633	−	1.23962i	0.193099	−	0.0517408i
$575$	3.53111	−	6.11607i	0.147258	−	0.255058i
$576$	9.34411	−	5.39483i	0.389338	−	0.224784i
$577$	11.3944	−	11.3944i	0.474354	−	0.474354i	−0.428966	−	0.903321i	$-0.641122\pi$
$577$	11.3944	−	11.3944i	0.474354	−	0.474354i	0.903321	+	0.428966i	$0.141122\pi$
$578$	−9.21393	+	34.3868i	−0.383249	+	1.43030i
$579$	−3.71561	−	0.995595i	−0.154416	−	0.0413755i
$580$	−19.4361	+	19.4361i	−0.807040	+	0.807040i
$581$	−1.15044	−	1.99262i	−0.0477283	−	0.0826679i
$582$	−20.2090	+	35.0031i	−0.837692	+	1.45092i
$583$	−2.21447	−	19.1583i	−0.0917140	−	0.793456i
$584$		−	2.02200i		−	0.0836711i
$585$	−7.15323	−	0.930003i	−0.295750	−	0.0384509i
$586$	7.05411			0.291402
$587$	7.52209	+	28.0728i	0.310470	+	1.15869i	0.928134	+	0.372247i	$0.121413\pi$
$587$	7.52209	+	28.0728i	0.310470	+	1.15869i	−0.617664	+	0.786442i	$0.711921\pi$
$588$	−8.29981	+	14.3757i	−0.342278	+	0.592844i
$589$	5.02858	+	8.70976i	0.207199	+	0.358880i
$590$	23.0957	+	23.0957i	0.950834	+	0.950834i
$591$	4.14017	−	15.4513i	0.170304	−	0.635583i
$592$	−3.52482	+	13.1548i	−0.144869	+	0.540660i
$593$	−22.1422	+	22.1422i	−0.909273	+	0.909273i	−0.996214	−	0.0869404i	$-0.972291\pi$
$593$	−22.1422	+	22.1422i	−0.909273	+	0.909273i	0.0869404	+	0.996214i	$0.472291\pi$
$594$	−2.55901	−	6.46549i	−0.104998	−	0.265282i
$595$	0.0648993	+	0.0374696i	0.00266061	+	0.00153610i
$596$	3.90659	+	14.5796i	0.160020	+	0.597203i
$597$		−	0.668447i		−	0.0273577i
$598$	53.0771	+	6.90064i	2.17048	+	0.282188i
$599$	28.8692			1.17956			0.589782	−	0.807563i	$-0.299214\pi$
$599$	28.8692			1.17956			0.589782	+	0.807563i	$0.299214\pi$
$600$	−0.798982	+	0.214087i	−0.0326183	+	0.00874005i
$601$	−21.7405	−	12.5519i	−0.886813	−	0.512002i	−0.0139140	−	0.999903i	$-0.504429\pi$
$601$	−21.7405	−	12.5519i	−0.886813	−	0.512002i	−0.872899	+	0.487902i	$0.837762\pi$
$602$	−1.84476	−	3.19522i	−0.0751868	−	0.130227i
$603$	−0.235939	+	0.235939i	−0.00960817	+	0.00960817i
$604$	7.28886	−	27.2024i	0.296580	−	1.10685i
$605$	−11.6011	+	18.7010i	−0.471650	+	0.760305i
$606$	−17.3908	−	17.3908i	−0.706452	−	0.706452i
$607$	−35.9574	+	20.7600i	−1.45947	+	0.842624i	−0.998985	−	0.0450444i	$-0.985657\pi$
$607$	−35.9574	+	20.7600i	−1.45947	+	0.842624i	−0.460483	+	0.887669i	$0.652324\pi$
$608$	15.9071	+	9.18395i	0.645117	+	0.372458i
$609$	1.47272	−	0.394614i	0.0596776	−	0.0159906i
$610$			12.3475i			0.499934i
$611$	13.1480	+	10.0551i	0.531910	+	0.406788i
$612$			0.337533i			0.0136440i
$613$	44.3989	−	11.8967i	1.79326	−	0.480501i	0.800363	−	0.599516i	$-0.204640\pi$
$613$	44.3989	−	11.8967i	1.79326	−	0.480501i	0.992892	+	0.119015i	$0.0379736\pi$
$614$	15.1012	−	26.1561i	0.609437	−	1.05558i
$615$	−8.59600	−	14.8887i	−0.346624	−	0.600370i
$616$	−0.435902	−	0.587083i	−0.0175630	−	0.0236543i
$617$	−45.0648	−	12.0751i	−1.81424	−	0.486124i	−0.818193	−	0.574943i	$-0.805024\pi$
$617$	−45.0648	−	12.0751i	−1.81424	−	0.486124i	−0.996048	+	0.0888189i	$0.971691\pi$
$618$	2.50838	+	0.672118i	0.100902	+	0.0270365i
$619$	−29.3676	−	29.3676i	−1.18038	−	1.18038i	−0.979645	−	0.200737i	$-0.935666\pi$
$619$	−29.3676	−	29.3676i	−1.18038	−	1.18038i	−0.200737	−	0.979645i	$-0.564334\pi$
$620$	−10.5731	−	18.3131i	−0.424625	−	0.735473i
$621$	6.13195	+	3.54029i	0.246067	+	0.142067i
$622$	−4.47601	−	16.7047i	−0.179472	−	0.669797i
$623$	4.60862			0.184640
$624$	6.71388	+	8.72053i	0.268770	+	0.349101i
$625$	19.0181			0.760725
$626$	−38.0383	+	10.1923i	−1.52032	+	0.407367i
$627$	4.69651	−	5.92413i	0.187561	−	0.236587i
$628$	41.9818	−	24.2382i	1.67526	−	0.967210i
$629$	−0.444520	−	0.444520i	−0.0177242	−	0.0177242i
$630$	−1.07709	−	0.288605i	−0.0429122	−	0.0114983i
$631$	−6.56590	+	24.5043i	−0.261384	+	0.975500i	0.703042	+	0.711148i	$0.251825\pi$
$631$	−6.56590	+	24.5043i	−0.261384	+	0.975500i	−0.964426	+	0.264351i	$0.914842\pi$
$632$	3.39391	+	3.39391i	0.135002	+	0.135002i
$633$	2.98094	−	1.72105i	0.118482	−	0.0684054i
$634$	8.33213	−	14.4317i	0.330911	−	0.573155i
$635$	8.16331	+	30.4659i	0.323951	+	1.20900i
$636$		−	13.9300i		−	0.552359i
$637$	−23.0976	−	9.52373i	−0.915162	−	0.377344i
$638$	5.83023	−	39.4510i	0.230821	−	1.56188i
$639$	2.26840	+	8.46578i	0.0897365	+	0.334901i
$640$	−11.2702	−	6.50687i	−0.445495	−	0.257207i
$641$	−11.2142	+	6.47454i	−0.442936	+	0.255729i	−0.704842	−	0.709364i	$-0.748982\pi$
$641$	−11.2142	+	6.47454i	−0.442936	+	0.255729i	0.261906	+	0.965093i	$0.415649\pi$
$642$	−20.1079	+	20.1079i	−0.793596	+	0.793596i
$643$	−24.2761	−	6.50477i	−0.957357	−	0.256523i	−0.253876	−	0.967237i	$-0.581705\pi$
$643$	−24.2761	−	6.50477i	−0.957357	−	0.256523i	−0.703481	+	0.710714i	$0.748372\pi$
$644$	4.35561	+	1.16708i	0.171635	+	0.0459895i
$645$	−9.36459	+	9.36459i	−0.368730	+	0.368730i
$646$	−0.583134	+	0.336672i	−0.0229431	+	0.0132462i
$647$	20.9845	+	12.1154i	0.824987	+	0.476306i	0.852133	−	0.523325i	$-0.175309\pi$
$647$	20.9845	+	12.1154i	0.824987	+	0.476306i	−0.0271464	+	0.999631i	$0.508642\pi$
$648$	−0.214643	−	0.801057i	−0.00843196	−	0.0314685i
$649$	−25.5489	−	3.77573i	−1.00288	−	0.148210i
$650$	−2.89654	−	6.96108i	−0.113612	−	0.273036i
$651$			1.17296i			0.0459720i
$652$	0.994304	+	3.71079i	0.0389399	+	0.145326i
$653$	−11.7379	+	20.3306i	−0.459339	+	0.795598i	−0.998926	−	0.0463313i	$-0.985247\pi$
$653$	−11.7379	+	20.3306i	−0.459339	+	0.795598i	0.539587	+	0.841930i	$0.318580\pi$
$654$	9.97328	−	5.75808i	0.389986	−	0.225159i
$655$	25.5651	+	25.5651i	0.998913	+	0.998913i
$656$	−6.78883	+	25.3363i	−0.265059	+	0.989215i
$657$	2.35508	+	0.631042i	0.0918805	+	0.0246193i
$658$	1.80928	+	1.80928i	0.0705331	+	0.0705331i
$659$	−39.9243	+	23.0503i	−1.55523	+	0.897912i	−0.557528	+	0.830158i	$0.688250\pi$
$659$	−39.9243	+	23.0503i	−1.55523	+	0.897912i	−0.997702	+	0.0677539i	$0.978417\pi$
$660$	−9.87488	+	12.4561i	−0.384379	+	0.484852i
$661$	16.1554	−	4.32882i	0.628372	−	0.168372i	0.0694410	−	0.997586i	$-0.477878\pi$
$661$	16.1554	−	4.32882i	0.628372	−	0.168372i	0.558931	+	0.829214i	$0.311212\pi$
$662$	46.6128			1.81166
$663$	−0.503566	+	0.0671224i	−0.0195569	+	0.00260682i
$664$	−7.17769			−0.278548
$665$	−0.313775	−	1.17102i	−0.0121677	−	0.0454104i
$666$	8.10095	+	4.67708i	0.313905	+	0.181233i
$667$	20.3041	+	35.1678i	0.786180	+	1.36170i
$668$	9.34788	+	9.34788i	0.361680	+	0.361680i
$669$	−4.91594	−	1.31722i	−0.190061	−	0.0509267i
$670$	1.35187	+	0.362233i	0.0522274	+	0.0139943i
$671$	−5.82022	−	7.83881i	−0.224687	−	0.302614i
$672$	1.07112	+	1.85523i	0.0413193	+	0.0715671i
$673$	−9.82203	+	17.0123i	−0.378612	+	0.655774i	−0.990860	−	0.134891i	$-0.956932\pi$
$673$	−9.82203	+	17.0123i	−0.378612	+	0.655774i	0.612249	+	0.790665i	$0.290265\pi$
$674$	71.0608	−	19.0407i	2.73716	−	0.733420i
$675$		−	0.997410i		−	0.0383903i
$676$	21.9498	−	22.0919i	0.844221	−	0.849687i
$677$			22.3258i			0.858050i	0.903293	+	0.429025i	$0.141143\pi$
$677$			22.3258i			0.858050i	−0.903293	+	0.429025i	$0.858857\pi$
$678$	−16.4707	+	4.41332i	−0.632554	+	0.169492i
$679$	−4.43843	−	2.56253i	−0.170331	−	0.0983407i
$680$	0.202456	−	0.116888i	0.00776382	−	0.00448244i
$681$	−0.800511	−	0.800511i	−0.0306756	−	0.0306756i
$682$	28.1555	+	12.1878i	1.07813	+	0.466694i
$683$	6.83303	−	25.5012i	0.261459	−	0.975777i	−0.702924	−	0.711265i	$-0.748122\pi$
$683$	6.83303	−	25.5012i	0.261459	−	0.975777i	0.964382	−	0.264512i	$-0.0852109\pi$
$684$	3.86112	−	3.86112i	0.147634	−	0.147634i
$685$	−14.3208	−	24.8044i	−0.547170	−	0.947726i
$686$	−6.72353	−	3.88183i	−0.256706	−	0.148209i
$687$	5.56273	−	1.49053i	0.212231	−	0.0568672i
$688$	20.2058			0.770339
$689$	20.7821	−	2.77014i	0.791737	−	0.105534i
$690$		−	29.6993i		−	1.13063i
$691$	−7.10353	−	26.5107i	−0.270231	−	1.00852i	−0.958970	−	0.283507i	$-0.908502\pi$
$691$	−7.10353	−	26.5107i	−0.270231	−	1.00852i	0.688739	−	0.725009i	$-0.258164\pi$
$692$	29.2738	+	16.9012i	1.11282	+	0.642489i
$693$	0.819831	−	0.324486i	0.0311428	−	0.0123262i
$694$	2.12615	−	2.12615i	0.0807075	−	0.0807075i
$695$	1.66874	−	6.22783i	0.0632990	−	0.236235i
$696$	1.23101	−	4.59420i	0.0466614	−	0.174143i
$697$	−0.856149	−	0.856149i	−0.0324290	−	0.0324290i
$698$	18.9558	+	32.8324i	0.717487	+	1.24272i
$699$	−0.814104	+	1.41007i	−0.0307922	+	0.0533337i
$700$	−0.164402	−	0.613556i	−0.00621381	−	0.0231902i
$701$	−16.3843			−0.618825			−0.309413	−	0.950928i	$-0.600132\pi$
$701$	−16.3843			−0.618825			−0.309413	+	0.950928i	$0.600132\pi$
$702$	6.97916	−	2.90406i	0.263411	−	0.109607i
$703$			10.1700i			0.383568i
$704$	35.5485	−	4.10899i	1.33979	−	0.154863i
$705$	4.59224	−	7.95399i	0.172954	−	0.299565i
$706$	−37.7547	−	65.3930i	−1.42092	−	2.46110i
$707$	2.20517	−	2.20517i	0.0829339	−	0.0829339i
$708$	−18.0185	−	4.82804i	−0.677177	−	0.181449i
$709$	−6.61629	+	24.6923i	−0.248480	+	0.927339i	0.723123	+	0.690720i	$0.242706\pi$
$709$	−6.61629	+	24.6923i	−0.248480	+	0.927339i	−0.971602	+	0.236620i	$0.923960\pi$
$710$	25.9948	−	25.9948i	0.975566	−	0.975566i
$711$	−5.01217	+	2.89378i	−0.187971	+	0.108525i
$712$	7.18838	−	12.4506i	0.269396	−	0.466607i
$713$	−30.1763	+	8.08572i	−1.13011	+	0.302813i
$714$	−0.0785318			−0.00293898
$715$	−20.5470	−	12.2553i	−0.768413	−	0.458323i
$716$	−46.3127			−1.73079
$717$	−25.5885	+	6.85641i	−0.955619	+	0.256057i
$718$	−16.6967	+	28.9195i	−0.623115	+	1.07927i
$719$	35.0456	−	20.2336i	1.30698	−	0.754586i	0.325391	−	0.945580i	$-0.394504\pi$
$719$	35.0456	−	20.2336i	1.30698	−	0.754586i	0.981591	+	0.190993i	$0.0611709\pi$
$720$	4.31816	−	4.31816i	0.160928	−	0.160928i
$721$	−0.0852252	+	0.318065i	−0.00317395	+	0.0118454i
$722$	−27.9554	−	7.49062i	−1.04039	−	0.278772i
$723$	12.4485	−	12.4485i	0.462966	−	0.462966i
$724$	13.9890	+	24.2297i	0.519898	+	0.900489i
$725$	2.86016	−	4.95394i	0.106224	−	0.183985i
$726$	0.729674	−	23.0506i	0.0270807	−	0.855488i
$727$			10.9688i			0.406809i	0.979095	+	0.203404i	$0.0652006\pi$
$727$			10.9688i			0.406809i	−0.979095	+	0.203404i	$0.934799\pi$
$728$	0.629868	−	0.484931i	0.0233445	−	0.0179727i
$729$	1.00000			0.0370370
$730$	−2.64689	−	9.87833i	−0.0979658	−	0.365613i
$731$	−0.466350	+	0.807742i	−0.0172486	+	0.0298754i
$732$	−3.52596	−	6.10714i	−0.130323	−	0.225726i
$733$	15.2065	+	15.2065i	0.561664	+	0.561664i	0.929780	−	0.368116i	$-0.119997\pi$
$733$	15.2065	+	15.2065i	0.561664	+	0.561664i	−0.368116	+	0.929780i	$0.619997\pi$
$734$	−15.2345	+	56.8558i	−0.562315	+	2.09859i
$735$	−3.58804	+	13.3908i	−0.132347	+	0.493926i
$736$	−40.3451	+	40.3451i	−1.48714	+	1.48714i
$737$	−1.02898	+	0.407268i	−0.0379031	+	0.0150019i
$738$	15.6025	+	9.00809i	0.574335	+	0.331592i
$739$	−3.57979	−	13.3600i	−0.131685	−	0.491454i	0.868305	−	0.496031i	$-0.165210\pi$
$739$	−3.57979	−	13.3600i	−0.131685	−	0.491454i	−0.999990	+	0.00457696i	$0.998543\pi$
$740$		−	21.3833i		−	0.786068i
$741$	6.52825	+	4.99259i	0.239821	+	0.183407i
$742$	3.24101			0.118981
$743$	−35.6639	+	9.55610i	−1.30838	+	0.350579i	−0.844613	−	0.535378i	$-0.820169\pi$
$743$	−35.6639	+	9.55610i	−1.30838	+	0.350579i	−0.463767	+	0.885957i	$0.653503\pi$
$744$	3.16887	+	1.82955i	0.116176	+	0.0670745i
$745$	6.30282	+	10.9168i	0.230918	+	0.399961i
$746$	−31.4617	+	31.4617i	−1.15189	+	1.15189i
$747$	2.24007	−	8.36004i	0.0819597	−	0.305878i
$748$	−0.444712	+	1.02735i	−0.0162603	+	0.0375635i
$749$	−2.54970	−	2.54970i	−0.0931641	−	0.0931641i
$750$	−21.7857	+	12.5780i	−0.795502	+	0.459283i
$751$	−3.21588	−	1.85669i	−0.117349	−	0.0677515i	0.440177	−	0.897911i	$-0.354916\pi$
$751$	−3.21588	−	1.85669i	−0.117349	−	0.0677515i	−0.557526	+	0.830160i	$0.688249\pi$
$752$	−13.5354	+	3.62680i	−0.493585	+	0.132256i
$753$		−	5.82155i		−	0.212149i
$754$	42.9918	+	5.58943i	1.56567	+	0.203555i
$755$		−	23.5194i		−	0.855960i
$756$	0.615150	−	0.164829i	0.0223728	−	0.00599477i
$757$	18.5204	−	32.0782i	0.673135	−	1.16590i	−0.303876	−	0.952712i	$-0.598281\pi$
$757$	18.5204	−	32.0782i	0.673135	−	1.16590i	0.977010	−	0.213192i	$-0.0683860\pi$
$758$	−37.8023	−	65.4754i	−1.37304	−	2.37818i
$759$	13.9993	+	18.8546i	0.508144	+	0.684380i
$760$	−3.65305	−	0.978833i	−0.132510	−	0.0355060i
$761$	0.735148	+	0.196982i	0.0266491	+	0.00714061i	0.272119	−	0.962264i	$-0.412276\pi$
$761$	0.735148	+	0.196982i	0.0266491	+	0.00714061i	−0.245470	+	0.969404i	$0.578942\pi$
$762$	−23.3718	−	23.3718i	−0.846670	−	0.846670i
$763$	0.730130	+	1.26462i	0.0264325	+	0.0457824i
$764$	0.463751	+	0.267747i	0.0167779	+	0.00968673i
$765$	0.0729584	+	0.272285i	0.00263782	+	0.00984447i
$766$	−16.4968			−0.596055
$767$	3.61978	−	27.8420i	0.130703	−	1.00531i
$768$	−7.94169			−0.286571
$769$	20.9679	−	5.61833i	0.756122	−	0.202602i	0.139890	−	0.990167i	$-0.455325\pi$
$769$	20.9679	−	5.61833i	0.756122	−	0.202602i	0.616232	+	0.787565i	$0.288658\pi$
$770$	−2.89808	−	2.29753i	−0.104440	−	0.0827973i
$771$	−4.30745	+	2.48691i	−0.155129	+	0.0895637i
$772$	−6.51596	−	6.51596i	−0.234515	−	0.234515i
$773$	−19.3508	−	5.18502i	−0.695999	−	0.186492i	−0.106561	−	0.994306i	$-0.533984\pi$
$773$	−19.3508	−	5.18502i	−0.695999	−	0.186492i	−0.589438	+	0.807814i	$0.700651\pi$
$774$	3.59200	−	13.4055i	0.129112	−	0.481852i
$775$	3.11181	+	3.11181i	0.111779	+	0.111779i
$776$	−13.8458	+	7.99389i	−0.497036	+	0.286964i
$777$	−0.593059	+	1.02721i	−0.0212759	+	0.0368509i
$778$	1.39146	+	5.19300i	0.0498863	+	0.186178i
$779$			19.5874i			0.701792i
$780$	−13.7263	−	10.4974i	−0.491480	−	0.375867i
$781$	−4.24967	+	28.7560i	−0.152065	+	1.02897i
$782$	−0.541353	−	2.02036i	−0.0193587	−	0.0722478i
$783$	4.96680	+	2.86759i	0.177499	+	0.102479i
$784$	18.3174	−	10.5756i	0.654194	−	0.377699i
$785$	28.6272	−	28.6272i	1.02175	−	1.02175i
$786$	−36.5968	−	9.80609i	−1.30537	−	0.349772i
$787$	−41.1092	−	11.0152i	−1.46538	−	0.392649i	−0.564038	−	0.825749i	$-0.690753\pi$
$787$	−41.1092	−	11.0152i	−1.46538	−	0.392649i	−0.901346	+	0.433100i	$0.857420\pi$
$788$	27.0966	−	27.0966i	0.965275	−	0.965275i
$789$	10.9912	−	6.34575i	0.391296	−	0.225915i
$790$	21.0234	+	12.1379i	0.747980	+	0.431847i
$791$	−0.559613	−	2.08850i	−0.0198976	−	0.0742587i
$792$	0.402117	−	2.72098i	0.0142886	−	0.0966857i
$793$	8.41008	−	6.47486i	0.298651	−	0.229929i
$794$		−	59.8372i		−	2.12354i
$795$	−3.01099	−	11.2372i	−0.106789	−	0.398542i
$796$	0.800653	−	1.38677i	0.0283784	−	0.0491528i
$797$	7.61613	−	4.39718i	0.269777	−	0.155756i	−0.359009	−	0.933334i	$-0.616885\pi$
$797$	7.61613	−	4.39718i	0.269777	−	0.155756i	0.628786	+	0.777578i	$0.283552\pi$
$798$	0.898346	+	0.898346i	0.0318011	+	0.0318011i
$799$	0.167413	−	0.624794i	0.00592264	−	0.0221036i
$800$	7.76345	+	2.08021i	0.274480	+	0.0735466i
$801$	12.2582	+	12.2582i	0.433121	+	0.433121i
$802$	−1.36000	+	0.785197i	−0.0480233	+	0.0277263i
$803$	6.33673	+	5.02361i	0.223618	+	0.177279i
$804$	−0.772085	+	0.206880i	−0.0272293	+	0.00729608i
$805$	3.76590			0.132731
$806$	−12.7139	+	30.8346i	−0.447826	+	1.08610i
$807$	28.7858			1.01331
$808$	−2.51793	−	9.39703i	−0.0885804	−	0.330586i
$809$	−3.73778	−	2.15801i	−0.131413	−	0.0758716i	0.432852	−	0.901465i	$-0.357507\pi$
$809$	−3.73778	−	2.15801i	−0.131413	−	0.0758716i	−0.564265	+	0.825593i	$0.690841\pi$
$810$	−2.09724	−	3.63252i	−0.0736894	−	0.127634i
$811$	22.9819	+	22.9819i	0.807003	+	0.807003i	0.984179	−	0.177176i	$-0.0566962\pi$
$811$	22.9819	+	22.9819i	0.807003	+	0.807003i	−0.177176	+	0.984179i	$0.556696\pi$
$812$	3.52799	+	0.945322i	0.123808	+	0.0331743i
$813$	25.2915	+	6.77684i	0.887011	+	0.237674i
$814$	18.4946	+	24.9089i	0.648235	+	0.873058i
$815$	1.60419	+	2.77854i	0.0561924	+	0.0973281i
$816$	0.215041	−	0.372462i	0.00752795	−	0.0130388i
$817$	14.5747	−	3.90527i	0.509903	−	0.136628i
$818$			47.4989i			1.66076i
$819$	0.368238	+	0.884965i	0.0128673	+	0.0309232i
$820$		−	41.1845i		−	1.43822i
$821$	44.3518	−	11.8840i	1.54789	−	0.414755i	0.619084	−	0.785325i	$-0.287504\pi$
$821$	44.3518	−	11.8840i	1.54789	−	0.414755i	0.928805	+	0.370570i	$0.120837\pi$
$822$	25.9935	+	15.0073i	0.906627	+	0.523441i
$823$	11.4046	−	6.58444i	0.397539	−	0.229519i	−0.287883	−	0.957666i	$-0.592951\pi$
$823$	11.4046	−	6.58444i	0.397539	−	0.229519i	0.685421	+	0.728147i	$0.259618\pi$
$824$	0.726352	+	0.726352i	0.0253037	+	0.0253037i
$825$	1.31413	−	3.03581i	0.0457520	−	0.105693i
$826$	1.12331	−	4.19226i	0.0390851	−	0.145868i
$827$	13.0208	−	13.0208i	0.452776	−	0.452776i	−0.443499	−	0.896275i	$-0.646263\pi$
$827$	13.0208	−	13.0208i	0.452776	−	0.452776i	0.896275	+	0.443499i	$0.146263\pi$
$828$	8.48097	+	14.6895i	0.294734	+	0.510494i
$829$	13.2034	+	7.62300i	0.458574	+	0.264758i	0.711444	−	0.702742i	$-0.248041\pi$
$829$	13.2034	+	7.62300i	0.458574	+	0.264758i	−0.252871	+	0.967500i	$0.581375\pi$
$830$	−35.0660	+	9.39590i	−1.21716	+	0.326137i
$831$	3.26117			0.113129
$832$	5.14003	+	38.5616i	0.178199	+	1.33688i
$833$			0.976337i			0.0338281i
$834$	1.74874	+	6.52640i	0.0605540	+	0.225991i
$835$	9.56142	+	5.52029i	0.330886	+	0.191037i
$836$	16.8393	−	6.66491i	0.582399	−	0.230511i
$837$	−3.11989	+	3.11989i	−0.107839	+	0.107839i
$838$	13.4165	−	50.0712i	0.463467	−	1.72968i
$839$	3.56179	−	13.2928i	0.122967	−	0.458918i	−0.876792	−	0.480869i	$-0.840321\pi$
$839$	3.56179	−	13.2928i	0.122967	−	0.458918i	0.999759	+	0.0219510i	$0.00698778\pi$
$840$	−0.311893	−	0.311893i	−0.0107613	−	0.0107613i
$841$	1.94610	+	3.37074i	0.0671069	+	0.116233i
$842$	7.72467	−	13.3795i	0.266210	−	0.461089i
$843$	0.835559	+	3.11835i	0.0287782	+	0.107402i
$844$	8.24574			0.283830
$845$	12.9315	−	22.5658i	0.444856	−	0.776287i
$846$			9.62479i			0.330907i
$847$	2.92284	+	0.0925234i	0.100430	+	0.00317914i
$848$	−8.87475	+	15.3715i	−0.304760	+	0.527860i
$849$	−0.687244	−	1.19034i	−0.0235862	−	0.0408524i
$850$	−0.208341	+	0.208341i	−0.00714603	+	0.00714603i
$851$	−30.5148	−	8.17641i	−1.04603	−	0.280284i
$852$	−5.43409	+	20.2803i	−0.186169	+	0.694791i
$853$	−6.92930	+	6.92930i	−0.237255	+	0.237255i	−0.815712	−	0.578458i	$-0.803655\pi$
$853$	−6.92930	+	6.92930i	−0.237255	+	0.237255i	0.578458	+	0.815712i	$0.303655\pi$
$854$	1.42091	−	0.820365i	0.0486227	−	0.0280723i
$855$	2.28014	−	3.94933i	0.0779793	−	0.135064i
$856$	−10.8652	+	2.91133i	−0.371365	+	0.0995071i
$857$	46.2894			1.58122			0.790608	−	0.612322i	$-0.209764\pi$
$857$	46.2894			1.58122			0.790608	+	0.612322i	$0.209764\pi$
$858$	25.0687	+	0.356226i	0.855830	+	0.0121613i
$859$	−26.8193			−0.915064			−0.457532	−	0.889193i	$-0.651266\pi$
$859$	−26.8193			−0.915064			−0.457532	+	0.889193i	$0.651266\pi$
$860$	−30.6446	+	8.21121i	−1.04497	+	0.280000i
$861$	−1.14224	+	1.97841i	−0.0389273	+	0.0674240i
$862$	−34.4022	+	19.8621i	−1.17174	+	0.676507i
$863$	14.9334	−	14.9334i	0.508340	−	0.508340i	−0.405677	−	0.914017i	$-0.632964\pi$
$863$	14.9334	−	14.9334i	0.508340	−	0.508340i	0.914017	+	0.405677i	$0.132964\pi$
$864$	−2.08561	+	7.78362i	−0.0709540	+	0.264804i
$865$	27.2682	+	7.30648i	0.927145	+	0.248428i
$866$	−32.9561	+	32.9561i	−1.11989	+	1.11989i
$867$	−8.49007	−	14.7052i	−0.288338	−	0.499416i
$868$	−1.40495	+	2.43345i	−0.0476871	+	0.0825965i
$869$	−19.0682	+	2.20406i	−0.646845	+	0.0747675i
$870$		−	24.0560i		−	0.815576i
$871$	−0.462182	−	1.11074i	−0.0156605	−	0.0376358i
$872$	4.55533			0.154263
$873$	−4.98959	−	18.6214i	−0.168872	−	0.630239i
$874$	−16.9187	+	29.3041i	−0.572284	+	0.991225i
$875$	−1.59490	−	2.76245i	−0.0539175	−	0.0933879i
$876$	4.13004	+	4.13004i	0.139541	+	0.139541i
$877$	12.0404	−	44.9355i	0.406577	−	1.51736i	−0.394553	−	0.918873i	$-0.629101\pi$
$877$	12.0404	−	44.9355i	0.406577	−	1.51736i	0.801129	−	0.598491i	$-0.204233\pi$
$878$	−3.95420	+	14.7573i	−0.133448	+	0.498035i
$879$	−2.37914	+	2.37914i	−0.0802464	+	0.0802464i
$880$	18.8325	−	7.45383i	0.634844	−	0.251268i
$881$	−11.7940	−	6.80926i	−0.397349	−	0.229410i	0.287990	−	0.957633i	$-0.407013\pi$
$881$	−11.7940	−	6.80926i	−0.397349	−	0.229410i	−0.685340	+	0.728224i	$0.740346\pi$
$882$	−3.76006	−	14.0327i	−0.126608	−	0.472506i
$883$			11.3800i			0.382967i	0.981496	+	0.191483i	$0.0613298\pi$
$883$			11.3800i			0.382967i	−0.981496	+	0.191483i	$0.938670\pi$
$884$	−1.12510	−	0.463908i	−0.0378413	−	0.0156029i
$885$	−15.5790			−0.523681
$886$	55.6420	−	14.9092i	1.86933	−	0.500886i
$887$	22.8021	+	13.1648i	0.765620	+	0.442031i	0.831310	−	0.555809i	$-0.187591\pi$
$887$	22.8021	+	13.1648i	0.765620	+	0.442031i	−0.0656898	+	0.997840i	$0.520925\pi$
$888$	1.85007	+	3.20441i	0.0620842	+	0.107533i
$889$	2.96356	−	2.96356i	0.0993948	−	0.0993948i
$890$	18.8198	−	70.2364i	0.630841	−	2.35433i
$891$	3.04370	+	1.31754i	0.101968	+	0.0441392i
$892$	−8.62094	−	8.62094i	−0.288650	−	0.288650i
$893$	−9.06226	+	5.23210i	−0.303257	+	0.175085i
$894$	−11.4402	−	6.60498i	−0.382616	−	0.220904i
$895$	−37.3600	+	10.0106i	−1.24881	+	0.334617i
$896$			1.72926i			0.0577707i
$897$	−20.2287	+	15.5739i	−0.675417	+	0.519999i
$898$		−	9.26104i		−	0.309045i
$899$	−24.4424	+	6.54933i	−0.815201	+	0.218432i
$900$	1.19468	−	2.06924i	0.0398226	−	0.0689747i
$901$	−0.409658	−	0.709549i	−0.0136477	−	0.0236385i
$902$	35.6207	+	47.9748i	1.18604	+	1.59738i
$903$	1.69983	+	0.455469i	0.0565670	+	0.0151571i
$904$	−6.51517	−	1.74573i	−0.216691	−	0.0580622i
$905$	16.5221	+	16.5221i	0.549214	+	0.549214i
$906$	12.3235	+	21.3449i	0.409420	+	0.709137i
$907$	−31.2122	−	18.0204i	−1.03638	−	0.598357i	−0.117577	−	0.993064i	$-0.537513\pi$
$907$	−31.2122	−	18.0204i	−1.03638	−	0.598357i	−0.918807	+	0.394707i	$0.870846\pi$
$908$	−0.701917	−	2.61959i	−0.0232939	−	0.0869341i
$909$	11.7308			0.389086
$910$	2.44237	−	3.19362i	0.0809638	−	0.105867i
$911$	28.9353			0.958670			0.479335	−	0.877632i	$-0.340878\pi$
$911$	28.9353			0.958670			0.479335	+	0.877632i	$0.340878\pi$
$912$	−6.72061	+	1.80078i	−0.222542	+	0.0596298i
$913$	17.8328	−	22.4941i	0.590178	−	0.744445i
$914$	−24.9618	+	14.4117i	−0.825662	+	0.476696i
$915$	−4.16443	−	4.16443i	−0.137672	−	0.137672i
$916$	13.3258	+	3.57065i	0.440298	+	0.117978i
$917$	1.24342	−	4.64051i	0.0410614	−	0.153243i
$918$	−0.208882	−	0.208882i	−0.00689413	−	0.00689413i
$919$	−15.6841	+	9.05524i	−0.517372	+	0.298705i	−0.735859	−	0.677135i	$-0.763221\pi$
$919$	−15.6841	+	9.05524i	−0.517372	+	0.298705i	0.218487	+	0.975840i	$0.429888\pi$
$920$	5.87393	−	10.1739i	0.193658	−	0.335425i
$921$	3.72848	+	13.9149i	0.122858	+	0.458511i
$922$			68.4516i			2.25433i
$923$	−31.3368	−	4.07415i	−1.03146	−	0.134102i
$924$	2.08950	+	0.308794i	0.0687394	+	0.0101586i
$925$	1.15178	+	4.29848i	0.0378701	+	0.141333i
$926$	−10.4755	−	6.04801i	−0.344245	−	0.198750i
$927$	−1.07269	+	0.619316i	−0.0352316	+	0.0203410i
$928$	−32.6790	+	32.6790i	−1.07274	+	1.07274i
$929$	−50.0499	−	13.4108i	−1.64208	−	0.439995i	−0.684703	−	0.728822i	$-0.740068\pi$
$929$	−50.0499	−	13.4108i	−1.64208	−	0.439995i	−0.957381	+	0.288827i	$0.906735\pi$
$930$	17.8762	+	4.78992i	0.586184	+	0.157068i
$931$	11.1686	−	11.1686i	0.366035	−	0.366035i
$932$	−3.37791	+	1.95024i	−0.110647	+	0.0638821i
$933$	7.14362	+	4.12437i	0.233872	+	0.135026i
$934$	18.2969	+	68.2848i	0.598692	+	2.23435i
$935$	−0.136682	+	0.924878i	−0.00446998	+	0.0302467i
$936$	2.96519	+	0.385508i	0.0969201	+	0.0126007i
$937$			17.3653i			0.567300i	0.958928	+	0.283650i	$0.0915455\pi$
$937$			17.3653i			0.567300i	−0.958928	+	0.283650i	$0.908455\pi$
$938$	−0.0481335	−	0.179637i	−0.00157161	−	0.00586535i
$939$	9.39161	−	16.2667i	0.306484	−	0.530845i
$940$	19.0543	−	11.0010i	0.621482	−	0.358813i
$941$	−35.5261	−	35.5261i	−1.15812	−	1.15812i	−0.984880	−	0.173237i	$-0.944577\pi$
$941$	−35.5261	−	35.5261i	−1.15812	−	1.15812i	−0.173237	−	0.984880i	$-0.555423\pi$
$942$	−10.9806	+	40.9802i	−0.357768	+	1.33521i
$943$	−58.7716	−	15.7478i	−1.91387	−	0.512819i
$944$	16.8072	+	16.8072i	0.547029	+	0.547029i
$945$	0.460608	−	0.265932i	0.0149836	−	0.00865076i
$946$	28.5953	−	36.0698i	0.929712	−	1.17273i
$947$	19.9065	−	5.33394i	0.646875	−	0.173330i	0.0795595	−	0.996830i	$-0.474649\pi$
$947$	19.9065	−	5.33394i	0.646875	−	0.173330i	0.567316	+	0.823500i	$0.307982\pi$
$948$	−13.8644			−0.450296
$949$	−5.34031	+	6.98292i	−0.173354	+	0.226675i
$950$	4.76653			0.154647
$951$	2.05719	+	7.67755i	0.0667091	+	0.248962i
$952$	−0.0269023	−	0.0155320i	−0.000871908	−	0.000503396i
$953$	−23.6210	−	40.9127i	−0.765158	−	1.32529i	−0.940163	−	0.340726i	$-0.889327\pi$
$953$	−23.6210	−	40.9127i	−0.765158	−	1.32529i	0.175004	−	0.984568i	$-0.444006\pi$
$954$	8.62055	+	8.62055i	0.279101	+	0.279101i
$955$	0.431978	+	0.115748i	0.0139785	+	0.00374552i
$956$	−61.2987	−	16.4249i	−1.98254	−	0.531221i
$957$	11.3393	+	15.2720i	0.366547	+	0.493674i
$958$	13.2390	+	22.9306i	0.427732	+	0.740854i
$959$	−1.90295	+	3.29600i	−0.0614493	+	0.106433i
$960$	20.8508	−	5.58694i	0.672955	−	0.180318i
$961$			11.5326i			0.372019i
$962$	−26.7242	+	20.5748i	−0.861623	+	0.663358i
$963$		−	13.5636i		−	0.437081i
$964$	40.7365	−	10.9153i	1.31203	−	0.351559i
$965$	−6.66481	−	3.84793i	−0.214548	−	0.123869i
$966$	−3.41772	+	1.97322i	−0.109963	+	0.0634873i
$967$	−20.3792	−	20.3792i	−0.655352	−	0.655352i	0.298925	−	0.954277i	$-0.403372\pi$
$967$	−20.3792	−	20.3792i	−0.655352	−	0.655352i	−0.954277	+	0.298925i	$0.903372\pi$
$968$	4.80891	−	7.75202i	0.154564	−	0.249159i
$969$	0.0831241	−	0.310223i	0.00267033	−	0.00996580i
$970$	−57.1783	+	57.1783i	−1.83588	+	1.83588i
$971$	0.187382	+	0.324554i	0.00601336	+	0.0104154i	0.869016	−	0.494783i	$-0.164753\pi$
$971$	0.187382	+	0.324554i	0.00601336	+	0.0104154i	−0.863003	+	0.505199i	$0.831419\pi$
$972$	2.07462	+	1.19778i	0.0665433	+	0.0384188i
$973$	−0.827554	+	0.221742i	−0.0265302	+	0.00710873i
$974$	−10.5418			−0.337780
$975$	3.32468	+	1.37085i	0.106475	+	0.0439023i
$976$			8.98552i			0.287620i
$977$	2.38720	+	8.90916i	0.0763734	+	0.285029i	0.993541	−	0.113472i	$-0.0361972\pi$
$977$	2.38720	+	8.90916i	0.0763734	+	0.285029i	−0.917168	+	0.398501i	$0.869530\pi$
$978$	−2.91175	−	1.68110i	−0.0931074	−	0.0537556i
$979$	21.1596	+	53.4608i	0.676262	+	1.70861i
$980$	−23.4830	+	23.4830i	−0.750137	+	0.750137i
$981$	−1.42166	+	5.30572i	−0.0453902	+	0.169399i
$982$	−22.8964	+	85.4504i	−0.730653	+	2.72683i
$983$	22.4618	+	22.4618i	0.716421	+	0.716421i	0.967870	−	0.251450i	$-0.0809073\pi$
$983$	22.4618	+	22.4618i	0.716421	+	0.716421i	−0.251450	+	0.967870i	$0.580907\pi$
$984$	3.56324	+	6.17172i	0.113592	+	0.196747i
$985$	16.0016	−	27.7155i	0.509852	−	0.883090i
$986$	−0.438489	−	1.63646i	−0.0139643	−	0.0521156i
$987$	−1.22043			−0.0388468
$988$	7.56359	+	18.1771i	0.240630	+	0.578291i
$989$			46.8707i			1.49040i
$990$	−1.59737	−	13.8195i	−0.0507677	−	0.439212i
$991$	−26.3697	+	45.6737i	−0.837661	+	1.45087i	0.0541835	+	0.998531i	$0.482744\pi$
$991$	−26.3697	+	45.6737i	−0.837661	+	1.45087i	−0.891845	+	0.452341i	$0.850589\pi$
$992$	−17.7771	−	30.7909i	−0.564424	−	0.977612i
$993$	−15.7211	+	15.7211i	−0.498894	+	0.498894i
$994$	−4.71850	−	1.26432i	−0.149662	−	0.0401017i
$995$	0.346126	−	1.29176i	0.0109729	−	0.0409515i
$996$	14.6608	−	14.6608i	0.464544	−	0.464544i
$997$	−53.9281	+	31.1354i	−1.70792	+	0.986069i	−0.770792	+	0.637087i	$0.780139\pi$
$997$	−53.9281	+	31.1354i	−1.70792	+	0.986069i	−0.937129	+	0.348982i	$0.886527\pi$
$998$	−3.81893	+	6.61458i	−0.120886	+	0.209381i
$999$	−4.30965	+	1.15477i	−0.136351	+	0.0365352i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bd.b.175.2	yes	56
11.10	odd	2	inner	429.2.bd.b.175.13	yes	56
13.11	odd	12	inner	429.2.bd.b.76.13	yes	56
143.76	even	12	inner	429.2.bd.b.76.2	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bd.b.76.2	✓	56	143.76	even	12	inner
429.2.bd.b.76.13	yes	56	13.11	odd	12	inner
429.2.bd.b.175.2	yes	56	1.1	even	1	trivial
429.2.bd.b.175.13	yes	56	11.10	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.02512 + 0.542629i) q^{2} +(0.500000 - 0.866025i) q^{3} +(2.07462 - 1.19778i) q^{4} +(1.41467 - 1.41467i) q^{5} +(-0.542629 + 2.02512i) q^{6} +(-0.256787 - 0.0688060i) q^{7} +(-0.586415 + 0.586415i) q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-2.02512 + 0.542629i) q^{2} +(0.500000 - 0.866025i) q^{3} +(2.07462 - 1.19778i) q^{4} +(1.41467 - 1.41467i) q^{5} +(-0.542629 + 2.02512i) q^{6} +(-0.256787 - 0.0688060i) q^{7} +(-0.586415 + 0.586415i) q^{8} +(-0.500000 - 0.866025i) q^{9} +(-2.09724 + 3.63252i) q^{10} +(-0.380826 - 3.29469i) q^{11} -2.39556i q^{12} +(3.57394 - 0.476385i) q^{13} +0.557361 q^{14} +(-0.517806 - 1.93248i) q^{15} +(-1.52621 + 2.64347i) q^{16} +(-0.0704496 - 0.122022i) q^{17} +(1.48249 + 1.48249i) q^{18} +(-0.589954 + 2.20174i) q^{19} +(1.24043 - 4.62937i) q^{20} +(-0.187981 + 0.187981i) q^{21} +(2.55901 + 6.46549i) q^{22} +(-6.13195 - 3.54029i) q^{23} +(0.214643 + 0.801057i) q^{24} +0.997410i q^{25} +(-6.97916 + 2.90406i) q^{26} -1.00000 q^{27} +(-0.615150 + 0.164829i) q^{28} +(-4.96680 - 2.86759i) q^{29} +(2.09724 + 3.63252i) q^{30} +(3.11989 - 3.11989i) q^{31} +(2.08561 - 7.78362i) q^{32} +(-3.04370 - 1.31754i) q^{33} +(0.208882 + 0.208882i) q^{34} +(-0.460608 + 0.265932i) q^{35} +(-2.07462 - 1.19778i) q^{36} +(4.30965 - 1.15477i) q^{37} -4.77891i q^{38} +(1.37441 - 3.33332i) q^{39} +1.65917i q^{40} +(8.30041 - 2.22409i) q^{41} +(0.278681 - 0.482689i) q^{42} +(-3.30981 - 5.73276i) q^{43} +(-4.73638 - 6.37907i) q^{44} +(-1.93248 - 0.517806i) q^{45} +(14.3390 + 3.84213i) q^{46} +(3.24615 + 3.24615i) q^{47} +(1.52621 + 2.64347i) q^{48} +(-6.00097 - 3.46466i) q^{49} +(-0.541224 - 2.01987i) q^{50} -0.140899 q^{51} +(6.84395 - 5.26911i) q^{52} +5.81491 q^{53} +(2.02512 - 0.542629i) q^{54} +(-5.19965 - 4.12216i) q^{55} +(0.190933 - 0.110235i) q^{56} +(1.61178 + 1.61178i) q^{57} +(11.6144 + 3.11207i) q^{58} +(2.01541 - 7.52163i) q^{59} +(-3.38893 - 3.38893i) q^{60} +(2.54936 - 1.47187i) q^{61} +(-4.62521 + 8.01109i) q^{62} +(0.0688060 + 0.256787i) q^{63} +10.7897i q^{64} +(4.38202 - 5.72988i) q^{65} +(6.87879 + 1.01658i) q^{66} +(-0.0863596 - 0.322298i) q^{67} +(-0.292312 - 0.168766i) q^{68} +(-6.13195 + 3.54029i) q^{69} +(0.788483 - 0.788483i) q^{70} +(-8.46578 - 2.26840i) q^{71} +(0.801057 + 0.214643i) q^{72} +(-1.72404 + 1.72404i) q^{73} +(-8.10095 + 4.67708i) q^{74} +(0.863782 + 0.498705i) q^{75} +(1.41327 + 5.27439i) q^{76} +(-0.128903 + 0.872237i) q^{77} +(-0.974588 + 7.49616i) q^{78} -5.78756i q^{79} +(1.58056 + 5.89871i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-15.6025 + 9.00809i) q^{82} +(6.11997 + 6.11997i) q^{83} +(-0.164829 + 0.615150i) q^{84} +(-0.272285 - 0.0729584i) q^{85} +(9.81353 + 9.81353i) q^{86} +(-4.96680 + 2.86759i) q^{87} +(2.15538 + 1.70873i) q^{88} +(-16.7450 + 4.48680i) q^{89} +4.19448 q^{90} +(-0.950521 - 0.123579i) q^{91} -16.9619 q^{92} +(-1.14196 - 4.26185i) q^{93} +(-8.33531 - 4.81239i) q^{94} +(2.28014 + 3.94933i) q^{95} +(-5.69800 - 5.69800i) q^{96} +(18.6214 + 4.98959i) q^{97} +(14.0327 + 3.76006i) q^{98} +(-2.66287 + 1.97715i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 28 q^{3} - 4 q^{5} - 28 q^{9}+O(q^{10}) \) 56 * q + 28 * q^3 - 4 * q^5 - 28 * q^9	\( 56 q + 28 q^{3} - 4 q^{5} - 28 q^{9} - 4 q^{11} - 24 q^{14} - 8 q^{15} + 4 q^{16} + 80 q^{20} - 10 q^{22} - 12 q^{23} + 40 q^{26} - 56 q^{27} - 12 q^{31} - 8 q^{33} - 16 q^{34} - 12 q^{37} - 12 q^{42} + 24 q^{44} - 4 q^{45} - 40 q^{47} - 4 q^{48} + 24 q^{49} - 88 q^{53} - 18 q^{55} + 72 q^{56} + 40 q^{58} + 8 q^{59} + 52 q^{60} - 20 q^{66} - 4 q^{67} - 12 q^{69} + 40 q^{70} - 24 q^{71} + 12 q^{75} - 4 q^{78} - 188 q^{80} - 28 q^{81} - 12 q^{82} + 32 q^{86} + 18 q^{88} - 16 q^{89} + 28 q^{91} - 96 q^{92} - 12 q^{93} - 28 q^{97} - 4 q^{99}+O(q^{100}) \) 56 * q + 28 * q^3 - 4 * q^5 - 28 * q^9 - 4 * q^11 - 24 * q^14 - 8 * q^15 + 4 * q^16 + 80 * q^20 - 10 * q^22 - 12 * q^23 + 40 * q^26 - 56 * q^27 - 12 * q^31 - 8 * q^33 - 16 * q^34 - 12 * q^37 - 12 * q^42 + 24 * q^44 - 4 * q^45 - 40 * q^47 - 4 * q^48 + 24 * q^49 - 88 * q^53 - 18 * q^55 + 72 * q^56 + 40 * q^58 + 8 * q^59 + 52 * q^60 - 20 * q^66 - 4 * q^67 - 12 * q^69 + 40 * q^70 - 24 * q^71 + 12 * q^75 - 4 * q^78 - 188 * q^80 - 28 * q^81 - 12 * q^82 + 32 * q^86 + 18 * q^88 - 16 * q^89 + 28 * q^91 - 96 * q^92 - 12 * q^93 - 28 * q^97 - 4 * q^99

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