LMFDB - Embedded newform 429.2.bq.a.29.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(29,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 21, 10]))

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

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

chi := DirichletCharacter("429.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bq (of order $30$, degree $8$, 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:	$416$
Relative dimension:	$52$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			29.5
Character	$\chi$	$=$	429.29
Dual form			429.2.bq.a.74.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.256618 + 2.44156i) q^{2} +(1.38266 + 1.04320i) q^{3} +(-3.93907 - 0.837274i) q^{4} +(1.76595 + 2.43063i) q^{5} +(-2.90184 + 3.10814i) q^{6} +(-0.156026 + 0.734044i) q^{7} +(1.53781 - 4.73290i) q^{8} +(0.823485 + 2.88477i) q^{9} +O(q^{10})$	\(q+(-0.256618 + 2.44156i) q^{2} +(1.38266 + 1.04320i) q^{3} +(-3.93907 - 0.837274i) q^{4} +(1.76595 + 2.43063i) q^{5} +(-2.90184 + 3.10814i) q^{6} +(-0.156026 + 0.734044i) q^{7} +(1.53781 - 4.73290i) q^{8} +(0.823485 + 2.88477i) q^{9} +(-6.38769 + 3.68794i) q^{10} +(-1.74541 - 2.82020i) q^{11} +(-4.57294 - 5.26688i) q^{12} +(3.60543 + 0.0299579i) q^{13} +(-1.75217 - 0.569316i) q^{14} +(-0.0939104 + 5.20296i) q^{15} +(3.80321 + 1.69330i) q^{16} +(0.0696395 + 0.662576i) q^{17} +(-7.25465 + 1.27030i) q^{18} +(3.53522 - 3.18313i) q^{19} +(-4.92110 - 11.0530i) q^{20} +(-0.981482 + 0.852166i) q^{21} +(7.33359 - 3.53782i) q^{22} +(-3.23872 + 1.86987i) q^{23} +(7.06361 - 4.93974i) q^{24} +(-1.24426 + 3.82945i) q^{25} +(-0.998362 + 8.79518i) q^{26} +(-1.87078 + 4.84770i) q^{27} +(1.22919 - 2.76081i) q^{28} +(4.34272 - 4.82308i) q^{29} +(-12.6792 - 1.56446i) q^{30} +(-6.99629 - 5.08310i) q^{31} +(-0.133799 + 0.231746i) q^{32} +(0.528712 - 5.72018i) q^{33} -1.63559 q^{34} +(-2.05972 + 0.917046i) q^{35} +(-0.828420 - 12.0528i) q^{36} +(0.316971 - 0.352032i) q^{37} +(6.86460 + 9.44831i) q^{38} +(4.95382 + 3.80259i) q^{39} +(14.2196 - 4.62023i) q^{40} +(-3.79981 + 0.807674i) q^{41} +(-1.82875 - 2.61503i) q^{42} +(-1.37938 - 0.796385i) q^{43} +(4.51402 + 12.5703i) q^{44} +(-5.55755 + 7.09594i) q^{45} +(-3.73429 - 8.38736i) q^{46} +(7.37983 + 2.39785i) q^{47} +(3.49210 + 6.30875i) q^{48} +(5.88034 + 2.61810i) q^{49} +(-9.03054 - 4.02066i) q^{50} +(-0.594909 + 0.988763i) q^{51} +(-14.1769 - 3.13674i) q^{52} +(4.36187 - 6.00360i) q^{53} +(-11.3559 - 5.81163i) q^{54} +(3.77253 - 9.22279i) q^{55} +(3.23422 + 1.86728i) q^{56} +(8.20863 - 0.713248i) q^{57} +(10.6614 + 11.8407i) q^{58} +(-0.699173 + 3.28935i) q^{59} +(4.72622 - 20.4162i) q^{60} +(7.98311 - 0.839059i) q^{61} +(14.2061 - 15.7774i) q^{62} +(-2.24603 + 0.154376i) q^{63} +(6.20461 + 4.50791i) q^{64} +(6.29420 + 8.81634i) q^{65} +(13.8305 + 2.75878i) q^{66} +(-2.57325 - 4.45699i) q^{67} +(0.280443 - 2.66824i) q^{68} +(-6.42868 - 0.793220i) q^{69} +(-1.71046 - 5.26426i) q^{70} +(-14.7292 + 1.54811i) q^{71} +(14.9197 + 0.538759i) q^{72} +(5.75591 - 1.87021i) q^{73} +(0.778167 + 0.864242i) q^{74} +(-5.71526 + 3.99681i) q^{75} +(-16.5906 + 9.57861i) q^{76} +(2.34248 - 0.841186i) q^{77} +(-10.5555 + 11.1192i) q^{78} +(-6.53147 + 8.98980i) q^{79} +(2.60052 + 12.2345i) q^{80} +(-7.64375 + 4.75112i) q^{81} +(-0.996885 - 9.48473i) q^{82} +(-2.87119 + 2.08604i) q^{83} +(4.57962 - 2.53497i) q^{84} +(-1.48749 + 1.33935i) q^{85} +(2.29840 - 3.16347i) q^{86} +(11.0359 - 2.13836i) q^{87} +(-16.0318 + 3.92393i) q^{88} +(-11.4515 + 6.61154i) q^{89} +(-15.8990 - 15.3900i) q^{90} +(-0.584530 + 2.64187i) q^{91} +(14.3231 - 4.65386i) q^{92} +(-4.37080 - 14.3267i) q^{93} +(-7.74830 + 17.4030i) q^{94} +(13.9800 + 2.97155i) q^{95} +(-0.426754 + 0.180847i) q^{96} +(-6.47388 + 2.88236i) q^{97} +(-7.90124 + 13.6854i) q^{98} +(6.69830 - 7.35750i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 416 q - 3 q^{3} + 42 q^{4} - 5 q^{6} - 10 q^{7} + 3 q^{9}+O(q^{10}) $ 416 * q - 3 * q^3 + 42 * q^4 - 5 * q^6 - 10 * q^7 + 3 * q^9	$ 416 q - 3 q^{3} + 42 q^{4} - 5 q^{6} - 10 q^{7} + 3 q^{9} - 52 q^{12} - 20 q^{13} - 3 q^{15} + 30 q^{16} - 20 q^{18} - 10 q^{19} + 4 q^{22} + 5 q^{24} + 60 q^{25} - 24 q^{27} - 10 q^{28} - 65 q^{30} - 8 q^{31} + 49 q^{33} - 24 q^{34} + 3 q^{36} - 6 q^{37} - 35 q^{39} - 120 q^{40} - 13 q^{42} - 32 q^{45} - 30 q^{46} - 33 q^{48} - 26 q^{49} - 100 q^{51} - 60 q^{52} - 42 q^{55} - 20 q^{57} - 34 q^{58} + 32 q^{60} - 30 q^{61} - 45 q^{63} + 40 q^{64} + 42 q^{66} + 32 q^{67} - 33 q^{69} - 268 q^{70} + 55 q^{72} - 40 q^{73} + 9 q^{75} - 32 q^{78} - 37 q^{81} + 28 q^{82} - 180 q^{84} - 10 q^{85} - 142 q^{88} - 30 q^{90} + 8 q^{91} - 26 q^{93} - 90 q^{94} + 330 q^{96} - 14 q^{97} - 4 q^{99}+O(q^{100}) $ 416 * q - 3 * q^3 + 42 * q^4 - 5 * q^6 - 10 * q^7 + 3 * q^9 - 52 * q^12 - 20 * q^13 - 3 * q^15 + 30 * q^16 - 20 * q^18 - 10 * q^19 + 4 * q^22 + 5 * q^24 + 60 * q^25 - 24 * q^27 - 10 * q^28 - 65 * q^30 - 8 * q^31 + 49 * q^33 - 24 * q^34 + 3 * q^36 - 6 * q^37 - 35 * q^39 - 120 * q^40 - 13 * q^42 - 32 * q^45 - 30 * q^46 - 33 * q^48 - 26 * q^49 - 100 * q^51 - 60 * q^52 - 42 * q^55 - 20 * q^57 - 34 * q^58 + 32 * q^60 - 30 * q^61 - 45 * q^63 + 40 * q^64 + 42 * q^66 + 32 * q^67 - 33 * q^69 - 268 * q^70 + 55 * q^72 - 40 * q^73 + 9 * q^75 - 32 * q^78 - 37 * q^81 + 28 * q^82 - 180 * q^84 - 10 * q^85 - 142 * q^88 - 30 * q^90 + 8 * q^91 - 26 * q^93 - 90 * q^94 + 330 * q^96 - 14 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{10}\right)$	$-1$

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 $

$2$	−0.256618	+	2.44156i	−0.181457	+	1.72644i	0.403156	+	0.915131i	$0.367913\pi$
$2$	−0.256618	+	2.44156i	−0.181457	+	1.72644i	−0.584613	+	0.811312i	$0.698754\pi$
$3$	1.38266	+	1.04320i	0.798278	+	0.602289i
$3$	1.38266	+	1.04320i	0.798278	+	0.602289i
$4$	−3.93907	−	0.837274i	−1.96953	−	0.418637i
$5$	1.76595	+	2.43063i	0.789758	+	1.08701i	0.994138	+	0.108117i	$0.0344821\pi$
$5$	1.76595	+	2.43063i	0.789758	+	1.08701i	−0.204380	+	0.978892i	$0.565518\pi$
$6$	−2.90184	+	3.10814i	−1.18467	+	1.26889i
$7$	−0.156026	+	0.734044i	−0.0589722	+	0.277443i	−0.997747	−	0.0670889i	$-0.978629\pi$
$7$	−0.156026	+	0.734044i	−0.0589722	+	0.277443i	0.938775	+	0.344531i	$0.111962\pi$
$8$	1.53781	−	4.73290i	0.543699	−	1.67333i
$9$	0.823485	+	2.88477i	0.274495	+	0.961589i
$10$	−6.38769	+	3.68794i	−2.01997	+	1.16623i
$11$	−1.74541	−	2.82020i	−0.526262	−	0.850322i
$11$	−1.74541	−	2.82020i	−0.526262	−	0.850322i
$12$	−4.57294	−	5.26688i	−1.32009	−	1.52042i
$13$	3.60543	+	0.0299579i	0.999965	+	0.00830881i
$13$	3.60543	+	0.0299579i	0.999965	+	0.00830881i
$14$	−1.75217	−	0.569316i	−0.468288	−	0.152156i
$15$	−0.0939104	+	5.20296i	−0.0242476	+	1.34340i
$16$	3.80321	+	1.69330i	0.950803	+	0.423325i
$17$	0.0696395	+	0.662576i	0.0168901	+	0.160698i	0.999716	−	0.0238376i	$-0.00758847\pi$
$17$	0.0696395	+	0.662576i	0.0168901	+	0.160698i	−0.982826	+	0.184536i	$0.940922\pi$
$18$	−7.25465	+	1.27030i	−1.70994	+	0.299413i
$19$	3.53522	−	3.18313i	0.811036	−	0.730260i	−0.155210	−	0.987882i	$-0.549605\pi$
$19$	3.53522	−	3.18313i	0.811036	−	0.730260i	0.966246	+	0.257621i	$0.0829387\pi$
$20$	−4.92110	−	11.0530i	−1.10039	−	2.47152i
$21$	−0.981482	+	0.852166i	−0.214177	+	0.185958i
$22$	7.33359	−	3.53782i	1.56353	−	0.754265i
$23$	−3.23872	+	1.86987i	−0.675319	+	0.389896i	−0.798089	−	0.602540i	$-0.794156\pi$
$23$	−3.23872	+	1.86987i	−0.675319	+	0.389896i	0.122770	+	0.992435i	$0.460822\pi$
$24$	7.06361	−	4.93974i	1.44185	−	1.00832i
$25$	−1.24426	+	3.82945i	−0.248853	+	0.765891i
$26$	−0.998362	+	8.79518i	−0.195795	+	1.72488i
$27$	−1.87078	+	4.84770i	−0.360032	+	0.932940i
$28$	1.22919	−	2.76081i	0.232296	−	0.521744i
$29$	4.34272	−	4.82308i	0.806423	−	0.895623i	−0.189856	−	0.981812i	$-0.560802\pi$
$29$	4.34272	−	4.82308i	0.806423	−	0.895623i	0.996279	+	0.0861889i	$0.0274689\pi$
$30$	−12.6792	−	1.56446i	−2.31490	−	0.285630i
$31$	−6.99629	−	5.08310i	−1.25657	−	0.912952i	−0.257987	−	0.966148i	$-0.583059\pi$
$31$	−6.99629	−	5.08310i	−1.25657	−	0.912952i	−0.998584	+	0.0531958i	$0.983059\pi$
$32$	−0.133799	+	0.231746i	−0.0236525	+	0.0409673i
$33$	0.528712	−	5.72018i	0.0920370	−	0.995756i
$34$	−1.63559			−0.280501
$35$	−2.05972	+	0.917046i	−0.348156	+	0.155009i
$36$	−0.828420	−	12.0528i	−0.138070	−	2.00879i
$37$	0.316971	−	0.352032i	0.0521098	−	0.0578738i	−0.716526	−	0.697560i	$-0.754269\pi$
$37$	0.316971	−	0.352032i	0.0521098	−	0.0578738i	0.768636	+	0.639686i	$0.220936\pi$
$38$	6.86460	+	9.44831i	1.11358	+	1.53272i
$39$	4.95382	+	3.80259i	0.793246	+	0.608901i
$40$	14.2196	−	4.62023i	2.24832	−	0.730523i
$41$	−3.79981	+	0.807674i	−0.593430	+	0.126138i	−0.494830	−	0.868990i	$-0.664770\pi$
$41$	−3.79981	+	0.807674i	−0.593430	+	0.126138i	−0.0986001	+	0.995127i	$0.531436\pi$
$42$	−1.82875	−	2.61503i	−0.282182	−	0.403508i
$43$	−1.37938	−	0.796385i	−0.210353	−	0.121448i	0.391122	−	0.920339i	$-0.372087\pi$
$43$	−1.37938	−	0.796385i	−0.210353	−	0.121448i	−0.601476	+	0.798891i	$0.705420\pi$
$44$	4.51402	+	12.5703i	0.680514	+	1.89505i
$45$	−5.55755	+	7.09594i	−0.828471	+	1.05780i
$46$	−3.73429	−	8.38736i	−0.550592	−	1.23665i
$47$	7.37983	+	2.39785i	1.07646	+	0.349763i	0.793000	−	0.609222i	$-0.208518\pi$
$47$	7.37983	+	2.39785i	1.07646	+	0.349763i	0.283459	+	0.958984i	$0.408518\pi$
$48$	3.49210	+	6.30875i	0.504041	+	0.910590i
$49$	5.88034	+	2.61810i	0.840049	+	0.374014i
$50$	−9.03054	−	4.02066i	−1.27711	−	0.568607i
$51$	−0.594909	+	0.988763i	−0.0833039	+	0.138455i
$52$	−14.1769	−	3.13674i	−1.96599	−	0.434987i
$53$	4.36187	−	6.00360i	0.599149	−	0.824658i	−0.396481	−	0.918043i	$-0.629769\pi$
$53$	4.36187	−	6.00360i	0.599149	−	0.824658i	0.995630	+	0.0933850i	$0.0297687\pi$
$54$	−11.3559	−	5.81163i	−1.54534	−	0.790862i
$55$	3.77253	−	9.22279i	0.508688	−	1.24360i
$56$	3.23422	+	1.86728i	0.432191	+	0.249525i
$57$	8.20863	−	0.713248i	1.08726	−	0.0944720i
$58$	10.6614	+	11.8407i	1.39991	+	1.55476i
$59$	−0.699173	+	3.28935i	−0.0910246	+	0.428237i	0.908912	+	0.416988i	$0.136914\pi$
$59$	−0.699173	+	3.28935i	−0.0910246	+	0.428237i	−0.999937	+	0.0112493i	$0.996419\pi$
$60$	4.72622	−	20.4162i	0.610153	−	2.63572i
$61$	7.98311	−	0.839059i	1.02213	−	0.107430i	0.421395	−	0.906877i	$-0.361540\pi$
$61$	7.98311	−	0.839059i	1.02213	−	0.107430i	0.600737	+	0.799447i	$0.294874\pi$
$62$	14.2061	−	15.7774i	1.80417	−	2.00374i
$63$	−2.24603	+	0.154376i	−0.282973	+	0.0194495i
$64$	6.20461	+	4.50791i	0.775576	+	0.563489i
$65$	6.29420	+	8.81634i	0.780699	+	1.09353i
$66$	13.8305	+	2.75878i	1.70242	+	0.339583i
$67$	−2.57325	−	4.45699i	−0.314372	−	0.544508i	0.664932	−	0.746904i	$-0.268461\pi$
$67$	−2.57325	−	4.45699i	−0.314372	−	0.544508i	−0.979304	+	0.202396i	$0.935127\pi$
$68$	0.280443	−	2.66824i	0.0340087	−	0.323571i
$69$	−6.42868	−	0.793220i	−0.773922	−	0.0954925i
$70$	−1.71046	−	5.26426i	−0.204439	−	0.629199i
$71$	−14.7292	+	1.54811i	−1.74804	+	0.183726i	−0.923893	−	0.382650i	$-0.875011\pi$
$71$	−14.7292	+	1.54811i	−1.74804	+	0.183726i	−0.824146	+	0.566377i	$0.808345\pi$
$72$	14.9197	+	0.538759i	1.75830	+	0.0634933i
$73$	5.75591	−	1.87021i	0.673678	−	0.218891i	0.0478526	−	0.998854i	$-0.484762\pi$
$73$	5.75591	−	1.87021i	0.673678	−	0.218891i	0.625825	+	0.779963i	$0.284762\pi$
$74$	0.778167	+	0.864242i	0.0904601	+	0.100466i
$75$	−5.71526	+	3.99681i	−0.659942	+	0.461512i
$76$	−16.5906	+	9.57861i	−1.90308	+	1.09874i
$77$	2.34248	−	0.841186i	0.266950	−	0.0958621i
$78$	−10.5555	+	11.1192i	−1.19517	+	1.25901i
$79$	−6.53147	+	8.98980i	−0.734848	+	1.01143i	0.264051	+	0.964509i	$0.414941\pi$
$79$	−6.53147	+	8.98980i	−0.734848	+	1.01143i	−0.998899	+	0.0469224i	$0.985059\pi$
$80$	2.60052	+	12.2345i	0.290747	+	1.36786i
$81$	−7.64375	+	4.75112i	−0.849305	+	0.527902i
$82$	−0.996885	−	9.48473i	−0.110088	−	1.04741i
$83$	−2.87119	+	2.08604i	−0.315154	+	0.228973i	−0.734105	−	0.679036i	$-0.762398\pi$
$83$	−2.87119	+	2.08604i	−0.315154	+	0.228973i	0.418951	+	0.908009i	$0.362398\pi$
$84$	4.57962	−	2.53497i	0.499677	−	0.276588i
$85$	−1.48749	+	1.33935i	−0.161341	+	0.145272i
$86$	2.29840	−	3.16347i	0.247842	−	0.341126i
$87$	11.0359	−	2.13836i	1.18317	−	0.229256i
$88$	−16.0318	+	3.92393i	−1.70900	+	0.418292i
$89$	−11.4515	+	6.61154i	−1.21386	+	0.700822i	−0.963598	−	0.267356i	$-0.913850\pi$
$89$	−11.4515	+	6.61154i	−1.21386	+	0.700822i	−0.250261	+	0.968178i	$0.580517\pi$
$90$	−15.8990	−	15.3900i	−1.67590	−	1.62225i
$91$	−0.584530	+	2.64187i	−0.0612754	+	0.276943i
$92$	14.3231	−	4.65386i	1.49329	−	0.485199i
$93$	−4.37080	−	14.3267i	−0.453231	−	1.48561i
$94$	−7.74830	+	17.4030i	−0.799176	+	1.79498i
$95$	13.9800	+	2.97155i	1.43432	+	0.304874i
$96$	−0.426754	+	0.180847i	−0.0435554	+	0.0184576i
$97$	−6.47388	+	2.88236i	−0.657323	+	0.292659i	−0.708164	−	0.706048i	$-0.750476\pi$
$97$	−6.47388	+	2.88236i	−0.657323	+	0.292659i	0.0508413	+	0.998707i	$0.483810\pi$
$98$	−7.90124	+	13.6854i	−0.798146	+	1.38243i
$99$	6.69830	−	7.35750i	0.673204	−	0.739457i
$100$	8.10755	−	14.0427i	0.810755	−	1.40427i
$101$	−0.977555	+	9.30081i	−0.0972703	+	0.925465i	0.831679	+	0.555257i	$0.187380\pi$
$101$	−0.977555	+	9.30081i	−0.0972703	+	0.925465i	−0.928949	+	0.370208i	$0.879286\pi$
$102$	−2.26146	−	1.70624i	−0.223918	−	0.168943i
$103$	5.33276	+	16.4126i	0.525453	+	1.61718i	0.763418	+	0.645904i	$0.223519\pi$
$103$	5.33276	+	16.4126i	0.525453	+	1.61718i	−0.237966	+	0.971274i	$0.576481\pi$
$104$	5.68626	−	17.0181i	0.557584	−	1.66876i
$105$	−3.80455	−	0.880730i	−0.371286	−	0.0859505i
$106$	13.5388	+	12.1904i	1.31501	+	1.18404i
$107$	16.5369	−	3.51503i	1.59868	−	0.339811i	0.679511	−	0.733666i	$-0.262192\pi$
$107$	16.5369	−	3.51503i	1.59868	−	0.339811i	0.919173	+	0.393855i	$0.128859\pi$
$108$	11.4280	−	17.5291i	1.09966	−	1.68673i
$109$		−	18.0010i		−	1.72418i	−0.506756	−	0.862089i	$-0.669156\pi$
$109$		−	18.0010i		−	1.72418i	0.506756	−	0.862089i	$-0.330844\pi$
$110$	21.5499	+	11.5776i	2.05470	+	1.10388i
$111$	0.805502	−	0.156077i	0.0764548	−	0.0148142i
$112$	−1.83636	+	2.52753i	−0.173519	+	0.238829i
$113$	−8.56076	+	7.70814i	−0.805328	+	0.725121i	−0.965057	−	0.262040i	$-0.915605\pi$
$113$	−8.56076	+	7.70814i	−0.805328	+	0.725121i	0.159729	+	0.987161i	$0.448938\pi$
$114$	−0.365048	+	20.2249i	−0.0341899	+	1.89424i
$115$	−10.2644	−	4.57000i	−0.957158	−	0.426154i
$116$	−21.1445	+	15.3624i	−1.96322	+	1.42636i
$117$	2.88259	+	10.4255i	0.266496	+	0.963836i
$118$	−7.85172	−	2.55118i	−0.722810	−	0.234855i
$119$	−0.497225	−	0.0522605i	−0.0455806	−	0.00479071i
$120$	24.4807	+	8.44564i	2.23477	+	0.770978i
$121$	−4.90706	+	9.84483i	−0.446097	+	0.894985i
$122$			19.7066i			1.78415i
$123$	−6.09640	−	2.84721i	−0.549694	−	0.256724i
$124$	23.3029	+	25.8805i	2.09266	+	2.32414i
$125$	2.78158	−	0.903789i	0.248792	−	0.0808373i
$126$	0.199455	−	5.52343i	0.0177688	−	0.492066i
$127$	8.50953	−	19.1127i	0.755099	−	1.69598i	0.0377278	−	0.999288i	$-0.487988\pi$
$127$	8.50953	−	19.1127i	0.755099	−	1.69598i	0.717371	−	0.696691i	$-0.245345\pi$
$128$	−12.9567	+	14.3898i	−1.14522	+	1.27189i
$129$	−1.07642	−	2.54009i	−0.0947739	−	0.223643i
$130$	−23.1408	+	13.1052i	−2.02959	+	1.14940i
$131$	−11.9312			−1.04243			−0.521217	−	0.853424i	$-0.674522\pi$
$131$	−11.9312			−1.04243			−0.521217	+	0.853424i	$0.674522\pi$
$132$	−6.87199	+	22.0895i	−0.598130	+	1.92264i
$133$	1.78497	+	3.09166i	0.154777	+	0.268081i
$134$	11.5424	−	5.13899i	0.997107	−	0.443941i
$135$	−15.0866	+	4.01365i	−1.29845	+	0.345440i
$136$	3.24300	+	0.689321i	0.278085	+	0.0591088i
$137$	2.74018	−	0.288005i	0.234109	−	0.0246059i	0.0132528	−	0.999912i	$-0.495781\pi$
$137$	2.74018	−	0.288005i	0.234109	−	0.0246059i	0.220857	+	0.975306i	$0.429115\pi$
$138$	3.58641	−	15.4924i	0.305296	−	1.31880i
$139$	−0.00742137	+	0.0349148i	−0.000629472	+	0.00296143i	−0.978461	−	0.206431i	$-0.933815\pi$
$139$	−0.00742137	+	0.0349148i	−0.000629472	+	0.00296143i	0.977832	+	0.209392i	$0.0671485\pi$
$140$	8.88119	−	1.88776i	0.750598	−	0.159544i
$141$	7.70235	+	11.0140i	0.648655	+	0.927548i
$142$		−	36.3596i		−	3.05123i
$143$	−6.20847	−	10.2203i	−0.519179	−	0.854666i
$144$	−1.75289	+	12.3658i	−0.146074	+	1.03048i
$145$	19.3921	+	2.03819i	1.61043	+	0.169263i
$146$	3.08915	+	14.5333i	0.255660	+	1.20279i
$147$	5.39931	+	9.75428i	0.445328	+	0.804519i
$148$	−1.54332	+	1.12129i	−0.126860	+	0.0921692i
$149$	0.665495	+	6.33177i	0.0545195	+	0.518718i	0.987367	+	0.158448i	$0.0506490\pi$
$149$	0.665495	+	6.33177i	0.0545195	+	0.518718i	−0.932848	+	0.360271i	$0.882684\pi$
$150$	−8.29181	−	14.9798i	−0.677024	−	1.22310i
$151$	2.05168	+	0.666632i	0.166964	+	0.0542498i	0.391306	−	0.920261i	$-0.372023\pi$
$151$	2.05168	+	0.666632i	0.166964	+	0.0542498i	−0.224342	+	0.974510i	$0.572023\pi$
$152$	−9.62893	−	21.6269i	−0.781009	−	1.75418i
$153$	−1.85403	+	0.746515i	−0.149889	+	0.0603521i
$154$	1.45268	+	5.93517i	0.117061	+	0.478270i
$155$		−	25.9819i		−	2.08692i
$156$	−16.3296	−	19.1264i	−1.30742	−	1.53133i
$157$	2.42896	−	7.47557i	0.193852	−	0.596616i	−0.806136	−	0.591730i	$-0.798445\pi$
$157$	2.42896	−	7.47557i	0.193852	−	0.596616i	0.999988	−	0.00488514i	$-0.00155499\pi$
$158$	−20.2730	−	18.2539i	−1.61284	−	1.45220i
$159$	12.2939	−	3.75064i	0.974970	−	0.297445i
$160$	−0.799570	+	0.0840382i	−0.0632116	+	0.00664380i
$161$	−0.867246	−	2.66911i	−0.0683485	−	0.210355i
$162$	−9.63862	−	19.8819i	−0.757281	−	1.56207i
$163$	6.97851	−	3.10703i	0.546599	−	0.243362i	−0.114809	−	0.993388i	$-0.536626\pi$
$163$	6.97851	−	3.10703i	0.546599	−	0.243362i	0.661408	+	0.750026i	$0.269959\pi$
$164$	15.6439			1.22159
$165$	14.8373	−	8.81647i	1.15508	−	0.686361i
$166$	−4.35640	−	7.54551i	−0.338122	−	0.585645i
$167$	−0.586935	+	5.58431i	−0.0454184	+	0.432127i	0.948059	+	0.318095i	$0.103043\pi$
$167$	−0.586935	+	5.58431i	−0.0454184	+	0.432127i	−0.993477	+	0.114032i	$0.963623\pi$
$168$	2.52388	+	5.95573i	0.194722	+	0.459494i
$169$	12.9982	+	0.216022i	0.999862	+	0.0166171i
$170$	−2.88837	−	3.97550i	−0.221528	−	0.304907i
$171$	12.0938	+	7.57703i	0.924835	+	0.579430i
$172$	4.76667	+	4.29193i	0.363456	+	0.327257i
$173$	0.651654	+	0.723735i	0.0495443	+	0.0550245i	0.767408	−	0.641160i	$-0.221546\pi$
$173$	0.651654	+	0.723735i	0.0495443	+	0.0550245i	−0.717863	+	0.696184i	$0.754880\pi$
$174$	2.38892	+	27.4936i	0.181103	+	2.08428i
$175$	−2.61685	−	1.51084i	−0.197815	−	0.114209i
$176$	−1.86274	−	13.6813i	−0.140409	−	1.03127i
$177$	−4.39815	+	3.81867i	−0.330585	+	0.287029i
$178$	−13.2038	−	29.6562i	−0.989667	−	2.22283i
$179$	−5.32963	−	25.0739i	−0.398355	−	1.87411i	−0.479708	−	0.877428i	$-0.659257\pi$
$179$	−5.32963	−	25.0739i	−0.398355	−	1.87411i	0.0813531	−	0.996685i	$-0.474076\pi$
$180$	27.8328	−	23.2982i	2.07453	−	1.73654i
$181$	−0.448674	+	0.325981i	−0.0333497	+	0.0242300i	−0.604335	−	0.796730i	$-0.706561\pi$
$181$	−0.448674	+	0.325981i	−0.0333497	+	0.0242300i	0.570986	+	0.820960i	$0.306561\pi$
$182$	−6.30028	−	2.10512i	−0.467008	−	0.156042i
$183$	11.9132	+	7.16782i	0.880650	+	0.529860i
$184$	3.86939	+	18.2040i	0.285255	+	1.34202i
$185$	1.41542	+	0.148766i	0.104063	+	0.0109375i
$186$	36.1011	−	6.99509i	2.64706	−	0.512905i
$187$	1.74705	−	1.35287i	0.127757	−	0.0989314i
$188$	−27.0620	−	15.6242i	−1.97370	−	1.13952i
$189$	−3.26653	−	2.12960i	−0.237605	−	0.154906i
$190$	−10.8427	+	33.3705i	−0.786615	+	2.42095i
$191$	4.82591	−	22.7041i	0.349191	−	1.64281i	−0.356502	−	0.934295i	$-0.616031\pi$
$191$	4.82591	−	22.7041i	0.349191	−	1.64281i	0.705693	−	0.708518i	$-0.250636\pi$
$192$	3.87621	+	12.7055i	0.279742	+	0.916942i
$193$	0.206059	−	0.462815i	0.0148324	−	0.0333142i	−0.905977	−	0.423326i	$-0.860862\pi$
$193$	0.206059	−	0.462815i	0.0148324	−	0.0333142i	0.920810	+	0.390012i	$0.127529\pi$
$194$	−5.37613	−	16.5460i	−0.385984	−	1.18794i
$195$	−0.494456	+	18.7561i	−0.0354088	+	1.34315i
$196$	−20.9710	−	15.2363i	−1.49793	−	1.08831i
$197$	−9.54391	−	16.5305i	−0.679975	−	1.17775i	−0.974988	−	0.222258i	$-0.928657\pi$
$197$	−9.54391	−	16.5305i	−0.679975	−	1.17775i	0.295013	−	0.955493i	$-0.404676\pi$
$198$	16.2449	+	18.2424i	1.15447	+	1.29643i
$199$	−9.11263	+	15.7835i	−0.645977	+	1.11887i	0.338098	+	0.941111i	$0.390217\pi$
$199$	−9.11263	+	15.7835i	−0.645977	+	1.11887i	−0.984075	+	0.177754i	$0.943117\pi$
$200$	16.2110	+	11.7780i	1.14629	+	0.832828i
$201$	1.09160	−	8.84689i	0.0769954	−	0.624012i
$202$	−22.4576	−	4.77352i	−1.58011	−	0.335863i
$203$	2.86277	+	3.94027i	0.200927	+	0.276553i
$204$	3.17125	−	3.39670i	0.222032	−	0.237817i
$205$	−8.67344	−	7.80960i	−0.605779	−	0.545446i
$206$	−41.4407	+	8.80850i	−2.88731	+	0.613717i
$207$	−8.06118	−	7.80312i	−0.560291	−	0.542355i
$208$	13.6615	+	6.21900i	0.947253	+	0.431210i
$209$	−15.1475	−	4.41416i	−1.04777	−	0.305334i
$210$	3.12667	−	9.06302i	0.215761	−	0.625408i
$211$	13.2076	+	1.38817i	0.909248	+	0.0955658i	0.547592	−	0.836746i	$-0.315545\pi$
$211$	13.2076	+	1.38817i	0.909248	+	0.0955658i	0.361656	+	0.932312i	$0.382211\pi$
$212$	−22.2084	+	19.9965i	−1.52528	+	1.37336i
$213$	−21.9805	−	13.2250i	−1.50608	−	0.906161i
$214$	4.33848	+	41.2779i	0.296572	+	2.82170i
$215$	−0.500205	−	4.75913i	−0.0341137	−	0.324570i
$216$	20.0668	+	16.3091i	1.36537	+	1.10969i
$217$	4.82282	−	4.34249i	0.327395	−	0.294787i
$218$	43.9504	+	4.61937i	2.97670	+	0.312863i
$219$	9.90944	+	3.41868i	0.669618	+	0.231013i
$220$	−22.5823	+	33.1705i	−1.52250	+	2.23636i
$221$	0.231231	+	2.39095i	0.0155543	+	0.160833i
$222$	0.174365	+	2.00673i	0.0117026	+	0.134683i
$223$	−3.58001	+	0.760954i	−0.239735	+	0.0509572i	−0.326212	−	0.945297i	$-0.605772\pi$
$223$	−3.58001	+	0.760954i	−0.239735	+	0.0509572i	0.0864772	+	0.996254i	$0.472439\pi$
$224$	−0.149236	−	0.134372i	−0.00997123	−	0.00897814i
$225$	−12.0717	−	0.435917i	−0.804781	−	0.0290611i
$226$	−16.6230	−	22.8797i	−1.10575	−	1.52193i
$227$	0.961573	+	0.204389i	0.0638219	+	0.0135658i	0.239712	−	0.970844i	$-0.422947\pi$
$227$	0.961573	+	0.204389i	0.0638219	+	0.0135658i	−0.175890	+	0.984410i	$0.556280\pi$
$228$	−32.9315	−	4.06335i	−2.18094	−	0.269102i
$229$	5.36278	+	3.89629i	0.354382	+	0.257474i	0.750705	−	0.660637i	$-0.229714\pi$
$229$	5.36278	+	3.89629i	0.354382	+	0.257474i	−0.396323	+	0.918111i	$0.629714\pi$
$230$	13.7919	−	23.8883i	0.909414	−	1.57515i
$231$	4.11637	+	1.28059i	0.270837	+	0.0842569i
$232$	−16.1489	−	27.9706i	−1.06022	−	1.83636i
$233$	4.99210	+	3.62697i	0.327043	+	0.237611i	0.739175	−	0.673513i	$-0.235216\pi$
$233$	4.99210	+	3.62697i	0.327043	+	0.237611i	−0.412132	+	0.911124i	$0.635216\pi$
$234$	−26.1942	+	4.36265i	−1.71237	+	0.285195i
$235$	7.20415	+	22.1721i	0.469947	+	1.44635i
$236$	5.50818	−	12.3716i	0.358552	−	0.805320i
$237$	−18.4089	+	5.61621i	−1.19579	+	0.364812i
$238$	0.255194	−	1.20059i	0.0165418	−	0.0778230i
$239$	4.13060	−	12.7127i	0.267187	−	0.822316i	−0.723995	−	0.689805i	$-0.757696\pi$
$239$	4.13060	−	12.7127i	0.267187	−	0.822316i	0.991182	−	0.132510i	$-0.0423038\pi$
$240$	−9.16732	+	19.6289i	−0.591748	+	1.26704i
$241$	−4.84569	−	2.79766i	−0.312138	−	0.180213i	0.335745	−	0.941953i	$-0.391012\pi$
$241$	−4.84569	−	2.79766i	−0.312138	−	0.180213i	−0.647883	+	0.761740i	$0.724345\pi$
$242$	−22.7775	−	14.5072i	−1.46419	−	0.932561i
$243$	−15.5250	−	1.40475i	−0.995931	−	0.0901149i
$244$	−32.1485	−	3.37895i	−2.05810	−	0.216315i
$245$	4.02079	+	18.9163i	0.256879	+	1.20852i
$246$	8.51608	−	14.1541i	0.542965	−	0.902431i
$247$	12.8414	−	11.3706i	0.817076	−	0.723496i
$248$	−34.8168	+	25.2959i	−2.21087	+	1.60629i
$249$	−6.14603	−	0.110932i	−0.389489	−	0.00703005i
$250$	1.49285	+	7.02331i	0.0944162	+	0.444193i
$251$	−3.17096	−	7.12210i	−0.200149	−	0.449543i	0.785387	−	0.619005i	$-0.212464\pi$
$251$	−3.17096	−	7.12210i	−0.200149	−	0.449543i	−0.985537	+	0.169462i	$0.945797\pi$
$252$	8.97651	+	1.27245i	0.565467	+	0.0801566i
$253$	10.9263	+	5.87012i	0.686932	+	0.369052i
$254$	44.4811	+	25.6812i	2.79100	+	1.61138i
$255$	−3.45389	+	0.300109i	−0.216291	+	0.0187935i
$256$	−21.5452	−	23.9283i	−1.34657	−	1.49552i
$257$	−11.7849	−	10.6112i	−0.735122	−	0.661906i	0.213994	−	0.976835i	$-0.431353\pi$
$257$	−11.7849	−	10.6112i	−0.735122	−	0.661906i	−0.949115	+	0.314929i	$0.898019\pi$
$258$	6.47802	−	1.97632i	0.403304	−	0.123040i
$259$	0.208952	+	0.287597i	0.0129836	+	0.0178704i
$260$	−17.4116	−	39.9981i	−1.07982	−	2.48058i
$261$	17.4896	+	8.55600i	1.08258	+	0.529603i
$262$	3.06177	−	29.1308i	0.189157	−	1.79970i
$263$	−10.9375	−	18.9443i	−0.674436	−	1.16816i	−0.976633	−	0.214912i	$-0.931054\pi$
$263$	−10.9375	−	18.9443i	−0.674436	−	1.16816i	0.302198	−	0.953245i	$-0.402280\pi$
$264$	−26.2600	−	11.2989i	−1.61619	−	0.695400i
$265$	22.2954			1.36959
$266$	−8.00653	+	3.56474i	−0.490912	+	0.218568i
$267$	−22.7307	−	2.80469i	−1.39109	−	0.171644i
$268$	6.40446	+	19.7109i	0.391215	+	1.20403i
$269$	4.78851	−	0.503292i	0.291960	−	0.0306863i	0.0425840	−	0.999093i	$-0.486441\pi$
$269$	4.78851	−	0.503292i	0.291960	−	0.0306863i	0.249377	+	0.968407i	$0.419774\pi$
$270$	−5.92805	−	37.8649i	−0.360769	−	2.30439i
$271$	−16.5363	−	14.8893i	−1.00451	−	0.904462i	−0.00907735	−	0.999959i	$-0.502889\pi$
$271$	−16.5363	−	14.8893i	−1.00451	−	0.904462i	−0.995430	+	0.0954965i	$0.969556\pi$
$272$	−0.857085	+	2.63784i	−0.0519684	+	0.159942i
$273$	−3.56419	+	3.04302i	−0.215715	+	0.184172i
$274$			6.76422i			0.408642i
$275$	12.9716	−	3.17490i	0.782216	−	0.191454i
$276$	24.6588	+	8.50711i	1.48429	+	0.512068i
$277$	−4.37700	−	9.83090i	−0.262988	−	0.590682i	0.732994	−	0.680236i	$-0.238123\pi$
$277$	−4.37700	−	9.83090i	−0.262988	−	0.590682i	−0.995982	+	0.0895540i	$0.971456\pi$
$278$	−0.0833421	−	0.0270795i	−0.00499852	−	0.00162412i
$279$	8.90223	−	24.3685i	0.532962	−	1.45891i
$280$	1.17283	+	11.1587i	0.0700898	+	0.666860i
$281$	6.16033	−	4.47574i	0.367494	−	0.267000i	−0.388677	−	0.921374i	$-0.627068\pi$
$281$	6.16033	−	4.47574i	0.367494	−	0.267000i	0.756171	+	0.654374i	$0.227068\pi$
$282$	−28.8680	+	15.9794i	−1.71906	+	0.951557i
$283$	2.48352	+	11.6841i	0.147630	+	0.694545i	0.988241	+	0.152905i	$0.0488629\pi$
$283$	2.48352	+	11.6841i	0.147630	+	0.694545i	−0.840611	+	0.541640i	$0.817804\pi$
$284$	59.3157	+	6.23433i	3.51974	+	0.369939i
$285$	16.2297	+	18.6925i	0.961364	+	1.10725i
$286$	26.5467	−	12.5356i	1.56974	−	0.741248i
$287$		−	2.91525i		−	0.172081i
$288$	−0.778714	−	0.195138i	−0.0458862	−	0.0114986i
$289$	16.1944	−	3.44222i	0.952609	−	0.202483i
$290$	−9.95275	+	46.8240i	−0.584445	+	2.74960i
$291$	−11.9580	−	2.76821i	−0.700992	−	0.162275i
$292$	−24.2388	+	2.54760i	−1.41847	+	0.149087i
$293$	−27.0933	−	5.75886i	−1.58281	−	0.336436i	−0.669215	−	0.743069i	$-0.733369\pi$
$293$	−27.0933	−	5.75886i	−1.58281	−	0.336436i	−0.913592	+	0.406633i	$0.866703\pi$
$294$	−25.2012	+	10.6796i	−1.46977	+	0.622848i
$295$	−9.22988	+	4.10941i	−0.537385	+	0.239259i
$296$	−1.17869	−	2.04155i	−0.0685101	−	0.118663i
$297$	16.9368	−	3.18527i	0.982771	−	0.184828i
$298$	−15.6302			−0.905431
$299$	−11.7330	+	6.64467i	−0.678535	+	0.384271i
$300$	25.8592	−	10.9585i	1.49298	−	0.632687i
$301$	0.799801	−	0.888269i	0.0460997	−	0.0511990i
$302$	−2.15412	+	4.83824i	−0.123956	+	0.278409i
$303$	−11.0542	+	11.8401i	−0.635047	+	0.680193i
$304$	18.8352	−	6.11993i	1.08027	−	0.351002i
$305$	16.1372	+	17.9222i	0.924015	+	1.02622i
$306$	−1.34688	−	4.71829i	−0.0769961	−	0.269727i
$307$			4.56418i			0.260492i	0.991482	+	0.130246i	$0.0415766\pi$
$307$			4.56418i			0.260492i	−0.991482	+	0.130246i	$0.958423\pi$
$308$	−9.93149	+	1.35219i	−0.565899	+	0.0770481i
$309$	−9.74813	+	28.2561i	−0.554552	+	1.60743i
$310$	63.4363	+	6.66743i	3.60294	+	0.378684i
$311$	31.9115	+	10.3687i	1.80954	+	0.587954i	1.00000		0.000883416i	$0.000281200\pi$
$311$	31.9115	+	10.3687i	1.80954	+	0.587954i	0.809536	+	0.587070i	$0.199719\pi$
$312$	25.6153	−	17.5983i	1.45018	−	0.996306i
$313$	4.28967	−	3.11663i	0.242466	−	0.176162i	−0.459915	−	0.887963i	$-0.652120\pi$
$313$	4.28967	−	3.11663i	0.242466	−	0.176162i	0.702381	+	0.711801i	$0.252120\pi$
$314$	17.6287	+	7.84882i	0.994847	+	0.442935i
$315$	−4.34161	−	5.18664i	−0.244622	−	0.292234i
$316$	33.2548	−	29.9428i	1.87073	−	1.68441i
$317$	−4.91686	+	6.76748i	−0.276158	+	0.380099i	−0.924457	−	0.381287i	$-0.875481\pi$
$317$	−4.91686	+	6.76748i	−0.276158	+	0.380099i	0.648298	+	0.761386i	$0.275481\pi$
$318$	6.00257	+	30.9788i	0.336607	+	1.73720i
$319$	−21.1819	−	3.82907i	−1.18596	−	0.214387i
$320$			23.0418i			1.28808i
$321$	26.5317	+	12.3912i	1.48086	+	0.691607i
$322$	6.73934	−	1.43249i	0.375569	−	0.0798296i
$323$	2.35526	+	2.12068i	0.131050	+	0.117998i
$324$	34.0872	−	12.3151i	1.89373	−	0.684170i
$325$	−4.60083	+	13.7695i	−0.255208	+	0.763797i
$326$	5.79519	+	17.8358i	0.320966	+	0.987832i
$327$	18.7785	−	24.8892i	1.03845	−	1.37637i
$328$	−2.02075	+	19.2262i	−0.111577	+	1.06159i
$329$	−2.91157	+	5.04299i	−0.160520	+	0.278029i
$330$	17.7184	+	38.4886i	0.975366	+	2.11873i
$331$	5.95160	−	10.3085i	0.327130	−	0.566605i	−0.654811	−	0.755792i	$-0.727252\pi$
$331$	5.95160	−	10.3085i	0.327130	−	0.566605i	0.981941	+	0.189187i	$0.0605852\pi$
$332$	13.0564	−	5.81309i	0.716564	−	0.319035i
$333$	1.27655	+	0.624495i	0.0699546	+	0.0342221i
$334$	−13.4838	−	2.86607i	−0.737801	−	0.156824i
$335$	6.28905	−	14.1254i	0.343607	−	0.771755i
$336$	−5.17576	+	1.57903i	−0.282361	+	0.0861429i
$337$	−0.0379401	+	0.0123275i	−0.00206673	+	0.000671521i	−0.310050	−	0.950720i	$-0.600346\pi$
$337$	−0.0379401	+	0.0123275i	−0.00206673	+	0.000671521i	0.307983	+	0.951392i	$0.400346\pi$
$338$	−3.86301	+	31.6805i	−0.210120	+	1.72319i
$339$	−19.8777	+	1.72717i	−1.07961	+	0.0938071i
$340$	6.98073	−	4.03033i	0.378583	−	0.218575i
$341$	−2.12395	+	28.6031i	−0.115018	+	1.54894i
$342$	−21.6033	+	27.5833i	−1.16817	+	1.49153i
$343$	−5.92698	+	8.15779i	−0.320027	+	0.440479i
$344$	−5.89044	+	5.30378i	−0.317591	+	0.285960i
$345$	−9.42472	−	17.0265i	−0.507410	−	0.916676i
$346$	−1.93427	+	1.40533i	−0.103987	+	0.0755509i
$347$	1.27073	+	12.0901i	0.0682161	+	0.649033i	0.974195	+	0.225710i	$0.0724700\pi$
$347$	1.27073	+	12.0901i	0.0682161	+	0.649033i	−0.905978	+	0.423324i	$0.860863\pi$
$348$	−45.2616	−	0.816945i	−2.42627	−	0.0437929i
$349$	−1.33696	−	6.28992i	−0.0715660	−	0.336692i	0.927769	−	0.373155i	$-0.121724\pi$
$349$	−1.33696	−	6.28992i	−0.0715660	−	0.336692i	−0.999335	+	0.0364635i	$0.988391\pi$
$350$	4.36034	−	6.00149i	0.233070	−	0.320793i
$351$	−6.89018	+	17.4220i	−0.367771	+	0.929917i
$352$	0.887104	−	0.0271537i	0.0472828	−	0.00144730i
$353$	−9.72645	+	5.61557i	−0.517687	+	0.298887i	−0.735988	−	0.676995i	$-0.763282\pi$
$353$	−9.72645	+	5.61557i	−0.517687	+	0.298887i	0.218301	+	0.975881i	$0.429949\pi$
$354$	−8.19487	−	11.7183i	−0.435552	−	0.622820i
$355$	−29.7740	−	33.0674i	−1.58024	−	1.75503i
$356$	50.6440	−	16.4552i	2.68413	−	0.872125i
$357$	−0.632975	−	0.590962i	−0.0335006	−	0.0312770i
$358$	62.5872	−	6.57818i	3.30784	−	0.347667i
$359$	−10.8934	−	33.5264i	−0.574931	−	1.76946i	−0.636414	−	0.771348i	$-0.719583\pi$
$359$	−10.8934	−	33.5264i	−0.574931	−	1.76946i	0.0614827	−	0.998108i	$-0.480417\pi$
$360$	25.0379	+	37.2156i	1.31961	+	1.96143i
$361$	0.379451	−	3.61024i	0.0199711	−	0.190012i
$362$	−0.680764	−	1.17912i	−0.0357802	−	0.0619731i
$363$	−17.0549	+	8.49301i	−0.895149	+	0.445767i
$364$	4.51447	−	9.91708i	0.236623	−	0.519796i
$365$	14.7104	+	10.6878i	0.769979	+	0.559423i
$366$	−20.5578	+	27.2474i	−1.07457	+	1.42425i
$367$	−12.1979	+	13.5471i	−0.636725	+	0.707154i	−0.972004	−	0.234964i	$-0.924503\pi$
$367$	−12.1979	+	13.5471i	−0.636725	+	0.707154i	0.335279	+	0.942119i	$0.391169\pi$
$368$	−15.4838	+	1.62741i	−0.807148	+	0.0848347i
$369$	−5.45904	−	10.2965i	−0.284186	−	0.536012i
$370$	−0.726443	+	3.41764i	−0.0377660	+	0.177675i
$371$	3.72634	+	4.13852i	0.193462	+	0.214861i
$372$	5.22151	+	60.0934i	0.270723	+	3.11570i
$373$	−18.4991	−	10.6805i	−0.957849	−	0.553015i	−0.0623390	−	0.998055i	$-0.519856\pi$
$373$	−18.4991	−	10.6805i	−0.957849	−	0.553015i	−0.895511	+	0.445040i	$0.853189\pi$
$374$	2.85478	+	4.61269i	0.147617	+	0.238517i
$375$	4.78880	+	1.65210i	0.247292	+	0.0853140i
$376$	22.6976	−	31.2406i	1.17054	−	1.61111i
$377$	15.8018	−	17.2592i	0.813836	−	0.888892i
$378$	6.03780	−	7.42894i	0.310551	−	0.382104i
$379$	11.0633	+	4.92568i	0.568281	+	0.253015i	0.670703	−	0.741726i	$-0.265993\pi$
$379$	11.0633	+	4.92568i	0.568281	+	0.253015i	−0.102422	+	0.994741i	$0.532659\pi$
$380$	−52.5803	−	23.4102i	−2.69731	−	1.20092i
$381$	31.7041	−	17.5492i	1.62425	−	0.899075i
$382$	54.1951	+	17.6090i	2.77286	+	0.900957i
$383$	−6.56179	−	14.7380i	−0.335292	−	0.753078i	−0.999982	−	0.00595911i	$-0.998103\pi$
$383$	−6.56179	−	14.7380i	−0.335292	−	0.753078i	0.664690	−	0.747119i	$-0.268564\pi$
$384$	−32.9260	+	6.37987i	−1.68025	+	0.325572i
$385$	6.18132	+	4.20820i	0.315029	+	0.214470i
$386$	1.07711	+	0.621872i	0.0548236	+	0.0316524i
$387$	1.16149	−	4.63500i	0.0590417	−	0.235610i
$388$	27.9144	−	5.93338i	1.41714	−	0.301222i
$389$	13.9064	−	4.51848i	0.705085	−	0.229096i	0.0655402	−	0.997850i	$-0.479123\pi$
$389$	13.9064	−	4.51848i	0.705085	−	0.229096i	0.639545	+	0.768754i	$0.279123\pi$
$390$	−45.6672	−	6.02039i	−2.31245	−	0.304855i
$391$	−1.46448	−	2.01568i	−0.0740617	−	0.101937i
$392$	21.4341	−	23.8049i	1.08258	−	1.20233i
$393$	−16.4968	−	12.4466i	−0.832152	−	0.627847i
$394$	42.8094	−	19.0600i	2.15671	−	0.960228i
$395$	−33.3851			−1.67979
$396$	−32.5453	+	23.3734i	−1.63546	+	1.17456i
$397$	−10.7481	+	18.6163i	−0.539433	+	0.934326i	0.459501	+	0.888177i	$0.348028\pi$
$397$	−10.7481	+	18.6163i	−0.539433	+	0.934326i	−0.998935	+	0.0461487i	$0.985305\pi$
$398$	−36.1980	−	26.2994i	−1.81444	−	1.31827i
$399$	−0.757204	+	6.13678i	−0.0379076	+	0.307223i
$400$	−11.2166	+	12.4573i	−0.560831	+	0.622866i
$401$	5.88090	−	13.2087i	0.293678	−	0.659612i	−0.705096	−	0.709112i	$-0.749096\pi$
$401$	5.88090	−	13.2087i	0.293678	−	0.659612i	0.998774	+	0.0495001i	$0.0157628\pi$
$402$	21.3201	+	4.93548i	1.06335	+	0.246159i
$403$	−25.0723	−	18.5364i	−1.24894	−	0.923362i
$404$	11.6380	−	35.8180i	0.579011	−	1.78201i
$405$	−25.0467	−	10.1888i	−1.24458	−	0.506287i
$406$	−10.3550	+	5.97849i	−0.513912	+	0.296707i
$407$	−1.54605	−	0.279481i	−0.0766348	−	0.0138533i
$408$	3.76486	+	4.33618i	0.186388	+	0.214673i
$409$	11.3307	+	25.4492i	0.560268	+	1.25838i	0.942466	+	0.334302i	$0.108501\pi$
$409$	11.3307	+	25.4492i	0.560268	+	1.25838i	−0.382198	+	0.924080i	$0.624833\pi$
$410$	21.2934	−	19.1726i	1.05160	−	0.946869i
$411$	4.08918	+	2.46033i	0.201704	+	0.121359i
$412$	−7.26430	−	69.1152i	−0.357886	−	3.40506i
$413$	−2.30544	−	1.02645i	−0.113443	−	0.0505082i
$414$	21.1204	−	17.6794i	1.03801	−	0.868896i
$415$	−10.1408	−	3.29494i	−0.497792	−	0.161742i
$416$	−0.489344	+	0.831535i	−0.0239921	+	0.0407694i
$417$	−0.0466842	+	0.0405333i	−0.00228613	+	0.00198492i
$418$	14.6646	−	35.8508i	0.717267	−	1.75352i
$419$	−17.5453	+	10.1298i	−0.857146	+	0.494874i	−0.863056	−	0.505109i	$-0.831452\pi$
$419$	−17.5453	+	10.1298i	−0.857146	+	0.494874i	0.00590935	+	0.999983i	$0.498119\pi$
$420$	14.2489	+	6.65470i	0.695277	+	0.324716i
$421$	−10.4002	+	32.0086i	−0.506876	+	1.56000i	0.290717	+	0.956809i	$0.406106\pi$
$421$	−10.4002	+	32.0086i	−0.506876	+	1.56000i	−0.797593	+	0.603195i	$0.793894\pi$
$422$	−6.77862	+	31.8909i	−0.329978	+	1.55242i
$423$	−0.840066	+	23.2637i	−0.0408454	+	1.13112i
$424$	−21.7067	−	29.8767i	−1.05417	−	1.45094i
$425$	−2.62395	−	0.557739i	−0.127280	−	0.0270543i
$426$	37.9302	−	50.2729i	1.83772	−	2.43573i
$427$	−0.629666	+	5.99087i	−0.0304717	+	0.289918i
$428$	−68.0830			−3.29092
$429$	2.07760	−	20.6079i	0.100307	−	0.994957i
$430$	11.7481			0.566542
$431$	−1.56630	+	14.9023i	−0.0754459	+	0.717819i	0.889778	+	0.456394i	$0.150859\pi$
$431$	−1.56630	+	14.9023i	−0.0754459	+	0.717819i	−0.965224	+	0.261425i	$0.915807\pi$
$432$	−15.3236	+	15.2690i	−0.737256	+	0.734632i
$433$	11.0080	+	2.33982i	0.529009	+	0.112444i	0.464670	−	0.885484i	$-0.346173\pi$
$433$	11.0080	+	2.33982i	0.529009	+	0.112444i	0.0643389	+	0.997928i	$0.479506\pi$
$434$	9.36483	+	12.8896i	0.449526	+	0.618719i
$435$	24.6864	+	23.0479i	1.18362	+	1.10506i
$436$	−15.0717	+	70.9069i	−0.721805	+	3.39583i
$437$	−5.49753	+	16.9197i	−0.262983	+	0.809378i
$438$	−10.8899	+	23.3172i	−0.520338	+	1.11414i
$439$	−26.0341	+	15.0308i	−1.24254	+	0.717381i	−0.969611	−	0.244652i	$-0.921326\pi$
$439$	−26.0341	+	15.0308i	−1.24254	+	0.717381i	−0.272930	+	0.962034i	$0.587993\pi$
$440$	−37.8491	−	32.0379i	−1.80438	−	1.52735i
$441$	−2.71023	+	19.1194i	−0.129058	+	0.910446i
$442$	−5.89700	−	0.0489987i	−0.280492	−	0.00233063i
$443$	19.3594	+	6.29025i	0.919792	+	0.298859i	0.730382	−	0.683039i	$-0.239342\pi$
$443$	19.3594	+	6.29025i	0.919792	+	0.298859i	0.189411	+	0.981898i	$0.439342\pi$
$444$	−3.30360	−	0.0596281i	−0.156782	−	0.00282983i
$445$	−36.2930	−	16.1587i	−1.72045	−	0.765996i
$446$	−0.939219	−	8.93607i	−0.0444733	−	0.423135i
$447$	−5.68512	+	9.44891i	−0.268897	+	0.446918i
$448$	−4.27708	+	3.85110i	−0.202073	+	0.181948i
$449$	14.6705	+	32.9505i	0.692344	+	1.55503i	0.825792	+	0.563975i	$0.190729\pi$
$449$	14.6705	+	32.9505i	0.692344	+	1.55503i	−0.133447	+	0.991056i	$0.542605\pi$
$450$	4.16214	−	29.3619i	0.196205	−	1.38414i
$451$	8.91004	+	9.30650i	0.419558	+	0.438226i
$452$	40.1752	−	23.1952i	1.88968	−	1.09101i
$453$	2.14135	+	3.06203i	0.100609	+	0.143867i
$454$	−0.745785	+	2.29529i	−0.0350014	+	0.107723i
$455$	−7.45364	+	3.24464i	−0.349432	+	0.152111i
$456$	9.24761	−	39.9475i	0.433059	−	1.87071i
$457$	−7.05150	+	15.8379i	−0.329855	+	0.740867i	−0.999999	−	0.00136447i	$-0.999566\pi$
$457$	−7.05150	+	15.8379i	−0.329855	+	0.740867i	0.670144	+	0.742231i	$0.266232\pi$
$458$	−10.8892	+	12.0937i	−0.508819	+	0.565101i
$459$	−3.34225	−	0.901941i	−0.156003	−	0.0420990i
$460$	36.6057	+	26.5956i	1.70675	+	1.24003i
$461$	10.9797	−	19.0174i	0.511377	−	0.885731i	−0.488536	−	0.872544i	$-0.662469\pi$
$461$	10.9797	−	19.0174i	0.511377	−	0.885731i	0.999913	−	0.0131870i	$-0.00419769\pi$
$462$	−4.18298	+	9.72174i	−0.194610	+	0.452296i
$463$	−11.3178			−0.525982			−0.262991	−	0.964798i	$-0.584709\pi$
$463$	−11.3178			−0.525982			−0.262991	+	0.964798i	$0.584709\pi$
$464$	24.6832	−	10.9897i	1.14589	−	0.510182i
$465$	27.1042	−	35.9241i	1.25693	−	1.66594i
$466$	−10.1365	+	11.2578i	−0.469566	+	0.521506i
$467$	11.7958	+	16.2356i	0.545847	+	0.751293i	0.989441	−	0.144934i	$-0.0462970\pi$
$467$	11.7958	+	16.2356i	0.545847	+	0.751293i	−0.443595	+	0.896228i	$0.646297\pi$
$468$	−2.62573	−	43.4802i	−0.121374	−	2.00987i
$469$	3.67312	−	1.19347i	0.169609	−	0.0551093i
$470$	−55.9832	+	11.8996i	−2.58231	+	0.548888i
$471$	11.1569	−	7.80227i	0.514083	−	0.359510i
$472$	14.4930	+	8.36752i	0.667093	+	0.385146i
$473$	0.161622	+	5.28015i	0.00743139	+	0.242782i
$474$	−8.98825	−	46.3877i	−0.412844	−	2.13066i
$475$	7.79089	+	17.4986i	0.357471	+	0.802892i
$476$	1.91485	+	0.622172i	0.0877669	+	0.0285172i
$477$	20.9109	+	7.63910i	0.957445	+	0.349771i
$478$	29.9788	+	13.3474i	1.37120	+	0.610497i
$479$	−15.3709	−	6.84355i	−0.702313	−	0.312690i	0.0243310	−	0.999704i	$-0.492254\pi$
$479$	−15.3709	−	6.84355i	−0.702313	−	0.312690i	−0.726644	+	0.687014i	$0.758921\pi$
$480$	−1.19320	−	0.717912i	−0.0544619	−	0.0327681i
$481$	1.15336	−	1.25973i	0.0525888	−	0.0574388i
$482$	8.07415	−	11.1131i	0.367767	−	0.506188i
$483$	1.58530	−	4.59517i	0.0721336	−	0.209087i
$484$	27.5721	−	34.6709i	1.25328	−	1.57595i
$485$	−18.4385	−	10.6455i	−0.837249	−	0.483386i
$486$	7.41379	−	37.5448i	0.336297	−	1.70307i
$487$	−21.7772	−	24.1860i	−0.986818	−	1.09597i	−0.995380	−	0.0960090i	$-0.969392\pi$
$487$	−21.7772	−	24.1860i	−0.986818	−	1.09597i	0.00856252	−	0.999963i	$-0.497274\pi$
$488$	8.30535	−	39.0736i	0.375965	−	1.76878i
$489$	12.8901	+	2.98399i	0.582912	+	0.134941i
$490$	−47.2172	+	4.96273i	−2.13305	+	0.224193i
$491$	−11.3052	+	12.5557i	−0.510197	+	0.566631i	−0.942119	−	0.335280i	$-0.891169\pi$
$491$	−11.3052	+	12.5557i	−0.510197	+	0.566631i	0.431922	+	0.901911i	$0.357836\pi$
$492$	21.6302	+	16.3197i	0.975166	+	0.735749i
$493$	3.49808	+	2.54150i	0.157546	+	0.114464i
$494$	24.4668	+	34.2708i	1.10081	+	1.54192i
$495$	29.7122	+	3.28805i	1.33546	+	0.147787i
$496$	−18.0012	−	31.1789i	−0.808277	−	1.39998i
$497$	1.16177	−	11.0535i	0.0521123	−	0.495815i
$498$	1.84803	−	14.9774i	0.0828123	−	0.671155i
$499$	−8.03501	−	24.7292i	−0.359696	−	1.10703i	−0.953236	−	0.302227i	$-0.902270\pi$
$499$	−8.03501	−	24.7292i	−0.359696	−	1.10703i	0.593539	−	0.804805i	$-0.297730\pi$
$500$	−11.7135	+	1.23114i	−0.523845	+	0.0550583i
$501$	−6.63706	+	7.10890i	−0.296522	+	0.317602i
$502$	18.2028	−	5.91443i	0.812429	−	0.263974i
$503$	14.6484	+	16.2687i	0.653141	+	0.725387i	0.975198	−	0.221334i	$-0.0710409\pi$
$503$	14.6484	+	16.2687i	0.653141	+	0.725387i	−0.322057	+	0.946720i	$0.604374\pi$
$504$	−2.72333	+	10.8676i	−0.121307	+	0.484083i
$505$	−24.3331	+	14.0487i	−1.08281	+	0.625160i
$506$	−17.1362	+	25.1709i	−0.761795	+	1.11898i
$507$	17.7467	+	13.8584i	0.788159	+	0.615471i
$508$	−49.5222	+	68.1614i	−2.19719	+	3.02418i
$509$	−1.44554	−	6.80071i	−0.0640723	−	0.301436i	0.934430	−	0.356147i	$-0.115910\pi$
$509$	−1.44554	−	6.80071i	−0.0640723	−	0.301436i	−0.998502	+	0.0547106i	$0.982576\pi$
$510$	0.153599	−	8.50990i	0.00680147	−	0.376825i
$511$	0.474744	+	4.51689i	0.0210014	+	0.199815i
$512$	32.6207	−	23.7003i	1.44164	−	1.04742i
$513$	8.81723	+	23.0926i	0.389290	+	1.01956i
$514$	28.9320	−	26.0505i	1.27614	−	1.14904i
$515$	−30.4754	+	41.9458i	−1.34291	+	1.84835i
$516$	2.11335	+	10.9068i	0.0930351	+	0.480147i
$517$	−6.11843	−	24.9978i	−0.269088	−	1.09940i
$518$	−0.755806	+	0.436365i	−0.0332082	+	0.0191728i
$519$	0.146017	+	1.68048i	0.00640943	+	0.0737649i
$520$	51.4062	−	16.2319i	2.25431	−	0.711817i
$521$	−0.580132	+	0.188496i	−0.0254160	+	0.00825817i	−0.321697	−	0.946843i	$-0.604253\pi$
$521$	−0.580132	+	0.188496i	−0.0254160	+	0.00825817i	0.296281	+	0.955101i	$0.404253\pi$
$522$	−25.3781	+	40.5063i	−1.11077	+	1.77291i
$523$	12.5530	−	28.1945i	0.548905	−	1.23286i	−0.399772	−	0.916615i	$-0.630911\pi$
$523$	12.5530	−	28.1945i	0.548905	−	1.23286i	0.948677	−	0.316247i	$-0.102423\pi$
$524$	46.9978	+	9.98970i	2.05311	+	0.436402i
$525$	−2.04211	−	4.81886i	−0.0891248	−	0.210312i
$526$	49.0605	−	21.8431i	2.13914	−	0.952405i
$527$	2.88072	−	4.98956i	0.125486	−	0.217349i
$528$	11.6968	−	20.8598i	0.509037	−	0.907806i
$529$	−4.50715	+	7.80661i	−0.195963	+	0.339418i
$530$	−5.72140	+	54.4355i	−0.248522	+	2.36452i
$531$	−10.0648	+	0.691779i	−0.436773	+	0.0300206i
$532$	−4.44255	−	13.6728i	−0.192609	−	0.592789i
$533$	−13.7241	+	2.79818i	−0.594458	+	0.121202i
$534$	12.6809	−	54.7786i	0.548757	−	2.37050i
$535$	37.7471	+	33.9876i	1.63195	+	1.46941i
$536$	−25.0517	+	5.32490i	−1.08207	+	0.230001i
$537$	18.7880	−	40.2285i	0.810761	−	1.73599i
$538$			11.8206i			0.509622i
$539$	−2.88007	−	21.1534i	−0.124053	−	0.911142i
$540$	62.7878	−	3.17835i	2.70196	−	0.136775i
$541$	4.38692	−	6.03808i	0.188609	−	0.259597i	−0.704232	−	0.709970i	$-0.748709\pi$
$541$	4.38692	−	6.03808i	0.188609	−	0.259597i	0.892841	+	0.450372i	$0.148709\pi$
$542$	40.5967	−	36.5534i	1.74378	−	1.57010i
$543$	−0.960425	−	0.0173351i	−0.0412158	−	0.000743921i
$544$	−0.162867	−	0.0725131i	−0.00698287	−	0.00310897i
$545$	43.7536	−	31.7888i	1.87420	−	1.36168i
$546$	−6.51508	−	9.48308i	−0.278820	−	0.405838i
$547$	−28.7276	−	9.33416i	−1.22830	−	0.399100i	−0.378204	−	0.925722i	$-0.623458\pi$
$547$	−28.7276	−	9.33416i	−1.22830	−	0.399100i	−0.850099	+	0.526623i	$0.823458\pi$
$548$	−11.0349	−	1.15981i	−0.471387	−	0.0495448i
$549$	8.99446	+	22.3385i	0.383874	+	0.953382i
$550$	4.42297	+	32.4856i	0.188596	+	1.38519i
$551$		−	30.8741i		−	1.31528i
$552$	−13.6403	+	29.2065i	−0.580571	+	1.24311i
$553$	−5.57983	−	6.19703i	−0.237278	−	0.263524i
$554$	25.1259	−	8.16392i	1.06750	−	0.346852i
$555$	1.80184	+	1.68225i	0.0764839	+	0.0714074i
$556$	0.0584665	−	0.131318i	0.00247953	−	0.00556912i
$557$	−6.42864	+	7.13973i	−0.272390	+	0.302520i	−0.863783	−	0.503863i	$-0.831911\pi$
$557$	−6.42864	+	7.13973i	−0.272390	+	0.302520i	0.591393	+	0.806383i	$0.298578\pi$
$558$	57.2127	+	27.9887i	2.42201	+	1.18486i
$559$	−4.94939	−	2.91263i	−0.209337	−	0.123191i
$560$	−9.38639			−0.396647
$561$	3.82687	−	0.0480388i	0.161571	−	0.00202820i
$562$	9.34693	+	16.1894i	0.394277	+	0.682907i
$563$	7.92397	−	3.52798i	0.333956	−	0.148687i	−0.232907	−	0.972499i	$-0.574824\pi$
$563$	7.92397	−	3.52798i	0.333956	−	0.148687i	0.566862	+	0.823812i	$0.308157\pi$
$564$	−21.1183	−	49.8339i	−0.889241	−	2.09839i
$565$	−33.8535	−	7.19578i	−1.42423	−	0.302729i
$566$	−29.1646	+	3.06533i	−1.22588	+	0.128845i
$567$	−2.29491	−	6.35214i	−0.0963771	−	0.266765i
$568$	−15.3238	+	72.0928i	−0.642972	+	3.02494i
$569$	−6.45719	+	1.37252i	−0.270700	+	0.0575390i	−0.341261	−	0.939968i	$-0.610854\pi$
$569$	−6.45719	+	1.37252i	−0.270700	+	0.0575390i	0.0705618	+	0.997507i	$0.477521\pi$
$570$	−49.8038	+	34.8289i	−2.08605	+	1.45882i
$571$			33.9407i			1.42037i	0.704014	+	0.710186i	$0.251389\pi$
$571$			33.9407i			1.42037i	−0.704014	+	0.710186i	$0.748611\pi$
$572$	15.8984	+	45.4567i	0.664745	+	1.90064i
$573$	30.3574	−	26.3577i	1.26820	−	1.10111i
$574$	7.11774	+	0.748105i	0.297089	+	0.0312253i
$575$	−3.13077	−	14.7291i	−0.130562	−	0.614247i
$576$	−7.89487	+	21.6110i	−0.328953	+	0.900460i
$577$	29.3978	−	21.3588i	1.22385	−	0.889177i	0.227433	−	0.973794i	$-0.426967\pi$
$577$	29.3978	−	21.3588i	1.22385	−	0.889177i	0.996414	+	0.0846167i	$0.0269666\pi$
$578$	4.24861	+	40.4228i	0.176719	+	1.68137i
$579$	0.767716	−	0.424956i	0.0319052	−	0.0176606i
$580$	−74.6803	−	24.2651i	−3.10093	−	1.00755i
$581$	−1.08327	−	2.43306i	−0.0449415	−	0.100940i
$582$	9.82740	−	28.4859i	0.407359	−	1.18078i
$583$	−24.5446	−	1.82258i	−1.01653	−	0.0754837i
$584$		−	30.1182i		−	1.24630i
$585$	−20.2499	+	25.4174i	−0.837231	+	1.05088i
$586$	21.0132	−	64.6720i	0.868048	−	2.67158i
$587$	−16.9336	−	15.2471i	−0.698926	−	0.629316i	0.241067	−	0.970508i	$-0.422503\pi$
$587$	−16.9336	−	15.2471i	−0.698926	−	0.629316i	−0.939993	+	0.341193i	$0.889169\pi$
$588$	−13.1012	−	42.9435i	−0.540286	−	1.77096i
$589$	−40.9136	+	4.30020i	−1.68582	+	0.177187i
$590$	−7.66481	−	23.5899i	−0.315555	−	0.971179i
$591$	4.04863	−	32.8122i	0.166538	−	1.34971i
$592$	1.80161	−	0.802127i	0.0740455	−	0.0329672i
$593$	20.8239			0.855135			0.427568	−	0.903983i	$-0.359371\pi$
$593$	20.8239			0.855135			0.427568	+	0.903983i	$0.359371\pi$
$594$	3.43074	+	42.1695i	0.140765	+	1.73024i
$595$	−0.751051	−	1.30086i	−0.0307901	−	0.0533300i
$596$	2.67999	−	25.4984i	0.109777	−	1.04446i
$597$	−29.0650	+	12.3170i	−1.18955	+	0.504100i
$598$	−13.2125	−	30.3519i	−0.540297	−	1.24118i
$599$	6.84608	+	9.42283i	0.279723	+	0.385006i	0.925642	−	0.378400i	$-0.123526\pi$
$599$	6.84608	+	9.42283i	0.279723	+	0.385006i	−0.645919	+	0.763406i	$0.723526\pi$
$600$	10.1275	+	33.1961i	0.413454	+	1.35523i
$601$	30.1153	+	27.1159i	1.22843	+	1.10608i	0.990886	+	0.134704i	$0.0430085\pi$
$601$	30.1153	+	27.1159i	1.22843	+	1.10608i	0.237542	+	0.971377i	$0.423658\pi$
$602$	1.96352	+	2.18071i	0.0800270	+	0.0888790i
$603$	10.7383	−	11.0935i	0.437299	−	0.451761i
$604$	−7.52356	−	4.34373i	−0.306129	−	0.176744i
$605$	−32.5947	+	5.45828i	−1.32516	+	0.221911i
$606$	−26.0715	−	30.0278i	−1.05908	−	1.21980i
$607$	13.6254	+	30.6031i	0.553036	+	1.24214i	0.946471	+	0.322787i	$0.104620\pi$
$607$	13.6254	+	30.6031i	0.553036	+	1.24214i	−0.393435	+	0.919352i	$0.628713\pi$
$608$	0.264670	+	1.24517i	0.0107338	+	0.0504984i
$609$	−0.152238	+	8.43448i	−0.00616898	+	0.341782i
$610$	−47.8993	+	34.8008i	−1.93938	+	1.40905i
$611$	26.5356	+	8.86637i	1.07352	+	0.358695i
$612$	7.92818	−	1.38824i	0.320478	−	0.0561163i
$613$	−4.69220	−	22.0750i	−0.189516	−	0.891603i	−0.965409	−	0.260739i	$-0.916034\pi$
$613$	−4.69220	−	22.0750i	−0.189516	−	0.891603i	0.775893	−	0.630864i	$-0.217299\pi$
$614$	−11.1437	−	1.17125i	−0.449724	−	0.0472679i
$615$	−3.84545	−	19.8461i	−0.155064	−	0.800272i
$616$	−0.378954	−	12.3803i	−0.0152685	−	0.498817i
$617$	3.55698	+	2.05362i	0.143199	+	0.0826758i	0.569888	−	0.821723i	$-0.306987\pi$
$617$	3.55698	+	2.05362i	0.143199	+	0.0826758i	−0.426689	+	0.904398i	$0.640320\pi$
$618$	−66.4873	−	31.0517i	−2.67451	−	1.24908i
$619$	−6.01902	+	18.5246i	−0.241925	+	0.744568i	0.754202	+	0.656642i	$0.228024\pi$
$619$	−6.01902	+	18.5246i	−0.241925	+	0.744568i	−0.996127	+	0.0879256i	$0.971976\pi$
$620$	−21.7540	+	102.344i	−0.873660	+	4.11025i
$621$	−3.00566	−	19.1984i	−0.120613	−	0.770407i
$622$	−33.5048	+	75.2531i	−1.34342	+	3.01737i
$623$	−3.06643	−	9.43749i	−0.122854	−	0.378105i
$624$	12.4015	+	22.8503i	0.496458	+	0.914746i
$625$	23.3965	+	16.9986i	0.935862	+	0.679943i
$626$	6.50862	+	11.2733i	0.260137	+	0.450570i
$627$	−16.3390	−	21.9051i	−0.652515	−	0.874805i
$628$	−15.8269	+	27.4131i	−0.631564	+	1.09390i
$629$	0.255322	+	0.185502i	0.0101804	+	0.00739646i
$630$	13.7776	−	9.26932i	0.548913	−	0.369298i
$631$	−33.5956	−	7.14096i	−1.33742	−	0.284277i	−0.516973	−	0.856002i	$-0.672941\pi$
$631$	−33.5956	−	7.14096i	−1.33742	−	0.284277i	−0.820445	+	0.571725i	$0.806274\pi$
$632$	32.5036	+	44.7374i	1.29293	+	1.77956i
$633$	16.8134	+	15.6975i	0.668274	+	0.623918i
$634$	−15.2614	−	13.7415i	−0.606109	−	0.545743i
$635$	61.4833	−	13.0687i	2.43989	−	0.518615i
$636$	−51.5668	+	4.48064i	−2.04476	+	0.177669i
$637$	21.1227	+	9.61552i	0.836912	+	0.380981i
$638$	14.7846	−	50.7342i	0.585327	−	2.00859i
$639$	−16.5952	−	41.2156i	−0.656497	−	1.63046i
$640$	−57.8571	−	6.08103i	−2.28700	−	0.240374i
$641$	−10.4929	+	9.44787i	−0.414445	+	0.373168i	−0.849813	−	0.527085i	$-0.823285\pi$
$641$	−10.4929	+	9.44787i	−0.414445	+	0.373168i	0.435367	+	0.900253i	$0.356618\pi$
$642$	−37.0623	+	61.5990i	−1.46273	+	2.43112i
$643$	1.85740	+	17.6720i	0.0732486	+	0.696914i	0.968102	+	0.250555i	$0.0806130\pi$
$643$	1.85740	+	17.6720i	0.0732486	+	0.696914i	−0.894854	+	0.446359i	$0.852720\pi$
$644$	1.18136	+	11.2399i	0.0465522	+	0.442915i
$645$	4.27310	−	7.10206i	0.168253	−	0.279644i
$646$	−5.78217	+	5.20629i	−0.227497	+	0.204839i
$647$	−19.4474	−	2.04401i	−0.764558	−	0.0803583i	−0.285781	−	0.958295i	$-0.592253\pi$
$647$	−19.4474	−	2.04401i	−0.764558	−	0.0803583i	−0.478777	+	0.877937i	$0.658920\pi$
$648$	10.7319	+	43.4834i	0.421590	+	1.70819i
$649$	10.4970	−	3.76947i	0.412042	−	0.147965i
$650$	−32.4385	−	14.7667i	−1.27234	−	0.579198i
$651$	11.1984	−	0.973027i	0.438899	−	0.0381359i
$652$	−30.0902	+	6.39588i	−1.17842	+	0.250482i
$653$	19.0414	+	17.1450i	0.745148	+	0.670934i	0.951536	−	0.307536i	$-0.0995045\pi$
$653$	19.0414	+	17.1450i	0.745148	+	0.670934i	−0.206389	+	0.978470i	$0.566171\pi$
$654$	55.9495	+	52.2359i	2.18780	+	2.04259i
$655$	−21.0700	−	29.0003i	−0.823271	−	1.13314i
$656$	−15.8191	−	3.36246i	−0.617633	−	0.131282i
$657$	10.1350	+	15.0644i	0.395404	+	0.587717i
$658$	−11.5656	−	8.40291i	−0.450874	−	0.327579i
$659$	1.27386	−	2.20639i	0.0496225	−	0.0859486i	−0.840147	−	0.542358i	$-0.817532\pi$
$659$	1.27386	−	2.20639i	0.0496225	−	0.0859486i	0.889770	+	0.456410i	$0.150865\pi$
$660$	−65.8269	+	22.3058i	−2.56231	+	0.868250i
$661$	−4.33211	−	7.50344i	−0.168500	−	0.291850i	0.769393	−	0.638776i	$-0.220559\pi$
$661$	−4.33211	−	7.50344i	−0.168500	−	0.291850i	−0.937893	+	0.346926i	$0.887226\pi$
$662$	23.6415	+	17.1765i	0.918852	+	0.667585i
$663$	−2.17452	+	3.54709i	−0.0844514	+	0.137758i
$664$	5.45768	+	16.7970i	0.211799	+	0.651851i
$665$	−4.36249	+	9.79832i	−0.169170	+	0.379963i
$666$	−1.85233	+	2.95652i	−0.0717763	+	0.114563i
$667$	−5.04629	+	23.7409i	−0.195393	+	0.919252i
$668$	6.98757	−	21.5055i	0.270357	−	0.832074i
$669$	−5.74375	−	2.68251i	−0.222066	−	0.103712i
$670$	32.8742	+	18.9799i	1.27004	+	0.733259i
$671$	−16.3001	−	21.0495i	−0.629260	−	0.812606i
$672$	−0.0661651	−	0.341473i	−0.00255238	−	0.0131726i
$673$	−29.3072	−	3.08032i	−1.12971	−	0.118737i	−0.478823	−	0.877911i	$-0.658937\pi$
$673$	−29.3072	−	3.08032i	−1.12971	−	0.118737i	−0.650888	+	0.759174i	$0.725603\pi$
$674$	−0.0203622	−	0.0957965i	−0.000784322	−	0.00368994i
$675$	−16.2363	−	13.1959i	−0.624935	−	0.507910i
$676$	−51.0199	−	11.7340i	−1.96230	−	0.451307i
$677$	−35.3719	+	25.6992i	−1.35945	+	0.987699i	−0.360971	+	0.932577i	$0.617555\pi$
$677$	−35.3719	+	25.6992i	−1.35945	+	0.987699i	−0.998480	+	0.0551218i	$0.982445\pi$
$678$	0.883985	−	48.9758i	0.0339492	−	1.88090i
$679$	−1.10568	−	5.20183i	−0.0424323	−	0.199628i
$680$	4.05150	+	9.09982i	0.155368	+	0.348962i
$681$	1.11631	+	1.28571i	0.0427771	+	0.0492685i
$682$	−69.2911	−	12.5258i	−2.65329	−	0.479638i
$683$	7.01184	+	4.04829i	0.268301	+	0.154903i	0.628115	−	0.778120i	$-0.283827\pi$
$683$	7.01184	+	4.04829i	0.268301	+	0.154903i	−0.359815	+	0.933024i	$0.617160\pi$
$684$	−41.2942	−	39.9723i	−1.57892	−	1.52838i
$685$	5.53906	+	6.15175i	0.211637	+	0.235046i
$686$	−18.3968	−	16.5645i	−0.702391	−	0.632436i
$687$	3.35030	+	10.9817i	0.127822	+	0.418976i
$688$	−3.89756	−	5.36453i	−0.148593	−	0.204521i
$689$	15.9063	−	21.5149i	0.605980	−	0.819651i
$690$	43.9898	−	18.6417i	1.67466	−	0.709678i
$691$	−2.45780	+	23.3844i	−0.0934991	+	0.889584i	0.842764	+	0.538284i	$0.180927\pi$
$691$	−2.45780	+	23.3844i	−0.0934991	+	0.889584i	−0.936263	+	0.351300i	$0.885740\pi$
$692$	−1.96094	−	3.39645i	−0.0745439	−	0.129114i
$693$	4.35562	+	6.06480i	0.165456	+	0.230383i
$694$	−29.8449			−1.13290
$695$	−0.0979705	+	0.0436193i	−0.00371623	+	0.00165457i
$696$	6.85052	−	55.5203i	0.259668	−	2.10449i
$697$	−0.799762	−	2.46142i	−0.0302932	−	0.0932328i
$698$	15.7003	−	1.65017i	0.594265	−	0.0624598i
$699$	3.11872	+	10.2226i	0.117961	+	0.386654i
$700$	9.04296	+	8.14232i	0.341792	+	0.307751i
$701$	−6.28948	+	19.3570i	−0.237550	+	0.731105i	0.759223	+	0.650831i	$0.225579\pi$
$701$	−6.28948	+	19.3570i	−0.237550	+	0.731105i	−0.996773	+	0.0802736i	$0.974421\pi$
$702$	−40.7687	−	21.2936i	−1.53871	−	0.803675i
$703$		−	2.25347i		−	0.0849914i
$704$	1.88361	−	25.3664i	0.0709911	−	0.956032i
$705$	−13.1690	+	38.1718i	−0.495972	+	1.43763i
$706$	−11.2148	−	25.1888i	−0.422073	−	0.947992i
$707$	−6.67468	−	2.16874i	−0.251027	−	0.0815637i
$708$	20.5219	−	11.3595i	0.771260	−	0.426917i
$709$	−1.58221	−	15.0537i	−0.0594212	−	0.565355i	−0.983213	−	0.182460i	$-0.941594\pi$
$709$	−1.58221	−	15.0537i	−0.0594212	−	0.565355i	0.923792	−	0.382895i	$-0.125073\pi$
$710$	88.3766	−	64.2093i	3.31671	−	2.40973i
$711$	−31.3120	−	11.4388i	−1.17429	−	0.428989i
$712$	13.6815	+	64.3662i	0.512735	+	2.41223i
$713$	32.1638	+	3.38055i	1.20454	+	0.126603i
$714$	1.60530	−	1.39379i	0.0600769	−	0.0521614i
$715$	13.8779	−	33.1391i	0.519003	−	1.23933i
$716$			103.230i			3.85789i
$717$	18.9730	−	13.2683i	0.708561	−	0.495513i
$718$	84.6522	−	17.9934i	3.15919	−	0.671507i
$719$	5.94247	−	27.9571i	0.221617	−	1.04262i	−0.716843	−	0.697235i	$-0.754413\pi$
$719$	5.94247	−	27.9571i	0.221617	−	1.04262i	0.938459	−	0.345390i	$-0.112253\pi$
$720$	−33.1521	+	17.5768i	−1.23551	+	0.655048i
$721$	−12.8796	+	1.35370i	−0.479661	+	0.0504144i
$722$	8.71723	+	1.85291i	0.324422	+	0.0689580i
$723$	−3.78142	−	8.92321i	−0.140633	−	0.331858i
$724$	2.04029	−	0.908397i	0.0758269	−	0.0337603i
$725$	13.0663	+	22.6314i	0.485269	+	0.840510i
$726$	−16.3596	−	43.8200i	−0.607161	−	1.62631i
$727$	8.98938			0.333398			0.166699	−	0.986008i	$-0.446689\pi$
$727$	8.98938			0.333398			0.166699	+	0.986008i	$0.446689\pi$
$728$	11.6048	+	6.82922i	0.430103	+	0.253108i
$729$	−20.0004	−	18.1379i	−0.740755	−	0.671776i
$730$	−29.8698	+	33.1737i	−1.10553	+	1.22781i
$731$	0.431606	−	0.969404i	0.0159635	−	0.0358547i
$732$	−40.9255	−	38.2091i	−1.51265	−	1.41225i
$733$	2.32176	−	0.754386i	0.0857563	−	0.0278639i	−0.265825	−	0.964021i	$-0.585644\pi$
$733$	2.32176	−	0.754386i	0.0857563	−	0.0278639i	0.351581	+	0.936158i	$0.385644\pi$
$734$	−29.9459	−	33.2583i	−1.10532	−	1.22759i
$735$	−14.1741	+	30.3493i	−0.522818	+	1.11945i
$736$		−	1.00075i		−	0.0368880i
$737$	−8.07823	+	15.0364i	−0.297566	+	0.553872i
$738$	26.5403	−	10.6863i	0.976962	−	0.393368i
$739$	18.0612	+	1.89830i	0.664391	+	0.0698303i	0.430720	−	0.902486i	$-0.358260\pi$
$739$	18.0612	+	1.89830i	0.664391	+	0.0698303i	0.233671	+	0.972316i	$0.424926\pi$
$740$	−5.45086	−	1.77109i	−0.200377	−	0.0651066i
$741$	29.6170	−	2.32565i	1.08801	−	0.0854349i
$742$	−11.0607	+	8.03607i	−0.406051	+	0.295013i
$743$	−6.70077	−	2.98337i	−0.245827	−	0.109449i	0.280125	−	0.959964i	$-0.409624\pi$
$743$	−6.70077	−	2.98337i	−0.245827	−	0.109449i	−0.525952	+	0.850514i	$0.676291\pi$
$744$	−74.5283	−	1.34519i	−2.73234	−	0.0493172i
$745$	−14.2149	+	12.7992i	−0.520794	+	0.468925i
$746$	30.8243	−	42.4260i	1.12856	−	1.55332i
$747$	−8.38213	−	6.56490i	−0.306686	−	0.240197i
$748$	−8.01445	+	3.86627i	−0.293037	+	0.141365i
$749$			12.6873i			0.463582i
$750$	−5.26259	+	11.2682i	−0.192163	+	0.411456i
$751$	9.35930	−	1.98938i	0.341526	−	0.0725935i	−0.0339561	−	0.999423i	$-0.510811\pi$
$751$	9.35930	−	1.98938i	0.341526	−	0.0725935i	0.375482	+	0.926830i	$0.377477\pi$
$752$	24.0068	+	21.6158i	0.875437	+	0.788247i
$753$	3.04539	−	13.1554i	0.110980	−	0.479408i
$754$	38.0842	+	43.0102i	1.38695	+	1.56634i
$755$	2.00284	+	6.16411i	0.0728909	+	0.224335i
$756$	11.0840	+	11.1236i	0.403122	+	0.404562i
$757$	4.15941	−	39.5741i	0.151176	−	1.43835i	−0.611335	−	0.791372i	$-0.709367\pi$
$757$	4.15941	−	39.5741i	0.151176	−	1.43835i	0.762511	−	0.646975i	$-0.223966\pi$
$758$	−14.8654	+	25.7476i	−0.539935	+	0.935194i
$759$	8.98366	+	19.5147i	0.326086	+	0.708337i
$760$	35.5627	−	61.5964i	1.29000	−	2.23434i
$761$	−39.4430	+	17.5611i	−1.42981	+	0.636591i	−0.968128	−	0.250456i	$-0.919419\pi$
$761$	−39.4430	+	17.5611i	−1.42981	+	0.636591i	−0.461679	+	0.887047i	$0.652753\pi$
$762$	34.7117	+	81.9109i	1.25747	+	2.96732i
$763$	13.2135	+	2.80861i	0.478361	+	0.101679i
$764$	−38.0192	+	85.3924i	−1.37548	+	3.08939i
$765$	−5.08862	−	3.18814i	−0.183980	−	0.115267i
$766$	37.6677	−	12.2390i	1.36099	−	0.442212i
$767$	−2.61936	+	11.8386i	−0.0945796	+	0.427466i
$768$	−4.82765	−	55.5605i	−0.174203	−	2.00487i
$769$	32.7023	−	18.8807i	1.17927	−	0.680854i	0.223428	−	0.974721i	$-0.428275\pi$
$769$	32.7023	−	18.8807i	1.17927	−	0.680854i	0.955847	+	0.293866i	$0.0949421\pi$
$770$	−11.8608	+	14.0122i	−0.427434	+	0.504963i
$771$	−5.22495	−	26.9656i	−0.188172	−	0.971141i
$772$	−1.19918	+	1.65053i	−0.0431595	+	0.0594040i
$773$	3.27707	−	2.95069i	0.117868	−	0.106129i	−0.608089	−	0.793869i	$-0.708064\pi$
$773$	3.27707	−	2.95069i	0.117868	−	0.106129i	0.725957	+	0.687740i	$0.241397\pi$
$774$	11.0186	+	4.02527i	0.396054	+	0.144685i
$775$	28.1708	−	20.4673i	1.01192	−	0.735205i
$776$	3.68630	+	35.0728i	0.132330	+	1.25904i
$777$	−0.0111117	+	0.615626i	−0.000398630	+	0.0220854i
$778$	7.46349	+	35.1129i	0.267579	+	1.25886i
$779$	−10.8622	+	14.9506i	−0.389180	+	0.535661i
$780$	17.6517	−	73.4674i	0.632031	−	2.63055i
$781$	30.0746	+	38.8373i	1.07615	+	1.38971i
$782$	5.29721	−	3.05834i	0.189428	−	0.109366i
$783$	15.2566	+	30.0751i	0.545225	+	1.07480i
$784$	17.9310	+	19.9144i	0.640392	+	0.711227i
$785$	22.4597	−	7.29761i	0.801622	−	0.260463i
$786$	34.6225	−	37.0839i	1.23494	−	1.32274i
$787$	28.9479	−	3.04254i	1.03188	−	0.108455i	0.426578	−	0.904451i	$-0.359719\pi$
$787$	28.9479	−	3.04254i	1.03188	−	0.108455i	0.605302	+	0.795996i	$0.293052\pi$
$788$	23.7535	+	73.1057i	0.846183	+	2.60428i
$789$	4.63981	−	37.6035i	0.165182	−	1.33872i
$790$	8.56722	−	81.5117i	0.304808	−	2.90006i
$791$	−4.32241	−	7.48664i	−0.153687	−	0.266194i
$792$	−24.5216	−	43.0168i	−0.871337	−	1.52854i
$793$	28.8077	−	2.78601i	1.02299	−	0.0989341i
$794$	−42.6947	−	31.0195i	−1.51518	−	1.10084i
$795$	30.8268	+	23.2584i	1.09332	+	0.824891i
$796$	49.1104	−	54.5426i	1.74067	−	1.93321i
$797$	6.77401	−	0.711977i	0.239948	−	0.0252195i	0.0162088	−	0.999869i	$-0.494840\pi$
$797$	6.77401	−	0.711977i	0.239948	−	0.0252195i	0.223739	+	0.974649i	$0.428174\pi$
$798$	−14.7890	−	3.42357i	−0.523525	−	0.121193i
$799$	−1.07483	+	5.05668i	−0.0380248	+	0.178893i
$800$	−0.720980	−	0.800729i	−0.0254905	−	0.0283101i
$801$	−28.5029	−	27.5905i	−1.00710	−	0.974861i
$802$	30.7407	+	17.7482i	1.08549	+	0.626709i
$803$	−15.3208	−	12.9685i	−0.540659	−	0.457649i
$804$	−11.7072	+	33.9345i	−0.412879	+	1.19678i
$805$	4.95609	−	6.82147i	0.174679	−	0.240425i
$806$	51.6916	−	56.4589i	1.82076	−	1.98868i
$807$	7.14590	+	4.29947i	0.251548	+	0.151349i
$808$	42.5165	+	18.9296i	1.49573	+	0.665940i
$809$	−19.8087	−	8.81942i	−0.696438	−	0.310074i	0.0278102	−	0.999613i	$-0.491147\pi$
$809$	−19.8087	−	8.81942i	−0.696438	−	0.310074i	−0.724249	+	0.689539i	$0.757813\pi$
$810$	31.3041	−	58.5383i	1.09991	−	2.05683i
$811$	6.99239	+	2.27197i	0.245536	+	0.0797795i	0.429200	−	0.903210i	$-0.358796\pi$
$811$	6.99239	+	2.27197i	0.245536	+	0.0797795i	−0.183664	+	0.982989i	$0.558796\pi$
$812$	−7.97757	−	17.9179i	−0.279958	−	0.628795i
$813$	−7.33152	−	37.8374i	−0.257128	−	1.32702i
$814$	1.07911	−	3.70305i	0.0378229	−	0.129792i
$815$	19.8757	+	11.4753i	0.696217	+	0.401961i
$816$	−3.93684	+	2.75312i	−0.137817	+	0.0963784i
$817$	−7.41141	+	1.57534i	−0.259293	+	0.0551143i
$818$	−65.0434	+	21.1339i	−2.27419	+	0.738929i
$819$	−8.10252	+	0.489304i	−0.283125	+	0.0170977i
$820$	27.6265	+	38.0246i	0.964758	+	1.32788i
$821$	14.9952	−	16.6538i	0.523335	−	0.581222i	−0.422299	−	0.906457i	$-0.638777\pi$
$821$	14.9952	−	16.6538i	0.523335	−	0.581222i	0.945633	+	0.325235i	$0.105443\pi$
$822$	−7.05641	+	9.35261i	−0.246121	+	0.326210i
$823$	−46.1957	+	20.5676i	−1.61028	+	0.716943i	−0.997319	−	0.0731714i	$-0.976688\pi$
$823$	−46.1957	+	20.5676i	−1.61028	+	0.716943i	−0.612960	+	0.790114i	$0.710021\pi$
$824$	85.8798			2.99177
$825$	21.2473	+	9.14210i	0.739736	+	0.318287i
$826$	3.09775	−	5.36546i	0.107785	−	0.186688i
$827$	4.79390	+	3.48297i	0.166700	+	0.121115i	0.668008	−	0.744155i	$-0.267147\pi$
$827$	4.79390	+	3.48297i	0.166700	+	0.121115i	−0.501307	+	0.865269i	$0.667147\pi$
$828$	25.2202	+	37.4864i	0.876461	+	1.30274i
$829$	−3.16924	+	3.51979i	−0.110072	+	0.122247i	−0.795663	−	0.605740i	$-0.792877\pi$
$829$	−3.16924	+	3.51979i	−0.110072	+	0.122247i	0.685591	+	0.727987i	$0.259544\pi$
$830$	10.6471	−	23.9138i	0.369566	−	0.830060i
$831$	4.20366	−	18.1588i	0.145823	−	0.629923i
$832$	22.2352	+	16.4388i	0.770867	+	0.569913i
$833$	−1.32518	+	4.07850i	−0.0459149	+	0.141311i
$834$	−0.0869843	−	0.124384i	−0.00301202	−	0.00430706i
$835$	−14.6099	+	8.43501i	−0.505595	+	0.291905i
$836$	55.9711	+	30.0703i	1.93580	+	1.04000i
$837$	37.7299	−	24.4066i	1.30414	−	0.843614i
$838$	−20.2301	−	45.4375i	−0.698837	−	1.56961i
$839$	10.6653	−	9.60303i	0.368205	−	0.331534i	−0.464170	−	0.885746i	$-0.653647\pi$
$839$	10.6653	−	9.60303i	0.368205	−	0.331534i	0.832375	+	0.554213i	$0.186981\pi$
$840$	−10.0191	+	16.6521i	−0.345691	+	0.574554i
$841$	−1.37155	−	13.0494i	−0.0472947	−	0.449979i
$842$	−75.4821	−	33.6068i	−2.60128	−	1.15817i
$843$	13.1867	+	0.238012i	0.454174	+	0.00819758i
$844$	−50.8633	−	16.5265i	−1.75079	−	0.568865i
$845$	22.4291	+	31.9752i	0.771586	+	1.09998i
$846$	−56.5841	−	8.02096i	−1.94540	−	0.275766i
$847$	−6.46091	−	5.13805i	−0.222000	−	0.176545i
$848$	26.7550	−	15.4470i	0.918771	−	0.530453i
$849$	−8.75489	+	18.7458i	−0.300467	+	0.643356i
$850$	2.03511	−	6.26341i	0.0698036	−	0.214833i
$851$	−0.368324	+	1.73283i	−0.0126260	+	0.0594006i
$852$	75.5096	+	70.4978i	2.58692	+	2.41521i
$853$	10.9597	+	15.0848i	0.375254	+	0.516492i	0.954319	−	0.298789i	$-0.0965825\pi$
$853$	10.9597	+	15.0848i	0.375254	+	0.516492i	−0.579066	+	0.815281i	$0.696583\pi$
$854$	−14.4655	−	3.07473i	−0.494999	−	0.105215i
$855$	2.94012	+	42.7761i	0.100550	+	1.46291i
$856$	8.79439	−	83.6730i	0.300586	−	2.85988i
$857$	−18.4028			−0.628629			−0.314314	−	0.949319i	$-0.601775\pi$
$857$	−18.4028			−0.628629			−0.314314	+	0.949319i	$0.601775\pi$
$858$	49.7822	+	10.3609i	1.69953	+	0.353716i
$859$	−4.02676			−0.137391			−0.0686956	−	0.997638i	$-0.521884\pi$
$859$	−4.02676			−0.137391			−0.0686956	+	0.997638i	$0.521884\pi$
$860$	−2.01436	+	19.1653i	−0.0686891	+	0.653533i
$861$	3.04117	−	4.03079i	0.103643	−	0.137369i
$862$	−35.9830	−	7.64841i	−1.22558	−	0.260506i
$863$	−1.14371	−	1.57418i	−0.0389324	−	0.0535859i	0.789107	−	0.614256i	$-0.210544\pi$
$863$	−1.14371	−	1.57418i	−0.0389324	−	0.0535859i	−0.828039	+	0.560670i	$0.810544\pi$
$864$	−0.873128	−	1.08216i	−0.0297044	−	0.0368159i
$865$	−0.608338	+	2.86201i	−0.0206841	+	0.0973112i
$866$	−8.53765	+	26.2762i	−0.290121	+	0.892901i
$867$	25.9822	+	12.1345i	0.882400	+	0.412108i
$868$	−22.6333	+	13.0673i	−0.768224	+	0.443534i
$869$	36.7531	+	2.72914i	1.24677	+	0.0925797i
$870$	−62.6078	+	54.3589i	−2.12260	+	1.84294i
$871$	−9.14413	−	16.1464i	−0.309837	−	0.547101i
$872$	−85.1967	−	27.6821i	−2.88513	−	0.937434i
$873$	−13.6461	−	16.3021i	−0.461849	−	0.551741i
$874$	−39.8996	−	17.7645i	−1.34962	−	0.600892i
$875$	0.229423	+	2.18281i	0.00775591	+	0.0737926i
$876$	−36.1716	−	21.7633i	−1.22212	−	0.735315i
$877$	−5.42925	+	4.88852i	−0.183333	+	0.165073i	−0.755687	−	0.654933i	$-0.772697\pi$
$877$	−5.42925	+	4.88852i	−0.183333	+	0.165073i	0.572354	+	0.820006i	$0.306030\pi$
$878$	−30.0178	−	67.4211i	−1.01305	−	2.27535i
$879$	−31.4531	−	36.2261i	−1.06089	−	1.22188i
$880$	29.9647	−	28.6882i	1.01011	−	0.967079i
$881$	0.624568	−	0.360594i	0.0210422	−	0.0121487i	−0.489442	−	0.872036i	$-0.662800\pi$
$881$	0.624568	−	0.360594i	0.0210422	−	0.0121487i	0.510484	+	0.859887i	$0.329466\pi$
$882$	−45.9856	−	11.5236i	−1.54842	−	0.388018i
$883$	0.578177	−	1.77945i	0.0194572	−	0.0598831i	−0.940856	−	0.338805i	$-0.889977\pi$
$883$	0.578177	−	1.77945i	0.0194572	−	0.0598831i	0.960314	+	0.278922i	$0.0899772\pi$
$884$	1.09105	−	9.61173i	0.0366960	−	0.323278i
$885$	−17.0487	−	3.94667i	−0.573085	−	0.132666i
$886$	−20.3260	+	45.6529i	−0.682865	+	1.53374i
$887$	37.5727	−	41.7287i	1.26157	−	1.40111i	0.382825	−	0.923821i	$-0.374951\pi$
$887$	37.5727	−	41.7287i	1.26157	−	1.40111i	0.878744	−	0.477293i	$-0.158382\pi$
$888$	0.500014	−	4.05238i	0.0167794	−	0.135989i
$889$	12.7019	+	9.22845i	0.426007	+	0.309512i
$890$	48.7659	−	84.4650i	1.63464	−	2.83127i
$891$	26.7406	+	13.2642i	0.895844	+	0.444368i
$892$	14.7390			0.493498
$893$	33.7220	−	15.0140i	1.12846	−	0.502425i
$894$	−21.6112	−	16.3053i	−0.722785	−	0.545332i
$895$	51.5334	−	57.2337i	1.72257	−	1.91311i
$896$	−8.54119	−	11.7559i	−0.285341	−	0.392739i
$897$	−23.1544	−	3.05249i	−0.773102	−	0.101920i
$898$	−84.2154	+	27.3632i	−2.81030	+	0.913123i
$899$	−54.8991	+	11.6692i	−1.83099	+	0.389189i
$900$	47.1863	+	11.8244i	1.57288	+	0.394148i
$901$	4.28160	+	2.47198i	0.142641	+	0.0823537i
$902$	−25.0089	+	19.3662i	−0.832704	+	0.644823i
$903$	2.03249	−	0.393823i	0.0676370	−	0.0131056i
$904$	23.3170	+	52.3709i	0.775513	+	1.74183i
$905$	−1.58468	−	0.514892i	−0.0526764	−	0.0171156i
$906$	−8.02564	+	4.44245i	−0.266634	+	0.147591i
$907$	40.5946	+	18.0739i	1.34792	+	0.600133i	0.948541	−	0.316653i	$-0.102559\pi$
$907$	40.5946	+	18.0739i	1.34792	+	0.600133i	0.399379	+	0.916786i	$0.369226\pi$
$908$	−3.61657	−	1.61020i	−0.120020	−	0.0534364i
$909$	−27.6357	+	4.83906i	−0.916617	+	0.160501i
$910$	−6.00924	−	19.0311i	−0.199204	−	0.630876i
$911$	−6.30694	+	8.68076i	−0.208958	+	0.287606i	−0.900613	−	0.434622i	$-0.856882\pi$
$911$	−6.30694	+	8.68076i	−0.208958	+	0.287606i	0.691655	+	0.722228i	$0.256882\pi$
$912$	32.4269	+	11.1870i	1.07376	+	0.370440i
$913$	10.8945	+	4.45633i	0.360555	+	0.147483i
$914$	−36.8597	−	21.2809i	−1.21921	−	0.703911i
$915$	3.61589	+	41.6146i	0.119538	+	1.37574i
$916$	−17.8621	−	19.8378i	−0.590179	−	0.655461i
$917$	1.86158	−	8.75803i	0.0614747	−	0.289216i
$918$	3.05983	−	7.92884i	0.100989	−	0.261691i
$919$	20.5629	−	2.16125i	0.678307	−	0.0712930i	0.240891	−	0.970552i	$-0.422560\pi$
$919$	20.5629	−	2.16125i	0.678307	−	0.0712930i	0.437416	+	0.899259i	$0.355894\pi$
$920$	−37.4140	+	41.5525i	−1.23350	+	1.36995i
$921$	−4.76134	+	6.31070i	−0.156891	+	0.207945i
$922$	43.6146	+	31.6879i	1.43637	+	1.04358i
$923$	−53.1516	+	5.14033i	−1.74951	+	0.169196i
$924$	−15.1424	−	8.49088i	−0.498150	−	0.279329i
$925$	0.953695	+	1.65185i	0.0313573	+	0.0543125i
$926$	2.90435	−	27.6330i	0.0954429	−	0.908078i
$927$	−42.9549	+	28.8993i	−1.41083	+	0.949177i
$928$	0.536679	+	1.65173i	0.0176174	+	0.0542207i
$929$	−30.8622	+	3.24375i	−1.01256	+	0.106424i	−0.596248	−	0.802800i	$-0.703343\pi$
$929$	−30.8622	+	3.24375i	−1.01256	+	0.106424i	−0.416307	+	0.909224i	$0.636676\pi$
$930$	80.7553	+	75.3953i	2.64807	+	2.47231i
$931$	29.1221	−	9.46233i	0.954437	−	0.310115i
$932$	−16.6274	−	18.4666i	−0.544650	−	0.604895i
$933$	33.3061	+	47.6263i	1.09039	+	1.55921i
$934$	−42.6672	+	24.6339i	−1.39611	+	0.806046i
$935$	6.37351	+	1.85732i	0.208436	+	0.0607408i
$936$	53.7757	+	2.38942i	1.75771	+	0.0781005i
$937$	5.60658	−	7.71680i	0.183159	−	0.252097i	−0.707558	−	0.706656i	$-0.750203\pi$
$937$	5.60658	−	7.71680i	0.183159	−	0.252097i	0.890717	+	0.454559i	$0.150203\pi$
$938$	1.97134	+	9.27441i	0.0643664	+	0.302820i
$939$	9.18240	+	0.165737i	0.299656	+	0.00540862i
$940$	−9.81350	−	93.3692i	−0.320081	−	3.04537i
$941$	0.0570729	−	0.0414659i	0.00186052	−	0.00135175i	−0.586855	−	0.809692i	$-0.699634\pi$
$941$	0.0570729	−	0.0414659i	0.00186052	−	0.00135175i	0.588715	+	0.808341i	$0.299634\pi$
$942$	16.1867	+	29.2425i	0.527390	+	0.952771i
$943$	10.7963	−	9.72099i	0.351574	−	0.316559i
$944$	−8.22896	+	11.3262i	−0.267830	+	0.368636i
$945$	−0.592285	−	11.7005i	−0.0192670	−	0.380617i
$946$	−12.9333	−	0.960373i	−0.420497	−	0.0312244i
$947$	37.8314	−	21.8420i	1.22936	−	0.709769i	0.262461	−	0.964943i	$-0.415466\pi$
$947$	37.8314	−	21.8420i	1.22936	−	0.709769i	0.966895	+	0.255174i	$0.0821327\pi$
$948$	77.2162	−	6.70931i	2.50787	−	0.217908i
$949$	20.8085	−	6.57046i	0.675473	−	0.213286i
$950$	−44.7232	+	14.5315i	−1.45101	+	0.471463i
$951$	−13.8581	+	4.22786i	−0.449381	+	0.137098i
$952$	−1.01198	+	2.27295i	−0.0327986	+	0.0736668i
$953$	−55.6369	−	11.8260i	−1.80225	−	0.383081i	−0.820260	−	0.571991i	$-0.806171\pi$
$953$	−55.6369	−	11.8260i	−1.80225	−	0.383081i	−0.981995	+	0.188909i	$0.939505\pi$
$954$	−24.0175	+	49.0949i	−0.777594	+	1.58951i
$955$	63.7075	−	28.3644i	2.06153	−	0.917851i
$956$	−26.9147	+	46.6177i	−0.870484	+	1.50772i
$957$	−25.2928	−	27.3912i	−0.817601	−	0.885430i
$958$	20.6534	−	35.7727i	0.667281	−	1.15576i
$959$	−0.216131	+	2.05635i	−0.00697924	+	0.0664030i
$960$	−24.0371	+	31.8590i	−0.775795	+	1.02824i
$961$	13.5306	+	41.6430i	0.436472	+	1.34332i
$962$	2.77973	+	3.13928i	0.0896222	+	0.101214i
$963$	23.7579	+	44.8105i	0.765588	+	1.44400i
$964$	16.7451	+	15.0773i	0.539323	+	0.485609i
$965$	1.48882	−	0.316459i	0.0479268	−	0.0101872i
$966$	10.8126	+	5.04981i	0.347889	+	0.162475i
$967$		−	18.1150i		−	0.582540i	−0.956641	−	0.291270i	$-0.905922\pi$
$967$		−	18.1150i		−	0.582540i	0.956641	−	0.291270i	$-0.0940778\pi$
$968$	39.0485	+	38.3642i	1.25507	+	1.23307i
$969$	1.04423	+	5.38917i	0.0335454	+	0.173125i
$970$	30.7232	−	42.2869i	0.986463	−	1.35775i
$971$	−9.20341	+	8.28679i	−0.295352	+	0.265936i	−0.803462	−	0.595356i	$-0.797011\pi$
$971$	−9.20341	+	8.28679i	−0.295352	+	0.265936i	0.508110	+	0.861292i	$0.330344\pi$
$972$	59.9780	+	18.5321i	1.92379	+	0.594418i
$973$	−0.0244711	−	0.0108952i	−0.000784506	−	0.000349285i
$974$	64.6400	−	46.9637i	2.07120	−	1.50481i
$975$	−20.7257	+	14.2390i	−0.663754	+	0.456013i
$976$	31.7822	+	10.3267i	1.01732	+	0.330549i
$977$	34.7671	+	3.65417i	1.11230	+	0.116907i	0.642806	−	0.766029i	$-0.277770\pi$
$977$	34.7671	+	3.65417i	1.11230	+	0.116907i	0.469492	+	0.882937i	$0.344437\pi$
$978$	−10.5934	+	30.7063i	−0.338741	+	0.981879i
$979$	38.6335	+	20.7557i	1.23473	+	0.663356i
$980$		−	77.8792i		−	2.48776i
$981$	51.9285	−	14.8235i	1.65795	−	0.473278i
$982$	−27.7544	−	30.8244i	−0.885678	−	0.983645i
$983$	16.5773	−	5.38629i	0.528733	−	0.171796i	−0.0324717	−	0.999473i	$-0.510338\pi$
$983$	16.5773	−	5.38629i	0.528733	−	0.171796i	0.561205	+	0.827677i	$0.310338\pi$
$984$	−22.8507	+	24.4752i	−0.728453	+	0.780240i
$985$	23.3254	−	52.3898i	0.743210	−	1.66928i
$986$	−7.10290	+	7.88857i	−0.226203	+	0.251223i
$987$	−9.28654	+	3.93539i	−0.295594	+	0.125265i
$988$	−60.1033	+	34.0379i	−1.91214	+	1.08289i
$989$	5.95656			0.189408
$990$	−15.6527	+	71.7003i	−0.497474	+	2.27879i
$991$	19.8988	+	34.4658i	0.632107	+	1.09484i	0.987120	+	0.159981i	$0.0511431\pi$
$991$	19.8988	+	34.4658i	0.632107	+	1.09484i	−0.355013	+	0.934861i	$0.615524\pi$
$992$	2.11408	−	0.941251i	0.0671222	−	0.0298847i
$993$	18.9828	−	8.04441i	0.602401	−	0.255282i
$994$	26.6895	+	5.67304i	0.846541	+	0.179938i
$995$	−54.4563	+	5.72359i	−1.72638	+	0.181450i
$996$	24.1167	+	5.58288i	0.764168	+	0.176900i
$997$	5.71295	−	26.8773i	0.180931	−	0.851213i	−0.790234	−	0.612805i	$-0.790041\pi$
$997$	5.71295	−	26.8773i	0.180931	−	0.851213i	0.971165	−	0.238408i	$-0.0766256\pi$
$998$	62.4398	−	13.2720i	1.97650	−	0.420117i
$999$	1.11356	+	2.19516i	0.0352316	+	0.0694517i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bq.a.29.5	✓	416
3.2	odd	2	inner	429.2.bq.a.29.48	yes	416
11.8	odd	10	inner	429.2.bq.a.107.5	yes	416
13.9	even	3	inner	429.2.bq.a.425.48	yes	416
33.8	even	10	inner	429.2.bq.a.107.48	yes	416
39.35	odd	6	inner	429.2.bq.a.425.5	yes	416
143.74	odd	30	inner	429.2.bq.a.74.48	yes	416
429.74	even	30	inner	429.2.bq.a.74.5	yes	416

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bq.a.29.5	✓	416	1.1	even	1	trivial
429.2.bq.a.29.48	yes	416	3.2	odd	2	inner
429.2.bq.a.74.5	yes	416	429.74	even	30	inner
429.2.bq.a.74.48	yes	416	143.74	odd	30	inner
429.2.bq.a.107.5	yes	416	11.8	odd	10	inner
429.2.bq.a.107.48	yes	416	33.8	even	10	inner
429.2.bq.a.425.5	yes	416	39.35	odd	6	inner
429.2.bq.a.425.48	yes	416	13.9	even	3	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.bq (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.256618 + 2.44156i) q^{2} +(1.38266 + 1.04320i) q^{3} +(-3.93907 - 0.837274i) q^{4} +(1.76595 + 2.43063i) q^{5} +(-2.90184 + 3.10814i) q^{6} +(-0.156026 + 0.734044i) q^{7} +(1.53781 - 4.73290i) q^{8} +(0.823485 + 2.88477i) q^{9} +O(q^{10})\)	\(q+(-0.256618 + 2.44156i) q^{2} +(1.38266 + 1.04320i) q^{3} +(-3.93907 - 0.837274i) q^{4} +(1.76595 + 2.43063i) q^{5} +(-2.90184 + 3.10814i) q^{6} +(-0.156026 + 0.734044i) q^{7} +(1.53781 - 4.73290i) q^{8} +(0.823485 + 2.88477i) q^{9} +(-6.38769 + 3.68794i) q^{10} +(-1.74541 - 2.82020i) q^{11} +(-4.57294 - 5.26688i) q^{12} +(3.60543 + 0.0299579i) q^{13} +(-1.75217 - 0.569316i) q^{14} +(-0.0939104 + 5.20296i) q^{15} +(3.80321 + 1.69330i) q^{16} +(0.0696395 + 0.662576i) q^{17} +(-7.25465 + 1.27030i) q^{18} +(3.53522 - 3.18313i) q^{19} +(-4.92110 - 11.0530i) q^{20} +(-0.981482 + 0.852166i) q^{21} +(7.33359 - 3.53782i) q^{22} +(-3.23872 + 1.86987i) q^{23} +(7.06361 - 4.93974i) q^{24} +(-1.24426 + 3.82945i) q^{25} +(-0.998362 + 8.79518i) q^{26} +(-1.87078 + 4.84770i) q^{27} +(1.22919 - 2.76081i) q^{28} +(4.34272 - 4.82308i) q^{29} +(-12.6792 - 1.56446i) q^{30} +(-6.99629 - 5.08310i) q^{31} +(-0.133799 + 0.231746i) q^{32} +(0.528712 - 5.72018i) q^{33} -1.63559 q^{34} +(-2.05972 + 0.917046i) q^{35} +(-0.828420 - 12.0528i) q^{36} +(0.316971 - 0.352032i) q^{37} +(6.86460 + 9.44831i) q^{38} +(4.95382 + 3.80259i) q^{39} +(14.2196 - 4.62023i) q^{40} +(-3.79981 + 0.807674i) q^{41} +(-1.82875 - 2.61503i) q^{42} +(-1.37938 - 0.796385i) q^{43} +(4.51402 + 12.5703i) q^{44} +(-5.55755 + 7.09594i) q^{45} +(-3.73429 - 8.38736i) q^{46} +(7.37983 + 2.39785i) q^{47} +(3.49210 + 6.30875i) q^{48} +(5.88034 + 2.61810i) q^{49} +(-9.03054 - 4.02066i) q^{50} +(-0.594909 + 0.988763i) q^{51} +(-14.1769 - 3.13674i) q^{52} +(4.36187 - 6.00360i) q^{53} +(-11.3559 - 5.81163i) q^{54} +(3.77253 - 9.22279i) q^{55} +(3.23422 + 1.86728i) q^{56} +(8.20863 - 0.713248i) q^{57} +(10.6614 + 11.8407i) q^{58} +(-0.699173 + 3.28935i) q^{59} +(4.72622 - 20.4162i) q^{60} +(7.98311 - 0.839059i) q^{61} +(14.2061 - 15.7774i) q^{62} +(-2.24603 + 0.154376i) q^{63} +(6.20461 + 4.50791i) q^{64} +(6.29420 + 8.81634i) q^{65} +(13.8305 + 2.75878i) q^{66} +(-2.57325 - 4.45699i) q^{67} +(0.280443 - 2.66824i) q^{68} +(-6.42868 - 0.793220i) q^{69} +(-1.71046 - 5.26426i) q^{70} +(-14.7292 + 1.54811i) q^{71} +(14.9197 + 0.538759i) q^{72} +(5.75591 - 1.87021i) q^{73} +(0.778167 + 0.864242i) q^{74} +(-5.71526 + 3.99681i) q^{75} +(-16.5906 + 9.57861i) q^{76} +(2.34248 - 0.841186i) q^{77} +(-10.5555 + 11.1192i) q^{78} +(-6.53147 + 8.98980i) q^{79} +(2.60052 + 12.2345i) q^{80} +(-7.64375 + 4.75112i) q^{81} +(-0.996885 - 9.48473i) q^{82} +(-2.87119 + 2.08604i) q^{83} +(4.57962 - 2.53497i) q^{84} +(-1.48749 + 1.33935i) q^{85} +(2.29840 - 3.16347i) q^{86} +(11.0359 - 2.13836i) q^{87} +(-16.0318 + 3.92393i) q^{88} +(-11.4515 + 6.61154i) q^{89} +(-15.8990 - 15.3900i) q^{90} +(-0.584530 + 2.64187i) q^{91} +(14.3231 - 4.65386i) q^{92} +(-4.37080 - 14.3267i) q^{93} +(-7.74830 + 17.4030i) q^{94} +(13.9800 + 2.97155i) q^{95} +(-0.426754 + 0.180847i) q^{96} +(-6.47388 + 2.88236i) q^{97} +(-7.90124 + 13.6854i) q^{98} +(6.69830 - 7.35750i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 416 q - 3 q^{3} + 42 q^{4} - 5 q^{6} - 10 q^{7} + 3 q^{9}+O(q^{10}) \) 416 * q - 3 * q^3 + 42 * q^4 - 5 * q^6 - 10 * q^7 + 3 * q^9	\( 416 q - 3 q^{3} + 42 q^{4} - 5 q^{6} - 10 q^{7} + 3 q^{9} - 52 q^{12} - 20 q^{13} - 3 q^{15} + 30 q^{16} - 20 q^{18} - 10 q^{19} + 4 q^{22} + 5 q^{24} + 60 q^{25} - 24 q^{27} - 10 q^{28} - 65 q^{30} - 8 q^{31} + 49 q^{33} - 24 q^{34} + 3 q^{36} - 6 q^{37} - 35 q^{39} - 120 q^{40} - 13 q^{42} - 32 q^{45} - 30 q^{46} - 33 q^{48} - 26 q^{49} - 100 q^{51} - 60 q^{52} - 42 q^{55} - 20 q^{57} - 34 q^{58} + 32 q^{60} - 30 q^{61} - 45 q^{63} + 40 q^{64} + 42 q^{66} + 32 q^{67} - 33 q^{69} - 268 q^{70} + 55 q^{72} - 40 q^{73} + 9 q^{75} - 32 q^{78} - 37 q^{81} + 28 q^{82} - 180 q^{84} - 10 q^{85} - 142 q^{88} - 30 q^{90} + 8 q^{91} - 26 q^{93} - 90 q^{94} + 330 q^{96} - 14 q^{97} - 4 q^{99}+O(q^{100}) \) 416 * q - 3 * q^3 + 42 * q^4 - 5 * q^6 - 10 * q^7 + 3 * q^9 - 52 * q^12 - 20 * q^13 - 3 * q^15 + 30 * q^16 - 20 * q^18 - 10 * q^19 + 4 * q^22 + 5 * q^24 + 60 * q^25 - 24 * q^27 - 10 * q^28 - 65 * q^30 - 8 * q^31 + 49 * q^33 - 24 * q^34 + 3 * q^36 - 6 * q^37 - 35 * q^39 - 120 * q^40 - 13 * q^42 - 32 * q^45 - 30 * q^46 - 33 * q^48 - 26 * q^49 - 100 * q^51 - 60 * q^52 - 42 * q^55 - 20 * q^57 - 34 * q^58 + 32 * q^60 - 30 * q^61 - 45 * q^63 + 40 * q^64 + 42 * q^66 + 32 * q^67 - 33 * q^69 - 268 * q^70 + 55 * q^72 - 40 * q^73 + 9 * q^75 - 32 * q^78 - 37 * q^81 + 28 * q^82 - 180 * q^84 - 10 * q^85 - 142 * q^88 - 30 * q^90 + 8 * q^91 - 26 * q^93 - 90 * q^94 + 330 * q^96 - 14 * q^97 - 4 * q^99

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