LMFDB - Embedded newform 425.2.k.b.86.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,2,Mod(86,425)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("425.86"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.k (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [76] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$19$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			86.10
Character	$\chi$	$=$	425.86
Dual form			425.2.k.b.341.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.382111 + 0.277620i) q^{2} +(0.549532 - 1.69129i) q^{3} +(-0.549098 + 1.68995i) q^{4} +(-0.894807 + 2.04922i) q^{5} +(0.259553 + 0.798821i) q^{6} +1.24434 q^{7} +(-0.551255 - 1.69659i) q^{8} +(-0.131414 - 0.0954780i) q^{9} +(-0.226990 - 1.03145i) q^{10} +(-4.29839 + 3.12296i) q^{11} +(2.55644 + 1.85736i) q^{12} +(-1.66410 - 1.20904i) q^{13} +(-0.475477 + 0.345454i) q^{14} +(2.97410 + 2.63949i) q^{15} +(-2.19347 - 1.59365i) q^{16} +(0.309017 + 0.951057i) q^{17} +0.0767215 q^{18} +(2.60229 + 8.00904i) q^{19} +(-2.97175 - 2.63740i) q^{20} +(0.683806 - 2.10454i) q^{21} +(0.775466 - 2.38664i) q^{22} +(-4.93396 + 3.58473i) q^{23} -3.17235 q^{24} +(-3.39864 - 3.66732i) q^{25} +0.971522 q^{26} +(4.08239 - 2.96603i) q^{27} +(-0.683266 + 2.10288i) q^{28} +(-0.901517 + 2.77458i) q^{29} +(-1.86921 - 0.182909i) q^{30} +(-0.466989 - 1.43725i) q^{31} +4.84837 q^{32} +(2.91972 + 8.98598i) q^{33} +(-0.382111 - 0.277620i) q^{34} +(-1.11345 + 2.54994i) q^{35} +(0.233512 - 0.169657i) q^{36} +(2.85583 + 2.07488i) q^{37} +(-3.21784 - 2.33789i) q^{38} +(-2.95930 + 2.15006i) q^{39} +(3.96995 + 0.388474i) q^{40} +(7.04170 + 5.11610i) q^{41} +(0.322972 + 0.994007i) q^{42} +10.2220 q^{43} +(-2.91741 - 8.97888i) q^{44} +(0.313246 - 0.183863i) q^{45} +(0.890128 - 2.73953i) q^{46} +(-0.660455 + 2.03267i) q^{47} +(-3.90069 + 2.83402i) q^{48} -5.45161 q^{49} +(2.31678 + 0.457793i) q^{50} +1.77832 q^{51} +(2.95696 - 2.14836i) q^{52} +(0.0480763 - 0.147964i) q^{53} +(-0.736497 + 2.26671i) q^{54} +(-2.55342 - 11.6028i) q^{55} +(-0.685949 - 2.11114i) q^{56} +14.9756 q^{57} +(-0.425800 - 1.31048i) q^{58} +(-6.47362 - 4.70336i) q^{59} +(-6.09368 + 3.57674i) q^{60} +(4.33169 - 3.14716i) q^{61} +(0.577450 + 0.419542i) q^{62} +(-0.163524 - 0.118807i) q^{63} +(2.53432 - 1.84129i) q^{64} +(3.96663 - 2.32825i) q^{65} +(-3.61035 - 2.62307i) q^{66} +(-1.53294 - 4.71789i) q^{67} -1.77692 q^{68} +(3.35144 + 10.3147i) q^{69} +(-0.282453 - 1.28347i) q^{70} +(0.918858 - 2.82796i) q^{71} +(-0.0895441 + 0.275588i) q^{72} +(-12.0599 + 8.76206i) q^{73} -1.66727 q^{74} +(-8.07015 + 3.73277i) q^{75} -14.9638 q^{76} +(-5.34867 + 3.88604i) q^{77} +(0.533883 - 1.64312i) q^{78} +(5.12699 - 15.7793i) q^{79} +(5.22847 - 3.06890i) q^{80} +(-2.92359 - 8.99787i) q^{81} -4.11104 q^{82} +(-1.43437 - 4.41453i) q^{83} +(3.18109 + 2.31120i) q^{84} +(-2.22544 - 0.217767i) q^{85} +(-3.90595 + 2.83784i) q^{86} +(4.19720 + 3.04945i) q^{87} +(7.66789 + 5.57105i) q^{88} +(-2.03508 + 1.47857i) q^{89} +(-0.0686509 + 0.157220i) q^{90} +(-2.07070 - 1.50445i) q^{91} +(-3.34879 - 10.3065i) q^{92} -2.68742 q^{93} +(-0.311943 - 0.960063i) q^{94} +(-18.7409 - 1.83386i) q^{95} +(2.66434 - 8.19999i) q^{96} +(-2.24987 + 6.92439i) q^{97} +(2.08312 - 1.51348i) q^{98} +0.863045 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 6 q^{2} - 7 q^{3} - 26 q^{4} + 13 q^{5} + 12 q^{6} + 22 q^{7} + 10 q^{8} - 24 q^{9} - 6 q^{10} - 16 q^{11} - 15 q^{12} - q^{13} - 19 q^{14} - 3 q^{15} + 30 q^{16} - 19 q^{17} + 6 q^{18} + 18 q^{19}+ \cdots - 64 q^{99}+O(q^{100}) $ 76 * q - 6 * q^2 - 7 * q^3 - 26 * q^4 + 13 * q^5 + 12 * q^6 + 22 * q^7 + 10 * q^8 - 24 * q^9 - 6 * q^10 - 16 * q^11 - 15 * q^12 - q^13 - 19 * q^14 - 3 * q^15 + 30 * q^16 - 19 * q^17 + 6 * q^18 + 18 * q^19 - 23 * q^20 - 22 * q^21 - 15 * q^22 - 8 * q^23 - 22 * q^24 + 35 * q^25 - 14 * q^26 - 10 * q^27 - 29 * q^28 - 25 * q^29 + 57 * q^30 + 22 * q^31 + 54 * q^32 - 22 * q^33 - 6 * q^34 - 19 * q^35 - 91 * q^36 - 49 * q^37 + 15 * q^38 + 25 * q^39 - 2 * q^40 + 16 * q^41 - 28 * q^42 + 104 * q^43 + 18 * q^44 + 10 * q^45 - 55 * q^46 - 26 * q^47 - 86 * q^48 + 2 * q^49 - 17 * q^50 + 18 * q^51 + 53 * q^52 - 41 * q^53 - 6 * q^54 + 67 * q^55 + 115 * q^56 + 84 * q^57 - 12 * q^58 - 7 * q^59 - 32 * q^60 - 21 * q^61 - 23 * q^62 - 21 * q^63 + 6 * q^64 - 72 * q^65 + 102 * q^66 - 15 * q^67 + 74 * q^68 + 48 * q^69 - 60 * q^70 - 8 * q^71 + 9 * q^72 - 25 * q^73 - 60 * q^74 + 68 * q^75 - 76 * q^76 - 36 * q^77 - 51 * q^78 + 2 * q^79 + 217 * q^80 + 20 * q^81 - 12 * q^82 - 41 * q^83 - 48 * q^84 - 7 * q^85 - 87 * q^86 - 54 * q^87 - 4 * q^88 + 77 * q^89 - 93 * q^90 + 79 * q^91 - 19 * q^92 + 72 * q^93 + 15 * q^94 + 57 * q^95 + 28 * q^96 + 13 * q^97 - 62 * q^98 - 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	−0.382111	+	0.277620i	−0.270193	+	0.196307i	−0.714629	−	0.699504i	$-0.753404\pi$
$2$	−0.382111	+	0.277620i	−0.270193	+	0.196307i	0.444435	+	0.895811i	$0.353404\pi$
$3$	0.549532	−	1.69129i	0.317273	−	0.976465i	−0.657536	−	0.753423i	$-0.728401\pi$
$3$	0.549532	−	1.69129i	0.317273	−	0.976465i	0.974809	−	0.223042i	$-0.0715987\pi$
$4$	−0.549098	+	1.68995i	−0.274549	+	0.844975i
$5$	−0.894807	+	2.04922i	−0.400170	+	0.916441i
$5$	−0.894807	+	2.04922i	−0.400170	+	0.916441i
$6$	0.259553	+	0.798821i	0.105962	+	0.326117i
$7$	1.24434			0.470317			0.235159	−	0.971957i	$-0.424439\pi$
$7$	1.24434			0.470317			0.235159	+	0.971957i	$0.424439\pi$
$8$	−0.551255	−	1.69659i	−0.194898	−	0.599834i
$9$	−0.131414	−	0.0954780i	−0.0438048	−	0.0318260i
$10$	−0.226990	−	1.03145i	−0.0717806	−	0.326173i
$11$	−4.29839	+	3.12296i	−1.29601	+	0.941609i	−0.999908	−	0.0135458i	$-0.995688\pi$
$11$	−4.29839	+	3.12296i	−1.29601	+	0.941609i	−0.296106	+	0.955155i	$0.595688\pi$
$12$	2.55644	+	1.85736i	0.737981	+	0.536175i
$13$	−1.66410	−	1.20904i	−0.461537	−	0.335326i	0.332597	−	0.943069i	$-0.392075\pi$
$13$	−1.66410	−	1.20904i	−0.461537	−	0.335326i	−0.794134	+	0.607743i	$0.792075\pi$
$14$	−0.475477	+	0.345454i	−0.127077	+	0.0923266i
$15$	2.97410	+	2.63949i	0.767910	+	0.681513i
$16$	−2.19347	−	1.59365i	−0.548367	−	0.398412i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$18$	0.0767215			0.0180834
$19$	2.60229	+	8.00904i	0.597007	+	1.83740i	0.544470	+	0.838781i	$0.316731\pi$
$19$	2.60229	+	8.00904i	0.597007	+	1.83740i	0.0525377	+	0.998619i	$0.483269\pi$
$20$	−2.97175	−	2.63740i	−0.664503	−	0.589741i
$21$	0.683806	−	2.10454i	0.149219	−	0.459248i
$22$	0.775466	−	2.38664i	0.165330	−	0.508833i
$23$	−4.93396	+	3.58473i	−1.02880	+	0.747468i	−0.968069	−	0.250686i	$-0.919344\pi$
$23$	−4.93396	+	3.58473i	−1.02880	+	0.747468i	−0.0607335	+	0.998154i	$0.519344\pi$
$24$	−3.17235			−0.647553
$25$	−3.39864	−	3.66732i	−0.679728	−	0.733464i
$26$	0.971522			0.190531
$27$	4.08239	−	2.96603i	0.785656	−	0.570812i
$28$	−0.683266	+	2.10288i	−0.129125	+	0.397406i
$29$	−0.901517	+	2.77458i	−0.167407	+	0.515227i	−0.999206	−	0.0398510i	$-0.987312\pi$
$29$	−0.901517	+	2.77458i	−0.167407	+	0.515227i	0.831798	+	0.555078i	$0.187312\pi$
$30$	−1.86921	−	0.182909i	−0.341270	−	0.0333944i
$31$	−0.466989	−	1.43725i	−0.0838737	−	0.258137i	0.900321	−	0.435227i	$-0.143332\pi$
$31$	−0.466989	−	1.43725i	−0.0838737	−	0.258137i	−0.984195	+	0.177090i	$0.943332\pi$
$32$	4.84837			0.857079
$33$	2.91972	+	8.98598i	0.508259	+	1.56426i
$34$	−0.382111	−	0.277620i	−0.0655315	−	0.0476115i
$35$	−1.11345	+	2.54994i	−0.188207	+	0.431018i
$36$	0.233512	−	0.169657i	0.0389187	−	0.0282761i
$37$	2.85583	+	2.07488i	0.469496	+	0.341109i	0.797245	−	0.603656i	$-0.206290\pi$
$37$	2.85583	+	2.07488i	0.469496	+	0.341109i	−0.327749	+	0.944765i	$0.606290\pi$
$38$	−3.21784	−	2.33789i	−0.522002	−	0.379257i
$39$	−2.95930	+	2.15006i	−0.473867	+	0.344285i
$40$	3.96995	+	0.388474i	0.627705	+	0.0614231i
$41$	7.04170	+	5.11610i	1.09973	+	0.799000i	0.981016	−	0.193929i	$-0.0621230\pi$
$41$	7.04170	+	5.11610i	1.09973	+	0.799000i	0.118713	+	0.992929i	$0.462123\pi$
$42$	0.322972	+	0.994007i	0.0498357	+	0.153379i
$43$	10.2220			1.55884			0.779422	−	0.626499i	$-0.215513\pi$
$43$	10.2220			1.55884			0.779422	+	0.626499i	$0.215513\pi$
$44$	−2.91741	−	8.97888i	−0.439817	−	1.35362i
$45$	0.313246	−	0.183863i	0.0466960	−	0.0274087i
$46$	0.890128	−	2.73953i	0.131242	−	0.403922i
$47$	−0.660455	+	2.03267i	−0.0963373	+	0.296496i	−0.987600	−	0.156992i	$-0.949820\pi$
$47$	−0.660455	+	2.03267i	−0.0963373	+	0.296496i	0.891263	+	0.453488i	$0.149820\pi$
$48$	−3.90069	+	2.83402i	−0.563017	+	0.409056i
$49$	−5.45161			−0.778802
$50$	2.31678	+	0.457793i	0.327642	+	0.0647418i
$51$	1.77832			0.249015
$52$	2.95696	−	2.14836i	0.410057	−	0.297924i
$53$	0.0480763	−	0.147964i	0.00660379	−	0.0203244i	−0.947700	−	0.319162i	$-0.896599\pi$
$53$	0.0480763	−	0.147964i	0.00660379	−	0.0203244i	0.954304	+	0.298837i	$0.0965987\pi$
$54$	−0.736497	+	2.26671i	−0.100225	+	0.308459i
$55$	−2.55342	−	11.6028i	−0.344304	−	1.56452i
$56$	−0.685949	−	2.11114i	−0.0916638	−	0.282112i
$57$	14.9756			1.98357
$58$	−0.425800	−	1.31048i	−0.0559103	−	0.172074i
$59$	−6.47362	−	4.70336i	−0.842794	−	0.612326i	0.0803558	−	0.996766i	$-0.474394\pi$
$59$	−6.47362	−	4.70336i	−0.842794	−	0.612326i	−0.923150	+	0.384441i	$0.874394\pi$
$60$	−6.09368	+	3.57674i	−0.786690	+	0.461755i
$61$	4.33169	−	3.14716i	0.554616	−	0.402952i	−0.274868	−	0.961482i	$-0.588634\pi$
$61$	4.33169	−	3.14716i	0.554616	−	0.402952i	0.829485	+	0.558530i	$0.188634\pi$
$62$	0.577450	+	0.419542i	0.0733362	+	0.0532819i
$63$	−0.163524	−	0.118807i	−0.0206021	−	0.0149683i
$64$	2.53432	−	1.84129i	0.316789	−	0.230161i
$65$	3.96663	−	2.32825i	0.492000	−	0.288784i
$66$	−3.61035	−	2.62307i	−0.444403	−	0.322878i
$67$	−1.53294	−	4.71789i	−0.187278	−	0.576382i	0.812702	−	0.582679i	$-0.197996\pi$
$67$	−1.53294	−	4.71789i	−0.187278	−	0.576382i	−0.999980	+	0.00629703i	$0.997996\pi$
$68$	−1.77692			−0.215483
$69$	3.35144	+	10.3147i	0.403466	+	1.24174i
$70$	−0.282453	−	1.28347i	−0.0337596	−	0.153405i
$71$	0.918858	−	2.82796i	0.109048	−	0.335617i	−0.881611	−	0.471977i	$-0.843541\pi$
$71$	0.918858	−	2.82796i	0.109048	−	0.335617i	0.990659	+	0.136360i	$0.0435405\pi$
$72$	−0.0895441	+	0.275588i	−0.0105529	+	0.0324784i
$73$	−12.0599	+	8.76206i	−1.41151	+	1.02552i	−0.418409	+	0.908259i	$0.637412\pi$
$73$	−12.0599	+	8.76206i	−1.41151	+	1.02552i	−0.993101	+	0.117263i	$0.962588\pi$
$74$	−1.66727			−0.193817
$75$	−8.07015	+	3.73277i	−0.931861	+	0.431023i
$76$	−14.9638			−1.71646
$77$	−5.34867	+	3.88604i	−0.609538	+	0.442855i
$78$	0.533883	−	1.64312i	0.0604503	−	0.186047i
$79$	5.12699	−	15.7793i	0.576832	−	1.77531i	−0.0530231	−	0.998593i	$-0.516886\pi$
$79$	5.12699	−	15.7793i	0.576832	−	1.77531i	0.629855	−	0.776713i	$-0.283114\pi$
$80$	5.22847	−	3.06890i	0.584561	−	0.343113i
$81$	−2.92359	−	8.99787i	−0.324843	−	0.999764i
$82$	−4.11104			−0.453989
$83$	−1.43437	−	4.41453i	−0.157442	−	0.484558i	0.840958	−	0.541101i	$-0.181992\pi$
$83$	−1.43437	−	4.41453i	−0.157442	−	0.484558i	−0.998400	+	0.0565427i	$0.981992\pi$
$84$	3.18109	+	2.31120i	0.347085	+	0.252172i
$85$	−2.22544	−	0.217767i	−0.241383	−	0.0236201i
$86$	−3.90595	+	2.83784i	−0.421190	+	0.306012i
$87$	4.19720	+	3.04945i	0.449988	+	0.326935i
$88$	7.66789	+	5.57105i	0.817400	+	0.593876i
$89$	−2.03508	+	1.47857i	−0.215718	+	0.156728i	−0.690397	−	0.723431i	$-0.742564\pi$
$89$	−2.03508	+	1.47857i	−0.215718	+	0.156728i	0.474679	+	0.880159i	$0.342564\pi$
$90$	−0.0686509	+	0.157220i	−0.00723644	+	0.0165724i
$91$	−2.07070	−	1.50445i	−0.217069	−	0.157710i
$92$	−3.34879	−	10.3065i	−0.349135	−	1.07453i
$93$	−2.68742			−0.278672
$94$	−0.311943	−	0.960063i	−0.0321745	−	0.0990229i
$95$	−18.7409	−	1.83386i	−1.92277	−	0.188150i
$96$	2.66434	−	8.19999i	0.271928	−	0.836908i
$97$	−2.24987	+	6.92439i	−0.228440	+	0.703065i	0.769484	+	0.638666i	$0.220513\pi$
$97$	−2.24987	+	6.92439i	−0.228440	+	0.703065i	−0.997924	+	0.0643997i	$0.979487\pi$
$98$	2.08312	−	1.51348i	0.210427	−	0.152884i
$99$	0.863045			0.0867392
$100$	8.06377	−	3.72981i	0.806377	−	0.372981i
$101$	15.4736			1.53968			0.769840	−	0.638237i	$-0.220336\pi$
$101$	15.4736			1.53968			0.769840	+	0.638237i	$0.220336\pi$
$102$	−0.679518	+	0.493699i	−0.0672823	+	0.0488834i
$103$	3.35431	−	10.3235i	0.330510	−	1.01720i	−0.638382	−	0.769719i	$-0.720396\pi$
$103$	3.35431	−	10.3235i	0.330510	−	1.01720i	0.968892	−	0.247484i	$-0.0796039\pi$
$104$	−1.13389	+	3.48977i	−0.111188	+	0.342200i
$105$	3.70080	+	3.28443i	0.361161	+	0.320528i
$106$	0.0227072	+	0.0698856i	0.00220552	+	0.00678789i
$107$	−4.51410			−0.436395			−0.218197	−	0.975905i	$-0.570018\pi$
$107$	−4.51410			−0.436395			−0.218197	+	0.975905i	$0.570018\pi$
$108$	2.77081	+	8.52767i	0.266621	+	0.820575i
$109$	12.0001	+	8.71856i	1.14940	+	0.835087i	0.988401	−	0.151868i	$-0.0485288\pi$
$109$	12.0001	+	8.71856i	1.14940	+	0.835087i	0.160998	+	0.986955i	$0.448529\pi$
$110$	4.19687	+	3.72469i	0.400156	+	0.355135i
$111$	5.07859	−	3.68982i	0.482039	−	0.350222i
$112$	−2.72942	−	1.98304i	−0.257906	−	0.187380i
$113$	8.86448	+	6.44042i	0.833900	+	0.605864i	0.920660	−	0.390365i	$-0.127651\pi$
$113$	8.86448	+	6.44042i	0.833900	+	0.605864i	−0.0867599	+	0.996229i	$0.527651\pi$
$114$	−5.72236	+	4.15754i	−0.535948	+	0.389389i
$115$	−2.93098	−	13.3184i	−0.273315	−	1.24195i
$116$	−4.19389	−	3.04704i	−0.389392	−	0.282910i
$117$	0.103249	+	0.317769i	0.00954541	+	0.0293778i
$118$	3.77939			0.347921
$119$	0.384523	+	1.18344i	0.0352492	+	0.108486i
$120$	2.83864	−	6.50085i	0.259131	−	0.593444i
$121$	5.32408	−	16.3858i	0.484007	−	1.48962i
$122$	−0.781474	+	2.40513i	−0.0707513	+	0.217750i
$123$	12.5224	−	9.09808i	1.12911	−	0.820346i
$124$	2.68529			0.241147
$125$	10.5563	−	3.68303i	0.944183	−	0.329421i
$126$	0.0954678			0.00850495
$127$	13.9657	−	10.1467i	1.23926	−	0.900374i	0.241710	−	0.970349i	$-0.422292\pi$
$127$	13.9657	−	10.1467i	1.23926	−	0.900374i	0.997549	+	0.0699746i	$0.0222918\pi$
$128$	−3.45367	+	10.6293i	−0.305264	+	0.939507i
$129$	5.61734	−	17.2884i	0.494579	−	1.52216i
$130$	−0.869325	+	1.99087i	−0.0762448	+	0.174611i
$131$	0.0654839	+	0.201539i	0.00572136	+	0.0176085i	0.953876	−	0.300199i	$-0.0970533\pi$
$131$	0.0654839	+	0.201539i	0.00572136	+	0.0176085i	−0.948155	+	0.317808i	$0.897053\pi$
$132$	−16.7891			−1.46130
$133$	3.23815	+	9.96599i	0.280783	+	0.864161i
$134$	1.89553	+	1.37719i	0.163749	+	0.118971i
$135$	2.42511	+	11.0197i	0.208720	+	0.948429i
$136$	1.44320	−	1.04855i	0.123754	−	0.0899123i
$137$	0.140028	+	0.101736i	0.0119634	+	0.00869192i	0.593751	−	0.804649i	$-0.297646\pi$
$137$	0.140028	+	0.101736i	0.0119634	+	0.00869192i	−0.581787	+	0.813341i	$0.697646\pi$
$138$	−4.14418	−	3.01093i	−0.352776	−	0.256307i
$139$	−7.02219	+	5.10192i	−0.595614	+	0.432739i	−0.844320	−	0.535840i	$-0.819995\pi$
$139$	−7.02219	+	5.10192i	−0.595614	+	0.432739i	0.248705	+	0.968579i	$0.419995\pi$
$140$	−3.69787	−	3.28183i	−0.312527	−	0.277365i
$141$	3.07489	+	2.23404i	0.258953	+	0.188140i
$142$	0.433991	+	1.33569i	0.0364197	+	0.112088i
$143$	10.9287			0.913905
$144$	0.136094	+	0.418856i	0.0113412	+	0.0349046i
$145$	−4.87906	−	4.33013i	−0.405184	−	0.359597i
$146$	2.17572	−	6.69617i	0.180064	−	0.554179i
$147$	−2.99584	+	9.22024i	−0.247093	+	0.760473i
$148$	−5.07458	+	3.68690i	−0.417128	+	0.303061i
$149$	−17.0648			−1.39800			−0.699002	−	0.715120i	$-0.746372\pi$
$149$	−17.0648			−1.39800			−0.699002	+	0.715120i	$0.746372\pi$
$150$	2.04741	−	3.66677i	0.167170	−	0.299390i
$151$	−3.26110			−0.265385			−0.132692	−	0.991157i	$-0.542362\pi$
$151$	−3.26110			−0.265385			−0.132692	+	0.991157i	$0.542362\pi$
$152$	12.1535	−	8.83004i	0.985779	−	0.716211i
$153$	0.0501958	−	0.154487i	0.00405809	−	0.0124895i
$154$	0.964946	−	2.96980i	0.0777575	−	0.239313i
$155$	3.36310	+	0.329091i	0.270131	+	0.0264332i
$156$	−2.00854	−	6.18166i	−0.160812	−	0.494929i
$157$	22.8047			1.82001			0.910005	−	0.414597i	$-0.136077\pi$
$157$	22.8047			1.82001			0.910005	+	0.414597i	$0.136077\pi$
$158$	2.42156	+	7.45279i	0.192649	+	0.592912i
$159$	−0.223830	−	0.162622i	−0.0177508	−	0.0128967i
$160$	−4.33836	+	9.93540i	−0.342977	+	0.785462i
$161$	−6.13954	+	4.46063i	−0.483863	+	0.351547i
$162$	3.61513	+	2.62654i	0.284031	+	0.206361i
$163$	15.9197	+	11.5664i	1.24693	+	0.905947i	0.998040	−	0.0625853i	$-0.0199346\pi$
$163$	15.9197	+	11.5664i	1.24693	+	0.905947i	0.248889	+	0.968532i	$0.419935\pi$
$164$	−12.5125	+	9.09088i	−0.977064	+	0.709879i
$165$	−21.0269	−	2.05755i	−1.63694	−	0.160180i
$166$	1.77365	+	1.28863i	0.137662	+	0.100017i
$167$	−2.80077	−	8.61988i	−0.216730	−	0.667026i	−0.999026	−	0.0441196i	$-0.985952\pi$
$167$	−2.80077	−	8.61988i	−0.216730	−	0.667026i	0.782296	−	0.622906i	$-0.214048\pi$
$168$	−3.94749			−0.304555
$169$	−2.70978	−	8.33983i	−0.208444	−	0.641526i
$170$	0.910822	−	0.534615i	0.0698568	−	0.0410031i
$171$	0.422709	−	1.30096i	0.0323253	−	0.0994872i
$172$	−5.61289	+	17.2747i	−0.427979	+	1.31718i
$173$	−8.06647	+	5.86063i	−0.613282	+	0.445575i	−0.850569	−	0.525864i	$-0.823742\pi$
$173$	−8.06647	+	5.86063i	−0.613282	+	0.445575i	0.237286	+	0.971440i	$0.423742\pi$
$174$	−2.45039			−0.185763
$175$	−4.22907	−	4.56340i	−0.319688	−	0.344961i
$176$	14.4053			1.08584
$177$	−11.5122	+	8.36410i	−0.865310	+	0.628685i
$178$	0.367146	−	1.12996i	0.0275187	−	0.0846939i
$179$	−2.61888	+	8.06009i	−0.195744	+	0.602439i	0.804223	+	0.594328i	$0.202582\pi$
$179$	−2.61888	+	8.06009i	−0.195744	+	0.602439i	−0.999967	+	0.00811131i	$0.997418\pi$
$180$	0.138716	+	0.630329i	0.0103393	+	0.0469820i
$181$	7.25494	+	22.3284i	0.539255	+	1.65966i	0.734271	+	0.678856i	$0.237524\pi$
$181$	7.25494	+	22.3284i	0.539255	+	1.65966i	−0.195016	+	0.980800i	$0.562476\pi$
$182$	1.20891			0.0896101
$183$	−2.94234	−	9.05560i	−0.217504	−	0.669409i
$184$	8.80168	+	6.39479i	0.648868	+	0.471430i
$185$	−6.80732	+	3.99562i	−0.500484	+	0.293764i
$186$	1.02689	−	0.746082i	0.0752955	−	0.0547054i
$187$	−4.29839	−	3.12296i	−0.314330	−	0.228374i
$188$	−3.07246	−	2.23227i	−0.224082	−	0.162805i
$189$	5.07989	−	3.69075i	0.369507	−	0.268463i
$190$	7.67021	−	4.50210i	0.556456	−	0.326617i
$191$	9.63633	+	7.00121i	0.697261	+	0.506589i	0.879039	−	0.476750i	$-0.158185\pi$
$191$	9.63633	+	7.00121i	0.697261	+	0.506589i	−0.181778	+	0.983340i	$0.558185\pi$
$192$	−1.72146	−	5.29810i	−0.124236	−	0.382358i
$193$	0.0806840			0.00580776			0.00290388	−	0.999996i	$-0.499076\pi$
$193$	0.0806840			0.00580776			0.00290388	+	0.999996i	$0.499076\pi$
$194$	−1.06265	−	3.27050i	−0.0762937	−	0.234808i
$195$	−1.75795	−	7.98816i	−0.125889	−	0.572044i
$196$	2.99347	−	9.21295i	0.213819	−	0.658068i
$197$	−2.73878	+	8.42911i	−0.195130	+	0.600549i	0.804845	+	0.593485i	$0.202249\pi$
$197$	−2.73878	+	8.42911i	−0.195130	+	0.600549i	−0.999975	+	0.00706385i	$0.997751\pi$
$198$	−0.329779	+	0.239599i	−0.0234364	+	0.0170275i
$199$	1.58796			0.112568			0.0562839	−	0.998415i	$-0.482075\pi$
$199$	1.58796			0.112568			0.0562839	+	0.998415i	$0.482075\pi$
$200$	−4.34841	+	7.78772i	−0.307479	+	0.550675i
$201$	−8.82171			−0.622235
$202$	−5.91264	+	4.29578i	−0.416012	+	0.302250i
$203$	−1.12180	+	3.45253i	−0.0787346	+	0.242320i
$204$	−0.976474	+	3.00528i	−0.0683669	+	0.210412i
$205$	−16.7850	+	9.85211i	−1.17231	+	0.688101i
$206$	1.58429	+	4.87595i	0.110383	+	0.339723i
$207$	0.990656			0.0688554
$208$	1.72336	+	5.30396i	0.119494	+	0.367763i
$209$	−36.1976	−	26.2991i	−2.50384	−	1.81915i
$210$	−2.32594	−	0.227601i	−0.160505	−	0.0157060i
$211$	−7.65432	+	5.56119i	−0.526945	+	0.382848i	−0.819214	−	0.573488i	$-0.805590\pi$
$211$	−7.65432	+	5.56119i	−0.526945	+	0.382848i	0.292269	+	0.956336i	$0.405590\pi$
$212$	0.223653	+	0.162493i	0.0153605	+	0.0111601i
$213$	−4.27794	−	3.10811i	−0.293120	−	0.212964i
$214$	1.72489	−	1.25321i	0.117911	−	0.0856674i
$215$	−9.14674	+	20.9472i	−0.623803	+	1.42859i
$216$	−7.28256	−	5.29109i	−0.495515	−	0.360013i
$217$	−0.581095	−	1.78843i	−0.0394473	−	0.121406i
$218$	−7.00581			−0.474493
$219$	8.19183	+	25.2119i	0.553553	+	1.70366i
$220$	21.0103	+	2.05593i	1.41651	+	0.138610i
$221$	0.635628	−	1.95626i	0.0427570	−	0.131592i
$222$	−0.916222	+	2.81984i	−0.0614928	+	0.189255i
$223$	8.38488	−	6.09197i	0.561493	−	0.407949i	−0.270512	−	0.962717i	$-0.587193\pi$
$223$	8.38488	−	6.09197i	0.561493	−	0.407949i	0.832005	+	0.554768i	$0.187193\pi$
$224$	6.03303			0.403099
$225$	0.0964813	+	0.806434i	0.00643209	+	0.0537623i
$226$	−5.17521			−0.344250
$227$	−10.4120	+	7.56473i	−0.691066	+	0.502089i	−0.877010	−	0.480471i	$-0.840466\pi$
$227$	−10.4120	+	7.56473i	−0.691066	+	0.502089i	0.185944	+	0.982560i	$0.440466\pi$
$228$	−8.22308	+	25.3081i	−0.544587	+	1.67607i
$229$	−3.44066	+	10.5893i	−0.227365	+	0.699757i	0.770678	+	0.637225i	$0.219918\pi$
$229$	−3.44066	+	10.5893i	−0.227365	+	0.699757i	−0.998043	+	0.0625326i	$0.980082\pi$
$230$	4.81743	+	4.27543i	0.317652	+	0.281913i
$231$	3.63314	+	11.1816i	0.239043	+	0.735698i
$232$	5.20429			0.341678
$233$	−0.0161234	−	0.0496227i	−0.00105628	−	0.00325089i	0.950527	−	0.310642i	$-0.100544\pi$
$233$	−0.0161234	−	0.0496227i	−0.00105628	−	0.00325089i	−0.951583	+	0.307391i	$0.900544\pi$
$234$	−0.127672	−	0.0927590i	−0.00834617	−	0.00606385i
$235$	−3.57442	−	3.17227i	−0.233170	−	0.206936i
$236$	11.5031	−	8.35749i	0.748788	−	0.544026i
$237$	−23.8698	−	17.3424i	−1.55051	−	1.12651i
$238$	−0.475477	−	0.345454i	−0.0308206	−	0.0223925i
$239$	4.69973	−	3.41455i	0.304000	−	0.220869i	−0.425318	−	0.905044i	$-0.639838\pi$
$239$	4.69973	−	3.41455i	0.304000	−	0.220869i	0.729318	+	0.684175i	$0.239838\pi$
$240$	−2.31718	−	10.5293i	−0.149573	−	0.679663i
$241$	4.10854	+	2.98503i	0.264654	+	0.192283i	0.712196	−	0.701980i	$-0.247701\pi$
$241$	4.10854	+	2.98503i	0.264654	+	0.192283i	−0.447542	+	0.894263i	$0.647701\pi$
$242$	2.51465	+	7.73928i	0.161648	+	0.497500i
$243$	−1.68627			−0.108174
$244$	2.94002	+	9.04844i	0.188215	+	0.579267i
$245$	4.87814	−	11.1716i	0.311653	−	0.713726i
$246$	−2.25915	+	6.95296i	−0.144038	+	0.443304i
$247$	5.35275	−	16.4741i	0.340587	−	1.04822i
$248$	−2.18098	+	1.58458i	−0.138492	+	0.100621i
$249$	−8.25448			−0.523106
$250$	−3.01119	+	4.33797i	−0.190445	+	0.274357i
$251$	−8.66556			−0.546965			−0.273483	−	0.961877i	$-0.588176\pi$
$251$	−8.66556			−0.546965			−0.273483	+	0.961877i	$0.588176\pi$
$252$	0.290569	−	0.211111i	0.0183041	−	0.0132987i
$253$	10.0131	−	30.8172i	0.629519	−	1.93746i
$254$	−2.51954	+	7.75434i	−0.158090	+	0.486550i
$255$	−1.59126	+	3.64419i	−0.0996484	+	0.228208i
$256$	0.304823	+	0.938149i	0.0190514	+	0.0586343i
$257$	6.61856			0.412855			0.206427	−	0.978462i	$-0.433816\pi$
$257$	6.61856			0.412855			0.206427	+	0.978462i	$0.433816\pi$
$258$	2.65315	+	8.16557i	0.165178	+	0.508366i
$259$	3.55363	+	2.58187i	0.220812	+	0.160429i
$260$	1.75656	+	7.98184i	0.108937	+	0.495013i
$261$	0.383384	−	0.278545i	0.0237309	−	0.0172415i
$262$	−0.0809734	−	0.0588306i	−0.00500255	−	0.00363457i
$263$	−18.9250	−	13.7498i	−1.16697	−	0.847852i	−0.176325	−	0.984332i	$-0.556421\pi$
$263$	−18.9250	−	13.7498i	−1.16697	−	0.847852i	−0.990643	+	0.136480i	$0.956421\pi$
$264$	13.6360	−	9.90713i	0.839237	−	0.609742i
$265$	0.260192	+	0.230918i	0.0159835	+	0.0141852i
$266$	−4.00409	−	2.90914i	−0.245507	−	0.178371i
$267$	1.38235	+	4.25443i	0.0845983	+	0.260367i
$268$	8.81473			0.538445
$269$	5.76021	+	17.7281i	0.351206	+	1.08090i	0.958177	+	0.286177i	$0.0923845\pi$
$269$	5.76021	+	17.7281i	0.351206	+	1.08090i	−0.606971	+	0.794724i	$0.707615\pi$
$270$	−3.98596	−	3.53751i	−0.242578	−	0.215286i
$271$	5.84408	−	17.9862i	0.355003	−	1.09259i	−0.601005	−	0.799245i	$-0.705233\pi$
$271$	5.84408	−	17.9862i	0.355003	−	1.09259i	0.956008	−	0.293341i	$-0.0947670\pi$
$272$	0.837830	−	2.57857i	0.0508009	−	0.156349i
$273$	−3.68238	+	2.67541i	−0.222868	+	0.161923i
$274$	−0.0817503			−0.00493872
$275$	26.0616	+	5.14974i	1.57157	+	0.310541i
$276$	−19.2715			−1.16001
$277$	−2.17343	+	1.57909i	−0.130589	+	0.0948784i	−0.651162	−	0.758939i	$-0.725718\pi$
$277$	−2.17343	+	1.57909i	−0.130589	+	0.0948784i	0.520573	+	0.853817i	$0.325718\pi$
$278$	1.26686	−	3.89900i	0.0759814	−	0.233847i
$279$	−0.0758563	+	0.233462i	−0.00454140	+	0.0139770i
$280$	4.93998	+	0.483394i	0.295220	+	0.0288883i
$281$	6.42461	+	19.7729i	0.383260	+	1.17955i	0.937735	+	0.347353i	$0.112919\pi$
$281$	6.42461	+	19.7729i	0.383260	+	1.17955i	−0.554475	+	0.832201i	$0.687081\pi$
$282$	−1.79516			−0.106901
$283$	−1.62376	−	4.99741i	−0.0965223	−	0.297065i	0.891125	−	0.453758i	$-0.149917\pi$
$283$	−1.62376	−	4.99741i	−0.0965223	−	0.297065i	−0.987647	+	0.156693i	$0.949917\pi$
$284$	4.27456	+	3.10565i	0.253648	+	0.184286i
$285$	−13.4003	+	30.6884i	−0.793765	+	1.81783i
$286$	−4.17598	+	3.03403i	−0.246931	+	0.179406i
$287$	8.76229	+	6.36617i	0.517221	+	0.375783i
$288$	−0.637145	−	0.462913i	−0.0375441	−	0.0272774i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	3.06647	+	0.300065i	0.180070	+	0.0176204i
$291$	10.4748	+	7.61035i	0.614041	+	0.446127i
$292$	−8.18535	−	25.1919i	−0.479012	−	1.47425i
$293$	21.9532			1.28252			0.641259	−	0.767324i	$-0.278412\pi$
$293$	21.9532			1.28252			0.641259	+	0.767324i	$0.278412\pi$
$294$	−1.41498	−	4.35486i	−0.0825233	−	0.253981i
$295$	15.4309	−	9.05731i	0.898421	−	0.527337i
$296$	1.94593	−	5.98896i	0.113105	−	0.348101i
$297$	−8.28490	+	25.4983i	−0.480739	+	1.47956i
$298$	6.52066	−	4.73754i	0.377732	−	0.274438i
$299$	12.5447			0.725476
$300$	−1.87688	−	15.6878i	−0.108362	−	0.905736i
$301$	12.7197			0.733152
$302$	1.24610	−	0.905347i	0.0717052	−	0.0520969i
$303$	8.50324	−	26.1703i	0.488499	−	1.50344i
$304$	7.05553	−	21.7147i	0.404663	−	1.24542i
$305$	2.57321	+	11.6927i	0.147341	+	0.669522i
$306$	0.0237082	+	0.0729665i	0.00135531	+	0.00417122i
$307$	6.60221			0.376808			0.188404	−	0.982092i	$-0.439669\pi$
$307$	6.60221			0.376808			0.188404	+	0.982092i	$0.439669\pi$
$308$	−3.63026	−	11.1728i	−0.206853	−	0.636629i
$309$	−15.6167	−	11.3462i	−0.888402	−	0.645462i
$310$	−1.37644	+	0.807916i	−0.0781766	+	0.0458865i
$311$	−14.0492	+	10.2074i	−0.796660	+	0.578807i	−0.909932	−	0.414757i	$-0.863867\pi$
$311$	−14.0492	+	10.2074i	−0.796660	+	0.578807i	0.113273	+	0.993564i	$0.463867\pi$
$312$	5.27909	+	3.83548i	0.298870	+	0.217141i
$313$	−12.8679	−	9.34907i	−0.727336	−	0.528441i	0.161383	−	0.986892i	$-0.448404\pi$
$313$	−12.8679	−	9.34907i	−0.727336	−	0.528441i	−0.888720	+	0.458451i	$0.848404\pi$
$314$	−8.71392	+	6.33103i	−0.491755	+	0.357281i
$315$	0.389786	−	0.228788i	0.0219619	−	0.0128908i
$316$	23.8509	+	17.3287i	1.34172	+	0.974817i
$317$	−1.82061	−	5.60325i	−0.102255	−	0.314710i	0.886821	−	0.462113i	$-0.152909\pi$
$317$	−1.82061	−	5.60325i	−0.102255	−	0.314710i	−0.989076	+	0.147403i	$0.952909\pi$
$318$	0.130675			0.00732789
$319$	−4.78985	−	14.7417i	−0.268180	−	0.825374i
$320$	1.50549	+	6.84098i	0.0841594	+	0.382422i
$321$	−2.48065	+	7.63464i	−0.138456	+	0.426124i
$322$	1.10762	−	3.40892i	0.0617255	−	0.189972i
$323$	−6.81290	+	4.94986i	−0.379080	+	0.275417i
$324$	16.8113			0.933960
$325$	1.22174	+	10.2118i	0.0677700	+	0.566452i
$326$	−9.29416			−0.514756
$327$	21.3400	−	15.5044i	1.18011	−	0.857397i
$328$	4.79813	−	14.7671i	0.264932	−	0.815378i
$329$	−0.821833	+	2.52934i	−0.0453091	+	0.139447i
$330$	8.60583	−	5.05127i	0.473735	−	0.278063i
$331$	6.73183	+	20.7184i	0.370015	+	1.13879i	0.946781	+	0.321879i	$0.104314\pi$
$331$	6.73183	+	20.7184i	0.370015	+	1.13879i	−0.576766	+	0.816909i	$0.695686\pi$
$332$	8.24795			0.452665
$333$	−0.177191	−	0.545338i	−0.00971002	−	0.0298844i
$334$	3.46326	+	2.51620i	0.189501	+	0.137680i
$335$	11.0397	+	1.08027i	0.603163	+	0.0590216i
$336$	−4.85380	+	3.52649i	−0.264796	+	0.192386i
$337$	0.0753389	+	0.0547369i	0.00410397	+	0.00298171i	0.589835	−	0.807524i	$-0.299193\pi$
$337$	0.0753389	+	0.0547369i	0.00410397	+	0.00298171i	−0.585731	+	0.810505i	$0.699193\pi$
$338$	3.35074	+	2.43446i	0.182256	+	0.132417i
$339$	15.7639	−	11.4532i	0.856179	−	0.622050i
$340$	1.59000	−	3.64130i	0.0862298	−	0.197477i
$341$	6.49577	+	4.71945i	0.351766	+	0.255573i
$342$	0.199652	+	0.614465i	0.0107959	+	0.0332265i
$343$	−15.4941			−0.836601
$344$	−5.63494	−	17.3426i	−0.303816	−	0.935048i
$345$	−24.1360	−	2.36179i	−1.29944	−	0.127154i
$346$	1.45526	−	4.47883i	0.0782352	−	0.240783i
$347$	9.99577	−	30.7638i	0.536601	−	1.65149i	−0.203564	−	0.979062i	$-0.565252\pi$
$347$	9.99577	−	30.7638i	0.536601	−	1.65149i	0.740164	−	0.672426i	$-0.234748\pi$
$348$	−7.45809	+	5.41862i	−0.399795	+	0.290468i
$349$	−3.65366			−0.195576			−0.0977880	−	0.995207i	$-0.531177\pi$
$349$	−3.65366			−0.195576			−0.0977880	+	0.995207i	$0.531177\pi$
$350$	2.88287	+	0.569652i	0.154096	+	0.0304492i
$351$	−10.3795			−0.554017
$352$	−20.8402	+	15.1413i	−1.11079	+	0.807034i
$353$	−5.80857	+	17.8769i	−0.309159	+	0.951494i	0.668933	+	0.743322i	$0.266751\pi$
$353$	−5.80857	+	17.8769i	−0.309159	+	0.951494i	−0.978092	+	0.208171i	$0.933249\pi$
$354$	2.07690	−	6.39204i	0.110386	−	0.339733i
$355$	4.97291	+	4.41342i	0.263935	+	0.234240i
$356$	−1.38125	−	4.25106i	−0.0732063	−	0.225306i
$357$	2.21284			0.117116
$358$	−1.23694	−	3.80691i	−0.0653742	−	0.201201i
$359$	16.8626	+	12.2514i	0.889973	+	0.646603i	0.935871	−	0.352343i	$-0.114615\pi$
$359$	16.8626	+	12.2514i	0.889973	+	0.646603i	−0.0458983	+	0.998946i	$0.514615\pi$
$360$	−0.484618	−	0.430094i	−0.0255416	−	0.0226680i
$361$	−42.0014	+	30.5158i	−2.21060	+	1.60610i
$362$	−8.97100	−	6.51782i	−0.471505	−	0.342569i
$363$	−24.7874	−	18.0091i	−1.30100	−	0.945232i
$364$	3.67947	−	2.67329i	0.192857	−	0.140119i
$365$	−7.16411	−	32.5539i	−0.374987	−	1.70395i
$366$	3.63832	+	2.64339i	0.190178	+	0.138172i
$367$	8.93144	+	27.4882i	0.466218	+	1.43487i	0.857445	+	0.514576i	$0.172051\pi$
$367$	8.93144	+	27.4882i	0.466218	+	1.43487i	−0.391227	+	0.920294i	$0.627949\pi$
$368$	16.5353			0.861961
$369$	−0.436905	−	1.34466i	−0.0227444	−	0.0700000i
$370$	1.49189	−	3.41662i	0.0775596	−	0.177622i
$371$	0.0598234	−	0.184118i	0.00310588	−	0.00955891i
$372$	1.47566	−	4.54160i	0.0765092	−	0.235471i
$373$	−7.72162	+	5.61008i	−0.399810	+	0.290479i	−0.769464	−	0.638691i	$-0.779476\pi$
$373$	−7.72162	+	5.61008i	−0.399810	+	0.290479i	0.369654	+	0.929170i	$0.379476\pi$
$374$	2.50946			0.129761
$375$	−0.428045	−	19.8777i	−0.0221042	−	1.02648i
$376$	3.81269			0.196624
$377$	4.85478	−	3.52721i	0.250034	−	0.181660i
$378$	−0.916455	+	2.82056i	−0.0471373	+	0.145074i
$379$	−7.16106	+	22.0395i	−0.367839	+	1.13209i	0.580345	+	0.814371i	$0.302918\pi$
$379$	−7.16106	+	22.0395i	−0.367839	+	1.13209i	−0.948184	+	0.317721i	$0.897082\pi$
$380$	13.3897	−	30.6642i	0.686877	−	1.57304i
$381$	−9.48636	−	29.1960i	−0.486001	−	1.49576i
$382$	−5.62583			−0.287842
$383$	−11.4015	−	35.0903i	−0.582590	−	1.79303i	−0.608739	−	0.793370i	$-0.708325\pi$
$383$	−11.4015	−	35.0903i	−0.582590	−	1.79303i	0.0261492	−	0.999658i	$-0.491675\pi$
$384$	16.0793	+	11.6823i	0.820543	+	0.596160i
$385$	−3.17733	−	14.4379i	−0.161932	−	0.735823i
$386$	−0.0308303	+	0.0223995i	−0.00156922	+	0.00114011i
$387$	−1.34332	−	0.975979i	−0.0682848	−	0.0496118i
$388$	−10.4665	−	7.60434i	−0.531355	−	0.386052i
$389$	0.635943	−	0.462040i	0.0322436	−	0.0234263i	−0.571547	−	0.820570i	$-0.693656\pi$
$389$	0.635943	−	0.462040i	0.0322436	−	0.0234263i	0.603790	+	0.797143i	$0.293656\pi$
$390$	2.88941	+	2.56432i	0.146311	+	0.129850i
$391$	−4.93396	−	3.58473i	−0.249521	−	0.181288i
$392$	3.00523	+	9.24913i	0.151787	+	0.467152i
$393$	0.376845			0.0190093
$394$	−1.29357	−	3.98120i	−0.0651691	−	0.200570i
$395$	27.7476	+	24.6258i	1.39613	+	1.23906i
$396$	−0.473896	+	1.45850i	−0.0238142	+	0.0732925i
$397$	7.18305	−	22.1071i	0.360507	−	1.10953i	−0.592240	−	0.805761i	$-0.701756\pi$
$397$	7.18305	−	22.1071i	0.360507	−	1.10953i	0.952747	−	0.303764i	$-0.0982436\pi$
$398$	−0.606779	+	0.440851i	−0.0304151	+	0.0220978i
$399$	18.6348			0.932907
$400$	1.61039	+	13.4604i	0.0805196	+	0.673019i
$401$	16.6629			0.832104			0.416052	−	0.909341i	$-0.363413\pi$
$401$	16.6629			0.832104			0.416052	+	0.909341i	$0.363413\pi$
$402$	3.37087	−	2.44908i	0.168124	−	0.122149i
$403$	−0.960566	+	2.95632i	−0.0478492	+	0.147265i
$404$	−8.49652	+	26.1496i	−0.422718	+	1.30099i
$405$	21.0547	+	2.06028i	1.04622	+	0.102376i
$406$	−0.529842	−	1.63068i	−0.0262956	−	0.0809295i
$407$	−18.7553			−0.929664
$408$	−0.980309	−	3.01708i	−0.0485325	−	0.149368i
$409$	−17.3603	−	12.6130i	−0.858414	−	0.623674i	0.0690392	−	0.997614i	$-0.478007\pi$
$409$	−17.3603	−	12.6130i	−0.858414	−	0.623674i	−0.927453	+	0.373940i	$0.878007\pi$
$410$	3.67859	−	8.42445i	0.181673	−	0.416054i
$411$	0.249015	−	0.180920i	0.0122830	−	0.00892413i
$412$	15.6043	+	11.3372i	0.768770	+	0.558544i
$413$	−8.05540	−	5.85259i	−0.396380	−	0.287987i
$414$	−0.378541	+	0.275026i	−0.0186043	+	0.0135168i
$415$	10.3299	+	1.01081i	0.507073	+	0.0496188i
$416$	−8.06815	−	5.86185i	−0.395574	−	0.287401i
$417$	4.76989	+	14.6802i	0.233582	+	0.718893i
$418$	21.1327			1.03363
$419$	−9.93279	−	30.5700i	−0.485249	−	1.49344i	−0.831620	−	0.555344i	$-0.812586\pi$
$419$	−9.93279	−	30.5700i	−0.485249	−	1.49344i	0.346372	−	0.938097i	$-0.387414\pi$
$420$	−7.58262	+	4.45069i	−0.369994	+	0.217171i
$421$	2.82722	−	8.70128i	0.137790	−	0.424074i	−0.858223	−	0.513276i	$-0.828432\pi$
$421$	2.82722	−	8.70128i	0.137790	−	0.424074i	0.996014	+	0.0892020i	$0.0284317\pi$
$422$	1.38090	−	4.24999i	0.0672214	−	0.206886i
$423$	0.280869	−	0.204063i	0.0136563	−	0.00992189i
$424$	−0.277536			−0.0134783
$425$	2.43759	−	4.36556i	0.118241	−	0.211761i
$426$	2.49752			0.121005
$427$	5.39011	−	3.91614i	0.260846	−	0.189515i
$428$	2.47868	−	7.62861i	0.119812	−	0.368743i
$429$	6.00568	−	18.4836i	0.289957	−	0.892396i
$430$	−2.32030	−	10.5435i	−0.111895	−	0.508452i
$431$	3.98496	+	12.2644i	0.191949	+	0.590757i	0.999999	+	0.00164321i	$0.000523052\pi$
$431$	3.98496	+	12.2644i	0.191949	+	0.590757i	−0.808050	+	0.589114i	$0.799477\pi$
$432$	−13.6814			−0.658246
$433$	−0.0317855	−	0.0978256i	−0.00152751	−	0.00470120i	0.950290	−	0.311367i	$-0.100787\pi$
$433$	−0.0317855	−	0.0978256i	−0.00152751	−	0.00470120i	−0.951817	+	0.306665i	$0.900787\pi$
$434$	0.718546	+	0.522054i	0.0344913	+	0.0250594i
$435$	−10.0047	+	5.87235i	−0.479688	+	0.281557i
$436$	−21.3231	+	15.4922i	−1.02119	+	0.741940i
$437$	−41.5499	−	30.1878i	−1.98760	−	1.44408i
$438$	−10.1295	−	7.35952i	−0.484007	−	0.351652i
$439$	−27.3989	+	19.9064i	−1.30768	+	0.950083i	−0.999999	−	0.00140767i	$-0.999552\pi$
$439$	−27.3989	+	19.9064i	−1.30768	+	0.950083i	−0.307678	+	0.951491i	$0.599552\pi$
$440$	−18.2776	+	10.7282i	−0.871351	+	0.511448i
$441$	0.716420	+	0.520509i	0.0341152	+	0.0247862i
$442$	0.300217	+	0.923973i	0.0142799	+	0.0439489i
$443$	−6.35171			−0.301779			−0.150889	−	0.988551i	$-0.548214\pi$
$443$	−6.35171			−0.301779			−0.150889	+	0.988551i	$0.548214\pi$
$444$	3.44696	+	10.6086i	0.163585	+	0.503464i
$445$	−1.20892	−	5.49337i	−0.0573084	−	0.260411i
$446$	−1.51270	+	4.65562i	−0.0716286	+	0.220450i
$447$	−9.37767	+	28.8615i	−0.443548	+	1.36510i
$448$	3.15356	−	2.29119i	0.148992	−	0.108249i
$449$	−2.76684			−0.130575			−0.0652877	−	0.997866i	$-0.520796\pi$
$449$	−2.76684			−0.130575			−0.0652877	+	0.997866i	$0.520796\pi$
$450$	−0.260749	−	0.281362i	−0.0122918	−	0.0132635i
$451$	−46.2454			−2.17761
$452$	−15.7515	+	11.4441i	−0.740886	+	0.538285i
$453$	−1.79208	+	5.51546i	−0.0841993	+	0.259139i
$454$	1.87841	−	5.78114i	0.0881580	−	0.271322i
$455$	4.93585	−	2.89714i	0.231396	−	0.135820i
$456$	−8.25538	−	25.4075i	−0.386594	−	1.18981i
$457$	−3.59643			−0.168234			−0.0841169	−	0.996456i	$-0.526807\pi$
$457$	−3.59643			−0.168234			−0.0841169	+	0.996456i	$0.526807\pi$
$458$	−1.62508	−	5.00147i	−0.0759348	−	0.233703i
$459$	4.08239	+	2.96603i	0.190549	+	0.138442i
$460$	24.1169	+	2.35992i	1.12446	+	0.110032i
$461$	8.79938	−	6.39312i	0.409828	−	0.297758i	−0.363704	−	0.931515i	$-0.618488\pi$
$461$	8.79938	−	6.39312i	0.409828	−	0.297758i	0.773532	+	0.633757i	$0.218488\pi$
$462$	−4.49251	−	3.26400i	−0.209011	−	0.151855i
$463$	11.5535	+	8.39409i	0.536935	+	0.390106i	0.822946	−	0.568120i	$-0.192329\pi$
$463$	11.5535	+	8.39409i	0.536935	+	0.390106i	−0.286010	+	0.958227i	$0.592329\pi$
$464$	6.39915	−	4.64926i	0.297073	−	0.215836i
$465$	2.40472	−	5.50713i	0.111516	−	0.255387i
$466$	0.0199372	+	0.0144852i	0.000923572	+	0.000671014i
$467$	0.862664	+	2.65501i	0.0399193	+	0.122859i	0.969030	−	0.246942i	$-0.0794258\pi$
$467$	0.862664	+	2.65501i	0.0399193	+	0.122859i	−0.929111	+	0.369801i	$0.879426\pi$
$468$	−0.593708			−0.0274442
$469$	−1.90750	−	5.87067i	−0.0880800	−	0.271082i
$470$	2.24651	+	0.219829i	0.103624	+	0.0101400i
$471$	12.5319	−	38.5692i	0.577440	−	1.77718i
$472$	−4.41105	+	13.5758i	−0.203035	+	0.624877i
$473$	−43.9383	+	31.9230i	−2.02028	+	1.46782i
$474$	13.9355			0.640080
$475$	20.5274	−	36.7633i	0.941864	−	1.68682i
$476$	−2.21109			−0.101345
$477$	−0.0204452	+	0.0148543i	−0.000936122	+	0.000680132i
$478$	−0.847871	+	2.60948i	−0.0387807	+	0.119355i
$479$	5.24966	−	16.1568i	0.239863	−	0.738222i	−0.756576	−	0.653906i	$-0.773129\pi$
$479$	5.24966	−	16.1568i	0.239863	−	0.738222i	0.996439	−	0.0843167i	$-0.0268707\pi$
$480$	14.4195	+	12.7972i	0.658159	+	0.584111i
$481$	−2.24377	−	6.90561i	−0.102307	−	0.314869i
$482$	−2.39862			−0.109254
$483$	4.17034	+	12.8350i	0.189757	+	0.584012i
$484$	24.7678	+	17.9949i	1.12581	+	0.817948i
$485$	−12.1764	−	10.8065i	−0.552903	−	0.490697i
$486$	0.644343	−	0.468143i	0.0292280	−	0.0212354i
$487$	1.50865	+	1.09610i	0.0683634	+	0.0496689i	0.621442	−	0.783460i	$-0.286547\pi$
$487$	1.50865	+	1.09610i	0.0683634	+	0.0496689i	−0.553079	+	0.833129i	$0.686547\pi$
$488$	−7.72729	−	5.61421i	−0.349798	−	0.254143i
$489$	28.3104	−	20.5687i	1.28024	−	0.930150i
$490$	1.23746	+	5.62306i	0.0559028	+	0.254024i
$491$	31.7042	+	23.0345i	1.43079	+	1.03953i	0.989869	+	0.141985i	$0.0453485\pi$
$491$	31.7042	+	23.0345i	1.43079	+	1.03953i	0.440922	+	0.897545i	$0.354651\pi$
$492$	8.49925	+	26.1580i	0.383176	+	1.17929i
$493$	−2.91737			−0.131392
$494$	2.52819	+	7.78096i	0.113749	+	0.350082i
$495$	−0.772258	+	1.76857i	−0.0347104	+	0.0794914i
$496$	−1.26614	+	3.89677i	−0.0568512	+	0.174970i
$497$	1.14337	−	3.51894i	0.0512874	−	0.157846i
$498$	3.15413	−	2.29161i	0.141340	−	0.102689i
$499$	8.22414			0.368163			0.184082	−	0.982911i	$-0.441069\pi$
$499$	8.22414			0.368163			0.184082	+	0.982911i	$0.441069\pi$
$500$	0.427707	+	19.8619i	0.0191276	+	0.888253i
$501$	−16.1178			−0.720090
$502$	3.31121	−	2.40573i	0.147786	−	0.107373i
$503$	13.1551	−	40.4872i	0.586556	−	1.80523i	−0.00637382	−	0.999980i	$-0.502029\pi$
$503$	13.1551	−	40.4872i	0.586556	−	1.80523i	0.592930	−	0.805254i	$-0.297971\pi$
$504$	−0.111424	+	0.342926i	−0.00496320	+	0.0152752i
$505$	−13.8459	+	31.7089i	−0.616134	+	1.41103i
$506$	4.72935	+	14.5554i	0.210245	+	0.647068i
$507$	−15.5942			−0.692561
$508$	9.47886	+	29.1729i	0.420556	+	1.29434i
$509$	8.37932	+	6.08793i	0.371407	+	0.269843i	0.757794	−	0.652494i	$-0.226277\pi$
$509$	8.37932	+	6.08793i	0.371407	+	0.269843i	−0.386387	+	0.922337i	$0.626277\pi$
$510$	−0.403662	−	1.83425i	−0.0178745	−	0.0812219i
$511$	−15.0067	+	10.9030i	−0.663857	+	0.482321i
$512$	−18.4606	−	13.4124i	−0.815850	−	0.592750i
$513$	34.3786	+	24.9775i	1.51785	+	1.10278i
$514$	−2.52903	+	1.83745i	−0.111551	+	0.0810463i
$515$	18.1537	+	16.1113i	0.799947	+	0.709947i
$516$	26.1320	+	18.9860i	1.15040	+	0.835813i
$517$	−3.50907	−	10.7998i	−0.154329	−	0.474975i
$518$	−2.07466			−0.0911554
$519$	5.47922	+	16.8633i	0.240511	+	0.740217i
$520$	−6.13670	−	5.44627i	−0.269112	−	0.238835i
$521$	1.30985	−	4.03129i	0.0573854	−	0.176614i	−0.918255	−	0.395989i	$-0.870402\pi$
$521$	1.30985	−	4.03129i	0.0573854	−	0.176614i	0.975641	+	0.219375i	$0.0704018\pi$
$522$	−0.0691657	+	0.212870i	−0.00302730	+	0.00931708i
$523$	4.39059	−	3.18995i	0.191987	−	0.139487i	−0.487639	−	0.873045i	$-0.662142\pi$
$523$	4.39059	−	3.18995i	0.191987	−	0.139487i	0.679626	+	0.733558i	$0.262142\pi$
$524$	−0.376547			−0.0164496
$525$	−10.0420	+	4.64484i	−0.438270	+	0.202717i
$526$	11.0487			0.481746
$527$	1.22259	−	0.888266i	0.0532570	−	0.0386935i
$528$	7.91617	−	24.3635i	0.344507	−	1.06028i
$529$	4.38627	−	13.4996i	0.190708	−	0.586938i
$530$	−0.163530	−	0.0160020i	−0.00710328	−	0.000695080i
$531$	0.401658	+	1.23618i	0.0174305	+	0.0536455i
$532$	−18.6201			−0.807283
$533$	−5.53252	−	17.0273i	−0.239640	−	0.737536i
$534$	−1.70932	−	1.24190i	−0.0739697	−	0.0537421i
$535$	4.03925	−	9.25041i	0.174632	−	0.399930i
$536$	−7.15927	+	5.20152i	−0.309234	+	0.224671i
$537$	12.1928	+	8.85856i	0.526157	+	0.382275i
$538$	−7.12272	−	5.17496i	−0.307082	−	0.223108i
$539$	23.4332	−	17.0252i	1.00934	−	0.733327i
$540$	−19.9544	−	1.95261i	−0.858702	−	0.0840269i
$541$	7.81892	+	5.68078i	0.336162	+	0.244236i	0.743041	−	0.669246i	$-0.233383\pi$
$541$	7.81892	+	5.68078i	0.336162	+	0.244236i	−0.406879	+	0.913482i	$0.633383\pi$
$542$	2.76025	+	8.49518i	0.118563	+	0.364899i
$543$	41.7505			1.79169
$544$	1.49823	+	4.61107i	0.0642360	+	0.197698i
$545$	−28.6040	+	16.7894i	−1.22526	+	0.719179i
$546$	0.664333	−	2.04461i	0.0284308	−	0.0875011i
$547$	6.93441	−	21.3419i	0.296494	−	0.912514i	−0.686222	−	0.727393i	$-0.740732\pi$
$547$	6.93441	−	21.3419i	0.296494	−	0.912514i	0.982716	−	0.185122i	$-0.0592680\pi$
$548$	−0.248818	+	0.180777i	−0.0106290	+	0.00772241i
$549$	−0.869730			−0.0371192
$550$	−11.3881	+	5.26745i	−0.485590	+	0.224605i
$551$	−24.5678			−1.04662
$552$	15.6522	−	11.3720i	0.666204	−	0.484025i
$553$	6.37974	−	19.6348i	0.271294	−	0.834957i
$554$	0.392106	−	1.20678i	0.0166590	−	0.0512710i
$555$	3.01690	+	13.7089i	0.128060	+	0.581908i
$556$	−4.76612	−	14.6686i	−0.202128	−	0.622087i
$557$	20.7504			0.879224			0.439612	−	0.898188i	$-0.355116\pi$
$557$	20.7504			0.879224			0.439612	+	0.898188i	$0.355116\pi$
$558$	−0.0358281	−	0.110268i	−0.00151672	−	0.00466800i
$559$	−17.0104	−	12.3588i	−0.719465	−	0.522722i
$560$	6.50601	−	3.81876i	0.274929	−	0.161372i
$561$	−7.64394	+	5.55364i	−0.322727	+	0.234475i
$562$	−7.94427	−	5.77185i	−0.335109	−	0.243471i
$563$	−27.4215	−	19.9229i	−1.15568	−	0.839651i	−0.166455	−	0.986049i	$-0.553232\pi$
$563$	−27.4215	−	19.9229i	−1.15568	−	0.839651i	−0.989226	+	0.146398i	$0.953232\pi$
$564$	−5.46383	+	3.96970i	−0.230069	+	0.167155i
$565$	−21.1299	+	12.4024i	−0.888940	+	0.521772i
$566$	2.00784	+	1.45878i	0.0843957	+	0.0613170i
$567$	−3.63794	−	11.1964i	−0.152779	−	0.470206i
$568$	−5.30440			−0.222568
$569$	−6.24642	−	19.2245i	−0.261864	−	0.805933i	−0.992399	−	0.123059i	$-0.960730\pi$
$569$	−6.24642	−	19.2245i	−0.261864	−	0.805933i	0.730536	−	0.682874i	$-0.239270\pi$
$570$	−3.39932	−	15.4466i	−0.142382	−	0.646986i
$571$	−9.74762	+	30.0001i	−0.407925	+	1.25546i	0.510503	+	0.859876i	$0.329459\pi$
$571$	−9.74762	+	30.0001i	−0.407925	+	1.25546i	−0.918428	+	0.395588i	$0.870541\pi$
$572$	−6.00093	+	18.4690i	−0.250912	+	0.772226i
$573$	17.1365	−	12.4504i	0.715889	−	0.520123i
$574$	−5.11555			−0.213519
$575$	29.9151	+	5.91120i	1.24755	+	0.246514i
$576$	−0.508848			−0.0212020
$577$	10.2243	−	7.42835i	0.425641	−	0.309246i	−0.354262	−	0.935146i	$-0.615268\pi$
$577$	10.2243	−	7.42835i	0.425641	−	0.309246i	0.779904	+	0.625900i	$0.215268\pi$
$578$	0.145954	−	0.449199i	0.00607087	−	0.0186842i
$579$	0.0443385	−	0.136460i	0.00184265	−	0.00567108i
$580$	9.99678	−	5.86770i	0.415094	−	0.243643i
$581$	−1.78485	−	5.49319i	−0.0740479	−	0.227896i
$582$	−6.11531			−0.253488
$583$	0.255435	+	0.786147i	0.0105790	+	0.0325589i
$584$	21.5137	+	15.6306i	0.890243	+	0.646800i
$585$	−0.743569	−	0.0727607i	−0.0307428	−	0.00300829i
$586$	−8.38856	+	6.09465i	−0.346528	+	0.251768i
$587$	29.8695	+	21.7015i	1.23285	+	0.895716i	0.997100	−	0.0760981i	$-0.0242462\pi$
$587$	29.8695	+	21.7015i	1.23285	+	0.895716i	0.235747	+	0.971814i	$0.424246\pi$
$588$	−13.9367	−	10.1256i	−0.574741	−	0.417574i
$589$	10.2957	−	7.48027i	0.424227	−	0.308219i
$590$	−3.38183	+	7.74482i	−0.139228	+	0.318849i
$591$	12.7510	+	9.26414i	0.524506	+	0.381076i
$592$	−2.95754	−	9.10237i	−0.121554	−	0.374105i
$593$	−13.2540			−0.544277			−0.272139	−	0.962258i	$-0.587731\pi$
$593$	−13.2540			−0.544277			−0.272139	+	0.962258i	$0.587731\pi$
$594$	−3.91309	−	12.0432i	−0.160556	−	0.494140i
$595$	−2.76921	−	0.270976i	−0.113526	−	0.0111090i
$596$	9.37025	−	28.8387i	0.383821	−	1.18128i
$597$	0.872637	−	2.68570i	0.0357147	−	0.109918i
$598$	−4.79345	+	3.48265i	−0.196019	+	0.142416i
$599$	14.8818			0.608056			0.304028	−	0.952663i	$-0.401668\pi$
$599$	14.8818			0.608056			0.304028	+	0.952663i	$0.401668\pi$
$600$	10.7817	+	11.6340i	0.440160	+	0.474957i
$601$	−35.0008			−1.42771			−0.713857	−	0.700292i	$-0.753053\pi$
$601$	−35.0008			−1.42771			−0.713857	+	0.700292i	$0.753053\pi$
$602$	−4.86034	+	3.53125i	−0.198093	+	0.143923i
$603$	−0.249005	+	0.766360i	−0.0101403	+	0.0312086i
$604$	1.79066	−	5.51110i	0.0728611	−	0.224243i
$605$	28.8142	+	25.5724i	1.17146	+	1.03967i
$606$	4.01621	+	12.3606i	0.163148	+	0.502117i
$607$	−34.9608			−1.41902			−0.709509	−	0.704697i	$-0.751083\pi$
$607$	−34.9608			−1.41902			−0.709509	+	0.704697i	$0.751083\pi$
$608$	12.6169	+	38.8308i	0.511682	+	1.57480i
$609$	5.22276	+	3.79456i	0.211637	+	0.153763i
$610$	−4.22938	−	3.75354i	−0.171243	−	0.151976i
$611$	3.55664	−	2.58405i	0.143886	−	0.104539i
$612$	0.233512	+	0.169657i	0.00943918	+	0.00685796i
$613$	21.4016	+	15.5492i	0.864404	+	0.628026i	0.929079	−	0.369880i	$-0.120601\pi$
$613$	21.4016	+	15.5492i	0.864404	+	0.628026i	−0.0646756	+	0.997906i	$0.520601\pi$
$614$	−2.52278	+	1.83291i	−0.101811	+	0.0739700i
$615$	7.43885	+	33.8023i	0.299963	+	1.36304i
$616$	9.54148	+	6.93229i	0.384437	+	0.279310i
$617$	−2.31793	−	7.13385i	−0.0933163	−	0.287198i	0.893495	−	0.449073i	$-0.148246\pi$
$617$	−2.31793	−	7.13385i	−0.0933163	−	0.287198i	−0.986811	+	0.161875i	$0.948246\pi$
$618$	9.11724			0.366749
$619$	−5.55383	−	17.0929i	−0.223227	−	0.687023i	−0.998467	−	0.0553557i	$-0.982371\pi$
$619$	−5.55383	−	17.0929i	−0.223227	−	0.687023i	0.775239	−	0.631668i	$-0.217629\pi$
$620$	−2.40282	+	5.50277i	−0.0964996	+	0.220997i
$621$	−9.50992	+	29.2685i	−0.381620	+	1.17451i
$622$	2.53460	−	7.80071i	0.101628	−	0.312780i
$623$	−2.53234	+	1.83985i	−0.101456	+	0.0737120i
$624$	9.91756			0.397020
$625$	−1.89848	+	24.9278i	−0.0759390	+	0.997112i
$626$	7.51246			0.300258
$627$	−64.3711	+	46.7684i	−2.57073	+	1.86775i
$628$	−12.5220	+	38.5387i	−0.499682	+	1.53786i
$629$	−1.09083	+	3.35723i	−0.0434943	+	0.133862i
$630$	−0.0854253	+	0.195635i	−0.00340342	+	0.00779428i
$631$	−14.2791	−	43.9466i	−0.568443	−	1.74949i	−0.657493	−	0.753460i	$-0.728383\pi$
$631$	−14.2791	−	43.9466i	−0.568443	−	1.74949i	0.0890504	−	0.996027i	$-0.471617\pi$
$632$	−29.5972			−1.17731
$633$	5.19927	+	16.0017i	0.206652	+	0.636011i
$634$	2.25125	+	1.63563i	0.0894085	+	0.0649591i
$635$	8.29623	+	37.6983i	0.329226	+	1.49601i
$636$	0.397727	−	0.288966i	0.0157709	−	0.0114582i
$637$	9.07200	+	6.59120i	0.359446	+	0.261153i
$638$	5.92284	+	4.30319i	0.234487	+	0.170365i
$639$	−0.390759	+	0.283903i	−0.0154582	+	0.0112310i
$640$	−18.6915	−	16.5885i	−0.738845	−	0.655719i
$641$	35.6682	+	25.9145i	1.40881	+	1.02356i	0.993494	+	0.113883i	$0.0363290\pi$
$641$	35.6682	+	25.9145i	1.40881	+	1.02356i	0.415316	+	0.909677i	$0.363671\pi$
$642$	−1.17165	−	3.60596i	−0.0462412	−	0.142316i
$643$	−18.4920			−0.729255			−0.364627	−	0.931154i	$-0.618804\pi$
$643$	−18.4920			−0.729255			−0.364627	+	0.931154i	$0.618804\pi$
$644$	−4.16704	−	12.8248i	−0.164204	−	0.505369i
$645$	30.4013	+	26.9809i	1.19705	+	1.06237i
$646$	1.22910	−	3.78279i	0.0483585	−	0.148832i
$647$	9.85527	−	30.3314i	0.387451	−	1.19245i	−0.547236	−	0.836978i	$-0.684320\pi$
$647$	9.85527	−	30.3314i	0.387451	−	1.19245i	0.934687	−	0.355473i	$-0.115680\pi$
$648$	−13.6540	+	9.92024i	−0.536381	+	0.389704i
$649$	42.5146			1.66884
$650$	−3.30186	−	3.56288i	−0.129509	−	0.139748i
$651$	−3.34407			−0.131064
$652$	−28.2880	+	20.5525i	−1.10784	+	0.804897i
$653$	3.96232	−	12.1948i	0.155058	−	0.477218i	−0.843109	−	0.537742i	$-0.819277\pi$
$653$	3.96232	−	12.1948i	0.155058	−	0.477218i	0.998167	+	0.0605244i	$0.0192773\pi$
$654$	−3.84992	+	11.8488i	−0.150544	+	0.463326i
$655$	−0.471594	−	0.0461470i	−0.0184267	−	0.00180311i
$656$	−7.29249	−	22.4440i	−0.284724	−	0.876290i
$657$	2.42143			0.0944691
$658$	−0.388164	−	1.19465i	−0.0151322	−	0.0465722i
$659$	−31.2002	−	22.6683i	−1.21539	−	0.883031i	−0.219679	−	0.975572i	$-0.570501\pi$
$659$	−31.2002	−	22.6683i	−1.21539	−	0.883031i	−0.995709	+	0.0925417i	$0.970501\pi$
$660$	15.0230	−	34.4046i	0.584769	−	1.33920i
$661$	22.1905	−	16.1223i	0.863110	−	0.627086i	−0.0656196	−	0.997845i	$-0.520902\pi$
$661$	22.1905	−	16.1223i	0.863110	−	0.627086i	0.928729	+	0.370759i	$0.120902\pi$
$662$	−8.32416	−	6.04786i	−0.323528	−	0.235057i
$663$	−2.95930	−	2.15006i	−0.114930	−	0.0835013i
$664$	−6.69894	+	4.86706i	−0.259969	+	0.188879i
$665$	−23.3201	−	2.28195i	−0.904313	−	0.0884901i
$666$	0.219104	+	0.159188i	0.00849009	+	0.00616842i
$667$	−5.49809	−	16.9214i	−0.212887	−	0.655199i
$668$	16.1051			0.623123
$669$	−5.69551	−	17.5290i	−0.220201	−	0.677709i
$670$	−4.51830	+	2.65206i	−0.174557	+	0.102458i
$671$	−8.79085	+	27.0554i	−0.339367	+	1.04446i
$672$	3.31535	−	10.2036i	0.127892	−	0.393612i
$673$	−13.7303	+	9.97567i	−0.529266	+	0.384534i	−0.820083	−	0.572245i	$-0.806073\pi$
$673$	−13.7303	+	9.97567i	−0.529266	+	0.384534i	0.290817	+	0.956779i	$0.406073\pi$
$674$	−0.0439839			−0.00169420
$675$	−24.7519	−	4.89096i	−0.952703	−	0.188253i
$676$	15.5818			0.599301
$677$	8.99947	−	6.53850i	0.345878	−	0.251295i	−0.401260	−	0.915964i	$-0.631428\pi$
$677$	8.99947	−	6.53850i	0.345878	−	0.251295i	0.747138	+	0.664669i	$0.231428\pi$
$678$	−2.84394	+	8.75276i	−0.109221	+	0.336148i
$679$	−2.79961	+	8.61631i	−0.107439	+	0.330664i
$680$	0.857323	+	3.89570i	0.0328768	+	0.149393i
$681$	7.07242	+	21.7667i	0.271016	+	0.834101i
$682$	−3.79232			−0.145215
$683$	11.7272	+	36.0925i	0.448727	+	1.38104i	0.878344	+	0.478029i	$0.158649\pi$
$683$	11.7272	+	36.0925i	0.448727	+	1.38104i	−0.429617	+	0.903011i	$0.641351\pi$
$684$	1.96645	+	1.42871i	0.0751893	+	0.0546282i
$685$	−0.333778	+	0.195914i	−0.0127530	+	0.00748550i
$686$	5.92046	−	4.30146i	0.226044	−	0.164231i
$687$	16.0187	+	11.6383i	0.611152	+	0.444028i
$688$	−22.4217	−	16.2903i	−0.854818	−	0.621062i
$689$	−0.258897	+	0.188100i	−0.00986320	+	0.00716603i
$690$	9.87830	−	5.79816i	0.376061	−	0.220732i
$691$	−14.0631	−	10.2174i	−0.534986	−	0.388690i	0.287234	−	0.957861i	$-0.407264\pi$
$691$	−14.0631	−	10.2174i	−0.534986	−	0.388690i	−0.822220	+	0.569171i	$0.807264\pi$
$692$	−5.47489	−	16.8500i	−0.208124	−	0.640540i
$693$	1.07392			0.0407950
$694$	4.72116	+	14.5302i	0.179213	+	0.551560i
$695$	−4.17147	−	18.9553i	−0.158233	−	0.719015i
$696$	2.85992	−	8.80194i	0.108405	−	0.333637i
$697$	−2.68969	+	8.27802i	−0.101879	+	0.313552i
$698$	1.39611	−	1.01433i	0.0528434	−	0.0383930i
$699$	−0.0927865			−0.00350951
$700$	10.0341	−	4.64117i	0.379253	−	0.175420i
$701$	13.2969			0.502217			0.251109	−	0.967959i	$-0.419205\pi$
$701$	13.2969			0.502217			0.251109	+	0.967959i	$0.419205\pi$
$702$	3.96613	−	2.88156i	0.149692	−	0.108758i
$703$	−9.18611	+	28.2719i	−0.346461	+	1.06630i
$704$	−5.14321	+	15.8292i	−0.193842	+	0.596584i
$705$	−7.32948	+	4.30211i	−0.276044	+	0.162027i
$706$	−2.74348	−	8.44356i	−0.103252	−	0.317778i
$707$	19.2545			0.724138
$708$	−7.81359	−	24.0477i	−0.293653	−	0.903770i
$709$	−31.2014	−	22.6691i	−1.17179	−	0.851358i	−0.180571	−	0.983562i	$-0.557794\pi$
$709$	−31.2014	−	22.6691i	−1.17179	−	0.851358i	−0.991222	+	0.132205i	$0.957794\pi$
$710$	−3.12546	−	0.305837i	−0.117296	−	0.0114779i
$711$	−2.18033	+	1.58410i	−0.0817689	+	0.0594086i
$712$	3.63037	+	2.63762i	0.136054	+	0.0988490i
$713$	7.45625	+	5.41728i	0.279239	+	0.202879i
$714$	−0.845553	+	0.614330i	−0.0316440	+	0.0229907i
$715$	−9.77909	+	22.3954i	−0.365717	+	0.837540i
$716$	−12.1831	−	8.85156i	−0.455305	−	0.330798i
$717$	−3.19234	−	9.82500i	−0.119220	−	0.366921i
$718$	−9.84461			−0.367397
$719$	−7.35958	−	22.6504i	−0.274466	−	0.844719i	−0.989360	−	0.145487i	$-0.953525\pi$
$719$	−7.35958	−	22.6504i	−0.274466	−	0.844719i	0.714894	−	0.699233i	$-0.246475\pi$
$720$	−0.980108	−	0.0959069i	−0.0365265	−	0.00357424i
$721$	4.17390	−	12.8460i	0.155444	−	0.478408i
$722$	7.57742	−	23.3209i	0.282002	−	0.867914i
$723$	7.30632	−	5.30835i	0.271725	−	0.197420i
$724$	−41.7175			−1.55042
$725$	13.2392	−	6.12366i	0.491692	−	0.227427i
$726$	14.4712			0.537078
$727$	−37.7483	+	27.4257i	−1.40001	+	1.01716i	−0.405324	+	0.914173i	$0.632841\pi$
$727$	−37.7483	+	27.4257i	−1.40001	+	1.01716i	−0.994682	+	0.102991i	$0.967159\pi$
$728$	−1.41095	+	4.34247i	−0.0522934	+	0.160943i
$729$	7.84410	−	24.1417i	0.290522	−	0.894135i
$730$	11.7751	+	10.4503i	0.435816	+	0.386783i
$731$	3.15878	+	9.72173i	0.116832	+	0.359571i
$732$	16.9191			0.625349
$733$	4.29744	+	13.2262i	0.158730	+	0.488519i	0.998520	−	0.0543919i	$-0.0173220\pi$
$733$	4.29744	+	13.2262i	0.158730	+	0.488519i	−0.839790	+	0.542911i	$0.817322\pi$
$734$	−11.0441	−	8.02399i	−0.407644	−	0.296171i
$735$	−16.2136	−	14.3895i	−0.598049	−	0.530764i
$736$	−23.9217	+	17.3801i	−0.881765	+	0.640639i
$737$	21.3230	+	15.4920i	0.785442	+	0.570657i
$738$	0.540250	+	0.392514i	0.0198869	+	0.0144487i
$739$	−5.62511	+	4.08688i	−0.206923	+	0.150338i	−0.686420	−	0.727205i	$-0.740819\pi$
$739$	−5.62511	+	4.08688i	−0.206923	+	0.150338i	0.479497	+	0.877543i	$0.340819\pi$
$740$	−3.01451	−	13.6980i	−0.110816	−	0.503549i
$741$	−24.9209	−	18.1061i	−0.915491	−	0.665143i
$742$	0.0282555	+	0.0869616i	0.00103729	+	0.00319246i
$743$	−9.32809			−0.342215			−0.171107	−	0.985252i	$-0.554734\pi$
$743$	−9.32809			−0.342215			−0.171107	+	0.985252i	$0.554734\pi$
$744$	1.48145	+	4.55944i	0.0543127	+	0.167157i
$745$	15.2697	−	34.9696i	0.559439	−	1.28119i
$746$	1.39304	−	4.28735i	0.0510030	−	0.156971i
$747$	−0.232995	+	0.717083i	−0.00852482	+	0.0262367i
$748$	7.63789	−	5.54925i	0.279269	−	0.202901i
$749$	−5.61709			−0.205244
$750$	5.68200	+	7.47664i	0.207477	+	0.273008i
$751$	−11.4531			−0.417929			−0.208964	−	0.977923i	$-0.567009\pi$
$751$	−11.4531			−0.417929			−0.208964	+	0.977923i	$0.567009\pi$
$752$	4.68805	−	3.40607i	0.170956	−	0.124206i
$753$	−4.76200	+	14.6559i	−0.173537	+	0.534092i
$754$	−0.875844	+	2.69557i	−0.0318963	+	0.0981669i
$755$	2.91806	−	6.68273i	0.106199	−	0.243209i
$756$	3.44783	+	10.6113i	0.125396	+	0.385931i
$757$	−9.75270			−0.354468			−0.177234	−	0.984169i	$-0.556715\pi$
$757$	−9.75270			−0.354468			−0.177234	+	0.984169i	$0.556715\pi$
$758$	−3.38228	−	10.4096i	−0.122850	−	0.378093i
$759$	−46.6182	−	33.8701i	−1.69213	−	1.22941i
$760$	7.21969	+	32.8064i	0.261886	+	1.19001i
$761$	15.4372	−	11.2158i	0.559599	−	0.406572i	−0.271713	−	0.962378i	$-0.587590\pi$
$761$	15.4372	−	11.2158i	0.559599	−	0.406572i	0.831312	+	0.555806i	$0.187590\pi$
$762$	11.7302	+	8.52252i	0.424942	+	0.308738i
$763$	14.9322	+	10.8489i	0.540582	+	0.392756i
$764$	−17.1230	+	12.4406i	−0.619487	+	0.450084i
$765$	0.271662	+	0.241098i	0.00982198	+	0.00871692i
$766$	14.0984	+	10.2431i	0.509396	+	0.370098i
$767$	5.08619	+	15.6537i	0.183652	+	0.565222i
$768$	1.75419			0.0632989
$769$	4.00083	+	12.3133i	0.144274	+	0.444028i	0.996917	−	0.0784652i	$-0.0250019\pi$
$769$	4.00083	+	12.3133i	0.144274	+	0.444028i	−0.852643	+	0.522493i	$0.825002\pi$
$770$	5.22234	+	4.63479i	0.188200	+	0.167026i
$771$	3.63711	−	11.1939i	0.130987	−	0.403138i
$772$	−0.0443034	+	0.136352i	−0.00159452	+	0.00490741i
$773$	13.7674	−	10.0026i	0.495178	−	0.359768i	−0.311994	−	0.950084i	$-0.600997\pi$
$773$	13.7674	−	10.0026i	0.495178	−	0.359768i	0.807172	+	0.590316i	$0.200997\pi$
$774$	0.784249			0.0281893
$775$	−3.68371	+	6.59728i	−0.132323	+	0.236981i
$776$	12.9881			0.466245
$777$	6.31951	−	4.59139i	0.226711	−	0.164715i
$778$	−0.114730	+	0.353101i	−0.00411325	+	0.0126593i
$779$	−22.6504	+	69.7108i	−0.811536	+	2.49765i
$780$	14.4649	+	1.41544i	0.517925	+	0.0506808i
$781$	4.88199	+	15.0252i	0.174691	+	0.537645i
$782$	2.88052			0.103007
$783$	4.54915	+	14.0008i	0.162573	+	0.500349i
$784$	11.9579	+	8.68794i	0.427069	+	0.310284i
$785$	−20.4058	+	46.7319i	−0.728313	+	1.66793i
$786$	−0.143997	+	0.104620i	−0.00513620	+	0.00373167i
$787$	32.9836	+	23.9640i	1.17574	+	0.854223i	0.991684	−	0.128694i	$-0.0410784\pi$
$787$	32.9836	+	23.9640i	1.17574	+	0.854223i	0.184052	+	0.982916i	$0.441078\pi$
$788$	−12.7409	−	9.25681i	−0.453876	−	0.329760i
$789$	−33.6548	+	24.4517i	−1.19814	+	0.870503i
$790$	−17.4393	−	1.70649i	−0.620461	−	0.0607143i
$791$	11.0304	+	8.01409i	0.392198	+	0.284948i
$792$	−0.475757	−	1.46423i	−0.0169053	−	0.0520292i
$793$	−11.0134			−0.391096
$794$	3.39266	+	10.4415i	0.120401	+	0.370557i
$795$	0.533533	−	0.313162i	0.0189225	−	0.0111067i
$796$	−0.871947	+	2.68358i	−0.0309054	+	0.0951169i
$797$	8.75693	−	26.9511i	0.310186	−	0.954655i	−0.667504	−	0.744606i	$-0.732637\pi$
$797$	8.75693	−	26.9511i	0.310186	−	0.954655i	0.977691	−	0.210050i	$-0.0673625\pi$
$798$	−7.12057	+	5.17340i	−0.252065	+	0.183136i
$799$	−2.13728			−0.0756115
$800$	−16.4779	−	17.7805i	−0.582581	−	0.628637i
$801$	0.408610			0.0144375
$802$	−6.36707	+	4.62595i	−0.224829	+	0.163348i
$803$	24.4748	−	75.3256i	0.863696	−	2.65818i
$804$	4.84398	−	14.9082i	0.170834	−	0.525773i
$805$	−3.64714	−	16.5727i	−0.128545	−	0.584111i
$806$	−0.453690	−	1.39632i	−0.0159806	−	0.0491831i
$807$	33.1487			1.16689
$808$	−8.52989	−	26.2523i	−0.300081	−	0.923553i
$809$	−6.14194	−	4.46238i	−0.215939	−	0.156889i	0.474558	−	0.880224i	$-0.342608\pi$
$809$	−6.14194	−	4.46238i	−0.215939	−	0.156889i	−0.690497	+	0.723335i	$0.742608\pi$
$810$	−8.61722	+	5.05796i	−0.302778	+	0.177718i
$811$	17.3140	−	12.5793i	0.607976	−	0.441720i	−0.240725	−	0.970593i	$-0.577385\pi$
$811$	17.3140	−	12.5793i	0.607976	−	0.441720i	0.848701	+	0.528873i	$0.177385\pi$
$812$	−5.21863	−	3.79156i	−0.183138	−	0.133058i
$813$	−27.2084	−	19.7680i	−0.954239	−	0.693295i
$814$	7.16660	−	5.20684i	0.251189	−	0.182500i
$815$	−37.9471	+	22.2734i	−1.32923	+	0.780204i
$816$	−3.90069	−	2.83402i	−0.136552	−	0.0992106i
$817$	26.6007	+	81.8686i	0.930642	+	2.86422i
$818$	10.1352			0.354369
$819$	0.128478	+	0.395414i	0.00448937	+	0.0138169i
$820$	−7.43296	−	33.7756i	−0.259570	−	1.17949i
$821$	−0.702597	+	2.16237i	−0.0245208	+	0.0754672i	−0.962568	−	0.271040i	$-0.912632\pi$
$821$	−0.702597	+	2.16237i	−0.0245208	+	0.0754672i	0.938047	+	0.346507i	$0.112632\pi$
$822$	−0.0449244	+	0.138263i	−0.00156692	+	0.00482248i
$823$	−0.592567	+	0.430525i	−0.0206556	+	0.0150072i	−0.598065	−	0.801447i	$-0.704064\pi$
$823$	−0.592567	+	0.430525i	−0.0206556	+	0.0150072i	0.577410	+	0.816455i	$0.304064\pi$
$824$	−19.3638			−0.674569
$825$	23.0314	−	41.2477i	0.801850	−	1.43606i
$826$	4.70286			0.163633
$827$	37.7332	−	27.4148i	1.31211	−	0.953305i	0.312117	−	0.950044i	$-0.398962\pi$
$827$	37.7332	−	27.4148i	1.31211	−	0.953305i	0.999995	−	0.00326130i	$-0.00103811\pi$
$828$	−0.543967	+	1.67416i	−0.0189042	+	0.0581810i
$829$	2.09041	−	6.43363i	0.0726031	−	0.223449i	−0.908170	−	0.418602i	$-0.862520\pi$
$829$	2.09041	−	6.43363i	0.0726031	−	0.223449i	0.980773	+	0.195153i	$0.0625202\pi$
$830$	−4.22778	+	2.48153i	−0.146748	+	0.0861353i
$831$	1.47632	+	4.54366i	0.0512131	+	0.157618i
$832$	−6.44353			−0.223389
$833$	−1.68464	−	5.18479i	−0.0583693	−	0.179642i
$834$	−5.89815	−	4.28526i	−0.204236	−	0.148386i
$835$	20.1702	+	1.97372i	0.698019	+	0.0683035i
$836$	64.3202	−	46.7314i	2.22456	−	1.61624i
$837$	−6.16934	−	4.48229i	−0.213244	−	0.154931i
$838$	12.2823	+	8.92360i	0.424284	+	0.308261i
$839$	17.1559	−	12.4645i	0.592286	−	0.430321i	−0.250846	−	0.968027i	$-0.580709\pi$
$839$	17.1559	−	12.4645i	0.592286	−	0.430321i	0.843133	+	0.537706i	$0.180709\pi$
$840$	3.53224	−	8.08928i	0.121874	−	0.279107i
$841$	16.5759	+	12.0431i	0.571583	+	0.415279i
$842$	1.33534	+	4.10975i	0.0460188	+	0.141631i
$843$	36.9722			1.27339
$844$	−5.19516	−	15.9890i	−0.178825	−	0.550366i
$845$	19.5149	+	1.90960i	0.671333	+	0.0656923i
$846$	−0.0506711	+	0.155950i	−0.00174211	+	0.00536166i
$847$	6.62498	−	20.3896i	0.227637	−	0.700595i
$848$	−0.341256	+	0.247937i	−0.0117188	+	0.00851419i
$849$	−9.34436			−0.320697
$850$	0.280537	+	2.34486i	0.00962235	+	0.0804279i
$851$	−21.5285			−0.737986
$852$	7.60155	−	5.52285i	0.260425	−	0.189210i
$853$	−0.773101	+	2.37936i	−0.0264705	+	0.0814678i	−0.963419	−	0.268000i	$-0.913637\pi$
$853$	−0.773101	+	2.37936i	−0.0264705	+	0.0814678i	0.936949	+	0.349467i	$0.113637\pi$
$854$	−0.972421	+	2.99280i	−0.0332756	+	0.102412i
$855$	2.28772	+	2.03034i	0.0782385	+	0.0694360i
$856$	2.48842	+	7.65857i	0.0850524	+	0.261764i
$857$	4.76229			0.162677			0.0813383	−	0.996687i	$-0.474081\pi$
$857$	4.76229			0.162677			0.0813383	+	0.996687i	$0.474081\pi$
$858$	2.83658	+	8.73008i	0.0968391	+	0.298040i
$859$	25.8186	+	18.7583i	0.880918	+	0.640025i	0.933494	−	0.358592i	$-0.116743\pi$
$859$	25.8186	+	18.7583i	0.880918	+	0.640025i	−0.0525761	+	0.998617i	$0.516743\pi$
$860$	−30.3773	−	26.9596i	−1.03586	−	0.919315i
$861$	15.5822	−	11.3211i	0.531040	−	0.385823i
$862$	−4.92755	−	3.58008i	−0.167833	−	0.121938i
$863$	21.6089	+	15.6998i	0.735574	+	0.534426i	0.891322	−	0.453371i	$-0.149779\pi$
$863$	21.6089	+	15.6998i	0.735574	+	0.534426i	−0.155748	+	0.987797i	$0.549779\pi$
$864$	19.7929	−	14.3804i	0.673369	−	0.489231i
$865$	−4.79182	−	21.7741i	−0.162927	−	0.740343i
$866$	0.0393039	+	0.0285560i	0.00133560	+	0.000970372i
$867$	0.549532	+	1.69129i	0.0186631	+	0.0574391i
$868$	3.34143			0.113415
$869$	27.2403	+	83.8369i	0.924062	+	2.84397i
$870$	2.19262	−	5.02139i	0.0743369	−	0.170241i
$871$	−3.15315	+	9.70440i	−0.106840	+	0.328821i
$872$	8.17671	−	25.1653i	0.276898	−	0.852205i
$873$	0.956792	−	0.695150i	0.0323825	−	0.0235273i
$874$	24.2574			0.820519
$875$	13.1356	−	4.58296i	0.444066	−	0.154932i
$876$	−47.1049			−1.59153
$877$	−8.86161	+	6.43834i	−0.299235	+	0.217407i	−0.727264	−	0.686358i	$-0.759208\pi$
$877$	−8.86161	+	6.43834i	−0.299235	+	0.217407i	0.428028	+	0.903765i	$0.359208\pi$
$878$	4.94299	−	15.2130i	0.166818	−	0.513412i
$879$	12.0640	−	37.1291i	0.406908	−	1.25233i
$880$	−12.8899	+	29.5197i	−0.434520	+	0.995107i
$881$	0.884791	+	2.72311i	0.0298094	+	0.0917438i	0.964854	−	0.262785i	$-0.0846411\pi$
$881$	0.884791	+	2.72311i	0.0298094	+	0.0917438i	−0.935045	+	0.354529i	$0.884641\pi$
$882$	−0.418256			−0.0140834
$883$	−2.28126	−	7.02100i	−0.0767706	−	0.236276i	0.905305	−	0.424761i	$-0.139642\pi$
$883$	−2.28126	−	7.02100i	−0.0767706	−	0.236276i	−0.982076	+	0.188486i	$0.939642\pi$
$884$	2.95696	+	2.14836i	0.0994534	+	0.0722571i
$885$	−6.83873	−	31.0753i	−0.229881	−	1.04459i
$886$	2.42706	−	1.76336i	0.0815387	−	0.0592413i
$887$	−30.7487	−	22.3402i	−1.03244	−	0.750112i	−0.0636449	−	0.997973i	$-0.520272\pi$
$887$	−30.7487	−	22.3402i	−1.03244	−	0.750112i	−0.968796	+	0.247861i	$0.920272\pi$
$888$	−9.05969	−	6.58225i	−0.304023	−	0.220886i
$889$	17.3782	−	12.6260i	0.582845	−	0.423461i
$890$	1.98701	+	1.76346i	0.0666048	+	0.0591113i
$891$	40.6668	+	29.5461i	1.36239	+	0.989833i
$892$	5.69101	+	17.5151i	0.190549	+	0.586449i
$893$	−17.9985			−0.602295
$894$	−4.42922	−	13.6317i	−0.148135	−	0.455913i
$895$	−14.1735	−	12.5789i	−0.473769	−	0.420466i
$896$	−4.29755	+	13.2265i	−0.143571	+	0.441866i
$897$	6.89369	−	21.2166i	0.230174	−	0.708402i
$898$	1.05724	−	0.768131i	0.0352806	−	0.0256329i
$899$	4.40876			0.147040
$900$	−1.41581	−	0.279762i	−0.0471937	−	0.00932542i
$901$	0.155578			0.00518307
$902$	17.6709	−	12.8386i	0.588376	−	0.427480i
$903$	6.98989	−	21.5127i	0.232609	−	0.715897i
$904$	6.04015	−	18.5897i	0.200892	−	0.618283i
$905$	−52.2477	−	5.11261i	−1.73677	−	0.169949i
$906$	−0.846428	−	2.60504i	−0.0281207	−	0.0865465i
$907$	41.6513			1.38301			0.691505	−	0.722372i	$-0.256948\pi$
$907$	41.6513			1.38301			0.691505	+	0.722372i	$0.256948\pi$
$908$	−7.06683	−	21.7495i	−0.234521	−	0.721782i
$909$	−2.03345	−	1.47739i	−0.0674453	−	0.0490019i
$910$	−1.08174	+	2.47732i	−0.0358593	+	0.0821224i
$911$	5.52369	−	4.01320i	0.183008	−	0.132963i	−0.492509	−	0.870307i	$-0.663920\pi$
$911$	5.52369	−	4.01320i	0.183008	−	0.132963i	0.675518	+	0.737344i	$0.263920\pi$
$912$	−32.8485	−	23.8659i	−1.08772	−	0.790278i
$913$	19.9519	+	14.4959i	0.660312	+	0.479745i
$914$	1.37424	−	0.998440i	0.0454557	−	0.0330255i
$915$	21.1898	+	2.07349i	0.700512	+	0.0685475i
$916$	−16.0060	−	11.6291i	−0.528855	−	0.384235i
$917$	0.0814844	+	0.250783i	0.00269085	+	0.00828159i
$918$	−2.38335			−0.0786624
$919$	−0.455687	−	1.40246i	−0.0150317	−	0.0462629i	0.943259	−	0.332057i	$-0.107743\pi$
$919$	−0.455687	−	1.40246i	−0.0150317	−	0.0462629i	−0.958291	+	0.285794i	$0.907743\pi$
$920$	−20.9802	+	12.3145i	−0.691696	+	0.405997i
$921$	3.62813	−	11.1662i	0.119551	−	0.367940i
$922$	−1.58748	+	4.88577i	−0.0522810	+	0.160904i
$923$	−4.94817	+	3.59505i	−0.162871	+	0.118333i
$924$	−20.8914			−0.687275
$925$	−2.09669	−	17.5250i	−0.0689386	−	0.576220i
$926$	−6.74508			−0.221657
$927$	−1.42647	+	1.03639i	−0.0468514	+	0.0340396i
$928$	−4.37089	+	13.4522i	−0.143481	+	0.441590i
$929$	−16.5889	+	51.0555i	−0.544266	+	1.67508i	0.178464	+	0.983946i	$0.442887\pi$
$929$	−16.5889	+	51.0555i	−0.544266	+	1.67508i	−0.722730	+	0.691131i	$0.757113\pi$
$930$	0.610018	+	2.77193i	0.0200033	+	0.0908953i
$931$	−14.1867	−	43.6622i	−0.464950	−	1.43097i
$932$	0.0927131			0.00303692
$933$	9.54308	+	29.3706i	0.312426	+	0.961550i
$934$	−1.06672	−	0.775016i	−0.0349041	−	0.0253593i
$935$	10.2459	−	6.01392i	0.335076	−	0.196676i
$936$	0.482206	−	0.350343i	0.0157614	−	0.0114513i
$937$	−33.3492	−	24.2296i	−1.08947	−	0.791547i	−0.110161	−	0.993914i	$-0.535137\pi$
$937$	−33.3492	−	24.2296i	−1.08947	−	0.791547i	−0.979310	+	0.202367i	$0.935137\pi$
$938$	2.35869	+	1.71369i	0.0770140	+	0.0559540i
$939$	−22.8833	+	16.6257i	−0.746768	+	0.542559i
$940$	7.32369	−	4.29871i	0.238872	−	0.140208i
$941$	−21.8879	−	15.9025i	−0.713524	−	0.518405i	0.170785	−	0.985308i	$-0.445370\pi$
$941$	−21.8879	−	15.9025i	−0.713524	−	0.518405i	−0.884308	+	0.466903i	$0.845370\pi$
$942$	5.91901	+	18.2168i	0.192852	+	0.593537i
$943$	−53.0833			−1.72863
$944$	6.70418	+	20.6333i	0.218202	+	0.671558i
$945$	3.01766	+	13.7123i	0.0981646	+	0.446062i
$946$	7.92684	−	24.3963i	0.257724	−	0.793192i
$947$	−4.82515	+	14.8503i	−0.156796	+	0.482570i	−0.998338	−	0.0576218i	$-0.981648\pi$
$947$	−4.82515	+	14.8503i	−0.156796	+	0.482570i	0.841542	+	0.540192i	$0.181648\pi$
$948$	42.4147	−	30.8161i	1.37757	−	1.00086i
$949$	30.6626			0.995349
$950$	2.36246	+	19.7465i	0.0766484	+	0.640661i
$951$	−10.4772			−0.339746
$952$	1.79584	−	1.30475i	0.0582035	−	0.0422873i
$953$	6.93835	−	21.3541i	0.224755	−	0.691726i	−0.773561	−	0.633722i	$-0.781526\pi$
$953$	6.93835	−	21.3541i	0.224755	−	0.691726i	0.998316	−	0.0580040i	$-0.0184736\pi$
$954$	0.00368849	−	0.0113520i	0.000119419	−	0.000367535i
$955$	−22.9697	+	13.4823i	−0.743282	+	0.436276i
$956$	3.18981	+	9.81723i	0.103166	+	0.317512i
$957$	−27.5645			−0.891035
$958$	2.47950	+	7.63110i	0.0801089	+	0.246550i
$959$	0.174243	+	0.126595i	0.00562659	+	0.00408796i
$960$	12.3974	+	1.21313i	0.400124	+	0.0391535i
$961$	23.2319	−	16.8790i	0.749417	−	0.544483i
$962$	2.77450	+	2.01580i	0.0894536	+	0.0649918i
$963$	0.593217	+	0.430998i	0.0191162	+	0.0138887i
$964$	−7.30054	+	5.30415i	−0.235135	+	0.170835i
$965$	−0.0721966	+	0.165340i	−0.00232409	+	0.00532247i
$966$	−5.15678	−	3.74662i	−0.165917	−	0.120546i
$967$	−7.64708	−	23.5353i	−0.245914	−	0.756844i	−0.995485	−	0.0949206i	$-0.969740\pi$
$967$	−7.64708	−	23.5353i	−0.245914	−	0.756844i	0.749571	−	0.661924i	$-0.230260\pi$
$968$	−30.7349			−0.987858
$969$	4.62772	+	14.2427i	0.148664	+	0.457540i
$970$	7.65285	+	0.748857i	0.245718	+	0.0240444i
$971$	6.90669	−	21.2566i	0.221646	−	0.682157i	−0.776968	−	0.629540i	$-0.783244\pi$
$971$	6.90669	−	21.2566i	0.221646	−	0.682157i	0.998615	−	0.0526176i	$-0.0167565\pi$
$972$	0.925928	−	2.84971i	0.0296991	−	0.0914046i
$973$	−8.73801	+	6.34854i	−0.280128	+	0.203525i
$974$	−0.880771			−0.0282217
$975$	17.9426	+	3.54543i	0.574622	+	0.113545i
$976$	−14.5169			−0.464674
$977$	28.7629	−	20.8975i	0.920206	−	0.668569i	−0.0233692	−	0.999727i	$-0.507439\pi$
$977$	28.7629	−	20.8975i	0.920206	−	0.668569i	0.943575	+	0.331158i	$0.107439\pi$
$978$	−5.10744	+	15.7191i	−0.163318	+	0.502641i
$979$	4.13004	−	12.7110i	0.131997	−	0.406244i
$980$	16.2008	+	14.3781i	0.517516	+	0.459292i
$981$	−0.744549	−	2.29149i	−0.0237716	−	0.0731615i
$982$	−18.5094			−0.590658
$983$	−4.26376	−	13.1225i	−0.135993	−	0.418543i	0.859750	−	0.510715i	$-0.170619\pi$
$983$	−4.26376	−	13.1225i	−0.135993	−	0.418543i	−0.995743	+	0.0921715i	$0.970619\pi$
$984$	−22.3387	−	16.2300i	−0.712132	−	0.517395i
$985$	−14.8225	−	13.1548i	−0.472283	−	0.419147i
$986$	1.11476	−	0.809921i	0.0355012	−	0.0257931i
$987$	3.82622	+	2.77991i	0.121790	+	0.0884855i
$988$	24.9012	+	18.0918i	0.792212	+	0.575575i
$989$	−50.4351	+	36.6432i	−1.60374	+	1.16519i
$990$	−0.195903	−	0.890186i	−0.00622619	−	0.0282920i
$991$	16.1363	+	11.7237i	0.512587	+	0.372416i	0.813804	−	0.581140i	$-0.197393\pi$
$991$	16.1363	+	11.7237i	0.512587	+	0.372416i	−0.301217	+	0.953556i	$0.597393\pi$
$992$	−2.26414	−	6.96830i	−0.0718864	−	0.221244i
$993$	38.7402			1.22938
$994$	0.540033	+	1.66205i	0.0171288	+	0.0527171i
$995$	−1.42092	+	3.25409i	−0.0450462	+	0.103162i
$996$	4.53252	−	13.9496i	0.143618	−	0.442012i
$997$	−12.8450	+	39.5328i	−0.406805	+	1.25202i	0.512574	+	0.858643i	$0.328692\pi$
$997$	−12.8450	+	39.5328i	−0.406805	+	1.25202i	−0.919379	+	0.393373i	$0.871308\pi$
$998$	−3.14254	+	2.28319i	−0.0994753	+	0.0722730i
$999$	17.8128			0.563571

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.k.b.86.10	✓	76
25.16	even	5	inner	425.2.k.b.341.10	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.k.b.86.10	✓	76	1.1	even	1	trivial
425.2.k.b.341.10	yes	76	25.16	even	5	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.382111 + 0.277620i) q^{2} +(0.549532 - 1.69129i) q^{3} +(-0.549098 + 1.68995i) q^{4} +(-0.894807 + 2.04922i) q^{5} +(0.259553 + 0.798821i) q^{6} +1.24434 q^{7} +(-0.551255 - 1.69659i) q^{8} +(-0.131414 - 0.0954780i) q^{9} +(-0.226990 - 1.03145i) q^{10} +(-4.29839 + 3.12296i) q^{11} +(2.55644 + 1.85736i) q^{12} +(-1.66410 - 1.20904i) q^{13} +(-0.475477 + 0.345454i) q^{14} +(2.97410 + 2.63949i) q^{15} +(-2.19347 - 1.59365i) q^{16} +(0.309017 + 0.951057i) q^{17} +0.0767215 q^{18} +(2.60229 + 8.00904i) q^{19} +(-2.97175 - 2.63740i) q^{20} +(0.683806 - 2.10454i) q^{21} +(0.775466 - 2.38664i) q^{22} +(-4.93396 + 3.58473i) q^{23} -3.17235 q^{24} +(-3.39864 - 3.66732i) q^{25} +0.971522 q^{26} +(4.08239 - 2.96603i) q^{27} +(-0.683266 + 2.10288i) q^{28} +(-0.901517 + 2.77458i) q^{29} +(-1.86921 - 0.182909i) q^{30} +(-0.466989 - 1.43725i) q^{31} +4.84837 q^{32} +(2.91972 + 8.98598i) q^{33} +(-0.382111 - 0.277620i) q^{34} +(-1.11345 + 2.54994i) q^{35} +(0.233512 - 0.169657i) q^{36} +(2.85583 + 2.07488i) q^{37} +(-3.21784 - 2.33789i) q^{38} +(-2.95930 + 2.15006i) q^{39} +(3.96995 + 0.388474i) q^{40} +(7.04170 + 5.11610i) q^{41} +(0.322972 + 0.994007i) q^{42} +10.2220 q^{43} +(-2.91741 - 8.97888i) q^{44} +(0.313246 - 0.183863i) q^{45} +(0.890128 - 2.73953i) q^{46} +(-0.660455 + 2.03267i) q^{47} +(-3.90069 + 2.83402i) q^{48} -5.45161 q^{49} +(2.31678 + 0.457793i) q^{50} +1.77832 q^{51} +(2.95696 - 2.14836i) q^{52} +(0.0480763 - 0.147964i) q^{53} +(-0.736497 + 2.26671i) q^{54} +(-2.55342 - 11.6028i) q^{55} +(-0.685949 - 2.11114i) q^{56} +14.9756 q^{57} +(-0.425800 - 1.31048i) q^{58} +(-6.47362 - 4.70336i) q^{59} +(-6.09368 + 3.57674i) q^{60} +(4.33169 - 3.14716i) q^{61} +(0.577450 + 0.419542i) q^{62} +(-0.163524 - 0.118807i) q^{63} +(2.53432 - 1.84129i) q^{64} +(3.96663 - 2.32825i) q^{65} +(-3.61035 - 2.62307i) q^{66} +(-1.53294 - 4.71789i) q^{67} -1.77692 q^{68} +(3.35144 + 10.3147i) q^{69} +(-0.282453 - 1.28347i) q^{70} +(0.918858 - 2.82796i) q^{71} +(-0.0895441 + 0.275588i) q^{72} +(-12.0599 + 8.76206i) q^{73} -1.66727 q^{74} +(-8.07015 + 3.73277i) q^{75} -14.9638 q^{76} +(-5.34867 + 3.88604i) q^{77} +(0.533883 - 1.64312i) q^{78} +(5.12699 - 15.7793i) q^{79} +(5.22847 - 3.06890i) q^{80} +(-2.92359 - 8.99787i) q^{81} -4.11104 q^{82} +(-1.43437 - 4.41453i) q^{83} +(3.18109 + 2.31120i) q^{84} +(-2.22544 - 0.217767i) q^{85} +(-3.90595 + 2.83784i) q^{86} +(4.19720 + 3.04945i) q^{87} +(7.66789 + 5.57105i) q^{88} +(-2.03508 + 1.47857i) q^{89} +(-0.0686509 + 0.157220i) q^{90} +(-2.07070 - 1.50445i) q^{91} +(-3.34879 - 10.3065i) q^{92} -2.68742 q^{93} +(-0.311943 - 0.960063i) q^{94} +(-18.7409 - 1.83386i) q^{95} +(2.66434 - 8.19999i) q^{96} +(-2.24987 + 6.92439i) q^{97} +(2.08312 - 1.51348i) q^{98} +0.863045 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 6 q^{2} - 7 q^{3} - 26 q^{4} + 13 q^{5} + 12 q^{6} + 22 q^{7} + 10 q^{8} - 24 q^{9} - 6 q^{10} - 16 q^{11} - 15 q^{12} - q^{13} - 19 q^{14} - 3 q^{15} + 30 q^{16} - 19 q^{17} + 6 q^{18} + 18 q^{19}+ \cdots - 64 q^{99}+O(q^{100}) \) 76 * q - 6 * q^2 - 7 * q^3 - 26 * q^4 + 13 * q^5 + 12 * q^6 + 22 * q^7 + 10 * q^8 - 24 * q^9 - 6 * q^10 - 16 * q^11 - 15 * q^12 - q^13 - 19 * q^14 - 3 * q^15 + 30 * q^16 - 19 * q^17 + 6 * q^18 + 18 * q^19 - 23 * q^20 - 22 * q^21 - 15 * q^22 - 8 * q^23 - 22 * q^24 + 35 * q^25 - 14 * q^26 - 10 * q^27 - 29 * q^28 - 25 * q^29 + 57 * q^30 + 22 * q^31 + 54 * q^32 - 22 * q^33 - 6 * q^34 - 19 * q^35 - 91 * q^36 - 49 * q^37 + 15 * q^38 + 25 * q^39 - 2 * q^40 + 16 * q^41 - 28 * q^42 + 104 * q^43 + 18 * q^44 + 10 * q^45 - 55 * q^46 - 26 * q^47 - 86 * q^48 + 2 * q^49 - 17 * q^50 + 18 * q^51 + 53 * q^52 - 41 * q^53 - 6 * q^54 + 67 * q^55 + 115 * q^56 + 84 * q^57 - 12 * q^58 - 7 * q^59 - 32 * q^60 - 21 * q^61 - 23 * q^62 - 21 * q^63 + 6 * q^64 - 72 * q^65 + 102 * q^66 - 15 * q^67 + 74 * q^68 + 48 * q^69 - 60 * q^70 - 8 * q^71 + 9 * q^72 - 25 * q^73 - 60 * q^74 + 68 * q^75 - 76 * q^76 - 36 * q^77 - 51 * q^78 + 2 * q^79 + 217 * q^80 + 20 * q^81 - 12 * q^82 - 41 * q^83 - 48 * q^84 - 7 * q^85 - 87 * q^86 - 54 * q^87 - 4 * q^88 + 77 * q^89 - 93 * q^90 + 79 * q^91 - 19 * q^92 + 72 * q^93 + 15 * q^94 + 57 * q^95 + 28 * q^96 + 13 * q^97 - 62 * q^98 - 64 * q^99

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