LMFDB - Embedded newform 87.2.g.a.52.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [87,2,Mod(7,87)] 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("87.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(87, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([0, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 87 = 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	87.g (of order $7$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [18,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$0.694698497585$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} + 18 x^{16} - 37 x^{15} + 71 x^{14} - 83 x^{13} + 225 x^{12} - 237 x^{11} + 485 x^{10} + \cdots + 64 $ x^18 - 6x^17 + 18x^16 - 37x^15 + 71x^14 - 83x^13 + 225x^12 - 237x^11 + 485x^10 - 319x^9 + 1092x^8 - 1080x^7 + 1833x^6 - 4032x^5 + 6004x^4 - 4480x^3 + 3200x^2 - 576*x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			52.1
Root			$0.491931 + 2.15529i$ of defining polynomial
Character	$\chi$	$=$	87.52
Dual form			87.2.g.a.82.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.754870 + 0.946578i) q^{2} +(-0.222521 + 0.974928i) q^{3} +(0.118862 + 0.520769i) q^{4} +(1.12131 - 1.40607i) q^{5} +(-0.754870 - 0.946578i) q^{6} +(-0.951706 + 4.16970i) q^{7} +(-2.76431 - 1.33122i) q^{8} +(-0.900969 - 0.433884i) q^{9} +(0.484517 + 2.12281i) q^{10} +(-0.951656 + 0.458293i) q^{11} -0.534161 q^{12} +(4.75885 - 2.29174i) q^{13} +(-3.22853 - 4.04845i) q^{14} +(1.12131 + 1.40607i) q^{15} +(2.38428 - 1.14821i) q^{16} +5.61769 q^{17} +(1.09082 - 0.525311i) q^{18} +(-1.42675 - 6.25099i) q^{19} +(0.865520 + 0.416812i) q^{20} +(-3.85338 - 1.85569i) q^{21} +(0.284567 - 1.24677i) q^{22} +(1.27587 + 1.59988i) q^{23} +(1.91296 - 2.39878i) q^{24} +(0.392890 + 1.72136i) q^{25} +(-1.42300 + 6.23459i) q^{26} +(0.623490 - 0.781831i) q^{27} -2.28457 q^{28} +(-4.54927 - 2.88169i) q^{29} -2.17740 q^{30} +(2.38467 - 2.99028i) q^{31} +(0.652504 - 2.85881i) q^{32} +(-0.235040 - 1.02978i) q^{33} +(-4.24063 + 5.31758i) q^{34} +(4.79575 + 6.01368i) q^{35} +(0.118862 - 0.520769i) q^{36} +(0.315606 + 0.151988i) q^{37} +(6.99406 + 3.36816i) q^{38} +(1.17534 + 5.14950i) q^{39} +(-4.97144 + 2.39412i) q^{40} -3.62240 q^{41} +(4.66536 - 2.24672i) q^{42} +(1.09049 + 1.36743i) q^{43} +(-0.351781 - 0.441119i) q^{44} +(-1.62033 + 0.780312i) q^{45} -2.47753 q^{46} +(-6.28881 + 3.02853i) q^{47} +(0.588868 + 2.58000i) q^{48} +(-10.1739 - 4.89947i) q^{49} +(-1.92598 - 0.927505i) q^{50} +(-1.25005 + 5.47684i) q^{51} +(1.75911 + 2.20586i) q^{52} +(-4.87488 + 6.11290i) q^{53} +(0.269410 + 1.18036i) q^{54} +(-0.422703 + 1.85198i) q^{55} +(8.18161 - 10.2594i) q^{56} +6.41175 q^{57} +(6.16185 - 2.13093i) q^{58} +0.382668 q^{59} +(-0.598958 + 0.751070i) q^{60} +(1.21640 - 5.32939i) q^{61} +(1.03041 + 4.51454i) q^{62} +(2.66662 - 3.34384i) q^{63} +(5.51347 + 6.91367i) q^{64} +(2.11377 - 9.26104i) q^{65} +(1.15219 + 0.554864i) q^{66} +(-7.03806 - 3.38935i) q^{67} +(0.667730 + 2.92552i) q^{68} +(-1.84368 + 0.887869i) q^{69} -9.31258 q^{70} +(14.0654 - 6.77356i) q^{71} +(1.91296 + 2.39878i) q^{72} +(-1.58547 - 1.98811i) q^{73} +(-0.382110 + 0.184015i) q^{74} -1.76563 q^{75} +(3.08574 - 1.48601i) q^{76} +(-1.00525 - 4.40428i) q^{77} +(-5.76163 - 2.77465i) q^{78} +(-9.25113 - 4.45511i) q^{79} +(1.05904 - 4.63996i) q^{80} +(0.623490 + 0.781831i) q^{81} +(2.73445 - 3.42889i) q^{82} +(-0.338541 - 1.48324i) q^{83} +(0.508365 - 2.22729i) q^{84} +(6.29915 - 7.89888i) q^{85} -2.11755 q^{86} +(3.82175 - 3.79397i) q^{87} +3.24076 q^{88} +(-11.1881 + 14.0295i) q^{89} +(0.484517 - 2.12281i) q^{90} +(5.02684 + 22.0240i) q^{91} +(-0.681518 + 0.854597i) q^{92} +(2.38467 + 2.99028i) q^{93} +(1.88050 - 8.23899i) q^{94} +(-10.3892 - 5.00316i) q^{95} +(2.64194 + 1.27229i) q^{96} +(1.51530 + 6.63895i) q^{97} +(12.3177 - 5.93188i) q^{98} +1.05626 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 4 q^{2} - 3 q^{3} - 6 q^{4} - q^{5} - 4 q^{6} - 4 q^{7} - 15 q^{8} - 3 q^{9} - 14 q^{10} + 26 q^{11} + 22 q^{12} + 9 q^{13} - 10 q^{14} - q^{15} - 14 q^{16} + 4 q^{17} - 4 q^{18} - 10 q^{19} - q^{20}+ \cdots - 2 q^{99}+O(q^{100}) $ 18 * q - 4 * q^2 - 3 * q^3 - 6 * q^4 - q^5 - 4 * q^6 - 4 * q^7 - 15 * q^8 - 3 * q^9 - 14 * q^10 + 26 * q^11 + 22 * q^12 + 9 * q^13 - 10 * q^14 - q^15 - 14 * q^16 + 4 * q^17 - 4 * q^18 - 10 * q^19 - q^20 - 4 * q^21 - 8 * q^22 - 8 * q^23 - 8 * q^24 + 16 * q^25 + 5 * q^26 - 3 * q^27 + 80 * q^28 + 8 * q^29 - 12 * q^31 + 9 * q^32 - 16 * q^33 - 22 * q^34 + 9 * q^35 - 6 * q^36 - 16 * q^37 - 32 * q^38 + 2 * q^39 + 33 * q^40 + 24 * q^41 - 3 * q^42 - 31 * q^43 - 52 * q^44 + 6 * q^45 - 44 * q^46 + 5 * q^47 - 47 * q^49 - 7 * q^50 + 11 * q^51 + 80 * q^52 + 5 * q^53 + 3 * q^54 - 17 * q^55 + 45 * q^56 + 18 * q^57 + 54 * q^58 - 32 * q^59 + 27 * q^60 - 28 * q^61 + 69 * q^62 + 3 * q^63 - 75 * q^64 + 22 * q^65 + 34 * q^66 + 6 * q^67 + 38 * q^68 + 20 * q^69 - 12 * q^70 + 46 * q^71 - 8 * q^72 - q^73 - 35 * q^74 + 2 * q^75 - 45 * q^76 - 36 * q^77 - 51 * q^78 - 15 * q^79 - 86 * q^80 - 3 * q^81 + 47 * q^82 - 16 * q^83 - 25 * q^84 + 19 * q^85 + 116 * q^86 + 43 * q^87 + 54 * q^88 - 72 * q^89 - 14 * q^90 - 47 * q^91 - 121 * q^92 - 12 * q^93 - 22 * q^94 - 72 * q^95 - 12 * q^96 + 43 * q^97 + 31 * q^98 - 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$e\left(\frac{5}{7}\right)$	$1$

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 $

$2$	−0.754870	+	0.946578i	−0.533774	+	0.669331i	−0.973470	−	0.228815i	$-0.926515\pi$
$2$	−0.754870	+	0.946578i	−0.533774	+	0.669331i	0.439696	+	0.898147i	$0.355086\pi$
$3$	−0.222521	+	0.974928i	−0.128473	+	0.562875i
$3$	−0.222521	+	0.974928i	−0.128473	+	0.562875i
$4$	0.118862	+	0.520769i	0.0594310	+	0.260384i
$5$	1.12131	−	1.40607i	0.501463	−	0.628815i	−0.465095	−	0.885261i	$-0.653980\pi$
$5$	1.12131	−	1.40607i	0.501463	−	0.628815i	0.966559	+	0.256445i	$0.0825514\pi$
$6$	−0.754870	−	0.946578i	−0.308175	−	0.386439i
$7$	−0.951706	+	4.16970i	−0.359711	+	1.57600i	0.394202	+	0.919024i	$0.371021\pi$
$7$	−0.951706	+	4.16970i	−0.359711	+	1.57600i	−0.753913	+	0.656974i	$0.771836\pi$
$8$	−2.76431	−	1.33122i	−0.977332	−	0.470658i
$9$	−0.900969	−	0.433884i	−0.300323	−	0.144628i
$10$	0.484517	+	2.12281i	0.153218	+	0.671290i
$11$	−0.951656	+	0.458293i	−0.286935	+	0.138181i	−0.571815	−	0.820383i	$-0.693761\pi$
$11$	−0.951656	+	0.458293i	−0.286935	+	0.138181i	0.284880	+	0.958563i	$0.408046\pi$
$12$	−0.534161			−0.154199
$13$	4.75885	−	2.29174i	1.31987	−	0.635615i	0.364547	−	0.931185i	$-0.381224\pi$
$13$	4.75885	−	2.29174i	1.31987	−	0.635615i	0.955321	+	0.295570i	$0.0955096\pi$
$14$	−3.22853	−	4.04845i	−0.862860	−	1.08199i
$15$	1.12131	+	1.40607i	0.289520	+	0.363047i
$16$	2.38428	−	1.14821i	0.596069	−	0.287052i
$17$	5.61769			1.36249			0.681245	−	0.732056i	$-0.261439\pi$
$17$	5.61769			1.36249			0.681245	+	0.732056i	$0.261439\pi$
$18$	1.09082	−	0.525311i	0.257109	−	0.123817i
$19$	−1.42675	−	6.25099i	−0.327319	−	1.43408i	−0.824220	−	0.566269i	$-0.808386\pi$
$19$	−1.42675	−	6.25099i	−0.327319	−	1.43408i	0.496902	−	0.867807i	$-0.334471\pi$
$20$	0.865520	+	0.416812i	0.193536	+	0.0932021i
$21$	−3.85338	−	1.85569i	−0.840877	−	0.404945i
$22$	0.284567	−	1.24677i	0.0606698	−	0.265812i
$23$	1.27587	+	1.59988i	0.266036	+	0.333599i	0.896850	−	0.442336i	$-0.145850\pi$
$23$	1.27587	+	1.59988i	0.266036	+	0.333599i	−0.630813	+	0.775935i	$0.717279\pi$
$24$	1.91296	−	2.39878i	0.390482	−	0.489649i
$25$	0.392890	+	1.72136i	0.0785779	+	0.344272i
$26$	−1.42300	+	6.23459i	−0.279074	+	1.22270i
$27$	0.623490	−	0.781831i	0.119991	−	0.150464i
$28$	−2.28457			−0.431743
$29$	−4.54927	−	2.88169i	−0.844778	−	0.535117i
$29$	−4.54927	−	2.88169i	−0.844778	−	0.535117i
$30$	−2.17740			−0.397537
$31$	2.38467	−	2.99028i	0.428299	−	0.537069i	−0.520119	−	0.854094i	$-0.674112\pi$
$31$	2.38467	−	2.99028i	0.428299	−	0.537069i	0.948417	+	0.317025i	$0.102684\pi$
$32$	0.652504	−	2.85881i	0.115348	−	0.505371i
$33$	−0.235040	−	1.02978i	−0.0409151	−	0.179261i
$34$	−4.24063	+	5.31758i	−0.727261	+	0.911957i
$35$	4.79575	+	6.01368i	0.810629	+	1.01650i
$36$	0.118862	−	0.520769i	0.0198103	−	0.0867948i
$37$	0.315606	+	0.151988i	0.0518854	+	0.0249867i	0.459647	−	0.888102i	$-0.347976\pi$
$37$	0.315606	+	0.151988i	0.0518854	+	0.0249867i	−0.407761	+	0.913089i	$0.633690\pi$
$38$	6.99406	+	3.36816i	1.13459	+	0.546388i
$39$	1.17534	+	5.14950i	0.188205	+	0.824579i
$40$	−4.97144	+	2.39412i	−0.786053	+	0.378543i
$41$	−3.62240			−0.565725			−0.282862	−	0.959161i	$-0.591284\pi$
$41$	−3.62240			−0.565725			−0.282862	+	0.959161i	$0.591284\pi$
$42$	4.66536	−	2.24672i	0.719880	−	0.346676i
$43$	1.09049	+	1.36743i	0.166298	+	0.208530i	0.857997	−	0.513655i	$-0.171709\pi$
$43$	1.09049	+	1.36743i	0.166298	+	0.208530i	−0.691699	+	0.722186i	$0.743138\pi$
$44$	−0.351781	−	0.441119i	−0.0530329	−	0.0665012i
$45$	−1.62033	+	0.780312i	−0.241545	+	0.116322i
$46$	−2.47753			−0.365292
$47$	−6.28881	+	3.02853i	−0.917317	+	0.441756i	−0.832112	−	0.554607i	$-0.812869\pi$
$47$	−6.28881	+	3.02853i	−0.917317	+	0.441756i	−0.0852043	+	0.996363i	$0.527154\pi$
$48$	0.588868	+	2.58000i	0.0849958	+	0.372391i
$49$	−10.1739	−	4.89947i	−1.45341	−	0.699924i
$50$	−1.92598	−	0.927505i	−0.272375	−	0.131169i
$51$	−1.25005	+	5.47684i	−0.175042	+	0.766911i
$52$	1.75911	+	2.20586i	0.243945	+	0.305898i
$53$	−4.87488	+	6.11290i	−0.669616	+	0.839672i	−0.994352	−	0.106133i	$-0.966153\pi$
$53$	−4.87488	+	6.11290i	−0.669616	+	0.839672i	0.324736	+	0.945805i	$0.394724\pi$
$54$	0.269410	+	1.18036i	0.0366621	+	0.160627i
$55$	−0.422703	+	1.85198i	−0.0569973	+	0.249722i
$56$	8.18161	−	10.2594i	1.09331	−	1.37097i
$57$	6.41175			0.849257
$58$	6.16185	−	2.13093i	0.809091	−	0.279805i
$59$	0.382668			0.0498191			0.0249096	−	0.999690i	$-0.492070\pi$
$59$	0.382668			0.0498191			0.0249096	+	0.999690i	$0.492070\pi$
$60$	−0.598958	+	0.751070i	−0.0773252	+	0.0969627i
$61$	1.21640	−	5.32939i	0.155744	−	0.682358i	−0.835409	−	0.549629i	$-0.814769\pi$
$61$	1.21640	−	5.32939i	0.155744	−	0.682358i	0.991152	−	0.132729i	$-0.0423740\pi$
$62$	1.03041	+	4.51454i	0.130863	+	0.573347i
$63$	2.66662	−	3.34384i	0.335963	−	0.421284i
$64$	5.51347	+	6.91367i	0.689184	+	0.864209i
$65$	2.11377	−	9.26104i	0.262181	−	1.14869i
$66$	1.15219	+	0.554864i	0.141824	+	0.0682990i
$67$	−7.03806	−	3.38935i	−0.859836	−	0.414075i	−0.0486169	−	0.998818i	$-0.515481\pi$
$67$	−7.03806	−	3.38935i	−0.859836	−	0.414075i	−0.811219	+	0.584742i	$0.801196\pi$
$68$	0.667730	+	2.92552i	0.0809742	+	0.354771i
$69$	−1.84368	+	0.887869i	−0.221953	+	0.106887i
$70$	−9.31258			−1.11307
$71$	14.0654	−	6.77356i	1.66926	−	0.803874i	0.671224	−	0.741255i	$-0.265769\pi$
$71$	14.0654	−	6.77356i	1.66926	−	0.803874i	0.998038	−	0.0626189i	$-0.0199452\pi$
$72$	1.91296	+	2.39878i	0.225445	+	0.282699i
$73$	−1.58547	−	1.98811i	−0.185565	−	0.232691i	0.680344	−	0.732893i	$-0.261830\pi$
$73$	−1.58547	−	1.98811i	−0.185565	−	0.232691i	−0.865909	+	0.500202i	$0.833259\pi$
$74$	−0.382110	+	0.184015i	−0.0444194	+	0.0213913i
$75$	−1.76563			−0.203877
$76$	3.08574	−	1.48601i	0.353958	−	0.170457i
$77$	−1.00525	−	4.40428i	−0.114559	−	0.501914i
$78$	−5.76163	−	2.77465i	−0.652376	−	0.314168i
$79$	−9.25113	−	4.45511i	−1.04083	−	0.501239i	−0.166235	−	0.986086i	$-0.553161\pi$
$79$	−9.25113	−	4.45511i	−1.04083	−	0.501239i	−0.874599	+	0.484847i	$0.838875\pi$
$80$	1.05904	−	4.63996i	0.118404	−	0.518764i
$81$	0.623490	+	0.781831i	0.0692766	+	0.0868702i
$82$	2.73445	−	3.42889i	0.301969	−	0.378657i
$83$	−0.338541	−	1.48324i	−0.0371597	−	0.162807i	0.952944	−	0.303148i	$-0.0980375\pi$
$83$	−0.338541	−	1.48324i	−0.0371597	−	0.162807i	−0.990103	+	0.140340i	$0.955180\pi$
$84$	0.508365	−	2.22729i	0.0554672	−	0.243017i
$85$	6.29915	−	7.89888i	0.683239	−	0.856754i
$86$	−2.11755			−0.228341
$87$	3.82175	−	3.79397i	0.409735	−	0.406756i
$88$	3.24076			0.345467
$89$	−11.1881	+	14.0295i	−1.18594	+	1.48712i	−0.351351	+	0.936244i	$0.614278\pi$
$89$	−11.1881	+	14.0295i	−1.18594	+	1.48712i	−0.834587	+	0.550876i	$0.814294\pi$
$90$	0.484517	−	2.12281i	0.0510725	−	0.223763i
$91$	5.02684	+	22.0240i	0.526956	+	2.30875i
$92$	−0.681518	+	0.854597i	−0.0710532	+	0.0890979i
$93$	2.38467	+	2.99028i	0.247278	+	0.310077i
$94$	1.88050	−	8.23899i	0.193958	−	0.849787i
$95$	−10.3892	−	5.00316i	−1.06591	−	0.513314i
$96$	2.64194	+	1.27229i	0.269641	+	0.129852i
$97$	1.51530	+	6.63895i	0.153855	+	0.674083i	0.991743	+	0.128241i	$0.0409331\pi$
$97$	1.51530	+	6.63895i	0.153855	+	0.674083i	−0.837888	+	0.545842i	$0.816210\pi$
$98$	12.3177	−	5.93188i	1.24427	−	0.599210i
$99$	1.05626			0.106158
$100$	−0.849732	+	0.409209i	−0.0849732	+	0.0409209i
$101$	2.94644	+	3.69472i	0.293182	+	0.367639i	0.906506	−	0.422193i	$-0.138739\pi$
$101$	2.94644	+	3.69472i	0.293182	+	0.367639i	−0.613324	+	0.789831i	$0.710168\pi$
$102$	−4.24063	−	5.31758i	−0.419885	−	0.526519i
$103$	−3.14881	+	1.51639i	−0.310261	+	0.149414i	−0.582534	−	0.812806i	$-0.697939\pi$
$103$	−3.14881	+	1.51639i	−0.310261	+	0.149414i	0.272273	+	0.962220i	$0.412225\pi$
$104$	−16.2058			−1.58911
$105$	−6.93006	+	3.33734i	−0.676304	+	0.325691i
$106$	−2.10644	−	9.22890i	−0.204595	−	0.896390i
$107$	4.43449	+	2.13554i	0.428699	+	0.206450i	0.635775	−	0.771874i	$-0.280681\pi$
$107$	4.43449	+	2.13554i	0.428699	+	0.206450i	−0.207076	+	0.978325i	$0.566395\pi$
$108$	0.481263	+	0.231764i	0.0463095	+	0.0223015i
$109$	3.31215	−	14.5115i	0.317246	−	1.38995i	−0.525114	−	0.851032i	$-0.675977\pi$
$109$	3.31215	−	14.5115i	0.317246	−	1.38995i	0.842360	−	0.538915i	$-0.181166\pi$
$110$	−1.43396	−	1.79813i	−0.136723	−	0.171445i
$111$	−0.218406	+	0.273873i	−0.0207302	+	0.0259949i
$112$	2.51855	+	11.0345i	0.237980	+	1.04266i
$113$	1.41140	−	6.18375i	0.132773	−	0.581718i	−0.864143	−	0.503246i	$-0.832139\pi$
$113$	1.41140	−	6.18375i	0.132773	−	0.581718i	0.996916	−	0.0784718i	$-0.0250041\pi$
$114$	−4.84004	+	6.06922i	−0.453311	+	0.568434i
$115$	3.68019			0.343180
$116$	0.959961	−	2.71164i	0.0891301	−	0.251770i
$117$	−5.28193			−0.488314
$118$	−0.288865	+	0.362225i	−0.0265922	+	0.0333455i
$119$	−5.34639	+	23.4241i	−0.490103	+	2.14728i
$120$	−1.22784	−	5.37953i	−0.112086	−	0.491082i
$121$	−6.16277	+	7.72787i	−0.560252	+	0.702534i
$122$	4.12646	+	5.17441i	0.373592	+	0.468469i
$123$	0.806061	−	3.53158i	0.0726801	−	0.318432i
$124$	1.84069	+	0.886429i	0.165299	+	0.0796037i
$125$	10.9626	+	5.27930i	0.980523	+	0.472195i
$126$	1.15225	+	5.04833i	0.102650	+	0.449741i
$127$	4.02345	−	1.93759i	0.357023	−	0.171933i	−0.246770	−	0.969074i	$-0.579369\pi$
$127$	4.02345	−	1.93759i	0.357023	−	0.171933i	0.603794	+	0.797141i	$0.293655\pi$
$128$	−4.84163			−0.427944
$129$	−1.57580	+	0.758864i	−0.138741	+	0.0668143i
$130$	7.17067	+	8.99173i	0.628909	+	0.788627i
$131$	0.00620961	+	0.00778660i	0.000542536	+	0.000680318i	0.782103	−	0.623150i	$-0.214147\pi$
$131$	0.00620961	+	0.00778660i	0.000542536	+	0.000680318i	−0.781560	+	0.623830i	$0.785576\pi$
$132$	0.508338	−	0.244803i	0.0442451	−	0.0213073i
$133$	27.4226			2.37784
$134$	8.52111	−	4.10355i	0.736112	−	0.354493i
$135$	−0.400190	−	1.75334i	−0.0344428	−	0.150904i
$136$	−15.5290	−	7.47839i	−1.33160	−	0.641267i
$137$	−11.0039	−	5.29921i	−0.940129	−	0.452742i	−0.0999140	−	0.994996i	$-0.531857\pi$
$137$	−11.0039	−	5.29921i	−0.940129	−	0.452742i	−0.840215	+	0.542254i	$0.817571\pi$
$138$	0.551302	−	2.41541i	0.0469299	−	0.205613i
$139$	3.08354	+	3.86663i	0.261542	+	0.327964i	0.895212	−	0.445640i	$-0.147024\pi$
$139$	3.08354	+	3.86663i	0.261542	+	0.327964i	−0.633670	+	0.773603i	$0.718452\pi$
$140$	−2.56170	+	3.21227i	−0.216503	+	0.271487i
$141$	−1.55321	−	6.80504i	−0.130804	−	0.573088i
$142$	−4.20589	+	18.4272i	−0.352950	+	1.54638i
$143$	−3.47850	+	4.36190i	−0.290887	+	0.364760i
$144$	−2.64635			−0.220529
$145$	−9.15299	+	3.16534i	−0.760115	+	0.262868i
$146$	3.07873			0.254797
$147$	7.04053	−	8.82854i	0.580693	−	0.728166i
$148$	−0.0416370	+	0.182424i	−0.00342254	+	0.0149951i
$149$	−3.11840	−	13.6626i	−0.255470	−	1.11929i	−0.926036	−	0.377436i	$-0.876806\pi$
$149$	−3.11840	−	13.6626i	−0.255470	−	1.11929i	0.670566	−	0.741850i	$-0.266051\pi$
$150$	1.33282	−	1.67131i	0.108824	−	0.136462i
$151$	1.82927	+	2.29383i	0.148864	+	0.186669i	0.850672	−	0.525697i	$-0.176195\pi$
$151$	1.82927	+	2.29383i	0.148864	+	0.186669i	−0.701809	+	0.712366i	$0.747624\pi$
$152$	−4.37749	+	19.1790i	−0.355061	+	1.55562i
$153$	−5.06136	−	2.43742i	−0.409187	−	0.197054i
$154$	4.92782	+	2.37311i	0.397095	+	0.191231i
$155$	−1.53061	−	6.70603i	−0.122941	−	0.538641i
$156$	−2.54199	+	1.22416i	−0.203522	+	0.0980112i
$157$	16.1919			1.29226			0.646128	−	0.763229i	$-0.276387\pi$
$157$	16.1919			1.29226			0.646128	+	0.763229i	$0.276387\pi$
$158$	11.2005	−	5.39388i	0.891065	−	0.429114i
$159$	−4.87488	−	6.11290i	−0.386603	−	0.484785i
$160$	−3.28804	−	4.12307i	−0.259942	−	0.325957i
$161$	−7.88529	+	3.79735i	−0.621448	+	0.299273i
$162$	−1.21072			−0.0951230
$163$	−12.2292	+	5.88927i	−0.957865	+	0.461284i	−0.846437	−	0.532489i	$-0.821257\pi$
$163$	−12.2292	+	5.88927i	−0.957865	+	0.461284i	−0.111428	+	0.993772i	$0.535543\pi$
$164$	−0.430567	−	1.88644i	−0.0336216	−	0.147306i
$165$	−1.71149	−	0.824211i	−0.133239	−	0.0641647i
$166$	1.65956	+	0.799202i	0.128807	+	0.0620301i
$167$	3.64080	−	15.9514i	0.281734	−	1.23436i	−0.613836	−	0.789434i	$-0.710374\pi$
$167$	3.64080	−	15.9514i	0.281734	−	1.23436i	0.895569	−	0.444922i	$-0.146769\pi$
$168$	8.18161	+	10.2594i	0.631225	+	0.791531i
$169$	9.28921	−	11.6483i	0.714555	−	0.896024i
$170$	2.72186	+	11.9253i	0.208757	+	0.914626i
$171$	−1.42675	+	6.25099i	−0.109106	+	0.478025i
$172$	−0.582495	+	0.730426i	−0.0444149	+	0.0556945i
$173$	−4.46374			−0.339372			−0.169686	−	0.985498i	$-0.554275\pi$
$173$	−4.46374			−0.339372			−0.169686	+	0.985498i	$0.554275\pi$
$174$	0.706362	+	6.48154i	0.0535491	+	0.491364i
$175$	−7.55148			−0.570838
$176$	−1.74280	+	2.18540i	−0.131368	+	0.164730i
$177$	−0.0851516	+	0.373074i	−0.00640039	+	0.0280419i
$178$	−4.83439	−	21.1808i	−0.362353	−	1.58757i
$179$	2.12026	−	2.65872i	0.158476	−	0.198722i	−0.696254	−	0.717795i	$-0.745151\pi$
$179$	2.12026	−	2.65872i	0.158476	−	0.198722i	0.854730	+	0.519073i	$0.173723\pi$
$180$	−0.598958	−	0.751070i	−0.0446437	−	0.0559815i
$181$	−1.47339	+	6.45532i	−0.109516	+	0.479820i	0.890190	+	0.455589i	$0.150571\pi$
$181$	−1.47339	+	6.45532i	−0.109516	+	0.479820i	−0.999706	+	0.0242319i	$0.992286\pi$
$182$	−24.6421	−	11.8670i	−1.82659	−	0.879640i
$183$	4.92510	+	2.37180i	0.364074	+	0.175329i
$184$	−1.39709	−	6.12104i	−0.102995	−	0.451249i
$185$	0.567598	−	0.273341i	0.0417306	−	0.0200964i
$186$	−4.63064			−0.339535
$187$	−5.34610	+	2.57455i	−0.390946	+	0.188270i
$188$	−2.32466	−	2.91504i	−0.169544	−	0.212601i
$189$	2.66662	+	3.34384i	0.193968	+	0.243228i
$190$	12.5784	−	6.05742i	0.912531	−	0.439452i
$191$	17.6196			1.27491			0.637454	−	0.770489i	$-0.279988\pi$
$191$	17.6196			1.27491			0.637454	+	0.770489i	$0.279988\pi$
$192$	−7.96720	+	3.83680i	−0.574983	+	0.276897i
$193$	2.98147	+	13.0627i	0.214611	+	0.940273i	0.961388	+	0.275198i	$0.0887434\pi$
$193$	2.98147	+	13.0627i	0.214611	+	0.940273i	−0.746776	+	0.665075i	$0.768399\pi$
$194$	−7.42813	−	3.57720i	−0.533309	−	0.256828i
$195$	8.55849	+	4.12155i	0.612886	+	0.295150i
$196$	1.34221	−	5.88059i	0.0958719	−	0.420042i
$197$	−5.11558	−	6.41474i	−0.364470	−	0.457031i	0.565455	−	0.824779i	$-0.308700\pi$
$197$	−5.11558	−	6.41474i	−0.364470	−	0.457031i	−0.929926	+	0.367748i	$0.880129\pi$
$198$	−0.797338	+	0.999830i	−0.0566643	+	0.0710548i
$199$	−5.45073	−	23.8812i	−0.386392	−	1.69290i	−0.676943	−	0.736036i	$-0.736696\pi$
$199$	−5.45073	−	23.8812i	−0.386392	−	1.69290i	0.290551	−	0.956860i	$-0.406162\pi$
$200$	1.20545	−	5.28141i	0.0852379	−	0.373452i
$201$	4.87049	−	6.10740i	0.343538	−	0.430783i
$202$	−5.72153			−0.402565
$203$	16.3454	−	16.2266i	1.14722	−	1.13888i
$204$	−3.00075			−0.210095
$205$	−4.06182	+	5.09337i	−0.283690	+	0.355736i
$206$	0.941565	−	4.12527i	0.0656019	−	0.287421i
$207$	−0.455351	−	1.99502i	−0.0316491	−	0.138664i
$208$	8.71503	−	10.9283i	0.604278	−	0.757741i
$209$	4.22256	+	5.29492i	0.292081	+	0.366258i
$210$	2.07224	−	9.07909i	0.142998	−	0.626517i
$211$	1.99243	+	0.959502i	0.137164	+	0.0660549i	0.501207	−	0.865327i	$-0.332890\pi$
$211$	1.99243	+	0.959502i	0.137164	+	0.0660549i	−0.364043	+	0.931382i	$0.618604\pi$
$212$	−3.76285	−	1.81209i	−0.258433	−	0.124455i
$213$	3.47388	+	15.2201i	0.238026	+	1.04286i
$214$	−5.36892	+	2.58554i	−0.367012	+	0.176744i
$215$	3.14547			0.214519
$216$	−2.76431	+	1.33122i	−0.188088	+	0.0905782i
$217$	10.1990	+	12.7892i	0.692356	+	0.868187i
$218$	11.2360	+	14.0895i	0.760997	+	0.954260i
$219$	2.29107	−	1.10332i	0.154816	−	0.0745554i
$220$	−1.01470			−0.0684110
$221$	26.7337	−	12.8743i	1.79831	−	0.866018i
$222$	−0.0943735	−	0.413477i	−0.00633393	−	0.0277508i
$223$	−2.43655	−	1.17338i	−0.163164	−	0.0785755i	0.350519	−	0.936555i	$-0.386005\pi$
$223$	−2.43655	−	1.17338i	−0.163164	−	0.0785755i	−0.513683	+	0.857980i	$0.671719\pi$
$224$	11.2994	+	5.44149i	0.754971	+	0.363575i
$225$	0.392890	−	1.72136i	0.0261926	−	0.114757i
$226$	4.78798	+	6.00393i	0.318491	+	0.399376i
$227$	8.99231	−	11.2760i	0.596840	−	0.748414i	−0.388041	−	0.921642i	$-0.626848\pi$
$227$	8.99231	−	11.2760i	0.596840	−	0.748414i	0.984882	+	0.173228i	$0.0554197\pi$
$228$	0.762114	+	3.33904i	0.0504722	+	0.221133i
$229$	−5.72917	+	25.1011i	−0.378594	+	1.65873i	0.323185	+	0.946336i	$0.395246\pi$
$229$	−5.72917	+	25.1011i	−0.378594	+	1.65873i	−0.701779	+	0.712394i	$0.747611\pi$
$230$	−2.77807	+	3.48359i	−0.183180	+	0.229701i
$231$	4.51754			0.297232
$232$	8.73942	+	14.0220i	0.573771	+	0.920589i
$233$	−22.6039			−1.48083			−0.740417	−	0.672148i	$-0.765372\pi$
$233$	−22.6039			−1.48083			−0.740417	+	0.672148i	$0.765372\pi$
$234$	3.98717	−	4.99975i	0.260649	−	0.326844i
$235$	−2.79334	+	12.2384i	−0.182218	+	0.798347i
$236$	0.0454847	+	0.199282i	0.00296080	+	0.0129721i
$237$	6.40198	−	8.02783i	0.415853	−	0.521464i
$238$	−18.1369	−	22.7429i	−1.17564	−	1.47420i
$239$	−5.21218	+	22.8361i	−0.337148	+	1.47714i	0.467820	+	0.883824i	$0.345040\pi$
$239$	−5.21218	+	22.8361i	−0.337148	+	1.47714i	−0.804968	+	0.593318i	$0.797818\pi$
$240$	4.28797	+	2.06498i	0.276787	+	0.133294i
$241$	−20.1661	−	9.71147i	−1.29901	−	0.625570i	−0.348805	−	0.937195i	$-0.613413\pi$
$241$	−20.1661	−	9.71147i	−1.29901	−	0.625570i	−0.950205	+	0.311625i	$0.899127\pi$
$242$	−2.66294	−	11.6671i	−0.171180	−	0.749989i
$243$	−0.900969	+	0.433884i	−0.0577972	+	0.0278337i
$244$	2.91996			0.186932
$245$	−18.2970	+	8.81138i	−1.16895	+	0.562939i
$246$	2.73445	+	3.42889i	0.174342	+	0.218618i
$247$	−21.1153	−	26.4778i	−1.34354	−	1.68474i
$248$	−10.5727	+	5.09154i	−0.671366	+	0.323313i
$249$	1.52139			0.0964141
$250$	−13.2726	+	6.39175i	−0.839433	+	0.404250i
$251$	1.32618	+	5.81039i	0.0837079	+	0.366748i	0.999381	−	0.0351751i	$-0.0111989\pi$
$251$	1.32618	+	5.81039i	0.0837079	+	0.366748i	−0.915673	+	0.401924i	$0.868342\pi$
$252$	2.05833	+	0.991238i	0.129662	+	0.0624421i
$253$	−1.94740	−	0.937819i	−0.122432	−	0.0589602i
$254$	−1.20310	+	5.27114i	−0.0754894	+	0.330741i
$255$	6.29915	+	7.89888i	0.394468	+	0.494647i
$256$	−7.37214	+	9.24437i	−0.460759	+	0.577773i
$257$	3.35390	+	14.6944i	0.209211	+	0.916612i	0.965094	+	0.261905i	$0.0843508\pi$
$257$	3.35390	+	14.6944i	0.209211	+	0.916612i	−0.755883	+	0.654707i	$0.772792\pi$
$258$	0.471199	−	2.06446i	0.0293356	−	0.128528i
$259$	−0.934109	+	1.17134i	−0.0580427	+	0.0727832i
$260$	5.07411			0.314683
$261$	2.84843	+	4.57017i	0.176313	+	0.282886i
$262$	−0.0120581			−0.000744950
$263$	−11.6750	+	14.6400i	−0.719911	+	0.902740i	−0.998333	−	0.0577193i	$-0.981617\pi$
$263$	−11.6750	+	14.6400i	−0.719911	+	0.902740i	0.278422	+	0.960459i	$0.410189\pi$
$264$	−0.721138	+	3.15951i	−0.0443830	+	0.194454i
$265$	3.12896	+	13.7089i	0.192210	+	0.842129i
$266$	−20.7005	+	25.9576i	−1.26923	+	1.59156i
$267$	−11.1881	−	14.0295i	−0.684702	−	0.858589i
$268$	0.928510	−	4.06807i	0.0567178	−	0.248497i
$269$	20.8357	+	10.0340i	1.27038	+	0.611781i	0.942899	−	0.333078i	$-0.108087\pi$
$269$	20.8357	+	10.0340i	1.27038	+	0.611781i	0.327477	+	0.944859i	$0.393802\pi$
$270$	1.96177	+	0.944738i	0.119389	+	0.0574949i
$271$	−4.75012	−	20.8116i	−0.288549	−	1.26422i	−0.886517	−	0.462697i	$-0.846882\pi$
$271$	−4.75012	−	20.8116i	−0.288549	−	1.26422i	0.597967	−	0.801521i	$-0.295975\pi$
$272$	13.3941	−	6.45027i	0.812138	−	0.391105i
$273$	−22.5904			−1.36723
$274$	13.3227	−	6.41585i	0.804851	−	0.387596i
$275$	−1.16278	−	1.45809i	−0.0701185	−	0.0879258i
$276$	−0.681518	−	0.854597i	−0.0410226	−	0.0514407i
$277$	7.49769	−	3.61070i	0.450493	−	0.216946i	−0.194859	−	0.980831i	$-0.562425\pi$
$277$	7.49769	−	3.61070i	0.450493	−	0.216946i	0.645352	+	0.763885i	$0.276711\pi$
$278$	−5.98774			−0.359121
$279$	−3.44594	+	1.65948i	−0.206303	+	0.0993503i
$280$	−5.25140	−	23.0079i	−0.313831	−	1.37498i
$281$	26.0562	+	12.5480i	1.55438	+	0.748552i	0.996675	−	0.0814850i	$-0.0259663\pi$
$281$	26.0562	+	12.5480i	1.55438	+	0.748552i	0.557709	+	0.830037i	$0.311681\pi$
$282$	7.61397	+	3.66670i	0.453405	+	0.218349i
$283$	−6.67116	+	29.2282i	−0.396559	+	1.73744i	0.244226	+	0.969718i	$0.421466\pi$
$283$	−6.67116	+	29.2282i	−0.396559	+	1.73744i	−0.640785	+	0.767721i	$0.721391\pi$
$284$	5.19931	+	6.51973i	0.308522	+	0.386875i
$285$	7.18953	−	9.01539i	0.425871	−	0.534026i
$286$	−1.50306	−	6.58534i	−0.0888778	−	0.389399i
$287$	3.44747	−	15.1043i	0.203497	−	0.891581i
$288$	−1.82828	+	2.29259i	−0.107732	+	0.135092i
$289$	14.5584			0.856378
$290$	3.91308	−	11.0534i	0.229784	−	0.649081i
$291$	−6.80968			−0.399191
$292$	0.846895	−	1.06197i	0.0495608	−	0.0621473i
$293$	−1.94796	+	8.53458i	−0.113801	+	0.498595i	0.885615	+	0.464421i	$0.153737\pi$
$293$	−1.94796	+	8.53458i	−0.113801	+	0.498595i	−0.999416	+	0.0341747i	$0.989120\pi$
$294$	3.04221	+	13.3288i	0.177426	+	0.777352i
$295$	0.429088	−	0.538059i	0.0249825	−	0.0313270i
$296$	−0.670105	−	0.840285i	−0.0389490	−	0.0488405i
$297$	−0.235040	+	1.02978i	−0.0136384	+	0.0597536i
$298$	15.2867	+	7.36170i	0.885536	+	0.426452i
$299$	9.73818	+	4.68966i	0.563173	+	0.271210i
$300$	−0.209867	−	0.919485i	−0.0121166	−	0.0530865i
$301$	−6.73958	+	3.24561i	−0.388463	+	0.187074i
$302$	−3.55215			−0.204403
$303$	−4.25773	+	2.05042i	−0.244600	+	0.117793i
$304$	−10.5792	−	13.2659i	−0.606759	−	0.760852i
$305$	−6.12956	−	7.68622i	−0.350977	−	0.440112i
$306$	6.12788	−	2.95103i	0.350308	−	0.168699i
$307$	−33.9161			−1.93570			−0.967848	−	0.251536i	$-0.919064\pi$
$307$	−33.9161			−1.93570			−0.967848	+	0.251536i	$0.919064\pi$
$308$	2.17412	−	1.04700i	0.123882	−	0.0596585i
$309$	−0.777691	−	3.40729i	−0.0442413	−	0.193834i
$310$	7.50319	+	3.61334i	0.426152	+	0.205224i
$311$	−7.32104	−	3.52563i	−0.415138	−	0.199920i	0.214643	−	0.976693i	$-0.431141\pi$
$311$	−7.32104	−	3.52563i	−0.415138	−	0.199920i	−0.629781	+	0.776773i	$0.716855\pi$
$312$	3.60612	−	15.7995i	0.204157	−	0.894468i
$313$	1.57580	+	1.97599i	0.0890693	+	0.111689i	0.824369	−	0.566053i	$-0.191530\pi$
$313$	1.57580	+	1.97599i	0.0890693	+	0.111689i	−0.735300	+	0.677742i	$0.762959\pi$
$314$	−12.2228	+	15.3269i	−0.689773	+	0.864948i
$315$	−1.71158	−	7.49893i	−0.0964367	−	0.422517i
$316$	1.22047	−	5.34724i	0.0686570	−	0.300806i
$317$	10.3738	−	13.0083i	0.582651	−	0.730621i	−0.399912	−	0.916554i	$-0.630959\pi$
$317$	10.3738	−	13.0083i	0.582651	−	0.730621i	0.982562	+	0.185933i	$0.0595306\pi$
$318$	9.46624			0.530840
$319$	5.65000	+	0.657481i	0.316339	+	0.0368119i
$320$	15.9034			0.889028
$321$	−3.06876	+	3.84811i	−0.171282	+	0.214780i
$322$	2.35788	−	10.3305i	0.131399	−	0.575699i
$323$	−8.01503	−	35.1161i	−0.445968	−	1.95391i
$324$	−0.333044	+	0.417624i	−0.0185025	+	0.0232013i
$325$	5.81462	+	7.29130i	0.322537	+	0.404449i
$326$	3.65681	−	16.0215i	0.202532	−	0.887350i
$327$	13.4106	+	6.45821i	0.741609	+	0.357140i
$328$	10.0135	+	4.82223i	0.552901	+	0.266263i
$329$	−6.64296	−	29.1047i	−0.366238	−	1.60459i
$330$	2.07213	−	0.997887i	0.114067	−	0.0549319i
$331$	12.9286			0.710619			0.355309	−	0.934749i	$-0.384375\pi$
$331$	12.9286			0.710619			0.355309	+	0.934749i	$0.384375\pi$
$332$	0.732188	−	0.352603i	0.0401840	−	0.0193516i
$333$	−0.218406	−	0.273873i	−0.0119686	−	0.0150081i
$334$	12.3509	+	15.4875i	0.675811	+	0.847440i
$335$	−12.6575	+	6.09553i	−0.691553	+	0.333034i
$336$	−11.3182			−0.617461
$337$	5.01185	−	2.41358i	0.273013	−	0.131476i	−0.292368	−	0.956306i	$-0.594443\pi$
$337$	5.01185	−	2.41358i	0.273013	−	0.131476i	0.565381	+	0.824830i	$0.308729\pi$
$338$	4.01387	+	17.5859i	0.218326	+	0.956548i
$339$	5.71464	+	2.75203i	0.310377	+	0.149470i
$340$	4.86222	+	2.34152i	0.263691	+	0.126987i
$341$	−0.898957	+	3.93859i	−0.0486813	+	0.213286i
$342$	−4.84004	−	6.06922i	−0.261719	−	0.328186i
$343$	11.4455	−	14.3522i	0.617998	−	0.774945i
$344$	−1.19409	−	5.23167i	−0.0643813	−	0.282073i
$345$	−0.818920	+	3.58792i	−0.0440891	+	0.193167i
$346$	3.36955	−	4.22528i	0.181148	−	0.227152i
$347$	−8.78686			−0.471703			−0.235852	−	0.971789i	$-0.575788\pi$
$347$	−8.78686			−0.471703			−0.235852	+	0.971789i	$0.575788\pi$
$348$	2.43004	+	1.53929i	0.130264	+	0.0825146i
$349$	15.1943			0.813332			0.406666	−	0.913577i	$-0.366691\pi$
$349$	15.1943			0.813332			0.406666	+	0.913577i	$0.366691\pi$
$350$	5.70039	−	7.14806i	0.304698	−	0.382080i
$351$	1.17534	−	5.14950i	0.0627350	−	0.274860i
$352$	0.689213	+	3.01964i	0.0367352	+	0.160947i
$353$	−7.71052	+	9.66868i	−0.410389	+	0.514612i	−0.943473	−	0.331451i	$-0.892462\pi$
$353$	−7.71052	+	9.66868i	−0.410389	+	0.514612i	0.533083	+	0.846063i	$0.321033\pi$
$354$	−0.288865	−	0.362225i	−0.0153530	−	0.0192520i
$355$	6.24754	−	27.3723i	0.331585	−	1.45277i
$356$	−8.63595	−	4.15885i	−0.457704	−	0.220419i
$357$	−21.6471	−	10.4247i	−1.14569	−	0.551733i
$358$	0.916165	+	4.01398i	0.0484208	+	0.212146i
$359$	14.4303	−	6.94924i	0.761600	−	0.366767i	−0.0124248	−	0.999923i	$-0.503955\pi$
$359$	14.4303	−	6.94924i	0.761600	−	0.366767i	0.774024	+	0.633156i	$0.218241\pi$
$360$	5.51788			0.290818
$361$	−19.9209	+	9.59340i	−1.04847	+	0.504916i
$362$	−4.99825	−	6.26761i	−0.262702	−	0.329418i
$363$	−6.16277	−	7.72787i	−0.323462	−	0.405608i
$364$	−10.8719	+	5.23565i	−0.569844	+	0.274422i
$365$	−4.57323			−0.239374
$366$	−5.96290	+	2.87158i	−0.311686	+	0.150100i
$367$	4.94990	+	21.6869i	0.258383	+	1.13205i	0.922980	+	0.384847i	$0.125746\pi$
$367$	4.94990	+	21.6869i	0.258383	+	1.13205i	−0.664597	+	0.747202i	$0.731397\pi$
$368$	4.87902	+	2.34961i	0.254336	+	0.122482i
$369$	3.26367	+	1.57170i	0.169900	+	0.0818196i
$370$	−0.169725	+	0.743612i	−0.00882356	+	0.0386585i
$371$	−20.8495	−	26.1445i	−1.08245	−	1.35735i
$372$	−1.27380	+	1.59729i	−0.0660433	+	0.0828156i
$373$	−1.54213	−	6.75653i	−0.0798487	−	0.349840i	0.919183	−	0.393830i	$-0.128850\pi$
$373$	−1.54213	−	6.75653i	−0.0798487	−	0.349840i	−0.999032	+	0.0439901i	$0.985993\pi$
$374$	1.59861	−	7.00395i	0.0826620	−	0.362166i
$375$	−7.58634	+	9.51297i	−0.391757	+	0.491248i
$376$	21.4159			1.10444
$377$	−28.2534	−	3.28780i	−1.45512	−	0.169330i
$378$	−5.17816			−0.266336
$379$	−4.85604	+	6.08928i	−0.249438	+	0.312785i	−0.890749	−	0.454496i	$-0.849819\pi$
$379$	−4.85604	+	6.08928i	−0.249438	+	0.312785i	0.641311	+	0.767281i	$0.278391\pi$
$380$	1.37061	−	6.00505i	0.0703110	−	0.308052i
$381$	0.993710	+	4.35373i	0.0509093	+	0.223048i
$382$	−13.3005	+	16.6783i	−0.680512	+	0.853335i
$383$	15.8756	+	19.9074i	0.811206	+	1.01722i	0.999384	+	0.0350856i	$0.0111704\pi$
$383$	15.8756	+	19.9074i	0.811206	+	1.01722i	−0.188178	+	0.982135i	$0.560258\pi$
$384$	1.07736	−	4.72024i	0.0549790	−	0.240879i
$385$	−7.31993	−	3.52509i	−0.373058	−	0.179655i
$386$	−14.6155	−	7.03844i	−0.743908	−	0.358247i
$387$	−0.389190	−	1.70515i	−0.0197836	−	0.0866778i
$388$	−3.27725	+	1.57824i	−0.166377	+	0.0801229i
$389$	10.9838			0.556902			0.278451	−	0.960450i	$-0.410179\pi$
$389$	10.9838			0.556902			0.278451	+	0.960450i	$0.410179\pi$
$390$	−10.3619	+	4.99004i	−0.524696	+	0.252680i
$391$	7.16741	+	8.98765i	0.362472	+	0.454525i
$392$	21.6014	+	27.0873i	1.09104	+	1.36812i
$393$	−0.00897314	+	0.00432124i	−0.000452635	+	0.000217978i
$394$	9.93365			0.500450
$395$	−16.6376	+	8.01223i	−0.837127	+	0.403139i
$396$	0.125549	+	0.550066i	0.00630908	+	0.0276419i
$397$	−4.59536	−	2.21301i	−0.230635	−	0.111068i	0.314998	−	0.949092i	$-0.397996\pi$
$397$	−4.59536	−	2.21301i	−0.230635	−	0.111068i	−0.545632	+	0.838025i	$0.683711\pi$
$398$	26.7200	+	12.8677i	1.33935	+	0.644999i
$399$	−6.10210	+	26.7351i	−0.305487	+	1.33843i
$400$	2.91324	+	3.65309i	0.145662	+	0.182654i
$401$	−12.1843	+	15.2786i	−0.608455	+	0.762979i	−0.986669	−	0.162740i	$-0.947967\pi$
$401$	−12.1843	+	15.2786i	−0.608455	+	0.762979i	0.378214	+	0.925718i	$0.376538\pi$
$402$	2.10454	+	9.22059i	0.104965	+	0.459881i
$403$	4.49533	−	19.6953i	0.223928	−	0.981093i
$404$	−1.57388	+	1.97358i	−0.0783033	+	0.0981892i
$405$	1.79844			0.0893650
$406$	3.02106	+	27.7211i	0.149933	+	1.37577i
$407$	−0.370004			−0.0183404
$408$	10.7464	−	13.4756i	0.532028	−	0.667142i
$409$	3.98856	−	17.4750i	0.197221	−	0.864083i	−0.775360	−	0.631520i	$-0.782431\pi$
$409$	3.98856	−	17.4750i	0.197221	−	0.864083i	0.972581	−	0.232564i	$-0.0747114\pi$
$410$	−1.75512	−	7.68966i	−0.0866790	−	0.379765i
$411$	7.61495	−	9.54885i	0.375618	−	0.471010i
$412$	−1.16396	−	1.45956i	−0.0573442	−	0.0719074i
$413$	−0.364188	+	1.59561i	−0.0179205	+	0.0785148i
$414$	2.23218	+	1.07496i	0.109705	+	0.0528314i
$415$	−2.46516	−	1.18716i	−0.121010	−	0.0582753i
$416$	−3.44648	−	15.1000i	−0.168978	−	0.740339i
$417$	−4.45584	+	2.14582i	−0.218204	+	0.105081i
$418$	−8.19954			−0.401053
$419$	−3.36801	+	1.62195i	−0.164538	+	0.0792373i	−0.514340	−	0.857586i	$-0.671963\pi$
$419$	−3.36801	+	1.62195i	−0.164538	+	0.0792373i	0.349802	+	0.936824i	$0.386249\pi$
$420$	−2.56170	−	3.21227i	−0.124998	−	0.156743i
$421$	5.16735	+	6.47965i	0.251841	+	0.315799i	0.891641	−	0.452742i	$-0.149554\pi$
$421$	5.16735	+	6.47965i	0.251841	+	0.315799i	−0.639800	+	0.768541i	$0.720983\pi$
$422$	−2.41227	+	1.16169i	−0.117427	+	0.0565500i
$423$	6.98005			0.339382
$424$	21.6133	−	10.4084i	1.04964	−	0.505478i
$425$	2.20713	+	9.67008i	0.107062	+	0.469068i
$426$	−17.0293	−	8.20087i	−0.825072	−	0.397334i
$427$	21.0643	+	10.1440i	1.01937	+	0.490904i
$428$	−0.585029	+	2.56318i	−0.0282785	+	0.123896i
$429$	−3.47850	−	4.36190i	−0.167943	−	0.210594i
$430$	−2.37442	+	2.97743i	−0.114505	+	0.143584i
$431$	−4.25670	−	18.6498i	−0.205038	−	0.898330i	−0.967814	−	0.251667i	$-0.919021\pi$
$431$	−4.25670	−	18.6498i	−0.205038	−	0.898330i	0.762776	−	0.646663i	$-0.223836\pi$
$432$	0.588868	−	2.58000i	0.0283319	−	0.124130i
$433$	−10.0699	+	12.6273i	−0.483929	+	0.606828i	−0.962520	−	0.271210i	$-0.912576\pi$
$433$	−10.0699	+	12.6273i	−0.483929	+	0.606828i	0.478591	+	0.878038i	$0.341148\pi$
$434$	−19.8049			−0.950667
$435$	−1.04925	−	9.62787i	−0.0503077	−	0.461621i
$436$	7.95081			0.380775
$437$	8.18053	−	10.2581i	0.391328	−	0.490710i
$438$	−0.685081	+	3.00154i	−0.0327344	+	0.143419i
$439$	−0.660522	−	2.89393i	−0.0315250	−	0.138120i	0.956716	−	0.291022i	$-0.0939953\pi$
$439$	−0.660522	−	2.89393i	−0.0315250	−	0.138120i	−0.988241	+	0.152902i	$0.951138\pi$
$440$	3.63389	−	4.55675i	0.173239	−	0.217235i
$441$	7.04053	+	8.82854i	0.335263	+	0.420407i
$442$	−7.99400	+	35.0240i	−0.380236	+	1.66592i
$443$	−9.45260	−	4.55213i	−0.449107	−	0.216278i	0.195638	−	0.980676i	$-0.437322\pi$
$443$	−9.45260	−	4.55213i	−0.449107	−	0.216278i	−0.644745	+	0.764398i	$0.723036\pi$
$444$	−0.168585	−	0.0811861i	−0.00800068	−	0.00385292i
$445$	7.18114	+	31.4626i	0.340419	+	1.49147i
$446$	2.94998	−	1.42064i	0.139686	−	0.0672691i
$447$	14.0140			0.662839
$448$	−34.0751	+	16.4097i	−1.60990	+	0.775287i
$449$	−2.74538	−	3.44260i	−0.129563	−	0.162466i	0.712819	−	0.701348i	$-0.247418\pi$
$449$	−2.74538	−	3.44260i	−0.129563	−	0.162466i	−0.842381	+	0.538882i	$0.818847\pi$
$450$	1.33282	+	1.67131i	0.0628298	+	0.0787861i
$451$	3.44728	−	1.66012i	0.162326	−	0.0781721i
$452$	3.38807			0.159361
$453$	−2.64337	+	1.27298i	−0.124196	+	0.0598097i
$454$	3.88558	+	17.0238i	0.182359	+	0.798968i
$455$	36.6040	+	17.6276i	1.71602	+	0.826394i
$456$	−17.7241	−	8.53547i	−0.830006	−	0.399710i
$457$	−2.52528	+	11.0640i	−0.118127	+	0.517550i	0.880894	+	0.473314i	$0.156943\pi$
$457$	−2.52528	+	11.0640i	−0.118127	+	0.517550i	−0.999021	+	0.0442360i	$0.985915\pi$
$458$	−19.4354	−	24.3712i	−0.908156	−	1.13879i
$459$	3.50257	−	4.39209i	0.163486	−	0.205005i
$460$	0.437435	+	1.91653i	0.0203955	+	0.0893586i
$461$	−4.38570	+	19.2150i	−0.204262	+	0.894932i	0.764044	+	0.645165i	$0.223211\pi$
$461$	−4.38570	+	19.2150i	−0.204262	+	0.894932i	−0.968306	+	0.249767i	$0.919646\pi$
$462$	−3.41016	+	4.27620i	−0.158655	+	0.198947i
$463$	0.753315			0.0350095			0.0175048	−	0.999847i	$-0.494428\pi$
$463$	0.753315			0.0350095			0.0175048	+	0.999847i	$0.494428\pi$
$464$	−14.1555	−	1.64725i	−0.657153	−	0.0764718i
$465$	6.87849			0.318982
$466$	17.0631	−	21.3964i	0.790431	−	0.991169i
$467$	−2.32424	+	10.1832i	−0.107553	+	0.471221i	0.892253	+	0.451535i	$0.149124\pi$
$467$	−2.32424	+	10.1832i	−0.107553	+	0.471221i	−0.999806	+	0.0196852i	$0.993734\pi$
$468$	−0.627821	−	2.75066i	−0.0290210	−	0.127149i
$469$	20.8307	−	26.1209i	0.961874	−	1.20615i
$470$	−9.47601	−	11.8825i	−0.437096	−	0.548101i
$471$	−3.60304	+	15.7860i	−0.166020	+	0.727379i
$472$	−1.05781	−	0.509416i	−0.0486898	−	0.0234478i
$473$	−1.66445	−	0.801556i	−0.0765314	−	0.0368556i
$474$	2.76630	+	12.1199i	0.127060	+	0.556688i
$475$	10.1997	−	4.91190i	0.467993	−	0.225374i
$476$	−12.8340			−0.588246
$477$	7.04440	−	3.39240i	0.322541	−	0.155328i
$478$	−17.6816	−	22.1720i	−0.808737	−	1.01412i
$479$	−8.71517	−	10.9285i	−0.398206	−	0.499335i	0.541793	−	0.840512i	$-0.317746\pi$
$479$	−8.71517	−	10.9285i	−0.398206	−	0.499335i	−0.939999	+	0.341177i	$0.889174\pi$
$480$	4.75135	−	2.28813i	0.216869	−	0.104438i
$481$	1.85024			0.0843637
$482$	24.4154	−	11.7578i	1.11209	−	0.535555i
$483$	−1.94750	−	8.53258i	−0.0886145	−	0.388246i
$484$	−4.75695	−	2.29083i	−0.216225	−	0.104129i
$485$	11.0340	+	5.31367i	0.501026	+	0.241282i
$486$	0.269410	−	1.18036i	0.0122207	−	0.0535424i
$487$	−0.910473	−	1.14170i	−0.0412575	−	0.0517352i	0.760775	−	0.649016i	$-0.224819\pi$
$487$	−0.910473	−	1.14170i	−0.0412575	−	0.0517352i	−0.802032	+	0.597281i	$0.796248\pi$
$488$	−10.4571	+	13.1128i	−0.473371	+	0.593589i
$489$	−3.02036	−	13.2331i	−0.136586	−	0.598420i
$490$	5.47123	−	23.9710i	0.247165	−	1.08290i
$491$	−7.57677	+	9.50097i	−0.341935	+	0.428773i	−0.922831	−	0.385205i	$-0.874131\pi$
$491$	−7.57677	+	9.50097i	−0.341935	+	0.428773i	0.580896	+	0.813978i	$0.302702\pi$
$492$	1.93495			0.0872342
$493$	−25.5564	−	16.1885i	−1.15100	−	0.729091i
$494$	41.0027			1.84480
$495$	1.18439	−	1.48518i	0.0532343	−	0.0667537i
$496$	2.25225	−	9.86774i	0.101129	−	0.443075i
$497$	14.8575	+	65.0951i	0.666451	+	2.91991i
$498$	−1.14845	+	1.44011i	−0.0514633	+	0.0645330i
$499$	−22.4256	−	28.1208i	−1.00391	−	1.25886i	−0.965719	−	0.259589i	$-0.916413\pi$
$499$	−22.4256	−	28.1208i	−1.00391	−	1.25886i	−0.0381883	−	0.999271i	$-0.512159\pi$
$500$	−1.44626	+	6.33648i	−0.0646787	+	0.283376i
$501$	14.7413	+	7.09904i	0.658593	+	0.317162i
$502$	−6.50108	−	3.13075i	−0.290157	−	0.139732i
$503$	3.19420	+	13.9947i	0.142422	+	0.623993i	0.994868	+	0.101178i	$0.0322612\pi$
$503$	3.19420	+	13.9947i	0.142422	+	0.623993i	−0.852446	+	0.522815i	$0.824882\pi$
$504$	−11.8228	+	5.69355i	−0.526628	+	0.253611i
$505$	8.49892			0.378197
$506$	2.35775	−	1.13543i	0.104815	−	0.0504762i
$507$	9.28921	+	11.6483i	0.412549	+	0.517319i
$508$	1.48727	+	1.86498i	0.0659871	+	0.0827452i
$509$	27.9345	−	13.4525i	1.23817	−	0.596273i	0.303857	−	0.952718i	$-0.401725\pi$
$509$	27.9345	−	13.4525i	1.23817	−	0.596273i	0.934316	+	0.356445i	$0.116011\pi$
$510$	−12.2319			−0.541640
$511$	9.79873	−	4.71882i	0.433470	−	0.208748i
$512$	−5.34023	−	23.3971i	−0.236007	−	1.03401i
$513$	−5.77679	−	2.78195i	−0.255051	−	0.122826i
$514$	−16.4412	−	7.91765i	−0.725189	−	0.349232i
$515$	−1.39863	+	6.12779i	−0.0616309	+	0.270023i
$516$	−0.582495	−	0.730426i	−0.0256429	−	0.0321552i
$517$	4.59682	−	5.76423i	0.202168	−	0.253511i
$518$	−0.403629	−	1.76841i	−0.0177344	−	0.0776996i
$519$	0.993276	−	4.35182i	0.0436000	−	0.191024i
$520$	−18.1716	+	22.7865i	−0.796879	+	0.999254i
$521$	−14.9084			−0.653150			−0.326575	−	0.945171i	$-0.605895\pi$
$521$	−14.9084			−0.653150			−0.326575	+	0.945171i	$0.605895\pi$
$522$	−6.47622	−	0.753627i	−0.283456	−	0.0329853i
$523$	−12.9505			−0.566284			−0.283142	−	0.959078i	$-0.591377\pi$
$523$	−12.9505			−0.566284			−0.283142	+	0.959078i	$0.591377\pi$
$524$	−0.00331693	+	0.00415930i	−0.000144901	+	0.000181700i
$525$	1.68036	−	7.36215i	0.0733370	−	0.321310i
$526$	−5.04477	−	22.1026i	−0.219962	−	0.963718i
$527$	13.3963	−	16.7984i	0.583552	−	0.731751i
$528$	−1.74280	−	2.18540i	−0.0758454	−	0.0951072i
$529$	4.18618	−	18.3409i	0.182008	−	0.797429i
$530$	−15.3385	−	7.38662i	−0.666260	−	0.320854i
$531$	−0.344772	−	0.166033i	−0.0149618	−	0.00720524i
$532$	3.25951	+	14.2808i	0.141318	+	0.619153i
$533$	−17.2385	+	8.30162i	−0.746682	+	0.359583i
$534$	21.7256			0.940157
$535$	7.97515	−	3.84063i	0.344796	−	0.166045i
$536$	14.9434	+	18.7385i	0.645457	+	0.809378i
$537$	2.12026	+	2.65872i	0.0914960	+	0.114732i
$538$	−25.2262	+	12.1483i	−1.08758	+	0.523750i
$539$	11.9274			0.513750
$540$	0.865520	−	0.416812i	0.0372461	−	0.0179368i
$541$	−2.41951	−	10.6006i	−0.104023	−	0.455754i	−0.999934	−	0.0115201i	$-0.996333\pi$
$541$	−2.41951	−	10.6006i	−0.104023	−	0.455754i	0.895911	−	0.444234i	$-0.146524\pi$
$542$	23.2856	+	11.2137i	1.00020	+	0.481671i
$543$	−5.96562	−	2.87289i	−0.256009	−	0.123287i
$544$	3.66557	−	16.0599i	0.157160	−	0.688562i
$545$	−16.6903	−	20.9289i	−0.714932	−	0.896497i
$546$	17.0528	−	21.3836i	0.729794	−	0.915133i
$547$	5.14692	+	22.5501i	0.220066	+	0.964174i	0.957427	+	0.288675i	$0.0932147\pi$
$547$	5.14692	+	22.5501i	0.220066	+	0.964174i	−0.737361	+	0.675499i	$0.763928\pi$
$548$	1.45171	−	6.36038i	0.0620142	−	0.271702i
$549$	−3.40827	+	4.27384i	−0.145462	+	0.182403i
$550$	2.25794			0.0962790
$551$	−11.5228	+	32.5489i	−0.490887	+	1.38663i
$552$	6.27846			0.267229
$553$	27.3808	−	34.3345i	1.16435	−	1.46005i
$554$	−2.24198	+	9.82275i	−0.0952526	+	0.417329i
$555$	0.140185	+	0.614191i	0.00595052	+	0.0260709i
$556$	−1.64711	+	2.06541i	−0.0698529	+	0.0875928i
$557$	−26.8909	−	33.7201i	−1.13940	−	1.42877i	−0.887375	−	0.461048i	$-0.847474\pi$
$557$	−26.8909	−	33.7201i	−1.13940	−	1.42877i	−0.252029	−	0.967720i	$-0.581098\pi$
$558$	1.03041	−	4.51454i	0.0436209	−	0.191116i
$559$	8.32325	+	4.00826i	0.352036	+	0.169532i
$560$	18.3393	+	8.83176i	0.774979	+	0.373210i
$561$	−1.32038	−	5.78496i	−0.0557464	−	0.244241i
$562$	−31.5467	+	15.1921i	−1.33072	+	0.640840i
$563$	34.1036			1.43729			0.718647	−	0.695375i	$-0.244762\pi$
$563$	34.1036			1.43729			0.718647	+	0.695375i	$0.244762\pi$
$564$	3.35924	−	1.61772i	0.141449	−	0.0681185i
$565$	−7.11219	−	8.91841i	−0.299212	−	0.375200i
$566$	−22.6309	−	28.3783i	−0.951250	−	1.19283i
$567$	−3.85338	+	1.85569i	−0.161827	+	0.0779317i
$568$	−47.8984			−2.00977
$569$	17.1914	−	8.27893i	0.720700	−	0.347071i	−0.0373190	−	0.999303i	$-0.511882\pi$
$569$	17.1914	−	8.27893i	0.720700	−	0.347071i	0.758019	+	0.652233i	$0.226167\pi$
$570$	3.10660	+	13.6109i	0.130121	+	0.570098i
$571$	5.91613	+	2.84906i	0.247582	+	0.119229i	0.553560	−	0.832809i	$-0.313269\pi$
$571$	5.91613	+	2.84906i	0.247582	+	0.119229i	−0.305978	+	0.952039i	$0.598983\pi$
$572$	−2.68500	−	1.29303i	−0.112266	−	0.0540642i
$573$	−3.92072	+	17.1778i	−0.163791	+	0.717613i
$574$	11.6950	+	14.6651i	0.488141	+	0.612110i
$575$	−2.25271	+	2.82480i	−0.0939444	+	0.117803i
$576$	−1.96773	−	8.62121i	−0.0819890	−	0.359217i
$577$	4.57508	−	20.0447i	0.190463	−	0.834474i	−0.785903	−	0.618350i	$-0.787801\pi$
$577$	4.57508	−	20.0447i	0.190463	−	0.834474i	0.976366	−	0.216124i	$-0.0693415\pi$
$578$	−10.9897	+	13.7807i	−0.457112	+	0.573200i
$579$	−13.3986			−0.556828
$580$	−2.73636	−	4.39036i	−0.113621	−	0.182300i
$581$	6.50687			0.269951
$582$	5.14043	−	6.44589i	0.213078	−	0.267191i
$583$	1.83770	−	8.05150i	0.0761098	−	0.333459i
$584$	1.73611	+	7.60637i	0.0718406	+	0.314754i
$585$	−5.92266	+	7.42678i	−0.244872	+	0.307059i
$586$	−6.60818	−	8.28640i	−0.272981	−	0.342308i
$587$	2.15654	−	9.44844i	0.0890101	−	0.389979i	−0.910725	−	0.413014i	$-0.864476\pi$
$587$	2.15654	−	9.44844i	0.0890101	−	0.389979i	0.999735	+	0.0230356i	$0.00733309\pi$
$588$	5.43448	+	2.61711i	0.224114	+	0.107928i
$589$	−22.0945	−	10.6402i	−0.910389	−	0.438420i
$590$	0.185409	+	0.812330i	0.00763317	+	0.0334431i
$591$	7.39223	−	3.55991i	0.304076	−	0.146435i
$592$	0.927007			0.0380997
$593$	11.8757	−	5.71902i	0.487675	−	0.234852i	−0.173854	−	0.984771i	$-0.555622\pi$
$593$	11.8757	−	5.71902i	0.487675	−	0.234852i	0.661529	+	0.749919i	$0.269908\pi$
$594$	−0.797338	−	0.999830i	−0.0327152	−	0.0410235i
$595$	26.9410	+	33.7830i	1.10447	+	1.38497i
$596$	6.74441	−	3.24794i	0.276262	−	0.133041i
$597$	24.4954			1.00253
$598$	−11.7902	+	5.67786i	−0.482137	+	0.232185i
$599$	3.21314	+	14.0777i	0.131285	+	0.575198i	0.997185	+	0.0749808i	$0.0238895\pi$
$599$	3.21314	+	14.0777i	0.131285	+	0.575198i	−0.865900	+	0.500218i	$0.833253\pi$
$600$	4.88075	+	2.35045i	0.199256	+	0.0959566i
$601$	−4.40415	−	2.12093i	−0.179649	−	0.0865143i	0.341898	−	0.939737i	$-0.388930\pi$
$601$	−4.40415	−	2.12093i	−0.179649	−	0.0865143i	−0.521546	+	0.853223i	$0.674645\pi$
$602$	2.01529	−	8.82955i	0.0821369	−	0.359865i
$603$	4.87049	+	6.10740i	0.198342	+	0.248713i
$604$	−0.977124	+	1.22527i	−0.0397586	+	0.0498557i
$605$	3.95560	+	17.3306i	0.160818	+	0.704590i
$606$	1.27316	−	5.57808i	0.0517186	−	0.226594i
$607$	−7.82778	+	9.81573i	−0.317720	+	0.398408i	−0.914888	−	0.403708i	$-0.867721\pi$
$607$	−7.82778	+	9.81573i	−0.317720	+	0.398408i	0.597168	+	0.802116i	$0.296293\pi$
$608$	−18.8014			−0.762496
$609$	12.1825	+	19.5463i	0.493661	+	0.792056i
$610$	11.9026			0.481923
$611$	−22.9869	+	28.8246i	−0.929950	+	1.16612i
$612$	0.667730	−	2.92552i	0.0269914	−	0.118257i
$613$	−0.778292	−	3.40992i	−0.0314349	−	0.137725i	0.956775	−	0.290828i	$-0.0939307\pi$
$613$	−0.778292	−	3.40992i	−0.0314349	−	0.137725i	−0.988210	+	0.153102i	$0.951074\pi$
$614$	25.6023	−	32.1042i	1.03322	−	1.29562i
$615$	−4.06182	−	5.09337i	−0.163789	−	0.205384i
$616$	−3.08426	+	13.5130i	−0.124268	+	0.544455i
$617$	24.5871	+	11.8405i	0.989838	+	0.476681i	0.857478	−	0.514521i	$-0.172030\pi$
$617$	24.5871	+	11.8405i	0.989838	+	0.476681i	0.132360	+	0.991202i	$0.457745\pi$
$618$	3.81232	+	1.83592i	0.153354	+	0.0738514i
$619$	5.68340	+	24.9006i	0.228435	+	1.00084i	0.950916	+	0.309449i	$0.100145\pi$
$619$	5.68340	+	24.9006i	0.228435	+	1.00084i	−0.722481	+	0.691391i	$0.756998\pi$
$620$	3.31036	−	1.59419i	0.132947	−	0.0640240i
$621$	2.04633			0.0821164
$622$	8.86372	−	4.26854i	0.355403	−	0.171153i
$623$	−47.8508	−	60.0030i	−1.91710	−	2.40397i
$624$	8.71503	+	10.9283i	0.348880	+	0.437482i
$625$	11.7616	−	5.66409i	0.470464	−	0.226564i
$626$	−3.05995			−0.122300
$627$	−6.10178	+	2.93846i	−0.243682	+	0.117351i
$628$	1.92461	+	8.43225i	0.0768002	+	0.336484i
$629$	1.77298	+	0.853821i	0.0706933	+	0.0340441i
$630$	8.39035	+	4.04058i	0.334279	+	0.160980i
$631$	−4.62745	+	20.2742i	−0.184216	+	0.807102i	0.795378	+	0.606114i	$0.207272\pi$
$631$	−4.62745	+	20.2742i	−0.184216	+	0.807102i	−0.979594	+	0.200988i	$0.935585\pi$
$632$	19.6423	+	24.6306i	0.781328	+	0.979754i
$633$	−1.37880	+	1.72896i	−0.0548025	+	0.0687201i
$634$	4.48252	+	19.6392i	0.178024	+	0.779973i
$635$	1.78712	−	7.82990i	0.0709198	−	0.310720i
$636$	2.60397	−	3.26528i	0.103254	−	0.129477i
$637$	−59.6442			−2.36319
$638$	−4.88737	+	4.85185i	−0.193493	+	0.192086i
$639$	−15.6115			−0.617580
$640$	−5.42895	+	6.80769i	−0.214598	+	0.269097i
$641$	3.14628	−	13.7848i	0.124271	−	0.544466i	−0.874013	−	0.485903i	$-0.838491\pi$
$641$	3.14628	−	13.7848i	0.124271	−	0.544466i	0.998284	−	0.0585631i	$-0.0186519\pi$
$642$	−1.32601	−	5.80965i	−0.0523336	−	0.229288i
$643$	22.1303	−	27.7505i	0.872734	−	1.09437i	−0.122066	−	0.992522i	$-0.538952\pi$
$643$	22.1303	−	27.7505i	0.872734	−	1.09437i	0.994800	−	0.101852i	$-0.0324768\pi$
$644$	−2.91481	−	3.65505i	−0.114859	−	0.144029i
$645$	−0.699933	+	3.06661i	−0.0275598	+	0.120747i
$646$	39.2905	+	18.9213i	1.54586	+	0.744448i
$647$	18.0758	+	8.70484i	0.710633	+	0.342223i	0.754034	−	0.656835i	$-0.228105\pi$
$647$	18.0758	+	8.70484i	0.710633	+	0.342223i	−0.0434016	+	0.999058i	$0.513819\pi$
$648$	−0.682729	−	2.99123i	−0.0268201	−	0.117507i
$649$	−0.364168	+	0.175374i	−0.0142948	+	0.00688404i
$650$	−11.2911			−0.442872
$651$	−14.7380	+	7.09747i	−0.577630	+	0.278172i
$652$	−4.52054	−	5.66858i	−0.177038	−	0.221999i
$653$	8.32587	+	10.4403i	0.325816	+	0.408561i	0.917580	−	0.397550i	$-0.130140\pi$
$653$	8.32587	+	10.4403i	0.325816	+	0.408561i	−0.591764	+	0.806111i	$0.701568\pi$
$654$	−16.2365	+	7.81907i	−0.634896	+	0.305750i
$655$	0.0179114			0.000699856
$656$	−8.63682	+	4.15927i	−0.337211	+	0.162392i
$657$	0.565847	+	2.47914i	0.0220758	+	0.0967203i
$658$	32.5644	+	15.6822i	1.26949	+	0.611356i
$659$	−10.2522	−	4.93720i	−0.399369	−	0.192326i	0.223408	−	0.974725i	$-0.428282\pi$
$659$	−10.2522	−	4.93720i	−0.399369	−	0.192326i	−0.622778	+	0.782399i	$0.713996\pi$
$660$	0.225792	−	0.989259i	0.00878893	−	0.0385068i
$661$	−23.0877	−	28.9510i	−0.898007	−	1.12606i	−0.991456	−	0.130441i	$-0.958361\pi$
$661$	−23.0877	−	28.9510i	−0.898007	−	1.12606i	0.0934495	−	0.995624i	$-0.470211\pi$
$662$	−9.75940	+	12.2379i	−0.379310	+	0.475640i
$663$	6.60269	+	28.9283i	0.256427	+	1.12348i
$664$	−1.03870	+	4.55082i	−0.0403092	+	0.176606i
$665$	30.7491	−	38.5582i	1.19240	−	1.49522i
$666$	0.424110			0.0164339
$667$	−1.19388	−	10.9550i	−0.0462271	−	0.424178i
$668$	8.73974			0.338151
$669$	1.68615	−	2.11436i	0.0651903	−	0.0817460i
$670$	3.78488	−	16.5826i	0.146223	−	0.640643i
$671$	1.28483	+	5.62921i	0.0496003	+	0.217313i
$672$	−7.81941	+	9.80523i	−0.301640	+	0.378245i
$673$	23.2210	+	29.1182i	0.895103	+	1.12242i	0.991888	+	0.127119i	$0.0405729\pi$
$673$	23.2210	+	29.1182i	0.895103	+	1.12242i	−0.0967842	+	0.995305i	$0.530856\pi$
$674$	−1.49866	+	6.56604i	−0.0577261	+	0.252915i
$675$	1.59078	+	0.766078i	0.0612291	+	0.0294864i
$676$	7.17021	+	3.45299i	0.275777	+	0.132807i
$677$	−9.99898	−	43.8084i	−0.384292	−	1.68369i	−0.683856	−	0.729617i	$-0.739698\pi$
$677$	−9.99898	−	43.8084i	−0.384292	−	1.68369i	0.299564	−	0.954076i	$-0.403159\pi$
$678$	−6.91882	+	3.33193i	−0.265716	+	0.127962i
$679$	−29.1245			−1.11770
$680$	−27.9280	+	13.4494i	−1.07099	+	0.515761i
$681$	8.99231	+	11.2760i	0.344586	+	0.432097i
$682$	−3.04958	−	3.82406i	−0.116775	−	0.146431i
$683$	−20.3639	+	9.80672i	−0.779201	+	0.375244i	−0.780821	−	0.624755i	$-0.785199\pi$
$683$	−20.3639	+	9.80672i	−0.779201	+	0.375244i	0.00161933	+	0.999999i	$0.499485\pi$
$684$	−3.42491			−0.130955
$685$	−19.7898	+	9.53029i	−0.756131	+	0.364134i
$686$	4.94560	+	21.6681i	0.188824	+	0.827291i
$687$	−23.1969	−	11.1711i	−0.885019	−	0.426202i
$688$	4.17011	+	2.00822i	0.158984	+	0.0765626i
$689$	−9.18962	+	40.2623i	−0.350097	+	1.53387i
$690$	−2.77807	−	3.48359i	−0.105759	−	0.132618i
$691$	−24.2367	+	30.3919i	−0.922009	+	1.15616i	0.0653818	+	0.997860i	$0.479173\pi$
$691$	−24.2367	+	30.3919i	−0.922009	+	1.15616i	−0.987391	+	0.158302i	$0.949398\pi$
$692$	−0.530569	−	2.32458i	−0.0201692	−	0.0883671i
$693$	−1.00525	+	4.40428i	−0.0381862	+	0.167305i
$694$	6.63294	−	8.31744i	0.251783	−	0.315726i
$695$	8.89436			0.337382
$696$	−15.6151	+	5.40012i	−0.591890	+	0.204691i
$697$	−20.3495			−0.770794
$698$	−11.4697	+	14.3826i	−0.434135	+	0.544388i
$699$	5.02985	−	22.0372i	0.190246	−	0.833524i
$700$	−0.897584	−	3.93257i	−0.0339255	−	0.148637i
$701$	−24.5921	+	30.8375i	−0.928831	+	1.16472i	0.0572342	+	0.998361i	$0.481772\pi$
$701$	−24.5921	+	30.8375i	−0.928831	+	1.16472i	−0.986066	+	0.166357i	$0.946800\pi$
$702$	3.98717	+	4.99975i	0.150486	+	0.188704i
$703$	0.499785	−	2.18970i	0.0188498	−	0.0825862i
$704$	−8.41541	−	4.05265i	−0.317168	−	0.152740i
$705$	−11.3100	−	5.44661i	−0.425960	−	0.205131i
$706$	−3.33172	−	14.5972i	−0.125391	−	0.549373i
$707$	−18.2100	+	8.76949i	−0.684859	+	0.329811i
$708$	−0.204406			−0.00768207
$709$	3.67038	−	1.76756i	0.137844	−	0.0663823i	−0.363690	−	0.931520i	$-0.618483\pi$
$709$	3.67038	−	1.76756i	0.137844	−	0.0663823i	0.501534	+	0.865138i	$0.332769\pi$
$710$	21.1939	+	26.5763i	0.795393	+	0.997391i
$711$	6.40198	+	8.02783i	0.240093	+	0.301067i
$712$	49.6038	−	23.8879i	1.85898	−	0.895238i
$713$	7.82661			0.293109
$714$	26.2085	−	12.6214i	0.980829	−	0.472343i
$715$	2.23269	+	9.78204i	0.0834978	+	0.365828i
$716$	1.63660	+	0.788144i	0.0611625	+	0.0294543i
$717$	−21.1037	−	10.1630i	−0.788132	−	0.379544i
$718$	−4.31497	+	18.9051i	−0.161033	+	0.705533i
$719$	−11.4911	−	14.4094i	−0.428546	−	0.537380i	0.519938	−	0.854204i	$-0.325955\pi$
$719$	−11.4911	−	14.4094i	−0.428546	−	0.537380i	−0.948484	+	0.316824i	$0.897384\pi$
$720$	−2.96737	+	3.72096i	−0.110587	+	0.138672i
$721$	−3.32613	−	14.5727i	−0.123872	−	0.542717i
$722$	5.95680	−	26.0985i	0.221689	−	0.971284i
$723$	13.9554	−	17.4995i	0.519005	−	0.650812i
$724$	−3.53686			−0.131446
$725$	3.17308	−	8.96313i	0.117845	−	0.332882i
$726$	11.9671			0.444142
$727$	10.9828	−	13.7720i	0.407330	−	0.510775i	−0.535279	−	0.844675i	$-0.679793\pi$
$727$	10.9828	−	13.7720i	0.407330	−	0.510775i	0.942608	+	0.333900i	$0.108365\pi$
$728$	15.4231	−	67.5732i	0.571619	−	2.50443i
$729$	−0.222521	−	0.974928i	−0.00824152	−	0.0361084i
$730$	3.45219	−	4.32891i	0.127771	−	0.160220i
$731$	6.12601	+	7.68177i	0.226579	+	0.284121i
$732$	−0.649753	+	2.84675i	−0.0240156	+	0.105219i
$733$	7.41249	+	3.56967i	0.273786	+	0.131849i	0.565739	−	0.824584i	$-0.308591\pi$
$733$	7.41249	+	3.56967i	0.273786	+	0.131849i	−0.291953	+	0.956433i	$0.594305\pi$
$734$	−24.2649	−	11.6854i	−0.895634	−	0.431315i
$735$	−4.51899	−	19.7990i	−0.166686	−	0.730297i
$736$	5.40627	−	2.60352i	0.199278	−	0.0959671i
$737$	8.25113			0.303934
$738$	−3.95139	+	1.90289i	−0.145453	+	0.0700463i
$739$	22.3350	+	28.0072i	0.821607	+	1.03026i	0.998936	+	0.0461112i	$0.0146829\pi$
$739$	22.3350	+	28.0072i	0.821607	+	1.03026i	−0.177329	+	0.984152i	$0.556746\pi$
$740$	0.209813	+	0.263097i	0.00771288	+	0.00967165i
$741$	30.5126	−	14.6941i	1.12091	−	0.539800i
$742$	40.4864			1.48630
$743$	−8.37415	+	4.03278i	−0.307218	+	0.147948i	−0.581140	−	0.813803i	$-0.697393\pi$
$743$	−8.37415	+	4.03278i	−0.307218	+	0.147948i	0.273922	+	0.961752i	$0.411679\pi$
$744$	−2.61124	−	11.4406i	−0.0957326	−	0.419432i
$745$	−22.7073	−	10.9353i	−0.831933	−	0.400638i
$746$	7.55969	+	3.64056i	0.276780	+	0.133290i
$747$	−0.338541	+	1.48324i	−0.0123866	+	0.0542691i
$748$	−1.97619	−	2.47807i	−0.0722568	−	0.0906071i
$749$	−13.1249	+	16.4581i	−0.479573	+	0.601366i
$750$	−3.27806	−	14.3621i	−0.119698	−	0.524431i
$751$	9.98479	−	43.7462i	0.364350	−	1.59632i	−0.377667	−	0.925941i	$-0.623274\pi$
$751$	9.98479	−	43.7462i	0.364350	−	1.59632i	0.742017	−	0.670381i	$-0.233869\pi$
$752$	−11.5169	+	14.4417i	−0.419977	+	0.526635i
$753$	−5.95981			−0.217188
$754$	24.4398	−	24.2622i	0.890045	−	0.883576i
$755$	5.27646			0.192030
$756$	−1.42441	+	1.78615i	−0.0518052	+	0.0649616i
$757$	−4.81041	+	21.0758i	−0.174837	+	0.766012i	0.809125	+	0.587636i	$0.199941\pi$
$757$	−4.81041	+	21.0758i	−0.174837	+	0.766012i	−0.983962	+	0.178376i	$0.942916\pi$
$758$	−2.09830	−	9.19323i	−0.0762135	−	0.333913i
$759$	1.34764	−	1.68989i	0.0489163	−	0.0613392i
$760$	22.0586	+	27.6606i	0.800150	+	1.00336i
$761$	8.76193	−	38.3885i	0.317620	−	1.39158i	−0.524094	−	0.851660i	$-0.675596\pi$
$761$	8.76193	−	38.3885i	0.317620	−	1.39158i	0.841714	−	0.539923i	$-0.181547\pi$
$762$	−4.87126	−	2.34588i	−0.176467	−	0.0849822i
$763$	57.3563	+	27.6213i	2.07644	+	0.999959i
$764$	2.09430	+	9.17572i	0.0757691	+	0.331966i
$765$	−9.10253	+	4.38355i	−0.329103	+	0.158488i
$766$	−30.8279			−1.11386
$767$	1.82106	−	0.876976i	0.0657547	−	0.0316658i
$768$	−7.37214	−	9.24437i	−0.266019	−	0.333577i
$769$	2.67820	+	3.35836i	0.0965784	+	0.121105i	0.827772	−	0.561064i	$-0.189608\pi$
$769$	2.67820	+	3.35836i	0.0965784	+	0.121105i	−0.731194	+	0.682170i	$0.761037\pi$
$770$	8.86237	−	4.26789i	0.319378	−	0.153804i
$771$	−15.0723			−0.542816
$772$	−6.44826	+	3.10532i	−0.232078	+	0.111763i
$773$	−6.20838	−	27.2007i	−0.223300	−	0.978341i	−0.954975	−	0.296687i	$-0.904118\pi$
$773$	−6.20838	−	27.2007i	−0.223300	−	0.978341i	0.731675	−	0.681654i	$-0.238739\pi$
$774$	1.90785	+	0.918771i	0.0685761	+	0.0330245i
$775$	6.08426	+	2.93002i	0.218553	+	0.105250i
$776$	4.64917	−	20.3693i	0.166895	−	0.731216i
$777$	−0.934109	−	1.17134i	−0.0335110	−	0.0420214i
$778$	−8.29137	+	10.3970i	−0.297260	+	0.372752i
$779$	5.16826	+	22.6436i	0.185172	+	0.811292i
$780$	−1.12910	+	4.94689i	−0.0404281	+	0.177127i
$781$	−10.2812	+	12.8922i	−0.367890	+	0.461319i
$782$	−13.9180			−0.497706
$783$	−5.08942	+	1.76005i	−0.181881	+	0.0628992i
$784$	−29.8829			−1.06725
$785$	18.1561	−	22.7670i	0.648019	−	0.812591i
$786$	0.00268317	−	0.0117557i	9.57056e−5	−	0.000419314i
$787$	1.31441	+	5.75879i	0.0468536	+	0.205279i	0.992937	−	0.118645i	$-0.0378550\pi$
$787$	1.31441	+	5.75879i	0.0468536	+	0.205279i	−0.946083	+	0.323924i	$0.894998\pi$
$788$	2.73255	−	3.42650i	0.0973429	−	0.122064i
$789$	−11.6750	−	14.6400i	−0.415641	−	0.521197i
$790$	4.97501	−	21.7969i	0.177003	−	0.775500i
$791$	24.4411	+	11.7702i	0.869027	+	0.418501i
$792$	−2.91983	−	1.40611i	−0.103752	−	0.0499641i
$793$	−6.42493	−	28.1494i	−0.228156	−	0.999616i
$794$	5.56369	−	2.67933i	0.197448	−	0.0950860i
$795$	−14.0614			−0.498707
$796$	11.7887	−	5.67715i	0.417840	−	0.201221i
$797$	−4.73789	−	5.94113i	−0.167825	−	0.210446i	0.690806	−	0.723040i	$-0.257256\pi$
$797$	−4.73789	−	5.94113i	−0.167825	−	0.210446i	−0.858631	+	0.512595i	$0.828684\pi$
$798$	−20.7005	−	25.9576i	−0.732790	−	0.918890i
$799$	−35.3286	+	17.0133i	−1.24983	+	0.601888i
$800$	5.17741			0.183049
$801$	16.1673	−	7.78576i	0.571244	−	0.275096i
$802$	−5.26484	−	23.0668i	−0.185908	−	0.814516i
$803$	2.41996	+	1.16539i	0.0853984	+	0.0411257i
$804$	3.75946	+	1.81046i	0.132586	+	0.0638500i
$805$	−3.50246	+	15.3453i	−0.123446	+	0.540850i
$806$	15.2498	+	19.1226i	0.537150	+	0.673564i
$807$	−14.4188	+	18.0806i	−0.507565	+	0.636466i
$808$	−3.22639	−	14.1357i	−0.113504	−	0.497294i
$809$	2.19189	−	9.60330i	0.0770628	−	0.337634i	−0.921669	−	0.387977i	$-0.873174\pi$
$809$	2.19189	−	9.60330i	0.0770628	−	0.337634i	0.998732	+	0.0503425i	$0.0160313\pi$
$810$	−1.35759	+	1.70236i	−0.0477007	+	0.0598148i
$811$	46.3250			1.62669			0.813346	−	0.581780i	$-0.197644\pi$
$811$	46.3250			1.62669			0.813346	+	0.581780i	$0.197644\pi$
$812$	10.3931	+	6.58343i	0.364727	+	0.231033i
$813$	21.3469			0.748667
$814$	0.279305	−	0.350237i	0.00978963	−	0.0122758i
$815$	−5.43193	+	23.7988i	−0.190272	+	0.833637i
$816$	3.30808	+	14.4936i	0.115806	+	0.507379i
$817$	6.99192	−	8.76759i	0.244616	−	0.306739i
$818$	13.5306	+	16.9668i	0.473087	+	0.593232i
$819$	5.02684	−	22.0240i	0.175652	−	0.769582i
$820$	−3.13526	−	1.50986i	−0.109488	−	0.0527267i
$821$	−16.2673	−	7.83393i	−0.567733	−	0.273406i	0.127919	−	0.991785i	$-0.459170\pi$
$821$	−16.2673	−	7.83393i	−0.567733	−	0.273406i	−0.695652	+	0.718379i	$0.744885\pi$
$822$	3.29042	+	14.4163i	0.114767	+	0.502826i
$823$	30.3038	−	14.5936i	1.05633	−	0.508700i	0.176650	−	0.984274i	$-0.443474\pi$
$823$	30.3038	−	14.5936i	1.05633	−	0.508700i	0.879676	+	0.475574i	$0.157760\pi$
$824$	10.7229			0.373551
$825$	1.68027	−	0.809176i	0.0584996	−	0.0281719i
$826$	−1.23545	−	1.54921i	−0.0429870	−	0.0539039i
$827$	25.6465	+	32.1597i	0.891817	+	1.11830i	0.992361	+	0.123370i	$0.0393702\pi$
$827$	25.6465	+	32.1597i	0.891817	+	1.11830i	−0.100544	+	0.994933i	$0.532058\pi$
$828$	0.984822	−	0.474265i	0.0342249	−	0.0164819i
$829$	7.95542			0.276303			0.138152	−	0.990411i	$-0.455884\pi$
$829$	7.95542			0.276303			0.138152	+	0.990411i	$0.455884\pi$
$830$	2.98461	−	1.43731i	0.103597	−	0.0498899i
$831$	1.85178	+	8.11316i	0.0642374	+	0.281442i
$832$	42.0821	+	20.2657i	1.45894	+	0.702586i
$833$	−57.1536	−	27.5237i	−1.98025	−	0.953640i
$834$	1.33240	−	5.83762i	0.0461372	−	0.202140i
$835$	−18.3464	−	23.0056i	−0.634903	−	0.796143i
$836$	−2.25553	+	2.82834i	−0.0780091	+	0.0978203i
$837$	−0.851077	−	3.72881i	−0.0294175	−	0.128887i
$838$	1.00711	−	4.41244i	0.0347901	−	0.152425i
$839$	−7.05968	+	8.85256i	−0.243727	+	0.305624i	−0.888616	−	0.458652i	$-0.848332\pi$
$839$	−7.05968	+	8.85256i	−0.243727	+	0.305624i	0.644889	+	0.764277i	$0.276904\pi$
$840$	23.5996			0.814263
$841$	12.3917	+	26.2192i	0.427299	+	0.904110i
$842$	−10.0342			−0.345801
$843$	−18.0315	+	22.6107i	−0.621036	+	0.778755i
$844$	−0.262855	+	1.15164i	−0.00904784	+	0.0396412i
$845$	−5.96232	−	26.1226i	−0.205110	−	0.898646i
$846$	−5.26903	+	6.60716i	−0.181153	+	0.227159i
$847$	−26.3577	−	33.0516i	−0.905663	−	1.13567i
$848$	−4.60418	+	20.1722i	−0.158108	+	0.692717i
$849$	−27.0110	−	13.0078i	−0.927014	−	0.446426i
$850$	−10.8196	−	5.21043i	−0.371108	−	0.178716i
$851$	0.159508	+	0.698850i	0.00546786	+	0.0239563i
$852$	−7.51322	+	3.61817i	−0.257399	+	0.123957i
$853$	14.5146			0.496971			0.248486	−	0.968636i	$-0.420067\pi$
$853$	14.5146			0.496971			0.248486	+	0.968636i	$0.420067\pi$
$854$	−25.5029	+	12.2816i	−0.872692	+	0.420266i
$855$	7.18953	+	9.01539i	0.245877	+	0.308320i
$856$	−9.41545	−	11.8066i	−0.321813	−	0.403541i
$857$	9.65562	−	4.64990i	0.329830	−	0.158838i	−0.261638	−	0.965166i	$-0.584263\pi$
$857$	9.65562	−	4.64990i	0.329830	−	0.158838i	0.591468	+	0.806328i	$0.298549\pi$
$858$	6.75469			0.230601
$859$	−14.1577	+	6.81799i	−0.483055	+	0.232627i	−0.659530	−	0.751678i	$-0.729245\pi$
$859$	−14.1577	+	6.81799i	−0.483055	+	0.232627i	0.176475	+	0.984305i	$0.443530\pi$
$860$	0.373877	+	1.63806i	0.0127491	+	0.0558575i
$861$	13.9585	+	6.72206i	0.475705	+	0.229087i
$862$	20.8667	+	10.0489i	0.710724	+	0.342267i
$863$	3.20755	−	14.0532i	0.109186	−	0.478377i	−0.890538	−	0.454908i	$-0.849672\pi$
$863$	3.20755	−	14.0532i	0.109186	−	0.478377i	0.999725	−	0.0234684i	$-0.00747089\pi$
$864$	−1.82828	−	2.29259i	−0.0621992	−	0.0779954i
$865$	−5.00522	+	6.27635i	−0.170183	+	0.213402i
$866$	−4.35122	−	19.0639i	−0.147860	−	0.647818i
$867$	−3.23955	+	14.1934i	−0.110021	+	0.482033i
$868$	−5.44794	+	6.83150i	−0.184915	+	0.231876i
$869$	10.8456			0.367913
$870$	9.90557	+	6.27460i	0.335830	+	0.212729i
$871$	−41.2606			−1.39806
$872$	−28.4738	+	35.7050i	−0.964245	+	1.20912i
$873$	1.51530	−	6.63895i	0.0512850	−	0.224694i
$874$	3.53481	+	15.4870i	0.119567	+	0.523856i
$875$	−32.4463	+	40.6863i	−1.09688	+	1.37545i
$876$	0.846895	+	1.06197i	0.0286139	+	0.0358807i
$877$	−3.02248	+	13.2424i	−0.102062	+	0.447163i	0.897914	+	0.440172i	$0.145082\pi$
$877$	−3.02248	+	13.2424i	−0.102062	+	0.447163i	−0.999976	+	0.00699099i	$0.997775\pi$
$878$	3.23794	+	1.55931i	0.109275	+	0.0526242i
$879$	−7.88714	−	3.79824i	−0.266026	−	0.128112i
$880$	1.11862	+	4.90100i	0.0377087	+	0.165213i
$881$	−19.2804	+	9.28496i	−0.649574	+	0.312818i	−0.729498	−	0.683983i	$-0.760246\pi$
$881$	−19.2804	+	9.28496i	−0.649574	+	0.312818i	0.0799246	+	0.996801i	$0.474532\pi$
$882$	−13.6716			−0.460346
$883$	10.0207	−	4.82569i	0.337222	−	0.162397i	−0.257607	−	0.966250i	$-0.582934\pi$
$883$	10.0207	−	4.82569i	0.337222	−	0.162397i	0.594829	+	0.803852i	$0.297220\pi$
$884$	9.88216	+	12.3918i	0.332373	+	0.416782i
$885$	0.429088	+	0.538059i	0.0144236	+	0.0180867i
$886$	11.4444	−	5.51135i	0.384483	−	0.185157i
$887$	−1.53319			−0.0514795			−0.0257397	−	0.999669i	$-0.508194\pi$
$887$	−1.53319			−0.0514795			−0.0257397	+	0.999669i	$0.508194\pi$
$888$	0.968329	−	0.466323i	0.0324950	−	0.0156488i
$889$	4.25003	+	18.6206i	0.142541	+	0.624514i
$890$	−35.2027	−	16.9527i	−1.18000	−	0.568256i
$891$	−0.951656	−	0.458293i	−0.0318817	−	0.0153534i
$892$	0.321447	−	1.40835i	0.0107629	−	0.0471551i
$893$	27.9039	+	34.9903i	0.933767	+	1.17091i
$894$	−10.5787	+	13.2653i	−0.353806	+	0.443659i
$895$	−1.36090	−	5.96248i	−0.0454898	−	0.199304i
$896$	4.60781	−	20.1881i	0.153936	−	0.674438i
$897$	−6.73903	+	8.45047i	−0.225010	+	0.282153i
$898$	5.33110			0.177901
$899$	−19.4655	+	6.73169i	−0.649212	+	0.224514i
$900$	0.943132			0.0314377
$901$	−27.3855	+	34.3404i	−0.912344	+	1.14404i
$902$	−1.03082	+	4.51630i	−0.0343224	+	0.150376i
$903$	−1.66454	−	7.29282i	−0.0553923	−	0.242690i
$904$	−12.1335	+	15.2149i	−0.403554	+	0.506041i
$905$	7.42454	+	9.31008i	0.246800	+	0.309478i
$906$	0.790427	−	3.46309i	0.0262602	−	0.115053i
$907$	−6.92799	−	3.33634i	−0.230040	−	0.110781i	0.315314	−	0.948988i	$-0.397890\pi$
$907$	−6.92799	−	3.33634i	−0.230040	−	0.110781i	−0.545354	+	0.838206i	$0.683605\pi$
$908$	6.94103	+	3.34262i	0.230346	+	0.110929i
$909$	−1.05157	−	4.60724i	−0.0348785	−	0.152813i
$910$	−44.3172	+	21.3420i	−1.46910	+	0.707481i
$911$	−29.5727			−0.979788			−0.489894	−	0.871782i	$-0.662964\pi$
$911$	−29.5727			−0.979788			−0.489894	+	0.871782i	$0.662964\pi$
$912$	15.2874	−	7.36202i	0.506216	−	0.243781i
$913$	1.00194	+	1.25639i	0.0331592	+	0.0415803i
$914$	−8.56664	−	10.7422i	−0.283359	−	0.355321i
$915$	8.85747	−	4.26553i	0.292819	−	0.141014i
$916$	−13.7529			−0.454408
$917$	−0.0383775	+	0.0184816i	−0.00126734	+	0.000610317i
$918$	1.51346	+	6.63091i	0.0499517	+	0.218853i
$919$	30.8397	+	14.8516i	1.01731	+	0.489910i	0.866778	−	0.498695i	$-0.166187\pi$
$919$	30.8397	+	14.8516i	1.01731	+	0.489910i	0.150532	+	0.988605i	$0.451901\pi$
$920$	−10.1732	−	4.89915i	−0.335400	−	0.161520i
$921$	7.54705	−	33.0658i	0.248684	−	1.08955i
$922$	−14.8779	−	18.6562i	−0.489976	−	0.614411i
$923$	51.4121	−	64.4687i	1.69225	−	2.12201i
$924$	0.536964	+	2.35259i	0.0176648	+	0.0773947i
$925$	−0.137628	+	0.602987i	−0.00452518	+	0.0198261i
$926$	−0.568656	+	0.713072i	−0.0186872	+	0.0234330i
$927$	3.49491			0.114788
$928$	−11.2066	+	11.1252i	−0.367876	+	0.365202i
$929$	48.1477			1.57967			0.789837	−	0.613317i	$-0.210165\pi$
$929$	48.1477			1.57967			0.789837	+	0.613317i	$0.210165\pi$
$930$	−5.19237	+	6.51102i	−0.170264	+	0.213505i
$931$	−16.1110	+	70.5870i	−0.528018	+	2.31340i
$932$	−2.68675	−	11.7714i	−0.0880075	−	0.385586i
$933$	5.06632	−	6.35296i	0.165864	−	0.207987i
$934$	−7.88466	−	9.88705i	−0.257994	−	0.323514i
$935$	−2.37462	+	10.4039i	−0.0776582	+	0.340243i
$936$	14.6009	+	7.03142i	0.477245	+	0.229829i
$937$	12.3770	+	5.96047i	0.404340	+	0.194720i	0.624989	−	0.780633i	$-0.285103\pi$
$937$	12.3770	+	5.96047i	0.404340	+	0.194720i	−0.220649	+	0.975353i	$0.570818\pi$
$938$	9.00097	+	39.4358i	0.293892	+	1.28763i
$939$	−2.27709	+	1.09659i	−0.0743101	+	0.0357859i
$940$	−6.70542			−0.218707
$941$	33.5624	−	16.1628i	1.09410	−	0.526892i	0.202303	−	0.979323i	$-0.435157\pi$
$941$	33.5624	−	16.1628i	1.09410	−	0.526892i	0.891800	+	0.452431i	$0.149443\pi$
$942$	−12.2228	−	15.3269i	−0.398241	−	0.499378i
$943$	−4.62170	−	5.79543i	−0.150503	−	0.188725i
$944$	0.912387	−	0.439382i	0.0296957	−	0.0143007i
$945$	7.69178			0.250214
$946$	2.01518	−	0.970459i	0.0655191	−	0.0315523i
$947$	−3.66686	−	16.0656i	−0.119157	−	0.522061i	−0.998912	−	0.0466336i	$-0.985151\pi$
$947$	−3.66686	−	16.0656i	−0.119157	−	0.522061i	0.879755	−	0.475427i	$-0.157706\pi$
$948$	4.94160	+	2.37975i	0.160496	+	0.0772906i
$949$	−12.1012	−	5.82765i	−0.392823	−	0.189174i
$950$	−3.04993	+	13.3626i	−0.0989529	+	0.433541i
$951$	10.3738	+	13.0083i	0.336394	+	0.421824i
$952$	45.9617	−	57.6342i	1.48963	−	1.86794i
$953$	6.18414	+	27.0945i	0.200324	+	0.877676i	0.970740	+	0.240134i	$0.0771915\pi$
$953$	6.18414	+	27.0945i	0.200324	+	0.877676i	−0.770416	+	0.637542i	$0.779951\pi$
$954$	−2.10644	+	9.22890i	−0.0681984	+	0.298797i
$955$	19.7569	−	24.7744i	0.639319	−	0.801681i
$956$	−12.5118			−0.404662
$957$	−1.89824	+	5.36204i	−0.0613614	+	0.173330i
$958$	16.9235			0.546773
$959$	32.5686	−	40.8397i	1.05170	−	1.31878i
$960$	−3.53884	+	15.5047i	−0.114216	+	0.500412i
$961$	3.64303	+	15.9612i	0.117517	+	0.514876i
$962$	−1.39669	+	1.75140i	−0.0450312	+	0.0564673i
$963$	−3.06876	−	3.84811i	−0.0988896	−	0.124004i
$964$	2.66045	−	11.6562i	0.0856873	−	0.375420i
$965$	21.7102	+	10.4551i	0.698878	+	0.336562i
$966$	9.54686	+	4.59753i	0.307165	+	0.147923i
$967$	11.5683	+	50.6842i	0.372012	+	1.62989i	0.721120	+	0.692810i	$0.243628\pi$
$967$	11.5683	+	50.6842i	0.372012	+	1.62989i	−0.349108	+	0.937083i	$0.613515\pi$
$968$	27.3233	−	13.1582i	0.878206	−	0.422922i
$969$	36.0192			1.15710
$970$	−13.3590	+	6.43336i	−0.428932	+	0.206563i
$971$	16.5938	+	20.8080i	0.532522	+	0.667761i	0.973215	−	0.229896i	$-0.0738387\pi$
$971$	16.5938	+	20.8080i	0.532522	+	0.667761i	−0.440693	+	0.897658i	$0.645267\pi$
$972$	−0.333044	−	0.417624i	−0.0106824	−	0.0133953i
$973$	−19.0573	+	9.17752i	−0.610950	+	0.294218i
$974$	1.76799			0.0566502
$975$	−8.40237	+	4.04637i	−0.269091	+	0.129588i
$976$	−3.21901	−	14.1034i	−0.103038	−	0.451440i
$977$	−54.8653	−	26.4217i	−1.75530	−	0.845306i	−0.975727	−	0.218989i	$-0.929724\pi$
$977$	−54.8653	−	26.4217i	−1.75530	−	0.845306i	−0.779568	−	0.626317i	$-0.784562\pi$
$978$	14.8061	+	7.13025i	0.473447	+	0.228000i
$979$	4.21763	−	18.4787i	0.134796	−	0.590580i
$980$	−6.76352	−	8.48118i	−0.216053	−	0.270921i
$981$	−9.28043	+	11.6373i	−0.296301	+	0.371550i
$982$	−3.27392	−	14.3440i	−0.104475	−	0.457735i
$983$	−10.4431	+	45.7541i	−0.333083	+	1.45933i	0.480044	+	0.877244i	$0.340621\pi$
$983$	−10.4431	+	45.7541i	−0.333083	+	1.45933i	−0.813127	+	0.582086i	$0.802237\pi$
$984$	−6.92953	+	8.68935i	−0.220905	+	0.277006i
$985$	−14.7557			−0.470156
$986$	34.6154	−	11.9709i	1.10238	−	0.381231i
$987$	29.8532			0.950237
$988$	11.2790	−	14.1434i	0.358833	−	0.449962i
$989$	−0.796411	+	3.48930i	−0.0253244	+	0.110953i
$990$	0.511775	+	2.24223i	0.0162653	+	0.0712628i
$991$	31.6674	−	39.7096i	1.00595	−	1.26142i	0.0409484	−	0.999161i	$-0.486962\pi$
$991$	31.6674	−	39.7096i	1.00595	−	1.26142i	0.964998	−	0.262256i	$-0.0844665\pi$
$992$	−6.99262	−	8.76847i	−0.222016	−	0.278399i
$993$	−2.87688	+	12.6044i	−0.0912950	+	0.399990i
$994$	−72.8331	−	35.0746i	−2.31012	−	1.11250i
$995$	−39.6907	−	19.1140i	−1.25828	−	0.605956i
$996$	0.180835	+	0.792292i	0.00572999	+	0.0251047i
$997$	41.2723	−	19.8757i	1.30711	−	0.629469i	0.354893	−	0.934907i	$-0.384517\pi$
$997$	41.2723	−	19.8757i	1.30711	−	0.629469i	0.952212	+	0.305438i	$0.0988029\pi$
$998$	43.5469			1.37845
$999$	0.315606	−	0.151988i	0.00998534	−	0.00480869i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	87.2.g.a.52.1	✓	18
3.2	odd	2		261.2.k.c.226.3		18
29.13	even	14		2523.2.a.o.1.8		9
29.16	even	7		2523.2.a.r.1.2		9
29.24	even	7	inner	87.2.g.a.82.1	yes	18
87.53	odd	14		261.2.k.c.82.3		18
87.71	odd	14		7569.2.a.bm.1.2		9
87.74	odd	14		7569.2.a.bj.1.8		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.g.a.52.1	✓	18	1.1	even	1	trivial
87.2.g.a.82.1	yes	18	29.24	even	7	inner
261.2.k.c.82.3		18	87.53	odd	14
261.2.k.c.226.3		18	3.2	odd	2
2523.2.a.o.1.8		9	29.13	even	14
2523.2.a.r.1.2		9	29.16	even	7
7569.2.a.bj.1.8		9	87.74	odd	14
7569.2.a.bm.1.2		9	87.71	odd	14

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:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	87.g (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.754870 + 0.946578i) q^{2} +(-0.222521 + 0.974928i) q^{3} +(0.118862 + 0.520769i) q^{4} +(1.12131 - 1.40607i) q^{5} +(-0.754870 - 0.946578i) q^{6} +(-0.951706 + 4.16970i) q^{7} +(-2.76431 - 1.33122i) q^{8} +(-0.900969 - 0.433884i) q^{9} +(0.484517 + 2.12281i) q^{10} +(-0.951656 + 0.458293i) q^{11} -0.534161 q^{12} +(4.75885 - 2.29174i) q^{13} +(-3.22853 - 4.04845i) q^{14} +(1.12131 + 1.40607i) q^{15} +(2.38428 - 1.14821i) q^{16} +5.61769 q^{17} +(1.09082 - 0.525311i) q^{18} +(-1.42675 - 6.25099i) q^{19} +(0.865520 + 0.416812i) q^{20} +(-3.85338 - 1.85569i) q^{21} +(0.284567 - 1.24677i) q^{22} +(1.27587 + 1.59988i) q^{23} +(1.91296 - 2.39878i) q^{24} +(0.392890 + 1.72136i) q^{25} +(-1.42300 + 6.23459i) q^{26} +(0.623490 - 0.781831i) q^{27} -2.28457 q^{28} +(-4.54927 - 2.88169i) q^{29} -2.17740 q^{30} +(2.38467 - 2.99028i) q^{31} +(0.652504 - 2.85881i) q^{32} +(-0.235040 - 1.02978i) q^{33} +(-4.24063 + 5.31758i) q^{34} +(4.79575 + 6.01368i) q^{35} +(0.118862 - 0.520769i) q^{36} +(0.315606 + 0.151988i) q^{37} +(6.99406 + 3.36816i) q^{38} +(1.17534 + 5.14950i) q^{39} +(-4.97144 + 2.39412i) q^{40} -3.62240 q^{41} +(4.66536 - 2.24672i) q^{42} +(1.09049 + 1.36743i) q^{43} +(-0.351781 - 0.441119i) q^{44} +(-1.62033 + 0.780312i) q^{45} -2.47753 q^{46} +(-6.28881 + 3.02853i) q^{47} +(0.588868 + 2.58000i) q^{48} +(-10.1739 - 4.89947i) q^{49} +(-1.92598 - 0.927505i) q^{50} +(-1.25005 + 5.47684i) q^{51} +(1.75911 + 2.20586i) q^{52} +(-4.87488 + 6.11290i) q^{53} +(0.269410 + 1.18036i) q^{54} +(-0.422703 + 1.85198i) q^{55} +(8.18161 - 10.2594i) q^{56} +6.41175 q^{57} +(6.16185 - 2.13093i) q^{58} +0.382668 q^{59} +(-0.598958 + 0.751070i) q^{60} +(1.21640 - 5.32939i) q^{61} +(1.03041 + 4.51454i) q^{62} +(2.66662 - 3.34384i) q^{63} +(5.51347 + 6.91367i) q^{64} +(2.11377 - 9.26104i) q^{65} +(1.15219 + 0.554864i) q^{66} +(-7.03806 - 3.38935i) q^{67} +(0.667730 + 2.92552i) q^{68} +(-1.84368 + 0.887869i) q^{69} -9.31258 q^{70} +(14.0654 - 6.77356i) q^{71} +(1.91296 + 2.39878i) q^{72} +(-1.58547 - 1.98811i) q^{73} +(-0.382110 + 0.184015i) q^{74} -1.76563 q^{75} +(3.08574 - 1.48601i) q^{76} +(-1.00525 - 4.40428i) q^{77} +(-5.76163 - 2.77465i) q^{78} +(-9.25113 - 4.45511i) q^{79} +(1.05904 - 4.63996i) q^{80} +(0.623490 + 0.781831i) q^{81} +(2.73445 - 3.42889i) q^{82} +(-0.338541 - 1.48324i) q^{83} +(0.508365 - 2.22729i) q^{84} +(6.29915 - 7.89888i) q^{85} -2.11755 q^{86} +(3.82175 - 3.79397i) q^{87} +3.24076 q^{88} +(-11.1881 + 14.0295i) q^{89} +(0.484517 - 2.12281i) q^{90} +(5.02684 + 22.0240i) q^{91} +(-0.681518 + 0.854597i) q^{92} +(2.38467 + 2.99028i) q^{93} +(1.88050 - 8.23899i) q^{94} +(-10.3892 - 5.00316i) q^{95} +(2.64194 + 1.27229i) q^{96} +(1.51530 + 6.63895i) q^{97} +(12.3177 - 5.93188i) q^{98} +1.05626 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 4 q^{2} - 3 q^{3} - 6 q^{4} - q^{5} - 4 q^{6} - 4 q^{7} - 15 q^{8} - 3 q^{9} - 14 q^{10} + 26 q^{11} + 22 q^{12} + 9 q^{13} - 10 q^{14} - q^{15} - 14 q^{16} + 4 q^{17} - 4 q^{18} - 10 q^{19} - q^{20}+ \cdots - 2 q^{99}+O(q^{100}) \) 18 * q - 4 * q^2 - 3 * q^3 - 6 * q^4 - q^5 - 4 * q^6 - 4 * q^7 - 15 * q^8 - 3 * q^9 - 14 * q^10 + 26 * q^11 + 22 * q^12 + 9 * q^13 - 10 * q^14 - q^15 - 14 * q^16 + 4 * q^17 - 4 * q^18 - 10 * q^19 - q^20 - 4 * q^21 - 8 * q^22 - 8 * q^23 - 8 * q^24 + 16 * q^25 + 5 * q^26 - 3 * q^27 + 80 * q^28 + 8 * q^29 - 12 * q^31 + 9 * q^32 - 16 * q^33 - 22 * q^34 + 9 * q^35 - 6 * q^36 - 16 * q^37 - 32 * q^38 + 2 * q^39 + 33 * q^40 + 24 * q^41 - 3 * q^42 - 31 * q^43 - 52 * q^44 + 6 * q^45 - 44 * q^46 + 5 * q^47 - 47 * q^49 - 7 * q^50 + 11 * q^51 + 80 * q^52 + 5 * q^53 + 3 * q^54 - 17 * q^55 + 45 * q^56 + 18 * q^57 + 54 * q^58 - 32 * q^59 + 27 * q^60 - 28 * q^61 + 69 * q^62 + 3 * q^63 - 75 * q^64 + 22 * q^65 + 34 * q^66 + 6 * q^67 + 38 * q^68 + 20 * q^69 - 12 * q^70 + 46 * q^71 - 8 * q^72 - q^73 - 35 * q^74 + 2 * q^75 - 45 * q^76 - 36 * q^77 - 51 * q^78 - 15 * q^79 - 86 * q^80 - 3 * q^81 + 47 * q^82 - 16 * q^83 - 25 * q^84 + 19 * q^85 + 116 * q^86 + 43 * q^87 + 54 * q^88 - 72 * q^89 - 14 * q^90 - 47 * q^91 - 121 * q^92 - 12 * q^93 - 22 * q^94 - 72 * q^95 - 12 * q^96 + 43 * q^97 + 31 * q^98 - 2 * q^99

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