LMFDB - Embedded newform 387.2.f.c.259.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,2,Mod(130,387)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("387.130");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	387.f (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.09021055822$
Analytic rank:	$0$
Dimension:	$38$
Relative dimension:	$19$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			259.19
Character	$\chi$	$=$	387.259
Dual form			387.2.f.c.130.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.27673 - 2.21136i) q^{2} +(-1.55815 + 0.756424i) q^{3} +(-2.26008 - 3.91458i) q^{4} +(-1.39974 - 2.42442i) q^{5} +(-0.316608 + 4.41138i) q^{6} +(0.0769910 - 0.133352i) q^{7} -6.43513 q^{8} +(1.85565 - 2.35724i) q^{9} +O(q^{10})$	\(q+(1.27673 - 2.21136i) q^{2} +(-1.55815 + 0.756424i) q^{3} +(-2.26008 - 3.91458i) q^{4} +(-1.39974 - 2.42442i) q^{5} +(-0.316608 + 4.41138i) q^{6} +(0.0769910 - 0.133352i) q^{7} -6.43513 q^{8} +(1.85565 - 2.35724i) q^{9} -7.14837 q^{10} +(-1.85795 + 3.21806i) q^{11} +(6.48262 + 4.38991i) q^{12} +(0.642256 + 1.11242i) q^{13} +(-0.196594 - 0.340510i) q^{14} +(4.01489 + 2.71881i) q^{15} +(-3.69577 + 6.40126i) q^{16} +0.563748 q^{17} +(-2.84355 - 7.11307i) q^{18} -6.62305 q^{19} +(-6.32706 + 10.9588i) q^{20} +(-0.0190925 + 0.266020i) q^{21} +(4.74420 + 8.21719i) q^{22} +(-3.02258 - 5.23526i) q^{23} +(10.0269 - 4.86769i) q^{24} +(-1.41855 + 2.45700i) q^{25} +3.27995 q^{26} +(-1.10830 + 5.07658i) q^{27} -0.696024 q^{28} +(4.34197 - 7.52050i) q^{29} +(11.1382 - 5.40719i) q^{30} +(0.846788 + 1.46668i) q^{31} +(3.00187 + 5.19939i) q^{32} +(0.460740 - 6.41961i) q^{33} +(0.719755 - 1.24665i) q^{34} -0.431070 q^{35} +(-13.4215 - 1.93652i) q^{36} +4.07664 q^{37} +(-8.45585 + 14.6460i) q^{38} +(-1.84219 - 1.24750i) q^{39} +(9.00752 + 15.6015i) q^{40} +(-5.55726 - 9.62547i) q^{41} +(0.563891 + 0.381857i) q^{42} +(-0.500000 + 0.866025i) q^{43} +16.7964 q^{44} +(-8.31237 - 1.19935i) q^{45} -15.4361 q^{46} +(3.69248 - 6.39556i) q^{47} +(0.916490 - 12.7697i) q^{48} +(3.48814 + 6.04164i) q^{49} +(3.62222 + 6.27386i) q^{50} +(-0.878403 + 0.426432i) q^{51} +(2.90310 - 5.02832i) q^{52} +2.30102 q^{53} +(9.81116 + 8.93228i) q^{54} +10.4026 q^{55} +(-0.495447 + 0.858140i) q^{56} +(10.3197 - 5.00983i) q^{57} +(-11.0870 - 19.2033i) q^{58} +(-2.94982 - 5.10923i) q^{59} +(1.56901 - 21.8613i) q^{60} +(2.07507 - 3.59412i) q^{61} +4.32448 q^{62} +(-0.171475 - 0.428941i) q^{63} +0.547229 q^{64} +(1.79798 - 3.11420i) q^{65} +(-13.6078 - 9.21497i) q^{66} +(-5.34393 - 9.25596i) q^{67} +(-1.27412 - 2.20683i) q^{68} +(8.66969 + 5.87095i) q^{69} +(-0.550360 + 0.953252i) q^{70} +12.6183 q^{71} +(-11.9413 + 15.1691i) q^{72} +1.47133 q^{73} +(5.20476 - 9.01492i) q^{74} +(0.351777 - 4.90140i) q^{75} +(14.9686 + 25.9264i) q^{76} +(0.286090 + 0.495523i) q^{77} +(-5.11065 + 2.48103i) q^{78} +(-4.16420 + 7.21261i) q^{79} +20.6925 q^{80} +(-2.11315 - 8.74841i) q^{81} -28.3805 q^{82} +(-3.48869 + 6.04259i) q^{83} +(1.08451 - 0.526489i) q^{84} +(-0.789102 - 1.36676i) q^{85} +(1.27673 + 2.21136i) q^{86} +(-1.07674 + 15.0024i) q^{87} +(11.9561 - 20.7086i) q^{88} +15.8842 q^{89} +(-13.2648 + 16.8504i) q^{90} +0.197792 q^{91} +(-13.6625 + 23.6642i) q^{92} +(-2.42885 - 1.64477i) q^{93} +(-9.42859 - 16.3308i) q^{94} +(9.27056 + 16.0571i) q^{95} +(-8.61029 - 5.83073i) q^{96} +(-8.27317 + 14.3296i) q^{97} +17.8137 q^{98} +(4.13804 + 10.3512i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 4 q^{2} - 7 q^{3} - 22 q^{4} - 9 q^{5} - 7 q^{7} + 24 q^{8} - 3 q^{9}+O(q^{10}) $ 38 * q - 4 * q^2 - 7 * q^3 - 22 * q^4 - 9 * q^5 - 7 * q^7 + 24 * q^8 - 3 * q^9	\( 38 q - 4 q^{2} - 7 q^{3} - 22 q^{4} - 9 q^{5} - 7 q^{7} + 24 q^{8} - 3 q^{9} - 14 q^{10} - 5 q^{11} + 11 q^{12} + 5 q^{13} - 17 q^{14} - 5 q^{15} - 24 q^{16} + 42 q^{17} - 23 q^{18} - 8 q^{19} - 21 q^{20} + 20 q^{22} - 22 q^{23} - 14 q^{24} - 10 q^{25} + 34 q^{26} - 4 q^{27} - 2 q^{28} - 30 q^{29} + 63 q^{30} + 5 q^{31} - 48 q^{32} - q^{33} + 6 q^{34} + 106 q^{35} - 20 q^{36} - 2 q^{37} - 21 q^{38} + 25 q^{39} - 16 q^{40} - 29 q^{41} - 47 q^{42} - 19 q^{43} + 58 q^{44} - 37 q^{45} - 32 q^{47} + 45 q^{48} + 10 q^{49} + 11 q^{50} - 53 q^{51} - q^{52} + 76 q^{53} - 41 q^{54} + 4 q^{55} - 46 q^{56} + 23 q^{57} - 30 q^{58} - 30 q^{59} - 87 q^{60} + 10 q^{61} + 50 q^{62} + 21 q^{63} + 28 q^{64} - 8 q^{65} + 91 q^{66} - 3 q^{67} - 47 q^{68} - 40 q^{69} - 56 q^{70} + 42 q^{71} + 3 q^{72} + 16 q^{73} - 28 q^{74} + 19 q^{75} + 36 q^{76} - 49 q^{77} - 105 q^{78} - 4 q^{79} + 140 q^{80} + 77 q^{81} - 8 q^{82} - 29 q^{83} + 145 q^{84} + 4 q^{85} - 4 q^{86} - 24 q^{87} + 47 q^{88} + 108 q^{89} - 8 q^{90} + 8 q^{91} - 12 q^{92} - 4 q^{93} + 23 q^{94} - 33 q^{95} - 147 q^{96} + 4 q^{97} + 98 q^{98} + 85 q^{99}+O(q^{100}) \) 38 * q - 4 * q^2 - 7 * q^3 - 22 * q^4 - 9 * q^5 - 7 * q^7 + 24 * q^8 - 3 * q^9 - 14 * q^10 - 5 * q^11 + 11 * q^12 + 5 * q^13 - 17 * q^14 - 5 * q^15 - 24 * q^16 + 42 * q^17 - 23 * q^18 - 8 * q^19 - 21 * q^20 + 20 * q^22 - 22 * q^23 - 14 * q^24 - 10 * q^25 + 34 * q^26 - 4 * q^27 - 2 * q^28 - 30 * q^29 + 63 * q^30 + 5 * q^31 - 48 * q^32 - q^33 + 6 * q^34 + 106 * q^35 - 20 * q^36 - 2 * q^37 - 21 * q^38 + 25 * q^39 - 16 * q^40 - 29 * q^41 - 47 * q^42 - 19 * q^43 + 58 * q^44 - 37 * q^45 - 32 * q^47 + 45 * q^48 + 10 * q^49 + 11 * q^50 - 53 * q^51 - q^52 + 76 * q^53 - 41 * q^54 + 4 * q^55 - 46 * q^56 + 23 * q^57 - 30 * q^58 - 30 * q^59 - 87 * q^60 + 10 * q^61 + 50 * q^62 + 21 * q^63 + 28 * q^64 - 8 * q^65 + 91 * q^66 - 3 * q^67 - 47 * q^68 - 40 * q^69 - 56 * q^70 + 42 * q^71 + 3 * q^72 + 16 * q^73 - 28 * q^74 + 19 * q^75 + 36 * q^76 - 49 * q^77 - 105 * q^78 - 4 * q^79 + 140 * q^80 + 77 * q^81 - 8 * q^82 - 29 * q^83 + 145 * q^84 + 4 * q^85 - 4 * q^86 - 24 * q^87 + 47 * q^88 + 108 * q^89 - 8 * q^90 + 8 * q^91 - 12 * q^92 - 4 * q^93 + 23 * q^94 - 33 * q^95 - 147 * q^96 + 4 * q^97 + 98 * q^98 + 85 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/387\mathbb{Z}\right)^\times$.

$n$	$46$	$173$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.27673	−	2.21136i	0.902785	−	1.56367i	0.0789211	−	0.996881i	$-0.474852\pi$
$2$	1.27673	−	2.21136i	0.902785	−	1.56367i	0.823864	−	0.566788i	$-0.191814\pi$
$3$	−1.55815	+	0.756424i	−0.899597	+	0.436721i
$3$	−1.55815	+	0.756424i	−0.899597	+	0.436721i
$4$	−2.26008	−	3.91458i	−1.13004	−	1.95729i
$5$	−1.39974	−	2.42442i	−0.625983	−	1.08423i	−0.988350	−	0.152199i	$-0.951364\pi$
$5$	−1.39974	−	2.42442i	−0.625983	−	1.08423i	0.362366	−	0.932036i	$-0.381969\pi$
$6$	−0.316608	+	4.41138i	−0.129255	+	1.80094i
$7$	0.0769910	−	0.133352i	0.0290999	−	0.0504024i	−0.851109	−	0.524989i	$-0.824069\pi$
$7$	0.0769910	−	0.133352i	0.0290999	−	0.0504024i	0.880209	+	0.474587i	$0.157403\pi$
$8$	−6.43513			−2.27516
$9$	1.85565	−	2.35724i	0.618549	−	0.785746i
$10$	−7.14837			−2.26051
$11$	−1.85795	+	3.21806i	−0.560192	+	0.970281i	0.437287	+	0.899322i	$0.355939\pi$
$11$	−1.85795	+	3.21806i	−0.560192	+	0.970281i	−0.997479	+	0.0709593i	$0.977394\pi$
$12$	6.48262	+	4.38991i	1.87137	+	1.26726i
$13$	0.642256	+	1.11242i	0.178130	+	0.308530i	0.941240	−	0.337739i	$-0.109662\pi$
$13$	0.642256	+	1.11242i	0.178130	+	0.308530i	−0.763110	+	0.646268i	$0.776329\pi$
$14$	−0.196594	−	0.340510i	−0.0525418	−	0.0910051i
$15$	4.01489	+	2.71881i	1.03664	+	0.701994i
$16$	−3.69577	+	6.40126i	−0.923942	+	1.60032i
$17$	0.563748			0.136729			0.0683645	−	0.997660i	$-0.478222\pi$
$17$	0.563748			0.136729			0.0683645	+	0.997660i	$0.478222\pi$
$18$	−2.84355	−	7.11307i	−0.670231	−	1.67657i
$19$	−6.62305			−1.51943			−0.759716	−	0.650255i	$-0.774662\pi$
$19$	−6.62305			−1.51943			−0.759716	+	0.650255i	$0.774662\pi$
$20$	−6.32706	+	10.9588i	−1.41477	+	2.45046i
$21$	−0.0190925	+	0.266020i	−0.00416632	+	0.0580504i
$22$	4.74420	+	8.21719i	1.01147	+	1.75191i
$23$	−3.02258	−	5.23526i	−0.630251	−	1.09163i	−0.987500	−	0.157617i	$-0.949619\pi$
$23$	−3.02258	−	5.23526i	−0.630251	−	1.09163i	0.357250	−	0.934009i	$-0.383715\pi$
$24$	10.0269	−	4.86769i	2.04673	−	0.993612i
$25$	−1.41855	+	2.45700i	−0.283710	+	0.491401i
$26$	3.27995			0.643251
$27$	−1.10830	+	5.07658i	−0.213293	+	0.976988i
$28$	−0.696024			−0.131536
$29$	4.34197	−	7.52050i	0.806283	−	1.39652i	−0.109139	−	0.994027i	$-0.534809\pi$
$29$	4.34197	−	7.52050i	0.806283	−	1.39652i	0.915422	−	0.402496i	$-0.131857\pi$
$30$	11.1382	−	5.40719i	2.03355	−	0.987214i
$31$	0.846788	+	1.46668i	0.152088	+	0.263424i	0.931995	−	0.362472i	$-0.118067\pi$
$31$	0.846788	+	1.46668i	0.152088	+	0.263424i	−0.779907	+	0.625895i	$0.784734\pi$
$32$	3.00187	+	5.19939i	0.530660	+	0.919131i
$33$	0.460740	−	6.41961i	0.0802046	−	1.11751i
$34$	0.719755	−	1.24665i	0.123437	−	0.213799i
$35$	−0.431070			−0.0728641
$36$	−13.4215	−	1.93652i	−2.23692	−	0.322753i
$37$	4.07664			0.670195			0.335097	−	0.942183i	$-0.391231\pi$
$37$	4.07664			0.670195			0.335097	+	0.942183i	$0.391231\pi$
$38$	−8.45585	+	14.6460i	−1.37172	+	2.37589i
$39$	−1.84219	−	1.24750i	−0.294986	−	0.199759i
$40$	9.00752	+	15.6015i	1.42421	+	2.46681i
$41$	−5.55726	−	9.62547i	−0.867899	−	1.50325i	−0.864140	−	0.503252i	$-0.832137\pi$
$41$	−5.55726	−	9.62547i	−0.867899	−	1.50325i	−0.00375938	−	0.999993i	$-0.501197\pi$
$42$	0.563891	+	0.381857i	0.0870103	+	0.0589218i
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i
$44$	16.7964			2.53216
$45$	−8.31237	−	1.19935i	−1.23913	−	0.178788i
$46$	−15.4361			−2.27592
$47$	3.69248	−	6.39556i	0.538603	−	0.932888i	−0.460377	−	0.887724i	$-0.652286\pi$
$47$	3.69248	−	6.39556i	0.538603	−	0.932888i	0.998980	−	0.0451639i	$-0.0143810\pi$
$48$	0.916490	−	12.7697i	0.132284	−	1.84314i
$49$	3.48814	+	6.04164i	0.498306	+	0.863092i
$50$	3.62222	+	6.27386i	0.512259	+	0.887258i
$51$	−0.878403	+	0.426432i	−0.123001	+	0.0597125i
$52$	2.90310	−	5.02832i	0.402588	−	0.697302i
$53$	2.30102			0.316069			0.158034	−	0.987434i	$-0.449484\pi$
$53$	2.30102			0.316069			0.158034	+	0.987434i	$0.449484\pi$
$54$	9.81116	+	8.93228i	1.33513	+	1.21553i
$55$	10.4026			1.40268
$56$	−0.495447	+	0.858140i	−0.0662070	+	0.114674i
$57$	10.3197	−	5.00983i	1.36688	−	0.663568i
$58$	−11.0870	−	19.2033i	−1.45580	−	2.52152i
$59$	−2.94982	−	5.10923i	−0.384033	−	0.665165i	0.607601	−	0.794242i	$-0.292132\pi$
$59$	−2.94982	−	5.10923i	−0.384033	−	0.665165i	−0.991635	+	0.129077i	$0.958799\pi$
$60$	1.56901	−	21.8613i	0.202558	−	2.82229i
$61$	2.07507	−	3.59412i	0.265685	−	0.460180i	−0.702058	−	0.712120i	$-0.747735\pi$
$61$	2.07507	−	3.59412i	0.265685	−	0.460180i	0.967743	+	0.251940i	$0.0810686\pi$
$62$	4.32448			0.549210
$63$	−0.171475	−	0.428941i	−0.0216038	−	0.0540415i
$64$	0.547229			0.0684037
$65$	1.79798	−	3.11420i	0.223013	−	0.386269i
$66$	−13.6078	−	9.21497i	−1.67501	−	1.13428i
$67$	−5.34393	−	9.25596i	−0.652865	−	1.13080i	−0.982424	−	0.186661i	$-0.940233\pi$
$67$	−5.34393	−	9.25596i	−0.652865	−	1.13080i	0.329559	−	0.944135i	$-0.393100\pi$
$68$	−1.27412	−	2.20683i	−0.154509	−	0.267618i
$69$	8.66969	+	5.87095i	1.04371	+	0.706780i
$70$	−0.550360	+	0.953252i	−0.0657806	+	0.113935i
$71$	12.6183			1.49752			0.748758	−	0.662843i	$-0.230650\pi$
$71$	12.6183			1.49752			0.748758	+	0.662843i	$0.230650\pi$
$72$	−11.9413	+	15.1691i	−1.40730	+	1.78770i
$73$	1.47133			0.172206			0.0861030	−	0.996286i	$-0.472559\pi$
$73$	1.47133			0.172206			0.0861030	+	0.996286i	$0.472559\pi$
$74$	5.20476	−	9.01492i	0.605042	−	1.04796i
$75$	0.351777	−	4.90140i	0.0406197	−	0.565965i
$76$	14.9686	+	25.9264i	1.71702	+	2.97397i
$77$	0.286090	+	0.495523i	0.0326030	+	0.0564701i
$78$	−5.11065	+	2.48103i	−0.578667	+	0.280922i
$79$	−4.16420	+	7.21261i	−0.468509	+	0.811482i	−0.999352	−	0.0359886i	$-0.988542\pi$
$79$	−4.16420	+	7.21261i	−0.468509	+	0.811482i	0.530843	+	0.847470i	$0.321875\pi$
$80$	20.6925			2.31349
$81$	−2.11315	−	8.74841i	−0.234794	−	0.972045i
$82$	−28.3805			−3.13410
$83$	−3.48869	+	6.04259i	−0.382933	+	0.663260i	−0.991480	−	0.130258i	$-0.958419\pi$
$83$	−3.48869	+	6.04259i	−0.382933	+	0.663260i	0.608547	+	0.793518i	$0.291753\pi$
$84$	1.08451	−	0.526489i	0.118329	−	0.0574446i
$85$	−0.789102	−	1.36676i	−0.0855901	−	0.148246i
$86$	1.27673	+	2.21136i	0.137673	+	0.238457i
$87$	−1.07674	+	15.0024i	−0.115438	+	1.60843i
$88$	11.9561	−	20.7086i	1.27453	−	2.20755i
$89$	15.8842			1.68373			0.841864	−	0.539690i	$-0.181459\pi$
$89$	15.8842			1.68373			0.841864	+	0.539690i	$0.181459\pi$
$90$	−13.2648	+	16.8504i	−1.39824	+	1.77619i
$91$	0.197792			0.0207342
$92$	−13.6625	+	23.6642i	−1.42442	+	2.46716i
$93$	−2.42885	−	1.64477i	−0.251860	−	0.170555i
$94$	−9.42859	−	16.3308i	−0.972485	−	1.68439i
$95$	9.27056	+	16.0571i	0.951139	+	1.64742i
$96$	−8.61029	−	5.83073i	−0.878785	−	0.595096i
$97$	−8.27317	+	14.3296i	−0.840013	+	1.45495i	0.0498688	+	0.998756i	$0.484120\pi$
$97$	−8.27317	+	14.3296i	−0.840013	+	1.45495i	−0.889882	+	0.456190i	$0.849214\pi$
$98$	17.8137			1.79945
$99$	4.13804	+	10.3512i	0.415889	+	1.04034i
$100$	12.8242			1.28242
$101$	−5.59941	+	9.69846i	−0.557162	+	0.965033i	0.440570	+	0.897718i	$0.354776\pi$
$101$	−5.59941	+	9.69846i	−0.557162	+	0.965033i	−0.997732	+	0.0673145i	$0.978557\pi$
$102$	−0.178487	+	2.48691i	−0.0176729	+	0.246240i
$103$	−7.19198	−	12.4569i	−0.708647	−	1.22741i	−0.965359	−	0.260924i	$-0.915973\pi$
$103$	−7.19198	−	12.4569i	−0.708647	−	1.22741i	0.256713	−	0.966488i	$-0.417361\pi$
$104$	−4.13300	−	7.15857i	−0.405274	−	0.701956i
$105$	0.671671	−	0.326071i	0.0655483	−	0.0318213i
$106$	2.93778	−	5.08838i	0.285342	−	0.494227i
$107$	−10.3317			−0.998801			−0.499400	−	0.866371i	$-0.666446\pi$
$107$	−10.3317			−0.998801			−0.499400	+	0.866371i	$0.666446\pi$
$108$	22.3775	−	7.13496i	2.15328	−	0.686562i
$109$	8.69073			0.832421			0.416211	−	0.909268i	$-0.363358\pi$
$109$	8.69073			0.832421			0.416211	+	0.909268i	$0.363358\pi$
$110$	13.2813	−	23.0039i	1.26632	−	2.19333i
$111$	−6.35200	+	3.08366i	−0.602905	+	0.292688i
$112$	0.569082	+	0.985679i	0.0537732	+	0.0931379i
$113$	−2.69829	−	4.67357i	−0.253834	−	0.439653i	0.710744	−	0.703450i	$-0.248358\pi$
$113$	−2.69829	−	4.67357i	−0.253834	−	0.439653i	−0.964578	+	0.263798i	$0.915025\pi$
$114$	2.09691	−	29.2168i	0.196394	−	2.73640i
$115$	−8.46165	+	14.6560i	−0.789053	+	1.36668i
$116$	−39.2528			−3.64453
$117$	3.81404	+	0.550308i	0.352608	+	0.0508760i
$118$	−15.0645			−1.38680
$119$	0.0434035	−	0.0751771i	0.00397880	−	0.00689148i
$120$	−25.8364	−	17.4959i	−2.35853	−	1.59715i
$121$	−1.40394	−	2.43169i	−0.127631	−	0.221063i
$122$	−5.29860	−	9.17744i	−0.479712	−	0.830886i
$123$	15.9400	+	10.7942i	1.43726	+	0.973285i
$124$	3.82762	−	6.62963i	0.343730	−	0.595359i
$125$	−6.05499			−0.541575
$126$	−1.16747	−	0.168448i	−0.104007	−	0.0150066i
$127$	8.93444			0.792803			0.396402	−	0.918077i	$-0.370259\pi$
$127$	8.93444			0.792803			0.396402	+	0.918077i	$0.370259\pi$
$128$	−5.30507	+	9.18866i	−0.468907	+	0.812170i
$129$	0.123992	−	1.72761i	0.0109169	−	0.152107i
$130$	−4.59108	−	7.95199i	−0.402665	−	0.697435i
$131$	4.50361	+	7.80048i	0.393482	+	0.681531i	0.992906	−	0.118901i	$-0.0379370\pi$
$131$	4.50361	+	7.80048i	0.393482	+	0.681531i	−0.599424	+	0.800432i	$0.704604\pi$
$132$	−26.1713	+	12.7052i	−2.27792	+	1.10585i
$133$	−0.509915	+	0.883199i	−0.0442153	+	0.0765831i
$134$	−27.2910			−2.35759
$135$	13.8591	−	4.41891i	1.19280	−	0.380319i
$136$	−3.62780			−0.311081
$137$	7.30352	−	12.6501i	0.623982	−	1.08077i	−0.364755	−	0.931104i	$-0.618847\pi$
$137$	7.30352	−	12.6501i	0.623982	−	1.08077i	0.988737	−	0.149665i	$-0.0478195\pi$
$138$	24.0517	−	11.6762i	2.04741	−	0.993944i
$139$	6.22405	+	10.7804i	0.527917	+	0.914379i	0.999470	+	0.0325417i	$0.0103602\pi$
$139$	6.22405	+	10.7804i	0.527917	+	0.914379i	−0.471553	+	0.881838i	$0.656307\pi$
$140$	0.974253	+	1.68746i	0.0823394	+	0.142616i
$141$	−0.915673	+	12.7583i	−0.0771136	+	1.07444i
$142$	16.1102	−	27.9036i	1.35194	−	2.34162i
$143$	−4.77311			−0.399148
$144$	8.23126	+	20.5903i	0.685938	+	1.71586i
$145$	−24.3105			−2.01888
$146$	1.87849	−	3.25364i	0.155465	−	0.269273i
$147$	−10.0051	−	6.77526i	−0.825206	−	0.558814i
$148$	−9.21353	−	15.9583i	−0.757347	−	1.31176i
$149$	−8.17481	−	14.1592i	−0.669706	−	1.15997i	−0.977986	−	0.208670i	$-0.933087\pi$
$149$	−8.17481	−	14.1592i	−0.669706	−	1.15997i	0.308280	−	0.951296i	$-0.400247\pi$
$150$	−10.3896	−	7.03567i	−0.848311	−	0.574460i
$151$	8.02286	−	13.8960i	0.652891	−	1.13084i	−0.329527	−	0.944146i	$-0.606889\pi$
$151$	8.02286	−	13.8960i	0.652891	−	1.13084i	0.982418	−	0.186694i	$-0.0597772\pi$
$152$	42.6202			3.45696
$153$	1.04612	−	1.32889i	0.0845736	−	0.107434i
$154$	1.46104			0.117734
$155$	2.37057	−	4.10595i	0.190409	−	0.329798i
$156$	−0.719921	+	10.0308i	−0.0576398	+	0.803110i
$157$	−0.757906	−	1.31273i	−0.0604875	−	0.104767i	0.834196	−	0.551468i	$-0.185932\pi$
$157$	−0.757906	−	1.31273i	−0.0604875	−	0.104767i	−0.894683	+	0.446701i	$0.852599\pi$
$158$	10.6331	+	18.4171i	0.845926	+	1.46519i
$159$	−3.58532	+	1.74054i	−0.284335	+	0.138034i
$160$	8.40368	−	14.5556i	0.664369	−	1.15072i
$161$	−0.930845			−0.0733608
$162$	−22.0438	−	6.49642i	−1.73193	−	0.510407i
$163$	18.1419			1.42098			0.710490	−	0.703707i	$-0.248473\pi$
$163$	18.1419			1.42098			0.710490	+	0.703707i	$0.248473\pi$
$164$	−25.1197	+	43.5087i	−1.96152	+	3.39746i
$165$	−16.2088	+	7.86876i	−1.26185	+	0.612582i
$166$	8.90823	+	15.4295i	0.691413	+	1.19756i
$167$	10.5220	+	18.2247i	0.814218	+	1.41027i	0.909888	+	0.414855i	$0.136168\pi$
$167$	10.5220	+	18.2247i	0.814218	+	1.41027i	−0.0956693	+	0.995413i	$0.530499\pi$
$168$	0.122863	−	1.71188i	0.00947907	−	0.132074i
$169$	5.67501	−	9.82941i	0.436540	−	0.756109i
$170$	−4.02988			−0.309078
$171$	−12.2900	+	15.6121i	−0.939843	+	1.19389i
$172$	4.52016			0.344659
$173$	−7.85288	+	13.6016i	−0.597043	+	1.03411i	0.396212	+	0.918159i	$0.370325\pi$
$173$	−7.85288	+	13.6016i	−0.597043	+	1.03411i	−0.993255	+	0.115950i	$0.963009\pi$
$174$	31.8011	+	21.5351i	2.41083	+	1.63257i
$175$	0.218431	+	0.378334i	0.0165119	+	0.0285994i
$176$	−13.7331	−	23.7864i	−1.03517	−	1.79297i
$177$	8.46099	+	5.72962i	0.635967	+	0.430665i
$178$	20.2799	−	35.1258i	1.52004	−	2.63279i
$179$	15.3843			1.14988			0.574939	−	0.818196i	$-0.305026\pi$
$179$	15.3843			1.14988			0.574939	+	0.818196i	$0.305026\pi$
$180$	14.0917	+	35.2500i	1.05033	+	2.62738i
$181$	−4.19026			−0.311460			−0.155730	−	0.987800i	$-0.549773\pi$
$181$	−4.19026			−0.311460			−0.155730	+	0.987800i	$0.549773\pi$
$182$	0.252527	−	0.437389i	0.0187185	−	0.0324214i
$183$	−0.514582	+	7.16979i	−0.0380390	+	0.530006i
$184$	19.4507	+	33.6896i	1.43392	+	2.48363i
$185$	−5.70624	−	9.88349i	−0.419531	−	0.726649i
$186$	−6.73818	+	3.27114i	−0.494067	+	0.239852i
$187$	−1.04741	+	1.81418i	−0.0765945	+	0.132666i
$188$	−33.3812			−2.43457
$189$	0.591645	+	0.538645i	0.0430358	+	0.0391807i
$190$	47.3440			3.43470
$191$	8.26169	−	14.3097i	0.597795	−	1.03541i	−0.395351	−	0.918530i	$-0.629377\pi$
$191$	8.26169	−	14.3097i	0.597795	−	1.03541i	0.993146	−	0.116881i	$-0.0372896\pi$
$192$	−0.852664	+	0.413937i	−0.0615357	+	0.0298733i
$193$	0.222898	+	0.386070i	0.0160445	+	0.0277899i	0.873936	−	0.486041i	$-0.161559\pi$
$193$	0.222898	+	0.386070i	0.0160445	+	0.0277899i	−0.857892	+	0.513831i	$0.828226\pi$
$194$	21.1252	+	36.5900i	1.51670	+	2.62701i
$195$	−0.445870	+	6.21242i	−0.0319294	+	0.444881i
$196$	15.7670	−	27.3092i	1.12621	−	1.95066i
$197$	2.28962			0.163128			0.0815642	−	0.996668i	$-0.474008\pi$
$197$	2.28962			0.163128			0.0815642	+	0.996668i	$0.474008\pi$
$198$	28.1734	+	4.06500i	2.00220	+	0.288887i
$199$	−3.92413			−0.278174			−0.139087	−	0.990280i	$-0.544417\pi$
$199$	−3.92413			−0.278174			−0.139087	+	0.990280i	$0.544417\pi$
$200$	9.12857	−	15.8111i	0.645487	−	1.11802i
$201$	15.3281	+	10.3799i	1.08116	+	0.732140i
$202$	14.2979	+	24.7646i	1.00599	+	1.74243i
$203$	−0.668585	−	1.15802i	−0.0469254	−	0.0812772i
$204$	3.65456	+	2.47480i	0.255871	+	0.173271i
$205$	−15.5575	+	26.9463i	−1.08658	+	1.88201i
$206$	−36.7289			−2.55902
$207$	−17.9496	−	2.58985i	−1.24758	−	0.180007i
$208$	−9.49452			−0.658327
$209$	12.3053	−	21.3134i	0.851174	−	1.47428i
$210$	0.136480	−	1.90161i	0.00941803	−	0.131224i
$211$	9.02888	+	15.6385i	0.621574	+	1.07660i	0.989193	+	0.146621i	$0.0468397\pi$
$211$	9.02888	+	15.6385i	0.621574	+	1.07660i	−0.367619	+	0.929977i	$0.619827\pi$
$212$	−5.20048	−	9.00750i	−0.357171	−	0.618638i
$213$	−19.6612	+	9.54478i	−1.34716	+	0.653997i
$214$	−13.1908	+	22.8471i	−0.901702	+	1.56179i
$215$	2.79948			0.190923
$216$	7.13206	−	32.6685i	0.485275	−	2.22281i
$217$	0.260780			0.0177029
$218$	11.0957	−	19.2184i	0.751497	−	1.30163i
$219$	−2.29255	+	1.11295i	−0.154916	+	0.0752060i
$220$	−23.5107	−	40.7217i	−1.58509	−	2.74546i
$221$	0.362071	+	0.627125i	0.0243555	+	0.0421850i
$222$	−1.29070	+	17.9836i	−0.0866258	+	1.20698i
$223$	4.15911	−	7.20379i	0.278515	−	0.482402i	−0.692501	−	0.721417i	$-0.743491\pi$
$223$	4.15911	−	7.20379i	0.278515	−	0.482402i	0.971016	+	0.239015i	$0.0768246\pi$
$224$	0.924468			0.0617686
$225$	3.15941	+	7.90319i	0.210627	+	0.526880i
$226$	−13.7799			−0.916628
$227$	6.96766	−	12.0683i	0.462460	−	0.801004i	−0.536623	−	0.843822i	$-0.680300\pi$
$227$	6.96766	−	12.0683i	0.462460	−	0.801004i	0.999083	+	0.0428182i	$0.0136336\pi$
$228$	−42.9347	−	29.0746i	−2.84342	−	1.92551i
$229$	0.834130	+	1.44476i	0.0551209	+	0.0954722i	0.892269	−	0.451504i	$-0.149112\pi$
$229$	0.834130	+	1.44476i	0.0551209	+	0.0954722i	−0.837148	+	0.546976i	$0.815779\pi$
$230$	21.6065	+	37.4235i	1.42469	+	2.46764i
$231$	−0.820596	−	0.555693i	−0.0539913	−	0.0365619i
$232$	−27.9411	+	48.3955i	−1.83443	+	3.17732i
$233$	0.0999337			0.00654687			0.00327344	−	0.999995i	$-0.498958\pi$
$233$	0.0999337			0.00654687			0.00327344	+	0.999995i	$0.498958\pi$
$234$	6.08643	−	7.73163i	0.397882	−	0.505432i
$235$	−20.6740			−1.34863
$236$	−13.3336	+	23.0946i	−0.867946	+	1.50333i
$237$	1.03265	−	14.3882i	0.0670780	−	0.934614i
$238$	−0.110829	−	0.191962i	−0.00718399	−	0.0124430i
$239$	−5.84080	−	10.1166i	−0.377810	−	0.654386i	0.612934	−	0.790134i	$-0.289989\pi$
$239$	−5.84080	−	10.1166i	−0.377810	−	0.654386i	−0.990743	+	0.135749i	$0.956656\pi$
$240$	−32.2419	+	15.6523i	−2.08121	+	1.01035i
$241$	2.50504	−	4.33885i	0.161364	−	0.279490i	−0.773994	−	0.633193i	$-0.781744\pi$
$241$	2.50504	−	4.33885i	0.161364	−	0.279490i	0.935358	+	0.353702i	$0.115077\pi$
$242$	−7.16979			−0.460892
$243$	9.91010	+	12.0329i	0.635733	+	0.771909i
$244$	−18.7593			−1.20094
$245$	9.76500	−	16.9135i	0.623863	−	1.08056i
$246$	44.2210	−	21.4677i	2.81943	−	1.36873i
$247$	−4.25369	−	7.36761i	−0.270656	−	0.468790i
$248$	−5.44920	−	9.43829i	−0.346024	−	0.599332i
$249$	0.865137	−	12.0542i	0.0548258	−	0.763902i
$250$	−7.73059	+	13.3898i	−0.488926	+	0.846844i
$251$	−4.73634			−0.298955			−0.149478	−	0.988765i	$-0.547759\pi$
$251$	−4.73634			−0.298955			−0.149478	+	0.988765i	$0.547759\pi$
$252$	−1.29157	+	1.64069i	−0.0813615	+	0.103354i
$253$	22.4631			1.41225
$254$	11.4069	−	19.7573i	0.715731	−	1.23968i
$255$	2.26339	+	1.53273i	0.141739	+	0.0959830i
$256$	14.0935	+	24.4107i	0.880845	+	1.52567i
$257$	−8.19567	−	14.1953i	−0.511232	−	0.885480i	−0.999915	−	0.0130184i	$-0.995856\pi$
$257$	−8.19567	−	14.1953i	−0.511232	−	0.885480i	0.488683	−	0.872461i	$-0.337477\pi$
$258$	−3.66206	−	2.47988i	−0.227990	−	0.154391i
$259$	0.313864	−	0.543629i	0.0195026	−	0.0337795i
$260$	−16.2544			−1.00805
$261$	−9.67047	−	24.1905i	−0.598587	−	1.49735i
$262$	22.9996			1.42092
$263$	−8.02200	+	13.8945i	−0.494658	+	0.856772i	−0.999981	−	0.00615770i	$-0.998040\pi$
$263$	−8.02200	+	13.8945i	−0.494658	+	0.856772i	0.505323	+	0.862930i	$0.331373\pi$
$264$	−2.96492	+	41.3110i	−0.182479	+	2.54252i
$265$	−3.22083	−	5.57864i	−0.197854	−	0.342693i
$266$	1.30205	+	2.25521i	0.0798337	+	0.138276i
$267$	−24.7500	+	12.0152i	−1.51468	+	0.735320i
$268$	−24.1554	+	41.8384i	−1.47553	+	2.55569i
$269$	15.7847			0.962412			0.481206	−	0.876607i	$-0.340199\pi$
$269$	15.7847			0.962412			0.481206	+	0.876607i	$0.340199\pi$
$270$	7.92254	−	36.2893i	0.482150	−	2.20849i
$271$	30.4843			1.85179			0.925894	−	0.377784i	$-0.123314\pi$
$271$	30.4843			1.85179			0.925894	+	0.377784i	$0.123314\pi$
$272$	−2.08348	+	3.60870i	−0.126330	+	0.218810i
$273$	−0.308189	+	0.149614i	−0.0186524	+	0.00905507i
$274$	−18.6493	−	32.3015i	−1.12664	−	1.95140i
$275$	−5.27119	−	9.12996i	−0.317865	−	0.550558i
$276$	3.38808	−	47.2070i	0.203939	−	2.84153i
$277$	−9.67683	+	16.7608i	−0.581424	+	1.00706i	0.413887	+	0.910328i	$0.364171\pi$
$277$	−9.67683	+	16.7608i	−0.581424	+	1.00706i	−0.995311	+	0.0967280i	$0.969162\pi$
$278$	31.7857			1.90638
$279$	5.02866	+	0.725559i	0.301058	+	0.0434381i
$280$	2.77399			0.165778
$281$	9.15517	−	15.8572i	0.546152	−	0.945962i	−0.452382	−	0.891824i	$-0.649426\pi$
$281$	9.15517	−	15.8572i	0.546152	−	0.945962i	0.998533	−	0.0541381i	$-0.0172411\pi$
$282$	27.0441	+	18.3138i	1.61045	+	1.09057i
$283$	−6.00971	−	10.4091i	−0.357240	−	0.618758i	0.630259	−	0.776385i	$-0.282949\pi$
$283$	−6.00971	−	10.4091i	−0.357240	−	0.618758i	−0.987499	+	0.157627i	$0.949616\pi$
$284$	−28.5184	−	49.3953i	−1.69225	−	2.93107i
$285$	−26.5908	−	18.0068i	−1.57511	−	1.06663i
$286$	−6.09398	+	10.5551i	−0.360344	+	0.624135i
$287$	−1.71144			−0.101023
$288$	17.8266	+	2.57211i	1.05044	+	0.151563i
$289$	−16.6822			−0.981305
$290$	−31.0380	+	53.7593i	−1.82261	+	3.15686i
$291$	2.05161	−	28.5856i	0.120268	−	1.67572i
$292$	−3.32532	−	5.75963i	−0.194600	−	0.337057i
$293$	−8.79180	−	15.2278i	−0.513623	−	0.889620i	−0.999875	−	0.0158021i	$-0.994970\pi$
$293$	−8.79180	−	15.2278i	−0.513623	−	0.889620i	0.486253	−	0.873818i	$-0.338364\pi$
$294$	−27.7563	+	13.4747i	−1.61878	+	0.785860i
$295$	−8.25796	+	14.3032i	−0.480797	+	0.832765i
$296$	−26.2337			−1.52480
$297$	−14.2776	−	12.9986i	−0.828469	−	0.754255i
$298$	−41.7481			−2.41840
$299$	3.88253	−	6.72475i	0.224533	−	0.388902i
$300$	−19.9819	+	9.70050i	−1.15366	+	0.560059i
$301$	0.0769910	+	0.133352i	0.00443769	+	0.00768630i
$302$	−20.4860	−	35.4829i	−1.17884	−	2.04181i
$303$	1.38856	−	19.3472i	0.0797707	−	1.11147i
$304$	24.4773	−	42.3959i	1.40387	−	2.43157i
$305$	−11.6182			−0.665257
$306$	−1.60304	−	4.00998i	−0.0916400	−	0.229235i
$307$	−9.91335			−0.565785			−0.282892	−	0.959152i	$-0.591294\pi$
$307$	−9.91335			−0.565785			−0.282892	+	0.959152i	$0.591294\pi$
$308$	1.29318	−	2.23985i	0.0736855	−	0.127627i
$309$	20.6288	+	13.9695i	1.17353	+	0.794695i
$310$	−6.05316	−	10.4844i	−0.343796	−	0.595472i
$311$	13.0471	+	22.5982i	0.739831	+	1.28143i	0.952571	+	0.304316i	$0.0984280\pi$
$311$	13.0471	+	22.5982i	0.739831	+	1.28143i	−0.212740	+	0.977109i	$0.568239\pi$
$312$	11.8547	+	8.02781i	0.671143	+	0.454485i
$313$	−2.38738	+	4.13507i	−0.134943	+	0.233728i	−0.925576	−	0.378563i	$-0.876418\pi$
$313$	−2.38738	+	4.13507i	−0.134943	+	0.233728i	0.790633	+	0.612291i	$0.209752\pi$
$314$	−3.87057			−0.218429
$315$	−0.799914	+	1.01613i	−0.0450700	+	0.0572527i
$316$	37.6457			2.11774
$317$	−10.6534	+	18.4523i	−0.598357	+	1.03639i	0.394706	+	0.918807i	$0.370846\pi$
$317$	−10.6534	+	18.4523i	−0.598357	+	1.03639i	−0.993064	+	0.117578i	$0.962487\pi$
$318$	−0.728520	+	10.1507i	−0.0408534	+	0.569220i
$319$	16.1343	+	27.9454i	0.903347	+	1.56464i
$320$	−0.765979	−	1.32672i	−0.0428195	−	0.0741656i
$321$	16.0983	−	7.81512i	0.898518	−	0.436198i
$322$	−1.18844	+	2.05843i	−0.0662290	+	0.114712i
$323$	−3.73373			−0.207750
$324$	−29.4704	+	28.0442i	−1.63724	+	1.55801i
$325$	−3.64429			−0.202149
$326$	23.1623	−	40.1182i	1.28284	−	2.22194i
$327$	−13.5414	+	6.57388i	−0.748844	+	0.363536i
$328$	35.7617	+	61.9412i	1.97461	+	3.42013i
$329$	−0.568575	−	0.984800i	−0.0313465	−	0.0542938i
$330$	−3.29354	+	45.8897i	−0.181303	+	2.52615i
$331$	−2.03831	+	3.53046i	−0.112036	+	0.194052i	−0.916591	−	0.399826i	$-0.869070\pi$
$331$	−2.03831	+	3.53046i	−0.112036	+	0.194052i	0.804555	+	0.593878i	$0.202404\pi$
$332$	31.5389			1.73092
$333$	7.56480	−	9.60960i	0.414548	−	0.526603i
$334$	53.7351			2.94026
$335$	−14.9602	+	25.9119i	−0.817365	+	1.41572i
$336$	−1.63230	−	1.10537i	−0.0890495	−	0.0603027i
$337$	−2.30238	−	3.98784i	−0.125419	−	0.217231i	0.796478	−	0.604668i	$-0.206694\pi$
$337$	−2.30238	−	3.98784i	−0.125419	−	0.217231i	−0.921896	+	0.387436i	$0.873361\pi$
$338$	−14.4909	−	25.0990i	−0.788203	−	1.36521i
$339$	7.73953	+	5.24106i	0.420354	+	0.284656i
$340$	−3.56687	+	6.17800i	−0.193441	+	0.335049i
$341$	−6.29315			−0.340793
$342$	18.8330	+	47.1102i	1.01837	+	2.54743i
$343$	2.15210			0.116202
$344$	3.21757	−	5.57299i	0.173480	−	0.300475i
$345$	2.09835	−	29.2368i	0.112971	−	1.57406i
$346$	20.0520	+	34.7311i	1.07800	+	1.86716i
$347$	−6.62588	−	11.4764i	−0.355696	−	0.616084i	0.631541	−	0.775343i	$-0.282423\pi$
$347$	−6.62588	−	11.4764i	−0.355696	−	0.616084i	−0.987237	+	0.159259i	$0.949090\pi$
$348$	61.1616	−	29.6917i	3.27861	−	1.59164i
$349$	−1.46592	+	2.53905i	−0.0784690	+	0.135912i	−0.902590	−	0.430502i	$-0.858336\pi$
$349$	−1.46592	+	2.53905i	−0.0784690	+	0.135912i	0.824121	+	0.566414i	$0.191670\pi$
$350$	1.11551			0.0596266
$351$	−6.35910	+	2.02757i	−0.339424	+	0.108224i
$352$	−22.3093			−1.18909
$353$	−14.7204	+	25.4964i	−0.783487	+	1.35704i	0.146412	+	0.989224i	$0.453227\pi$
$353$	−14.7204	+	25.4964i	−0.783487	+	1.35704i	−0.929899	+	0.367815i	$0.880106\pi$
$354$	23.4727	−	11.3951i	1.24756	−	0.605644i
$355$	−17.6624	−	30.5921i	−0.937420	−	1.62366i
$356$	−35.8997	−	62.1801i	−1.90268	−	3.29554i
$357$	−0.0107634	+	0.149969i	−0.000569657	+	0.00793718i
$358$	19.6416	−	34.0203i	1.03809	−	1.79803i
$359$	−35.4312			−1.86999			−0.934994	−	0.354664i	$-0.884595\pi$
$359$	−35.4312			−1.86999			−0.934994	+	0.354664i	$0.884595\pi$
$360$	53.4912	+	7.71797i	2.81923	+	0.406773i
$361$	24.8648			1.30867
$362$	−5.34983	+	9.26618i	−0.281181	+	0.487020i
$363$	4.02693	+	2.72696i	0.211359	+	0.143128i
$364$	−0.447025	−	0.774270i	−0.0234305	−	0.0405828i
$365$	−2.05948	−	3.56712i	−0.107798	−	0.186712i
$366$	15.1980	+	10.2918i	0.794414	+	0.537962i
$367$	3.95549	−	6.85111i	0.206475	−	0.357625i	−0.744127	−	0.668039i	$-0.767134\pi$
$367$	3.95549	−	6.85111i	0.206475	−	0.357625i	0.950602	+	0.310413i	$0.100467\pi$
$368$	44.6830			2.32926
$369$	−33.0018	−	4.76166i	−1.71801	−	0.247882i
$370$	−29.1413			−1.51498
$371$	0.177158	−	0.306846i	0.00919756	−	0.0159306i
$372$	−0.949186	+	13.2252i	−0.0492130	+	0.685697i
$373$	−0.971984	−	1.68353i	−0.0503274	−	0.0871697i	0.839764	−	0.542951i	$-0.182693\pi$
$373$	−0.971984	−	1.68353i	−0.0503274	−	0.0871697i	−0.890092	+	0.455782i	$0.849360\pi$
$374$	2.67453	+	4.63243i	0.138297	+	0.239537i
$375$	9.43457	−	4.58014i	0.487199	−	0.236517i
$376$	−23.7616	+	41.1563i	−1.22541	+	2.12247i
$377$	11.1546			0.574492
$378$	1.94651	−	0.620635i	0.100118	−	0.0319220i
$379$	8.52784			0.438046			0.219023	−	0.975720i	$-0.429713\pi$
$379$	8.52784			0.438046			0.219023	+	0.975720i	$0.429713\pi$
$380$	41.9044	−	72.5806i	2.14965	−	3.72331i
$381$	−13.9212	+	6.75822i	−0.713203	+	0.346234i
$382$	−21.0959	−	36.5392i	−1.07936	−	1.86951i
$383$	−5.04469	−	8.73766i	−0.257772	−	0.446474i	0.707873	−	0.706340i	$-0.249655\pi$
$383$	−5.04469	−	8.73766i	−0.257772	−	0.446474i	−0.965645	+	0.259866i	$0.916322\pi$
$384$	1.31557	−	18.3302i	0.0671349	−	0.935407i
$385$	0.800905	−	1.38721i	0.0408179	−	0.0706987i
$386$	1.13832			0.0579390
$387$	1.11361	+	2.78566i	0.0566077	+	0.141603i
$388$	74.7922			3.79700
$389$	−0.792197	+	1.37213i	−0.0401660	+	0.0695695i	−0.885410	−	0.464812i	$-0.846122\pi$
$389$	−0.792197	+	1.37213i	−0.0401660	+	0.0695695i	0.845244	+	0.534381i	$0.179455\pi$
$390$	13.1687	+	8.91757i	0.666821	+	0.451559i
$391$	−1.70397	−	2.95137i	−0.0861736	−	0.149257i
$392$	−22.4467	−	38.8788i	−1.13373	−	1.96368i
$393$	−12.9178	−	8.74766i	−0.651614	−	0.441261i
$394$	2.92322	−	5.06317i	0.147270	−	0.255079i
$395$	23.3152			1.17312
$396$	31.1683	−	39.5932i	1.56626	−	1.98963i
$397$	−5.37215			−0.269620			−0.134810	−	0.990871i	$-0.543042\pi$
$397$	−5.37215			−0.269620			−0.134810	+	0.990871i	$0.543042\pi$
$398$	−5.01005	+	8.67767i	−0.251131	+	0.434972i
$399$	0.126451	−	1.76187i	0.00633045	−	0.0882036i
$400$	−10.4853	−	18.1610i	−0.524264	−	0.908052i
$401$	6.75094	+	11.6930i	0.337126	+	0.583919i	0.983891	−	0.178770i	$-0.0572119\pi$
$401$	6.75094	+	11.6930i	0.337126	+	0.583919i	−0.646765	+	0.762689i	$0.723879\pi$
$402$	42.5235	−	20.6436i	2.12088	−	1.02961i
$403$	−1.08771	+	1.88397i	−0.0541827	+	0.0938471i
$404$	50.6205			2.51846
$405$	−18.2520	+	17.3687i	−0.906948	+	0.863056i
$406$	−3.41441			−0.169454
$407$	−7.57417	+	13.1189i	−0.375438	+	0.650277i
$408$	5.65264	−	2.74415i	0.279847	−	0.135856i
$409$	−9.36718	−	16.2244i	−0.463177	−	0.802247i	0.535940	−	0.844256i	$-0.319957\pi$
$409$	−9.36718	−	16.2244i	−0.463177	−	0.802247i	−0.999117	+	0.0420093i	$0.986624\pi$
$410$	39.7254	+	68.8064i	1.96190	+	3.39810i
$411$	−1.81115	+	25.2352i	−0.0893376	+	1.24476i
$412$	−32.5089	+	56.3071i	−1.60160	+	2.77405i
$413$	−0.908437			−0.0447013
$414$	−28.6439	+	36.3865i	−1.40777	+	1.78830i
$415$	19.5331			0.958840
$416$	−3.85594	+	6.67868i	−0.189053	+	0.327449i
$417$	−17.8525	−	12.0894i	−0.874241	−	0.592020i
$418$	−31.4210	−	54.4228i	−1.53685	−	2.66191i
$419$	−4.59794	−	7.96387i	−0.224624	−	0.389060i	0.731583	−	0.681753i	$-0.238782\pi$
$419$	−4.59794	−	7.96387i	−0.224624	−	0.389060i	−0.956207	+	0.292693i	$0.905449\pi$
$420$	−2.79446	−	1.89236i	−0.136356	−	0.0923376i
$421$	2.48856	−	4.31031i	0.121285	−	0.210072i	−0.798990	−	0.601345i	$-0.794632\pi$
$421$	2.48856	−	4.31031i	0.121285	−	0.210072i	0.920275	+	0.391273i	$0.127965\pi$
$422$	46.1098			2.24459
$423$	−8.22392	−	20.5719i	−0.399861	−	1.00024i
$424$	−14.8074			−0.719109
$425$	−0.799706	+	1.38513i	−0.0387914	+	0.0671887i
$426$	−3.99505	+	55.6641i	−0.193561	+	2.69693i
$427$	−0.319523	−	0.553430i	−0.0154628	−	0.0267823i
$428$	23.3504	+	40.4441i	1.12869	+	1.95494i
$429$	7.43721	−	3.61049i	0.359072	−	0.174316i
$430$	3.57418	−	6.19067i	0.172362	−	0.298541i
$431$	−2.97671			−0.143383			−0.0716916	−	0.997427i	$-0.522840\pi$
$431$	−2.97671			−0.143383			−0.0716916	+	0.997427i	$0.522840\pi$
$432$	−28.4005	−	25.8564i	−1.36642	−	1.24402i
$433$	−2.07208			−0.0995780			−0.0497890	−	0.998760i	$-0.515855\pi$
$433$	−2.07208			−0.0995780			−0.0497890	+	0.998760i	$0.515855\pi$
$434$	0.332946	−	0.576680i	0.0159819	−	0.0276815i
$435$	37.8794	−	18.3890i	1.81618	−	0.881687i
$436$	−19.6418	−	34.0205i	−0.940670	−	1.62929i
$437$	20.0187	+	34.6734i	0.957623	+	1.65865i
$438$	−0.465834	+	6.49058i	−0.0222584	+	0.310132i
$439$	10.8388	−	18.7734i	0.517310	−	0.896007i	−0.482488	−	0.875903i	$-0.660267\pi$
$439$	10.8388	−	18.7734i	0.517310	−	0.896007i	0.999798	−	0.0201044i	$-0.00639985\pi$
$440$	−66.9420			−3.19134
$441$	20.7144	+	2.98877i	0.986398	+	0.142322i
$442$	1.84907			0.0879511
$443$	−8.90773	+	15.4286i	−0.423219	+	0.733037i	−0.996252	−	0.0864954i	$-0.972433\pi$
$443$	−8.90773	+	15.4286i	−0.423219	+	0.733037i	0.573033	+	0.819532i	$0.305767\pi$
$444$	26.4273	+	17.8961i	1.25418	+	0.849309i
$445$	−22.2338	−	38.5101i	−1.05399	−	1.82556i
$446$	−10.6201	−	18.3946i	−0.502878	−	0.871010i
$447$	23.4479	+	15.8785i	1.10905	+	0.751026i
$448$	0.0421317	−	0.0729743i	0.00199054	−	0.00344771i
$449$	−39.1785			−1.84895			−0.924475	−	0.381243i	$-0.875496\pi$
$449$	−39.1785			−1.84895			−0.924475	+	0.381243i	$0.875496\pi$
$450$	21.5105	+	3.10364i	1.01402	+	0.146307i
$451$	41.3004			1.94476
$452$	−12.1967	+	21.1253i	−0.573684	+	0.993650i
$453$	−1.98954	+	27.7207i	−0.0934765	+	1.30243i
$454$	−17.7916	−	30.8160i	−0.835003	−	1.44627i
$455$	−0.276857	−	0.479531i	−0.0129793	−	0.0224807i
$456$	−66.4086	+	32.2389i	−3.10987	+	1.50973i
$457$	−1.53806	+	2.66400i	−0.0719474	+	0.124617i	−0.899755	−	0.436396i	$-0.856255\pi$
$457$	−1.53806	+	2.66400i	−0.0719474	+	0.124617i	0.827807	+	0.561012i	$0.189588\pi$
$458$	4.25984			0.199049
$459$	−0.624803	+	2.86191i	−0.0291633	+	0.133583i
$460$	76.4960			3.56665
$461$	2.07652	−	3.59664i	0.0967131	−	0.167512i	−0.813609	−	0.581412i	$-0.802500\pi$
$461$	2.07652	−	3.59664i	0.0967131	−	0.167512i	0.910322	+	0.413900i	$0.135834\pi$
$462$	−2.27652	+	1.10517i	−0.105913	+	0.0514170i
$463$	−3.54662	−	6.14292i	−0.164825	−	0.285486i	0.771768	−	0.635904i	$-0.219373\pi$
$463$	−3.54662	−	6.14292i	−0.164825	−	0.285486i	−0.936593	+	0.350418i	$0.886039\pi$
$464$	32.0938	+	55.5881i	1.48992	+	2.58061i
$465$	−0.587862	+	8.19082i	−0.0272614	+	0.379840i
$466$	0.127588	−	0.220990i	0.00591042	−	0.0102371i
$467$	−10.7211			−0.496112			−0.248056	−	0.968746i	$-0.579792\pi$
$467$	−10.7211			−0.496112			−0.248056	+	0.968746i	$0.579792\pi$
$468$	−6.46582	−	16.1741i	−0.298882	−	0.747647i
$469$	−1.64574			−0.0759932
$470$	−26.3952	+	45.7178i	−1.21752	+	2.10880i
$471$	2.17391	+	1.47213i	0.100169	+	0.0678323i
$472$	18.9825	+	32.8786i	0.873739	+	1.51336i
$473$	−1.85795	−	3.21806i	−0.0854285	−	0.147967i
$474$	−30.4991	−	20.6534i	−1.40087	−	0.948643i
$475$	9.39514	−	16.2729i	0.431078	−	0.746650i
$476$	−0.392382			−0.0179848
$477$	4.26987	−	5.42405i	0.195504	−	0.248350i
$478$	−29.8285			−1.36432
$479$	3.40786	−	5.90259i	0.155709	−	0.269696i	−0.777608	−	0.628750i	$-0.783567\pi$
$479$	3.40786	−	5.90259i	0.155709	−	0.269696i	0.933317	+	0.359053i	$0.116900\pi$
$480$	−2.08397	+	29.0365i	−0.0951199	+	1.32533i
$481$	2.61824	+	4.53493i	0.119382	+	0.206775i
$482$	−6.39652	−	11.0791i	−0.291353	−	0.504639i
$483$	1.45039	−	0.704113i	0.0659952	−	0.0320382i
$484$	−6.34602	+	10.9916i	−0.288455	+	0.499619i
$485$	46.3212			2.10334
$486$	39.2616	−	6.55208i	1.78094	−	0.297209i
$487$	−17.3377			−0.785645			−0.392823	−	0.919614i	$-0.628501\pi$
$487$	−17.3377			−0.785645			−0.392823	+	0.919614i	$0.628501\pi$
$488$	−13.3533	+	23.1286i	−0.604477	+	1.04698i
$489$	−28.2677	+	13.7229i	−1.27831	+	0.620572i
$490$	−24.9345	−	43.1879i	−1.12643	−	1.95103i
$491$	−7.95116	−	13.7718i	−0.358831	−	0.621514i	0.628935	−	0.777458i	$-0.283491\pi$
$491$	−7.95116	−	13.7718i	−0.358831	−	0.621514i	−0.987766	+	0.155944i	$0.950158\pi$
$492$	6.22928	−	86.7941i	0.280838	−	3.91298i
$493$	2.44778	−	4.23967i	0.110242	−	0.190945i
$494$	−21.7233			−0.977376
$495$	19.3035	−	24.5214i	0.867629	−	1.10215i
$496$	−12.5181			−0.562081
$497$	0.971496	−	1.68268i	0.0435775	−	0.0754785i
$498$	−25.5516	−	17.3031i	−1.14499	−	0.775368i
$499$	2.26248	+	3.91873i	0.101282	+	0.175426i	0.912213	−	0.409716i	$-0.134372\pi$
$499$	2.26248	+	3.91873i	0.101282	+	0.175426i	−0.810931	+	0.585142i	$0.801039\pi$
$500$	13.6848	+	23.7027i	0.612002	+	1.06002i
$501$	−30.1804	−	20.4376i	−1.34836	−	0.913086i
$502$	−6.04703	+	10.4738i	−0.269892	+	0.467467i
$503$	−19.5945			−0.873674			−0.436837	−	0.899541i	$-0.643901\pi$
$503$	−19.5945			−0.873674			−0.436837	+	0.899541i	$0.643901\pi$
$504$	1.10347	+	2.76029i	0.0491523	+	0.122953i
$505$	31.3509			1.39510
$506$	28.6794	−	49.6742i	1.27495	−	2.20829i
$507$	−1.40731	+	19.6084i	−0.0625008	+	0.870839i
$508$	−20.1926	−	34.9745i	−0.895900	−	1.55174i
$509$	14.4162	+	24.9696i	0.638988	+	1.10676i	0.985655	+	0.168772i	$0.0539800\pi$
$509$	14.4162	+	24.9696i	0.638988	+	1.10676i	−0.346667	+	0.937988i	$0.612687\pi$
$510$	6.27915	−	3.04830i	0.278045	−	0.134981i
$511$	0.113279	−	0.196205i	0.00501117	−	0.00867960i
$512$	50.7542			2.24304
$513$	7.34033	−	33.6224i	0.324083	−	1.48447i
$514$	−41.8546			−1.84613
$515$	−20.1338	+	34.8728i	−0.887202	+	1.53668i
$516$	−7.04308	+	3.41916i	−0.310054	+	0.150520i
$517$	13.7208	+	23.7652i	0.603442	+	1.04519i
$518$	−0.801440	−	1.38814i	−0.0352133	−	0.0609912i
$519$	1.94738	−	27.1334i	0.0854807	−	1.19102i
$520$	−11.5703	+	20.0403i	−0.507390	+	0.878825i
$521$	39.0982			1.71292			0.856461	−	0.516211i	$-0.172658\pi$
$521$	39.0982			1.71292			0.856461	+	0.516211i	$0.172658\pi$
$522$	−65.8404	−	9.49977i	−2.88176	−	0.415794i
$523$	−20.7298			−0.906453			−0.453226	−	0.891395i	$-0.649727\pi$
$523$	−20.7298			−0.906453			−0.453226	+	0.891395i	$0.649727\pi$
$524$	20.3570	−	35.2594i	0.889301	−	1.54032i
$525$	−0.626529	−	0.424274i	−0.0273440	−	0.0185168i
$526$	20.4839	+	35.4791i	0.893139	+	1.54696i
$527$	0.477375	+	0.826839i	0.0207948	+	0.0360177i
$528$	39.3908	+	26.6747i	1.71426	+	1.16087i
$529$	−6.77193	+	11.7293i	−0.294432	+	0.509971i
$530$	−16.4485			−0.714478
$531$	−17.5175	−	2.52751i	−0.760194	−	0.109685i
$532$	4.60980			0.199860
$533$	7.13837	−	12.3640i	0.309197	−	0.535545i
$534$	−5.02908	+	70.0714i	−0.217630	+	3.03229i
$535$	14.4617	+	25.0484i	0.625233	+	1.08293i
$536$	34.3889	+	59.5634i	1.48538	+	2.57275i
$537$	−23.9710	+	11.6371i	−1.03443	+	0.502176i
$538$	20.1529	−	34.9058i	0.868851	−	1.50489i
$539$	−25.9232			−1.11659
$540$	−48.6209	−	44.2654i	−2.09231	−	1.90488i
$541$	42.2499			1.81647			0.908233	−	0.418466i	$-0.137432\pi$
$541$	42.2499			1.81647			0.908233	+	0.418466i	$0.137432\pi$
$542$	38.9202	−	67.4117i	1.67177	−	2.89558i
$543$	6.52904	−	3.16961i	0.280188	−	0.136021i
$544$	1.69230	+	2.93115i	0.0725567	+	0.125672i
$545$	−12.1648	−	21.0700i	−0.521082	−	0.902540i
$546$	−0.0626224	+	0.872534i	−0.00267999	+	0.0373410i
$547$	6.84352	−	11.8533i	0.292608	−	0.506811i	−0.681818	−	0.731522i	$-0.738810\pi$
$547$	6.84352	−	11.8533i	0.292608	−	0.506811i	0.974426	+	0.224711i	$0.0721437\pi$
$548$	−66.0262			−2.82050
$549$	−4.62161	−	11.5608i	−0.197245	−	0.493405i
$550$	−26.9195			−1.14785
$551$	−28.7571	+	49.8087i	−1.22509	+	2.12192i
$552$	−55.7906	−	37.7804i	−2.37461	−	1.60804i
$553$	0.641212	+	1.11061i	0.0272671	+	0.0472280i
$554$	24.7094	+	42.7979i	1.04980	+	1.81831i
$555$	16.3673	+	11.0836i	0.694752	+	0.470473i
$556$	28.1337	−	48.7290i	1.19314	−	2.06657i
$557$	−19.8203			−0.839813			−0.419907	−	0.907567i	$-0.637937\pi$
$557$	−19.8203			−0.839813			−0.419907	+	0.907567i	$0.637937\pi$
$558$	8.02471	−	10.1938i	0.339713	−	0.431539i
$559$	−1.28451			−0.0543291
$560$	1.59314	−	2.75939i	0.0673223	−	0.116606i
$561$	0.259741	−	3.61904i	0.0109663	−	0.152796i
$562$	−23.3774	−	40.4908i	−0.986115	−	1.70800i
$563$	−20.6593	−	35.7830i	−0.870686	−	1.50807i	−0.861288	−	0.508117i	$-0.830342\pi$
$563$	−20.6593	−	35.7830i	−0.870686	−	1.50807i	−0.00939822	−	0.999956i	$-0.502992\pi$
$564$	52.0128	−	25.2503i	2.19013	−	1.06323i
$565$	−7.55381	+	13.0836i	−0.317791	+	0.550430i
$566$	−30.6911			−1.29004
$567$	−1.32931	−	0.391755i	−0.0558259	−	0.0164522i
$568$	−81.2005			−3.40710
$569$	−2.77982	+	4.81479i	−0.116536	+	0.201846i	−0.918393	−	0.395670i	$-0.870512\pi$
$569$	−2.77982	+	4.81479i	−0.116536	+	0.201846i	0.801857	+	0.597516i	$0.203846\pi$
$570$	−73.7689	+	35.8121i	−3.08984	+	1.50000i
$571$	21.1657	+	36.6600i	0.885756	+	1.53417i	0.844845	+	0.535011i	$0.179693\pi$
$571$	21.1657	+	36.6600i	0.885756	+	1.53417i	0.0409107	+	0.999163i	$0.486974\pi$
$572$	10.7876	+	18.6847i	0.451053	+	0.781247i
$573$	−2.04876	+	28.5459i	−0.0855883	+	1.19252i
$574$	−2.18504	+	3.78461i	−0.0912020	+	0.157966i
$575$	17.1507			0.715234
$576$	1.01546	−	1.28995i	0.0423110	−	0.0537479i
$577$	18.7514			0.780631			0.390316	−	0.920681i	$-0.372366\pi$
$577$	18.7514			0.780631			0.390316	+	0.920681i	$0.372366\pi$
$578$	−21.2987	+	36.8904i	−0.885907	+	1.53444i
$579$	−0.639340	−	0.432949i	−0.0265700	−	0.0179927i
$580$	54.9437	+	95.1653i	2.28141	+	3.95153i
$581$	0.537195	+	0.930450i	0.0222866	+	0.0386016i
$582$	−60.5937	−	41.0329i	−2.51169	−	1.70087i
$583$	−4.27517	+	7.40481i	−0.177059	+	0.306676i
$584$	−9.46820			−0.391797
$585$	−4.00449	−	10.0171i	−0.165565	−	0.414158i
$586$	−44.8990			−1.85476
$587$	6.01774	−	10.4230i	0.248379	−	0.430204i	−0.714698	−	0.699434i	$-0.753436\pi$
$587$	6.01774	−	10.4230i	0.248379	−	0.430204i	0.963076	+	0.269229i	$0.0867690\pi$
$588$	−3.90995	+	54.4783i	−0.161244	+	2.24665i
$589$	−5.60832	−	9.71390i	−0.231087	−	0.400254i
$590$	21.0864	+	36.5227i	0.868112	+	1.50361i
$591$	−3.56756	+	1.73192i	−0.146750	+	0.0712417i
$592$	−15.0663	+	26.0956i	−0.619221	+	1.07252i
$593$	15.9739			0.655970			0.327985	−	0.944683i	$-0.393630\pi$
$593$	15.9739			0.655970			0.327985	+	0.944683i	$0.393630\pi$
$594$	−46.9732	+	14.9772i	−1.92733	+	0.614521i
$595$	−0.243015			−0.00996264
$596$	−36.9515	+	64.0018i	−1.51359	+	2.62162i
$597$	6.11437	−	2.96830i	0.250244	−	0.121485i
$598$	−9.91390	−	17.1714i	−0.405410	−	0.702190i
$599$	−1.12275	−	1.94466i	−0.0458743	−	0.0794565i	0.842177	−	0.539202i	$-0.181274\pi$
$599$	−1.12275	−	1.94466i	−0.0458743	−	0.0794565i	−0.888051	+	0.459745i	$0.847941\pi$
$600$	−2.26373	+	31.5412i	−0.0924165	+	1.28766i
$601$	−2.39385	+	4.14626i	−0.0976470	+	0.169130i	−0.910710	−	0.413046i	$-0.864465\pi$
$601$	−2.39385	+	4.14626i	−0.0976470	+	0.169130i	0.813063	+	0.582175i	$0.197798\pi$
$602$	0.393187			0.0160251
$603$	−31.7350	−	4.57887i	−1.29235	−	0.186466i
$604$	−72.5292			−2.95117
$605$	−3.93029	+	6.80747i	−0.159789	+	0.276763i
$606$	−41.0107	−	27.7717i	−1.66595	−	1.12815i
$607$	−14.5002	−	25.1152i	−0.588547	−	1.01939i	−0.994423	−	0.105465i	$-0.966367\pi$
$607$	−14.5002	−	25.1152i	−0.588547	−	1.01939i	0.405876	−	0.913928i	$-0.366966\pi$
$608$	−19.8815	−	34.4358i	−0.806302	−	1.39656i
$609$	1.91771	+	1.29864i	0.0777095	+	0.0526234i
$610$	−14.8333	+	25.6921i	−0.600584	+	1.04024i
$611$	9.48606			0.383765
$612$	−7.56635	−	1.09171i	−0.305851	−	0.0441297i
$613$	−36.6015			−1.47832			−0.739160	−	0.673530i	$-0.764777\pi$
$613$	−36.6015			−1.47832			−0.739160	+	0.673530i	$0.764777\pi$
$614$	−12.6567	+	21.9220i	−0.510782	+	0.884700i
$615$	3.85799	−	53.7544i	0.155569	−	2.16759i
$616$	−1.84103	−	3.18876i	−0.0741772	−	0.128479i
$617$	17.9241	+	31.0455i	0.721599	+	1.24985i	0.960359	+	0.278767i	$0.0899257\pi$
$617$	17.9241	+	31.0455i	0.721599	+	1.24985i	−0.238760	+	0.971079i	$0.576741\pi$
$618$	57.2290	−	27.7826i	2.30209	−	1.11758i
$619$	16.4769	−	28.5388i	0.662261	−	1.14707i	−0.317759	−	0.948171i	$-0.602930\pi$
$619$	16.4769	−	28.5388i	0.662261	−	1.14707i	0.980020	−	0.198898i	$-0.0637363\pi$
$620$	−21.4307			−0.860678
$621$	29.9271	−	9.54212i	1.20093	−	0.382912i
$622$	66.6303			2.67163
$623$	1.22294	−	2.11820i	0.0489962	−	0.0848640i
$624$	14.7939	−	7.18188i	0.592228	−	0.287505i
$625$	15.5682	+	26.9649i	0.622727	+	1.07860i
$626$	6.09608	+	10.5587i	0.243649	+	0.422012i
$627$	−3.05151	+	42.5174i	−0.121865	+	1.69798i
$628$	−3.42586	+	5.93376i	−0.136707	+	0.236783i
$629$	2.29820			0.0916351
$630$	1.22577	+	3.06623i	0.0488358	+	0.122161i
$631$	10.8066			0.430203			0.215101	−	0.976592i	$-0.430992\pi$
$631$	10.8066			0.430203			0.215101	+	0.976592i	$0.430992\pi$
$632$	26.7972	−	46.4141i	1.06593	−	1.84625i
$633$	−25.8976	−	17.5374i	−1.02934	−	0.697049i
$634$	27.2032	+	47.1173i	1.08038	+	1.87127i
$635$	−12.5059	−	21.6609i	−0.496282	−	0.859585i
$636$	14.9166	+	10.1012i	0.591482	+	0.400541i
$637$	−4.48056	+	7.76056i	−0.177526	+	0.307485i
$638$	82.3965			3.26211
$639$	23.4151	−	29.7443i	0.926287	−	1.17667i
$640$	29.7029			1.17411
$641$	7.98234	−	13.8258i	0.315284	−	0.546087i	−0.664214	−	0.747542i	$-0.731234\pi$
$641$	7.98234	−	13.8258i	0.315284	−	0.546087i	0.979498	+	0.201455i	$0.0645670\pi$
$642$	3.27109	−	45.5769i	0.129100	−	1.79878i
$643$	−17.8131	−	30.8532i	−0.702481	−	1.21673i	−0.967593	−	0.252515i	$-0.918742\pi$
$643$	−17.8131	−	30.8532i	−0.702481	−	1.21673i	0.265113	−	0.964217i	$-0.414591\pi$
$644$	2.10378	+	3.64386i	0.0829007	+	0.143588i
$645$	−4.36201	+	2.11759i	−0.171754	+	0.0833802i
$646$	−4.76697	+	8.25664i	−0.187554	+	0.324853i
$647$	16.4474			0.646612			0.323306	−	0.946294i	$-0.395206\pi$
$647$	16.4474			0.646612			0.323306	+	0.946294i	$0.395206\pi$
$648$	13.5984	+	56.2972i	0.534196	+	2.21156i
$649$	21.9224			0.860530
$650$	−4.65278	+	8.05885i	−0.182497	+	0.316094i
$651$	−0.406334	+	0.197260i	−0.0159255	+	0.00773124i
$652$	−41.0021	−	71.0177i	−1.60577	−	2.78127i
$653$	2.91944	+	5.05662i	0.114246	+	0.197881i	0.917478	−	0.397786i	$-0.130221\pi$
$653$	2.91944	+	5.05662i	0.114246	+	0.197881i	−0.803232	+	0.595667i	$0.796888\pi$
$654$	−2.75156	+	38.3381i	−0.107594	+	1.49914i
$655$	12.6078	−	21.8373i	0.492626	−	0.853254i
$656$	82.1535			3.20755
$657$	2.73027	−	3.46827i	0.106518	−	0.135310i
$658$	−2.90367			−0.113197
$659$	−0.379323	+	0.657008i	−0.0147763	+	0.0255934i	−0.873319	−	0.487149i	$-0.838037\pi$
$659$	−0.379323	+	0.657008i	−0.0147763	+	0.0255934i	0.858543	+	0.512742i	$0.171370\pi$
$660$	67.4359	+	45.6664i	2.62494	+	1.77756i
$661$	22.5030	+	38.9764i	0.875266	+	1.51601i	0.856479	+	0.516182i	$0.172647\pi$
$661$	22.5030	+	38.9764i	0.875266	+	1.51601i	0.0187875	+	0.999823i	$0.494019\pi$
$662$	5.20475	+	9.01489i	0.202288	+	0.350374i
$663$	−1.03853	−	0.703274i	−0.0403332	−	0.0273129i
$664$	22.4502	−	38.8849i	0.871236	−	1.50903i
$665$	2.85500			0.110712
$666$	−11.5921	−	28.9974i	−0.449185	−	1.12363i
$667$	−52.4957			−2.03264
$668$	47.5612	−	82.3785i	1.84020	−	3.18732i
$669$	−1.03139	+	14.3706i	−0.0398759	+	0.555600i
$670$	38.2004	+	66.1650i	1.47581	+	2.55618i
$671$	7.71072	+	13.3554i	0.297669	+	0.515578i
$672$	−1.44046	+	0.699289i	−0.0555668	+	0.0269757i
$673$	8.44242	−	14.6227i	0.325431	−	0.563664i	−0.656168	−	0.754615i	$-0.727824\pi$
$673$	8.44242	−	14.6227i	0.325431	−	0.563664i	0.981600	+	0.190951i	$0.0611572\pi$
$674$	−11.7581			−0.452904
$675$	−10.9010	−	9.92449i	−0.419579	−	0.381994i
$676$	−51.3040			−1.97323
$677$	−17.8495	+	30.9163i	−0.686014	+	1.18821i	0.287103	+	0.957900i	$0.407308\pi$
$677$	−17.8495	+	30.9163i	−0.686014	+	1.18821i	−0.973117	+	0.230311i	$0.926026\pi$
$678$	21.4712	−	10.4235i	0.824596	−	0.400311i
$679$	1.27392	+	2.20649i	0.0488886	+	0.0846775i
$680$	5.07798	+	8.79531i	0.194731	+	0.337285i
$681$	−1.72786	+	24.0748i	−0.0662119	+	0.922547i
$682$	−8.03466	+	13.9164i	−0.307663	+	0.532888i
$683$	13.0146			0.497989			0.248995	−	0.968505i	$-0.419900\pi$
$683$	13.0146			0.497989			0.248995	+	0.968505i	$0.419900\pi$
$684$	88.8913	+	12.8257i	3.39884	+	0.490401i
$685$	−40.8922			−1.56241
$686$	2.74765	−	4.75907i	0.104906	−	0.181702i
$687$	−2.39255	−	1.62019i	−0.0912813	−	0.0618140i
$688$	−3.69577	−	6.40126i	−0.140900	−	0.244046i
$689$	1.47784	+	2.55970i	0.0563013	+	0.0975167i
$690$	−61.9741	−	41.9677i	−2.35932	−	1.59768i
$691$	0.417863	−	0.723760i	0.0158963	−	0.0275331i	−0.857968	−	0.513703i	$-0.828273\pi$
$691$	0.417863	−	0.723760i	0.0158963	−	0.0275331i	0.873864	+	0.486170i	$0.161607\pi$
$692$	70.9926			2.69873
$693$	1.69895	+	0.245133i	0.0645377	+	0.00931182i
$694$	−33.8379			−1.28447
$695$	17.4241	−	30.1795i	0.660935	−	1.14477i
$696$	6.92894	−	96.5426i	0.262641	−	3.65944i
$697$	−3.13290	−	5.42634i	−0.118667	−	0.205537i
$698$	3.74317	+	6.48337i	0.141681	+	0.245399i
$699$	−0.155711	+	0.0755922i	−0.00588955	+	0.00285916i
$700$	0.987345	−	1.71013i	0.0373181	−	0.0646369i
$701$	45.3676			1.71351			0.856755	−	0.515723i	$-0.172477\pi$
$701$	45.3676			1.71351			0.856755	+	0.515723i	$0.172477\pi$
$702$	−3.63517	+	16.6509i	−0.137201	+	0.628449i
$703$	−26.9998			−1.01832
$704$	−1.01672	+	1.76102i	−0.0383192	+	0.0663708i
$705$	32.2132	−	15.6383i	1.21322	−	0.588974i
$706$	37.5879	+	65.1042i	1.41464	+	2.45023i
$707$	0.862208	+	1.49339i	0.0324267	+	0.0561647i
$708$	3.30652	−	46.0706i	0.124267	−	1.73144i
$709$	−0.101566	+	0.175917i	−0.00381438	+	0.00660669i	−0.867926	−	0.496693i	$-0.834547\pi$
$709$	−0.101566	+	0.175917i	−0.00381438	+	0.00660669i	0.864112	+	0.503300i	$0.167881\pi$
$710$	−90.2003			−3.38516
$711$	9.27455	+	23.2001i	0.347823	+	0.870070i
$712$	−102.217			−3.83075
$713$	5.11896	−	8.86631i	0.191707	−	0.332046i
$714$	0.317893	+	0.215271i	0.0118968	+	0.00805632i
$715$	6.68112	+	11.5720i	0.249860	+	0.432770i
$716$	−34.7698	−	60.2230i	−1.29941	−	2.25064i
$717$	16.7532	+	11.3450i	0.625661	+	0.423686i
$718$	−45.2361	+	78.3512i	−1.68820	+	2.92404i
$719$	−15.9357			−0.594302			−0.297151	−	0.954830i	$-0.596037\pi$
$719$	−15.9357			−0.594302			−0.297151	+	0.954830i	$0.596037\pi$
$720$	38.3979	−	48.7771i	1.43101	−	1.81782i
$721$	−2.21487			−0.0824861
$722$	31.7456	−	54.9851i	1.18145	−	2.04633i
$723$	−0.621208	+	8.65544i	−0.0231030	+	0.321899i
$724$	9.47033	+	16.4031i	0.351962	+	0.609616i
$725$	12.3186	+	21.3364i	0.457501	+	0.792416i
$726$	11.1716	−	5.42340i	0.414617	−	0.201281i
$727$	22.9224	−	39.7028i	0.850146	−	1.47250i	−0.0309292	−	0.999522i	$-0.509847\pi$
$727$	22.9224	−	39.7028i	0.850146	−	1.47250i	0.881076	−	0.472975i	$-0.156820\pi$
$728$	−1.27282			−0.0471737
$729$	−24.5433	−	11.2528i	−0.909013	−	0.416769i
$730$	−10.5176			−0.389274
$731$	−0.281874	+	0.488220i	−0.0104255	+	0.0180575i
$732$	29.2297	−	14.1899i	1.08036	−	0.524476i
$733$	−3.17170	−	5.49354i	−0.117149	−	0.202908i	0.801488	−	0.598011i	$-0.204042\pi$
$733$	−3.17170	−	5.49354i	−0.117149	−	0.202908i	−0.918637	+	0.395103i	$0.870709\pi$
$734$	−10.1002	−	17.4940i	−0.372805	−	0.645717i
$735$	−2.42156	+	33.7402i	−0.0893205	+	1.24452i
$736$	18.1468	−	31.4311i	0.668898	−	1.15857i
$737$	39.7150			1.46292
$738$	−52.6642	+	66.8997i	−1.93860	+	2.46261i
$739$	32.6732			1.20190			0.600951	−	0.799286i	$-0.294789\pi$
$739$	32.6732			1.20190			0.600951	+	0.799286i	$0.294789\pi$
$740$	−25.7931	+	44.6750i	−0.948174	+	1.64228i
$741$	12.2009	+	8.26223i	0.448212	+	0.303521i
$742$	−0.452365	−	0.783519i	−0.0166068	−	0.0287639i
$743$	10.1642	+	17.6049i	0.372888	+	0.645861i	0.990009	−	0.141008i	$-0.0450342\pi$
$743$	10.1642	+	17.6049i	0.372888	+	0.645861i	−0.617120	+	0.786869i	$0.711701\pi$
$744$	15.6300	+	10.5843i	0.573023	+	0.388041i
$745$	−22.8852	+	39.6384i	−0.838450	+	1.45224i
$746$	−4.96385			−0.181739
$747$	7.77005	+	19.4366i	0.284291	+	0.711147i
$748$	9.46897			0.346220
$749$	−0.795446	+	1.37775i	−0.0290650	+	0.0503420i
$750$	1.91706	−	26.7109i	0.0700011	−	0.975343i
$751$	6.69532	+	11.5966i	0.244316	+	0.423167i	0.961939	−	0.273264i	$-0.0881034\pi$
$751$	6.69532	+	11.5966i	0.244316	+	0.423167i	−0.717623	+	0.696431i	$0.754770\pi$
$752$	27.2931	+	47.2730i	0.995276	+	1.72387i
$753$	7.37992	−	3.58268i	0.268939	−	0.130560i
$754$	14.2414	−	24.6669i	0.518642	−	0.898315i
$755$	−44.9197			−1.63479
$756$	0.771403	−	3.53342i	0.0280557	−	0.128509i
$757$	33.6454			1.22286			0.611432	−	0.791297i	$-0.290594\pi$
$757$	33.6454			1.22286			0.611432	+	0.791297i	$0.290594\pi$
$758$	10.8878	−	18.8581i	0.395461	−	0.684959i
$759$	−35.0009	+	16.9917i	−1.27045	+	0.616758i
$760$	−59.6573	−	103.329i	−2.16400	−	3.74815i
$761$	−7.03148	−	12.1789i	−0.254891	−	0.441484i	0.709975	−	0.704227i	$-0.248706\pi$
$761$	−7.03148	−	12.1789i	−0.254891	−	0.441484i	−0.964866	+	0.262743i	$0.915373\pi$
$762$	−2.82871	+	39.4132i	−0.102474	+	1.42779i
$763$	0.669108	−	1.15893i	0.0242233	−	0.0419561i
$764$	−74.6883			−2.70213
$765$	−4.68608	−	0.676131i	−0.169426	−	0.0244456i
$766$	−25.7628			−0.930849
$767$	3.78907	−	6.56287i	0.136816	−	0.236971i
$768$	−40.4246	−	27.3748i	−1.45870	−	0.987803i
$769$	1.83464	+	3.17768i	0.0661587	+	0.114590i	0.897207	−	0.441609i	$-0.145592\pi$
$769$	1.83464	+	3.17768i	0.0661587	+	0.114590i	−0.831049	+	0.556200i	$0.812259\pi$
$770$	−2.04508	−	3.54218i	−0.0736996	−	0.127651i
$771$	23.5077	+	15.9190i	0.846610	+	0.573309i
$772$	1.00753	−	1.74510i	0.0362619	−	0.0628075i
$773$	27.7108			0.996686			0.498343	−	0.866980i	$-0.333942\pi$
$773$	27.7108			0.996686			0.498343	+	0.866980i	$0.333942\pi$
$774$	7.58187	+	1.09395i	0.272525	+	0.0393212i
$775$	−4.80485			−0.172595
$776$	53.2390	−	92.2126i	1.91117	−	3.31024i
$777$	−0.0778331	+	1.08447i	−0.00279225	+	0.0389051i
$778$	2.02284	+	3.50367i	0.0725225	+	0.125613i
$779$	36.8060	+	63.7499i	1.31871	+	2.28408i
$780$	25.3267	−	12.2952i	0.906841	−	0.440238i
$781$	−23.4441	+	40.6064i	−0.838897	+	1.45301i
$782$	−8.70205			−0.311185
$783$	33.3662	+	30.3773i	1.19241	+	1.08560i
$784$	−51.5655			−1.84163
$785$	−2.12175	+	3.67497i	−0.0757283	+	0.131165i
$786$	−35.8367	+	17.3974i	−1.27825	+	0.620545i
$787$	13.6833	+	23.7002i	0.487757	+	0.844820i	0.999901	−	0.0140795i	$-0.00448178\pi$
$787$	13.6833	+	23.7002i	0.487757	+	0.844820i	−0.512144	+	0.858900i	$0.671148\pi$
$788$	−5.17472	−	8.96287i	−0.184342	−	0.319289i
$789$	1.98932	−	27.7177i	0.0708218	−	0.986777i
$790$	29.7672	−	51.5584i	1.05907	−	1.83436i
$791$	−0.830975			−0.0295461
$792$	−26.6288	−	66.6114i	−0.946215	−	2.36693i
$793$	5.33089			0.189306
$794$	−6.85879	+	11.8798i	−0.243409	+	0.421597i
$795$	9.23834	+	6.25603i	0.327650	+	0.221879i
$796$	8.86885	+	15.3613i	0.314348	+	0.544467i
$797$	−19.2017	−	33.2583i	−0.680159	−	1.17807i	−0.974932	−	0.222503i	$-0.928577\pi$
$797$	−19.2017	−	33.2583i	−0.680159	−	1.17807i	0.294773	−	0.955567i	$-0.404756\pi$
$798$	−3.73468	−	2.52906i	−0.132206	−	0.0895276i
$799$	2.08163	−	3.60548i	0.0736427	−	0.127553i
$800$	−17.0332			−0.602215
$801$	29.4756	−	37.4430i	1.04147	−	1.32298i
$802$	34.4765			1.21741
$803$	−2.73365	+	4.73482i	−0.0964684	+	0.167088i
$804$	5.99015	−	83.4622i	0.211256	−	2.94349i
$805$	1.30294	+	2.25676i	0.0459227	+	0.0795404i
$806$	2.77742	+	4.81064i	0.0978306	+	0.169448i
$807$	−24.5949	+	11.9399i	−0.865783	+	0.420306i
$808$	36.0329	−	62.4109i	1.26763	−	2.19561i
$809$	38.1968			1.34293			0.671464	−	0.741037i	$-0.265666\pi$
$809$	38.1968			1.34293			0.671464	+	0.741037i	$0.265666\pi$
$810$	15.1056	+	62.5368i	0.530756	+	2.19732i
$811$	−7.50867			−0.263665			−0.131833	−	0.991272i	$-0.542086\pi$
$811$	−7.50867			−0.263665			−0.131833	+	0.991272i	$0.542086\pi$
$812$	−3.02211	+	5.23445i	−0.106055	+	0.183693i
$813$	−47.4990	+	23.0590i	−1.66586	+	0.808715i
$814$	19.3404	+	33.4985i	0.677879	+	1.17412i
$815$	−25.3939	−	43.9835i	−0.889510	−	1.54068i
$816$	0.516670	−	7.19888i	0.0180871	−	0.252011i
$817$	3.31153	−	5.73573i	0.115856	−	0.200668i
$818$	−47.8375			−1.67260
$819$	0.367032	−	0.466242i	0.0128251	−	0.0162918i
$820$	140.645			4.91152
$821$	−3.60607	+	6.24590i	−0.125853	+	0.217984i	−0.922066	−	0.387033i	$-0.873500\pi$
$821$	−3.60607	+	6.24590i	−0.125853	+	0.217984i	0.796213	+	0.605016i	$0.206833\pi$
$822$	53.4919	+	36.2237i	1.86574	+	1.26345i
$823$	−1.95071	−	3.37873i	−0.0679975	−	0.117775i	0.830022	−	0.557730i	$-0.188328\pi$
$823$	−1.95071	−	3.37873i	−0.0679975	−	0.117775i	−0.898020	+	0.439955i	$0.854994\pi$
$824$	46.2814	+	80.1616i	1.61229	+	2.79256i
$825$	15.1194	+	10.2386i	0.526390	+	0.356462i
$826$	−1.15983	+	2.00888i	−0.0403556	+	0.0698980i
$827$	−56.2324			−1.95539			−0.977696	−	0.210023i	$-0.932646\pi$
$827$	−56.2324			−1.95539			−0.977696	+	0.210023i	$0.932646\pi$
$828$	30.4293	+	76.1183i	1.05749	+	2.64529i
$829$	−21.3784			−0.742502			−0.371251	−	0.928533i	$-0.621071\pi$
$829$	−21.3784			−0.742502			−0.371251	+	0.928533i	$0.621071\pi$
$830$	24.9384	−	43.1946i	0.865626	−	1.49931i
$831$	2.39969	−	33.4355i	0.0832444	−	1.15987i
$832$	0.351461	+	0.608749i	0.0121847	+	0.0211046i
$833$	1.96644	+	3.40597i	0.0681330	+	0.118010i
$834$	−49.5269	+	24.0435i	−1.71498	+	0.832558i
$835$	29.4562	−	51.0197i	1.01937	−	1.76561i
$836$	−111.244			−3.84744
$837$	−8.38422	+	2.67327i	−0.289801	+	0.0924016i
$838$	−23.4813			−0.811149
$839$	−16.2334	+	28.1171i	−0.560439	+	0.970709i	0.437019	+	0.899452i	$0.356034\pi$
$839$	−16.2334	+	28.1171i	−0.560439	+	0.970709i	−0.997458	+	0.0712567i	$0.977299\pi$
$840$	−4.32229	+	2.09831i	−0.149133	+	0.0723987i
$841$	−23.2053	−	40.1928i	−0.800184	−	1.38596i
$842$	−6.35444	−	11.0062i	−0.218989	−	0.379299i
$843$	−2.27033	+	31.6331i	−0.0781943	+	1.08950i
$844$	40.8120	−	70.6885i	1.40481	−	2.43320i
$845$	−31.7742			−1.09307
$846$	−55.9917	−	8.07875i	−1.92504	−	0.277753i
$847$	−0.432362			−0.0148561
$848$	−8.50403	+	14.7294i	−0.292030	+	0.505810i
$849$	17.2377	+	11.6731i	0.591597	+	0.400618i
$850$	2.04202	+	3.53688i	0.0700406	+	0.121314i
$851$	−12.3219	−	21.3422i	−0.422391	−	0.731602i
$852$	81.7996	+	55.3932i	2.80241	+	1.89774i
$853$	4.38253	−	7.59076i	0.150055	−	0.259903i	−0.781193	−	0.624290i	$-0.785388\pi$
$853$	4.38253	−	7.59076i	0.150055	−	0.259903i	0.931247	+	0.364387i	$0.118722\pi$
$854$	−1.63178			−0.0558383
$855$	55.0532	+	7.94335i	1.88278	+	0.271657i
$856$	66.4857			2.27244
$857$	−19.6447	+	34.0256i	−0.671049	+	1.16229i	0.306557	+	0.951852i	$0.400823\pi$
$857$	−19.6447	+	34.0256i	−0.671049	+	1.16229i	−0.977607	+	0.210440i	$0.932510\pi$
$858$	1.51120	−	21.0560i	0.0515917	−	0.718840i
$859$	18.7541	+	32.4830i	0.639880	+	1.10831i	0.985459	+	0.169915i	$0.0543494\pi$
$859$	18.7541	+	32.4830i	0.639880	+	1.10831i	−0.345578	+	0.938390i	$0.612317\pi$
$860$	−6.32706	−	10.9588i	−0.215751	−	0.373691i
$861$	2.66667	−	1.29457i	0.0908799	−	0.0441189i
$862$	−3.80046	+	6.58259i	−0.129444	+	0.224204i
$863$	35.2574			1.20018			0.600088	−	0.799934i	$-0.295132\pi$
$863$	35.2574			1.20018			0.600088	+	0.799934i	$0.295132\pi$
$864$	−29.7221	+	9.47674i	−1.01117	+	0.322405i
$865$	43.9680			1.49496
$866$	−2.64549	+	4.58213i	−0.0898975	+	0.155707i
$867$	25.9933	−	12.6188i	0.882779	−	0.428557i
$868$	−0.589385	−	1.02084i	−0.0200050	−	0.0346497i
$869$	−15.4737	−	26.8013i	−0.524910	−	0.909171i
$870$	7.69690	−	107.243i	0.260949	−	3.63587i
$871$	6.86434	−	11.8894i	0.232589	−	0.402857i
$872$	−55.9260			−1.89389
$873$	18.4261	+	46.0924i	0.623629	+	1.55999i
$874$	102.234			3.45811
$875$	−0.466180	+	0.807447i	−0.0157598	+	0.0272967i
$876$	9.53806	+	6.45899i	0.322261	+	0.218229i
$877$	4.40354	+	7.62715i	0.148697	+	0.257551i	0.930746	−	0.365666i	$-0.119159\pi$
$877$	4.40354	+	7.62715i	0.148697	+	0.257551i	−0.782049	+	0.623217i	$0.785825\pi$
$878$	−27.6766	−	47.9372i	−0.934039	−	1.61780i
$879$	25.2176	+	17.0769i	0.850569	+	0.575990i
$880$	−38.4455	+	66.5896i	−1.29600	+	2.24474i
$881$	−22.3061			−0.751512			−0.375756	−	0.926719i	$-0.622617\pi$
$881$	−22.3061			−0.751512			−0.375756	+	0.926719i	$0.622617\pi$
$882$	33.0559	−	41.9911i	1.11305	−	1.41391i
$883$	−12.9751			−0.436648			−0.218324	−	0.975876i	$-0.570059\pi$
$883$	−12.9751			−0.436648			−0.218324	+	0.975876i	$0.570059\pi$
$884$	1.63662	−	2.83471i	0.0550454	−	0.0953415i
$885$	2.04784	−	28.5330i	0.0688373	−	0.959127i
$886$	22.7455	+	39.3964i	0.764151	+	1.32355i
$887$	18.4547	+	31.9645i	0.619648	+	1.07326i	0.989550	+	0.144191i	$0.0460580\pi$
$887$	18.4547	+	31.9645i	0.619648	+	1.07326i	−0.369902	+	0.929071i	$0.620609\pi$
$888$	40.8760	−	19.8438i	1.37171	−	0.665914i
$889$	0.687871	−	1.19143i	0.0230705	−	0.0399592i
$890$	−113.546			−3.80609
$891$	32.0790	+	9.45384i	1.07469	+	0.316715i
$892$	−37.5997			−1.25893
$893$	−24.4555	+	42.3581i	−0.818370	+	1.41746i
$894$	65.0497	−	31.5792i	2.17559	−	1.05617i
$895$	−21.5341	−	37.2981i	−0.719804	−	1.24674i
$896$	0.816886	+	1.41489i	0.0272902	+	0.0472681i
$897$	−0.962804	+	13.4150i	−0.0321471	+	0.447913i
$898$	−50.0204	+	86.6379i	−1.66920	+	2.89115i
$899$	14.7069			0.490503
$900$	23.7971	−	30.2296i	0.793237	−	1.00765i
$901$	1.29719			0.0432158
$902$	52.7295	−	91.3302i	1.75570	−	3.04096i
$903$	−0.220834	−	0.149545i	−0.00734890	−	0.00497654i
$904$	17.3638	+	30.0751i	0.577513	+	1.00028i
$905$	5.86528	+	10.1590i	0.194969	+	0.337695i
$906$	58.7604	+	39.7914i	1.95218	+	1.32198i
$907$	−23.9021	+	41.3996i	−0.793656	+	1.37465i	0.130033	+	0.991510i	$0.458492\pi$
$907$	−23.9021	+	41.3996i	−0.793656	+	1.37465i	−0.923689	+	0.383143i	$0.874842\pi$
$908$	−62.9899			−2.09039
$909$	12.4711	+	31.1961i	0.413639	+	1.03471i
$910$	−1.41389			−0.0468699
$911$	−8.12177	+	14.0673i	−0.269086	+	0.466071i	−0.968626	−	0.248523i	$-0.920055\pi$
$911$	−8.12177	+	14.0673i	−0.269086	+	0.466071i	0.699540	+	0.714594i	$0.253388\pi$
$912$	−6.06996	+	84.5742i	−0.200996	+	2.80053i
$913$	−12.9636	−	22.4536i	−0.429033	−	0.743106i
$914$	3.92737	+	6.80241i	0.129906	+	0.225004i
$915$	18.1029	−	8.78829i	0.598463	−	0.290532i
$916$	3.77040	−	6.53053i	0.124578	−	0.215775i
$917$	1.38695			0.0458011
$918$	5.53102	+	5.03556i	0.182551	+	0.166198i
$919$	−16.1366			−0.532297			−0.266149	−	0.963932i	$-0.585751\pi$
$919$	−16.1366			−0.532297			−0.266149	+	0.963932i	$0.585751\pi$
$920$	54.4519	−	94.3134i	1.79522	−	3.10942i
$921$	15.4465	−	7.49869i	0.508978	−	0.247090i
$922$	−5.30231	−	9.18387i	−0.174622	−	0.302455i
$923$	8.10418	+	14.0368i	0.266752	+	0.462028i
$924$	−0.320686	+	4.46820i	−0.0105498	+	0.146993i
$925$	−5.78292	+	10.0163i	−0.190141	+	0.329334i
$926$	−18.1123			−0.595207
$927$	−42.7096	−	6.16235i	−1.40277	−	0.202398i
$928$	52.1360			1.71145
$929$	−7.13260	+	12.3540i	−0.234013	+	0.405322i	−0.958985	−	0.283456i	$-0.908519\pi$
$929$	−7.13260	+	12.3540i	−0.234013	+	0.405322i	0.724972	+	0.688778i	$0.241852\pi$
$930$	17.3623	+	11.7574i	0.569333	+	0.385542i
$931$	−23.1022	−	40.0141i	−0.757143	−	1.31141i
$932$	−0.225858	−	0.391198i	−0.00739823	−	0.0128141i
$933$	−37.4231	−	25.3422i	−1.22518	−	0.829666i
$934$	−13.6879	+	23.7082i	−0.447882	+	0.775755i
$935$	5.86444			0.191788
$936$	−24.5439	−	3.54131i	−0.802241	−	0.115751i
$937$	28.3390			0.925795			0.462897	−	0.886412i	$-0.346810\pi$
$937$	28.3390			0.925795			0.462897	+	0.886412i	$0.346810\pi$
$938$	−2.10116	+	3.63932i	−0.0686055	+	0.118828i
$939$	0.592031	−	8.24891i	0.0193202	−	0.269193i
$940$	46.7250	+	80.9301i	1.52400	+	2.63965i
$941$	−24.2002	−	41.9160i	−0.788904	−	1.36642i	−0.926639	−	0.375952i	$-0.877316\pi$
$941$	−24.2002	−	41.9160i	−0.788904	−	1.36642i	0.137735	−	0.990469i	$-0.456018\pi$
$942$	6.03091	−	2.92779i	0.196498	−	0.0953925i
$943$	−33.5945	+	58.1874i	−1.09399	+	1.89484i
$944$	43.6074			1.41930
$945$	0.477755	−	2.18836i	0.0155414	−	0.0711874i
$946$	−9.48839			−0.308494
$947$	17.3778	−	30.0992i	0.564703	−	0.978094i	−0.432374	−	0.901694i	$-0.642324\pi$
$947$	17.3778	−	30.0992i	0.564703	−	0.978094i	0.997077	−	0.0763999i	$-0.0243426\pi$
$948$	−58.6576	+	28.4761i	−1.90511	+	0.924861i
$949$	0.944969	+	1.63673i	0.0306750	+	0.0531307i
$950$	−23.9901	−	41.5521i	−0.778342	−	1.34813i
$951$	2.64188	−	36.8099i	0.0856688	−	1.19364i
$952$	−0.279308	+	0.483775i	−0.00905241	+	0.0156792i
$953$	−39.1055			−1.26675			−0.633375	−	0.773845i	$-0.718331\pi$
$953$	−39.1055			−1.26675			−0.633375	+	0.773845i	$0.718331\pi$
$954$	−6.54305	−	16.3673i	−0.211839	−	0.529910i
$955$	−46.2569			−1.49684
$956$	−26.4013	+	45.7285i	−0.853880	+	1.47896i
$957$	−46.2782	−	31.3387i	−1.49596	−	1.01304i
$958$	−8.70185	−	15.0720i	−0.281144	−	0.486955i
$959$	−1.12461	−	1.94788i	−0.0363156	−	0.0629004i
$960$	2.19707	+	1.48781i	0.0709100	+	0.0480190i
$961$	14.0659	−	24.3629i	0.453739	−	0.785898i
$962$	13.3712			0.431104
$963$	−19.1719	+	24.3542i	−0.617807	+	0.784804i
$964$	−22.6464			−0.729390
$965$	0.623998	−	1.08080i	0.0200872	−	0.0347921i
$966$	0.294713	−	4.10631i	0.00948223	−	0.132118i
$967$	2.84849	+	4.93373i	0.0916014	+	0.158658i	0.908185	−	0.418569i	$-0.137468\pi$
$967$	2.84849	+	4.93373i	0.0916014	+	0.158658i	−0.816584	+	0.577227i	$0.804135\pi$
$968$	9.03452	+	15.6482i	0.290380	+	0.502954i
$969$	5.81771	−	2.82428i	0.186892	−	0.0907291i
$970$	59.1397	−	102.433i	1.89886	−	3.28892i
$971$	24.9838			0.801768			0.400884	−	0.916129i	$-0.368703\pi$
$971$	24.9838			0.801768			0.400884	+	0.916129i	$0.368703\pi$
$972$	24.7059	−	65.9891i	0.792444	−	2.11660i
$973$	1.91678			0.0614493
$974$	−22.1355	+	38.3399i	−0.709268	+	1.22849i
$975$	5.67834	−	2.75663i	0.181853	−	0.0882828i
$976$	15.3379	+	26.5661i	0.490955	+	0.850359i
$977$	6.73626	+	11.6675i	0.215512	+	0.373278i	0.953431	−	0.301612i	$-0.0975246\pi$
$977$	6.73626	+	11.6675i	0.215512	+	0.373278i	−0.737919	+	0.674890i	$0.764191\pi$
$978$	−5.74386	+	80.0306i	−0.183668	+	2.55910i
$979$	−29.5121	+	51.1165i	−0.943211	+	1.63369i
$980$	−88.2788			−2.81996
$981$	16.1269	−	20.4861i	0.514893	−	0.654072i
$982$	−40.6060			−1.29579
$983$	5.61344	−	9.72276i	0.179041	−	0.310108i	−0.762511	−	0.646975i	$-0.776034\pi$
$983$	5.61344	−	9.72276i	0.179041	−	0.310108i	0.941552	+	0.336867i	$0.109367\pi$
$984$	−102.576	−	69.4624i	−3.27000	−	2.21438i
$985$	−3.20487	−	5.55100i	−0.102116	−	0.176870i
$986$	−6.25030	−	10.8258i	−0.199050	−	0.344765i
$987$	1.63085	+	1.10438i	0.0519105	+	0.0351528i
$988$	−19.2274	+	33.3028i	−0.611705	+	1.05950i
$989$	6.04515			0.192225
$990$	−29.5802	−	73.9942i	−0.940122	−	2.35169i
$991$	−55.8592			−1.77443			−0.887213	−	0.461360i	$-0.847362\pi$
$991$	−55.8592			−1.77443			−0.887213	+	0.461360i	$0.847362\pi$
$992$	−5.08390	+	8.80556i	−0.161414	+	0.279577i
$993$	0.505468	−	7.04281i	0.0160405	−	0.223497i
$994$	−2.48068	−	4.29666i	−0.0786823	−	0.136282i
$995$	5.49276	+	9.51374i	0.174132	+	0.301606i
$996$	−49.1422	+	23.8568i	−1.55713	+	0.755930i
$997$	26.8633	−	46.5286i	0.850769	−	1.47358i	−0.0297456	−	0.999558i	$-0.509470\pi$
$997$	26.8633	−	46.5286i	0.850769	−	1.47358i	0.880515	−	0.474018i	$-0.157197\pi$
$998$	11.5543			0.365745
$999$	−4.51814	+	20.6954i	−0.142948	+	0.654773i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.2.f.c.259.19	yes	38
3.2	odd	2		1161.2.f.c.775.1		38
9.2	odd	6		3483.2.a.r.1.19		19
9.4	even	3	inner	387.2.f.c.130.19	✓	38
9.5	odd	6		1161.2.f.c.388.1		38
9.7	even	3		3483.2.a.s.1.1		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
387.2.f.c.130.19	✓	38	9.4	even	3	inner
387.2.f.c.259.19	yes	38	1.1	even	1	trivial
1161.2.f.c.388.1		38	9.5	odd	6
1161.2.f.c.775.1		38	3.2	odd	2
3483.2.a.r.1.19		19	9.2	odd	6
3483.2.a.s.1.1		19	9.7	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	387.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.27673 - 2.21136i) q^{2} +(-1.55815 + 0.756424i) q^{3} +(-2.26008 - 3.91458i) q^{4} +(-1.39974 - 2.42442i) q^{5} +(-0.316608 + 4.41138i) q^{6} +(0.0769910 - 0.133352i) q^{7} -6.43513 q^{8} +(1.85565 - 2.35724i) q^{9} +O(q^{10})\)	\(q+(1.27673 - 2.21136i) q^{2} +(-1.55815 + 0.756424i) q^{3} +(-2.26008 - 3.91458i) q^{4} +(-1.39974 - 2.42442i) q^{5} +(-0.316608 + 4.41138i) q^{6} +(0.0769910 - 0.133352i) q^{7} -6.43513 q^{8} +(1.85565 - 2.35724i) q^{9} -7.14837 q^{10} +(-1.85795 + 3.21806i) q^{11} +(6.48262 + 4.38991i) q^{12} +(0.642256 + 1.11242i) q^{13} +(-0.196594 - 0.340510i) q^{14} +(4.01489 + 2.71881i) q^{15} +(-3.69577 + 6.40126i) q^{16} +0.563748 q^{17} +(-2.84355 - 7.11307i) q^{18} -6.62305 q^{19} +(-6.32706 + 10.9588i) q^{20} +(-0.0190925 + 0.266020i) q^{21} +(4.74420 + 8.21719i) q^{22} +(-3.02258 - 5.23526i) q^{23} +(10.0269 - 4.86769i) q^{24} +(-1.41855 + 2.45700i) q^{25} +3.27995 q^{26} +(-1.10830 + 5.07658i) q^{27} -0.696024 q^{28} +(4.34197 - 7.52050i) q^{29} +(11.1382 - 5.40719i) q^{30} +(0.846788 + 1.46668i) q^{31} +(3.00187 + 5.19939i) q^{32} +(0.460740 - 6.41961i) q^{33} +(0.719755 - 1.24665i) q^{34} -0.431070 q^{35} +(-13.4215 - 1.93652i) q^{36} +4.07664 q^{37} +(-8.45585 + 14.6460i) q^{38} +(-1.84219 - 1.24750i) q^{39} +(9.00752 + 15.6015i) q^{40} +(-5.55726 - 9.62547i) q^{41} +(0.563891 + 0.381857i) q^{42} +(-0.500000 + 0.866025i) q^{43} +16.7964 q^{44} +(-8.31237 - 1.19935i) q^{45} -15.4361 q^{46} +(3.69248 - 6.39556i) q^{47} +(0.916490 - 12.7697i) q^{48} +(3.48814 + 6.04164i) q^{49} +(3.62222 + 6.27386i) q^{50} +(-0.878403 + 0.426432i) q^{51} +(2.90310 - 5.02832i) q^{52} +2.30102 q^{53} +(9.81116 + 8.93228i) q^{54} +10.4026 q^{55} +(-0.495447 + 0.858140i) q^{56} +(10.3197 - 5.00983i) q^{57} +(-11.0870 - 19.2033i) q^{58} +(-2.94982 - 5.10923i) q^{59} +(1.56901 - 21.8613i) q^{60} +(2.07507 - 3.59412i) q^{61} +4.32448 q^{62} +(-0.171475 - 0.428941i) q^{63} +0.547229 q^{64} +(1.79798 - 3.11420i) q^{65} +(-13.6078 - 9.21497i) q^{66} +(-5.34393 - 9.25596i) q^{67} +(-1.27412 - 2.20683i) q^{68} +(8.66969 + 5.87095i) q^{69} +(-0.550360 + 0.953252i) q^{70} +12.6183 q^{71} +(-11.9413 + 15.1691i) q^{72} +1.47133 q^{73} +(5.20476 - 9.01492i) q^{74} +(0.351777 - 4.90140i) q^{75} +(14.9686 + 25.9264i) q^{76} +(0.286090 + 0.495523i) q^{77} +(-5.11065 + 2.48103i) q^{78} +(-4.16420 + 7.21261i) q^{79} +20.6925 q^{80} +(-2.11315 - 8.74841i) q^{81} -28.3805 q^{82} +(-3.48869 + 6.04259i) q^{83} +(1.08451 - 0.526489i) q^{84} +(-0.789102 - 1.36676i) q^{85} +(1.27673 + 2.21136i) q^{86} +(-1.07674 + 15.0024i) q^{87} +(11.9561 - 20.7086i) q^{88} +15.8842 q^{89} +(-13.2648 + 16.8504i) q^{90} +0.197792 q^{91} +(-13.6625 + 23.6642i) q^{92} +(-2.42885 - 1.64477i) q^{93} +(-9.42859 - 16.3308i) q^{94} +(9.27056 + 16.0571i) q^{95} +(-8.61029 - 5.83073i) q^{96} +(-8.27317 + 14.3296i) q^{97} +17.8137 q^{98} +(4.13804 + 10.3512i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 4 q^{2} - 7 q^{3} - 22 q^{4} - 9 q^{5} - 7 q^{7} + 24 q^{8} - 3 q^{9}+O(q^{10}) \) 38 * q - 4 * q^2 - 7 * q^3 - 22 * q^4 - 9 * q^5 - 7 * q^7 + 24 * q^8 - 3 * q^9	\( 38 q - 4 q^{2} - 7 q^{3} - 22 q^{4} - 9 q^{5} - 7 q^{7} + 24 q^{8} - 3 q^{9} - 14 q^{10} - 5 q^{11} + 11 q^{12} + 5 q^{13} - 17 q^{14} - 5 q^{15} - 24 q^{16} + 42 q^{17} - 23 q^{18} - 8 q^{19} - 21 q^{20} + 20 q^{22} - 22 q^{23} - 14 q^{24} - 10 q^{25} + 34 q^{26} - 4 q^{27} - 2 q^{28} - 30 q^{29} + 63 q^{30} + 5 q^{31} - 48 q^{32} - q^{33} + 6 q^{34} + 106 q^{35} - 20 q^{36} - 2 q^{37} - 21 q^{38} + 25 q^{39} - 16 q^{40} - 29 q^{41} - 47 q^{42} - 19 q^{43} + 58 q^{44} - 37 q^{45} - 32 q^{47} + 45 q^{48} + 10 q^{49} + 11 q^{50} - 53 q^{51} - q^{52} + 76 q^{53} - 41 q^{54} + 4 q^{55} - 46 q^{56} + 23 q^{57} - 30 q^{58} - 30 q^{59} - 87 q^{60} + 10 q^{61} + 50 q^{62} + 21 q^{63} + 28 q^{64} - 8 q^{65} + 91 q^{66} - 3 q^{67} - 47 q^{68} - 40 q^{69} - 56 q^{70} + 42 q^{71} + 3 q^{72} + 16 q^{73} - 28 q^{74} + 19 q^{75} + 36 q^{76} - 49 q^{77} - 105 q^{78} - 4 q^{79} + 140 q^{80} + 77 q^{81} - 8 q^{82} - 29 q^{83} + 145 q^{84} + 4 q^{85} - 4 q^{86} - 24 q^{87} + 47 q^{88} + 108 q^{89} - 8 q^{90} + 8 q^{91} - 12 q^{92} - 4 q^{93} + 23 q^{94} - 33 q^{95} - 147 q^{96} + 4 q^{97} + 98 q^{98} + 85 q^{99}+O(q^{100}) \) 38 * q - 4 * q^2 - 7 * q^3 - 22 * q^4 - 9 * q^5 - 7 * q^7 + 24 * q^8 - 3 * q^9 - 14 * q^10 - 5 * q^11 + 11 * q^12 + 5 * q^13 - 17 * q^14 - 5 * q^15 - 24 * q^16 + 42 * q^17 - 23 * q^18 - 8 * q^19 - 21 * q^20 + 20 * q^22 - 22 * q^23 - 14 * q^24 - 10 * q^25 + 34 * q^26 - 4 * q^27 - 2 * q^28 - 30 * q^29 + 63 * q^30 + 5 * q^31 - 48 * q^32 - q^33 + 6 * q^34 + 106 * q^35 - 20 * q^36 - 2 * q^37 - 21 * q^38 + 25 * q^39 - 16 * q^40 - 29 * q^41 - 47 * q^42 - 19 * q^43 + 58 * q^44 - 37 * q^45 - 32 * q^47 + 45 * q^48 + 10 * q^49 + 11 * q^50 - 53 * q^51 - q^52 + 76 * q^53 - 41 * q^54 + 4 * q^55 - 46 * q^56 + 23 * q^57 - 30 * q^58 - 30 * q^59 - 87 * q^60 + 10 * q^61 + 50 * q^62 + 21 * q^63 + 28 * q^64 - 8 * q^65 + 91 * q^66 - 3 * q^67 - 47 * q^68 - 40 * q^69 - 56 * q^70 + 42 * q^71 + 3 * q^72 + 16 * q^73 - 28 * q^74 + 19 * q^75 + 36 * q^76 - 49 * q^77 - 105 * q^78 - 4 * q^79 + 140 * q^80 + 77 * q^81 - 8 * q^82 - 29 * q^83 + 145 * q^84 + 4 * q^85 - 4 * q^86 - 24 * q^87 + 47 * q^88 + 108 * q^89 - 8 * q^90 + 8 * q^91 - 12 * q^92 - 4 * q^93 + 23 * q^94 - 33 * q^95 - 147 * q^96 + 4 * q^97 + 98 * q^98 + 85 * q^99

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