LMFDB - Embedded newform 11.3.d.a.6.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [11,3,Mod(2,11)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(11, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("11.2");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	11.d (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.299728290796$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			6.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	11.6
Dual form			11.3.d.a.2.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.690983 + 0.224514i) q^{2} +(-1.11803 - 0.812299i) q^{3} +(-2.80902 + 2.04087i) q^{4} +(1.23607 - 3.80423i) q^{5} +(0.954915 + 0.310271i) q^{6} +(5.85410 + 8.05748i) q^{7} +(3.19098 - 4.39201i) q^{8} +(-2.19098 - 6.74315i) q^{9} +O(q^{10})$	\(q+(-0.690983 + 0.224514i) q^{2} +(-1.11803 - 0.812299i) q^{3} +(-2.80902 + 2.04087i) q^{4} +(1.23607 - 3.80423i) q^{5} +(0.954915 + 0.310271i) q^{6} +(5.85410 + 8.05748i) q^{7} +(3.19098 - 4.39201i) q^{8} +(-2.19098 - 6.74315i) q^{9} +2.90617i q^{10} +(-10.3713 + 3.66547i) q^{11} +4.79837 q^{12} +(-5.00000 + 1.62460i) q^{13} +(-5.85410 - 4.25325i) q^{14} +(-4.47214 + 3.24920i) q^{15} +(3.07295 - 9.45756i) q^{16} +(14.5344 + 4.72253i) q^{17} +(3.02786 + 4.16750i) q^{18} +(1.21885 - 1.67760i) q^{19} +(4.29180 + 13.2088i) q^{20} -13.7638i q^{21} +(6.34346 - 4.86128i) q^{22} -2.76393 q^{23} +(-7.13525 + 2.31838i) q^{24} +(7.28115 + 5.29007i) q^{25} +(3.09017 - 2.24514i) q^{26} +(-6.87132 + 21.1478i) q^{27} +(-32.8885 - 10.6861i) q^{28} +(-16.7082 - 22.9969i) q^{29} +(2.36068 - 3.24920i) q^{30} +(-2.20163 - 6.77591i) q^{31} +28.9402i q^{32} +(14.5729 + 4.32650i) q^{33} -11.1033 q^{34} +(37.8885 - 12.3107i) q^{35} +(19.9164 + 14.4701i) q^{36} +(32.5623 - 23.6579i) q^{37} +(-0.465558 + 1.43284i) q^{38} +(6.90983 + 2.24514i) q^{39} +(-12.7639 - 17.5680i) q^{40} +(-41.2426 + 56.7656i) q^{41} +(3.09017 + 9.51057i) q^{42} -23.0624i q^{43} +(21.6525 - 31.4629i) q^{44} -28.3607 q^{45} +(1.90983 - 0.620541i) q^{46} +(-22.0344 - 16.0090i) q^{47} +(-11.1180 + 8.07772i) q^{48} +(-15.5106 + 47.7369i) q^{49} +(-6.21885 - 2.02063i) q^{50} +(-12.4139 - 17.0863i) q^{51} +(10.7295 - 14.7679i) q^{52} +(-3.54102 - 10.8981i) q^{53} -16.1554i q^{54} +(1.12461 + 43.9856i) q^{55} +54.0689 q^{56} +(-2.72542 + 0.885544i) q^{57} +(16.7082 + 12.1392i) q^{58} +(1.83688 - 1.33457i) q^{59} +(5.93112 - 18.2541i) q^{60} +(21.5066 + 6.98791i) q^{61} +(3.04257 + 4.18774i) q^{62} +(41.5066 - 57.1289i) q^{63} +(5.79431 + 17.8330i) q^{64} +21.0292i q^{65} +(-11.0410 + 0.282294i) q^{66} -38.4934 q^{67} +(-50.4656 + 16.3973i) q^{68} +(3.09017 + 2.24514i) q^{69} +(-23.4164 + 17.0130i) q^{70} +(23.5836 - 72.5828i) q^{71} +(-36.6074 - 11.8945i) q^{72} +(60.4656 + 83.2237i) q^{73} +(-17.1885 + 23.6579i) q^{74} +(-3.84346 - 11.8290i) q^{75} +7.19991i q^{76} +(-90.2492 - 62.1087i) q^{77} -5.27864 q^{78} +(-3.74265 + 1.21606i) q^{79} +(-32.1803 - 23.3804i) q^{80} +(-26.7639 + 19.4451i) q^{81} +(15.7533 - 48.4836i) q^{82} +(79.1697 + 25.7238i) q^{83} +(28.0902 + 38.6628i) q^{84} +(35.9311 - 49.4549i) q^{85} +(5.17783 + 15.9357i) q^{86} +39.2833i q^{87} +(-16.9959 + 57.2474i) q^{88} +123.297 q^{89} +(19.5967 - 6.36737i) q^{90} +(-42.3607 - 30.7768i) q^{91} +(7.76393 - 5.64083i) q^{92} +(-3.04257 + 9.36408i) q^{93} +(18.8197 + 6.11488i) q^{94} +(-4.87539 - 6.71040i) q^{95} +(23.5081 - 32.3562i) q^{96} +(-23.9205 - 73.6196i) q^{97} -36.4677i q^{98} +(47.4402 + 61.9044i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 5 q^{2} - 9 q^{4} - 4 q^{5} + 15 q^{6} + 10 q^{7} + 15 q^{8} - 11 q^{9}+O(q^{10}) $ 4 * q - 5 * q^2 - 9 * q^4 - 4 * q^5 + 15 * q^6 + 10 * q^7 + 15 * q^8 - 11 * q^9	\( 4 q - 5 q^{2} - 9 q^{4} - 4 q^{5} + 15 q^{6} + 10 q^{7} + 15 q^{8} - 11 q^{9} + q^{11} - 30 q^{12} - 20 q^{13} - 10 q^{14} + 19 q^{16} + 30 q^{18} + 25 q^{19} + 44 q^{20} - 35 q^{22} - 20 q^{23} + 5 q^{24} + 9 q^{25} - 10 q^{26} + 15 q^{27} - 60 q^{28} - 40 q^{29} - 80 q^{30} - 58 q^{31} + 65 q^{33} + 130 q^{34} + 80 q^{35} + 26 q^{36} + 90 q^{37} - 60 q^{38} + 50 q^{39} - 60 q^{40} - 80 q^{41} - 10 q^{42} + 24 q^{44} - 24 q^{45} + 30 q^{46} - 30 q^{47} - 40 q^{48} - 109 q^{49} - 45 q^{50} - 195 q^{51} + 110 q^{52} + 120 q^{53} - 76 q^{55} + 100 q^{56} + 45 q^{57} + 40 q^{58} + 23 q^{59} + 140 q^{60} + 10 q^{61} + 200 q^{62} + 90 q^{63} - 149 q^{64} + 90 q^{66} - 230 q^{67} - 260 q^{68} - 10 q^{69} - 40 q^{70} + 148 q^{71} - 95 q^{72} + 300 q^{73} - 270 q^{74} + 45 q^{75} - 200 q^{77} - 200 q^{78} + 70 q^{79} - 84 q^{80} - 116 q^{81} + 25 q^{82} + 225 q^{83} + 90 q^{84} + 260 q^{85} + 175 q^{86} + 55 q^{88} + 122 q^{89} - 20 q^{90} - 80 q^{91} + 40 q^{92} - 200 q^{93} + 120 q^{94} - 100 q^{95} + 340 q^{96} - 165 q^{97} + 31 q^{99}+O(q^{100}) \) 4 * q - 5 * q^2 - 9 * q^4 - 4 * q^5 + 15 * q^6 + 10 * q^7 + 15 * q^8 - 11 * q^9 + q^11 - 30 * q^12 - 20 * q^13 - 10 * q^14 + 19 * q^16 + 30 * q^18 + 25 * q^19 + 44 * q^20 - 35 * q^22 - 20 * q^23 + 5 * q^24 + 9 * q^25 - 10 * q^26 + 15 * q^27 - 60 * q^28 - 40 * q^29 - 80 * q^30 - 58 * q^31 + 65 * q^33 + 130 * q^34 + 80 * q^35 + 26 * q^36 + 90 * q^37 - 60 * q^38 + 50 * q^39 - 60 * q^40 - 80 * q^41 - 10 * q^42 + 24 * q^44 - 24 * q^45 + 30 * q^46 - 30 * q^47 - 40 * q^48 - 109 * q^49 - 45 * q^50 - 195 * q^51 + 110 * q^52 + 120 * q^53 - 76 * q^55 + 100 * q^56 + 45 * q^57 + 40 * q^58 + 23 * q^59 + 140 * q^60 + 10 * q^61 + 200 * q^62 + 90 * q^63 - 149 * q^64 + 90 * q^66 - 230 * q^67 - 260 * q^68 - 10 * q^69 - 40 * q^70 + 148 * q^71 - 95 * q^72 + 300 * q^73 - 270 * q^74 + 45 * q^75 - 200 * q^77 - 200 * q^78 + 70 * q^79 - 84 * q^80 - 116 * q^81 + 25 * q^82 + 225 * q^83 + 90 * q^84 + 260 * q^85 + 175 * q^86 + 55 * q^88 + 122 * q^89 - 20 * q^90 - 80 * q^91 + 40 * q^92 - 200 * q^93 + 120 * q^94 - 100 * q^95 + 340 * q^96 - 165 * q^97 + 31 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/11\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−0.690983	+	0.224514i	−0.345492	+	0.112257i	−0.476623	−	0.879108i	$-0.658139\pi$
$2$	−0.690983	+	0.224514i	−0.345492	+	0.112257i	0.131131	+	0.991365i	$0.458139\pi$
$3$	−1.11803	−	0.812299i	−0.372678	−	0.270766i	0.385643	−	0.922648i	$-0.373980\pi$
$3$	−1.11803	−	0.812299i	−0.372678	−	0.270766i	−0.758321	+	0.651882i	$0.773980\pi$
$4$	−2.80902	+	2.04087i	−0.702254	+	0.510218i
$5$	1.23607	−	3.80423i	0.247214	−	0.760845i	−0.748051	−	0.663641i	$-0.769010\pi$
$5$	1.23607	−	3.80423i	0.247214	−	0.760845i	0.995264	−	0.0972039i	$-0.0309899\pi$
$6$	0.954915	+	0.310271i	0.159153	+	0.0517118i
$7$	5.85410	+	8.05748i	0.836300	+	1.15107i	0.986717	+	0.162446i	$0.0519383\pi$
$7$	5.85410	+	8.05748i	0.836300	+	1.15107i	−0.150417	+	0.988623i	$0.548062\pi$
$8$	3.19098	−	4.39201i	0.398873	−	0.549001i
$9$	−2.19098	−	6.74315i	−0.243443	−	0.749239i
$10$			2.90617i			0.290617i
$11$	−10.3713	+	3.66547i	−0.942848	+	0.333224i
$11$	−10.3713	+	3.66547i	−0.942848	+	0.333224i
$12$	4.79837			0.399864
$13$	−5.00000	+	1.62460i	−0.384615	+	0.124969i	−0.494941	−	0.868926i	$-0.664810\pi$
$13$	−5.00000	+	1.62460i	−0.384615	+	0.124969i	0.110326	+	0.993895i	$0.464810\pi$
$14$	−5.85410	−	4.25325i	−0.418150	−	0.303804i
$15$	−4.47214	+	3.24920i	−0.298142	+	0.216613i
$16$	3.07295	−	9.45756i	0.192059	−	0.591098i
$17$	14.5344	+	4.72253i	0.854967	+	0.277796i	0.703525	−	0.710670i	$-0.251608\pi$
$17$	14.5344	+	4.72253i	0.854967	+	0.277796i	0.151442	+	0.988466i	$0.451608\pi$
$18$	3.02786	+	4.16750i	0.168215	+	0.231528i
$19$	1.21885	−	1.67760i	0.0641498	−	0.0882947i	−0.775737	−	0.631057i	$-0.782621\pi$
$19$	1.21885	−	1.67760i	0.0641498	−	0.0882947i	0.839886	+	0.542762i	$0.182621\pi$
$20$	4.29180	+	13.2088i	0.214590	+	0.660440i
$21$		−	13.7638i		−	0.655420i
$22$	6.34346	−	4.86128i	0.288339	−	0.220967i
$23$	−2.76393			−0.120171			−0.0600855	−	0.998193i	$-0.519137\pi$
$23$	−2.76393			−0.120171			−0.0600855	+	0.998193i	$0.519137\pi$
$24$	−7.13525	+	2.31838i	−0.297302	+	0.0965994i
$25$	7.28115	+	5.29007i	0.291246	+	0.211603i
$26$	3.09017	−	2.24514i	0.118853	−	0.0863515i
$27$	−6.87132	+	21.1478i	−0.254493	+	0.783250i
$28$	−32.8885	−	10.6861i	−1.17459	−	0.381648i
$29$	−16.7082	−	22.9969i	−0.576145	−	0.792996i	0.417121	−	0.908851i	$-0.363039\pi$
$29$	−16.7082	−	22.9969i	−0.576145	−	0.792996i	−0.993266	+	0.115855i	$0.963039\pi$
$30$	2.36068	−	3.24920i	0.0786893	−	0.108307i
$31$	−2.20163	−	6.77591i	−0.0710202	−	0.218578i	0.909246	−	0.416259i	$-0.136659\pi$
$31$	−2.20163	−	6.77591i	−0.0710202	−	0.218578i	−0.980266	+	0.197681i	$0.936659\pi$
$32$			28.9402i			0.904382i
$33$	14.5729	+	4.32650i	0.441605	+	0.131106i
$34$	−11.1033			−0.326568
$35$	37.8885	−	12.3107i	1.08253	−	0.351735i
$36$	19.9164	+	14.4701i	0.553234	+	0.401948i
$37$	32.5623	−	23.6579i	0.880062	−	0.639403i	−0.0532056	−	0.998584i	$-0.516944\pi$
$37$	32.5623	−	23.6579i	0.880062	−	0.639403i	0.933268	+	0.359181i	$0.116944\pi$
$38$	−0.465558	+	1.43284i	−0.0122515	+	0.0377063i
$39$	6.90983	+	2.24514i	0.177175	+	0.0575677i
$40$	−12.7639	−	17.5680i	−0.319098	−	0.439201i
$41$	−41.2426	+	56.7656i	−1.00592	+	1.38453i	−0.0842954	+	0.996441i	$0.526864\pi$
$41$	−41.2426	+	56.7656i	−1.00592	+	1.38453i	−0.921623	+	0.388087i	$0.873136\pi$
$42$	3.09017	+	9.51057i	0.0735755	+	0.226442i
$43$		−	23.0624i		−	0.536334i	−0.963372	−	0.268167i	$-0.913582\pi$
$43$		−	23.0624i		−	0.536334i	0.963372	−	0.268167i	$-0.0864180\pi$
$44$	21.6525	−	31.4629i	0.492102	−	0.715066i
$45$	−28.3607			−0.630237
$46$	1.90983	−	0.620541i	0.0415180	−	0.0134900i
$47$	−22.0344	−	16.0090i	−0.468818	−	0.340616i	0.328163	−	0.944621i	$-0.393571\pi$
$47$	−22.0344	−	16.0090i	−0.468818	−	0.340616i	−0.796980	+	0.604005i	$0.793571\pi$
$48$	−11.1180	+	8.07772i	−0.231626	+	0.168286i
$49$	−15.5106	+	47.7369i	−0.316544	+	0.974221i
$50$	−6.21885	−	2.02063i	−0.124377	−	0.0404125i
$51$	−12.4139	−	17.0863i	−0.243410	−	0.335025i
$52$	10.7295	−	14.7679i	0.206336	−	0.283998i
$53$	−3.54102	−	10.8981i	−0.0668117	−	0.205625i	0.912077	−	0.410019i	$-0.134478\pi$
$53$	−3.54102	−	10.8981i	−0.0668117	−	0.205625i	−0.978889	+	0.204393i	$0.934478\pi$
$54$		−	16.1554i		−	0.299175i
$55$	1.12461	+	43.9856i	0.0204475	+	0.799739i
$56$	54.0689			0.965516
$57$	−2.72542	+	0.885544i	−0.0478145	+	0.0155359i
$58$	16.7082	+	12.1392i	0.288072	+	0.209297i
$59$	1.83688	−	1.33457i	0.0311336	−	0.0226199i	−0.572110	−	0.820177i	$-0.693875\pi$
$59$	1.83688	−	1.33457i	0.0311336	−	0.0226199i	0.603243	+	0.797557i	$0.293875\pi$
$60$	5.93112	−	18.2541i	0.0988519	−	0.304235i
$61$	21.5066	+	6.98791i	0.352567	+	0.114556i	0.479946	−	0.877298i	$-0.340656\pi$
$61$	21.5066	+	6.98791i	0.352567	+	0.114556i	−0.127379	+	0.991854i	$0.540656\pi$
$62$	3.04257	+	4.18774i	0.0490737	+	0.0675442i
$63$	41.5066	−	57.1289i	0.658835	−	0.906808i
$64$	5.79431	+	17.8330i	0.0905361	+	0.278641i
$65$			21.0292i			0.323527i
$66$	−11.0410	+	0.282294i	−0.167288	+	0.00427718i
$67$	−38.4934			−0.574529			−0.287264	−	0.957851i	$-0.592746\pi$
$67$	−38.4934			−0.574529			−0.287264	+	0.957851i	$0.592746\pi$
$68$	−50.4656	+	16.3973i	−0.742141	+	0.241136i
$69$	3.09017	+	2.24514i	0.0447851	+	0.0325383i
$70$	−23.4164	+	17.0130i	−0.334520	+	0.243043i
$71$	23.5836	−	72.5828i	0.332163	−	1.02229i	−0.635939	−	0.771739i	$-0.719387\pi$
$71$	23.5836	−	72.5828i	0.332163	−	1.02229i	0.968103	−	0.250554i	$-0.0806129\pi$
$72$	−36.6074	−	11.8945i	−0.508436	−	0.165201i
$73$	60.4656	+	83.2237i	0.828295	+	1.14005i	0.988238	+	0.152924i	$0.0488691\pi$
$73$	60.4656	+	83.2237i	0.828295	+	1.14005i	−0.159943	+	0.987126i	$0.551131\pi$
$74$	−17.1885	+	23.6579i	−0.232277	+	0.319701i
$75$	−3.84346	−	11.8290i	−0.0512461	−	0.157719i
$76$			7.19991i			0.0947357i
$77$	−90.2492	−	62.1087i	−1.17207	−	0.806606i
$78$	−5.27864			−0.0676749
$79$	−3.74265	+	1.21606i	−0.0473753	+	0.0153932i	−0.332609	−	0.943065i	$-0.607929\pi$
$79$	−3.74265	+	1.21606i	−0.0473753	+	0.0153932i	0.285233	+	0.958458i	$0.407929\pi$
$80$	−32.1803	−	23.3804i	−0.402254	−	0.292255i
$81$	−26.7639	+	19.4451i	−0.330419	+	0.240063i
$82$	15.7533	−	48.4836i	0.192113	−	0.591264i
$83$	79.1697	+	25.7238i	0.953852	+	0.309925i	0.744280	−	0.667868i	$-0.232793\pi$
$83$	79.1697	+	25.7238i	0.953852	+	0.309925i	0.209572	+	0.977793i	$0.432793\pi$
$84$	28.0902	+	38.6628i	0.334407	+	0.460271i
$85$	35.9311	−	49.4549i	0.422719	−	0.581823i
$86$	5.17783	+	15.9357i	0.0602073	+	0.185299i
$87$			39.2833i			0.451533i
$88$	−16.9959	+	57.2474i	−0.193136	+	0.650539i
$89$	123.297			1.38536			0.692679	−	0.721246i	$-0.256430\pi$
$89$	123.297			1.38536			0.692679	+	0.721246i	$0.256430\pi$
$90$	19.5967	−	6.36737i	0.217742	−	0.0707485i
$91$	−42.3607	−	30.7768i	−0.465502	−	0.338207i
$92$	7.76393	−	5.64083i	0.0843906	−	0.0613133i
$93$	−3.04257	+	9.36408i	−0.0327158	+	0.100689i
$94$	18.8197	+	6.11488i	0.200209	+	0.0650519i
$95$	−4.87539	−	6.71040i	−0.0513199	−	0.0706357i
$96$	23.5081	−	32.3562i	0.244876	−	0.337043i
$97$	−23.9205	−	73.6196i	−0.246603	−	0.758965i	−0.995369	−	0.0961309i	$-0.969353\pi$
$97$	−23.9205	−	73.6196i	−0.246603	−	0.758965i	0.748766	−	0.662835i	$-0.230647\pi$
$98$		−	36.4677i		−	0.372119i
$99$	47.4402	+	61.9044i	0.479194	+	0.625297i
$100$	−31.2492			−0.312492
$101$	−107.159	+	34.8181i	−1.06098	+	0.344734i	−0.786969	−	0.616993i	$-0.788351\pi$
$101$	−107.159	+	34.8181i	−1.06098	+	0.344734i	−0.274012	+	0.961726i	$0.588351\pi$
$102$	12.4139	+	9.01922i	0.121705	+	0.0884238i
$103$	−74.9230	+	54.4347i	−0.727408	+	0.528493i	−0.888742	−	0.458407i	$-0.848420\pi$
$103$	−74.9230	+	54.4347i	−0.727408	+	0.528493i	0.161335	+	0.986900i	$0.448420\pi$
$104$	−8.81966	+	27.1441i	−0.0848044	+	0.261001i
$105$	−52.3607	−	17.0130i	−0.498673	−	0.162029i
$106$	4.89357	+	6.73542i	0.0461657	+	0.0635417i
$107$	−49.8607	+	68.6273i	−0.465988	+	0.641377i	−0.975737	−	0.218946i	$-0.929738\pi$
$107$	−49.8607	+	68.6273i	−0.465988	+	0.641377i	0.509749	+	0.860323i	$0.329738\pi$
$108$	−23.8582	−	73.4279i	−0.220909	−	0.679888i
$109$		−	94.0766i		−	0.863088i	−0.902092	−	0.431544i	$-0.857969\pi$
$109$		−	94.0766i		−	0.863088i	0.902092	−	0.431544i	$-0.142031\pi$
$110$	−10.6525	−	30.1408i	−0.0968407	−	0.274008i
$111$	−55.6231			−0.501109
$112$	94.1935	−	30.6053i	0.841013	−	0.273262i
$113$	6.87132	+	4.99231i	0.0608082	+	0.0441797i	0.617774	−	0.786356i	$-0.288035\pi$
$113$	6.87132	+	4.99231i	0.0608082	+	0.0441797i	−0.556966	+	0.830535i	$0.688035\pi$
$114$	1.68441	−	1.22379i	0.0147755	−	0.0107350i
$115$	−3.41641	+	10.5146i	−0.0297079	+	0.0914315i
$116$	93.8673	+	30.4993i	0.809200	+	0.262925i
$117$	21.9098	+	30.1563i	0.187264	+	0.257746i
$118$	−0.969623	+	1.33457i	−0.00821715	+	0.0113099i
$119$	47.0344	+	144.757i	0.395247	+	1.21645i
$120$			30.0098i			0.250082i
$121$	94.1287	−	76.0315i	0.777923	−	0.628360i
$122$	−16.4296			−0.134669
$123$	92.2214	−	29.9645i	0.749767	−	0.243614i
$124$	20.0132	+	14.5404i	0.161396	+	0.117261i
$125$	110.026	−	79.9388i	0.880210	−	0.639510i
$126$	−15.8541	+	48.7939i	−0.125826	+	0.387253i
$127$	−179.039	−	58.1734i	−1.40976	−	0.458059i	−0.497426	−	0.867506i	$-0.665721\pi$
$127$	−179.039	−	58.1734i	−1.40976	−	0.458059i	−0.912334	+	0.409448i	$0.865721\pi$
$128$	−76.0501	−	104.674i	−0.594141	−	0.817766i
$129$	−18.7336	+	25.7845i	−0.145221	+	0.199880i
$130$	−4.72136	−	14.5309i	−0.0363182	−	0.111776i
$131$			141.932i			1.08345i	0.840556	+	0.541725i	$0.182229\pi$
$131$			141.932i			1.08345i	−0.840556	+	0.541725i	$0.817771\pi$
$132$	−49.7655	+	17.5883i	−0.377011	+	0.133245i
$133$	20.6525			0.155282
$134$	26.5983	−	8.64231i	0.198495	−	0.0644949i
$135$	71.9574	+	52.2801i	0.533018	+	0.387260i
$136$	67.1205	−	48.7659i	0.493533	−	0.358573i
$137$	5.02380	−	15.4617i	0.0366701	−	0.112859i	−0.931046	−	0.364902i	$-0.881102\pi$
$137$	5.02380	−	15.4617i	0.0366701	−	0.112859i	0.967716	+	0.252043i	$0.0811025\pi$
$138$	−2.63932	−	0.857567i	−0.0191255	−	0.00621425i
$139$	−133.108	−	183.208i	−0.957614	−	1.31804i	−0.948061	−	0.318088i	$-0.896959\pi$
$139$	−133.108	−	183.208i	−0.957614	−	1.31804i	−0.00955293	−	0.999954i	$-0.503041\pi$
$140$	−81.3050	+	111.907i	−0.580750	+	0.799333i
$141$	11.6312	+	35.7971i	0.0824907	+	0.253880i
$142$			55.4484i			0.390481i
$143$	45.9017	−	35.1766i	0.320991	−	0.245990i
$144$	−70.5066			−0.489629
$145$	−108.138	+	35.1361i	−0.745778	+	0.242318i
$146$	−60.4656	−	43.9308i	−0.414148	−	0.300896i
$147$	56.1180	−	40.7721i	0.381755	−	0.277361i
$148$	−43.1854	+	132.911i	−0.291793	+	0.898047i
$149$	−63.8967	−	20.7613i	−0.428837	−	0.139338i	0.0866427	−	0.996239i	$-0.472386\pi$
$149$	−63.8967	−	20.7613i	−0.428837	−	0.139338i	−0.515479	+	0.856902i	$0.672386\pi$
$150$	5.31153	+	7.31069i	0.0354102	+	0.0487380i
$151$	59.0871	−	81.3264i	0.391305	−	0.538585i	−0.567230	−	0.823559i	$-0.691985\pi$
$151$	59.0871	−	81.3264i	0.391305	−	0.538585i	0.958535	+	0.284974i	$0.0919850\pi$
$152$	−3.47871	−	10.7064i	−0.0228863	−	0.0704367i
$153$		−	108.355i		−	0.708202i
$154$	76.3050	+	22.6538i	0.495487	+	0.147103i
$155$	−28.4984			−0.183861
$156$	−23.9919	+	7.79543i	−0.153794	+	0.0499707i
$157$	199.520	+	144.960i	1.27083	+	0.923309i	0.999235	−	0.0391033i	$-0.0124502\pi$
$157$	199.520	+	144.960i	1.27083	+	0.923309i	0.271591	+	0.962413i	$0.412450\pi$
$158$	2.31308	−	1.68055i	0.0146398	−	0.0106364i
$159$	−4.89357	+	15.0609i	−0.0307772	+	0.0947224i
$160$	110.095	+	35.7721i	0.688095	+	0.223576i
$161$	−16.1803	−	22.2703i	−0.100499	−	0.138325i
$162$	14.1277	−	19.4451i	0.0872081	−	0.120032i
$163$	53.8820	+	165.832i	0.330564	+	1.01737i	0.968866	+	0.247586i	$0.0796372\pi$
$163$	53.8820	+	165.832i	0.330564	+	1.01737i	−0.638302	+	0.769786i	$0.720363\pi$
$164$		−	243.627i		−	1.48553i
$165$	34.4721	−	50.0909i	0.208922	−	0.303581i
$166$	−60.4803			−0.364339
$167$	234.864	−	76.3120i	1.40637	−	0.456958i	0.495126	−	0.868821i	$-0.335122\pi$
$167$	234.864	−	76.3120i	1.40637	−	0.456958i	0.911246	+	0.411863i	$0.135122\pi$
$168$	−60.4508	−	43.9201i	−0.359826	−	0.261429i
$169$	−114.363	+	83.0897i	−0.676705	+	0.491655i
$170$	−13.7245	+	42.2396i	−0.0807321	+	0.248468i
$171$	−13.9828	−	4.54328i	−0.0817706	−	0.0265689i
$172$	47.0673	+	64.7826i	0.273647	+	0.376643i
$173$	−29.2411	+	40.2469i	−0.169024	+	0.232641i	−0.885123	−	0.465357i	$-0.845926\pi$
$173$	−29.2411	+	40.2469i	−0.169024	+	0.232641i	0.716099	+	0.697999i	$0.245926\pi$
$174$	−8.81966	−	27.1441i	−0.0506877	−	0.156001i
$175$			89.6363i			0.512208i
$176$	2.79586	+	109.351i	0.0158856	+	0.621314i
$177$	−3.13777			−0.0177275
$178$	−85.1960	+	27.6819i	−0.478629	+	0.155516i
$179$	−177.134	−	128.695i	−0.989574	−	0.718967i	−0.0297461	−	0.999557i	$-0.509470\pi$
$179$	−177.134	−	128.695i	−0.989574	−	0.718967i	−0.959828	+	0.280590i	$0.909470\pi$
$180$	79.6656	−	57.8805i	0.442587	−	0.321558i
$181$	12.0213	−	36.9977i	0.0664159	−	0.204407i	−0.912341	−	0.409431i	$-0.865727\pi$
$181$	12.0213	−	36.9977i	0.0664159	−	0.204407i	0.978757	+	0.205024i	$0.0657272\pi$
$182$	36.1803	+	11.7557i	0.198793	+	0.0645918i
$183$	−18.3688	−	25.2825i	−0.100376	−	0.138156i
$184$	−8.81966	+	12.1392i	−0.0479329	+	0.0659740i
$185$	−49.7508	−	153.117i	−0.268923	−	0.827660i
$186$		−	7.15352i		−	0.0384598i
$187$	−168.052	+	4.29670i	−0.898672	+	0.0229770i
$188$	94.5673			0.503018
$189$	−210.623	+	68.4356i	−1.11441	+	0.362093i
$190$	4.87539	+	3.54218i	0.0256599	+	0.0186430i
$191$	−96.9230	+	70.4187i	−0.507450	+	0.368684i	−0.811855	−	0.583858i	$-0.801542\pi$
$191$	−96.9230	+	70.4187i	−0.507450	+	0.368684i	0.304405	+	0.952543i	$0.401542\pi$
$192$	8.00754	−	24.6447i	0.0417059	−	0.128358i
$193$	27.7933	+	9.03061i	0.144007	+	0.0467907i	0.380134	−	0.924932i	$-0.375878\pi$
$193$	27.7933	+	9.03061i	0.144007	+	0.0467907i	−0.236127	+	0.971722i	$0.575878\pi$
$194$	33.0573	+	45.4994i	0.170398	+	0.234533i
$195$	17.0820	−	23.5114i	0.0876002	−	0.120571i
$196$	−53.8551	−	165.749i	−0.274771	−	0.845657i
$197$			282.037i			1.43166i	0.698275	+	0.715830i	$0.253951\pi$
$197$			282.037i			1.43166i	−0.698275	+	0.715830i	$0.746049\pi$
$198$	−46.6788	−	32.1239i	−0.235751	−	0.162242i
$199$	177.469			0.891804			0.445902	−	0.895082i	$-0.352883\pi$
$199$	177.469			0.891804			0.445902	+	0.895082i	$0.352883\pi$
$200$	46.4681	−	15.0984i	0.232340	−	0.0754920i
$201$	43.0370	+	31.2682i	0.214114	+	0.155563i
$202$	66.2279	−	48.1174i	0.327861	−	0.238205i
$203$	87.4853	−	269.252i	0.430962	−	1.32636i
$204$	69.7417	+	22.6604i	0.341871	+	0.111081i
$205$	164.971	+	227.063i	0.804735	+	1.10762i
$206$	39.5492	−	54.4347i	0.191986	−	0.264246i
$207$	6.05573	+	18.6376i	0.0292547	+	0.0900368i
$208$			52.2801i			0.251347i
$209$	−6.49187	+	21.8666i	−0.0310616	+	0.104625i
$210$	40.0000			0.190476
$211$	93.5354	−	30.3915i	0.443296	−	0.144036i	−0.0788599	−	0.996886i	$-0.525128\pi$
$211$	93.5354	−	30.3915i	0.443296	−	0.144036i	0.522156	+	0.852850i	$0.325128\pi$
$212$	32.1885	+	23.3863i	0.151832	+	0.110313i
$213$	−85.3262	+	61.9931i	−0.400593	+	0.291048i
$214$	19.0451	−	58.6147i	0.0889957	−	0.273901i
$215$	−87.7345	−	28.5067i	−0.408068	−	0.132589i
$216$	70.9549	+	97.6611i	0.328495	+	0.452135i
$217$	41.7082	−	57.4064i	0.192204	−	0.264546i
$218$	21.1215	+	65.0053i	0.0968876	+	0.298190i
$219$		−	142.163i		−	0.649146i
$220$	−92.9280	−	121.261i	−0.422400	−	0.551187i
$221$	−80.3444			−0.363549
$222$	38.4346	−	12.4882i	0.173129	−	0.0562529i
$223$	−215.220	−	156.366i	−0.965111	−	0.701194i	−0.0107791	−	0.999942i	$-0.503431\pi$
$223$	−215.220	−	156.366i	−0.965111	−	0.701194i	−0.954332	+	0.298748i	$0.903431\pi$
$224$	−233.185	+	169.419i	−1.04101	+	0.756335i
$225$	19.7188	−	60.6884i	0.0876393	−	0.269726i
$226$	−5.86881	−	1.90689i	−0.0259682	−	0.00843758i
$227$	149.606	+	205.915i	0.659057	+	0.907114i	0.999450	−	0.0331697i	$-0.0105602\pi$
$227$	149.606	+	205.915i	0.659057	+	0.907114i	−0.340393	+	0.940283i	$0.610560\pi$
$228$	5.84848	−	8.04975i	0.0256512	−	0.0353059i
$229$	−12.4245	−	38.2388i	−0.0542556	−	0.166982i	0.920257	−	0.391315i	$-0.127980\pi$
$229$	−12.4245	−	38.2388i	−0.0542556	−	0.166982i	−0.974513	+	0.224333i	$0.927980\pi$
$230$		−	8.03246i		−	0.0349237i
$231$	50.4508	+	142.749i	0.218402	+	0.617961i
$232$	−154.318			−0.665164
$233$	−219.639	+	71.3649i	−0.942655	+	0.306287i	−0.739728	−	0.672906i	$-0.765046\pi$
$233$	−219.639	+	71.3649i	−0.942655	+	0.306287i	−0.202928	+	0.979194i	$0.565046\pi$
$234$	−21.9098	−	15.9184i	−0.0936318	−	0.0680275i
$235$	−88.1378	+	64.0358i	−0.375054	+	0.272493i
$236$	−2.43614	+	7.49767i	−0.0103226	+	0.0317698i
$237$	5.17221	+	1.68055i	0.0218237	+	0.00709094i
$238$	−65.0000	−	89.4648i	−0.273109	−	0.375903i
$239$	185.249	−	254.974i	0.775101	−	1.06684i	−0.220704	−	0.975341i	$-0.570836\pi$
$239$	185.249	−	254.974i	0.775101	−	1.06684i	0.995806	−	0.0914947i	$-0.0291645\pi$
$240$	16.9868	+	52.2801i	0.0707785	+	0.217834i
$241$		−	270.933i		−	1.12420i	−0.827069	−	0.562101i	$-0.809993\pi$
$241$		−	270.933i		−	1.12420i	0.827069	−	0.562101i	$-0.190007\pi$
$242$	−47.9712	+	73.6697i	−0.198228	+	0.304420i
$243$	245.843			1.01170
$244$	−74.6738	+	24.2630i	−0.306040	+	0.0994384i
$245$	162.430	+	118.012i	0.662978	+	0.481682i
$246$	−56.9959	+	41.4100i	−0.231691	+	0.168333i
$247$	−3.36881	+	10.3681i	−0.0136389	+	0.0419762i
$248$	−36.7852	−	11.9522i	−0.148327	−	0.0481945i
$249$	−67.6190	−	93.0696i	−0.271562	−	0.373773i
$250$	−58.0789	+	79.9388i	−0.232316	+	0.319755i
$251$	3.44080	+	10.5897i	0.0137084	+	0.0421900i	0.957677	−	0.287846i	$-0.0929391\pi$
$251$	3.44080	+	10.5897i	0.0137084	+	0.0421900i	−0.943968	+	0.330036i	$0.892939\pi$
$252$			245.186i			0.972959i
$253$	28.6656	−	10.1311i	0.113303	−	0.0400439i
$254$	136.774			0.538480
$255$	−80.3444	+	26.1055i	−0.315076	+	0.102374i
$256$	15.3713	+	11.1679i	0.0600442	+	0.0436247i
$257$	326.261	−	237.042i	1.26950	−	0.922344i	0.270315	−	0.962772i	$-0.412872\pi$
$257$	326.261	−	237.042i	1.26950	−	0.922344i	0.999182	+	0.0404281i	$0.0128722\pi$
$258$	7.15558	−	22.0226i	0.0277348	−	0.0853590i
$259$	381.246	+	123.874i	1.47199	+	0.478279i
$260$	−42.9180	−	59.0715i	−0.165069	−	0.227198i
$261$	−118.464	+	163.052i	−0.453885	+	0.624719i
$262$	−31.8657	−	98.0726i	−0.121625	−	0.374323i
$263$		−	42.6636i		−	0.162219i	−0.996705	−	0.0811094i	$-0.974154\pi$
$263$		−	42.6636i		−	0.162219i	0.996705	−	0.0811094i	$-0.0258463\pi$
$264$	65.5041	−	50.1988i	0.248121	−	0.190147i
$265$	−45.8359			−0.172966
$266$	−14.2705	+	4.63677i	−0.0536485	+	0.0174315i
$267$	−137.850	−	100.154i	−0.516292	−	0.375108i
$268$	108.129	−	78.5601i	0.403465	−	0.293135i
$269$	−126.695	+	389.927i	−0.470985	+	1.44954i	0.380311	+	0.924859i	$0.375817\pi$
$269$	−126.695	+	389.927i	−0.470985	+	1.44954i	−0.851296	+	0.524685i	$0.824183\pi$
$270$	−61.4590	−	19.9692i	−0.227626	−	0.0739601i
$271$	−136.400	−	187.739i	−0.503322	−	0.692763i	0.479454	−	0.877567i	$-0.340835\pi$
$271$	−136.400	−	187.739i	−0.503322	−	0.692763i	−0.982775	+	0.184804i	$0.940835\pi$
$272$	89.3272	−	122.948i	0.328409	−	0.452016i
$273$	22.3607	+	68.8191i	0.0819073	+	0.252085i
$274$			11.8117i			0.0431082i
$275$	−94.9058	−	28.1762i	−0.345112	−	0.102459i
$276$	−13.2624			−0.0480521
$277$	291.305	−	94.6507i	1.05164	−	0.341699i	0.268330	−	0.963327i	$-0.413528\pi$
$277$	291.305	−	94.6507i	1.05164	−	0.341699i	0.783313	+	0.621628i	$0.213528\pi$
$278$	133.108	+	96.7089i	0.478807	+	0.347874i
$279$	−40.8673	+	29.6918i	−0.146478	+	0.106422i
$280$	66.8328	−	205.690i	0.238689	−	0.734608i
$281$	−123.114	−	40.0022i	−0.438128	−	0.142356i	0.0816438	−	0.996662i	$-0.473983\pi$
$281$	−123.114	−	40.0022i	−0.438128	−	0.142356i	−0.519772	+	0.854305i	$0.673983\pi$
$282$	−16.0739	−	22.1238i	−0.0569997	−	0.0784533i
$283$	−247.984	+	341.320i	−0.876268	+	1.20608i	0.101173	+	0.994869i	$0.467740\pi$
$283$	−247.984	+	341.320i	−0.876268	+	1.20608i	−0.977441	+	0.211210i	$0.932260\pi$
$284$	81.8854	+	252.017i	0.288329	+	0.887385i
$285$			11.4627i			0.0402201i
$286$	−23.8197	+	34.6120i	−0.0832855	+	0.121021i
$287$	−698.827			−2.43494
$288$	195.148	−	63.4076i	0.677599	−	0.220165i
$289$	−44.8582	−	32.5914i	−0.155219	−	0.112773i
$290$	66.8328	−	48.5569i	0.230458	−	0.167438i
$291$	−33.0573	+	101.740i	−0.113599	+	0.349621i
$292$	−339.698	−	110.374i	−1.16335	−	0.377995i
$293$	−37.8998	−	52.1646i	−0.129351	−	0.178036i	0.739429	−	0.673234i	$-0.235095\pi$
$293$	−37.8998	−	52.1646i	−0.129351	−	0.178036i	−0.868780	+	0.495198i	$0.835095\pi$
$294$	−29.6227	+	40.7721i	−0.100757	+	0.138681i
$295$	−2.80650	−	8.63753i	−0.00951357	−	0.0292798i
$296$		−	218.506i		−	0.738196i
$297$	−6.25174	−	244.517i	−0.0210496	−	0.823289i
$298$	48.8127			0.163801
$299$	13.8197	−	4.49028i	0.0462196	−	0.0150177i
$300$	34.9377	+	25.3837i	0.116459	+	0.0846124i
$301$	185.825	−	135.010i	0.617358	−	0.448537i
$302$	−22.5693	+	69.4610i	−0.0747326	+	0.230003i
$303$	148.090	+	48.1174i	0.488746	+	0.158803i
$304$	−12.1205	−	16.6825i	−0.0398702	−	0.0548766i
$305$	53.1672	−	73.1784i	0.174319	−	0.239929i
$306$	24.3272	+	74.8714i	0.0795006	+	0.244678i
$307$			356.512i			1.16128i	0.814161	+	0.580639i	$0.197197\pi$
$307$			356.512i			1.16128i	−0.814161	+	0.580639i	$0.802803\pi$
$308$	380.267	−	9.72257i	1.23463	−	0.0315668i
$309$	127.984			0.414187
$310$	19.6919	−	6.39830i	0.0635224	−	0.0206397i
$311$	449.177	+	326.346i	1.44430	+	1.04935i	0.987122	+	0.159970i	$0.0511397\pi$
$311$	449.177	+	326.346i	1.44430	+	1.04935i	0.457178	+	0.889375i	$0.348860\pi$
$312$	31.9098	−	23.1838i	0.102275	−	0.0743072i
$313$	−102.405	+	315.170i	−0.327172	+	1.00693i	0.643279	+	0.765632i	$0.277574\pi$
$313$	−102.405	+	315.170i	−0.327172	+	1.00693i	−0.970451	+	0.241300i	$0.922426\pi$
$314$	−170.410	−	55.3696i	−0.542708	−	0.176336i
$315$	−166.026	−	228.516i	−0.527068	−	0.725446i
$316$	8.03134	−	11.0542i	0.0254156	−	0.0349816i
$317$	−159.740	−	491.628i	−0.503910	−	1.55088i	−0.802595	−	0.596524i	$-0.796548\pi$
$317$	−159.740	−	491.628i	−0.503910	−	1.55088i	0.298685	−	0.954352i	$-0.403452\pi$
$318$		−	11.5055i		−	0.0361807i
$319$	257.580	+	177.265i	0.807462	+	0.555688i
$320$	75.0031			0.234385
$321$	111.492	−	36.2259i	0.347327	−	0.112853i
$322$	16.1803	+	11.7557i	0.0502495	+	0.0365084i
$323$	25.6378	−	18.6269i	0.0793739	−	0.0576685i
$324$	35.4953	−	109.243i	0.109554	−	0.337171i
$325$	−45.0000	−	14.6214i	−0.138462	−	0.0449889i
$326$	−74.4630	−	102.490i	−0.228414	−	0.314385i
$327$	−76.4183	+	105.181i	−0.233695	+	0.321654i
$328$	117.711	+	362.276i	0.358874	+	1.10450i
$329$		−	271.260i		−	0.824499i
$330$	−12.5735	+	42.3515i	−0.0381016	+	0.128338i
$331$	208.884			0.631068			0.315534	−	0.948914i	$-0.397816\pi$
$331$	208.884			0.631068			0.315534	+	0.948914i	$0.397816\pi$
$332$	−274.888	+	89.3165i	−0.827976	+	0.269026i
$333$	−230.872	−	167.739i	−0.693310	−	0.503719i
$334$	−145.154	+	105.461i	−0.434593	+	0.315750i
$335$	−47.5805	+	146.438i	−0.142031	+	0.437127i
$336$	−130.172	−	42.2955i	−0.387417	−	0.125880i
$337$	−79.3090	−	109.159i	−0.235338	−	0.323915i	0.674971	−	0.737844i	$-0.264156\pi$
$337$	−79.3090	−	109.159i	−0.235338	−	0.323915i	−0.910309	+	0.413929i	$0.864156\pi$
$338$	60.3682	−	83.0897i	0.178604	−	0.245828i
$339$	−3.62712	−	11.1631i	−0.0106995	−	0.0329296i
$340$			212.251i			0.624266i
$341$	47.6707	+	62.2051i	0.139797	+	0.182420i
$342$	10.6819			0.0312336
$343$	−11.3050	+	3.67320i	−0.0329590	+	0.0107090i
$344$	−101.290	−	73.5917i	−0.294448	−	0.213929i
$345$	12.3607	−	8.98056i	0.0358281	−	0.0260306i
$346$	11.1691	−	34.3750i	0.0322806	−	0.0993496i
$347$	−90.1393	−	29.2880i	−0.259767	−	0.0844036i	0.176238	−	0.984348i	$-0.443607\pi$
$347$	−90.1393	−	29.2880i	−0.259767	−	0.0844036i	−0.436005	+	0.899944i	$0.643607\pi$
$348$	−80.1722	−	110.348i	−0.230380	−	0.317091i
$349$	−100.997	+	139.010i	−0.289389	+	0.398310i	−0.928816	−	0.370542i	$-0.879172\pi$
$349$	−100.997	+	139.010i	−0.289389	+	0.398310i	0.639426	+	0.768852i	$0.279172\pi$
$350$	−20.1246	−	61.9372i	−0.0574989	−	0.176963i
$351$		−	116.902i		−	0.333054i
$352$	−106.080	−	300.149i	−0.301362	−	0.852695i
$353$	−119.644			−0.338936			−0.169468	−	0.985536i	$-0.554205\pi$
$353$	−119.644			−0.338936			−0.169468	+	0.985536i	$0.554205\pi$
$354$	2.16814	−	0.704473i	0.00612470	−	0.00199004i
$355$	−246.971	−	179.435i	−0.695692	−	0.505450i
$356$	−346.343	+	251.633i	−0.972873	+	0.706834i
$357$	65.0000	−	200.049i	0.182073	−	0.560363i
$358$	151.290	+	49.1572i	0.422598	+	0.137311i
$359$	274.681	+	378.066i	0.765127	+	1.05311i	0.996770	+	0.0803065i	$0.0255899\pi$
$359$	274.681	+	378.066i	0.765127	+	1.05311i	−0.231643	+	0.972801i	$0.574410\pi$
$360$	−90.4984	+	124.560i	−0.251385	+	0.346001i
$361$	110.226	+	339.242i	0.305336	+	0.939728i
$362$			28.2637i			0.0780766i
$363$	−166.999	+	8.54517i	−0.460053	+	0.0235404i
$364$	181.803			0.499460
$365$	391.341	−	127.155i	1.07217	−	0.348368i
$366$	18.3688	+	13.3457i	0.0501880	+	0.0364637i
$367$	266.026	−	193.279i	0.724867	−	0.526647i	−0.163068	−	0.986615i	$-0.552139\pi$
$367$	266.026	−	193.279i	0.724867	−	0.526647i	0.887936	+	0.459968i	$0.152139\pi$
$368$	−8.49342	+	26.1401i	−0.0230800	+	0.0710328i
$369$	473.141	+	153.733i	1.28223	+	0.416620i
$370$	68.7539	+	94.6316i	0.185821	+	0.255761i
$371$	67.0820	−	92.3305i	0.180814	−	0.248869i
$372$	−10.5642	−	32.5133i	−0.0283985	−	0.0874015i
$373$		−	214.135i		−	0.574088i	−0.957917	−	0.287044i	$-0.907327\pi$
$373$		−	214.135i		−	0.574088i	0.957917	−	0.287044i	$-0.0926726\pi$
$374$	115.156	−	40.6989i	0.307904	−	0.108821i
$375$	−187.947			−0.501193
$376$	−140.623	+	45.6912i	−0.373997	+	0.121519i
$377$	120.902	+	87.8402i	0.320694	+	0.232998i
$378$	130.172	−	94.5756i	0.344371	−	0.250200i
$379$	98.9630	−	304.577i	0.261116	−	0.803633i	−0.731447	−	0.681899i	$-0.761154\pi$
$379$	98.9630	−	304.577i	0.261116	−	0.803633i	0.992563	−	0.121734i	$-0.0388456\pi$
$380$	27.3901	+	8.89958i	0.0720792	+	0.0234200i
$381$	152.918	+	210.474i	0.401359	+	0.552424i
$382$	51.1622	−	70.4187i	0.133932	−	0.184342i
$383$	−169.205	−	520.759i	−0.441788	−	1.35968i	−0.885968	−	0.463746i	$-0.846505\pi$
$383$	−169.205	−	520.759i	−0.441788	−	1.35968i	0.444181	−	0.895937i	$-0.353495\pi$
$384$			178.805i			0.465637i
$385$	−347.830	+	266.558i	−0.903454	+	0.692358i
$386$	−21.2322			−0.0550058
$387$	−155.513	+	50.5293i	−0.401843	+	0.130567i
$388$	217.441	+	157.980i	0.560415	+	0.407166i
$389$	−272.259	+	197.808i	−0.699895	+	0.508504i	−0.879898	−	0.475162i	$-0.842389\pi$
$389$	−272.259	+	197.808i	−0.699895	+	0.508504i	0.180003	+	0.983666i	$0.442389\pi$
$390$	−6.52476	+	20.0811i	−0.0167301	+	0.0514901i
$391$	−40.1722	−	13.0527i	−0.102742	−	0.0333830i
$392$	160.167	+	220.450i	0.408588	+	0.562373i
$393$	115.291	−	158.685i	0.293362	−	0.403778i
$394$	−63.3212	−	194.883i	−0.160714	−	0.494626i
$395$			15.7410i			0.0398506i
$396$	−259.599	−	77.0713i	−0.655554	−	0.194624i
$397$	115.374			0.290614			0.145307	−	0.989387i	$-0.453583\pi$
$397$	115.374			0.290614			0.145307	+	0.989387i	$0.453583\pi$
$398$	−122.628	+	39.8443i	−0.308111	+	0.100111i
$399$	−23.0902	−	16.7760i	−0.0578701	−	0.0420451i
$400$	72.4058	−	52.6059i	0.181014	−	0.131515i
$401$	19.7138	−	60.6729i	0.0491617	−	0.151304i	−0.923462	−	0.383690i	$-0.874653\pi$
$401$	19.7138	−	60.6729i	0.0491617	−	0.151304i	0.972624	+	0.232386i	$0.0746532\pi$
$402$	−36.7579	−	11.9434i	−0.0914377	−	0.0297099i
$403$	22.0163	+	30.3028i	0.0546309	+	0.0751930i
$404$	229.952	−	316.502i	0.569189	−	0.783422i
$405$	40.8916	+	125.852i	0.100967	+	0.310745i
$406$			205.690i			0.506626i
$407$	−250.997	+	364.720i	−0.616700	+	0.896118i
$408$	−114.656			−0.281019
$409$	−581.745	+	189.020i	−1.42236	+	0.462152i	−0.916351	−	0.400377i	$-0.868879\pi$
$409$	−581.745	+	189.020i	−1.42236	+	0.462152i	−0.506008	+	0.862529i	$0.668879\pi$
$410$	−164.971	−	119.858i	−0.402367	−	0.292337i
$411$	−18.1763	+	13.2058i	−0.0442245	+	0.0321310i
$412$	99.3657	−	305.816i	0.241179	−	0.742272i
$413$	21.5066	+	6.98791i	0.0520740	+	0.0169199i
$414$	−8.36881	−	11.5187i	−0.0202145	−	0.0278229i
$415$	195.718	−	269.383i	0.471610	−	0.649116i
$416$	−47.0163	−	144.701i	−0.113020	−	0.347839i
$417$			312.957i			0.750495i
$418$	−0.423579	−	16.5669i	−0.00101335	−	0.0396338i
$419$	146.156			0.348821			0.174410	−	0.984673i	$-0.444198\pi$
$419$	146.156			0.348821			0.174410	+	0.984673i	$0.444198\pi$
$420$	181.803	−	59.0715i	0.432865	−	0.140646i
$421$	−480.079	−	348.798i	−1.14033	−	0.828498i	−0.153165	−	0.988201i	$-0.548947\pi$
$421$	−480.079	−	348.798i	−1.14033	−	0.828498i	−0.987165	+	0.159702i	$0.948947\pi$
$422$	−57.8081	+	42.0000i	−0.136986	+	0.0995261i
$423$	−59.6738	+	183.657i	−0.141073	+	0.434177i
$424$	−59.1641	−	19.2236i	−0.139538	−	0.0453386i
$425$	80.8450	+	111.274i	0.190224	+	0.261820i
$426$	45.0407	−	61.9931i	0.105729	−	0.145524i
$427$	69.5967	+	214.197i	0.162990	+	0.501632i
$428$		−	294.535i		−	0.688165i
$429$	−79.8936	+	2.04270i	−0.186232	+	0.00476153i
$430$	67.0232			0.155868
$431$	165.807	−	53.8738i	0.384702	−	0.124997i	−0.110280	−	0.993901i	$-0.535175\pi$
$431$	165.807	−	53.8738i	0.384702	−	0.124997i	0.494982	+	0.868903i	$0.335175\pi$
$432$	178.891	+	129.972i	0.414100	+	0.300861i
$433$	−502.109	+	364.804i	−1.15961	+	0.842503i	−0.989728	−	0.142962i	$-0.954337\pi$
$433$	−502.109	+	364.804i	−1.15961	+	0.842503i	−0.169878	+	0.985465i	$0.554337\pi$
$434$	−15.9311	+	49.0309i	−0.0367076	+	0.112975i
$435$	149.443	+	48.5569i	0.343546	+	0.111625i
$436$	191.998	+	264.263i	0.440363	+	0.606107i
$437$	−3.36881	+	4.63677i	−0.00770895	+	0.0106105i
$438$	31.9176	+	98.2323i	0.0728712	+	0.224275i
$439$		−	676.778i		−	1.54164i	−0.637055	−	0.770818i	$-0.719848\pi$
$439$		−	676.778i		−	1.54164i	0.637055	−	0.770818i	$-0.280152\pi$
$440$	196.774	+	135.418i	0.447214	+	0.307768i
$441$	355.880			0.806985
$442$	55.5166	−	18.0384i	0.125603	−	0.0408110i
$443$	209.784	+	152.417i	0.473552	+	0.344056i	0.798824	−	0.601565i	$-0.205456\pi$
$443$	209.784	+	152.417i	0.473552	+	0.344056i	−0.325272	+	0.945621i	$0.605456\pi$
$444$	156.246	−	113.519i	0.351906	−	0.255674i
$445$	152.403	−	469.049i	0.342479	−	1.05404i
$446$	183.820	+	59.7266i	0.412152	+	0.133916i
$447$	54.5743	+	75.1150i	0.122090	+	0.168043i
$448$	−109.769	+	151.084i	−0.245020	+	0.337241i
$449$	124.349	+	382.707i	0.276947	+	0.852354i	0.988698	+	0.149923i	$0.0479024\pi$
$449$	124.349	+	382.707i	0.276947	+	0.852354i	−0.711751	+	0.702432i	$0.752098\pi$
$450$			46.3618i			0.103026i
$451$	219.668	−	739.908i	0.487069	−	1.64059i
$452$	−29.4903			−0.0652441
$453$	−132.123	+	42.9293i	−0.291662	+	0.0947666i
$454$	−149.606	−	108.695i	−0.329528	−	0.239416i
$455$	−169.443	+	123.107i	−0.372402	+	0.270566i
$456$	−4.80746	+	14.7959i	−0.0105427	+	0.0324470i
$457$	243.209	+	79.0234i	0.532186	+	0.172918i	0.562769	−	0.826614i	$-0.309736\pi$
$457$	243.209	+	79.0234i	0.532186	+	0.172918i	−0.0305823	+	0.999532i	$0.509736\pi$
$458$	17.1703	+	23.6329i	0.0374897	+	0.0516002i
$459$	−199.742	+	274.921i	−0.435167	+	0.598956i
$460$	−11.8622	−	36.5082i	−0.0257875	−	0.0793656i
$461$			446.274i			0.968056i	0.875053	+	0.484028i	$0.160827\pi$
$461$			446.274i			0.968056i	−0.875053	+	0.484028i	$0.839173\pi$
$462$	−66.9098	−	87.3102i	−0.144826	−	0.188983i
$463$	73.1308			0.157950			0.0789750	−	0.996877i	$-0.474835\pi$
$463$	73.1308			0.157950			0.0789750	+	0.996877i	$0.474835\pi$
$464$	−268.838	+	87.3507i	−0.579392	+	0.188256i
$465$	31.8622	+	23.1493i	0.0685209	+	0.0497834i
$466$	135.744	−	98.6239i	0.291297	−	0.211639i
$467$	3.43459	−	10.5706i	0.00735458	−	0.0226351i	−0.947312	−	0.320313i	$-0.896212\pi$
$467$	3.43459	−	10.5706i	0.00735458	−	0.0226351i	0.954666	+	0.297678i	$0.0962120\pi$
$468$	−123.090	−	39.9944i	−0.263013	−	0.0854582i
$469$	−225.344	−	310.160i	−0.480479	−	0.661322i
$470$	46.5248	−	64.0358i	0.0989888	−	0.136246i
$471$	−105.319	−	324.139i	−0.223608	−	0.688194i
$472$		−	12.3262i		−	0.0261148i
$473$	84.5344	+	239.187i	0.178720	+	0.505682i
$474$	−3.95122			−0.00833590
$475$	17.7492	−	5.76707i	0.0373668	−	0.0121412i
$476$	−427.551	−	310.634i	−0.898217	−	0.652593i
$477$	−65.7295	+	47.7553i	−0.137798	+	0.100116i
$478$	−70.7589	+	217.774i	−0.148031	+	0.455593i
$479$	−545.546	−	177.259i	−1.13893	−	0.370060i	−0.321965	−	0.946752i	$-0.604343\pi$
$479$	−545.546	−	177.259i	−1.13893	−	0.370060i	−0.816962	+	0.576692i	$0.804343\pi$
$480$	−94.0325	−	129.425i	−0.195901	−	0.269635i
$481$	−124.377	+	171.190i	−0.258580	+	0.355905i
$482$	60.8282	+	187.210i	0.126199	+	0.388402i
$483$			38.0423i			0.0787624i
$484$	−109.239	+	405.678i	−0.225700	+	0.838178i
$485$	−309.633			−0.638419
$486$	−169.873	+	55.1952i	−0.349533	+	0.113570i
$487$	510.363	+	370.800i	1.04797	+	0.761397i	0.971826	−	0.235700i	$-0.0757383\pi$
$487$	510.363	+	370.800i	1.04797	+	0.761397i	0.0761466	+	0.997097i	$0.475738\pi$
$488$	99.3181	−	72.1588i	0.203521	−	0.147866i
$489$	74.4630	−	229.174i	0.152276	−	0.468658i
$490$	−138.731	−	45.0766i	−0.283125	−	0.0919930i
$491$	−256.297	−	352.763i	−0.521990	−	0.718458i	0.463893	−	0.885891i	$-0.346452\pi$
$491$	−256.297	−	352.763i	−0.521990	−	0.718458i	−0.985883	+	0.167433i	$0.946452\pi$
$492$	−197.898	+	272.383i	−0.402231	+	0.553623i
$493$	−134.241	−	413.152i	−0.272294	−	0.838036i
$494$		−	7.92055i		−	0.0160335i
$495$	294.138	−	103.955i	0.594218	−	0.210010i
$496$	−70.8491			−0.142841
$497$	722.895	−	234.883i	1.45452	−	0.472602i
$498$	67.6190	+	49.1281i	0.135781	+	0.0986508i
$499$	376.446	−	273.504i	0.754401	−	0.548105i	−0.142787	−	0.989753i	$-0.545606\pi$
$499$	376.446	−	273.504i	0.754401	−	0.548105i	0.897188	+	0.441649i	$0.145606\pi$
$500$	−145.921	+	449.099i	−0.291842	+	0.898198i
$501$	−324.574	−	105.461i	−0.647853	−	0.210500i
$502$	−4.75507	−	6.54479i	−0.00947225	−	0.0130374i
$503$	270.059	−	371.704i	0.536896	−	0.738974i	−0.451265	−	0.892390i	$-0.649027\pi$
$503$	270.059	−	371.704i	0.536896	−	0.738974i	0.988162	+	0.153415i	$0.0490273\pi$
$504$	−118.464	−	364.595i	−0.235048	−	0.723402i
$505$			450.695i			0.892465i
$506$	−17.5329	+	13.4363i	−0.0346500	+	0.0265539i
$507$	195.356			0.385317
$508$	621.649	−	201.986i	1.22372	−	0.397610i
$509$	194.705	+	141.462i	0.382525	+	0.277920i	0.762385	−	0.647123i	$-0.224028\pi$
$509$	194.705	+	141.462i	0.382525	+	0.277920i	−0.379861	+	0.925044i	$0.624028\pi$
$510$	49.6556	−	36.0769i	0.0973639	−	0.0707390i
$511$	−316.602	+	974.400i	−0.619573	+	1.90685i
$512$	479.078	+	155.662i	0.935699	+	0.304027i
$513$	27.1024	+	37.3032i	0.0528311	+	0.0727158i
$514$	−172.221	+	237.042i	−0.335061	+	0.461172i
$515$	114.472	+	352.309i	0.222276	+	0.684095i
$516$		−	110.662i		−	0.214461i
$517$	287.207	+	85.2675i	0.555525	+	0.164928i
$518$	−291.246			−0.562251
$519$	65.3851	−	21.2449i	0.125983	−	0.0409343i
$520$	92.3607	+	67.1040i	0.177617	+	0.129046i
$521$	564.504	−	410.136i	1.08350	−	0.787210i	0.105212	−	0.994450i	$-0.466448\pi$
$521$	564.504	−	410.136i	1.08350	−	0.787210i	0.978290	+	0.207240i	$0.0664480\pi$
$522$	45.2492	−	139.263i	0.0866843	−	0.266787i
$523$	−353.526	−	114.868i	−0.675959	−	0.219632i	−0.0491334	−	0.998792i	$-0.515646\pi$
$523$	−353.526	−	114.868i	−0.675959	−	0.219632i	−0.626825	+	0.779160i	$0.715646\pi$
$524$	−289.665	−	398.689i	−0.552795	−	0.760857i
$525$	72.8115	−	100.216i	0.138689	−	0.190889i
$526$	9.57857	+	29.4798i	0.0182102	+	0.0560452i
$527$		−	108.881i		−	0.206606i
$528$	85.7001	−	124.529i	0.162311	−	0.235851i
$529$	−521.361			−0.985559
$530$	31.6718	−	10.2908i	0.0597582	−	0.0194166i
$531$	−13.0238	−	9.46234i	−0.0245269	−	0.0178199i
$532$	−58.0132	+	42.1490i	−0.109047	+	0.0792275i
$533$	113.992	−	350.831i	0.213868	−	0.658219i
$534$	117.738	+	38.2554i	0.220483	+	0.0716393i
$535$	199.443	+	274.509i	0.372790	+	0.513102i
$536$	−122.832	+	169.064i	−0.229164	+	0.315417i
$537$	93.5025	+	287.771i	0.174120	+	0.535887i
$538$		−	297.878i		−	0.553676i
$539$	−14.1120	−	551.948i	−0.0261819	−	1.02402i
$540$	−308.827			−0.571901
$541$	−64.3657	+	20.9137i	−0.118975	+	0.0386575i	−0.367900	−	0.929866i	$-0.619923\pi$
$541$	−64.3657	+	20.9137i	−0.118975	+	0.0386575i	0.248924	+	0.968523i	$0.419923\pi$
$542$	136.400	+	99.1005i	0.251661	+	0.182842i
$543$	−43.4934	+	31.5998i	−0.0800984	+	0.0581949i
$544$	−136.671	+	420.630i	−0.251233	+	0.773217i
$545$	−357.889	−	116.285i	−0.656676	−	0.213367i
$546$	−30.9017	−	42.5325i	−0.0565965	−	0.0778984i
$547$	−436.380	+	600.625i	−0.797769	+	1.09804i	0.195328	+	0.980738i	$0.437423\pi$
$547$	−436.380	+	600.625i	−0.797769	+	1.09804i	−0.993097	+	0.117297i	$0.962577\pi$
$548$	17.4433	+	53.6850i	0.0318309	+	0.0979653i
$549$		−	160.333i		−	0.292045i
$550$	71.9042	−	1.83843i	0.130735	−	0.00334259i
$551$	−58.9443			−0.106977
$552$	19.7214	−	6.40786i	0.0357271	−	0.0116084i
$553$	−31.7082	−	23.0374i	−0.0573385	−	0.0416589i
$554$	−180.036	+	130.804i	−0.324975	+	0.236108i
$555$	−68.7539	+	211.603i	−0.123881	+	0.381266i
$556$	747.807	+	242.977i	1.34498	+	0.437010i
$557$	−441.323	−	607.429i	−0.792322	−	1.09054i	−0.993815	−	0.111047i	$-0.964579\pi$
$557$	−441.323	−	607.429i	−0.792322	−	1.09054i	0.201494	−	0.979490i	$-0.435421\pi$
$558$	21.5724	−	29.6918i	0.0386601	−	0.0532111i
$559$	37.4671	+	115.312i	0.0670252	+	0.206282i
$560$		−	396.164i		−	0.707435i
$561$	191.378	+	131.704i	0.341137	+	0.234767i
$562$	94.0507			0.167350
$563$	−991.673	+	322.214i	−1.76141	+	0.572316i	−0.997345	−	0.0728240i	$-0.976799\pi$
$563$	−991.673	+	322.214i	−1.76141	+	0.572316i	−0.764064	+	0.645140i	$0.776799\pi$
$564$	−105.729	−	76.8170i	−0.187464	−	0.136200i
$565$	27.4853	−	19.9692i	0.0486465	−	0.0353438i
$566$	94.7214	−	291.522i	0.167352	−	0.515057i
$567$	−313.358	−	101.816i	−0.552659	−	0.179570i
$568$	−243.530	−	335.190i	−0.428750	−	0.590123i
$569$	−136.967	+	188.518i	−0.240714	+	0.331315i	−0.912232	−	0.409673i	$-0.865643\pi$
$569$	−136.967	+	188.518i	−0.240714	+	0.331315i	0.671518	+	0.740988i	$0.265643\pi$
$570$	−2.57354	−	7.92055i	−0.00451499	−	0.0138957i
$571$			196.324i			0.343825i	0.985112	+	0.171912i	$0.0549946\pi$
$571$			196.324i			0.343825i	−0.985112	+	0.171912i	$0.945005\pi$
$572$	−57.1478	+	192.491i	−0.0999088	+	0.336523i
$573$	165.564			0.288943
$574$	482.877	−	156.896i	0.841250	−	0.273339i
$575$	−20.1246	−	14.6214i	−0.0349993	−	0.0254285i
$576$	107.556	−	78.1438i	0.186729	−	0.135666i
$577$	43.9884	−	135.382i	0.0762364	−	0.234631i	−0.905675	−	0.423973i	$-0.860635\pi$
$577$	43.9884	−	135.382i	0.0762364	−	0.234631i	0.981911	+	0.189341i	$0.0606352\pi$
$578$	38.3134	+	12.4488i	0.0662862	+	0.0215377i
$579$	−23.7384	−	32.6730i	−0.0409989	−	0.0564301i
$580$	232.053	−	319.393i	0.400091	−	0.550678i
$581$	256.199	+	788.498i	0.440961	+	1.35714i
$582$		−	77.7223i		−	0.133544i
$583$	76.6718	+	100.049i	0.131513	+	0.171610i
$584$	558.464			0.956274
$585$	141.803	−	46.0747i	0.242399	−	0.0787602i
$586$	37.8998	+	27.5358i	0.0646754	+	0.0469894i
$587$	193.847	−	140.838i	0.330233	−	0.239929i	−0.410296	−	0.911952i	$-0.634575\pi$
$587$	193.847	−	140.838i	0.330233	−	0.239929i	0.740530	+	0.672024i	$0.234575\pi$
$588$	−74.4259	+	229.059i	−0.126575	+	0.389557i
$589$	−14.0507	−	4.56535i	−0.0238552	−	0.00775102i
$590$	3.87849	+	5.33829i	0.00657372	+	0.00904795i
$591$	229.098	−	315.327i	0.387645	−	0.533548i
$592$	−123.684	−	380.660i	−0.208925	−	0.643006i
$593$			598.782i			1.00975i	0.863192	+	0.504875i	$0.168462\pi$
$593$			598.782i			1.00975i	−0.863192	+	0.504875i	$0.831538\pi$
$594$	59.2173	+	167.553i	0.0996924	+	0.282076i
$595$	608.827			1.02324
$596$	221.858	−	72.0860i	0.372245	−	0.120950i
$597$	−198.416	−	144.158i	−0.332356	−	0.241471i
$598$	−8.54102	+	6.20541i	−0.0142826	+	0.0103769i
$599$	93.8359	−	288.797i	0.156654	−	0.482132i	−0.841670	−	0.539992i	$-0.818427\pi$
$599$	93.8359	−	288.797i	0.156654	−	0.482132i	0.998325	+	0.0578592i	$0.0184274\pi$
$600$	−64.2173	−	20.8655i	−0.107029	−	0.0347758i
$601$	−107.416	−	147.845i	−0.178729	−	0.245999i	0.710248	−	0.703952i	$-0.248583\pi$
$601$	−107.416	−	147.845i	−0.178729	−	0.245999i	−0.888977	+	0.457953i	$0.848583\pi$
$602$	−98.0902	+	135.010i	−0.162940	+	0.224268i
$603$	84.3384	+	259.567i	0.139865	+	0.430459i
$604$			349.036i			0.577874i
$605$	−172.892	−	452.067i	−0.285771	−	0.747218i
$606$	−113.131			−0.186685
$607$	−769.237	+	249.940i	−1.26728	+	0.411763i	−0.864082	−	0.503351i	$-0.832100\pi$
$607$	−769.237	+	249.940i	−1.26728	+	0.411763i	−0.403195	+	0.915114i	$0.632100\pi$
$608$	48.5501	+	35.2737i	0.0798522	+	0.0580160i
$609$	−316.525	+	229.969i	−0.519745	+	0.377617i
$610$	−20.3081	+	62.5018i	−0.0332919	+	0.102462i
$611$	136.180	+	44.2477i	0.222881	+	0.0724185i
$612$	221.138	+	304.371i	0.361337	+	0.497338i
$613$	701.597	−	965.666i	1.14453	−	1.57531i	0.387585	−	0.921834i	$-0.373309\pi$
$613$	701.597	−	965.666i	1.14453	−	1.57531i	0.756946	−	0.653478i	$-0.226691\pi$
$614$	−80.0420	−	246.344i	−0.130362	−	0.401212i
$615$		−	387.869i		−	0.630681i
$616$	−560.766	+	198.188i	−0.910334	+	0.321733i
$617$	107.900			0.174878			0.0874390	−	0.996170i	$-0.472132\pi$
$617$	107.900			0.174878			0.0874390	+	0.996170i	$0.472132\pi$
$618$	−88.4346	+	28.7341i	−0.143098	+	0.0464954i
$619$	457.719	+	332.552i	0.739449	+	0.537241i	0.892539	−	0.450971i	$-0.148922\pi$
$619$	457.719	+	332.552i	0.739449	+	0.537241i	−0.153089	+	0.988212i	$0.548922\pi$
$620$	80.0526	−	58.1616i	0.129117	−	0.0938091i
$621$	18.9919	−	58.4510i	0.0305827	−	0.0941239i
$622$	−383.643	−	124.653i	−0.616790	−	0.200407i
$623$	721.792	+	993.462i	1.15857	+	1.59464i
$624$	42.4671	−	58.4510i	0.0680563	−	0.0936714i
$625$	−98.5764	−	303.387i	−0.157722	−	0.485419i
$626$		−	240.768i		−	0.384614i
$627$	25.0203	−	19.1742i	0.0399048	−	0.0305809i
$628$	−856.298			−1.36353
$629$	585.000	−	190.078i	0.930048	−	0.302191i
$630$	166.026	+	120.625i	0.263534	+	0.191469i
$631$	−558.872	+	406.044i	−0.885693	+	0.643494i	−0.934751	−	0.355302i	$-0.884378\pi$
$631$	−558.872	+	406.044i	−0.885693	+	0.643494i	0.0490585	+	0.998796i	$0.484378\pi$
$632$	−6.60177	+	20.3182i	−0.0104458	+	0.0321490i
$633$	−129.263	−	42.0000i	−0.204207	−	0.0663507i
$634$	220.755	+	303.843i	0.348193	+	0.479247i
$635$	−442.610	+	609.200i	−0.697023	+	0.959371i
$636$	−16.9911	−	52.2933i	−0.0267156	−	0.0822222i
$637$		−	263.883i		−	0.414259i
$638$	−217.782	−	64.6564i	−0.341351	−	0.101342i
$639$	−541.108			−0.846805
$640$	−492.207	+	159.928i	−0.769073	+	0.249887i
$641$	−624.756	−	453.912i	−0.974659	−	0.708131i	−0.0181501	−	0.999835i	$-0.505778\pi$
$641$	−624.756	−	453.912i	−0.974659	−	0.708131i	−0.956509	+	0.291704i	$0.905778\pi$
$642$	−68.9058	+	50.0630i	−0.107330	+	0.0779797i
$643$	291.864	−	898.264i	0.453909	−	1.39699i	−0.418502	−	0.908216i	$-0.637445\pi$
$643$	291.864	−	898.264i	0.453909	−	1.39699i	0.872411	−	0.488773i	$-0.162555\pi$
$644$	90.9017	+	29.5358i	0.141152	+	0.0458630i
$645$	74.9342	+	103.138i	0.116177	+	0.159904i
$646$	−13.5333	+	18.6269i	−0.0209493	+	0.0288343i
$647$	−301.400	−	927.614i	−0.465843	−	1.43372i	−0.857920	−	0.513784i	$-0.828243\pi$
$647$	−301.400	−	927.614i	−0.465843	−	1.43372i	0.392077	−	0.919932i	$-0.371757\pi$
$648$			179.597i			0.277155i
$649$	−14.1591	+	20.5743i	−0.0218167	+	0.0317016i
$650$	34.3769			0.0528876
$651$	−93.2624	+	30.3028i	−0.143260	+	0.0465481i
$652$	−489.796	−	355.858i	−0.751221	−	0.545794i
$653$	−194.615	+	141.396i	−0.298032	+	0.216533i	−0.726744	−	0.686908i	$-0.758967\pi$
$653$	−194.615	+	141.396i	−0.298032	+	0.216533i	0.428712	+	0.903441i	$0.358967\pi$
$654$	29.1892	−	89.8351i	0.0446318	−	0.137363i
$655$	539.941	+	175.438i	0.824338	+	0.267844i
$656$	410.128	+	564.493i	0.625195	+	0.860507i
$657$	428.711	−	590.070i	0.652528	−	0.898128i
$658$	60.9017	+	187.436i	0.0925558	+	0.284857i
$659$			937.713i			1.42293i	0.702720	+	0.711467i	$0.251969\pi$
$659$			937.713i			1.42293i	−0.702720	+	0.711467i	$0.748031\pi$
$660$	5.39631	+	211.059i	0.00817622	+	0.319787i
$661$	133.305			0.201672			0.100836	−	0.994903i	$-0.467848\pi$
$661$	133.305			0.201672			0.100836	+	0.994903i	$0.467848\pi$
$662$	−144.335	+	46.8973i	−0.218029	+	0.0708418i
$663$	89.8278	+	65.2637i	0.135487	+	0.0984370i
$664$	365.608	−	265.630i	0.550615	−	0.400045i
$665$	25.5279	−	78.5667i	0.0383878	−	0.118145i
$666$	197.188	+	64.0704i	0.296079	+	0.0962018i
$667$	46.1803	+	63.5618i	0.0692359	+	0.0952950i
$668$	−503.995	+	693.689i	−0.754483	+	1.03846i
$669$	113.607	+	349.646i	0.169816	+	0.522639i
$670$		−	111.868i		−	0.166968i
$671$	−248.666	+	6.35781i	−0.370590	+	0.00947513i
$672$	398.328			0.592750
$673$	860.230	−	279.506i	1.27820	−	0.415313i	0.410256	−	0.911971i	$-0.365439\pi$
$673$	860.230	−	279.506i	1.27820	−	0.415313i	0.867947	+	0.496657i	$0.165439\pi$
$674$	79.3090	+	57.6214i	0.117669	+	0.0854917i
$675$	−161.904	+	117.630i	−0.239858	+	0.174267i
$676$	151.673	−	466.801i	0.224368	−	0.690534i
$677$	574.798	+	186.763i	0.849037	+	0.275869i	0.701043	−	0.713119i	$-0.252718\pi$
$677$	574.798	+	186.763i	0.849037	+	0.275869i	0.147995	+	0.988988i	$0.452718\pi$
$678$	5.01256	+	6.89920i	0.00739316	+	0.0101758i
$679$	453.156	−	623.716i	0.667387	−	0.918580i
$680$	−102.551	−	315.620i	−0.150810	−	0.464147i
$681$		−	351.744i		−	0.516512i
$682$	−46.9055	−	32.2800i	−0.0687764	−	0.0473313i
$683$	1261.32			1.84673			0.923367	−	0.383919i	$-0.125426\pi$
$683$	1261.32			1.84673			0.923367	+	0.383919i	$0.125426\pi$
$684$	48.5501	−	15.7749i	0.0709797	−	0.0230627i
$685$	−52.6099	−	38.2233i	−0.0768028	−	0.0558005i
$686$	6.98684	−	5.07624i	0.0101849	−	0.00739977i
$687$	−17.1703	+	52.8447i	−0.0249931	+	0.0769210i
$688$	−218.114	−	70.8695i	−0.317026	−	0.103008i
$689$	35.4102	+	48.7380i	0.0513936	+	0.0707372i
$690$	−6.52476	+	8.98056i	−0.00945617	+	0.0130153i
$691$	−132.915	−	409.071i	−0.192352	−	0.591999i	−0.999997	−	0.00232993i	$-0.999258\pi$
$691$	−132.915	−	409.071i	−0.192352	−	0.591999i	0.807645	−	0.589669i	$-0.200742\pi$
$692$		−	172.732i		−	0.249612i
$693$	−221.074	+	744.643i	−0.319010	+	1.07452i
$694$	68.8603			0.0992224
$695$	−861.495	+	279.917i	−1.23956	+	0.402758i
$696$	172.533	+	125.352i	0.247892	+	0.180104i
$697$	−867.516	+	630.287i	−1.24464	+	0.904286i
$698$	38.5774	−	118.729i	0.0552685	−	0.170099i
$699$	303.533	+	98.6239i	0.434239	+	0.141093i
$700$	−182.936	−	251.790i	−0.261337	−	0.359700i
$701$	−299.098	+	411.673i	−0.426674	+	0.587266i	−0.967186	−	0.254070i	$-0.918231\pi$
$701$	−299.098	+	411.673i	−0.426674	+	0.587266i	0.540512	+	0.841336i	$0.318231\pi$
$702$	26.2461	+	80.7772i	0.0373876	+	0.115067i
$703$		−	83.4619i		−	0.118722i
$704$	−125.461	−	163.713i	−0.178212	−	0.232548i
$705$	150.557			0.213556
$706$	82.6722	−	26.8618i	0.117099	−	0.0380479i
$707$	−907.866	−	659.603i	−1.28411	−	0.932961i
$708$	8.81404	−	6.40378i	0.0124492	−	0.00904488i
$709$	−227.956	+	701.577i	−0.321518	+	0.989531i	0.651470	+	0.758674i	$0.274153\pi$
$709$	−227.956	+	701.577i	−0.321518	+	0.989531i	−0.972988	+	0.230856i	$0.925847\pi$
$710$	210.938	+	68.5379i	0.297096	+	0.0965323i
$711$	16.4001	+	22.5729i	0.0230663	+	0.0317481i
$712$	393.438	−	541.521i	0.552582	−	0.760563i
$713$	6.08514	+	18.7282i	0.00853457	+	0.0262667i
$714$			152.824i			0.214039i
$715$	−77.0820	−	218.101i	−0.107807	−	0.305036i
$716$	760.222			1.06176
$717$	−414.230	+	134.591i	−0.577726	+	0.187715i
$718$	−274.681	−	199.567i	−0.382564	−	0.277949i
$719$	425.782	−	309.349i	0.592187	−	0.430249i	−0.250910	−	0.968010i	$-0.580730\pi$
$719$	425.782	−	309.349i	0.592187	−	0.430249i	0.843097	+	0.537762i	$0.180730\pi$
$720$	−87.1509	+	268.223i	−0.121043	+	0.372532i
$721$	−877.214	−	285.024i	−1.21666	−	0.395318i
$722$	−152.329	−	209.663i	−0.210982	−	0.290392i
$723$	−220.078	+	302.912i	−0.304396	+	0.418965i
$724$	41.7395	+	128.461i	0.0576513	+	0.177432i
$725$		−	255.831i		−	0.352871i
$726$	113.475	−	43.3983i	0.156302	−	0.0597772i
$727$	−756.122			−1.04006			−0.520029	−	0.854149i	$-0.674079\pi$
$727$	−756.122			−1.04006			−0.520029	+	0.854149i	$0.674079\pi$
$728$	−270.344	+	87.8402i	−0.371352	+	0.120660i
$729$	−33.9853	−	24.6918i	−0.0466191	−	0.0338707i
$730$	−241.862	+	175.723i	−0.331318	+	0.240717i
$731$	108.913	−	335.199i	0.148991	−	0.458548i
$732$	103.197	+	33.5306i	0.140979	+	0.0458068i
$733$	250.381	+	344.620i	0.341584	+	0.470149i	0.944903	−	0.327350i	$-0.106156\pi$
$733$	250.381	+	344.620i	0.341584	+	0.470149i	−0.603320	+	0.797500i	$0.706156\pi$
$734$	−140.426	+	193.279i	−0.191316	+	0.263323i
$735$	−85.7407	−	263.883i	−0.116654	−	0.359024i
$736$		−	79.9888i		−	0.108680i
$737$	399.228	−	141.096i	0.541693	−	0.191447i
$738$	−361.448			−0.489767
$739$	184.618	−	59.9862i	0.249822	−	0.0811721i	−0.181429	−	0.983404i	$-0.558072\pi$
$739$	184.618	−	59.9862i	0.249822	−	0.0811721i	0.431251	+	0.902232i	$0.358072\pi$
$740$	452.243	+	328.574i	0.611139	+	0.444019i
$741$	12.1885	−	8.85544i	0.0164487	−	0.0119507i
$742$	−25.6231	+	78.8597i	−0.0345324	+	0.106280i
$743$	211.584	+	68.7477i	0.284769	+	0.0925272i	0.447919	−	0.894074i	$-0.352165\pi$
$743$	211.584	+	68.7477i	0.284769	+	0.0925272i	−0.163150	+	0.986601i	$0.552165\pi$
$744$	31.4183	+	43.2436i	0.0422289	+	0.0581231i
$745$	−157.961	+	217.415i	−0.212029	+	0.291832i
$746$	48.0763	+	147.964i	0.0644454	+	0.198343i
$747$		−	590.214i		−	0.790112i
$748$	463.291	−	355.041i	0.619373	−	0.474654i
$749$	−844.853			−1.12797
$750$	129.868	−	42.1968i	0.173158	−	0.0562624i
$751$	1186.49	+	862.033i	1.57987	+	1.14785i	0.916838	+	0.399260i	$0.130733\pi$
$751$	1186.49	+	862.033i	1.57987	+	1.14785i	0.663037	+	0.748587i	$0.269267\pi$
$752$	−219.116	+	159.197i	−0.291378	+	0.211699i
$753$	4.75507	−	14.6346i	0.00631483	−	0.0194351i
$754$	−103.262	−	33.5520i	−0.136953	−	0.0444986i
$755$	−236.348	−	325.305i	−0.313044	−	0.430868i
$756$	451.976	−	622.091i	0.597851	−	0.822872i
$757$	410.832	+	1264.41i	0.542710	+	1.67029i	0.726373	+	0.687301i	$0.241205\pi$
$757$	410.832	+	1264.41i	0.542710	+	1.67029i	−0.183663	+	0.982989i	$0.558795\pi$
$758$			232.676i			0.306961i
$759$	−40.2786	−	11.9581i	−0.0530680	−	0.0157551i
$760$	−45.0294			−0.0592492
$761$	654.725	−	212.733i	0.860348	−	0.279544i	0.154574	−	0.987981i	$-0.450599\pi$
$761$	654.725	−	212.733i	0.860348	−	0.279544i	0.705774	+	0.708437i	$0.250599\pi$
$762$	−152.918	−	111.101i	−0.200680	−	0.145802i
$763$	758.020	−	550.734i	0.993473	−	0.721801i
$764$	128.543	−	395.614i	0.168250	−	0.517820i
$765$	−412.207	−	133.934i	−0.538832	−	0.175077i
$766$	233.835	+	321.847i	0.305268	+	0.420165i
$767$	−7.01626	+	9.65706i	−0.00914767	+	0.0125907i
$768$	−8.11397	−	24.9722i	−0.0105651	−	0.0325159i
$769$			695.838i			0.904860i	0.891800	+	0.452430i	$0.149443\pi$
$769$			695.838i			0.904860i	−0.891800	+	0.452430i	$0.850557\pi$
$770$	180.498	−	262.280i	0.234414	−	0.340623i
$771$	−557.320			−0.722853
$772$	−96.5023	+	31.3555i	−0.125003	+	0.0406159i
$773$	−67.1591	−	48.7939i	−0.0868811	−	0.0631228i	0.543497	−	0.839411i	$-0.317100\pi$
$773$	−67.1591	−	48.7939i	−0.0868811	−	0.0631228i	−0.630378	+	0.776288i	$0.717100\pi$
$774$	96.1124	−	69.8298i	0.124176	−	0.0902193i
$775$	19.8146	−	60.9832i	0.0255673	−	0.0786880i
$776$	−399.668	−	129.860i	−0.515036	−	0.167345i
$777$	−325.623	−	448.182i	−0.419077	−	0.576810i
$778$	143.716	−	197.808i	0.184725	−	0.254252i
$779$	44.9615	+	138.377i	0.0577169	+	0.177634i
$780$			100.906i			0.129367i
$781$	21.4571	+	839.225i	0.0274738	+	1.07455i
$782$	30.6888			0.0392440
$783$	601.140	−	195.322i	0.767739	−	0.249454i
$784$	403.811	+	293.386i	0.515065	+	0.374217i
$785$	798.079	−	579.838i	1.01666	−	0.738647i
$786$	−44.0373	+	135.533i	−0.0560271	+	0.172434i
$787$	103.159	+	33.5185i	0.131079	+	0.0425903i	0.373822	−	0.927500i	$-0.378047\pi$
$787$	103.159	+	33.5185i	0.131079	+	0.0425903i	−0.242743	+	0.970091i	$0.578047\pi$
$788$	−575.601	−	792.246i	−0.730458	−	1.00539i
$789$	−34.6556	+	47.6993i	−0.0439234	+	0.0604554i
$790$	−3.53408	−	10.8768i	−0.00447351	−	0.0137681i
$791$			84.5910i			0.106942i
$792$	423.266	−	10.8219i	0.534427	−	0.0136641i
$793$	−118.885			−0.149919
$794$	−79.7214	+	25.9030i	−0.100405	+	0.0326235i
$795$	51.2461	+	37.2325i	0.0644605	+	0.0468333i
$796$	−498.514	+	362.191i	−0.626273	+	0.455014i
$797$	−308.596	+	949.759i	−0.387196	+	1.19167i	0.547678	+	0.836689i	$0.315512\pi$
$797$	−308.596	+	949.759i	−0.387196	+	1.19167i	−0.934874	+	0.354979i	$0.884488\pi$
$798$	19.7214	+	6.40786i	0.0247135	+	0.00802990i
$799$	−244.656	−	336.740i	−0.306202	−	0.421451i
$800$	−153.096	+	210.718i	−0.191370	+	0.263398i
$801$	−270.141	−	831.409i	−0.337255	−	1.03796i
$802$			46.3500i			0.0577930i
$803$	−932.162	−	641.505i	−1.16085	−	0.798886i
$804$	−184.706			−0.229734
$805$	−104.721	+	34.0260i	−0.130089	+	0.0422684i
$806$	−22.0163	−	15.9958i	−0.0273155	−	0.0198458i
$807$	458.387	−	333.038i	0.568014	−	0.412686i
$808$	−189.021	+	581.748i	−0.233937	+	0.719985i
$809$	71.6823	+	23.2910i	0.0886060	+	0.0287898i	0.352985	−	0.935629i	$-0.385167\pi$
$809$	71.6823	+	23.2910i	0.0886060	+	0.0287898i	−0.264379	+	0.964419i	$0.585167\pi$
$810$	−56.5109	−	77.7805i	−0.0697665	−	0.0960254i
$811$	−583.402	+	802.984i	−0.719361	+	0.990115i	0.280184	+	0.959946i	$0.409605\pi$
$811$	−583.402	+	802.984i	−0.719361	+	0.990115i	−0.999545	+	0.0301690i	$0.990395\pi$
$812$	303.761	+	934.880i	0.374090	+	1.15133i
$813$			320.696i			0.394460i
$814$	91.5499	−	308.368i	0.112469	−	0.378830i
$815$	697.463			0.855783
$816$	−199.742	+	64.9000i	−0.244781	+	0.0795343i
$817$	−38.6894	−	28.1095i	−0.0473555	−	0.0344058i
$818$	359.538	−	261.220i	0.439533	−	0.319339i
$819$	−114.721	+	353.076i	−0.140075	+	0.431106i
$820$	−926.810	−	301.139i	−1.13026	−	0.367243i
$821$	−733.079	−	1009.00i	−0.892910	−	1.22898i	−0.972675	−	0.232171i	$-0.925417\pi$
$821$	−733.079	−	1009.00i	−0.892910	−	1.22898i	0.0797652	−	0.996814i	$-0.474583\pi$
$822$	9.59460	−	13.2058i	0.0116723	−	0.0160655i
$823$	−165.319	−	508.800i	−0.200874	−	0.618227i	−0.999858	−	0.0168738i	$-0.994629\pi$
$823$	−165.319	−	508.800i	−0.200874	−	0.618227i	0.798984	−	0.601353i	$-0.205371\pi$
$824$			502.763i			0.610149i
$825$	83.2204	+	108.594i	0.100873	+	0.131629i
$826$	−16.4296			−0.0198905
$827$	53.4969	−	17.3822i	0.0646879	−	0.0210184i	−0.276494	−	0.961016i	$-0.589173\pi$
$827$	53.4969	−	17.3822i	0.0646879	−	0.0210184i	0.341182	+	0.939997i	$0.389173\pi$
$828$	−55.0476	−	39.9944i	−0.0664826	−	0.0483024i
$829$	660.320	−	479.751i	0.796526	−	0.578710i	−0.113367	−	0.993553i	$-0.536164\pi$
$829$	660.320	−	479.751i	0.796526	−	0.578710i	0.909893	+	0.414843i	$0.136164\pi$
$830$	−74.7577	+	230.081i	−0.0900695	+	0.277206i
$831$	−402.574	−	130.804i	−0.484445	−	0.157406i
$832$	−57.9431	−	79.7518i	−0.0696431	−	0.0958555i
$833$	−450.877	+	620.579i	−0.541269	+	0.744993i
$834$	−70.2631	−	216.248i	−0.0842483	−	0.259290i
$835$		−	987.803i		−	1.18300i
$836$	−26.3911	−	74.6726i	−0.0315682	−	0.0893213i
$837$	158.423			0.189275
$838$	−100.991	+	32.8141i	−0.120515	+	0.0391576i
$839$	−49.8216	−	36.1975i	−0.0593821	−	0.0431436i	0.557698	−	0.830044i	$-0.311685\pi$
$839$	−49.8216	−	36.1975i	−0.0593821	−	0.0431436i	−0.617080	+	0.786900i	$0.711685\pi$
$840$	−241.803	+	175.680i	−0.287861	+	0.209143i
$841$	10.1913	−	31.3657i	0.0121181	−	0.0372958i
$842$	410.036	+	133.229i	0.486979	+	0.158229i
$843$	105.152	+	144.729i	0.124735	+	0.171683i
$844$	−200.717	+	276.264i	−0.237817	+	0.327327i
$845$	174.731	+	537.768i	0.206783	+	0.636412i
$846$		−	140.301i		−	0.165841i
$847$	1163.66	+	313.344i	1.37386	+	0.369945i
$848$	−113.951			−0.134376
$849$	554.508	−	180.171i	0.653131	−	0.212215i
$850$	−80.8450	−	58.7373i	−0.0951118	−	0.0691028i
$851$	−90.0000	+	65.3888i	−0.105758	+	0.0768376i
$852$	113.163	−	348.280i	0.132820	−	0.408779i
$853$	1347.24	+	437.746i	1.57942	+	0.513184i	0.961907	−	0.273379i	$-0.0881412\pi$
$853$	1347.24	+	437.746i	1.57942	+	0.513184i	0.617511	+	0.786562i	$0.288141\pi$
$854$	−96.1803	−	132.381i	−0.112623	−	0.155013i
$855$	−34.5673	+	47.5778i	−0.0404296	+	0.0556466i
$856$	142.307	+	437.977i	0.166247	+	0.511656i
$857$		−	1249.64i		−	1.45815i	−0.684432	−	0.729077i	$-0.739950\pi$
$857$		−	1249.64i		−	1.45815i	0.684432	−	0.729077i	$-0.260050\pi$
$858$	54.7465	−	19.3487i	0.0638071	−	0.0225509i
$859$	−345.229			−0.401896			−0.200948	−	0.979602i	$-0.564402\pi$
$859$	−345.229			−0.401896			−0.200948	+	0.979602i	$0.564402\pi$
$860$	304.626	−	98.9790i	0.354216	−	0.115092i
$861$	781.312	+	567.656i	0.907447	+	0.659299i
$862$	−102.474	+	74.4518i	−0.118879	+	0.0863710i
$863$	−125.242	+	385.456i	−0.145124	+	0.446647i	−0.997027	−	0.0770535i	$-0.975449\pi$
$863$	−125.242	+	385.456i	−0.145124	+	0.446647i	0.851903	+	0.523700i	$0.175449\pi$
$864$	−612.021	−	198.858i	−0.708358	−	0.230159i
$865$	116.964	+	160.988i	0.135219	+	0.186113i
$866$	265.045	−	364.804i	0.306057	−	0.421251i
$867$	23.6790	+	72.8765i	0.0273114	+	0.0840560i
$868$			246.377i			0.283844i
$869$	34.3588	−	26.3307i	0.0395383	−	0.0303000i
$870$	−114.164			−0.131223
$871$	192.467	−	62.5364i	0.220973	−	0.0717983i
$872$	−413.185	−	300.197i	−0.473836	−	0.344262i
$873$	−444.019	+	322.599i	−0.508613	+	0.369529i
$874$	1.28677	−	3.96027i	0.00147228	−	0.00453121i
$875$	1288.21	+	418.565i	1.47224	+	0.478360i
$876$	290.136	+	399.338i	0.331206	+	0.455866i
$877$	209.069	−	287.759i	0.238391	−	0.328117i	−0.673012	−	0.739631i	$-0.735000\pi$
$877$	209.069	−	287.759i	0.238391	−	0.328117i	0.911403	+	0.411514i	$0.135000\pi$
$878$	151.946	+	467.642i	0.173059	+	0.532622i
$879$			89.1077i			0.101374i
$880$	419.453	+	124.529i	0.476651	+	0.141511i
$881$	−883.370			−1.00269			−0.501345	−	0.865248i	$-0.667161\pi$
$881$	−883.370			−1.00269			−0.501345	+	0.865248i	$0.667161\pi$
$882$	−245.907	+	79.9001i	−0.278806	+	0.0905897i
$883$	−674.512	−	490.062i	−0.763887	−	0.554996i	0.136213	−	0.990680i	$-0.456507\pi$
$883$	−674.512	−	490.062i	−0.763887	−	0.554996i	−0.900100	+	0.435683i	$0.856507\pi$
$884$	225.689	−	163.973i	0.255304	−	0.185489i
$885$	−3.87849	+	11.9368i	−0.00438248	+	0.0134879i
$886$	−179.177	−	58.2180i	−0.202231	−	0.0657088i
$887$	54.3406	+	74.7934i	0.0612633	+	0.0843217i	0.838549	−	0.544826i	$-0.183404\pi$
$887$	54.3406	+	74.7934i	0.0612633	+	0.0843217i	−0.777286	+	0.629147i	$0.783404\pi$
$888$	−177.492	+	244.297i	−0.199879	+	0.275109i
$889$	−579.384	−	1783.16i	−0.651725	−	2.00580i
$890$			358.322i			0.402608i
$891$	206.302	−	299.774i	0.231540	−	0.336447i
$892$	923.680			1.03552
$893$	−53.7132	+	17.4525i	−0.0601492	+	0.0195437i
$894$	−54.5743	−	39.6505i	−0.0610451	−	0.0443518i
$895$	−708.535	+	514.781i	−0.791659	+	0.575174i
$896$	398.204	−	1225.54i	0.444424	−	1.36780i
$897$	−19.0983	−	6.20541i	−0.0212913	−	0.00691796i
$898$	−171.846	−	236.526i	−0.191365	−	0.263392i
$899$	−119.039	+	163.844i	−0.132413	+	0.182251i
$900$	68.4665	+	210.718i	0.0760739	+	0.234131i
$901$		−	175.121i		−	0.194363i
$902$	14.3328	+	560.583i	0.0158900	+	0.621489i
$903$	−317.426			−0.351524
$904$	43.8525	−	14.2486i	0.0485095	−	0.0157617i
$905$	−125.889	−	91.4634i	−0.139103	−	0.101065i
$906$	81.6563	−	59.3268i	0.0901284	−	0.0654821i
$907$	−454.784	+	1399.68i	−0.501415	+	1.54320i	0.305299	+	0.952256i	$0.401243\pi$
$907$	−454.784	+	1399.68i	−0.501415	+	1.54320i	−0.806715	+	0.590941i	$0.798757\pi$
$908$	−840.491	−	273.092i	−0.925651	−	0.300762i
$909$	469.567	+	646.304i	0.516576	+	0.711005i
$910$	89.4427	−	123.107i	0.0982887	−	0.135283i
$911$	54.3525	+	167.280i	0.0596625	+	0.183622i	0.976446	−	0.215763i	$-0.0692237\pi$
$911$	54.3525	+	167.280i	0.0596625	+	0.183622i	−0.916783	+	0.399385i	$0.869224\pi$
$912$			28.4971i			0.0312468i
$913$	−915.384	+	23.4043i	−1.00261	+	0.0256345i
$914$	−185.795			−0.203277
$915$	−118.885	+	38.6282i	−0.129929	+	0.0422166i
$916$	112.941	+	82.0566i	0.123298	+	0.0895814i
$917$	−1143.61	+	830.884i	−1.24713	+	0.906089i
$918$	76.2945	−	234.810i	0.0831095	−	0.255785i
$919$	−1636.12	−	531.609i	−1.78033	−	0.578465i	−0.781371	−	0.624066i	$-0.785479\pi$
$919$	−1636.12	−	531.609i	−1.78033	−	0.578465i	−0.998960	+	0.0456019i	$0.985479\pi$
$920$	35.2786	+	48.5569i	0.0383463	+	0.0527792i
$921$	289.595	−	398.593i	0.314435	−	0.432783i
$922$	−100.195	−	308.368i	−0.108671	−	0.334455i
$923$			401.228i			0.434700i
$924$	−433.050	−	298.021i	−0.468668	−	0.322533i
$925$	362.243			0.391614
$926$	−50.5322	+	16.4189i	−0.0545704	+	0.0177310i
$927$	531.217	+	385.952i	0.573049	+	0.416345i
$928$	665.535	−	483.539i	0.717171	−	0.521055i
$929$	288.957	−	889.317i	0.311040	−	0.957284i	−0.666313	−	0.745672i	$-0.732129\pi$
$929$	288.957	−	889.317i	0.311040	−	0.957284i	0.977354	−	0.211612i	$-0.0678714\pi$
$930$	−27.2136	−	8.84223i	−0.0292619	−	0.00950778i
$931$	61.1782	+	84.2046i	0.0657123	+	0.0904453i
$932$	471.322	−	648.720i	0.505711	−	0.696051i
$933$	−237.105	−	729.733i	−0.254131	−	0.782136i
$934$			8.07520i			0.00864583i
$935$	−191.378	+	644.618i	−0.204682	+	0.689431i
$936$	202.361			0.216197
$937$	−853.544	+	277.333i	−0.910933	+	0.295980i	−0.726742	−	0.686910i	$-0.758967\pi$
$937$	−853.544	+	277.333i	−0.910933	+	0.295980i	−0.184191	+	0.982890i	$0.558967\pi$
$938$	225.344	+	163.722i	0.240239	+	0.174544i
$939$	370.504	−	269.187i	0.394573	−	0.286674i
$940$	116.892	−	359.756i	0.124353	−	0.382719i
$941$	437.800	+	142.250i	0.465250	+	0.151169i	0.532256	−	0.846584i	$-0.321345\pi$
$941$	437.800	+	142.250i	0.465250	+	0.151169i	−0.0670056	+	0.997753i	$0.521345\pi$
$942$	145.548	+	200.329i	0.154509	+	0.212664i
$943$	113.992	−	156.896i	0.120882	−	0.166380i
$944$	−6.97716	−	21.4735i	−0.00739106	−	0.0227473i
$945$			885.849i			0.937406i
$946$	−112.113	−	146.295i	−0.118512	−	0.154646i
$947$	1781.44			1.88114			0.940570	−	0.339600i	$-0.110292\pi$
$947$	1781.44			1.88114			0.940570	+	0.339600i	$0.110292\pi$
$948$	−17.9586	+	5.83511i	−0.0189437	+	0.00615518i
$949$	−437.533	−	317.886i	−0.461046	−	0.334970i
$950$	−10.9696	+	7.96990i	−0.0115470	+	0.00838937i
$951$	−220.755	+	679.413i	−0.232129	+	0.714419i
$952$	785.861	+	255.342i	0.825484	+	0.268216i
$953$	472.394	+	650.194i	0.495691	+	0.682260i	0.981425	−	0.191847i	$-0.0614476\pi$
$953$	472.394	+	650.194i	0.495691	+	0.682260i	−0.485734	+	0.874107i	$0.661448\pi$
$954$	34.6962	−	47.7553i	0.0363692	−	0.0500579i
$955$	148.085	+	455.759i	0.155063	+	0.477235i
$956$			1094.30i			1.14466i
$957$	−143.992	−	407.420i	−0.150462	−	0.425726i
$958$	416.760			0.435031
$959$	153.992	−	50.0350i	0.160575	−	0.0521741i
$960$	−83.8560	−	60.9250i	−0.0873500	−	0.0634635i
$961$	736.400	−	535.026i	0.766285	−	0.556738i
$962$	47.5078	−	146.214i	0.0493844	−	0.151989i
$963$	572.008	+	185.857i	0.593986	+	0.192998i
$964$	552.938	+	761.054i	0.573587	+	0.789475i
$965$	68.7089	−	94.5697i	0.0712010	−	0.0979997i
$966$	−8.54102	−	26.2866i	−0.00884164	−	0.0272118i
$967$		−	915.454i		−	0.946695i	−0.880876	−	0.473347i	$-0.843046\pi$
$967$		−	915.454i		−	0.946695i	0.880876	−	0.473347i	$-0.156954\pi$
$968$	−33.5683	−	656.030i	−0.0346780	−	0.677716i
$969$	−43.7945			−0.0451956
$970$	213.951	−	69.5170i	0.220568	−	0.0716670i
$971$	−596.366	−	433.285i	−0.614177	−	0.446226i	0.236706	−	0.971581i	$-0.423932\pi$
$971$	−596.366	−	433.285i	−0.614177	−	0.446226i	−0.850883	+	0.525356i	$0.823932\pi$
$972$	−690.577	+	501.733i	−0.710470	+	0.516187i
$973$	696.964	−	2145.04i	0.716305	−	2.20456i
$974$	−435.902	−	141.633i	−0.447538	−	0.145414i
$975$	38.4346	+	52.9007i	0.0394201	+	0.0542571i
$976$	132.177	−	181.926i	0.135427	−	0.186400i
$977$	59.1165	+	181.942i	0.0605082	+	0.186225i	0.976742	−	0.214420i	$-0.0687861\pi$
$977$	59.1165	+	181.942i	0.0605082	+	0.186225i	−0.916233	+	0.400645i	$0.868786\pi$
$978$			175.073i			0.179011i
$979$	−1278.75	+	451.941i	−1.30618	+	0.461635i
$980$	−697.115			−0.711341
$981$	−634.373	+	206.120i	−0.646659	+	0.210112i
$982$	256.297	+	186.211i	0.260995	+	0.189624i
$983$	−772.503	+	561.257i	−0.785863	+	0.570963i	−0.906733	−	0.421705i	$-0.861432\pi$
$983$	−772.503	+	561.257i	−0.785863	+	0.570963i	0.120870	+	0.992668i	$0.461432\pi$
$984$	162.672	−	500.654i	0.165317	−	0.508794i
$985$	1072.93	+	348.617i	1.08927	+	0.353926i
$986$	185.517	+	255.342i	0.188151	+	0.258967i
$987$	−220.344	+	303.278i	−0.223247	+	0.307273i
$988$	−11.6970	−	35.9996i	−0.0118390	−	0.0364368i
$989$			63.7429i			0.0644518i
$990$	−179.905	+	137.869i	−0.181722	+	0.139262i
$991$	−1076.02			−1.08580			−0.542898	−	0.839799i	$-0.682673\pi$
$991$	−1076.02			−1.08580			−0.542898	+	0.839799i	$0.682673\pi$
$992$	196.096	−	63.7156i	0.197678	−	0.0642294i
$993$	−233.539	−	169.676i	−0.235185	−	0.170872i
$994$	−446.774	+	324.600i	−0.449471	+	0.326560i
$995$	219.364	−	675.132i	0.220466	−	0.678525i
$996$	379.886	+	123.432i	0.381411	+	0.123928i
$997$	283.439	+	390.120i	0.284292	+	0.391294i	0.927150	−	0.374692i	$-0.122251\pi$
$997$	283.439	+	390.120i	0.284292	+	0.391294i	−0.642858	+	0.765986i	$0.722251\pi$
$998$	−198.712	+	273.504i	−0.199111	+	0.274052i
$999$	276.565	+	851.181i	0.276842	+	0.852033i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.3.d.a.6.1	yes	4
3.2	odd	2		99.3.k.a.28.1		4
4.3	odd	2		176.3.n.a.17.1		4
5.2	odd	4		275.3.q.d.149.1		8
5.3	odd	4		275.3.q.d.149.2		8
5.4	even	2		275.3.x.e.226.1		4
11.2	odd	10	inner	11.3.d.a.2.1	✓	4
11.3	even	5		121.3.b.b.120.3		4
11.4	even	5		121.3.d.c.118.1		4
11.5	even	5		121.3.d.a.40.1		4
11.6	odd	10		121.3.d.c.40.1		4
11.7	odd	10		121.3.d.a.118.1		4
11.8	odd	10		121.3.b.b.120.2		4
11.9	even	5		121.3.d.d.112.1		4
11.10	odd	2		121.3.d.d.94.1		4
33.2	even	10		99.3.k.a.46.1		4
33.8	even	10		1089.3.c.e.604.3		4
33.14	odd	10		1089.3.c.e.604.2		4
44.35	even	10		176.3.n.a.145.1		4
55.2	even	20		275.3.q.d.24.2		8
55.13	even	20		275.3.q.d.24.1		8
55.24	odd	10		275.3.x.e.101.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.3.d.a.2.1	✓	4	11.2	odd	10	inner
11.3.d.a.6.1	yes	4	1.1	even	1	trivial
99.3.k.a.28.1		4	3.2	odd	2
99.3.k.a.46.1		4	33.2	even	10
121.3.b.b.120.2		4	11.8	odd	10
121.3.b.b.120.3		4	11.3	even	5
121.3.d.a.40.1		4	11.5	even	5
121.3.d.a.118.1		4	11.7	odd	10
121.3.d.c.40.1		4	11.6	odd	10
121.3.d.c.118.1		4	11.4	even	5
121.3.d.d.94.1		4	11.10	odd	2
121.3.d.d.112.1		4	11.9	even	5
176.3.n.a.17.1		4	4.3	odd	2
176.3.n.a.145.1		4	44.35	even	10
275.3.q.d.24.1		8	55.13	even	20
275.3.q.d.24.2		8	55.2	even	20
275.3.q.d.149.1		8	5.2	odd	4
275.3.q.d.149.2		8	5.3	odd	4
275.3.x.e.101.1		4	55.24	odd	10
275.3.x.e.226.1		4	5.4	even	2
1089.3.c.e.604.2		4	33.14	odd	10
1089.3.c.e.604.3		4	33.8	even	10

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:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	11.d (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.690983 + 0.224514i) q^{2} +(-1.11803 - 0.812299i) q^{3} +(-2.80902 + 2.04087i) q^{4} +(1.23607 - 3.80423i) q^{5} +(0.954915 + 0.310271i) q^{6} +(5.85410 + 8.05748i) q^{7} +(3.19098 - 4.39201i) q^{8} +(-2.19098 - 6.74315i) q^{9} +O(q^{10})\)	\(q+(-0.690983 + 0.224514i) q^{2} +(-1.11803 - 0.812299i) q^{3} +(-2.80902 + 2.04087i) q^{4} +(1.23607 - 3.80423i) q^{5} +(0.954915 + 0.310271i) q^{6} +(5.85410 + 8.05748i) q^{7} +(3.19098 - 4.39201i) q^{8} +(-2.19098 - 6.74315i) q^{9} +2.90617i q^{10} +(-10.3713 + 3.66547i) q^{11} +4.79837 q^{12} +(-5.00000 + 1.62460i) q^{13} +(-5.85410 - 4.25325i) q^{14} +(-4.47214 + 3.24920i) q^{15} +(3.07295 - 9.45756i) q^{16} +(14.5344 + 4.72253i) q^{17} +(3.02786 + 4.16750i) q^{18} +(1.21885 - 1.67760i) q^{19} +(4.29180 + 13.2088i) q^{20} -13.7638i q^{21} +(6.34346 - 4.86128i) q^{22} -2.76393 q^{23} +(-7.13525 + 2.31838i) q^{24} +(7.28115 + 5.29007i) q^{25} +(3.09017 - 2.24514i) q^{26} +(-6.87132 + 21.1478i) q^{27} +(-32.8885 - 10.6861i) q^{28} +(-16.7082 - 22.9969i) q^{29} +(2.36068 - 3.24920i) q^{30} +(-2.20163 - 6.77591i) q^{31} +28.9402i q^{32} +(14.5729 + 4.32650i) q^{33} -11.1033 q^{34} +(37.8885 - 12.3107i) q^{35} +(19.9164 + 14.4701i) q^{36} +(32.5623 - 23.6579i) q^{37} +(-0.465558 + 1.43284i) q^{38} +(6.90983 + 2.24514i) q^{39} +(-12.7639 - 17.5680i) q^{40} +(-41.2426 + 56.7656i) q^{41} +(3.09017 + 9.51057i) q^{42} -23.0624i q^{43} +(21.6525 - 31.4629i) q^{44} -28.3607 q^{45} +(1.90983 - 0.620541i) q^{46} +(-22.0344 - 16.0090i) q^{47} +(-11.1180 + 8.07772i) q^{48} +(-15.5106 + 47.7369i) q^{49} +(-6.21885 - 2.02063i) q^{50} +(-12.4139 - 17.0863i) q^{51} +(10.7295 - 14.7679i) q^{52} +(-3.54102 - 10.8981i) q^{53} -16.1554i q^{54} +(1.12461 + 43.9856i) q^{55} +54.0689 q^{56} +(-2.72542 + 0.885544i) q^{57} +(16.7082 + 12.1392i) q^{58} +(1.83688 - 1.33457i) q^{59} +(5.93112 - 18.2541i) q^{60} +(21.5066 + 6.98791i) q^{61} +(3.04257 + 4.18774i) q^{62} +(41.5066 - 57.1289i) q^{63} +(5.79431 + 17.8330i) q^{64} +21.0292i q^{65} +(-11.0410 + 0.282294i) q^{66} -38.4934 q^{67} +(-50.4656 + 16.3973i) q^{68} +(3.09017 + 2.24514i) q^{69} +(-23.4164 + 17.0130i) q^{70} +(23.5836 - 72.5828i) q^{71} +(-36.6074 - 11.8945i) q^{72} +(60.4656 + 83.2237i) q^{73} +(-17.1885 + 23.6579i) q^{74} +(-3.84346 - 11.8290i) q^{75} +7.19991i q^{76} +(-90.2492 - 62.1087i) q^{77} -5.27864 q^{78} +(-3.74265 + 1.21606i) q^{79} +(-32.1803 - 23.3804i) q^{80} +(-26.7639 + 19.4451i) q^{81} +(15.7533 - 48.4836i) q^{82} +(79.1697 + 25.7238i) q^{83} +(28.0902 + 38.6628i) q^{84} +(35.9311 - 49.4549i) q^{85} +(5.17783 + 15.9357i) q^{86} +39.2833i q^{87} +(-16.9959 + 57.2474i) q^{88} +123.297 q^{89} +(19.5967 - 6.36737i) q^{90} +(-42.3607 - 30.7768i) q^{91} +(7.76393 - 5.64083i) q^{92} +(-3.04257 + 9.36408i) q^{93} +(18.8197 + 6.11488i) q^{94} +(-4.87539 - 6.71040i) q^{95} +(23.5081 - 32.3562i) q^{96} +(-23.9205 - 73.6196i) q^{97} -36.4677i q^{98} +(47.4402 + 61.9044i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 5 q^{2} - 9 q^{4} - 4 q^{5} + 15 q^{6} + 10 q^{7} + 15 q^{8} - 11 q^{9}+O(q^{10}) \) 4 * q - 5 * q^2 - 9 * q^4 - 4 * q^5 + 15 * q^6 + 10 * q^7 + 15 * q^8 - 11 * q^9	\( 4 q - 5 q^{2} - 9 q^{4} - 4 q^{5} + 15 q^{6} + 10 q^{7} + 15 q^{8} - 11 q^{9} + q^{11} - 30 q^{12} - 20 q^{13} - 10 q^{14} + 19 q^{16} + 30 q^{18} + 25 q^{19} + 44 q^{20} - 35 q^{22} - 20 q^{23} + 5 q^{24} + 9 q^{25} - 10 q^{26} + 15 q^{27} - 60 q^{28} - 40 q^{29} - 80 q^{30} - 58 q^{31} + 65 q^{33} + 130 q^{34} + 80 q^{35} + 26 q^{36} + 90 q^{37} - 60 q^{38} + 50 q^{39} - 60 q^{40} - 80 q^{41} - 10 q^{42} + 24 q^{44} - 24 q^{45} + 30 q^{46} - 30 q^{47} - 40 q^{48} - 109 q^{49} - 45 q^{50} - 195 q^{51} + 110 q^{52} + 120 q^{53} - 76 q^{55} + 100 q^{56} + 45 q^{57} + 40 q^{58} + 23 q^{59} + 140 q^{60} + 10 q^{61} + 200 q^{62} + 90 q^{63} - 149 q^{64} + 90 q^{66} - 230 q^{67} - 260 q^{68} - 10 q^{69} - 40 q^{70} + 148 q^{71} - 95 q^{72} + 300 q^{73} - 270 q^{74} + 45 q^{75} - 200 q^{77} - 200 q^{78} + 70 q^{79} - 84 q^{80} - 116 q^{81} + 25 q^{82} + 225 q^{83} + 90 q^{84} + 260 q^{85} + 175 q^{86} + 55 q^{88} + 122 q^{89} - 20 q^{90} - 80 q^{91} + 40 q^{92} - 200 q^{93} + 120 q^{94} - 100 q^{95} + 340 q^{96} - 165 q^{97} + 31 q^{99}+O(q^{100}) \) 4 * q - 5 * q^2 - 9 * q^4 - 4 * q^5 + 15 * q^6 + 10 * q^7 + 15 * q^8 - 11 * q^9 + q^11 - 30 * q^12 - 20 * q^13 - 10 * q^14 + 19 * q^16 + 30 * q^18 + 25 * q^19 + 44 * q^20 - 35 * q^22 - 20 * q^23 + 5 * q^24 + 9 * q^25 - 10 * q^26 + 15 * q^27 - 60 * q^28 - 40 * q^29 - 80 * q^30 - 58 * q^31 + 65 * q^33 + 130 * q^34 + 80 * q^35 + 26 * q^36 + 90 * q^37 - 60 * q^38 + 50 * q^39 - 60 * q^40 - 80 * q^41 - 10 * q^42 + 24 * q^44 - 24 * q^45 + 30 * q^46 - 30 * q^47 - 40 * q^48 - 109 * q^49 - 45 * q^50 - 195 * q^51 + 110 * q^52 + 120 * q^53 - 76 * q^55 + 100 * q^56 + 45 * q^57 + 40 * q^58 + 23 * q^59 + 140 * q^60 + 10 * q^61 + 200 * q^62 + 90 * q^63 - 149 * q^64 + 90 * q^66 - 230 * q^67 - 260 * q^68 - 10 * q^69 - 40 * q^70 + 148 * q^71 - 95 * q^72 + 300 * q^73 - 270 * q^74 + 45 * q^75 - 200 * q^77 - 200 * q^78 + 70 * q^79 - 84 * q^80 - 116 * q^81 + 25 * q^82 + 225 * q^83 + 90 * q^84 + 260 * q^85 + 175 * q^86 + 55 * q^88 + 122 * q^89 - 20 * q^90 - 80 * q^91 + 40 * q^92 - 200 * q^93 + 120 * q^94 - 100 * q^95 + 340 * q^96 - 165 * q^97 + 31 * q^99

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