LMFDB - Embedded newform 126.4.m.a.41.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,4,Mod(41,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("126.41");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	126.m (of order $6$, 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:	$7.43424066072$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			41.20
Character	$\chi$	$=$	126.41
Dual form			126.4.m.a.83.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.73205 - 1.00000i) q^{2} +(2.71645 + 4.42955i) q^{3} +(2.00000 - 3.46410i) q^{4} +(7.20413 - 12.4779i) q^{5} +(9.13458 + 4.95575i) q^{6} +(12.8262 - 13.3600i) q^{7} -8.00000i q^{8} +(-12.2418 + 24.0653i) q^{9} +O(q^{10})$	\(q+(1.73205 - 1.00000i) q^{2} +(2.71645 + 4.42955i) q^{3} +(2.00000 - 3.46410i) q^{4} +(7.20413 - 12.4779i) q^{5} +(9.13458 + 4.95575i) q^{6} +(12.8262 - 13.3600i) q^{7} -8.00000i q^{8} +(-12.2418 + 24.0653i) q^{9} -28.8165i q^{10} +(-14.4249 + 8.32823i) q^{11} +(20.7773 - 0.550969i) q^{12} +(-22.2962 - 12.8727i) q^{13} +(8.85557 - 35.9664i) q^{14} +(74.8412 - 1.98463i) q^{15} +(-8.00000 - 13.8564i) q^{16} +95.0816 q^{17} +(2.86191 + 53.9241i) q^{18} +29.3261i q^{19} +(-28.8165 - 49.9117i) q^{20} +(94.0204 + 20.5223i) q^{21} +(-16.6565 + 28.8498i) q^{22} +(82.8886 + 47.8557i) q^{23} +(35.4364 - 21.7316i) q^{24} +(-41.2991 - 71.5321i) q^{25} -51.4909 q^{26} +(-139.853 + 11.1467i) q^{27} +(-20.6281 - 71.1511i) q^{28} +(-189.673 + 109.508i) q^{29} +(127.644 - 78.2787i) q^{30} +(176.978 + 102.178i) q^{31} +(-27.7128 - 16.0000i) q^{32} +(-76.0749 - 41.2726i) q^{33} +(164.686 - 95.0816i) q^{34} +(-74.3037 - 256.291i) q^{35} +(58.8811 + 90.5374i) q^{36} -317.480 q^{37} +(29.3261 + 50.7942i) q^{38} +(-3.54623 - 133.730i) q^{39} +(-99.8234 - 57.6331i) q^{40} +(-182.596 + 316.266i) q^{41} +(183.370 - 58.4747i) q^{42} +(-189.535 - 328.285i) q^{43} +66.6258i q^{44} +(212.094 + 326.122i) q^{45} +191.423 q^{46} +(-128.656 - 222.839i) q^{47} +(39.6460 - 73.0766i) q^{48} +(-13.9791 - 342.715i) q^{49} +(-143.064 - 82.5982i) q^{50} +(258.284 + 421.168i) q^{51} +(-89.1849 + 51.4909i) q^{52} +610.363i q^{53} +(-231.085 + 159.159i) q^{54} +239.991i q^{55} +(-106.880 - 102.609i) q^{56} +(-129.901 + 79.6628i) q^{57} +(-219.015 + 379.346i) q^{58} +(-107.752 + 186.632i) q^{59} +(142.808 - 263.227i) q^{60} +(-52.4764 + 30.2972i) q^{61} +408.714 q^{62} +(164.497 + 472.216i) q^{63} -64.0000 q^{64} +(-321.250 + 185.474i) q^{65} +(-173.038 + 4.58859i) q^{66} +(411.812 - 713.279i) q^{67} +(190.163 - 329.372i) q^{68} +(13.1835 + 497.157i) q^{69} +(-384.989 - 369.606i) q^{70} +710.721i q^{71} +(192.522 + 97.9343i) q^{72} -219.032i q^{73} +(-549.892 + 317.480i) q^{74} +(204.668 - 377.250i) q^{75} +(101.588 + 58.6521i) q^{76} +(-73.7512 + 299.536i) q^{77} +(-139.873 - 228.081i) q^{78} +(56.3964 + 97.6814i) q^{79} -230.532 q^{80} +(-429.277 - 589.204i) q^{81} +730.385i q^{82} +(-550.407 - 953.334i) q^{83} +(259.132 - 284.652i) q^{84} +(684.980 - 1186.42i) q^{85} +(-656.570 - 379.071i) q^{86} +(-1000.31 - 542.693i) q^{87} +(66.6258 + 115.399i) q^{88} +190.308 q^{89} +(693.479 + 352.766i) q^{90} +(-457.955 + 132.770i) q^{91} +(331.554 - 191.423i) q^{92} +(28.1485 + 1061.50i) q^{93} +(-445.678 - 257.313i) q^{94} +(365.928 + 211.269i) q^{95} +(-4.40775 - 166.218i) q^{96} +(1281.74 - 740.015i) q^{97} +(-366.928 - 579.621i) q^{98} +(-23.8346 - 449.092i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 96 q^{4} - 12 q^{7} - 36 q^{9}+O(q^{10}) $ 48 * q + 96 * q^4 - 12 * q^7 - 36 * q^9	$ 48 q + 96 q^{4} - 12 q^{7} - 36 q^{9} + 24 q^{11} - 132 q^{14} - 120 q^{15} - 384 q^{16} + 120 q^{18} + 180 q^{21} + 348 q^{23} - 600 q^{25} - 96 q^{28} - 84 q^{29} + 192 q^{30} + 96 q^{36} - 672 q^{37} + 1368 q^{39} + 1128 q^{42} + 84 q^{43} - 1008 q^{46} - 42 q^{49} + 456 q^{50} + 2016 q^{51} - 528 q^{56} + 732 q^{57} + 504 q^{58} - 1008 q^{60} - 774 q^{63} - 3072 q^{64} - 6972 q^{65} + 1176 q^{67} + 216 q^{70} - 384 q^{72} + 2520 q^{74} + 1500 q^{77} + 2832 q^{78} + 348 q^{79} + 2268 q^{81} - 1080 q^{84} + 720 q^{85} + 1200 q^{86} + 180 q^{91} + 1392 q^{92} + 5232 q^{93} - 5892 q^{95} + 972 q^{99}+O(q^{100}) $ 48 * q + 96 * q^4 - 12 * q^7 - 36 * q^9 + 24 * q^11 - 132 * q^14 - 120 * q^15 - 384 * q^16 + 120 * q^18 + 180 * q^21 + 348 * q^23 - 600 * q^25 - 96 * q^28 - 84 * q^29 + 192 * q^30 + 96 * q^36 - 672 * q^37 + 1368 * q^39 + 1128 * q^42 + 84 * q^43 - 1008 * q^46 - 42 * q^49 + 456 * q^50 + 2016 * q^51 - 528 * q^56 + 732 * q^57 + 504 * q^58 - 1008 * q^60 - 774 * q^63 - 3072 * q^64 - 6972 * q^65 + 1176 * q^67 + 216 * q^70 - 384 * q^72 + 2520 * q^74 + 1500 * q^77 + 2832 * q^78 + 348 * q^79 + 2268 * q^81 - 1080 * q^84 + 720 * q^85 + 1200 * q^86 + 180 * q^91 + 1392 * q^92 + 5232 * q^93 - 5892 * q^95 + 972 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$3$	2.71645	+	4.42955i	0.522781	+	0.852467i
$3$	2.71645	+	4.42955i	0.522781	+	0.852467i
$4$	2.00000	−	3.46410i	0.250000	−	0.433013i
$5$	7.20413	−	12.4779i	0.644357	−	1.11606i	−0.340092	−	0.940392i	$-0.610458\pi$
$5$	7.20413	−	12.4779i	0.644357	−	1.11606i	0.984450	−	0.175667i	$-0.0562084\pi$
$6$	9.13458	+	4.95575i	0.621529	+	0.337196i
$7$	12.8262	−	13.3600i	0.692548	−	0.721372i
$7$	12.8262	−	13.3600i	0.692548	−	0.721372i
$8$		−	8.00000i		−	0.353553i
$9$	−12.2418	+	24.0653i	−0.453399	+	0.891307i
$10$		−	28.8165i		−	0.911259i
$11$	−14.4249	+	8.32823i	−0.395389	+	0.228278i	−0.684492	−	0.729020i	$-0.739976\pi$
$11$	−14.4249	+	8.32823i	−0.395389	+	0.228278i	0.289104	+	0.957298i	$0.406643\pi$
$12$	20.7773	−	0.550969i	0.499824	−	0.0132542i
$13$	−22.2962	−	12.8727i	−0.475681	−	0.274635i	0.242934	−	0.970043i	$-0.421890\pi$
$13$	−22.2962	−	12.8727i	−0.475681	−	0.274635i	−0.718615	+	0.695408i	$0.755224\pi$
$14$	8.85557	−	35.9664i	0.169054	−	0.686601i
$15$	74.8412	−	1.98463i	1.28826	−	0.0341619i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	95.0816			1.35651			0.678255	−	0.734827i	$-0.262736\pi$
$17$	95.0816			1.35651			0.678255	+	0.734827i	$0.262736\pi$
$18$	2.86191	+	53.9241i	0.0374755	+	0.706113i
$19$			29.3261i			0.354098i	0.984202	+	0.177049i	$0.0566551\pi$
$19$			29.3261i			0.354098i	−0.984202	+	0.177049i	$0.943345\pi$
$20$	−28.8165	−	49.9117i	−0.322179	−	0.558030i
$21$	94.0204	+	20.5223i	0.976997	+	0.213254i
$22$	−16.6565	+	28.8498i	−0.161417	+	0.279582i
$23$	82.8886	+	47.8557i	0.751455	+	0.433853i	0.826219	−	0.563348i	$-0.190487\pi$
$23$	82.8886	+	47.8557i	0.751455	+	0.433853i	−0.0747644	+	0.997201i	$0.523820\pi$
$24$	35.4364	−	21.7316i	0.301393	−	0.184831i
$25$	−41.2991	−	71.5321i	−0.330393	−	0.572257i
$26$	−51.4909			−0.388392
$27$	−139.853	+	11.1467i	−0.996839	+	0.0794509i
$28$	−20.6281	−	71.1511i	−0.139226	−	0.480225i
$29$	−189.673	+	109.508i	−1.21453	+	0.701209i	−0.963743	−	0.266833i	$-0.914023\pi$
$29$	−189.673	+	109.508i	−1.21453	+	0.701209i	−0.250787	+	0.968042i	$0.580690\pi$
$30$	127.644	−	78.2787i	0.776818	−	0.476389i
$31$	176.978	+	102.178i	1.02536	+	0.591993i	0.915653	−	0.401971i	$-0.131675\pi$
$31$	176.978	+	102.178i	1.02536	+	0.591993i	0.109710	+	0.993964i	$0.465008\pi$
$32$	−27.7128	−	16.0000i	−0.153093	−	0.0883883i
$33$	−76.0749	−	41.2726i	−0.401301	−	0.217716i
$34$	164.686	−	95.0816i	0.830689	−	0.479599i
$35$	−74.3037	−	256.291i	−0.358846	−	1.23775i
$36$	58.8811	+	90.5374i	0.272598	+	0.419155i
$37$	−317.480			−1.41063			−0.705317	−	0.708892i	$-0.749195\pi$
$37$	−317.480			−1.41063			−0.705317	+	0.708892i	$0.749195\pi$
$38$	29.3261	+	50.7942i	0.125193	+	0.216840i
$39$	−3.54623	−	133.730i	−0.0145603	−	0.549077i
$40$	−99.8234	−	57.6331i	−0.394587	−	0.227815i
$41$	−182.596	+	316.266i	−0.695530	+	1.20469i	0.274472	+	0.961595i	$0.411497\pi$
$41$	−182.596	+	316.266i	−0.695530	+	1.20469i	−0.970002	+	0.243098i	$0.921836\pi$
$42$	183.370	−	58.4747i	0.673683	−	0.214830i
$43$	−189.535	−	328.285i	−0.672183	−	1.16426i	−0.977284	−	0.211935i	$-0.932023\pi$
$43$	−189.535	−	328.285i	−0.672183	−	1.16426i	0.305101	−	0.952320i	$-0.401310\pi$
$44$			66.6258i			0.228278i
$45$	212.094	+	326.122i	0.702601	+	1.08034i
$46$	191.423			0.613560
$47$	−128.656	−	222.839i	−0.399286	−	0.691584i	0.594352	−	0.804205i	$-0.297409\pi$
$47$	−128.656	−	222.839i	−0.399286	−	0.691584i	−0.993638	+	0.112621i	$0.964075\pi$
$48$	39.6460	−	73.0766i	0.119217	−	0.219744i
$49$	−13.9791	−	342.715i	−0.0407555	−	0.999169i
$50$	−143.064	−	82.5982i	−0.404647	−	0.233623i
$51$	258.284	+	421.168i	0.709158	+	1.15638i
$52$	−89.1849	+	51.4909i	−0.237841	+	0.137317i
$53$			610.363i			1.58188i	0.611892	+	0.790941i	$0.290409\pi$
$53$			610.363i			1.58188i	−0.611892	+	0.790941i	$0.709591\pi$
$54$	−231.085	+	159.159i	−0.582346	+	0.401089i
$55$			239.991i			0.588370i
$56$	−106.880	−	102.609i	−0.255044	−	0.244853i
$57$	−129.901	+	79.6628i	−0.301857	+	0.185116i
$58$	−219.015	+	379.346i	−0.495830	+	0.858803i
$59$	−107.752	+	186.632i	−0.237764	+	0.411820i	−0.960072	−	0.279751i	$-0.909748\pi$
$59$	−107.752	+	186.632i	−0.237764	+	0.411820i	0.722308	+	0.691571i	$0.243081\pi$
$60$	142.808	−	263.227i	0.307273	−	0.566374i
$61$	−52.4764	+	30.2972i	−0.110146	+	0.0635929i	−0.554061	−	0.832476i	$-0.686923\pi$
$61$	−52.4764	+	30.2972i	−0.110146	+	0.0635929i	0.443915	+	0.896069i	$0.353589\pi$
$62$	408.714			0.837205
$63$	164.497	+	472.216i	0.328964	+	0.944343i
$64$	−64.0000			−0.125000
$65$	−321.250	+	185.474i	−0.613018	+	0.353926i
$66$	−173.038	+	4.58859i	−0.322720	+	0.00855783i
$67$	411.812	−	713.279i	0.750908	−	1.30061i	−0.196476	−	0.980509i	$-0.562950\pi$
$67$	411.812	−	713.279i	0.750908	−	1.30061i	0.947383	−	0.320101i	$-0.103717\pi$
$68$	190.163	−	329.372i	0.339128	−	0.587386i
$69$	13.1835	+	497.157i	0.0230016	+	0.867401i
$70$	−384.989	−	369.606i	−0.657357	−	0.631090i
$71$			710.721i			1.18799i	0.804470	+	0.593994i	$0.202450\pi$
$71$			710.721i			1.18799i	−0.804470	+	0.593994i	$0.797550\pi$
$72$	192.522	+	97.9343i	0.315125	+	0.160301i
$73$		−	219.032i		−	0.351175i	−0.984464	−	0.175588i	$-0.943817\pi$
$73$		−	219.032i		−	0.351175i	0.984464	−	0.175588i	$-0.0561825\pi$
$74$	−549.892	+	317.480i	−0.863833	+	0.498734i
$75$	204.668	−	377.250i	0.315107	−	0.580814i
$76$	101.588	+	58.6521i	0.153329	+	0.0885245i
$77$	−73.7512	+	299.536i	−0.109152	+	0.443316i
$78$	−139.873	−	228.081i	−0.203044	−	0.331092i
$79$	56.3964	+	97.6814i	0.0803175	+	0.139114i	0.903386	−	0.428828i	$-0.141073\pi$
$79$	56.3964	+	97.6814i	0.0803175	+	0.139114i	−0.823069	+	0.567942i	$0.807740\pi$
$80$	−230.532			−0.322179
$81$	−429.277	−	589.204i	−0.588858	−	0.808237i
$82$			730.385i			0.983628i
$83$	−550.407	−	953.334i	−0.727892	−	1.26075i	−0.957772	−	0.287528i	$-0.907167\pi$
$83$	−550.407	−	953.334i	−0.727892	−	1.26075i	0.229880	−	0.973219i	$-0.426167\pi$
$84$	259.132	−	284.652i	0.336591	−	0.369739i
$85$	684.980	−	1186.42i	0.874077	−	1.51395i
$86$	−656.570	−	379.071i	−0.823253	−	0.475305i
$87$	−1000.31	−	542.693i	−1.23269	−	0.668768i
$88$	66.6258	+	115.399i	0.0807084	+	0.139791i
$89$	190.308			0.226658			0.113329	−	0.993557i	$-0.463849\pi$
$89$	190.308			0.226658			0.113329	+	0.993557i	$0.463849\pi$
$90$	693.479	+	352.766i	0.812212	+	0.413164i
$91$	−457.955	+	132.770i	−0.527546	+	0.152946i
$92$	331.554	−	191.423i	0.375727	−	0.216926i
$93$	28.1485	+	1061.50i	0.0313857	+	1.18357i
$94$	−445.678	−	257.313i	−0.489024	−	0.282338i
$95$	365.928	+	211.269i	0.395194	+	0.228166i
$96$	−4.40775	−	166.218i	−0.00468608	−	0.176715i
$97$	1281.74	−	740.015i	1.34166	−	0.774610i	0.354612	−	0.935014i	$-0.384613\pi$
$97$	1281.74	−	740.015i	1.34166	−	0.774610i	0.987052	+	0.160404i	$0.0512796\pi$
$98$	−366.928	−	579.621i	−0.378217	−	0.597454i
$99$	−23.8346	−	449.092i	−0.0241967	−	0.455914i
$100$	−330.393			−0.330393
$101$	421.052	+	729.283i	0.414814	+	0.718479i	0.995409	−	0.0957139i	$-0.0305134\pi$
$101$	421.052	+	729.283i	0.414814	+	0.718479i	−0.580595	+	0.814192i	$0.697180\pi$
$102$	868.530	+	471.201i	0.843111	+	0.457410i
$103$	38.9564	+	22.4915i	0.0372669	+	0.0215160i	0.518518	−	0.855067i	$-0.326484\pi$
$103$	38.9564	+	22.4915i	0.0372669	+	0.0215160i	−0.481251	+	0.876583i	$0.659817\pi$
$104$	−102.982	+	178.370i	−0.0970981	+	0.168179i
$105$	933.411	−	1025.33i	0.867539	−	0.952975i
$106$	610.363	+	1057.18i	0.559280	+	0.968701i
$107$			1317.86i			1.19067i	0.803476	+	0.595337i	$0.202981\pi$
$107$			1317.86i			1.19067i	−0.803476	+	0.595337i	$0.797019\pi$
$108$	−241.092	+	506.757i	−0.214806	+	0.451507i
$109$	1197.29			1.05210			0.526052	−	0.850452i	$-0.323672\pi$
$109$	1197.29			1.05210			0.526052	+	0.850452i	$0.323672\pi$
$110$	239.991	+	415.676i	0.208020	+	0.360301i
$111$	−862.420	−	1406.29i	−0.737453	−	1.20252i
$112$	−287.731	−	70.8445i	−0.242750	−	0.0597695i
$113$	−602.558	−	347.887i	−0.501627	−	0.289615i	0.227758	−	0.973718i	$-0.426860\pi$
$113$	−602.558	−	347.887i	−0.501627	−	0.289615i	−0.729385	+	0.684103i	$0.760194\pi$
$114$	−145.333	+	267.881i	−0.119400	+	0.220082i
$115$	1194.28	−	689.518i	0.968411	−	0.559112i
$116$			876.062i			0.701209i
$117$	582.732	−	378.980i	0.460458	−	0.299459i
$118$			431.007i			0.336250i
$119$	1219.53	−	1270.29i	0.939448	−	0.978549i
$120$	−15.8770	−	598.730i	−0.0120780	−	0.455469i
$121$	−526.781	+	912.412i	−0.395779	+	0.685509i
$122$	−60.5945	+	104.953i	−0.0449670	+	0.0778850i
$123$	−1896.93	+	50.3024i	−1.39057	+	0.0368749i
$124$	707.913	−	408.714i	0.512681	−	0.295997i
$125$	610.937			0.437151
$126$	757.133	+	653.404i	0.535324	+	0.461983i
$127$	−599.549			−0.418908			−0.209454	−	0.977818i	$-0.567169\pi$
$127$	−599.549			−0.418908			−0.209454	+	0.977818i	$0.567169\pi$
$128$	−110.851	+	64.0000i	−0.0765466	+	0.0441942i
$129$	939.290	−	1731.33i	0.641084	−	1.18166i
$130$	−370.947	+	642.500i	−0.250263	+	0.433469i
$131$	488.538	−	846.173i	0.325830	−	0.564355i	−0.655850	−	0.754891i	$-0.727690\pi$
$131$	488.538	−	846.173i	0.325830	−	0.564355i	0.981680	+	0.190537i	$0.0610229\pi$
$132$	−295.122	+	180.986i	−0.194599	+	0.119339i
$133$	391.796	+	376.141i	0.255436	+	0.245230i
$134$		−	1647.25i		−	1.06194i
$135$	−868.430	+	1825.37i	−0.553648	+	1.16373i
$136$		−	760.653i		−	0.479599i
$137$	662.403	−	382.438i	0.413087	−	0.238496i	−0.279028	−	0.960283i	$-0.590012\pi$
$137$	662.403	−	382.438i	0.413087	−	0.238496i	0.692115	+	0.721787i	$0.256679\pi$
$138$	519.991	+	847.917i	0.320758	+	0.523040i
$139$	−1583.66	−	914.327i	−0.966363	−	0.557930i	−0.0682372	−	0.997669i	$-0.521737\pi$
$139$	−1583.66	−	914.327i	−0.966363	−	0.557930i	−0.898125	+	0.439739i	$0.855071\pi$
$140$	−1036.43	−	255.187i	−0.625671	−	0.154052i
$141$	637.588	−	1175.22i	0.380813	−	0.701925i
$142$	710.721	+	1231.01i	0.420017	+	0.727491i
$143$	428.828			0.250772
$144$	431.393	−	22.8953i	0.249649	−	0.0132496i
$145$			3155.63i			1.80732i
$146$	−219.032	−	379.375i	−0.124159	−	0.215050i
$147$	1480.10	−	992.890i	0.830452	−	0.557090i
$148$	−634.961	+	1099.78i	−0.352658	+	0.610822i
$149$	1859.43	+	1073.54i	1.02235	+	0.590256i	0.914785	−	0.403941i	$-0.132360\pi$
$149$	1859.43	+	1073.54i	1.02235	+	0.590256i	0.107569	+	0.994198i	$0.465693\pi$
$150$	−22.7545	−	858.084i	−0.0123860	−	0.467082i
$151$	95.3699	+	165.186i	0.0513980	+	0.0890239i	0.890580	−	0.454827i	$-0.150299\pi$
$151$	95.3699	+	165.186i	0.0513980	+	0.0890239i	−0.839182	+	0.543851i	$0.816966\pi$
$152$	234.609			0.125193
$153$	−1163.97	+	2288.17i	−0.615041	+	1.20907i
$154$	171.795	+	592.563i	0.0898939	+	0.310065i
$155$	2549.95	−	1472.21i	1.32140	−	0.762910i
$156$	−470.348	−	255.176i	−0.241397	−	0.130964i
$157$	−1953.25	−	1127.71i	−0.992909	−	0.573256i	−0.0867663	−	0.996229i	$-0.527653\pi$
$157$	−1953.25	−	1127.71i	−0.992909	−	0.573256i	−0.906143	+	0.422973i	$0.860987\pi$
$158$	195.363	+	112.793i	0.0983685	+	0.0567931i
$159$	−2703.63	+	1658.02i	−1.34850	+	0.826979i
$160$	−399.294	+	230.532i	−0.197293	+	0.113907i
$161$	1702.50	−	493.586i	0.833388	−	0.241615i
$162$	−1332.73	−	591.255i	−0.646355	−	0.286749i
$163$	−230.129			−0.110584			−0.0552918	−	0.998470i	$-0.517609\pi$
$163$	−230.129			−0.110584			−0.0552918	+	0.998470i	$0.517609\pi$
$164$	730.385	+	1265.06i	0.347765	+	0.602347i
$165$	−1063.05	+	651.923i	−0.501566	+	0.307589i
$166$	−1906.67	−	1100.81i	−0.891482	−	0.514698i
$167$	510.342	−	883.938i	0.236476	−	0.409588i	−0.723225	−	0.690613i	$-0.757341\pi$
$167$	510.342	−	883.938i	0.236476	−	0.409588i	0.959701	+	0.281025i	$0.0906743\pi$
$168$	164.178	−	752.163i	0.0753967	−	0.345421i
$169$	−767.086	−	1328.63i	−0.349151	−	0.604748i
$170$		−	2739.92i		−	1.23613i
$171$	−705.741	−	359.003i	−0.315610	−	0.160548i
$172$	−1516.28			−0.672183
$173$	−43.9107	−	76.0555i	−0.0192975	−	0.0334242i	0.856215	−	0.516619i	$-0.172810\pi$
$173$	−43.9107	−	76.0555i	−0.0192975	−	0.0334242i	−0.875513	+	0.483195i	$0.839476\pi$
$174$	−2275.28	+	60.3353i	−0.991311	+	0.0262874i
$175$	−1485.38	−	365.727i	−0.641623	−	0.157979i
$176$	230.799	+	133.252i	0.0988472	+	0.0570694i
$177$	−1119.40	+	29.6839i	−0.475362	+	0.0126055i
$178$	329.623	−	190.308i	0.138799	−	0.0801359i
$179$		−	4089.74i		−	1.70772i	−0.520505	−	0.853858i	$-0.674256\pi$
$179$		−	4089.74i		−	1.70772i	0.520505	−	0.853858i	$-0.325744\pi$
$180$	1553.91	−	82.4703i	0.643452	−	0.0341499i
$181$			3954.26i			1.62385i	0.583758	+	0.811927i	$0.301582\pi$
$181$			3954.26i			1.62385i	−0.583758	+	0.811927i	$0.698418\pi$
$182$	−660.431	+	687.919i	−0.268980	+	0.280175i
$183$	−276.753	−	150.146i	−0.111793	−	0.0606507i
$184$	382.846	−	663.109i	0.153390	−	0.265679i
$185$	−2287.17	+	3961.50i	−0.908952	+	1.57435i
$186$	1110.25	+	1810.42i	0.437675	+	0.713689i
$187$	−1371.54	+	791.861i	−0.536349	+	0.309661i
$188$	−1029.25			−0.399286
$189$	−1644.85	+	2011.40i	−0.633045	+	0.774115i
$190$	845.075			0.322675
$191$	−1742.80	+	1006.21i	−0.660233	+	0.381186i	−0.792366	−	0.610046i	$-0.791151\pi$
$191$	−1742.80	+	1006.21i	−0.660233	+	0.381186i	0.132133	+	0.991232i	$0.457817\pi$
$192$	−173.853	−	283.491i	−0.0653477	−	0.106558i
$193$	−2380.13	+	4122.51i	−0.887697	+	1.53754i	−0.0451062	+	0.998982i	$0.514363\pi$
$193$	−2380.13	+	4122.51i	−0.887697	+	1.53754i	−0.842591	+	0.538554i	$0.818971\pi$
$194$	1480.03	−	2563.49i	0.547732	−	0.948699i
$195$	−1694.22	−	919.161i	−0.622184	−	0.337551i
$196$	−1215.16	−	637.005i	−0.442842	−	0.232145i
$197$		−	1773.70i		−	0.641476i	−0.947168	−	0.320738i	$-0.896069\pi$
$197$		−	1773.70i		−	0.641476i	0.947168	−	0.320738i	$-0.103931\pi$
$198$	−490.375	−	754.016i	−0.176007	−	0.270634i
$199$		−	1392.74i		−	0.496124i	−0.968744	−	0.248062i	$-0.920206\pi$
$199$		−	1392.74i		−	0.496124i	0.968744	−	0.248062i	$-0.0797936\pi$
$200$	−572.257	+	330.393i	−0.202323	+	0.116811i
$201$	4278.17	−	113.448i	1.50129	−	0.0398108i
$202$	1458.57	+	842.103i	0.508041	+	0.293318i
$203$	−969.753	+	3938.59i	−0.335287	+	1.36175i
$204$	1975.54	−	52.3870i	0.678017	−	0.0179795i
$205$	2630.89	+	4556.84i	0.896340	+	1.55251i
$206$	89.9659			0.0304283
$207$	−2166.37	+	1408.90i	−0.727405	+	0.473069i
$208$			411.927i			0.137317i
$209$	−244.234	−	423.026i	−0.0808327	−	0.140006i
$210$	591.382	−	2709.34i	0.194330	−	0.890297i
$211$	2211.89	−	3831.10i	0.721671	−	1.24997i	−0.238659	−	0.971103i	$-0.576708\pi$
$211$	2211.89	−	3831.10i	0.721671	−	1.24997i	0.960330	−	0.278867i	$-0.0899588\pi$
$212$	2114.36	+	1220.73i	0.684975	+	0.395471i
$213$	−3148.17	+	1930.64i	−1.01272	+	0.621058i
$214$	1317.86	+	2282.60i	0.420967	+	0.729136i
$215$	−5461.75			−1.73250
$216$	89.1733	+	1118.82i	0.0280902	+	0.352436i
$217$	3635.06	−	1053.87i	1.13716	−	0.329684i
$218$	2073.76	−	1197.29i	0.644280	−	0.371975i
$219$	970.214	−	594.991i	0.299365	−	0.183588i
$220$	831.352	+	479.981i	0.254772	+	0.147092i
$221$	−2119.96	−	1223.96i	−0.645267	−	0.372545i
$222$	−2900.05	−	1573.35i	−0.876750	−	0.475660i
$223$	4663.03	−	2692.20i	1.40027	−	0.808445i	0.405848	−	0.913940i	$-0.366976\pi$
$223$	4663.03	−	2692.20i	1.40027	−	0.808445i	0.994420	+	0.105495i	$0.0336428\pi$
$224$	−569.209	+	165.025i	−0.169785	+	0.0492240i
$225$	2227.02	−	118.194i	0.659857	−	0.0350205i
$226$	−1391.55			−0.409577
$227$	2529.56	+	4381.33i	0.739616	+	1.28105i	0.952668	+	0.304011i	$0.0983261\pi$
$227$	2529.56	+	4381.33i	0.739616	+	1.28105i	−0.213053	+	0.977041i	$0.568341\pi$
$228$	16.1577	+	609.317i	0.00469330	+	0.176987i
$229$	503.193	+	290.519i	0.145205	+	0.0838341i	0.570842	−	0.821060i	$-0.306617\pi$
$229$	503.193	+	290.519i	0.145205	+	0.0838341i	−0.425637	+	0.904894i	$0.639950\pi$
$230$	1379.04	−	2388.56i	0.395352	−	0.684770i
$231$	−1527.15	+	486.991i	−0.434975	+	0.138708i
$232$	876.062	+	1517.38i	0.247915	+	0.429401i
$233$			1823.11i			0.512600i	0.966597	+	0.256300i	$0.0825034\pi$
$233$			1823.11i			0.512600i	−0.966597	+	0.256300i	$0.917497\pi$
$234$	630.341	−	1239.14i	0.176097	−	0.346177i
$235$	−3707.43			−1.02913
$236$	431.007	+	746.527i	0.118882	+	0.205910i
$237$	−279.486	+	515.157i	−0.0766016	+	0.141194i
$238$	842.001	−	3419.74i	0.229323	−	0.931381i
$239$	−766.333	−	442.443i	−0.207406	−	0.119746i	0.392699	−	0.919667i	$-0.371541\pi$
$239$	−766.333	−	442.443i	−0.207406	−	0.119746i	−0.600105	+	0.799921i	$0.704875\pi$
$240$	−626.230	−	1021.15i	−0.168429	−	0.274647i
$241$	2183.16	−	1260.45i	0.583527	−	0.336899i	−0.179007	−	0.983848i	$-0.557288\pi$
$241$	2183.16	−	1260.45i	0.583527	−	0.336899i	0.762534	+	0.646948i	$0.223955\pi$
$242$			2107.12i			0.559715i
$243$	1443.80	−	3502.05i	0.381151	−	0.924513i
$244$			242.378i			0.0635929i
$245$	−4377.08	−	2294.53i	−1.14139	−	0.598336i
$246$	−3235.27	+	1984.05i	−0.838510	+	0.514222i
$247$	377.506	−	653.860i	0.0972476	−	0.168438i
$248$	817.427	−	1415.83i	0.209301	−	0.362520i
$249$	2727.68	−	5027.74i	0.694216	−	1.27960i
$250$	1058.17	−	610.937i	0.267699	−	0.154556i
$251$	6977.12			1.75455			0.877275	−	0.479989i	$-0.159359\pi$
$251$	6977.12			1.75455			0.877275	+	0.479989i	$0.159359\pi$
$252$	1964.80	+	374.596i	0.491153	+	0.0936402i
$253$	−1594.21			−0.396156
$254$	−1038.45	+	599.549i	−0.256528	+	0.148106i
$255$	7116.02	−	188.701i	1.74754	−	0.0463409i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	3215.08	−	5568.68i	0.780354	−	1.35161i	−0.151382	−	0.988475i	$-0.548372\pi$
$257$	3215.08	−	5568.68i	0.780354	−	1.35161i	0.931736	−	0.363137i	$-0.118294\pi$
$258$	−104.428	−	3938.03i	−0.0251992	−	0.950276i
$259$	−4072.05	+	4241.54i	−0.976931	+	1.01759i
$260$			1483.79i			0.353926i
$261$	−313.401	−	5905.11i	−0.0743259	−	1.40045i
$262$		−	1954.15i		−	0.460794i
$263$	3431.49	−	1981.17i	0.804543	−	0.464503i	−0.0405141	−	0.999179i	$-0.512900\pi$
$263$	3431.49	−	1981.17i	0.804543	−	0.464503i	0.845057	+	0.534676i	$0.179566\pi$
$264$	−330.181	+	608.599i	−0.0769744	+	0.141881i
$265$	7616.06	+	4397.14i	1.76548	+	1.01930i
$266$	1054.75	+	259.699i	0.243124	+	0.0598615i
$267$	516.962	+	842.978i	0.118493	+	0.193219i
$268$	−1647.25	−	2853.12i	−0.375454	−	0.650305i
$269$	−1169.23			−0.265016			−0.132508	−	0.991182i	$-0.542303\pi$
$269$	−1169.23			−0.265016			−0.132508	+	0.991182i	$0.542303\pi$
$270$	321.208	+	4030.07i	0.0724004	+	0.908378i
$271$		−	835.613i		−	0.187306i	−0.995605	−	0.0936529i	$-0.970146\pi$
$271$		−	835.613i		−	0.187306i	0.995605	−	0.0936529i	$-0.0298544\pi$
$272$	−760.653	−	1317.49i	−0.169564	−	0.293693i
$273$	−1832.12	−	1667.87i	−0.406172	−	0.369758i
$274$	764.877	−	1324.81i	0.168642	−	0.292096i
$275$	1191.47	+	687.896i	0.261267	+	0.150843i
$276$	1748.57	+	948.644i	0.381346	+	0.206890i
$277$	−3587.91	−	6214.45i	−0.778255	−	1.34798i	−0.932947	−	0.360015i	$-0.882772\pi$
$277$	−3587.91	−	6214.45i	−0.778255	−	1.34798i	0.154691	−	0.987963i	$-0.450562\pi$
$278$	−3657.31			−0.789032
$279$	−4625.48	+	3008.19i	−0.992546	+	0.645504i
$280$	−2050.33	+	594.429i	−0.437609	+	0.126871i
$281$	−5988.97	+	3457.73i	−1.27143	+	0.734061i	−0.975257	−	0.221073i	$-0.929044\pi$
$281$	−5988.97	+	3457.73i	−1.27143	+	0.734061i	−0.296174	+	0.955134i	$0.595711\pi$
$282$	−70.8856	−	2673.13i	−0.0149687	−	0.564477i
$283$	−6379.54	−	3683.23i	−1.34001	−	0.773658i	−0.353205	−	0.935546i	$-0.614908\pi$
$283$	−6379.54	−	3683.23i	−1.34001	−	0.773658i	−0.986809	+	0.161888i	$0.948242\pi$
$284$	2462.01	+	1421.44i	0.514414	+	0.296997i
$285$	58.2012	+	2194.80i	0.0120966	+	0.456171i
$286$	742.752	−	428.828i	0.153566	−	0.0886613i
$287$	1883.30	+	6495.96i	0.387345	+	1.33604i
$288$	724.299	−	471.049i	0.148194	−	0.0963778i
$289$	4127.51			0.840120
$290$	3155.63	+	5465.72i	0.638983	+	1.10675i
$291$	6759.73	+	3667.33i	1.36173	+	0.738772i
$292$	−758.750	−	438.065i	−0.152063	−	0.0877938i
$293$	2617.56	−	4533.74i	0.521909	−	0.903973i	−0.477766	−	0.878487i	$-0.658553\pi$
$293$	2617.56	−	4533.74i	0.521909	−	0.903973i	0.999675	−	0.0254862i	$-0.00811337\pi$
$294$	1570.72	−	3199.83i	0.311585	−	0.634756i
$295$	1552.52	+	2689.04i	0.306410	+	0.530718i
$296$			2539.84i			0.498734i
$297$	1924.53	−	1325.51i	0.376002	−	0.258970i
$298$	4294.18			0.834749
$299$	−1232.07	−	2134.00i	−0.238302	−	0.412751i
$300$	−897.495	−	1463.49i	−0.172723	−	0.281649i
$301$	−6816.90	−	1678.44i	−1.30538	−	0.321408i
$302$	330.371	+	190.740i	0.0629494	+	0.0363438i
$303$	−2086.63	+	3846.13i	−0.395622	+	0.729222i
$304$	406.354	−	234.609i	0.0766644	−	0.0442622i
$305$			873.062i			0.163906i
$306$	272.115	+	5127.19i	0.0508359	+	0.957849i
$307$			2174.14i			0.404184i	0.979366	+	0.202092i	$0.0647741\pi$
$307$			2174.14i			0.404184i	−0.979366	+	0.202092i	$0.935226\pi$
$308$	890.121	+	854.554i	0.164673	+	0.158093i
$309$	6.19605	+	233.656i	0.00114072	+	0.0430170i
$310$	2944.43	−	5099.90i	0.539459	−	0.934370i
$311$	−2631.54	+	4557.96i	−0.479810	+	0.831056i	−0.999732	−	0.0231582i	$-0.992628\pi$
$311$	−2631.54	+	4557.96i	−0.479810	+	0.831056i	0.519922	+	0.854214i	$0.325961\pi$
$312$	−1069.84	+	28.3699i	−0.194128	+	0.00514785i
$313$	1285.21	−	742.016i	0.232090	−	0.133997i	−0.379446	−	0.925214i	$-0.623885\pi$
$313$	1285.21	−	742.016i	0.232090	−	0.133997i	0.611536	+	0.791217i	$0.290552\pi$
$314$	−4510.85			−0.810707
$315$	7077.33	+	1349.32i	1.26591	+	0.241351i
$316$	451.171			0.0803175
$317$	−2399.03	+	1385.08i	−0.425057	+	0.245407i	−0.697239	−	0.716839i	$-0.745588\pi$
$317$	−2399.03	+	1385.08i	−0.425057	+	0.245407i	0.272181	+	0.962246i	$0.412255\pi$
$318$	−3024.81	+	5575.41i	−0.533405	+	0.983187i
$319$	1824.01	−	3159.28i	0.320141	−	0.554501i
$320$	−461.065	+	798.587i	−0.0805447	+	0.139507i
$321$	−5837.51	+	3579.89i	−1.01501	+	0.622462i
$322$	2455.22	−	2557.41i	0.424920	−	0.442605i
$323$			2788.37i			0.480337i
$324$	−2899.62	+	308.652i	−0.497191	+	0.0529239i
$325$			2126.53i			0.362949i
$326$	−398.596	+	230.129i	−0.0677183	+	0.0390972i
$327$	3252.37	+	5303.44i	0.550020	+	0.896884i
$328$	2530.13	+	1460.77i	0.425923	+	0.245907i
$329$	−4627.30	−	1139.32i	−0.775414	−	0.190921i
$330$	−1189.33	+	2192.21i	−0.198396	+	0.365689i
$331$	−3911.89	−	6775.59i	−0.649598	−	1.12514i	−0.983219	−	0.182429i	$-0.941604\pi$
$331$	−3911.89	−	6775.59i	−0.649598	−	1.12514i	0.333621	−	0.942707i	$-0.391729\pi$
$332$	−4403.26			−0.727892
$333$	3886.53	−	7640.26i	0.639580	−	1.25731i
$334$		−	2041.37i		−	0.334427i
$335$	−5933.49	−	10277.1i	−0.967706	−	1.67612i
$336$	−467.798	−	1466.96i	−0.0759537	−	0.238183i
$337$	−4474.05	+	7749.29i	−0.723197	+	1.25261i	0.236515	+	0.971628i	$0.423995\pi$
$337$	−4474.05	+	7749.29i	−0.723197	+	1.25261i	−0.959712	+	0.280986i	$0.909339\pi$
$338$	−2657.26	−	1534.17i	−0.427621	−	0.246887i
$339$	−95.8374	−	3614.08i	−0.0153545	−	0.579026i
$340$	−2739.92	−	4745.68i	−0.437039	−	0.756973i
$341$	−3403.86			−0.540555
$342$	−1581.38	+	83.9286i	−0.250033	+	0.0132700i
$343$	−4757.97	−	4208.96i	−0.748998	−	0.662572i
$344$	−2626.28	+	1516.28i	−0.411626	+	0.237653i
$345$	6298.46	+	3417.08i	0.982892	+	0.533245i
$346$	−152.111	−	87.8213i	−0.0236345	−	0.0136454i
$347$	−5855.59	−	3380.72i	−0.905891	−	0.523017i	−0.0267844	−	0.999641i	$-0.508527\pi$
$347$	−5855.59	−	3380.72i	−0.905891	−	0.523017i	−0.879107	+	0.476625i	$0.841860\pi$
$348$	−3880.56	+	2379.78i	−0.597758	+	0.366579i
$349$	−6145.39	+	3548.05i	−0.942566	+	0.544191i	−0.890764	−	0.454467i	$-0.849830\pi$
$349$	−6145.39	+	3548.05i	−0.942566	+	0.544191i	−0.0518021	+	0.998657i	$0.516496\pi$
$350$	−2938.48	+	851.920i	−0.448766	+	0.130106i
$351$	3261.67	+	1551.76i	0.495998	+	0.235973i
$352$	533.007			0.0807084
$353$	−749.661	−	1298.45i	−0.113032	−	0.195778i	0.803959	−	0.594685i	$-0.202723\pi$
$353$	−749.661	−	1298.45i	−0.113032	−	0.195778i	−0.916992	+	0.398907i	$0.869390\pi$
$354$	−1909.17	+	1170.81i	−0.286642	+	0.175785i
$355$	8868.33	+	5120.13i	1.32586	+	0.765488i
$356$	380.616	−	659.246i	0.0566646	−	0.0981460i
$357$	8939.61	+	1951.29i	1.32531	+	0.289281i
$358$	−4089.74	−	7083.63i	−0.603769	−	1.04576i
$359$		−	6836.28i		−	1.00503i	−0.864569	−	0.502514i	$-0.832408\pi$
$359$		−	6836.28i		−	1.00503i	0.864569	−	0.502514i	$-0.167592\pi$
$360$	2608.97	−	1696.75i	0.381958	−	0.248407i
$361$	5998.98			0.874615
$362$	3954.26	+	6848.98i	0.574119	+	0.994404i
$363$	−5472.55	+	145.120i	−0.791279	+	0.0209830i
$364$	−455.981	+	1851.94i	−0.0656591	+	0.266671i
$365$	−2733.07	−	1577.94i	−0.391933	−	0.226282i
$366$	−629.495	+	16.6928i	−0.0899023	+	0.00238401i
$367$	5437.06	−	3139.09i	0.773331	−	0.446483i	−0.0607308	−	0.998154i	$-0.519343\pi$
$367$	5437.06	−	3139.09i	0.773331	−	0.446483i	0.834061	+	0.551672i	$0.186010\pi$
$368$		−	1531.38i		−	0.216926i
$369$	−5375.73	−	8265.89i	−0.758399	−	1.16614i
$370$			9148.68i			1.28545i
$371$	8154.45	+	7828.61i	1.14113	+	1.09553i
$372$	3733.43	+	2025.48i	0.520347	+	0.282302i
$373$	3509.77	−	6079.10i	0.487209	−	0.843871i	−0.512683	−	0.858578i	$-0.671348\pi$
$373$	3509.77	−	6079.10i	0.487209	−	0.843871i	0.999892	+	0.0147073i	$0.00468165\pi$
$374$	−1583.72	+	2743.09i	−0.218963	+	0.379256i
$375$	1659.58	+	2706.18i	0.228534	+	0.372657i
$376$	−1782.71	+	1029.25i	−0.244512	+	0.141169i
$377$	5638.65			0.770306
$378$	−837.569	+	5128.70i	−0.113968	+	0.697862i
$379$	−6751.65			−0.915064			−0.457532	−	0.889193i	$-0.651266\pi$
$379$	−6751.65			−0.915064			−0.457532	+	0.889193i	$0.651266\pi$
$380$	1463.71	−	845.075i	0.197597	−	0.114083i
$381$	−1628.64	−	2655.73i	−0.218997	−	0.357105i
$382$	−2012.41	+	3485.60i	−0.269539	+	0.466855i
$383$	−1814.70	+	3143.15i	−0.242107	+	0.419341i	−0.961314	−	0.275454i	$-0.911172\pi$
$383$	−1814.70	+	3143.15i	−0.242107	+	0.419341i	0.719207	+	0.694795i	$0.244505\pi$
$384$	−584.613	−	317.168i	−0.0776912	−	0.0421495i
$385$	3206.28	+	3078.16i	0.424434	+	0.407474i
$386$			9520.52i			1.25539i
$387$	10220.5	−	542.433i	1.34248	−	0.0712492i
$388$		−	5920.12i		−	0.774610i
$389$	−7221.16	+	4169.14i	−0.941201	+	0.543403i	−0.890337	−	0.455303i	$-0.849531\pi$
$389$	−7221.16	+	4169.14i	−0.941201	+	0.543403i	−0.0508644	+	0.998706i	$0.516198\pi$
$390$	−3853.64	+	102.190i	−0.500351	+	0.0132682i
$391$	7881.18	+	4550.20i	1.01936	+	0.588526i
$392$	−2741.72	+	111.833i	−0.353260	+	0.0144092i
$393$	5075.25	−	134.585i	0.651432	−	0.0172745i
$394$	−1773.70	−	3072.14i	−0.226796	−	0.392822i
$395$	1625.15			0.207013
$396$	−1603.37	−	815.619i	−0.203466	−	0.103501i
$397$		−	1836.42i		−	0.232160i	−0.993240	−	0.116080i	$-0.962967\pi$
$397$		−	1836.42i		−	0.232160i	0.993240	−	0.116080i	$-0.0370329\pi$
$398$	−1392.74	−	2412.29i	−0.175406	−	0.303813i
$399$	−601.839	+	2757.25i	−0.0755128	+	0.345953i
$400$	−660.785	+	1144.51i	−0.0825982	+	0.143064i
$401$	−5736.27	−	3311.84i	−0.714354	−	0.412432i	0.0983173	−	0.995155i	$-0.468654\pi$
$401$	−5736.27	−	3311.84i	−0.714354	−	0.412432i	−0.812671	+	0.582723i	$0.801987\pi$
$402$	7296.56	−	4474.67i	0.905272	−	0.555164i
$403$	−2630.63	−	4556.39i	−0.325164	−	0.563200i
$404$	3368.41			0.414814
$405$	−10444.6	+	1111.78i	−1.28148	+	0.136407i
$406$	2258.93	+	7791.60i	0.276130	+	0.952440i
$407$	4579.63	−	2644.05i	0.557749	−	0.322016i
$408$	3369.35	−	2066.28i	0.408842	−	0.250725i
$409$	−12384.8	−	7150.35i	−1.49728	−	0.864455i	−0.497285	−	0.867587i	$-0.665670\pi$
$409$	−12384.8	−	7150.35i	−1.49728	−	0.864455i	−0.999995	+	0.00313203i	$0.999003\pi$
$410$	9113.69	+	5261.79i	1.09779	+	0.633808i
$411$	3493.41	+	1895.27i	0.419264	+	0.227462i
$412$	155.826	−	89.9659i	0.0186334	−	0.0107580i
$413$	1111.36	+	3833.33i	0.132412	+	0.456722i
$414$	−2343.36	+	4606.65i	−0.278188	+	0.546871i
$415$	−15860.8			−1.87609
$416$	411.927	+	713.479i	0.0485490	+	0.0840894i
$417$	−251.883	−	9498.63i	−0.0295797	−	1.11547i
$418$	−846.052	−	488.468i	−0.0989994	−	0.0571573i
$419$	1312.06	−	2272.56i	0.152980	−	0.264968i	−0.779342	−	0.626599i	$-0.784446\pi$
$419$	1312.06	−	2272.56i	0.152980	−	0.264968i	0.932322	+	0.361630i	$0.117780\pi$
$420$	−1685.04	−	5284.10i	−0.195765	−	0.613899i
$421$	5563.34	+	9635.99i	0.644040	+	1.11551i	0.984522	+	0.175258i	$0.0560761\pi$
$421$	5563.34	+	9635.99i	0.644040	+	1.11551i	−0.340483	+	0.940251i	$0.610591\pi$
$422$		−	8847.54i		−	1.02060i
$423$	6937.68	−	368.203i	0.797450	−	0.0423230i
$424$	4882.90			0.559280
$425$	−3926.78	−	6801.39i	−0.448181	−	0.776272i
$426$	−3522.16	+	6492.14i	−0.400585	+	0.738369i
$427$	−268.299	+	1089.68i	−0.0304073	+	0.123497i
$428$	4565.19	+	2635.71i	0.515577	+	0.297668i
$429$	1164.89	+	1899.51i	0.131099	+	0.213775i
$430$	−9460.03	+	5461.75i	−1.06094	+	0.612533i
$431$		−	6147.08i		−	0.686994i	−0.939154	−	0.343497i	$-0.888388\pi$
$431$		−	6147.08i		−	0.686994i	0.939154	−	0.343497i	$-0.111612\pi$
$432$	1273.27	+	1848.68i	0.141806	+	0.205891i
$433$		−	9440.04i		−	1.04771i	−0.851807	−	0.523856i	$-0.824493\pi$
$433$		−	9440.04i		−	1.04771i	0.851807	−	0.523856i	$-0.175507\pi$
$434$	5242.23	−	5460.41i	0.579804	−	0.603936i
$435$	−13978.0	+	8572.12i	−1.54068	+	0.944832i
$436$	2394.58	−	4147.53i	0.263026	−	0.455574i
$437$	−1403.42	+	2430.80i	−0.153626	+	0.266089i
$438$	1085.47	−	2000.77i	0.118415	−	0.218266i
$439$	−5497.50	+	3173.98i	−0.597680	+	0.345071i	−0.768128	−	0.640296i	$-0.778812\pi$
$439$	−5497.50	+	3173.98i	−0.597680	+	0.345071i	0.170448	+	0.985367i	$0.445478\pi$
$440$	1919.93			0.208020
$441$	8418.67	+	3859.03i	0.909045	+	0.416697i
$442$	−4895.84			−0.526858
$443$	5493.00	−	3171.39i	0.589121	−	0.340129i	−0.175629	−	0.984456i	$-0.556196\pi$
$443$	5493.00	−	3171.39i	0.589121	−	0.340129i	0.764750	+	0.644327i	$0.222863\pi$
$444$	−6596.39	+	174.922i	−0.705069	+	0.0186969i
$445$	1371.00	−	2374.65i	0.146049	−	0.252964i
$446$	5384.41	−	9326.07i	0.571657	−	0.990139i
$447$	295.745	+	11152.7i	0.0312936	+	1.18010i
$448$	−820.874	+	855.040i	−0.0865685	+	0.0901715i
$449$			7435.21i			0.781491i	0.920499	+	0.390745i	$0.127783\pi$
$449$			7435.21i			0.781491i	−0.920499	+	0.390745i	$0.872217\pi$
$450$	3739.11	−	2431.73i	0.391696	−	0.254740i
$451$		−	6082.81i		−	0.635096i
$452$	−2410.23	+	1391.55i	−0.250814	+	0.144807i
$453$	−472.629	+	871.164i	−0.0490200	+	0.0903551i
$454$	8762.65	+	5059.12i	0.905841	+	0.522987i
$455$	−1642.47	+	6670.81i	−0.169232	+	0.687324i
$456$	637.303	+	1039.21i	0.0654483	+	0.106722i
$457$	6970.68	+	12073.6i	0.713512	+	1.23584i	0.963531	+	0.267597i	$0.0862297\pi$
$457$	6970.68	+	12073.6i	0.713512	+	1.23584i	−0.250019	+	0.968241i	$0.580437\pi$
$458$	1162.07			0.118559
$459$	−13297.4	+	1059.84i	−1.35222	+	0.107776i
$460$		−	5516.15i		−	0.559112i
$461$	−5890.29	−	10202.3i	−0.595094	−	1.03073i	−0.993534	−	0.113539i	$-0.963781\pi$
$461$	−5890.29	−	10202.3i	−0.595094	−	1.03073i	0.398440	−	0.917195i	$-0.369552\pi$
$462$	−2158.11	+	2370.64i	−0.217326	+	0.238728i
$463$	−2094.96	+	3628.57i	−0.210283	+	0.364220i	−0.951803	−	0.306710i	$-0.900772\pi$
$463$	−2094.96	+	3628.57i	−0.210283	+	0.364220i	0.741520	+	0.670931i	$0.234105\pi$
$464$	3034.77	+	1752.12i	0.303633	+	0.175302i
$465$	13448.1	+	7295.92i	1.34116	+	0.727614i
$466$	1823.11	+	3157.71i	0.181231	+	0.313902i
$467$	7787.83			0.771686			0.385843	−	0.922564i	$-0.373911\pi$
$467$	7787.83			0.771686			0.385843	+	0.922564i	$0.373911\pi$
$468$	−147.362	−	2776.60i	−0.0145552	−	0.274249i
$469$	−4247.44	−	14650.4i	−0.418185	−	1.44242i
$470$	−6421.45	+	3707.43i	−0.630212	+	0.363853i
$471$	−310.667	−	11715.4i	−0.0303923	−	1.14611i
$472$	1493.05	+	862.015i	0.145600	+	0.0840624i
$473$	5468.06	+	3156.99i	0.531547	+	0.306889i
$474$	31.0726	+	1171.76i	0.00301100	+	0.113546i
$475$	2097.75	−	1211.14i	0.202635	−	0.116991i
$476$	−1961.35	−	6765.16i	−0.188862	−	0.651430i
$477$	−14688.6	−	7471.93i	−1.40994	−	0.717225i
$478$	−1769.77			−0.169346
$479$	−3301.94	−	5719.13i	−0.314968	−	0.545540i	0.664463	−	0.747321i	$-0.268660\pi$
$479$	−3301.94	−	5719.13i	−0.314968	−	0.545540i	−0.979431	+	0.201781i	$0.935327\pi$
$480$	−2105.82	−	1142.46i	−0.200243	−	0.108637i
$481$	7078.61	+	4086.84i	0.671012	+	0.387409i
$482$	2520.90	−	4366.33i	0.238224	−	0.412616i
$483$	6811.11	+	6200.48i	0.641648	+	0.584124i
$484$	2107.12	+	3649.65i	0.197889	+	0.342754i
$485$		−	21324.7i		−	1.99650i
$486$	−1001.32	−	7509.53i	−0.0934584	−	0.700903i
$487$	17011.7			1.58290			0.791450	−	0.611234i	$-0.209326\pi$
$487$	17011.7			1.58290			0.791450	+	0.611234i	$0.209326\pi$
$488$	242.378	+	419.811i	0.0224835	+	0.0389425i
$489$	−625.135	−	1019.37i	−0.0578110	−	0.0942688i
$490$	−9875.86	+	402.830i	−0.910502	+	0.0371388i
$491$	553.160	+	319.367i	0.0508427	+	0.0293540i	0.525206	−	0.850975i	$-0.323988\pi$
$491$	553.160	+	319.367i	0.0508427	+	0.0293540i	−0.474363	+	0.880329i	$0.657322\pi$
$492$	−3619.60	+	6671.76i	−0.331676	+	0.611354i
$493$	−18034.4	+	10412.2i	−1.64752	+	0.951198i
$494$		−	1510.03i		−	0.137529i
$495$	−5775.45	−	2937.91i	−0.524418	−	0.266766i
$496$		−	3269.71i		−	0.295997i
$497$	9495.24	+	9115.83i	0.856981	+	0.822738i
$498$	−303.257	−	11436.0i	−0.0272877	−	1.02903i
$499$	−4567.63	+	7911.36i	−0.409769	+	0.709742i	−0.994864	−	0.101224i	$-0.967724\pi$
$499$	−4567.63	+	7911.36i	−0.409769	+	0.709742i	0.585094	+	0.810965i	$0.301058\pi$
$500$	1221.87	−	2116.35i	0.109288	−	0.189292i
$501$	5301.76	−	140.591i	0.472785	−	0.0125372i
$502$	12084.7	−	6977.12i	1.07444	−	0.620327i
$503$	17232.9			1.52759			0.763795	−	0.645459i	$-0.223334\pi$
$503$	17232.9			1.52759			0.763795	+	0.645459i	$0.223334\pi$
$504$	3777.73	−	1315.98i	0.333876	−	0.116306i
$505$	12133.2			1.06915
$506$	−2761.26	+	1594.21i	−0.242595	+	0.140062i
$507$	3801.48	−	7007.00i	0.332998	−	0.613791i
$508$	−1199.10	+	2076.90i	−0.104727	+	0.181393i
$509$	−8411.32	+	14568.8i	−0.732466	+	1.26867i	0.223360	+	0.974736i	$0.428297\pi$
$509$	−8411.32	+	14568.8i	−0.732466	+	1.26867i	−0.955826	+	0.293933i	$0.905036\pi$
$510$	12136.6	−	7442.86i	1.05376	−	0.646227i
$511$	−2926.27	−	2809.34i	−0.253328	−	0.243206i
$512$			512.000i			0.0441942i
$513$	−326.888	−	4101.33i	−0.0281334	−	0.352979i
$514$		−	12860.3i		−	1.10359i
$515$	561.294	−	324.063i	0.0480264	−	0.0277280i
$516$	−4118.91	−	6716.45i	−0.351405	−	0.573014i
$517$	3711.71	+	2142.96i	0.315746	+	0.182296i
$518$	−2811.47	+	11418.6i	−0.238473	+	0.968542i
$519$	217.610	−	401.105i	0.0184047	−	0.0339240i
$520$	1483.79	+	2570.00i	0.125132	+	0.216734i
$521$	−9552.67			−0.803282			−0.401641	−	0.915797i	$-0.631560\pi$
$521$	−9552.67			−0.803282			−0.401641	+	0.915797i	$0.631560\pi$
$522$	−6447.93	−	9914.54i	−0.540648	−	0.831317i
$523$			15218.3i			1.27237i	0.771535	+	0.636187i	$0.219489\pi$
$523$			15218.3i			1.27237i	−0.771535	+	0.636187i	$0.780511\pi$
$524$	−1954.15	−	3384.69i	−0.162915	−	0.282177i
$525$	−2414.95	−	7573.03i	−0.200756	−	0.629551i
$526$	3962.35	−	6862.98i	0.328453	−	0.568898i
$527$	16827.4	+	9715.29i	1.39091	+	0.803045i
$528$	36.7087	+	1384.31i	0.00302565	+	0.114099i
$529$	−1503.15	−	2603.54i	−0.123544	−	0.213984i
$530$	17588.5			1.44150
$531$	−3172.27	−	4877.79i	−0.259256	−	0.398640i
$532$	2086.58	−	604.940i	0.170047	−	0.0492998i
$533$	8142.41	−	4701.02i	0.661702	−	0.382034i
$534$	1738.38	+	943.119i	0.140875	+	0.0764284i
$535$	16444.1	+	9494.02i	1.32886	+	0.767219i
$536$	−5706.23	−	3294.49i	−0.459835	−	0.265486i
$537$	18115.7	−	11109.6i	1.45577	−	0.892763i
$538$	−2025.17	+	1169.23i	−0.162288	+	0.0936972i
$539$	3055.86	+	4827.21i	0.244202	+	0.385757i
$540$	4586.42	+	6659.07i	0.365496	+	0.530668i
$541$	13949.6			1.10858			0.554290	−	0.832323i	$-0.312990\pi$
$541$	13949.6			1.10858			0.554290	+	0.832323i	$0.312990\pi$
$542$	−835.613	−	1447.32i	−0.0662226	−	0.114701i
$543$	−17515.6	+	10741.6i	−1.38428	+	0.848921i
$544$	−2634.98	−	1521.31i	−0.207672	−	0.119900i
$545$	8625.42	−	14939.7i	0.677931	−	1.17421i
$546$	−4841.20	−	1056.71i	−0.379458	−	0.0828262i
$547$	−208.537	−	361.196i	−0.0163005	−	0.0282334i	0.857760	−	0.514050i	$-0.171856\pi$
$547$	−208.537	−	361.196i	−0.0163005	−	0.0282334i	−0.874061	+	0.485817i	$0.838522\pi$
$548$		−	3059.51i		−	0.238496i
$549$	−86.7080	−	1633.75i	−0.00674063	−	0.127007i
$550$	2751.59			0.213324
$551$	−3211.43	−	5562.36i	−0.248297	−	0.430063i
$552$	3977.25	−	105.468i	0.306672	−	0.00813228i
$553$	2028.37	+	499.422i	0.155977	+	0.0384043i
$554$	−12428.9	−	7175.82i	−0.953164	−	0.550310i
$555$	−23760.6	+	630.079i	−1.81727	+	0.0481899i
$556$	−6334.65	+	3657.31i	−0.483181	+	0.278965i
$557$			21202.7i			1.61290i	0.591301	+	0.806451i	$0.298615\pi$
$557$			21202.7i			1.61290i	−0.591301	+	0.806451i	$0.701385\pi$
$558$	−5003.38	+	9835.82i	−0.379588	+	0.746207i
$559$			9759.35i			0.738419i
$560$	−2956.84	+	3079.91i	−0.223124	+	0.232411i
$561$	−7233.32	−	3924.27i	−0.544369	−	0.295334i
$562$	−6915.47	+	11977.9i	−0.519059	+	0.899037i
$563$	−6082.19	+	10534.7i	−0.455299	+	0.788602i	−0.998705	−	0.0508682i	$-0.983801\pi$
$563$	−6082.19	+	10534.7i	−0.455299	+	0.788602i	0.543406	+	0.839470i	$0.317134\pi$
$564$	−2795.91	−	4559.11i	−0.208739	−	0.340378i
$565$	−8681.82	+	5012.45i	−0.646454	+	0.373231i
$566$	−14732.9			−1.09412
$567$	−13377.8	−	1822.09i	−0.990852	−	0.134957i
$568$	5685.77			0.420017
$569$	1944.63	−	1122.73i	0.143275	−	0.0827196i	−0.426649	−	0.904417i	$-0.640306\pi$
$569$	1944.63	−	1122.73i	0.143275	−	0.0827196i	0.569924	+	0.821698i	$0.306973\pi$
$570$	2295.61	+	3743.30i	0.168688	+	0.275070i
$571$	−6429.34	+	11135.9i	−0.471208	+	0.816155i	−0.999458	−	0.0329335i	$-0.989515\pi$
$571$	−6429.34	+	11135.9i	−0.471208	+	0.816155i	0.528250	+	0.849089i	$0.322848\pi$
$572$	857.656	−	1485.50i	0.0626930	−	0.108588i
$573$	−9191.26	−	4986.50i	−0.670106	−	0.363550i
$574$	9757.94	+	9368.03i	0.709562	+	0.681209i
$575$		−	7905.59i		−	0.573367i
$576$	783.474	−	1540.18i	0.0566749	−	0.111413i
$577$			15762.1i			1.13723i	0.822603	+	0.568617i	$0.192521\pi$
$577$			15762.1i			1.13723i	−0.822603	+	0.568617i	$0.807479\pi$
$578$	7149.05	−	4127.51i	0.514466	−	0.297027i
$579$	−24726.3	+	655.688i	−1.77477	+	0.0470630i
$580$	10931.4	+	6311.27i	0.782591	+	0.451829i
$581$	−19796.2	−	4874.17i	−1.41357	−	0.348046i
$582$	15375.5	−	407.725i	1.09508	−	0.0290391i
$583$	−5083.24	−	8804.43i	−0.361109	−	0.625459i
$584$	−1752.26			−0.124159
$585$	−530.809	−	10001.5i	−0.0375150	−	0.706857i
$586$		−	10470.2i		−	0.738091i
$587$	4505.49	+	7803.73i	0.316800	+	0.548713i	0.979818	−	0.199890i	$-0.0640584\pi$
$587$	4505.49	+	7803.73i	0.316800	+	0.548713i	−0.663019	+	0.748603i	$0.730725\pi$
$588$	−479.274	−	7112.99i	−0.0336138	−	0.498869i
$589$	−2996.49	+	5190.07i	−0.209624	+	0.363079i
$590$	5378.08	+	3105.04i	0.375275	+	0.216665i
$591$	7856.68	−	4818.17i	0.546837	−	0.335352i
$592$	2539.84	+	4399.14i	0.176329	+	0.305411i
$593$	307.650			0.0213047			0.0106523	−	0.999943i	$-0.496609\pi$
$593$	307.650			0.0213047			0.0106523	+	0.999943i	$0.496609\pi$
$594$	2007.87	−	4220.39i	0.138693	−	0.291523i
$595$	−7064.91	−	24368.6i	−0.486778	−	1.67901i
$596$	7437.74	−	4294.18i	0.511177	−	0.295128i
$597$	6169.20	−	3783.31i	0.422929	−	0.259364i
$598$	−4268.01	−	2464.14i	−0.291859	−	0.168505i
$599$	7087.63	+	4092.04i	0.483460	+	0.279126i	0.721857	−	0.692042i	$-0.243289\pi$
$599$	7087.63	+	4092.04i	0.483460	+	0.279126i	−0.238397	+	0.971168i	$0.576622\pi$
$600$	−3018.00	−	1637.34i	−0.205349	−	0.111407i
$601$	1353.50	−	781.442i	0.0918640	−	0.0530377i	−0.453364	−	0.891325i	$-0.649776\pi$
$601$	1353.50	−	781.442i	0.0918640	−	0.0530377i	0.545228	+	0.838288i	$0.316443\pi$
$602$	−13485.7	+	3909.75i	−0.913014	+	0.264700i
$603$	12124.0	+	18642.2i	0.818782	+	1.25899i
$604$	762.959			0.0513980
$605$	7590.00	+	13146.3i	0.510046	+	0.883425i
$606$	231.986	+	8748.32i	0.0155508	+	0.586429i
$607$	9228.15	+	5327.88i	0.617066	+	0.356263i	0.775726	−	0.631070i	$-0.217384\pi$
$607$	9228.15	+	5327.88i	0.617066	+	0.356263i	−0.158660	+	0.987333i	$0.550717\pi$
$608$	469.217	−	812.708i	0.0312981	−	0.0542099i
$609$	−20080.5	+	6403.43i	−1.33613	+	0.426076i
$610$	873.062	+	1512.19i	0.0579496	+	0.100372i
$611$			6624.63i			0.438632i
$612$	5598.51	+	8608.44i	0.369781	+	0.568587i
$613$	−1173.34			−0.0773093			−0.0386547	−	0.999253i	$-0.512307\pi$
$613$	−1173.34			−0.0773093			−0.0386547	+	0.999253i	$0.512307\pi$
$614$	2174.14	+	3765.72i	0.142901	+	0.247511i
$615$	−13038.1	+	24032.1i	−0.854870	+	1.57572i
$616$	2396.29	+	590.009i	0.156736	+	0.0385912i
$617$	−5900.92	−	3406.90i	−0.385028	−	0.222296i	0.294976	−	0.955505i	$-0.404688\pi$
$617$	−5900.92	−	3406.90i	−0.385028	−	0.222296i	−0.680003	+	0.733209i	$0.738022\pi$
$618$	244.388	+	398.508i	0.0159073	+	0.0259391i
$619$	−13281.1	+	7667.82i	−0.862376	+	0.497893i	−0.864807	−	0.502104i	$-0.832559\pi$
$619$	−13281.1	+	7667.82i	−0.862376	+	0.497893i	0.00243150	+	0.999997i	$0.499226\pi$
$620$		−	11777.7i		−	0.762910i
$621$	−12125.6	−	5768.82i	−0.783549	−	0.372777i
$622$			10526.2i			0.678554i
$623$	2440.92	−	2542.51i	0.156972	−	0.163505i
$624$	−1824.65	+	1118.98i	−0.117059	+	0.0717870i
$625$	9563.66	−	16564.7i	0.612074	−	1.06014i
$626$	1484.03	−	2570.42i	0.0947505	−	0.164113i
$627$	1210.36	−	2230.98i	0.0770929	−	0.142100i
$628$	−7813.02	+	4510.85i	−0.496454	+	0.286628i
$629$	−30186.5			−1.91354
$630$	13607.6	−	4740.24i	0.860540	−	0.299771i
$631$	28477.8			1.79665			0.898324	−	0.439334i	$-0.144785\pi$
$631$	28477.8			1.79665			0.898324	+	0.439334i	$0.144785\pi$
$632$	781.451	−	451.171i	0.0491842	−	0.0283965i
$633$	22978.5	−	609.340i	1.44283	−	0.0382608i
$634$	−2770.17	+	4798.07i	−0.173529	+	0.300561i
$635$	−4319.23	+	7481.12i	−0.269927	+	0.467527i
$636$	336.291	+	12681.7i	0.0209667	+	0.790663i
$637$	−4100.00	+	7821.20i	−0.255020	+	0.486479i
$638$		−	7296.04i		−	0.452748i
$639$	−17103.7	−	8700.50i	−1.05886	−	0.538633i
$640$			1844.26i			0.113907i
$641$	−4886.19	+	2821.04i	−0.301081	+	0.173829i	−0.642928	−	0.765926i	$-0.722281\pi$
$641$	−4886.19	+	2821.04i	−0.301081	+	0.173829i	0.341847	+	0.939756i	$0.388947\pi$
$642$	−6530.97	+	12038.1i	−0.401490	+	0.740039i
$643$	−9933.74	−	5735.25i	−0.609251	−	0.351751i	0.163421	−	0.986556i	$-0.447747\pi$
$643$	−9933.74	−	5735.25i	−0.609251	−	0.351751i	−0.772672	+	0.634805i	$0.781080\pi$
$644$	1695.16	−	6884.79i	0.103725	−	0.421271i
$645$	−14836.6	−	24193.1i	−0.905721	−	1.47690i
$646$	2788.37	+	4829.60i	0.169825	+	0.294145i
$647$	16234.3			0.986456			0.493228	−	0.869900i	$-0.335817\pi$
$647$	16234.3			0.986456			0.493228	+	0.869900i	$0.335817\pi$
$648$	−4713.64	+	3434.22i	−0.285755	+	0.208193i
$649$		−	3589.53i		−	0.217105i
$650$	2126.53	+	3683.25i	0.128322	+	0.222260i
$651$	14542.6	+	13238.9i	0.875531	+	0.797038i
$652$	−460.258	+	797.191i	−0.0276459	+	0.0478841i
$653$	4011.56	+	2316.08i	0.240405	+	0.138798i	0.615363	−	0.788244i	$-0.289009\pi$
$653$	4011.56	+	2316.08i	0.240405	+	0.138798i	−0.374958	+	0.927042i	$0.622343\pi$
$654$	10936.7	+	5933.46i	0.653914	+	0.354765i
$655$	−7038.99	−	12191.9i	−0.419902	−	0.727292i
$656$	5843.08			0.347765
$657$	5271.08	+	2681.35i	0.313005	+	0.159223i
$658$	−9154.04	+	2653.93i	−0.542343	+	0.157236i
$659$	25775.1	−	14881.3i	1.52361	−	0.879655i	0.523997	−	0.851720i	$-0.324440\pi$
$659$	25775.1	−	14881.3i	1.52361	−	0.879655i	0.999610	−	0.0279341i	$-0.00889287\pi$
$660$	132.227	+	4986.36i	0.00779840	+	0.294081i
$661$	−7437.89	−	4294.27i	−0.437671	−	0.252689i	0.264938	−	0.964265i	$-0.414648\pi$
$661$	−7437.89	−	4294.27i	−0.437671	−	0.252689i	−0.702609	+	0.711576i	$0.747982\pi$
$662$	−13551.2	−	7823.78i	−0.795592	−	0.459335i
$663$	−337.182	−	12715.3i	−0.0197512	−	0.744828i
$664$	−7626.67	+	4403.26i	−0.445741	+	0.257349i
$665$	7516.01	−	2179.03i	0.438283	−	0.127067i
$666$	−908.600	−	17119.8i	−0.0528642	−	0.996067i
$667$	−20962.3			−1.21689
$668$	−2041.37	−	3535.75i	−0.118238	−	0.204794i
$669$	24592.1	+	13341.9i	1.42121	+	0.771042i
$670$	−20554.2	−	11867.0i	−1.18519	−	0.684271i
$671$	504.645	−	874.070i	0.0290337	−	0.0502878i
$672$	−2277.21	−	2073.06i	−0.130722	−	0.119003i
$673$	−16922.2	−	29310.1i	−0.969245	−	1.67878i	−0.697749	−	0.716343i	$-0.745815\pi$
$673$	−16922.2	−	29310.1i	−0.969245	−	1.67878i	−0.271497	−	0.962439i	$-0.587519\pi$
$674$			17896.2i			1.02275i
$675$	6573.13	+	9543.60i	0.374815	+	0.544198i
$676$	−6136.69			−0.349151
$677$	−8030.19	−	13908.7i	−0.455872	−	0.789594i	0.542866	−	0.839819i	$-0.317339\pi$
$677$	−8030.19	−	13908.7i	−0.455872	−	0.789594i	−0.998738	+	0.0502259i	$0.984006\pi$
$678$	−3780.07	−	6163.93i	−0.214119	−	0.349151i
$679$	6553.25	−	26615.7i	0.370384	−	1.50429i
$680$	−9491.37	−	5479.84i	−0.535261	−	0.309033i
$681$	−12535.9	+	23106.5i	−0.705397	+	1.30021i
$682$	−5895.66	+	3403.86i	−0.331021	+	0.191115i
$683$		−	8213.30i		−	0.460136i	−0.973175	−	0.230068i	$-0.926105\pi$
$683$		−	8213.30i		−	0.460136i	0.973175	−	0.230068i	$-0.0738949\pi$
$684$	−2655.11	+	1726.75i	−0.148422	+	0.0965262i
$685$		−	11020.5i		−	0.614706i
$686$	−12450.0	−	2532.16i	−0.692920	−	0.140930i
$687$	80.0333	+	3018.10i	0.00444463	+	0.167609i
$688$	−3032.57	+	5252.56i	−0.168046	+	0.291064i
$689$	7857.04	−	13608.8i	0.434440	−	0.752472i
$690$	14326.3	−	379.903i	0.790426	−	0.0209604i
$691$	11819.3	−	6823.88i	0.650691	−	0.375677i	−0.138030	−	0.990428i	$-0.544077\pi$
$691$	11819.3	−	6823.88i	0.650691	−	0.375677i	0.788721	+	0.614751i	$0.210744\pi$
$692$	−351.285			−0.0192975
$693$	−6305.58	−	5441.70i	−0.345641	−	0.298287i
$694$	−13522.9			−0.739657
$695$	−22817.8	+	13173.9i	−1.24537	+	0.719012i
$696$	−4341.54	+	8002.46i	−0.236445	+	0.435822i
$697$	−17361.5	+	30071.1i	−0.943494	+	1.63418i
$698$	−7096.09	+	12290.8i	−0.384801	+	0.666495i
$699$	−8075.54	+	4952.38i	−0.436974	+	0.267977i
$700$	−4237.67	+	4414.04i	−0.228813	+	0.238336i
$701$			5763.39i			0.310528i	0.987873	+	0.155264i	$0.0496228\pi$
$701$			5763.39i			0.310528i	−0.987873	+	0.155264i	$0.950377\pi$
$702$	7201.14	−	573.952i	0.387165	−	0.0308581i
$703$		−	9310.45i		−	0.499502i
$704$	923.195	−	533.007i	0.0494236	−	0.0285347i
$705$	−10071.0	−	16422.2i	−0.538011	−	0.877301i
$706$	−2596.90	−	1499.32i	−0.138436	−	0.0799260i
$707$	15143.7	+	3728.65i	0.805569	+	0.198346i
$708$	−2135.97	+	3937.07i	−0.113382	+	0.208989i
$709$	15021.8	+	26018.5i	0.795706	+	1.37820i	0.922390	+	0.386261i	$0.126234\pi$
$709$	15021.8	+	26018.5i	0.795706	+	1.37820i	−0.126683	+	0.991943i	$0.540433\pi$
$710$	20480.5			1.08256
$711$	−3041.12	+	161.401i	−0.160409	+	0.00851339i
$712$		−	1522.46i		−	0.0801359i
$713$	9779.65	+	16938.9i	0.513676	+	0.889712i
$714$	17435.1	−	5559.87i	0.913857	−	0.291419i
$715$	3089.34	−	5350.89i	0.161587	−	0.279877i
$716$	−14167.3	−	8179.48i	−0.739463	−	0.426929i
$717$	−121.886	−	4596.38i	−0.00634856	−	0.239407i
$718$	−6836.28	−	11840.8i	−0.355331	−	0.615452i
$719$	−8515.35			−0.441682			−0.220841	−	0.975310i	$-0.570880\pi$
$719$	−8515.35			−0.441682			−0.220841	+	0.975310i	$0.570880\pi$
$720$	2822.13	−	5547.83i	0.146076	−	0.287160i
$721$	800.147	−	231.978i	0.0413302	−	0.0119824i
$722$	10390.5	−	5998.98i	0.535590	−	0.309223i
$723$	11513.7	+	6246.48i	0.592252	+	0.321313i
$724$	13698.0	+	7908.52i	0.703150	+	0.405964i
$725$	15666.6	+	9045.14i	0.802544	+	0.463349i
$726$	−9333.61	+	5723.90i	−0.477139	+	0.292609i
$727$	8836.77	−	5101.91i	0.450808	−	0.260274i	−0.257363	−	0.966315i	$-0.582854\pi$
$727$	8836.77	−	5101.91i	0.450808	−	0.260274i	0.708171	+	0.706041i	$0.249520\pi$
$728$	1062.16	+	3663.64i	0.0540745	+	0.186516i
$729$	19434.5	−	3117.78i	0.987375	−	0.158400i
$730$	−6311.75			−0.320012
$731$	−18021.3	−	31213.8i	−0.911823	−	1.57932i
$732$	−1073.62	+	658.408i	−0.0542108	+	0.0332452i
$733$	25285.7	+	14598.7i	1.27415	+	0.735629i	0.975766	−	0.218818i	$-0.0702202\pi$
$733$	25285.7	+	14598.7i	1.27415	+	0.735629i	0.298380	+	0.954447i	$0.403554\pi$
$734$	6278.18	−	10874.1i	0.315711	−	0.546827i
$735$	−1726.38	−	25621.5i	−0.0866372	−	1.28580i
$736$	−1531.38	−	2652.43i	−0.0766951	−	0.132840i
$737$			13718.6i			0.685662i
$738$	−17576.9	−	8941.21i	−0.876715	−	0.445976i
$739$	6461.73			0.321649			0.160825	−	0.986983i	$-0.448585\pi$
$739$	6461.73			0.321649			0.160825	+	0.986983i	$0.448585\pi$
$740$	9148.68	+	15846.0i	0.454476	+	0.787175i
$741$	3921.78	−	103.997i	0.194427	−	0.00515577i
$742$	21952.5	+	5405.11i	1.08612	+	0.267423i
$743$	15978.8	+	9225.34i	0.788969	+	0.455511i	0.839599	−	0.543206i	$-0.182790\pi$
$743$	15978.8	+	9225.34i	0.788969	+	0.455511i	−0.0506304	+	0.998717i	$0.516123\pi$
$744$	8491.97	−	225.188i	0.418455	−	0.0110965i
$745$	26791.2	−	15467.9i	1.31752	−	0.760672i
$746$		−	14039.1i		−	0.689018i
$747$	29680.2	−	1575.22i	1.45374	−	0.0771542i
$748$			6334.89i			0.309661i
$749$	17606.6	+	16903.0i	0.858919	+	0.824598i
$750$	5580.65	+	3027.65i	0.271702	+	0.147406i
$751$	7702.63	−	13341.3i	0.374265	−	0.648246i	−0.615952	−	0.787784i	$-0.711228\pi$
$751$	7702.63	−	13341.3i	0.374265	−	0.648246i	0.990217	+	0.139538i	$0.0445618\pi$
$752$	−2058.50	+	3565.43i	−0.0998215	+	0.172896i
$753$	18953.0	+	30905.5i	0.917246	+	1.49570i
$754$	9766.43	−	5638.65i	0.471714	−	0.272344i
$755$	2748.23			0.132475
$756$	3677.99	+	9720.74i	0.176941	+	0.467645i
$757$	−28232.7			−1.35553			−0.677765	−	0.735278i	$-0.737051\pi$
$757$	−28232.7			−1.35553			−0.677765	+	0.735278i	$0.737051\pi$
$758$	−11694.2	+	6751.65i	−0.560360	+	0.323524i
$759$	−4330.61	−	7061.65i	−0.207103	−	0.337710i
$760$	1690.15	−	2927.43i	0.0806687	−	0.139722i
$761$	9382.71	−	16251.3i	0.446942	−	0.774126i	−0.551243	−	0.834345i	$-0.685846\pi$
$761$	9382.71	−	16251.3i	0.446942	−	0.774126i	0.998185	+	0.0602184i	$0.0191797\pi$
$762$	−5476.63	−	2971.21i	−0.260364	−	0.141254i
$763$	15356.6	−	15995.8i	0.728632	−	0.758959i
$764$			8049.64i			0.381186i
$765$	20166.2	+	31008.2i	0.953085	+	1.46549i
$766$			7258.80i			0.342391i
$767$	4804.92	−	2774.12i	0.226200	−	0.130597i
$768$	−1329.75	+	35.2620i	−0.0624780	+	0.00165678i
$769$	1369.16	+	790.485i	0.0642044	+	0.0370684i	0.531759	−	0.846896i	$-0.321531\pi$
$769$	1369.16	+	790.485i	0.0642044	+	0.0370684i	−0.467554	+	0.883964i	$0.654865\pi$
$770$	8631.59	+	2125.25i	0.403975	+	0.0994660i
$771$	33400.3	−	885.703i	1.56016	−	0.0413720i
$772$	9520.52	+	16490.0i	0.443849	+	0.768768i
$773$	−20363.8			−0.947525			−0.473762	−	0.880653i	$-0.657104\pi$
$773$	−20363.8			−0.947525			−0.473762	+	0.880653i	$0.657104\pi$
$774$	17160.0	−	11160.0i	0.796905	−	0.518268i
$775$		−	16879.5i		−	0.782361i
$776$	−5920.12	−	10254.0i	−0.273866	−	0.474350i
$777$	−29849.6	−	6515.43i	−1.37818	−	0.300823i
$778$	−8338.27	+	14442.3i	−0.384244	+	0.665530i
$779$	−9274.83	−	5354.83i	−0.426579	−	0.246286i
$780$	−6572.52	+	4030.64i	−0.301710	+	0.185026i
$781$	−5919.05	−	10252.1i	−0.271191	−	0.469717i
$782$	18200.8			0.832301
$783$	25305.6	−	17429.2i	1.15498	−	0.795488i
$784$	−4636.97	+	2935.42i	−0.211232	+	0.133720i
$785$	−28143.0	+	16248.4i	−1.27958	+	0.738764i
$786$	8656.01	−	5308.36i	0.392811	−	0.240894i
$787$	−14833.3	−	8564.01i	−0.671856	−	0.387896i	0.124924	−	0.992166i	$-0.460131\pi$
$787$	−14833.3	−	8564.01i	−0.671856	−	0.387896i	−0.796779	+	0.604270i	$0.793465\pi$
$788$	−6144.27	−	3547.40i	−0.277767	−	0.160369i
$789$	18097.2	+	9818.20i	0.816574	+	0.443013i
$790$	2814.84	−	1625.15i	0.126769	−	0.0731901i
$791$	−12376.3	+	3588.12i	−0.556321	+	0.161288i
$792$	−3592.74	+	190.677i	−0.161190	+	0.00855482i
$793$	1560.03			0.0698593
$794$	−1836.42	−	3180.78i	−0.0820810	−	0.142168i
$795$	1211.34	+	45680.3i	0.0540401	+	2.03788i
$796$	−4824.59	−	2785.48i	−0.214828	−	0.124031i
$797$	6688.89	−	11585.5i	0.297280	−	0.514905i	−0.678232	−	0.734848i	$-0.737254\pi$
$797$	6688.89	−	11585.5i	0.297280	−	0.514905i	0.975513	+	0.219943i	$0.0705870\pi$
$798$	1714.83	+	5377.53i	0.0760707	+	0.238550i
$799$	−12232.8	−	21187.9i	−0.541636	−	0.938141i
$800$			2643.14i			0.116811i
$801$	−2329.71	+	4579.82i	−0.102767	+	0.202022i
$802$	−13247.4			−0.583267
$803$	1824.15	+	3159.52i	0.0801655	+	0.138851i
$804$	8163.34	−	15046.9i	0.358083	−	0.660029i
$805$	6106.08	−	24799.5i	0.267343	−	1.08580i
$806$	−9112.77	−	5261.26i	−0.398243	−	0.229926i
$807$	−3176.16	−	5179.16i	−0.138545	−	0.225917i
$808$	5834.26	−	3368.41i	0.254021	−	0.146659i
$809$			1355.00i			0.0588865i	0.999566	+	0.0294432i	$0.00937343\pi$
$809$			1355.00i			0.0588865i	−0.999566	+	0.0294432i	$0.990627\pi$
$810$	−16978.8	+	12370.3i	−0.736513	+	0.536602i
$811$			1809.85i			0.0783631i	0.999232	+	0.0391816i	$0.0124751\pi$
$811$			1809.85i			0.0783631i	−0.999232	+	0.0391816i	$0.987525\pi$
$812$	11704.2	+	11236.5i	0.505833	+	0.485621i
$813$	3701.39	−	2269.90i	0.159672	−	0.0979200i
$814$	5288.10	−	9159.25i	0.227700	−	0.394388i
$815$	−1657.88	+	2871.54i	−0.0712553	+	0.123418i
$816$	3769.60	−	6948.24i	0.161719	−	0.298085i
$817$	9627.30	−	5558.33i	0.412260	−	0.238019i
$818$	−28601.4			−1.22252
$819$	2411.04	−	12646.2i	0.102867	−	0.539551i
$820$	21047.2			0.896340
$821$	−31040.0	+	17921.0i	−1.31949	+	0.761810i	−0.983647	−	0.180107i	$-0.942356\pi$
$821$	−31040.0	+	17921.0i	−1.31949	+	0.761810i	−0.335846	+	0.941917i	$0.609022\pi$
$822$	7946.04	−	210.711i	0.337165	−	0.00894089i
$823$	−4594.24	+	7957.45i	−0.194587	+	0.337034i	−0.946765	−	0.321925i	$-0.895670\pi$
$823$	−4594.24	+	7957.45i	−0.194587	+	0.337034i	0.752178	+	0.658960i	$0.229003\pi$
$824$	179.932	−	311.651i	0.00760707	−	0.0131758i
$825$	189.505	+	7146.32i	0.00799722	+	0.301579i
$826$	5758.26	+	5528.17i	0.242561	+	0.232869i
$827$		−	4816.95i		−	0.202541i	−0.994859	−	0.101271i	$-0.967709\pi$
$827$		−	4816.95i		−	0.202541i	0.994859	−	0.101271i	$-0.0322908\pi$
$828$	547.835	+	10322.3i	0.0229935	+	0.433243i
$829$			18718.5i			0.784222i	0.919918	+	0.392111i	$0.128255\pi$
$829$			18718.5i			0.784222i	−0.919918	+	0.392111i	$0.871745\pi$
$830$	−27471.8	+	15860.8i	−1.14887	+	0.663298i
$831$	17780.8	−	32774.1i	0.742249	−	1.36813i
$832$	1426.96	+	823.855i	0.0594602	+	0.0343294i
$833$	−1329.16	−	32585.9i	−0.0552852	−	1.35538i
$834$	−9934.90	−	16200.2i	−0.412491	−	0.672623i
$835$	−7353.14	−	12736.0i	−0.304750	−	0.527842i
$836$	−1953.87			−0.0808327
$837$	−25889.8	−	12317.2i	−1.06916	−	0.508656i
$838$		−	5248.25i		−	0.216346i
$839$	8308.46	+	14390.7i	0.341883	+	0.592159i	0.984782	−	0.173792i	$-0.0556020\pi$
$839$	8308.46	+	14390.7i	0.341883	+	0.592159i	−0.642899	+	0.765951i	$0.722269\pi$
$840$	−8202.67	−	7467.29i	−0.336927	−	0.306721i
$841$	11789.4	−	20419.8i	0.483389	−	0.837255i
$842$	19272.0	+	11126.7i	0.788784	+	0.455405i
$843$	−31584.9	−	17135.7i	−1.29044	−	0.700099i
$844$	−8847.54	−	15324.4i	−0.360835	−	0.624985i
$845$	−22104.8			−0.899913
$846$	11648.2	−	7575.42i	0.473373	−	0.307859i
$847$	5433.24	+	18740.5i	0.220411	+	0.760251i
$848$	8457.44	−	4882.90i	0.342488	−	0.197735i
$849$	−1014.67	−	38263.8i	−0.0410170	−	1.54677i
$850$	−13602.8	−	7853.56i	−0.548907	−	0.316912i
$851$	−26315.5	−	15193.3i	−1.06003	−	0.612007i
$852$	391.585	+	14766.9i	0.0157459	+	0.593785i
$853$	16226.8	−	9368.56i	0.651343	−	0.376053i	−0.137628	−	0.990484i	$-0.543948\pi$
$853$	16226.8	−	9368.56i	0.651343	−	0.376053i	0.788971	+	0.614431i	$0.210614\pi$
$854$	624.974	+	2155.68i	0.0250423	+	0.0863770i
$855$	−9563.87	+	6219.87i	−0.382547	+	0.248790i
$856$	10542.9			0.420967
$857$	−2379.03	−	4120.60i	−0.0948262	−	0.164244i	0.814710	−	0.579869i	$-0.196896\pi$
$857$	−2379.03	−	4120.60i	−0.0948262	−	0.164244i	−0.909536	+	0.415625i	$0.863563\pi$
$858$	3917.16	+	2125.17i	0.155862	+	0.0845594i
$859$	−1174.41	−	678.044i	−0.0466476	−	0.0269320i	0.476495	−	0.879177i	$-0.341907\pi$
$859$	−1174.41	−	678.044i	−0.0466476	−	0.0269320i	−0.523142	+	0.852245i	$0.675240\pi$
$860$	−10923.5	+	18920.1i	−0.433126	+	0.750196i
$861$	−23658.3	+	25988.1i	−0.936436	+	1.02866i
$862$	−6147.08	−	10647.1i	−0.242889	−	0.420696i
$863$			11844.4i			0.467193i	0.972334	+	0.233597i	$0.0750495\pi$
$863$			11844.4i			0.467193i	−0.972334	+	0.233597i	$0.924951\pi$
$864$	4054.06	+	1928.74i	0.159632	+	0.0759455i
$865$	−1265.35			−0.0497379
$866$	−9440.04	−	16350.6i	−0.370422	−	0.641590i
$867$	11212.2	+	18283.0i	0.439199	+	0.716174i
$868$	3619.39	−	14699.9i	0.141532	−	0.574826i
$869$	−1627.03	−	939.363i	−0.0635133	−	0.0366694i
$870$	−15638.5	+	28825.4i	−0.609420	+	1.12330i
$871$	−18363.7	+	10602.3i	−0.714386	+	0.412451i
$872$		−	9578.30i		−	0.371975i
$873$	2117.86	+	39904.7i	0.0821061	+	1.54704i
$874$			5613.68i			0.217260i
$875$	7835.98	−	8162.12i	0.302748	−	0.315349i
$876$	−120.680	−	4550.90i	−0.00465456	−	0.175526i
$877$	12943.5	−	22418.8i	0.498371	−	0.863204i	−0.501627	−	0.865084i	$-0.667265\pi$
$877$	12943.5	−	22418.8i	0.498371	−	0.863204i	0.999998	+	0.00187967i	$0.000598316\pi$
$878$	−6347.97	+	10995.0i	−0.244002	+	0.422623i
$879$	27192.9	−	721.096i	1.04345	−	0.0276700i
$880$	3325.41	−	1919.93i	0.127386	−	0.0735462i
$881$	31994.5			1.22352			0.611761	−	0.791043i	$-0.290462\pi$
$881$	31994.5			1.22352			0.611761	+	0.791043i	$0.290462\pi$
$882$	18440.6	−	1734.63i	0.703999	−	0.0662223i
$883$	9087.39			0.346336			0.173168	−	0.984892i	$-0.444600\pi$
$883$	9087.39			0.346336			0.173168	+	0.984892i	$0.444600\pi$
$884$	−8479.84	+	4895.84i	−0.322633	+	0.186272i
$885$	−7693.89	+	14181.6i	−0.292234	+	0.538654i
$886$	6342.78	−	10986.0i	0.240508	−	0.416571i
$887$	−18903.8	+	32742.4i	−0.715591	+	1.23944i	0.247140	+	0.968980i	$0.420509\pi$
$887$	−18903.8	+	32742.4i	−0.715591	+	1.23944i	−0.962731	+	0.270460i	$0.912824\pi$
$888$	−11250.4	+	6899.36i	−0.425154	+	0.260729i
$889$	−7689.91	+	8009.97i	−0.290114	+	0.302189i
$890$		−	5484.02i		−	0.206545i
$891$	11099.3	+	4924.10i	0.417330	+	0.185144i
$892$		−	21537.6i		−	0.808445i
$893$	6535.00	−	3772.98i	0.244888	−	0.141386i
$894$	11664.9	+	19021.3i	0.436391	+	0.711596i
$895$	−51031.4	−	29463.0i	−1.90591	−	1.10038i
$896$	−566.756	+	2301.85i	−0.0211317	+	0.0858251i
$897$	6105.82	−	11254.4i	0.227277	−	0.418923i
$898$	7435.21	+	12878.2i	0.276299	+	0.478564i
$899$	−44757.3			−1.66044
$900$	4044.59	−	7951.00i	0.149800	−	0.294481i
$901$			58034.3i			2.14584i
$902$	−6082.81	−	10535.7i	−0.224540	−	0.388915i
$903$	−11083.0	−	34755.2i	−0.408439	−	1.28082i
$904$	−2783.10	+	4820.46i	−0.102394	+	0.177352i
$905$	49340.9	+	28487.0i	1.81232	+	1.04634i
$906$	52.5458	+	1981.53i	0.00192684	+	0.0726621i
$907$	8691.22	+	15053.6i	0.318178	+	0.551100i	0.980108	−	0.198465i	$-0.0635958\pi$
$907$	8691.22	+	15053.6i	0.318178	+	0.551100i	−0.661930	+	0.749566i	$0.730262\pi$
$908$	20236.5			0.739616
$909$	−22704.8	+	1205.01i	−0.828462	+	0.0439689i
$910$	3825.96	+	13196.7i	0.139373	+	0.480731i
$911$	−38266.0	+	22092.9i	−1.39167	+	0.803479i	−0.993500	−	0.113834i	$-0.963687\pi$
$911$	−38266.0	+	22092.9i	−1.39167	+	0.803479i	−0.398167	+	0.917313i	$0.630354\pi$
$912$	2143.05	+	1162.66i	0.0778108	+	0.0422144i
$913$	15879.2	+	9167.84i	0.575601	+	0.332323i
$914$	24147.2	+	13941.4i	0.873870	+	0.504529i
$915$	−3867.27	+	2371.63i	−0.139725	+	0.0856871i
$916$	2012.77	−	1162.07i	0.0726025	−	0.0419171i
$917$	−5038.80	−	17380.0i	−0.181457	−	0.625887i
$918$	−21971.9	+	15133.1i	−0.789959	+	0.544082i
$919$	−43321.6			−1.55500			−0.777502	−	0.628880i	$-0.783514\pi$
$919$	−43321.6			−1.55500			−0.777502	+	0.628880i	$0.783514\pi$
$920$	−5516.15	−	9554.25i	−0.197676	−	0.342385i
$921$	−9630.45	+	5905.94i	−0.344554	+	0.211300i
$922$	−20404.6	−	11780.6i	−0.728838	−	0.420795i
$923$	9148.92	−	15846.4i	0.326263	−	0.565104i
$924$	−1367.32	+	6264.19i	−0.0486812	+	0.223027i
$925$	13111.6	+	22710.0i	0.466063	+	0.807245i
$926$			8379.83i			0.297385i
$927$	−1018.16	+	662.161i	−0.0360742	+	0.0234609i
$928$	7008.49			0.247915
$929$	5439.82	+	9422.05i	0.192115	+	0.332753i	0.945951	−	0.324310i	$-0.105132\pi$
$929$	5439.82	+	9422.05i	0.192115	+	0.332753i	−0.753836	+	0.657063i	$0.771799\pi$
$930$	30588.6	−	811.144i	1.07854	−	0.0286005i
$931$	10050.5	−	409.953i	0.353804	−	0.0144314i
$932$	6315.43	+	3646.21i	0.221962	+	0.128150i
$933$	−27338.2	+	724.948i	−0.959283	+	0.0254381i
$934$	13488.9	−	7787.83i	0.472560	−	0.272832i
$935$			22818.7i			0.798129i
$936$	−3031.84	−	4661.85i	−0.105875	−	0.162796i
$937$		−	21.6097i		−	0.000753424i	−1.00000		0.000376712i	$-0.999880\pi$
$937$		−	21.6097i		−	0.000753424i	1.00000		0.000376712i	$-0.000119911\pi$
$938$	−22007.2	−	21127.9i	−0.766057	−	0.735447i
$939$	6778.00	+	3677.25i	0.235561	+	0.127798i
$940$	−7414.86	+	12842.9i	−0.257283	+	0.445627i
$941$	18953.2	−	32827.9i	0.656596	−	1.13726i	−0.324895	−	0.945750i	$-0.605329\pi$
$941$	18953.2	−	32827.9i	0.656596	−	1.13726i	0.981491	−	0.191508i	$-0.0613377\pi$
$942$	−12253.5	−	19981.0i	−0.423822	−	0.691101i
$943$	−30270.3	+	17476.6i	−1.04532	+	0.603515i
$944$	3448.06			0.118882
$945$	13248.4	+	35014.7i	0.456052	+	1.20532i
$946$	12627.9			0.434006
$947$	−11737.3	+	6776.51i	−0.402756	+	0.232531i	−0.687672	−	0.726021i	$-0.741367\pi$
$947$	−11737.3	+	6776.51i	−0.402756	+	0.232531i	0.284917	+	0.958552i	$0.408034\pi$
$948$	1225.58	+	1998.48i	0.0419885	+	0.0684680i
$949$	−2819.54	+	4883.59i	−0.0964450	+	0.167048i
$950$	2422.28	−	4195.51i	0.0827254	−	0.143285i
$951$	−12652.1	−	6864.12i	−0.431413	−	0.234053i
$952$	−10162.3	−	9756.25i	−0.345969	−	0.332145i
$953$		−	10271.9i		−	0.349151i	−0.984644	−	0.174575i	$-0.944145\pi$
$953$		−	10271.9i		−	0.349151i	0.984644	−	0.174575i	$-0.0558553\pi$
$954$	−32913.3	+	1746.80i	−1.11699	+	0.0592818i
$955$			28995.3i			0.982479i
$956$	−3065.33	+	1769.77i	−0.103703	+	0.0598729i
$957$	18949.0	−	502.486i	0.640057	−	0.0169729i
$958$	−11438.3	−	6603.89i	−0.385755	−	0.222716i
$959$	3386.71	−	13754.9i	0.114038	−	0.463159i
$960$	−4789.84	+	127.016i	−0.161033	+	0.00427023i
$961$	5985.36	+	10367.0i	0.200912	+	0.347989i
$962$	16347.4			0.547879
$963$	−31714.6	−	16132.9i	−1.06126	−	0.539851i
$964$		−	10083.6i		−	0.336899i
$965$	34293.6	+	59398.2i	1.14399	+	1.98145i
$966$	17997.7	+	3928.44i	0.599447	+	0.130844i
$967$	−14500.0	+	25114.7i	−0.482200	+	0.835195i	−0.999791	−	0.0204333i	$-0.993495\pi$
$967$	−14500.0	+	25114.7i	−0.482200	+	0.835195i	0.517591	+	0.855628i	$0.326829\pi$
$968$	7299.29	+	4214.25i	0.242364	+	0.139929i
$969$	−12351.2	+	7574.47i	−0.409472	+	0.251111i
$970$	−21324.7	−	36935.4i	−0.705870	−	1.22260i
$971$	−10453.4			−0.345483			−0.172742	−	0.984967i	$-0.555263\pi$
$971$	−10453.4			−0.345483			−0.172742	+	0.984967i	$0.555263\pi$
$972$	−9243.86	−	12005.6i	−0.305038	−	0.396171i
$973$	−32527.7	+	9430.40i	−1.07173	+	0.310714i
$974$	29465.1	−	17011.7i	0.969324	−	0.559640i
$975$	−9419.55	+	5776.61i	−0.309402	+	0.189743i
$976$	839.622	+	484.756i	0.0275365	+	0.0158982i
$977$	16226.7	+	9368.48i	0.531359	+	0.306780i	0.741570	−	0.670876i	$-0.234082\pi$
$977$	16226.7	+	9368.48i	0.531359	+	0.306780i	−0.210211	+	0.977656i	$0.567415\pi$
$978$	−2102.13	−	1140.46i	−0.0687309	−	0.0372883i
$979$	−2745.18	+	1584.93i	−0.0896182	+	0.0517411i
$980$	−16702.7	+	10573.6i	−0.544436	+	0.344654i
$981$	−14656.9	+	28813.1i	−0.477023	+	0.937748i
$982$	1277.47			0.0415129
$983$	15838.5	+	27433.2i	0.513908	+	0.890114i	0.999870	+	0.0161344i	$0.00513595\pi$
$983$	15838.5	+	27433.2i	0.513908	+	0.890114i	−0.485962	+	0.873980i	$0.661531\pi$
$984$	402.419	+	15175.4i	0.0130372	+	0.491641i
$985$	−22132.1	−	12778.0i	−0.715925	−	0.413340i
$986$	−20824.3	+	36068.8i	−0.672598	+	1.16497i
$987$	−7523.14	−	23591.8i	−0.242618	−	0.760825i
$988$	−1510.03	−	2615.44i	−0.0486238	−	0.0842189i
$989$		−	36281.4i		−	1.16651i
$990$	−12941.3	+	686.832i	−0.415456	+	0.0220494i
$991$	60390.6			1.93579			0.967896	−	0.251351i	$-0.0808750\pi$
$991$	60390.6			1.93579			0.967896	+	0.251351i	$0.0808750\pi$
$992$	−3269.71	−	5663.30i	−0.104651	−	0.181260i
$993$	19386.3	−	35733.5i	0.619544	−	1.14196i
$994$	25562.1	+	6293.84i	0.815673	+	0.200833i
$995$	−17378.5	−	10033.5i	−0.553704	−	0.319681i
$996$	−11961.2	−	19504.4i	−0.380529	−	0.620504i
$997$	28478.8	−	16442.3i	0.904647	−	0.522298i	0.0259423	−	0.999663i	$-0.491741\pi$
$997$	28478.8	−	16442.3i	0.904647	−	0.522298i	0.878705	+	0.477365i	$0.158408\pi$
$998$			18270.5i			0.579502i
$999$	44400.4	−	3538.84i	1.40617	−	0.112076i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.4.m.a.41.20	yes	48
3.2	odd	2		378.4.m.a.125.11		48
7.6	odd	2	inner	126.4.m.a.41.17	✓	48
9.2	odd	6	inner	126.4.m.a.83.17	yes	48
9.4	even	3		1134.4.d.b.1133.16		48
9.5	odd	6		1134.4.d.b.1133.33		48
9.7	even	3		378.4.m.a.251.12		48
21.20	even	2		378.4.m.a.125.12		48
63.13	odd	6		1134.4.d.b.1133.34		48
63.20	even	6	inner	126.4.m.a.83.20	yes	48
63.34	odd	6		378.4.m.a.251.11		48
63.41	even	6		1134.4.d.b.1133.15		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.4.m.a.41.17	✓	48	7.6	odd	2	inner
126.4.m.a.41.20	yes	48	1.1	even	1	trivial
126.4.m.a.83.17	yes	48	9.2	odd	6	inner
126.4.m.a.83.20	yes	48	63.20	even	6	inner
378.4.m.a.125.11		48	3.2	odd	2
378.4.m.a.125.12		48	21.20	even	2
378.4.m.a.251.11		48	63.34	odd	6
378.4.m.a.251.12		48	9.7	even	3
1134.4.d.b.1133.15		48	63.41	even	6
1134.4.d.b.1133.16		48	9.4	even	3
1134.4.d.b.1133.33		48	9.5	odd	6
1134.4.d.b.1133.34		48	63.13	odd	6

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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	126.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.73205 - 1.00000i) q^{2} +(2.71645 + 4.42955i) q^{3} +(2.00000 - 3.46410i) q^{4} +(7.20413 - 12.4779i) q^{5} +(9.13458 + 4.95575i) q^{6} +(12.8262 - 13.3600i) q^{7} -8.00000i q^{8} +(-12.2418 + 24.0653i) q^{9} +O(q^{10})\)	\(q+(1.73205 - 1.00000i) q^{2} +(2.71645 + 4.42955i) q^{3} +(2.00000 - 3.46410i) q^{4} +(7.20413 - 12.4779i) q^{5} +(9.13458 + 4.95575i) q^{6} +(12.8262 - 13.3600i) q^{7} -8.00000i q^{8} +(-12.2418 + 24.0653i) q^{9} -28.8165i q^{10} +(-14.4249 + 8.32823i) q^{11} +(20.7773 - 0.550969i) q^{12} +(-22.2962 - 12.8727i) q^{13} +(8.85557 - 35.9664i) q^{14} +(74.8412 - 1.98463i) q^{15} +(-8.00000 - 13.8564i) q^{16} +95.0816 q^{17} +(2.86191 + 53.9241i) q^{18} +29.3261i q^{19} +(-28.8165 - 49.9117i) q^{20} +(94.0204 + 20.5223i) q^{21} +(-16.6565 + 28.8498i) q^{22} +(82.8886 + 47.8557i) q^{23} +(35.4364 - 21.7316i) q^{24} +(-41.2991 - 71.5321i) q^{25} -51.4909 q^{26} +(-139.853 + 11.1467i) q^{27} +(-20.6281 - 71.1511i) q^{28} +(-189.673 + 109.508i) q^{29} +(127.644 - 78.2787i) q^{30} +(176.978 + 102.178i) q^{31} +(-27.7128 - 16.0000i) q^{32} +(-76.0749 - 41.2726i) q^{33} +(164.686 - 95.0816i) q^{34} +(-74.3037 - 256.291i) q^{35} +(58.8811 + 90.5374i) q^{36} -317.480 q^{37} +(29.3261 + 50.7942i) q^{38} +(-3.54623 - 133.730i) q^{39} +(-99.8234 - 57.6331i) q^{40} +(-182.596 + 316.266i) q^{41} +(183.370 - 58.4747i) q^{42} +(-189.535 - 328.285i) q^{43} +66.6258i q^{44} +(212.094 + 326.122i) q^{45} +191.423 q^{46} +(-128.656 - 222.839i) q^{47} +(39.6460 - 73.0766i) q^{48} +(-13.9791 - 342.715i) q^{49} +(-143.064 - 82.5982i) q^{50} +(258.284 + 421.168i) q^{51} +(-89.1849 + 51.4909i) q^{52} +610.363i q^{53} +(-231.085 + 159.159i) q^{54} +239.991i q^{55} +(-106.880 - 102.609i) q^{56} +(-129.901 + 79.6628i) q^{57} +(-219.015 + 379.346i) q^{58} +(-107.752 + 186.632i) q^{59} +(142.808 - 263.227i) q^{60} +(-52.4764 + 30.2972i) q^{61} +408.714 q^{62} +(164.497 + 472.216i) q^{63} -64.0000 q^{64} +(-321.250 + 185.474i) q^{65} +(-173.038 + 4.58859i) q^{66} +(411.812 - 713.279i) q^{67} +(190.163 - 329.372i) q^{68} +(13.1835 + 497.157i) q^{69} +(-384.989 - 369.606i) q^{70} +710.721i q^{71} +(192.522 + 97.9343i) q^{72} -219.032i q^{73} +(-549.892 + 317.480i) q^{74} +(204.668 - 377.250i) q^{75} +(101.588 + 58.6521i) q^{76} +(-73.7512 + 299.536i) q^{77} +(-139.873 - 228.081i) q^{78} +(56.3964 + 97.6814i) q^{79} -230.532 q^{80} +(-429.277 - 589.204i) q^{81} +730.385i q^{82} +(-550.407 - 953.334i) q^{83} +(259.132 - 284.652i) q^{84} +(684.980 - 1186.42i) q^{85} +(-656.570 - 379.071i) q^{86} +(-1000.31 - 542.693i) q^{87} +(66.6258 + 115.399i) q^{88} +190.308 q^{89} +(693.479 + 352.766i) q^{90} +(-457.955 + 132.770i) q^{91} +(331.554 - 191.423i) q^{92} +(28.1485 + 1061.50i) q^{93} +(-445.678 - 257.313i) q^{94} +(365.928 + 211.269i) q^{95} +(-4.40775 - 166.218i) q^{96} +(1281.74 - 740.015i) q^{97} +(-366.928 - 579.621i) q^{98} +(-23.8346 - 449.092i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 96 q^{4} - 12 q^{7} - 36 q^{9}+O(q^{10}) \) 48 * q + 96 * q^4 - 12 * q^7 - 36 * q^9	\( 48 q + 96 q^{4} - 12 q^{7} - 36 q^{9} + 24 q^{11} - 132 q^{14} - 120 q^{15} - 384 q^{16} + 120 q^{18} + 180 q^{21} + 348 q^{23} - 600 q^{25} - 96 q^{28} - 84 q^{29} + 192 q^{30} + 96 q^{36} - 672 q^{37} + 1368 q^{39} + 1128 q^{42} + 84 q^{43} - 1008 q^{46} - 42 q^{49} + 456 q^{50} + 2016 q^{51} - 528 q^{56} + 732 q^{57} + 504 q^{58} - 1008 q^{60} - 774 q^{63} - 3072 q^{64} - 6972 q^{65} + 1176 q^{67} + 216 q^{70} - 384 q^{72} + 2520 q^{74} + 1500 q^{77} + 2832 q^{78} + 348 q^{79} + 2268 q^{81} - 1080 q^{84} + 720 q^{85} + 1200 q^{86} + 180 q^{91} + 1392 q^{92} + 5232 q^{93} - 5892 q^{95} + 972 q^{99}+O(q^{100}) \) 48 * q + 96 * q^4 - 12 * q^7 - 36 * q^9 + 24 * q^11 - 132 * q^14 - 120 * q^15 - 384 * q^16 + 120 * q^18 + 180 * q^21 + 348 * q^23 - 600 * q^25 - 96 * q^28 - 84 * q^29 + 192 * q^30 + 96 * q^36 - 672 * q^37 + 1368 * q^39 + 1128 * q^42 + 84 * q^43 - 1008 * q^46 - 42 * q^49 + 456 * q^50 + 2016 * q^51 - 528 * q^56 + 732 * q^57 + 504 * q^58 - 1008 * q^60 - 774 * q^63 - 3072 * q^64 - 6972 * q^65 + 1176 * q^67 + 216 * q^70 - 384 * q^72 + 2520 * q^74 + 1500 * q^77 + 2832 * q^78 + 348 * q^79 + 2268 * q^81 - 1080 * q^84 + 720 * q^85 + 1200 * q^86 + 180 * q^91 + 1392 * q^92 + 5232 * q^93 - 5892 * q^95 + 972 * q^99

Introduction

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