LMFDB - Embedded newform 201.3.h.b.97.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,3,Mod(97,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("201.97");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	201.h (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:	$5.47685331364$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			97.8
Character	$\chi$	$=$	201.97
Dual form			201.3.h.b.172.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.15796 - 0.668551i) q^{2} +1.73205i q^{3} +(-1.10608 + 1.91579i) q^{4} +0.749427i q^{5} +(1.15796 + 2.00565i) q^{6} +(2.89468 + 1.67125i) q^{7} +8.30629i q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(1.15796 - 0.668551i) q^{2} +1.73205i q^{3} +(-1.10608 + 1.91579i) q^{4} +0.749427i q^{5} +(1.15796 + 2.00565i) q^{6} +(2.89468 + 1.67125i) q^{7} +8.30629i q^{8} -3.00000 q^{9} +(0.501030 + 0.867810i) q^{10} +(-6.87542 - 3.96953i) q^{11} +(-3.31824 - 1.91579i) q^{12} +(-14.8848 + 8.59375i) q^{13} +4.46925 q^{14} -1.29805 q^{15} +(1.12886 + 1.95525i) q^{16} +(9.50193 + 16.4578i) q^{17} +(-3.47389 + 2.00565i) q^{18} +(14.7724 + 25.5865i) q^{19} +(-1.43574 - 0.828925i) q^{20} +(-2.89468 + 5.01374i) q^{21} -10.6153 q^{22} +(-0.701183 - 1.21448i) q^{23} -14.3869 q^{24} +24.4384 q^{25} +(-11.4907 + 19.9025i) q^{26} -5.19615i q^{27} +(-6.40349 + 3.69706i) q^{28} +(26.1897 - 45.3619i) q^{29} +(-1.50309 + 0.867810i) q^{30} +(-16.5153 - 9.53514i) q^{31} +(-26.1595 - 15.1032i) q^{32} +(6.87542 - 11.9086i) q^{33} +(22.0058 + 12.7051i) q^{34} +(-1.25248 + 2.16935i) q^{35} +(3.31824 - 5.74736i) q^{36} +(-6.29733 - 10.9073i) q^{37} +(34.2117 + 19.7522i) q^{38} +(-14.8848 - 25.7812i) q^{39} -6.22496 q^{40} +(46.7236 + 26.9759i) q^{41} +7.74097i q^{42} +7.92633i q^{43} +(15.2095 - 8.78122i) q^{44} -2.24828i q^{45} +(-1.62389 - 0.937553i) q^{46} +(16.8595 - 29.2016i) q^{47} +(-3.38659 + 1.95525i) q^{48} +(-18.9139 - 32.7598i) q^{49} +(28.2987 - 16.3383i) q^{50} +(-28.5058 + 16.4578i) q^{51} -38.0215i q^{52} +26.7727i q^{53} +(-3.47389 - 6.01696i) q^{54} +(2.97487 - 5.15263i) q^{55} +(-13.8818 + 24.0441i) q^{56} +(-44.3171 + 25.5865i) q^{57} -70.0366i q^{58} +106.449 q^{59} +(1.43574 - 2.48678i) q^{60} +(-59.8814 + 34.5725i) q^{61} -25.4989 q^{62} +(-8.68404 - 5.01374i) q^{63} -49.4199 q^{64} +(-6.44039 - 11.1551i) q^{65} -18.3863i q^{66} +(47.9270 + 46.8189i) q^{67} -42.0396 q^{68} +(2.10355 - 1.21448i) q^{69} +3.34938i q^{70} +(15.3577 - 26.6004i) q^{71} -24.9189i q^{72} +(-56.9220 - 98.5918i) q^{73} +(-14.5842 - 8.42018i) q^{74} +42.3285i q^{75} -65.3576 q^{76} +(-13.2681 - 22.9810i) q^{77} +(-34.4722 - 19.9025i) q^{78} +(54.9541 + 31.7278i) q^{79} +(-1.46531 + 0.846000i) q^{80} +9.00000 q^{81} +72.1391 q^{82} +(-8.76783 - 15.1863i) q^{83} +(-6.40349 - 11.0912i) q^{84} +(-12.3339 + 7.12100i) q^{85} +(5.29915 + 9.17840i) q^{86} +(78.5691 + 45.3619i) q^{87} +(32.9720 - 57.1093i) q^{88} +123.476 q^{89} +(-1.50309 - 2.60343i) q^{90} -57.4490 q^{91} +3.10225 q^{92} +(16.5153 - 28.6054i) q^{93} -45.0859i q^{94} +(-19.1752 + 11.0708i) q^{95} +(26.1595 - 45.3095i) q^{96} +(-119.499 + 68.9929i) q^{97} +(-43.8032 - 25.2898i) q^{98} +(20.6263 + 11.9086i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 34 q^{4} + 21 q^{7} - 72 q^{9}+O(q^{10}) $ 24 * q + 34 * q^4 + 21 * q^7 - 72 * q^9	$ 24 q + 34 q^{4} + 21 q^{7} - 72 q^{9} + 30 q^{10} + 12 q^{11} + 102 q^{12} + 30 q^{13} + 6 q^{14} - 6 q^{15} - 98 q^{16} + 4 q^{17} + 39 q^{19} + 108 q^{20} - 21 q^{21} - 82 q^{22} - 13 q^{23} - 36 q^{24} - 222 q^{25} + 29 q^{26} + 189 q^{28} - 90 q^{30} - 93 q^{31} - 33 q^{32} - 12 q^{33} + 72 q^{34} - 93 q^{35} - 102 q^{36} - 33 q^{37} - 210 q^{38} + 30 q^{39} + 274 q^{40} - 15 q^{41} - 9 q^{44} - 228 q^{46} - 131 q^{47} + 294 q^{48} + 295 q^{49} - 423 q^{50} - 12 q^{51} - 56 q^{55} + 349 q^{56} - 117 q^{57} - 116 q^{59} - 108 q^{60} + 120 q^{61} + 282 q^{62} - 63 q^{63} - 276 q^{64} + 136 q^{65} - 25 q^{67} + 10 q^{68} + 39 q^{69} + 169 q^{71} + 187 q^{73} + 849 q^{74} + 386 q^{76} - 348 q^{77} + 87 q^{78} + 51 q^{80} + 216 q^{81} - 14 q^{82} + 104 q^{83} + 189 q^{84} - 243 q^{85} + 641 q^{86} - 766 q^{88} + 152 q^{89} - 90 q^{90} + 32 q^{91} - 216 q^{92} + 93 q^{93} + 762 q^{95} + 33 q^{96} - 84 q^{97} - 1086 q^{98} - 36 q^{99}+O(q^{100}) $ 24 * q + 34 * q^4 + 21 * q^7 - 72 * q^9 + 30 * q^10 + 12 * q^11 + 102 * q^12 + 30 * q^13 + 6 * q^14 - 6 * q^15 - 98 * q^16 + 4 * q^17 + 39 * q^19 + 108 * q^20 - 21 * q^21 - 82 * q^22 - 13 * q^23 - 36 * q^24 - 222 * q^25 + 29 * q^26 + 189 * q^28 - 90 * q^30 - 93 * q^31 - 33 * q^32 - 12 * q^33 + 72 * q^34 - 93 * q^35 - 102 * q^36 - 33 * q^37 - 210 * q^38 + 30 * q^39 + 274 * q^40 - 15 * q^41 - 9 * q^44 - 228 * q^46 - 131 * q^47 + 294 * q^48 + 295 * q^49 - 423 * q^50 - 12 * q^51 - 56 * q^55 + 349 * q^56 - 117 * q^57 - 116 * q^59 - 108 * q^60 + 120 * q^61 + 282 * q^62 - 63 * q^63 - 276 * q^64 + 136 * q^65 - 25 * q^67 + 10 * q^68 + 39 * q^69 + 169 * q^71 + 187 * q^73 + 849 * q^74 + 386 * q^76 - 348 * q^77 + 87 * q^78 + 51 * q^80 + 216 * q^81 - 14 * q^82 + 104 * q^83 + 189 * q^84 - 243 * q^85 + 641 * q^86 - 766 * q^88 + 152 * q^89 - 90 * q^90 + 32 * q^91 - 216 * q^92 + 93 * q^93 + 762 * q^95 + 33 * q^96 - 84 * q^97 - 1086 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	1.15796	−	0.668551i	0.578982	−	0.334276i	−0.181747	−	0.983345i	$-0.558175\pi$
$2$	1.15796	−	0.668551i	0.578982	−	0.334276i	0.760729	+	0.649070i	$0.224842\pi$
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	−1.10608	+	1.91579i	−0.276520	+	0.478946i
$5$			0.749427i			0.149885i	0.997188	+	0.0749427i	$0.0238774\pi$
$5$			0.749427i			0.149885i	−0.997188	+	0.0749427i	$0.976123\pi$
$6$	1.15796	+	2.00565i	0.192994	+	0.334276i
$7$	2.89468	+	1.67125i	0.413526	+	0.238749i	0.692304	−	0.721606i	$-0.256596\pi$
$7$	2.89468	+	1.67125i	0.413526	+	0.238749i	−0.278778	+	0.960356i	$0.589929\pi$
$8$			8.30629i			1.03829i
$9$	−3.00000			−0.333333
$10$	0.501030	+	0.867810i	0.0501030	+	0.0867810i
$11$	−6.87542	−	3.96953i	−0.625038	−	0.360866i	0.153790	−	0.988104i	$-0.450852\pi$
$11$	−6.87542	−	3.96953i	−0.625038	−	0.360866i	−0.778828	+	0.627238i	$0.784186\pi$
$12$	−3.31824	−	1.91579i	−0.276520	−	0.159649i
$13$	−14.8848	+	8.59375i	−1.14499	+	0.661058i	−0.947660	−	0.319281i	$-0.896559\pi$
$13$	−14.8848	+	8.59375i	−1.14499	+	0.661058i	−0.197325	+	0.980338i	$0.563225\pi$
$14$	4.46925			0.319232
$15$	−1.29805			−0.0865364
$16$	1.12886	+	1.95525i	0.0705539	+	0.122203i
$17$	9.50193	+	16.4578i	0.558937	+	0.968108i	0.997586	+	0.0694488i	$0.0221241\pi$
$17$	9.50193	+	16.4578i	0.558937	+	0.968108i	−0.438648	+	0.898659i	$0.644543\pi$
$18$	−3.47389	+	2.00565i	−0.192994	+	0.111425i
$19$	14.7724	+	25.5865i	0.777493	+	1.34666i	0.933383	+	0.358883i	$0.116842\pi$
$19$	14.7724	+	25.5865i	0.777493	+	1.34666i	−0.155890	+	0.987774i	$0.549824\pi$
$20$	−1.43574	−	0.828925i	−0.0717870	−	0.0414463i
$21$	−2.89468	+	5.01374i	−0.137842	+	0.238749i
$22$	−10.6153			−0.482515
$23$	−0.701183	−	1.21448i	−0.0304862	−	0.0528037i	0.850380	−	0.526169i	$-0.176372\pi$
$23$	−0.701183	−	1.21448i	−0.0304862	−	0.0528037i	−0.880866	+	0.473366i	$0.843039\pi$
$24$	−14.3869			−0.599455
$25$	24.4384			0.977534
$26$	−11.4907	+	19.9025i	−0.441951	+	0.765481i
$27$		−	5.19615i		−	0.192450i
$28$	−6.40349	+	3.69706i	−0.228696	+	0.132038i
$29$	26.1897	−	45.3619i	0.903093	−	1.56420i	0.0796365	−	0.996824i	$-0.474624\pi$
$29$	26.1897	−	45.3619i	0.903093	−	1.56420i	0.823457	−	0.567379i	$-0.192043\pi$
$30$	−1.50309	+	0.867810i	−0.0501030	+	0.0289270i
$31$	−16.5153	−	9.53514i	−0.532753	−	0.307585i	0.209384	−	0.977834i	$-0.432854\pi$
$31$	−16.5153	−	9.53514i	−0.532753	−	0.307585i	−0.742137	+	0.670248i	$0.766188\pi$
$32$	−26.1595	−	15.1032i	−0.817483	−	0.471974i
$33$	6.87542	−	11.9086i	0.208346	−	0.360866i
$34$	22.0058	+	12.7051i	0.647229	+	0.373678i
$35$	−1.25248	+	2.16935i	−0.0357850	+	0.0619815i
$36$	3.31824	−	5.74736i	0.0921733	−	0.159649i
$37$	−6.29733	−	10.9073i	−0.170198	−	0.294792i	0.768291	−	0.640101i	$-0.221107\pi$
$37$	−6.29733	−	10.9073i	−0.170198	−	0.294792i	−0.938489	+	0.345309i	$0.887774\pi$
$38$	34.2117	+	19.7522i	0.900309	+	0.519794i
$39$	−14.8848	−	25.7812i	−0.381662	−	0.661058i
$40$	−6.22496			−0.155624
$41$	46.7236	+	26.9759i	1.13960	+	0.657949i	0.946332	−	0.323197i	$-0.104758\pi$
$41$	46.7236	+	26.9759i	1.13960	+	0.657949i	0.193269	+	0.981146i	$0.438091\pi$
$42$			7.74097i			0.184309i
$43$			7.92633i			0.184333i	0.995744	+	0.0921666i	$0.0293792\pi$
$43$			7.92633i			0.184333i	−0.995744	+	0.0921666i	$0.970621\pi$
$44$	15.2095	−	8.78122i	0.345671	−	0.199573i
$45$		−	2.24828i		−	0.0499618i
$46$	−1.62389	−	0.937553i	−0.0353019	−	0.0203816i
$47$	16.8595	−	29.2016i	0.358714	−	0.621310i	−0.629032	−	0.777379i	$-0.716549\pi$
$47$	16.8595	−	29.2016i	0.358714	−	0.621310i	0.987746	+	0.156069i	$0.0498821\pi$
$48$	−3.38659	+	1.95525i	−0.0705539	+	0.0407343i
$49$	−18.9139	−	32.7598i	−0.385998	−	0.668567i
$50$	28.2987	−	16.3383i	0.565975	−	0.326766i
$51$	−28.5058	+	16.4578i	−0.558937	+	0.322703i
$52$		−	38.0215i		−	0.731182i
$53$			26.7727i			0.505146i	0.967578	+	0.252573i	$0.0812768\pi$
$53$			26.7727i			0.505146i	−0.967578	+	0.252573i	$0.918723\pi$
$54$	−3.47389	−	6.01696i	−0.0643314	−	0.111425i
$55$	2.97487	−	5.15263i	0.0540886	−	0.0936841i
$56$	−13.8818	+	24.0441i	−0.247890	+	0.429358i
$57$	−44.3171	+	25.5865i	−0.777493	+	0.448886i
$58$		−	70.0366i		−	1.20753i
$59$	106.449			1.80422			0.902108	−	0.431509i	$-0.142019\pi$
$59$	106.449			1.80422			0.902108	+	0.431509i	$0.142019\pi$
$60$	1.43574	−	2.48678i	0.0239290	−	0.0414463i
$61$	−59.8814	+	34.5725i	−0.981662	+	0.566763i	−0.902772	−	0.430120i	$-0.858471\pi$
$61$	−59.8814	+	34.5725i	−0.981662	+	0.566763i	−0.0788908	+	0.996883i	$0.525138\pi$
$62$	−25.4989			−0.411273
$63$	−8.68404	−	5.01374i	−0.137842	−	0.0795831i
$64$	−49.4199			−0.772185
$65$	−6.44039	−	11.1551i	−0.0990829	−	0.171617i
$66$		−	18.3863i		−	0.278580i
$67$	47.9270	+	46.8189i	0.715328	+	0.698789i
$67$	47.9270	+	46.8189i	0.715328	+	0.698789i
$68$	−42.0396			−0.618229
$69$	2.10355	−	1.21448i	0.0304862	−	0.0176012i
$70$			3.34938i			0.0478482i
$71$	15.3577	−	26.6004i	0.216306	−	0.374653i	−0.737370	−	0.675489i	$-0.763932\pi$
$71$	15.3577	−	26.6004i	0.216306	−	0.374653i	0.953676	+	0.300836i	$0.0972658\pi$
$72$		−	24.9189i		−	0.346095i
$73$	−56.9220	−	98.5918i	−0.779753	−	1.35057i	−0.932084	−	0.362243i	$-0.882011\pi$
$73$	−56.9220	−	98.5918i	−0.779753	−	1.35057i	0.152330	−	0.988330i	$-0.451322\pi$
$74$	−14.5842	−	8.42018i	−0.197083	−	0.113786i
$75$			42.3285i			0.564380i
$76$	−65.3576			−0.859969
$77$	−13.2681	−	22.9810i	−0.172313	−	0.298455i
$78$	−34.4722	−	19.9025i	−0.441951	−	0.255160i
$79$	54.9541	+	31.7278i	0.695622	+	0.401618i	0.805715	−	0.592304i	$-0.201781\pi$
$79$	54.9541	+	31.7278i	0.695622	+	0.401618i	−0.110093	+	0.993921i	$0.535115\pi$
$80$	−1.46531	+	0.846000i	−0.0183164	+	0.0105750i
$81$	9.00000			0.111111
$82$	72.1391			0.879745
$83$	−8.76783	−	15.1863i	−0.105636	−	0.182968i	0.808362	−	0.588686i	$-0.200355\pi$
$83$	−8.76783	−	15.1863i	−0.105636	−	0.182968i	−0.913998	+	0.405719i	$0.867021\pi$
$84$	−6.40349	−	11.0912i	−0.0762321	−	0.132038i
$85$	−12.3339	+	7.12100i	−0.145105	+	0.0837765i
$86$	5.29915	+	9.17840i	0.0616181	+	0.106726i
$87$	78.5691	+	45.3619i	0.903093	+	0.521401i
$88$	32.9720	−	57.1093i	0.374682	−	0.648969i
$89$	123.476			1.38737			0.693683	−	0.720281i	$-0.255987\pi$
$89$	123.476			1.38737			0.693683	+	0.720281i	$0.255987\pi$
$90$	−1.50309	−	2.60343i	−0.0167010	−	0.0289270i
$91$	−57.4490			−0.631308
$92$	3.10225			0.0337202
$93$	16.5153	−	28.6054i	0.177584	−	0.307585i
$94$		−	45.0859i		−	0.479637i
$95$	−19.1752	+	11.0708i	−0.201844	+	0.116535i
$96$	26.1595	−	45.3095i	0.272494	−	0.471974i
$97$	−119.499	+	68.9929i	−1.23195	+	0.711267i	−0.967436	−	0.253114i	$-0.918545\pi$
$97$	−119.499	+	68.9929i	−1.23195	+	0.711267i	−0.264515	+	0.964382i	$0.585212\pi$
$98$	−43.8032	−	25.2898i	−0.446971	−	0.258059i
$99$	20.6263	+	11.9086i	0.208346	+	0.120289i
$100$	−27.0308	+	46.8186i	−0.270308	+	0.468186i
$101$	37.1332	+	21.4389i	0.367656	+	0.212266i	0.672434	−	0.740157i	$-0.265249\pi$
$101$	37.1332	+	21.4389i	0.367656	+	0.212266i	−0.304778	+	0.952423i	$0.598582\pi$
$102$	−22.0058	+	38.1152i	−0.215743	+	0.373678i
$103$	−16.8251	+	29.1420i	−0.163351	+	0.282932i	−0.936068	−	0.351818i	$-0.885564\pi$
$103$	−16.8251	+	29.1420i	−0.163351	+	0.282932i	0.772718	+	0.634750i	$0.218897\pi$
$104$	−71.3822	−	123.638i	−0.686367	−	1.18882i
$105$	−3.75743	−	2.16935i	−0.0357850	−	0.0206605i
$106$	17.8989	+	31.0019i	0.168858	+	0.292471i
$107$	86.6687			0.809988			0.404994	−	0.914319i	$-0.367274\pi$
$107$	86.6687			0.809988			0.404994	+	0.914319i	$0.367274\pi$
$108$	9.95471	+	5.74736i	0.0921733	+	0.0532163i
$109$			80.9315i			0.742491i	0.928535	+	0.371245i	$0.121069\pi$
$109$			80.9315i			0.742491i	−0.928535	+	0.371245i	$0.878931\pi$
$110$		−	7.95541i		−	0.0723219i
$111$	18.8920	−	10.9073i	0.170198	−	0.0982640i
$112$			7.54642i			0.0673788i
$113$	−26.3773	−	15.2290i	−0.233428	−	0.134769i	0.378725	−	0.925509i	$-0.376363\pi$
$113$	−26.3773	−	15.2290i	−0.233428	−	0.134769i	−0.612152	+	0.790740i	$0.709696\pi$
$114$	−34.2117	+	59.2565i	−0.300103	+	0.519794i
$115$	0.910167	−	0.525485i	0.00791450	−	0.00456944i
$116$	57.9358	+	100.348i	0.499446	+	0.865066i
$117$	44.6544	−	25.7812i	0.381662	−	0.220353i
$118$	123.264	−	71.1664i	1.04461	−	0.603105i
$119$			63.5202i			0.533784i
$120$		−	10.7819i		−	0.0898495i
$121$	−28.9857	−	50.2047i	−0.239551	−	0.414915i
$122$	−46.2270	+	80.0676i	−0.378910	+	0.656291i
$123$	−46.7236	+	80.9277i	−0.379867	+	0.657949i
$124$	36.5346	−	21.0932i	0.294634	−	0.170107i
$125$			37.0504i			0.296403i
$126$	−13.4078			−0.106411
$127$	122.493	−	212.165i	0.964514	−	1.67059i	0.253600	−	0.967309i	$-0.418385\pi$
$127$	122.493	−	212.165i	0.964514	−	1.67059i	0.710915	−	0.703278i	$-0.248281\pi$
$128$	47.4114	−	27.3730i	0.370402	−	0.213852i
$129$	−13.7288			−0.106425
$130$	−14.9155	−	8.61145i	−0.114734	−	0.0662420i
$131$	−83.2783			−0.635712			−0.317856	−	0.948139i	$-0.602963\pi$
$131$	−83.2783			−0.635712			−0.317856	+	0.948139i	$0.602963\pi$
$132$	15.2095	+	26.3437i	0.115224	+	0.199573i
$133$			98.7530i			0.742504i
$134$	86.7985	+	22.1730i	0.647750	+	0.165470i
$135$	3.89414			0.0288455
$136$	−136.703	+	78.9258i	−1.00517	+	0.580337i
$137$			125.514i			0.916161i	0.888911	+	0.458081i	$0.151463\pi$
$137$			125.514i			0.916161i	−0.888911	+	0.458081i	$0.848537\pi$
$138$	1.62389	−	2.81266i	0.0117673	−	0.0203816i
$139$		−	10.1677i		−	0.0731490i	−0.999331	−	0.0365745i	$-0.988355\pi$
$139$		−	10.1677i		−	0.0731490i	0.999331	−	0.0365745i	$-0.0116446\pi$
$140$	−2.77068	−	4.79895i	−0.0197905	−	0.0342782i
$141$	50.5786	+	29.2016i	0.358714	+	0.207103i
$142$		−	41.0697i		−	0.289223i
$143$	136.452			0.954213
$144$	−3.38659	−	5.86574i	−0.0235180	−	0.0407343i
$145$	33.9954	+	19.6273i	0.234451	+	0.135360i
$146$	−131.827	−	76.1105i	−0.902927	−	0.521305i
$147$	56.7416	−	32.7598i	0.385998	−	0.222856i
$148$	27.8614			0.188253
$149$	−254.531			−1.70826			−0.854131	−	0.520058i	$-0.825910\pi$
$149$	−254.531			−1.70826			−0.854131	+	0.520058i	$0.825910\pi$
$150$	28.2987	+	49.0149i	0.188658	+	0.326766i
$151$	89.4358	+	154.907i	0.592290	+	1.02588i	0.993923	+	0.110075i	$0.0351093\pi$
$151$	89.4358	+	154.907i	0.592290	+	1.02588i	−0.401633	+	0.915801i	$0.631557\pi$
$152$	−212.529	+	122.704i	−1.39822	+	0.807260i
$153$	−28.5058	−	49.3735i	−0.186312	−	0.322703i
$154$	−30.7280	−	17.7408i	−0.199532	−	0.115200i
$155$	7.14589	−	12.3770i	0.0461025	−	0.0798519i
$156$	65.8551			0.422148
$157$	94.2421	+	163.232i	0.600268	+	1.03969i	0.992780	+	0.119948i	$0.0382728\pi$
$157$	94.2421	+	163.232i	0.600268	+	1.03969i	−0.392512	+	0.919747i	$0.628394\pi$
$158$	84.8466			0.537004
$159$	−46.3718			−0.291646
$160$	11.3187	−	19.6046i	0.0707420	−	0.122529i
$161$		−	4.68739i		−	0.0291142i
$162$	10.4217	−	6.01696i	0.0643314	−	0.0371417i
$163$	−146.881	+	254.406i	−0.901112	+	1.56077i	−0.0750603	+	0.997179i	$0.523915\pi$
$163$	−146.881	+	254.406i	−0.901112	+	1.56077i	−0.826052	+	0.563594i	$0.809418\pi$
$164$	−103.360	+	59.6750i	−0.630245	+	0.363872i
$165$	8.92461	+	5.15263i	0.0540886	+	0.0312280i
$166$	−20.3057	−	11.7235i	−0.122323	−	0.0706234i
$167$	1.60592	−	2.78153i	0.00961626	−	0.0166558i	−0.861177	−	0.508305i	$-0.830272\pi$
$167$	1.60592	−	2.78153i	0.00961626	−	0.0166558i	0.870793	+	0.491649i	$0.163606\pi$
$168$	−41.6455	−	24.0441i	−0.247890	−	0.143119i
$169$	63.2050	−	109.474i	0.373994	−	0.647777i
$170$	−9.52151	+	16.4917i	−0.0560089	+	0.0970102i
$171$	−44.3171	−	76.7595i	−0.259164	−	0.448886i
$172$	−15.1851	−	8.76714i	−0.0882857	−	0.0509718i
$173$	−77.7873	−	134.732i	−0.449638	−	0.778795i	0.548725	−	0.836003i	$-0.315114\pi$
$173$	−77.7873	−	134.732i	−0.449638	−	0.778795i	−0.998362	+	0.0572078i	$0.981780\pi$
$174$	121.307			0.697166
$175$	70.7413	+	40.8425i	0.404236	+	0.233386i
$176$		−	17.9242i		−	0.101842i
$177$			184.375i			1.04167i
$178$	142.980	−	82.5497i	0.803260	−	0.463762i
$179$		−	173.921i		−	0.971628i	−0.874062	−	0.485814i	$-0.838523\pi$
$179$		−	173.921i		−	0.971628i	0.874062	−	0.485814i	$-0.161477\pi$
$180$	4.30722	+	2.48678i	0.0239290	+	0.0138154i
$181$	−112.494	+	194.845i	−0.621512	+	1.07649i	0.367693	+	0.929947i	$0.380148\pi$
$181$	−112.494	+	194.845i	−0.621512	+	1.07649i	−0.989204	+	0.146542i	$0.953186\pi$
$182$	−66.5239	+	38.4076i	−0.365516	+	0.211031i
$183$	−59.8814	−	103.718i	−0.327221	−	0.566763i
$184$	10.0879	−	5.82423i	0.0548253	−	0.0316534i
$185$	8.17423	−	4.71939i	0.0441850	−	0.0255102i
$186$		−	44.1654i		−	0.237448i
$187$		−	150.873i		−	0.806806i
$188$	37.2960	+	64.5985i	0.198383	+	0.343609i
$189$	8.68404	−	15.0412i	0.0459473	−	0.0795831i
$190$	−14.8028	+	25.6392i	−0.0779095	+	0.134943i
$191$	−5.22956	+	3.01929i	−0.0273799	+	0.0158078i	−0.513627	−	0.858013i	$-0.671699\pi$
$191$	−5.22956	+	3.01929i	−0.0273799	+	0.0158078i	0.486248	+	0.873821i	$0.338365\pi$
$192$		−	85.5977i		−	0.445821i
$193$	−65.9203			−0.341556			−0.170778	−	0.985310i	$-0.554628\pi$
$193$	−65.9203			−0.341556			−0.170778	+	0.985310i	$0.554628\pi$
$194$	−92.2506	+	159.783i	−0.475519	+	0.823622i
$195$	19.3212	−	11.1551i	0.0990829	−	0.0572055i
$196$	83.6810			0.426944
$197$	−65.3058	−	37.7043i	−0.331502	−	0.191392i	0.325006	−	0.945712i	$-0.394634\pi$
$197$	−65.3058	−	37.7043i	−0.331502	−	0.191392i	−0.656508	+	0.754319i	$0.727967\pi$
$198$	31.8460			0.160838
$199$	−29.9041	−	51.7954i	−0.150272	−	0.260278i	0.781056	−	0.624462i	$-0.214682\pi$
$199$	−29.9041	−	51.7954i	−0.150272	−	0.260278i	−0.931327	+	0.364183i	$0.881348\pi$
$200$			202.992i			1.01496i
$201$	−81.0927	+	83.0119i	−0.403446	+	0.412995i
$202$	57.3320			0.283822
$203$	151.622	−	87.5388i	0.746905	−	0.431226i
$204$		−	72.8146i		−	0.356935i
$205$	−20.2165	+	35.0160i	−0.0986169	+	0.170810i
$206$			44.9938i			0.218417i
$207$	2.10355	+	3.64345i	0.0101621	+	0.0176012i
$208$	−33.6058	−	19.4023i	−0.161566	−	0.0932804i
$209$		−	234.557i		−	1.12228i
$210$	−5.80129			−0.0276252
$211$	−59.5448	−	103.135i	−0.282203	−	0.488789i	0.689724	−	0.724072i	$-0.257732\pi$
$211$	−59.5448	−	103.135i	−0.282203	−	0.488789i	−0.971927	+	0.235283i	$0.924398\pi$
$212$	−51.2908	−	29.6128i	−0.241938	−	0.139683i
$213$	46.0732	+	26.6004i	0.216306	+	0.124884i
$214$	100.359	−	57.9424i	0.468968	−	0.270759i
$215$	−5.94020			−0.0276288
$216$	43.1607			0.199818
$217$	−31.8711	−	55.2024i	−0.146872	−	0.254389i
$218$	54.1068	+	93.7158i	0.248197	+	0.429889i
$219$	170.766	−	98.5918i	0.779753	−	0.450191i
$220$	6.58088	+	11.3984i	0.0299131	+	0.0518110i
$221$	−282.869	−	163.314i	−1.27995	−	0.738979i
$222$	14.5842	−	25.2605i	0.0656945	−	0.113786i
$223$	385.483			1.72862			0.864311	−	0.502958i	$-0.167755\pi$
$223$	385.483			1.72862			0.864311	+	0.502958i	$0.167755\pi$
$224$	−50.4822	−	87.4378i	−0.225367	−	0.390347i
$225$	−73.3151			−0.325845
$226$	−40.7253			−0.180201
$227$	−39.1804	+	67.8624i	−0.172601	+	0.298953i	−0.939328	−	0.343019i	$-0.888550\pi$
$227$	−39.1804	+	67.8624i	−0.172601	+	0.298953i	0.766728	+	0.641973i	$0.221884\pi$
$228$		−	113.203i		−	0.496503i
$229$	252.887	−	146.004i	1.10431	−	0.637573i	0.166959	−	0.985964i	$-0.446605\pi$
$229$	252.887	−	146.004i	1.10431	−	0.637573i	0.937349	+	0.348391i	$0.113272\pi$
$230$	0.702628	−	1.21699i	0.00305490	−	0.00529125i
$231$	39.8043	−	22.9810i	0.172313	−	0.0994850i
$232$	376.789	+	217.539i	1.62409	+	0.937669i
$233$	−350.026	−	202.087i	−1.50226	−	0.867328i	−0.999997	−	0.00261117i	$-0.999169\pi$
$233$	−350.026	−	202.087i	−1.50226	−	0.867328i	−0.502260	−	0.864717i	$-0.667498\pi$
$234$	34.4722	−	59.7075i	0.147317	−	0.255160i
$235$	21.8845	+	12.6350i	0.0931254	+	0.0537659i
$236$	−117.741	+	203.933i	−0.498902	+	0.864123i
$237$	−54.9541	+	95.1834i	−0.231874	+	0.401618i
$238$	42.4665	+	73.5542i	0.178431	+	0.309051i
$239$	−166.891	−	96.3547i	−0.698290	−	0.403158i	0.108420	−	0.994105i	$-0.465421\pi$
$239$	−166.891	−	96.3547i	−0.698290	−	0.403158i	−0.806710	+	0.590947i	$0.798754\pi$
$240$	−1.46531	−	2.53800i	−0.00610548	−	0.0105750i
$241$	40.9945			0.170102			0.0850509	−	0.996377i	$-0.472895\pi$
$241$	40.9945			0.170102			0.0850509	+	0.996377i	$0.472895\pi$
$242$	−67.1288	−	38.7568i	−0.277392	−	0.160152i
$243$			15.5885i			0.0641500i
$244$		−	152.960i		−	0.626885i
$245$	24.5511	−	14.1746i	0.100208	−	0.0578554i
$246$			124.949i			0.507921i
$247$	−439.768	−	253.900i	−1.78044	−	1.02794i
$248$	79.2016	−	137.181i	0.319361	−	0.553150i
$249$	26.3035	−	15.1863i	0.105636	−	0.0609892i
$250$	24.7701	+	42.9031i	0.0990804	+	0.171612i
$251$	357.532	−	206.421i	1.42443	−	0.822394i	0.427755	−	0.903895i	$-0.359305\pi$
$251$	357.532	−	206.421i	1.42443	−	0.822394i	0.996673	+	0.0815005i	$0.0259712\pi$
$252$	19.2105	−	11.0912i	0.0762321	−	0.0440126i
$253$			11.1335i			0.0440058i
$254$		−	327.572i		−	1.28965i
$255$	−12.3339	−	21.3630i	−0.0483684	−	0.0837765i
$256$	135.440	−	234.589i	0.529063	−	0.916365i
$257$	65.1802	−	112.895i	0.253619	−	0.439282i	−0.710900	−	0.703293i	$-0.751712\pi$
$257$	65.1802	−	112.895i	0.253619	−	0.439282i	0.964520	+	0.264011i	$0.0850456\pi$
$258$	−15.8975	+	9.17840i	−0.0616181	+	0.0355752i
$259$		−	42.0976i		−	0.162539i
$260$	28.4943			0.109593
$261$	−78.5691	+	136.086i	−0.301031	+	0.521401i
$262$	−96.4333	+	55.6758i	−0.368066	+	0.212503i
$263$	77.7386			0.295584			0.147792	−	0.989018i	$-0.452783\pi$
$263$	77.7386			0.295584			0.147792	+	0.989018i	$0.452783\pi$
$264$	98.9161	+	57.1093i	0.374682	+	0.216323i
$265$	−20.0642			−0.0757140
$266$	66.0214	+	114.352i	0.248201	+	0.429896i
$267$			213.866i			0.800996i
$268$	−142.706	+	40.0324i	−0.532485	+	0.149375i
$269$	106.717			0.396716			0.198358	−	0.980130i	$-0.436439\pi$
$269$	106.717			0.396716			0.198358	+	0.980130i	$0.436439\pi$
$270$	4.50927	−	2.60343i	0.0167010	−	0.00964233i
$271$		−	432.931i		−	1.59753i	−0.601642	−	0.798766i	$-0.705486\pi$
$271$		−	432.931i		−	1.59753i	0.601642	−	0.798766i	$-0.294514\pi$
$272$	−21.4527	+	37.1572i	−0.0788704	+	0.136608i
$273$		−	99.5047i		−	0.364486i
$274$	83.9126	+	145.341i	0.306250	+	0.530441i
$275$	−168.024	−	97.0087i	−0.610997	−	0.352759i
$276$			5.37326i			0.0194683i
$277$	−40.5417			−0.146360			−0.0731800	−	0.997319i	$-0.523315\pi$
$277$	−40.5417			−0.146360			−0.0731800	+	0.997319i	$0.523315\pi$
$278$	−6.79763	−	11.7738i	−0.0244519	−	0.0423520i
$279$	49.5460	+	28.6054i	0.177584	+	0.102528i
$280$	−18.0193	−	10.4034i	−0.0643545	−	0.0371551i
$281$	−45.2616	+	26.1318i	−0.161073	+	0.0929958i	−0.578370	−	0.815775i	$-0.696311\pi$
$281$	−45.2616	+	26.1318i	−0.161073	+	0.0929958i	0.417297	+	0.908770i	$0.362978\pi$
$282$	78.0910			0.276918
$283$	58.0454			0.205107			0.102554	−	0.994727i	$-0.467299\pi$
$283$	58.0454			0.205107			0.102554	+	0.994727i	$0.467299\pi$
$284$	33.9737	+	58.8442i	0.119626	+	0.207198i
$285$	−19.1752	−	33.2124i	−0.0672814	−	0.116535i
$286$	158.007	−	91.2254i	0.552472	−	0.318970i
$287$	90.1667	+	156.173i	0.314170	+	0.544158i
$288$	78.4784	+	45.3095i	0.272494	+	0.157325i
$289$	−36.0734	+	62.4810i	−0.124822	+	0.216197i
$290$	52.4873			0.180991
$291$	−119.499	−	206.979i	−0.410650	−	0.711267i
$292$	251.841			0.862469
$293$	−272.517			−0.930092			−0.465046	−	0.885287i	$-0.653962\pi$
$293$	−272.517			−0.930092			−0.465046	+	0.885287i	$0.653962\pi$
$294$	43.8032	−	75.8694i	0.148990	−	0.258059i
$295$			79.7756i			0.270426i
$296$	90.5992	−	52.3075i	0.306078	−	0.176714i
$297$	−20.6263	+	35.7257i	−0.0694487	+	0.120289i
$298$	−294.738	+	170.167i	−0.989053	+	0.571030i
$299$	20.8739	+	12.0516i	0.0698125	+	0.0403063i
$300$	−81.0923	−	46.8186i	−0.270308	−	0.156062i
$301$	−13.2468	+	22.9442i	−0.0440094	+	0.0762266i
$302$	207.127	+	119.585i	0.685850	+	0.395976i
$303$	−37.1332	+	64.3167i	−0.122552	+	0.212266i
$304$	−33.3519	+	57.7672i	−0.109710	+	0.190024i
$305$	−25.9096	−	44.8767i	−0.0849495	−	0.147137i
$306$	−66.0174	−	38.1152i	−0.215743	−	0.124559i
$307$	−53.7131	−	93.0339i	−0.174961	−	0.303042i	0.765187	−	0.643809i	$-0.222647\pi$
$307$	−53.7131	−	93.0339i	−0.174961	−	0.303042i	−0.940148	+	0.340767i	$0.889313\pi$
$308$	58.7023			0.190592
$309$	−50.4754	−	29.1420i	−0.163351	−	0.0943106i
$310$		−	19.1096i		−	0.0616438i
$311$			29.8473i			0.0959720i	0.998848	+	0.0479860i	$0.0152803\pi$
$311$			29.8473i			0.0959720i	−0.998848	+	0.0479860i	$0.984720\pi$
$312$	214.146	−	123.638i	0.686367	−	0.396274i
$313$			196.412i			0.627515i	0.949503	+	0.313758i	$0.101588\pi$
$313$			196.412i			0.627515i	−0.949503	+	0.313758i	$0.898412\pi$
$314$	218.258	+	126.011i	0.695089	+	0.401310i
$315$	3.75743	−	6.50806i	0.0119283	−	0.0206605i
$316$	−121.567	+	70.1869i	−0.384706	+	0.222110i
$317$	−154.847	−	268.202i	−0.488475	−	0.846064i	0.511437	−	0.859321i	$-0.329113\pi$
$317$	−154.847	−	268.202i	−0.488475	−	0.846064i	−0.999912	+	0.0132572i	$0.995780\pi$
$318$	−53.6968	+	31.0019i	−0.168858	+	0.0974902i
$319$	−360.131	+	207.921i	−1.12894	+	0.651791i
$320$		−	37.0366i		−	0.115739i
$321$			150.115i			0.467647i
$322$	−3.13376	−	5.42784i	−0.00973218	−	0.0168566i
$323$	−280.732	+	486.242i	−0.869140	+	1.50539i
$324$	−9.95471	+	17.2421i	−0.0307244	+	0.0532163i
$325$	−363.760	+	210.017i	−1.11926	+	0.646207i
$326$			392.791i			1.20488i
$327$	−140.177			−0.428677
$328$	−224.070	+	388.100i	−0.683139	+	1.18323i
$329$	97.6060	−	56.3529i	0.296675	−	0.171285i
$330$	13.7792			0.0417551
$331$	−35.4351	−	20.4585i	−0.107055	−	0.0618081i	0.445517	−	0.895274i	$-0.353020\pi$
$331$	−35.4351	−	20.4585i	−0.107055	−	0.0618081i	−0.552571	+	0.833466i	$0.686353\pi$
$332$	38.7916			0.116842
$333$	18.8920	+	32.7219i	0.0567327	+	0.0982640i
$334$		−	4.29455i		−	0.0128579i
$335$	−35.0873	+	35.9178i	−0.104738	+	0.107217i
$336$	−13.0708			−0.0389011
$337$	−163.228	+	94.2397i	−0.484356	+	0.279643i	−0.722230	−	0.691653i	$-0.756883\pi$
$337$	−163.228	+	94.2397i	−0.484356	+	0.279643i	0.237874	+	0.971296i	$0.423549\pi$
$338$		−	169.023i		−	0.500068i
$339$	26.3773	−	45.6869i	0.0778092	−	0.134769i
$340$		−	31.5056i		−	0.0926635i
$341$	75.7000	+	131.116i	0.221994	+	0.384505i
$342$	−102.635	−	59.2565i	−0.300103	−	0.173265i
$343$		−	290.221i		−	0.846125i
$344$	−65.8384			−0.191391
$345$	0.910167	+	1.57646i	0.00263817	+	0.00456944i
$346$	−180.150	−	104.010i	−0.520665	−	0.300606i
$347$	349.009	+	201.501i	1.00579	+	0.580693i	0.909956	−	0.414704i	$-0.136115\pi$
$347$	349.009	+	201.501i	1.00579	+	0.580693i	0.0958339	+	0.995397i	$0.469448\pi$
$348$	−173.807	+	100.348i	−0.499446	+	0.288355i
$349$	105.636			0.302681			0.151340	−	0.988482i	$-0.451641\pi$
$349$	105.636			0.302681			0.151340	+	0.988482i	$0.451641\pi$
$350$	109.221			0.312060
$351$	44.6544	+	77.3437i	0.127221	+	0.220353i
$352$	119.905	+	207.681i	0.340639	+	0.590004i
$353$	493.213	−	284.757i	1.39720	−	0.806676i	0.403106	−	0.915153i	$-0.367931\pi$
$353$	493.213	−	284.757i	1.39720	−	0.806676i	0.994099	+	0.108477i	$0.0345974\pi$
$354$	123.264	+	213.499i	0.348203	+	0.603105i
$355$	19.9350	+	11.5095i	0.0561550	+	0.0324211i
$356$	−136.574	+	236.553i	−0.383634	+	0.664473i
$357$	−110.020			−0.308180
$358$	−116.275	−	201.395i	−0.324791	−	0.562555i
$359$	389.073			1.08377			0.541885	−	0.840453i	$-0.317711\pi$
$359$	389.073			1.08377			0.541885	+	0.840453i	$0.317711\pi$
$360$	18.6749			0.0518746
$361$	−255.946	+	443.311i	−0.708991	+	1.22801i
$362$			300.831i			0.831025i
$363$	86.9571	−	50.2047i	0.239551	−	0.138305i
$364$	63.5432	−	110.060i	0.174569	−	0.302363i
$365$	73.8873	−	42.6589i	0.202431	−	0.116874i
$366$	−138.681	−	80.0676i	−0.378910	−	0.218764i
$367$	501.094	+	289.306i	1.36538	+	0.788301i	0.990334	−	0.138706i	$-0.0442943\pi$
$367$	501.094	+	289.306i	1.36538	+	0.788301i	0.375044	+	0.927007i	$0.377628\pi$
$368$	1.58308	−	2.74197i	0.00430184	−	0.00745101i
$369$	−140.171	−	80.9277i	−0.379867	−	0.219316i
$370$	6.31031	−	10.9298i	0.0170549	−	0.0295399i
$371$	−44.7438	+	77.4986i	−0.120603	+	0.208891i
$372$	36.5346	+	63.2797i	0.0982112	+	0.170107i
$373$	−368.547	−	212.781i	−0.988062	−	0.570458i	−0.0833673	−	0.996519i	$-0.526567\pi$
$373$	−368.547	−	212.781i	−0.988062	−	0.570458i	−0.904694	+	0.426061i	$0.859901\pi$
$374$	−100.866	−	174.705i	−0.269695	−	0.467126i
$375$	−64.1732			−0.171129
$376$	242.557	+	140.040i	0.645098	+	0.372448i
$377$			900.271i			2.38799i
$378$		−	23.2229i		−	0.0614363i
$379$	276.410	−	159.585i	0.729313	−	0.421069i	−0.0888578	−	0.996044i	$-0.528322\pi$
$379$	276.410	−	159.585i	0.729313	−	0.421069i	0.818171	+	0.574975i	$0.194988\pi$
$380$		−	48.9808i		−	0.128897i
$381$	367.480	+	212.165i	0.964514	+	0.556863i
$382$	−4.03710	+	6.99246i	−0.0105683	+	0.0183049i
$383$	42.5618	−	24.5731i	0.111127	−	0.0641594i	−0.443406	−	0.896321i	$-0.646230\pi$
$383$	42.5618	−	24.5731i	0.111127	−	0.0641594i	0.554534	+	0.832161i	$0.312897\pi$
$384$	47.4114	+	82.1190i	0.123467	+	0.213852i
$385$	17.2226	−	9.94348i	0.0447340	−	0.0258272i
$386$	−76.3334	+	44.0711i	−0.197755	+	0.114174i
$387$		−	23.7790i		−	0.0614444i
$388$		−	305.247i		−	0.786718i
$389$	−229.401	−	397.334i	−0.589720	−	1.02143i	−0.994269	−	0.106909i	$-0.965905\pi$
$389$	−229.401	−	397.334i	−0.589720	−	1.02143i	0.404549	−	0.914516i	$-0.367429\pi$
$390$	14.9155	−	25.8344i	0.0382448	−	0.0662420i
$391$	13.3252	−	23.0799i	0.0340798	−	0.0590279i
$392$	272.112	−	157.104i	0.694164	−	0.400776i
$393$		−	144.242i		−	0.367028i
$394$	−100.829			−0.255911
$395$	−23.7777	+	41.1841i	−0.0601966	+	0.104264i
$396$	−45.6286	+	26.3437i	−0.115224	+	0.0665244i
$397$	−455.350			−1.14698			−0.573489	−	0.819213i	$-0.694411\pi$
$397$	−455.350			−1.14698			−0.573489	+	0.819213i	$0.694411\pi$
$398$	−69.2558	−	39.9848i	−0.174009	−	0.100464i
$399$	−171.045			−0.428685
$400$	27.5875	+	47.7830i	0.0689688	+	0.119458i
$401$			501.993i			1.25185i	0.779882	+	0.625926i	$0.215279\pi$
$401$			501.993i			1.25185i	−0.779882	+	0.625926i	$0.784721\pi$
$402$	−38.4047	+	150.339i	−0.0955341	+	0.373979i
$403$	327.770			0.813326
$404$	−82.1446	+	47.4262i	−0.203328	+	0.117392i
$405$			6.74484i			0.0166539i
$406$	117.048	−	202.734i	0.288296	−	0.499344i
$407$			99.9898i			0.245675i
$408$	−136.703	−	236.777i	−0.335058	−	0.580337i
$409$	397.310	+	229.387i	0.971417	+	0.560848i	0.899668	−	0.436575i	$-0.143809\pi$
$409$	397.310	+	229.387i	0.971417	+	0.560848i	0.0717493	+	0.997423i	$0.477142\pi$
$410$			54.0630i			0.131861i
$411$	−217.397			−0.528946
$412$	−37.2199	−	64.4667i	−0.0903395	−	0.156473i
$413$	308.135	+	177.902i	0.746090	+	0.430756i
$414$	4.87167	+	2.81266i	0.0117673	+	0.00679386i
$415$	11.3810	−	6.57084i	0.0274242	−	0.0158334i
$416$	519.172			1.24801
$417$	17.6110			0.0422326
$418$	−156.813	−	271.609i	−0.375152	−	0.649782i
$419$	−94.8848	−	164.345i	−0.226455	−	0.392232i	0.730300	−	0.683127i	$-0.239380\pi$
$419$	−94.8848	−	164.345i	−0.226455	−	0.392232i	−0.956755	+	0.290895i	$0.906047\pi$
$420$	8.31203	−	4.79895i	0.0197905	−	0.0114261i
$421$	−239.293	−	414.468i	−0.568393	−	0.984485i	−0.996725	−	0.0808636i	$-0.974232\pi$
$421$	−239.293	−	414.468i	−0.568393	−	0.984485i	0.428333	−	0.903621i	$-0.359101\pi$
$422$	−137.901	−	79.6174i	−0.326781	−	0.188667i
$423$	−50.5786	+	87.6048i	−0.119571	+	0.207103i
$424$	−222.382			−0.524486
$425$	232.212	+	402.202i	0.546380	+	0.946358i
$426$	71.1348			0.166983
$427$	−231.117			−0.541257
$428$	−95.8624	+	166.039i	−0.223978	+	0.387941i
$429$			236.343i			0.550915i
$430$	−6.87854	+	3.97133i	−0.0159966	+	0.00923565i
$431$	270.066	−	467.769i	0.626604	−	1.08531i	−0.361624	−	0.932324i	$-0.617778\pi$
$431$	270.066	−	467.769i	0.626604	−	1.08531i	0.988228	−	0.152986i	$-0.0488890\pi$
$432$	10.1598	−	5.86574i	0.0235180	−	0.0135781i
$433$	2.19298	+	1.26612i	0.00506463	+	0.00292406i	0.502530	−	0.864560i	$-0.332403\pi$
$433$	2.19298	+	1.26612i	0.00506463	+	0.00292406i	−0.497466	+	0.867484i	$0.665736\pi$
$434$	−73.8112	−	42.6149i	−0.170072	−	0.0981911i
$435$	−33.9954	+	58.8818i	−0.0781504	+	0.135360i
$436$	−155.047	−	89.5166i	−0.355613	−	0.205313i
$437$	20.7163	−	35.8816i	0.0474056	−	0.0821090i
$438$	131.827	−	228.332i	0.300976	−	0.521305i
$439$	−305.526	−	529.187i	−0.695959	−	1.20544i	−0.969856	−	0.243678i	$-0.921646\pi$
$439$	−305.526	−	529.187i	−0.695959	−	1.20544i	0.273897	−	0.961759i	$-0.411687\pi$
$440$	42.7992	+	24.7101i	0.0972709	+	0.0561594i
$441$	56.7416	+	98.2794i	0.128666	+	0.222856i
$442$	−436.736			−0.988091
$443$	−15.1675	−	8.75698i	−0.0342382	−	0.0197674i	0.482783	−	0.875740i	$-0.339626\pi$
$443$	−15.1675	−	8.75698i	−0.0342382	−	0.0197674i	−0.517021	+	0.855972i	$0.672959\pi$
$444$			48.2574i			0.108688i
$445$			92.5359i			0.207946i
$446$	446.375	−	257.715i	1.00084	−	0.577836i
$447$		−	440.861i		−	0.986266i
$448$	−143.055	−	82.5927i	−0.319319	−	0.184359i
$449$	273.537	−	473.781i	0.609215	−	1.05519i	−0.382156	−	0.924098i	$-0.624818\pi$
$449$	273.537	−	473.781i	0.609215	−	1.05519i	0.991370	−	0.131093i	$-0.0418485\pi$
$450$	−84.8962	+	49.0149i	−0.188658	+	0.108922i
$451$	−214.163	−	370.942i	−0.474863	−	0.822487i
$452$	58.3508	−	33.6888i	0.129095	−	0.0745329i
$453$	−268.307	+	154.907i	−0.592290	+	0.341959i
$454$			104.776i			0.230785i
$455$		−	43.0539i		−	0.0946239i
$456$	−212.529	−	368.111i	−0.466072	−	0.807260i
$457$	−5.98037	+	10.3583i	−0.0130861	+	0.0226659i	−0.872494	−	0.488624i	$-0.837499\pi$
$457$	−5.98037	+	10.3583i	−0.0130861	+	0.0226659i	0.859408	+	0.511290i	$0.170832\pi$
$458$	195.223	−	338.135i	0.426250	−	0.738287i
$459$	85.5174	−	49.3735i	0.186312	−	0.107568i
$460$			2.32491i			0.00505416i
$461$	243.724			0.528685			0.264343	−	0.964429i	$-0.414845\pi$
$461$	243.724			0.528685			0.264343	+	0.964429i	$0.414845\pi$
$462$	30.7280	−	53.2224i	0.0665108	−	0.115200i
$463$	768.776	−	443.853i	1.66042	−	0.958646i	0.687912	−	0.725794i	$-0.258528\pi$
$463$	768.776	−	443.853i	1.66042	−	0.958646i	0.972512	−	0.232852i	$-0.0748057\pi$
$464$	118.258			0.254867
$465$	21.4377	+	12.3770i	0.0461025	+	0.0266173i
$466$	−540.423			−1.15971
$467$	111.954	+	193.909i	0.239729	+	0.415223i	0.960637	−	0.277808i	$-0.0896080\pi$
$467$	111.954	+	193.909i	0.239729	+	0.415223i	−0.720907	+	0.693031i	$0.756275\pi$
$468$			114.064i			0.243727i
$469$	60.4875	+	215.623i	0.128971	+	0.459751i
$470$	33.7886			0.0718906
$471$	−282.726	+	163.232i	−0.600268	+	0.346565i
$472$			884.194i			1.87329i
$473$	31.4638	−	54.4968i	0.0665196	−	0.115215i
$474$			146.959i			0.310039i
$475$	361.012	+	625.292i	0.760026	+	1.31640i
$476$	−121.691	−	70.2584i	−0.255654	−	0.147602i
$477$		−	80.3182i		−	0.168382i
$478$	−257.672			−0.539063
$479$	−217.428	−	376.596i	−0.453920	−	0.786212i	0.544706	−	0.838627i	$-0.316641\pi$
$479$	−217.428	−	376.596i	−0.453920	−	0.786212i	−0.998625	+	0.0524153i	$0.983308\pi$
$480$	33.9562	+	19.6046i	0.0707420	+	0.0408429i
$481$	187.469	+	108.235i	0.389749	+	0.225022i
$482$	47.4702	−	27.4069i	0.0984859	−	0.0568608i
$483$	8.11880			0.0168091
$484$	128.242			0.264963
$485$	−51.7052	−	89.5560i	−0.106609	−	0.184651i
$486$	10.4217	+	18.0509i	0.0214438	+	0.0371417i
$487$	−434.732	+	250.992i	−0.892673	+	0.515385i	−0.874816	−	0.484456i	$-0.839018\pi$
$487$	−434.732	+	250.992i	−0.892673	+	0.515385i	−0.0178571	+	0.999841i	$0.505684\pi$
$488$	−287.170	−	497.392i	−0.588462	−	1.01925i
$489$	−440.644	−	254.406i	−0.901112	−	0.520258i
$490$	18.9528	−	32.8273i	0.0386793	−	0.0669945i
$491$	444.272			0.904831			0.452416	−	0.891807i	$-0.350562\pi$
$491$	444.272			0.904831			0.452416	+	0.891807i	$0.350562\pi$
$492$	−103.360	−	179.025i	−0.210082	−	0.363872i
$493$	995.411			2.01909
$494$	−678.980			−1.37445
$495$	−8.92461	+	15.4579i	−0.0180295	+	0.0312280i
$496$		−	43.0554i		−	0.0868053i
$497$	88.9115	−	51.3331i	0.178896	−	0.103286i
$498$	20.3057	−	35.1704i	0.0407744	−	0.0706234i
$499$	−215.052	+	124.161i	−0.430967	+	0.248819i	−0.699758	−	0.714380i	$-0.746709\pi$
$499$	−215.052	+	124.161i	−0.430967	+	0.248819i	0.268792	+	0.963198i	$0.413376\pi$
$500$	−70.9807	−	40.9807i	−0.141961	−	0.0819614i
$501$	4.81775	+	2.78153i	0.00961626	+	0.00555195i
$502$	276.006	−	478.056i	0.549812	−	0.952303i
$503$	97.6328	+	56.3683i	0.194101	+	0.112064i	0.593901	−	0.804538i	$-0.297587\pi$
$503$	97.6328	+	56.3683i	0.194101	+	0.112064i	−0.399800	+	0.916602i	$0.630920\pi$
$504$	41.6455	−	72.1322i	0.0826300	−	0.143119i
$505$	−16.0669	+	27.8287i	−0.0318156	+	0.0551062i
$506$	7.44328	+	12.8921i	0.0147100	+	0.0254786i
$507$	189.615	+	109.474i	0.373994	+	0.215926i
$508$	270.975	+	469.342i	0.533414	+	0.923901i
$509$	−472.689			−0.928663			−0.464332	−	0.885661i	$-0.653705\pi$
$509$	−472.689			−0.928663			−0.464332	+	0.885661i	$0.653705\pi$
$510$	−28.5645	−	16.4917i	−0.0560089	−	0.0323367i
$511$		−	380.522i		−	0.744662i
$512$		−	143.211i		−	0.279709i
$513$	132.951	−	76.7595i	0.259164	−	0.149629i
$514$		−	174.305i		−	0.339115i
$515$	−21.8398	−	12.6092i	−0.0424074	−	0.0244839i
$516$	15.1851	−	26.3014i	0.0294286	−	0.0509718i
$517$	−231.833	+	133.849i	−0.448420	+	0.258895i
$518$	−28.1444	−	48.7475i	−0.0543328	−	0.0941071i
$519$	233.362	−	134.732i	0.449638	−	0.259598i
$520$	92.6573	−	53.4957i	0.178187	−	0.102876i
$521$		−	603.114i		−	1.15761i	−0.815467	−	0.578804i	$-0.803520\pi$
$521$		−	603.114i		−	1.15761i	0.815467	−	0.578804i	$-0.196480\pi$
$522$			210.110i			0.402509i
$523$	51.3046	+	88.8622i	0.0980968	+	0.169909i	0.910897	−	0.412634i	$-0.135391\pi$
$523$	51.3046	+	88.8622i	0.0980968	+	0.169909i	−0.812800	+	0.582543i	$0.802058\pi$
$524$	92.1123	−	159.543i	0.175787	−	0.304472i
$525$	−70.7413	+	122.527i	−0.134745	+	0.233386i
$526$	90.0186	−	51.9722i	0.171138	−	0.0988065i
$527$		−	362.409i		−	0.687683i
$528$	31.0456			0.0587985
$529$	263.517	−	456.424i	0.498141	−	0.862806i
$530$	−23.2336	+	13.4140i	−0.0438371	+	0.0253093i
$531$	−319.346			−0.601406
$532$	−189.190	−	109.229i	−0.355619	−	0.205317i
$533$	−927.297			−1.73977
$534$	142.980	+	247.649i	0.267753	+	0.463762i
$535$			64.9518i			0.121405i
$536$	−388.891	+	398.095i	−0.725543	+	0.742715i
$537$	301.241			0.560970
$538$	123.574	−	71.3456i	0.229692	−	0.132613i
$539$			300.317i			0.557174i
$540$	−4.30722	+	7.46033i	−0.00797634	+	0.0138154i
$541$		−	87.9836i		−	0.162631i	−0.996688	−	0.0813157i	$-0.974088\pi$
$541$		−	87.9836i		−	0.162631i	0.996688	−	0.0813157i	$-0.0259122\pi$
$542$	−289.437	−	501.319i	−0.534016	−	0.924943i
$543$	−337.481	−	194.845i	−0.621512	−	0.358830i
$544$		−	574.037i		−	1.05522i
$545$	−60.6523			−0.111289
$546$	−66.5239	−	115.223i	−0.121839	−	0.211031i
$547$	435.645	+	251.520i	0.796426	+	0.459817i	0.842220	−	0.539134i	$-0.181248\pi$
$547$	435.645	+	251.520i	0.796426	+	0.459817i	−0.0457937	+	0.998951i	$0.514582\pi$
$548$	−240.458	−	138.828i	−0.438792	−	0.253337i
$549$	179.644	−	103.718i	0.327221	−	0.188921i
$550$	−259.421			−0.471675
$551$	1547.54			2.80859
$552$	10.0879	+	17.4727i	0.0182751	+	0.0316534i
$553$	106.050	+	183.684i	0.191772	+	0.332159i
$554$	−46.9458	+	27.1042i	−0.0847398	+	0.0489245i
$555$	8.17423	+	14.1582i	0.0147283	+	0.0255102i
$556$	19.4791	+	11.2463i	0.0350344	+	0.0202271i
$557$	−368.479	+	638.224i	−0.661542	+	1.14582i	0.318669	+	0.947866i	$0.396764\pi$
$557$	−368.479	+	638.224i	−0.661542	+	1.14582i	−0.980210	+	0.197958i	$0.936569\pi$
$558$	76.4967			0.137091
$559$	−68.1169	−	117.982i	−0.121855	−	0.211059i
$560$	−5.65549			−0.0100991
$561$	261.319			0.465810
$562$	−34.9409	+	60.5194i	−0.0621724	+	0.107686i
$563$			990.075i			1.75857i	0.476295	+	0.879285i	$0.341979\pi$
$563$			990.075i			1.75857i	−0.476295	+	0.879285i	$0.658021\pi$
$564$	−111.888	+	64.5985i	−0.198383	+	0.114536i
$565$	11.4130	−	19.7679i	0.0202000	−	0.0349874i
$566$	67.2145	−	38.8063i	0.118754	−	0.0685624i
$567$	26.0521	+	15.0412i	0.0459473	+	0.0265277i
$568$	220.950	+	127.566i	0.388997	+	0.224588i
$569$	5.12815	−	8.88221i	0.00901256	−	0.0156102i	−0.861484	−	0.507785i	$-0.830465\pi$
$569$	5.12815	−	8.88221i	0.00901256	−	0.0156102i	0.870497	+	0.492175i	$0.163798\pi$
$570$	−44.4084	−	25.6392i	−0.0779095	−	0.0449811i
$571$	−368.978	+	639.088i	−0.646196	+	1.11924i	0.337828	+	0.941208i	$0.390308\pi$
$571$	−368.978	+	639.088i	−0.646196	+	1.11924i	−0.984024	+	0.178036i	$0.943026\pi$
$572$	−150.927	+	261.414i	−0.263859	+	0.457017i
$573$	−5.22956	−	9.05786i	−0.00912663	−	0.0158078i
$574$	208.820	+	120.562i	0.363797	+	0.210039i
$575$	−17.1358	−	29.6800i	−0.0298013	−	0.0516174i
$576$	148.260			0.257395
$577$	815.828	+	471.019i	1.41391	+	0.816324i	0.995754	−	0.0920499i	$-0.0293419\pi$
$577$	815.828	+	471.019i	1.41391	+	0.816324i	0.418160	+	0.908374i	$0.362675\pi$
$578$			96.4678i			0.166899i
$579$		−	114.177i		−	0.197198i
$580$	−75.2033	+	43.4186i	−0.129661	+	0.0748597i
$581$		−	58.6127i		−	0.100883i
$582$	−276.752	−	159.783i	−0.475519	−	0.274541i
$583$	106.275	−	184.074i	0.182290	−	0.315736i
$584$	818.932	−	472.811i	1.40228	−	0.809607i
$585$	19.3212	+	33.4652i	0.0330276	+	0.0572055i
$586$	−315.565	+	182.191i	−0.538507	+	0.310907i
$587$	155.038	−	89.5112i	0.264119	−	0.152489i	−0.362093	−	0.932142i	$-0.617938\pi$
$587$	155.038	−	89.5112i	0.264119	−	0.152489i	0.626212	+	0.779653i	$0.284604\pi$
$588$			144.940i			0.246496i
$589$		−	563.426i		−	0.956581i
$590$	53.3341	+	92.3773i	0.0903967	+	0.156572i
$591$	65.3058	−	113.113i	0.110501	−	0.191392i
$592$	14.2176	−	24.6257i	0.0240163	−	0.0415974i
$593$	−560.565	+	323.643i	−0.945304	+	0.545772i	−0.891619	−	0.452786i	$-0.850430\pi$
$593$	−560.565	+	323.643i	−0.945304	+	0.545772i	−0.0536852	+	0.998558i	$0.517097\pi$
$594$			55.1589i			0.0928600i
$595$	−47.6038			−0.0800063
$596$	281.532	−	487.627i	0.472368	−	0.818166i
$597$	89.7123	−	51.7954i	0.150272	−	0.0867595i
$598$	32.2284			0.0538936
$599$	−621.502	−	358.825i	−1.03757	−	0.599039i	−0.118423	−	0.992963i	$-0.537784\pi$
$599$	−621.502	−	358.825i	−1.03757	−	0.599039i	−0.919143	+	0.393924i	$0.871117\pi$
$600$	−351.593			−0.585988
$601$	189.953	+	329.008i	0.316062	+	0.547435i	0.979663	−	0.200652i	$-0.0643060\pi$
$601$	189.953	+	329.008i	0.316062	+	0.547435i	−0.663601	+	0.748087i	$0.730973\pi$
$602$			35.4247i			0.0588451i
$603$	−143.781	−	140.457i	−0.238443	−	0.232930i
$604$	−395.692			−0.655119
$605$	37.6248	−	21.7227i	0.0621897	−	0.0359052i
$606$			99.3019i			0.163864i
$607$	−425.972	+	737.805i	−0.701766	+	1.21549i	0.266080	+	0.963951i	$0.414271\pi$
$607$	−425.972	+	737.805i	−0.701766	+	1.21549i	−0.967846	+	0.251543i	$0.919062\pi$
$608$		−	892.439i		−	1.46783i
$609$	151.622	+	262.616i	0.248968	+	0.431226i
$610$	−60.0048	−	34.6438i	−0.0983685	−	0.0567931i
$611$			579.547i			0.948522i
$612$	126.119			0.206076
$613$	−274.090	−	474.737i	−0.447129	−	0.774449i	0.551069	−	0.834460i	$-0.314220\pi$
$613$	−274.090	−	474.737i	−0.447129	−	0.774449i	−0.998198	+	0.0600101i	$0.980887\pi$
$614$	−124.396	−	71.8199i	−0.202599	−	0.116971i
$615$	−60.6494	−	35.0160i	−0.0986169	−	0.0569365i
$616$	190.887	−	110.209i	0.309882	−	0.178910i
$617$	−514.979			−0.834649			−0.417325	−	0.908757i	$-0.637032\pi$
$617$	−514.979			−0.834649			−0.417325	+	0.908757i	$0.637032\pi$
$618$	−77.9316			−0.126103
$619$	−182.410	−	315.944i	−0.294686	−	0.510410i	0.680226	−	0.733002i	$-0.261882\pi$
$619$	−182.410	−	315.944i	−0.294686	−	0.510410i	−0.974912	+	0.222592i	$0.928548\pi$
$620$	15.8078	+	27.3800i	0.0254965	+	0.0441613i
$621$	−6.31065	+	3.64345i	−0.0101621	+	0.00586707i
$622$	19.9544	+	34.5621i	0.0320811	+	0.0555661i
$623$	357.422	+	206.358i	0.573712	+	0.331233i
$624$	33.6058	−	58.2069i	0.0538554	−	0.0932804i
$625$	583.192			0.933108
$626$	131.312	+	227.438i	0.209763	+	0.363320i
$627$	406.265			0.647951
$628$	−416.957			−0.663944
$629$	119.674	−	207.281i	0.190260	−	0.329540i
$630$		−	10.0481i		−	0.0159494i
$631$	469.621	−	271.136i	0.744248	−	0.429692i	−0.0793637	−	0.996846i	$-0.525289\pi$
$631$	469.621	−	271.136i	0.744248	−	0.429692i	0.823612	+	0.567154i	$0.191956\pi$
$632$	−263.540	+	456.465i	−0.416994	+	0.722255i
$633$	178.634	−	103.135i	0.282203	−	0.162930i
$634$	−358.614	−	207.046i	−0.565637	−	0.326570i
$635$	159.002	+	91.7998i	0.250397	+	0.144567i
$636$	51.2908	−	88.8383i	0.0806460	−	0.139683i
$637$	563.059	+	325.082i	0.883923	+	0.510333i
$638$	−278.012	+	481.531i	−0.435756	+	0.754751i
$639$	−46.0732	+	79.8011i	−0.0721020	+	0.124884i
$640$	20.5141	+	35.5314i	0.0320532	+	0.0555178i
$641$	−491.604	−	283.828i	−0.766933	−	0.442789i	0.0648466	−	0.997895i	$-0.479344\pi$
$641$	−491.604	−	283.828i	−0.766933	−	0.442789i	−0.831779	+	0.555106i	$0.812678\pi$
$642$	100.359	+	173.827i	0.156323	+	0.270759i
$643$	646.459			1.00538			0.502689	−	0.864467i	$-0.332344\pi$
$643$	646.459			1.00538			0.502689	+	0.864467i	$0.332344\pi$
$644$	8.98004	+	5.18463i	0.0139442	+	0.00805067i
$645$		−	10.2887i		−	0.0159515i
$646$			750.735i			1.16213i
$647$	−152.282	+	87.9201i	−0.235366	+	0.135889i	−0.613045	−	0.790048i	$-0.710056\pi$
$647$	−152.282	+	87.9201i	−0.235366	+	0.135889i	0.377679	+	0.925937i	$0.376722\pi$
$648$			74.7566i			0.115365i
$649$	−731.880	−	422.551i	−1.12770	−	0.651081i
$650$	−280.814	+	486.385i	−0.432022	+	0.748284i
$651$	95.6134	−	55.2024i	0.146872	−	0.0847963i
$652$	−324.925	−	562.786i	−0.498351	−	0.863169i
$653$	−661.773	+	382.075i	−1.01344	+	0.585107i	−0.912196	−	0.409755i	$-0.865614\pi$
$653$	−661.773	+	382.075i	−1.01344	+	0.585107i	−0.101239	+	0.994862i	$0.532281\pi$
$654$	−162.321	+	93.7158i	−0.248197	+	0.143296i
$655$		−	62.4110i		−	0.0952839i
$656$			121.808i			0.185683i
$657$	170.766	+	295.775i	0.259918	+	0.450191i
$658$	75.3495	−	130.509i	0.114513	−	0.198342i
$659$	−626.656	+	1085.40i	−0.950920	+	1.64704i	−0.207479	+	0.978239i	$0.566526\pi$
$659$	−626.656	+	1085.40i	−0.950920	+	1.64704i	−0.743441	+	0.668802i	$0.766808\pi$
$660$	−19.7427	+	11.3984i	−0.0299131	+	0.0172703i
$661$		−	682.964i		−	1.03323i	−0.856218	−	0.516614i	$-0.827192\pi$
$661$		−	682.964i		−	1.03323i	0.856218	−	0.516614i	$-0.172808\pi$
$662$	−54.7101			−0.0826437
$663$	282.869	−	489.943i	0.426650	−	0.738979i
$664$	126.142	−	72.8281i	0.189973	−	0.109681i
$665$	−74.0081			−0.111290
$666$	43.7525	+	25.2605i	0.0656945	+	0.0379287i
$667$	−73.4551			−0.110128
$668$	3.55254	+	6.15318i	0.00531817	+	0.00921134i
$669$			667.675i			0.998020i
$670$	−16.6170	+	65.0491i	−0.0248015	+	0.0970883i
$671$	548.947			0.818102
$672$	151.447	−	87.4378i	0.225367	−	0.130116i
$673$			687.524i			1.02158i	0.859705	+	0.510790i	$0.170647\pi$
$673$			687.524i			1.02158i	−0.859705	+	0.510790i	$0.829353\pi$
$674$	−126.008	+	218.252i	−0.186956	+	0.323817i
$675$		−	126.985i		−	0.188127i
$676$	139.820	+	242.174i	0.206834	+	0.358246i
$677$	−236.910	−	136.780i	−0.349942	−	0.202039i	0.314718	−	0.949185i	$-0.398090\pi$
$677$	−236.910	−	136.780i	−0.349942	−	0.202039i	−0.664660	+	0.747146i	$0.731423\pi$
$678$		−	70.5383i		−	0.104039i
$679$	−461.216			−0.679258
$680$	−59.1491	−	102.449i	−0.0869840	−	0.150661i
$681$	−117.541	−	67.8624i	−0.172601	−	0.0996512i
$682$	175.316	+	101.219i	0.257061	+	0.148414i
$683$	−572.294	+	330.414i	−0.837912	+	0.483769i	−0.856554	−	0.516057i	$-0.827399\pi$
$683$	−572.294	+	330.414i	−0.837912	+	0.483769i	0.0186416	+	0.999826i	$0.494066\pi$
$684$	196.073			0.286656
$685$	−94.0636			−0.137319
$686$	−194.028	−	336.066i	−0.282839	−	0.489891i
$687$	252.887	+	438.013i	0.368103	+	0.637573i
$688$	−15.4979	+	8.94773i	−0.0225261	+	0.0130054i
$689$	−230.078	−	398.507i	−0.333931	−	0.578385i
$690$	2.10788	+	1.21699i	0.00305490	+	0.00176375i
$691$	−3.00190	+	5.19944i	−0.00434428	+	0.00752451i	−0.868189	−	0.496233i	$-0.834716\pi$
$691$	−3.00190	+	5.19944i	−0.00434428	+	0.00752451i	0.863845	+	0.503758i	$0.168049\pi$
$692$	344.156			0.497335
$693$	39.8043	+	68.9431i	0.0574377	+	0.0994850i
$694$	538.854			0.776446
$695$	7.61995			0.0109640
$696$	−376.789	+	652.618i	−0.541364	+	0.937669i
$697$			1025.29i			1.47101i
$698$	122.322	−	70.6228i	0.175247	−	0.101179i
$699$	350.026	−	606.262i	0.500752	−	0.867328i
$700$	−156.491	+	90.3500i	−0.223558	+	0.129071i
$701$	3.82698	+	2.20951i	0.00545932	+	0.00315194i	0.502727	−	0.864445i	$-0.332330\pi$
$701$	3.82698	+	2.20951i	0.00545932	+	0.00315194i	−0.497268	+	0.867597i	$0.665663\pi$
$702$	103.416	+	59.7075i	0.147317	+	0.0850535i
$703$	186.053	−	322.253i	0.264656	−	0.458397i
$704$	339.782	+	196.174i	0.482646	+	0.278656i
$705$	−21.8845	+	37.9050i	−0.0310418	+	0.0537659i
$706$	380.749	−	659.476i	0.539304	−	0.934103i
$707$	71.6593	+	124.118i	0.101357	+	0.175555i
$708$	−353.222	−	203.933i	−0.498902	−	0.288041i
$709$	120.464	+	208.650i	0.169907	+	0.294288i	0.938387	−	0.345586i	$-0.112320\pi$
$709$	120.464	+	208.650i	0.169907	+	0.294288i	−0.768480	+	0.639874i	$0.778987\pi$
$710$	30.7787			0.0433504
$711$	−164.862	−	95.1834i	−0.231874	−	0.133873i
$712$			1025.62i			1.44048i
$713$			26.7435i			0.0375084i
$714$	−127.400	+	73.5542i	−0.178431	+	0.103017i
$715$			102.261i			0.143023i
$716$	333.196	+	192.371i	0.465358	+	0.268674i
$717$	166.891	−	289.064i	0.232763	−	0.403158i
$718$	450.533	−	260.115i	0.627483	−	0.362278i
$719$	−468.951	−	812.247i	−0.652226	−	1.12969i	−0.982581	−	0.185832i	$-0.940502\pi$
$719$	−468.951	−	812.247i	−0.652226	−	1.12969i	0.330355	−	0.943857i	$-0.392832\pi$
$720$	4.39594	−	2.53800i	0.00610548	−	0.00352500i
$721$	−97.4068	+	56.2378i	−0.135100	+	0.0779998i
$722$			684.451i			0.947993i
$723$			71.0046i			0.0982083i
$724$	−248.854	−	431.027i	−0.343721	−	0.595341i
$725$	640.033	−	1108.57i	0.882805	−	1.52906i
$726$	67.1288	−	116.271i	0.0924640	−	0.160152i
$727$	357.572	−	206.444i	0.491846	−	0.283967i	−0.233494	−	0.972358i	$-0.575016\pi$
$727$	357.572	−	206.444i	0.491846	−	0.283967i	0.725340	+	0.688391i	$0.241683\pi$
$728$		−	477.188i		−	0.655479i
$729$	−27.0000			−0.0370370
$730$	57.0393	−	98.7949i	0.0781360	−	0.135335i
$731$	−130.450	+	75.3154i	−0.178454	+	0.103031i
$732$	264.934			0.361932
$733$	839.643	+	484.768i	1.14549	+	0.661348i	0.947784	−	0.318914i	$-0.103318\pi$
$733$	839.643	+	484.768i	1.14549	+	0.661348i	0.197704	+	0.980262i	$0.436651\pi$
$734$	773.665			1.05404
$735$	24.5511	+	42.5237i	0.0334028	+	0.0578554i
$736$			42.3604i			0.0575548i
$737$	−143.669	−	512.147i	−0.194938	−	0.694908i
$738$	−216.417			−0.293248
$739$	−337.258	+	194.716i	−0.456371	+	0.263486i	−0.710517	−	0.703680i	$-0.751539\pi$
$739$	−337.258	+	194.716i	−0.456371	+	0.263486i	0.254146	+	0.967166i	$0.418206\pi$
$740$			20.8801i			0.0282163i
$741$	439.768	−	761.700i	0.593479	−	1.02794i
$742$			119.654i			0.161259i
$743$	305.670	+	529.436i	0.411400	+	0.712565i	0.995043	−	0.0994451i	$-0.0317068\pi$
$743$	305.670	+	529.436i	0.411400	+	0.712565i	−0.583643	+	0.812010i	$0.698373\pi$
$744$	237.605	+	137.181i	0.319361	+	0.184383i
$745$		−	190.752i		−	0.256044i
$746$	−569.019			−0.762760
$747$	26.3035	+	45.5590i	0.0352122	+	0.0609892i
$748$	289.040	+	166.877i	0.386417	+	0.223098i
$749$	250.878	+	144.845i	0.334951	+	0.193384i
$750$	−74.3103	+	42.9031i	−0.0990804	+	0.0572041i
$751$	−1071.43			−1.42667			−0.713337	−	0.700822i	$-0.752817\pi$
$751$	−1071.43			−1.42667			−0.713337	+	0.700822i	$0.752817\pi$
$752$	76.1284			0.101235
$753$	357.532	+	619.263i	0.474809	+	0.822394i
$754$	601.877	+	1042.48i	0.798245	+	1.38260i
$755$	−116.092	+	67.0256i	−0.153764	+	0.0887756i
$756$	19.2105	+	33.2735i	0.0254107	+	0.0440126i
$757$	−296.300	−	171.069i	−0.391414	−	0.225983i	0.291359	−	0.956614i	$-0.405893\pi$
$757$	−296.300	−	171.069i	−0.391414	−	0.225983i	−0.682773	+	0.730631i	$0.739226\pi$
$758$	213.382	−	369.588i	0.281506	−	0.487583i
$759$	−19.2837			−0.0254067
$760$	−91.9573	−	159.275i	−0.120997	−	0.209572i
$761$	521.352			0.685088			0.342544	−	0.939502i	$-0.388711\pi$
$761$	521.352			0.685088			0.342544	+	0.939502i	$0.388711\pi$
$762$	567.372			0.744582
$763$	−135.256	+	234.271i	−0.177269	+	0.307039i
$764$		−	13.3583i		−	0.0174847i
$765$	37.0018	−	21.3630i	0.0483684	−	0.0279255i
$766$	32.8567	−	56.9094i	0.0428938	−	0.0742943i
$767$	−1584.47	+	914.794i	−2.06580	+	1.19269i
$768$	406.321	+	234.589i	0.529063	+	0.305455i
$769$	−988.345	−	570.621i	−1.28523	−	0.742030i	−0.307434	−	0.951569i	$-0.599470\pi$
$769$	−988.345	−	570.621i	−1.28523	−	0.742030i	−0.977800	+	0.209539i	$0.932804\pi$
$770$	13.2954	−	23.0284i	0.0172668	−	0.0299070i
$771$	195.541	+	112.895i	0.253619	+	0.146427i
$772$	72.9131	−	126.289i	0.0944470	−	0.163587i
$773$	632.585	−	1095.67i	0.818351	−	1.41742i	−0.0885463	−	0.996072i	$-0.528222\pi$
$773$	632.585	−	1095.67i	0.818351	−	1.41742i	0.906897	−	0.421353i	$-0.138445\pi$
$774$	−15.8975	−	27.5352i	−0.0205394	−	0.0355752i
$775$	−403.608	−	233.023i	−0.520785	−	0.300675i
$776$	−573.075	−	992.595i	−0.738499	−	1.27912i
$777$	72.9151			0.0938418
$778$	−531.277	−	306.733i	−0.682875	−	0.394258i
$779$			1593.99i			2.04620i
$780$			49.3536i			0.0632738i
$781$	−211.182	+	121.926i	−0.270399	+	0.156115i
$782$		−	35.6343i		−	0.0455681i
$783$	−235.707	−	136.086i	−0.301031	−	0.173800i
$784$	42.7023	−	73.9626i	0.0544672	−	0.0943400i
$785$	−122.331	+	70.6276i	−0.155835	+	0.0899714i
$786$	−96.4333	−	167.027i	−0.122689	−	0.212503i
$787$	115.733	−	66.8187i	0.147056	−	0.0849031i	−0.424666	−	0.905350i	$-0.639609\pi$
$787$	115.733	−	66.8187i	0.147056	−	0.0849031i	0.571723	+	0.820447i	$0.306275\pi$
$788$	144.467	−	83.4079i	0.183333	−	0.105848i
$789$			134.647i			0.170656i
$790$			63.5863i			0.0804890i
$791$	−50.9026	−	88.1659i	−0.0643522	−	0.111461i
$792$	−98.9161	+	171.328i	−0.124894	+	0.216323i
$793$	594.216	−	1029.21i	0.749326	−	1.29787i
$794$	−527.280	+	304.425i	−0.664080	+	0.383407i
$795$		−	34.7522i		−	0.0437135i
$796$	132.305			0.166213
$797$	−664.531	+	1151.00i	−0.833791	+	1.44417i	0.0612199	+	0.998124i	$0.480501\pi$
$797$	−664.531	+	1151.00i	−0.833791	+	1.44417i	−0.895011	+	0.446044i	$0.852832\pi$
$798$	−198.064	+	114.352i	−0.248201	+	0.143299i
$799$	640.793			0.801994
$800$	−639.294	−	369.097i	−0.799118	−	0.461371i
$801$	−370.427			−0.462455
$802$	335.608	+	581.290i	0.418464	+	0.724800i
$803$			903.814i			1.12555i
$804$	−69.3381	−	247.174i	−0.0862414	−	0.307430i
$805$	3.51286			0.00436380
$806$	379.546	−	219.131i	0.470901	−	0.271875i
$807$			184.839i			0.229044i
$808$	−178.078	+	308.440i	−0.220393	+	0.381732i
$809$		−	56.6686i		−	0.0700477i	−0.999386	−	0.0350238i	$-0.988849\pi$
$809$		−	56.6686i		−	0.0700477i	0.999386	−	0.0350238i	$-0.0111507\pi$
$810$	4.50927	+	7.81029i	0.00556700	+	0.00964233i
$811$	−937.868	−	541.479i	−1.15643	−	0.667668i	−0.205988	−	0.978555i	$-0.566041\pi$
$811$	−937.868	−	541.479i	−1.15643	−	0.667668i	−0.950447	+	0.310887i	$0.899374\pi$
$812$			387.299i			0.476970i
$813$	749.859			0.922336
$814$	66.8483	+	115.785i	0.0821232	+	0.142242i
$815$	−190.659	−	110.077i	−0.233937	−	0.135064i
$816$	−64.3582	−	37.1572i	−0.0788704	−	0.0455358i
$817$	−202.807	+	117.091i	−0.248234	+	0.143318i
$818$	613.427			0.749911
$819$	172.347			0.210436
$820$	−44.7220	−	77.4608i	−0.0545391	−	0.0944644i
$821$	637.082	+	1103.46i	0.775983	+	1.34404i	0.934240	+	0.356645i	$0.116079\pi$
$821$	637.082	+	1103.46i	0.775983	+	1.34404i	−0.158257	+	0.987398i	$0.550587\pi$
$822$	−251.738	+	145.341i	−0.306250	+	0.176814i
$823$	27.2783	+	47.2475i	0.0331450	+	0.0574088i	0.882122	−	0.471021i	$-0.156114\pi$
$823$	27.2783	+	47.2475i	0.0331450	+	0.0574088i	−0.848977	+	0.528430i	$0.822781\pi$
$824$	−242.062	−	139.754i	−0.293764	−	0.169605i
$825$	168.024	−	291.026i	0.203666	−	0.352759i
$826$	475.746			0.575964
$827$	−780.560	−	1351.97i	−0.943845	−	1.63479i	−0.758047	−	0.652200i	$-0.773846\pi$
$827$	−780.560	−	1351.97i	−0.943845	−	1.63479i	−0.185799	−	0.982588i	$-0.559487\pi$
$828$	−9.30676			−0.0112401
$829$	176.954			0.213455			0.106728	−	0.994288i	$-0.465963\pi$
$829$	176.954			0.213455			0.106728	+	0.994288i	$0.465963\pi$
$830$	8.78589	−	15.2176i	0.0105854	−	0.0183345i
$831$		−	70.2203i		−	0.0845010i
$832$	735.605	−	424.702i	0.884141	−	0.510459i
$833$	359.437	−	622.563i	0.431497	−	0.747374i
$834$	20.3929	−	11.7738i	0.0244519	−	0.0141173i
$835$	2.08455	+	1.20352i	0.00249647	+	0.00144134i
$836$	449.361	+	259.439i	0.537514	+	0.310334i
$837$	−49.5460	+	85.8163i	−0.0591948	+	0.102528i
$838$	−219.747	−	126.871i	−0.262227	−	0.151397i
$839$	19.9173	−	34.4978i	0.0237393	−	0.0411177i	−0.853912	−	0.520418i	$-0.825776\pi$
$839$	19.9173	−	34.4978i	0.0237393	−	0.0411177i	0.877651	+	0.479300i	$0.159109\pi$
$840$	18.0193	−	31.2103i	0.0214515	−	0.0371551i
$841$	−951.301	−	1647.70i	−1.13115	−	1.95922i
$842$	−554.186	−	319.960i	−0.658178	−	0.379999i
$843$	−45.2616	−	78.3954i	−0.0536911	−	0.0929958i
$844$	263.445			0.312138
$845$	82.0430	+	47.3675i	0.0970923	+	0.0560563i
$846$			135.258i			0.159879i
$847$		−	193.769i		−	0.228771i
$848$	−52.3473	+	30.2227i	−0.0617303	+	0.0356400i
$849$			100.538i			0.118419i
$850$	537.786	+	310.491i	0.632689	+	0.365283i
$851$	−8.83117	+	15.2960i	−0.0103774	+	0.0179742i
$852$	−101.921	+	58.8442i	−0.119626	+	0.0690660i
$853$	543.536	+	941.432i	0.637205	+	1.10367i	0.986043	+	0.166489i	$0.0532430\pi$
$853$	543.536	+	941.432i	0.637205	+	1.10367i	−0.348838	+	0.937183i	$0.613424\pi$
$854$	−267.625	+	154.513i	−0.313378	+	0.180929i
$855$	57.5256	−	33.2124i	0.0672814	−	0.0388449i
$856$			719.895i			0.840999i
$857$		−	1157.70i		−	1.35088i	−0.737416	−	0.675439i	$-0.763954\pi$
$857$		−	1157.70i		−	1.35088i	0.737416	−	0.675439i	$-0.236046\pi$
$858$	158.007	+	273.676i	0.184157	+	0.318970i
$859$	−483.385	+	837.248i	−0.562730	+	0.974677i	0.434527	+	0.900659i	$0.356916\pi$
$859$	−483.385	+	837.248i	−0.562730	+	0.974677i	−0.997257	+	0.0740184i	$0.976418\pi$
$860$	6.57033	−	11.3802i	0.00763992	−	0.0132327i
$861$	−270.500	+	156.173i	−0.314170	+	0.181386i
$862$		−	722.213i		−	0.837834i
$863$	−522.881			−0.605888			−0.302944	−	0.953008i	$-0.597969\pi$
$863$	−522.881			−0.605888			−0.302944	+	0.953008i	$0.597969\pi$
$864$	−78.4784	+	135.929i	−0.0908315	+	0.157325i
$865$	100.972	−	58.2959i	0.116730	−	0.0673941i
$866$	3.38586			0.00390977
$867$	−108.220	−	62.4810i	−0.124822	−	0.0720658i
$868$	141.008			0.162451
$869$	−251.889	−	436.284i	−0.289860	−	0.502053i
$870$			90.9107i			0.104495i
$871$	−1115.73	−	285.018i	−1.28098	−	0.327231i
$872$	−672.241			−0.770918
$873$	358.498	−	206.979i	0.410650	−	0.237089i
$874$		−	55.3995i		−	0.0633862i
$875$	−61.9204	+	107.249i	−0.0707661	+	0.122571i
$876$			436.201i			0.497947i
$877$	−669.229	−	1159.14i	−0.763089	−	1.32171i	−0.941251	−	0.337708i	$-0.890348\pi$
$877$	−669.229	−	1159.14i	−0.763089	−	1.32171i	0.178162	−	0.984001i	$-0.442985\pi$
$878$	−707.577	−	408.520i	−0.805896	−	0.465284i
$879$		−	472.013i		−	0.536989i
$880$	13.4329			0.0152646
$881$	−808.604	−	1400.54i	−0.917825	−	1.58972i	−0.802712	−	0.596367i	$-0.796610\pi$
$881$	−808.604	−	1400.54i	−0.917825	−	1.58972i	−0.115113	−	0.993352i	$-0.536723\pi$
$882$	131.410	+	75.8694i	0.148990	+	0.0860197i
$883$	−263.183	−	151.949i	−0.298055	−	0.172082i	0.343514	−	0.939148i	$-0.388383\pi$
$883$	−263.183	−	151.949i	−0.298055	−	0.172082i	−0.641569	+	0.767065i	$0.721716\pi$
$884$	625.751	−	361.277i	0.707863	−	0.408685i
$885$	−138.175			−0.156130
$886$	−23.4179			−0.0264311
$887$	214.806	+	372.055i	0.242172	+	0.419454i	0.961333	−	0.275390i	$-0.0888070\pi$
$887$	214.806	+	372.055i	0.242172	+	0.419454i	−0.719161	+	0.694843i	$0.755474\pi$
$888$	90.5992	+	156.922i	0.102026	+	0.176714i
$889$	709.158	−	409.433i	0.797703	−	0.460554i
$890$	61.8650	+	107.153i	0.0695112	+	0.120397i
$891$	−61.8788	−	35.7257i	−0.0694487	−	0.0400962i
$892$	−426.374	+	738.502i	−0.477998	+	0.827917i
$893$	996.222			1.11559
$894$	−294.738	−	510.501i	−0.329684	−	0.571030i
$895$	130.341			0.145633
$896$	182.988			0.204228
$897$	−20.8739	+	36.1547i	−0.0232708	+	0.0403063i
$898$		−	731.495i		−	0.814582i
$899$	−865.064	+	499.445i	−0.962251	+	0.555556i
$900$	81.0923	−	140.456i	0.0901025	−	0.156062i
$901$	−440.621	+	254.393i	−0.489036	+	0.282345i
$902$	−495.987	−	286.358i	−0.549874	−	0.317470i
$903$	−39.7405	−	22.9442i	−0.0440094	−	0.0254089i
$904$	126.496	−	219.098i	0.139929	−	0.242365i
$905$	−146.022	−	84.3057i	−0.161350	−	0.0931555i
$906$	−207.127	+	358.754i	−0.228617	+	0.395976i
$907$	464.858	−	805.158i	0.512523	−	0.887716i	−0.487372	−	0.873195i	$-0.662044\pi$
$907$	464.858	−	805.158i	0.512523	−	0.887716i	0.999895	−	0.0145209i	$-0.00462232\pi$
$908$	−86.6732	−	150.122i	−0.0954551	−	0.165333i
$909$	−111.400	−	64.3167i	−0.122552	−	0.0707554i
$910$	−28.7837	−	49.8548i	−0.0316304	−	0.0547855i
$911$	1727.28			1.89602			0.948012	−	0.318234i	$-0.103090\pi$
$911$	1727.28			1.89602			0.948012	+	0.318234i	$0.103090\pi$
$912$	−100.056	−	57.7672i	−0.109710	−	0.0633413i
$913$			139.216i			0.152482i
$914$			15.9927i			0.0174975i
$915$	77.7288	−	44.8767i	0.0849495	−	0.0490456i
$916$			645.969i			0.705206i
$917$	−241.064	−	139.178i	−0.262883	−	0.151776i
$918$	66.0174	−	114.345i	0.0719144	−	0.124559i
$919$	1152.60	−	665.454i	1.25419	−	0.724107i	0.282251	−	0.959341i	$-0.408919\pi$
$919$	1152.60	−	665.454i	1.25419	−	0.724107i	0.971939	+	0.235234i	$0.0755855\pi$
$920$	4.36483	+	7.56011i	0.00474438	+	0.00821751i
$921$	161.139	−	93.0339i	0.174961	−	0.101014i
$922$	282.224	−	162.942i	0.306099	−	0.176727i
$923$			527.922i			0.571963i
$924$			101.675i			0.110038i
$925$	−153.897	−	266.557i	−0.166375	−	0.288169i
$926$	593.477	−	1027.93i	0.640904	−	1.11008i
$927$	50.4754	−	87.4260i	0.0544503	−	0.0943106i
$928$	−1370.22	+	791.095i	−1.47653	+	0.852473i
$929$			219.268i			0.236026i	0.993012	+	0.118013i	$0.0376525\pi$
$929$			219.268i			0.236026i	−0.993012	+	0.118013i	$0.962348\pi$
$930$	33.0987			0.0355901
$931$	558.806	−	967.880i	0.600221	−	1.03961i
$932$	774.312	−	447.049i	0.830807	−	0.479667i
$933$	−51.6970			−0.0554094
$934$	259.276	+	149.693i	0.277598	+	0.160271i
$935$	113.068			0.120928
$936$	214.146	+	370.913i	0.228789	+	0.396274i
$937$			978.827i			1.04464i	0.852750	+	0.522320i	$0.174933\pi$
$937$			978.827i			1.04464i	−0.852750	+	0.522320i	$0.825067\pi$
$938$	214.198	+	209.245i	0.228356	+	0.223076i
$939$	−340.196			−0.362296
$940$	−48.4119	+	27.9506i	−0.0515020	+	0.0297347i
$941$		−	1428.30i		−	1.51785i	−0.651179	−	0.758924i	$-0.725725\pi$
$941$		−	1428.30i		−	1.51785i	0.651179	−	0.758924i	$-0.274275\pi$
$942$	−218.258	+	378.034i	−0.231696	+	0.401310i
$943$		−	75.6602i		−	0.0802335i
$944$	120.166	+	208.134i	0.127295	+	0.220481i
$945$	11.2723	+	6.50806i	0.0119283	+	0.00688683i
$946$		−	84.1405i		−	0.0889435i
$947$	455.723			0.481228			0.240614	−	0.970621i	$-0.422651\pi$
$947$	455.723			0.481228			0.240614	+	0.970621i	$0.422651\pi$
$948$	−121.567	−	210.561i	−0.128235	−	0.222110i
$949$	1694.55	+	978.347i	1.78561	+	1.03092i
$950$	836.079	+	482.710i	0.880083	+	0.508116i
$951$	464.540	−	268.202i	0.488475	−	0.282021i
$952$	−527.617			−0.554220
$953$	1121.51			1.17682			0.588411	−	0.808562i	$-0.299754\pi$
$953$	1121.51			1.17682			0.588411	+	0.808562i	$0.299754\pi$
$954$	−53.6968	−	93.0057i	−0.0562860	−	0.0974902i
$955$	−2.26274	−	3.91917i	−0.00236936	−	0.00410385i
$956$	369.190	−	213.152i	0.386182	−	0.222962i
$957$	−360.131	−	623.764i	−0.376312	−	0.651791i
$958$	−503.547	−	290.723i	−0.525623	−	0.303469i
$959$	−209.765	+	363.323i	−0.218733	+	0.378856i
$960$	64.1492			0.0668221
$961$	−298.662	−	517.298i	−0.310783	−	0.538291i
$962$	289.444			0.300877
$963$	−260.006			−0.269996
$964$	−45.3432	+	78.5367i	−0.0470365	+	0.0814696i
$965$		−	49.4025i		−	0.0511943i
$966$	9.40129	−	5.42784i	0.00973218	−	0.00561888i
$967$	−392.508	+	679.844i	−0.405903	+	0.703045i	−0.994426	−	0.105436i	$-0.966376\pi$
$967$	−392.508	+	679.844i	−0.405903	+	0.703045i	0.588523	+	0.808481i	$0.299710\pi$
$968$	417.015	−	240.764i	0.430801	−	0.248723i
$969$	−842.196	−	486.242i	−0.869140	−	0.501798i
$970$	−119.745	−	69.1351i	−0.123449	−	0.0712733i
$971$	−459.394	+	795.694i	−0.473115	+	0.819459i	−0.999526	−	0.0307711i	$-0.990204\pi$
$971$	−459.394	+	795.694i	−0.473115	+	0.819459i	0.526412	+	0.850230i	$0.323537\pi$
$972$	−29.8641	−	17.2421i	−0.0307244	−	0.0177388i
$973$	16.9927	−	29.4323i	0.0174643	−	0.0302490i
$974$	−335.603	+	581.281i	−0.344561	+	0.596797i
$975$	−363.760	−	630.051i	−0.373087	−	0.646207i
$976$	−135.196	−	78.0553i	−0.138520	−	0.0799747i
$977$	−48.6941	−	84.3406i	−0.0498404	−	0.0863261i	0.840029	−	0.542542i	$-0.182538\pi$
$977$	−48.6941	−	84.3406i	−0.0498404	−	0.0863261i	−0.889869	+	0.456216i	$0.849205\pi$
$978$	−680.333			−0.695637
$979$	−848.946	−	490.139i	−0.867157	−	0.500653i
$980$			62.7128i			0.0639926i
$981$		−	242.795i		−	0.247497i
$982$	514.451	−	297.019i	0.523881	−	0.302463i
$983$		−	1539.69i		−	1.56632i	−0.621823	−	0.783158i	$-0.713608\pi$
$983$		−	1539.69i		−	1.56632i	0.621823	−	0.783158i	$-0.286392\pi$
$984$	−672.209	−	388.100i	−0.683139	−	0.394411i
$985$	28.2566	−	48.9419i	0.0286869	−	0.0496872i
$986$	1152.65	−	665.483i	1.16902	−	0.674932i
$987$	97.6060	+	169.059i	0.0988916	+	0.171285i
$988$	972.836	−	561.667i	0.984652	−	0.568489i
$989$	9.62640	−	5.55780i	0.00973347	−	0.00561962i
$990$			23.8662i			0.0241073i
$991$		−	301.793i		−	0.304534i	−0.988339	−	0.152267i	$-0.951343\pi$
$991$		−	301.793i		−	0.304534i	0.988339	−	0.152267i	$-0.0486573\pi$
$992$	288.022	+	498.868i	0.290345	+	0.502892i
$993$	35.4351	−	61.3754i	0.0356849	−	0.0618081i
$994$	68.6376	−	118.884i	0.0690519	−	0.119601i
$995$	38.8169	−	22.4109i	0.0390119	−	0.0225236i
$996$			67.1891i			0.0674589i
$997$	1871.75			1.87739			0.938693	−	0.344756i	$-0.112038\pi$
$997$	1871.75			1.87739			0.938693	+	0.344756i	$0.112038\pi$
$998$	−166.015	+	287.547i	−0.166348	+	0.288123i
$999$	−56.6760	+	32.7219i	−0.0567327	+	0.0327547i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.h.b.97.8	✓	24
67.38	odd	6	inner	201.3.h.b.172.8	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.h.b.97.8	✓	24	1.1	even	1	trivial
201.3.h.b.172.8	yes	24	67.38	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	201.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.15796 - 0.668551i) q^{2} +1.73205i q^{3} +(-1.10608 + 1.91579i) q^{4} +0.749427i q^{5} +(1.15796 + 2.00565i) q^{6} +(2.89468 + 1.67125i) q^{7} +8.30629i q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(1.15796 - 0.668551i) q^{2} +1.73205i q^{3} +(-1.10608 + 1.91579i) q^{4} +0.749427i q^{5} +(1.15796 + 2.00565i) q^{6} +(2.89468 + 1.67125i) q^{7} +8.30629i q^{8} -3.00000 q^{9} +(0.501030 + 0.867810i) q^{10} +(-6.87542 - 3.96953i) q^{11} +(-3.31824 - 1.91579i) q^{12} +(-14.8848 + 8.59375i) q^{13} +4.46925 q^{14} -1.29805 q^{15} +(1.12886 + 1.95525i) q^{16} +(9.50193 + 16.4578i) q^{17} +(-3.47389 + 2.00565i) q^{18} +(14.7724 + 25.5865i) q^{19} +(-1.43574 - 0.828925i) q^{20} +(-2.89468 + 5.01374i) q^{21} -10.6153 q^{22} +(-0.701183 - 1.21448i) q^{23} -14.3869 q^{24} +24.4384 q^{25} +(-11.4907 + 19.9025i) q^{26} -5.19615i q^{27} +(-6.40349 + 3.69706i) q^{28} +(26.1897 - 45.3619i) q^{29} +(-1.50309 + 0.867810i) q^{30} +(-16.5153 - 9.53514i) q^{31} +(-26.1595 - 15.1032i) q^{32} +(6.87542 - 11.9086i) q^{33} +(22.0058 + 12.7051i) q^{34} +(-1.25248 + 2.16935i) q^{35} +(3.31824 - 5.74736i) q^{36} +(-6.29733 - 10.9073i) q^{37} +(34.2117 + 19.7522i) q^{38} +(-14.8848 - 25.7812i) q^{39} -6.22496 q^{40} +(46.7236 + 26.9759i) q^{41} +7.74097i q^{42} +7.92633i q^{43} +(15.2095 - 8.78122i) q^{44} -2.24828i q^{45} +(-1.62389 - 0.937553i) q^{46} +(16.8595 - 29.2016i) q^{47} +(-3.38659 + 1.95525i) q^{48} +(-18.9139 - 32.7598i) q^{49} +(28.2987 - 16.3383i) q^{50} +(-28.5058 + 16.4578i) q^{51} -38.0215i q^{52} +26.7727i q^{53} +(-3.47389 - 6.01696i) q^{54} +(2.97487 - 5.15263i) q^{55} +(-13.8818 + 24.0441i) q^{56} +(-44.3171 + 25.5865i) q^{57} -70.0366i q^{58} +106.449 q^{59} +(1.43574 - 2.48678i) q^{60} +(-59.8814 + 34.5725i) q^{61} -25.4989 q^{62} +(-8.68404 - 5.01374i) q^{63} -49.4199 q^{64} +(-6.44039 - 11.1551i) q^{65} -18.3863i q^{66} +(47.9270 + 46.8189i) q^{67} -42.0396 q^{68} +(2.10355 - 1.21448i) q^{69} +3.34938i q^{70} +(15.3577 - 26.6004i) q^{71} -24.9189i q^{72} +(-56.9220 - 98.5918i) q^{73} +(-14.5842 - 8.42018i) q^{74} +42.3285i q^{75} -65.3576 q^{76} +(-13.2681 - 22.9810i) q^{77} +(-34.4722 - 19.9025i) q^{78} +(54.9541 + 31.7278i) q^{79} +(-1.46531 + 0.846000i) q^{80} +9.00000 q^{81} +72.1391 q^{82} +(-8.76783 - 15.1863i) q^{83} +(-6.40349 - 11.0912i) q^{84} +(-12.3339 + 7.12100i) q^{85} +(5.29915 + 9.17840i) q^{86} +(78.5691 + 45.3619i) q^{87} +(32.9720 - 57.1093i) q^{88} +123.476 q^{89} +(-1.50309 - 2.60343i) q^{90} -57.4490 q^{91} +3.10225 q^{92} +(16.5153 - 28.6054i) q^{93} -45.0859i q^{94} +(-19.1752 + 11.0708i) q^{95} +(26.1595 - 45.3095i) q^{96} +(-119.499 + 68.9929i) q^{97} +(-43.8032 - 25.2898i) q^{98} +(20.6263 + 11.9086i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 34 q^{4} + 21 q^{7} - 72 q^{9}+O(q^{10}) \) 24 * q + 34 * q^4 + 21 * q^7 - 72 * q^9	\( 24 q + 34 q^{4} + 21 q^{7} - 72 q^{9} + 30 q^{10} + 12 q^{11} + 102 q^{12} + 30 q^{13} + 6 q^{14} - 6 q^{15} - 98 q^{16} + 4 q^{17} + 39 q^{19} + 108 q^{20} - 21 q^{21} - 82 q^{22} - 13 q^{23} - 36 q^{24} - 222 q^{25} + 29 q^{26} + 189 q^{28} - 90 q^{30} - 93 q^{31} - 33 q^{32} - 12 q^{33} + 72 q^{34} - 93 q^{35} - 102 q^{36} - 33 q^{37} - 210 q^{38} + 30 q^{39} + 274 q^{40} - 15 q^{41} - 9 q^{44} - 228 q^{46} - 131 q^{47} + 294 q^{48} + 295 q^{49} - 423 q^{50} - 12 q^{51} - 56 q^{55} + 349 q^{56} - 117 q^{57} - 116 q^{59} - 108 q^{60} + 120 q^{61} + 282 q^{62} - 63 q^{63} - 276 q^{64} + 136 q^{65} - 25 q^{67} + 10 q^{68} + 39 q^{69} + 169 q^{71} + 187 q^{73} + 849 q^{74} + 386 q^{76} - 348 q^{77} + 87 q^{78} + 51 q^{80} + 216 q^{81} - 14 q^{82} + 104 q^{83} + 189 q^{84} - 243 q^{85} + 641 q^{86} - 766 q^{88} + 152 q^{89} - 90 q^{90} + 32 q^{91} - 216 q^{92} + 93 q^{93} + 762 q^{95} + 33 q^{96} - 84 q^{97} - 1086 q^{98} - 36 q^{99}+O(q^{100}) \) 24 * q + 34 * q^4 + 21 * q^7 - 72 * q^9 + 30 * q^10 + 12 * q^11 + 102 * q^12 + 30 * q^13 + 6 * q^14 - 6 * q^15 - 98 * q^16 + 4 * q^17 + 39 * q^19 + 108 * q^20 - 21 * q^21 - 82 * q^22 - 13 * q^23 - 36 * q^24 - 222 * q^25 + 29 * q^26 + 189 * q^28 - 90 * q^30 - 93 * q^31 - 33 * q^32 - 12 * q^33 + 72 * q^34 - 93 * q^35 - 102 * q^36 - 33 * q^37 - 210 * q^38 + 30 * q^39 + 274 * q^40 - 15 * q^41 - 9 * q^44 - 228 * q^46 - 131 * q^47 + 294 * q^48 + 295 * q^49 - 423 * q^50 - 12 * q^51 - 56 * q^55 + 349 * q^56 - 117 * q^57 - 116 * q^59 - 108 * q^60 + 120 * q^61 + 282 * q^62 - 63 * q^63 - 276 * q^64 + 136 * q^65 - 25 * q^67 + 10 * q^68 + 39 * q^69 + 169 * q^71 + 187 * q^73 + 849 * q^74 + 386 * q^76 - 348 * q^77 + 87 * q^78 + 51 * q^80 + 216 * q^81 - 14 * q^82 + 104 * q^83 + 189 * q^84 - 243 * q^85 + 641 * q^86 - 766 * q^88 + 152 * q^89 - 90 * q^90 + 32 * q^91 - 216 * q^92 + 93 * q^93 + 762 * q^95 + 33 * q^96 - 84 * q^97 - 1086 * q^98 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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