LMFDB - Embedded newform 201.3.h.b.172.6

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			172.6
Character	$\chi$	$=$	201.172
Dual form			201.3.h.b.97.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415796 - 0.240060i) q^{2} -1.73205i q^{3} +(-1.88474 - 3.26447i) q^{4} -7.03218i q^{5} +(-0.415796 + 0.720180i) q^{6} +(1.25782 - 0.726201i) q^{7} +3.73029i q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(-0.415796 - 0.240060i) q^{2} -1.73205i q^{3} +(-1.88474 - 3.26447i) q^{4} -7.03218i q^{5} +(-0.415796 + 0.720180i) q^{6} +(1.25782 - 0.726201i) q^{7} +3.73029i q^{8} -3.00000 q^{9} +(-1.68815 + 2.92395i) q^{10} +(-2.57821 + 1.48853i) q^{11} +(-5.65423 + 3.26447i) q^{12} +(2.98391 + 1.72276i) q^{13} -0.697327 q^{14} -12.1801 q^{15} +(-6.64348 + 11.5068i) q^{16} +(-3.35174 + 5.80538i) q^{17} +(1.24739 + 0.720180i) q^{18} +(-3.81630 + 6.61002i) q^{19} +(-22.9563 + 13.2539i) q^{20} +(-1.25782 - 2.17860i) q^{21} +1.42935 q^{22} +(14.3514 - 24.8573i) q^{23} +6.46105 q^{24} -24.4516 q^{25} +(-0.827131 - 1.43263i) q^{26} +5.19615i q^{27} +(-4.74132 - 2.73740i) q^{28} +(-23.1262 - 40.0558i) q^{29} +(5.06444 + 2.92395i) q^{30} +(5.39189 - 3.11301i) q^{31} +(18.4468 - 10.6502i) q^{32} +(2.57821 + 4.46559i) q^{33} +(2.78728 - 1.60924i) q^{34} +(-5.10678 - 8.84520i) q^{35} +(5.65423 + 9.79341i) q^{36} +(-10.8367 + 18.7697i) q^{37} +(3.17360 - 1.83228i) q^{38} +(2.98391 - 5.16828i) q^{39} +26.2321 q^{40} +(16.2014 - 9.35386i) q^{41} +1.20781i q^{42} +3.54025i q^{43} +(9.71852 + 5.61099i) q^{44} +21.0965i q^{45} +(-11.9345 + 6.89039i) q^{46} +(-17.5471 - 30.3926i) q^{47} +(19.9304 + 11.5068i) q^{48} +(-23.4453 + 40.6084i) q^{49} +(10.1669 + 5.86985i) q^{50} +(10.0552 + 5.80538i) q^{51} -12.9878i q^{52} -52.6076i q^{53} +(1.24739 - 2.16054i) q^{54} +(10.4676 + 18.1304i) q^{55} +(2.70894 + 4.69202i) q^{56} +(11.4489 + 6.61002i) q^{57} +22.2067i q^{58} +32.9586 q^{59} +(22.9563 + 39.7616i) q^{60} +(2.92689 + 1.68984i) q^{61} -2.98924 q^{62} +(-3.77345 + 2.17860i) q^{63} +42.9210 q^{64} +(12.1148 - 20.9834i) q^{65} -2.47570i q^{66} +(51.7960 + 42.4991i) q^{67} +25.2686 q^{68} +(-43.0542 - 24.8573i) q^{69} +4.90373i q^{70} +(-46.4886 - 80.5207i) q^{71} -11.1909i q^{72} +(38.5009 - 66.6855i) q^{73} +(9.01169 - 5.20290i) q^{74} +42.3514i q^{75} +28.7710 q^{76} +(-2.16194 + 3.74460i) q^{77} +(-2.48139 + 1.43263i) q^{78} +(58.6569 - 33.8656i) q^{79} +(80.9182 + 46.7181i) q^{80} +9.00000 q^{81} -8.98196 q^{82} +(8.49146 - 14.7076i) q^{83} +(-4.74132 + 8.21221i) q^{84} +(40.8245 + 23.5700i) q^{85} +(0.849872 - 1.47202i) q^{86} +(-69.3787 + 40.0558i) q^{87} +(-5.55264 - 9.61746i) q^{88} +20.9872 q^{89} +(5.06444 - 8.77186i) q^{90} +5.00428 q^{91} -108.195 q^{92} +(-5.39189 - 9.33904i) q^{93} +16.8495i q^{94} +(46.4829 + 26.8369i) q^{95} +(-18.4468 - 31.9507i) q^{96} +(-75.2831 - 43.4647i) q^{97} +(19.4969 - 11.2565i) q^{98} +(7.73463 - 4.46559i) 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 $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.415796	−	0.240060i	−0.207898	−	0.120030i	0.392436	−	0.919779i	$-0.371632\pi$
$2$	−0.415796	−	0.240060i	−0.207898	−	0.120030i	−0.600334	+	0.799749i	$0.704966\pi$
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	−1.88474	−	3.26447i	−0.471186	−	0.816117i
$5$		−	7.03218i		−	1.40644i	−0.710974	−	0.703218i	$-0.751746\pi$
$5$		−	7.03218i		−	1.40644i	0.710974	−	0.703218i	$-0.248254\pi$
$6$	−0.415796	+	0.720180i	−0.0692994	+	0.120030i
$7$	1.25782	−	0.726201i	0.179688	−	0.103743i	−0.407458	−	0.913224i	$-0.633585\pi$
$7$	1.25782	−	0.726201i	0.179688	−	0.103743i	0.587146	+	0.809481i	$0.300251\pi$
$8$			3.73029i			0.466286i
$9$	−3.00000			−0.333333
$10$	−1.68815	+	2.92395i	−0.168815	+	0.292395i
$11$	−2.57821	+	1.48853i	−0.234383	+	0.135321i	−0.612592	−	0.790399i	$-0.709873\pi$
$11$	−2.57821	+	1.48853i	−0.234383	+	0.135321i	0.378210	+	0.925720i	$0.376540\pi$
$12$	−5.65423	+	3.26447i	−0.471186	+	0.272039i
$13$	2.98391	+	1.72276i	0.229531	+	0.132520i	0.610356	−	0.792127i	$-0.291026\pi$
$13$	2.98391	+	1.72276i	0.229531	+	0.132520i	−0.380825	+	0.924647i	$0.624360\pi$
$14$	−0.697327			−0.0498091
$15$	−12.1801			−0.812006
$16$	−6.64348	+	11.5068i	−0.415217	+	0.719177i
$17$	−3.35174	+	5.80538i	−0.197161	+	0.341493i	−0.947607	−	0.319439i	$-0.896506\pi$
$17$	−3.35174	+	5.80538i	−0.197161	+	0.341493i	0.750446	+	0.660932i	$0.229839\pi$
$18$	1.24739	+	0.720180i	0.0692994	+	0.0400100i
$19$	−3.81630	+	6.61002i	−0.200858	+	0.347896i	−0.948805	−	0.315862i	$-0.897706\pi$
$19$	−3.81630	+	6.61002i	−0.200858	+	0.347896i	0.747947	+	0.663758i	$0.231040\pi$
$20$	−22.9563	+	13.2539i	−1.14782	+	0.662693i
$21$	−1.25782	−	2.17860i	−0.0598960	−	0.103743i
$22$	1.42935			0.0649703
$23$	14.3514	−	24.8573i	0.623974	−	1.08075i	−0.364765	−	0.931100i	$-0.618851\pi$
$23$	14.3514	−	24.8573i	0.623974	−	1.08075i	0.988738	−	0.149654i	$-0.0478161\pi$
$24$	6.46105			0.269210
$25$	−24.4516			−0.978063
$26$	−0.827131	−	1.43263i	−0.0318127	−	0.0551013i
$27$			5.19615i			0.192450i
$28$	−4.74132	−	2.73740i	−0.169333	−	0.0977644i
$29$	−23.1262	−	40.0558i	−0.797456	−	1.38124i	−0.921268	−	0.388929i	$-0.872845\pi$
$29$	−23.1262	−	40.0558i	−0.797456	−	1.38124i	0.123811	−	0.992306i	$-0.460488\pi$
$30$	5.06444	+	2.92395i	0.168815	+	0.0974652i
$31$	5.39189	−	3.11301i	0.173932	−	0.100420i	−0.410507	−	0.911858i	$-0.634648\pi$
$31$	5.39189	−	3.11301i	0.173932	−	0.100420i	0.584439	+	0.811438i	$0.301315\pi$
$32$	18.4468	−	10.6502i	0.576461	−	0.332820i
$33$	2.57821	+	4.46559i	0.0781276	+	0.135321i
$34$	2.78728	−	1.60924i	0.0819788	−	0.0473305i
$35$	−5.10678	−	8.84520i	−0.145908	−	0.252720i
$36$	5.65423	+	9.79341i	0.157062	+	0.272039i
$37$	−10.8367	+	18.7697i	−0.292883	+	0.507288i	−0.974490	−	0.224430i	$-0.927948\pi$
$37$	−10.8367	+	18.7697i	−0.292883	+	0.507288i	0.681607	+	0.731718i	$0.261281\pi$
$38$	3.17360	−	1.83228i	0.0835159	−	0.0482179i
$39$	2.98391	−	5.16828i	0.0765104	−	0.132520i
$40$	26.2321			0.655801
$41$	16.2014	−	9.35386i	0.395155	−	0.228143i	−0.289236	−	0.957258i	$-0.593401\pi$
$41$	16.2014	−	9.35386i	0.395155	−	0.228143i	0.684391	+	0.729115i	$0.260068\pi$
$42$			1.20781i			0.0287573i
$43$			3.54025i			0.0823314i	0.999152	+	0.0411657i	$0.0131071\pi$
$43$			3.54025i			0.0823314i	−0.999152	+	0.0411657i	$0.986893\pi$
$44$	9.71852	+	5.61099i	0.220875	+	0.127523i
$45$			21.0965i			0.468812i
$46$	−11.9345	+	6.89039i	−0.259446	+	0.149791i
$47$	−17.5471	−	30.3926i	−0.373344	−	0.646650i	0.616734	−	0.787172i	$-0.288455\pi$
$47$	−17.5471	−	30.3926i	−0.373344	−	0.646650i	−0.990078	+	0.140522i	$0.955122\pi$
$48$	19.9304	+	11.5068i	0.415217	+	0.239726i
$49$	−23.4453	+	40.6084i	−0.478475	+	0.828743i
$50$	10.1669	+	5.86985i	0.203338	+	0.117397i
$51$	10.0552	+	5.80538i	0.197161	+	0.113831i
$52$		−	12.9878i		−	0.249766i
$53$		−	52.6076i		−	0.992595i	−0.868152	−	0.496298i	$-0.834692\pi$
$53$		−	52.6076i		−	0.992595i	0.868152	−	0.496298i	$-0.165308\pi$
$54$	1.24739	−	2.16054i	0.0230998	−	0.0400100i
$55$	10.4676	+	18.1304i	0.190320	+	0.329644i
$56$	2.70894	+	4.69202i	0.0483739	+	0.0837860i
$57$	11.4489	+	6.61002i	0.200858	+	0.115965i
$58$			22.2067i			0.382875i
$59$	32.9586			0.558620			0.279310	−	0.960201i	$-0.409894\pi$
$59$	32.9586			0.558620			0.279310	+	0.960201i	$0.409894\pi$
$60$	22.9563	+	39.7616i	0.382606	+	0.662693i
$61$	2.92689	+	1.68984i	0.0479818	+	0.0277023i	0.523799	−	0.851842i	$-0.324514\pi$
$61$	2.92689	+	1.68984i	0.0479818	+	0.0277023i	−0.475817	+	0.879544i	$0.657848\pi$
$62$	−2.98924			−0.0482135
$63$	−3.77345	+	2.17860i	−0.0598960	+	0.0345810i
$64$	42.9210			0.670641
$65$	12.1148	−	20.9834i	0.186381	−	0.322821i
$66$		−	2.47570i		−	0.0375106i
$67$	51.7960	+	42.4991i	0.773075	+	0.634314i
$67$	51.7960	+	42.4991i	0.773075	+	0.634314i
$68$	25.2686			0.371598
$69$	−43.0542	−	24.8573i	−0.623974	−	0.360251i
$70$			4.90373i			0.0700533i
$71$	−46.4886	−	80.5207i	−0.654770	−	1.13409i	−0.981952	−	0.189133i	$-0.939432\pi$
$71$	−46.4886	−	80.5207i	−0.654770	−	1.13409i	0.327182	−	0.944961i	$-0.393901\pi$
$72$		−	11.1909i		−	0.155429i
$73$	38.5009	−	66.6855i	0.527409	−	0.913500i	−0.472080	−	0.881556i	$-0.656497\pi$
$73$	38.5009	−	66.6855i	0.527409	−	0.913500i	0.999490	−	0.0319441i	$-0.0101699\pi$
$74$	9.01169	−	5.20290i	0.121780	−	0.0703095i
$75$			42.3514i			0.564685i
$76$	28.7710			0.378565
$77$	−2.16194	+	3.74460i	−0.0280772	+	0.0486311i
$78$	−2.48139	+	1.43263i	−0.0318127	+	0.0183671i
$79$	58.6569	−	33.8656i	0.742493	−	0.428679i	−0.0804820	−	0.996756i	$-0.525646\pi$
$79$	58.6569	−	33.8656i	0.742493	−	0.428679i	0.822975	+	0.568078i	$0.192313\pi$
$80$	80.9182	+	46.7181i	1.01148	+	0.583977i
$81$	9.00000			0.111111
$82$	−8.98196			−0.109536
$83$	8.49146	−	14.7076i	0.102307	−	0.177200i	−0.810328	−	0.585977i	$-0.800711\pi$
$83$	8.49146	−	14.7076i	0.102307	−	0.177200i	0.912635	+	0.408776i	$0.134044\pi$
$84$	−4.74132	+	8.21221i	−0.0564443	+	0.0977644i
$85$	40.8245	+	23.5700i	0.480288	+	0.277294i
$86$	0.849872	−	1.47202i	0.00988224	−	0.0171165i
$87$	−69.3787	+	40.0558i	−0.797456	+	0.460412i
$88$	−5.55264	−	9.61746i	−0.0630982	−	0.109289i
$89$	20.9872			0.235811			0.117906	−	0.993025i	$-0.462382\pi$
$89$	20.9872			0.235811			0.117906	+	0.993025i	$0.462382\pi$
$90$	5.06444	−	8.77186i	0.0562715	−	0.0974652i
$91$	5.00428			0.0549920
$92$	−108.195			−1.17603
$93$	−5.39189	−	9.33904i	−0.0579774	−	0.100420i
$94$			16.8495i			0.179250i
$95$	46.4829	+	26.8369i	0.489293	+	0.282494i
$96$	−18.4468	−	31.9507i	−0.192154	−	0.332820i
$97$	−75.2831	−	43.4647i	−0.776114	−	0.448090i	0.0589374	−	0.998262i	$-0.481229\pi$
$97$	−75.2831	−	43.4647i	−0.776114	−	0.448090i	−0.835051	+	0.550172i	$0.814562\pi$
$98$	19.4969	−	11.2565i	0.198948	−	0.114863i
$99$	7.73463	−	4.46559i	0.0781276	−	0.0451070i
$100$	46.0849	+	79.8214i	0.460849	+	0.798214i
$101$	−30.6119	+	17.6738i	−0.303088	+	0.174988i	−0.643830	−	0.765169i	$-0.722655\pi$
$101$	−30.6119	+	17.6738i	−0.303088	+	0.174988i	0.340741	+	0.940157i	$0.389322\pi$
$102$	−2.78728	−	4.82771i	−0.0273263	−	0.0473305i
$103$	−11.7101	−	20.2825i	−0.113690	−	0.196918i	0.803565	−	0.595217i	$-0.202934\pi$
$103$	−11.7101	−	20.2825i	−0.113690	−	0.196918i	−0.917256	+	0.398299i	$0.869601\pi$
$104$	−6.42638	+	11.1308i	−0.0617921	+	0.107027i
$105$	−15.3203	+	8.84520i	−0.145908	+	0.0842400i
$106$	−12.6290	+	21.8740i	−0.119141	+	0.206359i
$107$	56.4672			0.527731			0.263866	−	0.964559i	$-0.415002\pi$
$107$	56.4672			0.527731			0.263866	+	0.964559i	$0.415002\pi$
$108$	16.9627	−	9.79341i	0.157062	−	0.0906797i
$109$			29.1537i			0.267465i	0.991017	+	0.133733i	$0.0426964\pi$
$109$			29.1537i			0.267465i	−0.991017	+	0.133733i	$0.957304\pi$
$110$		−	10.0514i		−	0.0913766i
$111$	32.5100	+	18.7697i	0.292883	+	0.169096i
$112$			19.2980i			0.172304i
$113$	49.3125	−	28.4706i	0.436394	−	0.251952i	−0.265673	−	0.964063i	$-0.585594\pi$
$113$	49.3125	−	28.4706i	0.436394	−	0.251952i	0.702067	+	0.712111i	$0.252261\pi$
$114$	−3.17360	−	5.49684i	−0.0278386	−	0.0482179i
$115$	−174.801	−	100.922i	−1.52001	−	0.877579i
$116$	−87.1740	+	150.990i	−0.751500	+	1.30164i
$117$	−8.95172	−	5.16828i	−0.0765104	−	0.0441733i
$118$	−13.7040	−	7.91203i	−0.116136	−	0.0670511i
$119$			9.73614i			0.0818163i
$120$		−	45.4352i		−	0.378627i
$121$	−56.0686	+	97.1136i	−0.463377	+	0.802592i
$122$	−0.811327	−	1.40526i	−0.00665022	−	0.0115185i
$123$	−16.2014	−	28.0616i	−0.131718	−	0.228143i
$124$	−20.3247	−	11.7345i	−0.163909	−	0.0946327i
$125$		−	3.85656i		−	0.0308525i
$126$	2.09198			0.0166030
$127$	−115.765	−	200.511i	−0.911538	−	1.57883i	−0.811893	−	0.583807i	$-0.801563\pi$
$127$	−115.765	−	200.511i	−0.911538	−	1.57883i	−0.0996451	−	0.995023i	$-0.531771\pi$
$128$	−91.6334	−	52.9046i	−0.715886	−	0.413317i
$129$	6.13189			0.0475340
$130$	−10.0745	+	5.81654i	−0.0774964	+	0.0447426i
$131$	−68.7123			−0.524521			−0.262261	−	0.964997i	$-0.584468\pi$
$131$	−68.7123			−0.524521			−0.262261	+	0.964997i	$0.584468\pi$
$132$	9.71852	−	16.8330i	0.0736252	−	0.127523i
$133$			11.0856i			0.0833504i
$134$	−11.3343	−	30.1051i	−0.0845841	−	0.224665i
$135$	36.5403			0.270669
$136$	−21.6557	−	12.5029i	−0.159233	−	0.0919334i
$137$			171.957i			1.25516i	0.778553	+	0.627579i	$0.215954\pi$
$137$			171.957i			1.25516i	−0.778553	+	0.627579i	$0.784046\pi$
$138$	11.9345	+	20.6712i	0.0864820	+	0.149791i
$139$		−	218.610i		−	1.57273i	−0.617761	−	0.786366i	$-0.711960\pi$
$139$		−	218.610i		−	1.57273i	0.617761	−	0.786366i	$-0.288040\pi$
$140$	−19.2499	+	33.3418i	−0.137499	+	0.238156i
$141$	−52.6414	+	30.3926i	−0.373344	+	0.215550i
$142$			44.6403i			0.314368i
$143$	−10.2575			−0.0717308
$144$	19.9304	−	34.5205i	0.138406	−	0.239726i
$145$	−281.680	+	162.628i	−1.94262	+	1.12157i
$146$	−32.0170	+	18.4850i	−0.219295	+	0.126610i
$147$	70.3358	+	40.6084i	0.478475	+	0.276248i
$148$	81.6973			0.552009
$149$	205.053			1.37620			0.688098	−	0.725618i	$-0.258446\pi$
$149$	205.053			1.37620			0.688098	+	0.725618i	$0.258446\pi$
$150$	10.1669	−	17.6095i	0.0677792	−	0.117397i
$151$	111.913	−	193.840i	0.741148	−	1.28371i	−0.210825	−	0.977524i	$-0.567615\pi$
$151$	111.913	−	193.840i	0.741148	−	1.28371i	0.951973	−	0.306182i	$-0.0990516\pi$
$152$	−24.6573	−	14.2359i	−0.162219	−	0.0936571i
$153$	10.0552	−	17.4161i	0.0657203	−	0.113831i
$154$	1.79786	−	1.03799i	0.0116744	−	0.00674021i
$155$	−21.8913	−	37.9168i	−0.141234	−	0.244624i
$156$	−22.4956			−0.144202
$157$	−100.524	+	174.113i	−0.640283	+	1.10900i	0.345086	+	0.938571i	$0.387850\pi$
$157$	−100.524	+	174.113i	−0.640283	+	1.10900i	−0.985369	+	0.170432i	$0.945484\pi$
$158$	−32.5191			−0.205817
$159$	−91.1190			−0.573075
$160$	−74.8944	−	129.721i	−0.468090	−	0.810756i
$161$		−	41.6880i		−	0.258932i
$162$	−3.74217	−	2.16054i	−0.0230998	−	0.0133367i
$163$	143.984	+	249.387i	0.883336	+	1.52998i	0.847609	+	0.530622i	$0.178042\pi$
$163$	143.984	+	249.387i	0.883336	+	1.52998i	0.0357279	+	0.999362i	$0.488625\pi$
$164$	−61.0708	−	35.2592i	−0.372383	−	0.214995i
$165$	31.4028	−	18.1304i	0.190320	−	0.109881i
$166$	−7.06143	+	4.07692i	−0.0425387	+	0.0245598i
$167$	−70.7252	−	122.500i	−0.423504	−	0.733530i	0.572775	−	0.819712i	$-0.305867\pi$
$167$	−70.7252	−	122.500i	−0.423504	−	0.733530i	−0.996279	+	0.0861819i	$0.972533\pi$
$168$	8.12681	−	4.69202i	0.0483739	−	0.0279287i
$169$	−78.5642	−	136.077i	−0.464877	−	0.805191i
$170$	−11.3164	−	19.6007i	−0.0665673	−	0.115298i
$171$	11.4489	−	19.8301i	0.0669526	−	0.115965i
$172$	11.5570	−	6.67246i	0.0671921	−	0.0387934i
$173$	−62.0061	+	107.398i	−0.358417	+	0.620796i	−0.987696	−	0.156383i	$-0.950017\pi$
$173$	−62.0061	+	107.398i	−0.358417	+	0.620796i	0.629280	+	0.777179i	$0.283350\pi$
$174$	38.4632			0.221053
$175$	−30.7556	+	17.7568i	−0.175746	+	0.101467i
$176$		−	39.5561i		−	0.224750i
$177$		−	57.0859i		−	0.322519i
$178$	−8.72641	−	5.03819i	−0.0490248	−	0.0283045i
$179$			243.950i			1.36285i	0.731889	+	0.681424i	$0.238639\pi$
$179$			243.950i			1.36285i	−0.731889	+	0.681424i	$0.761361\pi$
$180$	68.8690	−	39.7616i	0.382606	−	0.220898i
$181$	138.270	+	239.490i	0.763921	+	1.32315i	0.940815	+	0.338921i	$0.110062\pi$
$181$	138.270	+	239.490i	0.763921	+	1.32315i	−0.176894	+	0.984230i	$0.556605\pi$
$182$	−2.08076	−	1.20133i	−0.0114327	−	0.00660070i
$183$	2.92689	−	5.06952i	0.0159939	−	0.0277023i
$184$	92.7250	+	53.5348i	0.503940	+	0.290950i
$185$	131.992	+	76.2054i	0.713468	+	0.411921i
$186$			5.17751i			0.0278361i
$187$		−	19.9566i		−	0.106720i
$188$	−66.1437	+	114.564i	−0.351828	+	0.609384i
$189$	3.77345	+	6.53581i	0.0199653	+	0.0345810i
$190$	−12.8849	−	22.3174i	−0.0678155	−	0.117460i
$191$	169.175	+	97.6730i	0.885731	+	0.511377i	0.872544	−	0.488536i	$-0.162469\pi$
$191$	169.175	+	97.6730i	0.885731	+	0.511377i	0.0131873	+	0.999913i	$0.495802\pi$
$192$		−	74.3414i		−	0.387195i
$193$	216.835			1.12350			0.561749	−	0.827308i	$-0.310129\pi$
$193$	216.835			1.12350			0.561749	+	0.827308i	$0.310129\pi$
$194$	20.8683	+	36.1449i	0.107568	+	0.186314i
$195$	−36.3443	−	20.9834i	−0.186381	−	0.107607i
$196$	176.753			0.901802
$197$	−222.537	+	128.482i	−1.12963	+	0.652193i	−0.943842	−	0.330396i	$-0.892818\pi$
$197$	−222.537	+	128.482i	−1.12963	+	0.652193i	−0.185789	+	0.982590i	$0.559484\pi$
$198$	−4.28804			−0.0216568
$199$	176.868	−	306.344i	0.888782	−	1.53942i	0.0474658	−	0.998873i	$-0.484885\pi$
$199$	176.868	−	306.344i	0.888782	−	1.53942i	0.841316	−	0.540543i	$-0.181781\pi$
$200$		−	91.2114i		−	0.456057i
$201$	73.6105	−	89.7134i	0.366222	−	0.446335i
$202$	16.9711			0.0840154
$203$	−58.1772	−	33.5886i	−0.286587	−	0.165461i
$204$		−	43.7666i		−	0.214542i
$205$	−65.7781	−	113.931i	−0.320869	−	0.555761i
$206$			11.2445i			0.0545851i
$207$	−43.0542	+	74.5720i	−0.207991	+	0.360251i
$208$	−39.6470	+	22.8902i	−0.190611	+	0.110049i
$209$		−	22.7227i		−	0.108721i
$210$	8.49352			0.0404453
$211$	67.7159	−	117.287i	0.320928	−	0.555864i	−0.659752	−	0.751484i	$-0.729338\pi$
$211$	67.7159	−	117.287i	0.320928	−	0.555864i	0.980680	+	0.195620i	$0.0626718\pi$
$212$	−171.736	+	99.1517i	−0.810074	+	0.467697i
$213$	−139.466	+	80.5207i	−0.654770	+	0.378031i
$214$	−23.4789	−	13.5555i	−0.109714	−	0.0633436i
$215$	24.8957			0.115794
$216$	−19.3831			−0.0897367
$217$	4.52134	−	7.83120i	0.0208357	−	0.0360885i
$218$	6.99865	−	12.1220i	0.0321039	−	0.0556056i
$219$	−115.503	−	66.6855i	−0.527409	−	0.304500i
$220$	39.4575	−	68.3424i	0.179352	−	0.310647i
$221$	−20.0025	+	11.5485i	−0.0905092	+	0.0522555i
$222$	−9.01169	−	15.6087i	−0.0405932	−	0.0703095i
$223$	181.824			0.815352			0.407676	−	0.913127i	$-0.366339\pi$
$223$	181.824			0.815352			0.407676	+	0.913127i	$0.366339\pi$
$224$	15.4684	−	26.7921i	0.0690555	−	0.119608i
$225$	73.3548			0.326021
$226$	−27.3386			−0.120967
$227$	4.62606	+	8.01257i	0.0203791	+	0.0352977i	0.876035	−	0.482247i	$-0.160179\pi$
$227$	4.62606	+	8.01257i	0.0203791	+	0.0352977i	−0.855656	+	0.517545i	$0.826846\pi$
$228$		−	49.8328i		−	0.218565i
$229$	230.458	+	133.055i	1.00637	+	0.581026i	0.910126	−	0.414332i	$-0.135985\pi$
$229$	230.458	+	133.055i	1.00637	+	0.581026i	0.0962411	+	0.995358i	$0.469318\pi$
$230$	48.4545	+	83.9257i	0.210672	+	0.364894i
$231$	6.48583	+	3.74460i	0.0280772	+	0.0162104i
$232$	149.420	−	86.2675i	0.644050	−	0.371843i
$233$	139.909	−	80.7765i	0.600468	−	0.346680i	−0.168758	−	0.985658i	$-0.553976\pi$
$233$	139.909	−	80.7765i	0.600468	−	0.346680i	0.769226	+	0.638977i	$0.220642\pi$
$234$	2.48139	+	4.29790i	0.0106042	+	0.0183671i
$235$	−213.726	+	123.395i	−0.909472	+	0.525084i
$236$	−62.1184	−	107.592i	−0.263214	−	0.455899i
$237$	−58.6569	−	101.597i	−0.247498	−	0.428679i
$238$	2.33726	−	4.04825i	0.00982042	−	0.0170095i
$239$	49.2668	−	28.4442i	0.206137	−	0.119013i	−0.393378	−	0.919377i	$-0.628694\pi$
$239$	49.2668	−	28.4442i	0.206137	−	0.119013i	0.599515	+	0.800364i	$0.295360\pi$
$240$	80.9182	−	140.154i	0.337159	−	0.583977i
$241$	52.2364			0.216748			0.108374	−	0.994110i	$-0.465436\pi$
$241$	52.2364			0.216748			0.108374	+	0.994110i	$0.465436\pi$
$242$	46.6262	−	26.9196i	0.192670	−	0.111238i
$243$		−	15.5885i		−	0.0641500i
$244$		−	12.7397i		−	0.0522117i
$245$	285.566	+	164.871i	1.16557	+	0.672944i
$246$			15.5572i			0.0632407i
$247$	−22.7749	+	13.1491i	−0.0922063	+	0.0532353i
$248$	11.6124	+	20.1133i	0.0468243	+	0.0811021i
$249$	−25.4744	−	14.7076i	−0.102307	−	0.0590668i
$250$	−0.925807	+	1.60354i	−0.00370323	+	0.00641418i
$251$	28.3104	+	16.3450i	0.112790	+	0.0651196i	0.555334	−	0.831627i	$-0.312590\pi$
$251$	28.3104	+	16.3450i	0.112790	+	0.0651196i	−0.442544	+	0.896747i	$0.645924\pi$
$252$	14.2240	+	8.21221i	0.0564443	+	0.0325881i
$253$			85.4499i			0.337747i
$254$			111.163i			0.437648i
$255$	40.8245	−	70.7101i	0.160096	−	0.277294i
$256$	−60.4415	−	104.688i	−0.236100	−	0.408936i
$257$	55.4208	+	95.9917i	0.215645	+	0.373508i	0.953472	−	0.301482i	$-0.0974812\pi$
$257$	55.4208	+	95.9917i	0.215645	+	0.373508i	−0.737827	+	0.674990i	$0.764148\pi$
$258$	−2.54962	−	1.47202i	−0.00988224	−	0.00570551i
$259$			31.4784i			0.121538i
$260$	−91.3327			−0.351280
$261$	69.3787	+	120.167i	0.265819	+	0.460412i
$262$	28.5703	+	16.4951i	0.109047	+	0.0629583i
$263$	130.375			0.495722			0.247861	−	0.968796i	$-0.420272\pi$
$263$	130.375			0.495722			0.247861	+	0.968796i	$0.420272\pi$
$264$	−16.6579	+	9.61746i	−0.0630982	+	0.0364298i
$265$	−369.946			−1.39602
$266$	2.66121	−	4.60935i	0.0100045	−	0.0173284i
$267$		−	36.3509i		−	0.136146i
$268$	41.1147	−	249.186i	0.153413	−	0.929800i
$269$	459.779			1.70922			0.854608	−	0.519273i	$-0.173797\pi$
$269$	459.779			1.70922			0.854608	+	0.519273i	$0.173797\pi$
$270$	−15.1933	−	8.77186i	−0.0562715	−	0.0324884i
$271$			260.404i			0.960899i	0.877022	+	0.480449i	$0.159526\pi$
$271$			260.404i			0.960899i	−0.877022	+	0.480449i	$0.840474\pi$
$272$	−44.5344	−	77.1358i	−0.163729	−	0.283588i
$273$		−	8.66766i		−	0.0317497i
$274$	41.2799	−	71.4989i	0.150657	−	0.260945i
$275$	63.0413	−	36.3969i	0.229241	−	0.132352i
$276$			187.399i			0.678981i
$277$	−339.522			−1.22571			−0.612856	−	0.790194i	$-0.709980\pi$
$277$	−339.522			−1.22571			−0.612856	+	0.790194i	$0.709980\pi$
$278$	−52.4795	+	90.8971i	−0.188775	+	0.326968i
$279$	−16.1757	+	9.33904i	−0.0579774	+	0.0334732i
$280$	32.9951	−	19.0497i	0.117840	−	0.0680348i
$281$	389.602	+	224.937i	1.38648	+	0.800487i	0.992917	−	0.118810i	$-0.0379078\pi$
$281$	389.602	+	224.937i	1.38648	+	0.800487i	0.393566	+	0.919296i	$0.371241\pi$
$282$	29.1842			0.103490
$283$	320.294			1.13178			0.565890	−	0.824481i	$-0.308533\pi$
$283$	320.294			1.13178			0.565890	+	0.824481i	$0.308533\pi$
$284$	−175.238	+	303.522i	−0.617036	+	1.06874i
$285$	46.4829	−	80.5107i	0.163098	−	0.282494i
$286$	4.26503	+	2.46242i	0.0149127	+	0.00860986i
$287$	13.5856	−	23.5309i	0.0473365	−	0.0819892i
$288$	−55.3403	+	31.9507i	−0.192154	+	0.110940i
$289$	122.032	+	211.365i	0.422255	+	0.731367i
$290$	156.162			0.538489
$291$	−75.2831	+	130.394i	−0.258705	+	0.448090i
$292$	−290.257			−0.994031
$293$	−512.585			−1.74944			−0.874719	−	0.484631i	$-0.838954\pi$
$293$	−512.585			−1.74944			−0.874719	+	0.484631i	$0.838954\pi$
$294$	−19.4969	−	33.7696i	−0.0663160	−	0.114863i
$295$		−	231.771i		−	0.785663i
$296$	−70.0162	−	40.4239i	−0.236541	−	0.136567i
$297$	−7.73463	−	13.3968i	−0.0260425	−	0.0451070i
$298$	−85.2603	−	49.2251i	−0.286108	−	0.165185i
$299$	85.6464	−	49.4480i	0.286443	−	0.165378i
$300$	138.255	−	79.8214i	0.460849	−	0.266071i
$301$	2.57093	+	4.45299i	0.00854130	+	0.0147940i
$302$	−93.0663	+	53.7318i	−0.308167	+	0.177920i
$303$	30.6119	+	53.0214i	0.101029	+	0.174988i
$304$	−50.7070	−	87.8271i	−0.166799	−	0.288905i
$305$	11.8833	−	20.5824i	0.0389615	−	0.0674834i
$306$	−8.36184	+	4.82771i	−0.0273263	+	0.0157768i
$307$	−100.335	+	173.785i	−0.326824	+	0.566075i	−0.981880	−	0.189505i	$-0.939312\pi$
$307$	−100.335	+	173.785i	−0.326824	+	0.566075i	0.655056	+	0.755580i	$0.272645\pi$
$308$	16.2988			0.0529183
$309$	−35.1304	+	20.2825i	−0.113690	+	0.0656392i
$310$			21.0209i			0.0678093i
$311$		−	482.442i		−	1.55126i	−0.631188	−	0.775630i	$-0.717432\pi$
$311$		−	482.442i		−	1.55126i	0.631188	−	0.775630i	$-0.282568\pi$
$312$	19.2791	+	11.1308i	0.0617921	+	0.0356757i
$313$			114.658i			0.366320i	0.983083	+	0.183160i	$0.0586326\pi$
$313$			114.658i			0.366320i	−0.983083	+	0.183160i	$0.941367\pi$
$314$	83.5954	−	48.2638i	0.266227	−	0.153706i
$315$	15.3203	+	26.5356i	0.0486360	+	0.0842400i
$316$	−221.106	−	127.656i	−0.699704	−	0.403974i
$317$	−127.328	+	220.539i	−0.401667	+	0.695708i	−0.993927	−	0.110039i	$-0.964902\pi$
$317$	−127.328	+	220.539i	−0.401667	+	0.695708i	0.592260	+	0.805747i	$0.298236\pi$
$318$	37.8869	+	21.8740i	0.119141	+	0.0687862i
$319$	119.249	+	68.8482i	0.373820	+	0.215825i
$320$		−	301.828i		−	0.943214i
$321$		−	97.8041i		−	0.304686i
$322$	−10.0076	+	17.3337i	−0.0310796	+	0.0538314i
$323$	−25.5825	−	44.3101i	−0.0792027	−	0.137183i
$324$	−16.9627	−	29.3802i	−0.0523540	−	0.0906797i
$325$	−72.9612	−	42.1242i	−0.224496	−	0.129613i
$326$		−	138.259i		−	0.424108i
$327$	50.4957			0.154421
$328$	34.8926	+	60.4357i	0.106380	+	0.184255i
$329$	−44.1422	−	25.4855i	−0.134171	−	0.0774636i
$330$	−17.4096			−0.0527563
$331$	1.74798	−	1.00920i	0.00528090	−	0.00304893i	−0.497357	−	0.867546i	$-0.665696\pi$
$331$	1.74798	−	1.00920i	0.00528090	−	0.00304893i	0.502638	+	0.864497i	$0.332363\pi$
$332$	−64.0168			−0.192822
$333$	32.5100	−	56.3090i	0.0976276	−	0.169096i
$334$			67.9132i			0.203333i
$335$	298.861	−	364.239i	0.892123	−	1.08728i
$336$	33.4251			0.0994795
$337$	−469.293	−	270.946i	−1.39256	−	0.803995i	−0.398961	−	0.916968i	$-0.630629\pi$
$337$	−469.293	−	270.946i	−1.39256	−	0.803995i	−0.993598	+	0.112973i	$0.963963\pi$
$338$			75.4405i			0.223197i
$339$	−49.3125	−	85.4118i	−0.145465	−	0.251952i
$340$		−	177.694i		−	0.522629i
$341$	−9.26762	+	16.0520i	−0.0271778	+	0.0470733i
$342$	−9.52081	+	5.49684i	−0.0278386	+	0.0160726i
$343$			139.272i			0.406040i
$344$	−13.2061			−0.0383899
$345$	−174.801	+	302.765i	−0.506671	+	0.877579i
$346$	51.5638	−	29.7704i	0.149028	−	0.0860415i
$347$	−525.892	+	303.624i	−1.51554	+	0.874997i	−0.515705	+	0.856766i	$0.672470\pi$
$347$	−525.892	+	303.624i	−1.51554	+	0.874997i	−0.999834	+	0.0182302i	$0.994197\pi$
$348$	261.522	+	150.990i	0.751500	+	0.433879i
$349$	−116.157			−0.332829			−0.166415	−	0.986056i	$-0.553219\pi$
$349$	−116.157			−0.332829			−0.166415	+	0.986056i	$0.553219\pi$
$350$	17.0508			0.0487165
$351$	−8.95172	+	15.5048i	−0.0255035	+	0.0441733i
$352$	−31.7064	+	54.9171i	−0.0900750	+	0.156014i
$353$	−351.820	−	203.123i	−0.996657	−	0.575420i	−0.0893997	−	0.995996i	$-0.528495\pi$
$353$	−351.820	−	203.123i	−0.996657	−	0.575420i	−0.907258	+	0.420575i	$0.861828\pi$
$354$	−13.7040	+	23.7361i	−0.0387120	+	0.0670511i
$355$	−566.236	+	326.917i	−1.59503	+	0.920892i
$356$	−39.5555	−	68.5121i	−0.111111	−	0.192450i
$357$	16.8635			0.0472367
$358$	58.5626	−	101.433i	0.163583	−	0.283334i
$359$	55.1955			0.153748			0.0768739	−	0.997041i	$-0.475506\pi$
$359$	55.1955			0.153748			0.0768739	+	0.997041i	$0.475506\pi$
$360$	−78.6962			−0.218600
$361$	151.372	+	262.184i	0.419312	+	0.726270i
$362$		−	132.772i		−	0.366774i
$363$	168.206	+	97.1136i	0.463377	+	0.267531i
$364$	−9.43177	−	16.3363i	−0.0259115	−	0.0448800i
$365$	−468.944	−	270.745i	−1.28478	−	0.741768i
$366$	−2.43398	+	1.40526i	−0.00665022	+	0.00383951i
$367$	447.549	−	258.393i	1.21948	−	0.704067i	0.254673	−	0.967027i	$-0.418032\pi$
$367$	447.549	−	258.393i	1.21948	−	0.704067i	0.964807	+	0.262960i	$0.0846987\pi$
$368$	190.686	+	330.278i	0.518169	+	0.897496i
$369$	−48.6041	+	28.0616i	−0.131718	+	0.0760477i
$370$	−36.5877	−	63.3718i	−0.0988858	−	0.171275i
$371$	−38.2037	−	66.1707i	−0.102975	−	0.178358i
$372$	−20.3247	+	35.2034i	−0.0546362	+	0.0946327i
$373$	−118.251	+	68.2720i	−0.317025	+	0.183035i	−0.650066	−	0.759878i	$-0.725259\pi$
$373$	−118.251	+	68.2720i	−0.317025	+	0.183035i	0.333040	+	0.942913i	$0.391925\pi$
$374$	−4.79079	+	8.29790i	−0.0128096	+	0.0221869i
$375$	−6.67976			−0.0178127
$376$	113.373	−	65.4559i	0.301524	−	0.174085i
$377$		−	159.364i		−	0.422715i
$378$		−	3.62342i		−	0.00958577i
$379$	413.436	+	238.697i	1.09086	+	0.629808i	0.933805	−	0.357781i	$-0.116467\pi$
$379$	413.436	+	238.697i	1.09086	+	0.629808i	0.157055	+	0.987590i	$0.449800\pi$
$380$		−	202.323i		−	0.532428i
$381$	−347.296	+	200.511i	−0.911538	+	0.526277i
$382$	−46.8948	−	81.2242i	−0.122761	−	0.212629i
$383$	58.8217	+	33.9607i	0.153582	+	0.0886703i	0.574821	−	0.818279i	$-0.305072\pi$
$383$	58.8217	+	33.9607i	0.153582	+	0.0886703i	−0.421240	+	0.906949i	$0.638405\pi$
$384$	−91.6334	+	158.714i	−0.238629	+	0.413317i
$385$	26.3327	+	15.2032i	0.0683966	+	0.0394888i
$386$	−90.1593	−	52.0535i	−0.233573	−	0.134854i
$387$		−	10.6207i		−	0.0274438i
$388$			327.679i			0.844533i
$389$	−114.243	+	197.875i	−0.293685	+	0.508677i	−0.974678	−	0.223613i	$-0.928215\pi$
$389$	−114.243	+	197.875i	−0.293685	+	0.508677i	0.680993	+	0.732289i	$0.261548\pi$
$390$	10.0745	+	17.4496i	0.0258321	+	0.0447426i
$391$	96.2042	+	166.631i	0.246047	+	0.426165i
$392$	−151.481	−	87.4575i	−0.386431	−	0.223106i
$393$			119.013i			0.302832i
$394$	123.374			0.313131
$395$	−238.149	−	412.486i	−0.602909	−	1.04427i
$396$	−29.1556	−	16.8330i	−0.0736252	−	0.0425075i
$397$	115.310			0.290453			0.145226	−	0.989398i	$-0.453609\pi$
$397$	115.310			0.290453			0.145226	+	0.989398i	$0.453609\pi$
$398$	−147.082	+	84.9177i	−0.369552	+	0.213361i
$399$	19.2008			0.0481224
$400$	162.444	−	281.360i	0.406109	−	0.703401i
$401$		−	263.225i		−	0.656420i	−0.944605	−	0.328210i	$-0.893555\pi$
$401$		−	263.225i		−	0.656420i	0.944605	−	0.328210i	$-0.106445\pi$
$402$	−52.1436	+	19.6315i	−0.129710	+	0.0488347i
$403$	21.4519			0.0532305
$404$	115.391	+	66.6212i	0.285622	+	0.164904i
$405$		−	63.2896i		−	0.156271i
$406$	16.1266	+	27.9320i	0.0397206	+	0.0687981i
$407$		−	64.5228i		−	0.158533i
$408$	−21.6557	+	37.5088i	−0.0530778	+	0.0919334i
$409$	−229.203	+	132.330i	−0.560399	+	0.323546i	−0.753305	−	0.657671i	$-0.771542\pi$
$409$	−229.203	+	132.330i	−0.560399	+	0.323546i	0.192907	+	0.981217i	$0.438208\pi$
$410$			63.1628i			0.154056i
$411$	297.838			0.724666
$412$	−44.1411	+	76.4546i	−0.107139	+	0.185570i
$413$	41.4558	−	23.9345i	0.100377	−	0.0579529i
$414$	35.8035	−	20.6712i	0.0864820	−	0.0499304i
$415$	−103.427	−	59.7135i	−0.249221	−	0.143888i
$416$	73.3912			0.176421
$417$	−378.643			−0.908017
$418$	−5.45481	+	9.44801i	−0.0130498	+	0.0226029i
$419$	236.463	−	409.565i	0.564350	−	0.977483i	−0.432760	−	0.901509i	$-0.642460\pi$
$419$	236.463	−	409.565i	0.564350	−	0.977483i	0.997110	−	0.0759736i	$-0.0242065\pi$
$420$	57.7498	+	33.3418i	0.137499	+	0.0793853i
$421$	111.634	−	193.355i	0.265163	−	0.459275i	−0.702443	−	0.711740i	$-0.747908\pi$
$421$	111.634	−	193.355i	0.265163	−	0.459275i	0.967606	+	0.252464i	$0.0812410\pi$
$422$	−56.3120	+	32.5118i	−0.133441	+	0.0770421i
$423$	52.6414	+	91.1777i	0.124448	+	0.215550i
$424$	196.241			0.462833
$425$	81.9553	−	141.951i	0.192836	−	0.334002i
$426$	77.3192			0.181501
$427$	4.90866			0.0114957
$428$	−106.426	−	184.336i	−0.248659	−	0.430691i
$429$			17.7665i			0.0414138i
$430$	−10.3515	−	5.97646i	−0.0240733	−	0.0138987i
$431$	−291.832	−	505.468i	−0.677104	−	1.17278i	−0.975849	−	0.218446i	$-0.929901\pi$
$431$	−291.832	−	505.468i	−0.677104	−	1.17278i	0.298745	−	0.954333i	$-0.403432\pi$
$432$	−59.7913	−	34.5205i	−0.138406	−	0.0799086i
$433$	−196.678	+	113.552i	−0.454222	+	0.262245i	−0.709612	−	0.704593i	$-0.751130\pi$
$433$	−196.678	+	113.552i	−0.454222	+	0.262245i	0.255390	+	0.966838i	$0.417796\pi$
$434$	−3.75992	+	2.17079i	−0.00866340	+	0.00500182i
$435$	281.680	+	487.884i	0.647540	+	1.12157i
$436$	95.1715	−	54.9473i	0.218283	−	0.126026i
$437$	109.538	+	189.726i	0.250660	+	0.434156i
$438$	32.0170	+	55.4551i	0.0730983	+	0.126610i
$439$	−237.788	+	411.862i	−0.541659	+	0.938181i	0.457150	+	0.889390i	$0.348870\pi$
$439$	−237.788	+	411.862i	−0.541659	+	0.938181i	−0.998809	+	0.0487915i	$0.984463\pi$
$440$	−67.6317	+	39.0472i	−0.153708	+	0.0887436i
$441$	70.3358	−	121.825i	0.159492	−	0.276248i
$442$	11.0893			0.0250889
$443$	171.329	−	98.9169i	0.386748	−	0.223289i	−0.294002	−	0.955805i	$-0.594987\pi$
$443$	171.329	−	98.9169i	0.386748	−	0.223289i	0.680750	+	0.732516i	$0.261654\pi$
$444$		−	141.504i		−	0.318702i
$445$		−	147.586i		−	0.331654i
$446$	−75.6016	−	43.6486i	−0.169510	−	0.0978668i
$447$		−	355.162i		−	0.794547i
$448$	53.9868	−	31.1693i	0.120506	−	0.0695743i
$449$	219.367	+	379.954i	0.488567	+	0.846223i	0.999914	−	0.0131518i	$-0.00418647\pi$
$449$	219.367	+	379.954i	0.488567	+	0.846223i	−0.511347	+	0.859375i	$0.670853\pi$
$450$	−30.5006	−	17.6095i	−0.0677792	−	0.0391323i
$451$	−27.8470	+	48.2324i	−0.0617450	+	0.106946i
$452$	−185.883	−	107.319i	−0.411245	−	0.237432i
$453$	−335.740	−	193.840i	−0.741148	−	0.427902i
$454$		−	4.44213i		−	0.00978442i
$455$		−	35.1910i		−	0.0773428i
$456$	−24.6573	+	42.7076i	−0.0540730	+	0.0936571i
$457$	−231.747	−	401.397i	−0.507104	−	0.878331i	−0.999966	−	0.00822292i	$-0.997383\pi$
$457$	−231.747	−	401.397i	−0.507104	−	0.878331i	0.492862	−	0.870108i	$-0.335951\pi$
$458$	−63.8824	−	110.648i	−0.139481	−	0.241589i
$459$	−30.1656	−	17.4161i	−0.0657203	−	0.0379437i
$460$			760.845i			1.65401i
$461$	371.634			0.806148			0.403074	−	0.915167i	$-0.367942\pi$
$461$	371.634			0.806148			0.403074	+	0.915167i	$0.367942\pi$
$462$	−1.79786	−	3.11398i	−0.00389146	−	0.00674021i
$463$	212.430	+	122.646i	0.458811	+	0.264895i	0.711544	−	0.702641i	$-0.247996\pi$
$463$	212.430	+	122.646i	0.458811	+	0.264895i	−0.252733	+	0.967536i	$0.581329\pi$
$464$	614.554			1.32447
$465$	−65.6738	+	37.9168i	−0.141234	+	0.0815415i
$466$	−77.5648			−0.166448
$467$	−47.6261	+	82.4908i	−0.101983	+	0.176640i	−0.912502	−	0.409073i	$-0.865852\pi$
$467$	−47.6261	+	82.4908i	−0.101983	+	0.176640i	0.810519	+	0.585713i	$0.199185\pi$
$468$			38.9635i			0.0832553i
$469$	96.0128	+	15.8417i	0.204718	+	0.0337776i
$470$	118.489			0.252103
$471$	301.573	+	174.113i	0.640283	+	0.369668i
$472$			122.945i			0.260476i
$473$	−5.26977	−	9.12750i	−0.0111412	−	0.0192970i
$474$			56.3248i			0.118829i
$475$	93.3145	−	161.626i	0.196452	−	0.340264i
$476$	31.7833	−	18.3501i	0.0667717	−	0.0385507i
$477$			157.823i			0.330865i
$478$	−27.3132			−0.0571407
$479$	−134.658	+	233.234i	−0.281123	+	0.486920i	−0.971662	−	0.236376i	$-0.924040\pi$
$479$	−134.658	+	233.234i	−0.281123	+	0.486920i	0.690539	+	0.723296i	$0.257374\pi$
$480$	−224.683	+	129.721i	−0.468090	+	0.270252i
$481$	−64.6712	+	37.3379i	−0.134451	+	0.0776256i
$482$	−21.7197	−	12.5399i	−0.0450616	−	0.0260163i
$483$	−72.2057			−0.149494
$484$	422.699			0.873345
$485$	−305.652	+	529.404i	−0.630209	+	1.09155i
$486$	−3.74217	+	6.48162i	−0.00769993	+	0.0133367i
$487$	315.157	+	181.956i	0.647139	+	0.373626i	0.787359	−	0.616494i	$-0.211448\pi$
$487$	315.157	+	181.956i	0.647139	+	0.373626i	−0.140220	+	0.990120i	$0.544781\pi$
$488$	−6.30359	+	10.9181i	−0.0129172	+	0.0223732i
$489$	431.952	−	249.387i	0.883336	−	0.509995i
$490$	−79.1581	−	137.106i	−0.161547	−	0.279808i
$491$	289.711			0.590042			0.295021	−	0.955491i	$-0.404673\pi$
$491$	289.711			0.590042			0.295021	+	0.955491i	$0.404673\pi$
$492$	−61.0708	+	105.778i	−0.124128	+	0.214995i
$493$	310.052			0.628909
$494$	12.6263			0.0255593
$495$	−31.4028	−	54.3913i	−0.0634401	−	0.109881i
$496$			82.7249i			0.166784i
$497$	−116.948	−	67.5202i	−0.235309	−	0.135856i
$498$	7.06143	+	12.2308i	0.0141796	+	0.0245598i
$499$	−192.983	−	111.419i	−0.386740	−	0.223285i	0.294006	−	0.955803i	$-0.405011\pi$
$499$	−192.983	−	111.419i	−0.386740	−	0.223285i	−0.680747	+	0.732519i	$0.738345\pi$
$500$	−12.5896	+	7.26863i	−0.0251793	+	0.0145373i
$501$	−212.175	+	122.500i	−0.423504	+	0.244510i
$502$	−7.84757	−	13.5924i	−0.0156326	−	0.0270765i
$503$	725.392	−	418.805i	1.44213	−	0.832614i	0.444139	−	0.895958i	$-0.353510\pi$
$503$	725.392	−	418.805i	1.44213	−	0.832614i	0.997992	+	0.0633438i	$0.0201765\pi$
$504$	−8.12681	−	14.0761i	−0.0161246	−	0.0279287i
$505$	124.285	+	215.269i	0.246110	+	0.426275i
$506$	20.5131	−	35.5298i	0.0405398	−	0.0702169i
$507$	−235.693	+	136.077i	−0.464877	+	0.268397i
$508$	−436.376	+	755.825i	−0.859007	+	1.48784i
$509$	620.621			1.21930			0.609648	−	0.792673i	$-0.291311\pi$
$509$	620.621			1.21930			0.609648	+	0.792673i	$0.291311\pi$
$510$	−33.9493	+	19.6007i	−0.0665673	+	0.0384327i
$511$		−	111.838i		−	0.218860i
$512$			481.275i			0.939990i
$513$	−34.3467	−	19.8301i	−0.0669526	−	0.0386551i
$514$		−	53.2173i		−	0.103536i
$515$	−142.630	+	82.3477i	−0.276952	+	0.159898i
$516$	−11.5570	−	20.0174i	−0.0223974	−	0.0387934i
$517$	90.4804	+	52.2389i	0.175011	+	0.101042i
$518$	7.55670	−	13.0886i	0.0145882	−	0.0252676i
$519$	186.018	+	107.398i	0.358417	+	0.206932i
$520$	78.2740	+	45.1915i	0.150527	+	0.0869067i
$521$		−	679.715i		−	1.30464i	−0.757946	−	0.652318i	$-0.773797\pi$
$521$		−	679.715i		−	1.30464i	0.757946	−	0.652318i	$-0.226203\pi$
$522$		−	66.6202i		−	0.127625i
$523$	70.2494	−	121.675i	0.134320	−	0.232649i	−0.791017	−	0.611794i	$-0.790448\pi$
$523$	70.2494	−	121.675i	0.134320	−	0.232649i	0.925337	+	0.379144i	$0.123782\pi$
$524$	129.505	+	224.309i	0.247147	+	0.428071i
$525$	30.7556	+	53.2703i	0.0585821	+	0.101467i
$526$	−54.2094	−	31.2978i	−0.103060	−	0.0595016i
$527$			41.7360i			0.0791954i
$528$	−68.5131			−0.129760
$529$	−147.425	−	255.348i	−0.278686	−	0.482699i
$530$	153.822	+	88.8092i	0.290230	+	0.167565i
$531$	−98.8757			−0.186207
$532$	36.1886	−	20.8935i	0.0680237	−	0.0392735i
$533$	64.4578			0.120934
$534$	−8.72641	+	15.1146i	−0.0163416	+	0.0283045i
$535$		−	397.088i		−	0.742220i
$536$	−158.534	+	193.214i	−0.295772	+	0.360474i
$537$	422.533			0.786841
$538$	−191.175	−	110.375i	−0.355343	−	0.205157i
$539$		−	139.596i		−	0.258991i
$540$	−68.8690	−	119.285i	−0.127535	−	0.220898i
$541$		−	521.918i		−	0.964729i	−0.875971	−	0.482364i	$-0.839778\pi$
$541$		−	521.918i		−	0.964729i	0.875971	−	0.482364i	$-0.160222\pi$
$542$	62.5125	−	108.275i	0.115337	−	0.199769i
$543$	414.809	−	239.490i	0.763921	−	0.441050i
$544$			142.787i			0.262477i
$545$	205.014			0.376173
$546$	−2.08076	+	3.60398i	−0.00381091	+	0.00660070i
$547$	462.509	−	267.029i	0.845537	−	0.488171i	−0.0136056	−	0.999907i	$-0.504331\pi$
$547$	462.509	−	267.029i	0.845537	−	0.488171i	0.859142	+	0.511737i	$0.170998\pi$
$548$	561.347	−	324.094i	1.02436	−	0.591413i
$549$	−8.78067	−	5.06952i	−0.0159939	−	0.00923410i
$550$	−34.9498			−0.0635451
$551$	353.026			0.640701
$552$	92.7250	−	160.604i	0.167980	−	0.290950i
$553$	49.1865	−	85.1935i	0.0889448	−	0.154057i
$554$	141.172	+	81.5058i	0.254823	+	0.147122i
$555$	131.992	−	228.616i	0.237823	−	0.411921i
$556$	−713.645	+	412.023i	−1.28353	+	0.741048i
$557$	39.9730	+	69.2353i	0.0717648	+	0.124300i	0.899675	−	0.436561i	$-0.143804\pi$
$557$	39.9730	+	69.2353i	0.0717648	+	0.124300i	−0.827910	+	0.560861i	$0.810470\pi$
$558$	8.96772			0.0160712
$559$	−6.09899	+	10.5638i	−0.0109105	+	0.0188976i
$560$	135.707			0.242334
$561$	−34.5659			−0.0616148
$562$	−107.997	−	187.056i	−0.192165	−	0.332839i
$563$		−	237.994i		−	0.422724i	−0.977408	−	0.211362i	$-0.932210\pi$
$563$		−	237.994i		−	0.422724i	0.977408	−	0.211362i	$-0.0677900\pi$
$564$	198.431	+	114.564i	0.351828	+	0.203128i
$565$	−200.210	−	346.775i	−0.354355	−	0.613760i
$566$	−133.177	−	76.8897i	−0.235295	−	0.135848i
$567$	11.3204	−	6.53581i	0.0199653	−	0.0115270i
$568$	300.365	−	173.416i	0.528812	−	0.305310i
$569$	236.116	+	408.965i	0.414967	+	0.718743i	0.995425	−	0.0955468i	$-0.0304599\pi$
$569$	236.116	+	408.965i	0.414967	+	0.718743i	−0.580458	+	0.814290i	$0.697127\pi$
$570$	−38.6548	+	22.3174i	−0.0678155	+	0.0391533i
$571$	−160.271	−	277.597i	−0.280684	−	0.486159i	0.690869	−	0.722980i	$-0.257228\pi$
$571$	−160.271	−	277.597i	−0.280684	−	0.486159i	−0.971553	+	0.236820i	$0.923895\pi$
$572$	19.3328	+	33.4853i	0.0337985	+	0.0585408i
$573$	169.175	−	293.019i	0.295244	−	0.511377i
$574$	−11.2977	+	6.52271i	−0.0196823	+	0.0113636i
$575$	−350.914	+	607.801i	−0.610286	+	1.05705i
$576$	−128.763			−0.223547
$577$	−637.189	+	367.881i	−1.10431	+	0.637575i	−0.937350	−	0.348388i	$-0.886729\pi$
$577$	−637.189	+	367.881i	−1.10431	+	0.637575i	−0.166963	+	0.985963i	$0.553396\pi$
$578$		−	117.180i		−	0.202733i
$579$		−	375.570i		−	0.648652i
$580$	1061.79	+	613.023i	1.83067	+	1.05694i
$581$		−	24.6660i		−	0.0424544i
$582$	62.6048	−	36.1449i	0.107568	−	0.0621047i
$583$	78.3079	+	135.633i	0.134319	+	0.232647i
$584$	248.756	+	143.619i	0.425952	+	0.245923i
$585$	−36.3443	+	62.9501i	−0.0621269	+	0.107607i
$586$	213.131	+	123.051i	0.363705	+	0.209985i
$587$	−865.145	−	499.492i	−1.47384	−	0.850923i	−0.474276	−	0.880376i	$-0.657290\pi$
$587$	−865.145	−	499.492i	−1.47384	−	0.850923i	−0.999566	+	0.0294531i	$0.990623\pi$
$588$		−	306.145i		−	0.520655i
$589$			47.5207i			0.0806803i
$590$	−55.6389	+	96.3693i	−0.0943032	+	0.163338i
$591$	222.537	+	385.446i	0.376544	+	0.652193i
$592$	−143.986	−	249.391i	−0.243220	−	0.421269i
$593$	−419.821	−	242.384i	−0.707962	−	0.408742i	0.102344	−	0.994749i	$-0.467366\pi$
$593$	−419.821	−	242.384i	−0.707962	−	0.408742i	−0.810306	+	0.586007i	$0.800699\pi$
$594$			7.42710i			0.0125035i
$595$	68.4663			0.115069
$596$	−386.472	−	669.389i	−0.648443	−	1.12314i
$597$	−530.603	−	306.344i	−0.888782	−	0.513139i
$598$	−47.4819			−0.0794012
$599$	−376.237	+	217.220i	−0.628108	+	0.362638i	−0.780019	−	0.625756i	$-0.784791\pi$
$599$	−376.237	+	217.220i	−0.628108	+	0.362638i	0.151911	+	0.988394i	$0.451457\pi$
$600$	−157.983			−0.263305
$601$	532.692	−	922.649i	0.886342	−	1.53519i	0.0421749	−	0.999110i	$-0.486571\pi$
$601$	532.692	−	922.649i	0.886342	−	1.53519i	0.844167	−	0.536080i	$-0.180095\pi$
$602$		−	2.46871i		−	0.00410085i
$603$	−155.388	−	127.497i	−0.257692	−	0.211438i
$604$	−843.711			−1.39687
$605$	682.920	+	394.284i	1.12879	+	0.651710i
$606$		−	29.3948i		−	0.0485063i
$607$	279.477	+	484.069i	0.460424	+	0.797478i	0.998982	−	0.0451107i	$-0.0143641\pi$
$607$	279.477	+	484.069i	0.460424	+	0.797478i	−0.538558	+	0.842588i	$0.681031\pi$
$608$			162.578i			0.267398i
$609$	−58.1772	+	100.766i	−0.0955290	+	0.165461i
$610$	−9.88204	+	5.70540i	−0.0162001	+	0.00935311i
$611$		−	120.918i		−	0.197902i
$612$	−75.8059			−0.123866
$613$	31.0639	−	53.8042i	0.0506751	−	0.0877719i	−0.839575	−	0.543244i	$-0.817196\pi$
$613$	31.0639	−	53.8042i	0.0506751	−	0.0877719i	0.890250	+	0.455472i	$0.150529\pi$
$614$	83.4378	−	48.1728i	0.135892	−	0.0784573i
$615$	−197.334	+	113.931i	−0.320869	+	0.185254i
$616$	−13.9684	−	8.06467i	−0.0226760	−	0.0130920i
$617$	337.079			0.546319			0.273160	−	0.961969i	$-0.411931\pi$
$617$	337.079			0.546319			0.273160	+	0.961969i	$0.411931\pi$
$618$	19.4761			0.0315147
$619$	475.530	−	823.643i	0.768223	−	1.33060i	−0.170302	−	0.985392i	$-0.554474\pi$
$619$	475.530	−	823.643i	0.768223	−	1.33060i	0.938525	−	0.345210i	$-0.112192\pi$
$620$	−82.5188	+	142.927i	−0.133095	+	0.230527i
$621$	129.163	+	74.5720i	0.207991	+	0.120084i
$622$	−115.815	+	200.598i	−0.186198	+	0.322504i
$623$	26.3981	−	15.2409i	0.0423725	−	0.0244638i
$624$	39.6470	+	68.6706i	0.0635369	+	0.110049i
$625$	−638.410			−1.02146
$626$	27.5248	−	47.6744i	0.0439694	−	0.0761572i
$627$	−39.3569			−0.0627701
$628$	757.851			1.20677
$629$	−72.6433	−	125.822i	−0.115490	−	0.200035i
$630$		−	14.7112i		−	0.0233511i
$631$	641.367	+	370.294i	1.01643	+	0.586836i	0.913068	−	0.407808i	$-0.133707\pi$
$631$	641.367	+	370.294i	1.01643	+	0.586836i	0.103362	+	0.994644i	$0.467040\pi$
$632$	126.328	+	218.807i	0.199887	+	0.346214i
$633$	−203.148	−	117.287i	−0.320928	−	0.185288i
$634$	105.885	−	61.1329i	0.167012	−	0.0964242i
$635$	−1410.03	+	814.083i	−2.22052	+	1.28202i
$636$	171.736	+	297.455i	0.270025	+	0.467697i
$637$	−139.917	+	80.7811i	−0.219650	+	0.126815i
$638$	−33.0554	−	57.2536i	−0.0518110	−	0.0897392i
$639$	139.466	+	241.562i	0.218257	+	0.378031i
$640$	−372.035	+	644.383i	−0.581304	+	1.00685i
$641$	−1047.38	+	604.705i	−1.63398	+	0.943378i	−0.651130	+	0.758966i	$0.725705\pi$
$641$	−1047.38	+	604.705i	−1.63398	+	0.943378i	−0.982849	+	0.184412i	$0.940962\pi$
$642$	−23.4789	+	40.6666i	−0.0365714	+	0.0633436i
$643$	−975.863			−1.51767			−0.758836	−	0.651282i	$-0.774232\pi$
$643$	−975.863			−1.51767			−0.758836	+	0.651282i	$0.774232\pi$
$644$	−136.089	+	78.5711i	−0.211319	+	0.122005i
$645$		−	43.1206i		−	0.0668536i
$646$			24.5653i			0.0380268i
$647$	282.780	+	163.263i	0.437064	+	0.252339i	0.702351	−	0.711830i	$-0.252134\pi$
$647$	282.780	+	163.263i	0.437064	+	0.252339i	−0.265287	+	0.964169i	$0.585467\pi$
$648$			33.5726i			0.0518095i
$649$	−84.9741	+	49.0598i	−0.130931	+	0.0755929i
$650$	20.2247	+	35.0301i	0.0311149	+	0.0538925i
$651$	−13.5640	−	7.83120i	−0.0208357	−	0.0120295i
$652$	542.745	−	940.062i	0.832431	−	1.44181i
$653$	−183.656	−	106.034i	−0.281250	−	0.162380i	0.352739	−	0.935722i	$-0.385250\pi$
$653$	−183.656	−	106.034i	−0.281250	−	0.162380i	−0.633989	+	0.773342i	$0.718584\pi$
$654$	−20.9959	−	12.1220i	−0.0321039	−	0.0185352i
$655$			483.197i			0.737706i
$656$			248.569i			0.378916i
$657$	−115.503	+	200.056i	−0.175803	+	0.304500i
$658$	12.2361	+	21.1936i	0.0185959	+	0.0322091i
$659$	75.1882	+	130.230i	0.114094	+	0.197617i	0.917417	−	0.397926i	$-0.130270\pi$
$659$	75.1882	+	130.230i	0.114094	+	0.197617i	−0.803323	+	0.595544i	$0.796937\pi$
$660$	−118.373	−	68.3424i	−0.179352	−	0.103549i
$661$			286.923i			0.434074i	0.976163	+	0.217037i	$0.0696392\pi$
$661$			286.923i			0.434074i	−0.976163	+	0.217037i	$0.930361\pi$
$662$	−0.969070			−0.00146385
$663$	20.0025	+	34.6454i	0.0301697	+	0.0522555i
$664$	54.8637	+	31.6756i	0.0826260	+	0.0477042i
$665$	77.9559			0.117227
$666$	−27.0351	+	15.6087i	−0.0405932	+	0.0234365i
$667$	−1327.57			−1.99037
$668$	−266.597	+	461.760i	−0.399098	+	0.691258i
$669$		−	314.928i		−	0.470744i
$670$	−211.705	+	79.7046i	−0.315977	+	0.118962i
$671$	−10.0615			−0.0149948
$672$	−46.4053	−	26.7921i	−0.0690555	−	0.0398692i
$673$		−	755.959i		−	1.12327i	−0.827386	−	0.561634i	$-0.810173\pi$
$673$		−	755.959i		−	1.12327i	0.827386	−	0.561634i	$-0.189827\pi$
$674$	130.087	+	225.317i	0.193007	+	0.334298i
$675$		−	127.054i		−	0.188228i
$676$	−296.147	+	512.941i	−0.438087	+	0.758788i
$677$	−842.899	+	486.648i	−1.24505	+	0.718830i	−0.970118	−	0.242633i	$-0.921989\pi$
$677$	−842.899	+	486.648i	−1.24505	+	0.718830i	−0.274933	+	0.961463i	$0.588656\pi$
$678$			47.3519i			0.0698405i
$679$	−126.256			−0.185945
$680$	−87.9230	+	152.287i	−0.129298	+	0.223952i
$681$	13.8782	−	8.01257i	0.0203791	−	0.0117659i
$682$	7.70689	−	4.44957i	0.0113004	−	0.00652430i
$683$	−502.811	−	290.298i	−0.736180	−	0.425034i	0.0844985	−	0.996424i	$-0.473071\pi$
$683$	−502.811	−	290.298i	−0.736180	−	0.425034i	−0.820679	+	0.571390i	$0.806405\pi$
$684$	−86.3129			−0.126188
$685$	1209.23			1.76530
$686$	33.4335	−	57.9086i	0.0487370	−	0.0844149i
$687$	230.458	−	399.165i	0.335456	−	0.581026i
$688$	−40.7371	−	23.5196i	−0.0592109	−	0.0341854i
$689$	90.6301	−	156.976i	0.131539	−	0.227832i
$690$	145.364	−	83.9257i	0.210672	−	0.121631i
$691$	285.709	+	494.863i	0.413472	+	0.716155i	0.995267	−	0.0971810i	$-0.0309826\pi$
$691$	285.709	+	494.863i	0.413472	+	0.716155i	−0.581795	+	0.813336i	$0.697649\pi$
$692$	467.462			0.675523
$693$	6.48583	−	11.2338i	0.00935906	−	0.0162104i
$694$	291.552			0.420103
$695$	−1537.30			−2.21195
$696$	−149.420	−	258.802i	−0.214683	−	0.371843i
$697$			125.407i			0.179924i
$698$	48.2978	+	27.8848i	0.0691946	+	0.0399495i
$699$	−139.909	−	242.329i	−0.200156	−	0.346680i
$700$	115.933	+	66.9339i	0.165618	+	0.0956198i
$701$	−778.853	+	449.671i	−1.11106	+	0.641471i	−0.939104	−	0.343634i	$-0.888342\pi$
$701$	−778.853	+	449.671i	−1.11106	+	0.641471i	−0.171956	+	0.985105i	$0.555009\pi$
$702$	7.44418	−	4.29790i	0.0106042	−	0.00612236i
$703$	−82.7119	−	143.261i	−0.117656	−	0.203785i
$704$	−110.659	+	63.8892i	−0.157187	+	0.0907517i
$705$	213.726	+	370.184i	0.303157	+	0.525084i
$706$	97.5236	+	168.916i	0.138135	+	0.239258i
$707$	−25.6695	+	44.4608i	−0.0363076	+	0.0628866i
$708$	−186.355	+	107.592i	−0.263214	+	0.151966i
$709$	−382.376	+	662.295i	−0.539318	+	0.934126i	0.459623	+	0.888114i	$0.347985\pi$
$709$	−382.376	+	662.295i	−0.539318	+	0.934126i	−0.998941	+	0.0460119i	$0.985349\pi$
$710$	313.918			0.442139
$711$	−175.971	+	101.597i	−0.247498	+	0.142893i
$712$			78.2883i			0.109956i
$713$		−	178.704i		−	0.250637i
$714$	−7.01178	−	4.04825i	−0.00982042	−	0.00566982i
$715$			72.1327i			0.100885i
$716$	796.367	−	459.783i	1.11224	−	0.642154i
$717$	−49.2668	−	85.3325i	−0.0687123	−	0.119013i
$718$	−22.9501	−	13.2502i	−0.0319639	−	0.0184544i
$719$	82.8384	−	143.480i	0.115213	−	0.199555i	−0.802652	−	0.596448i	$-0.796578\pi$
$719$	82.8384	−	143.480i	0.115213	−	0.199555i	0.917865	+	0.396893i	$0.129911\pi$
$720$	−242.755	−	140.154i	−0.337159	−	0.194659i
$721$	−29.4584	−	17.0078i	−0.0408577	−	0.0235892i
$722$		−	145.353i		−	0.201320i
$723$		−	90.4760i		−	0.125140i
$724$	521.206	−	902.755i	0.719897	−	1.24690i
$725$	565.473	+	979.428i	0.779963	+	1.35094i
$726$	−46.6262	−	80.7589i	−0.0642234	−	0.111238i
$727$	−1252.25	−	722.989i	−1.72249	−	0.994482i	−0.913699	−	0.406392i	$-0.866787\pi$
$727$	−1252.25	−	722.989i	−1.72249	−	0.994482i	−0.808795	−	0.588090i	$-0.799880\pi$
$728$			18.6674i			0.0256420i
$729$	−27.0000			−0.0370370
$730$	129.990	+	225.150i	0.178069	+	0.308424i
$731$	−20.5525	−	11.8660i	−0.0281156	−	0.0162325i
$732$	−22.0657			−0.0301444
$733$	1126.84	−	650.579i	1.53729	−	0.887557i	0.538298	−	0.842755i	$-0.319067\pi$
$733$	1126.84	−	650.579i	1.53729	−	0.887557i	0.998996	−	0.0448025i	$-0.0142658\pi$
$734$	−248.119			−0.338037
$735$	285.566	−	494.614i	0.388525	−	0.672944i
$736$		−	611.383i		−	0.830684i
$737$	−196.802	−	32.4715i	−0.267031	−	0.0440591i
$738$	26.9459			0.0365120
$739$	−640.668	−	369.890i	−0.866939	−	0.500527i	−0.000608988	−	1.00000i	$-0.500194\pi$
$739$	−640.668	−	369.890i	−0.866939	−	0.500527i	−0.866330	+	0.499473i	$0.833527\pi$
$740$		−	574.510i		−	0.776365i
$741$	22.7749	+	39.4474i	0.0307354	+	0.0532353i
$742$			36.6847i			0.0494403i
$743$	−486.268	+	842.240i	−0.654465	+	1.13357i	0.327562	+	0.944830i	$0.393773\pi$
$743$	−486.268	+	842.240i	−0.654465	+	1.13357i	−0.982028	+	0.188738i	$0.939560\pi$
$744$	34.8373	−	20.1133i	0.0468243	−	0.0270340i
$745$		−	1441.97i		−	1.93553i
$746$	65.5575			0.0878787
$747$	−25.4744	+	44.1229i	−0.0341022	+	0.0590668i
$748$	−65.1479	+	37.6131i	−0.0870961	+	0.0502849i
$749$	71.0255	−	41.0066i	0.0948271	−	0.0547484i
$750$	2.77742	+	1.60354i	0.00370323	+	0.00213806i
$751$	−284.406			−0.378703			−0.189351	−	0.981909i	$-0.560639\pi$
$751$	−284.406			−0.378703			−0.189351	+	0.981909i	$0.560639\pi$
$752$	466.296			0.620075
$753$	28.3104	−	49.0351i	0.0375968	−	0.0651196i
$754$	−38.2569	+	66.2628i	−0.0507385	+	0.0878817i
$755$	−1363.12	−	786.995i	−1.80545	−	1.04238i
$756$	14.2240	−	24.6366i	0.0188148	−	0.0325881i
$757$	362.567	−	209.328i	0.478953	−	0.276524i	−0.241027	−	0.970518i	$-0.577484\pi$
$757$	362.567	−	209.328i	0.478953	−	0.276524i	0.719980	+	0.693995i	$0.244151\pi$
$758$	−114.603	−	198.499i	−0.151192	−	0.261872i
$759$	148.004			0.194998
$760$	−100.109	+	173.394i	−0.131723	+	0.228151i
$761$	1336.17			1.75581			0.877904	−	0.478837i	$-0.158941\pi$
$761$	1336.17			1.75581			0.877904	+	0.478837i	$0.158941\pi$
$762$	192.539			0.252676
$763$	21.1715	+	36.6701i	0.0277477	+	0.0480604i
$764$		−	736.354i		−	0.963814i
$765$	−122.473	−	70.7101i	−0.160096	−	0.0924315i
$766$	−16.3052	−	28.2415i	−0.0212862	−	0.0368688i
$767$	98.3452	+	56.7796i	0.128221	+	0.0740282i
$768$	−181.324	+	104.688i	−0.236100	+	0.136312i
$769$	697.289	−	402.580i	0.906748	−	0.523511i	0.0273646	−	0.999626i	$-0.491288\pi$
$769$	697.289	−	402.580i	0.906748	−	0.523511i	0.879383	+	0.476114i	$0.157955\pi$
$770$	−7.29935	−	12.6429i	−0.00947968	−	0.0164193i
$771$	166.262	−	95.9917i	0.215645	−	0.124503i
$772$	−408.679	−	707.852i	−0.529376	−	0.916907i
$773$	399.205	+	691.444i	0.516436	+	0.894494i	0.999818	+	0.0190839i	$0.00607498\pi$
$773$	399.205	+	691.444i	0.516436	+	0.894494i	−0.483382	+	0.875410i	$0.660592\pi$
$774$	−2.54962	+	4.41607i	−0.00329408	+	0.00570551i
$775$	−131.840	+	76.1181i	−0.170117	+	0.0982169i
$776$	162.136	−	280.827i	0.208938	−	0.361891i
$777$	54.5222			0.0701701
$778$	95.0039	−	54.8505i	0.122113	−	0.0705019i
$779$			142.789i			0.183297i
$780$			158.193i			0.202811i
$781$	239.715	+	138.399i	0.306933	+	0.177208i
$782$		−	92.3792i		−	0.118132i
$783$	208.136	−	120.167i	0.265819	−	0.153471i
$784$	−311.516	−	539.562i	−0.397342	−	0.688217i
$785$	1224.40	+	706.906i	1.55974	+	0.900518i
$786$	28.5703	−	49.4852i	0.0363490	−	0.0629583i
$787$	111.643	+	64.4571i	0.141859	+	0.0819022i	0.569250	−	0.822165i	$-0.307234\pi$
$787$	111.643	+	64.4571i	0.141859	+	0.0819022i	−0.427391	+	0.904067i	$0.640567\pi$
$788$	838.852	+	484.311i	1.06453	+	0.614608i
$789$		−	225.816i		−	0.286205i
$790$			228.680i			0.289469i
$791$	41.3507	−	71.6216i	0.0522765	−	0.0905456i
$792$	16.6579	+	28.8524i	0.0210327	+	0.0364298i
$793$	5.82238	+	10.0847i	0.00734221	+	0.0127171i
$794$	−47.9453	−	27.6812i	−0.0603845	−	0.0348630i
$795$			640.765i			0.805994i
$796$	−1333.40			−1.67513
$797$	273.670	+	474.010i	0.343375	+	0.594743i	0.985057	−	0.172228i	$-0.0550965\pi$
$797$	273.670	+	474.010i	0.343375	+	0.594743i	−0.641682	+	0.766971i	$0.721763\pi$
$798$	−7.98363	−	4.60935i	−0.0100045	−	0.00577613i
$799$	235.254			0.294435
$800$	−451.052	+	260.415i	−0.563815	+	0.325519i
$801$	−62.9617			−0.0786038
$802$	−63.1897	+	109.448i	−0.0787902	+	0.136469i
$803$			229.239i			0.285478i
$804$	−431.603	−	71.2128i	−0.536820	−	0.0885731i
$805$	−293.158			−0.364171
$806$	−8.91961	−	5.14974i	−0.0110665	−	0.00638925i
$807$		−	796.361i		−	0.986817i
$808$	−65.9284	−	114.191i	−0.0815945	−	0.141326i
$809$			730.265i			0.902676i	0.892353	+	0.451338i	$0.149053\pi$
$809$			730.265i			0.902676i	−0.892353	+	0.451338i	$0.850947\pi$
$810$	−15.1933	+	26.3156i	−0.0187572	+	0.0324884i
$811$	146.704	−	84.6996i	0.180893	−	0.104438i	−0.406819	−	0.913509i	$-0.633362\pi$
$811$	146.704	−	84.6996i	0.180893	−	0.104438i	0.587712	+	0.809070i	$0.300029\pi$
$812$			253.223i			0.311851i
$813$	451.032			0.554775
$814$	−15.4893	+	26.8283i	−0.0190287	+	0.0329586i
$815$	1753.74	−	1012.52i	2.15182	−	1.24236i
$816$	−133.603	+	77.1358i	−0.163729	+	0.0945292i
$817$	−23.4011	−	13.5106i	−0.0286427	−	0.0165369i
$818$	127.069			0.155341
$819$	−15.0128			−0.0183307
$820$	−247.949	+	429.461i	−0.302377	+	0.523733i
$821$	253.895	−	439.759i	0.309251	−	0.535639i	−0.668948	−	0.743310i	$-0.733255\pi$
$821$	253.895	−	439.759i	0.309251	−	0.535639i	0.978199	+	0.207671i	$0.0665883\pi$
$822$	−123.840	−	71.4989i	−0.150657	−	0.0869817i
$823$	−360.162	+	623.819i	−0.437621	+	0.757982i	−0.997505	−	0.0705889i	$-0.977512\pi$
$823$	−360.162	+	623.819i	−0.437621	+	0.757982i	0.559885	+	0.828571i	$0.310845\pi$
$824$	75.6596	−	43.6821i	0.0918199	−	0.0530122i
$825$	−63.0413	−	109.191i	−0.0764137	−	0.132352i
$826$	−22.9829			−0.0278243
$827$	61.6217	−	106.732i	0.0745124	−	0.129059i	−0.826362	−	0.563140i	$-0.809593\pi$
$827$	61.6217	−	106.732i	0.0745124	−	0.129059i	0.900874	+	0.434080i	$0.142927\pi$
$828$	324.584			0.392010
$829$	329.970			0.398034			0.199017	−	0.979996i	$-0.436225\pi$
$829$	329.970			0.398034			0.199017	+	0.979996i	$0.436225\pi$
$830$	28.6696	+	49.6573i	0.0345417	+	0.0598280i
$831$			588.070i			0.707666i
$832$	128.072	+	73.9426i	0.153933	+	0.0888733i
$833$	−157.165	−	272.217i	−0.188673	−	0.326792i
$834$	157.438	+	90.8971i	0.188775	+	0.108989i
$835$	−861.439	+	497.352i	−1.03166	+	0.595631i
$836$	−74.1775	+	42.8264i	−0.0887291	+	0.0512278i
$837$	16.1757	+	28.0171i	0.0193258	+	0.0334732i
$838$	−196.641	+	113.530i	−0.234655	+	0.135478i
$839$	403.939	+	699.642i	0.481452	+	0.833900i	0.999773	−	0.0212861i	$-0.00677609\pi$
$839$	403.939	+	699.642i	0.481452	+	0.833900i	−0.518321	+	0.855186i	$0.673443\pi$
$840$	−32.9951	−	57.1492i	−0.0392799	−	0.0680348i
$841$	−649.146	+	1124.35i	−0.771874	+	1.33692i
$842$	−92.8336	+	53.5975i	−0.110254	+	0.0636550i
$843$	389.602	−	674.810i	0.462161	−	0.800487i
$844$	−510.508			−0.604867
$845$	−956.920	+	552.478i	−1.13245	+	0.653820i
$846$		−	50.5484i		−	0.0597499i
$847$			162.868i			0.192288i
$848$	605.347	+	349.497i	0.713852	+	0.412143i
$849$		−	554.765i		−	0.653433i
$850$	−68.1534	+	39.3484i	−0.0801805	+	0.0462922i
$851$	311.042	+	538.741i	0.365502	+	0.633069i
$852$	525.715	+	303.522i	0.617036	+	0.356246i
$853$	372.607	−	645.374i	0.436820	−	0.756594i	−0.560623	−	0.828071i	$-0.689438\pi$
$853$	372.607	−	645.374i	0.436820	−	0.756594i	0.997442	+	0.0714777i	$0.0227715\pi$
$854$	−2.04100	−	1.17837i	−0.00238993	−	0.00137983i
$855$	−139.449	−	80.5107i	−0.163098	−	0.0941646i
$856$			210.639i			0.246074i
$857$			1275.89i			1.48879i	0.667739	+	0.744396i	$0.267262\pi$
$857$			1275.89i			1.48879i	−0.667739	+	0.744396i	$0.732738\pi$
$858$	4.26503	−	7.38726i	0.00497090	−	0.00860986i
$859$	380.956	+	659.835i	0.443488	+	0.768143i	0.997945	−	0.0640686i	$-0.0204077\pi$
$859$	380.956	+	659.835i	0.443488	+	0.768143i	−0.554458	+	0.832212i	$0.687074\pi$
$860$	−46.9219	−	81.2712i	−0.0545604	−	0.0945014i
$861$	−40.7567	−	23.5309i	−0.0473365	−	0.0273297i
$862$			280.229i			0.325091i
$863$	141.225			0.163645			0.0818223	−	0.996647i	$-0.473926\pi$
$863$	141.225			0.163645			0.0818223	+	0.996647i	$0.473926\pi$
$864$	55.3403	+	95.8522i	0.0640512	+	0.110940i
$865$	755.240	+	436.038i	0.873110	+	0.504090i
$866$	109.037			0.125909
$867$	366.095	−	211.365i	0.422255	−	0.243789i
$868$	−34.0863			−0.0392699
$869$	−100.820	+	174.625i	−0.116018	+	0.200950i
$870$		−	270.480i		−	0.310897i
$871$	81.3389	+	216.045i	0.0933856	+	0.248043i
$872$	−108.752			−0.124715
$873$	225.849	+	130.394i	0.258705	+	0.149363i
$874$		−	105.183i		−	0.120347i
$875$	−2.80064	−	4.85085i	−0.00320073	−	0.00554383i
$876$			502.740i			0.573904i
$877$	509.516	−	882.508i	0.580976	−	1.00628i	−0.414388	−	0.910100i	$-0.636004\pi$
$877$	509.516	−	882.508i	0.580976	−	1.00628i	0.995364	−	0.0961800i	$-0.0306624\pi$
$878$	197.743	−	114.167i	0.225220	−	0.130031i
$879$			887.823i			1.01004i
$880$	−278.165			−0.316097
$881$	140.838	−	243.939i	0.159862	−	0.276889i	−0.774957	−	0.632014i	$-0.782228\pi$
$881$	140.838	−	243.939i	0.159862	−	0.276889i	0.934819	+	0.355125i	$0.115562\pi$
$882$	−58.4907	+	33.7696i	−0.0663160	+	0.0382876i
$883$	512.718	−	296.018i	0.580655	−	0.335241i	−0.180739	−	0.983531i	$-0.557849\pi$
$883$	512.718	−	296.018i	0.580655	−	0.335241i	0.761394	+	0.648290i	$0.224515\pi$
$884$	75.3993	+	43.5318i	0.0852933	+	0.0492441i
$885$	−401.438			−0.453603
$886$	−94.9840			−0.107205
$887$	−161.925	+	280.463i	−0.182554	+	0.316193i	−0.942750	−	0.333501i	$-0.891770\pi$
$887$	−161.925	+	280.463i	−0.182554	+	0.316193i	0.760196	+	0.649694i	$0.225103\pi$
$888$	−70.0162	+	121.272i	−0.0788470	+	0.136567i
$889$	−291.223	−	168.138i	−0.327585	−	0.189131i
$890$	−35.4295	+	61.3657i	−0.0398084	+	0.0689502i
$891$	−23.2039	+	13.3968i	−0.0260425	+	0.0150357i
$892$	−342.691	−	593.558i	−0.384182	−	0.665423i
$893$	267.861			0.299956
$894$	−85.2603	+	147.675i	−0.0953695	+	0.165185i
$895$	1715.50			1.91676
$896$	−153.677			−0.171515
$897$	−85.6464	−	148.344i	−0.0954809	−	0.165378i
$898$		−	210.645i		−	0.234571i
$899$	−249.388	−	143.984i	−0.277407	−	0.160161i
$900$	−138.255	−	239.464i	−0.153616	−	0.266071i
$901$	305.407	+	176.327i	0.338964	+	0.195701i
$902$	23.1574	−	13.3699i	0.0256734	−	0.0148225i
$903$	7.71280	−	4.45299i	0.00854130	−	0.00493132i
$904$	106.203	+	183.950i	0.117482	+	0.203484i
$905$	1684.14	−	972.338i	1.86093	−	1.07441i
$906$	93.0663	+	161.196i	0.102722	+	0.177920i
$907$	744.835	+	1290.09i	0.821208	+	1.42237i	0.904784	+	0.425872i	$0.140033\pi$
$907$	744.835	+	1290.09i	0.821208	+	1.42237i	−0.0835760	+	0.996501i	$0.526634\pi$
$908$	17.4379	−	30.2033i	0.0192047	−	0.0332635i
$909$	91.8358	−	53.0214i	0.101029	−	0.0583294i
$910$	−8.44795	+	14.6323i	−0.00928346	+	0.0160794i
$911$	−1659.64			−1.82178			−0.910890	−	0.412649i	$-0.864604\pi$
$911$	−1659.64			−1.82178			−0.910890	+	0.412649i	$0.864604\pi$
$912$	−152.121	+	87.8271i	−0.166799	+	0.0963016i
$913$			50.5591i			0.0553769i
$914$			222.533i			0.243471i
$915$	−35.6498	−	20.5824i	−0.0389615	−	0.0224945i
$916$		−	1003.10i		−	1.09508i
$917$	−86.4275	+	49.8989i	−0.0942503	+	0.0544154i
$918$	8.36184	+	14.4831i	0.00910876	+	0.0157768i
$919$	1516.57	+	875.589i	1.65023	+	0.952763i	0.976974	+	0.213357i	$0.0684398\pi$
$919$	1516.57	+	875.589i	1.65023	+	0.952763i	0.673260	+	0.739406i	$0.264894\pi$
$920$	376.466	−	652.059i	0.409203	−	0.708760i
$921$	301.005	+	173.785i	0.326824	+	0.188692i
$922$	−154.524	−	89.2146i	−0.167597	−	0.0967620i
$923$		−	320.355i		−	0.347080i
$924$		−	28.2304i		−	0.0305524i
$925$	264.974	−	458.948i	0.286458	−	0.496160i
$926$	−58.8850	−	101.992i	−0.0635907	−	0.110142i
$927$	35.1304	+	60.8476i	0.0378968	+	0.0656392i
$928$	−853.208	−	492.600i	−0.919405	−	0.530819i
$929$		−	1234.35i		−	1.32869i	−0.747427	−	0.664344i	$-0.768711\pi$
$929$		−	1234.35i		−	1.32869i	0.747427	−	0.664344i	$-0.231289\pi$
$930$	36.4092			0.0391497
$931$	−178.948	−	309.947i	−0.192211	−	0.332919i
$932$	−527.385	−	304.486i	−0.565863	−	0.326701i
$933$	−835.614			−0.895621
$934$	39.6055	−	22.8662i	0.0424042	−	0.0244821i
$935$	−140.339			−0.150095
$936$	19.2791	−	33.3925i	0.0205974	−	0.0356757i
$937$		−	593.069i		−	0.632945i	−0.948602	−	0.316472i	$-0.897502\pi$
$937$		−	593.069i		−	0.632945i	0.948602	−	0.316472i	$-0.102498\pi$
$938$	−36.1188	−	29.6358i	−0.0385062	−	0.0315946i
$939$	198.594			0.211495
$940$	805.637	+	465.135i	0.857060	+	0.494824i
$941$		−	1322.42i		−	1.40533i	−0.711520	−	0.702666i	$-0.751993\pi$
$941$		−	1322.42i		−	1.40533i	0.711520	−	0.702666i	$-0.248007\pi$
$942$	−83.5954	−	144.791i	−0.0887425	−	0.153706i
$943$		−	536.964i		−	0.569421i
$944$	−218.959	+	379.249i	−0.231949	+	0.401747i
$945$	45.9610	−	26.5356i	0.0486360	−	0.0280800i
$946$			5.06024i			0.00534909i
$947$	159.685			0.168622			0.0843108	−	0.996440i	$-0.473131\pi$
$947$	159.685			0.168622			0.0843108	+	0.996440i	$0.473131\pi$
$948$	−221.106	+	382.968i	−0.233235	+	0.403974i
$949$	229.766	−	132.655i	0.242114	−	0.139784i
$950$	−77.5997	+	44.8022i	−0.0816839	+	0.0471602i
$951$	381.985	+	220.539i	0.401667	+	0.231903i
$952$	−36.3186			−0.0381498
$953$	999.577			1.04887			0.524437	−	0.851449i	$-0.324276\pi$
$953$	999.577			1.04887			0.524437	+	0.851449i	$0.324276\pi$
$954$	37.8869	−	65.6221i	0.0397138	−	0.0687862i
$955$	686.854	−	1189.67i	0.719219	−	1.24572i
$956$	−185.710	−	107.220i	−0.194258	−	0.112155i
$957$	119.249	−	206.545i	0.124607	−	0.215825i
$958$	111.981	−	64.6520i	0.116890	−	0.0674864i
$959$	124.875	+	216.290i	0.130214	+	0.225537i
$960$	−522.782			−0.544565
$961$	−461.118	+	798.680i	−0.479832	+	0.831093i
$962$	35.8534			0.0372696
$963$	−169.402			−0.175910
$964$	−98.4521	−	170.524i	−0.102129	−	0.176892i
$965$		−	1524.82i		−	1.58013i
$966$	30.0229	+	17.3337i	0.0310796	+	0.0179438i
$967$	282.512	+	489.325i	0.292153	+	0.506024i	0.974319	−	0.225174i	$-0.0722950\pi$
$967$	282.512	+	489.325i	0.292153	+	0.506024i	−0.682166	+	0.731198i	$0.738962\pi$
$968$	−362.261	−	209.152i	−0.374237	−	0.216066i
$969$	−76.7474	+	44.3101i	−0.0792027	+	0.0457277i
$970$	254.178	−	146.749i	0.262039	−	0.151288i
$971$	99.2999	+	171.992i	0.102266	+	0.177129i	0.912618	−	0.408814i	$-0.134058\pi$
$971$	99.2999	+	171.992i	0.102266	+	0.177129i	−0.810352	+	0.585943i	$0.800724\pi$
$972$	−50.8880	+	29.3802i	−0.0523540	+	0.0302266i
$973$	−158.755	−	274.971i	−0.163160	−	0.282601i
$974$	−87.3607	−	151.313i	−0.0896927	−	0.155352i
$975$	−72.9612	+	126.373i	−0.0748320	+	0.129613i
$976$	−38.8895	+	22.4528i	−0.0398457	+	0.0230050i
$977$	−551.642	+	955.471i	−0.564628	+	0.977964i	0.432456	+	0.901655i	$0.357647\pi$
$977$	−551.642	+	955.471i	−0.564628	+	0.977964i	−0.997084	+	0.0763094i	$0.975686\pi$
$978$	−239.472			−0.244859
$979$	−54.1094	+	31.2401i	−0.0552701	+	0.0319102i
$980$		−	1242.96i		−	1.26833i
$981$		−	87.4612i		−	0.0891551i
$982$	−120.461	−	69.5480i	−0.122669	−	0.0708228i
$983$			0.200034i			0.000203493i	1.00000		0.000101747i	$3.23869e-5\pi$
$983$			0.200034i			0.000203493i	−1.00000		0.000101747i	$0.999968\pi$
$984$	104.678	−	60.4357i	0.106380	−	0.0614184i
$985$	903.509	+	1564.92i	0.917268	+	1.58876i
$986$	−128.919	−	74.4312i	−0.130749	−	0.0754880i
$987$	−44.1422	+	76.4565i	−0.0447236	+	0.0774636i
$988$	85.8498	+	49.5654i	0.0868925	+	0.0501674i
$989$	88.0012	+	50.8075i	0.0889800	+	0.0513726i
$990$			30.1543i			0.0304589i
$991$			1331.73i			1.34383i	0.740629	+	0.671914i	$0.234528\pi$
$991$			1331.73i			1.34383i	−0.740629	+	0.671914i	$0.765472\pi$
$992$	66.3086	−	114.850i	0.0668434	−	0.115776i
$993$	−1.74798	−	3.02759i	−0.00176030	−	0.00304893i
$994$	32.4178	+	56.1493i	0.0326135	+	0.0564882i
$995$	−2154.27	−	1243.77i	−2.16509	−	1.25002i
$996$			110.880i			0.111326i
$997$	363.558			0.364652			0.182326	−	0.983238i	$-0.441637\pi$
$997$	363.558			0.364652			0.182326	+	0.983238i	$0.441637\pi$
$998$	53.4945	+	92.6552i	0.0536017	+	0.0928409i
$999$	−97.5300	−	56.3090i	−0.0976276	−	0.0563653i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.h.b.172.6	yes	24
67.30	odd	6	inner	201.3.h.b.97.6	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.h.b.97.6	✓	24	67.30	odd	6	inner
201.3.h.b.172.6	yes	24	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-0.415796 - 0.240060i) q^{2} -1.73205i q^{3} +(-1.88474 - 3.26447i) q^{4} -7.03218i q^{5} +(-0.415796 + 0.720180i) q^{6} +(1.25782 - 0.726201i) q^{7} +3.73029i q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(-0.415796 - 0.240060i) q^{2} -1.73205i q^{3} +(-1.88474 - 3.26447i) q^{4} -7.03218i q^{5} +(-0.415796 + 0.720180i) q^{6} +(1.25782 - 0.726201i) q^{7} +3.73029i q^{8} -3.00000 q^{9} +(-1.68815 + 2.92395i) q^{10} +(-2.57821 + 1.48853i) q^{11} +(-5.65423 + 3.26447i) q^{12} +(2.98391 + 1.72276i) q^{13} -0.697327 q^{14} -12.1801 q^{15} +(-6.64348 + 11.5068i) q^{16} +(-3.35174 + 5.80538i) q^{17} +(1.24739 + 0.720180i) q^{18} +(-3.81630 + 6.61002i) q^{19} +(-22.9563 + 13.2539i) q^{20} +(-1.25782 - 2.17860i) q^{21} +1.42935 q^{22} +(14.3514 - 24.8573i) q^{23} +6.46105 q^{24} -24.4516 q^{25} +(-0.827131 - 1.43263i) q^{26} +5.19615i q^{27} +(-4.74132 - 2.73740i) q^{28} +(-23.1262 - 40.0558i) q^{29} +(5.06444 + 2.92395i) q^{30} +(5.39189 - 3.11301i) q^{31} +(18.4468 - 10.6502i) q^{32} +(2.57821 + 4.46559i) q^{33} +(2.78728 - 1.60924i) q^{34} +(-5.10678 - 8.84520i) q^{35} +(5.65423 + 9.79341i) q^{36} +(-10.8367 + 18.7697i) q^{37} +(3.17360 - 1.83228i) q^{38} +(2.98391 - 5.16828i) q^{39} +26.2321 q^{40} +(16.2014 - 9.35386i) q^{41} +1.20781i q^{42} +3.54025i q^{43} +(9.71852 + 5.61099i) q^{44} +21.0965i q^{45} +(-11.9345 + 6.89039i) q^{46} +(-17.5471 - 30.3926i) q^{47} +(19.9304 + 11.5068i) q^{48} +(-23.4453 + 40.6084i) q^{49} +(10.1669 + 5.86985i) q^{50} +(10.0552 + 5.80538i) q^{51} -12.9878i q^{52} -52.6076i q^{53} +(1.24739 - 2.16054i) q^{54} +(10.4676 + 18.1304i) q^{55} +(2.70894 + 4.69202i) q^{56} +(11.4489 + 6.61002i) q^{57} +22.2067i q^{58} +32.9586 q^{59} +(22.9563 + 39.7616i) q^{60} +(2.92689 + 1.68984i) q^{61} -2.98924 q^{62} +(-3.77345 + 2.17860i) q^{63} +42.9210 q^{64} +(12.1148 - 20.9834i) q^{65} -2.47570i q^{66} +(51.7960 + 42.4991i) q^{67} +25.2686 q^{68} +(-43.0542 - 24.8573i) q^{69} +4.90373i q^{70} +(-46.4886 - 80.5207i) q^{71} -11.1909i q^{72} +(38.5009 - 66.6855i) q^{73} +(9.01169 - 5.20290i) q^{74} +42.3514i q^{75} +28.7710 q^{76} +(-2.16194 + 3.74460i) q^{77} +(-2.48139 + 1.43263i) q^{78} +(58.6569 - 33.8656i) q^{79} +(80.9182 + 46.7181i) q^{80} +9.00000 q^{81} -8.98196 q^{82} +(8.49146 - 14.7076i) q^{83} +(-4.74132 + 8.21221i) q^{84} +(40.8245 + 23.5700i) q^{85} +(0.849872 - 1.47202i) q^{86} +(-69.3787 + 40.0558i) q^{87} +(-5.55264 - 9.61746i) q^{88} +20.9872 q^{89} +(5.06444 - 8.77186i) q^{90} +5.00428 q^{91} -108.195 q^{92} +(-5.39189 - 9.33904i) q^{93} +16.8495i q^{94} +(46.4829 + 26.8369i) q^{95} +(-18.4468 - 31.9507i) q^{96} +(-75.2831 - 43.4647i) q^{97} +(19.4969 - 11.2565i) q^{98} +(7.73463 - 4.46559i) 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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