LMFDB - Embedded newform 126.3.r.a.11.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [126,3,Mod(11,126)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(126, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 4])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("126.11"); S:= CuspForms(chi, 3); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$3.43325133094$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.1
Character	$\chi$	$=$	126.11
Dual form			126.3.r.a.23.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.41421i q^{2} +(-2.92705 + 0.657548i) q^{3} -2.00000 q^{4} +(2.90307 + 1.67609i) q^{5} +(0.929913 + 4.13948i) q^{6} +(5.64984 + 4.13271i) q^{7} +2.82843i q^{8} +(8.13526 - 3.84935i) q^{9} +(2.37035 - 4.10556i) q^{10} +(12.2880 - 7.09448i) q^{11} +(5.85410 - 1.31510i) q^{12} +(-8.31908 - 14.4091i) q^{13} +(5.84453 - 7.99008i) q^{14} +(-9.59954 - 2.99709i) q^{15} +4.00000 q^{16} +(13.5532 + 7.82495i) q^{17} +(-5.44381 - 11.5050i) q^{18} +(17.3162 + 29.9925i) q^{19} +(-5.80614 - 3.35218i) q^{20} +(-19.2548 - 8.38161i) q^{21} +(-10.0331 - 17.3779i) q^{22} +(22.7453 + 13.1320i) q^{23} +(-1.85983 - 8.27895i) q^{24} +(-6.88146 - 11.9190i) q^{25} +(-20.3775 + 11.7650i) q^{26} +(-21.2812 + 16.6166i) q^{27} +(-11.2997 - 8.26542i) q^{28} +(18.2368 + 10.5290i) q^{29} +(-4.23852 + 13.5758i) q^{30} -33.7477 q^{31} -5.65685i q^{32} +(-31.3027 + 28.8459i) q^{33} +(11.0662 - 19.1671i) q^{34} +(9.47510 + 21.4672i) q^{35} +(-16.2705 + 7.69871i) q^{36} +(-31.9815 - 55.3936i) q^{37} +(42.4158 - 24.4888i) q^{38} +(33.8250 + 36.7059i) q^{39} +(-4.74069 + 8.21112i) q^{40} +(5.44200 - 3.14194i) q^{41} +(-11.8534 + 27.2304i) q^{42} +(0.0742627 - 0.128627i) q^{43} +(-24.5760 + 14.1890i) q^{44} +(30.0691 + 2.46047i) q^{45} +(18.5715 - 32.1667i) q^{46} +41.9794i q^{47} +(-11.7082 + 2.63019i) q^{48} +(14.8414 + 46.6983i) q^{49} +(-16.8561 + 9.73185i) q^{50} +(-44.8162 - 13.9921i) q^{51} +(16.6382 + 28.8182i) q^{52} +(-38.6074 - 22.2900i) q^{53} +(23.4994 + 30.0962i) q^{54} +47.5639 q^{55} +(-11.6891 + 15.9802i) q^{56} +(-70.4069 - 76.4034i) q^{57} +(14.8903 - 25.7907i) q^{58} -41.4581i q^{59} +(19.1991 + 5.99418i) q^{60} +15.9995 q^{61} +47.7264i q^{62} +(61.8712 + 11.8724i) q^{63} -8.00000 q^{64} -55.7741i q^{65} +(40.7942 + 44.2686i) q^{66} -85.3249 q^{67} +(-27.1064 - 15.6499i) q^{68} +(-75.2116 - 23.4819i) q^{69} +(30.3592 - 13.3998i) q^{70} -56.4376i q^{71} +(10.8876 + 23.0100i) q^{72} +(4.42855 - 7.67047i) q^{73} +(-78.3383 + 45.2287i) q^{74} +(27.9797 + 30.3627i) q^{75} +(-34.6324 - 59.9850i) q^{76} +(98.7447 + 10.7001i) q^{77} +(51.9100 - 47.8358i) q^{78} +29.1408 q^{79} +(11.6123 + 6.70435i) q^{80} +(51.3650 - 62.6310i) q^{81} +(-4.44338 - 7.69616i) q^{82} +(-48.8531 - 28.2054i) q^{83} +(38.5097 + 16.7632i) q^{84} +(26.2306 + 45.4328i) q^{85} +(-0.181906 - 0.105023i) q^{86} +(-60.3033 - 18.8274i) q^{87} +(20.0662 + 34.7557i) q^{88} +(-5.43082 + 3.13549i) q^{89} +(3.47963 - 42.5241i) q^{90} +(12.5470 - 115.789i) q^{91} +(-45.4906 - 26.2640i) q^{92} +(98.7812 - 22.1907i) q^{93} +59.3679 q^{94} +116.094i q^{95} +(3.71965 + 16.5579i) q^{96} +(-32.1934 + 55.7605i) q^{97} +(66.0414 - 20.9889i) q^{98} +(72.6569 - 105.016i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 64 q^{4} + 8 q^{6} + 2 q^{7} - 20 q^{9} - 36 q^{11} + 10 q^{13} + 36 q^{14} + 10 q^{15} + 128 q^{16} - 54 q^{17} + 28 q^{19} + 28 q^{21} - 126 q^{23} - 16 q^{24} + 80 q^{25} - 72 q^{26} - 126 q^{27}+ \cdots + 394 q^{99}+O(q^{100}) $ 32 * q - 64 * q^4 + 8 * q^6 + 2 * q^7 - 20 * q^9 - 36 * q^11 + 10 * q^13 + 36 * q^14 + 10 * q^15 + 128 * q^16 - 54 * q^17 + 28 * q^19 + 28 * q^21 - 126 * q^23 - 16 * q^24 + 80 * q^25 - 72 * q^26 - 126 * q^27 - 4 * q^28 + 36 * q^29 + 76 * q^30 + 16 * q^31 - 40 * q^33 - 90 * q^35 + 40 * q^36 + 22 * q^37 + 46 * q^39 + 72 * q^41 + 120 * q^42 + 16 * q^43 + 72 * q^44 + 464 * q^45 - 12 * q^46 + 2 * q^49 - 288 * q^50 - 286 * q^51 - 20 * q^52 - 72 * q^53 - 160 * q^54 - 24 * q^55 - 72 * q^56 - 282 * q^57 - 24 * q^58 - 20 * q^60 + 124 * q^61 + 66 * q^63 - 256 * q^64 - 16 * q^66 - 140 * q^67 + 108 * q^68 + 218 * q^69 + 72 * q^70 + 196 * q^73 + 216 * q^74 + 658 * q^75 - 56 * q^76 + 486 * q^77 + 32 * q^78 + 76 * q^79 - 380 * q^81 - 56 * q^84 + 60 * q^85 - 144 * q^86 - 740 * q^87 - 486 * q^89 + 296 * q^90 - 122 * q^91 + 252 * q^92 + 238 * q^93 - 336 * q^94 + 32 * q^96 - 38 * q^97 + 288 * q^98 + 394 * q^99

Character values

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

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		−	1.41421i		−	0.707107i
$2$		−	1.41421i		−	0.707107i
$3$	−2.92705	+	0.657548i	−0.975684	+	0.219183i
$3$	−2.92705	+	0.657548i	−0.975684	+	0.219183i
$4$	−2.00000			−0.500000
$5$	2.90307	+	1.67609i	0.580614	+	0.335218i	0.761377	−	0.648309i	$-0.224523\pi$
$5$	2.90307	+	1.67609i	0.580614	+	0.335218i	−0.180763	+	0.983527i	$0.557857\pi$
$6$	0.929913	+	4.13948i	0.154986	+	0.689913i
$7$	5.64984	+	4.13271i	0.807120	+	0.590387i
$7$	5.64984	+	4.13271i	0.807120	+	0.590387i
$8$			2.82843i			0.353553i
$9$	8.13526	−	3.84935i	0.903918	−	0.427706i
$10$	2.37035	−	4.10556i	0.237035	−	0.410556i
$11$	12.2880	−	7.09448i	1.11709	−	0.644953i	0.176434	−	0.984312i	$-0.443544\pi$
$11$	12.2880	−	7.09448i	1.11709	−	0.644953i	0.940657	+	0.339360i	$0.110210\pi$
$12$	5.85410	−	1.31510i	0.487842	−	0.109591i
$13$	−8.31908	−	14.4091i	−0.639930	−	1.10839i	−0.985448	−	0.169978i	$-0.945630\pi$
$13$	−8.31908	−	14.4091i	−0.639930	−	1.10839i	0.345518	−	0.938412i	$-0.387703\pi$
$14$	5.84453	−	7.99008i	0.417467	−	0.570720i
$15$	−9.59954	−	2.99709i	−0.639970	−	0.199806i
$16$	4.00000			0.250000
$17$	13.5532	+	7.82495i	0.797248	+	0.460291i	0.842508	−	0.538684i	$-0.181078\pi$
$17$	13.5532	+	7.82495i	0.797248	+	0.460291i	−0.0452601	+	0.998975i	$0.514412\pi$
$18$	−5.44381	−	11.5050i	−0.302434	−	0.639166i
$19$	17.3162	+	29.9925i	0.911378	+	1.57855i	0.812120	+	0.583491i	$0.198314\pi$
$19$	17.3162	+	29.9925i	0.911378	+	1.57855i	0.0992583	+	0.995062i	$0.468353\pi$
$20$	−5.80614	−	3.35218i	−0.290307	−	0.167609i
$21$	−19.2548	−	8.38161i	−0.916897	−	0.399124i
$22$	−10.0331	−	17.3779i	−0.456050	−	0.789903i
$23$	22.7453	+	13.1320i	0.988926	+	0.570956i	0.904953	−	0.425512i	$-0.139906\pi$
$23$	22.7453	+	13.1320i	0.988926	+	0.570956i	0.0839727	+	0.996468i	$0.473239\pi$
$24$	−1.85983	−	8.27895i	−0.0774928	−	0.344956i
$25$	−6.88146	−	11.9190i	−0.275258	−	0.476761i
$26$	−20.3775	+	11.7650i	−0.783750	+	0.452499i
$27$	−21.2812	+	16.6166i	−0.788192	+	0.615429i
$28$	−11.2997	−	8.26542i	−0.403560	−	0.295194i
$29$	18.2368	+	10.5290i	0.628855	+	0.363069i	0.780308	−	0.625395i	$-0.215062\pi$
$29$	18.2368	+	10.5290i	0.628855	+	0.363069i	−0.151454	+	0.988464i	$0.548395\pi$
$30$	−4.23852	+	13.5758i	−0.141284	+	0.452527i
$31$	−33.7477			−1.08863			−0.544317	−	0.838879i	$-0.683211\pi$
$31$	−33.7477			−1.08863			−0.544317	+	0.838879i	$0.683211\pi$
$32$		−	5.65685i		−	0.176777i
$33$	−31.3027	+	28.8459i	−0.948565	+	0.874117i
$34$	11.0662	−	19.1671i	0.325475	−	0.563739i
$35$	9.47510	+	21.4672i	0.270717	+	0.613348i
$36$	−16.2705	+	7.69871i	−0.451959	+	0.213853i
$37$	−31.9815	−	55.3936i	−0.864365	−	1.49712i	−0.867677	−	0.497129i	$-0.834388\pi$
$37$	−31.9815	−	55.3936i	−0.864365	−	1.49712i	0.00331203	−	0.999995i	$-0.498946\pi$
$38$	42.4158	−	24.4888i	1.11621	−	0.644441i
$39$	33.8250	+	36.7059i	0.867309	+	0.941177i
$40$	−4.74069	+	8.21112i	−0.118517	+	0.205278i
$41$	5.44200	−	3.14194i	0.132732	−	0.0766328i	−0.432164	−	0.901795i	$-0.642250\pi$
$41$	5.44200	−	3.14194i	0.132732	−	0.0766328i	0.564896	+	0.825162i	$0.308916\pi$
$42$	−11.8534	+	27.2304i	−0.282224	+	0.648344i
$43$	0.0742627	−	0.128627i	0.00172704	−	0.00299132i	−0.865161	−	0.501495i	$-0.832784\pi$
$43$	0.0742627	−	0.128627i	0.00172704	−	0.00299132i	0.866888	+	0.498504i	$0.166117\pi$
$44$	−24.5760	+	14.1890i	−0.558545	+	0.322476i
$45$	30.0691	+	2.46047i	0.668202	+	0.0546772i
$46$	18.5715	−	32.1667i	0.403727	−	0.699276i
$47$			41.9794i			0.893179i	0.894739	+	0.446590i	$0.147362\pi$
$47$			41.9794i			0.893179i	−0.894739	+	0.446590i	$0.852638\pi$
$48$	−11.7082	+	2.63019i	−0.243921	+	0.0547957i
$49$	14.8414	+	46.6983i	0.302886	+	0.953027i
$50$	−16.8561	+	9.73185i	−0.337121	+	0.194637i
$51$	−44.8162	−	13.9921i	−0.878750	−	0.274356i
$52$	16.6382	+	28.8182i	0.319965	+	0.554195i
$53$	−38.6074	−	22.2900i	−0.728442	−	0.420566i	0.0894100	−	0.995995i	$-0.471502\pi$
$53$	−38.6074	−	22.2900i	−0.728442	−	0.420566i	−0.817852	+	0.575429i	$0.804835\pi$
$54$	23.4994	+	30.0962i	0.435174	+	0.557336i
$55$	47.5639			0.864798
$56$	−11.6891	+	15.9802i	−0.208733	+	0.285360i
$57$	−70.4069	−	76.4034i	−1.23521	−	1.34041i
$58$	14.8903	−	25.7907i	0.256729	−	0.444667i
$59$		−	41.4581i		−	0.702679i	−0.936248	−	0.351340i	$-0.885726\pi$
$59$		−	41.4581i		−	0.702679i	0.936248	−	0.351340i	$-0.114274\pi$
$60$	19.1991	+	5.99418i	0.319985	+	0.0999030i
$61$	15.9995			0.262287			0.131144	−	0.991363i	$-0.458135\pi$
$61$	15.9995			0.262287			0.131144	+	0.991363i	$0.458135\pi$
$62$			47.7264i			0.769781i
$63$	61.8712	+	11.8724i	0.982083	+	0.188451i
$64$	−8.00000			−0.125000
$65$		−	55.7741i		−	0.858063i
$66$	40.7942	+	44.2686i	0.618094	+	0.670737i
$67$	−85.3249			−1.27351			−0.636753	−	0.771068i	$-0.719723\pi$
$67$	−85.3249			−1.27351			−0.636753	+	0.771068i	$0.719723\pi$
$68$	−27.1064	−	15.6499i	−0.398624	−	0.230146i
$69$	−75.2116	−	23.4819i	−1.09002	−	0.340318i
$70$	30.3592	−	13.3998i	0.433702	−	0.191426i
$71$		−	56.4376i		−	0.794896i	−0.917625	−	0.397448i	$-0.869896\pi$
$71$		−	56.4376i		−	0.794896i	0.917625	−	0.397448i	$-0.130104\pi$
$72$	10.8876	+	23.0100i	0.151217	+	0.319583i
$73$	4.42855	−	7.67047i	0.0606650	−	0.105075i	−0.834098	−	0.551617i	$-0.814011\pi$
$73$	4.42855	−	7.67047i	0.0606650	−	0.105075i	0.894763	+	0.446542i	$0.147345\pi$
$74$	−78.3383	+	45.2287i	−1.05863	+	0.611198i
$75$	27.9797	+	30.3627i	0.373063	+	0.404836i
$76$	−34.6324	−	59.9850i	−0.455689	−	0.789276i
$77$	98.7447	+	10.7001i	1.28240	+	0.138962i
$78$	51.9100	−	47.8358i	0.665513	−	0.613280i
$79$	29.1408			0.368870			0.184435	−	0.982845i	$-0.440954\pi$
$79$	29.1408			0.368870			0.184435	+	0.982845i	$0.440954\pi$
$80$	11.6123	+	6.70435i	0.145153	+	0.0838044i
$81$	51.3650	−	62.6310i	0.634135	−	0.773222i
$82$	−4.44338	−	7.69616i	−0.0541875	−	0.0938556i
$83$	−48.8531	−	28.2054i	−0.588592	−	0.339824i	0.175949	−	0.984399i	$-0.443701\pi$
$83$	−48.8531	−	28.2054i	−0.588592	−	0.339824i	−0.764540	+	0.644576i	$0.777034\pi$
$84$	38.5097	+	16.7632i	0.458448	+	0.199562i
$85$	26.2306	+	45.4328i	0.308595	+	0.534503i
$86$	−0.181906	−	0.105023i	−0.00211518	−	0.00122120i
$87$	−60.3033	−	18.8274i	−0.693142	−	0.216407i
$88$	20.0662	+	34.7557i	0.228025	+	0.394951i
$89$	−5.43082	+	3.13549i	−0.0610205	+	0.0352302i	−0.530200	−	0.847873i	$-0.677883\pi$
$89$	−5.43082	+	3.13549i	−0.0610205	+	0.0352302i	0.469179	+	0.883103i	$0.344550\pi$
$90$	3.47963	−	42.5241i	0.0386626	−	0.472490i
$91$	12.5470	−	115.789i	0.137879	−	1.27241i
$92$	−45.4906	−	26.2640i	−0.494463	−	0.285478i
$93$	98.7812	−	22.1907i	1.06216	−	0.238610i
$94$	59.3679			0.631573
$95$			116.094i			1.22204i
$96$	3.71965	+	16.5579i	0.0387464	+	0.172478i
$97$	−32.1934	+	55.7605i	−0.331890	+	0.574851i	−0.982883	−	0.184233i	$-0.941020\pi$
$97$	−32.1934	+	55.7605i	−0.331890	+	0.574851i	0.650992	+	0.759084i	$0.274353\pi$
$98$	66.0414	−	20.9889i	0.673892	−	0.214173i
$99$	72.6569	−	105.016i	0.733908	−	1.06077i
$100$	13.7629	+	23.8381i	0.137629	+	0.238381i
$101$	80.7285	−	46.6086i	0.799292	−	0.461472i	−0.0439314	−	0.999035i	$-0.513988\pi$
$101$	80.7285	−	46.6086i	0.799292	−	0.461472i	0.843224	+	0.537563i	$0.180655\pi$
$102$	−19.7879	+	63.3797i	−0.193999	+	0.621370i
$103$	−64.5523	+	111.808i	−0.626721	+	1.08551i	0.361484	+	0.932378i	$0.382270\pi$
$103$	−64.5523	+	111.808i	−0.626721	+	1.08551i	−0.988205	+	0.153135i	$0.951063\pi$
$104$	40.7550	−	23.5299i	0.391875	−	0.226249i
$105$	−41.8498	−	56.6052i	−0.398570	−	0.539097i
$106$	−31.5228	+	54.5991i	−0.297385	+	0.515086i
$107$	92.8758	−	53.6219i	0.867998	−	0.501139i	0.00131550	−	0.999999i	$-0.499581\pi$
$107$	92.8758	−	53.6219i	0.867998	−	0.501139i	0.866682	+	0.498860i	$0.166248\pi$
$108$	42.5624	−	33.2332i	0.394096	−	0.307714i
$109$	−16.5505	+	28.6662i	−0.151839	+	0.262993i	−0.931904	−	0.362706i	$-0.881853\pi$
$109$	−16.5505	+	28.6662i	−0.151839	+	0.262993i	0.780064	+	0.625699i	$0.215186\pi$
$110$		−	67.2655i		−	0.611505i
$111$	130.035	+	141.110i	1.17149	+	1.27127i
$112$	22.5994	+	16.5308i	0.201780	+	0.147597i
$113$	−146.122	+	84.3635i	−1.29311	+	0.746580i	−0.979205	−	0.202874i	$-0.934972\pi$
$113$	−146.122	+	84.3635i	−1.29311	+	0.746580i	−0.313909	+	0.949453i	$0.601639\pi$
$114$	−108.051	+	99.5703i	−0.947813	+	0.873424i
$115$	44.0208	+	76.2462i	0.382789	+	0.663011i
$116$	−36.4736	−	21.0580i	−0.314427	−	0.181535i
$117$	−123.144	−	85.1985i	−1.05251	−	0.728192i
$118$	−58.6306			−0.496869
$119$	44.2353	+	100.221i	0.371725	+	0.842195i
$120$	8.47705	−	27.1516i	0.0706421	−	0.226263i
$121$	40.1633	−	69.5649i	0.331928	−	0.574916i
$122$		−	22.6267i		−	0.185465i
$123$	−13.8630	+	12.7750i	−0.112708	+	0.103862i
$124$	67.4954			0.544317
$125$		−	129.940i		−	1.03952i
$126$	16.7902	−	87.4991i	0.133255	−	0.694437i
$127$	75.2845			0.592792			0.296396	−	0.955065i	$-0.404215\pi$
$127$	75.2845			0.592792			0.296396	+	0.955065i	$0.404215\pi$
$128$			11.3137i			0.0883883i
$129$	−0.132792	+	0.425328i	−0.00102940	+	0.00329712i
$130$	−78.8765			−0.606742
$131$	−135.527	−	78.2467i	−1.03456	−	0.597303i	−0.116272	−	0.993217i	$-0.537094\pi$
$131$	−135.527	−	78.2467i	−1.03456	−	0.597303i	−0.918288	+	0.395914i	$0.870428\pi$
$132$	62.6053	−	57.6917i	0.474283	−	0.437058i
$133$	−26.1166	+	241.016i	−0.196366	+	1.81215i
$134$			120.668i			0.900505i
$135$	−89.6317	+	12.5699i	−0.663938	+	0.0931106i
$136$	−22.1323	+	38.3343i	−0.162738	+	0.281870i
$137$	−71.6146	+	41.3467i	−0.522734	+	0.301801i	−0.738053	−	0.674743i	$-0.764254\pi$
$137$	−71.6146	+	41.3467i	−0.522734	+	0.301801i	0.215318	+	0.976544i	$0.430921\pi$
$138$	−33.2084	+	106.365i	−0.240641	+	0.770762i
$139$	50.4535	+	87.3880i	0.362975	+	0.628690i	0.988449	−	0.151554i	$-0.0484279\pi$
$139$	50.4535	+	87.3880i	0.362975	+	0.628690i	−0.625474	+	0.780245i	$0.715095\pi$
$140$	−18.9502	−	42.9344i	−0.135359	−	0.306674i
$141$	−27.6035	−	122.876i	−0.195769	−	0.871461i
$142$	−79.8148			−0.562076
$143$	−204.450	−	118.039i	−1.42972	−	0.825449i
$144$	32.5410	−	15.3974i	0.225979	−	0.106926i
$145$	35.2951	+	61.1329i	0.243415	+	0.421606i
$146$	−10.8477	−	6.26291i	−0.0742992	−	0.0428967i
$147$	−74.1480	−	126.929i	−0.504408	−	0.863465i
$148$	63.9630	+	110.787i	0.432182	+	0.748562i
$149$	104.181	+	60.1490i	0.699203	+	0.403685i	0.807050	−	0.590483i	$-0.201063\pi$
$149$	104.181	+	60.1490i	0.699203	+	0.403685i	−0.107848	+	0.994167i	$0.534396\pi$
$150$	42.9394	−	39.5693i	0.286263	−	0.263795i
$151$	−36.8571	−	63.8384i	−0.244087	−	0.422771i	0.717788	−	0.696262i	$-0.245155\pi$
$151$	−36.8571	−	63.8384i	−0.244087	−	0.422771i	−0.961875	+	0.273491i	$0.911822\pi$
$152$	−84.8316	+	48.9776i	−0.558103	+	0.322221i
$153$	140.380	+	11.4869i	0.917516	+	0.0750779i
$154$	15.1322	−	139.646i	0.0982608	−	0.906793i
$155$	−97.9719	−	56.5641i	−0.632077	−	0.364930i
$156$	−67.6501	−	73.4118i	−0.433654	−	0.470589i
$157$	−263.591			−1.67893			−0.839463	−	0.543417i	$-0.817130\pi$
$157$	−263.591			−1.67893			−0.839463	+	0.543417i	$0.817130\pi$
$158$		−	41.2113i		−	0.260831i
$159$	127.663	+	39.8578i	0.802910	+	0.250678i
$160$	9.48139	−	16.4222i	0.0592587	−	0.102639i
$161$	74.2365	+	168.193i	0.461097	+	1.04468i
$162$	−88.5736	−	72.6410i	−0.546751	−	0.448401i
$163$	−36.3832	−	63.0176i	−0.223210	−	0.386611i	0.732571	−	0.680691i	$-0.238320\pi$
$163$	−36.3832	−	63.0176i	−0.223210	−	0.386611i	−0.955781	+	0.294080i	$0.904987\pi$
$164$	−10.8840	+	6.28389i	−0.0663659	+	0.0383164i
$165$	−139.222	+	31.2755i	−0.843770	+	0.189549i
$166$	−39.8884	+	69.0887i	−0.240292	+	0.416197i
$167$	−172.653	+	99.6811i	−1.03385	+	0.596893i	−0.918085	−	0.396384i	$-0.870265\pi$
$167$	−172.653	+	99.6811i	−1.03385	+	0.596893i	−0.115764	+	0.993277i	$0.536932\pi$
$168$	23.7068	−	54.4609i	0.141112	−	0.324172i
$169$	−53.9143	+	93.3824i	−0.319020	+	0.552558i
$170$	64.2516	−	37.0957i	0.377951	−	0.218210i
$171$	256.323	+	177.341i	1.49897	+	1.03708i
$172$	−0.148525	+	0.257253i	−0.000863519	+	0.00149566i
$173$		−	249.497i		−	1.44218i	−0.692841	−	0.721090i	$-0.743641\pi$
$173$		−	249.497i		−	1.44218i	0.692841	−	0.721090i	$-0.256359\pi$
$174$	−26.6260	+	85.2818i	−0.153023	+	0.490125i
$175$	10.3788	−	95.7797i	0.0593072	−	0.547313i
$176$	49.1520	−	28.3779i	0.279273	−	0.161238i
$177$	27.2607	+	121.350i	0.154015	+	0.685593i
$178$	4.43425	+	7.68034i	0.0249115	+	0.0431480i
$179$	178.420	+	103.011i	0.996760	+	0.575479i	0.907288	−	0.420510i	$-0.138149\pi$
$179$	178.420	+	103.011i	0.996760	+	0.575479i	0.0894717	+	0.995989i	$0.471482\pi$
$180$	−60.1382	−	4.92095i	−0.334101	−	0.0273386i
$181$	−68.0662			−0.376056			−0.188028	−	0.982164i	$-0.560210\pi$
$181$	−68.0662			−0.376056			−0.188028	+	0.982164i	$0.560210\pi$
$182$	−163.751	−	17.7442i	−0.899730	−	0.0974955i
$183$	−46.8314	+	10.5205i	−0.255909	+	0.0574888i
$184$	−37.1429	+	64.3334i	−0.201864	+	0.349638i
$185$		−	214.415i		−	1.15900i
$186$	−31.3824	−	139.698i	−0.168723	−	0.751063i
$187$	222.056			1.18746
$188$		−	83.9588i		−	0.446590i
$189$	−188.907	+	5.93205i	−0.999507	+	0.0313865i
$190$	164.181			0.864113
$191$			258.142i			1.35153i	0.737117	+	0.675765i	$0.236187\pi$
$191$			258.142i			1.35153i	−0.737117	+	0.675765i	$0.763813\pi$
$192$	23.4164	−	5.26038i	0.121960	−	0.0273978i
$193$	159.600			0.826945			0.413473	−	0.910516i	$-0.364316\pi$
$193$	159.600			0.826945			0.413473	+	0.910516i	$0.364316\pi$
$194$	78.8573	+	45.5283i	0.406481	+	0.234682i
$195$	36.6741	+	163.254i	0.188072	+	0.837198i
$196$	−29.6828	−	93.3966i	−0.151443	−	0.476513i
$197$		−	173.797i		−	0.882219i	−0.897453	−	0.441109i	$-0.854585\pi$
$197$		−	173.797i		−	0.882219i	0.897453	−	0.441109i	$-0.145415\pi$
$198$	−148.515	−	102.752i	−0.750078	−	0.518952i
$199$	48.3082	−	83.6723i	0.242755	−	0.420464i	−0.718743	−	0.695276i	$-0.755282\pi$
$199$	48.3082	−	83.6723i	0.242755	−	0.420464i	0.961498	+	0.274812i	$0.0886156\pi$
$200$	33.7121	−	19.4637i	0.168561	−	0.0973185i
$201$	249.751	−	56.1052i	1.24254	−	0.279131i
$202$	−65.9146	−	114.167i	−0.326310	−	0.565185i
$203$	59.5216	+	134.855i	0.293210	+	0.664308i
$204$	89.6325	+	27.9843i	0.439375	+	0.137178i
$205$	21.0647			0.102755
$206$	158.120	+	91.2907i	0.767574	+	0.443159i
$207$	235.589	+	19.2776i	1.13811	+	0.0931284i
$208$	−33.2763	−	57.6363i	−0.159982	−	0.277098i
$209$	425.562	+	245.699i	2.03618	+	1.17559i
$210$	−80.0518	+	59.1846i	−0.381199	+	0.281831i
$211$	8.68169	+	15.0371i	0.0411455	+	0.0712660i	0.885865	−	0.463944i	$-0.153566\pi$
$211$	8.68169	+	15.0371i	0.0411455	+	0.0712660i	−0.844719	+	0.535210i	$0.820233\pi$
$212$	77.2148	+	44.5800i	0.364221	+	0.210283i
$213$	37.1104	+	165.196i	0.174227	+	0.775567i
$214$	−75.8328	−	131.346i	−0.354359	−	0.613767i
$215$	0.431179	−	0.248942i	0.00200549	−	0.00115787i
$216$	−46.9988	−	60.1923i	−0.217587	−	0.278668i
$217$	−190.669	−	139.469i	−0.878659	−	0.642716i
$218$	40.5402	+	23.4059i	0.185964	+	0.107366i
$219$	−7.91889	+	25.3638i	−0.0361593	+	0.115817i
$220$	−95.1278			−0.432399
$221$		−	260.386i		−	1.17822i
$222$	199.560	−	183.898i	0.898920	−	0.828369i
$223$	147.273	−	255.085i	0.660418	−	1.14388i	−0.320088	−	0.947388i	$-0.603713\pi$
$223$	147.273	−	255.085i	0.660418	−	1.14388i	0.980506	−	0.196489i	$-0.0629541\pi$
$224$	23.3781	−	31.9603i	0.104367	−	0.142680i
$225$	−101.863	−	70.4753i	−0.452725	−	0.313223i
$226$	119.308	+	206.648i	0.527912	+	0.914370i
$227$	−194.224	+	112.135i	−0.855612	+	0.493988i	−0.862541	−	0.505988i	$-0.831128\pi$
$227$	−194.224	+	112.135i	−0.855612	+	0.493988i	0.00692812	+	0.999976i	$0.497795\pi$
$228$	140.814	+	152.807i	0.617604	+	0.670205i
$229$	51.7349	−	89.6074i	0.225916	−	0.391299i	−0.730678	−	0.682723i	$-0.760796\pi$
$229$	51.7349	−	89.6074i	0.225916	−	0.391299i	0.956594	+	0.291424i	$0.0941290\pi$
$230$	107.828	−	62.2548i	0.468819	−	0.270673i
$231$	−296.067	+	33.6098i	−1.28167	+	0.145497i
$232$	−29.7805	+	51.5814i	−0.128364	+	0.222334i
$233$	−187.439	+	108.218i	−0.804457	+	0.464454i	−0.845027	−	0.534723i	$-0.820416\pi$
$233$	−187.439	+	108.218i	−0.804457	+	0.464454i	0.0405700	+	0.999177i	$0.487083\pi$
$234$	−120.489	+	174.151i	−0.514910	+	0.744236i
$235$	−70.3612	+	121.869i	−0.299409	+	0.518592i
$236$			82.9162i			0.351340i
$237$	−85.2965	+	19.1614i	−0.359901	+	0.0808500i
$238$	141.734	−	62.5581i	0.595522	−	0.262849i
$239$	−387.074	+	223.477i	−1.61956	+	0.935052i	−0.632524	+	0.774541i	$0.717981\pi$
$239$	−387.074	+	223.477i	−1.61956	+	0.935052i	−0.987034	+	0.160511i	$0.948686\pi$
$240$	−38.3982	−	11.9884i	−0.159992	−	0.0499515i
$241$	41.3755	+	71.6645i	0.171683	+	0.297363i	0.939008	−	0.343895i	$-0.111746\pi$
$241$	41.3755	+	71.6645i	0.171683	+	0.297363i	−0.767326	+	0.641258i	$0.778413\pi$
$242$	−98.3796	−	56.7995i	−0.406527	−	0.234709i
$243$	−109.165	+	217.099i	−0.449239	+	0.893412i
$244$	−31.9991			−0.131144
$245$	−35.1848	+	160.444i	−0.143611	+	0.654873i
$246$	18.0666	+	19.6053i	0.0734414	+	0.0796964i
$247$	288.110	−	499.020i	1.16644	−	2.02033i
$248$		−	95.4529i		−	0.384891i
$249$	161.542	+	50.4353i	0.648763	+	0.202551i
$250$	−183.763			−0.735052
$251$		−	228.368i		−	0.909831i	−0.890535	−	0.454916i	$-0.849669\pi$
$251$		−	228.368i		−	0.909831i	0.890535	−	0.454916i	$-0.150331\pi$
$252$	−123.742	−	23.7449i	−0.491041	−	0.0942257i
$253$	372.659			1.47296
$254$		−	106.468i		−	0.419167i
$255$	−106.653	−	115.736i	−0.418245	−	0.453867i
$256$	16.0000			0.0625000
$257$	66.3878	+	38.3290i	0.258318	+	0.149140i	0.623567	−	0.781770i	$-0.285683\pi$
$257$	66.3878	+	38.3290i	0.258318	+	0.149140i	−0.365249	+	0.930910i	$0.619016\pi$
$258$	0.601505	+	0.187797i	0.00233142	+	0.000727895i
$259$	48.2352	−	445.135i	0.186236	−	1.71867i
$260$			111.548i			0.429031i
$261$	188.891	+	15.4564i	0.723720	+	0.0592201i
$262$	−110.658	+	191.665i	−0.422357	+	0.731544i
$263$	306.958	−	177.222i	1.16714	−	0.673849i	0.214136	−	0.976804i	$-0.431306\pi$
$263$	306.958	−	177.222i	1.16714	−	0.673849i	0.953005	+	0.302955i	$0.0979731\pi$
$264$	−81.5884	−	88.5373i	−0.309047	−	0.335368i
$265$	−74.7200	−	129.419i	−0.281962	−	0.488373i
$266$	340.848	+	36.9345i	1.28138	+	0.138852i
$267$	13.8346	−	12.7488i	0.0518149	−	0.0477482i
$268$	170.650			0.636753
$269$	−87.8658	−	50.7294i	−0.326639	−	0.188585i	0.327709	−	0.944779i	$-0.393723\pi$
$269$	−87.8658	−	50.7294i	−0.326639	−	0.188585i	−0.654348	+	0.756194i	$0.727057\pi$
$270$	17.7766	+	126.758i	0.0658392	+	0.469475i
$271$	−37.9220	−	65.6829i	−0.139934	−	0.242372i	0.787538	−	0.616267i	$-0.211356\pi$
$271$	−37.9220	−	65.6829i	−0.139934	−	0.242372i	−0.927471	+	0.373894i	$0.878022\pi$
$272$	54.2129	+	31.2998i	0.199312	+	0.115073i
$273$	39.4113	+	347.172i	0.144364	+	1.27169i
$274$	58.4731	+	101.278i	0.213405	+	0.369629i
$275$	−169.119	−	97.6407i	−0.614977	−	0.355057i
$276$	150.423	+	46.9638i	0.545011	+	0.170159i
$277$	−134.061	−	232.200i	−0.483973	−	0.838266i	0.515857	−	0.856674i	$-0.327473\pi$
$277$	−134.061	−	232.200i	−0.483973	−	0.838266i	−0.999831	+	0.0184083i	$0.994140\pi$
$278$	123.585	−	71.3520i	0.444551	−	0.256662i
$279$	−274.546	+	129.907i	−0.984037	+	0.465616i
$280$	−60.7183	+	26.7996i	−0.216851	+	0.0957130i
$281$	423.951	+	244.768i	1.50872	+	0.871060i	0.999948	+	0.0101594i	$0.00323390\pi$
$281$	423.951	+	244.768i	1.50872	+	0.871060i	0.508773	+	0.860901i	$0.330099\pi$
$282$	−173.773	+	39.0372i	−0.616216	+	0.138430i
$283$	−523.237			−1.84889			−0.924446	−	0.381312i	$-0.875472\pi$
$283$	−523.237			−1.84889			−0.924446	+	0.381312i	$0.875472\pi$
$284$			112.875i			0.397448i
$285$	−76.3372	−	339.812i	−0.267850	−	1.19232i
$286$	−166.933	+	289.136i	−0.583680	+	1.01096i
$287$	43.7312	+	4.73875i	0.152374	+	0.0165113i
$288$	−21.7752	−	46.0200i	−0.0756084	−	0.159792i
$289$	−22.0403	−	38.1749i	−0.0762639	−	0.132093i
$290$	86.4550	−	49.9148i	0.298121	−	0.172120i
$291$	57.5664	−	184.383i	0.197823	−	0.633617i
$292$	−8.85710	+	15.3409i	−0.0303325	+	0.0525375i
$293$	64.1639	−	37.0450i	0.218989	−	0.126434i	−0.386493	−	0.922292i	$-0.626314\pi$
$293$	64.1639	−	37.0450i	0.218989	−	0.126434i	0.605482	+	0.795859i	$0.292980\pi$
$294$	−179.505	+	104.861i	−0.610562	+	0.356670i
$295$	69.4874	−	120.356i	0.235551	−	0.407985i
$296$	156.677	−	90.4573i	0.529313	−	0.305599i
$297$	−143.617	+	355.164i	−0.483560	+	1.19584i
$298$	85.0636	−	147.334i	0.285448	−	0.494411i
$299$		−	436.985i		−	1.46149i
$300$	−55.9594	−	60.7255i	−0.186531	−	0.202418i
$301$	0.951149	−	0.419815i	0.00315996	−	0.00139473i
$302$	−90.2811	+	52.1238i	−0.298944	+	0.172596i
$303$	−205.649	+	189.509i	−0.678710	+	0.625441i
$304$	69.2647	+	119.970i	0.227844	+	0.394638i
$305$	46.4477	+	26.8166i	0.152288	+	0.0879233i
$306$	16.2449	−	198.527i	0.0530881	−	0.648782i
$307$	−159.112			−0.518280			−0.259140	−	0.965840i	$-0.583439\pi$
$307$	−159.112			−0.518280			−0.259140	+	0.965840i	$0.583439\pi$
$308$	−197.489	−	21.4001i	−0.641199	−	0.0694808i
$309$	115.429	−	369.714i	0.373556	−	1.19648i
$310$	−79.9937	+	138.553i	−0.258044	+	0.446946i
$311$		−	446.556i		−	1.43587i	−0.696109	−	0.717936i	$-0.745087\pi$
$311$		−	446.556i		−	1.43587i	0.696109	−	0.717936i	$-0.254913\pi$
$312$	−103.820	+	95.6717i	−0.332756	+	0.306640i
$313$	−196.307			−0.627178			−0.313589	−	0.949559i	$-0.601531\pi$
$313$	−196.307			−0.627178			−0.313589	+	0.949559i	$0.601531\pi$
$314$			372.774i			1.18718i
$315$	159.717	+	138.168i	0.507039	+	0.438629i
$316$	−58.2815			−0.184435
$317$			340.779i			1.07501i	0.843260	+	0.537506i	$0.180633\pi$
$317$			340.779i			1.07501i	−0.843260	+	0.537506i	$0.819367\pi$
$318$	56.3674	−	180.542i	0.177256	−	0.567743i
$319$	298.791			0.936650
$320$	−23.2246	−	13.4087i	−0.0725767	−	0.0419022i
$321$	−236.593	+	218.024i	−0.737051	+	0.679203i
$322$	237.861	−	104.986i	0.738700	−	0.326044i
$323$			541.993i			1.67800i
$324$	−102.730	+	125.262i	−0.317068	+	0.386611i
$325$	−114.495	+	198.311i	−0.352292	+	0.610187i
$326$	−89.1204	+	51.4537i	−0.273375	+	0.157833i
$327$	29.5946	−	94.7903i	0.0905034	−	0.289879i
$328$	8.88676	+	15.3923i	0.0270938	+	0.0469278i
$329$	−173.489	+	237.177i	−0.527322	+	0.720903i
$330$	44.2303	+	196.890i	0.134031	+	0.596635i
$331$	−563.578			−1.70265			−0.851326	−	0.524638i	$-0.824201\pi$
$331$	−563.578			−1.70265			−0.851326	+	0.524638i	$0.824201\pi$
$332$	97.7062	+	56.4107i	0.294296	+	0.169912i
$333$	−473.407	−	327.533i	−1.42164	−	0.983583i
$334$	140.970	+	244.168i	0.422067	+	0.731041i
$335$	−247.704	−	143.012i	−0.739416	−	0.426902i
$336$	−77.0193	−	33.5265i	−0.229224	−	0.0997811i
$337$	303.340	+	525.401i	0.900119	+	1.55905i	0.827338	+	0.561704i	$0.189854\pi$
$337$	303.340	+	525.401i	0.900119	+	1.55905i	0.0727808	+	0.997348i	$0.476813\pi$
$338$	132.063	+	76.2464i	0.390718	+	0.225581i
$339$	372.233	−	343.018i	1.09803	−	1.01185i
$340$	−52.4612	−	90.8655i	−0.154298	−	0.267252i
$341$	−414.692	+	239.422i	−1.21610	+	0.702118i
$342$	250.798	−	362.496i	0.733327	−	1.05993i
$343$	−109.139	+	325.173i	−0.318189	+	0.948027i
$344$	0.363811	+	0.210047i	0.00105759	+	0.000610600i
$345$	−178.987	−	194.231i	−0.518802	−	0.562988i
$346$	−352.842			−1.01978
$347$			52.3842i			0.150963i	0.997147	+	0.0754816i	$0.0240494\pi$
$347$			52.3842i			0.150963i	−0.997147	+	0.0754816i	$0.975951\pi$
$348$	120.607	+	37.6548i	0.346571	+	0.108203i
$349$	−4.33946	+	7.51616i	−0.0124340	+	0.0215363i	−0.872175	−	0.489193i	$-0.837291\pi$
$349$	−4.33946	+	7.51616i	−0.0124340	+	0.0215363i	0.859741	+	0.510729i	$0.170625\pi$
$350$	−135.453	−	14.6778i	−0.387008	−	0.0419365i
$351$	416.470	+	168.408i	1.18652	+	0.479794i
$352$	−40.1324	−	69.5114i	−0.114013	−	0.197476i
$353$	103.990	−	60.0388i	0.294590	−	0.170082i	−0.345420	−	0.938448i	$-0.612264\pi$
$353$	103.990	−	60.0388i	0.294590	−	0.170082i	0.640010	+	0.768367i	$0.278930\pi$
$354$	171.615	−	38.5524i	0.484787	−	0.108905i
$355$	94.5944	−	163.842i	0.266463	−	0.461528i
$356$	10.8616	−	6.27097i	0.0305102	−	0.0176151i
$357$	−195.379	−	264.266i	−0.547280	−	0.740241i
$358$	145.679	−	252.324i	0.406925	−	0.704816i
$359$	101.066	−	58.3503i	0.281520	−	0.162536i	−0.352591	−	0.935777i	$-0.614699\pi$
$359$	101.066	−	58.3503i	0.281520	−	0.162536i	0.634111	+	0.773242i	$0.281366\pi$
$360$	−6.95927	+	85.0482i	−0.0193313	+	0.236245i
$361$	−419.200	+	726.076i	−1.16122	+	2.01129i
$362$			96.2602i			0.265912i
$363$	−71.8178	+	230.029i	−0.197845	+	0.633690i
$364$	−25.0940	+	231.579i	−0.0689397	+	0.636205i
$365$	25.7128	−	14.8453i	0.0704459	−	0.0406720i
$366$	14.8782	+	66.2297i	0.0406507	+	0.180955i
$367$	−148.299	−	256.861i	−0.404085	−	0.699895i	0.590130	−	0.807308i	$-0.299077\pi$
$367$	−148.299	−	256.861i	−0.404085	−	0.699895i	−0.994214	+	0.107413i	$0.965743\pi$
$368$	90.9812	+	52.5280i	0.247231	+	0.142739i
$369$	32.1777	−	46.5087i	0.0872024	−	0.126040i
$370$	−303.229			−0.819538
$371$	−126.008	−	285.488i	−0.339643	−	0.769510i
$372$	−197.562	+	44.3814i	−0.531082	+	0.119305i
$373$	208.053	−	360.359i	0.557783	−	0.966109i	−0.439898	−	0.898048i	$-0.644985\pi$
$373$	208.053	−	360.359i	0.557783	−	0.966109i	0.997681	−	0.0680609i	$-0.0216812\pi$
$374$		−	314.034i		−	0.839664i
$375$	85.4419	+	380.341i	0.227845	+	1.01424i
$376$	−118.736			−0.315787
$377$		−	350.367i		−	0.929355i
$378$	8.38918	+	267.155i	0.0221936	+	0.706758i
$379$	315.897			0.833501			0.416750	−	0.909021i	$-0.363169\pi$
$379$	315.897			0.833501			0.416750	+	0.909021i	$0.363169\pi$
$380$		−	232.188i		−	0.611020i
$381$	−220.362	+	49.5032i	−0.578377	+	0.129930i
$382$	365.068			0.955676
$383$	348.813	+	201.387i	0.910740	+	0.525816i	0.880669	−	0.473732i	$-0.157093\pi$
$383$	348.813	+	201.387i	0.910740	+	0.525816i	0.0300707	+	0.999548i	$0.490427\pi$
$384$	−7.43931	−	33.1158i	−0.0193732	−	0.0862391i
$385$	268.729	+	196.568i	0.697996	+	0.510566i
$386$		−	225.709i		−	0.584739i
$387$	0.109017	−	1.33228i	0.000281696	−	0.00344257i
$388$	64.3867	−	111.521i	0.165945	−	0.287425i
$389$	314.791	−	181.745i	0.809232	−	0.467210i	−0.0374573	−	0.999298i	$-0.511926\pi$
$389$	314.791	−	181.745i	0.809232	−	0.467210i	0.846689	+	0.532088i	$0.178592\pi$
$390$	230.875	−	51.8651i	0.591988	−	0.132987i
$391$	205.515	+	355.962i	0.525613	+	0.910388i
$392$	−132.083	+	41.9779i	−0.336946	+	0.107086i
$393$	448.146	+	139.916i	1.14032	+	0.356022i
$394$	−245.786			−0.623823
$395$	84.5977	+	48.8425i	0.214171	+	0.123652i
$396$	−145.314	+	210.033i	−0.366954	+	0.530385i
$397$	32.4146	+	56.1437i	0.0816489	+	0.141420i	0.903958	−	0.427621i	$-0.140648\pi$
$397$	32.4146	+	56.1437i	0.0816489	+	0.141420i	−0.822309	+	0.569041i	$0.807315\pi$
$398$	−118.330	−	68.3181i	−0.297313	−	0.171654i
$399$	−82.0346	−	722.638i	−0.205600	−	1.81112i
$400$	−27.5258	−	47.6761i	−0.0688146	−	0.119190i
$401$	430.383	+	248.482i	1.07328	+	0.619656i	0.929074	−	0.369893i	$-0.120606\pi$
$401$	430.383	+	248.482i	1.07328	+	0.619656i	0.144201	+	0.989548i	$0.453939\pi$
$402$	−79.3448	−	353.201i	−0.197375	−	0.878608i
$403$	280.750	+	486.273i	0.696650	+	1.20663i
$404$	−161.457	+	93.2173i	−0.399646	+	0.230736i
$405$	254.091	−	95.7300i	0.627385	−	0.236370i
$406$	190.713	−	84.1762i	0.469737	−	0.207331i
$407$	−785.977	−	453.784i	−1.93115	−	1.11495i
$408$	39.5758	−	126.759i	0.0969994	−	0.310685i
$409$	493.994			1.20781			0.603905	−	0.797056i	$-0.293611\pi$
$409$	493.994			1.20781			0.603905	+	0.797056i	$0.293611\pi$
$410$		−	29.7900i		−	0.0726585i
$411$	182.432	−	168.114i	0.443874	−	0.409036i
$412$	129.105	−	223.616i	0.313361	−	0.542757i
$413$	171.334	−	234.232i	0.414853	−	0.567147i
$414$	27.2626	−	333.173i	0.0658517	−	0.804765i
$415$	−94.5493	−	163.764i	−0.227830	−	0.394613i
$416$	−81.5100	+	47.0598i	−0.195938	+	0.113125i
$417$	−205.142	−	222.613i	−0.491946	−	0.533845i
$418$	347.470	−	601.836i	0.831269	−	1.43980i
$419$	229.187	−	132.321i	0.546987	−	0.315803i	−0.200919	−	0.979608i	$-0.564393\pi$
$419$	229.187	−	132.321i	0.546987	−	0.315803i	0.747906	+	0.663805i	$0.231060\pi$
$420$	83.6996	+	113.210i	0.199285	+	0.269549i
$421$	−41.2156	+	71.3876i	−0.0978994	+	0.169567i	−0.910815	−	0.412815i	$-0.864546\pi$
$421$	−41.2156	+	71.3876i	−0.0978994	+	0.169567i	0.812916	+	0.582382i	$0.197879\pi$
$422$	21.2657	−	12.2778i	0.0503927	−	0.0290942i
$423$	161.594	+	341.514i	0.382018	+	0.807361i
$424$	63.0456	−	109.198i	0.148693	−	0.257543i
$425$		−	215.388i		−	0.506796i
$426$	233.622	−	52.4821i	0.548409	−	0.123197i
$427$	90.3948	+	66.1214i	0.211697	+	0.154851i
$428$	−185.752	+	107.244i	−0.433999	+	0.250569i
$429$	676.052	+	211.071i	1.57588	+	0.492007i
$430$	−0.352057	−	0.609780i	−0.000818736	−	0.00141809i
$431$	−409.848	−	236.626i	−0.950924	−	0.549016i	−0.0575561	−	0.998342i	$-0.518331\pi$
$431$	−409.848	−	236.626i	−0.950924	−	0.549016i	−0.893368	+	0.449326i	$0.851664\pi$
$432$	−85.1248	+	66.4663i	−0.197048	+	0.153857i
$433$	140.867			0.325328			0.162664	−	0.986681i	$-0.447991\pi$
$433$	140.867			0.325328			0.162664	+	0.986681i	$0.447991\pi$
$434$	−197.239	+	269.647i	−0.454469	+	0.621306i
$435$	−143.508	−	155.731i	−0.329904	−	0.358002i
$436$	33.1009	−	57.3325i	0.0759195	−	0.131497i
$437$			909.584i			2.08143i
$438$	35.8699	+	11.1990i	0.0818947	+	0.0255685i
$439$	−255.155			−0.581218			−0.290609	−	0.956842i	$-0.593858\pi$
$439$	−255.155			−0.581218			−0.290609	+	0.956842i	$0.593858\pi$
$440$			134.531i			0.305752i
$441$	300.497	+	322.773i	0.681399	+	0.731912i
$442$	−368.241			−0.833124
$443$			466.380i			1.05278i	0.850244	+	0.526388i	$0.176454\pi$
$443$			466.380i			1.05278i	−0.850244	+	0.526388i	$0.823546\pi$
$444$	−260.071	−	282.221i	−0.585745	−	0.635633i
$445$	−21.0214			−0.0472391
$446$	−360.744	−	208.276i	−0.808843	−	0.466986i
$447$	−344.495	−	107.555i	−0.770681	−	0.240616i
$448$	−45.1987	−	33.0617i	−0.100890	−	0.0737984i
$449$		−	383.226i		−	0.853509i	−0.904367	−	0.426755i	$-0.859657\pi$
$449$		−	383.226i		−	0.853509i	0.904367	−	0.426755i	$-0.140343\pi$
$450$	−99.6671	+	144.056i	−0.221482	+	0.320125i
$451$	44.5809	−	77.2164i	0.0988490	−	0.171212i
$452$	292.244	−	168.727i	0.646557	−	0.373290i
$453$	149.860	+	162.623i	0.330816	+	0.358991i
$454$	158.583	+	274.674i	0.349302	+	0.605009i
$455$	230.498	−	315.115i	0.506589	−	0.692560i
$456$	216.101	−	199.141i	0.473907	−	0.436712i
$457$	−483.494			−1.05797			−0.528987	−	0.848630i	$-0.677428\pi$
$457$	−483.494			−1.05797			−0.528987	+	0.848630i	$0.677428\pi$
$458$	−126.724	−	73.1641i	−0.276690	−	0.159747i
$459$	−418.452	+	58.6838i	−0.911661	+	0.127851i
$460$	−88.0416	−	152.492i	−0.191395	−	0.331505i
$461$	−391.665	−	226.128i	−0.849599	−	0.490516i	0.0109166	−	0.999940i	$-0.496525\pi$
$461$	−391.665	−	226.128i	−0.849599	−	0.490516i	−0.860516	+	0.509424i	$0.829858\pi$
$462$	47.5314	+	418.701i	0.102882	+	0.906280i
$463$	−157.167	−	272.221i	−0.339454	−	0.587951i	0.644876	−	0.764287i	$-0.276909\pi$
$463$	−157.167	−	272.221i	−0.339454	−	0.587951i	−0.984330	+	0.176336i	$0.943575\pi$
$464$	72.9471	+	42.1160i	0.157214	+	0.0907673i
$465$	323.962	+	101.145i	0.696693	+	0.217516i
$466$	153.043	+	265.078i	0.328418	+	0.568837i
$467$	258.779	−	149.406i	0.554130	−	0.319927i	−0.196656	−	0.980473i	$-0.563008\pi$
$467$	258.779	−	149.406i	0.554130	−	0.319927i	0.750786	+	0.660545i	$0.229675\pi$
$468$	246.287	+	170.397i	0.526255	+	0.364096i
$469$	−482.072	−	352.623i	−1.02787	−	0.751862i
$470$	172.349	+	99.5058i	0.366700	+	0.211714i
$471$	771.545	−	173.324i	1.63810	−	0.367991i
$472$	117.261			0.248435
$473$		−	2.10742i		−	0.00445543i
$474$	27.0984	+	120.627i	0.0571696	+	0.254488i
$475$	238.321	−	412.784i	0.501729	−	0.869019i
$476$	−88.4705	−	200.442i	−0.185862	−	0.421098i
$477$	−399.884	−	32.7214i	−0.838330	−	0.0685983i
$478$	316.045	+	547.406i	0.661182	+	1.14520i
$479$	−436.436	+	251.976i	−0.911139	+	0.526047i	−0.880798	−	0.473493i	$-0.842993\pi$
$479$	−436.436	+	251.976i	−0.911139	+	0.526047i	−0.0303418	+	0.999540i	$0.509660\pi$
$480$	−16.9541	+	54.3032i	−0.0353210	+	0.113132i
$481$	−532.113	+	921.648i	−1.10626	+	1.91611i
$482$	101.349	−	58.5138i	0.210267	−	0.121398i
$483$	−327.889	−	443.497i	−0.678860	−	0.918213i
$484$	−80.3266	+	139.130i	−0.165964	+	0.287458i
$485$	−186.919	+	107.918i	−0.385400	+	0.222511i
$486$	307.024	+	154.383i	0.631738	+	0.317660i
$487$	146.436	−	253.634i	0.300690	−	0.520810i	−0.675603	−	0.737266i	$-0.736116\pi$
$487$	146.436	−	253.634i	0.300690	−	0.520810i	0.976292	+	0.216456i	$0.0694498\pi$
$488$			45.2535i			0.0927326i
$489$	147.933	+	160.532i	0.302521	+	0.328287i
$490$	226.902	+	49.7588i	0.463065	+	0.101549i
$491$	−370.452	+	213.881i	−0.754485	+	0.435602i	−0.827312	−	0.561743i	$-0.810131\pi$
$491$	−370.452	+	213.881i	−0.754485	+	0.435602i	0.0728274	+	0.997345i	$0.476798\pi$
$492$	27.7261	−	25.5500i	0.0563539	−	0.0519309i
$493$	164.778	+	285.404i	0.334235	+	0.578913i
$494$	−705.721	−	407.448i	−1.42859	−	0.824794i
$495$	386.945	−	183.090i	0.781707	−	0.369879i
$496$	−134.991			−0.272159
$497$	233.240	−	318.864i	0.469296	−	0.641577i
$498$	71.3262	−	228.455i	0.143225	−	0.458745i
$499$	−103.195	+	178.740i	−0.206804	+	0.358196i	−0.950706	−	0.310093i	$-0.899640\pi$
$499$	−103.195	+	178.740i	−0.206804	+	0.358196i	0.743902	+	0.668289i	$0.232973\pi$
$500$			259.880i			0.519760i
$501$	439.818	−	405.299i	0.877881	−	0.808980i
$502$	−322.961			−0.643348
$503$			415.249i			0.825546i	0.910834	+	0.412773i	$0.135440\pi$
$503$			415.249i			0.825546i	−0.910834	+	0.412773i	$0.864560\pi$
$504$	−33.5803	+	174.998i	−0.0666276	+	0.347219i
$505$	312.481			0.618774
$506$		−	527.019i		−	1.04154i
$507$	96.4066	−	308.786i	0.190151	−	0.609046i
$508$	−150.569			−0.296396
$509$	333.324	+	192.445i	0.654860	+	0.378084i	0.790316	−	0.612700i	$-0.209916\pi$
$509$	333.324	+	192.445i	0.654860	+	0.378084i	−0.135455	+	0.990783i	$0.543250\pi$
$510$	−163.676	+	150.830i	−0.320933	+	0.295744i
$511$	56.7204	−	25.0350i	0.110999	−	0.0489922i
$512$		−	22.6274i		−	0.0441942i
$513$	−866.882	−	350.541i	−1.68983	−	0.683315i
$514$	54.2054	−	93.8865i	0.105458	−	0.182659i
$515$	−374.800	+	216.391i	−0.727766	+	0.420176i
$516$	0.265585	−	0.850657i	0.000514699	−	0.00164856i
$517$	297.822	+	515.843i	0.576058	+	0.997762i
$518$	−629.516	−	68.2149i	−1.21528	−	0.131689i
$519$	164.056	+	730.291i	0.316101	+	1.40711i
$520$	157.753			0.303371
$521$	191.141	+	110.355i	0.366874	+	0.211815i	0.672092	−	0.740468i	$-0.265396\pi$
$521$	191.141	+	110.355i	0.366874	+	0.211815i	−0.305218	+	0.952282i	$0.598729\pi$
$522$	21.8587	−	267.132i	0.0418749	−	0.511747i
$523$	389.796	+	675.146i	0.745308	+	1.29091i	0.950051	+	0.312095i	$0.101031\pi$
$523$	389.796	+	675.146i	0.745308	+	1.29091i	−0.204743	+	0.978816i	$0.565636\pi$
$524$	271.055	+	156.493i	0.517280	+	0.298652i
$525$	32.6006	+	287.177i	0.0620963	+	0.547003i
$526$	−250.630	−	434.104i	−0.476483	−	0.825293i
$527$	−457.390	−	264.074i	−0.867912	−	0.501089i
$528$	−125.211	+	115.383i	−0.237141	+	0.218529i
$529$	80.3988	+	139.255i	0.151983	+	0.263242i
$530$	−183.026	+	105.670i	−0.345332	+	0.199377i
$531$	−159.587	−	337.272i	−0.300540	−	0.635164i
$532$	52.2333	−	482.031i	0.0981829	−	0.906074i
$533$	−90.5450	−	52.2762i	−0.169878	−	0.0980791i
$534$	−18.0295	−	19.5650i	−0.0337630	−	0.0366386i
$535$	359.500			0.671962
$536$		−	241.335i		−	0.450253i
$537$	−589.979	−	184.198i	−1.09866	−	0.343014i
$538$	−71.7422	+	124.261i	−0.133350	+	0.230969i
$539$	513.672	+	468.537i	0.953009	+	0.869270i
$540$	179.263	−	25.1399i	0.331969	−	0.0465553i
$541$	108.437	+	187.818i	0.200437	+	0.347168i	0.948669	−	0.316269i	$-0.102430\pi$
$541$	108.437	+	187.818i	0.200437	+	0.347168i	−0.748232	+	0.663437i	$0.769097\pi$
$542$	−92.8896	+	53.6299i	−0.171383	+	0.0989481i
$543$	199.233	−	44.7568i	0.366912	−	0.0824250i
$544$	44.2646	−	76.6686i	0.0813688	−	0.140935i
$545$	−96.0943	+	55.4801i	−0.176320	+	0.101798i
$546$	490.975	−	55.7360i	0.899221	−	0.102081i
$547$	−330.752	+	572.879i	−0.604665	+	1.04731i	0.387440	+	0.921895i	$0.373360\pi$
$547$	−330.752	+	572.879i	−0.604665	+	1.04731i	−0.992104	+	0.125415i	$0.959974\pi$
$548$	143.229	−	82.6934i	0.261367	−	0.150900i
$549$	130.160	−	61.5878i	0.237086	−	0.112182i
$550$	−138.085	+	239.170i	−0.251063	+	0.434854i
$551$			729.289i			1.32357i
$552$	66.4169	−	212.730i	0.120320	−	0.385381i
$553$	164.641	+	120.430i	0.297723	+	0.217776i
$554$	−328.380	+	189.590i	−0.592744	+	0.342221i
$555$	140.988	+	627.604i	0.254033	+	1.13082i
$556$	−100.907	−	174.776i	−0.181487	−	0.314345i
$557$	159.762	+	92.2387i	0.286826	+	0.165599i	0.636510	−	0.771269i	$-0.280378\pi$
$557$	159.762	+	92.2387i	0.286826	+	0.165599i	−0.349684	+	0.936868i	$0.613711\pi$
$558$	183.716	+	388.267i	0.329240	+	0.695819i
$559$	−2.47119			−0.00442073
$560$	37.9004	+	85.8687i	0.0676793	+	0.153337i
$561$	−649.969	+	146.012i	−1.15859	+	0.260272i
$562$	346.154	−	599.557i	0.615933	−	1.06683i
$563$		−	1043.84i		−	1.85407i	−0.374981	−	0.927033i	$-0.622351\pi$
$563$		−	1043.84i		−	1.85407i	0.374981	−	0.927033i	$-0.377649\pi$
$564$	55.2070	+	245.752i	0.0978847	+	0.435730i
$565$	−565.603			−1.00107
$566$			739.968i			1.30736i
$567$	549.040	−	141.579i	0.968324	−	0.249698i
$568$	159.630			0.281038
$569$			75.8394i			0.133285i	0.997777	+	0.0666427i	$0.0212288\pi$
$569$			75.8394i			0.133285i	−0.997777	+	0.0666427i	$0.978771\pi$
$570$	−480.567	+	107.957i	−0.843101	+	0.189398i
$571$	−770.837			−1.34998			−0.674988	−	0.737829i	$-0.735851\pi$
$571$	−770.837			−1.34998			−0.674988	+	0.737829i	$0.735851\pi$
$572$	408.900	+	236.078i	0.714860	+	0.412724i
$573$	−169.741	−	755.596i	−0.296232	−	1.31867i
$574$	6.70160	−	61.8453i	0.0116753	−	0.107744i
$575$		−	361.469i		−	0.628642i
$576$	−65.0821	+	30.7948i	−0.112990	+	0.0534632i
$577$	435.383	−	754.105i	0.754563	−	1.30694i	−0.191028	−	0.981585i	$-0.561182\pi$
$577$	435.383	−	754.105i	0.754563	−	1.30694i	0.945591	−	0.325357i	$-0.105484\pi$
$578$	−53.9874	+	31.1697i	−0.0934039	+	0.0539267i
$579$	−467.159	+	104.945i	−0.806837	+	0.181252i
$580$	−70.5902	−	122.266i	−0.121707	−	0.210803i
$581$	−159.448	−	361.252i	−0.274437	−	0.621775i
$582$	−260.756	−	81.4112i	−0.448035	−	0.139882i
$583$	−632.544			−1.08498
$584$	21.6954	+	12.5258i	0.0371496	+	0.0214483i
$585$	−214.694	−	453.737i	−0.366999	−	0.775618i
$586$	−52.3896	−	90.7414i	−0.0894020	−	0.154849i
$587$	520.453	+	300.484i	0.886633	+	0.511898i	0.872840	−	0.488007i	$-0.162276\pi$
$587$	520.453	+	300.484i	0.886633	+	0.511898i	0.0137932	+	0.999905i	$0.495609\pi$
$588$	148.296	+	253.859i	0.252204	+	0.431733i
$589$	−584.381	−	1012.18i	−0.992158	−	1.71847i
$590$	−170.209	−	98.2700i	−0.288489	−	0.166559i
$591$	114.280	+	508.713i	0.193367	+	0.860766i
$592$	−127.926	−	221.574i	−0.216091	−	0.374281i
$593$	−288.796	+	166.736i	−0.487008	+	0.281174i	−0.723332	−	0.690500i	$-0.757391\pi$
$593$	−288.796	+	166.736i	−0.487008	+	0.281174i	0.236324	+	0.971674i	$0.424057\pi$
$594$	502.277	+	203.106i	0.845584	+	0.341929i
$595$	−39.5616	+	365.091i	−0.0664901	+	0.613599i
$596$	−208.362	−	120.298i	−0.349601	−	0.201842i
$597$	−86.3821	+	276.678i	−0.144694	+	0.463447i
$598$	−617.990			−1.03343
$599$			410.366i			0.685086i	0.939502	+	0.342543i	$0.111288\pi$
$599$			410.366i			0.685086i	−0.939502	+	0.342543i	$0.888712\pi$
$600$	−85.8788	+	79.1386i	−0.143131	+	0.131898i
$601$	204.315	−	353.884i	0.339958	−	0.588825i	−0.644466	−	0.764633i	$-0.722920\pi$
$601$	204.315	−	353.884i	0.339958	−	0.588825i	0.984424	+	0.175808i	$0.0562538\pi$
$602$	−0.593707	−	1.34513i	−0.000986225	−	0.00223443i
$603$	−694.141	+	328.446i	−1.15115	+	0.544686i
$604$	73.7142	+	127.677i	0.122043	+	0.211385i
$605$	233.194	−	134.634i	0.385444	−	0.222536i
$606$	268.006	+	290.832i	0.442254	+	0.479920i
$607$	114.081	−	197.594i	0.187942	−	0.325526i	−0.756622	−	0.653853i	$-0.773152\pi$
$607$	114.081	−	197.594i	0.187942	−	0.325526i	0.944564	+	0.328327i	$0.106485\pi$
$608$	169.663	−	97.9551i	0.279051	−	0.161110i
$609$	−262.896	−	355.588i	−0.431685	−	0.583888i
$610$	37.9244	−	65.6870i	0.0621712	−	0.107684i
$611$	604.885	−	349.230i	0.989991	−	0.571572i
$612$	−280.760	−	22.9738i	−0.458758	−	0.0375389i
$613$	−59.5738	+	103.185i	−0.0971840	+	0.168328i	−0.910518	−	0.413469i	$-0.864317\pi$
$613$	−59.5738	+	103.185i	−0.0971840	+	0.168328i	0.813334	+	0.581797i	$0.197650\pi$
$614$			225.018i			0.366479i
$615$	−61.6574	+	13.8510i	−0.100256	+	0.0225220i
$616$	−30.2643	+	279.292i	−0.0491304	+	0.453396i
$617$	1004.18	−	579.761i	1.62751	−	0.939645i	0.642682	−	0.766133i	$-0.277822\pi$
$617$	1004.18	−	579.761i	1.62751	−	0.939645i	0.984832	−	0.173512i	$-0.0555116\pi$
$618$	−522.854	−	163.241i	−0.846042	−	0.264144i
$619$	382.915	+	663.228i	0.618603	+	1.07145i	0.989741	+	0.142873i	$0.0456342\pi$
$619$	382.915	+	663.228i	0.618603	+	1.07145i	−0.371138	+	0.928578i	$0.621032\pi$
$620$	195.944	+	113.128i	0.316038	+	0.182465i
$621$	−702.256	+	98.4843i	−1.13085	+	0.158590i
$622$	−631.526			−1.01531
$623$	−43.6413	−	4.72901i	−0.0700503	−	0.00759071i
$624$	135.300	+	146.824i	0.216827	+	0.235294i
$625$	45.7547	−	79.2494i	0.0732075	−	0.126799i
$626$			277.620i			0.443482i
$627$	−1407.20	−	439.345i	−2.24434	−	0.700709i
$628$	527.183			0.839463
$629$		−	1001.01i		−	1.59144i
$630$	195.399	−	225.874i	0.310157	−	0.358530i
$631$	−562.217			−0.890994			−0.445497	−	0.895283i	$-0.646973\pi$
$631$	−562.217			−0.890994			−0.445497	+	0.895283i	$0.646973\pi$
$632$			82.4225i			0.130415i
$633$	−35.2994	−	38.3058i	−0.0557652	−	0.0605147i
$634$	481.934			0.760148
$635$	218.556	+	126.184i	0.344183	+	0.198714i
$636$	−255.325	−	79.7155i	−0.401455	−	0.125339i
$637$	549.413	−	602.338i	0.862500	−	0.945586i
$638$		−	422.555i		−	0.662312i
$639$	−217.248	−	459.135i	−0.339982	−	0.718521i
$640$	−18.9628	+	32.8445i	−0.0296293	+	0.0513195i
$641$	608.106	−	351.090i	0.948684	−	0.547723i	0.0560121	−	0.998430i	$-0.482161\pi$
$641$	608.106	−	351.090i	0.948684	−	0.547723i	0.892672	+	0.450707i	$0.148828\pi$
$642$	308.333	+	334.593i	0.480269	+	0.521173i
$643$	110.674	+	191.694i	0.172122	+	0.298124i	0.939161	−	0.343476i	$-0.111604\pi$
$643$	110.674	+	191.694i	0.172122	+	0.298124i	−0.767040	+	0.641600i	$0.778271\pi$
$644$	−148.473	−	336.387i	−0.230548	−	0.522340i
$645$	−1.09839	+	1.01219i	−0.00170294	+	0.00156928i
$646$	766.494			1.18652
$647$	501.744	+	289.682i	0.775494	+	0.447731i	0.834831	−	0.550507i	$-0.185565\pi$
$647$	501.744	+	289.682i	0.775494	+	0.447731i	−0.0593372	+	0.998238i	$0.518899\pi$
$648$	177.147	+	145.282i	0.273375	+	0.224201i
$649$	−294.124	−	509.437i	−0.453195	−	0.784957i
$650$	280.454	+	161.920i	0.431468	+	0.249108i
$651$	649.806	+	282.860i	0.998166	+	0.434501i
$652$	72.7665	+	126.035i	0.111605	+	0.193306i
$653$	−926.464	−	534.894i	−1.41878	−	0.819134i	−0.422589	−	0.906321i	$-0.638879\pi$
$653$	−926.464	−	534.894i	−1.41878	−	0.819134i	−0.996192	+	0.0871874i	$0.972212\pi$
$654$	−134.054	−	41.8531i	−0.204975	−	0.0639956i
$655$	−262.297	−	454.311i	−0.400453	−	0.693605i
$656$	21.7680	−	12.5678i	0.0331830	−	0.0191582i
$657$	6.50104	−	79.4483i	0.00989504	−	0.120926i
$658$	335.419	+	245.350i	0.509755	+	0.372873i
$659$	740.124	+	427.311i	1.12310	+	0.648423i	0.942191	−	0.335076i	$-0.108762\pi$
$659$	740.124	+	427.311i	1.12310	+	0.648423i	0.180911	+	0.983499i	$0.442095\pi$
$660$	278.444	−	62.5511i	0.421885	−	0.0947744i
$661$	−1180.67			−1.78619			−0.893094	−	0.449870i	$-0.851470\pi$
$661$	−1180.67			−1.78619			−0.893094	+	0.449870i	$0.851470\pi$
$662$			797.019i			1.20396i
$663$	171.216	+	762.162i	0.258244	+	1.14957i
$664$	79.7768	−	138.177i	0.120146	−	0.208099i
$665$	−479.782	+	655.911i	−0.721477	+	0.986333i
$666$	−463.202	+	669.499i	−0.695498	+	1.00525i
$667$	276.534	+	478.971i	0.414594	+	0.718097i
$668$	345.305	−	199.362i	0.516924	−	0.298446i
$669$	−263.346	+	843.485i	−0.393641	+	1.26081i
$670$	−202.250	+	350.307i	−0.301865	+	0.522846i
$671$	196.602	−	113.508i	0.292999	−	0.169163i
$672$	−47.4136	+	108.922i	−0.0705559	+	0.162086i
$673$	232.243	−	402.257i	0.345086	−	0.597707i	−0.640283	−	0.768139i	$-0.721183\pi$
$673$	232.243	−	402.257i	0.345086	−	0.597707i	0.985369	+	0.170432i	$0.0545163\pi$
$674$	743.029	−	428.988i	1.10242	−	0.636480i
$675$	344.499	+	139.305i	0.510369	+	0.206378i
$676$	107.829	−	186.765i	0.159510	−	0.276279i
$677$		−	182.958i		−	0.270248i	−0.990829	−	0.135124i	$-0.956857\pi$
$677$		−	182.958i		−	0.270248i	0.990829	−	0.135124i	$-0.0431433\pi$
$678$	−485.101	−	526.417i	−0.715489	−	0.776427i
$679$	−412.330	+	181.992i	−0.607260	+	0.268030i
$680$	−128.503	+	74.1914i	−0.188975	+	0.109105i
$681$	494.769	−	455.937i	0.726534	−	0.669512i
$682$	338.594	+	586.462i	0.496472	+	0.859916i
$683$	878.043	+	506.938i	1.28557	+	0.742223i	0.977861	−	0.209258i	$-0.0671048\pi$
$683$	878.043	+	506.938i	1.28557	+	0.742223i	0.307708	+	0.951481i	$0.400438\pi$
$684$	−512.647	−	354.681i	−0.749484	−	0.518540i
$685$	−277.203			−0.404676
$686$	459.865	+	154.346i	0.670356	+	0.224994i
$687$	−92.5094	+	296.304i	−0.134657	+	0.431301i
$688$	0.297051	−	0.514507i	0.000431760	−	0.000747830i
$689$			741.730i			1.07653i
$690$	−274.684	+	253.125i	−0.398093	+	0.366848i
$691$	1002.41			1.45066			0.725331	−	0.688400i	$-0.241687\pi$
$691$	1002.41			1.45066			0.725331	+	0.688400i	$0.241687\pi$
$692$			498.995i			0.721090i
$693$	844.502	−	293.056i	1.21862	−	0.422880i
$694$	74.0825			0.106747
$695$			338.258i			0.486702i
$696$	53.2519	−	170.564i	0.0765114	−	0.245063i
$697$	98.3422			0.141094
$698$	10.6295	+	6.13692i	0.0152285	+	0.00879215i
$699$	477.484	−	440.009i	0.683096	−	0.629483i
$700$	−20.7575	+	191.559i	−0.0296536	+	0.273656i
$701$		−	77.0590i		−	0.109927i	−0.998488	−	0.0549636i	$-0.982496\pi$
$701$		−	77.0590i		−	0.109927i	0.998488	−	0.0549636i	$-0.0175043\pi$
$702$	238.164	−	588.977i	0.339265	−	0.838999i
$703$	1107.59	−	1918.41i	1.57553	−	2.72889i
$704$	−98.3040	+	56.7558i	−0.139636	+	0.0806191i
$705$	125.816	−	402.983i	0.178462	−	0.571608i
$706$	−84.9077	−	147.064i	−0.120266	−	0.208306i
$707$	648.723	+	70.2962i	0.917572	+	0.0994288i
$708$	−54.5214	−	242.700i	−0.0770076	−	0.342796i
$709$	906.235			1.27819			0.639093	−	0.769129i	$-0.279310\pi$
$709$	906.235			1.27819			0.639093	+	0.769129i	$0.279310\pi$
$710$	−231.708	−	133.777i	−0.326349	−	0.188418i
$711$	237.068	−	112.173i	0.333429	−	0.157768i
$712$	−8.86850	−	15.3607i	−0.0124558	−	0.0215740i
$713$	−767.601	−	443.175i	−1.07658	−	0.621563i
$714$	−373.728	+	276.308i	−0.523429	+	0.386986i
$715$	−395.688	−	685.352i	−0.553410	−	0.958534i
$716$	−356.840	−	206.022i	−0.498380	−	0.287740i
$717$	986.039	−	908.650i	1.37523	−	1.26729i
$718$	−82.5198	−	142.928i	−0.114930	−	0.199065i
$719$	20.7034	−	11.9531i	0.0287947	−	0.0166246i	−0.485534	−	0.874218i	$-0.661375\pi$
$719$	20.7034	−	11.9531i	0.0287947	−	0.0166246i	0.514328	+	0.857593i	$0.328041\pi$
$720$	120.276	+	9.84189i	0.167050	+	0.0136693i
$721$	−826.780	+	364.921i	−1.14671	+	0.506131i
$722$	1026.83	+	592.838i	1.42220	+	0.821106i
$723$	−168.231	−	182.559i	−0.232685	−	0.252503i
$724$	136.132			0.188028
$725$		−	289.820i		−	0.399751i
$726$	325.311	+	101.566i	0.448086	+	0.139898i
$727$	185.455	−	321.217i	0.255096	−	0.441839i	−0.709826	−	0.704377i	$-0.751226\pi$
$727$	185.455	−	321.217i	0.255096	−	0.441839i	0.964921	+	0.262539i	$0.0845597\pi$
$728$	327.502	+	35.4883i	0.449865	+	0.0487477i
$729$	176.778	−	707.241i	0.242494	−	0.970153i
$730$	−20.9944	−	36.3633i	−0.0287594	−	0.0498128i
$731$	2.01300	−	1.16220i	0.00275376	−	0.00158988i
$732$	93.6629	−	21.0409i	0.127955	−	0.0287444i
$733$	309.948	−	536.846i	0.422849	−	0.732396i	−0.573368	−	0.819298i	$-0.694363\pi$
$733$	309.948	−	536.846i	0.422849	−	0.732396i	0.996217	+	0.0869020i	$0.0276967\pi$
$734$	−363.257	+	209.726i	−0.494900	+	0.285731i
$735$	−2.51186	−	492.764i	−0.00341750	−	0.670427i
$736$	74.2858	−	128.667i	0.100932	−	0.174819i
$737$	−1048.47	+	605.336i	−1.42262	+	0.821352i
$738$	−65.7733	−	45.5061i	−0.0891237	−	0.0616614i
$739$	−304.105	+	526.725i	−0.411508	+	0.712754i	−0.995055	−	0.0993262i	$-0.968331\pi$
$739$	−304.105	+	526.725i	−0.411508	+	0.712754i	0.583546	+	0.812080i	$0.301665\pi$
$740$			428.830i			0.579501i
$741$	−515.182	+	1650.10i	−0.695252	+	2.22686i
$742$	−403.741	+	178.202i	−0.544126	+	0.240164i
$743$	723.866	−	417.924i	0.974248	−	0.562482i	0.0737195	−	0.997279i	$-0.476513\pi$
$743$	723.866	−	417.924i	0.974248	−	0.562482i	0.900529	+	0.434797i	$0.143180\pi$
$744$	62.7648	+	279.395i	0.0843613	+	0.375532i
$745$	201.630	+	349.234i	0.270645	+	0.468770i
$746$	−509.624	−	294.232i	−0.683142	−	0.394412i
$747$	−506.005	−	41.4050i	−0.677383	−	0.0554284i
$748$	−444.112			−0.593732
$749$	746.337	+	80.8737i	0.996445	+	0.107976i
$750$	537.884	−	120.833i	0.717179	−	0.161111i
$751$	−521.619	+	903.470i	−0.694566	+	1.20302i	0.275761	+	0.961226i	$0.411070\pi$
$751$	−521.619	+	903.470i	−0.694566	+	1.20302i	−0.970327	+	0.241797i	$0.922263\pi$
$752$			167.918i			0.223295i
$753$	150.163	+	668.444i	0.199419	+	0.887708i
$754$	−495.494			−0.657153
$755$		−	247.103i		−	0.327289i
$756$	377.814	−	11.8641i	0.499754	−	0.0156932i
$757$	441.367			0.583047			0.291524	−	0.956564i	$-0.405838\pi$
$757$	441.367			0.583047			0.291524	+	0.956564i	$0.405838\pi$
$758$		−	446.745i		−	0.589374i
$759$	−1090.79	+	245.041i	−1.43714	+	0.322847i
$760$	−328.363			−0.432056
$761$	−257.357	−	148.585i	−0.338182	−	0.195249i	0.321286	−	0.946982i	$-0.395885\pi$
$761$	−257.357	−	148.585i	−0.338182	−	0.195249i	−0.659468	+	0.751733i	$0.729218\pi$
$762$	70.0081	+	311.639i	0.0918741	+	0.408975i
$763$	−211.977	+	93.5615i	−0.277820	+	0.122623i
$764$		−	516.285i		−	0.675765i
$765$	388.280	+	268.636i	0.507555	+	0.351159i
$766$	284.805	−	493.297i	0.371808	−	0.643990i
$767$	−597.373	+	344.893i	−0.778843	+	0.449665i
$768$	−46.8328	+	10.5208i	−0.0609802	+	0.0136989i
$769$	−79.6447	−	137.949i	−0.103569	−	0.179387i	0.809584	−	0.587005i	$-0.199693\pi$
$769$	−79.6447	−	137.949i	−0.103569	−	0.179387i	−0.913153	+	0.407618i	$0.866360\pi$
$770$	277.989	−	380.039i	0.361024	−	0.493558i
$771$	−219.524	−	68.5378i	−0.284726	−	0.0888947i
$772$	−319.201			−0.413473
$773$	767.592	+	443.170i	0.993004	+	0.573311i	0.906171	−	0.422912i	$-0.138992\pi$
$773$	767.592	+	443.170i	0.993004	+	0.573311i	0.0868334	+	0.996223i	$0.472325\pi$
$774$	−1.88412	−	0.154173i	−0.00243427	−	0.000199189i
$775$	232.233	+	402.240i	0.299656	+	0.519019i
$776$	−157.715	−	91.0566i	−0.203241	−	0.117341i
$777$	151.511	+	1334.65i	0.194995	+	1.71770i
$778$	−257.026	−	445.182i	−0.330367	−	0.572213i
$779$	188.469	+	108.813i	0.241938	+	0.139683i
$780$	−73.3483	−	326.507i	−0.0940362	−	0.418599i
$781$	−400.396	−	693.505i	−0.512670	−	0.887971i
$782$	503.406	−	290.641i	0.643741	−	0.371664i
$783$	−563.057	+	78.9630i	−0.719102	+	0.100847i
$784$	59.3657	+	186.793i	0.0757215	+	0.238257i
$785$	−765.224	−	441.802i	−0.974808	−	0.562805i
$786$	197.872	−	633.775i	0.251745	−	0.806329i
$787$	989.314			1.25707			0.628535	−	0.777781i	$-0.283655\pi$
$787$	989.314			1.25707			0.628535	+	0.777781i	$0.283655\pi$
$788$			347.594i			0.441109i
$789$	−781.950	+	720.579i	−0.991065	+	0.913281i
$790$	69.0737	−	119.639i	0.0874351	−	0.151442i
$791$	−1174.22	−	127.239i	−1.48447	−	0.160858i
$792$	297.031	+	205.505i	0.375039	+	0.259476i
$793$	−133.101	−	230.538i	−0.167845	−	0.290717i
$794$	79.3992	−	45.8412i	0.0999991	−	0.0577345i
$795$	303.808	+	329.684i	0.382149	+	0.414696i
$796$	−96.6164	+	167.345i	−0.121377	+	0.210232i
$797$	−1020.06	+	588.934i	−1.27988	+	0.738939i	−0.976826	−	0.214034i	$-0.931340\pi$
$797$	−1020.06	+	588.934i	−1.27988	+	0.738939i	−0.303054	+	0.952973i	$0.598006\pi$
$798$	−1021.96	+	116.014i	−1.28066	+	0.145381i
$799$	−328.487	+	568.956i	−0.411123	+	0.712085i
$800$	−67.4242	+	38.9274i	−0.0842803	+	0.0486592i
$801$	−32.1116	+	46.4132i	−0.0400893	+	0.0579440i
$802$	351.407	−	608.654i	0.438163	−	0.758920i
$803$		−	125.673i		−	0.156504i
$804$	−499.501	+	112.210i	−0.621270	+	0.139565i
$805$	−66.3931	+	612.704i	−0.0824759	+	0.761123i
$806$	687.694	−	397.040i	0.853218	−	0.492606i
$807$	290.545	+	90.7115i	0.360031	+	0.112406i
$808$	131.829	+	228.335i	0.163155	+	0.282592i
$809$	240.690	+	138.963i	0.297516	+	0.171771i	0.641326	−	0.767268i	$-0.278384\pi$
$809$	240.690	+	138.963i	0.297516	+	0.171771i	−0.343810	+	0.939039i	$0.611718\pi$
$810$	−135.383	−	359.339i	−0.167139	−	0.443629i
$811$	−594.387			−0.732906			−0.366453	−	0.930437i	$-0.619428\pi$
$811$	−594.387			−0.732906			−0.366453	+	0.930437i	$0.619428\pi$
$812$	−119.043	−	269.709i	−0.146605	−	0.332154i
$813$	154.189	+	167.322i	0.189655	+	0.205808i
$814$	−641.748	+	1111.54i	−0.788388	+	1.36553i
$815$		−	243.926i		−	0.299296i
$816$	−179.265	−	55.9686i	−0.219687	−	0.0685890i
$817$	5.14378			0.00629594
$818$		−	698.613i		−	0.854050i
$819$	−343.641	−	990.275i	−0.419586	−	1.20913i
$820$	−42.1294			−0.0513773
$821$		−	135.048i		−	0.164492i	−0.996612	−	0.0822460i	$-0.973791\pi$
$821$		−	135.048i		−	0.164492i	0.996612	−	0.0822460i	$-0.0262093\pi$
$822$	−237.749	−	257.998i	−0.289232	−	0.313866i
$823$	383.153			0.465557			0.232778	−	0.972530i	$-0.425218\pi$
$823$	383.153			0.465557			0.232778	+	0.972530i	$0.425218\pi$
$824$	−316.240	−	182.581i	−0.383787	−	0.221579i
$825$	559.223	+	174.596i	0.677846	+	0.211631i
$826$	−331.253	−	242.303i	−0.401033	−	0.293345i
$827$			1194.80i			1.44474i	0.691504	+	0.722372i	$0.256948\pi$
$827$			1194.80i			1.44474i	−0.691504	+	0.722372i	$0.743052\pi$
$828$	−471.177	−	38.5552i	−0.569055	−	0.0465642i
$829$	484.580	−	839.318i	0.584536	−	1.01245i	−0.410397	−	0.911907i	$-0.634610\pi$
$829$	484.580	−	839.318i	0.584536	−	1.01245i	0.994933	−	0.100539i	$-0.0320567\pi$
$830$	−231.598	+	133.713i	−0.279033	+	0.161100i
$831$	545.085	+	591.509i	0.655938	+	0.711804i
$832$	66.5527	+	115.273i	0.0799912	+	0.138549i
$833$	−164.263	+	749.046i	−0.197195	+	0.899214i
$834$	−314.823	+	290.114i	−0.377486	+	0.347859i
$835$	−668.297			−0.800356
$836$	−851.125	−	491.397i	−1.01809	−	0.587796i
$837$	718.191	−	560.771i	0.858054	−	0.669977i
$838$	−187.131	−	324.120i	−0.223306	−	0.386778i
$839$	−766.287	−	442.416i	−0.913334	−	0.527314i	−0.0318317	−	0.999493i	$-0.510134\pi$
$839$	−766.287	−	442.416i	−0.913334	−	0.527314i	−0.881502	+	0.472180i	$0.843467\pi$
$840$	160.104	−	118.369i	0.190600	−	0.140916i
$841$	−198.780	−	344.297i	−0.236361	−	0.409390i
$842$	100.957	+	58.2877i	0.119902	+	0.0692253i
$843$	−1401.87	−	437.681i	−1.66296	−	0.519194i
$844$	−17.3634	−	30.0743i	−0.0205727	−	0.0356330i
$845$	−313.034	+	180.730i	−0.370455	+	0.213882i
$846$	482.973	−	228.528i	0.570890	−	0.270128i
$847$	514.408	−	227.047i	0.607329	−	0.268061i
$848$	−154.430	−	89.1600i	−0.182110	−	0.105142i
$849$	1531.54	−	344.053i	1.80393	−	0.405245i
$850$	−304.605			−0.358359
$851$		−	1679.92i		−	1.97406i
$852$	−74.2209	−	330.392i	−0.0871137	−	0.387784i
$853$	−91.3479	+	158.219i	−0.107090	+	0.185486i	−0.914590	−	0.404382i	$-0.867487\pi$
$853$	−91.3479	+	158.219i	−0.107090	+	0.185486i	0.807500	+	0.589867i	$0.200820\pi$
$854$	93.5098	−	127.838i	0.109496	−	0.149693i
$855$	446.886	+	944.453i	0.522674	+	1.10462i
$856$	151.666	+	262.692i	0.177179	+	0.306884i
$857$	−1043.89	+	602.693i	−1.21808	+	0.703259i	−0.964507	−	0.264058i	$-0.914939\pi$
$857$	−1043.89	+	602.693i	−1.21808	+	0.703259i	−0.253573	+	0.967316i	$0.581606\pi$
$858$	298.500	−	956.081i	0.347902	−	1.11431i
$859$	518.743	−	898.489i	0.603892	−	1.04597i	−0.388334	−	0.921519i	$-0.626949\pi$
$859$	518.743	−	898.489i	0.603892	−	1.04597i	0.992226	−	0.124452i	$-0.0397174\pi$
$860$	−0.862359	+	0.497883i	−0.00100274	+	0.000578934i
$861$	−131.119	+	14.8848i	−0.152287	+	0.0172878i
$862$	−334.640	+	579.613i	−0.388213	+	0.672405i
$863$	−908.692	+	524.634i	−1.05295	+	0.607919i	−0.923473	−	0.383664i	$-0.874662\pi$
$863$	−908.692	+	524.634i	−1.05295	+	0.607919i	−0.129473	+	0.991583i	$0.541329\pi$
$864$	93.9976	+	120.385i	0.108793	+	0.139334i
$865$	418.179	−	724.308i	0.483444	−	0.837350i
$866$		−	199.216i		−	0.230042i
$867$	89.6148	+	97.2473i	0.103362	+	0.112165i
$868$	381.338	+	278.939i	0.439330	+	0.321358i
$869$	358.082	−	206.739i	0.412062	−	0.237904i
$870$	−220.237	+	202.952i	−0.253146	+	0.233278i
$871$	709.825	+	1229.45i	0.814955	+	1.41154i
$872$	−81.0804	−	46.8118i	−0.0929821	−	0.0536832i
$873$	−47.2594	+	577.550i	−0.0541345	+	0.661570i
$874$	1286.35			1.47179
$875$	537.005	−	734.141i	0.613720	−	0.839018i
$876$	15.8378	−	50.7277i	0.0180796	−	0.0579083i
$877$	532.536	−	922.379i	0.607224	−	1.05174i	−0.384471	−	0.923137i	$-0.625616\pi$
$877$	532.536	−	922.379i	0.607224	−	1.05174i	0.991696	−	0.128606i	$-0.0410504\pi$
$878$			360.843i			0.410983i
$879$	−163.452	+	150.624i	−0.185952	+	0.171358i
$880$	190.256			0.216200
$881$			963.331i			1.09345i	0.837312	+	0.546726i	$0.184126\pi$
$881$			963.331i			1.09345i	−0.837312	+	0.546726i	$0.815874\pi$
$882$	456.470	−	424.967i	0.517540	−	0.481822i
$883$	−1212.68			−1.37336			−0.686681	−	0.726959i	$-0.740933\pi$
$883$	−1212.68			−1.37336			−0.686681	+	0.726959i	$0.740933\pi$
$884$			520.771i			0.589108i
$885$	−124.254	+	397.979i	−0.140399	+	0.449693i
$886$	659.561			0.744426
$887$	404.747	+	233.681i	0.456310	+	0.263450i	0.710491	−	0.703706i	$-0.248473\pi$
$887$	404.747	+	233.681i	0.456310	+	0.263450i	−0.254182	+	0.967157i	$0.581806\pi$
$888$	−399.121	+	367.796i	−0.449460	+	0.414184i
$889$	425.346	+	311.129i	0.478454	+	0.349977i
$890$			29.7288i			0.0334031i
$891$	186.838	−	1134.02i	0.209695	−	1.27275i
$892$	−294.546	+	510.169i	−0.330209	+	0.571939i
$893$	−1259.07	+	726.923i	−1.40993	+	0.814024i
$894$	−152.106	+	487.189i	−0.170141	+	0.544954i
$895$	345.310	+	598.095i	0.385822	+	0.668263i
$896$	−46.7563	+	63.9207i	−0.0521833	+	0.0713400i
$897$	287.338	+	1279.08i	0.320333	+	1.42595i
$898$	−541.963			−0.603522
$899$	−615.449	−	355.330i	−0.684593	−	0.395250i
$900$	203.726	+	140.951i	0.226362	+	0.156612i
$901$	−348.836	−	604.202i	−0.387166	−	0.670591i
$902$	−109.200	−	63.0469i	−0.121065	−	0.0698968i
$903$	−2.50801	+	1.85425i	−0.00277742	+	0.00205343i
$904$	−238.616	−	413.295i	−0.263956	−	0.457185i
$905$	−197.601	−	114.085i	−0.218344	−	0.126061i
$906$	229.984	−	211.933i	0.253845	−	0.233922i
$907$	525.571	+	910.316i	0.579461	+	1.00366i	0.995541	+	0.0943280i	$0.0300702\pi$
$907$	525.571	+	910.316i	0.579461	+	1.00366i	−0.416080	+	0.909328i	$0.636596\pi$
$908$	388.448	−	224.271i	0.427806	−	0.246994i
$909$	477.334	−	689.926i	0.525120	−	0.758994i
$910$	−445.639	−	325.973i	−0.489714	−	0.358213i
$911$	1182.79	+	682.886i	1.29835	+	0.749601i	0.980118	−	0.198413i	$-0.0635788\pi$
$911$	1182.79	+	682.886i	1.29835	+	0.749601i	0.318228	+	0.948014i	$0.396912\pi$
$912$	−281.627	−	305.614i	−0.308802	−	0.335103i
$913$	−800.409			−0.876681
$914$			683.764i			0.748101i
$915$	−153.588	−	47.9520i	−0.167856	−	0.0524066i
$916$	−103.470	+	179.215i	−0.112958	+	0.195649i
$917$	−442.337	−	1002.18i	−0.482374	−	1.09289i
$918$	82.9914	+	591.781i	0.0904045	+	0.644642i
$919$	87.7536	+	151.994i	0.0954881	+	0.165390i	0.909812	−	0.415020i	$-0.136225\pi$
$919$	87.7536	+	151.994i	0.0954881	+	0.165390i	−0.814324	+	0.580410i	$0.802892\pi$
$920$	−215.657	+	124.510i	−0.234410	+	0.135336i
$921$	465.729	−	104.624i	0.505678	−	0.113598i
$922$	−319.793	+	553.898i	−0.346847	+	0.600757i
$923$	−813.214	+	469.509i	−0.881055	+	0.508677i
$924$	592.133	−	67.2195i	0.640837	−	0.0727484i
$925$	−440.158	+	762.377i	−0.475847	+	0.824191i
$926$	−384.979	+	222.268i	−0.415744	+	0.240030i
$927$	−94.7618	+	1158.07i	−0.102224	+	1.24927i
$928$	59.5611	−	103.163i	0.0641822	−	0.111167i
$929$		−	1052.24i		−	1.13266i	−0.824179	−	0.566329i	$-0.808363\pi$
$929$		−	1052.24i		−	1.13266i	0.824179	−	0.566329i	$-0.191637\pi$
$930$	143.040	−	458.152i	0.153807	−	0.492637i
$931$	−1143.60	+	1253.77i	−1.22836	+	1.34669i
$932$	374.877	−	216.435i	0.402229	−	0.232227i
$933$	293.632	+	1307.09i	0.314718	+	1.40096i
$934$	−211.292	−	365.969i	−0.226223	−	0.391829i
$935$	644.644	+	372.185i	0.689458	+	0.398059i
$936$	240.978	−	348.303i	0.257455	−	0.372118i
$937$	1548.61			1.65274			0.826368	−	0.563131i	$-0.190403\pi$
$937$	1548.61			1.65274			0.826368	+	0.563131i	$0.190403\pi$
$938$	−498.685	+	681.753i	−0.531647	+	0.726816i
$939$	574.600	−	129.081i	0.611927	−	0.137467i
$940$	140.722	−	243.738i	0.149705	−	0.259296i
$941$			572.102i			0.607972i	0.952677	+	0.303986i	$0.0983176\pi$
$941$			572.102i			0.607972i	−0.952677	+	0.303986i	$0.901682\pi$
$942$	−245.117	−	1091.13i	−0.260209	−	1.15831i
$943$	165.040			0.175016
$944$		−	165.832i		−	0.175670i
$945$	−558.353	−	299.403i	−0.590849	−	0.316829i
$946$	−2.98034			−0.00315047
$947$		−	959.484i		−	1.01318i	−0.862186	−	0.506591i	$-0.830905\pi$
$947$		−	959.484i		−	1.01318i	0.862186	−	0.506591i	$-0.169095\pi$
$948$	170.593	−	38.3229i	0.179950	−	0.0404250i
$949$	−147.366			−0.155285
$950$	−583.765	−	337.037i	−0.614490	−	0.354776i
$951$	−224.078	−	997.477i	−0.235624	−	1.04887i
$952$	−283.468	+	125.116i	−0.297761	+	0.131425i
$953$		−	1308.52i		−	1.37305i	−0.727104	−	0.686527i	$-0.759134\pi$
$953$		−	1308.52i		−	1.37305i	0.727104	−	0.686527i	$-0.240866\pi$
$954$	−46.2750	+	565.521i	−0.0485063	+	0.592789i
$955$	−432.669	+	749.405i	−0.453057	+	0.784717i
$956$	774.149	−	446.955i	0.809779	−	0.467526i
$957$	−874.578	+	196.470i	−0.913875	+	0.205298i
$958$	356.348	+	617.213i	0.371971	+	0.644273i
$959$	−575.485	−	62.3600i	−0.600089	−	0.0650261i
$960$	76.7963	+	23.9767i	0.0799962	+	0.0249757i
$961$	177.906			0.185126
$962$	1303.41	+	752.522i	1.35489	+	0.782247i
$963$	549.159	−	793.739i	0.570259	−	0.824236i
$964$	−82.7511	−	143.329i	−0.0858413	−	0.148682i
$965$	463.331	+	267.504i	0.480136	+	0.277207i
$966$	−627.199	+	463.706i	−0.649274	+	0.480027i
$967$	85.8474	+	148.692i	0.0887770	+	0.153766i	0.906994	−	0.421143i	$-0.138371\pi$
$967$	85.8474	+	148.692i	0.0887770	+	0.153766i	−0.818217	+	0.574909i	$0.805037\pi$
$968$	196.759	+	113.599i	0.203264	+	0.117354i
$969$	−356.386	−	1586.44i	−0.367788	−	1.63719i
$970$	152.619	+	264.344i	0.157339	+	0.272519i
$971$	803.642	−	463.983i	0.827644	−	0.477840i	−0.0254013	−	0.999677i	$-0.508086\pi$
$971$	803.642	−	463.983i	0.827644	−	0.477840i	0.853045	+	0.521837i	$0.174753\pi$
$972$	218.330	−	434.198i	0.224619	−	0.446706i
$973$	−76.0950	+	702.238i	−0.0782066	+	0.721724i
$974$	−358.693	−	207.092i	−0.368268	−	0.212620i
$975$	204.733	−	655.752i	0.209983	−	0.672566i
$976$	63.9981			0.0655718
$977$			1422.61i			1.45610i	0.685523	+	0.728051i	$0.259574\pi$
$977$			1422.61i			1.45610i	−0.685523	+	0.728051i	$0.740426\pi$
$978$	227.027	−	209.209i	0.232134	−	0.213915i
$979$	−44.4893	+	77.0577i	−0.0454436	+	0.0787107i
$980$	70.3696	−	320.888i	0.0718057	−	0.327437i
$981$	−24.2958	+	296.916i	−0.0247664	+	0.302667i
$982$	302.473	+	523.898i	0.308017	+	0.533501i
$983$	−244.614	+	141.228i	−0.248844	+	0.143670i	−0.619235	−	0.785206i	$-0.712557\pi$
$983$	−244.614	+	141.228i	−0.248844	+	0.143670i	0.370391	+	0.928876i	$0.379224\pi$
$984$	−36.1332	−	39.2106i	−0.0367207	−	0.0398482i
$985$	291.299	−	504.545i	0.295735	−	0.512228i
$986$	403.622	−	233.031i	0.409353	−	0.236340i
$987$	351.855	−	808.307i	0.356490	−	0.818953i
$988$	−576.219	+	998.041i	−0.583218	+	1.01016i
$989$	3.37825	−	1.95043i	0.00341583	−	0.00197213i
$990$	−258.929	−	547.223i	−0.261544	−	0.552750i
$991$	587.805	−	1018.11i	0.593143	−	1.02735i	−0.400663	−	0.916226i	$-0.631220\pi$
$991$	587.805	−	1018.11i	0.593143	−	1.02735i	0.993806	−	0.111129i	$-0.0354465\pi$
$992$			190.906i			0.192445i
$993$	1649.62	−	370.579i	1.66125	−	0.373192i
$994$	−450.941	−	329.852i	−0.453663	−	0.331843i
$995$	280.484	−	161.938i	0.281894	−	0.162751i
$996$	−323.084	−	100.871i	−0.324381	−	0.101276i
$997$	357.930	+	619.953i	0.359007	+	0.621818i	0.987795	−	0.155758i	$-0.0497821\pi$
$997$	357.930	+	619.953i	0.359007	+	0.621818i	−0.628788	+	0.777577i	$0.716449\pi$
$998$	252.776	+	145.940i	0.253283	+	0.146233i
$999$	1601.06	+	647.418i	1.60266	+	0.648066i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.3.r.a.11.1	yes	32
3.2	odd	2		378.3.r.a.305.10		32
7.2	even	3		126.3.i.a.65.6	✓	32
9.4	even	3		378.3.i.a.179.10		32
9.5	odd	6		126.3.i.a.95.6	yes	32
21.2	odd	6		378.3.i.a.359.15		32
63.23	odd	6	inner	126.3.r.a.23.9	yes	32
63.58	even	3		378.3.r.a.233.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.i.a.65.6	✓	32	7.2	even	3
126.3.i.a.95.6	yes	32	9.5	odd	6
126.3.r.a.11.1	yes	32	1.1	even	1	trivial
126.3.r.a.23.9	yes	32	63.23	odd	6	inner
378.3.i.a.179.10		32	9.4	even	3
378.3.i.a.359.15		32	21.2	odd	6
378.3.r.a.233.2		32	63.58	even	3
378.3.r.a.305.10		32	3.2	odd	2

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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +(-2.92705 + 0.657548i) q^{3} -2.00000 q^{4} +(2.90307 + 1.67609i) q^{5} +(0.929913 + 4.13948i) q^{6} +(5.64984 + 4.13271i) q^{7} +2.82843i q^{8} +(8.13526 - 3.84935i) q^{9} +(2.37035 - 4.10556i) q^{10} +(12.2880 - 7.09448i) q^{11} +(5.85410 - 1.31510i) q^{12} +(-8.31908 - 14.4091i) q^{13} +(5.84453 - 7.99008i) q^{14} +(-9.59954 - 2.99709i) q^{15} +4.00000 q^{16} +(13.5532 + 7.82495i) q^{17} +(-5.44381 - 11.5050i) q^{18} +(17.3162 + 29.9925i) q^{19} +(-5.80614 - 3.35218i) q^{20} +(-19.2548 - 8.38161i) q^{21} +(-10.0331 - 17.3779i) q^{22} +(22.7453 + 13.1320i) q^{23} +(-1.85983 - 8.27895i) q^{24} +(-6.88146 - 11.9190i) q^{25} +(-20.3775 + 11.7650i) q^{26} +(-21.2812 + 16.6166i) q^{27} +(-11.2997 - 8.26542i) q^{28} +(18.2368 + 10.5290i) q^{29} +(-4.23852 + 13.5758i) q^{30} -33.7477 q^{31} -5.65685i q^{32} +(-31.3027 + 28.8459i) q^{33} +(11.0662 - 19.1671i) q^{34} +(9.47510 + 21.4672i) q^{35} +(-16.2705 + 7.69871i) q^{36} +(-31.9815 - 55.3936i) q^{37} +(42.4158 - 24.4888i) q^{38} +(33.8250 + 36.7059i) q^{39} +(-4.74069 + 8.21112i) q^{40} +(5.44200 - 3.14194i) q^{41} +(-11.8534 + 27.2304i) q^{42} +(0.0742627 - 0.128627i) q^{43} +(-24.5760 + 14.1890i) q^{44} +(30.0691 + 2.46047i) q^{45} +(18.5715 - 32.1667i) q^{46} +41.9794i q^{47} +(-11.7082 + 2.63019i) q^{48} +(14.8414 + 46.6983i) q^{49} +(-16.8561 + 9.73185i) q^{50} +(-44.8162 - 13.9921i) q^{51} +(16.6382 + 28.8182i) q^{52} +(-38.6074 - 22.2900i) q^{53} +(23.4994 + 30.0962i) q^{54} +47.5639 q^{55} +(-11.6891 + 15.9802i) q^{56} +(-70.4069 - 76.4034i) q^{57} +(14.8903 - 25.7907i) q^{58} -41.4581i q^{59} +(19.1991 + 5.99418i) q^{60} +15.9995 q^{61} +47.7264i q^{62} +(61.8712 + 11.8724i) q^{63} -8.00000 q^{64} -55.7741i q^{65} +(40.7942 + 44.2686i) q^{66} -85.3249 q^{67} +(-27.1064 - 15.6499i) q^{68} +(-75.2116 - 23.4819i) q^{69} +(30.3592 - 13.3998i) q^{70} -56.4376i q^{71} +(10.8876 + 23.0100i) q^{72} +(4.42855 - 7.67047i) q^{73} +(-78.3383 + 45.2287i) q^{74} +(27.9797 + 30.3627i) q^{75} +(-34.6324 - 59.9850i) q^{76} +(98.7447 + 10.7001i) q^{77} +(51.9100 - 47.8358i) q^{78} +29.1408 q^{79} +(11.6123 + 6.70435i) q^{80} +(51.3650 - 62.6310i) q^{81} +(-4.44338 - 7.69616i) q^{82} +(-48.8531 - 28.2054i) q^{83} +(38.5097 + 16.7632i) q^{84} +(26.2306 + 45.4328i) q^{85} +(-0.181906 - 0.105023i) q^{86} +(-60.3033 - 18.8274i) q^{87} +(20.0662 + 34.7557i) q^{88} +(-5.43082 + 3.13549i) q^{89} +(3.47963 - 42.5241i) q^{90} +(12.5470 - 115.789i) q^{91} +(-45.4906 - 26.2640i) q^{92} +(98.7812 - 22.1907i) q^{93} +59.3679 q^{94} +116.094i q^{95} +(3.71965 + 16.5579i) q^{96} +(-32.1934 + 55.7605i) q^{97} +(66.0414 - 20.9889i) q^{98} +(72.6569 - 105.016i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 64 q^{4} + 8 q^{6} + 2 q^{7} - 20 q^{9} - 36 q^{11} + 10 q^{13} + 36 q^{14} + 10 q^{15} + 128 q^{16} - 54 q^{17} + 28 q^{19} + 28 q^{21} - 126 q^{23} - 16 q^{24} + 80 q^{25} - 72 q^{26} - 126 q^{27}+ \cdots + 394 q^{99}+O(q^{100}) \) 32 * q - 64 * q^4 + 8 * q^6 + 2 * q^7 - 20 * q^9 - 36 * q^11 + 10 * q^13 + 36 * q^14 + 10 * q^15 + 128 * q^16 - 54 * q^17 + 28 * q^19 + 28 * q^21 - 126 * q^23 - 16 * q^24 + 80 * q^25 - 72 * q^26 - 126 * q^27 - 4 * q^28 + 36 * q^29 + 76 * q^30 + 16 * q^31 - 40 * q^33 - 90 * q^35 + 40 * q^36 + 22 * q^37 + 46 * q^39 + 72 * q^41 + 120 * q^42 + 16 * q^43 + 72 * q^44 + 464 * q^45 - 12 * q^46 + 2 * q^49 - 288 * q^50 - 286 * q^51 - 20 * q^52 - 72 * q^53 - 160 * q^54 - 24 * q^55 - 72 * q^56 - 282 * q^57 - 24 * q^58 - 20 * q^60 + 124 * q^61 + 66 * q^63 - 256 * q^64 - 16 * q^66 - 140 * q^67 + 108 * q^68 + 218 * q^69 + 72 * q^70 + 196 * q^73 + 216 * q^74 + 658 * q^75 - 56 * q^76 + 486 * q^77 + 32 * q^78 + 76 * q^79 - 380 * q^81 - 56 * q^84 + 60 * q^85 - 144 * q^86 - 740 * q^87 - 486 * q^89 + 296 * q^90 - 122 * q^91 + 252 * q^92 + 238 * q^93 - 336 * q^94 + 32 * q^96 - 38 * q^97 + 288 * q^98 + 394 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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